Properties

Label 126.3.n.b.73.2
Level $126$
Weight $3$
Character 126.73
Analytic conductor $3.433$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.43325133094\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 73.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 126.73
Dual form 126.3.n.b.19.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-4.24264 + 2.44949i) q^{5} +(3.50000 + 6.06218i) q^{7} -2.82843 q^{8} +O(q^{10})\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-4.24264 + 2.44949i) q^{5} +(3.50000 + 6.06218i) q^{7} -2.82843 q^{8} +(-6.00000 - 3.46410i) q^{10} +(-8.48528 + 14.6969i) q^{11} -1.73205i q^{13} +(-4.94975 + 8.57321i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(4.24264 + 2.44949i) q^{17} +(25.5000 - 14.7224i) q^{19} -9.79796i q^{20} -24.0000 q^{22} +(-4.24264 - 7.34847i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(2.12132 - 1.22474i) q^{26} -14.0000 q^{28} +33.9411 q^{29} +(-10.5000 - 6.06218i) q^{31} +(2.82843 - 4.89898i) q^{32} +6.92820i q^{34} +(-29.6985 - 17.1464i) q^{35} +(23.5000 + 40.7032i) q^{37} +(36.0624 + 20.8207i) q^{38} +(12.0000 - 6.92820i) q^{40} -68.5857i q^{41} +31.0000 q^{43} +(-16.9706 - 29.3939i) q^{44} +(6.00000 - 10.3923i) q^{46} +(72.1249 - 41.6413i) q^{47} +(-24.5000 + 42.4352i) q^{49} -1.41421 q^{50} +(3.00000 + 1.73205i) q^{52} +(-38.1838 + 66.1362i) q^{53} -83.1384i q^{55} +(-9.89949 - 17.1464i) q^{56} +(24.0000 + 41.5692i) q^{58} +(72.1249 + 41.6413i) q^{59} +(-72.0000 + 41.5692i) q^{61} -17.1464i q^{62} +8.00000 q^{64} +(4.24264 + 7.34847i) q^{65} +(15.5000 - 26.8468i) q^{67} +(-8.48528 + 4.89898i) q^{68} -48.4974i q^{70} -59.3970 q^{71} +(-70.5000 - 40.7032i) q^{73} +(-33.2340 + 57.5630i) q^{74} +58.8897i q^{76} -118.794 q^{77} +(-20.5000 - 35.5070i) q^{79} +(16.9706 + 9.79796i) q^{80} +(84.0000 - 48.4974i) q^{82} +4.89898i q^{83} -24.0000 q^{85} +(21.9203 + 37.9671i) q^{86} +(24.0000 - 41.5692i) q^{88} +(-50.9117 + 29.3939i) q^{89} +(10.5000 - 6.06218i) q^{91} +16.9706 q^{92} +(102.000 + 58.8897i) q^{94} +(-72.1249 + 124.924i) q^{95} +41.5692i q^{97} -69.2965 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} + 14 q^{7} + O(q^{10}) \) \( 4 q - 4 q^{4} + 14 q^{7} - 24 q^{10} - 8 q^{16} + 102 q^{19} - 96 q^{22} - 2 q^{25} - 56 q^{28} - 42 q^{31} + 94 q^{37} + 48 q^{40} + 124 q^{43} + 24 q^{46} - 98 q^{49} + 12 q^{52} + 96 q^{58} - 288 q^{61} + 32 q^{64} + 62 q^{67} - 282 q^{73} - 82 q^{79} + 336 q^{82} - 96 q^{85} + 96 q^{88} + 42 q^{91} + 408 q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 1.22474i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) −4.24264 + 2.44949i −0.848528 + 0.489898i −0.860154 0.510034i \(-0.829633\pi\)
0.0116258 + 0.999932i \(0.496299\pi\)
\(6\) 0 0
\(7\) 3.50000 + 6.06218i 0.500000 + 0.866025i
\(8\) −2.82843 −0.353553
\(9\) 0 0
\(10\) −6.00000 3.46410i −0.600000 0.346410i
\(11\) −8.48528 + 14.6969i −0.771389 + 1.33609i 0.165412 + 0.986224i \(0.447104\pi\)
−0.936802 + 0.349861i \(0.886229\pi\)
\(12\) 0 0
\(13\) 1.73205i 0.133235i −0.997779 0.0666173i \(-0.978779\pi\)
0.997779 0.0666173i \(-0.0212207\pi\)
\(14\) −4.94975 + 8.57321i −0.353553 + 0.612372i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 4.24264 + 2.44949i 0.249567 + 0.144088i 0.619566 0.784945i \(-0.287309\pi\)
−0.369999 + 0.929032i \(0.620642\pi\)
\(18\) 0 0
\(19\) 25.5000 14.7224i 1.34211 0.774865i 0.354989 0.934870i \(-0.384485\pi\)
0.987116 + 0.160006i \(0.0511512\pi\)
\(20\) 9.79796i 0.489898i
\(21\) 0 0
\(22\) −24.0000 −1.09091
\(23\) −4.24264 7.34847i −0.184463 0.319499i 0.758933 0.651169i \(-0.225721\pi\)
−0.943395 + 0.331670i \(0.892388\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(26\) 2.12132 1.22474i 0.0815892 0.0471056i
\(27\) 0 0
\(28\) −14.0000 −0.500000
\(29\) 33.9411 1.17038 0.585192 0.810895i \(-0.301019\pi\)
0.585192 + 0.810895i \(0.301019\pi\)
\(30\) 0 0
\(31\) −10.5000 6.06218i −0.338710 0.195554i 0.320992 0.947082i \(-0.395984\pi\)
−0.659701 + 0.751528i \(0.729317\pi\)
\(32\) 2.82843 4.89898i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 6.92820i 0.203771i
\(35\) −29.6985 17.1464i −0.848528 0.489898i
\(36\) 0 0
\(37\) 23.5000 + 40.7032i 0.635135 + 1.10009i 0.986486 + 0.163843i \(0.0523889\pi\)
−0.351351 + 0.936244i \(0.614278\pi\)
\(38\) 36.0624 + 20.8207i 0.949012 + 0.547912i
\(39\) 0 0
\(40\) 12.0000 6.92820i 0.300000 0.173205i
\(41\) 68.5857i 1.67282i −0.548103 0.836411i \(-0.684650\pi\)
0.548103 0.836411i \(-0.315350\pi\)
\(42\) 0 0
\(43\) 31.0000 0.720930 0.360465 0.932773i \(-0.382618\pi\)
0.360465 + 0.932773i \(0.382618\pi\)
\(44\) −16.9706 29.3939i −0.385695 0.668043i
\(45\) 0 0
\(46\) 6.00000 10.3923i 0.130435 0.225920i
\(47\) 72.1249 41.6413i 1.53457 0.885986i 0.535430 0.844580i \(-0.320150\pi\)
0.999142 0.0414059i \(-0.0131837\pi\)
\(48\) 0 0
\(49\) −24.5000 + 42.4352i −0.500000 + 0.866025i
\(50\) −1.41421 −0.0282843
\(51\) 0 0
\(52\) 3.00000 + 1.73205i 0.0576923 + 0.0333087i
\(53\) −38.1838 + 66.1362i −0.720448 + 1.24785i 0.240372 + 0.970681i \(0.422731\pi\)
−0.960820 + 0.277172i \(0.910603\pi\)
\(54\) 0 0
\(55\) 83.1384i 1.51161i
\(56\) −9.89949 17.1464i −0.176777 0.306186i
\(57\) 0 0
\(58\) 24.0000 + 41.5692i 0.413793 + 0.716711i
\(59\) 72.1249 + 41.6413i 1.22246 + 0.705785i 0.965441 0.260622i \(-0.0839277\pi\)
0.257015 + 0.966407i \(0.417261\pi\)
\(60\) 0 0
\(61\) −72.0000 + 41.5692i −1.18033 + 0.681463i −0.956090 0.293072i \(-0.905322\pi\)
−0.224237 + 0.974535i \(0.571989\pi\)
\(62\) 17.1464i 0.276555i
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) 4.24264 + 7.34847i 0.0652714 + 0.113053i
\(66\) 0 0
\(67\) 15.5000 26.8468i 0.231343 0.400698i −0.726860 0.686785i \(-0.759021\pi\)
0.958204 + 0.286087i \(0.0923546\pi\)
\(68\) −8.48528 + 4.89898i −0.124784 + 0.0720438i
\(69\) 0 0
\(70\) 48.4974i 0.692820i
\(71\) −59.3970 −0.836577 −0.418289 0.908314i \(-0.637370\pi\)
−0.418289 + 0.908314i \(0.637370\pi\)
\(72\) 0 0
\(73\) −70.5000 40.7032i −0.965753 0.557578i −0.0678144 0.997698i \(-0.521603\pi\)
−0.897939 + 0.440120i \(0.854936\pi\)
\(74\) −33.2340 + 57.5630i −0.449108 + 0.777878i
\(75\) 0 0
\(76\) 58.8897i 0.774865i
\(77\) −118.794 −1.54278
\(78\) 0 0
\(79\) −20.5000 35.5070i −0.259494 0.449456i 0.706613 0.707601i \(-0.250222\pi\)
−0.966106 + 0.258144i \(0.916889\pi\)
\(80\) 16.9706 + 9.79796i 0.212132 + 0.122474i
\(81\) 0 0
\(82\) 84.0000 48.4974i 1.02439 0.591432i
\(83\) 4.89898i 0.0590238i 0.999564 + 0.0295119i \(0.00939530\pi\)
−0.999564 + 0.0295119i \(0.990605\pi\)
\(84\) 0 0
\(85\) −24.0000 −0.282353
\(86\) 21.9203 + 37.9671i 0.254887 + 0.441478i
\(87\) 0 0
\(88\) 24.0000 41.5692i 0.272727 0.472377i
\(89\) −50.9117 + 29.3939i −0.572041 + 0.330268i −0.757964 0.652296i \(-0.773806\pi\)
0.185923 + 0.982564i \(0.440473\pi\)
\(90\) 0 0
\(91\) 10.5000 6.06218i 0.115385 0.0666173i
\(92\) 16.9706 0.184463
\(93\) 0 0
\(94\) 102.000 + 58.8897i 1.08511 + 0.626486i
\(95\) −72.1249 + 124.924i −0.759209 + 1.31499i
\(96\) 0 0
\(97\) 41.5692i 0.428549i 0.976774 + 0.214274i \(0.0687387\pi\)
−0.976774 + 0.214274i \(0.931261\pi\)
\(98\) −69.2965 −0.707107
\(99\) 0 0
\(100\) −1.00000 1.73205i −0.0100000 0.0173205i
\(101\) 152.735 + 88.1816i 1.51223 + 0.873085i 0.999898 + 0.0142971i \(0.00455107\pi\)
0.512331 + 0.858788i \(0.328782\pi\)
\(102\) 0 0
\(103\) −25.5000 + 14.7224i −0.247573 + 0.142936i −0.618652 0.785665i \(-0.712321\pi\)
0.371080 + 0.928601i \(0.378988\pi\)
\(104\) 4.89898i 0.0471056i
\(105\) 0 0
\(106\) −108.000 −1.01887
\(107\) −72.1249 124.924i −0.674064 1.16751i −0.976741 0.214421i \(-0.931214\pi\)
0.302677 0.953093i \(-0.402120\pi\)
\(108\) 0 0
\(109\) −84.5000 + 146.358i −0.775229 + 1.34274i 0.159436 + 0.987208i \(0.449032\pi\)
−0.934665 + 0.355528i \(0.884301\pi\)
\(110\) 101.823 58.7878i 0.925667 0.534434i
\(111\) 0 0
\(112\) 14.0000 24.2487i 0.125000 0.216506i
\(113\) 59.3970 0.525637 0.262818 0.964845i \(-0.415348\pi\)
0.262818 + 0.964845i \(0.415348\pi\)
\(114\) 0 0
\(115\) 36.0000 + 20.7846i 0.313043 + 0.180736i
\(116\) −33.9411 + 58.7878i −0.292596 + 0.506791i
\(117\) 0 0
\(118\) 117.779i 0.998131i
\(119\) 34.2929i 0.288175i
\(120\) 0 0
\(121\) −83.5000 144.626i −0.690083 1.19526i
\(122\) −101.823 58.7878i −0.834618 0.481867i
\(123\) 0 0
\(124\) 21.0000 12.1244i 0.169355 0.0977771i
\(125\) 127.373i 1.01899i
\(126\) 0 0
\(127\) 209.000 1.64567 0.822835 0.568281i \(-0.192391\pi\)
0.822835 + 0.568281i \(0.192391\pi\)
\(128\) 5.65685 + 9.79796i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −6.00000 + 10.3923i −0.0461538 + 0.0799408i
\(131\) 50.9117 29.3939i 0.388639 0.224381i −0.292931 0.956133i \(-0.594631\pi\)
0.681570 + 0.731753i \(0.261297\pi\)
\(132\) 0 0
\(133\) 178.500 + 103.057i 1.34211 + 0.774865i
\(134\) 43.8406 0.327169
\(135\) 0 0
\(136\) −12.0000 6.92820i −0.0882353 0.0509427i
\(137\) 76.3675 132.272i 0.557427 0.965492i −0.440283 0.897859i \(-0.645122\pi\)
0.997710 0.0676333i \(-0.0215448\pi\)
\(138\) 0 0
\(139\) 195.722i 1.40807i −0.710165 0.704035i \(-0.751380\pi\)
0.710165 0.704035i \(-0.248620\pi\)
\(140\) 59.3970 34.2929i 0.424264 0.244949i
\(141\) 0 0
\(142\) −42.0000 72.7461i −0.295775 0.512297i
\(143\) 25.4558 + 14.6969i 0.178013 + 0.102776i
\(144\) 0 0
\(145\) −144.000 + 83.1384i −0.993103 + 0.573369i
\(146\) 115.126i 0.788534i
\(147\) 0 0
\(148\) −94.0000 −0.635135
\(149\) 25.4558 + 44.0908i 0.170845 + 0.295912i 0.938715 0.344693i \(-0.112017\pi\)
−0.767871 + 0.640605i \(0.778684\pi\)
\(150\) 0 0
\(151\) −5.00000 + 8.66025i −0.0331126 + 0.0573527i −0.882107 0.471049i \(-0.843875\pi\)
0.848994 + 0.528402i \(0.177209\pi\)
\(152\) −72.1249 + 41.6413i −0.474506 + 0.273956i
\(153\) 0 0
\(154\) −84.0000 145.492i −0.545455 0.944755i
\(155\) 59.3970 0.383206
\(156\) 0 0
\(157\) 36.0000 + 20.7846i 0.229299 + 0.132386i 0.610249 0.792210i \(-0.291069\pi\)
−0.380949 + 0.924596i \(0.624403\pi\)
\(158\) 28.9914 50.2145i 0.183490 0.317814i
\(159\) 0 0
\(160\) 27.7128i 0.173205i
\(161\) 29.6985 51.4393i 0.184463 0.319499i
\(162\) 0 0
\(163\) −43.0000 74.4782i −0.263804 0.456921i 0.703446 0.710749i \(-0.251644\pi\)
−0.967250 + 0.253828i \(0.918310\pi\)
\(164\) 118.794 + 68.5857i 0.724353 + 0.418206i
\(165\) 0 0
\(166\) −6.00000 + 3.46410i −0.0361446 + 0.0208681i
\(167\) 181.262i 1.08540i −0.839926 0.542701i \(-0.817402\pi\)
0.839926 0.542701i \(-0.182598\pi\)
\(168\) 0 0
\(169\) 166.000 0.982249
\(170\) −16.9706 29.3939i −0.0998268 0.172905i
\(171\) 0 0
\(172\) −31.0000 + 53.6936i −0.180233 + 0.312172i
\(173\) 38.1838 22.0454i 0.220715 0.127430i −0.385566 0.922680i \(-0.625994\pi\)
0.606281 + 0.795250i \(0.292660\pi\)
\(174\) 0 0
\(175\) −7.00000 −0.0400000
\(176\) 67.8823 0.385695
\(177\) 0 0
\(178\) −72.0000 41.5692i −0.404494 0.233535i
\(179\) −4.24264 + 7.34847i −0.0237019 + 0.0410529i −0.877633 0.479333i \(-0.840879\pi\)
0.853931 + 0.520386i \(0.174212\pi\)
\(180\) 0 0
\(181\) 43.3013i 0.239234i 0.992820 + 0.119617i \(0.0381666\pi\)
−0.992820 + 0.119617i \(0.961833\pi\)
\(182\) 14.8492 + 8.57321i 0.0815892 + 0.0471056i
\(183\) 0 0
\(184\) 12.0000 + 20.7846i 0.0652174 + 0.112960i
\(185\) −199.404 115.126i −1.07786 0.622303i
\(186\) 0 0
\(187\) −72.0000 + 41.5692i −0.385027 + 0.222295i
\(188\) 166.565i 0.885986i
\(189\) 0 0
\(190\) −204.000 −1.07368
\(191\) 38.1838 + 66.1362i 0.199915 + 0.346263i 0.948501 0.316775i \(-0.102600\pi\)
−0.748586 + 0.663038i \(0.769267\pi\)
\(192\) 0 0
\(193\) 143.500 248.549i 0.743523 1.28782i −0.207358 0.978265i \(-0.566487\pi\)
0.950882 0.309555i \(-0.100180\pi\)
\(194\) −50.9117 + 29.3939i −0.262431 + 0.151515i
\(195\) 0 0
\(196\) −49.0000 84.8705i −0.250000 0.433013i
\(197\) −127.279 −0.646087 −0.323044 0.946384i \(-0.604706\pi\)
−0.323044 + 0.946384i \(0.604706\pi\)
\(198\) 0 0
\(199\) 180.000 + 103.923i 0.904523 + 0.522226i 0.878665 0.477439i \(-0.158435\pi\)
0.0258579 + 0.999666i \(0.491768\pi\)
\(200\) 1.41421 2.44949i 0.00707107 0.0122474i
\(201\) 0 0
\(202\) 249.415i 1.23473i
\(203\) 118.794 + 205.757i 0.585192 + 1.01358i
\(204\) 0 0
\(205\) 168.000 + 290.985i 0.819512 + 1.41944i
\(206\) −36.0624 20.8207i −0.175060 0.101071i
\(207\) 0 0
\(208\) −6.00000 + 3.46410i −0.0288462 + 0.0166543i
\(209\) 499.696i 2.39089i
\(210\) 0 0
\(211\) 82.0000 0.388626 0.194313 0.980940i \(-0.437752\pi\)
0.194313 + 0.980940i \(0.437752\pi\)
\(212\) −76.3675 132.272i −0.360224 0.623927i
\(213\) 0 0
\(214\) 102.000 176.669i 0.476636 0.825557i
\(215\) −131.522 + 75.9342i −0.611730 + 0.353182i
\(216\) 0 0
\(217\) 84.8705i 0.391108i
\(218\) −239.002 −1.09634
\(219\) 0 0
\(220\) 144.000 + 83.1384i 0.654545 + 0.377902i
\(221\) 4.24264 7.34847i 0.0191975 0.0332510i
\(222\) 0 0
\(223\) 41.5692i 0.186409i −0.995647 0.0932045i \(-0.970289\pi\)
0.995647 0.0932045i \(-0.0297110\pi\)
\(224\) 39.5980 0.176777
\(225\) 0 0
\(226\) 42.0000 + 72.7461i 0.185841 + 0.321886i
\(227\) −330.926 191.060i −1.45782 0.841675i −0.458920 0.888478i \(-0.651763\pi\)
−0.998904 + 0.0468029i \(0.985097\pi\)
\(228\) 0 0
\(229\) −70.5000 + 40.7032i −0.307860 + 0.177743i −0.645969 0.763364i \(-0.723546\pi\)
0.338108 + 0.941107i \(0.390213\pi\)
\(230\) 58.7878i 0.255599i
\(231\) 0 0
\(232\) −96.0000 −0.413793
\(233\) 114.551 + 198.409i 0.491636 + 0.851539i 0.999954 0.00963059i \(-0.00306556\pi\)
−0.508317 + 0.861170i \(0.669732\pi\)
\(234\) 0 0
\(235\) −204.000 + 353.338i −0.868085 + 1.50357i
\(236\) −144.250 + 83.2827i −0.611228 + 0.352893i
\(237\) 0 0
\(238\) −42.0000 + 24.2487i −0.176471 + 0.101885i
\(239\) 67.8823 0.284026 0.142013 0.989865i \(-0.454642\pi\)
0.142013 + 0.989865i \(0.454642\pi\)
\(240\) 0 0
\(241\) −396.000 228.631i −1.64315 0.948675i −0.979703 0.200455i \(-0.935758\pi\)
−0.663451 0.748220i \(-0.730909\pi\)
\(242\) 118.087 204.532i 0.487962 0.845175i
\(243\) 0 0
\(244\) 166.277i 0.681463i
\(245\) 240.050i 0.979796i
\(246\) 0 0
\(247\) −25.5000 44.1673i −0.103239 0.178815i
\(248\) 29.6985 + 17.1464i 0.119752 + 0.0691388i
\(249\) 0 0
\(250\) 156.000 90.0666i 0.624000 0.360267i
\(251\) 347.828i 1.38577i 0.721050 + 0.692884i \(0.243660\pi\)
−0.721050 + 0.692884i \(0.756340\pi\)
\(252\) 0 0
\(253\) 144.000 0.569170
\(254\) 147.785 + 255.972i 0.581832 + 1.00776i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −140.007 + 80.8332i −0.544775 + 0.314526i −0.747012 0.664811i \(-0.768512\pi\)
0.202237 + 0.979337i \(0.435179\pi\)
\(258\) 0 0
\(259\) −164.500 + 284.922i −0.635135 + 1.10009i
\(260\) −16.9706 −0.0652714
\(261\) 0 0
\(262\) 72.0000 + 41.5692i 0.274809 + 0.158661i
\(263\) 127.279 220.454i 0.483951 0.838228i −0.515879 0.856662i \(-0.672534\pi\)
0.999830 + 0.0184332i \(0.00586781\pi\)
\(264\) 0 0
\(265\) 374.123i 1.41178i
\(266\) 291.489i 1.09582i
\(267\) 0 0
\(268\) 31.0000 + 53.6936i 0.115672 + 0.200349i
\(269\) −16.9706 9.79796i −0.0630876 0.0364236i 0.468124 0.883663i \(-0.344930\pi\)
−0.531212 + 0.847239i \(0.678263\pi\)
\(270\) 0 0
\(271\) 36.0000 20.7846i 0.132841 0.0766960i −0.432107 0.901823i \(-0.642230\pi\)
0.564948 + 0.825127i \(0.308896\pi\)
\(272\) 19.5959i 0.0720438i
\(273\) 0 0
\(274\) 216.000 0.788321
\(275\) −8.48528 14.6969i −0.0308556 0.0534434i
\(276\) 0 0
\(277\) 168.500 291.851i 0.608303 1.05361i −0.383217 0.923658i \(-0.625184\pi\)
0.991520 0.129954i \(-0.0414829\pi\)
\(278\) 239.709 138.396i 0.862263 0.497828i
\(279\) 0 0
\(280\) 84.0000 + 48.4974i 0.300000 + 0.173205i
\(281\) −246.073 −0.875705 −0.437853 0.899047i \(-0.644261\pi\)
−0.437853 + 0.899047i \(0.644261\pi\)
\(282\) 0 0
\(283\) −169.500 97.8609i −0.598940 0.345798i 0.169685 0.985498i \(-0.445725\pi\)
−0.768624 + 0.639700i \(0.779058\pi\)
\(284\) 59.3970 102.879i 0.209144 0.362248i
\(285\) 0 0
\(286\) 41.5692i 0.145347i
\(287\) 415.779 240.050i 1.44871 0.836411i
\(288\) 0 0
\(289\) −132.500 229.497i −0.458478 0.794106i
\(290\) −203.647 117.576i −0.702230 0.405433i
\(291\) 0 0
\(292\) 141.000 81.4064i 0.482877 0.278789i
\(293\) 97.9796i 0.334401i −0.985923 0.167201i \(-0.946527\pi\)
0.985923 0.167201i \(-0.0534728\pi\)
\(294\) 0 0
\(295\) −408.000 −1.38305
\(296\) −66.4680 115.126i −0.224554 0.388939i
\(297\) 0 0
\(298\) −36.0000 + 62.3538i −0.120805 + 0.209241i
\(299\) −12.7279 + 7.34847i −0.0425683 + 0.0245768i
\(300\) 0 0
\(301\) 108.500 + 187.928i 0.360465 + 0.624344i
\(302\) −14.1421 −0.0468283
\(303\) 0 0
\(304\) −102.000 58.8897i −0.335526 0.193716i
\(305\) 203.647 352.727i 0.667694 1.15648i
\(306\) 0 0
\(307\) 71.0141i 0.231316i −0.993289 0.115658i \(-0.963102\pi\)
0.993289 0.115658i \(-0.0368977\pi\)
\(308\) 118.794 205.757i 0.385695 0.668043i
\(309\) 0 0
\(310\) 42.0000 + 72.7461i 0.135484 + 0.234665i
\(311\) −186.676 107.778i −0.600245 0.346552i 0.168893 0.985634i \(-0.445981\pi\)
−0.769138 + 0.639083i \(0.779314\pi\)
\(312\) 0 0
\(313\) 253.500 146.358i 0.809904 0.467598i −0.0370184 0.999315i \(-0.511786\pi\)
0.846923 + 0.531716i \(0.178453\pi\)
\(314\) 58.7878i 0.187222i
\(315\) 0 0
\(316\) 82.0000 0.259494
\(317\) −118.794 205.757i −0.374744 0.649076i 0.615544 0.788102i \(-0.288936\pi\)
−0.990289 + 0.139026i \(0.955603\pi\)
\(318\) 0 0
\(319\) −288.000 + 498.831i −0.902821 + 1.56373i
\(320\) −33.9411 + 19.5959i −0.106066 + 0.0612372i
\(321\) 0 0
\(322\) 84.0000 0.260870
\(323\) 144.250 0.446594
\(324\) 0 0
\(325\) 1.50000 + 0.866025i 0.00461538 + 0.00266469i
\(326\) 60.8112 105.328i 0.186537 0.323092i
\(327\) 0 0
\(328\) 193.990i 0.591432i
\(329\) 504.874 + 291.489i 1.53457 + 0.885986i
\(330\) 0 0
\(331\) 92.5000 + 160.215i 0.279456 + 0.484032i 0.971250 0.238063i \(-0.0765125\pi\)
−0.691794 + 0.722095i \(0.743179\pi\)
\(332\) −8.48528 4.89898i −0.0255581 0.0147560i
\(333\) 0 0
\(334\) 222.000 128.172i 0.664671 0.383748i
\(335\) 151.868i 0.453338i
\(336\) 0 0
\(337\) −359.000 −1.06528 −0.532641 0.846341i \(-0.678800\pi\)
−0.532641 + 0.846341i \(0.678800\pi\)
\(338\) 117.380 + 203.308i 0.347277 + 0.601502i
\(339\) 0 0
\(340\) 24.0000 41.5692i 0.0705882 0.122262i
\(341\) 178.191 102.879i 0.522554 0.301697i
\(342\) 0 0
\(343\) −343.000 −1.00000
\(344\) −87.6812 −0.254887
\(345\) 0 0
\(346\) 54.0000 + 31.1769i 0.156069 + 0.0901067i
\(347\) 233.345 404.166i 0.672465 1.16474i −0.304738 0.952436i \(-0.598569\pi\)
0.977203 0.212307i \(-0.0680976\pi\)
\(348\) 0 0
\(349\) 581.969i 1.66753i 0.552117 + 0.833767i \(0.313820\pi\)
−0.552117 + 0.833767i \(0.686180\pi\)
\(350\) −4.94975 8.57321i −0.0141421 0.0244949i
\(351\) 0 0
\(352\) 48.0000 + 83.1384i 0.136364 + 0.236189i
\(353\) −250.316 144.520i −0.709110 0.409405i 0.101621 0.994823i \(-0.467597\pi\)
−0.810731 + 0.585418i \(0.800930\pi\)
\(354\) 0 0
\(355\) 252.000 145.492i 0.709859 0.409837i
\(356\) 117.576i 0.330268i
\(357\) 0 0
\(358\) −12.0000 −0.0335196
\(359\) 169.706 + 293.939i 0.472718 + 0.818771i 0.999512 0.0312215i \(-0.00993973\pi\)
−0.526795 + 0.849992i \(0.676606\pi\)
\(360\) 0 0
\(361\) 253.000 438.209i 0.700831 1.21387i
\(362\) −53.0330 + 30.6186i −0.146500 + 0.0845818i
\(363\) 0 0
\(364\) 24.2487i 0.0666173i
\(365\) 398.808 1.09263
\(366\) 0 0
\(367\) 133.500 + 77.0763i 0.363760 + 0.210017i 0.670729 0.741703i \(-0.265981\pi\)
−0.306969 + 0.951720i \(0.599315\pi\)
\(368\) −16.9706 + 29.3939i −0.0461157 + 0.0798747i
\(369\) 0 0
\(370\) 325.626i 0.880069i
\(371\) −534.573 −1.44090
\(372\) 0 0
\(373\) 144.500 + 250.281i 0.387399 + 0.670996i 0.992099 0.125458i \(-0.0400401\pi\)
−0.604699 + 0.796454i \(0.706707\pi\)
\(374\) −101.823 58.7878i −0.272255 0.157187i
\(375\) 0 0
\(376\) −204.000 + 117.779i −0.542553 + 0.313243i
\(377\) 58.7878i 0.155936i
\(378\) 0 0
\(379\) 7.00000 0.0184697 0.00923483 0.999957i \(-0.497060\pi\)
0.00923483 + 0.999957i \(0.497060\pi\)
\(380\) −144.250 249.848i −0.379605 0.657495i
\(381\) 0 0
\(382\) −54.0000 + 93.5307i −0.141361 + 0.244845i
\(383\) −428.507 + 247.398i −1.11882 + 0.645949i −0.941099 0.338132i \(-0.890205\pi\)
−0.177718 + 0.984081i \(0.556871\pi\)
\(384\) 0 0
\(385\) 504.000 290.985i 1.30909 0.755804i
\(386\) 405.879 1.05150
\(387\) 0 0
\(388\) −72.0000 41.5692i −0.185567 0.107137i
\(389\) −114.551 + 198.409i −0.294476 + 0.510048i −0.974863 0.222805i \(-0.928479\pi\)
0.680387 + 0.732853i \(0.261812\pi\)
\(390\) 0 0
\(391\) 41.5692i 0.106315i
\(392\) 69.2965 120.025i 0.176777 0.306186i
\(393\) 0 0
\(394\) −90.0000 155.885i −0.228426 0.395646i
\(395\) 173.948 + 100.429i 0.440375 + 0.254251i
\(396\) 0 0
\(397\) 70.5000 40.7032i 0.177582 0.102527i −0.408574 0.912725i \(-0.633974\pi\)
0.586156 + 0.810198i \(0.300641\pi\)
\(398\) 293.939i 0.738540i
\(399\) 0 0
\(400\) 4.00000 0.0100000
\(401\) −46.6690 80.8332i −0.116382 0.201579i 0.801950 0.597392i \(-0.203796\pi\)
−0.918331 + 0.395813i \(0.870463\pi\)
\(402\) 0 0
\(403\) −10.5000 + 18.1865i −0.0260546 + 0.0451279i
\(404\) −305.470 + 176.363i −0.756114 + 0.436543i
\(405\) 0 0
\(406\) −168.000 + 290.985i −0.413793 + 0.716711i
\(407\) −797.616 −1.95975
\(408\) 0 0
\(409\) −361.500 208.712i −0.883863 0.510299i −0.0119329 0.999929i \(-0.503798\pi\)
−0.871930 + 0.489630i \(0.837132\pi\)
\(410\) −237.588 + 411.514i −0.579483 + 1.00369i
\(411\) 0 0
\(412\) 58.8897i 0.142936i
\(413\) 582.979i 1.41157i
\(414\) 0 0
\(415\) −12.0000 20.7846i −0.0289157 0.0500834i
\(416\) −8.48528 4.89898i −0.0203973 0.0117764i
\(417\) 0 0
\(418\) −612.000 + 353.338i −1.46411 + 0.845307i
\(419\) 19.5959i 0.0467683i −0.999727 0.0233842i \(-0.992556\pi\)
0.999727 0.0233842i \(-0.00744408\pi\)
\(420\) 0 0
\(421\) 407.000 0.966746 0.483373 0.875415i \(-0.339412\pi\)
0.483373 + 0.875415i \(0.339412\pi\)
\(422\) 57.9828 + 100.429i 0.137400 + 0.237984i
\(423\) 0 0
\(424\) 108.000 187.061i 0.254717 0.441183i
\(425\) −4.24264 + 2.44949i −0.00998268 + 0.00576351i
\(426\) 0 0
\(427\) −504.000 290.985i −1.18033 0.681463i
\(428\) 288.500 0.674064
\(429\) 0 0
\(430\) −186.000 107.387i −0.432558 0.249738i
\(431\) −80.6102 + 139.621i −0.187031 + 0.323946i −0.944259 0.329204i \(-0.893220\pi\)
0.757228 + 0.653150i \(0.226553\pi\)
\(432\) 0 0
\(433\) 168.009i 0.388011i −0.981000 0.194006i \(-0.937852\pi\)
0.981000 0.194006i \(-0.0621480\pi\)
\(434\) 103.945 60.0125i 0.239504 0.138278i
\(435\) 0 0
\(436\) −169.000 292.717i −0.387615 0.671368i
\(437\) −216.375 124.924i −0.495137 0.285867i
\(438\) 0 0
\(439\) −468.000 + 270.200i −1.06606 + 0.615490i −0.927102 0.374809i \(-0.877708\pi\)
−0.138957 + 0.990298i \(0.544375\pi\)
\(440\) 235.151i 0.534434i
\(441\) 0 0
\(442\) 12.0000 0.0271493
\(443\) 63.6396 + 110.227i 0.143656 + 0.248819i 0.928871 0.370404i \(-0.120781\pi\)
−0.785215 + 0.619224i \(0.787447\pi\)
\(444\) 0 0
\(445\) 144.000 249.415i 0.323596 0.560484i
\(446\) 50.9117 29.3939i 0.114152 0.0659056i
\(447\) 0 0
\(448\) 28.0000 + 48.4974i 0.0625000 + 0.108253i
\(449\) −110.309 −0.245676 −0.122838 0.992427i \(-0.539200\pi\)
−0.122838 + 0.992427i \(0.539200\pi\)
\(450\) 0 0
\(451\) 1008.00 + 581.969i 2.23503 + 1.29040i
\(452\) −59.3970 + 102.879i −0.131409 + 0.227607i
\(453\) 0 0
\(454\) 540.400i 1.19031i
\(455\) −29.6985 + 51.4393i −0.0652714 + 0.113053i
\(456\) 0 0
\(457\) −12.5000 21.6506i −0.0273523 0.0473756i 0.852025 0.523501i \(-0.175374\pi\)
−0.879378 + 0.476125i \(0.842041\pi\)
\(458\) −99.7021 57.5630i −0.217690 0.125683i
\(459\) 0 0
\(460\) −72.0000 + 41.5692i −0.156522 + 0.0903679i
\(461\) 78.3837i 0.170030i 0.996380 + 0.0850148i \(0.0270938\pi\)
−0.996380 + 0.0850148i \(0.972906\pi\)
\(462\) 0 0
\(463\) 521.000 1.12527 0.562635 0.826705i \(-0.309788\pi\)
0.562635 + 0.826705i \(0.309788\pi\)
\(464\) −67.8823 117.576i −0.146298 0.253395i
\(465\) 0 0
\(466\) −162.000 + 280.592i −0.347639 + 0.602129i
\(467\) 190.919 110.227i 0.408820 0.236032i −0.281463 0.959572i \(-0.590820\pi\)
0.690283 + 0.723540i \(0.257486\pi\)
\(468\) 0 0
\(469\) 217.000 0.462687
\(470\) −576.999 −1.22766
\(471\) 0 0
\(472\) −204.000 117.779i −0.432203 0.249533i
\(473\) −263.044 + 455.605i −0.556118 + 0.963224i
\(474\) 0 0
\(475\) 29.4449i 0.0619892i
\(476\) −59.3970 34.2929i −0.124784 0.0720438i
\(477\) 0 0
\(478\) 48.0000 + 83.1384i 0.100418 + 0.173930i
\(479\) 759.433 + 438.459i 1.58545 + 0.915363i 0.994043 + 0.108993i \(0.0347626\pi\)
0.591412 + 0.806370i \(0.298571\pi\)
\(480\) 0 0
\(481\) 70.5000 40.7032i 0.146570 0.0846220i
\(482\) 646.665i 1.34163i
\(483\) 0 0
\(484\) 334.000 0.690083
\(485\) −101.823 176.363i −0.209945 0.363636i
\(486\) 0 0
\(487\) −63.5000 + 109.985i −0.130390 + 0.225842i −0.923827 0.382810i \(-0.874956\pi\)
0.793437 + 0.608653i \(0.208290\pi\)
\(488\) 203.647 117.576i 0.417309 0.240933i
\(489\) 0 0
\(490\) 294.000 169.741i 0.600000 0.346410i
\(491\) 627.911 1.27884 0.639420 0.768857i \(-0.279174\pi\)
0.639420 + 0.768857i \(0.279174\pi\)
\(492\) 0 0
\(493\) 144.000 + 83.1384i 0.292089 + 0.168638i
\(494\) 36.0624 62.4620i 0.0730009 0.126441i
\(495\) 0 0
\(496\) 48.4974i 0.0977771i
\(497\) −207.889 360.075i −0.418289 0.724497i
\(498\) 0 0
\(499\) 116.500 + 201.784i 0.233467 + 0.404377i 0.958826 0.283994i \(-0.0916596\pi\)
−0.725359 + 0.688371i \(0.758326\pi\)
\(500\) 220.617 + 127.373i 0.441235 + 0.254747i
\(501\) 0 0
\(502\) −426.000 + 245.951i −0.848606 + 0.489943i
\(503\) 538.888i 1.07135i −0.844425 0.535674i \(-0.820058\pi\)
0.844425 0.535674i \(-0.179942\pi\)
\(504\) 0 0
\(505\) −864.000 −1.71089
\(506\) 101.823 + 176.363i 0.201232 + 0.348544i
\(507\) 0 0
\(508\) −209.000 + 361.999i −0.411417 + 0.712596i
\(509\) −275.772 + 159.217i −0.541791 + 0.312803i −0.745805 0.666165i \(-0.767935\pi\)
0.204013 + 0.978968i \(0.434601\pi\)
\(510\) 0 0
\(511\) 569.845i 1.11516i
\(512\) −22.6274 −0.0441942
\(513\) 0 0
\(514\) −198.000 114.315i −0.385214 0.222403i
\(515\) 72.1249 124.924i 0.140048 0.242571i
\(516\) 0 0
\(517\) 1413.35i 2.73376i
\(518\) −465.276 −0.898217
\(519\) 0 0
\(520\) −12.0000 20.7846i −0.0230769 0.0399704i
\(521\) 492.146 + 284.141i 0.944619 + 0.545376i 0.891405 0.453207i \(-0.149720\pi\)
0.0532135 + 0.998583i \(0.483054\pi\)
\(522\) 0 0
\(523\) 457.500 264.138i 0.874761 0.505043i 0.00583355 0.999983i \(-0.498143\pi\)
0.868927 + 0.494939i \(0.164810\pi\)
\(524\) 117.576i 0.224381i
\(525\) 0 0
\(526\) 360.000 0.684411
\(527\) −29.6985 51.4393i −0.0563539 0.0976078i
\(528\) 0 0
\(529\) 228.500 395.774i 0.431947 0.748154i
\(530\) 458.205 264.545i 0.864538 0.499141i
\(531\) 0 0
\(532\) −357.000 + 206.114i −0.671053 + 0.387432i
\(533\) −118.794 −0.222878
\(534\) 0 0
\(535\) 612.000 + 353.338i 1.14393 + 0.660446i
\(536\) −43.8406 + 75.9342i −0.0817922 + 0.141668i
\(537\) 0 0
\(538\) 27.7128i 0.0515108i
\(539\) −415.779 720.150i −0.771389 1.33609i
\(540\) 0 0
\(541\) −167.500 290.119i −0.309612 0.536263i 0.668666 0.743563i \(-0.266866\pi\)
−0.978277 + 0.207300i \(0.933532\pi\)
\(542\) 50.9117 + 29.3939i 0.0939330 + 0.0542322i
\(543\) 0 0
\(544\) 24.0000 13.8564i 0.0441176 0.0254713i
\(545\) 827.928i 1.51913i
\(546\) 0 0
\(547\) −658.000 −1.20293 −0.601463 0.798901i \(-0.705415\pi\)
−0.601463 + 0.798901i \(0.705415\pi\)
\(548\) 152.735 + 264.545i 0.278714 + 0.482746i
\(549\) 0 0
\(550\) 12.0000 20.7846i 0.0218182 0.0377902i
\(551\) 865.499 499.696i 1.57078 0.906889i
\(552\) 0 0
\(553\) 143.500 248.549i 0.259494 0.449456i
\(554\) 476.590 0.860271
\(555\) 0 0
\(556\) 339.000 + 195.722i 0.609712 + 0.352018i
\(557\) −135.765 + 235.151i −0.243742 + 0.422174i −0.961777 0.273833i \(-0.911708\pi\)
0.718035 + 0.696007i \(0.245042\pi\)
\(558\) 0 0
\(559\) 53.6936i 0.0960529i
\(560\) 137.171i 0.244949i
\(561\) 0 0
\(562\) −174.000 301.377i −0.309609 0.536258i
\(563\) 12.7279 + 7.34847i 0.0226073 + 0.0130523i 0.511261 0.859425i \(-0.329179\pi\)
−0.488654 + 0.872478i \(0.662512\pi\)
\(564\) 0 0
\(565\) −252.000 + 145.492i −0.446018 + 0.257508i
\(566\) 276.792i 0.489032i
\(567\) 0 0
\(568\) 168.000 0.295775
\(569\) −424.264 734.847i −0.745631 1.29147i −0.949899 0.312556i \(-0.898815\pi\)
0.204268 0.978915i \(-0.434519\pi\)
\(570\) 0 0
\(571\) −224.500 + 388.845i −0.393170 + 0.680990i −0.992866 0.119238i \(-0.961955\pi\)
0.599696 + 0.800228i \(0.295288\pi\)
\(572\) −50.9117 + 29.3939i −0.0890064 + 0.0513879i
\(573\) 0 0
\(574\) 588.000 + 339.482i 1.02439 + 0.591432i
\(575\) 8.48528 0.0147570
\(576\) 0 0
\(577\) −253.500 146.358i −0.439341 0.253654i 0.263977 0.964529i \(-0.414966\pi\)
−0.703318 + 0.710875i \(0.748299\pi\)
\(578\) 187.383 324.557i 0.324193 0.561518i
\(579\) 0 0
\(580\) 332.554i 0.573369i
\(581\) −29.6985 + 17.1464i −0.0511162 + 0.0295119i
\(582\) 0 0
\(583\) −648.000 1122.37i −1.11149 1.92516i
\(584\) 199.404 + 115.126i 0.341445 + 0.197134i
\(585\) 0 0
\(586\) 120.000 69.2820i 0.204778 0.118229i
\(587\) 529.090i 0.901345i 0.892689 + 0.450673i \(0.148816\pi\)
−0.892689 + 0.450673i \(0.851184\pi\)
\(588\) 0 0
\(589\) −357.000 −0.606112
\(590\) −288.500 499.696i −0.488982 0.846942i
\(591\) 0 0
\(592\) 94.0000 162.813i 0.158784 0.275022i
\(593\) 907.925 524.191i 1.53107 0.883964i 0.531758 0.846896i \(-0.321531\pi\)
0.999313 0.0370681i \(-0.0118018\pi\)
\(594\) 0 0
\(595\) −84.0000 145.492i −0.141176 0.244525i
\(596\) −101.823 −0.170845
\(597\) 0 0
\(598\) −18.0000 10.3923i −0.0301003 0.0173784i
\(599\) −322.441 + 558.484i −0.538298 + 0.932360i 0.460698 + 0.887557i \(0.347599\pi\)
−0.998996 + 0.0448028i \(0.985734\pi\)
\(600\) 0 0
\(601\) 458.993i 0.763716i 0.924221 + 0.381858i \(0.124716\pi\)
−0.924221 + 0.381858i \(0.875284\pi\)
\(602\) −153.442 + 265.770i −0.254887 + 0.441478i
\(603\) 0 0
\(604\) −10.0000 17.3205i −0.0165563 0.0286763i
\(605\) 708.521 + 409.065i 1.17111 + 0.676140i
\(606\) 0 0
\(607\) 910.500 525.677i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(608\) 166.565i 0.273956i
\(609\) 0 0
\(610\) 576.000 0.944262
\(611\) −72.1249 124.924i −0.118044 0.204458i
\(612\) 0 0
\(613\) −145.000 + 251.147i −0.236542 + 0.409702i −0.959720 0.280960i \(-0.909347\pi\)
0.723178 + 0.690662i \(0.242681\pi\)
\(614\) 86.9741 50.2145i 0.141652 0.0817826i
\(615\) 0 0
\(616\) 336.000 0.545455
\(617\) 729.734 1.18271 0.591357 0.806410i \(-0.298593\pi\)
0.591357 + 0.806410i \(0.298593\pi\)
\(618\) 0 0
\(619\) −709.500 409.630i −1.14620 0.661761i −0.198244 0.980153i \(-0.563524\pi\)
−0.947959 + 0.318392i \(0.896857\pi\)
\(620\) −59.3970 + 102.879i −0.0958016 + 0.165933i
\(621\) 0 0
\(622\) 304.841i 0.490098i
\(623\) −356.382 205.757i −0.572041 0.330268i
\(624\) 0 0
\(625\) 299.500 + 518.749i 0.479200 + 0.829999i
\(626\) 358.503 + 206.982i 0.572689 + 0.330642i
\(627\) 0 0
\(628\) −72.0000 + 41.5692i −0.114650 + 0.0661930i
\(629\) 230.252i 0.366060i
\(630\) 0 0
\(631\) −58.0000 −0.0919176 −0.0459588 0.998943i \(-0.514634\pi\)
−0.0459588 + 0.998943i \(0.514634\pi\)
\(632\) 57.9828 + 100.429i 0.0917449 + 0.158907i
\(633\) 0 0
\(634\) 168.000 290.985i 0.264984 0.458966i
\(635\) −886.712 + 511.943i −1.39640 + 0.806210i
\(636\) 0 0
\(637\) 73.5000 + 42.4352i 0.115385 + 0.0666173i
\(638\) −814.587 −1.27678
\(639\) 0 0
\(640\) −48.0000 27.7128i −0.0750000 0.0433013i
\(641\) −479.418 + 830.377i −0.747923 + 1.29544i 0.200894 + 0.979613i \(0.435615\pi\)
−0.948817 + 0.315827i \(0.897718\pi\)
\(642\) 0 0
\(643\) 760.370i 1.18254i −0.806475 0.591268i \(-0.798628\pi\)
0.806475 0.591268i \(-0.201372\pi\)
\(644\) 59.3970 + 102.879i 0.0922313 + 0.159749i
\(645\) 0 0
\(646\) 102.000 + 176.669i 0.157895 + 0.273482i
\(647\) −305.470 176.363i −0.472133 0.272586i 0.244999 0.969523i \(-0.421212\pi\)
−0.717132 + 0.696937i \(0.754546\pi\)
\(648\) 0 0
\(649\) −1224.00 + 706.677i −1.88598 + 1.08887i
\(650\) 2.44949i 0.00376845i
\(651\) 0 0
\(652\) 172.000 0.263804
\(653\) 220.617 + 382.120i 0.337852 + 0.585177i 0.984028 0.178011i \(-0.0569664\pi\)
−0.646177 + 0.763188i \(0.723633\pi\)
\(654\) 0 0
\(655\) −144.000 + 249.415i −0.219847 + 0.380787i
\(656\) −237.588 + 137.171i −0.362177 + 0.209103i
\(657\) 0 0
\(658\) 824.456i 1.25297i
\(659\) 161.220 0.244644 0.122322 0.992490i \(-0.460966\pi\)
0.122322 + 0.992490i \(0.460966\pi\)
\(660\) 0 0
\(661\) −721.500 416.558i −1.09153 0.630194i −0.157545 0.987512i \(-0.550358\pi\)
−0.933983 + 0.357318i \(0.883691\pi\)
\(662\) −130.815 + 226.578i −0.197605 + 0.342263i
\(663\) 0 0
\(664\) 13.8564i 0.0208681i
\(665\) −1009.75 −1.51842
\(666\) 0 0
\(667\) −144.000 249.415i −0.215892 0.373936i
\(668\) 313.955 + 181.262i 0.469993 + 0.271351i
\(669\) 0 0
\(670\) −186.000 + 107.387i −0.277612 + 0.160279i
\(671\) 1410.91i 2.10269i
\(672\) 0 0
\(673\) −263.000 −0.390788 −0.195394 0.980725i \(-0.562598\pi\)
−0.195394 + 0.980725i \(0.562598\pi\)
\(674\) −253.851 439.683i −0.376634 0.652349i
\(675\) 0 0
\(676\) −166.000 + 287.520i −0.245562 + 0.425326i
\(677\) 432.749 249.848i 0.639216 0.369052i −0.145096 0.989418i \(-0.546349\pi\)
0.784313 + 0.620366i \(0.213016\pi\)
\(678\) 0 0
\(679\) −252.000 + 145.492i −0.371134 + 0.214274i
\(680\) 67.8823 0.0998268
\(681\) 0 0
\(682\) 252.000 + 145.492i 0.369501 + 0.213332i
\(683\) −479.418 + 830.377i −0.701930 + 1.21578i 0.265858 + 0.964012i \(0.414345\pi\)
−0.967788 + 0.251767i \(0.918988\pi\)
\(684\) 0 0
\(685\) 748.246i 1.09233i
\(686\) −242.538 420.087i −0.353553 0.612372i
\(687\) 0 0
\(688\) −62.0000 107.387i −0.0901163 0.156086i
\(689\) 114.551 + 66.1362i 0.166257 + 0.0959887i
\(690\) 0 0
\(691\) 1069.50 617.476i 1.54776 0.893598i 0.549444 0.835530i \(-0.314839\pi\)
0.998313 0.0580674i \(-0.0184938\pi\)
\(692\) 88.1816i 0.127430i
\(693\) 0 0
\(694\) 660.000 0.951009
\(695\) 479.418 + 830.377i 0.689811 + 1.19479i
\(696\) 0 0
\(697\) 168.000 290.985i 0.241033 0.417481i
\(698\) −712.764 + 411.514i −1.02115 + 0.589562i
\(699\) 0 0
\(700\) 7.00000 12.1244i 0.0100000 0.0173205i
\(701\) −975.807 −1.39202 −0.696011 0.718031i \(-0.745044\pi\)
−0.696011 + 0.718031i \(0.745044\pi\)
\(702\) 0 0
\(703\) 1198.50 + 691.954i 1.70484 + 0.984288i
\(704\) −67.8823 + 117.576i −0.0964237 + 0.167011i
\(705\) 0 0
\(706\) 408.764i 0.578986i
\(707\) 1234.54i 1.74617i
\(708\) 0 0
\(709\) 553.000 + 957.824i 0.779972 + 1.35095i 0.931957 + 0.362568i \(0.118100\pi\)
−0.151986 + 0.988383i \(0.548567\pi\)
\(710\) 356.382 + 205.757i 0.501946 + 0.289799i
\(711\) 0 0
\(712\) 144.000 83.1384i 0.202247 0.116767i
\(713\) 102.879i 0.144290i
\(714\) 0 0
\(715\) −144.000 −0.201399
\(716\) −8.48528 14.6969i −0.0118510 0.0205265i
\(717\) 0 0
\(718\) −240.000 + 415.692i −0.334262 + 0.578958i
\(719\) −593.970 + 342.929i −0.826105 + 0.476952i −0.852517 0.522699i \(-0.824925\pi\)
0.0264120 + 0.999651i \(0.491592\pi\)
\(720\) 0 0
\(721\) −178.500 103.057i −0.247573 0.142936i
\(722\) 715.592 0.991125
\(723\) 0 0
\(724\) −75.0000 43.3013i −0.103591 0.0598084i
\(725\) −16.9706 + 29.3939i −0.0234077 + 0.0405433i
\(726\) 0 0
\(727\) 427.817i 0.588468i −0.955733 0.294234i \(-0.904935\pi\)
0.955733 0.294234i \(-0.0950646\pi\)
\(728\) −29.6985 + 17.1464i −0.0407946 + 0.0235528i
\(729\) 0 0
\(730\) 282.000 + 488.438i 0.386301 + 0.669094i
\(731\) 131.522 + 75.9342i 0.179920 + 0.103877i
\(732\) 0 0
\(733\) 34.5000 19.9186i 0.0470668 0.0271741i −0.476282 0.879293i \(-0.658016\pi\)
0.523349 + 0.852119i \(0.324682\pi\)
\(734\) 218.005i 0.297009i
\(735\) 0 0
\(736\) −48.0000 −0.0652174
\(737\) 263.044 + 455.605i 0.356911 + 0.618189i
\(738\) 0 0
\(739\) 243.500 421.754i 0.329499 0.570710i −0.652913 0.757433i \(-0.726453\pi\)
0.982413 + 0.186723i \(0.0597867\pi\)
\(740\) 398.808 230.252i 0.538930 0.311151i
\(741\) 0 0
\(742\) −378.000 654.715i −0.509434 0.882366i
\(743\) 509.117 0.685218 0.342609 0.939478i \(-0.388689\pi\)
0.342609 + 0.939478i \(0.388689\pi\)
\(744\) 0 0
\(745\) −216.000 124.708i −0.289933 0.167393i
\(746\) −204.354 + 353.951i −0.273933 + 0.474466i
\(747\) 0 0
\(748\) 166.277i 0.222295i
\(749\) 504.874 874.468i 0.674064 1.16751i
\(750\) 0 0
\(751\) 272.500 + 471.984i 0.362850 + 0.628474i 0.988429 0.151687i \(-0.0484706\pi\)
−0.625579 + 0.780161i \(0.715137\pi\)
\(752\) −288.500 166.565i −0.383643 0.221496i
\(753\) 0 0
\(754\) 72.0000 41.5692i 0.0954907 0.0551316i
\(755\) 48.9898i 0.0648871i
\(756\) 0 0
\(757\) −770.000 −1.01717 −0.508587 0.861011i \(-0.669832\pi\)
−0.508587 + 0.861011i \(0.669832\pi\)
\(758\) 4.94975 + 8.57321i 0.00653001 + 0.0113103i
\(759\) 0 0
\(760\) 204.000 353.338i 0.268421 0.464919i
\(761\) −148.492 + 85.7321i −0.195128 + 0.112657i −0.594381 0.804184i \(-0.702603\pi\)
0.399253 + 0.916841i \(0.369270\pi\)
\(762\) 0 0
\(763\) −1183.00 −1.55046
\(764\) −152.735 −0.199915
\(765\) 0 0
\(766\) −606.000 349.874i −0.791123 0.456755i
\(767\) 72.1249 124.924i 0.0940351 0.162874i
\(768\) 0 0
\(769\) 704.945i 0.916703i 0.888771 + 0.458352i \(0.151560\pi\)
−0.888771 + 0.458352i \(0.848440\pi\)
\(770\) 712.764 + 411.514i 0.925667 + 0.534434i
\(771\) 0 0
\(772\) 287.000 + 497.099i 0.371762 + 0.643910i
\(773\) −797.616 460.504i −1.03185 0.595736i −0.114333 0.993443i \(-0.536473\pi\)
−0.917513 + 0.397706i \(0.869806\pi\)
\(774\) 0 0
\(775\) 10.5000 6.06218i 0.0135484 0.00782216i
\(776\) 117.576i 0.151515i
\(777\) 0 0
\(778\) −324.000 −0.416452
\(779\) −1009.75 1748.94i −1.29621 2.24510i
\(780\) 0 0
\(781\) 504.000 872.954i 0.645327 1.11774i
\(782\) 50.9117 29.3939i 0.0651045 0.0375881i
\(783\) 0 0
\(784\) 196.000 0.250000
\(785\) −203.647 −0.259423
\(786\) 0 0
\(787\) 396.000 + 228.631i 0.503177 + 0.290509i 0.730024 0.683421i \(-0.239509\pi\)
−0.226848 + 0.973930i \(0.572842\pi\)