Properties

Label 225.4.e.c.76.1
Level $225$
Weight $4$
Character 225.76
Analytic conductor $13.275$
Analytic rank $0$
Dimension $6$
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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.15759792.1
Defining polynomial: \(x^{6} - 3 x^{5} + 16 x^{4} - 27 x^{3} + 52 x^{2} - 39 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 76.1
Root \(0.500000 - 2.88506i\) of defining polynomial
Character \(\chi\) \(=\) 225.76
Dual form 225.4.e.c.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.28679 - 3.96084i) q^{2} +(-3.36330 + 3.96084i) q^{3} +(-6.45882 + 11.1870i) q^{4} +(23.3794 + 4.26387i) q^{6} +(-10.0573 - 17.4197i) q^{7} +22.4912 q^{8} +(-4.37646 - 26.6429i) q^{9} +O(q^{10})\) \(q+(-2.28679 - 3.96084i) q^{2} +(-3.36330 + 3.96084i) q^{3} +(-6.45882 + 11.1870i) q^{4} +(23.3794 + 4.26387i) q^{6} +(-10.0573 - 17.4197i) q^{7} +22.4912 q^{8} +(-4.37646 - 26.6429i) q^{9} +(-33.1708 - 57.4535i) q^{11} +(-22.5870 - 63.2076i) q^{12} +(-23.4003 + 40.5305i) q^{13} +(-45.9977 + 79.6704i) q^{14} +(0.237854 + 0.411975i) q^{16} +47.6233 q^{17} +(-95.5203 + 78.2613i) q^{18} -9.95276 q^{19} +(102.822 + 18.7524i) q^{21} +(-151.709 + 262.768i) q^{22} +(4.79602 - 8.30695i) q^{23} +(-75.6447 + 89.0841i) q^{24} +214.046 q^{26} +(120.248 + 72.2737i) q^{27} +259.832 q^{28} +(89.3675 + 154.789i) q^{29} +(-77.0186 + 133.400i) q^{31} +(91.0527 - 157.708i) q^{32} +(339.127 + 61.8491i) q^{33} +(-108.905 - 188.628i) q^{34} +(326.322 + 123.123i) q^{36} -248.864 q^{37} +(22.7599 + 39.4213i) q^{38} +(-81.8326 - 229.001i) q^{39} +(-124.832 + 216.216i) q^{41} +(-160.857 - 450.145i) q^{42} +(-106.122 - 183.809i) q^{43} +856.976 q^{44} -43.8700 q^{46} +(237.847 + 411.963i) q^{47} +(-2.43174 - 0.443494i) q^{48} +(-30.7973 + 53.3425i) q^{49} +(-160.171 + 188.628i) q^{51} +(-302.277 - 523.559i) q^{52} +546.314 q^{53} +(11.2831 - 641.556i) q^{54} +(-226.200 - 391.790i) q^{56} +(33.4741 - 39.4213i) q^{57} +(408.729 - 707.940i) q^{58} +(209.648 - 363.121i) q^{59} +(272.605 + 472.165i) q^{61} +704.502 q^{62} +(-420.097 + 344.192i) q^{63} -829.068 q^{64} +(-530.538 - 1484.66i) q^{66} +(-223.938 + 387.872i) q^{67} +(-307.590 + 532.762i) q^{68} +(16.7720 + 46.9350i) q^{69} +409.542 q^{71} +(-98.4319 - 599.232i) q^{72} +358.548 q^{73} +(569.100 + 985.710i) q^{74} +(64.2831 - 111.342i) q^{76} +(-667.215 + 1155.65i) q^{77} +(-719.902 + 847.803i) q^{78} +(325.776 + 564.260i) q^{79} +(-690.693 + 233.204i) q^{81} +1141.86 q^{82} +(-406.571 - 704.202i) q^{83} +(-873.893 + 1029.15i) q^{84} +(-485.359 + 840.667i) q^{86} +(-913.663 - 166.631i) q^{87} +(-746.051 - 1292.20i) q^{88} -201.000 q^{89} +941.373 q^{91} +(61.9532 + 107.306i) q^{92} +(-269.340 - 753.723i) q^{93} +(1087.81 - 1884.14i) q^{94} +(318.418 + 891.064i) q^{96} +(126.074 + 218.367i) q^{97} +281.708 q^{98} +(-1385.56 + 1135.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 9 q^{3} - 11 q^{4} + 84 q^{6} - 43 q^{7} + 54 q^{8} + 57 q^{9} + O(q^{10}) \) \( 6 q - q^{2} - 9 q^{3} - 11 q^{4} + 84 q^{6} - 43 q^{7} + 54 q^{8} + 57 q^{9} - 14 q^{11} - 75 q^{12} + 40 q^{13} + 27 q^{14} + 13 q^{16} + 332 q^{17} - 3 q^{18} - 328 q^{19} - 144 q^{21} - 376 q^{22} + 171 q^{23} - 63 q^{24} + 868 q^{26} - 162 q^{27} + 1034 q^{28} + 335 q^{29} + 352 q^{31} - 77 q^{32} + 708 q^{33} + 52 q^{34} + 1086 q^{36} - 804 q^{37} - 178 q^{38} - 390 q^{39} - 187 q^{41} - 513 q^{42} - 602 q^{43} + 1964 q^{44} - 402 q^{46} + 665 q^{47} + 1074 q^{48} - 430 q^{49} - 180 q^{51} - 456 q^{52} + 1460 q^{53} + 639 q^{54} - 705 q^{56} + 486 q^{57} + 217 q^{58} + 298 q^{59} + 1439 q^{61} + 3228 q^{62} - 2205 q^{63} - 3138 q^{64} - 966 q^{66} - 1849 q^{67} - 710 q^{68} - 873 q^{69} + 140 q^{71} - 261 q^{72} + 736 q^{73} + 320 q^{74} - 204 q^{76} - 948 q^{77} + 432 q^{78} + 382 q^{79} - 1251 q^{81} + 1150 q^{82} - 831 q^{83} - 909 q^{84} - 1580 q^{86} - 258 q^{87} - 1428 q^{88} + 3438 q^{89} - 1420 q^{91} - 1623 q^{92} - 2178 q^{93} + 2077 q^{94} + 1155 q^{96} - 282 q^{97} - 4328 q^{98} - 762 q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28679 3.96084i −0.808502 1.40037i −0.913901 0.405937i \(-0.866945\pi\)
0.105398 0.994430i \(-0.466388\pi\)
\(3\) −3.36330 + 3.96084i −0.647267 + 0.762263i
\(4\) −6.45882 + 11.1870i −0.807352 + 1.39838i
\(5\) 0 0
\(6\) 23.3794 + 4.26387i 1.59077 + 0.290120i
\(7\) −10.0573 17.4197i −0.543041 0.940575i −0.998727 0.0504348i \(-0.983939\pi\)
0.455686 0.890141i \(-0.349394\pi\)
\(8\) 22.4912 0.993981
\(9\) −4.37646 26.6429i −0.162091 0.986776i
\(10\) 0 0
\(11\) −33.1708 57.4535i −0.909215 1.57481i −0.815157 0.579240i \(-0.803349\pi\)
−0.0940582 0.995567i \(-0.529984\pi\)
\(12\) −22.5870 63.2076i −0.543358 1.52054i
\(13\) −23.4003 + 40.5305i −0.499237 + 0.864703i −1.00000 0.000881222i \(-0.999719\pi\)
0.500763 + 0.865584i \(0.333053\pi\)
\(14\) −45.9977 + 79.6704i −0.878101 + 1.52092i
\(15\) 0 0
\(16\) 0.237854 + 0.411975i 0.00371647 + 0.00643711i
\(17\) 47.6233 0.679432 0.339716 0.940528i \(-0.389669\pi\)
0.339716 + 0.940528i \(0.389669\pi\)
\(18\) −95.5203 + 78.2613i −1.25080 + 1.02480i
\(19\) −9.95276 −0.120175 −0.0600874 0.998193i \(-0.519138\pi\)
−0.0600874 + 0.998193i \(0.519138\pi\)
\(20\) 0 0
\(21\) 102.822 + 18.7524i 1.06846 + 0.194863i
\(22\) −151.709 + 262.768i −1.47021 + 2.54647i
\(23\) 4.79602 8.30695i 0.0434800 0.0753095i −0.843466 0.537182i \(-0.819489\pi\)
0.886946 + 0.461872i \(0.152822\pi\)
\(24\) −75.6447 + 89.0841i −0.643371 + 0.757675i
\(25\) 0 0
\(26\) 214.046 1.61454
\(27\) 120.248 + 72.2737i 0.857099 + 0.515151i
\(28\) 259.832 1.75370
\(29\) 89.3675 + 154.789i 0.572246 + 0.991158i 0.996335 + 0.0855380i \(0.0272609\pi\)
−0.424089 + 0.905620i \(0.639406\pi\)
\(30\) 0 0
\(31\) −77.0186 + 133.400i −0.446224 + 0.772883i −0.998137 0.0610190i \(-0.980565\pi\)
0.551912 + 0.833902i \(0.313898\pi\)
\(32\) 91.0527 157.708i 0.503000 0.871222i
\(33\) 339.127 + 61.8491i 1.78892 + 0.326259i
\(34\) −108.905 188.628i −0.549323 0.951455i
\(35\) 0 0
\(36\) 326.322 + 123.123i 1.51075 + 0.570012i
\(37\) −248.864 −1.10576 −0.552878 0.833262i \(-0.686471\pi\)
−0.552878 + 0.833262i \(0.686471\pi\)
\(38\) 22.7599 + 39.4213i 0.0971616 + 0.168289i
\(39\) −81.8326 229.001i −0.335992 0.940244i
\(40\) 0 0
\(41\) −124.832 + 216.216i −0.475500 + 0.823590i −0.999606 0.0280628i \(-0.991066\pi\)
0.524106 + 0.851653i \(0.324400\pi\)
\(42\) −160.857 450.145i −0.590972 1.65378i
\(43\) −106.122 183.809i −0.376361 0.651876i 0.614169 0.789175i \(-0.289491\pi\)
−0.990530 + 0.137299i \(0.956158\pi\)
\(44\) 856.976 2.93623
\(45\) 0 0
\(46\) −43.8700 −0.140615
\(47\) 237.847 + 411.963i 0.738160 + 1.27853i 0.953323 + 0.301953i \(0.0976384\pi\)
−0.215163 + 0.976578i \(0.569028\pi\)
\(48\) −2.43174 0.443494i −0.00731232 0.00133360i
\(49\) −30.7973 + 53.3425i −0.0897880 + 0.155517i
\(50\) 0 0
\(51\) −160.171 + 188.628i −0.439774 + 0.517906i
\(52\) −302.277 523.559i −0.806120 1.39624i
\(53\) 546.314 1.41589 0.707944 0.706269i \(-0.249623\pi\)
0.707944 + 0.706269i \(0.249623\pi\)
\(54\) 11.2831 641.556i 0.0284341 1.61675i
\(55\) 0 0
\(56\) −226.200 391.790i −0.539773 0.934914i
\(57\) 33.4741 39.4213i 0.0777851 0.0916048i
\(58\) 408.729 707.940i 0.925324 1.60271i
\(59\) 209.648 363.121i 0.462608 0.801261i −0.536482 0.843912i \(-0.680247\pi\)
0.999090 + 0.0426512i \(0.0135804\pi\)
\(60\) 0 0
\(61\) 272.605 + 472.165i 0.572188 + 0.991059i 0.996341 + 0.0854682i \(0.0272386\pi\)
−0.424153 + 0.905591i \(0.639428\pi\)
\(62\) 704.502 1.44309
\(63\) −420.097 + 344.192i −0.840115 + 0.688319i
\(64\) −829.068 −1.61927
\(65\) 0 0
\(66\) −530.538 1484.66i −0.989466 2.76893i
\(67\) −223.938 + 387.872i −0.408335 + 0.707256i −0.994703 0.102788i \(-0.967224\pi\)
0.586369 + 0.810044i \(0.300557\pi\)
\(68\) −307.590 + 532.762i −0.548541 + 0.950102i
\(69\) 16.7720 + 46.9350i 0.0292625 + 0.0818885i
\(70\) 0 0
\(71\) 409.542 0.684559 0.342279 0.939598i \(-0.388801\pi\)
0.342279 + 0.939598i \(0.388801\pi\)
\(72\) −98.4319 599.232i −0.161115 0.980836i
\(73\) 358.548 0.574861 0.287431 0.957801i \(-0.407199\pi\)
0.287431 + 0.957801i \(0.407199\pi\)
\(74\) 569.100 + 985.710i 0.894007 + 1.54847i
\(75\) 0 0
\(76\) 64.2831 111.342i 0.0970234 0.168049i
\(77\) −667.215 + 1155.65i −0.987483 + 1.71037i
\(78\) −719.902 + 847.803i −1.04504 + 1.23070i
\(79\) 325.776 + 564.260i 0.463958 + 0.803598i 0.999154 0.0411297i \(-0.0130957\pi\)
−0.535196 + 0.844728i \(0.679762\pi\)
\(80\) 0 0
\(81\) −690.693 + 233.204i −0.947453 + 0.319895i
\(82\) 1141.86 1.53777
\(83\) −406.571 704.202i −0.537675 0.931280i −0.999029 0.0440636i \(-0.985970\pi\)
0.461354 0.887216i \(-0.347364\pi\)
\(84\) −873.893 + 1029.15i −1.13511 + 1.33678i
\(85\) 0 0
\(86\) −485.359 + 840.667i −0.608577 + 1.05409i
\(87\) −913.663 166.631i −1.12592 0.205342i
\(88\) −746.051 1292.20i −0.903743 1.56533i
\(89\) −201.000 −0.239393 −0.119696 0.992811i \(-0.538192\pi\)
−0.119696 + 0.992811i \(0.538192\pi\)
\(90\) 0 0
\(91\) 941.373 1.08442
\(92\) 61.9532 + 107.306i 0.0702073 + 0.121603i
\(93\) −269.340 753.723i −0.300314 0.840402i
\(94\) 1087.81 1884.14i 1.19361 2.06739i
\(95\) 0 0
\(96\) 318.418 + 891.064i 0.338525 + 0.947331i
\(97\) 126.074 + 218.367i 0.131968 + 0.228576i 0.924435 0.381339i \(-0.124537\pi\)
−0.792467 + 0.609915i \(0.791204\pi\)
\(98\) 281.708 0.290375
\(99\) −1385.56 + 1135.21i −1.40661 + 1.15245i
\(100\) 0 0
\(101\) −21.8013 37.7610i −0.0214783 0.0372016i 0.855086 0.518485i \(-0.173504\pi\)
−0.876565 + 0.481284i \(0.840171\pi\)
\(102\) 1113.40 + 203.060i 1.08082 + 0.197117i
\(103\) −720.176 + 1247.38i −0.688942 + 1.19328i 0.283238 + 0.959050i \(0.408591\pi\)
−0.972180 + 0.234233i \(0.924742\pi\)
\(104\) −526.301 + 911.581i −0.496232 + 0.859498i
\(105\) 0 0
\(106\) −1249.31 2163.86i −1.14475 1.98276i
\(107\) −355.755 −0.321422 −0.160711 0.987002i \(-0.551379\pi\)
−0.160711 + 0.987002i \(0.551379\pi\)
\(108\) −1585.18 + 878.409i −1.41236 + 0.782638i
\(109\) −1522.51 −1.33789 −0.668946 0.743311i \(-0.733254\pi\)
−0.668946 + 0.743311i \(0.733254\pi\)
\(110\) 0 0
\(111\) 837.004 985.710i 0.715720 0.842878i
\(112\) 4.78432 8.28669i 0.00403639 0.00699124i
\(113\) −406.499 + 704.077i −0.338409 + 0.586142i −0.984134 0.177429i \(-0.943222\pi\)
0.645725 + 0.763570i \(0.276555\pi\)
\(114\) −232.689 42.4373i −0.191170 0.0348650i
\(115\) 0 0
\(116\) −2308.83 −1.84802
\(117\) 1182.26 + 446.073i 0.934190 + 0.352474i
\(118\) −1917.69 −1.49608
\(119\) −478.960 829.584i −0.368960 0.639057i
\(120\) 0 0
\(121\) −1535.10 + 2658.87i −1.15334 + 1.99765i
\(122\) 1246.78 2159.49i 0.925231 1.60255i
\(123\) −436.547 1221.64i −0.320017 0.895539i
\(124\) −994.899 1723.22i −0.720521 1.24798i
\(125\) 0 0
\(126\) 2323.96 + 876.841i 1.64313 + 0.619962i
\(127\) 864.662 0.604144 0.302072 0.953285i \(-0.402322\pi\)
0.302072 + 0.953285i \(0.402322\pi\)
\(128\) 1167.48 + 2022.14i 0.806187 + 1.39636i
\(129\) 1084.96 + 197.872i 0.740507 + 0.135052i
\(130\) 0 0
\(131\) 1089.26 1886.65i 0.726482 1.25830i −0.231879 0.972745i \(-0.574487\pi\)
0.958361 0.285559i \(-0.0921792\pi\)
\(132\) −2882.27 + 3394.34i −1.90052 + 2.23818i
\(133\) 100.098 + 173.374i 0.0652599 + 0.113033i
\(134\) 2048.40 1.32056
\(135\) 0 0
\(136\) 1071.11 0.675343
\(137\) −1149.58 1991.13i −0.716900 1.24171i −0.962222 0.272266i \(-0.912227\pi\)
0.245322 0.969442i \(-0.421106\pi\)
\(138\) 147.548 173.762i 0.0910152 0.107185i
\(139\) 1066.98 1848.06i 0.651077 1.12770i −0.331785 0.943355i \(-0.607651\pi\)
0.982862 0.184343i \(-0.0590157\pi\)
\(140\) 0 0
\(141\) −2431.67 443.481i −1.45236 0.264878i
\(142\) −936.536 1622.13i −0.553467 0.958634i
\(143\) 3104.83 1.81565
\(144\) 9.93528 8.14012i 0.00574958 0.00471072i
\(145\) 0 0
\(146\) −819.924 1420.15i −0.464777 0.805017i
\(147\) −107.700 301.390i −0.0604284 0.169103i
\(148\) 1607.37 2784.04i 0.892735 1.54626i
\(149\) −875.309 + 1516.08i −0.481263 + 0.833572i −0.999769 0.0215024i \(-0.993155\pi\)
0.518506 + 0.855074i \(0.326488\pi\)
\(150\) 0 0
\(151\) −437.977 758.598i −0.236040 0.408833i 0.723534 0.690288i \(-0.242516\pi\)
−0.959574 + 0.281455i \(0.909183\pi\)
\(152\) −223.850 −0.119451
\(153\) −208.421 1268.83i −0.110130 0.670447i
\(154\) 6103.12 3.19353
\(155\) 0 0
\(156\) 3090.38 + 563.615i 1.58608 + 0.289265i
\(157\) −129.697 + 224.642i −0.0659298 + 0.114194i −0.897106 0.441815i \(-0.854335\pi\)
0.831176 + 0.556009i \(0.187668\pi\)
\(158\) 1489.96 2580.69i 0.750222 1.29942i
\(159\) −1837.42 + 2163.86i −0.916457 + 1.07928i
\(160\) 0 0
\(161\) −192.939 −0.0944457
\(162\) 2503.15 + 2202.44i 1.21399 + 1.06815i
\(163\) 1201.80 0.577498 0.288749 0.957405i \(-0.406761\pi\)
0.288749 + 0.957405i \(0.406761\pi\)
\(164\) −1612.54 2792.99i −0.767792 1.32986i
\(165\) 0 0
\(166\) −1859.49 + 3220.72i −0.869422 + 1.50588i
\(167\) −839.452 + 1453.97i −0.388975 + 0.673724i −0.992312 0.123762i \(-0.960504\pi\)
0.603337 + 0.797486i \(0.293837\pi\)
\(168\) 2312.60 + 421.765i 1.06203 + 0.193690i
\(169\) 3.35162 + 5.80518i 0.00152554 + 0.00264232i
\(170\) 0 0
\(171\) 43.5578 + 265.171i 0.0194792 + 0.118586i
\(172\) 2741.70 1.21542
\(173\) 465.899 + 806.961i 0.204749 + 0.354636i 0.950053 0.312089i \(-0.101029\pi\)
−0.745303 + 0.666725i \(0.767695\pi\)
\(174\) 1429.36 + 3999.92i 0.622754 + 1.74272i
\(175\) 0 0
\(176\) 15.7796 27.3311i 0.00675814 0.0117054i
\(177\) 733.155 + 2051.67i 0.311341 + 0.871259i
\(178\) 459.644 + 796.127i 0.193549 + 0.335237i
\(179\) 1023.40 0.427333 0.213667 0.976907i \(-0.431459\pi\)
0.213667 + 0.976907i \(0.431459\pi\)
\(180\) 0 0
\(181\) 2639.93 1.08411 0.542056 0.840342i \(-0.317646\pi\)
0.542056 + 0.840342i \(0.317646\pi\)
\(182\) −2152.72 3728.62i −0.876760 1.51859i
\(183\) −2787.02 508.289i −1.12581 0.205322i
\(184\) 107.868 186.833i 0.0432182 0.0748562i
\(185\) 0 0
\(186\) −2369.45 + 2790.42i −0.934067 + 1.10002i
\(187\) −1579.70 2736.13i −0.617750 1.06997i
\(188\) −6144.84 −2.38382
\(189\) 49.6230 2821.56i 0.0190981 1.08591i
\(190\) 0 0
\(191\) 406.640 + 704.322i 0.154050 + 0.266822i 0.932713 0.360621i \(-0.117435\pi\)
−0.778663 + 0.627442i \(0.784102\pi\)
\(192\) 2788.40 3283.80i 1.04810 1.23431i
\(193\) −407.121 + 705.154i −0.151840 + 0.262995i −0.931904 0.362705i \(-0.881853\pi\)
0.780064 + 0.625700i \(0.215187\pi\)
\(194\) 576.612 998.720i 0.213393 0.369608i
\(195\) 0 0
\(196\) −397.828 689.059i −0.144981 0.251115i
\(197\) −4078.41 −1.47500 −0.737499 0.675348i \(-0.763994\pi\)
−0.737499 + 0.675348i \(0.763994\pi\)
\(198\) 7664.87 + 2891.99i 2.75110 + 1.03800i
\(199\) −1342.49 −0.478224 −0.239112 0.970992i \(-0.576856\pi\)
−0.239112 + 0.970992i \(0.576856\pi\)
\(200\) 0 0
\(201\) −783.129 2191.51i −0.274814 0.769042i
\(202\) −99.7101 + 172.703i −0.0347306 + 0.0601551i
\(203\) 1797.58 3113.51i 0.621506 1.07648i
\(204\) −1075.67 3010.15i −0.369175 1.03310i
\(205\) 0 0
\(206\) 6587.56 2.22805
\(207\) −242.311 91.4250i −0.0813613 0.0306980i
\(208\) −22.2634 −0.00742159
\(209\) 330.141 + 571.821i 0.109265 + 0.189252i
\(210\) 0 0
\(211\) 1477.49 2559.08i 0.482059 0.834950i −0.517729 0.855545i \(-0.673222\pi\)
0.999788 + 0.0205943i \(0.00655583\pi\)
\(212\) −3528.55 + 6111.62i −1.14312 + 1.97994i
\(213\) −1377.41 + 1622.13i −0.443092 + 0.521814i
\(214\) 813.536 + 1409.09i 0.259870 + 0.450108i
\(215\) 0 0
\(216\) 2704.52 + 1625.52i 0.851940 + 0.512050i
\(217\) 3098.39 0.969273
\(218\) 3481.66 + 6030.42i 1.08169 + 1.87354i
\(219\) −1205.90 + 1420.15i −0.372089 + 0.438196i
\(220\) 0 0
\(221\) −1114.40 + 1930.20i −0.339198 + 0.587507i
\(222\) −5818.29 1061.12i −1.75900 0.320802i
\(223\) 1753.43 + 3037.03i 0.526539 + 0.911993i 0.999522 + 0.0309212i \(0.00984409\pi\)
−0.472982 + 0.881072i \(0.656823\pi\)
\(224\) −3662.97 −1.09260
\(225\) 0 0
\(226\) 3718.31 1.09442
\(227\) 326.413 + 565.364i 0.0954396 + 0.165306i 0.909792 0.415064i \(-0.136241\pi\)
−0.814352 + 0.580371i \(0.802908\pi\)
\(228\) 224.803 + 629.090i 0.0652979 + 0.182730i
\(229\) −2291.78 + 3969.47i −0.661331 + 1.14546i 0.318935 + 0.947776i \(0.396675\pi\)
−0.980266 + 0.197682i \(0.936659\pi\)
\(230\) 0 0
\(231\) −2333.30 6529.52i −0.664588 1.85979i
\(232\) 2009.98 + 3481.39i 0.568801 + 0.985192i
\(233\) −317.527 −0.0892785 −0.0446392 0.999003i \(-0.514214\pi\)
−0.0446392 + 0.999003i \(0.514214\pi\)
\(234\) −936.765 5702.83i −0.261702 1.59319i
\(235\) 0 0
\(236\) 2708.16 + 4690.67i 0.746975 + 1.29380i
\(237\) −3330.62 607.430i −0.912858 0.166485i
\(238\) −2190.56 + 3794.17i −0.596610 + 1.03336i
\(239\) −928.835 + 1608.79i −0.251386 + 0.435414i −0.963908 0.266236i \(-0.914220\pi\)
0.712521 + 0.701650i \(0.247553\pi\)
\(240\) 0 0
\(241\) 1633.47 + 2829.25i 0.436602 + 0.756217i 0.997425 0.0717190i \(-0.0228485\pi\)
−0.560823 + 0.827936i \(0.689515\pi\)
\(242\) 14041.8 3.72993
\(243\) 1399.33 3520.06i 0.369411 0.929266i
\(244\) −7042.82 −1.84783
\(245\) 0 0
\(246\) −3840.41 + 4522.72i −0.995349 + 1.17219i
\(247\) 232.898 403.390i 0.0599956 0.103915i
\(248\) −1732.24 + 3000.33i −0.443538 + 0.768231i
\(249\) 4156.65 + 758.079i 1.05790 + 0.192937i
\(250\) 0 0
\(251\) −5641.37 −1.41865 −0.709323 0.704884i \(-0.750999\pi\)
−0.709323 + 0.704884i \(0.750999\pi\)
\(252\) −1137.15 6922.70i −0.284260 1.73051i
\(253\) −636.351 −0.158131
\(254\) −1977.30 3424.78i −0.488452 0.846024i
\(255\) 0 0
\(256\) 2023.31 3504.47i 0.493971 0.855584i
\(257\) −586.731 + 1016.25i −0.142410 + 0.246661i −0.928404 0.371574i \(-0.878818\pi\)
0.785994 + 0.618234i \(0.212152\pi\)
\(258\) −1697.34 4749.84i −0.409580 1.14617i
\(259\) 2502.89 + 4335.14i 0.600472 + 1.04005i
\(260\) 0 0
\(261\) 3732.92 3058.44i 0.885295 0.725336i
\(262\) −9963.64 −2.34945
\(263\) −1448.98 2509.71i −0.339726 0.588423i 0.644655 0.764474i \(-0.277001\pi\)
−0.984381 + 0.176051i \(0.943668\pi\)
\(264\) 7627.38 + 1391.06i 1.77815 + 0.324295i
\(265\) 0 0
\(266\) 457.804 792.940i 0.105526 0.182776i
\(267\) 676.022 796.127i 0.154951 0.182480i
\(268\) −2892.75 5010.40i −0.659340 1.14201i
\(269\) 2930.13 0.664138 0.332069 0.943255i \(-0.392253\pi\)
0.332069 + 0.943255i \(0.392253\pi\)
\(270\) 0 0
\(271\) −668.881 −0.149932 −0.0749661 0.997186i \(-0.523885\pi\)
−0.0749661 + 0.997186i \(0.523885\pi\)
\(272\) 11.3274 + 19.6196i 0.00252509 + 0.00437358i
\(273\) −3166.12 + 3728.62i −0.701912 + 0.826617i
\(274\) −5257.70 + 9106.60i −1.15923 + 2.00785i
\(275\) 0 0
\(276\) −633.389 115.516i −0.138136 0.0251929i
\(277\) −316.315 547.874i −0.0686121 0.118840i 0.829679 0.558241i \(-0.188524\pi\)
−0.898291 + 0.439402i \(0.855190\pi\)
\(278\) −9759.80 −2.10559
\(279\) 3891.24 + 1468.18i 0.834991 + 0.315046i
\(280\) 0 0
\(281\) 1797.65 + 3113.62i 0.381633 + 0.661007i 0.991296 0.131653i \(-0.0420286\pi\)
−0.609663 + 0.792661i \(0.708695\pi\)
\(282\) 3804.16 + 10645.6i 0.803313 + 2.24800i
\(283\) 252.184 436.796i 0.0529710 0.0917485i −0.838324 0.545172i \(-0.816464\pi\)
0.891295 + 0.453424i \(0.149798\pi\)
\(284\) −2645.16 + 4581.55i −0.552680 + 0.957270i
\(285\) 0 0
\(286\) −7100.08 12297.7i −1.46796 2.54258i
\(287\) 5021.88 1.03286
\(288\) −4600.29 1735.71i −0.941232 0.355131i
\(289\) −2645.02 −0.538372
\(290\) 0 0
\(291\) −1288.94 235.074i −0.259654 0.0473549i
\(292\) −2315.80 + 4011.08i −0.464116 + 0.803872i
\(293\) 3099.25 5368.06i 0.617953 1.07033i −0.371906 0.928270i \(-0.621296\pi\)
0.989859 0.142055i \(-0.0453710\pi\)
\(294\) −947.467 + 1115.80i −0.187950 + 0.221343i
\(295\) 0 0
\(296\) −5597.26 −1.09910
\(297\) 163.666 9306.02i 0.0319760 1.81815i
\(298\) 8006.60 1.55641
\(299\) 224.457 + 388.770i 0.0434136 + 0.0751945i
\(300\) 0 0
\(301\) −2134.60 + 3697.24i −0.408759 + 0.707991i
\(302\) −2003.12 + 3469.51i −0.381678 + 0.661086i
\(303\) 222.889 + 40.6500i 0.0422596 + 0.00770719i
\(304\) −2.36730 4.10029i −0.000446626 0.000773578i
\(305\) 0 0
\(306\) −4548.99 + 3727.06i −0.849832 + 0.696281i
\(307\) 1966.79 0.365636 0.182818 0.983147i \(-0.441478\pi\)
0.182818 + 0.983147i \(0.441478\pi\)
\(308\) −8618.84 14928.3i −1.59449 2.76174i
\(309\) −2518.51 7047.81i −0.463666 1.29753i
\(310\) 0 0
\(311\) 1153.05 1997.15i 0.210237 0.364141i −0.741552 0.670896i \(-0.765910\pi\)
0.951789 + 0.306755i \(0.0992431\pi\)
\(312\) −1840.51 5150.51i −0.333970 0.934584i
\(313\) 5151.20 + 8922.14i 0.930234 + 1.61121i 0.782920 + 0.622122i \(0.213729\pi\)
0.147314 + 0.989090i \(0.452937\pi\)
\(314\) 1186.36 0.213218
\(315\) 0 0
\(316\) −8416.51 −1.49831
\(317\) −850.916 1473.83i −0.150764 0.261131i 0.780745 0.624850i \(-0.214840\pi\)
−0.931509 + 0.363719i \(0.881507\pi\)
\(318\) 12772.5 + 2329.41i 2.25235 + 0.410777i
\(319\) 5928.78 10268.9i 1.04059 1.80235i
\(320\) 0 0
\(321\) 1196.51 1409.09i 0.208046 0.245008i
\(322\) 441.212 + 764.201i 0.0763596 + 0.132259i
\(323\) −473.983 −0.0816506
\(324\) 1852.21 9233.01i 0.317595 1.58316i
\(325\) 0 0
\(326\) −2748.26 4760.13i −0.466908 0.808709i
\(327\) 5120.66 6030.42i 0.865973 1.01983i
\(328\) −2807.63 + 4862.95i −0.472638 + 0.818633i
\(329\) 4784.18 8286.44i 0.801703 1.38859i
\(330\) 0 0
\(331\) 4175.74 + 7232.60i 0.693413 + 1.20103i 0.970713 + 0.240243i \(0.0772271\pi\)
−0.277300 + 0.960783i \(0.589440\pi\)
\(332\) 10503.9 1.73637
\(333\) 1089.14 + 6630.47i 0.179233 + 1.09113i
\(334\) 7678.61 1.25795
\(335\) 0 0
\(336\) 16.7311 + 46.8205i 0.00271654 + 0.00760199i
\(337\) −3928.71 + 6804.73i −0.635046 + 1.09993i 0.351459 + 0.936203i \(0.385686\pi\)
−0.986505 + 0.163729i \(0.947648\pi\)
\(338\) 15.3289 26.5504i 0.00246681 0.00427264i
\(339\) −1421.56 3978.10i −0.227753 0.637347i
\(340\) 0 0
\(341\) 10219.1 1.62286
\(342\) 950.691 778.916i 0.150314 0.123155i
\(343\) −5660.34 −0.891048
\(344\) −2386.82 4134.10i −0.374095 0.647952i
\(345\) 0 0
\(346\) 2130.83 3690.70i 0.331081 0.573449i
\(347\) 606.088 1049.78i 0.0937652 0.162406i −0.815327 0.579000i \(-0.803443\pi\)
0.909093 + 0.416594i \(0.136776\pi\)
\(348\) 7765.29 9144.91i 1.19616 1.40867i
\(349\) −699.332 1211.28i −0.107262 0.185783i 0.807398 0.590007i \(-0.200875\pi\)
−0.914660 + 0.404224i \(0.867542\pi\)
\(350\) 0 0
\(351\) −5743.12 + 3182.47i −0.873348 + 0.483954i
\(352\) −12081.2 −1.82934
\(353\) 1314.21 + 2276.28i 0.198154 + 0.343214i 0.947930 0.318479i \(-0.103172\pi\)
−0.749776 + 0.661692i \(0.769839\pi\)
\(354\) 6449.75 7595.64i 0.968362 1.14041i
\(355\) 0 0
\(356\) 1298.22 2248.59i 0.193274 0.334761i
\(357\) 4896.73 + 893.053i 0.725946 + 0.132396i
\(358\) −2340.31 4053.53i −0.345500 0.598424i
\(359\) 3677.48 0.540640 0.270320 0.962770i \(-0.412870\pi\)
0.270320 + 0.962770i \(0.412870\pi\)
\(360\) 0 0
\(361\) −6759.94 −0.985558
\(362\) −6036.96 10456.3i −0.876507 1.51815i
\(363\) −5368.36 15022.9i −0.776215 2.17217i
\(364\) −6080.16 + 10531.1i −0.875513 + 1.51643i
\(365\) 0 0
\(366\) 4360.08 + 12201.3i 0.622692 + 1.74255i
\(367\) 5714.88 + 9898.47i 0.812846 + 1.40789i 0.910864 + 0.412706i \(0.135416\pi\)
−0.0980185 + 0.995185i \(0.531250\pi\)
\(368\) 4.56301 0.000646368
\(369\) 6306.94 + 2379.64i 0.889773 + 0.335715i
\(370\) 0 0
\(371\) −5494.43 9516.63i −0.768886 1.33175i
\(372\) 10171.5 + 1855.05i 1.41766 + 0.258549i
\(373\) 1129.95 1957.13i 0.156854 0.271679i −0.776879 0.629650i \(-0.783198\pi\)
0.933733 + 0.357971i \(0.116531\pi\)
\(374\) −7224.90 + 12513.9i −0.998905 + 1.73015i
\(375\) 0 0
\(376\) 5349.47 + 9265.55i 0.733717 + 1.27084i
\(377\) −8364.90 −1.14274
\(378\) −11289.2 + 6255.76i −1.53612 + 0.851221i
\(379\) −11815.8 −1.60142 −0.800709 0.599053i \(-0.795544\pi\)
−0.800709 + 0.599053i \(0.795544\pi\)
\(380\) 0 0
\(381\) −2908.12 + 3424.78i −0.391043 + 0.460517i
\(382\) 1859.80 3221.27i 0.249099 0.431452i
\(383\) −4040.11 + 6997.68i −0.539008 + 0.933589i 0.459950 + 0.887945i \(0.347867\pi\)
−0.998958 + 0.0456440i \(0.985466\pi\)
\(384\) −11936.0 2176.85i −1.58621 0.289289i
\(385\) 0 0
\(386\) 3724.00 0.491054
\(387\) −4432.78 + 3631.85i −0.582251 + 0.477047i
\(388\) −3257.17 −0.426180
\(389\) −1550.22 2685.05i −0.202054 0.349968i 0.747136 0.664671i \(-0.231428\pi\)
−0.949190 + 0.314703i \(0.898095\pi\)
\(390\) 0 0
\(391\) 228.402 395.604i 0.0295417 0.0511677i
\(392\) −692.669 + 1199.74i −0.0892476 + 0.154581i
\(393\) 3809.22 + 10659.8i 0.488931 + 1.36823i
\(394\) 9326.47 + 16153.9i 1.19254 + 2.06554i
\(395\) 0 0
\(396\) −3750.52 22832.4i −0.475936 2.89740i
\(397\) 11990.1 1.51578 0.757890 0.652382i \(-0.226230\pi\)
0.757890 + 0.652382i \(0.226230\pi\)
\(398\) 3069.99 + 5317.38i 0.386645 + 0.669689i
\(399\) −1023.36 186.638i −0.128402 0.0234176i
\(400\) 0 0
\(401\) −6426.63 + 11131.3i −0.800326 + 1.38620i 0.119076 + 0.992885i \(0.462007\pi\)
−0.919402 + 0.393320i \(0.871327\pi\)
\(402\) −6889.38 + 8113.38i −0.854753 + 1.00661i
\(403\) −3604.52 6243.21i −0.445543 0.771703i
\(404\) 563.243 0.0693623
\(405\) 0 0
\(406\) −16442.8 −2.00996
\(407\) 8255.02 + 14298.1i 1.00537 + 1.74135i
\(408\) −3602.45 + 4242.48i −0.437127 + 0.514789i
\(409\) −1112.54 + 1926.98i −0.134503 + 0.232966i −0.925408 0.378974i \(-0.876277\pi\)
0.790904 + 0.611940i \(0.209610\pi\)
\(410\) 0 0
\(411\) 11752.9 + 2143.47i 1.41053 + 0.257249i
\(412\) −9302.97 16113.2i −1.11244 1.92680i
\(413\) −8433.95 −1.00486
\(414\) 191.995 + 1168.82i 0.0227924 + 0.138755i
\(415\) 0 0
\(416\) 4261.32 + 7380.83i 0.502232 + 0.869891i
\(417\) 3731.29 + 10441.7i 0.438183 + 1.22621i
\(418\) 1509.93 2615.27i 0.176682 0.306021i
\(419\) −4838.33 + 8380.23i −0.564123 + 0.977090i 0.433007 + 0.901390i \(0.357452\pi\)
−0.997131 + 0.0756998i \(0.975881\pi\)
\(420\) 0 0
\(421\) 4981.30 + 8627.87i 0.576660 + 0.998804i 0.995859 + 0.0909098i \(0.0289775\pi\)
−0.419199 + 0.907894i \(0.637689\pi\)
\(422\) −13514.8 −1.55898
\(423\) 9934.98 8139.88i 1.14197 0.935637i
\(424\) 12287.3 1.40737
\(425\) 0 0
\(426\) 9574.84 + 1746.23i 1.08897 + 0.198604i
\(427\) 5483.32 9497.39i 0.621444 1.07637i
\(428\) 2297.76 3979.83i 0.259500 0.449468i
\(429\) −10442.5 + 12297.7i −1.17521 + 1.38401i
\(430\) 0 0
\(431\) −2461.47 −0.275092 −0.137546 0.990495i \(-0.543922\pi\)
−0.137546 + 0.990495i \(0.543922\pi\)
\(432\) −1.17358 + 66.7297i −0.000130704 + 0.00743179i
\(433\) −7818.49 −0.867743 −0.433871 0.900975i \(-0.642853\pi\)
−0.433871 + 0.900975i \(0.642853\pi\)
\(434\) −7085.36 12272.2i −0.783660 1.35734i
\(435\) 0 0
\(436\) 9833.63 17032.3i 1.08015 1.87087i
\(437\) −47.7336 + 82.6770i −0.00522519 + 0.00905030i
\(438\) 8382.64 + 1528.80i 0.914470 + 0.166779i
\(439\) −3105.91 5379.60i −0.337670 0.584862i 0.646324 0.763063i \(-0.276306\pi\)
−0.983994 + 0.178201i \(0.942972\pi\)
\(440\) 0 0
\(441\) 1555.98 + 587.080i 0.168015 + 0.0633927i
\(442\) 10193.6 1.09697
\(443\) 1492.17 + 2584.52i 0.160034 + 0.277188i 0.934881 0.354962i \(-0.115506\pi\)
−0.774846 + 0.632150i \(0.782173\pi\)
\(444\) 5621.08 + 15730.1i 0.600822 + 1.68134i
\(445\) 0 0
\(446\) 8019.45 13890.1i 0.851417 1.47470i
\(447\) −3061.02 8565.99i −0.323896 0.906392i
\(448\) 8338.16 + 14442.1i 0.879333 + 1.52305i
\(449\) −810.476 −0.0851865 −0.0425932 0.999092i \(-0.513562\pi\)
−0.0425932 + 0.999092i \(0.513562\pi\)
\(450\) 0 0
\(451\) 16563.1 1.72933
\(452\) −5251.01 9095.01i −0.546431 0.946446i
\(453\) 4477.73 + 816.637i 0.464420 + 0.0846996i
\(454\) 1492.88 2585.74i 0.154326 0.267301i
\(455\) 0 0
\(456\) 752.873 886.632i 0.0773169 0.0910534i
\(457\) 785.887 + 1361.20i 0.0804425 + 0.139331i 0.903440 0.428714i \(-0.141033\pi\)
−0.822998 + 0.568045i \(0.807700\pi\)
\(458\) 20963.2 2.13875
\(459\) 5726.59 + 3441.91i 0.582341 + 0.350010i
\(460\) 0 0
\(461\) −1031.35 1786.34i −0.104196 0.180474i 0.809213 0.587515i \(-0.199894\pi\)
−0.913410 + 0.407042i \(0.866560\pi\)
\(462\) −20526.6 + 24173.5i −2.06707 + 2.43431i
\(463\) 1391.62 2410.35i 0.139684 0.241940i −0.787693 0.616068i \(-0.788725\pi\)
0.927377 + 0.374128i \(0.122058\pi\)
\(464\) −42.5128 + 73.6344i −0.00425347 + 0.00736722i
\(465\) 0 0
\(466\) 726.118 + 1257.67i 0.0721819 + 0.125023i
\(467\) −10939.7 −1.08400 −0.541999 0.840379i \(-0.682332\pi\)
−0.541999 + 0.840379i \(0.682332\pi\)
\(468\) −12626.2 + 10344.9i −1.24711 + 1.02178i
\(469\) 9008.83 0.886970
\(470\) 0 0
\(471\) −453.561 1269.25i −0.0443716 0.124170i
\(472\) 4715.24 8167.04i 0.459823 0.796438i
\(473\) −7040.33 + 12194.2i −0.684386 + 1.18539i
\(474\) 5210.51 + 14581.1i 0.504908 + 1.41294i
\(475\) 0 0
\(476\) 12374.1 1.19152
\(477\) −2390.92 14555.4i −0.229503 1.39716i
\(478\) 8496.21 0.812986
\(479\) −7311.85 12664.5i −0.697467 1.20805i −0.969342 0.245716i \(-0.920977\pi\)
0.271875 0.962333i \(-0.412356\pi\)
\(480\) 0 0
\(481\) 5823.49 10086.6i 0.552034 0.956151i
\(482\) 7470.81 12939.8i 0.705987 1.22281i
\(483\) 648.913 764.201i 0.0611316 0.0719925i
\(484\) −19829.9 34346.4i −1.86231 3.22562i
\(485\) 0 0
\(486\) −17142.3 + 2507.13i −1.59998 + 0.234003i
\(487\) −16473.6 −1.53284 −0.766419 0.642341i \(-0.777963\pi\)
−0.766419 + 0.642341i \(0.777963\pi\)
\(488\) 6131.22 + 10619.6i 0.568744 + 0.985093i
\(489\) −4042.01 + 4760.13i −0.373795 + 0.440206i
\(490\) 0 0
\(491\) −10264.6 + 17778.8i −0.943450 + 1.63410i −0.184626 + 0.982809i \(0.559107\pi\)
−0.758825 + 0.651295i \(0.774226\pi\)
\(492\) 16486.0 + 3006.68i 1.51067 + 0.275511i
\(493\) 4255.97 + 7371.56i 0.388802 + 0.673425i
\(494\) −2130.35 −0.194026
\(495\) 0 0
\(496\) −73.2768 −0.00663352
\(497\) −4118.87 7134.10i −0.371744 0.643879i
\(498\) −6502.76 18197.4i −0.585132 1.63744i
\(499\) 7202.31 12474.8i 0.646131 1.11913i −0.337908 0.941179i \(-0.609719\pi\)
0.984039 0.177953i \(-0.0569475\pi\)
\(500\) 0 0
\(501\) −2935.63 8215.08i −0.261785 0.732580i
\(502\) 12900.6 + 22344.5i 1.14698 + 1.98663i
\(503\) 2953.63 0.261821 0.130910 0.991394i \(-0.458210\pi\)
0.130910 + 0.991394i \(0.458210\pi\)
\(504\) −9448.49 + 7741.30i −0.835058 + 0.684176i
\(505\) 0 0
\(506\) 1455.20 + 2520.48i 0.127849 + 0.221441i
\(507\) −34.2659 6.24932i −0.00300158 0.000547420i
\(508\) −5584.69 + 9672.98i −0.487757 + 0.844821i
\(509\) 8684.44 15041.9i 0.756250 1.30986i −0.188500 0.982073i \(-0.560363\pi\)
0.944750 0.327790i \(-0.106304\pi\)
\(510\) 0 0
\(511\) −3606.02 6245.80i −0.312174 0.540701i
\(512\) 172.223 0.0148657
\(513\) −1196.80 719.323i −0.103002 0.0619082i
\(514\) 5366.92 0.460554
\(515\) 0 0
\(516\) −9221.16 + 10859.4i −0.786703 + 0.926473i
\(517\) 15779.1 27330.3i 1.34229 2.32492i
\(518\) 11447.2 19827.1i 0.970966 1.68176i
\(519\) −4763.20 868.699i −0.402854 0.0734714i
\(520\) 0 0
\(521\) −6146.30 −0.516841 −0.258421 0.966033i \(-0.583202\pi\)
−0.258421 + 0.966033i \(0.583202\pi\)
\(522\) −20650.4 7791.48i −1.73150 0.653303i
\(523\) 4554.68 0.380807 0.190404 0.981706i \(-0.439020\pi\)
0.190404 + 0.981706i \(0.439020\pi\)
\(524\) 14070.7 + 24371.1i 1.17305 + 2.03179i
\(525\) 0 0
\(526\) −6627.03 + 11478.4i −0.549339 + 0.951483i
\(527\) −3667.88 + 6352.96i −0.303179 + 0.525122i
\(528\) 55.1824 + 154.423i 0.00454831 + 0.0127280i
\(529\) 6037.50 + 10457.3i 0.496219 + 0.859476i
\(530\) 0 0
\(531\) −10592.1 3996.46i −0.865649 0.326613i
\(532\) −2586.05 −0.210751
\(533\) −5842.22 10119.0i −0.474774 0.822333i
\(534\) −4699.25 857.037i −0.380817 0.0694525i
\(535\) 0 0
\(536\) −5036.64 + 8723.72i −0.405877 + 0.702999i
\(537\) −3442.01 + 4053.53i −0.276599 + 0.325741i
\(538\) −6700.59 11605.8i −0.536957 0.930037i
\(539\) 4086.28 0.326547
\(540\) 0 0
\(541\) 18091.8 1.43776 0.718879 0.695135i \(-0.244655\pi\)
0.718879 + 0.695135i \(0.244655\pi\)
\(542\) 1529.59 + 2649.33i 0.121221 + 0.209960i
\(543\) −8878.86 + 10456.3i −0.701710 + 0.826379i
\(544\) 4336.23 7510.58i 0.341754 0.591936i
\(545\) 0 0
\(546\) 22008.7 + 4013.89i 1.72507 + 0.314613i
\(547\) 7890.69 + 13667.1i 0.616786 + 1.06830i 0.990068 + 0.140586i \(0.0448987\pi\)
−0.373283 + 0.927718i \(0.621768\pi\)
\(548\) 29699.7 2.31516
\(549\) 11386.8 9329.41i 0.885206 0.725263i
\(550\) 0 0
\(551\) −889.453 1540.58i −0.0687694 0.119112i
\(552\) 377.223 + 1055.62i 0.0290864 + 0.0813956i
\(553\) 6552.83 11349.8i 0.503896 0.872774i
\(554\) −1446.69 + 2505.75i −0.110946 + 0.192164i
\(555\) 0 0
\(556\) 13782.8 + 23872.5i 1.05130 + 1.82090i
\(557\) 13954.5 1.06153 0.530766 0.847519i \(-0.321904\pi\)
0.530766 + 0.847519i \(0.321904\pi\)
\(558\) −3083.22 18770.0i −0.233913 1.42401i
\(559\) 9933.18 0.751572
\(560\) 0 0
\(561\) 16150.4 + 2945.46i 1.21545 + 0.221671i
\(562\) 8221.69 14240.4i 0.617102 1.06885i
\(563\) −6801.97 + 11781.4i −0.509181 + 0.881927i 0.490762 + 0.871293i \(0.336718\pi\)
−0.999943 + 0.0106339i \(0.996615\pi\)
\(564\) 20666.9 24338.7i 1.54297 1.81710i
\(565\) 0 0
\(566\) −2306.77 −0.171309
\(567\) 11008.8 + 9686.28i 0.815392 + 0.717435i
\(568\) 9211.10 0.680438
\(569\) 6229.30 + 10789.5i 0.458956 + 0.794935i 0.998906 0.0467619i \(-0.0148902\pi\)
−0.539950 + 0.841697i \(0.681557\pi\)
\(570\) 0 0
\(571\) 6728.56 11654.2i 0.493137 0.854139i −0.506831 0.862045i \(-0.669183\pi\)
0.999969 + 0.00790629i \(0.00251668\pi\)
\(572\) −20053.5 + 34733.7i −1.46587 + 2.53897i
\(573\) −4157.36 758.207i −0.303100 0.0552785i
\(574\) −11484.0 19890.8i −0.835074 1.44639i
\(575\) 0 0
\(576\) 3628.38 + 22088.8i 0.262470 + 1.59786i
\(577\) −3722.70 −0.268592 −0.134296 0.990941i \(-0.542877\pi\)
−0.134296 + 0.990941i \(0.542877\pi\)
\(578\) 6048.61 + 10476.5i 0.435275 + 0.753918i
\(579\) −1423.73 3984.18i −0.102190 0.285971i
\(580\) 0 0
\(581\) −8177.99 + 14164.7i −0.583959 + 1.01145i
\(582\) 2016.45 + 5642.86i 0.143616 + 0.401897i
\(583\) −18121.7 31387.7i −1.28735 2.22975i
\(584\) 8064.19 0.571401
\(585\) 0 0
\(586\) −28349.3 −1.99847
\(587\) −8770.16 15190.4i −0.616667 1.06810i −0.990090 0.140437i \(-0.955149\pi\)
0.373423 0.927661i \(-0.378184\pi\)
\(588\) 4067.27 + 741.777i 0.285257 + 0.0520244i
\(589\) 766.548 1327.70i 0.0536249 0.0928810i
\(590\) 0 0
\(591\) 13716.9 16153.9i 0.954718 1.12434i
\(592\) −59.1933 102.526i −0.00410951 0.00711788i
\(593\) 22350.6 1.54777 0.773886 0.633325i \(-0.218310\pi\)
0.773886 + 0.633325i \(0.218310\pi\)
\(594\) −37233.9 + 20632.7i −2.57193 + 1.42520i
\(595\) 0 0
\(596\) −11306.9 19584.2i −0.777097 1.34597i
\(597\) 4515.19 5317.38i 0.309539 0.364533i
\(598\) 1026.57 1778.07i 0.0702000 0.121590i
\(599\) 1280.81 2218.43i 0.0873665 0.151323i −0.819031 0.573750i \(-0.805488\pi\)
0.906397 + 0.422427i \(0.138822\pi\)
\(600\) 0 0
\(601\) −6692.51 11591.8i −0.454232 0.786752i 0.544412 0.838818i \(-0.316753\pi\)
−0.998644 + 0.0520656i \(0.983420\pi\)
\(602\) 19525.6 1.32193
\(603\) 11314.1 + 4268.87i 0.764091 + 0.288295i
\(604\) 11315.3 0.762270
\(605\) 0 0
\(606\) −348.693 975.786i −0.0233741 0.0654103i
\(607\) −14314.3 + 24793.1i −0.957166 + 1.65786i −0.227835 + 0.973700i \(0.573165\pi\)
−0.729331 + 0.684161i \(0.760169\pi\)
\(608\) −906.226 + 1569.63i −0.0604479 + 0.104699i
\(609\) 6286.29 + 17591.6i 0.418281 + 1.17052i
\(610\) 0 0
\(611\) −22262.8 −1.47407
\(612\) 15540.5 + 5863.50i 1.02645 + 0.387284i
\(613\) −7188.12 −0.473614 −0.236807 0.971557i \(-0.576101\pi\)
−0.236807 + 0.971557i \(0.576101\pi\)
\(614\) −4497.63 7790.12i −0.295618 0.512025i
\(615\) 0 0
\(616\) −15006.5 + 25992.0i −0.981539 + 1.70008i
\(617\) 7766.88 13452.6i 0.506779 0.877767i −0.493190 0.869922i \(-0.664169\pi\)
0.999969 0.00784559i \(-0.00249736\pi\)
\(618\) −22155.9 + 26092.3i −1.44214 + 1.69836i
\(619\) 11079.9 + 19191.0i 0.719450 + 1.24612i 0.961218 + 0.275789i \(0.0889392\pi\)
−0.241769 + 0.970334i \(0.577728\pi\)
\(620\) 0 0
\(621\) 1177.08 652.265i 0.0760624 0.0421490i
\(622\) −10547.2 −0.679908
\(623\) 2021.51 + 3501.36i 0.130000 + 0.225167i
\(624\) 74.8785 88.1818i 0.00480375 0.00565721i
\(625\) 0 0
\(626\) 23559.4 40806.1i 1.50419 2.60534i
\(627\) −3375.25 615.569i −0.214983 0.0392081i
\(628\) −1675.38 2901.85i −0.106457 0.184389i
\(629\) −11851.7 −0.751287
\(630\) 0 0
\(631\) −25582.8 −1.61400 −0.807002 0.590549i \(-0.798911\pi\)
−0.807002 + 0.590549i \(0.798911\pi\)
\(632\) 7327.10 + 12690.9i 0.461165 + 0.798761i
\(633\) 5166.88 + 14459.0i 0.324431 + 0.907891i
\(634\) −3891.73 + 6740.68i −0.243786 + 0.422250i
\(635\) 0 0
\(636\) −12339.6 34531.2i −0.769334 2.15291i
\(637\) −1441.33 2496.46i −0.0896510 0.155280i
\(638\) −54231.5 −3.36527
\(639\) −1792.34 10911.4i −0.110961 0.675506i
\(640\) 0 0
\(641\) −1905.34 3300.14i −0.117405 0.203351i 0.801334 0.598217i \(-0.204124\pi\)
−0.918738 + 0.394867i \(0.870791\pi\)
\(642\) −8317.33 1516.89i −0.511306 0.0932507i
\(643\) 13360.0 23140.3i 0.819391 1.41923i −0.0867402 0.996231i \(-0.527645\pi\)
0.906131 0.422996i \(-0.139022\pi\)
\(644\) 1246.16 2158.41i 0.0762509 0.132071i
\(645\) 0 0
\(646\) 1083.90 + 1877.37i 0.0660147 + 0.114341i
\(647\) −5114.23 −0.310759 −0.155380 0.987855i \(-0.549660\pi\)
−0.155380 + 0.987855i \(0.549660\pi\)
\(648\) −15534.5 + 5245.03i −0.941750 + 0.317970i
\(649\) −27816.8 −1.68244
\(650\) 0 0
\(651\) −10420.8 + 12272.2i −0.627378 + 0.738842i
\(652\) −7762.20 + 13444.5i −0.466244 + 0.807559i
\(653\) −4435.53 + 7682.56i −0.265813 + 0.460401i −0.967776 0.251812i \(-0.918974\pi\)
0.701964 + 0.712213i \(0.252307\pi\)
\(654\) −35595.4 6491.79i −2.12827 0.388148i
\(655\) 0 0
\(656\) −118.767 −0.00706872
\(657\) −1569.17 9552.78i −0.0931799 0.567259i
\(658\) −43761.7 −2.59272
\(659\) 12102.2 + 20961.7i 0.715382 + 1.23908i 0.962812 + 0.270172i \(0.0870805\pi\)
−0.247430 + 0.968906i \(0.579586\pi\)
\(660\) 0 0
\(661\) −10689.8 + 18515.2i −0.629023 + 1.08950i 0.358726 + 0.933443i \(0.383211\pi\)
−0.987748 + 0.156056i \(0.950122\pi\)
\(662\) 19098.1 33078.9i 1.12125 1.94207i
\(663\) −3897.14 10905.8i −0.228284 0.638832i
\(664\) −9144.28 15838.4i −0.534438 0.925674i
\(665\) 0 0
\(666\) 23771.6 19476.4i 1.38308 1.13318i
\(667\) 1714.43 0.0995248
\(668\) −10843.7 18781.9i −0.628079 1.08787i
\(669\) −17926.5 3269.38i −1.03599 0.188941i
\(670\) 0 0
\(671\) 18085.0 31324.2i 1.04048 1.80217i
\(672\) 12319.6 14508.4i 0.707203 0.832849i
\(673\) 14850.7 + 25722.1i 0.850597 + 1.47328i 0.880670 + 0.473730i \(0.157093\pi\)
−0.0300732 + 0.999548i \(0.509574\pi\)
\(674\) 35936.6 2.05375
\(675\) 0 0
\(676\) −86.5900 −0.00492661
\(677\) 1330.74 + 2304.91i 0.0755459 + 0.130849i 0.901324 0.433147i \(-0.142597\pi\)
−0.825778 + 0.563996i \(0.809263\pi\)
\(678\) −12505.8 + 14727.6i −0.708381 + 0.834235i
\(679\) 2535.93 4392.36i 0.143328 0.248252i
\(680\) 0 0
\(681\) −3337.14 608.618i −0.187782 0.0342471i
\(682\) −23368.9 40476.1i −1.31208 2.27259i
\(683\) −28698.1 −1.60776 −0.803882 0.594789i \(-0.797235\pi\)
−0.803882 + 0.594789i \(0.797235\pi\)
\(684\) −3247.80 1225.41i −0.181554 0.0685010i
\(685\) 0 0
\(686\) 12944.0 + 22419.7i 0.720415 + 1.24780i
\(687\) −8014.51 22427.9i −0.445084 1.24553i
\(688\) 50.4833 87.4396i 0.00279747 0.00484535i
\(689\) −12783.9 + 22142.4i −0.706863 + 1.22432i
\(690\) 0 0
\(691\) −8412.62 14571.1i −0.463142 0.802186i 0.535973 0.844235i \(-0.319945\pi\)
−0.999116 + 0.0420492i \(0.986611\pi\)
\(692\) −12036.6 −0.661220
\(693\) 33710.0 + 12718.9i 1.84781 + 0.697189i
\(694\) −5543.99 −0.303238
\(695\) 0 0
\(696\) −20549.4 3747.74i −1.11914 0.204106i
\(697\) −5944.92 + 10296.9i −0.323070 + 0.559574i
\(698\) −3198.45 + 5539.88i −0.173443 + 0.300412i
\(699\) 1067.94 1257.67i 0.0577870 0.0680537i
\(700\) 0 0
\(701\) −998.795 −0.0538145 −0.0269073 0.999638i \(-0.508566\pi\)
−0.0269073 + 0.999638i \(0.508566\pi\)
\(702\) 25738.6 + 15469.9i 1.38382 + 0.831730i
\(703\) 2476.88 0.132884
\(704\) 27500.8 + 47632.9i 1.47227 + 2.55004i
\(705\) 0 0
\(706\) 6010.66 10410.8i 0.320417 0.554978i
\(707\) −438.523 + 759.545i −0.0233272 + 0.0404040i
\(708\) −27687.3 5049.54i −1.46971 0.268041i
\(709\) −16626.9 28798.6i −0.880727 1.52546i −0.850534 0.525921i \(-0.823721\pi\)
−0.0301937 0.999544i \(-0.509612\pi\)
\(710\) 0 0
\(711\) 13607.8 11149.1i 0.717768 0.588078i
\(712\) −4520.73 −0.237952
\(713\) 738.765 + 1279.58i 0.0388036 + 0.0672099i
\(714\) −7660.56 21437.4i −0.401526 1.12363i
\(715\) 0 0
\(716\) −6609.97 + 11448.8i −0.345009 + 0.597573i
\(717\) −3248.21 9089.81i −0.169186 0.473452i
\(718\) −8409.62 14565.9i −0.437109 0.757095i
\(719\) 1178.94 0.0611503 0.0305752 0.999532i \(-0.490266\pi\)
0.0305752 + 0.999532i \(0.490266\pi\)
\(720\) 0 0
\(721\) 28972.0 1.49650
\(722\) 15458.6 + 26775.0i 0.796826 + 1.38014i
\(723\) −16700.1 3045.71i −0.859034 0.156668i
\(724\) −17050.8 + 29532.9i −0.875260 + 1.51600i
\(725\) 0 0
\(726\) −47226.8 + 55617.4i −2.41426 + 2.84319i
\(727\) 6338.35 + 10978.3i 0.323351 + 0.560061i 0.981177 0.193109i \(-0.0618571\pi\)
−0.657826 + 0.753170i \(0.728524\pi\)
\(728\) 21172.6 1.07790
\(729\) 9236.02 + 17381.5i 0.469238 + 0.883072i
\(730\) 0 0
\(731\) −5053.90 8753.61i −0.255712 0.442906i
\(732\) 23687.1 27895.5i 1.19604 1.40853i
\(733\) 4903.42 8492.98i 0.247083 0.427961i −0.715632 0.698478i \(-0.753861\pi\)
0.962715 + 0.270517i \(0.0871945\pi\)
\(734\) 26137.5 45271.4i 1.31438 2.27657i
\(735\) 0 0
\(736\) −873.381 1512.74i −0.0437408 0.0757613i
\(737\) 29712.8 1.48506
\(738\) −4997.30 30422.5i −0.249259 1.51744i
\(739\) −29970.4 −1.49185 −0.745927 0.666028i \(-0.767993\pi\)
−0.745927 + 0.666028i \(0.767993\pi\)
\(740\) 0 0
\(741\) 814.460 + 2279.19i 0.0403778 + 0.112994i
\(742\) −25129.2 + 43525.1i −1.24329 + 2.15345i
\(743\) 10848.8 18790.6i 0.535670 0.927808i −0.463460 0.886118i \(-0.653392\pi\)
0.999131 0.0416904i \(-0.0132743\pi\)
\(744\) −6057.78 16952.1i −0.298507 0.835344i
\(745\) 0 0
\(746\) −10335.8 −0.507267
\(747\) −16982.7 + 13914.2i −0.831812 + 0.681516i
\(748\) 40812.1 1.99497
\(749\) 3577.92 + 6197.14i 0.174545 + 0.302321i
\(750\) 0 0
\(751\) −8512.10 + 14743.4i −0.413596 + 0.716370i −0.995280 0.0970452i \(-0.969061\pi\)
0.581684 + 0.813415i \(0.302394\pi\)
\(752\) −113.146 + 195.974i −0.00548670 + 0.00950324i
\(753\) 18973.6 22344.5i 0.918243 1.08138i
\(754\) 19128.8 + 33132.0i 0.923911 + 1.60026i
\(755\) 0 0
\(756\) 31244.2 + 18779.0i 1.50310 + 0.903422i
\(757\) −30745.2 −1.47616 −0.738080 0.674714i \(-0.764267\pi\)
−0.738080 + 0.674714i \(0.764267\pi\)
\(758\) 27020.3 + 46800.5i 1.29475 + 2.24257i
\(759\) 2140.24 2520.48i 0.102353 0.120537i
\(760\) 0 0
\(761\) −10748.3 + 18616.6i −0.511992 + 0.886797i 0.487911 + 0.872893i \(0.337759\pi\)
−0.999903 + 0.0139035i \(0.995574\pi\)
\(762\) 20215.3 + 3686.81i 0.961052 + 0.175274i
\(763\) 15312.3 + 26521.7i 0.726530 + 1.25839i
\(764\) −10505.7 −0.497489
\(765\) 0 0
\(766\) 36955.5 1.74316
\(767\) 9811.66 + 16994.3i 0.461902 + 0.800037i
\(768\) 7075.65 + 19800.6i 0.332449 + 0.930327i
\(769\) −11028.7 + 19102.4i −0.517174 + 0.895772i 0.482627 + 0.875826i \(0.339683\pi\)
−0.999801 + 0.0199457i \(0.993651\pi\)
\(770\) 0 0
\(771\) −2051.84 5741.89i −0.0958434 0.268209i
\(772\) −5259.04 9108.93i −0.245178 0.424660i
\(773\) −30155.8 −1.40314 −0.701570 0.712601i \(-0.747517\pi\)
−0.701570 + 0.712601i \(0.747517\pi\)
\(774\) 24522.0 + 9252.26i 1.13879 + 0.429671i
\(775\) 0 0
\(776\) 2835.57 + 4911.35i 0.131174 + 0.227200i
\(777\) −25588.7 4666.81i −1.18146 0.215471i
\(778\) −7090.04 + 12280.3i