Properties

Label 400.2.u.b.81.1
Level $400$
Weight $2$
Character 400.81
Analytic conductor $3.194$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.u (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 81.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 400.81
Dual form 400.2.u.b.321.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{3} +(-0.690983 + 2.12663i) q^{5} -0.618034 q^{7} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})\) \(q+(0.809017 - 0.587785i) q^{3} +(-0.690983 + 2.12663i) q^{5} -0.618034 q^{7} +(-0.618034 + 1.90211i) q^{9} +(1.61803 + 4.97980i) q^{11} +(0.572949 - 1.76336i) q^{13} +(0.690983 + 2.12663i) q^{15} +(4.23607 + 3.07768i) q^{17} +(0.690983 + 0.502029i) q^{19} +(-0.500000 + 0.363271i) q^{21} +(-1.16312 - 3.57971i) q^{23} +(-4.04508 - 2.93893i) q^{25} +(1.54508 + 4.75528i) q^{27} +(2.92705 - 2.12663i) q^{29} +(-2.42705 - 1.76336i) q^{31} +(4.23607 + 3.07768i) q^{33} +(0.427051 - 1.31433i) q^{35} +(-0.0729490 + 0.224514i) q^{37} +(-0.572949 - 1.76336i) q^{39} +(-0.236068 + 0.726543i) q^{41} +4.85410 q^{43} +(-3.61803 - 2.62866i) q^{45} +(0.500000 - 0.363271i) q^{47} -6.61803 q^{49} +5.23607 q^{51} +(2.80902 - 2.04087i) q^{53} -11.7082 q^{55} +0.854102 q^{57} +(3.35410 - 10.3229i) q^{59} +(2.69098 + 8.28199i) q^{61} +(0.381966 - 1.17557i) q^{63} +(3.35410 + 2.43690i) q^{65} +(3.85410 + 2.80017i) q^{67} +(-3.04508 - 2.21238i) q^{69} +(-5.35410 + 3.88998i) q^{71} +(-2.78115 - 8.55951i) q^{73} -5.00000 q^{75} +(-1.00000 - 3.07768i) q^{77} +(-6.54508 + 4.75528i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-5.04508 - 3.66547i) q^{83} +(-9.47214 + 6.88191i) q^{85} +(1.11803 - 3.44095i) q^{87} +(-2.76393 - 8.50651i) q^{89} +(-0.354102 + 1.08981i) q^{91} -3.00000 q^{93} +(-1.54508 + 1.12257i) q^{95} +(3.11803 - 2.26538i) q^{97} -10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{3} - 5 q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{3} - 5 q^{5} + 2 q^{7} + 2 q^{9} + 2 q^{11} + 9 q^{13} + 5 q^{15} + 8 q^{17} + 5 q^{19} - 2 q^{21} + 11 q^{23} - 5 q^{25} - 5 q^{27} + 5 q^{29} - 3 q^{31} + 8 q^{33} - 5 q^{35} - 7 q^{37} - 9 q^{39} + 8 q^{41} + 6 q^{43} - 10 q^{45} + 2 q^{47} - 22 q^{49} + 12 q^{51} + 9 q^{53} - 20 q^{55} - 10 q^{57} + 13 q^{61} + 6 q^{63} + 2 q^{67} - q^{69} - 8 q^{71} + 9 q^{73} - 20 q^{75} - 4 q^{77} - 15 q^{79} - q^{81} - 9 q^{83} - 20 q^{85} - 20 q^{89} + 12 q^{91} - 12 q^{93} + 5 q^{95} + 8 q^{97} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(1\)

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
\(3\) 0.809017 0.587785i 0.467086 0.339358i −0.329218 0.944254i \(-0.606785\pi\)
0.796305 + 0.604896i \(0.206785\pi\)
\(4\) 0 0
\(5\) −0.690983 + 2.12663i −0.309017 + 0.951057i
\(6\) 0 0
\(7\) −0.618034 −0.233595 −0.116797 0.993156i \(-0.537263\pi\)
−0.116797 + 0.993156i \(0.537263\pi\)
\(8\) 0 0
\(9\) −0.618034 + 1.90211i −0.206011 + 0.634038i
\(10\) 0 0
\(11\) 1.61803 + 4.97980i 0.487856 + 1.50147i 0.827802 + 0.561020i \(0.189591\pi\)
−0.339946 + 0.940445i \(0.610409\pi\)
\(12\) 0 0
\(13\) 0.572949 1.76336i 0.158907 0.489067i −0.839628 0.543161i \(-0.817227\pi\)
0.998536 + 0.0540944i \(0.0172272\pi\)
\(14\) 0 0
\(15\) 0.690983 + 2.12663i 0.178411 + 0.549093i
\(16\) 0 0
\(17\) 4.23607 + 3.07768i 1.02740 + 0.746448i 0.967786 0.251774i \(-0.0810139\pi\)
0.0596113 + 0.998222i \(0.481014\pi\)
\(18\) 0 0
\(19\) 0.690983 + 0.502029i 0.158522 + 0.115173i 0.664219 0.747538i \(-0.268764\pi\)
−0.505696 + 0.862712i \(0.668764\pi\)
\(20\) 0 0
\(21\) −0.500000 + 0.363271i −0.109109 + 0.0792723i
\(22\) 0 0
\(23\) −1.16312 3.57971i −0.242527 0.746422i −0.996033 0.0889808i \(-0.971639\pi\)
0.753506 0.657441i \(-0.228361\pi\)
\(24\) 0 0
\(25\) −4.04508 2.93893i −0.809017 0.587785i
\(26\) 0 0
\(27\) 1.54508 + 4.75528i 0.297352 + 0.915155i
\(28\) 0 0
\(29\) 2.92705 2.12663i 0.543540 0.394905i −0.281858 0.959456i \(-0.590951\pi\)
0.825398 + 0.564551i \(0.190951\pi\)
\(30\) 0 0
\(31\) −2.42705 1.76336i −0.435911 0.316708i 0.348097 0.937459i \(-0.386828\pi\)
−0.784008 + 0.620750i \(0.786828\pi\)
\(32\) 0 0
\(33\) 4.23607 + 3.07768i 0.737405 + 0.535756i
\(34\) 0 0
\(35\) 0.427051 1.31433i 0.0721848 0.222162i
\(36\) 0 0
\(37\) −0.0729490 + 0.224514i −0.0119927 + 0.0369099i −0.956874 0.290504i \(-0.906177\pi\)
0.944881 + 0.327414i \(0.106177\pi\)
\(38\) 0 0
\(39\) −0.572949 1.76336i −0.0917453 0.282363i
\(40\) 0 0
\(41\) −0.236068 + 0.726543i −0.0368676 + 0.113467i −0.967797 0.251733i \(-0.918999\pi\)
0.930929 + 0.365200i \(0.118999\pi\)
\(42\) 0 0
\(43\) 4.85410 0.740244 0.370122 0.928983i \(-0.379316\pi\)
0.370122 + 0.928983i \(0.379316\pi\)
\(44\) 0 0
\(45\) −3.61803 2.62866i −0.539345 0.391857i
\(46\) 0 0
\(47\) 0.500000 0.363271i 0.0729325 0.0529886i −0.550722 0.834689i \(-0.685647\pi\)
0.623654 + 0.781700i \(0.285647\pi\)
\(48\) 0 0
\(49\) −6.61803 −0.945433
\(50\) 0 0
\(51\) 5.23607 0.733196
\(52\) 0 0
\(53\) 2.80902 2.04087i 0.385848 0.280335i −0.377904 0.925845i \(-0.623355\pi\)
0.763752 + 0.645510i \(0.223355\pi\)
\(54\) 0 0
\(55\) −11.7082 −1.57873
\(56\) 0 0
\(57\) 0.854102 0.113129
\(58\) 0 0
\(59\) 3.35410 10.3229i 0.436667 1.34392i −0.454702 0.890644i \(-0.650254\pi\)
0.891369 0.453279i \(-0.149746\pi\)
\(60\) 0 0
\(61\) 2.69098 + 8.28199i 0.344545 + 1.06040i 0.961827 + 0.273659i \(0.0882338\pi\)
−0.617282 + 0.786742i \(0.711766\pi\)
\(62\) 0 0
\(63\) 0.381966 1.17557i 0.0481232 0.148108i
\(64\) 0 0
\(65\) 3.35410 + 2.43690i 0.416025 + 0.302260i
\(66\) 0 0
\(67\) 3.85410 + 2.80017i 0.470853 + 0.342095i 0.797774 0.602957i \(-0.206011\pi\)
−0.326920 + 0.945052i \(0.606011\pi\)
\(68\) 0 0
\(69\) −3.04508 2.21238i −0.366585 0.266340i
\(70\) 0 0
\(71\) −5.35410 + 3.88998i −0.635415 + 0.461656i −0.858272 0.513195i \(-0.828462\pi\)
0.222857 + 0.974851i \(0.428462\pi\)
\(72\) 0 0
\(73\) −2.78115 8.55951i −0.325509 1.00181i −0.971210 0.238224i \(-0.923435\pi\)
0.645701 0.763590i \(-0.276565\pi\)
\(74\) 0 0
\(75\) −5.00000 −0.577350
\(76\) 0 0
\(77\) −1.00000 3.07768i −0.113961 0.350735i
\(78\) 0 0
\(79\) −6.54508 + 4.75528i −0.736380 + 0.535011i −0.891575 0.452873i \(-0.850399\pi\)
0.155196 + 0.987884i \(0.450399\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 0 0
\(83\) −5.04508 3.66547i −0.553770 0.402337i 0.275404 0.961329i \(-0.411189\pi\)
−0.829174 + 0.558991i \(0.811189\pi\)
\(84\) 0 0
\(85\) −9.47214 + 6.88191i −1.02740 + 0.746448i
\(86\) 0 0
\(87\) 1.11803 3.44095i 0.119866 0.368909i
\(88\) 0 0
\(89\) −2.76393 8.50651i −0.292976 0.901688i −0.983894 0.178754i \(-0.942793\pi\)
0.690918 0.722934i \(-0.257207\pi\)
\(90\) 0 0
\(91\) −0.354102 + 1.08981i −0.0371200 + 0.114244i
\(92\) 0 0
\(93\) −3.00000 −0.311086
\(94\) 0 0
\(95\) −1.54508 + 1.12257i −0.158522 + 0.115173i
\(96\) 0 0
\(97\) 3.11803 2.26538i 0.316588 0.230015i −0.418130 0.908387i \(-0.637314\pi\)
0.734718 + 0.678372i \(0.237314\pi\)
\(98\) 0 0
\(99\) −10.4721 −1.05249
\(100\) 0 0
\(101\) 1.47214 0.146483 0.0732415 0.997314i \(-0.476666\pi\)
0.0732415 + 0.997314i \(0.476666\pi\)
\(102\) 0 0
\(103\) 6.92705 5.03280i 0.682543 0.495896i −0.191658 0.981462i \(-0.561386\pi\)
0.874200 + 0.485566i \(0.161386\pi\)
\(104\) 0 0
\(105\) −0.427051 1.31433i −0.0416759 0.128265i
\(106\) 0 0
\(107\) 16.4164 1.58703 0.793517 0.608548i \(-0.208248\pi\)
0.793517 + 0.608548i \(0.208248\pi\)
\(108\) 0 0
\(109\) 3.09017 9.51057i 0.295985 0.910947i −0.686904 0.726748i \(-0.741031\pi\)
0.982889 0.184199i \(-0.0589691\pi\)
\(110\) 0 0
\(111\) 0.0729490 + 0.224514i 0.00692401 + 0.0213099i
\(112\) 0 0
\(113\) 5.20820 16.0292i 0.489947 1.50790i −0.334740 0.942311i \(-0.608648\pi\)
0.824687 0.565590i \(-0.191352\pi\)
\(114\) 0 0
\(115\) 8.41641 0.784834
\(116\) 0 0
\(117\) 3.00000 + 2.17963i 0.277350 + 0.201507i
\(118\) 0 0
\(119\) −2.61803 1.90211i −0.239995 0.174366i
\(120\) 0 0
\(121\) −13.2812 + 9.64932i −1.20738 + 0.877211i
\(122\) 0 0
\(123\) 0.236068 + 0.726543i 0.0212855 + 0.0655101i
\(124\) 0 0
\(125\) 9.04508 6.57164i 0.809017 0.587785i
\(126\) 0 0
\(127\) −6.14590 18.9151i −0.545360 1.67845i −0.720132 0.693837i \(-0.755919\pi\)
0.174772 0.984609i \(-0.444081\pi\)
\(128\) 0 0
\(129\) 3.92705 2.85317i 0.345758 0.251208i
\(130\) 0 0
\(131\) 5.50000 + 3.99598i 0.480537 + 0.349131i 0.801534 0.597950i \(-0.204018\pi\)
−0.320996 + 0.947080i \(0.604018\pi\)
\(132\) 0 0
\(133\) −0.427051 0.310271i −0.0370300 0.0269039i
\(134\) 0 0
\(135\) −11.1803 −0.962250
\(136\) 0 0
\(137\) −3.69098 + 11.3597i −0.315342 + 0.970523i 0.660271 + 0.751027i \(0.270441\pi\)
−0.975613 + 0.219496i \(0.929559\pi\)
\(138\) 0 0
\(139\) −1.54508 4.75528i −0.131052 0.403338i 0.863903 0.503659i \(-0.168013\pi\)
−0.994955 + 0.100321i \(0.968013\pi\)
\(140\) 0 0
\(141\) 0.190983 0.587785i 0.0160837 0.0495004i
\(142\) 0 0
\(143\) 9.70820 0.811841
\(144\) 0 0
\(145\) 2.50000 + 7.69421i 0.207614 + 0.638969i
\(146\) 0 0
\(147\) −5.35410 + 3.88998i −0.441599 + 0.320840i
\(148\) 0 0
\(149\) −3.94427 −0.323127 −0.161564 0.986862i \(-0.551654\pi\)
−0.161564 + 0.986862i \(0.551654\pi\)
\(150\) 0 0
\(151\) −14.5623 −1.18506 −0.592532 0.805547i \(-0.701872\pi\)
−0.592532 + 0.805547i \(0.701872\pi\)
\(152\) 0 0
\(153\) −8.47214 + 6.15537i −0.684932 + 0.497632i
\(154\) 0 0
\(155\) 5.42705 3.94298i 0.435911 0.316708i
\(156\) 0 0
\(157\) 13.1803 1.05191 0.525953 0.850514i \(-0.323709\pi\)
0.525953 + 0.850514i \(0.323709\pi\)
\(158\) 0 0
\(159\) 1.07295 3.30220i 0.0850904 0.261881i
\(160\) 0 0
\(161\) 0.718847 + 2.21238i 0.0566531 + 0.174360i
\(162\) 0 0
\(163\) −3.39919 + 10.4616i −0.266245 + 0.819417i 0.725159 + 0.688581i \(0.241766\pi\)
−0.991404 + 0.130836i \(0.958234\pi\)
\(164\) 0 0
\(165\) −9.47214 + 6.88191i −0.737405 + 0.535756i
\(166\) 0 0
\(167\) 11.7812 + 8.55951i 0.911653 + 0.662355i 0.941432 0.337202i \(-0.109480\pi\)
−0.0297794 + 0.999556i \(0.509480\pi\)
\(168\) 0 0
\(169\) 7.73607 + 5.62058i 0.595082 + 0.432352i
\(170\) 0 0
\(171\) −1.38197 + 1.00406i −0.105682 + 0.0767822i
\(172\) 0 0
\(173\) 5.83688 + 17.9641i 0.443770 + 1.36578i 0.883827 + 0.467813i \(0.154958\pi\)
−0.440057 + 0.897970i \(0.645042\pi\)
\(174\) 0 0
\(175\) 2.50000 + 1.81636i 0.188982 + 0.137304i
\(176\) 0 0
\(177\) −3.35410 10.3229i −0.252110 0.775914i
\(178\) 0 0
\(179\) −0.427051 + 0.310271i −0.0319193 + 0.0231907i −0.603631 0.797264i \(-0.706280\pi\)
0.571711 + 0.820455i \(0.306280\pi\)
\(180\) 0 0
\(181\) −0.236068 0.171513i −0.0175468 0.0127485i 0.578977 0.815344i \(-0.303452\pi\)
−0.596524 + 0.802595i \(0.703452\pi\)
\(182\) 0 0
\(183\) 7.04508 + 5.11855i 0.520788 + 0.378374i
\(184\) 0 0
\(185\) −0.427051 0.310271i −0.0313974 0.0228116i
\(186\) 0 0
\(187\) −8.47214 + 26.0746i −0.619544 + 1.90676i
\(188\) 0 0
\(189\) −0.954915 2.93893i −0.0694598 0.213775i
\(190\) 0 0
\(191\) 0.562306 1.73060i 0.0406870 0.125222i −0.928650 0.370958i \(-0.879030\pi\)
0.969337 + 0.245736i \(0.0790295\pi\)
\(192\) 0 0
\(193\) 7.70820 0.554849 0.277424 0.960747i \(-0.410519\pi\)
0.277424 + 0.960747i \(0.410519\pi\)
\(194\) 0 0
\(195\) 4.14590 0.296894
\(196\) 0 0
\(197\) −3.00000 + 2.17963i −0.213741 + 0.155292i −0.689505 0.724281i \(-0.742172\pi\)
0.475764 + 0.879573i \(0.342172\pi\)
\(198\) 0 0
\(199\) 17.5623 1.24496 0.622479 0.782636i \(-0.286125\pi\)
0.622479 + 0.782636i \(0.286125\pi\)
\(200\) 0 0
\(201\) 4.76393 0.336022
\(202\) 0 0
\(203\) −1.80902 + 1.31433i −0.126968 + 0.0922477i
\(204\) 0 0
\(205\) −1.38197 1.00406i −0.0965207 0.0701264i
\(206\) 0 0
\(207\) 7.52786 0.523223
\(208\) 0 0
\(209\) −1.38197 + 4.25325i −0.0955926 + 0.294204i
\(210\) 0 0
\(211\) 2.83688 + 8.73102i 0.195299 + 0.601068i 0.999973 + 0.00735149i \(0.00234007\pi\)
−0.804674 + 0.593717i \(0.797660\pi\)
\(212\) 0 0
\(213\) −2.04508 + 6.29412i −0.140127 + 0.431266i
\(214\) 0 0
\(215\) −3.35410 + 10.3229i −0.228748 + 0.704014i
\(216\) 0 0
\(217\) 1.50000 + 1.08981i 0.101827 + 0.0739814i
\(218\) 0 0
\(219\) −7.28115 5.29007i −0.492015 0.357470i
\(220\) 0 0
\(221\) 7.85410 5.70634i 0.528324 0.383850i
\(222\) 0 0
\(223\) 0.0557281 + 0.171513i 0.00373183 + 0.0114854i 0.952905 0.303269i \(-0.0980780\pi\)
−0.949173 + 0.314754i \(0.898078\pi\)
\(224\) 0 0
\(225\) 8.09017 5.87785i 0.539345 0.391857i
\(226\) 0 0
\(227\) −4.56231 14.0413i −0.302811 0.931956i −0.980485 0.196594i \(-0.937012\pi\)
0.677674 0.735362i \(-0.262988\pi\)
\(228\) 0 0
\(229\) −17.5623 + 12.7598i −1.16055 + 0.843189i −0.989847 0.142134i \(-0.954604\pi\)
−0.170702 + 0.985323i \(0.554604\pi\)
\(230\) 0 0
\(231\) −2.61803 1.90211i −0.172254 0.125150i
\(232\) 0 0
\(233\) 2.38197 + 1.73060i 0.156048 + 0.113375i 0.663069 0.748558i \(-0.269254\pi\)
−0.507021 + 0.861933i \(0.669254\pi\)
\(234\) 0 0
\(235\) 0.427051 + 1.31433i 0.0278577 + 0.0857373i
\(236\) 0 0
\(237\) −2.50000 + 7.69421i −0.162392 + 0.499793i
\(238\) 0 0
\(239\) 6.34346 + 19.5232i 0.410324 + 1.26285i 0.916367 + 0.400340i \(0.131108\pi\)
−0.506043 + 0.862508i \(0.668892\pi\)
\(240\) 0 0
\(241\) 0.781153 2.40414i 0.0503185 0.154864i −0.922740 0.385423i \(-0.874055\pi\)
0.973058 + 0.230559i \(0.0740554\pi\)
\(242\) 0 0
\(243\) −16.0000 −1.02640
\(244\) 0 0
\(245\) 4.57295 14.0741i 0.292155 0.899161i
\(246\) 0 0
\(247\) 1.28115 0.930812i 0.0815178 0.0592262i
\(248\) 0 0
\(249\) −6.23607 −0.395195
\(250\) 0 0
\(251\) 29.1803 1.84185 0.920923 0.389744i \(-0.127436\pi\)
0.920923 + 0.389744i \(0.127436\pi\)
\(252\) 0 0
\(253\) 15.9443 11.5842i 1.00241 0.728292i
\(254\) 0 0
\(255\) −3.61803 + 11.1352i −0.226570 + 0.697311i
\(256\) 0 0
\(257\) 22.8541 1.42560 0.712800 0.701367i \(-0.247427\pi\)
0.712800 + 0.701367i \(0.247427\pi\)
\(258\) 0 0
\(259\) 0.0450850 0.138757i 0.00280144 0.00862196i
\(260\) 0 0
\(261\) 2.23607 + 6.88191i 0.138409 + 0.425980i
\(262\) 0 0
\(263\) 3.37132 10.3759i 0.207885 0.639803i −0.791698 0.610913i \(-0.790803\pi\)
0.999583 0.0288905i \(-0.00919740\pi\)
\(264\) 0 0
\(265\) 2.39919 + 7.38394i 0.147381 + 0.453592i
\(266\) 0 0
\(267\) −7.23607 5.25731i −0.442840 0.321742i
\(268\) 0 0
\(269\) 10.3262 + 7.50245i 0.629602 + 0.457433i 0.856262 0.516541i \(-0.172781\pi\)
−0.226660 + 0.973974i \(0.572781\pi\)
\(270\) 0 0
\(271\) −6.47214 + 4.70228i −0.393154 + 0.285643i −0.766747 0.641950i \(-0.778126\pi\)
0.373593 + 0.927593i \(0.378126\pi\)
\(272\) 0 0
\(273\) 0.354102 + 1.08981i 0.0214312 + 0.0659585i
\(274\) 0 0
\(275\) 8.09017 24.8990i 0.487856 1.50147i
\(276\) 0 0
\(277\) −7.63525 23.4989i −0.458758 1.41191i −0.866666 0.498889i \(-0.833742\pi\)
0.407908 0.913023i \(-0.366258\pi\)
\(278\) 0 0
\(279\) 4.85410 3.52671i 0.290607 0.211139i
\(280\) 0 0
\(281\) −8.16312 5.93085i −0.486971 0.353805i 0.317047 0.948410i \(-0.397309\pi\)
−0.804018 + 0.594605i \(0.797309\pi\)
\(282\) 0 0
\(283\) −24.1525 17.5478i −1.43572 1.04311i −0.988916 0.148474i \(-0.952564\pi\)
−0.446799 0.894634i \(-0.647436\pi\)
\(284\) 0 0
\(285\) −0.590170 + 1.81636i −0.0349587 + 0.107592i
\(286\) 0 0
\(287\) 0.145898 0.449028i 0.00861209 0.0265053i
\(288\) 0 0
\(289\) 3.21885 + 9.90659i 0.189344 + 0.582741i
\(290\) 0 0
\(291\) 1.19098 3.66547i 0.0698167 0.214874i
\(292\) 0 0
\(293\) −19.5279 −1.14083 −0.570415 0.821357i \(-0.693218\pi\)
−0.570415 + 0.821357i \(0.693218\pi\)
\(294\) 0 0
\(295\) 19.6353 + 14.2658i 1.14321 + 0.830590i
\(296\) 0 0
\(297\) −21.1803 + 15.3884i −1.22901 + 0.892927i
\(298\) 0 0
\(299\) −6.97871 −0.403589
\(300\) 0 0
\(301\) −3.00000 −0.172917
\(302\) 0 0
\(303\) 1.19098 0.865300i 0.0684202 0.0497102i
\(304\) 0 0
\(305\) −19.4721 −1.11497
\(306\) 0 0
\(307\) −9.23607 −0.527130 −0.263565 0.964642i \(-0.584898\pi\)
−0.263565 + 0.964642i \(0.584898\pi\)
\(308\) 0 0
\(309\) 2.64590 8.14324i 0.150520 0.463253i
\(310\) 0 0
\(311\) −2.62868 8.09024i −0.149059 0.458755i 0.848452 0.529272i \(-0.177535\pi\)
−0.997511 + 0.0705172i \(0.977535\pi\)
\(312\) 0 0
\(313\) −5.18034 + 15.9434i −0.292810 + 0.901177i 0.691138 + 0.722723i \(0.257110\pi\)
−0.983948 + 0.178454i \(0.942890\pi\)
\(314\) 0 0
\(315\) 2.23607 + 1.62460i 0.125988 + 0.0915358i
\(316\) 0 0
\(317\) −6.19098 4.49801i −0.347720 0.252634i 0.400192 0.916431i \(-0.368944\pi\)
−0.747912 + 0.663798i \(0.768944\pi\)
\(318\) 0 0
\(319\) 15.3262 + 11.1352i 0.858105 + 0.623449i
\(320\) 0 0
\(321\) 13.2812 9.64932i 0.741282 0.538573i
\(322\) 0 0
\(323\) 1.38197 + 4.25325i 0.0768946 + 0.236657i
\(324\) 0 0
\(325\) −7.50000 + 5.44907i −0.416025 + 0.302260i
\(326\) 0 0
\(327\) −3.09017 9.51057i −0.170887 0.525935i
\(328\) 0 0
\(329\) −0.309017 + 0.224514i −0.0170367 + 0.0123779i
\(330\) 0 0
\(331\) −18.7082 13.5923i −1.02830 0.747101i −0.0603290 0.998179i \(-0.519215\pi\)
−0.967967 + 0.251078i \(0.919215\pi\)
\(332\) 0 0
\(333\) −0.381966 0.277515i −0.0209316 0.0152077i
\(334\) 0 0
\(335\) −8.61803 + 6.26137i −0.470853 + 0.342095i
\(336\) 0 0
\(337\) 2.42705 7.46969i 0.132210 0.406900i −0.862936 0.505314i \(-0.831377\pi\)
0.995146 + 0.0984135i \(0.0313768\pi\)
\(338\) 0 0
\(339\) −5.20820 16.0292i −0.282871 0.870587i
\(340\) 0 0
\(341\) 4.85410 14.9394i 0.262864 0.809013i
\(342\) 0 0
\(343\) 8.41641 0.454443
\(344\) 0 0
\(345\) 6.80902 4.94704i 0.366585 0.266340i
\(346\) 0 0
\(347\) −16.1074 + 11.7027i −0.864690 + 0.628234i −0.929157 0.369686i \(-0.879465\pi\)
0.0644668 + 0.997920i \(0.479465\pi\)
\(348\) 0 0
\(349\) 21.7082 1.16201 0.581007 0.813899i \(-0.302659\pi\)
0.581007 + 0.813899i \(0.302659\pi\)
\(350\) 0 0
\(351\) 9.27051 0.494823
\(352\) 0 0
\(353\) −10.4443 + 7.58821i −0.555893 + 0.403880i −0.829953 0.557833i \(-0.811633\pi\)
0.274061 + 0.961712i \(0.411633\pi\)
\(354\) 0 0
\(355\) −4.57295 14.0741i −0.242707 0.746975i
\(356\) 0 0
\(357\) −3.23607 −0.171271
\(358\) 0 0
\(359\) −4.24671 + 13.0700i −0.224133 + 0.689810i 0.774246 + 0.632885i \(0.218130\pi\)
−0.998378 + 0.0569247i \(0.981870\pi\)
\(360\) 0 0
\(361\) −5.64590 17.3763i −0.297153 0.914541i
\(362\) 0 0
\(363\) −5.07295 + 15.6129i −0.266261 + 0.819466i
\(364\) 0 0
\(365\) 20.1246 1.05337
\(366\) 0 0
\(367\) −20.6803 15.0251i −1.07950 0.784306i −0.101908 0.994794i \(-0.532495\pi\)
−0.977597 + 0.210488i \(0.932495\pi\)
\(368\) 0 0
\(369\) −1.23607 0.898056i −0.0643471 0.0467509i
\(370\) 0 0
\(371\) −1.73607 + 1.26133i −0.0901322 + 0.0654848i
\(372\) 0 0
\(373\) −8.73607 26.8869i −0.452336 1.39215i −0.874234 0.485505i \(-0.838636\pi\)
0.421897 0.906644i \(-0.361364\pi\)
\(374\) 0 0
\(375\) 3.45492 10.6331i 0.178411 0.549093i
\(376\) 0 0
\(377\) −2.07295 6.37988i −0.106762 0.328581i
\(378\) 0 0
\(379\) 11.8090 8.57975i 0.606588 0.440712i −0.241623 0.970370i \(-0.577680\pi\)
0.848211 + 0.529658i \(0.177680\pi\)
\(380\) 0 0
\(381\) −16.0902 11.6902i −0.824324 0.598907i
\(382\) 0 0
\(383\) 26.9894 + 19.6089i 1.37909 + 1.00197i 0.996964 + 0.0778591i \(0.0248084\pi\)
0.382127 + 0.924110i \(0.375192\pi\)
\(384\) 0 0
\(385\) 7.23607 0.368784
\(386\) 0 0
\(387\) −3.00000 + 9.23305i −0.152499 + 0.469342i
\(388\) 0 0
\(389\) 4.63525 + 14.2658i 0.235017 + 0.723307i 0.997119 + 0.0758507i \(0.0241672\pi\)
−0.762102 + 0.647456i \(0.775833\pi\)
\(390\) 0 0
\(391\) 6.09017 18.7436i 0.307993 0.947905i
\(392\) 0 0
\(393\) 6.79837 0.342933
\(394\) 0 0
\(395\) −5.59017 17.2048i −0.281272 0.865666i
\(396\) 0 0
\(397\) −23.4894 + 17.0660i −1.17890 + 0.856519i −0.992047 0.125870i \(-0.959828\pi\)
−0.186850 + 0.982388i \(0.559828\pi\)
\(398\) 0 0
\(399\) −0.527864 −0.0264263
\(400\) 0 0
\(401\) 26.5967 1.32818 0.664089 0.747653i \(-0.268820\pi\)
0.664089 + 0.747653i \(0.268820\pi\)
\(402\) 0 0
\(403\) −4.50000 + 3.26944i −0.224161 + 0.162862i
\(404\) 0 0
\(405\) 1.80902 1.31433i 0.0898908 0.0653095i
\(406\) 0 0
\(407\) −1.23607 −0.0612696
\(408\) 0 0
\(409\) 0.489357 1.50609i 0.0241971 0.0744711i −0.938229 0.346016i \(-0.887534\pi\)
0.962426 + 0.271544i \(0.0875344\pi\)
\(410\) 0 0
\(411\) 3.69098 + 11.3597i 0.182063 + 0.560332i
\(412\) 0 0
\(413\) −2.07295 + 6.37988i −0.102003 + 0.313933i
\(414\) 0 0
\(415\) 11.2812 8.19624i 0.553770 0.402337i
\(416\) 0 0
\(417\) −4.04508 2.93893i −0.198089 0.143920i
\(418\) 0 0
\(419\) −7.66312 5.56758i −0.374368 0.271994i 0.384652 0.923062i \(-0.374321\pi\)
−0.759020 + 0.651068i \(0.774321\pi\)
\(420\) 0 0
\(421\) −25.8885 + 18.8091i −1.26173 + 0.916701i −0.998841 0.0481252i \(-0.984675\pi\)
−0.262889 + 0.964826i \(0.584675\pi\)
\(422\) 0 0
\(423\) 0.381966 + 1.17557i 0.0185718 + 0.0571582i
\(424\) 0 0
\(425\) −8.09017 24.8990i −0.392431 1.20778i
\(426\) 0 0
\(427\) −1.66312 5.11855i −0.0804840 0.247704i
\(428\) 0 0
\(429\) 7.85410 5.70634i 0.379200 0.275505i
\(430\) 0 0
\(431\) −24.1353 17.5353i −1.16255 0.844645i −0.172456 0.985017i \(-0.555170\pi\)
−0.990099 + 0.140372i \(0.955170\pi\)
\(432\) 0 0
\(433\) −21.7254 15.7844i −1.04406 0.758552i −0.0729839 0.997333i \(-0.523252\pi\)
−0.971073 + 0.238781i \(0.923252\pi\)
\(434\) 0 0
\(435\) 6.54508 + 4.75528i 0.313813 + 0.227998i
\(436\) 0 0
\(437\) 0.993422 3.05744i 0.0475218 0.146257i
\(438\) 0 0
\(439\) 12.6631 + 38.9731i 0.604378 + 1.86008i 0.501013 + 0.865440i \(0.332961\pi\)
0.103365 + 0.994644i \(0.467039\pi\)
\(440\) 0 0
\(441\) 4.09017 12.5882i 0.194770 0.599440i
\(442\) 0 0
\(443\) −29.9443 −1.42270 −0.711348 0.702840i \(-0.751915\pi\)
−0.711348 + 0.702840i \(0.751915\pi\)
\(444\) 0 0
\(445\) 20.0000 0.948091
\(446\) 0 0
\(447\) −3.19098 + 2.31838i −0.150928 + 0.109656i
\(448\) 0 0
\(449\) 4.67376 0.220568 0.110284 0.993900i \(-0.464824\pi\)
0.110284 + 0.993900i \(0.464824\pi\)
\(450\) 0 0
\(451\) −4.00000 −0.188353
\(452\) 0 0
\(453\) −11.7812 + 8.55951i −0.553527 + 0.402161i
\(454\) 0 0
\(455\) −2.07295 1.50609i −0.0971813 0.0706064i
\(456\) 0 0
\(457\) −21.4164 −1.00182 −0.500909 0.865500i \(-0.667001\pi\)
−0.500909 + 0.865500i \(0.667001\pi\)
\(458\) 0 0
\(459\) −8.09017 + 24.8990i −0.377617 + 1.16218i
\(460\) 0 0
\(461\) 0.253289 + 0.779543i 0.0117968 + 0.0363069i 0.956782 0.290807i \(-0.0939238\pi\)
−0.944985 + 0.327114i \(0.893924\pi\)
\(462\) 0 0
\(463\) 7.45492 22.9439i 0.346459 1.06629i −0.614339 0.789042i \(-0.710577\pi\)
0.960798 0.277250i \(-0.0894229\pi\)
\(464\) 0 0
\(465\) 2.07295 6.37988i 0.0961307 0.295860i
\(466\) 0 0
\(467\) 22.2082 + 16.1352i 1.02767 + 0.746648i 0.967842 0.251560i \(-0.0809437\pi\)
0.0598315 + 0.998208i \(0.480944\pi\)
\(468\) 0 0
\(469\) −2.38197 1.73060i −0.109989 0.0799117i
\(470\) 0 0
\(471\) 10.6631 7.74721i 0.491331 0.356973i
\(472\) 0 0
\(473\) 7.85410 + 24.1724i 0.361132 + 1.11145i
\(474\) 0 0
\(475\) −1.31966 4.06150i −0.0605502 0.186354i
\(476\) 0 0
\(477\) 2.14590 + 6.60440i 0.0982539 + 0.302394i
\(478\) 0 0
\(479\) −8.78115 + 6.37988i −0.401221 + 0.291504i −0.770038 0.637998i \(-0.779763\pi\)
0.368817 + 0.929502i \(0.379763\pi\)
\(480\) 0 0
\(481\) 0.354102 + 0.257270i 0.0161457 + 0.0117305i
\(482\) 0 0
\(483\) 1.88197 + 1.36733i 0.0856324 + 0.0622156i
\(484\) 0 0
\(485\) 2.66312 + 8.19624i 0.120926 + 0.372172i
\(486\) 0 0
\(487\) 11.2533 34.6341i 0.509935 1.56942i −0.282377 0.959303i \(-0.591123\pi\)
0.792312 0.610116i \(-0.208877\pi\)
\(488\) 0 0
\(489\) 3.39919 + 10.4616i 0.153717 + 0.473091i
\(490\) 0 0
\(491\) 13.3647 41.1325i 0.603143 1.85628i 0.0940550 0.995567i \(-0.470017\pi\)
0.509088 0.860715i \(-0.329983\pi\)
\(492\) 0 0
\(493\) 18.9443 0.853207
\(494\) 0 0
\(495\) 7.23607 22.2703i 0.325237 1.00098i
\(496\) 0 0
\(497\) 3.30902 2.40414i 0.148430 0.107840i
\(498\) 0 0
\(499\) −7.56231 −0.338535 −0.169268 0.985570i \(-0.554140\pi\)
−0.169268 + 0.985570i \(0.554140\pi\)
\(500\) 0 0
\(501\) 14.5623 0.650596
\(502\) 0 0
\(503\) −30.2705 + 21.9928i −1.34970 + 0.980611i −0.350669 + 0.936500i \(0.614046\pi\)
−0.999027 + 0.0441115i \(0.985954\pi\)
\(504\) 0 0
\(505\) −1.01722 + 3.13068i −0.0452657 + 0.139314i
\(506\) 0 0
\(507\) 9.56231 0.424677
\(508\) 0 0
\(509\) −6.28115 + 19.3314i −0.278407 + 0.856849i 0.709891 + 0.704312i \(0.248744\pi\)
−0.988298 + 0.152537i \(0.951256\pi\)
\(510\) 0 0
\(511\) 1.71885 + 5.29007i 0.0760373 + 0.234019i
\(512\) 0 0
\(513\) −1.31966 + 4.06150i −0.0582644 + 0.179319i
\(514\) 0 0
\(515\) 5.91641 + 18.2088i 0.260708 + 0.802377i
\(516\) 0 0
\(517\) 2.61803 + 1.90211i 0.115141 + 0.0836548i
\(518\) 0 0
\(519\) 15.2812 + 11.1024i 0.670768 + 0.487342i
\(520\) 0 0
\(521\) −23.7533 + 17.2578i −1.04065 + 0.756077i −0.970412 0.241453i \(-0.922376\pi\)
−0.0702381 + 0.997530i \(0.522376\pi\)
\(522\) 0 0
\(523\) 4.06231 + 12.5025i 0.177632 + 0.546696i 0.999744 0.0226305i \(-0.00720412\pi\)
−0.822112 + 0.569326i \(0.807204\pi\)
\(524\) 0 0
\(525\) 3.09017 0.134866
\(526\) 0 0
\(527\) −4.85410 14.9394i −0.211448 0.650770i
\(528\) 0 0
\(529\) 7.14590 5.19180i 0.310691 0.225730i
\(530\) 0 0
\(531\) 17.5623 + 12.7598i 0.762139 + 0.553727i
\(532\) 0 0
\(533\) 1.14590 + 0.832544i 0.0496344 + 0.0360615i
\(534\) 0 0
\(535\) −11.3435 + 34.9116i −0.490420 + 1.50936i
\(536\) 0 0
\(537\) −0.163119 + 0.502029i −0.00703910 + 0.0216641i
\(538\) 0 0
\(539\) −10.7082 32.9565i −0.461235 1.41954i
\(540\) 0 0
\(541\) 8.38197 25.7970i 0.360369 1.10910i −0.592462 0.805599i \(-0.701844\pi\)
0.952831 0.303503i \(-0.0981561\pi\)
\(542\) 0 0
\(543\) −0.291796 −0.0125222
\(544\) 0 0
\(545\) 18.0902 + 13.1433i 0.774898 + 0.562996i
\(546\) 0 0
\(547\) −17.2254 + 12.5150i −0.736506 + 0.535103i −0.891615 0.452794i \(-0.850427\pi\)
0.155109 + 0.987897i \(0.450427\pi\)
\(548\) 0 0
\(549\) −17.4164 −0.743314
\(550\) 0 0
\(551\) 3.09017 0.131646
\(552\) 0 0
\(553\) 4.04508 2.93893i 0.172015 0.124976i
\(554\) 0 0
\(555\) −0.527864 −0.0224066
\(556\) 0 0
\(557\) 4.76393 0.201854 0.100927 0.994894i \(-0.467819\pi\)
0.100927 + 0.994894i \(0.467819\pi\)
\(558\) 0 0
\(559\) 2.78115 8.55951i 0.117630 0.362029i
\(560\) 0 0
\(561\) 8.47214 + 26.0746i 0.357694 + 1.10087i
\(562\) 0 0
\(563\) −2.28115 + 7.02067i −0.0961391 + 0.295886i −0.987549 0.157312i \(-0.949717\pi\)
0.891410 + 0.453198i \(0.149717\pi\)
\(564\) 0 0
\(565\) 30.4894 + 22.1518i 1.28270 + 0.931934i
\(566\) 0 0
\(567\) 0.500000 + 0.363271i 0.0209980 + 0.0152560i
\(568\) 0 0
\(569\) −16.6074 12.0660i −0.696218 0.505832i 0.182480 0.983210i \(-0.441587\pi\)
−0.878698 + 0.477377i \(0.841587\pi\)
\(570\) 0 0
\(571\) −6.57295 + 4.77553i −0.275069 + 0.199850i −0.716764 0.697316i \(-0.754377\pi\)
0.441695 + 0.897165i \(0.354377\pi\)
\(572\) 0 0
\(573\) −0.562306 1.73060i −0.0234907 0.0722968i
\(574\) 0 0
\(575\) −5.81559 + 17.8986i −0.242527 + 0.746422i
\(576\) 0 0
\(577\) −10.4377 32.1239i −0.434527 1.33734i −0.893571 0.448923i \(-0.851808\pi\)
0.459044 0.888414i \(-0.348192\pi\)
\(578\) 0 0
\(579\) 6.23607 4.53077i 0.259162 0.188292i
\(580\) 0 0
\(581\) 3.11803 + 2.26538i 0.129358 + 0.0939840i
\(582\) 0 0
\(583\) 14.7082 + 10.6861i 0.609152 + 0.442575i
\(584\) 0 0
\(585\) −6.70820 + 4.87380i −0.277350 + 0.201507i
\(586\) 0 0
\(587\) −1.63525 + 5.03280i −0.0674942 + 0.207726i −0.979115 0.203306i \(-0.934831\pi\)
0.911621 + 0.411032i \(0.134831\pi\)
\(588\) 0 0
\(589\) −0.791796 2.43690i −0.0326254 0.100411i
\(590\) 0 0
\(591\) −1.14590 + 3.52671i −0.0471359 + 0.145070i
\(592\) 0 0
\(593\) −10.9098 −0.448013 −0.224007 0.974588i \(-0.571914\pi\)
−0.224007 + 0.974588i \(0.571914\pi\)
\(594\) 0 0
\(595\) 5.85410 4.25325i 0.239995 0.174366i
\(596\) 0 0
\(597\) 14.2082 10.3229i 0.581503 0.422487i
\(598\) 0 0
\(599\) 9.47214 0.387021 0.193510 0.981098i \(-0.438013\pi\)
0.193510 + 0.981098i \(0.438013\pi\)
\(600\) 0 0
\(601\) 2.72949 0.111338 0.0556691 0.998449i \(-0.482271\pi\)
0.0556691 + 0.998449i \(0.482271\pi\)
\(602\) 0 0
\(603\) −7.70820 + 5.60034i −0.313902 + 0.228063i
\(604\) 0 0
\(605\) −11.3435 34.9116i −0.461177 1.41936i
\(606\) 0 0
\(607\) 35.5623 1.44343 0.721715 0.692191i \(-0.243354\pi\)
0.721715 + 0.692191i \(0.243354\pi\)
\(608\) 0 0
\(609\) −0.690983 + 2.12663i −0.0280000 + 0.0861753i
\(610\) 0 0
\(611\) −0.354102 1.08981i −0.0143254 0.0440891i
\(612\) 0 0
\(613\) −4.62868 + 14.2456i −0.186951 + 0.575374i −0.999977 0.00685287i \(-0.997819\pi\)
0.813026 + 0.582227i \(0.197819\pi\)
\(614\) 0 0
\(615\) −1.70820 −0.0688814
\(616\) 0 0
\(617\) −11.5172 8.36775i −0.463666 0.336873i 0.331302 0.943525i \(-0.392512\pi\)
−0.794968 + 0.606652i \(0.792512\pi\)
\(618\) 0 0
\(619\) 24.6976 + 17.9438i 0.992679 + 0.721223i 0.960506 0.278259i \(-0.0897573\pi\)
0.0321727 + 0.999482i \(0.489757\pi\)
\(620\) 0 0
\(621\) 15.2254 11.0619i 0.610975 0.443900i
\(622\) 0 0
\(623\) 1.70820 + 5.25731i 0.0684377 + 0.210630i
\(624\) 0 0
\(625\) 7.72542 + 23.7764i 0.309017 + 0.951057i
\(626\) 0 0
\(627\) 1.38197 + 4.25325i 0.0551904 + 0.169859i
\(628\) 0 0
\(629\) −1.00000 + 0.726543i −0.0398726 + 0.0289691i
\(630\) 0 0
\(631\) −8.28115 6.01661i −0.329667 0.239517i 0.410622 0.911806i \(-0.365312\pi\)
−0.740290 + 0.672288i \(0.765312\pi\)
\(632\) 0 0
\(633\) 7.42705 + 5.39607i 0.295199 + 0.214474i
\(634\) 0 0
\(635\) 44.4721 1.76482
\(636\) 0 0
\(637\) −3.79180 + 11.6699i −0.150236 + 0.462380i
\(638\) 0 0
\(639\) −4.09017 12.5882i −0.161805 0.497983i
\(640\) 0 0
\(641\) −0.336881 + 1.03681i −0.0133060 + 0.0409517i −0.957489 0.288470i \(-0.906854\pi\)
0.944183 + 0.329421i \(0.106854\pi\)
\(642\) 0 0
\(643\) 30.8328 1.21593 0.607964 0.793965i \(-0.291987\pi\)
0.607964 + 0.793965i \(0.291987\pi\)
\(644\) 0 0
\(645\) 3.35410 + 10.3229i 0.132068 + 0.406462i
\(646\) 0 0
\(647\) −29.5623 + 21.4783i −1.16221 + 0.844398i −0.990056 0.140671i \(-0.955074\pi\)
−0.172158 + 0.985069i \(0.555074\pi\)
\(648\) 0 0
\(649\) 56.8328 2.23088
\(650\) 0 0
\(651\) 1.85410 0.0726680
\(652\) 0 0
\(653\) −15.4443 + 11.2209i −0.604381 + 0.439109i −0.847431 0.530905i \(-0.821852\pi\)
0.243050 + 0.970014i \(0.421852\pi\)
\(654\) 0 0
\(655\) −12.2984 + 8.93529i −0.480537 + 0.349131i
\(656\) 0 0
\(657\) 18.0000 0.702247
\(658\) 0 0
\(659\) −4.79837 + 14.7679i −0.186918 + 0.575275i −0.999976 0.00690786i \(-0.997801\pi\)
0.813058 + 0.582183i \(0.197801\pi\)
\(660\) 0 0
\(661\) 6.08359 + 18.7234i 0.236624 + 0.728255i 0.996902 + 0.0786563i \(0.0250630\pi\)
−0.760277 + 0.649598i \(0.774937\pi\)
\(662\) 0 0
\(663\) 3.00000 9.23305i 0.116510 0.358582i
\(664\) 0 0
\(665\) 0.954915 0.693786i 0.0370300 0.0269039i
\(666\) 0 0
\(667\) −11.0172 8.00448i −0.426588 0.309935i
\(668\) 0 0
\(669\) 0.145898 + 0.106001i 0.00564074 + 0.00409824i
\(670\) 0 0
\(671\) −36.8885 + 26.8011i −1.42407 + 1.03464i
\(672\) 0 0
\(673\) 3.76393 + 11.5842i 0.145089 + 0.446538i 0.997022 0.0771122i \(-0.0245700\pi\)
−0.851934 + 0.523650i \(0.824570\pi\)
\(674\) 0 0
\(675\) 7.72542 23.7764i 0.297352 0.915155i
\(676\) 0 0
\(677\) 3.28115 + 10.0984i 0.126105 + 0.388111i 0.994101 0.108460i \(-0.0345921\pi\)
−0.867996 + 0.496571i \(0.834592\pi\)
\(678\) 0 0
\(679\) −1.92705 + 1.40008i −0.0739534 + 0.0537303i
\(680\) 0 0
\(681\) −11.9443 8.67802i −0.457705 0.332543i
\(682\) 0 0
\(683\) −10.8992 7.91872i −0.417046 0.303002i 0.359402 0.933183i \(-0.382981\pi\)
−0.776448 + 0.630181i \(0.782981\pi\)
\(684\) 0 0
\(685\) −21.6074 15.6987i −0.825576 0.599816i
\(686\) 0 0
\(687\) −6.70820 + 20.6457i −0.255934 + 0.787684i
\(688\) 0 0
\(689\) −1.98936 6.12261i −0.0757885 0.233253i
\(690\) 0 0
\(691\) −11.2082 + 34.4953i −0.426380 + 1.31226i 0.475286 + 0.879831i \(0.342344\pi\)
−0.901667 + 0.432432i \(0.857656\pi\)
\(692\) 0 0
\(693\) 6.47214 0.245856
\(694\) 0 0
\(695\) 11.1803 0.424094
\(696\) 0 0
\(697\) −3.23607 + 2.35114i −0.122575 + 0.0890558i
\(698\) 0 0
\(699\) 2.94427 0.111363
\(700\) 0 0
\(701\) −41.0132 −1.54905 −0.774523 0.632546i \(-0.782010\pi\)
−0.774523 + 0.632546i \(0.782010\pi\)
\(702\) 0 0
\(703\) −0.163119 + 0.118513i −0.00615215 + 0.00446980i
\(704\) 0 0
\(705\) 1.11803 + 0.812299i 0.0421076 + 0.0305930i
\(706\) 0 0
\(707\) −0.909830 −0.0342177
\(708\) 0 0
\(709\) −10.3647 + 31.8994i −0.389256 + 1.19801i 0.544089 + 0.839027i \(0.316875\pi\)
−0.933345 + 0.358980i \(0.883125\pi\)
\(710\) 0 0
\(711\) −5.00000 15.3884i −0.187515 0.577111i
\(712\) 0 0
\(713\) −3.48936 + 10.7391i −0.130677 + 0.402184i
\(714\) 0 0
\(715\) −6.70820 + 20.6457i −0.250873 + 0.772106i
\(716\) 0 0
\(717\) 16.6074 + 12.0660i 0.620214 + 0.450612i
\(718\) 0 0
\(719\) −18.8435 13.6906i −0.702742 0.510572i 0.178082 0.984016i \(-0.443011\pi\)
−0.880824 + 0.473443i \(0.843011\pi\)
\(720\) 0 0
\(721\) −4.28115 + 3.11044i −0.159438 + 0.115839i
\(722\) 0 0
\(723\) −0.781153 2.40414i −0.0290514 0.0894110i
\(724\) 0 0
\(725\) −18.0902 −0.671852
\(726\) 0 0
\(727\) −7.59017 23.3601i −0.281504 0.866380i −0.987425 0.158089i \(-0.949467\pi\)
0.705921 0.708291i \(-0.250533\pi\)
\(728\) 0 0
\(729\) −10.5172 + 7.64121i −0.389527 + 0.283008i
\(730\) 0 0
\(731\) 20.5623 + 14.9394i 0.760524 + 0.552553i
\(732\) 0 0
\(733\) 16.1631 + 11.7432i 0.596998 + 0.433745i 0.844812 0.535063i \(-0.179712\pi\)
−0.247814 + 0.968808i \(0.579712\pi\)
\(734\) 0 0
\(735\) −4.57295 14.0741i −0.168676 0.519131i
\(736\) 0 0
\(737\) −7.70820 + 23.7234i −0.283935 + 0.873863i
\(738\) 0 0
\(739\) −4.93769 15.1967i −0.181636 0.559018i 0.818238 0.574879i \(-0.194951\pi\)
−0.999874 + 0.0158612i \(0.994951\pi\)
\(740\) 0 0
\(741\) 0.489357 1.50609i 0.0179770 0.0553274i
\(742\) 0 0
\(743\) −28.3607 −1.04045 −0.520226 0.854029i \(-0.674152\pi\)
−0.520226 + 0.854029i \(0.674152\pi\)
\(744\) 0 0
\(745\) 2.72542 8.38800i 0.0998518 0.307312i
\(746\) 0 0
\(747\) 10.0902 7.33094i 0.369180 0.268225i
\(748\) 0 0
\(749\) −10.1459 −0.370723
\(750\) 0 0
\(751\) 5.11146 0.186520 0.0932598 0.995642i \(-0.470271\pi\)
0.0932598 + 0.995642i \(0.470271\pi\)
\(752\) 0 0
\(753\) 23.6074 17.1518i 0.860301 0.625045i
\(754\) 0 0
\(755\) 10.0623 30.9686i 0.366205 1.12706i
\(756\) 0 0
\(757\) 30.4164 1.10550 0.552752 0.833346i \(-0.313578\pi\)
0.552752 + 0.833346i \(0.313578\pi\)
\(758\) 0 0
\(759\) 6.09017 18.7436i 0.221059 0.680350i
\(760\) 0 0
\(761\) −5.70163 17.5478i −0.206684 0.636107i −0.999640 0.0268287i \(-0.991459\pi\)
0.792956 0.609279i \(-0.208541\pi\)
\(762\) 0 0
\(763\) −1.90983 + 5.87785i −0.0691405 + 0.212793i
\(764\) 0 0
\(765\) −7.23607 22.2703i −0.261621 0.805185i
\(766\) 0 0
\(767\) −16.2812 11.8290i −0.587878 0.427119i
\(768\) 0 0
\(769\) −10.8541 7.88597i −0.391409 0.284375i 0.374624 0.927177i \(-0.377772\pi\)
−0.766033 + 0.642802i \(0.777772\pi\)
\(770\) 0 0
\(771\) 18.4894 13.4333i 0.665878 0.483789i
\(772\) 0 0
\(773\) −11.1738 34.3893i −0.401892 1.23690i −0.923462 0.383689i \(-0.874654\pi\)
0.521570 0.853208i \(-0.325346\pi\)
\(774\) 0 0
\(775\) 4.63525 + 14.2658i 0.166503 + 0.512444i
\(776\) 0 0
\(777\) −0.0450850 0.138757i −0.00161741 0.00497789i
\(778\) 0 0
\(779\) −0.527864 + 0.383516i −0.0189127 + 0.0137409i
\(780\) 0 0
\(781\) −28.0344 20.3682i −1.00315 0.728832i
\(782\) 0 0
\(783\) 14.6353 + 10.6331i 0.523021 + 0.379997i
\(784\) 0 0
\(785\) −9.10739 + 28.0297i −0.325057 + 1.00042i
\(786\) 0 0
\(787\) 3.65248 11.2412i 0.130197 0.400704i −0.864615 0.502434i \(-0.832438\pi\)
0.994812 + 0.101730i \(0.0324378\pi\)
\(788\) 0 0
\(789\) −3.37132 10.3759i −0.120022 0.369391i
\(790\) 0 0
\(791\) −3.21885 + 9.90659i −0.114449 + 0.352238i
\(792\) 0 0
\(793\) 16.1459