Properties

Label 405.2.r.a.152.8
Level $405$
Weight $2$
Character 405.152
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 152.8
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0928047 - 0.0649826i) q^{2} +(-0.679650 - 1.86732i) q^{4} +(-0.584024 - 2.15845i) q^{5} +(0.344848 + 0.739528i) q^{7} +(-0.116914 + 0.436329i) q^{8} +O(q^{10})\) \(q+(-0.0928047 - 0.0649826i) q^{2} +(-0.679650 - 1.86732i) q^{4} +(-0.584024 - 2.15845i) q^{5} +(0.344848 + 0.739528i) q^{7} +(-0.116914 + 0.436329i) q^{8} +(-0.0860616 + 0.238266i) q^{10} +(0.792138 + 0.944033i) q^{11} +(-2.08344 - 2.97546i) q^{13} +(0.0160530 - 0.0910408i) q^{14} +(-3.00531 + 2.52175i) q^{16} +(-1.65815 - 6.18829i) q^{17} +(-2.78289 + 1.60671i) q^{19} +(-3.63360 + 2.55755i) q^{20} +(-0.0121684 - 0.139086i) q^{22} +(-0.471164 - 0.219707i) q^{23} +(-4.31783 + 2.52118i) q^{25} +0.411524i q^{26} +(1.14656 - 1.14656i) q^{28} +(-0.754929 - 4.28141i) q^{29} +(-6.93274 + 2.52331i) q^{31} +(1.34278 - 0.117478i) q^{32} +(-0.248247 + 0.682053i) q^{34} +(1.39484 - 1.17624i) q^{35} +(8.35299 - 2.23818i) q^{37} +(0.362674 + 0.0317298i) q^{38} +(1.01007 - 0.00247331i) q^{40} +(8.94143 + 1.57662i) q^{41} +(0.490289 - 5.60402i) q^{43} +(1.22444 - 2.12079i) q^{44} +(0.0294491 + 0.0510073i) q^{46} +(-2.14663 + 1.00099i) q^{47} +(4.07153 - 4.85226i) q^{49} +(0.564548 + 0.0466068i) q^{50} +(-4.14014 + 5.91273i) q^{52} +(-4.55111 - 4.55111i) q^{53} +(1.57502 - 2.26113i) q^{55} +(-0.362995 + 0.0640058i) q^{56} +(-0.208156 + 0.446393i) q^{58} +(10.5708 + 8.86992i) q^{59} +(3.01780 + 1.09839i) q^{61} +(0.807362 + 0.216332i) q^{62} +(6.66285 + 3.84680i) q^{64} +(-5.20561 + 6.23475i) q^{65} +(9.77239 - 6.84270i) q^{67} +(-10.4286 + 7.30217i) q^{68} +(-0.205883 + 0.0185205i) q^{70} +(-4.14187 - 2.39131i) q^{71} +(-5.46389 - 1.46405i) q^{73} +(-0.920640 - 0.335086i) q^{74} +(4.89163 + 4.10457i) q^{76} +(-0.424972 + 0.911356i) q^{77} +(9.54938 - 1.68381i) q^{79} +(7.19826 + 5.01405i) q^{80} +(-0.727355 - 0.727355i) q^{82} +(-4.76170 + 6.80042i) q^{83} +(-12.3887 + 7.19314i) q^{85} +(-0.409665 + 0.488220i) q^{86} +(-0.504521 + 0.235262i) q^{88} +(0.689073 + 1.19351i) q^{89} +(1.48197 - 2.56685i) q^{91} +(-0.0900380 + 1.02914i) q^{92} +(0.264265 + 0.0465970i) q^{94} +(5.09327 + 5.06839i) q^{95} +(-6.18004 - 0.540683i) q^{97} +(-0.693170 + 0.185734i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0928047 0.0649826i −0.0656229 0.0459496i 0.540305 0.841469i \(-0.318309\pi\)
−0.605928 + 0.795520i \(0.707198\pi\)
\(3\) 0 0
\(4\) −0.679650 1.86732i −0.339825 0.933662i
\(5\) −0.584024 2.15845i −0.261183 0.965289i
\(6\) 0 0
\(7\) 0.344848 + 0.739528i 0.130340 + 0.279515i 0.960637 0.277805i \(-0.0896071\pi\)
−0.830297 + 0.557321i \(0.811829\pi\)
\(8\) −0.116914 + 0.436329i −0.0413353 + 0.154265i
\(9\) 0 0
\(10\) −0.0860616 + 0.238266i −0.0272151 + 0.0753463i
\(11\) 0.792138 + 0.944033i 0.238839 + 0.284637i 0.872127 0.489279i \(-0.162740\pi\)
−0.633289 + 0.773916i \(0.718295\pi\)
\(12\) 0 0
\(13\) −2.08344 2.97546i −0.577843 0.825245i 0.418718 0.908116i \(-0.362480\pi\)
−0.996560 + 0.0828718i \(0.973591\pi\)
\(14\) 0.0160530 0.0910408i 0.00429033 0.0243317i
\(15\) 0 0
\(16\) −3.00531 + 2.52175i −0.751327 + 0.630438i
\(17\) −1.65815 6.18829i −0.402160 1.50088i −0.809234 0.587486i \(-0.800118\pi\)
0.407074 0.913395i \(-0.366549\pi\)
\(18\) 0 0
\(19\) −2.78289 + 1.60671i −0.638440 + 0.368603i −0.784013 0.620744i \(-0.786831\pi\)
0.145573 + 0.989347i \(0.453497\pi\)
\(20\) −3.63360 + 2.55755i −0.812497 + 0.571887i
\(21\) 0 0
\(22\) −0.0121684 0.139086i −0.00259432 0.0296532i
\(23\) −0.471164 0.219707i −0.0982444 0.0458121i 0.372875 0.927882i \(-0.378372\pi\)
−0.471119 + 0.882070i \(0.656150\pi\)
\(24\) 0 0
\(25\) −4.31783 + 2.52118i −0.863566 + 0.504235i
\(26\) 0.411524i 0.0807066i
\(27\) 0 0
\(28\) 1.14656 1.14656i 0.216680 0.216680i
\(29\) −0.754929 4.28141i −0.140187 0.795038i −0.971107 0.238646i \(-0.923296\pi\)
0.830920 0.556392i \(-0.187815\pi\)
\(30\) 0 0
\(31\) −6.93274 + 2.52331i −1.24516 + 0.453200i −0.878762 0.477260i \(-0.841630\pi\)
−0.366394 + 0.930460i \(0.619408\pi\)
\(32\) 1.34278 0.117478i 0.237372 0.0207674i
\(33\) 0 0
\(34\) −0.248247 + 0.682053i −0.0425740 + 0.116971i
\(35\) 1.39484 1.17624i 0.235771 0.198821i
\(36\) 0 0
\(37\) 8.35299 2.23818i 1.37322 0.367954i 0.504569 0.863372i \(-0.331652\pi\)
0.868655 + 0.495417i \(0.164985\pi\)
\(38\) 0.362674 + 0.0317298i 0.0588334 + 0.00514726i
\(39\) 0 0
\(40\) 1.01007 0.00247331i 0.159707 0.000391065i
\(41\) 8.94143 + 1.57662i 1.39642 + 0.246226i 0.820670 0.571402i \(-0.193600\pi\)
0.575747 + 0.817628i \(0.304711\pi\)
\(42\) 0 0
\(43\) 0.490289 5.60402i 0.0747683 0.854606i −0.862514 0.506034i \(-0.831111\pi\)
0.937282 0.348572i \(-0.113333\pi\)
\(44\) 1.22444 2.12079i 0.184591 0.319721i
\(45\) 0 0
\(46\) 0.0294491 + 0.0510073i 0.00434203 + 0.00752062i
\(47\) −2.14663 + 1.00099i −0.313118 + 0.146010i −0.572824 0.819678i \(-0.694152\pi\)
0.259706 + 0.965688i \(0.416374\pi\)
\(48\) 0 0
\(49\) 4.07153 4.85226i 0.581647 0.693180i
\(50\) 0.564548 + 0.0466068i 0.0798391 + 0.00659120i
\(51\) 0 0
\(52\) −4.14014 + 5.91273i −0.574134 + 0.819949i
\(53\) −4.55111 4.55111i −0.625143 0.625143i 0.321699 0.946842i \(-0.395746\pi\)
−0.946842 + 0.321699i \(0.895746\pi\)
\(54\) 0 0
\(55\) 1.57502 2.26113i 0.212376 0.304891i
\(56\) −0.362995 + 0.0640058i −0.0485072 + 0.00855313i
\(57\) 0 0
\(58\) −0.208156 + 0.446393i −0.0273323 + 0.0586142i
\(59\) 10.5708 + 8.86992i 1.37620 + 1.15477i 0.970596 + 0.240714i \(0.0773817\pi\)
0.405600 + 0.914051i \(0.367063\pi\)
\(60\) 0 0
\(61\) 3.01780 + 1.09839i 0.386390 + 0.140634i 0.527908 0.849301i \(-0.322976\pi\)
−0.141519 + 0.989936i \(0.545199\pi\)
\(62\) 0.807362 + 0.216332i 0.102535 + 0.0274742i
\(63\) 0 0
\(64\) 6.66285 + 3.84680i 0.832856 + 0.480850i
\(65\) −5.20561 + 6.23475i −0.645677 + 0.773325i
\(66\) 0 0
\(67\) 9.77239 6.84270i 1.19389 0.835969i 0.204160 0.978938i \(-0.434554\pi\)
0.989727 + 0.142969i \(0.0456649\pi\)
\(68\) −10.4286 + 7.30217i −1.26465 + 0.885518i
\(69\) 0 0
\(70\) −0.205883 + 0.0185205i −0.0246077 + 0.00221362i
\(71\) −4.14187 2.39131i −0.491550 0.283796i 0.233667 0.972317i \(-0.424927\pi\)
−0.725217 + 0.688520i \(0.758261\pi\)
\(72\) 0 0
\(73\) −5.46389 1.46405i −0.639500 0.171354i −0.0755232 0.997144i \(-0.524063\pi\)
−0.563977 + 0.825790i \(0.690729\pi\)
\(74\) −0.920640 0.335086i −0.107022 0.0389529i
\(75\) 0 0
\(76\) 4.89163 + 4.10457i 0.561109 + 0.470826i
\(77\) −0.424972 + 0.911356i −0.0484301 + 0.103859i
\(78\) 0 0
\(79\) 9.54938 1.68381i 1.07439 0.189444i 0.391656 0.920112i \(-0.371902\pi\)
0.682733 + 0.730668i \(0.260791\pi\)
\(80\) 7.19826 + 5.01405i 0.804790 + 0.560588i
\(81\) 0 0
\(82\) −0.727355 0.727355i −0.0803229 0.0803229i
\(83\) −4.76170 + 6.80042i −0.522665 + 0.746443i −0.990521 0.137362i \(-0.956138\pi\)
0.467856 + 0.883805i \(0.345027\pi\)
\(84\) 0 0
\(85\) −12.3887 + 7.19314i −1.34375 + 0.780206i
\(86\) −0.409665 + 0.488220i −0.0441753 + 0.0526461i
\(87\) 0 0
\(88\) −0.504521 + 0.235262i −0.0537821 + 0.0250790i
\(89\) 0.689073 + 1.19351i 0.0730416 + 0.126512i 0.900233 0.435409i \(-0.143396\pi\)
−0.827191 + 0.561920i \(0.810063\pi\)
\(90\) 0 0
\(91\) 1.48197 2.56685i 0.155353 0.269079i
\(92\) −0.0900380 + 1.02914i −0.00938711 + 0.107295i
\(93\) 0 0
\(94\) 0.264265 + 0.0465970i 0.0272568 + 0.00480611i
\(95\) 5.09327 + 5.06839i 0.522559 + 0.520006i
\(96\) 0 0
\(97\) −6.18004 0.540683i −0.627488 0.0548981i −0.231023 0.972948i \(-0.574207\pi\)
−0.396464 + 0.918050i \(0.629763\pi\)
\(98\) −0.693170 + 0.185734i −0.0700207 + 0.0187620i
\(99\) 0 0
\(100\) 7.64247 + 6.34927i 0.764247 + 0.634927i
\(101\) 0.358110 0.983900i 0.0356333 0.0979017i −0.920600 0.390507i \(-0.872300\pi\)
0.956233 + 0.292605i \(0.0945221\pi\)
\(102\) 0 0
\(103\) 5.46070 0.477749i 0.538058 0.0470740i 0.185112 0.982717i \(-0.440735\pi\)
0.352947 + 0.935643i \(0.385180\pi\)
\(104\) 1.54186 0.561192i 0.151192 0.0550294i
\(105\) 0 0
\(106\) 0.126622 + 0.718107i 0.0122986 + 0.0697487i
\(107\) 7.41541 7.41541i 0.716875 0.716875i −0.251089 0.967964i \(-0.580789\pi\)
0.967964 + 0.251089i \(0.0807888\pi\)
\(108\) 0 0
\(109\) 13.2925i 1.27319i 0.771199 + 0.636595i \(0.219658\pi\)
−0.771199 + 0.636595i \(0.780342\pi\)
\(110\) −0.293104 + 0.107495i −0.0279463 + 0.0102492i
\(111\) 0 0
\(112\) −2.90128 1.35289i −0.274145 0.127836i
\(113\) −1.20301 13.7505i −0.113170 1.29353i −0.814276 0.580477i \(-0.802866\pi\)
0.701107 0.713056i \(-0.252690\pi\)
\(114\) 0 0
\(115\) −0.199057 + 1.14530i −0.0185621 + 0.106800i
\(116\) −7.48170 + 4.31956i −0.694658 + 0.401061i
\(117\) 0 0
\(118\) −0.404626 1.51009i −0.0372489 0.139015i
\(119\) 4.00461 3.36027i 0.367102 0.308035i
\(120\) 0 0
\(121\) 1.64641 9.33728i 0.149674 0.848843i
\(122\) −0.208690 0.298040i −0.0188939 0.0269833i
\(123\) 0 0
\(124\) 9.42367 + 11.2307i 0.846271 + 1.00855i
\(125\) 7.96355 + 7.84741i 0.712282 + 0.701893i
\(126\) 0 0
\(127\) 3.01921 11.2678i 0.267911 0.999858i −0.692533 0.721386i \(-0.743505\pi\)
0.960444 0.278472i \(-0.0898280\pi\)
\(128\) −1.50767 3.23321i −0.133261 0.285778i
\(129\) 0 0
\(130\) 0.888256 0.240340i 0.0779052 0.0210792i
\(131\) 2.06228 + 5.66608i 0.180182 + 0.495047i 0.996598 0.0824178i \(-0.0262642\pi\)
−0.816415 + 0.577465i \(0.804042\pi\)
\(132\) 0 0
\(133\) −2.14788 1.50396i −0.186245 0.130410i
\(134\) −1.35158 −0.116759
\(135\) 0 0
\(136\) 2.89399 0.248157
\(137\) 10.9750 + 7.68477i 0.937657 + 0.656554i 0.939173 0.343444i \(-0.111594\pi\)
−0.00151614 + 0.999999i \(0.500483\pi\)
\(138\) 0 0
\(139\) −2.32343 6.38357i −0.197071 0.541447i 0.801315 0.598242i \(-0.204134\pi\)
−0.998386 + 0.0567952i \(0.981912\pi\)
\(140\) −3.14442 1.80518i −0.265752 0.152566i
\(141\) 0 0
\(142\) 0.228992 + 0.491074i 0.0192166 + 0.0412100i
\(143\) 1.15856 4.32381i 0.0968839 0.361575i
\(144\) 0 0
\(145\) −8.80033 + 4.12993i −0.730828 + 0.342972i
\(146\) 0.411938 + 0.490928i 0.0340922 + 0.0406295i
\(147\) 0 0
\(148\) −9.85652 14.0766i −0.810201 1.15709i
\(149\) 2.75408 15.6192i 0.225623 1.27957i −0.635868 0.771798i \(-0.719358\pi\)
0.861491 0.507773i \(-0.169531\pi\)
\(150\) 0 0
\(151\) −0.777628 + 0.652507i −0.0632825 + 0.0531003i −0.673880 0.738841i \(-0.735374\pi\)
0.610598 + 0.791941i \(0.290929\pi\)
\(152\) −0.375692 1.40210i −0.0304727 0.113726i
\(153\) 0 0
\(154\) 0.0986617 0.0569624i 0.00795039 0.00459016i
\(155\) 9.49533 + 13.4903i 0.762683 + 1.08357i
\(156\) 0 0
\(157\) 1.36005 + 15.5455i 0.108544 + 1.24066i 0.833754 + 0.552136i \(0.186187\pi\)
−0.725210 + 0.688528i \(0.758257\pi\)
\(158\) −0.995646 0.464278i −0.0792094 0.0369359i
\(159\) 0 0
\(160\) −1.03779 2.82972i −0.0820442 0.223709i
\(161\) 0.424205i 0.0334320i
\(162\) 0 0
\(163\) 1.25033 1.25033i 0.0979331 0.0979331i −0.656443 0.754376i \(-0.727940\pi\)
0.754376 + 0.656443i \(0.227940\pi\)
\(164\) −3.13299 17.7681i −0.244646 1.38746i
\(165\) 0 0
\(166\) 0.883817 0.321683i 0.0685975 0.0249675i
\(167\) −4.87345 + 0.426371i −0.377119 + 0.0329936i −0.274140 0.961690i \(-0.588393\pi\)
−0.102979 + 0.994684i \(0.532837\pi\)
\(168\) 0 0
\(169\) −0.0663864 + 0.182395i −0.00510665 + 0.0140304i
\(170\) 1.61716 + 0.137494i 0.124031 + 0.0105453i
\(171\) 0 0
\(172\) −10.7978 + 2.89325i −0.823321 + 0.220608i
\(173\) −2.34398 0.205071i −0.178209 0.0155913i −0.00229816 0.999997i \(-0.500732\pi\)
−0.175911 + 0.984406i \(0.556287\pi\)
\(174\) 0 0
\(175\) −3.35348 2.32374i −0.253499 0.175658i
\(176\) −4.76124 0.839535i −0.358892 0.0632823i
\(177\) 0 0
\(178\) 0.0136081 0.155541i 0.00101997 0.0116583i
\(179\) −9.70081 + 16.8023i −0.725073 + 1.25586i 0.233871 + 0.972268i \(0.424861\pi\)
−0.958944 + 0.283595i \(0.908473\pi\)
\(180\) 0 0
\(181\) −2.02017 3.49903i −0.150158 0.260081i 0.781128 0.624371i \(-0.214645\pi\)
−0.931285 + 0.364291i \(0.881312\pi\)
\(182\) −0.304334 + 0.141913i −0.0225587 + 0.0105193i
\(183\) 0 0
\(184\) 0.150950 0.179895i 0.0111282 0.0132621i
\(185\) −9.70935 16.7224i −0.713846 1.22945i
\(186\) 0 0
\(187\) 4.52847 6.46733i 0.331155 0.472938i
\(188\) 3.32813 + 3.32813i 0.242729 + 0.242729i
\(189\) 0 0
\(190\) −0.143323 0.801345i −0.0103977 0.0581357i
\(191\) 0.548539 0.0967222i 0.0396909 0.00699857i −0.153767 0.988107i \(-0.549141\pi\)
0.193458 + 0.981108i \(0.438030\pi\)
\(192\) 0 0
\(193\) −8.39357 + 18.0001i −0.604183 + 1.29567i 0.331708 + 0.943382i \(0.392375\pi\)
−0.935890 + 0.352292i \(0.885403\pi\)
\(194\) 0.538402 + 0.451773i 0.0386550 + 0.0324354i
\(195\) 0 0
\(196\) −11.8280 4.30503i −0.844854 0.307502i
\(197\) −16.1238 4.32035i −1.14877 0.307812i −0.366299 0.930497i \(-0.619375\pi\)
−0.782473 + 0.622685i \(0.786042\pi\)
\(198\) 0 0
\(199\) −20.8934 12.0628i −1.48110 0.855112i −0.481327 0.876541i \(-0.659845\pi\)
−0.999770 + 0.0214296i \(0.993178\pi\)
\(200\) −0.595246 2.17875i −0.0420903 0.154061i
\(201\) 0 0
\(202\) −0.0971707 + 0.0680397i −0.00683691 + 0.00478725i
\(203\) 2.90589 2.03473i 0.203954 0.142810i
\(204\) 0 0
\(205\) −1.81896 20.2204i −0.127042 1.41226i
\(206\) −0.537824 0.310513i −0.0374720 0.0216344i
\(207\) 0 0
\(208\) 13.7648 + 3.68826i 0.954415 + 0.255735i
\(209\) −3.72122 1.35441i −0.257402 0.0936867i
\(210\) 0 0
\(211\) 21.4119 + 17.9667i 1.47406 + 1.23688i 0.912265 + 0.409601i \(0.134332\pi\)
0.561792 + 0.827279i \(0.310112\pi\)
\(212\) −5.40523 + 11.5916i −0.371233 + 0.796111i
\(213\) 0 0
\(214\) −1.17006 + 0.206313i −0.0799835 + 0.0141032i
\(215\) −12.3824 + 2.21462i −0.844470 + 0.151036i
\(216\) 0 0
\(217\) −4.25680 4.25680i −0.288970 0.288970i
\(218\) 0.863780 1.23361i 0.0585026 0.0835503i
\(219\) 0 0
\(220\) −5.29273 1.40430i −0.356836 0.0946779i
\(221\) −14.9584 + 17.8267i −1.00621 + 1.19915i
\(222\) 0 0
\(223\) 3.93150 1.83329i 0.263273 0.122766i −0.286500 0.958080i \(-0.592492\pi\)
0.549773 + 0.835314i \(0.314714\pi\)
\(224\) 0.549933 + 0.952512i 0.0367440 + 0.0636424i
\(225\) 0 0
\(226\) −0.781895 + 1.35428i −0.0520109 + 0.0900855i
\(227\) 2.21851 25.3576i 0.147247 1.68305i −0.459521 0.888167i \(-0.651979\pi\)
0.606768 0.794879i \(-0.292466\pi\)
\(228\) 0 0
\(229\) −5.08120 0.895953i −0.335775 0.0592062i 0.00321862 0.999995i \(-0.498975\pi\)
−0.338994 + 0.940789i \(0.610087\pi\)
\(230\) 0.0928979 0.0933539i 0.00612550 0.00615558i
\(231\) 0 0
\(232\) 1.95636 + 0.171160i 0.128442 + 0.0112372i
\(233\) 7.55194 2.02354i 0.494744 0.132566i −0.00281565 0.999996i \(-0.500896\pi\)
0.497560 + 0.867430i \(0.334230\pi\)
\(234\) 0 0
\(235\) 3.41428 + 4.04880i 0.222723 + 0.264115i
\(236\) 9.37859 25.7675i 0.610494 1.67732i
\(237\) 0 0
\(238\) −0.590005 + 0.0516188i −0.0382444 + 0.00334595i
\(239\) 10.8598 3.95265i 0.702462 0.255675i 0.0340005 0.999422i \(-0.489175\pi\)
0.668462 + 0.743746i \(0.266953\pi\)
\(240\) 0 0
\(241\) 2.63129 + 14.9228i 0.169496 + 0.961259i 0.944307 + 0.329066i \(0.106734\pi\)
−0.774811 + 0.632193i \(0.782155\pi\)
\(242\) −0.759555 + 0.759555i −0.0488261 + 0.0488261i
\(243\) 0 0
\(244\) 6.38173i 0.408548i
\(245\) −12.8512 5.95437i −0.821036 0.380411i
\(246\) 0 0
\(247\) 10.5787 + 4.93292i 0.673106 + 0.313874i
\(248\) −0.290459 3.31996i −0.0184442 0.210818i
\(249\) 0 0
\(250\) −0.229111 1.24577i −0.0144902 0.0787893i
\(251\) 13.8298 7.98465i 0.872930 0.503986i 0.00460934 0.999989i \(-0.498533\pi\)
0.868321 + 0.496003i \(0.165199\pi\)
\(252\) 0 0
\(253\) −0.165816 0.618833i −0.0104247 0.0389057i
\(254\) −1.01241 + 0.849512i −0.0635242 + 0.0533031i
\(255\) 0 0
\(256\) 2.60177 14.7554i 0.162611 0.922212i
\(257\) −13.2591 18.9360i −0.827080 1.18119i −0.981172 0.193136i \(-0.938134\pi\)
0.154092 0.988057i \(-0.450755\pi\)
\(258\) 0 0
\(259\) 4.53571 + 5.40545i 0.281835 + 0.335878i
\(260\) 15.1803 + 5.48312i 0.941442 + 0.340048i
\(261\) 0 0
\(262\) 0.176807 0.659851i 0.0109231 0.0407657i
\(263\) −0.0491363 0.105373i −0.00302987 0.00649758i 0.904787 0.425864i \(-0.140030\pi\)
−0.907817 + 0.419367i \(0.862252\pi\)
\(264\) 0 0
\(265\) −7.16539 + 12.4813i −0.440167 + 0.766721i
\(266\) 0.101602 + 0.279149i 0.00622962 + 0.0171158i
\(267\) 0 0
\(268\) −19.4193 13.5976i −1.18622 0.830604i
\(269\) −16.5806 −1.01094 −0.505468 0.862845i \(-0.668680\pi\)
−0.505468 + 0.862845i \(0.668680\pi\)
\(270\) 0 0
\(271\) −31.4952 −1.91320 −0.956599 0.291408i \(-0.905876\pi\)
−0.956599 + 0.291408i \(0.905876\pi\)
\(272\) 20.5886 + 14.4163i 1.24837 + 0.874116i
\(273\) 0 0
\(274\) −0.519155 1.42637i −0.0313633 0.0861700i
\(275\) −5.80039 2.07906i −0.349777 0.125372i
\(276\) 0 0
\(277\) −0.477906 1.02487i −0.0287146 0.0615786i 0.891427 0.453164i \(-0.149705\pi\)
−0.920142 + 0.391585i \(0.871927\pi\)
\(278\) −0.199196 + 0.743408i −0.0119470 + 0.0445866i
\(279\) 0 0
\(280\) 0.350151 + 0.746126i 0.0209255 + 0.0445896i
\(281\) 15.9976 + 19.0652i 0.954338 + 1.13734i 0.990434 + 0.137988i \(0.0440634\pi\)
−0.0360958 + 0.999348i \(0.511492\pi\)
\(282\) 0 0
\(283\) 13.1825 + 18.8266i 0.783618 + 1.11912i 0.990057 + 0.140664i \(0.0449236\pi\)
−0.206439 + 0.978459i \(0.566187\pi\)
\(284\) −1.65033 + 9.35947i −0.0979289 + 0.555382i
\(285\) 0 0
\(286\) −0.388493 + 0.325984i −0.0229721 + 0.0192758i
\(287\) 1.91748 + 7.15614i 0.113185 + 0.422413i
\(288\) 0 0
\(289\) −20.8231 + 12.0222i −1.22489 + 0.707188i
\(290\) 1.08509 + 0.188591i 0.0637184 + 0.0110745i
\(291\) 0 0
\(292\) 0.979689 + 11.1979i 0.0573320 + 0.655307i
\(293\) 15.8638 + 7.39741i 0.926773 + 0.432161i 0.826588 0.562807i \(-0.190279\pi\)
0.100185 + 0.994969i \(0.468056\pi\)
\(294\) 0 0
\(295\) 12.9717 27.9967i 0.755243 1.63003i
\(296\) 3.90632i 0.227050i
\(297\) 0 0
\(298\) −1.27056 + 1.27056i −0.0736018 + 0.0736018i
\(299\) 0.327911 + 1.85968i 0.0189636 + 0.107548i
\(300\) 0 0
\(301\) 4.31341 1.56995i 0.248621 0.0904906i
\(302\) 0.114569 0.0100235i 0.00659272 0.000576788i
\(303\) 0 0
\(304\) 4.31174 11.8464i 0.247295 0.679439i
\(305\) 0.608353 7.15526i 0.0348342 0.409709i
\(306\) 0 0
\(307\) 0.890598 0.238635i 0.0508291 0.0136196i −0.233315 0.972401i \(-0.574957\pi\)
0.284144 + 0.958782i \(0.408291\pi\)
\(308\) 1.99063 + 0.174158i 0.113427 + 0.00992355i
\(309\) 0 0
\(310\) −0.00457650 1.86900i −0.000259928 0.106152i
\(311\) −8.25248 1.45513i −0.467955 0.0825131i −0.0653015 0.997866i \(-0.520801\pi\)
−0.402653 + 0.915352i \(0.631912\pi\)
\(312\) 0 0
\(313\) 0.138297 1.58074i 0.00781702 0.0893490i −0.991284 0.131743i \(-0.957943\pi\)
0.999101 + 0.0423936i \(0.0134983\pi\)
\(314\) 0.883965 1.53107i 0.0498851 0.0864034i
\(315\) 0 0
\(316\) −9.63446 16.6874i −0.541981 0.938739i
\(317\) 9.24972 4.31321i 0.519516 0.242254i −0.145130 0.989413i \(-0.546360\pi\)
0.664646 + 0.747158i \(0.268582\pi\)
\(318\) 0 0
\(319\) 3.44379 4.10415i 0.192815 0.229788i
\(320\) 4.41186 16.6281i 0.246631 0.929537i
\(321\) 0 0
\(322\) −0.0275659 + 0.0393682i −0.00153619 + 0.00219390i
\(323\) 14.5572 + 14.5572i 0.809985 + 0.809985i
\(324\) 0 0
\(325\) 16.4976 + 7.59482i 0.915123 + 0.421285i
\(326\) −0.197286 + 0.0347868i −0.0109266 + 0.00192666i
\(327\) 0 0
\(328\) −1.73330 + 3.71707i −0.0957055 + 0.205241i
\(329\) −1.48052 1.24231i −0.0816238 0.0684905i
\(330\) 0 0
\(331\) 7.45973 + 2.71512i 0.410024 + 0.149236i 0.538793 0.842438i \(-0.318880\pi\)
−0.128769 + 0.991675i \(0.541103\pi\)
\(332\) 15.9349 + 4.26974i 0.874540 + 0.234332i
\(333\) 0 0
\(334\) 0.479986 + 0.277120i 0.0262636 + 0.0151633i
\(335\) −20.4769 17.0969i −1.11878 0.934105i
\(336\) 0 0
\(337\) 1.96309 1.37457i 0.106937 0.0748778i −0.518885 0.854844i \(-0.673653\pi\)
0.625822 + 0.779966i \(0.284764\pi\)
\(338\) 0.0180135 0.0126132i 0.000979805 0.000686067i
\(339\) 0 0
\(340\) 21.8519 + 18.2450i 1.18509 + 0.989472i
\(341\) −7.87377 4.54592i −0.426389 0.246176i
\(342\) 0 0
\(343\) 10.5097 + 2.81606i 0.567469 + 0.152053i
\(344\) 2.38787 + 0.869115i 0.128746 + 0.0468595i
\(345\) 0 0
\(346\) 0.204206 + 0.171349i 0.0109782 + 0.00921179i
\(347\) −10.1468 + 21.7598i −0.544708 + 1.16813i 0.420656 + 0.907220i \(0.361800\pi\)
−0.965363 + 0.260909i \(0.915978\pi\)
\(348\) 0 0
\(349\) 18.2123 3.21131i 0.974880 0.171898i 0.336554 0.941664i \(-0.390738\pi\)
0.638326 + 0.769767i \(0.279627\pi\)
\(350\) 0.160216 + 0.433571i 0.00856391 + 0.0231754i
\(351\) 0 0
\(352\) 1.17457 + 1.17457i 0.0626048 + 0.0626048i
\(353\) −16.5605 + 23.6509i −0.881429 + 1.25881i 0.0835552 + 0.996503i \(0.473373\pi\)
−0.964984 + 0.262308i \(0.915516\pi\)
\(354\) 0 0
\(355\) −2.74258 + 10.3366i −0.145561 + 0.548610i
\(356\) 1.76034 2.09789i 0.0932978 0.111188i
\(357\) 0 0
\(358\) 1.99214 0.928949i 0.105288 0.0490965i
\(359\) 14.8587 + 25.7360i 0.784210 + 1.35829i 0.929470 + 0.368899i \(0.120265\pi\)
−0.145259 + 0.989394i \(0.546402\pi\)
\(360\) 0 0
\(361\) −4.33700 + 7.51190i −0.228263 + 0.395363i
\(362\) −0.0398950 + 0.456002i −0.00209684 + 0.0239670i
\(363\) 0 0
\(364\) −5.80035 1.02276i −0.304021 0.0536071i
\(365\) 0.0309719 + 12.6486i 0.00162114 + 0.662057i
\(366\) 0 0
\(367\) −11.9998 1.04985i −0.626385 0.0548016i −0.230456 0.973083i \(-0.574022\pi\)
−0.395929 + 0.918281i \(0.629577\pi\)
\(368\) 1.97004 0.527871i 0.102695 0.0275172i
\(369\) 0 0
\(370\) −0.185590 + 2.18286i −0.00964838 + 0.113481i
\(371\) 1.79623 4.93511i 0.0932558 0.256218i
\(372\) 0 0
\(373\) 10.0076 0.875548i 0.518172 0.0453341i 0.174929 0.984581i \(-0.444030\pi\)
0.343242 + 0.939247i \(0.388475\pi\)
\(374\) −0.840527 + 0.305927i −0.0434626 + 0.0158191i
\(375\) 0 0
\(376\) −0.185790 1.05367i −0.00958138 0.0543387i
\(377\) −11.1663 + 11.1663i −0.575095 + 0.575095i
\(378\) 0 0
\(379\) 10.8604i 0.557863i −0.960311 0.278932i \(-0.910020\pi\)
0.960311 0.278932i \(-0.0899803\pi\)
\(380\) 6.00268 12.9555i 0.307931 0.664604i
\(381\) 0 0
\(382\) −0.0571923 0.0266692i −0.00292621 0.00136451i
\(383\) −0.230605 2.63583i −0.0117834 0.134685i 0.988024 0.154299i \(-0.0493118\pi\)
−0.999808 + 0.0196141i \(0.993756\pi\)
\(384\) 0 0
\(385\) 2.21531 + 0.385029i 0.112903 + 0.0196229i
\(386\) 1.94865 1.12506i 0.0991839 0.0572639i
\(387\) 0 0
\(388\) 3.19063 + 11.9076i 0.161980 + 0.604517i
\(389\) −21.4540 + 18.0020i −1.08776 + 0.912739i −0.996542 0.0830919i \(-0.973520\pi\)
−0.0912181 + 0.995831i \(0.529076\pi\)
\(390\) 0 0
\(391\) −0.578353 + 3.28001i −0.0292486 + 0.165877i
\(392\) 1.64116 + 2.34382i 0.0828912 + 0.118381i
\(393\) 0 0
\(394\) 1.21561 + 1.44871i 0.0612418 + 0.0729851i
\(395\) −9.21150 19.6285i −0.463481 0.987617i
\(396\) 0 0
\(397\) 1.22098 4.55674i 0.0612790 0.228696i −0.928494 0.371347i \(-0.878896\pi\)
0.989773 + 0.142651i \(0.0455626\pi\)
\(398\) 1.15514 + 2.47720i 0.0579018 + 0.124171i
\(399\) 0 0
\(400\) 6.61863 18.4654i 0.330932 0.923271i
\(401\) −1.42496 3.91506i −0.0711593 0.195509i 0.899015 0.437919i \(-0.144284\pi\)
−0.970174 + 0.242410i \(0.922062\pi\)
\(402\) 0 0
\(403\) 21.9520 + 15.3709i 1.09351 + 0.765681i
\(404\) −2.08065 −0.103516
\(405\) 0 0
\(406\) −0.401902 −0.0199461
\(407\) 8.72964 + 6.11256i 0.432712 + 0.302988i
\(408\) 0 0
\(409\) −4.16426 11.4412i −0.205910 0.565732i 0.793153 0.609023i \(-0.208438\pi\)
−0.999063 + 0.0432906i \(0.986216\pi\)
\(410\) −1.14517 + 1.99475i −0.0565558 + 0.0985138i
\(411\) 0 0
\(412\) −4.60348 9.87218i −0.226797 0.486368i
\(413\) −2.91426 + 10.8761i −0.143401 + 0.535180i
\(414\) 0 0
\(415\) 17.4593 + 6.30630i 0.857044 + 0.309564i
\(416\) −3.14715 3.75063i −0.154302 0.183890i
\(417\) 0 0
\(418\) 0.257334 + 0.367510i 0.0125866 + 0.0179755i
\(419\) 1.06706 6.05161i 0.0521294 0.295641i −0.947586 0.319501i \(-0.896485\pi\)
0.999715 + 0.0238606i \(0.00759578\pi\)
\(420\) 0 0
\(421\) −3.35083 + 2.81168i −0.163309 + 0.137033i −0.720780 0.693164i \(-0.756216\pi\)
0.557471 + 0.830197i \(0.311772\pi\)
\(422\) −0.819602 3.05880i −0.0398976 0.148900i
\(423\) 0 0
\(424\) 2.51787 1.45369i 0.122278 0.0705975i
\(425\) 22.7614 + 22.5395i 1.10409 + 1.09333i
\(426\) 0 0
\(427\) 0.228391 + 2.61052i 0.0110526 + 0.126332i
\(428\) −18.8869 8.80709i −0.912931 0.425707i
\(429\) 0 0
\(430\) 1.29305 + 0.599110i 0.0623566 + 0.0288917i
\(431\) 30.2828i 1.45867i −0.684157 0.729335i \(-0.739830\pi\)
0.684157 0.729335i \(-0.260170\pi\)
\(432\) 0 0
\(433\) 10.8459 10.8459i 0.521222 0.521222i −0.396718 0.917941i \(-0.629851\pi\)
0.917941 + 0.396718i \(0.129851\pi\)
\(434\) 0.118433 + 0.671669i 0.00568498 + 0.0322411i
\(435\) 0 0
\(436\) 24.8214 9.03424i 1.18873 0.432662i
\(437\) 1.66420 0.145599i 0.0796097 0.00696494i
\(438\) 0 0
\(439\) −7.27898 + 19.9988i −0.347407 + 0.954492i 0.635777 + 0.771873i \(0.280680\pi\)
−0.983184 + 0.182619i \(0.941543\pi\)
\(440\) 0.802453 + 0.951585i 0.0382555 + 0.0453650i
\(441\) 0 0
\(442\) 2.54663 0.682368i 0.121131 0.0324569i
\(443\) 38.2232 + 3.34409i 1.81604 + 0.158883i 0.943869 0.330321i \(-0.107157\pi\)
0.872169 + 0.489204i \(0.162713\pi\)
\(444\) 0 0
\(445\) 2.17370 2.18437i 0.103043 0.103549i
\(446\) −0.483993 0.0853411i −0.0229177 0.00404102i
\(447\) 0 0
\(448\) −0.547148 + 6.25393i −0.0258503 + 0.295470i
\(449\) −13.8474 + 23.9843i −0.653497 + 1.13189i 0.328771 + 0.944410i \(0.393366\pi\)
−0.982268 + 0.187481i \(0.939968\pi\)
\(450\) 0 0
\(451\) 5.59447 + 9.68991i 0.263433 + 0.456280i
\(452\) −24.8589 + 11.5919i −1.16927 + 0.545237i
\(453\) 0 0
\(454\) −1.85369 + 2.20915i −0.0869981 + 0.103680i
\(455\) −6.40592 1.69966i −0.300314 0.0796813i
\(456\) 0 0
\(457\) −9.23637 + 13.1909i −0.432059 + 0.617044i −0.974860 0.222817i \(-0.928475\pi\)
0.542801 + 0.839861i \(0.317364\pi\)
\(458\) 0.413338 + 0.413338i 0.0193140 + 0.0193140i
\(459\) 0 0
\(460\) 2.27393 0.406699i 0.106023 0.0189625i
\(461\) 4.66067 0.821802i 0.217069 0.0382751i −0.0640559 0.997946i \(-0.520404\pi\)
0.281125 + 0.959671i \(0.409292\pi\)
\(462\) 0 0
\(463\) −0.268361 + 0.575502i −0.0124718 + 0.0267458i −0.912445 0.409199i \(-0.865808\pi\)
0.899973 + 0.435945i \(0.143586\pi\)
\(464\) 13.0655 + 10.9632i 0.606549 + 0.508955i
\(465\) 0 0
\(466\) −0.832350 0.302951i −0.0385579 0.0140339i
\(467\) −10.3035 2.76083i −0.476791 0.127756i 0.0124169 0.999923i \(-0.496047\pi\)
−0.489208 + 0.872167i \(0.662714\pi\)
\(468\) 0 0
\(469\) 8.43036 + 4.86727i 0.389278 + 0.224750i
\(470\) −0.0537595 0.597616i −0.00247974 0.0275660i
\(471\) 0 0
\(472\) −5.10607 + 3.57531i −0.235026 + 0.164567i
\(473\) 5.67876 3.97631i 0.261110 0.182831i
\(474\) 0 0
\(475\) 7.96529 13.9537i 0.365472 0.640237i
\(476\) −8.99644 5.19410i −0.412351 0.238071i
\(477\) 0 0
\(478\) −1.26469 0.338874i −0.0578458 0.0154997i
\(479\) −6.25290 2.27587i −0.285702 0.103987i 0.195194 0.980765i \(-0.437466\pi\)
−0.480896 + 0.876777i \(0.659689\pi\)
\(480\) 0 0
\(481\) −24.0626 20.1909i −1.09716 0.920626i
\(482\) 0.725524 1.55589i 0.0330467 0.0708689i
\(483\) 0 0
\(484\) −18.5547 + 3.27169i −0.843396 + 0.148713i
\(485\) 2.44225 + 13.6551i 0.110897 + 0.620045i
\(486\) 0 0
\(487\) −9.82088 9.82088i −0.445027 0.445027i 0.448671 0.893697i \(-0.351898\pi\)
−0.893697 + 0.448671i \(0.851898\pi\)
\(488\) −0.832081 + 1.18833i −0.0376665 + 0.0537934i
\(489\) 0 0
\(490\) 0.805726 + 1.38770i 0.0363990 + 0.0626899i
\(491\) 3.96956 4.73074i 0.179144 0.213495i −0.668999 0.743264i \(-0.733277\pi\)
0.848142 + 0.529769i \(0.177721\pi\)
\(492\) 0 0
\(493\) −25.2428 + 11.7709i −1.13688 + 0.530136i
\(494\) −0.661198 1.14523i −0.0297487 0.0515263i
\(495\) 0 0
\(496\) 14.4719 25.0660i 0.649805 1.12550i
\(497\) 0.340127 3.88767i 0.0152568 0.174386i
\(498\) 0 0
\(499\) −0.467311 0.0823996i −0.0209197 0.00368871i 0.163179 0.986597i \(-0.447825\pi\)
−0.184098 + 0.982908i \(0.558936\pi\)
\(500\) 9.24122 20.2040i 0.413280 0.903552i
\(501\) 0 0
\(502\) −1.80234 0.157684i −0.0804422 0.00703778i
\(503\) 18.5422 4.96837i 0.826756 0.221529i 0.179458 0.983766i \(-0.442566\pi\)
0.647298 + 0.762237i \(0.275899\pi\)
\(504\) 0 0
\(505\) −2.33285 0.198343i −0.103810 0.00882614i
\(506\) −0.0248249 + 0.0682057i −0.00110360 + 0.00303211i
\(507\) 0 0
\(508\) −23.0927 + 2.02035i −1.02457 + 0.0896385i
\(509\) 4.28872 1.56097i 0.190094 0.0691886i −0.245219 0.969468i \(-0.578860\pi\)
0.435313 + 0.900279i \(0.356638\pi\)
\(510\) 0 0
\(511\) −0.801508 4.54558i −0.0354566 0.201084i
\(512\) −6.24544 + 6.24544i −0.276012 + 0.276012i
\(513\) 0 0
\(514\) 2.61896i 0.115517i
\(515\) −4.22038 11.5076i −0.185972 0.507087i
\(516\) 0 0
\(517\) −2.64540 1.23357i −0.116344 0.0542523i
\(518\) −0.0696754 0.796393i −0.00306136 0.0349915i
\(519\) 0 0
\(520\) −2.11179 3.00029i −0.0926081 0.131571i
\(521\) −12.7475 + 7.35977i −0.558478 + 0.322437i −0.752534 0.658553i \(-0.771169\pi\)
0.194057 + 0.980990i \(0.437835\pi\)
\(522\) 0 0
\(523\) 3.33822 + 12.4584i 0.145970 + 0.544768i 0.999710 + 0.0240685i \(0.00766199\pi\)
−0.853740 + 0.520699i \(0.825671\pi\)
\(524\) 9.17877 7.70190i 0.400976 0.336459i
\(525\) 0 0
\(526\) −0.00228734 + 0.0129721i −9.97326e−5 + 0.000565611i
\(527\) 27.1105 + 38.7178i 1.18095 + 1.68657i
\(528\) 0 0
\(529\) −14.6104 17.4120i −0.635234 0.757043i
\(530\) 1.47605 0.692699i 0.0641155 0.0300889i
\(531\) 0 0
\(532\) −1.34858 + 5.03295i −0.0584682 + 0.218206i
\(533\) −13.9378 29.8897i −0.603712 1.29467i
\(534\) 0 0
\(535\) −20.3366 11.6750i −0.879227 0.504756i
\(536\) 1.84314 + 5.06398i 0.0796114 + 0.218731i
\(537\) 0 0
\(538\) 1.53876 + 1.07745i 0.0663405 + 0.0464521i
\(539\) 7.80591 0.336224
\(540\) 0 0
\(541\) 26.5994 1.14360 0.571798 0.820394i \(-0.306246\pi\)
0.571798 + 0.820394i \(0.306246\pi\)
\(542\) 2.92290 + 2.04664i 0.125550 + 0.0879107i
\(543\) 0 0
\(544\) −2.95352 8.11472i −0.126631 0.347916i
\(545\) 28.6912 7.76313i 1.22900 0.332536i
\(546\) 0 0
\(547\) 2.39975 + 5.14628i 0.102606 + 0.220039i 0.950908 0.309473i \(-0.100153\pi\)
−0.848302 + 0.529512i \(0.822375\pi\)
\(548\) 6.89080 25.7168i 0.294360 1.09857i
\(549\) 0 0
\(550\) 0.403201 + 0.569871i 0.0171926 + 0.0242994i
\(551\) 8.97986 + 10.7018i 0.382555 + 0.455911i
\(552\) 0 0
\(553\) 4.53831 + 6.48138i 0.192989 + 0.275616i
\(554\) −0.0222469 + 0.126169i −0.000945181 + 0.00536039i
\(555\) 0 0
\(556\) −10.3411 + 8.67719i −0.438559 + 0.367995i
\(557\) −8.94116 33.3689i −0.378849 1.41388i −0.847638 0.530575i \(-0.821976\pi\)
0.468789 0.883310i \(-0.344690\pi\)
\(558\) 0 0
\(559\) −17.6960 + 10.2168i −0.748463 + 0.432125i
\(560\) −1.22573 + 7.05240i −0.0517966 + 0.298018i
\(561\) 0 0
\(562\) −0.245748 2.80891i −0.0103662 0.118487i
\(563\) 20.2108 + 9.42446i 0.851785 + 0.397194i 0.798941 0.601409i \(-0.205394\pi\)
0.0528435 + 0.998603i \(0.483172\pi\)
\(564\) 0 0
\(565\) −28.9771 + 10.6272i −1.21908 + 0.447091i
\(566\) 2.60383i 0.109447i
\(567\) 0 0
\(568\) 1.52764 1.52764i 0.0640983 0.0640983i
\(569\) −7.59648 43.0818i −0.318461 1.80608i −0.552121 0.833764i \(-0.686181\pi\)
0.233660 0.972318i \(-0.424930\pi\)
\(570\) 0 0
\(571\) −6.30344 + 2.29426i −0.263791 + 0.0960119i −0.470530 0.882384i \(-0.655937\pi\)
0.206739 + 0.978396i \(0.433715\pi\)
\(572\) −8.86138 + 0.775270i −0.370513 + 0.0324157i
\(573\) 0 0
\(574\) 0.287073 0.788726i 0.0119822 0.0329208i
\(575\) 2.58833 0.239228i 0.107941 0.00997648i
\(576\) 0 0
\(577\) 4.79931 1.28597i 0.199798 0.0535357i −0.157532 0.987514i \(-0.550354\pi\)
0.357330 + 0.933978i \(0.383687\pi\)
\(578\) 2.71371 + 0.237419i 0.112876 + 0.00987533i
\(579\) 0 0
\(580\) 13.6931 + 13.6262i 0.568573 + 0.565796i
\(581\) −6.67116 1.17631i −0.276767 0.0488014i
\(582\) 0 0
\(583\) 0.691292 7.90150i 0.0286304 0.327247i
\(584\) 1.27761 2.21288i 0.0528679 0.0915698i
\(585\) 0 0
\(586\) −0.991533 1.71739i −0.0409599 0.0709446i
\(587\) −38.3006 + 17.8599i −1.58084 + 0.737156i −0.997194 0.0748562i \(-0.976150\pi\)
−0.583641 + 0.812012i \(0.698372\pi\)
\(588\) 0 0
\(589\) 15.2389 18.1610i 0.627906 0.748310i
\(590\) −3.02314 + 1.75529i −0.124461 + 0.0722643i
\(591\) 0 0
\(592\) −19.4592 + 27.7906i −0.799768 + 1.14219i
\(593\) −5.82461 5.82461i −0.239188 0.239188i 0.577326 0.816514i \(-0.304096\pi\)
−0.816514 + 0.577326i \(0.804096\pi\)
\(594\) 0 0
\(595\) −9.59176 6.68128i −0.393224 0.273906i
\(596\) −31.0378 + 5.47281i −1.27136 + 0.224175i
\(597\) 0 0
\(598\) 0.0904149 0.193895i 0.00369734 0.00792897i
\(599\) −4.98951 4.18670i −0.203866 0.171064i 0.535139 0.844764i \(-0.320259\pi\)
−0.739005 + 0.673700i \(0.764704\pi\)
\(600\) 0 0
\(601\) 22.5591 + 8.21084i 0.920205 + 0.334927i 0.758320 0.651882i \(-0.226020\pi\)
0.161885 + 0.986810i \(0.448243\pi\)
\(602\) −0.502325 0.134597i −0.0204732 0.00548578i
\(603\) 0 0
\(604\) 1.74696 + 1.00861i 0.0710827 + 0.0410396i
\(605\) −21.1156 + 1.89949i −0.858472 + 0.0772252i
\(606\) 0 0
\(607\) −24.5836 + 17.2136i −0.997817 + 0.698679i −0.953828 0.300353i \(-0.902896\pi\)
−0.0439890 + 0.999032i \(0.514007\pi\)
\(608\) −3.54806 + 2.48438i −0.143893 + 0.100755i
\(609\) 0 0
\(610\) −0.521425 + 0.624510i −0.0211119 + 0.0252857i
\(611\) 7.45079 + 4.30172i 0.301427 + 0.174029i
\(612\) 0 0
\(613\) −8.77093 2.35016i −0.354255 0.0949223i 0.0773029 0.997008i \(-0.475369\pi\)
−0.431558 + 0.902085i \(0.642036\pi\)
\(614\) −0.0981589 0.0357269i −0.00396137 0.00144182i
\(615\) 0 0
\(616\) −0.347966 0.291978i −0.0140199 0.0117641i
\(617\) 5.96112 12.7837i 0.239986 0.514651i −0.749017 0.662551i \(-0.769474\pi\)
0.989002 + 0.147900i \(0.0472515\pi\)
\(618\) 0 0
\(619\) 3.14514 0.554573i 0.126414 0.0222902i −0.110083 0.993922i \(-0.535112\pi\)
0.236497 + 0.971632i \(0.424001\pi\)
\(620\) 18.7373 26.8995i 0.752507 1.08031i
\(621\) 0 0
\(622\) 0.671311 + 0.671311i 0.0269171 + 0.0269171i
\(623\) −0.645009 + 0.921168i −0.0258417 + 0.0369058i
\(624\) 0 0
\(625\) 12.2873 21.7720i 0.491494 0.870881i
\(626\) −0.115556 + 0.137714i −0.00461853 + 0.00550415i
\(627\) 0 0
\(628\) 28.1041 13.1051i 1.12147 0.522952i
\(629\) −27.7010 47.9795i −1.10451 1.91307i
\(630\) 0 0
\(631\) 4.87996 8.45234i 0.194268 0.336482i −0.752392 0.658715i \(-0.771100\pi\)
0.946660 + 0.322233i \(0.104434\pi\)
\(632\) −0.381759 + 4.36353i −0.0151856 + 0.173572i
\(633\) 0 0
\(634\) −1.13870 0.200784i −0.0452236 0.00797414i
\(635\) −26.0844 + 0.0638713i −1.03513 + 0.00253465i
\(636\) 0 0
\(637\) −22.9205 2.00529i −0.908144 0.0794523i
\(638\) −0.586298 + 0.157098i −0.0232118 + 0.00621957i
\(639\) 0 0
\(640\) −6.09822 + 5.14251i −0.241053 + 0.203276i
\(641\) 3.49998 9.61611i 0.138241 0.379813i −0.851183 0.524870i \(-0.824114\pi\)
0.989423 + 0.145056i \(0.0463363\pi\)
\(642\) 0 0
\(643\) −13.9040 + 1.21644i −0.548320 + 0.0479718i −0.357950 0.933741i \(-0.616524\pi\)
−0.190370 + 0.981712i \(0.560969\pi\)
\(644\) −0.792127 + 0.288311i −0.0312142 + 0.0113610i
\(645\) 0 0
\(646\) −0.405013 2.29694i −0.0159350 0.0903720i
\(647\) 26.7302 26.7302i 1.05087 1.05087i 0.0522394 0.998635i \(-0.483364\pi\)
0.998635 0.0522394i \(-0.0166359\pi\)
\(648\) 0 0
\(649\) 17.0053i 0.667518i
\(650\) −1.03753 1.77689i −0.0406951 0.0696955i
\(651\) 0 0
\(652\) −3.18455 1.48498i −0.124717 0.0581563i
\(653\) −0.358345 4.09590i −0.0140231 0.160285i 0.985954 0.167016i \(-0.0534131\pi\)
−0.999977 + 0.00673072i \(0.997858\pi\)
\(654\) 0 0
\(655\) 11.0255 7.76046i 0.430803 0.303226i
\(656\) −30.8476 + 17.8099i −1.20440 + 0.695359i
\(657\) 0 0
\(658\) 0.0566713 + 0.211500i 0.00220928 + 0.00824513i
\(659\) −23.3538 + 19.5962i −0.909736 + 0.763359i −0.972069 0.234697i \(-0.924590\pi\)
0.0623330 + 0.998055i \(0.480146\pi\)
\(660\) 0 0
\(661\) −2.49857 + 14.1701i −0.0971833 + 0.551154i 0.896873 + 0.442288i \(0.145833\pi\)
−0.994056 + 0.108866i \(0.965278\pi\)
\(662\) −0.515863 0.736728i −0.0200496 0.0286338i
\(663\) 0 0
\(664\) −2.41051 2.87273i −0.0935458 0.111484i
\(665\) −1.99182 + 5.51444i −0.0772393 + 0.213841i
\(666\) 0 0
\(667\) −0.584963 + 2.18311i −0.0226498 + 0.0845304i
\(668\) 4.10841 + 8.81052i 0.158959 + 0.340889i
\(669\) 0 0
\(670\) 0.789355 + 2.91732i 0.0304955 + 0.112706i
\(671\) 1.35360 + 3.71898i 0.0522550 + 0.143570i
\(672\) 0 0
\(673\) 3.89377 + 2.72645i 0.150094 + 0.105097i 0.646211 0.763159i \(-0.276353\pi\)
−0.496117 + 0.868255i \(0.665241\pi\)
\(674\) −0.271508 −0.0104581
\(675\) 0 0
\(676\) 0.385711 0.0148350
\(677\) 24.2852 + 17.0047i 0.933356 + 0.653543i 0.938070 0.346446i \(-0.112612\pi\)
−0.00471373 + 0.999989i \(0.501500\pi\)
\(678\) 0 0
\(679\) −1.73132 4.75677i −0.0664420 0.182548i
\(680\) −1.69016 6.24654i −0.0648146 0.239544i
\(681\) 0 0
\(682\) 0.435318 + 0.933541i 0.0166692 + 0.0357472i
\(683\) −2.52954 + 9.44037i −0.0967901 + 0.361226i −0.997285 0.0736414i \(-0.976538\pi\)
0.900495 + 0.434867i \(0.143205\pi\)
\(684\) 0 0
\(685\) 10.1776 28.1771i 0.388864 1.07659i
\(686\) −0.792353 0.944289i −0.0302522 0.0360531i
\(687\) 0 0
\(688\) 12.6585 + 18.0782i 0.482601 + 0.689225i
\(689\) −4.05968 + 23.0236i −0.154662 + 0.877130i
\(690\) 0 0
\(691\) 5.93833 4.98285i 0.225905 0.189556i −0.522809 0.852450i \(-0.675116\pi\)
0.748714 + 0.662893i \(0.230672\pi\)
\(692\) 1.21015 + 4.51634i 0.0460030 + 0.171685i
\(693\) 0 0
\(694\) 2.35568 1.36005i 0.0894204 0.0516269i
\(695\) −12.4217 + 8.74317i −0.471181 + 0.331647i
\(696\) 0 0
\(697\) −5.06966 57.9464i −0.192027 2.19488i
\(698\) −1.89886 0.885454i −0.0718730 0.0335149i
\(699\) 0 0
\(700\) −2.05998 + 7.84135i −0.0778599 + 0.296375i
\(701\) 11.8234i 0.446564i 0.974754 + 0.223282i \(0.0716771\pi\)
−0.974754 + 0.223282i \(0.928323\pi\)
\(702\) 0 0
\(703\) −19.6494 + 19.6494i −0.741092 + 0.741092i
\(704\) 1.64639 + 9.33714i 0.0620507 + 0.351907i
\(705\) 0 0
\(706\) 3.07379 1.11877i 0.115684 0.0421055i
\(707\) 0.851116 0.0744630i 0.0320095 0.00280047i
\(708\) 0 0
\(709\) −9.00610 + 24.7441i −0.338231 + 0.929283i 0.647665 + 0.761925i \(0.275746\pi\)
−0.985896 + 0.167357i \(0.946477\pi\)
\(710\) 0.926224 0.781067i 0.0347606 0.0293129i
\(711\) 0 0
\(712\) −0.601324 + 0.161124i −0.0225356 + 0.00603839i
\(713\) 3.82084 + 0.334281i 0.143092 + 0.0125189i
\(714\) 0 0
\(715\) −10.0094 + 0.0245094i −0.374329 + 0.000916599i
\(716\) 37.9685 + 6.69487i 1.41895 + 0.250199i
\(717\) 0 0
\(718\) 0.293435 3.35397i 0.0109509 0.125169i
\(719\) 15.9538 27.6328i 0.594977 1.03053i −0.398573 0.917136i \(-0.630495\pi\)
0.993550 0.113393i \(-0.0361721\pi\)
\(720\) 0 0
\(721\) 2.23642 + 3.87359i 0.0832885 + 0.144260i
\(722\) 0.890637 0.415311i 0.0331461 0.0154563i
\(723\) 0 0
\(724\) −5.16082 + 6.15042i −0.191800 + 0.228579i
\(725\) 14.0539 + 16.5831i 0.521947 + 0.615881i
\(726\) 0 0
\(727\) 12.2503 17.4952i 0.454338 0.648863i −0.524997 0.851104i \(-0.675934\pi\)
0.979336 + 0.202241i \(0.0648225\pi\)
\(728\) 0.946725 + 0.946725i 0.0350880 + 0.0350880i
\(729\) 0 0
\(730\) 0.819064 1.17586i 0.0303149 0.0435206i
\(731\) −35.4923 + 6.25825i −1.31273 + 0.231470i
\(732\) 0 0
\(733\) 15.6653 33.5943i 0.578611 1.24083i −0.371358 0.928490i \(-0.621108\pi\)
0.949969 0.312345i \(-0.101114\pi\)
\(734\) 1.04542 + 0.877209i 0.0385870 + 0.0323784i
\(735\) 0 0
\(736\) −0.658480 0.239667i −0.0242719 0.00883425i
\(737\) 14.2008 + 3.80510i 0.523094 + 0.140163i
\(738\) 0 0
\(739\) −0.0105302 0.00607959i −0.000387358 0.000223641i 0.499806 0.866137i \(-0.333405\pi\)
−0.500194 + 0.865914i \(0.666738\pi\)
\(740\) −24.6272 + 29.4959i −0.905312 + 1.08429i
\(741\) 0 0
\(742\) −0.487396 + 0.341278i −0.0178929 + 0.0125287i
\(743\) 16.1496 11.3081i 0.592471 0.414852i −0.238521 0.971137i \(-0.576663\pi\)
0.830992 + 0.556285i \(0.187774\pi\)
\(744\) 0 0
\(745\) −35.3216 + 3.17741i −1.29408 + 0.116411i
\(746\) −0.985644 0.569062i −0.0360870 0.0208348i
\(747\) 0 0
\(748\) −15.1544 4.06060i −0.554099 0.148470i
\(749\) 8.04109 + 2.92672i 0.293815 + 0.106940i
\(750\) 0 0
\(751\) −25.5632 21.4501i −0.932814 0.782724i 0.0435062 0.999053i \(-0.486147\pi\)
−0.976321 + 0.216329i \(0.930592\pi\)
\(752\) 3.92704 8.42156i 0.143204 0.307103i
\(753\) 0 0
\(754\) 1.76191 0.310672i 0.0641648 0.0113140i
\(755\) 1.86256 + 1.29739i 0.0677855 + 0.0472170i
\(756\) 0 0
\(757\) 28.4224 + 28.4224i 1.03303 + 1.03303i 0.999436 + 0.0335950i \(0.0106956\pi\)
0.0335950 + 0.999436i \(0.489304\pi\)
\(758\) −0.705739 + 1.00790i −0.0256336 + 0.0366086i
\(759\) 0 0
\(760\) −2.80696 + 1.62978i −0.101819 + 0.0591182i
\(761\) 14.3996 17.1608i 0.521985 0.622078i −0.439064 0.898456i \(-0.644690\pi\)
0.961049 + 0.276378i \(0.0891342\pi\)
\(762\) 0 0
\(763\) −9.83017 + 4.58388i −0.355876 + 0.165948i
\(764\) −0.553426 0.958563i −0.0200223 0.0346796i
\(765\) 0 0
\(766\) −0.149882 + 0.259603i −0.00541545 + 0.00937983i
\(767\) 4.36856 49.9328i 0.157739 1.80297i
\(768\) 0 0
\(769\) 3.68867 + 0.650412i 0.133017 + 0.0234545i 0.239760 0.970832i \(-0.422931\pi\)
−0.106743 + 0.994287i \(0.534042\pi\)
\(770\) −0.180571 0.179689i −0.00650734 0.00647555i
\(771\) 0 0
\(772\) 39.3167 + 3.43976i 1.41504 + 0.123800i
\(773\) −10.7936 + 2.89214i −0.388220 + 0.104023i −0.447649 0.894209i \(-0.647739\pi\)
0.0594292 + 0.998233i \(0.481072\pi\)
\(774\) 0 0
\(775\) 23.5727 28.3739i 0.846756 1.01922i
\(776\) 0.958447 2.63331i 0.0344063 0.0945304i
\(777\) 0 0
\(778\) 3.16085 0.276538i 0.113322 0.00991439i
\(779\) −27.4162 + 9.97869i −0.982288 + 0.357524i
\(780\) 0 0
\(781\) −1.02346 5.80431i −0.0366222 0.207695i
\(782\) 0.266817 0.266817i 0.00954136 0.00954136i
\(783\) 0 0
\(784\) 24.8499i 0.887498i
\(785\) 32.7598 12.0145i 1.16925 0.428817i
\(786\) 0 0