Properties

Label 576.2.bd.a.37.7
Level $576$
Weight $2$
Character 576.37
Analytic conductor $4.599$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bd (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(7\) over \(\Q(\zeta_{16})\)
Twist minimal: no (minimal twist has level 64)
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 37.7
Character \(\chi\) \(=\) 576.37
Dual form 576.2.bd.a.109.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.35786 + 0.395231i) q^{2} +(1.68758 + 1.07334i) q^{4} +(-0.154331 + 0.775873i) q^{5} +(1.53949 - 3.71667i) q^{7} +(1.86729 + 2.12443i) q^{8} +O(q^{10})\) \(q+(1.35786 + 0.395231i) q^{2} +(1.68758 + 1.07334i) q^{4} +(-0.154331 + 0.775873i) q^{5} +(1.53949 - 3.71667i) q^{7} +(1.86729 + 2.12443i) q^{8} +(-0.516209 + 0.992533i) q^{10} +(1.83415 - 1.22554i) q^{11} +(0.559685 + 2.81373i) q^{13} +(3.55936 - 4.43827i) q^{14} +(1.69589 + 3.62270i) q^{16} +(2.73419 - 2.73419i) q^{17} +(-5.68264 + 1.13035i) q^{19} +(-1.09322 + 1.14370i) q^{20} +(2.97490 - 0.939205i) q^{22} +(-2.55179 + 1.05698i) q^{23} +(4.04124 + 1.67394i) q^{25} +(-0.352096 + 4.04186i) q^{26} +(6.58727 - 4.61979i) q^{28} +(2.96252 + 1.97949i) q^{29} -0.201957i q^{31} +(0.870977 + 5.58940i) q^{32} +(4.79329 - 2.63202i) q^{34} +(2.64607 + 1.76805i) q^{35} +(-8.82594 - 1.75559i) q^{37} +(-8.16299 - 0.711098i) q^{38} +(-1.93647 + 1.12092i) q^{40} +(-7.85196 + 3.25239i) q^{41} +(1.06440 + 1.59299i) q^{43} +(4.41071 - 0.0995378i) q^{44} +(-3.88273 + 0.426695i) q^{46} +(7.56082 - 7.56082i) q^{47} +(-6.49382 - 6.49382i) q^{49} +(4.82586 + 3.87020i) q^{50} +(-2.07557 + 5.34913i) q^{52} +(-11.1942 + 7.47973i) q^{53} +(0.667799 + 1.61221i) q^{55} +(10.7705 - 3.66955i) q^{56} +(3.24034 + 3.85875i) q^{58} +(1.71321 - 8.61290i) q^{59} +(-2.32214 + 3.47533i) q^{61} +(0.0798198 - 0.274231i) q^{62} +(-1.02644 + 7.93388i) q^{64} -2.26947 q^{65} +(5.15244 - 7.71118i) q^{67} +(7.54888 - 1.67946i) q^{68} +(2.89421 + 3.44657i) q^{70} +(-1.98817 + 4.79986i) q^{71} +(-6.11102 - 14.7533i) q^{73} +(-11.2906 - 5.87213i) q^{74} +(-10.8032 - 4.19184i) q^{76} +(-1.73126 - 8.70365i) q^{77} +(-2.91841 - 2.91841i) q^{79} +(-3.07248 + 0.756698i) q^{80} +(-11.9473 + 1.31296i) q^{82} +(0.190374 - 0.0378677i) q^{83} +(1.69941 + 2.54335i) q^{85} +(0.815713 + 2.58375i) q^{86} +(6.02849 + 1.60809i) q^{88} +(-0.659812 - 0.273303i) q^{89} +(11.3193 + 2.25155i) q^{91} +(-5.44086 - 0.955181i) q^{92} +(13.2548 - 7.27829i) q^{94} -4.58345i q^{95} +2.80442i q^{97} +(-6.25116 - 11.3843i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} + O(q^{10}) \) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} - 8q^{10} + 8q^{11} - 8q^{13} + 8q^{14} - 8q^{16} + 8q^{17} - 8q^{19} + 8q^{20} + 8q^{23} - 8q^{25} - 32q^{26} + 32q^{28} + 8q^{29} - 32q^{32} + 32q^{34} + 8q^{35} - 8q^{37} - 32q^{38} + 32q^{40} + 8q^{41} - 8q^{43} - 8q^{46} + 8q^{47} - 8q^{49} + 32q^{50} - 56q^{52} + 8q^{53} + 56q^{55} + 64q^{56} - 80q^{58} - 56q^{59} - 8q^{61} + 40q^{62} - 104q^{64} + 16q^{65} + 72q^{67} + 56q^{68} - 104q^{70} - 56q^{71} - 8q^{73} + 64q^{74} - 72q^{76} + 8q^{77} + 24q^{79} - 32q^{80} + 72q^{82} + 8q^{83} - 8q^{85} - 96q^{86} + 72q^{88} + 8q^{89} - 8q^{91} - 144q^{92} + 88q^{94} - 128q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{9}{16}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35786 + 0.395231i 0.960154 + 0.279470i
\(3\) 0 0
\(4\) 1.68758 + 1.07334i 0.843792 + 0.536670i
\(5\) −0.154331 + 0.775873i −0.0690188 + 0.346981i −0.999828 0.0185235i \(-0.994103\pi\)
0.930810 + 0.365504i \(0.119103\pi\)
\(6\) 0 0
\(7\) 1.53949 3.71667i 0.581874 1.40477i −0.309238 0.950985i \(-0.600074\pi\)
0.891112 0.453783i \(-0.149926\pi\)
\(8\) 1.86729 + 2.12443i 0.660188 + 0.751101i
\(9\) 0 0
\(10\) −0.516209 + 0.992533i −0.163240 + 0.313866i
\(11\) 1.83415 1.22554i 0.553018 0.369515i −0.247440 0.968903i \(-0.579589\pi\)
0.800459 + 0.599388i \(0.204589\pi\)
\(12\) 0 0
\(13\) 0.559685 + 2.81373i 0.155229 + 0.780387i 0.977441 + 0.211207i \(0.0677393\pi\)
−0.822213 + 0.569180i \(0.807261\pi\)
\(14\) 3.55936 4.43827i 0.951280 1.18618i
\(15\) 0 0
\(16\) 1.69589 + 3.62270i 0.423972 + 0.905676i
\(17\) 2.73419 2.73419i 0.663138 0.663138i −0.292981 0.956118i \(-0.594647\pi\)
0.956118 + 0.292981i \(0.0946472\pi\)
\(18\) 0 0
\(19\) −5.68264 + 1.13035i −1.30369 + 0.259319i −0.797612 0.603171i \(-0.793904\pi\)
−0.506074 + 0.862490i \(0.668904\pi\)
\(20\) −1.09322 + 1.14370i −0.244452 + 0.255740i
\(21\) 0 0
\(22\) 2.97490 0.939205i 0.634251 0.200239i
\(23\) −2.55179 + 1.05698i −0.532084 + 0.220396i −0.632516 0.774548i \(-0.717978\pi\)
0.100432 + 0.994944i \(0.467978\pi\)
\(24\) 0 0
\(25\) 4.04124 + 1.67394i 0.808247 + 0.334787i
\(26\) −0.352096 + 4.04186i −0.0690517 + 0.792674i
\(27\) 0 0
\(28\) 6.58727 4.61979i 1.24488 0.873058i
\(29\) 2.96252 + 1.97949i 0.550125 + 0.367582i 0.799352 0.600863i \(-0.205176\pi\)
−0.249226 + 0.968445i \(0.580176\pi\)
\(30\) 0 0
\(31\) 0.201957i 0.0362726i −0.999836 0.0181363i \(-0.994227\pi\)
0.999836 0.0181363i \(-0.00577328\pi\)
\(32\) 0.870977 + 5.58940i 0.153968 + 0.988076i
\(33\) 0 0
\(34\) 4.79329 2.63202i 0.822042 0.451387i
\(35\) 2.64607 + 1.76805i 0.447267 + 0.298854i
\(36\) 0 0
\(37\) −8.82594 1.75559i −1.45098 0.288617i −0.594204 0.804314i \(-0.702533\pi\)
−0.856771 + 0.515697i \(0.827533\pi\)
\(38\) −8.16299 0.711098i −1.32421 0.115355i
\(39\) 0 0
\(40\) −1.93647 + 1.12092i −0.306183 + 0.177232i
\(41\) −7.85196 + 3.25239i −1.22627 + 0.507938i −0.899398 0.437131i \(-0.855995\pi\)
−0.326872 + 0.945069i \(0.605995\pi\)
\(42\) 0 0
\(43\) 1.06440 + 1.59299i 0.162320 + 0.242929i 0.903710 0.428146i \(-0.140833\pi\)
−0.741390 + 0.671074i \(0.765833\pi\)
\(44\) 4.41071 0.0995378i 0.664940 0.0150059i
\(45\) 0 0
\(46\) −3.88273 + 0.426695i −0.572477 + 0.0629128i
\(47\) 7.56082 7.56082i 1.10286 1.10286i 0.108795 0.994064i \(-0.465301\pi\)
0.994064 0.108795i \(-0.0346993\pi\)
\(48\) 0 0
\(49\) −6.49382 6.49382i −0.927688 0.927688i
\(50\) 4.82586 + 3.87020i 0.682479 + 0.547329i
\(51\) 0 0
\(52\) −2.07557 + 5.34913i −0.287829 + 0.741791i
\(53\) −11.1942 + 7.47973i −1.53764 + 1.02742i −0.557256 + 0.830341i \(0.688146\pi\)
−0.980387 + 0.197080i \(0.936854\pi\)
\(54\) 0 0
\(55\) 0.667799 + 1.61221i 0.0900460 + 0.217390i
\(56\) 10.7705 3.66955i 1.43927 0.490364i
\(57\) 0 0
\(58\) 3.24034 + 3.85875i 0.425477 + 0.506679i
\(59\) 1.71321 8.61290i 0.223041 1.12130i −0.693221 0.720725i \(-0.743809\pi\)
0.916262 0.400579i \(-0.131191\pi\)
\(60\) 0 0
\(61\) −2.32214 + 3.47533i −0.297320 + 0.444970i −0.949810 0.312826i \(-0.898724\pi\)
0.652491 + 0.757797i \(0.273724\pi\)
\(62\) 0.0798198 0.274231i 0.0101371 0.0348273i
\(63\) 0 0
\(64\) −1.02644 + 7.93388i −0.128305 + 0.991735i
\(65\) −2.26947 −0.281493
\(66\) 0 0
\(67\) 5.15244 7.71118i 0.629471 0.942070i −0.370442 0.928856i \(-0.620794\pi\)
0.999913 0.0132144i \(-0.00420639\pi\)
\(68\) 7.54888 1.67946i 0.915436 0.203665i
\(69\) 0 0
\(70\) 2.89421 + 3.44657i 0.345925 + 0.411944i
\(71\) −1.98817 + 4.79986i −0.235952 + 0.569639i −0.996857 0.0792247i \(-0.974756\pi\)
0.760905 + 0.648864i \(0.224756\pi\)
\(72\) 0 0
\(73\) −6.11102 14.7533i −0.715240 1.72674i −0.686472 0.727157i \(-0.740841\pi\)
−0.0287686 0.999586i \(-0.509159\pi\)
\(74\) −11.2906 5.87213i −1.31250 0.682622i
\(75\) 0 0
\(76\) −10.8032 4.19184i −1.23921 0.480837i
\(77\) −1.73126 8.70365i −0.197296 0.991873i
\(78\) 0 0
\(79\) −2.91841 2.91841i −0.328346 0.328346i 0.523611 0.851957i \(-0.324585\pi\)
−0.851957 + 0.523611i \(0.824585\pi\)
\(80\) −3.07248 + 0.756698i −0.343514 + 0.0846014i
\(81\) 0 0
\(82\) −11.9473 + 1.31296i −1.31936 + 0.144992i
\(83\) 0.190374 0.0378677i 0.0208962 0.00415652i −0.184631 0.982808i \(-0.559109\pi\)
0.205527 + 0.978651i \(0.434109\pi\)
\(84\) 0 0
\(85\) 1.69941 + 2.54335i 0.184327 + 0.275865i
\(86\) 0.815713 + 2.58375i 0.0879606 + 0.278612i
\(87\) 0 0
\(88\) 6.02849 + 1.60809i 0.642639 + 0.171423i
\(89\) −0.659812 0.273303i −0.0699399 0.0289701i 0.347439 0.937702i \(-0.387051\pi\)
−0.417379 + 0.908732i \(0.637051\pi\)
\(90\) 0 0
\(91\) 11.3193 + 2.25155i 1.18659 + 0.236027i
\(92\) −5.44086 0.955181i −0.567249 0.0995845i
\(93\) 0 0
\(94\) 13.2548 7.27829i 1.36713 0.750699i
\(95\) 4.58345i 0.470252i
\(96\) 0 0
\(97\) 2.80442i 0.284746i 0.989813 + 0.142373i \(0.0454732\pi\)
−0.989813 + 0.142373i \(0.954527\pi\)
\(98\) −6.25116 11.3843i −0.631463 1.14999i
\(99\) 0 0
\(100\) 5.02323 + 7.16253i 0.502323 + 0.716253i
\(101\) −6.80113 1.35283i −0.676738 0.134612i −0.155257 0.987874i \(-0.549620\pi\)
−0.521481 + 0.853263i \(0.674620\pi\)
\(102\) 0 0
\(103\) −12.7910 5.29822i −1.26034 0.522049i −0.350324 0.936629i \(-0.613929\pi\)
−0.910013 + 0.414580i \(0.863929\pi\)
\(104\) −4.93248 + 6.44306i −0.483669 + 0.631794i
\(105\) 0 0
\(106\) −18.1564 + 5.73216i −1.76351 + 0.556756i
\(107\) 6.64476 + 9.94459i 0.642373 + 0.961380i 0.999625 + 0.0273716i \(0.00871374\pi\)
−0.357252 + 0.934008i \(0.616286\pi\)
\(108\) 0 0
\(109\) 4.24802 0.844985i 0.406887 0.0809348i 0.0125963 0.999921i \(-0.495990\pi\)
0.394291 + 0.918986i \(0.370990\pi\)
\(110\) 0.269585 + 2.45309i 0.0257039 + 0.233893i
\(111\) 0 0
\(112\) 16.0752 0.725916i 1.51896 0.0685926i
\(113\) 4.08315 + 4.08315i 0.384110 + 0.384110i 0.872581 0.488470i \(-0.162445\pi\)
−0.488470 + 0.872581i \(0.662445\pi\)
\(114\) 0 0
\(115\) −0.426266 2.14299i −0.0397496 0.199834i
\(116\) 2.87483 + 6.52034i 0.266922 + 0.605399i
\(117\) 0 0
\(118\) 5.73039 11.0180i 0.527526 1.01429i
\(119\) −5.95280 14.3713i −0.545692 1.31742i
\(120\) 0 0
\(121\) −2.34735 + 5.66701i −0.213396 + 0.515182i
\(122\) −4.52671 + 3.80124i −0.409829 + 0.344148i
\(123\) 0 0
\(124\) 0.216769 0.340820i 0.0194664 0.0306066i
\(125\) −4.11993 + 6.16591i −0.368498 + 0.551496i
\(126\) 0 0
\(127\) −7.68361 −0.681810 −0.340905 0.940098i \(-0.610733\pi\)
−0.340905 + 0.940098i \(0.610733\pi\)
\(128\) −4.52947 + 10.3674i −0.400353 + 0.916361i
\(129\) 0 0
\(130\) −3.08163 0.896964i −0.270277 0.0786690i
\(131\) −3.11524 + 4.66229i −0.272180 + 0.407346i −0.942228 0.334971i \(-0.891273\pi\)
0.670048 + 0.742318i \(0.266273\pi\)
\(132\) 0 0
\(133\) −4.54726 + 22.8606i −0.394298 + 1.98227i
\(134\) 10.0440 8.43432i 0.867670 0.728614i
\(135\) 0 0
\(136\) 10.9141 + 0.703071i 0.935878 + 0.0602879i
\(137\) −3.02379 7.30007i −0.258339 0.623687i 0.740489 0.672068i \(-0.234594\pi\)
−0.998829 + 0.0483813i \(0.984594\pi\)
\(138\) 0 0
\(139\) −0.706120 + 0.471814i −0.0598923 + 0.0400188i −0.585156 0.810921i \(-0.698967\pi\)
0.525264 + 0.850940i \(0.323967\pi\)
\(140\) 2.56775 + 5.82386i 0.217015 + 0.492206i
\(141\) 0 0
\(142\) −4.59672 + 5.73177i −0.385748 + 0.481000i
\(143\) 4.47489 + 4.47489i 0.374209 + 0.374209i
\(144\) 0 0
\(145\) −1.99304 + 1.99304i −0.165513 + 0.165513i
\(146\) −2.46696 22.4482i −0.204167 1.85783i
\(147\) 0 0
\(148\) −13.0102 12.4359i −1.06943 1.02223i
\(149\) −0.819641 1.22668i −0.0671476 0.100493i 0.796376 0.604802i \(-0.206748\pi\)
−0.863524 + 0.504308i \(0.831748\pi\)
\(150\) 0 0
\(151\) −5.92201 + 2.45298i −0.481927 + 0.199621i −0.610401 0.792092i \(-0.708992\pi\)
0.128475 + 0.991713i \(0.458992\pi\)
\(152\) −13.0125 9.96170i −1.05545 0.808000i
\(153\) 0 0
\(154\) 1.08913 12.5026i 0.0877649 1.00749i
\(155\) 0.156693 + 0.0311682i 0.0125859 + 0.00250349i
\(156\) 0 0
\(157\) −4.13123 2.76040i −0.329708 0.220304i 0.379687 0.925115i \(-0.376032\pi\)
−0.709395 + 0.704811i \(0.751032\pi\)
\(158\) −2.80935 5.11624i −0.223500 0.407026i
\(159\) 0 0
\(160\) −4.47108 0.186849i −0.353470 0.0147717i
\(161\) 11.1114i 0.875698i
\(162\) 0 0
\(163\) 18.6548 + 12.4647i 1.46115 + 0.976311i 0.995836 + 0.0911673i \(0.0290598\pi\)
0.465317 + 0.885144i \(0.345940\pi\)
\(164\) −16.7418 2.93913i −1.30731 0.229508i
\(165\) 0 0
\(166\) 0.273468 + 0.0238224i 0.0212252 + 0.00184898i
\(167\) 1.14501 + 0.474279i 0.0886036 + 0.0367008i 0.426545 0.904466i \(-0.359731\pi\)
−0.337941 + 0.941167i \(0.609731\pi\)
\(168\) 0 0
\(169\) 4.40663 1.82529i 0.338972 0.140407i
\(170\) 1.30236 + 4.12518i 0.0998863 + 0.316387i
\(171\) 0 0
\(172\) 0.0864500 + 3.83077i 0.00659175 + 0.292093i
\(173\) 3.23710 0.643899i 0.246112 0.0489547i −0.0704926 0.997512i \(-0.522457\pi\)
0.316605 + 0.948558i \(0.397457\pi\)
\(174\) 0 0
\(175\) 12.4429 12.4429i 0.940596 0.940596i
\(176\) 7.55029 + 4.56621i 0.569125 + 0.344191i
\(177\) 0 0
\(178\) −0.787916 0.631886i −0.0590568 0.0473619i
\(179\) −1.34019 6.73758i −0.100170 0.503591i −0.997998 0.0632437i \(-0.979855\pi\)
0.897828 0.440347i \(-0.145145\pi\)
\(180\) 0 0
\(181\) 5.57875 3.72760i 0.414665 0.277070i −0.330688 0.943740i \(-0.607281\pi\)
0.745353 + 0.666670i \(0.232281\pi\)
\(182\) 14.4802 + 7.53104i 1.07334 + 0.558238i
\(183\) 0 0
\(184\) −7.01042 3.44740i −0.516815 0.254146i
\(185\) 2.72423 6.57686i 0.200289 0.483541i
\(186\) 0 0
\(187\) 1.66406 8.36578i 0.121688 0.611767i
\(188\) 20.8749 4.64420i 1.52246 0.338713i
\(189\) 0 0
\(190\) 1.81152 6.22370i 0.131422 0.451515i
\(191\) −12.7735 −0.924258 −0.462129 0.886813i \(-0.652914\pi\)
−0.462129 + 0.886813i \(0.652914\pi\)
\(192\) 0 0
\(193\) 19.9599 1.43675 0.718373 0.695659i \(-0.244887\pi\)
0.718373 + 0.695659i \(0.244887\pi\)
\(194\) −1.10839 + 3.80802i −0.0795780 + 0.273400i
\(195\) 0 0
\(196\) −3.98880 17.9289i −0.284914 1.28064i
\(197\) −1.38429 + 6.95930i −0.0986267 + 0.495830i 0.899622 + 0.436670i \(0.143842\pi\)
−0.998249 + 0.0591600i \(0.981158\pi\)
\(198\) 0 0
\(199\) −2.35849 + 5.69389i −0.167189 + 0.403629i −0.985162 0.171627i \(-0.945098\pi\)
0.817973 + 0.575256i \(0.195098\pi\)
\(200\) 3.99001 + 11.7111i 0.282136 + 0.828097i
\(201\) 0 0
\(202\) −8.70033 4.52498i −0.612153 0.318376i
\(203\) 11.9179 7.96327i 0.836471 0.558912i
\(204\) 0 0
\(205\) −1.31164 6.59406i −0.0916090 0.460549i
\(206\) −15.2744 12.2497i −1.06422 0.853474i
\(207\) 0 0
\(208\) −9.24413 + 6.79933i −0.640965 + 0.471449i
\(209\) −9.03754 + 9.03754i −0.625140 + 0.625140i
\(210\) 0 0
\(211\) 22.5419 4.48387i 1.55185 0.308682i 0.656599 0.754240i \(-0.271995\pi\)
0.895253 + 0.445558i \(0.146995\pi\)
\(212\) −26.9195 + 0.607499i −1.84884 + 0.0417232i
\(213\) 0 0
\(214\) 5.09227 + 16.1296i 0.348100 + 1.10260i
\(215\) −1.40023 + 0.579993i −0.0954947 + 0.0395552i
\(216\) 0 0
\(217\) −0.750608 0.310912i −0.0509546 0.0211061i
\(218\) 6.10220 + 0.531577i 0.413293 + 0.0360030i
\(219\) 0 0
\(220\) −0.603480 + 3.43751i −0.0406866 + 0.231757i
\(221\) 9.22353 + 6.16297i 0.620442 + 0.414566i
\(222\) 0 0
\(223\) 14.8044i 0.991375i 0.868501 + 0.495688i \(0.165084\pi\)
−0.868501 + 0.495688i \(0.834916\pi\)
\(224\) 22.1148 + 5.36771i 1.47761 + 0.358645i
\(225\) 0 0
\(226\) 3.93057 + 7.15814i 0.261458 + 0.476153i
\(227\) 9.66687 + 6.45920i 0.641613 + 0.428712i 0.833359 0.552733i \(-0.186415\pi\)
−0.191746 + 0.981445i \(0.561415\pi\)
\(228\) 0 0
\(229\) −12.7938 2.54484i −0.845435 0.168168i −0.246677 0.969098i \(-0.579339\pi\)
−0.598758 + 0.800930i \(0.704339\pi\)
\(230\) 0.268163 3.07836i 0.0176821 0.202981i
\(231\) 0 0
\(232\) 1.32659 + 9.98995i 0.0870949 + 0.655873i
\(233\) 15.7633 6.52939i 1.03269 0.427755i 0.199008 0.979998i \(-0.436228\pi\)
0.833683 + 0.552243i \(0.186228\pi\)
\(234\) 0 0
\(235\) 4.69937 + 7.03310i 0.306553 + 0.458789i
\(236\) 12.1358 12.6961i 0.789971 0.826449i
\(237\) 0 0
\(238\) −2.40309 21.8670i −0.155769 1.41743i
\(239\) −4.07054 + 4.07054i −0.263301 + 0.263301i −0.826394 0.563093i \(-0.809611\pi\)
0.563093 + 0.826394i \(0.309611\pi\)
\(240\) 0 0
\(241\) 8.38424 + 8.38424i 0.540076 + 0.540076i 0.923551 0.383475i \(-0.125273\pi\)
−0.383475 + 0.923551i \(0.625273\pi\)
\(242\) −5.42716 + 6.76727i −0.348871 + 0.435017i
\(243\) 0 0
\(244\) −7.64902 + 3.37247i −0.489678 + 0.215900i
\(245\) 6.04057 4.03618i 0.385918 0.257862i
\(246\) 0 0
\(247\) −6.36097 15.3567i −0.404739 0.977126i
\(248\) 0.429045 0.377114i 0.0272444 0.0239467i
\(249\) 0 0
\(250\) −8.03126 + 6.74414i −0.507942 + 0.426537i
\(251\) 3.80254 19.1167i 0.240014 1.20663i −0.653264 0.757130i \(-0.726601\pi\)
0.893278 0.449504i \(-0.148399\pi\)
\(252\) 0 0
\(253\) −3.38499 + 5.06599i −0.212812 + 0.318496i
\(254\) −10.4333 3.03680i −0.654643 0.190546i
\(255\) 0 0
\(256\) −10.2479 + 12.2874i −0.640496 + 0.767961i
\(257\) 10.7354 0.669657 0.334828 0.942279i \(-0.391322\pi\)
0.334828 + 0.942279i \(0.391322\pi\)
\(258\) 0 0
\(259\) −20.1124 + 30.1004i −1.24972 + 1.87034i
\(260\) −3.82992 2.43591i −0.237522 0.151069i
\(261\) 0 0
\(262\) −6.07276 + 5.09951i −0.375176 + 0.315049i
\(263\) 6.13406 14.8089i 0.378242 0.913158i −0.614053 0.789265i \(-0.710462\pi\)
0.992296 0.123893i \(-0.0395380\pi\)
\(264\) 0 0
\(265\) −4.07571 9.83964i −0.250369 0.604444i
\(266\) −15.2098 + 29.2444i −0.932572 + 1.79309i
\(267\) 0 0
\(268\) 16.9719 7.48295i 1.03672 0.457094i
\(269\) 6.17273 + 31.0324i 0.376358 + 1.89208i 0.446925 + 0.894571i \(0.352519\pi\)
−0.0705674 + 0.997507i \(0.522481\pi\)
\(270\) 0 0
\(271\) 2.32497 + 2.32497i 0.141232 + 0.141232i 0.774188 0.632956i \(-0.218159\pi\)
−0.632956 + 0.774188i \(0.718159\pi\)
\(272\) 14.5420 + 5.26827i 0.881739 + 0.319436i
\(273\) 0 0
\(274\) −1.22068 11.1076i −0.0737437 0.671034i
\(275\) 9.46373 1.88245i 0.570684 0.113516i
\(276\) 0 0
\(277\) 7.64613 + 11.4432i 0.459411 + 0.687557i 0.986778 0.162081i \(-0.0518204\pi\)
−0.527366 + 0.849638i \(0.676820\pi\)
\(278\) −1.14529 + 0.361579i −0.0686899 + 0.0216860i
\(279\) 0 0
\(280\) 1.18489 + 8.92286i 0.0708106 + 0.533243i
\(281\) −5.95182 2.46532i −0.355056 0.147069i 0.198024 0.980197i \(-0.436548\pi\)
−0.553080 + 0.833128i \(0.686548\pi\)
\(282\) 0 0
\(283\) −17.8358 3.54776i −1.06023 0.210893i −0.365976 0.930624i \(-0.619265\pi\)
−0.694252 + 0.719732i \(0.744265\pi\)
\(284\) −8.50709 + 5.96620i −0.504803 + 0.354029i
\(285\) 0 0
\(286\) 4.30767 + 7.84490i 0.254718 + 0.463879i
\(287\) 34.1901i 2.01818i
\(288\) 0 0
\(289\) 2.04845i 0.120497i
\(290\) −3.49399 + 1.91856i −0.205174 + 0.112662i
\(291\) 0 0
\(292\) 5.52243 31.4566i 0.323176 1.84086i
\(293\) −2.52796 0.502842i −0.147685 0.0293763i 0.120694 0.992690i \(-0.461488\pi\)
−0.268379 + 0.963313i \(0.586488\pi\)
\(294\) 0 0
\(295\) 6.41812 + 2.65847i 0.373677 + 0.154782i
\(296\) −12.7510 22.0283i −0.741136 1.28037i
\(297\) 0 0
\(298\) −0.628138 1.98961i −0.0363871 0.115255i
\(299\) −4.40226 6.58845i −0.254589 0.381020i
\(300\) 0 0
\(301\) 7.55925 1.50363i 0.435708 0.0866677i
\(302\) −9.01078 + 0.990246i −0.518512 + 0.0569822i
\(303\) 0 0
\(304\) −13.7320 18.6696i −0.787585 1.07077i
\(305\) −2.33804 2.33804i −0.133876 0.133876i
\(306\) 0 0
\(307\) 1.65226 + 8.30646i 0.0942993 + 0.474075i 0.998860 + 0.0477304i \(0.0151988\pi\)
−0.904561 + 0.426344i \(0.859801\pi\)
\(308\) 6.42032 16.5464i 0.365832 0.942818i
\(309\) 0 0
\(310\) 0.200449 + 0.104252i 0.0113848 + 0.00592113i
\(311\) 0.633352 + 1.52905i 0.0359141 + 0.0867042i 0.940819 0.338910i \(-0.110058\pi\)
−0.904905 + 0.425614i \(0.860058\pi\)
\(312\) 0 0
\(313\) 6.07939 14.6769i 0.343628 0.829590i −0.653715 0.756740i \(-0.726791\pi\)
0.997343 0.0728497i \(-0.0232094\pi\)
\(314\) −4.51865 5.38104i −0.255002 0.303670i
\(315\) 0 0
\(316\) −1.79262 8.05750i −0.100843 0.453270i
\(317\) 8.81780 13.1968i 0.495257 0.741204i −0.496680 0.867934i \(-0.665448\pi\)
0.991937 + 0.126729i \(0.0404479\pi\)
\(318\) 0 0
\(319\) 7.85966 0.440057
\(320\) −5.99727 2.02082i −0.335258 0.112968i
\(321\) 0 0
\(322\) −4.39155 + 15.0877i −0.244732 + 0.840805i
\(323\) −12.4468 + 18.6280i −0.692559 + 1.03649i
\(324\) 0 0
\(325\) −2.44817 + 12.3078i −0.135800 + 0.682714i
\(326\) 20.4042 + 24.2983i 1.13008 + 1.34576i
\(327\) 0 0
\(328\) −21.5714 10.6078i −1.19108 0.585718i
\(329\) −16.4612 39.7409i −0.907536 2.19099i
\(330\) 0 0
\(331\) 17.9691 12.0066i 0.987671 0.659941i 0.0468703 0.998901i \(-0.485075\pi\)
0.940801 + 0.338960i \(0.110075\pi\)
\(332\) 0.361917 + 0.140431i 0.0198628 + 0.00770713i
\(333\) 0 0
\(334\) 1.36732 + 1.09655i 0.0748164 + 0.0600005i
\(335\) 5.18771 + 5.18771i 0.283435 + 0.283435i
\(336\) 0 0
\(337\) 0.918442 0.918442i 0.0500307 0.0500307i −0.681649 0.731680i \(-0.738737\pi\)
0.731680 + 0.681649i \(0.238737\pi\)
\(338\) 6.70501 0.736852i 0.364705 0.0400795i
\(339\) 0 0
\(340\) 0.138025 + 6.11616i 0.00748547 + 0.331696i
\(341\) −0.247507 0.370421i −0.0134033 0.0200594i
\(342\) 0 0
\(343\) −8.11589 + 3.36171i −0.438217 + 0.181515i
\(344\) −1.39665 + 5.23583i −0.0753024 + 0.282297i
\(345\) 0 0
\(346\) 4.65003 + 0.405075i 0.249987 + 0.0217770i
\(347\) 0.170754 + 0.0339651i 0.00916656 + 0.00182334i 0.199671 0.979863i \(-0.436013\pi\)
−0.190505 + 0.981686i \(0.561013\pi\)
\(348\) 0 0
\(349\) 0.883430 + 0.590289i 0.0472889 + 0.0315974i 0.578990 0.815335i \(-0.303447\pi\)
−0.531701 + 0.846932i \(0.678447\pi\)
\(350\) 21.8136 11.9780i 1.16599 0.640249i
\(351\) 0 0
\(352\) 8.44756 + 9.18440i 0.450256 + 0.489530i
\(353\) 0.638175i 0.0339666i 0.999856 + 0.0169833i \(0.00540622\pi\)
−0.999856 + 0.0169833i \(0.994594\pi\)
\(354\) 0 0
\(355\) −3.41725 2.28333i −0.181369 0.121187i
\(356\) −0.820141 1.16942i −0.0434674 0.0619793i
\(357\) 0 0
\(358\) 0.843109 9.67840i 0.0445597 0.511519i
\(359\) −14.2385 5.89779i −0.751480 0.311273i −0.0261347 0.999658i \(-0.508320\pi\)
−0.725345 + 0.688385i \(0.758320\pi\)
\(360\) 0 0
\(361\) 13.4610 5.57571i 0.708472 0.293459i
\(362\) 9.04844 2.85668i 0.475575 0.150144i
\(363\) 0 0
\(364\) 16.6856 + 15.9491i 0.874564 + 0.835962i
\(365\) 12.3898 2.46448i 0.648512 0.128997i
\(366\) 0 0
\(367\) 5.81483 5.81483i 0.303531 0.303531i −0.538862 0.842394i \(-0.681146\pi\)
0.842394 + 0.538862i \(0.181146\pi\)
\(368\) −8.15668 7.45183i −0.425196 0.388454i
\(369\) 0 0
\(370\) 6.29851 7.85378i 0.327444 0.408299i
\(371\) 10.5663 + 53.1202i 0.548573 + 2.75786i
\(372\) 0 0
\(373\) −4.87425 + 3.25687i −0.252379 + 0.168634i −0.675324 0.737521i \(-0.735996\pi\)
0.422945 + 0.906155i \(0.360996\pi\)
\(374\) 5.56598 10.7019i 0.287810 0.553382i
\(375\) 0 0
\(376\) 30.1807 + 1.94420i 1.55645 + 0.100264i
\(377\) −3.91167 + 9.44360i −0.201461 + 0.486370i
\(378\) 0 0
\(379\) 2.02175 10.1640i 0.103850 0.522090i −0.893482 0.449098i \(-0.851745\pi\)
0.997333 0.0729916i \(-0.0232546\pi\)
\(380\) 4.91960 7.73496i 0.252370 0.396795i
\(381\) 0 0
\(382\) −17.3447 5.04848i −0.887430 0.258303i
\(383\) 35.5967 1.81890 0.909452 0.415808i \(-0.136501\pi\)
0.909452 + 0.415808i \(0.136501\pi\)
\(384\) 0 0
\(385\) 7.02012 0.357778
\(386\) 27.1028 + 7.88877i 1.37950 + 0.401528i
\(387\) 0 0
\(388\) −3.01009 + 4.73269i −0.152814 + 0.240266i
\(389\) −6.65141 + 33.4389i −0.337240 + 1.69542i 0.324663 + 0.945830i \(0.394749\pi\)
−0.661903 + 0.749590i \(0.730251\pi\)
\(390\) 0 0
\(391\) −4.08707 + 9.86705i −0.206692 + 0.498998i
\(392\) 1.66983 25.9215i 0.0843390 1.30924i
\(393\) 0 0
\(394\) −4.63021 + 8.90267i −0.233267 + 0.448510i
\(395\) 2.71471 1.81391i 0.136592 0.0912679i
\(396\) 0 0
\(397\) 5.24522 + 26.3695i 0.263250 + 1.32345i 0.855546 + 0.517727i \(0.173222\pi\)
−0.592295 + 0.805721i \(0.701778\pi\)
\(398\) −5.45290 + 6.79938i −0.273329 + 0.340822i
\(399\) 0 0
\(400\) 0.789309 + 17.4790i 0.0394655 + 0.873950i
\(401\) 8.87445 8.87445i 0.443169 0.443169i −0.449907 0.893076i \(-0.648543\pi\)
0.893076 + 0.449907i \(0.148543\pi\)
\(402\) 0 0
\(403\) 0.568253 0.113032i 0.0283067 0.00563055i
\(404\) −10.0254 9.58294i −0.498784 0.476769i
\(405\) 0 0
\(406\) 19.3302 6.10272i 0.959341 0.302873i
\(407\) −18.3397 + 7.59655i −0.909064 + 0.376547i
\(408\) 0 0
\(409\) −10.8015 4.47412i −0.534099 0.221231i 0.0992984 0.995058i \(-0.468340\pi\)
−0.633398 + 0.773827i \(0.718340\pi\)
\(410\) 0.825149 9.47224i 0.0407512 0.467800i
\(411\) 0 0
\(412\) −15.8992 22.6703i −0.783295 1.11689i
\(413\) −29.3738 19.6269i −1.44539 0.965779i
\(414\) 0 0
\(415\) 0.153550i 0.00753747i
\(416\) −15.2396 + 5.57899i −0.747181 + 0.273533i
\(417\) 0 0
\(418\) −15.8437 + 8.69983i −0.774939 + 0.425523i
\(419\) −13.3738 8.93607i −0.653351 0.436555i 0.184219 0.982885i \(-0.441025\pi\)
−0.837570 + 0.546330i \(0.816025\pi\)
\(420\) 0 0
\(421\) 25.6227 + 5.09667i 1.24877 + 0.248397i 0.774836 0.632162i \(-0.217832\pi\)
0.473938 + 0.880558i \(0.342832\pi\)
\(422\) 32.3810 + 2.82079i 1.57628 + 0.137314i
\(423\) 0 0
\(424\) −36.7931 9.81451i −1.78683 0.476635i
\(425\) 15.6263 6.47265i 0.757989 0.313969i
\(426\) 0 0
\(427\) 9.34172 + 13.9809i 0.452077 + 0.676582i
\(428\) 0.539683 + 23.9144i 0.0260866 + 1.15595i
\(429\) 0 0
\(430\) −2.13055 + 0.234138i −0.102744 + 0.0112911i
\(431\) 6.74058 6.74058i 0.324682 0.324682i −0.525878 0.850560i \(-0.676263\pi\)
0.850560 + 0.525878i \(0.176263\pi\)
\(432\) 0 0
\(433\) −8.98452 8.98452i −0.431769 0.431769i 0.457461 0.889230i \(-0.348759\pi\)
−0.889230 + 0.457461i \(0.848759\pi\)
\(434\) −0.896341 0.718840i −0.0430258 0.0345054i
\(435\) 0 0
\(436\) 8.07586 + 3.13359i 0.386763 + 0.150072i
\(437\) 13.3061 8.89086i 0.636518 0.425308i
\(438\) 0 0
\(439\) −12.2357 29.5395i −0.583976 1.40984i −0.889181 0.457556i \(-0.848725\pi\)
0.305205 0.952287i \(-0.401275\pi\)
\(440\) −2.17806 + 4.42916i −0.103835 + 0.211152i
\(441\) 0 0
\(442\) 10.0885 + 12.0139i 0.479861 + 0.571443i
\(443\) −5.01357 + 25.2049i −0.238202 + 1.19752i 0.657704 + 0.753277i \(0.271528\pi\)
−0.895906 + 0.444244i \(0.853472\pi\)
\(444\) 0 0
\(445\) 0.313877 0.469751i 0.0148792 0.0222683i
\(446\) −5.85115 + 20.1023i −0.277060 + 0.951873i
\(447\) 0 0
\(448\) 27.9074 + 16.0291i 1.31850 + 0.757303i
\(449\) 26.9484 1.27177 0.635887 0.771782i \(-0.280635\pi\)
0.635887 + 0.771782i \(0.280635\pi\)
\(450\) 0 0
\(451\) −10.4158 + 15.5883i −0.490459 + 0.734024i
\(452\) 2.50806 + 11.2733i 0.117969 + 0.530250i
\(453\) 0 0
\(454\) 10.5734 + 12.5914i 0.496235 + 0.590942i
\(455\) −3.49383 + 8.43486i −0.163793 + 0.395432i
\(456\) 0 0
\(457\) 4.39604 + 10.6130i 0.205638 + 0.496454i 0.992727 0.120385i \(-0.0384128\pi\)
−0.787089 + 0.616839i \(0.788413\pi\)
\(458\) −16.3664 8.51203i −0.764750 0.397741i
\(459\) 0 0
\(460\) 1.58079 4.07400i 0.0737047 0.189951i
\(461\) −3.51862 17.6893i −0.163878 0.823872i −0.972023 0.234888i \(-0.924528\pi\)
0.808144 0.588985i \(-0.200472\pi\)
\(462\) 0 0
\(463\) 9.97845 + 9.97845i 0.463738 + 0.463738i 0.899879 0.436141i \(-0.143655\pi\)
−0.436141 + 0.899879i \(0.643655\pi\)
\(464\) −2.14701 + 14.0893i −0.0996726 + 0.654079i
\(465\) 0 0
\(466\) 23.9851 2.63586i 1.11109 0.122104i
\(467\) −35.3990 + 7.04130i −1.63807 + 0.325832i −0.926360 0.376640i \(-0.877079\pi\)
−0.711711 + 0.702473i \(0.752079\pi\)
\(468\) 0 0
\(469\) −20.7277 31.0212i −0.957117 1.43243i
\(470\) 3.60140 + 11.4073i 0.166120 + 0.526181i
\(471\) 0 0
\(472\) 21.4966 12.4432i 0.989462 0.572745i
\(473\) 3.90455 + 1.61732i 0.179531 + 0.0743644i
\(474\) 0 0
\(475\) −24.8570 4.94437i −1.14052 0.226863i
\(476\) 5.37945 30.6422i 0.246567 1.40448i
\(477\) 0 0
\(478\) −7.13604 + 3.91843i −0.326395 + 0.179225i
\(479\) 37.7961i 1.72695i −0.504393 0.863474i \(-0.668284\pi\)
0.504393 0.863474i \(-0.331716\pi\)
\(480\) 0 0
\(481\) 25.8163i 1.17712i
\(482\) 8.07094 + 14.6984i 0.367621 + 0.669492i
\(483\) 0 0
\(484\) −10.0440 + 7.04405i −0.456544 + 0.320184i
\(485\) −2.17587 0.432808i −0.0988012 0.0196528i
\(486\) 0 0
\(487\) 17.7628 + 7.35758i 0.804908 + 0.333404i 0.746920 0.664914i \(-0.231532\pi\)
0.0579876 + 0.998317i \(0.481532\pi\)
\(488\) −11.7192 + 1.55622i −0.530504 + 0.0704469i
\(489\) 0 0
\(490\) 9.79750 3.09316i 0.442606 0.139735i
\(491\) −19.8604 29.7231i −0.896285 1.34139i −0.939582 0.342323i \(-0.888786\pi\)
0.0432969 0.999062i \(-0.486214\pi\)
\(492\) 0 0
\(493\) 13.5124 2.68778i 0.608566 0.121051i
\(494\) −2.56787 23.3664i −0.115534 1.05130i
\(495\) 0 0
\(496\) 0.731632 0.342497i 0.0328512 0.0153786i
\(497\) 14.7787 + 14.7787i 0.662916 + 0.662916i
\(498\) 0 0
\(499\) −5.52124 27.7572i −0.247165 1.24258i −0.882488 0.470335i \(-0.844133\pi\)
0.635323 0.772246i \(-0.280867\pi\)
\(500\) −13.5708 + 5.98342i −0.606907 + 0.267587i
\(501\) 0 0
\(502\) 12.7188 24.4549i 0.567669 1.09148i
\(503\) −3.74555 9.04255i −0.167006 0.403187i 0.818114 0.575056i \(-0.195020\pi\)
−0.985120 + 0.171868i \(0.945020\pi\)
\(504\) 0 0
\(505\) 2.09925 5.06803i 0.0934153 0.225524i
\(506\) −6.59859 + 5.54108i −0.293343 + 0.246331i
\(507\) 0 0
\(508\) −12.9667 8.24712i −0.575306 0.365907i
\(509\) 13.6199 20.3836i 0.603691 0.903488i −0.396201 0.918164i \(-0.629672\pi\)
0.999892 + 0.0146761i \(0.00467173\pi\)
\(510\) 0 0
\(511\) −64.2409 −2.84185
\(512\) −18.7717 + 12.6343i −0.829598 + 0.558361i
\(513\) 0 0
\(514\) 14.5772 + 4.24297i 0.642974 + 0.187149i
\(515\) 6.08479 9.10653i 0.268128 0.401282i
\(516\) 0 0
\(517\) 4.60160 23.1338i 0.202378 1.01742i
\(518\) −39.2065 + 32.9231i −1.72263 + 1.44656i
\(519\) 0 0
\(520\) −4.23776 4.82134i −0.185838 0.211430i
\(521\) 1.21410 + 2.93109i 0.0531905 + 0.128413i 0.948241 0.317552i \(-0.102861\pi\)
−0.895050 + 0.445965i \(0.852861\pi\)
\(522\) 0 0
\(523\) 32.5809 21.7698i 1.42466 0.951929i 0.425772 0.904830i \(-0.360003\pi\)
0.998890 0.0470985i \(-0.0149975\pi\)
\(524\) −10.2615 + 4.52430i −0.448274 + 0.197645i
\(525\) 0 0
\(526\) 14.1822 17.6841i 0.618372 0.771065i
\(527\) −0.552189 0.552189i −0.0240537 0.0240537i
\(528\) 0 0
\(529\) −10.8691 + 10.8691i −0.472568 + 0.472568i
\(530\) −1.64533 14.9717i −0.0714685 0.650330i
\(531\) 0 0
\(532\) −32.2111 + 33.6985i −1.39653 + 1.46101i
\(533\) −13.5459 20.2729i −0.586740 0.878118i
\(534\) 0 0
\(535\) −8.74123 + 3.62073i −0.377916 + 0.156538i
\(536\) 26.0030 3.45300i 1.12316 0.149147i
\(537\) 0 0
\(538\) −3.88324 + 44.5774i −0.167419 + 1.92187i
\(539\) −19.8691 3.95221i −0.855824 0.170234i
\(540\) 0 0
\(541\) −15.3762 10.2741i −0.661075 0.441716i 0.179247 0.983804i \(-0.442634\pi\)
−0.840322 + 0.542088i \(0.817634\pi\)
\(542\) 2.23809 + 4.07590i 0.0961343 + 0.175075i
\(543\) 0 0
\(544\) 17.6639 + 12.9010i 0.757333 + 0.553128i
\(545\) 3.42633i 0.146768i
\(546\) 0 0
\(547\) −12.2578 8.19037i −0.524104 0.350195i 0.265204 0.964192i \(-0.414561\pi\)
−0.789308 + 0.613997i \(0.789561\pi\)
\(548\) 2.73255 15.5650i 0.116729 0.664905i
\(549\) 0 0
\(550\) 13.5945 + 1.18425i 0.579670 + 0.0504964i
\(551\) −19.0724 7.90005i −0.812512 0.336553i
\(552\) 0 0
\(553\) −15.3396 + 6.35388i −0.652307 + 0.270194i
\(554\) 5.85967 + 18.5603i 0.248954 + 0.788553i
\(555\) 0 0
\(556\) −1.69805 + 0.0383205i −0.0720135 + 0.00162515i
\(557\) 18.6390 3.70752i 0.789758 0.157093i 0.216299 0.976327i \(-0.430601\pi\)
0.573459 + 0.819234i \(0.305601\pi\)
\(558\) 0 0
\(559\) −3.88650 + 3.88650i −0.164382 + 0.164382i
\(560\) −1.91768 + 12.5843i −0.0810366 + 0.531785i
\(561\) 0 0
\(562\) −7.10738 5.69992i −0.299807 0.240436i
\(563\) −5.99694 30.1487i −0.252741 1.27061i −0.873582 0.486678i \(-0.838209\pi\)
0.620841 0.783937i \(-0.286791\pi\)
\(564\) 0 0
\(565\) −3.79816 + 2.53785i −0.159790 + 0.106768i
\(566\) −22.8164 11.8666i −0.959045 0.498792i
\(567\) 0 0
\(568\) −13.9095 + 4.73902i −0.583629 + 0.198845i
\(569\) −1.35295 + 3.26632i −0.0567187 + 0.136931i −0.949699 0.313166i \(-0.898610\pi\)
0.892980 + 0.450097i \(0.148610\pi\)
\(570\) 0 0
\(571\) −7.21231 + 36.2587i −0.301826 + 1.51738i 0.470641 + 0.882325i \(0.344023\pi\)
−0.772467 + 0.635055i \(0.780977\pi\)
\(572\) 2.74868 + 12.3548i 0.114928 + 0.516581i
\(573\) 0 0
\(574\) −13.5130 + 46.4255i −0.564022 + 1.93776i
\(575\) −12.0817 −0.503842
\(576\) 0 0
\(577\) −13.4288 −0.559050 −0.279525 0.960138i \(-0.590177\pi\)
−0.279525 + 0.960138i \(0.590177\pi\)
\(578\) −0.809610 + 2.78151i −0.0336753 + 0.115696i
\(579\) 0 0
\(580\) −5.50263 + 1.22422i −0.228484 + 0.0508328i
\(581\) 0.152338 0.765853i 0.00632003 0.0317729i
\(582\) 0 0
\(583\) −11.3652 + 27.4380i −0.470698 + 1.13636i
\(584\) 19.9313 40.5312i 0.824765 1.67719i
\(585\) 0 0
\(586\) −3.23388 1.68192i −0.133590 0.0694793i
\(587\) −4.86470 + 3.25049i −0.200788 + 0.134162i −0.651899 0.758305i \(-0.726028\pi\)
0.451112 + 0.892467i \(0.351028\pi\)
\(588\) 0 0
\(589\) 0.228282 + 1.14765i 0.00940619 + 0.0472881i
\(590\) 7.66421 + 6.14648i 0.315531 + 0.253046i
\(591\) 0 0
\(592\) −8.60781 34.9510i −0.353779 1.43648i
\(593\) −22.6469 + 22.6469i −0.929995 + 0.929995i −0.997705 0.0677097i \(-0.978431\pi\)
0.0677097 + 0.997705i \(0.478431\pi\)
\(594\) 0 0
\(595\) 12.0690 2.40068i 0.494781 0.0984181i
\(596\) −0.0665707 2.94988i −0.00272684 0.120832i
\(597\) 0 0
\(598\) −3.37371 10.6861i −0.137961 0.436988i
\(599\) −40.9799 + 16.9744i −1.67439 + 0.693557i −0.999035 0.0439314i \(-0.986012\pi\)
−0.675360 + 0.737488i \(0.736012\pi\)
\(600\) 0 0
\(601\) 19.0417 + 7.88732i 0.776727 + 0.321731i 0.735594 0.677423i \(-0.236903\pi\)
0.0411328 + 0.999154i \(0.486903\pi\)
\(602\) 10.8587 + 0.945928i 0.442568 + 0.0385531i
\(603\) 0 0
\(604\) −12.6268 2.21672i −0.513776 0.0901970i
\(605\) −4.03461 2.69584i −0.164030 0.109601i
\(606\) 0 0
\(607\) 19.4092i 0.787793i 0.919155 + 0.393897i \(0.128873\pi\)
−0.919155 + 0.393897i \(0.871127\pi\)
\(608\) −11.2674 30.7780i −0.456954 1.24821i
\(609\) 0 0
\(610\) −2.25067 4.09880i −0.0911269 0.165955i
\(611\) 25.5058 + 17.0424i 1.03185 + 0.689462i
\(612\) 0 0
\(613\) −17.2993 3.44105i −0.698712 0.138983i −0.167062 0.985946i \(-0.553428\pi\)
−0.531650 + 0.846964i \(0.678428\pi\)
\(614\) −1.03943 + 11.9321i −0.0419480 + 0.481539i
\(615\) 0 0
\(616\) 15.2576 19.9302i 0.614745 0.803012i
\(617\) −19.6710 + 8.14801i −0.791926 + 0.328027i −0.741718 0.670712i \(-0.765989\pi\)
−0.0502085 + 0.998739i \(0.515989\pi\)
\(618\) 0 0
\(619\) −8.49755 12.7175i −0.341545 0.511159i 0.620442 0.784252i \(-0.286953\pi\)
−0.961987 + 0.273094i \(0.911953\pi\)
\(620\) 0.230979 + 0.220784i 0.00927634 + 0.00886690i
\(621\) 0 0
\(622\) 0.255678 + 2.32656i 0.0102518 + 0.0932864i
\(623\) −2.03155 + 2.03155i −0.0813924 + 0.0813924i
\(624\) 0 0
\(625\) 11.3170 + 11.3170i 0.452681 + 0.452681i
\(626\) 14.0558 17.5265i 0.561781 0.700501i
\(627\) 0 0
\(628\) −4.00896 9.09263i −0.159975 0.362835i
\(629\) −28.9319 + 19.3317i −1.15359 + 0.770804i
\(630\) 0 0
\(631\) −15.2549 36.8286i −0.607289 1.46613i −0.865937 0.500153i \(-0.833277\pi\)
0.258648 0.965972i \(-0.416723\pi\)
\(632\) 0.750442 11.6495i 0.0298510 0.463392i
\(633\) 0 0
\(634\) 17.1891 14.4343i 0.682668 0.573261i
\(635\) 1.18582 5.96150i 0.0470577 0.236575i
\(636\) 0 0
\(637\) 14.6373 21.9063i 0.579952 0.867960i
\(638\) 10.6723 + 3.10638i 0.422522 + 0.122983i
\(639\) 0 0
\(640\) −7.34478 5.11431i −0.290328 0.202161i
\(641\) 29.8562 1.17925 0.589624 0.807678i \(-0.299276\pi\)
0.589624 + 0.807678i \(0.299276\pi\)
\(642\) 0 0
\(643\) −16.7593 + 25.0820i −0.660921 + 0.989138i 0.337928 + 0.941172i \(0.390274\pi\)
−0.998849 + 0.0479657i \(0.984726\pi\)
\(644\) −11.9263 + 18.7514i −0.469960 + 0.738907i
\(645\) 0 0
\(646\) −24.2634 + 20.3749i −0.954631 + 0.801638i
\(647\) −9.93240 + 23.9789i −0.390483 + 0.942709i 0.599352 + 0.800486i \(0.295425\pi\)
−0.989835 + 0.142223i \(0.954575\pi\)
\(648\) 0 0
\(649\) −7.41318 17.8970i −0.290993 0.702519i
\(650\) −8.18871 + 15.7447i −0.321188 + 0.617559i
\(651\) 0 0
\(652\) 18.1026 + 41.0581i 0.708953 + 1.60796i
\(653\) 1.64465 + 8.26822i 0.0643602 + 0.323560i 0.999531 0.0306378i \(-0.00975384\pi\)
−0.935170 + 0.354198i \(0.884754\pi\)
\(654\) 0 0
\(655\) −3.13657 3.13657i −0.122556 0.122556i
\(656\) −25.0985 22.9296i −0.979930 0.895251i
\(657\) 0 0
\(658\) −6.64525 60.4687i −0.259059 2.35731i
\(659\) 4.11710 0.818941i 0.160379 0.0319014i −0.114248 0.993452i \(-0.536446\pi\)
0.274627 + 0.961551i \(0.411446\pi\)
\(660\) 0 0
\(661\) −16.0973 24.0913i −0.626112 0.937043i −0.999954 0.00955074i \(-0.996960\pi\)
0.373842 0.927492i \(-0.378040\pi\)
\(662\) 29.1449 9.20133i 1.13275 0.357620i
\(663\) 0 0
\(664\) 0.435931 + 0.333726i 0.0169174 + 0.0129511i
\(665\) −17.0352 7.05619i −0.660595 0.273627i
\(666\) 0 0
\(667\) −9.65200 1.91990i −0.373727 0.0743389i
\(668\) 1.42324 + 2.02937i 0.0550669 + 0.0785187i
\(669\) 0 0
\(670\) 4.99386 + 9.09455i 0.192930 + 0.351353i
\(671\) 9.22017i 0.355941i
\(672\) 0 0
\(673\) 3.38922i 0.130645i 0.997864 + 0.0653224i \(0.0208076\pi\)
−0.997864 + 0.0653224i \(0.979192\pi\)
\(674\) 1.61012 0.884122i 0.0620193 0.0340551i
\(675\) 0 0
\(676\) 9.39572 + 1.64948i 0.361374 + 0.0634417i
\(677\) −22.4472 4.46503i −0.862717 0.171605i −0.256150 0.966637i \(-0.582454\pi\)
−0.606568 + 0.795032i \(0.707454\pi\)
\(678\) 0 0
\(679\) 10.4231 + 4.31738i 0.400001 + 0.165686i
\(680\) −2.22988 + 8.35947i −0.0855119 + 0.320571i
\(681\) 0 0
\(682\) −0.189679 0.600804i −0.00726320 0.0230060i
\(683\) 10.4891 + 15.6981i 0.401355 + 0.600670i 0.976010 0.217726i \(-0.0698638\pi\)
−0.574655 + 0.818396i \(0.694864\pi\)
\(684\) 0 0
\(685\) 6.13059 1.21945i 0.234238 0.0465928i
\(686\) −12.3489 + 1.35709i −0.471484 + 0.0518141i
\(687\) 0 0
\(688\) −3.96582 + 6.55754i −0.151196 + 0.250004i
\(689\) −27.3111 27.3111i −1.04047 1.04047i
\(690\) 0 0
\(691\) −1.70364 8.56476i −0.0648094 0.325819i 0.934756 0.355290i \(-0.115618\pi\)
−0.999566 + 0.0294708i \(0.990618\pi\)
\(692\) 6.15400 + 2.38787i 0.233940 + 0.0907732i
\(693\) 0 0
\(694\) 0.218437 + 0.113607i 0.00829174 + 0.00431247i
\(695\) −0.257092 0.620674i −0.00975205 0.0235435i
\(696\) 0 0
\(697\) −12.5761 + 30.3613i −0.476353 + 1.15002i
\(698\) 0.966276 + 1.15069i 0.0365741 + 0.0435543i
\(699\) 0 0
\(700\) 34.3539 7.64301i 1.29846 0.288879i
\(701\) 26.3880 39.4924i 0.996661 1.49161i 0.130746 0.991416i \(-0.458263\pi\)
0.865914 0.500192i \(-0.166737\pi\)
\(702\) 0 0
\(703\) 52.1390 1.96646
\(704\) 7.84066 + 15.8099i 0.295506 + 0.595858i
\(705\) 0 0
\(706\) −0.252226 + 0.866554i −0.00949267 + 0.0326132i
\(707\) −15.4983 + 23.1949i −0.582874 + 0.872333i
\(708\) 0 0
\(709\) 1.30250 6.54810i 0.0489163 0.245919i −0.948589 0.316511i \(-0.897489\pi\)
0.997505 + 0.0705917i \(0.0224887\pi\)
\(710\) −3.73771 4.45106i −0.140274 0.167045i
\(711\) 0 0
\(712\) −0.651447 1.91206i −0.0244140 0.0716576i
\(713\) 0.213466 + 0.515352i 0.00799436 + 0.0193001i
\(714\) 0 0
\(715\) −4.16256 + 2.78133i −0.155671 + 0.104016i
\(716\) 4.97003 12.8087i 0.185739 0.478684i
\(717\) 0 0
\(718\) −17.0030 13.6359i −0.634545 0.508887i
\(719\) 6.09983 + 6.09983i 0.227485 + 0.227485i 0.811641 0.584156i \(-0.198574\pi\)
−0.584156 + 0.811641i \(0.698574\pi\)
\(720\) 0 0
\(721\) −39.3834 + 39.3834i −1.46671 + 1.46671i
\(722\) 20.4818 2.25087i 0.762255 0.0837686i
\(723\) 0 0
\(724\) 13.4156 0.302753i 0.498586 0.0112517i
\(725\) 8.65869 + 12.9586i 0.321576 + 0.481272i
\(726\) 0 0
\(727\) 3.50465 1.45167i 0.129980 0.0538395i −0.316745 0.948511i \(-0.602590\pi\)
0.446725 + 0.894671i \(0.352590\pi\)
\(728\) 16.3532 + 28.2514i 0.606090 + 1.04707i
\(729\) 0 0
\(730\) 17.7977 + 1.55040i 0.658722 + 0.0573829i
\(731\) 7.26580 + 1.44526i 0.268735 + 0.0534548i
\(732\) 0 0
\(733\) −6.66476 4.45325i −0.246169 0.164485i 0.426365 0.904551i \(-0.359794\pi\)
−0.672534 + 0.740067i \(0.734794\pi\)
\(734\) 10.1939 5.59754i 0.376265 0.206609i
\(735\) 0 0
\(736\) −8.13046 13.3423i −0.299693 0.491805i
\(737\) 20.4580i 0.753581i
\(738\) 0 0
\(739\) −24.1533 16.1387i −0.888492 0.593671i 0.0253784 0.999678i \(-0.491921\pi\)
−0.913870 + 0.406007i \(0.866921\pi\)
\(740\) 11.6566 8.17500i 0.428504 0.300519i
\(741\) 0 0
\(742\) −6.64720 + 76.3060i −0.244026 + 2.80128i
\(743\) 27.7230 + 11.4832i 1.01706 + 0.421279i 0.828025 0.560691i \(-0.189465\pi\)
0.189033 + 0.981971i \(0.439465\pi\)
\(744\) 0 0
\(745\) 1.07824 0.446623i 0.0395037 0.0163630i
\(746\) −7.90579 + 2.49593i −0.289451 + 0.0913825i
\(747\) 0 0
\(748\) 11.7876 12.3319i 0.430996 0.450898i
\(749\) 47.1903 9.38673i 1.72430 0.342984i
\(750\) 0 0
\(751\) 18.6881 18.6881i 0.681937 0.681937i −0.278499 0.960436i \(-0.589837\pi\)
0.960436 + 0.278499i \(0.0898370\pi\)
\(752\) 40.2129 + 14.5683i 1.46641 + 0.531252i
\(753\) 0 0
\(754\) −9.04391 + 11.2771i −0.329360 + 0.410688i
\(755\) −0.989251 4.97330i −0.0360025 0.180997i
\(756\) 0 0
\(757\) 0.988973 0.660810i 0.0359448 0.0240176i −0.537468 0.843284i \(-0.680619\pi\)
0.573413 + 0.819267i \(0.305619\pi\)
\(758\) 6.76238 13.0023i 0.245621 0.472264i
\(759\) 0 0
\(760\) 9.73724 8.55864i 0.353207 0.310455i
\(761\) 3.73816 9.02472i 0.135508 0.327146i −0.841530 0.540211i \(-0.818345\pi\)
0.977038 + 0.213065i \(0.0683445\pi\)
\(762\) 0 0
\(763\) 3.39928 17.0893i 0.123062 0.618675i
\(764\) −21.5564 13.7103i −0.779882 0.496021i
\(765\) 0 0
\(766\) 48.3354 + 14.0689i 1.74643 + 0.508330i
\(767\) 25.1932 0.909674
\(768\) 0 0
\(769\) 53.0775 1.91402 0.957012 0.290049i \(-0.0936716\pi\)
0.957012 + 0.290049i \(0.0936716\pi\)
\(770\) 9.53236 + 2.77457i 0.343522 + 0.0999885i
\(771\) 0 0
\(772\) 33.6840 + 21.4237i 1.21231 + 0.771057i
\(773\) 4.23170 21.2742i 0.152204 0.765179i −0.826985 0.562225i \(-0.809946\pi\)
0.979188 0.202955i \(-0.0650544\pi\)
\(774\) 0 0
\(775\) 0.338064 0.816158i 0.0121436 0.0293173i
\(776\) −5.95780 + 5.23667i −0.213873 + 0.187985i
\(777\) 0 0
\(778\) −22.2478 + 42.7766i −0.797622 + 1.53362i
\(779\) 40.9435 27.3576i 1.46695 0.980187i
\(780\) 0 0
\(781\) 2.23583 + 11.2403i 0.0800043 + 0.402209i
\(782\) −9.44944 + 11.7828i −0.337911 + 0.421351i
\(783\) 0 0
\(784\) 12.5124 34.5380i 0.446871 1.23350i
\(785\) 2.77930 2.77930i 0.0991974 0.0991974i
\(786\) 0 0
\(787\) −23.2249 + 4.61971i −0.827877 + 0.164675i −0.590802 0.806816i \(-0.701189\pi\)
−0.237075 + 0.971491i \(0.576189\pi\)
\(788\) −9.80580 + 10.2586i −0.3493