Properties

Label 105.3.l.a.43.8
Level 105
Weight 3
Character 105.43
Analytic conductor 2.861
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.8
Character \(\chi\) \(=\) 105.43
Dual form 105.3.l.a.22.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.992944 - 0.992944i) q^{2} +(1.22474 + 1.22474i) q^{3} +2.02813i q^{4} +(-2.01954 + 4.57400i) q^{5} +2.43221 q^{6} +(1.87083 - 1.87083i) q^{7} +(5.98559 + 5.98559i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(0.992944 - 0.992944i) q^{2} +(1.22474 + 1.22474i) q^{3} +2.02813i q^{4} +(-2.01954 + 4.57400i) q^{5} +2.43221 q^{6} +(1.87083 - 1.87083i) q^{7} +(5.98559 + 5.98559i) q^{8} +3.00000i q^{9} +(2.53644 + 6.54701i) q^{10} +6.89922 q^{11} +(-2.48394 + 2.48394i) q^{12} +(-11.8879 - 11.8879i) q^{13} -3.71526i q^{14} +(-8.07540 + 3.12856i) q^{15} +3.77421 q^{16} +(16.7997 - 16.7997i) q^{17} +(2.97883 + 2.97883i) q^{18} -8.54896i q^{19} +(-9.27664 - 4.09587i) q^{20} +4.58258 q^{21} +(6.85053 - 6.85053i) q^{22} +(12.4881 + 12.4881i) q^{23} +14.6616i q^{24} +(-16.8429 - 18.4747i) q^{25} -23.6079 q^{26} +(-3.67423 + 3.67423i) q^{27} +(3.79427 + 3.79427i) q^{28} +1.33880i q^{29} +(-4.91193 + 11.1249i) q^{30} -18.4055 q^{31} +(-20.1948 + 20.1948i) q^{32} +(8.44978 + 8.44978i) q^{33} -33.3623i q^{34} +(4.77896 + 12.3354i) q^{35} -6.08438 q^{36} +(31.4003 - 31.4003i) q^{37} +(-8.48863 - 8.48863i) q^{38} -29.1192i q^{39} +(-39.4662 + 15.2900i) q^{40} -26.7387 q^{41} +(4.55024 - 4.55024i) q^{42} +(-15.5575 - 15.5575i) q^{43} +13.9925i q^{44} +(-13.7220 - 6.05861i) q^{45} +24.7999 q^{46} +(-22.1535 + 22.1535i) q^{47} +(4.62244 + 4.62244i) q^{48} -7.00000i q^{49} +(-35.0685 - 1.62028i) q^{50} +41.1506 q^{51} +(24.1101 - 24.1101i) q^{52} +(66.4707 + 66.4707i) q^{53} +7.29662i q^{54} +(-13.9332 + 31.5570i) q^{55} +22.3960 q^{56} +(10.4703 - 10.4703i) q^{57} +(1.32935 + 1.32935i) q^{58} -81.8790i q^{59} +(-6.34512 - 16.3779i) q^{60} -92.0711 q^{61} +(-18.2756 + 18.2756i) q^{62} +(5.61249 + 5.61249i) q^{63} +55.2014i q^{64} +(78.3830 - 30.3671i) q^{65} +16.7803 q^{66} +(79.2670 - 79.2670i) q^{67} +(34.0719 + 34.0719i) q^{68} +30.5894i q^{69} +(16.9936 + 7.50310i) q^{70} -63.1779 q^{71} +(-17.9568 + 17.9568i) q^{72} +(92.9816 + 92.9816i) q^{73} -62.3574i q^{74} +(1.99853 - 43.2551i) q^{75} +17.3384 q^{76} +(12.9072 - 12.9072i) q^{77} +(-28.9137 - 28.9137i) q^{78} -8.46427i q^{79} +(-7.62216 + 17.2632i) q^{80} -9.00000 q^{81} +(-26.5501 + 26.5501i) q^{82} +(36.2768 + 36.2768i) q^{83} +9.29404i q^{84} +(42.9141 + 110.769i) q^{85} -30.8955 q^{86} +(-1.63969 + 1.63969i) q^{87} +(41.2959 + 41.2959i) q^{88} -32.5098i q^{89} +(-19.6410 + 7.60931i) q^{90} -44.4803 q^{91} +(-25.3273 + 25.3273i) q^{92} +(-22.5420 - 22.5420i) q^{93} +43.9943i q^{94} +(39.1029 + 17.2649i) q^{95} -49.4669 q^{96} +(-79.2404 + 79.2404i) q^{97} +(-6.95061 - 6.95061i) q^{98} +20.6976i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} - 40q^{10} - 48q^{12} + 64q^{13} - 184q^{16} + 24q^{17} + 24q^{18} + 72q^{20} + 8q^{22} + 8q^{23} - 136q^{25} - 80q^{26} + 96q^{30} + 96q^{31} + 56q^{32} - 72q^{33} + 168q^{36} + 8q^{37} + 56q^{38} + 232q^{40} + 320q^{41} - 112q^{43} - 72q^{45} + 320q^{46} + 64q^{47} + 192q^{48} - 256q^{50} - 192q^{51} + 96q^{52} - 72q^{53} - 80q^{55} - 336q^{56} + 48q^{57} - 512q^{58} - 192q^{60} - 496q^{61} - 776q^{62} + 312q^{65} - 192q^{66} - 192q^{67} + 568q^{68} + 112q^{70} - 144q^{71} + 144q^{72} + 224q^{73} + 144q^{75} + 416q^{76} + 112q^{77} - 216q^{78} - 528q^{80} - 216q^{81} + 352q^{82} - 32q^{83} + 24q^{85} + 240q^{86} + 384q^{87} + 216q^{88} - 24q^{90} + 1304q^{92} + 376q^{95} + 168q^{96} - 816q^{97} - 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.992944 0.992944i 0.496472 0.496472i −0.413866 0.910338i \(-0.635822\pi\)
0.910338 + 0.413866i \(0.135822\pi\)
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) 2.02813i 0.507031i
\(5\) −2.01954 + 4.57400i −0.403908 + 0.914800i
\(6\) 2.43221 0.405368
\(7\) 1.87083 1.87083i 0.267261 0.267261i
\(8\) 5.98559 + 5.98559i 0.748199 + 0.748199i
\(9\) 3.00000i 0.333333i
\(10\) 2.53644 + 6.54701i 0.253644 + 0.654701i
\(11\) 6.89922 0.627201 0.313601 0.949555i \(-0.398465\pi\)
0.313601 + 0.949555i \(0.398465\pi\)
\(12\) −2.48394 + 2.48394i −0.206995 + 0.206995i
\(13\) −11.8879 11.8879i −0.914450 0.914450i 0.0821681 0.996618i \(-0.473816\pi\)
−0.996618 + 0.0821681i \(0.973816\pi\)
\(14\) 3.71526i 0.265375i
\(15\) −8.07540 + 3.12856i −0.538360 + 0.208571i
\(16\) 3.77421 0.235888
\(17\) 16.7997 16.7997i 0.988216 0.988216i −0.0117149 0.999931i \(-0.503729\pi\)
0.999931 + 0.0117149i \(0.00372905\pi\)
\(18\) 2.97883 + 2.97883i 0.165491 + 0.165491i
\(19\) 8.54896i 0.449945i −0.974365 0.224973i \(-0.927771\pi\)
0.974365 0.224973i \(-0.0722292\pi\)
\(20\) −9.27664 4.09587i −0.463832 0.204794i
\(21\) 4.58258 0.218218
\(22\) 6.85053 6.85053i 0.311388 0.311388i
\(23\) 12.4881 + 12.4881i 0.542959 + 0.542959i 0.924395 0.381436i \(-0.124570\pi\)
−0.381436 + 0.924395i \(0.624570\pi\)
\(24\) 14.6616i 0.610902i
\(25\) −16.8429 18.4747i −0.673717 0.738989i
\(26\) −23.6079 −0.907998
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) 3.79427 + 3.79427i 0.135510 + 0.135510i
\(29\) 1.33880i 0.0461655i 0.999734 + 0.0230828i \(0.00734813\pi\)
−0.999734 + 0.0230828i \(0.992652\pi\)
\(30\) −4.91193 + 11.1249i −0.163731 + 0.370830i
\(31\) −18.4055 −0.593726 −0.296863 0.954920i \(-0.595940\pi\)
−0.296863 + 0.954920i \(0.595940\pi\)
\(32\) −20.1948 + 20.1948i −0.631087 + 0.631087i
\(33\) 8.44978 + 8.44978i 0.256054 + 0.256054i
\(34\) 33.3623i 0.981243i
\(35\) 4.77896 + 12.3354i 0.136542 + 0.352439i
\(36\) −6.08438 −0.169010
\(37\) 31.4003 31.4003i 0.848656 0.848656i −0.141309 0.989966i \(-0.545131\pi\)
0.989966 + 0.141309i \(0.0451311\pi\)
\(38\) −8.48863 8.48863i −0.223385 0.223385i
\(39\) 29.1192i 0.746646i
\(40\) −39.4662 + 15.2900i −0.986655 + 0.382249i
\(41\) −26.7387 −0.652164 −0.326082 0.945341i \(-0.605729\pi\)
−0.326082 + 0.945341i \(0.605729\pi\)
\(42\) 4.55024 4.55024i 0.108339 0.108339i
\(43\) −15.5575 15.5575i −0.361803 0.361803i 0.502673 0.864476i \(-0.332350\pi\)
−0.864476 + 0.502673i \(0.832350\pi\)
\(44\) 13.9925i 0.318011i
\(45\) −13.7220 6.05861i −0.304933 0.134636i
\(46\) 24.7999 0.539128
\(47\) −22.1535 + 22.1535i −0.471350 + 0.471350i −0.902351 0.431001i \(-0.858160\pi\)
0.431001 + 0.902351i \(0.358160\pi\)
\(48\) 4.62244 + 4.62244i 0.0963009 + 0.0963009i
\(49\) 7.00000i 0.142857i
\(50\) −35.0685 1.62028i −0.701369 0.0324055i
\(51\) 41.1506 0.806875
\(52\) 24.1101 24.1101i 0.463655 0.463655i
\(53\) 66.4707 + 66.4707i 1.25416 + 1.25416i 0.953836 + 0.300328i \(0.0970960\pi\)
0.300328 + 0.953836i \(0.402904\pi\)
\(54\) 7.29662i 0.135123i
\(55\) −13.9332 + 31.5570i −0.253331 + 0.573764i
\(56\) 22.3960 0.399929
\(57\) 10.4703 10.4703i 0.183689 0.183689i
\(58\) 1.32935 + 1.32935i 0.0229199 + 0.0229199i
\(59\) 81.8790i 1.38778i −0.720081 0.693890i \(-0.755895\pi\)
0.720081 0.693890i \(-0.244105\pi\)
\(60\) −6.34512 16.3779i −0.105752 0.272965i
\(61\) −92.0711 −1.50936 −0.754681 0.656092i \(-0.772208\pi\)
−0.754681 + 0.656092i \(0.772208\pi\)
\(62\) −18.2756 + 18.2756i −0.294768 + 0.294768i
\(63\) 5.61249 + 5.61249i 0.0890871 + 0.0890871i
\(64\) 55.2014i 0.862522i
\(65\) 78.3830 30.3671i 1.20589 0.467186i
\(66\) 16.7803 0.254247
\(67\) 79.2670 79.2670i 1.18309 1.18309i 0.204149 0.978940i \(-0.434557\pi\)
0.978940 0.204149i \(-0.0654428\pi\)
\(68\) 34.0719 + 34.0719i 0.501057 + 0.501057i
\(69\) 30.5894i 0.443324i
\(70\) 16.9936 + 7.50310i 0.242765 + 0.107187i
\(71\) −63.1779 −0.889829 −0.444915 0.895573i \(-0.646766\pi\)
−0.444915 + 0.895573i \(0.646766\pi\)
\(72\) −17.9568 + 17.9568i −0.249400 + 0.249400i
\(73\) 92.9816 + 92.9816i 1.27372 + 1.27372i 0.944121 + 0.329600i \(0.106914\pi\)
0.329600 + 0.944121i \(0.393086\pi\)
\(74\) 62.3574i 0.842668i
\(75\) 1.99853 43.2551i 0.0266470 0.576735i
\(76\) 17.3384 0.228136
\(77\) 12.9072 12.9072i 0.167627 0.167627i
\(78\) −28.9137 28.9137i −0.370689 0.370689i
\(79\) 8.46427i 0.107143i −0.998564 0.0535713i \(-0.982940\pi\)
0.998564 0.0535713i \(-0.0170605\pi\)
\(80\) −7.62216 + 17.2632i −0.0952769 + 0.215790i
\(81\) −9.00000 −0.111111
\(82\) −26.5501 + 26.5501i −0.323781 + 0.323781i
\(83\) 36.2768 + 36.2768i 0.437070 + 0.437070i 0.891025 0.453955i \(-0.149987\pi\)
−0.453955 + 0.891025i \(0.649987\pi\)
\(84\) 9.29404i 0.110643i
\(85\) 42.9141 + 110.769i 0.504872 + 1.30317i
\(86\) −30.8955 −0.359250
\(87\) −1.63969 + 1.63969i −0.0188470 + 0.0188470i
\(88\) 41.2959 + 41.2959i 0.469271 + 0.469271i
\(89\) 32.5098i 0.365279i −0.983180 0.182639i \(-0.941536\pi\)
0.983180 0.182639i \(-0.0584641\pi\)
\(90\) −19.6410 + 7.60931i −0.218234 + 0.0845479i
\(91\) −44.4803 −0.488794
\(92\) −25.3273 + 25.3273i −0.275297 + 0.275297i
\(93\) −22.5420 22.5420i −0.242387 0.242387i
\(94\) 43.9943i 0.468024i
\(95\) 39.1029 + 17.2649i 0.411610 + 0.181736i
\(96\) −49.4669 −0.515280
\(97\) −79.2404 + 79.2404i −0.816911 + 0.816911i −0.985659 0.168748i \(-0.946028\pi\)
0.168748 + 0.985659i \(0.446028\pi\)
\(98\) −6.95061 6.95061i −0.0709246 0.0709246i
\(99\) 20.6976i 0.209067i
\(100\) 37.4691 34.1596i 0.374691 0.341596i
\(101\) 58.6380 0.580575 0.290287 0.956940i \(-0.406249\pi\)
0.290287 + 0.956940i \(0.406249\pi\)
\(102\) 40.8603 40.8603i 0.400591 0.400591i
\(103\) −99.0052 99.0052i −0.961215 0.961215i 0.0380601 0.999275i \(-0.487882\pi\)
−0.999275 + 0.0380601i \(0.987882\pi\)
\(104\) 142.312i 1.36838i
\(105\) −9.25468 + 20.9607i −0.0881398 + 0.199626i
\(106\) 132.003 1.24531
\(107\) 1.04612 1.04612i 0.00977686 0.00977686i −0.702201 0.711978i \(-0.747799\pi\)
0.711978 + 0.702201i \(0.247799\pi\)
\(108\) −7.45181 7.45181i −0.0689982 0.0689982i
\(109\) 157.350i 1.44358i 0.692111 + 0.721791i \(0.256681\pi\)
−0.692111 + 0.721791i \(0.743319\pi\)
\(110\) 17.4994 + 45.1692i 0.159086 + 0.410629i
\(111\) 76.9147 0.692925
\(112\) 7.06090 7.06090i 0.0630437 0.0630437i
\(113\) −127.762 127.762i −1.13063 1.13063i −0.990072 0.140562i \(-0.955109\pi\)
−0.140562 0.990072i \(-0.544891\pi\)
\(114\) 20.7928i 0.182393i
\(115\) −82.3405 + 31.9003i −0.716004 + 0.277394i
\(116\) −2.71525 −0.0234074
\(117\) 35.6636 35.6636i 0.304817 0.304817i
\(118\) −81.3013 81.3013i −0.688994 0.688994i
\(119\) 62.8586i 0.528224i
\(120\) −67.0623 29.6097i −0.558853 0.246748i
\(121\) −73.4008 −0.606618
\(122\) −91.4214 + 91.4214i −0.749356 + 0.749356i
\(123\) −32.7481 32.7481i −0.266245 0.266245i
\(124\) 37.3286i 0.301037i
\(125\) 118.518 39.7292i 0.948147 0.317833i
\(126\) 11.1458 0.0884585
\(127\) −15.3568 + 15.3568i −0.120920 + 0.120920i −0.764977 0.644057i \(-0.777250\pi\)
0.644057 + 0.764977i \(0.277250\pi\)
\(128\) −25.9672 25.9672i −0.202869 0.202869i
\(129\) 38.1080i 0.295411i
\(130\) 47.6771 107.983i 0.366747 0.830636i
\(131\) −176.678 −1.34869 −0.674344 0.738417i \(-0.735574\pi\)
−0.674344 + 0.738417i \(0.735574\pi\)
\(132\) −17.1372 + 17.1372i −0.129827 + 0.129827i
\(133\) −15.9936 15.9936i −0.120253 0.120253i
\(134\) 157.415i 1.17474i
\(135\) −9.38569 24.2262i −0.0695236 0.179453i
\(136\) 201.112 1.47876
\(137\) −18.0301 + 18.0301i −0.131607 + 0.131607i −0.769842 0.638235i \(-0.779665\pi\)
0.638235 + 0.769842i \(0.279665\pi\)
\(138\) 30.3735 + 30.3735i 0.220098 + 0.220098i
\(139\) 158.415i 1.13968i 0.821756 + 0.569839i \(0.192994\pi\)
−0.821756 + 0.569839i \(0.807006\pi\)
\(140\) −25.0177 + 9.69233i −0.178698 + 0.0692309i
\(141\) −54.2647 −0.384856
\(142\) −62.7321 + 62.7321i −0.441775 + 0.441775i
\(143\) −82.0169 82.0169i −0.573545 0.573545i
\(144\) 11.3226i 0.0786293i
\(145\) −6.12367 2.70376i −0.0422322 0.0186466i
\(146\) 184.651 1.26473
\(147\) 8.57321 8.57321i 0.0583212 0.0583212i
\(148\) 63.6837 + 63.6837i 0.430295 + 0.430295i
\(149\) 140.085i 0.940169i 0.882621 + 0.470085i \(0.155777\pi\)
−0.882621 + 0.470085i \(0.844223\pi\)
\(150\) −40.9655 44.9343i −0.273103 0.299562i
\(151\) −215.189 −1.42509 −0.712546 0.701625i \(-0.752458\pi\)
−0.712546 + 0.701625i \(0.752458\pi\)
\(152\) 51.1705 51.1705i 0.336648 0.336648i
\(153\) 50.3990 + 50.3990i 0.329405 + 0.329405i
\(154\) 25.6323i 0.166444i
\(155\) 37.1706 84.1867i 0.239810 0.543140i
\(156\) 59.0573 0.378573
\(157\) 49.6844 49.6844i 0.316461 0.316461i −0.530945 0.847406i \(-0.678163\pi\)
0.847406 + 0.530945i \(0.178163\pi\)
\(158\) −8.40455 8.40455i −0.0531933 0.0531933i
\(159\) 162.819i 1.02402i
\(160\) −51.5868 133.155i −0.322417 0.832219i
\(161\) 46.7260 0.290224
\(162\) −8.93649 + 8.93649i −0.0551635 + 0.0551635i
\(163\) −173.503 173.503i −1.06443 1.06443i −0.997776 0.0666571i \(-0.978767\pi\)
−0.0666571 0.997776i \(-0.521233\pi\)
\(164\) 54.2295i 0.330668i
\(165\) −55.7139 + 21.5846i −0.337660 + 0.130816i
\(166\) 72.0417 0.433986
\(167\) −177.701 + 177.701i −1.06408 + 1.06408i −0.0662778 + 0.997801i \(0.521112\pi\)
−0.997801 + 0.0662778i \(0.978888\pi\)
\(168\) 27.4294 + 27.4294i 0.163270 + 0.163270i
\(169\) 113.642i 0.672439i
\(170\) 152.599 + 67.3764i 0.897641 + 0.396332i
\(171\) 25.6469 0.149982
\(172\) 31.5526 31.5526i 0.183445 0.183445i
\(173\) 216.483 + 216.483i 1.25135 + 1.25135i 0.955116 + 0.296233i \(0.0957304\pi\)
0.296233 + 0.955116i \(0.404270\pi\)
\(174\) 3.25624i 0.0187140i
\(175\) −66.0733 3.05280i −0.377562 0.0174446i
\(176\) 26.0391 0.147949
\(177\) 100.281 100.281i 0.566559 0.566559i
\(178\) −32.2804 32.2804i −0.181351 0.181351i
\(179\) 243.651i 1.36118i 0.732665 + 0.680590i \(0.238276\pi\)
−0.732665 + 0.680590i \(0.761724\pi\)
\(180\) 12.2876 27.8299i 0.0682646 0.154611i
\(181\) 255.169 1.40977 0.704887 0.709320i \(-0.250998\pi\)
0.704887 + 0.709320i \(0.250998\pi\)
\(182\) −44.1664 + 44.1664i −0.242673 + 0.242673i
\(183\) −112.764 112.764i −0.616194 0.616194i
\(184\) 149.497i 0.812483i
\(185\) 80.2108 + 207.039i 0.433572 + 1.11913i
\(186\) −44.7659 −0.240677
\(187\) 115.905 115.905i 0.619811 0.619811i
\(188\) −44.9300 44.9300i −0.238989 0.238989i
\(189\) 13.7477i 0.0727393i
\(190\) 55.9701 21.6839i 0.294580 0.114126i
\(191\) 7.77927 0.0407292 0.0203646 0.999793i \(-0.493517\pi\)
0.0203646 + 0.999793i \(0.493517\pi\)
\(192\) −67.6076 + 67.6076i −0.352123 + 0.352123i
\(193\) 142.113 + 142.113i 0.736339 + 0.736339i 0.971867 0.235528i \(-0.0756821\pi\)
−0.235528 + 0.971867i \(0.575682\pi\)
\(194\) 157.363i 0.811147i
\(195\) 133.191 + 58.8073i 0.683031 + 0.301576i
\(196\) 14.1969 0.0724330
\(197\) 25.0644 25.0644i 0.127230 0.127230i −0.640624 0.767855i \(-0.721324\pi\)
0.767855 + 0.640624i \(0.221324\pi\)
\(198\) 20.5516 + 20.5516i 0.103796 + 0.103796i
\(199\) 84.2722i 0.423479i −0.977326 0.211739i \(-0.932087\pi\)
0.977326 0.211739i \(-0.0679128\pi\)
\(200\) 9.76722 211.397i 0.0488361 1.05699i
\(201\) 194.164 0.965988
\(202\) 58.2243 58.2243i 0.288239 0.288239i
\(203\) 2.50467 + 2.50467i 0.0123383 + 0.0123383i
\(204\) 83.4587i 0.409111i
\(205\) 53.9999 122.303i 0.263414 0.596600i
\(206\) −196.613 −0.954433
\(207\) −37.4642 + 37.4642i −0.180986 + 0.180986i
\(208\) −44.8672 44.8672i −0.215708 0.215708i
\(209\) 58.9811i 0.282206i
\(210\) 11.6234 + 30.0022i 0.0553496 + 0.142868i
\(211\) 365.560 1.73251 0.866255 0.499601i \(-0.166520\pi\)
0.866255 + 0.499601i \(0.166520\pi\)
\(212\) −134.811 + 134.811i −0.635900 + 0.635900i
\(213\) −77.3768 77.3768i −0.363271 0.363271i
\(214\) 2.07749i 0.00970788i
\(215\) 102.579 39.7411i 0.477112 0.184842i
\(216\) −43.9849 −0.203634
\(217\) −34.4335 + 34.4335i −0.158680 + 0.158680i
\(218\) 156.240 + 156.240i 0.716698 + 0.716698i
\(219\) 227.758i 1.03999i
\(220\) −64.0016 28.2583i −0.290916 0.128447i
\(221\) −399.424 −1.80735
\(222\) 76.3720 76.3720i 0.344018 0.344018i
\(223\) −258.830 258.830i −1.16067 1.16067i −0.984329 0.176343i \(-0.943573\pi\)
−0.176343 0.984329i \(-0.556427\pi\)
\(224\) 75.5620i 0.337330i
\(225\) 55.4242 50.5288i 0.246330 0.224572i
\(226\) −253.720 −1.12266
\(227\) 107.905 107.905i 0.475354 0.475354i −0.428288 0.903642i \(-0.640883\pi\)
0.903642 + 0.428288i \(0.140883\pi\)
\(228\) 21.2351 + 21.2351i 0.0931362 + 0.0931362i
\(229\) 253.800i 1.10829i −0.832419 0.554147i \(-0.813044\pi\)
0.832419 0.554147i \(-0.186956\pi\)
\(230\) −50.0843 + 113.435i −0.217758 + 0.493194i
\(231\) 31.6162 0.136867
\(232\) −8.01351 + 8.01351i −0.0345410 + 0.0345410i
\(233\) −242.257 242.257i −1.03973 1.03973i −0.999177 0.0405526i \(-0.987088\pi\)
−0.0405526 0.999177i \(-0.512912\pi\)
\(234\) 70.8238i 0.302666i
\(235\) −56.5901 146.070i −0.240809 0.621573i
\(236\) 166.061 0.703648
\(237\) 10.3666 10.3666i 0.0437408 0.0437408i
\(238\) −62.4151 62.4151i −0.262248 0.262248i
\(239\) 65.4432i 0.273821i −0.990583 0.136910i \(-0.956283\pi\)
0.990583 0.136910i \(-0.0437172\pi\)
\(240\) −30.4782 + 11.8079i −0.126993 + 0.0491994i
\(241\) 72.8224 0.302168 0.151084 0.988521i \(-0.451724\pi\)
0.151084 + 0.988521i \(0.451724\pi\)
\(242\) −72.8829 + 72.8829i −0.301169 + 0.301169i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 186.732i 0.765294i
\(245\) 32.0180 + 14.1368i 0.130686 + 0.0577011i
\(246\) −65.0341 −0.264366
\(247\) −101.629 + 101.629i −0.411452 + 0.411452i
\(248\) −110.168 110.168i −0.444225 0.444225i
\(249\) 88.8597i 0.356866i
\(250\) 78.2332 157.131i 0.312933 0.628524i
\(251\) 77.1502 0.307371 0.153686 0.988120i \(-0.450886\pi\)
0.153686 + 0.988120i \(0.450886\pi\)
\(252\) −11.3828 + 11.3828i −0.0451699 + 0.0451699i
\(253\) 86.1578 + 86.1578i 0.340545 + 0.340545i
\(254\) 30.4969i 0.120066i
\(255\) −83.1053 + 188.223i −0.325903 + 0.738129i
\(256\) −272.374 −1.06396
\(257\) 321.516 321.516i 1.25104 1.25104i 0.295779 0.955256i \(-0.404421\pi\)
0.955256 0.295779i \(-0.0955793\pi\)
\(258\) −37.8391 37.8391i −0.146663 0.146663i
\(259\) 117.489i 0.453626i
\(260\) 61.5882 + 158.971i 0.236878 + 0.611425i
\(261\) −4.01640 −0.0153885
\(262\) −175.432 + 175.432i −0.669586 + 0.669586i
\(263\) 52.5498 + 52.5498i 0.199809 + 0.199809i 0.799918 0.600109i \(-0.204876\pi\)
−0.600109 + 0.799918i \(0.704876\pi\)
\(264\) 101.154i 0.383158i
\(265\) −438.277 + 169.797i −1.65387 + 0.640743i
\(266\) −31.7616 −0.119404
\(267\) 39.8162 39.8162i 0.149125 0.149125i
\(268\) 160.763 + 160.763i 0.599863 + 0.599863i
\(269\) 25.6548i 0.0953709i −0.998862 0.0476855i \(-0.984815\pi\)
0.998862 0.0476855i \(-0.0151845\pi\)
\(270\) −33.3747 14.7358i −0.123610 0.0545770i
\(271\) −62.2867 −0.229840 −0.114920 0.993375i \(-0.536661\pi\)
−0.114920 + 0.993375i \(0.536661\pi\)
\(272\) 63.4055 63.4055i 0.233108 0.233108i
\(273\) −54.4770 54.4770i −0.199549 0.199549i
\(274\) 35.8058i 0.130678i
\(275\) −116.203 127.461i −0.422557 0.463495i
\(276\) −62.0391 −0.224779
\(277\) 50.5633 50.5633i 0.182539 0.182539i −0.609922 0.792461i \(-0.708799\pi\)
0.792461 + 0.609922i \(0.208799\pi\)
\(278\) 157.297 + 157.297i 0.565818 + 0.565818i
\(279\) 55.2165i 0.197909i
\(280\) −45.2296 + 102.439i −0.161534 + 0.365855i
\(281\) −30.1715 −0.107372 −0.0536859 0.998558i \(-0.517097\pi\)
−0.0536859 + 0.998558i \(0.517097\pi\)
\(282\) −53.8818 + 53.8818i −0.191070 + 0.191070i
\(283\) 17.6667 + 17.6667i 0.0624264 + 0.0624264i 0.737631 0.675204i \(-0.235945\pi\)
−0.675204 + 0.737631i \(0.735945\pi\)
\(284\) 128.133i 0.451171i
\(285\) 26.7460 + 69.0362i 0.0938455 + 0.242232i
\(286\) −162.876 −0.569497
\(287\) −50.0236 + 50.0236i −0.174298 + 0.174298i
\(288\) −60.5843 60.5843i −0.210362 0.210362i
\(289\) 275.459i 0.953144i
\(290\) −8.76514 + 3.39578i −0.0302246 + 0.0117096i
\(291\) −194.099 −0.667005
\(292\) −188.578 + 188.578i −0.645816 + 0.645816i
\(293\) 58.3820 + 58.3820i 0.199256 + 0.199256i 0.799681 0.600425i \(-0.205002\pi\)
−0.600425 + 0.799681i \(0.705002\pi\)
\(294\) 17.0254i 0.0579097i
\(295\) 374.515 + 165.358i 1.26954 + 0.560535i
\(296\) 375.898 1.26993
\(297\) −25.3493 + 25.3493i −0.0853513 + 0.0853513i
\(298\) 139.097 + 139.097i 0.466768 + 0.466768i
\(299\) 296.912i 0.993018i
\(300\) 87.7268 + 4.05326i 0.292423 + 0.0135109i
\(301\) −58.2109 −0.193392
\(302\) −213.671 + 213.671i −0.707519 + 0.707519i
\(303\) 71.8166 + 71.8166i 0.237019 + 0.237019i
\(304\) 32.2655i 0.106137i
\(305\) 185.941 421.133i 0.609643 1.38076i
\(306\) 100.087 0.327081
\(307\) 148.513 148.513i 0.483756 0.483756i −0.422573 0.906329i \(-0.638873\pi\)
0.906329 + 0.422573i \(0.138873\pi\)
\(308\) 26.1775 + 26.1775i 0.0849919 + 0.0849919i
\(309\) 242.512i 0.784829i
\(310\) −46.6844 120.501i −0.150595 0.388713i
\(311\) −200.767 −0.645555 −0.322777 0.946475i \(-0.604616\pi\)
−0.322777 + 0.946475i \(0.604616\pi\)
\(312\) 174.295 174.295i 0.558639 0.558639i
\(313\) 288.120 + 288.120i 0.920511 + 0.920511i 0.997065 0.0765549i \(-0.0243920\pi\)
−0.0765549 + 0.997065i \(0.524392\pi\)
\(314\) 98.6676i 0.314228i
\(315\) −37.0061 + 14.3369i −0.117480 + 0.0455139i
\(316\) 17.1666 0.0543247
\(317\) 85.7613 85.7613i 0.270540 0.270540i −0.558777 0.829318i \(-0.688729\pi\)
0.829318 + 0.558777i \(0.188729\pi\)
\(318\) 161.670 + 161.670i 0.508397 + 0.508397i
\(319\) 9.23667i 0.0289551i
\(320\) −252.491 111.481i −0.789035 0.348379i
\(321\) 2.56247 0.00798277
\(322\) 46.3963 46.3963i 0.144088 0.144088i
\(323\) −143.620 143.620i −0.444643 0.444643i
\(324\) 18.2531i 0.0563368i
\(325\) −19.3985 + 419.851i −0.0596876 + 1.29185i
\(326\) −344.557 −1.05692
\(327\) −192.714 + 192.714i −0.589340 + 0.589340i
\(328\) −160.047 160.047i −0.487949 0.487949i
\(329\) 82.8906i 0.251947i
\(330\) −33.8885 + 76.7531i −0.102692 + 0.232585i
\(331\) 118.330 0.357494 0.178747 0.983895i \(-0.442796\pi\)
0.178747 + 0.983895i \(0.442796\pi\)
\(332\) −73.5739 + 73.5739i −0.221608 + 0.221608i
\(333\) 94.2009 + 94.2009i 0.282885 + 0.282885i
\(334\) 352.895i 1.05657i
\(335\) 202.484 + 522.650i 0.604431 + 1.56015i
\(336\) 17.2956 0.0514750
\(337\) 64.4724 64.4724i 0.191313 0.191313i −0.604950 0.796263i \(-0.706807\pi\)
0.796263 + 0.604950i \(0.206807\pi\)
\(338\) 112.840 + 112.840i 0.333847 + 0.333847i
\(339\) 312.951i 0.923158i
\(340\) −224.654 + 87.0352i −0.660747 + 0.255986i
\(341\) −126.983 −0.372385
\(342\) 25.4659 25.4659i 0.0744617 0.0744617i
\(343\) −13.0958 13.0958i −0.0381802 0.0381802i
\(344\) 186.242i 0.541401i
\(345\) −139.916 61.7764i −0.405553 0.179062i
\(346\) 429.911 1.24252
\(347\) 88.5274 88.5274i 0.255122 0.255122i −0.567945 0.823067i \(-0.692261\pi\)
0.823067 + 0.567945i \(0.192261\pi\)
\(348\) −3.32549 3.32549i −0.00955602 0.00955602i
\(349\) 286.340i 0.820458i 0.911982 + 0.410229i \(0.134551\pi\)
−0.911982 + 0.410229i \(0.865449\pi\)
\(350\) −68.6383 + 62.5758i −0.196110 + 0.178788i
\(351\) 87.3575 0.248882
\(352\) −139.328 + 139.328i −0.395819 + 0.395819i
\(353\) 99.9512 + 99.9512i 0.283148 + 0.283148i 0.834363 0.551215i \(-0.185836\pi\)
−0.551215 + 0.834363i \(0.685836\pi\)
\(354\) 199.147i 0.562561i
\(355\) 127.590 288.976i 0.359409 0.814016i
\(356\) 65.9340 0.185208
\(357\) 76.9858 76.9858i 0.215647 0.215647i
\(358\) 241.932 + 241.932i 0.675788 + 0.675788i
\(359\) 166.393i 0.463491i 0.972776 + 0.231745i \(0.0744437\pi\)
−0.972776 + 0.231745i \(0.925556\pi\)
\(360\) −45.8699 118.399i −0.127416 0.328885i
\(361\) 287.915 0.797549
\(362\) 253.369 253.369i 0.699913 0.699913i
\(363\) −89.8973 89.8973i −0.247651 0.247651i
\(364\) 90.2116i 0.247834i
\(365\) −613.078 + 237.518i −1.67967 + 0.650734i
\(366\) −223.936 −0.611846
\(367\) −185.150 + 185.150i −0.504495 + 0.504495i −0.912832 0.408336i \(-0.866109\pi\)
0.408336 + 0.912832i \(0.366109\pi\)
\(368\) 47.1325 + 47.1325i 0.128078 + 0.128078i
\(369\) 80.2162i 0.217388i
\(370\) 285.223 + 125.933i 0.770873 + 0.340360i
\(371\) 248.710 0.670379
\(372\) 45.7181 45.7181i 0.122898 0.122898i
\(373\) 302.569 + 302.569i 0.811176 + 0.811176i 0.984810 0.173634i \(-0.0555511\pi\)
−0.173634 + 0.984810i \(0.555551\pi\)
\(374\) 230.174i 0.615437i
\(375\) 193.813 + 96.4966i 0.516834 + 0.257324i
\(376\) −265.203 −0.705327
\(377\) 15.9155 15.9155i 0.0422161 0.0422161i
\(378\) 13.6507 + 13.6507i 0.0361130 + 0.0361130i
\(379\) 651.952i 1.72019i −0.510134 0.860095i \(-0.670404\pi\)
0.510134 0.860095i \(-0.329596\pi\)
\(380\) −35.0155 + 79.3056i −0.0921459 + 0.208699i
\(381\) −37.6163 −0.0987305
\(382\) 7.72438 7.72438i 0.0202209 0.0202209i
\(383\) 262.099 + 262.099i 0.684333 + 0.684333i 0.960973 0.276641i \(-0.0892212\pi\)
−0.276641 + 0.960973i \(0.589221\pi\)
\(384\) 63.6065i 0.165642i
\(385\) 32.9711 + 85.1044i 0.0856392 + 0.221050i
\(386\) 282.221 0.731143
\(387\) 46.6726 46.6726i 0.120601 0.120601i
\(388\) −160.709 160.709i −0.414200 0.414200i
\(389\) 143.489i 0.368866i 0.982845 + 0.184433i \(0.0590449\pi\)
−0.982845 + 0.184433i \(0.940955\pi\)
\(390\) 190.644 73.8590i 0.488830 0.189382i
\(391\) 419.591 1.07312
\(392\) 41.8991 41.8991i 0.106886 0.106886i
\(393\) −216.386 216.386i −0.550600 0.550600i
\(394\) 49.7751i 0.126333i
\(395\) 38.7156 + 17.0939i 0.0980141 + 0.0432757i
\(396\) −41.9774 −0.106004
\(397\) −96.1908 + 96.1908i −0.242294 + 0.242294i −0.817799 0.575504i \(-0.804806\pi\)
0.575504 + 0.817799i \(0.304806\pi\)
\(398\) −83.6776 83.6776i −0.210245 0.210245i
\(399\) 39.1762i 0.0981861i
\(400\) −63.5687 69.7275i −0.158922 0.174319i
\(401\) −537.127 −1.33947 −0.669735 0.742600i \(-0.733592\pi\)
−0.669735 + 0.742600i \(0.733592\pi\)
\(402\) 192.794 192.794i 0.479586 0.479586i
\(403\) 218.802 + 218.802i 0.542933 + 0.542933i
\(404\) 118.925i 0.294369i
\(405\) 18.1758 41.1660i 0.0448786 0.101644i
\(406\) 4.97399 0.0122512
\(407\) 216.637 216.637i 0.532279 0.532279i
\(408\) 246.311 + 246.311i 0.603703 + 0.603703i
\(409\) 63.6521i 0.155629i 0.996968 + 0.0778144i \(0.0247941\pi\)
−0.996968 + 0.0778144i \(0.975206\pi\)
\(410\) −67.8211 175.059i −0.165417 0.426973i
\(411\) −44.1646 −0.107456
\(412\) 200.795 200.795i 0.487366 0.487366i
\(413\) −153.182 153.182i −0.370900 0.370900i
\(414\) 74.3997i 0.179709i
\(415\) −239.193 + 92.6677i −0.576368 + 0.223296i
\(416\) 480.145 1.15420
\(417\) −194.018 + 194.018i −0.465271 + 0.465271i
\(418\) −58.5649 58.5649i −0.140107 0.140107i
\(419\) 259.412i 0.619123i 0.950879 + 0.309561i \(0.100182\pi\)
−0.950879 + 0.309561i \(0.899818\pi\)
\(420\) −42.5109 18.7697i −0.101216 0.0446897i
\(421\) −691.062 −1.64148 −0.820739 0.571303i \(-0.806438\pi\)
−0.820739 + 0.571303i \(0.806438\pi\)
\(422\) 362.980 362.980i 0.860143 0.860143i
\(423\) −66.4604 66.4604i −0.157117 0.157117i
\(424\) 795.732i 1.87673i
\(425\) −593.325 27.4135i −1.39606 0.0645024i
\(426\) −153.662 −0.360708
\(427\) −172.249 + 172.249i −0.403394 + 0.403394i
\(428\) 2.12167 + 2.12167i 0.00495717 + 0.00495717i
\(429\) 200.899i 0.468297i
\(430\) 62.3946 141.316i 0.145104 0.328642i
\(431\) 22.7256 0.0527277 0.0263639 0.999652i \(-0.491607\pi\)
0.0263639 + 0.999652i \(0.491607\pi\)
\(432\) −13.8673 + 13.8673i −0.0321003 + 0.0321003i
\(433\) 120.702 + 120.702i 0.278757 + 0.278757i 0.832612 0.553856i \(-0.186844\pi\)
−0.553856 + 0.832612i \(0.686844\pi\)
\(434\) 68.3811i 0.157560i
\(435\) −4.18852 10.8113i −0.00962879 0.0248537i
\(436\) −319.126 −0.731941
\(437\) 106.760 106.760i 0.244302 0.244302i
\(438\) 226.150 + 226.150i 0.516325 + 0.516325i
\(439\) 330.633i 0.753151i 0.926386 + 0.376576i \(0.122899\pi\)
−0.926386 + 0.376576i \(0.877101\pi\)
\(440\) −272.286 + 105.489i −0.618831 + 0.239747i
\(441\) 21.0000 0.0476190
\(442\) −396.606 + 396.606i −0.897298 + 0.897298i
\(443\) −13.7007 13.7007i −0.0309271 0.0309271i 0.691474 0.722401i \(-0.256962\pi\)
−0.722401 + 0.691474i \(0.756962\pi\)
\(444\) 155.993i 0.351335i
\(445\) 148.700 + 65.6548i 0.334157 + 0.147539i
\(446\) −514.007 −1.15248
\(447\) −171.569 + 171.569i −0.383822 + 0.383822i
\(448\) 103.272 + 103.272i 0.230519 + 0.230519i
\(449\) 205.185i 0.456982i 0.973546 + 0.228491i \(0.0733792\pi\)
−0.973546 + 0.228491i \(0.926621\pi\)
\(450\) 4.86083 105.205i 0.0108018 0.233790i
\(451\) −184.476 −0.409038
\(452\) 259.117 259.117i 0.573267 0.573267i
\(453\) −263.552 263.552i −0.581792 0.581792i
\(454\) 214.288i 0.472000i
\(455\) 89.8296 203.453i 0.197428 0.447149i
\(456\) 125.342 0.274872
\(457\) 354.569 354.569i 0.775863 0.775863i −0.203262 0.979124i \(-0.565154\pi\)
0.979124 + 0.203262i \(0.0651542\pi\)
\(458\) −252.009 252.009i −0.550237 0.550237i
\(459\) 123.452i 0.268958i
\(460\) −64.6977 166.997i −0.140647 0.363037i
\(461\) 15.0039 0.0325465 0.0162733 0.999868i \(-0.494820\pi\)
0.0162733 + 0.999868i \(0.494820\pi\)
\(462\) 31.3931 31.3931i 0.0679504 0.0679504i
\(463\) −281.077 281.077i −0.607078 0.607078i 0.335103 0.942181i \(-0.391229\pi\)
−0.942181 + 0.335103i \(0.891229\pi\)
\(464\) 5.05291i 0.0108899i
\(465\) 148.632 57.5828i 0.319638 0.123834i
\(466\) −481.095 −1.03239
\(467\) −336.527 + 336.527i −0.720616 + 0.720616i −0.968731 0.248115i \(-0.920189\pi\)
0.248115 + 0.968731i \(0.420189\pi\)
\(468\) 72.3302 + 72.3302i 0.154552 + 0.154552i
\(469\) 296.590i 0.632388i
\(470\) −201.230 88.8481i −0.428148 0.189038i
\(471\) 121.701 0.258389
\(472\) 490.094 490.094i 1.03834 1.03834i
\(473\) −107.335 107.335i −0.226923 0.226923i
\(474\) 20.5868i 0.0434322i
\(475\) −157.940 + 143.990i −0.332504 + 0.303136i
\(476\) 127.485 0.267826
\(477\) −199.412 + 199.412i −0.418055 + 0.418055i
\(478\) −64.9814 64.9814i −0.135944 0.135944i
\(479\) 778.915i 1.62613i 0.582175 + 0.813063i \(0.302202\pi\)
−0.582175 + 0.813063i \(0.697798\pi\)
\(480\) 99.9003 226.262i 0.208126 0.471378i
\(481\) −746.564 −1.55211
\(482\) 72.3086 72.3086i 0.150018 0.150018i
\(483\) 57.2275 + 57.2275i 0.118483 + 0.118483i
\(484\) 148.866i 0.307575i
\(485\) −202.417 522.475i −0.417354 1.07727i
\(486\) −21.8899 −0.0450408
\(487\) 644.143 644.143i 1.32268 1.32268i 0.411074 0.911602i \(-0.365154\pi\)
0.911602 0.411074i \(-0.134846\pi\)
\(488\) −551.100 551.100i −1.12930 1.12930i
\(489\) 424.993i 0.869106i
\(490\) 45.8291 17.7551i 0.0935287 0.0362348i
\(491\) 582.633 1.18662 0.593312 0.804972i \(-0.297820\pi\)
0.593312 + 0.804972i \(0.297820\pi\)
\(492\) 66.4173 66.4173i 0.134995 0.134995i
\(493\) 22.4914 + 22.4914i 0.0456215 + 0.0456215i
\(494\) 201.823i 0.408549i
\(495\) −94.6710 41.7997i −0.191255 0.0844438i
\(496\) −69.4662 −0.140053
\(497\) −118.195 + 118.195i −0.237817 + 0.237817i
\(498\) 88.2327 + 88.2327i 0.177174 + 0.177174i
\(499\) 656.490i 1.31561i −0.753188 0.657806i \(-0.771485\pi\)
0.753188 0.657806i \(-0.228515\pi\)
\(500\) 80.5757 + 240.370i 0.161151 + 0.480740i
\(501\) −435.277 −0.868817
\(502\) 76.6058 76.6058i 0.152601 0.152601i
\(503\) 72.1236 + 72.1236i 0.143387 + 0.143387i 0.775156 0.631769i \(-0.217671\pi\)
−0.631769 + 0.775156i \(0.717671\pi\)
\(504\) 67.1881i 0.133310i
\(505\) −118.422 + 268.210i −0.234498 + 0.531109i
\(506\) 171.100 0.338142
\(507\) −139.183 + 139.183i −0.274522 + 0.274522i
\(508\) −31.1455 31.1455i −0.0613100 0.0613100i
\(509\) 143.879i 0.282670i −0.989962 0.141335i \(-0.954860\pi\)
0.989962 0.141335i \(-0.0451395\pi\)
\(510\) 104.376 + 269.414i 0.204659 + 0.528262i
\(511\) 347.905 0.680832
\(512\) −166.583 + 166.583i −0.325357 + 0.325357i
\(513\) 31.4109 + 31.4109i 0.0612298 + 0.0612298i
\(514\) 638.495i 1.24221i
\(515\) 652.794 252.905i 1.26756 0.491078i
\(516\) 77.2878 0.149783
\(517\) −152.841 + 152.841i −0.295631 + 0.295631i
\(518\) −116.660 116.660i −0.225213 0.225213i
\(519\) 530.274i 1.02172i
\(520\) 650.933 + 287.404i 1.25179 + 0.552699i
\(521\) 731.203 1.40346 0.701730 0.712443i \(-0.252411\pi\)
0.701730 + 0.712443i \(0.252411\pi\)
\(522\) −3.98806 + 3.98806i −0.00763996 + 0.00763996i
\(523\) −351.808 351.808i −0.672674 0.672674i 0.285658 0.958332i \(-0.407788\pi\)
−0.958332 + 0.285658i \(0.907788\pi\)
\(524\) 358.326i 0.683827i
\(525\) −77.1840 84.6618i −0.147017 0.161261i
\(526\) 104.358 0.198399
\(527\) −309.206 + 309.206i −0.586729 + 0.586729i
\(528\) 31.8912 + 31.8912i 0.0604000 + 0.0604000i
\(529\) 217.097i 0.410391i
\(530\) −266.586 + 603.783i −0.502992 + 1.13921i
\(531\) 245.637 0.462593
\(532\) 32.4371 32.4371i 0.0609720 0.0609720i
\(533\) 317.866 + 317.866i 0.596372 + 0.596372i
\(534\) 79.0706i 0.148072i
\(535\) 2.67228 + 6.89766i 0.00499492 + 0.0128928i
\(536\) 948.919 1.77037
\(537\) −298.411 + 298.411i −0.555699 + 0.555699i
\(538\) −25.4737 25.4737i −0.0473490 0.0473490i
\(539\) 48.2945i 0.0896002i
\(540\) 49.1338 19.0354i 0.0909885 0.0352507i
\(541\) 562.933 1.04054 0.520271 0.854001i \(-0.325831\pi\)
0.520271 + 0.854001i \(0.325831\pi\)
\(542\) −61.8472 + 61.8472i −0.114109 + 0.114109i
\(543\) 312.517 + 312.517i 0.575538 + 0.575538i
\(544\) 678.532i 1.24730i
\(545\) −719.721 317.775i −1.32059 0.583074i
\(546\) −108.185 −0.198141
\(547\) −300.932 + 300.932i −0.550149 + 0.550149i −0.926484 0.376334i \(-0.877184\pi\)
0.376334 + 0.926484i \(0.377184\pi\)
\(548\) −36.5673 36.5673i −0.0667287 0.0667287i
\(549\) 276.213i 0.503121i
\(550\) −241.945 11.1786i −0.439900 0.0203248i
\(551\) 11.4453 0.0207720
\(552\) −183.095 + 183.095i −0.331695 + 0.331695i
\(553\) −15.8352 15.8352i −0.0286351 0.0286351i
\(554\) 100.413i 0.181251i
\(555\) −155.332 + 351.808i −0.279878 + 0.633888i
\(556\) −321.286 −0.577852
\(557\) −134.801 + 134.801i −0.242013 + 0.242013i −0.817682 0.575670i \(-0.804741\pi\)
0.575670 + 0.817682i \(0.304741\pi\)
\(558\) −54.8269 54.8269i −0.0982560 0.0982560i
\(559\) 369.891i 0.661702i
\(560\) 18.0368 + 46.5563i 0.0322086 + 0.0831362i
\(561\) 283.907 0.506073
\(562\) −29.9586 + 29.9586i −0.0533070 + 0.0533070i
\(563\) −202.903 202.903i −0.360395 0.360395i 0.503563 0.863958i \(-0.332022\pi\)
−0.863958 + 0.503563i \(0.832022\pi\)
\(564\) 110.056i 0.195134i
\(565\) 842.401 326.362i 1.49097 0.577632i
\(566\) 35.0840 0.0619859
\(567\) −16.8375 + 16.8375i −0.0296957 + 0.0296957i
\(568\) −378.157 378.157i −0.665769 0.665769i
\(569\) 924.085i 1.62405i 0.583622 + 0.812025i \(0.301635\pi\)
−0.583622 + 0.812025i \(0.698365\pi\)
\(570\) 95.1063 + 41.9919i 0.166853 + 0.0736700i
\(571\) 303.388 0.531328 0.265664 0.964066i \(-0.414409\pi\)
0.265664 + 0.964066i \(0.414409\pi\)
\(572\) 166.340 166.340i 0.290805 0.290805i
\(573\) 9.52762 + 9.52762i 0.0166276 + 0.0166276i
\(574\) 99.3413i 0.173068i
\(575\) 20.3779 441.049i 0.0354398 0.767042i
\(576\) −165.604 −0.287507
\(577\) −143.967 + 143.967i −0.249510 + 0.249510i −0.820770 0.571259i \(-0.806455\pi\)
0.571259 + 0.820770i \(0.306455\pi\)
\(578\) −273.515 273.515i −0.473209 0.473209i
\(579\) 348.105i 0.601218i
\(580\) 5.48356 12.4196i 0.00945441 0.0214131i
\(581\) 135.735 0.233624
\(582\) −192.729 + 192.729i −0.331149 + 0.331149i
\(583\) 458.596 + 458.596i 0.786613 + 0.786613i
\(584\) 1113.10i 1.90599i
\(585\) 91.1012 + 235.149i 0.155729 + 0.401964i
\(586\) 115.940 0.197850
\(587\) 19.0650 19.0650i 0.0324788 0.0324788i −0.690681 0.723160i \(-0.742689\pi\)
0.723160 + 0.690681i \(0.242689\pi\)
\(588\) 17.3876 + 17.3876i 0.0295707 + 0.0295707i
\(589\) 157.348i 0.267144i
\(590\) 536.063 207.681i 0.908581 0.352002i
\(591\) 61.3950 0.103883
\(592\) 118.511 118.511i 0.200188 0.200188i
\(593\) 355.233 + 355.233i 0.599044 + 0.599044i 0.940058 0.341014i \(-0.110770\pi\)
−0.341014 + 0.940058i \(0.610770\pi\)
\(594\) 50.3409i 0.0847490i
\(595\) 287.515 + 126.945i 0.483219 + 0.213354i
\(596\) −284.110 −0.476695
\(597\) 103.212 103.212i 0.172884 0.172884i
\(598\) −294.817 294.817i −0.493006 0.493006i
\(599\) 869.938i 1.45232i 0.687527 + 0.726159i \(0.258696\pi\)
−0.687527 + 0.726159i \(0.741304\pi\)
\(600\) 270.870 246.945i 0.451450 0.411575i
\(601\) 136.014 0.226312 0.113156 0.993577i \(-0.463904\pi\)
0.113156 + 0.993577i \(0.463904\pi\)
\(602\) −57.8002 + 57.8002i −0.0960136 + 0.0960136i
\(603\) 237.801 + 237.801i 0.394363 + 0.394363i
\(604\) 436.430i 0.722567i
\(605\) 148.236 335.735i 0.245018 0.554934i
\(606\) 142.620 0.235346
\(607\) −530.632 + 530.632i −0.874189 + 0.874189i −0.992926 0.118737i \(-0.962115\pi\)
0.118737 + 0.992926i \(0.462115\pi\)
\(608\) 172.644 + 172.644i 0.283954 + 0.283954i
\(609\) 6.13515i 0.0100741i
\(610\) −233.532 602.790i −0.382840 0.988181i
\(611\) 526.714 0.862052
\(612\) −102.216 + 102.216i −0.167019 + 0.167019i
\(613\) −600.328 600.328i −0.979328 0.979328i 0.0204626 0.999791i \(-0.493486\pi\)
−0.999791 + 0.0204626i \(0.993486\pi\)
\(614\) 294.931i 0.480343i
\(615\) 215.926 83.6539i 0.351099 0.136023i
\(616\) 154.515 0.250836
\(617\) 549.965 549.965i 0.891354 0.891354i −0.103297 0.994651i \(-0.532939\pi\)
0.994651 + 0.103297i \(0.0329391\pi\)
\(618\) −240.801 240.801i −0.389646 0.389646i
\(619\) 63.1436i 0.102009i 0.998698 + 0.0510046i \(0.0162423\pi\)
−0.998698 + 0.0510046i \(0.983758\pi\)
\(620\) 170.741 + 75.3866i 0.275389 + 0.121591i
\(621\) −91.7681 −0.147775
\(622\) −199.351 + 199.351i −0.320500 + 0.320500i
\(623\) −60.8203 60.8203i −0.0976249 0.0976249i
\(624\) 109.902i 0.176125i
\(625\) −57.6310 + 622.337i −0.0922096 + 0.995740i
\(626\) 572.174 0.914015
\(627\) 72.2368 72.2368i 0.115210 0.115210i
\(628\) 100.766 + 100.766i 0.160456 + 0.160456i
\(629\) 1055.03i 1.67731i
\(630\) −22.5093 + 50.9807i −0.0357290 + 0.0809218i
\(631\) −463.289 −0.734213 −0.367107 0.930179i \(-0.619652\pi\)
−0.367107 + 0.930179i \(0.619652\pi\)
\(632\) 50.6636 50.6636i 0.0801640 0.0801640i
\(633\) 447.717 + 447.717i 0.707295 + 0.707295i
\(634\) 170.312i 0.268631i
\(635\) −39.2283 101.256i −0.0617769 0.159458i
\(636\) −330.218 −0.519210
\(637\) −83.2150 + 83.2150i −0.130636 + 0.130636i
\(638\) 9.17150 + 9.17150i 0.0143754 + 0.0143754i
\(639\) 189.534i 0.296610i
\(640\) 171.216 66.3323i 0.267525 0.103644i
\(641\) −741.985 −1.15754 −0.578772 0.815490i \(-0.696468\pi\)
−0.578772 + 0.815490i \(0.696468\pi\)
\(642\) 2.54439 2.54439i 0.00396322 0.00396322i
\(643\) −230.657 230.657i −0.358720 0.358720i 0.504621 0.863341i \(-0.331632\pi\)
−0.863341 + 0.504621i \(0.831632\pi\)
\(644\) 94.7663i 0.147153i
\(645\) 174.306 + 76.9605i 0.270242 + 0.119319i
\(646\) −285.213 −0.441506
\(647\) −763.503 + 763.503i −1.18007 + 1.18007i −0.200341 + 0.979726i \(0.564205\pi\)
−0.979726 + 0.200341i \(0.935795\pi\)
\(648\) −53.8703 53.8703i −0.0831332 0.0831332i
\(649\) 564.901i 0.870418i
\(650\) 397.627 + 436.150i 0.611734 + 0.671000i
\(651\) −84.3446 −0.129562
\(652\) 351.885 351.885i 0.539701 0.539701i
\(653\) 381.398 + 381.398i 0.584070 + 0.584070i 0.936019 0.351949i \(-0.114481\pi\)
−0.351949 + 0.936019i \(0.614481\pi\)
\(654\) 382.709i 0.585181i
\(655\) 356.808 808.126i 0.544745 1.23378i
\(656\) −100.918 −0.153838
\(657\) −278.945 + 278.945i −0.424574 + 0.424574i
\(658\) 82.3057 + 82.3057i 0.125085 + 0.125085i
\(659\) 608.628i 0.923563i 0.886994 + 0.461781i \(0.152790\pi\)
−0.886994 + 0.461781i \(0.847210\pi\)
\(660\) −43.7763 112.995i −0.0663278 0.171204i
\(661\) 108.770 0.164554 0.0822770 0.996609i \(-0.473781\pi\)
0.0822770 + 0.996609i \(0.473781\pi\)
\(662\) 117.495 117.495i 0.177486 0.177486i
\(663\) −489.193 489.193i −0.737847 0.737847i
\(664\) 434.276i 0.654031i
\(665\) 105.455 40.8551i 0.158578 0.0614363i
\(666\) 187.072 0.280889
\(667\) −16.7190 + 16.7190i −0.0250660 + 0.0250660i
\(668\) −360.400 360.400i −0.539521 0.539521i
\(669\) 634.001i 0.947685i
\(670\) 720.017 + 317.906i 1.07465 + 0.474487i
\(671\) −635.218 −0.946674
\(672\) −92.5441 + 92.5441i −0.137714 + 0.137714i
\(673\) −717.128 717.128i −1.06557 1.06557i −0.997694 0.0678751i \(-0.978378\pi\)
−0.0678751 0.997694i \(-0.521622\pi\)
\(674\) 128.035i 0.189963i
\(675\) 129.765 + 5.99558i 0.192245 + 0.00888234i
\(676\) −230.481 −0.340948
\(677\) −120.083 + 120.083i −0.177376 + 0.177376i −0.790211 0.612835i \(-0.790029\pi\)
0.612835 + 0.790211i \(0.290029\pi\)
\(678\) −310.742 310.742i −0.458322 0.458322i
\(679\) 296.490i 0.436658i
\(680\) −406.153 + 919.886i −0.597284 + 1.35277i
\(681\) 264.313 0.388125
\(682\) −126.087 + 126.087i −0.184879 + 0.184879i
\(683\) −382.924 382.924i −0.560651 0.560651i 0.368842 0.929492i \(-0.379755\pi\)
−0.929492 + 0.368842i \(0.879755\pi\)
\(684\) 52.0151i 0.0760454i
\(685\) −46.0572 118.882i −0.0672369 0.173551i
\(686\) −26.0068 −0.0379108
\(687\) 310.840 310.840i 0.452459 0.452459i
\(688\) −58.7173 58.7173i −0.0853450 0.0853450i
\(689\) 1580.39i 2.29374i
\(690\) −200.269 + 77.5880i −0.290245 + 0.112446i
\(691\) 1016.89 1.47162 0.735809 0.677190i \(-0.236802\pi\)
0.735809 + 0.677190i \(0.236802\pi\)
\(692\) −439.055 + 439.055i −0.634473 + 0.634473i
\(693\) 38.7217 + 38.7217i 0.0558755 + 0.0558755i
\(694\) 175.806i 0.253322i
\(695\) −724.591 319.925i −1.04258 0.460324i
\(696\) −19.6290 −0.0282026
\(697\) −449.202 + 449.202i −0.644480 + 0.644480i
\(698\) 284.319 + 284.319i 0.407335 + 0.407335i
\(699\) 593.406i 0.848936i
\(700\) 6.19146 134.005i 0.00884494 0.191436i
\(701\) −603.636 −0.861106 −0.430553 0.902565i \(-0.641682\pi\)
−0.430553 + 0.902565i \(0.641682\pi\)
\(702\) 86.7411 86.7411i 0.123563 0.123563i
\(703\) −268.440 268.440i −0.381849 0.381849i
\(704\) 380.846i 0.540975i
\(705\) 109.590 248.206i 0.155446 0.352066i
\(706\) 198.492 0.281150
\(707\) 109.702 109.702i 0.155165 0.155165i
\(708\) 203.382 + 203.382i 0.287263 + 0.287263i
\(709\) 137.621i 0.194106i 0.995279 + 0.0970528i \(0.0309416\pi\)
−0.995279 + 0.0970528i \(0.969058\pi\)
\(710\) −160.247 413.626i −0.225700 0.582572i
\(711\) 25.3928 0.0357142
\(712\) 194.591 194.591i 0.273301 0.273301i
\(713\) −229.849 229.849i −0.322369 0.322369i
\(714\) 152.885i 0.214125i
\(715\) 540.781 209.509i 0.756337 0.293019i
\(716\) −494.155 −0.690161
\(717\) 80.1512 80.1512i 0.111787 0.111787i
\(718\) 165.219 + 165.219i 0.230110 + 0.230110i
\(719\) 171.289i 0.238233i 0.992880 + 0.119116i \(0.0380062\pi\)
−0.992880 + 0.119116i \(0.961994\pi\)
\(720\) −51.7897 22.8665i −0.0719301 0.0317590i
\(721\) −370.443 −0.513791
\(722\) 285.884 285.884i 0.395961 0.395961i
\(723\) 89.1889 + 89.1889i 0.123359 + 0.123359i
\(724\) 517.515i 0.714799i
\(725\) 24.7340 22.5493i 0.0341158 0.0311025i
\(726\) −178.526 −0.245903
\(727\) 277.598 277.598i 0.381840 0.381840i −0.489925 0.871765i \(-0.662976\pi\)
0.871765 + 0.489925i \(0.162976\pi\)
\(728\) −266.241 266.241i −0.365715 0.365715i
\(729\) 27.0000i 0.0370370i
\(730\) −372.910 + 844.594i −0.510835 + 1.15698i
\(731\) −522.723 −0.715079
\(732\) 228.699 228.699i 0.312430 0.312430i
\(733\) 41.4717 + 41.4717i 0.0565780 + 0.0565780i 0.734830 0.678252i \(-0.237262\pi\)
−0.678252 + 0.734830i \(0.737262\pi\)
\(734\) 367.687i 0.500936i
\(735\) 21.8999 + 56.5278i 0.0297958 + 0.0769086i
\(736\) −504.387 −0.685309
\(737\) 546.880 546.880i 0.742035 0.742035i
\(738\) −79.6502 79.6502i −0.107927 0.107927i
\(739\) 991.780i 1.34206i −0.741432 0.671028i \(-0.765853\pi\)
0.741432 0.671028i \(-0.234147\pi\)
\(740\) −419.901 + 162.678i −0.567434 + 0.219835i
\(741\) −248.939 −0.335949
\(742\) 246.956 246.956i 0.332824 0.332824i
\(743\) 569.850 + 569.850i 0.766958 + 0.766958i 0.977570 0.210611i \(-0.0675455\pi\)
−0.210611 + 0.977570i \(0.567545\pi\)
\(744\) 269.855i 0.362708i
\(745\) −640.750 282.907i −0.860067 0.379741i
\(746\) 600.867 0.805452
\(747\) −108.830 + 108.830i −0.145690 + 0.145690i
\(748\) 235.069 + 235.069i 0.314263 + 0.314263i
\(749\) 3.91424i 0.00522595i
\(750\) 288.261 96.6295i 0.384348 0.128839i
\(751\) −774.252 −1.03096 −0.515480 0.856901i \(-0.672387\pi\)
−0.515480 + 0.856901i \(0.672387\pi\)
\(752\) −83.6117 + 83.6117i −0.111186 + 0.111186i
\(753\) 94.4894 + 94.4894i 0.125484 + 0.125484i
\(754\) 31.6063i 0.0419182i
\(755\) 434.582 984.274i 0.575606 1.30367i
\(756\) −27.8821 −0.0368811
\(757\) −404.173 + 404.173i −0.533914 + 0.533914i −0.921735 0.387821i \(-0.873228\pi\)
0.387821 + 0.921735i \(0.373228\pi\)
\(758\) −647.352 647.352i −0.854026 0.854026i
\(759\) 211.043i 0.278054i
\(760\) 130.713 + 337.395i 0.171991 + 0.443941i
\(761\) 287.708 0.378065 0.189033 0.981971i \(-0.439465\pi\)
0.189033 + 0.981971i \(0.439465\pi\)
\(762\) −37.3509 + 37.3509i −0.0490169 + 0.0490169i
\(763\) 294.376 + 294.376i 0.385814 + 0.385814i
\(764\) 15.7773i 0.0206510i
\(765\) −332.308 + 128.742i −0.434389 + 0.168291i
\(766\) 520.500 0.679504
\(767\) −973.366 + 973.366i −1.26906 + 1.26906i
\(768\) −333.588 333.588i −0.434360 0.434360i
\(769\) 1001.09i 1.30181i 0.759160 + 0.650905i \(0.225610\pi\)
−0.759160 + 0.650905i \(0.774390\pi\)
\(770\) 117.242 + 51.7655i 0.152263 + 0.0672279i
\(771\) 787.550 1.02147
\(772\) −288.224 + 288.224i −0.373347 + 0.373347i