Properties

Label 105.3.l.a.22.8
Level 105
Weight 3
Character 105.22
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 22.8
Character \(\chi\) \(=\) 105.22
Dual form 105.3.l.a.43.8

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.992944 + 0.992944i 0.496472 + 0.496472i 0.910338 0.413866i \(-0.135822\pi\)
−0.413866 + 0.910338i \(0.635822\pi\)
\(3\) 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 −0.996618 0.0821681i \(-0.973816\pi\)
0.0821681 + 0.996618i \(0.473816\pi\)
\(14\) 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 0.999931 0.0117149i \(-0.00372905\pi\)
−0.0117149 + 0.999931i \(0.503729\pi\)
\(18\) 2.97883 2.97883i 0.165491 0.165491i
\(19\) 8.54896i 0.449945i 0.974365 + 0.224973i \(0.0722292\pi\)
−0.974365 + 0.224973i \(0.927771\pi\)
\(20\) −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 −0.381436 0.924395i \(-0.624570\pi\)
0.924395 + 0.381436i \(0.124570\pi\)
\(24\) 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 \(-0.992652\pi\)
0.999734 0.0230828i \(-0.00734813\pi\)
\(30\) −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 0.989966 0.141309i \(-0.0451311\pi\)
−0.141309 + 0.989966i \(0.545131\pi\)
\(38\) −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 −0.864476 0.502673i \(-0.832350\pi\)
0.502673 + 0.864476i \(0.332350\pi\)
\(44\) 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 0.431001 0.902351i \(-0.358160\pi\)
−0.902351 + 0.431001i \(0.858160\pi\)
\(48\) 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 0.300328 0.953836i \(-0.402904\pi\)
0.953836 0.300328i \(-0.0970960\pi\)
\(54\) 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 \(0.244105\pi\)
−0.720081 + 0.693890i \(0.755895\pi\)
\(60\) −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 0.978940 + 0.204149i \(0.0654428\pi\)
0.204149 + 0.978940i \(0.434557\pi\)
\(68\) 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 0.329600 0.944121i \(-0.393086\pi\)
0.944121 0.329600i \(-0.106914\pi\)
\(74\) 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 \(0.0170605\pi\)
−0.998564 + 0.0535713i \(0.982940\pi\)
\(80\) −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 −0.453955 0.891025i \(-0.649987\pi\)
0.891025 + 0.453955i \(0.149987\pi\)
\(84\) 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 \(0.0584641\pi\)
−0.983180 + 0.182639i \(0.941536\pi\)
\(90\) −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 0.168748 0.985659i \(-0.446028\pi\)
−0.985659 + 0.168748i \(0.946028\pi\)
\(98\) −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 −0.999275 0.0380601i \(-0.987882\pi\)
0.0380601 + 0.999275i \(0.487882\pi\)
\(104\) 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 0.711978 0.702201i \(-0.247799\pi\)
−0.702201 + 0.711978i \(0.747799\pi\)
\(108\) −7.45181 + 7.45181i −0.0689982 + 0.0689982i
\(109\) 157.350i 1.44358i −0.692111 0.721791i \(-0.743319\pi\)
0.692111 0.721791i \(-0.256681\pi\)
\(110\) 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 −0.140562 + 0.990072i \(0.544891\pi\)
−0.990072 + 0.140562i \(0.955109\pi\)
\(114\) 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 0.644057 0.764977i \(-0.277250\pi\)
−0.764977 + 0.644057i \(0.777250\pi\)
\(128\) −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 0.638235 0.769842i \(-0.279665\pi\)
−0.769842 + 0.638235i \(0.779665\pi\)
\(138\) 30.3735 30.3735i 0.220098 0.220098i
\(139\) 158.415i 1.13968i −0.821756 0.569839i \(-0.807006\pi\)
0.821756 0.569839i \(-0.192994\pi\)
\(140\) −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 \(-0.844223\pi\)
0.882621 0.470085i \(-0.155777\pi\)
\(150\) −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 0.847406 0.530945i \(-0.178163\pi\)
−0.530945 + 0.847406i \(0.678163\pi\)
\(158\) −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 −0.0666571 + 0.997776i \(0.521233\pi\)
−0.997776 + 0.0666571i \(0.978767\pi\)
\(164\) 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 −0.997801 0.0662778i \(-0.978888\pi\)
−0.0662778 0.997801i \(-0.521112\pi\)
\(168\) 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 0.296233 0.955116i \(-0.404270\pi\)
0.955116 0.296233i \(-0.0957304\pi\)
\(174\) 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 \(-0.761724\pi\)
0.732665 0.680590i \(-0.238276\pi\)
\(180\) 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 −0.235528 0.971867i \(-0.575682\pi\)
0.971867 + 0.235528i \(0.0756821\pi\)
\(194\) 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 0.767855 0.640624i \(-0.221324\pi\)
−0.640624 + 0.767855i \(0.721324\pi\)
\(198\) 20.5516 20.5516i 0.103796 0.103796i
\(199\) 84.2722i 0.423479i 0.977326 + 0.211739i \(0.0679128\pi\)
−0.977326 + 0.211739i \(0.932087\pi\)
\(200\) 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 −0.176343 + 0.984329i \(0.556427\pi\)
−0.984329 + 0.176343i \(0.943573\pi\)
\(224\) 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 0.903642 0.428288i \(-0.140883\pi\)
−0.428288 + 0.903642i \(0.640883\pi\)
\(228\) 21.2351 21.2351i 0.0931362 0.0931362i
\(229\) 253.800i 1.10829i 0.832419 + 0.554147i \(0.186956\pi\)
−0.832419 + 0.554147i \(0.813044\pi\)
\(230\) −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 −0.0405526 + 0.999177i \(0.512912\pi\)
−0.999177 + 0.0405526i \(0.987088\pi\)
\(234\) 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 \(0.0437172\pi\)
−0.990583 + 0.136910i \(0.956283\pi\)
\(240\) −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 0.955256 + 0.295779i \(0.0955793\pi\)
0.295779 + 0.955256i \(0.404421\pi\)
\(258\) −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 −0.600109 0.799918i \(-0.704876\pi\)
0.799918 + 0.600109i \(0.204876\pi\)
\(264\) 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 \(0.0151845\pi\)
−0.998862 + 0.0476855i \(0.984815\pi\)
\(270\) −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 0.792461 0.609922i \(-0.208799\pi\)
−0.609922 + 0.792461i \(0.708799\pi\)
\(278\) 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 −0.675204 0.737631i \(-0.735945\pi\)
0.737631 + 0.675204i \(0.235945\pi\)
\(284\) 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 −0.600425 0.799681i \(-0.705002\pi\)
0.799681 + 0.600425i \(0.205002\pi\)
\(294\) 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 0.906329 0.422573i \(-0.138873\pi\)
−0.422573 + 0.906329i \(0.638873\pi\)
\(308\) 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 −0.0765549 0.997065i \(-0.524392\pi\)
0.997065 + 0.0765549i \(0.0243920\pi\)
\(314\) 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 0.829318 0.558777i \(-0.188729\pi\)
−0.558777 + 0.829318i \(0.688729\pi\)
\(318\) 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 0.796263 0.604950i \(-0.206807\pi\)
−0.604950 + 0.796263i \(0.706807\pi\)
\(338\) 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 0.823067 0.567945i \(-0.192261\pi\)
−0.567945 + 0.823067i \(0.692261\pi\)
\(348\) −3.32549 + 3.32549i −0.00955602 + 0.00955602i
\(349\) 286.340i 0.820458i −0.911982 0.410229i \(-0.865449\pi\)
0.911982 0.410229i \(-0.134551\pi\)
\(350\) −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 −0.551215 0.834363i \(-0.685836\pi\)
0.834363 + 0.551215i \(0.185836\pi\)
\(354\) 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 \(-0.925556\pi\)
0.972776 0.231745i \(-0.0744437\pi\)
\(360\) −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 0.408336 0.912832i \(-0.366109\pi\)
−0.912832 + 0.408336i \(0.866109\pi\)
\(368\) 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 −0.173634 0.984810i \(-0.555551\pi\)
0.984810 + 0.173634i \(0.0555511\pi\)
\(374\) 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 \(0.329596\pi\)
−0.510134 + 0.860095i \(0.670404\pi\)
\(380\) −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 −0.276641 0.960973i \(-0.589221\pi\)
0.960973 + 0.276641i \(0.0892212\pi\)
\(384\) 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 \(-0.940955\pi\)
0.982845 0.184433i \(-0.0590449\pi\)
\(390\) 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 0.575504 0.817799i \(-0.304806\pi\)
−0.817799 + 0.575504i \(0.804806\pi\)
\(398\) −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 \(-0.975206\pi\)
0.996968 0.0778144i \(-0.0247941\pi\)
\(410\) −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 \(-0.899818\pi\)
0.950879 0.309561i \(-0.100182\pi\)
\(420\) −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 −0.553856 0.832612i \(-0.686844\pi\)
0.832612 + 0.553856i \(0.186844\pi\)
\(434\) 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 \(-0.877101\pi\)
0.926386 0.376576i \(-0.122899\pi\)
\(440\) −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 −0.722401 0.691474i \(-0.756962\pi\)
0.691474 + 0.722401i \(0.256962\pi\)
\(444\) 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 \(-0.926621\pi\)
0.973546 0.228491i \(-0.0733792\pi\)
\(450\) 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 0.979124 0.203262i \(-0.0651542\pi\)
−0.203262 + 0.979124i \(0.565154\pi\)
\(458\) −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 −0.942181 0.335103i \(-0.891229\pi\)
0.335103 + 0.942181i \(0.391229\pi\)
\(464\) 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 0.248115 0.968731i \(-0.420189\pi\)
−0.968731 + 0.248115i \(0.920189\pi\)
\(468\) 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 \(-0.697798\pi\)
0.582175 0.813063i \(-0.302202\pi\)
\(480\) 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 0.911602 + 0.411074i \(0.134846\pi\)
0.411074 + 0.911602i \(0.365154\pi\)
\(488\) −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 \(0.228515\pi\)
−0.753188 + 0.657806i \(0.771485\pi\)
\(500\) 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 −0.631769 0.775156i \(-0.717671\pi\)
0.775156 + 0.631769i \(0.217671\pi\)
\(504\) 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 \(0.0451395\pi\)
−0.989962 + 0.141335i \(0.954860\pi\)
\(510\) 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 −0.958332 0.285658i \(-0.907788\pi\)
0.285658 + 0.958332i \(0.407788\pi\)
\(524\) 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 0.376334 0.926484i \(-0.377184\pi\)
−0.926484 + 0.376334i \(0.877184\pi\)
\(548\) −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 0.575670 0.817682i \(-0.304741\pi\)
−0.817682 + 0.575670i \(0.804741\pi\)
\(558\) −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 −0.863958 0.503563i \(-0.832022\pi\)
0.503563 + 0.863958i \(0.332022\pi\)
\(564\) 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 \(-0.698365\pi\)
0.583622 0.812025i \(-0.301635\pi\)
\(570\) 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 0.571259 0.820770i \(-0.306455\pi\)
−0.820770 + 0.571259i \(0.806455\pi\)
\(578\) −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 0.723160 0.690681i \(-0.242689\pi\)
−0.690681 + 0.723160i \(0.742689\pi\)
\(588\) 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 −0.341014 0.940058i \(-0.610770\pi\)
0.940058 + 0.341014i \(0.110770\pi\)
\(594\) 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 \(-0.741304\pi\)
0.687527 0.726159i \(-0.258696\pi\)
\(600\) 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 0.118737 0.992926i \(-0.462115\pi\)
−0.992926 + 0.118737i \(0.962115\pi\)
\(608\) 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 −0.999791 0.0204626i \(-0.993486\pi\)
0.0204626 + 0.999791i \(0.493486\pi\)
\(614\) 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 0.994651 0.103297i \(-0.0329391\pi\)
−0.103297 + 0.994651i \(0.532939\pi\)
\(618\) −240.801 + 240.801i −0.389646 + 0.389646i
\(619\) 63.1436i 0.102009i −0.998698 0.0510046i \(-0.983758\pi\)
0.998698 0.0510046i \(-0.0162423\pi\)
\(620\) 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 −0.863341 0.504621i \(-0.831632\pi\)
0.504621 + 0.863341i \(0.331632\pi\)
\(644\) 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 −0.979726 0.200341i \(-0.935795\pi\)
−0.200341 0.979726i \(-0.564205\pi\)
\(648\) −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 −0.351949 0.936019i \(-0.614481\pi\)
0.936019 + 0.351949i \(0.114481\pi\)
\(654\) 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 \(-0.847210\pi\)
0.886994 0.461781i \(-0.152790\pi\)
\(660\) −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 −0.0678751 + 0.997694i \(0.521622\pi\)
−0.997694 + 0.0678751i \(0.978378\pi\)
\(674\) 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 0.612835 0.790211i \(-0.290029\pi\)
−0.790211 + 0.612835i \(0.790029\pi\)
\(678\) −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 −0.929492 0.368842i \(-0.879755\pi\)
0.368842 + 0.929492i \(0.379755\pi\)
\(684\) 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 \(-0.969058\pi\)
0.995279 0.0970528i \(-0.0309416\pi\)
\(710\) −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 \(-0.961994\pi\)
0.992880 0.119116i \(-0.0380062\pi\)
\(720\) −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 0.871765 0.489925i \(-0.162976\pi\)
−0.489925 + 0.871765i \(0.662976\pi\)
\(728\) −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 −0.678252 0.734830i \(-0.737262\pi\)
0.734830 + 0.678252i \(0.237262\pi\)
\(734\) 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 \(0.234147\pi\)
−0.741432 + 0.671028i \(0.765853\pi\)
\(740\) −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 −0.210611 0.977570i \(-0.567545\pi\)
0.977570 + 0.210611i \(0.0675455\pi\)
\(744\) 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 0.387821 0.921735i \(-0.373228\pi\)
−0.921735 + 0.387821i \(0.873228\pi\)
\(758\) −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 \(-0.774390\pi\)
0.759160 0.650905i \(-0.225610\pi\)
\(770\) 117.242 51.7655i 0.152263 0.0672279i
\(771\) 787.550 1.02147
\(772\) −288.224 288.224i −0.373347 0.373347i