Properties

Label 405.2.r.a.368.2
Level $405$
Weight $2$
Character 405.368
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 368.2
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.2

$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.08671 0.182563i −1.47552 0.129092i −0.679196 0.733956i \(-0.737672\pi\)
−0.796328 + 0.604865i \(0.793227\pi\)
\(3\) 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 0.997879 0.0651011i \(-0.0207370\pi\)
0.280120 + 0.959965i \(0.409626\pi\)
\(8\) −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 0.384546 + 0.923106i \(0.374358\pi\)
−0.887940 + 0.459958i \(0.847864\pi\)
\(12\) 0 0
\(13\) −0.223275 2.55204i −0.0619252 0.707809i −0.962175 0.272434i \(-0.912171\pi\)
0.900249 0.435375i \(-0.143384\pi\)
\(14\) −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 0.0391524 0.999233i \(-0.487534\pi\)
0.533524 + 0.845785i \(0.320868\pi\)
\(18\) 0 0
\(19\) −4.05431 + 2.34076i −0.930123 + 0.537007i −0.886850 0.462057i \(-0.847112\pi\)
−0.0432724 + 0.999063i \(0.513778\pi\)
\(20\) 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 0.532462 0.846454i \(-0.321267\pi\)
−0.977519 + 0.210846i \(0.932378\pi\)
\(24\) 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 −0.840920 0.541159i \(-0.817986\pi\)
0.386913 + 0.922116i \(0.373541\pi\)
\(30\) 0 0
\(31\) −0.272295 + 1.54426i −0.0489057 + 0.277358i −0.999447 0.0332389i \(-0.989418\pi\)
0.950542 + 0.310597i \(0.100529\pi\)
\(32\) 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 0.997384 0.0722918i \(-0.0230313\pi\)
−0.899905 + 0.436085i \(0.856365\pi\)
\(38\) 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 −0.305579 0.952167i \(-0.598850\pi\)
0.990764 + 0.135594i \(0.0432944\pi\)
\(42\) 0 0
\(43\) 0.553045 + 1.18601i 0.0843385 + 0.180865i 0.943954 0.330077i \(-0.107075\pi\)
−0.859616 + 0.510941i \(0.829297\pi\)
\(44\) −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 −0.802763 0.596298i \(-0.796638\pi\)
0.834898 + 0.550405i \(0.185527\pi\)
\(48\) 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 −0.719213 0.694790i \(-0.755497\pi\)
0.694790 + 0.719213i \(0.255497\pi\)
\(54\) 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 −0.289610 0.957145i \(-0.593526\pi\)
0.393387 + 0.919373i \(0.371303\pi\)
\(60\) 0 0
\(61\) 1.38646 + 7.86300i 0.177518 + 1.00675i 0.935197 + 0.354127i \(0.115222\pi\)
−0.757679 + 0.652627i \(0.773667\pi\)
\(62\) 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 0.419083 0.907948i \(-0.362351\pi\)
0.570380 + 0.821381i \(0.306796\pi\)
\(68\) 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 0.886629 0.462481i \(-0.153041\pi\)
0.0427939 + 0.999084i \(0.486374\pi\)
\(72\) 0 0
\(73\) 3.19228 11.9138i 0.373628 1.39440i −0.481710 0.876330i \(-0.659984\pi\)
0.855339 0.518069i \(-0.173349\pi\)
\(74\) −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 0.217376 0.976088i \(-0.430250\pi\)
−0.999006 + 0.0445777i \(0.985806\pi\)
\(80\) −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 0.957257 + 0.289237i \(0.0934016\pi\)
−0.992940 + 0.118617i \(0.962154\pi\)
\(84\) 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 −0.916981 0.398932i \(-0.869381\pi\)
0.113006 0.993594i \(-0.463952\pi\)
\(90\) 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 −0.485058 0.874482i \(-0.661201\pi\)
0.358103 + 0.933682i \(0.383424\pi\)
\(98\) −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 −0.199232 0.979952i \(-0.563845\pi\)
0.147946 + 0.988995i \(0.452734\pi\)
\(102\) 0 0
\(103\) 3.14419 + 1.46616i 0.309806 + 0.144465i 0.571303 0.820739i \(-0.306438\pi\)
−0.261496 + 0.965204i \(0.584216\pi\)
\(104\) −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 0.875941 0.482418i \(-0.160241\pi\)
−0.482418 + 0.875941i \(0.660241\pi\)
\(108\) 0 0
\(109\) 10.3288i 0.989319i −0.869087 0.494660i \(-0.835293\pi\)
0.869087 0.494660i \(-0.164707\pi\)
\(110\) 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 −0.767136 0.641484i \(-0.778319\pi\)
0.984511 + 0.175323i \(0.0560969\pi\)
\(114\) 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 0.555019 0.831838i \(-0.312711\pi\)
0.0647416 + 0.997902i \(0.479378\pi\)
\(128\) 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 −0.163098 0.986610i \(-0.552149\pi\)
−0.490702 + 0.871327i \(0.663260\pi\)
\(132\) 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 −0.294070 0.955784i \(-0.595010\pi\)
−0.455573 + 0.890199i \(0.650565\pi\)
\(138\) 0 0
\(139\) 0.637180 + 0.112352i 0.0540449 + 0.00952958i 0.200605 0.979672i \(-0.435709\pi\)
−0.146560 + 0.989202i \(0.546820\pi\)
\(140\) 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 0.999995 0.00304137i \(-0.000968099\pi\)
0.170652 + 0.985331i \(0.445413\pi\)
\(150\) 0 0
\(151\) 11.1465 + 4.05701i 0.907092 + 0.330155i 0.753091 0.657916i \(-0.228562\pi\)
0.154001 + 0.988071i \(0.450784\pi\)
\(152\) 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 −0.889582 0.456775i \(-0.849005\pi\)
0.921722 + 0.387851i \(0.126782\pi\)
\(158\) 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 0.999016 0.0443429i \(-0.0141194\pi\)
−0.0443429 + 0.999016i \(0.514119\pi\)
\(164\) 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 0.592346 0.805684i \(-0.298202\pi\)
−0.236437 + 0.971647i \(0.575980\pi\)
\(168\) 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 −0.364166 0.931334i \(-0.618646\pi\)
0.479362 + 0.877617i \(0.340868\pi\)
\(174\) 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 0.463255 + 0.886225i \(0.346681\pi\)
−0.999121 + 0.0419217i \(0.986652\pi\)
\(180\) 0 0
\(181\) −10.7361 18.5955i −0.798011 1.38220i −0.920910 0.389776i \(-0.872552\pi\)
0.122899 0.992419i \(-0.460781\pi\)
\(182\) −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 0.967459 0.253029i \(-0.0814267\pi\)
−0.417182 + 0.908823i \(0.636982\pi\)
\(192\) 0 0
\(193\) −13.1725 + 9.22349i −0.948178 + 0.663922i −0.941841 0.336058i \(-0.890906\pi\)
−0.00633721 + 0.999980i \(0.502017\pi\)
\(194\) 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 0.0864206 0.996259i \(-0.472457\pi\)
0.423287 0.905996i \(-0.360876\pi\)
\(198\) 0 0
\(199\) −17.2147 9.93892i −1.22032 0.704551i −0.255332 0.966853i \(-0.582185\pi\)
−0.964986 + 0.262302i \(0.915518\pi\)
\(200\) −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 0.518105 0.855317i \(-0.326638\pi\)
0.946678 + 0.322180i \(0.104416\pi\)
\(212\) −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 −0.577143 0.816643i \(-0.695832\pi\)
0.964788 + 0.263029i \(0.0847213\pi\)
\(224\) 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 −0.874684 0.484694i \(-0.838931\pi\)
0.190939 0.981602i \(-0.438847\pi\)
\(228\) 0 0
\(229\) −5.75242 + 6.85547i −0.380131 + 0.453022i −0.921855 0.387534i \(-0.873327\pi\)
0.541725 + 0.840556i \(0.317771\pi\)
\(230\) 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 −0.915496 0.402328i \(-0.868201\pi\)
0.591679 0.806174i \(-0.298465\pi\)
\(234\) 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 −0.967544 0.252704i \(-0.918680\pi\)
0.995623 + 0.0934552i \(0.0297912\pi\)
\(240\) 0 0
\(241\) 16.4029 13.7637i 1.05660 0.886595i 0.0628307 0.998024i \(-0.479987\pi\)
0.993772 + 0.111429i \(0.0355428\pi\)
\(242\) 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 −0.864725 0.502246i \(-0.832507\pi\)
0.00259539 + 0.999997i \(0.499174\pi\)
\(252\) 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 0.999039 0.0438287i \(-0.0139556\pi\)
−0.991472 + 0.130318i \(0.958400\pi\)
\(258\) 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 −0.254420 0.967094i \(-0.581884\pi\)
−0.995788 + 0.0916894i \(0.970773\pi\)
\(264\) 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 0.422126 0.906537i \(-0.361284\pi\)
−0.707491 + 0.706723i \(0.750173\pi\)
\(278\) −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 −0.681089 0.732201i \(-0.738493\pi\)
0.992394 0.123103i \(-0.0392846\pi\)
\(282\) 0 0
\(283\) −2.06765 23.6334i −0.122909 1.40486i −0.767852 0.640627i \(-0.778674\pi\)
0.644943 0.764231i \(-0.276881\pi\)
\(284\) 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 0.654690 0.755897i \(-0.272799\pi\)
−0.934228 + 0.356676i \(0.883910\pi\)
\(294\) 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 −0.912321 0.409476i \(-0.865711\pi\)
0.585355 0.810777i \(-0.300955\pi\)
\(308\) −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 0.0163937 + 0.999866i \(0.494781\pi\)
−0.987522 + 0.157480i \(0.949663\pi\)
\(312\) 0 0
\(313\) −0.188967 0.405241i −0.0106810 0.0229056i 0.900895 0.434037i \(-0.142911\pi\)
−0.911576 + 0.411132i \(0.865134\pi\)
\(314\) −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 −0.832718 0.553697i \(-0.813217\pi\)
0.805111 + 0.593124i \(0.202105\pi\)
\(318\) 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 0.743181 + 0.669091i \(0.233316\pi\)
−0.469519 + 0.882922i \(0.655573\pi\)
\(332\) −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 −0.289535 0.957167i \(-0.593501\pi\)
−0.118926 + 0.992903i \(0.537945\pi\)
\(338\) −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 0.159099 0.987263i \(-0.449141\pi\)
0.982138 + 0.188160i \(0.0602524\pi\)
\(348\) 0 0
\(349\) 11.2260 + 13.3786i 0.600915 + 0.716143i 0.977664 0.210173i \(-0.0674026\pi\)
−0.376749 + 0.926315i \(0.622958\pi\)
\(350\) 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 −0.946190 0.323611i \(-0.895103\pi\)
0.988010 0.154390i \(-0.0493413\pi\)
\(354\) 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 0.578345 0.815792i \(-0.303699\pi\)
−0.995669 + 0.0929655i \(0.970365\pi\)
\(360\) 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 0.163589 0.986529i \(-0.447693\pi\)
0.860878 + 0.508812i \(0.169915\pi\)
\(368\) 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 −0.241845 0.970315i \(-0.577753\pi\)
−0.898760 + 0.438442i \(0.855530\pi\)
\(374\) 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 \(-0.842239\pi\)
0.879673 0.475578i \(-0.157761\pi\)
\(380\) −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 −0.879158 0.476530i \(-0.841895\pi\)
0.930155 + 0.367167i \(0.119672\pi\)
\(384\) 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 0.0785096 0.996913i \(-0.474984\pi\)
−0.580662 + 0.814145i \(0.697206\pi\)
\(390\) 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 0.0648910 0.997892i \(-0.479330\pi\)
−0.442749 + 0.896646i \(0.645997\pi\)
\(398\) 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 0.835677 0.549222i \(-0.185076\pi\)
0.597434 + 0.801918i \(0.296187\pi\)
\(402\) 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 −0.0818277 0.996646i \(-0.526076\pi\)
−0.417766 + 0.908555i \(0.637187\pi\)
\(410\) −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 0.917496 0.397744i \(-0.130207\pi\)
−0.232380 + 0.972625i \(0.574651\pi\)
\(420\) 0 0
\(421\) −28.8617 10.5048i −1.40664 0.511973i −0.476495 0.879177i \(-0.658093\pi\)
−0.930140 + 0.367204i \(0.880315\pi\)
\(422\) −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 \(0.101570\pi\)
−0.949521 + 0.313703i \(0.898430\pi\)
\(432\) 0 0
\(433\) 24.3815 + 24.3815i 1.17170 + 1.17170i 0.981804 + 0.189896i \(0.0608150\pi\)
0.189896 + 0.981804i \(0.439185\pi\)
\(434\) 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 0.353386 0.935477i \(-0.385030\pi\)
0.652027 + 0.758196i \(0.273919\pi\)
\(440\) 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 0.260527 0.965466i \(-0.416104\pi\)
0.907054 + 0.421014i \(0.138326\pi\)
\(444\) 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 −0.892393 0.451259i \(-0.850975\pi\)
0.836998 + 0.547205i \(0.184308\pi\)
\(450\) 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 −0.995047 0.0994013i \(-0.968307\pi\)
0.997191 + 0.0748970i \(0.0238628\pi\)
\(458\) 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 0.887038 0.461696i \(-0.152759\pi\)
−0.608715 + 0.793389i \(0.708315\pi\)
\(462\) 0 0
\(463\) −18.1131 + 12.6829i −0.841787 + 0.589426i −0.912965 0.408038i \(-0.866213\pi\)
0.0711780 + 0.997464i \(0.477324\pi\)
\(464\) 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 0.625992 + 0.779830i \(0.284694\pi\)
−0.932040 + 0.362356i \(0.881972\pi\)
\(468\) 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 −0.993772 0.111431i \(-0.964457\pi\)
0.895729 0.444601i \(-0.146655\pi\)
\(480\) 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 −0.229538 0.973300i \(-0.573722\pi\)
0.973300 + 0.229538i \(0.0737215\pi\)
\(488\) 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 0.834129 0.551569i \(-0.185971\pi\)
−0.993522 + 0.113641i \(0.963749\pi\)
\(492\) 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 0.0323314 + 0.999477i \(0.489707\pi\)
−0.989907 + 0.141717i \(0.954738\pi\)
\(500\) −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 0.905549 + 0.424241i \(0.139459\pi\)
−0.572108 + 0.820178i \(0.693874\pi\)
\(504\) 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 0.883613 + 0.468218i \(0.155104\pi\)
−0.990465 + 0.137768i \(0.956007\pi\)
\(510\) 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 −0.587299 0.809370i \(-0.699809\pi\)
0.407285 + 0.913301i \(0.366475\pi\)
\(522\) 0 0
\(523\) −39.4721 + 10.5765i −1.72599 + 0.462478i −0.979254 0.202638i \(-0.935048\pi\)
−0.746739 + 0.665117i \(0.768382\pi\)
\(524\) −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 0.907784 0.419437i \(-0.137773\pi\)
−0.0836614 + 0.996494i \(0.526661\pi\)
\(548\) −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 0.282547 0.959253i \(-0.408821\pi\)
0.724320 + 0.689464i \(0.242154\pi\)
\(558\) 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 0.946421 0.322936i \(-0.104670\pi\)
−0.627156 + 0.778894i \(0.715781\pi\)
\(564\) 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 −0.824762 0.565481i \(-0.808691\pi\)
0.413671 + 0.910426i \(0.364246\pi\)
\(570\) 0 0
\(571\) 1.27813 7.24862i 0.0534879 0.303345i −0.946314 0.323249i \(-0.895225\pi\)
0.999802 + 0.0199038i \(0.00633599\pi\)
\(572\) 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 0.970462 + 0.241253i \(0.0775585\pi\)
−0.719818 + 0.694163i \(0.755775\pi\)
\(578\) 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 −0.672847 0.739781i \(-0.734929\pi\)
0.925294 + 0.379249i \(0.123818\pi\)
\(588\) 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 −0.281969 + 0.959424i \(0.590987\pi\)
−0.959424 + 0.281969i \(0.909013\pi\)
\(594\) 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 −0.689634 0.724158i \(-0.742228\pi\)
−0.0628100 + 0.998026i \(0.520006\pi\)
\(600\) 0 0
\(601\) −5.44723 30.8927i −0.222197 1.26014i −0.867972 0.496614i \(-0.834577\pi\)
0.645775 0.763528i \(-0.276534\pi\)
\(602\) 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 −0.378233 0.925710i \(-0.623468\pi\)
−0.211739 + 0.977326i \(0.567913\pi\)
\(608\) −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 −0.848873 0.528596i \(-0.822719\pi\)
0.999444 0.0333409i \(-0.0106147\pi\)
\(614\) 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 −0.529366 0.848394i \(-0.677570\pi\)
0.616175 + 0.787609i \(0.288681\pi\)
\(618\) 0 0
\(619\) −14.0882 16.7897i −0.566254 0.674836i 0.404603 0.914492i \(-0.367410\pi\)
−0.970858 + 0.239657i \(0.922965\pi\)
\(620\) −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 −0.999955 0.00945434i \(-0.996991\pi\)
0.508165 + 0.861260i \(0.330324\pi\)
\(632\) 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 −0.152434 0.988314i \(-0.548711\pi\)
0.194782 + 0.980847i \(0.437600\pi\)
\(642\) 0 0
\(643\) 38.6292 + 18.0131i 1.52339 + 0.710367i 0.990715 0.135954i \(-0.0434099\pi\)
0.532673 + 0.846321i \(0.321188\pi\)
\(644\) 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 0.529273 0.848452i \(-0.322465\pi\)
−0.848452 + 0.529273i \(0.822465\pi\)
\(648\) 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 −0.162125 + 0.986770i \(0.551835\pi\)
−0.651698 + 0.758479i \(0.725943\pi\)
\(654\) 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 0.625233 0.780438i \(-0.285004\pi\)
−0.0226995 + 0.999742i \(0.507226\pi\)
\(660\) 0 0
\(661\) 5.35212 + 4.49096i 0.208173 + 0.174678i 0.740913 0.671601i \(-0.234393\pi\)
−0.532740 + 0.846279i \(0.678838\pi\)
\(662\) −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 −0.0429476 0.999077i \(-0.513675\pi\)
−0.215783 + 0.976441i \(0.569230\pi\)
\(674\) 15.7666 0.607307
\(675\) 0 0
\(676\) 15.3700 0.591155
\(677\) −5.61594 0.491331i −0.215838 0.0188834i −0.0212762 0.999774i \(-0.506773\pi\)
−0.194562 + 0.980890i \(0.562328\pi\)
\(678\) 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 0.573958 0.818885i \(-0.305407\pi\)
0.0876196 + 0.996154i \(0.472074\pi\)
\(684\) 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 −0.230302 0.973119i \(-0.573971\pi\)
−0.801930 + 0.597417i \(0.796194\pi\)
\(692\) 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 \(-0.872277\pi\)
0.920572 0.390573i \(-0.127723\pi\)
\(702\) 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 −0.517808 0.855497i \(-0.673252\pi\)
−0.193983 + 0.981005i \(0.562141\pi\)
\(710\) −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 −0.768573 0.639763i \(-0.779033\pi\)
0.938337 + 0.345722i \(0.112366\pi\)
\(720\) 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 0.953054 + 0.302801i \(0.0979216\pi\)
−0.991156 + 0.132704i \(0.957634\pi\)
\(728\) −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 0.368896 0.929471i \(-0.379736\pi\)
0.999587 0.0287512i \(-0.00915305\pi\)
\(734\) −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 0.988240 0.152911i \(-0.0488648\pi\)
0.361695 + 0.932296i \(0.382198\pi\)
\(740\) −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 −0.299603 0.954064i \(-0.596854\pi\)
−0.129379 + 0.991595i \(0.541299\pi\)
\(744\) 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 0.301338 0.953517i \(-0.402567\pi\)
0.843747 + 0.536741i \(0.180345\pi\)
\(752\) −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 −0.344580 0.938757i \(-0.611979\pi\)
0.938757 + 0.344580i \(0.111979\pi\)
\(758\) −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 0.807207 0.590269i \(-0.200978\pi\)
−0.997774 + 0.0666905i \(0.978756\pi\)
\(762\) 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 −0.315225 0.949017i \(-0.602080\pi\)
0.989337 + 0.145641i \(0.0465246\pi\)
\(770\) 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 0.906071 0.423127i \(-0.139067\pi\)
−0.996243 + 0.0865969i \(0.972401\pi\)
\(774\) 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