Properties

Label 1386.2.r.c.89.2
Level $1386$
Weight $2$
Character 1386.89
Analytic conductor $11.067$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.2
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1386.89
Dual form 1386.2.r.c.1277.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.96593 - 3.40508i) q^{5} +(2.19067 + 1.48356i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.96593 - 3.40508i) q^{5} +(2.19067 + 1.48356i) q^{7} -1.00000i q^{8} +(-3.40508 + 1.96593i) q^{10} +(-0.866025 + 0.500000i) q^{11} -2.44949i q^{13} +(-1.15539 - 2.38014i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.64626 - 6.31552i) q^{17} +(3.17914 + 1.83548i) q^{19} +3.93185 q^{20} +1.00000 q^{22} +(2.94098 + 1.69798i) q^{23} +(-5.22973 - 9.05816i) q^{25} +(-1.22474 + 2.12132i) q^{26} +(-0.189469 + 2.63896i) q^{28} -5.16088i q^{29} +(-1.99465 + 1.15161i) q^{31} +(0.866025 - 0.500000i) q^{32} +7.29253i q^{34} +(9.35835 - 4.54284i) q^{35} +(1.98709 - 3.44174i) q^{37} +(-1.83548 - 3.17914i) q^{38} +(-3.40508 - 1.96593i) q^{40} +5.92480 q^{41} -10.7128 q^{43} +(-0.866025 - 0.500000i) q^{44} +(-1.69798 - 2.94098i) q^{46} +(-4.31199 + 7.46859i) q^{47} +(2.59808 + 6.50000i) q^{49} +10.4595i q^{50} +(2.12132 - 1.22474i) q^{52} +(11.5854 - 6.68885i) q^{53} +3.93185i q^{55} +(1.48356 - 2.19067i) q^{56} +(-2.58044 + 4.46945i) q^{58} +(0.975056 + 1.68885i) q^{59} +(5.16813 + 2.98382i) q^{61} +2.30323 q^{62} -1.00000 q^{64} +(-8.34072 - 4.81552i) q^{65} +(-2.33378 - 4.04222i) q^{67} +(3.64626 - 6.31552i) q^{68} +(-10.3760 - 0.744963i) q^{70} +8.90754i q^{71} +(-2.37466 + 1.37101i) q^{73} +(-3.44174 + 1.98709i) q^{74} +3.67095i q^{76} +(-2.63896 - 0.189469i) q^{77} +(7.69798 - 13.3333i) q^{79} +(1.96593 + 3.40508i) q^{80} +(-5.13103 - 2.96240i) q^{82} -6.05521 q^{83} -28.6731 q^{85} +(9.27755 + 5.35640i) q^{86} +(0.500000 + 0.866025i) q^{88} +(-5.87404 + 10.1741i) q^{89} +(3.63397 - 5.36603i) q^{91} +3.39595i q^{92} +(7.46859 - 4.31199i) q^{94} +(12.4999 - 7.21682i) q^{95} +5.85765i q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + 8q^{5} + O(q^{10}) \) \( 8q + 4q^{4} + 8q^{5} - 4q^{16} - 4q^{17} + 24q^{19} + 16q^{20} + 8q^{22} + 24q^{23} - 4q^{25} + 12q^{31} + 16q^{35} + 12q^{37} - 8q^{38} + 16q^{41} - 32q^{43} + 8q^{46} + 48q^{53} - 4q^{58} + 16q^{59} + 24q^{62} - 8q^{64} - 12q^{65} - 24q^{67} + 4q^{68} - 20q^{70} - 24q^{73} - 12q^{74} + 40q^{79} + 8q^{80} + 12q^{82} + 72q^{83} - 32q^{85} - 24q^{86} + 4q^{88} - 16q^{89} + 36q^{91} + 24q^{95} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.96593 3.40508i 0.879189 1.52280i 0.0269561 0.999637i \(-0.491419\pi\)
0.852233 0.523163i \(-0.175248\pi\)
\(6\) 0 0
\(7\) 2.19067 + 1.48356i 0.827996 + 0.560734i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −3.40508 + 1.96593i −1.07678 + 0.621680i
\(11\) −0.866025 + 0.500000i −0.261116 + 0.150756i
\(12\) 0 0
\(13\) 2.44949i 0.679366i −0.940540 0.339683i \(-0.889680\pi\)
0.940540 0.339683i \(-0.110320\pi\)
\(14\) −1.15539 2.38014i −0.308792 0.636119i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.64626 6.31552i −0.884349 1.53174i −0.846458 0.532456i \(-0.821269\pi\)
−0.0378910 0.999282i \(-0.512064\pi\)
\(18\) 0 0
\(19\) 3.17914 + 1.83548i 0.729344 + 0.421087i 0.818182 0.574959i \(-0.194982\pi\)
−0.0888382 + 0.996046i \(0.528315\pi\)
\(20\) 3.93185 0.879189
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 2.94098 + 1.69798i 0.613237 + 0.354053i 0.774231 0.632903i \(-0.218137\pi\)
−0.160994 + 0.986955i \(0.551470\pi\)
\(24\) 0 0
\(25\) −5.22973 9.05816i −1.04595 1.81163i
\(26\) −1.22474 + 2.12132i −0.240192 + 0.416025i
\(27\) 0 0
\(28\) −0.189469 + 2.63896i −0.0358062 + 0.498716i
\(29\) 5.16088i 0.958351i −0.877719 0.479175i \(-0.840936\pi\)
0.877719 0.479175i \(-0.159064\pi\)
\(30\) 0 0
\(31\) −1.99465 + 1.15161i −0.358250 + 0.206836i −0.668313 0.743880i \(-0.732983\pi\)
0.310063 + 0.950716i \(0.399650\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 7.29253i 1.25066i
\(35\) 9.35835 4.54284i 1.58185 0.767880i
\(36\) 0 0
\(37\) 1.98709 3.44174i 0.326675 0.565818i −0.655175 0.755477i \(-0.727405\pi\)
0.981850 + 0.189659i \(0.0607383\pi\)
\(38\) −1.83548 3.17914i −0.297753 0.515724i
\(39\) 0 0
\(40\) −3.40508 1.96593i −0.538391 0.310840i
\(41\) 5.92480 0.925299 0.462649 0.886541i \(-0.346899\pi\)
0.462649 + 0.886541i \(0.346899\pi\)
\(42\) 0 0
\(43\) −10.7128 −1.63369 −0.816843 0.576860i \(-0.804278\pi\)
−0.816843 + 0.576860i \(0.804278\pi\)
\(44\) −0.866025 0.500000i −0.130558 0.0753778i
\(45\) 0 0
\(46\) −1.69798 2.94098i −0.250353 0.433624i
\(47\) −4.31199 + 7.46859i −0.628969 + 1.08941i 0.358791 + 0.933418i \(0.383189\pi\)
−0.987759 + 0.155987i \(0.950144\pi\)
\(48\) 0 0
\(49\) 2.59808 + 6.50000i 0.371154 + 0.928571i
\(50\) 10.4595i 1.47919i
\(51\) 0 0
\(52\) 2.12132 1.22474i 0.294174 0.169842i
\(53\) 11.5854 6.68885i 1.59138 0.918784i 0.598309 0.801265i \(-0.295839\pi\)
0.993071 0.117519i \(-0.0374940\pi\)
\(54\) 0 0
\(55\) 3.93185i 0.530171i
\(56\) 1.48356 2.19067i 0.198250 0.292741i
\(57\) 0 0
\(58\) −2.58044 + 4.46945i −0.338828 + 0.586868i
\(59\) 0.975056 + 1.68885i 0.126941 + 0.219869i 0.922490 0.386021i \(-0.126151\pi\)
−0.795549 + 0.605890i \(0.792817\pi\)
\(60\) 0 0
\(61\) 5.16813 + 2.98382i 0.661711 + 0.382039i 0.792929 0.609314i \(-0.208555\pi\)
−0.131217 + 0.991354i \(0.541889\pi\)
\(62\) 2.30323 0.292510
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −8.34072 4.81552i −1.03454 0.597291i
\(66\) 0 0
\(67\) −2.33378 4.04222i −0.285116 0.493835i 0.687521 0.726164i \(-0.258699\pi\)
−0.972637 + 0.232329i \(0.925365\pi\)
\(68\) 3.64626 6.31552i 0.442175 0.765869i
\(69\) 0 0
\(70\) −10.3760 0.744963i −1.24017 0.0890401i
\(71\) 8.90754i 1.05713i 0.848893 + 0.528565i \(0.177270\pi\)
−0.848893 + 0.528565i \(0.822730\pi\)
\(72\) 0 0
\(73\) −2.37466 + 1.37101i −0.277933 + 0.160464i −0.632487 0.774571i \(-0.717966\pi\)
0.354554 + 0.935035i \(0.384633\pi\)
\(74\) −3.44174 + 1.98709i −0.400094 + 0.230994i
\(75\) 0 0
\(76\) 3.67095i 0.421087i
\(77\) −2.63896 0.189469i −0.300737 0.0215920i
\(78\) 0 0
\(79\) 7.69798 13.3333i 0.866090 1.50011i 0.000129281 1.00000i \(-0.499959\pi\)
0.865961 0.500112i \(-0.166708\pi\)
\(80\) 1.96593 + 3.40508i 0.219797 + 0.380700i
\(81\) 0 0
\(82\) −5.13103 2.96240i −0.566628 0.327143i
\(83\) −6.05521 −0.664646 −0.332323 0.943166i \(-0.607832\pi\)
−0.332323 + 0.943166i \(0.607832\pi\)
\(84\) 0 0
\(85\) −28.6731 −3.11004
\(86\) 9.27755 + 5.35640i 1.00042 + 0.577595i
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) −5.87404 + 10.1741i −0.622647 + 1.07846i 0.366344 + 0.930479i \(0.380609\pi\)
−0.988991 + 0.147976i \(0.952724\pi\)
\(90\) 0 0
\(91\) 3.63397 5.36603i 0.380944 0.562512i
\(92\) 3.39595i 0.354053i
\(93\) 0 0
\(94\) 7.46859 4.31199i 0.770326 0.444748i
\(95\) 12.4999 7.21682i 1.28246 0.740430i
\(96\) 0 0
\(97\) 5.85765i 0.594754i 0.954760 + 0.297377i \(0.0961119\pi\)
−0.954760 + 0.297377i \(0.903888\pi\)
\(98\) 1.00000 6.92820i 0.101015 0.699854i
\(99\) 0 0
\(100\) 5.22973 9.05816i 0.522973 0.905816i
\(101\) −7.76028 13.4412i −0.772177 1.33745i −0.936368 0.351021i \(-0.885835\pi\)
0.164191 0.986429i \(-0.447499\pi\)
\(102\) 0 0
\(103\) 10.7413 + 6.20150i 1.05837 + 0.611052i 0.924982 0.380011i \(-0.124080\pi\)
0.133391 + 0.991063i \(0.457413\pi\)
\(104\) −2.44949 −0.240192
\(105\) 0 0
\(106\) −13.3777 −1.29936
\(107\) −11.9441 6.89595i −1.15468 0.666657i −0.204660 0.978833i \(-0.565609\pi\)
−0.950024 + 0.312176i \(0.898942\pi\)
\(108\) 0 0
\(109\) −2.45534 4.25277i −0.235179 0.407341i 0.724146 0.689647i \(-0.242234\pi\)
−0.959325 + 0.282306i \(0.908901\pi\)
\(110\) 1.96593 3.40508i 0.187444 0.324662i
\(111\) 0 0
\(112\) −2.38014 + 1.15539i −0.224902 + 0.109175i
\(113\) 16.1270i 1.51710i −0.651614 0.758551i \(-0.725908\pi\)
0.651614 0.758551i \(-0.274092\pi\)
\(114\) 0 0
\(115\) 11.5635 6.67619i 1.07830 0.622558i
\(116\) 4.46945 2.58044i 0.414978 0.239588i
\(117\) 0 0
\(118\) 1.95011i 0.179522i
\(119\) 1.38171 19.2447i 0.126661 1.76416i
\(120\) 0 0
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) −2.98382 5.16813i −0.270143 0.467901i
\(123\) 0 0
\(124\) −1.99465 1.15161i −0.179125 0.103418i
\(125\) −21.4658 −1.91996
\(126\) 0 0
\(127\) 9.94522 0.882495 0.441248 0.897385i \(-0.354536\pi\)
0.441248 + 0.897385i \(0.354536\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 4.81552 + 8.34072i 0.422349 + 0.731529i
\(131\) 9.24264 16.0087i 0.807533 1.39869i −0.107034 0.994255i \(-0.534135\pi\)
0.914567 0.404433i \(-0.132531\pi\)
\(132\) 0 0
\(133\) 4.24140 + 8.73737i 0.367776 + 0.757626i
\(134\) 4.66755i 0.403215i
\(135\) 0 0
\(136\) −6.31552 + 3.64626i −0.541551 + 0.312665i
\(137\) −2.41786 + 1.39595i −0.206572 + 0.119264i −0.599717 0.800212i \(-0.704720\pi\)
0.393145 + 0.919476i \(0.371387\pi\)
\(138\) 0 0
\(139\) 5.10583i 0.433071i −0.976275 0.216535i \(-0.930524\pi\)
0.976275 0.216535i \(-0.0694757\pi\)
\(140\) 8.61339 + 5.83315i 0.727965 + 0.492991i
\(141\) 0 0
\(142\) 4.45377 7.71415i 0.373752 0.647358i
\(143\) 1.22474 + 2.12132i 0.102418 + 0.177394i
\(144\) 0 0
\(145\) −17.5732 10.1459i −1.45938 0.842571i
\(146\) 2.74202 0.226931
\(147\) 0 0
\(148\) 3.97418 0.326675
\(149\) 5.93596 + 3.42713i 0.486292 + 0.280761i 0.723035 0.690811i \(-0.242746\pi\)
−0.236743 + 0.971572i \(0.576080\pi\)
\(150\) 0 0
\(151\) 7.23351 + 12.5288i 0.588655 + 1.01958i 0.994409 + 0.105598i \(0.0336756\pi\)
−0.405754 + 0.913982i \(0.632991\pi\)
\(152\) 1.83548 3.17914i 0.148877 0.257862i
\(153\) 0 0
\(154\) 2.19067 + 1.48356i 0.176529 + 0.119549i
\(155\) 9.05594i 0.727391i
\(156\) 0 0
\(157\) 14.4305 8.33145i 1.15168 0.664922i 0.202383 0.979306i \(-0.435131\pi\)
0.949296 + 0.314384i \(0.101798\pi\)
\(158\) −13.3333 + 7.69798i −1.06074 + 0.612418i
\(159\) 0 0
\(160\) 3.93185i 0.310840i
\(161\) 3.92367 + 8.08284i 0.309228 + 0.637017i
\(162\) 0 0
\(163\) −0.481740 + 0.834398i −0.0377328 + 0.0653551i −0.884275 0.466966i \(-0.845347\pi\)
0.846542 + 0.532321i \(0.178680\pi\)
\(164\) 2.96240 + 5.13103i 0.231325 + 0.400666i
\(165\) 0 0
\(166\) 5.24397 + 3.02761i 0.407011 + 0.234988i
\(167\) −1.93426 −0.149677 −0.0748386 0.997196i \(-0.523844\pi\)
−0.0748386 + 0.997196i \(0.523844\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 24.8317 + 14.3366i 1.90450 + 1.09956i
\(171\) 0 0
\(172\) −5.35640 9.27755i −0.408421 0.707407i
\(173\) −9.87902 + 17.1110i −0.751088 + 1.30092i 0.196208 + 0.980562i \(0.437137\pi\)
−0.947296 + 0.320360i \(0.896196\pi\)
\(174\) 0 0
\(175\) 1.98174 27.6021i 0.149805 2.08652i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) 10.1741 5.87404i 0.762583 0.440278i
\(179\) −9.13593 + 5.27463i −0.682852 + 0.394245i −0.800929 0.598760i \(-0.795660\pi\)
0.118077 + 0.993004i \(0.462327\pi\)
\(180\) 0 0
\(181\) 4.12560i 0.306653i 0.988176 + 0.153327i \(0.0489987\pi\)
−0.988176 + 0.153327i \(0.951001\pi\)
\(182\) −5.83013 + 2.83013i −0.432158 + 0.209783i
\(183\) 0 0
\(184\) 1.69798 2.94098i 0.125176 0.216812i
\(185\) −7.81294 13.5324i −0.574418 0.994922i
\(186\) 0 0
\(187\) 6.31552 + 3.64626i 0.461836 + 0.266641i
\(188\) −8.62398 −0.628969
\(189\) 0 0
\(190\) −14.4336 −1.04713
\(191\) −19.9354 11.5097i −1.44248 0.832813i −0.444461 0.895798i \(-0.646605\pi\)
−0.998014 + 0.0629850i \(0.979938\pi\)
\(192\) 0 0
\(193\) −4.60708 7.97970i −0.331625 0.574391i 0.651206 0.758901i \(-0.274264\pi\)
−0.982831 + 0.184510i \(0.940930\pi\)
\(194\) 2.92883 5.07287i 0.210277 0.364211i
\(195\) 0 0
\(196\) −4.33013 + 5.50000i −0.309295 + 0.392857i
\(197\) 6.52180i 0.464659i 0.972637 + 0.232330i \(0.0746348\pi\)
−0.972637 + 0.232330i \(0.925365\pi\)
\(198\) 0 0
\(199\) −12.9813 + 7.49473i −0.920217 + 0.531288i −0.883704 0.468046i \(-0.844958\pi\)
−0.0365128 + 0.999333i \(0.511625\pi\)
\(200\) −9.05816 + 5.22973i −0.640508 + 0.369798i
\(201\) 0 0
\(202\) 15.5206i 1.09202i
\(203\) 7.65649 11.3058i 0.537380 0.793510i
\(204\) 0 0
\(205\) 11.6477 20.1744i 0.813512 1.40904i
\(206\) −6.20150 10.7413i −0.432079 0.748383i
\(207\) 0 0
\(208\) 2.12132 + 1.22474i 0.147087 + 0.0849208i
\(209\) −3.67095 −0.253925
\(210\) 0 0
\(211\) −9.10759 −0.626992 −0.313496 0.949589i \(-0.601500\pi\)
−0.313496 + 0.949589i \(0.601500\pi\)
\(212\) 11.5854 + 6.68885i 0.795690 + 0.459392i
\(213\) 0 0
\(214\) 6.89595 + 11.9441i 0.471398 + 0.816485i
\(215\) −21.0606 + 36.4780i −1.43632 + 2.48778i
\(216\) 0 0
\(217\) −6.07812 0.436389i −0.412609 0.0296240i
\(218\) 4.91067i 0.332593i
\(219\) 0 0
\(220\) −3.40508 + 1.96593i −0.229571 + 0.132543i
\(221\) −15.4698 + 8.93149i −1.04061 + 0.600797i
\(222\) 0 0
\(223\) 7.28788i 0.488033i −0.969771 0.244016i \(-0.921535\pi\)
0.969771 0.244016i \(-0.0784651\pi\)
\(224\) 2.63896 + 0.189469i 0.176323 + 0.0126594i
\(225\) 0 0
\(226\) −8.06350 + 13.9664i −0.536376 + 0.929031i
\(227\) −0.465428 0.806145i −0.0308915 0.0535057i 0.850166 0.526514i \(-0.176501\pi\)
−0.881058 + 0.473009i \(0.843168\pi\)
\(228\) 0 0
\(229\) 20.8048 + 12.0117i 1.37482 + 0.793753i 0.991530 0.129874i \(-0.0414574\pi\)
0.383291 + 0.923628i \(0.374791\pi\)
\(230\) −13.3524 −0.880430
\(231\) 0 0
\(232\) −5.16088 −0.338828
\(233\) 15.1427 + 8.74264i 0.992031 + 0.572749i 0.905881 0.423533i \(-0.139210\pi\)
0.0861503 + 0.996282i \(0.472543\pi\)
\(234\) 0 0
\(235\) 16.9541 + 29.3654i 1.10596 + 1.91559i
\(236\) −0.975056 + 1.68885i −0.0634707 + 0.109935i
\(237\) 0 0
\(238\) −10.8189 + 15.9755i −0.701287 + 1.03554i
\(239\) 0.712115i 0.0460629i 0.999735 + 0.0230315i \(0.00733179\pi\)
−0.999735 + 0.0230315i \(0.992668\pi\)
\(240\) 0 0
\(241\) −13.5097 + 7.79983i −0.870237 + 0.502432i −0.867427 0.497565i \(-0.834228\pi\)
−0.00280996 + 0.999996i \(0.500894\pi\)
\(242\) −0.866025 + 0.500000i −0.0556702 + 0.0321412i
\(243\) 0 0
\(244\) 5.96764i 0.382039i
\(245\) 27.2407 + 3.93185i 1.74034 + 0.251197i
\(246\) 0 0
\(247\) 4.49598 7.78726i 0.286072 0.495492i
\(248\) 1.15161 + 1.99465i 0.0731275 + 0.126661i
\(249\) 0 0
\(250\) 18.5899 + 10.7329i 1.17573 + 0.678807i
\(251\) 22.2326 1.40331 0.701655 0.712516i \(-0.252445\pi\)
0.701655 + 0.712516i \(0.252445\pi\)
\(252\) 0 0
\(253\) −3.39595 −0.213502
\(254\) −8.61281 4.97261i −0.540416 0.312009i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.47443 + 2.55379i −0.0919727 + 0.159301i −0.908341 0.418230i \(-0.862651\pi\)
0.816368 + 0.577531i \(0.195984\pi\)
\(258\) 0 0
\(259\) 9.45909 4.59174i 0.587759 0.285317i
\(260\) 9.63103i 0.597291i
\(261\) 0 0
\(262\) −16.0087 + 9.24264i −0.989022 + 0.571012i
\(263\) −16.4066 + 9.47237i −1.01168 + 0.584091i −0.911682 0.410897i \(-0.865216\pi\)
−0.0999939 + 0.994988i \(0.531882\pi\)
\(264\) 0 0
\(265\) 52.5991i 3.23114i
\(266\) 0.695530 9.68749i 0.0426457 0.593978i
\(267\) 0 0
\(268\) 2.33378 4.04222i 0.142558 0.246918i
\(269\) 12.1165 + 20.9863i 0.738754 + 1.27956i 0.953057 + 0.302792i \(0.0979189\pi\)
−0.214302 + 0.976767i \(0.568748\pi\)
\(270\) 0 0
\(271\) 19.4275 + 11.2165i 1.18013 + 0.681351i 0.956046 0.293218i \(-0.0947261\pi\)
0.224089 + 0.974569i \(0.428059\pi\)
\(272\) 7.29253 0.442175
\(273\) 0 0
\(274\) 2.79191 0.168665
\(275\) 9.05816 + 5.22973i 0.546227 + 0.315365i
\(276\) 0 0
\(277\) 4.92392 + 8.52849i 0.295850 + 0.512427i 0.975182 0.221404i \(-0.0710638\pi\)
−0.679332 + 0.733831i \(0.737731\pi\)
\(278\) −2.55291 + 4.42178i −0.153114 + 0.265201i
\(279\) 0 0
\(280\) −4.54284 9.35835i −0.271487 0.559269i
\(281\) 10.8623i 0.647990i 0.946059 + 0.323995i \(0.105026\pi\)
−0.946059 + 0.323995i \(0.894974\pi\)
\(282\) 0 0
\(283\) −8.32792 + 4.80813i −0.495044 + 0.285814i −0.726664 0.686993i \(-0.758930\pi\)
0.231621 + 0.972806i \(0.425597\pi\)
\(284\) −7.71415 + 4.45377i −0.457751 + 0.264283i
\(285\) 0 0
\(286\) 2.44949i 0.144841i
\(287\) 12.9793 + 8.78982i 0.766143 + 0.518847i
\(288\) 0 0
\(289\) −18.0905 + 31.3336i −1.06415 + 1.84316i
\(290\) 10.1459 + 17.5732i 0.595788 + 1.03193i
\(291\) 0 0
\(292\) −2.37466 1.37101i −0.138966 0.0802322i
\(293\) −14.4546 −0.844450 −0.422225 0.906491i \(-0.638751\pi\)
−0.422225 + 0.906491i \(0.638751\pi\)
\(294\) 0 0
\(295\) 7.66755 0.446422
\(296\) −3.44174 1.98709i −0.200047 0.115497i
\(297\) 0 0
\(298\) −3.42713 5.93596i −0.198528 0.343861i
\(299\) 4.15918 7.20390i 0.240531 0.416613i
\(300\) 0 0
\(301\) −23.4682 15.8931i −1.35268 0.916064i
\(302\) 14.4670i 0.832484i
\(303\) 0 0
\(304\) −3.17914 + 1.83548i −0.182336 + 0.105272i
\(305\) 20.3203 11.7319i 1.16354 0.671769i
\(306\) 0 0
\(307\) 0.928932i 0.0530170i −0.999649 0.0265085i \(-0.991561\pi\)
0.999649 0.0265085i \(-0.00843890\pi\)
\(308\) −1.15539 2.38014i −0.0658347 0.135621i
\(309\) 0 0
\(310\) 4.52797 7.84267i 0.257171 0.445434i
\(311\) 13.3841 + 23.1819i 0.758940 + 1.31452i 0.943392 + 0.331681i \(0.107616\pi\)
−0.184451 + 0.982842i \(0.559051\pi\)
\(312\) 0 0
\(313\) 6.88437 + 3.97469i 0.389127 + 0.224663i 0.681782 0.731555i \(-0.261205\pi\)
−0.292655 + 0.956218i \(0.594539\pi\)
\(314\) −16.6629 −0.940342
\(315\) 0 0
\(316\) 15.3960 0.866090
\(317\) 14.4394 + 8.33657i 0.810995 + 0.468228i 0.847301 0.531112i \(-0.178226\pi\)
−0.0363060 + 0.999341i \(0.511559\pi\)
\(318\) 0 0
\(319\) 2.58044 + 4.46945i 0.144477 + 0.250241i
\(320\) −1.96593 + 3.40508i −0.109899 + 0.190350i
\(321\) 0 0
\(322\) 0.643427 8.96178i 0.0358568 0.499420i
\(323\) 26.7705i 1.48955i
\(324\) 0 0
\(325\) −22.1879 + 12.8102i −1.23076 + 0.710580i
\(326\) 0.834398 0.481740i 0.0462130 0.0266811i
\(327\) 0 0
\(328\) 5.92480i 0.327143i
\(329\) −20.5263 + 9.96410i −1.13165 + 0.549339i
\(330\) 0 0
\(331\) 1.58933 2.75280i 0.0873574 0.151307i −0.819036 0.573742i \(-0.805491\pi\)
0.906393 + 0.422435i \(0.138824\pi\)
\(332\) −3.02761 5.24397i −0.166161 0.287800i
\(333\) 0 0
\(334\) 1.67511 + 0.967128i 0.0916582 + 0.0529189i
\(335\) −18.3521 −1.00268
\(336\) 0 0
\(337\) 15.7473 0.857812 0.428906 0.903349i \(-0.358899\pi\)
0.428906 + 0.903349i \(0.358899\pi\)
\(338\) −6.06218 3.50000i −0.329739 0.190375i
\(339\) 0 0
\(340\) −14.3366 24.8317i −0.777510 1.34669i
\(341\) 1.15161 1.99465i 0.0623633 0.108016i
\(342\) 0 0
\(343\) −3.95164 + 18.0938i −0.213368 + 0.976972i
\(344\) 10.7128i 0.577595i
\(345\) 0 0
\(346\) 17.1110 9.87902i 0.919891 0.531099i
\(347\) 22.7976 13.1622i 1.22384 0.706584i 0.258105 0.966117i \(-0.416902\pi\)
0.965734 + 0.259533i \(0.0835686\pi\)
\(348\) 0 0
\(349\) 32.9044i 1.76133i 0.473737 + 0.880666i \(0.342905\pi\)
−0.473737 + 0.880666i \(0.657095\pi\)
\(350\) −15.5173 + 22.9132i −0.829433 + 1.22476i
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 4.74943 + 8.22626i 0.252787 + 0.437839i 0.964292 0.264841i \(-0.0853196\pi\)
−0.711505 + 0.702681i \(0.751986\pi\)
\(354\) 0 0
\(355\) 30.3309 + 17.5116i 1.60980 + 0.929417i
\(356\) −11.7481 −0.622647
\(357\) 0 0
\(358\) 10.5493 0.557546
\(359\) −2.59578 1.49867i −0.137000 0.0790970i 0.429933 0.902861i \(-0.358537\pi\)
−0.566933 + 0.823764i \(0.691870\pi\)
\(360\) 0 0
\(361\) −2.76206 4.78403i −0.145372 0.251791i
\(362\) 2.06280 3.57287i 0.108418 0.187786i
\(363\) 0 0
\(364\) 6.46410 + 0.464102i 0.338811 + 0.0243255i
\(365\) 10.7812i 0.564314i
\(366\) 0 0
\(367\) 14.3336 8.27551i 0.748208 0.431978i −0.0768379 0.997044i \(-0.524482\pi\)
0.825046 + 0.565065i \(0.191149\pi\)
\(368\) −2.94098 + 1.69798i −0.153309 + 0.0885132i
\(369\) 0 0
\(370\) 15.6259i 0.812350i
\(371\) 35.3032 + 2.53465i 1.83285 + 0.131593i
\(372\) 0 0
\(373\) 9.73753 16.8659i 0.504190 0.873283i −0.495798 0.868438i \(-0.665124\pi\)
0.999988 0.00484535i \(-0.00154233\pi\)
\(374\) −3.64626 6.31552i −0.188544 0.326568i
\(375\) 0 0
\(376\) 7.46859 + 4.31199i 0.385163 + 0.222374i
\(377\) −12.6415 −0.651071
\(378\) 0 0
\(379\) 2.20809 0.113422 0.0567111 0.998391i \(-0.481939\pi\)
0.0567111 + 0.998391i \(0.481939\pi\)
\(380\) 12.4999 + 7.21682i 0.641231 + 0.370215i
\(381\) 0 0
\(382\) 11.5097 + 19.9354i 0.588888 + 1.01998i
\(383\) −1.41849 + 2.45690i −0.0724816 + 0.125542i −0.899988 0.435914i \(-0.856425\pi\)
0.827507 + 0.561456i \(0.189759\pi\)
\(384\) 0 0
\(385\) −5.83315 + 8.61339i −0.297285 + 0.438979i
\(386\) 9.21416i 0.468989i
\(387\) 0 0
\(388\) −5.07287 + 2.92883i −0.257536 + 0.148689i
\(389\) 16.4686 9.50814i 0.834991 0.482082i −0.0205678 0.999788i \(-0.506547\pi\)
0.855558 + 0.517706i \(0.173214\pi\)
\(390\) 0 0
\(391\) 24.7651i 1.25242i
\(392\) 6.50000 2.59808i 0.328300 0.131223i
\(393\) 0 0
\(394\) 3.26090 5.64805i 0.164282 0.284544i
\(395\) −30.2673 52.4245i −1.52291 2.63776i
\(396\) 0 0
\(397\) 9.23729 + 5.33315i 0.463606 + 0.267663i 0.713559 0.700595i \(-0.247082\pi\)
−0.249953 + 0.968258i \(0.580415\pi\)
\(398\) 14.9895 0.751354
\(399\) 0 0
\(400\) 10.4595 0.522973
\(401\) 28.4216 + 16.4092i 1.41931 + 0.819437i 0.996238 0.0866614i \(-0.0276198\pi\)
0.423068 + 0.906098i \(0.360953\pi\)
\(402\) 0 0
\(403\) 2.82086 + 4.88588i 0.140517 + 0.243383i
\(404\) 7.76028 13.4412i 0.386088 0.668725i
\(405\) 0 0
\(406\) −12.2836 + 5.96285i −0.609625 + 0.295931i
\(407\) 3.97418i 0.196993i
\(408\) 0 0
\(409\) −6.25334 + 3.61037i −0.309208 + 0.178521i −0.646572 0.762853i \(-0.723798\pi\)
0.337364 + 0.941374i \(0.390465\pi\)
\(410\) −20.1744 + 11.6477i −0.996345 + 0.575240i
\(411\) 0 0
\(412\) 12.4030i 0.611052i
\(413\) −0.369485 + 5.14626i −0.0181812 + 0.253231i
\(414\) 0 0
\(415\) −11.9041 + 20.6185i −0.584349 + 1.01212i
\(416\) −1.22474 2.12132i −0.0600481 0.104006i
\(417\) 0 0
\(418\) 3.17914 + 1.83548i 0.155497 + 0.0897760i
\(419\) −15.9184 −0.777665 −0.388832 0.921309i \(-0.627121\pi\)
−0.388832 + 0.921309i \(0.627121\pi\)
\(420\) 0 0
\(421\) 4.23889 0.206591 0.103295 0.994651i \(-0.467061\pi\)
0.103295 + 0.994651i \(0.467061\pi\)
\(422\) 7.88740 + 4.55379i 0.383953 + 0.221675i
\(423\) 0 0
\(424\) −6.68885 11.5854i −0.324839 0.562638i
\(425\) −38.1379 + 66.0569i −1.84996 + 3.20423i
\(426\) 0 0
\(427\) 6.89498 + 14.2038i 0.333672 + 0.687371i
\(428\) 13.7919i 0.666657i
\(429\) 0 0
\(430\) 36.4780 21.0606i 1.75912 1.01563i
\(431\) −17.4567 + 10.0786i −0.840860 + 0.485471i −0.857556 0.514390i \(-0.828018\pi\)
0.0166966 + 0.999861i \(0.494685\pi\)
\(432\) 0 0
\(433\) 5.81292i 0.279351i −0.990197 0.139676i \(-0.955394\pi\)
0.990197 0.139676i \(-0.0446060\pi\)
\(434\) 5.04561 + 3.41698i 0.242197 + 0.164020i
\(435\) 0 0
\(436\) 2.45534 4.25277i 0.117589 0.203671i
\(437\) 6.23319 + 10.7962i 0.298174 + 0.516452i
\(438\) 0 0
\(439\) 24.0204 + 13.8682i 1.14643 + 0.661893i 0.948015 0.318225i \(-0.103087\pi\)
0.198416 + 0.980118i \(0.436420\pi\)
\(440\) 3.93185 0.187444
\(441\) 0 0
\(442\) 17.8630 0.849655
\(443\) 11.4746 + 6.62486i 0.545175 + 0.314757i 0.747173 0.664629i \(-0.231410\pi\)
−0.201999 + 0.979386i \(0.564744\pi\)
\(444\) 0 0
\(445\) 23.0958 + 40.0032i 1.09485 + 1.89633i
\(446\) −3.64394 + 6.31149i −0.172546 + 0.298858i
\(447\) 0 0
\(448\) −2.19067 1.48356i −0.103499 0.0700918i
\(449\) 21.9232i 1.03462i 0.855798 + 0.517310i \(0.173067\pi\)
−0.855798 + 0.517310i \(0.826933\pi\)
\(450\) 0 0
\(451\) −5.13103 + 2.96240i −0.241611 + 0.139494i
\(452\) 13.9664 8.06350i 0.656924 0.379275i
\(453\) 0 0
\(454\) 0.930856i 0.0436872i
\(455\) −11.1276 22.9232i −0.521672 1.07466i
\(456\) 0 0
\(457\) 16.3092 28.2483i 0.762911 1.32140i −0.178433 0.983952i \(-0.557103\pi\)
0.941344 0.337449i \(-0.109564\pi\)
\(458\) −12.0117 20.8048i −0.561268 0.972145i
\(459\) 0 0
\(460\) 11.5635 + 6.67619i 0.539151 + 0.311279i
\(461\) −31.6262 −1.47298 −0.736489 0.676450i \(-0.763518\pi\)
−0.736489 + 0.676450i \(0.763518\pi\)
\(462\) 0 0
\(463\) 11.5687 0.537642 0.268821 0.963190i \(-0.413366\pi\)
0.268821 + 0.963190i \(0.413366\pi\)
\(464\) 4.46945 + 2.58044i 0.207489 + 0.119794i
\(465\) 0 0
\(466\) −8.74264 15.1427i −0.404995 0.701472i
\(467\) 3.92392 6.79643i 0.181578 0.314501i −0.760840 0.648939i \(-0.775213\pi\)
0.942418 + 0.334438i \(0.108546\pi\)
\(468\) 0 0
\(469\) 0.884355 12.3175i 0.0408357 0.568768i
\(470\) 33.9082i 1.56407i
\(471\) 0 0
\(472\) 1.68885 0.975056i 0.0777355 0.0448806i
\(473\) 9.27755 5.35640i 0.426582 0.246287i
\(474\) 0 0
\(475\) 38.3962i 1.76174i
\(476\) 17.3572 8.42575i 0.795568 0.386194i
\(477\) 0 0
\(478\) 0.356058 0.616710i 0.0162857 0.0282077i
\(479\) −20.3161 35.1885i −0.928267 1.60781i −0.786221 0.617945i \(-0.787965\pi\)
−0.142046 0.989860i \(-0.545368\pi\)
\(480\) 0 0
\(481\) −8.43050 4.86735i −0.384398 0.221932i
\(482\) 15.5997 0.710545
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 19.9458 + 11.5157i 0.905692 + 0.522901i
\(486\) 0 0
\(487\) 12.6074 + 21.8367i 0.571297 + 0.989515i 0.996433 + 0.0843858i \(0.0268928\pi\)
−0.425136 + 0.905129i \(0.639774\pi\)
\(488\) 2.98382 5.16813i 0.135071 0.233950i
\(489\) 0 0
\(490\) −21.6252 17.0254i −0.976926 0.769130i
\(491\) 2.83551i 0.127965i −0.997951 0.0639824i \(-0.979620\pi\)
0.997951 0.0639824i \(-0.0203802\pi\)
\(492\) 0 0
\(493\) −32.5936 + 18.8179i −1.46794 + 0.847516i
\(494\) −7.78726 + 4.49598i −0.350365 + 0.202284i
\(495\) 0 0
\(496\) 2.30323i 0.103418i
\(497\) −13.2149 + 19.5135i −0.592769 + 0.875299i
\(498\) 0 0
\(499\) −7.29858 + 12.6415i −0.326729 + 0.565912i −0.981861 0.189603i \(-0.939280\pi\)
0.655131 + 0.755515i \(0.272613\pi\)
\(500\) −10.7329 18.5899i −0.479989 0.831366i
\(501\) 0 0
\(502\) −19.2540 11.1163i −0.859349 0.496145i
\(503\) −14.4955 −0.646322 −0.323161 0.946344i \(-0.604745\pi\)
−0.323161 + 0.946344i \(0.604745\pi\)
\(504\) 0 0
\(505\) −61.0245 −2.71556
\(506\) 2.94098 + 1.69798i 0.130743 + 0.0754843i
\(507\) 0 0
\(508\) 4.97261 + 8.61281i 0.220624 + 0.382132i
\(509\) 14.4421 25.0144i 0.640134 1.10874i −0.345269 0.938504i \(-0.612212\pi\)
0.985403 0.170240i \(-0.0544544\pi\)
\(510\) 0 0
\(511\) −7.23607 0.519527i −0.320105 0.0229825i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 2.55379 1.47443i 0.112643 0.0650345i
\(515\) 42.2333 24.3834i 1.86102 1.07446i
\(516\) 0 0
\(517\) 8.62398i 0.379282i
\(518\) −10.4877 0.752982i −0.460802 0.0330841i
\(519\) 0 0
\(520\) −4.81552 + 8.34072i −0.211174 + 0.365765i
\(521\) −2.96937 5.14310i −0.130090 0.225323i 0.793621 0.608413i \(-0.208193\pi\)
−0.923711 + 0.383090i \(0.874860\pi\)
\(522\) 0 0
\(523\) −15.6424 9.03115i −0.683995 0.394905i 0.117364 0.993089i \(-0.462556\pi\)
−0.801358 + 0.598184i \(0.795889\pi\)
\(524\) 18.4853 0.807533
\(525\) 0 0
\(526\) 18.9447 0.826030
\(527\) 14.5461 + 8.39817i 0.633636 + 0.365830i
\(528\) 0 0
\(529\) −5.73375 9.93115i −0.249294 0.431789i
\(530\) −26.2996 + 45.5522i −1.14238 + 1.97866i
\(531\) 0 0
\(532\) −5.44609 + 8.04184i −0.236118 + 0.348658i
\(533\) 14.5127i 0.628617i
\(534\) 0 0
\(535\) −46.9626 + 27.1139i −2.03037 + 1.17223i
\(536\) −4.04222 + 2.33378i −0.174597 + 0.100804i
\(537\) 0 0
\(538\) 24.2329i 1.04476i
\(539\) −5.50000 4.33013i −0.236902 0.186512i
\(540\) 0 0
\(541\) 7.59039 13.1469i 0.326336 0.565231i −0.655446 0.755242i \(-0.727519\pi\)
0.981782 + 0.190011i \(0.0608525\pi\)
\(542\) −11.2165 19.4275i −0.481788 0.834481i
\(543\) 0 0
\(544\) −6.31552 3.64626i −0.270775 0.156332i
\(545\) −19.3080 −0.827065
\(546\) 0 0
\(547\) 12.6498 0.540865 0.270433 0.962739i \(-0.412833\pi\)
0.270433 + 0.962739i \(0.412833\pi\)
\(548\) −2.41786 1.39595i −0.103286 0.0596322i
\(549\) 0 0
\(550\) −5.22973 9.05816i −0.222996 0.386241i
\(551\) 9.47266 16.4071i 0.403549 0.698967i
\(552\) 0 0
\(553\) 36.6445 17.7884i 1.55828 0.756440i
\(554\) 9.84785i 0.418395i
\(555\) 0 0
\(556\) 4.42178 2.55291i 0.187525 0.108268i
\(557\) 2.43639 1.40665i 0.103233 0.0596017i −0.447495 0.894287i \(-0.647684\pi\)
0.550728 + 0.834685i \(0.314350\pi\)
\(558\) 0 0
\(559\) 26.2409i 1.10987i
\(560\) −0.744963 + 10.3760i −0.0314804 + 0.438466i
\(561\) 0 0
\(562\) 5.43115 9.40702i 0.229099 0.396811i
\(563\) −2.94887 5.10759i −0.124280 0.215259i 0.797171 0.603753i \(-0.206329\pi\)
−0.921451 + 0.388494i \(0.872995\pi\)
\(564\) 0 0
\(565\) −54.9138 31.7045i −2.31024 1.33382i
\(566\) 9.61625 0.404201
\(567\) 0 0
\(568\) 8.90754 0.373752
\(569\) 24.4687 + 14.1270i 1.02578 + 0.592235i 0.915773 0.401696i \(-0.131579\pi\)
0.110008 + 0.993931i \(0.464912\pi\)
\(570\) 0 0
\(571\) 16.6142 + 28.7766i 0.695281 + 1.20426i 0.970086 + 0.242762i \(0.0780535\pi\)
−0.274805 + 0.961500i \(0.588613\pi\)
\(572\) −1.22474 + 2.12132i −0.0512092 + 0.0886969i
\(573\) 0 0
\(574\) −6.84549 14.1019i −0.285725 0.588600i
\(575\) 35.5198i 1.48128i
\(576\) 0 0
\(577\) −7.80012 + 4.50340i −0.324723 + 0.187479i −0.653496 0.756930i \(-0.726698\pi\)
0.328773 + 0.944409i \(0.393365\pi\)
\(578\) 31.3336 18.0905i 1.30331 0.752465i
\(579\) 0 0
\(580\) 20.2918i 0.842571i
\(581\) −13.2650 8.98329i −0.550324 0.372690i
\(582\) 0 0
\(583\) −6.68885 + 11.5854i −0.277024 + 0.479819i
\(584\) 1.37101 + 2.37466i 0.0567328 + 0.0982640i
\(585\) 0 0
\(586\) 12.5181 + 7.22732i 0.517118 + 0.298558i
\(587\) 39.5783 1.63357 0.816785 0.576942i \(-0.195754\pi\)
0.816785 + 0.576942i \(0.195754\pi\)
\(588\) 0 0
\(589\) −8.45503 −0.348383
\(590\) −6.64029 3.83378i −0.273377 0.157834i
\(591\) 0 0
\(592\) 1.98709 + 3.44174i 0.0816688 + 0.141455i
\(593\) −17.9542 + 31.0976i −0.737290 + 1.27702i 0.216421 + 0.976300i \(0.430562\pi\)
−0.953711 + 0.300724i \(0.902772\pi\)
\(594\) 0 0
\(595\) −62.8134 42.5384i −2.57510 1.74391i
\(596\) 6.85425i 0.280761i
\(597\) 0 0
\(598\) −7.20390 + 4.15918i −0.294590 + 0.170081i
\(599\) −28.9870 + 16.7357i −1.18438 + 0.683800i −0.957023 0.290012i \(-0.906341\pi\)
−0.227354 + 0.973812i \(0.573007\pi\)
\(600\) 0 0
\(601\) 27.5546i 1.12398i 0.827146 + 0.561988i \(0.189963\pi\)
−0.827146 + 0.561988i \(0.810037\pi\)
\(602\) 12.3775 + 25.4979i 0.504469 + 1.03922i
\(603\) 0 0
\(604\) −7.23351 + 12.5288i −0.294327 + 0.509790i
\(605\) −1.96593 3.40508i −0.0799263 0.138436i
\(606\) 0 0
\(607\) −39.1116 22.5811i −1.58749 0.916539i −0.993719 0.111906i \(-0.964305\pi\)
−0.593773 0.804633i \(-0.702362\pi\)
\(608\) 3.67095 0.148877
\(609\) 0 0
\(610\) −23.4639 −0.950025
\(611\) 18.2942 + 10.5622i 0.740105 + 0.427300i
\(612\) 0 0
\(613\) 13.4202 + 23.2445i 0.542037 + 0.938836i 0.998787 + 0.0492407i \(0.0156802\pi\)
−0.456750 + 0.889595i \(0.650987\pi\)
\(614\) −0.464466 + 0.804479i −0.0187443 + 0.0324661i
\(615\) 0 0
\(616\) −0.189469 + 2.63896i −0.00763391 + 0.106327i
\(617\) 37.4317i 1.50694i −0.657481 0.753471i \(-0.728378\pi\)
0.657481 0.753471i \(-0.271622\pi\)
\(618\) 0 0
\(619\) −10.7567 + 6.21039i −0.432349 + 0.249617i −0.700347 0.713803i \(-0.746971\pi\)
0.267998 + 0.963419i \(0.413638\pi\)
\(620\) −7.84267 + 4.52797i −0.314969 + 0.181848i
\(621\) 0 0
\(622\) 26.7681i 1.07330i
\(623\) −27.9620 + 13.5737i −1.12028 + 0.543817i
\(624\) 0 0
\(625\) −16.0515 + 27.8020i −0.642059 + 1.11208i
\(626\) −3.97469 6.88437i −0.158861 0.275155i
\(627\) 0 0
\(628\) 14.4305 + 8.33145i 0.575840 + 0.332461i
\(629\) −28.9818 −1.15558
\(630\) 0 0
\(631\) −5.57938 −0.222112 −0.111056 0.993814i \(-0.535423\pi\)
−0.111056 + 0.993814i \(0.535423\pi\)
\(632\) −13.3333 7.69798i −0.530370 0.306209i
\(633\) 0 0
\(634\) −8.33657 14.4394i −0.331088 0.573460i
\(635\) 19.5516 33.8643i 0.775880 1.34386i
\(636\) 0 0
\(637\) 15.9217 6.36396i 0.630840 0.252149i
\(638\) 5.16088i 0.204321i
\(639\) 0 0
\(640\) 3.40508 1.96593i 0.134598 0.0777100i
\(641\) −29.7432 + 17.1723i −1.17479 + 0.678263i −0.954803 0.297240i \(-0.903934\pi\)
−0.219984 + 0.975504i \(0.570600\pi\)
\(642\) 0 0
\(643\) 21.2432i 0.837748i 0.908044 + 0.418874i \(0.137575\pi\)
−0.908044 + 0.418874i \(0.862425\pi\)
\(644\) −5.03811 + 7.43942i −0.198529 + 0.293154i
\(645\) 0 0
\(646\) −13.3853 + 23.1839i −0.526636 + 0.912160i
\(647\) −12.0354 20.8459i −0.473160 0.819537i 0.526368 0.850257i \(-0.323553\pi\)
−0.999528 + 0.0307199i \(0.990220\pi\)
\(648\) 0 0
\(649\) −1.68885 0.975056i −0.0662930 0.0382743i
\(650\) 25.6203 1.00491
\(651\) 0 0
\(652\) −0.963479 −0.0377328
\(653\) 25.2388 + 14.5716i 0.987672 + 0.570233i 0.904578 0.426309i \(-0.140186\pi\)
0.0830943 + 0.996542i \(0.473520\pi\)
\(654\) 0 0
\(655\) −36.3407 62.9439i −1.41995 2.45942i
\(656\) −2.96240 + 5.13103i −0.115662 + 0.200333i
\(657\) 0 0
\(658\) 22.7583 + 1.63397i 0.887212 + 0.0636990i
\(659\) 39.4790i 1.53788i 0.639318 + 0.768942i \(0.279217\pi\)
−0.639318 + 0.768942i \(0.720783\pi\)
\(660\) 0 0
\(661\) −33.0582 + 19.0861i −1.28581 + 0.742365i −0.977905 0.209051i \(-0.932962\pi\)
−0.307909 + 0.951416i \(0.599629\pi\)
\(662\) −2.75280 + 1.58933i −0.106990 + 0.0617710i
\(663\) 0 0
\(664\) 6.05521i 0.234988i
\(665\) 38.0898 + 2.73472i 1.47706 + 0.106048i
\(666\) 0 0
\(667\) 8.76305 15.1780i 0.339307 0.587696i
\(668\) −0.967128 1.67511i −0.0374193 0.0648121i
\(669\) 0 0
\(670\) 15.8934 + 9.17606i 0.614016 + 0.354502i
\(671\) −5.96764 −0.230378
\(672\) 0 0
\(673\) −10.7014 −0.412509 −0.206255 0.978498i \(-0.566128\pi\)
−0.206255 + 0.978498i \(0.566128\pi\)
\(674\) −13.6376 7.87367i −0.525301 0.303282i
\(675\) 0 0
\(676\) 3.50000 + 6.06218i 0.134615 + 0.233161i
\(677\) 8.12925 14.0803i 0.312432 0.541149i −0.666456 0.745544i \(-0.732190\pi\)
0.978888 + 0.204396i \(0.0655229\pi\)
\(678\) 0 0
\(679\) −8.69020 + 12.8322i −0.333499 + 0.492454i
\(680\) 28.6731i 1.09956i
\(681\) 0 0
\(682\) −1.99465 + 1.15161i −0.0763792 + 0.0440975i
\(683\) −0.845958 + 0.488414i −0.0323697 + 0.0186887i −0.516098 0.856530i \(-0.672616\pi\)
0.483728 + 0.875218i \(0.339282\pi\)
\(684\) 0 0
\(685\) 10.9774i 0.419423i
\(686\) 12.4691 13.6938i 0.476073 0.522834i
\(687\) 0 0
\(688\) 5.35640 9.27755i 0.204211 0.353703i
\(689\) −16.3843 28.3784i −0.624191 1.08113i
\(690\) 0 0
\(691\) 15.3783 + 8.87869i 0.585020 + 0.337761i 0.763126 0.646250i \(-0.223664\pi\)
−0.178106 + 0.984011i \(0.556997\pi\)
\(692\) −19.7580 −0.751088
\(693\) 0 0
\(694\) −26.3244 −0.999261
\(695\) −17.3858 10.0377i −0.659480 0.380751i
\(696\) 0 0
\(697\) −21.6034 37.4182i −0.818287 1.41731i
\(698\) 16.4522 28.4961i 0.622725 1.07859i
\(699\) 0 0
\(700\) 24.8950 12.0848i 0.940941 0.456762i
\(701\) 9.85160i 0.372090i −0.982541 0.186045i \(-0.940433\pi\)
0.982541 0.186045i \(-0.0595670\pi\)
\(702\) 0 0
\(703\) 12.6344 7.29450i 0.476517 0.275117i
\(704\) 0.866025 0.500000i 0.0326396 0.0188445i
\(705\) 0 0
\(706\) 9.49886i 0.357494i
\(707\) 2.94066 40.9581i 0.110595 1.54039i
\(708\) 0 0
\(709\) 19.4994 33.7739i 0.732314 1.26840i −0.223578 0.974686i \(-0.571774\pi\)
0.955892 0.293718i \(-0.0948928\pi\)
\(710\) −17.5116 30.3309i −0.657197 1.13830i
\(711\) 0 0
\(712\) 10.1741 + 5.87404i 0.381292 + 0.220139i
\(713\) −7.82165 −0.292923
\(714\) 0 0
\(715\) 9.63103 0.360180
\(716\) −9.13593 5.27463i −0.341426 0.197122i
\(717\) 0 0
\(718\) 1.49867 + 2.59578i 0.0559300 + 0.0968736i
\(719\) −6.32864 + 10.9615i −0.236019 + 0.408796i −0.959568 0.281476i \(-0.909176\pi\)
0.723550 + 0.690272i \(0.242509\pi\)
\(720\) 0 0
\(721\) 14.3304 + 29.5209i 0.533690 + 1.09941i
\(722\) 5.52412i 0.205587i
\(723\) 0 0
\(724\) −3.57287 + 2.06280i −0.132785 + 0.0766634i
\(725\) −46.7480 + 26.9900i −1.73618 + 1.00238i
\(726\) 0 0
\(727\) 15.8671i 0.588478i −0.955732 0.294239i \(-0.904934\pi\)
0.955732 0.294239i \(-0.0950662\pi\)
\(728\) −5.36603 3.63397i −0.198878 0.134684i
\(729\) 0 0
\(730\) 5.39060 9.33680i 0.199515 0.345571i
\(731\) 39.0617 + 67.6568i 1.44475 + 2.50238i
\(732\) 0 0
\(733\) −21.8797 12.6322i −0.808144 0.466582i 0.0381669 0.999271i \(-0.487848\pi\)
−0.846311 + 0.532689i \(0.821181\pi\)
\(734\) −16.5510 −0.610910
\(735\) 0 0
\(736\) 3.39595 0.125176
\(737\) 4.04222 + 2.33378i 0.148897 + 0.0859657i
\(738\) 0 0
\(739\) 2.35023 + 4.07072i 0.0864546 + 0.149744i 0.906010 0.423256i \(-0.139113\pi\)
−0.819556 + 0.573000i \(0.805780\pi\)
\(740\) 7.81294 13.5324i 0.287209 0.497461i
\(741\) 0 0
\(742\) −29.3061 19.8467i −1.07586 0.728594i
\(743\) 37.5807i 1.37870i 0.724427 + 0.689352i \(0.242105\pi\)
−0.724427 + 0.689352i \(0.757895\pi\)
\(744\) 0 0
\(745\) 23.3393 13.4749i 0.855086 0.493684i
\(746\) −16.8659 + 9.73753i −0.617505 + 0.356516i
\(747\) 0 0
\(748\) 7.29253i 0.266641i
\(749\) −15.9351 32.8267i −0.582256 1.19946i
\(750\) 0 0
\(751\) 13.6493 23.6413i 0.498070 0.862682i −0.501928 0.864910i \(-0.667376\pi\)
0.999998 + 0.00222750i \(0.000709036\pi\)
\(752\) −4.31199 7.46859i −0.157242 0.272351i
\(753\) 0 0
\(754\) 10.9479 + 6.32076i 0.398698 + 0.230188i
\(755\) 56.8822 2.07015
\(756\) 0 0
\(757\) −1.76874 −0.0642858 −0.0321429 0.999483i \(-0.510233\pi\)
−0.0321429 + 0.999483i \(0.510233\pi\)
\(758\) −1.91227 1.10405i −0.0694566 0.0401008i
\(759\) 0 0
\(760\) −7.21682 12.4999i −0.261781 0.453419i
\(761\) −15.4241 + 26.7153i −0.559122 + 0.968428i 0.438448 + 0.898757i \(0.355528\pi\)
−0.997570 + 0.0696715i \(0.977805\pi\)
\(762\) 0 0
\(763\) 0.930419 12.9591i 0.0336834 0.469149i
\(764\) 23.0194i 0.832813i
\(765\) 0 0
\(766\) 2.45690 1.41849i 0.0887715 0.0512522i
\(767\) 4.13681 2.38839i 0.149372 0.0862398i
\(768\) 0 0
\(769\) 39.1842i 1.41302i −0.707704 0.706509i \(-0.750269\pi\)
0.707704 0.706509i \(-0.249731\pi\)
\(770\) 9.35835 4.54284i 0.337252 0.163713i
\(771\) 0 0
\(772\) 4.60708 7.97970i 0.165813 0.287196i
\(773\) 27.0296 + 46.8166i 0.972186 + 1.68388i 0.688924 + 0.724834i \(0.258084\pi\)
0.283263 + 0.959042i \(0.408583\pi\)
\(774\) 0 0
\(775\) 20.8630 + 12.0452i 0.749420 + 0.432678i
\(776\) 5.85765 0.210277
\(777\) 0 0
\(778\) −19.0163 −0.681767
\(779\) 18.8358 + 10.8748i 0.674861 + 0.389631i
\(780\) 0 0
\(781\) −4.45377 7.71415i −0.159368 0.276034i
\(782\) −12.3825 + 21.4472i −0.442799 + 0.766950i
\(783\) 0 0
\(784\) −6.92820 1.00000i −0.247436 0.0357143i
\(785\) 65.5161i 2.33837i
\(786\) 0 0
\(787\) −8.76131 + 5.05834i −0.312307 + 0.180311i −0.647958 0.761676i \(-0.724377\pi\)
0.335651 + 0.941986i \(0.391044\pi\)
\(788\) −5.64805 + 3.26090i −0.201203 + 0.116165i
\(789\) 0 0