Properties

Label 273.2.g.a.272.1
Level $273$
Weight $2$
Character 273.272
Analytic conductor $2.180$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 272.1
Character \(\chi\) \(=\) 273.272
Dual form 273.2.g.a.272.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.35085 q^{2} +(-0.813690 - 1.52902i) q^{3} +3.52651 q^{4} -0.514868i q^{5} +(1.91287 + 3.59451i) q^{6} +(-1.49028 + 2.18611i) q^{7} -3.58861 q^{8} +(-1.67582 + 2.48830i) q^{9} +O(q^{10})\) \(q-2.35085 q^{2} +(-0.813690 - 1.52902i) q^{3} +3.52651 q^{4} -0.514868i q^{5} +(1.91287 + 3.59451i) q^{6} +(-1.49028 + 2.18611i) q^{7} -3.58861 q^{8} +(-1.67582 + 2.48830i) q^{9} +1.21038i q^{10} +2.08851 q^{11} +(-2.86949 - 5.39212i) q^{12} +(-2.92002 + 2.11506i) q^{13} +(3.50342 - 5.13923i) q^{14} +(-0.787245 + 0.418943i) q^{15} +1.38328 q^{16} +0.359522 q^{17} +(3.93960 - 5.84963i) q^{18} +3.55174 q^{19} -1.81569i q^{20} +(4.55523 + 0.499847i) q^{21} -4.90979 q^{22} +1.93858i q^{23} +(2.92002 + 5.48707i) q^{24} +4.73491 q^{25} +(6.86454 - 4.97220i) q^{26} +(5.16826 + 0.537655i) q^{27} +(-5.25548 + 7.70935i) q^{28} +8.77503i q^{29} +(1.85070 - 0.984875i) q^{30} +7.37747 q^{31} +3.92534 q^{32} +(-1.69940 - 3.19338i) q^{33} -0.845183 q^{34} +(1.12556 + 0.767296i) q^{35} +(-5.90979 + 8.77503i) q^{36} +2.76971i q^{37} -8.34962 q^{38} +(5.60997 + 2.74377i) q^{39} +1.84766i q^{40} -5.37332i q^{41} +(-10.7087 - 1.17507i) q^{42} -0.383277 q^{43} +7.36518 q^{44} +(1.28115 + 0.862825i) q^{45} -4.55733i q^{46} +6.90164i q^{47} +(-1.12556 - 2.11506i) q^{48} +(-2.55816 - 6.51581i) q^{49} -11.1311 q^{50} +(-0.292539 - 0.549717i) q^{51} +(-10.2975 + 7.45880i) q^{52} -9.21019i q^{53} +(-12.1498 - 1.26395i) q^{54} -1.07531i q^{55} +(5.34802 - 7.84511i) q^{56} +(-2.89002 - 5.43069i) q^{57} -20.6288i q^{58} -1.01344i q^{59} +(-2.77623 + 1.47741i) q^{60} +10.7842i q^{61} -17.3434 q^{62} +(-2.94227 - 7.37177i) q^{63} -11.9945 q^{64} +(1.08898 + 1.50343i) q^{65} +(3.99505 + 7.50718i) q^{66} +3.71944i q^{67} +1.26786 q^{68} +(2.96414 - 1.57741i) q^{69} +(-2.64603 - 1.80380i) q^{70} +2.79049 q^{71} +(6.01386 - 8.92955i) q^{72} -6.83815 q^{73} -6.51119i q^{74} +(-3.85275 - 7.23978i) q^{75} +12.5253 q^{76} +(-3.11246 + 4.56572i) q^{77} +(-13.1882 - 6.45020i) q^{78} +9.78607 q^{79} -0.712206i q^{80} +(-3.38328 - 8.33987i) q^{81} +12.6319i q^{82} +14.8929i q^{83} +(16.0641 + 1.76272i) q^{84} -0.185106i q^{85} +0.901029 q^{86} +(13.4172 - 7.14015i) q^{87} -7.49487 q^{88} +15.0466i q^{89} +(-3.01179 - 2.02838i) q^{90} +(-0.272125 - 9.53551i) q^{91} +6.83644i q^{92} +(-6.00298 - 11.2803i) q^{93} -16.2247i q^{94} -1.82868i q^{95} +(-3.19401 - 6.00194i) q^{96} -8.34372 q^{97} +(6.01386 + 15.3177i) q^{98} +(-3.49997 + 5.19685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 16q^{4} + O(q^{10}) \) \( 32q + 16q^{4} - 16q^{16} - 16q^{25} + 16q^{30} - 32q^{36} - 48q^{42} + 48q^{43} - 32q^{49} - 16q^{51} - 80q^{64} + 32q^{78} + 80q^{79} - 48q^{81} - 96q^{88} + 32q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.35085 −1.66230 −0.831152 0.556045i \(-0.812318\pi\)
−0.831152 + 0.556045i \(0.812318\pi\)
\(3\) −0.813690 1.52902i −0.469784 0.882781i
\(4\) 3.52651 1.76326
\(5\) 0.514868i 0.230256i −0.993351 0.115128i \(-0.963272\pi\)
0.993351 0.115128i \(-0.0367278\pi\)
\(6\) 1.91287 + 3.59451i 0.780925 + 1.46745i
\(7\) −1.49028 + 2.18611i −0.563271 + 0.826272i
\(8\) −3.58861 −1.26877
\(9\) −1.67582 + 2.48830i −0.558606 + 0.829433i
\(10\) 1.21038i 0.382756i
\(11\) 2.08851 0.629711 0.314855 0.949140i \(-0.398044\pi\)
0.314855 + 0.949140i \(0.398044\pi\)
\(12\) −2.86949 5.39212i −0.828351 1.55657i
\(13\) −2.92002 + 2.11506i −0.809868 + 0.586613i
\(14\) 3.50342 5.13923i 0.936328 1.37352i
\(15\) −0.787245 + 0.418943i −0.203266 + 0.108171i
\(16\) 1.38328 0.345819
\(17\) 0.359522 0.0871968 0.0435984 0.999049i \(-0.486118\pi\)
0.0435984 + 0.999049i \(0.486118\pi\)
\(18\) 3.93960 5.84963i 0.928573 1.37877i
\(19\) 3.55174 0.814825 0.407412 0.913244i \(-0.366431\pi\)
0.407412 + 0.913244i \(0.366431\pi\)
\(20\) 1.81569i 0.406001i
\(21\) 4.55523 + 0.499847i 0.994033 + 0.109076i
\(22\) −4.90979 −1.04677
\(23\) 1.93858i 0.404223i 0.979363 + 0.202111i \(0.0647803\pi\)
−0.979363 + 0.202111i \(0.935220\pi\)
\(24\) 2.92002 + 5.48707i 0.596047 + 1.12004i
\(25\) 4.73491 0.946982
\(26\) 6.86454 4.97220i 1.34625 0.975129i
\(27\) 5.16826 + 0.537655i 0.994632 + 0.103472i
\(28\) −5.25548 + 7.70935i −0.993192 + 1.45693i
\(29\) 8.77503i 1.62948i 0.579825 + 0.814741i \(0.303121\pi\)
−0.579825 + 0.814741i \(0.696879\pi\)
\(30\) 1.85070 0.984875i 0.337890 0.179813i
\(31\) 7.37747 1.32503 0.662517 0.749047i \(-0.269488\pi\)
0.662517 + 0.749047i \(0.269488\pi\)
\(32\) 3.92534 0.693909
\(33\) −1.69940 3.19338i −0.295828 0.555897i
\(34\) −0.845183 −0.144948
\(35\) 1.12556 + 0.767296i 0.190254 + 0.129697i
\(36\) −5.90979 + 8.77503i −0.984965 + 1.46250i
\(37\) 2.76971i 0.455338i 0.973739 + 0.227669i \(0.0731104\pi\)
−0.973739 + 0.227669i \(0.926890\pi\)
\(38\) −8.34962 −1.35449
\(39\) 5.60997 + 2.74377i 0.898314 + 0.439355i
\(40\) 1.84766i 0.292141i
\(41\) 5.37332i 0.839172i −0.907716 0.419586i \(-0.862175\pi\)
0.907716 0.419586i \(-0.137825\pi\)
\(42\) −10.7087 1.17507i −1.65239 0.181317i
\(43\) −0.383277 −0.0584492 −0.0292246 0.999573i \(-0.509304\pi\)
−0.0292246 + 0.999573i \(0.509304\pi\)
\(44\) 7.36518 1.11034
\(45\) 1.28115 + 0.862825i 0.190982 + 0.128622i
\(46\) 4.55733i 0.671941i
\(47\) 6.90164i 1.00671i 0.864081 + 0.503354i \(0.167901\pi\)
−0.864081 + 0.503354i \(0.832099\pi\)
\(48\) −1.12556 2.11506i −0.162460 0.305283i
\(49\) −2.55816 6.51581i −0.365451 0.930830i
\(50\) −11.1311 −1.57417
\(51\) −0.292539 0.549717i −0.0409637 0.0769757i
\(52\) −10.2975 + 7.45880i −1.42801 + 1.03435i
\(53\) 9.21019i 1.26512i −0.774513 0.632558i \(-0.782005\pi\)
0.774513 0.632558i \(-0.217995\pi\)
\(54\) −12.1498 1.26395i −1.65338 0.172002i
\(55\) 1.07531i 0.144995i
\(56\) 5.34802 7.84511i 0.714660 1.04835i
\(57\) −2.89002 5.43069i −0.382792 0.719312i
\(58\) 20.6288i 2.70870i
\(59\) 1.01344i 0.131939i −0.997822 0.0659696i \(-0.978986\pi\)
0.997822 0.0659696i \(-0.0210140\pi\)
\(60\) −2.77623 + 1.47741i −0.358410 + 0.190733i
\(61\) 10.7842i 1.38078i 0.723437 + 0.690390i \(0.242561\pi\)
−0.723437 + 0.690390i \(0.757439\pi\)
\(62\) −17.3434 −2.20261
\(63\) −2.94227 7.37177i −0.370691 0.928756i
\(64\) −11.9945 −1.49931
\(65\) 1.08898 + 1.50343i 0.135071 + 0.186477i
\(66\) 3.99505 + 7.50718i 0.491757 + 0.924070i
\(67\) 3.71944i 0.454402i 0.973848 + 0.227201i \(0.0729574\pi\)
−0.973848 + 0.227201i \(0.927043\pi\)
\(68\) 1.26786 0.153750
\(69\) 2.96414 1.57741i 0.356840 0.189897i
\(70\) −2.64603 1.80380i −0.316261 0.215595i
\(71\) 2.79049 0.331170 0.165585 0.986196i \(-0.447049\pi\)
0.165585 + 0.986196i \(0.447049\pi\)
\(72\) 6.01386 8.92955i 0.708740 1.05236i
\(73\) −6.83815 −0.800345 −0.400173 0.916440i \(-0.631050\pi\)
−0.400173 + 0.916440i \(0.631050\pi\)
\(74\) 6.51119i 0.756911i
\(75\) −3.85275 7.23978i −0.444877 0.835978i
\(76\) 12.5253 1.43675
\(77\) −3.11246 + 4.56572i −0.354698 + 0.520312i
\(78\) −13.1882 6.45020i −1.49327 0.730342i
\(79\) 9.78607 1.10102 0.550509 0.834829i \(-0.314433\pi\)
0.550509 + 0.834829i \(0.314433\pi\)
\(80\) 0.712206i 0.0796270i
\(81\) −3.38328 8.33987i −0.375920 0.926652i
\(82\) 12.6319i 1.39496i
\(83\) 14.8929i 1.63471i 0.576136 + 0.817354i \(0.304560\pi\)
−0.576136 + 0.817354i \(0.695440\pi\)
\(84\) 16.0641 + 1.76272i 1.75274 + 0.192328i
\(85\) 0.185106i 0.0200776i
\(86\) 0.901029 0.0971605
\(87\) 13.4172 7.14015i 1.43848 0.765505i
\(88\) −7.49487 −0.798956
\(89\) 15.0466i 1.59494i 0.603358 + 0.797470i \(0.293829\pi\)
−0.603358 + 0.797470i \(0.706171\pi\)
\(90\) −3.01179 2.02838i −0.317471 0.213810i
\(91\) −0.272125 9.53551i −0.0285265 0.999593i
\(92\) 6.83644i 0.712749i
\(93\) −6.00298 11.2803i −0.622480 1.16971i
\(94\) 16.2247i 1.67345i
\(95\) 1.82868i 0.187618i
\(96\) −3.19401 6.00194i −0.325988 0.612570i
\(97\) −8.34372 −0.847176 −0.423588 0.905855i \(-0.639230\pi\)
−0.423588 + 0.905855i \(0.639230\pi\)
\(98\) 6.01386 + 15.3177i 0.607491 + 1.54732i
\(99\) −3.49997 + 5.19685i −0.351760 + 0.522303i
\(100\) 16.6977 1.66977
\(101\) −16.8574 −1.67738 −0.838688 0.544612i \(-0.816677\pi\)
−0.838688 + 0.544612i \(0.816677\pi\)
\(102\) 0.687717 + 1.29230i 0.0680941 + 0.127957i
\(103\) 3.69533i 0.364111i −0.983288 0.182056i \(-0.941725\pi\)
0.983288 0.182056i \(-0.0582751\pi\)
\(104\) 10.4788 7.59014i 1.02753 0.744274i
\(105\) 0.257355 2.34535i 0.0251153 0.228882i
\(106\) 21.6518i 2.10301i
\(107\) 13.7205i 1.32641i 0.748439 + 0.663204i \(0.230804\pi\)
−0.748439 + 0.663204i \(0.769196\pi\)
\(108\) 18.2260 + 1.89605i 1.75379 + 0.182447i
\(109\) 10.8614i 1.04033i 0.854065 + 0.520166i \(0.174130\pi\)
−0.854065 + 0.520166i \(0.825870\pi\)
\(110\) 2.52790i 0.241025i
\(111\) 4.23495 2.25369i 0.401964 0.213911i
\(112\) −2.06146 + 3.02400i −0.194790 + 0.285741i
\(113\) 13.7516i 1.29364i −0.762641 0.646822i \(-0.776098\pi\)
0.762641 0.646822i \(-0.223902\pi\)
\(114\) 6.79400 + 12.7668i 0.636317 + 1.19572i
\(115\) 0.998115 0.0930747
\(116\) 30.9453i 2.87320i
\(117\) −0.369491 10.8103i −0.0341594 0.999416i
\(118\) 2.38246i 0.219323i
\(119\) −0.535786 + 0.785954i −0.0491155 + 0.0720483i
\(120\) 2.82512 1.50343i 0.257897 0.137243i
\(121\) −6.63811 −0.603464
\(122\) 25.3522i 2.29528i
\(123\) −8.21593 + 4.37222i −0.740806 + 0.394230i
\(124\) 26.0168 2.33637
\(125\) 5.01220i 0.448305i
\(126\) 6.91685 + 17.3300i 0.616202 + 1.54388i
\(127\) 8.11819 0.720373 0.360186 0.932880i \(-0.382713\pi\)
0.360186 + 0.932880i \(0.382713\pi\)
\(128\) 20.3466 1.79840
\(129\) 0.311869 + 0.586039i 0.0274585 + 0.0515979i
\(130\) −2.56003 3.53433i −0.224529 0.309982i
\(131\) 16.9323 1.47939 0.739693 0.672945i \(-0.234971\pi\)
0.739693 + 0.672945i \(0.234971\pi\)
\(132\) −5.99297 11.2615i −0.521621 0.980189i
\(133\) −5.29307 + 7.76450i −0.458967 + 0.673267i
\(134\) 8.74386i 0.755355i
\(135\) 0.276822 2.66097i 0.0238250 0.229020i
\(136\) −1.29018 −0.110632
\(137\) 9.93920 0.849163 0.424582 0.905390i \(-0.360421\pi\)
0.424582 + 0.905390i \(0.360421\pi\)
\(138\) −6.96825 + 3.70825i −0.593177 + 0.315667i
\(139\) 1.24868i 0.105912i −0.998597 0.0529559i \(-0.983136\pi\)
0.998597 0.0529559i \(-0.0168643\pi\)
\(140\) 3.96930 + 2.70588i 0.335467 + 0.228689i
\(141\) 10.5528 5.61579i 0.888702 0.472935i
\(142\) −6.56003 −0.550505
\(143\) −6.09850 + 4.41734i −0.509982 + 0.369396i
\(144\) −2.31812 + 3.44201i −0.193177 + 0.286834i
\(145\) 4.51798 0.375198
\(146\) 16.0755 1.33042
\(147\) −7.88127 + 9.21333i −0.650036 + 0.759903i
\(148\) 9.76744i 0.802878i
\(149\) −14.5206 −1.18958 −0.594789 0.803882i \(-0.702764\pi\)
−0.594789 + 0.803882i \(0.702764\pi\)
\(150\) 9.05725 + 17.0197i 0.739522 + 1.38965i
\(151\) 3.27828i 0.266783i 0.991063 + 0.133391i \(0.0425867\pi\)
−0.991063 + 0.133391i \(0.957413\pi\)
\(152\) −12.7458 −1.03382
\(153\) −0.602492 + 0.894598i −0.0487086 + 0.0723240i
\(154\) 7.31694 10.7333i 0.589616 0.864918i
\(155\) 3.79843i 0.305097i
\(156\) 19.7836 + 9.67594i 1.58396 + 0.774696i
\(157\) 17.9756i 1.43461i 0.696758 + 0.717306i \(0.254625\pi\)
−0.696758 + 0.717306i \(0.745375\pi\)
\(158\) −23.0056 −1.83023
\(159\) −14.0826 + 7.49424i −1.11682 + 0.594332i
\(160\) 2.02104i 0.159777i
\(161\) −4.23796 2.88902i −0.333998 0.227687i
\(162\) 7.95359 + 19.6058i 0.624893 + 1.54038i
\(163\) 16.4417i 1.28781i −0.765104 0.643907i \(-0.777313\pi\)
0.765104 0.643907i \(-0.222687\pi\)
\(164\) 18.9491i 1.47968i
\(165\) −1.64417 + 0.874969i −0.127999 + 0.0681163i
\(166\) 35.0110i 2.71738i
\(167\) 11.5628i 0.894753i −0.894346 0.447376i \(-0.852358\pi\)
0.894346 0.447376i \(-0.147642\pi\)
\(168\) −16.3470 1.79376i −1.26120 0.138391i
\(169\) 4.05303 12.3520i 0.311772 0.950157i
\(170\) 0.435158i 0.0333751i
\(171\) −5.95206 + 8.83779i −0.455166 + 0.675843i
\(172\) −1.35163 −0.103061
\(173\) −12.6080 −0.958570 −0.479285 0.877659i \(-0.659104\pi\)
−0.479285 + 0.877659i \(0.659104\pi\)
\(174\) −31.5419 + 16.7855i −2.39119 + 1.27250i
\(175\) −7.05632 + 10.3510i −0.533408 + 0.782465i
\(176\) 2.88899 0.217766
\(177\) −1.54958 + 0.824630i −0.116473 + 0.0619830i
\(178\) 35.3725i 2.65128i
\(179\) 11.4566i 0.856309i −0.903706 0.428154i \(-0.859164\pi\)
0.903706 0.428154i \(-0.140836\pi\)
\(180\) 4.51798 + 3.04277i 0.336751 + 0.226794i
\(181\) 6.85014i 0.509167i 0.967051 + 0.254583i \(0.0819384\pi\)
−0.967051 + 0.254583i \(0.918062\pi\)
\(182\) 0.639726 + 22.4166i 0.0474197 + 1.66163i
\(183\) 16.4893 8.77503i 1.21893 0.648669i
\(184\) 6.95683i 0.512864i
\(185\) 1.42604 0.104844
\(186\) 14.1121 + 26.5184i 1.03475 + 1.94442i
\(187\) 0.750866 0.0549088
\(188\) 24.3387i 1.77508i
\(189\) −8.87751 + 10.4971i −0.645744 + 0.763554i
\(190\) 4.29896i 0.311879i
\(191\) 4.65135i 0.336560i 0.985739 + 0.168280i \(0.0538212\pi\)
−0.985739 + 0.168280i \(0.946179\pi\)
\(192\) 9.75978 + 18.3398i 0.704351 + 1.32356i
\(193\) 9.76744i 0.703075i −0.936174 0.351538i \(-0.885659\pi\)
0.936174 0.351538i \(-0.114341\pi\)
\(194\) 19.6149 1.40827
\(195\) 1.41268 2.88839i 0.101164 0.206842i
\(196\) −9.02139 22.9781i −0.644385 1.64129i
\(197\) 20.0181 1.42623 0.713116 0.701046i \(-0.247283\pi\)
0.713116 + 0.701046i \(0.247283\pi\)
\(198\) 8.22791 12.2170i 0.584732 0.868227i
\(199\) 16.0897i 1.14057i −0.821448 0.570283i \(-0.806833\pi\)
0.821448 0.570283i \(-0.193167\pi\)
\(200\) −16.9918 −1.20150
\(201\) 5.68711 3.02647i 0.401138 0.213471i
\(202\) 39.6293 2.78831
\(203\) −19.1832 13.0772i −1.34640 0.917840i
\(204\) −1.03164 1.93858i −0.0722295 0.135728i
\(205\) −2.76655 −0.193225
\(206\) 8.68718i 0.605264i
\(207\) −4.82378 3.24871i −0.335276 0.225801i
\(208\) −4.03920 + 2.92572i −0.280068 + 0.202862i
\(209\) 7.41786 0.513104
\(210\) −0.605005 + 5.51357i −0.0417493 + 0.380472i
\(211\) 7.13770 0.491380 0.245690 0.969348i \(-0.420986\pi\)
0.245690 + 0.969348i \(0.420986\pi\)
\(212\) 32.4799i 2.23073i
\(213\) −2.27059 4.26672i −0.155578 0.292351i
\(214\) 32.2548i 2.20489i
\(215\) 0.197337i 0.0134583i
\(216\) −18.5469 1.92944i −1.26196 0.131281i
\(217\) −10.9945 + 16.1280i −0.746353 + 1.09484i
\(218\) 25.5335i 1.72935i
\(219\) 5.56414 + 10.4557i 0.375990 + 0.706530i
\(220\) 3.79210i 0.255663i
\(221\) −1.04981 + 0.760411i −0.0706179 + 0.0511507i
\(222\) −9.95576 + 5.29809i −0.668187 + 0.355585i
\(223\) 13.7655 0.921806 0.460903 0.887450i \(-0.347526\pi\)
0.460903 + 0.887450i \(0.347526\pi\)
\(224\) −5.84984 + 8.58124i −0.390859 + 0.573358i
\(225\) −7.93484 + 11.7819i −0.528989 + 0.785459i
\(226\) 32.3281i 2.15043i
\(227\) 16.6621i 1.10591i −0.833213 0.552953i \(-0.813501\pi\)
0.833213 0.552953i \(-0.186499\pi\)
\(228\) −10.1917 19.1514i −0.674961 1.26833i
\(229\) −24.1786 −1.59777 −0.798883 0.601486i \(-0.794576\pi\)
−0.798883 + 0.601486i \(0.794576\pi\)
\(230\) −2.34642 −0.154719
\(231\) 9.51367 + 1.04394i 0.625954 + 0.0686861i
\(232\) 31.4902i 2.06743i
\(233\) 6.58993i 0.431721i −0.976424 0.215860i \(-0.930744\pi\)
0.976424 0.215860i \(-0.0692556\pi\)
\(234\) 0.868619 + 25.4135i 0.0567834 + 1.66133i
\(235\) 3.55343 0.231801
\(236\) 3.57393i 0.232643i
\(237\) −7.96283 14.9631i −0.517241 0.971959i
\(238\) 1.25956 1.84766i 0.0816449 0.119766i
\(239\) −5.44285 −0.352069 −0.176034 0.984384i \(-0.556327\pi\)
−0.176034 + 0.984384i \(0.556327\pi\)
\(240\) −1.08898 + 0.579515i −0.0702932 + 0.0374075i
\(241\) 1.44312 0.0929593 0.0464797 0.998919i \(-0.485200\pi\)
0.0464797 + 0.998919i \(0.485200\pi\)
\(242\) 15.6052 1.00314
\(243\) −9.99891 + 11.9592i −0.641430 + 0.767181i
\(244\) 38.0308i 2.43467i
\(245\) −3.35479 + 1.31712i −0.214329 + 0.0841474i
\(246\) 19.3145 10.2785i 1.23144 0.655330i
\(247\) −10.3711 + 7.51215i −0.659900 + 0.477986i
\(248\) −26.4749 −1.68116
\(249\) 22.7716 12.1182i 1.44309 0.767960i
\(250\) 11.7829i 0.745219i
\(251\) −28.3665 −1.79048 −0.895239 0.445587i \(-0.852995\pi\)
−0.895239 + 0.445587i \(0.852995\pi\)
\(252\) −10.3760 25.9967i −0.653624 1.63764i
\(253\) 4.04876i 0.254543i
\(254\) −19.0847 −1.19748
\(255\) −0.283032 + 0.150619i −0.0177241 + 0.00943214i
\(256\) −23.8428 −1.49018
\(257\) 23.8529 1.48790 0.743951 0.668234i \(-0.232950\pi\)
0.743951 + 0.668234i \(0.232950\pi\)
\(258\) −0.733159 1.37769i −0.0456445 0.0857714i
\(259\) −6.05490 4.12764i −0.376233 0.256479i
\(260\) 3.84030 + 5.30185i 0.238165 + 0.328807i
\(261\) −21.8349 14.7053i −1.35155 0.910238i
\(262\) −39.8055 −2.45919
\(263\) 15.1763i 0.935812i 0.883778 + 0.467906i \(0.154991\pi\)
−0.883778 + 0.467906i \(0.845009\pi\)
\(264\) 6.09850 + 11.4598i 0.375337 + 0.705303i
\(265\) −4.74203 −0.291301
\(266\) 12.4432 18.2532i 0.762944 1.11918i
\(267\) 23.0066 12.2433i 1.40798 0.749278i
\(268\) 13.1167i 0.801228i
\(269\) 16.6681 1.01627 0.508137 0.861276i \(-0.330334\pi\)
0.508137 + 0.861276i \(0.330334\pi\)
\(270\) −0.650767 + 6.25556i −0.0396044 + 0.380701i
\(271\) −1.41125 −0.0857271 −0.0428636 0.999081i \(-0.513648\pi\)
−0.0428636 + 0.999081i \(0.513648\pi\)
\(272\) 0.497318 0.0301543
\(273\) −14.3586 + 8.17504i −0.869021 + 0.494776i
\(274\) −23.3656 −1.41157
\(275\) 9.88893 0.596325
\(276\) 10.4531 5.56275i 0.629201 0.334838i
\(277\) −2.02977 −0.121957 −0.0609787 0.998139i \(-0.519422\pi\)
−0.0609787 + 0.998139i \(0.519422\pi\)
\(278\) 2.93547i 0.176058i
\(279\) −12.3633 + 18.3574i −0.740171 + 1.09903i
\(280\) −4.03920 2.75353i −0.241388 0.164555i
\(281\) 15.9966 0.954279 0.477139 0.878828i \(-0.341674\pi\)
0.477139 + 0.878828i \(0.341674\pi\)
\(282\) −24.8080 + 13.2019i −1.47729 + 0.786162i
\(283\) 30.3700i 1.80531i 0.430367 + 0.902654i \(0.358384\pi\)
−0.430367 + 0.902654i \(0.641616\pi\)
\(284\) 9.84070 0.583938
\(285\) −2.79609 + 1.48798i −0.165626 + 0.0881402i
\(286\) 14.3367 10.3845i 0.847746 0.614049i
\(287\) 11.7467 + 8.00773i 0.693385 + 0.472682i
\(288\) −6.57816 + 9.76744i −0.387622 + 0.575552i
\(289\) −16.8707 −0.992397
\(290\) −10.6211 −0.623694
\(291\) 6.78920 + 12.7577i 0.397990 + 0.747871i
\(292\) −24.1149 −1.41122
\(293\) 24.4561i 1.42874i −0.699769 0.714369i \(-0.746714\pi\)
0.699769 0.714369i \(-0.253286\pi\)
\(294\) 18.5277 21.6592i 1.08056 1.26319i
\(295\) −0.521790 −0.0303798
\(296\) 9.93943i 0.577718i
\(297\) 10.7940 + 1.12290i 0.626331 + 0.0651573i
\(298\) 34.1359 1.97744
\(299\) −4.10022 5.66070i −0.237122 0.327367i
\(300\) −13.5868 25.5312i −0.784433 1.47404i
\(301\) 0.571189 0.837887i 0.0329228 0.0482950i
\(302\) 7.70676i 0.443474i
\(303\) 13.7167 + 25.7754i 0.788005 + 1.48076i
\(304\) 4.91304 0.281782
\(305\) 5.55246 0.317933
\(306\) 1.41637 2.10307i 0.0809686 0.120224i
\(307\) 9.83678 0.561415 0.280707 0.959793i \(-0.409431\pi\)
0.280707 + 0.959793i \(0.409431\pi\)
\(308\) −10.9761 + 16.1011i −0.625424 + 0.917445i
\(309\) −5.65024 + 3.00685i −0.321431 + 0.171054i
\(310\) 8.92955i 0.507164i
\(311\) 21.5814 1.22377 0.611884 0.790948i \(-0.290412\pi\)
0.611884 + 0.790948i \(0.290412\pi\)
\(312\) −20.1320 9.84633i −1.13975 0.557439i
\(313\) 9.13704i 0.516456i −0.966084 0.258228i \(-0.916861\pi\)
0.966084 0.258228i \(-0.0831386\pi\)
\(314\) 42.2581i 2.38476i
\(315\) −3.79549 + 1.51488i −0.213852 + 0.0853540i
\(316\) 34.5107 1.94138
\(317\) −0.763354 −0.0428743 −0.0214371 0.999770i \(-0.506824\pi\)
−0.0214371 + 0.999770i \(0.506824\pi\)
\(318\) 33.1061 17.6179i 1.85650 0.987961i
\(319\) 18.3268i 1.02610i
\(320\) 6.17557i 0.345225i
\(321\) 20.9789 11.1642i 1.17093 0.623125i
\(322\) 9.96282 + 6.79167i 0.555206 + 0.378485i
\(323\) 1.27693 0.0710501
\(324\) −11.9312 29.4107i −0.662843 1.63393i
\(325\) −13.8260 + 10.0146i −0.766930 + 0.555512i
\(326\) 38.6520i 2.14074i
\(327\) 16.6073 8.83779i 0.918385 0.488731i
\(328\) 19.2828i 1.06471i
\(329\) −15.0877 10.2853i −0.831814 0.567049i
\(330\) 3.86521 2.05692i 0.212773 0.113230i
\(331\) 6.95683i 0.382382i −0.981553 0.191191i \(-0.938765\pi\)
0.981553 0.191191i \(-0.0612350\pi\)
\(332\) 52.5200i 2.88241i
\(333\) −6.89188 4.64153i −0.377673 0.254354i
\(334\) 27.1824i 1.48735i
\(335\) 1.91502 0.104629
\(336\) 6.30115 + 0.691427i 0.343756 + 0.0377204i
\(337\) 14.6708 0.799170 0.399585 0.916696i \(-0.369154\pi\)
0.399585 + 0.916696i \(0.369154\pi\)
\(338\) −9.52808 + 29.0378i −0.518259 + 1.57945i
\(339\) −21.0265 + 11.1896i −1.14201 + 0.607734i
\(340\) 0.652780i 0.0354020i
\(341\) 15.4080 0.834388
\(342\) 13.9924 20.7764i 0.756624 1.12346i
\(343\) 18.0566 + 4.11794i 0.974967 + 0.222348i
\(344\) 1.37543 0.0741584
\(345\) −0.812157 1.52614i −0.0437250 0.0821646i
\(346\) 29.6396 1.59344
\(347\) 27.1157i 1.45565i −0.685765 0.727823i \(-0.740532\pi\)
0.685765 0.727823i \(-0.259468\pi\)
\(348\) 47.3160 25.1799i 2.53640 1.34978i
\(349\) 8.10159 0.433668 0.216834 0.976208i \(-0.430427\pi\)
0.216834 + 0.976208i \(0.430427\pi\)
\(350\) 16.5884 24.3338i 0.886686 1.30070i
\(351\) −16.2286 + 9.36123i −0.866219 + 0.499665i
\(352\) 8.19814 0.436962
\(353\) 25.1410i 1.33812i 0.743209 + 0.669059i \(0.233303\pi\)
−0.743209 + 0.669059i \(0.766697\pi\)
\(354\) 3.64283 1.93858i 0.193614 0.103035i
\(355\) 1.43673i 0.0762539i
\(356\) 53.0622i 2.81229i
\(357\) 1.63771 + 0.179706i 0.0866766 + 0.00951104i
\(358\) 26.9329i 1.42345i
\(359\) −6.28685 −0.331807 −0.165904 0.986142i \(-0.553054\pi\)
−0.165904 + 0.986142i \(0.553054\pi\)
\(360\) −4.59754 3.09635i −0.242312 0.163192i
\(361\) −6.38515 −0.336060
\(362\) 16.1037i 0.846391i
\(363\) 5.40136 + 10.1498i 0.283498 + 0.532727i
\(364\) −0.959653 33.6271i −0.0502995 1.76254i
\(365\) 3.52075i 0.184284i
\(366\) −38.7640 + 20.6288i −2.02623 + 1.07829i
\(367\) 22.3791i 1.16818i −0.811689 0.584091i \(-0.801451\pi\)
0.811689 0.584091i \(-0.198549\pi\)
\(368\) 2.68160i 0.139788i
\(369\) 13.3704 + 9.00471i 0.696038 + 0.468766i
\(370\) −3.35241 −0.174283
\(371\) 20.1345 + 13.7257i 1.04533 + 0.712604i
\(372\) −21.1696 39.7802i −1.09759 2.06251i
\(373\) 27.3311 1.41515 0.707576 0.706637i \(-0.249789\pi\)
0.707576 + 0.706637i \(0.249789\pi\)
\(374\) −1.76518 −0.0912751
\(375\) −7.66376 + 4.07838i −0.395755 + 0.210606i
\(376\) 24.7673i 1.27728i
\(377\) −18.5597 25.6233i −0.955874 1.31966i
\(378\) 20.8697 24.6772i 1.07342 1.26926i
\(379\) 11.9962i 0.616204i −0.951353 0.308102i \(-0.900306\pi\)
0.951353 0.308102i \(-0.0996938\pi\)
\(380\) 6.44886i 0.330820i
\(381\) −6.60569 12.4129i −0.338420 0.635932i
\(382\) 10.9346i 0.559465i
\(383\) 10.5766i 0.540440i 0.962799 + 0.270220i \(0.0870964\pi\)
−0.962799 + 0.270220i \(0.912904\pi\)
\(384\) −16.5558 31.1103i −0.844859 1.58759i
\(385\) 2.35075 + 1.60251i 0.119805 + 0.0816714i
\(386\) 22.9618i 1.16873i
\(387\) 0.642303 0.953709i 0.0326501 0.0484798i
\(388\) −29.4242 −1.49379
\(389\) 18.6357i 0.944868i −0.881366 0.472434i \(-0.843375\pi\)
0.881366 0.472434i \(-0.156625\pi\)
\(390\) −3.32100 + 6.79019i −0.168166 + 0.343835i
\(391\) 0.696963i 0.0352469i
\(392\) 9.18024 + 23.3827i 0.463672 + 1.18101i
\(393\) −13.7777 25.8899i −0.694992 1.30597i
\(394\) −47.0597 −2.37083
\(395\) 5.03854i 0.253516i
\(396\) −12.3427 + 18.3268i −0.620243 + 0.920955i
\(397\) −13.1051 −0.657727 −0.328864 0.944377i \(-0.606666\pi\)
−0.328864 + 0.944377i \(0.606666\pi\)
\(398\) 37.8245i 1.89597i
\(399\) 16.1790 + 1.77533i 0.809963 + 0.0888775i
\(400\) 6.54969 0.327485
\(401\) 2.36431 0.118068 0.0590341 0.998256i \(-0.481198\pi\)
0.0590341 + 0.998256i \(0.481198\pi\)
\(402\) −13.3696 + 7.11480i −0.666813 + 0.354854i
\(403\) −21.5424 + 15.6038i −1.07310 + 0.777281i
\(404\) −59.4479 −2.95765
\(405\) −4.29394 + 1.74194i −0.213367 + 0.0865578i
\(406\) 45.0969 + 30.7426i 2.23812 + 1.52573i
\(407\) 5.78459i 0.286731i
\(408\) 1.04981 + 1.97272i 0.0519734 + 0.0976642i
\(409\) 23.0987 1.14216 0.571078 0.820896i \(-0.306525\pi\)
0.571078 + 0.820896i \(0.306525\pi\)
\(410\) 6.50377 0.321198
\(411\) −8.08743 15.1973i −0.398924 0.749626i
\(412\) 13.0316i 0.642022i
\(413\) 2.21550 + 1.51031i 0.109018 + 0.0743175i
\(414\) 11.3400 + 7.63725i 0.557331 + 0.375350i
\(415\) 7.66788 0.376402
\(416\) −11.4621 + 8.30234i −0.561975 + 0.407056i
\(417\) −1.90926 + 1.01604i −0.0934970 + 0.0497557i
\(418\) −17.4383 −0.852935
\(419\) −5.80253 −0.283472 −0.141736 0.989904i \(-0.545268\pi\)
−0.141736 + 0.989904i \(0.545268\pi\)
\(420\) 0.907568 8.27090i 0.0442848 0.403578i
\(421\) 39.7670i 1.93812i −0.246820 0.969061i \(-0.579386\pi\)
0.246820 0.969061i \(-0.420614\pi\)
\(422\) −16.7797 −0.816823
\(423\) −17.1733 11.5659i −0.834997 0.562352i
\(424\) 33.0518i 1.60514i
\(425\) 1.70230 0.0825738
\(426\) 5.33783 + 10.0304i 0.258619 + 0.485976i
\(427\) −23.5755 16.0715i −1.14090 0.777754i
\(428\) 48.3854i 2.33880i
\(429\) 11.7165 + 5.73040i 0.565678 + 0.276666i
\(430\) 0.463911i 0.0223718i
\(431\) −36.2007 −1.74372 −0.871862 0.489751i \(-0.837088\pi\)
−0.871862 + 0.489751i \(0.837088\pi\)
\(432\) 7.14914 + 0.743726i 0.343963 + 0.0357825i
\(433\) 1.61582i 0.0776516i −0.999246 0.0388258i \(-0.987638\pi\)
0.999246 0.0388258i \(-0.0123617\pi\)
\(434\) 25.8464 37.9145i 1.24067 1.81995i
\(435\) −3.67624 6.90810i −0.176262 0.331218i
\(436\) 38.3028i 1.83437i
\(437\) 6.88534i 0.329371i
\(438\) −13.0805 24.5798i −0.625009 1.17447i
\(439\) 17.9868i 0.858465i −0.903194 0.429233i \(-0.858784\pi\)
0.903194 0.429233i \(-0.141216\pi\)
\(440\) 3.85887i 0.183964i
\(441\) 20.5003 + 4.55384i 0.976205 + 0.216850i
\(442\) 2.46795 1.78761i 0.117388 0.0850281i
\(443\) 3.25336i 0.154572i 0.997009 + 0.0772860i \(0.0246255\pi\)
−0.997009 + 0.0772860i \(0.975375\pi\)
\(444\) 14.9346 7.94767i 0.708766 0.377180i
\(445\) 7.74704 0.367245
\(446\) −32.3607 −1.53232
\(447\) 11.8153 + 22.2024i 0.558845 + 1.05014i
\(448\) 17.8751 26.2212i 0.844517 1.23884i
\(449\) −40.1506 −1.89482 −0.947411 0.320019i \(-0.896311\pi\)
−0.947411 + 0.320019i \(0.896311\pi\)
\(450\) 18.6537 27.6975i 0.879342 1.30567i
\(451\) 11.2223i 0.528436i
\(452\) 48.4953i 2.28103i
\(453\) 5.01256 2.66751i 0.235511 0.125330i
\(454\) 39.1703i 1.83835i
\(455\) −4.90953 + 0.140109i −0.230162 + 0.00656839i
\(456\) 10.3711 + 19.4886i 0.485674 + 0.912639i
\(457\) 0.467674i 0.0218769i 0.999940 + 0.0109384i \(0.00348188\pi\)
−0.999940 + 0.0109384i \(0.996518\pi\)
\(458\) 56.8403 2.65598
\(459\) 1.85810 + 0.193299i 0.0867288 + 0.00902241i
\(460\) 3.51987 0.164115
\(461\) 25.9844i 1.21021i 0.796144 + 0.605107i \(0.206870\pi\)
−0.796144 + 0.605107i \(0.793130\pi\)
\(462\) −22.3653 2.45415i −1.04053 0.114177i
\(463\) 18.8412i 0.875625i 0.899066 + 0.437812i \(0.144247\pi\)
−0.899066 + 0.437812i \(0.855753\pi\)
\(464\) 12.1383i 0.563506i
\(465\) −5.80788 + 3.09074i −0.269334 + 0.143330i
\(466\) 15.4920i 0.717652i
\(467\) 7.90380 0.365744 0.182872 0.983137i \(-0.441461\pi\)
0.182872 + 0.983137i \(0.441461\pi\)
\(468\) −1.30301 38.1228i −0.0602319 1.76223i
\(469\) −8.13111 5.54299i −0.375460 0.255952i
\(470\) −8.35361 −0.385323
\(471\) 27.4851 14.6266i 1.26645 0.673958i
\(472\) 3.63686i 0.167400i
\(473\) −0.800480 −0.0368061
\(474\) 18.7194 + 35.1761i 0.859813 + 1.61569i
\(475\) 16.8172 0.771625
\(476\) −1.88946 + 2.77168i −0.0866032 + 0.127040i
\(477\) 22.9177 + 15.4346i 1.04933 + 0.706701i
\(478\) 12.7953 0.585245
\(479\) 14.3507i 0.655701i −0.944730 0.327851i \(-0.893676\pi\)
0.944730 0.327851i \(-0.106324\pi\)
\(480\) −3.09021 + 1.64450i −0.141048 + 0.0750607i
\(481\) −5.85811 8.08762i −0.267107 0.368764i
\(482\) −3.39256 −0.154527
\(483\) −0.968995 + 8.83070i −0.0440908 + 0.401811i
\(484\) −23.4094 −1.06406
\(485\) 4.29592i 0.195068i
\(486\) 23.5060 28.1143i 1.06625 1.27529i
\(487\) 31.9722i 1.44880i 0.689380 + 0.724400i \(0.257883\pi\)
−0.689380 + 0.724400i \(0.742117\pi\)
\(488\) 38.7005i 1.75189i
\(489\) −25.1397 + 13.3784i −1.13686 + 0.604994i
\(490\) 7.88661 3.09635i 0.356281 0.139879i
\(491\) 18.2619i 0.824148i 0.911150 + 0.412074i \(0.135196\pi\)
−0.911150 + 0.412074i \(0.864804\pi\)
\(492\) −28.9736 + 15.4187i −1.30623 + 0.695129i
\(493\) 3.15481i 0.142086i
\(494\) 24.3811 17.6600i 1.09696 0.794559i
\(495\) 2.67569 + 1.80202i 0.120264 + 0.0809949i
\(496\) 10.2051 0.458222
\(497\) −4.15859 + 6.10031i −0.186538 + 0.273636i
\(498\) −53.5326 + 28.4881i −2.39885 + 1.27658i
\(499\) 27.3031i 1.22225i −0.791533 0.611127i \(-0.790717\pi\)
0.791533 0.611127i \(-0.209283\pi\)
\(500\) 17.6756i 0.790476i
\(501\) −17.6797 + 9.40850i −0.789871 + 0.420341i
\(502\) 66.6855 2.97632
\(503\) −0.0424911 −0.00189459 −0.000947293 1.00000i \(-0.500302\pi\)
−0.000947293 1.00000i \(0.500302\pi\)
\(504\) 10.5587 + 26.4544i 0.470321 + 1.17837i
\(505\) 8.67935i 0.386226i
\(506\) 9.51804i 0.423129i
\(507\) −22.1845 + 3.85356i −0.985246 + 0.171143i
\(508\) 28.6289 1.27020
\(509\) 19.8553i 0.880069i −0.897981 0.440034i \(-0.854966\pi\)
0.897981 0.440034i \(-0.145034\pi\)
\(510\) 0.665366 0.354084i 0.0294629 0.0156791i
\(511\) 10.1907 14.9490i 0.450811 0.661303i
\(512\) 15.3579 0.678731
\(513\) 18.3563 + 1.90961i 0.810451 + 0.0843114i
\(514\) −56.0746 −2.47335
\(515\) −1.90261 −0.0838389
\(516\) 1.09981 + 2.06668i 0.0484165 + 0.0909804i
\(517\) 14.4142i 0.633934i
\(518\) 14.2342 + 9.70347i 0.625414 + 0.426346i
\(519\) 10.2590 + 19.2779i 0.450321 + 0.846208i
\(520\) −3.90792 5.39521i −0.171374 0.236596i
\(521\) 12.5037 0.547798 0.273899 0.961759i \(-0.411687\pi\)
0.273899 + 0.961759i \(0.411687\pi\)
\(522\) 51.3307 + 34.5701i 2.24668 + 1.51309i
\(523\) 4.40349i 0.192551i −0.995355 0.0962757i \(-0.969307\pi\)
0.995355 0.0962757i \(-0.0306930\pi\)
\(524\) 59.7122 2.60854
\(525\) 21.5686 + 2.36673i 0.941332 + 0.103293i
\(526\) 35.6773i 1.55560i
\(527\) 2.65236 0.115539
\(528\) −2.35075 4.41734i −0.102303 0.192240i
\(529\) 19.2419 0.836604
\(530\) 11.1478 0.484231
\(531\) 2.52175 + 1.69835i 0.109435 + 0.0737020i
\(532\) −18.6661 + 27.3816i −0.809278 + 1.18714i
\(533\) 11.3649 + 15.6902i 0.492269 + 0.679619i
\(534\) −54.0853 + 28.7822i −2.34050 + 1.24553i
\(535\) 7.06423 0.305413
\(536\) 13.3476i 0.576530i
\(537\) −17.5174 + 9.32214i −0.755933 + 0.402280i
\(538\) −39.1843 −1.68936
\(539\) −5.34275 13.6084i −0.230129 0.586154i
\(540\) 0.976215 9.38397i 0.0420096 0.403822i
\(541\) 33.8573i 1.45564i 0.685768 + 0.727820i \(0.259466\pi\)
−0.685768 + 0.727820i \(0.740534\pi\)
\(542\) 3.31763 0.142505
\(543\) 10.4740 5.57389i 0.449483 0.239199i
\(544\) 1.41125 0.0605067
\(545\) 5.59218 0.239543
\(546\) 33.7549 19.2183i 1.44458 0.822468i
\(547\) −25.7777 −1.10217 −0.551087 0.834448i \(-0.685787\pi\)
−0.551087 + 0.834448i \(0.685787\pi\)
\(548\) 35.0507 1.49729
\(549\) −26.8344 18.0724i −1.14527 0.771311i
\(550\) −23.2474 −0.991274
\(551\) 31.1666i 1.32774i
\(552\) −10.6371 + 5.66070i −0.452747 + 0.240936i
\(553\) −14.5839 + 21.3934i −0.620172 + 0.909741i
\(554\) 4.77170 0.202730
\(555\) −1.16035 2.18044i −0.0492542 0.0925547i
\(556\) 4.40349i 0.186750i
\(557\) −13.2935 −0.563265 −0.281633 0.959522i \(-0.590876\pi\)
−0.281633 + 0.959522i \(0.590876\pi\)
\(558\) 29.0643 43.1555i 1.23039 1.82692i
\(559\) 1.11918 0.810655i 0.0473362 0.0342871i
\(560\) 1.55696 + 1.06138i 0.0657936 + 0.0448516i
\(561\) −0.610972 1.14809i −0.0257953 0.0484724i
\(562\) −37.6057 −1.58630
\(563\) −3.97380 −0.167476 −0.0837379 0.996488i \(-0.526686\pi\)
−0.0837379 + 0.996488i \(0.526686\pi\)
\(564\) 37.2144 19.8042i 1.56701 0.833906i
\(565\) −7.08028 −0.297870
\(566\) 71.3954i 3.00097i
\(567\) 23.2739 + 5.03248i 0.977412 + 0.211344i
\(568\) −10.0140 −0.420177
\(569\) 16.3233i 0.684309i −0.939644 0.342155i \(-0.888843\pi\)
0.939644 0.342155i \(-0.111157\pi\)
\(570\) 6.57320 3.49802i 0.275321 0.146516i
\(571\) −22.2039 −0.929205 −0.464603 0.885519i \(-0.653803\pi\)
−0.464603 + 0.885519i \(0.653803\pi\)
\(572\) −21.5065 + 15.5778i −0.899230 + 0.651341i
\(573\) 7.11201 3.78476i 0.297109 0.158110i
\(574\) −27.6147 18.8250i −1.15262 0.785741i
\(575\) 9.17902i 0.382792i
\(576\) 20.1005 29.8458i 0.837522 1.24358i
\(577\) 23.2603 0.968338 0.484169 0.874975i \(-0.339122\pi\)
0.484169 + 0.874975i \(0.339122\pi\)
\(578\) 39.6607 1.64967
\(579\) −14.9346 + 7.94767i −0.620662 + 0.330294i
\(580\) 15.9327 0.661571
\(581\) −32.5575 22.1945i −1.35071 0.920784i
\(582\) −15.9604 29.9916i −0.661581 1.24319i
\(583\) 19.2356i 0.796657i
\(584\) 24.5395 1.01545
\(585\) −5.56590 + 0.190239i −0.230122 + 0.00786542i
\(586\) 57.4926i 2.37500i
\(587\) 12.5987i 0.520006i 0.965608 + 0.260003i \(0.0837235\pi\)
−0.965608 + 0.260003i \(0.916277\pi\)
\(588\) −27.7934 + 32.4910i −1.14618 + 1.33990i
\(589\) 26.2029 1.07967
\(590\) 1.22665 0.0505005
\(591\) −16.2885 30.6081i −0.670021 1.25905i
\(592\) 3.83128i 0.157465i
\(593\) 30.1206i 1.23690i −0.785823 0.618452i \(-0.787760\pi\)
0.785823 0.618452i \(-0.212240\pi\)
\(594\) −25.3751 2.63977i −1.04115 0.108311i
\(595\) 0.404663 + 0.275859i 0.0165896 + 0.0113091i
\(596\) −51.2073 −2.09753
\(597\) −24.6015 + 13.0920i −1.00687 + 0.535820i
\(598\) 9.63903 + 13.3075i 0.394169 + 0.544184i
\(599\) 5.44292i 0.222392i 0.993799 + 0.111196i \(0.0354681\pi\)
−0.993799 + 0.111196i \(0.964532\pi\)
\(600\) 13.8260 + 25.9808i 0.564445 + 1.06066i
\(601\) 6.01932i 0.245533i 0.992436 + 0.122767i \(0.0391766\pi\)
−0.992436 + 0.122767i \(0.960823\pi\)
\(602\) −1.34278 + 1.96975i −0.0547277 + 0.0802810i
\(603\) −9.25509 6.23310i −0.376896 0.253831i
\(604\) 11.5609i 0.470407i
\(605\) 3.41775i 0.138951i
\(606\) −32.2460 60.5941i −1.30990 2.46147i
\(607\) 3.15481i 0.128050i −0.997948 0.0640250i \(-0.979606\pi\)
0.997948 0.0640250i \(-0.0203937\pi\)
\(608\) 13.9418 0.565415
\(609\) −4.38617 + 39.9723i −0.177737 + 1.61976i
\(610\) −13.0530 −0.528502
\(611\) −14.5974 20.1529i −0.590547 0.815300i
\(612\) −2.12470 + 3.15481i −0.0858858 + 0.127526i
\(613\) 28.6230i 1.15607i −0.816011 0.578036i \(-0.803819\pi\)
0.816011 0.578036i \(-0.196181\pi\)
\(614\) −23.1248 −0.933242
\(615\) 2.25112 + 4.23012i 0.0907739 + 0.170575i
\(616\) 11.1694 16.3846i 0.450029 0.660155i
\(617\) −4.18768 −0.168590 −0.0842949 0.996441i \(-0.526864\pi\)
−0.0842949 + 0.996441i \(0.526864\pi\)
\(618\) 13.2829 7.06867i 0.534316 0.284344i
\(619\) −8.46124 −0.340086 −0.170043 0.985437i \(-0.554391\pi\)
−0.170043 + 0.985437i \(0.554391\pi\)
\(620\) 13.3952i 0.537965i
\(621\) −1.04229 + 10.0191i −0.0418256 + 0.402053i
\(622\) −50.7347 −2.03428
\(623\) −32.8936 22.4236i −1.31786 0.898384i
\(624\) 7.76014 + 3.79539i 0.310654 + 0.151937i
\(625\) 21.0939 0.843757
\(626\) 21.4799i 0.858508i
\(627\) −6.03584 11.3421i −0.241048 0.452959i
\(628\) 63.3913i 2.52959i
\(629\) 0.995772i 0.0397040i
\(630\) 8.92265 3.56127i 0.355487 0.141884i
\(631\) 34.5892i 1.37698i −0.725248 0.688488i \(-0.758275\pi\)
0.725248 0.688488i \(-0.241725\pi\)
\(632\) −35.1184 −1.39694
\(633\) −5.80788 10.9137i −0.230842 0.433781i
\(634\) 1.79453 0.0712701
\(635\) 4.17980i 0.165870i
\(636\) −49.6624 + 26.4285i −1.96924 + 1.04796i
\(637\) 21.2512 + 13.6156i 0.842004 + 0.539471i
\(638\) 43.0836i 1.70569i
\(639\) −4.67635 + 6.94357i −0.184993 + 0.274683i
\(640\) 10.4758i 0.414092i
\(641\) 32.3388i 1.27731i 0.769495 + 0.638653i \(0.220508\pi\)
−0.769495 + 0.638653i \(0.779492\pi\)
\(642\) −49.3183 + 26.2454i −1.94644 + 1.03582i
\(643\) −19.4259 −0.766081 −0.383041 0.923731i \(-0.625123\pi\)
−0.383041 + 0.923731i \(0.625123\pi\)
\(644\) −14.9452 10.1882i −0.588924 0.401471i
\(645\) 0.301733 0.160571i 0.0118807 0.00632250i
\(646\) −3.00187 −0.118107
\(647\) 19.2229 0.755731 0.377865 0.925861i \(-0.376658\pi\)
0.377865 + 0.925861i \(0.376658\pi\)
\(648\) 12.1413 + 29.9286i 0.476954 + 1.17571i
\(649\) 2.11659i 0.0830835i
\(650\) 32.5030 23.5429i 1.27487 0.923430i
\(651\) 33.6061 + 3.68761i 1.31713 + 0.144529i
\(652\) 57.9819i 2.27075i
\(653\) 10.6175i 0.415494i 0.978183 + 0.207747i \(0.0666131\pi\)
−0.978183 + 0.207747i \(0.933387\pi\)
\(654\) −39.0413 + 20.7764i −1.52664 + 0.812420i
\(655\) 8.71793i 0.340638i
\(656\) 7.43280i 0.290202i
\(657\) 11.4595 17.0154i 0.447077 0.663833i
\(658\) 35.4691 + 24.1793i 1.38273 + 0.942608i
\(659\) 15.7690i 0.614271i −0.951666 0.307136i \(-0.900629\pi\)
0.951666 0.307136i \(-0.0993705\pi\)
\(660\) −5.79820 + 3.08559i −0.225695 + 0.120106i
\(661\) 22.0381 0.857183 0.428591 0.903498i \(-0.359010\pi\)
0.428591 + 0.903498i \(0.359010\pi\)
\(662\) 16.3545i 0.635635i
\(663\) 2.01690 + 0.986445i 0.0783301 + 0.0383103i
\(664\) 53.4449i 2.07406i
\(665\) 3.99769 + 2.72523i 0.155024 + 0.105680i
\(666\) 16.2018 + 10.9116i 0.627807 + 0.422815i
\(667\) −17.0111 −0.658673
\(668\) 40.7762i 1.57768i
\(669\) −11.2009 21.0478i −0.433050 0.813753i
\(670\) −4.50194 −0.173925
\(671\) 22.5230i 0.869492i
\(672\) 17.8809 + 1.96207i 0.689769 + 0.0756886i
\(673\) 5.62885 0.216976 0.108488 0.994098i \(-0.465399\pi\)
0.108488 + 0.994098i \(0.465399\pi\)
\(674\) −34.4889 −1.32846
\(675\) 24.4713 + 2.54575i 0.941899 + 0.0979859i
\(676\) 14.2931 43.5597i 0.549733 1.67537i
\(677\) 25.1231 0.965560 0.482780 0.875742i \(-0.339627\pi\)
0.482780 + 0.875742i \(0.339627\pi\)
\(678\) 49.4303 26.3050i 1.89836 1.01024i
\(679\) 12.4344 18.2403i 0.477190 0.699998i
\(680\) 0.664275i 0.0254738i
\(681\) −25.4768 + 13.5578i −0.976273 + 0.519537i
\(682\) −36.2219 −1.38701
\(683\) 19.7688 0.756432 0.378216 0.925717i \(-0.376538\pi\)
0.378216 + 0.925717i \(0.376538\pi\)
\(684\) −20.9900 + 31.1666i −0.802574 + 1.19169i
\(685\) 5.11738i 0.195525i
\(686\) −42.4485 9.68067i −1.62069 0.369610i
\(687\) 19.6739 + 36.9696i 0.750606 + 1.41048i
\(688\) −0.530179 −0.0202129
\(689\) 19.4801 + 26.8939i 0.742133 + 1.02458i
\(690\) 1.90926 + 3.58773i 0.0726844 + 0.136583i
\(691\) 26.7444 1.01741 0.508703 0.860942i \(-0.330125\pi\)
0.508703 + 0.860942i \(0.330125\pi\)
\(692\) −44.4624 −1.69021
\(693\) −6.14498 15.3961i −0.233428 0.584848i
\(694\) 63.7450i 2.41973i
\(695\) −0.642907 −0.0243868
\(696\) −48.1492 + 25.6233i −1.82509 + 0.971247i
\(697\) 1.93183i 0.0731732i
\(698\) −19.0457 −0.720889
\(699\) −10.0762 + 5.36216i −0.381115 + 0.202816i
\(700\) −24.8842 + 36.5031i −0.940535 + 1.37969i
\(701\) 7.90471i 0.298557i −0.988795 0.149278i \(-0.952305\pi\)
0.988795 0.149278i \(-0.0476951\pi\)
\(702\) 38.1511 22.0069i 1.43992 0.830596i
\(703\) 9.83730i 0.371021i
\(704\) −25.0506 −0.944131
\(705\) −2.89139 5.43328i −0.108896 0.204629i
\(706\) 59.1028i 2.22436i
\(707\) 25.1222 36.8522i 0.944818 1.38597i
\(708\) −5.46461 + 2.90807i −0.205373 + 0.109292i
\(709\) 40.7899i 1.53190i 0.642901 + 0.765949i \(0.277731\pi\)
−0.642901 + 0.765949i \(0.722269\pi\)
\(710\) 3.37755i 0.126757i
\(711\) −16.3997 + 24.3507i −0.615035 + 0.913222i
\(712\) 53.9966i 2.02361i
\(713\) 14.3018i 0.535608i
\(714\) −3.85001 0.422462i −0.144083 0.0158103i
\(715\) 2.27435 + 3.13993i 0.0850557 + 0.117427i
\(716\) 40.4020i 1.50989i
\(717\) 4.42879 + 8.32224i 0.165396 + 0.310800i
\(718\) 14.7795 0.551565
\(719\) 16.2571 0.606288 0.303144 0.952945i \(-0.401964\pi\)
0.303144 + 0.952945i \(0.401964\pi\)
\(720\) 1.77218 + 1.19353i 0.0660453 + 0.0444801i
\(721\) 8.07839 + 5.50706i 0.300855 + 0.205093i
\(722\) 15.0105 0.558635
\(723\) −1.17425 2.20656i −0.0436708 0.0820628i
\(724\) 24.1571i 0.897792i
\(725\) 41.5490i 1.54309i
\(726\) −12.6978 23.8607i −0.471260 0.885555i
\(727\) 19.1679i 0.710897i −0.934696 0.355449i \(-0.884328\pi\)
0.934696 0.355449i \(-0.115672\pi\)
\(728\) 0.976552 + 34.2193i 0.0361934 + 1.26825i
\(729\) 26.4219 + 5.55748i 0.978587 + 0.205833i
\(730\) 8.27677i 0.306337i
\(731\) −0.137797 −0.00509659
\(732\) 58.1499 30.9453i 2.14928 1.14377i
\(733\) −31.3124 −1.15655 −0.578274 0.815842i \(-0.696274\pi\)
−0.578274 + 0.815842i \(0.696274\pi\)
\(734\) 52.6101i 1.94187i
\(735\) 4.74365 + 4.05782i 0.174972 + 0.149675i
\(736\) 7.60961i 0.280494i
\(737\) 7.76811i 0.286142i
\(738\) −31.4320 21.1688i −1.15703 0.779232i
\(739\) 38.9147i 1.43150i −0.698357 0.715750i \(-0.746085\pi\)
0.698357 0.715750i \(-0.253915\pi\)
\(740\) 5.02894 0.184868
\(741\) 19.9251 + 9.74515i 0.731968 + 0.357997i
\(742\) −47.3332 32.2671i −1.73766 1.18456i
\(743\) 3.18656 0.116903 0.0584517 0.998290i \(-0.481384\pi\)
0.0584517 + 0.998290i \(0.481384\pi\)
\(744\) 21.5424 + 40.4807i 0.789781 + 1.48409i
\(745\) 7.47622i 0.273907i
\(746\) −64.2515 −2.35241
\(747\) −37.0580 24.9578i −1.35588 0.913157i
\(748\) 2.64794 0.0968183
\(749\) −29.9945 20.4473i −1.09597 0.747127i
\(750\) 18.0164 9.58767i 0.657865 0.350092i
\(751\) −0.0203251 −0.000741673 −0.000370837 1.00000i \(-0.500118\pi\)
−0.000370837 1.00000i \(0.500118\pi\)
\(752\) 9.54688i 0.348139i
\(753\) 23.0815 + 43.3730i 0.841138 + 1.58060i
\(754\) 43.6312 + 60.2365i 1.58895 + 2.19369i
\(755\) 1.68788 0.0614284
\(756\) −31.3067 + 37.0183i −1.13861 + 1.34634i
\(757\) 15.7117 0.571052 0.285526 0.958371i \(-0.407832\pi\)
0.285526 + 0.958371i \(0.407832\pi\)
\(758\) 28.2013i 1.02432i
\(759\) 6.19064 3.29444i 0.224706 0.119580i
\(760\) 6.56242i 0.238044i
\(761\) 27.8139i 1.00825i 0.863629 + 0.504127i \(0.168186\pi\)
−0.863629 + 0.504127i \(0.831814\pi\)
\(762\) 15.5290 + 29.1809i 0.562557 + 1.05711i
\(763\) −23.7442 16.1864i −0.859597 0.585988i
\(764\) 16.4030i 0.593441i
\(765\) 0.460600 + 0.310204i 0.0166530 + 0.0112155i
\(766\) 24.8641i 0.898376i
\(767\) 2.14350 + 2.95928i 0.0773972 + 0.106853i
\(768\) 19.4007 + 36.4562i 0.700062 + 1.31550i
\(769\) 32.8282 1.18381 0.591907 0.806006i \(-0.298375\pi\)
0.591907 + 0.806006i \(0.298375\pi\)
\(770\) −5.52626 3.76726i −0.199153 0.135763i
\(771\) −19.4089 36.4716i −0.698993 1.31349i
\(772\) 34.4450i 1.23970i
\(773\) 18.4141i 0.662310i −0.943576 0.331155i \(-0.892562\pi\)
0.943576 0.331155i \(-0.107438\pi\)
\(774\) −1.50996 + 2.24203i −0.0542744 + 0.0805881i
\(775\) 34.9317 1.25478
\(776\) 29.9424 1.07487
\(777\) −1.38443 + 12.6167i −0.0496663 + 0.452621i
\(778\) 43.8099i 1.57066i
\(779\) 19.0846i 0.683778i
\(780\) 4.98184 10.1860i 0.178378 0.364716i
\(781\) 5.82797 0.208541
\(782\) 1.63846i 0.0585911i
\(783\) −4.71794 + 45.3516i −0.168605 + 1.62074i
\(784\) −3.53864 9.01318i −0.126380 0.321899i
\(785\) 9.25509 0.330328