Properties

Label 1110.2.o.a.253.14
Level $1110$
Weight $2$
Character 1110.253
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.o (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 253.14
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.14

$q$-expansion

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

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000 0.500000
\(5\) −2.02734 + 0.943349i −0.906652 + 0.421878i
\(6\) −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 \(0.294058\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) 2.02734 0.943349i 0.641100 0.298313i
\(11\) 0.497352i 0.149957i −0.997185 0.0749787i \(-0.976111\pi\)
0.997185 0.0749787i \(-0.0238889\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) −1.53056 −0.424500 −0.212250 0.977215i \(-0.568079\pi\)
−0.212250 + 0.977215i \(0.568079\pi\)
\(14\) 0.516238 0.516238i 0.137970 0.137970i
\(15\) −0.766495 + 2.10059i −0.197908 + 0.542370i
\(16\) 1.00000 0.250000
\(17\) 2.55573i 0.619856i −0.950760 0.309928i \(-0.899695\pi\)
0.950760 0.309928i \(-0.100305\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 2.36425 + 2.36425i 0.542396 + 0.542396i 0.924231 0.381835i \(-0.124708\pi\)
−0.381835 + 0.924231i \(0.624708\pi\)
\(20\) −2.02734 + 0.943349i −0.453326 + 0.210939i
\(21\) 0.730071i 0.159315i
\(22\) 0.497352i 0.106036i
\(23\) 5.13868 1.07149 0.535744 0.844380i \(-0.320031\pi\)
0.535744 + 0.844380i \(0.320031\pi\)
\(24\) −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 −0.617504 + 0.786568i \(0.711856\pi\)
−0.786568 + 0.617504i \(0.788144\pi\)
\(30\) 0.766495 2.10059i 0.139942 0.383514i
\(31\) 5.92380 + 5.92380i 1.06395 + 1.06395i 0.997811 + 0.0661351i \(0.0210668\pi\)
0.0661351 + 0.997811i \(0.478933\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.351681 0.351681i −0.0612198 0.0612198i
\(34\) 2.55573i 0.438305i
\(35\) 0.559596 1.53358i 0.0945890 0.259223i
\(36\) 1.00000i 0.166667i
\(37\) 4.64120 + 3.93182i 0.763009 + 0.646388i
\(38\) −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 \(-0.932289\pi\)
0.977460 0.211119i \(-0.0677108\pi\)
\(42\) 0.730071i 0.112652i
\(43\) 9.05230 1.38046 0.690232 0.723588i \(-0.257509\pi\)
0.690232 + 0.723588i \(0.257509\pi\)
\(44\) 0.497352i 0.0749787i
\(45\) 0.943349 + 2.02734i 0.140626 + 0.302217i
\(46\) −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
\(50\) −3.22019 + 3.82497i −0.455403 + 0.540933i
\(51\) −1.80718 1.80718i −0.253055 0.253055i
\(52\) −1.53056 −0.212250
\(53\) −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
\(55\) 0.469177 + 1.00830i 0.0632638 + 0.135959i
\(56\) 0.516238 0.516238i 0.0689852 0.0689852i
\(57\) 3.34355 0.442865
\(58\) 7.56116 7.56116i 0.992829 0.992829i
\(59\) 5.91307 + 5.91307i 0.769817 + 0.769817i 0.978074 0.208257i \(-0.0667792\pi\)
−0.208257 + 0.978074i \(0.566779\pi\)
\(60\) −0.766495 + 2.10059i −0.0989541 + 0.271185i
\(61\) 10.7956 + 10.7956i 1.38223 + 1.38223i 0.840645 + 0.541586i \(0.182176\pi\)
0.541586 + 0.840645i \(0.317824\pi\)
\(62\) −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 \(-0.953150\pi\)
−0.146653 0.989188i \(-0.546850\pi\)
\(68\) 2.55573i 0.309928i
\(69\) 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 \(0.578350\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −2.63103 + 2.63103i −0.307938 + 0.307938i −0.844109 0.536171i \(-0.819870\pi\)
0.536171 + 0.844109i \(0.319870\pi\)
\(74\) −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 \(-0.270981\pi\)
−0.752146 + 0.658997i \(0.770981\pi\)
\(80\) −2.02734 + 0.943349i −0.226663 + 0.105470i
\(81\) −1.00000 −0.111111
\(82\) 2.70364i 0.298567i
\(83\) 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
\(87\) 10.6931i 1.14642i
\(88\) 0.497352i 0.0530179i
\(89\) 6.24255 6.24255i 0.661709 0.661709i −0.294074 0.955783i \(-0.595011\pi\)
0.955783 + 0.294074i \(0.0950112\pi\)
\(90\) −0.943349 2.02734i −0.0994377 0.213700i
\(91\) 0.790132 0.790132i 0.0828284 0.0828284i
\(92\) 5.13868 0.535744
\(93\) 8.37752 0.868708
\(94\) 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
\(97\) 3.13965i 0.318783i −0.987215 0.159391i \(-0.949047\pi\)
0.987215 0.159391i \(-0.0509532\pi\)
\(98\) 6.46700i 0.653265i
\(99\) −0.497352 −0.0499858
\(100\) 3.22019 3.82497i 0.322019 0.382497i
\(101\) 4.17592i 0.415519i −0.978180 0.207760i \(-0.933383\pi\)
0.978180 0.207760i \(-0.0666172\pi\)
\(102\) 1.80718 + 1.80718i 0.178937 + 0.178937i
\(103\) 15.6656i 1.54357i −0.635881 0.771787i \(-0.719363\pi\)
0.635881 0.771787i \(-0.280637\pi\)
\(104\) 1.53056 0.150083
\(105\) −0.688712 1.48010i −0.0672114 0.144443i
\(106\) 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 \(-0.255512\pi\)
−0.719245 + 0.694756i \(0.755512\pi\)
\(110\) −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
\(113\) 12.8460i 1.20845i −0.796813 0.604226i \(-0.793482\pi\)
0.796813 0.604226i \(-0.206518\pi\)
\(114\) −3.34355 −0.313153
\(115\) −10.4178 + 4.84756i −0.971467 + 0.452038i
\(116\) −7.56116 + 7.56116i −0.702036 + 0.702036i
\(117\) 1.53056i 0.141500i
\(118\) −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
\(125\) −2.92012 + 10.7923i −0.261183 + 0.965289i
\(126\) −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 \(0.260071\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 6.40095 6.40095i 0.563572 0.563572i
\(130\) −3.10295 + 1.44385i −0.272147 + 0.126634i
\(131\) 15.2212 + 15.2212i 1.32988 + 1.32988i 0.905472 + 0.424407i \(0.139517\pi\)
0.424407 + 0.905472i \(0.360483\pi\)
\(132\) −0.351681 0.351681i −0.0306099 0.0306099i
\(133\) −2.44103 −0.211664
\(134\) 9.29726 + 9.29726i 0.803161 + 0.803161i
\(135\) 2.10059 + 0.766495i 0.180790 + 0.0659694i
\(136\) 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 \(-0.498498\pi\)
0.00471819 + 0.999989i \(0.498498\pi\)
\(140\) 0.559596 1.53358i 0.0472945 0.129611i
\(141\) 13.1085i 1.10393i
\(142\) 4.10631 0.344594
\(143\) 0.761226i 0.0636569i
\(144\) 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
\(148\) 4.64120 + 3.93182i 0.381505 + 0.323194i
\(149\) 16.2537i 1.33155i 0.746150 + 0.665777i \(0.231900\pi\)
−0.746150 + 0.665777i \(0.768100\pi\)
\(150\) 0.427648 + 4.98168i 0.0349173 + 0.406752i
\(151\) 15.7270i 1.27985i 0.768438 + 0.639924i \(0.221034\pi\)
−0.768438 + 0.639924i \(0.778966\pi\)
\(152\) −2.36425 2.36425i −0.191766 0.191766i
\(153\) −2.55573 −0.206619
\(154\) −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
\(162\) 1.00000 0.0785674
\(163\) 12.0896i 0.946929i 0.880813 + 0.473465i \(0.156997\pi\)
−0.880813 + 0.473465i \(0.843003\pi\)
\(164\) 2.70364i 0.211119i
\(165\) 1.04473 + 0.381218i 0.0813324 + 0.0296778i
\(166\) −11.2038 11.2038i −0.869583 0.869583i
\(167\) 11.3927i 0.881596i −0.897606 0.440798i \(-0.854695\pi\)
0.897606 0.440798i \(-0.145305\pi\)
\(168\) 0.730071i 0.0563262i
\(169\) −10.6574 −0.819800
\(170\) −2.41095 5.18133i −0.184911 0.397390i
\(171\) 2.36425 2.36425i 0.180799 0.180799i
\(172\) 9.05230 0.690232
\(173\) 13.4370 13.4370i 1.02160 1.02160i 0.0218360 0.999762i \(-0.493049\pi\)
0.999762 0.0218360i \(-0.00695117\pi\)
\(174\) 10.6931i 0.810641i
\(175\) 0.312213 + 3.63698i 0.0236011 + 0.274930i
\(176\) 0.497352i 0.0374893i
\(177\) 8.36235 0.628553
\(178\) −6.24255 + 6.24255i −0.467899 + 0.467899i
\(179\) −7.63199 + 7.63199i −0.570442 + 0.570442i −0.932252 0.361810i \(-0.882159\pi\)
0.361810 + 0.932252i \(0.382159\pi\)
\(180\) 0.943349 + 2.02734i 0.0703131 + 0.151109i
\(181\) 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
\(183\) 15.2672 1.12859
\(184\) −5.13868 −0.378828
\(185\) −13.1184 3.59286i −0.964481 0.264152i
\(186\) −8.37752 −0.614269
\(187\) −1.27110 −0.0929520
\(188\) −9.26908 + 9.26908i −0.676017 + 0.676017i
\(189\) 0.730071 0.0531049
\(190\) 7.02344 + 2.56282i 0.509534 + 0.185926i
\(191\) 13.3339 13.3339i 0.964808 0.964808i −0.0345933 0.999401i \(-0.511014\pi\)
0.999401 + 0.0345933i \(0.0110136\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) 8.67065 0.624127 0.312064 0.950061i \(-0.398980\pi\)
0.312064 + 0.950061i \(0.398980\pi\)
\(194\) 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 \(0.162970\pi\)
\(198\) 0.497352 0.0353453
\(199\) −13.1621 + 13.1621i −0.933037 + 0.933037i −0.997895 0.0648573i \(-0.979341\pi\)
0.0648573 + 0.997895i \(0.479341\pi\)
\(200\) −3.22019 + 3.82497i −0.227702 + 0.270466i
\(201\) −13.1483 −0.927410
\(202\) 4.17592i 0.293816i
\(203\) 7.80672i 0.547924i
\(204\) −1.80718 1.80718i −0.126528 0.126528i
\(205\) 2.55048 + 5.48119i 0.178133 + 0.382823i
\(206\) 15.6656i 1.09147i
\(207\) 5.13868i 0.357163i
\(208\) −1.53056 −0.106125
\(209\) 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
\(217\) −6.11618 −0.415194
\(218\) 0.255676 + 0.255676i 0.0173166 + 0.0173166i
\(219\) 3.72083i 0.251431i
\(220\) 0.469177 + 1.00830i 0.0316319 + 0.0679796i
\(221\) 3.91170i 0.263129i
\(222\) −6.06205 + 0.501607i −0.406858 + 0.0336657i
\(223\) −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
\(227\) 28.9019i 1.91829i −0.282922 0.959143i \(-0.591304\pi\)
0.282922 0.959143i \(-0.408696\pi\)
\(228\) 3.34355 0.221432
\(229\) 27.5614i 1.82131i −0.413171 0.910654i \(-0.635579\pi\)
0.413171 0.910654i \(-0.364421\pi\)
\(230\) 10.4178 4.84756i 0.686931 0.319639i
\(231\) 0.363102 0.0238904
\(232\) 7.56116 7.56116i 0.496414 0.496414i
\(233\) −7.51093 + 7.51093i −0.492057 + 0.492057i −0.908954 0.416897i \(-0.863118\pi\)
0.416897 + 0.908954i \(0.363118\pi\)
\(234\) 1.53056i 0.100056i
\(235\) 10.0476 27.5355i 0.655431 1.79622i
\(236\) 5.91307 + 5.91307i 0.384908 + 0.384908i
\(237\) −1.17086 −0.0760557
\(238\) −1.31937 1.31937i −0.0855219 0.0855219i
\(239\) −6.73852 6.73852i −0.435879 0.435879i 0.454744 0.890622i \(-0.349731\pi\)
−0.890622 + 0.454744i \(0.849731\pi\)
\(240\) −0.766495 + 2.10059i −0.0494770 + 0.135593i
\(241\) −8.91683 + 8.91683i −0.574384 + 0.574384i −0.933350 0.358967i \(-0.883129\pi\)
0.358967 + 0.933350i \(0.383129\pi\)
\(242\) −10.7526 −0.691206
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 10.7956 + 10.7956i 0.691116 + 0.691116i
\(245\) −6.10063 13.1108i −0.389755 0.837617i
\(246\) 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 0.375795 0.926703i \(-0.377370\pi\)
−0.926703 + 0.375795i \(0.877370\pi\)
\(252\) 0.516238 + 0.516238i 0.0325200 + 0.0325200i
\(253\) 2.55573i 0.160677i
\(254\) 0.504136 0.504136i 0.0316323 0.0316323i
\(255\) 5.36855 + 1.95896i 0.336192 + 0.122675i
\(256\) 1.00000 0.0625000
\(257\) 6.57411i 0.410082i 0.978753 + 0.205041i \(0.0657327\pi\)
−0.978753 + 0.205041i \(0.934267\pi\)
\(258\) −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 −0.680685 0.732577i \(-0.738318\pi\)
0.732577 + 0.680685i \(0.238318\pi\)
\(264\) 0.351681 + 0.351681i 0.0216445 + 0.0216445i
\(265\) 1.22925 + 0.448546i 0.0755121 + 0.0275540i
\(266\) 2.44103 0.149669
\(267\) 8.82830i 0.540283i
\(268\) −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 \(0.465327\pi\)
\(272\) 2.55573i 0.154964i
\(273\) 1.11742i 0.0676291i
\(274\) 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
\(277\) −11.1501 −0.669946 −0.334973 0.942228i \(-0.608727\pi\)
−0.334973 + 0.942228i \(0.608727\pi\)
\(278\) −0.111253 −0.00667252
\(279\) 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 −0.967863 0.251480i \(-0.919083\pi\)
0.251480 + 0.967863i \(0.419083\pi\)
\(282\) 13.1085i 0.780597i
\(283\) 23.9142i 1.42155i −0.703419 0.710776i \(-0.748344\pi\)
0.703419 0.710776i \(-0.251656\pi\)
\(284\) −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
\(288\) 1.00000i 0.0589256i
\(289\) 10.4682 0.615778
\(290\) −8.19620 + 22.4618i −0.481297 + 1.31900i
\(291\) −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
\(298\) 16.2537i 0.941552i
\(299\) −7.86504 −0.454847
\(300\) −0.427648 4.98168i −0.0246902 0.287617i
\(301\) −4.67315 + 4.67315i −0.269356 + 0.269356i
\(302\) 15.7270i 0.904989i
\(303\) −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 0.509095 0.860710i \(-0.329980\pi\)
−0.860710 + 0.509095i \(0.829980\pi\)
\(308\) 0.256752 + 0.256752i 0.0146298 + 0.0146298i
\(309\) −11.0772 11.0772i −0.630161 0.630161i
\(310\) 17.5977 + 6.42132i 0.999485 + 0.364707i
\(311\) −12.1752 12.1752i −0.690392 0.690392i 0.271926 0.962318i \(-0.412339\pi\)
−0.962318 + 0.271926i \(0.912339\pi\)
\(312\) 1.08227 1.08227i 0.0612713 0.0612713i
\(313\) 3.47014 0.196144 0.0980720 0.995179i \(-0.468732\pi\)
0.0980720 + 0.995179i \(0.468732\pi\)
\(314\) 3.60469 3.60469i 0.203424 0.203424i
\(315\) −1.53358 0.559596i −0.0864075 0.0315297i
\(316\) −0.827925 0.827925i −0.0465744 0.0465744i
\(317\) 6.39255 + 6.39255i 0.359041 + 0.359041i 0.863460 0.504418i \(-0.168293\pi\)
−0.504418 + 0.863460i \(0.668293\pi\)
\(318\) 0.585191 0.0328159
\(319\) 3.76056 + 3.76056i 0.210551 + 0.210551i
\(320\) −2.02734 + 0.943349i −0.113332 + 0.0527348i
\(321\) 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
\(325\) −4.92868 + 5.85434i −0.273394 + 0.324740i
\(326\) 12.0896i 0.669580i
\(327\) −0.361581 −0.0199955
\(328\) 2.70364i 0.149284i
\(329\) 9.57011i 0.527617i
\(330\) −1.04473 0.381218i −0.0575107 0.0209854i
\(331\) −12.6298 + 12.6298i −0.694194 + 0.694194i −0.963152 0.268958i \(-0.913321\pi\)
0.268958 + 0.963152i \(0.413321\pi\)
\(332\) 11.2038 + 11.2038i 0.614888 + 0.614888i
\(333\) 3.93182 4.64120i 0.215463 0.254336i
\(334\) 11.3927i 0.623383i
\(335\) 27.6192 + 10.0781i 1.50900 + 0.550626i
\(336\) 0.730071i 0.0398286i
\(337\) 11.4706 + 11.4706i 0.624845 + 0.624845i 0.946766 0.321921i \(-0.104329\pi\)
−0.321921 + 0.946766i \(0.604329\pi\)
\(338\) 10.6574 0.579686
\(339\) −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
\(347\) −2.52563 −0.135583 −0.0677914 0.997700i \(-0.521595\pi\)
−0.0677914 + 0.997700i \(0.521595\pi\)
\(348\) 10.6931i 0.573210i
\(349\) 5.42724i 0.290514i 0.989394 + 0.145257i \(0.0464008\pi\)
−0.989394 + 0.145257i \(0.953599\pi\)
\(350\) −0.312213 3.63698i −0.0166885 0.194405i
\(351\) 1.08227 + 1.08227i 0.0577672 + 0.0577672i
\(352\) 0.497352i 0.0265090i
\(353\) 16.8913i 0.899034i 0.893272 + 0.449517i \(0.148404\pi\)
−0.893272 + 0.449517i \(0.851596\pi\)
\(354\) −8.36235 −0.444454
\(355\) 8.32486 3.87368i 0.441838 0.205594i
\(356\) 6.24255 6.24255i 0.330854 0.330854i
\(357\) 1.86587 0.0987522
\(358\) 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
\(362\) −9.48047 −0.498282
\(363\) 7.60327 7.60327i 0.399068 0.399068i
\(364\) 0.790132 0.790132i 0.0414142 0.0414142i
\(365\) 2.85200 7.81595i 0.149280 0.409105i
\(366\) −15.2672 −0.798032
\(367\) −13.8736 + 13.8736i −0.724195 + 0.724195i −0.969457 0.245262i \(-0.921126\pi\)
0.245262 + 0.969457i \(0.421126\pi\)
\(368\) 5.13868 0.267872
\(369\) −2.70364 −0.140746
\(370\) 13.1184 + 3.59286i 0.681991 + 0.186784i
\(371\) 0.427231 0.0221807
\(372\) 8.37752 0.434354
\(373\) −6.36168 + 6.36168i −0.329395 + 0.329395i −0.852356 0.522961i \(-0.824827\pi\)
0.522961 + 0.852356i \(0.324827\pi\)
\(374\) 1.27110 0.0657270
\(375\) 5.56645 + 9.69612i 0.287450 + 0.500705i
\(376\) 9.26908 9.26908i 0.478016 0.478016i
\(377\) 11.5728 11.5728i 0.596029 0.596029i
\(378\) −0.730071 −0.0375508
\(379\) 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
\(383\) −20.7631 −1.06094 −0.530472 0.847703i \(-0.677985\pi\)
−0.530472 + 0.847703i \(0.677985\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −0.762730 0.278316i −0.0388723 0.0141843i
\(386\) −8.67065 −0.441325
\(387\) 9.05230i 0.460154i
\(388\) 3.13965i 0.159391i
\(389\) 20.8063 + 20.8063i 1.05492 + 1.05492i 0.998401 + 0.0565210i \(0.0180008\pi\)
0.0565210 + 0.998401i \(0.481999\pi\)
\(390\) −1.17316 + 3.21508i −0.0594055 + 0.162802i
\(391\) 13.1331i 0.664169i
\(392\) 6.46700i 0.326633i
\(393\) 21.5260 1.08584
\(394\) −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 0.839156 0.543891i \(-0.183050\pi\)
−0.543891 + 0.839156i \(0.683050\pi\)
\(398\) 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 0.243090 0.970004i \(-0.421839\pi\)
−0.970004 + 0.243090i \(0.921839\pi\)
\(402\) 13.1483 0.655778
\(403\) −9.06671 9.06671i −0.451645 0.451645i
\(404\) 4.17592i 0.207760i
\(405\) 2.02734 0.943349i 0.100739 0.0468754i
\(406\) 7.80672i 0.387441i
\(407\) 1.95550 2.30831i 0.0969306 0.114419i
\(408\) 1.80718 + 1.80718i 0.0894686 + 0.0894686i
\(409\) 11.0869 11.0869i 0.548211 0.548211i −0.377712 0.925923i \(-0.623289\pi\)
0.925923 + 0.377712i \(0.123289\pi\)
\(410\) −2.55048 5.48119i −0.125959 0.270697i
\(411\) 14.8551i 0.732749i
\(412\) 15.6656i 0.771787i
\(413\) −6.10511 −0.300413
\(414\) 5.13868i 0.252552i
\(415\) −33.2830 12.1448i −1.63380 0.596164i
\(416\) 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 \(-0.180822\pi\)
\(420\) −0.688712 1.48010i −0.0336057 0.0722215i
\(421\) 22.6650 + 22.6650i 1.10463 + 1.10463i 0.993845 + 0.110782i \(0.0353356\pi\)
0.110782 + 0.993845i \(0.464664\pi\)
\(422\) 24.6681 1.20083
\(423\) 9.26908 + 9.26908i 0.450678 + 0.450678i
\(424\) 0.413793 + 0.413793i 0.0200956 + 0.0200956i
\(425\) −9.77561 8.22994i −0.474187 0.399211i
\(426\) 2.90360 2.90360i 0.140680 0.140680i
\(427\) −11.1462 −0.539401
\(428\) −0.609066 + 0.609066i −0.0294403 + 0.0294403i
\(429\) 0.538268 + 0.538268i 0.0259878 + 0.0259878i
\(430\) 18.3521 8.53948i 0.885015 0.411810i
\(431\) 17.9692 + 17.9692i 0.865547 + 0.865547i 0.991976 0.126428i \(-0.0403514\pi\)
−0.126428 + 0.991976i \(0.540351\pi\)
\(432\) −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
\(438\) 3.72083i 0.177788i
\(439\) −24.7771 + 24.7771i −1.18255 + 1.18255i −0.203463 + 0.979083i \(0.565220\pi\)
−0.979083 + 0.203463i \(0.934780\pi\)
\(440\) −0.469177 1.00830i −0.0223671 0.0480688i
\(441\) 6.46700 0.307952
\(442\) 3.91170i 0.186060i
\(443\) −11.6985 + 11.6985i −0.555811 + 0.555811i −0.928112 0.372301i \(-0.878569\pi\)
0.372301 + 0.928112i \(0.378569\pi\)
\(444\) 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 \(-0.0658740\pi\)
−0.205475 + 0.978662i \(0.565874\pi\)
\(450\) 3.82497 + 3.22019i 0.180311 + 0.151801i
\(451\) −1.34466 −0.0633177
\(452\) 12.8460i 0.604226i
\(453\) 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
\(457\) 36.6470i 1.71427i 0.515089 + 0.857137i \(0.327759\pi\)
−0.515089 + 0.857137i \(0.672241\pi\)
\(458\) 27.5614i 1.28786i
\(459\) −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 −0.811550 0.584283i \(-0.801376\pi\)
0.584283 + 0.811550i \(0.301376\pi\)
\(462\) −0.363102 −0.0168931
\(463\) 3.03199 0.140908 0.0704542 0.997515i \(-0.477555\pi\)
0.0704542 + 0.997515i \(0.477555\pi\)
\(464\) −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
\(467\) 7.88298i 0.364781i 0.983226 + 0.182390i \(0.0583835\pi\)
−0.983226 + 0.182390i \(0.941616\pi\)
\(468\) 1.53056i 0.0707500i
\(469\) 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
\(473\) 4.50218i 0.207011i
\(474\) 1.17086 0.0537795
\(475\) 16.6565 1.42986i 0.764253 0.0656066i
\(476\) 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 0.999818 + 0.0190898i \(0.00607685\pi\)
0.0190898 + 0.999818i \(0.493923\pi\)
\(480\) 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
\(483\) 3.75160i 0.170704i
\(484\) 10.7526 0.488756
\(485\) 2.96178 + 6.36512i 0.134488 + 0.289025i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 12.8810i 0.583695i −0.956465 0.291847i \(-0.905730\pi\)
0.956465 0.291847i \(-0.0942699\pi\)
\(488\) −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
\(495\) 1.00830 0.469177i 0.0453197 0.0210879i
\(496\) 5.92380 + 5.92380i 0.265986 + 0.265986i
\(497\) 2.11983 2.11983i 0.0950875 0.0950875i
\(498\) −15.8446 −0.710012
\(499\) 17.8190 17.8190i 0.797689 0.797689i −0.185042 0.982731i \(-0.559242\pi\)
0.982731 + 0.185042i \(0.0592421\pi\)
\(500\) −2.92012 + 10.7923i −0.130592 + 0.482645i
\(501\) −8.05588 8.05588i −0.359910 0.359910i
\(502\) 8.72803 + 8.72803i 0.389551 + 0.389551i
\(503\) 17.9635 0.800955 0.400477 0.916307i \(-0.368844\pi\)
0.400477 + 0.916307i \(0.368844\pi\)
\(504\) −0.516238 0.516238i −0.0229951 0.0229951i
\(505\) 3.93935 + 8.46599i 0.175299 + 0.376731i
\(506\) 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 \(-0.440649\pi\)
0.185378 + 0.982667i \(0.440649\pi\)
\(510\) −5.36855 1.95896i −0.237723 0.0867441i
\(511\) 2.71647i 0.120170i
\(512\) −1.00000 −0.0441942
\(513\) 3.34355i 0.147622i
\(514\) 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
\(518\) 4.42572 0.366209i 0.194455 0.0160903i
\(519\) 19.0028i 0.834131i
\(520\) −3.10295 + 1.44385i −0.136074 + 0.0633170i
\(521\) 16.5234i 0.723904i −0.932197 0.361952i \(-0.882110\pi\)
0.932197 0.361952i \(-0.117890\pi\)
\(522\) −7.56116 7.56116i −0.330943 0.330943i
\(523\) 14.2767 0.624278 0.312139 0.950036i \(-0.398954\pi\)
0.312139 + 0.950036i \(0.398954\pi\)
\(524\) 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
\(532\) −2.44103 −0.105832
\(533\) 4.13808i 0.179240i
\(534\) 8.82830i 0.382038i
\(535\) 0.660220 1.80934i 0.0285438 0.0782247i
\(536\) 9.29726 + 9.29726i 0.401580 + 0.401580i
\(537\) 10.7933i 0.465764i
\(538\) 16.4147i 0.707689i
\(539\) 3.21637 0.138539
\(540\) 2.10059 + 0.766495i 0.0903951 + 0.0329847i
\(541\) −2.99943 + 2.99943i −0.128955 + 0.128955i −0.768639 0.639683i \(-0.779066\pi\)
0.639683 + 0.768639i \(0.279066\pi\)
\(542\) −3.57932 −0.153745
\(543\) 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
\(547\) −20.8842 −0.892944 −0.446472 0.894798i \(-0.647320\pi\)
−0.446472 + 0.894798i \(0.647320\pi\)
\(548\) −10.5042 + 10.5042i −0.448715 + 0.448715i
\(549\) 10.7956 10.7956i 0.460744 0.460744i
\(550\) 1.90236 + 1.60157i 0.0811168 + 0.0682910i
\(551\) −35.7529 −1.52313
\(552\) −3.63359 + 3.63359i −0.154656 + 0.154656i
\(553\) 0.854813 0.0363504
\(554\) 11.1501 0.473723
\(555\) −11.8166 + 6.73555i −0.501587 + 0.285908i
\(556\) 0.111253 0.00471819
\(557\) −10.1584 −0.430426 −0.215213 0.976567i \(-0.569045\pi\)
−0.215213 + 0.976567i \(0.569045\pi\)
\(558\) −5.92380 + 5.92380i −0.250774 + 0.250774i
\(559\) −13.8551 −0.586007
\(560\) 0.559596 1.53358i 0.0236472 0.0648056i
\(561\) −0.898803 + 0.898803i −0.0379475 + 0.0379475i
\(562\) 12.0088 12.0088i 0.506559 0.506559i
\(563\) 13.4772 0.567996 0.283998 0.958825i \(-0.408339\pi\)
0.283998 + 0.958825i \(0.408339\pi\)
\(564\) 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
\(568\) 4.10631 0.172297
\(569\) 0.956429 0.956429i 0.0400956 0.0400956i −0.686775 0.726870i \(-0.740974\pi\)
0.726870 + 0.686775i \(0.240974\pi\)
\(570\) 6.77851 3.15414i 0.283920 0.132112i
\(571\) −1.80272 −0.0754415 −0.0377208 0.999288i \(-0.512010\pi\)
−0.0377208 + 0.999288i \(0.512010\pi\)
\(572\) 0.761226i 0.0318285i
\(573\) 18.8570i 0.787763i
\(574\) −1.39572 1.39572i −0.0582564 0.0582564i
\(575\) 16.5475 19.6553i 0.690078 0.819682i
\(576\) 1.00000i 0.0416667i
\(577\) 21.8641i 0.910216i 0.890436 + 0.455108i \(0.150399\pi\)
−0.890436 + 0.455108i \(0.849601\pi\)
\(578\) −10.4682 −0.435421
\(579\) 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
\(587\) 13.4925 0.556896 0.278448 0.960451i \(-0.410180\pi\)
0.278448 + 0.960451i \(0.410180\pi\)
\(588\) 4.57286 + 4.57286i 0.188581 + 0.188581i
\(589\) 28.0107i 1.15416i
\(590\) 17.5659 + 6.40970i 0.723176 + 0.263883i
\(591\) 7.57983i 0.311793i
\(592\) 4.64120 + 3.93182i 0.190752 + 0.161597i
\(593\) −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
\(597\) 18.6140i 0.761822i
\(598\) 7.86504 0.321625
\(599\) 1.58656i 0.0648249i 0.999475 + 0.0324125i \(0.0103190\pi\)
−0.999475 + 0.0324125i \(0.989681\pi\)
\(600\) 0.427648 + 4.98168i 0.0174586 + 0.203376i
\(601\) 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
\(605\) −21.7992 + 10.1435i −0.886264 + 0.412392i
\(606\) 2.95282 + 2.95282i 0.119950 + 0.119950i
\(607\) −29.3879 −1.19282 −0.596409 0.802680i \(-0.703407\pi\)
−0.596409 + 0.802680i \(0.703407\pi\)
\(608\) −2.36425 2.36425i −0.0958830 0.0958830i
\(609\) −5.52018 5.52018i −0.223689 0.223689i
\(610\) 32.0702 + 11.7023i 1.29849 + 0.473811i
\(611\) 14.1869 14.1869i 0.573939 0.573939i
\(612\) −2.55573 −0.103309
\(613\) 11.9588 11.9588i 0.483011 0.483011i −0.423081 0.906092i \(-0.639051\pi\)
0.906092 + 0.423081i \(0.139051\pi\)
\(614\) 6.16080 + 6.16080i 0.248630 + 0.248630i
\(615\) 5.67925 + 2.07233i 0.229009 + 0.0835644i
\(616\) −0.256752 0.256752i −0.0103448 0.0103448i
\(617\) 19.8923 + 19.8923i 0.800835 + 0.800835i 0.983226 0.182391i \(-0.0583836\pi\)
−0.182391 + 0.983226i \(0.558384\pi\)
\(618\) 11.0772 + 11.0772i 0.445591 + 0.445591i
\(619\) −25.0352 −1.00625 −0.503125 0.864213i \(-0.667817\pi\)
−0.503125 + 0.864213i \(0.667817\pi\)
\(620\) −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
\(623\) 6.44528i 0.258225i
\(624\) −1.08227 + 1.08227i −0.0433254 + 0.0433254i
\(625\) −4.26081 24.6342i −0.170432 0.985369i
\(626\) −3.47014 −0.138695
\(627\) 1.66292i 0.0664108i
\(628\) −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 0.352733 0.935724i \(-0.385252\pi\)
−0.935724 + 0.352733i \(0.885252\pi\)
\(632\) 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
\(635\) 0.546478 1.49763i 0.0216863 0.0594317i
\(636\) −0.585191 −0.0232043
\(637\) 9.89811i 0.392177i
\(638\) −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 \(0.379134\pi\)
\(642\) 0.861349i 0.0339947i
\(643\) 33.3318i 1.31448i −0.753683 0.657238i \(-0.771725\pi\)
0.753683 0.657238i \(-0.228275\pi\)
\(644\) −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
\(647\) 20.5310 0.807156 0.403578 0.914945i \(-0.367766\pi\)
0.403578 + 0.914945i \(0.367766\pi\)
\(648\) 1.00000 0.0392837
\(649\) 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
\(652\) 12.0896i 0.473465i
\(653\) 26.4235i 1.03403i 0.855976 + 0.517016i \(0.172957\pi\)
−0.855976 + 0.517016i \(0.827043\pi\)
\(654\) 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
\(658\) 9.57011i 0.373082i
\(659\) 39.4006 1.53483 0.767414 0.641152i \(-0.221543\pi\)
0.767414 + 0.641152i \(0.221543\pi\)
\(660\) 1.04473 + 0.381218i 0.0406662 + 0.0148389i
\(661\) 7.90042 + 7.90042i 0.307291 + 0.307291i 0.843858 0.536567i \(-0.180279\pi\)
−0.536567 + 0.843858i \(0.680279\pi\)
\(662\) 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
\(668\) 11.3927i 0.440798i
\(669\) −15.6137 −0.603659
\(670\) −27.6192 10.0781i −1.06702 0.389351i
\(671\) 5.36920 5.36920i 0.207276 0.207276i
\(672\) 0.730071i 0.0281631i
\(673\) −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 0.984800 0.173690i \(-0.0555691\pi\)
−0.173690 + 0.984800i \(0.555569\pi\)
\(678\) 9.08351 + 9.08351i 0.348850 + 0.348850i
\(679\) 1.62081 + 1.62081i 0.0622008 + 0.0622008i
\(680\) −2.41095 5.18133i −0.0924556 0.198695i
\(681\) −20.4367 20.4367i −0.783137 0.783137i
\(682\) −2.94621 + 2.94621i −0.112816 + 0.112816i
\(683\) 35.4086 1.35487 0.677437 0.735581i \(-0.263091\pi\)
0.677437 + 0.735581i \(0.263091\pi\)
\(684\) 2.36425 2.36425i 0.0903993 0.0903993i
\(685\) 11.3864 31.2045i 0.435051 1.19226i
\(686\) 6.95218 + 6.95218i 0.265435 + 0.265435i
\(687\) −19.4888 19.4888i −0.743546 0.743546i
\(688\) 9.05230 0.345116
\(689\) 0.633334 + 0.633334i 0.0241281 + 0.0241281i
\(690\) 3.93877 10.7943i 0.149946 0.410930i
\(691\) 22.4704i 0.854814i −0.904059 0.427407i \(-0.859427\pi\)
0.904059 0.427407i \(-0.140573\pi\)
\(692\) 13.4370 13.4370i 0.510799 0.510799i
\(693\) 0.256752 0.256752i 0.00975321 0.00975321i
\(694\) 2.52563 0.0958715
\(695\) −0.225548 + 0.104951i −0.00855551 + 0.00398100i
\(696\) 10.6931i 0.405321i
\(697\) −6.90979 −0.261727
\(698\) 5.42724i 0.205424i
\(699\) 10.6221i 0.401763i
\(700\) 0.312213 + 3.63698i 0.0118005 + 0.137465i
\(701\) 15.2902 15.2902i 0.577504 0.577504i −0.356711 0.934215i \(-0.616102\pi\)
0.934215 + 0.356711i \(0.116102\pi\)
\(702\) −1.08227 1.08227i −0.0408475 0.0408475i
\(703\) 1.67715 + 20.2688i 0.0632549 + 0.764451i
\(704\) 0.497352i 0.0187447i
\(705\) −12.3658 26.5753i −0.465725 1.00088i
\(706\) 16.8913i 0.635713i
\(707\) 2.15577 + 2.15577i 0.0810760 + 0.0810760i
\(708\) 8.36235 0.314276
\(709\) 11.5740 + 11.5740i 0.434672 + 0.434672i 0.890214 0.455542i \(-0.150555\pi\)
−0.455542 + 0.890214i \(0.650555\pi\)
\(710\) −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
\(717\) −9.52971 −0.355893
\(718\) 10.2084i 0.380976i
\(719\) 33.1940i 1.23793i −0.785420 0.618963i \(-0.787553\pi\)
0.785420 0.618963i \(-0.212447\pi\)
\(720\) 0.943349 + 2.02734i 0.0351565 + 0.0755544i
\(721\) 8.08716 + 8.08716i 0.301182 + 0.301182i
\(722\) 7.82065i 0.291054i
\(723\) 12.6103i 0.468982i
\(724\) 9.48047 0.352339
\(725\) 4.57288 + 53.2695i 0.169832 + 1.97838i
\(726\) −7.60327 + 7.60327i −0.282184 + 0.282184i
\(727\) 25.8130 0.957352 0.478676 0.877992i \(-0.341117\pi\)
0.478676 + 0.877992i \(0.341117\pi\)
\(728\) −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
\(732\) 15.2672 0.564294
\(733\) −29.0185 + 29.0185i −1.07182 + 1.07182i −0.0746110 + 0.997213i \(0.523772\pi\)
−0.997213 + 0.0746110i \(0.976228\pi\)
\(734\) 13.8736 13.8736i 0.512083 0.512083i
\(735\) −13.5845 4.95692i −0.501073 0.182839i
\(736\) −5.13868 −0.189414
\(737\) −4.62401 + 4.62401i −0.170328 + 0.170328i
\(738\) 2.70364 0.0995225
\(739\) −33.6130 −1.23647 −0.618236 0.785992i \(-0.712153\pi\)
−0.618236 + 0.785992i \(0.712153\pi\)
\(740\) −13.1184 3.59286i −0.482241 0.132076i
\(741\) −5.11750 −0.187996
\(742\) −0.427231 −0.0156842
\(743\) −15.7302 + 15.7302i −0.577084 + 0.577084i −0.934099 0.357015i \(-0.883795\pi\)
0.357015 + 0.934099i \(0.383795\pi\)
\(744\) −8.37752 −0.307135
\(745\) −15.3329 32.9517i −0.561754 1.20726i
\(746\) 6.36168 6.36168i 0.232918 0.232918i
\(747\) 11.2038 11.2038i 0.409926 0.409926i
\(748\) −1.27110 −0.0464760
\(749\) 0.628846i 0.0229775i
\(750\) −5.56645 9.69612i −0.203258 0.354052i
\(751\) 12.7266i 0.464401i −0.972668 0.232201i \(-0.925407\pi\)
0.972668 0.232201i \(-0.0745926\pi\)
\(752\) −9.26908 + 9.26908i −0.338009 + 0.338009i
\(753\) −12.3433 −0.449815
\(754\) −11.5728 + 11.5728i −0.421456 + 0.421456i
\(755\) −14.8361 31.8840i −0.539940 1.16038i
\(756\) 0.730071 0.0265524
\(757\) 49.4794i 1.79836i −0.437578 0.899181i \(-0.644164\pi\)
0.437578 0.899181i \(-0.355836\pi\)
\(758\) 10.4081i 0.378038i
\(759\) −1.80718 1.80718i −0.0655963 0.0655963i
\(760\) 7.02344 + 2.56282i 0.254767 + 0.0929632i
\(761\) 10.2526i 0.371657i −0.982582 0.185828i \(-0.940503\pi\)
0.982582 0.185828i \(-0.0594968\pi\)
\(762\) 0.712957i 0.0258277i
\(763\) 0.263980 0.00955671
\(764\) 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 \(-0.902604\pi\)
0.301226 + 0.953553i \(0.402604\pi\)
\(770\) 0.762730 + 0.278316i 0.0274869 + 0.0100298i
\(771\) 4.64860 + 4.64860i 0.167415 + 0.167415i
\(772\) 8.67065 0.312064
\(773\) 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
\(775\) 41.7341 3.58263i 1.49913 0.128692i
\(776\) 3.13965i 0.112707i
\(777\) −2.87051 + 3.38841i −0.102979 + 0.121558i
\(778\) −20.8063 20.8063i −0.745943 0.745943i
\(779\) 6.39209 6.39209i 0.229020 0.229020i