Properties

Label 1950.2.z.n.1699.4
Level $1950$
Weight $2$
Character 1950.1699
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.z (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
Defining polynomial: \(x^{8} - 9 x^{6} + 65 x^{4} - 144 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1699.4
Root \(1.35234 - 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1699
Dual form 1950.2.z.n.1849.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(0.486319 - 0.280776i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(0.486319 - 0.280776i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.06155 + 3.57071i) q^{11} -1.00000i q^{12} +(-2.21837 + 2.84233i) q^{13} +0.561553 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.70469 - 1.56155i) q^{17} +1.00000i q^{18} +(0.280776 + 0.486319i) q^{19} -0.561553 q^{21} +(-3.57071 + 2.06155i) q^{22} +(-4.05703 - 2.34233i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-3.34233 + 1.35234i) q^{26} -1.00000i q^{27} +(0.486319 + 0.280776i) q^{28} +(1.21922 - 2.11176i) q^{29} -6.68466 q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.57071 - 2.06155i) q^{33} +3.12311 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-3.57071 - 2.06155i) q^{37} +0.561553i q^{38} +(3.34233 - 1.35234i) q^{39} +(-6.12311 + 10.6055i) q^{41} +(-0.486319 - 0.280776i) q^{42} +(0.379706 - 0.219224i) q^{43} -4.12311 q^{44} +(-2.34233 - 4.05703i) q^{46} -7.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(-3.34233 + 5.78908i) q^{49} -3.12311 q^{51} +(-3.57071 - 0.500000i) q^{52} +8.56155i q^{53} +(0.500000 - 0.866025i) q^{54} +(0.280776 + 0.486319i) q^{56} -0.561553i q^{57} +(2.11176 - 1.21922i) q^{58} +(3.21922 + 5.57586i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(-5.78908 - 3.34233i) q^{62} +(0.486319 + 0.280776i) q^{63} -1.00000 q^{64} +4.12311 q^{66} +(-1.94528 - 1.12311i) q^{67} +(2.70469 + 1.56155i) q^{68} +(2.34233 + 4.05703i) q^{69} +(6.56155 + 11.3649i) q^{71} +(-0.866025 + 0.500000i) q^{72} +9.36932i q^{73} +(-2.06155 - 3.57071i) q^{74} +(-0.280776 + 0.486319i) q^{76} +2.31534i q^{77} +(3.57071 + 0.500000i) q^{78} -11.5616 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-10.6055 + 6.12311i) q^{82} -7.12311i q^{83} +(-0.280776 - 0.486319i) q^{84} +0.438447 q^{86} +(-2.11176 + 1.21922i) q^{87} +(-3.57071 - 2.06155i) q^{88} +(-9.40388 + 16.2880i) q^{89} +(-0.280776 + 2.00514i) q^{91} -4.68466i q^{92} +(5.78908 + 3.34233i) q^{93} +(3.50000 - 6.06218i) q^{94} +1.00000 q^{96} +(6.16879 - 3.56155i) q^{97} +(-5.78908 + 3.34233i) q^{98} -4.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} - 4q^{6} + 4q^{9} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{6} + 4q^{9} - 12q^{14} - 4q^{16} - 6q^{19} + 12q^{21} + 4q^{24} - 2q^{26} + 18q^{29} - 4q^{31} - 8q^{34} - 4q^{36} + 2q^{39} - 16q^{41} + 6q^{46} - 2q^{49} + 8q^{51} + 4q^{54} - 6q^{56} + 34q^{59} - 24q^{61} - 8q^{64} - 6q^{69} + 36q^{71} + 6q^{76} - 76q^{79} - 4q^{81} + 6q^{84} + 20q^{86} - 34q^{89} + 6q^{91} + 28q^{94} + 8q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 0.486319 0.280776i 0.183811 0.106124i −0.405271 0.914197i \(-0.632823\pi\)
0.589082 + 0.808073i \(0.299489\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −2.06155 + 3.57071i −0.621582 + 1.07661i 0.367610 + 0.929980i \(0.380176\pi\)
−0.989191 + 0.146631i \(0.953157\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −2.21837 + 2.84233i −0.615265 + 0.788320i
\(14\) 0.561553 0.150081
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.70469 1.56155i 0.655983 0.378732i −0.134761 0.990878i \(-0.543027\pi\)
0.790745 + 0.612146i \(0.209693\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0.280776 + 0.486319i 0.0644145 + 0.111569i 0.896434 0.443177i \(-0.146149\pi\)
−0.832020 + 0.554746i \(0.812815\pi\)
\(20\) 0 0
\(21\) −0.561553 −0.122541
\(22\) −3.57071 + 2.06155i −0.761279 + 0.439525i
\(23\) −4.05703 2.34233i −0.845950 0.488409i 0.0133324 0.999911i \(-0.495756\pi\)
−0.859282 + 0.511502i \(0.829089\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0 0
\(26\) −3.34233 + 1.35234i −0.655485 + 0.265217i
\(27\) 1.00000i 0.192450i
\(28\) 0.486319 + 0.280776i 0.0919057 + 0.0530618i
\(29\) 1.21922 2.11176i 0.226404 0.392143i −0.730336 0.683088i \(-0.760636\pi\)
0.956740 + 0.290945i \(0.0939697\pi\)
\(30\) 0 0
\(31\) −6.68466 −1.20060 −0.600300 0.799775i \(-0.704952\pi\)
−0.600300 + 0.799775i \(0.704952\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 3.57071 2.06155i 0.621582 0.358870i
\(34\) 3.12311 0.535608
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −3.57071 2.06155i −0.587022 0.338917i 0.176897 0.984229i \(-0.443394\pi\)
−0.763919 + 0.645312i \(0.776727\pi\)
\(38\) 0.561553i 0.0910959i
\(39\) 3.34233 1.35234i 0.535201 0.216548i
\(40\) 0 0
\(41\) −6.12311 + 10.6055i −0.956268 + 1.65631i −0.224830 + 0.974398i \(0.572183\pi\)
−0.731438 + 0.681908i \(0.761151\pi\)
\(42\) −0.486319 0.280776i −0.0750407 0.0433247i
\(43\) 0.379706 0.219224i 0.0579047 0.0334313i −0.470768 0.882257i \(-0.656023\pi\)
0.528673 + 0.848826i \(0.322690\pi\)
\(44\) −4.12311 −0.621582
\(45\) 0 0
\(46\) −2.34233 4.05703i −0.345358 0.598177i
\(47\) 7.00000i 1.02105i −0.859861 0.510527i \(-0.829450\pi\)
0.859861 0.510527i \(-0.170550\pi\)
\(48\) 0.866025 0.500000i 0.125000 0.0721688i
\(49\) −3.34233 + 5.78908i −0.477476 + 0.827012i
\(50\) 0 0
\(51\) −3.12311 −0.437322
\(52\) −3.57071 0.500000i −0.495169 0.0693375i
\(53\) 8.56155i 1.17602i 0.808854 + 0.588010i \(0.200088\pi\)
−0.808854 + 0.588010i \(0.799912\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 0.280776 + 0.486319i 0.0375203 + 0.0649871i
\(57\) 0.561553i 0.0743795i
\(58\) 2.11176 1.21922i 0.277287 0.160092i
\(59\) 3.21922 + 5.57586i 0.419107 + 0.725915i 0.995850 0.0910109i \(-0.0290098\pi\)
−0.576743 + 0.816926i \(0.695676\pi\)
\(60\) 0 0
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) −5.78908 3.34233i −0.735214 0.424476i
\(63\) 0.486319 + 0.280776i 0.0612704 + 0.0353745i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 4.12311 0.507519
\(67\) −1.94528 1.12311i −0.237653 0.137209i 0.376444 0.926439i \(-0.377147\pi\)
−0.614098 + 0.789230i \(0.710480\pi\)
\(68\) 2.70469 + 1.56155i 0.327992 + 0.189366i
\(69\) 2.34233 + 4.05703i 0.281983 + 0.488409i
\(70\) 0 0
\(71\) 6.56155 + 11.3649i 0.778713 + 1.34877i 0.932684 + 0.360695i \(0.117461\pi\)
−0.153971 + 0.988075i \(0.549206\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 9.36932i 1.09660i 0.836283 + 0.548298i \(0.184724\pi\)
−0.836283 + 0.548298i \(0.815276\pi\)
\(74\) −2.06155 3.57071i −0.239651 0.415087i
\(75\) 0 0
\(76\) −0.280776 + 0.486319i −0.0322073 + 0.0557846i
\(77\) 2.31534i 0.263858i
\(78\) 3.57071 + 0.500000i 0.404304 + 0.0566139i
\(79\) −11.5616 −1.30078 −0.650388 0.759602i \(-0.725394\pi\)
−0.650388 + 0.759602i \(0.725394\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −10.6055 + 6.12311i −1.17118 + 0.676184i
\(83\) 7.12311i 0.781862i −0.920420 0.390931i \(-0.872153\pi\)
0.920420 0.390931i \(-0.127847\pi\)
\(84\) −0.280776 0.486319i −0.0306352 0.0530618i
\(85\) 0 0
\(86\) 0.438447 0.0472790
\(87\) −2.11176 + 1.21922i −0.226404 + 0.130714i
\(88\) −3.57071 2.06155i −0.380639 0.219762i
\(89\) −9.40388 + 16.2880i −0.996810 + 1.72652i −0.429281 + 0.903171i \(0.641233\pi\)
−0.567529 + 0.823354i \(0.692100\pi\)
\(90\) 0 0
\(91\) −0.280776 + 2.00514i −0.0294334 + 0.210196i
\(92\) 4.68466i 0.488409i
\(93\) 5.78908 + 3.34233i 0.600300 + 0.346583i
\(94\) 3.50000 6.06218i 0.360997 0.625266i
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 6.16879 3.56155i 0.626346 0.361621i −0.152990 0.988228i \(-0.548890\pi\)
0.779335 + 0.626607i \(0.215557\pi\)
\(98\) −5.78908 + 3.34233i −0.584786 + 0.337626i
\(99\) −4.12311 −0.414388
\(100\) 0 0
\(101\) 4.43845 7.68762i 0.441642 0.764946i −0.556170 0.831069i \(-0.687729\pi\)
0.997812 + 0.0661225i \(0.0210628\pi\)
\(102\) −2.70469 1.56155i −0.267804 0.154617i
\(103\) 4.56155i 0.449463i 0.974421 + 0.224732i \(0.0721505\pi\)
−0.974421 + 0.224732i \(0.927849\pi\)
\(104\) −2.84233 2.21837i −0.278713 0.217529i
\(105\) 0 0
\(106\) −4.28078 + 7.41452i −0.415786 + 0.720162i
\(107\) 1.73205 + 1.00000i 0.167444 + 0.0966736i 0.581380 0.813632i \(-0.302513\pi\)
−0.413936 + 0.910306i \(0.635846\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 3.75379 0.359548 0.179774 0.983708i \(-0.442463\pi\)
0.179774 + 0.983708i \(0.442463\pi\)
\(110\) 0 0
\(111\) 2.06155 + 3.57071i 0.195674 + 0.338917i
\(112\) 0.561553i 0.0530618i
\(113\) 7.52113 4.34233i 0.707529 0.408492i −0.102617 0.994721i \(-0.532721\pi\)
0.810145 + 0.586229i \(0.199388\pi\)
\(114\) 0.280776 0.486319i 0.0262971 0.0455479i
\(115\) 0 0
\(116\) 2.43845 0.226404
\(117\) −3.57071 0.500000i −0.330113 0.0462250i
\(118\) 6.43845i 0.592707i
\(119\) 0.876894 1.51883i 0.0803848 0.139231i
\(120\) 0 0
\(121\) −3.00000 5.19615i −0.272727 0.472377i
\(122\) 6.00000i 0.543214i
\(123\) 10.6055 6.12311i 0.956268 0.552102i
\(124\) −3.34233 5.78908i −0.300150 0.519875i
\(125\) 0 0
\(126\) 0.280776 + 0.486319i 0.0250136 + 0.0433247i
\(127\) −7.41452 4.28078i −0.657932 0.379857i 0.133556 0.991041i \(-0.457360\pi\)
−0.791489 + 0.611184i \(0.790694\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −0.438447 −0.0386031
\(130\) 0 0
\(131\) −2.12311 −0.185497 −0.0927483 0.995690i \(-0.529565\pi\)
−0.0927483 + 0.995690i \(0.529565\pi\)
\(132\) 3.57071 + 2.06155i 0.310791 + 0.179435i
\(133\) 0.273094 + 0.157671i 0.0236802 + 0.0136718i
\(134\) −1.12311 1.94528i −0.0970215 0.168046i
\(135\) 0 0
\(136\) 1.56155 + 2.70469i 0.133902 + 0.231925i
\(137\) −10.2258 + 5.90388i −0.873651 + 0.504403i −0.868560 0.495584i \(-0.834954\pi\)
−0.00509126 + 0.999987i \(0.501621\pi\)
\(138\) 4.68466i 0.398785i
\(139\) 6.28078 + 10.8786i 0.532729 + 0.922713i 0.999270 + 0.0382133i \(0.0121666\pi\)
−0.466541 + 0.884500i \(0.654500\pi\)
\(140\) 0 0
\(141\) −3.50000 + 6.06218i −0.294753 + 0.510527i
\(142\) 13.1231i 1.10127i
\(143\) −5.57586 13.7808i −0.466277 1.15241i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −4.68466 + 8.11407i −0.387705 + 0.671525i
\(147\) 5.78908 3.34233i 0.477476 0.275671i
\(148\) 4.12311i 0.338917i
\(149\) −1.09612 1.89853i −0.0897975 0.155534i 0.817628 0.575747i \(-0.195289\pi\)
−0.907425 + 0.420213i \(0.861955\pi\)
\(150\) 0 0
\(151\) −15.3693 −1.25074 −0.625369 0.780329i \(-0.715051\pi\)
−0.625369 + 0.780329i \(0.715051\pi\)
\(152\) −0.486319 + 0.280776i −0.0394457 + 0.0227740i
\(153\) 2.70469 + 1.56155i 0.218661 + 0.126244i
\(154\) −1.15767 + 2.00514i −0.0932878 + 0.161579i
\(155\) 0 0
\(156\) 2.84233 + 2.21837i 0.227568 + 0.177612i
\(157\) 13.8769i 1.10750i −0.832684 0.553748i \(-0.813197\pi\)
0.832684 0.553748i \(-0.186803\pi\)
\(158\) −10.0126 5.78078i −0.796560 0.459894i
\(159\) 4.28078 7.41452i 0.339488 0.588010i
\(160\) 0 0
\(161\) −2.63068 −0.207327
\(162\) −0.866025 + 0.500000i −0.0680414 + 0.0392837i
\(163\) −12.5041 + 7.21922i −0.979394 + 0.565453i −0.902087 0.431554i \(-0.857965\pi\)
−0.0773067 + 0.997007i \(0.524632\pi\)
\(164\) −12.2462 −0.956268
\(165\) 0 0
\(166\) 3.56155 6.16879i 0.276430 0.478791i
\(167\) 3.78394 + 2.18466i 0.292810 + 0.169054i 0.639208 0.769034i \(-0.279262\pi\)
−0.346398 + 0.938087i \(0.612595\pi\)
\(168\) 0.561553i 0.0433247i
\(169\) −3.15767 12.6107i −0.242898 0.970052i
\(170\) 0 0
\(171\) −0.280776 + 0.486319i −0.0214715 + 0.0371897i
\(172\) 0.379706 + 0.219224i 0.0289523 + 0.0167156i
\(173\) 17.4739 10.0885i 1.32851 0.767018i 0.343444 0.939173i \(-0.388407\pi\)
0.985070 + 0.172156i \(0.0550732\pi\)
\(174\) −2.43845 −0.184858
\(175\) 0 0
\(176\) −2.06155 3.57071i −0.155395 0.269153i
\(177\) 6.43845i 0.483943i
\(178\) −16.2880 + 9.40388i −1.22084 + 0.704851i
\(179\) −6.34233 + 10.9852i −0.474048 + 0.821075i −0.999559 0.0297120i \(-0.990541\pi\)
0.525511 + 0.850787i \(0.323874\pi\)
\(180\) 0 0
\(181\) 2.87689 0.213838 0.106919 0.994268i \(-0.465901\pi\)
0.106919 + 0.994268i \(0.465901\pi\)
\(182\) −1.24573 + 1.59612i −0.0923398 + 0.118312i
\(183\) 6.00000i 0.443533i
\(184\) 2.34233 4.05703i 0.172679 0.299088i
\(185\) 0 0
\(186\) 3.34233 + 5.78908i 0.245071 + 0.424476i
\(187\) 12.8769i 0.941652i
\(188\) 6.06218 3.50000i 0.442130 0.255264i
\(189\) −0.280776 0.486319i −0.0204235 0.0353745i
\(190\) 0 0
\(191\) −5.43845 9.41967i −0.393512 0.681583i 0.599398 0.800451i \(-0.295407\pi\)
−0.992910 + 0.118868i \(0.962073\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 7.12311 0.511409
\(195\) 0 0
\(196\) −6.68466 −0.477476
\(197\) 11.0918 + 6.40388i 0.790262 + 0.456258i 0.840055 0.542502i \(-0.182523\pi\)
−0.0497931 + 0.998760i \(0.515856\pi\)
\(198\) −3.57071 2.06155i −0.253760 0.146508i
\(199\) 1.43845 + 2.49146i 0.101969 + 0.176615i 0.912496 0.409086i \(-0.134152\pi\)
−0.810527 + 0.585701i \(0.800819\pi\)
\(200\) 0 0
\(201\) 1.12311 + 1.94528i 0.0792178 + 0.137209i
\(202\) 7.68762 4.43845i 0.540899 0.312288i
\(203\) 1.36932i 0.0961072i
\(204\) −1.56155 2.70469i −0.109331 0.189366i
\(205\) 0 0
\(206\) −2.28078 + 3.95042i −0.158909 + 0.275239i
\(207\) 4.68466i 0.325606i
\(208\) −1.35234 3.34233i −0.0937682 0.231749i
\(209\) −2.31534 −0.160156
\(210\) 0 0
\(211\) 10.9654 18.9927i 0.754892 1.30751i −0.190536 0.981680i \(-0.561023\pi\)
0.945428 0.325831i \(-0.105644\pi\)
\(212\) −7.41452 + 4.28078i −0.509231 + 0.294005i
\(213\) 13.1231i 0.899180i
\(214\) 1.00000 + 1.73205i 0.0683586 + 0.118401i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −3.25088 + 1.87689i −0.220684 + 0.127412i
\(218\) 3.25088 + 1.87689i 0.220177 + 0.127119i
\(219\) 4.68466 8.11407i 0.316560 0.548298i
\(220\) 0 0
\(221\) −1.56155 + 11.1517i −0.105041 + 0.750146i
\(222\) 4.12311i 0.276725i
\(223\) −23.6427 13.6501i −1.58323 0.914078i −0.994384 0.105832i \(-0.966249\pi\)
−0.588845 0.808246i \(-0.700417\pi\)
\(224\) −0.280776 + 0.486319i −0.0187602 + 0.0324936i
\(225\) 0 0
\(226\) 8.68466 0.577695
\(227\) 17.3205 10.0000i 1.14960 0.663723i 0.200812 0.979630i \(-0.435642\pi\)
0.948790 + 0.315906i \(0.102309\pi\)
\(228\) 0.486319 0.280776i 0.0322073 0.0185949i
\(229\) 24.2462 1.60223 0.801117 0.598507i \(-0.204239\pi\)
0.801117 + 0.598507i \(0.204239\pi\)
\(230\) 0 0
\(231\) 1.15767 2.00514i 0.0761691 0.131929i
\(232\) 2.11176 + 1.21922i 0.138644 + 0.0800460i
\(233\) 5.31534i 0.348220i −0.984726 0.174110i \(-0.944295\pi\)
0.984726 0.174110i \(-0.0557048\pi\)
\(234\) −2.84233 2.21837i −0.185809 0.145019i
\(235\) 0 0
\(236\) −3.21922 + 5.57586i −0.209554 + 0.362957i
\(237\) 10.0126 + 5.78078i 0.650388 + 0.375502i
\(238\) 1.51883 0.876894i 0.0984508 0.0568406i
\(239\) 11.3693 0.735420 0.367710 0.929941i \(-0.380142\pi\)
0.367710 + 0.929941i \(0.380142\pi\)
\(240\) 0 0
\(241\) 14.0616 + 24.3553i 0.905784 + 1.56886i 0.819861 + 0.572563i \(0.194051\pi\)
0.0859232 + 0.996302i \(0.472616\pi\)
\(242\) 6.00000i 0.385695i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) 3.00000 5.19615i 0.192055 0.332650i
\(245\) 0 0
\(246\) 12.2462 0.780790
\(247\) −2.00514 0.280776i −0.127584 0.0178654i
\(248\) 6.68466i 0.424476i
\(249\) −3.56155 + 6.16879i −0.225704 + 0.390931i
\(250\) 0 0
\(251\) 4.06155 + 7.03482i 0.256363 + 0.444034i 0.965265 0.261273i \(-0.0841424\pi\)
−0.708902 + 0.705307i \(0.750809\pi\)
\(252\) 0.561553i 0.0353745i
\(253\) 16.7276 9.65767i 1.05165 0.607173i
\(254\) −4.28078 7.41452i −0.268600 0.465229i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.81645 2.78078i −0.300442 0.173460i 0.342200 0.939627i \(-0.388828\pi\)
−0.642641 + 0.766167i \(0.722161\pi\)
\(258\) −0.379706 0.219224i −0.0236395 0.0136483i
\(259\) −2.31534 −0.143868
\(260\) 0 0
\(261\) 2.43845 0.150936
\(262\) −1.83866 1.06155i −0.113593 0.0655830i
\(263\) 11.2583 + 6.50000i 0.694218 + 0.400807i 0.805190 0.593016i \(-0.202063\pi\)
−0.110972 + 0.993824i \(0.535396\pi\)
\(264\) 2.06155 + 3.57071i 0.126880 + 0.219762i
\(265\) 0 0
\(266\) 0.157671 + 0.273094i 0.00966742 + 0.0167445i
\(267\) 16.2880 9.40388i 0.996810 0.575508i
\(268\) 2.24621i 0.137209i
\(269\) 10.6847 + 18.5064i 0.651455 + 1.12835i 0.982770 + 0.184833i \(0.0591745\pi\)
−0.331315 + 0.943520i \(0.607492\pi\)
\(270\) 0 0
\(271\) 6.58854 11.4117i 0.400225 0.693211i −0.593528 0.804814i \(-0.702265\pi\)
0.993753 + 0.111603i \(0.0355985\pi\)
\(272\) 3.12311i 0.189366i
\(273\) 1.24573 1.59612i 0.0753951 0.0966015i
\(274\) −11.8078 −0.713333
\(275\) 0 0
\(276\) −2.34233 + 4.05703i −0.140992 + 0.244205i
\(277\) 0.866025 0.500000i 0.0520344 0.0300421i −0.473757 0.880656i \(-0.657103\pi\)
0.525792 + 0.850613i \(0.323769\pi\)
\(278\) 12.5616i 0.753392i
\(279\) −3.34233 5.78908i −0.200100 0.346583i
\(280\) 0 0
\(281\) 16.2462 0.969168 0.484584 0.874745i \(-0.338971\pi\)
0.484584 + 0.874745i \(0.338971\pi\)
\(282\) −6.06218 + 3.50000i −0.360997 + 0.208422i
\(283\) −13.4767 7.78078i −0.801107 0.462519i 0.0427513 0.999086i \(-0.486388\pi\)
−0.843858 + 0.536567i \(0.819721\pi\)
\(284\) −6.56155 + 11.3649i −0.389357 + 0.674385i
\(285\) 0 0
\(286\) 2.06155 14.7224i 0.121902 0.870556i
\(287\) 6.87689i 0.405930i
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) −3.62311 + 6.27540i −0.213124 + 0.369141i
\(290\) 0 0
\(291\) −7.12311 −0.417564
\(292\) −8.11407 + 4.68466i −0.474840 + 0.274149i
\(293\) 3.40423 1.96543i 0.198877 0.114822i −0.397254 0.917709i \(-0.630037\pi\)
0.596132 + 0.802887i \(0.296704\pi\)
\(294\) 6.68466 0.389857
\(295\) 0 0
\(296\) 2.06155 3.57071i 0.119825 0.207544i
\(297\) 3.57071 + 2.06155i 0.207194 + 0.119623i
\(298\) 2.19224i 0.126993i
\(299\) 15.6577 6.33527i 0.905506 0.366378i
\(300\) 0 0
\(301\) 0.123106 0.213225i 0.00709569 0.0122901i
\(302\) −13.3102 7.68466i −0.765917 0.442202i
\(303\) −7.68762 + 4.43845i −0.441642 + 0.254982i
\(304\) −0.561553 −0.0322073
\(305\) 0 0
\(306\) 1.56155 + 2.70469i 0.0892680 + 0.154617i
\(307\) 25.6155i 1.46196i −0.682401 0.730978i \(-0.739064\pi\)
0.682401 0.730978i \(-0.260936\pi\)
\(308\) −2.00514 + 1.15767i −0.114254 + 0.0659644i
\(309\) 2.28078 3.95042i 0.129749 0.224732i
\(310\) 0 0
\(311\) 30.7386 1.74303 0.871514 0.490371i \(-0.163139\pi\)
0.871514 + 0.490371i \(0.163139\pi\)
\(312\) 1.35234 + 3.34233i 0.0765614 + 0.189222i
\(313\) 31.3693i 1.77310i 0.462634 + 0.886549i \(0.346904\pi\)
−0.462634 + 0.886549i \(0.653096\pi\)
\(314\) 6.93845 12.0177i 0.391559 0.678200i
\(315\) 0 0
\(316\) −5.78078 10.0126i −0.325194 0.563253i
\(317\) 24.8078i 1.39334i 0.717390 + 0.696671i \(0.245336\pi\)
−0.717390 + 0.696671i \(0.754664\pi\)
\(318\) 7.41452 4.28078i 0.415786 0.240054i
\(319\) 5.02699 + 8.70700i 0.281457 + 0.487498i
\(320\) 0 0
\(321\) −1.00000 1.73205i −0.0558146 0.0966736i
\(322\) −2.27824 1.31534i −0.126961 0.0733011i
\(323\) 1.51883 + 0.876894i 0.0845097 + 0.0487917i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −14.4384 −0.799672
\(327\) −3.25088 1.87689i −0.179774 0.103792i
\(328\) −10.6055 6.12311i −0.585592 0.338092i
\(329\) −1.96543 3.40423i −0.108358 0.187681i
\(330\) 0 0
\(331\) −15.3693 26.6204i −0.844774 1.46319i −0.885817 0.464034i \(-0.846401\pi\)
0.0410432 0.999157i \(-0.486932\pi\)
\(332\) 6.16879 3.56155i 0.338556 0.195466i
\(333\) 4.12311i 0.225945i
\(334\) 2.18466 + 3.78394i 0.119539 + 0.207048i
\(335\) 0 0
\(336\) 0.280776 0.486319i 0.0153176 0.0265309i
\(337\) 6.00000i 0.326841i 0.986557 + 0.163420i \(0.0522527\pi\)
−0.986557 + 0.163420i \(0.947747\pi\)
\(338\) 3.57071 12.5000i 0.194221 0.679910i
\(339\) −8.68466 −0.471686
\(340\) 0 0
\(341\) 13.7808 23.8690i 0.746271 1.29258i
\(342\) −0.486319 + 0.280776i −0.0262971 + 0.0151826i
\(343\) 7.68466i 0.414933i
\(344\) 0.219224 + 0.379706i 0.0118197 + 0.0204724i
\(345\) 0 0
\(346\) 20.1771 1.08473
\(347\) −0.759413 + 0.438447i −0.0407674 + 0.0235371i −0.520245 0.854017i \(-0.674159\pi\)
0.479478 + 0.877554i \(0.340826\pi\)
\(348\) −2.11176 1.21922i −0.113202 0.0653572i
\(349\) 4.24621 7.35465i 0.227294 0.393686i −0.729711 0.683756i \(-0.760345\pi\)
0.957005 + 0.290070i \(0.0936787\pi\)
\(350\) 0 0
\(351\) 2.84233 + 2.21837i 0.151712 + 0.118408i
\(352\) 4.12311i 0.219762i
\(353\) 22.3969 + 12.9309i 1.19207 + 0.688241i 0.958775 0.284166i \(-0.0917166\pi\)
0.233293 + 0.972407i \(0.425050\pi\)
\(354\) 3.21922 5.57586i 0.171100 0.296354i
\(355\) 0 0
\(356\) −18.8078 −0.996810
\(357\) −1.51883 + 0.876894i −0.0803848 + 0.0464102i
\(358\) −10.9852 + 6.34233i −0.580588 + 0.335203i
\(359\) −13.1231 −0.692611 −0.346306 0.938122i \(-0.612564\pi\)
−0.346306 + 0.938122i \(0.612564\pi\)
\(360\) 0 0
\(361\) 9.34233 16.1814i 0.491702 0.851652i
\(362\) 2.49146 + 1.43845i 0.130948 + 0.0756031i
\(363\) 6.00000i 0.314918i
\(364\) −1.87689 + 0.759413i −0.0983760 + 0.0398040i
\(365\) 0 0
\(366\) −3.00000 + 5.19615i −0.156813 + 0.271607i
\(367\) 10.8188 + 6.24621i 0.564734 + 0.326050i 0.755044 0.655675i \(-0.227616\pi\)
−0.190309 + 0.981724i \(0.560949\pi\)
\(368\) 4.05703 2.34233i 0.211487 0.122102i
\(369\) −12.2462 −0.637512
\(370\) 0 0
\(371\) 2.40388 + 4.16365i 0.124803 + 0.216166i
\(372\) 6.68466i 0.346583i
\(373\) −22.3502 + 12.9039i −1.15725 + 0.668138i −0.950643 0.310287i \(-0.899575\pi\)
−0.206605 + 0.978424i \(0.566242\pi\)
\(374\) −6.43845 + 11.1517i −0.332924 + 0.576642i
\(375\) 0 0
\(376\) 7.00000 0.360997
\(377\) 3.29762 + 8.15009i 0.169836 + 0.419751i
\(378\) 0.561553i 0.0288832i
\(379\) −8.84233 + 15.3154i −0.454200 + 0.786697i −0.998642 0.0521012i \(-0.983408\pi\)
0.544442 + 0.838799i \(0.316741\pi\)
\(380\) 0 0
\(381\) 4.28078 + 7.41452i 0.219311 + 0.379857i
\(382\) 10.8769i 0.556510i
\(383\) 0.166481 0.0961180i 0.00850679 0.00491140i −0.495741 0.868471i \(-0.665103\pi\)
0.504247 + 0.863559i \(0.331770\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) 0 0
\(387\) 0.379706 + 0.219224i 0.0193016 + 0.0111438i
\(388\) 6.16879 + 3.56155i 0.313173 + 0.180810i
\(389\) 18.0540 0.915373 0.457686 0.889114i \(-0.348678\pi\)
0.457686 + 0.889114i \(0.348678\pi\)
\(390\) 0 0
\(391\) −14.6307 −0.739905
\(392\) −5.78908 3.34233i −0.292393 0.168813i
\(393\) 1.83866 + 1.06155i 0.0927483 + 0.0535483i
\(394\) 6.40388 + 11.0918i 0.322623 + 0.558799i
\(395\) 0 0
\(396\) −2.06155 3.57071i −0.103597 0.179435i
\(397\) 17.4271 10.0616i 0.874642 0.504975i 0.00575403 0.999983i \(-0.498168\pi\)
0.868888 + 0.495009i \(0.164835\pi\)
\(398\) 2.87689i 0.144206i
\(399\) −0.157671 0.273094i −0.00789341 0.0136718i
\(400\) 0 0
\(401\) −0.157671 + 0.273094i −0.00787370 + 0.0136377i −0.869935 0.493166i \(-0.835840\pi\)
0.862062 + 0.506803i \(0.169173\pi\)
\(402\) 2.24621i 0.112031i
\(403\) 14.8290 19.0000i 0.738687 0.946457i
\(404\) 8.87689 0.441642
\(405\) 0 0
\(406\) 0.684658 1.18586i 0.0339790 0.0588534i
\(407\) 14.7224 8.50000i 0.729764 0.421329i
\(408\) 3.12311i 0.154617i
\(409\) −9.40388 16.2880i −0.464992 0.805390i 0.534209 0.845352i \(-0.320609\pi\)
−0.999201 + 0.0399625i \(0.987276\pi\)
\(410\) 0 0
\(411\) 11.8078 0.582434
\(412\) −3.95042 + 2.28078i −0.194623 + 0.112366i
\(413\) 3.13114 + 1.80776i 0.154073 + 0.0889543i
\(414\) 2.34233 4.05703i 0.115119 0.199392i
\(415\) 0 0
\(416\) 0.500000 3.57071i 0.0245145 0.175069i
\(417\) 12.5616i 0.615142i
\(418\) −2.00514 1.15767i −0.0980748 0.0566235i
\(419\) 16.2462 28.1393i 0.793679 1.37469i −0.129995 0.991515i \(-0.541496\pi\)
0.923674 0.383178i \(-0.125171\pi\)
\(420\) 0 0
\(421\) −32.4924 −1.58358 −0.791792 0.610791i \(-0.790852\pi\)
−0.791792 + 0.610791i \(0.790852\pi\)
\(422\) 18.9927 10.9654i 0.924550 0.533789i
\(423\) 6.06218 3.50000i 0.294753 0.170176i
\(424\) −8.56155 −0.415786
\(425\) 0 0
\(426\) 6.56155 11.3649i 0.317908 0.550633i
\(427\) −2.91791 1.68466i −0.141208 0.0815263i
\(428\) 2.00000i 0.0966736i
\(429\) −2.06155 + 14.7224i −0.0995327 + 0.710806i
\(430\) 0 0
\(431\) 11.3693 19.6922i 0.547641 0.948542i −0.450795 0.892628i \(-0.648859\pi\)
0.998436 0.0559140i \(-0.0178073\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) −16.2281 + 9.36932i −0.779874 + 0.450261i −0.836386 0.548141i \(-0.815336\pi\)
0.0565114 + 0.998402i \(0.482002\pi\)
\(434\) −3.75379 −0.180188
\(435\) 0 0
\(436\) 1.87689 + 3.25088i 0.0898869 + 0.155689i
\(437\) 2.63068i 0.125843i
\(438\) 8.11407 4.68466i 0.387705 0.223842i
\(439\) 12.5616 21.7572i 0.599530 1.03842i −0.393360 0.919384i \(-0.628687\pi\)
0.992890 0.119032i \(-0.0379792\pi\)
\(440\) 0 0
\(441\) −6.68466 −0.318317
\(442\) −6.92820 + 8.87689i −0.329541 + 0.422231i
\(443\) 13.1231i 0.623498i −0.950165 0.311749i \(-0.899085\pi\)
0.950165 0.311749i \(-0.100915\pi\)
\(444\) −2.06155 + 3.57071i −0.0978370 + 0.169459i
\(445\) 0 0
\(446\) −13.6501 23.6427i −0.646351 1.11951i
\(447\) 2.19224i 0.103689i
\(448\) −0.486319 + 0.280776i −0.0229764 + 0.0132654i
\(449\) −10.0885 17.4739i −0.476108 0.824643i 0.523518 0.852015i \(-0.324619\pi\)
−0.999625 + 0.0273722i \(0.991286\pi\)
\(450\) 0 0
\(451\) −25.2462 43.7277i −1.18880 2.05906i
\(452\) 7.52113 + 4.34233i 0.353764 + 0.204246i
\(453\) 13.3102 + 7.68466i 0.625369 + 0.361057i
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) 0.561553 0.0262971
\(457\) 17.5337 + 10.1231i 0.820193 + 0.473539i 0.850483 0.526002i \(-0.176310\pi\)
−0.0302897 + 0.999541i \(0.509643\pi\)
\(458\) 20.9978 + 12.1231i 0.981164 + 0.566476i
\(459\) −1.56155 2.70469i −0.0728870 0.126244i
\(460\) 0 0
\(461\) 15.0270 + 26.0275i 0.699877 + 1.21222i 0.968509 + 0.248979i \(0.0800950\pi\)
−0.268632 + 0.963243i \(0.586572\pi\)
\(462\) 2.00514 1.15767i 0.0932878 0.0538597i
\(463\) 7.61553i 0.353924i −0.984218 0.176962i \(-0.943373\pi\)
0.984218 0.176962i \(-0.0566269\pi\)
\(464\) 1.21922 + 2.11176i 0.0566010 + 0.0980359i
\(465\) 0 0
\(466\) 2.65767 4.60322i 0.123114 0.213240i
\(467\) 17.8617i 0.826543i 0.910608 + 0.413271i \(0.135614\pi\)
−0.910608 + 0.413271i \(0.864386\pi\)
\(468\) −1.35234 3.34233i −0.0625121 0.154499i
\(469\) −1.26137 −0.0582445
\(470\) 0 0
\(471\) −6.93845 + 12.0177i −0.319707 + 0.553748i
\(472\) −5.57586 + 3.21922i −0.256650 + 0.148177i
\(473\) 1.80776i 0.0831211i
\(474\) 5.78078 + 10.0126i 0.265520 + 0.459894i
\(475\) 0 0
\(476\) 1.75379 0.0803848
\(477\) −7.41452 + 4.28078i −0.339488 + 0.196003i
\(478\) 9.84612 + 5.68466i 0.450351 + 0.260010i
\(479\) −19.1231 + 33.1222i −0.873757 + 1.51339i −0.0156760 + 0.999877i \(0.504990\pi\)
−0.858081 + 0.513514i \(0.828343\pi\)
\(480\) 0 0
\(481\) 13.7808 5.57586i 0.628349 0.254237i
\(482\) 28.1231i 1.28097i
\(483\) 2.27824 + 1.31534i 0.103663 + 0.0598501i
\(484\) 3.00000 5.19615i 0.136364 0.236189i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) −11.3051 + 6.52699i −0.512282 + 0.295766i −0.733771 0.679397i \(-0.762242\pi\)
0.221489 + 0.975163i \(0.428908\pi\)
\(488\) 5.19615 3.00000i 0.235219 0.135804i
\(489\) 14.4384 0.652929
\(490\) 0 0
\(491\) 8.71922 15.1021i 0.393493 0.681550i −0.599415 0.800439i \(-0.704600\pi\)
0.992908 + 0.118889i \(0.0379332\pi\)
\(492\) 10.6055 + 6.12311i 0.478134 + 0.276051i
\(493\) 7.61553i 0.342986i
\(494\) −1.59612 1.24573i −0.0718127 0.0560481i
\(495\) 0 0
\(496\) 3.34233 5.78908i 0.150075 0.259938i
\(497\) 6.38202 + 3.68466i 0.286273 + 0.165280i
\(498\) −6.16879 + 3.56155i −0.276430 + 0.159597i
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) −2.18466 3.78394i −0.0976033 0.169054i
\(502\) 8.12311i 0.362552i
\(503\) −37.2858 + 21.5270i −1.66249 + 0.959841i −0.690974 + 0.722879i \(0.742818\pi\)
−0.971519 + 0.236962i \(0.923848\pi\)
\(504\) −0.280776 + 0.486319i −0.0125068 + 0.0216624i
\(505\) 0 0
\(506\) 19.3153 0.858672
\(507\) −3.57071 + 12.5000i −0.158581 + 0.555144i
\(508\) 8.56155i 0.379857i
\(509\) 20.2732 35.1142i 0.898594 1.55641i 0.0693009 0.997596i \(-0.477923\pi\)
0.829293 0.558814i \(-0.188744\pi\)
\(510\) 0 0
\(511\) 2.63068 + 4.55648i 0.116375 + 0.201567i
\(512\) 1.00000i 0.0441942i
\(513\) 0.486319 0.280776i 0.0214715 0.0123966i
\(514\) −2.78078 4.81645i −0.122655 0.212444i
\(515\) 0 0
\(516\) −0.219224 0.379706i −0.00965078 0.0167156i
\(517\) 24.9950 + 14.4309i 1.09928 + 0.634669i
\(518\) −2.00514 1.15767i −0.0881010 0.0508651i
\(519\) −20.1771 −0.885676
\(520\) 0 0
\(521\) −6.31534 −0.276680 −0.138340 0.990385i \(-0.544177\pi\)
−0.138340 + 0.990385i \(0.544177\pi\)
\(522\) 2.11176 + 1.21922i 0.0924291 + 0.0533640i
\(523\) 25.8143 + 14.9039i 1.12878 + 0.651701i 0.943628 0.331009i \(-0.107389\pi\)
0.185152 + 0.982710i \(0.440722\pi\)
\(524\) −1.06155 1.83866i −0.0463741 0.0803224i
\(525\) 0 0
\(526\) 6.50000 + 11.2583i 0.283413 + 0.490887i
\(527\) −18.0799 + 10.4384i −0.787574 + 0.454706i
\(528\) 4.12311i 0.179435i
\(529\) −0.526988 0.912769i −0.0229125 0.0396856i
\(530\) 0 0
\(531\) −3.21922 + 5.57586i −0.139702 + 0.241972i
\(532\) 0.315342i 0.0136718i
\(533\) −16.5611 40.9309i −0.717341 1.77291i
\(534\) 18.8078 0.813892
\(535\) 0 0
\(536\) 1.12311 1.94528i 0.0485108 0.0840231i
\(537\) 10.9852 6.34233i 0.474048 0.273692i
\(538\) 21.3693i 0.921297i
\(539\) −13.7808 23.8690i −0.593580 1.02811i
\(540\) 0 0
\(541\) −27.3693 −1.17670 −0.588349 0.808607i \(-0.700222\pi\)
−0.588349 + 0.808607i \(0.700222\pi\)
\(542\) 11.4117 6.58854i 0.490174 0.283002i
\(543\) −2.49146 1.43845i −0.106919 0.0617297i
\(544\) −1.56155 + 2.70469i −0.0669510 + 0.115963i
\(545\) 0 0
\(546\) 1.87689 0.759413i 0.0803237 0.0324999i
\(547\) 5.61553i 0.240103i 0.992768 + 0.120051i \(0.0383059\pi\)
−0.992768 + 0.120051i \(0.961694\pi\)
\(548\) −10.2258 5.90388i −0.436826 0.252201i
\(549\) 3.00000 5.19615i 0.128037 0.221766i
\(550\) 0 0
\(551\) 1.36932 0.0583349
\(552\) −4.05703 + 2.34233i −0.172679 + 0.0996962i
\(553\) −5.62260 + 3.24621i −0.239097 + 0.138043i
\(554\) 1.00000 0.0424859
\(555\) 0 0
\(556\) −6.28078 + 10.8786i −0.266364 + 0.461356i
\(557\) −7.41452 4.28078i −0.314163 0.181382i 0.334625 0.942352i \(-0.391390\pi\)
−0.648788 + 0.760969i \(0.724724\pi\)
\(558\) 6.68466i 0.282984i
\(559\) −0.219224 + 1.56557i −0.00927217 + 0.0662165i
\(560\) 0 0
\(561\) 6.43845 11.1517i 0.271831 0.470826i
\(562\) 14.0696 + 8.12311i 0.593492 + 0.342653i
\(563\) −28.5657 + 16.4924i −1.20390 + 0.695073i −0.961420 0.275083i \(-0.911295\pi\)
−0.242481 + 0.970156i \(0.577961\pi\)
\(564\) −7.00000 −0.294753
\(565\) 0 0
\(566\) −7.78078 13.4767i −0.327050 0.566468i
\(567\) 0.561553i 0.0235830i
\(568\) −11.3649 + 6.56155i −0.476862 + 0.275317i
\(569\) 13.0885 22.6700i 0.548700 0.950377i −0.449664 0.893198i \(-0.648456\pi\)
0.998364 0.0571787i \(-0.0182105\pi\)
\(570\) 0 0
\(571\) 23.6847 0.991172 0.495586 0.868559i \(-0.334953\pi\)
0.495586 + 0.868559i \(0.334953\pi\)
\(572\) 9.14657 11.7192i 0.382437 0.490005i
\(573\) 10.8769i 0.454389i
\(574\) −3.43845 + 5.95557i −0.143518 + 0.248580i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 40.7386i 1.69597i 0.530019 + 0.847986i \(0.322185\pi\)
−0.530019 + 0.847986i \(0.677815\pi\)
\(578\) −6.27540 + 3.62311i −0.261022 + 0.150701i
\(579\) 0 0
\(580\) 0 0
\(581\) −2.00000 3.46410i −0.0829740 0.143715i
\(582\) −6.16879 3.56155i −0.255705 0.147631i
\(583\) −30.5709 17.6501i −1.26612 0.730992i
\(584\) −9.36932 −0.387705
\(585\) 0 0
\(586\) 3.93087 0.162383
\(587\) −34.8542 20.1231i −1.43859 0.830569i −0.440837 0.897587i \(-0.645318\pi\)
−0.997752 + 0.0670179i \(0.978652\pi\)
\(588\) 5.78908 + 3.34233i 0.238738 + 0.137835i
\(589\) −1.87689 3.25088i −0.0773361 0.133950i
\(590\) 0 0
\(591\) −6.40388 11.0918i −0.263421 0.456258i
\(592\) 3.57071 2.06155i 0.146755 0.0847293i
\(593\) 33.1771i 1.36242i 0.732088 + 0.681210i \(0.238546\pi\)
−0.732088 + 0.681210i \(0.761454\pi\)
\(594\) 2.06155 + 3.57071i 0.0845865 + 0.146508i
\(595\) 0 0
\(596\) 1.09612 1.89853i 0.0448987 0.0777669i
\(597\) 2.87689i 0.117743i
\(598\) 16.7276 + 2.34233i 0.684041 + 0.0957850i
\(599\) 14.0000 0.572024 0.286012 0.958226i \(-0.407670\pi\)
0.286012 + 0.958226i \(0.407670\pi\)
\(600\) 0 0
\(601\) −14.9924 + 25.9676i −0.611554 + 1.05924i 0.379425 + 0.925222i \(0.376122\pi\)
−0.990979 + 0.134020i \(0.957212\pi\)
\(602\) 0.213225 0.123106i 0.00869041 0.00501741i
\(603\) 2.24621i 0.0914728i
\(604\) −7.68466 13.3102i −0.312684 0.541585i
\(605\) 0 0
\(606\) −8.87689 −0.360599
\(607\) −28.0794 + 16.2116i −1.13971 + 0.658010i −0.946358 0.323120i \(-0.895268\pi\)
−0.193349 + 0.981130i \(0.561935\pi\)
\(608\) −0.486319 0.280776i −0.0197228 0.0113870i
\(609\) −0.684658 + 1.18586i −0.0277438 + 0.0480536i
\(610\) 0 0
\(611\) 19.8963 + 15.5286i 0.804918 + 0.628219i
\(612\) 3.12311i 0.126244i
\(613\) −17.2139 9.93845i −0.695263 0.401410i 0.110318 0.993896i \(-0.464813\pi\)
−0.805581 + 0.592486i \(0.798146\pi\)
\(614\) 12.8078 22.1837i 0.516879 0.895261i
\(615\) 0 0
\(616\) −2.31534 −0.0932878
\(617\) 25.3878 14.6577i 1.02208 0.590096i 0.107371 0.994219i \(-0.465757\pi\)
0.914704 + 0.404123i \(0.132423\pi\)
\(618\) 3.95042 2.28078i 0.158909 0.0917463i
\(619\) 20.5616 0.826439 0.413219 0.910632i \(-0.364404\pi\)
0.413219 + 0.910632i \(0.364404\pi\)
\(620\) 0 0
\(621\) −2.34233 + 4.05703i −0.0939944 + 0.162803i
\(622\) 26.6204 + 15.3693i 1.06738 + 0.616253i
\(623\) 10.5616i 0.423140i
\(624\) −0.500000 + 3.57071i −0.0200160 + 0.142943i
\(625\) 0 0
\(626\) −15.6847 + 27.1666i −0.626885 + 1.08580i
\(627\) 2.00514 + 1.15767i 0.0800778 + 0.0462329i
\(628\) 12.0177 6.93845i 0.479560 0.276874i
\(629\) −12.8769 −0.513435
\(630\) 0 0
\(631\) 6.87689 + 11.9111i 0.273765 + 0.474175i 0.969823 0.243811i \(-0.0783977\pi\)
−0.696058 + 0.717986i \(0.745064\pi\)
\(632\) 11.5616i 0.459894i
\(633\) −18.9927 + 10.9654i −0.754892 + 0.435837i
\(634\) −12.4039 + 21.4842i −0.492621 + 0.853245i
\(635\) 0 0
\(636\) 8.56155 0.339488
\(637\) −9.03996 22.3423i −0.358176 0.885235i
\(638\) 10.0540i 0.398041i
\(639\) −6.56155 + 11.3649i −0.259571 + 0.449590i
\(640\) 0 0
\(641\) 5.71922 + 9.90599i 0.225896 + 0.391263i 0.956588 0.291444i \(-0.0941358\pi\)
−0.730692 + 0.682707i \(0.760802\pi\)
\(642\) 2.00000i 0.0789337i
\(643\) 18.8393 10.8769i 0.742951 0.428943i −0.0801904 0.996780i \(-0.525553\pi\)
0.823141 + 0.567837i \(0.192220\pi\)
\(644\) −1.31534 2.27824i −0.0518317 0.0897752i
\(645\) 0 0
\(646\) 0.876894 + 1.51883i 0.0345009 + 0.0597574i
\(647\) 30.3576 + 17.5270i 1.19348 + 0.689057i 0.959094 0.283086i \(-0.0913583\pi\)
0.234387 + 0.972143i \(0.424692\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −26.5464 −1.04204
\(650\) 0 0
\(651\) 3.75379 0.147123
\(652\) −12.5041 7.21922i −0.489697 0.282727i
\(653\) 38.5914 + 22.2808i 1.51020 + 0.871914i 0.999929 + 0.0119002i \(0.00378803\pi\)
0.510270 + 0.860014i \(0.329545\pi\)
\(654\) −1.87689 3.25088i −0.0733924 0.127119i
\(655\) 0 0
\(656\) −6.12311 10.6055i −0.239067 0.414076i
\(657\) −8.11407 + 4.68466i −0.316560 + 0.182766i
\(658\) 3.93087i 0.153241i
\(659\) −3.02699 5.24290i −0.117915 0.204234i 0.801026 0.598629i \(-0.204288\pi\)
−0.918941 + 0.394395i \(0.870954\pi\)
\(660\) 0 0
\(661\) −14.8078 + 25.6478i −0.575955 + 0.997584i 0.419982 + 0.907532i \(0.362036\pi\)
−0.995937 + 0.0900513i \(0.971297\pi\)
\(662\) 30.7386i 1.19469i
\(663\) 6.92820 8.87689i 0.269069 0.344750i
\(664\) 7.12311 0.276430
\(665\) 0 0
\(666\) 2.06155 3.57071i 0.0798835 0.138362i
\(667\) −9.89286 + 5.71165i −0.383053 + 0.221156i
\(668\) 4.36932i 0.169054i
\(669\) 13.6501 + 23.6427i 0.527743 + 0.914078i
\(670\) 0 0
\(671\) 24.7386 0.955024
\(672\) 0.486319 0.280776i 0.0187602 0.0108312i
\(673\) −22.3034 12.8769i −0.859734 0.496368i 0.00418904 0.999991i \(-0.498667\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(674\) −3.00000 + 5.19615i −0.115556 + 0.200148i
\(675\) 0 0
\(676\) 9.34233 9.03996i 0.359320 0.347691i
\(677\) 37.1231i 1.42676i 0.700779 + 0.713378i \(0.252836\pi\)
−0.700779 + 0.713378i \(0.747164\pi\)
\(678\) −7.52113 4.34233i −0.288847 0.166766i
\(679\) 2.00000 3.46410i 0.0767530 0.132940i
\(680\) 0 0
\(681\) −20.0000 −0.766402
\(682\) 23.8690 13.7808i 0.913991 0.527693i
\(683\) 14.8290 8.56155i 0.567418 0.327599i −0.188700 0.982035i \(-0.560427\pi\)
0.756117 + 0.654436i \(0.227094\pi\)
\(684\) −0.561553 −0.0214715
\(685\) 0 0
\(686\) −3.84233 + 6.65511i −0.146701 + 0.254093i
\(687\) −20.9978 12.1231i −0.801117 0.462525i
\(688\) 0.438447i 0.0167156i
\(689\) −24.3348 18.9927i −0.927080 0.723564i
\(690\) 0 0
\(691\) 10.2808 17.8068i 0.391099 0.677404i −0.601496 0.798876i \(-0.705428\pi\)
0.992595 + 0.121472i \(0.0387616\pi\)
\(692\) 17.4739 + 10.0885i 0.664257 + 0.383509i
\(693\) −2.00514 + 1.15767i −0.0761691 + 0.0439763i
\(694\) −0.876894 −0.0332865
\(695\) 0 0
\(696\) −1.21922 2.11176i −0.0462146 0.0800460i
\(697\) 38.2462i 1.44868i
\(698\) 7.35465 4.24621i 0.278378 0.160721i
\(699\) −2.65767 + 4.60322i −0.100522 + 0.174110i
\(700\) 0 0
\(701\) −36.3002 −1.37104 −0.685520 0.728054i \(-0.740425\pi\)
−0.685520 + 0.728054i \(0.740425\pi\)
\(702\) 1.35234 + 3.34233i 0.0510410 + 0.126148i
\(703\) 2.31534i 0.0873248i
\(704\) 2.06155 3.57071i 0.0776977 0.134576i
\(705\) 0 0
\(706\) 12.9309 + 22.3969i 0.486660 + 0.842919i
\(707\) 4.98485i 0.187474i
\(708\) 5.57586 3.21922i 0.209554 0.120986i
\(709\) 17.1231 + 29.6581i 0.643072 + 1.11383i 0.984743 + 0.174013i \(0.0556736\pi\)
−0.341672 + 0.939819i \(0.610993\pi\)
\(710\) 0 0
\(711\) −5.78078 10.0126i −0.216796 0.375502i
\(712\) −16.2880 9.40388i −0.610419 0.352425i
\(713\) 27.1199 + 15.6577i 1.01565 + 0.586384i
\(714\) −1.75379 −0.0656339
\(715\) 0 0
\(716\) −12.6847 −0.474048
\(717\) −9.84612 5.68466i −0.367710 0.212297i
\(718\) −11.3649 6.56155i −0.424136 0.244875i
\(719\) 22.4924 + 38.9580i 0.838826 + 1.45289i 0.890877 + 0.454245i \(0.150091\pi\)
−0.0520512 + 0.998644i \(0.516576\pi\)
\(720\) 0 0
\(721\) 1.28078 + 2.21837i 0.0476986 + 0.0826164i
\(722\) 16.1814 9.34233i 0.602209 0.347685i
\(723\) 28.1231i 1.04591i
\(724\) 1.43845 + 2.49146i 0.0534595 + 0.0925945i
\(725\) 0 0
\(726\) −3.00000 + 5.19615i −0.111340 + 0.192847i
\(727\) 38.4233i 1.42504i −0.701651 0.712521i \(-0.747554\pi\)
0.701651 0.712521i \(-0.252446\pi\)
\(728\) −2.00514 0.280776i −0.0743156 0.0104063i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0.684658 1.18586i 0.0253230 0.0438607i
\(732\) −5.19615 + 3.00000i −0.192055 + 0.110883i
\(733\) 20.0691i 0.741270i 0.928779 + 0.370635i \(0.120860\pi\)
−0.928779 + 0.370635i \(0.879140\pi\)
\(734\) 6.24621 + 10.8188i 0.230552 + 0.399328i
\(735\) 0 0
\(736\) 4.68466 0.172679
\(737\) 8.02058 4.63068i 0.295442 0.170573i
\(738\) −10.6055 6.12311i −0.390395 0.225395i
\(739\) −13.7732 + 23.8559i −0.506655 + 0.877553i 0.493315 + 0.869851i \(0.335785\pi\)
−0.999970 + 0.00770202i \(0.997548\pi\)
\(740\) 0 0
\(741\) 1.59612 + 1.24573i 0.0586349 + 0.0457631i
\(742\) 4.80776i 0.176499i
\(743\) −11.4117 6.58854i −0.418654 0.241710i 0.275847 0.961202i \(-0.411042\pi\)
−0.694501 + 0.719491i \(0.744375\pi\)
\(744\) −3.34233 + 5.78908i −0.122536 + 0.212238i
\(745\) 0 0
\(746\) −25.8078 −0.944889
\(747\) 6.16879 3.56155i 0.225704 0.130310i
\(748\) −11.1517 + 6.43845i −0.407747 + 0.235413i
\(749\) 1.12311 0.0410374
\(750\) 0 0
\(751\) 11.9039 20.6181i 0.434379 0.752366i −0.562866 0.826548i \(-0.690301\pi\)
0.997245 + 0.0741820i \(0.0236346\pi\)
\(752\) 6.06218 + 3.50000i 0.221065 + 0.127632i
\(753\) 8.12311i 0.296022i
\(754\) −1.21922 + 8.70700i −0.0444015 + 0.317090i
\(755\) 0 0
\(756\) 0.280776 0.486319i 0.0102117 0.0176873i
\(757\) −24.6153 14.2116i −0.894658 0.516531i −0.0191948 0.999816i \(-0.506110\pi\)
−0.875463 + 0.483285i \(0.839444\pi\)
\(758\) −15.3154 + 8.84233i −0.556279 + 0.321168i
\(759\) −19.3153 −0.701102
\(760\) 0 0
\(761\) 8.96543 + 15.5286i 0.324997 + 0.562911i 0.981512 0.191402i \(-0.0613035\pi\)
−0.656515 + 0.754313i \(0.727970\pi\)
\(762\) 8.56155i 0.310152i
\(763\) 1.82554 1.05398i 0.0660889 0.0381565i
\(764\) 5.43845 9.41967i 0.196756 0.340792i
\(765\) 0 0
\(766\) 0.192236 0.00694577
\(767\) −22.9899 3.21922i −0.830116 0.116239i
\(768\) 1.00000i 0.0360844i
\(769\) −16.6577 + 28.8519i −0.600691 + 1.04043i 0.392026 + 0.919954i \(0.371774\pi\)
−0.992717 + 0.120473i \(0.961559\pi\)
\(770\) 0 0
\(771\) 2.78078 + 4.81645i 0.100147 + 0.173460i
\(772\) 0 0
\(773\) 20.9380 12.0885i 0.753086 0.434795i −0.0737217 0.997279i \(-0.523488\pi\)
0.826808 + 0.562484i \(0.190154\pi\)
\(774\) 0.219224 + 0.379706i 0.00787983 + 0.0136483i
\(775\) 0 0
\(776\) 3.56155 + 6.16879i 0.127852 + 0.221447i
\(777\) 2.00514 + 1.15767i 0.0719342 + 0.0415312i
\(778\) 15.6352 + 9.02699i 0.560549 + 0.323633i
\(779\) −6.87689 −0.246390
\(780\) 0 0
\(781\) −54.1080 −1.93613
\(782\) −12.6705 7.31534i −0.453098 0.261596i
\(783\) −2.11176 1.21922i −0.0754680 0.0435715i
\(784\) −3.34233 5.78908i −0.119369 0.206753i
\(785\) 0 0