Properties

Label 490.2.g.c.293.1
Level $490$
Weight $2$
Character 490.293
Analytic conductor $3.913$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.91266969904\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 10 x^{14} + 61 x^{12} + 266 x^{10} + 852 x^{8} + 1438 x^{6} + 1933 x^{4} + 3038 x^{2} + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 293.1
Root \(0.587308 - 2.01725i\) of defining polynomial
Character \(\chi\) \(=\) 490.293
Dual form 490.2.g.c.97.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-2.05532 + 2.05532i) q^{3} -1.00000i q^{4} +(-0.830578 - 2.07609i) q^{5} -2.90667i q^{6} +(0.707107 + 0.707107i) q^{8} -5.44871i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-2.05532 + 2.05532i) q^{3} -1.00000i q^{4} +(-0.830578 - 2.07609i) q^{5} -2.90667i q^{6} +(0.707107 + 0.707107i) q^{8} -5.44871i q^{9} +(2.05532 + 0.880708i) q^{10} +3.67114 q^{11} +(2.05532 + 2.05532i) q^{12} +(-0.830578 + 0.830578i) q^{13} +(5.97414 + 2.55992i) q^{15} -1.00000 q^{16} +(0.557436 + 0.557436i) q^{17} +(3.85282 + 3.85282i) q^{18} +2.18923 q^{19} +(-2.07609 + 0.830578i) q^{20} +(-2.59589 + 2.59589i) q^{22} +(3.32739 + 3.32739i) q^{23} -2.90667 q^{24} +(-3.62028 + 3.44871i) q^{25} -1.17462i q^{26} +(5.03288 + 5.03288i) q^{27} -2.62236i q^{29} +(-6.03449 + 2.41421i) q^{30} -0.0415289i q^{31} +(0.707107 - 0.707107i) q^{32} +(-7.54538 + 7.54538i) q^{33} -0.788333 q^{34} -5.44871 q^{36} +(0.181676 - 0.181676i) q^{37} +(-1.54802 + 1.54802i) q^{38} -3.41421i q^{39} +(0.880708 - 2.05532i) q^{40} +8.98026i q^{41} +(-0.474569 - 0.474569i) q^{43} -3.67114i q^{44} +(-11.3120 + 4.52558i) q^{45} -4.70563 q^{46} +(4.52558 + 4.52558i) q^{47} +(2.05532 - 2.05532i) q^{48} +(0.121320 - 4.99853i) q^{50} -2.29142 q^{51} +(0.830578 + 0.830578i) q^{52} +(5.59589 + 5.59589i) q^{53} -7.11757 q^{54} +(-3.04917 - 7.62161i) q^{55} +(-4.49957 + 4.49957i) q^{57} +(1.85429 + 1.85429i) q^{58} +10.7123 q^{59} +(2.55992 - 5.97414i) q^{60} +1.99231i q^{61} +(0.0293654 + 0.0293654i) q^{62} +1.00000i q^{64} +(2.41421 + 1.03449i) q^{65} -10.6708i q^{66} +(-4.68272 + 4.68272i) q^{67} +(0.557436 - 0.557436i) q^{68} -13.6777 q^{69} +8.11777 q^{71} +(3.85282 - 3.85282i) q^{72} +(6.97578 - 6.97578i) q^{73} +0.256928i q^{74} +(0.352638 - 14.5291i) q^{75} -2.18923i q^{76} +(2.41421 + 2.41421i) q^{78} +13.4113i q^{79} +(0.830578 + 2.07609i) q^{80} -4.34228 q^{81} +(-6.35000 - 6.35000i) q^{82} +(9.73033 - 9.73033i) q^{83} +(0.694291 - 1.62028i) q^{85} +0.671142 q^{86} +(5.38980 + 5.38980i) q^{87} +(2.59589 + 2.59589i) q^{88} +1.43026 q^{89} +(4.79872 - 11.1989i) q^{90} +(3.32739 - 3.32739i) q^{92} +(0.0853553 + 0.0853553i) q^{93} -6.40013 q^{94} +(-1.81832 - 4.54503i) q^{95} +2.90667i q^{96} +(3.16693 + 3.16693i) q^{97} -20.0030i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q + 24 q^{11} + 16 q^{15} - 16 q^{16} + 16 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{25} - 40 q^{30} - 8 q^{36} - 8 q^{37} - 8 q^{43} + 16 q^{46} - 32 q^{50} + 32 q^{51} + 56 q^{53} + 8 q^{57} + 64 q^{58} - 16 q^{60} + 16 q^{65} - 64 q^{67} + 16 q^{71} + 16 q^{72} + 16 q^{78} + 24 q^{85} - 24 q^{86} + 8 q^{88} + 8 q^{92} - 56 q^{93} - 40 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −2.05532 + 2.05532i −1.18664 + 1.18664i −0.208651 + 0.977990i \(0.566907\pi\)
−0.977990 + 0.208651i \(0.933093\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −0.830578 2.07609i −0.371446 0.928455i
\(6\) 2.90667i 1.18664i
\(7\) 0 0
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 5.44871i 1.81624i
\(10\) 2.05532 + 0.880708i 0.649950 + 0.278504i
\(11\) 3.67114 1.10689 0.553445 0.832885i \(-0.313313\pi\)
0.553445 + 0.832885i \(0.313313\pi\)
\(12\) 2.05532 + 2.05532i 0.593321 + 0.593321i
\(13\) −0.830578 + 0.830578i −0.230361 + 0.230361i −0.812843 0.582482i \(-0.802082\pi\)
0.582482 + 0.812843i \(0.302082\pi\)
\(14\) 0 0
\(15\) 5.97414 + 2.55992i 1.54252 + 0.660970i
\(16\) −1.00000 −0.250000
\(17\) 0.557436 + 0.557436i 0.135198 + 0.135198i 0.771467 0.636269i \(-0.219523\pi\)
−0.636269 + 0.771467i \(0.719523\pi\)
\(18\) 3.85282 + 3.85282i 0.908118 + 0.908118i
\(19\) 2.18923 0.502243 0.251122 0.967956i \(-0.419201\pi\)
0.251122 + 0.967956i \(0.419201\pi\)
\(20\) −2.07609 + 0.830578i −0.464227 + 0.185723i
\(21\) 0 0
\(22\) −2.59589 + 2.59589i −0.553445 + 0.553445i
\(23\) 3.32739 + 3.32739i 0.693808 + 0.693808i 0.963068 0.269260i \(-0.0867790\pi\)
−0.269260 + 0.963068i \(0.586779\pi\)
\(24\) −2.90667 −0.593321
\(25\) −3.62028 + 3.44871i −0.724056 + 0.689741i
\(26\) 1.17462i 0.230361i
\(27\) 5.03288 + 5.03288i 0.968579 + 0.968579i
\(28\) 0 0
\(29\) 2.62236i 0.486960i −0.969906 0.243480i \(-0.921711\pi\)
0.969906 0.243480i \(-0.0782891\pi\)
\(30\) −6.03449 + 2.41421i −1.10174 + 0.440773i
\(31\) 0.0415289i 0.00745881i −0.999993 0.00372940i \(-0.998813\pi\)
0.999993 0.00372940i \(-0.00118711\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −7.54538 + 7.54538i −1.31348 + 1.31348i
\(34\) −0.788333 −0.135198
\(35\) 0 0
\(36\) −5.44871 −0.908118
\(37\) 0.181676 0.181676i 0.0298673 0.0298673i −0.692015 0.721883i \(-0.743277\pi\)
0.721883 + 0.692015i \(0.243277\pi\)
\(38\) −1.54802 + 1.54802i −0.251122 + 0.251122i
\(39\) 3.41421i 0.546712i
\(40\) 0.880708 2.05532i 0.139252 0.324975i
\(41\) 8.98026i 1.40248i 0.712925 + 0.701241i \(0.247370\pi\)
−0.712925 + 0.701241i \(0.752630\pi\)
\(42\) 0 0
\(43\) −0.474569 0.474569i −0.0723711 0.0723711i 0.669995 0.742366i \(-0.266296\pi\)
−0.742366 + 0.669995i \(0.766296\pi\)
\(44\) 3.67114i 0.553445i
\(45\) −11.3120 + 4.52558i −1.68629 + 0.674633i
\(46\) −4.70563 −0.693808
\(47\) 4.52558 + 4.52558i 0.660123 + 0.660123i 0.955409 0.295286i \(-0.0954148\pi\)
−0.295286 + 0.955409i \(0.595415\pi\)
\(48\) 2.05532 2.05532i 0.296660 0.296660i
\(49\) 0 0
\(50\) 0.121320 4.99853i 0.0171573 0.706899i
\(51\) −2.29142 −0.320863
\(52\) 0.830578 + 0.830578i 0.115180 + 0.115180i
\(53\) 5.59589 + 5.59589i 0.768654 + 0.768654i 0.977870 0.209215i \(-0.0670909\pi\)
−0.209215 + 0.977870i \(0.567091\pi\)
\(54\) −7.11757 −0.968579
\(55\) −3.04917 7.62161i −0.411150 1.02770i
\(56\) 0 0
\(57\) −4.49957 + 4.49957i −0.595982 + 0.595982i
\(58\) 1.85429 + 1.85429i 0.243480 + 0.243480i
\(59\) 10.7123 1.39462 0.697312 0.716768i \(-0.254379\pi\)
0.697312 + 0.716768i \(0.254379\pi\)
\(60\) 2.55992 5.97414i 0.330485 0.771258i
\(61\) 1.99231i 0.255090i 0.991833 + 0.127545i \(0.0407097\pi\)
−0.991833 + 0.127545i \(0.959290\pi\)
\(62\) 0.0293654 + 0.0293654i 0.00372940 + 0.00372940i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 2.41421 + 1.03449i 0.299446 + 0.128313i
\(66\) 10.6708i 1.31348i
\(67\) −4.68272 + 4.68272i −0.572085 + 0.572085i −0.932711 0.360626i \(-0.882563\pi\)
0.360626 + 0.932711i \(0.382563\pi\)
\(68\) 0.557436 0.557436i 0.0675990 0.0675990i
\(69\) −13.6777 −1.64660
\(70\) 0 0
\(71\) 8.11777 0.963402 0.481701 0.876336i \(-0.340019\pi\)
0.481701 + 0.876336i \(0.340019\pi\)
\(72\) 3.85282 3.85282i 0.454059 0.454059i
\(73\) 6.97578 6.97578i 0.816454 0.816454i −0.169139 0.985592i \(-0.554099\pi\)
0.985592 + 0.169139i \(0.0540985\pi\)
\(74\) 0.256928i 0.0298673i
\(75\) 0.352638 14.5291i 0.0407191 1.67767i
\(76\) 2.18923i 0.251122i
\(77\) 0 0
\(78\) 2.41421 + 2.41421i 0.273356 + 0.273356i
\(79\) 13.4113i 1.50889i 0.656366 + 0.754443i \(0.272093\pi\)
−0.656366 + 0.754443i \(0.727907\pi\)
\(80\) 0.830578 + 2.07609i 0.0928615 + 0.232114i
\(81\) −4.34228 −0.482476
\(82\) −6.35000 6.35000i −0.701241 0.701241i
\(83\) 9.73033 9.73033i 1.06804 1.06804i 0.0705331 0.997509i \(-0.477530\pi\)
0.997509 0.0705331i \(-0.0224700\pi\)
\(84\) 0 0
\(85\) 0.694291 1.62028i 0.0753065 0.175744i
\(86\) 0.671142 0.0723711
\(87\) 5.38980 + 5.38980i 0.577847 + 0.577847i
\(88\) 2.59589 + 2.59589i 0.276723 + 0.276723i
\(89\) 1.43026 0.151607 0.0758036 0.997123i \(-0.475848\pi\)
0.0758036 + 0.997123i \(0.475848\pi\)
\(90\) 4.79872 11.1989i 0.505829 1.18046i
\(91\) 0 0
\(92\) 3.32739 3.32739i 0.346904 0.346904i
\(93\) 0.0853553 + 0.0853553i 0.00885093 + 0.00885093i
\(94\) −6.40013 −0.660123
\(95\) −1.81832 4.54503i −0.186556 0.466310i
\(96\) 2.90667i 0.296660i
\(97\) 3.16693 + 3.16693i 0.321553 + 0.321553i 0.849363 0.527810i \(-0.176987\pi\)
−0.527810 + 0.849363i \(0.676987\pi\)
\(98\) 0 0
\(99\) 20.0030i 2.01037i
\(100\) 3.44871 + 3.62028i 0.344871 + 0.362028i
\(101\) 0.0719071i 0.00715503i 0.999994 + 0.00357751i \(0.00113876\pi\)
−0.999994 + 0.00357751i \(0.998861\pi\)
\(102\) 1.62028 1.62028i 0.160432 0.160432i
\(103\) 11.7237 11.7237i 1.15517 1.15517i 0.169664 0.985502i \(-0.445732\pi\)
0.985502 0.169664i \(-0.0542684\pi\)
\(104\) −1.17462 −0.115180
\(105\) 0 0
\(106\) −7.91378 −0.768654
\(107\) 3.23107 3.23107i 0.312359 0.312359i −0.533464 0.845823i \(-0.679110\pi\)
0.845823 + 0.533464i \(0.179110\pi\)
\(108\) 5.03288 5.03288i 0.484289 0.484289i
\(109\) 18.1026i 1.73392i −0.498381 0.866958i \(-0.666072\pi\)
0.498381 0.866958i \(-0.333928\pi\)
\(110\) 7.54538 + 3.23320i 0.719424 + 0.308274i
\(111\) 0.746804i 0.0708835i
\(112\) 0 0
\(113\) 1.52064 + 1.52064i 0.143049 + 0.143049i 0.775005 0.631955i \(-0.217747\pi\)
−0.631955 + 0.775005i \(0.717747\pi\)
\(114\) 6.36335i 0.595982i
\(115\) 4.14429 9.67160i 0.386457 0.901881i
\(116\) −2.62236 −0.243480
\(117\) 4.52558 + 4.52558i 0.418390 + 0.418390i
\(118\) −7.57475 + 7.57475i −0.697312 + 0.697312i
\(119\) 0 0
\(120\) 2.41421 + 6.03449i 0.220387 + 0.550871i
\(121\) 2.47728 0.225207
\(122\) −1.40878 1.40878i −0.127545 0.127545i
\(123\) −18.4573 18.4573i −1.66424 1.66424i
\(124\) −0.0415289 −0.00372940
\(125\) 10.1667 + 4.65160i 0.909341 + 0.416051i
\(126\) 0 0
\(127\) −13.2527 + 13.2527i −1.17599 + 1.17599i −0.195234 + 0.980757i \(0.562547\pi\)
−0.980757 + 0.195234i \(0.937453\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 1.95078 0.171757
\(130\) −2.43860 + 0.975610i −0.213880 + 0.0855666i
\(131\) 14.1946i 1.24019i 0.784527 + 0.620095i \(0.212906\pi\)
−0.784527 + 0.620095i \(0.787094\pi\)
\(132\) 7.54538 + 7.54538i 0.656741 + 0.656741i
\(133\) 0 0
\(134\) 6.62236i 0.572085i
\(135\) 6.26850 14.6289i 0.539507 1.25906i
\(136\) 0.788333i 0.0675990i
\(137\) −13.4113 + 13.4113i −1.14580 + 1.14580i −0.158432 + 0.987370i \(0.550644\pi\)
−0.987370 + 0.158432i \(0.949356\pi\)
\(138\) 9.67160 9.67160i 0.823301 0.823301i
\(139\) −8.23706 −0.698658 −0.349329 0.937000i \(-0.613591\pi\)
−0.349329 + 0.937000i \(0.613591\pi\)
\(140\) 0 0
\(141\) −18.6030 −1.56666
\(142\) −5.74013 + 5.74013i −0.481701 + 0.481701i
\(143\) −3.04917 + 3.04917i −0.254984 + 0.254984i
\(144\) 5.44871i 0.454059i
\(145\) −5.44425 + 2.17808i −0.452120 + 0.180879i
\(146\) 9.86525i 0.816454i
\(147\) 0 0
\(148\) −0.181676 0.181676i −0.0149336 0.0149336i
\(149\) 4.84185i 0.396660i −0.980135 0.198330i \(-0.936448\pi\)
0.980135 0.198330i \(-0.0635518\pi\)
\(150\) 10.0242 + 10.5229i 0.818476 + 0.859195i
\(151\) 10.0458 0.817519 0.408759 0.912642i \(-0.365962\pi\)
0.408759 + 0.912642i \(0.365962\pi\)
\(152\) 1.54802 + 1.54802i 0.125561 + 0.125561i
\(153\) 3.03730 3.03730i 0.245551 0.245551i
\(154\) 0 0
\(155\) −0.0862176 + 0.0344930i −0.00692516 + 0.00277054i
\(156\) −3.41421 −0.273356
\(157\) −17.3147 17.3147i −1.38186 1.38186i −0.841310 0.540553i \(-0.818215\pi\)
−0.540553 0.841310i \(-0.681785\pi\)
\(158\) −9.48320 9.48320i −0.754443 0.754443i
\(159\) −23.0027 −1.82423
\(160\) −2.05532 0.880708i −0.162488 0.0696261i
\(161\) 0 0
\(162\) 3.07046 3.07046i 0.241238 0.241238i
\(163\) −15.5320 15.5320i −1.21656 1.21656i −0.968829 0.247729i \(-0.920316\pi\)
−0.247729 0.968829i \(-0.579684\pi\)
\(164\) 8.98026 0.701241
\(165\) 21.9319 + 9.39784i 1.70740 + 0.731621i
\(166\) 13.7608i 1.06804i
\(167\) 3.14616 + 3.14616i 0.243457 + 0.243457i 0.818279 0.574821i \(-0.194928\pi\)
−0.574821 + 0.818279i \(0.694928\pi\)
\(168\) 0 0
\(169\) 11.6203i 0.893868i
\(170\) 0.654772 + 1.63665i 0.0502188 + 0.125525i
\(171\) 11.9285i 0.912192i
\(172\) −0.474569 + 0.474569i −0.0361855 + 0.0361855i
\(173\) 3.69572 3.69572i 0.280980 0.280980i −0.552520 0.833500i \(-0.686334\pi\)
0.833500 + 0.552520i \(0.186334\pi\)
\(174\) −7.62233 −0.577847
\(175\) 0 0
\(176\) −3.67114 −0.276723
\(177\) −22.0173 + 22.0173i −1.65492 + 1.65492i
\(178\) −1.01135 + 1.01135i −0.0758036 + 0.0758036i
\(179\) 12.5686i 0.939418i 0.882821 + 0.469709i \(0.155641\pi\)
−0.882821 + 0.469709i \(0.844359\pi\)
\(180\) 4.52558 + 11.3120i 0.337317 + 0.843146i
\(181\) 11.6742i 0.867740i −0.900976 0.433870i \(-0.857148\pi\)
0.900976 0.433870i \(-0.142852\pi\)
\(182\) 0 0
\(183\) −4.09485 4.09485i −0.302700 0.302700i
\(184\) 4.70563i 0.346904i
\(185\) −0.528070 0.226279i −0.0388245 0.0166363i
\(186\) −0.120711 −0.00885093
\(187\) 2.04643 + 2.04643i 0.149649 + 0.149649i
\(188\) 4.52558 4.52558i 0.330062 0.330062i
\(189\) 0 0
\(190\) 4.49957 + 1.92807i 0.326433 + 0.139877i
\(191\) 15.5034 1.12179 0.560894 0.827888i \(-0.310458\pi\)
0.560894 + 0.827888i \(0.310458\pi\)
\(192\) −2.05532 2.05532i −0.148330 0.148330i
\(193\) 6.36249 + 6.36249i 0.457982 + 0.457982i 0.897993 0.440011i \(-0.145025\pi\)
−0.440011 + 0.897993i \(0.645025\pi\)
\(194\) −4.47871 −0.321553
\(195\) −7.08821 + 2.83577i −0.507597 + 0.203074i
\(196\) 0 0
\(197\) 12.1951 12.1951i 0.868865 0.868865i −0.123482 0.992347i \(-0.539406\pi\)
0.992347 + 0.123482i \(0.0394061\pi\)
\(198\) 14.1442 + 14.1442i 1.00519 + 1.00519i
\(199\) 8.73115 0.618935 0.309467 0.950910i \(-0.399849\pi\)
0.309467 + 0.950910i \(0.399849\pi\)
\(200\) −4.99853 0.121320i −0.353449 0.00857864i
\(201\) 19.2490i 1.35772i
\(202\) −0.0508460 0.0508460i −0.00357751 0.00357751i
\(203\) 0 0
\(204\) 2.29142i 0.160432i
\(205\) 18.6438 7.45881i 1.30214 0.520946i
\(206\) 16.5798i 1.15517i
\(207\) 18.1300 18.1300i 1.26012 1.26012i
\(208\) 0.830578 0.830578i 0.0575902 0.0575902i
\(209\) 8.03696 0.555928
\(210\) 0 0
\(211\) −11.1745 −0.769288 −0.384644 0.923065i \(-0.625676\pi\)
−0.384644 + 0.923065i \(0.625676\pi\)
\(212\) 5.59589 5.59589i 0.384327 0.384327i
\(213\) −16.6846 + 16.6846i −1.14321 + 1.14321i
\(214\) 4.56942i 0.312359i
\(215\) −0.591080 + 1.37941i −0.0403113 + 0.0940752i
\(216\) 7.11757i 0.484289i
\(217\) 0 0
\(218\) 12.8005 + 12.8005i 0.866958 + 0.866958i
\(219\) 28.6750i 1.93768i
\(220\) −7.62161 + 3.04917i −0.513849 + 0.205575i
\(221\) −0.925988 −0.0622887
\(222\) −0.528070 0.528070i −0.0354418 0.0354418i
\(223\) −0.746804 + 0.746804i −0.0500097 + 0.0500097i −0.731669 0.681660i \(-0.761258\pi\)
0.681660 + 0.731669i \(0.261258\pi\)
\(224\) 0 0
\(225\) 18.7910 + 19.7258i 1.25273 + 1.31506i
\(226\) −2.15051 −0.143049
\(227\) 2.20643 + 2.20643i 0.146446 + 0.146446i 0.776528 0.630082i \(-0.216979\pi\)
−0.630082 + 0.776528i \(0.716979\pi\)
\(228\) 4.49957 + 4.49957i 0.297991 + 0.297991i
\(229\) 8.42181 0.556529 0.278264 0.960504i \(-0.410241\pi\)
0.278264 + 0.960504i \(0.410241\pi\)
\(230\) 3.90840 + 9.76931i 0.257712 + 0.644169i
\(231\) 0 0
\(232\) 1.85429 1.85429i 0.121740 0.121740i
\(233\) −16.1198 16.1198i −1.05605 1.05605i −0.998333 0.0577132i \(-0.981619\pi\)
−0.0577132 0.998333i \(-0.518381\pi\)
\(234\) −6.40013 −0.418390
\(235\) 5.63665 13.1543i 0.367694 0.858095i
\(236\) 10.7123i 0.697312i
\(237\) −27.5645 27.5645i −1.79051 1.79051i
\(238\) 0 0
\(239\) 23.9971i 1.55224i −0.630585 0.776120i \(-0.717185\pi\)
0.630585 0.776120i \(-0.282815\pi\)
\(240\) −5.97414 2.55992i −0.385629 0.165242i
\(241\) 24.7875i 1.59670i 0.602194 + 0.798350i \(0.294294\pi\)
−0.602194 + 0.798350i \(0.705706\pi\)
\(242\) −1.75170 + 1.75170i −0.112604 + 0.112604i
\(243\) −6.17385 + 6.17385i −0.396053 + 0.396053i
\(244\) 1.99231 0.127545
\(245\) 0 0
\(246\) 26.1026 1.66424
\(247\) −1.81832 + 1.81832i −0.115697 + 0.115697i
\(248\) 0.0293654 0.0293654i 0.00186470 0.00186470i
\(249\) 39.9979i 2.53477i
\(250\) −10.4781 + 3.89980i −0.662696 + 0.246645i
\(251\) 11.1158i 0.701623i 0.936446 + 0.350811i \(0.114094\pi\)
−0.936446 + 0.350811i \(0.885906\pi\)
\(252\) 0 0
\(253\) 12.2153 + 12.2153i 0.767970 + 0.767970i
\(254\) 18.7422i 1.17599i
\(255\) 1.90320 + 4.75719i 0.119183 + 0.297907i
\(256\) 1.00000 0.0625000
\(257\) −17.8850 17.8850i −1.11564 1.11564i −0.992374 0.123262i \(-0.960664\pi\)
−0.123262 0.992374i \(-0.539336\pi\)
\(258\) −1.37941 + 1.37941i −0.0858785 + 0.0858785i
\(259\) 0 0
\(260\) 1.03449 2.41421i 0.0641565 0.149723i
\(261\) −14.2885 −0.884435
\(262\) −10.0371 10.0371i −0.620095 0.620095i
\(263\) 8.02292 + 8.02292i 0.494714 + 0.494714i 0.909788 0.415074i \(-0.136244\pi\)
−0.415074 + 0.909788i \(0.636244\pi\)
\(264\) −10.6708 −0.656741
\(265\) 6.96973 16.2654i 0.428147 0.999174i
\(266\) 0 0
\(267\) −2.93964 + 2.93964i −0.179903 + 0.179903i
\(268\) 4.68272 + 4.68272i 0.286042 + 0.286042i
\(269\) −8.06692 −0.491849 −0.245924 0.969289i \(-0.579092\pi\)
−0.245924 + 0.969289i \(0.579092\pi\)
\(270\) 5.91170 + 14.7767i 0.359775 + 0.899281i
\(271\) 8.39951i 0.510234i 0.966910 + 0.255117i \(0.0821140\pi\)
−0.966910 + 0.255117i \(0.917886\pi\)
\(272\) −0.557436 0.557436i −0.0337995 0.0337995i
\(273\) 0 0
\(274\) 18.9664i 1.14580i
\(275\) −13.2906 + 12.6607i −0.801451 + 0.763468i
\(276\) 13.6777i 0.823301i
\(277\) 4.01637 4.01637i 0.241320 0.241320i −0.576076 0.817396i \(-0.695417\pi\)
0.817396 + 0.576076i \(0.195417\pi\)
\(278\) 5.82448 5.82448i 0.349329 0.349329i
\(279\) −0.226279 −0.0135470
\(280\) 0 0
\(281\) 7.27627 0.434066 0.217033 0.976164i \(-0.430362\pi\)
0.217033 + 0.976164i \(0.430362\pi\)
\(282\) 13.1543 13.1543i 0.783330 0.783330i
\(283\) −5.45180 + 5.45180i −0.324076 + 0.324076i −0.850328 0.526253i \(-0.823597\pi\)
0.526253 + 0.850328i \(0.323597\pi\)
\(284\) 8.11777i 0.481701i
\(285\) 13.0787 + 5.60425i 0.774718 + 0.331967i
\(286\) 4.31218i 0.254984i
\(287\) 0 0
\(288\) −3.85282 3.85282i −0.227029 0.227029i
\(289\) 16.3785i 0.963443i
\(290\) 2.30953 5.38980i 0.135621 0.316500i
\(291\) −13.0181 −0.763136
\(292\) −6.97578 6.97578i −0.408227 0.408227i
\(293\) −3.35198 + 3.35198i −0.195824 + 0.195824i −0.798207 0.602383i \(-0.794218\pi\)
0.602383 + 0.798207i \(0.294218\pi\)
\(294\) 0 0
\(295\) −8.89741 22.2397i −0.518027 1.29485i
\(296\) 0.256928 0.0149336
\(297\) 18.4764 + 18.4764i 1.07211 + 1.07211i
\(298\) 3.42371 + 3.42371i 0.198330 + 0.198330i
\(299\) −5.52731 −0.319653
\(300\) −14.5291 0.352638i −0.838835 0.0203595i
\(301\) 0 0
\(302\) −7.10348 + 7.10348i −0.408759 + 0.408759i
\(303\) −0.147792 0.147792i −0.00849045 0.00849045i
\(304\) −2.18923 −0.125561
\(305\) 4.13622 1.65477i 0.236839 0.0947520i
\(306\) 4.29540i 0.245551i
\(307\) 1.06546 + 1.06546i 0.0608089 + 0.0608089i 0.736857 0.676048i \(-0.236309\pi\)
−0.676048 + 0.736857i \(0.736309\pi\)
\(308\) 0 0
\(309\) 48.1918i 2.74154i
\(310\) 0.0365748 0.0853553i 0.00207731 0.00484785i
\(311\) 13.8083i 0.782999i −0.920178 0.391500i \(-0.871956\pi\)
0.920178 0.391500i \(-0.128044\pi\)
\(312\) 2.41421 2.41421i 0.136678 0.136678i
\(313\) −16.5089 + 16.5089i −0.933136 + 0.933136i −0.997901 0.0647646i \(-0.979370\pi\)
0.0647646 + 0.997901i \(0.479370\pi\)
\(314\) 24.4867 1.38186
\(315\) 0 0
\(316\) 13.4113 0.754443
\(317\) 9.32591 9.32591i 0.523796 0.523796i −0.394920 0.918716i \(-0.629228\pi\)
0.918716 + 0.394920i \(0.129228\pi\)
\(318\) 16.2654 16.2654i 0.912117 0.912117i
\(319\) 9.62706i 0.539012i
\(320\) 2.07609 0.830578i 0.116057 0.0464307i
\(321\) 13.2818i 0.741316i
\(322\) 0 0
\(323\) 1.22035 + 1.22035i 0.0679023 + 0.0679023i
\(324\) 4.34228i 0.241238i
\(325\) 0.142505 5.87135i 0.00790474 0.325684i
\(326\) 21.9655 1.21656
\(327\) 37.2067 + 37.2067i 2.05754 + 2.05754i
\(328\) −6.35000 + 6.35000i −0.350620 + 0.350620i
\(329\) 0 0
\(330\) −22.1535 + 8.86292i −1.21951 + 0.487888i
\(331\) −19.0960 −1.04961 −0.524805 0.851223i \(-0.675862\pi\)
−0.524805 + 0.851223i \(0.675862\pi\)
\(332\) −9.73033 9.73033i −0.534021 0.534021i
\(333\) −0.989897 0.989897i −0.0542460 0.0542460i
\(334\) −4.44935 −0.243457
\(335\) 13.6111 + 5.83237i 0.743653 + 0.318656i
\(336\) 0 0
\(337\) 0.488226 0.488226i 0.0265953 0.0265953i −0.693684 0.720279i \(-0.744014\pi\)
0.720279 + 0.693684i \(0.244014\pi\)
\(338\) −8.21678 8.21678i −0.446934 0.446934i
\(339\) −6.25080 −0.339497
\(340\) −1.62028 0.694291i −0.0878720 0.0376532i
\(341\) 0.152458i 0.00825609i
\(342\) 8.43469 + 8.43469i 0.456096 + 0.456096i
\(343\) 0 0
\(344\) 0.671142i 0.0361855i
\(345\) 11.3604 + 28.3961i 0.611624 + 1.52880i
\(346\) 5.22653i 0.280980i
\(347\) 2.69406 2.69406i 0.144625 0.144625i −0.631087 0.775712i \(-0.717391\pi\)
0.775712 + 0.631087i \(0.217391\pi\)
\(348\) 5.38980 5.38980i 0.288924 0.288924i
\(349\) 7.91303 0.423575 0.211787 0.977316i \(-0.432072\pi\)
0.211787 + 0.977316i \(0.432072\pi\)
\(350\) 0 0
\(351\) −8.36041 −0.446246
\(352\) 2.59589 2.59589i 0.138361 0.138361i
\(353\) −18.2283 + 18.2283i −0.970196 + 0.970196i −0.999569 0.0293725i \(-0.990649\pi\)
0.0293725 + 0.999569i \(0.490649\pi\)
\(354\) 31.1371i 1.65492i
\(355\) −6.74244 16.8532i −0.357852 0.894475i
\(356\) 1.43026i 0.0758036i
\(357\) 0 0
\(358\) −8.88731 8.88731i −0.469709 0.469709i
\(359\) 10.3865i 0.548179i −0.961704 0.274089i \(-0.911624\pi\)
0.961704 0.274089i \(-0.0883764\pi\)
\(360\) −11.1989 4.79872i −0.590231 0.252915i
\(361\) −14.2073 −0.747752
\(362\) 8.25494 + 8.25494i 0.433870 + 0.433870i
\(363\) −5.09161 + 5.09161i −0.267240 + 0.267240i
\(364\) 0 0
\(365\) −20.2763 8.68840i −1.06131 0.454772i
\(366\) 5.79099 0.302700
\(367\) 6.14194 + 6.14194i 0.320607 + 0.320607i 0.849000 0.528393i \(-0.177205\pi\)
−0.528393 + 0.849000i \(0.677205\pi\)
\(368\) −3.32739 3.32739i −0.173452 0.173452i
\(369\) 48.9308 2.54724
\(370\) 0.533405 0.213399i 0.0277304 0.0110941i
\(371\) 0 0
\(372\) 0.0853553 0.0853553i 0.00442546 0.00442546i
\(373\) 9.41127 + 9.41127i 0.487297 + 0.487297i 0.907452 0.420155i \(-0.138024\pi\)
−0.420155 + 0.907452i \(0.638024\pi\)
\(374\) −2.89408 −0.149649
\(375\) −30.4565 + 11.3354i −1.57277 + 0.585358i
\(376\) 6.40013i 0.330062i
\(377\) 2.17808 + 2.17808i 0.112177 + 0.112177i
\(378\) 0 0
\(379\) 25.3453i 1.30190i 0.759121 + 0.650949i \(0.225629\pi\)
−0.759121 + 0.650949i \(0.774371\pi\)
\(380\) −4.54503 + 1.81832i −0.233155 + 0.0932781i
\(381\) 54.4773i 2.79096i
\(382\) −10.9626 + 10.9626i −0.560894 + 0.560894i
\(383\) −13.0114 + 13.0114i −0.664852 + 0.664852i −0.956520 0.291668i \(-0.905790\pi\)
0.291668 + 0.956520i \(0.405790\pi\)
\(384\) 2.90667 0.148330
\(385\) 0 0
\(386\) −8.99792 −0.457982
\(387\) −2.58579 + 2.58579i −0.131443 + 0.131443i
\(388\) 3.16693 3.16693i 0.160776 0.160776i
\(389\) 22.3575i 1.13357i −0.823866 0.566784i \(-0.808187\pi\)
0.823866 0.566784i \(-0.191813\pi\)
\(390\) 3.00693 7.01731i 0.152262 0.355335i
\(391\) 3.70961i 0.187603i
\(392\) 0 0
\(393\) −29.1745 29.1745i −1.47166 1.47166i
\(394\) 17.2465i 0.868865i
\(395\) 27.8430 11.1391i 1.40093 0.560469i
\(396\) −20.0030 −1.00519
\(397\) −11.1609 11.1609i −0.560151 0.560151i 0.369199 0.929350i \(-0.379632\pi\)
−0.929350 + 0.369199i \(0.879632\pi\)
\(398\) −6.17385 + 6.17385i −0.309467 + 0.309467i
\(399\) 0 0
\(400\) 3.62028 3.44871i 0.181014 0.172435i
\(401\) 13.9706 0.697657 0.348828 0.937187i \(-0.386580\pi\)
0.348828 + 0.937187i \(0.386580\pi\)
\(402\) 13.6111 + 13.6111i 0.678860 + 0.678860i
\(403\) 0.0344930 + 0.0344930i 0.00171822 + 0.00171822i
\(404\) 0.0719071 0.00357751
\(405\) 3.60661 + 9.01496i 0.179214 + 0.447957i
\(406\) 0 0
\(407\) 0.666957 0.666957i 0.0330598 0.0330598i
\(408\) −1.62028 1.62028i −0.0802158 0.0802158i
\(409\) −0.313362 −0.0154947 −0.00774737 0.999970i \(-0.502466\pi\)
−0.00774737 + 0.999970i \(0.502466\pi\)
\(410\) −7.90899 + 18.4573i −0.390597 + 0.911543i
\(411\) 55.1290i 2.71931i
\(412\) −11.7237 11.7237i −0.577583 0.577583i
\(413\) 0 0
\(414\) 25.6396i 1.26012i
\(415\) −28.2828 12.1192i −1.38835 0.594909i
\(416\) 1.17462i 0.0575902i
\(417\) 16.9298 16.9298i 0.829057 0.829057i
\(418\) −5.68299 + 5.68299i −0.277964 + 0.277964i
\(419\) −31.6254 −1.54500 −0.772501 0.635014i \(-0.780994\pi\)
−0.772501 + 0.635014i \(0.780994\pi\)
\(420\) 0 0
\(421\) 24.2137 1.18011 0.590053 0.807365i \(-0.299107\pi\)
0.590053 + 0.807365i \(0.299107\pi\)
\(422\) 7.90160 7.90160i 0.384644 0.384644i
\(423\) 24.6585 24.6585i 1.19894 1.19894i
\(424\) 7.91378i 0.384327i
\(425\) −3.94051 0.0956409i −0.191143 0.00463926i
\(426\) 23.5956i 1.14321i
\(427\) 0 0
\(428\) −3.23107 3.23107i −0.156179 0.156179i
\(429\) 12.5341i 0.605150i
\(430\) −0.557436 1.39335i −0.0268819 0.0671933i
\(431\) 1.55807 0.0750498 0.0375249 0.999296i \(-0.488053\pi\)
0.0375249 + 0.999296i \(0.488053\pi\)
\(432\) −5.03288 5.03288i −0.242145 0.242145i
\(433\) −6.28166 + 6.28166i −0.301877 + 0.301877i −0.841748 0.539871i \(-0.818473\pi\)
0.539871 + 0.841748i \(0.318473\pi\)
\(434\) 0 0
\(435\) 6.71305 15.6663i 0.321866 0.751144i
\(436\) −18.1026 −0.866958
\(437\) 7.28440 + 7.28440i 0.348460 + 0.348460i
\(438\) −20.2763 20.2763i −0.968838 0.968838i
\(439\) 23.9142 1.14136 0.570681 0.821172i \(-0.306679\pi\)
0.570681 + 0.821172i \(0.306679\pi\)
\(440\) 3.23320 7.54538i 0.154137 0.359712i
\(441\) 0 0
\(442\) 0.654772 0.654772i 0.0311443 0.0311443i
\(443\) 9.09485 + 9.09485i 0.432109 + 0.432109i 0.889345 0.457236i \(-0.151161\pi\)
−0.457236 + 0.889345i \(0.651161\pi\)
\(444\) 0.746804 0.0354418
\(445\) −1.18794 2.96934i −0.0563139 0.140760i
\(446\) 1.05614i 0.0500097i
\(447\) 9.95157 + 9.95157i 0.470693 + 0.470693i
\(448\) 0 0
\(449\) 17.8932i 0.844435i −0.906495 0.422217i \(-0.861252\pi\)
0.906495 0.422217i \(-0.138748\pi\)
\(450\) −27.2355 0.661039i −1.28389 0.0311617i
\(451\) 32.9678i 1.55239i
\(452\) 1.52064 1.52064i 0.0715247 0.0715247i
\(453\) −20.6474 + 20.6474i −0.970101 + 0.970101i
\(454\) −3.12036 −0.146446
\(455\) 0 0
\(456\) −6.36335 −0.297991
\(457\) 24.1909 24.1909i 1.13160 1.13160i 0.141693 0.989911i \(-0.454746\pi\)
0.989911 0.141693i \(-0.0452545\pi\)
\(458\) −5.95512 + 5.95512i −0.278264 + 0.278264i
\(459\) 5.61102i 0.261900i
\(460\) −9.67160 4.14429i −0.450941 0.193229i
\(461\) 23.3471i 1.08738i −0.839286 0.543690i \(-0.817027\pi\)
0.839286 0.543690i \(-0.182973\pi\)
\(462\) 0 0
\(463\) 3.98510 + 3.98510i 0.185203 + 0.185203i 0.793619 0.608415i \(-0.208195\pi\)
−0.608415 + 0.793619i \(0.708195\pi\)
\(464\) 2.62236i 0.121740i
\(465\) 0.106311 0.248099i 0.00493004 0.0115053i
\(466\) 22.7969 1.05605
\(467\) −3.45478 3.45478i −0.159868 0.159868i 0.622640 0.782508i \(-0.286060\pi\)
−0.782508 + 0.622640i \(0.786060\pi\)
\(468\) 4.52558 4.52558i 0.209195 0.209195i
\(469\) 0 0
\(470\) 5.31581 + 13.2872i 0.245200 + 0.612895i
\(471\) 71.1746 3.27955
\(472\) 7.57475 + 7.57475i 0.348656 + 0.348656i
\(473\) −1.74221 1.74221i −0.0801069 0.0801069i
\(474\) 38.9821 1.79051
\(475\) −7.92561 + 7.55000i −0.363652 + 0.346418i
\(476\) 0 0
\(477\) 30.4904 30.4904i 1.39606 1.39606i
\(478\) 16.9685 + 16.9685i 0.776120 + 0.776120i
\(479\) −17.1114 −0.781841 −0.390921 0.920424i \(-0.627843\pi\)
−0.390921 + 0.920424i \(0.627843\pi\)
\(480\) 6.03449 2.41421i 0.275436 0.110193i
\(481\) 0.301792i 0.0137605i
\(482\) −17.5274 17.5274i −0.798350 0.798350i
\(483\) 0 0
\(484\) 2.47728i 0.112604i
\(485\) 3.94444 9.20520i 0.179108 0.417987i
\(486\) 8.73115i 0.396053i
\(487\) 0.0921357 0.0921357i 0.00417507 0.00417507i −0.705016 0.709191i \(-0.749060\pi\)
0.709191 + 0.705016i \(0.249060\pi\)
\(488\) −1.40878 + 1.40878i −0.0637724 + 0.0637724i
\(489\) 63.8465 2.88724
\(490\) 0 0
\(491\) 26.9895 1.21802 0.609011 0.793162i \(-0.291567\pi\)
0.609011 + 0.793162i \(0.291567\pi\)
\(492\) −18.4573 + 18.4573i −0.832121 + 0.832121i
\(493\) 1.46180 1.46180i 0.0658361 0.0658361i
\(494\) 2.57150i 0.115697i
\(495\) −41.5279 + 16.6140i −1.86654 + 0.746745i
\(496\) 0.0415289i 0.00186470i
\(497\) 0 0
\(498\) −28.2828 28.2828i −1.26738 1.26738i
\(499\) 0.0962993i 0.00431095i 0.999998 + 0.00215548i \(0.000686110\pi\)
−0.999998 + 0.00215548i \(0.999314\pi\)
\(500\) 4.65160 10.1667i 0.208026 0.454671i
\(501\) −12.9328 −0.577793
\(502\) −7.86005 7.86005i −0.350811 0.350811i
\(503\) 13.6334 13.6334i 0.607883 0.607883i −0.334509 0.942392i \(-0.608571\pi\)
0.942392 + 0.334509i \(0.108571\pi\)
\(504\) 0 0
\(505\) 0.149286 0.0597245i 0.00664312 0.00265771i
\(506\) −17.2751 −0.767970
\(507\) −23.8834 23.8834i −1.06070 1.06070i
\(508\) 13.2527 + 13.2527i 0.587995 + 0.587995i
\(509\) −12.3273 −0.546399 −0.273199 0.961957i \(-0.588082\pi\)
−0.273199 + 0.961957i \(0.588082\pi\)
\(510\) −4.70961 2.01807i −0.208545 0.0893618i
\(511\) 0 0
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 11.0181 + 11.0181i 0.486462 + 0.486462i
\(514\) 25.2932 1.11564
\(515\) −34.0768 14.6019i −1.50160 0.643438i
\(516\) 1.95078i 0.0858785i
\(517\) 16.6140 + 16.6140i 0.730684 + 0.730684i
\(518\) 0 0
\(519\) 15.1918i 0.666845i
\(520\) 0.975610 + 2.43860i 0.0427833 + 0.106940i
\(521\) 16.3292i 0.715396i −0.933837 0.357698i \(-0.883562\pi\)
0.933837 0.357698i \(-0.116438\pi\)
\(522\) 10.1035 10.1035i 0.442217 0.442217i
\(523\) 19.3776 19.3776i 0.847323 0.847323i −0.142475 0.989798i \(-0.545506\pi\)
0.989798 + 0.142475i \(0.0455060\pi\)
\(524\) 14.1946 0.620095
\(525\) 0 0
\(526\) −11.3461 −0.494714
\(527\) 0.0231497 0.0231497i 0.00100842 0.00100842i
\(528\) 7.54538 7.54538i 0.328371 0.328371i
\(529\) 0.857002i 0.0372610i
\(530\) 6.57302 + 16.4297i 0.285514 + 0.713661i
\(531\) 58.3682i 2.53297i
\(532\) 0 0
\(533\) −7.45881 7.45881i −0.323077 0.323077i
\(534\) 4.15729i 0.179903i
\(535\) −9.39163 4.02432i −0.406036 0.173987i
\(536\) −6.62236 −0.286042
\(537\) −25.8324 25.8324i −1.11475 1.11475i
\(538\) 5.70417 5.70417i 0.245924 0.245924i
\(539\) 0 0
\(540\) −14.6289 6.26850i −0.629528 0.269753i
\(541\) −41.1547 −1.76938 −0.884689 0.466181i \(-0.845630\pi\)
−0.884689 + 0.466181i \(0.845630\pi\)
\(542\) −5.93935 5.93935i −0.255117 0.255117i
\(543\) 23.9943 + 23.9943i 1.02970 + 1.02970i
\(544\) 0.788333 0.0337995
\(545\) −37.5826 + 15.0356i −1.60986 + 0.644056i
\(546\) 0 0
\(547\) 8.06541 8.06541i 0.344852 0.344852i −0.513336 0.858188i \(-0.671590\pi\)
0.858188 + 0.513336i \(0.171590\pi\)
\(548\) 13.4113 + 13.4113i 0.572901 + 0.572901i
\(549\) 10.8555 0.463303
\(550\) 0.445384 18.3503i 0.0189912 0.782460i
\(551\) 5.74094i 0.244572i
\(552\) −9.67160 9.67160i −0.411651 0.411651i
\(553\) 0 0
\(554\) 5.68000i 0.241320i
\(555\) 1.55043 0.620279i 0.0658121 0.0263294i
\(556\) 8.23706i 0.349329i
\(557\) −18.1422 + 18.1422i −0.768708 + 0.768708i −0.977879 0.209171i \(-0.932923\pi\)
0.209171 + 0.977879i \(0.432923\pi\)
\(558\) 0.160003 0.160003i 0.00677348 0.00677348i
\(559\) 0.788333 0.0333429
\(560\) 0 0
\(561\) −8.41213 −0.355160
\(562\) −5.14510 + 5.14510i −0.217033 + 0.217033i
\(563\) −9.05904 + 9.05904i −0.381793 + 0.381793i −0.871748 0.489955i \(-0.837013\pi\)
0.489955 + 0.871748i \(0.337013\pi\)
\(564\) 18.6030i 0.783330i
\(565\) 1.89397 4.41998i 0.0796798 0.185950i
\(566\) 7.71000i 0.324076i
\(567\) 0 0
\(568\) 5.74013 + 5.74013i 0.240850 + 0.240850i
\(569\) 34.4437i 1.44395i 0.691917 + 0.721977i \(0.256766\pi\)
−0.691917 + 0.721977i \(0.743234\pi\)
\(570\) −13.2109 + 5.28526i −0.553343 + 0.221375i
\(571\) −8.23970 −0.344821 −0.172410 0.985025i \(-0.555155\pi\)
−0.172410 + 0.985025i \(0.555155\pi\)
\(572\) 3.04917 + 3.04917i 0.127492 + 0.127492i
\(573\) −31.8645 + 31.8645i −1.33116 + 1.33116i
\(574\) 0 0
\(575\) −23.5212 0.570889i −0.980904 0.0238077i
\(576\) 5.44871 0.227029
\(577\) 2.48640 + 2.48640i 0.103510 + 0.103510i 0.756965 0.653455i \(-0.226681\pi\)
−0.653455 + 0.756965i \(0.726681\pi\)
\(578\) 11.5814 + 11.5814i 0.481721 + 0.481721i
\(579\) −26.1539 −1.08692
\(580\) 2.17808 + 5.44425i 0.0904397 + 0.226060i
\(581\) 0 0
\(582\) 9.20520 9.20520i 0.381568 0.381568i
\(583\) 20.5433 + 20.5433i 0.850817 + 0.850817i
\(584\) 9.86525 0.408227
\(585\) 5.63665 13.1543i 0.233047 0.543865i
\(586\) 4.74041i 0.195824i
\(587\) 5.37485 + 5.37485i 0.221844 + 0.221844i 0.809275 0.587431i \(-0.199861\pi\)
−0.587431 + 0.809275i \(0.699861\pi\)
\(588\) 0 0
\(589\) 0.0909162i 0.00374613i
\(590\) 22.0173 + 9.43442i 0.906436 + 0.388409i
\(591\) 50.1297i 2.06206i
\(592\) −0.181676 + 0.181676i −0.00746682 + 0.00746682i
\(593\) −0.519513 + 0.519513i −0.0213338 + 0.0213338i −0.717693 0.696359i \(-0.754802\pi\)
0.696359 + 0.717693i \(0.254802\pi\)
\(594\) −26.1296 −1.07211
\(595\) 0 0
\(596\) −4.84185 −0.198330
\(597\) −17.9453 + 17.9453i −0.734454 + 0.734454i
\(598\) 3.90840 3.90840i 0.159826 0.159826i
\(599\) 8.35746i 0.341477i 0.985316 + 0.170738i \(0.0546153\pi\)
−0.985316 + 0.170738i \(0.945385\pi\)
\(600\) 10.5229 10.0242i 0.429597 0.409238i
\(601\) 39.9236i 1.62852i 0.580501 + 0.814259i \(0.302857\pi\)
−0.580501 + 0.814259i \(0.697143\pi\)
\(602\) 0 0
\(603\) 25.5147 + 25.5147i 1.03904 + 1.03904i
\(604\) 10.0458i 0.408759i
\(605\) −2.05758 5.14305i −0.0836524 0.209095i
\(606\) 0.209010 0.00849045
\(607\) 24.3596 + 24.3596i 0.988726 + 0.988726i 0.999937 0.0112116i \(-0.00356883\pi\)
−0.0112116 + 0.999937i \(0.503569\pi\)
\(608\) 1.54802 1.54802i 0.0627804 0.0627804i
\(609\) 0 0
\(610\) −1.75465 + 4.09485i −0.0710436 + 0.165796i
\(611\) −7.51769 −0.304133
\(612\) −3.03730 3.03730i −0.122776 0.122776i
\(613\) −23.1359 23.1359i −0.934449 0.934449i 0.0635309 0.997980i \(-0.479764\pi\)
−0.997980 + 0.0635309i \(0.979764\pi\)
\(614\) −1.50679 −0.0608089
\(615\) −22.9888 + 53.6493i −0.926997 + 2.16335i
\(616\) 0 0
\(617\) −15.5005 + 15.5005i −0.624025 + 0.624025i −0.946558 0.322533i \(-0.895466\pi\)
0.322533 + 0.946558i \(0.395466\pi\)
\(618\) −34.0768 34.0768i −1.37077 1.37077i
\(619\) 8.62275 0.346578 0.173289 0.984871i \(-0.444561\pi\)
0.173289 + 0.984871i \(0.444561\pi\)
\(620\) 0.0344930 + 0.0862176i 0.00138527 + 0.00346258i
\(621\) 33.4927i 1.34402i
\(622\) 9.76397 + 9.76397i 0.391500 + 0.391500i
\(623\) 0 0
\(624\) 3.41421i 0.136678i
\(625\) 1.21285 24.9706i 0.0485138 0.998823i
\(626\) 23.3471i 0.933136i
\(627\) −16.5186 + 16.5186i −0.659688 + 0.659688i
\(628\) −17.3147 + 17.3147i −0.690931 + 0.690931i
\(629\) 0.202545 0.00807600
\(630\) 0 0
\(631\) −4.13675 −0.164682 −0.0823408 0.996604i \(-0.526240\pi\)
−0.0823408 + 0.996604i \(0.526240\pi\)
\(632\) −9.48320 + 9.48320i −0.377221 + 0.377221i
\(633\) 22.9673 22.9673i 0.912868 0.912868i
\(634\) 13.1888i 0.523796i
\(635\) 38.5213 + 16.5064i 1.52867 + 0.655037i
\(636\) 23.0027i 0.912117i
\(637\) 0 0
\(638\) 6.80736 + 6.80736i 0.269506 + 0.269506i
\(639\) 44.2313i 1.74976i
\(640\) −0.880708 + 2.05532i −0.0348130 + 0.0812438i
\(641\) 10.8561 0.428792 0.214396 0.976747i \(-0.431222\pi\)
0.214396 + 0.976747i \(0.431222\pi\)
\(642\) −9.39163 9.39163i −0.370658 0.370658i
\(643\) 8.06230 8.06230i 0.317946 0.317946i −0.530032 0.847978i \(-0.677820\pi\)
0.847978 + 0.530032i \(0.177820\pi\)
\(644\) 0 0
\(645\) −1.62028 4.05000i −0.0637984 0.159469i
\(646\) −1.72584 −0.0679023
\(647\) 7.37284 + 7.37284i 0.289856 + 0.289856i 0.837023 0.547167i \(-0.184294\pi\)
−0.547167 + 0.837023i \(0.684294\pi\)
\(648\) −3.07046 3.07046i −0.120619 0.120619i
\(649\) 39.3264 1.54370
\(650\) 4.05090 + 4.25243i 0.158889 + 0.166794i
\(651\) 0 0
\(652\) −15.5320 + 15.5320i −0.608279 + 0.608279i
\(653\) −4.69937 4.69937i −0.183900 0.183900i 0.609153 0.793053i \(-0.291510\pi\)
−0.793053 + 0.609153i \(0.791510\pi\)
\(654\) −52.6183 −2.05754
\(655\) 29.4693 11.7897i 1.15146 0.460664i
\(656\) 8.98026i 0.350620i
\(657\) −38.0090 38.0090i −1.48287 1.48287i
\(658\) 0 0
\(659\) 22.0345i 0.858343i 0.903223 + 0.429172i \(0.141194\pi\)
−0.903223 + 0.429172i \(0.858806\pi\)
\(660\) 9.39784 21.9319i 0.365811 0.853698i
\(661\) 11.4809i 0.446557i 0.974755 + 0.223278i \(0.0716759\pi\)
−0.974755 + 0.223278i \(0.928324\pi\)
\(662\) 13.5029 13.5029i 0.524805 0.524805i
\(663\) 1.90320 1.90320i 0.0739143 0.0739143i
\(664\) 13.7608 0.534021
\(665\) 0 0
\(666\) 1.39993 0.0542460
\(667\) 8.72561 8.72561i 0.337857 0.337857i
\(668\) 3.14616 3.14616i 0.121729 0.121729i
\(669\) 3.06985i 0.118687i
\(670\) −13.7486 + 5.50039i −0.531155 + 0.212499i
\(671\) 7.31407i 0.282356i
\(672\) 0 0
\(673\) −15.2073 15.2073i −0.586198 0.586198i 0.350402 0.936600i \(-0.386045\pi\)
−0.936600 + 0.350402i \(0.886045\pi\)
\(674\) 0.690455i 0.0265953i
\(675\) −35.5774 0.863506i −1.36937 0.0332364i
\(676\) 11.6203 0.446934
\(677\) −4.05773 4.05773i −0.155951 0.155951i 0.624819 0.780770i \(-0.285173\pi\)
−0.780770 + 0.624819i \(0.785173\pi\)
\(678\) 4.41998 4.41998i 0.169748 0.169748i
\(679\) 0 0
\(680\) 1.63665 0.654772i 0.0627626 0.0251094i
\(681\) −9.06985 −0.347557
\(682\) 0.107804 + 0.107804i 0.00412804 + 0.00412804i
\(683\) 13.7395 + 13.7395i 0.525727 + 0.525727i 0.919295 0.393568i \(-0.128759\pi\)
−0.393568 + 0.919295i \(0.628759\pi\)
\(684\) −11.9285 −0.456096
\(685\) 38.9821 + 16.7039i 1.48943 + 0.638222i
\(686\) 0 0
\(687\) −17.3095 + 17.3095i −0.660400 + 0.660400i
\(688\) 0.474569 + 0.474569i 0.0180928 + 0.0180928i
\(689\) −9.29565 −0.354136
\(690\) −28.1121 12.0461i −1.07021 0.458586i
\(691\) 22.0448i 0.838624i 0.907842 + 0.419312i \(0.137729\pi\)
−0.907842 + 0.419312i \(0.862271\pi\)
\(692\) −3.69572 3.69572i −0.140490 0.140490i
\(693\) 0 0
\(694\) 3.80998i 0.144625i
\(695\) 6.84152 + 17.1009i 0.259514 + 0.648673i
\(696\) 7.62233i 0.288924i
\(697\) −5.00592 + 5.00592i −0.189613 + 0.189613i
\(698\) −5.59536 + 5.59536i −0.211787 + 0.211787i
\(699\) 66.2630 2.50630
\(700\) 0 0
\(701\) −18.0270 −0.680870 −0.340435 0.940268i \(-0.610574\pi\)
−0.340435 + 0.940268i \(0.610574\pi\)
\(702\) 5.91170 5.91170i 0.223123 0.223123i
\(703\) 0.397729 0.397729i 0.0150006 0.0150006i
\(704\) 3.67114i 0.138361i
\(705\) 15.4513 + 38.6216i 0.581929 + 1.45457i
\(706\) 25.7787i 0.970196i
\(707\) 0 0
\(708\) 22.0173 + 22.0173i 0.827459 + 0.827459i
\(709\) 42.7949i 1.60719i 0.595173 + 0.803597i \(0.297083\pi\)
−0.595173 + 0.803597i \(0.702917\pi\)
\(710\) 16.6846 + 7.14938i 0.626163 + 0.268312i
\(711\) 73.0741 2.74049
\(712\) 1.01135 + 1.01135i 0.0379018 + 0.0379018i
\(713\) 0.138183 0.138183i 0.00517498 0.00517498i
\(714\) 0 0
\(715\) 8.86292 + 3.79777i 0.331454 + 0.142029i
\(716\) 12.5686 0.469709
\(717\) 49.3217 + 49.3217i 1.84195 + 1.84195i
\(718\) 7.34437 + 7.34437i 0.274089 + 0.274089i
\(719\) −5.45382 −0.203393 −0.101697 0.994815i \(-0.532427\pi\)
−0.101697 + 0.994815i \(0.532427\pi\)
\(720\) 11.3120 4.52558i 0.421573 0.168658i
\(721\) 0 0
\(722\) 10.0461 10.0461i 0.373876 0.373876i
\(723\) −50.9462 50.9462i −1.89471 1.89471i
\(724\) −11.6742 −0.433870
\(725\) 9.04375 + 9.49368i 0.335877 + 0.352586i
\(726\) 7.20063i 0.267240i
\(727\) −16.6781 16.6781i −0.618555 0.618555i 0.326606 0.945161i \(-0.394095\pi\)
−0.945161 + 0.326606i \(0.894095\pi\)
\(728\) 0 0
\(729\) 38.4054i 1.42242i
\(730\) 20.4811 8.19386i 0.758040 0.303268i
\(731\) 0.529083i 0.0195689i
\(732\) −4.09485 + 4.09485i −0.151350 + 0.151350i
\(733\) 24.0409 24.0409i 0.887973 0.887973i −0.106356 0.994328i \(-0.533918\pi\)
0.994328 + 0.106356i \(0.0339182\pi\)
\(734\) −8.68601 −0.320607
\(735\) 0 0
\(736\) 4.70563 0.173452
\(737\) −17.1909 + 17.1909i −0.633236 + 0.633236i
\(738\) −34.5993 + 34.5993i −1.27362 + 1.27362i
\(739\) 28.9521i 1.06502i 0.846424 + 0.532510i \(0.178751\pi\)
−0.846424 + 0.532510i \(0.821249\pi\)
\(740\) −0.226279 + 0.528070i −0.00831817 + 0.0194123i
\(741\) 7.47449i 0.274582i
\(742\) 0 0
\(743\) 34.0351 + 34.0351i 1.24863 + 1.24863i 0.956327 + 0.292300i \(0.0944206\pi\)
0.292300 + 0.956327i \(0.405579\pi\)
\(744\) 0.120711i 0.00442546i
\(745\) −10.0521 + 4.02154i −0.368281 + 0.147338i
\(746\) −13.3095 −0.487297
\(747\) −53.0177 53.0177i −1.93982 1.93982i
\(748\) 2.04643 2.04643i 0.0748247 0.0748247i
\(749\) 0 0
\(750\) 13.5206 29.5513i 0.493704 1.07906i
\(751\) −18.6114 −0.679139 −0.339569 0.940581i \(-0.610281\pi\)
−0.339569 + 0.940581i \(0.610281\pi\)
\(752\) −4.52558 4.52558i −0.165031 0.165031i
\(753\) −22.8466 22.8466i −0.832575 0.832575i
\(754\) −3.08027 −0.112177
\(755\) −8.34385 20.8560i −0.303664 0.759029i
\(756\) 0 0
\(757\) 29.7422 29.7422i 1.08100 1.08100i 0.0845825 0.996416i \(-0.473044\pi\)
0.996416 0.0845825i \(-0.0269557\pi\)
\(758\) −17.9218 17.9218i −0.650949 0.650949i
\(759\) −50.2128 −1.82261
\(760\) 1.92807 4.49957i 0.0699384 0.163217i
\(761\) 20.3775i 0.738682i 0.929294 + 0.369341i \(0.120417\pi\)
−0.929294 + 0.369341i \(0.879583\pi\)
\(762\) 38.5213 + 38.5213i 1.39548 + 1.39548i
\(763\) 0 0
\(764\) 15.5034i 0.560894i
\(765\) −8.82843 3.78299i −0.319192 0.136774i
\(766\) 18.4009i 0.664852i
\(767\) −8.89741 + 8.89741i −0.321267 + 0.321267i
\(768\) −2.05532 + 2.05532i −0.0741651 + 0.0741651i
\(769\) −40.9728 −1.47752 −0.738759 0.673970i \(-0.764588\pi\)
−0.738759 + 0.673970i \(0.764588\pi\)
\(770\) 0 0
\(771\) 73.5189 2.64772
\(772\) 6.36249 6.36249i 0.228991 0.228991i
\(773\) 17.4650 17.4650i 0.628174 0.628174i −0.319435 0.947608i \(-0.603493\pi\)
0.947608 + 0.319435i \(0.103493\pi\)
\(774\) 3.65685i 0.131443i
\(775\) 0.143221 + 0.150346i 0.00514465 + 0.00540059i
\(776\) 4.47871i 0.160776i
\(777\) 0 0
\(778\) 15.8091 + 15.8091i 0.566784 + 0.566784i
\(779\) 19.6598i 0.704386i
\(780\) 2.83577 + 7.08821i 0.101537 + 0.253799i
\(781\) 29.8015 1.06638
\(782\) −2.62309 2.62309i −0.0938015 0.0938015i
\(783\) 13.1980 13.1980i 0.471659 0.471659i
\(784\) 0 0