Properties

Label 405.2.r.a.368.15
Level $405$
Weight $2$
Character 405.368
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 368.15
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.15

$q$-expansion

\(f(q)\) \(=\) \(q+(2.45457 + 0.214747i) q^{2} +(4.00918 + 0.706926i) q^{4} +(-1.21103 + 1.87974i) q^{5} +(1.02748 + 0.719449i) q^{7} +(4.92901 + 1.32073i) q^{8} +O(q^{10})\) \(q+(2.45457 + 0.214747i) q^{2} +(4.00918 + 0.706926i) q^{4} +(-1.21103 + 1.87974i) q^{5} +(1.02748 + 0.719449i) q^{7} +(4.92901 + 1.32073i) q^{8} +(-3.37621 + 4.35388i) q^{10} +(-0.955177 + 2.62433i) q^{11} +(-0.519069 - 5.93299i) q^{13} +(2.36752 + 1.98658i) q^{14} +(4.16396 + 1.51556i) q^{16} +(5.37628 - 1.44057i) q^{17} +(-1.75284 + 1.01200i) q^{19} +(-6.18405 + 6.68010i) q^{20} +(-2.90811 + 6.23647i) q^{22} +(-2.67978 - 3.82712i) q^{23} +(-2.06683 - 4.55282i) q^{25} -14.6744i q^{26} +(3.61075 + 3.61075i) q^{28} +(-2.13514 + 1.79159i) q^{29} +(0.860131 - 4.87805i) q^{31} +(0.645681 + 0.301086i) q^{32} +(13.5058 - 2.38144i) q^{34} +(-2.59668 + 1.06012i) q^{35} +(0.354589 + 1.32334i) q^{37} +(-4.51978 + 2.10761i) q^{38} +(-8.45178 + 7.66582i) q^{40} +(0.207426 - 0.247201i) q^{41} +(3.79373 + 8.13568i) q^{43} +(-5.68468 + 9.84615i) q^{44} +(-5.75583 - 9.96940i) q^{46} +(0.213694 - 0.305187i) q^{47} +(-1.85603 - 5.09941i) q^{49} +(-4.09548 - 11.6191i) q^{50} +(2.11314 - 24.1534i) q^{52} +(-7.96878 + 7.96878i) q^{53} +(-3.77630 - 4.97361i) q^{55} +(4.11426 + 4.90319i) q^{56} +(-5.62558 + 3.93908i) q^{58} +(-2.97238 + 1.08186i) q^{59} +(-0.0275256 - 0.156106i) q^{61} +(3.15880 - 11.7888i) q^{62} +(-6.15484 - 3.55350i) q^{64} +(11.7811 + 6.20929i) q^{65} +(8.09208 - 0.707965i) q^{67} +(22.5728 - 1.97487i) q^{68} +(-6.60139 + 2.04451i) q^{70} +(-7.01095 - 4.04777i) q^{71} +(-1.41949 + 5.29760i) q^{73} +(0.586179 + 3.32439i) q^{74} +(-7.74284 + 2.81816i) q^{76} +(-2.86949 + 2.00924i) q^{77} +(10.3148 + 12.2927i) q^{79} +(-7.89151 + 5.99177i) q^{80} +(0.562227 - 0.562227i) q^{82} +(0.151375 - 1.73023i) q^{83} +(-3.80292 + 11.8506i) q^{85} +(7.56486 + 20.7843i) q^{86} +(-8.17410 + 11.6738i) q^{88} +(-6.44892 - 11.1699i) q^{89} +(3.73515 - 6.46947i) q^{91} +(-8.03821 - 17.2380i) q^{92} +(0.590066 - 0.703213i) q^{94} +(0.220434 - 4.52043i) q^{95} +(-3.21455 + 1.49897i) q^{97} +(-3.46068 - 12.9154i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.45457 + 0.214747i 1.73564 + 0.151849i 0.910618 0.413249i \(-0.135606\pi\)
0.825024 + 0.565098i \(0.191162\pi\)
\(3\) 0 0
\(4\) 4.00918 + 0.706926i 2.00459 + 0.353463i
\(5\) −1.21103 + 1.87974i −0.541587 + 0.840645i
\(6\) 0 0
\(7\) 1.02748 + 0.719449i 0.388351 + 0.271926i 0.751404 0.659842i \(-0.229377\pi\)
−0.363054 + 0.931768i \(0.618266\pi\)
\(8\) 4.92901 + 1.32073i 1.74267 + 0.466947i
\(9\) 0 0
\(10\) −3.37621 + 4.35388i −1.06765 + 1.37682i
\(11\) −0.955177 + 2.62433i −0.287997 + 0.791264i 0.708350 + 0.705862i \(0.249440\pi\)
−0.996347 + 0.0854029i \(0.972782\pi\)
\(12\) 0 0
\(13\) −0.519069 5.93299i −0.143964 1.64552i −0.633652 0.773618i \(-0.718445\pi\)
0.489688 0.871898i \(-0.337111\pi\)
\(14\) 2.36752 + 1.98658i 0.632746 + 0.530937i
\(15\) 0 0
\(16\) 4.16396 + 1.51556i 1.04099 + 0.378889i
\(17\) 5.37628 1.44057i 1.30394 0.349390i 0.461001 0.887400i \(-0.347490\pi\)
0.842938 + 0.538010i \(0.180824\pi\)
\(18\) 0 0
\(19\) −1.75284 + 1.01200i −0.402128 + 0.232169i −0.687402 0.726277i \(-0.741249\pi\)
0.285274 + 0.958446i \(0.407916\pi\)
\(20\) −6.18405 + 6.68010i −1.38280 + 1.49372i
\(21\) 0 0
\(22\) −2.90811 + 6.23647i −0.620012 + 1.32962i
\(23\) −2.67978 3.82712i −0.558772 0.798009i 0.436020 0.899937i \(-0.356388\pi\)
−0.994792 + 0.101928i \(0.967499\pi\)
\(24\) 0 0
\(25\) −2.06683 4.55282i −0.413367 0.910565i
\(26\) 14.6744i 2.87789i
\(27\) 0 0
\(28\) 3.61075 + 3.61075i 0.682367 + 0.682367i
\(29\) −2.13514 + 1.79159i −0.396485 + 0.332691i −0.819133 0.573603i \(-0.805545\pi\)
0.422648 + 0.906294i \(0.361101\pi\)
\(30\) 0 0
\(31\) 0.860131 4.87805i 0.154484 0.876123i −0.804772 0.593584i \(-0.797712\pi\)
0.959256 0.282539i \(-0.0911765\pi\)
\(32\) 0.645681 + 0.301086i 0.114141 + 0.0532250i
\(33\) 0 0
\(34\) 13.5058 2.38144i 2.31623 0.408413i
\(35\) −2.59668 + 1.06012i −0.438919 + 0.179193i
\(36\) 0 0
\(37\) 0.354589 + 1.32334i 0.0582941 + 0.217556i 0.988928 0.148394i \(-0.0474105\pi\)
−0.930634 + 0.365951i \(0.880744\pi\)
\(38\) −4.51978 + 2.10761i −0.733206 + 0.341899i
\(39\) 0 0
\(40\) −8.45178 + 7.66582i −1.33634 + 1.21207i
\(41\) 0.207426 0.247201i 0.0323945 0.0386063i −0.749604 0.661887i \(-0.769756\pi\)
0.781998 + 0.623280i \(0.214200\pi\)
\(42\) 0 0
\(43\) 3.79373 + 8.13568i 0.578538 + 1.24068i 0.950005 + 0.312234i \(0.101077\pi\)
−0.371467 + 0.928446i \(0.621145\pi\)
\(44\) −5.68468 + 9.84615i −0.856997 + 1.48436i
\(45\) 0 0
\(46\) −5.75583 9.96940i −0.848652 1.46991i
\(47\) 0.213694 0.305187i 0.0311705 0.0445161i −0.803264 0.595623i \(-0.796905\pi\)
0.834435 + 0.551107i \(0.185794\pi\)
\(48\) 0 0
\(49\) −1.85603 5.09941i −0.265148 0.728487i
\(50\) −4.09548 11.6191i −0.579188 1.64318i
\(51\) 0 0
\(52\) 2.11314 24.1534i 0.293040 3.34947i
\(53\) −7.96878 + 7.96878i −1.09460 + 1.09460i −0.0995653 + 0.995031i \(0.531745\pi\)
−0.995031 + 0.0995653i \(0.968255\pi\)
\(54\) 0 0
\(55\) −3.77630 4.97361i −0.509197 0.670642i
\(56\) 4.11426 + 4.90319i 0.549792 + 0.655216i
\(57\) 0 0
\(58\) −5.62558 + 3.93908i −0.738675 + 0.517226i
\(59\) −2.97238 + 1.08186i −0.386971 + 0.140846i −0.528177 0.849134i \(-0.677124\pi\)
0.141206 + 0.989980i \(0.454902\pi\)
\(60\) 0 0
\(61\) −0.0275256 0.156106i −0.00352429 0.0199873i 0.982995 0.183633i \(-0.0587858\pi\)
−0.986519 + 0.163646i \(0.947675\pi\)
\(62\) 3.15880 11.7888i 0.401168 1.49718i
\(63\) 0 0
\(64\) −6.15484 3.55350i −0.769355 0.444187i
\(65\) 11.7811 + 6.20929i 1.46126 + 0.770168i
\(66\) 0 0
\(67\) 8.09208 0.707965i 0.988605 0.0864917i 0.418633 0.908156i \(-0.362509\pi\)
0.569972 + 0.821664i \(0.306954\pi\)
\(68\) 22.5728 1.97487i 2.73736 0.239488i
\(69\) 0 0
\(70\) −6.60139 + 2.04451i −0.789017 + 0.244366i
\(71\) −7.01095 4.04777i −0.832046 0.480382i 0.0225065 0.999747i \(-0.492835\pi\)
−0.854553 + 0.519365i \(0.826169\pi\)
\(72\) 0 0
\(73\) −1.41949 + 5.29760i −0.166139 + 0.620037i 0.831754 + 0.555145i \(0.187337\pi\)
−0.997892 + 0.0648926i \(0.979330\pi\)
\(74\) 0.586179 + 3.32439i 0.0681419 + 0.386452i
\(75\) 0 0
\(76\) −7.74284 + 2.81816i −0.888165 + 0.323266i
\(77\) −2.86949 + 2.00924i −0.327009 + 0.228974i
\(78\) 0 0
\(79\) 10.3148 + 12.2927i 1.16051 + 1.38304i 0.909838 + 0.414964i \(0.136206\pi\)
0.250668 + 0.968073i \(0.419350\pi\)
\(80\) −7.89151 + 5.99177i −0.882298 + 0.669900i
\(81\) 0 0
\(82\) 0.562227 0.562227i 0.0620876 0.0620876i
\(83\) 0.151375 1.73023i 0.0166156 0.189917i −0.983351 0.181718i \(-0.941834\pi\)
0.999966 0.00819974i \(-0.00261009\pi\)
\(84\) 0 0
\(85\) −3.80292 + 11.8506i −0.412485 + 1.28537i
\(86\) 7.56486 + 20.7843i 0.815740 + 2.24123i
\(87\) 0 0
\(88\) −8.17410 + 11.6738i −0.871361 + 1.24443i
\(89\) −6.44892 11.1699i −0.683584 1.18400i −0.973879 0.227066i \(-0.927087\pi\)
0.290295 0.956937i \(-0.406247\pi\)
\(90\) 0 0
\(91\) 3.73515 6.46947i 0.391550 0.678185i
\(92\) −8.03821 17.2380i −0.838041 1.79719i
\(93\) 0 0
\(94\) 0.590066 0.703213i 0.0608606 0.0725309i
\(95\) 0.220434 4.52043i 0.0226161 0.463787i
\(96\) 0 0
\(97\) −3.21455 + 1.49897i −0.326388 + 0.152197i −0.578904 0.815395i \(-0.696520\pi\)
0.252517 + 0.967593i \(0.418742\pi\)
\(98\) −3.46068 12.9154i −0.349581 1.30466i
\(99\) 0 0
\(100\) −5.06779 19.7142i −0.506779 1.97142i
\(101\) 9.18834 1.62015i 0.914274 0.161211i 0.303330 0.952885i \(-0.401901\pi\)
0.610943 + 0.791674i \(0.290790\pi\)
\(102\) 0 0
\(103\) −0.625323 0.291593i −0.0616149 0.0287315i 0.391567 0.920150i \(-0.371933\pi\)
−0.453181 + 0.891418i \(0.649711\pi\)
\(104\) 5.27735 29.9293i 0.517487 2.93481i
\(105\) 0 0
\(106\) −21.2712 + 17.8487i −2.06604 + 1.73361i
\(107\) 7.01111 + 7.01111i 0.677790 + 0.677790i 0.959500 0.281710i \(-0.0909016\pi\)
−0.281710 + 0.959500i \(0.590902\pi\)
\(108\) 0 0
\(109\) 3.98129i 0.381339i 0.981654 + 0.190669i \(0.0610658\pi\)
−0.981654 + 0.190669i \(0.938934\pi\)
\(110\) −8.20113 13.0190i −0.781947 1.24131i
\(111\) 0 0
\(112\) 3.18801 + 4.55296i 0.301239 + 0.430214i
\(113\) −5.38280 + 11.5434i −0.506371 + 1.08592i 0.472480 + 0.881341i \(0.343359\pi\)
−0.978851 + 0.204575i \(0.934419\pi\)
\(114\) 0 0
\(115\) 10.4393 0.402540i 0.973466 0.0375371i
\(116\) −9.82667 + 5.67343i −0.912383 + 0.526765i
\(117\) 0 0
\(118\) −7.52823 + 2.01718i −0.693030 + 0.185697i
\(119\) 6.56043 + 2.38780i 0.601394 + 0.218889i
\(120\) 0 0
\(121\) 2.45176 + 2.05727i 0.222887 + 0.187024i
\(122\) −0.0340403 0.389083i −0.00308187 0.0352259i
\(123\) 0 0
\(124\) 6.89684 18.9489i 0.619354 1.70166i
\(125\) 11.0611 + 1.62848i 0.989335 + 0.145656i
\(126\) 0 0
\(127\) −1.43624 0.384839i −0.127445 0.0341489i 0.194532 0.980896i \(-0.437681\pi\)
−0.321978 + 0.946747i \(0.604348\pi\)
\(128\) −15.5115 10.8613i −1.37104 0.960012i
\(129\) 0 0
\(130\) 27.5840 + 17.7711i 2.41928 + 1.55863i
\(131\) 4.86082 + 0.857093i 0.424691 + 0.0748846i 0.381909 0.924200i \(-0.375267\pi\)
0.0427823 + 0.999084i \(0.486378\pi\)
\(132\) 0 0
\(133\) −2.52909 0.221266i −0.219300 0.0191862i
\(134\) 20.0146 1.72900
\(135\) 0 0
\(136\) 28.4024 2.43548
\(137\) −9.23718 0.808148i −0.789185 0.0690448i −0.314566 0.949236i \(-0.601859\pi\)
−0.474620 + 0.880191i \(0.657414\pi\)
\(138\) 0 0
\(139\) 0.653880 + 0.115297i 0.0554614 + 0.00977934i 0.201310 0.979528i \(-0.435480\pi\)
−0.145849 + 0.989307i \(0.546591\pi\)
\(140\) −11.1600 + 2.41455i −0.943190 + 0.204067i
\(141\) 0 0
\(142\) −16.3396 11.4411i −1.37119 0.960117i
\(143\) 16.0659 + 4.30485i 1.34350 + 0.359990i
\(144\) 0 0
\(145\) −0.782020 6.18317i −0.0649432 0.513484i
\(146\) −4.62188 + 12.6985i −0.382509 + 1.05094i
\(147\) 0 0
\(148\) 0.486104 + 5.55619i 0.0399575 + 0.456716i
\(149\) −3.98025 3.33983i −0.326075 0.273610i 0.465023 0.885298i \(-0.346046\pi\)
−0.791098 + 0.611689i \(0.790490\pi\)
\(150\) 0 0
\(151\) 3.92942 + 1.43019i 0.319772 + 0.116387i 0.496919 0.867797i \(-0.334465\pi\)
−0.177147 + 0.984184i \(0.556687\pi\)
\(152\) −9.97633 + 2.67315i −0.809187 + 0.216821i
\(153\) 0 0
\(154\) −7.47485 + 4.31561i −0.602340 + 0.347761i
\(155\) 8.12781 + 7.52426i 0.652841 + 0.604363i
\(156\) 0 0
\(157\) 5.80347 12.4456i 0.463168 0.993266i −0.526538 0.850151i \(-0.676510\pi\)
0.989706 0.143115i \(-0.0457119\pi\)
\(158\) 22.6786 + 32.3884i 1.80421 + 2.57668i
\(159\) 0 0
\(160\) −1.34790 + 0.849088i −0.106561 + 0.0671263i
\(161\) 5.86025i 0.461852i
\(162\) 0 0
\(163\) 14.8723 + 14.8723i 1.16489 + 1.16489i 0.983391 + 0.181498i \(0.0580947\pi\)
0.181498 + 0.983391i \(0.441905\pi\)
\(164\) 1.00636 0.844437i 0.0785835 0.0659394i
\(165\) 0 0
\(166\) 0.743123 4.21446i 0.0576775 0.327105i
\(167\) 3.30546 + 1.54136i 0.255784 + 0.119274i 0.546281 0.837602i \(-0.316043\pi\)
−0.290497 + 0.956876i \(0.593821\pi\)
\(168\) 0 0
\(169\) −22.1284 + 3.90184i −1.70219 + 0.300142i
\(170\) −11.8794 + 28.2714i −0.911109 + 2.16831i
\(171\) 0 0
\(172\) 9.45841 + 35.2993i 0.721197 + 2.69154i
\(173\) 7.42544 3.46254i 0.564546 0.263252i −0.119325 0.992855i \(-0.538073\pi\)
0.683871 + 0.729603i \(0.260295\pi\)
\(174\) 0 0
\(175\) 1.15190 6.16491i 0.0870751 0.466024i
\(176\) −7.95463 + 9.47996i −0.599603 + 0.714579i
\(177\) 0 0
\(178\) −13.4306 28.8021i −1.00667 2.15881i
\(179\) −3.07632 + 5.32834i −0.229935 + 0.398259i −0.957789 0.287474i \(-0.907185\pi\)
0.727854 + 0.685732i \(0.240518\pi\)
\(180\) 0 0
\(181\) −4.75332 8.23298i −0.353311 0.611953i 0.633516 0.773729i \(-0.281611\pi\)
−0.986827 + 0.161777i \(0.948278\pi\)
\(182\) 10.5575 15.0776i 0.782573 1.11763i
\(183\) 0 0
\(184\) −8.15408 22.4032i −0.601127 1.65158i
\(185\) −2.91696 0.936070i −0.214459 0.0688212i
\(186\) 0 0
\(187\) −1.35477 + 15.4851i −0.0990708 + 1.13238i
\(188\) 1.07248 1.07248i 0.0782189 0.0782189i
\(189\) 0 0
\(190\) 1.51182 11.0484i 0.109679 0.801534i
\(191\) −8.71630 10.3877i −0.630690 0.751627i 0.352179 0.935933i \(-0.385441\pi\)
−0.982869 + 0.184306i \(0.940996\pi\)
\(192\) 0 0
\(193\) 14.3226 10.0288i 1.03096 0.721888i 0.0697136 0.997567i \(-0.477791\pi\)
0.961250 + 0.275679i \(0.0889026\pi\)
\(194\) −8.21222 + 2.98900i −0.589603 + 0.214598i
\(195\) 0 0
\(196\) −3.83626 21.7565i −0.274019 1.55404i
\(197\) 0.482608 1.80112i 0.0343844 0.128324i −0.946600 0.322410i \(-0.895507\pi\)
0.980985 + 0.194085i \(0.0621739\pi\)
\(198\) 0 0
\(199\) −6.71379 3.87621i −0.475928 0.274777i 0.242790 0.970079i \(-0.421937\pi\)
−0.718718 + 0.695302i \(0.755271\pi\)
\(200\) −4.17442 25.1706i −0.295176 1.77983i
\(201\) 0 0
\(202\) 22.9013 2.00361i 1.61133 0.140973i
\(203\) −3.48277 + 0.304703i −0.244443 + 0.0213859i
\(204\) 0 0
\(205\) 0.213474 + 0.689273i 0.0149097 + 0.0481409i
\(206\) −1.47228 0.850021i −0.102579 0.0592237i
\(207\) 0 0
\(208\) 6.83040 25.4914i 0.473603 1.76751i
\(209\) −0.981552 5.56666i −0.0678954 0.385054i
\(210\) 0 0
\(211\) −20.1076 + 7.31857i −1.38426 + 0.503831i −0.923468 0.383675i \(-0.874658\pi\)
−0.460796 + 0.887506i \(0.652436\pi\)
\(212\) −37.5816 + 26.3149i −2.58111 + 1.80732i
\(213\) 0 0
\(214\) 15.7036 + 18.7149i 1.07348 + 1.27932i
\(215\) −19.8873 2.72130i −1.35630 0.185591i
\(216\) 0 0
\(217\) 4.39327 4.39327i 0.298235 0.298235i
\(218\) −0.854971 + 9.77236i −0.0579059 + 0.661868i
\(219\) 0 0
\(220\) −11.6239 22.6097i −0.783683 1.52434i
\(221\) −11.3376 31.1497i −0.762646 2.09535i
\(222\) 0 0
\(223\) −13.2104 + 18.8664i −0.884633 + 1.26339i 0.0791939 + 0.996859i \(0.474765\pi\)
−0.963827 + 0.266528i \(0.914124\pi\)
\(224\) 0.446808 + 0.773894i 0.0298536 + 0.0517079i
\(225\) 0 0
\(226\) −15.6914 + 27.1782i −1.04377 + 1.80787i
\(227\) 10.0438 + 21.5391i 0.666633 + 1.42960i 0.890502 + 0.454979i \(0.150353\pi\)
−0.223869 + 0.974619i \(0.571869\pi\)
\(228\) 0 0
\(229\) −9.86052 + 11.7513i −0.651602 + 0.776549i −0.986155 0.165828i \(-0.946970\pi\)
0.334553 + 0.942377i \(0.391415\pi\)
\(230\) 25.7103 + 1.25374i 1.69529 + 0.0826689i
\(231\) 0 0
\(232\) −12.8903 + 6.01086i −0.846291 + 0.394632i
\(233\) −3.29342 12.2912i −0.215759 0.805223i −0.985898 0.167347i \(-0.946480\pi\)
0.770139 0.637876i \(-0.220187\pi\)
\(234\) 0 0
\(235\) 0.314883 + 0.771279i 0.0205407 + 0.0503127i
\(236\) −12.6816 + 2.23611i −0.825501 + 0.145558i
\(237\) 0 0
\(238\) 15.5903 + 7.26986i 1.01057 + 0.471235i
\(239\) 0.944310 5.35545i 0.0610824 0.346415i −0.938915 0.344149i \(-0.888167\pi\)
0.999997 0.00226637i \(-0.000721408\pi\)
\(240\) 0 0
\(241\) 5.71656 4.79676i 0.368236 0.308987i −0.439827 0.898082i \(-0.644960\pi\)
0.808063 + 0.589096i \(0.200516\pi\)
\(242\) 5.57622 + 5.57622i 0.358453 + 0.358453i
\(243\) 0 0
\(244\) 0.645313i 0.0413119i
\(245\) 11.8333 + 2.68666i 0.755999 + 0.171644i
\(246\) 0 0
\(247\) 6.91404 + 9.87427i 0.439930 + 0.628285i
\(248\) 10.6822 22.9080i 0.678318 1.45466i
\(249\) 0 0
\(250\) 26.8005 + 6.37256i 1.69501 + 0.403036i
\(251\) −4.37402 + 2.52534i −0.276086 + 0.159398i −0.631650 0.775254i \(-0.717622\pi\)
0.355564 + 0.934652i \(0.384289\pi\)
\(252\) 0 0
\(253\) 12.6033 3.37704i 0.792361 0.212312i
\(254\) −3.44270 1.25304i −0.216014 0.0786228i
\(255\) 0 0
\(256\) −24.8532 20.8543i −1.55332 1.30339i
\(257\) 2.32628 + 26.5895i 0.145109 + 1.65861i 0.624514 + 0.781013i \(0.285297\pi\)
−0.479405 + 0.877594i \(0.659147\pi\)
\(258\) 0 0
\(259\) −0.587745 + 1.61482i −0.0365207 + 0.100340i
\(260\) 42.8429 + 33.2225i 2.65700 + 2.06037i
\(261\) 0 0
\(262\) 11.7471 + 3.14764i 0.725741 + 0.194462i
\(263\) 21.4619 + 15.0278i 1.32340 + 0.926654i 0.999809 0.0195432i \(-0.00622118\pi\)
0.323590 + 0.946197i \(0.395110\pi\)
\(264\) 0 0
\(265\) −5.32882 24.6296i −0.327347 1.51299i
\(266\) −6.16030 1.08623i −0.377712 0.0666009i
\(267\) 0 0
\(268\) 32.9431 + 2.88214i 2.01232 + 0.176055i
\(269\) 2.30251 0.140387 0.0701934 0.997533i \(-0.477638\pi\)
0.0701934 + 0.997533i \(0.477638\pi\)
\(270\) 0 0
\(271\) 6.12068 0.371805 0.185902 0.982568i \(-0.440479\pi\)
0.185902 + 0.982568i \(0.440479\pi\)
\(272\) 24.5699 + 2.14958i 1.48977 + 0.130338i
\(273\) 0 0
\(274\) −22.4997 3.96731i −1.35926 0.239674i
\(275\) 13.9223 1.07529i 0.839546 0.0648426i
\(276\) 0 0
\(277\) 8.67336 + 6.07315i 0.521132 + 0.364901i 0.804351 0.594155i \(-0.202513\pi\)
−0.283219 + 0.959055i \(0.591402\pi\)
\(278\) 1.58023 + 0.423423i 0.0947762 + 0.0253952i
\(279\) 0 0
\(280\) −14.1992 + 1.79585i −0.848564 + 0.107323i
\(281\) 2.07965 5.71378i 0.124061 0.340856i −0.862078 0.506776i \(-0.830837\pi\)
0.986139 + 0.165920i \(0.0530594\pi\)
\(282\) 0 0
\(283\) 0.312211 + 3.56859i 0.0185590 + 0.212131i 0.999812 + 0.0194049i \(0.00617717\pi\)
−0.981253 + 0.192726i \(0.938267\pi\)
\(284\) −25.2466 21.1845i −1.49811 1.25707i
\(285\) 0 0
\(286\) 38.5104 + 14.0167i 2.27717 + 0.828822i
\(287\) 0.390974 0.104761i 0.0230785 0.00618386i
\(288\) 0 0
\(289\) 12.1067 6.98981i 0.712160 0.411166i
\(290\) −0.591705 15.3449i −0.0347461 0.901086i
\(291\) 0 0
\(292\) −9.43599 + 20.2355i −0.552200 + 1.18420i
\(293\) −15.2979 21.8477i −0.893714 1.27636i −0.960412 0.278582i \(-0.910135\pi\)
0.0666984 0.997773i \(-0.478753\pi\)
\(294\) 0 0
\(295\) 1.56602 6.89745i 0.0911771 0.401585i
\(296\) 6.99110i 0.406349i
\(297\) 0 0
\(298\) −9.05259 9.05259i −0.524403 0.524403i
\(299\) −21.3153 + 17.8856i −1.23269 + 1.03435i
\(300\) 0 0
\(301\) −1.95523 + 11.0886i −0.112697 + 0.639138i
\(302\) 9.33791 + 4.35434i 0.537336 + 0.250564i
\(303\) 0 0
\(304\) −8.83248 + 1.55741i −0.506578 + 0.0893233i
\(305\) 0.326772 + 0.137307i 0.0187109 + 0.00786217i
\(306\) 0 0
\(307\) 3.38428 + 12.6303i 0.193151 + 0.720850i 0.992738 + 0.120299i \(0.0383854\pi\)
−0.799586 + 0.600551i \(0.794948\pi\)
\(308\) −12.9247 + 6.02688i −0.736453 + 0.343413i
\(309\) 0 0
\(310\) 18.3345 + 20.2142i 1.04133 + 1.14809i
\(311\) 7.01743 8.36305i 0.397922 0.474225i −0.529463 0.848333i \(-0.677607\pi\)
0.927385 + 0.374108i \(0.122051\pi\)
\(312\) 0 0
\(313\) −2.03021 4.35380i −0.114754 0.246091i 0.840539 0.541751i \(-0.182238\pi\)
−0.955293 + 0.295660i \(0.904461\pi\)
\(314\) 16.9177 29.3023i 0.954720 1.65362i
\(315\) 0 0
\(316\) 32.6638 + 56.5754i 1.83748 + 3.18262i
\(317\) 18.1287 25.8905i 1.01821 1.45415i 0.131787 0.991278i \(-0.457929\pi\)
0.886423 0.462876i \(-0.153182\pi\)
\(318\) 0 0
\(319\) −2.66229 7.31459i −0.149060 0.409538i
\(320\) 14.1333 7.26611i 0.790076 0.406188i
\(321\) 0 0
\(322\) 1.25847 14.3844i 0.0701318 0.801610i
\(323\) −7.96588 + 7.96588i −0.443234 + 0.443234i
\(324\) 0 0
\(325\) −25.9390 + 14.6257i −1.43884 + 0.811290i
\(326\) 33.3113 + 39.6989i 1.84494 + 2.19872i
\(327\) 0 0
\(328\) 1.34889 0.944503i 0.0744800 0.0521515i
\(329\) 0.439133 0.159831i 0.0242102 0.00881179i
\(330\) 0 0
\(331\) −4.86664 27.6001i −0.267495 1.51704i −0.761835 0.647771i \(-0.775701\pi\)
0.494340 0.869268i \(-0.335410\pi\)
\(332\) 1.83003 6.82978i 0.100436 0.374833i
\(333\) 0 0
\(334\) 7.78247 + 4.49321i 0.425838 + 0.245858i
\(335\) −8.46893 + 16.0684i −0.462707 + 0.877908i
\(336\) 0 0
\(337\) −35.9100 + 3.14172i −1.95614 + 0.171140i −0.994620 0.103586i \(-0.966968\pi\)
−0.961522 + 0.274727i \(0.911413\pi\)
\(338\) −55.1537 + 4.82532i −2.99997 + 0.262463i
\(339\) 0 0
\(340\) −23.6240 + 44.8226i −1.28119 + 2.43085i
\(341\) 11.9800 + 6.91666i 0.648754 + 0.374558i
\(342\) 0 0
\(343\) 4.03422 15.0559i 0.217828 0.812944i
\(344\) 7.95435 + 45.1114i 0.428870 + 2.43224i
\(345\) 0 0
\(346\) 18.9698 6.90445i 1.01982 0.371186i
\(347\) −13.1696 + 9.22149i −0.706984 + 0.495035i −0.870913 0.491437i \(-0.836472\pi\)
0.163930 + 0.986472i \(0.447583\pi\)
\(348\) 0 0
\(349\) −3.65928 4.36096i −0.195877 0.233437i 0.659162 0.752001i \(-0.270911\pi\)
−0.855039 + 0.518564i \(0.826467\pi\)
\(350\) 4.15130 14.8848i 0.221896 0.795628i
\(351\) 0 0
\(352\) −1.40689 + 1.40689i −0.0749873 + 0.0749873i
\(353\) 1.22287 13.9775i 0.0650869 0.743946i −0.891599 0.452825i \(-0.850416\pi\)
0.956686 0.291121i \(-0.0940282\pi\)
\(354\) 0 0
\(355\) 16.0992 8.27679i 0.854456 0.439286i
\(356\) −17.9586 49.3408i −0.951804 2.61506i
\(357\) 0 0
\(358\) −8.69528 + 12.4181i −0.459560 + 0.656319i
\(359\) 3.44870 + 5.97333i 0.182016 + 0.315260i 0.942567 0.334018i \(-0.108405\pi\)
−0.760551 + 0.649278i \(0.775071\pi\)
\(360\) 0 0
\(361\) −7.45171 + 12.9067i −0.392195 + 0.679302i
\(362\) −9.89933 21.2292i −0.520297 1.11578i
\(363\) 0 0
\(364\) 19.5483 23.2968i 1.02461 1.22108i
\(365\) −8.23907 9.08380i −0.431253 0.475468i
\(366\) 0 0
\(367\) −3.23085 + 1.50657i −0.168649 + 0.0786424i −0.505110 0.863055i \(-0.668548\pi\)
0.336460 + 0.941698i \(0.390770\pi\)
\(368\) −5.35826 19.9973i −0.279319 1.04243i
\(369\) 0 0
\(370\) −6.95886 2.92406i −0.361774 0.152014i
\(371\) −13.9209 + 2.45463i −0.722736 + 0.127438i
\(372\) 0 0
\(373\) −11.1529 5.20069i −0.577476 0.269282i 0.111859 0.993724i \(-0.464319\pi\)
−0.689335 + 0.724443i \(0.742097\pi\)
\(374\) −6.65076 + 37.7184i −0.343903 + 1.95037i
\(375\) 0 0
\(376\) 1.45637 1.22204i 0.0751066 0.0630219i
\(377\) 11.7378 + 11.7378i 0.604527 + 0.604527i
\(378\) 0 0
\(379\) 15.9996i 0.821843i −0.911671 0.410922i \(-0.865207\pi\)
0.911671 0.410922i \(-0.134793\pi\)
\(380\) 4.07937 17.9674i 0.209267 0.921708i
\(381\) 0 0
\(382\) −19.1640 27.3691i −0.980518 1.40032i
\(383\) 10.5466 22.6172i 0.538904 1.15568i −0.428755 0.903421i \(-0.641048\pi\)
0.967659 0.252262i \(-0.0811746\pi\)
\(384\) 0 0
\(385\) −0.301816 7.82714i −0.0153820 0.398908i
\(386\) 37.3095 21.5406i 1.89900 1.09639i
\(387\) 0 0
\(388\) −13.9473 + 3.73718i −0.708069 + 0.189726i
\(389\) −17.5837 6.39994i −0.891529 0.324490i −0.144676 0.989479i \(-0.546214\pi\)
−0.746853 + 0.664989i \(0.768436\pi\)
\(390\) 0 0
\(391\) −19.9205 16.7153i −1.00742 0.845327i
\(392\) −2.41350 27.5864i −0.121900 1.39332i
\(393\) 0 0
\(394\) 1.57138 4.31732i 0.0791649 0.217504i
\(395\) −35.5986 + 4.50235i −1.79116 + 0.226538i
\(396\) 0 0
\(397\) −9.00214 2.41212i −0.451805 0.121061i 0.0257391 0.999669i \(-0.491806\pi\)
−0.477544 + 0.878608i \(0.658473\pi\)
\(398\) −15.6471 10.9562i −0.784316 0.549184i
\(399\) 0 0
\(400\) −1.70614 22.0902i −0.0853070 1.10451i
\(401\) 21.8705 + 3.85636i 1.09216 + 0.192578i 0.690588 0.723249i \(-0.257352\pi\)
0.401575 + 0.915826i \(0.368463\pi\)
\(402\) 0 0
\(403\) −29.3879 2.57111i −1.46391 0.128076i
\(404\) 37.9830 1.88972
\(405\) 0 0
\(406\) −8.61413 −0.427512
\(407\) −3.81158 0.333470i −0.188933 0.0165295i
\(408\) 0 0
\(409\) −2.79062 0.492062i −0.137987 0.0243309i 0.104228 0.994553i \(-0.466763\pi\)
−0.242215 + 0.970223i \(0.577874\pi\)
\(410\) 0.375968 + 1.73771i 0.0185678 + 0.0858195i
\(411\) 0 0
\(412\) −2.30089 1.61110i −0.113357 0.0793734i
\(413\) −3.83240 1.02689i −0.188580 0.0505299i
\(414\) 0 0
\(415\) 3.06906 + 2.37990i 0.150654 + 0.116825i
\(416\) 1.45119 3.98710i 0.0711503 0.195484i
\(417\) 0 0
\(418\) −1.21386 13.8745i −0.0593720 0.678626i
\(419\) −3.08697 2.59027i −0.150808 0.126543i 0.564262 0.825596i \(-0.309161\pi\)
−0.715070 + 0.699053i \(0.753605\pi\)
\(420\) 0 0
\(421\) −4.12343 1.50080i −0.200964 0.0731448i 0.239577 0.970877i \(-0.422991\pi\)
−0.440541 + 0.897733i \(0.645213\pi\)
\(422\) −50.9271 + 13.6459i −2.47909 + 0.664271i
\(423\) 0 0
\(424\) −49.8028 + 28.7537i −2.41864 + 1.39640i
\(425\) −17.6705 21.4998i −0.857147 1.04290i
\(426\) 0 0
\(427\) 0.0840279 0.180198i 0.00406640 0.00872041i
\(428\) 23.1524 + 33.0651i 1.11912 + 1.59826i
\(429\) 0 0
\(430\) −48.2302 10.9503i −2.32587 0.528073i
\(431\) 14.3108i 0.689325i −0.938727 0.344662i \(-0.887993\pi\)
0.938727 0.344662i \(-0.112007\pi\)
\(432\) 0 0
\(433\) −10.5706 10.5706i −0.507988 0.507988i 0.405920 0.913909i \(-0.366951\pi\)
−0.913909 + 0.405920i \(0.866951\pi\)
\(434\) 11.7270 9.84015i 0.562915 0.472342i
\(435\) 0 0
\(436\) −2.81448 + 15.9617i −0.134789 + 0.764427i
\(437\) 8.57026 + 3.99638i 0.409971 + 0.191173i
\(438\) 0 0
\(439\) 23.9432 4.22183i 1.14275 0.201497i 0.429940 0.902857i \(-0.358535\pi\)
0.712807 + 0.701360i \(0.247424\pi\)
\(440\) −12.0447 29.5025i −0.574208 1.40647i
\(441\) 0 0
\(442\) −21.1395 78.8937i −1.00550 3.75259i
\(443\) 6.12987 2.85840i 0.291239 0.135807i −0.271508 0.962436i \(-0.587522\pi\)
0.562747 + 0.826629i \(0.309745\pi\)
\(444\) 0 0
\(445\) 28.8062 + 1.40470i 1.36555 + 0.0665894i
\(446\) −36.4773 + 43.4720i −1.72725 + 2.05846i
\(447\) 0 0
\(448\) −3.76741 8.07923i −0.177993 0.381708i
\(449\) −1.79424 + 3.10771i −0.0846753 + 0.146662i −0.905253 0.424873i \(-0.860319\pi\)
0.820577 + 0.571535i \(0.193652\pi\)
\(450\) 0 0
\(451\) 0.450607 + 0.780474i 0.0212183 + 0.0367511i
\(452\) −29.7409 + 42.4745i −1.39890 + 1.99783i
\(453\) 0 0
\(454\) 20.0278 + 55.0260i 0.939953 + 2.58250i
\(455\) 7.63755 + 14.8558i 0.358054 + 0.696451i
\(456\) 0 0
\(457\) 2.64330 30.2131i 0.123648 1.41331i −0.640347 0.768086i \(-0.721209\pi\)
0.763995 0.645222i \(-0.223235\pi\)
\(458\) −26.7269 + 26.7269i −1.24887 + 1.24887i
\(459\) 0 0
\(460\) 42.1374 + 5.76593i 1.96467 + 0.268838i
\(461\) −25.6308 30.5456i −1.19375 1.42265i −0.881197 0.472750i \(-0.843261\pi\)
−0.312550 0.949901i \(-0.601183\pi\)
\(462\) 0 0
\(463\) 14.0626 9.84673i 0.653544 0.457616i −0.199191 0.979961i \(-0.563831\pi\)
0.852735 + 0.522344i \(0.174942\pi\)
\(464\) −11.6059 + 4.22420i −0.538790 + 0.196103i
\(465\) 0 0
\(466\) −5.44442 30.8768i −0.252208 1.43034i
\(467\) 4.75144 17.7326i 0.219870 0.820568i −0.764525 0.644595i \(-0.777026\pi\)
0.984395 0.175973i \(-0.0563072\pi\)
\(468\) 0 0
\(469\) 8.82379 + 5.09442i 0.407445 + 0.235238i
\(470\) 0.607271 + 1.96078i 0.0280113 + 0.0904439i
\(471\) 0 0
\(472\) −16.0797 + 1.40679i −0.740129 + 0.0647529i
\(473\) −24.9744 + 2.18497i −1.14832 + 0.100465i
\(474\) 0 0
\(475\) 8.23028 + 5.88872i 0.377631 + 0.270193i
\(476\) 24.6139 + 14.2109i 1.12818 + 0.651354i
\(477\) 0 0
\(478\) 3.46794 12.9425i 0.158620 0.591978i
\(479\) −4.07702 23.1219i −0.186284 1.05647i −0.924295 0.381679i \(-0.875346\pi\)
0.738011 0.674789i \(-0.235765\pi\)
\(480\) 0 0
\(481\) 7.66733 2.79068i 0.349600 0.127244i
\(482\) 15.0618 10.5464i 0.686046 0.480374i
\(483\) 0 0
\(484\) 8.37519 + 9.98117i 0.380691 + 0.453689i
\(485\) 1.07523 7.85779i 0.0488238 0.356804i
\(486\) 0 0
\(487\) 7.21511 7.21511i 0.326948 0.326948i −0.524477 0.851425i \(-0.675739\pi\)
0.851425 + 0.524477i \(0.175739\pi\)
\(488\) 0.0704984 0.805800i 0.00319131 0.0364768i
\(489\) 0 0
\(490\) 28.4686 + 9.13575i 1.28608 + 0.412711i
\(491\) 11.3506 + 31.1854i 0.512243 + 1.40738i 0.878893 + 0.477018i \(0.158282\pi\)
−0.366650 + 0.930359i \(0.619495\pi\)
\(492\) 0 0
\(493\) −8.89818 + 12.7079i −0.400754 + 0.572336i
\(494\) 14.8505 + 25.7218i 0.668156 + 1.15728i
\(495\) 0 0
\(496\) 10.9745 19.0084i 0.492770 0.853502i
\(497\) −4.29144 9.20302i −0.192497 0.412812i
\(498\) 0 0
\(499\) −15.7113 + 18.7240i −0.703333 + 0.838200i −0.992899 0.118958i \(-0.962044\pi\)
0.289566 + 0.957158i \(0.406489\pi\)
\(500\) 43.1947 + 14.3483i 1.93173 + 0.641674i
\(501\) 0 0
\(502\) −11.2786 + 5.25932i −0.503391 + 0.234735i
\(503\) 9.98672 + 37.2709i 0.445286 + 1.66183i 0.715181 + 0.698939i \(0.246344\pi\)
−0.269896 + 0.962890i \(0.586989\pi\)
\(504\) 0 0
\(505\) −8.08185 + 19.2337i −0.359638 + 0.855889i
\(506\) 31.6608 5.58265i 1.40749 0.248179i
\(507\) 0 0
\(508\) −5.48608 2.55820i −0.243405 0.113502i
\(509\) −0.294649 + 1.67104i −0.0130601 + 0.0740674i −0.990641 0.136492i \(-0.956417\pi\)
0.977581 + 0.210559i \(0.0675284\pi\)
\(510\) 0 0
\(511\) −5.26985 + 4.42193i −0.233124 + 0.195615i
\(512\) −29.7458 29.7458i −1.31459 1.31459i
\(513\) 0 0
\(514\) 65.7653i 2.90078i
\(515\) 1.30540 0.822317i 0.0575228 0.0362356i
\(516\) 0 0
\(517\) 0.596795 + 0.852312i 0.0262470 + 0.0374846i
\(518\) −1.78944 + 3.83746i −0.0786234 + 0.168608i
\(519\) 0 0
\(520\) 49.8683 + 46.1652i 2.18687 + 2.02448i
\(521\) −22.9824 + 13.2689i −1.00688 + 0.581322i −0.910276 0.414001i \(-0.864131\pi\)
−0.0966024 + 0.995323i \(0.530798\pi\)
\(522\) 0 0
\(523\) 14.6802 3.93354i 0.641920 0.172002i 0.0768469 0.997043i \(-0.475515\pi\)
0.565073 + 0.825041i \(0.308848\pi\)
\(524\) 18.8820 + 6.87247i 0.824863 + 0.300225i
\(525\) 0 0
\(526\) 49.4526 + 41.4957i 2.15624 + 1.80930i
\(527\) −2.40286 27.4648i −0.104670 1.19639i
\(528\) 0 0
\(529\) 0.400836 1.10129i 0.0174277 0.0478821i
\(530\) −7.79083 61.5995i −0.338412 2.67571i
\(531\) 0 0
\(532\) −9.98314 2.67497i −0.432824 0.115975i
\(533\) −1.57431 1.10234i −0.0681909 0.0477478i
\(534\) 0 0
\(535\) −21.6697 + 4.68842i −0.936862 + 0.202698i
\(536\) 40.8210 + 7.19784i 1.76320 + 0.310900i
\(537\) 0 0
\(538\) 5.65168 + 0.494458i 0.243661 + 0.0213176i
\(539\) 15.1554 0.652788
\(540\) 0 0
\(541\) 6.56072 0.282068 0.141034 0.990005i \(-0.454957\pi\)
0.141034 + 0.990005i \(0.454957\pi\)
\(542\) 15.0236 + 1.31440i 0.645320 + 0.0564582i
\(543\) 0 0
\(544\) 3.90510 + 0.688574i 0.167430 + 0.0295224i
\(545\) −7.48379 4.82145i −0.320570 0.206528i
\(546\) 0 0
\(547\) 29.4654 + 20.6319i 1.25985 + 0.882156i 0.996585 0.0825680i \(-0.0263122\pi\)
0.263264 + 0.964724i \(0.415201\pi\)
\(548\) −36.4622 9.77001i −1.55759 0.417354i
\(549\) 0 0
\(550\) 34.4041 + 0.350390i 1.46700 + 0.0149407i
\(551\) 1.92945 5.30113i 0.0821975 0.225836i
\(552\) 0 0
\(553\) 1.75428 + 20.0515i 0.0745994 + 0.852675i
\(554\) 19.9852 + 16.7696i 0.849089 + 0.712470i
\(555\) 0 0
\(556\) 2.54002 + 0.924490i 0.107721 + 0.0392071i
\(557\) 4.37675 1.17275i 0.185449 0.0496908i −0.164899 0.986310i \(-0.552730\pi\)
0.350348 + 0.936620i \(0.386063\pi\)
\(558\) 0 0
\(559\) 46.2997 26.7312i 1.95827 1.13061i
\(560\) −12.4191 + 0.478885i −0.524804 + 0.0202366i
\(561\) 0 0
\(562\) 6.33165 13.5783i 0.267085 0.572765i
\(563\) −1.52340 2.17564i −0.0642037 0.0916924i 0.785766 0.618524i \(-0.212269\pi\)
−0.849970 + 0.526831i \(0.823380\pi\)
\(564\) 0 0
\(565\) −15.1800 24.0977i −0.638625 1.01380i
\(566\) 8.82639i 0.371001i
\(567\) 0 0
\(568\) −29.2111 29.2111i −1.22567 1.22567i
\(569\) −22.4581 + 18.8446i −0.941494 + 0.790007i −0.977845 0.209332i \(-0.932871\pi\)
0.0363507 + 0.999339i \(0.488427\pi\)
\(570\) 0 0
\(571\) −2.73020 + 15.4837i −0.114255 + 0.647973i 0.872861 + 0.487969i \(0.162262\pi\)
−0.987116 + 0.160004i \(0.948849\pi\)
\(572\) 61.3679 + 28.6163i 2.56592 + 1.19651i
\(573\) 0 0
\(574\) 0.982170 0.173183i 0.0409950 0.00722852i
\(575\) −11.8855 + 20.1106i −0.495661 + 0.838668i
\(576\) 0 0
\(577\) 7.02870 + 26.2315i 0.292609 + 1.09203i 0.943098 + 0.332515i \(0.107897\pi\)
−0.650489 + 0.759515i \(0.725436\pi\)
\(578\) 31.2178 14.5571i 1.29849 0.605496i
\(579\) 0 0
\(580\) 1.23579 25.3422i 0.0513133 1.05228i
\(581\) 1.40035 1.66887i 0.0580961 0.0692363i
\(582\) 0 0
\(583\) −13.3011 28.5243i −0.550875 1.18136i
\(584\) −13.9934 + 24.2372i −0.579049 + 1.00294i
\(585\) 0 0
\(586\) −32.8581 56.9118i −1.35735 2.35101i
\(587\) −0.208890 + 0.298326i −0.00862180 + 0.0123132i −0.823440 0.567404i \(-0.807948\pi\)
0.814818 + 0.579717i \(0.196837\pi\)
\(588\) 0 0
\(589\) 3.42892 + 9.42087i 0.141286 + 0.388180i
\(590\) 5.32511 16.5940i 0.219231 0.683163i
\(591\) 0 0
\(592\) −0.529109 + 6.04775i −0.0217463 + 0.248561i
\(593\) 5.77411 5.77411i 0.237114 0.237114i −0.578540 0.815654i \(-0.696377\pi\)
0.815654 + 0.578540i \(0.196377\pi\)
\(594\) 0 0
\(595\) −12.4333 + 9.44021i −0.509715 + 0.387011i
\(596\) −13.5965 16.2037i −0.556936 0.663730i
\(597\) 0 0
\(598\) −56.1607 + 39.3241i −2.29658 + 1.60808i
\(599\) 22.4110 8.15692i 0.915687 0.333283i 0.159166 0.987252i \(-0.449120\pi\)
0.756521 + 0.653969i \(0.226897\pi\)
\(600\) 0 0
\(601\) −0.792095 4.49219i −0.0323102 0.183240i 0.964381 0.264515i \(-0.0852120\pi\)
−0.996692 + 0.0812748i \(0.974101\pi\)
\(602\) −7.18049 + 26.7979i −0.292655 + 1.09220i
\(603\) 0 0
\(604\) 14.7427 + 8.51171i 0.599872 + 0.346336i
\(605\) −6.83627 + 2.11726i −0.277934 + 0.0860788i
\(606\) 0 0
\(607\) −40.4825 + 3.54176i −1.64313 + 0.143756i −0.870859 0.491533i \(-0.836437\pi\)
−0.772275 + 0.635289i \(0.780881\pi\)
\(608\) −1.43647 + 0.125675i −0.0582566 + 0.00509680i
\(609\) 0 0
\(610\) 0.772598 + 0.407202i 0.0312816 + 0.0164871i
\(611\) −1.92160 1.10943i −0.0777394 0.0448829i
\(612\) 0 0
\(613\) −5.74347 + 21.4349i −0.231977 + 0.865749i 0.747512 + 0.664249i \(0.231248\pi\)
−0.979488 + 0.201500i \(0.935418\pi\)
\(614\) 5.59463 + 31.7288i 0.225781 + 1.28047i
\(615\) 0 0
\(616\) −16.7974 + 6.11376i −0.676788 + 0.246331i
\(617\) 10.6418 7.45148i 0.428423 0.299985i −0.339406 0.940640i \(-0.610226\pi\)
0.767829 + 0.640655i \(0.221337\pi\)
\(618\) 0 0
\(619\) −7.80404 9.30049i −0.313671 0.373818i 0.586057 0.810270i \(-0.300679\pi\)
−0.899728 + 0.436452i \(0.856235\pi\)
\(620\) 27.2667 + 35.9119i 1.09506 + 1.44225i
\(621\) 0 0
\(622\) 19.0207 19.0207i 0.762661 0.762661i
\(623\) 1.41001 16.1165i 0.0564908 0.645693i
\(624\) 0 0
\(625\) −16.4564 + 18.8198i −0.658256 + 0.752794i
\(626\) −4.04832 11.1227i −0.161804 0.444552i
\(627\) 0 0
\(628\) 32.0653 45.7939i 1.27954 1.82738i
\(629\) 3.81274 + 6.60386i 0.152024 + 0.263313i
\(630\) 0 0
\(631\) 11.6365 20.1551i 0.463243 0.802360i −0.535877 0.844296i \(-0.680019\pi\)
0.999120 + 0.0419354i \(0.0133524\pi\)
\(632\) 34.6065 + 74.2139i 1.37657 + 2.95207i
\(633\) 0 0
\(634\) 50.0581 59.6569i 1.98806 2.36928i
\(635\) 2.46272 2.23370i 0.0977299 0.0886417i
\(636\) 0 0
\(637\) −29.2913 + 13.6588i −1.16057 + 0.541181i
\(638\) −4.96400 18.5259i −0.196526 0.733447i
\(639\) 0 0
\(640\) 39.2013 16.0043i 1.54957 0.632627i
\(641\) 36.8613 6.49963i 1.45593 0.256720i 0.611016 0.791618i \(-0.290761\pi\)
0.844916 + 0.534898i \(0.179650\pi\)
\(642\) 0 0
\(643\) 29.5339 + 13.7719i 1.16470 + 0.543110i 0.906179 0.422895i \(-0.138986\pi\)
0.258524 + 0.966005i \(0.416764\pi\)
\(644\) 4.14276 23.4948i 0.163248 0.925823i
\(645\) 0 0
\(646\) −21.2635 + 17.8422i −0.836600 + 0.701991i
\(647\) −25.9188 25.9188i −1.01897 1.01897i −0.999816 0.0191583i \(-0.993901\pi\)
−0.0191583 0.999816i \(-0.506099\pi\)
\(648\) 0 0
\(649\) 8.83386i 0.346759i
\(650\) −66.8100 + 30.3295i −2.62050 + 1.18962i
\(651\) 0 0
\(652\) 49.1121 + 70.1394i 1.92338 + 2.74687i
\(653\) 14.6418 31.3994i 0.572978 1.22875i −0.379795 0.925071i \(-0.624006\pi\)
0.952773 0.303684i \(-0.0982167\pi\)
\(654\) 0 0
\(655\) −7.49768 + 8.09910i −0.292959 + 0.316458i
\(656\) 1.23836 0.714967i 0.0483498 0.0279148i
\(657\) 0 0
\(658\) 1.11221 0.298015i 0.0433583 0.0116178i
\(659\) 14.1890 + 5.16436i 0.552723 + 0.201175i 0.603256 0.797548i \(-0.293870\pi\)
−0.0505327 + 0.998722i \(0.516092\pi\)
\(660\) 0 0
\(661\) 26.1426 + 21.9363i 1.01683 + 0.853222i 0.989226 0.146397i \(-0.0467677\pi\)
0.0276043 + 0.999619i \(0.491212\pi\)
\(662\) −6.01847 68.7915i −0.233915 2.67366i
\(663\) 0 0
\(664\) 3.03129 8.32839i 0.117637 0.323204i
\(665\) 3.47871 4.48606i 0.134899 0.173962i
\(666\) 0 0
\(667\) 12.5783 + 3.37035i 0.487035 + 0.130501i
\(668\) 12.1625 + 8.51630i 0.470582 + 0.329505i
\(669\) 0 0
\(670\) −24.2382 + 37.6222i −0.936404 + 1.45347i
\(671\) 0.435964 + 0.0768722i 0.0168302 + 0.00296762i
\(672\) 0 0
\(673\) 44.9802 + 3.93526i 1.73386 + 0.151693i 0.909865 0.414905i \(-0.136185\pi\)
0.823995 + 0.566598i \(0.191741\pi\)
\(674\) −88.8183 −3.42115
\(675\) 0 0
\(676\) −91.4752 −3.51828
\(677\) −15.7890 1.38136i −0.606822 0.0530900i −0.220396 0.975411i \(-0.570735\pi\)
−0.386426 + 0.922321i \(0.626290\pi\)
\(678\) 0 0
\(679\) −4.38131 0.772543i −0.168139 0.0296475i
\(680\) −34.3960 + 53.3890i −1.31903 + 2.04737i
\(681\) 0 0
\(682\) 27.9204 + 19.5501i 1.06913 + 0.748612i
\(683\) 7.02767 + 1.88306i 0.268906 + 0.0720532i 0.390753 0.920496i \(-0.372215\pi\)
−0.121846 + 0.992549i \(0.538881\pi\)
\(684\) 0 0
\(685\) 12.7056 16.3848i 0.485455 0.626030i
\(686\) 13.1355 36.0895i 0.501515 1.37790i
\(687\) 0 0
\(688\) 3.46685 + 39.6262i 0.132172 + 1.51074i
\(689\) 51.4151 + 43.1424i 1.95876 + 1.64359i
\(690\) 0 0
\(691\) 42.1583 + 15.3444i 1.60378 + 0.583728i 0.980196 0.198030i \(-0.0634544\pi\)
0.623582 + 0.781758i \(0.285677\pi\)
\(692\) 32.2177 8.63269i 1.22473 0.328166i
\(693\) 0 0
\(694\) −34.3061 + 19.8066i −1.30224 + 0.751849i
\(695\) −1.00859 + 1.08950i −0.0382581 + 0.0413270i
\(696\) 0 0
\(697\) 0.759071 1.62783i 0.0287519 0.0616585i
\(698\) −8.04544 11.4901i −0.304525 0.434906i
\(699\) 0 0
\(700\) 8.97629 23.9019i 0.339272 0.903407i
\(701\) 23.7146i 0.895688i 0.894112 + 0.447844i \(0.147808\pi\)
−0.894112 + 0.447844i \(0.852192\pi\)
\(702\) 0 0
\(703\) −1.96076 1.96076i −0.0739516 0.0739516i
\(704\) 15.2045 12.7581i 0.573041 0.480839i
\(705\) 0 0
\(706\) 6.00324 34.0461i 0.225935 1.28134i
\(707\) 10.6064 + 4.94586i 0.398896 + 0.186008i
\(708\) 0 0
\(709\) −35.6845 + 6.29214i −1.34016 + 0.236306i −0.797334 0.603539i \(-0.793757\pi\)
−0.542826 + 0.839845i \(0.682646\pi\)
\(710\) 41.2940 16.8587i 1.54974 0.632696i
\(711\) 0 0
\(712\) −17.0345 63.5736i −0.638395 2.38252i
\(713\) −20.9738 + 9.78025i −0.785476 + 0.366273i
\(714\) 0 0
\(715\) −27.5482 + 24.9864i −1.03025 + 0.934439i
\(716\) −16.1002 + 19.1875i −0.601694 + 0.717071i
\(717\) 0 0
\(718\) 7.18233 + 15.4026i 0.268042 + 0.574818i
\(719\) 3.82026 6.61689i 0.142472 0.246768i −0.785955 0.618284i \(-0.787828\pi\)
0.928427 + 0.371515i \(0.121162\pi\)
\(720\) 0 0
\(721\) −0.432720 0.749493i −0.0161153 0.0279126i
\(722\) −21.0624 + 30.0802i −0.783862 + 1.11947i
\(723\) 0 0
\(724\) −13.2368 36.3677i −0.491941 1.35160i
\(725\) 12.5698 + 6.01798i 0.466830 + 0.223502i
\(726\) 0 0
\(727\) −4.09954 + 46.8579i −0.152043 + 1.73786i 0.411175 + 0.911557i \(0.365119\pi\)
−0.563218 + 0.826308i \(0.690437\pi\)
\(728\) 26.9550 26.9550i 0.999018 0.999018i
\(729\) 0 0
\(730\) −18.2726 24.0661i −0.676301 0.890727i
\(731\) 32.1162 + 38.2746i 1.18786 + 1.41564i
\(732\) 0 0
\(733\) 38.5374 26.9842i 1.42341 0.996682i 0.427723 0.903910i \(-0.359316\pi\)
0.995687 0.0927724i \(-0.0295729\pi\)
\(734\) −8.25389 + 3.00417i −0.304657 + 0.110886i
\(735\) 0 0
\(736\) −0.577989 3.27794i −0.0213050 0.120826i
\(737\) −5.87144 + 21.9125i −0.216277 + 0.807157i
\(738\) 0 0
\(739\) −40.7581 23.5317i −1.49931 0.865628i −0.499311 0.866423i \(-0.666414\pi\)
−1.00000 0.000795196i \(0.999747\pi\)
\(740\) −11.0329 5.81494i −0.405576 0.213761i
\(741\) 0 0
\(742\) −34.6969 + 3.03559i −1.27376 + 0.111440i
\(743\) 5.97266 0.522540i 0.219115 0.0191701i 0.0229307 0.999737i \(-0.492700\pi\)
0.196185 + 0.980567i \(0.437145\pi\)
\(744\) 0 0
\(745\) 11.0982 3.43722i 0.406607 0.125930i
\(746\) −26.2588 15.1605i −0.961402 0.555066i
\(747\) 0 0
\(748\) −16.3784 + 61.1248i −0.598852 + 2.23495i
\(749\) 2.15964 + 12.2479i 0.0789114 + 0.447529i
\(750\) 0 0
\(751\) 30.7152 11.1794i 1.12081 0.407943i 0.285865 0.958270i \(-0.407719\pi\)
0.834949 + 0.550327i \(0.185497\pi\)
\(752\) 1.35234 0.946921i 0.0493149 0.0345306i
\(753\) 0 0
\(754\) 26.2906 + 31.3319i 0.957446 + 1.14104i
\(755\) −7.44702 + 5.65429i −0.271025 + 0.205781i
\(756\) 0 0
\(757\) −6.11549 + 6.11549i −0.222271 + 0.222271i −0.809454 0.587183i \(-0.800237\pi\)
0.587183 + 0.809454i \(0.300237\pi\)
\(758\) 3.43586 39.2721i 0.124796 1.42643i
\(759\) 0 0
\(760\) 7.05677 21.9901i 0.255976 0.797667i
\(761\) 8.81390 + 24.2160i 0.319503 + 0.877829i 0.990641 + 0.136495i \(0.0435839\pi\)
−0.671137 + 0.741333i \(0.734194\pi\)
\(762\) 0 0
\(763\) −2.86434 + 4.09070i −0.103696 + 0.148093i
\(764\) −27.6019 47.8078i −0.998601 1.72963i
\(765\) 0 0
\(766\) 30.7442 53.2505i 1.11083 1.92402i
\(767\) 7.96152 + 17.0735i 0.287474 + 0.616490i
\(768\) 0 0
\(769\) 17.3950 20.7306i 0.627281 0.747565i −0.355023 0.934858i \(-0.615527\pi\)
0.982304 + 0.187293i \(0.0599713\pi\)
\(770\) 0.940025 19.2771i 0.0338762 0.694697i
\(771\) 0 0
\(772\) 64.5115 30.0822i 2.32182 1.08268i
\(773\) 11.1567 + 41.6374i 0.401279 + 1.49759i 0.810817 + 0.585299i \(0.199023\pi\)
−0.409539 + 0.912293i \(0.634310\pi\)
\(774\) 0 0
\(775\) −23.9866 + 6.16608i −0.861625 + 0.221492i
\(776\) −17.8243 + 3.14290i −0.639854 + 0.112823i
\(777\) 0 0
\(778\) −41.7860 19.4851i −1.49810 0.698576i
\(779\) −0.113417 + 0.643218i −0.00406357 + 0.0230457i
\(780\) 0 0
\(781\) 17.3194 14.5327i 0.619736 0.520020i
\(782\) −45.3066 45.3066i −1.62016 1.62016i
\(783\) 0 0
\(784\) 24.0467i 0.858809i
\(785\) 16.3663 + 25.9809i 0.584138 + 0.927300i
\(786\) 0 0
\(787\) −14.3355 20.4732i −0.511006