Properties

Label 225.4.e.c.151.1
Level $225$
Weight $4$
Character 225.151
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 151.1
Root \(0.500000 + 2.88506i\) of defining polynomial
Character \(\chi\) \(=\) 225.151
Dual form 225.4.e.c.76.1

$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28679 + 3.96084i −0.808502 + 1.40037i 0.105398 + 0.994430i \(0.466388\pi\)
−0.913901 + 0.405937i \(0.866945\pi\)
\(3\) −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 0.455686 + 0.890141i \(0.349394\pi\)
−0.998727 + 0.0504348i \(0.983939\pi\)
\(8\) 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 −0.0940582 + 0.995567i \(0.529984\pi\)
−0.815157 + 0.579240i \(0.803349\pi\)
\(12\) −22.5870 + 63.2076i −0.543358 + 1.52054i
\(13\) −23.4003 40.5305i −0.499237 0.864703i 0.500763 0.865584i \(-0.333053\pi\)
−1.00000 0.000881222i \(0.999719\pi\)
\(14\) −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 0.886946 0.461872i \(-0.152822\pi\)
−0.843466 + 0.537182i \(0.819489\pi\)
\(24\) −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 −0.424089 0.905620i \(-0.639406\pi\)
0.996335 0.0855380i \(-0.0272609\pi\)
\(30\) 0 0
\(31\) −77.0186 133.400i −0.446224 0.772883i 0.551912 0.833902i \(-0.313898\pi\)
−0.998137 + 0.0610190i \(0.980565\pi\)
\(32\) 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 0.524106 0.851653i \(-0.324400\pi\)
−0.999606 + 0.0280628i \(0.991066\pi\)
\(42\) −160.857 + 450.145i −0.590972 + 1.65378i
\(43\) −106.122 + 183.809i −0.376361 + 0.651876i −0.990530 0.137299i \(-0.956158\pi\)
0.614169 + 0.789175i \(0.289491\pi\)
\(44\) 856.976 2.93623
\(45\) 0 0
\(46\) −43.8700 −0.140615
\(47\) 237.847 411.963i 0.738160 1.27853i −0.215163 0.976578i \(-0.569028\pi\)
0.953323 0.301953i \(-0.0976384\pi\)
\(48\) −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 0.999090 0.0426512i \(-0.0135804\pi\)
−0.536482 + 0.843912i \(0.680247\pi\)
\(60\) 0 0
\(61\) 272.605 472.165i 0.572188 0.991059i −0.424153 0.905591i \(-0.639428\pi\)
0.996341 0.0854682i \(-0.0272386\pi\)
\(62\) 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 0.586369 0.810044i \(-0.300557\pi\)
−0.994703 + 0.102788i \(0.967224\pi\)
\(68\) −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 −0.535196 0.844728i \(-0.679762\pi\)
0.999154 + 0.0411297i \(0.0130957\pi\)
\(80\) 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 0.461354 + 0.887216i \(0.347364\pi\)
−0.999029 + 0.0440636i \(0.985970\pi\)
\(84\) −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 −0.792467 0.609915i \(-0.791204\pi\)
0.924435 + 0.381339i \(0.124537\pi\)
\(98\) 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 −0.876565 0.481284i \(-0.840171\pi\)
0.855086 + 0.518485i \(0.173504\pi\)
\(102\) 1113.40 203.060i 1.08082 0.197117i
\(103\) −720.176 1247.38i −0.688942 1.19328i −0.972180 0.234233i \(-0.924742\pi\)
0.283238 0.959050i \(-0.408591\pi\)
\(104\) −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 0.645725 0.763570i \(-0.276555\pi\)
−0.984134 + 0.177429i \(0.943222\pi\)
\(114\) −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 0.958361 + 0.285559i \(0.0921792\pi\)
−0.231879 + 0.972745i \(0.574487\pi\)
\(132\) −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 0.245322 + 0.969442i \(0.421106\pi\)
−0.962222 + 0.272266i \(0.912227\pi\)
\(138\) 147.548 + 173.762i 0.0910152 + 0.107185i
\(139\) 1066.98 + 1848.06i 0.651077 + 1.12770i 0.982862 + 0.184343i \(0.0590157\pi\)
−0.331785 + 0.943355i \(0.607651\pi\)
\(140\) 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 0.518506 0.855074i \(-0.326488\pi\)
−0.999769 + 0.0215024i \(0.993155\pi\)
\(150\) 0 0
\(151\) −437.977 + 758.598i −0.236040 + 0.408833i −0.959574 0.281455i \(-0.909183\pi\)
0.723534 + 0.690288i \(0.242516\pi\)
\(152\) −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 0.831176 0.556009i \(-0.187668\pi\)
−0.897106 + 0.441815i \(0.854335\pi\)
\(158\) 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 0.603337 0.797486i \(-0.293837\pi\)
−0.992312 + 0.123762i \(0.960504\pi\)
\(168\) 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 −0.745303 0.666725i \(-0.767695\pi\)
0.950053 + 0.312089i \(0.101029\pi\)
\(174\) 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 −0.778663 0.627442i \(-0.784102\pi\)
0.932713 + 0.360621i \(0.117435\pi\)
\(192\) 2788.40 + 3283.80i 1.04810 + 1.23431i
\(193\) −407.121 705.154i −0.151840 0.262995i 0.780064 0.625700i \(-0.215187\pi\)
−0.931904 + 0.362705i \(0.881853\pi\)
\(194\) 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 0.999788 0.0205943i \(-0.00655583\pi\)
−0.517729 + 0.855545i \(0.673222\pi\)
\(212\) −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 −0.472982 0.881072i \(-0.656823\pi\)
0.999522 0.0309212i \(-0.00984409\pi\)
\(224\) −3662.97 −1.09260
\(225\) 0 0
\(226\) 3718.31 1.09442
\(227\) 326.413 565.364i 0.0954396 0.165306i −0.814352 0.580371i \(-0.802908\pi\)
0.909792 + 0.415064i \(0.136241\pi\)
\(228\) 224.803 629.090i 0.0652979 0.182730i
\(229\) −2291.78 3969.47i −0.661331 1.14546i −0.980266 0.197682i \(-0.936659\pi\)
0.318935 0.947776i \(-0.396675\pi\)
\(230\) 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 0.712521 0.701650i \(-0.247553\pi\)
−0.963908 + 0.266236i \(0.914220\pi\)
\(240\) 0 0
\(241\) 1633.47 2829.25i 0.436602 0.756217i −0.560823 0.827936i \(-0.689515\pi\)
0.997425 + 0.0717190i \(0.0228485\pi\)
\(242\) 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 0.785994 0.618234i \(-0.212152\pi\)
−0.928404 + 0.371574i \(0.878818\pi\)
\(258\) −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 −0.984381 0.176051i \(-0.943668\pi\)
0.644655 + 0.764474i \(0.277001\pi\)
\(264\) 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 −0.898291 0.439402i \(-0.855190\pi\)
0.829679 + 0.558241i \(0.188524\pi\)
\(278\) −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 −0.609663 0.792661i \(-0.708695\pi\)
0.991296 + 0.131653i \(0.0420286\pi\)
\(282\) 3804.16 10645.6i 0.803313 2.24800i
\(283\) 252.184 + 436.796i 0.0529710 + 0.0917485i 0.891295 0.453424i \(-0.149798\pi\)
−0.838324 + 0.545172i \(0.816464\pi\)
\(284\) −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 0.989859 + 0.142055i \(0.0453710\pi\)
−0.371906 + 0.928270i \(0.621296\pi\)
\(294\) −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 0.951789 0.306755i \(-0.0992431\pi\)
−0.741552 + 0.670896i \(0.765910\pi\)
\(312\) −1840.51 + 5150.51i −0.333970 + 0.934584i
\(313\) 5151.20 8922.14i 0.930234 1.61121i 0.147314 0.989090i \(-0.452937\pi\)
0.782920 0.622122i \(-0.213729\pi\)
\(314\) 1186.36 0.213218
\(315\) 0 0
\(316\) −8416.51 −1.49831
\(317\) −850.916 + 1473.83i −0.150764 + 0.261131i −0.931509 0.363719i \(-0.881507\pi\)
0.780745 + 0.624850i \(0.214840\pi\)
\(318\) 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 −0.277300 0.960783i \(-0.589440\pi\)
0.970713 0.240243i \(-0.0772271\pi\)
\(332\) 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 −0.986505 0.163729i \(-0.947648\pi\)
0.351459 0.936203i \(-0.385686\pi\)
\(338\) 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 0.909093 0.416594i \(-0.136776\pi\)
−0.815327 + 0.579000i \(0.803443\pi\)
\(348\) 7765.29 + 9144.91i 1.19616 + 1.40867i
\(349\) −699.332 + 1211.28i −0.107262 + 0.185783i −0.914660 0.404224i \(-0.867542\pi\)
0.807398 + 0.590007i \(0.200875\pi\)
\(350\) 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 −0.749776 0.661692i \(-0.769839\pi\)
0.947930 + 0.318479i \(0.103172\pi\)
\(354\) 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 −0.0980185 0.995185i \(-0.531250\pi\)
0.910864 0.412706i \(-0.135416\pi\)
\(368\) 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 0.933733 0.357971i \(-0.116531\pi\)
−0.776879 + 0.629650i \(0.783198\pi\)
\(374\) −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 −0.998958 0.0456440i \(-0.985466\pi\)
0.459950 0.887945i \(-0.347867\pi\)
\(384\) −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 −0.949190 0.314703i \(-0.898095\pi\)
0.747136 + 0.664671i \(0.231428\pi\)
\(390\) 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 −0.919402 0.393320i \(-0.871327\pi\)
0.119076 0.992885i \(-0.462007\pi\)
\(402\) −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 0.790904 0.611940i \(-0.209610\pi\)
−0.925408 + 0.378974i \(0.876277\pi\)
\(410\) 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 −0.997131 0.0756998i \(-0.975881\pi\)
0.433007 0.901390i \(-0.357452\pi\)
\(420\) 0 0
\(421\) 4981.30 8627.87i 0.576660 0.998804i −0.419199 0.907894i \(-0.637689\pi\)
0.995859 0.0909098i \(-0.0289775\pi\)
\(422\) −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 −0.983994 0.178201i \(-0.942972\pi\)
0.646324 + 0.763063i \(0.276306\pi\)
\(440\) 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 −0.774846 0.632150i \(-0.782173\pi\)
0.934881 + 0.354962i \(0.115506\pi\)
\(444\) 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 −0.822998 0.568045i \(-0.807700\pi\)
0.903440 + 0.428714i \(0.141033\pi\)
\(458\) 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 −0.913410 0.407042i \(-0.866560\pi\)
0.809213 + 0.587515i \(0.199894\pi\)
\(462\) −20526.6 24173.5i −2.06707 2.43431i
\(463\) 1391.62 + 2410.35i 0.139684 + 0.241940i 0.927377 0.374128i \(-0.122058\pi\)
−0.787693 + 0.616068i \(0.788725\pi\)
\(464\) −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 0.271875 + 0.962333i \(0.412356\pi\)
−0.969342 + 0.245716i \(0.920977\pi\)
\(480\) 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 −0.758825 0.651295i \(-0.774226\pi\)
−0.184626 0.982809i \(-0.559107\pi\)
\(492\) 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 0.984039 + 0.177953i \(0.0569475\pi\)
−0.337908 + 0.941179i \(0.609719\pi\)
\(500\) 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 0.944750 + 0.327790i \(0.106304\pi\)
−0.188500 + 0.982073i \(0.560363\pi\)
\(510\) 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 −0.373283 0.927718i \(-0.621768\pi\)
0.990068 0.140586i \(-0.0448987\pi\)
\(548\) 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 −0.999943 0.0106339i \(-0.996615\pi\)
0.490762 0.871293i \(-0.336718\pi\)
\(564\) 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 −0.539950 0.841697i \(-0.681557\pi\)
0.998906 + 0.0467619i \(0.0148902\pi\)
\(570\) 0 0
\(571\) 6728.56 + 11654.2i 0.493137 + 0.854139i 0.999969 0.00790629i \(-0.00251668\pi\)
−0.506831 + 0.862045i \(0.669183\pi\)
\(572\) −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 0.373423 + 0.927661i \(0.378184\pi\)
−0.990090 + 0.140437i \(0.955149\pi\)
\(588\) 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 0.906397 0.422427i \(-0.138822\pi\)
−0.819031 + 0.573750i \(0.805488\pi\)
\(600\) 0 0
\(601\) −6692.51 + 11591.8i −0.454232 + 0.786752i −0.998644 0.0520656i \(-0.983420\pi\)
0.544412 + 0.838818i \(0.316753\pi\)
\(602\) 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 −0.729331 0.684161i \(-0.760169\pi\)
−0.227835 0.973700i \(-0.573165\pi\)
\(608\) −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 0.999969 + 0.00784559i \(0.00249736\pi\)
−0.493190 + 0.869922i \(0.664169\pi\)
\(618\) −22155.9 26092.3i −1.44214 1.69836i
\(619\) 11079.9 19191.0i 0.719450 1.24612i −0.241769 0.970334i \(-0.577728\pi\)
0.961218 0.275789i \(-0.0889392\pi\)
\(620\) 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 −0.918738 0.394867i \(-0.870791\pi\)
0.801334 + 0.598217i \(0.204124\pi\)
\(642\) −8317.33 + 1516.89i −0.511306 + 0.0932507i
\(643\) 13360.0 + 23140.3i 0.819391 + 1.41923i 0.906131 + 0.422996i \(0.139022\pi\)
−0.0867402 + 0.996231i \(0.527645\pi\)
\(644\) 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 0.701964 0.712213i \(-0.252307\pi\)
−0.967776 + 0.251812i \(0.918974\pi\)
\(654\) −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 −0.247430 0.968906i \(-0.579586\pi\)
0.962812 0.270172i \(-0.0870805\pi\)
\(660\) 0 0
\(661\) −10689.8 18515.2i −0.629023 1.08950i −0.987748 0.156056i \(-0.950122\pi\)
0.358726 0.933443i \(-0.383211\pi\)
\(662\) 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 −0.0300732 0.999548i \(-0.509574\pi\)
0.880670 0.473730i \(-0.157093\pi\)
\(674\) 35936.6 2.05375
\(675\) 0 0
\(676\) −86.5900 −0.00492661
\(677\) 1330.74 2304.91i 0.0755459 0.130849i −0.825778 0.563996i \(-0.809263\pi\)
0.901324 + 0.433147i \(0.142597\pi\)
\(678\) −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 −0.999116 0.0420492i \(-0.986611\pi\)
0.535973 + 0.844235i \(0.319945\pi\)
\(692\) −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 −0.0301937 + 0.999544i \(0.509612\pi\)
−0.850534 + 0.525921i \(0.823721\pi\)
\(710\) 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 −0.657826 0.753170i \(-0.728524\pi\)
0.981177 + 0.193109i \(0.0618571\pi\)
\(728\) 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 0.962715 0.270517i \(-0.0871945\pi\)
−0.715632 + 0.698478i \(0.753861\pi\)
\(734\) 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 0.999131 + 0.0416904i \(0.0132743\pi\)
−0.463460 + 0.886118i \(0.653392\pi\)
\(744\) −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 0.581684 0.813415i \(-0.302394\pi\)
−0.995280 + 0.0970452i \(0.969061\pi\)
\(752\) −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 −0.999903 0.0139035i \(-0.995574\pi\)
0.487911 0.872893i \(-0.337759\pi\)
\(762\) 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 −0.999801 0.0199457i \(-0.993651\pi\)
0.482627 0.875826i \(-0.339683\pi\)
\(770\) 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
\(778\)