Properties

Label 225.2.h.b.46.1
Level $225$
Weight $2$
Character 225.46
Analytic conductor $1.797$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.79663404548\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 46.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 225.46
Dual form 225.2.h.b.181.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 1.53884i) q^{2} +(-0.500000 - 0.363271i) q^{4} +(0.690983 + 2.12663i) q^{5} +0.618034 q^{7} +(1.80902 - 1.31433i) q^{8} +O(q^{10})\) \(q+(0.500000 - 1.53884i) q^{2} +(-0.500000 - 0.363271i) q^{4} +(0.690983 + 2.12663i) q^{5} +0.618034 q^{7} +(1.80902 - 1.31433i) q^{8} +3.61803 q^{10} +(1.61803 - 4.97980i) q^{11} +(0.572949 + 1.76336i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-1.50000 - 4.61653i) q^{16} +(-4.23607 + 3.07768i) q^{17} +(-0.690983 + 0.502029i) q^{19} +(0.427051 - 1.31433i) q^{20} +(-6.85410 - 4.97980i) q^{22} +(-1.16312 + 3.57971i) q^{23} +(-4.04508 + 2.93893i) q^{25} +3.00000 q^{26} +(-0.309017 - 0.224514i) q^{28} +(-2.92705 - 2.12663i) q^{29} +(2.42705 - 1.76336i) q^{31} -3.38197 q^{32} +(2.61803 + 8.05748i) q^{34} +(0.427051 + 1.31433i) q^{35} +(-0.0729490 - 0.224514i) q^{37} +(0.427051 + 1.31433i) q^{38} +(4.04508 + 2.93893i) q^{40} +(0.236068 + 0.726543i) q^{41} -4.85410 q^{43} +(-2.61803 + 1.90211i) q^{44} +(4.92705 + 3.57971i) q^{46} +(0.500000 + 0.363271i) q^{47} -6.61803 q^{49} +(2.50000 + 7.69421i) q^{50} +(0.354102 - 1.08981i) q^{52} +(-2.80902 - 2.04087i) q^{53} +11.7082 q^{55} +(1.11803 - 0.812299i) q^{56} +(-4.73607 + 3.44095i) q^{58} +(3.35410 + 10.3229i) q^{59} +(2.69098 - 8.28199i) q^{61} +(-1.50000 - 4.61653i) q^{62} +(1.30902 - 4.02874i) q^{64} +(-3.35410 + 2.43690i) q^{65} +(-3.85410 + 2.80017i) q^{67} +3.23607 q^{68} +2.23607 q^{70} +(-5.35410 - 3.88998i) q^{71} +(-2.78115 + 8.55951i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(1.00000 - 3.07768i) q^{77} +(6.54508 + 4.75528i) q^{79} +(8.78115 - 6.37988i) q^{80} +1.23607 q^{82} +(-5.04508 + 3.66547i) q^{83} +(-9.47214 - 6.88191i) q^{85} +(-2.42705 + 7.46969i) q^{86} +(-3.61803 - 11.1352i) q^{88} +(2.76393 - 8.50651i) q^{89} +(0.354102 + 1.08981i) q^{91} +(1.88197 - 1.36733i) q^{92} +(0.809017 - 0.587785i) q^{94} +(-1.54508 - 1.12257i) q^{95} +(3.11803 + 2.26538i) q^{97} +(-3.30902 + 10.1841i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8} + 10 q^{10} + 2 q^{11} + 9 q^{13} - q^{14} - 6 q^{16} - 8 q^{17} - 5 q^{19} - 5 q^{20} - 14 q^{22} + 11 q^{23} - 5 q^{25} + 12 q^{26} + q^{28} - 5 q^{29} + 3 q^{31} - 18 q^{32} + 6 q^{34} - 5 q^{35} - 7 q^{37} - 5 q^{38} + 5 q^{40} - 8 q^{41} - 6 q^{43} - 6 q^{44} + 13 q^{46} + 2 q^{47} - 22 q^{49} + 10 q^{50} - 12 q^{52} - 9 q^{53} + 20 q^{55} - 10 q^{58} + 13 q^{61} - 6 q^{62} + 3 q^{64} - 2 q^{67} + 4 q^{68} - 8 q^{71} + 9 q^{73} - 6 q^{74} + 20 q^{76} + 4 q^{77} + 15 q^{79} + 15 q^{80} - 4 q^{82} - 9 q^{83} - 20 q^{85} - 3 q^{86} - 10 q^{88} + 20 q^{89} - 12 q^{91} + 12 q^{92} + q^{94} + 5 q^{95} + 8 q^{97} - 11 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 1.53884i 0.353553 1.08813i −0.603290 0.797522i \(-0.706144\pi\)
0.956844 0.290604i \(-0.0938561\pi\)
\(3\) 0 0
\(4\) −0.500000 0.363271i −0.250000 0.181636i
\(5\) 0.690983 + 2.12663i 0.309017 + 0.951057i
\(6\) 0 0
\(7\) 0.618034 0.233595 0.116797 0.993156i \(-0.462737\pi\)
0.116797 + 0.993156i \(0.462737\pi\)
\(8\) 1.80902 1.31433i 0.639584 0.464685i
\(9\) 0 0
\(10\) 3.61803 1.14412
\(11\) 1.61803 4.97980i 0.487856 1.50147i −0.339946 0.940445i \(-0.610409\pi\)
0.827802 0.561020i \(-0.189591\pi\)
\(12\) 0 0
\(13\) 0.572949 + 1.76336i 0.158907 + 0.489067i 0.998536 0.0540944i \(-0.0172272\pi\)
−0.839628 + 0.543161i \(0.817227\pi\)
\(14\) 0.309017 0.951057i 0.0825883 0.254181i
\(15\) 0 0
\(16\) −1.50000 4.61653i −0.375000 1.15413i
\(17\) −4.23607 + 3.07768i −1.02740 + 0.746448i −0.967786 0.251774i \(-0.918986\pi\)
−0.0596113 + 0.998222i \(0.518986\pi\)
\(18\) 0 0
\(19\) −0.690983 + 0.502029i −0.158522 + 0.115173i −0.664219 0.747538i \(-0.731236\pi\)
0.505696 + 0.862712i \(0.331236\pi\)
\(20\) 0.427051 1.31433i 0.0954915 0.293893i
\(21\) 0 0
\(22\) −6.85410 4.97980i −1.46130 1.06170i
\(23\) −1.16312 + 3.57971i −0.242527 + 0.746422i 0.753506 + 0.657441i \(0.228361\pi\)
−0.996033 + 0.0889808i \(0.971639\pi\)
\(24\) 0 0
\(25\) −4.04508 + 2.93893i −0.809017 + 0.587785i
\(26\) 3.00000 0.588348
\(27\) 0 0
\(28\) −0.309017 0.224514i −0.0583987 0.0424292i
\(29\) −2.92705 2.12663i −0.543540 0.394905i 0.281858 0.959456i \(-0.409049\pi\)
−0.825398 + 0.564551i \(0.809049\pi\)
\(30\) 0 0
\(31\) 2.42705 1.76336i 0.435911 0.316708i −0.348097 0.937459i \(-0.613172\pi\)
0.784008 + 0.620750i \(0.213172\pi\)
\(32\) −3.38197 −0.597853
\(33\) 0 0
\(34\) 2.61803 + 8.05748i 0.448989 + 1.38185i
\(35\) 0.427051 + 1.31433i 0.0721848 + 0.222162i
\(36\) 0 0
\(37\) −0.0729490 0.224514i −0.0119927 0.0369099i 0.944881 0.327414i \(-0.106177\pi\)
−0.956874 + 0.290504i \(0.906177\pi\)
\(38\) 0.427051 + 1.31433i 0.0692768 + 0.213212i
\(39\) 0 0
\(40\) 4.04508 + 2.93893i 0.639584 + 0.464685i
\(41\) 0.236068 + 0.726543i 0.0368676 + 0.113467i 0.967797 0.251733i \(-0.0810006\pi\)
−0.930929 + 0.365200i \(0.881001\pi\)
\(42\) 0 0
\(43\) −4.85410 −0.740244 −0.370122 0.928983i \(-0.620684\pi\)
−0.370122 + 0.928983i \(0.620684\pi\)
\(44\) −2.61803 + 1.90211i −0.394683 + 0.286754i
\(45\) 0 0
\(46\) 4.92705 + 3.57971i 0.726454 + 0.527800i
\(47\) 0.500000 + 0.363271i 0.0729325 + 0.0529886i 0.623654 0.781700i \(-0.285647\pi\)
−0.550722 + 0.834689i \(0.685647\pi\)
\(48\) 0 0
\(49\) −6.61803 −0.945433
\(50\) 2.50000 + 7.69421i 0.353553 + 1.08813i
\(51\) 0 0
\(52\) 0.354102 1.08981i 0.0491051 0.151130i
\(53\) −2.80902 2.04087i −0.385848 0.280335i 0.377904 0.925845i \(-0.376645\pi\)
−0.763752 + 0.645510i \(0.776645\pi\)
\(54\) 0 0
\(55\) 11.7082 1.57873
\(56\) 1.11803 0.812299i 0.149404 0.108548i
\(57\) 0 0
\(58\) −4.73607 + 3.44095i −0.621876 + 0.451820i
\(59\) 3.35410 + 10.3229i 0.436667 + 1.34392i 0.891369 + 0.453279i \(0.149746\pi\)
−0.454702 + 0.890644i \(0.650254\pi\)
\(60\) 0 0
\(61\) 2.69098 8.28199i 0.344545 1.06040i −0.617282 0.786742i \(-0.711766\pi\)
0.961827 0.273659i \(-0.0882338\pi\)
\(62\) −1.50000 4.61653i −0.190500 0.586299i
\(63\) 0 0
\(64\) 1.30902 4.02874i 0.163627 0.503593i
\(65\) −3.35410 + 2.43690i −0.416025 + 0.302260i
\(66\) 0 0
\(67\) −3.85410 + 2.80017i −0.470853 + 0.342095i −0.797774 0.602957i \(-0.793989\pi\)
0.326920 + 0.945052i \(0.393989\pi\)
\(68\) 3.23607 0.392431
\(69\) 0 0
\(70\) 2.23607 0.267261
\(71\) −5.35410 3.88998i −0.635415 0.461656i 0.222857 0.974851i \(-0.428462\pi\)
−0.858272 + 0.513195i \(0.828462\pi\)
\(72\) 0 0
\(73\) −2.78115 + 8.55951i −0.325509 + 1.00181i 0.645701 + 0.763590i \(0.276565\pi\)
−0.971210 + 0.238224i \(0.923435\pi\)
\(74\) −0.381966 −0.0444026
\(75\) 0 0
\(76\) 0.527864 0.0605502
\(77\) 1.00000 3.07768i 0.113961 0.350735i
\(78\) 0 0
\(79\) 6.54508 + 4.75528i 0.736380 + 0.535011i 0.891575 0.452873i \(-0.149601\pi\)
−0.155196 + 0.987884i \(0.549601\pi\)
\(80\) 8.78115 6.37988i 0.981763 0.713292i
\(81\) 0 0
\(82\) 1.23607 0.136501
\(83\) −5.04508 + 3.66547i −0.553770 + 0.402337i −0.829174 0.558991i \(-0.811189\pi\)
0.275404 + 0.961329i \(0.411189\pi\)
\(84\) 0 0
\(85\) −9.47214 6.88191i −1.02740 0.746448i
\(86\) −2.42705 + 7.46969i −0.261716 + 0.805478i
\(87\) 0 0
\(88\) −3.61803 11.1352i −0.385684 1.18701i
\(89\) 2.76393 8.50651i 0.292976 0.901688i −0.690918 0.722934i \(-0.742793\pi\)
0.983894 0.178754i \(-0.0572068\pi\)
\(90\) 0 0
\(91\) 0.354102 + 1.08981i 0.0371200 + 0.114244i
\(92\) 1.88197 1.36733i 0.196209 0.142554i
\(93\) 0 0
\(94\) 0.809017 0.587785i 0.0834437 0.0606254i
\(95\) −1.54508 1.12257i −0.158522 0.115173i
\(96\) 0 0
\(97\) 3.11803 + 2.26538i 0.316588 + 0.230015i 0.734718 0.678372i \(-0.237314\pi\)
−0.418130 + 0.908387i \(0.637314\pi\)
\(98\) −3.30902 + 10.1841i −0.334261 + 1.02875i
\(99\) 0 0
\(100\) 3.09017 0.309017
\(101\) −1.47214 −0.146483 −0.0732415 0.997314i \(-0.523334\pi\)
−0.0732415 + 0.997314i \(0.523334\pi\)
\(102\) 0 0
\(103\) −6.92705 5.03280i −0.682543 0.495896i 0.191658 0.981462i \(-0.438614\pi\)
−0.874200 + 0.485566i \(0.838614\pi\)
\(104\) 3.35410 + 2.43690i 0.328897 + 0.238957i
\(105\) 0 0
\(106\) −4.54508 + 3.30220i −0.441458 + 0.320738i
\(107\) 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 0.982889 + 0.184199i \(0.0589691\pi\)
−0.686904 + 0.726748i \(0.741031\pi\)
\(110\) 5.85410 18.0171i 0.558167 1.71786i
\(111\) 0 0
\(112\) −0.927051 2.85317i −0.0875981 0.269599i
\(113\) −5.20820 16.0292i −0.489947 1.50790i −0.824687 0.565590i \(-0.808648\pi\)
0.334740 0.942311i \(-0.391352\pi\)
\(114\) 0 0
\(115\) −8.41641 −0.784834
\(116\) 0.690983 + 2.12663i 0.0641562 + 0.197452i
\(117\) 0 0
\(118\) 17.5623 1.61674
\(119\) −2.61803 + 1.90211i −0.239995 + 0.174366i
\(120\) 0 0
\(121\) −13.2812 9.64932i −1.20738 0.877211i
\(122\) −11.3992 8.28199i −1.03203 0.749817i
\(123\) 0 0
\(124\) −1.85410 −0.166503
\(125\) −9.04508 6.57164i −0.809017 0.587785i
\(126\) 0 0
\(127\) 6.14590 18.9151i 0.545360 1.67845i −0.174772 0.984609i \(-0.555919\pi\)
0.720132 0.693837i \(-0.244081\pi\)
\(128\) −11.0172 8.00448i −0.973794 0.707503i
\(129\) 0 0
\(130\) 2.07295 + 6.37988i 0.181810 + 0.559553i
\(131\) 5.50000 3.99598i 0.480537 0.349131i −0.320996 0.947080i \(-0.604018\pi\)
0.801534 + 0.597950i \(0.204018\pi\)
\(132\) 0 0
\(133\) −0.427051 + 0.310271i −0.0370300 + 0.0269039i
\(134\) 2.38197 + 7.33094i 0.205771 + 0.633297i
\(135\) 0 0
\(136\) −3.61803 + 11.1352i −0.310244 + 0.954832i
\(137\) 3.69098 + 11.3597i 0.315342 + 0.970523i 0.975613 + 0.219496i \(0.0704412\pi\)
−0.660271 + 0.751027i \(0.729559\pi\)
\(138\) 0 0
\(139\) 1.54508 4.75528i 0.131052 0.403338i −0.863903 0.503659i \(-0.831987\pi\)
0.994955 + 0.100321i \(0.0319869\pi\)
\(140\) 0.263932 0.812299i 0.0223063 0.0686518i
\(141\) 0 0
\(142\) −8.66312 + 6.29412i −0.726993 + 0.528191i
\(143\) 9.70820 0.811841
\(144\) 0 0
\(145\) 2.50000 7.69421i 0.207614 0.638969i
\(146\) 11.7812 + 8.55951i 0.975015 + 0.708390i
\(147\) 0 0
\(148\) −0.0450850 + 0.138757i −0.00370596 + 0.0114058i
\(149\) 3.94427 0.323127 0.161564 0.986862i \(-0.448346\pi\)
0.161564 + 0.986862i \(0.448346\pi\)
\(150\) 0 0
\(151\) 14.5623 1.18506 0.592532 0.805547i \(-0.298128\pi\)
0.592532 + 0.805547i \(0.298128\pi\)
\(152\) −0.590170 + 1.81636i −0.0478691 + 0.147326i
\(153\) 0 0
\(154\) −4.23607 3.07768i −0.341352 0.248007i
\(155\) 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 \(0.323709\pi\)
\(158\) 10.5902 7.69421i 0.842509 0.612118i
\(159\) 0 0
\(160\) −2.33688 7.19218i −0.184747 0.568592i
\(161\) −0.718847 + 2.21238i −0.0566531 + 0.174360i
\(162\) 0 0
\(163\) 3.39919 + 10.4616i 0.266245 + 0.819417i 0.991404 + 0.130836i \(0.0417662\pi\)
−0.725159 + 0.688581i \(0.758234\pi\)
\(164\) 0.145898 0.449028i 0.0113927 0.0350632i
\(165\) 0 0
\(166\) 3.11803 + 9.59632i 0.242006 + 0.744819i
\(167\) 11.7812 8.55951i 0.911653 0.662355i −0.0297794 0.999556i \(-0.509480\pi\)
0.941432 + 0.337202i \(0.109480\pi\)
\(168\) 0 0
\(169\) 7.73607 5.62058i 0.595082 0.432352i
\(170\) −15.3262 + 11.1352i −1.17547 + 0.854028i
\(171\) 0 0
\(172\) 2.42705 + 1.76336i 0.185061 + 0.134455i
\(173\) −5.83688 + 17.9641i −0.443770 + 1.36578i 0.440057 + 0.897970i \(0.354958\pi\)
−0.883827 + 0.467813i \(0.845042\pi\)
\(174\) 0 0
\(175\) −2.50000 + 1.81636i −0.188982 + 0.137304i
\(176\) −25.4164 −1.91583
\(177\) 0 0
\(178\) −11.7082 8.50651i −0.877567 0.637590i
\(179\) −0.427051 0.310271i −0.0319193 0.0231907i 0.571711 0.820455i \(-0.306280\pi\)
−0.603631 + 0.797264i \(0.706280\pi\)
\(180\) 0 0
\(181\) −0.236068 + 0.171513i −0.0175468 + 0.0127485i −0.596524 0.802595i \(-0.703452\pi\)
0.578977 + 0.815344i \(0.303452\pi\)
\(182\) 1.85410 0.137435
\(183\) 0 0
\(184\) 2.60081 + 8.00448i 0.191734 + 0.590098i
\(185\) 0.427051 0.310271i 0.0313974 0.0228116i
\(186\) 0 0
\(187\) 8.47214 + 26.0746i 0.619544 + 1.90676i
\(188\) −0.118034 0.363271i −0.00860851 0.0264943i
\(189\) 0 0
\(190\) −2.50000 + 1.81636i −0.181369 + 0.131772i
\(191\) 0.562306 + 1.73060i 0.0406870 + 0.125222i 0.969337 0.245736i \(-0.0790295\pi\)
−0.928650 + 0.370958i \(0.879030\pi\)
\(192\) 0 0
\(193\) 7.70820 0.554849 0.277424 0.960747i \(-0.410519\pi\)
0.277424 + 0.960747i \(0.410519\pi\)
\(194\) 5.04508 3.66547i 0.362216 0.263165i
\(195\) 0 0
\(196\) 3.30902 + 2.40414i 0.236358 + 0.171724i
\(197\) 3.00000 + 2.17963i 0.213741 + 0.155292i 0.689505 0.724281i \(-0.257828\pi\)
−0.475764 + 0.879573i \(0.657828\pi\)
\(198\) 0 0
\(199\) −17.5623 −1.24496 −0.622479 0.782636i \(-0.713875\pi\)
−0.622479 + 0.782636i \(0.713875\pi\)
\(200\) −3.45492 + 10.6331i −0.244299 + 0.751876i
\(201\) 0 0
\(202\) −0.736068 + 2.26538i −0.0517896 + 0.159392i
\(203\) −1.80902 1.31433i −0.126968 0.0922477i
\(204\) 0 0
\(205\) −1.38197 + 1.00406i −0.0965207 + 0.0701264i
\(206\) −11.2082 + 8.14324i −0.780913 + 0.567366i
\(207\) 0 0
\(208\) 7.28115 5.29007i 0.504857 0.366800i
\(209\) 1.38197 + 4.25325i 0.0955926 + 0.294204i
\(210\) 0 0
\(211\) −2.83688 + 8.73102i −0.195299 + 0.601068i 0.804674 + 0.593717i \(0.202340\pi\)
−0.999973 + 0.00735149i \(0.997660\pi\)
\(212\) 0.663119 + 2.04087i 0.0455432 + 0.140168i
\(213\) 0 0
\(214\) 8.20820 25.2623i 0.561101 1.72689i
\(215\) −3.35410 10.3229i −0.228748 0.704014i
\(216\) 0 0
\(217\) 1.50000 1.08981i 0.101827 0.0739814i
\(218\) 16.1803 1.09587
\(219\) 0 0
\(220\) −5.85410 4.25325i −0.394683 0.286754i
\(221\) −7.85410 5.70634i −0.528324 0.383850i
\(222\) 0 0
\(223\) −0.0557281 + 0.171513i −0.00373183 + 0.0114854i −0.952905 0.303269i \(-0.901922\pi\)
0.949173 + 0.314754i \(0.101922\pi\)
\(224\) −2.09017 −0.139655
\(225\) 0 0
\(226\) −27.2705 −1.81401
\(227\) −4.56231 + 14.0413i −0.302811 + 0.931956i 0.677674 + 0.735362i \(0.262988\pi\)
−0.980485 + 0.196594i \(0.937012\pi\)
\(228\) 0 0
\(229\) −17.5623 12.7598i −1.16055 0.843189i −0.170702 0.985323i \(-0.554604\pi\)
−0.989847 + 0.142134i \(0.954604\pi\)
\(230\) −4.20820 + 12.9515i −0.277481 + 0.853998i
\(231\) 0 0
\(232\) −8.09017 −0.531146
\(233\) −2.38197 + 1.73060i −0.156048 + 0.113375i −0.663069 0.748558i \(-0.730746\pi\)
0.507021 + 0.861933i \(0.330746\pi\)
\(234\) 0 0
\(235\) −0.427051 + 1.31433i −0.0278577 + 0.0857373i
\(236\) 2.07295 6.37988i 0.134937 0.415295i
\(237\) 0 0
\(238\) 1.61803 + 4.97980i 0.104882 + 0.322792i
\(239\) 6.34346 19.5232i 0.410324 1.26285i −0.506043 0.862508i \(-0.668892\pi\)
0.916367 0.400340i \(-0.131108\pi\)
\(240\) 0 0
\(241\) 0.781153 + 2.40414i 0.0503185 + 0.154864i 0.973058 0.230559i \(-0.0740554\pi\)
−0.922740 + 0.385423i \(0.874055\pi\)
\(242\) −21.4894 + 15.6129i −1.38139 + 1.00364i
\(243\) 0 0
\(244\) −4.35410 + 3.16344i −0.278743 + 0.202519i
\(245\) −4.57295 14.0741i −0.292155 0.899161i
\(246\) 0 0
\(247\) −1.28115 0.930812i −0.0815178 0.0592262i
\(248\) 2.07295 6.37988i 0.131632 0.405123i
\(249\) 0 0
\(250\) −14.6353 + 10.6331i −0.925615 + 0.672499i
\(251\) 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
\(254\) −26.0344 18.9151i −1.63355 1.18684i
\(255\) 0 0
\(256\) −10.9721 + 7.97172i −0.685758 + 0.498233i
\(257\) −22.8541 −1.42560 −0.712800 0.701367i \(-0.752573\pi\)
−0.712800 + 0.701367i \(0.752573\pi\)
\(258\) 0 0
\(259\) −0.0450850 0.138757i −0.00280144 0.00862196i
\(260\) 2.56231 0.158907
\(261\) 0 0
\(262\) −3.39919 10.4616i −0.210002 0.646321i
\(263\) 3.37132 + 10.3759i 0.207885 + 0.639803i 0.999583 + 0.0288905i \(0.00919740\pi\)
−0.791698 + 0.610913i \(0.790803\pi\)
\(264\) 0 0
\(265\) 2.39919 7.38394i 0.147381 0.453592i
\(266\) 0.263932 + 0.812299i 0.0161827 + 0.0498053i
\(267\) 0 0
\(268\) 2.94427 0.179850
\(269\) −10.3262 + 7.50245i −0.629602 + 0.457433i −0.856262 0.516541i \(-0.827219\pi\)
0.226660 + 0.973974i \(0.427219\pi\)
\(270\) 0 0
\(271\) 6.47214 + 4.70228i 0.393154 + 0.285643i 0.766747 0.641950i \(-0.221874\pi\)
−0.373593 + 0.927593i \(0.621874\pi\)
\(272\) 20.5623 + 14.9394i 1.24677 + 0.905834i
\(273\) 0 0
\(274\) 19.3262 1.16754
\(275\) 8.09017 + 24.8990i 0.487856 + 1.50147i
\(276\) 0 0
\(277\) −7.63525 + 23.4989i −0.458758 + 1.41191i 0.407908 + 0.913023i \(0.366258\pi\)
−0.866666 + 0.498889i \(0.833742\pi\)
\(278\) −6.54508 4.75528i −0.392548 0.285203i
\(279\) 0 0
\(280\) 2.50000 + 1.81636i 0.149404 + 0.108548i
\(281\) 8.16312 5.93085i 0.486971 0.353805i −0.317047 0.948410i \(-0.602691\pi\)
0.804018 + 0.594605i \(0.202691\pi\)
\(282\) 0 0
\(283\) 24.1525 17.5478i 1.43572 1.04311i 0.446799 0.894634i \(-0.352564\pi\)
0.988916 0.148474i \(-0.0474362\pi\)
\(284\) 1.26393 + 3.88998i 0.0750006 + 0.230828i
\(285\) 0 0
\(286\) 4.85410 14.9394i 0.287029 0.883385i
\(287\) 0.145898 + 0.449028i 0.00861209 + 0.0265053i
\(288\) 0 0
\(289\) 3.21885 9.90659i 0.189344 0.582741i
\(290\) −10.5902 7.69421i −0.621876 0.451820i
\(291\) 0 0
\(292\) 4.50000 3.26944i 0.263343 0.191330i
\(293\) 19.5279 1.14083 0.570415 0.821357i \(-0.306782\pi\)
0.570415 + 0.821357i \(0.306782\pi\)
\(294\) 0 0
\(295\) −19.6353 + 14.2658i −1.14321 + 0.830590i
\(296\) −0.427051 0.310271i −0.0248218 0.0180341i
\(297\) 0 0
\(298\) 1.97214 6.06961i 0.114243 0.351603i
\(299\) −6.97871 −0.403589
\(300\) 0 0
\(301\) −3.00000 −0.172917
\(302\) 7.28115 22.4091i 0.418983 1.28950i
\(303\) 0 0
\(304\) 3.35410 + 2.43690i 0.192371 + 0.139766i
\(305\) 19.4721 1.11497
\(306\) 0 0
\(307\) 9.23607 0.527130 0.263565 0.964642i \(-0.415102\pi\)
0.263565 + 0.964642i \(0.415102\pi\)
\(308\) −1.61803 + 1.17557i −0.0921960 + 0.0669843i
\(309\) 0 0
\(310\) 8.78115 6.37988i 0.498736 0.362353i
\(311\) −2.62868 + 8.09024i −0.149059 + 0.458755i −0.997511 0.0705172i \(-0.977535\pi\)
0.848452 + 0.529272i \(0.177535\pi\)
\(312\) 0 0
\(313\) −5.18034 15.9434i −0.292810 0.901177i −0.983948 0.178454i \(-0.942890\pi\)
0.691138 0.722723i \(-0.257110\pi\)
\(314\) 6.59017 20.2825i 0.371905 1.14461i
\(315\) 0 0
\(316\) −1.54508 4.75528i −0.0869178 0.267506i
\(317\) 6.19098 4.49801i 0.347720 0.252634i −0.400192 0.916431i \(-0.631056\pi\)
0.747912 + 0.663798i \(0.231056\pi\)
\(318\) 0 0
\(319\) −15.3262 + 11.1352i −0.858105 + 0.623449i
\(320\) 9.47214 0.529508
\(321\) 0 0
\(322\) 3.04508 + 2.21238i 0.169696 + 0.123291i
\(323\) 1.38197 4.25325i 0.0768946 0.236657i
\(324\) 0 0
\(325\) −7.50000 5.44907i −0.416025 0.302260i
\(326\) 17.7984 0.985761
\(327\) 0 0
\(328\) 1.38197 + 1.00406i 0.0763063 + 0.0554398i
\(329\) 0.309017 + 0.224514i 0.0170367 + 0.0123779i
\(330\) 0 0
\(331\) 18.7082 13.5923i 1.02830 0.747101i 0.0603290 0.998179i \(-0.480785\pi\)
0.967967 + 0.251078i \(0.0807850\pi\)
\(332\) 3.85410 0.211521
\(333\) 0 0
\(334\) −7.28115 22.4091i −0.398407 1.22617i
\(335\) −8.61803 6.26137i −0.470853 0.342095i
\(336\) 0 0
\(337\) 2.42705 + 7.46969i 0.132210 + 0.406900i 0.995146 0.0984135i \(-0.0313768\pi\)
−0.862936 + 0.505314i \(0.831377\pi\)
\(338\) −4.78115 14.7149i −0.260060 0.800384i
\(339\) 0 0
\(340\) 2.23607 + 6.88191i 0.121268 + 0.373224i
\(341\) −4.85410 14.9394i −0.262864 0.809013i
\(342\) 0 0
\(343\) −8.41641 −0.454443
\(344\) −8.78115 + 6.37988i −0.473448 + 0.343980i
\(345\) 0 0
\(346\) 24.7254 + 17.9641i 1.32925 + 0.965755i
\(347\) −16.1074 11.7027i −0.864690 0.628234i 0.0644668 0.997920i \(-0.479465\pi\)
−0.929157 + 0.369686i \(0.879465\pi\)
\(348\) 0 0
\(349\) 21.7082 1.16201 0.581007 0.813899i \(-0.302659\pi\)
0.581007 + 0.813899i \(0.302659\pi\)
\(350\) 1.54508 + 4.75528i 0.0825883 + 0.254181i
\(351\) 0 0
\(352\) −5.47214 + 16.8415i −0.291666 + 0.897655i
\(353\) 10.4443 + 7.58821i 0.555893 + 0.403880i 0.829953 0.557833i \(-0.188367\pi\)
−0.274061 + 0.961712i \(0.588367\pi\)
\(354\) 0 0
\(355\) 4.57295 14.0741i 0.242707 0.746975i
\(356\) −4.47214 + 3.24920i −0.237023 + 0.172207i
\(357\) 0 0
\(358\) −0.690983 + 0.502029i −0.0365196 + 0.0265330i
\(359\) −4.24671 13.0700i −0.224133 0.689810i −0.998378 0.0569247i \(-0.981870\pi\)
0.774246 0.632885i \(-0.218130\pi\)
\(360\) 0 0
\(361\) −5.64590 + 17.3763i −0.297153 + 0.914541i
\(362\) 0.145898 + 0.449028i 0.00766823 + 0.0236004i
\(363\) 0 0
\(364\) 0.218847 0.673542i 0.0114707 0.0353032i
\(365\) −20.1246 −1.05337
\(366\) 0 0
\(367\) 20.6803 15.0251i 1.07950 0.784306i 0.101908 0.994794i \(-0.467505\pi\)
0.977597 + 0.210488i \(0.0675051\pi\)
\(368\) 18.2705 0.952416
\(369\) 0 0
\(370\) −0.263932 0.812299i −0.0137212 0.0422294i
\(371\) −1.73607 1.26133i −0.0901322 0.0654848i
\(372\) 0 0
\(373\) −8.73607 + 26.8869i −0.452336 + 1.39215i 0.421897 + 0.906644i \(0.361364\pi\)
−0.874234 + 0.485505i \(0.838636\pi\)
\(374\) 44.3607 2.29384
\(375\) 0 0
\(376\) 1.38197 0.0712695
\(377\) 2.07295 6.37988i 0.106762 0.328581i
\(378\) 0 0
\(379\) −11.8090 8.57975i −0.606588 0.440712i 0.241623 0.970370i \(-0.422320\pi\)
−0.848211 + 0.529658i \(0.822320\pi\)
\(380\) 0.364745 + 1.12257i 0.0187110 + 0.0575866i
\(381\) 0 0
\(382\) 2.94427 0.150642
\(383\) 26.9894 19.6089i 1.37909 1.00197i 0.382127 0.924110i \(-0.375192\pi\)
0.996964 0.0778591i \(-0.0248084\pi\)
\(384\) 0 0
\(385\) 7.23607 0.368784
\(386\) 3.85410 11.8617i 0.196169 0.603745i
\(387\) 0 0
\(388\) −0.736068 2.26538i −0.0373682 0.115007i
\(389\) −4.63525 + 14.2658i −0.235017 + 0.723307i 0.762102 + 0.647456i \(0.224167\pi\)
−0.997119 + 0.0758507i \(0.975833\pi\)
\(390\) 0 0
\(391\) −6.09017 18.7436i −0.307993 0.947905i
\(392\) −11.9721 + 8.69827i −0.604684 + 0.439329i
\(393\) 0 0
\(394\) 4.85410 3.52671i 0.244546 0.177673i
\(395\) −5.59017 + 17.2048i −0.281272 + 0.865666i
\(396\) 0 0
\(397\) −23.4894 17.0660i −1.17890 0.856519i −0.186850 0.982388i \(-0.559828\pi\)
−0.992047 + 0.125870i \(0.959828\pi\)
\(398\) −8.78115 + 27.0256i −0.440159 + 1.35467i
\(399\) 0 0
\(400\) 19.6353 + 14.2658i 0.981763 + 0.713292i
\(401\) −26.5967 −1.32818 −0.664089 0.747653i \(-0.731180\pi\)
−0.664089 + 0.747653i \(0.731180\pi\)
\(402\) 0 0
\(403\) 4.50000 + 3.26944i 0.224161 + 0.162862i
\(404\) 0.736068 + 0.534785i 0.0366208 + 0.0266065i
\(405\) 0 0
\(406\) −2.92705 + 2.12663i −0.145267 + 0.105543i
\(407\) −1.23607 −0.0612696
\(408\) 0 0
\(409\) 0.489357 + 1.50609i 0.0241971 + 0.0744711i 0.962426 0.271544i \(-0.0875344\pi\)
−0.938229 + 0.346016i \(0.887534\pi\)
\(410\) 0.854102 + 2.62866i 0.0421811 + 0.129820i
\(411\) 0 0
\(412\) 1.63525 + 5.03280i 0.0805632 + 0.247948i
\(413\) 2.07295 + 6.37988i 0.102003 + 0.313933i
\(414\) 0 0
\(415\) −11.2812 8.19624i −0.553770 0.402337i
\(416\) −1.93769 5.96361i −0.0950033 0.292390i
\(417\) 0 0
\(418\) 7.23607 0.353928
\(419\) −7.66312 + 5.56758i −0.374368 + 0.271994i −0.759020 0.651068i \(-0.774321\pi\)
0.384652 + 0.923062i \(0.374321\pi\)
\(420\) 0 0
\(421\) −25.8885 18.8091i −1.26173 0.916701i −0.262889 0.964826i \(-0.584675\pi\)
−0.998841 + 0.0481252i \(0.984675\pi\)
\(422\) 12.0172 + 8.73102i 0.584989 + 0.425020i
\(423\) 0 0
\(424\) −7.76393 −0.377050
\(425\) 8.09017 24.8990i 0.392431 1.20778i
\(426\) 0 0
\(427\) 1.66312 5.11855i 0.0804840 0.247704i
\(428\) −8.20820 5.96361i −0.396759 0.288262i
\(429\) 0 0
\(430\) −17.5623 −0.846930
\(431\) −24.1353 + 17.5353i −1.16255 + 0.844645i −0.990099 0.140372i \(-0.955170\pi\)
−0.172456 + 0.985017i \(0.555170\pi\)
\(432\) 0 0
\(433\) −21.7254 + 15.7844i −1.04406 + 0.758552i −0.971073 0.238781i \(-0.923252\pi\)
−0.0729839 + 0.997333i \(0.523252\pi\)
\(434\) −0.927051 2.85317i −0.0444999 0.136957i
\(435\) 0 0
\(436\) 1.90983 5.87785i 0.0914643 0.281498i
\(437\) −0.993422 3.05744i −0.0475218 0.146257i
\(438\) 0 0
\(439\) −12.6631 + 38.9731i −0.604378 + 1.86008i −0.103365 + 0.994644i \(0.532961\pi\)
−0.501013 + 0.865440i \(0.667039\pi\)
\(440\) 21.1803 15.3884i 1.00973 0.733614i
\(441\) 0 0
\(442\) −12.7082 + 9.23305i −0.604468 + 0.439171i
\(443\) −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
\(446\) 0.236068 + 0.171513i 0.0111781 + 0.00812140i
\(447\) 0 0
\(448\) 0.809017 2.48990i 0.0382225 0.117637i
\(449\) −4.67376 −0.220568 −0.110284 0.993900i \(-0.535176\pi\)
−0.110284 + 0.993900i \(0.535176\pi\)
\(450\) 0 0
\(451\) 4.00000 0.188353
\(452\) −3.21885 + 9.90659i −0.151402 + 0.465967i
\(453\) 0 0
\(454\) 19.3262 + 14.0413i 0.907025 + 0.658992i
\(455\) −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 \(0.667001\pi\)
\(458\) −28.4164 + 20.6457i −1.32781 + 0.964712i
\(459\) 0 0
\(460\) 4.20820 + 3.05744i 0.196209 + 0.142554i
\(461\) −0.253289 + 0.779543i −0.0117968 + 0.0363069i −0.956782 0.290807i \(-0.906076\pi\)
0.944985 + 0.327114i \(0.106076\pi\)
\(462\) 0 0
\(463\) −7.45492 22.9439i −0.346459 1.06629i −0.960798 0.277250i \(-0.910577\pi\)
0.614339 0.789042i \(-0.289423\pi\)
\(464\) −5.42705 + 16.7027i −0.251945 + 0.775405i
\(465\) 0 0
\(466\) 1.47214 + 4.53077i 0.0681954 + 0.209884i
\(467\) 22.2082 16.1352i 1.02767 0.746648i 0.0598315 0.998208i \(-0.480944\pi\)
0.967842 + 0.251560i \(0.0809437\pi\)
\(468\) 0 0
\(469\) −2.38197 + 1.73060i −0.109989 + 0.0799117i
\(470\) 1.80902 + 1.31433i 0.0834437 + 0.0606254i
\(471\) 0 0
\(472\) 19.6353 + 14.2658i 0.903786 + 0.656639i
\(473\) −7.85410 + 24.1724i −0.361132 + 1.11145i
\(474\) 0 0
\(475\) 1.31966 4.06150i 0.0605502 0.186354i
\(476\) 2.00000 0.0916698
\(477\) 0 0
\(478\) −26.8713 19.5232i −1.22907 0.892969i
\(479\) −8.78115 6.37988i −0.401221 0.291504i 0.368817 0.929502i \(-0.379763\pi\)
−0.770038 + 0.637998i \(0.779763\pi\)
\(480\) 0 0
\(481\) 0.354102 0.257270i 0.0161457 0.0117305i
\(482\) 4.09017 0.186302
\(483\) 0 0
\(484\) 3.13525 + 9.64932i 0.142512 + 0.438606i
\(485\) −2.66312 + 8.19624i −0.120926 + 0.372172i
\(486\) 0 0
\(487\) −11.2533 34.6341i −0.509935 1.56942i −0.792312 0.610116i \(-0.791123\pi\)
0.282377 0.959303i \(-0.408877\pi\)
\(488\) −6.01722 18.5191i −0.272387 0.838320i
\(489\) 0 0
\(490\) −23.9443 −1.08169
\(491\) 13.3647 + 41.1325i 0.603143 + 1.85628i 0.509088 + 0.860715i \(0.329983\pi\)
0.0940550 + 0.995567i \(0.470017\pi\)
\(492\) 0 0
\(493\) 18.9443 0.853207
\(494\) −2.07295 + 1.50609i −0.0932664 + 0.0677620i
\(495\) 0 0
\(496\) −11.7812 8.55951i −0.528989 0.384333i
\(497\) −3.30902 2.40414i −0.148430 0.107840i
\(498\) 0 0
\(499\) 7.56231 0.338535 0.169268 0.985570i \(-0.445860\pi\)
0.169268 + 0.985570i \(0.445860\pi\)
\(500\) 2.13525 + 6.57164i 0.0954915 + 0.293893i
\(501\) 0 0
\(502\) 14.5902 44.9039i 0.651191 2.00416i
\(503\) −30.2705 21.9928i −1.34970 0.980611i −0.999027 0.0441115i \(-0.985954\pi\)
−0.350669 0.936500i \(-0.614046\pi\)
\(504\) 0 0
\(505\) −1.01722 3.13068i −0.0452657 0.139314i
\(506\) 25.7984 18.7436i 1.14688 0.833255i
\(507\) 0 0
\(508\) −9.94427 + 7.22494i −0.441206 + 0.320555i
\(509\) 6.28115 + 19.3314i 0.278407 + 0.856849i 0.988298 + 0.152537i \(0.0487444\pi\)
−0.709891 + 0.704312i \(0.751256\pi\)
\(510\) 0 0
\(511\) −1.71885 + 5.29007i −0.0760373 + 0.234019i
\(512\) −1.63525 5.03280i −0.0722687 0.222420i
\(513\) 0 0
\(514\) −11.4271 + 35.1688i −0.504026 + 1.55123i
\(515\) 5.91641 18.2088i 0.260708 0.802377i
\(516\) 0 0
\(517\) 2.61803 1.90211i 0.115141 0.0836548i
\(518\) −0.236068 −0.0103722
\(519\) 0 0
\(520\) −2.86475 + 8.81678i −0.125627 + 0.386641i
\(521\) 23.7533 + 17.2578i 1.04065 + 0.756077i 0.970412 0.241453i \(-0.0776241\pi\)
0.0702381 + 0.997530i \(0.477624\pi\)
\(522\) 0 0
\(523\) −4.06231 + 12.5025i −0.177632 + 0.546696i −0.999744 0.0226305i \(-0.992796\pi\)
0.822112 + 0.569326i \(0.192796\pi\)
\(524\) −4.20163 −0.183549
\(525\) 0 0
\(526\) 17.6525 0.769685
\(527\) −4.85410 + 14.9394i −0.211448 + 0.650770i
\(528\) 0 0
\(529\) 7.14590 + 5.19180i 0.310691 + 0.225730i
\(530\) −10.1631 7.38394i −0.441458 0.320738i
\(531\) 0 0
\(532\) 0.326238 0.0141442
\(533\) −1.14590 + 0.832544i −0.0496344 + 0.0360615i
\(534\) 0 0
\(535\) 11.3435 + 34.9116i 0.490420 + 1.50936i
\(536\) −3.29180 + 10.1311i −0.142184 + 0.437597i
\(537\) 0 0
\(538\) 6.38197 + 19.6417i 0.275146 + 0.846813i
\(539\) −10.7082 + 32.9565i −0.461235 + 1.41954i
\(540\) 0 0
\(541\) 8.38197 + 25.7970i 0.360369 + 1.10910i 0.952831 + 0.303503i \(0.0981561\pi\)
−0.592462 + 0.805599i \(0.701844\pi\)
\(542\) 10.4721 7.60845i 0.449817 0.326811i
\(543\) 0 0
\(544\) 14.3262 10.4086i 0.614232 0.446266i
\(545\) −18.0902 + 13.1433i −0.774898 + 0.562996i
\(546\) 0 0
\(547\) 17.2254 + 12.5150i 0.736506 + 0.535103i 0.891615 0.452794i \(-0.149573\pi\)
−0.155109 + 0.987897i \(0.549573\pi\)
\(548\) 2.28115 7.02067i 0.0974460 0.299908i
\(549\) 0 0
\(550\) 42.3607 1.80627
\(551\) 3.09017 0.131646
\(552\) 0 0
\(553\) 4.04508 + 2.93893i 0.172015 + 0.124976i
\(554\) 32.3435 + 23.4989i 1.37414 + 0.998373i
\(555\) 0 0
\(556\) −2.50000 + 1.81636i −0.106024 + 0.0770307i
\(557\) −4.76393 −0.201854 −0.100927 0.994894i \(-0.532181\pi\)
−0.100927 + 0.994894i \(0.532181\pi\)
\(558\) 0 0
\(559\) −2.78115 8.55951i −0.117630 0.362029i
\(560\) 5.42705 3.94298i 0.229335 0.166621i
\(561\) 0 0
\(562\) −5.04508 15.5272i −0.212814 0.654974i
\(563\) −2.28115 7.02067i −0.0961391 0.295886i 0.891410 0.453198i \(-0.149717\pi\)
−0.987549 + 0.157312i \(0.949717\pi\)
\(564\) 0 0
\(565\) 30.4894 22.1518i 1.28270 0.931934i
\(566\) −14.9271 45.9407i −0.627431 1.93103i
\(567\) 0 0
\(568\) −14.7984 −0.620926
\(569\) 16.6074 12.0660i 0.696218 0.505832i −0.182480 0.983210i \(-0.558413\pi\)
0.878698 + 0.477377i \(0.158413\pi\)
\(570\) 0 0
\(571\) 6.57295 + 4.77553i 0.275069 + 0.199850i 0.716764 0.697316i \(-0.245623\pi\)
−0.441695 + 0.897165i \(0.645623\pi\)
\(572\) −4.85410 3.52671i −0.202960 0.147459i
\(573\) 0 0
\(574\) 0.763932 0.0318859
\(575\) −5.81559 17.8986i −0.242527 0.746422i
\(576\) 0 0
\(577\) −10.4377 + 32.1239i −0.434527 + 1.33734i 0.459044 + 0.888414i \(0.348192\pi\)
−0.893571 + 0.448923i \(0.851808\pi\)
\(578\) −13.6353 9.90659i −0.567152 0.412060i
\(579\) 0 0
\(580\) −4.04508 + 2.93893i −0.167963 + 0.122032i
\(581\) −3.11803 + 2.26538i −0.129358 + 0.0939840i
\(582\) 0 0
\(583\) −14.7082 + 10.6861i −0.609152 + 0.442575i
\(584\) 6.21885 + 19.1396i 0.257338 + 0.792004i
\(585\) 0 0
\(586\) 9.76393 30.0503i 0.403344 1.24137i
\(587\) −1.63525 5.03280i −0.0674942 0.207726i 0.911621 0.411032i \(-0.134831\pi\)
−0.979115 + 0.203306i \(0.934831\pi\)
\(588\) 0 0
\(589\) −0.791796 + 2.43690i −0.0326254 + 0.100411i
\(590\) 12.1353 + 37.3485i 0.499601 + 1.53761i
\(591\) 0 0
\(592\) −0.927051 + 0.673542i −0.0381016 + 0.0276824i
\(593\) 10.9098 0.448013 0.224007 0.974588i \(-0.428086\pi\)
0.224007 + 0.974588i \(0.428086\pi\)
\(594\) 0 0
\(595\) −5.85410 4.25325i −0.239995 0.174366i
\(596\) −1.97214 1.43284i −0.0807818 0.0586914i
\(597\) 0 0
\(598\) −3.48936 + 10.7391i −0.142690 + 0.439156i
\(599\) 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 \(0.482271\pi\)
\(602\) −1.50000 + 4.61653i −0.0611354 + 0.188156i
\(603\) 0 0
\(604\) −7.28115 5.29007i −0.296266 0.215250i
\(605\) 11.3435 34.9116i 0.461177 1.41936i
\(606\) 0 0
\(607\) −35.5623 −1.44343 −0.721715 0.692191i \(-0.756646\pi\)
−0.721715 + 0.692191i \(0.756646\pi\)
\(608\) 2.33688 1.69784i 0.0947730 0.0688566i
\(609\) 0 0
\(610\) 9.73607 29.9645i 0.394202 1.21323i
\(611\) −0.354102 + 1.08981i −0.0143254 + 0.0440891i
\(612\) 0 0
\(613\) −4.62868 14.2456i −0.186951 0.575374i 0.813026 0.582227i \(-0.197819\pi\)
−0.999977 + 0.00685287i \(0.997819\pi\)
\(614\) 4.61803 14.2128i 0.186369 0.573584i
\(615\) 0 0
\(616\) −2.23607 6.88191i −0.0900937 0.277280i
\(617\) 11.5172 8.36775i 0.463666 0.336873i −0.331302 0.943525i \(-0.607488\pi\)
0.794968 + 0.606652i \(0.207488\pi\)
\(618\) 0 0
\(619\) −24.6976 + 17.9438i −0.992679 + 0.721223i −0.960506 0.278259i \(-0.910243\pi\)
−0.0321727 + 0.999482i \(0.510243\pi\)
\(620\) −1.28115 3.94298i −0.0514523 0.158354i
\(621\) 0 0
\(622\) 11.1353 + 8.09024i 0.446483 + 0.324389i
\(623\) 1.70820 5.25731i 0.0684377 0.210630i
\(624\) 0 0
\(625\) 7.72542 23.7764i 0.309017 0.951057i
\(626\) −27.1246 −1.08412
\(627\) 0 0
\(628\) −6.59017 4.78804i −0.262976 0.191064i
\(629\) 1.00000 + 0.726543i 0.0398726 + 0.0289691i
\(630\) 0 0
\(631\) 8.28115 6.01661i 0.329667 0.239517i −0.410622 0.911806i \(-0.634688\pi\)
0.740290 + 0.672288i \(0.234688\pi\)
\(632\) 18.0902 0.719588
\(633\) 0 0
\(634\) −3.82624 11.7759i −0.151959 0.467683i
\(635\) 44.4721 1.76482
\(636\) 0 0
\(637\) −3.79180 11.6699i −0.150236 0.462380i
\(638\) 9.47214 + 29.1522i 0.375005 + 1.15415i
\(639\) 0 0
\(640\) 9.40983 28.9605i 0.371956 1.14476i
\(641\) 0.336881 + 1.03681i 0.0133060 + 0.0409517i 0.957489 0.288470i \(-0.0931464\pi\)
−0.944183 + 0.329421i \(0.893146\pi\)
\(642\) 0 0
\(643\) −30.8328 −1.21593 −0.607964 0.793965i \(-0.708013\pi\)
−0.607964 + 0.793965i \(0.708013\pi\)
\(644\) 1.16312 0.845055i 0.0458333 0.0332998i
\(645\) 0 0
\(646\) −5.85410 4.25325i −0.230327 0.167342i
\(647\) −29.5623 21.4783i −1.16221 0.844398i −0.172158 0.985069i \(-0.555074\pi\)
−0.990056 + 0.140671i \(0.955074\pi\)
\(648\) 0 0
\(649\) 56.8328 2.23088
\(650\) −12.1353 + 8.81678i −0.475984 + 0.345823i
\(651\) 0 0
\(652\) 2.10081 6.46564i 0.0822742 0.253214i
\(653\) 15.4443 + 11.2209i 0.604381 + 0.439109i 0.847431 0.530905i \(-0.178148\pi\)
−0.243050 + 0.970014i \(0.578148\pi\)
\(654\) 0 0
\(655\) 12.2984 + 8.93529i 0.480537 + 0.349131i
\(656\) 3.00000 2.17963i 0.117130 0.0851002i
\(657\) 0 0
\(658\) 0.500000 0.363271i 0.0194920 0.0141618i
\(659\) −4.79837 14.7679i −0.186918 0.575275i 0.813058 0.582183i \(-0.197801\pi\)
−0.999976 + 0.00690786i \(0.997801\pi\)
\(660\) 0 0
\(661\) 6.08359 18.7234i 0.236624 0.728255i −0.760277 0.649598i \(-0.774937\pi\)
0.996902 0.0786563i \(-0.0250630\pi\)
\(662\) −11.5623 35.5851i −0.449382 1.38305i
\(663\) 0 0
\(664\) −4.30902 + 13.2618i −0.167222 + 0.514657i
\(665\) −0.954915 0.693786i −0.0370300 0.0269039i
\(666\) 0 0
\(667\) 11.0172 8.00448i 0.426588 0.309935i
\(668\) −9.00000 −0.348220
\(669\) 0 0
\(670\) −13.9443 + 10.1311i −0.538714 + 0.391399i
\(671\) −36.8885 26.8011i −1.42407 1.03464i
\(672\) 0 0
\(673\) 3.76393 11.5842i 0.145089 0.446538i −0.851934 0.523650i \(-0.824570\pi\)
0.997022 + 0.0771122i \(0.0245700\pi\)
\(674\) 12.7082 0.489502
\(675\) 0 0
\(676\) −5.90983 −0.227301
\(677\) −3.28115 + 10.0984i −0.126105 + 0.388111i −0.994101 0.108460i \(-0.965408\pi\)
0.867996 + 0.496571i \(0.165408\pi\)
\(678\) 0 0
\(679\) 1.92705 + 1.40008i 0.0739534 + 0.0537303i
\(680\) −26.1803 −1.00397
\(681\) 0 0
\(682\) −25.4164 −0.973245
\(683\) −10.8992 + 7.91872i −0.417046 + 0.303002i −0.776448 0.630181i \(-0.782981\pi\)
0.359402 + 0.933183i \(0.382981\pi\)
\(684\) 0 0
\(685\) −21.6074 + 15.6987i −0.825576 + 0.599816i
\(686\) −4.20820 + 12.9515i −0.160670 + 0.494491i
\(687\) 0 0
\(688\) 7.28115 + 22.4091i 0.277591 + 0.854338i
\(689\) 1.98936 6.12261i 0.0757885 0.233253i
\(690\) 0 0
\(691\) 11.2082 + 34.4953i 0.426380 + 1.31226i 0.901667 + 0.432432i \(0.142344\pi\)
−0.475286 + 0.879831i \(0.657656\pi\)
\(692\) 9.44427 6.86167i 0.359017 0.260841i
\(693\) 0 0
\(694\) −26.0623 + 18.9354i −0.989312 + 0.718777i
\(695\) 11.1803 0.424094
\(696\) 0 0
\(697\) −3.23607 2.35114i −0.122575 0.0890558i
\(698\) 10.8541 33.4055i 0.410834 1.26442i
\(699\) 0 0
\(700\) 1.90983 0.0721848
\(701\) 41.0132 1.54905 0.774523 0.632546i \(-0.217990\pi\)
0.774523 + 0.632546i \(0.217990\pi\)
\(702\) 0 0
\(703\) 0.163119 + 0.118513i 0.00615215 + 0.00446980i
\(704\) −17.9443 13.0373i −0.676300 0.491361i
\(705\) 0 0
\(706\) 16.8992 12.2780i 0.636009 0.462088i
\(707\) −0.909830 −0.0342177
\(708\) 0 0
\(709\) −10.3647 31.8994i −0.389256 1.19801i −0.933345 0.358980i \(-0.883125\pi\)
0.544089 0.839027i \(-0.316875\pi\)
\(710\) −19.3713 14.0741i −0.726993 0.528191i
\(711\) 0 0
\(712\) −6.18034 19.0211i −0.231618 0.712847i
\(713\) 3.48936 + 10.7391i 0.130677 + 0.402184i
\(714\) 0 0
\(715\) 6.70820 + 20.6457i 0.250873 + 0.772106i
\(716\) 0.100813 + 0.310271i 0.00376756 + 0.0115954i
\(717\) 0 0
\(718\) −22.2361 −0.829843
\(719\) −18.8435 + 13.6906i −0.702742 + 0.510572i −0.880824 0.473443i \(-0.843011\pi\)
0.178082 + 0.984016i \(0.443011\pi\)
\(720\) 0 0
\(721\) −4.28115 3.11044i −0.159438 0.115839i
\(722\) 23.9164 + 17.3763i 0.890077 + 0.646678i
\(723\) 0 0
\(724\) 0.180340 0.00670228
\(725\) 18.0902 0.671852
\(726\) 0 0
\(727\) 7.59017 23.3601i 0.281504 0.866380i −0.705921 0.708291i \(-0.749467\pi\)
0.987425 0.158089i \(-0.0505333\pi\)
\(728\) 2.07295 + 1.50609i 0.0768286 + 0.0558192i
\(729\) 0 0
\(730\) −10.0623 + 30.9686i −0.372423 + 1.14620i
\(731\) 20.5623 14.9394i 0.760524 0.552553i
\(732\) 0 0
\(733\) 16.1631 11.7432i 0.596998 0.433745i −0.247814 0.968808i \(-0.579712\pi\)
0.844812 + 0.535063i \(0.179712\pi\)
\(734\) −12.7812 39.3363i −0.471761 1.45193i
\(735\) 0 0
\(736\) 3.93363 12.1065i 0.144995 0.446250i
\(737\) 7.70820 + 23.7234i 0.283935 + 0.873863i
\(738\) 0 0
\(739\) 4.93769 15.1967i 0.181636 0.559018i −0.818238 0.574879i \(-0.805049\pi\)
0.999874 + 0.0158612i \(0.00504898\pi\)
\(740\) −0.326238 −0.0119927
\(741\) 0 0
\(742\) −2.80902 + 2.04087i −0.103122 + 0.0749227i
\(743\) −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
\(746\) 37.0066 + 26.8869i 1.35491 + 0.984398i
\(747\) 0 0
\(748\) 5.23607 16.1150i 0.191450 0.589221i
\(749\) 10.1459 0.370723
\(750\) 0 0
\(751\) −5.11146 −0.186520 −0.0932598 0.995642i \(-0.529729\pi\)
−0.0932598 + 0.995642i \(0.529729\pi\)
\(752\) 0.927051 2.85317i 0.0338061 0.104044i
\(753\) 0 0
\(754\) −8.78115 6.37988i −0.319791 0.232342i
\(755\) 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 \(0.313578\pi\)
\(758\) −19.1074 + 13.8823i −0.694012 + 0.504229i
\(759\) 0 0
\(760\) −4.27051 −0.154908
\(761\) 5.70163 17.5478i 0.206684 0.636107i −0.792956 0.609279i \(-0.791459\pi\)
0.999640 0.0268287i \(-0.00854087\pi\)
\(762\) 0 0
\(763\) 1.90983 + 5.87785i 0.0691405 + 0.212793i
\(764\) 0.347524 1.06957i 0.0125730 0.0386957i
\(765\) 0 0
\(766\) −16.6803 51.3368i −0.602685 1.85487i
\(767\) −16.2812 + 11.8290i −0.587878 + 0.427119i
\(768\) 0 0
\(769\) −10.8541 + 7.88597i −0.391409 + 0.284375i −0.766033 0.642802i \(-0.777772\pi\)
0.374624 + 0.927177i \(0.377772\pi\)
\(770\) 3.61803 11.1352i 0.130385 0.401283i
\(771\) 0 0
\(772\) −3.85410 2.80017i −0.138712 0.100780i
\(773\) 11.1738 34.3893i 0.401892 1.23690i −0.521570 0.853208i \(-0.674654\pi\)
0.923462 0.383689i \(-0.125346\pi\)
\(774\) 0 0
\(775\) −4.63525 + 14.2658i −0.166503 + 0.512444i
\(776\) 8.61803 0.309369
\(777\) 0 0
\(778\) 19.6353 + 14.2658i 0.703958 + 0.511455i
\(779\) −0.527864 0.383516i −0.0189127 0.0137409i
\(780\) 0 0
\(781\) −28.0344 + 20.3682i −1.00315 + 0.728832i
\(782\) −31.8885 −1.14033
\(783\) 0 0
\(784\) 9.92705 + 30.5523i 0.354538 + 1.09115i
\(785\) 9.10739 + 28.0297i 0.325057 + 1.00042i
\(786\) 0 0