Properties

Label 912.2.cc.c.545.3
Level $912$
Weight $2$
Character 912.545
Analytic conductor $7.282$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.cc (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + 162 x^{7} + 270 x^{6} + 2916 x^{5} - 4374 x^{4} - 729 x^{3} + 19683\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 545.3
Root \(1.40849 + 1.00804i\) of defining polynomial
Character \(\chi\) \(=\) 912.545
Dual form 912.2.cc.c.497.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.748148 + 1.56214i) q^{3} +(-0.262261 + 0.0462437i) q^{5} +(-0.604656 + 1.04730i) q^{7} +(-1.88055 + 2.33742i) q^{9} +O(q^{10})\) \(q+(0.748148 + 1.56214i) q^{3} +(-0.262261 + 0.0462437i) q^{5} +(-0.604656 + 1.04730i) q^{7} +(-1.88055 + 2.33742i) q^{9} +(-2.03630 + 1.17566i) q^{11} +(1.01749 + 2.79553i) q^{13} +(-0.268449 - 0.375091i) q^{15} +(0.576470 + 0.687011i) q^{17} +(-1.97979 - 3.88335i) q^{19} +(-2.08839 - 0.161024i) q^{21} +(-5.53770 - 0.976446i) q^{23} +(-4.63182 + 1.68584i) q^{25} +(-5.05830 - 1.18894i) q^{27} +(1.92487 + 1.61516i) q^{29} +(8.98131 + 5.18536i) q^{31} +(-3.36000 - 2.30141i) q^{33} +(0.110147 - 0.302626i) q^{35} +3.95916i q^{37} +(-3.60577 + 3.68093i) q^{39} +(-10.4227 - 3.79356i) q^{41} +(0.834031 + 4.73003i) q^{43} +(0.385104 - 0.699978i) q^{45} +(-1.24341 + 1.48183i) q^{47} +(2.76878 + 4.79567i) q^{49} +(-0.641920 + 1.41451i) q^{51} +(0.998339 - 5.66186i) q^{53} +(0.479676 - 0.402496i) q^{55} +(4.58516 - 5.99803i) q^{57} +(9.78136 - 8.20754i) q^{59} +(-0.153642 + 0.871345i) q^{61} +(-1.31088 - 3.38283i) q^{63} +(-0.396123 - 0.686106i) q^{65} +(-3.28864 + 3.91925i) q^{67} +(-2.61768 - 9.38117i) q^{69} +(1.64669 + 9.33885i) q^{71} +(0.320853 + 0.116781i) q^{73} +(-6.09881 - 5.97428i) q^{75} -2.84348i q^{77} +(-2.33914 + 6.42674i) q^{79} +(-1.92708 - 8.79127i) q^{81} +(-12.2240 - 7.05752i) q^{83} +(-0.182956 - 0.153518i) q^{85} +(-1.08301 + 4.21529i) q^{87} +(-11.5580 + 4.20677i) q^{89} +(-3.54297 - 0.624722i) q^{91} +(-1.38090 + 17.9095i) q^{93} +(0.698802 + 0.926900i) q^{95} +(3.88456 + 4.62944i) q^{97} +(1.08135 - 6.97057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 3q^{3} - 3q^{9} + O(q^{10}) \) \( 18q - 3q^{3} - 3q^{9} - 12q^{13} - 18q^{15} + 6q^{17} + 6q^{19} - 18q^{25} + 6q^{27} - 6q^{29} - 24q^{33} + 24q^{35} - 6q^{39} + 3q^{41} + 6q^{43} - 54q^{45} - 30q^{47} + 21q^{49} - 42q^{51} - 60q^{53} - 30q^{55} + 12q^{57} - 3q^{59} + 54q^{61} + 18q^{63} + 24q^{65} + 15q^{67} + 30q^{69} - 36q^{71} - 42q^{73} + 6q^{79} - 3q^{81} - 36q^{83} - 60q^{89} + 18q^{91} - 66q^{93} - 6q^{95} + 9q^{97} + 102q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.748148 + 1.56214i 0.431944 + 0.901901i
\(4\) 0 0
\(5\) −0.262261 + 0.0462437i −0.117287 + 0.0206808i −0.231983 0.972720i \(-0.574522\pi\)
0.114697 + 0.993401i \(0.463410\pi\)
\(6\) 0 0
\(7\) −0.604656 + 1.04730i −0.228539 + 0.395840i −0.957375 0.288847i \(-0.906728\pi\)
0.728837 + 0.684688i \(0.240061\pi\)
\(8\) 0 0
\(9\) −1.88055 + 2.33742i −0.626849 + 0.779140i
\(10\) 0 0
\(11\) −2.03630 + 1.17566i −0.613968 + 0.354474i −0.774517 0.632553i \(-0.782007\pi\)
0.160549 + 0.987028i \(0.448674\pi\)
\(12\) 0 0
\(13\) 1.01749 + 2.79553i 0.282201 + 0.775340i 0.997099 + 0.0761119i \(0.0242506\pi\)
−0.714899 + 0.699228i \(0.753527\pi\)
\(14\) 0 0
\(15\) −0.268449 0.375091i −0.0693133 0.0968480i
\(16\) 0 0
\(17\) 0.576470 + 0.687011i 0.139815 + 0.166625i 0.831408 0.555663i \(-0.187535\pi\)
−0.691593 + 0.722287i \(0.743091\pi\)
\(18\) 0 0
\(19\) −1.97979 3.88335i −0.454194 0.890903i
\(20\) 0 0
\(21\) −2.08839 0.161024i −0.455724 0.0351383i
\(22\) 0 0
\(23\) −5.53770 0.976446i −1.15469 0.203603i −0.436668 0.899623i \(-0.643841\pi\)
−0.718022 + 0.696020i \(0.754952\pi\)
\(24\) 0 0
\(25\) −4.63182 + 1.68584i −0.926364 + 0.337169i
\(26\) 0 0
\(27\) −5.05830 1.18894i −0.973471 0.228811i
\(28\) 0 0
\(29\) 1.92487 + 1.61516i 0.357440 + 0.299928i 0.803769 0.594941i \(-0.202825\pi\)
−0.446329 + 0.894869i \(0.647269\pi\)
\(30\) 0 0
\(31\) 8.98131 + 5.18536i 1.61309 + 0.931319i 0.988648 + 0.150249i \(0.0480075\pi\)
0.624443 + 0.781070i \(0.285326\pi\)
\(32\) 0 0
\(33\) −3.36000 2.30141i −0.584900 0.400625i
\(34\) 0 0
\(35\) 0.110147 0.302626i 0.0186182 0.0511532i
\(36\) 0 0
\(37\) 3.95916i 0.650882i 0.945562 + 0.325441i \(0.105513\pi\)
−0.945562 + 0.325441i \(0.894487\pi\)
\(38\) 0 0
\(39\) −3.60577 + 3.68093i −0.577385 + 0.589420i
\(40\) 0 0
\(41\) −10.4227 3.79356i −1.62776 0.592455i −0.642920 0.765934i \(-0.722277\pi\)
−0.984838 + 0.173479i \(0.944499\pi\)
\(42\) 0 0
\(43\) 0.834031 + 4.73003i 0.127189 + 0.721322i 0.979984 + 0.199077i \(0.0637944\pi\)
−0.852795 + 0.522245i \(0.825095\pi\)
\(44\) 0 0
\(45\) 0.385104 0.699978i 0.0574079 0.104347i
\(46\) 0 0
\(47\) −1.24341 + 1.48183i −0.181369 + 0.216147i −0.849067 0.528285i \(-0.822835\pi\)
0.667698 + 0.744432i \(0.267280\pi\)
\(48\) 0 0
\(49\) 2.76878 + 4.79567i 0.395540 + 0.685096i
\(50\) 0 0
\(51\) −0.641920 + 1.41451i −0.0898868 + 0.198071i
\(52\) 0 0
\(53\) 0.998339 5.66186i 0.137132 0.777717i −0.836219 0.548396i \(-0.815239\pi\)
0.973351 0.229320i \(-0.0736504\pi\)
\(54\) 0 0
\(55\) 0.479676 0.402496i 0.0646794 0.0542725i
\(56\) 0 0
\(57\) 4.58516 5.99803i 0.607319 0.794458i
\(58\) 0 0
\(59\) 9.78136 8.20754i 1.27342 1.06853i 0.279310 0.960201i \(-0.409894\pi\)
0.994115 0.108329i \(-0.0345501\pi\)
\(60\) 0 0
\(61\) −0.153642 + 0.871345i −0.0196718 + 0.111564i −0.993063 0.117587i \(-0.962484\pi\)
0.973391 + 0.229152i \(0.0735951\pi\)
\(62\) 0 0
\(63\) −1.31088 3.38283i −0.165156 0.426196i
\(64\) 0 0
\(65\) −0.396123 0.686106i −0.0491331 0.0851010i
\(66\) 0 0
\(67\) −3.28864 + 3.91925i −0.401771 + 0.478812i −0.928559 0.371184i \(-0.878952\pi\)
0.526788 + 0.849997i \(0.323396\pi\)
\(68\) 0 0
\(69\) −2.61768 9.38117i −0.315131 1.12936i
\(70\) 0 0
\(71\) 1.64669 + 9.33885i 0.195426 + 1.10832i 0.911810 + 0.410612i \(0.134685\pi\)
−0.716384 + 0.697706i \(0.754204\pi\)
\(72\) 0 0
\(73\) 0.320853 + 0.116781i 0.0375530 + 0.0136682i 0.360728 0.932671i \(-0.382528\pi\)
−0.323175 + 0.946339i \(0.604750\pi\)
\(74\) 0 0
\(75\) −6.09881 5.97428i −0.704230 0.689850i
\(76\) 0 0
\(77\) 2.84348i 0.324044i
\(78\) 0 0
\(79\) −2.33914 + 6.42674i −0.263174 + 0.723064i 0.735775 + 0.677226i \(0.236818\pi\)
−0.998949 + 0.0458383i \(0.985404\pi\)
\(80\) 0 0
\(81\) −1.92708 8.79127i −0.214120 0.976807i
\(82\) 0 0
\(83\) −12.2240 7.05752i −1.34176 0.774663i −0.354691 0.934984i \(-0.615414\pi\)
−0.987065 + 0.160320i \(0.948747\pi\)
\(84\) 0 0
\(85\) −0.182956 0.153518i −0.0198443 0.0166514i
\(86\) 0 0
\(87\) −1.08301 + 4.21529i −0.116111 + 0.451927i
\(88\) 0 0
\(89\) −11.5580 + 4.20677i −1.22515 + 0.445917i −0.871933 0.489626i \(-0.837133\pi\)
−0.353213 + 0.935543i \(0.614911\pi\)
\(90\) 0 0
\(91\) −3.54297 0.624722i −0.371405 0.0654887i
\(92\) 0 0
\(93\) −1.38090 + 17.9095i −0.143192 + 1.85713i
\(94\) 0 0
\(95\) 0.698802 + 0.926900i 0.0716956 + 0.0950979i
\(96\) 0 0
\(97\) 3.88456 + 4.62944i 0.394418 + 0.470049i 0.926309 0.376764i \(-0.122963\pi\)
−0.531892 + 0.846812i \(0.678519\pi\)
\(98\) 0 0
\(99\) 1.08135 6.97057i 0.108680 0.700569i
\(100\) 0 0
\(101\) 3.54557 + 9.74137i 0.352797 + 0.969302i 0.981467 + 0.191630i \(0.0613774\pi\)
−0.628670 + 0.777672i \(0.716400\pi\)
\(102\) 0 0
\(103\) 12.7994 7.38973i 1.26116 0.728131i 0.287861 0.957672i \(-0.407056\pi\)
0.973299 + 0.229541i \(0.0737224\pi\)
\(104\) 0 0
\(105\) 0.555150 0.0543446i 0.0541771 0.00530349i
\(106\) 0 0
\(107\) 8.08439 14.0026i 0.781547 1.35368i −0.149493 0.988763i \(-0.547764\pi\)
0.931040 0.364917i \(-0.118903\pi\)
\(108\) 0 0
\(109\) 17.9876 3.17170i 1.72290 0.303794i 0.777302 0.629128i \(-0.216588\pi\)
0.945599 + 0.325334i \(0.105477\pi\)
\(110\) 0 0
\(111\) −6.18475 + 2.96204i −0.587030 + 0.281144i
\(112\) 0 0
\(113\) 2.40020 0.225792 0.112896 0.993607i \(-0.463987\pi\)
0.112896 + 0.993607i \(0.463987\pi\)
\(114\) 0 0
\(115\) 1.49748 0.139640
\(116\) 0 0
\(117\) −8.44777 2.87883i −0.780996 0.266148i
\(118\) 0 0
\(119\) −1.06807 + 0.188329i −0.0979098 + 0.0172641i
\(120\) 0 0
\(121\) −2.73565 + 4.73829i −0.248696 + 0.430754i
\(122\) 0 0
\(123\) −1.87168 19.1199i −0.168764 1.72398i
\(124\) 0 0
\(125\) 2.28993 1.32209i 0.204818 0.118251i
\(126\) 0 0
\(127\) 2.02408 + 5.56112i 0.179608 + 0.493470i 0.996526 0.0832849i \(-0.0265411\pi\)
−0.816918 + 0.576754i \(0.804319\pi\)
\(128\) 0 0
\(129\) −6.76497 + 4.84163i −0.595623 + 0.426282i
\(130\) 0 0
\(131\) 11.1080 + 13.2379i 0.970506 + 1.15660i 0.987638 + 0.156751i \(0.0501020\pi\)
−0.0171319 + 0.999853i \(0.505454\pi\)
\(132\) 0 0
\(133\) 5.26411 + 0.274672i 0.456456 + 0.0238171i
\(134\) 0 0
\(135\) 1.38158 + 0.0778975i 0.118907 + 0.00670435i
\(136\) 0 0
\(137\) 18.0150 + 3.17653i 1.53912 + 0.271389i 0.877917 0.478813i \(-0.158933\pi\)
0.661208 + 0.750203i \(0.270044\pi\)
\(138\) 0 0
\(139\) 2.16057 0.786381i 0.183257 0.0667000i −0.248762 0.968565i \(-0.580024\pi\)
0.432019 + 0.901865i \(0.357801\pi\)
\(140\) 0 0
\(141\) −3.24508 0.833740i −0.273285 0.0702135i
\(142\) 0 0
\(143\) −5.35850 4.49632i −0.448100 0.376001i
\(144\) 0 0
\(145\) −0.579510 0.334580i −0.0481257 0.0277854i
\(146\) 0 0
\(147\) −5.42004 + 7.91309i −0.447037 + 0.652661i
\(148\) 0 0
\(149\) −2.67853 + 7.35921i −0.219434 + 0.602890i −0.999747 0.0224995i \(-0.992838\pi\)
0.780313 + 0.625389i \(0.215060\pi\)
\(150\) 0 0
\(151\) 11.1343i 0.906098i 0.891486 + 0.453049i \(0.149664\pi\)
−0.891486 + 0.453049i \(0.850336\pi\)
\(152\) 0 0
\(153\) −2.68991 + 0.0554973i −0.217467 + 0.00448669i
\(154\) 0 0
\(155\) −2.59524 0.944590i −0.208455 0.0758713i
\(156\) 0 0
\(157\) −3.68519 20.8997i −0.294110 1.66798i −0.670798 0.741640i \(-0.734048\pi\)
0.376688 0.926340i \(-0.377063\pi\)
\(158\) 0 0
\(159\) 9.59152 2.67637i 0.760657 0.212250i
\(160\) 0 0
\(161\) 4.37103 5.20919i 0.344485 0.410542i
\(162\) 0 0
\(163\) −1.74061 3.01482i −0.136335 0.236139i 0.789772 0.613401i \(-0.210199\pi\)
−0.926107 + 0.377262i \(0.876866\pi\)
\(164\) 0 0
\(165\) 0.987622 + 0.448193i 0.0768863 + 0.0348918i
\(166\) 0 0
\(167\) −3.56671 + 20.2278i −0.276000 + 1.56527i 0.459767 + 0.888040i \(0.347933\pi\)
−0.735767 + 0.677235i \(0.763178\pi\)
\(168\) 0 0
\(169\) 3.17888 2.66740i 0.244529 0.205185i
\(170\) 0 0
\(171\) 12.8001 + 2.67524i 0.978850 + 0.204581i
\(172\) 0 0
\(173\) 6.38346 5.35636i 0.485326 0.407237i −0.367022 0.930212i \(-0.619623\pi\)
0.852348 + 0.522976i \(0.175178\pi\)
\(174\) 0 0
\(175\) 1.03508 5.87024i 0.0782448 0.443748i
\(176\) 0 0
\(177\) 20.1392 + 9.13938i 1.51376 + 0.686958i
\(178\) 0 0
\(179\) 4.51280 + 7.81640i 0.337302 + 0.584225i 0.983924 0.178586i \(-0.0571522\pi\)
−0.646622 + 0.762811i \(0.723819\pi\)
\(180\) 0 0
\(181\) 5.90976 7.04297i 0.439269 0.523500i −0.500304 0.865850i \(-0.666778\pi\)
0.939573 + 0.342350i \(0.111223\pi\)
\(182\) 0 0
\(183\) −1.47611 + 0.411886i −0.109117 + 0.0304475i
\(184\) 0 0
\(185\) −0.183086 1.03833i −0.0134608 0.0763398i
\(186\) 0 0
\(187\) −1.98156 0.721228i −0.144906 0.0527414i
\(188\) 0 0
\(189\) 4.30370 4.57864i 0.313048 0.333047i
\(190\) 0 0
\(191\) 7.33252i 0.530562i 0.964171 + 0.265281i \(0.0854648\pi\)
−0.964171 + 0.265281i \(0.914535\pi\)
\(192\) 0 0
\(193\) 0.613121 1.68453i 0.0441334 0.121255i −0.915668 0.401935i \(-0.868338\pi\)
0.959801 + 0.280680i \(0.0905599\pi\)
\(194\) 0 0
\(195\) 0.775433 1.13211i 0.0555299 0.0810720i
\(196\) 0 0
\(197\) −6.85271 3.95642i −0.488236 0.281883i 0.235607 0.971849i \(-0.424292\pi\)
−0.723842 + 0.689966i \(0.757626\pi\)
\(198\) 0 0
\(199\) 8.01318 + 6.72386i 0.568039 + 0.476642i 0.880995 0.473126i \(-0.156875\pi\)
−0.312955 + 0.949768i \(0.601319\pi\)
\(200\) 0 0
\(201\) −8.58280 2.20513i −0.605384 0.155538i
\(202\) 0 0
\(203\) −2.85543 + 1.03929i −0.200412 + 0.0729441i
\(204\) 0 0
\(205\) 2.90891 + 0.512919i 0.203167 + 0.0358238i
\(206\) 0 0
\(207\) 12.6963 11.1077i 0.882452 0.772037i
\(208\) 0 0
\(209\) 8.59694 + 5.58012i 0.594663 + 0.385985i
\(210\) 0 0
\(211\) −8.93046 10.6429i −0.614799 0.732688i 0.365368 0.930863i \(-0.380943\pi\)
−0.980167 + 0.198175i \(0.936499\pi\)
\(212\) 0 0
\(213\) −13.3566 + 9.55921i −0.915180 + 0.654986i
\(214\) 0 0
\(215\) −0.437468 1.20193i −0.0298351 0.0819712i
\(216\) 0 0
\(217\) −10.8612 + 6.27072i −0.737307 + 0.425684i
\(218\) 0 0
\(219\) 0.0576176 + 0.588585i 0.00389344 + 0.0397729i
\(220\) 0 0
\(221\) −1.33401 + 2.31057i −0.0897349 + 0.155425i
\(222\) 0 0
\(223\) 12.2714 2.16379i 0.821757 0.144898i 0.253066 0.967449i \(-0.418561\pi\)
0.568691 + 0.822551i \(0.307450\pi\)
\(224\) 0 0
\(225\) 4.76983 13.9968i 0.317989 0.933122i
\(226\) 0 0
\(227\) −1.63948 −0.108816 −0.0544081 0.998519i \(-0.517327\pi\)
−0.0544081 + 0.998519i \(0.517327\pi\)
\(228\) 0 0
\(229\) −12.1547 −0.803204 −0.401602 0.915814i \(-0.631546\pi\)
−0.401602 + 0.915814i \(0.631546\pi\)
\(230\) 0 0
\(231\) 4.44190 2.12734i 0.292256 0.139969i
\(232\) 0 0
\(233\) 2.37239 0.418316i 0.155420 0.0274048i −0.0953966 0.995439i \(-0.530412\pi\)
0.250817 + 0.968035i \(0.419301\pi\)
\(234\) 0 0
\(235\) 0.257571 0.446127i 0.0168021 0.0291021i
\(236\) 0 0
\(237\) −11.7895 + 1.15409i −0.765809 + 0.0749663i
\(238\) 0 0
\(239\) 16.5806 9.57284i 1.07251 0.619215i 0.143646 0.989629i \(-0.454117\pi\)
0.928867 + 0.370414i \(0.120784\pi\)
\(240\) 0 0
\(241\) 1.43503 + 3.94271i 0.0924383 + 0.253972i 0.977292 0.211897i \(-0.0679641\pi\)
−0.884854 + 0.465869i \(0.845742\pi\)
\(242\) 0 0
\(243\) 12.2914 9.58753i 0.788496 0.615040i
\(244\) 0 0
\(245\) −0.947913 1.12968i −0.0605600 0.0721726i
\(246\) 0 0
\(247\) 8.84162 9.48582i 0.562579 0.603568i
\(248\) 0 0
\(249\) 1.87947 24.3756i 0.119106 1.54474i
\(250\) 0 0
\(251\) −4.15098 0.731929i −0.262007 0.0461990i 0.0411012 0.999155i \(-0.486913\pi\)
−0.303109 + 0.952956i \(0.598024\pi\)
\(252\) 0 0
\(253\) 12.4244 4.52211i 0.781114 0.284302i
\(254\) 0 0
\(255\) 0.102938 0.400656i 0.00644625 0.0250901i
\(256\) 0 0
\(257\) 13.6150 + 11.4244i 0.849282 + 0.712632i 0.959631 0.281260i \(-0.0907525\pi\)
−0.110349 + 0.993893i \(0.535197\pi\)
\(258\) 0 0
\(259\) −4.14641 2.39393i −0.257645 0.148752i
\(260\) 0 0
\(261\) −7.39512 + 1.46185i −0.457747 + 0.0904863i
\(262\) 0 0
\(263\) −0.383160 + 1.05272i −0.0236267 + 0.0649138i −0.950945 0.309359i \(-0.899885\pi\)
0.927319 + 0.374273i \(0.122108\pi\)
\(264\) 0 0
\(265\) 1.53105i 0.0940519i
\(266\) 0 0
\(267\) −15.2187 14.9079i −0.931366 0.912349i
\(268\) 0 0
\(269\) 18.2909 + 6.65734i 1.11522 + 0.405905i 0.832904 0.553418i \(-0.186677\pi\)
0.282311 + 0.959323i \(0.408899\pi\)
\(270\) 0 0
\(271\) 0.0552285 + 0.313217i 0.00335489 + 0.0190266i 0.986439 0.164127i \(-0.0524806\pi\)
−0.983084 + 0.183153i \(0.941370\pi\)
\(272\) 0 0
\(273\) −1.67477 6.00200i −0.101362 0.363257i
\(274\) 0 0
\(275\) 7.44980 8.87833i 0.449240 0.535383i
\(276\) 0 0
\(277\) 10.9678 + 18.9968i 0.658993 + 1.14141i 0.980877 + 0.194630i \(0.0623506\pi\)
−0.321884 + 0.946779i \(0.604316\pi\)
\(278\) 0 0
\(279\) −29.0102 + 11.2418i −1.73679 + 0.673028i
\(280\) 0 0
\(281\) 2.62001 14.8588i 0.156297 0.886403i −0.801294 0.598271i \(-0.795855\pi\)
0.957591 0.288132i \(-0.0930342\pi\)
\(282\) 0 0
\(283\) 5.08697 4.26848i 0.302389 0.253735i −0.478949 0.877843i \(-0.658982\pi\)
0.781338 + 0.624108i \(0.214538\pi\)
\(284\) 0 0
\(285\) −0.925138 + 1.78508i −0.0548005 + 0.105739i
\(286\) 0 0
\(287\) 10.2751 8.62187i 0.606523 0.508933i
\(288\) 0 0
\(289\) 2.81235 15.9496i 0.165433 0.938215i
\(290\) 0 0
\(291\) −4.32560 + 9.53173i −0.253571 + 0.558760i
\(292\) 0 0
\(293\) −14.2028 24.5999i −0.829735 1.43714i −0.898246 0.439493i \(-0.855158\pi\)
0.0685112 0.997650i \(-0.478175\pi\)
\(294\) 0 0
\(295\) −2.18572 + 2.60484i −0.127258 + 0.151660i
\(296\) 0 0
\(297\) 11.6980 3.52580i 0.678787 0.204588i
\(298\) 0 0
\(299\) −2.90487 16.4743i −0.167993 0.952734i
\(300\) 0 0
\(301\) −5.45804 1.98656i −0.314596 0.114504i
\(302\) 0 0
\(303\) −12.5647 + 12.8266i −0.721826 + 0.736872i
\(304\) 0 0
\(305\) 0.235625i 0.0134918i
\(306\) 0 0
\(307\) −1.49097 + 4.09641i −0.0850942 + 0.233794i −0.974940 0.222466i \(-0.928589\pi\)
0.889846 + 0.456261i \(0.150812\pi\)
\(308\) 0 0
\(309\) 21.1196 + 14.4658i 1.20145 + 0.822930i
\(310\) 0 0
\(311\) −4.11082 2.37338i −0.233103 0.134582i 0.378900 0.925438i \(-0.376303\pi\)
−0.612003 + 0.790856i \(0.709636\pi\)
\(312\) 0 0
\(313\) 14.5023 + 12.1689i 0.819718 + 0.687825i 0.952906 0.303265i \(-0.0980769\pi\)
−0.133188 + 0.991091i \(0.542521\pi\)
\(314\) 0 0
\(315\) 0.500228 + 0.826563i 0.0281847 + 0.0465716i
\(316\) 0 0
\(317\) −29.4488 + 10.7185i −1.65401 + 0.602010i −0.989404 0.145186i \(-0.953622\pi\)
−0.664604 + 0.747196i \(0.731400\pi\)
\(318\) 0 0
\(319\) −5.81850 1.02596i −0.325773 0.0574426i
\(320\) 0 0
\(321\) 27.9223 + 2.15293i 1.55847 + 0.120165i
\(322\) 0 0
\(323\) 1.52662 3.59877i 0.0849432 0.200241i
\(324\) 0 0
\(325\) −9.42565 11.2331i −0.522841 0.623098i
\(326\) 0 0
\(327\) 18.4120 + 25.7262i 1.01819 + 1.42266i
\(328\) 0 0
\(329\) −0.800083 2.19821i −0.0441100 0.121191i
\(330\) 0 0
\(331\) 3.20610 1.85104i 0.176223 0.101742i −0.409294 0.912403i \(-0.634225\pi\)
0.585517 + 0.810660i \(0.300892\pi\)
\(332\) 0 0
\(333\) −9.25422 7.44539i −0.507128 0.408005i
\(334\) 0 0
\(335\) 0.681242 1.17995i 0.0372202 0.0644673i
\(336\) 0 0
\(337\) −19.7344 + 3.47971i −1.07500 + 0.189552i −0.683004 0.730415i \(-0.739327\pi\)
−0.391997 + 0.919967i \(0.628216\pi\)
\(338\) 0 0
\(339\) 1.79570 + 3.74944i 0.0975292 + 0.203642i
\(340\) 0 0
\(341\) −24.3849 −1.32051
\(342\) 0 0
\(343\) −15.1618 −0.818662
\(344\) 0 0
\(345\) 1.12034 + 2.33927i 0.0603168 + 0.125942i
\(346\) 0 0
\(347\) −0.281016 + 0.0495507i −0.0150857 + 0.00266002i −0.181186 0.983449i \(-0.557994\pi\)
0.166100 + 0.986109i \(0.446882\pi\)
\(348\) 0 0
\(349\) 6.98873 12.1048i 0.374098 0.647957i −0.616093 0.787673i \(-0.711286\pi\)
0.990192 + 0.139716i \(0.0446190\pi\)
\(350\) 0 0
\(351\) −1.82306 15.3504i −0.0973077 0.819342i
\(352\) 0 0
\(353\) −17.7647 + 10.2564i −0.945519 + 0.545895i −0.891686 0.452654i \(-0.850477\pi\)
−0.0538327 + 0.998550i \(0.517144\pi\)
\(354\) 0 0
\(355\) −0.863726 2.37307i −0.0458418 0.125949i
\(356\) 0 0
\(357\) −1.09327 1.52757i −0.0578620 0.0808477i
\(358\) 0 0
\(359\) 17.9876 + 21.4368i 0.949348 + 1.13139i 0.991214 + 0.132266i \(0.0422254\pi\)
−0.0418658 + 0.999123i \(0.513330\pi\)
\(360\) 0 0
\(361\) −11.1609 + 15.3764i −0.587415 + 0.809286i
\(362\) 0 0
\(363\) −9.44854 0.728524i −0.495920 0.0382376i
\(364\) 0 0
\(365\) −0.0895476 0.0157897i −0.00468713 0.000826468i
\(366\) 0 0
\(367\) −1.43051 + 0.520662i −0.0746719 + 0.0271783i −0.379086 0.925361i \(-0.623762\pi\)
0.304414 + 0.952540i \(0.401539\pi\)
\(368\) 0 0
\(369\) 28.4676 17.2283i 1.48196 0.896871i
\(370\) 0 0
\(371\) 5.32599 + 4.46904i 0.276512 + 0.232021i
\(372\) 0 0
\(373\) 4.13495 + 2.38731i 0.214100 + 0.123610i 0.603215 0.797578i \(-0.293886\pi\)
−0.389116 + 0.921189i \(0.627219\pi\)
\(374\) 0 0
\(375\) 3.77850 + 2.58806i 0.195121 + 0.133647i
\(376\) 0 0
\(377\) −2.55669 + 7.02444i −0.131676 + 0.361777i
\(378\) 0 0
\(379\) 13.4129i 0.688972i −0.938791 0.344486i \(-0.888053\pi\)
0.938791 0.344486i \(-0.111947\pi\)
\(380\) 0 0
\(381\) −7.17292 + 7.32244i −0.367480 + 0.375140i
\(382\) 0 0
\(383\) −30.5956 11.1359i −1.56336 0.569017i −0.591857 0.806043i \(-0.701605\pi\)
−0.971503 + 0.237026i \(0.923827\pi\)
\(384\) 0 0
\(385\) 0.131493 + 0.745733i 0.00670150 + 0.0380061i
\(386\) 0 0
\(387\) −12.6245 6.94556i −0.641739 0.353063i
\(388\) 0 0
\(389\) 8.33624 9.93474i 0.422664 0.503711i −0.512127 0.858910i \(-0.671142\pi\)
0.934791 + 0.355199i \(0.115587\pi\)
\(390\) 0 0
\(391\) −2.52149 4.36735i −0.127517 0.220866i
\(392\) 0 0
\(393\) −12.3691 + 27.2561i −0.623938 + 1.37489i
\(394\) 0 0
\(395\) 0.316270 1.79365i 0.0159132 0.0902485i
\(396\) 0 0
\(397\) 18.9635 15.9123i 0.951752 0.798615i −0.0278396 0.999612i \(-0.508863\pi\)
0.979592 + 0.200997i \(0.0644183\pi\)
\(398\) 0 0
\(399\) 3.50926 + 8.42876i 0.175683 + 0.421966i
\(400\) 0 0
\(401\) 4.89417 4.10670i 0.244403 0.205079i −0.512354 0.858774i \(-0.671227\pi\)
0.756758 + 0.653695i \(0.226782\pi\)
\(402\) 0 0
\(403\) −5.35744 + 30.3836i −0.266873 + 1.51351i
\(404\) 0 0
\(405\) 0.911938 + 2.21649i 0.0453146 + 0.110138i
\(406\) 0 0
\(407\) −4.65462 8.06204i −0.230721 0.399620i
\(408\) 0 0
\(409\) −18.5835 + 22.1469i −0.918894 + 1.09510i 0.0762911 + 0.997086i \(0.475692\pi\)
−0.995185 + 0.0980100i \(0.968752\pi\)
\(410\) 0 0
\(411\) 8.51571 + 30.5184i 0.420049 + 1.50536i
\(412\) 0 0
\(413\) 2.68135 + 15.2067i 0.131941 + 0.748273i
\(414\) 0 0
\(415\) 3.53224 + 1.28563i 0.173391 + 0.0631091i
\(416\) 0 0
\(417\) 2.84486 + 2.78677i 0.139313 + 0.136469i
\(418\) 0 0
\(419\) 19.2304i 0.939467i −0.882808 0.469733i \(-0.844350\pi\)
0.882808 0.469733i \(-0.155650\pi\)
\(420\) 0 0
\(421\) −11.8370 + 32.5219i −0.576900 + 1.58502i 0.216476 + 0.976288i \(0.430544\pi\)
−0.793376 + 0.608732i \(0.791678\pi\)
\(422\) 0 0
\(423\) −1.12538 5.69302i −0.0547180 0.276804i
\(424\) 0 0
\(425\) −3.82830 2.21027i −0.185700 0.107214i
\(426\) 0 0
\(427\) −0.819655 0.687772i −0.0396659 0.0332836i
\(428\) 0 0
\(429\) 3.01491 11.7346i 0.145561 0.566553i
\(430\) 0 0
\(431\) −30.2120 + 10.9963i −1.45526 + 0.529671i −0.944055 0.329788i \(-0.893023\pi\)
−0.511205 + 0.859459i \(0.670801\pi\)
\(432\) 0 0
\(433\) −22.7212 4.00636i −1.09191 0.192534i −0.401435 0.915888i \(-0.631488\pi\)
−0.690477 + 0.723354i \(0.742599\pi\)
\(434\) 0 0
\(435\) 0.0891011 1.15559i 0.00427207 0.0554063i
\(436\) 0 0
\(437\) 7.17158 + 23.4380i 0.343063 + 1.12119i
\(438\) 0 0
\(439\) −7.57338 9.02561i −0.361458 0.430769i 0.554413 0.832242i \(-0.312943\pi\)
−0.915871 + 0.401473i \(0.868498\pi\)
\(440\) 0 0
\(441\) −16.4163 2.54668i −0.781730 0.121271i
\(442\) 0 0
\(443\) 7.28357 + 20.0114i 0.346053 + 0.950772i 0.983600 + 0.180361i \(0.0577267\pi\)
−0.637548 + 0.770411i \(0.720051\pi\)
\(444\) 0 0
\(445\) 2.83668 1.63776i 0.134471 0.0776371i
\(446\) 0 0
\(447\) −13.5000 + 1.32154i −0.638530 + 0.0625068i
\(448\) 0 0
\(449\) 5.96300 10.3282i 0.281411 0.487419i −0.690321 0.723503i \(-0.742531\pi\)
0.971733 + 0.236084i \(0.0758641\pi\)
\(450\) 0 0
\(451\) 25.6837 4.52874i 1.20940 0.213250i
\(452\) 0 0
\(453\) −17.3933 + 8.33012i −0.817211 + 0.391383i
\(454\) 0 0
\(455\) 0.958074 0.0449152
\(456\) 0 0
\(457\) −19.1338 −0.895044 −0.447522 0.894273i \(-0.647693\pi\)
−0.447522 + 0.894273i \(0.647693\pi\)
\(458\) 0 0
\(459\) −2.09915 4.16050i −0.0979799 0.194195i
\(460\) 0 0
\(461\) 29.6765 5.23277i 1.38217 0.243715i 0.567376 0.823459i \(-0.307959\pi\)
0.814798 + 0.579744i \(0.196848\pi\)
\(462\) 0 0
\(463\) −12.7896 + 22.1523i −0.594385 + 1.02950i 0.399248 + 0.916843i \(0.369271\pi\)
−0.993633 + 0.112662i \(0.964062\pi\)
\(464\) 0 0
\(465\) −0.466044 4.76082i −0.0216123 0.220778i
\(466\) 0 0
\(467\) −24.6450 + 14.2288i −1.14044 + 0.658431i −0.946539 0.322591i \(-0.895446\pi\)
−0.193898 + 0.981022i \(0.562113\pi\)
\(468\) 0 0
\(469\) −2.11611 5.81397i −0.0977131 0.268464i
\(470\) 0 0
\(471\) 29.8912 21.3929i 1.37731 0.985732i
\(472\) 0 0
\(473\) −7.25924 8.65122i −0.333780 0.397784i
\(474\) 0 0
\(475\) 15.7168 + 14.6494i 0.721134 + 0.672160i
\(476\) 0 0
\(477\) 11.3567 + 12.9809i 0.519989 + 0.594357i
\(478\) 0 0
\(479\) 12.1691 + 2.14575i 0.556022 + 0.0980417i 0.444596 0.895731i \(-0.353347\pi\)
0.111426 + 0.993773i \(0.464458\pi\)
\(480\) 0 0
\(481\) −11.0679 + 4.02840i −0.504655 + 0.183679i
\(482\) 0 0
\(483\) 11.4077 + 2.93090i 0.519066 + 0.133361i
\(484\) 0 0
\(485\) −1.23285 1.03449i −0.0559810 0.0469736i
\(486\) 0 0
\(487\) −24.3442 14.0551i −1.10314 0.636899i −0.166097 0.986109i \(-0.553117\pi\)
−0.937044 + 0.349210i \(0.886450\pi\)
\(488\) 0 0
\(489\) 3.40734 4.97461i 0.154085 0.224959i
\(490\) 0 0
\(491\) −1.17147 + 3.21859i −0.0528678 + 0.145253i −0.963316 0.268371i \(-0.913515\pi\)
0.910448 + 0.413624i \(0.135737\pi\)
\(492\) 0 0
\(493\) 2.25350i 0.101493i
\(494\) 0 0
\(495\) 0.0387486 + 1.87812i 0.00174162 + 0.0844151i
\(496\) 0 0
\(497\) −10.7762 3.92222i −0.483379 0.175936i
\(498\) 0 0
\(499\) −6.64566 37.6894i −0.297500 1.68721i −0.656862 0.754010i \(-0.728117\pi\)
0.359362 0.933198i \(-0.382994\pi\)
\(500\) 0 0
\(501\) −34.2670 + 9.56171i −1.53094 + 0.427186i
\(502\) 0 0
\(503\) −10.1578 + 12.1056i −0.452916 + 0.539764i −0.943387 0.331693i \(-0.892380\pi\)
0.490472 + 0.871457i \(0.336825\pi\)
\(504\) 0 0
\(505\) −1.38034 2.39082i −0.0614244 0.106390i
\(506\) 0 0
\(507\) 6.54512 + 2.97024i 0.290679 + 0.131913i
\(508\) 0 0
\(509\) −1.72136 + 9.76234i −0.0762981 + 0.432708i 0.922599 + 0.385760i \(0.126061\pi\)
−0.998897 + 0.0469483i \(0.985050\pi\)
\(510\) 0 0
\(511\) −0.316310 + 0.265415i −0.0139927 + 0.0117413i
\(512\) 0 0
\(513\) 5.39730 + 21.9970i 0.238296 + 0.971192i
\(514\) 0 0
\(515\) −3.01505 + 2.52993i −0.132859 + 0.111482i
\(516\) 0 0
\(517\) 0.789817 4.47928i 0.0347361 0.196998i
\(518\) 0 0
\(519\) 13.1431 + 5.96449i 0.576920 + 0.261812i
\(520\) 0 0
\(521\) 6.93036 + 12.0037i 0.303625 + 0.525894i 0.976954 0.213449i \(-0.0684697\pi\)
−0.673329 + 0.739343i \(0.735136\pi\)
\(522\) 0 0
\(523\) −24.0581 + 28.6713i −1.05199 + 1.25371i −0.0856778 + 0.996323i \(0.527306\pi\)
−0.966309 + 0.257386i \(0.917139\pi\)
\(524\) 0 0
\(525\) 9.94452 2.77487i 0.434014 0.121105i
\(526\) 0 0
\(527\) 1.61506 + 9.15947i 0.0703532 + 0.398993i
\(528\) 0 0
\(529\) 8.09973 + 2.94806i 0.352162 + 0.128177i
\(530\) 0 0
\(531\) 0.790147 + 38.2978i 0.0342895 + 1.66198i
\(532\) 0 0
\(533\) 32.9970i 1.42926i
\(534\) 0 0
\(535\) −1.47269 + 4.04618i −0.0636699 + 0.174932i
\(536\) 0 0
\(537\) −8.83404 + 12.8974i −0.381217 + 0.556565i
\(538\) 0 0
\(539\) −11.2761 6.51028i −0.485698 0.280418i
\(540\) 0 0
\(541\) 6.17119 + 5.17824i 0.265320 + 0.222630i 0.765736 0.643155i \(-0.222375\pi\)
−0.500416 + 0.865785i \(0.666819\pi\)
\(542\) 0 0
\(543\) 15.4235 + 3.96266i 0.661884 + 0.170054i
\(544\) 0 0
\(545\) −4.57078 + 1.66363i −0.195791 + 0.0712620i
\(546\) 0 0
\(547\) −25.2004 4.44352i −1.07749 0.189991i −0.393386 0.919373i \(-0.628697\pi\)
−0.684106 + 0.729382i \(0.739808\pi\)
\(548\) 0 0
\(549\) −1.74777 1.99773i −0.0745930 0.0852611i
\(550\) 0 0
\(551\) 2.46140 10.6726i 0.104859 0.454670i
\(552\) 0 0
\(553\) −5.31631 6.33574i −0.226073 0.269423i
\(554\) 0 0
\(555\) 1.48504 1.06283i 0.0630366 0.0451147i
\(556\) 0 0
\(557\) −4.99606 13.7266i −0.211690 0.581613i 0.787718 0.616037i \(-0.211263\pi\)
−0.999407 + 0.0344238i \(0.989040\pi\)
\(558\) 0 0
\(559\) −12.3743 + 7.14431i −0.523377 + 0.302172i
\(560\) 0 0
\(561\) −0.355841 3.63505i −0.0150236 0.153472i
\(562\) 0 0
\(563\) −12.5968 + 21.8184i −0.530893 + 0.919534i 0.468457 + 0.883486i \(0.344810\pi\)
−0.999350 + 0.0360479i \(0.988523\pi\)
\(564\) 0 0
\(565\) −0.629478 + 0.110994i −0.0264824 + 0.00466955i
\(566\) 0 0
\(567\) 10.3723 + 3.29748i 0.435594 + 0.138481i
\(568\) 0 0
\(569\) −42.1013 −1.76498 −0.882490 0.470332i \(-0.844134\pi\)
−0.882490 + 0.470332i \(0.844134\pi\)
\(570\) 0 0
\(571\) 12.9487 0.541887 0.270944 0.962595i \(-0.412664\pi\)
0.270944 + 0.962595i \(0.412664\pi\)
\(572\) 0 0
\(573\) −11.4544 + 5.48581i −0.478515 + 0.229173i
\(574\) 0 0
\(575\) 27.2958 4.81298i 1.13831 0.200715i
\(576\) 0 0
\(577\) 6.43762 11.1503i 0.268002 0.464192i −0.700344 0.713805i \(-0.746970\pi\)
0.968346 + 0.249613i \(0.0803034\pi\)
\(578\) 0 0
\(579\) 3.09018 0.302503i 0.128424 0.0125716i
\(580\) 0 0
\(581\) 14.7826 8.53474i 0.613286 0.354081i
\(582\) 0 0
\(583\) 4.62350 + 12.7030i 0.191486 + 0.526103i
\(584\) 0 0
\(585\) 2.34865 + 0.364348i 0.0971046 + 0.0150639i
\(586\) 0 0
\(587\) 11.6998 + 13.9432i 0.482900 + 0.575498i 0.951397 0.307967i \(-0.0996486\pi\)
−0.468497 + 0.883465i \(0.655204\pi\)
\(588\) 0 0
\(589\) 2.35551 45.1435i 0.0970573 1.86011i
\(590\) 0 0
\(591\) 1.05362 13.6649i 0.0433402 0.562098i
\(592\) 0 0
\(593\) 6.08719 + 1.07334i 0.249971 + 0.0440766i 0.297230 0.954806i \(-0.403937\pi\)
−0.0472585 + 0.998883i \(0.515048\pi\)
\(594\) 0 0
\(595\) 0.271404 0.0987830i 0.0111265 0.00404971i
\(596\) 0 0
\(597\) −4.50854 + 17.5481i −0.184522 + 0.718197i
\(598\) 0 0
\(599\) −27.9659 23.4662i −1.14266 0.958803i −0.143135 0.989703i \(-0.545718\pi\)
−0.999522 + 0.0308999i \(0.990163\pi\)
\(600\) 0 0
\(601\) 2.01662 + 1.16430i 0.0822597 + 0.0474927i 0.540566 0.841302i \(-0.318210\pi\)
−0.458306 + 0.888795i \(0.651544\pi\)
\(602\) 0 0
\(603\) −2.97649 15.0573i −0.121212 0.613180i
\(604\) 0 0
\(605\) 0.498339 1.36918i 0.0202604 0.0556649i
\(606\) 0 0
\(607\) 24.4621i 0.992887i −0.868069 0.496443i \(-0.834639\pi\)
0.868069 0.496443i \(-0.165361\pi\)
\(608\) 0 0
\(609\) −3.75981 3.68304i −0.152355 0.149244i
\(610\) 0 0
\(611\) −5.40766 1.96823i −0.218770 0.0796259i
\(612\) 0 0
\(613\) −6.30039 35.7313i −0.254470 1.44317i −0.797428 0.603414i \(-0.793807\pi\)
0.542958 0.839760i \(-0.317304\pi\)
\(614\) 0 0
\(615\) 1.37504 + 4.92785i 0.0554471 + 0.198710i
\(616\) 0 0
\(617\) 10.3830 12.3740i 0.418006 0.498160i −0.515416 0.856940i \(-0.672363\pi\)
0.933422 + 0.358780i \(0.116807\pi\)
\(618\) 0 0
\(619\) 15.2492 + 26.4123i 0.612916 + 1.06160i 0.990746 + 0.135726i \(0.0433368\pi\)
−0.377831 + 0.925875i \(0.623330\pi\)
\(620\) 0 0
\(621\) 26.8504 + 11.5231i 1.07747 + 0.462408i
\(622\) 0 0
\(623\) 2.58289 14.6483i 0.103481 0.586871i
\(624\) 0 0
\(625\) 18.3401 15.3891i 0.733602 0.615565i
\(626\) 0 0
\(627\) −2.28513 + 17.6044i −0.0912594 + 0.703051i
\(628\) 0 0
\(629\) −2.71998 + 2.28234i −0.108453 + 0.0910028i
\(630\) 0 0
\(631\) 5.03370 28.5475i 0.200388 1.13646i −0.704145 0.710056i \(-0.748670\pi\)
0.904533 0.426403i \(-0.140219\pi\)
\(632\) 0 0
\(633\) 9.94438 21.9131i 0.395254 0.870967i
\(634\) 0 0
\(635\) −0.788005 1.36486i −0.0312710 0.0541630i
\(636\) 0 0
\(637\) −10.5892 + 12.6198i −0.419561 + 0.500013i
\(638\) 0 0
\(639\) −24.9255 13.7132i −0.986038 0.542484i
\(640\) 0 0
\(641\) 4.38869 + 24.8895i 0.173343 + 0.983076i 0.940039 + 0.341066i \(0.110788\pi\)
−0.766696 + 0.642010i \(0.778101\pi\)
\(642\) 0 0
\(643\) −11.3227 4.12111i −0.446522 0.162521i 0.108966 0.994046i \(-0.465246\pi\)
−0.555488 + 0.831525i \(0.687468\pi\)
\(644\) 0 0
\(645\) 1.55029 1.58261i 0.0610428 0.0623152i
\(646\) 0 0
\(647\) 27.8093i 1.09330i −0.837362 0.546649i \(-0.815903\pi\)
0.837362 0.546649i \(-0.184097\pi\)
\(648\) 0 0
\(649\) −10.2685 + 28.2126i −0.403075 + 1.10744i
\(650\) 0 0
\(651\) −17.9215 12.2753i −0.702400 0.481106i
\(652\) 0 0
\(653\) 2.53710 + 1.46480i 0.0992846 + 0.0573220i 0.548820 0.835940i \(-0.315077\pi\)
−0.449536 + 0.893262i \(0.648411\pi\)
\(654\) 0 0
\(655\) −3.52536 2.95812i −0.137747 0.115583i
\(656\) 0 0
\(657\) −0.876345 + 0.530356i −0.0341895 + 0.0206912i
\(658\) 0 0
\(659\) 25.4128 9.24952i 0.989944 0.360310i 0.204245 0.978920i \(-0.434526\pi\)
0.785699 + 0.618610i \(0.212304\pi\)
\(660\) 0 0
\(661\) 13.9832 + 2.46561i 0.543883 + 0.0959013i 0.438838 0.898566i \(-0.355390\pi\)
0.105045 + 0.994467i \(0.466501\pi\)
\(662\) 0 0
\(663\) −4.60746 0.355255i −0.178939 0.0137970i
\(664\) 0 0
\(665\) −1.39327 + 0.171396i −0.0540288 + 0.00664645i
\(666\) 0 0
\(667\) −9.08225 10.8238i −0.351666 0.419099i
\(668\) 0 0
\(669\) 12.5610 + 17.5509i 0.485636 + 0.678555i
\(670\) 0 0
\(671\) −0.711543 1.95495i −0.0274688 0.0754700i
\(672\) 0 0
\(673\) −4.68491 + 2.70483i −0.180590 + 0.104264i −0.587570 0.809173i \(-0.699915\pi\)
0.406980 + 0.913437i \(0.366582\pi\)
\(674\) 0 0
\(675\) 25.4335 3.02057i 0.978936 0.116262i
\(676\) 0 0
\(677\) −11.2154 + 19.4256i −0.431043 + 0.746588i −0.996963 0.0778720i \(-0.975187\pi\)
0.565921 + 0.824460i \(0.308521\pi\)
\(678\) 0 0
\(679\) −7.19722 + 1.26906i −0.276204 + 0.0487022i
\(680\) 0 0
\(681\) −1.22658 2.56110i −0.0470025 0.0981414i
\(682\) 0 0
\(683\) −5.63051 −0.215446 −0.107723 0.994181i \(-0.534356\pi\)
−0.107723 + 0.994181i \(0.534356\pi\)
\(684\) 0 0
\(685\) −4.87153 −0.186131
\(686\) 0 0
\(687\) −9.09350 18.9873i −0.346939 0.724410i
\(688\) 0 0
\(689\) 16.8437 2.97000i 0.641694 0.113148i
\(690\) 0 0
\(691\) −8.10408 + 14.0367i −0.308294 + 0.533980i −0.977989 0.208655i \(-0.933091\pi\)
0.669696 + 0.742636i \(0.266425\pi\)
\(692\) 0 0
\(693\) 6.64640 + 5.34730i 0.252476 + 0.203127i
\(694\) 0 0
\(695\) −0.530267 + 0.306150i −0.0201142 + 0.0116129i
\(696\) 0 0
\(697\) −3.40218 9.34740i −0.128867 0.354058i
\(698\) 0 0
\(699\) 2.42836 + 3.39303i 0.0918491 + 0.128336i
\(700\) 0 0
\(701\) 25.1621 + 29.9870i 0.950360 + 1.13260i 0.991059 + 0.133424i \(0.0425971\pi\)
−0.0406990 + 0.999171i \(0.512958\pi\)
\(702\) 0 0
\(703\) 15.3748 7.83829i 0.579872 0.295627i
\(704\) 0 0
\(705\) 0.889613 + 0.0685930i 0.0335048 + 0.00258336i
\(706\) 0 0
\(707\) −12.3459 2.17692i −0.464317 0.0818715i
\(708\) 0 0
\(709\) −0.294067 + 0.107032i −0.0110439 + 0.00401966i −0.347536 0.937667i \(-0.612982\pi\)
0.336492 + 0.941686i \(0.390759\pi\)
\(710\) 0 0
\(711\) −10.6231 17.5533i −0.398398 0.658302i
\(712\) 0 0
\(713\) −44.6726 37.4847i −1.67300 1.40381i
\(714\) 0 0
\(715\) 1.61325 + 0.931412i 0.0603322 + 0.0348328i
\(716\) 0 0
\(717\) 27.3589 + 18.7393i 1.02174 + 0.699833i
\(718\) 0 0
\(719\) 9.97683 27.4111i 0.372073 1.02226i −0.602486 0.798130i \(-0.705823\pi\)
0.974559 0.224132i \(-0.0719548\pi\)
\(720\) 0 0
\(721\) 17.8730i 0.665624i
\(722\) 0 0
\(723\) −5.08544 + 5.19144i −0.189129 + 0.193072i
\(724\) 0 0
\(725\) −11.6386 4.23609i −0.432246 0.157325i
\(726\) 0 0
\(727\) −1.39364 7.90374i −0.0516873 0.293133i 0.947996 0.318281i \(-0.103106\pi\)
−0.999684 + 0.0251476i \(0.991994\pi\)
\(728\) 0 0
\(729\) 24.1729 + 12.0280i 0.895291 + 0.445482i
\(730\) 0 0
\(731\) −2.76878 + 3.29971i −0.102407 + 0.122044i
\(732\) 0 0
\(733\) −8.60205 14.8992i −0.317724 0.550314i 0.662289 0.749249i \(-0.269585\pi\)
−0.980013 + 0.198935i \(0.936252\pi\)
\(734\) 0 0
\(735\) 1.05553 2.32594i 0.0389340 0.0857936i
\(736\) 0 0
\(737\) 2.08896 11.8471i 0.0769479 0.436393i
\(738\) 0 0
\(739\) 19.8776 16.6793i 0.731210 0.613558i −0.199251 0.979948i \(-0.563851\pi\)
0.930461 + 0.366390i \(0.119407\pi\)
\(740\) 0 0
\(741\) 21.4330 + 6.71502i 0.787361 + 0.246682i
\(742\) 0 0
\(743\) 35.8677 30.0966i 1.31586 1.10414i 0.328693 0.944437i \(-0.393392\pi\)
0.987166 0.159700i \(-0.0510527\pi\)
\(744\) 0 0
\(745\) 0.362158 2.05390i 0.0132684 0.0752491i
\(746\) 0 0
\(747\) 39.4842 15.3006i 1.44465 0.559819i
\(748\) 0 0
\(749\) 9.77655 + 16.9335i 0.357227 + 0.618736i
\(750\) 0 0
\(751\) 1.93570 2.30687i 0.0706346 0.0841791i −0.729570 0.683906i \(-0.760280\pi\)
0.800205 + 0.599727i \(0.204724\pi\)
\(752\) 0 0
\(753\) −1.96217 7.03199i −0.0715055 0.256260i
\(754\) 0 0
\(755\) −0.514892 2.92010i −0.0187389 0.106273i
\(756\) 0 0
\(757\) 6.18347 + 2.25060i 0.224742 + 0.0817994i 0.451937 0.892050i \(-0.350733\pi\)
−0.227195 + 0.973849i \(0.572955\pi\)
\(758\) 0 0
\(759\) 16.3594 + 16.0254i 0.593810 + 0.581685i
\(760\) 0 0
\(761\) 12.0756i 0.437741i 0.975754 + 0.218870i \(0.0702372\pi\)
−0.975754 + 0.218870i \(0.929763\pi\)
\(762\) 0 0
\(763\) −7.55461 + 20.7561i −0.273495 + 0.751422i
\(764\) 0 0
\(765\) 0.702893 0.138946i 0.0254132 0.00502362i
\(766\) 0 0
\(767\) 32.8968 + 18.9930i 1.18784 + 0.685797i
\(768\) 0 0
\(769\) −28.1846 23.6497i −1.01636 0.852830i −0.0271972 0.999630i \(-0.508658\pi\)
−0.989166 + 0.146800i \(0.953103\pi\)
\(770\) 0 0
\(771\) −7.66037 + 29.8157i −0.275882 + 1.07379i
\(772\) 0 0
\(773\) 15.8791 5.77952i 0.571132 0.207875i −0.0402788 0.999188i \(-0.512825\pi\)
0.611411 + 0.791314i \(0.290602\pi\)
\(774\) 0 0
\(775\) −50.3416 8.87657i −1.80832 0.318856i
\(776\) 0 0
\(777\) 0.637520 8.26827i 0.0228709 0.296623i
\(778\) 0 0
\(779\) 5.90304 + 47.9856i 0.211498 + 1.71926i
\(780\) 0 0
\(781\) −14.3325 17.0808i −0.512856 0.611198i
\(782\) 0 0
\(783\) −7.81626 10.4585i −0.279330 0.373757i
\(784\) 0 0
\(785\) 1.93296 + 5.31077i 0.0689904 + 0.189550i
\(786\) 0 0
\(787\) 19.2256 11.0999i 0.685319 0.395669i −0.116537 0.993186i \(-0.537179\pi\)
0.801856 + 0.597517i \(0.203846\pi\)
\(788\) 0 0
\(789\) −1.93116 + 0.189045i −0.0687512 + 0.00673017i
\(790\) 0 0
\(791\) −1.45129 + 2.51372i −0.0516021 + 0.0893774i
\(792\) 0 0
\(793\) −2.59220 + 0.457074i −0.0920516 + 0.0162312i