Properties

Label 405.2.r.a.197.2
Level $405$
Weight $2$
Character 405.197
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 197.2
Character \(\chi\) \(=\) 405.197
Dual form 405.2.r.a.368.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.08671 + 0.182563i) q^{2} +(2.35140 - 0.414615i) q^{4} +(1.98370 - 1.03196i) q^{5} +(3.38127 - 2.36759i) q^{7} +(-0.784385 + 0.210175i) q^{8} +O(q^{10})\) \(q+(-2.08671 + 0.182563i) q^{2} +(2.35140 - 0.414615i) q^{4} +(1.98370 - 1.03196i) q^{5} +(3.38127 - 2.36759i) q^{7} +(-0.784385 + 0.210175i) q^{8} +(-3.95100 + 2.51554i) q^{10} +(-1.66957 - 4.58710i) q^{11} +(-0.223275 + 2.55204i) q^{13} +(-6.62348 + 5.55776i) q^{14} +(-2.88895 + 1.05149i) q^{16} +(2.36120 + 0.632683i) q^{17} +(-4.05431 - 2.34076i) q^{19} +(4.23661 - 3.24902i) q^{20} +(4.32134 + 9.26714i) q^{22} +(-2.13442 + 3.04827i) q^{23} +(2.87013 - 4.09419i) q^{25} -5.36612i q^{26} +(6.96907 - 6.96907i) q^{28} +(-2.44490 - 2.05152i) q^{29} +(-0.272295 - 1.54426i) q^{31} +(7.30837 - 3.40795i) q^{32} +(-5.04264 - 0.889154i) q^{34} +(4.26417 - 8.18590i) q^{35} +(0.592937 - 2.21287i) q^{37} +(8.88750 + 4.14431i) q^{38} +(-1.33909 + 1.22638i) q^{40} +(4.38733 + 5.22862i) q^{41} +(0.553045 - 1.18601i) q^{43} +(-5.82771 - 10.0939i) q^{44} +(3.89741 - 6.75051i) q^{46} +(0.220307 + 0.314631i) q^{47} +(3.43334 - 9.43304i) q^{49} +(-5.24167 + 9.06735i) q^{50} +(0.533107 + 6.09344i) q^{52} +(-0.177802 - 0.177802i) q^{53} +(-8.04562 - 7.37651i) q^{55} +(-2.15461 + 2.56776i) q^{56} +(5.47633 + 3.83457i) q^{58} +(0.797126 + 0.290130i) q^{59} +(1.38646 - 7.86300i) q^{61} +(0.850126 + 3.17272i) q^{62} +(-9.30332 + 5.37128i) q^{64} +(2.19069 + 5.29289i) q^{65} +(8.09911 + 0.708580i) q^{67} +(5.81446 + 0.508699i) q^{68} +(-7.40362 + 17.8601i) q^{70} +(7.83146 - 4.52149i) q^{71} +(3.19228 + 11.9138i) q^{73} +(-0.833296 + 4.72586i) q^{74} +(-10.5038 - 3.82308i) q^{76} +(-16.5056 - 11.5574i) q^{77} +(-6.94728 + 8.27944i) q^{79} +(-4.64572 + 5.06712i) q^{80} +(-10.1096 - 10.1096i) q^{82} +(-0.325084 - 3.71573i) q^{83} +(5.33682 - 1.18161i) q^{85} +(-0.937521 + 2.57582i) q^{86} +(2.27368 + 3.24715i) q^{88} +(-7.58469 + 13.1371i) q^{89} +(5.28723 + 9.15775i) q^{91} +(-3.75502 + 8.05267i) q^{92} +(-0.517156 - 0.616322i) q^{94} +(-10.4581 - 0.459486i) q^{95} +(-1.25036 - 0.583050i) q^{97} +(-5.44226 + 20.3108i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.08671 + 0.182563i −1.47552 + 0.129092i −0.796328 0.604865i \(-0.793227\pi\)
−0.679196 + 0.733956i \(0.737672\pi\)
\(3\) 0 0
\(4\) 2.35140 0.414615i 1.17570 0.207308i
\(5\) 1.98370 1.03196i 0.887138 0.461505i
\(6\) 0 0
\(7\) 3.38127 2.36759i 1.27800 0.894864i 0.280120 0.959965i \(-0.409626\pi\)
0.997879 + 0.0651011i \(0.0207370\pi\)
\(8\) −0.784385 + 0.210175i −0.277322 + 0.0743082i
\(9\) 0 0
\(10\) −3.95100 + 2.51554i −1.24942 + 0.795484i
\(11\) −1.66957 4.58710i −0.503394 1.38306i −0.887940 0.459958i \(-0.847864\pi\)
0.384546 0.923106i \(-0.374358\pi\)
\(12\) 0 0
\(13\) −0.223275 + 2.55204i −0.0619252 + 0.707809i 0.900249 + 0.435375i \(0.143384\pi\)
−0.962175 + 0.272434i \(0.912171\pi\)
\(14\) −6.62348 + 5.55776i −1.77020 + 1.48537i
\(15\) 0 0
\(16\) −2.88895 + 1.05149i −0.722238 + 0.262873i
\(17\) 2.36120 + 0.632683i 0.572676 + 0.153448i 0.533524 0.845785i \(-0.320868\pi\)
0.0391524 + 0.999233i \(0.487534\pi\)
\(18\) 0 0
\(19\) −4.05431 2.34076i −0.930123 0.537007i −0.0432724 0.999063i \(-0.513778\pi\)
−0.886850 + 0.462057i \(0.847112\pi\)
\(20\) 4.23661 3.24902i 0.947335 0.726502i
\(21\) 0 0
\(22\) 4.32134 + 9.26714i 0.921313 + 1.97576i
\(23\) −2.13442 + 3.04827i −0.445058 + 0.635608i −0.977519 0.210846i \(-0.932378\pi\)
0.532462 + 0.846454i \(0.321267\pi\)
\(24\) 0 0
\(25\) 2.87013 4.09419i 0.574026 0.818837i
\(26\) 5.36612i 1.05238i
\(27\) 0 0
\(28\) 6.96907 6.96907i 1.31703 1.31703i
\(29\) −2.44490 2.05152i −0.454007 0.380957i 0.386913 0.922116i \(-0.373541\pi\)
−0.840920 + 0.541159i \(0.817986\pi\)
\(30\) 0 0
\(31\) −0.272295 1.54426i −0.0489057 0.277358i 0.950542 0.310597i \(-0.100529\pi\)
−0.999447 + 0.0332389i \(0.989418\pi\)
\(32\) 7.30837 3.40795i 1.29195 0.602446i
\(33\) 0 0
\(34\) −5.04264 0.889154i −0.864806 0.152489i
\(35\) 4.26417 8.18590i 0.720776 1.38367i
\(36\) 0 0
\(37\) 0.592937 2.21287i 0.0974782 0.363793i −0.899905 0.436085i \(-0.856365\pi\)
0.997384 + 0.0722918i \(0.0230313\pi\)
\(38\) 8.88750 + 4.14431i 1.44174 + 0.672295i
\(39\) 0 0
\(40\) −1.33909 + 1.22638i −0.211729 + 0.193907i
\(41\) 4.38733 + 5.22862i 0.685186 + 0.816573i 0.990764 0.135594i \(-0.0432944\pi\)
−0.305579 + 0.952167i \(0.598850\pi\)
\(42\) 0 0
\(43\) 0.553045 1.18601i 0.0843385 0.180865i −0.859616 0.510941i \(-0.829297\pi\)
0.943954 + 0.330077i \(0.107075\pi\)
\(44\) −5.82771 10.0939i −0.878561 1.52171i
\(45\) 0 0
\(46\) 3.89741 6.75051i 0.574642 0.995309i
\(47\) 0.220307 + 0.314631i 0.0321351 + 0.0458936i 0.834898 0.550405i \(-0.185527\pi\)
−0.802763 + 0.596298i \(0.796638\pi\)
\(48\) 0 0
\(49\) 3.43334 9.43304i 0.490478 1.34758i
\(50\) −5.24167 + 9.06735i −0.741284 + 1.28232i
\(51\) 0 0
\(52\) 0.533107 + 6.09344i 0.0739287 + 0.845009i
\(53\) −0.177802 0.177802i −0.0244229 0.0244229i 0.694790 0.719213i \(-0.255497\pi\)
−0.719213 + 0.694790i \(0.755497\pi\)
\(54\) 0 0
\(55\) −8.04562 7.37651i −1.08487 0.994649i
\(56\) −2.15461 + 2.56776i −0.287921 + 0.343131i
\(57\) 0 0
\(58\) 5.47633 + 3.83457i 0.719077 + 0.503503i
\(59\) 0.797126 + 0.290130i 0.103777 + 0.0377717i 0.393387 0.919373i \(-0.371303\pi\)
−0.289610 + 0.957145i \(0.593526\pi\)
\(60\) 0 0
\(61\) 1.38646 7.86300i 0.177518 1.00675i −0.757679 0.652627i \(-0.773667\pi\)
0.935197 0.354127i \(-0.115222\pi\)
\(62\) 0.850126 + 3.17272i 0.107966 + 0.402935i
\(63\) 0 0
\(64\) −9.30332 + 5.37128i −1.16292 + 0.671410i
\(65\) 2.19069 + 5.29289i 0.271721 + 0.656502i
\(66\) 0 0
\(67\) 8.09911 + 0.708580i 0.989463 + 0.0865668i 0.570380 0.821381i \(-0.306796\pi\)
0.419083 + 0.907948i \(0.362351\pi\)
\(68\) 5.81446 + 0.508699i 0.705106 + 0.0616888i
\(69\) 0 0
\(70\) −7.40362 + 17.8601i −0.884902 + 2.13469i
\(71\) 7.83146 4.52149i 0.929423 0.536603i 0.0427939 0.999084i \(-0.486374\pi\)
0.886629 + 0.462481i \(0.153041\pi\)
\(72\) 0 0
\(73\) 3.19228 + 11.9138i 0.373628 + 1.39440i 0.855339 + 0.518069i \(0.173349\pi\)
−0.481710 + 0.876330i \(0.659984\pi\)
\(74\) −0.833296 + 4.72586i −0.0968687 + 0.549370i
\(75\) 0 0
\(76\) −10.5038 3.82308i −1.20487 0.438537i
\(77\) −16.5056 11.5574i −1.88099 1.31708i
\(78\) 0 0
\(79\) −6.94728 + 8.27944i −0.781630 + 0.931510i −0.999006 0.0445777i \(-0.985806\pi\)
0.217376 + 0.976088i \(0.430250\pi\)
\(80\) −4.64572 + 5.06712i −0.519407 + 0.566521i
\(81\) 0 0
\(82\) −10.1096 10.1096i −1.11642 1.11642i
\(83\) −0.325084 3.71573i −0.0356826 0.407854i −0.992940 0.118617i \(-0.962154\pi\)
0.957257 0.289237i \(-0.0934016\pi\)
\(84\) 0 0
\(85\) 5.33682 1.18161i 0.578859 0.128163i
\(86\) −0.937521 + 2.57582i −0.101095 + 0.277758i
\(87\) 0 0
\(88\) 2.27368 + 3.24715i 0.242375 + 0.346148i
\(89\) −7.58469 + 13.1371i −0.803975 + 1.39253i 0.113006 + 0.993594i \(0.463952\pi\)
−0.916981 + 0.398932i \(0.869381\pi\)
\(90\) 0 0
\(91\) 5.28723 + 9.15775i 0.554252 + 0.959993i
\(92\) −3.75502 + 8.05267i −0.391488 + 0.839549i
\(93\) 0 0
\(94\) −0.517156 0.616322i −0.0533406 0.0635688i
\(95\) −10.4581 0.459486i −1.07298 0.0471422i
\(96\) 0 0
\(97\) −1.25036 0.583050i −0.126954 0.0591998i 0.358103 0.933682i \(-0.383424\pi\)
−0.485058 + 0.874482i \(0.661201\pi\)
\(98\) −5.44226 + 20.3108i −0.549751 + 2.05170i
\(99\) 0 0
\(100\) 5.05131 10.8171i 0.505131 1.08171i
\(101\) −0.515416 0.0908818i −0.0512858 0.00904308i 0.147946 0.988995i \(-0.452734\pi\)
−0.199232 + 0.979952i \(0.563845\pi\)
\(102\) 0 0
\(103\) 3.14419 1.46616i 0.309806 0.144465i −0.261496 0.965204i \(-0.584216\pi\)
0.571303 + 0.820739i \(0.306438\pi\)
\(104\) −0.361243 2.04871i −0.0354228 0.200892i
\(105\) 0 0
\(106\) 0.403480 + 0.338560i 0.0391894 + 0.0328838i
\(107\) 4.07064 4.07064i 0.393524 0.393524i −0.482418 0.875941i \(-0.660241\pi\)
0.875941 + 0.482418i \(0.160241\pi\)
\(108\) 0 0
\(109\) 10.3288i 0.989319i 0.869087 + 0.494660i \(0.164707\pi\)
−0.869087 + 0.494660i \(0.835293\pi\)
\(110\) 18.1355 + 13.9238i 1.72916 + 1.32758i
\(111\) 0 0
\(112\) −7.27881 + 10.3952i −0.687783 + 0.982256i
\(113\) 2.31072 + 4.95536i 0.217375 + 0.466161i 0.984511 0.175323i \(-0.0560969\pi\)
−0.767136 + 0.641484i \(0.778319\pi\)
\(114\) 0 0
\(115\) −1.08837 + 8.24948i −0.101491 + 0.769268i
\(116\) −6.59954 3.81025i −0.612752 0.353773i
\(117\) 0 0
\(118\) −1.71634 0.459891i −0.158001 0.0423364i
\(119\) 9.48179 3.45109i 0.869194 0.316361i
\(120\) 0 0
\(121\) −9.82758 + 8.24632i −0.893416 + 0.749665i
\(122\) −1.45764 + 16.6609i −0.131968 + 1.50841i
\(123\) 0 0
\(124\) −1.28055 3.51829i −0.114997 0.315951i
\(125\) 1.46845 11.0835i 0.131342 0.991337i
\(126\) 0 0
\(127\) 6.98435 1.87145i 0.619760 0.166064i 0.0647416 0.997902i \(-0.479378\pi\)
0.555019 + 0.831838i \(0.312711\pi\)
\(128\) 5.22160 3.65620i 0.461528 0.323166i
\(129\) 0 0
\(130\) −5.53761 10.6448i −0.485680 0.933608i
\(131\) −7.48308 + 1.31947i −0.653800 + 0.115283i −0.490702 0.871327i \(-0.663260\pi\)
−0.163098 + 0.986610i \(0.552149\pi\)
\(132\) 0 0
\(133\) −19.2507 + 1.68421i −1.66924 + 0.146040i
\(134\) −17.0298 −1.47115
\(135\) 0 0
\(136\) −1.98507 −0.170218
\(137\) −8.77434 + 0.767656i −0.749643 + 0.0655852i −0.455573 0.890199i \(-0.650565\pi\)
−0.294070 + 0.955784i \(0.595010\pi\)
\(138\) 0 0
\(139\) 0.637180 0.112352i 0.0540449 0.00952958i −0.146560 0.989202i \(-0.546820\pi\)
0.200605 + 0.979672i \(0.435709\pi\)
\(140\) 6.63277 21.0163i 0.560571 1.77620i
\(141\) 0 0
\(142\) −15.5165 + 10.8648i −1.30212 + 0.911751i
\(143\) 12.0792 3.23662i 1.01012 0.270660i
\(144\) 0 0
\(145\) −6.96703 1.54656i −0.578581 0.128435i
\(146\) −8.83637 24.2777i −0.731303 2.00924i
\(147\) 0 0
\(148\) 0.476742 5.44918i 0.0391879 0.447920i
\(149\) 14.2896 11.9904i 1.17065 0.982290i 0.170652 0.985331i \(-0.445413\pi\)
0.999995 + 0.00304137i \(0.000968099\pi\)
\(150\) 0 0
\(151\) 11.1465 4.05701i 0.907092 0.330155i 0.154001 0.988071i \(-0.450784\pi\)
0.753091 + 0.657916i \(0.228562\pi\)
\(152\) 3.67211 + 0.983939i 0.297847 + 0.0798080i
\(153\) 0 0
\(154\) 36.5524 + 21.1035i 2.94547 + 1.70057i
\(155\) −2.13377 2.78236i −0.171388 0.223484i
\(156\) 0 0
\(157\) 0.402710 + 0.863615i 0.0321398 + 0.0689240i 0.921722 0.387851i \(-0.126782\pi\)
−0.889582 + 0.456775i \(0.849005\pi\)
\(158\) 12.9854 18.5451i 1.03306 1.47537i
\(159\) 0 0
\(160\) 10.9808 14.3023i 0.868105 1.13069i
\(161\) 15.3604i 1.21057i
\(162\) 0 0
\(163\) 12.1885 12.1885i 0.954673 0.954673i −0.0443429 0.999016i \(-0.514119\pi\)
0.999016 + 0.0443429i \(0.0141194\pi\)
\(164\) 12.4842 + 10.4755i 0.974855 + 0.818001i
\(165\) 0 0
\(166\) 1.35671 + 7.69429i 0.105301 + 0.597193i
\(167\) 4.59936 2.14472i 0.355909 0.165963i −0.236437 0.971647i \(-0.575980\pi\)
0.592346 + 0.805684i \(0.298202\pi\)
\(168\) 0 0
\(169\) 6.33944 + 1.11781i 0.487649 + 0.0859858i
\(170\) −10.9207 + 3.43998i −0.837577 + 0.263834i
\(171\) 0 0
\(172\) 0.808693 3.01808i 0.0616622 0.230127i
\(173\) 1.51516 + 0.706530i 0.115195 + 0.0537164i 0.479362 0.877617i \(-0.340868\pi\)
−0.364166 + 0.931334i \(0.618646\pi\)
\(174\) 0 0
\(175\) 0.0113268 20.6388i 0.000856228 1.56015i
\(176\) 9.64661 + 11.4964i 0.727140 + 0.866572i
\(177\) 0 0
\(178\) 13.4287 28.7979i 1.00652 2.15849i
\(179\) −7.16939 12.4178i −0.535866 0.928147i −0.999121 0.0419217i \(-0.986652\pi\)
0.463255 0.886225i \(-0.346681\pi\)
\(180\) 0 0
\(181\) −10.7361 + 18.5955i −0.798011 + 1.38220i 0.122899 + 0.992419i \(0.460781\pi\)
−0.920910 + 0.389776i \(0.872552\pi\)
\(182\) −12.7048 18.1443i −0.941740 1.34494i
\(183\) 0 0
\(184\) 1.03354 2.83962i 0.0761933 0.209339i
\(185\) −1.10738 5.00155i −0.0814160 0.367722i
\(186\) 0 0
\(187\) −1.04001 11.8874i −0.0760532 0.869292i
\(188\) 0.648481 + 0.648481i 0.0472953 + 0.0472953i
\(189\) 0 0
\(190\) 21.9069 0.950452i 1.58929 0.0689530i
\(191\) 7.60498 9.06326i 0.550277 0.655794i −0.417182 0.908823i \(-0.636982\pi\)
0.967459 + 0.253029i \(0.0814267\pi\)
\(192\) 0 0
\(193\) −13.1725 9.22349i −0.948178 0.663922i −0.00633721 0.999980i \(-0.502017\pi\)
−0.941841 + 0.336058i \(0.890906\pi\)
\(194\) 2.71557 + 0.988386i 0.194967 + 0.0709620i
\(195\) 0 0
\(196\) 4.16209 23.6044i 0.297292 1.68603i
\(197\) 7.15409 + 26.6994i 0.509708 + 1.90225i 0.423287 + 0.905996i \(0.360876\pi\)
0.0864206 + 0.996259i \(0.472457\pi\)
\(198\) 0 0
\(199\) −17.2147 + 9.93892i −1.22032 + 0.704551i −0.964986 0.262302i \(-0.915518\pi\)
−0.255332 + 0.966853i \(0.582185\pi\)
\(200\) −1.39079 + 3.81465i −0.0983437 + 0.269736i
\(201\) 0 0
\(202\) 1.09211 + 0.0955476i 0.0768409 + 0.00672271i
\(203\) −13.1240 1.14820i −0.921126 0.0805881i
\(204\) 0 0
\(205\) 14.0988 + 5.84447i 0.984706 + 0.408195i
\(206\) −6.29334 + 3.63346i −0.438478 + 0.253155i
\(207\) 0 0
\(208\) −2.03842 7.60749i −0.141339 0.527484i
\(209\) −3.96835 + 22.5056i −0.274496 + 1.55675i
\(210\) 0 0
\(211\) 21.2772 + 7.74427i 1.46478 + 0.533137i 0.946678 0.322180i \(-0.104416\pi\)
0.518105 + 0.855317i \(0.326638\pi\)
\(212\) −0.491802 0.344364i −0.0337771 0.0236510i
\(213\) 0 0
\(214\) −7.75108 + 9.23738i −0.529853 + 0.631454i
\(215\) −0.126835 2.92340i −0.00865006 0.199374i
\(216\) 0 0
\(217\) −4.57688 4.57688i −0.310699 0.310699i
\(218\) −1.88566 21.5532i −0.127713 1.45976i
\(219\) 0 0
\(220\) −21.9769 14.0093i −1.48168 0.944507i
\(221\) −2.14183 + 5.88462i −0.144075 + 0.395843i
\(222\) 0 0
\(223\) 5.78878 + 8.26723i 0.387645 + 0.553615i 0.964788 0.263029i \(-0.0847213\pi\)
−0.577143 + 0.816643i \(0.695832\pi\)
\(224\) 16.6429 28.8264i 1.11200 1.92604i
\(225\) 0 0
\(226\) −5.72647 9.91853i −0.380919 0.659771i
\(227\) −10.3017 + 22.0920i −0.683745 + 1.46630i 0.190939 + 0.981602i \(0.438847\pi\)
−0.874684 + 0.484694i \(0.838931\pi\)
\(228\) 0 0
\(229\) −5.75242 6.85547i −0.380131 0.453022i 0.541725 0.840556i \(-0.317771\pi\)
−0.921855 + 0.387534i \(0.873327\pi\)
\(230\) 0.765053 17.4129i 0.0504461 1.14818i
\(231\) 0 0
\(232\) 2.34892 + 1.09532i 0.154214 + 0.0719114i
\(233\) −4.94285 + 18.4470i −0.323817 + 1.20850i 0.591679 + 0.806174i \(0.298465\pi\)
−0.915496 + 0.402328i \(0.868201\pi\)
\(234\) 0 0
\(235\) 0.761708 + 0.396786i 0.0496884 + 0.0258835i
\(236\) 1.99466 + 0.351712i 0.129841 + 0.0228945i
\(237\) 0 0
\(238\) −19.1557 + 8.93244i −1.24168 + 0.579004i
\(239\) 0.434105 + 2.46193i 0.0280799 + 0.159249i 0.995623 0.0934552i \(-0.0297912\pi\)
−0.967544 + 0.252704i \(0.918680\pi\)
\(240\) 0 0
\(241\) 16.4029 + 13.7637i 1.05660 + 0.886595i 0.993772 0.111429i \(-0.0355428\pi\)
0.0628307 + 0.998024i \(0.479987\pi\)
\(242\) 19.0018 19.0018i 1.22148 1.22148i
\(243\) 0 0
\(244\) 19.0639i 1.22044i
\(245\) −2.92376 22.2554i −0.186792 1.42184i
\(246\) 0 0
\(247\) 6.87893 9.82413i 0.437696 0.625095i
\(248\) 0.538151 + 1.15407i 0.0341726 + 0.0732834i
\(249\) 0 0
\(250\) −1.04079 + 23.3961i −0.0658255 + 1.47970i
\(251\) −13.6587 7.88585i −0.862129 0.497751i 0.00259539 0.999997i \(-0.499174\pi\)
−0.864725 + 0.502246i \(0.832507\pi\)
\(252\) 0 0
\(253\) 17.5463 + 4.70152i 1.10313 + 0.295582i
\(254\) −14.2326 + 5.18025i −0.893034 + 0.325038i
\(255\) 0 0
\(256\) 6.23009 5.22767i 0.389381 0.326729i
\(257\) 0.121306 1.38654i 0.00756687 0.0864897i −0.991472 0.130318i \(-0.958400\pi\)
0.999039 + 0.0438287i \(0.0139556\pi\)
\(258\) 0 0
\(259\) −3.23429 8.88613i −0.200969 0.552157i
\(260\) 7.34570 + 11.5374i 0.455561 + 0.715520i
\(261\) 0 0
\(262\) 15.3741 4.11948i 0.949816 0.254502i
\(263\) −20.2750 + 14.1967i −1.25021 + 0.875405i −0.995788 0.0916894i \(-0.970773\pi\)
−0.254420 + 0.967094i \(0.581884\pi\)
\(264\) 0 0
\(265\) −0.536189 0.169221i −0.0329378 0.0103952i
\(266\) 39.8630 7.02892i 2.44416 0.430971i
\(267\) 0 0
\(268\) 19.3380 1.69186i 1.18126 0.103347i
\(269\) 30.2129 1.84212 0.921058 0.389426i \(-0.127327\pi\)
0.921058 + 0.389426i \(0.127327\pi\)
\(270\) 0 0
\(271\) −30.1849 −1.83360 −0.916802 0.399341i \(-0.869239\pi\)
−0.916802 + 0.399341i \(0.869239\pi\)
\(272\) −7.48666 + 0.654998i −0.453946 + 0.0397151i
\(273\) 0 0
\(274\) 18.1693 3.20374i 1.09765 0.193545i
\(275\) −23.5723 6.33006i −1.42147 0.381717i
\(276\) 0 0
\(277\) −4.74942 + 3.32558i −0.285365 + 0.199815i −0.707491 0.706723i \(-0.750173\pi\)
0.422126 + 0.906537i \(0.361284\pi\)
\(278\) −1.30910 + 0.350772i −0.0785144 + 0.0210379i
\(279\) 0 0
\(280\) −1.62427 + 7.31712i −0.0970689 + 0.437282i
\(281\) 5.21843 + 14.3375i 0.311305 + 0.855304i 0.992394 + 0.123103i \(0.0392846\pi\)
−0.681089 + 0.732201i \(0.738493\pi\)
\(282\) 0 0
\(283\) −2.06765 + 23.6334i −0.122909 + 1.40486i 0.644943 + 0.764231i \(0.276881\pi\)
−0.767852 + 0.640627i \(0.778674\pi\)
\(284\) 16.5402 13.8789i 0.981481 0.823561i
\(285\) 0 0
\(286\) −24.6150 + 8.95911i −1.45551 + 0.529764i
\(287\) 27.2139 + 7.29195i 1.60639 + 0.430430i
\(288\) 0 0
\(289\) −9.54744 5.51222i −0.561614 0.324248i
\(290\) 14.8205 + 1.95529i 0.870290 + 0.114819i
\(291\) 0 0
\(292\) 12.4460 + 26.6905i 0.728345 + 1.56194i
\(293\) −4.78492 + 6.83357i −0.279538 + 0.399221i −0.934228 0.356676i \(-0.883910\pi\)
0.654690 + 0.755897i \(0.272799\pi\)
\(294\) 0 0
\(295\) 1.88066 0.247069i 0.109496 0.0143849i
\(296\) 1.86036i 0.108131i
\(297\) 0 0
\(298\) −27.6292 + 27.6292i −1.60051 + 1.60051i
\(299\) −7.30274 6.12773i −0.422329 0.354376i
\(300\) 0 0
\(301\) −0.937987 5.31959i −0.0540647 0.306616i
\(302\) −22.5189 + 10.5007i −1.29582 + 0.604249i
\(303\) 0 0
\(304\) 14.1740 + 2.49926i 0.812934 + 0.143342i
\(305\) −5.36396 17.0286i −0.307139 0.975055i
\(306\) 0 0
\(307\) −5.72891 + 21.3806i −0.326966 + 1.22025i 0.585355 + 0.810777i \(0.300955\pi\)
−0.912321 + 0.409476i \(0.865711\pi\)
\(308\) −43.6032 20.3325i −2.48452 1.15855i
\(309\) 0 0
\(310\) 4.96050 + 5.41642i 0.281738 + 0.307632i
\(311\) −17.1260 20.4100i −0.971128 1.15735i −0.987522 0.157480i \(-0.949663\pi\)
0.0163937 0.999866i \(-0.494781\pi\)
\(312\) 0 0
\(313\) −0.188967 + 0.405241i −0.0106810 + 0.0229056i −0.911576 0.411132i \(-0.865134\pi\)
0.900895 + 0.434037i \(0.142911\pi\)
\(314\) −0.998003 1.72859i −0.0563206 0.0975501i
\(315\) 0 0
\(316\) −12.9031 + 22.3487i −0.725853 + 1.25722i
\(317\) −0.491526 0.701972i −0.0276069 0.0394267i 0.805111 0.593124i \(-0.202105\pi\)
−0.832718 + 0.553697i \(0.813217\pi\)
\(318\) 0 0
\(319\) −5.32859 + 14.6402i −0.298344 + 0.819693i
\(320\) −12.9121 + 20.2556i −0.721807 + 1.13232i
\(321\) 0 0
\(322\) −2.80425 32.0527i −0.156275 1.78623i
\(323\) −8.09210 8.09210i −0.450256 0.450256i
\(324\) 0 0
\(325\) 9.80770 + 8.23881i 0.544033 + 0.457007i
\(326\) −23.2086 + 27.6589i −1.28540 + 1.53188i
\(327\) 0 0
\(328\) −4.54028 3.17914i −0.250695 0.175539i
\(329\) 1.48983 + 0.542255i 0.0821371 + 0.0298955i
\(330\) 0 0
\(331\) 4.97884 28.2364i 0.273662 1.55201i −0.469519 0.882922i \(-0.655573\pi\)
0.743181 0.669091i \(-0.233316\pi\)
\(332\) −2.30500 8.60238i −0.126503 0.472117i
\(333\) 0 0
\(334\) −9.20598 + 5.31507i −0.503729 + 0.290828i
\(335\) 16.7974 6.95232i 0.917741 0.379846i
\(336\) 0 0
\(337\) −7.49834 0.656020i −0.408461 0.0357357i −0.118926 0.992903i \(-0.537945\pi\)
−0.289535 + 0.957167i \(0.593501\pi\)
\(338\) −13.4326 1.17520i −0.730639 0.0639226i
\(339\) 0 0
\(340\) 12.0591 4.99116i 0.653996 0.270684i
\(341\) −6.62908 + 3.82730i −0.358985 + 0.207260i
\(342\) 0 0
\(343\) −3.24609 12.1146i −0.175272 0.654125i
\(344\) −0.184530 + 1.04652i −0.00994921 + 0.0564248i
\(345\) 0 0
\(346\) −3.29068 1.19771i −0.176908 0.0643892i
\(347\) 21.2589 + 14.8856i 1.14124 + 0.799103i 0.982138 0.188160i \(-0.0602524\pi\)
0.159099 + 0.987263i \(0.449141\pi\)
\(348\) 0 0
\(349\) 11.2260 13.3786i 0.600915 0.716143i −0.376749 0.926315i \(-0.622958\pi\)
0.977664 + 0.210173i \(0.0674026\pi\)
\(350\) 3.74425 + 43.0692i 0.200139 + 2.30215i
\(351\) 0 0
\(352\) −27.8345 27.8345i −1.48358 1.48358i
\(353\) 0.785720 + 8.98082i 0.0418196 + 0.478001i 0.988010 + 0.154390i \(0.0493413\pi\)
−0.946190 + 0.323611i \(0.895103\pi\)
\(354\) 0 0
\(355\) 10.8693 17.0510i 0.576881 0.904974i
\(356\) −12.3878 + 34.0352i −0.656553 + 1.80386i
\(357\) 0 0
\(358\) 17.2275 + 24.6033i 0.910499 + 1.30033i
\(359\) −7.90716 + 13.6956i −0.417324 + 0.722827i −0.995669 0.0929655i \(-0.970365\pi\)
0.578345 + 0.815792i \(0.303699\pi\)
\(360\) 0 0
\(361\) 1.45829 + 2.52584i 0.0767523 + 0.132939i
\(362\) 19.0083 40.7635i 0.999055 2.14248i
\(363\) 0 0
\(364\) 16.2293 + 19.3414i 0.850648 + 1.01376i
\(365\) 18.6270 + 20.3390i 0.974982 + 1.06459i
\(366\) 0 0
\(367\) 19.6260 + 9.15174i 1.02447 + 0.477717i 0.860878 0.508812i \(-0.169915\pi\)
0.163589 + 0.986529i \(0.447693\pi\)
\(368\) 2.96101 11.0506i 0.154353 0.576054i
\(369\) 0 0
\(370\) 3.22387 + 10.2346i 0.167601 + 0.532072i
\(371\) −1.02216 0.180234i −0.0530677 0.00935726i
\(372\) 0 0
\(373\) −22.0287 + 10.2722i −1.14060 + 0.531873i −0.898760 0.438442i \(-0.855530\pi\)
−0.241845 + 0.970315i \(0.577753\pi\)
\(374\) 4.34040 + 24.6156i 0.224437 + 1.27284i
\(375\) 0 0
\(376\) −0.238933 0.200489i −0.0123220 0.0103394i
\(377\) 5.78144 5.78144i 0.297759 0.297759i
\(378\) 0 0
\(379\) 18.5170i 0.951157i 0.879673 + 0.475578i \(0.157761\pi\)
−0.879673 + 0.475578i \(0.842239\pi\)
\(380\) −24.7817 + 3.25565i −1.27127 + 0.167012i
\(381\) 0 0
\(382\) −14.2147 + 20.3008i −0.727289 + 1.03868i
\(383\) 0.998023 + 2.14027i 0.0509966 + 0.109363i 0.930155 0.367167i \(-0.119672\pi\)
−0.879158 + 0.476530i \(0.841895\pi\)
\(384\) 0 0
\(385\) −44.6689 5.89325i −2.27654 0.300348i
\(386\) 29.1711 + 16.8419i 1.48477 + 0.857231i
\(387\) 0 0
\(388\) −3.18183 0.852569i −0.161533 0.0432826i
\(389\) −9.90399 + 3.60476i −0.502152 + 0.182768i −0.580662 0.814145i \(-0.697206\pi\)
0.0785096 + 0.996913i \(0.474984\pi\)
\(390\) 0 0
\(391\) −6.96839 + 5.84717i −0.352407 + 0.295704i
\(392\) −0.710472 + 8.12074i −0.0358843 + 0.410159i
\(393\) 0 0
\(394\) −19.8028 54.4078i −0.997651 2.74102i
\(395\) −5.23728 + 23.5932i −0.263516 + 1.18710i
\(396\) 0 0
\(397\) −7.52877 + 2.01733i −0.377858 + 0.101247i −0.442749 0.896646i \(-0.645997\pi\)
0.0648910 + 0.997892i \(0.479330\pi\)
\(398\) 34.1076 23.8824i 1.70966 1.19712i
\(399\) 0 0
\(400\) −3.98666 + 14.8458i −0.199333 + 0.742291i
\(401\) 28.6980 5.06024i 1.43311 0.252696i 0.597434 0.801918i \(-0.296187\pi\)
0.835677 + 0.549222i \(0.185076\pi\)
\(402\) 0 0
\(403\) 4.00182 0.350114i 0.199345 0.0174404i
\(404\) −1.24963 −0.0621715
\(405\) 0 0
\(406\) 27.5956 1.36955
\(407\) −11.1406 + 0.974677i −0.552220 + 0.0483130i
\(408\) 0 0
\(409\) −10.1037 + 1.78155i −0.499594 + 0.0880918i −0.417766 0.908555i \(-0.637187\pi\)
−0.0818277 + 0.996646i \(0.526076\pi\)
\(410\) −30.4872 9.62176i −1.50565 0.475185i
\(411\) 0 0
\(412\) 6.78536 4.75116i 0.334291 0.234073i
\(413\) 3.38220 0.906258i 0.166427 0.0445941i
\(414\) 0 0
\(415\) −4.47934 7.03542i −0.219882 0.345355i
\(416\) 7.06545 + 19.4122i 0.346412 + 0.951760i
\(417\) 0 0
\(418\) 4.17208 47.6871i 0.204063 2.33245i
\(419\) 14.0240 11.7675i 0.685117 0.574881i −0.232380 0.972625i \(-0.574651\pi\)
0.917496 + 0.397744i \(0.130207\pi\)
\(420\) 0 0
\(421\) −28.8617 + 10.5048i −1.40664 + 0.511973i −0.930140 0.367204i \(-0.880315\pi\)
−0.476495 + 0.879177i \(0.658093\pi\)
\(422\) −45.8131 12.2756i −2.23015 0.597566i
\(423\) 0 0
\(424\) 0.176834 + 0.102095i 0.00858784 + 0.00495819i
\(425\) 9.36728 7.85132i 0.454380 0.380845i
\(426\) 0 0
\(427\) −13.9284 29.8695i −0.674040 1.44548i
\(428\) 7.88396 11.2595i 0.381085 0.544246i
\(429\) 0 0
\(430\) 0.798373 + 6.07713i 0.0385010 + 0.293065i
\(431\) 13.0253i 0.627407i −0.949521 0.313703i \(-0.898430\pi\)
0.949521 0.313703i \(-0.101570\pi\)
\(432\) 0 0
\(433\) 24.3815 24.3815i 1.17170 1.17170i 0.189896 0.981804i \(-0.439185\pi\)
0.981804 0.189896i \(-0.0608150\pi\)
\(434\) 10.3862 + 8.71504i 0.498553 + 0.418335i
\(435\) 0 0
\(436\) 4.28248 + 24.2871i 0.205093 + 1.16314i
\(437\) 15.7889 7.36247i 0.755284 0.352195i
\(438\) 0 0
\(439\) 21.0657 + 3.71446i 1.00541 + 0.177281i 0.652027 0.758196i \(-0.273919\pi\)
0.353386 + 0.935477i \(0.385030\pi\)
\(440\) 7.86122 + 4.09504i 0.374769 + 0.195223i
\(441\) 0 0
\(442\) 3.39505 12.6705i 0.161486 0.602674i
\(443\) 24.5747 + 11.4594i 1.16758 + 0.544452i 0.907054 0.421014i \(-0.138326\pi\)
0.260527 + 0.965466i \(0.416104\pi\)
\(444\) 0 0
\(445\) −1.48886 + 33.8871i −0.0705786 + 1.60640i
\(446\) −13.5888 16.1945i −0.643447 0.766830i
\(447\) 0 0
\(448\) −18.7400 + 40.1882i −0.885384 + 1.89871i
\(449\) −1.17379 2.03306i −0.0553944 0.0959459i 0.836998 0.547205i \(-0.184308\pi\)
−0.892393 + 0.451259i \(0.850975\pi\)
\(450\) 0 0
\(451\) 16.6593 28.8547i 0.784454 1.35871i
\(452\) 7.48801 + 10.6940i 0.352206 + 0.503003i
\(453\) 0 0
\(454\) 17.4634 47.9802i 0.819596 2.25182i
\(455\) 19.9387 + 12.7100i 0.934740 + 0.595855i
\(456\) 0 0
\(457\) 0.0458303 + 0.523843i 0.00214385 + 0.0245043i 0.997191 0.0748970i \(-0.0238628\pi\)
−0.995047 + 0.0994013i \(0.968307\pi\)
\(458\) 13.2552 + 13.2552i 0.619374 + 0.619374i
\(459\) 0 0
\(460\) 0.861173 + 19.8491i 0.0401524 + 0.925469i
\(461\) 5.97585 7.12174i 0.278323 0.331693i −0.608715 0.793389i \(-0.708315\pi\)
0.887038 + 0.461696i \(0.152759\pi\)
\(462\) 0 0
\(463\) −18.1131 12.6829i −0.841787 0.589426i 0.0711780 0.997464i \(-0.477324\pi\)
−0.912965 + 0.408038i \(0.866213\pi\)
\(464\) 9.22036 + 3.35594i 0.428045 + 0.155795i
\(465\) 0 0
\(466\) 6.94655 39.3958i 0.321793 1.82498i
\(467\) −6.61375 24.6828i −0.306048 1.14219i −0.932040 0.362356i \(-0.881972\pi\)
0.625992 0.779830i \(-0.284694\pi\)
\(468\) 0 0
\(469\) 29.0629 16.7794i 1.34200 0.774803i
\(470\) −1.66190 0.688916i −0.0766577 0.0317773i
\(471\) 0 0
\(472\) −0.686232 0.0600375i −0.0315864 0.00276345i
\(473\) −6.36369 0.556751i −0.292603 0.0255994i
\(474\) 0 0
\(475\) −21.2199 + 9.88083i −0.973636 + 0.453363i
\(476\) 20.8646 12.0462i 0.956328 0.552136i
\(477\) 0 0
\(478\) −1.35531 5.05807i −0.0619903 0.231351i
\(479\) −2.14579 + 12.1694i −0.0980435 + 0.556032i 0.895729 + 0.444601i \(0.146655\pi\)
−0.993772 + 0.111431i \(0.964457\pi\)
\(480\) 0 0
\(481\) 5.51494 + 2.00728i 0.251460 + 0.0915239i
\(482\) −36.7408 25.7262i −1.67350 1.17179i
\(483\) 0 0
\(484\) −19.6895 + 23.4651i −0.894979 + 1.06659i
\(485\) −3.08201 + 0.133716i −0.139947 + 0.00607174i
\(486\) 0 0
\(487\) 16.4134 + 16.4134i 0.743762 + 0.743762i 0.973300 0.229538i \(-0.0737215\pi\)
−0.229538 + 0.973300i \(0.573722\pi\)
\(488\) 0.565091 + 6.45902i 0.0255805 + 0.292386i
\(489\) 0 0
\(490\) 10.1641 + 45.9067i 0.459165 + 2.07385i
\(491\) −3.53191 + 9.70384i −0.159393 + 0.437928i −0.993522 0.113641i \(-0.963749\pi\)
0.834129 + 0.551569i \(0.185971\pi\)
\(492\) 0 0
\(493\) −4.47496 6.39090i −0.201542 0.287832i
\(494\) −12.5608 + 21.7559i −0.565137 + 0.978846i
\(495\) 0 0
\(496\) 2.41043 + 4.17499i 0.108231 + 0.187462i
\(497\) 15.7752 33.8300i 0.707615 1.51748i
\(498\) 0 0
\(499\) −21.3906 25.4924i −0.957576 1.14119i −0.989907 0.141717i \(-0.954738\pi\)
0.0323314 0.999477i \(-0.489707\pi\)
\(500\) −1.14247 26.6706i −0.0510926 1.19274i
\(501\) 0 0
\(502\) 29.9414 + 13.9619i 1.33635 + 0.623150i
\(503\) 7.47831 27.9094i 0.333441 1.24442i −0.572108 0.820178i \(-0.693874\pi\)
0.905549 0.424241i \(-0.139459\pi\)
\(504\) 0 0
\(505\) −1.11622 + 0.351605i −0.0496710 + 0.0156462i
\(506\) −37.4723 6.60738i −1.66585 0.293734i
\(507\) 0 0
\(508\) 15.6471 7.29635i 0.694226 0.323723i
\(509\) −2.41068 13.6717i −0.106852 0.605986i −0.990465 0.137768i \(-0.956007\pi\)
0.883613 0.468218i \(-0.155104\pi\)
\(510\) 0 0
\(511\) 39.0008 + 32.7256i 1.72529 + 1.44769i
\(512\) −21.0607 + 21.0607i −0.930762 + 0.930762i
\(513\) 0 0
\(514\) 2.91544i 0.128594i
\(515\) 4.72412 6.15309i 0.208169 0.271138i
\(516\) 0 0
\(517\) 1.07543 1.53587i 0.0472972 0.0675474i
\(518\) 8.37129 + 17.9523i 0.367813 + 0.788778i
\(519\) 0 0
\(520\) −2.83078 3.69124i −0.124138 0.161871i
\(521\) −4.10889 2.37227i −0.180014 0.103931i 0.407285 0.913301i \(-0.366475\pi\)
−0.587299 + 0.809370i \(0.699809\pi\)
\(522\) 0 0
\(523\) −39.4721 10.5765i −1.72599 0.462478i −0.746739 0.665117i \(-0.768382\pi\)
−0.979254 + 0.202638i \(0.935048\pi\)
\(524\) −17.0487 + 6.20521i −0.744774 + 0.271076i
\(525\) 0 0
\(526\) 39.7161 33.3258i 1.73170 1.45307i
\(527\) 0.334084 3.81860i 0.0145529 0.166341i
\(528\) 0 0
\(529\) 3.13027 + 8.60035i 0.136099 + 0.373928i
\(530\) 1.14976 + 0.255227i 0.0499425 + 0.0110864i
\(531\) 0 0
\(532\) −44.5677 + 11.9419i −1.93226 + 0.517746i
\(533\) −14.3232 + 10.0292i −0.620407 + 0.434414i
\(534\) 0 0
\(535\) 3.87420 12.2757i 0.167496 0.530723i
\(536\) −6.50174 + 1.14643i −0.280833 + 0.0495184i
\(537\) 0 0
\(538\) −63.0456 + 5.51577i −2.71809 + 0.237802i
\(539\) −49.0025 −2.11069
\(540\) 0 0
\(541\) −14.7870 −0.635743 −0.317871 0.948134i \(-0.602968\pi\)
−0.317871 + 0.948134i \(0.602968\pi\)
\(542\) 62.9871 5.51066i 2.70553 0.236703i
\(543\) 0 0
\(544\) 19.4127 3.42298i 0.832313 0.146759i
\(545\) 10.6589 + 20.4892i 0.456576 + 0.877662i
\(546\) 0 0
\(547\) 19.2746 13.4962i 0.824123 0.577057i −0.0836614 0.996494i \(-0.526661\pi\)
0.907784 + 0.419437i \(0.137773\pi\)
\(548\) −20.3137 + 5.44304i −0.867759 + 0.232515i
\(549\) 0 0
\(550\) 50.3442 + 8.90553i 2.14668 + 0.379733i
\(551\) 5.11030 + 14.0404i 0.217706 + 0.598142i
\(552\) 0 0
\(553\) −3.88828 + 44.4433i −0.165347 + 1.88992i
\(554\) 9.30352 7.80658i 0.395269 0.331670i
\(555\) 0 0
\(556\) 1.45168 0.528370i 0.0615651 0.0224079i
\(557\) 23.7629 + 6.36725i 1.00687 + 0.269789i 0.724320 0.689464i \(-0.242154\pi\)
0.282547 + 0.959253i \(0.408821\pi\)
\(558\) 0 0
\(559\) 2.90326 + 1.67620i 0.122795 + 0.0708956i
\(560\) −3.71156 + 28.1324i −0.156842 + 1.18881i
\(561\) 0 0
\(562\) −13.5068 28.9655i −0.569751 1.22184i
\(563\) 7.57539 10.8188i 0.319265 0.455957i −0.627156 0.778894i \(-0.715781\pi\)
0.946421 + 0.322936i \(0.104670\pi\)
\(564\) 0 0
\(565\) 9.69750 + 7.44538i 0.407977 + 0.313230i
\(566\) 49.6934i 2.08877i
\(567\) 0 0
\(568\) −5.19257 + 5.19257i −0.217875 + 0.217875i
\(569\) −9.80603 8.22824i −0.411090 0.344946i 0.413671 0.910426i \(-0.364246\pi\)
−0.824762 + 0.565481i \(0.808691\pi\)
\(570\) 0 0
\(571\) 1.27813 + 7.24862i 0.0534879 + 0.303345i 0.999802 0.0199038i \(-0.00633599\pi\)
−0.946314 + 0.323249i \(0.895225\pi\)
\(572\) 27.0612 12.6188i 1.13149 0.527620i
\(573\) 0 0
\(574\) −58.1187 10.2479i −2.42583 0.427739i
\(575\) 6.35412 + 17.4876i 0.264985 + 0.729285i
\(576\) 0 0
\(577\) 6.02067 22.4695i 0.250644 0.935416i −0.719818 0.694163i \(-0.755775\pi\)
0.970462 0.241253i \(-0.0775585\pi\)
\(578\) 20.9290 + 9.75937i 0.870533 + 0.405936i
\(579\) 0 0
\(580\) −17.0235 0.747943i −0.706863 0.0310567i
\(581\) −9.89651 11.7942i −0.410576 0.489306i
\(582\) 0 0
\(583\) −0.518743 + 1.11245i −0.0214841 + 0.0460729i
\(584\) −5.00795 8.67403i −0.207231 0.358934i
\(585\) 0 0
\(586\) 8.73716 15.1332i 0.360929 0.625147i
\(587\) 6.11631 + 8.73500i 0.252447 + 0.360532i 0.925294 0.379249i \(-0.123818\pi\)
−0.672847 + 0.739781i \(0.734929\pi\)
\(588\) 0 0
\(589\) −2.51078 + 6.89830i −0.103455 + 0.284240i
\(590\) −3.87928 + 0.858899i −0.159707 + 0.0353603i
\(591\) 0 0
\(592\) 0.613850 + 7.01634i 0.0252291 + 0.288370i
\(593\) −30.2299 30.2299i −1.24139 1.24139i −0.959424 0.281969i \(-0.909013\pi\)
−0.281969 0.959424i \(-0.590987\pi\)
\(594\) 0 0
\(595\) 15.2476 16.6307i 0.625093 0.681793i
\(596\) 28.6291 34.1189i 1.17269 1.39756i
\(597\) 0 0
\(598\) 16.3574 + 11.4536i 0.668903 + 0.468371i
\(599\) −18.4157 6.70275i −0.752444 0.273867i −0.0628100 0.998026i \(-0.520006\pi\)
−0.689634 + 0.724158i \(0.742228\pi\)
\(600\) 0 0
\(601\) −5.44723 + 30.8927i −0.222197 + 1.26014i 0.645775 + 0.763528i \(0.276534\pi\)
−0.867972 + 0.496614i \(0.834577\pi\)
\(602\) 2.92847 + 10.9292i 0.119355 + 0.445440i
\(603\) 0 0
\(604\) 24.5279 14.1612i 0.998025 0.576210i
\(605\) −10.9851 + 26.4999i −0.446609 + 1.07737i
\(606\) 0 0
\(607\) −14.5354 1.27168i −0.589972 0.0516159i −0.211739 0.977326i \(-0.567913\pi\)
−0.378233 + 0.925710i \(0.623468\pi\)
\(608\) −37.6076 3.29024i −1.52519 0.133437i
\(609\) 0 0
\(610\) 14.3018 + 34.5544i 0.579063 + 1.39907i
\(611\) −0.852139 + 0.491983i −0.0344739 + 0.0199035i
\(612\) 0 0
\(613\) 3.72795 + 13.9129i 0.150571 + 0.561937i 0.999444 + 0.0333409i \(0.0106147\pi\)
−0.848873 + 0.528596i \(0.822719\pi\)
\(614\) 8.05124 45.6609i 0.324922 1.84272i
\(615\) 0 0
\(616\) 15.3758 + 5.59635i 0.619510 + 0.225483i
\(617\) 2.15631 + 1.50986i 0.0868096 + 0.0607847i 0.616175 0.787609i \(-0.288681\pi\)
−0.529366 + 0.848394i \(0.677570\pi\)
\(618\) 0 0
\(619\) −14.0882 + 16.7897i −0.566254 + 0.674836i −0.970858 0.239657i \(-0.922965\pi\)
0.404603 + 0.914492i \(0.367410\pi\)
\(620\) −6.17095 5.65775i −0.247831 0.227221i
\(621\) 0 0
\(622\) 39.4631 + 39.4631i 1.58233 + 1.58233i
\(623\) 5.45731 + 62.3773i 0.218642 + 2.49909i
\(624\) 0 0
\(625\) −8.52471 23.5017i −0.340989 0.940067i
\(626\) 0.320337 0.880118i 0.0128032 0.0351766i
\(627\) 0 0
\(628\) 1.30500 + 1.86374i 0.0520753 + 0.0743712i
\(629\) 2.80009 4.84989i 0.111647 0.193378i
\(630\) 0 0
\(631\) −12.3536 21.3971i −0.491790 0.851805i 0.508165 0.861260i \(-0.330324\pi\)
−0.999955 + 0.00945434i \(0.996991\pi\)
\(632\) 3.70921 7.95442i 0.147544 0.316410i
\(633\) 0 0
\(634\) 1.15383 + 1.37508i 0.0458243 + 0.0546112i
\(635\) 11.9236 10.9199i 0.473173 0.433345i
\(636\) 0 0
\(637\) 23.3069 + 10.8682i 0.923453 + 0.430613i
\(638\) 8.44645 31.5226i 0.334398 1.24799i
\(639\) 0 0
\(640\) 6.58504 12.6413i 0.260297 0.499690i
\(641\) 1.07217 + 0.189053i 0.0423482 + 0.00746712i 0.194782 0.980847i \(-0.437600\pi\)
−0.152434 + 0.988314i \(0.548711\pi\)
\(642\) 0 0
\(643\) 38.6292 18.0131i 1.52339 0.710367i 0.532673 0.846321i \(-0.321188\pi\)
0.990715 + 0.135954i \(0.0434099\pi\)
\(644\) 6.36868 + 36.1186i 0.250961 + 1.42327i
\(645\) 0 0
\(646\) 18.3632 + 15.4085i 0.722489 + 0.606240i
\(647\) −8.11871 + 8.11871i −0.319179 + 0.319179i −0.848452 0.529273i \(-0.822465\pi\)
0.529273 + 0.848452i \(0.322465\pi\)
\(648\) 0 0
\(649\) 4.14089i 0.162544i
\(650\) −21.9699 15.4015i −0.861730 0.604095i
\(651\) 0 0
\(652\) 23.6064 33.7135i 0.924499 1.32032i
\(653\) −20.7963 44.5979i −0.813823 1.74525i −0.651698 0.758479i \(-0.725943\pi\)
−0.162125 0.986770i \(-0.551835\pi\)
\(654\) 0 0
\(655\) −13.4826 + 10.3397i −0.526807 + 0.404004i
\(656\) −18.1726 10.4920i −0.709522 0.409643i
\(657\) 0 0
\(658\) −3.20784 0.859538i −0.125055 0.0335083i
\(659\) 15.4676 5.62976i 0.602534 0.219304i −0.0226995 0.999742i \(-0.507226\pi\)
0.625233 + 0.780438i \(0.285004\pi\)
\(660\) 0 0
\(661\) 5.35212 4.49096i 0.208173 0.174678i −0.532740 0.846279i \(-0.678838\pi\)
0.740913 + 0.671601i \(0.234393\pi\)
\(662\) −5.23445 + 59.8301i −0.203443 + 2.32536i
\(663\) 0 0
\(664\) 1.03595 + 2.84624i 0.0402025 + 0.110455i
\(665\) −36.4495 + 23.2068i −1.41345 + 0.899922i
\(666\) 0 0
\(667\) 11.4720 3.07392i 0.444199 0.119023i
\(668\) 9.92571 6.95006i 0.384037 0.268906i
\(669\) 0 0
\(670\) −33.7821 + 17.5740i −1.30511 + 0.678945i
\(671\) −38.3832 + 6.76799i −1.48177 + 0.261276i
\(672\) 0 0
\(673\) −6.71205 + 0.587229i −0.258731 + 0.0226360i −0.215783 0.976441i \(-0.569230\pi\)
−0.0429476 + 0.999077i \(0.513675\pi\)
\(674\) 15.7666 0.607307
\(675\) 0 0
\(676\) 15.3700 0.591155
\(677\) −5.61594 + 0.491331i −0.215838 + 0.0188834i −0.194562 0.980890i \(-0.562328\pi\)
−0.0212762 + 0.999774i \(0.506773\pi\)
\(678\) 0 0
\(679\) −5.60821 + 0.988878i −0.215223 + 0.0379497i
\(680\) −3.93778 + 2.04850i −0.151007 + 0.0785565i
\(681\) 0 0
\(682\) 13.1342 9.19669i 0.502936 0.352159i
\(683\) 17.2898 4.63280i 0.661577 0.177269i 0.0876196 0.996154i \(-0.472074\pi\)
0.573958 + 0.818885i \(0.305407\pi\)
\(684\) 0 0
\(685\) −16.6135 + 10.5775i −0.634768 + 0.404147i
\(686\) 8.98530 + 24.6869i 0.343060 + 0.942551i
\(687\) 0 0
\(688\) −0.350641 + 4.00784i −0.0133681 + 0.152798i
\(689\) 0.493456 0.414058i 0.0187992 0.0157744i
\(690\) 0 0
\(691\) −27.1342 + 9.87603i −1.03223 + 0.375702i −0.801930 0.597417i \(-0.796194\pi\)
−0.230302 + 0.973119i \(0.573971\pi\)
\(692\) 3.85568 + 1.03313i 0.146571 + 0.0392736i
\(693\) 0 0
\(694\) −47.0786 27.1809i −1.78708 1.03177i
\(695\) 1.14803 0.880416i 0.0435473 0.0333961i
\(696\) 0 0
\(697\) 7.05132 + 15.1216i 0.267088 + 0.572772i
\(698\) −20.9830 + 29.9668i −0.794217 + 1.13426i
\(699\) 0 0
\(700\) −8.53054 48.5348i −0.322424 1.83444i
\(701\) 20.6819i 0.781145i 0.920572 + 0.390573i \(0.127723\pi\)
−0.920572 + 0.390573i \(0.872277\pi\)
\(702\) 0 0
\(703\) −7.58374 + 7.58374i −0.286026 + 0.286026i
\(704\) 40.1712 + 33.7076i 1.51401 + 1.27040i
\(705\) 0 0
\(706\) −3.27913 18.5969i −0.123412 0.699903i
\(707\) −1.95793 + 0.912998i −0.0736355 + 0.0343368i
\(708\) 0 0
\(709\) −18.9529 3.34191i −0.711791 0.125508i −0.193983 0.981005i \(-0.562141\pi\)
−0.517808 + 0.855497i \(0.673252\pi\)
\(710\) −19.5681 + 37.5648i −0.734378 + 1.40978i
\(711\) 0 0
\(712\) 3.18823 11.8986i 0.119484 0.445920i
\(713\) 5.28853 + 2.46608i 0.198057 + 0.0923554i
\(714\) 0 0
\(715\) 20.6215 18.8858i 0.771202 0.706287i
\(716\) −22.0067 26.2266i −0.822430 0.980133i
\(717\) 0 0
\(718\) 13.9996 30.0223i 0.522461 1.12042i
\(719\) 4.55209 + 7.88446i 0.169764 + 0.294041i 0.938337 0.345722i \(-0.112366\pi\)
−0.768573 + 0.639763i \(0.779033\pi\)
\(720\) 0 0
\(721\) 7.16008 12.4016i 0.266655 0.461861i
\(722\) −3.50416 5.00446i −0.130411 0.186247i
\(723\) 0 0
\(724\) −17.5350 + 48.1769i −0.651682 + 1.79048i
\(725\) −15.4165 + 4.12177i −0.572554 + 0.153079i
\(726\) 0 0
\(727\) −1.02733 11.7425i −0.0381017 0.435505i −0.991156 0.132704i \(-0.957634\pi\)
0.953054 0.302801i \(-0.0979216\pi\)
\(728\) −6.07195 6.07195i −0.225042 0.225042i
\(729\) 0 0
\(730\) −42.5823 39.0410i −1.57604 1.44497i
\(731\) 2.05622 2.45051i 0.0760520 0.0906352i
\(732\) 0 0
\(733\) 37.0503 + 25.9429i 1.36848 + 0.958222i 0.999587 + 0.0287512i \(0.00915305\pi\)
0.368896 + 0.929471i \(0.379736\pi\)
\(734\) −42.6244 15.5140i −1.57330 0.572633i
\(735\) 0 0
\(736\) −5.21080 + 29.5519i −0.192072 + 1.08930i
\(737\) −10.2717 38.3345i −0.378363 1.41207i
\(738\) 0 0
\(739\) 36.6974 21.1872i 1.34994 0.779385i 0.361695 0.932296i \(-0.382198\pi\)
0.988240 + 0.152911i \(0.0488648\pi\)
\(740\) −4.67761 11.3015i −0.171952 0.415452i
\(741\) 0 0
\(742\) 2.16584 + 0.189487i 0.0795106 + 0.00695628i
\(743\) −11.6932 1.02302i −0.428982 0.0375311i −0.129379 0.991595i \(-0.541299\pi\)
−0.299603 + 0.954064i \(0.596854\pi\)
\(744\) 0 0
\(745\) 15.9727 38.5315i 0.585193 1.41169i
\(746\) 44.0922 25.4566i 1.61433 0.932034i
\(747\) 0 0
\(748\) −7.37418 27.5208i −0.269627 1.00626i
\(749\) 4.12632 23.4015i 0.150772 0.855073i
\(750\) 0 0
\(751\) 31.3803 + 11.4215i 1.14509 + 0.416777i 0.843747 0.536741i \(-0.180345\pi\)
0.301338 + 0.953517i \(0.402567\pi\)
\(752\) −0.967287 0.677302i −0.0352733 0.0246987i
\(753\) 0 0
\(754\) −11.0087 + 13.1197i −0.400913 + 0.477790i
\(755\) 17.9247 19.5506i 0.652348 0.711520i
\(756\) 0 0
\(757\) 16.3480 + 16.3480i 0.594177 + 0.594177i 0.938757 0.344580i \(-0.111979\pi\)
−0.344580 + 0.938757i \(0.611979\pi\)
\(758\) −3.38053 38.6396i −0.122786 1.40345i
\(759\) 0 0
\(760\) 8.29975 1.83762i 0.301063 0.0666575i
\(761\) −5.25702 + 14.4435i −0.190567 + 0.523578i −0.997774 0.0666905i \(-0.978756\pi\)
0.807207 + 0.590269i \(0.200978\pi\)
\(762\) 0 0
\(763\) 24.4543 + 34.9244i 0.885306 + 1.26435i
\(764\) 14.1246 24.4645i 0.511010 0.885095i
\(765\) 0 0
\(766\) −2.47331 4.28391i −0.0893645 0.154784i
\(767\) −0.918402 + 1.96952i −0.0331616 + 0.0711152i
\(768\) 0 0
\(769\) 18.6937 + 22.2783i 0.674112 + 0.803376i 0.989337 0.145641i \(-0.0465246\pi\)
−0.315225 + 0.949017i \(0.602080\pi\)
\(770\) 94.2868 + 4.14257i 3.39786 + 0.149288i
\(771\) 0 0
\(772\) −34.7981 16.2266i −1.25241 0.584008i
\(773\) −2.50707 + 9.35650i −0.0901729 + 0.336530i −0.996243 0.0865969i \(-0.972401\pi\)
0.906071 + 0.423127i \(0.139067\pi\)
\(774\) 0 0
\(775\) −7.10403 3.31741i −0.255184 0.119165i
\(776\) 1.10330 + 0.194542i 0.0396063 + 0.00698365i
\(777\) 0 0
\(778\) 20.0086 9.33018i 0.717344 0.334503i
\(779\) −5.54868 31.4681i −0.198802 1.12746i
\(780\) 0 0
\(781\) −33.8157 28.3748i −1.21002 1.01533i
\(782\) 13.4735 13.4735i 0.481812 0.481812i
\(783\) 0 0
\(784\) 30.8617i 1.10220i
\(785\) 1.69007 + 1.29757i 0.0603212 + 0.0463124i
\(786\) 0 0
\(787\) −10.8021 + 15.4269i