Properties

Label 690.2.d.c.139.4
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 139.4
Root \(0.403032 - 0.403032i\) of defining polynomial
Character \(\chi\) \(=\) 690.139
Dual form 690.2.d.c.139.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.67513 + 1.48119i) q^{5} -1.00000 q^{6} -2.96239i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-1.67513 + 1.48119i) q^{5} -1.00000 q^{6} -2.96239i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-1.48119 - 1.67513i) q^{10} -3.35026 q^{11} -1.00000i q^{12} -4.96239i q^{13} +2.96239 q^{14} +(-1.48119 - 1.67513i) q^{15} +1.00000 q^{16} -1.35026i q^{17} -1.00000i q^{18} +4.96239 q^{19} +(1.67513 - 1.48119i) q^{20} +2.96239 q^{21} -3.35026i q^{22} -1.00000i q^{23} +1.00000 q^{24} +(0.612127 - 4.96239i) q^{25} +4.96239 q^{26} -1.00000i q^{27} +2.96239i q^{28} -7.73813 q^{29} +(1.67513 - 1.48119i) q^{30} -4.00000 q^{31} +1.00000i q^{32} -3.35026i q^{33} +1.35026 q^{34} +(4.38787 + 4.96239i) q^{35} +1.00000 q^{36} +7.61213i q^{37} +4.96239i q^{38} +4.96239 q^{39} +(1.48119 + 1.67513i) q^{40} +4.70052 q^{41} +2.96239i q^{42} -10.3127i q^{43} +3.35026 q^{44} +(1.67513 - 1.48119i) q^{45} +1.00000 q^{46} -3.22425i q^{47} +1.00000i q^{48} -1.77575 q^{49} +(4.96239 + 0.612127i) q^{50} +1.35026 q^{51} +4.96239i q^{52} -6.96239i q^{53} +1.00000 q^{54} +(5.61213 - 4.96239i) q^{55} -2.96239 q^{56} +4.96239i q^{57} -7.73813i q^{58} -1.22425 q^{59} +(1.48119 + 1.67513i) q^{60} -11.0884 q^{61} -4.00000i q^{62} +2.96239i q^{63} -1.00000 q^{64} +(7.35026 + 8.31265i) q^{65} +3.35026 q^{66} +7.61213i q^{67} +1.35026i q^{68} +1.00000 q^{69} +(-4.96239 + 4.38787i) q^{70} -2.18664 q^{71} +1.00000i q^{72} -9.92478i q^{73} -7.61213 q^{74} +(4.96239 + 0.612127i) q^{75} -4.96239 q^{76} +9.92478i q^{77} +4.96239i q^{78} +4.12601 q^{79} +(-1.67513 + 1.48119i) q^{80} +1.00000 q^{81} +4.70052i q^{82} -6.38787i q^{83} -2.96239 q^{84} +(2.00000 + 2.26187i) q^{85} +10.3127 q^{86} -7.73813i q^{87} +3.35026i q^{88} -9.92478 q^{89} +(1.48119 + 1.67513i) q^{90} -14.7005 q^{91} +1.00000i q^{92} -4.00000i q^{93} +3.22425 q^{94} +(-8.31265 + 7.35026i) q^{95} -1.00000 q^{96} -12.8872i q^{97} -1.77575i q^{98} +3.35026 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} - 6q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 6q^{4} - 6q^{6} - 6q^{9} + 2q^{10} - 4q^{14} + 2q^{15} + 6q^{16} + 8q^{19} - 4q^{21} + 6q^{24} + 2q^{25} + 8q^{26} - 28q^{29} - 24q^{31} - 12q^{34} + 28q^{35} + 6q^{36} + 8q^{39} - 2q^{40} - 12q^{41} + 6q^{46} - 14q^{49} + 8q^{50} - 12q^{51} + 6q^{54} + 32q^{55} + 4q^{56} - 4q^{59} - 2q^{60} - 28q^{61} - 6q^{64} + 24q^{65} + 6q^{69} - 8q^{70} + 12q^{71} - 44q^{74} + 8q^{75} - 8q^{76} + 8q^{79} + 6q^{81} + 4q^{84} + 12q^{85} + 20q^{86} - 16q^{89} - 2q^{90} - 48q^{91} + 16q^{94} - 8q^{95} - 6q^{96} + O(q^{100}) \)

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
\(5\) −1.67513 + 1.48119i −0.749141 + 0.662410i
\(6\) −1.00000 −0.408248
\(7\) 2.96239i 1.11968i −0.828602 0.559839i \(-0.810863\pi\)
0.828602 0.559839i \(-0.189137\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −1.48119 1.67513i −0.468395 0.529723i
\(11\) −3.35026 −1.01014 −0.505071 0.863078i \(-0.668534\pi\)
−0.505071 + 0.863078i \(0.668534\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 4.96239i 1.37632i −0.725559 0.688159i \(-0.758419\pi\)
0.725559 0.688159i \(-0.241581\pi\)
\(14\) 2.96239 0.791732
\(15\) −1.48119 1.67513i −0.382443 0.432517i
\(16\) 1.00000 0.250000
\(17\) 1.35026i 0.327487i −0.986503 0.163743i \(-0.947643\pi\)
0.986503 0.163743i \(-0.0523569\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.96239 1.13845 0.569225 0.822182i \(-0.307243\pi\)
0.569225 + 0.822182i \(0.307243\pi\)
\(20\) 1.67513 1.48119i 0.374571 0.331205i
\(21\) 2.96239 0.646446
\(22\) 3.35026i 0.714278i
\(23\) 1.00000i 0.208514i
\(24\) 1.00000 0.204124
\(25\) 0.612127 4.96239i 0.122425 0.992478i
\(26\) 4.96239 0.973204
\(27\) 1.00000i 0.192450i
\(28\) 2.96239i 0.559839i
\(29\) −7.73813 −1.43694 −0.718468 0.695560i \(-0.755156\pi\)
−0.718468 + 0.695560i \(0.755156\pi\)
\(30\) 1.67513 1.48119i 0.305836 0.270428i
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 3.35026i 0.583206i
\(34\) 1.35026 0.231568
\(35\) 4.38787 + 4.96239i 0.741686 + 0.838797i
\(36\) 1.00000 0.166667
\(37\) 7.61213i 1.25143i 0.780053 + 0.625713i \(0.215192\pi\)
−0.780053 + 0.625713i \(0.784808\pi\)
\(38\) 4.96239i 0.805006i
\(39\) 4.96239 0.794618
\(40\) 1.48119 + 1.67513i 0.234197 + 0.264861i
\(41\) 4.70052 0.734098 0.367049 0.930202i \(-0.380368\pi\)
0.367049 + 0.930202i \(0.380368\pi\)
\(42\) 2.96239i 0.457106i
\(43\) 10.3127i 1.57266i −0.617804 0.786332i \(-0.711977\pi\)
0.617804 0.786332i \(-0.288023\pi\)
\(44\) 3.35026 0.505071
\(45\) 1.67513 1.48119i 0.249714 0.220803i
\(46\) 1.00000 0.147442
\(47\) 3.22425i 0.470306i −0.971958 0.235153i \(-0.924441\pi\)
0.971958 0.235153i \(-0.0755591\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −1.77575 −0.253678
\(50\) 4.96239 + 0.612127i 0.701788 + 0.0865678i
\(51\) 1.35026 0.189074
\(52\) 4.96239i 0.688159i
\(53\) 6.96239i 0.956358i −0.878263 0.478179i \(-0.841297\pi\)
0.878263 0.478179i \(-0.158703\pi\)
\(54\) 1.00000 0.136083
\(55\) 5.61213 4.96239i 0.756739 0.669128i
\(56\) −2.96239 −0.395866
\(57\) 4.96239i 0.657284i
\(58\) 7.73813i 1.01607i
\(59\) −1.22425 −0.159384 −0.0796921 0.996820i \(-0.525394\pi\)
−0.0796921 + 0.996820i \(0.525394\pi\)
\(60\) 1.48119 + 1.67513i 0.191221 + 0.216258i
\(61\) −11.0884 −1.41972 −0.709862 0.704341i \(-0.751243\pi\)
−0.709862 + 0.704341i \(0.751243\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 2.96239i 0.373226i
\(64\) −1.00000 −0.125000
\(65\) 7.35026 + 8.31265i 0.911688 + 1.03106i
\(66\) 3.35026 0.412389
\(67\) 7.61213i 0.929969i 0.885319 + 0.464985i \(0.153940\pi\)
−0.885319 + 0.464985i \(0.846060\pi\)
\(68\) 1.35026i 0.163743i
\(69\) 1.00000 0.120386
\(70\) −4.96239 + 4.38787i −0.593119 + 0.524451i
\(71\) −2.18664 −0.259507 −0.129753 0.991546i \(-0.541419\pi\)
−0.129753 + 0.991546i \(0.541419\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 9.92478i 1.16161i −0.814044 0.580804i \(-0.802738\pi\)
0.814044 0.580804i \(-0.197262\pi\)
\(74\) −7.61213 −0.884892
\(75\) 4.96239 + 0.612127i 0.573007 + 0.0706823i
\(76\) −4.96239 −0.569225
\(77\) 9.92478i 1.13103i
\(78\) 4.96239i 0.561880i
\(79\) 4.12601 0.464212 0.232106 0.972690i \(-0.425438\pi\)
0.232106 + 0.972690i \(0.425438\pi\)
\(80\) −1.67513 + 1.48119i −0.187285 + 0.165603i
\(81\) 1.00000 0.111111
\(82\) 4.70052i 0.519086i
\(83\) 6.38787i 0.701160i −0.936533 0.350580i \(-0.885984\pi\)
0.936533 0.350580i \(-0.114016\pi\)
\(84\) −2.96239 −0.323223
\(85\) 2.00000 + 2.26187i 0.216930 + 0.245334i
\(86\) 10.3127 1.11204
\(87\) 7.73813i 0.829615i
\(88\) 3.35026i 0.357139i
\(89\) −9.92478 −1.05202 −0.526012 0.850477i \(-0.676313\pi\)
−0.526012 + 0.850477i \(0.676313\pi\)
\(90\) 1.48119 + 1.67513i 0.156132 + 0.176574i
\(91\) −14.7005 −1.54103
\(92\) 1.00000i 0.104257i
\(93\) 4.00000i 0.414781i
\(94\) 3.22425 0.332556
\(95\) −8.31265 + 7.35026i −0.852860 + 0.754121i
\(96\) −1.00000 −0.102062
\(97\) 12.8872i 1.30849i −0.756281 0.654247i \(-0.772986\pi\)
0.756281 0.654247i \(-0.227014\pi\)
\(98\) 1.77575i 0.179377i
\(99\) 3.35026 0.336714
\(100\) −0.612127 + 4.96239i −0.0612127 + 0.496239i
\(101\) 4.26187 0.424071 0.212036 0.977262i \(-0.431991\pi\)
0.212036 + 0.977262i \(0.431991\pi\)
\(102\) 1.35026i 0.133696i
\(103\) 0.261865i 0.0258023i −0.999917 0.0129012i \(-0.995893\pi\)
0.999917 0.0129012i \(-0.00410668\pi\)
\(104\) −4.96239 −0.486602
\(105\) −4.96239 + 4.38787i −0.484280 + 0.428213i
\(106\) 6.96239 0.676247
\(107\) 9.08840i 0.878608i 0.898338 + 0.439304i \(0.144775\pi\)
−0.898338 + 0.439304i \(0.855225\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −18.9380 −1.81393 −0.906963 0.421210i \(-0.861606\pi\)
−0.906963 + 0.421210i \(0.861606\pi\)
\(110\) 4.96239 + 5.61213i 0.473145 + 0.535095i
\(111\) −7.61213 −0.722511
\(112\) 2.96239i 0.279919i
\(113\) 6.64974i 0.625555i −0.949826 0.312777i \(-0.898741\pi\)
0.949826 0.312777i \(-0.101259\pi\)
\(114\) −4.96239 −0.464770
\(115\) 1.48119 + 1.67513i 0.138122 + 0.156207i
\(116\) 7.73813 0.718468
\(117\) 4.96239i 0.458773i
\(118\) 1.22425i 0.112702i
\(119\) −4.00000 −0.366679
\(120\) −1.67513 + 1.48119i −0.152918 + 0.135214i
\(121\) 0.224254 0.0203867
\(122\) 11.0884i 1.00390i
\(123\) 4.70052i 0.423832i
\(124\) 4.00000 0.359211
\(125\) 6.32487 + 9.21933i 0.565713 + 0.824602i
\(126\) −2.96239 −0.263911
\(127\) 0.186642i 0.0165618i −0.999966 0.00828091i \(-0.997364\pi\)
0.999966 0.00828091i \(-0.00263593\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 10.3127 0.907978
\(130\) −8.31265 + 7.35026i −0.729068 + 0.644661i
\(131\) 7.92478 0.692391 0.346196 0.938162i \(-0.387473\pi\)
0.346196 + 0.938162i \(0.387473\pi\)
\(132\) 3.35026i 0.291603i
\(133\) 14.7005i 1.27470i
\(134\) −7.61213 −0.657588
\(135\) 1.48119 + 1.67513i 0.127481 + 0.144172i
\(136\) −1.35026 −0.115784
\(137\) 9.19982i 0.785993i −0.919540 0.392997i \(-0.871438\pi\)
0.919540 0.392997i \(-0.128562\pi\)
\(138\) 1.00000i 0.0851257i
\(139\) −8.62530 −0.731588 −0.365794 0.930696i \(-0.619203\pi\)
−0.365794 + 0.930696i \(0.619203\pi\)
\(140\) −4.38787 4.96239i −0.370843 0.419398i
\(141\) 3.22425 0.271531
\(142\) 2.18664i 0.183499i
\(143\) 16.6253i 1.39028i
\(144\) −1.00000 −0.0833333
\(145\) 12.9624 11.4617i 1.07647 0.951841i
\(146\) 9.92478 0.821380
\(147\) 1.77575i 0.146461i
\(148\) 7.61213i 0.625713i
\(149\) −4.64974 −0.380921 −0.190461 0.981695i \(-0.560998\pi\)
−0.190461 + 0.981695i \(0.560998\pi\)
\(150\) −0.612127 + 4.96239i −0.0499799 + 0.405177i
\(151\) 10.7005 0.870796 0.435398 0.900238i \(-0.356608\pi\)
0.435398 + 0.900238i \(0.356608\pi\)
\(152\) 4.96239i 0.402503i
\(153\) 1.35026i 0.109162i
\(154\) −9.92478 −0.799761
\(155\) 6.70052 5.92478i 0.538199 0.475890i
\(156\) −4.96239 −0.397309
\(157\) 17.0132i 1.35780i 0.734231 + 0.678900i \(0.237543\pi\)
−0.734231 + 0.678900i \(0.762457\pi\)
\(158\) 4.12601i 0.328248i
\(159\) 6.96239 0.552153
\(160\) −1.48119 1.67513i −0.117099 0.132431i
\(161\) −2.96239 −0.233469
\(162\) 1.00000i 0.0785674i
\(163\) 12.6253i 0.988890i 0.869209 + 0.494445i \(0.164629\pi\)
−0.869209 + 0.494445i \(0.835371\pi\)
\(164\) −4.70052 −0.367049
\(165\) 4.96239 + 5.61213i 0.386321 + 0.436903i
\(166\) 6.38787 0.495795
\(167\) 24.6253i 1.90556i 0.303657 + 0.952781i \(0.401792\pi\)
−0.303657 + 0.952781i \(0.598208\pi\)
\(168\) 2.96239i 0.228553i
\(169\) −11.6253 −0.894254
\(170\) −2.26187 + 2.00000i −0.173477 + 0.153393i
\(171\) −4.96239 −0.379483
\(172\) 10.3127i 0.786332i
\(173\) 4.44851i 0.338214i −0.985598 0.169107i \(-0.945912\pi\)
0.985598 0.169107i \(-0.0540883\pi\)
\(174\) 7.73813 0.586626
\(175\) −14.7005 1.81336i −1.11126 0.137077i
\(176\) −3.35026 −0.252535
\(177\) 1.22425i 0.0920205i
\(178\) 9.92478i 0.743894i
\(179\) 13.8496 1.03516 0.517582 0.855634i \(-0.326832\pi\)
0.517582 + 0.855634i \(0.326832\pi\)
\(180\) −1.67513 + 1.48119i −0.124857 + 0.110402i
\(181\) −22.6859 −1.68623 −0.843116 0.537732i \(-0.819281\pi\)
−0.843116 + 0.537732i \(0.819281\pi\)
\(182\) 14.7005i 1.08968i
\(183\) 11.0884i 0.819678i
\(184\) −1.00000 −0.0737210
\(185\) −11.2750 12.7513i −0.828957 0.937495i
\(186\) 4.00000 0.293294
\(187\) 4.52373i 0.330808i
\(188\) 3.22425i 0.235153i
\(189\) −2.96239 −0.215482
\(190\) −7.35026 8.31265i −0.533244 0.603063i
\(191\) −19.3258 −1.39837 −0.699184 0.714942i \(-0.746453\pi\)
−0.699184 + 0.714942i \(0.746453\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 5.92478i 0.426475i −0.977000 0.213237i \(-0.931599\pi\)
0.977000 0.213237i \(-0.0684008\pi\)
\(194\) 12.8872 0.925245
\(195\) −8.31265 + 7.35026i −0.595281 + 0.526363i
\(196\) 1.77575 0.126839
\(197\) 8.07522i 0.575336i −0.957730 0.287668i \(-0.907120\pi\)
0.957730 0.287668i \(-0.0928799\pi\)
\(198\) 3.35026i 0.238093i
\(199\) −15.9756 −1.13248 −0.566239 0.824241i \(-0.691602\pi\)
−0.566239 + 0.824241i \(0.691602\pi\)
\(200\) −4.96239 0.612127i −0.350894 0.0432839i
\(201\) −7.61213 −0.536918
\(202\) 4.26187i 0.299864i
\(203\) 22.9234i 1.60890i
\(204\) −1.35026 −0.0945372
\(205\) −7.87399 + 6.96239i −0.549943 + 0.486274i
\(206\) 0.261865 0.0182450
\(207\) 1.00000i 0.0695048i
\(208\) 4.96239i 0.344080i
\(209\) −16.6253 −1.15000
\(210\) −4.38787 4.96239i −0.302792 0.342437i
\(211\) 21.7743 1.49901 0.749503 0.662000i \(-0.230292\pi\)
0.749503 + 0.662000i \(0.230292\pi\)
\(212\) 6.96239i 0.478179i
\(213\) 2.18664i 0.149826i
\(214\) −9.08840 −0.621270
\(215\) 15.2750 + 17.2750i 1.04175 + 1.17815i
\(216\) −1.00000 −0.0680414
\(217\) 11.8496i 0.804400i
\(218\) 18.9380i 1.28264i
\(219\) 9.92478 0.670654
\(220\) −5.61213 + 4.96239i −0.378370 + 0.334564i
\(221\) −6.70052 −0.450726
\(222\) 7.61213i 0.510893i
\(223\) 3.81336i 0.255361i −0.991815 0.127681i \(-0.959247\pi\)
0.991815 0.127681i \(-0.0407533\pi\)
\(224\) 2.96239 0.197933
\(225\) −0.612127 + 4.96239i −0.0408085 + 0.330826i
\(226\) 6.64974 0.442334
\(227\) 16.9380i 1.12421i 0.827065 + 0.562106i \(0.190009\pi\)
−0.827065 + 0.562106i \(0.809991\pi\)
\(228\) 4.96239i 0.328642i
\(229\) 26.9380 1.78011 0.890055 0.455853i \(-0.150666\pi\)
0.890055 + 0.455853i \(0.150666\pi\)
\(230\) −1.67513 + 1.48119i −0.110455 + 0.0976671i
\(231\) −9.92478 −0.653002
\(232\) 7.73813i 0.508033i
\(233\) 27.4010i 1.79510i −0.440910 0.897551i \(-0.645344\pi\)
0.440910 0.897551i \(-0.354656\pi\)
\(234\) −4.96239 −0.324401
\(235\) 4.77575 + 5.40105i 0.311535 + 0.352325i
\(236\) 1.22425 0.0796921
\(237\) 4.12601i 0.268013i
\(238\) 4.00000i 0.259281i
\(239\) −7.48612 −0.484237 −0.242118 0.970247i \(-0.577842\pi\)
−0.242118 + 0.970247i \(0.577842\pi\)
\(240\) −1.48119 1.67513i −0.0956107 0.108129i
\(241\) −13.0738 −0.842158 −0.421079 0.907024i \(-0.638348\pi\)
−0.421079 + 0.907024i \(0.638348\pi\)
\(242\) 0.224254i 0.0144156i
\(243\) 1.00000i 0.0641500i
\(244\) 11.0884 0.709862
\(245\) 2.97461 2.63023i 0.190041 0.168039i
\(246\) −4.70052 −0.299694
\(247\) 24.6253i 1.56687i
\(248\) 4.00000i 0.254000i
\(249\) 6.38787 0.404815
\(250\) −9.21933 + 6.32487i −0.583082 + 0.400020i
\(251\) −5.02302 −0.317050 −0.158525 0.987355i \(-0.550674\pi\)
−0.158525 + 0.987355i \(0.550674\pi\)
\(252\) 2.96239i 0.186613i
\(253\) 3.35026i 0.210629i
\(254\) 0.186642 0.0117110
\(255\) −2.26187 + 2.00000i −0.141643 + 0.125245i
\(256\) 1.00000 0.0625000
\(257\) 19.4010i 1.21020i −0.796148 0.605102i \(-0.793132\pi\)
0.796148 0.605102i \(-0.206868\pi\)
\(258\) 10.3127i 0.642038i
\(259\) 22.5501 1.40119
\(260\) −7.35026 8.31265i −0.455844 0.515529i
\(261\) 7.73813 0.478979
\(262\) 7.92478i 0.489594i
\(263\) 15.4763i 0.954308i 0.878820 + 0.477154i \(0.158332\pi\)
−0.878820 + 0.477154i \(0.841668\pi\)
\(264\) −3.35026 −0.206194
\(265\) 10.3127 + 11.6629i 0.633501 + 0.716447i
\(266\) 14.7005 0.901347
\(267\) 9.92478i 0.607387i
\(268\) 7.61213i 0.464985i
\(269\) 20.2130 1.23241 0.616204 0.787587i \(-0.288670\pi\)
0.616204 + 0.787587i \(0.288670\pi\)
\(270\) −1.67513 + 1.48119i −0.101945 + 0.0901426i
\(271\) 30.3996 1.84665 0.923323 0.384024i \(-0.125462\pi\)
0.923323 + 0.384024i \(0.125462\pi\)
\(272\) 1.35026i 0.0818716i
\(273\) 14.7005i 0.889716i
\(274\) 9.19982 0.555781
\(275\) −2.05079 + 16.6253i −0.123667 + 1.00254i
\(276\) −1.00000 −0.0601929
\(277\) 20.8119i 1.25047i −0.780437 0.625234i \(-0.785003\pi\)
0.780437 0.625234i \(-0.214997\pi\)
\(278\) 8.62530i 0.517311i
\(279\) 4.00000 0.239474
\(280\) 4.96239 4.38787i 0.296559 0.262226i
\(281\) 19.8496 1.18413 0.592063 0.805892i \(-0.298314\pi\)
0.592063 + 0.805892i \(0.298314\pi\)
\(282\) 3.22425i 0.192002i
\(283\) 12.3879i 0.736383i 0.929750 + 0.368191i \(0.120023\pi\)
−0.929750 + 0.368191i \(0.879977\pi\)
\(284\) 2.18664 0.129753
\(285\) −7.35026 8.31265i −0.435392 0.492399i
\(286\) −16.6253 −0.983075
\(287\) 13.9248i 0.821954i
\(288\) 1.00000i 0.0589256i
\(289\) 15.1768 0.892753
\(290\) 11.4617 + 12.9624i 0.673053 + 0.761178i
\(291\) 12.8872 0.755459
\(292\) 9.92478i 0.580804i
\(293\) 9.03761i 0.527983i 0.964525 + 0.263991i \(0.0850391\pi\)
−0.964525 + 0.263991i \(0.914961\pi\)
\(294\) 1.77575 0.103564
\(295\) 2.05079 1.81336i 0.119401 0.105578i
\(296\) 7.61213 0.442446
\(297\) 3.35026i 0.194402i
\(298\) 4.64974i 0.269352i
\(299\) −4.96239 −0.286982
\(300\) −4.96239 0.612127i −0.286504 0.0353412i
\(301\) −30.5501 −1.76088
\(302\) 10.7005i 0.615746i
\(303\) 4.26187i 0.244838i
\(304\) 4.96239 0.284613
\(305\) 18.5745 16.4241i 1.06357 0.940440i
\(306\) −1.35026 −0.0771893
\(307\) 30.5501i 1.74359i 0.489875 + 0.871793i \(0.337042\pi\)
−0.489875 + 0.871793i \(0.662958\pi\)
\(308\) 9.92478i 0.565517i
\(309\) 0.261865 0.0148970
\(310\) 5.92478 + 6.70052i 0.336505 + 0.380564i
\(311\) 14.4387 0.818741 0.409371 0.912368i \(-0.365748\pi\)
0.409371 + 0.912368i \(0.365748\pi\)
\(312\) 4.96239i 0.280940i
\(313\) 27.9610i 1.58045i 0.612818 + 0.790224i \(0.290036\pi\)
−0.612818 + 0.790224i \(0.709964\pi\)
\(314\) −17.0132 −0.960109
\(315\) −4.38787 4.96239i −0.247229 0.279599i
\(316\) −4.12601 −0.232106
\(317\) 1.47627i 0.0829156i −0.999140 0.0414578i \(-0.986800\pi\)
0.999140 0.0414578i \(-0.0132002\pi\)
\(318\) 6.96239i 0.390431i
\(319\) 25.9248 1.45151
\(320\) 1.67513 1.48119i 0.0936427 0.0828013i
\(321\) −9.08840 −0.507265
\(322\) 2.96239i 0.165087i
\(323\) 6.70052i 0.372827i
\(324\) −1.00000 −0.0555556
\(325\) −24.6253 3.03761i −1.36597 0.168496i
\(326\) −12.6253 −0.699251
\(327\) 18.9380i 1.04727i
\(328\) 4.70052i 0.259543i
\(329\) −9.55149 −0.526591
\(330\) −5.61213 + 4.96239i −0.308937 + 0.273171i
\(331\) 23.1754 1.27383 0.636917 0.770932i \(-0.280209\pi\)
0.636917 + 0.770932i \(0.280209\pi\)
\(332\) 6.38787i 0.350580i
\(333\) 7.61213i 0.417142i
\(334\) −24.6253 −1.34744
\(335\) −11.2750 12.7513i −0.616021 0.696678i
\(336\) 2.96239 0.161612
\(337\) 21.0376i 1.14599i 0.819558 + 0.572996i \(0.194219\pi\)
−0.819558 + 0.572996i \(0.805781\pi\)
\(338\) 11.6253i 0.632333i
\(339\) 6.64974 0.361164
\(340\) −2.00000 2.26187i −0.108465 0.122667i
\(341\) 13.4010 0.725707
\(342\) 4.96239i 0.268335i
\(343\) 15.4763i 0.835640i
\(344\) −10.3127 −0.556021
\(345\) −1.67513 + 1.48119i −0.0901860 + 0.0797448i
\(346\) 4.44851 0.239153
\(347\) 3.37470i 0.181163i −0.995889 0.0905817i \(-0.971127\pi\)
0.995889 0.0905817i \(-0.0288726\pi\)
\(348\) 7.73813i 0.414808i
\(349\) 4.44851 0.238123 0.119062 0.992887i \(-0.462011\pi\)
0.119062 + 0.992887i \(0.462011\pi\)
\(350\) 1.81336 14.7005i 0.0969280 0.785776i
\(351\) −4.96239 −0.264873
\(352\) 3.35026i 0.178570i
\(353\) 35.4010i 1.88421i −0.335321 0.942104i \(-0.608845\pi\)
0.335321 0.942104i \(-0.391155\pi\)
\(354\) 1.22425 0.0650684
\(355\) 3.66291 3.23884i 0.194407 0.171900i
\(356\) 9.92478 0.526012
\(357\) 4.00000i 0.211702i
\(358\) 13.8496i 0.731972i
\(359\) 34.5501 1.82348 0.911742 0.410764i \(-0.134738\pi\)
0.911742 + 0.410764i \(0.134738\pi\)
\(360\) −1.48119 1.67513i −0.0780658 0.0882871i
\(361\) 5.62530 0.296068
\(362\) 22.6859i 1.19235i
\(363\) 0.224254i 0.0117703i
\(364\) 14.7005 0.770517
\(365\) 14.7005 + 16.6253i 0.769461 + 0.870208i
\(366\) 11.0884 0.579600
\(367\) 22.8119i 1.19077i −0.803439 0.595387i \(-0.796999\pi\)
0.803439 0.595387i \(-0.203001\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) −4.70052 −0.244699
\(370\) 12.7513 11.2750i 0.662909 0.586161i
\(371\) −20.6253 −1.07081
\(372\) 4.00000i 0.207390i
\(373\) 10.8364i 0.561087i 0.959841 + 0.280543i \(0.0905146\pi\)
−0.959841 + 0.280543i \(0.909485\pi\)
\(374\) −4.52373 −0.233917
\(375\) −9.21933 + 6.32487i −0.476084 + 0.326615i
\(376\) −3.22425 −0.166278
\(377\) 38.3996i 1.97768i
\(378\) 2.96239i 0.152369i
\(379\) 32.4387 1.66626 0.833131 0.553076i \(-0.186546\pi\)
0.833131 + 0.553076i \(0.186546\pi\)
\(380\) 8.31265 7.35026i 0.426430 0.377060i
\(381\) 0.186642 0.00956198
\(382\) 19.3258i 0.988795i
\(383\) 32.9986i 1.68615i −0.537797 0.843074i \(-0.680743\pi\)
0.537797 0.843074i \(-0.319257\pi\)
\(384\) 1.00000 0.0510310
\(385\) −14.7005 16.6253i −0.749208 0.847304i
\(386\) 5.92478 0.301563
\(387\) 10.3127i 0.524221i
\(388\) 12.8872i 0.654247i
\(389\) −29.1246 −1.47668 −0.738338 0.674431i \(-0.764389\pi\)
−0.738338 + 0.674431i \(0.764389\pi\)
\(390\) −7.35026 8.31265i −0.372195 0.420927i
\(391\) −1.35026 −0.0682857
\(392\) 1.77575i 0.0896887i
\(393\) 7.92478i 0.399752i
\(394\) 8.07522 0.406824
\(395\) −6.91160 + 6.11142i −0.347761 + 0.307499i
\(396\) −3.35026 −0.168357
\(397\) 13.7381i 0.689497i −0.938695 0.344749i \(-0.887964\pi\)
0.938695 0.344749i \(-0.112036\pi\)
\(398\) 15.9756i 0.800783i
\(399\) 14.7005 0.735947
\(400\) 0.612127 4.96239i 0.0306063 0.248119i
\(401\) −1.44992 −0.0724057 −0.0362028 0.999344i \(-0.511526\pi\)
−0.0362028 + 0.999344i \(0.511526\pi\)
\(402\) 7.61213i 0.379658i
\(403\) 19.8496i 0.988777i
\(404\) −4.26187 −0.212036
\(405\) −1.67513 + 1.48119i −0.0832379 + 0.0736011i
\(406\) −22.9234 −1.13767
\(407\) 25.5026i 1.26412i
\(408\) 1.35026i 0.0668479i
\(409\) 17.8496 0.882604 0.441302 0.897359i \(-0.354517\pi\)
0.441302 + 0.897359i \(0.354517\pi\)
\(410\) −6.96239 7.87399i −0.343848 0.388869i
\(411\) 9.19982 0.453793
\(412\) 0.261865i 0.0129012i
\(413\) 3.62672i 0.178459i
\(414\) −1.00000 −0.0491473
\(415\) 9.46168 + 10.7005i 0.464456 + 0.525268i
\(416\) 4.96239 0.243301
\(417\) 8.62530i 0.422383i
\(418\) 16.6253i 0.813170i
\(419\) −17.9003 −0.874489 −0.437244 0.899343i \(-0.644046\pi\)
−0.437244 + 0.899343i \(0.644046\pi\)
\(420\) 4.96239 4.38787i 0.242140 0.214106i
\(421\) 7.61213 0.370992 0.185496 0.982645i \(-0.440611\pi\)
0.185496 + 0.982645i \(0.440611\pi\)
\(422\) 21.7743i 1.05996i
\(423\) 3.22425i 0.156769i
\(424\) −6.96239 −0.338123
\(425\) −6.70052 0.826531i −0.325023 0.0400927i
\(426\) 2.18664 0.105943
\(427\) 32.8481i 1.58963i
\(428\) 9.08840i 0.439304i
\(429\) −16.6253 −0.802677
\(430\) −17.2750 + 15.2750i −0.833076 + 0.736628i
\(431\) −22.9525 −1.10558 −0.552792 0.833319i \(-0.686438\pi\)
−0.552792 + 0.833319i \(0.686438\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 33.7645i 1.62262i 0.584618 + 0.811309i \(0.301244\pi\)
−0.584618 + 0.811309i \(0.698756\pi\)
\(434\) −11.8496 −0.568797
\(435\) 11.4617 + 12.9624i 0.549546 + 0.621499i
\(436\) 18.9380 0.906963
\(437\) 4.96239i 0.237383i
\(438\) 9.92478i 0.474224i
\(439\) 23.4763 1.12046 0.560231 0.828337i \(-0.310713\pi\)
0.560231 + 0.828337i \(0.310713\pi\)
\(440\) −4.96239 5.61213i −0.236573 0.267548i
\(441\) 1.77575 0.0845593
\(442\) 6.70052i 0.318711i
\(443\) 30.5501i 1.45148i −0.687970 0.725739i \(-0.741498\pi\)
0.687970 0.725739i \(-0.258502\pi\)
\(444\) 7.61213 0.361256
\(445\) 16.6253 14.7005i 0.788115 0.696872i
\(446\) 3.81336 0.180568
\(447\) 4.64974i 0.219925i
\(448\) 2.96239i 0.139960i
\(449\) −32.7005 −1.54323 −0.771617 0.636088i \(-0.780552\pi\)
−0.771617 + 0.636088i \(0.780552\pi\)
\(450\) −4.96239 0.612127i −0.233929 0.0288559i
\(451\) −15.7480 −0.741544
\(452\) 6.64974i 0.312777i
\(453\) 10.7005i 0.502754i
\(454\) −16.9380 −0.794937
\(455\) 24.6253 21.7743i 1.15445 1.02080i
\(456\) 4.96239 0.232385
\(457\) 5.81336i 0.271937i −0.990713 0.135969i \(-0.956585\pi\)
0.990713 0.135969i \(-0.0434147\pi\)
\(458\) 26.9380i 1.25873i
\(459\) −1.35026 −0.0630248
\(460\) −1.48119 1.67513i −0.0690610 0.0781034i
\(461\) −23.9902 −1.11733 −0.558666 0.829392i \(-0.688687\pi\)
−0.558666 + 0.829392i \(0.688687\pi\)
\(462\) 9.92478i 0.461742i
\(463\) 35.3620i 1.64341i −0.569911 0.821706i \(-0.693022\pi\)
0.569911 0.821706i \(-0.306978\pi\)
\(464\) −7.73813 −0.359234
\(465\) 5.92478 + 6.70052i 0.274755 + 0.310729i
\(466\) 27.4010 1.26933
\(467\) 1.98541i 0.0918739i 0.998944 + 0.0459369i \(0.0146273\pi\)
−0.998944 + 0.0459369i \(0.985373\pi\)
\(468\) 4.96239i 0.229386i
\(469\) 22.5501 1.04127
\(470\) −5.40105 + 4.77575i −0.249132 + 0.220289i
\(471\) −17.0132 −0.783926
\(472\) 1.22425i 0.0563508i
\(473\) 34.5501i 1.58861i
\(474\) −4.12601 −0.189514
\(475\) 3.03761 24.6253i 0.139375 1.12989i
\(476\) 4.00000 0.183340
\(477\) 6.96239i 0.318786i
\(478\) 7.48612i 0.342407i
\(479\) −11.0738 −0.505975 −0.252988 0.967470i \(-0.581413\pi\)
−0.252988 + 0.967470i \(0.581413\pi\)
\(480\) 1.67513 1.48119i 0.0764589 0.0676070i
\(481\) 37.7743 1.72236
\(482\) 13.0738i 0.595496i
\(483\) 2.96239i 0.134793i
\(484\) −0.224254 −0.0101934
\(485\) 19.0884 + 21.5877i 0.866759 + 0.980246i
\(486\) −1.00000 −0.0453609
\(487\) 17.4372i 0.790157i −0.918647 0.395078i \(-0.870717\pi\)
0.918647 0.395078i \(-0.129283\pi\)
\(488\) 11.0884i 0.501948i
\(489\) −12.6253 −0.570936
\(490\) 2.63023 + 2.97461i 0.118821 + 0.134379i
\(491\) 14.8773 0.671404 0.335702 0.941968i \(-0.391027\pi\)
0.335702 + 0.941968i \(0.391027\pi\)
\(492\) 4.70052i 0.211916i
\(493\) 10.4485i 0.470577i
\(494\) 24.6253 1.10794
\(495\) −5.61213 + 4.96239i −0.252246 + 0.223043i
\(496\) −4.00000 −0.179605
\(497\) 6.47768i 0.290564i
\(498\) 6.38787i 0.286247i
\(499\) 16.1016 0.720805 0.360403 0.932797i \(-0.382639\pi\)
0.360403 + 0.932797i \(0.382639\pi\)
\(500\) −6.32487 9.21933i −0.282857 0.412301i
\(501\) −24.6253 −1.10018
\(502\) 5.02302i 0.224188i
\(503\) 38.8021i 1.73010i 0.501686 + 0.865050i \(0.332713\pi\)
−0.501686 + 0.865050i \(0.667287\pi\)
\(504\) 2.96239 0.131955
\(505\) −7.13918 + 6.31265i −0.317689 + 0.280909i
\(506\) −3.35026 −0.148937
\(507\) 11.6253i 0.516298i
\(508\) 0.186642i 0.00828091i
\(509\) −23.4372 −1.03884 −0.519419 0.854520i \(-0.673852\pi\)
−0.519419 + 0.854520i \(0.673852\pi\)
\(510\) −2.00000 2.26187i −0.0885615 0.100157i
\(511\) −29.4010 −1.30063
\(512\) 1.00000i 0.0441942i
\(513\) 4.96239i 0.219095i
\(514\) 19.4010 0.855743
\(515\) 0.387873 + 0.438658i 0.0170917 + 0.0193296i
\(516\) −10.3127 −0.453989
\(517\) 10.8021i 0.475076i
\(518\) 22.5501i 0.990794i
\(519\) 4.44851 0.195268
\(520\) 8.31265 7.35026i 0.364534 0.322330i
\(521\) 21.1490 0.926556 0.463278 0.886213i \(-0.346673\pi\)
0.463278 + 0.886213i \(0.346673\pi\)
\(522\) 7.73813i 0.338689i
\(523\) 11.7626i 0.514341i 0.966366 + 0.257171i \(0.0827903\pi\)
−0.966366 + 0.257171i \(0.917210\pi\)
\(524\) −7.92478 −0.346196
\(525\) 1.81336 14.7005i 0.0791414 0.641583i
\(526\) −15.4763 −0.674797
\(527\) 5.40105i 0.235273i
\(528\) 3.35026i 0.145801i
\(529\) −1.00000 −0.0434783
\(530\) −11.6629 + 10.3127i −0.506605 + 0.447953i
\(531\) 1.22425 0.0531281
\(532\) 14.7005i 0.637349i
\(533\) 23.3258i 1.01035i
\(534\) 9.92478 0.429487
\(535\) −13.4617 15.2243i −0.581999 0.658202i
\(536\) 7.61213 0.328794
\(537\) 13.8496i 0.597652i
\(538\) 20.2130i 0.871444i
\(539\) 5.94921 0.256251
\(540\) −1.48119 1.67513i −0.0637405 0.0720862i
\(541\) −21.1754 −0.910401 −0.455200 0.890389i \(-0.650432\pi\)
−0.455200 + 0.890389i \(0.650432\pi\)
\(542\) 30.3996i 1.30578i
\(543\) 22.6859i 0.973547i
\(544\) 1.35026 0.0578920
\(545\) 31.7235 28.0508i 1.35889 1.20156i
\(546\) 14.7005 0.629124
\(547\) 5.29948i 0.226589i −0.993561 0.113295i \(-0.963860\pi\)
0.993561 0.113295i \(-0.0361404\pi\)
\(548\) 9.19982i 0.392997i
\(549\) 11.0884 0.473241
\(550\) −16.6253 2.05079i −0.708905 0.0874458i
\(551\) −38.3996 −1.63588
\(552\) 1.00000i 0.0425628i
\(553\) 12.2228i 0.519768i
\(554\) 20.8119 0.884215
\(555\) 12.7513 11.2750i 0.541263 0.478599i
\(556\) 8.62530 0.365794
\(557\) 7.99015i 0.338554i 0.985569 + 0.169277i \(0.0541432\pi\)
−0.985569 + 0.169277i \(0.945857\pi\)
\(558\) 4.00000i 0.169334i
\(559\) −51.1754 −2.16449
\(560\) 4.38787 + 4.96239i 0.185421 + 0.209699i
\(561\) −4.52373 −0.190992
\(562\) 19.8496i 0.837303i
\(563\) 15.1636i 0.639070i 0.947574 + 0.319535i \(0.103527\pi\)
−0.947574 + 0.319535i \(0.896473\pi\)
\(564\) −3.22425 −0.135766
\(565\) 9.84955 + 11.1392i 0.414374 + 0.468629i
\(566\) −12.3879 −0.520701
\(567\) 2.96239i 0.124409i
\(568\) 2.18664i 0.0917495i
\(569\) 25.5223 1.06995 0.534976 0.844868i \(-0.320321\pi\)
0.534976 + 0.844868i \(0.320321\pi\)
\(570\) 8.31265 7.35026i 0.348179 0.307869i
\(571\) 6.76590 0.283144 0.141572 0.989928i \(-0.454784\pi\)
0.141572 + 0.989928i \(0.454784\pi\)
\(572\) 16.6253i 0.695139i
\(573\) 19.3258i 0.807348i
\(574\) 13.9248 0.581209
\(575\) −4.96239 0.612127i −0.206946 0.0255275i
\(576\) 1.00000 0.0416667
\(577\) 4.00000i 0.166522i −0.996528 0.0832611i \(-0.973466\pi\)
0.996528 0.0832611i \(-0.0265335\pi\)
\(578\) 15.1768i 0.631271i
\(579\) 5.92478 0.246225
\(580\) −12.9624 + 11.4617i −0.538234 + 0.475920i
\(581\) −18.9234 −0.785073
\(582\) 12.8872i 0.534190i
\(583\) 23.3258i 0.966057i
\(584\) −9.92478 −0.410690
\(585\) −7.35026 8.31265i −0.303896 0.343686i
\(586\) −9.03761 −0.373340
\(587\) 12.8773i 0.531504i 0.964041 + 0.265752i \(0.0856202\pi\)
−0.964041 + 0.265752i \(0.914380\pi\)
\(588\) 1.77575i 0.0732305i
\(589\) −19.8496 −0.817887
\(590\) 1.81336 + 2.05079i 0.0746548 + 0.0844295i
\(591\) 8.07522 0.332170
\(592\) 7.61213i 0.312856i
\(593\) 16.2981i 0.669281i 0.942346 + 0.334641i \(0.108615\pi\)
−0.942346 + 0.334641i \(0.891385\pi\)
\(594\) −3.35026 −0.137463
\(595\) 6.70052 5.92478i 0.274695 0.242892i
\(596\) 4.64974 0.190461
\(597\) 15.9756i 0.653836i
\(598\) 4.96239i 0.202927i
\(599\) −9.91493 −0.405113 −0.202556 0.979271i \(-0.564925\pi\)
−0.202556 + 0.979271i \(0.564925\pi\)
\(600\) 0.612127 4.96239i 0.0249900 0.202589i
\(601\) −7.40105 −0.301895 −0.150948 0.988542i \(-0.548232\pi\)
−0.150948 + 0.988542i \(0.548232\pi\)
\(602\) 30.5501i 1.24513i
\(603\) 7.61213i 0.309990i
\(604\) −10.7005 −0.435398
\(605\) −0.375654 + 0.332163i −0.0152725 + 0.0135044i
\(606\) −4.26187 −0.173126
\(607\) 13.9610i 0.566658i 0.959023 + 0.283329i \(0.0914389\pi\)
−0.959023 + 0.283329i \(0.908561\pi\)
\(608\) 4.96239i 0.201251i
\(609\) −22.9234 −0.928902
\(610\) 16.4241 + 18.5745i 0.664991 + 0.752060i
\(611\) −16.0000 −0.647291
\(612\) 1.35026i 0.0545811i
\(613\) 41.3865i 1.67158i −0.549047 0.835792i \(-0.685009\pi\)
0.549047 0.835792i \(-0.314991\pi\)
\(614\) −30.5501 −1.23290
\(615\) −6.96239 7.87399i −0.280751 0.317510i
\(616\) 9.92478 0.399881
\(617\) 29.3014i 1.17963i −0.807539 0.589815i \(-0.799201\pi\)
0.807539 0.589815i \(-0.200799\pi\)
\(618\) 0.261865i 0.0105338i
\(619\) 19.0376 0.765186 0.382593 0.923917i \(-0.375031\pi\)
0.382593 + 0.923917i \(0.375031\pi\)
\(620\) −6.70052 + 5.92478i −0.269099 + 0.237945i
\(621\) −1.00000 −0.0401286
\(622\) 14.4387i 0.578937i
\(623\) 29.4010i 1.17793i
\(624\) 4.96239 0.198655
\(625\) −24.2506 6.07522i −0.970024 0.243009i
\(626\) −27.9610 −1.11755
\(627\) 16.6253i 0.663951i
\(628\) 17.0132i 0.678900i
\(629\) 10.2784 0.409825
\(630\) 4.96239 4.38787i 0.197706 0.174817i
\(631\) 12.4993 0.497589 0.248794 0.968556i \(-0.419966\pi\)
0.248794 + 0.968556i \(0.419966\pi\)
\(632\) 4.12601i 0.164124i
\(633\) 21.7743i 0.865452i
\(634\) 1.47627 0.0586302
\(635\) 0.276454 + 0.312650i 0.0109707 + 0.0124072i
\(636\) −6.96239 −0.276077
\(637\) 8.81194i 0.349142i
\(638\) 25.9248i 1.02637i
\(639\) 2.18664 0.0865022
\(640\) 1.48119 + 1.67513i 0.0585493 + 0.0662154i
\(641\) −34.0263 −1.34396 −0.671980 0.740569i \(-0.734556\pi\)
−0.671980 + 0.740569i \(0.734556\pi\)
\(642\) 9.08840i 0.358690i
\(643\) 7.34041i 0.289478i −0.989470 0.144739i \(-0.953766\pi\)
0.989470 0.144739i \(-0.0462342\pi\)
\(644\) 2.96239 0.116734
\(645\) −17.2750 + 15.2750i −0.680204 + 0.601454i
\(646\) 6.70052 0.263629
\(647\) 14.9525i 0.587845i 0.955829 + 0.293922i \(0.0949608\pi\)
−0.955829 + 0.293922i \(0.905039\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 4.10157 0.161001
\(650\) 3.03761 24.6253i 0.119145 0.965884i
\(651\) −11.8496 −0.464421
\(652\) 12.6253i 0.494445i
\(653\) 20.4485i 0.800212i 0.916469 + 0.400106i \(0.131027\pi\)
−0.916469 + 0.400106i \(0.868973\pi\)
\(654\) 18.9380 0.740532
\(655\) −13.2750 + 11.7381i −0.518699 + 0.458647i
\(656\) 4.70052 0.183525
\(657\) 9.92478i 0.387202i
\(658\) 9.55149i 0.372356i
\(659\) −38.4241 −1.49679 −0.748395 0.663254i \(-0.769175\pi\)
−0.748395 + 0.663254i \(0.769175\pi\)
\(660\) −4.96239 5.61213i −0.193161 0.218452i
\(661\) −39.3112 −1.52903 −0.764515 0.644606i \(-0.777021\pi\)
−0.764515 + 0.644606i \(0.777021\pi\)
\(662\) 23.1754i 0.900737i
\(663\) 6.70052i 0.260227i
\(664\) −6.38787 −0.247898
\(665\) 21.7743 + 24.6253i 0.844372 + 0.954928i
\(666\) 7.61213 0.294964
\(667\) 7.73813i 0.299622i
\(668\) 24.6253i 0.952781i
\(669\) 3.81336 0.147433
\(670\) 12.7513 11.2750i 0.492626 0.435593i
\(671\) 37.1490 1.43412
\(672\) 2.96239i 0.114277i
\(673\) 25.5515i 0.984938i 0.870330 + 0.492469i \(0.163905\pi\)
−0.870330 + 0.492469i \(0.836095\pi\)
\(674\) −21.0376 −0.810339
\(675\) −4.96239 0.612127i −0.191002 0.0235608i
\(676\) 11.6253 0.447127
\(677\) 36.2130i 1.39178i −0.718149 0.695889i \(-0.755010\pi\)
0.718149 0.695889i \(-0.244990\pi\)
\(678\) 6.64974i 0.255382i
\(679\) −38.1768 −1.46509
\(680\) 2.26187 2.00000i 0.0867386 0.0766965i
\(681\) −16.9380 −0.649064
\(682\) 13.4010i 0.513153i
\(683\) 15.4763i 0.592183i −0.955160 0.296092i \(-0.904317\pi\)
0.955160 0.296092i \(-0.0956833\pi\)
\(684\) 4.96239 0.189742
\(685\) 13.6267 + 15.4109i 0.520650 + 0.588820i
\(686\) 15.4763 0.590887
\(687\) 26.9380i 1.02775i
\(688\) 10.3127i 0.393166i
\(689\) −34.5501 −1.31625
\(690\) −1.48119 1.67513i −0.0563881 0.0637711i
\(691\) −37.6531 −1.43239 −0.716195 0.697900i \(-0.754118\pi\)
−0.716195 + 0.697900i \(0.754118\pi\)
\(692\) 4.44851i 0.169107i
\(693\) 9.92478i 0.377011i
\(694\) 3.37470 0.128102
\(695\) 14.4485 12.7757i 0.548063 0.484612i
\(696\) −7.73813 −0.293313
\(697\) 6.34694i 0.240407i
\(698\) 4.44851i 0.168378i
\(699\) 27.4010 1.03640
\(700\) 14.7005 + 1.81336i 0.555628 + 0.0685385i
\(701\) 28.3488 1.07072 0.535361 0.844624i \(-0.320176\pi\)
0.535361 + 0.844624i \(0.320176\pi\)
\(702\) 4.96239i 0.187293i
\(703\) 37.7743i 1.42469i
\(704\) 3.35026 0.126268
\(705\) −5.40105 + 4.77575i −0.203415 + 0.179865i
\(706\) 35.4010 1.33234
\(707\) 12.6253i 0.474823i
\(708\) 1.22425i 0.0460103i
\(709\) 43.5633 1.63605 0.818026 0.575181i \(-0.195068\pi\)
0.818026 + 0.575181i \(0.195068\pi\)
\(710\) 3.23884 + 3.66291i 0.121552 + 0.137467i
\(711\) −4.12601 −0.154737
\(712\) 9.92478i 0.371947i
\(713\) 4.00000i 0.149801i
\(714\) 4.00000 0.149696
\(715\) −24.6253 27.8496i −0.920934 1.04151i
\(716\) −13.8496 −0.517582
\(717\) 7.48612i 0.279574i
\(718\) 34.5501i 1.28940i
\(719\) −32.3634 −1.20695 −0.603476 0.797381i \(-0.706218\pi\)
−0.603476 + 0.797381i \(0.706218\pi\)
\(720\) 1.67513 1.48119i 0.0624284 0.0552009i
\(721\) −0.775746 −0.0288903
\(722\) 5.62530i 0.209352i
\(723\) 13.0738i 0.486220i
\(724\) 22.6859 0.843116
\(725\) −4.73672 + 38.3996i −0.175917 + 1.42613i
\(726\) −0.224254 −0.00832284
\(727\) 6.96239i 0.258221i 0.991630 + 0.129110i \(0.0412121\pi\)
−0.991630 + 0.129110i \(0.958788\pi\)
\(728\) 14.7005i 0.544838i
\(729\) −1.00000 −0.0370370
\(730\) −16.6253 + 14.7005i −0.615330 + 0.544091i
\(731\) −13.9248 −0.515026
\(732\) 11.0884i 0.409839i
\(733\) 9.68735i 0.357810i 0.983866 + 0.178905i \(0.0572555\pi\)
−0.983866 + 0.178905i \(0.942744\pi\)
\(734\) 22.8119 0.842004
\(735\) 2.63023 + 2.97461i 0.0970173 + 0.109720i
\(736\) 1.00000 0.0368605
\(737\) 25.5026i 0.939401i
\(738\) 4.70052i 0.173029i
\(739\) 42.9234 1.57896 0.789481 0.613775i \(-0.210350\pi\)
0.789481 + 0.613775i \(0.210350\pi\)
\(740\) 11.2750 + 12.7513i 0.414479 + 0.468747i
\(741\) 24.6253 0.904633
\(742\) 20.6253i 0.757179i
\(743\) 16.9986i 0.623618i −0.950145 0.311809i \(-0.899065\pi\)
0.950145 0.311809i \(-0.100935\pi\)
\(744\) −4.00000 −0.146647
\(745\) 7.78892 6.88717i 0.285364 0.252326i
\(746\) −10.8364 −0.396748
\(747\) 6.38787i 0.233720i
\(748\) 4.52373i 0.165404i
\(749\) 26.9234 0.983758
\(750\) −6.32487 9.21933i −0.230952 0.336642i
\(751\) −17.9003 −0.653193 −0.326596 0.945164i \(-0.605902\pi\)
−0.326596 + 0.945164i \(0.605902\pi\)
\(752\) 3.22425i 0.117576i
\(753\) 5.02302i 0.183049i
\(754\) −38.3996 −1.39843
\(755\) −17.9248 + 15.8496i −0.652349 + 0.576824i
\(756\) 2.96239 0.107741
\(757\) 12.3879i 0.450245i −0.974330 0.225122i \(-0.927722\pi\)
0.974330 0.225122i \(-0.0722782\pi\)
\(758\) 32.4387i 1.17823i
\(759\) −3.35026 −0.121607
\(760\) 7.35026 + 8.31265i 0.266622 + 0.301532i
\(761\) 38.5764 1.39839 0.699197 0.714929i \(-0.253541\pi\)
0.699197 + 0.714929i \(0.253541\pi\)
\(762\) 0.186642i 0.00676134i
\(763\) 56.1016i 2.03101i
\(764\) 19.3258 0.699184
\(765\) −2.00000 2.26187i −0.0723102 0.0817779i
\(766\) 32.9986 1.19229
\(767\) 6.07522i 0.219364i
\(768\) 1.00000i 0.0360844i
\(769\) −34.2228 −1.23411 −0.617054 0.786921i \(-0.711674\pi\)
−0.617054 + 0.786921i \(0.711674\pi\)
\(770\) 16.6253 14.7005i 0.599134 0.529770i
\(771\) 19.4010 0.698712
\(772\) 5.92478i 0.213237i
\(773\) 13.5613i 0.487768i −0.969804 0.243884i \(-0.921578\pi\)
0.969804 0.243884i \(-0.0784215\pi\)
\(774\) −10.3127 −0.370681
\(775\) −2.44851 + 19.8496i −0.0879530 + 0.713017i
\(776\) −12.8872 −0.462622
\(777\) 22.5501i 0.808980i
\(778\) 29.1246i 1.04417i
\(779\) 23.3258 0.835734
\(780\) 8.31265 7.35026i 0.297641 0.263182i
\(781\) 7.32582 0.262139
\(782\) 1.35026i 0.0482853i
\(783\) 7.73813i 0.276538i
\(784\) −1.77575 −0.0634195
\(785\) −25.1998 28.4993i −0.899420 1.01718i
\(786\) −7.92478 −0.282667
\(787\) 37.0132i 1.31938i −0.751539 0.659689i \(-0.770688\pi\)
0.751539 0.659689i \(-0.229312\pi\)
\(788\) 8.07522i