Properties

Label 1110.2.l.b.697.20
Level $1110$
Weight $2$
Character 1110.697
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 697.20
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.b.43.20

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.73553 + 1.40994i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-3.05055 - 3.05055i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.73553 + 1.40994i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-3.05055 - 3.05055i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-1.40994 + 1.73553i) q^{10} -3.00583i q^{11} +(-0.707107 - 0.707107i) q^{12} -6.48482i q^{13} +(3.05055 - 3.05055i) q^{14} +(0.230232 + 2.22418i) q^{15} +1.00000 q^{16} +6.00301 q^{17} -1.00000 q^{18} +(-4.44125 - 4.44125i) q^{19} +(-1.73553 - 1.40994i) q^{20} -4.31413i q^{21} +3.00583 q^{22} -4.23386i q^{23} +(0.707107 - 0.707107i) q^{24} +(1.02416 + 4.89399i) q^{25} +6.48482 q^{26} +(-0.707107 + 0.707107i) q^{27} +(3.05055 + 3.05055i) q^{28} +(1.51474 - 1.51474i) q^{29} +(-2.22418 + 0.230232i) q^{30} +(1.07252 + 1.07252i) q^{31} +1.00000i q^{32} +(2.12544 - 2.12544i) q^{33} +6.00301i q^{34} +(-0.993249 - 9.59541i) q^{35} -1.00000i q^{36} +(-1.11161 + 5.98033i) q^{37} +(4.44125 - 4.44125i) q^{38} +(4.58546 - 4.58546i) q^{39} +(1.40994 - 1.73553i) q^{40} +6.80482i q^{41} +4.31413 q^{42} -11.7951i q^{43} +3.00583i q^{44} +(-1.40994 + 1.73553i) q^{45} +4.23386 q^{46} +(5.31277 + 5.31277i) q^{47} +(0.707107 + 0.707107i) q^{48} +11.6117i q^{49} +(-4.89399 + 1.02416i) q^{50} +(4.24477 + 4.24477i) q^{51} +6.48482i q^{52} +(-5.63889 + 5.63889i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(4.23804 - 5.21672i) q^{55} +(-3.05055 + 3.05055i) q^{56} -6.28088i q^{57} +(1.51474 + 1.51474i) q^{58} +(-4.46968 - 4.46968i) q^{59} +(-0.230232 - 2.22418i) q^{60} +(-7.40088 - 7.40088i) q^{61} +(-1.07252 + 1.07252i) q^{62} +(3.05055 - 3.05055i) q^{63} -1.00000 q^{64} +(9.14318 - 11.2546i) q^{65} +(2.12544 + 2.12544i) q^{66} +(-2.42395 + 2.42395i) q^{67} -6.00301 q^{68} +(2.99379 - 2.99379i) q^{69} +(9.59541 - 0.993249i) q^{70} -9.18996 q^{71} +1.00000 q^{72} +(-2.01404 - 2.01404i) q^{73} +(-5.98033 - 1.11161i) q^{74} +(-2.73638 + 4.18476i) q^{75} +(4.44125 + 4.44125i) q^{76} +(-9.16944 + 9.16944i) q^{77} +(4.58546 + 4.58546i) q^{78} +(6.59707 + 6.59707i) q^{79} +(1.73553 + 1.40994i) q^{80} -1.00000 q^{81} -6.80482 q^{82} +(-0.481307 + 0.481307i) q^{83} +4.31413i q^{84} +(10.4184 + 8.46387i) q^{85} +11.7951 q^{86} +2.14216 q^{87} -3.00583 q^{88} +(4.35292 - 4.35292i) q^{89} +(-1.73553 - 1.40994i) q^{90} +(-19.7823 + 19.7823i) q^{91} +4.23386i q^{92} +1.51677i q^{93} +(-5.31277 + 5.31277i) q^{94} +(-1.44606 - 13.9698i) q^{95} +(-0.707107 + 0.707107i) q^{96} +16.2572 q^{97} -11.6117 q^{98} +3.00583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{4} - 4q^{7} + O(q^{10}) \) \( 40q - 40q^{4} - 4q^{7} + 4q^{14} + 40q^{16} + 24q^{17} - 40q^{18} + 4q^{19} + 8q^{22} + 8q^{25} + 8q^{26} + 4q^{28} + 28q^{31} - 4q^{33} + 20q^{35} + 20q^{37} - 4q^{38} + 4q^{39} + 16q^{42} - 16q^{47} + 16q^{51} + 20q^{53} + 16q^{55} - 4q^{56} - 4q^{59} - 8q^{61} - 28q^{62} + 4q^{63} - 40q^{64} - 4q^{65} - 4q^{66} + 16q^{67} - 24q^{68} - 8q^{69} + 12q^{70} + 40q^{71} + 40q^{72} + 8q^{73} - 8q^{74} + 16q^{75} - 4q^{76} - 24q^{77} + 4q^{78} - 12q^{79} - 40q^{81} - 24q^{82} - 8q^{83} - 8q^{85} + 8q^{87} - 8q^{88} + 12q^{89} - 24q^{91} + 16q^{94} - 28q^{95} + 40q^{97} - 56q^{98} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) −1.00000 −0.500000
\(5\) 1.73553 + 1.40994i 0.776154 + 0.630543i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) −3.05055 3.05055i −1.15300 1.15300i −0.985948 0.167051i \(-0.946576\pi\)
−0.167051 0.985948i \(-0.553424\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) −1.40994 + 1.73553i −0.445861 + 0.548824i
\(11\) 3.00583i 0.906293i −0.891436 0.453146i \(-0.850301\pi\)
0.891436 0.453146i \(-0.149699\pi\)
\(12\) −0.707107 0.707107i −0.204124 0.204124i
\(13\) 6.48482i 1.79856i −0.437369 0.899282i \(-0.644090\pi\)
0.437369 0.899282i \(-0.355910\pi\)
\(14\) 3.05055 3.05055i 0.815294 0.815294i
\(15\) 0.230232 + 2.22418i 0.0594456 + 0.574282i
\(16\) 1.00000 0.250000
\(17\) 6.00301 1.45594 0.727972 0.685607i \(-0.240463\pi\)
0.727972 + 0.685607i \(0.240463\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.44125 4.44125i −1.01889 1.01889i −0.999818 0.0190753i \(-0.993928\pi\)
−0.0190753 0.999818i \(-0.506072\pi\)
\(20\) −1.73553 1.40994i −0.388077 0.315272i
\(21\) 4.31413i 0.941420i
\(22\) 3.00583 0.640846
\(23\) 4.23386i 0.882821i −0.897305 0.441410i \(-0.854478\pi\)
0.897305 0.441410i \(-0.145522\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) 1.02416 + 4.89399i 0.204831 + 0.978797i
\(26\) 6.48482 1.27178
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 3.05055 + 3.05055i 0.576500 + 0.576500i
\(29\) 1.51474 1.51474i 0.281280 0.281280i −0.552339 0.833619i \(-0.686265\pi\)
0.833619 + 0.552339i \(0.186265\pi\)
\(30\) −2.22418 + 0.230232i −0.406079 + 0.0420344i
\(31\) 1.07252 + 1.07252i 0.192631 + 0.192631i 0.796832 0.604201i \(-0.206508\pi\)
−0.604201 + 0.796832i \(0.706508\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.12544 2.12544i 0.369992 0.369992i
\(34\) 6.00301i 1.02951i
\(35\) −0.993249 9.59541i −0.167890 1.62192i
\(36\) 1.00000i 0.166667i
\(37\) −1.11161 + 5.98033i −0.182747 + 0.983160i
\(38\) 4.44125 4.44125i 0.720466 0.720466i
\(39\) 4.58546 4.58546i 0.734261 0.734261i
\(40\) 1.40994 1.73553i 0.222931 0.274412i
\(41\) 6.80482i 1.06273i 0.847142 + 0.531367i \(0.178322\pi\)
−0.847142 + 0.531367i \(0.821678\pi\)
\(42\) 4.31413 0.665684
\(43\) 11.7951i 1.79874i −0.437191 0.899369i \(-0.644027\pi\)
0.437191 0.899369i \(-0.355973\pi\)
\(44\) 3.00583i 0.453146i
\(45\) −1.40994 + 1.73553i −0.210181 + 0.258718i
\(46\) 4.23386 0.624249
\(47\) 5.31277 + 5.31277i 0.774946 + 0.774946i 0.978967 0.204020i \(-0.0654008\pi\)
−0.204020 + 0.978967i \(0.565401\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 11.6117i 1.65881i
\(50\) −4.89399 + 1.02416i −0.692114 + 0.144837i
\(51\) 4.24477 + 4.24477i 0.594387 + 0.594387i
\(52\) 6.48482i 0.899282i
\(53\) −5.63889 + 5.63889i −0.774562 + 0.774562i −0.978900 0.204339i \(-0.934496\pi\)
0.204339 + 0.978900i \(0.434496\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) 4.23804 5.21672i 0.571457 0.703423i
\(56\) −3.05055 + 3.05055i −0.407647 + 0.407647i
\(57\) 6.28088i 0.831923i
\(58\) 1.51474 + 1.51474i 0.198895 + 0.198895i
\(59\) −4.46968 4.46968i −0.581903 0.581903i 0.353523 0.935426i \(-0.384984\pi\)
−0.935426 + 0.353523i \(0.884984\pi\)
\(60\) −0.230232 2.22418i −0.0297228 0.287141i
\(61\) −7.40088 7.40088i −0.947586 0.947586i 0.0511071 0.998693i \(-0.483725\pi\)
−0.998693 + 0.0511071i \(0.983725\pi\)
\(62\) −1.07252 + 1.07252i −0.136210 + 0.136210i
\(63\) 3.05055 3.05055i 0.384333 0.384333i
\(64\) −1.00000 −0.125000
\(65\) 9.14318 11.2546i 1.13407 1.39596i
\(66\) 2.12544 + 2.12544i 0.261624 + 0.261624i
\(67\) −2.42395 + 2.42395i −0.296132 + 0.296132i −0.839497 0.543364i \(-0.817150\pi\)
0.543364 + 0.839497i \(0.317150\pi\)
\(68\) −6.00301 −0.727972
\(69\) 2.99379 2.99379i 0.360410 0.360410i
\(70\) 9.59541 0.993249i 1.14687 0.118716i
\(71\) −9.18996 −1.09065 −0.545324 0.838225i \(-0.683593\pi\)
−0.545324 + 0.838225i \(0.683593\pi\)
\(72\) 1.00000 0.117851
\(73\) −2.01404 2.01404i −0.235725 0.235725i 0.579352 0.815077i \(-0.303306\pi\)
−0.815077 + 0.579352i \(0.803306\pi\)
\(74\) −5.98033 1.11161i −0.695199 0.129222i
\(75\) −2.73638 + 4.18476i −0.315970 + 0.483214i
\(76\) 4.44125 + 4.44125i 0.509447 + 0.509447i
\(77\) −9.16944 + 9.16944i −1.04495 + 1.04495i
\(78\) 4.58546 + 4.58546i 0.519201 + 0.519201i
\(79\) 6.59707 + 6.59707i 0.742228 + 0.742228i 0.973006 0.230778i \(-0.0741272\pi\)
−0.230778 + 0.973006i \(0.574127\pi\)
\(80\) 1.73553 + 1.40994i 0.194039 + 0.157636i
\(81\) −1.00000 −0.111111
\(82\) −6.80482 −0.751467
\(83\) −0.481307 + 0.481307i −0.0528303 + 0.0528303i −0.733028 0.680198i \(-0.761894\pi\)
0.680198 + 0.733028i \(0.261894\pi\)
\(84\) 4.31413i 0.470710i
\(85\) 10.4184 + 8.46387i 1.13004 + 0.918036i
\(86\) 11.7951 1.27190
\(87\) 2.14216 0.229664
\(88\) −3.00583 −0.320423
\(89\) 4.35292 4.35292i 0.461409 0.461409i −0.437708 0.899117i \(-0.644210\pi\)
0.899117 + 0.437708i \(0.144210\pi\)
\(90\) −1.73553 1.40994i −0.182941 0.148620i
\(91\) −19.7823 + 19.7823i −2.07374 + 2.07374i
\(92\) 4.23386i 0.441410i
\(93\) 1.51677i 0.157282i
\(94\) −5.31277 + 5.31277i −0.547970 + 0.547970i
\(95\) −1.44606 13.9698i −0.148362 1.43327i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) 16.2572 1.65067 0.825336 0.564643i \(-0.190986\pi\)
0.825336 + 0.564643i \(0.190986\pi\)
\(98\) −11.6117 −1.17296
\(99\) 3.00583 0.302098
\(100\) −1.02416 4.89399i −0.102416 0.489399i
\(101\) 16.3032i 1.62223i −0.584887 0.811115i \(-0.698861\pi\)
0.584887 0.811115i \(-0.301139\pi\)
\(102\) −4.24477 + 4.24477i −0.420295 + 0.420295i
\(103\) 8.32869 0.820650 0.410325 0.911939i \(-0.365415\pi\)
0.410325 + 0.911939i \(0.365415\pi\)
\(104\) −6.48482 −0.635889
\(105\) 6.08265 7.48731i 0.593606 0.730687i
\(106\) −5.63889 5.63889i −0.547698 0.547698i
\(107\) 7.63911 + 7.63911i 0.738501 + 0.738501i 0.972288 0.233787i \(-0.0751119\pi\)
−0.233787 + 0.972288i \(0.575112\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) −6.00958 6.00958i −0.575613 0.575613i 0.358079 0.933691i \(-0.383432\pi\)
−0.933691 + 0.358079i \(0.883432\pi\)
\(110\) 5.21672 + 4.23804i 0.497395 + 0.404081i
\(111\) −5.01476 + 3.44271i −0.475980 + 0.326767i
\(112\) −3.05055 3.05055i −0.288250 0.288250i
\(113\) 9.17752 0.863348 0.431674 0.902030i \(-0.357923\pi\)
0.431674 + 0.902030i \(0.357923\pi\)
\(114\) 6.28088 0.588258
\(115\) 5.96948 7.34801i 0.556657 0.685205i
\(116\) −1.51474 + 1.51474i −0.140640 + 0.140640i
\(117\) 6.48482 0.599522
\(118\) 4.46968 4.46968i 0.411467 0.411467i
\(119\) −18.3125 18.3125i −1.67870 1.67870i
\(120\) 2.22418 0.230232i 0.203039 0.0210172i
\(121\) 1.96497 0.178634
\(122\) 7.40088 7.40088i 0.670045 0.670045i
\(123\) −4.81173 + 4.81173i −0.433859 + 0.433859i
\(124\) −1.07252 1.07252i −0.0963153 0.0963153i
\(125\) −5.12276 + 9.93767i −0.458193 + 0.888853i
\(126\) 3.05055 + 3.05055i 0.271765 + 0.271765i
\(127\) 8.41071 + 8.41071i 0.746330 + 0.746330i 0.973788 0.227458i \(-0.0730415\pi\)
−0.227458 + 0.973788i \(0.573042\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 8.34040 8.34040i 0.734331 0.734331i
\(130\) 11.2546 + 9.14318i 0.987095 + 0.801910i
\(131\) 1.85417 + 1.85417i 0.161999 + 0.161999i 0.783452 0.621452i \(-0.213457\pi\)
−0.621452 + 0.783452i \(0.713457\pi\)
\(132\) −2.12544 + 2.12544i −0.184996 + 0.184996i
\(133\) 27.0965i 2.34957i
\(134\) −2.42395 2.42395i −0.209397 0.209397i
\(135\) −2.22418 + 0.230232i −0.191427 + 0.0198152i
\(136\) 6.00301i 0.514754i
\(137\) 6.46226 + 6.46226i 0.552108 + 0.552108i 0.927049 0.374941i \(-0.122337\pi\)
−0.374941 + 0.927049i \(0.622337\pi\)
\(138\) 2.99379 + 2.99379i 0.254848 + 0.254848i
\(139\) 11.3845 0.965623 0.482812 0.875724i \(-0.339616\pi\)
0.482812 + 0.875724i \(0.339616\pi\)
\(140\) 0.993249 + 9.59541i 0.0839449 + 0.810960i
\(141\) 7.51338i 0.632741i
\(142\) 9.18996i 0.771204i
\(143\) −19.4923 −1.63003
\(144\) 1.00000i 0.0833333i
\(145\) 4.76456 0.493194i 0.395676 0.0409575i
\(146\) 2.01404 2.01404i 0.166683 0.166683i
\(147\) −8.21071 + 8.21071i −0.677208 + 0.677208i
\(148\) 1.11161 5.98033i 0.0913735 0.491580i
\(149\) 21.2592i 1.74162i −0.491619 0.870811i \(-0.663595\pi\)
0.491619 0.870811i \(-0.336405\pi\)
\(150\) −4.18476 2.73638i −0.341684 0.223425i
\(151\) 0.529983i 0.0431294i 0.999767 + 0.0215647i \(0.00686480\pi\)
−0.999767 + 0.0215647i \(0.993135\pi\)
\(152\) −4.44125 + 4.44125i −0.360233 + 0.360233i
\(153\) 6.00301i 0.485315i
\(154\) −9.16944 9.16944i −0.738895 0.738895i
\(155\) 0.349210 + 3.37358i 0.0280492 + 0.270973i
\(156\) −4.58546 + 4.58546i −0.367130 + 0.367130i
\(157\) −9.06045 9.06045i −0.723103 0.723103i 0.246133 0.969236i \(-0.420840\pi\)
−0.969236 + 0.246133i \(0.920840\pi\)
\(158\) −6.59707 + 6.59707i −0.524835 + 0.524835i
\(159\) −7.97460 −0.632427
\(160\) −1.40994 + 1.73553i −0.111465 + 0.137206i
\(161\) −12.9156 + 12.9156i −1.01789 + 1.01789i
\(162\) 1.00000i 0.0785674i
\(163\) 21.1810 1.65902 0.829512 0.558489i \(-0.188619\pi\)
0.829512 + 0.558489i \(0.188619\pi\)
\(164\) 6.80482i 0.531367i
\(165\) 6.68552 0.692038i 0.520467 0.0538751i
\(166\) −0.481307 0.481307i −0.0373567 0.0373567i
\(167\) −12.7951 −0.990113 −0.495057 0.868861i \(-0.664853\pi\)
−0.495057 + 0.868861i \(0.664853\pi\)
\(168\) −4.31413 −0.332842
\(169\) −29.0528 −2.23483
\(170\) −8.46387 + 10.4184i −0.649149 + 0.799057i
\(171\) 4.44125 4.44125i 0.339631 0.339631i
\(172\) 11.7951i 0.899369i
\(173\) 4.92625 + 4.92625i 0.374536 + 0.374536i 0.869126 0.494590i \(-0.164682\pi\)
−0.494590 + 0.869126i \(0.664682\pi\)
\(174\) 2.14216i 0.162397i
\(175\) 11.8051 18.0536i 0.892383 1.36472i
\(176\) 3.00583i 0.226573i
\(177\) 6.32108i 0.475122i
\(178\) 4.35292 + 4.35292i 0.326265 + 0.326265i
\(179\) 7.25672 7.25672i 0.542393 0.542393i −0.381837 0.924230i \(-0.624708\pi\)
0.924230 + 0.381837i \(0.124708\pi\)
\(180\) 1.40994 1.73553i 0.105091 0.129359i
\(181\) 9.70338 0.721247 0.360623 0.932712i \(-0.382564\pi\)
0.360623 + 0.932712i \(0.382564\pi\)
\(182\) −19.7823 19.7823i −1.46636 1.46636i
\(183\) 10.4664i 0.773701i
\(184\) −4.23386 −0.312124
\(185\) −10.3611 + 8.81177i −0.761764 + 0.647854i
\(186\) −1.51677 −0.111215
\(187\) 18.0441i 1.31951i
\(188\) −5.31277 5.31277i −0.387473 0.387473i
\(189\) 4.31413 0.313807
\(190\) 13.9698 1.44606i 1.01348 0.104908i
\(191\) −7.13391 + 7.13391i −0.516192 + 0.516192i −0.916417 0.400225i \(-0.868932\pi\)
0.400225 + 0.916417i \(0.368932\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) 19.3360i 1.39184i 0.718121 + 0.695918i \(0.245002\pi\)
−0.718121 + 0.695918i \(0.754998\pi\)
\(194\) 16.2572i 1.16720i
\(195\) 14.4234 1.49301i 1.03288 0.106917i
\(196\) 11.6117i 0.829407i
\(197\) −8.51405 8.51405i −0.606601 0.606601i 0.335455 0.942056i \(-0.391110\pi\)
−0.942056 + 0.335455i \(0.891110\pi\)
\(198\) 3.00583i 0.213615i
\(199\) −4.71139 + 4.71139i −0.333982 + 0.333982i −0.854096 0.520115i \(-0.825889\pi\)
0.520115 + 0.854096i \(0.325889\pi\)
\(200\) 4.89399 1.02416i 0.346057 0.0724187i
\(201\) −3.42798 −0.241791
\(202\) 16.3032 1.14709
\(203\) −9.24157 −0.648631
\(204\) −4.24477 4.24477i −0.297193 0.297193i
\(205\) −9.59437 + 11.8100i −0.670100 + 0.824846i
\(206\) 8.32869i 0.580287i
\(207\) 4.23386 0.294274
\(208\) 6.48482i 0.449641i
\(209\) −13.3497 + 13.3497i −0.923416 + 0.923416i
\(210\) 7.48731 + 6.08265i 0.516674 + 0.419743i
\(211\) −19.7786 −1.36161 −0.680806 0.732464i \(-0.738370\pi\)
−0.680806 + 0.732464i \(0.738370\pi\)
\(212\) 5.63889 5.63889i 0.387281 0.387281i
\(213\) −6.49828 6.49828i −0.445255 0.445255i
\(214\) −7.63911 + 7.63911i −0.522199 + 0.522199i
\(215\) 16.6304 20.4708i 1.13418 1.39610i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) 6.54356i 0.444206i
\(218\) 6.00958 6.00958i 0.407020 0.407020i
\(219\) 2.84828i 0.192469i
\(220\) −4.23804 + 5.21672i −0.285728 + 0.351711i
\(221\) 38.9284i 2.61861i
\(222\) −3.44271 5.01476i −0.231059 0.336568i
\(223\) 4.53283 4.53283i 0.303540 0.303540i −0.538857 0.842397i \(-0.681144\pi\)
0.842397 + 0.538857i \(0.181144\pi\)
\(224\) 3.05055 3.05055i 0.203823 0.203823i
\(225\) −4.89399 + 1.02416i −0.326266 + 0.0682770i
\(226\) 9.17752i 0.610479i
\(227\) 12.5323 0.831799 0.415899 0.909411i \(-0.363467\pi\)
0.415899 + 0.909411i \(0.363467\pi\)
\(228\) 6.28088i 0.415961i
\(229\) 20.0623i 1.32575i 0.748728 + 0.662877i \(0.230665\pi\)
−0.748728 + 0.662877i \(0.769335\pi\)
\(230\) 7.34801 + 5.96948i 0.484513 + 0.393616i
\(231\) −12.9675 −0.853202
\(232\) −1.51474 1.51474i −0.0994474 0.0994474i
\(233\) −4.10021 4.10021i −0.268614 0.268614i 0.559928 0.828542i \(-0.310829\pi\)
−0.828542 + 0.559928i \(0.810829\pi\)
\(234\) 6.48482i 0.423926i
\(235\) 1.72982 + 16.7111i 0.112841 + 1.09012i
\(236\) 4.46968 + 4.46968i 0.290951 + 0.290951i
\(237\) 9.32966i 0.606027i
\(238\) 18.3125 18.3125i 1.18702 1.18702i
\(239\) −9.03944 9.03944i −0.584713 0.584713i 0.351482 0.936195i \(-0.385678\pi\)
−0.936195 + 0.351482i \(0.885678\pi\)
\(240\) 0.230232 + 2.22418i 0.0148614 + 0.143570i
\(241\) 7.69908 7.69908i 0.495942 0.495942i −0.414230 0.910172i \(-0.635949\pi\)
0.910172 + 0.414230i \(0.135949\pi\)
\(242\) 1.96497i 0.126313i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 7.40088 + 7.40088i 0.473793 + 0.473793i
\(245\) −16.3718 + 20.1525i −1.04595 + 1.28750i
\(246\) −4.81173 4.81173i −0.306785 0.306785i
\(247\) −28.8007 + 28.8007i −1.83255 + 1.83255i
\(248\) 1.07252 1.07252i 0.0681052 0.0681052i
\(249\) −0.680671 −0.0431358
\(250\) −9.93767 5.12276i −0.628514 0.323992i
\(251\) 9.83570 + 9.83570i 0.620824 + 0.620824i 0.945742 0.324918i \(-0.105337\pi\)
−0.324918 + 0.945742i \(0.605337\pi\)
\(252\) −3.05055 + 3.05055i −0.192167 + 0.192167i
\(253\) −12.7263 −0.800094
\(254\) −8.41071 + 8.41071i −0.527735 + 0.527735i
\(255\) 1.38208 + 13.3518i 0.0865495 + 0.836122i
\(256\) 1.00000 0.0625000
\(257\) 3.77576 0.235525 0.117763 0.993042i \(-0.462428\pi\)
0.117763 + 0.993042i \(0.462428\pi\)
\(258\) 8.34040 + 8.34040i 0.519251 + 0.519251i
\(259\) 21.6343 14.8523i 1.34429 0.922876i
\(260\) −9.14318 + 11.2546i −0.567036 + 0.697982i
\(261\) 1.51474 + 1.51474i 0.0937599 + 0.0937599i
\(262\) −1.85417 + 1.85417i −0.114551 + 0.114551i
\(263\) 9.85731 + 9.85731i 0.607828 + 0.607828i 0.942378 0.334550i \(-0.108584\pi\)
−0.334550 + 0.942378i \(0.608584\pi\)
\(264\) −2.12544 2.12544i −0.130812 0.130812i
\(265\) −17.7370 + 1.83601i −1.08957 + 0.112785i
\(266\) −27.0965 −1.66139
\(267\) 6.15596 0.376739
\(268\) 2.42395 2.42395i 0.148066 0.148066i
\(269\) 25.0749i 1.52884i 0.644716 + 0.764422i \(0.276975\pi\)
−0.644716 + 0.764422i \(0.723025\pi\)
\(270\) −0.230232 2.22418i −0.0140115 0.135360i
\(271\) −24.0884 −1.46326 −0.731632 0.681700i \(-0.761241\pi\)
−0.731632 + 0.681700i \(0.761241\pi\)
\(272\) 6.00301 0.363986
\(273\) −27.9763 −1.69320
\(274\) −6.46226 + 6.46226i −0.390399 + 0.390399i
\(275\) 14.7105 3.07844i 0.887077 0.185637i
\(276\) −2.99379 + 2.99379i −0.180205 + 0.180205i
\(277\) 16.3414i 0.981859i −0.871199 0.490929i \(-0.836657\pi\)
0.871199 0.490929i \(-0.163343\pi\)
\(278\) 11.3845i 0.682799i
\(279\) −1.07252 + 1.07252i −0.0642102 + 0.0642102i
\(280\) −9.59541 + 0.993249i −0.573436 + 0.0593580i
\(281\) −11.9540 + 11.9540i −0.713117 + 0.713117i −0.967186 0.254069i \(-0.918231\pi\)
0.254069 + 0.967186i \(0.418231\pi\)
\(282\) −7.51338 −0.447416
\(283\) −10.0542 −0.597658 −0.298829 0.954307i \(-0.596596\pi\)
−0.298829 + 0.954307i \(0.596596\pi\)
\(284\) 9.18996 0.545324
\(285\) 8.85565 10.9007i 0.524563 0.645701i
\(286\) 19.4923i 1.15260i
\(287\) 20.7584 20.7584i 1.22533 1.22533i
\(288\) −1.00000 −0.0589256
\(289\) 19.0362 1.11977
\(290\) 0.493194 + 4.76456i 0.0289613 + 0.279785i
\(291\) 11.4956 + 11.4956i 0.673884 + 0.673884i
\(292\) 2.01404 + 2.01404i 0.117863 + 0.117863i
\(293\) 8.47560 8.47560i 0.495150 0.495150i −0.414774 0.909924i \(-0.636139\pi\)
0.909924 + 0.414774i \(0.136139\pi\)
\(294\) −8.21071 8.21071i −0.478858 0.478858i
\(295\) −1.45531 14.0592i −0.0847316 0.818561i
\(296\) 5.98033 + 1.11161i 0.347600 + 0.0646108i
\(297\) 2.12544 + 2.12544i 0.123331 + 0.123331i
\(298\) 21.2592 1.23151
\(299\) −27.4558 −1.58781
\(300\) 2.73638 4.18476i 0.157985 0.241607i
\(301\) −35.9816 + 35.9816i −2.07394 + 2.07394i
\(302\) −0.529983 −0.0304971
\(303\) 11.5281 11.5281i 0.662273 0.662273i
\(304\) −4.44125 4.44125i −0.254723 0.254723i
\(305\) −2.40970 23.2793i −0.137979 1.33297i
\(306\) −6.00301 −0.343169
\(307\) −2.69632 + 2.69632i −0.153887 + 0.153887i −0.779852 0.625964i \(-0.784706\pi\)
0.625964 + 0.779852i \(0.284706\pi\)
\(308\) 9.16944 9.16944i 0.522477 0.522477i
\(309\) 5.88927 + 5.88927i 0.335029 + 0.335029i
\(310\) −3.37358 + 0.349210i −0.191607 + 0.0198338i
\(311\) −6.10837 6.10837i −0.346374 0.346374i 0.512383 0.858757i \(-0.328763\pi\)
−0.858757 + 0.512383i \(0.828763\pi\)
\(312\) −4.58546 4.58546i −0.259600 0.259600i
\(313\) 22.7166i 1.28402i −0.766697 0.642009i \(-0.778101\pi\)
0.766697 0.642009i \(-0.221899\pi\)
\(314\) 9.06045 9.06045i 0.511311 0.511311i
\(315\) 9.59541 0.993249i 0.540640 0.0559632i
\(316\) −6.59707 6.59707i −0.371114 0.371114i
\(317\) 17.3373 17.3373i 0.973762 0.973762i −0.0259029 0.999664i \(-0.508246\pi\)
0.999664 + 0.0259029i \(0.00824608\pi\)
\(318\) 7.97460i 0.447193i
\(319\) −4.55305 4.55305i −0.254922 0.254922i
\(320\) −1.73553 1.40994i −0.0970193 0.0788179i
\(321\) 10.8033i 0.602983i
\(322\) −12.9156 12.9156i −0.719758 0.719758i
\(323\) −26.6609 26.6609i −1.48345 1.48345i
\(324\) 1.00000 0.0555556
\(325\) 31.7366 6.64146i 1.76043 0.368402i
\(326\) 21.1810i 1.17311i
\(327\) 8.49882i 0.469986i
\(328\) 6.80482 0.375733
\(329\) 32.4137i 1.78703i
\(330\) 0.692038 + 6.68552i 0.0380954 + 0.368026i
\(331\) −0.296981 + 0.296981i −0.0163236 + 0.0163236i −0.715221 0.698898i \(-0.753674\pi\)
0.698898 + 0.715221i \(0.253674\pi\)
\(332\) 0.481307 0.481307i 0.0264152 0.0264152i
\(333\) −5.98033 1.11161i −0.327720 0.0609157i
\(334\) 12.7951i 0.700116i
\(335\) −7.62446 + 0.789230i −0.416569 + 0.0431202i
\(336\) 4.31413i 0.235355i
\(337\) −12.3894 + 12.3894i −0.674892 + 0.674892i −0.958840 0.283948i \(-0.908356\pi\)
0.283948 + 0.958840i \(0.408356\pi\)
\(338\) 29.0528i 1.58027i
\(339\) 6.48948 + 6.48948i 0.352460 + 0.352460i
\(340\) −10.4184 8.46387i −0.565019 0.459018i
\(341\) 3.22382 3.22382i 0.174580 0.174580i
\(342\) 4.44125 + 4.44125i 0.240155 + 0.240155i
\(343\) 14.0682 14.0682i 0.759612 0.759612i
\(344\) −11.7951 −0.635950
\(345\) 9.41688 0.974769i 0.506988 0.0524798i
\(346\) −4.92625 + 4.92625i −0.264837 + 0.264837i
\(347\) 21.8151i 1.17110i 0.810637 + 0.585549i \(0.199121\pi\)
−0.810637 + 0.585549i \(0.800879\pi\)
\(348\) −2.14216 −0.114832
\(349\) 0.296683i 0.0158811i 0.999968 + 0.00794054i \(0.00252758\pi\)
−0.999968 + 0.00794054i \(0.997472\pi\)
\(350\) 18.0536 + 11.8051i 0.965005 + 0.631010i
\(351\) 4.58546 + 4.58546i 0.244754 + 0.244754i
\(352\) 3.00583 0.160211
\(353\) −1.99266 −0.106058 −0.0530292 0.998593i \(-0.516888\pi\)
−0.0530292 + 0.998593i \(0.516888\pi\)
\(354\) 6.32108 0.335962
\(355\) −15.9495 12.9573i −0.846511 0.687700i
\(356\) −4.35292 + 4.35292i −0.230704 + 0.230704i
\(357\) 25.8978i 1.37066i
\(358\) 7.25672 + 7.25672i 0.383530 + 0.383530i
\(359\) 10.3520i 0.546358i 0.961963 + 0.273179i \(0.0880752\pi\)
−0.961963 + 0.273179i \(0.911925\pi\)
\(360\) 1.73553 + 1.40994i 0.0914707 + 0.0743102i
\(361\) 20.4495i 1.07629i
\(362\) 9.70338i 0.509998i
\(363\) 1.38944 + 1.38944i 0.0729268 + 0.0729268i
\(364\) 19.7823 19.7823i 1.03687 1.03687i
\(365\) −0.655764 6.33510i −0.0343243 0.331594i
\(366\) 10.4664 0.547089
\(367\) 0.446811 + 0.446811i 0.0233233 + 0.0233233i 0.718672 0.695349i \(-0.244750\pi\)
−0.695349 + 0.718672i \(0.744750\pi\)
\(368\) 4.23386i 0.220705i
\(369\) −6.80482 −0.354245
\(370\) −8.81177 10.3611i −0.458102 0.538649i
\(371\) 34.4034 1.78614
\(372\) 1.51677i 0.0786411i
\(373\) 19.8830 + 19.8830i 1.02950 + 1.02950i 0.999551 + 0.0299526i \(0.00953562\pi\)
0.0299526 + 0.999551i \(0.490464\pi\)
\(374\) 18.0441 0.933036
\(375\) −10.6493 + 3.40466i −0.549929 + 0.175816i
\(376\) 5.31277 5.31277i 0.273985 0.273985i
\(377\) −9.82280 9.82280i −0.505900 0.505900i
\(378\) 4.31413i 0.221895i
\(379\) 2.16219i 0.111064i 0.998457 + 0.0555322i \(0.0176855\pi\)
−0.998457 + 0.0555322i \(0.982314\pi\)
\(380\) 1.44606 + 13.9698i 0.0741812 + 0.716637i
\(381\) 11.8945i 0.609376i
\(382\) −7.13391 7.13391i −0.365003 0.365003i
\(383\) 28.0841i 1.43503i −0.696543 0.717515i \(-0.745279\pi\)
0.696543 0.717515i \(-0.254721\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) −28.8422 + 2.98554i −1.46994 + 0.152157i
\(386\) −19.3360 −0.984177
\(387\) 11.7951 0.599579
\(388\) −16.2572 −0.825336
\(389\) −8.88959 8.88959i −0.450720 0.450720i 0.444873 0.895594i \(-0.353249\pi\)
−0.895594 + 0.444873i \(0.853249\pi\)
\(390\) 1.49301 + 14.4234i 0.0756015 + 0.730358i
\(391\) 25.4159i 1.28534i
\(392\) 11.6117 0.586479
\(393\) 2.62219i 0.132272i
\(394\) 8.51405 8.51405i 0.428932 0.428932i
\(395\) 2.14798 + 20.7509i 0.108077 + 1.04409i
\(396\) −3.00583 −0.151049
\(397\) −2.71530 + 2.71530i −0.136277 + 0.136277i −0.771955 0.635678i \(-0.780721\pi\)
0.635678 + 0.771955i \(0.280721\pi\)
\(398\) −4.71139 4.71139i −0.236161 0.236161i
\(399\) −19.1601 + 19.1601i −0.959206 + 0.959206i
\(400\) 1.02416 + 4.89399i 0.0512078 + 0.244699i
\(401\) 12.5140 + 12.5140i 0.624919 + 0.624919i 0.946785 0.321866i \(-0.104310\pi\)
−0.321866 + 0.946785i \(0.604310\pi\)
\(402\) 3.42798i 0.170972i
\(403\) 6.95511 6.95511i 0.346458 0.346458i
\(404\) 16.3032i 0.811115i
\(405\) −1.73553 1.40994i −0.0862394 0.0700603i
\(406\) 9.24157i 0.458651i
\(407\) 17.9759 + 3.34130i 0.891031 + 0.165622i
\(408\) 4.24477 4.24477i 0.210148 0.210148i
\(409\) −19.7886 + 19.7886i −0.978486 + 0.978486i −0.999773 0.0212876i \(-0.993223\pi\)
0.0212876 + 0.999773i \(0.493223\pi\)
\(410\) −11.8100 9.59437i −0.583254 0.473832i
\(411\) 9.13901i 0.450794i
\(412\) −8.32869 −0.410325
\(413\) 27.2700i 1.34187i
\(414\) 4.23386i 0.208083i
\(415\) −1.51394 + 0.156712i −0.0743163 + 0.00769269i
\(416\) 6.48482 0.317944
\(417\) 8.05008 + 8.05008i 0.394214 + 0.394214i
\(418\) −13.3497 13.3497i −0.652953 0.652953i
\(419\) 21.0888i 1.03026i 0.857113 + 0.515129i \(0.172256\pi\)
−0.857113 + 0.515129i \(0.827744\pi\)
\(420\) −6.08265 + 7.48731i −0.296803 + 0.365344i
\(421\) 0.620287 + 0.620287i 0.0302309 + 0.0302309i 0.722061 0.691830i \(-0.243195\pi\)
−0.691830 + 0.722061i \(0.743195\pi\)
\(422\) 19.7786i 0.962805i
\(423\) −5.31277 + 5.31277i −0.258315 + 0.258315i
\(424\) 5.63889 + 5.63889i 0.273849 + 0.273849i
\(425\) 6.14802 + 29.3787i 0.298223 + 1.42507i
\(426\) 6.49828 6.49828i 0.314843 0.314843i
\(427\) 45.1535i 2.18513i
\(428\) −7.63911 7.63911i −0.369250 0.369250i
\(429\) −13.7831 13.7831i −0.665455 0.665455i
\(430\) 20.4708 + 16.6304i 0.987190 + 0.801987i
\(431\) 19.6454 + 19.6454i 0.946286 + 0.946286i 0.998629 0.0523433i \(-0.0166690\pi\)
−0.0523433 + 0.998629i \(0.516669\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) −26.4568 + 26.4568i −1.27143 + 1.27143i −0.326095 + 0.945337i \(0.605733\pi\)
−0.945337 + 0.326095i \(0.894267\pi\)
\(434\) 6.54356 0.314101
\(435\) 3.71780 + 3.02032i 0.178255 + 0.144813i
\(436\) 6.00958 + 6.00958i 0.287806 + 0.287806i
\(437\) −18.8036 + 18.8036i −0.899500 + 0.899500i
\(438\) 2.84828 0.136096
\(439\) 15.3968 15.3968i 0.734850 0.734850i −0.236726 0.971576i \(-0.576074\pi\)
0.971576 + 0.236726i \(0.0760744\pi\)
\(440\) −5.21672 4.23804i −0.248698 0.202040i
\(441\) −11.6117 −0.552938
\(442\) 38.9284 1.85164
\(443\) 13.4474 + 13.4474i 0.638907 + 0.638907i 0.950286 0.311379i \(-0.100791\pi\)
−0.311379 + 0.950286i \(0.600791\pi\)
\(444\) 5.01476 3.44271i 0.237990 0.163384i
\(445\) 13.6920 1.41730i 0.649062 0.0671863i
\(446\) 4.53283 + 4.53283i 0.214636 + 0.214636i
\(447\) 15.0325 15.0325i 0.711014 0.711014i
\(448\) 3.05055 + 3.05055i 0.144125 + 0.144125i
\(449\) 0.109620 + 0.109620i 0.00517328 + 0.00517328i 0.709689 0.704515i \(-0.248836\pi\)
−0.704515 + 0.709689i \(0.748836\pi\)
\(450\) −1.02416 4.89399i −0.0482791 0.230705i
\(451\) 20.4542 0.963148
\(452\) −9.17752 −0.431674
\(453\) −0.374755 + 0.374755i −0.0176075 + 0.0176075i
\(454\) 12.5323i 0.588170i
\(455\) −62.2245 + 6.44104i −2.91713 + 0.301960i
\(456\) −6.28088 −0.294129
\(457\) −7.05088 −0.329826 −0.164913 0.986308i \(-0.552734\pi\)
−0.164913 + 0.986308i \(0.552734\pi\)
\(458\) −20.0623 −0.937450
\(459\) −4.24477 + 4.24477i −0.198129 + 0.198129i
\(460\) −5.96948 + 7.34801i −0.278328 + 0.342603i
\(461\) 0.0298156 0.0298156i 0.00138865 0.00138865i −0.706412 0.707801i \(-0.749687\pi\)
0.707801 + 0.706412i \(0.249687\pi\)
\(462\) 12.9675i 0.603305i
\(463\) 5.26855i 0.244850i 0.992478 + 0.122425i \(0.0390671\pi\)
−0.992478 + 0.122425i \(0.960933\pi\)
\(464\) 1.51474 1.51474i 0.0703200 0.0703200i
\(465\) −2.13856 + 2.63241i −0.0991732 + 0.122075i
\(466\) 4.10021 4.10021i 0.189939 0.189939i
\(467\) 8.16999 0.378062 0.189031 0.981971i \(-0.439465\pi\)
0.189031 + 0.981971i \(0.439465\pi\)
\(468\) −6.48482 −0.299761
\(469\) 14.7887 0.682881
\(470\) −16.7111 + 1.72982i −0.770828 + 0.0797906i
\(471\) 12.8134i 0.590411i
\(472\) −4.46968 + 4.46968i −0.205734 + 0.205734i
\(473\) −35.4541 −1.63018
\(474\) −9.32966 −0.428526
\(475\) 17.1869 26.2840i 0.788589 1.20599i
\(476\) 18.3125 + 18.3125i 0.839352 + 0.839352i
\(477\) −5.63889 5.63889i −0.258187 0.258187i
\(478\) 9.03944 9.03944i 0.413454 0.413454i
\(479\) 8.69240 + 8.69240i 0.397166 + 0.397166i 0.877232 0.480066i \(-0.159387\pi\)
−0.480066 + 0.877232i \(0.659387\pi\)
\(480\) −2.22418 + 0.230232i −0.101520 + 0.0105086i
\(481\) 38.7813 + 7.20856i 1.76828 + 0.328682i
\(482\) 7.69908 + 7.69908i 0.350684 + 0.350684i
\(483\) −18.2654 −0.831105
\(484\) −1.96497 −0.0893168
\(485\) 28.2150 + 22.9217i 1.28118 + 1.04082i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 25.3749 1.14984 0.574922 0.818208i \(-0.305032\pi\)
0.574922 + 0.818208i \(0.305032\pi\)
\(488\) −7.40088 + 7.40088i −0.335022 + 0.335022i
\(489\) 14.9772 + 14.9772i 0.677294 + 0.677294i
\(490\) −20.1525 16.3718i −0.910397 0.739601i
\(491\) −34.9666 −1.57802 −0.789009 0.614381i \(-0.789406\pi\)
−0.789009 + 0.614381i \(0.789406\pi\)
\(492\) 4.81173 4.81173i 0.216930 0.216930i
\(493\) 9.09299 9.09299i 0.409528 0.409528i
\(494\) −28.8007 28.8007i −1.29581 1.29581i
\(495\) 5.21672 + 4.23804i 0.234474 + 0.190486i
\(496\) 1.07252 + 1.07252i 0.0481576 + 0.0481576i
\(497\) 28.0344 + 28.0344i 1.25752 + 1.25752i
\(498\) 0.680671i 0.0305016i
\(499\) −0.199787 + 0.199787i −0.00894368 + 0.00894368i −0.711564 0.702621i \(-0.752013\pi\)
0.702621 + 0.711564i \(0.252013\pi\)
\(500\) 5.12276 9.93767i 0.229097 0.444426i
\(501\) −9.04749 9.04749i −0.404212 0.404212i
\(502\) −9.83570 + 9.83570i −0.438989 + 0.438989i
\(503\) 16.3722i 0.729999i 0.931008 + 0.365000i \(0.118931\pi\)
−0.931008 + 0.365000i \(0.881069\pi\)
\(504\) −3.05055 3.05055i −0.135882 0.135882i
\(505\) 22.9865 28.2948i 1.02289 1.25910i
\(506\) 12.7263i 0.565752i
\(507\) −20.5435 20.5435i −0.912367 0.912367i
\(508\) −8.41071 8.41071i −0.373165 0.373165i
\(509\) 32.3903 1.43568 0.717838 0.696210i \(-0.245132\pi\)
0.717838 + 0.696210i \(0.245132\pi\)
\(510\) −13.3518 + 1.38208i −0.591228 + 0.0611997i
\(511\) 12.2878i 0.543582i
\(512\) 1.00000i 0.0441942i
\(513\) 6.28088 0.277308
\(514\) 3.77576i 0.166541i
\(515\) 14.4547 + 11.7429i 0.636951 + 0.517455i
\(516\) −8.34040 + 8.34040i −0.367166 + 0.367166i
\(517\) 15.9693 15.9693i 0.702328 0.702328i
\(518\) 14.8523 + 21.6343i 0.652572 + 0.950556i
\(519\) 6.96677i 0.305807i
\(520\) −11.2546 9.14318i −0.493548 0.400955i
\(521\) 17.4138i 0.762914i 0.924387 + 0.381457i \(0.124578\pi\)
−0.924387 + 0.381457i \(0.875422\pi\)
\(522\) −1.51474 + 1.51474i −0.0662983 + 0.0662983i
\(523\) 38.1149i 1.66665i −0.552784 0.833325i \(-0.686434\pi\)
0.552784 0.833325i \(-0.313566\pi\)
\(524\) −1.85417 1.85417i −0.0809997 0.0809997i
\(525\) 21.1133 4.41834i 0.921459 0.192832i
\(526\) −9.85731 + 9.85731i −0.429799 + 0.429799i
\(527\) 6.43836 + 6.43836i 0.280459 + 0.280459i
\(528\) 2.12544 2.12544i 0.0924981 0.0924981i
\(529\) 5.07442 0.220627
\(530\) −1.83601 17.7370i −0.0797510 0.770445i
\(531\) 4.46968 4.46968i 0.193968 0.193968i
\(532\) 27.0965i 1.17478i
\(533\) 44.1280 1.91140
\(534\) 6.15596i 0.266394i
\(535\) 2.48727 + 24.0286i 0.107534 + 1.03885i
\(536\) 2.42395 + 2.42395i 0.104699 + 0.104699i
\(537\) 10.2626 0.442862
\(538\) −25.0749 −1.08106
\(539\) 34.9028 1.50337
\(540\) 2.22418 0.230232i 0.0957136 0.00990759i
\(541\) −27.4040 + 27.4040i −1.17819 + 1.17819i −0.197986 + 0.980205i \(0.563440\pi\)
−0.980205 + 0.197986i \(0.936560\pi\)
\(542\) 24.0884i 1.03468i
\(543\) 6.86133 + 6.86133i 0.294448 + 0.294448i
\(544\) 6.00301i 0.257377i
\(545\) −1.95670 18.9029i −0.0838158 0.809713i
\(546\) 27.9763i 1.19728i
\(547\) 4.61554i 0.197346i 0.995120 + 0.0986731i \(0.0314598\pi\)
−0.995120 + 0.0986731i \(0.968540\pi\)
\(548\) −6.46226 6.46226i −0.276054 0.276054i
\(549\) 7.40088 7.40088i 0.315862 0.315862i
\(550\) 3.07844 + 14.7105i 0.131265 + 0.627258i
\(551\) −13.4547 −0.573188
\(552\) −2.99379 2.99379i −0.127424 0.127424i
\(553\) 40.2494i 1.71158i
\(554\) 16.3414 0.694279
\(555\) −13.5573 1.09556i −0.575474 0.0465037i
\(556\) −11.3845 −0.482812
\(557\) 6.03445i 0.255688i 0.991794 + 0.127844i \(0.0408056\pi\)
−0.991794 + 0.127844i \(0.959194\pi\)
\(558\) −1.07252 1.07252i −0.0454035 0.0454035i
\(559\) −76.4891 −3.23514
\(560\) −0.993249 9.59541i −0.0419724 0.405480i
\(561\) 12.7591 12.7591i 0.538689 0.538689i
\(562\) −11.9540 11.9540i −0.504250 0.504250i
\(563\) 16.8876i 0.711727i 0.934538 + 0.355863i \(0.115813\pi\)
−0.934538 + 0.355863i \(0.884187\pi\)
\(564\) 7.51338i 0.316371i
\(565\) 15.9279 + 12.9397i 0.670091 + 0.544378i
\(566\) 10.0542i 0.422608i
\(567\) 3.05055 + 3.05055i 0.128111 + 0.128111i
\(568\) 9.18996i 0.385602i
\(569\) 22.0925 22.0925i 0.926168 0.926168i −0.0712881 0.997456i \(-0.522711\pi\)
0.997456 + 0.0712881i \(0.0227110\pi\)
\(570\) 10.9007 + 8.85565i 0.456579 + 0.370922i
\(571\) 28.0375 1.17333 0.586666 0.809829i \(-0.300440\pi\)
0.586666 + 0.809829i \(0.300440\pi\)
\(572\) 19.4923 0.815013
\(573\) −10.0889 −0.421469
\(574\) 20.7584 + 20.7584i 0.866440 + 0.866440i
\(575\) 20.7205 4.33613i 0.864103 0.180829i
\(576\) 1.00000i 0.0416667i
\(577\) 27.2016 1.13242 0.566208 0.824262i \(-0.308410\pi\)
0.566208 + 0.824262i \(0.308410\pi\)
\(578\) 19.0362i 0.791800i
\(579\) −13.6726 + 13.6726i −0.568215 + 0.568215i
\(580\) −4.76456 + 0.493194i −0.197838 + 0.0204788i
\(581\) 2.93650 0.121827
\(582\) −11.4956 + 11.4956i −0.476508 + 0.476508i
\(583\) 16.9496 + 16.9496i 0.701979 + 0.701979i
\(584\) −2.01404 + 2.01404i −0.0833415 + 0.0833415i
\(585\) 11.2546 + 9.14318i 0.465321 + 0.378024i
\(586\) 8.47560 + 8.47560i 0.350124 + 0.350124i
\(587\) 8.46791i 0.349508i −0.984612 0.174754i \(-0.944087\pi\)
0.984612 0.174754i \(-0.0559131\pi\)
\(588\) 8.21071 8.21071i 0.338604 0.338604i
\(589\) 9.52668i 0.392540i
\(590\) 14.0592 1.45531i 0.578810 0.0599143i
\(591\) 12.0407i 0.495288i
\(592\) −1.11161 + 5.98033i −0.0456867 + 0.245790i
\(593\) 6.22133 6.22133i 0.255479 0.255479i −0.567733 0.823213i \(-0.692179\pi\)
0.823213 + 0.567733i \(0.192179\pi\)
\(594\) −2.12544 + 2.12544i −0.0872081 + 0.0872081i
\(595\) −5.96249 57.6014i −0.244438 2.36143i
\(596\) 21.2592i 0.870811i
\(597\) −6.66291 −0.272695
\(598\) 27.4558i 1.12275i
\(599\) 31.7305i 1.29647i −0.761439 0.648236i \(-0.775507\pi\)
0.761439 0.648236i \(-0.224493\pi\)
\(600\) 4.18476 + 2.73638i 0.170842 + 0.111712i
\(601\) −7.01914 −0.286317 −0.143158 0.989700i \(-0.545726\pi\)
−0.143158 + 0.989700i \(0.545726\pi\)
\(602\) −35.9816 35.9816i −1.46650 1.46650i
\(603\) −2.42395 2.42395i −0.0987108 0.0987108i
\(604\) 0.529983i 0.0215647i
\(605\) 3.41027 + 2.77048i 0.138647 + 0.112636i
\(606\) 11.5281 + 11.5281i 0.468297 + 0.468297i
\(607\) 20.9319i 0.849600i 0.905287 + 0.424800i \(0.139656\pi\)
−0.905287 + 0.424800i \(0.860344\pi\)
\(608\) 4.44125 4.44125i 0.180117 0.180117i
\(609\) −6.53477 6.53477i −0.264802 0.264802i
\(610\) 23.2793 2.40970i 0.942550 0.0975661i
\(611\) 34.4523 34.4523i 1.39379 1.39379i
\(612\) 6.00301i 0.242657i
\(613\) −3.66683 3.66683i −0.148102 0.148102i 0.629168 0.777270i \(-0.283396\pi\)
−0.777270 + 0.629168i \(0.783396\pi\)
\(614\) −2.69632 2.69632i −0.108815 0.108815i
\(615\) −15.1352 + 1.56669i −0.610309 + 0.0631748i
\(616\) 9.16944 + 9.16944i 0.369447 + 0.369447i
\(617\) −3.93991 + 3.93991i −0.158615 + 0.158615i −0.781953 0.623338i \(-0.785776\pi\)
0.623338 + 0.781953i \(0.285776\pi\)
\(618\) −5.88927 + 5.88927i −0.236901 + 0.236901i
\(619\) −17.6521 −0.709496 −0.354748 0.934962i \(-0.615433\pi\)
−0.354748 + 0.934962i \(0.615433\pi\)
\(620\) −0.349210 3.37358i −0.0140246 0.135486i
\(621\) 2.99379 + 2.99379i 0.120137 + 0.120137i
\(622\) 6.10837 6.10837i 0.244924 0.244924i
\(623\) −26.5576 −1.06401
\(624\) 4.58546 4.58546i 0.183565 0.183565i
\(625\) −22.9022 + 10.0244i −0.916088 + 0.400976i
\(626\) 22.7166 0.907938
\(627\) −18.8793 −0.753966
\(628\) 9.06045 + 9.06045i 0.361551 + 0.361551i
\(629\) −6.67299 + 35.9000i −0.266069 + 1.43143i
\(630\) 0.993249 + 9.59541i 0.0395720 + 0.382290i
\(631\) −14.6419 14.6419i −0.582883 0.582883i 0.352811 0.935695i \(-0.385226\pi\)
−0.935695 + 0.352811i \(0.885226\pi\)
\(632\) 6.59707 6.59707i 0.262417 0.262417i
\(633\) −13.9855 13.9855i −0.555876 0.555876i
\(634\) 17.3373 + 17.3373i 0.688553 + 0.688553i
\(635\) 2.73850 + 26.4556i 0.108674 + 1.04986i
\(636\) 7.97460 0.316213
\(637\) 75.2997 2.98348
\(638\) 4.55305 4.55305i 0.180257 0.180257i
\(639\) 9.18996i 0.363549i
\(640\) 1.40994 1.73553i 0.0557327 0.0686030i
\(641\) 41.2135 1.62783 0.813917 0.580981i \(-0.197331\pi\)
0.813917 + 0.580981i \(0.197331\pi\)
\(642\) −10.8033 −0.426374
\(643\) −16.5141 −0.651254 −0.325627 0.945498i \(-0.605575\pi\)
−0.325627 + 0.945498i \(0.605575\pi\)
\(644\) 12.9156 12.9156i 0.508946 0.508946i
\(645\) 26.2345 2.71561i 1.03298 0.106927i
\(646\) 26.6609 26.6609i 1.04896 1.04896i
\(647\) 48.9342i 1.92380i −0.273401 0.961900i \(-0.588149\pi\)
0.273401 0.961900i \(-0.411851\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −13.4351 + 13.4351i −0.527374 + 0.527374i
\(650\) 6.64146 + 31.7366i 0.260499 + 1.24481i
\(651\) 4.62699 4.62699i 0.181346 0.181346i
\(652\) −21.1810 −0.829512
\(653\) 15.4749 0.605581 0.302791 0.953057i \(-0.402082\pi\)
0.302791 + 0.953057i \(0.402082\pi\)
\(654\) 8.49882 0.332330
\(655\) 0.603711 + 5.83223i 0.0235889 + 0.227884i
\(656\) 6.80482i 0.265684i
\(657\) 2.01404 2.01404i 0.0785751 0.0785751i
\(658\) 32.4137 1.26362
\(659\) 36.9284 1.43853 0.719264 0.694737i \(-0.244479\pi\)
0.719264 + 0.694737i \(0.244479\pi\)
\(660\) −6.68552 + 0.692038i −0.260234 + 0.0269375i
\(661\) −11.4256 11.4256i −0.444405 0.444405i 0.449084 0.893489i \(-0.351750\pi\)
−0.893489 + 0.449084i \(0.851750\pi\)
\(662\) −0.296981 0.296981i −0.0115425 0.0115425i
\(663\) 27.5266 27.5266i 1.06904 1.06904i
\(664\) 0.481307 + 0.481307i 0.0186783 + 0.0186783i
\(665\) −38.2044 + 47.0269i −1.48150 + 1.82363i
\(666\) 1.11161 5.98033i 0.0430739 0.231733i
\(667\) −6.41319 6.41319i −0.248320 0.248320i
\(668\) 12.7951 0.495057
\(669\) 6.41038 0.247840
\(670\) −0.789230 7.62446i −0.0304906 0.294559i
\(671\) −22.2458 + 22.2458i −0.858790 + 0.858790i
\(672\) 4.31413 0.166421
\(673\) 21.5091 21.5091i 0.829113 0.829113i −0.158281 0.987394i \(-0.550595\pi\)
0.987394 + 0.158281i \(0.0505952\pi\)
\(674\) −12.3894 12.3894i −0.477220 0.477220i
\(675\) −4.18476 2.73638i −0.161071 0.105323i
\(676\) 29.0528 1.11742
\(677\) 10.9295 10.9295i 0.420053 0.420053i −0.465169 0.885222i \(-0.654006\pi\)
0.885222 + 0.465169i \(0.154006\pi\)
\(678\) −6.48948 + 6.48948i −0.249227 + 0.249227i
\(679\) −49.5935 49.5935i −1.90322 1.90322i
\(680\) 8.46387 10.4184i 0.324575 0.399529i
\(681\) 8.86168 + 8.86168i 0.339580 + 0.339580i
\(682\) 3.22382 + 3.22382i 0.123446 + 0.123446i
\(683\) 14.1654i 0.542024i 0.962576 + 0.271012i \(0.0873584\pi\)
−0.962576 + 0.271012i \(0.912642\pi\)
\(684\) −4.44125 + 4.44125i −0.169816 + 0.169816i
\(685\) 2.10409 + 20.3268i 0.0803932 + 0.776649i
\(686\) 14.0682 + 14.0682i 0.537127 + 0.537127i
\(687\) −14.1862 + 14.1862i −0.541237 + 0.541237i
\(688\) 11.7951i 0.449684i
\(689\) 36.5672 + 36.5672i 1.39310 + 1.39310i
\(690\) 0.974769 + 9.41688i 0.0371088 + 0.358495i
\(691\) 3.21102i 0.122153i −0.998133 0.0610765i \(-0.980547\pi\)
0.998133 0.0610765i \(-0.0194533\pi\)
\(692\) −4.92625 4.92625i −0.187268 0.187268i
\(693\) −9.16944 9.16944i −0.348318 0.348318i
\(694\) −21.8151 −0.828091
\(695\) 19.7582 + 16.0515i 0.749473 + 0.608867i
\(696\) 2.14216i 0.0811985i
\(697\) 40.8494i 1.54728i
\(698\) −0.296683 −0.0112296
\(699\) 5.79858i 0.219322i
\(700\) −11.8051 + 18.0536i −0.446191 + 0.682361i
\(701\) 7.77755 7.77755i 0.293754 0.293754i −0.544807 0.838561i \(-0.683397\pi\)
0.838561 + 0.544807i \(0.183397\pi\)
\(702\) −4.58546 + 4.58546i −0.173067 + 0.173067i
\(703\) 31.4971 21.6232i 1.18793 0.815536i
\(704\) 3.00583i 0.113287i
\(705\) −10.5934 + 13.0397i −0.398970 + 0.491105i
\(706\) 1.99266i 0.0749946i
\(707\) −49.7337 + 49.7337i −1.87043 + 1.87043i
\(708\) 6.32108i 0.237561i
\(709\) 23.8317 + 23.8317i 0.895018 + 0.895018i 0.994990 0.0999719i \(-0.0318753\pi\)
−0.0999719 + 0.994990i \(0.531875\pi\)
\(710\) 12.9573 15.9495i 0.486278 0.598574i
\(711\) −6.59707 + 6.59707i −0.247409 + 0.247409i
\(712\) −4.35292 4.35292i −0.163133 0.163133i
\(713\) 4.54091 4.54091i 0.170058 0.170058i
\(714\) 25.8978 0.969200
\(715\) −33.8295 27.4829i −1.26515 1.02780i
\(716\) −7.25672 + 7.25672i −0.271196 + 0.271196i
\(717\) 12.7837i 0.477416i
\(718\) −10.3520 −0.386334
\(719\) 35.0794i 1.30824i −0.756391 0.654120i \(-0.773039\pi\)
0.756391 0.654120i \(-0.226961\pi\)
\(720\) −1.40994 + 1.73553i −0.0525453 + 0.0646795i
\(721\) −25.4071 25.4071i −0.946209 0.946209i
\(722\) −20.4495 −0.761050
\(723\) 10.8881 0.404935
\(724\) −9.70338 −0.360623
\(725\) 8.96444 + 5.86178i 0.332931 + 0.217701i
\(726\) −1.38944 + 1.38944i −0.0515671 + 0.0515671i
\(727\) 8.98773i 0.333336i −0.986013 0.166668i \(-0.946699\pi\)
0.986013 0.166668i \(-0.0533009\pi\)
\(728\) 19.7823 + 19.7823i 0.733179 + 0.733179i
\(729\) 1.00000i 0.0370370i
\(730\) 6.33510 0.655764i 0.234473 0.0242709i
\(731\) 70.8062i 2.61886i
\(732\) 10.4664i 0.386850i
\(733\) 1.69194 + 1.69194i 0.0624931 + 0.0624931i 0.737663 0.675170i \(-0.235930\pi\)
−0.675170 + 0.737663i \(0.735930\pi\)
\(734\) −0.446811 + 0.446811i −0.0164921 + 0.0164921i
\(735\) −25.8266 + 2.67338i −0.952627 + 0.0986092i
\(736\) 4.23386 0.156062
\(737\) 7.28598 + 7.28598i 0.268383 + 0.268383i
\(738\) 6.80482i 0.250489i
\(739\) 8.19699 0.301531 0.150765 0.988570i \(-0.451826\pi\)
0.150765 + 0.988570i \(0.451826\pi\)
\(740\) 10.3611 8.81177i 0.380882 0.323927i
\(741\) −40.7304 −1.49627
\(742\) 34.4034i 1.26299i
\(743\) −5.18593 5.18593i −0.190253 0.190253i 0.605552 0.795806i \(-0.292952\pi\)
−0.795806 + 0.605552i \(0.792952\pi\)
\(744\) 1.51677 0.0556076
\(745\) 29.9741 36.8961i 1.09817 1.35177i
\(746\) −19.8830 + 19.8830i −0.727969 + 0.727969i
\(747\) −0.481307 0.481307i −0.0176101 0.0176101i
\(748\) 18.0441i 0.659756i
\(749\) 46.6070i 1.70298i
\(750\) −3.40466 10.6493i −0.124321 0.388859i
\(751\) 7.11165i 0.259508i 0.991546 + 0.129754i \(0.0414187\pi\)
−0.991546 + 0.129754i \(0.958581\pi\)
\(752\) 5.31277 + 5.31277i 0.193737 + 0.193737i
\(753\) 13.9098i 0.506901i
\(754\) 9.82280 9.82280i 0.357725 0.357725i
\(755\) −0.747243 + 0.919804i −0.0271950 + 0.0334751i
\(756\) −4.31413 −0.156903
\(757\) 23.4049 0.850665 0.425332 0.905037i \(-0.360157\pi\)
0.425332 + 0.905037i \(0.360157\pi\)
\(758\) −2.16219 −0.0785343
\(759\) −8.99884 8.99884i −0.326637 0.326637i
\(760\) −13.9698 + 1.44606i −0.506739 + 0.0524540i
\(761\) 10.2257i 0.370683i −0.982674 0.185341i \(-0.940661\pi\)
0.982674 0.185341i \(-0.0593391\pi\)
\(762\) −11.8945 −0.430894
\(763\) 36.6650i 1.32736i
\(764\) 7.13391 7.13391i 0.258096 0.258096i
\(765\) −8.46387 + 10.4184i −0.306012 + 0.376679i
\(766\) 28.0841 1.01472
\(767\) −28.9851 + 28.9851i −1.04659 + 1.04659i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) −35.6398 + 35.6398i −1.28520 + 1.28520i −0.347537 + 0.937666i \(0.612982\pi\)
−0.937666 + 0.347537i \(0.887018\pi\)
\(770\) −2.98554 28.8422i −0.107591 1.03940i
\(771\) 2.66986 + 2.66986i 0.0961528 + 0.0961528i
\(772\) 19.3360i 0.695918i
\(773\) −9.02172 + 9.02172i −0.324489 + 0.324489i −0.850486 0.525997i \(-0.823692\pi\)
0.525997 + 0.850486i \(0.323692\pi\)
\(774\) 11.7951i 0.423966i
\(775\) −4.15048 + 6.34733i −0.149090 + 0.228003i
\(776\) 16.2572i 0.583600i
\(777\) 25.7999 + 4.79561i 0.925566 + 0.172042i
\(778\) 8.88959 8.88959i 0.318707 0.318707i
\(779\) 30.2219 30.2219i 1.08281 1.08281i
\(780\) −14.4234 + 1.49301i −0.516441 + 0.0534583i