Properties

Label 600.2.d.g.349.1
Level 600
Weight 2
Character 600.349
Analytic conductor 4.791
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.214798336.3
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 349.1
Root \(-1.08003 + 0.912978i\) of \(x^{8} - 2 x^{7} - 2 x^{5} + 9 x^{4} - 4 x^{3} - 16 x + 16\)
Character \(\chi\) \(=\) 600.349
Dual form 600.2.d.g.349.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41298 - 0.0591148i) q^{2} -1.00000 q^{3} +(1.99301 + 0.167056i) q^{4} +(1.41298 + 0.0591148i) q^{6} -1.33411i q^{7} +(-2.80620 - 0.353863i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-1.41298 - 0.0591148i) q^{2} -1.00000 q^{3} +(1.99301 + 0.167056i) q^{4} +(1.41298 + 0.0591148i) q^{6} -1.33411i q^{7} +(-2.80620 - 0.353863i) q^{8} +1.00000 q^{9} +2.94418i q^{11} +(-1.99301 - 0.167056i) q^{12} +2.04184 q^{13} +(-0.0788658 + 1.88507i) q^{14} +(3.94418 + 0.665888i) q^{16} -3.61241i q^{17} +(-1.41298 - 0.0591148i) q^{18} -5.35964i q^{19} +1.33411i q^{21} +(0.174045 - 4.16007i) q^{22} +8.59609i q^{23} +(2.80620 + 0.353863i) q^{24} +(-2.88507 - 0.120703i) q^{26} -1.00000 q^{27} +(0.222871 - 2.65890i) q^{28} -5.26432i q^{29} -2.08134 q^{31} +(-5.53368 - 1.17404i) q^{32} -2.94418i q^{33} +(-0.213547 + 5.10425i) q^{34} +(1.99301 + 0.167056i) q^{36} +6.55659 q^{37} +(-0.316834 + 7.57304i) q^{38} -2.04184 q^{39} +7.02786 q^{41} +(0.0788658 - 1.88507i) q^{42} +8.50078 q^{43} +(-0.491843 + 5.86779i) q^{44} +(0.508157 - 12.1461i) q^{46} -9.97204i q^{47} +(-3.94418 - 0.665888i) q^{48} +5.22015 q^{49} +3.61241i q^{51} +(4.06940 + 0.341101i) q^{52} +6.12318 q^{53} +(1.41298 + 0.0591148i) q^{54} +(-0.472092 + 3.74379i) q^{56} +5.35964i q^{57} +(-0.311199 + 7.43836i) q^{58} -4.75190i q^{59} -8.51476i q^{61} +(2.94089 + 0.123038i) q^{62} -1.33411i q^{63} +(7.74956 + 1.98602i) q^{64} +(-0.174045 + 4.16007i) q^{66} +10.6961 q^{67} +(0.603474 - 7.19957i) q^{68} -8.59609i q^{69} -2.62405 q^{71} +(-2.80620 - 0.353863i) q^{72} -15.3875i q^{73} +(-9.26432 - 0.387592i) q^{74} +(0.895358 - 10.6818i) q^{76} +3.92787 q^{77} +(2.88507 + 0.120703i) q^{78} -10.4450 q^{79} +1.00000 q^{81} +(-9.93021 - 0.415451i) q^{82} -1.52708 q^{83} +(-0.222871 + 2.65890i) q^{84} +(-12.0114 - 0.502522i) q^{86} +5.26432i q^{87} +(1.04184 - 8.26198i) q^{88} +12.7193 q^{89} -2.72404i q^{91} +(-1.43603 + 17.1321i) q^{92} +2.08134 q^{93} +(-0.589496 + 14.0903i) q^{94} +(5.53368 + 1.17404i) q^{96} +13.4450i q^{97} +(-7.37595 - 0.308588i) q^{98} +2.94418i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{2} - 8q^{3} - 4q^{4} + 2q^{6} - 8q^{8} + 8q^{9} + O(q^{10}) \) \( 8q - 2q^{2} - 8q^{3} - 4q^{4} + 2q^{6} - 8q^{8} + 8q^{9} + 4q^{12} + 6q^{14} + 8q^{16} - 2q^{18} + 20q^{22} + 8q^{24} - 2q^{26} - 8q^{27} + 24q^{28} + 8q^{31} - 12q^{32} - 12q^{34} - 4q^{36} + 14q^{38} - 6q^{42} - 8q^{43} + 12q^{44} + 20q^{46} - 8q^{48} + 24q^{52} + 8q^{53} + 2q^{54} + 8q^{56} - 20q^{58} + 26q^{62} + 32q^{64} - 20q^{66} + 24q^{67} + 36q^{68} - 40q^{71} - 8q^{72} - 8q^{74} - 20q^{76} - 24q^{77} + 2q^{78} + 16q^{79} + 8q^{81} - 16q^{82} - 32q^{83} - 24q^{84} - 18q^{86} - 8q^{88} + 28q^{92} - 8q^{93} + 4q^{94} + 12q^{96} - 40q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41298 0.0591148i −0.999126 0.0418005i
\(3\) −1.00000 −0.577350
\(4\) 1.99301 + 0.167056i 0.996505 + 0.0835279i
\(5\) 0 0
\(6\) 1.41298 + 0.0591148i 0.576846 + 0.0241335i
\(7\) 1.33411i 0.504247i −0.967695 0.252123i \(-0.918871\pi\)
0.967695 0.252123i \(-0.0811289\pi\)
\(8\) −2.80620 0.353863i −0.992143 0.125109i
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.94418i 0.887705i 0.896100 + 0.443853i \(0.146389\pi\)
−0.896100 + 0.443853i \(0.853611\pi\)
\(12\) −1.99301 0.167056i −0.575333 0.0482249i
\(13\) 2.04184 0.566304 0.283152 0.959075i \(-0.408620\pi\)
0.283152 + 0.959075i \(0.408620\pi\)
\(14\) −0.0788658 + 1.88507i −0.0210778 + 0.503806i
\(15\) 0 0
\(16\) 3.94418 + 0.665888i 0.986046 + 0.166472i
\(17\) 3.61241i 0.876138i −0.898941 0.438069i \(-0.855663\pi\)
0.898941 0.438069i \(-0.144337\pi\)
\(18\) −1.41298 0.0591148i −0.333042 0.0139335i
\(19\) 5.35964i 1.22958i −0.788689 0.614792i \(-0.789240\pi\)
0.788689 0.614792i \(-0.210760\pi\)
\(20\) 0 0
\(21\) 1.33411i 0.291127i
\(22\) 0.174045 4.16007i 0.0371065 0.886929i
\(23\) 8.59609i 1.79241i 0.443641 + 0.896205i \(0.353687\pi\)
−0.443641 + 0.896205i \(0.646313\pi\)
\(24\) 2.80620 + 0.353863i 0.572814 + 0.0722319i
\(25\) 0 0
\(26\) −2.88507 0.120703i −0.565809 0.0236718i
\(27\) −1.00000 −0.192450
\(28\) 0.222871 2.65890i 0.0421187 0.502485i
\(29\) 5.26432i 0.977559i −0.872407 0.488780i \(-0.837442\pi\)
0.872407 0.488780i \(-0.162558\pi\)
\(30\) 0 0
\(31\) −2.08134 −0.373820 −0.186910 0.982377i \(-0.559847\pi\)
−0.186910 + 0.982377i \(0.559847\pi\)
\(32\) −5.53368 1.17404i −0.978226 0.207544i
\(33\) 2.94418i 0.512517i
\(34\) −0.213547 + 5.10425i −0.0366230 + 0.875372i
\(35\) 0 0
\(36\) 1.99301 + 0.167056i 0.332168 + 0.0278426i
\(37\) 6.55659 1.07790 0.538949 0.842339i \(-0.318822\pi\)
0.538949 + 0.842339i \(0.318822\pi\)
\(38\) −0.316834 + 7.57304i −0.0513973 + 1.22851i
\(39\) −2.04184 −0.326956
\(40\) 0 0
\(41\) 7.02786 1.09757 0.548784 0.835964i \(-0.315091\pi\)
0.548784 + 0.835964i \(0.315091\pi\)
\(42\) 0.0788658 1.88507i 0.0121693 0.290873i
\(43\) 8.50078 1.29636 0.648178 0.761489i \(-0.275531\pi\)
0.648178 + 0.761489i \(0.275531\pi\)
\(44\) −0.491843 + 5.86779i −0.0741482 + 0.884603i
\(45\) 0 0
\(46\) 0.508157 12.1461i 0.0749236 1.79084i
\(47\) 9.97204i 1.45457i −0.686334 0.727286i \(-0.740781\pi\)
0.686334 0.727286i \(-0.259219\pi\)
\(48\) −3.94418 0.665888i −0.569294 0.0961127i
\(49\) 5.22015 0.745735
\(50\) 0 0
\(51\) 3.61241i 0.505838i
\(52\) 4.06940 + 0.341101i 0.564325 + 0.0473022i
\(53\) 6.12318 0.841083 0.420541 0.907273i \(-0.361840\pi\)
0.420541 + 0.907273i \(0.361840\pi\)
\(54\) 1.41298 + 0.0591148i 0.192282 + 0.00804451i
\(55\) 0 0
\(56\) −0.472092 + 3.74379i −0.0630860 + 0.500285i
\(57\) 5.35964i 0.709901i
\(58\) −0.311199 + 7.43836i −0.0408625 + 0.976705i
\(59\) 4.75190i 0.618644i −0.950957 0.309322i \(-0.899898\pi\)
0.950957 0.309322i \(-0.100102\pi\)
\(60\) 0 0
\(61\) 8.51476i 1.09020i −0.838370 0.545101i \(-0.816491\pi\)
0.838370 0.545101i \(-0.183509\pi\)
\(62\) 2.94089 + 0.123038i 0.373493 + 0.0156258i
\(63\) 1.33411i 0.168082i
\(64\) 7.74956 + 1.98602i 0.968695 + 0.248253i
\(65\) 0 0
\(66\) −0.174045 + 4.16007i −0.0214235 + 0.512069i
\(67\) 10.6961 1.30673 0.653367 0.757041i \(-0.273356\pi\)
0.653367 + 0.757041i \(0.273356\pi\)
\(68\) 0.603474 7.19957i 0.0731820 0.873076i
\(69\) 8.59609i 1.03485i
\(70\) 0 0
\(71\) −2.62405 −0.311418 −0.155709 0.987803i \(-0.549766\pi\)
−0.155709 + 0.987803i \(0.549766\pi\)
\(72\) −2.80620 0.353863i −0.330714 0.0417031i
\(73\) 15.3875i 1.80097i −0.434887 0.900485i \(-0.643212\pi\)
0.434887 0.900485i \(-0.356788\pi\)
\(74\) −9.26432 0.387592i −1.07696 0.0450566i
\(75\) 0 0
\(76\) 0.895358 10.6818i 0.102705 1.22529i
\(77\) 3.92787 0.447622
\(78\) 2.88507 + 0.120703i 0.326670 + 0.0136669i
\(79\) −10.4450 −1.17515 −0.587575 0.809170i \(-0.699917\pi\)
−0.587575 + 0.809170i \(0.699917\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −9.93021 0.415451i −1.09661 0.0458789i
\(83\) −1.52708 −0.167619 −0.0838095 0.996482i \(-0.526709\pi\)
−0.0838095 + 0.996482i \(0.526709\pi\)
\(84\) −0.222871 + 2.65890i −0.0243172 + 0.290110i
\(85\) 0 0
\(86\) −12.0114 0.502522i −1.29522 0.0541883i
\(87\) 5.26432i 0.564394i
\(88\) 1.04184 8.26198i 0.111060 0.880730i
\(89\) 12.7193 1.34824 0.674120 0.738622i \(-0.264523\pi\)
0.674120 + 0.738622i \(0.264523\pi\)
\(90\) 0 0
\(91\) 2.72404i 0.285557i
\(92\) −1.43603 + 17.1321i −0.149716 + 1.78615i
\(93\) 2.08134 0.215825
\(94\) −0.589496 + 14.0903i −0.0608018 + 1.45330i
\(95\) 0 0
\(96\) 5.53368 + 1.17404i 0.564779 + 0.119825i
\(97\) 13.4450i 1.36513i 0.730825 + 0.682565i \(0.239135\pi\)
−0.730825 + 0.682565i \(0.760865\pi\)
\(98\) −7.37595 0.308588i −0.745083 0.0311721i
\(99\) 2.94418i 0.295902i
\(100\) 0 0
\(101\) 10.1232i 1.00729i 0.863910 + 0.503647i \(0.168009\pi\)
−0.863910 + 0.503647i \(0.831991\pi\)
\(102\) 0.213547 5.10425i 0.0211443 0.505396i
\(103\) 10.7472i 1.05896i 0.848324 + 0.529478i \(0.177612\pi\)
−0.848324 + 0.529478i \(0.822388\pi\)
\(104\) −5.72981 0.722530i −0.561854 0.0708499i
\(105\) 0 0
\(106\) −8.65191 0.361971i −0.840348 0.0351577i
\(107\) −4.86518 −0.470335 −0.235167 0.971955i \(-0.575564\pi\)
−0.235167 + 0.971955i \(0.575564\pi\)
\(108\) −1.99301 0.167056i −0.191778 0.0160750i
\(109\) 15.4573i 1.48054i 0.672310 + 0.740270i \(0.265302\pi\)
−0.672310 + 0.740270i \(0.734698\pi\)
\(110\) 0 0
\(111\) −6.55659 −0.622324
\(112\) 0.888369 5.26198i 0.0839430 0.497211i
\(113\) 9.88837i 0.930220i −0.885253 0.465110i \(-0.846015\pi\)
0.885253 0.465110i \(-0.153985\pi\)
\(114\) 0.316834 7.57304i 0.0296742 0.709281i
\(115\) 0 0
\(116\) 0.879435 10.4918i 0.0816535 0.974143i
\(117\) 2.04184 0.188768
\(118\) −0.280908 + 6.71432i −0.0258596 + 0.618104i
\(119\) −4.81936 −0.441790
\(120\) 0 0
\(121\) 2.33178 0.211980
\(122\) −0.503348 + 12.0312i −0.0455710 + 1.08925i
\(123\) −7.02786 −0.633681
\(124\) −4.14813 0.347700i −0.372513 0.0312244i
\(125\) 0 0
\(126\) −0.0788658 + 1.88507i −0.00702592 + 0.167935i
\(127\) 8.75190i 0.776605i 0.921532 + 0.388303i \(0.126938\pi\)
−0.921532 + 0.388303i \(0.873062\pi\)
\(128\) −10.8326 3.26432i −0.957472 0.288528i
\(129\) −8.50078 −0.748452
\(130\) 0 0
\(131\) 0.471266i 0.0411747i −0.999788 0.0205874i \(-0.993446\pi\)
0.999788 0.0205874i \(-0.00655362\pi\)
\(132\) 0.491843 5.86779i 0.0428095 0.510726i
\(133\) −7.15035 −0.620014
\(134\) −15.1133 0.632297i −1.30559 0.0546222i
\(135\) 0 0
\(136\) −1.27830 + 10.1372i −0.109613 + 0.869254i
\(137\) 1.30382i 0.111393i −0.998448 0.0556964i \(-0.982262\pi\)
0.998448 0.0556964i \(-0.0177379\pi\)
\(138\) −0.508157 + 12.1461i −0.0432572 + 1.03394i
\(139\) 8.74723i 0.741930i −0.928647 0.370965i \(-0.879027\pi\)
0.928647 0.370965i \(-0.120973\pi\)
\(140\) 0 0
\(141\) 9.97204i 0.839798i
\(142\) 3.70773 + 0.155120i 0.311145 + 0.0130174i
\(143\) 6.01155i 0.502711i
\(144\) 3.94418 + 0.665888i 0.328682 + 0.0554907i
\(145\) 0 0
\(146\) −0.909629 + 21.7422i −0.0752814 + 1.79940i
\(147\) −5.22015 −0.430550
\(148\) 13.0674 + 1.09532i 1.07413 + 0.0900345i
\(149\) 15.1411i 1.24041i −0.784439 0.620205i \(-0.787049\pi\)
0.784439 0.620205i \(-0.212951\pi\)
\(150\) 0 0
\(151\) −23.2782 −1.89435 −0.947176 0.320713i \(-0.896078\pi\)
−0.947176 + 0.320713i \(0.896078\pi\)
\(152\) −1.89657 + 15.0402i −0.153833 + 1.21992i
\(153\) 3.61241i 0.292046i
\(154\) −5.54999 0.232195i −0.447231 0.0187108i
\(155\) 0 0
\(156\) −4.06940 0.341101i −0.325813 0.0273099i
\(157\) −21.8976 −1.74762 −0.873809 0.486270i \(-0.838357\pi\)
−0.873809 + 0.486270i \(0.838357\pi\)
\(158\) 14.7585 + 0.617452i 1.17412 + 0.0491219i
\(159\) −6.12318 −0.485599
\(160\) 0 0
\(161\) 11.4682 0.903817
\(162\) −1.41298 0.0591148i −0.111014 0.00464450i
\(163\) 11.1643 0.874458 0.437229 0.899350i \(-0.355960\pi\)
0.437229 + 0.899350i \(0.355960\pi\)
\(164\) 14.0066 + 1.17404i 1.09373 + 0.0916775i
\(165\) 0 0
\(166\) 2.15773 + 0.0902732i 0.167472 + 0.00700656i
\(167\) 10.0952i 0.781192i −0.920562 0.390596i \(-0.872269\pi\)
0.920562 0.390596i \(-0.127731\pi\)
\(168\) 0.472092 3.74379i 0.0364227 0.288840i
\(169\) −8.83090 −0.679300
\(170\) 0 0
\(171\) 5.35964i 0.409862i
\(172\) 16.9421 + 1.42010i 1.29183 + 0.108282i
\(173\) −13.8162 −1.05043 −0.525215 0.850970i \(-0.676015\pi\)
−0.525215 + 0.850970i \(0.676015\pi\)
\(174\) 0.311199 7.43836i 0.0235920 0.563901i
\(175\) 0 0
\(176\) −1.96050 + 11.6124i −0.147778 + 0.875318i
\(177\) 4.75190i 0.357174i
\(178\) −17.9720 0.751898i −1.34706 0.0563571i
\(179\) 21.9441i 1.64018i 0.572236 + 0.820089i \(0.306076\pi\)
−0.572236 + 0.820089i \(0.693924\pi\)
\(180\) 0 0
\(181\) 1.93021i 0.143471i −0.997424 0.0717356i \(-0.977146\pi\)
0.997424 0.0717356i \(-0.0228538\pi\)
\(182\) −0.161031 + 3.84901i −0.0119364 + 0.285307i
\(183\) 8.51476i 0.629429i
\(184\) 3.04184 24.1224i 0.224247 1.77833i
\(185\) 0 0
\(186\) −2.94089 0.123038i −0.215636 0.00902158i
\(187\) 10.6356 0.777752
\(188\) 1.66589 19.8744i 0.121497 1.44949i
\(189\) 1.33411i 0.0970423i
\(190\) 0 0
\(191\) 12.1232 0.877202 0.438601 0.898682i \(-0.355474\pi\)
0.438601 + 0.898682i \(0.355474\pi\)
\(192\) −7.74956 1.98602i −0.559276 0.143329i
\(193\) 1.27431i 0.0917267i −0.998948 0.0458634i \(-0.985396\pi\)
0.998948 0.0458634i \(-0.0146039\pi\)
\(194\) 0.794797 18.9974i 0.0570631 1.36394i
\(195\) 0 0
\(196\) 10.4038 + 0.872056i 0.743129 + 0.0622897i
\(197\) −3.30849 −0.235720 −0.117860 0.993030i \(-0.537603\pi\)
−0.117860 + 0.993030i \(0.537603\pi\)
\(198\) 0.174045 4.16007i 0.0123688 0.295643i
\(199\) −9.02718 −0.639920 −0.319960 0.947431i \(-0.603669\pi\)
−0.319960 + 0.947431i \(0.603669\pi\)
\(200\) 0 0
\(201\) −10.6961 −0.754443
\(202\) 0.598430 14.3038i 0.0421054 1.00641i
\(203\) −7.02319 −0.492931
\(204\) −0.603474 + 7.19957i −0.0422516 + 0.504071i
\(205\) 0 0
\(206\) 0.635321 15.1856i 0.0442649 1.05803i
\(207\) 8.59609i 0.597470i
\(208\) 8.05338 + 1.35964i 0.558402 + 0.0942738i
\(209\) 15.7798 1.09151
\(210\) 0 0
\(211\) 6.61241i 0.455217i 0.973753 + 0.227608i \(0.0730906\pi\)
−0.973753 + 0.227608i \(0.926909\pi\)
\(212\) 12.2036 + 1.02291i 0.838144 + 0.0702539i
\(213\) 2.62405 0.179797
\(214\) 6.87439 + 0.287604i 0.469924 + 0.0196602i
\(215\) 0 0
\(216\) 2.80620 + 0.353863i 0.190938 + 0.0240773i
\(217\) 2.77674i 0.188497i
\(218\) 0.913755 21.8408i 0.0618873 1.47925i
\(219\) 15.3875i 1.03979i
\(220\) 0 0
\(221\) 7.37595i 0.496160i
\(222\) 9.26432 + 0.387592i 0.621780 + 0.0260135i
\(223\) 0.833237i 0.0557976i 0.999611 + 0.0278988i \(0.00888162\pi\)
−0.999611 + 0.0278988i \(0.991118\pi\)
\(224\) −1.56631 + 7.38255i −0.104653 + 0.493267i
\(225\) 0 0
\(226\) −0.584549 + 13.9720i −0.0388836 + 0.929407i
\(227\) −10.9999 −0.730089 −0.365045 0.930990i \(-0.618946\pi\)
−0.365045 + 0.930990i \(0.618946\pi\)
\(228\) −0.895358 + 10.6818i −0.0592966 + 0.707420i
\(229\) 15.2061i 1.00485i 0.864622 + 0.502423i \(0.167558\pi\)
−0.864622 + 0.502423i \(0.832442\pi\)
\(230\) 0 0
\(231\) −3.92787 −0.258435
\(232\) −1.86285 + 14.7728i −0.122302 + 0.969879i
\(233\) 2.47594i 0.162204i 0.996706 + 0.0811020i \(0.0258439\pi\)
−0.996706 + 0.0811020i \(0.974156\pi\)
\(234\) −2.88507 0.120703i −0.188603 0.00789059i
\(235\) 0 0
\(236\) 0.793832 9.47058i 0.0516741 0.616482i
\(237\) 10.4450 0.678473
\(238\) 6.80964 + 0.284895i 0.441404 + 0.0184670i
\(239\) 21.0737 1.36314 0.681572 0.731751i \(-0.261297\pi\)
0.681572 + 0.731751i \(0.261297\pi\)
\(240\) 0 0
\(241\) −6.10852 −0.393484 −0.196742 0.980455i \(-0.563036\pi\)
−0.196742 + 0.980455i \(0.563036\pi\)
\(242\) −3.29475 0.137843i −0.211794 0.00886086i
\(243\) −1.00000 −0.0641500
\(244\) 1.42244 16.9700i 0.0910624 1.08639i
\(245\) 0 0
\(246\) 9.93021 + 0.415451i 0.633127 + 0.0264882i
\(247\) 10.9435i 0.696318i
\(248\) 5.84066 + 0.736508i 0.370882 + 0.0467683i
\(249\) 1.52708 0.0967748
\(250\) 0 0
\(251\) 22.5286i 1.42199i −0.703195 0.710997i \(-0.748244\pi\)
0.703195 0.710997i \(-0.251756\pi\)
\(252\) 0.222871 2.65890i 0.0140396 0.167495i
\(253\) −25.3085 −1.59113
\(254\) 0.517367 12.3662i 0.0324625 0.775927i
\(255\) 0 0
\(256\) 15.1132 + 5.25277i 0.944574 + 0.328298i
\(257\) 14.5286i 0.906271i −0.891442 0.453136i \(-0.850305\pi\)
0.891442 0.453136i \(-0.149695\pi\)
\(258\) 12.0114 + 0.502522i 0.747798 + 0.0312857i
\(259\) 8.74723i 0.543526i
\(260\) 0 0
\(261\) 5.26432i 0.325853i
\(262\) −0.0278588 + 0.665888i −0.00172112 + 0.0411387i
\(263\) 5.29694i 0.326624i 0.986575 + 0.163312i \(0.0522177\pi\)
−0.986575 + 0.163312i \(0.947782\pi\)
\(264\) −1.04184 + 8.26198i −0.0641206 + 0.508490i
\(265\) 0 0
\(266\) 10.1033 + 0.422692i 0.619472 + 0.0259169i
\(267\) −12.7193 −0.778407
\(268\) 21.3174 + 1.78684i 1.30217 + 0.109149i
\(269\) 27.0737i 1.65071i 0.564613 + 0.825356i \(0.309025\pi\)
−0.564613 + 0.825356i \(0.690975\pi\)
\(270\) 0 0
\(271\) 15.8604 0.963451 0.481726 0.876322i \(-0.340010\pi\)
0.481726 + 0.876322i \(0.340010\pi\)
\(272\) 2.40546 14.2480i 0.145852 0.863912i
\(273\) 2.72404i 0.164866i
\(274\) −0.0770751 + 1.84227i −0.00465628 + 0.111296i
\(275\) 0 0
\(276\) 1.43603 17.1321i 0.0864387 1.03123i
\(277\) −9.98592 −0.599996 −0.299998 0.953940i \(-0.596986\pi\)
−0.299998 + 0.953940i \(0.596986\pi\)
\(278\) −0.517091 + 12.3596i −0.0310130 + 0.741282i
\(279\) −2.08134 −0.124607
\(280\) 0 0
\(281\) 13.4218 0.800676 0.400338 0.916368i \(-0.368893\pi\)
0.400338 + 0.916368i \(0.368893\pi\)
\(282\) 0.589496 14.0903i 0.0351040 0.839064i
\(283\) −3.83722 −0.228099 −0.114050 0.993475i \(-0.536382\pi\)
−0.114050 + 0.993475i \(0.536382\pi\)
\(284\) −5.22976 0.438363i −0.310329 0.0260121i
\(285\) 0 0
\(286\) 0.355372 8.49418i 0.0210136 0.502271i
\(287\) 9.37595i 0.553445i
\(288\) −5.53368 1.17404i −0.326075 0.0691813i
\(289\) 3.95051 0.232383
\(290\) 0 0
\(291\) 13.4450i 0.788158i
\(292\) 2.57057 30.6674i 0.150431 1.79468i
\(293\) 26.4450 1.54493 0.772466 0.635057i \(-0.219023\pi\)
0.772466 + 0.635057i \(0.219023\pi\)
\(294\) 7.37595 + 0.308588i 0.430174 + 0.0179972i
\(295\) 0 0
\(296\) −18.3991 2.32013i −1.06943 0.134855i
\(297\) 2.94418i 0.170839i
\(298\) −0.895066 + 21.3941i −0.0518498 + 1.23933i
\(299\) 17.5518i 1.01505i
\(300\) 0 0
\(301\) 11.3410i 0.653684i
\(302\) 32.8916 + 1.37609i 1.89270 + 0.0791849i
\(303\) 10.1232i 0.581561i
\(304\) 3.56892 21.1394i 0.204692 1.21243i
\(305\) 0 0
\(306\) −0.213547 + 5.10425i −0.0122077 + 0.291791i
\(307\) 1.27596 0.0728230 0.0364115 0.999337i \(-0.488407\pi\)
0.0364115 + 0.999337i \(0.488407\pi\)
\(308\) 7.82829 + 0.656174i 0.446058 + 0.0373890i
\(309\) 10.7472i 0.611388i
\(310\) 0 0
\(311\) 2.44496 0.138641 0.0693205 0.997594i \(-0.477917\pi\)
0.0693205 + 0.997594i \(0.477917\pi\)
\(312\) 5.72981 + 0.722530i 0.324387 + 0.0409052i
\(313\) 22.8325i 1.29057i 0.763943 + 0.645283i \(0.223261\pi\)
−0.763943 + 0.645283i \(0.776739\pi\)
\(314\) 30.9408 + 1.29447i 1.74609 + 0.0730513i
\(315\) 0 0
\(316\) −20.8169 1.74489i −1.17104 0.0981579i
\(317\) −2.11163 −0.118601 −0.0593005 0.998240i \(-0.518887\pi\)
−0.0593005 + 0.998240i \(0.518887\pi\)
\(318\) 8.65191 + 0.361971i 0.485175 + 0.0202983i
\(319\) 15.4991 0.867784
\(320\) 0 0
\(321\) 4.86518 0.271548
\(322\) −16.2042 0.677938i −0.903027 0.0377800i
\(323\) −19.3612 −1.07729
\(324\) 1.99301 + 0.167056i 0.110723 + 0.00928088i
\(325\) 0 0
\(326\) −15.7749 0.659978i −0.873694 0.0365528i
\(327\) 15.4573i 0.854790i
\(328\) −19.7216 2.48690i −1.08894 0.137316i
\(329\) −13.3038 −0.733463
\(330\) 0 0
\(331\) 23.2248i 1.27655i 0.769808 + 0.638276i \(0.220352\pi\)
−0.769808 + 0.638276i \(0.779648\pi\)
\(332\) −3.04349 0.255108i −0.167033 0.0140009i
\(333\) 6.55659 0.359299
\(334\) −0.596777 + 14.2643i −0.0326542 + 0.780509i
\(335\) 0 0
\(336\) −0.888369 + 5.26198i −0.0484645 + 0.287065i
\(337\) 12.8884i 0.702074i −0.936362 0.351037i \(-0.885829\pi\)
0.936362 0.351037i \(-0.114171\pi\)
\(338\) 12.4779 + 0.522037i 0.678706 + 0.0283951i
\(339\) 9.88837i 0.537063i
\(340\) 0 0
\(341\) 6.12785i 0.331841i
\(342\) −0.316834 + 7.57304i −0.0171324 + 0.409503i
\(343\) 16.3030i 0.880281i
\(344\) −23.8549 3.00811i −1.28617 0.162186i
\(345\) 0 0
\(346\) 19.5220 + 0.816745i 1.04951 + 0.0439085i
\(347\) −6.79827 −0.364951 −0.182475 0.983210i \(-0.558411\pi\)
−0.182475 + 0.983210i \(0.558411\pi\)
\(348\) −0.879435 + 10.4918i −0.0471427 + 0.562422i
\(349\) 34.6076i 1.85250i 0.376904 + 0.926252i \(0.376989\pi\)
−0.376904 + 0.926252i \(0.623011\pi\)
\(350\) 0 0
\(351\) −2.04184 −0.108985
\(352\) 3.45661 16.2922i 0.184238 0.868376i
\(353\) 12.2433i 0.651647i 0.945431 + 0.325823i \(0.105642\pi\)
−0.945431 + 0.325823i \(0.894358\pi\)
\(354\) 0.280908 6.71432i 0.0149301 0.356862i
\(355\) 0 0
\(356\) 25.3496 + 2.12483i 1.34353 + 0.112616i
\(357\) 4.81936 0.255067
\(358\) 1.29722 31.0065i 0.0685603 1.63874i
\(359\) 2.01622 0.106412 0.0532059 0.998584i \(-0.483056\pi\)
0.0532059 + 0.998584i \(0.483056\pi\)
\(360\) 0 0
\(361\) −9.72569 −0.511878
\(362\) −0.114104 + 2.72734i −0.00599716 + 0.143346i
\(363\) −2.33178 −0.122387
\(364\) 0.455067 5.42904i 0.0238520 0.284559i
\(365\) 0 0
\(366\) 0.503348 12.0312i 0.0263104 0.628879i
\(367\) 13.4131i 0.700159i 0.936720 + 0.350079i \(0.113845\pi\)
−0.936720 + 0.350079i \(0.886155\pi\)
\(368\) −5.72404 + 33.9046i −0.298386 + 1.76740i
\(369\) 7.02786 0.365856
\(370\) 0 0
\(371\) 8.16900i 0.424113i
\(372\) 4.14813 + 0.347700i 0.215071 + 0.0180274i
\(373\) −10.0976 −0.522832 −0.261416 0.965226i \(-0.584189\pi\)
−0.261416 + 0.965226i \(0.584189\pi\)
\(374\) −15.0279 0.628722i −0.777072 0.0325104i
\(375\) 0 0
\(376\) −3.52873 + 27.9836i −0.181981 + 1.44314i
\(377\) 10.7489i 0.553595i
\(378\) 0.0788658 1.88507i 0.00405642 0.0969575i
\(379\) 18.2775i 0.938853i −0.882972 0.469426i \(-0.844461\pi\)
0.882972 0.469426i \(-0.155539\pi\)
\(380\) 0 0
\(381\) 8.75190i 0.448373i
\(382\) −17.1298 0.716660i −0.876436 0.0366675i
\(383\) 11.7734i 0.601594i −0.953688 0.300797i \(-0.902747\pi\)
0.953688 0.300797i \(-0.0972527\pi\)
\(384\) 10.8326 + 3.26432i 0.552796 + 0.166582i
\(385\) 0 0
\(386\) −0.0753305 + 1.80057i −0.00383422 + 0.0916466i
\(387\) 8.50078 0.432119
\(388\) −2.24606 + 26.7960i −0.114026 + 1.36036i
\(389\) 33.4270i 1.69482i −0.530942 0.847408i \(-0.678162\pi\)
0.530942 0.847408i \(-0.321838\pi\)
\(390\) 0 0
\(391\) 31.0526 1.57040
\(392\) −14.6488 1.84721i −0.739876 0.0932984i
\(393\) 0.471266i 0.0237722i
\(394\) 4.67482 + 0.195581i 0.235514 + 0.00985322i
\(395\) 0 0
\(396\) −0.491843 + 5.86779i −0.0247161 + 0.294868i
\(397\) −39.0434 −1.95953 −0.979766 0.200147i \(-0.935858\pi\)
−0.979766 + 0.200147i \(0.935858\pi\)
\(398\) 12.7552 + 0.533640i 0.639360 + 0.0267490i
\(399\) 7.15035 0.357965
\(400\) 0 0
\(401\) −24.6140 −1.22916 −0.614581 0.788853i \(-0.710675\pi\)
−0.614581 + 0.788853i \(0.710675\pi\)
\(402\) 15.1133 + 0.632297i 0.753784 + 0.0315361i
\(403\) −4.24976 −0.211695
\(404\) −1.69114 + 20.1756i −0.0841372 + 1.00377i
\(405\) 0 0
\(406\) 9.92361 + 0.415175i 0.492500 + 0.0206048i
\(407\) 19.3038i 0.956855i
\(408\) 1.27830 10.1372i 0.0632851 0.501864i
\(409\) 14.5024 0.717099 0.358550 0.933511i \(-0.383271\pi\)
0.358550 + 0.933511i \(0.383271\pi\)
\(410\) 0 0
\(411\) 1.30382i 0.0643127i
\(412\) −1.79539 + 21.4193i −0.0884524 + 1.05526i
\(413\) −6.33956 −0.311949
\(414\) 0.508157 12.1461i 0.0249745 0.596948i
\(415\) 0 0
\(416\) −11.2989 2.39721i −0.553973 0.117533i
\(417\) 8.74723i 0.428354i
\(418\) −22.2964 0.932818i −1.09055 0.0456256i
\(419\) 12.6419i 0.617598i −0.951127 0.308799i \(-0.900073\pi\)
0.951127 0.308799i \(-0.0999271\pi\)
\(420\) 0 0
\(421\) 16.8389i 0.820677i 0.911933 + 0.410338i \(0.134589\pi\)
−0.911933 + 0.410338i \(0.865411\pi\)
\(422\) 0.390891 9.34318i 0.0190283 0.454819i
\(423\) 9.97204i 0.484857i
\(424\) −17.1829 2.16676i −0.834474 0.105227i
\(425\) 0 0
\(426\) −3.70773 0.155120i −0.179640 0.00751561i
\(427\) −11.3596 −0.549731
\(428\) −9.69636 0.812757i −0.468691 0.0392861i
\(429\) 6.01155i 0.290240i
\(430\) 0 0
\(431\) 5.98845 0.288454 0.144227 0.989545i \(-0.453930\pi\)
0.144227 + 0.989545i \(0.453930\pi\)
\(432\) −3.94418 0.665888i −0.189765 0.0320376i
\(433\) 2.22482i 0.106918i −0.998570 0.0534589i \(-0.982975\pi\)
0.998570 0.0534589i \(-0.0170246\pi\)
\(434\) 0.164146 3.92347i 0.00787928 0.188333i
\(435\) 0 0
\(436\) −2.58223 + 30.8065i −0.123666 + 1.47537i
\(437\) 46.0719 2.20392
\(438\) 0.909629 21.7422i 0.0434638 1.03888i
\(439\) 2.30460 0.109993 0.0549963 0.998487i \(-0.482485\pi\)
0.0549963 + 0.998487i \(0.482485\pi\)
\(440\) 0 0
\(441\) 5.22015 0.248578
\(442\) −0.436028 + 10.4220i −0.0207397 + 0.495726i
\(443\) 22.1347 1.05165 0.525826 0.850592i \(-0.323756\pi\)
0.525826 + 0.850592i \(0.323756\pi\)
\(444\) −13.0674 1.09532i −0.620149 0.0519815i
\(445\) 0 0
\(446\) 0.0492566 1.17734i 0.00233237 0.0557489i
\(447\) 15.1411i 0.716151i
\(448\) 2.64957 10.3388i 0.125181 0.488462i
\(449\) −21.5861 −1.01871 −0.509356 0.860556i \(-0.670116\pi\)
−0.509356 + 0.860556i \(0.670116\pi\)
\(450\) 0 0
\(451\) 20.6913i 0.974316i
\(452\) 1.65191 19.7076i 0.0776993 0.926969i
\(453\) 23.2782 1.09371
\(454\) 15.5426 + 0.650257i 0.729451 + 0.0305181i
\(455\) 0 0
\(456\) 1.89657 15.0402i 0.0888153 0.704323i
\(457\) 2.50088i 0.116986i 0.998288 + 0.0584930i \(0.0186295\pi\)
−0.998288 + 0.0584930i \(0.981370\pi\)
\(458\) 0.898904 21.4858i 0.0420030 1.00397i
\(459\) 3.61241i 0.168613i
\(460\) 0 0
\(461\) 2.59609i 0.120912i 0.998171 + 0.0604561i \(0.0192555\pi\)
−0.998171 + 0.0604561i \(0.980744\pi\)
\(462\) 5.54999 + 0.232195i 0.258209 + 0.0108027i
\(463\) 27.8604i 1.29478i −0.762158 0.647392i \(-0.775860\pi\)
0.762158 0.647392i \(-0.224140\pi\)
\(464\) 3.50545 20.7634i 0.162736 0.963919i
\(465\) 0 0
\(466\) 0.146365 3.49844i 0.00678021 0.162062i
\(467\) −5.75200 −0.266171 −0.133085 0.991105i \(-0.542488\pi\)
−0.133085 + 0.991105i \(0.542488\pi\)
\(468\) 4.06940 + 0.341101i 0.188108 + 0.0157674i
\(469\) 14.2698i 0.658917i
\(470\) 0 0
\(471\) 21.8976 1.00899
\(472\) −1.68152 + 13.3348i −0.0773982 + 0.613784i
\(473\) 25.0279i 1.15078i
\(474\) −14.7585 0.617452i −0.677880 0.0283605i
\(475\) 0 0
\(476\) −9.60503 0.805102i −0.440246 0.0369018i
\(477\) 6.12318 0.280361
\(478\) −29.7766 1.24577i −1.36195 0.0569801i
\(479\) 12.5473 0.573299 0.286649 0.958036i \(-0.407459\pi\)
0.286649 + 0.958036i \(0.407459\pi\)
\(480\) 0 0
\(481\) 13.3875 0.610417
\(482\) 8.63119 + 0.361104i 0.393140 + 0.0164478i
\(483\) −11.4682 −0.521819
\(484\) 4.64726 + 0.389537i 0.211239 + 0.0177062i
\(485\) 0 0
\(486\) 1.41298 + 0.0591148i 0.0640940 + 0.00268150i
\(487\) 8.60530i 0.389944i 0.980809 + 0.194972i \(0.0624615\pi\)
−0.980809 + 0.194972i \(0.937538\pi\)
\(488\) −3.01305 + 23.8941i −0.136395 + 1.08164i
\(489\) −11.1643 −0.504868
\(490\) 0 0
\(491\) 36.8866i 1.66467i 0.554273 + 0.832335i \(0.312996\pi\)
−0.554273 + 0.832335i \(0.687004\pi\)
\(492\) −14.0066 1.17404i −0.631466 0.0529300i
\(493\) −19.0169 −0.856477
\(494\) −0.646923 + 15.4629i −0.0291065 + 0.695710i
\(495\) 0 0
\(496\) −8.20919 1.38594i −0.368603 0.0622305i
\(497\) 3.50078i 0.157031i
\(498\) −2.15773 0.0902732i −0.0966903 0.00404524i
\(499\) 36.2496i 1.62275i −0.584524 0.811377i \(-0.698719\pi\)
0.584524 0.811377i \(-0.301281\pi\)
\(500\) 0 0
\(501\) 10.0952i 0.451021i
\(502\) −1.33178 + 31.8325i −0.0594401 + 1.42075i
\(503\) 23.3527i 1.04124i −0.853787 0.520622i \(-0.825700\pi\)
0.853787 0.520622i \(-0.174300\pi\)
\(504\) −0.472092 + 3.74379i −0.0210287 + 0.166762i
\(505\) 0 0
\(506\) 35.7603 + 1.49611i 1.58974 + 0.0665101i
\(507\) 8.83090 0.392194
\(508\) −1.46206 + 17.4426i −0.0648682 + 0.773891i
\(509\) 3.35506i 0.148711i 0.997232 + 0.0743553i \(0.0236899\pi\)
−0.997232 + 0.0743553i \(0.976310\pi\)
\(510\) 0 0
\(511\) −20.5286 −0.908133
\(512\) −21.0441 8.31546i −0.930025 0.367495i
\(513\) 5.35964i 0.236634i
\(514\) −0.858858 + 20.5286i −0.0378826 + 0.905479i
\(515\) 0 0
\(516\) −16.9421 1.42010i −0.745836 0.0625166i
\(517\) 29.3595 1.29123
\(518\) −0.517091 + 12.3596i −0.0227197 + 0.543051i
\(519\) 13.8162 0.606466
\(520\) 0 0
\(521\) −33.6029 −1.47217 −0.736084 0.676890i \(-0.763327\pi\)
−0.736084 + 0.676890i \(0.763327\pi\)
\(522\) −0.311199 + 7.43836i −0.0136208 + 0.325568i
\(523\) 0.965721 0.0422280 0.0211140 0.999777i \(-0.493279\pi\)
0.0211140 + 0.999777i \(0.493279\pi\)
\(524\) 0.0787277 0.939238i 0.00343924 0.0410308i
\(525\) 0 0
\(526\) 0.313128 7.48446i 0.0136530 0.326338i
\(527\) 7.51865i 0.327517i
\(528\) 1.96050 11.6124i 0.0853197 0.505365i
\(529\) −50.8928 −2.21273
\(530\) 0 0
\(531\) 4.75190i 0.206215i
\(532\) −14.2507 1.19451i −0.617848 0.0517885i
\(533\) 14.3497 0.621556
\(534\) 17.9720 + 0.751898i 0.777726 + 0.0325378i
\(535\) 0 0
\(536\) −30.0154 3.78494i −1.29647 0.163485i
\(537\) 21.9441i 0.946957i
\(538\) 1.60046 38.2545i 0.0690006 1.64927i
\(539\) 15.3691i 0.661993i
\(540\) 0 0
\(541\) 6.34877i 0.272955i −0.990643 0.136478i \(-0.956422\pi\)
0.990643 0.136478i \(-0.0435781\pi\)
\(542\) −22.4104 0.937586i −0.962609 0.0402728i
\(543\) 1.93021i 0.0828331i
\(544\) −4.24113 + 19.9899i −0.181837 + 0.857060i
\(545\) 0 0
\(546\) 0.161031 3.84901i 0.00689149 0.164722i
\(547\) 2.07433 0.0886921 0.0443460 0.999016i \(-0.485880\pi\)
0.0443460 + 0.999016i \(0.485880\pi\)
\(548\) 0.217811 2.59853i 0.00930442 0.111004i
\(549\) 8.51476i 0.363401i
\(550\) 0 0
\(551\) −28.2148 −1.20199
\(552\) −3.04184 + 24.1224i −0.129469 + 1.02672i
\(553\) 13.9347i 0.592566i
\(554\) 14.1099 + 0.590316i 0.599472 + 0.0250801i
\(555\) 0 0
\(556\) 1.46128 17.4333i 0.0619719 0.739337i
\(557\) −27.6931 −1.17339 −0.586696 0.809807i \(-0.699572\pi\)
−0.586696 + 0.809807i \(0.699572\pi\)
\(558\) 2.94089 + 0.123038i 0.124498 + 0.00520861i
\(559\) 17.3572 0.734131
\(560\) 0 0
\(561\) −10.6356 −0.449035
\(562\) −18.9647 0.793426i −0.799976 0.0334687i
\(563\) 3.80771 0.160476 0.0802380 0.996776i \(-0.474432\pi\)
0.0802380 + 0.996776i \(0.474432\pi\)
\(564\) −1.66589 + 19.8744i −0.0701466 + 0.836863i
\(565\) 0 0
\(566\) 5.42191 + 0.226837i 0.227900 + 0.00953467i
\(567\) 1.33411i 0.0560274i
\(568\) 7.36362 + 0.928554i 0.308971 + 0.0389613i
\(569\) −38.6371 −1.61975 −0.809875 0.586603i \(-0.800465\pi\)
−0.809875 + 0.586603i \(0.800465\pi\)
\(570\) 0 0
\(571\) 6.24976i 0.261544i −0.991412 0.130772i \(-0.958254\pi\)
0.991412 0.130772i \(-0.0417456\pi\)
\(572\) −1.00426 + 11.9811i −0.0419904 + 0.500954i
\(573\) −12.1232 −0.506453
\(574\) −0.554258 + 13.2480i −0.0231343 + 0.552961i
\(575\) 0 0
\(576\) 7.74956 + 1.98602i 0.322898 + 0.0827509i
\(577\) 2.17377i 0.0904952i 0.998976 + 0.0452476i \(0.0144077\pi\)
−0.998976 + 0.0452476i \(0.985592\pi\)
\(578\) −5.58198 0.233534i −0.232180 0.00971372i
\(579\) 1.27431i 0.0529585i
\(580\) 0 0
\(581\) 2.03730i 0.0845213i
\(582\) −0.794797 + 18.9974i −0.0329454 + 0.787469i
\(583\) 18.0278i 0.746634i
\(584\) −5.44506 + 43.1804i −0.225318 + 1.78682i
\(585\) 0 0
\(586\) −37.3661 1.56329i −1.54358 0.0645789i
\(587\) 34.1688 1.41030 0.705149 0.709059i \(-0.250880\pi\)
0.705149 + 0.709059i \(0.250880\pi\)
\(588\) −10.4038 0.872056i −0.429046 0.0359630i
\(589\) 11.1552i 0.459643i
\(590\) 0 0
\(591\) 3.30849 0.136093
\(592\) 25.8604 + 4.36596i 1.06286 + 0.179440i
\(593\) 12.9952i 0.533650i 0.963745 + 0.266825i \(0.0859746\pi\)
−0.963745 + 0.266825i \(0.914025\pi\)
\(594\) −0.174045 + 4.16007i −0.00714115 + 0.170690i
\(595\) 0 0
\(596\) 2.52942 30.1765i 0.103609 1.23608i
\(597\) 9.02718 0.369458
\(598\) 1.03757 24.8003i 0.0424295 1.01416i
\(599\) −47.2572 −1.93088 −0.965439 0.260628i \(-0.916071\pi\)
−0.965439 + 0.260628i \(0.916071\pi\)
\(600\) 0 0
\(601\) −23.5007 −0.958613 −0.479306 0.877648i \(-0.659112\pi\)
−0.479306 + 0.877648i \(0.659112\pi\)
\(602\) −0.670421 + 16.0246i −0.0273243 + 0.653112i
\(603\) 10.6961 0.435578
\(604\) −46.3937 3.88876i −1.88773 0.158231i
\(605\) 0 0
\(606\) −0.598430 + 14.3038i −0.0243096 + 0.581053i
\(607\) 0.218591i 0.00887233i 0.999990 + 0.00443617i \(0.00141208\pi\)
−0.999990 + 0.00443617i \(0.998588\pi\)
\(608\) −6.29245 + 29.6585i −0.255193 + 1.20281i
\(609\) 7.02319 0.284594
\(610\) 0 0
\(611\) 20.3613i 0.823730i
\(612\) 0.603474 7.19957i 0.0243940 0.291025i
\(613\) 35.7488 1.44388 0.721940 0.691956i \(-0.243251\pi\)
0.721940 + 0.691956i \(0.243251\pi\)
\(614\) −1.80290 0.0754282i −0.0727593 0.00304404i
\(615\) 0 0
\(616\) −11.0224 1.38993i −0.444105 0.0560018i
\(617\) 33.0836i 1.33189i 0.745999 + 0.665947i \(0.231972\pi\)
−0.745999 + 0.665947i \(0.768028\pi\)
\(618\) −0.635321 + 15.1856i −0.0255563 + 0.610854i
\(619\) 25.1084i 1.00919i −0.863355 0.504596i \(-0.831641\pi\)
0.863355 0.504596i \(-0.168359\pi\)
\(620\) 0 0
\(621\) 8.59609i 0.344949i
\(622\) −3.45468 0.144534i −0.138520 0.00579527i
\(623\) 16.9689i 0.679846i
\(624\) −8.05338 1.35964i −0.322393 0.0544290i
\(625\) 0 0
\(626\) 1.34974 32.2617i 0.0539463 1.28944i
\(627\) −15.7798 −0.630183
\(628\) −43.6421 3.65812i −1.74151 0.145975i
\(629\) 23.6851i 0.944386i
\(630\) 0 0
\(631\) 23.2829 0.926876 0.463438 0.886129i \(-0.346616\pi\)
0.463438 + 0.886129i \(0.346616\pi\)
\(632\) 29.3107 + 3.69608i 1.16592 + 0.147022i
\(633\) 6.61241i 0.262820i
\(634\) 2.98369 + 0.124829i 0.118497 + 0.00495758i
\(635\) 0 0
\(636\) −12.2036 1.02291i −0.483902 0.0405611i
\(637\) 10.6587 0.422313
\(638\) −21.8999 0.916228i −0.867026 0.0362738i
\(639\) −2.62405 −0.103806
\(640\) 0 0
\(641\) −38.3021 −1.51284 −0.756420 0.654086i \(-0.773054\pi\)
−0.756420 + 0.654086i \(0.773054\pi\)
\(642\) −6.87439 0.287604i −0.271311 0.0113508i
\(643\) 45.8045 1.80635 0.903177 0.429269i \(-0.141229\pi\)
0.903177 + 0.429269i \(0.141229\pi\)
\(644\) 22.8561 + 1.91582i 0.900658 + 0.0754940i
\(645\) 0 0
\(646\) 27.3569 + 1.14453i 1.07634 + 0.0450311i
\(647\) 48.1114i 1.89146i 0.324960 + 0.945728i \(0.394649\pi\)
−0.324960 + 0.945728i \(0.605351\pi\)
\(648\) −2.80620 0.353863i −0.110238 0.0139010i
\(649\) 13.9905 0.549174
\(650\) 0 0
\(651\) 2.77674i 0.108829i
\(652\) 22.2506 + 1.86507i 0.871402 + 0.0730417i
\(653\) 38.3331 1.50009 0.750046 0.661386i \(-0.230031\pi\)
0.750046 + 0.661386i \(0.230031\pi\)
\(654\) −0.913755 + 21.8408i −0.0357306 + 0.854043i
\(655\) 0 0
\(656\) 27.7192 + 4.67977i 1.08225 + 0.182714i
\(657\) 15.3875i 0.600323i
\(658\) 18.7980 + 0.786453i 0.732822 + 0.0306591i
\(659\) 5.03253i 0.196040i −0.995184 0.0980198i \(-0.968749\pi\)
0.995184 0.0980198i \(-0.0312508\pi\)
\(660\) 0 0
\(661\) 17.4665i 0.679368i 0.940540 + 0.339684i \(0.110320\pi\)
−0.940540 + 0.339684i \(0.889680\pi\)
\(662\) 1.37293 32.8161i 0.0533605 1.27544i
\(663\) 7.37595i 0.286458i
\(664\) 4.28530 + 0.540377i 0.166302 + 0.0209707i
\(665\) 0 0
\(666\) −9.26432 0.387592i −0.358985 0.0150189i
\(667\) 45.2526 1.75219
\(668\) 1.68647 20.1199i 0.0652513 0.778462i
\(669\) 0.833237i 0.0322148i
\(670\) 0 0
\(671\) 25.0690 0.967779
\(672\) 1.56631 7.38255i 0.0604216 0.284788i
\(673\) 32.4448i 1.25065i 0.780363 + 0.625327i \(0.215034\pi\)
−0.780363 + 0.625327i \(0.784966\pi\)
\(674\) −0.761894 + 18.2110i −0.0293471 + 0.701461i
\(675\) 0 0
\(676\) −17.6001 1.47525i −0.676926 0.0567405i
\(677\) 8.07213 0.310237 0.155119 0.987896i \(-0.450424\pi\)
0.155119 + 0.987896i \(0.450424\pi\)
\(678\) 0.584549 13.9720i 0.0224495 0.536593i
\(679\) 17.9371 0.688362
\(680\) 0 0
\(681\) 10.9999 0.421517
\(682\) −0.362247 + 8.65851i −0.0138711 + 0.331551i
\(683\) −36.3380 −1.39043 −0.695217 0.718799i \(-0.744692\pi\)
−0.695217 + 0.718799i \(0.744692\pi\)
\(684\) 0.895358 10.6818i 0.0342349 0.408429i
\(685\) 0 0
\(686\) −0.963751 + 23.0358i −0.0367962 + 0.879512i
\(687\) 15.2061i 0.580148i
\(688\) 33.5286 + 5.66057i 1.27827 + 0.215807i
\(689\) 12.5025 0.476308
\(690\) 0 0
\(691\) 15.0016i 0.570686i −0.958425 0.285343i \(-0.907892\pi\)
0.958425 0.285343i \(-0.0921075\pi\)
\(692\) −27.5359 2.30808i −1.04676 0.0877402i
\(693\) 3.92787 0.149207
\(694\) 9.60581 + 0.401879i 0.364632 + 0.0152551i
\(695\) 0 0
\(696\) 1.86285 14.7728i 0.0706110 0.559960i
\(697\) 25.3875i 0.961620i
\(698\) 2.04582 48.8998i 0.0774356 1.85089i
\(699\) 2.47594i 0.0936485i
\(700\) 0 0
\(701\) 13.2874i 0.501859i 0.968005 + 0.250929i \(0.0807362\pi\)
−0.968005 + 0.250929i \(0.919264\pi\)
\(702\) 2.88507 + 0.120703i 0.108890 + 0.00455564i
\(703\) 35.1409i 1.32537i
\(704\) −5.84721 + 22.8161i −0.220375 + 0.859916i
\(705\) 0 0
\(706\) 0.723763 17.2996i 0.0272392 0.651077i
\(707\) 13.5054 0.507925
\(708\) −0.793832 + 9.47058i −0.0298340 + 0.355926i
\(709\) 37.8976i 1.42327i −0.702548 0.711637i \(-0.747954\pi\)
0.702548 0.711637i \(-0.252046\pi\)
\(710\) 0 0
\(711\) −10.4450 −0.391717
\(712\) −35.6929 4.50088i −1.33765 0.168677i
\(713\) 17.8914i 0.670038i
\(714\) −6.80964 0.284895i −0.254844 0.0106619i
\(715\) 0 0
\(716\) −3.66589 + 43.7348i −0.137001 + 1.63445i
\(717\) −21.0737 −0.787011
\(718\) −2.84887 0.119188i −0.106319 0.00444807i
\(719\) 4.17909 0.155854 0.0779269 0.996959i \(-0.475170\pi\)
0.0779269 + 0.996959i \(0.475170\pi\)
\(720\) 0 0
\(721\) 14.3380 0.533975
\(722\) 13.7422 + 0.574933i 0.511431 + 0.0213968i
\(723\) 6.10852 0.227178
\(724\) 0.322452 3.84692i 0.0119838 0.142970i
\(725\) 0 0
\(726\) 3.29475 + 0.137843i 0.122280 + 0.00511582i
\(727\) 26.7727i 0.992943i −0.868053 0.496471i \(-0.834629\pi\)
0.868053 0.496471i \(-0.165371\pi\)
\(728\) −0.963936 + 7.64421i −0.0357258 + 0.283313i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 30.7083i 1.13579i
\(732\) −1.42244 + 16.9700i −0.0525749 + 0.627229i
\(733\) −21.3364 −0.788080 −0.394040 0.919093i \(-0.628923\pi\)
−0.394040 + 0.919093i \(0.628923\pi\)
\(734\) 0.792914 18.9524i 0.0292670 0.699547i
\(735\) 0 0
\(736\) 10.0922 47.5680i 0.372003 1.75338i
\(737\) 31.4912i 1.15999i
\(738\) −9.93021 0.415451i −0.365536 0.0152930i
\(739\) 13.1038i 0.482033i 0.970521 + 0.241016i \(0.0774807\pi\)
−0.970521 + 0.241016i \(0.922519\pi\)
\(740\) 0 0
\(741\) 10.9435i 0.402020i
\(742\) −0.482909 + 11.5426i −0.0177282 + 0.423743i
\(743\) 33.3595i 1.22384i −0.790919 0.611921i \(-0.790397\pi\)
0.790919 0.611921i \(-0.209603\pi\)
\(744\) −5.84066 0.736508i −0.214129 0.0270017i
\(745\) 0 0
\(746\) 14.2676 + 0.596915i 0.522375 + 0.0218546i
\(747\) −1.52708 −0.0558730
\(748\) 21.1969 + 1.77674i 0.775034 + 0.0649640i
\(749\) 6.49069i 0.237165i
\(750\) 0 0
\(751\) −1.92100 −0.0700981 −0.0350491 0.999386i \(-0.511159\pi\)
−0.0350491 + 0.999386i \(0.511159\pi\)
\(752\) 6.64027 39.3316i 0.242146 1.43428i
\(753\) 22.5286i 0.820989i
\(754\) −0.635418 + 15.1879i −0.0231406 + 0.553112i
\(755\) 0 0
\(756\) −0.222871 + 2.65890i −0.00810575 + 0.0967032i
\(757\) 13.9908 0.508504 0.254252 0.967138i \(-0.418171\pi\)
0.254252 + 0.967138i \(0.418171\pi\)
\(758\) −1.08047 + 25.8257i −0.0392445 + 0.938032i
\(759\) 25.3085 0.918640
\(760\) 0 0
\(761\) 25.6618 0.930240 0.465120 0.885248i \(-0.346011\pi\)
0.465120 + 0.885248i \(0.346011\pi\)
\(762\) −0.517367 + 12.3662i −0.0187422 + 0.447981i
\(763\) 20.6217 0.746557
\(764\) 24.1616 + 2.02525i 0.874137 + 0.0732709i
\(765\) 0 0
\(766\) −0.695985 + 16.6356i −0.0251469 + 0.601069i
\(767\) 9.70260i 0.350341i
\(768\) −15.1132 5.25277i −0.545350 0.189543i
\(769\) 12.3922 0.446873 0.223436 0.974719i \(-0.428272\pi\)
0.223436 + 0.974719i \(0.428272\pi\)
\(770\) 0 0
\(771\) 14.5286i 0.523236i
\(772\) 0.212881 2.53971i 0.00766174 0.0914062i
\(773\) −38.4843 −1.38418 −0.692091 0.721810i \(-0.743311\pi\)
−0.692091 + 0.721810i \(0.743311\pi\)
\(774\) −12.0114 0.502522i −0.431741 0.0180628i
\(775\) 0 0
\(776\) 4.75767 37.7293i 0.170790 1.35440i
\(777\) 8.74723i 0.313805i
\(778\) −1.97603 + 47.2316i −0.0708442 + 1.69333i
\(779\) 37.6668i 1.34955i
\(780\) 0 0
\(781\) 7.72569i 0.276447i
\(782\) −43.8766 1.83567i −1.56903 0.0656434i
\(783\) 5.26432i 0.188131i
\(784\) 20.5892 + 3.47603i 0.735329 + 0.124144i
\(785\) 0 0
\(786\) 0.0278588 0.665888i 0.000993691 0.0237514i
\(787\) 0.389147 0.0138716 0.00693579 0.999976i \(-0.497792\pi\)
0.00693579 + 0.999976i