Properties

Label 1260.2.c.e.811.2
Level $1260$
Weight $2$
Character 1260.811
Analytic conductor $10.061$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + 24 x^{7} - 28 x^{6} + 16 x^{5} + 48 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 811.2
Root \(1.40936 + 0.117062i\) of defining polynomial
Character \(\chi\) \(=\) 1260.811
Dual form 1260.2.c.e.811.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.40936 + 0.117062i) q^{2} +(1.97259 - 0.329965i) q^{4} +1.00000i q^{5} +(-0.776136 + 2.52935i) q^{7} +(-2.74147 + 0.695955i) q^{8} +O(q^{10})\) \(q+(-1.40936 + 0.117062i) q^{2} +(1.97259 - 0.329965i) q^{4} +1.00000i q^{5} +(-0.776136 + 2.52935i) q^{7} +(-2.74147 + 0.695955i) q^{8} +(-0.117062 - 1.40936i) q^{10} -0.556350i q^{11} +0.182384i q^{13} +(0.797764 - 3.65562i) q^{14} +(3.78225 - 1.30177i) q^{16} +2.39449i q^{17} -3.08109 q^{19} +(0.329965 + 1.97259i) q^{20} +(0.0651274 + 0.784098i) q^{22} +3.94362i q^{23} -1.00000 q^{25} +(-0.0213502 - 0.257045i) q^{26} +(-0.696403 + 5.24548i) q^{28} +3.20026 q^{29} -5.68747 q^{31} +(-5.17816 + 2.27742i) q^{32} +(-0.280303 - 3.37469i) q^{34} +(-2.52935 - 0.776136i) q^{35} -4.98180 q^{37} +(4.34237 - 0.360678i) q^{38} +(-0.695955 - 2.74147i) q^{40} -9.64809i q^{41} -0.643697i q^{43} +(-0.183576 - 1.09745i) q^{44} +(-0.461647 - 5.55798i) q^{46} -3.63668 q^{47} +(-5.79523 - 3.92624i) q^{49} +(1.40936 - 0.117062i) q^{50} +(0.0601803 + 0.359769i) q^{52} +6.97060 q^{53} +0.556350 q^{55} +(0.367437 - 7.47429i) q^{56} +(-4.51031 + 0.374628i) q^{58} -8.79962 q^{59} +14.3787i q^{61} +(8.01569 - 0.665786i) q^{62} +(7.03129 - 3.81588i) q^{64} -0.182384 q^{65} +10.0692i q^{67} +(0.790096 + 4.72335i) q^{68} +(3.65562 + 0.797764i) q^{70} +1.36136i q^{71} -10.1087i q^{73} +(7.02115 - 0.583179i) q^{74} +(-6.07774 + 1.01665i) q^{76} +(1.40721 + 0.431803i) q^{77} -13.0596i q^{79} +(1.30177 + 3.78225i) q^{80} +(1.12942 + 13.5976i) q^{82} -9.45272 q^{83} -2.39449 q^{85} +(0.0753523 + 0.907200i) q^{86} +(0.387195 + 1.52522i) q^{88} +8.01600i q^{89} +(-0.461313 - 0.141555i) q^{91} +(1.30125 + 7.77915i) q^{92} +(5.12540 - 0.425717i) q^{94} -3.08109i q^{95} -0.445387i q^{97} +(8.62718 + 4.85508i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} + O(q^{10}) \) \( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40936 + 0.117062i −0.996568 + 0.0827753i
\(3\) 0 0
\(4\) 1.97259 0.329965i 0.986297 0.164982i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −0.776136 + 2.52935i −0.293352 + 0.956005i
\(8\) −2.74147 + 0.695955i −0.969255 + 0.246057i
\(9\) 0 0
\(10\) −0.117062 1.40936i −0.0370182 0.445679i
\(11\) 0.556350i 0.167746i −0.996476 0.0838730i \(-0.973271\pi\)
0.996476 0.0838730i \(-0.0267290\pi\)
\(12\) 0 0
\(13\) 0.182384i 0.0505842i 0.999680 + 0.0252921i \(0.00805158\pi\)
−0.999680 + 0.0252921i \(0.991948\pi\)
\(14\) 0.797764 3.65562i 0.213211 0.977006i
\(15\) 0 0
\(16\) 3.78225 1.30177i 0.945562 0.325443i
\(17\) 2.39449i 0.580748i 0.956913 + 0.290374i \(0.0937797\pi\)
−0.956913 + 0.290374i \(0.906220\pi\)
\(18\) 0 0
\(19\) −3.08109 −0.706851 −0.353425 0.935463i \(-0.614983\pi\)
−0.353425 + 0.935463i \(0.614983\pi\)
\(20\) 0.329965 + 1.97259i 0.0737824 + 0.441085i
\(21\) 0 0
\(22\) 0.0651274 + 0.784098i 0.0138852 + 0.167170i
\(23\) 3.94362i 0.822301i 0.911568 + 0.411150i \(0.134873\pi\)
−0.911568 + 0.411150i \(0.865127\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −0.0213502 0.257045i −0.00418712 0.0504106i
\(27\) 0 0
\(28\) −0.696403 + 5.24548i −0.131608 + 0.991302i
\(29\) 3.20026 0.594273 0.297136 0.954835i \(-0.403968\pi\)
0.297136 + 0.954835i \(0.403968\pi\)
\(30\) 0 0
\(31\) −5.68747 −1.02150 −0.510750 0.859729i \(-0.670632\pi\)
−0.510750 + 0.859729i \(0.670632\pi\)
\(32\) −5.17816 + 2.27742i −0.915378 + 0.402595i
\(33\) 0 0
\(34\) −0.280303 3.37469i −0.0480716 0.578755i
\(35\) −2.52935 0.776136i −0.427538 0.131191i
\(36\) 0 0
\(37\) −4.98180 −0.819002 −0.409501 0.912310i \(-0.634297\pi\)
−0.409501 + 0.912310i \(0.634297\pi\)
\(38\) 4.34237 0.360678i 0.704425 0.0585098i
\(39\) 0 0
\(40\) −0.695955 2.74147i −0.110040 0.433464i
\(41\) 9.64809i 1.50678i −0.657575 0.753389i \(-0.728418\pi\)
0.657575 0.753389i \(-0.271582\pi\)
\(42\) 0 0
\(43\) 0.643697i 0.0981628i −0.998795 0.0490814i \(-0.984371\pi\)
0.998795 0.0490814i \(-0.0156294\pi\)
\(44\) −0.183576 1.09745i −0.0276751 0.165447i
\(45\) 0 0
\(46\) −0.461647 5.55798i −0.0680662 0.819479i
\(47\) −3.63668 −0.530465 −0.265232 0.964184i \(-0.585449\pi\)
−0.265232 + 0.964184i \(0.585449\pi\)
\(48\) 0 0
\(49\) −5.79523 3.92624i −0.827890 0.560891i
\(50\) 1.40936 0.117062i 0.199314 0.0165551i
\(51\) 0 0
\(52\) 0.0601803 + 0.359769i 0.00834550 + 0.0498910i
\(53\) 6.97060 0.957485 0.478743 0.877955i \(-0.341093\pi\)
0.478743 + 0.877955i \(0.341093\pi\)
\(54\) 0 0
\(55\) 0.556350 0.0750183
\(56\) 0.367437 7.47429i 0.0491009 0.998794i
\(57\) 0 0
\(58\) −4.51031 + 0.374628i −0.592233 + 0.0491911i
\(59\) −8.79962 −1.14561 −0.572807 0.819691i \(-0.694145\pi\)
−0.572807 + 0.819691i \(0.694145\pi\)
\(60\) 0 0
\(61\) 14.3787i 1.84100i 0.390743 + 0.920500i \(0.372218\pi\)
−0.390743 + 0.920500i \(0.627782\pi\)
\(62\) 8.01569 0.665786i 1.01799 0.0845549i
\(63\) 0 0
\(64\) 7.03129 3.81588i 0.878912 0.476984i
\(65\) −0.182384 −0.0226219
\(66\) 0 0
\(67\) 10.0692i 1.23015i 0.788467 + 0.615077i \(0.210875\pi\)
−0.788467 + 0.615077i \(0.789125\pi\)
\(68\) 0.790096 + 4.72335i 0.0958132 + 0.572790i
\(69\) 0 0
\(70\) 3.65562 + 0.797764i 0.436930 + 0.0953511i
\(71\) 1.36136i 0.161564i 0.996732 + 0.0807821i \(0.0257418\pi\)
−0.996732 + 0.0807821i \(0.974258\pi\)
\(72\) 0 0
\(73\) 10.1087i 1.18314i −0.806255 0.591569i \(-0.798509\pi\)
0.806255 0.591569i \(-0.201491\pi\)
\(74\) 7.02115 0.583179i 0.816192 0.0677931i
\(75\) 0 0
\(76\) −6.07774 + 1.01665i −0.697164 + 0.116618i
\(77\) 1.40721 + 0.431803i 0.160366 + 0.0492086i
\(78\) 0 0
\(79\) 13.0596i 1.46932i −0.678438 0.734658i \(-0.737343\pi\)
0.678438 0.734658i \(-0.262657\pi\)
\(80\) 1.30177 + 3.78225i 0.145543 + 0.422868i
\(81\) 0 0
\(82\) 1.12942 + 13.5976i 0.124724 + 1.50161i
\(83\) −9.45272 −1.03757 −0.518785 0.854905i \(-0.673616\pi\)
−0.518785 + 0.854905i \(0.673616\pi\)
\(84\) 0 0
\(85\) −2.39449 −0.259718
\(86\) 0.0753523 + 0.907200i 0.00812545 + 0.0978259i
\(87\) 0 0
\(88\) 0.387195 + 1.52522i 0.0412751 + 0.162589i
\(89\) 8.01600i 0.849694i 0.905265 + 0.424847i \(0.139672\pi\)
−0.905265 + 0.424847i \(0.860328\pi\)
\(90\) 0 0
\(91\) −0.461313 0.141555i −0.0483587 0.0148390i
\(92\) 1.30125 + 7.77915i 0.135665 + 0.811032i
\(93\) 0 0
\(94\) 5.12540 0.425717i 0.528645 0.0439094i
\(95\) 3.08109i 0.316113i
\(96\) 0 0
\(97\) 0.445387i 0.0452222i −0.999744 0.0226111i \(-0.992802\pi\)
0.999744 0.0226111i \(-0.00719796\pi\)
\(98\) 8.62718 + 4.85508i 0.871476 + 0.490437i
\(99\) 0 0
\(100\) −1.97259 + 0.329965i −0.197259 + 0.0329965i
\(101\) 12.8540i 1.27902i −0.768781 0.639512i \(-0.779136\pi\)
0.768781 0.639512i \(-0.220864\pi\)
\(102\) 0 0
\(103\) −14.3031 −1.40933 −0.704664 0.709542i \(-0.748902\pi\)
−0.704664 + 0.709542i \(0.748902\pi\)
\(104\) −0.126931 0.500000i −0.0124466 0.0490290i
\(105\) 0 0
\(106\) −9.82408 + 0.815991i −0.954199 + 0.0792561i
\(107\) 18.3230i 1.77136i 0.464301 + 0.885678i \(0.346306\pi\)
−0.464301 + 0.885678i \(0.653694\pi\)
\(108\) 0 0
\(109\) −4.03790 −0.386760 −0.193380 0.981124i \(-0.561945\pi\)
−0.193380 + 0.981124i \(0.561945\pi\)
\(110\) −0.784098 + 0.0651274i −0.0747608 + 0.00620966i
\(111\) 0 0
\(112\) 0.357103 + 10.5770i 0.0337430 + 0.999431i
\(113\) −3.14680 −0.296026 −0.148013 0.988985i \(-0.547288\pi\)
−0.148013 + 0.988985i \(0.547288\pi\)
\(114\) 0 0
\(115\) −3.94362 −0.367744
\(116\) 6.31280 1.05597i 0.586129 0.0980445i
\(117\) 0 0
\(118\) 12.4018 1.03010i 1.14168 0.0948284i
\(119\) −6.05649 1.85845i −0.555198 0.170363i
\(120\) 0 0
\(121\) 10.6905 0.971861
\(122\) −1.68319 20.2647i −0.152389 1.83468i
\(123\) 0 0
\(124\) −11.2191 + 1.87666i −1.00750 + 0.168529i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 11.8445i 1.05103i 0.850784 + 0.525516i \(0.176128\pi\)
−0.850784 + 0.525516i \(0.823872\pi\)
\(128\) −9.46293 + 6.20104i −0.836413 + 0.548100i
\(129\) 0 0
\(130\) 0.257045 0.0213502i 0.0225443 0.00187254i
\(131\) −16.6337 −1.45329 −0.726647 0.687011i \(-0.758922\pi\)
−0.726647 + 0.687011i \(0.758922\pi\)
\(132\) 0 0
\(133\) 2.39134 7.79316i 0.207356 0.675753i
\(134\) −1.17872 14.1912i −0.101826 1.22593i
\(135\) 0 0
\(136\) −1.66645 6.56441i −0.142897 0.562893i
\(137\) −9.88658 −0.844667 −0.422334 0.906440i \(-0.638789\pi\)
−0.422334 + 0.906440i \(0.638789\pi\)
\(138\) 0 0
\(139\) −20.5861 −1.74609 −0.873047 0.487636i \(-0.837859\pi\)
−0.873047 + 0.487636i \(0.837859\pi\)
\(140\) −5.24548 0.696403i −0.443324 0.0588568i
\(141\) 0 0
\(142\) −0.159364 1.91865i −0.0133735 0.161010i
\(143\) 0.101469 0.00848529
\(144\) 0 0
\(145\) 3.20026i 0.265767i
\(146\) 1.18335 + 14.2468i 0.0979345 + 1.17908i
\(147\) 0 0
\(148\) −9.82706 + 1.64382i −0.807779 + 0.135121i
\(149\) −7.28607 −0.596898 −0.298449 0.954426i \(-0.596469\pi\)
−0.298449 + 0.954426i \(0.596469\pi\)
\(150\) 0 0
\(151\) 15.1807i 1.23539i 0.786418 + 0.617694i \(0.211933\pi\)
−0.786418 + 0.617694i \(0.788067\pi\)
\(152\) 8.44671 2.14430i 0.685119 0.173926i
\(153\) 0 0
\(154\) −2.03381 0.443836i −0.163889 0.0357654i
\(155\) 5.68747i 0.456829i
\(156\) 0 0
\(157\) 10.7177i 0.855366i −0.903929 0.427683i \(-0.859330\pi\)
0.903929 0.427683i \(-0.140670\pi\)
\(158\) 1.52878 + 18.4056i 0.121623 + 1.46427i
\(159\) 0 0
\(160\) −2.27742 5.17816i −0.180046 0.409370i
\(161\) −9.97479 3.06078i −0.786123 0.241223i
\(162\) 0 0
\(163\) 20.7486i 1.62515i −0.582853 0.812577i \(-0.698064\pi\)
0.582853 0.812577i \(-0.301936\pi\)
\(164\) −3.18353 19.0318i −0.248592 1.48613i
\(165\) 0 0
\(166\) 13.3223 1.10655i 1.03401 0.0858852i
\(167\) −8.37483 −0.648064 −0.324032 0.946046i \(-0.605039\pi\)
−0.324032 + 0.946046i \(0.605039\pi\)
\(168\) 0 0
\(169\) 12.9667 0.997441
\(170\) 3.37469 0.280303i 0.258827 0.0214983i
\(171\) 0 0
\(172\) −0.212397 1.26975i −0.0161951 0.0968176i
\(173\) 21.8554i 1.66163i 0.556546 + 0.830817i \(0.312126\pi\)
−0.556546 + 0.830817i \(0.687874\pi\)
\(174\) 0 0
\(175\) 0.776136 2.52935i 0.0586703 0.191201i
\(176\) −0.724242 2.10425i −0.0545918 0.158614i
\(177\) 0 0
\(178\) −0.938368 11.2974i −0.0703337 0.846778i
\(179\) 18.3538i 1.37182i −0.727684 0.685912i \(-0.759403\pi\)
0.727684 0.685912i \(-0.240597\pi\)
\(180\) 0 0
\(181\) 12.7452i 0.947341i 0.880702 + 0.473670i \(0.157071\pi\)
−0.880702 + 0.473670i \(0.842929\pi\)
\(182\) 0.666726 + 0.145499i 0.0494211 + 0.0107851i
\(183\) 0 0
\(184\) −2.74458 10.8113i −0.202333 0.797019i
\(185\) 4.98180i 0.366269i
\(186\) 0 0
\(187\) 1.33217 0.0974181
\(188\) −7.17370 + 1.19998i −0.523196 + 0.0875174i
\(189\) 0 0
\(190\) 0.360678 + 4.34237i 0.0261664 + 0.315028i
\(191\) 21.4663i 1.55324i 0.629967 + 0.776622i \(0.283068\pi\)
−0.629967 + 0.776622i \(0.716932\pi\)
\(192\) 0 0
\(193\) 5.27923 0.380008 0.190004 0.981783i \(-0.439150\pi\)
0.190004 + 0.981783i \(0.439150\pi\)
\(194\) 0.0521379 + 0.627711i 0.00374328 + 0.0450670i
\(195\) 0 0
\(196\) −12.7271 5.83265i −0.909082 0.416618i
\(197\) 8.44807 0.601900 0.300950 0.953640i \(-0.402696\pi\)
0.300950 + 0.953640i \(0.402696\pi\)
\(198\) 0 0
\(199\) 18.5300 1.31356 0.656778 0.754084i \(-0.271919\pi\)
0.656778 + 0.754084i \(0.271919\pi\)
\(200\) 2.74147 0.695955i 0.193851 0.0492114i
\(201\) 0 0
\(202\) 1.50472 + 18.1160i 0.105872 + 1.27463i
\(203\) −2.48383 + 8.09457i −0.174331 + 0.568127i
\(204\) 0 0
\(205\) 9.64809 0.673852
\(206\) 20.1582 1.67435i 1.40449 0.116657i
\(207\) 0 0
\(208\) 0.237422 + 0.689821i 0.0164623 + 0.0478305i
\(209\) 1.71417i 0.118571i
\(210\) 0 0
\(211\) 17.4456i 1.20101i 0.799622 + 0.600504i \(0.205033\pi\)
−0.799622 + 0.600504i \(0.794967\pi\)
\(212\) 13.7502 2.30005i 0.944364 0.157968i
\(213\) 0 0
\(214\) −2.14493 25.8238i −0.146624 1.76528i
\(215\) 0.643697 0.0438997
\(216\) 0 0
\(217\) 4.41425 14.3856i 0.299659 0.976558i
\(218\) 5.69085 0.472684i 0.385433 0.0320142i
\(219\) 0 0
\(220\) 1.09745 0.183576i 0.0739903 0.0123767i
\(221\) −0.436716 −0.0293767
\(222\) 0 0
\(223\) 11.9173 0.798038 0.399019 0.916943i \(-0.369351\pi\)
0.399019 + 0.916943i \(0.369351\pi\)
\(224\) −1.74145 14.8650i −0.116355 0.993208i
\(225\) 0 0
\(226\) 4.43498 0.368371i 0.295010 0.0245037i
\(227\) −2.13795 −0.141901 −0.0709505 0.997480i \(-0.522603\pi\)
−0.0709505 + 0.997480i \(0.522603\pi\)
\(228\) 0 0
\(229\) 7.10530i 0.469531i 0.972052 + 0.234766i \(0.0754323\pi\)
−0.972052 + 0.234766i \(0.924568\pi\)
\(230\) 5.55798 0.461647i 0.366482 0.0304401i
\(231\) 0 0
\(232\) −8.77340 + 2.22723i −0.576002 + 0.146225i
\(233\) −10.8641 −0.711732 −0.355866 0.934537i \(-0.615814\pi\)
−0.355866 + 0.934537i \(0.615814\pi\)
\(234\) 0 0
\(235\) 3.63668i 0.237231i
\(236\) −17.3581 + 2.90357i −1.12991 + 0.189006i
\(237\) 0 0
\(238\) 8.75333 + 1.91023i 0.567394 + 0.123822i
\(239\) 15.3760i 0.994592i −0.867581 0.497296i \(-0.834326\pi\)
0.867581 0.497296i \(-0.165674\pi\)
\(240\) 0 0
\(241\) 0.518574i 0.0334043i −0.999861 0.0167022i \(-0.994683\pi\)
0.999861 0.0167022i \(-0.00531671\pi\)
\(242\) −15.0667 + 1.25145i −0.968526 + 0.0804461i
\(243\) 0 0
\(244\) 4.74445 + 28.3633i 0.303733 + 1.81577i
\(245\) 3.92624 5.79523i 0.250838 0.370243i
\(246\) 0 0
\(247\) 0.561941i 0.0357555i
\(248\) 15.5920 3.95822i 0.990094 0.251347i
\(249\) 0 0
\(250\) 0.117062 + 1.40936i 0.00740364 + 0.0891358i
\(251\) 19.8979 1.25594 0.627972 0.778236i \(-0.283885\pi\)
0.627972 + 0.778236i \(0.283885\pi\)
\(252\) 0 0
\(253\) 2.19403 0.137938
\(254\) −1.38654 16.6932i −0.0869995 1.04743i
\(255\) 0 0
\(256\) 12.6108 9.84725i 0.788174 0.615453i
\(257\) 30.1252i 1.87916i 0.342335 + 0.939578i \(0.388782\pi\)
−0.342335 + 0.939578i \(0.611218\pi\)
\(258\) 0 0
\(259\) 3.86655 12.6007i 0.240256 0.782970i
\(260\) −0.359769 + 0.0601803i −0.0223119 + 0.00373222i
\(261\) 0 0
\(262\) 23.4429 1.94717i 1.44831 0.120297i
\(263\) 4.44397i 0.274027i −0.990569 0.137013i \(-0.956250\pi\)
0.990569 0.137013i \(-0.0437503\pi\)
\(264\) 0 0
\(265\) 6.97060i 0.428200i
\(266\) −2.45798 + 11.2633i −0.150709 + 0.690597i
\(267\) 0 0
\(268\) 3.32250 + 19.8625i 0.202954 + 1.21330i
\(269\) 8.40266i 0.512319i −0.966634 0.256160i \(-0.917543\pi\)
0.966634 0.256160i \(-0.0824573\pi\)
\(270\) 0 0
\(271\) 28.7730 1.74783 0.873916 0.486077i \(-0.161572\pi\)
0.873916 + 0.486077i \(0.161572\pi\)
\(272\) 3.11708 + 9.05653i 0.189000 + 0.549133i
\(273\) 0 0
\(274\) 13.9338 1.15734i 0.841769 0.0699176i
\(275\) 0.556350i 0.0335492i
\(276\) 0 0
\(277\) −3.93122 −0.236204 −0.118102 0.993001i \(-0.537681\pi\)
−0.118102 + 0.993001i \(0.537681\pi\)
\(278\) 29.0133 2.40985i 1.74010 0.144533i
\(279\) 0 0
\(280\) 7.47429 + 0.367437i 0.446674 + 0.0219586i
\(281\) −17.8653 −1.06575 −0.532876 0.846193i \(-0.678889\pi\)
−0.532876 + 0.846193i \(0.678889\pi\)
\(282\) 0 0
\(283\) −4.34129 −0.258063 −0.129031 0.991641i \(-0.541187\pi\)
−0.129031 + 0.991641i \(0.541187\pi\)
\(284\) 0.449202 + 2.68542i 0.0266552 + 0.159350i
\(285\) 0 0
\(286\) −0.143007 + 0.0118782i −0.00845617 + 0.000702372i
\(287\) 24.4034 + 7.48823i 1.44049 + 0.442016i
\(288\) 0 0
\(289\) 11.2664 0.662732
\(290\) −0.374628 4.51031i −0.0219989 0.264855i
\(291\) 0 0
\(292\) −3.33553 19.9404i −0.195197 1.16692i
\(293\) 0.535106i 0.0312612i 0.999878 + 0.0156306i \(0.00497558\pi\)
−0.999878 + 0.0156306i \(0.995024\pi\)
\(294\) 0 0
\(295\) 8.79962i 0.512334i
\(296\) 13.6574 3.46711i 0.793822 0.201521i
\(297\) 0 0
\(298\) 10.2687 0.852922i 0.594850 0.0494084i
\(299\) −0.719252 −0.0415954
\(300\) 0 0
\(301\) 1.62813 + 0.499596i 0.0938441 + 0.0287962i
\(302\) −1.77708 21.3951i −0.102260 1.23115i
\(303\) 0 0
\(304\) −11.6534 + 4.01088i −0.668371 + 0.230040i
\(305\) −14.3787 −0.823320
\(306\) 0 0
\(307\) 20.4818 1.16896 0.584478 0.811409i \(-0.301299\pi\)
0.584478 + 0.811409i \(0.301299\pi\)
\(308\) 2.91832 + 0.387444i 0.166287 + 0.0220767i
\(309\) 0 0
\(310\) 0.665786 + 8.01569i 0.0378141 + 0.455261i
\(311\) 29.6598 1.68185 0.840927 0.541149i \(-0.182010\pi\)
0.840927 + 0.541149i \(0.182010\pi\)
\(312\) 0 0
\(313\) 11.7015i 0.661406i 0.943735 + 0.330703i \(0.107286\pi\)
−0.943735 + 0.330703i \(0.892714\pi\)
\(314\) 1.25464 + 15.1051i 0.0708032 + 0.852431i
\(315\) 0 0
\(316\) −4.30920 25.7612i −0.242411 1.44918i
\(317\) 16.0488 0.901388 0.450694 0.892678i \(-0.351177\pi\)
0.450694 + 0.892678i \(0.351177\pi\)
\(318\) 0 0
\(319\) 1.78046i 0.0996868i
\(320\) 3.81588 + 7.03129i 0.213314 + 0.393061i
\(321\) 0 0
\(322\) 14.4164 + 3.14608i 0.803393 + 0.175324i
\(323\) 7.37763i 0.410502i
\(324\) 0 0
\(325\) 0.182384i 0.0101168i
\(326\) 2.42887 + 29.2422i 0.134523 + 1.61958i
\(327\) 0 0
\(328\) 6.71464 + 26.4499i 0.370754 + 1.46045i
\(329\) 2.82256 9.19845i 0.155613 0.507127i
\(330\) 0 0
\(331\) 10.9660i 0.602746i 0.953506 + 0.301373i \(0.0974450\pi\)
−0.953506 + 0.301373i \(0.902555\pi\)
\(332\) −18.6464 + 3.11906i −1.02335 + 0.171181i
\(333\) 0 0
\(334\) 11.8032 0.980374i 0.645840 0.0536437i
\(335\) −10.0692 −0.550142
\(336\) 0 0
\(337\) −7.87907 −0.429200 −0.214600 0.976702i \(-0.568845\pi\)
−0.214600 + 0.976702i \(0.568845\pi\)
\(338\) −18.2748 + 1.51791i −0.994018 + 0.0825635i
\(339\) 0 0
\(340\) −4.72335 + 0.790096i −0.256159 + 0.0428490i
\(341\) 3.16423i 0.171352i
\(342\) 0 0
\(343\) 14.4287 11.6109i 0.779077 0.626928i
\(344\) 0.447984 + 1.76467i 0.0241537 + 0.0951448i
\(345\) 0 0
\(346\) −2.55843 30.8021i −0.137542 1.65593i
\(347\) 14.2548i 0.765240i −0.923906 0.382620i \(-0.875022\pi\)
0.923906 0.382620i \(-0.124978\pi\)
\(348\) 0 0
\(349\) 6.69632i 0.358446i −0.983809 0.179223i \(-0.942642\pi\)
0.983809 0.179223i \(-0.0573583\pi\)
\(350\) −0.797764 + 3.65562i −0.0426423 + 0.195401i
\(351\) 0 0
\(352\) 1.26705 + 2.88087i 0.0675338 + 0.153551i
\(353\) 18.6741i 0.993920i −0.867773 0.496960i \(-0.834449\pi\)
0.867773 0.496960i \(-0.165551\pi\)
\(354\) 0 0
\(355\) −1.36136 −0.0722537
\(356\) 2.64500 + 15.8123i 0.140185 + 0.838051i
\(357\) 0 0
\(358\) 2.14853 + 25.8671i 0.113553 + 1.36712i
\(359\) 20.9659i 1.10654i −0.833003 0.553269i \(-0.813380\pi\)
0.833003 0.553269i \(-0.186620\pi\)
\(360\) 0 0
\(361\) −9.50688 −0.500362
\(362\) −1.49197 17.9625i −0.0784164 0.944090i
\(363\) 0 0
\(364\) −0.956690 0.127013i −0.0501442 0.00665727i
\(365\) 10.1087 0.529115
\(366\) 0 0
\(367\) 21.4633 1.12038 0.560189 0.828365i \(-0.310729\pi\)
0.560189 + 0.828365i \(0.310729\pi\)
\(368\) 5.13369 + 14.9157i 0.267612 + 0.777536i
\(369\) 0 0
\(370\) 0.583179 + 7.02115i 0.0303180 + 0.365012i
\(371\) −5.41013 + 17.6311i −0.280880 + 0.915360i
\(372\) 0 0
\(373\) −36.3356 −1.88139 −0.940693 0.339260i \(-0.889823\pi\)
−0.940693 + 0.339260i \(0.889823\pi\)
\(374\) −1.87751 + 0.155947i −0.0970838 + 0.00806381i
\(375\) 0 0
\(376\) 9.96985 2.53097i 0.514156 0.130525i
\(377\) 0.583675i 0.0300608i
\(378\) 0 0
\(379\) 11.1047i 0.570412i 0.958466 + 0.285206i \(0.0920621\pi\)
−0.958466 + 0.285206i \(0.907938\pi\)
\(380\) −1.01665 6.07774i −0.0521531 0.311781i
\(381\) 0 0
\(382\) −2.51288 30.2537i −0.128570 1.54791i
\(383\) 23.6321 1.20754 0.603772 0.797157i \(-0.293664\pi\)
0.603772 + 0.797157i \(0.293664\pi\)
\(384\) 0 0
\(385\) −0.431803 + 1.40721i −0.0220067 + 0.0717178i
\(386\) −7.44034 + 0.617997i −0.378704 + 0.0314552i
\(387\) 0 0
\(388\) −0.146962 0.878568i −0.00746087 0.0446025i
\(389\) 22.7913 1.15557 0.577783 0.816190i \(-0.303918\pi\)
0.577783 + 0.816190i \(0.303918\pi\)
\(390\) 0 0
\(391\) −9.44293 −0.477549
\(392\) 18.6199 + 6.73044i 0.940448 + 0.339939i
\(393\) 0 0
\(394\) −11.9064 + 0.988947i −0.599834 + 0.0498224i
\(395\) 13.0596 0.657098
\(396\) 0 0
\(397\) 10.5426i 0.529118i 0.964370 + 0.264559i \(0.0852264\pi\)
−0.964370 + 0.264559i \(0.914774\pi\)
\(398\) −26.1154 + 2.16916i −1.30905 + 0.108730i
\(399\) 0 0
\(400\) −3.78225 + 1.30177i −0.189112 + 0.0650886i
\(401\) 28.1602 1.40625 0.703126 0.711065i \(-0.251787\pi\)
0.703126 + 0.711065i \(0.251787\pi\)
\(402\) 0 0
\(403\) 1.03730i 0.0516717i
\(404\) −4.24138 25.3558i −0.211017 1.26150i
\(405\) 0 0
\(406\) 2.55305 11.6989i 0.126706 0.580608i
\(407\) 2.77163i 0.137384i
\(408\) 0 0
\(409\) 23.3091i 1.15256i −0.817253 0.576280i \(-0.804504\pi\)
0.817253 0.576280i \(-0.195496\pi\)
\(410\) −13.5976 + 1.12942i −0.671540 + 0.0557783i
\(411\) 0 0
\(412\) −28.2142 + 4.71952i −1.39001 + 0.232514i
\(413\) 6.82970 22.2573i 0.336068 1.09521i
\(414\) 0 0
\(415\) 9.45272i 0.464016i
\(416\) −0.415365 0.944413i −0.0203650 0.0463037i
\(417\) 0 0
\(418\) −0.200664 2.41588i −0.00981478 0.118164i
\(419\) 22.9252 1.11997 0.559984 0.828503i \(-0.310807\pi\)
0.559984 + 0.828503i \(0.310807\pi\)
\(420\) 0 0
\(421\) −30.2880 −1.47614 −0.738072 0.674722i \(-0.764264\pi\)
−0.738072 + 0.674722i \(0.764264\pi\)
\(422\) −2.04222 24.5872i −0.0994137 1.19689i
\(423\) 0 0
\(424\) −19.1097 + 4.85122i −0.928048 + 0.235596i
\(425\) 2.39449i 0.116150i
\(426\) 0 0
\(427\) −36.3687 11.1598i −1.76000 0.540060i
\(428\) 6.04596 + 36.1439i 0.292242 + 1.74708i
\(429\) 0 0
\(430\) −0.907200 + 0.0753523i −0.0437491 + 0.00363381i
\(431\) 17.6787i 0.851551i 0.904829 + 0.425776i \(0.139999\pi\)
−0.904829 + 0.425776i \(0.860001\pi\)
\(432\) 0 0
\(433\) 30.2797i 1.45515i 0.686029 + 0.727574i \(0.259352\pi\)
−0.686029 + 0.727574i \(0.740648\pi\)
\(434\) −4.53726 + 20.7912i −0.217795 + 0.998011i
\(435\) 0 0
\(436\) −7.96513 + 1.33236i −0.381460 + 0.0638086i
\(437\) 12.1506i 0.581244i
\(438\) 0 0
\(439\) 3.51474 0.167749 0.0838747 0.996476i \(-0.473270\pi\)
0.0838747 + 0.996476i \(0.473270\pi\)
\(440\) −1.52522 + 0.387195i −0.0727119 + 0.0184588i
\(441\) 0 0
\(442\) 0.615490 0.0511228i 0.0292759 0.00243166i
\(443\) 3.34004i 0.158690i −0.996847 0.0793450i \(-0.974717\pi\)
0.996847 0.0793450i \(-0.0252829\pi\)
\(444\) 0 0
\(445\) −8.01600 −0.379995
\(446\) −16.7957 + 1.39506i −0.795300 + 0.0660578i
\(447\) 0 0
\(448\) 4.19445 + 20.7462i 0.198169 + 0.980168i
\(449\) 30.3020 1.43004 0.715019 0.699105i \(-0.246418\pi\)
0.715019 + 0.699105i \(0.246418\pi\)
\(450\) 0 0
\(451\) −5.36772 −0.252756
\(452\) −6.20736 + 1.03833i −0.291970 + 0.0488391i
\(453\) 0 0
\(454\) 3.01315 0.250273i 0.141414 0.0117459i
\(455\) 0.141555 0.461313i 0.00663618 0.0216267i
\(456\) 0 0
\(457\) −7.65632 −0.358148 −0.179074 0.983836i \(-0.557310\pi\)
−0.179074 + 0.983836i \(0.557310\pi\)
\(458\) −0.831760 10.0139i −0.0388656 0.467920i
\(459\) 0 0
\(460\) −7.77915 + 1.30125i −0.362705 + 0.0606713i
\(461\) 7.75351i 0.361117i 0.983564 + 0.180559i \(0.0577905\pi\)
−0.983564 + 0.180559i \(0.942209\pi\)
\(462\) 0 0
\(463\) 21.4187i 0.995410i −0.867346 0.497705i \(-0.834176\pi\)
0.867346 0.497705i \(-0.165824\pi\)
\(464\) 12.1042 4.16600i 0.561921 0.193402i
\(465\) 0 0
\(466\) 15.3114 1.27177i 0.709289 0.0589138i
\(467\) 11.8414 0.547954 0.273977 0.961736i \(-0.411661\pi\)
0.273977 + 0.961736i \(0.411661\pi\)
\(468\) 0 0
\(469\) −25.4686 7.81510i −1.17603 0.360868i
\(470\) 0.425717 + 5.12540i 0.0196369 + 0.236417i
\(471\) 0 0
\(472\) 24.1239 6.12414i 1.11039 0.281886i
\(473\) −0.358121 −0.0164664
\(474\) 0 0
\(475\) 3.08109 0.141370
\(476\) −12.5602 1.66753i −0.575697 0.0764310i
\(477\) 0 0
\(478\) 1.79995 + 21.6704i 0.0823276 + 0.991179i
\(479\) −19.5650 −0.893948 −0.446974 0.894547i \(-0.647498\pi\)
−0.446974 + 0.894547i \(0.647498\pi\)
\(480\) 0 0
\(481\) 0.908600i 0.0414286i
\(482\) 0.0607053 + 0.730858i 0.00276505 + 0.0332897i
\(483\) 0 0
\(484\) 21.0880 3.52748i 0.958543 0.160340i
\(485\) 0.445387 0.0202240
\(486\) 0 0
\(487\) 2.69121i 0.121950i 0.998139 + 0.0609752i \(0.0194210\pi\)
−0.998139 + 0.0609752i \(0.980579\pi\)
\(488\) −10.0069 39.4187i −0.452991 1.78440i
\(489\) 0 0
\(490\) −4.85508 + 8.62718i −0.219330 + 0.389736i
\(491\) 0.816644i 0.0368546i −0.999830 0.0184273i \(-0.994134\pi\)
0.999830 0.0184273i \(-0.00586593\pi\)
\(492\) 0 0
\(493\) 7.66297i 0.345123i
\(494\) 0.0657819 + 0.791978i 0.00295967 + 0.0356328i
\(495\) 0 0
\(496\) −21.5114 + 7.40379i −0.965891 + 0.332440i
\(497\) −3.44337 1.05660i −0.154456 0.0473951i
\(498\) 0 0
\(499\) 6.19049i 0.277124i 0.990354 + 0.138562i \(0.0442481\pi\)
−0.990354 + 0.138562i \(0.955752\pi\)
\(500\) −0.329965 1.97259i −0.0147565 0.0882170i
\(501\) 0 0
\(502\) −28.0433 + 2.32928i −1.25163 + 0.103961i
\(503\) 23.4882 1.04729 0.523643 0.851938i \(-0.324573\pi\)
0.523643 + 0.851938i \(0.324573\pi\)
\(504\) 0 0
\(505\) 12.8540 0.571997
\(506\) −3.09218 + 0.256838i −0.137464 + 0.0114178i
\(507\) 0 0
\(508\) 3.90828 + 23.3644i 0.173402 + 1.03663i
\(509\) 31.9990i 1.41833i 0.705042 + 0.709165i \(0.250928\pi\)
−0.705042 + 0.709165i \(0.749072\pi\)
\(510\) 0 0
\(511\) 25.5685 + 7.84575i 1.13108 + 0.347075i
\(512\) −16.6204 + 15.3546i −0.734524 + 0.678582i
\(513\) 0 0
\(514\) −3.52651 42.4572i −0.155548 1.87271i
\(515\) 14.3031i 0.630270i
\(516\) 0 0
\(517\) 2.02327i 0.0889834i
\(518\) −3.97430 + 18.2116i −0.174621 + 0.800170i
\(519\) 0 0
\(520\) 0.500000 0.126931i 0.0219264 0.00556629i
\(521\) 38.3707i 1.68105i 0.541773 + 0.840525i \(0.317753\pi\)
−0.541773 + 0.840525i \(0.682247\pi\)
\(522\) 0 0
\(523\) −27.0855 −1.18437 −0.592183 0.805804i \(-0.701734\pi\)
−0.592183 + 0.805804i \(0.701734\pi\)
\(524\) −32.8115 + 5.48854i −1.43338 + 0.239768i
\(525\) 0 0
\(526\) 0.520219 + 6.26315i 0.0226826 + 0.273086i
\(527\) 13.6186i 0.593234i
\(528\) 0 0
\(529\) 7.44790 0.323822
\(530\) −0.815991 9.82408i −0.0354444 0.426731i
\(531\) 0 0
\(532\) 2.14568 16.1618i 0.0930271 0.700702i
\(533\) 1.75966 0.0762192
\(534\) 0 0
\(535\) −18.3230 −0.792174
\(536\) −7.00774 27.6045i −0.302688 1.19233i
\(537\) 0 0
\(538\) 0.983632 + 11.8424i 0.0424074 + 0.510561i
\(539\) −2.18436 + 3.22418i −0.0940872 + 0.138875i
\(540\) 0 0
\(541\) 12.3048 0.529024 0.264512 0.964382i \(-0.414789\pi\)
0.264512 + 0.964382i \(0.414789\pi\)
\(542\) −40.5515 + 3.36822i −1.74183 + 0.144677i
\(543\) 0 0
\(544\) −5.45326 12.3990i −0.233806 0.531604i
\(545\) 4.03790i 0.172964i
\(546\) 0 0
\(547\) 7.41113i 0.316877i −0.987369 0.158438i \(-0.949354\pi\)
0.987369 0.158438i \(-0.0506460\pi\)
\(548\) −19.5022 + 3.26222i −0.833093 + 0.139355i
\(549\) 0 0
\(550\) −0.0651274 0.784098i −0.00277704 0.0334341i
\(551\) −9.86028 −0.420062
\(552\) 0 0
\(553\) 33.0322 + 10.1360i 1.40467 + 0.431026i
\(554\) 5.54051 0.460196i 0.235394 0.0195519i
\(555\) 0 0
\(556\) −40.6081 + 6.79270i −1.72217 + 0.288075i
\(557\) 0.317738 0.0134630 0.00673149 0.999977i \(-0.497857\pi\)
0.00673149 + 0.999977i \(0.497857\pi\)
\(558\) 0 0
\(559\) 0.117400 0.00496549
\(560\) −10.5770 + 0.357103i −0.446959 + 0.0150903i
\(561\) 0 0
\(562\) 25.1786 2.09134i 1.06210 0.0882179i
\(563\) −2.50413 −0.105537 −0.0527683 0.998607i \(-0.516804\pi\)
−0.0527683 + 0.998607i \(0.516804\pi\)
\(564\) 0 0
\(565\) 3.14680i 0.132387i
\(566\) 6.11844 0.508200i 0.257177 0.0213612i
\(567\) 0 0
\(568\) −0.947448 3.73214i −0.0397540 0.156597i
\(569\) −25.4990 −1.06897 −0.534487 0.845177i \(-0.679495\pi\)
−0.534487 + 0.845177i \(0.679495\pi\)
\(570\) 0 0
\(571\) 43.8357i 1.83447i 0.398350 + 0.917233i \(0.369583\pi\)
−0.398350 + 0.917233i \(0.630417\pi\)
\(572\) 0.200158 0.0334813i 0.00836902 0.00139992i
\(573\) 0 0
\(574\) −35.2698 7.69690i −1.47213 0.321262i
\(575\) 3.94362i 0.164460i
\(576\) 0 0
\(577\) 4.18046i 0.174035i 0.996207 + 0.0870175i \(0.0277336\pi\)
−0.996207 + 0.0870175i \(0.972266\pi\)
\(578\) −15.8785 + 1.31887i −0.660457 + 0.0548578i
\(579\) 0 0
\(580\) 1.05597 + 6.31280i 0.0438468 + 0.262125i
\(581\) 7.33659 23.9092i 0.304373 0.991922i
\(582\) 0 0
\(583\) 3.87810i 0.160614i
\(584\) 7.03522 + 27.7128i 0.291119 + 1.14676i
\(585\) 0 0
\(586\) −0.0626405 0.754157i −0.00258766 0.0311540i
\(587\) −34.7799 −1.43552 −0.717761 0.696290i \(-0.754833\pi\)
−0.717761 + 0.696290i \(0.754833\pi\)
\(588\) 0 0
\(589\) 17.5236 0.722048
\(590\) 1.03010 + 12.4018i 0.0424086 + 0.510576i
\(591\) 0 0
\(592\) −18.8424 + 6.48517i −0.774417 + 0.266539i
\(593\) 5.30521i 0.217859i −0.994049 0.108929i \(-0.965258\pi\)
0.994049 0.108929i \(-0.0347423\pi\)
\(594\) 0 0
\(595\) 1.85845 6.05649i 0.0761888 0.248292i
\(596\) −14.3725 + 2.40415i −0.588719 + 0.0984777i
\(597\) 0 0
\(598\) 1.01369 0.0841970i 0.0414527 0.00344307i
\(599\) 1.76214i 0.0719991i 0.999352 + 0.0359996i \(0.0114615\pi\)
−0.999352 + 0.0359996i \(0.988539\pi\)
\(600\) 0 0
\(601\) 20.8508i 0.850523i −0.905071 0.425262i \(-0.860182\pi\)
0.905071 0.425262i \(-0.139818\pi\)
\(602\) −2.35311 0.513518i −0.0959057 0.0209294i
\(603\) 0 0
\(604\) 5.00910 + 29.9454i 0.203817 + 1.21846i
\(605\) 10.6905i 0.434630i
\(606\) 0 0
\(607\) −5.84505 −0.237243 −0.118622 0.992940i \(-0.537848\pi\)
−0.118622 + 0.992940i \(0.537848\pi\)
\(608\) 15.9544 7.01695i 0.647036 0.284575i
\(609\) 0 0
\(610\) 20.2647 1.68319i 0.820495 0.0681505i
\(611\) 0.663273i 0.0268331i
\(612\) 0 0
\(613\) 10.6913 0.431816 0.215908 0.976414i \(-0.430729\pi\)
0.215908 + 0.976414i \(0.430729\pi\)
\(614\) −28.8662 + 2.39764i −1.16495 + 0.0967607i
\(615\) 0 0
\(616\) −4.15832 0.204424i −0.167544 0.00823648i
\(617\) −31.3037 −1.26024 −0.630120 0.776497i \(-0.716994\pi\)
−0.630120 + 0.776497i \(0.716994\pi\)
\(618\) 0 0
\(619\) 13.7799 0.553861 0.276930 0.960890i \(-0.410683\pi\)
0.276930 + 0.960890i \(0.410683\pi\)
\(620\) −1.87666 11.2191i −0.0753687 0.450568i
\(621\) 0 0
\(622\) −41.8014 + 3.47203i −1.67608 + 0.139216i
\(623\) −20.2753 6.22150i −0.812312 0.249259i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −1.36980 16.4916i −0.0547481 0.659137i
\(627\) 0 0
\(628\) −3.53647 21.1417i −0.141120 0.843645i
\(629\) 11.9288i 0.475634i
\(630\) 0 0
\(631\) 15.3886i 0.612610i −0.951933 0.306305i \(-0.900907\pi\)
0.951933 0.306305i \(-0.0990928\pi\)
\(632\) 9.08887 + 35.8024i 0.361536 + 1.42414i
\(633\) 0 0
\(634\) −22.6185 + 1.87870i −0.898295 + 0.0746126i
\(635\) −11.8445 −0.470036
\(636\) 0 0
\(637\) 0.716082 1.05696i 0.0283722 0.0418781i
\(638\) 0.208424 + 2.50931i 0.00825160 + 0.0993447i
\(639\) 0 0
\(640\) −6.20104 9.46293i −0.245118 0.374055i
\(641\) 4.57385 0.180656 0.0903282 0.995912i \(-0.471208\pi\)
0.0903282 + 0.995912i \(0.471208\pi\)
\(642\) 0 0
\(643\) −40.9959 −1.61672 −0.808360 0.588689i \(-0.799644\pi\)
−0.808360 + 0.588689i \(0.799644\pi\)
\(644\) −20.6861 2.74635i −0.815148 0.108221i
\(645\) 0 0
\(646\) 0.863639 + 10.3977i 0.0339794 + 0.409093i
\(647\) 6.26797 0.246419 0.123210 0.992381i \(-0.460681\pi\)
0.123210 + 0.992381i \(0.460681\pi\)
\(648\) 0 0
\(649\) 4.89567i 0.192172i
\(650\) 0.0213502 + 0.257045i 0.000837424 + 0.0100821i
\(651\) 0 0
\(652\) −6.84630 40.9285i −0.268122 1.60288i
\(653\) −27.6655 −1.08263 −0.541316 0.840819i \(-0.682074\pi\)
−0.541316 + 0.840819i \(0.682074\pi\)
\(654\) 0 0
\(655\) 16.6337i 0.649932i
\(656\) −12.5596 36.4915i −0.490371 1.42475i
\(657\) 0 0
\(658\) −2.90122 + 13.2943i −0.113101 + 0.518267i
\(659\) 33.8406i 1.31824i 0.752036 + 0.659122i \(0.229072\pi\)
−0.752036 + 0.659122i \(0.770928\pi\)
\(660\) 0 0
\(661\) 15.9944i 0.622109i −0.950392 0.311054i \(-0.899318\pi\)
0.950392 0.311054i \(-0.100682\pi\)
\(662\) −1.28370 15.4551i −0.0498925 0.600678i
\(663\) 0 0
\(664\) 25.9143 6.57866i 1.00567 0.255302i
\(665\) 7.79316 + 2.39134i 0.302206 + 0.0927324i
\(666\) 0 0
\(667\) 12.6206i 0.488671i
\(668\) −16.5201 + 2.76340i −0.639183 + 0.106919i
\(669\) 0 0
\(670\) 14.1912 1.17872i 0.548254 0.0455381i
\(671\) 7.99958 0.308820
\(672\) 0 0
\(673\) 1.91279 0.0737326 0.0368663 0.999320i \(-0.488262\pi\)
0.0368663 + 0.999320i \(0.488262\pi\)
\(674\) 11.1045 0.922339i 0.427728 0.0355272i
\(675\) 0 0
\(676\) 25.5781 4.27857i 0.983773 0.164560i
\(677\) 7.67384i 0.294930i −0.989067 0.147465i \(-0.952889\pi\)
0.989067 0.147465i \(-0.0471113\pi\)
\(678\) 0 0
\(679\) 1.12654 + 0.345681i 0.0432327 + 0.0132660i
\(680\) 6.56441 1.66645i 0.251733 0.0639056i
\(681\) 0 0
\(682\) −0.370410 4.45954i −0.0141837 0.170764i
\(683\) 21.8303i 0.835314i −0.908605 0.417657i \(-0.862851\pi\)
0.908605 0.417657i \(-0.137149\pi\)
\(684\) 0 0
\(685\) 9.88658i 0.377747i
\(686\) −18.9761 + 18.0529i −0.724510 + 0.689265i
\(687\) 0 0
\(688\) −0.837947 2.43462i −0.0319464 0.0928190i
\(689\) 1.27132i 0.0484336i
\(690\) 0 0
\(691\) 19.9109 0.757446 0.378723 0.925510i \(-0.376363\pi\)
0.378723 + 0.925510i \(0.376363\pi\)
\(692\) 7.21151 + 43.1118i 0.274140 + 1.63886i
\(693\) 0 0
\(694\) 1.66870 + 20.0902i 0.0633429 + 0.762614i
\(695\) 20.5861i 0.780877i
\(696\) 0 0
\(697\) 23.1022 0.875059
\(698\) 0.783884 + 9.43752i 0.0296704 + 0.357215i
\(699\) 0 0
\(700\) 0.696403 5.24548i 0.0263216 0.198260i
\(701\) −41.1901 −1.55573 −0.777864 0.628433i \(-0.783697\pi\)
−0.777864 + 0.628433i \(0.783697\pi\)
\(702\) 0 0
\(703\) 15.3494 0.578912
\(704\) −2.12296 3.91186i −0.0800122 0.147434i
\(705\) 0 0
\(706\) 2.18602 + 26.3185i 0.0822720 + 0.990509i
\(707\) 32.5124 + 9.97647i 1.22275 + 0.375204i
\(708\) 0 0
\(709\) −5.89330 −0.221327 −0.110664 0.993858i \(-0.535298\pi\)
−0.110664 + 0.993858i \(0.535298\pi\)
\(710\) 1.91865 0.159364i 0.0720057 0.00598082i
\(711\) 0 0
\(712\) −5.57877 21.9756i −0.209073 0.823571i
\(713\) 22.4292i 0.839980i
\(714\) 0 0
\(715\) 0.101469i 0.00379474i
\(716\) −6.05610 36.2045i −0.226327 1.35303i
\(717\) 0 0
\(718\) 2.45431 + 29.5485i 0.0915940 + 1.10274i
\(719\) 35.2121 1.31319 0.656595 0.754243i \(-0.271996\pi\)
0.656595 + 0.754243i \(0.271996\pi\)
\(720\) 0 0
\(721\) 11.1012 36.1776i 0.413429 1.34732i
\(722\) 13.3986 1.11289i 0.498645 0.0414176i
\(723\) 0 0
\(724\) 4.20546 + 25.1410i 0.156295 + 0.934359i
\(725\) −3.20026 −0.118855
\(726\) 0 0
\(727\) 44.9984 1.66890 0.834449 0.551085i \(-0.185786\pi\)
0.834449 + 0.551085i \(0.185786\pi\)
\(728\) 1.36319 + 0.0670147i 0.0505232 + 0.00248373i
\(729\) 0 0
\(730\) −14.2468 + 1.18335i −0.527299 + 0.0437976i
\(731\) 1.54132 0.0570079
\(732\) 0 0
\(733\) 4.38540i 0.161978i −0.996715 0.0809892i \(-0.974192\pi\)
0.996715 0.0809892i \(-0.0258079\pi\)
\(734\) −30.2496 + 2.51254i −1.11653 + 0.0927395i
\(735\) 0 0
\(736\) −8.98128 20.4207i −0.331054 0.752716i
\(737\) 5.60203 0.206353
\(738\) 0 0
\(739\) 29.0684i 1.06930i 0.845075 + 0.534648i \(0.179556\pi\)
−0.845075 + 0.534648i \(0.820444\pi\)
\(740\) −1.64382 9.82706i −0.0604279 0.361250i
\(741\) 0 0
\(742\) 5.56089 25.4819i 0.204147 0.935469i
\(743\) 21.0881i 0.773647i 0.922154 + 0.386824i \(0.126428\pi\)
−0.922154 + 0.386824i \(0.873572\pi\)
\(744\) 0 0
\(745\) 7.28607i 0.266941i
\(746\) 51.2099 4.25351i 1.87493 0.155732i
\(747\) 0 0
\(748\) 2.62784 0.439570i 0.0960832 0.0160723i
\(749\) −46.3454 14.2212i −1.69342 0.519630i
\(750\) 0 0
\(751\) 41.9734i 1.53163i 0.643061 + 0.765815i \(0.277664\pi\)
−0.643061 + 0.765815i \(0.722336\pi\)
\(752\) −13.7548 + 4.73414i −0.501587 + 0.172636i
\(753\) 0 0
\(754\) −0.0683261 0.822608i −0.00248829 0.0299576i
\(755\) −15.1807 −0.552483
\(756\) 0 0
\(757\) 3.52848 0.128245 0.0641224 0.997942i \(-0.479575\pi\)
0.0641224 + 0.997942i \(0.479575\pi\)
\(758\) −1.29994 15.6506i −0.0472160 0.568455i
\(759\) 0 0
\(760\) 2.14430 + 8.44671i 0.0777819 + 0.306394i
\(761\) 43.3157i 1.57019i 0.619374 + 0.785096i \(0.287387\pi\)
−0.619374 + 0.785096i \(0.712613\pi\)
\(762\) 0 0
\(763\) 3.13396 10.2133i 0.113457 0.369745i
\(764\) 7.08311 + 42.3442i 0.256258 + 1.53196i
\(765\) 0 0
\(766\) −33.3061 + 2.76642i −1.20340 + 0.0999548i
\(767\) 1.60491i 0.0579499i
\(768\) 0 0
\(769\) 36.5255i 1.31714i 0.752518 + 0.658572i \(0.228839\pi\)
−0.752518 + 0.658572i \(0.771161\pi\)
\(770\) 0.443836 2.03381i 0.0159948 0.0732933i
\(771\) 0 0
\(772\) 10.4138 1.74196i 0.374800 0.0626946i
\(773\) 38.9312i 1.40026i 0.714017 + 0.700128i \(0.246874\pi\)
−0.714017 + 0.700128i \(0.753126\pi\)
\(774\) 0 0
\(775\) 5.68747 0.204300
\(776\) 0.309969 + 1.22102i 0.0111273 + 0.0438319i
\(777\) 0 0
\(778\) −32.1212 + 2.66800i −1.15160 + 0.0956524i
\(779\) 29.7266i 1.06507i
\(780\) 0 0
\(781\) 0.757395 0.0271017
\(782\) 13.3085 1.10541i 0.475911 0.0395293i
\(783\) 0 0
\(784\) −27.0300 7.30593i −0.965359 0.260926i
\(785\) 10.7177 0.382531
\(786\) 0 0
\(787\) −36.3954 −1.29736 −0.648679 0.761063i \(-0.724678\pi\)
−0.648679 + 0.761063i \(0.724678\pi\)
\(788\) 16.6646 2.78756i 0.593652 0.0993029i
\(789\) 0 0
\(790\) −18.4056 + 1.52878i −0.654843 + 0.0543915i
\(791\) 2.44235 7.95937i 0.0868398 0.283003i
\(792\)