Properties

Label 1110.2.l.a.43.5
Level $1110$
Weight $2$
Character 1110.43
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
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: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.5
Character \(\chi\) \(=\) 1110.43
Dual form 1110.2.l.a.697.5

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.943349 - 2.02734i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-0.516238 + 0.516238i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.943349 - 2.02734i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-0.516238 + 0.516238i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(2.02734 - 0.943349i) q^{10} +0.497352i q^{11} +(0.707107 - 0.707107i) q^{12} -1.53056i q^{13} +(-0.516238 - 0.516238i) q^{14} +(2.10059 + 0.766495i) q^{15} +1.00000 q^{16} +2.55573 q^{17} +1.00000 q^{18} +(-2.36425 + 2.36425i) q^{19} +(0.943349 + 2.02734i) q^{20} -0.730071i q^{21} -0.497352 q^{22} +5.13868i q^{23} +(0.707107 + 0.707107i) q^{24} +(-3.22019 + 3.82497i) q^{25} +1.53056 q^{26} +(0.707107 + 0.707107i) q^{27} +(0.516238 - 0.516238i) q^{28} +(7.56116 + 7.56116i) q^{29} +(-0.766495 + 2.10059i) q^{30} +(5.92380 - 5.92380i) q^{31} +1.00000i q^{32} +(-0.351681 - 0.351681i) q^{33} +2.55573i q^{34} +(1.53358 + 0.559596i) q^{35} +1.00000i q^{36} +(-3.93182 - 4.64120i) q^{37} +(-2.36425 - 2.36425i) q^{38} +(1.08227 + 1.08227i) q^{39} +(-2.02734 + 0.943349i) q^{40} +2.70364i q^{41} +0.730071 q^{42} +9.05230i q^{43} -0.497352i q^{44} +(-2.02734 + 0.943349i) q^{45} -5.13868 q^{46} +(-9.26908 + 9.26908i) q^{47} +(-0.707107 + 0.707107i) q^{48} +6.46700i q^{49} +(-3.82497 - 3.22019i) q^{50} +(-1.80718 + 1.80718i) q^{51} +1.53056i q^{52} +(-0.413793 - 0.413793i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(1.00830 - 0.469177i) q^{55} +(0.516238 + 0.516238i) q^{56} -3.34355i q^{57} +(-7.56116 + 7.56116i) q^{58} +(-5.91307 + 5.91307i) q^{59} +(-2.10059 - 0.766495i) q^{60} +(10.7956 - 10.7956i) q^{61} +(5.92380 + 5.92380i) q^{62} +(0.516238 + 0.516238i) q^{63} -1.00000 q^{64} +(-3.10295 + 1.44385i) q^{65} +(0.351681 - 0.351681i) q^{66} +(9.29726 + 9.29726i) q^{67} -2.55573 q^{68} +(-3.63359 - 3.63359i) q^{69} +(-0.559596 + 1.53358i) q^{70} -4.10631 q^{71} -1.00000 q^{72} +(2.63103 - 2.63103i) q^{73} +(4.64120 - 3.93182i) q^{74} +(-0.427648 - 4.98168i) q^{75} +(2.36425 - 2.36425i) q^{76} +(-0.256752 - 0.256752i) q^{77} +(-1.08227 + 1.08227i) q^{78} +(0.827925 - 0.827925i) q^{79} +(-0.943349 - 2.02734i) q^{80} -1.00000 q^{81} -2.70364 q^{82} +(11.2038 + 11.2038i) q^{83} +0.730071i q^{84} +(-2.41095 - 5.18133i) q^{85} -9.05230 q^{86} -10.6931 q^{87} +0.497352 q^{88} +(-6.24255 - 6.24255i) q^{89} +(-0.943349 - 2.02734i) q^{90} +(0.790132 + 0.790132i) q^{91} -5.13868i q^{92} +8.37752i q^{93} +(-9.26908 - 9.26908i) q^{94} +(7.02344 + 2.56282i) q^{95} +(-0.707107 - 0.707107i) q^{96} +3.13965 q^{97} -6.46700 q^{98} +0.497352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{4} + 4q^{7} + O(q^{10}) \) \( 36q - 36q^{4} + 4q^{7} - 4q^{10} + 4q^{14} + 36q^{16} - 32q^{17} + 36q^{18} + 4q^{19} + 8q^{22} - 4q^{25} + 8q^{26} - 4q^{28} + 36q^{29} - 4q^{31} + 4q^{33} - 12q^{35} - 4q^{37} + 4q^{38} + 4q^{39} + 4q^{40} - 16q^{42} + 4q^{45} + 16q^{47} - 16q^{50} - 8q^{53} + 16q^{55} - 4q^{56} - 36q^{58} - 4q^{59} - 4q^{61} - 4q^{62} - 4q^{63} - 36q^{64} + 52q^{65} - 4q^{66} + 16q^{67} + 32q^{68} - 8q^{69} - 28q^{70} - 8q^{71} - 36q^{72} - 4q^{73} + 28q^{74} + 16q^{75} - 4q^{76} + 8q^{77} - 4q^{78} - 12q^{79} - 36q^{81} - 8q^{82} + 8q^{83} + 8q^{85} + 32q^{86} - 8q^{87} - 8q^{88} - 24q^{89} + 56q^{91} + 16q^{94} - 20q^{95} + 40q^{97} - 12q^{98} - 8q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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
\(5\) −0.943349 2.02734i −0.421878 0.906652i
\(6\) −0.707107 0.707107i −0.288675 0.288675i
\(7\) −0.516238 + 0.516238i −0.195120 + 0.195120i −0.797904 0.602784i \(-0.794058\pi\)
0.602784 + 0.797904i \(0.294058\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) 2.02734 0.943349i 0.641100 0.298313i
\(11\) 0.497352i 0.149957i 0.997185 + 0.0749787i \(0.0238889\pi\)
−0.997185 + 0.0749787i \(0.976111\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) 1.53056i 0.424500i −0.977215 0.212250i \(-0.931921\pi\)
0.977215 0.212250i \(-0.0680791\pi\)
\(14\) −0.516238 0.516238i −0.137970 0.137970i
\(15\) 2.10059 + 0.766495i 0.542370 + 0.197908i
\(16\) 1.00000 0.250000
\(17\) 2.55573 0.619856 0.309928 0.950760i \(-0.399695\pi\)
0.309928 + 0.950760i \(0.399695\pi\)
\(18\) 1.00000 0.235702
\(19\) −2.36425 + 2.36425i −0.542396 + 0.542396i −0.924231 0.381835i \(-0.875292\pi\)
0.381835 + 0.924231i \(0.375292\pi\)
\(20\) 0.943349 + 2.02734i 0.210939 + 0.453326i
\(21\) 0.730071i 0.159315i
\(22\) −0.497352 −0.106036
\(23\) 5.13868i 1.07149i 0.844380 + 0.535744i \(0.179969\pi\)
−0.844380 + 0.535744i \(0.820031\pi\)
\(24\) 0.707107 + 0.707107i 0.144338 + 0.144338i
\(25\) −3.22019 + 3.82497i −0.644037 + 0.764994i
\(26\) 1.53056 0.300167
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 0.516238 0.516238i 0.0975599 0.0975599i
\(29\) 7.56116 + 7.56116i 1.40407 + 1.40407i 0.786568 + 0.617504i \(0.211856\pi\)
0.617504 + 0.786568i \(0.288144\pi\)
\(30\) −0.766495 + 2.10059i −0.139942 + 0.383514i
\(31\) 5.92380 5.92380i 1.06395 1.06395i 0.0661351 0.997811i \(-0.478933\pi\)
0.997811 0.0661351i \(-0.0210668\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −0.351681 0.351681i −0.0612198 0.0612198i
\(34\) 2.55573i 0.438305i
\(35\) 1.53358 + 0.559596i 0.259223 + 0.0945890i
\(36\) 1.00000i 0.166667i
\(37\) −3.93182 4.64120i −0.646388 0.763009i
\(38\) −2.36425 2.36425i −0.383532 0.383532i
\(39\) 1.08227 + 1.08227i 0.173301 + 0.173301i
\(40\) −2.02734 + 0.943349i −0.320550 + 0.149157i
\(41\) 2.70364i 0.422238i 0.977460 + 0.211119i \(0.0677108\pi\)
−0.977460 + 0.211119i \(0.932289\pi\)
\(42\) 0.730071 0.112652
\(43\) 9.05230i 1.38046i 0.723588 + 0.690232i \(0.242491\pi\)
−0.723588 + 0.690232i \(0.757509\pi\)
\(44\) 0.497352i 0.0749787i
\(45\) −2.02734 + 0.943349i −0.302217 + 0.140626i
\(46\) −5.13868 −0.757656
\(47\) −9.26908 + 9.26908i −1.35203 + 1.35203i −0.468650 + 0.883384i \(0.655260\pi\)
−0.883384 + 0.468650i \(0.844740\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 6.46700i 0.923857i
\(50\) −3.82497 3.22019i −0.540933 0.455403i
\(51\) −1.80718 + 1.80718i −0.253055 + 0.253055i
\(52\) 1.53056i 0.212250i
\(53\) −0.413793 0.413793i −0.0568388 0.0568388i 0.678116 0.734955i \(-0.262797\pi\)
−0.734955 + 0.678116i \(0.762797\pi\)
\(54\) −0.707107 + 0.707107i −0.0962250 + 0.0962250i
\(55\) 1.00830 0.469177i 0.135959 0.0632638i
\(56\) 0.516238 + 0.516238i 0.0689852 + 0.0689852i
\(57\) 3.34355i 0.442865i
\(58\) −7.56116 + 7.56116i −0.992829 + 0.992829i
\(59\) −5.91307 + 5.91307i −0.769817 + 0.769817i −0.978074 0.208257i \(-0.933221\pi\)
0.208257 + 0.978074i \(0.433221\pi\)
\(60\) −2.10059 0.766495i −0.271185 0.0989541i
\(61\) 10.7956 10.7956i 1.38223 1.38223i 0.541586 0.840645i \(-0.317824\pi\)
0.840645 0.541586i \(-0.182176\pi\)
\(62\) 5.92380 + 5.92380i 0.752323 + 0.752323i
\(63\) 0.516238 + 0.516238i 0.0650399 + 0.0650399i
\(64\) −1.00000 −0.125000
\(65\) −3.10295 + 1.44385i −0.384874 + 0.179087i
\(66\) 0.351681 0.351681i 0.0432889 0.0432889i
\(67\) 9.29726 + 9.29726i 1.13584 + 1.13584i 0.989188 + 0.146653i \(0.0468500\pi\)
0.146653 + 0.989188i \(0.453150\pi\)
\(68\) −2.55573 −0.309928
\(69\) −3.63359 3.63359i −0.437433 0.437433i
\(70\) −0.559596 + 1.53358i −0.0668845 + 0.183298i
\(71\) −4.10631 −0.487329 −0.243664 0.969860i \(-0.578350\pi\)
−0.243664 + 0.969860i \(0.578350\pi\)
\(72\) −1.00000 −0.117851
\(73\) 2.63103 2.63103i 0.307938 0.307938i −0.536171 0.844109i \(-0.680130\pi\)
0.844109 + 0.536171i \(0.180130\pi\)
\(74\) 4.64120 3.93182i 0.539529 0.457065i
\(75\) −0.427648 4.98168i −0.0493805 0.575235i
\(76\) 2.36425 2.36425i 0.271198 0.271198i
\(77\) −0.256752 0.256752i −0.0292596 0.0292596i
\(78\) −1.08227 + 1.08227i −0.122543 + 0.122543i
\(79\) 0.827925 0.827925i 0.0931489 0.0931489i −0.658997 0.752146i \(-0.729019\pi\)
0.752146 + 0.658997i \(0.229019\pi\)
\(80\) −0.943349 2.02734i −0.105470 0.226663i
\(81\) −1.00000 −0.111111
\(82\) −2.70364 −0.298567
\(83\) 11.2038 + 11.2038i 1.22978 + 1.22978i 0.964048 + 0.265729i \(0.0856126\pi\)
0.265729 + 0.964048i \(0.414387\pi\)
\(84\) 0.730071i 0.0796573i
\(85\) −2.41095 5.18133i −0.261504 0.561994i
\(86\) −9.05230 −0.976135
\(87\) −10.6931 −1.14642
\(88\) 0.497352 0.0530179
\(89\) −6.24255 6.24255i −0.661709 0.661709i 0.294074 0.955783i \(-0.404989\pi\)
−0.955783 + 0.294074i \(0.904989\pi\)
\(90\) −0.943349 2.02734i −0.0994377 0.213700i
\(91\) 0.790132 + 0.790132i 0.0828284 + 0.0828284i
\(92\) 5.13868i 0.535744i
\(93\) 8.37752i 0.868708i
\(94\) −9.26908 9.26908i −0.956032 0.956032i
\(95\) 7.02344 + 2.56282i 0.720590 + 0.262940i
\(96\) −0.707107 0.707107i −0.0721688 0.0721688i
\(97\) 3.13965 0.318783 0.159391 0.987215i \(-0.449047\pi\)
0.159391 + 0.987215i \(0.449047\pi\)
\(98\) −6.46700 −0.653265
\(99\) 0.497352 0.0499858
\(100\) 3.22019 3.82497i 0.322019 0.382497i
\(101\) 4.17592i 0.415519i 0.978180 + 0.207760i \(0.0666172\pi\)
−0.978180 + 0.207760i \(0.933383\pi\)
\(102\) −1.80718 1.80718i −0.178937 0.178937i
\(103\) −15.6656 −1.54357 −0.771787 0.635881i \(-0.780637\pi\)
−0.771787 + 0.635881i \(0.780637\pi\)
\(104\) −1.53056 −0.150083
\(105\) −1.48010 + 0.688712i −0.144443 + 0.0672114i
\(106\) 0.413793 0.413793i 0.0401911 0.0401911i
\(107\) −0.609066 + 0.609066i −0.0588806 + 0.0588806i −0.735934 0.677053i \(-0.763257\pi\)
0.677053 + 0.735934i \(0.263257\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 0.255676 0.255676i 0.0244894 0.0244894i −0.694756 0.719245i \(-0.744488\pi\)
0.719245 + 0.694756i \(0.244488\pi\)
\(110\) 0.469177 + 1.00830i 0.0447342 + 0.0961376i
\(111\) 6.06205 + 0.501607i 0.575384 + 0.0476104i
\(112\) −0.516238 + 0.516238i −0.0487799 + 0.0487799i
\(113\) −12.8460 −1.20845 −0.604226 0.796813i \(-0.706518\pi\)
−0.604226 + 0.796813i \(0.706518\pi\)
\(114\) 3.34355 0.313153
\(115\) 10.4178 4.84756i 0.971467 0.452038i
\(116\) −7.56116 7.56116i −0.702036 0.702036i
\(117\) −1.53056 −0.141500
\(118\) −5.91307 5.91307i −0.544343 0.544343i
\(119\) −1.31937 + 1.31937i −0.120946 + 0.120946i
\(120\) 0.766495 2.10059i 0.0699711 0.191757i
\(121\) 10.7526 0.977513
\(122\) 10.7956 + 10.7956i 0.977385 + 0.977385i
\(123\) −1.91176 1.91176i −0.172378 0.172378i
\(124\) −5.92380 + 5.92380i −0.531973 + 0.531973i
\(125\) 10.7923 + 2.92012i 0.965289 + 0.261183i
\(126\) −0.516238 + 0.516238i −0.0459902 + 0.0459902i
\(127\) −0.504136 + 0.504136i −0.0447349 + 0.0447349i −0.729120 0.684385i \(-0.760071\pi\)
0.684385 + 0.729120i \(0.260071\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −6.40095 6.40095i −0.563572 0.563572i
\(130\) −1.44385 3.10295i −0.126634 0.272147i
\(131\) 15.2212 15.2212i 1.32988 1.32988i 0.424407 0.905472i \(-0.360483\pi\)
0.905472 0.424407i \(-0.139517\pi\)
\(132\) 0.351681 + 0.351681i 0.0306099 + 0.0306099i
\(133\) 2.44103i 0.211664i
\(134\) −9.29726 + 9.29726i −0.803161 + 0.803161i
\(135\) 0.766495 2.10059i 0.0659694 0.180790i
\(136\) 2.55573i 0.219152i
\(137\) −10.5042 + 10.5042i −0.897430 + 0.897430i −0.995208 0.0977781i \(-0.968826\pi\)
0.0977781 + 0.995208i \(0.468826\pi\)
\(138\) 3.63359 3.63359i 0.309312 0.309312i
\(139\) −0.111253 −0.00943637 −0.00471819 0.999989i \(-0.501502\pi\)
−0.00471819 + 0.999989i \(0.501502\pi\)
\(140\) −1.53358 0.559596i −0.129611 0.0472945i
\(141\) 13.1085i 1.10393i
\(142\) 4.10631i 0.344594i
\(143\) 0.761226 0.0636569
\(144\) 1.00000i 0.0833333i
\(145\) 8.19620 22.4618i 0.680657 1.86535i
\(146\) 2.63103 + 2.63103i 0.217745 + 0.217745i
\(147\) −4.57286 4.57286i −0.377163 0.377163i
\(148\) 3.93182 + 4.64120i 0.323194 + 0.381505i
\(149\) 16.2537i 1.33155i 0.746150 + 0.665777i \(0.231900\pi\)
−0.746150 + 0.665777i \(0.768100\pi\)
\(150\) 4.98168 0.427648i 0.406752 0.0349173i
\(151\) 15.7270i 1.27985i −0.768438 0.639924i \(-0.778966\pi\)
0.768438 0.639924i \(-0.221034\pi\)
\(152\) 2.36425 + 2.36425i 0.191766 + 0.191766i
\(153\) 2.55573i 0.206619i
\(154\) 0.256752 0.256752i 0.0206897 0.0206897i
\(155\) −17.5977 6.42132i −1.41348 0.515773i
\(156\) −1.08227 1.08227i −0.0866507 0.0866507i
\(157\) −3.60469 + 3.60469i −0.287685 + 0.287685i −0.836164 0.548479i \(-0.815207\pi\)
0.548479 + 0.836164i \(0.315207\pi\)
\(158\) 0.827925 + 0.827925i 0.0658662 + 0.0658662i
\(159\) 0.585191 0.0464087
\(160\) 2.02734 0.943349i 0.160275 0.0745783i
\(161\) −2.65278 2.65278i −0.209068 0.209068i
\(162\) 1.00000i 0.0785674i
\(163\) 12.0896 0.946929 0.473465 0.880813i \(-0.343003\pi\)
0.473465 + 0.880813i \(0.343003\pi\)
\(164\) 2.70364i 0.211119i
\(165\) −0.381218 + 1.04473i −0.0296778 + 0.0813324i
\(166\) −11.2038 + 11.2038i −0.869583 + 0.869583i
\(167\) 11.3927 0.881596 0.440798 0.897606i \(-0.354695\pi\)
0.440798 + 0.897606i \(0.354695\pi\)
\(168\) −0.730071 −0.0563262
\(169\) 10.6574 0.819800
\(170\) 5.18133 2.41095i 0.397390 0.184911i
\(171\) 2.36425 + 2.36425i 0.180799 + 0.180799i
\(172\) 9.05230i 0.690232i
\(173\) −13.4370 + 13.4370i −1.02160 + 1.02160i −0.0218360 + 0.999762i \(0.506951\pi\)
−0.999762 + 0.0218360i \(0.993049\pi\)
\(174\) 10.6931i 0.810641i
\(175\) −0.312213 3.63698i −0.0236011 0.274930i
\(176\) 0.497352i 0.0374893i
\(177\) 8.36235i 0.628553i
\(178\) 6.24255 6.24255i 0.467899 0.467899i
\(179\) 7.63199 + 7.63199i 0.570442 + 0.570442i 0.932252 0.361810i \(-0.117841\pi\)
−0.361810 + 0.932252i \(0.617841\pi\)
\(180\) 2.02734 0.943349i 0.151109 0.0703131i
\(181\) 9.48047 0.704677 0.352339 0.935873i \(-0.385387\pi\)
0.352339 + 0.935873i \(0.385387\pi\)
\(182\) −0.790132 + 0.790132i −0.0585685 + 0.0585685i
\(183\) 15.2672i 1.12859i
\(184\) 5.13868 0.378828
\(185\) −5.70020 + 12.3494i −0.419087 + 0.907946i
\(186\) −8.37752 −0.614269
\(187\) 1.27110i 0.0929520i
\(188\) 9.26908 9.26908i 0.676017 0.676017i
\(189\) −0.730071 −0.0531049
\(190\) −2.56282 + 7.02344i −0.185926 + 0.509534i
\(191\) 13.3339 + 13.3339i 0.964808 + 0.964808i 0.999401 0.0345933i \(-0.0110136\pi\)
−0.0345933 + 0.999401i \(0.511014\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) 8.67065i 0.624127i 0.950061 + 0.312064i \(0.101020\pi\)
−0.950061 + 0.312064i \(0.898980\pi\)
\(194\) 3.13965i 0.225413i
\(195\) 1.17316 3.21508i 0.0840120 0.230236i
\(196\) 6.46700i 0.461928i
\(197\) 5.35975 5.35975i 0.381867 0.381867i −0.489908 0.871774i \(-0.662970\pi\)
0.871774 + 0.489908i \(0.162970\pi\)
\(198\) 0.497352i 0.0353453i
\(199\) 13.1621 + 13.1621i 0.933037 + 0.933037i 0.997895 0.0648573i \(-0.0206592\pi\)
−0.0648573 + 0.997895i \(0.520659\pi\)
\(200\) 3.82497 + 3.22019i 0.270466 + 0.227702i
\(201\) −13.1483 −0.927410
\(202\) −4.17592 −0.293816
\(203\) −7.80672 −0.547924
\(204\) 1.80718 1.80718i 0.126528 0.126528i
\(205\) 5.48119 2.55048i 0.382823 0.178133i
\(206\) 15.6656i 1.09147i
\(207\) 5.13868 0.357163
\(208\) 1.53056i 0.106125i
\(209\) −1.17586 1.17586i −0.0813363 0.0813363i
\(210\) −0.688712 1.48010i −0.0475256 0.102137i
\(211\) −24.6681 −1.69822 −0.849112 0.528213i \(-0.822862\pi\)
−0.849112 + 0.528213i \(0.822862\pi\)
\(212\) 0.413793 + 0.413793i 0.0284194 + 0.0284194i
\(213\) 2.90360 2.90360i 0.198951 0.198951i
\(214\) −0.609066 0.609066i −0.0416349 0.0416349i
\(215\) 18.3521 8.53948i 1.25160 0.582388i
\(216\) 0.707107 0.707107i 0.0481125 0.0481125i
\(217\) 6.11618i 0.415194i
\(218\) 0.255676 + 0.255676i 0.0173166 + 0.0173166i
\(219\) 3.72083i 0.251431i
\(220\) −1.00830 + 0.469177i −0.0679796 + 0.0316319i
\(221\) 3.91170i 0.263129i
\(222\) −0.501607 + 6.06205i −0.0336657 + 0.406858i
\(223\) −11.0405 11.0405i −0.739328 0.739328i 0.233120 0.972448i \(-0.425106\pi\)
−0.972448 + 0.233120i \(0.925106\pi\)
\(224\) −0.516238 0.516238i −0.0344926 0.0344926i
\(225\) 3.82497 + 3.22019i 0.254998 + 0.214679i
\(226\) 12.8460i 0.854505i
\(227\) 28.9019 1.91829 0.959143 0.282922i \(-0.0913038\pi\)
0.959143 + 0.282922i \(0.0913038\pi\)
\(228\) 3.34355i 0.221432i
\(229\) 27.5614i 1.82131i −0.413171 0.910654i \(-0.635579\pi\)
0.413171 0.910654i \(-0.364421\pi\)
\(230\) 4.84756 + 10.4178i 0.319639 + 0.686931i
\(231\) 0.363102 0.0238904
\(232\) 7.56116 7.56116i 0.496414 0.496414i
\(233\) 7.51093 7.51093i 0.492057 0.492057i −0.416897 0.908954i \(-0.636882\pi\)
0.908954 + 0.416897i \(0.136882\pi\)
\(234\) 1.53056i 0.100056i
\(235\) 27.5355 + 10.0476i 1.79622 + 0.655431i
\(236\) 5.91307 5.91307i 0.384908 0.384908i
\(237\) 1.17086i 0.0760557i
\(238\) −1.31937 1.31937i −0.0855219 0.0855219i
\(239\) 6.73852 6.73852i 0.435879 0.435879i −0.454744 0.890622i \(-0.650269\pi\)
0.890622 + 0.454744i \(0.150269\pi\)
\(240\) 2.10059 + 0.766495i 0.135593 + 0.0494770i
\(241\) −8.91683 8.91683i −0.574384 0.574384i 0.358967 0.933350i \(-0.383129\pi\)
−0.933350 + 0.358967i \(0.883129\pi\)
\(242\) 10.7526i 0.691206i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −10.7956 + 10.7956i −0.691116 + 0.691116i
\(245\) 13.1108 6.10063i 0.837617 0.389755i
\(246\) 1.91176 1.91176i 0.121890 0.121890i
\(247\) 3.61862 + 3.61862i 0.230247 + 0.230247i
\(248\) −5.92380 5.92380i −0.376162 0.376162i
\(249\) −15.8446 −1.00411
\(250\) −2.92012 + 10.7923i −0.184684 + 0.682563i
\(251\) −8.72803 + 8.72803i −0.550908 + 0.550908i −0.926703 0.375795i \(-0.877370\pi\)
0.375795 + 0.926703i \(0.377370\pi\)
\(252\) −0.516238 0.516238i −0.0325200 0.0325200i
\(253\) −2.55573 −0.160677
\(254\) −0.504136 0.504136i −0.0316323 0.0316323i
\(255\) 5.36855 + 1.95896i 0.336192 + 0.122675i
\(256\) 1.00000 0.0625000
\(257\) −6.57411 −0.410082 −0.205041 0.978753i \(-0.565733\pi\)
−0.205041 + 0.978753i \(0.565733\pi\)
\(258\) 6.40095 6.40095i 0.398505 0.398505i
\(259\) 4.42572 + 0.366209i 0.275001 + 0.0227551i
\(260\) 3.10295 1.44385i 0.192437 0.0895437i
\(261\) 7.56116 7.56116i 0.468024 0.468024i
\(262\) 15.2212 + 15.2212i 0.940366 + 0.940366i
\(263\) −0.841547 + 0.841547i −0.0518920 + 0.0518920i −0.732577 0.680685i \(-0.761682\pi\)
0.680685 + 0.732577i \(0.261682\pi\)
\(264\) −0.351681 + 0.351681i −0.0216445 + 0.0216445i
\(265\) −0.448546 + 1.22925i −0.0275540 + 0.0755121i
\(266\) 2.44103 0.149669
\(267\) 8.82830 0.540283
\(268\) −9.29726 9.29726i −0.567920 0.567920i
\(269\) 16.4147i 1.00082i −0.865788 0.500412i \(-0.833182\pi\)
0.865788 0.500412i \(-0.166818\pi\)
\(270\) 2.10059 + 0.766495i 0.127838 + 0.0466474i
\(271\) 3.57932 0.217428 0.108714 0.994073i \(-0.465327\pi\)
0.108714 + 0.994073i \(0.465327\pi\)
\(272\) 2.55573 0.154964
\(273\) −1.11742 −0.0676291
\(274\) −10.5042 10.5042i −0.634579 0.634579i
\(275\) −1.90236 1.60157i −0.114716 0.0965781i
\(276\) 3.63359 + 3.63359i 0.218717 + 0.218717i
\(277\) 11.1501i 0.669946i 0.942228 + 0.334973i \(0.108727\pi\)
−0.942228 + 0.334973i \(0.891273\pi\)
\(278\) 0.111253i 0.00667252i
\(279\) −5.92380 5.92380i −0.354649 0.354649i
\(280\) 0.559596 1.53358i 0.0334422 0.0916490i
\(281\) −12.0088 12.0088i −0.716383 0.716383i 0.251480 0.967863i \(-0.419083\pi\)
−0.967863 + 0.251480i \(0.919083\pi\)
\(282\) 13.1085 0.780597
\(283\) −23.9142 −1.42155 −0.710776 0.703419i \(-0.751656\pi\)
−0.710776 + 0.703419i \(0.751656\pi\)
\(284\) 4.10631 0.243664
\(285\) −6.77851 + 3.15414i −0.401524 + 0.186835i
\(286\) 0.761226i 0.0450122i
\(287\) −1.39572 1.39572i −0.0823870 0.0823870i
\(288\) 1.00000 0.0589256
\(289\) −10.4682 −0.615778
\(290\) 22.4618 + 8.19620i 1.31900 + 0.481297i
\(291\) −2.22007 + 2.22007i −0.130143 + 0.130143i
\(292\) −2.63103 + 2.63103i −0.153969 + 0.153969i
\(293\) 17.4755 + 17.4755i 1.02093 + 1.02093i 0.999776 + 0.0211515i \(0.00673323\pi\)
0.0211515 + 0.999776i \(0.493267\pi\)
\(294\) 4.57286 4.57286i 0.266694 0.266694i
\(295\) 17.5659 + 6.40970i 1.02273 + 0.373187i
\(296\) −4.64120 + 3.93182i −0.269764 + 0.228533i
\(297\) −0.351681 + 0.351681i −0.0204066 + 0.0204066i
\(298\) −16.2537 −0.941552
\(299\) 7.86504 0.454847
\(300\) 0.427648 + 4.98168i 0.0246902 + 0.287617i
\(301\) −4.67315 4.67315i −0.269356 0.269356i
\(302\) 15.7270 0.904989
\(303\) −2.95282 2.95282i −0.169635 0.169635i
\(304\) −2.36425 + 2.36425i −0.135599 + 0.135599i
\(305\) −32.0702 11.7023i −1.83634 0.670070i
\(306\) 2.55573 0.146102
\(307\) 6.16080 + 6.16080i 0.351615 + 0.351615i 0.860710 0.509095i \(-0.170020\pi\)
−0.509095 + 0.860710i \(0.670020\pi\)
\(308\) 0.256752 + 0.256752i 0.0146298 + 0.0146298i
\(309\) 11.0772 11.0772i 0.630161 0.630161i
\(310\) 6.42132 17.5977i 0.364707 0.999485i
\(311\) −12.1752 + 12.1752i −0.690392 + 0.690392i −0.962318 0.271926i \(-0.912339\pi\)
0.271926 + 0.962318i \(0.412339\pi\)
\(312\) 1.08227 1.08227i 0.0612713 0.0612713i
\(313\) 3.47014i 0.196144i 0.995179 + 0.0980720i \(0.0312675\pi\)
−0.995179 + 0.0980720i \(0.968732\pi\)
\(314\) −3.60469 3.60469i −0.203424 0.203424i
\(315\) 0.559596 1.53358i 0.0315297 0.0864075i
\(316\) −0.827925 + 0.827925i −0.0465744 + 0.0465744i
\(317\) −6.39255 6.39255i −0.359041 0.359041i 0.504418 0.863460i \(-0.331707\pi\)
−0.863460 + 0.504418i \(0.831707\pi\)
\(318\) 0.585191i 0.0328159i
\(319\) −3.76056 + 3.76056i −0.210551 + 0.210551i
\(320\) 0.943349 + 2.02734i 0.0527348 + 0.113332i
\(321\) 0.861349i 0.0480758i
\(322\) 2.65278 2.65278i 0.147834 0.147834i
\(323\) −6.04239 + 6.04239i −0.336208 + 0.336208i
\(324\) 1.00000 0.0555556
\(325\) 5.85434 + 4.92868i 0.324740 + 0.273394i
\(326\) 12.0896i 0.669580i
\(327\) 0.361581i 0.0199955i
\(328\) 2.70364 0.149284
\(329\) 9.57011i 0.527617i
\(330\) −1.04473 0.381218i −0.0575107 0.0209854i
\(331\) −12.6298 12.6298i −0.694194 0.694194i 0.268958 0.963152i \(-0.413321\pi\)
−0.963152 + 0.268958i \(0.913321\pi\)
\(332\) −11.2038 11.2038i −0.614888 0.614888i
\(333\) −4.64120 + 3.93182i −0.254336 + 0.215463i
\(334\) 11.3927i 0.623383i
\(335\) 10.0781 27.6192i 0.550626 1.50900i
\(336\) 0.730071i 0.0398286i
\(337\) −11.4706 11.4706i −0.624845 0.624845i 0.321921 0.946766i \(-0.395671\pi\)
−0.946766 + 0.321921i \(0.895671\pi\)
\(338\) 10.6574i 0.579686i
\(339\) 9.08351 9.08351i 0.493349 0.493349i
\(340\) 2.41095 + 5.18133i 0.130752 + 0.280997i
\(341\) 2.94621 + 2.94621i 0.159546 + 0.159546i
\(342\) −2.36425 + 2.36425i −0.127844 + 0.127844i
\(343\) −6.95218 6.95218i −0.375382 0.375382i
\(344\) 9.05230 0.488068
\(345\) −3.93877 + 10.7943i −0.212056 + 0.581143i
\(346\) −13.4370 13.4370i −0.722379 0.722379i
\(347\) 2.52563i 0.135583i 0.997700 + 0.0677914i \(0.0215952\pi\)
−0.997700 + 0.0677914i \(0.978405\pi\)
\(348\) 10.6931 0.573210
\(349\) 5.42724i 0.290514i 0.989394 + 0.145257i \(0.0464008\pi\)
−0.989394 + 0.145257i \(0.953599\pi\)
\(350\) 3.63698 0.312213i 0.194405 0.0166885i
\(351\) 1.08227 1.08227i 0.0577672 0.0577672i
\(352\) −0.497352 −0.0265090
\(353\) 16.8913 0.899034 0.449517 0.893272i \(-0.351596\pi\)
0.449517 + 0.893272i \(0.351596\pi\)
\(354\) 8.36235 0.444454
\(355\) 3.87368 + 8.32486i 0.205594 + 0.441838i
\(356\) 6.24255 + 6.24255i 0.330854 + 0.330854i
\(357\) 1.86587i 0.0987522i
\(358\) −7.63199 + 7.63199i −0.403363 + 0.403363i
\(359\) 10.2084i 0.538781i −0.963031 0.269391i \(-0.913178\pi\)
0.963031 0.269391i \(-0.0868223\pi\)
\(360\) 0.943349 + 2.02734i 0.0497189 + 0.106850i
\(361\) 7.82065i 0.411613i
\(362\) 9.48047i 0.498282i
\(363\) −7.60327 + 7.60327i −0.399068 + 0.399068i
\(364\) −0.790132 0.790132i −0.0414142 0.0414142i
\(365\) −7.81595 2.85200i −0.409105 0.149280i
\(366\) −15.2672 −0.798032
\(367\) −13.8736 + 13.8736i −0.724195 + 0.724195i −0.969457 0.245262i \(-0.921126\pi\)
0.245262 + 0.969457i \(0.421126\pi\)
\(368\) 5.13868i 0.267872i
\(369\) 2.70364 0.140746
\(370\) −12.3494 5.70020i −0.642015 0.296339i
\(371\) 0.427231 0.0221807
\(372\) 8.37752i 0.434354i
\(373\) 6.36168 6.36168i 0.329395 0.329395i −0.522961 0.852356i \(-0.675173\pi\)
0.852356 + 0.522961i \(0.175173\pi\)
\(374\) −1.27110 −0.0657270
\(375\) −9.69612 + 5.56645i −0.500705 + 0.287450i
\(376\) 9.26908 + 9.26908i 0.478016 + 0.478016i
\(377\) 11.5728 11.5728i 0.596029 0.596029i
\(378\) 0.730071i 0.0375508i
\(379\) 10.4081i 0.534627i −0.963610 0.267313i \(-0.913864\pi\)
0.963610 0.267313i \(-0.0861359\pi\)
\(380\) −7.02344 2.56282i −0.360295 0.131470i
\(381\) 0.712957i 0.0365259i
\(382\) −13.3339 + 13.3339i −0.682222 + 0.682222i
\(383\) 20.7631i 1.06094i −0.847703 0.530472i \(-0.822015\pi\)
0.847703 0.530472i \(-0.177985\pi\)
\(384\) 0.707107 + 0.707107i 0.0360844 + 0.0360844i
\(385\) −0.278316 + 0.762730i −0.0141843 + 0.0388723i
\(386\) −8.67065 −0.441325
\(387\) 9.05230 0.460154
\(388\) −3.13965 −0.159391
\(389\) −20.8063 + 20.8063i −1.05492 + 1.05492i −0.0565210 + 0.998401i \(0.518001\pi\)
−0.998401 + 0.0565210i \(0.981999\pi\)
\(390\) 3.21508 + 1.17316i 0.162802 + 0.0594055i
\(391\) 13.1331i 0.664169i
\(392\) 6.46700 0.326633
\(393\) 21.5260i 1.08584i
\(394\) 5.35975 + 5.35975i 0.270020 + 0.270020i
\(395\) −2.45951 0.897461i −0.123751 0.0451561i
\(396\) −0.497352 −0.0249929
\(397\) −5.88311 5.88311i −0.295265 0.295265i 0.543891 0.839156i \(-0.316950\pi\)
−0.839156 + 0.543891i \(0.816950\pi\)
\(398\) −13.1621 + 13.1621i −0.659757 + 0.659757i
\(399\) 1.72607 + 1.72607i 0.0864116 + 0.0864116i
\(400\) −3.22019 + 3.82497i −0.161009 + 0.191249i
\(401\) −14.5564 + 14.5564i −0.726914 + 0.726914i −0.970004 0.243090i \(-0.921839\pi\)
0.243090 + 0.970004i \(0.421839\pi\)
\(402\) 13.1483i 0.655778i
\(403\) −9.06671 9.06671i −0.451645 0.451645i
\(404\) 4.17592i 0.207760i
\(405\) 0.943349 + 2.02734i 0.0468754 + 0.100739i
\(406\) 7.80672i 0.387441i
\(407\) 2.30831 1.95550i 0.114419 0.0969306i
\(408\) 1.80718 + 1.80718i 0.0894686 + 0.0894686i
\(409\) −11.0869 11.0869i −0.548211 0.548211i 0.377712 0.925923i \(-0.376711\pi\)
−0.925923 + 0.377712i \(0.876711\pi\)
\(410\) 2.55048 + 5.48119i 0.125959 + 0.270697i
\(411\) 14.8551i 0.732749i
\(412\) 15.6656 0.771787
\(413\) 6.10511i 0.300413i
\(414\) 5.13868i 0.252552i
\(415\) 12.1448 33.2830i 0.596164 1.63380i
\(416\) 1.53056 0.0750417
\(417\) 0.0786679 0.0786679i 0.00385238 0.00385238i
\(418\) 1.17586 1.17586i 0.0575134 0.0575134i
\(419\) 22.0253i 1.07601i −0.842942 0.538004i \(-0.819178\pi\)
0.842942 0.538004i \(-0.180822\pi\)
\(420\) 1.48010 0.688712i 0.0722215 0.0336057i
\(421\) 22.6650 22.6650i 1.10463 1.10463i 0.110782 0.993845i \(-0.464664\pi\)
0.993845 0.110782i \(-0.0353356\pi\)
\(422\) 24.6681i 1.20083i
\(423\) 9.26908 + 9.26908i 0.450678 + 0.450678i
\(424\) −0.413793 + 0.413793i −0.0200956 + 0.0200956i
\(425\) −8.22994 + 9.77561i −0.399211 + 0.474187i
\(426\) 2.90360 + 2.90360i 0.140680 + 0.140680i
\(427\) 11.1462i 0.539401i
\(428\) 0.609066 0.609066i 0.0294403 0.0294403i
\(429\) −0.538268 + 0.538268i −0.0259878 + 0.0259878i
\(430\) 8.53948 + 18.3521i 0.411810 + 0.885015i
\(431\) 17.9692 17.9692i 0.865547 0.865547i −0.126428 0.991976i \(-0.540351\pi\)
0.991976 + 0.126428i \(0.0403514\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) −18.0984 18.0984i −0.869755 0.869755i 0.122690 0.992445i \(-0.460848\pi\)
−0.992445 + 0.122690i \(0.960848\pi\)
\(434\) −6.11618 −0.293586
\(435\) 10.0873 + 21.6785i 0.483650 + 1.03940i
\(436\) −0.255676 + 0.255676i −0.0122447 + 0.0122447i
\(437\) −12.1491 12.1491i −0.581171 0.581171i
\(438\) −3.72083 −0.177788
\(439\) 24.7771 + 24.7771i 1.18255 + 1.18255i 0.979083 + 0.203463i \(0.0652198\pi\)
0.203463 + 0.979083i \(0.434780\pi\)
\(440\) −0.469177 1.00830i −0.0223671 0.0480688i
\(441\) 6.46700 0.307952
\(442\) 3.91170 0.186060
\(443\) 11.6985 11.6985i 0.555811 0.555811i −0.372301 0.928112i \(-0.621431\pi\)
0.928112 + 0.372301i \(0.121431\pi\)
\(444\) −6.06205 0.501607i −0.287692 0.0238052i
\(445\) −6.76685 + 18.5446i −0.320779 + 0.879101i
\(446\) 11.0405 11.0405i 0.522784 0.522784i
\(447\) −11.4931 11.4931i −0.543605 0.543605i
\(448\) 0.516238 0.516238i 0.0243900 0.0243900i
\(449\) −16.3835 + 16.3835i −0.773187 + 0.773187i −0.978662 0.205475i \(-0.934126\pi\)
0.205475 + 0.978662i \(0.434126\pi\)
\(450\) −3.22019 + 3.82497i −0.151801 + 0.180311i
\(451\) −1.34466 −0.0633177
\(452\) 12.8460 0.604226
\(453\) 11.1207 + 11.1207i 0.522496 + 0.522496i
\(454\) 28.9019i 1.35643i
\(455\) 0.856493 2.34723i 0.0401530 0.110040i
\(456\) −3.34355 −0.156576
\(457\) −36.6470 −1.71427 −0.857137 0.515089i \(-0.827759\pi\)
−0.857137 + 0.515089i \(0.827759\pi\)
\(458\) 27.5614 1.28786
\(459\) 1.80718 + 1.80718i 0.0843518 + 0.0843518i
\(460\) −10.4178 + 4.84756i −0.485734 + 0.226019i
\(461\) −4.87965 4.87965i −0.227268 0.227268i 0.584283 0.811550i \(-0.301376\pi\)
−0.811550 + 0.584283i \(0.801376\pi\)
\(462\) 0.363102i 0.0168931i
\(463\) 3.03199i 0.140908i 0.997515 + 0.0704542i \(0.0224449\pi\)
−0.997515 + 0.0704542i \(0.977555\pi\)
\(464\) 7.56116 + 7.56116i 0.351018 + 0.351018i
\(465\) 16.9840 7.90292i 0.787616 0.366489i
\(466\) 7.51093 + 7.51093i 0.347937 + 0.347937i
\(467\) −7.88298 −0.364781 −0.182390 0.983226i \(-0.558384\pi\)
−0.182390 + 0.983226i \(0.558384\pi\)
\(468\) 1.53056 0.0707500
\(469\) −9.59920 −0.443250
\(470\) −10.0476 + 27.5355i −0.463460 + 1.27012i
\(471\) 5.09780i 0.234894i
\(472\) 5.91307 + 5.91307i 0.272171 + 0.272171i
\(473\) −4.50218 −0.207011
\(474\) −1.17086 −0.0537795
\(475\) −1.42986 16.6565i −0.0656066 0.764253i
\(476\) 1.31937 1.31937i 0.0604731 0.0604731i
\(477\) −0.413793 + 0.413793i −0.0189463 + 0.0189463i
\(478\) 6.73852 + 6.73852i 0.308213 + 0.308213i
\(479\) −22.2999 + 22.2999i −1.01891 + 1.01891i −0.0190898 + 0.999818i \(0.506077\pi\)
−0.999818 + 0.0190898i \(0.993923\pi\)
\(480\) −0.766495 + 2.10059i −0.0349855 + 0.0958785i
\(481\) −7.10363 + 6.01788i −0.323897 + 0.274392i
\(482\) 8.91683 8.91683i 0.406151 0.406151i
\(483\) 3.75160 0.170704
\(484\) −10.7526 −0.488756
\(485\) −2.96178 6.36512i −0.134488 0.289025i
\(486\) 0.707107 + 0.707107i 0.0320750 + 0.0320750i
\(487\) 12.8810 0.583695 0.291847 0.956465i \(-0.405730\pi\)
0.291847 + 0.956465i \(0.405730\pi\)
\(488\) −10.7956 10.7956i −0.488693 0.488693i
\(489\) −8.54863 + 8.54863i −0.386582 + 0.386582i
\(490\) 6.10063 + 13.1108i 0.275599 + 0.592285i
\(491\) 0.897235 0.0404916 0.0202458 0.999795i \(-0.493555\pi\)
0.0202458 + 0.999795i \(0.493555\pi\)
\(492\) 1.91176 + 1.91176i 0.0861890 + 0.0861890i
\(493\) 19.3243 + 19.3243i 0.870323 + 0.870323i
\(494\) −3.61862 + 3.61862i −0.162809 + 0.162809i
\(495\) −0.469177 1.00830i −0.0210879 0.0453197i
\(496\) 5.92380 5.92380i 0.265986 0.265986i
\(497\) 2.11983 2.11983i 0.0950875 0.0950875i
\(498\) 15.8446i 0.710012i
\(499\) −17.8190 17.8190i −0.797689 0.797689i 0.185042 0.982731i \(-0.440758\pi\)
−0.982731 + 0.185042i \(0.940758\pi\)
\(500\) −10.7923 2.92012i −0.482645 0.130592i
\(501\) −8.05588 + 8.05588i −0.359910 + 0.359910i
\(502\) −8.72803 8.72803i −0.389551 0.389551i
\(503\) 17.9635i 0.800955i 0.916307 + 0.400477i \(0.131156\pi\)
−0.916307 + 0.400477i \(0.868844\pi\)
\(504\) 0.516238 0.516238i 0.0229951 0.0229951i
\(505\) 8.46599 3.93935i 0.376731 0.175299i
\(506\) 2.55573i 0.113616i
\(507\) −7.53592 + 7.53592i −0.334682 + 0.334682i
\(508\) 0.504136 0.504136i 0.0223674 0.0223674i
\(509\) −8.36462 −0.370755 −0.185378 0.982667i \(-0.559351\pi\)
−0.185378 + 0.982667i \(0.559351\pi\)
\(510\) −1.95896 + 5.36855i −0.0867441 + 0.237723i
\(511\) 2.71647i 0.120170i
\(512\) 1.00000i 0.0441942i
\(513\) −3.34355 −0.147622
\(514\) 6.57411i 0.289972i
\(515\) 14.7781 + 31.7594i 0.651200 + 1.39948i
\(516\) 6.40095 + 6.40095i 0.281786 + 0.281786i
\(517\) −4.61000 4.61000i −0.202747 0.202747i
\(518\) −0.366209 + 4.42572i −0.0160903 + 0.194455i
\(519\) 19.0028i 0.834131i
\(520\) 1.44385 + 3.10295i 0.0633170 + 0.136074i
\(521\) 16.5234i 0.723904i 0.932197 + 0.361952i \(0.117890\pi\)
−0.932197 + 0.361952i \(0.882110\pi\)
\(522\) 7.56116 + 7.56116i 0.330943 + 0.330943i
\(523\) 14.2767i 0.624278i 0.950036 + 0.312139i \(0.101046\pi\)
−0.950036 + 0.312139i \(0.898954\pi\)
\(524\) −15.2212 + 15.2212i −0.664939 + 0.664939i
\(525\) 2.79250 + 2.35096i 0.121875 + 0.102605i
\(526\) −0.841547 0.841547i −0.0366932 0.0366932i
\(527\) 15.1397 15.1397i 0.659494 0.659494i
\(528\) −0.351681 0.351681i −0.0153050 0.0153050i
\(529\) −3.40599 −0.148087
\(530\) −1.22925 0.448546i −0.0533951 0.0194836i
\(531\) 5.91307 + 5.91307i 0.256606 + 0.256606i
\(532\) 2.44103i 0.105832i
\(533\) 4.13808 0.179240
\(534\) 8.82830i 0.382038i
\(535\) 1.80934 + 0.660220i 0.0782247 + 0.0285438i
\(536\) 9.29726 9.29726i 0.401580 0.401580i
\(537\) −10.7933 −0.465764
\(538\) 16.4147 0.707689
\(539\) −3.21637 −0.138539
\(540\) −0.766495 + 2.10059i −0.0329847 + 0.0903951i
\(541\) −2.99943 2.99943i −0.128955 0.128955i 0.639683 0.768639i \(-0.279066\pi\)
−0.768639 + 0.639683i \(0.779066\pi\)
\(542\) 3.57932i 0.153745i
\(543\) −6.70370 + 6.70370i −0.287683 + 0.287683i
\(544\) 2.55573i 0.109576i
\(545\) −0.759534 0.277150i −0.0325349 0.0118718i
\(546\) 1.11742i 0.0478210i
\(547\) 20.8842i 0.892944i 0.894798 + 0.446472i \(0.147320\pi\)
−0.894798 + 0.446472i \(0.852680\pi\)
\(548\) 10.5042 10.5042i 0.448715 0.448715i
\(549\) −10.7956 10.7956i −0.460744 0.460744i
\(550\) 1.60157 1.90236i 0.0682910 0.0811168i
\(551\) −35.7529 −1.52313
\(552\) −3.63359 + 3.63359i −0.154656 + 0.154656i
\(553\) 0.854813i 0.0363504i
\(554\) −11.1501 −0.473723
\(555\) −4.70170 12.7630i −0.199576 0.541759i
\(556\) 0.111253 0.00471819
\(557\) 10.1584i 0.430426i 0.976567 + 0.215213i \(0.0690446\pi\)
−0.976567 + 0.215213i \(0.930955\pi\)
\(558\) 5.92380 5.92380i 0.250774 0.250774i
\(559\) 13.8551 0.586007
\(560\) 1.53358 + 0.559596i 0.0648056 + 0.0236472i
\(561\) −0.898803 0.898803i −0.0379475 0.0379475i
\(562\) 12.0088 12.0088i 0.506559 0.506559i
\(563\) 13.4772i 0.567996i 0.958825 + 0.283998i \(0.0916610\pi\)
−0.958825 + 0.283998i \(0.908339\pi\)
\(564\) 13.1085i 0.551966i
\(565\) 12.1183 + 26.0432i 0.509820 + 1.09565i
\(566\) 23.9142i 1.00519i
\(567\) 0.516238 0.516238i 0.0216800 0.0216800i
\(568\) 4.10631i 0.172297i
\(569\) −0.956429 0.956429i −0.0400956 0.0400956i 0.686775 0.726870i \(-0.259026\pi\)
−0.726870 + 0.686775i \(0.759026\pi\)
\(570\) −3.15414 6.77851i −0.132112 0.283920i
\(571\) −1.80272 −0.0754415 −0.0377208 0.999288i \(-0.512010\pi\)
−0.0377208 + 0.999288i \(0.512010\pi\)
\(572\) −0.761226 −0.0318285
\(573\) −18.8570 −0.787763
\(574\) 1.39572 1.39572i 0.0582564 0.0582564i
\(575\) −19.6553 16.5475i −0.819682 0.690078i
\(576\) 1.00000i 0.0416667i
\(577\) −21.8641 −0.910216 −0.455108 0.890436i \(-0.650399\pi\)
−0.455108 + 0.890436i \(0.650399\pi\)
\(578\) 10.4682i 0.435421i
\(579\) −6.13108 6.13108i −0.254799 0.254799i
\(580\) −8.19620 + 22.4618i −0.340329 + 0.932676i
\(581\) −11.5677 −0.479907
\(582\) −2.22007 2.22007i −0.0920247 0.0920247i
\(583\) 0.205801 0.205801i 0.00852340 0.00852340i
\(584\) −2.63103 2.63103i −0.108873 0.108873i
\(585\) 1.44385 + 3.10295i 0.0596958 + 0.128291i
\(586\) −17.4755 + 17.4755i −0.721905 + 0.721905i
\(587\) 13.4925i 0.556896i −0.960451 0.278448i \(-0.910180\pi\)
0.960451 0.278448i \(-0.0898200\pi\)
\(588\) 4.57286 + 4.57286i 0.188581 + 0.188581i
\(589\) 28.0107i 1.15416i
\(590\) −6.40970 + 17.5659i −0.263883 + 0.723176i
\(591\) 7.57983i 0.311793i
\(592\) −3.93182 4.64120i −0.161597 0.190752i
\(593\) −21.6151 21.6151i −0.887628 0.887628i 0.106667 0.994295i \(-0.465982\pi\)
−0.994295 + 0.106667i \(0.965982\pi\)
\(594\) −0.351681 0.351681i −0.0144296 0.0144296i
\(595\) 3.91942 + 1.43018i 0.160681 + 0.0586316i
\(596\) 16.2537i 0.665777i
\(597\) −18.6140 −0.761822
\(598\) 7.86504i 0.321625i
\(599\) 1.58656i 0.0648249i 0.999475 + 0.0324125i \(0.0103190\pi\)
−0.999475 + 0.0324125i \(0.989681\pi\)
\(600\) −4.98168 + 0.427648i −0.203376 + 0.0174586i
\(601\) 39.5787 1.61445 0.807224 0.590245i \(-0.200969\pi\)
0.807224 + 0.590245i \(0.200969\pi\)
\(602\) 4.67315 4.67315i 0.190463 0.190463i
\(603\) 9.29726 9.29726i 0.378614 0.378614i
\(604\) 15.7270i 0.639924i
\(605\) −10.1435 21.7992i −0.412392 0.886264i
\(606\) 2.95282 2.95282i 0.119950 0.119950i
\(607\) 29.3879i 1.19282i 0.802680 + 0.596409i \(0.203407\pi\)
−0.802680 + 0.596409i \(0.796593\pi\)
\(608\) −2.36425 2.36425i −0.0958830 0.0958830i
\(609\) 5.52018 5.52018i 0.223689 0.223689i
\(610\) 11.7023 32.0702i 0.473811 1.29849i
\(611\) 14.1869 + 14.1869i 0.573939 + 0.573939i
\(612\) 2.55573i 0.103309i
\(613\) −11.9588 + 11.9588i −0.483011 + 0.483011i −0.906092 0.423081i \(-0.860949\pi\)
0.423081 + 0.906092i \(0.360949\pi\)
\(614\) −6.16080 + 6.16080i −0.248630 + 0.248630i
\(615\) −2.07233 + 5.67925i −0.0835644 + 0.229009i
\(616\) −0.256752 + 0.256752i −0.0103448 + 0.0103448i
\(617\) −19.8923 19.8923i −0.800835 0.800835i 0.182391 0.983226i \(-0.441616\pi\)
−0.983226 + 0.182391i \(0.941616\pi\)
\(618\) 11.0772 + 11.0772i 0.445591 + 0.445591i
\(619\) 25.0352 1.00625 0.503125 0.864213i \(-0.332183\pi\)
0.503125 + 0.864213i \(0.332183\pi\)
\(620\) 17.5977 + 6.42132i 0.706742 + 0.257887i
\(621\) −3.63359 + 3.63359i −0.145811 + 0.145811i
\(622\) −12.1752 12.1752i −0.488181 0.488181i
\(623\) 6.44528 0.258225
\(624\) 1.08227 + 1.08227i 0.0433254 + 0.0433254i
\(625\) −4.26081 24.6342i −0.170432 0.985369i
\(626\) −3.47014 −0.138695
\(627\) 1.66292 0.0664108
\(628\) 3.60469 3.60469i 0.143843 0.143843i
\(629\) −10.0487 11.8617i −0.400668 0.472956i
\(630\) 1.53358 + 0.559596i 0.0610993 + 0.0222948i
\(631\) −14.6446 + 14.6446i −0.582990 + 0.582990i −0.935724 0.352733i \(-0.885252\pi\)
0.352733 + 0.935724i \(0.385252\pi\)
\(632\) −0.827925 0.827925i −0.0329331 0.0329331i
\(633\) 17.4430 17.4430i 0.693297 0.693297i
\(634\) 6.39255 6.39255i 0.253881 0.253881i
\(635\) 1.49763 + 0.546478i 0.0594317 + 0.0216863i
\(636\) −0.585191 −0.0232043
\(637\) 9.89811 0.392177
\(638\) −3.76056 3.76056i −0.148882 0.148882i
\(639\) 4.10631i 0.162443i
\(640\) −2.02734 + 0.943349i −0.0801375 + 0.0372891i
\(641\) 18.7683 0.741305 0.370652 0.928772i \(-0.379134\pi\)
0.370652 + 0.928772i \(0.379134\pi\)
\(642\) 0.861349 0.0339947
\(643\) −33.3318 −1.31448 −0.657238 0.753683i \(-0.728275\pi\)
−0.657238 + 0.753683i \(0.728275\pi\)
\(644\) 2.65278 + 2.65278i 0.104534 + 0.104534i
\(645\) −6.93855 + 19.0152i −0.273205 + 0.748723i
\(646\) −6.04239 6.04239i −0.237735 0.237735i
\(647\) 20.5310i 0.807156i −0.914945 0.403578i \(-0.867766\pi\)
0.914945 0.403578i \(-0.132234\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −2.94088 2.94088i −0.115440 0.115440i
\(650\) −4.92868 + 5.85434i −0.193319 + 0.229626i
\(651\) −4.32479 4.32479i −0.169502 0.169502i
\(652\) −12.0896 −0.473465
\(653\) 26.4235 1.03403 0.517016 0.855976i \(-0.327043\pi\)
0.517016 + 0.855976i \(0.327043\pi\)
\(654\) −0.361581 −0.0141389
\(655\) −45.2173 16.4995i −1.76678 0.644690i
\(656\) 2.70364i 0.105560i
\(657\) −2.63103 2.63103i −0.102646 0.102646i
\(658\) 9.57011 0.373082
\(659\) −39.4006 −1.53483 −0.767414 0.641152i \(-0.778457\pi\)
−0.767414 + 0.641152i \(0.778457\pi\)
\(660\) 0.381218 1.04473i 0.0148389 0.0406662i
\(661\) 7.90042 7.90042i 0.307291 0.307291i −0.536567 0.843858i \(-0.680279\pi\)
0.843858 + 0.536567i \(0.180279\pi\)
\(662\) 12.6298 12.6298i 0.490870 0.490870i
\(663\) 2.76599 + 2.76599i 0.107422 + 0.107422i
\(664\) 11.2038 11.2038i 0.434792 0.434792i
\(665\) −4.94879 + 2.30274i −0.191906 + 0.0892966i
\(666\) −3.93182 4.64120i −0.152355 0.179843i
\(667\) −38.8543 + 38.8543i −1.50445 + 1.50445i
\(668\) −11.3927 −0.440798
\(669\) 15.6137 0.603659
\(670\) 27.6192 + 10.0781i 1.06702 + 0.389351i
\(671\) 5.36920 + 5.36920i 0.207276 + 0.207276i
\(672\) 0.730071 0.0281631
\(673\) −31.7666 31.7666i −1.22451 1.22451i −0.966011 0.258503i \(-0.916771\pi\)
−0.258503 0.966011i \(-0.583229\pi\)
\(674\) 11.4706 11.4706i 0.441832 0.441832i
\(675\) −4.98168 + 0.427648i −0.191745 + 0.0164602i
\(676\) −10.6574 −0.409900
\(677\) −21.1045 21.1045i −0.811110 0.811110i 0.173690 0.984800i \(-0.444431\pi\)
−0.984800 + 0.173690i \(0.944431\pi\)
\(678\) 9.08351 + 9.08351i 0.348850 + 0.348850i
\(679\) −1.62081 + 1.62081i −0.0622008 + 0.0622008i
\(680\) −5.18133 + 2.41095i −0.198695 + 0.0924556i
\(681\) −20.4367 + 20.4367i −0.783137 + 0.783137i
\(682\) −2.94621 + 2.94621i −0.112816 + 0.112816i
\(683\) 35.4086i 1.35487i 0.735581 + 0.677437i \(0.236909\pi\)
−0.735581 + 0.677437i \(0.763091\pi\)
\(684\) −2.36425 2.36425i −0.0903993 0.0903993i
\(685\) 31.2045 + 11.3864i 1.19226 + 0.435051i
\(686\) 6.95218 6.95218i 0.265435 0.265435i
\(687\) 19.4888 + 19.4888i 0.743546 + 0.743546i
\(688\) 9.05230i 0.345116i
\(689\) −0.633334 + 0.633334i −0.0241281 + 0.0241281i
\(690\) −10.7943 3.93877i −0.410930 0.149946i
\(691\) 22.4704i 0.854814i 0.904059 + 0.427407i \(0.140573\pi\)
−0.904059 + 0.427407i \(0.859427\pi\)
\(692\) 13.4370 13.4370i 0.510799 0.510799i
\(693\) −0.256752 + 0.256752i −0.00975321 + 0.00975321i
\(694\) −2.52563 −0.0958715
\(695\) 0.104951 + 0.225548i 0.00398100 + 0.00855551i
\(696\) 10.6931i 0.405321i
\(697\) 6.90979i 0.261727i
\(698\) −5.42724 −0.205424
\(699\) 10.6221i 0.401763i
\(700\) 0.312213 + 3.63698i 0.0118005 + 0.137465i
\(701\) 15.2902 + 15.2902i 0.577504 + 0.577504i 0.934215 0.356711i \(-0.116102\pi\)
−0.356711 + 0.934215i \(0.616102\pi\)
\(702\) 1.08227 + 1.08227i 0.0408475 + 0.0408475i
\(703\) 20.2688 + 1.67715i 0.764451 + 0.0632549i
\(704\) 0.497352i 0.0187447i
\(705\) −26.5753 + 12.3658i −1.00088 + 0.465725i
\(706\) 16.8913i 0.635713i
\(707\) −2.15577 2.15577i −0.0810760 0.0810760i
\(708\) 8.36235i 0.314276i
\(709\) −11.5740 + 11.5740i −0.434672 + 0.434672i −0.890214 0.455542i \(-0.849445\pi\)
0.455542 + 0.890214i \(0.349445\pi\)
\(710\) −8.32486 + 3.87368i −0.312427 + 0.145377i
\(711\) −0.827925 0.827925i −0.0310496 0.0310496i
\(712\) −6.24255 + 6.24255i −0.233949 + 0.233949i
\(713\) 30.4405 + 30.4405i 1.14001 + 1.14001i
\(714\) 1.86587 0.0698283
\(715\) −0.718102 1.54326i −0.0268555 0.0577147i
\(716\) −7.63199 7.63199i −0.285221 0.285221i
\(717\) 9.52971i 0.355893i
\(718\) 10.2084 0.380976
\(719\) 33.1940i 1.23793i −0.785420 0.618963i \(-0.787553\pi\)
0.785420 0.618963i \(-0.212447\pi\)
\(720\) −2.02734 + 0.943349i −0.0755544 + 0.0351565i
\(721\) 8.08716 8.08716i 0.301182 0.301182i
\(722\) −7.82065 −0.291054
\(723\) 12.6103 0.468982
\(724\) −9.48047 −0.352339
\(725\) −53.2695 + 4.57288i −1.97838 + 0.169832i
\(726\) −7.60327 7.60327i −0.282184 0.282184i
\(727\) 25.8130i 0.957352i −0.877992 0.478676i \(-0.841117\pi\)
0.877992 0.478676i \(-0.158883\pi\)
\(728\) 0.790132 0.790132i 0.0292842 0.0292842i
\(729\) 1.00000i 0.0370370i
\(730\) 2.85200 7.81595i 0.105557 0.289281i
\(731\) 23.1353i 0.855689i
\(732\) 15.2672i 0.564294i
\(733\) 29.0185 29.0185i 1.07182 1.07182i 0.0746110 0.997213i \(-0.476228\pi\)
0.997213 0.0746110i \(-0.0237715\pi\)
\(734\) −13.8736 13.8736i −0.512083 0.512083i
\(735\) −4.95692 + 13.5845i −0.182839 + 0.501073i
\(736\) −5.13868 −0.189414
\(737\) −4.62401 + 4.62401i −0.170328 + 0.170328i
\(738\) 2.70364i 0.0995225i
\(739\) 33.6130 1.23647 0.618236 0.785992i \(-0.287847\pi\)
0.618236 + 0.785992i \(0.287847\pi\)
\(740\) 5.70020 12.3494i 0.209543 0.453973i
\(741\) −5.11750 −0.187996
\(742\) 0.427231i 0.0156842i
\(743\) 15.7302 15.7302i 0.577084 0.577084i −0.357015 0.934099i \(-0.616205\pi\)
0.934099 + 0.357015i \(0.116205\pi\)
\(744\) 8.37752 0.307135
\(745\) 32.9517 15.3329i 1.20726 0.561754i
\(746\) 6.36168 + 6.36168i 0.232918 + 0.232918i
\(747\) 11.2038 11.2038i 0.409926 0.409926i
\(748\) 1.27110i 0.0464760i
\(749\) 0.628846i 0.0229775i
\(750\) −5.56645 9.69612i −0.203258 0.354052i
\(751\) 12.7266i 0.464401i 0.972668 + 0.232201i \(0.0745926\pi\)
−0.972668 + 0.232201i \(0.925407\pi\)
\(752\) −9.26908 + 9.26908i −0.338009 + 0.338009i
\(753\) 12.3433i 0.449815i
\(754\) 11.5728 + 11.5728i 0.421456 + 0.421456i
\(755\) −31.8840 + 14.8361i −1.16038 + 0.539940i
\(756\) 0.730071 0.0265524
\(757\) 49.4794 1.79836 0.899181 0.437578i \(-0.144164\pi\)
0.899181 + 0.437578i \(0.144164\pi\)
\(758\) 10.4081 0.378038
\(759\) 1.80718 1.80718i 0.0655963 0.0655963i
\(760\) 2.56282 7.02344i 0.0929632 0.254767i
\(761\) 10.2526i 0.371657i 0.982582 + 0.185828i \(0.0594968\pi\)
−0.982582 + 0.185828i \(0.940503\pi\)
\(762\) 0.712957 0.0258277
\(763\) 0.263980i 0.00955671i
\(764\) −13.3339 13.3339i −0.482404 0.482404i
\(765\) −5.18133 + 2.41095i −0.187331 + 0.0871680i
\(766\) 20.7631 0.750200
\(767\) 9.05030 + 9.05030i 0.326787 + 0.326787i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 18.0896 + 18.0896i 0.652327 + 0.652327i 0.953553 0.301226i \(-0.0973959\pi\)
−0.301226 + 0.953553i \(0.597396\pi\)
\(770\) −0.762730 0.278316i −0.0274869 0.0100298i
\(771\) 4.64860 4.64860i 0.167415 0.167415i
\(772\) 8.67065i 0.312064i
\(773\) 21.4323 + 21.4323i 0.770866 + 0.770866i 0.978258 0.207392i \(-0.0664976\pi\)
−0.207392 + 0.978258i \(0.566498\pi\)
\(774\) 9.05230i 0.325378i
\(775\) 3.58263 + 41.7341i 0.128692 + 1.49913i
\(776\) 3.13965i 0.112707i
\(777\) −3.38841 + 2.87051i −0.121558 + 0.102979i
\(778\) −20.8063 20.8063i −0.745943 0.745943i
\(779\) −6.39209 6.39209i −0.229020 0.229020i
\(780\) −1.17316 +