Properties

Label 690.3.k.b.277.12
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.12
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(1.48797 - 4.77346i) q^{5} +2.44949 q^{6} +(-9.54800 - 9.54800i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(1.48797 - 4.77346i) q^{5} +2.44949 q^{6} +(-9.54800 - 9.54800i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-6.26143 + 3.28550i) q^{10} -15.2672 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-8.82448 + 8.82448i) q^{13} +19.0960i q^{14} +(4.02390 + 7.66865i) q^{15} -4.00000 q^{16} +(5.29413 + 5.29413i) q^{17} +(-3.00000 + 3.00000i) q^{18} -0.807134i q^{19} +(9.54693 + 2.97593i) q^{20} +23.3877 q^{21} +(15.2672 + 15.2672i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(-20.5719 - 14.2055i) q^{25} +17.6490 q^{26} +(3.67423 + 3.67423i) q^{27} +(19.0960 - 19.0960i) q^{28} +14.0088i q^{29} +(3.64476 - 11.6926i) q^{30} +29.6842 q^{31} +(4.00000 + 4.00000i) q^{32} +(18.6984 - 18.6984i) q^{33} -10.5883i q^{34} +(-59.7841 + 31.3699i) q^{35} +6.00000 q^{36} +(-6.74933 - 6.74933i) q^{37} +(-0.807134 + 0.807134i) q^{38} -21.6155i q^{39} +(-6.57100 - 12.5229i) q^{40} +70.9103 q^{41} +(-23.3877 - 23.3877i) q^{42} +(36.3155 - 36.3155i) q^{43} -30.5344i q^{44} +(-14.3204 - 4.46390i) q^{45} -6.78233 q^{46} +(-32.5756 - 32.5756i) q^{47} +(4.89898 - 4.89898i) q^{48} +133.329i q^{49} +(6.36642 + 34.7774i) q^{50} -12.9679 q^{51} +(-17.6490 - 17.6490i) q^{52} +(-41.7961 + 41.7961i) q^{53} -7.34847i q^{54} +(-22.7170 + 72.8773i) q^{55} -38.1920 q^{56} +(0.988533 + 0.988533i) q^{57} +(14.0088 - 14.0088i) q^{58} +103.898i q^{59} +(-15.3373 + 8.04779i) q^{60} +63.7279 q^{61} +(-29.6842 - 29.6842i) q^{62} +(-28.6440 + 28.6440i) q^{63} -8.00000i q^{64} +(28.9928 + 55.2539i) q^{65} -37.3968 q^{66} +(-31.8570 - 31.8570i) q^{67} +(-10.5883 + 10.5883i) q^{68} +8.30662i q^{69} +(91.1541 + 28.4142i) q^{70} -61.7411 q^{71} +(-6.00000 - 6.00000i) q^{72} +(80.7054 - 80.7054i) q^{73} +13.4987i q^{74} +(42.5935 - 7.79724i) q^{75} +1.61427 q^{76} +(145.771 + 145.771i) q^{77} +(-21.6155 + 21.6155i) q^{78} +132.668i q^{79} +(-5.95186 + 19.0939i) q^{80} -9.00000 q^{81} +(-70.9103 - 70.9103i) q^{82} +(-59.6101 + 59.6101i) q^{83} +46.7755i q^{84} +(33.1488 - 17.3939i) q^{85} -72.6310 q^{86} +(-17.1572 - 17.1572i) q^{87} +(-30.5344 + 30.5344i) q^{88} -87.8622i q^{89} +(9.85650 + 18.7843i) q^{90} +168.512 q^{91} +(6.78233 + 6.78233i) q^{92} +(-36.3556 + 36.3556i) q^{93} +65.1511i q^{94} +(-3.85283 - 1.20099i) q^{95} -9.79796 q^{96} +(71.4213 + 71.4213i) q^{97} +(133.329 - 133.329i) q^{98} +45.8015i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 1.48797 4.77346i 0.297593 0.954693i
\(6\) 2.44949 0.408248
\(7\) −9.54800 9.54800i −1.36400 1.36400i −0.868751 0.495249i \(-0.835077\pi\)
−0.495249 0.868751i \(-0.664923\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −6.26143 + 3.28550i −0.626143 + 0.328550i
\(11\) −15.2672 −1.38793 −0.693963 0.720011i \(-0.744137\pi\)
−0.693963 + 0.720011i \(0.744137\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −8.82448 + 8.82448i −0.678806 + 0.678806i −0.959730 0.280924i \(-0.909359\pi\)
0.280924 + 0.959730i \(0.409359\pi\)
\(14\) 19.0960i 1.36400i
\(15\) 4.02390 + 7.66865i 0.268260 + 0.511244i
\(16\) −4.00000 −0.250000
\(17\) 5.29413 + 5.29413i 0.311419 + 0.311419i 0.845459 0.534040i \(-0.179327\pi\)
−0.534040 + 0.845459i \(0.679327\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 0.807134i 0.0424807i −0.999774 0.0212404i \(-0.993238\pi\)
0.999774 0.0212404i \(-0.00676153\pi\)
\(20\) 9.54693 + 2.97593i 0.477346 + 0.148797i
\(21\) 23.3877 1.11370
\(22\) 15.2672 + 15.2672i 0.693963 + 0.693963i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −20.5719 14.2055i −0.822877 0.568220i
\(26\) 17.6490 0.678806
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 19.0960 19.0960i 0.682000 0.682000i
\(29\) 14.0088i 0.483062i 0.970393 + 0.241531i \(0.0776495\pi\)
−0.970393 + 0.241531i \(0.922350\pi\)
\(30\) 3.64476 11.6926i 0.121492 0.389752i
\(31\) 29.6842 0.957556 0.478778 0.877936i \(-0.341080\pi\)
0.478778 + 0.877936i \(0.341080\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 18.6984 18.6984i 0.566618 0.566618i
\(34\) 10.5883i 0.311419i
\(35\) −59.7841 + 31.3699i −1.70812 + 0.896284i
\(36\) 6.00000 0.166667
\(37\) −6.74933 6.74933i −0.182414 0.182414i 0.609993 0.792407i \(-0.291172\pi\)
−0.792407 + 0.609993i \(0.791172\pi\)
\(38\) −0.807134 + 0.807134i −0.0212404 + 0.0212404i
\(39\) 21.6155i 0.554243i
\(40\) −6.57100 12.5229i −0.164275 0.313071i
\(41\) 70.9103 1.72952 0.864759 0.502187i \(-0.167471\pi\)
0.864759 + 0.502187i \(0.167471\pi\)
\(42\) −23.3877 23.3877i −0.556851 0.556851i
\(43\) 36.3155 36.3155i 0.844546 0.844546i −0.144900 0.989446i \(-0.546286\pi\)
0.989446 + 0.144900i \(0.0462860\pi\)
\(44\) 30.5344i 0.693963i
\(45\) −14.3204 4.46390i −0.318231 0.0991977i
\(46\) −6.78233 −0.147442
\(47\) −32.5756 32.5756i −0.693097 0.693097i 0.269815 0.962912i \(-0.413037\pi\)
−0.962912 + 0.269815i \(0.913037\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 133.329i 2.72099i
\(50\) 6.36642 + 34.7774i 0.127328 + 0.695548i
\(51\) −12.9679 −0.254273
\(52\) −17.6490 17.6490i −0.339403 0.339403i
\(53\) −41.7961 + 41.7961i −0.788606 + 0.788606i −0.981266 0.192659i \(-0.938289\pi\)
0.192659 + 0.981266i \(0.438289\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −22.7170 + 72.8773i −0.413037 + 1.32504i
\(56\) −38.1920 −0.682000
\(57\) 0.988533 + 0.988533i 0.0173427 + 0.0173427i
\(58\) 14.0088 14.0088i 0.241531 0.241531i
\(59\) 103.898i 1.76099i 0.474056 + 0.880495i \(0.342790\pi\)
−0.474056 + 0.880495i \(0.657210\pi\)
\(60\) −15.3373 + 8.04779i −0.255622 + 0.134130i
\(61\) 63.7279 1.04472 0.522360 0.852725i \(-0.325052\pi\)
0.522360 + 0.852725i \(0.325052\pi\)
\(62\) −29.6842 29.6842i −0.478778 0.478778i
\(63\) −28.6440 + 28.6440i −0.454667 + 0.454667i
\(64\) 8.00000i 0.125000i
\(65\) 28.9928 + 55.2539i 0.446043 + 0.850060i
\(66\) −37.3968 −0.566618
\(67\) −31.8570 31.8570i −0.475477 0.475477i 0.428204 0.903682i \(-0.359146\pi\)
−0.903682 + 0.428204i \(0.859146\pi\)
\(68\) −10.5883 + 10.5883i −0.155710 + 0.155710i
\(69\) 8.30662i 0.120386i
\(70\) 91.1541 + 28.4142i 1.30220 + 0.405917i
\(71\) −61.7411 −0.869593 −0.434796 0.900529i \(-0.643180\pi\)
−0.434796 + 0.900529i \(0.643180\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) 80.7054 80.7054i 1.10555 1.10555i 0.111826 0.993728i \(-0.464330\pi\)
0.993728 0.111826i \(-0.0356700\pi\)
\(74\) 13.4987i 0.182414i
\(75\) 42.5935 7.79724i 0.567913 0.103963i
\(76\) 1.61427 0.0212404
\(77\) 145.771 + 145.771i 1.89313 + 1.89313i
\(78\) −21.6155 + 21.6155i −0.277122 + 0.277122i
\(79\) 132.668i 1.67934i 0.543099 + 0.839669i \(0.317251\pi\)
−0.543099 + 0.839669i \(0.682749\pi\)
\(80\) −5.95186 + 19.0939i −0.0743983 + 0.238673i
\(81\) −9.00000 −0.111111
\(82\) −70.9103 70.9103i −0.864759 0.864759i
\(83\) −59.6101 + 59.6101i −0.718194 + 0.718194i −0.968235 0.250041i \(-0.919556\pi\)
0.250041 + 0.968235i \(0.419556\pi\)
\(84\) 46.7755i 0.556851i
\(85\) 33.1488 17.3939i 0.389986 0.204634i
\(86\) −72.6310 −0.844546
\(87\) −17.1572 17.1572i −0.197209 0.197209i
\(88\) −30.5344 + 30.5344i −0.346981 + 0.346981i
\(89\) 87.8622i 0.987215i −0.869685 0.493608i \(-0.835678\pi\)
0.869685 0.493608i \(-0.164322\pi\)
\(90\) 9.85650 + 18.7843i 0.109517 + 0.208714i
\(91\) 168.512 1.85178
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) −36.3556 + 36.3556i −0.390921 + 0.390921i
\(94\) 65.1511i 0.693097i
\(95\) −3.85283 1.20099i −0.0405561 0.0126420i
\(96\) −9.79796 −0.102062
\(97\) 71.4213 + 71.4213i 0.736302 + 0.736302i 0.971860 0.235559i \(-0.0756919\pi\)
−0.235559 + 0.971860i \(0.575692\pi\)
\(98\) 133.329 133.329i 1.36050 1.36050i
\(99\) 45.8015i 0.462642i
\(100\) 28.4110 41.1438i 0.284110 0.411438i
\(101\) −109.722 −1.08636 −0.543180 0.839617i \(-0.682780\pi\)
−0.543180 + 0.839617i \(0.682780\pi\)
\(102\) 12.9679 + 12.9679i 0.127136 + 0.127136i
\(103\) 78.8523 78.8523i 0.765556 0.765556i −0.211765 0.977321i \(-0.567921\pi\)
0.977321 + 0.211765i \(0.0679210\pi\)
\(104\) 35.2979i 0.339403i
\(105\) 34.8001 111.640i 0.331430 1.06324i
\(106\) 83.5923 0.788606
\(107\) −106.500 106.500i −0.995324 0.995324i 0.00466549 0.999989i \(-0.498515\pi\)
−0.999989 + 0.00466549i \(0.998515\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 163.472i 1.49974i 0.661583 + 0.749872i \(0.269885\pi\)
−0.661583 + 0.749872i \(0.730115\pi\)
\(110\) 95.5944 50.1603i 0.869040 0.456003i
\(111\) 16.5324 0.148941
\(112\) 38.1920 + 38.1920i 0.341000 + 0.341000i
\(113\) −35.0186 + 35.0186i −0.309899 + 0.309899i −0.844870 0.534971i \(-0.820323\pi\)
0.534971 + 0.844870i \(0.320323\pi\)
\(114\) 1.97707i 0.0173427i
\(115\) −11.1417 21.2335i −0.0968841 0.184639i
\(116\) −28.0176 −0.241531
\(117\) 26.4734 + 26.4734i 0.226269 + 0.226269i
\(118\) 103.898 103.898i 0.880495 0.880495i
\(119\) 101.097i 0.849552i
\(120\) 23.3851 + 7.28951i 0.194876 + 0.0607459i
\(121\) 112.087 0.926337
\(122\) −63.7279 63.7279i −0.522360 0.522360i
\(123\) −86.8470 + 86.8470i −0.706073 + 0.706073i
\(124\) 59.3685i 0.478778i
\(125\) −98.4197 + 77.0620i −0.787358 + 0.616496i
\(126\) 57.2880 0.454667
\(127\) 17.8774 + 17.8774i 0.140767 + 0.140767i 0.773979 0.633212i \(-0.218264\pi\)
−0.633212 + 0.773979i \(0.718264\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 88.9544i 0.689569i
\(130\) 26.2611 84.2467i 0.202008 0.648052i
\(131\) −115.204 −0.879421 −0.439710 0.898140i \(-0.644919\pi\)
−0.439710 + 0.898140i \(0.644919\pi\)
\(132\) 37.3968 + 37.3968i 0.283309 + 0.283309i
\(133\) −7.70652 + 7.70652i −0.0579437 + 0.0579437i
\(134\) 63.7140i 0.475477i
\(135\) 23.0060 12.0717i 0.170415 0.0894199i
\(136\) 21.1765 0.155710
\(137\) 113.671 + 113.671i 0.829715 + 0.829715i 0.987477 0.157762i \(-0.0504278\pi\)
−0.157762 + 0.987477i \(0.550428\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 27.5466i 0.198177i 0.995079 + 0.0990884i \(0.0315927\pi\)
−0.995079 + 0.0990884i \(0.968407\pi\)
\(140\) −62.7399 119.568i −0.448142 0.854059i
\(141\) 79.7935 0.565912
\(142\) 61.7411 + 61.7411i 0.434796 + 0.434796i
\(143\) 134.725 134.725i 0.942133 0.942133i
\(144\) 12.0000i 0.0833333i
\(145\) 66.8705 + 20.8446i 0.461176 + 0.143756i
\(146\) −161.411 −1.10555
\(147\) −163.294 163.294i −1.11084 1.11084i
\(148\) 13.4987 13.4987i 0.0912072 0.0912072i
\(149\) 44.7097i 0.300065i 0.988681 + 0.150033i \(0.0479379\pi\)
−0.988681 + 0.150033i \(0.952062\pi\)
\(150\) −50.3907 34.7962i −0.335938 0.231975i
\(151\) −181.710 −1.20338 −0.601689 0.798730i \(-0.705505\pi\)
−0.601689 + 0.798730i \(0.705505\pi\)
\(152\) −1.61427 1.61427i −0.0106202 0.0106202i
\(153\) 15.8824 15.8824i 0.103806 0.103806i
\(154\) 291.542i 1.89313i
\(155\) 44.1691 141.697i 0.284962 0.914172i
\(156\) 43.2310 0.277122
\(157\) −105.941 105.941i −0.674783 0.674783i 0.284032 0.958815i \(-0.408328\pi\)
−0.958815 + 0.284032i \(0.908328\pi\)
\(158\) 132.668 132.668i 0.839669 0.839669i
\(159\) 102.379i 0.643894i
\(160\) 25.0457 13.1420i 0.156536 0.0821375i
\(161\) −64.7577 −0.402222
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 88.1818 88.1818i 0.540993 0.540993i −0.382827 0.923820i \(-0.625050\pi\)
0.923820 + 0.382827i \(0.125050\pi\)
\(164\) 141.821i 0.864759i
\(165\) −61.4336 117.079i −0.372325 0.709568i
\(166\) 119.220 0.718194
\(167\) 140.172 + 140.172i 0.839354 + 0.839354i 0.988774 0.149420i \(-0.0477406\pi\)
−0.149420 + 0.988774i \(0.547741\pi\)
\(168\) 46.7755 46.7755i 0.278425 0.278425i
\(169\) 13.2570i 0.0784439i
\(170\) −50.5427 15.7550i −0.297310 0.0926762i
\(171\) −2.42140 −0.0141602
\(172\) 72.6310 + 72.6310i 0.422273 + 0.422273i
\(173\) −108.261 + 108.261i −0.625788 + 0.625788i −0.947005 0.321218i \(-0.895908\pi\)
0.321218 + 0.947005i \(0.395908\pi\)
\(174\) 34.3144i 0.197209i
\(175\) 60.7865 + 332.055i 0.347352 + 1.89746i
\(176\) 61.0687 0.346981
\(177\) −127.249 127.249i −0.718921 0.718921i
\(178\) −87.8622 + 87.8622i −0.493608 + 0.493608i
\(179\) 89.5979i 0.500547i −0.968175 0.250273i \(-0.919480\pi\)
0.968175 0.250273i \(-0.0805205\pi\)
\(180\) 8.92779 28.6408i 0.0495989 0.159115i
\(181\) −56.2745 −0.310909 −0.155454 0.987843i \(-0.549684\pi\)
−0.155454 + 0.987843i \(0.549684\pi\)
\(182\) −168.512 168.512i −0.925892 0.925892i
\(183\) −78.0504 + 78.0504i −0.426505 + 0.426505i
\(184\) 13.5647i 0.0737210i
\(185\) −42.2605 + 22.1749i −0.228435 + 0.119864i
\(186\) 72.7113 0.390921
\(187\) −80.8264 80.8264i −0.432227 0.432227i
\(188\) 65.1511 65.1511i 0.346549 0.346549i
\(189\) 70.1632i 0.371234i
\(190\) 2.65184 + 5.05381i 0.0139570 + 0.0265990i
\(191\) −94.4885 −0.494704 −0.247352 0.968926i \(-0.579560\pi\)
−0.247352 + 0.968926i \(0.579560\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) −234.734 + 234.734i −1.21624 + 1.21624i −0.247299 + 0.968939i \(0.579543\pi\)
−0.968939 + 0.247299i \(0.920457\pi\)
\(194\) 142.843i 0.736302i
\(195\) −103.181 32.1631i −0.529132 0.164939i
\(196\) −266.657 −1.36050
\(197\) −42.4399 42.4399i −0.215431 0.215431i 0.591139 0.806570i \(-0.298678\pi\)
−0.806570 + 0.591139i \(0.798678\pi\)
\(198\) 45.8015 45.8015i 0.231321 0.231321i
\(199\) 96.7373i 0.486117i −0.970012 0.243059i \(-0.921849\pi\)
0.970012 0.243059i \(-0.0781508\pi\)
\(200\) −69.5548 + 12.7328i −0.347774 + 0.0636642i
\(201\) 78.0334 0.388226
\(202\) 109.722 + 109.722i 0.543180 + 0.543180i
\(203\) 133.756 133.756i 0.658896 0.658896i
\(204\) 25.9358i 0.127136i
\(205\) 105.512 338.488i 0.514693 1.65116i
\(206\) −157.705 −0.765556
\(207\) −10.1735 10.1735i −0.0491473 0.0491473i
\(208\) 35.2979 35.2979i 0.169702 0.169702i
\(209\) 12.3227i 0.0589601i
\(210\) −146.441 + 76.8403i −0.697336 + 0.365906i
\(211\) −43.2445 −0.204950 −0.102475 0.994736i \(-0.532676\pi\)
−0.102475 + 0.994736i \(0.532676\pi\)
\(212\) −83.5923 83.5923i −0.394303 0.394303i
\(213\) 75.6171 75.6171i 0.355010 0.355010i
\(214\) 212.999i 0.995324i
\(215\) −119.314 227.387i −0.554951 1.05761i
\(216\) 14.6969 0.0680414
\(217\) −283.425 283.425i −1.30611 1.30611i
\(218\) 163.472 163.472i 0.749872 0.749872i
\(219\) 197.687i 0.902681i
\(220\) −145.755 45.4341i −0.662521 0.206519i
\(221\) −93.4359 −0.422787
\(222\) −16.5324 16.5324i −0.0744703 0.0744703i
\(223\) −60.9713 + 60.9713i −0.273414 + 0.273414i −0.830473 0.557059i \(-0.811930\pi\)
0.557059 + 0.830473i \(0.311930\pi\)
\(224\) 76.3840i 0.341000i
\(225\) −42.6165 + 61.7158i −0.189407 + 0.274292i
\(226\) 70.0373 0.309899
\(227\) 5.19640 + 5.19640i 0.0228916 + 0.0228916i 0.718460 0.695568i \(-0.244847\pi\)
−0.695568 + 0.718460i \(0.744847\pi\)
\(228\) −1.97707 + 1.97707i −0.00867135 + 0.00867135i
\(229\) 8.93888i 0.0390344i −0.999810 0.0195172i \(-0.993787\pi\)
0.999810 0.0195172i \(-0.00621292\pi\)
\(230\) −10.0919 + 32.3752i −0.0438777 + 0.140762i
\(231\) −357.065 −1.54573
\(232\) 28.0176 + 28.0176i 0.120765 + 0.120765i
\(233\) −302.154 + 302.154i −1.29680 + 1.29680i −0.366304 + 0.930495i \(0.619377\pi\)
−0.930495 + 0.366304i \(0.880623\pi\)
\(234\) 52.9469i 0.226269i
\(235\) −203.970 + 107.027i −0.867956 + 0.455434i
\(236\) −207.797 −0.880495
\(237\) −162.484 162.484i −0.685587 0.685587i
\(238\) −101.097 + 101.097i −0.424776 + 0.424776i
\(239\) 83.3390i 0.348699i −0.984684 0.174349i \(-0.944218\pi\)
0.984684 0.174349i \(-0.0557822\pi\)
\(240\) −16.0956 30.6746i −0.0670650 0.127811i
\(241\) 418.251 1.73548 0.867741 0.497016i \(-0.165571\pi\)
0.867741 + 0.497016i \(0.165571\pi\)
\(242\) −112.087 112.087i −0.463168 0.463168i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 127.456i 0.522360i
\(245\) 636.439 + 198.388i 2.59771 + 0.809748i
\(246\) 173.694 0.706073
\(247\) 7.12254 + 7.12254i 0.0288362 + 0.0288362i
\(248\) 59.3685 59.3685i 0.239389 0.239389i
\(249\) 146.014i 0.586403i
\(250\) 175.482 + 21.3577i 0.701927 + 0.0854310i
\(251\) 54.6126 0.217580 0.108790 0.994065i \(-0.465302\pi\)
0.108790 + 0.994065i \(0.465302\pi\)
\(252\) −57.2880 57.2880i −0.227333 0.227333i
\(253\) −51.7735 + 51.7735i −0.204638 + 0.204638i
\(254\) 35.7547i 0.140767i
\(255\) −19.2958 + 61.9019i −0.0756698 + 0.242752i
\(256\) 16.0000 0.0625000
\(257\) 290.966 + 290.966i 1.13216 + 1.13216i 0.989817 + 0.142346i \(0.0454645\pi\)
0.142346 + 0.989817i \(0.454535\pi\)
\(258\) 88.9544 88.9544i 0.344785 0.344785i
\(259\) 128.885i 0.497626i
\(260\) −110.508 + 57.9856i −0.425030 + 0.223022i
\(261\) 42.0264 0.161021
\(262\) 115.204 + 115.204i 0.439710 + 0.439710i
\(263\) 72.2816 72.2816i 0.274835 0.274835i −0.556208 0.831043i \(-0.687744\pi\)
0.831043 + 0.556208i \(0.187744\pi\)
\(264\) 74.7936i 0.283309i
\(265\) 137.321 + 261.704i 0.518193 + 0.987561i
\(266\) 15.4130 0.0579437
\(267\) 107.609 + 107.609i 0.403029 + 0.403029i
\(268\) 63.7140 63.7140i 0.237739 0.237739i
\(269\) 403.498i 1.49999i 0.661443 + 0.749995i \(0.269944\pi\)
−0.661443 + 0.749995i \(0.730056\pi\)
\(270\) −35.0777 10.9343i −0.129917 0.0404973i
\(271\) −181.559 −0.669959 −0.334979 0.942225i \(-0.608729\pi\)
−0.334979 + 0.942225i \(0.608729\pi\)
\(272\) −21.1765 21.1765i −0.0778548 0.0778548i
\(273\) −206.385 + 206.385i −0.755988 + 0.755988i
\(274\) 227.342i 0.829715i
\(275\) 314.075 + 216.878i 1.14209 + 0.788647i
\(276\) −16.6132 −0.0601929
\(277\) −302.137 302.137i −1.09075 1.09075i −0.995449 0.0952968i \(-0.969620\pi\)
−0.0952968 0.995449i \(-0.530380\pi\)
\(278\) 27.5466 27.5466i 0.0990884 0.0990884i
\(279\) 89.0527i 0.319185i
\(280\) −56.8284 + 182.308i −0.202959 + 0.651100i
\(281\) 175.916 0.626037 0.313019 0.949747i \(-0.398660\pi\)
0.313019 + 0.949747i \(0.398660\pi\)
\(282\) −79.7935 79.7935i −0.282956 0.282956i
\(283\) 228.430 228.430i 0.807174 0.807174i −0.177032 0.984205i \(-0.556649\pi\)
0.984205 + 0.177032i \(0.0566495\pi\)
\(284\) 123.482i 0.434796i
\(285\) 6.18963 3.24782i 0.0217180 0.0113959i
\(286\) −269.450 −0.942133
\(287\) −677.051 677.051i −2.35906 2.35906i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 232.944i 0.806036i
\(290\) −46.0259 87.7151i −0.158710 0.302466i
\(291\) −174.946 −0.601188
\(292\) 161.411 + 161.411i 0.552777 + 0.552777i
\(293\) 206.779 206.779i 0.705729 0.705729i −0.259905 0.965634i \(-0.583691\pi\)
0.965634 + 0.259905i \(0.0836913\pi\)
\(294\) 326.587i 1.11084i
\(295\) 495.955 + 154.597i 1.68120 + 0.524058i
\(296\) −26.9973 −0.0912072
\(297\) −56.0952 56.0952i −0.188873 0.188873i
\(298\) 44.7097 44.7097i 0.150033 0.150033i
\(299\) 59.8506i 0.200169i
\(300\) 15.5945 + 85.1869i 0.0519816 + 0.283956i
\(301\) −693.481 −2.30392
\(302\) 181.710 + 181.710i 0.601689 + 0.601689i
\(303\) 134.382 134.382i 0.443504 0.443504i
\(304\) 3.22854i 0.0106202i
\(305\) 94.8249 304.203i 0.310901 0.997386i
\(306\) −31.7648 −0.103806
\(307\) −136.705 136.705i −0.445294 0.445294i 0.448493 0.893787i \(-0.351961\pi\)
−0.893787 + 0.448493i \(0.851961\pi\)
\(308\) −291.542 + 291.542i −0.946565 + 0.946565i
\(309\) 193.148i 0.625074i
\(310\) −185.866 + 97.5275i −0.599567 + 0.314605i
\(311\) −380.382 −1.22309 −0.611547 0.791208i \(-0.709452\pi\)
−0.611547 + 0.791208i \(0.709452\pi\)
\(312\) −43.2310 43.2310i −0.138561 0.138561i
\(313\) 319.660 319.660i 1.02128 1.02128i 0.0215083 0.999769i \(-0.493153\pi\)
0.999769 0.0215083i \(-0.00684684\pi\)
\(314\) 211.882i 0.674783i
\(315\) 94.1098 + 179.352i 0.298761 + 0.569373i
\(316\) −265.335 −0.839669
\(317\) −220.290 220.290i −0.694920 0.694920i 0.268391 0.963310i \(-0.413508\pi\)
−0.963310 + 0.268391i \(0.913508\pi\)
\(318\) −102.379 + 102.379i −0.321947 + 0.321947i
\(319\) 213.875i 0.670454i
\(320\) −38.1877 11.9037i −0.119337 0.0371991i
\(321\) 260.870 0.812678
\(322\) 64.7577 + 64.7577i 0.201111 + 0.201111i
\(323\) 4.27307 4.27307i 0.0132293 0.0132293i
\(324\) 18.0000i 0.0555556i
\(325\) 306.893 56.1803i 0.944285 0.172863i
\(326\) −176.364 −0.540993
\(327\) −200.212 200.212i −0.612268 0.612268i
\(328\) 141.821 141.821i 0.432380 0.432380i
\(329\) 622.063i 1.89077i
\(330\) −55.6451 + 178.512i −0.168622 + 0.540946i
\(331\) 351.499 1.06193 0.530965 0.847394i \(-0.321830\pi\)
0.530965 + 0.847394i \(0.321830\pi\)
\(332\) −119.220 119.220i −0.359097 0.359097i
\(333\) −20.2480 + 20.2480i −0.0608048 + 0.0608048i
\(334\) 280.344i 0.839354i
\(335\) −199.470 + 104.666i −0.595434 + 0.312436i
\(336\) −93.5509 −0.278425
\(337\) 2.49301 + 2.49301i 0.00739767 + 0.00739767i 0.710796 0.703398i \(-0.248335\pi\)
−0.703398 + 0.710796i \(0.748335\pi\)
\(338\) 13.2570 13.2570i 0.0392219 0.0392219i
\(339\) 85.7778i 0.253032i
\(340\) 34.7877 + 66.2976i 0.102317 + 0.194993i
\(341\) −453.195 −1.32902
\(342\) 2.42140 + 2.42140i 0.00708012 + 0.00708012i
\(343\) 805.170 805.170i 2.34743 2.34743i
\(344\) 145.262i 0.422273i
\(345\) 39.6514 + 12.3600i 0.114932 + 0.0358260i
\(346\) 216.523 0.625788
\(347\) −0.135782 0.135782i −0.000391302 0.000391302i 0.706911 0.707302i \(-0.250088\pi\)
−0.707302 + 0.706911i \(0.750088\pi\)
\(348\) 34.3144 34.3144i 0.0986046 0.0986046i
\(349\) 437.421i 1.25336i −0.779278 0.626678i \(-0.784414\pi\)
0.779278 0.626678i \(-0.215586\pi\)
\(350\) 271.268 392.841i 0.775052 1.12240i
\(351\) −64.8464 −0.184748
\(352\) −61.0687 61.0687i −0.173491 0.173491i
\(353\) −279.219 + 279.219i −0.790989 + 0.790989i −0.981655 0.190666i \(-0.938935\pi\)
0.190666 + 0.981655i \(0.438935\pi\)
\(354\) 254.498i 0.718921i
\(355\) −91.8686 + 294.719i −0.258785 + 0.830194i
\(356\) 175.724 0.493608
\(357\) 123.818 + 123.818i 0.346828 + 0.346828i
\(358\) −89.5979 + 89.5979i −0.250273 + 0.250273i
\(359\) 245.162i 0.682903i 0.939899 + 0.341452i \(0.110919\pi\)
−0.939899 + 0.341452i \(0.889081\pi\)
\(360\) −37.5686 + 19.7130i −0.104357 + 0.0547583i
\(361\) 360.349 0.998195
\(362\) 56.2745 + 56.2745i 0.155454 + 0.155454i
\(363\) −137.278 + 137.278i −0.378175 + 0.378175i
\(364\) 337.025i 0.925892i
\(365\) −265.158 505.331i −0.726459 1.38447i
\(366\) 156.101 0.426505
\(367\) −242.695 242.695i −0.661295 0.661295i 0.294390 0.955685i \(-0.404883\pi\)
−0.955685 + 0.294390i \(0.904883\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 212.731i 0.576506i
\(370\) 64.4354 + 20.0855i 0.174150 + 0.0542852i
\(371\) 798.139 2.15132
\(372\) −72.7113 72.7113i −0.195460 0.195460i
\(373\) −236.803 + 236.803i −0.634862 + 0.634862i −0.949283 0.314422i \(-0.898189\pi\)
0.314422 + 0.949283i \(0.398189\pi\)
\(374\) 161.653i 0.432227i
\(375\) 26.1578 214.920i 0.0697541 0.573121i
\(376\) −130.302 −0.346549
\(377\) −123.620 123.620i −0.327905 0.327905i
\(378\) −70.1632 + 70.1632i −0.185617 + 0.185617i
\(379\) 282.098i 0.744323i 0.928168 + 0.372161i \(0.121383\pi\)
−0.928168 + 0.372161i \(0.878617\pi\)
\(380\) 2.40198 7.70565i 0.00632099 0.0202780i
\(381\) −43.7904 −0.114935
\(382\) 94.4885 + 94.4885i 0.247352 + 0.247352i
\(383\) −296.066 + 296.066i −0.773019 + 0.773019i −0.978633 0.205614i \(-0.934081\pi\)
0.205614 + 0.978633i \(0.434081\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 912.735 478.930i 2.37074 1.24398i
\(386\) 469.468 1.21624
\(387\) −108.946 108.946i −0.281515 0.281515i
\(388\) −142.843 + 142.843i −0.368151 + 0.368151i
\(389\) 28.9682i 0.0744684i 0.999307 + 0.0372342i \(0.0118548\pi\)
−0.999307 + 0.0372342i \(0.988145\pi\)
\(390\) 71.0176 + 135.344i 0.182096 + 0.347035i
\(391\) 35.9065 0.0918326
\(392\) 266.657 + 266.657i 0.680248 + 0.680248i
\(393\) 141.096 141.096i 0.359022 0.359022i
\(394\) 84.8797i 0.215431i
\(395\) 633.284 + 197.405i 1.60325 + 0.499759i
\(396\) −91.6031 −0.231321
\(397\) 306.025 + 306.025i 0.770845 + 0.770845i 0.978254 0.207410i \(-0.0665033\pi\)
−0.207410 + 0.978254i \(0.566503\pi\)
\(398\) −96.7373 + 96.7373i −0.243059 + 0.243059i
\(399\) 18.8770i 0.0473109i
\(400\) 82.2877 + 56.8220i 0.205719 + 0.142055i
\(401\) 652.488 1.62715 0.813576 0.581458i \(-0.197518\pi\)
0.813576 + 0.581458i \(0.197518\pi\)
\(402\) −78.0334 78.0334i −0.194113 0.194113i
\(403\) −261.948 + 261.948i −0.649995 + 0.649995i
\(404\) 219.445i 0.543180i
\(405\) −13.3917 + 42.9612i −0.0330659 + 0.106077i
\(406\) −267.512 −0.658896
\(407\) 103.043 + 103.043i 0.253177 + 0.253177i
\(408\) −25.9358 + 25.9358i −0.0635682 + 0.0635682i
\(409\) 169.896i 0.415394i −0.978193 0.207697i \(-0.933403\pi\)
0.978193 0.207697i \(-0.0665968\pi\)
\(410\) −444.000 + 232.976i −1.08293 + 0.568233i
\(411\) −278.436 −0.677460
\(412\) 157.705 + 157.705i 0.382778 + 0.382778i
\(413\) 992.022 992.022i 2.40199 2.40199i
\(414\) 20.3470i 0.0491473i
\(415\) 195.849 + 373.244i 0.471925 + 0.899384i
\(416\) −70.5959 −0.169702
\(417\) −33.7375 33.7375i −0.0809054 0.0809054i
\(418\) 12.3227 12.3227i 0.0294801 0.0294801i
\(419\) 453.781i 1.08301i 0.840697 + 0.541505i \(0.182145\pi\)
−0.840697 + 0.541505i \(0.817855\pi\)
\(420\) 223.281 + 69.6003i 0.531621 + 0.165715i
\(421\) 690.644 1.64048 0.820242 0.572017i \(-0.193839\pi\)
0.820242 + 0.572017i \(0.193839\pi\)
\(422\) 43.2445 + 43.2445i 0.102475 + 0.102475i
\(423\) −97.7267 + 97.7267i −0.231032 + 0.231032i
\(424\) 167.185i 0.394303i
\(425\) −33.7046 184.116i −0.0793050 0.433214i
\(426\) −151.234 −0.355010
\(427\) −608.474 608.474i −1.42500 1.42500i
\(428\) 212.999 212.999i 0.497662 0.497662i
\(429\) 330.007i 0.769248i
\(430\) −108.072 + 346.701i −0.251331 + 0.806282i
\(431\) 221.482 0.513879 0.256940 0.966427i \(-0.417286\pi\)
0.256940 + 0.966427i \(0.417286\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) 33.2597 33.2597i 0.0768122 0.0768122i −0.667657 0.744469i \(-0.732703\pi\)
0.744469 + 0.667657i \(0.232703\pi\)
\(434\) 566.850i 1.30611i
\(435\) −107.429 + 56.3699i −0.246962 + 0.129586i
\(436\) −326.944 −0.749872
\(437\) −2.73713 2.73713i −0.00626344 0.00626344i
\(438\) 197.687 197.687i 0.451341 0.451341i
\(439\) 497.481i 1.13321i 0.823988 + 0.566607i \(0.191744\pi\)
−0.823988 + 0.566607i \(0.808256\pi\)
\(440\) 100.321 + 191.189i 0.228001 + 0.434520i
\(441\) 399.986 0.906997
\(442\) 93.4359 + 93.4359i 0.211393 + 0.211393i
\(443\) −179.340 + 179.340i −0.404831 + 0.404831i −0.879931 0.475101i \(-0.842412\pi\)
0.475101 + 0.879931i \(0.342412\pi\)
\(444\) 33.0648i 0.0744703i
\(445\) −419.407 130.736i −0.942487 0.293788i
\(446\) 121.943 0.273414
\(447\) −54.7580 54.7580i −0.122501 0.122501i
\(448\) −76.3840 + 76.3840i −0.170500 + 0.170500i
\(449\) 322.045i 0.717249i 0.933482 + 0.358624i \(0.116754\pi\)
−0.933482 + 0.358624i \(0.883246\pi\)
\(450\) 104.332 19.0992i 0.231849 0.0424428i
\(451\) −1082.60 −2.40044
\(452\) −70.0373 70.0373i −0.154950 0.154950i
\(453\) 222.548 222.548i 0.491277 0.491277i
\(454\) 10.3928i 0.0228916i
\(455\) 250.741 804.387i 0.551078 1.76788i
\(456\) 3.95413 0.00867135
\(457\) −8.39176 8.39176i −0.0183627 0.0183627i 0.697866 0.716229i \(-0.254133\pi\)
−0.716229 + 0.697866i \(0.754133\pi\)
\(458\) −8.93888 + 8.93888i −0.0195172 + 0.0195172i
\(459\) 38.9037i 0.0847576i
\(460\) 42.4671 22.2833i 0.0923197 0.0484420i
\(461\) −284.927 −0.618063 −0.309031 0.951052i \(-0.600005\pi\)
−0.309031 + 0.951052i \(0.600005\pi\)
\(462\) 357.065 + 357.065i 0.772867 + 0.772867i
\(463\) −473.858 + 473.858i −1.02345 + 1.02345i −0.0237337 + 0.999718i \(0.507555\pi\)
−0.999718 + 0.0237337i \(0.992445\pi\)
\(464\) 56.0352i 0.120765i
\(465\) 119.446 + 227.638i 0.256874 + 0.489545i
\(466\) 604.309 1.29680
\(467\) 527.960 + 527.960i 1.13053 + 1.13053i 0.990088 + 0.140446i \(0.0448537\pi\)
0.140446 + 0.990088i \(0.455146\pi\)
\(468\) −52.9469 + 52.9469i −0.113134 + 0.113134i
\(469\) 608.341i 1.29710i
\(470\) 310.997 + 96.9427i 0.661695 + 0.206261i
\(471\) 259.501 0.550958
\(472\) 207.797 + 207.797i 0.440247 + 0.440247i
\(473\) −554.435 + 554.435i −1.17217 + 1.17217i
\(474\) 324.968i 0.685587i
\(475\) −11.4657 + 16.6043i −0.0241384 + 0.0349564i
\(476\) 202.193 0.424776
\(477\) 125.388 + 125.388i 0.262869 + 0.262869i
\(478\) −83.3390 + 83.3390i −0.174349 + 0.174349i
\(479\) 169.005i 0.352829i −0.984316 0.176415i \(-0.943550\pi\)
0.984316 0.176415i \(-0.0564499\pi\)
\(480\) −14.5790 + 46.7702i −0.0303730 + 0.0974379i
\(481\) 119.119 0.247648
\(482\) −418.251 418.251i −0.867741 0.867741i
\(483\) 79.3116 79.3116i 0.164206 0.164206i
\(484\) 224.173i 0.463168i
\(485\) 447.199 234.654i 0.922060 0.483824i
\(486\) −22.0454 −0.0453609
\(487\) 235.015 + 235.015i 0.482578 + 0.482578i 0.905954 0.423376i \(-0.139155\pi\)
−0.423376 + 0.905954i \(0.639155\pi\)
\(488\) 127.456 127.456i 0.261180 0.261180i
\(489\) 216.000i 0.441719i
\(490\) −438.051 834.828i −0.893981 1.70373i
\(491\) −104.029 −0.211872 −0.105936 0.994373i \(-0.533784\pi\)
−0.105936 + 0.994373i \(0.533784\pi\)
\(492\) −173.694 173.694i −0.353036 0.353036i
\(493\) −74.1644 + 74.1644i −0.150435 + 0.150435i
\(494\) 14.2451i 0.0288362i
\(495\) 218.632 + 68.1511i 0.441681 + 0.137679i
\(496\) −118.737 −0.239389
\(497\) 589.504 + 589.504i 1.18612 + 1.18612i
\(498\) −146.014 + 146.014i −0.293201 + 0.293201i
\(499\) 106.509i 0.213445i −0.994289 0.106723i \(-0.965964\pi\)
0.994289 0.106723i \(-0.0340357\pi\)
\(500\) −154.124 196.839i −0.308248 0.393679i
\(501\) −343.350 −0.685330
\(502\) −54.6126 54.6126i −0.108790 0.108790i
\(503\) −480.602 + 480.602i −0.955472 + 0.955472i −0.999050 0.0435785i \(-0.986124\pi\)
0.0435785 + 0.999050i \(0.486124\pi\)
\(504\) 114.576i 0.227333i
\(505\) −163.263 + 523.755i −0.323293 + 1.03714i
\(506\) 103.547 0.204638
\(507\) −16.2365 16.2365i −0.0320246 0.0320246i
\(508\) −35.7547 + 35.7547i −0.0703833 + 0.0703833i
\(509\) 415.566i 0.816435i 0.912885 + 0.408218i \(0.133850\pi\)
−0.912885 + 0.408218i \(0.866150\pi\)
\(510\) 81.1977 42.6061i 0.159211 0.0835413i
\(511\) −1541.15 −3.01595
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 2.96560 2.96560i 0.00578090 0.00578090i
\(514\) 581.932i 1.13216i
\(515\) −259.069 493.728i −0.503047 0.958695i
\(516\) −177.909 −0.344785
\(517\) 497.337 + 497.337i 0.961967 + 0.961967i
\(518\) 128.885 128.885i 0.248813 0.248813i
\(519\) 265.185i 0.510953i
\(520\) 168.493 + 52.5221i 0.324026 + 0.101004i
\(521\) −148.312 −0.284667 −0.142333 0.989819i \(-0.545461\pi\)
−0.142333 + 0.989819i \(0.545461\pi\)
\(522\) −42.0264 42.0264i −0.0805103 0.0805103i
\(523\) −504.625 + 504.625i −0.964866 + 0.964866i −0.999403 0.0345373i \(-0.989004\pi\)
0.0345373 + 0.999403i \(0.489004\pi\)
\(524\) 230.408i 0.439710i
\(525\) −481.130 332.234i −0.916439 0.632827i
\(526\) −144.563 −0.274835
\(527\) 157.152 + 157.152i 0.298202 + 0.298202i
\(528\) −74.7936 + 74.7936i −0.141655 + 0.141655i
\(529\) 23.0000i 0.0434783i
\(530\) 124.382 399.025i 0.234684 0.752877i
\(531\) 311.695 0.586997
\(532\) −15.4130 15.4130i −0.0289719 0.0289719i
\(533\) −625.746 + 625.746i −1.17401 + 1.17401i
\(534\) 215.217i 0.403029i
\(535\) −666.840 + 349.904i −1.24643 + 0.654027i
\(536\) −127.428 −0.237739
\(537\) 109.735 + 109.735i 0.204347 + 0.204347i
\(538\) 403.498 403.498i 0.749995 0.749995i
\(539\) 2035.55i 3.77653i
\(540\) 24.1434 + 46.0119i 0.0447100 + 0.0852073i
\(541\) 105.629 0.195247 0.0976236 0.995223i \(-0.468876\pi\)
0.0976236 + 0.995223i \(0.468876\pi\)
\(542\) 181.559 + 181.559i 0.334979 + 0.334979i
\(543\) 68.9219 68.9219i 0.126928 0.126928i
\(544\) 42.3530i 0.0778548i
\(545\) 780.328 + 243.241i 1.43180 + 0.446314i
\(546\) 412.769 0.755988
\(547\) 212.307 + 212.307i 0.388131 + 0.388131i 0.874020 0.485890i \(-0.161504\pi\)
−0.485890 + 0.874020i \(0.661504\pi\)
\(548\) −227.342 + 227.342i −0.414858 + 0.414858i
\(549\) 191.184i 0.348240i
\(550\) −97.1972 530.953i −0.176722 0.965369i
\(551\) 11.3070 0.0205208
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) 1266.71 1266.71i 2.29062 2.29062i
\(554\) 604.273i 1.09075i
\(555\) 24.5997 78.9169i 0.0443237 0.142193i
\(556\) −55.0932 −0.0990884
\(557\) −593.376 593.376i −1.06531 1.06531i −0.997713 0.0675950i \(-0.978467\pi\)
−0.0675950 0.997713i \(-0.521533\pi\)
\(558\) −89.0527 + 89.0527i −0.159593 + 0.159593i
\(559\) 640.931i 1.14657i
\(560\) 239.137 125.480i 0.427029 0.224071i
\(561\) 197.983 0.352912
\(562\) −175.916 175.916i −0.313019 0.313019i
\(563\) −177.134 + 177.134i −0.314625 + 0.314625i −0.846698 0.532074i \(-0.821413\pi\)
0.532074 + 0.846698i \(0.321413\pi\)
\(564\) 159.587i 0.282956i
\(565\) 115.054 + 219.267i 0.203635 + 0.388083i
\(566\) −456.860 −0.807174
\(567\) 85.9320 + 85.9320i 0.151556 + 0.151556i
\(568\) −123.482 + 123.482i −0.217398 + 0.217398i
\(569\) 1086.68i 1.90981i −0.296907 0.954907i \(-0.595955\pi\)
0.296907 0.954907i \(-0.404045\pi\)
\(570\) −9.43746 2.94181i −0.0165569 0.00516107i
\(571\) −812.228 −1.42247 −0.711233 0.702956i \(-0.751863\pi\)
−0.711233 + 0.702956i \(0.751863\pi\)
\(572\) 269.450 + 269.450i 0.471066 + 0.471066i
\(573\) 115.724 115.724i 0.201962 0.201962i
\(574\) 1354.10i 2.35906i
\(575\) −117.936 + 21.5896i −0.205106 + 0.0375471i
\(576\) −24.0000 −0.0416667
\(577\) −387.764 387.764i −0.672035 0.672035i 0.286150 0.958185i \(-0.407624\pi\)
−0.958185 + 0.286150i \(0.907624\pi\)
\(578\) −232.944 + 232.944i −0.403018 + 0.403018i
\(579\) 574.978i 0.993054i
\(580\) −41.6892 + 133.741i −0.0718779 + 0.230588i
\(581\) 1138.31 1.95923
\(582\) 174.946 + 174.946i 0.300594 + 0.300594i
\(583\) 638.109 638.109i 1.09453 1.09453i
\(584\) 322.822i 0.552777i
\(585\) 165.762 86.9785i 0.283353 0.148681i
\(586\) −413.557 −0.705729
\(587\) 738.060 + 738.060i 1.25734 + 1.25734i 0.952357 + 0.304986i \(0.0986516\pi\)
0.304986 + 0.952357i \(0.401348\pi\)
\(588\) 326.587 326.587i 0.555420 0.555420i
\(589\) 23.9592i 0.0406777i
\(590\) −341.358 650.553i −0.578573 1.10263i
\(591\) 103.956 0.175898
\(592\) 26.9973 + 26.9973i 0.0456036 + 0.0456036i
\(593\) −598.064 + 598.064i −1.00854 + 1.00854i −0.00857559 + 0.999963i \(0.502730\pi\)
−0.999963 + 0.00857559i \(0.997270\pi\)
\(594\) 112.190i 0.188873i
\(595\) −482.581 150.428i −0.811061 0.252821i
\(596\) −89.4195 −0.150033
\(597\) 118.479 + 118.479i 0.198457 + 0.198457i
\(598\) 59.8506 59.8506i 0.100085 0.100085i
\(599\) 170.664i 0.284914i −0.989801 0.142457i \(-0.954500\pi\)
0.989801 0.142457i \(-0.0455003\pi\)
\(600\) 69.5925 100.781i 0.115987 0.167969i
\(601\) −578.991 −0.963380 −0.481690 0.876342i \(-0.659977\pi\)
−0.481690 + 0.876342i \(0.659977\pi\)
\(602\) 693.481 + 693.481i 1.15196 + 1.15196i
\(603\) −95.5710 + 95.5710i −0.158492 + 0.158492i
\(604\) 363.420i 0.601689i
\(605\) 166.781 535.042i 0.275671 0.884367i
\(606\) −268.764 −0.443504
\(607\) −57.5503 57.5503i −0.0948110 0.0948110i 0.658110 0.752921i \(-0.271356\pi\)
−0.752921 + 0.658110i \(0.771356\pi\)
\(608\) 3.22854 3.22854i 0.00531009 0.00531009i
\(609\) 327.634i 0.537987i
\(610\) −399.028 + 209.378i −0.654143 + 0.343242i
\(611\) 574.925 0.940958
\(612\) 31.7648 + 31.7648i 0.0519032 + 0.0519032i
\(613\) −619.940 + 619.940i −1.01132 + 1.01132i −0.0113863 + 0.999935i \(0.503624\pi\)
−0.999935 + 0.0113863i \(0.996376\pi\)
\(614\) 273.410i 0.445294i
\(615\) 285.336 + 543.786i 0.463960 + 0.884205i
\(616\) 583.084 0.946565
\(617\) 238.014 + 238.014i 0.385760 + 0.385760i 0.873172 0.487412i \(-0.162059\pi\)
−0.487412 + 0.873172i \(0.662059\pi\)
\(618\) 193.148 193.148i 0.312537 0.312537i
\(619\) 95.4435i 0.154190i −0.997024 0.0770949i \(-0.975436\pi\)
0.997024 0.0770949i \(-0.0245644\pi\)
\(620\) 283.393 + 88.3383i 0.457086 + 0.142481i
\(621\) 24.9199 0.0401286
\(622\) 380.382 + 380.382i 0.611547 + 0.611547i
\(623\) −838.908 + 838.908i −1.34656 + 1.34656i
\(624\) 86.4619i 0.138561i
\(625\) 221.408 + 584.469i 0.354252 + 0.935150i
\(626\) −639.319 −1.02128
\(627\) −15.0921 15.0921i −0.0240704 0.0240704i
\(628\) 211.882 211.882i 0.337391 0.337391i
\(629\) 71.4636i 0.113615i
\(630\) 85.2426 273.462i 0.135306 0.434067i
\(631\) 298.665 0.473320 0.236660 0.971592i \(-0.423947\pi\)
0.236660 + 0.971592i \(0.423947\pi\)
\(632\) 265.335 + 265.335i 0.419834 + 0.419834i
\(633\) 52.9635 52.9635i 0.0836706 0.0836706i
\(634\) 440.579i 0.694920i
\(635\) 111.938 58.7361i 0.176280 0.0924977i
\(636\) 204.758 0.321947
\(637\) −1176.56 1176.56i −1.84703 1.84703i
\(638\) −213.875 + 213.875i −0.335227 + 0.335227i
\(639\) 185.223i 0.289864i
\(640\) 26.2840 + 50.0914i 0.0410687 + 0.0782679i
\(641\) −174.918 −0.272882 −0.136441 0.990648i \(-0.543566\pi\)
−0.136441 + 0.990648i \(0.543566\pi\)
\(642\) −260.870 260.870i −0.406339 0.406339i
\(643\) −296.575 + 296.575i −0.461236 + 0.461236i −0.899060 0.437825i \(-0.855749\pi\)
0.437825 + 0.899060i \(0.355749\pi\)
\(644\) 129.515i 0.201111i
\(645\) 424.621 + 132.361i 0.658327 + 0.205211i
\(646\) −8.54614 −0.0132293
\(647\) 372.708 + 372.708i 0.576056 + 0.576056i 0.933814 0.357759i \(-0.116459\pi\)
−0.357759 + 0.933814i \(0.616459\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 1586.24i 2.44412i
\(650\) −363.073 250.712i −0.558574 0.385711i
\(651\) 694.247 1.06643
\(652\) 176.364 + 176.364i 0.270496 + 0.270496i
\(653\) 336.400 336.400i 0.515162 0.515162i −0.400942 0.916103i \(-0.631317\pi\)
0.916103 + 0.400942i \(0.131317\pi\)
\(654\) 400.423i 0.612268i
\(655\) −171.420 + 549.923i −0.261710 + 0.839577i
\(656\) −283.641 −0.432380
\(657\) −242.116 242.116i −0.368518 0.368518i
\(658\) 622.063 622.063i 0.945385 0.945385i
\(659\) 441.117i 0.669374i 0.942329 + 0.334687i \(0.108631\pi\)
−0.942329 + 0.334687i \(0.891369\pi\)
\(660\) 234.157 122.867i 0.354784 0.186162i
\(661\) 153.009 0.231481 0.115740 0.993279i \(-0.463076\pi\)
0.115740 + 0.993279i \(0.463076\pi\)
\(662\) −351.499 351.499i −0.530965 0.530965i
\(663\) 114.435 114.435i 0.172602 0.172602i
\(664\) 238.440i 0.359097i
\(665\) 25.3197 + 48.2538i 0.0380748 + 0.0725621i
\(666\) 40.4960 0.0608048
\(667\) 47.5061 + 47.5061i 0.0712236 + 0.0712236i
\(668\) −280.344 + 280.344i −0.419677 + 0.419677i
\(669\) 149.349i 0.223242i
\(670\) 304.136 + 94.8042i 0.453935 + 0.141499i
\(671\) −972.945 −1.44999
\(672\) 93.5509 + 93.5509i 0.139213 + 0.139213i
\(673\) −716.575 + 716.575i −1.06475 + 1.06475i −0.0669937 + 0.997753i \(0.521341\pi\)
−0.997753 + 0.0669937i \(0.978659\pi\)
\(674\) 4.98603i 0.00739767i
\(675\) −23.3917 127.780i −0.0346544 0.189304i
\(676\) −26.5140 −0.0392219
\(677\) 31.0480 + 31.0480i 0.0458611 + 0.0458611i 0.729665 0.683804i \(-0.239676\pi\)
−0.683804 + 0.729665i \(0.739676\pi\)
\(678\) −85.7778 + 85.7778i −0.126516 + 0.126516i
\(679\) 1363.86i 2.00863i
\(680\) 31.5099 101.085i 0.0463381 0.148655i
\(681\) −12.7285 −0.0186909
\(682\) 453.195 + 453.195i 0.664508 + 0.664508i
\(683\) −242.458 + 242.458i −0.354990 + 0.354990i −0.861962 0.506972i \(-0.830765\pi\)
0.506972 + 0.861962i \(0.330765\pi\)
\(684\) 4.84280i 0.00708012i
\(685\) 711.743 373.466i 1.03904 0.545206i
\(686\) −1610.34 −2.34743
\(687\) 10.9479 + 10.9479i 0.0159357 + 0.0159357i
\(688\) −145.262 + 145.262i −0.211137 + 0.211137i
\(689\) 737.659i 1.07062i
\(690\) −27.2914 52.0113i −0.0395528 0.0753788i
\(691\) 532.561 0.770711 0.385356 0.922768i \(-0.374079\pi\)
0.385356 + 0.922768i \(0.374079\pi\)
\(692\) −216.523 216.523i −0.312894 0.312894i
\(693\) 437.313 437.313i 0.631043 0.631043i
\(694\) 0.271564i 0.000391302i
\(695\) 131.493 + 40.9884i 0.189198 + 0.0589761i
\(696\) −68.6288 −0.0986046
\(697\) 375.408 + 375.408i 0.538605 + 0.538605i
\(698\) −437.421 + 437.421i −0.626678 + 0.626678i
\(699\) 740.124i 1.05883i
\(700\) −664.110 + 121.573i −0.948728 + 0.173676i
\(701\) −1075.73 −1.53457 −0.767285 0.641307i \(-0.778393\pi\)
−0.767285 + 0.641307i \(0.778393\pi\)
\(702\) 64.8464 + 64.8464i 0.0923738 + 0.0923738i
\(703\) −5.44761 + 5.44761i −0.00774910 + 0.00774910i
\(704\) 122.137i 0.173491i
\(705\) 118.730 380.892i 0.168411 0.540272i
\(706\) 558.439 0.790989
\(707\) 1047.63 + 1047.63i 1.48179 + 1.48179i
\(708\) 254.498 254.498i 0.359461 0.359461i
\(709\) 87.1267i 0.122887i 0.998111 + 0.0614434i \(0.0195704\pi\)
−0.998111 + 0.0614434i \(0.980430\pi\)
\(710\) 386.588 202.850i 0.544489 0.285705i
\(711\) 398.003 0.559779
\(712\) −175.724 175.724i −0.246804 0.246804i
\(713\) 100.664 100.664i 0.141184 0.141184i
\(714\) 247.635i 0.346828i
\(715\) −442.639 843.571i −0.619075 1.17982i
\(716\) 179.196 0.250273
\(717\) 102.069 + 102.069i 0.142356 + 0.142356i
\(718\) 245.162 245.162i 0.341452 0.341452i
\(719\) 143.978i 0.200247i −0.994975 0.100123i \(-0.968076\pi\)
0.994975 0.100123i \(-0.0319238\pi\)
\(720\) 57.2816 + 17.8556i 0.0795577 + 0.0247994i
\(721\) −1505.76 −2.08844
\(722\) −360.349 360.349i −0.499098 0.499098i
\(723\) −512.251 + 512.251i −0.708508 + 0.708508i
\(724\) 112.549i 0.155454i
\(725\) 199.002 288.188i 0.274485 0.397500i
\(726\) 274.555 0.378175
\(727\) −568.660 568.660i −0.782201 0.782201i 0.198001 0.980202i \(-0.436555\pi\)
−0.980202 + 0.198001i \(0.936555\pi\)
\(728\) 337.025 337.025i 0.462946 0.462946i
\(729\) 27.0000i 0.0370370i
\(730\) −240.174 + 770.489i −0.329005 + 1.05546i
\(731\) 384.518 0.526016
\(732\) −156.101 156.101i −0.213252 0.213252i
\(733\) −540.647 + 540.647i −0.737582 + 0.737582i −0.972109 0.234528i \(-0.924646\pi\)
0.234528 + 0.972109i \(0.424646\pi\)
\(734\) 485.390i 0.661295i
\(735\) −1022.45 + 536.501i −1.39109 + 0.729933i
\(736\) 27.1293 0.0368605
\(737\) 486.366 + 486.366i 0.659927 + 0.659927i
\(738\) −212.731 + 212.731i −0.288253 + 0.288253i
\(739\) 1453.38i 1.96669i −0.181746 0.983346i \(-0.558175\pi\)
0.181746 0.983346i \(-0.441825\pi\)
\(740\) −44.3498 84.5209i −0.0599322 0.114217i
\(741\) −17.4466 −0.0235447
\(742\) −798.139 798.139i −1.07566 1.07566i
\(743\) 705.443 705.443i 0.949452 0.949452i −0.0493305 0.998783i \(-0.515709\pi\)
0.998783 + 0.0493305i \(0.0157088\pi\)
\(744\) 145.423i 0.195460i
\(745\) 213.420 + 66.5265i 0.286470 + 0.0892974i
\(746\) 473.607 0.634862
\(747\) 178.830 + 178.830i 0.239398 + 0.239398i
\(748\) 161.653 161.653i 0.216113 0.216113i
\(749\) 2033.72i 2.71524i
\(750\) −241.078 + 188.763i −0.321438 + 0.251683i
\(751\) 429.630 0.572077 0.286039 0.958218i \(-0.407661\pi\)
0.286039 + 0.958218i \(0.407661\pi\)
\(752\) 130.302 + 130.302i 0.173274 + 0.173274i
\(753\) −66.8865 + 66.8865i −0.0888267 + 0.0888267i
\(754\) 247.241i 0.327905i
\(755\) −270.378 + 867.387i −0.358117 + 1.14886i
\(756\) 140.326 0.185617
\(757\) −365.273 365.273i −0.482527 0.482527i 0.423411 0.905938i \(-0.360833\pi\)
−0.905938 + 0.423411i \(0.860833\pi\)
\(758\) 282.098 282.098i 0.372161 0.372161i
\(759\) 126.819i 0.167087i
\(760\) −10.1076 + 5.30368i −0.0132995 + 0.00697852i
\(761\) 25.4087 0.0333886 0.0166943 0.999861i \(-0.494686\pi\)
0.0166943 + 0.999861i \(0.494686\pi\)
\(762\) 43.7904 + 43.7904i 0.0574677 + 0.0574677i
\(763\) 1560.83 1560.83i 2.04565 2.04565i
\(764\) 188.977i 0.247352i
\(765\) −52.1816 99.4464i −0.0682112 0.129995i
\(766\) 592.133 0.773019
\(767\) −916.850 916.850i −1.19537 1.19537i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 217.638i 0.283015i −0.989937 0.141507i \(-0.954805\pi\)
0.989937 0.141507i \(-0.0451949\pi\)
\(770\) −1391.67 433.805i −1.80736 0.563382i
\(771\) −712.718 −0.924407
\(772\) −469.468 469.468i −0.608119 0.608119i
\(773\) 784.910 784.910i 1.01541 1.01541i 0.0155284 0.999879i \(-0.495057\pi\)
0.999879 0.0155284i \(-0.00494303\pi\)
\(774\) 217.893i 0.281515i
\(775\) −610.662 421.680i −0.787951 0.544103i
\(776\) 285.685 0.368151
\(777\) −157.851 157.851i −0.203155 0.203155i
\(778\) 28.9682 28.9682i 0.0372342 0.0372342i
\(779\)