Properties

Label 570.2.d.d.229.4
Level $570$
Weight $2$
Character 570.229
Analytic conductor $4.551$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 229.4
Root \(0.403032 - 0.403032i\) of defining polynomial
Character \(\chi\) \(=\) 570.229
Dual form 570.2.d.d.229.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.48119 - 1.67513i) q^{5} +1.00000 q^{6} +3.35026i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.48119 - 1.67513i) q^{5} +1.00000 q^{6} +3.35026i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(1.67513 - 1.48119i) q^{10} -1.61213 q^{11} +1.00000i q^{12} +1.35026i q^{13} -3.35026 q^{14} +(-1.67513 + 1.48119i) q^{15} +1.00000 q^{16} +6.96239i q^{17} -1.00000i q^{18} +1.00000 q^{19} +(1.48119 + 1.67513i) q^{20} +3.35026 q^{21} -1.61213i q^{22} +1.35026i q^{23} -1.00000 q^{24} +(-0.612127 + 4.96239i) q^{25} -1.35026 q^{26} +1.00000i q^{27} -3.35026i q^{28} -3.61213 q^{29} +(-1.48119 - 1.67513i) q^{30} -2.31265 q^{31} +1.00000i q^{32} +1.61213i q^{33} -6.96239 q^{34} +(5.61213 - 4.96239i) q^{35} +1.00000 q^{36} +11.2750i q^{37} +1.00000i q^{38} +1.35026 q^{39} +(-1.67513 + 1.48119i) q^{40} -3.35026 q^{41} +3.35026i q^{42} +10.3127i q^{43} +1.61213 q^{44} +(1.48119 + 1.67513i) q^{45} -1.35026 q^{46} -4.57452i q^{47} -1.00000i q^{48} -4.22425 q^{49} +(-4.96239 - 0.612127i) q^{50} +6.96239 q^{51} -1.35026i q^{52} -11.9248i q^{53} -1.00000 q^{54} +(2.38787 + 2.70052i) q^{55} +3.35026 q^{56} -1.00000i q^{57} -3.61213i q^{58} -1.03761 q^{59} +(1.67513 - 1.48119i) q^{60} +2.00000 q^{61} -2.31265i q^{62} -3.35026i q^{63} -1.00000 q^{64} +(2.26187 - 2.00000i) q^{65} -1.61213 q^{66} -9.92478i q^{67} -6.96239i q^{68} +1.35026 q^{69} +(4.96239 + 5.61213i) q^{70} -0.775746 q^{71} +1.00000i q^{72} +3.22425i q^{73} -11.2750 q^{74} +(4.96239 + 0.612127i) q^{75} -1.00000 q^{76} -5.40105i q^{77} +1.35026i q^{78} -14.3127 q^{79} +(-1.48119 - 1.67513i) q^{80} +1.00000 q^{81} -3.35026i q^{82} -10.8872i q^{83} -3.35026 q^{84} +(11.6629 - 10.3127i) q^{85} -10.3127 q^{86} +3.61213i q^{87} +1.61213i q^{88} +2.57452 q^{89} +(-1.67513 + 1.48119i) q^{90} -4.52373 q^{91} -1.35026i q^{92} +2.31265i q^{93} +4.57452 q^{94} +(-1.48119 - 1.67513i) q^{95} +1.00000 q^{96} -1.16362i q^{97} -4.22425i q^{98} +1.61213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} + 2q^{5} + 6q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 6q^{4} + 2q^{5} + 6q^{6} - 6q^{9} - 8q^{11} + 6q^{16} + 6q^{19} - 2q^{20} - 6q^{24} - 2q^{25} + 12q^{26} - 20q^{29} + 2q^{30} + 28q^{31} - 20q^{34} + 32q^{35} + 6q^{36} - 12q^{39} + 8q^{44} - 2q^{45} + 12q^{46} - 22q^{49} - 8q^{50} + 20q^{51} - 6q^{54} + 16q^{55} - 28q^{59} + 12q^{61} - 6q^{64} + 32q^{65} - 8q^{66} - 12q^{69} + 8q^{70} - 8q^{71} - 4q^{74} + 8q^{75} - 6q^{76} - 44q^{79} + 2q^{80} + 6q^{81} + 8q^{85} - 20q^{86} - 8q^{89} - 64q^{91} + 4q^{94} + 2q^{95} + 6q^{96} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) −1.48119 1.67513i −0.662410 0.749141i
\(6\) 1.00000 0.408248
\(7\) 3.35026i 1.26628i 0.774037 + 0.633140i \(0.218234\pi\)
−0.774037 + 0.633140i \(0.781766\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 1.67513 1.48119i 0.529723 0.468395i
\(11\) −1.61213 −0.486075 −0.243037 0.970017i \(-0.578144\pi\)
−0.243037 + 0.970017i \(0.578144\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.35026i 0.374495i 0.982313 + 0.187248i \(0.0599567\pi\)
−0.982313 + 0.187248i \(0.940043\pi\)
\(14\) −3.35026 −0.895395
\(15\) −1.67513 + 1.48119i −0.432517 + 0.382443i
\(16\) 1.00000 0.250000
\(17\) 6.96239i 1.68863i 0.535849 + 0.844314i \(0.319992\pi\)
−0.535849 + 0.844314i \(0.680008\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.00000 0.229416
\(20\) 1.48119 + 1.67513i 0.331205 + 0.374571i
\(21\) 3.35026 0.731087
\(22\) 1.61213i 0.343707i
\(23\) 1.35026i 0.281549i 0.990042 + 0.140775i \(0.0449593\pi\)
−0.990042 + 0.140775i \(0.955041\pi\)
\(24\) −1.00000 −0.204124
\(25\) −0.612127 + 4.96239i −0.122425 + 0.992478i
\(26\) −1.35026 −0.264808
\(27\) 1.00000i 0.192450i
\(28\) 3.35026i 0.633140i
\(29\) −3.61213 −0.670755 −0.335378 0.942084i \(-0.608864\pi\)
−0.335378 + 0.942084i \(0.608864\pi\)
\(30\) −1.48119 1.67513i −0.270428 0.305836i
\(31\) −2.31265 −0.415364 −0.207682 0.978196i \(-0.566592\pi\)
−0.207682 + 0.978196i \(0.566592\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.61213i 0.280635i
\(34\) −6.96239 −1.19404
\(35\) 5.61213 4.96239i 0.948623 0.838797i
\(36\) 1.00000 0.166667
\(37\) 11.2750i 1.85360i 0.375549 + 0.926802i \(0.377454\pi\)
−0.375549 + 0.926802i \(0.622546\pi\)
\(38\) 1.00000i 0.162221i
\(39\) 1.35026 0.216215
\(40\) −1.67513 + 1.48119i −0.264861 + 0.234197i
\(41\) −3.35026 −0.523223 −0.261611 0.965173i \(-0.584254\pi\)
−0.261611 + 0.965173i \(0.584254\pi\)
\(42\) 3.35026i 0.516957i
\(43\) 10.3127i 1.57266i 0.617804 + 0.786332i \(0.288023\pi\)
−0.617804 + 0.786332i \(0.711977\pi\)
\(44\) 1.61213 0.243037
\(45\) 1.48119 + 1.67513i 0.220803 + 0.249714i
\(46\) −1.35026 −0.199085
\(47\) 4.57452i 0.667262i −0.942704 0.333631i \(-0.891726\pi\)
0.942704 0.333631i \(-0.108274\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −4.22425 −0.603465
\(50\) −4.96239 0.612127i −0.701788 0.0865678i
\(51\) 6.96239 0.974929
\(52\) 1.35026i 0.187248i
\(53\) 11.9248i 1.63799i −0.573798 0.818997i \(-0.694530\pi\)
0.573798 0.818997i \(-0.305470\pi\)
\(54\) −1.00000 −0.136083
\(55\) 2.38787 + 2.70052i 0.321981 + 0.364139i
\(56\) 3.35026 0.447698
\(57\) 1.00000i 0.132453i
\(58\) 3.61213i 0.474295i
\(59\) −1.03761 −0.135085 −0.0675427 0.997716i \(-0.521516\pi\)
−0.0675427 + 0.997716i \(0.521516\pi\)
\(60\) 1.67513 1.48119i 0.216258 0.191221i
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 2.31265i 0.293707i
\(63\) 3.35026i 0.422093i
\(64\) −1.00000 −0.125000
\(65\) 2.26187 2.00000i 0.280550 0.248069i
\(66\) −1.61213 −0.198439
\(67\) 9.92478i 1.21250i −0.795272 0.606252i \(-0.792672\pi\)
0.795272 0.606252i \(-0.207328\pi\)
\(68\) 6.96239i 0.844314i
\(69\) 1.35026 0.162552
\(70\) 4.96239 + 5.61213i 0.593119 + 0.670777i
\(71\) −0.775746 −0.0920641 −0.0460321 0.998940i \(-0.514658\pi\)
−0.0460321 + 0.998940i \(0.514658\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 3.22425i 0.377370i 0.982038 + 0.188685i \(0.0604226\pi\)
−0.982038 + 0.188685i \(0.939577\pi\)
\(74\) −11.2750 −1.31070
\(75\) 4.96239 + 0.612127i 0.573007 + 0.0706823i
\(76\) −1.00000 −0.114708
\(77\) 5.40105i 0.615506i
\(78\) 1.35026i 0.152887i
\(79\) −14.3127 −1.61030 −0.805149 0.593072i \(-0.797915\pi\)
−0.805149 + 0.593072i \(0.797915\pi\)
\(80\) −1.48119 1.67513i −0.165603 0.187285i
\(81\) 1.00000 0.111111
\(82\) 3.35026i 0.369975i
\(83\) 10.8872i 1.19502i −0.801861 0.597511i \(-0.796156\pi\)
0.801861 0.597511i \(-0.203844\pi\)
\(84\) −3.35026 −0.365544
\(85\) 11.6629 10.3127i 1.26502 1.11856i
\(86\) −10.3127 −1.11204
\(87\) 3.61213i 0.387261i
\(88\) 1.61213i 0.171853i
\(89\) 2.57452 0.272898 0.136449 0.990647i \(-0.456431\pi\)
0.136449 + 0.990647i \(0.456431\pi\)
\(90\) −1.67513 + 1.48119i −0.176574 + 0.156132i
\(91\) −4.52373 −0.474216
\(92\) 1.35026i 0.140775i
\(93\) 2.31265i 0.239811i
\(94\) 4.57452 0.471825
\(95\) −1.48119 1.67513i −0.151967 0.171865i
\(96\) 1.00000 0.102062
\(97\) 1.16362i 0.118148i −0.998254 0.0590738i \(-0.981185\pi\)
0.998254 0.0590738i \(-0.0188147\pi\)
\(98\) 4.22425i 0.426714i
\(99\) 1.61213 0.162025
\(100\) 0.612127 4.96239i 0.0612127 0.496239i
\(101\) 8.88717 0.884306 0.442153 0.896940i \(-0.354215\pi\)
0.442153 + 0.896940i \(0.354215\pi\)
\(102\) 6.96239i 0.689379i
\(103\) 7.03761i 0.693436i 0.937969 + 0.346718i \(0.112704\pi\)
−0.937969 + 0.346718i \(0.887296\pi\)
\(104\) 1.35026 0.132404
\(105\) −4.96239 5.61213i −0.484280 0.547688i
\(106\) 11.9248 1.15824
\(107\) 0.775746i 0.0749942i 0.999297 + 0.0374971i \(0.0119385\pi\)
−0.999297 + 0.0374971i \(0.988062\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 20.1622 1.93119 0.965594 0.260052i \(-0.0837399\pi\)
0.965594 + 0.260052i \(0.0837399\pi\)
\(110\) −2.70052 + 2.38787i −0.257485 + 0.227675i
\(111\) 11.2750 1.07018
\(112\) 3.35026i 0.316570i
\(113\) 11.1490i 1.04881i 0.851468 + 0.524406i \(0.175713\pi\)
−0.851468 + 0.524406i \(0.824287\pi\)
\(114\) 1.00000 0.0936586
\(115\) 2.26187 2.00000i 0.210920 0.186501i
\(116\) 3.61213 0.335378
\(117\) 1.35026i 0.124832i
\(118\) 1.03761i 0.0955199i
\(119\) −23.3258 −2.13827
\(120\) 1.48119 + 1.67513i 0.135214 + 0.152918i
\(121\) −8.40105 −0.763732
\(122\) 2.00000i 0.181071i
\(123\) 3.35026i 0.302083i
\(124\) 2.31265 0.207682
\(125\) 9.21933 6.32487i 0.824602 0.565713i
\(126\) 3.35026 0.298465
\(127\) 13.7381i 1.21906i −0.792762 0.609531i \(-0.791358\pi\)
0.792762 0.609531i \(-0.208642\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 10.3127 0.907978
\(130\) 2.00000 + 2.26187i 0.175412 + 0.198379i
\(131\) 5.61213 0.490334 0.245167 0.969481i \(-0.421157\pi\)
0.245167 + 0.969481i \(0.421157\pi\)
\(132\) 1.61213i 0.140318i
\(133\) 3.35026i 0.290505i
\(134\) 9.92478 0.857370
\(135\) 1.67513 1.48119i 0.144172 0.127481i
\(136\) 6.96239 0.597020
\(137\) 17.6629i 1.50904i 0.656275 + 0.754522i \(0.272131\pi\)
−0.656275 + 0.754522i \(0.727869\pi\)
\(138\) 1.35026i 0.114942i
\(139\) −10.7005 −0.907607 −0.453803 0.891102i \(-0.649933\pi\)
−0.453803 + 0.891102i \(0.649933\pi\)
\(140\) −5.61213 + 4.96239i −0.474311 + 0.419398i
\(141\) −4.57452 −0.385244
\(142\) 0.775746i 0.0650992i
\(143\) 2.17679i 0.182033i
\(144\) −1.00000 −0.0833333
\(145\) 5.35026 + 6.05079i 0.444315 + 0.502490i
\(146\) −3.22425 −0.266841
\(147\) 4.22425i 0.348411i
\(148\) 11.2750i 0.926802i
\(149\) −1.03761 −0.0850044 −0.0425022 0.999096i \(-0.513533\pi\)
−0.0425022 + 0.999096i \(0.513533\pi\)
\(150\) −0.612127 + 4.96239i −0.0499799 + 0.405177i
\(151\) 1.16362 0.0946940 0.0473470 0.998879i \(-0.484923\pi\)
0.0473470 + 0.998879i \(0.484923\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 6.96239i 0.562876i
\(154\) 5.40105 0.435229
\(155\) 3.42548 + 3.87399i 0.275142 + 0.311167i
\(156\) −1.35026 −0.108107
\(157\) 10.9624i 0.874894i −0.899244 0.437447i \(-0.855883\pi\)
0.899244 0.437447i \(-0.144117\pi\)
\(158\) 14.3127i 1.13865i
\(159\) −11.9248 −0.945696
\(160\) 1.67513 1.48119i 0.132431 0.117099i
\(161\) −4.52373 −0.356520
\(162\) 1.00000i 0.0785674i
\(163\) 21.0132i 1.64588i 0.568129 + 0.822939i \(0.307667\pi\)
−0.568129 + 0.822939i \(0.692333\pi\)
\(164\) 3.35026 0.261611
\(165\) 2.70052 2.38787i 0.210235 0.185896i
\(166\) 10.8872 0.845008
\(167\) 9.92478i 0.768002i −0.923333 0.384001i \(-0.874546\pi\)
0.923333 0.384001i \(-0.125454\pi\)
\(168\) 3.35026i 0.258478i
\(169\) 11.1768 0.859753
\(170\) 10.3127 + 11.6629i 0.790944 + 0.894505i
\(171\) −1.00000 −0.0764719
\(172\) 10.3127i 0.786332i
\(173\) 14.6253i 1.11194i 0.831202 + 0.555971i \(0.187653\pi\)
−0.831202 + 0.555971i \(0.812347\pi\)
\(174\) −3.61213 −0.273835
\(175\) −16.6253 2.05079i −1.25675 0.155025i
\(176\) −1.61213 −0.121519
\(177\) 1.03761i 0.0779916i
\(178\) 2.57452i 0.192968i
\(179\) −11.7381 −0.877349 −0.438675 0.898646i \(-0.644552\pi\)
−0.438675 + 0.898646i \(0.644552\pi\)
\(180\) −1.48119 1.67513i −0.110402 0.124857i
\(181\) 21.4617 1.59523 0.797617 0.603164i \(-0.206094\pi\)
0.797617 + 0.603164i \(0.206094\pi\)
\(182\) 4.52373i 0.335321i
\(183\) 2.00000i 0.147844i
\(184\) 1.35026 0.0995426
\(185\) 18.8872 16.7005i 1.38861 1.22785i
\(186\) −2.31265 −0.169572
\(187\) 11.2243i 0.820799i
\(188\) 4.57452i 0.333631i
\(189\) −3.35026 −0.243696
\(190\) 1.67513 1.48119i 0.121527 0.107457i
\(191\) −21.2750 −1.53941 −0.769704 0.638401i \(-0.779596\pi\)
−0.769704 + 0.638401i \(0.779596\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 14.1622i 1.01942i −0.860347 0.509709i \(-0.829753\pi\)
0.860347 0.509709i \(-0.170247\pi\)
\(194\) 1.16362 0.0835430
\(195\) −2.00000 2.26187i −0.143223 0.161976i
\(196\) 4.22425 0.301732
\(197\) 3.87399i 0.276011i −0.990431 0.138005i \(-0.955931\pi\)
0.990431 0.138005i \(-0.0440691\pi\)
\(198\) 1.61213i 0.114569i
\(199\) −3.47627 −0.246426 −0.123213 0.992380i \(-0.539320\pi\)
−0.123213 + 0.992380i \(0.539320\pi\)
\(200\) 4.96239 + 0.612127i 0.350894 + 0.0432839i
\(201\) −9.92478 −0.700040
\(202\) 8.88717i 0.625299i
\(203\) 12.1016i 0.849364i
\(204\) −6.96239 −0.487465
\(205\) 4.96239 + 5.61213i 0.346588 + 0.391968i
\(206\) −7.03761 −0.490334
\(207\) 1.35026i 0.0938497i
\(208\) 1.35026i 0.0936238i
\(209\) −1.61213 −0.111513
\(210\) 5.61213 4.96239i 0.387274 0.342437i
\(211\) 9.92478 0.683250 0.341625 0.939836i \(-0.389023\pi\)
0.341625 + 0.939836i \(0.389023\pi\)
\(212\) 11.9248i 0.818997i
\(213\) 0.775746i 0.0531533i
\(214\) −0.775746 −0.0530289
\(215\) 17.2750 15.2750i 1.17815 1.04175i
\(216\) 1.00000 0.0680414
\(217\) 7.74798i 0.525967i
\(218\) 20.1622i 1.36556i
\(219\) 3.22425 0.217875
\(220\) −2.38787 2.70052i −0.160990 0.182069i
\(221\) −9.40105 −0.632383
\(222\) 11.2750i 0.756731i
\(223\) 7.03761i 0.471273i 0.971841 + 0.235637i \(0.0757175\pi\)
−0.971841 + 0.235637i \(0.924282\pi\)
\(224\) −3.35026 −0.223849
\(225\) 0.612127 4.96239i 0.0408085 0.330826i
\(226\) −11.1490 −0.741623
\(227\) 14.5501i 0.965723i 0.875697 + 0.482861i \(0.160402\pi\)
−0.875697 + 0.482861i \(0.839598\pi\)
\(228\) 1.00000i 0.0662266i
\(229\) −11.4010 −0.753402 −0.376701 0.926335i \(-0.622942\pi\)
−0.376701 + 0.926335i \(0.622942\pi\)
\(230\) 2.00000 + 2.26187i 0.131876 + 0.149143i
\(231\) −5.40105 −0.355363
\(232\) 3.61213i 0.237148i
\(233\) 21.9149i 1.43569i 0.696201 + 0.717847i \(0.254872\pi\)
−0.696201 + 0.717847i \(0.745128\pi\)
\(234\) 1.35026 0.0882694
\(235\) −7.66291 + 6.77575i −0.499873 + 0.442001i
\(236\) 1.03761 0.0675427
\(237\) 14.3127i 0.929707i
\(238\) 23.3258i 1.51199i
\(239\) 13.2750 0.858691 0.429345 0.903140i \(-0.358744\pi\)
0.429345 + 0.903140i \(0.358744\pi\)
\(240\) −1.67513 + 1.48119i −0.108129 + 0.0956107i
\(241\) 21.3258 1.37372 0.686859 0.726791i \(-0.258989\pi\)
0.686859 + 0.726791i \(0.258989\pi\)
\(242\) 8.40105i 0.540040i
\(243\) 1.00000i 0.0641500i
\(244\) −2.00000 −0.128037
\(245\) 6.25694 + 7.07618i 0.399741 + 0.452080i
\(246\) −3.35026 −0.213605
\(247\) 1.35026i 0.0859151i
\(248\) 2.31265i 0.146853i
\(249\) −10.8872 −0.689946
\(250\) 6.32487 + 9.21933i 0.400020 + 0.583082i
\(251\) 16.3127 1.02965 0.514823 0.857297i \(-0.327858\pi\)
0.514823 + 0.857297i \(0.327858\pi\)
\(252\) 3.35026i 0.211047i
\(253\) 2.17679i 0.136854i
\(254\) 13.7381 0.862007
\(255\) −10.3127 11.6629i −0.645803 0.730360i
\(256\) 1.00000 0.0625000
\(257\) 24.5501i 1.53139i 0.643203 + 0.765696i \(0.277605\pi\)
−0.643203 + 0.765696i \(0.722395\pi\)
\(258\) 10.3127i 0.642038i
\(259\) −37.7743 −2.34718
\(260\) −2.26187 + 2.00000i −0.140275 + 0.124035i
\(261\) 3.61213 0.223585
\(262\) 5.61213i 0.346718i
\(263\) 30.3488i 1.87139i −0.352810 0.935695i \(-0.614774\pi\)
0.352810 0.935695i \(-0.385226\pi\)
\(264\) 1.61213 0.0992195
\(265\) −19.9756 + 17.6629i −1.22709 + 1.08502i
\(266\) −3.35026 −0.205418
\(267\) 2.57452i 0.157558i
\(268\) 9.92478i 0.606252i
\(269\) −14.3127 −0.872658 −0.436329 0.899787i \(-0.643722\pi\)
−0.436329 + 0.899787i \(0.643722\pi\)
\(270\) 1.48119 + 1.67513i 0.0901426 + 0.101945i
\(271\) −7.32582 −0.445012 −0.222506 0.974931i \(-0.571424\pi\)
−0.222506 + 0.974931i \(0.571424\pi\)
\(272\) 6.96239i 0.422157i
\(273\) 4.52373i 0.273789i
\(274\) −17.6629 −1.06706
\(275\) 0.986826 8.00000i 0.0595079 0.482418i
\(276\) −1.35026 −0.0812762
\(277\) 14.4387i 0.867535i −0.901025 0.433767i \(-0.857184\pi\)
0.901025 0.433767i \(-0.142816\pi\)
\(278\) 10.7005i 0.641775i
\(279\) 2.31265 0.138455
\(280\) −4.96239 5.61213i −0.296559 0.335389i
\(281\) −11.9756 −0.714402 −0.357201 0.934028i \(-0.616269\pi\)
−0.357201 + 0.934028i \(0.616269\pi\)
\(282\) 4.57452i 0.272408i
\(283\) 24.4894i 1.45575i 0.685712 + 0.727873i \(0.259491\pi\)
−0.685712 + 0.727873i \(0.740509\pi\)
\(284\) 0.775746 0.0460321
\(285\) −1.67513 + 1.48119i −0.0992262 + 0.0877384i
\(286\) 2.17679 0.128716
\(287\) 11.2243i 0.662547i
\(288\) 1.00000i 0.0589256i
\(289\) −31.4749 −1.85146
\(290\) −6.05079 + 5.35026i −0.355314 + 0.314178i
\(291\) −1.16362 −0.0682126
\(292\) 3.22425i 0.188685i
\(293\) 18.1016i 1.05751i 0.848776 + 0.528753i \(0.177340\pi\)
−0.848776 + 0.528753i \(0.822660\pi\)
\(294\) −4.22425 −0.246363
\(295\) 1.53690 + 1.73813i 0.0894820 + 0.101198i
\(296\) 11.2750 0.655348
\(297\) 1.61213i 0.0935451i
\(298\) 1.03761i 0.0601072i
\(299\) −1.82321 −0.105439
\(300\) −4.96239 0.612127i −0.286504 0.0353412i
\(301\) −34.5501 −1.99143
\(302\) 1.16362i 0.0669588i
\(303\) 8.88717i 0.510554i
\(304\) 1.00000 0.0573539
\(305\) −2.96239 3.35026i −0.169626 0.191835i
\(306\) 6.96239 0.398013
\(307\) 29.9248i 1.70790i −0.520357 0.853949i \(-0.674201\pi\)
0.520357 0.853949i \(-0.325799\pi\)
\(308\) 5.40105i 0.307753i
\(309\) 7.03761 0.400356
\(310\) −3.87399 + 3.42548i −0.220028 + 0.194554i
\(311\) −21.2750 −1.20640 −0.603198 0.797591i \(-0.706107\pi\)
−0.603198 + 0.797591i \(0.706107\pi\)
\(312\) 1.35026i 0.0764435i
\(313\) 17.4010i 0.983565i 0.870718 + 0.491783i \(0.163655\pi\)
−0.870718 + 0.491783i \(0.836345\pi\)
\(314\) 10.9624 0.618643
\(315\) −5.61213 + 4.96239i −0.316208 + 0.279599i
\(316\) 14.3127 0.805149
\(317\) 14.1016i 0.792023i −0.918246 0.396012i \(-0.870394\pi\)
0.918246 0.396012i \(-0.129606\pi\)
\(318\) 11.9248i 0.668708i
\(319\) 5.82321 0.326037
\(320\) 1.48119 + 1.67513i 0.0828013 + 0.0936427i
\(321\) 0.775746 0.0432979
\(322\) 4.52373i 0.252098i
\(323\) 6.96239i 0.387398i
\(324\) −1.00000 −0.0555556
\(325\) −6.70052 0.826531i −0.371678 0.0458477i
\(326\) −21.0132 −1.16381
\(327\) 20.1622i 1.11497i
\(328\) 3.35026i 0.184987i
\(329\) 15.3258 0.844940
\(330\) 2.38787 + 2.70052i 0.131448 + 0.148659i
\(331\) 6.85097 0.376563 0.188282 0.982115i \(-0.439708\pi\)
0.188282 + 0.982115i \(0.439708\pi\)
\(332\) 10.8872i 0.597511i
\(333\) 11.2750i 0.617868i
\(334\) 9.92478 0.543060
\(335\) −16.6253 + 14.7005i −0.908337 + 0.803175i
\(336\) 3.35026 0.182772
\(337\) 24.2374i 1.32030i −0.751135 0.660148i \(-0.770493\pi\)
0.751135 0.660148i \(-0.229507\pi\)
\(338\) 11.1768i 0.607937i
\(339\) 11.1490 0.605532
\(340\) −11.6629 + 10.3127i −0.632510 + 0.559282i
\(341\) 3.72829 0.201898
\(342\) 1.00000i 0.0540738i
\(343\) 9.29948i 0.502125i
\(344\) 10.3127 0.556021
\(345\) −2.00000 2.26187i −0.107676 0.121775i
\(346\) −14.6253 −0.786261
\(347\) 0.962389i 0.0516637i −0.999666 0.0258319i \(-0.991777\pi\)
0.999666 0.0258319i \(-0.00822345\pi\)
\(348\) 3.61213i 0.193630i
\(349\) 1.37470 0.0735860 0.0367930 0.999323i \(-0.488286\pi\)
0.0367930 + 0.999323i \(0.488286\pi\)
\(350\) 2.05079 16.6253i 0.109619 0.888660i
\(351\) −1.35026 −0.0720716
\(352\) 1.61213i 0.0859267i
\(353\) 28.7367i 1.52950i 0.644326 + 0.764751i \(0.277138\pi\)
−0.644326 + 0.764751i \(0.722862\pi\)
\(354\) −1.03761 −0.0551484
\(355\) 1.14903 + 1.29948i 0.0609842 + 0.0689691i
\(356\) −2.57452 −0.136449
\(357\) 23.3258i 1.23453i
\(358\) 11.7381i 0.620380i
\(359\) −31.1998 −1.64666 −0.823332 0.567561i \(-0.807887\pi\)
−0.823332 + 0.567561i \(0.807887\pi\)
\(360\) 1.67513 1.48119i 0.0882871 0.0780658i
\(361\) 1.00000 0.0526316
\(362\) 21.4617i 1.12800i
\(363\) 8.40105i 0.440941i
\(364\) 4.52373 0.237108
\(365\) 5.40105 4.77575i 0.282704 0.249974i
\(366\) 2.00000 0.104542
\(367\) 20.1260i 1.05057i −0.850927 0.525285i \(-0.823959\pi\)
0.850927 0.525285i \(-0.176041\pi\)
\(368\) 1.35026i 0.0703873i
\(369\) 3.35026 0.174408
\(370\) 16.7005 + 18.8872i 0.868219 + 0.981897i
\(371\) 39.9511 2.07416
\(372\) 2.31265i 0.119905i
\(373\) 17.9756i 0.930739i −0.885116 0.465370i \(-0.845921\pi\)
0.885116 0.465370i \(-0.154079\pi\)
\(374\) 11.2243 0.580392
\(375\) −6.32487 9.21933i −0.326615 0.476084i
\(376\) −4.57452 −0.235913
\(377\) 4.87732i 0.251195i
\(378\) 3.35026i 0.172319i
\(379\) −1.67276 −0.0859240 −0.0429620 0.999077i \(-0.513679\pi\)
−0.0429620 + 0.999077i \(0.513679\pi\)
\(380\) 1.48119 + 1.67513i 0.0759837 + 0.0859324i
\(381\) −13.7381 −0.703826
\(382\) 21.2750i 1.08853i
\(383\) 31.8496i 1.62744i 0.581260 + 0.813718i \(0.302560\pi\)
−0.581260 + 0.813718i \(0.697440\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −9.04746 + 8.00000i −0.461101 + 0.407718i
\(386\) 14.1622 0.720837
\(387\) 10.3127i 0.524221i
\(388\) 1.16362i 0.0590738i
\(389\) 10.3371 0.524111 0.262056 0.965053i \(-0.415600\pi\)
0.262056 + 0.965053i \(0.415600\pi\)
\(390\) 2.26187 2.00000i 0.114534 0.101274i
\(391\) −9.40105 −0.475431
\(392\) 4.22425i 0.213357i
\(393\) 5.61213i 0.283094i
\(394\) 3.87399 0.195169
\(395\) 21.1998 + 23.9756i 1.06668 + 1.20634i
\(396\) −1.61213 −0.0810124
\(397\) 31.4372i 1.57779i 0.614528 + 0.788895i \(0.289346\pi\)
−0.614528 + 0.788895i \(0.710654\pi\)
\(398\) 3.47627i 0.174250i
\(399\) 3.35026 0.167723
\(400\) −0.612127 + 4.96239i −0.0306063 + 0.248119i
\(401\) 5.94921 0.297090 0.148545 0.988906i \(-0.452541\pi\)
0.148545 + 0.988906i \(0.452541\pi\)
\(402\) 9.92478i 0.495003i
\(403\) 3.12268i 0.155552i
\(404\) −8.88717 −0.442153
\(405\) −1.48119 1.67513i −0.0736011 0.0832379i
\(406\) 12.1016 0.600591
\(407\) 18.1768i 0.900990i
\(408\) 6.96239i 0.344690i
\(409\) 30.9986 1.53278 0.766391 0.642375i \(-0.222051\pi\)
0.766391 + 0.642375i \(0.222051\pi\)
\(410\) −5.61213 + 4.96239i −0.277163 + 0.245075i
\(411\) 17.6629 0.871247
\(412\) 7.03761i 0.346718i
\(413\) 3.47627i 0.171056i
\(414\) 1.35026 0.0663617
\(415\) −18.2374 + 16.1260i −0.895240 + 0.791595i
\(416\) −1.35026 −0.0662020
\(417\) 10.7005i 0.524007i
\(418\) 1.61213i 0.0788517i
\(419\) 34.3390 1.67757 0.838785 0.544463i \(-0.183266\pi\)
0.838785 + 0.544463i \(0.183266\pi\)
\(420\) 4.96239 + 5.61213i 0.242140 + 0.273844i
\(421\) 22.8627 1.11426 0.557131 0.830425i \(-0.311902\pi\)
0.557131 + 0.830425i \(0.311902\pi\)
\(422\) 9.92478i 0.483131i
\(423\) 4.57452i 0.222421i
\(424\) −11.9248 −0.579118
\(425\) −34.5501 4.26187i −1.67592 0.206731i
\(426\) −0.775746 −0.0375850
\(427\) 6.70052i 0.324261i
\(428\) 0.775746i 0.0374971i
\(429\) −2.17679 −0.105097
\(430\) 15.2750 + 17.2750i 0.736628 + 0.833076i
\(431\) 11.5975 0.558634 0.279317 0.960199i \(-0.409892\pi\)
0.279317 + 0.960199i \(0.409892\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 27.8350i 1.33766i 0.743414 + 0.668832i \(0.233205\pi\)
−0.743414 + 0.668832i \(0.766795\pi\)
\(434\) 7.74798 0.371915
\(435\) 6.05079 5.35026i 0.290113 0.256525i
\(436\) −20.1622 −0.965594
\(437\) 1.35026i 0.0645918i
\(438\) 3.22425i 0.154061i
\(439\) 38.7875 1.85123 0.925613 0.378471i \(-0.123550\pi\)
0.925613 + 0.378471i \(0.123550\pi\)
\(440\) 2.70052 2.38787i 0.128742 0.113837i
\(441\) 4.22425 0.201155
\(442\) 9.40105i 0.447162i
\(443\) 29.2144i 1.38802i −0.719966 0.694009i \(-0.755843\pi\)
0.719966 0.694009i \(-0.244157\pi\)
\(444\) −11.2750 −0.535090
\(445\) −3.81336 4.31265i −0.180770 0.204439i
\(446\) −7.03761 −0.333241
\(447\) 1.03761i 0.0490773i
\(448\) 3.35026i 0.158285i
\(449\) 20.4993 0.967421 0.483711 0.875228i \(-0.339289\pi\)
0.483711 + 0.875228i \(0.339289\pi\)
\(450\) 4.96239 + 0.612127i 0.233929 + 0.0288559i
\(451\) 5.40105 0.254325
\(452\) 11.1490i 0.524406i
\(453\) 1.16362i 0.0546716i
\(454\) −14.5501 −0.682869
\(455\) 6.70052 + 7.57784i 0.314125 + 0.355255i
\(456\) −1.00000 −0.0468293
\(457\) 6.44851i 0.301648i −0.988561 0.150824i \(-0.951807\pi\)
0.988561 0.150824i \(-0.0481927\pi\)
\(458\) 11.4010i 0.532736i
\(459\) −6.96239 −0.324976
\(460\) −2.26187 + 2.00000i −0.105460 + 0.0932505i
\(461\) −13.5125 −0.629338 −0.314669 0.949201i \(-0.601894\pi\)
−0.314669 + 0.949201i \(0.601894\pi\)
\(462\) 5.40105i 0.251279i
\(463\) 6.20123i 0.288196i 0.989563 + 0.144098i \(0.0460280\pi\)
−0.989563 + 0.144098i \(0.953972\pi\)
\(464\) −3.61213 −0.167689
\(465\) 3.87399 3.42548i 0.179652 0.158853i
\(466\) −21.9149 −1.01519
\(467\) 16.5599i 0.766302i 0.923686 + 0.383151i \(0.125161\pi\)
−0.923686 + 0.383151i \(0.874839\pi\)
\(468\) 1.35026i 0.0624159i
\(469\) 33.2506 1.53537
\(470\) −6.77575 7.66291i −0.312542 0.353464i
\(471\) −10.9624 −0.505120
\(472\) 1.03761i 0.0477599i
\(473\) 16.6253i 0.764432i
\(474\) −14.3127 −0.657402
\(475\) −0.612127 + 4.96239i −0.0280863 + 0.227690i
\(476\) 23.3258 1.06914
\(477\) 11.9248i 0.545998i
\(478\) 13.2750i 0.607186i
\(479\) 30.5256 1.39475 0.697376 0.716705i \(-0.254351\pi\)
0.697376 + 0.716705i \(0.254351\pi\)
\(480\) −1.48119 1.67513i −0.0676070 0.0764589i
\(481\) −15.2243 −0.694166
\(482\) 21.3258i 0.971365i
\(483\) 4.52373i 0.205837i
\(484\) 8.40105 0.381866
\(485\) −1.94921 + 1.72355i −0.0885093 + 0.0782622i
\(486\) 1.00000 0.0453609
\(487\) 2.51388i 0.113915i 0.998377 + 0.0569574i \(0.0181399\pi\)
−0.998377 + 0.0569574i \(0.981860\pi\)
\(488\) 2.00000i 0.0905357i
\(489\) 21.0132 0.950249
\(490\) −7.07618 + 6.25694i −0.319669 + 0.282660i
\(491\) 1.46168 0.0659648 0.0329824 0.999456i \(-0.489499\pi\)
0.0329824 + 0.999456i \(0.489499\pi\)
\(492\) 3.35026i 0.151041i
\(493\) 25.1490i 1.13266i
\(494\) −1.35026 −0.0607511
\(495\) −2.38787 2.70052i −0.107327 0.121380i
\(496\) −2.31265 −0.103841
\(497\) 2.59895i 0.116579i
\(498\) 10.8872i 0.487866i
\(499\) 5.55149 0.248519 0.124259 0.992250i \(-0.460344\pi\)
0.124259 + 0.992250i \(0.460344\pi\)
\(500\) −9.21933 + 6.32487i −0.412301 + 0.282857i
\(501\) −9.92478 −0.443406
\(502\) 16.3127i 0.728069i
\(503\) 6.90175i 0.307734i 0.988092 + 0.153867i \(0.0491727\pi\)
−0.988092 + 0.153867i \(0.950827\pi\)
\(504\) −3.35026 −0.149233
\(505\) −13.1636 14.8872i −0.585773 0.662470i
\(506\) 2.17679 0.0967703
\(507\) 11.1768i 0.496379i
\(508\) 13.7381i 0.609531i
\(509\) −8.76116 −0.388331 −0.194166 0.980969i \(-0.562200\pi\)
−0.194166 + 0.980969i \(0.562200\pi\)
\(510\) 11.6629 10.3127i 0.516442 0.456652i
\(511\) −10.8021 −0.477857
\(512\) 1.00000i 0.0441942i
\(513\) 1.00000i 0.0441511i
\(514\) −24.5501 −1.08286
\(515\) 11.7889 10.4241i 0.519482 0.459339i
\(516\) −10.3127 −0.453989
\(517\) 7.37470i 0.324339i
\(518\) 37.7743i 1.65971i
\(519\) 14.6253 0.641979
\(520\) −2.00000 2.26187i −0.0877058 0.0991893i
\(521\) 39.4518 1.72842 0.864208 0.503135i \(-0.167820\pi\)
0.864208 + 0.503135i \(0.167820\pi\)
\(522\) 3.61213i 0.158098i
\(523\) 37.5026i 1.63987i −0.572453 0.819937i \(-0.694008\pi\)
0.572453 0.819937i \(-0.305992\pi\)
\(524\) −5.61213 −0.245167
\(525\) −2.05079 + 16.6253i −0.0895036 + 0.725588i
\(526\) 30.3488 1.32327
\(527\) 16.1016i 0.701395i
\(528\) 1.61213i 0.0701588i
\(529\) 21.1768 0.920730
\(530\) −17.6629 19.9756i −0.767228 0.867683i
\(531\) 1.03761 0.0450285
\(532\) 3.35026i 0.145252i
\(533\) 4.52373i 0.195945i
\(534\) 2.57452 0.111410
\(535\) 1.29948 1.14903i 0.0561813 0.0496769i
\(536\) −9.92478 −0.428685
\(537\) 11.7381i 0.506538i
\(538\) 14.3127i 0.617062i
\(539\) 6.81003 0.293329
\(540\) −1.67513 + 1.48119i −0.0720862 + 0.0637405i
\(541\) −30.7757 −1.32315 −0.661576 0.749878i \(-0.730112\pi\)
−0.661576 + 0.749878i \(0.730112\pi\)
\(542\) 7.32582i 0.314671i
\(543\) 21.4617i 0.921009i
\(544\) −6.96239 −0.298510
\(545\) −29.8641 33.7743i −1.27924 1.44673i
\(546\) −4.52373 −0.193598
\(547\) 1.77433i 0.0758649i 0.999280 + 0.0379325i \(0.0120772\pi\)
−0.999280 + 0.0379325i \(0.987923\pi\)
\(548\) 17.6629i 0.754522i
\(549\) −2.00000 −0.0853579
\(550\) 8.00000 + 0.986826i 0.341121 + 0.0420784i
\(551\) −3.61213 −0.153882
\(552\) 1.35026i 0.0574710i
\(553\) 47.9511i 2.03909i
\(554\) 14.4387 0.613440
\(555\) −16.7005 18.8872i −0.708898 0.801716i
\(556\) 10.7005 0.453803
\(557\) 8.90175i 0.377179i 0.982056 + 0.188590i \(0.0603916\pi\)
−0.982056 + 0.188590i \(0.939608\pi\)
\(558\) 2.31265i 0.0979023i
\(559\) −13.9248 −0.588955
\(560\) 5.61213 4.96239i 0.237156 0.209699i
\(561\) −11.2243 −0.473888
\(562\) 11.9756i 0.505159i
\(563\) 10.9525i 0.461595i −0.973002 0.230797i \(-0.925867\pi\)
0.973002 0.230797i \(-0.0741334\pi\)
\(564\) 4.57452 0.192622
\(565\) 18.6761 16.5139i 0.785709 0.694744i
\(566\) −24.4894 −1.02937
\(567\) 3.35026i 0.140698i
\(568\) 0.775746i 0.0325496i
\(569\) 10.2012 0.427658 0.213829 0.976871i \(-0.431406\pi\)
0.213829 + 0.976871i \(0.431406\pi\)
\(570\) −1.48119 1.67513i −0.0620404 0.0701635i
\(571\) −25.6531 −1.07355 −0.536774 0.843726i \(-0.680357\pi\)
−0.536774 + 0.843726i \(0.680357\pi\)
\(572\) 2.17679i 0.0910163i
\(573\) 21.2750i 0.888778i
\(574\) 11.2243 0.468491
\(575\) −6.70052 0.826531i −0.279431 0.0344687i
\(576\) 1.00000 0.0416667
\(577\) 6.44851i 0.268455i −0.990951 0.134227i \(-0.957145\pi\)
0.990951 0.134227i \(-0.0428553\pi\)
\(578\) 31.4749i 1.30918i
\(579\) −14.1622 −0.588561
\(580\) −5.35026 6.05079i −0.222158 0.251245i
\(581\) 36.4749 1.51323
\(582\) 1.16362i 0.0482336i
\(583\) 19.2243i 0.796187i
\(584\) 3.22425 0.133421
\(585\) −2.26187 + 2.00000i −0.0935166 + 0.0826898i
\(586\) −18.1016 −0.747769
\(587\) 41.8397i 1.72691i 0.504426 + 0.863455i \(0.331704\pi\)
−0.504426 + 0.863455i \(0.668296\pi\)
\(588\) 4.22425i 0.174205i
\(589\) −2.31265 −0.0952911
\(590\) −1.73813 + 1.53690i −0.0715579 + 0.0632733i
\(591\) −3.87399 −0.159355
\(592\) 11.2750i 0.463401i
\(593\) 8.73672i 0.358774i 0.983779 + 0.179387i \(0.0574114\pi\)
−0.983779 + 0.179387i \(0.942589\pi\)
\(594\) 1.61213 0.0661464
\(595\) 34.5501 + 39.0738i 1.41642 + 1.60187i
\(596\) 1.03761 0.0425022
\(597\) 3.47627i 0.142274i
\(598\) 1.82321i 0.0745565i
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0.612127 4.96239i 0.0249900 0.202589i
\(601\) 30.6253 1.24923 0.624616 0.780932i \(-0.285255\pi\)
0.624616 + 0.780932i \(0.285255\pi\)
\(602\) 34.5501i 1.40816i
\(603\) 9.92478i 0.404168i
\(604\) −1.16362 −0.0473470
\(605\) 12.4436 + 14.0729i 0.505904 + 0.572143i
\(606\) 8.88717 0.361016
\(607\) 2.51388i 0.102035i 0.998698 + 0.0510176i \(0.0162465\pi\)
−0.998698 + 0.0510176i \(0.983754\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) −12.1016 −0.490380
\(610\) 3.35026 2.96239i 0.135648 0.119944i
\(611\) 6.17679 0.249886
\(612\) 6.96239i 0.281438i
\(613\) 2.96239i 0.119650i −0.998209 0.0598249i \(-0.980946\pi\)
0.998209 0.0598249i \(-0.0190542\pi\)
\(614\) 29.9248 1.20767
\(615\) 5.61213 4.96239i 0.226303 0.200103i
\(616\) −5.40105 −0.217614
\(617\) 18.3371i 0.738223i 0.929385 + 0.369112i \(0.120338\pi\)
−0.929385 + 0.369112i \(0.879662\pi\)
\(618\) 7.03761i 0.283094i
\(619\) 40.7269 1.63695 0.818476 0.574541i \(-0.194820\pi\)
0.818476 + 0.574541i \(0.194820\pi\)
\(620\) −3.42548 3.87399i −0.137571 0.155583i
\(621\) −1.35026 −0.0541841
\(622\) 21.2750i 0.853051i
\(623\) 8.62530i 0.345565i
\(624\) 1.35026 0.0540537
\(625\) −24.2506 6.07522i −0.970024 0.243009i
\(626\) −17.4010 −0.695486
\(627\) 1.61213i 0.0643821i
\(628\) 10.9624i 0.437447i
\(629\) −78.5012 −3.13005
\(630\) −4.96239 5.61213i −0.197706 0.223592i
\(631\) −5.92478 −0.235862 −0.117931 0.993022i \(-0.537626\pi\)
−0.117931 + 0.993022i \(0.537626\pi\)
\(632\) 14.3127i 0.569327i
\(633\) 9.92478i 0.394474i
\(634\) 14.1016 0.560045
\(635\) −23.0132 + 20.3488i −0.913250 + 0.807519i
\(636\) 11.9248 0.472848
\(637\) 5.70385i 0.225995i
\(638\) 5.82321i 0.230543i
\(639\) 0.775746 0.0306880
\(640\) −1.67513 + 1.48119i −0.0662154 + 0.0585493i
\(641\) 19.0494 0.752405 0.376202 0.926537i \(-0.377230\pi\)
0.376202 + 0.926537i \(0.377230\pi\)
\(642\) 0.775746i 0.0306163i
\(643\) 1.06205i 0.0418831i −0.999781 0.0209416i \(-0.993334\pi\)
0.999781 0.0209416i \(-0.00666639\pi\)
\(644\) 4.52373 0.178260
\(645\) −15.2750 17.2750i −0.601454 0.680204i
\(646\) −6.96239 −0.273932
\(647\) 26.6497i 1.04771i −0.851808 0.523855i \(-0.824493\pi\)
0.851808 0.523855i \(-0.175507\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 1.67276 0.0656616
\(650\) 0.826531 6.70052i 0.0324192 0.262816i
\(651\) −7.74798 −0.303667
\(652\) 21.0132i 0.822939i
\(653\) 9.64832i 0.377568i −0.982019 0.188784i \(-0.939545\pi\)
0.982019 0.188784i \(-0.0604546\pi\)
\(654\) 20.1622 0.788405
\(655\) −8.31265 9.40105i −0.324802 0.367329i
\(656\) −3.35026 −0.130806
\(657\) 3.22425i 0.125790i
\(658\) 15.3258i 0.597463i
\(659\) −10.0654 −0.392091 −0.196046 0.980595i \(-0.562810\pi\)
−0.196046 + 0.980595i \(0.562810\pi\)
\(660\) −2.70052 + 2.38787i −0.105118 + 0.0929478i
\(661\) 13.5633 0.527549 0.263775 0.964584i \(-0.415032\pi\)
0.263775 + 0.964584i \(0.415032\pi\)
\(662\) 6.85097i 0.266270i
\(663\) 9.40105i 0.365106i
\(664\) −10.8872 −0.422504
\(665\) 5.61213 4.96239i 0.217629 0.192433i
\(666\) 11.2750 0.436899
\(667\) 4.87732i 0.188850i
\(668\) 9.92478i 0.384001i
\(669\) 7.03761 0.272090
\(670\) −14.7005 16.6253i −0.567931 0.642291i
\(671\) −3.22425 −0.124471
\(672\) 3.35026i 0.129239i
\(673\) 5.93937i 0.228946i −0.993426 0.114473i \(-0.963482\pi\)
0.993426 0.114473i \(-0.0365179\pi\)
\(674\) 24.2374 0.933591
\(675\) −4.96239 0.612127i −0.191002 0.0235608i
\(676\) −11.1768 −0.429877
\(677\) 24.9525i 0.959004i 0.877541 + 0.479502i \(0.159183\pi\)
−0.877541 + 0.479502i \(0.840817\pi\)
\(678\) 11.1490i 0.428176i
\(679\) 3.89843 0.149608
\(680\) −10.3127 11.6629i −0.395472 0.447252i
\(681\) 14.5501 0.557560
\(682\) 3.72829i 0.142763i
\(683\) 45.6239i 1.74575i 0.487944 + 0.872875i \(0.337747\pi\)
−0.487944 + 0.872875i \(0.662253\pi\)
\(684\) 1.00000 0.0382360
\(685\) 29.5877 26.1622i 1.13049 0.999606i
\(686\) −9.29948 −0.355056
\(687\) 11.4010i 0.434977i
\(688\) 10.3127i 0.393166i
\(689\) 16.1016 0.613421
\(690\) 2.26187 2.00000i 0.0861077 0.0761387i
\(691\) −11.7480 −0.446914 −0.223457 0.974714i \(-0.571734\pi\)
−0.223457 + 0.974714i \(0.571734\pi\)
\(692\) 14.6253i 0.555971i
\(693\) 5.40105i 0.205169i
\(694\) 0.962389 0.0365318
\(695\) 15.8496 + 17.9248i 0.601208 + 0.679926i
\(696\) 3.61213 0.136917
\(697\) 23.3258i 0.883529i
\(698\) 1.37470i 0.0520331i
\(699\) 21.9149 0.828899
\(700\) 16.6253 + 2.05079i 0.628377 + 0.0775124i
\(701\) −43.8105 −1.65470 −0.827350 0.561686i \(-0.810153\pi\)
−0.827350 + 0.561686i \(0.810153\pi\)
\(702\) 1.35026i 0.0509623i
\(703\) 11.2750i 0.425246i
\(704\) 1.61213 0.0607593
\(705\) 6.77575 + 7.66291i 0.255189 + 0.288602i
\(706\) −28.7367 −1.08152
\(707\) 29.7743i 1.11978i
\(708\) 1.03761i 0.0389958i
\(709\) 29.5975 1.11156 0.555779 0.831330i \(-0.312420\pi\)
0.555779 + 0.831330i \(0.312420\pi\)
\(710\) −1.29948 + 1.14903i −0.0487685 + 0.0431224i
\(711\) 14.3127 0.536766
\(712\) 2.57452i 0.0964840i
\(713\) 3.12268i 0.116945i
\(714\) −23.3258 −0.872947
\(715\) −3.64641 + 3.22425i −0.136368 + 0.120580i
\(716\) 11.7381 0.438675
\(717\) 13.2750i 0.495765i
\(718\) 31.1998i 1.16437i
\(719\) −7.45183 −0.277906 −0.138953 0.990299i \(-0.544374\pi\)
−0.138953 + 0.990299i \(0.544374\pi\)
\(720\) 1.48119 + 1.67513i 0.0552009 + 0.0624284i
\(721\) −23.5778 −0.878085
\(722\) 1.00000i 0.0372161i
\(723\) 21.3258i 0.793116i
\(724\) −21.4617 −0.797617
\(725\) 2.21108 17.9248i 0.0821174 0.665710i
\(726\) −8.40105 −0.311792
\(727\) 0.600863i 0.0222848i 0.999938 + 0.0111424i \(0.00354681\pi\)
−0.999938 + 0.0111424i \(0.996453\pi\)
\(728\) 4.52373i 0.167661i
\(729\) −1.00000 −0.0370370
\(730\) 4.77575 + 5.40105i 0.176758 + 0.199902i
\(731\) −71.8007 −2.65564
\(732\) 2.00000i 0.0739221i
\(733\) 36.0625i 1.33200i −0.745952 0.666000i \(-0.768005\pi\)
0.745952 0.666000i \(-0.231995\pi\)
\(734\) 20.1260 0.742865
\(735\) 7.07618 6.25694i 0.261009 0.230791i
\(736\) −1.35026 −0.0497713
\(737\) 16.0000i 0.589368i
\(738\) 3.35026i 0.123325i
\(739\) 14.1768 0.521502 0.260751 0.965406i \(-0.416030\pi\)
0.260751 + 0.965406i \(0.416030\pi\)
\(740\) −18.8872 + 16.7005i −0.694306 + 0.613923i
\(741\) 1.35026 0.0496031
\(742\) 39.9511i 1.46665i
\(743\) 24.9986i 0.917109i −0.888666 0.458555i \(-0.848367\pi\)
0.888666 0.458555i \(-0.151633\pi\)
\(744\) 2.31265 0.0847859
\(745\) 1.53690 + 1.73813i 0.0563078 + 0.0636803i
\(746\) 17.9756 0.658132
\(747\) 10.8872i 0.398341i
\(748\) 11.2243i 0.410399i
\(749\) −2.59895 −0.0949637
\(750\) 9.21933 6.32487i 0.336642 0.230952i
\(751\) −10.2111 −0.372608 −0.186304 0.982492i \(-0.559651\pi\)
−0.186304 + 0.982492i \(0.559651\pi\)
\(752\) 4.57452i 0.166815i
\(753\) 16.3127i 0.594466i
\(754\) 4.87732 0.177621
\(755\) −1.72355 1.94921i −0.0627263 0.0709392i
\(756\) 3.35026 0.121848
\(757\) 44.4847i 1.61682i 0.588617 + 0.808412i \(0.299673\pi\)
−0.588617 + 0.808412i \(0.700327\pi\)
\(758\) 1.67276i 0.0607574i
\(759\) −2.17679 −0.0790126
\(760\) −1.67513 + 1.48119i −0.0607634 + 0.0537286i
\(761\) 27.1490 0.984152 0.492076 0.870552i \(-0.336238\pi\)
0.492076 + 0.870552i \(0.336238\pi\)
\(762\) 13.7381i 0.497680i
\(763\) 67.5487i 2.44543i
\(764\) 21.2750 0.769704
\(765\) −11.6629 + 10.3127i −0.421673 + 0.372855i
\(766\) −31.8496 −1.15077
\(767\) 1.40105i 0.0505889i
\(768\) 1.00000i 0.0360844i
\(769\) 31.4010 1.13235 0.566175 0.824285i \(-0.308422\pi\)
0.566175 + 0.824285i \(0.308422\pi\)
\(770\) −8.00000 9.04746i −0.288300 0.326048i
\(771\) 24.5501 0.884149
\(772\) 14.1622i 0.509709i
\(773\) 4.02635i 0.144818i −0.997375 0.0724088i \(-0.976931\pi\)
0.997375 0.0724088i \(-0.0230686\pi\)
\(774\) 10.3127 0.370681
\(775\) 1.41564 11.4763i 0.0508511 0.412240i
\(776\) −1.16362 −0.0417715
\(777\) 37.7743i 1.35515i
\(778\) 10.3371i 0.370603i
\(779\) −3.35026 −0.120036
\(780\) 2.00000 + 2.26187i 0.0716115 + 0.0809878i
\(781\) 1.25060 0.0447500
\(782\) 9.40105i 0.336181i
\(783\) 3.61213i 0.129087i
\(784\) −4.22425 −0.150866
\(785\) −18.3634 + 16.2374i −0.655419 + 0.579539i
\(786\) 5.61213 0.200178
\(787\) 18.2981i 0.652255i 0.945326 + 0.326128i \(0.105744\pi\)
−0.945326 + 0.326128i \(0.894256\pi\)
\(788\) 3.87399i