Properties

Label 675.2.r.a.46.2
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 46.2
Character \(\chi\) \(=\) 675.46
Dual form 675.2.r.a.631.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.69452 - 1.88195i) q^{2} +(-0.461298 + 4.38896i) q^{4} +(2.12223 - 0.704374i) q^{5} +(-1.03406 + 1.79105i) q^{7} +(4.94396 - 3.59200i) q^{8} +O(q^{10})\) \(q+(-1.69452 - 1.88195i) q^{2} +(-0.461298 + 4.38896i) q^{4} +(2.12223 - 0.704374i) q^{5} +(-1.03406 + 1.79105i) q^{7} +(4.94396 - 3.59200i) q^{8} +(-4.92175 - 2.80036i) q^{10} +(-1.63896 - 1.82025i) q^{11} +(-1.19441 + 1.32652i) q^{13} +(5.12291 - 1.08891i) q^{14} +(-6.50420 - 1.38251i) q^{16} +(-3.67466 + 2.66979i) q^{17} +(5.85004 - 4.25031i) q^{19} +(2.11249 + 9.63931i) q^{20} +(-0.648378 + 6.16890i) q^{22} +(2.31553 - 0.492181i) q^{23} +(4.00772 - 2.98968i) q^{25} +4.52040 q^{26} +(-7.38384 - 5.36467i) q^{28} +(7.47301 - 3.32720i) q^{29} +(6.20029 + 2.76055i) q^{31} +(2.30859 + 3.99860i) q^{32} +(11.2512 + 2.39152i) q^{34} +(-0.932951 + 4.52939i) q^{35} +(1.53985 + 4.73917i) q^{37} +(-17.9119 - 3.80729i) q^{38} +(7.96211 - 11.1054i) q^{40} +(3.20347 - 3.55781i) q^{41} +(4.14034 - 7.17127i) q^{43} +(8.74507 - 6.35367i) q^{44} +(-4.84997 - 3.52371i) q^{46} +(9.25434 - 4.12030i) q^{47} +(1.36143 + 2.35806i) q^{49} +(-12.4176 - 2.47626i) q^{50} +(-5.27108 - 5.85413i) q^{52} +(2.52356 + 1.83348i) q^{53} +(-4.76039 - 2.70855i) q^{55} +(1.32108 + 12.5692i) q^{56} +(-18.9248 - 8.42585i) q^{58} +(-6.99016 + 7.76336i) q^{59} +(-1.76446 - 1.95963i) q^{61} +(-5.31128 - 16.3465i) q^{62} +(-0.496397 + 1.52775i) q^{64} +(-1.60044 + 3.65649i) q^{65} +(-1.48939 - 0.663118i) q^{67} +(-10.0225 - 17.3595i) q^{68} +(10.1050 - 5.91936i) q^{70} +(-8.24169 - 5.98794i) q^{71} +(-0.608028 + 1.87132i) q^{73} +(6.30959 - 10.9285i) q^{74} +(15.9558 + 27.6363i) q^{76} +(4.95496 - 1.05321i) q^{77} +(13.6290 - 6.06801i) q^{79} +(-14.7772 + 1.64738i) q^{80} -12.1240 q^{82} +(0.424422 + 4.03811i) q^{83} +(-5.91793 + 8.25424i) q^{85} +(-20.5119 + 4.35993i) q^{86} +(-14.6413 - 3.11211i) q^{88} +(-0.105993 + 0.326212i) q^{89} +(-1.14078 - 3.51095i) q^{91} +(1.09201 + 10.3898i) q^{92} +(-23.4358 - 10.4343i) q^{94} +(9.42133 - 13.1407i) q^{95} +(-10.0640 + 4.48076i) q^{97} +(2.13079 - 6.55791i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.69452 1.88195i −1.19821 1.33074i −0.930080 0.367358i \(-0.880263\pi\)
−0.268125 0.963384i \(-0.586404\pi\)
\(3\) 0 0
\(4\) −0.461298 + 4.38896i −0.230649 + 2.19448i
\(5\) 2.12223 0.704374i 0.949090 0.315005i
\(6\) 0 0
\(7\) −1.03406 + 1.79105i −0.390839 + 0.676953i −0.992560 0.121753i \(-0.961148\pi\)
0.601721 + 0.798706i \(0.294482\pi\)
\(8\) 4.94396 3.59200i 1.74795 1.26996i
\(9\) 0 0
\(10\) −4.92175 2.80036i −1.55640 0.885552i
\(11\) −1.63896 1.82025i −0.494166 0.548827i 0.443541 0.896254i \(-0.353722\pi\)
−0.937707 + 0.347427i \(0.887055\pi\)
\(12\) 0 0
\(13\) −1.19441 + 1.32652i −0.331269 + 0.367911i −0.885651 0.464351i \(-0.846288\pi\)
0.554383 + 0.832262i \(0.312954\pi\)
\(14\) 5.12291 1.08891i 1.36916 0.291023i
\(15\) 0 0
\(16\) −6.50420 1.38251i −1.62605 0.345628i
\(17\) −3.67466 + 2.66979i −0.891235 + 0.647520i −0.936200 0.351469i \(-0.885682\pi\)
0.0449649 + 0.998989i \(0.485682\pi\)
\(18\) 0 0
\(19\) 5.85004 4.25031i 1.34209 0.975087i 0.342728 0.939435i \(-0.388649\pi\)
0.999364 0.0356524i \(-0.0113509\pi\)
\(20\) 2.11249 + 9.63931i 0.472367 + 2.15542i
\(21\) 0 0
\(22\) −0.648378 + 6.16890i −0.138235 + 1.31521i
\(23\) 2.31553 0.492181i 0.482821 0.102627i 0.0399305 0.999202i \(-0.487286\pi\)
0.442891 + 0.896576i \(0.353953\pi\)
\(24\) 0 0
\(25\) 4.00772 2.98968i 0.801543 0.597937i
\(26\) 4.52040 0.886523
\(27\) 0 0
\(28\) −7.38384 5.36467i −1.39541 1.01383i
\(29\) 7.47301 3.32720i 1.38770 0.617845i 0.429273 0.903175i \(-0.358770\pi\)
0.958429 + 0.285330i \(0.0921031\pi\)
\(30\) 0 0
\(31\) 6.20029 + 2.76055i 1.11361 + 0.495809i 0.879259 0.476344i \(-0.158038\pi\)
0.234346 + 0.972153i \(0.424705\pi\)
\(32\) 2.30859 + 3.99860i 0.408105 + 0.706859i
\(33\) 0 0
\(34\) 11.2512 + 2.39152i 1.92956 + 0.410141i
\(35\) −0.932951 + 4.52939i −0.157698 + 0.765606i
\(36\) 0 0
\(37\) 1.53985 + 4.73917i 0.253150 + 0.779115i 0.994189 + 0.107653i \(0.0343334\pi\)
−0.741039 + 0.671462i \(0.765667\pi\)
\(38\) −17.9119 3.80729i −2.90569 0.617624i
\(39\) 0 0
\(40\) 7.96211 11.1054i 1.25892 1.75592i
\(41\) 3.20347 3.55781i 0.500297 0.555636i −0.439113 0.898432i \(-0.644707\pi\)
0.939410 + 0.342796i \(0.111374\pi\)
\(42\) 0 0
\(43\) 4.14034 7.17127i 0.631395 1.09361i −0.355871 0.934535i \(-0.615816\pi\)
0.987267 0.159074i \(-0.0508508\pi\)
\(44\) 8.74507 6.35367i 1.31837 0.957851i
\(45\) 0 0
\(46\) −4.84997 3.52371i −0.715088 0.519542i
\(47\) 9.25434 4.12030i 1.34988 0.601007i 0.400839 0.916148i \(-0.368719\pi\)
0.949045 + 0.315141i \(0.102052\pi\)
\(48\) 0 0
\(49\) 1.36143 + 2.35806i 0.194489 + 0.336866i
\(50\) −12.4176 2.47626i −1.75611 0.350196i
\(51\) 0 0
\(52\) −5.27108 5.85413i −0.730967 0.811821i
\(53\) 2.52356 + 1.83348i 0.346638 + 0.251847i 0.747457 0.664310i \(-0.231274\pi\)
−0.400819 + 0.916157i \(0.631274\pi\)
\(54\) 0 0
\(55\) −4.76039 2.70855i −0.641891 0.365221i
\(56\) 1.32108 + 12.5692i 0.176537 + 1.67963i
\(57\) 0 0
\(58\) −18.9248 8.42585i −2.48494 1.10637i
\(59\) −6.99016 + 7.76336i −0.910041 + 1.01070i 0.0898499 + 0.995955i \(0.471361\pi\)
−0.999891 + 0.0147480i \(0.995305\pi\)
\(60\) 0 0
\(61\) −1.76446 1.95963i −0.225916 0.250905i 0.619521 0.784980i \(-0.287327\pi\)
−0.845437 + 0.534075i \(0.820660\pi\)
\(62\) −5.31128 16.3465i −0.674534 2.07600i
\(63\) 0 0
\(64\) −0.496397 + 1.52775i −0.0620496 + 0.190969i
\(65\) −1.60044 + 3.65649i −0.198510 + 0.453532i
\(66\) 0 0
\(67\) −1.48939 0.663118i −0.181958 0.0810127i 0.313736 0.949510i \(-0.398419\pi\)
−0.495693 + 0.868498i \(0.665086\pi\)
\(68\) −10.0225 17.3595i −1.21541 2.10515i
\(69\) 0 0
\(70\) 10.1050 5.91936i 1.20778 0.707498i
\(71\) −8.24169 5.98794i −0.978109 0.710638i −0.0208238 0.999783i \(-0.506629\pi\)
−0.957285 + 0.289145i \(0.906629\pi\)
\(72\) 0 0
\(73\) −0.608028 + 1.87132i −0.0711643 + 0.219021i −0.980313 0.197451i \(-0.936734\pi\)
0.909148 + 0.416472i \(0.136734\pi\)
\(74\) 6.30959 10.9285i 0.733475 1.27042i
\(75\) 0 0
\(76\) 15.9558 + 27.6363i 1.83026 + 3.17010i
\(77\) 4.95496 1.05321i 0.564670 0.120024i
\(78\) 0 0
\(79\) 13.6290 6.06801i 1.53338 0.682704i 0.545525 0.838094i \(-0.316330\pi\)
0.987853 + 0.155390i \(0.0496635\pi\)
\(80\) −14.7772 + 1.64738i −1.65214 + 0.184183i
\(81\) 0 0
\(82\) −12.1240 −1.33887
\(83\) 0.424422 + 4.03811i 0.0465864 + 0.443240i 0.992808 + 0.119720i \(0.0381996\pi\)
−0.946221 + 0.323520i \(0.895134\pi\)
\(84\) 0 0
\(85\) −5.91793 + 8.25424i −0.641890 + 0.895298i
\(86\) −20.5119 + 4.35993i −2.21185 + 0.470144i
\(87\) 0 0
\(88\) −14.6413 3.11211i −1.56077 0.331752i
\(89\) −0.105993 + 0.326212i −0.0112352 + 0.0345784i −0.956517 0.291677i \(-0.905787\pi\)
0.945282 + 0.326255i \(0.105787\pi\)
\(90\) 0 0
\(91\) −1.14078 3.51095i −0.119586 0.368048i
\(92\) 1.09201 + 10.3898i 0.113850 + 1.08321i
\(93\) 0 0
\(94\) −23.4358 10.4343i −2.41722 1.07622i
\(95\) 9.42133 13.1407i 0.966608 1.34821i
\(96\) 0 0
\(97\) −10.0640 + 4.48076i −1.02184 + 0.454953i −0.848098 0.529839i \(-0.822252\pi\)
−0.173742 + 0.984791i \(0.555586\pi\)
\(98\) 2.13079 6.55791i 0.215243 0.662449i
\(99\) 0 0
\(100\) 11.2729 + 18.9688i 1.12729 + 1.89688i
\(101\) −6.38861 + 11.0654i −0.635691 + 1.10105i 0.350677 + 0.936496i \(0.385951\pi\)
−0.986368 + 0.164553i \(0.947382\pi\)
\(102\) 0 0
\(103\) 0.959675 9.13070i 0.0945596 0.899674i −0.839693 0.543062i \(-0.817265\pi\)
0.934252 0.356613i \(-0.116068\pi\)
\(104\) −1.14023 + 10.8486i −0.111809 + 1.06379i
\(105\) 0 0
\(106\) −0.825708 7.85609i −0.0801999 0.763051i
\(107\) −0.980681 −0.0948061 −0.0474030 0.998876i \(-0.515095\pi\)
−0.0474030 + 0.998876i \(0.515095\pi\)
\(108\) 0 0
\(109\) −2.74384 8.44467i −0.262812 0.808853i −0.992189 0.124741i \(-0.960190\pi\)
0.729377 0.684112i \(-0.239810\pi\)
\(110\) 2.96920 + 13.5485i 0.283103 + 1.29180i
\(111\) 0 0
\(112\) 9.20190 10.2197i 0.869498 0.965675i
\(113\) −4.53863 + 5.04065i −0.426958 + 0.474185i −0.917788 0.397070i \(-0.870027\pi\)
0.490830 + 0.871255i \(0.336694\pi\)
\(114\) 0 0
\(115\) 4.56740 2.67552i 0.425913 0.249493i
\(116\) 11.1557 + 34.3336i 1.03578 + 3.18779i
\(117\) 0 0
\(118\) 26.4552 2.43540
\(119\) −0.981908 9.34223i −0.0900113 0.856401i
\(120\) 0 0
\(121\) 0.522693 4.97309i 0.0475175 0.452099i
\(122\) −0.698024 + 6.64126i −0.0631962 + 0.601271i
\(123\) 0 0
\(124\) −14.9761 + 25.9394i −1.34490 + 2.32943i
\(125\) 6.39944 9.16773i 0.572383 0.819986i
\(126\) 0 0
\(127\) 3.08193 9.48521i 0.273477 0.841676i −0.716141 0.697955i \(-0.754093\pi\)
0.989618 0.143721i \(-0.0459067\pi\)
\(128\) 12.1523 5.41057i 1.07412 0.478231i
\(129\) 0 0
\(130\) 9.59332 3.18405i 0.841390 0.279259i
\(131\) 12.5686 + 5.59591i 1.09813 + 0.488917i 0.874139 0.485675i \(-0.161426\pi\)
0.223986 + 0.974592i \(0.428093\pi\)
\(132\) 0 0
\(133\) 1.56320 + 14.8728i 0.135546 + 1.28964i
\(134\) 1.27584 + 3.92662i 0.110215 + 0.339208i
\(135\) 0 0
\(136\) −8.57746 + 26.3987i −0.735511 + 2.26367i
\(137\) −8.34276 1.77331i −0.712770 0.151504i −0.162764 0.986665i \(-0.552041\pi\)
−0.550005 + 0.835161i \(0.685374\pi\)
\(138\) 0 0
\(139\) 9.12603 1.93980i 0.774060 0.164532i 0.196086 0.980587i \(-0.437177\pi\)
0.577974 + 0.816055i \(0.303843\pi\)
\(140\) −19.4489 6.18409i −1.64374 0.522651i
\(141\) 0 0
\(142\) 2.69667 + 25.6571i 0.226300 + 2.15310i
\(143\) 4.37219 0.365621
\(144\) 0 0
\(145\) 13.5158 12.3249i 1.12243 1.02352i
\(146\) 4.55205 2.02670i 0.376730 0.167731i
\(147\) 0 0
\(148\) −21.5104 + 4.57217i −1.76814 + 0.375830i
\(149\) 3.47298 + 6.01538i 0.284518 + 0.492799i 0.972492 0.232936i \(-0.0748332\pi\)
−0.687974 + 0.725735i \(0.741500\pi\)
\(150\) 0 0
\(151\) 0.394205 0.682783i 0.0320800 0.0555641i −0.849540 0.527525i \(-0.823120\pi\)
0.881620 + 0.471961i \(0.156454\pi\)
\(152\) 13.6553 42.0267i 1.10759 3.40881i
\(153\) 0 0
\(154\) −10.3783 7.54031i −0.836311 0.607616i
\(155\) 15.1029 + 1.49119i 1.21309 + 0.119776i
\(156\) 0 0
\(157\) −1.94393 3.36698i −0.155142 0.268714i 0.777969 0.628303i \(-0.216250\pi\)
−0.933111 + 0.359589i \(0.882917\pi\)
\(158\) −34.5142 15.3667i −2.74580 1.22251i
\(159\) 0 0
\(160\) 7.71587 + 6.85983i 0.609993 + 0.542318i
\(161\) −1.51288 + 4.65617i −0.119232 + 0.366958i
\(162\) 0 0
\(163\) 2.59370 + 7.98258i 0.203154 + 0.625244i 0.999784 + 0.0207767i \(0.00661392\pi\)
−0.796630 + 0.604467i \(0.793386\pi\)
\(164\) 14.1373 + 15.7011i 1.10394 + 1.22605i
\(165\) 0 0
\(166\) 6.88033 7.64139i 0.534018 0.593087i
\(167\) −9.87343 4.39594i −0.764029 0.340168i −0.0125472 0.999921i \(-0.503994\pi\)
−0.751482 + 0.659754i \(0.770661\pi\)
\(168\) 0 0
\(169\) 1.02581 + 9.75997i 0.0789088 + 0.750767i
\(170\) 25.5621 2.84970i 1.96053 0.218562i
\(171\) 0 0
\(172\) 29.5645 + 21.4799i 2.25427 + 1.63783i
\(173\) 11.0146 + 12.2329i 0.837422 + 0.930051i 0.998379 0.0569100i \(-0.0181248\pi\)
−0.160957 + 0.986961i \(0.551458\pi\)
\(174\) 0 0
\(175\) 1.21044 + 10.2695i 0.0915009 + 0.776305i
\(176\) 8.14362 + 14.1052i 0.613849 + 1.06322i
\(177\) 0 0
\(178\) 0.793522 0.353299i 0.0594770 0.0264809i
\(179\) 0.422707 + 0.307115i 0.0315946 + 0.0229548i 0.603471 0.797385i \(-0.293784\pi\)
−0.571876 + 0.820340i \(0.693784\pi\)
\(180\) 0 0
\(181\) −18.6716 + 13.5657i −1.38785 + 1.00833i −0.391756 + 0.920069i \(0.628132\pi\)
−0.996097 + 0.0882646i \(0.971868\pi\)
\(182\) −4.67438 + 8.09626i −0.346488 + 0.600134i
\(183\) 0 0
\(184\) 9.67997 10.7507i 0.713617 0.792552i
\(185\) 6.60606 + 8.97298i 0.485687 + 0.659706i
\(186\) 0 0
\(187\) 10.8823 + 2.31311i 0.795794 + 0.169151i
\(188\) 13.8148 + 42.5176i 1.00755 + 3.10092i
\(189\) 0 0
\(190\) −40.6949 + 4.53672i −2.95232 + 0.329128i
\(191\) −0.982006 0.208732i −0.0710555 0.0151033i 0.172247 0.985054i \(-0.444897\pi\)
−0.243302 + 0.969951i \(0.578231\pi\)
\(192\) 0 0
\(193\) 6.92614 + 11.9964i 0.498554 + 0.863521i 0.999999 0.00166856i \(-0.000531120\pi\)
−0.501444 + 0.865190i \(0.667198\pi\)
\(194\) 25.4861 + 11.3472i 1.82980 + 0.814679i
\(195\) 0 0
\(196\) −10.9775 + 4.88748i −0.784104 + 0.349105i
\(197\) −6.40803 4.65571i −0.456553 0.331705i 0.335624 0.941996i \(-0.391053\pi\)
−0.792178 + 0.610291i \(0.791053\pi\)
\(198\) 0 0
\(199\) 14.6161 1.03611 0.518053 0.855348i \(-0.326657\pi\)
0.518053 + 0.855348i \(0.326657\pi\)
\(200\) 9.07505 29.1766i 0.641703 2.06310i
\(201\) 0 0
\(202\) 31.6502 6.72746i 2.22690 0.473342i
\(203\) −1.76839 + 16.8251i −0.124116 + 1.18089i
\(204\) 0 0
\(205\) 4.29246 9.80692i 0.299799 0.684945i
\(206\) −18.8097 + 13.6661i −1.31054 + 0.952160i
\(207\) 0 0
\(208\) 9.60259 6.97669i 0.665820 0.483746i
\(209\) −17.3246 3.68246i −1.19837 0.254721i
\(210\) 0 0
\(211\) −13.0287 + 2.76934i −0.896933 + 0.190649i −0.633238 0.773957i \(-0.718275\pi\)
−0.263695 + 0.964606i \(0.584941\pi\)
\(212\) −9.21118 + 10.2300i −0.632626 + 0.702603i
\(213\) 0 0
\(214\) 1.66178 + 1.84560i 0.113597 + 0.126162i
\(215\) 3.73549 18.1354i 0.254758 1.23683i
\(216\) 0 0
\(217\) −11.3558 + 8.25045i −0.770880 + 0.560077i
\(218\) −11.2430 + 19.4734i −0.761471 + 1.31891i
\(219\) 0 0
\(220\) 14.0837 19.6437i 0.949522 1.32438i
\(221\) 0.847490 8.06333i 0.0570084 0.542398i
\(222\) 0 0
\(223\) 2.44141 + 2.71146i 0.163489 + 0.181573i 0.819323 0.573332i \(-0.194350\pi\)
−0.655834 + 0.754905i \(0.727683\pi\)
\(224\) −9.54893 −0.638014
\(225\) 0 0
\(226\) 17.1771 1.14260
\(227\) −10.5152 11.6783i −0.697915 0.775114i 0.285127 0.958490i \(-0.407964\pi\)
−0.983043 + 0.183376i \(0.941297\pi\)
\(228\) 0 0
\(229\) −0.627978 + 5.97482i −0.0414980 + 0.394827i 0.953983 + 0.299862i \(0.0969406\pi\)
−0.995481 + 0.0949650i \(0.969726\pi\)
\(230\) −12.7747 4.06193i −0.842342 0.267835i
\(231\) 0 0
\(232\) 24.9950 43.2926i 1.64100 2.84230i
\(233\) 0.484321 0.351880i 0.0317289 0.0230524i −0.571808 0.820388i \(-0.693758\pi\)
0.603537 + 0.797335i \(0.293758\pi\)
\(234\) 0 0
\(235\) 16.7376 15.2627i 1.09184 0.995630i
\(236\) −30.8485 34.2608i −2.00807 2.23019i
\(237\) 0 0
\(238\) −15.9178 + 17.6785i −1.03180 + 1.14593i
\(239\) 1.14937 0.244307i 0.0743469 0.0158029i −0.170588 0.985342i \(-0.554567\pi\)
0.244935 + 0.969540i \(0.421233\pi\)
\(240\) 0 0
\(241\) −17.5785 3.73642i −1.13233 0.240684i −0.396621 0.917982i \(-0.629817\pi\)
−0.735709 + 0.677298i \(0.763151\pi\)
\(242\) −10.2448 + 7.44331i −0.658563 + 0.478474i
\(243\) 0 0
\(244\) 9.41469 6.84017i 0.602714 0.437897i
\(245\) 4.55021 + 4.04539i 0.290702 + 0.258450i
\(246\) 0 0
\(247\) −1.34920 + 12.8368i −0.0858477 + 0.816787i
\(248\) 40.5699 8.62339i 2.57619 0.547586i
\(249\) 0 0
\(250\) −28.0972 + 3.49144i −1.77702 + 0.220818i
\(251\) −0.313172 −0.0197673 −0.00988364 0.999951i \(-0.503146\pi\)
−0.00988364 + 0.999951i \(0.503146\pi\)
\(252\) 0 0
\(253\) −4.69096 3.40818i −0.294918 0.214270i
\(254\) −23.0731 + 10.2728i −1.44773 + 0.644573i
\(255\) 0 0
\(256\) −27.8398 12.3951i −1.73999 0.774692i
\(257\) −1.48530 2.57262i −0.0926507 0.160476i 0.815975 0.578087i \(-0.196201\pi\)
−0.908626 + 0.417611i \(0.862867\pi\)
\(258\) 0 0
\(259\) −10.0804 2.14265i −0.626365 0.133138i
\(260\) −15.3099 8.71099i −0.949482 0.540233i
\(261\) 0 0
\(262\) −10.7665 33.1359i −0.665158 2.04714i
\(263\) −7.94955 1.68973i −0.490190 0.104193i −0.0438160 0.999040i \(-0.513952\pi\)
−0.446374 + 0.894847i \(0.647285\pi\)
\(264\) 0 0
\(265\) 6.64704 + 2.11353i 0.408324 + 0.129833i
\(266\) 25.3411 28.1441i 1.55376 1.72563i
\(267\) 0 0
\(268\) 3.59745 6.23097i 0.219749 0.380617i
\(269\) −18.6230 + 13.5304i −1.13547 + 0.824965i −0.986481 0.163874i \(-0.947601\pi\)
−0.148986 + 0.988839i \(0.547601\pi\)
\(270\) 0 0
\(271\) −18.3049 13.2993i −1.11194 0.807874i −0.128974 0.991648i \(-0.541169\pi\)
−0.982969 + 0.183774i \(0.941169\pi\)
\(272\) 27.5917 12.2846i 1.67299 0.744865i
\(273\) 0 0
\(274\) 10.7997 + 18.7056i 0.652432 + 1.13005i
\(275\) −12.0105 2.39507i −0.724259 0.144428i
\(276\) 0 0
\(277\) −6.92921 7.69566i −0.416336 0.462388i 0.498100 0.867120i \(-0.334031\pi\)
−0.914435 + 0.404732i \(0.867365\pi\)
\(278\) −19.1148 13.8877i −1.14643 0.832931i
\(279\) 0 0
\(280\) 11.6571 + 25.7443i 0.696643 + 1.53851i
\(281\) −2.65920 25.3006i −0.158635 1.50931i −0.727060 0.686574i \(-0.759114\pi\)
0.568425 0.822735i \(-0.307553\pi\)
\(282\) 0 0
\(283\) −15.1378 6.73980i −0.899851 0.400639i −0.0959386 0.995387i \(-0.530585\pi\)
−0.803912 + 0.594748i \(0.797252\pi\)
\(284\) 30.0827 33.4102i 1.78508 1.98253i
\(285\) 0 0
\(286\) −7.40876 8.22826i −0.438089 0.486547i
\(287\) 3.05963 + 9.41657i 0.180604 + 0.555842i
\(288\) 0 0
\(289\) 1.12201 3.45318i 0.0660004 0.203128i
\(290\) −46.0977 4.55148i −2.70695 0.267272i
\(291\) 0 0
\(292\) −7.93266 3.53185i −0.464224 0.206686i
\(293\) 6.06420 + 10.5035i 0.354274 + 0.613621i 0.986993 0.160760i \(-0.0513946\pi\)
−0.632719 + 0.774381i \(0.718061\pi\)
\(294\) 0 0
\(295\) −9.36642 + 21.3993i −0.545334 + 1.24592i
\(296\) 24.6360 + 17.8991i 1.43194 + 1.04037i
\(297\) 0 0
\(298\) 5.43564 16.7292i 0.314878 0.969095i
\(299\) −2.11279 + 3.65946i −0.122186 + 0.211632i
\(300\) 0 0
\(301\) 8.56274 + 14.8311i 0.493548 + 0.854851i
\(302\) −1.95295 + 0.415113i −0.112380 + 0.0238871i
\(303\) 0 0
\(304\) −43.9259 + 19.5571i −2.51933 + 1.12168i
\(305\) −5.12490 2.91595i −0.293451 0.166967i
\(306\) 0 0
\(307\) −11.7705 −0.671776 −0.335888 0.941902i \(-0.609036\pi\)
−0.335888 + 0.941902i \(0.609036\pi\)
\(308\) 2.33678 + 22.2330i 0.133150 + 1.26684i
\(309\) 0 0
\(310\) −22.7858 30.9498i −1.29414 1.75783i
\(311\) 9.67624 2.05675i 0.548689 0.116628i 0.0747782 0.997200i \(-0.476175\pi\)
0.473911 + 0.880573i \(0.342842\pi\)
\(312\) 0 0
\(313\) 33.6648 + 7.15567i 1.90285 + 0.404462i 0.999691 0.0248538i \(-0.00791202\pi\)
0.903154 + 0.429316i \(0.141245\pi\)
\(314\) −3.04248 + 9.36378i −0.171697 + 0.528429i
\(315\) 0 0
\(316\) 20.3452 + 62.6162i 1.14451 + 3.52243i
\(317\) 2.32443 + 22.1155i 0.130553 + 1.24213i 0.842034 + 0.539425i \(0.181358\pi\)
−0.711481 + 0.702706i \(0.751975\pi\)
\(318\) 0 0
\(319\) −18.3043 8.14961i −1.02485 0.456290i
\(320\) 0.0226404 + 3.59189i 0.00126564 + 0.200793i
\(321\) 0 0
\(322\) 11.3263 5.04280i 0.631190 0.281024i
\(323\) −10.1495 + 31.2368i −0.564731 + 1.73806i
\(324\) 0 0
\(325\) −0.820957 + 8.88722i −0.0455385 + 0.492974i
\(326\) 10.6278 18.4078i 0.588618 1.01952i
\(327\) 0 0
\(328\) 3.05817 29.0965i 0.168859 1.60659i
\(329\) −2.18991 + 20.8356i −0.120734 + 1.14871i
\(330\) 0 0
\(331\) 1.36800 + 13.0156i 0.0751920 + 0.715404i 0.965563 + 0.260169i \(0.0837781\pi\)
−0.890371 + 0.455235i \(0.849555\pi\)
\(332\) −17.9189 −0.983426
\(333\) 0 0
\(334\) 8.45777 + 26.0303i 0.462788 + 1.42432i
\(335\) −3.62790 0.358203i −0.198214 0.0195707i
\(336\) 0 0
\(337\) 9.72209 10.7975i 0.529596 0.588176i −0.417680 0.908594i \(-0.637157\pi\)
0.947276 + 0.320418i \(0.103823\pi\)
\(338\) 16.6295 18.4690i 0.904528 1.00458i
\(339\) 0 0
\(340\) −33.4976 29.7812i −1.81666 1.61511i
\(341\) −5.13715 15.8105i −0.278192 0.856188i
\(342\) 0 0
\(343\) −20.1081 −1.08573
\(344\) −5.28954 50.3266i −0.285193 2.71343i
\(345\) 0 0
\(346\) 4.35739 41.4578i 0.234255 2.22878i
\(347\) 1.16703 11.1035i 0.0626493 0.596068i −0.917490 0.397759i \(-0.869788\pi\)
0.980139 0.198310i \(-0.0635452\pi\)
\(348\) 0 0
\(349\) 4.08628 7.07765i 0.218734 0.378858i −0.735687 0.677321i \(-0.763141\pi\)
0.954421 + 0.298463i \(0.0964740\pi\)
\(350\) 17.2757 19.6799i 0.923424 1.05194i
\(351\) 0 0
\(352\) 3.49476 10.7558i 0.186272 0.573285i
\(353\) 20.5995 9.17150i 1.09640 0.488150i 0.222836 0.974856i \(-0.428468\pi\)
0.873566 + 0.486706i \(0.161802\pi\)
\(354\) 0 0
\(355\) −21.7085 6.90255i −1.15217 0.366349i
\(356\) −1.38284 0.615679i −0.0732903 0.0326309i
\(357\) 0 0
\(358\) −0.138310 1.31593i −0.00730989 0.0695489i
\(359\) 7.75846 + 23.8781i 0.409476 + 1.26024i 0.917100 + 0.398658i \(0.130524\pi\)
−0.507624 + 0.861579i \(0.669476\pi\)
\(360\) 0 0
\(361\) 10.2866 31.6589i 0.541400 1.66626i
\(362\) 57.1695 + 12.1518i 3.00476 + 0.638682i
\(363\) 0 0
\(364\) 15.9357 3.38723i 0.835256 0.177539i
\(365\) 0.0277319 + 4.39965i 0.00145155 + 0.230288i
\(366\) 0 0
\(367\) 0.674667 + 6.41903i 0.0352173 + 0.335071i 0.997918 + 0.0645007i \(0.0205455\pi\)
−0.962700 + 0.270570i \(0.912788\pi\)
\(368\) −15.7411 −0.820562
\(369\) 0 0
\(370\) 5.69263 27.6372i 0.295946 1.43679i
\(371\) −5.89338 + 2.62390i −0.305969 + 0.136226i
\(372\) 0 0
\(373\) 23.5755 5.01112i 1.22069 0.259466i 0.447875 0.894096i \(-0.352181\pi\)
0.772816 + 0.634630i \(0.218848\pi\)
\(374\) −14.0871 24.3996i −0.728428 1.26167i
\(375\) 0 0
\(376\) 30.9530 53.6121i 1.59628 2.76484i
\(377\) −4.51220 + 13.8871i −0.232390 + 0.715224i
\(378\) 0 0
\(379\) −0.345496 0.251018i −0.0177469 0.0128939i 0.578876 0.815415i \(-0.303491\pi\)
−0.596623 + 0.802521i \(0.703491\pi\)
\(380\) 53.3282 + 47.4117i 2.73568 + 2.43217i
\(381\) 0 0
\(382\) 1.27120 + 2.20179i 0.0650404 + 0.112653i
\(383\) −20.8402 9.27864i −1.06488 0.474117i −0.201930 0.979400i \(-0.564721\pi\)
−0.862953 + 0.505283i \(0.831388\pi\)
\(384\) 0 0
\(385\) 9.77370 5.72529i 0.498114 0.291788i
\(386\) 10.8402 33.3628i 0.551753 1.69812i
\(387\) 0 0
\(388\) −15.0234 46.2373i −0.762698 2.34734i
\(389\) −8.29913 9.21712i −0.420783 0.467327i 0.495063 0.868857i \(-0.335145\pi\)
−0.915846 + 0.401531i \(0.868478\pi\)
\(390\) 0 0
\(391\) −7.19475 + 7.99058i −0.363854 + 0.404101i
\(392\) 15.2010 + 6.76791i 0.767765 + 0.341831i
\(393\) 0 0
\(394\) 2.09670 + 19.9488i 0.105630 + 1.00501i
\(395\) 24.6496 22.4776i 1.24026 1.13097i
\(396\) 0 0
\(397\) −2.26012 1.64207i −0.113432 0.0824133i 0.529623 0.848233i \(-0.322333\pi\)
−0.643055 + 0.765820i \(0.722333\pi\)
\(398\) −24.7672 27.5068i −1.24147 1.37879i
\(399\) 0 0
\(400\) −30.2003 + 13.9048i −1.51001 + 0.695240i
\(401\) 18.1027 + 31.3549i 0.904008 + 1.56579i 0.822244 + 0.569136i \(0.192722\pi\)
0.0817642 + 0.996652i \(0.473945\pi\)
\(402\) 0 0
\(403\) −11.0676 + 4.92761i −0.551316 + 0.245462i
\(404\) −45.6186 33.1438i −2.26961 1.64897i
\(405\) 0 0
\(406\) 34.6605 25.1824i 1.72017 1.24978i
\(407\) 6.10273 10.5702i 0.302501 0.523947i
\(408\) 0 0
\(409\) −14.8526 + 16.4955i −0.734414 + 0.815649i −0.988450 0.151546i \(-0.951575\pi\)
0.254037 + 0.967195i \(0.418242\pi\)
\(410\) −25.7298 + 8.53979i −1.27071 + 0.421750i
\(411\) 0 0
\(412\) 39.6316 + 8.42395i 1.95251 + 0.415018i
\(413\) −6.67630 20.5475i −0.328519 1.01108i
\(414\) 0 0
\(415\) 3.74506 + 8.27084i 0.183838 + 0.405999i
\(416\) −8.06163 1.71355i −0.395254 0.0840138i
\(417\) 0 0
\(418\) 22.4267 + 38.8441i 1.09692 + 1.89993i
\(419\) 29.2051 + 13.0030i 1.42676 + 0.635236i 0.967456 0.253041i \(-0.0814308\pi\)
0.459308 + 0.888277i \(0.348097\pi\)
\(420\) 0 0
\(421\) −1.27594 + 0.568087i −0.0621857 + 0.0276869i −0.437594 0.899173i \(-0.644169\pi\)
0.375408 + 0.926860i \(0.377503\pi\)
\(422\) 27.2891 + 19.8267i 1.32841 + 0.965150i
\(423\) 0 0
\(424\) 19.0622 0.925745
\(425\) −6.74513 + 21.6858i −0.327187 + 1.05192i
\(426\) 0 0
\(427\) 5.33436 1.13385i 0.258148 0.0548710i
\(428\) 0.452387 4.30417i 0.0218669 0.208050i
\(429\) 0 0
\(430\) −40.4599 + 23.7008i −1.95115 + 1.14295i
\(431\) 0.506575 0.368048i 0.0244009 0.0177283i −0.575518 0.817789i \(-0.695200\pi\)
0.599919 + 0.800061i \(0.295200\pi\)
\(432\) 0 0
\(433\) −4.64257 + 3.37302i −0.223108 + 0.162097i −0.693724 0.720241i \(-0.744031\pi\)
0.470617 + 0.882338i \(0.344031\pi\)
\(434\) 34.7695 + 7.39049i 1.66899 + 0.354755i
\(435\) 0 0
\(436\) 38.3291 8.14710i 1.83563 0.390175i
\(437\) 11.4540 12.7210i 0.547920 0.608527i
\(438\) 0 0
\(439\) −15.5049 17.2199i −0.740007 0.821861i 0.249190 0.968455i \(-0.419836\pi\)
−0.989197 + 0.146594i \(0.953169\pi\)
\(440\) −33.2643 + 3.70835i −1.58581 + 0.176789i
\(441\) 0 0
\(442\) −16.6109 + 12.0685i −0.790100 + 0.574041i
\(443\) −10.9667 + 18.9950i −0.521046 + 0.902477i 0.478655 + 0.878003i \(0.341125\pi\)
−0.999700 + 0.0244742i \(0.992209\pi\)
\(444\) 0 0
\(445\) 0.00483427 + 0.766955i 0.000229167 + 0.0363572i
\(446\) 0.965829 9.18925i 0.0457333 0.435124i
\(447\) 0 0
\(448\) −2.22298 2.46887i −0.105026 0.116643i
\(449\) 12.6712 0.597990 0.298995 0.954255i \(-0.403349\pi\)
0.298995 + 0.954255i \(0.403349\pi\)
\(450\) 0 0
\(451\) −11.7265 −0.552178
\(452\) −20.0296 22.2451i −0.942112 1.04632i
\(453\) 0 0
\(454\) −4.15982 + 39.5781i −0.195230 + 1.85749i
\(455\) −4.89401 6.64751i −0.229435 0.311640i
\(456\) 0 0
\(457\) 0.0638731 0.110631i 0.00298786 0.00517512i −0.864528 0.502585i \(-0.832382\pi\)
0.867515 + 0.497410i \(0.165716\pi\)
\(458\) 12.3084 8.94261i 0.575136 0.417861i
\(459\) 0 0
\(460\) 9.63581 + 21.2804i 0.449272 + 0.992203i
\(461\) 4.84829 + 5.38457i 0.225807 + 0.250785i 0.845393 0.534144i \(-0.179366\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(462\) 0 0
\(463\) 15.2392 16.9248i 0.708225 0.786564i −0.276438 0.961032i \(-0.589154\pi\)
0.984663 + 0.174468i \(0.0558206\pi\)
\(464\) −53.2058 + 11.3092i −2.47002 + 0.525018i
\(465\) 0 0
\(466\) −1.48291 0.315203i −0.0686945 0.0146015i
\(467\) 7.87672 5.72277i 0.364491 0.264818i −0.390432 0.920632i \(-0.627674\pi\)
0.754923 + 0.655814i \(0.227674\pi\)
\(468\) 0 0
\(469\) 2.72780 1.98186i 0.125958 0.0915138i
\(470\) −57.0859 5.63641i −2.63318 0.259988i
\(471\) 0 0
\(472\) −6.67311 + 63.4904i −0.307155 + 2.92238i
\(473\) −19.8394 + 4.21699i −0.912216 + 0.193897i
\(474\) 0 0
\(475\) 10.7382 34.5238i 0.492704 1.58406i
\(476\) 41.4556 1.90012
\(477\) 0 0
\(478\) −2.40741 1.74909i −0.110112 0.0800013i
\(479\) 10.2812 4.57749i 0.469761 0.209151i −0.158183 0.987410i \(-0.550564\pi\)
0.627944 + 0.778259i \(0.283897\pi\)
\(480\) 0 0
\(481\) −8.12582 3.61785i −0.370506 0.164960i
\(482\) 22.7553 + 39.4133i 1.03648 + 1.79523i
\(483\) 0 0
\(484\) 21.5856 + 4.58816i 0.981163 + 0.208553i
\(485\) −18.2019 + 16.5980i −0.826506 + 0.753676i
\(486\) 0 0
\(487\) −2.45081 7.54283i −0.111057 0.341798i 0.880047 0.474886i \(-0.157511\pi\)
−0.991104 + 0.133088i \(0.957511\pi\)
\(488\) −15.7624 3.35040i −0.713531 0.151666i
\(489\) 0 0
\(490\) −0.0971844 15.4183i −0.00439035 0.696526i
\(491\) −9.84430 + 10.9332i −0.444267 + 0.493409i −0.923134 0.384479i \(-0.874381\pi\)
0.478867 + 0.877888i \(0.341048\pi\)
\(492\) 0 0
\(493\) −18.5778 + 32.1777i −0.836702 + 1.44921i
\(494\) 26.4445 19.2131i 1.18980 0.864437i
\(495\) 0 0
\(496\) −36.5114 26.5271i −1.63941 1.19110i
\(497\) 19.2471 8.56938i 0.863352 0.384389i
\(498\) 0 0
\(499\) −11.7212 20.3017i −0.524714 0.908831i −0.999586 0.0287762i \(-0.990839\pi\)
0.474872 0.880055i \(-0.342494\pi\)
\(500\) 37.2847 + 32.3159i 1.66742 + 1.44521i
\(501\) 0 0
\(502\) 0.530676 + 0.589376i 0.0236852 + 0.0263051i
\(503\) 11.6643 + 8.47463i 0.520087 + 0.377865i 0.816637 0.577152i \(-0.195836\pi\)
−0.296550 + 0.955017i \(0.595836\pi\)
\(504\) 0 0
\(505\) −5.76393 + 27.9833i −0.256491 + 1.24524i
\(506\) 1.53488 + 14.6034i 0.0682336 + 0.649200i
\(507\) 0 0
\(508\) 40.2085 + 17.9020i 1.78396 + 0.794272i
\(509\) −0.258484 + 0.287075i −0.0114571 + 0.0127244i −0.748846 0.662744i \(-0.769392\pi\)
0.737389 + 0.675468i \(0.236058\pi\)
\(510\) 0 0
\(511\) −2.72289 3.02407i −0.120453 0.133777i
\(512\) 15.6267 + 48.0942i 0.690611 + 2.12548i
\(513\) 0 0
\(514\) −2.32468 + 7.15462i −0.102537 + 0.315577i
\(515\) −4.39477 20.0534i −0.193657 0.883659i
\(516\) 0 0
\(517\) −22.6675 10.0922i −0.996915 0.443855i
\(518\) 13.0490 + 22.6016i 0.573342 + 0.993057i
\(519\) 0 0
\(520\) 5.22162 + 23.8263i 0.228983 + 1.04485i
\(521\) −35.3256 25.6656i −1.54764 1.12443i −0.945304 0.326190i \(-0.894235\pi\)
−0.602340 0.798240i \(-0.705765\pi\)
\(522\) 0 0
\(523\) −6.03504 + 18.5739i −0.263894 + 0.812182i 0.728052 + 0.685522i \(0.240426\pi\)
−0.991946 + 0.126660i \(0.959574\pi\)
\(524\) −30.3581 + 52.5818i −1.32620 + 2.29705i
\(525\) 0 0
\(526\) 10.2907 + 17.8239i 0.448694 + 0.777161i
\(527\) −30.1540 + 6.40943i −1.31353 + 0.279199i
\(528\) 0 0
\(529\) −15.8921 + 7.07563i −0.690962 + 0.307636i
\(530\) −7.28596 16.0908i −0.316482 0.698940i
\(531\) 0 0
\(532\) −65.9973 −2.86135
\(533\) 0.893274 + 8.49894i 0.0386920 + 0.368130i
\(534\) 0 0
\(535\) −2.08123 + 0.690766i −0.0899795 + 0.0298644i
\(536\) −9.74539 + 2.07145i −0.420937 + 0.0894728i
\(537\) 0 0
\(538\) 57.0207 + 12.1201i 2.45834 + 0.522536i
\(539\) 2.06094 6.34291i 0.0887708 0.273208i
\(540\) 0 0
\(541\) −5.67479 17.4652i −0.243978 0.750888i −0.995803 0.0915249i \(-0.970826\pi\)
0.751824 0.659363i \(-0.229174\pi\)
\(542\) 5.98935 + 56.9848i 0.257264 + 2.44771i
\(543\) 0 0
\(544\) −19.1587 8.53001i −0.821423 0.365721i
\(545\) −11.7713 15.9888i −0.504225 0.684887i
\(546\) 0 0
\(547\) 35.1535 15.6513i 1.50306 0.669203i 0.520278 0.853997i \(-0.325828\pi\)
0.982777 + 0.184794i \(0.0591616\pi\)
\(548\) 11.6315 35.7980i 0.496872 1.52922i
\(549\) 0 0
\(550\) 15.8446 + 26.6616i 0.675614 + 1.13686i
\(551\) 29.5758 51.2268i 1.25997 2.18234i
\(552\) 0 0
\(553\) −3.22511 + 30.6849i −0.137146 + 1.30485i
\(554\) −2.74121 + 26.0809i −0.116463 + 1.10807i
\(555\) 0 0
\(556\) 4.30388 + 40.9486i 0.182525 + 1.73661i
\(557\) −34.0992 −1.44483 −0.722414 0.691461i \(-0.756968\pi\)
−0.722414 + 0.691461i \(0.756968\pi\)
\(558\) 0 0
\(559\) 4.56761 + 14.0577i 0.193189 + 0.594576i
\(560\) 12.3300 28.1702i 0.521039 1.19041i
\(561\) 0 0
\(562\) −43.1085 + 47.8769i −1.81842 + 2.01956i
\(563\) 16.6117 18.4492i 0.700100 0.777540i −0.283292 0.959034i \(-0.591427\pi\)
0.983392 + 0.181494i \(0.0580933\pi\)
\(564\) 0 0
\(565\) −6.08150 + 13.8943i −0.255851 + 0.584538i
\(566\) 12.9674 + 39.9094i 0.545058 + 1.67752i
\(567\) 0 0
\(568\) −62.2553 −2.61217
\(569\) −2.96097 28.1717i −0.124130 1.18102i −0.862297 0.506403i \(-0.830975\pi\)
0.738167 0.674618i \(-0.235692\pi\)
\(570\) 0 0
\(571\) −3.33890 + 31.7675i −0.139729 + 1.32943i 0.669884 + 0.742465i \(0.266344\pi\)
−0.809613 + 0.586964i \(0.800323\pi\)
\(572\) −2.01689 + 19.1894i −0.0843303 + 0.802349i
\(573\) 0 0
\(574\) 12.5369 21.7146i 0.523282 0.906351i
\(575\) 7.80852 8.89522i 0.325638 0.370956i
\(576\) 0 0
\(577\) −4.21265 + 12.9652i −0.175375 + 0.539748i −0.999650 0.0264408i \(-0.991583\pi\)
0.824276 + 0.566189i \(0.191583\pi\)
\(578\) −8.39998 + 3.73991i −0.349393 + 0.155560i
\(579\) 0 0
\(580\) 47.8585 + 65.0060i 1.98722 + 2.69923i
\(581\) −7.67133 3.41550i −0.318260 0.141699i
\(582\) 0 0
\(583\) −0.798637 7.59853i −0.0330762 0.314699i
\(584\) 3.71570 + 11.4358i 0.153757 + 0.473215i
\(585\) 0 0
\(586\) 9.49120 29.2109i 0.392078 1.20669i
\(587\) −38.8559 8.25908i −1.60376 0.340889i −0.682815 0.730592i \(-0.739244\pi\)
−0.920941 + 0.389703i \(0.872578\pi\)
\(588\) 0 0
\(589\) 48.0051 10.2038i 1.97802 0.420441i
\(590\) 56.1441 18.6344i 2.31141 0.767165i
\(591\) 0 0
\(592\) −3.46354 32.9534i −0.142351 1.35438i
\(593\) −16.9892 −0.697663 −0.348832 0.937185i \(-0.613421\pi\)
−0.348832 + 0.937185i \(0.613421\pi\)
\(594\) 0 0
\(595\) −8.66425 19.1347i −0.355200 0.784447i
\(596\) −28.0034 + 12.4679i −1.14706 + 0.510705i
\(597\) 0 0
\(598\) 10.4671 2.22485i 0.428032 0.0909810i
\(599\) 7.81800 + 13.5412i 0.319435 + 0.553277i 0.980370 0.197166i \(-0.0631736\pi\)
−0.660935 + 0.750443i \(0.729840\pi\)
\(600\) 0 0
\(601\) −0.702116 + 1.21610i −0.0286399 + 0.0496058i −0.879990 0.474992i \(-0.842451\pi\)
0.851350 + 0.524598i \(0.175784\pi\)
\(602\) 13.4017 41.2462i 0.546213 1.68107i
\(603\) 0 0
\(604\) 2.81486 + 2.04512i 0.114535 + 0.0832147i
\(605\) −2.39364 10.9222i −0.0973152 0.444051i
\(606\) 0 0
\(607\) −3.79337 6.57031i −0.153968 0.266681i 0.778715 0.627378i \(-0.215872\pi\)
−0.932683 + 0.360698i \(0.882539\pi\)
\(608\) 30.5006 + 13.5798i 1.23696 + 0.550732i
\(609\) 0 0
\(610\) 3.19656 + 14.5859i 0.129425 + 0.590568i
\(611\) −5.58777 + 17.1974i −0.226057 + 0.695732i
\(612\) 0 0
\(613\) 9.44377 + 29.0649i 0.381430 + 1.17392i 0.939037 + 0.343816i \(0.111720\pi\)
−0.557607 + 0.830105i \(0.688280\pi\)
\(614\) 19.9453 + 22.1515i 0.804925 + 0.893960i
\(615\) 0 0
\(616\) 20.7140 23.0052i 0.834590 0.926906i
\(617\) −0.925938 0.412254i −0.0372768 0.0165967i 0.388014 0.921654i \(-0.373161\pi\)
−0.425290 + 0.905057i \(0.639828\pi\)
\(618\) 0 0
\(619\) −4.81309 45.7935i −0.193454 1.84059i −0.473724 0.880673i \(-0.657091\pi\)
0.280270 0.959921i \(-0.409576\pi\)
\(620\) −13.5117 + 65.5981i −0.542644 + 2.63448i
\(621\) 0 0
\(622\) −20.2673 14.7250i −0.812644 0.590420i
\(623\) −0.474659 0.527162i −0.0190168 0.0211203i
\(624\) 0 0
\(625\) 7.12357 23.9636i 0.284943 0.958545i
\(626\) −43.5789 75.4809i −1.74176 3.01682i
\(627\) 0 0
\(628\) 15.6743 6.97863i 0.625471 0.278478i
\(629\) −18.3110 13.3037i −0.730108 0.530455i
\(630\) 0 0
\(631\) −6.24556 + 4.53767i −0.248632 + 0.180642i −0.705120 0.709088i \(-0.749107\pi\)
0.456488 + 0.889729i \(0.349107\pi\)
\(632\) 45.5848 78.9552i 1.81327 3.14067i
\(633\) 0 0
\(634\) 37.6815 41.8496i 1.49653 1.66206i
\(635\) −0.140565 22.3006i −0.00557816 0.884973i
\(636\) 0 0
\(637\) −4.75411 1.01052i −0.188365 0.0400382i
\(638\) 15.6798 + 48.2575i 0.620770 + 1.91053i
\(639\) 0 0
\(640\) 21.9790 20.0422i 0.868795 0.792239i
\(641\) 27.3002 + 5.80283i 1.07829 + 0.229198i 0.712623 0.701547i \(-0.247507\pi\)
0.365669 + 0.930745i \(0.380840\pi\)
\(642\) 0 0
\(643\) −3.87285 6.70797i −0.152730 0.264537i 0.779500 0.626402i \(-0.215473\pi\)
−0.932230 + 0.361866i \(0.882140\pi\)
\(644\) −19.7379 8.78787i −0.777782 0.346291i
\(645\) 0 0
\(646\) 75.9847 33.8305i 2.98958 1.33105i
\(647\) 27.8778 + 20.2544i 1.09599 + 0.796283i 0.980401 0.197015i \(-0.0631246\pi\)
0.115588 + 0.993297i \(0.463125\pi\)
\(648\) 0 0
\(649\) 25.5879 1.00441
\(650\) 18.1165 13.5146i 0.710586 0.530085i
\(651\) 0 0
\(652\) −36.2317 + 7.70129i −1.41894 + 0.301606i
\(653\) −1.25103 + 11.9028i −0.0489567 + 0.465792i 0.942389 + 0.334518i \(0.108573\pi\)
−0.991346 + 0.131274i \(0.958093\pi\)
\(654\) 0 0
\(655\) 30.6151 + 3.02280i 1.19623 + 0.118111i
\(656\) −25.7547 + 18.7119i −1.00555 + 0.730576i
\(657\) 0 0
\(658\) 42.9225 31.1850i 1.67329 1.21572i
\(659\) 9.12961 + 1.94056i 0.355639 + 0.0755934i 0.382267 0.924052i \(-0.375144\pi\)
−0.0266278 + 0.999645i \(0.508477\pi\)
\(660\) 0 0
\(661\) −4.71132 + 1.00142i −0.183249 + 0.0389508i −0.298622 0.954371i \(-0.596527\pi\)
0.115373 + 0.993322i \(0.463194\pi\)
\(662\) 22.1767 24.6297i 0.861922 0.957261i
\(663\) 0 0
\(664\) 16.6032 + 18.4397i 0.644329 + 0.715600i
\(665\) 13.7935 + 30.4624i 0.534888 + 1.18128i
\(666\) 0 0
\(667\) 15.6664 11.3823i 0.606605 0.440724i
\(668\) 23.8482 41.3063i 0.922714 1.59819i
\(669\) 0 0
\(670\) 5.47342 + 7.43452i 0.211457 + 0.287221i
\(671\) −0.675140 + 6.42352i −0.0260635 + 0.247977i
\(672\) 0 0
\(673\) −11.9310 13.2507i −0.459907 0.510779i 0.467929 0.883766i \(-0.345000\pi\)
−0.927837 + 0.372987i \(0.878334\pi\)
\(674\) −36.7946 −1.41728
\(675\) 0 0
\(676\) −43.3093 −1.66574
\(677\) −10.2517 11.3857i −0.394005 0.437586i 0.513205 0.858266i \(-0.328458\pi\)
−0.907209 + 0.420680i \(0.861792\pi\)
\(678\) 0 0
\(679\) 2.38150 22.6584i 0.0913935 0.869551i
\(680\) 0.391213 + 62.0658i 0.0150024 + 2.38012i
\(681\) 0 0
\(682\) −21.0497 + 36.4591i −0.806034 + 1.39609i
\(683\) 22.9889 16.7024i 0.879645 0.639100i −0.0535124 0.998567i \(-0.517042\pi\)
0.933158 + 0.359468i \(0.117042\pi\)
\(684\) 0 0
\(685\) −18.9543 + 2.11305i −0.724207 + 0.0807355i
\(686\) 34.0735 + 37.8425i 1.30093 + 1.44483i
\(687\) 0 0
\(688\) −36.8439 + 40.9193i −1.40466 + 1.56004i
\(689\) −5.44631 + 1.15765i −0.207488 + 0.0441029i
\(690\) 0 0
\(691\) −21.4992 4.56981i −0.817870 0.173844i −0.220065 0.975485i \(-0.570627\pi\)
−0.597805 + 0.801642i \(0.703960\pi\)
\(692\) −58.7708 + 42.6995i −2.23413 + 1.62319i
\(693\) 0 0
\(694\) −22.8739 + 16.6188i −0.868280 + 0.630842i
\(695\) 18.0012 10.5448i 0.682824 0.399988i
\(696\) 0 0
\(697\) −2.27302 + 21.6263i −0.0860966 + 0.819155i
\(698\) −20.2441 + 4.30301i −0.766250 + 0.162871i
\(699\) 0 0
\(700\) −45.6310 + 0.575266i −1.72469 + 0.0217430i
\(701\) −6.44692 −0.243497 −0.121748 0.992561i \(-0.538850\pi\)
−0.121748 + 0.992561i \(0.538850\pi\)
\(702\) 0 0
\(703\) 29.1511 + 21.1795i 1.09946 + 0.798801i
\(704\) 3.59447 1.60036i 0.135472 0.0603159i
\(705\) 0 0
\(706\) −52.1666 23.2261i −1.96332 0.874124i
\(707\) −13.2125 22.8847i −0.496906 0.860666i
\(708\) 0 0
\(709\) 4.80312 + 1.02094i 0.180385 + 0.0383420i 0.297218 0.954809i \(-0.403941\pi\)
−0.116833 + 0.993152i \(0.537274\pi\)
\(710\) 23.7952 + 52.5509i 0.893017 + 1.97220i
\(711\) 0 0
\(712\) 0.647729 + 1.99351i 0.0242747 + 0.0747098i
\(713\) 15.7156 + 3.34046i 0.588555 + 0.125101i
\(714\) 0 0
\(715\) 9.27880 3.07966i 0.347007 0.115173i
\(716\) −1.54291 + 1.71358i −0.0576613 + 0.0640393i
\(717\) 0 0
\(718\) 31.7906 55.0629i 1.18641 2.05493i
\(719\) −38.7957 + 28.1867i −1.44683 + 1.05119i −0.460277 + 0.887775i \(0.652250\pi\)
−0.986558 + 0.163412i \(0.947750\pi\)
\(720\) 0 0
\(721\) 15.3612 + 11.1605i 0.572080 + 0.415640i
\(722\) −77.0113 + 34.2877i −2.86607 + 1.27605i
\(723\) 0 0
\(724\) −50.9263 88.2070i −1.89266 3.27819i
\(725\) 20.0024 35.6764i 0.742871 1.32499i
\(726\) 0 0
\(727\) 6.94241 + 7.71033i 0.257480 + 0.285960i 0.858000 0.513649i \(-0.171707\pi\)
−0.600521 + 0.799609i \(0.705040\pi\)
\(728\) −18.2513 13.2603i −0.676437 0.491461i
\(729\) 0 0
\(730\) 8.23293 7.50747i 0.304715 0.277864i
\(731\) 3.93151 + 37.4058i 0.145412 + 1.38350i
\(732\) 0 0
\(733\) −8.79421 3.91543i −0.324822 0.144620i 0.237847 0.971303i \(-0.423558\pi\)
−0.562668 + 0.826683i \(0.690225\pi\)
\(734\) 10.9371 12.1469i 0.403695 0.448349i
\(735\) 0 0
\(736\) 7.31365 + 8.12263i 0.269585 + 0.299404i
\(737\) 1.23401 + 3.79789i 0.0454553 + 0.139897i
\(738\) 0 0
\(739\) −10.9628 + 33.7400i −0.403273 + 1.24115i 0.519056 + 0.854740i \(0.326284\pi\)
−0.922329 + 0.386406i \(0.873716\pi\)
\(740\) −42.4294 + 24.8545i −1.55974 + 0.913671i
\(741\) 0 0
\(742\) 14.9245 + 6.64481i 0.547895 + 0.243939i
\(743\) −1.41943 2.45852i −0.0520738 0.0901944i 0.838814 0.544419i \(-0.183250\pi\)
−0.890887 + 0.454224i \(0.849916\pi\)
\(744\) 0 0
\(745\) 11.6075 + 10.3197i 0.425268 + 0.378086i
\(746\) −49.3797 35.8765i −1.80792 1.31353i
\(747\) 0 0
\(748\) −15.1721 + 46.6951i −0.554749 + 1.70734i
\(749\) 1.01409 1.75645i 0.0370539 0.0641793i
\(750\) 0 0
\(751\) −19.4018 33.6049i −0.707983 1.22626i −0.965604 0.260016i \(-0.916272\pi\)
0.257622 0.966246i \(-0.417061\pi\)
\(752\) −65.8884 + 14.0050i −2.40270 + 0.510710i
\(753\) 0 0
\(754\) 33.7809 15.0402i 1.23023 0.547734i
\(755\) 0.355659 1.72669i 0.0129438 0.0628407i
\(756\) 0 0
\(757\) 32.7437 1.19009 0.595046 0.803692i \(-0.297134\pi\)
0.595046 + 0.803692i \(0.297134\pi\)
\(758\) 0.113046 + 1.07556i 0.00410602 + 0.0390662i
\(759\) 0 0
\(760\) −0.622811 98.8087i −0.0225917 3.58417i
\(761\) −0.437407 + 0.0929737i −0.0158560 + 0.00337029i −0.215833 0.976430i \(-0.569247\pi\)
0.199977 + 0.979801i \(0.435913\pi\)
\(762\) 0 0
\(763\) 17.9621 + 3.81797i 0.650273 + 0.138220i
\(764\) 1.36911 4.21370i 0.0495328 0.152446i
\(765\) 0 0
\(766\) 17.8521 + 54.9431i 0.645022 + 1.98517i
\(767\) −1.94918 18.5452i −0.0703808 0.669629i
\(768\) 0 0
\(769\) −6.84396 3.04713i −0.246800 0.109882i 0.279609 0.960114i \(-0.409795\pi\)
−0.526409 + 0.850232i \(0.676462\pi\)
\(770\) −27.3364 8.69204i −0.985137 0.313239i
\(771\) 0 0
\(772\) −55.8469 + 24.8646i −2.00997 + 0.894897i
\(773\) 5.48853 16.8920i 0.197409 0.607562i −0.802531 0.596610i \(-0.796514\pi\)
0.999940 0.0109516i \(-0.00348607\pi\)
\(774\) 0 0
\(775\) 33.1022 7.47343i 1.18906 0.268453i
\(776\) −33.6609 + 58.3024i −1.20836 + 2.09293i
\(777\) 0 0
\(778\) −3.28316 + 31.2372i −0.117707 + 1.11991i
\(779\) 3.61864 34.4290i 0.129651 1.23355i
\(780\) 0 0
\(781\) 2.60826 + 24.8160i 0.0933310 + 0.887985i
\(782\) 27.2295 0.973726
\(783\) 0 0
\(784\) −5.59494 17.2195i −0.199819 0.614981i
\(785\) −6.49706 5.77625i −0.231890 0.206163i
\(786\) 0 0
\(787\) 9.21203 10.2310i 0.328373