Properties

Label 70.2.g.a.27.1
Level $70$
Weight $2$
Character 70.27
Analytic conductor $0.559$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 70.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.558952814149\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{16})\)
Defining polynomial: \(x^{8} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 27.1
Root \(-0.382683 - 0.923880i\) of defining polynomial
Character \(\chi\) \(=\) 70.27
Dual form 70.2.g.a.13.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.30656 - 1.30656i) q^{3} +1.00000i q^{4} +(-0.158513 - 2.23044i) q^{5} +1.84776i q^{6} +(-2.47247 - 0.941740i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.414214i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.30656 - 1.30656i) q^{3} +1.00000i q^{4} +(-0.158513 - 2.23044i) q^{5} +1.84776i q^{6} +(-2.47247 - 0.941740i) q^{7} +(0.707107 - 0.707107i) q^{8} +0.414214i q^{9} +(-1.46508 + 1.68925i) q^{10} +2.82843 q^{11} +(1.30656 - 1.30656i) q^{12} +(4.23671 + 4.23671i) q^{13} +(1.08239 + 2.41421i) q^{14} +(-2.70711 + 3.12132i) q^{15} -1.00000 q^{16} +(3.69552 - 3.69552i) q^{17} +(0.292893 - 0.292893i) q^{18} -1.39942 q^{19} +(2.23044 - 0.158513i) q^{20} +(2.00000 + 4.46088i) q^{21} +(-2.00000 - 2.00000i) q^{22} +(0.414214 - 0.414214i) q^{23} -1.84776 q^{24} +(-4.94975 + 0.707107i) q^{25} -5.99162i q^{26} +(-3.37849 + 3.37849i) q^{27} +(0.941740 - 2.47247i) q^{28} -0.828427i q^{29} +(4.12132 - 0.292893i) q^{30} -1.53073i q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.69552 - 3.69552i) q^{33} -5.22625 q^{34} +(-1.70858 + 5.66399i) q^{35} -0.414214 q^{36} +(2.58579 + 2.58579i) q^{37} +(0.989538 + 0.989538i) q^{38} -11.0711i q^{39} +(-1.68925 - 1.46508i) q^{40} -3.69552i q^{41} +(1.74011 - 4.56854i) q^{42} +(4.00000 - 4.00000i) q^{43} +2.82843i q^{44} +(0.923880 - 0.0656581i) q^{45} -0.585786 q^{46} +(-1.08239 + 1.08239i) q^{47} +(1.30656 + 1.30656i) q^{48} +(5.22625 + 4.65685i) q^{49} +(4.00000 + 3.00000i) q^{50} -9.65685 q^{51} +(-4.23671 + 4.23671i) q^{52} +(-8.24264 + 8.24264i) q^{53} +4.77791 q^{54} +(-0.448342 - 6.30864i) q^{55} +(-2.41421 + 1.08239i) q^{56} +(1.82843 + 1.82843i) q^{57} +(-0.585786 + 0.585786i) q^{58} +9.23880 q^{59} +(-3.12132 - 2.70711i) q^{60} +6.43996i q^{61} +(-1.08239 + 1.08239i) q^{62} +(0.390081 - 1.02413i) q^{63} -1.00000i q^{64} +(8.77817 - 10.1213i) q^{65} +5.22625i q^{66} +(10.4853 + 10.4853i) q^{67} +(3.69552 + 3.69552i) q^{68} -1.08239 q^{69} +(5.21319 - 2.79690i) q^{70} -0.585786 q^{71} +(0.292893 + 0.292893i) q^{72} +(-4.14386 - 4.14386i) q^{73} -3.65685i q^{74} +(7.39104 + 5.54328i) q^{75} -1.39942i q^{76} +(-6.99321 - 2.66364i) q^{77} +(-7.82843 + 7.82843i) q^{78} +5.07107i q^{79} +(0.158513 + 2.23044i) q^{80} +10.0711 q^{81} +(-2.61313 + 2.61313i) q^{82} +(-5.31911 - 5.31911i) q^{83} +(-4.46088 + 2.00000i) q^{84} +(-8.82843 - 7.65685i) q^{85} -5.65685 q^{86} +(-1.08239 + 1.08239i) q^{87} +(2.00000 - 2.00000i) q^{88} -11.3492 q^{89} +(-0.699709 - 0.606854i) q^{90} +(-6.48528 - 14.4650i) q^{91} +(0.414214 + 0.414214i) q^{92} +(-2.00000 + 2.00000i) q^{93} +1.53073 q^{94} +(0.221825 + 3.12132i) q^{95} -1.84776i q^{96} +(4.59220 - 4.59220i) q^{97} +(-0.402625 - 6.98841i) q^{98} +1.17157i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{7} + O(q^{10}) \) \( 8 q - 8 q^{7} - 16 q^{15} - 8 q^{16} + 8 q^{18} + 16 q^{21} - 16 q^{22} - 8 q^{23} + 8 q^{28} + 16 q^{30} - 8 q^{35} + 8 q^{36} + 32 q^{37} + 32 q^{43} - 16 q^{46} + 32 q^{50} - 32 q^{51} - 32 q^{53} - 8 q^{56} - 8 q^{57} - 16 q^{58} - 8 q^{60} + 8 q^{65} + 16 q^{67} - 24 q^{70} - 16 q^{71} + 8 q^{72} - 16 q^{77} - 40 q^{78} + 24 q^{81} - 48 q^{85} + 16 q^{88} + 16 q^{91} - 8 q^{92} - 16 q^{93} + 64 q^{95} + 32 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(57\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) −1.30656 1.30656i −0.754344 0.754344i 0.220942 0.975287i \(-0.429087\pi\)
−0.975287 + 0.220942i \(0.929087\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −0.158513 2.23044i −0.0708890 0.997484i
\(6\) 1.84776i 0.754344i
\(7\) −2.47247 0.941740i −0.934507 0.355944i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0.414214i 0.138071i
\(10\) −1.46508 + 1.68925i −0.463298 + 0.534187i
\(11\) 2.82843 0.852803 0.426401 0.904534i \(-0.359781\pi\)
0.426401 + 0.904534i \(0.359781\pi\)
\(12\) 1.30656 1.30656i 0.377172 0.377172i
\(13\) 4.23671 + 4.23671i 1.17505 + 1.17505i 0.980989 + 0.194064i \(0.0621670\pi\)
0.194064 + 0.980989i \(0.437833\pi\)
\(14\) 1.08239 + 2.41421i 0.289281 + 0.645226i
\(15\) −2.70711 + 3.12132i −0.698972 + 0.805921i
\(16\) −1.00000 −0.250000
\(17\) 3.69552 3.69552i 0.896295 0.896295i −0.0988114 0.995106i \(-0.531504\pi\)
0.995106 + 0.0988114i \(0.0315040\pi\)
\(18\) 0.292893 0.292893i 0.0690356 0.0690356i
\(19\) −1.39942 −0.321048 −0.160524 0.987032i \(-0.551318\pi\)
−0.160524 + 0.987032i \(0.551318\pi\)
\(20\) 2.23044 0.158513i 0.498742 0.0354445i
\(21\) 2.00000 + 4.46088i 0.436436 + 0.973445i
\(22\) −2.00000 2.00000i −0.426401 0.426401i
\(23\) 0.414214 0.414214i 0.0863695 0.0863695i −0.662602 0.748972i \(-0.730548\pi\)
0.748972 + 0.662602i \(0.230548\pi\)
\(24\) −1.84776 −0.377172
\(25\) −4.94975 + 0.707107i −0.989949 + 0.141421i
\(26\) 5.99162i 1.17505i
\(27\) −3.37849 + 3.37849i −0.650191 + 0.650191i
\(28\) 0.941740 2.47247i 0.177972 0.467254i
\(29\) 0.828427i 0.153835i −0.997037 0.0769175i \(-0.975492\pi\)
0.997037 0.0769175i \(-0.0245078\pi\)
\(30\) 4.12132 0.292893i 0.752447 0.0534747i
\(31\) 1.53073i 0.274928i −0.990507 0.137464i \(-0.956105\pi\)
0.990507 0.137464i \(-0.0438951\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −3.69552 3.69552i −0.643307 0.643307i
\(34\) −5.22625 −0.896295
\(35\) −1.70858 + 5.66399i −0.288802 + 0.957389i
\(36\) −0.414214 −0.0690356
\(37\) 2.58579 + 2.58579i 0.425101 + 0.425101i 0.886956 0.461855i \(-0.152816\pi\)
−0.461855 + 0.886956i \(0.652816\pi\)
\(38\) 0.989538 + 0.989538i 0.160524 + 0.160524i
\(39\) 11.0711i 1.77279i
\(40\) −1.68925 1.46508i −0.267093 0.231649i
\(41\) 3.69552i 0.577143i −0.957458 0.288571i \(-0.906820\pi\)
0.957458 0.288571i \(-0.0931803\pi\)
\(42\) 1.74011 4.56854i 0.268505 0.704940i
\(43\) 4.00000 4.00000i 0.609994 0.609994i −0.332950 0.942944i \(-0.608044\pi\)
0.942944 + 0.332950i \(0.108044\pi\)
\(44\) 2.82843i 0.426401i
\(45\) 0.923880 0.0656581i 0.137724 0.00978773i
\(46\) −0.585786 −0.0863695
\(47\) −1.08239 + 1.08239i −0.157883 + 0.157883i −0.781628 0.623745i \(-0.785610\pi\)
0.623745 + 0.781628i \(0.285610\pi\)
\(48\) 1.30656 + 1.30656i 0.188586 + 0.188586i
\(49\) 5.22625 + 4.65685i 0.746607 + 0.665265i
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) −9.65685 −1.35223
\(52\) −4.23671 + 4.23671i −0.587527 + 0.587527i
\(53\) −8.24264 + 8.24264i −1.13221 + 1.13221i −0.142405 + 0.989808i \(0.545484\pi\)
−0.989808 + 0.142405i \(0.954516\pi\)
\(54\) 4.77791 0.650191
\(55\) −0.448342 6.30864i −0.0604544 0.850657i
\(56\) −2.41421 + 1.08239i −0.322613 + 0.144641i
\(57\) 1.82843 + 1.82843i 0.242181 + 0.242181i
\(58\) −0.585786 + 0.585786i −0.0769175 + 0.0769175i
\(59\) 9.23880 1.20279 0.601394 0.798952i \(-0.294612\pi\)
0.601394 + 0.798952i \(0.294612\pi\)
\(60\) −3.12132 2.70711i −0.402961 0.349486i
\(61\) 6.43996i 0.824552i 0.911059 + 0.412276i \(0.135266\pi\)
−0.911059 + 0.412276i \(0.864734\pi\)
\(62\) −1.08239 + 1.08239i −0.137464 + 0.137464i
\(63\) 0.390081 1.02413i 0.0491456 0.129029i
\(64\) 1.00000i 0.125000i
\(65\) 8.77817 10.1213i 1.08880 1.25540i
\(66\) 5.22625i 0.643307i
\(67\) 10.4853 + 10.4853i 1.28098 + 1.28098i 0.940110 + 0.340871i \(0.110722\pi\)
0.340871 + 0.940110i \(0.389278\pi\)
\(68\) 3.69552 + 3.69552i 0.448147 + 0.448147i
\(69\) −1.08239 −0.130305
\(70\) 5.21319 2.79690i 0.623096 0.334293i
\(71\) −0.585786 −0.0695201 −0.0347600 0.999396i \(-0.511067\pi\)
−0.0347600 + 0.999396i \(0.511067\pi\)
\(72\) 0.292893 + 0.292893i 0.0345178 + 0.0345178i
\(73\) −4.14386 4.14386i −0.485002 0.485002i 0.421723 0.906725i \(-0.361426\pi\)
−0.906725 + 0.421723i \(0.861426\pi\)
\(74\) 3.65685i 0.425101i
\(75\) 7.39104 + 5.54328i 0.853443 + 0.640083i
\(76\) 1.39942i 0.160524i
\(77\) −6.99321 2.66364i −0.796950 0.303550i
\(78\) −7.82843 + 7.82843i −0.886395 + 0.886395i
\(79\) 5.07107i 0.570540i 0.958447 + 0.285270i \(0.0920832\pi\)
−0.958447 + 0.285270i \(0.907917\pi\)
\(80\) 0.158513 + 2.23044i 0.0177223 + 0.249371i
\(81\) 10.0711 1.11901
\(82\) −2.61313 + 2.61313i −0.288571 + 0.288571i
\(83\) −5.31911 5.31911i −0.583848 0.583848i 0.352111 0.935958i \(-0.385464\pi\)
−0.935958 + 0.352111i \(0.885464\pi\)
\(84\) −4.46088 + 2.00000i −0.486722 + 0.218218i
\(85\) −8.82843 7.65685i −0.957577 0.830502i
\(86\) −5.65685 −0.609994
\(87\) −1.08239 + 1.08239i −0.116045 + 0.116045i
\(88\) 2.00000 2.00000i 0.213201 0.213201i
\(89\) −11.3492 −1.20301 −0.601506 0.798869i \(-0.705432\pi\)
−0.601506 + 0.798869i \(0.705432\pi\)
\(90\) −0.699709 0.606854i −0.0737558 0.0639680i
\(91\) −6.48528 14.4650i −0.679842 1.51635i
\(92\) 0.414214 + 0.414214i 0.0431847 + 0.0431847i
\(93\) −2.00000 + 2.00000i −0.207390 + 0.207390i
\(94\) 1.53073 0.157883
\(95\) 0.221825 + 3.12132i 0.0227588 + 0.320241i
\(96\) 1.84776i 0.188586i
\(97\) 4.59220 4.59220i 0.466267 0.466267i −0.434436 0.900703i \(-0.643052\pi\)
0.900703 + 0.434436i \(0.143052\pi\)
\(98\) −0.402625 6.98841i −0.0406713 0.705936i
\(99\) 1.17157i 0.117748i
\(100\) −0.707107 4.94975i −0.0707107 0.494975i
\(101\) 2.74444i 0.273082i 0.990634 + 0.136541i \(0.0435986\pi\)
−0.990634 + 0.136541i \(0.956401\pi\)
\(102\) 6.82843 + 6.82843i 0.676115 + 0.676115i
\(103\) 10.0042 + 10.0042i 0.985739 + 0.985739i 0.999900 0.0141603i \(-0.00450753\pi\)
−0.0141603 + 0.999900i \(0.504508\pi\)
\(104\) 5.99162 0.587527
\(105\) 9.63272 5.16799i 0.940057 0.504344i
\(106\) 11.6569 1.13221
\(107\) −3.65685 3.65685i −0.353521 0.353521i 0.507897 0.861418i \(-0.330423\pi\)
−0.861418 + 0.507897i \(0.830423\pi\)
\(108\) −3.37849 3.37849i −0.325096 0.325096i
\(109\) 12.1421i 1.16301i −0.813544 0.581503i \(-0.802465\pi\)
0.813544 0.581503i \(-0.197535\pi\)
\(110\) −4.14386 + 4.77791i −0.395102 + 0.455556i
\(111\) 6.75699i 0.641345i
\(112\) 2.47247 + 0.941740i 0.233627 + 0.0889861i
\(113\) 1.17157 1.17157i 0.110212 0.110212i −0.649850 0.760062i \(-0.725168\pi\)
0.760062 + 0.649850i \(0.225168\pi\)
\(114\) 2.58579i 0.242181i
\(115\) −0.989538 0.858221i −0.0922749 0.0800296i
\(116\) 0.828427 0.0769175
\(117\) −1.75490 + 1.75490i −0.162241 + 0.162241i
\(118\) −6.53281 6.53281i −0.601394 0.601394i
\(119\) −12.6173 + 5.65685i −1.15662 + 0.518563i
\(120\) 0.292893 + 4.12132i 0.0267374 + 0.376223i
\(121\) −3.00000 −0.272727
\(122\) 4.55374 4.55374i 0.412276 0.412276i
\(123\) −4.82843 + 4.82843i −0.435365 + 0.435365i
\(124\) 1.53073 0.137464
\(125\) 2.36176 + 10.9280i 0.211242 + 0.977434i
\(126\) −1.00000 + 0.448342i −0.0890871 + 0.0399414i
\(127\) 3.58579 + 3.58579i 0.318187 + 0.318187i 0.848071 0.529883i \(-0.177764\pi\)
−0.529883 + 0.848071i \(0.677764\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −10.4525 −0.920292
\(130\) −13.3640 + 0.949747i −1.17210 + 0.0832984i
\(131\) 14.6508i 1.28004i 0.768357 + 0.640021i \(0.221074\pi\)
−0.768357 + 0.640021i \(0.778926\pi\)
\(132\) 3.69552 3.69552i 0.321654 0.321654i
\(133\) 3.46002 + 1.31789i 0.300022 + 0.114275i
\(134\) 14.8284i 1.28098i
\(135\) 8.07107 + 7.00000i 0.694647 + 0.602464i
\(136\) 5.22625i 0.448147i
\(137\) −8.17157 8.17157i −0.698145 0.698145i 0.265866 0.964010i \(-0.414342\pi\)
−0.964010 + 0.265866i \(0.914342\pi\)
\(138\) 0.765367 + 0.765367i 0.0651524 + 0.0651524i
\(139\) 8.60474 0.729845 0.364922 0.931038i \(-0.381095\pi\)
0.364922 + 0.931038i \(0.381095\pi\)
\(140\) −5.66399 1.70858i −0.478694 0.144401i
\(141\) 2.82843 0.238197
\(142\) 0.414214 + 0.414214i 0.0347600 + 0.0347600i
\(143\) 11.9832 + 11.9832i 1.00209 + 1.00209i
\(144\) 0.414214i 0.0345178i
\(145\) −1.84776 + 0.131316i −0.153448 + 0.0109052i
\(146\) 5.86030i 0.485002i
\(147\) −0.743954 12.9129i −0.0613603 1.06504i
\(148\) −2.58579 + 2.58579i −0.212550 + 0.212550i
\(149\) 17.3137i 1.41839i 0.705010 + 0.709197i \(0.250942\pi\)
−0.705010 + 0.709197i \(0.749058\pi\)
\(150\) −1.30656 9.14594i −0.106680 0.746763i
\(151\) −8.82843 −0.718447 −0.359224 0.933252i \(-0.616958\pi\)
−0.359224 + 0.933252i \(0.616958\pi\)
\(152\) −0.989538 + 0.989538i −0.0802621 + 0.0802621i
\(153\) 1.53073 + 1.53073i 0.123752 + 0.123752i
\(154\) 3.06147 + 6.82843i 0.246700 + 0.550250i
\(155\) −3.41421 + 0.242641i −0.274236 + 0.0194894i
\(156\) 11.0711 0.886395
\(157\) −10.2283 + 10.2283i −0.816310 + 0.816310i −0.985571 0.169261i \(-0.945862\pi\)
0.169261 + 0.985571i \(0.445862\pi\)
\(158\) 3.58579 3.58579i 0.285270 0.285270i
\(159\) 21.5391 1.70816
\(160\) 1.46508 1.68925i 0.115824 0.133547i
\(161\) −1.41421 + 0.634051i −0.111456 + 0.0499702i
\(162\) −7.12132 7.12132i −0.559504 0.559504i
\(163\) 13.6569 13.6569i 1.06969 1.06969i 0.0723048 0.997383i \(-0.476965\pi\)
0.997383 0.0723048i \(-0.0230354\pi\)
\(164\) 3.69552 0.288571
\(165\) −7.65685 + 8.82843i −0.596085 + 0.687292i
\(166\) 7.52235i 0.583848i
\(167\) 1.71644 1.71644i 0.132822 0.132822i −0.637570 0.770392i \(-0.720060\pi\)
0.770392 + 0.637570i \(0.220060\pi\)
\(168\) 4.56854 + 1.74011i 0.352470 + 0.134252i
\(169\) 22.8995i 1.76150i
\(170\) 0.828427 + 11.6569i 0.0635375 + 0.894040i
\(171\) 0.579658i 0.0443275i
\(172\) 4.00000 + 4.00000i 0.304997 + 0.304997i
\(173\) −13.2898 13.2898i −1.01040 1.01040i −0.999945 0.0104595i \(-0.996671\pi\)
−0.0104595 0.999945i \(-0.503329\pi\)
\(174\) 1.53073 0.116045
\(175\) 12.9040 + 2.91307i 0.975453 + 0.220208i
\(176\) −2.82843 −0.213201
\(177\) −12.0711 12.0711i −0.907317 0.907317i
\(178\) 8.02509 + 8.02509i 0.601506 + 0.601506i
\(179\) 13.6569i 1.02076i −0.859949 0.510381i \(-0.829505\pi\)
0.859949 0.510381i \(-0.170495\pi\)
\(180\) 0.0656581 + 0.923880i 0.00489387 + 0.0688619i
\(181\) 8.79045i 0.653389i 0.945130 + 0.326695i \(0.105935\pi\)
−0.945130 + 0.326695i \(0.894065\pi\)
\(182\) −5.64255 + 14.8141i −0.418253 + 1.09810i
\(183\) 8.41421 8.41421i 0.621997 0.621997i
\(184\) 0.585786i 0.0431847i
\(185\) 5.35757 6.17733i 0.393896 0.454166i
\(186\) 2.82843 0.207390
\(187\) 10.4525 10.4525i 0.764363 0.764363i
\(188\) −1.08239 1.08239i −0.0789416 0.0789416i
\(189\) 11.5349 5.17157i 0.839040 0.376177i
\(190\) 2.05025 2.36396i 0.148741 0.171500i
\(191\) 1.75736 0.127158 0.0635790 0.997977i \(-0.479749\pi\)
0.0635790 + 0.997977i \(0.479749\pi\)
\(192\) −1.30656 + 1.30656i −0.0942931 + 0.0942931i
\(193\) 8.24264 8.24264i 0.593318 0.593318i −0.345208 0.938526i \(-0.612192\pi\)
0.938526 + 0.345208i \(0.112192\pi\)
\(194\) −6.49435 −0.466267
\(195\) −24.6934 + 1.75490i −1.76833 + 0.125671i
\(196\) −4.65685 + 5.22625i −0.332632 + 0.373304i
\(197\) 0.585786 + 0.585786i 0.0417356 + 0.0417356i 0.727667 0.685931i \(-0.240605\pi\)
−0.685931 + 0.727667i \(0.740605\pi\)
\(198\) 0.828427 0.828427i 0.0588738 0.0588738i
\(199\) −28.0334 −1.98724 −0.993618 0.112798i \(-0.964019\pi\)
−0.993618 + 0.112798i \(0.964019\pi\)
\(200\) −3.00000 + 4.00000i −0.212132 + 0.282843i
\(201\) 27.3994i 1.93260i
\(202\) 1.94061 1.94061i 0.136541 0.136541i
\(203\) −0.780163 + 2.04826i −0.0547567 + 0.143760i
\(204\) 9.65685i 0.676115i
\(205\) −8.24264 + 0.585786i −0.575691 + 0.0409131i
\(206\) 14.1480i 0.985739i
\(207\) 0.171573 + 0.171573i 0.0119251 + 0.0119251i
\(208\) −4.23671 4.23671i −0.293763 0.293763i
\(209\) −3.95815 −0.273791
\(210\) −10.4657 3.15704i −0.722201 0.217857i
\(211\) −10.3431 −0.712052 −0.356026 0.934476i \(-0.615868\pi\)
−0.356026 + 0.934476i \(0.615868\pi\)
\(212\) −8.24264 8.24264i −0.566107 0.566107i
\(213\) 0.765367 + 0.765367i 0.0524421 + 0.0524421i
\(214\) 5.17157i 0.353521i
\(215\) −9.55582 8.28772i −0.651702 0.565218i
\(216\) 4.77791i 0.325096i
\(217\) −1.44155 + 3.78470i −0.0978590 + 0.256922i
\(218\) −8.58579 + 8.58579i −0.581503 + 0.581503i
\(219\) 10.8284i 0.731717i
\(220\) 6.30864 0.448342i 0.425329 0.0302272i
\(221\) 31.3137 2.10639
\(222\) −4.77791 + 4.77791i −0.320672 + 0.320672i
\(223\) −6.75699 6.75699i −0.452481 0.452481i 0.443696 0.896177i \(-0.353667\pi\)
−0.896177 + 0.443696i \(0.853667\pi\)
\(224\) −1.08239 2.41421i −0.0723204 0.161306i
\(225\) −0.292893 2.05025i −0.0195262 0.136684i
\(226\) −1.65685 −0.110212
\(227\) 8.38057 8.38057i 0.556238 0.556238i −0.371996 0.928234i \(-0.621327\pi\)
0.928234 + 0.371996i \(0.121327\pi\)
\(228\) −1.82843 + 1.82843i −0.121091 + 0.121091i
\(229\) −7.70806 −0.509363 −0.254682 0.967025i \(-0.581971\pi\)
−0.254682 + 0.967025i \(0.581971\pi\)
\(230\) 0.0928546 + 1.30656i 0.00612265 + 0.0861522i
\(231\) 5.65685 + 12.6173i 0.372194 + 0.830157i
\(232\) −0.585786 0.585786i −0.0384588 0.0384588i
\(233\) 3.00000 3.00000i 0.196537 0.196537i −0.601977 0.798513i \(-0.705620\pi\)
0.798513 + 0.601977i \(0.205620\pi\)
\(234\) 2.48181 0.162241
\(235\) 2.58579 + 2.24264i 0.168678 + 0.146294i
\(236\) 9.23880i 0.601394i
\(237\) 6.62567 6.62567i 0.430383 0.430383i
\(238\) 12.9218 + 4.92177i 0.837594 + 0.319031i
\(239\) 6.48528i 0.419498i −0.977755 0.209749i \(-0.932735\pi\)
0.977755 0.209749i \(-0.0672647\pi\)
\(240\) 2.70711 3.12132i 0.174743 0.201480i
\(241\) 6.75699i 0.435256i 0.976032 + 0.217628i \(0.0698319\pi\)
−0.976032 + 0.217628i \(0.930168\pi\)
\(242\) 2.12132 + 2.12132i 0.136364 + 0.136364i
\(243\) −3.02301 3.02301i −0.193926 0.193926i
\(244\) −6.43996 −0.412276
\(245\) 9.55842 12.3950i 0.610665 0.791889i
\(246\) 6.82843 0.435365
\(247\) −5.92893 5.92893i −0.377249 0.377249i
\(248\) −1.08239 1.08239i −0.0687320 0.0687320i
\(249\) 13.8995i 0.880845i
\(250\) 6.05728 9.39731i 0.383096 0.594338i
\(251\) 14.0936i 0.889582i 0.895634 + 0.444791i \(0.146722\pi\)
−0.895634 + 0.444791i \(0.853278\pi\)
\(252\) 1.02413 + 0.390081i 0.0645143 + 0.0245728i
\(253\) 1.17157 1.17157i 0.0736562 0.0736562i
\(254\) 5.07107i 0.318187i
\(255\) 1.53073 + 21.5391i 0.0958583 + 1.34883i
\(256\) 1.00000 0.0625000
\(257\) 7.83938 7.83938i 0.489007 0.489007i −0.418986 0.907993i \(-0.637614\pi\)
0.907993 + 0.418986i \(0.137614\pi\)
\(258\) 7.39104 + 7.39104i 0.460146 + 0.460146i
\(259\) −3.95815 8.82843i −0.245948 0.548572i
\(260\) 10.1213 + 8.77817i 0.627698 + 0.544399i
\(261\) 0.343146 0.0212402
\(262\) 10.3596 10.3596i 0.640021 0.640021i
\(263\) −19.4142 + 19.4142i −1.19713 + 1.19713i −0.222110 + 0.975022i \(0.571294\pi\)
−0.975022 + 0.222110i \(0.928706\pi\)
\(264\) −5.22625 −0.321654
\(265\) 19.6913 + 17.0782i 1.20963 + 1.04910i
\(266\) −1.51472 3.37849i −0.0928734 0.207149i
\(267\) 14.8284 + 14.8284i 0.907485 + 0.907485i
\(268\) −10.4853 + 10.4853i −0.640490 + 0.640490i
\(269\) 26.8966 1.63992 0.819958 0.572424i \(-0.193997\pi\)
0.819958 + 0.572424i \(0.193997\pi\)
\(270\) −0.757359 10.6569i −0.0460914 0.648555i
\(271\) 18.7402i 1.13839i −0.822203 0.569194i \(-0.807255\pi\)
0.822203 0.569194i \(-0.192745\pi\)
\(272\) −3.69552 + 3.69552i −0.224074 + 0.224074i
\(273\) −10.4261 + 27.3729i −0.631014 + 1.65668i
\(274\) 11.5563i 0.698145i
\(275\) −14.0000 + 2.00000i −0.844232 + 0.120605i
\(276\) 1.08239i 0.0651524i
\(277\) −1.75736 1.75736i −0.105589 0.105589i 0.652338 0.757928i \(-0.273788\pi\)
−0.757928 + 0.652338i \(0.773788\pi\)
\(278\) −6.08447 6.08447i −0.364922 0.364922i
\(279\) 0.634051 0.0379596
\(280\) 2.79690 + 5.21319i 0.167147 + 0.311548i
\(281\) −5.65685 −0.337460 −0.168730 0.985662i \(-0.553967\pi\)
−0.168730 + 0.985662i \(0.553967\pi\)
\(282\) −2.00000 2.00000i −0.119098 0.119098i
\(283\) −3.15432 3.15432i −0.187505 0.187505i 0.607112 0.794617i \(-0.292328\pi\)
−0.794617 + 0.607112i \(0.792328\pi\)
\(284\) 0.585786i 0.0347600i
\(285\) 3.78837 4.36803i 0.224404 0.258740i
\(286\) 16.9469i 1.00209i
\(287\) −3.48022 + 9.13707i −0.205431 + 0.539344i
\(288\) −0.292893 + 0.292893i −0.0172589 + 0.0172589i
\(289\) 10.3137i 0.606689i
\(290\) 1.39942 + 1.21371i 0.0821766 + 0.0712714i
\(291\) −12.0000 −0.703452
\(292\) 4.14386 4.14386i 0.242501 0.242501i
\(293\) 2.38896 + 2.38896i 0.139564 + 0.139564i 0.773437 0.633873i \(-0.218536\pi\)
−0.633873 + 0.773437i \(0.718536\pi\)
\(294\) −8.60474 + 9.65685i −0.501839 + 0.563199i
\(295\) −1.46447 20.6066i −0.0852645 1.19976i
\(296\) 3.65685 0.212550
\(297\) −9.55582 + 9.55582i −0.554485 + 0.554485i
\(298\) 12.2426 12.2426i 0.709197 0.709197i
\(299\) 3.50981 0.202977
\(300\) −5.54328 + 7.39104i −0.320041 + 0.426722i
\(301\) −13.6569 + 6.12293i −0.787168 + 0.352920i
\(302\) 6.24264 + 6.24264i 0.359224 + 0.359224i
\(303\) 3.58579 3.58579i 0.205998 0.205998i
\(304\) 1.39942 0.0802621
\(305\) 14.3640 1.02082i 0.822478 0.0584517i
\(306\) 2.16478i 0.123752i
\(307\) −23.1626 + 23.1626i −1.32196 + 1.32196i −0.409776 + 0.912186i \(0.634393\pi\)
−0.912186 + 0.409776i \(0.865607\pi\)
\(308\) 2.66364 6.99321i 0.151775 0.398475i
\(309\) 26.1421i 1.48717i
\(310\) 2.58579 + 2.24264i 0.146863 + 0.127373i
\(311\) 3.43289i 0.194661i −0.995252 0.0973305i \(-0.968970\pi\)
0.995252 0.0973305i \(-0.0310304\pi\)
\(312\) −7.82843 7.82843i −0.443197 0.443197i
\(313\) 6.75699 + 6.75699i 0.381927 + 0.381927i 0.871796 0.489869i \(-0.162955\pi\)
−0.489869 + 0.871796i \(0.662955\pi\)
\(314\) 14.4650 0.816310
\(315\) −2.34610 0.707716i −0.132188 0.0398753i
\(316\) −5.07107 −0.285270
\(317\) 21.8995 + 21.8995i 1.23000 + 1.23000i 0.963963 + 0.266035i \(0.0857136\pi\)
0.266035 + 0.963963i \(0.414286\pi\)
\(318\) −15.2304 15.2304i −0.854079 0.854079i
\(319\) 2.34315i 0.131191i
\(320\) −2.23044 + 0.158513i −0.124686 + 0.00886113i
\(321\) 9.55582i 0.533354i
\(322\) 1.44834 + 0.551658i 0.0807129 + 0.0307427i
\(323\) −5.17157 + 5.17157i −0.287754 + 0.287754i
\(324\) 10.0711i 0.559504i
\(325\) −23.9665 17.9749i −1.32942 0.997066i
\(326\) −19.3137 −1.06969
\(327\) −15.8645 + 15.8645i −0.877307 + 0.877307i
\(328\) −2.61313 2.61313i −0.144286 0.144286i
\(329\) 3.69552 1.65685i 0.203741 0.0913453i
\(330\) 11.6569 0.828427i 0.641689 0.0456034i
\(331\) 23.3137 1.28144 0.640719 0.767776i \(-0.278637\pi\)
0.640719 + 0.767776i \(0.278637\pi\)
\(332\) 5.31911 5.31911i 0.291924 0.291924i
\(333\) −1.07107 + 1.07107i −0.0586942 + 0.0586942i
\(334\) −2.42742 −0.132822
\(335\) 21.7248 25.0489i 1.18695 1.36857i
\(336\) −2.00000 4.46088i −0.109109 0.243361i
\(337\) 3.75736 + 3.75736i 0.204676 + 0.204676i 0.802000 0.597324i \(-0.203769\pi\)
−0.597324 + 0.802000i \(0.703769\pi\)
\(338\) 16.1924 16.1924i 0.880750 0.880750i
\(339\) −3.06147 −0.166276
\(340\) 7.65685 8.82843i 0.415251 0.478789i
\(341\) 4.32957i 0.234459i
\(342\) −0.409880 + 0.409880i −0.0221638 + 0.0221638i
\(343\) −8.53622 16.4357i −0.460913 0.887445i
\(344\) 5.65685i 0.304997i
\(345\) 0.171573 + 2.41421i 0.00923717 + 0.129977i
\(346\) 18.7946i 1.01040i
\(347\) −5.31371 5.31371i −0.285255 0.285255i 0.549946 0.835200i \(-0.314648\pi\)
−0.835200 + 0.549946i \(0.814648\pi\)
\(348\) −1.08239 1.08239i −0.0580223 0.0580223i
\(349\) −2.66752 −0.142789 −0.0713945 0.997448i \(-0.522745\pi\)
−0.0713945 + 0.997448i \(0.522745\pi\)
\(350\) −7.06467 11.1844i −0.377623 0.597830i
\(351\) −28.6274 −1.52802
\(352\) 2.00000 + 2.00000i 0.106600 + 0.106600i
\(353\) −8.47343 8.47343i −0.450995 0.450995i 0.444690 0.895685i \(-0.353314\pi\)
−0.895685 + 0.444690i \(0.853314\pi\)
\(354\) 17.0711i 0.907317i
\(355\) 0.0928546 + 1.30656i 0.00492821 + 0.0693452i
\(356\) 11.3492i 0.601506i
\(357\) 23.8763 + 9.09425i 1.26367 + 0.481318i
\(358\) −9.65685 + 9.65685i −0.510381 + 0.510381i
\(359\) 16.9706i 0.895672i −0.894116 0.447836i \(-0.852195\pi\)
0.894116 0.447836i \(-0.147805\pi\)
\(360\) 0.606854 0.699709i 0.0319840 0.0368779i
\(361\) −17.0416 −0.896928
\(362\) 6.21579 6.21579i 0.326695 0.326695i
\(363\) 3.91969 + 3.91969i 0.205730 + 0.205730i
\(364\) 14.4650 6.48528i 0.758174 0.339921i
\(365\) −8.58579 + 9.89949i −0.449401 + 0.518163i
\(366\) −11.8995 −0.621997
\(367\) −3.06147 + 3.06147i −0.159807 + 0.159807i −0.782481 0.622674i \(-0.786046\pi\)
0.622674 + 0.782481i \(0.286046\pi\)
\(368\) −0.414214 + 0.414214i −0.0215924 + 0.0215924i
\(369\) 1.53073 0.0796868
\(370\) −8.15640 + 0.579658i −0.424031 + 0.0301350i
\(371\) 28.1421 12.6173i 1.46107 0.655057i
\(372\) −2.00000 2.00000i −0.103695 0.103695i
\(373\) −15.0711 + 15.0711i −0.780350 + 0.780350i −0.979890 0.199539i \(-0.936055\pi\)
0.199539 + 0.979890i \(0.436055\pi\)
\(374\) −14.7821 −0.764363
\(375\) 11.1924 17.3640i 0.577972 0.896671i
\(376\) 1.53073i 0.0789416i
\(377\) 3.50981 3.50981i 0.180764 0.180764i
\(378\) −11.8133 4.49955i −0.607608 0.231432i
\(379\) 6.14214i 0.315500i 0.987479 + 0.157750i \(0.0504241\pi\)
−0.987479 + 0.157750i \(0.949576\pi\)
\(380\) −3.12132 + 0.221825i −0.160120 + 0.0113794i
\(381\) 9.37011i 0.480045i
\(382\) −1.24264 1.24264i −0.0635790 0.0635790i
\(383\) 10.6382 + 10.6382i 0.543587 + 0.543587i 0.924579 0.380991i \(-0.124417\pi\)
−0.380991 + 0.924579i \(0.624417\pi\)
\(384\) 1.84776 0.0942931
\(385\) −4.83259 + 16.0202i −0.246292 + 0.816464i
\(386\) −11.6569 −0.593318
\(387\) 1.65685 + 1.65685i 0.0842226 + 0.0842226i
\(388\) 4.59220 + 4.59220i 0.233134 + 0.233134i
\(389\) 0.142136i 0.00720656i 0.999994 + 0.00360328i \(0.00114696\pi\)
−0.999994 + 0.00360328i \(0.998853\pi\)
\(390\) 18.7018 + 16.2200i 0.947001 + 0.821329i
\(391\) 3.06147i 0.154825i
\(392\) 6.98841 0.402625i 0.352968 0.0203356i
\(393\) 19.1421 19.1421i 0.965593 0.965593i
\(394\) 0.828427i 0.0417356i
\(395\) 11.3107 0.803828i 0.569104 0.0404450i
\(396\) −1.17157 −0.0588738
\(397\) −1.12085 + 1.12085i −0.0562540 + 0.0562540i −0.734674 0.678420i \(-0.762665\pi\)
0.678420 + 0.734674i \(0.262665\pi\)
\(398\) 19.8226 + 19.8226i 0.993618 + 0.993618i
\(399\) −2.79884 6.24264i −0.140117 0.312523i
\(400\) 4.94975 0.707107i 0.247487 0.0353553i
\(401\) −19.7574 −0.986635 −0.493318 0.869849i \(-0.664216\pi\)
−0.493318 + 0.869849i \(0.664216\pi\)
\(402\) −19.3743 + 19.3743i −0.966301 + 0.966301i
\(403\) 6.48528 6.48528i 0.323055 0.323055i
\(404\) −2.74444 −0.136541
\(405\) −1.59639 22.4629i −0.0793253 1.11619i
\(406\) 2.00000 0.896683i 0.0992583 0.0445016i
\(407\) 7.31371 + 7.31371i 0.362527 + 0.362527i
\(408\) −6.82843 + 6.82843i −0.338058 + 0.338058i
\(409\) 24.9719 1.23478 0.617392 0.786656i \(-0.288189\pi\)
0.617392 + 0.786656i \(0.288189\pi\)
\(410\) 6.24264 + 5.41421i 0.308302 + 0.267389i
\(411\) 21.3533i 1.05328i
\(412\) −10.0042 + 10.0042i −0.492870 + 0.492870i
\(413\) −22.8427 8.70054i −1.12401 0.428126i
\(414\) 0.242641i 0.0119251i
\(415\) −11.0208 + 12.7071i −0.540991 + 0.623767i
\(416\) 5.99162i 0.293763i
\(417\) −11.2426 11.2426i −0.550554 0.550554i
\(418\) 2.79884 + 2.79884i 0.136895 + 0.136895i
\(419\) −11.5893 −0.566174 −0.283087 0.959094i \(-0.591358\pi\)
−0.283087 + 0.959094i \(0.591358\pi\)
\(420\) 5.16799 + 9.63272i 0.252172 + 0.470029i
\(421\) 17.7990 0.867470 0.433735 0.901041i \(-0.357195\pi\)
0.433735 + 0.901041i \(0.357195\pi\)
\(422\) 7.31371 + 7.31371i 0.356026 + 0.356026i
\(423\) −0.448342 0.448342i −0.0217991 0.0217991i
\(424\) 11.6569i 0.566107i
\(425\) −15.6788 + 20.9050i −0.760531 + 1.01404i
\(426\) 1.08239i 0.0524421i
\(427\) 6.06477 15.9226i 0.293495 0.770550i
\(428\) 3.65685 3.65685i 0.176761 0.176761i
\(429\) 31.3137i 1.51184i
\(430\) 0.896683 + 12.6173i 0.0432419 + 0.608460i
\(431\) 5.65685 0.272481 0.136241 0.990676i \(-0.456498\pi\)
0.136241 + 0.990676i \(0.456498\pi\)
\(432\) 3.37849 3.37849i 0.162548 0.162548i
\(433\) 10.4525 + 10.4525i 0.502315 + 0.502315i 0.912157 0.409841i \(-0.134416\pi\)
−0.409841 + 0.912157i \(0.634416\pi\)
\(434\) 3.69552 1.65685i 0.177391 0.0795315i
\(435\) 2.58579 + 2.24264i 0.123979 + 0.107526i
\(436\) 12.1421 0.581503
\(437\) −0.579658 + 0.579658i −0.0277288 + 0.0277288i
\(438\) 7.65685 7.65685i 0.365859 0.365859i
\(439\) 13.8854 0.662713 0.331357 0.943506i \(-0.392494\pi\)
0.331357 + 0.943506i \(0.392494\pi\)
\(440\) −4.77791 4.14386i −0.227778 0.197551i
\(441\) −1.92893 + 2.16478i −0.0918539 + 0.103085i
\(442\) −22.1421 22.1421i −1.05319 1.05319i
\(443\) −4.14214 + 4.14214i −0.196799 + 0.196799i −0.798626 0.601827i \(-0.794440\pi\)
0.601827 + 0.798626i \(0.294440\pi\)
\(444\) 6.75699 0.320672
\(445\) 1.79899 + 25.3137i 0.0852803 + 1.19998i
\(446\) 9.55582i 0.452481i
\(447\) 22.6215 22.6215i 1.06996 1.06996i
\(448\) −0.941740 + 2.47247i −0.0444930 + 0.116813i
\(449\) 25.6569i 1.21082i 0.795913 + 0.605411i \(0.206991\pi\)
−0.795913 + 0.605411i \(0.793009\pi\)
\(450\) −1.24264 + 1.65685i −0.0585786 + 0.0781049i
\(451\) 10.4525i 0.492189i
\(452\) 1.17157 + 1.17157i 0.0551062 + 0.0551062i
\(453\) 11.5349 + 11.5349i 0.541957 + 0.541957i
\(454\) −11.8519 −0.556238
\(455\) −31.2355 + 16.7579i −1.46434 + 0.785624i
\(456\) 2.58579 0.121091
\(457\) −1.65685 1.65685i −0.0775044 0.0775044i 0.667292 0.744796i \(-0.267453\pi\)
−0.744796 + 0.667292i \(0.767453\pi\)
\(458\) 5.45042 + 5.45042i 0.254682 + 0.254682i
\(459\) 24.9706i 1.16553i
\(460\) 0.858221 0.989538i 0.0400148 0.0461374i
\(461\) 34.0250i 1.58470i −0.610064 0.792352i \(-0.708856\pi\)
0.610064 0.792352i \(-0.291144\pi\)
\(462\) 4.92177 12.9218i 0.228981 0.601175i
\(463\) −12.9706 + 12.9706i −0.602793 + 0.602793i −0.941053 0.338260i \(-0.890162\pi\)
0.338260 + 0.941053i \(0.390162\pi\)
\(464\) 0.828427i 0.0384588i
\(465\) 4.77791 + 4.14386i 0.221570 + 0.192167i
\(466\) −4.24264 −0.196537
\(467\) −17.4337 + 17.4337i −0.806734 + 0.806734i −0.984138 0.177404i \(-0.943230\pi\)
0.177404 + 0.984138i \(0.443230\pi\)
\(468\) −1.75490 1.75490i −0.0811205 0.0811205i
\(469\) −16.0502 35.7990i −0.741128 1.65304i
\(470\) −0.242641 3.41421i −0.0111922 0.157486i
\(471\) 26.7279 1.23156
\(472\) 6.53281 6.53281i 0.300697 0.300697i
\(473\) 11.3137 11.3137i 0.520205 0.520205i
\(474\) −9.37011 −0.430383
\(475\) 6.92676 0.989538i 0.317822 0.0454031i
\(476\) −5.65685 12.6173i −0.259281 0.578312i
\(477\) −3.41421 3.41421i −0.156326 0.156326i
\(478\) −4.58579 + 4.58579i −0.209749 + 0.209749i
\(479\) 11.0866 0.506558 0.253279 0.967393i \(-0.418491\pi\)
0.253279 + 0.967393i \(0.418491\pi\)
\(480\) −4.12132 + 0.292893i −0.188112 + 0.0133687i
\(481\) 21.9105i 0.999032i
\(482\) 4.77791 4.77791i 0.217628 0.217628i
\(483\) 2.67619 + 1.01933i 0.121771 + 0.0463812i
\(484\) 3.00000i 0.136364i
\(485\) −10.9706 9.51472i −0.498148 0.432041i
\(486\) 4.27518i 0.193926i
\(487\) 1.10051 + 1.10051i 0.0498686 + 0.0498686i 0.731601 0.681733i \(-0.238773\pi\)
−0.681733 + 0.731601i \(0.738773\pi\)
\(488\) 4.55374 + 4.55374i 0.206138 + 0.206138i
\(489\) −35.6871 −1.61383
\(490\) −15.5234 + 2.00578i −0.701277 + 0.0906121i
\(491\) 25.1716 1.13598 0.567989 0.823036i \(-0.307722\pi\)
0.567989 + 0.823036i \(0.307722\pi\)
\(492\) −4.82843 4.82843i −0.217682 0.217682i
\(493\) −3.06147 3.06147i −0.137882 0.137882i
\(494\) 8.38478i 0.377249i
\(495\) 2.61313 0.185709i 0.117451 0.00834701i
\(496\) 1.53073i 0.0687320i
\(497\) 1.44834 + 0.551658i 0.0649670 + 0.0247453i
\(498\) 9.82843 9.82843i 0.440422 0.440422i
\(499\) 7.51472i 0.336405i 0.985752 + 0.168203i \(0.0537963\pi\)
−0.985752 + 0.168203i \(0.946204\pi\)
\(500\) −10.9280 + 2.36176i −0.488717 + 0.105621i
\(501\) −4.48528 −0.200388
\(502\) 9.96570 9.96570i 0.444791 0.444791i
\(503\) −18.1062 18.1062i −0.807314 0.807314i 0.176912 0.984227i \(-0.443389\pi\)
−0.984227 + 0.176912i \(0.943389\pi\)
\(504\) −0.448342 1.00000i −0.0199707 0.0445435i
\(505\) 6.12132 0.435029i 0.272395 0.0193585i
\(506\) −1.65685 −0.0736562
\(507\) 29.9196 29.9196i 1.32878 1.32878i
\(508\) −3.58579 + 3.58579i −0.159094 + 0.159094i
\(509\) −14.4650 −0.641152 −0.320576 0.947223i \(-0.603876\pi\)
−0.320576 + 0.947223i \(0.603876\pi\)
\(510\) 14.1480 16.3128i 0.626485 0.722343i
\(511\) 6.34315 + 14.1480i 0.280604 + 0.625872i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 4.72792 4.72792i 0.208743 0.208743i
\(514\) −11.0866 −0.489007
\(515\) 20.7279 23.8995i 0.913381 1.05314i
\(516\) 10.4525i 0.460146i
\(517\) −3.06147 + 3.06147i −0.134643 + 0.134643i
\(518\) −3.44381 + 9.04148i −0.151312 + 0.397260i
\(519\) 34.7279i 1.52439i
\(520\) −0.949747 13.3640i −0.0416492 0.586048i
\(521\) 36.6925i 1.60753i 0.594947 + 0.803765i \(0.297173\pi\)
−0.594947 + 0.803765i \(0.702827\pi\)
\(522\) −0.242641 0.242641i −0.0106201 0.0106201i
\(523\) −1.75490 1.75490i −0.0767366 0.0767366i 0.667697 0.744433i \(-0.267280\pi\)
−0.744433 + 0.667697i \(0.767280\pi\)
\(524\) −14.6508 −0.640021
\(525\) −13.0538 20.6660i −0.569715 0.901940i
\(526\) 27.4558 1.19713
\(527\) −5.65685 5.65685i −0.246416 0.246416i
\(528\) 3.69552 + 3.69552i 0.160827 + 0.160827i
\(529\) 22.6569i 0.985081i
\(530\) −1.84776 25.9999i −0.0802615 1.12937i
\(531\) 3.82683i 0.166070i
\(532\) −1.31789 + 3.46002i −0.0571377 + 0.150011i
\(533\) 15.6569 15.6569i 0.678174 0.678174i
\(534\) 20.9706i 0.907485i
\(535\) −7.57675 + 8.73606i −0.327571 + 0.377693i
\(536\) 14.8284 0.640490
\(537\) −17.8435 + 17.8435i −0.770006 + 0.770006i
\(538\) −19.0188 19.0188i −0.819958 0.819958i
\(539\) 14.7821 + 13.1716i 0.636709 + 0.567340i
\(540\) −7.00000 + 8.07107i −0.301232 + 0.347323i
\(541\) 10.9706 0.471661 0.235831 0.971794i \(-0.424219\pi\)
0.235831 + 0.971794i \(0.424219\pi\)
\(542\) −13.2513 + 13.2513i −0.569194 + 0.569194i
\(543\) 11.4853 11.4853i 0.492881 0.492881i
\(544\) 5.22625 0.224074
\(545\) −27.0823 + 1.92468i −1.16008 + 0.0824443i
\(546\) 26.7279 11.9832i 1.14385 0.512835i
\(547\) −30.6274 30.6274i −1.30953 1.30953i −0.921751 0.387783i \(-0.873241\pi\)
−0.387783 0.921751i \(-0.626759\pi\)
\(548\) 8.17157 8.17157i 0.349072 0.349072i
\(549\) −2.66752 −0.113847
\(550\) 11.3137 + 8.48528i 0.482418 + 0.361814i
\(551\) 1.15932i 0.0493885i
\(552\) −0.765367 + 0.765367i −0.0325762 + 0.0325762i
\(553\) 4.77563 12.5381i 0.203080 0.533173i
\(554\) 2.48528i 0.105589i
\(555\) −15.0711 + 1.07107i −0.639731 + 0.0454643i
\(556\) 8.60474i 0.364922i
\(557\) −26.7279 26.7279i −1.13250 1.13250i −0.989761 0.142738i \(-0.954409\pi\)
−0.142738 0.989761i \(-0.545591\pi\)
\(558\) −0.448342 0.448342i −0.0189798 0.0189798i
\(559\) 33.8937 1.43355
\(560\) 1.70858 5.66399i 0.0722006 0.239347i
\(561\) −27.3137 −1.15319
\(562\) 4.00000 + 4.00000i 0.168730 + 0.168730i
\(563\) −3.54827 3.54827i −0.149542 0.149542i 0.628372 0.777913i \(-0.283722\pi\)
−0.777913 + 0.628372i \(0.783722\pi\)
\(564\) 2.82843i 0.119098i
\(565\) −2.79884 2.42742i −0.117748 0.102122i
\(566\) 4.46088i 0.187505i
\(567\) −24.9004 9.48433i −1.04572 0.398304i
\(568\) −0.414214 + 0.414214i −0.0173800 + 0.0173800i
\(569\) 1.41421i 0.0592869i 0.999561 + 0.0296435i \(0.00943719\pi\)
−0.999561 + 0.0296435i \(0.990563\pi\)
\(570\) −5.76745 + 0.409880i −0.241572 + 0.0171680i
\(571\) −25.4558 −1.06529 −0.532647 0.846338i \(-0.678803\pi\)
−0.532647 + 0.846338i \(0.678803\pi\)
\(572\) −11.9832 + 11.9832i −0.501044 + 0.501044i
\(573\) −2.29610 2.29610i −0.0959210 0.0959210i
\(574\) 8.92177 4.00000i 0.372387 0.166957i
\(575\) −1.75736 + 2.34315i −0.0732869 + 0.0977159i
\(576\) 0.414214 0.0172589
\(577\) 26.3170 26.3170i 1.09559 1.09559i 0.100670 0.994920i \(-0.467901\pi\)
0.994920 0.100670i \(-0.0320986\pi\)
\(578\) −7.29289 + 7.29289i −0.303344 + 0.303344i
\(579\) −21.5391 −0.895133
\(580\) −0.131316 1.84776i −0.00545261 0.0767240i
\(581\) 8.14214 + 18.1606i 0.337793 + 0.753427i
\(582\) 8.48528 + 8.48528i 0.351726 + 0.351726i
\(583\) −23.3137 + 23.3137i −0.965555 + 0.965555i
\(584\) −5.86030 −0.242501
\(585\) 4.19239 + 3.63604i 0.173334 + 0.150332i
\(586\) 3.37849i 0.139564i
\(587\) −16.0886 + 16.0886i −0.664049 + 0.664049i −0.956332 0.292283i \(-0.905585\pi\)
0.292283 + 0.956332i \(0.405585\pi\)
\(588\) 12.9129 0.743954i 0.532519 0.0306801i
\(589\) 2.14214i 0.0882652i
\(590\) −13.5355 + 15.6066i −0.557249 + 0.642514i
\(591\) 1.53073i 0.0629660i
\(592\) −2.58579 2.58579i −0.106275 0.106275i
\(593\) 22.8841 + 22.8841i 0.939737 + 0.939737i 0.998285 0.0585480i \(-0.0186471\pi\)
−0.0585480 + 0.998285i \(0.518647\pi\)
\(594\) 13.5140 0.554485
\(595\) 14.6173 + 27.2455i 0.599250 + 1.11695i
\(596\) −17.3137 −0.709197
\(597\) 36.6274 + 36.6274i 1.49906 + 1.49906i
\(598\) −2.48181 2.48181i −0.101489 0.101489i
\(599\) 18.5269i 0.756989i 0.925604 + 0.378495i \(0.123558\pi\)
−0.925604 + 0.378495i \(0.876442\pi\)
\(600\) 9.14594 1.30656i 0.373381 0.0533402i
\(601\) 16.5754i 0.676126i −0.941123 0.338063i \(-0.890228\pi\)
0.941123 0.338063i \(-0.109772\pi\)
\(602\) 13.9864 + 5.32729i 0.570044 + 0.217124i
\(603\) −4.34315 + 4.34315i −0.176867 + 0.176867i
\(604\) 8.82843i 0.359224i
\(605\) 0.475538 + 6.69133i 0.0193334 + 0.272041i
\(606\) −5.07107 −0.205998
\(607\) 21.5391 21.5391i 0.874243 0.874243i −0.118688 0.992932i \(-0.537869\pi\)
0.992932 + 0.118688i \(0.0378689\pi\)
\(608\) −0.989538 0.989538i −0.0401311 0.0401311i
\(609\) 3.69552 1.65685i 0.149750 0.0671391i
\(610\) −10.8787 9.43503i −0.440465 0.382013i
\(611\) −9.17157 −0.371042
\(612\) −1.53073 + 1.53073i −0.0618762 + 0.0618762i
\(613\) 19.8995 19.8995i 0.803733 0.803733i −0.179944 0.983677i \(-0.557592\pi\)
0.983677 + 0.179944i \(0.0575916\pi\)
\(614\) 32.7569 1.32196
\(615\) 11.5349 + 10.0042i 0.465132 + 0.403407i
\(616\) −6.82843 + 3.06147i −0.275125 + 0.123350i
\(617\) −28.4853 28.4853i −1.14677 1.14677i −0.987183 0.159591i \(-0.948982\pi\)
−0.159591 0.987183i \(-0.551018\pi\)
\(618\) −18.4853 + 18.4853i −0.743587 + 0.743587i
\(619\) 0.688444 0.0276709 0.0138354 0.999904i \(-0.495596\pi\)
0.0138354 + 0.999904i \(0.495596\pi\)
\(620\) −0.242641 3.41421i −0.00974468 0.137118i
\(621\) 2.79884i 0.112313i
\(622\) −2.42742 + 2.42742i −0.0973305 + 0.0973305i
\(623\) 28.0606 + 10.6880i 1.12422 + 0.428205i
\(624\) 11.0711i 0.443197i
\(625\) 24.0000 7.00000i 0.960000 0.280000i
\(626\) 9.55582i 0.381927i
\(627\) 5.17157 + 5.17157i 0.206533 + 0.206533i
\(628\) −10.2283 10.2283i −0.408155 0.408155i
\(629\) 19.1116 0.762031
\(630\) 1.15851 + 2.15937i 0.0461562 + 0.0860315i
\(631\) 41.3553 1.64633 0.823165 0.567802i \(-0.192206\pi\)
0.823165 + 0.567802i \(0.192206\pi\)
\(632\) 3.58579 + 3.58579i 0.142635 + 0.142635i
\(633\) 13.5140 + 13.5140i 0.537132 + 0.537132i
\(634\) 30.9706i 1.23000i
\(635\) 7.42950 8.56628i 0.294831 0.339943i
\(636\) 21.5391i 0.854079i
\(637\) 2.41237 + 41.8719i 0.0955818 + 1.65902i
\(638\) −1.65685 + 1.65685i −0.0655955 + 0.0655955i
\(639\) 0.242641i 0.00959872i
\(640\) 1.68925 + 1.46508i 0.0667733 + 0.0579122i
\(641\) −37.2132 −1.46983 −0.734917 0.678158i \(-0.762779\pi\)
−0.734917 + 0.678158i \(0.762779\pi\)
\(642\) 6.75699 6.75699i 0.266677 0.266677i
\(643\) 20.9435 + 20.9435i 0.825930 + 0.825930i 0.986951 0.161021i \(-0.0514787\pi\)
−0.161021 + 0.986951i \(0.551479\pi\)
\(644\) −0.634051 1.41421i −0.0249851 0.0557278i
\(645\) 1.65685 + 23.3137i 0.0652386 + 0.917976i
\(646\) 7.31371 0.287754
\(647\) −23.8896 + 23.8896i −0.939195 + 0.939195i −0.998254 0.0590593i \(-0.981190\pi\)
0.0590593 + 0.998254i \(0.481190\pi\)
\(648\) 7.12132 7.12132i 0.279752 0.279752i
\(649\) 26.1313 1.02574
\(650\) 4.23671 + 29.6570i 0.166178 + 1.16324i
\(651\) 6.82843 3.06147i 0.267627 0.119988i
\(652\) 13.6569 + 13.6569i 0.534844 + 0.534844i
\(653\) 8.72792 8.72792i 0.341550 0.341550i −0.515400 0.856950i \(-0.672357\pi\)
0.856950 + 0.515400i \(0.172357\pi\)
\(654\) 22.4357 0.877307
\(655\) 32.6777 2.32233i 1.27682 0.0907410i
\(656\) 3.69552i 0.144286i
\(657\) 1.71644 1.71644i 0.0669648 0.0669648i
\(658\) −3.78470 1.44155i −0.147543 0.0561976i
\(659\) 29.6569i 1.15527i −0.816296 0.577634i \(-0.803976\pi\)
0.816296 0.577634i \(-0.196024\pi\)
\(660\) −8.82843 7.65685i −0.343646 0.298043i
\(661\) 47.5390i 1.84905i −0.381118 0.924526i \(-0.624461\pi\)
0.381118 0.924526i \(-0.375539\pi\)
\(662\) −16.4853 16.4853i −0.640719 0.640719i
\(663\) −40.9133 40.9133i −1.58894 1.58894i
\(664\) −7.52235 −0.291924
\(665\) 2.39101 7.92628i 0.0927196 0.307368i
\(666\) 1.51472 0.0586942
\(667\) −0.343146 0.343146i −0.0132867 0.0132867i
\(668\) 1.71644 + 1.71644i 0.0664112 + 0.0664112i
\(669\) 17.6569i 0.682653i
\(670\) −33.0740 + 2.35049i −1.27776 + 0.0908075i
\(671\) 18.2150i 0.703181i
\(672\) −1.74011 + 4.56854i −0.0671261 + 0.176235i
\(673\) −22.7990 + 22.7990i −0.878836 + 0.878836i −0.993414 0.114578i \(-0.963448\pi\)
0.114578 + 0.993414i \(0.463448\pi\)
\(674\) 5.31371i 0.204676i
\(675\) 14.3337 19.1116i 0.551706 0.735607i
\(676\) −22.8995 −0.880750
\(677\) 22.4742 22.4742i 0.863754 0.863754i −0.128018 0.991772i \(-0.540862\pi\)
0.991772 + 0.128018i \(0.0408615\pi\)
\(678\) 2.16478 + 2.16478i 0.0831380 + 0.0831380i
\(679\) −15.6788 + 7.02944i −0.601695 + 0.269765i
\(680\) −11.6569 + 0.828427i −0.447020 + 0.0317687i
\(681\) −21.8995 −0.839190
\(682\) −3.06147 + 3.06147i −0.117230 + 0.117230i
\(683\) −25.3137 + 25.3137i −0.968602 + 0.968602i −0.999522 0.0309197i \(-0.990156\pi\)
0.0309197 + 0.999522i \(0.490156\pi\)
\(684\) 0.579658 0.0221638
\(685\) −16.9309 + 19.5215i −0.646897 + 0.745879i
\(686\) −5.58579 + 17.6578i −0.213266 + 0.674179i
\(687\) 10.0711 + 10.0711i 0.384235 + 0.384235i
\(688\) −4.00000 + 4.00000i −0.152499 + 0.152499i
\(689\) −69.8434 −2.66082
\(690\) 1.58579 1.82843i 0.0603699 0.0696070i
\(691\) 25.1033i 0.954973i −0.878639 0.477487i \(-0.841548\pi\)
0.878639 0.477487i \(-0.158452\pi\)
\(692\) 13.2898 13.2898i 0.505202 0.505202i
\(693\) 1.10332 2.89668i 0.0419115 0.110036i
\(694\) 7.51472i 0.285255i
\(695\) −1.36396 19.1924i −0.0517380 0.728009i
\(696\) 1.53073i 0.0580223i
\(697\) −13.6569 13.6569i −0.517290 0.517290i
\(698\) 1.88622 + 1.88622i 0.0713945 + 0.0713945i
\(699\) −7.83938 −0.296512
\(700\) −2.91307 + 12.9040i −0.110104 + 0.487727i
\(701\) −13.1127 −0.495260 −0.247630 0.968855i \(-0.579652\pi\)
−0.247630 + 0.968855i \(0.579652\pi\)
\(702\) 20.2426 + 20.2426i 0.764009 + 0.764009i
\(703\) −3.61859 3.61859i −0.136478 0.136478i
\(704\) 2.82843i 0.106600i
\(705\) −0.448342 6.30864i −0.0168855 0.237597i
\(706\) 11.9832i 0.450995i
\(707\) 2.58455 6.78556i 0.0972020 0.255197i
\(708\) 12.0711 12.0711i 0.453659 0.453659i
\(709\) 41.3137i 1.55157i −0.630998 0.775784i \(-0.717354\pi\)
0.630998 0.775784i \(-0.282646\pi\)
\(710\) 0.858221 0.989538i 0.0322085 0.0371367i
\(711\) −2.10051 −0.0787751
\(712\) −8.02509 + 8.02509i −0.300753 + 0.300753i
\(713\) −0.634051 0.634051i −0.0237454 0.0237454i
\(714\) −10.4525 23.3137i −0.391175 0.872494i
\(715\) 24.8284 28.6274i 0.928531 1.07060i
\(716\) 13.6569 0.510381
\(717\) −8.47343 + 8.47343i −0.316446 + 0.316446i
\(718\) −12.0000 + 12.0000i −0.447836 + 0.447836i
\(719\) −43.7122 −1.63019 −0.815094 0.579328i \(-0.803315\pi\)
−0.815094 + 0.579328i \(0.803315\pi\)
\(720\) −0.923880 + 0.0656581i −0.0344310 + 0.00244693i
\(721\) −15.3137 34.1563i −0.570312 1.27205i
\(722\) 12.0503 + 12.0503i 0.448464 + 0.448464i
\(723\) 8.82843 8.82843i 0.328333 0.328333i
\(724\) −8.79045 −0.326695
\(725\) 0.585786 + 4.10051i 0.0217556 + 0.152289i
\(726\) 5.54328i 0.205730i
\(727\) 22.8841 22.8841i 0.848724 0.848724i −0.141250 0.989974i \(-0.545112\pi\)
0.989974 + 0.141250i \(0.0451122\pi\)
\(728\) −14.8141 5.64255i −0.549048 0.209127i
\(729\) 22.3137i 0.826434i
\(730\) 13.0711 0.928932i 0.483782 0.0343813i
\(731\) 29.5641i 1.09347i
\(732\) 8.41421 + 8.41421i 0.310998 + 0.310998i
\(733\) −21.9489 21.9489i −0.810703 0.810703i 0.174037 0.984739i \(-0.444319\pi\)
−0.984739 + 0.174037i \(0.944319\pi\)
\(734\) 4.32957 0.159807
\(735\) −28.6836 + 3.70620i −1.05801 + 0.136705i
\(736\) 0.585786 0.0215924
\(737\) 29.6569 + 29.6569i 1.09242 + 1.09242i
\(738\) −1.08239 1.08239i −0.0398434 0.0398434i
\(739\) 9.65685i 0.355233i −0.984100 0.177617i \(-0.943161\pi\)
0.984100 0.177617i \(-0.0568387\pi\)
\(740\) 6.17733 + 5.35757i 0.227083 + 0.196948i
\(741\) 15.4930i 0.569151i
\(742\) −28.8213 10.9777i −1.05806 0.403005i
\(743\) 27.0416 27.0416i 0.992061 0.992061i −0.00790753 0.999969i \(-0.502517\pi\)
0.999969 + 0.00790753i \(0.00251707\pi\)
\(744\) 2.82843i 0.103695i
\(745\) 38.6172 2.74444i 1.41483 0.100549i
\(746\) 21.3137 0.780350
\(747\) 2.20325 2.20325i 0.0806126 0.0806126i
\(748\) 10.4525 + 10.4525i 0.382181 + 0.382181i
\(749\) 5.59767 + 12.4853i 0.204534 + 0.456202i
\(750\) −20.1924 + 4.36396i −0.737322 + 0.159349i
\(751\) −2.48528 −0.0906892 −0.0453446 0.998971i \(-0.514439\pi\)
−0.0453446 + 0.998971i \(0.514439\pi\)
\(752\) 1.08239 1.08239i 0.0394708 0.0394708i
\(753\) 18.4142 18.4142i 0.671051 0.671051i
\(754\) −4.96362 −0.180764
\(755\) 1.39942 + 19.6913i 0.0509300 + 0.716640i
\(756\) 5.17157 + 11.5349i 0.188088 + 0.419520i
\(757\) 7.89949 + 7.89949i 0.287112 + 0.287112i 0.835937 0.548825i \(-0.184925\pi\)
−0.548825 + 0.835937i \(0.684925\pi\)
\(758\) 4.34315 4.34315i 0.157750 0.157750i
\(759\) −3.06147 −0.111124
\(760\) 2.36396 + 2.05025i 0.0857499 + 0.0743705i
\(761\) 26.3939i 0.956778i −0.878148 0.478389i \(-0.841221\pi\)
0.878148 0.478389i \(-0.158779\pi\)
\(762\) −6.62567 + 6.62567i −0.240023 + 0.240023i
\(763\) −11.4347 + 30.0211i −0.413965 + 1.08684i
\(764\) 1.75736i 0.0635790i
\(765\) 3.17157 3.65685i 0.114668 0.132214i
\(766\) 15.0447i 0.543587i
\(767\) 39.1421 + 39.1421i 1.41334 + 1.41334i
\(768\) −1.30656 1.30656i −0.0471465 0.0471465i
\(769\) 17.5809 0.633984 0.316992 0.948428i \(-0.397327\pi\)
0.316992 + 0.948428i \(0.397327\pi\)
\(770\) 14.7451 7.91082i 0.531378 0.285086i
\(771\) −20.4853 −0.737759
\(772\) 8.24264 + 8.24264i 0.296659 + 0.296659i
\(773\) 14.6892 + 14.6892i 0.528334 + 0.528334i 0.920076 0.391741i \(-0.128127\pi\)
−0.391741 + 0.920076i \(0.628127\pi\)
\(774\) 2.34315i 0.0842226i
\(775\) 1.08239 + 7.57675i 0.0388807 + 0.272165i
\(776\) 6.49435i 0.233134i
\(777\) −6.36332 + 16.7065i −0.228283 +