Properties

Label 1008.2.r.l.673.1
Level 1008
Weight 2
Character 1008.673
Analytic conductor 8.049
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.2091141441.1
Defining polynomial: \(x^{8} - x^{7} + x^{6} + 3 x^{5} - 15 x^{4} + 9 x^{3} + 9 x^{2} - 27 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.1
Root \(0.199732 - 1.72050i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.l.337.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.58986 + 0.687275i) q^{3} +(-0.300268 - 0.520080i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.05531 - 2.18534i) q^{9} +O(q^{10})\) \(q+(-1.58986 + 0.687275i) q^{3} +(-0.300268 - 0.520080i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.05531 - 2.18534i) q^{9} +(-0.800268 + 1.38611i) q^{11} +(-0.165178 - 0.286096i) q^{13} +(0.834822 + 0.620487i) q^{15} -1.44990 q^{17} -2.57918 q^{19} +(0.199732 - 1.72050i) q^{21} +(0.924682 + 1.60160i) q^{23} +(2.31968 - 4.01780i) q^{25} +(-1.76571 + 4.88695i) q^{27} +(-1.75950 + 3.04755i) q^{29} +(-4.81034 - 8.33176i) q^{31} +(0.319678 - 2.75372i) q^{33} +0.600537 q^{35} +0.600537 q^{37} +(0.459236 + 0.341330i) q^{39} +(-3.31034 - 5.73368i) q^{41} +(1.81481 - 3.14334i) q^{43} +(-1.75370 - 0.412734i) q^{45} +(1.95477 - 3.38576i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(2.30514 - 0.996481i) q^{51} -9.27166 q^{53} +0.961181 q^{55} +(4.10054 - 1.77261i) q^{57} +(-6.93476 - 12.0113i) q^{59} +(2.59433 - 4.49351i) q^{61} +(0.864909 + 2.87262i) q^{63} +(-0.0991952 + 0.171811i) q^{65} +(-5.90467 - 10.2272i) q^{67} +(-2.57085 - 1.91080i) q^{69} +4.17972 q^{71} +4.13969 q^{73} +(-0.926627 + 7.98199i) q^{75} +(-0.800268 - 1.38611i) q^{77} +(4.06538 - 7.04144i) q^{79} +(-0.551441 - 8.98309i) q^{81} +(-2.78959 + 4.83171i) q^{83} +(0.435359 + 0.754064i) q^{85} +(0.702858 - 6.05444i) q^{87} -3.83069 q^{89} +0.330355 q^{91} +(13.3740 + 9.94029i) q^{93} +(0.774447 + 1.34138i) q^{95} +(0.974782 - 1.68837i) q^{97} +(1.38432 + 4.59773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{3} - 3q^{5} - 4q^{7} - q^{9} + O(q^{10}) \) \( 8q + q^{3} - 3q^{5} - 4q^{7} - q^{9} - 7q^{11} + 3q^{13} + 11q^{15} + 6q^{17} + 8q^{19} + q^{21} - 2q^{23} - 5q^{25} - 11q^{27} - 9q^{29} - 3q^{31} - 21q^{33} + 6q^{35} + 6q^{37} - 2q^{39} + 9q^{41} - 8q^{43} + 7q^{45} - 3q^{47} - 4q^{49} + 18q^{51} + 12q^{53} + 56q^{55} + 34q^{57} - 10q^{59} + 20q^{61} + 2q^{63} + q^{65} - 11q^{67} - 17q^{69} + 6q^{71} - 48q^{73} - 52q^{75} - 7q^{77} - 21q^{79} - 25q^{81} - 8q^{83} + 9q^{85} + 15q^{87} + 12q^{89} - 6q^{91} + 29q^{93} - 36q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(3\) −1.58986 + 0.687275i −0.917906 + 0.396799i
\(4\) 0 0
\(5\) −0.300268 0.520080i −0.134284 0.232587i 0.791040 0.611765i \(-0.209540\pi\)
−0.925324 + 0.379178i \(0.876207\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 0 0
\(9\) 2.05531 2.18534i 0.685102 0.728447i
\(10\) 0 0
\(11\) −0.800268 + 1.38611i −0.241290 + 0.417926i −0.961082 0.276263i \(-0.910904\pi\)
0.719792 + 0.694190i \(0.244237\pi\)
\(12\) 0 0
\(13\) −0.165178 0.286096i −0.0458120 0.0793487i 0.842210 0.539149i \(-0.181254\pi\)
−0.888022 + 0.459801i \(0.847921\pi\)
\(14\) 0 0
\(15\) 0.834822 + 0.620487i 0.215550 + 0.160209i
\(16\) 0 0
\(17\) −1.44990 −0.351652 −0.175826 0.984421i \(-0.556260\pi\)
−0.175826 + 0.984421i \(0.556260\pi\)
\(18\) 0 0
\(19\) −2.57918 −0.591705 −0.295852 0.955234i \(-0.595604\pi\)
−0.295852 + 0.955234i \(0.595604\pi\)
\(20\) 0 0
\(21\) 0.199732 1.72050i 0.0435850 0.375443i
\(22\) 0 0
\(23\) 0.924682 + 1.60160i 0.192809 + 0.333956i 0.946180 0.323640i \(-0.104907\pi\)
−0.753371 + 0.657596i \(0.771573\pi\)
\(24\) 0 0
\(25\) 2.31968 4.01780i 0.463936 0.803560i
\(26\) 0 0
\(27\) −1.76571 + 4.88695i −0.339812 + 0.940493i
\(28\) 0 0
\(29\) −1.75950 + 3.04755i −0.326732 + 0.565916i −0.981861 0.189601i \(-0.939281\pi\)
0.655130 + 0.755517i \(0.272614\pi\)
\(30\) 0 0
\(31\) −4.81034 8.33176i −0.863963 1.49643i −0.868073 0.496436i \(-0.834642\pi\)
0.00411031 0.999992i \(-0.498692\pi\)
\(32\) 0 0
\(33\) 0.319678 2.75372i 0.0556488 0.479361i
\(34\) 0 0
\(35\) 0.600537 0.101509
\(36\) 0 0
\(37\) 0.600537 0.0987276 0.0493638 0.998781i \(-0.484281\pi\)
0.0493638 + 0.998781i \(0.484281\pi\)
\(38\) 0 0
\(39\) 0.459236 + 0.341330i 0.0735366 + 0.0546565i
\(40\) 0 0
\(41\) −3.31034 5.73368i −0.516989 0.895450i −0.999805 0.0197291i \(-0.993720\pi\)
0.482817 0.875721i \(-0.339614\pi\)
\(42\) 0 0
\(43\) 1.81481 3.14334i 0.276756 0.479355i −0.693821 0.720148i \(-0.744074\pi\)
0.970577 + 0.240793i \(0.0774074\pi\)
\(44\) 0 0
\(45\) −1.75370 0.412734i −0.261425 0.0615267i
\(46\) 0 0
\(47\) 1.95477 3.38576i 0.285132 0.493864i −0.687509 0.726176i \(-0.741296\pi\)
0.972641 + 0.232312i \(0.0746291\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) 2.30514 0.996481i 0.322784 0.139535i
\(52\) 0 0
\(53\) −9.27166 −1.27356 −0.636780 0.771046i \(-0.719734\pi\)
−0.636780 + 0.771046i \(0.719734\pi\)
\(54\) 0 0
\(55\) 0.961181 0.129606
\(56\) 0 0
\(57\) 4.10054 1.77261i 0.543129 0.234788i
\(58\) 0 0
\(59\) −6.93476 12.0113i −0.902828 1.56374i −0.823806 0.566872i \(-0.808154\pi\)
−0.0790221 0.996873i \(-0.525180\pi\)
\(60\) 0 0
\(61\) 2.59433 4.49351i 0.332169 0.575334i −0.650768 0.759277i \(-0.725553\pi\)
0.982937 + 0.183943i \(0.0588861\pi\)
\(62\) 0 0
\(63\) 0.864909 + 2.87262i 0.108968 + 0.361916i
\(64\) 0 0
\(65\) −0.0991952 + 0.171811i −0.0123036 + 0.0213105i
\(66\) 0 0
\(67\) −5.90467 10.2272i −0.721370 1.24945i −0.960451 0.278450i \(-0.910179\pi\)
0.239081 0.971000i \(-0.423154\pi\)
\(68\) 0 0
\(69\) −2.57085 1.91080i −0.309494 0.230033i
\(70\) 0 0
\(71\) 4.17972 0.496041 0.248021 0.968755i \(-0.420220\pi\)
0.248021 + 0.968755i \(0.420220\pi\)
\(72\) 0 0
\(73\) 4.13969 0.484514 0.242257 0.970212i \(-0.422112\pi\)
0.242257 + 0.970212i \(0.422112\pi\)
\(74\) 0 0
\(75\) −0.926627 + 7.98199i −0.106998 + 0.921681i
\(76\) 0 0
\(77\) −0.800268 1.38611i −0.0911990 0.157961i
\(78\) 0 0
\(79\) 4.06538 7.04144i 0.457391 0.792224i −0.541431 0.840745i \(-0.682117\pi\)
0.998822 + 0.0485208i \(0.0154507\pi\)
\(80\) 0 0
\(81\) −0.551441 8.98309i −0.0612713 0.998121i
\(82\) 0 0
\(83\) −2.78959 + 4.83171i −0.306197 + 0.530349i −0.977527 0.210809i \(-0.932390\pi\)
0.671330 + 0.741159i \(0.265723\pi\)
\(84\) 0 0
\(85\) 0.435359 + 0.754064i 0.0472213 + 0.0817897i
\(86\) 0 0
\(87\) 0.702858 6.05444i 0.0753542 0.649104i
\(88\) 0 0
\(89\) −3.83069 −0.406053 −0.203026 0.979173i \(-0.565078\pi\)
−0.203026 + 0.979173i \(0.565078\pi\)
\(90\) 0 0
\(91\) 0.330355 0.0346306
\(92\) 0 0
\(93\) 13.3740 + 9.94029i 1.38682 + 1.03076i
\(94\) 0 0
\(95\) 0.774447 + 1.34138i 0.0794565 + 0.137623i
\(96\) 0 0
\(97\) 0.974782 1.68837i 0.0989741 0.171428i −0.812286 0.583259i \(-0.801777\pi\)
0.911260 + 0.411831i \(0.135111\pi\)
\(98\) 0 0
\(99\) 1.38432 + 4.59773i 0.139129 + 0.462089i
\(100\) 0 0
\(101\) −8.79520 + 15.2337i −0.875155 + 1.51581i −0.0185572 + 0.999828i \(0.505907\pi\)
−0.856598 + 0.515985i \(0.827426\pi\)
\(102\) 0 0
\(103\) −5.30547 9.18935i −0.522764 0.905454i −0.999649 0.0264880i \(-0.991568\pi\)
0.476885 0.878966i \(-0.341766\pi\)
\(104\) 0 0
\(105\) −0.954769 + 0.412734i −0.0931759 + 0.0402787i
\(106\) 0 0
\(107\) 3.43949 0.332508 0.166254 0.986083i \(-0.446833\pi\)
0.166254 + 0.986083i \(0.446833\pi\)
\(108\) 0 0
\(109\) −5.55010 −0.531603 −0.265802 0.964028i \(-0.585637\pi\)
−0.265802 + 0.964028i \(0.585637\pi\)
\(110\) 0 0
\(111\) −0.954769 + 0.412734i −0.0906226 + 0.0391750i
\(112\) 0 0
\(113\) −4.38079 7.58775i −0.412110 0.713796i 0.583010 0.812465i \(-0.301875\pi\)
−0.995120 + 0.0986691i \(0.968541\pi\)
\(114\) 0 0
\(115\) 0.555305 0.961817i 0.0517825 0.0896899i
\(116\) 0 0
\(117\) −0.964708 0.227045i −0.0891873 0.0209903i
\(118\) 0 0
\(119\) 0.724950 1.25565i 0.0664561 0.115105i
\(120\) 0 0
\(121\) 4.21914 + 7.30777i 0.383558 + 0.664342i
\(122\) 0 0
\(123\) 9.20360 + 6.84063i 0.829860 + 0.616799i
\(124\) 0 0
\(125\) −5.78879 −0.517765
\(126\) 0 0
\(127\) 11.1521 0.989590 0.494795 0.869010i \(-0.335243\pi\)
0.494795 + 0.869010i \(0.335243\pi\)
\(128\) 0 0
\(129\) −0.724950 + 6.24474i −0.0638283 + 0.549819i
\(130\) 0 0
\(131\) −2.59993 4.50322i −0.227157 0.393448i 0.729807 0.683653i \(-0.239610\pi\)
−0.956964 + 0.290205i \(0.906276\pi\)
\(132\) 0 0
\(133\) 1.28959 2.23364i 0.111822 0.193681i
\(134\) 0 0
\(135\) 3.07179 0.549083i 0.264378 0.0472575i
\(136\) 0 0
\(137\) −4.39399 + 7.61062i −0.375404 + 0.650219i −0.990387 0.138321i \(-0.955829\pi\)
0.614983 + 0.788540i \(0.289163\pi\)
\(138\) 0 0
\(139\) −4.50934 7.81040i −0.382477 0.662469i 0.608939 0.793217i \(-0.291596\pi\)
−0.991416 + 0.130748i \(0.958262\pi\)
\(140\) 0 0
\(141\) −0.780859 + 6.72634i −0.0657602 + 0.566460i
\(142\) 0 0
\(143\) 0.528746 0.0442159
\(144\) 0 0
\(145\) 2.11329 0.175499
\(146\) 0 0
\(147\) 1.39013 + 1.03322i 0.114656 + 0.0852186i
\(148\) 0 0
\(149\) 0.525620 + 0.910400i 0.0430604 + 0.0745829i 0.886752 0.462245i \(-0.152956\pi\)
−0.843692 + 0.536828i \(0.819623\pi\)
\(150\) 0 0
\(151\) −6.48932 + 11.2398i −0.528094 + 0.914685i 0.471370 + 0.881936i \(0.343760\pi\)
−0.999464 + 0.0327494i \(0.989574\pi\)
\(152\) 0 0
\(153\) −2.97999 + 3.16853i −0.240918 + 0.256160i
\(154\) 0 0
\(155\) −2.88879 + 5.00352i −0.232033 + 0.401893i
\(156\) 0 0
\(157\) 9.86699 + 17.0901i 0.787471 + 1.36394i 0.927511 + 0.373795i \(0.121944\pi\)
−0.140040 + 0.990146i \(0.544723\pi\)
\(158\) 0 0
\(159\) 14.7406 6.37218i 1.16901 0.505347i
\(160\) 0 0
\(161\) −1.84936 −0.145750
\(162\) 0 0
\(163\) 22.9214 1.79534 0.897672 0.440664i \(-0.145257\pi\)
0.897672 + 0.440664i \(0.145257\pi\)
\(164\) 0 0
\(165\) −1.52814 + 0.660596i −0.118966 + 0.0514273i
\(166\) 0 0
\(167\) 1.61508 + 2.79740i 0.124978 + 0.216469i 0.921725 0.387845i \(-0.126780\pi\)
−0.796746 + 0.604314i \(0.793447\pi\)
\(168\) 0 0
\(169\) 6.44543 11.1638i 0.495803 0.858755i
\(170\) 0 0
\(171\) −5.30101 + 5.63640i −0.405378 + 0.431026i
\(172\) 0 0
\(173\) −7.08052 + 12.2638i −0.538322 + 0.932401i 0.460672 + 0.887570i \(0.347608\pi\)
−0.998995 + 0.0448312i \(0.985725\pi\)
\(174\) 0 0
\(175\) 2.31968 + 4.01780i 0.175351 + 0.303717i
\(176\) 0 0
\(177\) 19.2804 + 14.3303i 1.44920 + 1.07713i
\(178\) 0 0
\(179\) −7.06790 −0.528280 −0.264140 0.964484i \(-0.585088\pi\)
−0.264140 + 0.964484i \(0.585088\pi\)
\(180\) 0 0
\(181\) −19.6207 −1.45839 −0.729197 0.684304i \(-0.760106\pi\)
−0.729197 + 0.684304i \(0.760106\pi\)
\(182\) 0 0
\(183\) −1.03634 + 8.92706i −0.0766084 + 0.659907i
\(184\) 0 0
\(185\) −0.180322 0.312327i −0.0132575 0.0229627i
\(186\) 0 0
\(187\) 1.16031 2.00971i 0.0848502 0.146965i
\(188\) 0 0
\(189\) −3.34936 3.97263i −0.243630 0.288966i
\(190\) 0 0
\(191\) −10.1096 + 17.5104i −0.731505 + 1.26700i 0.224734 + 0.974420i \(0.427849\pi\)
−0.956240 + 0.292584i \(0.905485\pi\)
\(192\) 0 0
\(193\) −8.89473 15.4061i −0.640257 1.10896i −0.985375 0.170398i \(-0.945495\pi\)
0.345119 0.938559i \(-0.387839\pi\)
\(194\) 0 0
\(195\) 0.0396248 0.341330i 0.00283759 0.0244431i
\(196\) 0 0
\(197\) 8.04150 0.572933 0.286467 0.958090i \(-0.407519\pi\)
0.286467 + 0.958090i \(0.407519\pi\)
\(198\) 0 0
\(199\) −14.0332 −0.994790 −0.497395 0.867524i \(-0.665710\pi\)
−0.497395 + 0.867524i \(0.665710\pi\)
\(200\) 0 0
\(201\) 16.4165 + 12.2017i 1.15793 + 0.860638i
\(202\) 0 0
\(203\) −1.75950 3.04755i −0.123493 0.213896i
\(204\) 0 0
\(205\) −1.98798 + 3.44328i −0.138847 + 0.240489i
\(206\) 0 0
\(207\) 5.40054 + 1.27102i 0.375363 + 0.0883421i
\(208\) 0 0
\(209\) 2.06404 3.57502i 0.142772 0.247289i
\(210\) 0 0
\(211\) 7.32622 + 12.6894i 0.504358 + 0.873574i 0.999987 + 0.00503962i \(0.00160417\pi\)
−0.495629 + 0.868534i \(0.665062\pi\)
\(212\) 0 0
\(213\) −6.64516 + 2.87262i −0.455319 + 0.196829i
\(214\) 0 0
\(215\) −2.17972 −0.148656
\(216\) 0 0
\(217\) 9.62068 0.653095
\(218\) 0 0
\(219\) −6.58153 + 2.84511i −0.444738 + 0.192255i
\(220\) 0 0
\(221\) 0.239491 + 0.414811i 0.0161099 + 0.0279032i
\(222\) 0 0
\(223\) −7.02696 + 12.1711i −0.470560 + 0.815034i −0.999433 0.0336670i \(-0.989281\pi\)
0.528873 + 0.848701i \(0.322615\pi\)
\(224\) 0 0
\(225\) −4.01262 13.3271i −0.267508 0.888473i
\(226\) 0 0
\(227\) 2.40601 4.16733i 0.159692 0.276596i −0.775065 0.631881i \(-0.782283\pi\)
0.934758 + 0.355286i \(0.115616\pi\)
\(228\) 0 0
\(229\) −1.68419 2.91710i −0.111294 0.192767i 0.804998 0.593277i \(-0.202166\pi\)
−0.916292 + 0.400510i \(0.868833\pi\)
\(230\) 0 0
\(231\) 2.22495 + 1.65371i 0.146391 + 0.108806i
\(232\) 0 0
\(233\) 20.9137 1.37010 0.685051 0.728495i \(-0.259780\pi\)
0.685051 + 0.728495i \(0.259780\pi\)
\(234\) 0 0
\(235\) −2.34782 −0.153155
\(236\) 0 0
\(237\) −1.62397 + 13.9889i −0.105488 + 0.908679i
\(238\) 0 0
\(239\) 9.60614 + 16.6383i 0.621370 + 1.07624i 0.989231 + 0.146363i \(0.0467568\pi\)
−0.367861 + 0.929881i \(0.619910\pi\)
\(240\) 0 0
\(241\) 8.88912 15.3964i 0.572599 0.991770i −0.423699 0.905803i \(-0.639269\pi\)
0.996298 0.0859672i \(-0.0273980\pi\)
\(242\) 0 0
\(243\) 7.05057 + 13.9029i 0.452294 + 0.891869i
\(244\) 0 0
\(245\) −0.300268 + 0.520080i −0.0191834 + 0.0332267i
\(246\) 0 0
\(247\) 0.426023 + 0.737894i 0.0271072 + 0.0469510i
\(248\) 0 0
\(249\) 1.11434 9.59896i 0.0706184 0.608309i
\(250\) 0 0
\(251\) −20.5531 −1.29730 −0.648649 0.761088i \(-0.724665\pi\)
−0.648649 + 0.761088i \(0.724665\pi\)
\(252\) 0 0
\(253\) −2.95997 −0.186092
\(254\) 0 0
\(255\) −1.21041 0.899644i −0.0757988 0.0563379i
\(256\) 0 0
\(257\) 12.6943 + 21.9871i 0.791846 + 1.37152i 0.924823 + 0.380399i \(0.124213\pi\)
−0.132976 + 0.991119i \(0.542453\pi\)
\(258\) 0 0
\(259\) −0.300268 + 0.520080i −0.0186578 + 0.0323162i
\(260\) 0 0
\(261\) 3.04362 + 10.1088i 0.188396 + 0.625717i
\(262\) 0 0
\(263\) −15.3557 + 26.5969i −0.946874 + 1.64003i −0.194918 + 0.980820i \(0.562444\pi\)
−0.751956 + 0.659213i \(0.770889\pi\)
\(264\) 0 0
\(265\) 2.78398 + 4.82200i 0.171019 + 0.296213i
\(266\) 0 0
\(267\) 6.09026 2.63274i 0.372718 0.161121i
\(268\) 0 0
\(269\) 13.7402 0.837757 0.418878 0.908042i \(-0.362423\pi\)
0.418878 + 0.908042i \(0.362423\pi\)
\(270\) 0 0
\(271\) −7.64977 −0.464690 −0.232345 0.972633i \(-0.574640\pi\)
−0.232345 + 0.972633i \(0.574640\pi\)
\(272\) 0 0
\(273\) −0.525218 + 0.227045i −0.0317877 + 0.0137414i
\(274\) 0 0
\(275\) 3.71273 + 6.43064i 0.223886 + 0.387782i
\(276\) 0 0
\(277\) 4.19174 7.26030i 0.251857 0.436229i −0.712180 0.701997i \(-0.752292\pi\)
0.964037 + 0.265768i \(0.0856254\pi\)
\(278\) 0 0
\(279\) −28.0945 6.61206i −1.68197 0.395854i
\(280\) 0 0
\(281\) 12.7786 22.1333i 0.762310 1.32036i −0.179347 0.983786i \(-0.557398\pi\)
0.941657 0.336574i \(-0.109268\pi\)
\(282\) 0 0
\(283\) 5.46132 + 9.45928i 0.324641 + 0.562296i 0.981440 0.191771i \(-0.0614230\pi\)
−0.656798 + 0.754066i \(0.728090\pi\)
\(284\) 0 0
\(285\) −2.15316 1.60035i −0.127542 0.0947965i
\(286\) 0 0
\(287\) 6.62068 0.390807
\(288\) 0 0
\(289\) −14.8978 −0.876341
\(290\) 0 0
\(291\) −0.389390 + 3.35422i −0.0228264 + 0.196628i
\(292\) 0 0
\(293\) −13.9994 24.2477i −0.817853 1.41656i −0.907261 0.420569i \(-0.861831\pi\)
0.0894073 0.995995i \(-0.471503\pi\)
\(294\) 0 0
\(295\) −4.16457 + 7.21325i −0.242471 + 0.419972i
\(296\) 0 0
\(297\) −5.36078 6.35833i −0.311064 0.368948i
\(298\) 0 0
\(299\) 0.305473 0.529095i 0.0176660 0.0305984i
\(300\) 0 0
\(301\) 1.81481 + 3.14334i 0.104604 + 0.181179i
\(302\) 0 0
\(303\) 3.51336 30.2642i 0.201837 1.73863i
\(304\) 0 0
\(305\) −3.11598 −0.178420
\(306\) 0 0
\(307\) 33.0259 1.88489 0.942443 0.334367i \(-0.108523\pi\)
0.942443 + 0.334367i \(0.108523\pi\)
\(308\) 0 0
\(309\) 14.7506 + 10.9635i 0.839131 + 0.623689i
\(310\) 0 0
\(311\) −13.0143 22.5415i −0.737975 1.27821i −0.953406 0.301692i \(-0.902449\pi\)
0.215430 0.976519i \(-0.430885\pi\)
\(312\) 0 0
\(313\) 5.46618 9.46771i 0.308967 0.535146i −0.669170 0.743110i \(-0.733350\pi\)
0.978137 + 0.207963i \(0.0666834\pi\)
\(314\) 0 0
\(315\) 1.23429 1.31238i 0.0695441 0.0739441i
\(316\) 0 0
\(317\) 5.98593 10.3679i 0.336203 0.582321i −0.647512 0.762055i \(-0.724190\pi\)
0.983715 + 0.179734i \(0.0575237\pi\)
\(318\) 0 0
\(319\) −2.81615 4.87772i −0.157674 0.273100i
\(320\) 0 0
\(321\) −5.46830 + 2.36388i −0.305211 + 0.131939i
\(322\) 0 0
\(323\) 3.73956 0.208074
\(324\) 0 0
\(325\) −1.53264 −0.0850153
\(326\) 0 0
\(327\) 8.82388 3.81445i 0.487962 0.210939i
\(328\) 0 0
\(329\) 1.95477 + 3.38576i 0.107770 + 0.186663i
\(330\) 0 0
\(331\) 11.6176 20.1223i 0.638561 1.10602i −0.347188 0.937796i \(-0.612863\pi\)
0.985749 0.168224i \(-0.0538034\pi\)
\(332\) 0 0
\(333\) 1.23429 1.31238i 0.0676384 0.0719179i
\(334\) 0 0
\(335\) −3.54597 + 6.14180i −0.193737 + 0.335562i
\(336\) 0 0
\(337\) −3.89594 6.74796i −0.212225 0.367585i 0.740185 0.672403i \(-0.234738\pi\)
−0.952411 + 0.304818i \(0.901404\pi\)
\(338\) 0 0
\(339\) 12.1797 + 9.05265i 0.661512 + 0.491672i
\(340\) 0 0
\(341\) 15.3983 0.833862
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −0.221824 + 1.91080i −0.0119426 + 0.102874i
\(346\) 0 0
\(347\) −9.26198 16.0422i −0.497209 0.861192i 0.502785 0.864411i \(-0.332309\pi\)
−0.999995 + 0.00321932i \(0.998975\pi\)
\(348\) 0 0
\(349\) 0.958498 1.66017i 0.0513072 0.0888667i −0.839231 0.543775i \(-0.816995\pi\)
0.890538 + 0.454908i \(0.150328\pi\)
\(350\) 0 0
\(351\) 1.68979 0.302050i 0.0901944 0.0161223i
\(352\) 0 0
\(353\) 0.869778 1.50650i 0.0462936 0.0801829i −0.841950 0.539555i \(-0.818592\pi\)
0.888244 + 0.459372i \(0.151926\pi\)
\(354\) 0 0
\(355\) −1.25504 2.17379i −0.0666104 0.115373i
\(356\) 0 0
\(357\) −0.289591 + 2.49455i −0.0153268 + 0.132025i
\(358\) 0 0
\(359\) 3.07616 0.162354 0.0811768 0.996700i \(-0.474132\pi\)
0.0811768 + 0.996700i \(0.474132\pi\)
\(360\) 0 0
\(361\) −12.3478 −0.649885
\(362\) 0 0
\(363\) −11.7303 8.71861i −0.615681 0.457608i
\(364\) 0 0
\(365\) −1.24302 2.15297i −0.0650625 0.112692i
\(366\) 0 0
\(367\) −6.17871 + 10.7018i −0.322526 + 0.558632i −0.981009 0.193964i \(-0.937865\pi\)
0.658482 + 0.752596i \(0.271199\pi\)
\(368\) 0 0
\(369\) −19.3338 4.55023i −1.00648 0.236876i
\(370\) 0 0
\(371\) 4.63583 8.02949i 0.240680 0.416870i
\(372\) 0 0
\(373\) −12.3999 21.4773i −0.642044 1.11205i −0.984976 0.172693i \(-0.944753\pi\)
0.342931 0.939360i \(-0.388580\pi\)
\(374\) 0 0
\(375\) 9.20335 3.97849i 0.475259 0.205448i
\(376\) 0 0
\(377\) 1.16252 0.0598730
\(378\) 0 0
\(379\) 11.9650 0.614602 0.307301 0.951612i \(-0.400574\pi\)
0.307301 + 0.951612i \(0.400574\pi\)
\(380\) 0 0
\(381\) −17.7303 + 7.66457i −0.908350 + 0.392668i
\(382\) 0 0
\(383\) 5.85810 + 10.1465i 0.299335 + 0.518463i 0.975984 0.217843i \(-0.0699020\pi\)
−0.676649 + 0.736306i \(0.736569\pi\)
\(384\) 0 0
\(385\) −0.480590 + 0.832407i −0.0244932 + 0.0424234i
\(386\) 0 0
\(387\) −3.13929 10.4265i −0.159579 0.530009i
\(388\) 0 0
\(389\) −19.1360 + 33.1445i −0.970232 + 1.68049i −0.275384 + 0.961334i \(0.588805\pi\)
−0.694848 + 0.719156i \(0.744528\pi\)
\(390\) 0 0
\(391\) −1.34070 2.32215i −0.0678019 0.117436i
\(392\) 0 0
\(393\) 7.22848 + 5.37261i 0.364628 + 0.271012i
\(394\) 0 0
\(395\) −4.88282 −0.245681
\(396\) 0 0
\(397\) 12.8396 0.644402 0.322201 0.946671i \(-0.395577\pi\)
0.322201 + 0.946671i \(0.395577\pi\)
\(398\) 0 0
\(399\) −0.515144 + 4.43747i −0.0257895 + 0.222152i
\(400\) 0 0
\(401\) −11.1570 19.3245i −0.557155 0.965021i −0.997732 0.0673063i \(-0.978560\pi\)
0.440577 0.897715i \(-0.354774\pi\)
\(402\) 0 0
\(403\) −1.58912 + 2.75244i −0.0791598 + 0.137109i
\(404\) 0 0
\(405\) −4.50634 + 2.98413i −0.223922 + 0.148283i
\(406\) 0 0
\(407\) −0.480590 + 0.832407i −0.0238220 + 0.0412609i
\(408\) 0 0
\(409\) 3.76605 + 6.52299i 0.186219 + 0.322541i 0.943987 0.329984i \(-0.107043\pi\)
−0.757767 + 0.652525i \(0.773710\pi\)
\(410\) 0 0
\(411\) 1.75524 15.1197i 0.0865796 0.745799i
\(412\) 0 0
\(413\) 13.8695 0.682474
\(414\) 0 0
\(415\) 3.35050 0.164470
\(416\) 0 0
\(417\) 12.5371 + 9.31828i 0.613945 + 0.456318i
\(418\) 0 0
\(419\) −14.1245 24.4644i −0.690029 1.19517i −0.971828 0.235692i \(-0.924264\pi\)
0.281798 0.959474i \(-0.409069\pi\)
\(420\) 0 0
\(421\) −9.53395 + 16.5133i −0.464656 + 0.804808i −0.999186 0.0403414i \(-0.987155\pi\)
0.534530 + 0.845150i \(0.320489\pi\)
\(422\) 0 0
\(423\) −3.38140 11.2306i −0.164409 0.546051i
\(424\) 0 0
\(425\) −3.36330 + 5.82541i −0.163144 + 0.282574i
\(426\) 0 0
\(427\) 2.59433 + 4.49351i 0.125548 + 0.217456i
\(428\) 0 0
\(429\) −0.840631 + 0.363394i −0.0405860 + 0.0175448i
\(430\) 0 0
\(431\) 22.9786 1.10684 0.553421 0.832902i \(-0.313322\pi\)
0.553421 + 0.832902i \(0.313322\pi\)
\(432\) 0 0
\(433\) −29.0806 −1.39752 −0.698762 0.715354i \(-0.746265\pi\)
−0.698762 + 0.715354i \(0.746265\pi\)
\(434\) 0 0
\(435\) −3.35984 + 1.45241i −0.161092 + 0.0696379i
\(436\) 0 0
\(437\) −2.38492 4.13081i −0.114086 0.197603i
\(438\) 0 0
\(439\) −7.36777 + 12.7613i −0.351644 + 0.609066i −0.986538 0.163534i \(-0.947711\pi\)
0.634893 + 0.772600i \(0.281044\pi\)
\(440\) 0 0
\(441\) −2.92021 0.687275i −0.139058 0.0327274i
\(442\) 0 0
\(443\) −17.2548 + 29.8861i −0.819799 + 1.41993i 0.0860314 + 0.996292i \(0.472581\pi\)
−0.905830 + 0.423641i \(0.860752\pi\)
\(444\) 0 0
\(445\) 1.15024 + 1.99227i 0.0545264 + 0.0944425i
\(446\) 0 0
\(447\) −1.46136 1.08616i −0.0691198 0.0513737i
\(448\) 0 0
\(449\) 11.5508 0.545115 0.272557 0.962140i \(-0.412131\pi\)
0.272557 + 0.962140i \(0.412131\pi\)
\(450\) 0 0
\(451\) 10.5966 0.498977
\(452\) 0 0
\(453\) 2.59225 22.3297i 0.121794 1.04914i
\(454\) 0 0
\(455\) −0.0991952 0.171811i −0.00465034 0.00805463i
\(456\) 0 0
\(457\) −18.6995 + 32.3884i −0.874724 + 1.51507i −0.0176677 + 0.999844i \(0.505624\pi\)
−0.857056 + 0.515223i \(0.827709\pi\)
\(458\) 0 0
\(459\) 2.56011 7.08558i 0.119496 0.330727i
\(460\) 0 0
\(461\) 9.13929 15.8297i 0.425659 0.737263i −0.570823 0.821073i \(-0.693376\pi\)
0.996482 + 0.0838101i \(0.0267089\pi\)
\(462\) 0 0
\(463\) 4.24610 + 7.35447i 0.197333 + 0.341791i 0.947663 0.319273i \(-0.103439\pi\)
−0.750330 + 0.661064i \(0.770105\pi\)
\(464\) 0 0
\(465\) 1.15396 9.94029i 0.0535138 0.460970i
\(466\) 0 0
\(467\) 14.6746 0.679060 0.339530 0.940595i \(-0.389732\pi\)
0.339530 + 0.940595i \(0.389732\pi\)
\(468\) 0 0
\(469\) 11.8093 0.545305
\(470\) 0 0
\(471\) −27.4327 20.3896i −1.26403 0.939501i
\(472\) 0 0
\(473\) 2.90467 + 5.03103i 0.133557 + 0.231327i
\(474\) 0 0
\(475\) −5.98287 + 10.3626i −0.274513 + 0.475470i
\(476\) 0 0
\(477\) −19.0561 + 20.2617i −0.872518 + 0.927722i
\(478\) 0 0
\(479\) 18.7151 32.4156i 0.855117 1.48111i −0.0214198 0.999771i \(-0.506819\pi\)
0.876537 0.481335i \(-0.159848\pi\)
\(480\) 0 0
\(481\) −0.0991952 0.171811i −0.00452291 0.00783391i
\(482\) 0 0
\(483\) 2.94023 1.27102i 0.133785 0.0578335i
\(484\) 0 0
\(485\) −1.17078 −0.0531626
\(486\) 0 0
\(487\) −33.3216 −1.50994 −0.754972 0.655757i \(-0.772350\pi\)
−0.754972 + 0.655757i \(0.772350\pi\)
\(488\) 0 0
\(489\) −36.4418 + 15.7533i −1.64796 + 0.712390i
\(490\) 0 0
\(491\) −19.9456 34.5467i −0.900131 1.55907i −0.827323 0.561726i \(-0.810137\pi\)
−0.0728078 0.997346i \(-0.523196\pi\)
\(492\) 0 0
\(493\) 2.55110 4.41864i 0.114896 0.199006i
\(494\) 0 0
\(495\) 1.97552 2.10051i 0.0887930 0.0944108i
\(496\) 0 0
\(497\) −2.08986 + 3.61974i −0.0937430 + 0.162368i
\(498\) 0 0
\(499\) 11.0370 + 19.1167i 0.494086 + 0.855781i 0.999977 0.00681602i \(-0.00216962\pi\)
−0.505891 + 0.862597i \(0.668836\pi\)
\(500\) 0 0
\(501\) −4.49033 3.33746i −0.200613 0.149107i
\(502\) 0 0
\(503\) 9.30820 0.415032 0.207516 0.978232i \(-0.433462\pi\)
0.207516 + 0.978232i \(0.433462\pi\)
\(504\) 0 0
\(505\) 10.5637 0.470077
\(506\) 0 0
\(507\) −2.57471 + 22.1787i −0.114347 + 0.984990i
\(508\) 0 0
\(509\) 2.88466 + 4.99637i 0.127860 + 0.221460i 0.922847 0.385166i \(-0.125856\pi\)
−0.794987 + 0.606626i \(0.792522\pi\)
\(510\) 0 0
\(511\) −2.06985 + 3.58508i −0.0915646 + 0.158595i
\(512\) 0 0
\(513\) 4.55410 12.6043i 0.201068 0.556495i
\(514\) 0 0
\(515\) −3.18613 + 5.51854i −0.140398 + 0.243176i
\(516\) 0 0
\(517\) 3.12868 + 5.41903i 0.137599 + 0.238329i
\(518\) 0 0
\(519\) 2.82841 24.3640i 0.124153 1.06946i
\(520\) 0 0
\(521\) −13.2989 −0.582634 −0.291317 0.956627i \(-0.594093\pi\)
−0.291317 + 0.956627i \(0.594093\pi\)
\(522\) 0 0
\(523\) −4.27523 −0.186943 −0.0934713 0.995622i \(-0.529796\pi\)
−0.0934713 + 0.995622i \(0.529796\pi\)
\(524\) 0 0
\(525\) −6.44930 4.79348i −0.281470 0.209205i
\(526\) 0 0
\(527\) 6.97451 + 12.0802i 0.303815 + 0.526222i
\(528\) 0 0
\(529\) 9.78993 16.9567i 0.425649 0.737246i
\(530\) 0 0
\(531\) −40.5019 9.53217i −1.75763 0.413661i
\(532\) 0 0
\(533\) −1.09359 + 1.89415i −0.0473686 + 0.0820448i
\(534\) 0 0
\(535\) −1.03277 1.78881i −0.0446505 0.0773370i
\(536\) 0 0
\(537\) 11.2370 4.85759i 0.484911 0.209621i
\(538\) 0 0
\(539\) 1.60054 0.0689400
\(540\) 0 0
\(541\) −12.2130 −0.525076 −0.262538 0.964922i \(-0.584560\pi\)
−0.262538 + 0.964922i \(0.584560\pi\)
\(542\) 0 0
\(543\) 31.1941 13.4848i 1.33867 0.578689i
\(544\) 0 0
\(545\) 1.66652 + 2.88650i 0.0713858 + 0.123644i
\(546\) 0 0
\(547\) 19.0910 33.0666i 0.816272 1.41382i −0.0921387 0.995746i \(-0.529370\pi\)
0.908411 0.418079i \(-0.137296\pi\)
\(548\) 0 0
\(549\) −4.48771 14.9050i −0.191531 0.636131i
\(550\) 0 0
\(551\) 4.53808 7.86019i 0.193329 0.334855i
\(552\) 0 0
\(553\) 4.06538 + 7.04144i 0.172877 + 0.299433i
\(554\) 0 0
\(555\) 0.501341 + 0.372625i 0.0212808 + 0.0158171i
\(556\) 0 0
\(557\) 36.8404 1.56098 0.780490 0.625169i \(-0.214970\pi\)
0.780490 + 0.625169i \(0.214970\pi\)
\(558\) 0 0
\(559\) −1.19906 −0.0507150
\(560\) 0 0
\(561\) −0.463501 + 3.99261i −0.0195690 + 0.168568i
\(562\) 0 0
\(563\) 9.56265 + 16.5630i 0.403018 + 0.698047i 0.994089 0.108572i \(-0.0346279\pi\)
−0.591071 + 0.806620i \(0.701295\pi\)
\(564\) 0 0
\(565\) −2.63083 + 4.55672i −0.110680 + 0.191703i
\(566\) 0 0
\(567\) 8.05531 + 4.01398i 0.338291 + 0.168571i
\(568\) 0 0
\(569\) 12.9576 22.4433i 0.543212 0.940871i −0.455505 0.890233i \(-0.650541\pi\)
0.998717 0.0506376i \(-0.0161253\pi\)
\(570\) 0 0
\(571\) −19.5679 33.8925i −0.818889 1.41836i −0.906501 0.422203i \(-0.861257\pi\)
0.0876117 0.996155i \(-0.472077\pi\)
\(572\) 0 0
\(573\) 4.03842 34.7871i 0.168707 1.45325i
\(574\) 0 0
\(575\) 8.57985 0.357805
\(576\) 0 0
\(577\) 9.72008 0.404652 0.202326 0.979318i \(-0.435150\pi\)
0.202326 + 0.979318i \(0.435150\pi\)
\(578\) 0 0
\(579\) 24.7296 + 18.3804i 1.02773 + 0.763865i
\(580\) 0 0
\(581\) −2.78959 4.83171i −0.115732 0.200453i
\(582\) 0 0
\(583\) 7.41981 12.8515i 0.307297 0.532254i
\(584\) 0 0
\(585\) 0.171590 + 0.569900i 0.00709436 + 0.0235625i
\(586\) 0 0
\(587\) 6.91088 11.9700i 0.285242 0.494054i −0.687425 0.726255i \(-0.741259\pi\)
0.972668 + 0.232200i \(0.0745925\pi\)
\(588\) 0 0
\(589\) 12.4067 + 21.4891i 0.511211 + 0.885444i
\(590\) 0 0
\(591\) −12.7849 + 5.52673i −0.525899 + 0.227339i
\(592\) 0 0
\(593\) −22.1361 −0.909022 −0.454511 0.890741i \(-0.650186\pi\)
−0.454511 + 0.890741i \(0.650186\pi\)
\(594\) 0 0
\(595\) −0.870718 −0.0356960
\(596\) 0 0
\(597\) 22.3109 9.64470i 0.913123 0.394731i
\(598\) 0 0
\(599\) 2.28059 + 3.95010i 0.0931824 + 0.161397i 0.908849 0.417126i \(-0.136963\pi\)
−0.815666 + 0.578523i \(0.803629\pi\)
\(600\) 0 0
\(601\) −10.2116 + 17.6870i −0.416541 + 0.721469i −0.995589 0.0938238i \(-0.970091\pi\)
0.579048 + 0.815293i \(0.303424\pi\)
\(602\) 0 0
\(603\) −34.4858 8.11627i −1.40437 0.330520i
\(604\) 0 0
\(605\) 2.53375 4.38858i 0.103012 0.178421i
\(606\) 0 0
\(607\) 7.11206 + 12.3184i 0.288670 + 0.499990i 0.973492 0.228719i \(-0.0734538\pi\)
−0.684823 + 0.728710i \(0.740120\pi\)
\(608\) 0 0
\(609\) 4.89187 + 3.63591i 0.198229 + 0.147335i
\(610\) 0 0
\(611\) −1.29154 −0.0522499
\(612\) 0 0
\(613\) −31.3892 −1.26780 −0.633899 0.773416i \(-0.718546\pi\)
−0.633899 + 0.773416i \(0.718546\pi\)
\(614\) 0 0
\(615\) 0.794126 6.84063i 0.0320222 0.275841i
\(616\) 0 0
\(617\) −2.51767 4.36073i −0.101357 0.175556i 0.810887 0.585203i \(-0.198985\pi\)
−0.912244 + 0.409647i \(0.865652\pi\)
\(618\) 0 0
\(619\) −19.1803 + 33.2212i −0.770920 + 1.33527i 0.166140 + 0.986102i \(0.446870\pi\)
−0.937060 + 0.349170i \(0.886464\pi\)
\(620\) 0 0
\(621\) −9.45964 + 1.69091i −0.379602 + 0.0678539i
\(622\) 0 0
\(623\) 1.91535 3.31748i 0.0767367 0.132912i
\(624\) 0 0
\(625\) −9.86020 17.0784i −0.394408 0.683135i
\(626\) 0 0
\(627\) −0.824508 + 7.10234i −0.0329277 + 0.283640i
\(628\) 0 0
\(629\) −0.870718 −0.0347178
\(630\) 0 0
\(631\) −24.0768 −0.958480 −0.479240 0.877684i \(-0.659088\pi\)
−0.479240 + 0.877684i \(0.659088\pi\)
\(632\) 0 0
\(633\) −20.3688 15.1392i −0.809586 0.601730i
\(634\) 0 0
\(635\) −3.34863 5.79999i −0.132886 0.230166i
\(636\) 0 0
\(637\) −0.165178 + 0.286096i −0.00654457 + 0.0113355i
\(638\) 0 0
\(639\) 8.59060 9.13412i 0.339839 0.361340i
\(640\) 0 0
\(641\) −20.7800 + 35.9920i −0.820760 + 1.42160i 0.0843567 + 0.996436i \(0.473116\pi\)
−0.905117 + 0.425163i \(0.860217\pi\)
\(642\) 0 0
\(643\) −0.924345 1.60101i −0.0364526 0.0631378i 0.847224 0.531237i \(-0.178272\pi\)
−0.883676 + 0.468099i \(0.844939\pi\)
\(644\) 0 0
\(645\) 3.46545 1.49807i 0.136452 0.0589863i
\(646\) 0 0
\(647\) 38.8480 1.52727 0.763637 0.645646i \(-0.223412\pi\)
0.763637 + 0.645646i \(0.223412\pi\)
\(648\) 0 0
\(649\) 22.1987 0.871374
\(650\) 0 0
\(651\) −15.2955 + 6.61206i −0.599479 + 0.259147i
\(652\) 0 0
\(653\) −20.3225 35.1996i −0.795281 1.37747i −0.922661 0.385613i \(-0.873990\pi\)
0.127380 0.991854i \(-0.459343\pi\)
\(654\) 0 0
\(655\) −1.56135 + 2.70435i −0.0610072 + 0.105668i
\(656\) 0 0
\(657\) 8.50833 9.04664i 0.331942 0.352943i
\(658\) 0 0
\(659\) 19.2140 33.2796i 0.748471 1.29639i −0.200084 0.979779i \(-0.564121\pi\)
0.948555 0.316612i \(-0.102545\pi\)
\(660\) 0 0
\(661\) 5.72841 + 9.92190i 0.222809 + 0.385917i 0.955660 0.294472i \(-0.0951439\pi\)
−0.732851 + 0.680390i \(0.761811\pi\)
\(662\) 0 0
\(663\) −0.665846 0.494894i −0.0258593 0.0192201i
\(664\) 0 0
\(665\) −1.54889 −0.0600635
\(666\) 0 0
\(667\) −6.50793 −0.251988
\(668\) 0 0
\(669\) 2.80701 24.1797i 0.108525 0.934842i
\(670\) 0 0
\(671\) 4.15231 + 7.19202i 0.160298 + 0.277645i
\(672\) 0 0
\(673\) −23.4933 + 40.6916i −0.905601 + 1.56855i −0.0854925 + 0.996339i \(0.527246\pi\)
−0.820108 + 0.572208i \(0.806087\pi\)
\(674\) 0 0
\(675\) 15.5389 + 18.4304i 0.598092 + 0.709388i
\(676\) 0 0
\(677\) 8.03942 13.9247i 0.308980 0.535169i −0.669159 0.743119i \(-0.733346\pi\)
0.978140 + 0.207950i \(0.0666790\pi\)
\(678\) 0 0
\(679\) 0.974782 + 1.68837i 0.0374087 + 0.0647938i
\(680\) 0 0
\(681\) −0.961113 + 8.27906i −0.0368299 + 0.317254i
\(682\) 0 0
\(683\) 5.20464 0.199150 0.0995750 0.995030i \(-0.468252\pi\)
0.0995750 + 0.995030i \(0.468252\pi\)
\(684\) 0 0
\(685\) 5.27750 0.201643
\(686\) 0 0
\(687\) 4.68247 + 3.48027i 0.178647 + 0.132781i
\(688\) 0 0
\(689\) 1.53147 + 2.65258i 0.0583444 + 0.101055i
\(690\) 0 0
\(691\) 0.783381 1.35686i 0.0298012 0.0516172i −0.850740 0.525587i \(-0.823846\pi\)
0.880541 + 0.473969i \(0.157179\pi\)
\(692\) 0 0
\(693\) −4.67391 1.10001i −0.177547 0.0417859i
\(694\) 0 0
\(695\) −2.70802 + 4.69043i −0.102721 + 0.177918i
\(696\) 0 0
\(697\) 4.79966 + 8.31326i 0.181800 + 0.314887i
\(698\) 0 0
\(699\) −33.2498 + 14.3735i −1.25762 + 0.543654i
\(700\) 0 0
\(701\) 5.94479 0.224532 0.112266 0.993678i \(-0.464189\pi\)
0.112266 + 0.993678i \(0.464189\pi\)
\(702\) 0 0
\(703\) −1.54889 −0.0584176
\(704\) 0 0
\(705\) 3.73270 1.61360i 0.140582 0.0607716i
\(706\) 0 0
\(707\) −8.79520 15.2337i −0.330777 0.572923i
\(708\) 0 0
\(709\) 6.53916 11.3262i 0.245583 0.425362i −0.716712 0.697369i \(-0.754354\pi\)
0.962295 + 0.272007i \(0.0876872\pi\)
\(710\) 0 0
\(711\) −7.03237 23.3566i −0.263734 0.875939i
\(712\) 0 0
\(713\) 8.89607 15.4084i 0.333160 0.577051i
\(714\) 0 0
\(715\) −0.158766 0.274990i −0.00593749 0.0102840i
\(716\) 0 0
\(717\) −26.7075 19.8505i −0.997411 0.741332i
\(718\) 0 0
\(719\) 10.5600 0.393821 0.196910 0.980422i \(-0.436909\pi\)
0.196910 + 0.980422i \(0.436909\pi\)
\(720\) 0 0
\(721\) 10.6109 0.395172
\(722\) 0 0
\(723\) −3.55088 + 30.5874i −0.132059 + 1.13756i
\(724\) 0 0
\(725\) 8.16297 + 14.1387i 0.303165 + 0.525097i
\(726\) 0 0
\(727\) −5.08052 + 8.79972i −0.188426 + 0.326364i −0.944726 0.327862i \(-0.893672\pi\)
0.756300 + 0.654226i \(0.227005\pi\)
\(728\) 0 0
\(729\) −20.7645 17.2579i −0.769056 0.639182i
\(730\) 0 0
\(731\) −2.63129 + 4.55753i −0.0973218 + 0.168566i
\(732\) 0 0
\(733\) −13.2280 22.9116i −0.488589 0.846260i 0.511325 0.859387i \(-0.329155\pi\)
−0.999914 + 0.0131270i \(0.995821\pi\)
\(734\) 0 0
\(735\) 0.119946 1.03322i 0.00442428 0.0381109i
\(736\) 0 0
\(737\) 18.9013 0.696237
\(738\) 0 0
\(739\) −24.3880 −0.897127 −0.448563 0.893751i \(-0.648064\pi\)
−0.448563 + 0.893751i \(0.648064\pi\)
\(740\) 0 0
\(741\) −1.18445 0.880352i −0.0435120 0.0323405i
\(742\) 0 0
\(743\) 8.21961 + 14.2368i 0.301548 + 0.522297i 0.976487 0.215577i \(-0.0691632\pi\)
−0.674939 + 0.737874i \(0.735830\pi\)
\(744\) 0 0
\(745\) 0.315654 0.546728i 0.0115647 0.0200306i
\(746\) 0 0
\(747\) 4.82549 + 16.0269i 0.176555 + 0.586392i
\(748\) 0 0
\(749\) −1.71974 + 2.97869i −0.0628381 + 0.108839i
\(750\) 0 0
\(751\) −0.0653789 0.113240i −0.00238571 0.00413217i 0.864830 0.502065i \(-0.167426\pi\)
−0.867216 + 0.497932i \(0.834093\pi\)
\(752\) 0 0
\(753\) 32.6765 14.1256i 1.19080 0.514766i
\(754\) 0 0
\(755\) 7.79415 0.283658
\(756\) 0 0
\(757\) 36.1017 1.31214 0.656069 0.754701i \(-0.272218\pi\)
0.656069 + 0.754701i \(0.272218\pi\)
\(758\) 0 0
\(759\) 4.70594 2.03432i 0.170815 0.0738410i
\(760\) 0 0
\(761\) 4.61027 + 7.98523i 0.167122 + 0.289464i 0.937407 0.348236i \(-0.113219\pi\)
−0.770285 + 0.637700i \(0.779886\pi\)
\(762\) 0 0
\(763\) 2.77505 4.80653i 0.100464 0.174008i
\(764\) 0 0
\(765\) 2.54268 + 0.598423i 0.0919309 + 0.0216360i
\(766\) 0 0
\(767\) −2.29093 + 3.96801i −0.0827208 + 0.143277i
\(768\) 0 0
\(769\) 22.8660 + 39.6050i 0.824568 + 1.42819i 0.902249 + 0.431216i \(0.141915\pi\)
−0.0776802 + 0.996978i \(0.524751\pi\)
\(770\) 0 0
\(771\) −35.2933 26.2319i −1.27106 0.944721i
\(772\) 0 0
\(773\) 25.9709 0.934109 0.467054 0.884229i \(-0.345315\pi\)
0.467054 + 0.884229i \(0.345315\pi\)
\(774\) 0 0
\(775\) −44.6338 −1.60329
\(776\) 0 0
\(777\) 0.119946 1.03322i 0.00430305 0.0370666i
\(778\) 0 0
\(779\) 8.53797 + 14.7882i 0.305905 + 0.529842i
\(780\) 0 0
\(781\) −3.34490 + 5.79353i −0.119690 + 0.207309i
\(782\) 0 0
\(783\) −11.7864 13.9797i −0.421213 0.499594i
\(784\) 0 0
\(785\) 5.92549 10.2632i 0.211490 0.366311i
\(786\) 0 0
\(787\) 25.3821 + 43.9630i 0.904773 + 1.56711i 0.821222 + 0.570609i \(0.193293\pi\)
0.0835512 + 0.996503i \(0.473374\pi\)
\(788\) 0 0
\(789\) 6.13404 52.8389i 0.218378 1.88111i
\(790\) 0 0
\(791\) 8.76158 0.311526
\(792\) 0 0
\(793\) −1.71410 −0.0608694
\(794\) 0 0
\(795\) −7.74019 5.75294i −0.274516 0.204036i
\(796\) 0 0
\(797\) −13.2977 23.0322i −0.471027 0.815843i 0.528424 0.848981i \(-0.322783\pi\)
−0.999451 + 0.0331379i \(0.989450\pi\)