Properties

Label 490.2.g.c.293.2
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 293.2
Root \(1.45333 + 1.51725i\) of defining polynomial
Character \(\chi\) \(=\) 490.293
Dual form 490.2.g.c.97.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.830578 + 0.830578i) q^{3} -1.00000i q^{4} +(-2.05532 + 0.880708i) q^{5} -1.17462i q^{6} +(0.707107 + 0.707107i) q^{8} +1.62028i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.830578 + 0.830578i) q^{3} -1.00000i q^{4} +(-2.05532 + 0.880708i) q^{5} -1.17462i q^{6} +(0.707107 + 0.707107i) q^{8} +1.62028i q^{9} +(0.830578 - 2.07609i) q^{10} +0.743072 q^{11} +(0.830578 + 0.830578i) q^{12} +(-2.05532 + 2.05532i) q^{13} +(0.975610 - 2.43860i) q^{15} -1.00000 q^{16} +(-4.63872 - 4.63872i) q^{17} +(-1.14571 - 1.14571i) q^{18} +1.89205 q^{19} +(0.880708 + 2.05532i) q^{20} +(-0.525431 + 0.525431i) q^{22} +(-3.74160 - 3.74160i) q^{23} -1.17462 q^{24} +(3.44871 - 3.62028i) q^{25} -2.90667i q^{26} +(-3.83750 - 3.83750i) q^{27} -9.69135i q^{29} +(1.03449 + 2.41421i) q^{30} +3.42257i q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.617179 + 0.617179i) q^{33} +6.56014 q^{34} +1.62028 q^{36} +(-1.88878 + 1.88878i) q^{37} +(-1.33788 + 1.33788i) q^{38} -3.41421i q^{39} +(-2.07609 - 0.830578i) q^{40} -0.817699i q^{41} +(1.59589 + 1.59589i) q^{43} -0.743072i q^{44} +(-1.42699 - 3.33020i) q^{45} +5.29142 q^{46} +(-3.33020 - 3.33020i) q^{47} +(0.830578 - 0.830578i) q^{48} +(0.121320 + 4.99853i) q^{50} +7.70563 q^{51} +(2.05532 + 2.05532i) q^{52} +(3.52543 + 3.52543i) q^{53} +5.42705 q^{54} +(-1.52725 + 0.654429i) q^{55} +(-1.57150 + 1.57150i) q^{57} +(6.85282 + 6.85282i) q^{58} -2.54975 q^{59} +(-2.43860 - 0.975610i) q^{60} -6.07359i q^{61} +(-2.42012 - 2.42012i) q^{62} +1.00000i q^{64} +(2.41421 - 6.03449i) q^{65} -0.872823i q^{66} +(-9.68124 + 9.68124i) q^{67} +(-4.63872 + 4.63872i) q^{68} +6.21538 q^{69} -16.0173 q^{71} +(-1.14571 + 1.14571i) q^{72} +(6.25834 - 6.25834i) q^{73} -2.67114i q^{74} +(0.142505 + 5.87135i) q^{75} -1.89205i q^{76} +(2.41421 + 2.41421i) q^{78} -6.58284i q^{79} +(2.05532 - 0.880708i) q^{80} +1.51386 q^{81} +(0.578200 + 0.578200i) q^{82} +(-9.23519 + 9.23519i) q^{83} +(13.6194 + 5.44871i) q^{85} -2.25693 q^{86} +(8.04942 + 8.04942i) q^{87} +(0.525431 + 0.525431i) q^{88} +6.03207 q^{89} +(3.36384 + 1.34577i) q^{90} +(-3.74160 + 3.74160i) q^{92} +(-2.84271 - 2.84271i) q^{93} +4.70961 q^{94} +(-3.88878 + 1.66635i) q^{95} +1.17462i q^{96} +(-3.16693 - 3.16693i) q^{97} +1.20398i 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
\(3\) −0.830578 + 0.830578i −0.479535 + 0.479535i −0.904983 0.425448i \(-0.860116\pi\)
0.425448 + 0.904983i \(0.360116\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −2.05532 + 0.880708i −0.919168 + 0.393865i
\(6\) 1.17462i 0.479535i
\(7\) 0 0
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.62028i 0.540093i
\(10\) 0.830578 2.07609i 0.262652 0.656517i
\(11\) 0.743072 0.224045 0.112022 0.993706i \(-0.464267\pi\)
0.112022 + 0.993706i \(0.464267\pi\)
\(12\) 0.830578 + 0.830578i 0.239767 + 0.239767i
\(13\) −2.05532 + 2.05532i −0.570044 + 0.570044i −0.932141 0.362097i \(-0.882061\pi\)
0.362097 + 0.932141i \(0.382061\pi\)
\(14\) 0 0
\(15\) 0.975610 2.43860i 0.251901 0.629645i
\(16\) −1.00000 −0.250000
\(17\) −4.63872 4.63872i −1.12505 1.12505i −0.990970 0.134084i \(-0.957191\pi\)
−0.134084 0.990970i \(-0.542809\pi\)
\(18\) −1.14571 1.14571i −0.270047 0.270047i
\(19\) 1.89205 0.434067 0.217033 0.976164i \(-0.430362\pi\)
0.217033 + 0.976164i \(0.430362\pi\)
\(20\) 0.880708 + 2.05532i 0.196932 + 0.459584i
\(21\) 0 0
\(22\) −0.525431 + 0.525431i −0.112022 + 0.112022i
\(23\) −3.74160 3.74160i −0.780177 0.780177i 0.199683 0.979861i \(-0.436009\pi\)
−0.979861 + 0.199683i \(0.936009\pi\)
\(24\) −1.17462 −0.239767
\(25\) 3.44871 3.62028i 0.689741 0.724056i
\(26\) 2.90667i 0.570044i
\(27\) −3.83750 3.83750i −0.738528 0.738528i
\(28\) 0 0
\(29\) 9.69135i 1.79964i −0.436263 0.899819i \(-0.643698\pi\)
0.436263 0.899819i \(-0.356302\pi\)
\(30\) 1.03449 + 2.41421i 0.188872 + 0.440773i
\(31\) 3.42257i 0.614712i 0.951595 + 0.307356i \(0.0994443\pi\)
−0.951595 + 0.307356i \(0.900556\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −0.617179 + 0.617179i −0.107437 + 0.107437i
\(34\) 6.56014 1.12505
\(35\) 0 0
\(36\) 1.62028 0.270047
\(37\) −1.88878 + 1.88878i −0.310514 + 0.310514i −0.845109 0.534595i \(-0.820464\pi\)
0.534595 + 0.845109i \(0.320464\pi\)
\(38\) −1.33788 + 1.33788i −0.217033 + 0.217033i
\(39\) 3.41421i 0.546712i
\(40\) −2.07609 0.830578i −0.328258 0.131326i
\(41\) 0.817699i 0.127703i −0.997959 0.0638515i \(-0.979662\pi\)
0.997959 0.0638515i \(-0.0203384\pi\)
\(42\) 0 0
\(43\) 1.59589 + 1.59589i 0.243371 + 0.243371i 0.818243 0.574872i \(-0.194948\pi\)
−0.574872 + 0.818243i \(0.694948\pi\)
\(44\) 0.743072i 0.112022i
\(45\) −1.42699 3.33020i −0.212724 0.496437i
\(46\) 5.29142 0.780177
\(47\) −3.33020 3.33020i −0.485759 0.485759i 0.421206 0.906965i \(-0.361607\pi\)
−0.906965 + 0.421206i \(0.861607\pi\)
\(48\) 0.830578 0.830578i 0.119884 0.119884i
\(49\) 0 0
\(50\) 0.121320 + 4.99853i 0.0171573 + 0.706899i
\(51\) 7.70563 1.07900
\(52\) 2.05532 + 2.05532i 0.285022 + 0.285022i
\(53\) 3.52543 + 3.52543i 0.484255 + 0.484255i 0.906488 0.422232i \(-0.138753\pi\)
−0.422232 + 0.906488i \(0.638753\pi\)
\(54\) 5.42705 0.738528
\(55\) −1.52725 + 0.654429i −0.205935 + 0.0882432i
\(56\) 0 0
\(57\) −1.57150 + 1.57150i −0.208150 + 0.208150i
\(58\) 6.85282 + 6.85282i 0.899819 + 0.899819i
\(59\) −2.54975 −0.331949 −0.165975 0.986130i \(-0.553077\pi\)
−0.165975 + 0.986130i \(0.553077\pi\)
\(60\) −2.43860 0.975610i −0.314822 0.125951i
\(61\) 6.07359i 0.777644i −0.921313 0.388822i \(-0.872882\pi\)
0.921313 0.388822i \(-0.127118\pi\)
\(62\) −2.42012 2.42012i −0.307356 0.307356i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 2.41421 6.03449i 0.299446 0.748487i
\(66\) 0.872823i 0.107437i
\(67\) −9.68124 + 9.68124i −1.18275 + 1.18275i −0.203724 + 0.979028i \(0.565304\pi\)
−0.979028 + 0.203724i \(0.934696\pi\)
\(68\) −4.63872 + 4.63872i −0.562527 + 0.562527i
\(69\) 6.21538 0.748244
\(70\) 0 0
\(71\) −16.0173 −1.90090 −0.950450 0.310879i \(-0.899377\pi\)
−0.950450 + 0.310879i \(0.899377\pi\)
\(72\) −1.14571 + 1.14571i −0.135023 + 0.135023i
\(73\) 6.25834 6.25834i 0.732484 0.732484i −0.238627 0.971111i \(-0.576697\pi\)
0.971111 + 0.238627i \(0.0766975\pi\)
\(74\) 2.67114i 0.310514i
\(75\) 0.142505 + 5.87135i 0.0164550 + 0.677965i
\(76\) 1.89205i 0.217033i
\(77\) 0 0
\(78\) 2.41421 + 2.41421i 0.273356 + 0.273356i
\(79\) 6.58284i 0.740628i −0.928907 0.370314i \(-0.879250\pi\)
0.928907 0.370314i \(-0.120750\pi\)
\(80\) 2.05532 0.880708i 0.229792 0.0984662i
\(81\) 1.51386 0.168206
\(82\) 0.578200 + 0.578200i 0.0638515 + 0.0638515i
\(83\) −9.23519 + 9.23519i −1.01369 + 1.01369i −0.0137887 + 0.999905i \(0.504389\pi\)
−0.999905 + 0.0137887i \(0.995611\pi\)
\(84\) 0 0
\(85\) 13.6194 + 5.44871i 1.47723 + 0.590995i
\(86\) −2.25693 −0.243371
\(87\) 8.04942 + 8.04942i 0.862989 + 0.862989i
\(88\) 0.525431 + 0.525431i 0.0560111 + 0.0560111i
\(89\) 6.03207 0.639398 0.319699 0.947519i \(-0.396418\pi\)
0.319699 + 0.947519i \(0.396418\pi\)
\(90\) 3.36384 + 1.34577i 0.354580 + 0.141856i
\(91\) 0 0
\(92\) −3.74160 + 3.74160i −0.390089 + 0.390089i
\(93\) −2.84271 2.84271i −0.294776 0.294776i
\(94\) 4.70961 0.485759
\(95\) −3.88878 + 1.66635i −0.398981 + 0.170964i
\(96\) 1.17462i 0.119884i
\(97\) −3.16693 3.16693i −0.321553 0.321553i 0.527810 0.849363i \(-0.323013\pi\)
−0.849363 + 0.527810i \(0.823013\pi\)
\(98\) 0 0
\(99\) 1.20398i 0.121005i
\(100\) −3.62028 3.44871i −0.362028 0.344871i
\(101\) 11.1817i 1.11262i 0.830976 + 0.556308i \(0.187782\pi\)
−0.830976 + 0.556308i \(0.812218\pi\)
\(102\) −5.44871 + 5.44871i −0.539502 + 0.539502i
\(103\) 1.71557 1.71557i 0.169040 0.169040i −0.617517 0.786557i \(-0.711862\pi\)
0.786557 + 0.617517i \(0.211862\pi\)
\(104\) −2.90667 −0.285022
\(105\) 0 0
\(106\) −4.98571 −0.484255
\(107\) −4.69553 + 4.69553i −0.453934 + 0.453934i −0.896658 0.442724i \(-0.854012\pi\)
0.442724 + 0.896658i \(0.354012\pi\)
\(108\) −3.83750 + 3.83750i −0.369264 + 0.369264i
\(109\) 8.96048i 0.858258i 0.903243 + 0.429129i \(0.141180\pi\)
−0.903243 + 0.429129i \(0.858820\pi\)
\(110\) 0.617179 1.54268i 0.0588457 0.147089i
\(111\) 3.13756i 0.297804i
\(112\) 0 0
\(113\) 0.307790 + 0.307790i 0.0289545 + 0.0289545i 0.721436 0.692481i \(-0.243482\pi\)
−0.692481 + 0.721436i \(0.743482\pi\)
\(114\) 2.22244i 0.208150i
\(115\) 10.9855 + 4.39494i 1.02440 + 0.409830i
\(116\) −9.69135 −0.899819
\(117\) −3.33020 3.33020i −0.307877 0.307877i
\(118\) 1.80295 1.80295i 0.165975 0.165975i
\(119\) 0 0
\(120\) 2.41421 1.03449i 0.220387 0.0944359i
\(121\) −10.4478 −0.949804
\(122\) 4.29468 + 4.29468i 0.388822 + 0.388822i
\(123\) 0.679163 + 0.679163i 0.0612380 + 0.0612380i
\(124\) 3.42257 0.307356
\(125\) −3.89980 + 10.4781i −0.348808 + 0.937194i
\(126\) 0 0
\(127\) −11.1823 + 11.1823i −0.992267 + 0.992267i −0.999970 0.00770296i \(-0.997548\pi\)
0.00770296 + 0.999970i \(0.497548\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −2.65102 −0.233409
\(130\) 2.55992 + 5.97414i 0.224520 + 0.523967i
\(131\) 9.59282i 0.838129i 0.907957 + 0.419064i \(0.137642\pi\)
−0.907957 + 0.419064i \(0.862358\pi\)
\(132\) 0.617179 + 0.617179i 0.0537186 + 0.0537186i
\(133\) 0 0
\(134\) 13.6913i 1.18275i
\(135\) 11.2670 + 4.50759i 0.969712 + 0.387952i
\(136\) 6.56014i 0.562527i
\(137\) 6.58284 6.58284i 0.562410 0.562410i −0.367581 0.929991i \(-0.619814\pi\)
0.929991 + 0.367581i \(0.119814\pi\)
\(138\) −4.39494 + 4.39494i −0.374122 + 0.374122i
\(139\) 22.1714 1.88056 0.940278 0.340408i \(-0.110565\pi\)
0.940278 + 0.340408i \(0.110565\pi\)
\(140\) 0 0
\(141\) 5.53198 0.465877
\(142\) 11.3259 11.3259i 0.950450 0.950450i
\(143\) −1.52725 + 1.52725i −0.127715 + 0.127715i
\(144\) 1.62028i 0.135023i
\(145\) 8.53525 + 19.9189i 0.708814 + 1.65417i
\(146\) 8.85064i 0.732484i
\(147\) 0 0
\(148\) 1.88878 + 1.88878i 0.155257 + 0.155257i
\(149\) 3.94236i 0.322970i 0.986875 + 0.161485i \(0.0516284\pi\)
−0.986875 + 0.161485i \(0.948372\pi\)
\(150\) −4.25243 4.05090i −0.347210 0.330755i
\(151\) −19.9453 −1.62313 −0.811564 0.584264i \(-0.801383\pi\)
−0.811564 + 0.584264i \(0.801383\pi\)
\(152\) 1.33788 + 1.33788i 0.108517 + 0.108517i
\(153\) 7.51602 7.51602i 0.607634 0.607634i
\(154\) 0 0
\(155\) −3.01429 7.03449i −0.242113 0.565024i
\(156\) −3.41421 −0.273356
\(157\) −5.27738 5.27738i −0.421181 0.421181i 0.464430 0.885610i \(-0.346259\pi\)
−0.885610 + 0.464430i \(0.846259\pi\)
\(158\) 4.65477 + 4.65477i 0.370314 + 0.370314i
\(159\) −5.85629 −0.464434
\(160\) −0.830578 + 2.07609i −0.0656630 + 0.164129i
\(161\) 0 0
\(162\) −1.07046 + 1.07046i −0.0841031 + 0.0841031i
\(163\) 8.60305 + 8.60305i 0.673843 + 0.673843i 0.958600 0.284757i \(-0.0919129\pi\)
−0.284757 + 0.958600i \(0.591913\pi\)
\(164\) −0.817699 −0.0638515
\(165\) 0.724948 1.81206i 0.0564371 0.141069i
\(166\) 13.0605i 1.01369i
\(167\) −1.45564 1.45564i −0.112641 0.112641i 0.648540 0.761181i \(-0.275380\pi\)
−0.761181 + 0.648540i \(0.775380\pi\)
\(168\) 0 0
\(169\) 4.55129i 0.350099i
\(170\) −13.4832 + 5.77756i −1.03411 + 0.443119i
\(171\) 3.06566i 0.234437i
\(172\) 1.59589 1.59589i 0.121685 0.121685i
\(173\) 6.65251 6.65251i 0.505781 0.505781i −0.407448 0.913229i \(-0.633581\pi\)
0.913229 + 0.407448i \(0.133581\pi\)
\(174\) −11.3836 −0.862989
\(175\) 0 0
\(176\) −0.743072 −0.0560111
\(177\) 2.11777 2.11777i 0.159181 0.159181i
\(178\) −4.26531 + 4.26531i −0.319699 + 0.319699i
\(179\) 4.49749i 0.336158i −0.985774 0.168079i \(-0.946244\pi\)
0.985774 0.168079i \(-0.0537564\pi\)
\(180\) −3.33020 + 1.42699i −0.248218 + 0.106362i
\(181\) 17.8850i 1.32938i −0.747118 0.664691i \(-0.768563\pi\)
0.747118 0.664691i \(-0.231437\pi\)
\(182\) 0 0
\(183\) 5.04460 + 5.04460i 0.372907 + 0.372907i
\(184\) 5.29142i 0.390089i
\(185\) 2.21859 5.54552i 0.163114 0.407715i
\(186\) 4.02021 0.294776
\(187\) −3.44690 3.44690i −0.252062 0.252062i
\(188\) −3.33020 + 3.33020i −0.242880 + 0.242880i
\(189\) 0 0
\(190\) 1.57150 3.92807i 0.114009 0.284972i
\(191\) −2.77548 −0.200827 −0.100413 0.994946i \(-0.532017\pi\)
−0.100413 + 0.994946i \(0.532017\pi\)
\(192\) −0.830578 0.830578i −0.0599418 0.0599418i
\(193\) −3.63457 3.63457i −0.261622 0.261622i 0.564091 0.825713i \(-0.309227\pi\)
−0.825713 + 0.564091i \(0.809227\pi\)
\(194\) 4.47871 0.321553
\(195\) 3.00693 + 7.01731i 0.215330 + 0.502520i
\(196\) 0 0
\(197\) 1.34043 1.34043i 0.0955019 0.0955019i −0.657742 0.753244i \(-0.728488\pi\)
0.753244 + 0.657742i \(0.228488\pi\)
\(198\) −0.851345 0.851345i −0.0605025 0.0605025i
\(199\) −14.5030 −1.02809 −0.514043 0.857764i \(-0.671853\pi\)
−0.514043 + 0.857764i \(0.671853\pi\)
\(200\) 4.99853 0.121320i 0.353449 0.00857864i
\(201\) 16.0821i 1.13434i
\(202\) −7.90662 7.90662i −0.556308 0.556308i
\(203\) 0 0
\(204\) 7.70563i 0.539502i
\(205\) 0.720154 + 1.68063i 0.0502977 + 0.117381i
\(206\) 2.42618i 0.169040i
\(207\) 6.06244 6.06244i 0.421369 0.421369i
\(208\) 2.05532 2.05532i 0.142511 0.142511i
\(209\) 1.40593 0.0972504
\(210\) 0 0
\(211\) 10.0324 0.690660 0.345330 0.938481i \(-0.387767\pi\)
0.345330 + 0.938481i \(0.387767\pi\)
\(212\) 3.52543 3.52543i 0.242128 0.242128i
\(213\) 13.3036 13.3036i 0.911547 0.911547i
\(214\) 6.64048i 0.453934i
\(215\) −4.68558 1.87456i −0.319554 0.127844i
\(216\) 5.42705i 0.369264i
\(217\) 0 0
\(218\) −6.33602 6.33602i −0.429129 0.429129i
\(219\) 10.3961i 0.702503i
\(220\) 0.654429 + 1.52725i 0.0441216 + 0.102967i
\(221\) 19.0681 1.28266
\(222\) 2.21859 + 2.21859i 0.148902 + 0.148902i
\(223\) 3.13756 3.13756i 0.210107 0.210107i −0.594206 0.804313i \(-0.702534\pi\)
0.804313 + 0.594206i \(0.202534\pi\)
\(224\) 0 0
\(225\) 5.86586 + 5.58787i 0.391058 + 0.372525i
\(226\) −0.435281 −0.0289545
\(227\) 0.474378 + 0.474378i 0.0314856 + 0.0314856i 0.722674 0.691189i \(-0.242913\pi\)
−0.691189 + 0.722674i \(0.742913\pi\)
\(228\) 1.57150 + 1.57150i 0.104075 + 0.104075i
\(229\) −13.2033 −0.872501 −0.436250 0.899825i \(-0.643694\pi\)
−0.436250 + 0.899825i \(0.643694\pi\)
\(230\) −10.8756 + 4.66020i −0.717115 + 0.307284i
\(231\) 0 0
\(232\) 6.85282 6.85282i 0.449910 0.449910i
\(233\) −6.12279 6.12279i −0.401117 0.401117i 0.477509 0.878627i \(-0.341540\pi\)
−0.878627 + 0.477509i \(0.841540\pi\)
\(234\) 4.70961 0.307877
\(235\) 9.77756 + 3.91170i 0.637818 + 0.255171i
\(236\) 2.54975i 0.165975i
\(237\) 5.46757 + 5.46757i 0.355157 + 0.355157i
\(238\) 0 0
\(239\) 4.00294i 0.258929i −0.991584 0.129464i \(-0.958674\pi\)
0.991584 0.129464i \(-0.0413258\pi\)
\(240\) −0.975610 + 2.43860i −0.0629753 + 0.157411i
\(241\) 17.3251i 1.11601i −0.829838 0.558005i \(-0.811567\pi\)
0.829838 0.558005i \(-0.188433\pi\)
\(242\) 7.38774 7.38774i 0.474902 0.474902i
\(243\) 10.2551 10.2551i 0.657867 0.657867i
\(244\) −6.07359 −0.388822
\(245\) 0 0
\(246\) −0.960481 −0.0612380
\(247\) −3.88878 + 3.88878i −0.247437 + 0.247437i
\(248\) −2.42012 + 2.42012i −0.153678 + 0.153678i
\(249\) 15.3411i 0.972202i
\(250\) −4.65160 10.1667i −0.294193 0.643001i
\(251\) 5.49938i 0.347118i 0.984824 + 0.173559i \(0.0555267\pi\)
−0.984824 + 0.173559i \(0.944473\pi\)
\(252\) 0 0
\(253\) −2.78028 2.78028i −0.174795 0.174795i
\(254\) 15.8141i 0.992267i
\(255\) −15.8376 + 6.78641i −0.991787 + 0.424982i
\(256\) 1.00000 0.0625000
\(257\) −11.6742 11.6742i −0.728219 0.728219i 0.242046 0.970265i \(-0.422182\pi\)
−0.970265 + 0.242046i \(0.922182\pi\)
\(258\) 1.87456 1.87456i 0.116705 0.116705i
\(259\) 0 0
\(260\) −6.03449 2.41421i −0.374243 0.149723i
\(261\) 15.7027 0.971972
\(262\) −6.78315 6.78315i −0.419064 0.419064i
\(263\) −6.97267 6.97267i −0.429953 0.429953i 0.458659 0.888612i \(-0.348330\pi\)
−0.888612 + 0.458659i \(0.848330\pi\)
\(264\) −0.872823 −0.0537186
\(265\) −10.3508 4.14102i −0.635843 0.254381i
\(266\) 0 0
\(267\) −5.01010 + 5.01010i −0.306613 + 0.306613i
\(268\) 9.68124 + 9.68124i 0.591376 + 0.591376i
\(269\) −8.95844 −0.546206 −0.273103 0.961985i \(-0.588050\pi\)
−0.273103 + 0.961985i \(0.588050\pi\)
\(270\) −11.1543 + 4.77965i −0.678832 + 0.290880i
\(271\) 22.8503i 1.38805i 0.719949 + 0.694027i \(0.244165\pi\)
−0.719949 + 0.694027i \(0.755835\pi\)
\(272\) 4.63872 + 4.63872i 0.281264 + 0.281264i
\(273\) 0 0
\(274\) 9.30954i 0.562410i
\(275\) 2.56264 2.69013i 0.154533 0.162221i
\(276\) 6.21538i 0.374122i
\(277\) 15.2263 15.2263i 0.914858 0.914858i −0.0817915 0.996649i \(-0.526064\pi\)
0.996649 + 0.0817915i \(0.0260642\pi\)
\(278\) −15.6776 + 15.6776i −0.940278 + 0.940278i
\(279\) −5.54552 −0.332002
\(280\) 0 0
\(281\) −5.64885 −0.336982 −0.168491 0.985703i \(-0.553889\pi\)
−0.168491 + 0.985703i \(0.553889\pi\)
\(282\) −3.91170 + 3.91170i −0.232938 + 0.232938i
\(283\) 2.07075 2.07075i 0.123093 0.123093i −0.642876 0.765970i \(-0.722259\pi\)
0.765970 + 0.642876i \(0.222259\pi\)
\(284\) 16.0173i 0.950450i
\(285\) 1.84591 4.61397i 0.109342 0.273308i
\(286\) 2.15986i 0.127715i
\(287\) 0 0
\(288\) 1.14571 + 1.14571i 0.0675116 + 0.0675116i
\(289\) 26.0354i 1.53149i
\(290\) −20.1201 8.04942i −1.18149 0.472678i
\(291\) 5.26076 0.308391
\(292\) −6.25834 6.25834i −0.366242 0.366242i
\(293\) −10.7875 + 10.7875i −0.630212 + 0.630212i −0.948121 0.317909i \(-0.897019\pi\)
0.317909 + 0.948121i \(0.397019\pi\)
\(294\) 0 0
\(295\) 5.24056 2.24558i 0.305117 0.130743i
\(296\) −2.67114 −0.155257
\(297\) −2.85154 2.85154i −0.165463 0.165463i
\(298\) −2.78767 2.78767i −0.161485 0.161485i
\(299\) 15.3804 0.889471
\(300\) 5.87135 0.142505i 0.338982 0.00822751i
\(301\) 0 0
\(302\) 14.1035 14.1035i 0.811564 0.811564i
\(303\) −9.28724 9.28724i −0.533538 0.533538i
\(304\) −1.89205 −0.108517
\(305\) 5.34906 + 12.4832i 0.306287 + 0.714786i
\(306\) 10.6293i 0.607634i
\(307\) 6.89201 + 6.89201i 0.393348 + 0.393348i 0.875879 0.482531i \(-0.160282\pi\)
−0.482531 + 0.875879i \(0.660282\pi\)
\(308\) 0 0
\(309\) 2.84982i 0.162121i
\(310\) 7.10556 + 2.84271i 0.403569 + 0.161455i
\(311\) 0.126019i 0.00714589i −0.999994 0.00357294i \(-0.998863\pi\)
0.999994 0.00357294i \(-0.00113731\pi\)
\(312\) 2.41421 2.41421i 0.136678 0.136678i
\(313\) −8.26887 + 8.26887i −0.467384 + 0.467384i −0.901066 0.433682i \(-0.857214\pi\)
0.433682 + 0.901066i \(0.357214\pi\)
\(314\) 7.46334 0.421181
\(315\) 0 0
\(316\) −6.58284 −0.370314
\(317\) −7.74013 + 7.74013i −0.434729 + 0.434729i −0.890233 0.455505i \(-0.849459\pi\)
0.455505 + 0.890233i \(0.349459\pi\)
\(318\) 4.14102 4.14102i 0.232217 0.232217i
\(319\) 7.20137i 0.403199i
\(320\) −0.880708 2.05532i −0.0492331 0.114896i
\(321\) 7.80001i 0.435354i
\(322\) 0 0
\(323\) −8.77670 8.77670i −0.488349 0.488349i
\(324\) 1.51386i 0.0841031i
\(325\) 0.352638 + 14.5291i 0.0195608 + 0.805927i
\(326\) −12.1665 −0.673843
\(327\) −7.44238 7.44238i −0.411565 0.411565i
\(328\) 0.578200 0.578200i 0.0319258 0.0319258i
\(329\) 0 0
\(330\) 0.768703 + 1.79393i 0.0423157 + 0.0987528i
\(331\) −5.46038 −0.300129 −0.150065 0.988676i \(-0.547948\pi\)
−0.150065 + 0.988676i \(0.547948\pi\)
\(332\) 9.23519 + 9.23519i 0.506847 + 0.506847i
\(333\) −3.06036 3.06036i −0.167706 0.167706i
\(334\) 2.05859 0.112641
\(335\) 11.3717 28.4244i 0.621304 1.55299i
\(336\) 0 0
\(337\) 20.4823 20.4823i 1.11574 1.11574i 0.123385 0.992359i \(-0.460625\pi\)
0.992359 0.123385i \(-0.0393751\pi\)
\(338\) −3.21825 3.21825i −0.175050 0.175050i
\(339\) −0.511288 −0.0277694
\(340\) 5.44871 13.6194i 0.295498 0.738617i
\(341\) 2.54322i 0.137723i
\(342\) −2.16775 2.16775i −0.117218 0.117218i
\(343\) 0 0
\(344\) 2.25693i 0.121685i
\(345\) −12.7746 + 5.47394i −0.687762 + 0.294707i
\(346\) 9.40807i 0.505781i
\(347\) −15.2296 + 15.2296i −0.817567 + 0.817567i −0.985755 0.168188i \(-0.946209\pi\)
0.168188 + 0.985755i \(0.446209\pi\)
\(348\) 8.04942 8.04942i 0.431494 0.431494i
\(349\) −12.5744 −0.673093 −0.336546 0.941667i \(-0.609259\pi\)
−0.336546 + 0.941667i \(0.609259\pi\)
\(350\) 0 0
\(351\) 15.7746 0.841987
\(352\) 0.525431 0.525431i 0.0280056 0.0280056i
\(353\) −0.487554 + 0.487554i −0.0259499 + 0.0259499i −0.719963 0.694013i \(-0.755841\pi\)
0.694013 + 0.719963i \(0.255841\pi\)
\(354\) 2.99497i 0.159181i
\(355\) 32.9206 14.1065i 1.74725 0.748697i
\(356\) 6.03207i 0.319699i
\(357\) 0 0
\(358\) 3.18020 + 3.18020i 0.168079 + 0.168079i
\(359\) 22.0988i 1.16633i −0.812354 0.583165i \(-0.801814\pi\)
0.812354 0.583165i \(-0.198186\pi\)
\(360\) 1.34577 3.36384i 0.0709282 0.177290i
\(361\) −15.4201 −0.811586
\(362\) 12.6466 + 12.6466i 0.664691 + 0.664691i
\(363\) 8.67775 8.67775i 0.455464 0.455464i
\(364\) 0 0
\(365\) −7.35115 + 18.3747i −0.384777 + 0.961775i
\(366\) −7.13414 −0.372907
\(367\) 9.48295 + 9.48295i 0.495006 + 0.495006i 0.909879 0.414873i \(-0.136174\pi\)
−0.414873 + 0.909879i \(0.636174\pi\)
\(368\) 3.74160 + 3.74160i 0.195044 + 0.195044i
\(369\) 1.32490 0.0689715
\(370\) 2.35250 + 5.49006i 0.122300 + 0.285415i
\(371\) 0 0
\(372\) −2.84271 + 2.84271i −0.147388 + 0.147388i
\(373\) −10.5828 10.5828i −0.547959 0.547959i 0.377891 0.925850i \(-0.376649\pi\)
−0.925850 + 0.377891i \(0.876649\pi\)
\(374\) 4.87465 0.252062
\(375\) −5.46384 11.9420i −0.282151 0.616683i
\(376\) 4.70961i 0.242880i
\(377\) 19.9189 + 19.9189i 1.02587 + 1.02587i
\(378\) 0 0
\(379\) 1.71784i 0.0882395i −0.999026 0.0441198i \(-0.985952\pi\)
0.999026 0.0441198i \(-0.0140483\pi\)
\(380\) 1.66635 + 3.88878i 0.0854818 + 0.199490i
\(381\) 18.5755i 0.951653i
\(382\) 1.96256 1.96256i 0.100413 0.100413i
\(383\) −7.39499 + 7.39499i −0.377866 + 0.377866i −0.870332 0.492465i \(-0.836096\pi\)
0.492465 + 0.870332i \(0.336096\pi\)
\(384\) 1.17462 0.0599418
\(385\) 0 0
\(386\) 5.14005 0.261622
\(387\) −2.58579 + 2.58579i −0.131443 + 0.131443i
\(388\) −3.16693 + 3.16693i −0.160776 + 0.160776i
\(389\) 21.7717i 1.10387i 0.833888 + 0.551934i \(0.186110\pi\)
−0.833888 + 0.551934i \(0.813890\pi\)
\(390\) −7.08821 2.83577i −0.358925 0.143595i
\(391\) 34.7124i 1.75548i
\(392\) 0 0
\(393\) −7.96759 7.96759i −0.401912 0.401912i
\(394\) 1.89566i 0.0955019i
\(395\) 5.79756 + 13.5299i 0.291707 + 0.680762i
\(396\) 1.20398 0.0605025
\(397\) 22.4145 + 22.4145i 1.12495 + 1.12495i 0.990986 + 0.133965i \(0.0427709\pi\)
0.133965 + 0.990986i \(0.457229\pi\)
\(398\) 10.2551 10.2551i 0.514043 0.514043i
\(399\) 0 0
\(400\) −3.44871 + 3.62028i −0.172435 + 0.181014i
\(401\) 13.9706 0.697657 0.348828 0.937187i \(-0.386580\pi\)
0.348828 + 0.937187i \(0.386580\pi\)
\(402\) 11.3717 + 11.3717i 0.567171 + 0.567171i
\(403\) −7.03449 7.03449i −0.350413 0.350413i
\(404\) 11.1817 0.556308
\(405\) −3.11146 + 1.33327i −0.154610 + 0.0662505i
\(406\) 0 0
\(407\) −1.40350 + 1.40350i −0.0695690 + 0.0695690i
\(408\) 5.44871 + 5.44871i 0.269751 + 0.269751i
\(409\) 18.7392 0.926594 0.463297 0.886203i \(-0.346666\pi\)
0.463297 + 0.886203i \(0.346666\pi\)
\(410\) −1.69761 0.679163i −0.0838392 0.0335415i
\(411\) 10.9351i 0.539390i
\(412\) −1.71557 1.71557i −0.0845198 0.0845198i
\(413\) 0 0
\(414\) 8.57358i 0.421369i
\(415\) 10.8478 27.1148i 0.532497 1.33101i
\(416\) 2.90667i 0.142511i
\(417\) −18.4151 + 18.4151i −0.901792 + 0.901792i
\(418\) −0.994144 + 0.994144i −0.0486252 + 0.0486252i
\(419\) −31.5744 −1.54251 −0.771255 0.636526i \(-0.780371\pi\)
−0.771255 + 0.636526i \(0.780371\pi\)
\(420\) 0 0
\(421\) −13.5569 −0.660722 −0.330361 0.943855i \(-0.607171\pi\)
−0.330361 + 0.943855i \(0.607171\pi\)
\(422\) −7.09399 + 7.09399i −0.345330 + 0.345330i
\(423\) 5.39585 5.39585i 0.262355 0.262355i
\(424\) 4.98571i 0.242128i
\(425\) −32.7910 + 0.795878i −1.59060 + 0.0386058i
\(426\) 18.8141i 0.911547i
\(427\) 0 0
\(428\) 4.69553 + 4.69553i 0.226967 + 0.226967i
\(429\) 2.53701i 0.122488i
\(430\) 4.63872 1.98769i 0.223699 0.0958552i
\(431\) 13.2704 0.639210 0.319605 0.947551i \(-0.396450\pi\)
0.319605 + 0.947551i \(0.396450\pi\)
\(432\) 3.83750 + 3.83750i 0.184632 + 0.184632i
\(433\) 12.0535 12.0535i 0.579252 0.579252i −0.355445 0.934697i \(-0.615671\pi\)
0.934697 + 0.355445i \(0.115671\pi\)
\(434\) 0 0
\(435\) −23.6334 9.45497i −1.13313 0.453331i
\(436\) 8.96048 0.429129
\(437\) −7.07931 7.07931i −0.338649 0.338649i
\(438\) −7.35115 7.35115i −0.351251 0.351251i
\(439\) −35.0476 −1.67273 −0.836366 0.548172i \(-0.815324\pi\)
−0.836366 + 0.548172i \(0.815324\pi\)
\(440\) −1.54268 0.617179i −0.0735445 0.0294229i
\(441\) 0 0
\(442\) −13.4832 + 13.4832i −0.641330 + 0.641330i
\(443\) −0.0445958 0.0445958i −0.00211881 0.00211881i 0.706047 0.708165i \(-0.250477\pi\)
−0.708165 + 0.706047i \(0.750477\pi\)
\(444\) −3.13756 −0.148902
\(445\) −12.3978 + 5.31249i −0.587714 + 0.251836i
\(446\) 4.43718i 0.210107i
\(447\) −3.27444 3.27444i −0.154876 0.154876i
\(448\) 0 0
\(449\) 24.5207i 1.15720i 0.815611 + 0.578601i \(0.196401\pi\)
−0.815611 + 0.578601i \(0.803599\pi\)
\(450\) −8.09901 + 0.196573i −0.381791 + 0.00926653i
\(451\) 0.607609i 0.0286112i
\(452\) 0.307790 0.307790i 0.0144772 0.0144772i
\(453\) 16.5662 16.5662i 0.778346 0.778346i
\(454\) −0.670872 −0.0314856
\(455\) 0 0
\(456\) −2.22244 −0.104075
\(457\) 14.1939 14.1939i 0.663961 0.663961i −0.292350 0.956311i \(-0.594437\pi\)
0.956311 + 0.292350i \(0.0944374\pi\)
\(458\) 9.33616 9.33616i 0.436250 0.436250i
\(459\) 35.6022i 1.66177i
\(460\) 4.39494 10.9855i 0.204915 0.512199i
\(461\) 11.6940i 0.544642i −0.962207 0.272321i \(-0.912209\pi\)
0.962207 0.272321i \(-0.0877912\pi\)
\(462\) 0 0
\(463\) 2.77226 + 2.77226i 0.128838 + 0.128838i 0.768585 0.639747i \(-0.220961\pi\)
−0.639747 + 0.768585i \(0.720961\pi\)
\(464\) 9.69135i 0.449910i
\(465\) 8.34630 + 3.33910i 0.387050 + 0.154847i
\(466\) 8.65894 0.401117
\(467\) 14.7933 + 14.7933i 0.684552 + 0.684552i 0.961022 0.276470i \(-0.0891648\pi\)
−0.276470 + 0.961022i \(0.589165\pi\)
\(468\) −3.33020 + 3.33020i −0.153938 + 0.153938i
\(469\) 0 0
\(470\) −9.67977 + 4.14779i −0.446495 + 0.191323i
\(471\) 8.76655 0.403941
\(472\) −1.80295 1.80295i −0.0829873 0.0829873i
\(473\) 1.18586 + 1.18586i 0.0545259 + 0.0545259i
\(474\) −7.73231 −0.355157
\(475\) 6.52514 6.84976i 0.299394 0.314289i
\(476\) 0 0
\(477\) −5.71218 + 5.71218i −0.261543 + 0.261543i
\(478\) 2.83051 + 2.83051i 0.129464 + 0.129464i
\(479\) 24.2837 1.10955 0.554775 0.832000i \(-0.312804\pi\)
0.554775 + 0.832000i \(0.312804\pi\)
\(480\) −1.03449 2.41421i −0.0472179 0.110193i
\(481\) 7.76412i 0.354013i
\(482\) 12.2507 + 12.2507i 0.558005 + 0.558005i
\(483\) 0 0
\(484\) 10.4478i 0.474902i
\(485\) 9.29820 + 3.71992i 0.422210 + 0.168913i
\(486\) 14.5030i 0.657867i
\(487\) 1.80736 1.80736i 0.0818993 0.0818993i −0.664970 0.746870i \(-0.731556\pi\)
0.746870 + 0.664970i \(0.231556\pi\)
\(488\) 4.29468 4.29468i 0.194411 0.194411i
\(489\) −14.2910 −0.646262
\(490\) 0 0
\(491\) 14.5668 0.657391 0.328695 0.944436i \(-0.393391\pi\)
0.328695 + 0.944436i \(0.393391\pi\)
\(492\) 0.679163 0.679163i 0.0306190 0.0306190i
\(493\) −44.9554 + 44.9554i −2.02469 + 2.02469i
\(494\) 5.49957i 0.247437i
\(495\) −1.06036 2.47458i −0.0476596 0.111224i
\(496\) 3.42257i 0.153678i
\(497\) 0 0
\(498\) 10.8478 + 10.8478i 0.486101 + 0.486101i
\(499\) 30.0875i 1.34690i 0.739233 + 0.673450i \(0.235188\pi\)
−0.739233 + 0.673450i \(0.764812\pi\)
\(500\) 10.4781 + 3.89980i 0.468597 + 0.174404i
\(501\) 2.41805 0.108030
\(502\) −3.88865 3.88865i −0.173559 0.173559i
\(503\) −24.6819 + 24.6819i −1.10051 + 1.10051i −0.106161 + 0.994349i \(0.533856\pi\)
−0.994349 + 0.106161i \(0.966144\pi\)
\(504\) 0 0
\(505\) −9.84777 22.9819i −0.438220 1.02268i
\(506\) 3.93191 0.174795
\(507\) −3.78021 3.78021i −0.167885 0.167885i
\(508\) 11.1823 + 11.1823i 0.496134 + 0.496134i
\(509\) −12.4504 −0.551855 −0.275927 0.961178i \(-0.588985\pi\)
−0.275927 + 0.961178i \(0.588985\pi\)
\(510\) 6.40013 15.9976i 0.283403 0.708384i
\(511\) 0 0
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −7.26076 7.26076i −0.320571 0.320571i
\(514\) 16.5099 0.728219
\(515\) −2.01513 + 5.03695i −0.0887972 + 0.221955i
\(516\) 2.65102i 0.116705i
\(517\) −2.47458 2.47458i −0.108832 0.108832i
\(518\) 0 0
\(519\) 11.0509i 0.485079i
\(520\) 5.97414 2.55992i 0.261983 0.112260i
\(521\) 35.3351i 1.54806i 0.633149 + 0.774030i \(0.281762\pi\)
−0.633149 + 0.774030i \(0.718238\pi\)
\(522\) −11.1035 + 11.1035i −0.485986 + 0.485986i
\(523\) −11.6252 + 11.6252i −0.508336 + 0.508336i −0.914015 0.405680i \(-0.867035\pi\)
0.405680 + 0.914015i \(0.367035\pi\)
\(524\) 9.59282 0.419064
\(525\) 0 0
\(526\) 9.86084 0.429953
\(527\) 15.8763 15.8763i 0.691584 0.691584i
\(528\) 0.617179 0.617179i 0.0268593 0.0268593i
\(529\) 4.99914i 0.217354i
\(530\) 10.2473 4.39096i 0.445112 0.190731i
\(531\) 4.13131i 0.179283i
\(532\) 0 0
\(533\) 1.68063 + 1.68063i 0.0727964 + 0.0727964i
\(534\) 7.08536i 0.306613i
\(535\) 5.51544 13.7862i 0.238453 0.596031i
\(536\) −13.6913 −0.591376
\(537\) 3.73552 + 3.73552i 0.161199 + 0.161199i
\(538\) 6.33457 6.33457i 0.273103 0.273103i
\(539\) 0 0
\(540\) 4.50759 11.2670i 0.193976 0.484856i
\(541\) −26.5143 −1.13994 −0.569970 0.821665i \(-0.693045\pi\)
−0.569970 + 0.821665i \(0.693045\pi\)
\(542\) −16.1576 16.1576i −0.694027 0.694027i
\(543\) 14.8549 + 14.8549i 0.637485 + 0.637485i
\(544\) −6.56014 −0.281264
\(545\) −7.89157 18.4167i −0.338038 0.788884i
\(546\) 0 0
\(547\) −1.07403 + 1.07403i −0.0459223 + 0.0459223i −0.729695 0.683773i \(-0.760338\pi\)
0.683773 + 0.729695i \(0.260338\pi\)
\(548\) −6.58284 6.58284i −0.281205 0.281205i
\(549\) 9.84092 0.420000
\(550\) 0.0901497 + 3.71427i 0.00384400 + 0.158377i
\(551\) 18.3366i 0.781163i
\(552\) 4.39494 + 4.39494i 0.187061 + 0.187061i
\(553\) 0 0
\(554\) 21.5332i 0.914858i
\(555\) 2.76328 + 6.44871i 0.117295 + 0.273732i
\(556\) 22.1714i 0.940278i
\(557\) 10.9914 10.9914i 0.465721 0.465721i −0.434804 0.900525i \(-0.643182\pi\)
0.900525 + 0.434804i \(0.143182\pi\)
\(558\) 3.92128 3.92128i 0.166001 0.166001i
\(559\) −6.56014 −0.277464
\(560\) 0 0
\(561\) 5.72584 0.241745
\(562\) 3.99434 3.99434i 0.168491 0.168491i
\(563\) 19.4073 19.4073i 0.817919 0.817919i −0.167887 0.985806i \(-0.553695\pi\)
0.985806 + 0.167887i \(0.0536945\pi\)
\(564\) 5.53198i 0.232938i
\(565\) −0.903682 0.361535i −0.0380182 0.0152099i
\(566\) 2.92849i 0.123093i
\(567\) 0 0
\(568\) −11.3259 11.3259i −0.475225 0.475225i
\(569\) 6.75739i 0.283284i −0.989918 0.141642i \(-0.954762\pi\)
0.989918 0.141642i \(-0.0452383\pi\)
\(570\) 1.95732 + 4.56782i 0.0819830 + 0.191325i
\(571\) 11.7544 0.491907 0.245953 0.969282i \(-0.420899\pi\)
0.245953 + 0.969282i \(0.420899\pi\)
\(572\) 1.52725 + 1.52725i 0.0638576 + 0.0638576i
\(573\) 2.30526 2.30526i 0.0963034 0.0963034i
\(574\) 0 0
\(575\) −26.4493 + 0.641957i −1.10301 + 0.0267715i
\(576\) −1.62028 −0.0675116
\(577\) 1.59488 + 1.59488i 0.0663958 + 0.0663958i 0.739525 0.673129i \(-0.235050\pi\)
−0.673129 + 0.739525i \(0.735050\pi\)
\(578\) −18.4098 18.4098i −0.765747 0.765747i
\(579\) 6.03758 0.250913
\(580\) 19.9189 8.53525i 0.827085 0.354407i
\(581\) 0 0
\(582\) −3.71992 + 3.71992i −0.154196 + 0.154196i
\(583\) 2.61965 + 2.61965i 0.108495 + 0.108495i
\(584\) 8.85064 0.366242
\(585\) 9.77756 + 3.91170i 0.404253 + 0.161729i
\(586\) 15.2558i 0.630212i
\(587\) −12.8372 12.8372i −0.529847 0.529847i 0.390680 0.920527i \(-0.372240\pi\)
−0.920527 + 0.390680i \(0.872240\pi\)
\(588\) 0 0
\(589\) 6.47569i 0.266826i
\(590\) −2.11777 + 5.29350i −0.0871871 + 0.217930i
\(591\) 2.22667i 0.0915929i
\(592\) 1.88878 1.88878i 0.0776285 0.0776285i
\(593\) 25.7074 25.7074i 1.05568 1.05568i 0.0573221 0.998356i \(-0.481744\pi\)
0.998356 0.0573221i \(-0.0182562\pi\)
\(594\) 4.03269 0.165463
\(595\) 0 0
\(596\) 3.94236 0.161485
\(597\) 12.0458 12.0458i 0.493003 0.493003i
\(598\) −10.8756 + 10.8756i −0.444736 + 0.444736i
\(599\) 35.7717i 1.46159i −0.682596 0.730796i \(-0.739149\pi\)
0.682596 0.730796i \(-0.260851\pi\)
\(600\) −4.05090 + 4.25243i −0.165377 + 0.173605i
\(601\) 45.6631i 1.86264i 0.364204 + 0.931319i \(0.381341\pi\)
−0.364204 + 0.931319i \(0.618659\pi\)
\(602\) 0 0
\(603\) −15.6863 15.6863i −0.638796 0.638796i
\(604\) 19.9453i 0.811564i
\(605\) 21.4737 9.20150i 0.873030 0.374094i
\(606\) 13.1341 0.533538
\(607\) 0.828325 + 0.828325i 0.0336207 + 0.0336207i 0.723717 0.690097i \(-0.242432\pi\)
−0.690097 + 0.723717i \(0.742432\pi\)
\(608\) 1.33788 1.33788i 0.0542584 0.0542584i
\(609\) 0 0
\(610\) −12.6093 5.04460i −0.510536 0.204250i
\(611\) 13.6893 0.553808
\(612\) −7.51602 7.51602i −0.303817 0.303817i
\(613\) −9.85551 9.85551i −0.398060 0.398060i 0.479488 0.877548i \(-0.340822\pi\)
−0.877548 + 0.479488i \(0.840822\pi\)
\(614\) −9.74677 −0.393348
\(615\) −1.99404 0.797755i −0.0804076 0.0321686i
\(616\) 0 0
\(617\) 22.7725 22.7725i 0.916788 0.916788i −0.0800065 0.996794i \(-0.525494\pi\)
0.996794 + 0.0800065i \(0.0254941\pi\)
\(618\) −2.01513 2.01513i −0.0810604 0.0810604i
\(619\) −22.6773 −0.911476 −0.455738 0.890114i \(-0.650625\pi\)
−0.455738 + 0.890114i \(0.650625\pi\)
\(620\) −7.03449 + 3.01429i −0.282512 + 0.121057i
\(621\) 28.7168i 1.15237i
\(622\) 0.0891090 + 0.0891090i 0.00357294 + 0.00357294i
\(623\) 0 0
\(624\) 3.41421i 0.136678i
\(625\) −1.21285 24.9706i −0.0485138 0.998823i
\(626\) 11.6940i 0.467384i
\(627\) −1.16774 + 1.16774i −0.0466349 + 0.0466349i
\(628\) −5.27738 + 5.27738i −0.210590 + 0.210590i
\(629\) 17.5231 0.698690
\(630\) 0 0
\(631\) 32.4210 1.29066 0.645330 0.763904i \(-0.276720\pi\)
0.645330 + 0.763904i \(0.276720\pi\)
\(632\) 4.65477 4.65477i 0.185157 0.185157i
\(633\) −8.33270 + 8.33270i −0.331195 + 0.331195i
\(634\) 10.9462i 0.434729i
\(635\) 13.1349 32.8315i 0.521242 1.30288i
\(636\) 5.85629i 0.232217i
\(637\) 0 0
\(638\) 5.09214 + 5.09214i 0.201600 + 0.201600i
\(639\) 25.9524i 1.02666i
\(640\) 2.07609 + 0.830578i 0.0820646 + 0.0328315i
\(641\) −0.856140 −0.0338155 −0.0169077 0.999857i \(-0.505382\pi\)
−0.0169077 + 0.999857i \(0.505382\pi\)
\(642\) 5.51544 + 5.51544i 0.217677 + 0.217677i
\(643\) 16.4254 16.4254i 0.647754 0.647754i −0.304696 0.952450i \(-0.598555\pi\)
0.952450 + 0.304696i \(0.0985548\pi\)
\(644\) 0 0
\(645\) 5.44871 2.33478i 0.214543 0.0919317i
\(646\) 12.4121 0.488349
\(647\) −33.5510 33.5510i −1.31903 1.31903i −0.914546 0.404482i \(-0.867452\pi\)
−0.404482 0.914546i \(-0.632548\pi\)
\(648\) 1.07046 + 1.07046i 0.0420516 + 0.0420516i
\(649\) −1.89465 −0.0743714
\(650\) −10.5229 10.0242i −0.412744 0.393183i
\(651\) 0 0
\(652\) 8.60305 8.60305i 0.336921 0.336921i
\(653\) 18.5780 + 18.5780i 0.727015 + 0.727015i 0.970024 0.243009i \(-0.0781344\pi\)
−0.243009 + 0.970024i \(0.578134\pi\)
\(654\) 10.5251 0.411565
\(655\) −8.44848 19.7163i −0.330109 0.770381i
\(656\) 0.817699i 0.0319258i
\(657\) 10.1403 + 10.1403i 0.395609 + 0.395609i
\(658\) 0 0
\(659\) 26.2355i 1.02199i −0.859583 0.510996i \(-0.829277\pi\)
0.859583 0.510996i \(-0.170723\pi\)
\(660\) −1.81206 0.724948i −0.0705343 0.0282186i
\(661\) 14.5719i 0.566782i −0.959004 0.283391i \(-0.908541\pi\)
0.959004 0.283391i \(-0.0914595\pi\)
\(662\) 3.86107 3.86107i 0.150065 0.150065i
\(663\) −15.8376 + 15.8376i −0.615080 + 0.615080i
\(664\) −13.0605 −0.506847
\(665\) 0 0
\(666\) 4.32800 0.167706
\(667\) −36.2611 + 36.2611i −1.40404 + 1.40404i
\(668\) −1.45564 + 1.45564i −0.0563205 + 0.0563205i
\(669\) 5.21198i 0.201507i
\(670\) 12.0581 + 28.1401i 0.465844 + 1.08715i
\(671\) 4.51312i 0.174227i
\(672\) 0 0
\(673\) −16.4201 16.4201i −0.632950 0.632950i 0.315857 0.948807i \(-0.397708\pi\)
−0.948807 + 0.315857i \(0.897708\pi\)
\(674\) 28.9664i 1.11574i
\(675\) −27.1273 + 0.658412i −1.04413 + 0.0253423i
\(676\) 4.55129 0.175050
\(677\) 16.0965 + 16.0965i 0.618638 + 0.618638i 0.945182 0.326544i \(-0.105884\pi\)
−0.326544 + 0.945182i \(0.605884\pi\)
\(678\) 0.361535 0.361535i 0.0138847 0.0138847i
\(679\) 0 0
\(680\) 5.77756 + 13.4832i 0.221559 + 0.517057i
\(681\) −0.788016 −0.0301968
\(682\) −1.79833 1.79833i −0.0688615 0.0688615i
\(683\) 21.6661 + 21.6661i 0.829030 + 0.829030i 0.987383 0.158353i \(-0.0506183\pi\)
−0.158353 + 0.987383i \(0.550618\pi\)
\(684\) 3.06566 0.117218
\(685\) −7.73231 + 19.3274i −0.295436 + 0.738463i
\(686\) 0 0
\(687\) 10.9664 10.9664i 0.418394 0.418394i
\(688\) −1.59589 1.59589i −0.0608427 0.0608427i
\(689\) −14.4918 −0.552094
\(690\) 5.16236 12.9037i 0.196528 0.491235i
\(691\) 32.0180i 1.21802i −0.793161 0.609012i \(-0.791566\pi\)
0.793161 0.609012i \(-0.208434\pi\)
\(692\) −6.65251 6.65251i −0.252891 0.252891i
\(693\) 0 0
\(694\) 21.5379i 0.817567i
\(695\) −45.5694 + 19.5266i −1.72855 + 0.740684i
\(696\) 11.3836i 0.431494i
\(697\) −3.79307 + 3.79307i −0.143673 + 0.143673i
\(698\) 8.89145 8.89145i 0.336546 0.336546i
\(699\) 10.1709 0.384699
\(700\) 0 0
\(701\) −18.5294 −0.699844 −0.349922 0.936779i \(-0.613792\pi\)
−0.349922 + 0.936779i \(0.613792\pi\)
\(702\) −11.1543 + 11.1543i −0.420993 + 0.420993i
\(703\) −3.57368 + 3.57368i −0.134784 + 0.134784i
\(704\) 0.743072i 0.0280056i
\(705\) −11.3700 + 4.87206i −0.428219 + 0.183492i
\(706\) 0.689506i 0.0259499i
\(707\) 0 0
\(708\) −2.11777 2.11777i −0.0795905 0.0795905i
\(709\) 26.6822i 1.00207i −0.865427 0.501035i \(-0.832953\pi\)
0.865427 0.501035i \(-0.167047\pi\)
\(710\) −13.3036 + 33.2532i −0.499275 + 1.24797i
\(711\) 10.6660 0.400008
\(712\) 4.26531 + 4.26531i 0.159849 + 0.159849i
\(713\) 12.8059 12.8059i 0.479585 0.479585i
\(714\) 0 0
\(715\) 1.79393 4.48406i 0.0670893 0.167694i
\(716\) −4.49749 −0.168079
\(717\) 3.32476 + 3.32476i 0.124165 + 0.124165i
\(718\) 15.6262 + 15.6262i 0.583165 + 0.583165i
\(719\) −31.9779 −1.19258 −0.596288 0.802771i \(-0.703358\pi\)
−0.596288 + 0.802771i \(0.703358\pi\)
\(720\) 1.42699 + 3.33020i 0.0531809 + 0.124109i
\(721\) 0 0
\(722\) 10.9037 10.9037i 0.405793 0.405793i
\(723\) 14.3899 + 14.3899i 0.535165 + 0.535165i
\(724\) −17.8850 −0.664691
\(725\) −35.0854 33.4226i −1.30304 1.24128i
\(726\) 12.2722i 0.455464i
\(727\) −21.4539 21.4539i −0.795683 0.795683i 0.186729 0.982412i \(-0.440211\pi\)
−0.982412 + 0.186729i \(0.940211\pi\)
\(728\) 0 0
\(729\) 21.5770i 0.799146i
\(730\) −7.79483 18.1909i −0.288499 0.673276i
\(731\) 14.8058i 0.547611i
\(732\) 5.04460 5.04460i 0.186454 0.186454i
\(733\) −9.20125 + 9.20125i −0.339856 + 0.339856i −0.856313 0.516457i \(-0.827251\pi\)
0.516457 + 0.856313i \(0.327251\pi\)
\(734\) −13.4109 −0.495006
\(735\) 0 0
\(736\) −5.29142 −0.195044
\(737\) −7.19386 + 7.19386i −0.264989 + 0.264989i
\(738\) −0.936846 + 0.936846i −0.0344858 + 0.0344858i
\(739\) 3.60424i 0.132584i 0.997800 + 0.0662920i \(0.0211169\pi\)
−0.997800 + 0.0662920i \(0.978883\pi\)
\(740\) −5.54552 2.21859i −0.203858 0.0815571i
\(741\) 6.45988i 0.237309i
\(742\) 0 0
\(743\) 31.1070 + 31.1070i 1.14121 + 1.14121i 0.988230 + 0.152977i \(0.0488859\pi\)
0.152977 + 0.988230i \(0.451114\pi\)
\(744\) 4.02021i 0.147388i
\(745\) −3.47207 8.10282i −0.127207 0.296864i
\(746\) 14.9664 0.547959
\(747\) −14.9636 14.9636i −0.547489 0.547489i
\(748\) −3.44690 + 3.44690i −0.126031 + 0.126031i
\(749\) 0 0
\(750\) 12.3078 + 4.58076i 0.449417 + 0.167266i
\(751\) −51.0282 −1.86205 −0.931023 0.364960i \(-0.881083\pi\)
−0.931023 + 0.364960i \(0.881083\pi\)
\(752\) 3.33020 + 3.33020i 0.121440 + 0.121440i
\(753\) −4.56766 4.56766i −0.166455 0.166455i
\(754\) −28.1695 −1.02587
\(755\) 40.9941 17.5660i 1.49193 0.639293i
\(756\) 0 0
\(757\) 26.8141 26.8141i 0.974576 0.974576i −0.0251083 0.999685i \(-0.507993\pi\)
0.999685 + 0.0251083i \(0.00799305\pi\)
\(758\) 1.21470 + 1.21470i 0.0441198 + 0.0441198i
\(759\) 4.61848 0.167640
\(760\) −3.92807 1.57150i −0.142486 0.0570043i
\(761\) 29.8782i 1.08309i 0.840673 + 0.541543i \(0.182160\pi\)
−0.840673 + 0.541543i \(0.817840\pi\)
\(762\) 13.1349 + 13.1349i 0.475827 + 0.475827i
\(763\) 0 0
\(764\) 2.77548i 0.100413i
\(765\) −8.82843 + 22.0673i −0.319192 + 0.797844i
\(766\) 10.4581i 0.377866i
\(767\) 5.24056 5.24056i 0.189226 0.189226i
\(768\) −0.830578 + 0.830578i −0.0299709 + 0.0299709i
\(769\) −44.7341 −1.61315 −0.806576 0.591130i \(-0.798682\pi\)
−0.806576 + 0.591130i \(0.798682\pi\)
\(770\) 0 0
\(771\) 19.3927 0.698413
\(772\) −3.63457 + 3.63457i −0.130811 + 0.130811i
\(773\) 17.0808 17.0808i 0.614355 0.614355i −0.329723 0.944078i \(-0.606955\pi\)
0.944078 + 0.329723i \(0.106955\pi\)
\(774\) 3.65685i 0.131443i
\(775\) 12.3907 + 11.8034i 0.445086 + 0.423992i
\(776\) 4.47871i 0.160776i
\(777\) 0 0
\(778\) −15.3949 15.3949i −0.551934 0.551934i
\(779\) 1.54713i 0.0554317i
\(780\) 7.01731 3.00693i 0.251260 0.107665i
\(781\) −11.9020 −0.425886
\(782\) −24.5454 24.5454i −0.877742 0.877742i
\(783\) −37.1906 + 37.1906i −1.32908 + 1.32908i
\(784\) 0 0