Properties

Label 675.2.r.a.46.7
Level $675$
Weight $2$
Character 675.46
Analytic conductor $5.390$
Analytic rank $0$
Dimension $224$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.r (of order \(15\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 225)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 46.7
Character \(\chi\) \(=\) 675.46
Dual form 675.2.r.a.631.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.956880 - 1.06272i) q^{2} +(-0.00470356 + 0.0447514i) q^{4} +(2.07212 - 0.840433i) q^{5} +(1.92019 - 3.32586i) q^{7} +(-2.26178 + 1.64328i) q^{8} +O(q^{10})\) \(q+(-0.956880 - 1.06272i) q^{2} +(-0.00470356 + 0.0447514i) q^{4} +(2.07212 - 0.840433i) q^{5} +(1.92019 - 3.32586i) q^{7} +(-2.26178 + 1.64328i) q^{8} +(-2.87591 - 1.39789i) q^{10} +(-3.49787 - 3.88478i) q^{11} +(-2.25011 + 2.49900i) q^{13} +(-5.37185 + 1.14182i) q^{14} +(3.99864 + 0.849937i) q^{16} +(3.90998 - 2.84077i) q^{17} +(-1.90903 + 1.38699i) q^{19} +(0.0278642 + 0.0966831i) q^{20} +(-0.781401 + 7.43453i) q^{22} +(-4.56147 + 0.969570i) q^{23} +(3.58734 - 3.48295i) q^{25} +4.80884 q^{26} +(0.139805 + 0.101574i) q^{28} +(6.71254 - 2.98862i) q^{29} +(0.593962 + 0.264449i) q^{31} +(-0.127249 - 0.220402i) q^{32} +(-6.76033 - 1.43695i) q^{34} +(1.18369 - 8.50536i) q^{35} +(0.315262 + 0.970276i) q^{37} +(3.30069 + 0.701584i) q^{38} +(-3.30561 + 5.30596i) q^{40} +(2.50903 - 2.78656i) q^{41} +(-2.34851 + 4.06773i) q^{43} +(0.190302 - 0.138262i) q^{44} +(5.39516 + 3.91981i) q^{46} +(-10.9118 + 4.85827i) q^{47} +(-3.87423 - 6.71036i) q^{49} +(-7.13407 - 0.479583i) q^{50} +(-0.101250 - 0.112450i) q^{52} +(-2.92011 - 2.12158i) q^{53} +(-10.5129 - 5.10999i) q^{55} +(1.12228 + 10.6778i) q^{56} +(-9.59917 - 4.27383i) q^{58} +(5.20768 - 5.78372i) q^{59} +(-4.40843 - 4.89605i) q^{61} +(-0.287314 - 0.884263i) q^{62} +(2.41404 - 7.42965i) q^{64} +(-2.56225 + 7.06930i) q^{65} +(-0.930565 - 0.414314i) q^{67} +(0.108737 + 0.188339i) q^{68} +(-10.1715 + 6.88068i) q^{70} +(2.82082 + 2.04945i) q^{71} +(-1.38140 + 4.25150i) q^{73} +(0.729467 - 1.26347i) q^{74} +(-0.0530904 - 0.0919553i) q^{76} +(-19.6368 + 4.17393i) q^{77} +(1.49826 - 0.667070i) q^{79} +(8.99997 - 1.59942i) q^{80} -5.36219 q^{82} +(1.18152 + 11.2414i) q^{83} +(5.71446 - 9.17248i) q^{85} +(6.57011 - 1.39652i) q^{86} +(14.2952 + 3.03854i) q^{88} +(0.935178 - 2.87818i) q^{89} +(3.99070 + 12.2821i) q^{91} +(-0.0219345 - 0.208692i) q^{92} +(15.6043 + 6.94749i) q^{94} +(-2.79006 + 4.47841i) q^{95} +(14.8057 - 6.59193i) q^{97} +(-3.42408 + 10.5382i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.956880 1.06272i −0.676616 0.751458i 0.302856 0.953036i \(-0.402060\pi\)
−0.979472 + 0.201578i \(0.935393\pi\)
\(3\) 0 0
\(4\) −0.00470356 + 0.0447514i −0.00235178 + 0.0223757i
\(5\) 2.07212 0.840433i 0.926679 0.375853i
\(6\) 0 0
\(7\) 1.92019 3.32586i 0.725762 1.25706i −0.232897 0.972501i \(-0.574821\pi\)
0.958660 0.284556i \(-0.0918460\pi\)
\(8\) −2.26178 + 1.64328i −0.799662 + 0.580988i
\(9\) 0 0
\(10\) −2.87591 1.39789i −0.909444 0.442052i
\(11\) −3.49787 3.88478i −1.05465 1.17131i −0.984790 0.173748i \(-0.944412\pi\)
−0.0698578 0.997557i \(-0.522255\pi\)
\(12\) 0 0
\(13\) −2.25011 + 2.49900i −0.624069 + 0.693099i −0.969429 0.245371i \(-0.921090\pi\)
0.345360 + 0.938470i \(0.387757\pi\)
\(14\) −5.37185 + 1.14182i −1.43569 + 0.305165i
\(15\) 0 0
\(16\) 3.99864 + 0.849937i 0.999660 + 0.212484i
\(17\) 3.90998 2.84077i 0.948309 0.688987i −0.00209712 0.999998i \(-0.500668\pi\)
0.950406 + 0.311011i \(0.100668\pi\)
\(18\) 0 0
\(19\) −1.90903 + 1.38699i −0.437961 + 0.318197i −0.784824 0.619719i \(-0.787247\pi\)
0.346863 + 0.937916i \(0.387247\pi\)
\(20\) 0.0278642 + 0.0966831i 0.00623063 + 0.0216190i
\(21\) 0 0
\(22\) −0.781401 + 7.43453i −0.166595 + 1.58505i
\(23\) −4.56147 + 0.969570i −0.951132 + 0.202169i −0.657250 0.753672i \(-0.728281\pi\)
−0.293882 + 0.955842i \(0.594947\pi\)
\(24\) 0 0
\(25\) 3.58734 3.48295i 0.717469 0.696591i
\(26\) 4.80884 0.943090
\(27\) 0 0
\(28\) 0.139805 + 0.101574i 0.0264207 + 0.0191957i
\(29\) 6.71254 2.98862i 1.24649 0.554972i 0.325862 0.945417i \(-0.394346\pi\)
0.920626 + 0.390445i \(0.127679\pi\)
\(30\) 0 0
\(31\) 0.593962 + 0.264449i 0.106679 + 0.0474964i 0.459382 0.888239i \(-0.348071\pi\)
−0.352703 + 0.935735i \(0.614738\pi\)
\(32\) −0.127249 0.220402i −0.0224947 0.0389619i
\(33\) 0 0
\(34\) −6.76033 1.43695i −1.15939 0.246435i
\(35\) 1.18369 8.50536i 0.200080 1.43767i
\(36\) 0 0
\(37\) 0.315262 + 0.970276i 0.0518287 + 0.159512i 0.973621 0.228172i \(-0.0732749\pi\)
−0.921792 + 0.387685i \(0.873275\pi\)
\(38\) 3.30069 + 0.701584i 0.535443 + 0.113812i
\(39\) 0 0
\(40\) −3.30561 + 5.30596i −0.522664 + 0.838945i
\(41\) 2.50903 2.78656i 0.391845 0.435188i −0.514653 0.857399i \(-0.672079\pi\)
0.906498 + 0.422211i \(0.138746\pi\)
\(42\) 0 0
\(43\) −2.34851 + 4.06773i −0.358144 + 0.620324i −0.987651 0.156671i \(-0.949924\pi\)
0.629507 + 0.776995i \(0.283257\pi\)
\(44\) 0.190302 0.138262i 0.0286890 0.0208438i
\(45\) 0 0
\(46\) 5.39516 + 3.91981i 0.795473 + 0.577945i
\(47\) −10.9118 + 4.85827i −1.59166 + 0.708651i −0.995548 0.0942531i \(-0.969954\pi\)
−0.596108 + 0.802904i \(0.703287\pi\)
\(48\) 0 0
\(49\) −3.87423 6.71036i −0.553461 0.958623i
\(50\) −7.13407 0.479583i −1.00891 0.0678233i
\(51\) 0 0
\(52\) −0.101250 0.112450i −0.0140409 0.0155940i
\(53\) −2.92011 2.12158i −0.401108 0.291422i 0.368884 0.929475i \(-0.379740\pi\)
−0.769992 + 0.638054i \(0.779740\pi\)
\(54\) 0 0
\(55\) −10.5129 5.10999i −1.41756 0.689031i
\(56\) 1.12228 + 10.6778i 0.149971 + 1.42688i
\(57\) 0 0
\(58\) −9.59917 4.27383i −1.26043 0.561181i
\(59\) 5.20768 5.78372i 0.677982 0.752976i −0.301728 0.953394i \(-0.597563\pi\)
0.979710 + 0.200418i \(0.0642302\pi\)
\(60\) 0 0
\(61\) −4.40843 4.89605i −0.564441 0.626875i 0.391590 0.920140i \(-0.371925\pi\)
−0.956031 + 0.293264i \(0.905258\pi\)
\(62\) −0.287314 0.884263i −0.0364890 0.112301i
\(63\) 0 0
\(64\) 2.41404 7.42965i 0.301755 0.928707i
\(65\) −2.56225 + 7.06930i −0.317808 + 0.876839i
\(66\) 0 0
\(67\) −0.930565 0.414314i −0.113687 0.0506165i 0.349105 0.937084i \(-0.386486\pi\)
−0.462792 + 0.886467i \(0.653152\pi\)
\(68\) 0.108737 + 0.188339i 0.0131863 + 0.0228394i
\(69\) 0 0
\(70\) −10.1715 + 6.88068i −1.21573 + 0.822398i
\(71\) 2.82082 + 2.04945i 0.334770 + 0.243225i 0.742452 0.669899i \(-0.233663\pi\)
−0.407682 + 0.913124i \(0.633663\pi\)
\(72\) 0 0
\(73\) −1.38140 + 4.25150i −0.161680 + 0.497601i −0.998776 0.0494551i \(-0.984252\pi\)
0.837096 + 0.547056i \(0.184252\pi\)
\(74\) 0.729467 1.26347i 0.0847988 0.146876i
\(75\) 0 0
\(76\) −0.0530904 0.0919553i −0.00608989 0.0105480i
\(77\) −19.6368 + 4.17393i −2.23782 + 0.475663i
\(78\) 0 0
\(79\) 1.49826 0.667070i 0.168568 0.0750513i −0.320718 0.947175i \(-0.603924\pi\)
0.489286 + 0.872123i \(0.337257\pi\)
\(80\) 8.99997 1.59942i 1.00623 0.178821i
\(81\) 0 0
\(82\) −5.36219 −0.592154
\(83\) 1.18152 + 11.2414i 0.129688 + 1.23390i 0.844873 + 0.534967i \(0.179676\pi\)
−0.715185 + 0.698936i \(0.753657\pi\)
\(84\) 0 0
\(85\) 5.71446 9.17248i 0.619820 0.994895i
\(86\) 6.57011 1.39652i 0.708473 0.150591i
\(87\) 0 0
\(88\) 14.2952 + 3.03854i 1.52388 + 0.323910i
\(89\) 0.935178 2.87818i 0.0991286 0.305087i −0.889179 0.457559i \(-0.848724\pi\)
0.988308 + 0.152473i \(0.0487237\pi\)
\(90\) 0 0
\(91\) 3.99070 + 12.2821i 0.418339 + 1.28752i
\(92\) −0.0219345 0.208692i −0.00228682 0.0217577i
\(93\) 0 0
\(94\) 15.6043 + 6.94749i 1.60946 + 0.716579i
\(95\) −2.79006 + 4.47841i −0.286254 + 0.459475i
\(96\) 0 0
\(97\) 14.8057 6.59193i 1.50329 0.669309i 0.520474 0.853878i \(-0.325755\pi\)
0.982820 + 0.184569i \(0.0590888\pi\)
\(98\) −3.42408 + 10.5382i −0.345885 + 1.06452i
\(99\) 0 0
\(100\) 0.138994 + 0.176921i 0.0138994 + 0.0176921i
\(101\) 2.79104 4.83422i 0.277719 0.481023i −0.693099 0.720843i \(-0.743755\pi\)
0.970817 + 0.239820i \(0.0770884\pi\)
\(102\) 0 0
\(103\) −0.0651481 + 0.619843i −0.00641923 + 0.0610749i −0.997263 0.0739417i \(-0.976442\pi\)
0.990843 + 0.135017i \(0.0431088\pi\)
\(104\) 0.982702 9.34978i 0.0963618 0.916822i
\(105\) 0 0
\(106\) 0.539538 + 5.13336i 0.0524046 + 0.498596i
\(107\) −8.51791 −0.823458 −0.411729 0.911306i \(-0.635075\pi\)
−0.411729 + 0.911306i \(0.635075\pi\)
\(108\) 0 0
\(109\) −3.14970 9.69377i −0.301686 0.928495i −0.980893 0.194548i \(-0.937676\pi\)
0.679207 0.733947i \(-0.262324\pi\)
\(110\) 4.62908 + 16.0619i 0.441365 + 1.53145i
\(111\) 0 0
\(112\) 10.5049 11.6669i 0.992620 1.10242i
\(113\) 4.24309 4.71243i 0.399156 0.443308i −0.509741 0.860328i \(-0.670259\pi\)
0.908897 + 0.417020i \(0.136926\pi\)
\(114\) 0 0
\(115\) −8.63704 + 5.84268i −0.805408 + 0.544832i
\(116\) 0.102172 + 0.314453i 0.00948642 + 0.0291962i
\(117\) 0 0
\(118\) −11.1296 −1.02456
\(119\) −1.94010 18.4588i −0.177849 1.69212i
\(120\) 0 0
\(121\) −1.70660 + 16.2372i −0.155145 + 1.47611i
\(122\) −0.984813 + 9.36987i −0.0891607 + 0.848308i
\(123\) 0 0
\(124\) −0.0146282 + 0.0253368i −0.00131365 + 0.00227531i
\(125\) 4.50621 10.2320i 0.403047 0.915179i
\(126\) 0 0
\(127\) 4.60449 14.1712i 0.408583 1.25749i −0.509284 0.860599i \(-0.670090\pi\)
0.917867 0.396889i \(-0.129910\pi\)
\(128\) −10.6706 + 4.75086i −0.943157 + 0.419920i
\(129\) 0 0
\(130\) 9.96447 4.04151i 0.873942 0.354464i
\(131\) 12.3027 + 5.47750i 1.07489 + 0.478571i 0.866347 0.499442i \(-0.166462\pi\)
0.208542 + 0.978014i \(0.433128\pi\)
\(132\) 0 0
\(133\) 0.947245 + 9.01243i 0.0821365 + 0.781477i
\(134\) 0.450138 + 1.38538i 0.0388860 + 0.119679i
\(135\) 0 0
\(136\) −4.17535 + 12.8504i −0.358033 + 1.10191i
\(137\) 8.93278 + 1.89872i 0.763179 + 0.162219i 0.573028 0.819536i \(-0.305769\pi\)
0.190151 + 0.981755i \(0.439102\pi\)
\(138\) 0 0
\(139\) −11.4759 + 2.43928i −0.973376 + 0.206897i −0.667037 0.745025i \(-0.732438\pi\)
−0.306339 + 0.951922i \(0.599104\pi\)
\(140\) 0.375059 + 0.0929771i 0.0316983 + 0.00785800i
\(141\) 0 0
\(142\) −0.521193 4.95882i −0.0437376 0.416135i
\(143\) 17.5787 1.47000
\(144\) 0 0
\(145\) 11.3974 11.8342i 0.946507 0.982778i
\(146\) 5.84000 2.60014i 0.483322 0.215189i
\(147\) 0 0
\(148\) −0.0449040 + 0.00954465i −0.00369109 + 0.000784565i
\(149\) 4.73317 + 8.19809i 0.387756 + 0.671614i 0.992147 0.125074i \(-0.0399169\pi\)
−0.604391 + 0.796688i \(0.706584\pi\)
\(150\) 0 0
\(151\) 7.67377 13.2914i 0.624482 1.08164i −0.364158 0.931337i \(-0.618643\pi\)
0.988641 0.150298i \(-0.0480234\pi\)
\(152\) 2.03859 6.27414i 0.165352 0.508900i
\(153\) 0 0
\(154\) 23.2258 + 16.8745i 1.87159 + 1.35979i
\(155\) 1.45301 + 0.0487838i 0.116709 + 0.00391841i
\(156\) 0 0
\(157\) 10.9037 + 18.8858i 0.870210 + 1.50725i 0.861780 + 0.507283i \(0.169350\pi\)
0.00843010 + 0.999964i \(0.497317\pi\)
\(158\) −2.14257 0.953934i −0.170454 0.0758909i
\(159\) 0 0
\(160\) −0.448909 0.349755i −0.0354893 0.0276505i
\(161\) −5.53422 + 17.0326i −0.436157 + 1.34235i
\(162\) 0 0
\(163\) −3.56614 10.9754i −0.279321 0.859663i −0.988044 0.154175i \(-0.950728\pi\)
0.708722 0.705488i \(-0.249272\pi\)
\(164\) 0.112901 + 0.125389i 0.00881609 + 0.00979126i
\(165\) 0 0
\(166\) 10.8159 12.0123i 0.839477 0.932334i
\(167\) 3.85690 + 1.71720i 0.298456 + 0.132881i 0.550501 0.834834i \(-0.314437\pi\)
−0.252045 + 0.967715i \(0.581103\pi\)
\(168\) 0 0
\(169\) 0.176859 + 1.68270i 0.0136045 + 0.129438i
\(170\) −15.2159 + 2.70407i −1.16700 + 0.207393i
\(171\) 0 0
\(172\) −0.170990 0.124232i −0.0130379 0.00947258i
\(173\) 6.60700 + 7.33782i 0.502321 + 0.557884i 0.939968 0.341263i \(-0.110855\pi\)
−0.437647 + 0.899147i \(0.644188\pi\)
\(174\) 0 0
\(175\) −4.69545 18.6189i −0.354943 1.40746i
\(176\) −10.6849 18.5068i −0.805405 1.39500i
\(177\) 0 0
\(178\) −3.95356 + 1.76024i −0.296332 + 0.131935i
\(179\) 2.85965 + 2.07766i 0.213740 + 0.155292i 0.689504 0.724281i \(-0.257828\pi\)
−0.475764 + 0.879573i \(0.657828\pi\)
\(180\) 0 0
\(181\) 12.3513 8.97372i 0.918062 0.667011i −0.0249788 0.999688i \(-0.507952\pi\)
0.943041 + 0.332677i \(0.107952\pi\)
\(182\) 9.23386 15.9935i 0.684459 1.18552i
\(183\) 0 0
\(184\) 8.72379 9.68874i 0.643126 0.714264i
\(185\) 1.46871 + 1.74557i 0.107982 + 0.128337i
\(186\) 0 0
\(187\) −24.7124 5.25277i −1.80715 0.384121i
\(188\) −0.166090 0.511171i −0.0121133 0.0372810i
\(189\) 0 0
\(190\) 7.42906 1.32025i 0.538960 0.0957808i
\(191\) 18.1452 + 3.85689i 1.31294 + 0.279075i 0.810603 0.585596i \(-0.199139\pi\)
0.502340 + 0.864670i \(0.332473\pi\)
\(192\) 0 0
\(193\) −5.82208 10.0841i −0.419082 0.725872i 0.576765 0.816910i \(-0.304315\pi\)
−0.995847 + 0.0910384i \(0.970981\pi\)
\(194\) −21.1727 9.42669i −1.52011 0.676797i
\(195\) 0 0
\(196\) 0.318520 0.141814i 0.0227515 0.0101296i
\(197\) −6.93084 5.03555i −0.493802 0.358768i 0.312843 0.949805i \(-0.398719\pi\)
−0.806645 + 0.591037i \(0.798719\pi\)
\(198\) 0 0
\(199\) 17.3700 1.23133 0.615663 0.788010i \(-0.288888\pi\)
0.615663 + 0.788010i \(0.288888\pi\)
\(200\) −2.39032 + 13.7727i −0.169021 + 0.973878i
\(201\) 0 0
\(202\) −7.80812 + 1.65967i −0.549378 + 0.116774i
\(203\) 2.94961 28.0637i 0.207022 1.96968i
\(204\) 0 0
\(205\) 2.85709 7.88276i 0.199548 0.550556i
\(206\) 0.721060 0.523881i 0.0502386 0.0365005i
\(207\) 0 0
\(208\) −11.1214 + 8.08016i −0.771129 + 0.560258i
\(209\) 12.0657 + 2.56464i 0.834600 + 0.177400i
\(210\) 0 0
\(211\) 4.59169 0.975994i 0.316105 0.0671902i −0.0471270 0.998889i \(-0.515007\pi\)
0.363232 + 0.931699i \(0.381673\pi\)
\(212\) 0.108679 0.120700i 0.00746407 0.00828969i
\(213\) 0 0
\(214\) 8.15062 + 9.05218i 0.557165 + 0.618794i
\(215\) −1.44772 + 10.4026i −0.0987340 + 0.709450i
\(216\) 0 0
\(217\) 2.02004 1.46764i 0.137129 0.0996301i
\(218\) −7.28791 + 12.6230i −0.493599 + 0.854939i
\(219\) 0 0
\(220\) 0.278127 0.446431i 0.0187513 0.0300984i
\(221\) −1.69881 + 16.1631i −0.114274 + 1.08725i
\(222\) 0 0
\(223\) 10.5491 + 11.7160i 0.706422 + 0.784561i 0.984385 0.176031i \(-0.0563259\pi\)
−0.277963 + 0.960592i \(0.589659\pi\)
\(224\) −0.977368 −0.0653032
\(225\) 0 0
\(226\) −9.06813 −0.603203
\(227\) −4.82528 5.35901i −0.320265 0.355690i 0.561418 0.827532i \(-0.310256\pi\)
−0.881683 + 0.471842i \(0.843589\pi\)
\(228\) 0 0
\(229\) −1.07910 + 10.2669i −0.0713086 + 0.678456i 0.899224 + 0.437488i \(0.144132\pi\)
−0.970533 + 0.240968i \(0.922535\pi\)
\(230\) 14.4738 + 3.58804i 0.954371 + 0.236589i
\(231\) 0 0
\(232\) −10.2712 + 17.7902i −0.674337 + 1.16799i
\(233\) 10.0148 7.27620i 0.656094 0.476680i −0.209248 0.977863i \(-0.567102\pi\)
0.865341 + 0.501183i \(0.167102\pi\)
\(234\) 0 0
\(235\) −18.5276 + 19.2376i −1.20861 + 1.25492i
\(236\) 0.234334 + 0.260255i 0.0152539 + 0.0169411i
\(237\) 0 0
\(238\) −17.7602 + 19.7247i −1.15122 + 1.27856i
\(239\) 15.6686 3.33046i 1.01352 0.215430i 0.328925 0.944356i \(-0.393314\pi\)
0.684592 + 0.728927i \(0.259980\pi\)
\(240\) 0 0
\(241\) 2.86314 + 0.608580i 0.184431 + 0.0392021i 0.299201 0.954190i \(-0.403280\pi\)
−0.114770 + 0.993392i \(0.536613\pi\)
\(242\) 18.8886 13.7234i 1.21421 0.882173i
\(243\) 0 0
\(244\) 0.239840 0.174254i 0.0153542 0.0111555i
\(245\) −13.6675 10.6486i −0.873183 0.680316i
\(246\) 0 0
\(247\) 0.829435 7.89155i 0.0527757 0.502127i
\(248\) −1.77798 + 0.377921i −0.112902 + 0.0239980i
\(249\) 0 0
\(250\) −15.1857 + 5.00196i −0.960427 + 0.316352i
\(251\) 4.72015 0.297933 0.148967 0.988842i \(-0.452405\pi\)
0.148967 + 0.988842i \(0.452405\pi\)
\(252\) 0 0
\(253\) 19.7220 + 14.3289i 1.23991 + 0.900849i
\(254\) −19.4660 + 8.66681i −1.22140 + 0.543804i
\(255\) 0 0
\(256\) 0.986086 + 0.439034i 0.0616304 + 0.0274396i
\(257\) 10.6050 + 18.3684i 0.661523 + 1.14579i 0.980215 + 0.197934i \(0.0634230\pi\)
−0.318692 + 0.947858i \(0.603244\pi\)
\(258\) 0 0
\(259\) 3.83236 + 0.814594i 0.238132 + 0.0506164i
\(260\) −0.304309 0.147915i −0.0188725 0.00917331i
\(261\) 0 0
\(262\) −5.95111 18.3156i −0.367661 1.13154i
\(263\) −7.23524 1.53790i −0.446144 0.0948309i −0.0206393 0.999787i \(-0.506570\pi\)
−0.425505 + 0.904956i \(0.639904\pi\)
\(264\) 0 0
\(265\) −7.83385 1.94201i −0.481230 0.119297i
\(266\) 8.67131 9.63047i 0.531672 0.590482i
\(267\) 0 0
\(268\) 0.0229181 0.0396953i 0.00139994 0.00242478i
\(269\) −22.6424 + 16.4507i −1.38053 + 1.00301i −0.383700 + 0.923458i \(0.625350\pi\)
−0.996830 + 0.0795565i \(0.974650\pi\)
\(270\) 0 0
\(271\) −16.6545 12.1002i −1.01169 0.735034i −0.0471255 0.998889i \(-0.515006\pi\)
−0.964562 + 0.263855i \(0.915006\pi\)
\(272\) 18.0491 8.03596i 1.09439 0.487252i
\(273\) 0 0
\(274\) −6.52978 11.3099i −0.394479 0.683257i
\(275\) −26.0786 1.75312i −1.57260 0.105717i
\(276\) 0 0
\(277\) −1.82156 2.02305i −0.109447 0.121553i 0.685932 0.727666i \(-0.259395\pi\)
−0.795379 + 0.606112i \(0.792728\pi\)
\(278\) 13.5734 + 9.86163i 0.814077 + 0.591461i
\(279\) 0 0
\(280\) 11.2995 + 21.1824i 0.675272 + 1.26589i
\(281\) −2.51223 23.9023i −0.149867 1.42589i −0.768319 0.640067i \(-0.778907\pi\)
0.618452 0.785822i \(-0.287760\pi\)
\(282\) 0 0
\(283\) 7.03966 + 3.13426i 0.418464 + 0.186312i 0.605157 0.796106i \(-0.293110\pi\)
−0.186693 + 0.982418i \(0.559777\pi\)
\(284\) −0.104983 + 0.116596i −0.00622962 + 0.00691869i
\(285\) 0 0
\(286\) −16.8207 18.6813i −0.994628 1.10465i
\(287\) −4.44991 13.6954i −0.262670 0.808415i
\(288\) 0 0
\(289\) 1.96470 6.04671i 0.115570 0.355689i
\(290\) −23.4825 0.788408i −1.37894 0.0462969i
\(291\) 0 0
\(292\) −0.183763 0.0818166i −0.0107539 0.00478795i
\(293\) 13.7967 + 23.8965i 0.806010 + 1.39605i 0.915607 + 0.402074i \(0.131711\pi\)
−0.109597 + 0.993976i \(0.534956\pi\)
\(294\) 0 0
\(295\) 5.93010 16.3612i 0.345264 0.952589i
\(296\) −2.30749 1.67649i −0.134120 0.0974441i
\(297\) 0 0
\(298\) 4.18322 12.8746i 0.242327 0.745807i
\(299\) 7.84086 13.5808i 0.453449 0.785397i
\(300\) 0 0
\(301\) 9.01914 + 15.6216i 0.519855 + 0.900415i
\(302\) −21.4679 + 4.56314i −1.23534 + 0.262579i
\(303\) 0 0
\(304\) −8.81236 + 3.92352i −0.505423 + 0.225029i
\(305\) −13.2496 6.44021i −0.758669 0.368765i
\(306\) 0 0
\(307\) −29.8034 −1.70097 −0.850485 0.526000i \(-0.823691\pi\)
−0.850485 + 0.526000i \(0.823691\pi\)
\(308\) −0.0944262 0.898406i −0.00538043 0.0511914i
\(309\) 0 0
\(310\) −1.33851 1.59083i −0.0760224 0.0903529i
\(311\) −5.41338 + 1.15065i −0.306964 + 0.0652473i −0.358818 0.933407i \(-0.616820\pi\)
0.0518541 + 0.998655i \(0.483487\pi\)
\(312\) 0 0
\(313\) −5.60052 1.19043i −0.316560 0.0672869i 0.0468916 0.998900i \(-0.485068\pi\)
−0.363452 + 0.931613i \(0.618402\pi\)
\(314\) 9.63679 29.6590i 0.543836 1.67375i
\(315\) 0 0
\(316\) 0.0228051 + 0.0701870i 0.00128289 + 0.00394833i
\(317\) 1.21704 + 11.5794i 0.0683559 + 0.650363i 0.974035 + 0.226399i \(0.0726952\pi\)
−0.905679 + 0.423964i \(0.860638\pi\)
\(318\) 0 0
\(319\) −35.0897 15.6230i −1.96465 0.874718i
\(320\) −1.24195 17.4240i −0.0694272 0.974029i
\(321\) 0 0
\(322\) 23.3965 10.4168i 1.30383 0.580504i
\(323\) −3.52414 + 10.8462i −0.196089 + 0.603498i
\(324\) 0 0
\(325\) 0.631986 + 16.8018i 0.0350563 + 0.931998i
\(326\) −8.25148 + 14.2920i −0.457007 + 0.791560i
\(327\) 0 0
\(328\) −1.09578 + 10.4257i −0.0605044 + 0.575661i
\(329\) −4.79486 + 45.6201i −0.264349 + 2.51511i
\(330\) 0 0
\(331\) 2.09180 + 19.9021i 0.114976 + 1.09392i 0.888095 + 0.459659i \(0.152028\pi\)
−0.773120 + 0.634260i \(0.781305\pi\)
\(332\) −0.508625 −0.0279144
\(333\) 0 0
\(334\) −1.86568 5.74198i −0.102086 0.314187i
\(335\) −2.27644 0.0764300i −0.124375 0.00417582i
\(336\) 0 0
\(337\) −2.65966 + 2.95385i −0.144881 + 0.160907i −0.811217 0.584745i \(-0.801195\pi\)
0.666337 + 0.745651i \(0.267861\pi\)
\(338\) 1.61901 1.79809i 0.0880625 0.0978033i
\(339\) 0 0
\(340\) 0.383603 + 0.298873i 0.0208038 + 0.0162087i
\(341\) −1.05028 3.23242i −0.0568757 0.175045i
\(342\) 0 0
\(343\) −2.87436 −0.155201
\(344\) −1.37262 13.0596i −0.0740067 0.704126i
\(345\) 0 0
\(346\) 1.47596 14.0428i 0.0793481 0.754946i
\(347\) 3.83972 36.5325i 0.206127 1.96117i −0.0628621 0.998022i \(-0.520023\pi\)
0.268989 0.963143i \(-0.413311\pi\)
\(348\) 0 0
\(349\) 5.56763 9.64341i 0.298028 0.516200i −0.677657 0.735378i \(-0.737004\pi\)
0.975685 + 0.219179i \(0.0703377\pi\)
\(350\) −15.2938 + 22.8060i −0.817486 + 1.21903i
\(351\) 0 0
\(352\) −0.411112 + 1.26527i −0.0219124 + 0.0674393i
\(353\) 2.71907 1.21061i 0.144722 0.0644343i −0.333098 0.942892i \(-0.608094\pi\)
0.477820 + 0.878458i \(0.341427\pi\)
\(354\) 0 0
\(355\) 7.56750 + 1.87598i 0.401641 + 0.0995668i
\(356\) 0.124404 + 0.0553882i 0.00659339 + 0.00293557i
\(357\) 0 0
\(358\) −0.528368 5.02709i −0.0279251 0.265690i
\(359\) −0.714480 2.19894i −0.0377088 0.116056i 0.930430 0.366469i \(-0.119433\pi\)
−0.968139 + 0.250413i \(0.919433\pi\)
\(360\) 0 0
\(361\) −4.15068 + 12.7745i −0.218457 + 0.672341i
\(362\) −21.3552 4.53920i −1.12241 0.238575i
\(363\) 0 0
\(364\) −0.568412 + 0.120820i −0.0297929 + 0.00633267i
\(365\) 0.710688 + 9.97059i 0.0371991 + 0.521885i
\(366\) 0 0
\(367\) 1.77075 + 16.8476i 0.0924324 + 0.879435i 0.938249 + 0.345961i \(0.112447\pi\)
−0.845816 + 0.533474i \(0.820886\pi\)
\(368\) −19.0637 −0.993766
\(369\) 0 0
\(370\) 0.449676 3.23113i 0.0233775 0.167979i
\(371\) −12.6632 + 5.63803i −0.657442 + 0.292712i
\(372\) 0 0
\(373\) 24.6592 5.24148i 1.27681 0.271394i 0.480880 0.876787i \(-0.340317\pi\)
0.795927 + 0.605393i \(0.206984\pi\)
\(374\) 18.0645 + 31.2886i 0.934094 + 1.61790i
\(375\) 0 0
\(376\) 16.6967 28.9196i 0.861069 1.49141i
\(377\) −7.63542 + 23.4994i −0.393244 + 1.21028i
\(378\) 0 0
\(379\) 19.7932 + 14.3806i 1.01671 + 0.738681i 0.965605 0.260012i \(-0.0837266\pi\)
0.0511021 + 0.998693i \(0.483727\pi\)
\(380\) −0.187292 0.145923i −0.00960787 0.00748570i
\(381\) 0 0
\(382\) −13.2640 22.9739i −0.678645 1.17545i
\(383\) 0.00459473 + 0.00204571i 0.000234780 + 0.000104531i 0.406854 0.913493i \(-0.366626\pi\)
−0.406619 + 0.913598i \(0.633292\pi\)
\(384\) 0 0
\(385\) −37.1818 + 25.1523i −1.89496 + 1.28188i
\(386\) −5.14561 + 15.8365i −0.261904 + 0.806059i
\(387\) 0 0
\(388\) 0.225358 + 0.693582i 0.0114408 + 0.0352113i
\(389\) −6.97691 7.74865i −0.353744 0.392872i 0.539841 0.841767i \(-0.318484\pi\)
−0.893584 + 0.448895i \(0.851818\pi\)
\(390\) 0 0
\(391\) −15.0809 + 16.7491i −0.762675 + 0.847037i
\(392\) 19.7897 + 8.81094i 0.999531 + 0.445020i
\(393\) 0 0
\(394\) 1.28059 + 12.1840i 0.0645151 + 0.613820i
\(395\) 2.54395 2.64144i 0.128000 0.132905i
\(396\) 0 0
\(397\) −4.80180 3.48871i −0.240996 0.175094i 0.460731 0.887540i \(-0.347587\pi\)
−0.701727 + 0.712446i \(0.747587\pi\)
\(398\) −16.6210 18.4595i −0.833135 0.925290i
\(399\) 0 0
\(400\) 17.3048 10.8781i 0.865239 0.543903i
\(401\) −9.95507 17.2427i −0.497133 0.861059i 0.502862 0.864367i \(-0.332280\pi\)
−0.999995 + 0.00330780i \(0.998947\pi\)
\(402\) 0 0
\(403\) −1.99734 + 0.889274i −0.0994946 + 0.0442979i
\(404\) 0.203210 + 0.147641i 0.0101101 + 0.00734540i
\(405\) 0 0
\(406\) −32.6463 + 23.7190i −1.62021 + 1.17715i
\(407\) 2.66656 4.61862i 0.132177 0.228937i
\(408\) 0 0
\(409\) −3.27138 + 3.63324i −0.161759 + 0.179652i −0.818576 0.574399i \(-0.805236\pi\)
0.656816 + 0.754051i \(0.271903\pi\)
\(410\) −11.1111 + 4.50656i −0.548737 + 0.222563i
\(411\) 0 0
\(412\) −0.0274324 0.00583093i −0.00135150 0.000287269i
\(413\) −9.23611 28.4258i −0.454479 1.39874i
\(414\) 0 0
\(415\) 11.8959 + 22.3005i 0.583946 + 1.09469i
\(416\) 0.837111 + 0.177933i 0.0410427 + 0.00872390i
\(417\) 0 0
\(418\) −8.81990 15.2765i −0.431395 0.747199i
\(419\) −11.6448 5.18460i −0.568886 0.253284i 0.102075 0.994777i \(-0.467452\pi\)
−0.670961 + 0.741492i \(0.734118\pi\)
\(420\) 0 0
\(421\) −16.0386 + 7.14085i −0.781674 + 0.348024i −0.758471 0.651707i \(-0.774053\pi\)
−0.0232033 + 0.999731i \(0.507387\pi\)
\(422\) −5.43091 3.94579i −0.264372 0.192078i
\(423\) 0 0
\(424\) 10.0910 0.490063
\(425\) 4.13218 23.8091i 0.200440 1.15491i
\(426\) 0 0
\(427\) −24.7486 + 5.26047i −1.19767 + 0.254572i
\(428\) 0.0400645 0.381188i 0.00193659 0.0184254i
\(429\) 0 0
\(430\) 12.4404 8.41549i 0.599927 0.405831i
\(431\) −23.8727 + 17.3445i −1.14991 + 0.835456i −0.988469 0.151427i \(-0.951613\pi\)
−0.161438 + 0.986883i \(0.551613\pi\)
\(432\) 0 0
\(433\) 15.9668 11.6006i 0.767316 0.557488i −0.133830 0.991004i \(-0.542727\pi\)
0.901146 + 0.433517i \(0.142727\pi\)
\(434\) −3.49263 0.742382i −0.167652 0.0356355i
\(435\) 0 0
\(436\) 0.448624 0.0953580i 0.0214852 0.00456682i
\(437\) 7.36318 8.17764i 0.352229 0.391190i
\(438\) 0 0
\(439\) 8.21559 + 9.12433i 0.392109 + 0.435481i 0.906585 0.422024i \(-0.138680\pi\)
−0.514476 + 0.857505i \(0.672014\pi\)
\(440\) 32.1751 5.71796i 1.53389 0.272593i
\(441\) 0 0
\(442\) 18.8024 13.6608i 0.894341 0.649777i
\(443\) 11.4062 19.7562i 0.541926 0.938643i −0.456868 0.889535i \(-0.651029\pi\)
0.998793 0.0491085i \(-0.0156380\pi\)
\(444\) 0 0
\(445\) −0.481121 6.74988i −0.0228073 0.319975i
\(446\) 2.35660 22.4216i 0.111588 1.06169i
\(447\) 0 0
\(448\) −20.0746 22.2951i −0.948435 1.05334i
\(449\) 4.10374 0.193668 0.0968338 0.995301i \(-0.469128\pi\)
0.0968338 + 0.995301i \(0.469128\pi\)
\(450\) 0 0
\(451\) −19.6015 −0.922997
\(452\) 0.190930 + 0.212049i 0.00898058 + 0.00997395i
\(453\) 0 0
\(454\) −1.07793 + 10.2559i −0.0505900 + 0.481331i
\(455\) 18.5915 + 22.0961i 0.871583 + 1.03588i
\(456\) 0 0
\(457\) 9.06472 15.7006i 0.424030 0.734441i −0.572299 0.820045i \(-0.693948\pi\)
0.996329 + 0.0856035i \(0.0272818\pi\)
\(458\) 11.9434 8.67742i 0.558080 0.405469i
\(459\) 0 0
\(460\) −0.220843 0.414001i −0.0102968 0.0193029i
\(461\) −15.7461 17.4878i −0.733370 0.814490i 0.254939 0.966957i \(-0.417945\pi\)
−0.988308 + 0.152468i \(0.951278\pi\)
\(462\) 0 0
\(463\) −2.39487 + 2.65977i −0.111299 + 0.123610i −0.796220 0.605008i \(-0.793170\pi\)
0.684921 + 0.728617i \(0.259837\pi\)
\(464\) 29.3812 6.24516i 1.36399 0.289924i
\(465\) 0 0
\(466\) −17.3156 3.68054i −0.802129 0.170498i
\(467\) −12.8399 + 9.32877i −0.594162 + 0.431684i −0.843802 0.536655i \(-0.819688\pi\)
0.249640 + 0.968339i \(0.419688\pi\)
\(468\) 0 0
\(469\) −3.16481 + 2.29937i −0.146137 + 0.106175i
\(470\) 38.1729 + 1.28163i 1.76078 + 0.0591171i
\(471\) 0 0
\(472\) −2.27437 + 21.6392i −0.104686 + 0.996026i
\(473\) 24.0170 5.10498i 1.10430 0.234727i
\(474\) 0 0
\(475\) −2.01752 + 11.6247i −0.0925700 + 0.533376i
\(476\) 0.835184 0.0382806
\(477\) 0 0
\(478\) −18.5323 13.4645i −0.847648 0.615852i
\(479\) 15.3830 6.84896i 0.702868 0.312937i −0.0240023 0.999712i \(-0.507641\pi\)
0.726870 + 0.686775i \(0.240974\pi\)
\(480\) 0 0
\(481\) −3.13410 1.39539i −0.142903 0.0636244i
\(482\) −2.09293 3.62506i −0.0953304 0.165117i
\(483\) 0 0
\(484\) −0.718609 0.152745i −0.0326640 0.00694295i
\(485\) 25.1391 26.1025i 1.14151 1.18525i
\(486\) 0 0
\(487\) −3.07445 9.46219i −0.139317 0.428773i 0.856920 0.515450i \(-0.172375\pi\)
−0.996236 + 0.0866771i \(0.972375\pi\)
\(488\) 18.0165 + 3.82953i 0.815569 + 0.173355i
\(489\) 0 0
\(490\) 1.76159 + 24.7142i 0.0795804 + 1.11647i
\(491\) −7.86619 + 8.73629i −0.354996 + 0.394263i −0.894020 0.448027i \(-0.852127\pi\)
0.539024 + 0.842291i \(0.318793\pi\)
\(492\) 0 0
\(493\) 17.7559 30.7542i 0.799688 1.38510i
\(494\) −9.18019 + 6.66980i −0.413036 + 0.300089i
\(495\) 0 0
\(496\) 2.15027 + 1.56227i 0.0965502 + 0.0701478i
\(497\) 12.2327 5.44634i 0.548710 0.244302i
\(498\) 0 0
\(499\) 12.7440 + 22.0733i 0.570501 + 0.988137i 0.996514 + 0.0834204i \(0.0265844\pi\)
−0.426013 + 0.904717i \(0.640082\pi\)
\(500\) 0.436701 + 0.249786i 0.0195299 + 0.0111708i
\(501\) 0 0
\(502\) −4.51661 5.01621i −0.201586 0.223884i
\(503\) 3.86329 + 2.80684i 0.172256 + 0.125151i 0.670573 0.741844i \(-0.266048\pi\)
−0.498317 + 0.866995i \(0.666048\pi\)
\(504\) 0 0
\(505\) 1.72052 12.3628i 0.0765621 0.550135i
\(506\) −3.64397 34.6700i −0.161994 1.54127i
\(507\) 0 0
\(508\) 0.612521 + 0.272712i 0.0271762 + 0.0120996i
\(509\) 0.140363 0.155889i 0.00622150 0.00690968i −0.740026 0.672578i \(-0.765187\pi\)
0.746248 + 0.665669i \(0.231854\pi\)
\(510\) 0 0
\(511\) 11.4874 + 12.7580i 0.508171 + 0.564381i
\(512\) 6.74190 + 20.7494i 0.297953 + 0.917005i
\(513\) 0 0
\(514\) 9.37282 28.8466i 0.413417 1.27237i
\(515\) 0.385942 + 1.33914i 0.0170066 + 0.0590095i
\(516\) 0 0
\(517\) 57.0415 + 25.3965i 2.50868 + 1.11694i
\(518\) −2.80142 4.85221i −0.123088 0.213194i
\(519\) 0 0
\(520\) −5.82160 20.1997i −0.255294 0.885818i
\(521\) 10.5015 + 7.62978i 0.460079 + 0.334267i 0.793562 0.608489i \(-0.208224\pi\)
−0.333484 + 0.942756i \(0.608224\pi\)
\(522\) 0 0
\(523\) 11.1175 34.2162i 0.486136 1.49617i −0.344194 0.938899i \(-0.611848\pi\)
0.830329 0.557273i \(-0.188152\pi\)
\(524\) −0.302992 + 0.524797i −0.0132363 + 0.0229259i
\(525\) 0 0
\(526\) 5.28890 + 9.16064i 0.230607 + 0.399423i
\(527\) 3.07362 0.653317i 0.133889 0.0284590i
\(528\) 0 0
\(529\) −1.14461 + 0.509612i −0.0497655 + 0.0221570i
\(530\) 5.43223 + 10.1835i 0.235961 + 0.442342i
\(531\) 0 0
\(532\) −0.407774 −0.0176792
\(533\) 1.31802 + 12.5402i 0.0570900 + 0.543175i
\(534\) 0 0
\(535\) −17.6501 + 7.15874i −0.763081 + 0.309499i
\(536\) 2.78557 0.592092i 0.120318 0.0255745i
\(537\) 0 0
\(538\) 39.1485 + 8.32127i 1.68781 + 0.358756i
\(539\) −12.5167 + 38.5225i −0.539133 + 1.65928i
\(540\) 0 0
\(541\) 5.95413 + 18.3249i 0.255988 + 0.787850i 0.993633 + 0.112661i \(0.0359376\pi\)
−0.737646 + 0.675188i \(0.764062\pi\)
\(542\) 3.07719 + 29.2775i 0.132177 + 1.25758i
\(543\) 0 0
\(544\) −1.12365 0.500282i −0.0481762 0.0214494i
\(545\) −14.6735 17.4395i −0.628544 0.747027i
\(546\) 0 0
\(547\) 39.9472 17.7856i 1.70802 0.760459i 0.709578 0.704627i \(-0.248885\pi\)
0.998440 0.0558322i \(-0.0177812\pi\)
\(548\) −0.126986 + 0.390823i −0.00542458 + 0.0166951i
\(549\) 0 0
\(550\) 23.0910 + 29.3918i 0.984603 + 1.25327i
\(551\) −8.66924 + 15.0156i −0.369322 + 0.639685i
\(552\) 0 0
\(553\) 0.658364 6.26392i 0.0279965 0.266369i
\(554\) −0.406925 + 3.87163i −0.0172886 + 0.164490i
\(555\) 0 0
\(556\) −0.0551836 0.525037i −0.00234031 0.0222665i
\(557\) −42.9035 −1.81788 −0.908939 0.416929i \(-0.863106\pi\)
−0.908939 + 0.416929i \(0.863106\pi\)
\(558\) 0 0
\(559\) −4.88088 15.0218i −0.206439 0.635354i
\(560\) 11.9622 33.0038i 0.505494 1.39467i
\(561\) 0 0
\(562\) −22.9976 + 25.5414i −0.970094 + 1.07740i
\(563\) −10.6413 + 11.8183i −0.448476 + 0.498083i −0.924411 0.381397i \(-0.875443\pi\)
0.475935 + 0.879480i \(0.342110\pi\)
\(564\) 0 0
\(565\) 4.83170 13.3307i 0.203271 0.560828i
\(566\) −3.40526 10.4803i −0.143134 0.440520i
\(567\) 0 0
\(568\) −9.74791 −0.409013
\(569\) 2.46904 + 23.4914i 0.103508 + 0.984810i 0.915820 + 0.401588i \(0.131542\pi\)
−0.812313 + 0.583222i \(0.801792\pi\)
\(570\) 0 0
\(571\) 0.122040 1.16113i 0.00510720 0.0485917i −0.991671 0.128793i \(-0.958890\pi\)
0.996779 + 0.0802014i \(0.0255563\pi\)
\(572\) −0.0826824 + 0.786670i −0.00345712 + 0.0328923i
\(573\) 0 0
\(574\) −10.2964 + 17.8339i −0.429763 + 0.744372i
\(575\) −12.9866 + 19.3656i −0.541578 + 0.807600i
\(576\) 0 0
\(577\) −10.2147 + 31.4377i −0.425244 + 1.30877i 0.477516 + 0.878623i \(0.341537\pi\)
−0.902760 + 0.430144i \(0.858463\pi\)
\(578\) −8.30596 + 3.69805i −0.345482 + 0.153819i
\(579\) 0 0
\(580\) 0.475989 + 0.565714i 0.0197643 + 0.0234900i
\(581\) 39.6560 + 17.6560i 1.64521 + 0.732494i
\(582\) 0 0
\(583\) 1.97228 + 18.7650i 0.0816835 + 0.777167i
\(584\) −3.86200 11.8860i −0.159811 0.491847i
\(585\) 0 0
\(586\) 12.1936 37.5281i 0.503714 1.55027i
\(587\) 3.60347 + 0.765941i 0.148731 + 0.0316138i 0.281675 0.959510i \(-0.409110\pi\)
−0.132944 + 0.991123i \(0.542443\pi\)
\(588\) 0 0
\(589\) −1.50068 + 0.318979i −0.0618343 + 0.0131433i
\(590\) −23.0619 + 9.35369i −0.949442 + 0.385085i
\(591\) 0 0
\(592\) 0.435945 + 4.14774i 0.0179172 + 0.170471i
\(593\) −18.3600 −0.753956 −0.376978 0.926222i \(-0.623037\pi\)
−0.376978 + 0.926222i \(0.623037\pi\)
\(594\) 0 0
\(595\) −19.5335 36.6184i −0.800797 1.50121i
\(596\) −0.389138 + 0.173256i −0.0159397 + 0.00709682i
\(597\) 0 0
\(598\) −21.9354 + 4.66250i −0.897004 + 0.190664i
\(599\) −21.7553 37.6813i −0.888897 1.53961i −0.841181 0.540754i \(-0.818139\pi\)
−0.0477161 0.998861i \(-0.515194\pi\)
\(600\) 0 0
\(601\) 4.47712 7.75460i 0.182626 0.316317i −0.760148 0.649750i \(-0.774874\pi\)
0.942774 + 0.333433i \(0.108207\pi\)
\(602\) 7.97120 24.5328i 0.324882 0.999884i
\(603\) 0 0
\(604\) 0.558712 + 0.405928i 0.0227337 + 0.0165170i
\(605\) 10.1100 + 35.0796i 0.411030 + 1.42619i
\(606\) 0 0
\(607\) 2.21210 + 3.83147i 0.0897864 + 0.155515i 0.907421 0.420223i \(-0.138048\pi\)
−0.817634 + 0.575738i \(0.804715\pi\)
\(608\) 0.548617 + 0.244260i 0.0222494 + 0.00990605i
\(609\) 0 0
\(610\) 5.83410 + 20.2431i 0.236216 + 0.819621i
\(611\) 12.4121 38.2004i 0.502138 1.54542i
\(612\) 0 0
\(613\) −6.60377 20.3243i −0.266724 0.820891i −0.991291 0.131687i \(-0.957960\pi\)
0.724568 0.689204i \(-0.242040\pi\)
\(614\) 28.5183 + 31.6727i 1.15090 + 1.27821i
\(615\) 0 0
\(616\) 37.5553 41.7093i 1.51314 1.68052i
\(617\) 29.4288 + 13.1026i 1.18476 + 0.527489i 0.902014 0.431706i \(-0.142088\pi\)
0.282745 + 0.959195i \(0.408755\pi\)
\(618\) 0 0
\(619\) 4.20729 + 40.0297i 0.169105 + 1.60893i 0.669284 + 0.743007i \(0.266601\pi\)
−0.500178 + 0.865922i \(0.666732\pi\)
\(620\) −0.00901746 + 0.0647948i −0.000362150 + 0.00260222i
\(621\) 0 0
\(622\) 6.40277 + 4.65188i 0.256728 + 0.186524i
\(623\) −7.77671 8.63691i −0.311567 0.346031i
\(624\) 0 0
\(625\) 0.738068 24.9891i 0.0295227 0.999564i
\(626\) 4.09393 + 7.09089i 0.163626 + 0.283409i
\(627\) 0 0
\(628\) −0.896449 + 0.399125i −0.0357722 + 0.0159268i
\(629\) 3.98900 + 2.89817i 0.159052 + 0.115558i
\(630\) 0 0
\(631\) −0.646758 + 0.469897i −0.0257470 + 0.0187063i −0.600584 0.799561i \(-0.705065\pi\)
0.574837 + 0.818268i \(0.305065\pi\)
\(632\) −2.29257 + 3.97084i −0.0911934 + 0.157952i
\(633\) 0 0
\(634\) 11.1411 12.3735i 0.442470 0.491413i
\(635\) −2.36887 33.2341i −0.0940059 1.31885i
\(636\) 0 0
\(637\) 25.4867 + 5.41736i 1.00982 + 0.214644i
\(638\) 16.9738 + 52.2399i 0.671999 + 2.06820i
\(639\) 0 0
\(640\) −18.1180 + 18.8123i −0.716175 + 0.743620i
\(641\) −28.1541 5.98433i −1.11202 0.236367i −0.384954 0.922936i \(-0.625783\pi\)
−0.727065 + 0.686569i \(0.759116\pi\)
\(642\) 0 0
\(643\) 24.5329 + 42.4923i 0.967484 + 1.67573i 0.702789 + 0.711399i \(0.251938\pi\)
0.264695 + 0.964332i \(0.414729\pi\)
\(644\) −0.736200 0.327777i −0.0290103 0.0129162i
\(645\) 0 0
\(646\) 14.8987 6.63332i 0.586180 0.260984i
\(647\) 11.9156 + 8.65721i 0.468452 + 0.340350i 0.796838 0.604194i \(-0.206505\pi\)
−0.328386 + 0.944544i \(0.606505\pi\)
\(648\) 0 0
\(649\) −40.6843 −1.59700
\(650\) 17.2509 16.7490i 0.676638 0.656948i
\(651\) 0 0
\(652\) 0.507939 0.107966i 0.0198924 0.00422827i
\(653\) −2.79240 + 26.5679i −0.109275 + 1.03968i 0.793206 + 0.608954i \(0.208410\pi\)
−0.902481 + 0.430730i \(0.858256\pi\)
\(654\) 0 0
\(655\) 30.0960 + 1.01045i 1.17595 + 0.0394817i
\(656\) 12.4011 9.00994i 0.484182 0.351779i
\(657\) 0 0
\(658\) 53.0696 38.5573i 2.06887 1.50312i
\(659\) −5.26842 1.11984i −0.205228 0.0436226i 0.104150 0.994562i \(-0.466788\pi\)
−0.309379 + 0.950939i \(0.600121\pi\)
\(660\) 0 0
\(661\) 23.7568 5.04966i 0.924032 0.196409i 0.278759 0.960361i \(-0.410077\pi\)
0.645273 + 0.763952i \(0.276744\pi\)
\(662\) 19.1488 21.2669i 0.744240 0.826563i
\(663\) 0 0
\(664\) −21.1451 23.4840i −0.820590 0.911357i
\(665\) 9.53715 + 17.8787i 0.369835 + 0.693307i
\(666\) 0 0
\(667\) −27.7214 + 20.1408i −1.07338 + 0.779854i
\(668\) −0.0949884 + 0.164525i −0.00367521 + 0.00636565i
\(669\) 0 0
\(670\) 2.09706 + 2.49236i 0.0810164 + 0.0962883i
\(671\) −3.59998 + 34.2515i −0.138976 + 1.32227i
\(672\) 0 0
\(673\) 22.8188 + 25.3428i 0.879599 + 0.976893i 0.999874 0.0158471i \(-0.00504451\pi\)
−0.120276 + 0.992741i \(0.538378\pi\)
\(674\) 5.68410 0.218943
\(675\) 0 0
\(676\) −0.0761349 −0.00292826
\(677\) −3.34059 3.71010i −0.128389 0.142591i 0.675522 0.737339i \(-0.263918\pi\)
−0.803912 + 0.594749i \(0.797252\pi\)
\(678\) 0 0
\(679\) 6.50590 61.8995i 0.249673 2.37548i
\(680\) 2.14809 + 30.1367i 0.0823756 + 1.15569i
\(681\) 0 0
\(682\) −2.43018 + 4.20919i −0.0930563 + 0.161178i
\(683\) −6.26357 + 4.55075i −0.239669 + 0.174130i −0.701136 0.713028i \(-0.747323\pi\)
0.461467 + 0.887157i \(0.347323\pi\)
\(684\) 0 0
\(685\) 20.1055 3.57303i 0.768192 0.136519i
\(686\) 2.75042 + 3.05465i 0.105012 + 0.116627i
\(687\) 0 0
\(688\) −12.8481 + 14.2693i −0.489831 + 0.544013i
\(689\) 11.8724 2.52356i 0.452303 0.0961400i
\(690\) 0 0
\(691\) −31.3939 6.67298i −1.19428 0.253852i −0.432468 0.901649i \(-0.642357\pi\)
−0.761813 + 0.647797i \(0.775690\pi\)
\(692\) −0.359454 + 0.261158i −0.0136644 + 0.00992775i
\(693\) 0 0
\(694\) −42.4980 + 30.8766i −1.61320 + 1.17206i
\(695\) −21.7294 + 14.6992i −0.824244 + 0.557574i
\(696\) 0 0
\(697\) 1.89429 18.0230i 0.0717514 0.682669i
\(698\) −15.5758 + 3.31074i −0.589553 + 0.125313i
\(699\) 0 0
\(700\) 0.855307 0.122553i 0.0323276 0.00463205i
\(701\) 2.23365 0.0843639 0.0421819 0.999110i \(-0.486569\pi\)
0.0421819 + 0.999110i \(0.486569\pi\)
\(702\) 0 0
\(703\) −1.94761 1.41502i −0.0734553 0.0533684i
\(704\) −37.3066 + 16.6100i −1.40604 + 0.626011i
\(705\) 0 0
\(706\) −3.88837 1.73121i −0.146341 0.0651551i
\(707\) −10.7186 18.5652i −0.403115 0.698216i
\(708\) 0 0
\(709\) −40.0642 8.51592i −1.50464 0.319822i −0.619447 0.785038i \(-0.712643\pi\)
−0.885197 + 0.465216i \(0.845976\pi\)
\(710\) −5.24754 9.83724i −0.196936 0.369185i
\(711\) 0 0
\(712\) 2.61449 + 8.04659i 0.0979823 + 0.301559i
\(713\) −2.96574 0.630388i −0.111068 0.0236082i
\(714\) 0 0
\(715\) 36.4251 14.7737i 1.36222 0.552506i
\(716\) −0.106429 + 0.118201i −0.00397742 + 0.00441738i
\(717\) 0 0
\(718\) −1.65319 + 2.86342i −0.0616967 + 0.106862i
\(719\) −11.5919 + 8.42199i −0.432304 + 0.314087i −0.782570 0.622563i \(-0.786091\pi\)
0.350265 + 0.936650i \(0.386091\pi\)
\(720\) 0 0
\(721\) 1.93641 + 1.40689i 0.0721158 + 0.0523952i
\(722\) 17.5474 7.81262i 0.653048 0.290756i
\(723\) 0 0
\(724\) 0.343491 + 0.594944i 0.0127657 + 0.0221109i
\(725\) 13.6710 34.1007i 0.507728 1.26647i
\(726\) 0 0
\(727\) −22.8565 25.3847i −0.847700 0.941466i 0.151193 0.988504i \(-0.451688\pi\)
−0.998893 + 0.0470382i \(0.985022\pi\)
\(728\) −29.2091 21.2217i −1.08256 0.786527i
\(729\) 0 0
\(730\) 9.91593 10.2959i 0.367005 0.381069i
\(731\) 2.37287 + 22.5763i 0.0877636 + 0.835015i
\(732\) 0 0
\(733\) −40.6252 18.0875i −1.50053 0.668078i −0.518202 0.855258i \(-0.673398\pi\)
−0.982326 + 0.187180i \(0.940065\pi\)
\(734\) 16.2099 18.0029i 0.598318 0.664499i
\(735\) 0 0
\(736\) 0.794139 + 0.881980i 0.0292723 + 0.0325102i
\(737\) 1.64548 + 5.06426i 0.0606119 + 0.186544i
\(738\) 0 0
\(739\) −6.83528 + 21.0368i −0.251440 + 0.773852i 0.743071 + 0.669213i \(0.233369\pi\)
−0.994510 + 0.104639i \(0.966631\pi\)
\(740\) −0.0850248 + 0.0575165i −0.00312557 + 0.00211435i
\(741\) 0 0
\(742\) 18.1089 + 8.06258i 0.664797 + 0.295987i
\(743\) −5.42519 9.39670i −0.199031 0.344732i 0.749184 0.662362i \(-0.230446\pi\)
−0.948214 + 0.317631i \(0.897113\pi\)
\(744\) 0 0
\(745\) 16.6976 + 13.0095i 0.611754 + 0.476631i
\(746\) −29.1662 21.1905i −1.06785 0.775838i
\(747\) 0 0
\(748\) 0.351305 1.08120i 0.0128450 0.0395328i
\(749\) −16.3560 + 28.3294i −0.597635 + 1.03513i
\(750\) 0 0
\(751\) 7.68498 + 13.3108i 0.280429 + 0.485717i 0.971490 0.237079i \(-0.0761900\pi\)
−0.691062 + 0.722796i \(0.742857\pi\)
\(752\) −47.7618 + 10.1521i −1.74169 + 0.370208i
\(753\) 0 0
\(754\) 32.2795 14.3718i 1.17555 0.523389i
\(755\) 4.73045 33.9905i 0.172159 1.23704i
\(756\) 0 0
\(757\) −32.9738 −1.19845 −0.599226 0.800580i \(-0.704525\pi\)
−0.599226 + 0.800580i \(0.704525\pi\)
\(758\) −3.65712 34.7952i −0.132833 1.26382i
\(759\) 0 0
\(760\) −1.04879 14.7141i −0.0380438 0.533735i
\(761\) −31.3838 + 6.67084i −1.13766 + 0.241818i −0.737971 0.674832i \(-0.764216\pi\)
−0.399691 + 0.916650i \(0.630883\pi\)
\(762\) 0 0
\(763\) −38.2881 8.13839i −1.38612 0.294630i
\(764\) −0.257948 + 0.793883i −0.00933224 + 0.0287217i
\(765\) 0 0
\(766\) −0.00222259 0.00684042i −8.03054e−5 0.000247155i
\(767\) 2.73566 + 26.0280i 0.0987788 + 0.939818i
\(768\) 0 0
\(769\) −38.7820 17.2669i −1.39852 0.622659i −0.437516 0.899211i \(-0.644142\pi\)
−0.960999 + 0.276552i \(0.910808\pi\)
\(770\) 62.3085 + 15.4463i 2.24544 + 0.556645i
\(771\) 0 0
\(772\) 0.478663 0.213114i 0.0172275 0.00767016i
\(773\) −0.355723 + 1.09480i −0.0127945 + 0.0393773i −0.957250 0.289262i \(-0.906590\pi\)
0.944455 + 0.328639i \(0.106590\pi\)
\(774\) 0 0
\(775\) 3.05181 1.12007i 0.109624 0.0402342i
\(776\) −22.6549 + 39.2395i −0.813265 + 1.40862i
\(777\) 0 0
\(778\) −1.55860 + 14.8290i −0.0558783 + 0.531647i
\(779\) −0.924877 + 8.79962i −0.0331372 + 0.315279i
\(780\) 0 0
\(781\) −1.90522 18.1270i −0.0681742 0.648634i
\(782\) 32.2302 1.15255
\(783\) 0 0
\(784\) −9.78826 30.1252i −0.349581 1.07590i
\(785\) 38.4660 + 29.9697i 1.37291 + 1.06966i
\(786\) 0 0
\(787\) 6.85895