Properties

Label 225.4.e.f.151.8
Level $225$
Weight $4$
Character 225.151
Analytic conductor $13.275$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 151.8
Character \(\chi\) \(=\) 225.151
Dual form 225.4.e.f.76.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.07290 - 1.85832i) q^{2} +(-2.66146 + 4.46280i) q^{3} +(1.69777 + 2.94063i) q^{4} +(5.43782 + 9.73398i) q^{6} +(11.6282 - 20.1406i) q^{7} +24.4526 q^{8} +(-12.8333 - 23.7552i) q^{9} +O(q^{10})\) \(q+(1.07290 - 1.85832i) q^{2} +(-2.66146 + 4.46280i) q^{3} +(1.69777 + 2.94063i) q^{4} +(5.43782 + 9.73398i) q^{6} +(11.6282 - 20.1406i) q^{7} +24.4526 q^{8} +(-12.8333 - 23.7552i) q^{9} +(-6.24976 + 10.8249i) q^{11} +(-17.6420 - 0.249540i) q^{12} +(25.3078 + 43.8344i) q^{13} +(-24.9518 - 43.2178i) q^{14} +(12.6529 - 21.9155i) q^{16} +63.6794 q^{17} +(-57.9134 - 1.63865i) q^{18} +5.41153 q^{19} +(58.9358 + 105.498i) q^{21} +(13.4107 + 23.2281i) q^{22} +(44.2335 + 76.6146i) q^{23} +(-65.0795 + 109.127i) q^{24} +108.611 q^{26} +(140.170 + 5.95112i) q^{27} +78.9683 q^{28} +(-72.2845 + 125.200i) q^{29} +(138.980 + 240.720i) q^{31} +(70.6596 + 122.386i) q^{32} +(-31.6759 - 56.7015i) q^{33} +(68.3216 - 118.337i) q^{34} +(48.0672 - 78.0687i) q^{36} +243.269 q^{37} +(5.80603 - 10.0563i) q^{38} +(-262.980 - 3.71976i) q^{39} +(-234.286 - 405.796i) q^{41} +(259.281 + 3.66743i) q^{42} +(249.205 - 431.637i) q^{43} -42.4427 q^{44} +189.832 q^{46} +(-226.262 + 391.897i) q^{47} +(64.1294 + 114.795i) q^{48} +(-98.9304 - 171.352i) q^{49} +(-169.480 + 284.189i) q^{51} +(-85.9339 + 148.842i) q^{52} -223.885 q^{53} +(161.447 - 254.095i) q^{54} +(284.339 - 492.490i) q^{56} +(-14.4026 + 24.1506i) q^{57} +(155.108 + 268.655i) q^{58} +(-57.9657 - 100.400i) q^{59} +(-41.3965 + 71.7008i) q^{61} +596.444 q^{62} +(-627.672 - 17.7599i) q^{63} +505.689 q^{64} +(-139.354 - 1.97112i) q^{66} +(-405.064 - 701.592i) q^{67} +(108.113 + 187.258i) q^{68} +(-459.642 - 6.50146i) q^{69} -134.171 q^{71} +(-313.806 - 580.874i) q^{72} +707.508 q^{73} +(261.003 - 452.070i) q^{74} +(9.18755 + 15.9133i) q^{76} +(145.347 + 251.748i) q^{77} +(-289.064 + 484.710i) q^{78} +(-208.821 + 361.689i) q^{79} +(-399.615 + 609.712i) q^{81} -1005.46 q^{82} +(461.443 - 799.243i) q^{83} +(-210.171 + 352.420i) q^{84} +(-534.745 - 926.205i) q^{86} +(-366.363 - 655.808i) q^{87} +(-152.823 + 264.696i) q^{88} +114.544 q^{89} +1177.14 q^{91} +(-150.197 + 260.149i) q^{92} +(-1444.17 - 20.4273i) q^{93} +(485.513 + 840.932i) q^{94} +(-734.242 - 10.3856i) q^{96} +(-180.777 + 313.115i) q^{97} -424.569 q^{98} +(337.352 + 9.54534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} - 29 q^{11} + 77 q^{12} - 24 q^{13} + 69 q^{14} - 192 q^{16} - 158 q^{17} - 125 q^{18} - 150 q^{19} - 60 q^{21} + 18 q^{22} + 318 q^{23} + 342 q^{24} - 308 q^{26} + 394 q^{27} + 192 q^{28} - 106 q^{29} - 60 q^{31} + 914 q^{32} + 80 q^{33} + 108 q^{34} + 1303 q^{36} - 168 q^{37} + 640 q^{38} - 410 q^{39} + 353 q^{41} - 1521 q^{42} + 426 q^{43} + 1142 q^{44} + 540 q^{46} + 1210 q^{47} - 2680 q^{48} - 666 q^{49} - 1369 q^{51} + 75 q^{52} - 896 q^{53} - 2128 q^{54} + 570 q^{56} - 1544 q^{57} - 594 q^{58} - 482 q^{59} - 402 q^{61} - 5088 q^{62} + 1038 q^{63} + 1950 q^{64} + 2041 q^{66} + 201 q^{67} + 3437 q^{68} + 2856 q^{69} - 1888 q^{71} + 5493 q^{72} - 906 q^{73} - 10 q^{74} + 462 q^{76} + 2652 q^{77} + 4589 q^{78} - 258 q^{79} + 3071 q^{81} + 1746 q^{82} + 3012 q^{83} - 2703 q^{84} - 1952 q^{86} - 2708 q^{87} + 216 q^{88} - 1476 q^{89} - 1236 q^{91} + 5232 q^{92} - 3024 q^{93} - 63 q^{94} - 10424 q^{96} + 318 q^{97} - 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.07290 1.85832i 0.379327 0.657014i −0.611637 0.791138i \(-0.709489\pi\)
0.990965 + 0.134124i \(0.0428221\pi\)
\(3\) −2.66146 + 4.46280i −0.512198 + 0.858867i
\(4\) 1.69777 + 2.94063i 0.212222 + 0.367579i
\(5\) 0 0
\(6\) 5.43782 + 9.73398i 0.369997 + 0.662313i
\(7\) 11.6282 20.1406i 0.627864 1.08749i −0.360115 0.932908i \(-0.617263\pi\)
0.987980 0.154585i \(-0.0494040\pi\)
\(8\) 24.4526 1.08066
\(9\) −12.8333 23.7552i −0.475306 0.879821i
\(10\) 0 0
\(11\) −6.24976 + 10.8249i −0.171307 + 0.296712i −0.938877 0.344253i \(-0.888132\pi\)
0.767570 + 0.640965i \(0.221466\pi\)
\(12\) −17.6420 0.249540i −0.424401 0.00600299i
\(13\) 25.3078 + 43.8344i 0.539933 + 0.935191i 0.998907 + 0.0467417i \(0.0148838\pi\)
−0.458974 + 0.888450i \(0.651783\pi\)
\(14\) −24.9518 43.2178i −0.476332 0.825031i
\(15\) 0 0
\(16\) 12.6529 21.9155i 0.197702 0.342430i
\(17\) 63.6794 0.908502 0.454251 0.890874i \(-0.349907\pi\)
0.454251 + 0.890874i \(0.349907\pi\)
\(18\) −57.9134 1.63865i −0.758351 0.0214575i
\(19\) 5.41153 0.0653416 0.0326708 0.999466i \(-0.489599\pi\)
0.0326708 + 0.999466i \(0.489599\pi\)
\(20\) 0 0
\(21\) 58.9358 + 105.498i 0.612421 + 1.09626i
\(22\) 13.4107 + 23.2281i 0.129963 + 0.225102i
\(23\) 44.2335 + 76.6146i 0.401014 + 0.694576i 0.993849 0.110748i \(-0.0353247\pi\)
−0.592835 + 0.805324i \(0.701991\pi\)
\(24\) −65.0795 + 109.127i −0.553512 + 0.928144i
\(25\) 0 0
\(26\) 108.611 0.819245
\(27\) 140.170 + 5.95112i 0.999100 + 0.0424183i
\(28\) 78.9683 0.532986
\(29\) −72.2845 + 125.200i −0.462858 + 0.801694i −0.999102 0.0423690i \(-0.986510\pi\)
0.536244 + 0.844063i \(0.319843\pi\)
\(30\) 0 0
\(31\) 138.980 + 240.720i 0.805208 + 1.39466i 0.916150 + 0.400835i \(0.131280\pi\)
−0.110942 + 0.993827i \(0.535387\pi\)
\(32\) 70.6596 + 122.386i 0.390343 + 0.676093i
\(33\) −31.6759 56.7015i −0.167093 0.299105i
\(34\) 68.3216 118.337i 0.344619 0.596898i
\(35\) 0 0
\(36\) 48.0672 78.0687i 0.222533 0.361429i
\(37\) 243.269 1.08090 0.540448 0.841378i \(-0.318255\pi\)
0.540448 + 0.841378i \(0.318255\pi\)
\(38\) 5.80603 10.0563i 0.0247858 0.0429303i
\(39\) −262.980 3.71976i −1.07976 0.0152728i
\(40\) 0 0
\(41\) −234.286 405.796i −0.892424 1.54572i −0.836961 0.547263i \(-0.815670\pi\)
−0.0554628 0.998461i \(-0.517663\pi\)
\(42\) 259.281 + 3.66743i 0.952569 + 0.0134737i
\(43\) 249.205 431.637i 0.883802 1.53079i 0.0367211 0.999326i \(-0.488309\pi\)
0.847081 0.531464i \(-0.178358\pi\)
\(44\) −42.4427 −0.145420
\(45\) 0 0
\(46\) 189.832 0.608462
\(47\) −226.262 + 391.897i −0.702206 + 1.21626i 0.265484 + 0.964115i \(0.414468\pi\)
−0.967690 + 0.252142i \(0.918865\pi\)
\(48\) 64.1294 + 114.795i 0.192839 + 0.345192i
\(49\) −98.9304 171.352i −0.288427 0.499570i
\(50\) 0 0
\(51\) −169.480 + 284.189i −0.465333 + 0.780282i
\(52\) −85.9339 + 148.842i −0.229171 + 0.396936i
\(53\) −223.885 −0.580244 −0.290122 0.956990i \(-0.593696\pi\)
−0.290122 + 0.956990i \(0.593696\pi\)
\(54\) 161.447 254.095i 0.406855 0.640332i
\(55\) 0 0
\(56\) 284.339 492.490i 0.678508 1.17521i
\(57\) −14.4026 + 24.1506i −0.0334679 + 0.0561197i
\(58\) 155.108 + 268.655i 0.351150 + 0.608209i
\(59\) −57.9657 100.400i −0.127907 0.221541i 0.794959 0.606663i \(-0.207492\pi\)
−0.922865 + 0.385123i \(0.874159\pi\)
\(60\) 0 0
\(61\) −41.3965 + 71.7008i −0.0868898 + 0.150497i −0.906195 0.422860i \(-0.861026\pi\)
0.819305 + 0.573358i \(0.194359\pi\)
\(62\) 596.444 1.22175
\(63\) −627.672 17.7599i −1.25523 0.0355165i
\(64\) 505.689 0.987675
\(65\) 0 0
\(66\) −139.354 1.97112i −0.259899 0.00367617i
\(67\) −405.064 701.592i −0.738604 1.27930i −0.953124 0.302580i \(-0.902152\pi\)
0.214520 0.976720i \(-0.431181\pi\)
\(68\) 108.113 + 187.258i 0.192804 + 0.333946i
\(69\) −459.642 6.50146i −0.801947 0.0113432i
\(70\) 0 0
\(71\) −134.171 −0.224270 −0.112135 0.993693i \(-0.535769\pi\)
−0.112135 + 0.993693i \(0.535769\pi\)
\(72\) −313.806 580.874i −0.513644 0.950787i
\(73\) 707.508 1.13435 0.567175 0.823597i \(-0.308036\pi\)
0.567175 + 0.823597i \(0.308036\pi\)
\(74\) 261.003 452.070i 0.410013 0.710163i
\(75\) 0 0
\(76\) 9.18755 + 15.9133i 0.0138669 + 0.0240182i
\(77\) 145.347 + 251.748i 0.215115 + 0.372589i
\(78\) −289.064 + 484.710i −0.419616 + 0.703623i
\(79\) −208.821 + 361.689i −0.297396 + 0.515104i −0.975539 0.219825i \(-0.929451\pi\)
0.678144 + 0.734929i \(0.262785\pi\)
\(80\) 0 0
\(81\) −399.615 + 609.712i −0.548169 + 0.836368i
\(82\) −1005.46 −1.35408
\(83\) 461.443 799.243i 0.610240 1.05697i −0.380959 0.924592i \(-0.624406\pi\)
0.991200 0.132376i \(-0.0422605\pi\)
\(84\) −210.171 + 352.420i −0.272994 + 0.457764i
\(85\) 0 0
\(86\) −534.745 926.205i −0.670500 1.16134i
\(87\) −366.363 655.808i −0.451474 0.808160i
\(88\) −152.823 + 264.696i −0.185124 + 0.320645i
\(89\) 114.544 0.136423 0.0682116 0.997671i \(-0.478271\pi\)
0.0682116 + 0.997671i \(0.478271\pi\)
\(90\) 0 0
\(91\) 1177.14 1.35602
\(92\) −150.197 + 260.149i −0.170208 + 0.294808i
\(93\) −1444.17 20.4273i −1.61026 0.0227765i
\(94\) 485.513 + 840.932i 0.532732 + 0.922719i
\(95\) 0 0
\(96\) −734.242 10.3856i −0.780607 0.0110414i
\(97\) −180.777 + 313.115i −0.189228 + 0.327753i −0.944993 0.327090i \(-0.893932\pi\)
0.755765 + 0.654843i \(0.227265\pi\)
\(98\) −424.569 −0.437633
\(99\) 337.352 + 9.54534i 0.342476 + 0.00969033i
\(100\) 0 0
\(101\) −144.611 + 250.473i −0.142469 + 0.246763i −0.928426 0.371518i \(-0.878837\pi\)
0.785957 + 0.618281i \(0.212171\pi\)
\(102\) 346.277 + 619.854i 0.336143 + 0.601713i
\(103\) 241.404 + 418.124i 0.230934 + 0.399990i 0.958083 0.286490i \(-0.0924884\pi\)
−0.727149 + 0.686480i \(0.759155\pi\)
\(104\) 618.841 + 1071.86i 0.583484 + 1.01062i
\(105\) 0 0
\(106\) −240.206 + 416.049i −0.220102 + 0.381229i
\(107\) −1796.65 −1.62326 −0.811628 0.584175i \(-0.801418\pi\)
−0.811628 + 0.584175i \(0.801418\pi\)
\(108\) 220.477 + 422.291i 0.196439 + 0.376250i
\(109\) 1507.20 1.32443 0.662216 0.749313i \(-0.269616\pi\)
0.662216 + 0.749313i \(0.269616\pi\)
\(110\) 0 0
\(111\) −647.450 + 1085.66i −0.553633 + 0.928346i
\(112\) −294.262 509.677i −0.248260 0.429999i
\(113\) −1075.02 1861.98i −0.894948 1.55010i −0.833869 0.551962i \(-0.813879\pi\)
−0.0610790 0.998133i \(-0.519454\pi\)
\(114\) 29.4269 + 52.6757i 0.0241762 + 0.0432766i
\(115\) 0 0
\(116\) −490.891 −0.392914
\(117\) 716.512 1163.73i 0.566168 0.919546i
\(118\) −248.765 −0.194074
\(119\) 740.478 1282.54i 0.570416 0.987989i
\(120\) 0 0
\(121\) 587.381 + 1017.37i 0.441308 + 0.764368i
\(122\) 88.8285 + 153.855i 0.0659193 + 0.114176i
\(123\) 2434.53 + 34.4355i 1.78467 + 0.0252435i
\(124\) −471.912 + 817.375i −0.341765 + 0.591955i
\(125\) 0 0
\(126\) −706.432 + 1147.36i −0.499476 + 0.811229i
\(127\) −1288.35 −0.900180 −0.450090 0.892983i \(-0.648608\pi\)
−0.450090 + 0.892983i \(0.648608\pi\)
\(128\) −22.7226 + 39.3567i −0.0156907 + 0.0271772i
\(129\) 1263.06 + 2260.94i 0.862063 + 1.54314i
\(130\) 0 0
\(131\) −851.472 1474.79i −0.567889 0.983612i −0.996774 0.0802534i \(-0.974427\pi\)
0.428886 0.903359i \(-0.358906\pi\)
\(132\) 112.960 189.414i 0.0744839 0.124896i
\(133\) 62.9264 108.992i 0.0410256 0.0710585i
\(134\) −1738.37 −1.12069
\(135\) 0 0
\(136\) 1557.12 0.981782
\(137\) 110.241 190.944i 0.0687486 0.119076i −0.829602 0.558355i \(-0.811433\pi\)
0.898351 + 0.439279i \(0.144766\pi\)
\(138\) −505.231 + 847.184i −0.311653 + 0.522588i
\(139\) −1512.99 2620.58i −0.923241 1.59910i −0.794366 0.607440i \(-0.792197\pi\)
−0.128875 0.991661i \(-0.541137\pi\)
\(140\) 0 0
\(141\) −1146.77 2052.78i −0.684934 1.22607i
\(142\) −143.952 + 249.332i −0.0850716 + 0.147348i
\(143\) −632.671 −0.369976
\(144\) −682.985 19.3250i −0.395246 0.0111834i
\(145\) 0 0
\(146\) 759.085 1314.77i 0.430290 0.745284i
\(147\) 1028.01 + 14.5408i 0.576796 + 0.00815856i
\(148\) 413.015 + 715.363i 0.229390 + 0.397314i
\(149\) −964.264 1670.15i −0.530172 0.918284i −0.999380 0.0351969i \(-0.988794\pi\)
0.469209 0.883087i \(-0.344539\pi\)
\(150\) 0 0
\(151\) 546.916 947.285i 0.294751 0.510523i −0.680176 0.733049i \(-0.738097\pi\)
0.974927 + 0.222526i \(0.0714301\pi\)
\(152\) 132.326 0.0706121
\(153\) −817.214 1512.72i −0.431816 0.799319i
\(154\) 623.771 0.326395
\(155\) 0 0
\(156\) −435.543 779.643i −0.223534 0.400137i
\(157\) −287.034 497.157i −0.145910 0.252723i 0.783802 0.621010i \(-0.213278\pi\)
−0.929712 + 0.368288i \(0.879944\pi\)
\(158\) 448.089 + 776.113i 0.225620 + 0.390786i
\(159\) 595.861 999.154i 0.297200 0.498353i
\(160\) 0 0
\(161\) 2057.42 1.00713
\(162\) 704.291 + 1396.77i 0.341570 + 0.677412i
\(163\) −2279.16 −1.09520 −0.547601 0.836740i \(-0.684459\pi\)
−0.547601 + 0.836740i \(0.684459\pi\)
\(164\) 795.530 1377.90i 0.378783 0.656072i
\(165\) 0 0
\(166\) −990.164 1715.01i −0.462962 0.801873i
\(167\) 1567.06 + 2714.23i 0.726125 + 1.25769i 0.958509 + 0.285061i \(0.0920140\pi\)
−0.232384 + 0.972624i \(0.574653\pi\)
\(168\) 1441.13 + 2579.69i 0.661819 + 1.18469i
\(169\) −182.472 + 316.051i −0.0830552 + 0.143856i
\(170\) 0 0
\(171\) −69.4475 128.552i −0.0310572 0.0574889i
\(172\) 1692.38 0.750248
\(173\) 2091.71 3622.95i 0.919249 1.59219i 0.118690 0.992931i \(-0.462130\pi\)
0.800559 0.599254i \(-0.204536\pi\)
\(174\) −1611.77 22.7979i −0.702229 0.00993276i
\(175\) 0 0
\(176\) 158.156 + 273.934i 0.0677354 + 0.117321i
\(177\) 602.337 + 8.51982i 0.255788 + 0.00361802i
\(178\) 122.894 212.859i 0.0517490 0.0896319i
\(179\) −2760.46 −1.15266 −0.576331 0.817216i \(-0.695516\pi\)
−0.576331 + 0.817216i \(0.695516\pi\)
\(180\) 0 0
\(181\) 2563.75 1.05283 0.526414 0.850229i \(-0.323536\pi\)
0.526414 + 0.850229i \(0.323536\pi\)
\(182\) 1262.95 2187.50i 0.514375 0.890923i
\(183\) −209.812 375.573i −0.0847525 0.151711i
\(184\) 1081.62 + 1873.42i 0.433360 + 0.750601i
\(185\) 0 0
\(186\) −1587.41 + 2661.81i −0.625778 + 1.04932i
\(187\) −397.981 + 689.323i −0.155632 + 0.269563i
\(188\) −1536.57 −0.596094
\(189\) 1749.78 2753.91i 0.673429 1.05988i
\(190\) 0 0
\(191\) −2180.95 + 3777.51i −0.826219 + 1.43105i 0.0747649 + 0.997201i \(0.476179\pi\)
−0.900984 + 0.433852i \(0.857154\pi\)
\(192\) −1345.87 + 2256.79i −0.505885 + 0.848281i
\(193\) 1384.57 + 2398.15i 0.516393 + 0.894419i 0.999819 + 0.0190333i \(0.00605887\pi\)
−0.483426 + 0.875385i \(0.660608\pi\)
\(194\) 387.911 + 671.882i 0.143559 + 0.248651i
\(195\) 0 0
\(196\) 335.923 581.835i 0.122421 0.212039i
\(197\) 547.622 0.198053 0.0990264 0.995085i \(-0.468427\pi\)
0.0990264 + 0.995085i \(0.468427\pi\)
\(198\) 379.683 616.665i 0.136277 0.221336i
\(199\) −2077.15 −0.739927 −0.369963 0.929046i \(-0.620630\pi\)
−0.369963 + 0.929046i \(0.620630\pi\)
\(200\) 0 0
\(201\) 4209.13 + 59.5365i 1.47706 + 0.0208925i
\(202\) 310.306 + 537.466i 0.108084 + 0.187208i
\(203\) 1681.08 + 2911.71i 0.581224 + 1.00671i
\(204\) −1123.43 15.8905i −0.385569 0.00545373i
\(205\) 0 0
\(206\) 1036.01 0.350399
\(207\) 1252.33 2033.99i 0.420498 0.682956i
\(208\) 1280.87 0.426984
\(209\) −33.8208 + 58.5793i −0.0111934 + 0.0193876i
\(210\) 0 0
\(211\) 305.993 + 529.995i 0.0998360 + 0.172921i 0.911617 0.411041i \(-0.134835\pi\)
−0.811781 + 0.583962i \(0.801502\pi\)
\(212\) −380.106 658.363i −0.123140 0.213286i
\(213\) 357.090 598.778i 0.114871 0.192618i
\(214\) −1927.62 + 3338.74i −0.615745 + 1.06650i
\(215\) 0 0
\(216\) 3427.51 + 145.520i 1.07969 + 0.0458398i
\(217\) 6464.33 2.02225
\(218\) 1617.07 2800.85i 0.502393 0.870171i
\(219\) −1883.01 + 3157.47i −0.581012 + 0.974256i
\(220\) 0 0
\(221\) 1611.59 + 2791.35i 0.490530 + 0.849623i
\(222\) 1322.85 + 2367.97i 0.399928 + 0.715891i
\(223\) −89.6685 + 155.310i −0.0269267 + 0.0466384i −0.879175 0.476500i \(-0.841905\pi\)
0.852248 + 0.523138i \(0.175239\pi\)
\(224\) 3286.58 0.980328
\(225\) 0 0
\(226\) −4613.54 −1.35791
\(227\) 106.893 185.144i 0.0312544 0.0541342i −0.849975 0.526823i \(-0.823383\pi\)
0.881230 + 0.472689i \(0.156716\pi\)
\(228\) −95.4703 1.35039i −0.0277310 0.000392245i
\(229\) −1452.45 2515.72i −0.419130 0.725955i 0.576722 0.816941i \(-0.304332\pi\)
−0.995852 + 0.0909854i \(0.970998\pi\)
\(230\) 0 0
\(231\) −1510.34 21.3632i −0.430186 0.00608482i
\(232\) −1767.54 + 3061.47i −0.500193 + 0.866359i
\(233\) −2683.70 −0.754570 −0.377285 0.926097i \(-0.623142\pi\)
−0.377285 + 0.926097i \(0.623142\pi\)
\(234\) −1393.83 2580.07i −0.389392 0.720789i
\(235\) 0 0
\(236\) 196.825 340.911i 0.0542891 0.0940315i
\(237\) −1058.38 1894.55i −0.290081 0.519259i
\(238\) −1588.92 2752.08i −0.432748 0.749542i
\(239\) 1999.45 + 3463.14i 0.541144 + 0.937289i 0.998839 + 0.0481794i \(0.0153419\pi\)
−0.457695 + 0.889109i \(0.651325\pi\)
\(240\) 0 0
\(241\) −1221.72 + 2116.09i −0.326548 + 0.565598i −0.981824 0.189791i \(-0.939219\pi\)
0.655276 + 0.755389i \(0.272552\pi\)
\(242\) 2520.80 0.669601
\(243\) −1657.47 3406.13i −0.437557 0.899190i
\(244\) −281.127 −0.0737596
\(245\) 0 0
\(246\) 2676.00 4487.18i 0.693559 1.16298i
\(247\) 136.954 + 237.211i 0.0352801 + 0.0611069i
\(248\) 3398.40 + 5886.21i 0.870157 + 1.50716i
\(249\) 2338.75 + 4186.48i 0.595230 + 1.06549i
\(250\) 0 0
\(251\) 665.021 0.167234 0.0836170 0.996498i \(-0.473353\pi\)
0.0836170 + 0.996498i \(0.473353\pi\)
\(252\) −1013.42 1875.90i −0.253331 0.468932i
\(253\) −1105.79 −0.274785
\(254\) −1382.27 + 2394.17i −0.341463 + 0.591431i
\(255\) 0 0
\(256\) 2071.52 + 3587.97i 0.505741 + 0.875969i
\(257\) −1000.94 1733.67i −0.242944 0.420792i 0.718607 0.695416i \(-0.244780\pi\)
−0.961552 + 0.274624i \(0.911447\pi\)
\(258\) 5556.68 + 78.5971i 1.34087 + 0.0189660i
\(259\) 2828.78 4899.59i 0.678656 1.17547i
\(260\) 0 0
\(261\) 3901.80 + 110.401i 0.925347 + 0.0261826i
\(262\) −3654.17 −0.861663
\(263\) −2190.68 + 3794.37i −0.513624 + 0.889623i 0.486251 + 0.873819i \(0.338364\pi\)
−0.999875 + 0.0158039i \(0.994969\pi\)
\(264\) −774.557 1386.50i −0.180571 0.323231i
\(265\) 0 0
\(266\) −135.027 233.874i −0.0311243 0.0539088i
\(267\) −304.855 + 511.188i −0.0698757 + 0.117169i
\(268\) 1375.41 2382.29i 0.313496 0.542990i
\(269\) −99.0813 −0.0224576 −0.0112288 0.999937i \(-0.503574\pi\)
−0.0112288 + 0.999937i \(0.503574\pi\)
\(270\) 0 0
\(271\) −7951.92 −1.78245 −0.891227 0.453558i \(-0.850155\pi\)
−0.891227 + 0.453558i \(0.850155\pi\)
\(272\) 805.732 1395.57i 0.179613 0.311098i
\(273\) −3132.91 + 5253.34i −0.694550 + 1.16464i
\(274\) −236.556 409.727i −0.0521564 0.0903375i
\(275\) 0 0
\(276\) −761.249 1362.67i −0.166021 0.297186i
\(277\) 2882.82 4993.20i 0.625314 1.08308i −0.363166 0.931725i \(-0.618304\pi\)
0.988480 0.151352i \(-0.0483625\pi\)
\(278\) −6493.16 −1.40084
\(279\) 3934.77 6390.70i 0.844332 1.37133i
\(280\) 0 0
\(281\) −2789.94 + 4832.31i −0.592290 + 1.02588i 0.401633 + 0.915801i \(0.368443\pi\)
−0.993923 + 0.110076i \(0.964890\pi\)
\(282\) −5045.09 71.3609i −1.06536 0.0150691i
\(283\) −377.022 653.022i −0.0791931 0.137167i 0.823709 0.567013i \(-0.191901\pi\)
−0.902902 + 0.429846i \(0.858568\pi\)
\(284\) −227.792 394.547i −0.0475949 0.0824368i
\(285\) 0 0
\(286\) −678.793 + 1175.70i −0.140342 + 0.243080i
\(287\) −10897.3 −2.24128
\(288\) 2000.51 3249.14i 0.409309 0.664782i
\(289\) −857.930 −0.174625
\(290\) 0 0
\(291\) −916.240 1640.12i −0.184574 0.330396i
\(292\) 1201.19 + 2080.52i 0.240734 + 0.416963i
\(293\) 4834.85 + 8374.21i 0.964010 + 1.66971i 0.712251 + 0.701925i \(0.247676\pi\)
0.251759 + 0.967790i \(0.418991\pi\)
\(294\) 1129.97 1894.77i 0.224155 0.375868i
\(295\) 0 0
\(296\) 5948.54 1.16808
\(297\) −940.448 + 1480.13i −0.183738 + 0.289178i
\(298\) −4138.23 −0.804434
\(299\) −2238.91 + 3877.90i −0.433041 + 0.750049i
\(300\) 0 0
\(301\) −5795.63 10038.3i −1.10981 1.92226i
\(302\) −1173.57 2032.68i −0.223614 0.387311i
\(303\) −732.938 1312.00i −0.138964 0.248753i
\(304\) 68.4717 118.597i 0.0129182 0.0223749i
\(305\) 0 0
\(306\) −3687.89 104.349i −0.688963 0.0194941i
\(307\) 1601.00 0.297635 0.148817 0.988865i \(-0.452453\pi\)
0.148817 + 0.988865i \(0.452453\pi\)
\(308\) −493.533 + 854.824i −0.0913040 + 0.158143i
\(309\) −2508.49 35.4817i −0.461822 0.00653230i
\(310\) 0 0
\(311\) −2980.08 5161.64i −0.543359 0.941125i −0.998708 0.0508122i \(-0.983819\pi\)
0.455349 0.890313i \(-0.349514\pi\)
\(312\) −6430.54 90.9576i −1.16685 0.0165047i
\(313\) 1835.78 3179.67i 0.331517 0.574204i −0.651293 0.758826i \(-0.725773\pi\)
0.982809 + 0.184623i \(0.0591064\pi\)
\(314\) −1231.83 −0.221390
\(315\) 0 0
\(316\) −1418.13 −0.252455
\(317\) 1171.21 2028.59i 0.207512 0.359422i −0.743418 0.668827i \(-0.766797\pi\)
0.950930 + 0.309405i \(0.100130\pi\)
\(318\) −1217.45 2179.29i −0.214689 0.384303i
\(319\) −903.521 1564.94i −0.158581 0.274671i
\(320\) 0 0
\(321\) 4781.70 8018.08i 0.831429 1.39416i
\(322\) 2207.41 3823.34i 0.382031 0.661697i
\(323\) 344.603 0.0593629
\(324\) −2471.39 139.968i −0.423764 0.0240000i
\(325\) 0 0
\(326\) −2445.31 + 4235.41i −0.415440 + 0.719563i
\(327\) −4011.34 + 6726.32i −0.678372 + 1.13751i
\(328\) −5728.90 9922.74i −0.964407 1.67040i
\(329\) 5262.04 + 9114.12i 0.881780 + 1.52729i
\(330\) 0 0
\(331\) 672.393 1164.62i 0.111656 0.193394i −0.804782 0.593570i \(-0.797718\pi\)
0.916438 + 0.400177i \(0.131051\pi\)
\(332\) 3133.70 0.518025
\(333\) −3121.93 5778.89i −0.513756 0.950994i
\(334\) 6725.20 1.10176
\(335\) 0 0
\(336\) 3057.75 + 43.2508i 0.496471 + 0.00702239i
\(337\) −968.133 1676.86i −0.156491 0.271051i 0.777110 0.629365i \(-0.216685\pi\)
−0.933601 + 0.358314i \(0.883352\pi\)
\(338\) 391.549 + 678.183i 0.0630102 + 0.109137i
\(339\) 11170.8 + 158.007i 1.78972 + 0.0253149i
\(340\) 0 0
\(341\) −3474.35 −0.551750
\(342\) −313.400 8.86762i −0.0495519 0.00140206i
\(343\) 3375.42 0.531357
\(344\) 6093.71 10554.6i 0.955090 1.65426i
\(345\) 0 0
\(346\) −4488.40 7774.13i −0.697392 1.20792i
\(347\) 1895.80 + 3283.61i 0.293290 + 0.507993i 0.974586 0.224015i \(-0.0719165\pi\)
−0.681296 + 0.732008i \(0.738583\pi\)
\(348\) 1306.49 2190.75i 0.201250 0.337461i
\(349\) −451.754 + 782.461i −0.0692890 + 0.120012i −0.898589 0.438792i \(-0.855406\pi\)
0.829300 + 0.558804i \(0.188740\pi\)
\(350\) 0 0
\(351\) 3286.53 + 6294.88i 0.499778 + 0.957253i
\(352\) −1766.42 −0.267473
\(353\) 4041.75 7000.51i 0.609406 1.05552i −0.381932 0.924190i \(-0.624741\pi\)
0.991338 0.131332i \(-0.0419255\pi\)
\(354\) 662.079 1110.19i 0.0994043 0.166684i
\(355\) 0 0
\(356\) 194.470 + 336.832i 0.0289520 + 0.0501463i
\(357\) 3752.99 + 6718.05i 0.556385 + 0.995958i
\(358\) −2961.70 + 5129.81i −0.437236 + 0.757316i
\(359\) −3688.92 −0.542322 −0.271161 0.962534i \(-0.587408\pi\)
−0.271161 + 0.962534i \(0.587408\pi\)
\(360\) 0 0
\(361\) −6829.72 −0.995730
\(362\) 2750.64 4764.25i 0.399366 0.691722i
\(363\) −6103.63 86.3336i −0.882528 0.0124830i
\(364\) 1998.52 + 3461.53i 0.287777 + 0.498444i
\(365\) 0 0
\(366\) −923.040 13.0561i −0.131825 0.00186462i
\(367\) −1518.23 + 2629.65i −0.215943 + 0.374024i −0.953564 0.301191i \(-0.902616\pi\)
0.737621 + 0.675215i \(0.235949\pi\)
\(368\) 2238.73 0.317125
\(369\) −6633.09 + 10773.2i −0.935785 + 1.51986i
\(370\) 0 0
\(371\) −2603.38 + 4509.18i −0.364315 + 0.631011i
\(372\) −2391.81 4281.46i −0.333359 0.596729i
\(373\) 2490.02 + 4312.84i 0.345653 + 0.598688i 0.985472 0.169837i \(-0.0543242\pi\)
−0.639819 + 0.768525i \(0.720991\pi\)
\(374\) 853.987 + 1479.15i 0.118071 + 0.204505i
\(375\) 0 0
\(376\) −5532.68 + 9582.89i −0.758846 + 1.31436i
\(377\) −7317.45 −0.999650
\(378\) −3240.29 6206.32i −0.440907 0.844494i
\(379\) −6027.99 −0.816984 −0.408492 0.912762i \(-0.633945\pi\)
−0.408492 + 0.912762i \(0.633945\pi\)
\(380\) 0 0
\(381\) 3428.90 5749.67i 0.461071 0.773135i
\(382\) 4679.88 + 8105.78i 0.626815 + 1.08568i
\(383\) 1892.57 + 3278.03i 0.252496 + 0.437335i 0.964212 0.265131i \(-0.0854153\pi\)
−0.711717 + 0.702467i \(0.752082\pi\)
\(384\) −115.166 206.153i −0.0153048 0.0273964i
\(385\) 0 0
\(386\) 5942.03 0.783527
\(387\) −13451.7 380.615i −1.76690 0.0499942i
\(388\) −1227.67 −0.160633
\(389\) −2871.46 + 4973.51i −0.374264 + 0.648244i −0.990217 0.139539i \(-0.955438\pi\)
0.615953 + 0.787783i \(0.288771\pi\)
\(390\) 0 0
\(391\) 2816.76 + 4878.77i 0.364322 + 0.631024i
\(392\) −2419.10 4190.00i −0.311691 0.539865i
\(393\) 8847.87 + 125.150i 1.13566 + 0.0160635i
\(394\) 587.543 1017.65i 0.0751269 0.130124i
\(395\) 0 0
\(396\) 544.678 + 1008.23i 0.0691189 + 0.127944i
\(397\) −899.327 −0.113693 −0.0568463 0.998383i \(-0.518104\pi\)
−0.0568463 + 0.998383i \(0.518104\pi\)
\(398\) −2228.58 + 3860.01i −0.280674 + 0.486142i
\(399\) 318.933 + 570.905i 0.0400165 + 0.0716316i
\(400\) 0 0
\(401\) 2838.95 + 4917.20i 0.353542 + 0.612352i 0.986867 0.161533i \(-0.0516439\pi\)
−0.633326 + 0.773886i \(0.718311\pi\)
\(402\) 4626.61 7758.02i 0.574016 0.962524i
\(403\) −7034.54 + 12184.2i −0.869517 + 1.50605i
\(404\) −982.067 −0.120940
\(405\) 0 0
\(406\) 7214.51 0.881897
\(407\) −1520.37 + 2633.36i −0.185165 + 0.320714i
\(408\) −4144.23 + 6949.14i −0.502867 + 0.843220i
\(409\) 1815.75 + 3144.97i 0.219518 + 0.380217i 0.954661 0.297696i \(-0.0962180\pi\)
−0.735142 + 0.677913i \(0.762885\pi\)
\(410\) 0 0
\(411\) 558.741 + 1000.17i 0.0670576 + 0.120036i
\(412\) −819.699 + 1419.76i −0.0980186 + 0.169773i
\(413\) −2696.15 −0.321232
\(414\) −2436.16 4509.49i −0.289205 0.535337i
\(415\) 0 0
\(416\) −3576.48 + 6194.64i −0.421518 + 0.730090i
\(417\) 15721.9 + 222.381i 1.84630 + 0.0261152i
\(418\) 72.5725 + 125.699i 0.00849196 + 0.0147085i
\(419\) 1459.14 + 2527.31i 0.170128 + 0.294671i 0.938465 0.345376i \(-0.112248\pi\)
−0.768336 + 0.640046i \(0.778915\pi\)
\(420\) 0 0
\(421\) 7154.67 12392.3i 0.828260 1.43459i −0.0711420 0.997466i \(-0.522664\pi\)
0.899402 0.437122i \(-0.144002\pi\)
\(422\) 1313.20 0.151482
\(423\) 12213.3 + 345.573i 1.40385 + 0.0397218i
\(424\) −5474.56 −0.627047
\(425\) 0 0
\(426\) −729.597 1306.02i −0.0829791 0.148537i
\(427\) 962.733 + 1667.50i 0.109110 + 0.188984i
\(428\) −3050.30 5283.27i −0.344490 0.596674i
\(429\) 1683.83 2823.49i 0.189501 0.317761i
\(430\) 0 0
\(431\) −3222.12 −0.360102 −0.180051 0.983657i \(-0.557626\pi\)
−0.180051 + 0.983657i \(0.557626\pi\)
\(432\) 1903.98 2996.60i 0.212050 0.333736i
\(433\) −997.716 −0.110732 −0.0553662 0.998466i \(-0.517633\pi\)
−0.0553662 + 0.998466i \(0.517633\pi\)
\(434\) 6935.58 12012.8i 0.767093 1.32864i
\(435\) 0 0
\(436\) 2558.88 + 4432.10i 0.281073 + 0.486833i
\(437\) 239.371 + 414.602i 0.0262029 + 0.0453847i
\(438\) 3847.30 + 6886.87i 0.419706 + 0.751295i
\(439\) 4468.16 7739.08i 0.485771 0.841380i −0.514095 0.857733i \(-0.671872\pi\)
0.999866 + 0.0163529i \(0.00520553\pi\)
\(440\) 0 0
\(441\) −2800.91 + 4549.12i −0.302441 + 0.491212i
\(442\) 6916.29 0.744286
\(443\) 3346.27 5795.91i 0.358885 0.621607i −0.628890 0.777494i \(-0.716490\pi\)
0.987775 + 0.155887i \(0.0498236\pi\)
\(444\) −4291.75 60.7052i −0.458733 0.00648861i
\(445\) 0 0
\(446\) 192.411 + 333.265i 0.0204280 + 0.0353824i
\(447\) 10019.9 + 141.728i 1.06024 + 0.0149967i
\(448\) 5880.26 10184.9i 0.620125 1.07409i
\(449\) −17877.3 −1.87903 −0.939513 0.342514i \(-0.888721\pi\)
−0.939513 + 0.342514i \(0.888721\pi\)
\(450\) 0 0
\(451\) 5856.93 0.611513
\(452\) 3650.27 6322.46i 0.379855 0.657928i
\(453\) 2771.96 + 4961.94i 0.287501 + 0.514641i
\(454\) −229.371 397.282i −0.0237113 0.0410691i
\(455\) 0 0
\(456\) −352.180 + 590.544i −0.0361674 + 0.0606464i
\(457\) 4579.33 7931.63i 0.468735 0.811873i −0.530626 0.847606i \(-0.678043\pi\)
0.999361 + 0.0357331i \(0.0113766\pi\)
\(458\) −6233.35 −0.635950
\(459\) 8925.94 + 378.964i 0.907684 + 0.0385371i
\(460\) 0 0
\(461\) 8436.12 14611.8i 0.852298 1.47622i −0.0268321 0.999640i \(-0.508542\pi\)
0.879130 0.476583i \(-0.158125\pi\)
\(462\) −1660.14 + 2783.77i −0.167179 + 0.280330i
\(463\) 490.023 + 848.746i 0.0491864 + 0.0851934i 0.889570 0.456798i \(-0.151004\pi\)
−0.840384 + 0.541992i \(0.817670\pi\)
\(464\) 1829.22 + 3168.31i 0.183016 + 0.316993i
\(465\) 0 0
\(466\) −2879.34 + 4987.16i −0.286229 + 0.495763i
\(467\) 7396.39 0.732900 0.366450 0.930438i \(-0.380573\pi\)
0.366450 + 0.930438i \(0.380573\pi\)
\(468\) 4638.58 + 131.248i 0.458159 + 0.0129636i
\(469\) −18840.7 −1.85497
\(470\) 0 0
\(471\) 2982.65 + 42.1884i 0.291790 + 0.00412726i
\(472\) −1417.41 2455.02i −0.138224 0.239410i
\(473\) 3114.95 + 5395.25i 0.302802 + 0.524469i
\(474\) −4656.21 65.8603i −0.451196 0.00638199i
\(475\) 0 0
\(476\) 5028.65 0.484218
\(477\) 2873.17 + 5318.42i 0.275793 + 0.510511i
\(478\) 8580.82 0.821082
\(479\) 2256.79 3908.88i 0.215273 0.372863i −0.738084 0.674708i \(-0.764269\pi\)
0.953357 + 0.301846i \(0.0976027\pi\)
\(480\) 0 0
\(481\) 6156.60 + 10663.5i 0.583611 + 1.01084i
\(482\) 2621.57 + 4540.69i 0.247737 + 0.429093i
\(483\) −5475.75 + 9181.88i −0.515850 + 0.864989i
\(484\) −1994.48 + 3454.54i −0.187310 + 0.324431i
\(485\) 0 0
\(486\) −8107.96 574.340i −0.756758 0.0536061i
\(487\) −14036.0 −1.30602 −0.653012 0.757348i \(-0.726495\pi\)
−0.653012 + 0.757348i \(0.726495\pi\)
\(488\) −1012.25 + 1753.27i −0.0938983 + 0.162637i
\(489\) 6065.91 10171.5i 0.560961 0.940633i
\(490\) 0 0
\(491\) 3597.57 + 6231.17i 0.330664 + 0.572727i 0.982642 0.185511i \(-0.0593940\pi\)
−0.651978 + 0.758238i \(0.726061\pi\)
\(492\) 4032.02 + 7217.52i 0.369467 + 0.661364i
\(493\) −4603.04 + 7972.69i −0.420508 + 0.728341i
\(494\) 587.752 0.0535308
\(495\) 0 0
\(496\) 7034.00 0.636766
\(497\) −1560.17 + 2702.29i −0.140811 + 0.243892i
\(498\) 10289.1 + 145.535i 0.925831 + 0.0130955i
\(499\) 2738.51 + 4743.24i 0.245676 + 0.425524i 0.962322 0.271914i \(-0.0876566\pi\)
−0.716645 + 0.697438i \(0.754323\pi\)
\(500\) 0 0
\(501\) −16283.8 230.328i −1.45210 0.0205395i
\(502\) 713.500 1235.82i 0.0634364 0.109875i
\(503\) −1253.89 −0.111149 −0.0555747 0.998455i \(-0.517699\pi\)
−0.0555747 + 0.998455i \(0.517699\pi\)
\(504\) −15348.2 434.275i −1.35647 0.0383813i
\(505\) 0 0
\(506\) −1186.41 + 2054.91i −0.104234 + 0.180538i
\(507\) −924.833 1655.50i −0.0810124 0.145016i
\(508\) −2187.33 3788.57i −0.191038 0.330887i
\(509\) −6341.09 10983.1i −0.552188 0.956418i −0.998116 0.0613492i \(-0.980460\pi\)
0.445928 0.895069i \(-0.352874\pi\)
\(510\) 0 0
\(511\) 8227.05 14249.7i 0.712218 1.23360i
\(512\) 8526.55 0.735984
\(513\) 758.533 + 32.2047i 0.0652828 + 0.00277168i
\(514\) −4295.61 −0.368621
\(515\) 0 0
\(516\) −4504.20 + 7552.75i −0.384276 + 0.644363i
\(517\) −2828.17 4898.53i −0.240585 0.416706i
\(518\) −6069.99 10513.5i −0.514865 0.891772i
\(519\) 10601.5 + 18977.3i 0.896638 + 1.60503i
\(520\) 0 0
\(521\) 10532.9 0.885710 0.442855 0.896593i \(-0.353966\pi\)
0.442855 + 0.896593i \(0.353966\pi\)
\(522\) 4391.40 7132.33i 0.368211 0.598034i
\(523\) 4327.58 0.361820 0.180910 0.983500i \(-0.442096\pi\)
0.180910 + 0.983500i \(0.442096\pi\)
\(524\) 2891.21 5007.73i 0.241037 0.417488i
\(525\) 0 0
\(526\) 4700.76 + 8141.95i 0.389663 + 0.674916i
\(527\) 8850.14 + 15328.9i 0.731533 + 1.26705i
\(528\) −1643.44 23.2458i −0.135457 0.00191599i
\(529\) 2170.30 3759.07i 0.178376 0.308956i
\(530\) 0 0
\(531\) −1641.12 + 2665.44i −0.134121 + 0.217834i
\(532\) 427.339 0.0348261
\(533\) 11858.6 20539.6i 0.963698 1.66917i
\(534\) 622.871 + 1114.97i 0.0504761 + 0.0903548i
\(535\) 0 0
\(536\) −9904.85 17155.7i −0.798180 1.38249i
\(537\) 7346.86 12319.4i 0.590392 0.989984i
\(538\) −106.304 + 184.124i −0.00851877 + 0.0147549i
\(539\) 2473.16 0.197638
\(540\) 0 0
\(541\) −9235.00 −0.733907 −0.366953 0.930239i \(-0.619599\pi\)
−0.366953 + 0.930239i \(0.619599\pi\)
\(542\) −8531.61 + 14777.2i −0.676133 + 1.17110i
\(543\) −6823.31 + 11441.5i −0.539256 + 0.904239i
\(544\) 4499.56 + 7793.47i 0.354627 + 0.614232i
\(545\) 0 0
\(546\) 6401.07 + 11458.2i 0.501723 + 0.898109i
\(547\) −10390.8 + 17997.3i −0.812206 + 1.40678i 0.0991101 + 0.995076i \(0.468400\pi\)
−0.911317 + 0.411706i \(0.864933\pi\)
\(548\) 748.660 0.0583598
\(549\) 2234.52 + 63.2254i 0.173710 + 0.00491511i
\(550\) 0 0
\(551\) −391.170 + 677.526i −0.0302439 + 0.0523840i
\(552\) −11239.4 158.977i −0.866632 0.0122582i
\(553\) 4856.44 + 8411.60i 0.373448 + 0.646831i
\(554\) −6185.96 10714.4i −0.474397 0.821680i
\(555\) 0 0
\(556\) 5137.44 8898.31i 0.391864 0.678728i
\(557\) 14486.4 1.10199 0.550996 0.834508i \(-0.314248\pi\)
0.550996 + 0.834508i \(0.314248\pi\)
\(558\) −7654.32 14168.6i −0.580705 1.07492i
\(559\) 25227.4 1.90878
\(560\) 0 0
\(561\) −2017.10 3610.72i −0.151804 0.271737i
\(562\) 5986.64 + 10369.2i 0.449344 + 0.778286i
\(563\) −10947.8 18962.2i −0.819532 1.41947i −0.906027 0.423219i \(-0.860900\pi\)
0.0864949 0.996252i \(-0.472433\pi\)
\(564\) 4089.51 6857.40i 0.305318 0.511965i
\(565\) 0 0
\(566\) −1618.03 −0.120160
\(567\) 7633.18 + 15138.4i 0.565368 + 1.12125i
\(568\) −3280.82 −0.242359
\(569\) −9961.73 + 17254.2i −0.733950 + 1.27124i 0.221233 + 0.975221i \(0.428992\pi\)
−0.955183 + 0.296017i \(0.904341\pi\)
\(570\) 0 0
\(571\) −1225.64 2122.86i −0.0898271 0.155585i 0.817611 0.575771i \(-0.195298\pi\)
−0.907438 + 0.420186i \(0.861965\pi\)
\(572\) −1074.13 1860.45i −0.0785170 0.135996i
\(573\) −11053.8 19786.8i −0.805897 1.44260i
\(574\) −11691.7 + 20250.7i −0.850180 + 1.47255i
\(575\) 0 0
\(576\) −6489.64 12012.7i −0.469447 0.868977i
\(577\) −4268.82 −0.307995 −0.153998 0.988071i \(-0.549215\pi\)
−0.153998 + 0.988071i \(0.549215\pi\)
\(578\) −920.473 + 1594.31i −0.0662398 + 0.114731i
\(579\) −14387.5 203.505i −1.03268 0.0146069i
\(580\) 0 0
\(581\) −10731.5 18587.5i −0.766296 1.32726i
\(582\) −4030.89 57.0153i −0.287089 0.00406076i
\(583\) 1399.23 2423.53i 0.0993997 0.172165i
\(584\) 17300.4 1.22585
\(585\) 0 0
\(586\) 20749.2 1.46270
\(587\) 1407.06 2437.09i 0.0989360 0.171362i −0.812309 0.583228i \(-0.801789\pi\)
0.911244 + 0.411866i \(0.135123\pi\)
\(588\) 1702.57 + 3047.69i 0.119410 + 0.213749i
\(589\) 752.092 + 1302.66i 0.0526136 + 0.0911294i
\(590\) 0 0
\(591\) −1457.47 + 2443.93i −0.101442 + 0.170101i
\(592\) 3078.06 5331.36i 0.213695 0.370131i
\(593\) 7066.19 0.489331 0.244666 0.969607i \(-0.421322\pi\)
0.244666 + 0.969607i \(0.421322\pi\)
\(594\) 1741.55 + 3335.68i 0.120297 + 0.230412i
\(595\) 0 0
\(596\) 3274.20 5671.09i 0.225028 0.389760i
\(597\) 5528.26 9269.92i 0.378989 0.635499i
\(598\) 4804.24 + 8321.19i 0.328528 + 0.569028i
\(599\) −3623.12 6275.43i −0.247140 0.428059i 0.715591 0.698519i \(-0.246157\pi\)
−0.962731 + 0.270461i \(0.912824\pi\)
\(600\) 0 0
\(601\) −928.919 + 1608.93i −0.0630472 + 0.109201i −0.895826 0.444405i \(-0.853415\pi\)
0.832779 + 0.553606i \(0.186749\pi\)
\(602\) −24872.5 −1.68393
\(603\) −11468.1 + 18626.1i −0.774492 + 1.25790i
\(604\) 3714.16 0.250210
\(605\) 0 0
\(606\) −3224.47 45.6089i −0.216147 0.00305732i
\(607\) −7826.04 13555.1i −0.523310 0.906400i −0.999632 0.0271286i \(-0.991364\pi\)
0.476322 0.879271i \(-0.341970\pi\)
\(608\) 382.376 + 662.295i 0.0255056 + 0.0441770i
\(609\) −17468.5 247.086i −1.16233 0.0164408i
\(610\) 0 0
\(611\) −22904.8 −1.51658
\(612\) 3060.89 4971.37i 0.202172 0.328359i
\(613\) −421.560 −0.0277760 −0.0138880 0.999904i \(-0.504421\pi\)
−0.0138880 + 0.999904i \(0.504421\pi\)
\(614\) 1717.71 2975.16i 0.112901 0.195550i
\(615\) 0 0
\(616\) 3554.10 + 6155.89i 0.232466 + 0.402643i
\(617\) −7436.70 12880.7i −0.485235 0.840452i 0.514621 0.857418i \(-0.327933\pi\)
−0.999856 + 0.0169657i \(0.994599\pi\)
\(618\) −2757.30 + 4623.50i −0.179474 + 0.300946i
\(619\) 11751.5 20354.1i 0.763054 1.32165i −0.178215 0.983992i \(-0.557032\pi\)
0.941269 0.337657i \(-0.109635\pi\)
\(620\) 0 0
\(621\) 5744.25 + 11002.3i 0.371190 + 0.710961i
\(622\) −12789.3 −0.824443
\(623\) 1331.94 2306.99i 0.0856552 0.148359i
\(624\) −3408.99 + 5716.29i −0.218700 + 0.366722i
\(625\) 0 0
\(626\) −3939.22 6822.94i −0.251507 0.435622i
\(627\) −171.415 306.842i −0.0109181 0.0195440i
\(628\) 974.637 1688.12i 0.0619304 0.107267i
\(629\) 15491.2 0.981995
\(630\) 0 0
\(631\) −3402.59 −0.214667 −0.107333 0.994223i \(-0.534231\pi\)
−0.107333 + 0.994223i \(0.534231\pi\)
\(632\) −5106.22 + 8844.23i −0.321384 + 0.556653i
\(633\) −3179.65 44.9750i −0.199652 0.00282400i
\(634\) −2513.17 4352.94i −0.157430 0.272677i
\(635\) 0 0
\(636\) 3949.78 + 55.8681i 0.246256 + 0.00348320i
\(637\) 5007.43 8673.12i 0.311462 0.539468i
\(638\) −3877.55 −0.240617
\(639\) 1721.85 + 3187.25i 0.106597 + 0.197317i
\(640\) 0 0
\(641\) 4328.19 7496.64i 0.266697 0.461933i −0.701310 0.712857i \(-0.747401\pi\)
0.968007 + 0.250923i \(0.0807342\pi\)
\(642\) −9769.85 17488.5i −0.600600 1.07510i
\(643\) 5641.51 + 9771.38i 0.346002 + 0.599293i 0.985535 0.169470i \(-0.0542056\pi\)
−0.639533 + 0.768764i \(0.720872\pi\)
\(644\) 3493.04 + 6050.12i 0.213735 + 0.370199i
\(645\) 0 0
\(646\) 369.725 640.382i 0.0225180 0.0390023i
\(647\) −18232.2 −1.10785 −0.553927 0.832565i \(-0.686871\pi\)
−0.553927 + 0.832565i \(0.686871\pi\)
\(648\) −9771.61 + 14909.0i −0.592385 + 0.903829i
\(649\) 1449.09 0.0876450
\(650\) 0 0
\(651\) −17204.6 + 28849.0i −1.03579 + 1.73684i
\(652\) −3869.51 6702.18i −0.232426 0.402573i
\(653\) 9852.12 + 17064.4i 0.590418 + 1.02263i 0.994176 + 0.107769i \(0.0343706\pi\)
−0.403758 + 0.914866i \(0.632296\pi\)
\(654\) 8195.86 + 14671.0i 0.490036 + 0.877189i
\(655\) 0 0
\(656\) −11857.6 −0.705736
\(657\) −9079.63 16807.0i −0.539163 0.998025i
\(658\) 22582.6 1.33793
\(659\) 2227.87 3858.79i 0.131693 0.228099i −0.792636 0.609695i \(-0.791292\pi\)
0.924329 + 0.381596i \(0.124625\pi\)
\(660\) 0 0
\(661\) 8793.82 + 15231.3i 0.517458 + 0.896264i 0.999794 + 0.0202777i \(0.00645502\pi\)
−0.482336 + 0.875986i \(0.660212\pi\)
\(662\) −1442.82 2499.04i −0.0847082 0.146719i
\(663\) −16746.4 236.872i −0.980962 0.0138753i
\(664\) 11283.5 19543.5i 0.659463 1.14222i
\(665\) 0 0
\(666\) −14088.5 398.633i −0.819698 0.0231933i
\(667\) −12789.6 −0.742450
\(668\) −5321.03 + 9216.30i −0.308199 + 0.533816i
\(669\) −454.471 813.526i −0.0262644 0.0470145i
\(670\) 0 0
\(671\) −517.436 896.225i −0.0297696 0.0515624i
\(672\) −8747.09 + 14667.3i −0.502123 + 0.841972i
\(673\) 3885.57 6730.00i 0.222552 0.385472i −0.733030 0.680196i \(-0.761895\pi\)
0.955582 + 0.294725i \(0.0952279\pi\)
\(674\) −4154.84 −0.237446
\(675\) 0 0
\(676\) −1239.19 −0.0705045
\(677\) 724.033 1254.06i 0.0411032 0.0711928i −0.844742 0.535174i \(-0.820246\pi\)
0.885845 + 0.463981i \(0.153579\pi\)
\(678\) 12278.8 20589.3i 0.695521 1.16627i
\(679\) 4204.22 + 7281.93i 0.237619 + 0.411568i
\(680\) 0 0
\(681\) 541.771 + 969.797i 0.0304856 + 0.0545708i
\(682\) −3727.63 + 6456.45i −0.209294 + 0.362508i
\(683\) −19014.6 −1.06526 −0.532630 0.846348i \(-0.678796\pi\)
−0.532630 + 0.846348i \(0.678796\pi\)
\(684\) 260.117 422.471i 0.0145407 0.0236164i
\(685\) 0 0
\(686\) 3621.48 6272.59i 0.201558 0.349109i
\(687\) 15092.8 + 213.482i 0.838177 + 0.0118557i
\(688\) −6306.36 10922.9i −0.349459 0.605281i
\(689\) −5666.04 9813.87i −0.313293 0.542639i
\(690\) 0 0
\(691\) −16149.2 + 27971.2i −0.889064 + 1.53990i −0.0480796 + 0.998844i \(0.515310\pi\)
−0.840984 + 0.541060i \(0.818023\pi\)
\(692\) 14205.0 0.780338
\(693\) 4115.05 6683.49i 0.225567 0.366356i
\(694\) 8135.99 0.445012
\(695\) 0 0
\(696\) −8958.50 16036.2i −0.487890 0.873347i
\(697\) −14919.2 25840.8i −0.810769 1.40429i
\(698\) 969.374 + 1679.00i 0.0525664 + 0.0910476i
\(699\) 7142.55 11976.8i 0.386490 0.648075i
\(700\) 0 0
\(701\) 8389.52 0.452022 0.226011 0.974125i \(-0.427431\pi\)
0.226011 + 0.974125i \(0.427431\pi\)
\(702\) 15224.0 + 646.357i 0.818508 + 0.0347510i
\(703\) 1316.46 0.0706274
\(704\) −3160.44 + 5474.04i −0.169195 + 0.293055i
\(705\) 0 0
\(706\) −8672.77 15021.7i −0.462329 0.800777i
\(707\) 3363.13 + 5825.11i 0.178902 + 0.309867i
\(708\) 997.578 + 1785.71i 0.0529538 + 0.0947899i
\(709\) 76.8578 133.122i 0.00407117 0.00705147i −0.863983 0.503522i \(-0.832037\pi\)
0.868054 + 0.496470i \(0.165371\pi\)
\(710\) 0 0
\(711\) 11271.8 + 318.936i 0.594553 + 0.0168228i
\(712\) 2800.90 0.147427
\(713\) −12295.1 + 21295.7i −0.645799 + 1.11856i
\(714\) 16510.8 + 233.540i 0.865410 + 0.0122409i
\(715\) 0 0
\(716\) −4686.64 8117.50i −0.244620 0.423694i
\(717\) −20776.8 293.880i −1.08218 0.0153070i
\(718\) −3957.83 + 6855.17i −0.205717 + 0.356313i
\(719\) −271.312 −0.0140726 −0.00703632 0.999975i \(-0.502240\pi\)
−0.00703632 + 0.999975i \(0.502240\pi\)
\(720\) 0 0
\(721\) 11228.4 0.579982
\(722\) −7327.60 + 12691.8i −0.377708 + 0.654209i
\(723\) −6192.11 11084.2i −0.318516 0.570160i
\(724\) 4352.66 + 7539.03i 0.223433 + 0.386997i
\(725\) 0 0
\(726\) −6709.02 + 11249.9i −0.342968 + 0.575098i
\(727\) 8057.68 13956.3i 0.411063 0.711982i −0.583943 0.811795i \(-0.698491\pi\)
0.995006 + 0.0998123i \(0.0318242\pi\)
\(728\) 28784.0 1.46540
\(729\) 19612.2 + 1668.34i 0.996401 + 0.0847602i
\(730\) 0 0
\(731\) 15869.3 27486.4i 0.802936 1.39073i
\(732\) 748.210 1254.62i 0.0377795 0.0633497i
\(733\) −13007.0 22528.8i −0.655424 1.13523i −0.981787 0.189983i \(-0.939157\pi\)
0.326364 0.945244i \(-0.394177\pi\)
\(734\) 3257.82 + 5642.71i 0.163826 + 0.283755i
\(735\) 0 0
\(736\) −6251.03 + 10827.1i −0.313065 + 0.542245i
\(737\) 10126.2 0.506111
\(738\) 12903.4 + 23884.9i 0.643603 + 1.19135i
\(739\) 16758.4 0.834192 0.417096 0.908862i \(-0.363048\pi\)
0.417096 + 0.908862i \(0.363048\pi\)
\(740\) 0 0
\(741\) −1423.13 20.1296i −0.0705531 0.000997947i
\(742\) 5586.33 + 9675.80i 0.276389 + 0.478720i
\(743\) −12022.9 20824.3i −0.593645 1.02822i −0.993737 0.111748i \(-0.964355\pi\)
0.400092 0.916475i \(-0.368978\pi\)
\(744\) −35313.7 499.499i −1.74014 0.0246136i
\(745\) 0 0
\(746\) 10686.2 0.524462
\(747\) −24908.0 704.768i −1.21999 0.0345196i
\(748\) −2702.73 −0.132114
\(749\) −20891.8 + 36185.6i −1.01918 + 1.76528i
\(750\) 0 0
\(751\) −8658.97 14997.8i −0.420733 0.728730i 0.575279 0.817958i \(-0.304894\pi\)
−0.996011 + 0.0892271i \(0.971560\pi\)
\(752\) 5725.76 + 9917.30i 0.277655 + 0.480913i
\(753\) −1769.93 + 2967.86i −0.0856570 + 0.143632i
\(754\) −7850.89 + 13598.1i −0.379194 + 0.656784i
\(755\) 0 0
\(756\) 11069.0 + 469.950i 0.532506 + 0.0226083i
\(757\) 9907.10 0.475667 0.237833 0.971306i \(-0.423563\pi\)
0.237833 + 0.971306i \(0.423563\pi\)
\(758\) −6467.43 + 11201.9i −0.309904 + 0.536770i
\(759\) 2943.03 4934.94i 0.140745 0.236004i
\(760\) 0 0
\(761\) 15587.5 + 26998.3i 0.742504 + 1.28606i 0.951352 + 0.308107i \(0.0996955\pi\)
−0.208847 + 0.977948i \(0.566971\pi\)
\(762\) −7005.84 12540.8i −0.333064 0.596201i
\(763\) 17526.0 30355.9i 0.831564 1.44031i
\(764\) −14811.0 −0.701367
\(765\) 0 0
\(766\) 8122.15 0.383114
\(767\) 2933.97 5081.79i 0.138122 0.239234i
\(768\) −21525.7 304.472i −1.01138 0.0143056i
\(769\) −12703.5 22003.0i −0.595706 1.03179i −0.993447 0.114296i \(-0.963539\pi\)
0.397740 0.917498i \(-0.369794\pi\)
\(770\) 0 0
\(771\) 10401.0 + 147.118i 0.485840 + 0.00687202i
\(772\) −4701.39 + 8143.04i −0.219180 + 0.379630i
\(773\) 18107.2 0.842521 0.421261 0.906940i \(-0.361588\pi\)
0.421261 + 0.906940i \(0.361588\pi\)
\(774\) −15139.6 + 24589.2i −0.703079 + 1.14191i
\(775\) 0 0
\(776\) −4420.46 + 7656.46i −0.204491 + 0.354189i
\(777\) 14337.2 + 25664.4i 0.661963 + 1.18495i
\(778\) 6161.57 + 10672.2i 0.283937 + 0.491793i
\(779\) −1267.85 2195.98i −0.0583124 0.101000i