Properties

Label 668.2.e.a.9.7
Level $668$
Weight $2$
Character 668.9
Analytic conductor $5.334$
Analytic rank $0$
Dimension $1148$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.e (of order \(83\), degree \(82\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.33400685502\)
Analytic rank: \(0\)
Dimension: \(1148\)
Relative dimension: \(14\) over \(\Q(\zeta_{83})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label 9.7
Character \(\chi\) \(=\) 668.9
Dual form 668.2.e.a.297.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0142693 - 0.107081i) q^{3} +(2.37141 + 1.04866i) q^{5} +(-0.709794 + 1.52635i) q^{7} +(2.88405 - 0.782538i) q^{9} +O(q^{10})\) \(q+(-0.0142693 - 0.107081i) q^{3} +(2.37141 + 1.04866i) q^{5} +(-0.709794 + 1.52635i) q^{7} +(2.88405 - 0.782538i) q^{9} +(-3.35961 + 4.30756i) q^{11} +(-2.66055 + 5.19729i) q^{13} +(0.0784527 - 0.268896i) q^{15} +(-0.517944 - 0.0392840i) q^{17} +(1.49067 - 2.24242i) q^{19} +(0.173570 + 0.0542253i) q^{21} +(-1.78155 - 0.708489i) q^{23} +(1.15954 + 1.27481i) q^{25} +(-0.250384 - 0.596482i) q^{27} +(9.05639 - 3.60155i) q^{29} +(-3.29354 + 0.761104i) q^{31} +(0.509196 + 0.298283i) q^{33} +(-3.28383 + 2.87526i) q^{35} +(6.35944 + 1.72552i) q^{37} +(0.594493 + 0.210732i) q^{39} +(-10.1623 + 4.96177i) q^{41} +(0.0217449 - 0.229112i) q^{43} +(7.65989 + 1.16867i) q^{45} +(0.0934650 + 4.93805i) q^{47} +(2.68486 + 3.18606i) q^{49} +(0.00318414 + 0.0560224i) q^{51} +(-0.741992 - 4.31406i) q^{53} +(-12.4842 + 6.69193i) q^{55} +(-0.261390 - 0.127625i) q^{57} +(11.2284 - 0.851629i) q^{59} +(4.47266 - 4.55812i) q^{61} +(-0.852659 + 4.95750i) q^{63} +(-11.7594 + 9.53490i) q^{65} +(2.01203 - 0.889737i) q^{67} +(-0.0504440 + 0.200880i) q^{69} +(12.5514 - 1.43139i) q^{71} +(5.08275 - 3.81172i) q^{73} +(0.119961 - 0.142355i) q^{75} +(-4.19020 - 8.18540i) q^{77} +(1.89257 - 5.03445i) q^{79} +(7.67518 - 4.49606i) q^{81} +(-2.31465 + 3.21134i) q^{83} +(-1.18706 - 0.636305i) q^{85} +(-0.514884 - 0.918372i) q^{87} +(-1.63105 - 5.59042i) q^{89} +(-6.04441 - 7.74993i) q^{91} +(0.128496 + 0.341814i) q^{93} +(5.88653 - 3.75449i) q^{95} +(-3.78589 - 0.874881i) q^{97} +(-6.31845 + 15.0523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1148q - 2q^{5} - 14q^{9} + O(q^{10}) \) \( 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(335\)
\(\chi(n)\) \(e\left(\frac{11}{83}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.0142693 0.107081i −0.00823837 0.0618231i 0.986636 0.162937i \(-0.0520967\pi\)
−0.994875 + 0.101114i \(0.967759\pi\)
\(4\) 0 0
\(5\) 2.37141 + 1.04866i 1.06053 + 0.468974i 0.859778 0.510668i \(-0.170602\pi\)
0.200750 + 0.979643i \(0.435662\pi\)
\(6\) 0 0
\(7\) −0.709794 + 1.52635i −0.268277 + 0.576904i −0.993786 0.111308i \(-0.964496\pi\)
0.725509 + 0.688213i \(0.241604\pi\)
\(8\) 0 0
\(9\) 2.88405 0.782538i 0.961350 0.260846i
\(10\) 0 0
\(11\) −3.35961 + 4.30756i −1.01296 + 1.29878i −0.0591882 + 0.998247i \(0.518851\pi\)
−0.953771 + 0.300533i \(0.902836\pi\)
\(12\) 0 0
\(13\) −2.66055 + 5.19729i −0.737905 + 1.44147i 0.153447 + 0.988157i \(0.450962\pi\)
−0.891352 + 0.453312i \(0.850242\pi\)
\(14\) 0 0
\(15\) 0.0784527 0.268896i 0.0202564 0.0694286i
\(16\) 0 0
\(17\) −0.517944 0.0392840i −0.125620 0.00952777i 0.0126686 0.999920i \(-0.495967\pi\)
−0.138289 + 0.990392i \(0.544160\pi\)
\(18\) 0 0
\(19\) 1.49067 2.24242i 0.341984 0.514446i −0.621069 0.783756i \(-0.713302\pi\)
0.963054 + 0.269310i \(0.0867955\pi\)
\(20\) 0 0
\(21\) 0.173570 + 0.0542253i 0.0378761 + 0.0118329i
\(22\) 0 0
\(23\) −1.78155 0.708489i −0.371480 0.147730i 0.176334 0.984330i \(-0.443576\pi\)
−0.547814 + 0.836600i \(0.684540\pi\)
\(24\) 0 0
\(25\) 1.15954 + 1.27481i 0.231909 + 0.254961i
\(26\) 0 0
\(27\) −0.250384 0.596482i −0.0481864 0.114793i
\(28\) 0 0
\(29\) 9.05639 3.60155i 1.68173 0.668791i 0.683595 0.729861i \(-0.260415\pi\)
0.998133 + 0.0610708i \(0.0194515\pi\)
\(30\) 0 0
\(31\) −3.29354 + 0.761104i −0.591538 + 0.136698i −0.510300 0.859997i \(-0.670466\pi\)
−0.0812377 + 0.996695i \(0.525887\pi\)
\(32\) 0 0
\(33\) 0.509196 + 0.298283i 0.0886397 + 0.0519244i
\(34\) 0 0
\(35\) −3.28383 + 2.87526i −0.555068 + 0.486008i
\(36\) 0 0
\(37\) 6.35944 + 1.72552i 1.04548 + 0.283674i 0.742868 0.669438i \(-0.233465\pi\)
0.302617 + 0.953112i \(0.402140\pi\)
\(38\) 0 0
\(39\) 0.594493 + 0.210732i 0.0951951 + 0.0337442i
\(40\) 0 0
\(41\) −10.1623 + 4.96177i −1.58708 + 0.774898i −0.999415 0.0342055i \(-0.989110\pi\)
−0.587667 + 0.809103i \(0.699953\pi\)
\(42\) 0 0
\(43\) 0.0217449 0.229112i 0.00331607 0.0349392i −0.993715 0.111940i \(-0.964293\pi\)
0.997031 + 0.0770010i \(0.0245345\pi\)
\(44\) 0 0
\(45\) 7.65989 + 1.16867i 1.14187 + 0.174214i
\(46\) 0 0
\(47\) 0.0934650 + 4.93805i 0.0136333 + 0.720288i 0.939521 + 0.342490i \(0.111270\pi\)
−0.925888 + 0.377798i \(0.876681\pi\)
\(48\) 0 0
\(49\) 2.68486 + 3.18606i 0.383551 + 0.455151i
\(50\) 0 0
\(51\) 0.00318414 + 0.0560224i 0.000445868 + 0.00784470i
\(52\) 0 0
\(53\) −0.741992 4.31406i −0.101920 0.592582i −0.990896 0.134628i \(-0.957016\pi\)
0.888976 0.457954i \(-0.151418\pi\)
\(54\) 0 0
\(55\) −12.4842 + 6.69193i −1.68337 + 0.902339i
\(56\) 0 0
\(57\) −0.261390 0.127625i −0.0346220 0.0169043i
\(58\) 0 0
\(59\) 11.2284 0.851629i 1.46181 0.110873i 0.679462 0.733710i \(-0.262213\pi\)
0.782351 + 0.622838i \(0.214020\pi\)
\(60\) 0 0
\(61\) 4.47266 4.55812i 0.572665 0.583607i −0.365060 0.930984i \(-0.618952\pi\)
0.937726 + 0.347377i \(0.112928\pi\)
\(62\) 0 0
\(63\) −0.852659 + 4.95750i −0.107425 + 0.624586i
\(64\) 0 0
\(65\) −11.7594 + 9.53490i −1.45858 + 1.18266i
\(66\) 0 0
\(67\) 2.01203 0.889737i 0.245809 0.108699i −0.277857 0.960622i \(-0.589624\pi\)
0.523666 + 0.851924i \(0.324564\pi\)
\(68\) 0 0
\(69\) −0.0504440 + 0.200880i −0.00607274 + 0.0241831i
\(70\) 0 0
\(71\) 12.5514 1.43139i 1.48958 0.169875i 0.669796 0.742545i \(-0.266382\pi\)
0.819786 + 0.572670i \(0.194092\pi\)
\(72\) 0 0
\(73\) 5.08275 3.81172i 0.594890 0.446128i −0.259512 0.965740i \(-0.583562\pi\)
0.854403 + 0.519611i \(0.173923\pi\)
\(74\) 0 0
\(75\) 0.119961 0.142355i 0.0138519 0.0164378i
\(76\) 0 0
\(77\) −4.19020 8.18540i −0.477518 0.932813i
\(78\) 0 0
\(79\) 1.89257 5.03445i 0.212930 0.566420i −0.785707 0.618598i \(-0.787701\pi\)
0.998638 + 0.0521786i \(0.0166165\pi\)
\(80\) 0 0
\(81\) 7.67518 4.49606i 0.852798 0.499562i
\(82\) 0 0
\(83\) −2.31465 + 3.21134i −0.254066 + 0.352490i −0.918893 0.394508i \(-0.870915\pi\)
0.664827 + 0.746998i \(0.268505\pi\)
\(84\) 0 0
\(85\) −1.18706 0.636305i −0.128755 0.0690170i
\(86\) 0 0
\(87\) −0.514884 0.918372i −0.0552014 0.0984599i
\(88\) 0 0
\(89\) −1.63105 5.59042i −0.172891 0.592583i −0.999553 0.0298847i \(-0.990486\pi\)
0.826662 0.562699i \(-0.190237\pi\)
\(90\) 0 0
\(91\) −6.04441 7.74993i −0.633627 0.812413i
\(92\) 0 0
\(93\) 0.128496 + 0.341814i 0.0133244 + 0.0354445i
\(94\) 0 0
\(95\) 5.88653 3.75449i 0.603945 0.385202i
\(96\) 0 0
\(97\) −3.78589 0.874881i −0.384399 0.0888307i 0.0285320 0.999593i \(-0.490917\pi\)
−0.412931 + 0.910762i \(0.635495\pi\)
\(98\) 0 0
\(99\) −6.31845 + 15.0523i −0.635028 + 1.51281i
\(100\) 0 0
\(101\) −0.388847 4.09701i −0.0386917 0.407668i −0.993781 0.111351i \(-0.964482\pi\)
0.955089 0.296318i \(-0.0957587\pi\)
\(102\) 0 0
\(103\) 1.79910 1.24570i 0.177271 0.122743i −0.477309 0.878736i \(-0.658388\pi\)
0.654580 + 0.755993i \(0.272846\pi\)
\(104\) 0 0
\(105\) 0.354743 + 0.310606i 0.0346193 + 0.0303121i
\(106\) 0 0
\(107\) −7.59949 5.26190i −0.734670 0.508687i 0.141948 0.989874i \(-0.454664\pi\)
−0.876618 + 0.481187i \(0.840206\pi\)
\(108\) 0 0
\(109\) −1.24003 0.790903i −0.118773 0.0757548i 0.477021 0.878892i \(-0.341717\pi\)
−0.595794 + 0.803137i \(0.703163\pi\)
\(110\) 0 0
\(111\) 0.0940256 0.705595i 0.00892452 0.0669721i
\(112\) 0 0
\(113\) −7.47163 + 12.2185i −0.702872 + 1.14942i 0.279075 + 0.960269i \(0.409972\pi\)
−0.981947 + 0.189154i \(0.939425\pi\)
\(114\) 0 0
\(115\) −3.48183 3.54836i −0.324683 0.330886i
\(116\) 0 0
\(117\) −3.60610 + 17.0712i −0.333384 + 1.57824i
\(118\) 0 0
\(119\) 0.427595 0.762678i 0.0391975 0.0699146i
\(120\) 0 0
\(121\) −4.58906 18.2747i −0.417187 1.66134i
\(122\) 0 0
\(123\) 0.676318 + 1.01738i 0.0609815 + 0.0917343i
\(124\) 0 0
\(125\) −2.68660 8.06037i −0.240297 0.720941i
\(126\) 0 0
\(127\) −15.4843 1.76586i −1.37401 0.156695i −0.605149 0.796112i \(-0.706887\pi\)
−0.768860 + 0.639417i \(0.779176\pi\)
\(128\) 0 0
\(129\) −0.0248437 0.000940797i −0.00218737 8.28325e-5i
\(130\) 0 0
\(131\) 0.230395 4.05363i 0.0201297 0.354167i −0.972494 0.232929i \(-0.925169\pi\)
0.992623 0.121238i \(-0.0386864\pi\)
\(132\) 0 0
\(133\) 2.36463 + 3.86694i 0.205040 + 0.335306i
\(134\) 0 0
\(135\) 0.0317428 1.67707i 0.00273199 0.144339i
\(136\) 0 0
\(137\) 19.1824 6.79966i 1.63886 0.580934i 0.654343 0.756198i \(-0.272945\pi\)
0.984522 + 0.175263i \(0.0560777\pi\)
\(138\) 0 0
\(139\) −12.9380 12.2235i −1.09738 1.03678i −0.999133 0.0416216i \(-0.986748\pi\)
−0.0982507 0.995162i \(-0.531325\pi\)
\(140\) 0 0
\(141\) 0.527436 0.0804707i 0.0444181 0.00677685i
\(142\) 0 0
\(143\) −13.4492 28.9214i −1.12468 2.41853i
\(144\) 0 0
\(145\) 25.2532 + 0.956304i 2.09716 + 0.0794167i
\(146\) 0 0
\(147\) 0.302854 0.332959i 0.0249790 0.0274620i
\(148\) 0 0
\(149\) 3.16211 + 2.56393i 0.259050 + 0.210045i 0.750517 0.660851i \(-0.229804\pi\)
−0.491467 + 0.870896i \(0.663539\pi\)
\(150\) 0 0
\(151\) −2.90048 2.17517i −0.236038 0.177013i 0.475383 0.879779i \(-0.342309\pi\)
−0.711421 + 0.702766i \(0.751948\pi\)
\(152\) 0 0
\(153\) −1.52452 + 0.292014i −0.123250 + 0.0236079i
\(154\) 0 0
\(155\) −8.60848 1.64891i −0.691450 0.132444i
\(156\) 0 0
\(157\) −0.231445 1.09566i −0.0184713 0.0874431i 0.968196 0.250193i \(-0.0804939\pi\)
−0.986667 + 0.162749i \(0.947964\pi\)
\(158\) 0 0
\(159\) −0.451365 + 0.141012i −0.0357956 + 0.0111829i
\(160\) 0 0
\(161\) 2.34593 2.21638i 0.184885 0.174676i
\(162\) 0 0
\(163\) 5.41008 16.2314i 0.423751 1.27134i −0.492352 0.870396i \(-0.663863\pi\)
0.916102 0.400945i \(-0.131318\pi\)
\(164\) 0 0
\(165\) 0.894716 + 1.24132i 0.0696536 + 0.0966370i
\(166\) 0 0
\(167\) 7.49551 + 10.5270i 0.580020 + 0.814602i
\(168\) 0 0
\(169\) −12.3319 17.1093i −0.948610 1.31610i
\(170\) 0 0
\(171\) 2.54441 7.63376i 0.194576 0.583768i
\(172\) 0 0
\(173\) −1.32033 + 1.24741i −0.100382 + 0.0948391i −0.735303 0.677738i \(-0.762960\pi\)
0.634921 + 0.772577i \(0.281033\pi\)
\(174\) 0 0
\(175\) −2.76883 + 0.865015i −0.209304 + 0.0653890i
\(176\) 0 0
\(177\) −0.251414 1.19019i −0.0188974 0.0894603i
\(178\) 0 0
\(179\) −4.50338 0.862599i −0.336598 0.0644737i 0.0170431 0.999855i \(-0.494575\pi\)
−0.353641 + 0.935381i \(0.615057\pi\)
\(180\) 0 0
\(181\) 2.91010 0.557414i 0.216306 0.0414323i −0.0788278 0.996888i \(-0.525118\pi\)
0.295134 + 0.955456i \(0.404636\pi\)
\(182\) 0 0
\(183\) −0.551908 0.413894i −0.0407982 0.0305960i
\(184\) 0 0
\(185\) 13.2714 + 10.7608i 0.975729 + 0.791150i
\(186\) 0 0
\(187\) 1.90931 2.09910i 0.139622 0.153501i
\(188\) 0 0
\(189\) 1.08816 + 0.0412070i 0.0791519 + 0.00299737i
\(190\) 0 0
\(191\) 8.02581 + 17.2587i 0.580727 + 1.24880i 0.947877 + 0.318637i \(0.103225\pi\)
−0.367150 + 0.930162i \(0.619666\pi\)
\(192\) 0 0
\(193\) −10.2835 + 1.56896i −0.740226 + 0.112936i −0.509968 0.860194i \(-0.670343\pi\)
−0.230258 + 0.973130i \(0.573957\pi\)
\(194\) 0 0
\(195\) 1.18880 + 1.12315i 0.0851319 + 0.0804307i
\(196\) 0 0
\(197\) 16.0211 5.67905i 1.14145 0.404616i 0.304838 0.952404i \(-0.401398\pi\)
0.836617 + 0.547789i \(0.184530\pi\)
\(198\) 0 0
\(199\) −0.0811298 + 4.28634i −0.00575114 + 0.303851i 0.985335 + 0.170630i \(0.0545802\pi\)
−0.991086 + 0.133221i \(0.957468\pi\)
\(200\) 0 0
\(201\) −0.123984 0.202754i −0.00874514 0.0143011i
\(202\) 0 0
\(203\) −0.930961 + 16.3795i −0.0653406 + 1.14962i
\(204\) 0 0
\(205\) −29.3021 + 1.10963i −2.04655 + 0.0775000i
\(206\) 0 0
\(207\) −5.69251 0.649186i −0.395657 0.0451215i
\(208\) 0 0
\(209\) 4.65128 + 13.9548i 0.321736 + 0.965275i
\(210\) 0 0
\(211\) 6.83736 + 10.2854i 0.470703 + 0.708078i 0.989130 0.147044i \(-0.0469760\pi\)
−0.518426 + 0.855122i \(0.673482\pi\)
\(212\) 0 0
\(213\) −0.332374 1.32359i −0.0227739 0.0906910i
\(214\) 0 0
\(215\) 0.291826 0.520515i 0.0199024 0.0354988i
\(216\) 0 0
\(217\) 1.17603 5.56731i 0.0798340 0.377933i
\(218\) 0 0
\(219\) −0.480689 0.489873i −0.0324819 0.0331026i
\(220\) 0 0
\(221\) 1.58219 2.58739i 0.106430 0.174047i
\(222\) 0 0
\(223\) 3.28526 24.6535i 0.219997 1.65092i −0.438790 0.898590i \(-0.644593\pi\)
0.658787 0.752330i \(-0.271070\pi\)
\(224\) 0 0
\(225\) 4.34177 + 2.76922i 0.289451 + 0.184615i
\(226\) 0 0
\(227\) −1.29664 0.897798i −0.0860612 0.0595889i 0.525451 0.850824i \(-0.323896\pi\)
−0.611513 + 0.791235i \(0.709439\pi\)
\(228\) 0 0
\(229\) −9.04161 7.91668i −0.597487 0.523149i 0.305851 0.952079i \(-0.401059\pi\)
−0.903337 + 0.428931i \(0.858890\pi\)
\(230\) 0 0
\(231\) −0.816707 + 0.565489i −0.0537354 + 0.0372065i
\(232\) 0 0
\(233\) 2.64172 + 27.8340i 0.173065 + 1.82347i 0.486302 + 0.873791i \(0.338346\pi\)
−0.313237 + 0.949675i \(0.601413\pi\)
\(234\) 0 0
\(235\) −4.95668 + 11.8082i −0.323338 + 0.770279i
\(236\) 0 0
\(237\) −0.566098 0.130819i −0.0367720 0.00849763i
\(238\) 0 0
\(239\) −6.62001 + 4.22231i −0.428213 + 0.273118i −0.734221 0.678911i \(-0.762452\pi\)
0.306008 + 0.952029i \(0.401007\pi\)
\(240\) 0 0
\(241\) 0.141916 + 0.377512i 0.00914158 + 0.0243177i 0.940537 0.339692i \(-0.110323\pi\)
−0.931395 + 0.364010i \(0.881407\pi\)
\(242\) 0 0
\(243\) −1.78449 2.28801i −0.114475 0.146776i
\(244\) 0 0
\(245\) 3.02581 + 10.3709i 0.193312 + 0.662576i
\(246\) 0 0
\(247\) 7.68848 + 13.7135i 0.489206 + 0.872572i
\(248\) 0 0
\(249\) 0.376900 + 0.202031i 0.0238851 + 0.0128032i
\(250\) 0 0
\(251\) −14.4093 + 19.9914i −0.909507 + 1.26185i 0.0551879 + 0.998476i \(0.482424\pi\)
−0.964695 + 0.263370i \(0.915166\pi\)
\(252\) 0 0
\(253\) 9.03718 5.29391i 0.568163 0.332825i
\(254\) 0 0
\(255\) −0.0511974 + 0.136191i −0.00320611 + 0.00852862i
\(256\) 0 0
\(257\) 7.63412 + 14.9130i 0.476204 + 0.930246i 0.997062 + 0.0766024i \(0.0244072\pi\)
−0.520858 + 0.853643i \(0.674388\pi\)
\(258\) 0 0
\(259\) −7.14763 + 8.48193i −0.444132 + 0.527041i
\(260\) 0 0
\(261\) 23.3007 17.4740i 1.44228 1.08161i
\(262\) 0 0
\(263\) 15.7109 1.79170i 0.968773 0.110481i 0.385457 0.922726i \(-0.374044\pi\)
0.583316 + 0.812245i \(0.301755\pi\)
\(264\) 0 0
\(265\) 2.76441 11.0085i 0.169816 0.676248i
\(266\) 0 0
\(267\) −0.575352 + 0.254426i −0.0352110 + 0.0155706i
\(268\) 0 0
\(269\) 14.3735 11.6545i 0.876369 0.710585i −0.0818427 0.996645i \(-0.526081\pi\)
0.958212 + 0.286060i \(0.0923456\pi\)
\(270\) 0 0
\(271\) 4.70731 27.3691i 0.285949 1.66255i −0.386409 0.922328i \(-0.626285\pi\)
0.672358 0.740226i \(-0.265282\pi\)
\(272\) 0 0
\(273\) −0.743618 + 0.757826i −0.0450058 + 0.0458657i
\(274\) 0 0
\(275\) −9.38693 + 0.711961i −0.566053 + 0.0429328i
\(276\) 0 0
\(277\) −28.3524 13.8432i −1.70353 0.831755i −0.991575 0.129531i \(-0.958653\pi\)
−0.711956 0.702224i \(-0.752191\pi\)
\(278\) 0 0
\(279\) −8.90315 + 4.77238i −0.533018 + 0.285715i
\(280\) 0 0
\(281\) −2.22668 12.9463i −0.132832 0.772309i −0.973143 0.230203i \(-0.926061\pi\)
0.840310 0.542106i \(-0.182373\pi\)
\(282\) 0 0
\(283\) −1.15895 20.3907i −0.0688922 1.21210i −0.827845 0.560957i \(-0.810433\pi\)
0.758952 0.651146i \(-0.225711\pi\)
\(284\) 0 0
\(285\) −0.486029 0.576760i −0.0287899 0.0341643i
\(286\) 0 0
\(287\) −0.360247 19.0330i −0.0212647 1.12348i
\(288\) 0 0
\(289\) −16.5388 2.52332i −0.972871 0.148431i
\(290\) 0 0
\(291\) −0.0396609 + 0.417880i −0.00232496 + 0.0244966i
\(292\) 0 0
\(293\) −14.3945 + 7.02817i −0.840937 + 0.410590i −0.808224 0.588875i \(-0.799571\pi\)
−0.0327126 + 0.999465i \(0.510415\pi\)
\(294\) 0 0
\(295\) 27.5202 + 9.75519i 1.60229 + 0.567969i
\(296\) 0 0
\(297\) 3.41058 + 0.925401i 0.197902 + 0.0536972i
\(298\) 0 0
\(299\) 8.42214 7.37428i 0.487065 0.426465i
\(300\) 0 0
\(301\) 0.334269 + 0.195812i 0.0192670 + 0.0112864i
\(302\) 0 0
\(303\) −0.433163 + 0.100099i −0.0248845 + 0.00575056i
\(304\) 0 0
\(305\) 15.3864 6.11888i 0.881024 0.350366i
\(306\) 0 0
\(307\) 12.2452 + 29.1713i 0.698868 + 1.66489i 0.745950 + 0.666002i \(0.231996\pi\)
−0.0470814 + 0.998891i \(0.514992\pi\)
\(308\) 0 0
\(309\) −0.159062 0.174874i −0.00904875 0.00994822i
\(310\) 0 0
\(311\) 11.4757 + 4.56366i 0.650728 + 0.258782i 0.671502 0.741002i \(-0.265649\pi\)
−0.0207745 + 0.999784i \(0.506613\pi\)
\(312\) 0 0
\(313\) −9.61498 3.00383i −0.543471 0.169786i 0.0141232 0.999900i \(-0.495504\pi\)
−0.557594 + 0.830114i \(0.688275\pi\)
\(314\) 0 0
\(315\) −7.22073 + 10.8621i −0.406842 + 0.612011i
\(316\) 0 0
\(317\) −4.95030 0.375460i −0.278036 0.0210879i −0.0641280 0.997942i \(-0.520427\pi\)
−0.213908 + 0.976854i \(0.568619\pi\)
\(318\) 0 0
\(319\) −14.9120 + 51.1108i −0.834912 + 2.86165i
\(320\) 0 0
\(321\) −0.455008 + 0.888842i −0.0253961 + 0.0496103i
\(322\) 0 0
\(323\) −0.860178 + 1.10289i −0.0478616 + 0.0613663i
\(324\) 0 0
\(325\) −9.71057 + 2.63480i −0.538646 + 0.146152i
\(326\) 0 0
\(327\) −0.0669961 + 0.144069i −0.00370489 + 0.00796703i
\(328\) 0 0
\(329\) −7.60351 3.36234i −0.419195 0.185372i
\(330\) 0 0
\(331\) −2.37953 17.8567i −0.130791 0.981492i −0.926628 0.375981i \(-0.877306\pi\)
0.795837 0.605511i \(-0.207031\pi\)
\(332\) 0 0
\(333\) 19.6912 1.07907
\(334\) 0 0
\(335\) 5.70438 0.311664
\(336\) 0 0
\(337\) 4.43306 + 33.2669i 0.241484 + 1.81216i 0.522697 + 0.852518i \(0.324926\pi\)
−0.281213 + 0.959645i \(0.590737\pi\)
\(338\) 0 0
\(339\) 1.41498 + 0.625718i 0.0768514 + 0.0339843i
\(340\) 0 0
\(341\) 7.78650 16.7442i 0.421663 0.906747i
\(342\) 0 0
\(343\) −18.1407 + 4.92217i −0.979507 + 0.265772i
\(344\) 0 0
\(345\) −0.330277 + 0.423469i −0.0177815 + 0.0227988i
\(346\) 0 0
\(347\) −5.78234 + 11.2956i −0.310412 + 0.606378i −0.992126 0.125240i \(-0.960030\pi\)
0.681714 + 0.731618i \(0.261235\pi\)
\(348\) 0 0
\(349\) 1.89422 6.49242i 0.101395 0.347531i −0.893421 0.449220i \(-0.851702\pi\)
0.994816 + 0.101689i \(0.0324247\pi\)
\(350\) 0 0
\(351\) 3.76625 + 0.285655i 0.201028 + 0.0152471i
\(352\) 0 0
\(353\) −18.7865 + 28.2605i −0.999905 + 1.50415i −0.142314 + 0.989822i \(0.545454\pi\)
−0.857591 + 0.514332i \(0.828040\pi\)
\(354\) 0 0
\(355\) 31.2657 + 9.76775i 1.65941 + 0.518418i
\(356\) 0 0
\(357\) −0.0877696 0.0349042i −0.00464526 0.00184733i
\(358\) 0 0
\(359\) 5.28041 + 5.80530i 0.278689 + 0.306392i 0.863067 0.505090i \(-0.168541\pi\)
−0.584377 + 0.811482i \(0.698661\pi\)
\(360\) 0 0
\(361\) 4.54763 + 10.8337i 0.239349 + 0.570194i
\(362\) 0 0
\(363\) −1.89138 + 0.752166i −0.0992719 + 0.0394785i
\(364\) 0 0
\(365\) 16.0505 3.70910i 0.840120 0.194143i
\(366\) 0 0
\(367\) −30.8715 18.0843i −1.61148 0.943992i −0.986578 0.163289i \(-0.947790\pi\)
−0.624901 0.780704i \(-0.714861\pi\)
\(368\) 0 0
\(369\) −25.4258 + 22.2624i −1.32361 + 1.15893i
\(370\) 0 0
\(371\) 7.11141 + 1.92956i 0.369206 + 0.100178i
\(372\) 0 0
\(373\) 26.0473 + 9.23309i 1.34868 + 0.478071i 0.907766 0.419478i \(-0.137787\pi\)
0.440914 + 0.897549i \(0.354654\pi\)
\(374\) 0 0
\(375\) −0.824774 + 0.402698i −0.0425911 + 0.0207953i
\(376\) 0 0
\(377\) −5.37671 + 56.6508i −0.276915 + 2.91766i
\(378\) 0 0
\(379\) 14.0746 + 2.14735i 0.722962 + 0.110302i 0.501860 0.864949i \(-0.332649\pi\)
0.221102 + 0.975251i \(0.429035\pi\)
\(380\) 0 0
\(381\) 0.0318600 + 1.68327i 0.00163224 + 0.0862363i
\(382\) 0 0
\(383\) 12.0872 + 14.3436i 0.617627 + 0.732924i 0.979975 0.199119i \(-0.0638080\pi\)
−0.362348 + 0.932043i \(0.618025\pi\)
\(384\) 0 0
\(385\) −1.35300 23.8050i −0.0689555 1.21322i
\(386\) 0 0
\(387\) −0.116575 0.677786i −0.00592584 0.0344538i
\(388\) 0 0
\(389\) −1.38633 + 0.743117i −0.0702896 + 0.0376775i −0.507209 0.861823i \(-0.669323\pi\)
0.436919 + 0.899501i \(0.356070\pi\)
\(390\) 0 0
\(391\) 0.894913 + 0.436944i 0.0452577 + 0.0220972i
\(392\) 0 0
\(393\) −0.437353 + 0.0331714i −0.0220615 + 0.00167328i
\(394\) 0 0
\(395\) 9.76747 9.95409i 0.491455 0.500845i
\(396\) 0 0
\(397\) 0.761591 4.42801i 0.0382231 0.222236i −0.960134 0.279542i \(-0.909817\pi\)
0.998357 + 0.0573063i \(0.0182512\pi\)
\(398\) 0 0
\(399\) 0.380333 0.308385i 0.0190404 0.0154386i
\(400\) 0 0
\(401\) 20.1681 8.91852i 1.00715 0.445370i 0.165972 0.986130i \(-0.446924\pi\)
0.841176 + 0.540761i \(0.181864\pi\)
\(402\) 0 0
\(403\) 4.80697 19.1424i 0.239452 0.953553i
\(404\) 0 0
\(405\) 22.9158 2.61337i 1.13870 0.129859i
\(406\) 0 0
\(407\) −28.7980 + 21.5966i −1.42746 + 1.07050i
\(408\) 0 0
\(409\) −8.92036 + 10.5856i −0.441083 + 0.523424i −0.939054 0.343771i \(-0.888296\pi\)
0.497970 + 0.867194i \(0.334079\pi\)
\(410\) 0 0
\(411\) −1.00183 1.95704i −0.0494167 0.0965337i
\(412\) 0 0
\(413\) −6.66997 + 17.7429i −0.328208 + 0.873071i
\(414\) 0 0
\(415\) −8.85659 + 5.18812i −0.434753 + 0.254675i
\(416\) 0 0
\(417\) −1.12428 + 1.55983i −0.0550565 + 0.0763850i
\(418\) 0 0
\(419\) 31.0784 + 16.6591i 1.51828 + 0.813848i 0.999165 0.0408563i \(-0.0130086\pi\)
0.519115 + 0.854704i \(0.326262\pi\)
\(420\) 0 0
\(421\) −11.0293 19.6724i −0.537536 0.958775i −0.997488 0.0708318i \(-0.977435\pi\)
0.459952 0.887944i \(-0.347867\pi\)
\(422\) 0 0
\(423\) 4.13377 + 14.1684i 0.200991 + 0.688893i
\(424\) 0 0
\(425\) −0.550500 0.705831i −0.0267032 0.0342378i
\(426\) 0 0
\(427\) 3.78259 + 10.0621i 0.183053 + 0.486941i
\(428\) 0 0
\(429\) −2.90501 + 1.85284i −0.140255 + 0.0894560i
\(430\) 0 0
\(431\) 30.1977 + 6.97838i 1.45457 + 0.336137i 0.877114 0.480283i \(-0.159466\pi\)
0.577459 + 0.816420i \(0.304044\pi\)
\(432\) 0 0
\(433\) −4.58216 + 10.9159i −0.220204 + 0.524587i −0.994067 0.108767i \(-0.965310\pi\)
0.773863 + 0.633353i \(0.218322\pi\)
\(434\) 0 0
\(435\) −0.257943 2.71778i −0.0123674 0.130307i
\(436\) 0 0
\(437\) −4.24444 + 2.93886i −0.203039 + 0.140585i
\(438\) 0 0
\(439\) −24.0198 21.0313i −1.14640 1.00377i −0.999894 0.0145598i \(-0.995365\pi\)
−0.146508 0.989210i \(-0.546803\pi\)
\(440\) 0 0
\(441\) 10.2365 + 7.08775i 0.487451 + 0.337512i
\(442\) 0 0
\(443\) −13.3165 8.49338i −0.632685 0.403533i 0.182113 0.983278i \(-0.441706\pi\)
−0.814798 + 0.579745i \(0.803152\pi\)
\(444\) 0 0
\(445\) 1.99454 14.9676i 0.0945504 0.709533i
\(446\) 0 0
\(447\) 0.229426 0.375186i 0.0108515 0.0177457i
\(448\) 0 0
\(449\) −13.9611 14.2278i −0.658864 0.671452i 0.300449 0.953798i \(-0.402863\pi\)
−0.959313 + 0.282346i \(0.908888\pi\)
\(450\) 0 0
\(451\) 12.7681 60.4443i 0.601228 2.84621i
\(452\) 0 0
\(453\) −0.191531 + 0.341623i −0.00899889 + 0.0160509i
\(454\) 0 0
\(455\) −6.20677 24.7168i −0.290978 1.15874i
\(456\) 0 0
\(457\) −12.2063 18.3618i −0.570984 0.858930i 0.428010 0.903774i \(-0.359215\pi\)
−0.998994 + 0.0448440i \(0.985721\pi\)
\(458\) 0 0
\(459\) 0.106253 + 0.318781i 0.00495945 + 0.0148794i
\(460\) 0 0
\(461\) 18.4391 + 2.10283i 0.858794 + 0.0979386i 0.531576 0.847010i \(-0.321600\pi\)
0.327217 + 0.944949i \(0.393889\pi\)
\(462\) 0 0
\(463\) 26.9953 1.02227i 1.25458 0.0475090i 0.597831 0.801622i \(-0.296029\pi\)
0.656745 + 0.754113i \(0.271933\pi\)
\(464\) 0 0
\(465\) −0.0537296 + 0.945330i −0.00249165 + 0.0438386i
\(466\) 0 0
\(467\) −2.81174 4.59811i −0.130112 0.212775i 0.781419 0.624007i \(-0.214496\pi\)
−0.911531 + 0.411232i \(0.865099\pi\)
\(468\) 0 0
\(469\) −0.0700807 + 3.70258i −0.00323602 + 0.170969i
\(470\) 0 0
\(471\) −0.114021 + 0.0404175i −0.00525383 + 0.00186234i
\(472\) 0 0
\(473\) 0.913859 + 0.863393i 0.0420193 + 0.0396989i
\(474\) 0 0
\(475\) 4.58715 0.699860i 0.210473 0.0321118i
\(476\) 0 0
\(477\) −5.51586 11.8613i −0.252554 0.543094i
\(478\) 0 0
\(479\) 3.75042 + 0.142023i 0.171361 + 0.00648921i 0.123383 0.992359i \(-0.460626\pi\)
0.0479784 + 0.998848i \(0.484722\pi\)
\(480\) 0 0
\(481\) −25.8877 + 28.4610i −1.18038 + 1.29771i
\(482\) 0 0
\(483\) −0.270807 0.219578i −0.0123221 0.00999114i
\(484\) 0 0
\(485\) −8.06046 6.04481i −0.366007 0.274481i
\(486\) 0 0
\(487\) 29.3397 5.61986i 1.32951 0.254660i 0.526269 0.850318i \(-0.323591\pi\)
0.803238 + 0.595658i \(0.203109\pi\)
\(488\) 0 0
\(489\) −1.81527 0.347705i −0.0820892 0.0157238i
\(490\) 0 0
\(491\) −4.36502 20.6640i −0.196991 0.932552i −0.958653 0.284578i \(-0.908147\pi\)
0.761662 0.647974i \(-0.224384\pi\)
\(492\) 0 0
\(493\) −4.83219 + 1.50963i −0.217631 + 0.0679903i
\(494\) 0 0
\(495\) −30.7683 + 29.0692i −1.38293 + 1.30656i
\(496\) 0 0
\(497\) −6.72413 + 20.1738i −0.301619 + 0.904920i
\(498\) 0 0
\(499\) 22.7499 + 31.5631i 1.01843 + 1.41296i 0.907949 + 0.419081i \(0.137648\pi\)
0.110478 + 0.993879i \(0.464762\pi\)
\(500\) 0 0
\(501\) 1.02028 0.952837i 0.0455828 0.0425696i
\(502\) 0 0
\(503\) −18.8248 26.1174i −0.839356 1.16452i −0.984548 0.175114i \(-0.943970\pi\)
0.145192 0.989403i \(-0.453620\pi\)
\(504\) 0 0
\(505\) 3.37425 10.1235i 0.150152 0.450489i
\(506\) 0 0
\(507\) −1.65610 + 1.56465i −0.0735501 + 0.0694885i
\(508\) 0 0
\(509\) −22.6142 + 7.06492i −1.00235 + 0.313147i −0.754962 0.655768i \(-0.772345\pi\)
−0.247393 + 0.968915i \(0.579574\pi\)
\(510\) 0 0
\(511\) 2.21030 + 10.4636i 0.0977781 + 0.462881i
\(512\) 0 0
\(513\) −1.71080 0.327696i −0.0755338 0.0144681i
\(514\) 0 0
\(515\) 5.57273 1.06743i 0.245564 0.0470365i
\(516\) 0 0
\(517\) −21.5850 16.1873i −0.949306 0.711916i
\(518\) 0 0
\(519\) 0.152414 + 0.123582i 0.00669023 + 0.00542463i
\(520\) 0 0
\(521\) −7.17874 + 7.89234i −0.314506 + 0.345770i −0.876526 0.481354i \(-0.840145\pi\)
0.562020 + 0.827124i \(0.310025\pi\)
\(522\) 0 0
\(523\) 26.0869 + 0.987875i 1.14070 + 0.0431968i 0.601423 0.798931i \(-0.294601\pi\)
0.539278 + 0.842128i \(0.318697\pi\)
\(524\) 0 0
\(525\) 0.132136 + 0.284145i 0.00576687 + 0.0124011i
\(526\) 0 0
\(527\) 1.73577 0.264826i 0.0756113 0.0115360i
\(528\) 0 0
\(529\) −14.0466 13.2709i −0.610720 0.576994i
\(530\) 0 0
\(531\) 31.7169 11.2428i 1.37639 0.487895i
\(532\) 0 0
\(533\) 1.24954 66.0174i 0.0541238 2.85953i
\(534\) 0 0
\(535\) −12.5036 20.4474i −0.540577 0.884018i
\(536\) 0 0
\(537\) −0.0281077 + 0.494533i −0.00121294 + 0.0213407i
\(538\) 0 0
\(539\) −22.7442 + 0.861291i −0.979663 + 0.0370985i
\(540\) 0 0
\(541\) −21.3616 2.43612i −0.918407 0.104737i −0.358724 0.933444i \(-0.616788\pi\)
−0.559683 + 0.828707i \(0.689077\pi\)
\(542\) 0 0
\(543\) −0.101213 0.303661i −0.00434348 0.0130314i
\(544\) 0 0
\(545\) −2.11123 3.17592i −0.0904354 0.136042i
\(546\) 0 0
\(547\) 7.83601 + 31.2048i 0.335044 + 1.33422i 0.871543 + 0.490320i \(0.163120\pi\)
−0.536499 + 0.843901i \(0.680254\pi\)
\(548\) 0 0
\(549\) 9.33248 16.6459i 0.398301 0.710428i
\(550\) 0 0
\(551\) 5.42395 25.6769i 0.231068 1.09387i
\(552\) 0 0
\(553\) 6.34097 + 6.46213i 0.269646 + 0.274798i
\(554\) 0 0
\(555\) 0.962901 1.57465i 0.0408729 0.0668404i
\(556\) 0 0
\(557\) 2.95469 22.1728i 0.125194 0.939492i −0.810266 0.586062i \(-0.800678\pi\)
0.935461 0.353431i \(-0.114985\pi\)
\(558\) 0 0
\(559\) 1.13291 + 0.722579i 0.0479168 + 0.0305618i
\(560\) 0 0
\(561\) −0.252017 0.174497i −0.0106402 0.00736728i
\(562\) 0 0
\(563\) 8.25236 + 7.22562i 0.347796 + 0.304524i 0.814812 0.579725i \(-0.196840\pi\)
−0.467017 + 0.884248i \(0.654671\pi\)
\(564\) 0 0
\(565\) −30.5314 + 21.1400i −1.28447 + 0.889366i
\(566\) 0 0
\(567\) 1.41475 + 14.9062i 0.0594138 + 0.626004i
\(568\) 0 0
\(569\) −5.75532 + 13.7107i −0.241276 + 0.574784i −0.996764 0.0803777i \(-0.974387\pi\)
0.755489 + 0.655161i \(0.227399\pi\)
\(570\) 0 0
\(571\) −29.2671 6.76333i −1.22479 0.283037i −0.437273 0.899329i \(-0.644056\pi\)
−0.787518 + 0.616292i \(0.788634\pi\)
\(572\) 0 0
\(573\) 1.73356 1.10568i 0.0724203 0.0461904i
\(574\) 0 0
\(575\) −1.16260 3.09266i −0.0484839 0.128973i
\(576\) 0 0
\(577\) 7.54151 + 9.66945i 0.313957 + 0.402544i 0.919387 0.393354i \(-0.128685\pi\)
−0.605430 + 0.795899i \(0.706999\pi\)
\(578\) 0 0
\(579\) 0.314744 + 1.07878i 0.0130803 + 0.0448326i
\(580\) 0 0
\(581\) −3.25868 5.81234i −0.135193 0.241137i
\(582\) 0 0
\(583\) 21.0759 + 11.2974i 0.872875 + 0.467890i
\(584\) 0 0
\(585\) −26.4534 + 36.7013i −1.09371 + 1.51741i
\(586\) 0 0
\(587\) 7.45606 4.36770i 0.307745 0.180274i −0.343479 0.939160i \(-0.611605\pi\)
0.651224 + 0.758886i \(0.274256\pi\)
\(588\) 0 0
\(589\) −3.20289 + 8.52005i −0.131973 + 0.351063i
\(590\) 0 0
\(591\) −0.836726 1.63451i −0.0344183 0.0672348i
\(592\) 0 0
\(593\) −6.31659 + 7.49575i −0.259391 + 0.307814i −0.878738 0.477304i \(-0.841614\pi\)
0.619347 + 0.785117i \(0.287397\pi\)
\(594\) 0 0
\(595\) 1.81379 1.36022i 0.0743582 0.0557637i
\(596\) 0 0
\(597\) 0.460142 0.0524756i 0.0188324 0.00214768i
\(598\) 0 0
\(599\) 7.40875 29.5033i 0.302713 1.20547i −0.608505 0.793550i \(-0.708230\pi\)
0.911218 0.411924i \(-0.135143\pi\)
\(600\) 0 0
\(601\) −24.9229 + 11.0211i −1.01662 + 0.449560i −0.844523 0.535519i \(-0.820116\pi\)
−0.172102 + 0.985079i \(0.555056\pi\)
\(602\) 0 0
\(603\) 5.10654 4.14053i 0.207955 0.168616i
\(604\) 0 0
\(605\) 8.28136 48.1492i 0.336685 1.95754i
\(606\) 0 0
\(607\) −0.474909 + 0.483983i −0.0192760 + 0.0196443i −0.723337 0.690496i \(-0.757392\pi\)
0.704061 + 0.710140i \(0.251368\pi\)
\(608\) 0 0
\(609\) 1.76721 0.134036i 0.0716112 0.00543142i
\(610\) 0 0
\(611\) −25.9131 12.6522i −1.04833 0.511852i
\(612\) 0 0
\(613\) 21.8751 11.7258i 0.883526 0.473599i 0.0329535 0.999457i \(-0.489509\pi\)
0.850572 + 0.525858i \(0.176256\pi\)
\(614\) 0 0
\(615\) 0.536940 + 3.12186i 0.0216515 + 0.125886i
\(616\) 0 0
\(617\) −0.246612 4.33894i −0.00992822 0.174679i −0.999525 0.0308119i \(-0.990191\pi\)
0.989597 0.143867i \(-0.0459539\pi\)
\(618\) 0 0
\(619\) 24.8799 + 29.5244i 1.00001 + 1.18668i 0.982390 + 0.186840i \(0.0598246\pi\)
0.0176163 + 0.999845i \(0.494392\pi\)
\(620\) 0 0
\(621\) 0.0234712 + 1.24006i 0.000941868 + 0.0497619i
\(622\) 0 0
\(623\) 9.69062 + 1.47849i 0.388247 + 0.0592346i
\(624\) 0 0
\(625\) 2.89566 30.5096i 0.115826 1.22038i
\(626\) 0 0
\(627\) 1.42792 0.697187i 0.0570257 0.0278430i
\(628\) 0 0
\(629\) −3.22605 1.14355i −0.128631 0.0455963i
\(630\) 0 0
\(631\) 20.9683 + 5.68938i 0.834734 + 0.226491i 0.653478 0.756945i \(-0.273309\pi\)
0.181256 + 0.983436i \(0.441984\pi\)
\(632\) 0 0
\(633\) 1.00381 0.878915i 0.0398977 0.0349337i
\(634\) 0 0
\(635\) −34.8678 20.4253i −1.38369 0.810554i
\(636\) 0 0
\(637\) −23.7021 + 5.47730i −0.939110 + 0.217019i
\(638\) 0 0
\(639\) 35.0789 13.9502i 1.38770 0.551861i
\(640\) 0 0
\(641\) −10.8152 25.7647i −0.427175 1.01765i −0.982542 0.186041i \(-0.940434\pi\)
0.555367 0.831605i \(-0.312578\pi\)
\(642\) 0 0
\(643\) −2.57687 2.83302i −0.101622 0.111723i 0.686835 0.726813i \(-0.258999\pi\)
−0.788457 + 0.615090i \(0.789120\pi\)
\(644\) 0 0
\(645\) −0.0599012 0.0238216i −0.00235861 0.000937973i
\(646\) 0 0
\(647\) −29.8244 9.31748i −1.17252 0.366308i −0.350936 0.936399i \(-0.614137\pi\)
−0.821581 + 0.570092i \(0.806908\pi\)
\(648\) 0 0
\(649\) −34.0546 + 51.2282i −1.33676 + 2.01088i
\(650\) 0 0
\(651\) −0.612932 0.0464884i −0.0240227 0.00182203i
\(652\) 0 0
\(653\) 2.77035 9.49534i 0.108412 0.371582i −0.887620 0.460577i \(-0.847643\pi\)
0.996032 + 0.0889951i \(0.0283655\pi\)
\(654\) 0 0
\(655\) 4.79723 9.37121i 0.187443 0.366164i
\(656\) 0 0
\(657\) 11.6761 14.9706i 0.455527 0.584060i
\(658\) 0 0
\(659\) 38.7726 10.5203i 1.51036 0.409811i 0.592128 0.805844i \(-0.298288\pi\)
0.918237 + 0.396032i \(0.129613\pi\)
\(660\) 0 0
\(661\) 19.7252 42.4172i 0.767221 1.64984i 0.00716859 0.999974i \(-0.497718\pi\)
0.760052 0.649862i \(-0.225173\pi\)
\(662\) 0 0
\(663\) −0.299636 0.132502i −0.0116369 0.00514594i
\(664\) 0 0
\(665\) 1.55242 + 11.6498i 0.0602002 + 0.451759i
\(666\) 0 0
\(667\) −18.6861 −0.723528
\(668\) 0 0
\(669\) −2.68679 −0.103877
\(670\) 0 0
\(671\) 4.60800 + 34.5798i 0.177890 + 1.33494i
\(672\) 0 0
\(673\) −2.40544 1.06371i −0.0927228 0.0410028i 0.357549 0.933894i \(-0.383613\pi\)
−0.450272 + 0.892892i \(0.648673\pi\)
\(674\) 0 0
\(675\) 0.470069 1.01084i 0.0180929 0.0389072i
\(676\) 0 0
\(677\) −28.1532 + 7.63889i −1.08202 + 0.293586i −0.757860 0.652417i \(-0.773755\pi\)
−0.324156 + 0.946004i \(0.605080\pi\)
\(678\) 0 0
\(679\) 4.02257 5.15760i 0.154372 0.197930i
\(680\) 0 0
\(681\) −0.0776346 + 0.151656i −0.00297496 + 0.00581148i
\(682\) 0 0
\(683\) −6.19687 + 21.2397i −0.237117 + 0.812715i 0.751171 + 0.660108i \(0.229490\pi\)
−0.988287 + 0.152606i \(0.951233\pi\)
\(684\) 0 0
\(685\) 52.6199 + 3.99101i 2.01050 + 0.152489i
\(686\) 0 0
\(687\) −0.718706 + 1.08115i −0.0274203 + 0.0412483i
\(688\) 0 0
\(689\) 24.3956 + 7.62145i 0.929397 + 0.290354i
\(690\) 0 0
\(691\) 18.0537 + 7.17960i 0.686794 + 0.273125i 0.686769 0.726875i \(-0.259028\pi\)
2.49947e−5 1.00000i \(0.499992\pi\)
\(692\) 0 0
\(693\) −18.4901 20.3281i −0.702382 0.772202i
\(694\) 0 0
\(695\) −17.8630 42.5544i −0.677581 1.61418i
\(696\) 0 0
\(697\) 5.45841 2.17070i 0.206752 0.0822213i
\(698\) 0 0
\(699\) 2.94279 0.680048i 0.111306 0.0257218i
\(700\) 0 0
\(701\) −15.2442 8.92993i −0.575765 0.337279i 0.188609 0.982052i \(-0.439602\pi\)
−0.764374 + 0.644774i \(0.776952\pi\)
\(702\) 0 0
\(703\) 13.3492 11.6883i 0.503474 0.440833i
\(704\) 0 0
\(705\) 1.33515 + 0.362271i 0.0502848 + 0.0136439i
\(706\) 0 0
\(707\) 6.52946 + 2.31452i 0.245566 + 0.0870465i
\(708\) 0 0
\(709\) −1.81034 + 0.883904i −0.0679887 + 0.0331957i −0.472429 0.881369i \(-0.656623\pi\)
0.404441 + 0.914564i \(0.367466\pi\)
\(710\) 0 0
\(711\) 1.51861 16.0006i 0.0569525 0.600070i
\(712\) 0 0
\(713\) 6.40685 + 0.977491i 0.239939 + 0.0366073i
\(714\) 0 0
\(715\) −1.56508 82.6881i −0.0585307 3.09236i
\(716\) 0 0
\(717\) 0.546590 + 0.648626i 0.0204128 + 0.0242234i
\(718\) 0 0
\(719\) 1.92751 + 33.9129i 0.0718838 + 1.26474i 0.808528 + 0.588458i \(0.200265\pi\)
−0.736644 + 0.676281i \(0.763591\pi\)
\(720\) 0 0
\(721\) 0.624379 + 3.63024i 0.0232531 + 0.135197i
\(722\) 0 0
\(723\) 0.0383992 0.0205832i 0.00142808 0.000765499i
\(724\) 0 0
\(725\) 15.0926 + 7.36899i 0.560524 + 0.273677i
\(726\) 0 0
\(727\) 25.2795 1.91735i 0.937564 0.0711104i 0.402032 0.915626i \(-0.368304\pi\)
0.535532 + 0.844515i \(0.320111\pi\)
\(728\) 0 0
\(729\) 18.4704 18.8233i 0.684090 0.697161i
\(730\) 0 0
\(731\) −0.0202631 + 0.117813i −0.000749457 + 0.00435747i
\(732\) 0 0
\(733\) −29.5945 + 23.9961i −1.09310 + 0.886316i −0.994067 0.108768i \(-0.965309\pi\)
−0.0990312 + 0.995084i \(0.531574\pi\)
\(734\) 0 0
\(735\) 1.06735 0.471992i 0.0393699 0.0174097i
\(736\) 0 0
\(737\) −2.92703 + 11.6561i −0.107819 + 0.429358i
\(738\) 0 0
\(739\) −35.2231 + 4.01691i −1.29570 + 0.147764i −0.733758 0.679411i \(-0.762235\pi\)
−0.561943 + 0.827176i \(0.689946\pi\)
\(740\) 0 0
\(741\) 1.35875 1.01897i 0.0499148 0.0374328i
\(742\) 0 0
\(743\) −9.35988 + 11.1072i −0.343381 + 0.407482i −0.908740 0.417363i \(-0.862954\pi\)
0.565359 + 0.824845i \(0.308738\pi\)
\(744\) 0 0
\(745\) 4.80997 + 9.39610i 0.176224 + 0.344246i
\(746\) 0 0
\(747\) −4.16258 + 11.0730i −0.152301 + 0.405138i
\(748\) 0 0
\(749\) 13.4255 7.86458i 0.490559 0.287365i
\(750\) 0 0
\(751\) −16.6678 + 23.1248i −0.608216 + 0.843835i −0.996993 0.0774965i \(-0.975307\pi\)
0.388777 + 0.921332i \(0.372898\pi\)
\(752\) 0 0
\(753\) 2.34630 + 1.25769i 0.0855040 + 0.0458330i
\(754\) 0 0
\(755\) −4.59722 8.19982i −0.167310 0.298422i
\(756\) 0 0
\(757\) −5.87342 20.1311i −0.213473 0.731678i −0.994271 0.106893i \(-0.965910\pi\)
0.780797 0.624784i \(-0.214813\pi\)
\(758\) 0 0
\(759\) −0.695830 0.892167i −0.0252570 0.0323836i
\(760\) 0 0
\(761\) 0.988960 + 2.63075i 0.0358498 + 0.0953646i 0.952754 0.303742i \(-0.0982360\pi\)
−0.916905 + 0.399106i \(0.869320\pi\)
\(762\) 0 0
\(763\) 2.08736 1.33134i 0.0755674 0.0481976i
\(764\) 0 0
\(765\) −3.92148 0.906215i −0.141782 0.0327643i
\(766\) 0 0
\(767\) −25.4476 + 60.6231i −0.918859 + 2.18897i
\(768\) 0 0
\(769\) −1.61357 17.0011i −0.0581867 0.613074i −0.976251 0.216643i \(-0.930489\pi\)
0.918064 0.396432i \(-0.129752\pi\)
\(770\) 0 0
\(771\) 1.48796 1.03026i 0.0535875 0.0371041i
\(772\) 0 0
\(773\) 14.2381 + 12.4666i 0.512108 + 0.448393i 0.875482 0.483251i \(-0.160544\pi\)
−0.363374 + 0.931643i \(0.618375\pi\)
\(774\) 0 0
\(775\) −4.78927 3.31610i −0.172036 0.119118i
\(776\) 0 0
\(777\) 1.01024 + 0.644342i 0.0362422 + 0.0231156i
\(778\) 0 0
\(779\) −4.02230 + 30.1845i −0.144114 + 1.08147i
\(780\) 0 0
\(781\) −36.0021 + 58.8751i −1.28826 + 2.10671i
\(782\) 0 0
\(783\) −4.41583 4.50020i −0.157809 0.160824i
\(784\) 0 0
\(785\) 0.600120 2.84096i 0.0214192 0.101398i
\(786\) 0 0
\(787\) 9.98500 17.8097i 0.355927 0.634849i −0.634494 0.772928i \(-0.718792\pi\)
0.990421 + 0.138079i \(0.0440928\pi\)
\(788\) 0 0
\(789\) −0.416039 1.65676i −0.0148114 0.0589823i
\(790\) 0 0
\(791\) −13.3464 20.0769i −0.474543 0.713854i
\(792\) 0 0
\(793\) 11.7901 + 35.3728i 0.418679 + 1.25613i
\(794\) 0 0
\(795\) −1.21825 0.138931i −0.0432067 0.00492739i
\(796\) 0