Properties

Label 432.2.be.a.335.1
Level $432$
Weight $2$
Character 432.335
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 335.1
Character \(\chi\) \(=\) 432.335
Dual form 432.2.be.a.383.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.64221 + 0.550590i) q^{3} +(-1.00608 + 2.76418i) q^{5} +(-0.201339 - 0.0355015i) q^{7} +(2.39370 - 1.80837i) q^{9} +O(q^{10})\) \(q+(-1.64221 + 0.550590i) q^{3} +(-1.00608 + 2.76418i) q^{5} +(-0.201339 - 0.0355015i) q^{7} +(2.39370 - 1.80837i) q^{9} +(-2.91100 + 1.05952i) q^{11} +(1.23448 - 1.03585i) q^{13} +(0.130261 - 5.09330i) q^{15} +(-2.86450 + 1.65382i) q^{17} +(-5.98415 - 3.45495i) q^{19} +(0.350187 - 0.0525544i) q^{21} +(-1.21573 - 6.89473i) q^{23} +(-2.79827 - 2.34802i) q^{25} +(-2.93529 + 4.28767i) q^{27} +(-2.70909 + 3.22857i) q^{29} +(0.173262 - 0.0305507i) q^{31} +(4.19711 - 3.34272i) q^{33} +(0.300695 - 0.520819i) q^{35} +(-5.46424 - 9.46434i) q^{37} +(-1.45694 + 2.38077i) q^{39} +(-0.982963 - 1.17145i) q^{41} +(3.57898 + 9.83317i) q^{43} +(2.59040 + 8.43598i) q^{45} +(-1.76136 + 9.98915i) q^{47} +(-6.53857 - 2.37985i) q^{49} +(3.79353 - 4.29308i) q^{51} +3.56595i q^{53} -9.11248i q^{55} +(11.7295 + 2.37894i) q^{57} +(4.69955 + 1.71050i) q^{59} +(1.18103 - 6.69796i) q^{61} +(-0.546144 + 0.279115i) q^{63} +(1.62129 + 4.45446i) q^{65} +(2.60404 + 3.10337i) q^{67} +(5.79265 + 10.6532i) q^{69} +(-2.61271 - 4.52534i) q^{71} +(-4.68403 + 8.11298i) q^{73} +(5.88814 + 2.31525i) q^{75} +(0.623712 - 0.109977i) q^{77} +(6.13899 - 7.31617i) q^{79} +(2.45960 - 8.65739i) q^{81} +(8.47037 + 7.10748i) q^{83} +(-1.68954 - 9.58186i) q^{85} +(2.67127 - 6.79358i) q^{87} +(2.64985 + 1.52989i) q^{89} +(-0.285322 + 0.164731i) q^{91} +(-0.267711 + 0.145567i) q^{93} +(15.5706 - 13.0653i) q^{95} +(-1.58670 + 0.577510i) q^{97} +(-5.05206 + 7.80033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 6 q^{5} - 12 q^{9} + O(q^{10}) \) \( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\)

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
\(3\) −1.64221 + 0.550590i −0.948130 + 0.317884i
\(4\) 0 0
\(5\) −1.00608 + 2.76418i −0.449932 + 1.23618i 0.482839 + 0.875709i \(0.339606\pi\)
−0.932771 + 0.360469i \(0.882617\pi\)
\(6\) 0 0
\(7\) −0.201339 0.0355015i −0.0760989 0.0134183i 0.135469 0.990782i \(-0.456746\pi\)
−0.211568 + 0.977363i \(0.567857\pi\)
\(8\) 0 0
\(9\) 2.39370 1.80837i 0.797900 0.602790i
\(10\) 0 0
\(11\) −2.91100 + 1.05952i −0.877700 + 0.319457i −0.741281 0.671195i \(-0.765781\pi\)
−0.136419 + 0.990651i \(0.543559\pi\)
\(12\) 0 0
\(13\) 1.23448 1.03585i 0.342382 0.287293i −0.455340 0.890318i \(-0.650482\pi\)
0.797723 + 0.603025i \(0.206038\pi\)
\(14\) 0 0
\(15\) 0.130261 5.09330i 0.0336333 1.31508i
\(16\) 0 0
\(17\) −2.86450 + 1.65382i −0.694743 + 0.401110i −0.805386 0.592750i \(-0.798042\pi\)
0.110644 + 0.993860i \(0.464709\pi\)
\(18\) 0 0
\(19\) −5.98415 3.45495i −1.37286 0.792621i −0.381572 0.924339i \(-0.624617\pi\)
−0.991287 + 0.131718i \(0.957951\pi\)
\(20\) 0 0
\(21\) 0.350187 0.0525544i 0.0764171 0.0114683i
\(22\) 0 0
\(23\) −1.21573 6.89473i −0.253497 1.43765i −0.799902 0.600130i \(-0.795115\pi\)
0.546406 0.837521i \(-0.315996\pi\)
\(24\) 0 0
\(25\) −2.79827 2.34802i −0.559653 0.469605i
\(26\) 0 0
\(27\) −2.93529 + 4.28767i −0.564896 + 0.825162i
\(28\) 0 0
\(29\) −2.70909 + 3.22857i −0.503065 + 0.599530i −0.956490 0.291765i \(-0.905758\pi\)
0.453425 + 0.891294i \(0.350202\pi\)
\(30\) 0 0
\(31\) 0.173262 0.0305507i 0.0311187 0.00548707i −0.158067 0.987428i \(-0.550526\pi\)
0.189186 + 0.981941i \(0.439415\pi\)
\(32\) 0 0
\(33\) 4.19711 3.34272i 0.730623 0.581893i
\(34\) 0 0
\(35\) 0.300695 0.520819i 0.0508267 0.0880345i
\(36\) 0 0
\(37\) −5.46424 9.46434i −0.898315 1.55593i −0.829647 0.558288i \(-0.811459\pi\)
−0.0686675 0.997640i \(-0.521875\pi\)
\(38\) 0 0
\(39\) −1.45694 + 2.38077i −0.233297 + 0.381229i
\(40\) 0 0
\(41\) −0.982963 1.17145i −0.153513 0.182950i 0.683807 0.729663i \(-0.260323\pi\)
−0.837320 + 0.546713i \(0.815879\pi\)
\(42\) 0 0
\(43\) 3.57898 + 9.83317i 0.545789 + 1.49954i 0.839343 + 0.543601i \(0.182940\pi\)
−0.293554 + 0.955942i \(0.594838\pi\)
\(44\) 0 0
\(45\) 2.59040 + 8.43598i 0.386155 + 1.25756i
\(46\) 0 0
\(47\) −1.76136 + 9.98915i −0.256920 + 1.45707i 0.534175 + 0.845374i \(0.320622\pi\)
−0.791095 + 0.611693i \(0.790489\pi\)
\(48\) 0 0
\(49\) −6.53857 2.37985i −0.934082 0.339978i
\(50\) 0 0
\(51\) 3.79353 4.29308i 0.531200 0.601152i
\(52\) 0 0
\(53\) 3.56595i 0.489820i 0.969546 + 0.244910i \(0.0787585\pi\)
−0.969546 + 0.244910i \(0.921242\pi\)
\(54\) 0 0
\(55\) 9.11248i 1.22873i
\(56\) 0 0
\(57\) 11.7295 + 2.37894i 1.55361 + 0.315098i
\(58\) 0 0
\(59\) 4.69955 + 1.71050i 0.611829 + 0.222688i 0.629303 0.777160i \(-0.283340\pi\)
−0.0174743 + 0.999847i \(0.505563\pi\)
\(60\) 0 0
\(61\) 1.18103 6.69796i 0.151216 0.857586i −0.810949 0.585117i \(-0.801049\pi\)
0.962164 0.272469i \(-0.0878403\pi\)
\(62\) 0 0
\(63\) −0.546144 + 0.279115i −0.0688077 + 0.0351652i
\(64\) 0 0
\(65\) 1.62129 + 4.45446i 0.201097 + 0.552508i
\(66\) 0 0
\(67\) 2.60404 + 3.10337i 0.318134 + 0.379137i 0.901285 0.433226i \(-0.142625\pi\)
−0.583151 + 0.812364i \(0.698181\pi\)
\(68\) 0 0
\(69\) 5.79265 + 10.6532i 0.697353 + 1.28250i
\(70\) 0 0
\(71\) −2.61271 4.52534i −0.310071 0.537059i 0.668306 0.743886i \(-0.267020\pi\)
−0.978377 + 0.206827i \(0.933686\pi\)
\(72\) 0 0
\(73\) −4.68403 + 8.11298i −0.548225 + 0.949553i 0.450172 + 0.892942i \(0.351363\pi\)
−0.998396 + 0.0566108i \(0.981971\pi\)
\(74\) 0 0
\(75\) 5.88814 + 2.31525i 0.679904 + 0.267342i
\(76\) 0 0
\(77\) 0.623712 0.109977i 0.0710786 0.0125331i
\(78\) 0 0
\(79\) 6.13899 7.31617i 0.690691 0.823133i −0.300748 0.953704i \(-0.597236\pi\)
0.991439 + 0.130570i \(0.0416808\pi\)
\(80\) 0 0
\(81\) 2.45960 8.65739i 0.273289 0.961932i
\(82\) 0 0
\(83\) 8.47037 + 7.10748i 0.929743 + 0.780147i 0.975771 0.218793i \(-0.0702119\pi\)
−0.0460279 + 0.998940i \(0.514656\pi\)
\(84\) 0 0
\(85\) −1.68954 9.58186i −0.183256 1.03930i
\(86\) 0 0
\(87\) 2.67127 6.79358i 0.286390 0.728348i
\(88\) 0 0
\(89\) 2.64985 + 1.52989i 0.280884 + 0.162168i 0.633823 0.773478i \(-0.281485\pi\)
−0.352940 + 0.935646i \(0.614818\pi\)
\(90\) 0 0
\(91\) −0.285322 + 0.164731i −0.0299099 + 0.0172685i
\(92\) 0 0
\(93\) −0.267711 + 0.145567i −0.0277604 + 0.0150946i
\(94\) 0 0
\(95\) 15.5706 13.0653i 1.59751 1.34047i
\(96\) 0 0
\(97\) −1.58670 + 0.577510i −0.161105 + 0.0586373i −0.421314 0.906915i \(-0.638431\pi\)
0.260209 + 0.965552i \(0.416209\pi\)
\(98\) 0 0
\(99\) −5.05206 + 7.80033i −0.507752 + 0.783963i
\(100\) 0 0
\(101\) −7.31576 1.28997i −0.727946 0.128356i −0.202620 0.979258i \(-0.564946\pi\)
−0.525326 + 0.850901i \(0.676057\pi\)
\(102\) 0 0
\(103\) −5.55315 + 15.2572i −0.547169 + 1.50333i 0.290348 + 0.956921i \(0.406229\pi\)
−0.837516 + 0.546412i \(0.815993\pi\)
\(104\) 0 0
\(105\) −0.207046 + 1.02085i −0.0202056 + 0.0996251i
\(106\) 0 0
\(107\) −13.3992 −1.29535 −0.647676 0.761916i \(-0.724259\pi\)
−0.647676 + 0.761916i \(0.724259\pi\)
\(108\) 0 0
\(109\) 14.6377 1.40204 0.701021 0.713141i \(-0.252728\pi\)
0.701021 + 0.713141i \(0.252728\pi\)
\(110\) 0 0
\(111\) 14.1844 + 12.5339i 1.34632 + 1.18966i
\(112\) 0 0
\(113\) −6.06668 + 16.6681i −0.570705 + 1.56800i 0.232689 + 0.972551i \(0.425247\pi\)
−0.803394 + 0.595448i \(0.796975\pi\)
\(114\) 0 0
\(115\) 20.2814 + 3.57616i 1.89125 + 0.333478i
\(116\) 0 0
\(117\) 1.08177 4.71190i 0.100010 0.435616i
\(118\) 0 0
\(119\) 0.635448 0.231284i 0.0582514 0.0212018i
\(120\) 0 0
\(121\) −1.07514 + 0.902150i −0.0977400 + 0.0820136i
\(122\) 0 0
\(123\) 2.25922 + 1.38256i 0.203707 + 0.124661i
\(124\) 0 0
\(125\) −3.43177 + 1.98133i −0.306947 + 0.177216i
\(126\) 0 0
\(127\) 3.62718 + 2.09415i 0.321860 + 0.185826i 0.652221 0.758029i \(-0.273837\pi\)
−0.330361 + 0.943855i \(0.607171\pi\)
\(128\) 0 0
\(129\) −11.2915 14.1776i −0.994159 1.24826i
\(130\) 0 0
\(131\) 2.37574 + 13.4735i 0.207570 + 1.17719i 0.893345 + 0.449372i \(0.148352\pi\)
−0.685775 + 0.727814i \(0.740537\pi\)
\(132\) 0 0
\(133\) 1.08219 + 0.908062i 0.0938375 + 0.0787390i
\(134\) 0 0
\(135\) −8.89875 12.4274i −0.765883 1.06958i
\(136\) 0 0
\(137\) −0.304060 + 0.362365i −0.0259776 + 0.0309589i −0.778877 0.627177i \(-0.784210\pi\)
0.752899 + 0.658136i \(0.228655\pi\)
\(138\) 0 0
\(139\) −20.9825 + 3.69979i −1.77972 + 0.313812i −0.964250 0.264994i \(-0.914630\pi\)
−0.815465 + 0.578806i \(0.803519\pi\)
\(140\) 0 0
\(141\) −2.60741 17.3741i −0.219584 1.46316i
\(142\) 0 0
\(143\) −2.49606 + 4.32331i −0.208731 + 0.361533i
\(144\) 0 0
\(145\) −6.19878 10.7366i −0.514781 0.891626i
\(146\) 0 0
\(147\) 12.0480 + 0.308128i 0.993704 + 0.0254140i
\(148\) 0 0
\(149\) −12.3756 14.7487i −1.01385 1.20826i −0.977936 0.208904i \(-0.933011\pi\)
−0.0359129 0.999355i \(-0.511434\pi\)
\(150\) 0 0
\(151\) −4.21217 11.5729i −0.342782 0.941786i −0.984584 0.174915i \(-0.944035\pi\)
0.641802 0.766871i \(-0.278187\pi\)
\(152\) 0 0
\(153\) −3.86604 + 9.13882i −0.312550 + 0.738829i
\(154\) 0 0
\(155\) −0.0898674 + 0.509663i −0.00721832 + 0.0409371i
\(156\) 0 0
\(157\) 15.0345 + 5.47210i 1.19988 + 0.436721i 0.863183 0.504892i \(-0.168468\pi\)
0.336698 + 0.941613i \(0.390690\pi\)
\(158\) 0 0
\(159\) −1.96338 5.85603i −0.155706 0.464413i
\(160\) 0 0
\(161\) 1.43134i 0.112805i
\(162\) 0 0
\(163\) 12.5222i 0.980811i −0.871494 0.490406i \(-0.836849\pi\)
0.871494 0.490406i \(-0.163151\pi\)
\(164\) 0 0
\(165\) 5.01725 + 14.9646i 0.390592 + 1.16499i
\(166\) 0 0
\(167\) 6.06389 + 2.20708i 0.469238 + 0.170789i 0.565807 0.824538i \(-0.308565\pi\)
−0.0965691 + 0.995326i \(0.530787\pi\)
\(168\) 0 0
\(169\) −1.80648 + 10.2450i −0.138960 + 0.788080i
\(170\) 0 0
\(171\) −20.5721 + 2.55144i −1.57319 + 0.195113i
\(172\) 0 0
\(173\) −1.34451 3.69400i −0.102221 0.280850i 0.878031 0.478605i \(-0.158857\pi\)
−0.980252 + 0.197755i \(0.936635\pi\)
\(174\) 0 0
\(175\) 0.480041 + 0.572091i 0.0362877 + 0.0432460i
\(176\) 0 0
\(177\) −8.65942 0.221465i −0.650882 0.0166463i
\(178\) 0 0
\(179\) −13.2327 22.9198i −0.989061 1.71310i −0.622276 0.782798i \(-0.713792\pi\)
−0.366785 0.930306i \(-0.619542\pi\)
\(180\) 0 0
\(181\) −2.77259 + 4.80227i −0.206085 + 0.356950i −0.950478 0.310792i \(-0.899406\pi\)
0.744393 + 0.667742i \(0.232739\pi\)
\(182\) 0 0
\(183\) 1.74833 + 11.6497i 0.129241 + 0.861172i
\(184\) 0 0
\(185\) 31.6586 5.58226i 2.32758 0.410416i
\(186\) 0 0
\(187\) 6.58631 7.84925i 0.481638 0.573994i
\(188\) 0 0
\(189\) 0.743205 0.759067i 0.0540602 0.0552140i
\(190\) 0 0
\(191\) 7.21805 + 6.05666i 0.522280 + 0.438245i 0.865426 0.501037i \(-0.167048\pi\)
−0.343146 + 0.939282i \(0.611493\pi\)
\(192\) 0 0
\(193\) 2.81540 + 15.9670i 0.202657 + 1.14933i 0.901084 + 0.433645i \(0.142773\pi\)
−0.698427 + 0.715682i \(0.746116\pi\)
\(194\) 0 0
\(195\) −5.11508 6.42249i −0.366299 0.459924i
\(196\) 0 0
\(197\) −12.4926 7.21263i −0.890063 0.513878i −0.0161001 0.999870i \(-0.505125\pi\)
−0.873963 + 0.485992i \(0.838458\pi\)
\(198\) 0 0
\(199\) 3.37317 1.94750i 0.239118 0.138055i −0.375653 0.926760i \(-0.622582\pi\)
0.614771 + 0.788705i \(0.289248\pi\)
\(200\) 0 0
\(201\) −5.98506 3.66263i −0.422154 0.258342i
\(202\) 0 0
\(203\) 0.660064 0.553859i 0.0463274 0.0388733i
\(204\) 0 0
\(205\) 4.22704 1.53852i 0.295229 0.107455i
\(206\) 0 0
\(207\) −15.3783 14.3054i −1.06887 0.994297i
\(208\) 0 0
\(209\) 21.0805 + 3.71705i 1.45817 + 0.257114i
\(210\) 0 0
\(211\) −7.01625 + 19.2770i −0.483018 + 1.32708i 0.423874 + 0.905721i \(0.360670\pi\)
−0.906893 + 0.421361i \(0.861552\pi\)
\(212\) 0 0
\(213\) 6.78222 + 5.99302i 0.464710 + 0.410635i
\(214\) 0 0
\(215\) −30.7814 −2.09927
\(216\) 0 0
\(217\) −0.0359689 −0.00244173
\(218\) 0 0
\(219\) 3.22523 15.9022i 0.217941 1.07457i
\(220\) 0 0
\(221\) −1.82305 + 5.00879i −0.122632 + 0.336928i
\(222\) 0 0
\(223\) 5.04386 + 0.889368i 0.337762 + 0.0595565i 0.339957 0.940441i \(-0.389588\pi\)
−0.00219496 + 0.999998i \(0.500699\pi\)
\(224\) 0 0
\(225\) −10.9443 0.560168i −0.729621 0.0373446i
\(226\) 0 0
\(227\) 2.64745 0.963595i 0.175718 0.0639560i −0.252663 0.967554i \(-0.581306\pi\)
0.428381 + 0.903598i \(0.359084\pi\)
\(228\) 0 0
\(229\) −7.12439 + 5.97807i −0.470793 + 0.395042i −0.847084 0.531459i \(-0.821644\pi\)
0.376291 + 0.926502i \(0.377199\pi\)
\(230\) 0 0
\(231\) −0.963713 + 0.524015i −0.0634076 + 0.0344777i
\(232\) 0 0
\(233\) 20.4589 11.8120i 1.34031 0.773828i 0.353458 0.935451i \(-0.385006\pi\)
0.986853 + 0.161622i \(0.0516726\pi\)
\(234\) 0 0
\(235\) −25.8397 14.9186i −1.68560 0.973180i
\(236\) 0 0
\(237\) −6.05330 + 15.3947i −0.393204 + 0.999996i
\(238\) 0 0
\(239\) −3.21197 18.2160i −0.207765 1.17829i −0.893029 0.449999i \(-0.851424\pi\)
0.685264 0.728295i \(-0.259687\pi\)
\(240\) 0 0
\(241\) 2.33009 + 1.95517i 0.150094 + 0.125944i 0.714743 0.699388i \(-0.246544\pi\)
−0.564649 + 0.825331i \(0.690988\pi\)
\(242\) 0 0
\(243\) 0.727493 + 15.5715i 0.0466687 + 0.998910i
\(244\) 0 0
\(245\) 13.1566 15.6795i 0.840547 1.00172i
\(246\) 0 0
\(247\) −10.9661 + 1.93362i −0.697757 + 0.123033i
\(248\) 0 0
\(249\) −17.8234 7.00827i −1.12951 0.444131i
\(250\) 0 0
\(251\) 1.32283 2.29121i 0.0834963 0.144620i −0.821253 0.570564i \(-0.806725\pi\)
0.904749 + 0.425944i \(0.140058\pi\)
\(252\) 0 0
\(253\) 10.8441 + 18.7825i 0.681761 + 1.18084i
\(254\) 0 0
\(255\) 8.05026 + 14.8052i 0.504127 + 0.927135i
\(256\) 0 0
\(257\) −9.61198 11.4551i −0.599579 0.714551i 0.377838 0.925872i \(-0.376668\pi\)
−0.977417 + 0.211321i \(0.932223\pi\)
\(258\) 0 0
\(259\) 0.764165 + 2.09953i 0.0474829 + 0.130458i
\(260\) 0 0
\(261\) −0.646307 + 12.6273i −0.0400054 + 0.781607i
\(262\) 0 0
\(263\) −4.11650 + 23.3458i −0.253834 + 1.43957i 0.545213 + 0.838298i \(0.316449\pi\)
−0.799047 + 0.601268i \(0.794662\pi\)
\(264\) 0 0
\(265\) −9.85691 3.58762i −0.605505 0.220386i
\(266\) 0 0
\(267\) −5.19396 1.05342i −0.317865 0.0644683i
\(268\) 0 0
\(269\) 17.9967i 1.09728i −0.836060 0.548638i \(-0.815146\pi\)
0.836060 0.548638i \(-0.184854\pi\)
\(270\) 0 0
\(271\) 6.89090i 0.418592i 0.977852 + 0.209296i \(0.0671173\pi\)
−0.977852 + 0.209296i \(0.932883\pi\)
\(272\) 0 0
\(273\) 0.377860 0.427618i 0.0228691 0.0258806i
\(274\) 0 0
\(275\) 10.6335 + 3.87029i 0.641226 + 0.233387i
\(276\) 0 0
\(277\) −0.940086 + 5.33149i −0.0564843 + 0.320338i −0.999938 0.0111670i \(-0.996445\pi\)
0.943453 + 0.331505i \(0.107556\pi\)
\(278\) 0 0
\(279\) 0.359490 0.386451i 0.0215221 0.0231362i
\(280\) 0 0
\(281\) −6.04984 16.6218i −0.360903 0.991573i −0.978711 0.205244i \(-0.934201\pi\)
0.617808 0.786329i \(-0.288021\pi\)
\(282\) 0 0
\(283\) −3.98533 4.74953i −0.236903 0.282330i 0.634474 0.772944i \(-0.281217\pi\)
−0.871377 + 0.490614i \(0.836772\pi\)
\(284\) 0 0
\(285\) −18.3766 + 30.0290i −1.08854 + 1.77877i
\(286\) 0 0
\(287\) 0.156320 + 0.270755i 0.00922731 + 0.0159822i
\(288\) 0 0
\(289\) −3.02977 + 5.24771i −0.178222 + 0.308689i
\(290\) 0 0
\(291\) 2.28772 1.82201i 0.134108 0.106808i
\(292\) 0 0
\(293\) 12.7111 2.24131i 0.742589 0.130938i 0.210461 0.977602i \(-0.432504\pi\)
0.532128 + 0.846664i \(0.321392\pi\)
\(294\) 0 0
\(295\) −9.45623 + 11.2695i −0.550563 + 0.656135i
\(296\) 0 0
\(297\) 4.00176 15.5914i 0.232206 0.904704i
\(298\) 0 0
\(299\) −8.64269 7.25208i −0.499820 0.419399i
\(300\) 0 0
\(301\) −0.371496 2.10686i −0.0214127 0.121437i
\(302\) 0 0
\(303\) 12.7243 1.90959i 0.730989 0.109703i
\(304\) 0 0
\(305\) 17.3262 + 10.0033i 0.992093 + 0.572785i
\(306\) 0 0
\(307\) 12.4699 7.19947i 0.711692 0.410896i −0.0999951 0.994988i \(-0.531883\pi\)
0.811687 + 0.584092i \(0.198549\pi\)
\(308\) 0 0
\(309\) 0.718990 28.1130i 0.0409019 1.59929i
\(310\) 0 0
\(311\) 5.88767 4.94034i 0.333859 0.280141i −0.460411 0.887706i \(-0.652298\pi\)
0.794270 + 0.607565i \(0.207854\pi\)
\(312\) 0 0
\(313\) −6.11474 + 2.22558i −0.345625 + 0.125797i −0.508999 0.860767i \(-0.669984\pi\)
0.163374 + 0.986564i \(0.447762\pi\)
\(314\) 0 0
\(315\) −0.222059 1.79045i −0.0125116 0.100881i
\(316\) 0 0
\(317\) −19.2668 3.39726i −1.08213 0.190809i −0.395974 0.918262i \(-0.629593\pi\)
−0.686158 + 0.727452i \(0.740704\pi\)
\(318\) 0 0
\(319\) 4.46544 12.2687i 0.250016 0.686915i
\(320\) 0 0
\(321\) 22.0043 7.37749i 1.22816 0.411771i
\(322\) 0 0
\(323\) 22.8555 1.27171
\(324\) 0 0
\(325\) −5.88660 −0.326530
\(326\) 0 0
\(327\) −24.0382 + 8.05940i −1.32932 + 0.445686i
\(328\) 0 0
\(329\) 0.709259 1.94867i 0.0391027 0.107434i
\(330\) 0 0
\(331\) 24.5610 + 4.33077i 1.35000 + 0.238041i 0.801441 0.598073i \(-0.204067\pi\)
0.548555 + 0.836114i \(0.315178\pi\)
\(332\) 0 0
\(333\) −30.1948 12.7734i −1.65466 0.699979i
\(334\) 0 0
\(335\) −11.1981 + 4.07579i −0.611820 + 0.222684i
\(336\) 0 0
\(337\) 13.7434 11.5321i 0.748650 0.628192i −0.186496 0.982456i \(-0.559713\pi\)
0.935145 + 0.354264i \(0.115269\pi\)
\(338\) 0 0
\(339\) 0.785478 30.7127i 0.0426613 1.66808i
\(340\) 0 0
\(341\) −0.471996 + 0.272507i −0.0255600 + 0.0147571i
\(342\) 0 0
\(343\) 2.47136 + 1.42684i 0.133441 + 0.0770422i
\(344\) 0 0
\(345\) −35.2753 + 5.29394i −1.89916 + 0.285016i
\(346\) 0 0
\(347\) −3.12290 17.7109i −0.167646 0.950769i −0.946294 0.323307i \(-0.895205\pi\)
0.778648 0.627461i \(-0.215906\pi\)
\(348\) 0 0
\(349\) 16.9984 + 14.2633i 0.909901 + 0.763498i 0.972100 0.234566i \(-0.0753669\pi\)
−0.0621990 + 0.998064i \(0.519811\pi\)
\(350\) 0 0
\(351\) 0.817836 + 8.33354i 0.0436529 + 0.444812i
\(352\) 0 0
\(353\) −9.79906 + 11.6781i −0.521551 + 0.621561i −0.960947 0.276733i \(-0.910748\pi\)
0.439395 + 0.898294i \(0.355193\pi\)
\(354\) 0 0
\(355\) 15.1374 2.66914i 0.803411 0.141663i
\(356\) 0 0
\(357\) −0.916195 + 0.729688i −0.0484902 + 0.0386192i
\(358\) 0 0
\(359\) −3.52298 + 6.10199i −0.185936 + 0.322051i −0.943892 0.330256i \(-0.892865\pi\)
0.757956 + 0.652306i \(0.226198\pi\)
\(360\) 0 0
\(361\) 14.3734 + 24.8955i 0.756495 + 1.31029i
\(362\) 0 0
\(363\) 1.26889 2.07348i 0.0665995 0.108830i
\(364\) 0 0
\(365\) −17.7132 21.1098i −0.927153 1.10494i
\(366\) 0 0
\(367\) 4.13340 + 11.3564i 0.215762 + 0.592800i 0.999603 0.0281603i \(-0.00896488\pi\)
−0.783842 + 0.620961i \(0.786743\pi\)
\(368\) 0 0
\(369\) −4.47133 1.02654i −0.232768 0.0534395i
\(370\) 0 0
\(371\) 0.126596 0.717963i 0.00657255 0.0372748i
\(372\) 0 0
\(373\) 14.2735 + 5.19514i 0.739056 + 0.268994i 0.683993 0.729489i \(-0.260242\pi\)
0.0550629 + 0.998483i \(0.482464\pi\)
\(374\) 0 0
\(375\) 4.54478 5.14326i 0.234691 0.265597i
\(376\) 0 0
\(377\) 6.79180i 0.349796i
\(378\) 0 0
\(379\) 23.4726i 1.20571i −0.797852 0.602853i \(-0.794031\pi\)
0.797852 0.602853i \(-0.205969\pi\)
\(380\) 0 0
\(381\) −7.10961 1.44195i −0.364236 0.0738732i
\(382\) 0 0
\(383\) 5.57744 + 2.03002i 0.284994 + 0.103729i 0.480562 0.876961i \(-0.340433\pi\)
−0.195568 + 0.980690i \(0.562655\pi\)
\(384\) 0 0
\(385\) −0.323507 + 1.83470i −0.0164874 + 0.0935048i
\(386\) 0 0
\(387\) 26.3490 + 17.0655i 1.33940 + 0.867490i
\(388\) 0 0
\(389\) 6.24510 + 17.1583i 0.316639 + 0.869958i 0.991275 + 0.131808i \(0.0420783\pi\)
−0.674636 + 0.738150i \(0.735700\pi\)
\(390\) 0 0
\(391\) 14.8851 + 17.7394i 0.752771 + 0.897118i
\(392\) 0 0
\(393\) −11.3199 20.8183i −0.571011 1.05014i
\(394\) 0 0
\(395\) 14.0469 + 24.3299i 0.706775 + 1.22417i
\(396\) 0 0
\(397\) 12.7443 22.0738i 0.639620 1.10785i −0.345897 0.938273i \(-0.612425\pi\)
0.985516 0.169581i \(-0.0542414\pi\)
\(398\) 0 0
\(399\) −2.27715 0.895387i −0.114000 0.0448254i
\(400\) 0 0
\(401\) 29.3971 5.18350i 1.46802 0.258852i 0.618240 0.785989i \(-0.287846\pi\)
0.849780 + 0.527138i \(0.176735\pi\)
\(402\) 0 0
\(403\) 0.182242 0.217187i 0.00907811 0.0108189i
\(404\) 0 0
\(405\) 21.4560 + 15.5088i 1.06616 + 0.770638i
\(406\) 0 0
\(407\) 25.9340 + 21.7612i 1.28550 + 1.07866i
\(408\) 0 0
\(409\) 5.05387 + 28.6619i 0.249898 + 1.41724i 0.808838 + 0.588032i \(0.200097\pi\)
−0.558940 + 0.829208i \(0.688792\pi\)
\(410\) 0 0
\(411\) 0.299816 0.762492i 0.0147888 0.0376110i
\(412\) 0 0
\(413\) −0.885476 0.511230i −0.0435714 0.0251560i
\(414\) 0 0
\(415\) −28.1682 + 16.2629i −1.38272 + 0.798315i
\(416\) 0 0
\(417\) 32.4206 17.6286i 1.58765 0.863277i
\(418\) 0 0
\(419\) −3.66441 + 3.07481i −0.179018 + 0.150214i −0.727894 0.685690i \(-0.759501\pi\)
0.548875 + 0.835904i \(0.315056\pi\)
\(420\) 0 0
\(421\) 17.1855 6.25501i 0.837570 0.304851i 0.112608 0.993639i \(-0.464079\pi\)
0.724962 + 0.688789i \(0.241857\pi\)
\(422\) 0 0
\(423\) 13.8479 + 27.0962i 0.673308 + 1.31746i
\(424\) 0 0
\(425\) 11.8988 + 2.09809i 0.577178 + 0.101772i
\(426\) 0 0
\(427\) −0.475575 + 1.30663i −0.0230147 + 0.0632323i
\(428\) 0 0
\(429\) 1.71869 8.47409i 0.0829789 0.409133i
\(430\) 0 0
\(431\) 15.9894 0.770181 0.385091 0.922879i \(-0.374170\pi\)
0.385091 + 0.922879i \(0.374170\pi\)
\(432\) 0 0
\(433\) −19.0614 −0.916031 −0.458016 0.888944i \(-0.651440\pi\)
−0.458016 + 0.888944i \(0.651440\pi\)
\(434\) 0 0
\(435\) 16.0912 + 14.2188i 0.771512 + 0.681737i
\(436\) 0 0
\(437\) −16.5459 + 45.4594i −0.791497 + 2.17462i
\(438\) 0 0
\(439\) −21.2264 3.74279i −1.01308 0.178634i −0.357625 0.933865i \(-0.616413\pi\)
−0.655458 + 0.755232i \(0.727524\pi\)
\(440\) 0 0
\(441\) −19.9550 + 6.12751i −0.950239 + 0.291786i
\(442\) 0 0
\(443\) −13.7234 + 4.99490i −0.652018 + 0.237315i −0.646786 0.762671i \(-0.723887\pi\)
−0.00523142 + 0.999986i \(0.501665\pi\)
\(444\) 0 0
\(445\) −6.89486 + 5.78547i −0.326848 + 0.274258i
\(446\) 0 0
\(447\) 28.4438 + 17.4065i 1.34535 + 0.823300i
\(448\) 0 0
\(449\) −18.2978 + 10.5643i −0.863528 + 0.498558i −0.865192 0.501440i \(-0.832804\pi\)
0.00166397 + 0.999999i \(0.499470\pi\)
\(450\) 0 0
\(451\) 4.10258 + 2.36863i 0.193183 + 0.111534i
\(452\) 0 0
\(453\) 13.2892 + 16.6859i 0.624380 + 0.783970i
\(454\) 0 0
\(455\) −0.168289 0.954414i −0.00788951 0.0447436i
\(456\) 0 0
\(457\) −1.17150 0.983008i −0.0548006 0.0459832i 0.614976 0.788546i \(-0.289166\pi\)
−0.669777 + 0.742563i \(0.733610\pi\)
\(458\) 0 0
\(459\) 1.31709 17.1364i 0.0614766 0.799861i
\(460\) 0 0
\(461\) 9.11059 10.8576i 0.424322 0.505688i −0.510953 0.859609i \(-0.670707\pi\)
0.935275 + 0.353921i \(0.115152\pi\)
\(462\) 0 0
\(463\) 35.5679 6.27159i 1.65298 0.291465i 0.732068 0.681231i \(-0.238555\pi\)
0.920914 + 0.389766i \(0.127444\pi\)
\(464\) 0 0
\(465\) −0.133035 0.886453i −0.00616933 0.0411083i
\(466\) 0 0
\(467\) 13.2029 22.8680i 0.610956 1.05821i −0.380124 0.924936i \(-0.624119\pi\)
0.991080 0.133271i \(-0.0425480\pi\)
\(468\) 0 0
\(469\) −0.414120 0.717276i −0.0191223 0.0331207i
\(470\) 0 0
\(471\) −27.7026 0.708495i −1.27647 0.0326457i
\(472\) 0 0
\(473\) −20.8368 24.8324i −0.958078 1.14179i
\(474\) 0 0
\(475\) 8.63295 + 23.7188i 0.396107 + 1.08829i
\(476\) 0 0
\(477\) 6.44855 + 8.53581i 0.295259 + 0.390828i
\(478\) 0 0
\(479\) 0.459687 2.60701i 0.0210036 0.119117i −0.972503 0.232889i \(-0.925182\pi\)
0.993507 + 0.113772i \(0.0362932\pi\)
\(480\) 0 0
\(481\) −16.5491 6.02338i −0.754574 0.274643i
\(482\) 0 0
\(483\) −0.788080 2.35055i −0.0358589 0.106954i
\(484\) 0 0
\(485\) 4.96693i 0.225537i
\(486\) 0 0
\(487\) 9.95003i 0.450879i 0.974257 + 0.225440i \(0.0723818\pi\)
−0.974257 + 0.225440i \(0.927618\pi\)
\(488\) 0 0
\(489\) 6.89458 + 20.5640i 0.311784 + 0.929936i
\(490\) 0 0
\(491\) −19.7065 7.17257i −0.889341 0.323694i −0.143368 0.989669i \(-0.545793\pi\)
−0.745973 + 0.665976i \(0.768015\pi\)
\(492\) 0 0
\(493\) 2.42072 13.7286i 0.109024 0.618303i
\(494\) 0 0
\(495\) −16.4787 21.8126i −0.740664 0.980402i
\(496\) 0 0
\(497\) 0.365383 + 1.00388i 0.0163897 + 0.0450302i
\(498\) 0 0
\(499\) −4.59699 5.47848i −0.205789 0.245250i 0.653271 0.757124i \(-0.273396\pi\)
−0.859061 + 0.511874i \(0.828952\pi\)
\(500\) 0 0
\(501\) −11.1734 0.285759i −0.499189 0.0127668i
\(502\) 0 0
\(503\) −2.12080 3.67334i −0.0945619 0.163786i 0.814864 0.579653i \(-0.196812\pi\)
−0.909426 + 0.415866i \(0.863478\pi\)
\(504\) 0 0
\(505\) 10.9259 18.9243i 0.486198 0.842119i
\(506\) 0 0
\(507\) −2.67421 17.8191i −0.118766 0.791375i
\(508\) 0 0
\(509\) 35.9453 6.33812i 1.59325 0.280932i 0.694530 0.719463i \(-0.255612\pi\)
0.898716 + 0.438531i \(0.144501\pi\)
\(510\) 0 0
\(511\) 1.23110 1.46717i 0.0544607 0.0649037i
\(512\) 0 0
\(513\) 32.3789 15.5168i 1.42956 0.685083i
\(514\) 0 0
\(515\) −36.5866 30.6998i −1.61220 1.35280i
\(516\) 0 0
\(517\) −5.45637 30.9446i −0.239971 1.36094i
\(518\) 0 0
\(519\) 4.24184 + 5.32605i 0.186196 + 0.233788i
\(520\) 0 0
\(521\) −20.7979 12.0077i −0.911174 0.526067i −0.0303652 0.999539i \(-0.509667\pi\)
−0.880809 + 0.473472i \(0.843000\pi\)
\(522\) 0 0
\(523\) 3.54766 2.04824i 0.155128 0.0895633i −0.420426 0.907327i \(-0.638120\pi\)
0.575555 + 0.817763i \(0.304786\pi\)
\(524\) 0 0
\(525\) −1.10332 0.675187i −0.0481527 0.0294676i
\(526\) 0 0
\(527\) −0.445783 + 0.374056i −0.0194186 + 0.0162941i
\(528\) 0 0
\(529\) −24.4464 + 8.89776i −1.06289 + 0.386859i
\(530\) 0 0
\(531\) 14.3425 4.40410i 0.622412 0.191122i
\(532\) 0 0
\(533\) −2.42689 0.427927i −0.105120 0.0185356i
\(534\) 0 0
\(535\) 13.4807 37.0379i 0.582820 1.60129i
\(536\) 0 0
\(537\) 34.3503 + 30.3532i 1.48233 + 1.30984i
\(538\) 0 0
\(539\) 21.5553 0.928451
\(540\) 0 0
\(541\) −28.7933 −1.23792 −0.618960 0.785423i \(-0.712446\pi\)
−0.618960 + 0.785423i \(0.712446\pi\)
\(542\) 0 0
\(543\) 1.90909 9.41289i 0.0819269 0.403946i
\(544\) 0 0
\(545\) −14.7267 + 40.4613i −0.630823 + 1.73317i
\(546\) 0 0
\(547\) −32.0427 5.64999i −1.37005 0.241576i −0.560267 0.828312i \(-0.689302\pi\)
−0.809778 + 0.586736i \(0.800413\pi\)
\(548\) 0 0
\(549\) −9.28535 18.1687i −0.396289 0.775419i
\(550\) 0 0
\(551\) 27.3662 9.96047i 1.16584 0.424330i
\(552\) 0 0
\(553\) −1.49575 + 1.25509i −0.0636059 + 0.0533716i
\(554\) 0 0
\(555\) −48.9164 + 26.5981i −2.07639 + 1.12903i
\(556\) 0 0
\(557\) 2.09638 1.21034i 0.0888264 0.0512840i −0.454929 0.890528i \(-0.650335\pi\)
0.543755 + 0.839244i \(0.317002\pi\)
\(558\) 0 0
\(559\) 14.6039 + 8.43154i 0.617677 + 0.356616i
\(560\) 0 0
\(561\) −6.49437 + 16.5165i −0.274192 + 0.697326i
\(562\) 0 0
\(563\) 6.64509 + 37.6862i 0.280057 + 1.58828i 0.722426 + 0.691449i \(0.243027\pi\)
−0.442369 + 0.896833i \(0.645862\pi\)
\(564\) 0 0
\(565\) −39.9699 33.5388i −1.68155 1.41099i
\(566\) 0 0
\(567\) −0.802563 + 1.65575i −0.0337045 + 0.0695349i
\(568\) 0 0
\(569\) 3.36673 4.01232i 0.141141 0.168205i −0.690843 0.723005i \(-0.742761\pi\)
0.831984 + 0.554799i \(0.187205\pi\)
\(570\) 0 0
\(571\) −25.6895 + 4.52974i −1.07507 + 0.189564i −0.683034 0.730386i \(-0.739340\pi\)
−0.392036 + 0.919950i \(0.628229\pi\)
\(572\) 0 0
\(573\) −15.1883 5.97212i −0.634500 0.249489i
\(574\) 0 0
\(575\) −12.7871 + 22.1479i −0.533258 + 0.923629i
\(576\) 0 0
\(577\) 0.175577 + 0.304109i 0.00730939 + 0.0126602i 0.869657 0.493657i \(-0.164340\pi\)
−0.862348 + 0.506317i \(0.831007\pi\)
\(578\) 0 0
\(579\) −13.4147 24.6709i −0.557497 1.02529i
\(580\) 0 0
\(581\) −1.45309 1.73172i −0.0602842 0.0718439i
\(582\) 0 0
\(583\) −3.77818 10.3805i −0.156476 0.429915i
\(584\) 0 0
\(585\) 11.9362 + 7.73076i 0.493501 + 0.319627i
\(586\) 0 0
\(587\) 1.48582 8.42649i 0.0613262 0.347798i −0.938669 0.344819i \(-0.887940\pi\)
0.999996 0.00297975i \(-0.000948484\pi\)
\(588\) 0 0
\(589\) −1.14238 0.415791i −0.0470708 0.0171324i
\(590\) 0 0
\(591\) 24.4867 + 4.96631i 1.00725 + 0.204287i
\(592\) 0 0
\(593\) 0.724041i 0.0297328i −0.999889 0.0148664i \(-0.995268\pi\)
0.999889 0.0148664i \(-0.00473230\pi\)
\(594\) 0 0
\(595\) 1.98918i 0.0815484i
\(596\) 0 0
\(597\) −4.46718 + 5.05544i −0.182829 + 0.206905i
\(598\) 0 0
\(599\) −37.8615 13.7805i −1.54698 0.563055i −0.579274 0.815133i \(-0.696664\pi\)
−0.967707 + 0.252078i \(0.918886\pi\)
\(600\) 0 0
\(601\) −0.501839 + 2.84607i −0.0204704 + 0.116094i −0.993331 0.115299i \(-0.963217\pi\)
0.972860 + 0.231393i \(0.0743284\pi\)
\(602\) 0 0
\(603\) 11.8453 + 2.71948i 0.482379 + 0.110746i
\(604\) 0 0
\(605\) −1.41203 3.87951i −0.0574071 0.157725i
\(606\) 0 0
\(607\) −14.3491 17.1005i −0.582410 0.694089i 0.391718 0.920085i \(-0.371881\pi\)
−0.974128 + 0.225996i \(0.927436\pi\)
\(608\) 0 0
\(609\) −0.779013 + 1.27298i −0.0315672 + 0.0515836i
\(610\) 0 0
\(611\) 8.17290 + 14.1559i 0.330640 + 0.572686i
\(612\) 0 0
\(613\) 15.4658 26.7875i 0.624657 1.08194i −0.363950 0.931419i \(-0.618572\pi\)
0.988607 0.150520i \(-0.0480946\pi\)
\(614\) 0 0
\(615\) −6.09458 + 4.85393i −0.245757 + 0.195729i
\(616\) 0 0
\(617\) −28.0462 + 4.94530i −1.12910 + 0.199090i −0.706831 0.707382i \(-0.749876\pi\)
−0.422265 + 0.906472i \(0.638765\pi\)
\(618\) 0 0
\(619\) 6.86139 8.17709i 0.275783 0.328665i −0.610319 0.792156i \(-0.708959\pi\)
0.886102 + 0.463491i \(0.153403\pi\)
\(620\) 0 0
\(621\) 33.1308 + 15.0254i 1.32949 + 0.602947i
\(622\) 0 0
\(623\) −0.479205 0.402100i −0.0191989 0.0161098i
\(624\) 0 0
\(625\) −5.19570 29.4663i −0.207828 1.17865i
\(626\) 0 0
\(627\) −36.6651 + 5.50252i −1.46426 + 0.219750i
\(628\) 0 0
\(629\) 31.3046 + 18.0737i 1.24820 + 0.720646i
\(630\) 0 0
\(631\) 0.930324 0.537123i 0.0370356 0.0213825i −0.481368 0.876519i \(-0.659860\pi\)
0.518403 + 0.855136i \(0.326527\pi\)
\(632\) 0 0
\(633\) 0.908423 35.5199i 0.0361066 1.41179i
\(634\) 0 0
\(635\) −9.43784 + 7.91929i −0.374529 + 0.314267i
\(636\) 0 0
\(637\) −10.5369 + 3.83511i −0.417486 + 0.151953i
\(638\) 0 0
\(639\) −14.4375 6.10757i −0.571139 0.241612i
\(640\) 0 0
\(641\) −14.2400 2.51090i −0.562448 0.0991748i −0.114807 0.993388i \(-0.536625\pi\)
−0.447642 + 0.894213i \(0.647736\pi\)
\(642\) 0 0
\(643\) −8.89665 + 24.4433i −0.350850 + 0.963951i 0.631248 + 0.775581i \(0.282543\pi\)
−0.982098 + 0.188371i \(0.939679\pi\)
\(644\) 0 0
\(645\) 50.5494 16.9479i 1.99038 0.667324i
\(646\) 0 0
\(647\) −40.7872 −1.60351 −0.801754 0.597654i \(-0.796100\pi\)
−0.801754 + 0.597654i \(0.796100\pi\)
\(648\) 0 0
\(649\) −15.4927 −0.608141
\(650\) 0 0
\(651\) 0.0590685 0.0198041i 0.00231508 0.000776186i
\(652\) 0 0
\(653\) 0.910599 2.50185i 0.0356345 0.0979050i −0.920599 0.390508i \(-0.872299\pi\)
0.956234 + 0.292603i \(0.0945215\pi\)
\(654\) 0 0
\(655\) −39.6334 6.98843i −1.54860 0.273061i
\(656\) 0 0
\(657\) 3.45910 + 27.8905i 0.134952 + 1.08811i
\(658\) 0 0
\(659\) 4.60227 1.67509i 0.179279 0.0652522i −0.250821 0.968033i \(-0.580701\pi\)
0.430100 + 0.902781i \(0.358478\pi\)
\(660\) 0 0
\(661\) −1.04237 + 0.874649i −0.0405434 + 0.0340199i −0.662834 0.748766i \(-0.730647\pi\)
0.622291 + 0.782786i \(0.286202\pi\)
\(662\) 0 0
\(663\) 0.236038 9.22924i 0.00916695 0.358434i
\(664\) 0 0
\(665\) −3.59881 + 2.07777i −0.139556 + 0.0805726i
\(666\) 0 0
\(667\) 25.5536 + 14.7534i 0.989440 + 0.571253i
\(668\) 0 0
\(669\) −8.77275 + 1.31657i −0.339174 + 0.0509016i
\(670\) 0 0
\(671\) 3.65863 + 20.7491i 0.141240 + 0.801010i
\(672\) 0 0
\(673\) 5.96510 + 5.00532i 0.229938 + 0.192941i 0.750476 0.660898i \(-0.229824\pi\)
−0.520538 + 0.853838i \(0.674269\pi\)
\(674\) 0 0
\(675\) 18.2813 5.10592i 0.703646 0.196527i
\(676\) 0 0
\(677\) −30.5599 + 36.4198i −1.17451 + 1.39973i −0.275783 + 0.961220i \(0.588937\pi\)
−0.898727 + 0.438508i \(0.855507\pi\)
\(678\) 0 0
\(679\) 0.339966 0.0599452i 0.0130467 0.00230048i
\(680\) 0 0
\(681\) −3.81713 + 3.04009i −0.146273 + 0.116496i
\(682\) 0 0
\(683\) 1.48629 2.57432i 0.0568712 0.0985037i −0.836188 0.548443i \(-0.815221\pi\)
0.893059 + 0.449939i \(0.148554\pi\)
\(684\) 0 0
\(685\) −0.695733 1.20505i −0.0265826 0.0460424i
\(686\) 0 0
\(687\) 8.40827 13.7399i 0.320795 0.524209i
\(688\) 0 0
\(689\) 3.69378 + 4.40208i 0.140722 + 0.167706i
\(690\) 0 0
\(691\) −14.9301 41.0201i −0.567967 1.56048i −0.807672 0.589632i \(-0.799273\pi\)
0.239705 0.970846i \(-0.422949\pi\)
\(692\) 0 0
\(693\) 1.29410 1.39115i 0.0491588 0.0528456i
\(694\) 0 0
\(695\) 10.8832 61.7217i 0.412824 2.34124i
\(696\) 0 0
\(697\) 4.75306 + 1.72997i 0.180035 + 0.0655274i
\(698\) 0 0
\(699\) −27.0943 + 30.6622i −1.02480 + 1.15975i
\(700\) 0 0
\(701\) 47.5239i 1.79495i 0.441063 + 0.897476i \(0.354602\pi\)
−0.441063 + 0.897476i \(0.645398\pi\)
\(702\) 0 0
\(703\) 75.5147i 2.84809i
\(704\) 0 0
\(705\) 50.6482 + 10.2723i 1.90752 + 0.386877i
\(706\) 0 0
\(707\) 1.42715 + 0.519441i 0.0536735 + 0.0195356i
\(708\) 0 0
\(709\) −1.48937 + 8.44661i −0.0559343 + 0.317219i −0.999918 0.0127717i \(-0.995935\pi\)
0.943984 + 0.329991i \(0.107046\pi\)
\(710\) 0 0
\(711\) 1.46458 28.6143i 0.0549260 1.07312i
\(712\) 0 0
\(713\) −0.421278 1.15745i −0.0157770 0.0433469i
\(714\) 0 0
\(715\) −9.43916 11.2492i −0.353005 0.420695i
\(716\) 0 0
\(717\) 15.3043 + 28.1460i 0.571548 + 1.05113i
\(718\) 0 0
\(719\) −11.5537 20.0116i −0.430881 0.746308i 0.566068 0.824358i \(-0.308464\pi\)
−0.996949 + 0.0780505i \(0.975130\pi\)
\(720\) 0 0
\(721\) 1.65972 2.87471i 0.0618111 0.107060i
\(722\) 0 0
\(723\) −4.90299 1.92788i −0.182344 0.0716987i
\(724\) 0 0
\(725\) 15.1615 2.67338i 0.563084 0.0992870i
\(726\) 0 0
\(727\) −7.97816 + 9.50800i −0.295893 + 0.352632i −0.893424 0.449214i \(-0.851704\pi\)
0.597531 + 0.801846i \(0.296149\pi\)
\(728\) 0 0
\(729\) −9.76820 25.1711i −0.361785 0.932261i
\(730\) 0 0
\(731\) −26.5143 22.2481i −0.980665 0.822876i
\(732\) 0 0
\(733\) −1.42442 8.07829i −0.0526122 0.298379i 0.947136 0.320833i \(-0.103963\pi\)
−0.999748 + 0.0224548i \(0.992852\pi\)
\(734\) 0 0
\(735\) −12.9730 + 32.9929i −0.478516 + 1.21696i
\(736\) 0 0
\(737\) −10.8684 6.27489i −0.400344 0.231139i
\(738\) 0 0
\(739\) 25.6088 14.7852i 0.942034 0.543884i 0.0514367 0.998676i \(-0.483620\pi\)
0.890597 + 0.454793i \(0.150287\pi\)
\(740\) 0 0
\(741\) 16.9440 9.21325i 0.622454 0.338457i
\(742\) 0 0
\(743\) −22.1792 + 18.6105i −0.813675 + 0.682754i −0.951482 0.307705i \(-0.900439\pi\)
0.137807 + 0.990459i \(0.455995\pi\)
\(744\) 0 0
\(745\) 53.2188 19.3701i 1.94979 0.709664i
\(746\) 0 0
\(747\) 33.1285 + 1.69563i 1.21211 + 0.0620399i
\(748\) 0 0
\(749\) 2.69778 + 0.475692i 0.0985749 + 0.0173814i
\(750\) 0 0
\(751\) 13.6007 37.3675i 0.496295 1.36356i −0.398536 0.917153i \(-0.630482\pi\)
0.894831 0.446406i \(-0.147296\pi\)
\(752\) 0 0
\(753\) −0.910845 + 4.49098i −0.0331930 + 0.163660i
\(754\) 0 0
\(755\) 36.2272 1.31844
\(756\) 0 0
\(757\) 8.11133 0.294811 0.147406 0.989076i \(-0.452908\pi\)
0.147406 + 0.989076i \(0.452908\pi\)
\(758\) 0 0
\(759\) −28.1497 24.8741i −1.02177 0.902873i
\(760\) 0 0
\(761\) −11.2460 + 30.8982i −0.407668 + 1.12006i 0.550744 + 0.834674i \(0.314344\pi\)
−0.958413 + 0.285386i \(0.907878\pi\)
\(762\) 0 0
\(763\) −2.94714 0.519661i −0.106694 0.0188130i
\(764\) 0 0
\(765\) −21.3718 19.8808i −0.772699 0.718791i
\(766\) 0 0
\(767\) 7.57330 2.75646i 0.273456 0.0995299i
\(768\) 0 0
\(769\) 5.60501 4.70316i 0.202122 0.169600i −0.536109 0.844149i \(-0.680106\pi\)
0.738230 + 0.674549i \(0.235662\pi\)
\(770\) 0 0
\(771\) 22.0920 + 13.5194i 0.795623 + 0.486890i
\(772\) 0 0
\(773\) −30.5895 + 17.6608i −1.10023 + 0.635216i −0.936281 0.351253i \(-0.885756\pi\)
−0.163946 + 0.986469i \(0.552422\pi\)
\(774\) 0 0
\(775\) −0.556567 0.321334i −0.0199925 0.0115427i
\(776\) 0 0
\(777\) −2.41090 3.02712i −0.0864905 0.108597i
\(778\) 0 0
\(779\) 1.83490 + 10.4062i 0.0657421 + 0.372842i
\(780\) 0 0
\(781\) 12.4003 + 10.4051i 0.443716 + 0.372322i
\(782\) 0 0
\(783\) −5.89107 21.0924i −0.210530 0.753782i
\(784\) 0 0
\(785\) −30.2517 + 36.0526i −1.07973 + 1.28677i
\(786\) 0 0
\(787\) −10.2798 + 1.81261i −0.366437 + 0.0646127i −0.353835 0.935308i \(-0.615123\pi\)
−0.0126019 + 0.999921i \(0.504011\pi\)
\(788\) 0 0
\(789\) −6.09384 40.6052i −0.216946 1.44558i
\(790\) 0 0
\(791\) 1.81320 3.14055i 0.0644699 0.111665i
\(792\) 0 0
\(793\) −5.48013 9.49186i −0.194605 0.337066i
\(794\) 0 0
\(795\) 18.1624 + 0.464504i 0.644155 + 0.0164743i