Properties

Label 225.4.k.c.124.6
Level $225$
Weight $4$
Character 225.124
Analytic conductor $13.275$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 23 x^{10} + 198 x^{8} - 719 x^{6} + 886 x^{4} + 585 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.6
Root \(2.88506 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 225.124
Dual form 225.4.k.c.49.6

$q$-expansion

\(f(q)\) \(=\) \(q+(3.96084 + 2.28679i) q^{2} +(3.96084 - 3.36330i) q^{3} +(6.45882 + 11.1870i) q^{4} +(23.3794 - 4.26387i) q^{6} +(17.4197 + 10.0573i) q^{7} +22.4912i q^{8} +(4.37646 - 26.6429i) q^{9} +O(q^{10})\) \(q+(3.96084 + 2.28679i) q^{2} +(3.96084 - 3.36330i) q^{3} +(6.45882 + 11.1870i) q^{4} +(23.3794 - 4.26387i) q^{6} +(17.4197 + 10.0573i) q^{7} +22.4912i q^{8} +(4.37646 - 26.6429i) q^{9} +(-33.1708 + 57.4535i) q^{11} +(63.2076 + 22.5870i) q^{12} +(40.5305 - 23.4003i) q^{13} +(45.9977 + 79.6704i) q^{14} +(0.237854 - 0.411975i) q^{16} -47.6233i q^{17} +(78.2613 - 95.5203i) q^{18} +9.95276 q^{19} +(102.822 - 18.7524i) q^{21} +(-262.768 + 151.709i) q^{22} +(-8.30695 + 4.79602i) q^{23} +(75.6447 + 89.0841i) q^{24} +214.046 q^{26} +(-72.2737 - 120.248i) q^{27} +259.832i q^{28} +(-89.3675 + 154.789i) q^{29} +(-77.0186 - 133.400i) q^{31} +(157.708 - 91.0527i) q^{32} +(61.8491 + 339.127i) q^{33} +(108.905 - 188.628i) q^{34} +(326.322 - 123.123i) q^{36} +248.864i q^{37} +(39.4213 + 22.7599i) q^{38} +(81.8326 - 229.001i) q^{39} +(-124.832 - 216.216i) q^{41} +(450.145 + 160.857i) q^{42} +(-183.809 - 106.122i) q^{43} -856.976 q^{44} -43.8700 q^{46} +(-411.963 - 237.847i) q^{47} +(-0.443494 - 2.43174i) q^{48} +(30.7973 + 53.3425i) q^{49} +(-160.171 - 188.628i) q^{51} +(523.559 + 302.277i) q^{52} +546.314i q^{53} +(-11.2831 - 641.556i) q^{54} +(-226.200 + 391.790i) q^{56} +(39.4213 - 33.4741i) q^{57} +(-707.940 + 408.729i) q^{58} +(-209.648 - 363.121i) q^{59} +(272.605 - 472.165i) q^{61} -704.502i q^{62} +(344.192 - 420.097i) q^{63} +829.068 q^{64} +(-530.538 + 1484.66i) q^{66} +(-387.872 + 223.938i) q^{67} +(532.762 - 307.590i) q^{68} +(-16.7720 + 46.9350i) q^{69} +409.542 q^{71} +(599.232 + 98.4319i) q^{72} +358.548i q^{73} +(-569.100 + 985.710i) q^{74} +(64.2831 + 111.342i) q^{76} +(-1155.65 + 667.215i) q^{77} +(847.803 - 719.902i) q^{78} +(-325.776 + 564.260i) q^{79} +(-690.693 - 233.204i) q^{81} -1141.86i q^{82} +(-704.202 - 406.571i) q^{83} +(873.893 + 1029.15i) q^{84} +(-485.359 - 840.667i) q^{86} +(166.631 + 913.663i) q^{87} +(-1292.20 - 746.051i) q^{88} +201.000 q^{89} +941.373 q^{91} +(-107.306 - 61.9532i) q^{92} +(-753.723 - 269.340i) q^{93} +(-1087.81 - 1884.14i) q^{94} +(318.418 - 891.064i) q^{96} +(-218.367 - 126.074i) q^{97} +281.708i q^{98} +(1385.56 + 1135.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} + O(q^{10}) \) \( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} - 28 q^{11} - 54 q^{14} + 26 q^{16} + 656 q^{19} - 288 q^{21} + 126 q^{24} + 1736 q^{26} - 670 q^{29} + 704 q^{31} - 104 q^{34} + 2172 q^{36} + 780 q^{39} - 374 q^{41} - 3928 q^{44} - 804 q^{46} + 860 q^{49} - 360 q^{51} - 1278 q^{54} - 1410 q^{56} - 596 q^{59} + 2878 q^{61} + 6276 q^{64} - 1932 q^{66} + 1746 q^{69} + 280 q^{71} - 640 q^{74} - 408 q^{76} - 764 q^{79} - 2502 q^{81} + 1818 q^{84} - 3160 q^{86} - 6876 q^{89} - 2840 q^{91} - 4154 q^{94} + 2310 q^{96} + 1524 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.96084 + 2.28679i 1.40037 + 0.808502i 0.994430 0.105398i \(-0.0336118\pi\)
0.405937 + 0.913901i \(0.366945\pi\)
\(3\) 3.96084 3.36330i 0.762263 0.647267i
\(4\) 6.45882 + 11.1870i 0.807352 + 1.39838i
\(5\) 0 0
\(6\) 23.3794 4.26387i 1.59077 0.290120i
\(7\) 17.4197 + 10.0573i 0.940575 + 0.543041i 0.890141 0.455686i \(-0.150606\pi\)
0.0504348 + 0.998727i \(0.483939\pi\)
\(8\) 22.4912i 0.993981i
\(9\) 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 \(0.803349\pi\)
\(12\) 63.2076 + 22.5870i 1.52054 + 0.543358i
\(13\) 40.5305 23.4003i 0.864703 0.499237i −0.000881222 1.00000i \(-0.500281\pi\)
0.865584 + 0.500763i \(0.166947\pi\)
\(14\) 45.9977 + 79.6704i 0.878101 + 1.52092i
\(15\) 0 0
\(16\) 0.237854 0.411975i 0.00371647 0.00643711i
\(17\) 47.6233i 0.679432i −0.940528 0.339716i \(-0.889669\pi\)
0.940528 0.339716i \(-0.110331\pi\)
\(18\) 78.2613 95.5203i 1.02480 1.25080i
\(19\) 9.95276 0.120175 0.0600874 0.998193i \(-0.480862\pi\)
0.0600874 + 0.998193i \(0.480862\pi\)
\(20\) 0 0
\(21\) 102.822 18.7524i 1.06846 0.194863i
\(22\) −262.768 + 151.709i −2.54647 + 1.47021i
\(23\) −8.30695 + 4.79602i −0.0753095 + 0.0434800i −0.537182 0.843466i \(-0.680511\pi\)
0.461872 + 0.886946i \(0.347178\pi\)
\(24\) 75.6447 + 89.0841i 0.643371 + 0.757675i
\(25\) 0 0
\(26\) 214.046 1.61454
\(27\) −72.2737 120.248i −0.515151 0.857099i
\(28\) 259.832i 1.75370i
\(29\) −89.3675 + 154.789i −0.572246 + 0.991158i 0.424089 + 0.905620i \(0.360594\pi\)
−0.996335 + 0.0855380i \(0.972739\pi\)
\(30\) 0 0
\(31\) −77.0186 133.400i −0.446224 0.772883i 0.551912 0.833902i \(-0.313898\pi\)
−0.998137 + 0.0610190i \(0.980565\pi\)
\(32\) 157.708 91.0527i 0.871222 0.503000i
\(33\) 61.8491 + 339.127i 0.326259 + 1.78892i
\(34\) 108.905 188.628i 0.549323 0.951455i
\(35\) 0 0
\(36\) 326.322 123.123i 1.51075 0.570012i
\(37\) 248.864i 1.10576i 0.833262 + 0.552878i \(0.186471\pi\)
−0.833262 + 0.552878i \(0.813529\pi\)
\(38\) 39.4213 + 22.7599i 0.168289 + 0.0971616i
\(39\) 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 \(0.991066\pi\)
\(42\) 450.145 + 160.857i 1.65378 + 0.590972i
\(43\) −183.809 106.122i −0.651876 0.376361i 0.137299 0.990530i \(-0.456158\pi\)
−0.789175 + 0.614169i \(0.789491\pi\)
\(44\) −856.976 −2.93623
\(45\) 0 0
\(46\) −43.8700 −0.140615
\(47\) −411.963 237.847i −1.27853 0.738160i −0.301953 0.953323i \(-0.597638\pi\)
−0.976578 + 0.215163i \(0.930972\pi\)
\(48\) −0.443494 2.43174i −0.00133360 0.00731232i
\(49\) 30.7973 + 53.3425i 0.0897880 + 0.155517i
\(50\) 0 0
\(51\) −160.171 188.628i −0.439774 0.517906i
\(52\) 523.559 + 302.277i 1.39624 + 0.806120i
\(53\) 546.314i 1.41589i 0.706269 + 0.707944i \(0.250377\pi\)
−0.706269 + 0.707944i \(0.749623\pi\)
\(54\) −11.2831 641.556i −0.0284341 1.61675i
\(55\) 0 0
\(56\) −226.200 + 391.790i −0.539773 + 0.934914i
\(57\) 39.4213 33.4741i 0.0916048 0.0777851i
\(58\) −707.940 + 408.729i −1.60271 + 0.925324i
\(59\) −209.648 363.121i −0.462608 0.801261i 0.536482 0.843912i \(-0.319753\pi\)
−0.999090 + 0.0426512i \(0.986420\pi\)
\(60\) 0 0
\(61\) 272.605 472.165i 0.572188 0.991059i −0.424153 0.905591i \(-0.639428\pi\)
0.996341 0.0854682i \(-0.0272386\pi\)
\(62\) 704.502i 1.44309i
\(63\) 344.192 420.097i 0.688319 0.840115i
\(64\) 829.068 1.61927
\(65\) 0 0
\(66\) −530.538 + 1484.66i −0.989466 + 2.76893i
\(67\) −387.872 + 223.938i −0.707256 + 0.408335i −0.810044 0.586369i \(-0.800557\pi\)
0.102788 + 0.994703i \(0.467224\pi\)
\(68\) 532.762 307.590i 0.950102 0.548541i
\(69\) −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 \(0.388801\pi\)
\(72\) 599.232 + 98.4319i 0.980836 + 0.161115i
\(73\) 358.548i 0.574861i 0.957801 + 0.287431i \(0.0928011\pi\)
−0.957801 + 0.287431i \(0.907199\pi\)
\(74\) −569.100 + 985.710i −0.894007 + 1.54847i
\(75\) 0 0
\(76\) 64.2831 + 111.342i 0.0970234 + 0.168049i
\(77\) −1155.65 + 667.215i −1.71037 + 0.987483i
\(78\) 847.803 719.902i 1.23070 1.04504i
\(79\) −325.776 + 564.260i −0.463958 + 0.803598i −0.999154 0.0411297i \(-0.986904\pi\)
0.535196 + 0.844728i \(0.320238\pi\)
\(80\) 0 0
\(81\) −690.693 233.204i −0.947453 0.319895i
\(82\) 1141.86i 1.53777i
\(83\) −704.202 406.571i −0.931280 0.537675i −0.0440636 0.999029i \(-0.514030\pi\)
−0.887216 + 0.461354i \(0.847364\pi\)
\(84\) 873.893 + 1029.15i 1.13511 + 1.33678i
\(85\) 0 0
\(86\) −485.359 840.667i −0.608577 1.05409i
\(87\) 166.631 + 913.663i 0.205342 + 1.12592i
\(88\) −1292.20 746.051i −1.56533 0.903743i
\(89\) 201.000 0.239393 0.119696 0.992811i \(-0.461808\pi\)
0.119696 + 0.992811i \(0.461808\pi\)
\(90\) 0 0
\(91\) 941.373 1.08442
\(92\) −107.306 61.9532i −0.121603 0.0702073i
\(93\) −753.723 269.340i −0.840402 0.300314i
\(94\) −1087.81 1884.14i −1.19361 2.06739i
\(95\) 0 0
\(96\) 318.418 891.064i 0.338525 0.947331i
\(97\) −218.367 126.074i −0.228576 0.131968i 0.381339 0.924435i \(-0.375463\pi\)
−0.609915 + 0.792467i \(0.708796\pi\)
\(98\) 281.708i 0.290375i
\(99\) 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 \(0.173504\pi\)
\(102\) −203.060 1113.40i −0.197117 1.08082i
\(103\) 1247.38 720.176i 1.19328 0.688942i 0.234233 0.972180i \(-0.424742\pi\)
0.959050 + 0.283238i \(0.0914087\pi\)
\(104\) 526.301 + 911.581i 0.496232 + 0.859498i
\(105\) 0 0
\(106\) −1249.31 + 2163.86i −1.14475 + 1.98276i
\(107\) 355.755i 0.321422i 0.987002 + 0.160711i \(0.0513786\pi\)
−0.987002 + 0.160711i \(0.948621\pi\)
\(108\) 878.409 1585.18i 0.782638 1.41236i
\(109\) 1522.51 1.33789 0.668946 0.743311i \(-0.266746\pi\)
0.668946 + 0.743311i \(0.266746\pi\)
\(110\) 0 0
\(111\) 837.004 + 985.710i 0.715720 + 0.842878i
\(112\) 8.28669 4.78432i 0.00699124 0.00403639i
\(113\) 704.077 406.499i 0.586142 0.338409i −0.177429 0.984134i \(-0.556778\pi\)
0.763570 + 0.645725i \(0.223445\pi\)
\(114\) 232.689 42.4373i 0.191170 0.0348650i
\(115\) 0 0
\(116\) −2308.83 −1.84802
\(117\) −446.073 1182.26i −0.352474 0.934190i
\(118\) 1917.69i 1.49608i
\(119\) 478.960 829.584i 0.368960 0.639057i
\(120\) 0 0
\(121\) −1535.10 2658.87i −1.15334 1.99765i
\(122\) 2159.49 1246.78i 1.60255 0.925231i
\(123\) −1221.64 436.547i −0.895539 0.320017i
\(124\) 994.899 1723.22i 0.720521 1.24798i
\(125\) 0 0
\(126\) 2323.96 876.841i 1.64313 0.619962i
\(127\) 864.662i 0.604144i −0.953285 0.302072i \(-0.902322\pi\)
0.953285 0.302072i \(-0.0976784\pi\)
\(128\) 2022.14 + 1167.48i 1.39636 + 0.806187i
\(129\) −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 \(0.574487\pi\)
\(132\) −3394.34 + 2882.27i −2.23818 + 1.90052i
\(133\) 173.374 + 100.098i 0.113033 + 0.0652599i
\(134\) −2048.40 −1.32056
\(135\) 0 0
\(136\) 1071.11 0.675343
\(137\) 1991.13 + 1149.58i 1.24171 + 0.716900i 0.969442 0.245322i \(-0.0788937\pi\)
0.272266 + 0.962222i \(0.412227\pi\)
\(138\) −173.762 + 147.548i −0.107185 + 0.0910152i
\(139\) −1066.98 1848.06i −0.651077 1.12770i −0.982862 0.184343i \(-0.940984\pi\)
0.331785 0.943355i \(-0.392349\pi\)
\(140\) 0 0
\(141\) −2431.67 + 443.481i −1.45236 + 0.264878i
\(142\) 1622.13 + 936.536i 0.958634 + 0.553467i
\(143\) 3104.83i 1.81565i
\(144\) −9.93528 8.14012i −0.00574958 0.00471072i
\(145\) 0 0
\(146\) −819.924 + 1420.15i −0.464777 + 0.805017i
\(147\) 301.390 + 107.700i 0.169103 + 0.0604284i
\(148\) −2784.04 + 1607.37i −1.54626 + 0.892735i
\(149\) 875.309 + 1516.08i 0.481263 + 0.833572i 0.999769 0.0215024i \(-0.00684497\pi\)
−0.518506 + 0.855074i \(0.673512\pi\)
\(150\) 0 0
\(151\) −437.977 + 758.598i −0.236040 + 0.408833i −0.959574 0.281455i \(-0.909183\pi\)
0.723534 + 0.690288i \(0.242516\pi\)
\(152\) 223.850i 0.119451i
\(153\) −1268.83 208.421i −0.670447 0.110130i
\(154\) −6103.12 −3.19353
\(155\) 0 0
\(156\) 3090.38 563.615i 1.58608 0.289265i
\(157\) −224.642 + 129.697i −0.114194 + 0.0659298i −0.556009 0.831176i \(-0.687668\pi\)
0.441815 + 0.897106i \(0.354335\pi\)
\(158\) −2580.69 + 1489.96i −1.29942 + 0.750222i
\(159\) 1837.42 + 2163.86i 0.916457 + 1.07928i
\(160\) 0 0
\(161\) −192.939 −0.0944457
\(162\) −2202.44 2503.15i −1.06815 1.21399i
\(163\) 1201.80i 0.577498i 0.957405 + 0.288749i \(0.0932393\pi\)
−0.957405 + 0.288749i \(0.906761\pi\)
\(164\) 1612.54 2792.99i 0.767792 1.32986i
\(165\) 0 0
\(166\) −1859.49 3220.72i −0.869422 1.50588i
\(167\) −1453.97 + 839.452i −0.673724 + 0.388975i −0.797486 0.603337i \(-0.793837\pi\)
0.123762 + 0.992312i \(0.460504\pi\)
\(168\) 421.765 + 2312.60i 0.193690 + 1.06203i
\(169\) −3.35162 + 5.80518i −0.00152554 + 0.00264232i
\(170\) 0 0
\(171\) 43.5578 265.171i 0.0194792 0.118586i
\(172\) 2741.70i 1.21542i
\(173\) 806.961 + 465.899i 0.354636 + 0.204749i 0.666725 0.745303i \(-0.267695\pi\)
−0.312089 + 0.950053i \(0.601029\pi\)
\(174\) −1429.36 + 3999.92i −0.622754 + 1.74272i
\(175\) 0 0
\(176\) 15.7796 + 27.3311i 0.00675814 + 0.0117054i
\(177\) −2051.67 733.155i −0.871259 0.311341i
\(178\) 796.127 + 459.644i 0.335237 + 0.193549i
\(179\) −1023.40 −0.427333 −0.213667 0.976907i \(-0.568541\pi\)
−0.213667 + 0.976907i \(0.568541\pi\)
\(180\) 0 0
\(181\) 2639.93 1.08411 0.542056 0.840342i \(-0.317646\pi\)
0.542056 + 0.840342i \(0.317646\pi\)
\(182\) 3728.62 + 2152.72i 1.51859 + 0.876760i
\(183\) −508.289 2787.02i −0.205322 1.12581i
\(184\) −107.868 186.833i −0.0432182 0.0748562i
\(185\) 0 0
\(186\) −2369.45 2790.42i −0.934067 1.10002i
\(187\) 2736.13 + 1579.70i 1.06997 + 0.617750i
\(188\) 6144.84i 2.38382i
\(189\) −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 \(0.117435\pi\)
\(192\) 3283.80 2788.40i 1.23431 1.04810i
\(193\) 705.154 407.121i 0.262995 0.151840i −0.362705 0.931904i \(-0.618147\pi\)
0.625700 + 0.780064i \(0.284813\pi\)
\(194\) −576.612 998.720i −0.213393 0.369608i
\(195\) 0 0
\(196\) −397.828 + 689.059i −0.144981 + 0.251115i
\(197\) 4078.41i 1.47500i 0.675348 + 0.737499i \(0.263994\pi\)
−0.675348 + 0.737499i \(0.736006\pi\)
\(198\) 2891.99 + 7664.87i 1.03800 + 2.75110i
\(199\) 1342.49 0.478224 0.239112 0.970992i \(-0.423144\pi\)
0.239112 + 0.970992i \(0.423144\pi\)
\(200\) 0 0
\(201\) −783.129 + 2191.51i −0.274814 + 0.769042i
\(202\) −172.703 + 99.7101i −0.0601551 + 0.0347306i
\(203\) −3113.51 + 1797.58i −1.07648 + 0.621506i
\(204\) 1075.67 3010.15i 0.369175 1.03310i
\(205\) 0 0
\(206\) 6587.56 2.22805
\(207\) 91.4250 + 242.311i 0.0306980 + 0.0813613i
\(208\) 22.2634i 0.00742159i
\(209\) −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 \(0.673222\pi\)
\(212\) −6111.62 + 3528.55i −1.97994 + 1.14312i
\(213\) 1622.13 1377.41i 0.521814 0.443092i
\(214\) −813.536 + 1409.09i −0.259870 + 0.450108i
\(215\) 0 0
\(216\) 2704.52 1625.52i 0.851940 0.512050i
\(217\) 3098.39i 0.969273i
\(218\) 6030.42 + 3481.66i 1.87354 + 1.08169i
\(219\) 1205.90 + 1420.15i 0.372089 + 0.438196i
\(220\) 0 0
\(221\) −1114.40 1930.20i −0.339198 0.587507i
\(222\) 1061.12 + 5818.29i 0.320802 + 1.75900i
\(223\) 3037.03 + 1753.43i 0.911993 + 0.526539i 0.881072 0.472982i \(-0.156823\pi\)
0.0309212 + 0.999522i \(0.490156\pi\)
\(224\) 3662.97 1.09260
\(225\) 0 0
\(226\) 3718.31 1.09442
\(227\) −565.364 326.413i −0.165306 0.0954396i 0.415064 0.909792i \(-0.363759\pi\)
−0.580371 + 0.814352i \(0.697092\pi\)
\(228\) 629.090 + 224.803i 0.182730 + 0.0652979i
\(229\) 2291.78 + 3969.47i 0.661331 + 1.14546i 0.980266 + 0.197682i \(0.0633414\pi\)
−0.318935 + 0.947776i \(0.603325\pi\)
\(230\) 0 0
\(231\) −2333.30 + 6529.52i −0.664588 + 1.85979i
\(232\) −3481.39 2009.98i −0.985192 0.568801i
\(233\) 317.527i 0.0892785i −0.999003 0.0446392i \(-0.985786\pi\)
0.999003 0.0446392i \(-0.0142138\pi\)
\(234\) 936.765 5702.83i 0.261702 1.59319i
\(235\) 0 0
\(236\) 2708.16 4690.67i 0.746975 1.29380i
\(237\) 607.430 + 3330.62i 0.166485 + 0.912858i
\(238\) 3794.17 2190.56i 1.03336 0.596610i
\(239\) 928.835 + 1608.79i 0.251386 + 0.435414i 0.963908 0.266236i \(-0.0857802\pi\)
−0.712521 + 0.701650i \(0.752447\pi\)
\(240\) 0 0
\(241\) 1633.47 2829.25i 0.436602 0.756217i −0.560823 0.827936i \(-0.689515\pi\)
0.997425 + 0.0717190i \(0.0228485\pi\)
\(242\) 14041.8i 3.72993i
\(243\) −3520.06 + 1399.33i −0.929266 + 0.369411i
\(244\) 7042.82 1.84783
\(245\) 0 0
\(246\) −3840.41 4522.72i −0.995349 1.17219i
\(247\) 403.390 232.898i 0.103915 0.0599956i
\(248\) 3000.33 1732.24i 0.768231 0.443538i
\(249\) −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 \(0.750999\pi\)
\(252\) 6922.70 + 1137.15i 1.73051 + 0.284260i
\(253\) 636.351i 0.158131i
\(254\) 1977.30 3424.78i 0.488452 0.846024i
\(255\) 0 0
\(256\) 2023.31 + 3504.47i 0.493971 + 0.855584i
\(257\) −1016.25 + 586.731i −0.246661 + 0.142410i −0.618234 0.785994i \(-0.712152\pi\)
0.371574 + 0.928404i \(0.378818\pi\)
\(258\) −4749.84 1697.34i −1.14617 0.409580i
\(259\) −2502.89 + 4335.14i −0.600472 + 1.04005i
\(260\) 0 0
\(261\) 3732.92 + 3058.44i 0.885295 + 0.725336i
\(262\) 9963.64i 2.34945i
\(263\) −2509.71 1448.98i −0.588423 0.339726i 0.176051 0.984381i \(-0.443668\pi\)
−0.764474 + 0.644655i \(0.777001\pi\)
\(264\) −7627.38 + 1391.06i −1.77815 + 0.324295i
\(265\) 0 0
\(266\) 457.804 + 792.940i 0.105526 + 0.182776i
\(267\) 796.127 676.022i 0.182480 0.154951i
\(268\) −5010.40 2892.75i −1.14201 0.659340i
\(269\) −2930.13 −0.664138 −0.332069 0.943255i \(-0.607747\pi\)
−0.332069 + 0.943255i \(0.607747\pi\)
\(270\) 0 0
\(271\) −668.881 −0.149932 −0.0749661 0.997186i \(-0.523885\pi\)
−0.0749661 + 0.997186i \(0.523885\pi\)
\(272\) −19.6196 11.3274i −0.00437358 0.00252509i
\(273\) 3728.62 3166.12i 0.826617 0.701912i
\(274\) 5257.70 + 9106.60i 1.15923 + 2.00785i
\(275\) 0 0
\(276\) −633.389 + 115.516i −0.138136 + 0.0251929i
\(277\) 547.874 + 316.315i 0.118840 + 0.0686121i 0.558241 0.829679i \(-0.311476\pi\)
−0.439402 + 0.898291i \(0.644810\pi\)
\(278\) 9759.80i 2.10559i
\(279\) −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 \(0.0420286\pi\)
\(282\) −10645.6 3804.16i −2.24800 0.803313i
\(283\) −436.796 + 252.184i −0.0917485 + 0.0529710i −0.545172 0.838324i \(-0.683536\pi\)
0.453424 + 0.891295i \(0.350202\pi\)
\(284\) 2645.16 + 4581.55i 0.552680 + 0.957270i
\(285\) 0 0
\(286\) −7100.08 + 12297.7i −1.46796 + 2.54258i
\(287\) 5021.88i 1.03286i
\(288\) −1735.71 4600.29i −0.355131 0.941232i
\(289\) 2645.02 0.538372
\(290\) 0 0
\(291\) −1288.94 + 235.074i −0.259654 + 0.0473549i
\(292\) −4011.08 + 2315.80i −0.803872 + 0.464116i
\(293\) −5368.06 + 3099.25i −1.07033 + 0.617953i −0.928270 0.371906i \(-0.878704\pi\)
−0.142055 + 0.989859i \(0.545371\pi\)
\(294\) 947.467 + 1115.80i 0.187950 + 0.221343i
\(295\) 0 0
\(296\) −5597.26 −1.09910
\(297\) 9306.02 163.666i 1.81815 0.0319760i
\(298\) 8006.60i 1.55641i
\(299\) −224.457 + 388.770i −0.0434136 + 0.0751945i
\(300\) 0 0
\(301\) −2134.60 3697.24i −0.408759 0.707991i
\(302\) −3469.51 + 2003.12i −0.661086 + 0.381678i
\(303\) 40.6500 + 222.889i 0.00770719 + 0.0422596i
\(304\) 2.36730 4.10029i 0.000446626 0.000773578i
\(305\) 0 0
\(306\) −4548.99 3727.06i −0.849832 0.696281i
\(307\) 1966.79i 0.365636i −0.983147 0.182818i \(-0.941478\pi\)
0.983147 0.182818i \(-0.0585220\pi\)
\(308\) −14928.3 8618.84i −2.76174 1.59449i
\(309\) 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 \(0.765910\pi\)
\(312\) 5150.51 + 1840.51i 0.934584 + 0.333970i
\(313\) 8922.14 + 5151.20i 1.61121 + 0.930234i 0.989090 + 0.147314i \(0.0470627\pi\)
0.622122 + 0.782920i \(0.286271\pi\)
\(314\) −1186.36 −0.213218
\(315\) 0 0
\(316\) −8416.51 −1.49831
\(317\) 1473.83 + 850.916i 0.261131 + 0.150764i 0.624850 0.780745i \(-0.285160\pi\)
−0.363719 + 0.931509i \(0.618493\pi\)
\(318\) 2329.41 + 12772.5i 0.410777 + 2.25235i
\(319\) −5928.78 10268.9i −1.04059 1.80235i
\(320\) 0 0
\(321\) 1196.51 + 1409.09i 0.208046 + 0.245008i
\(322\) −764.201 441.212i −0.132259 0.0763596i
\(323\) 473.983i 0.0816506i
\(324\) −1852.21 9233.01i −0.317595 1.58316i
\(325\) 0 0
\(326\) −2748.26 + 4760.13i −0.466908 + 0.808709i
\(327\) 6030.42 5120.66i 1.01983 0.865973i
\(328\) 4862.95 2807.63i 0.818633 0.472638i
\(329\) −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 \(-0.0772271\pi\)
\(332\) 10503.9i 1.73637i
\(333\) 6630.47 + 1089.14i 1.09113 + 0.179233i
\(334\) −7678.61 −1.25795
\(335\) 0 0
\(336\) 16.7311 46.8205i 0.00271654 0.00760199i
\(337\) −6804.73 + 3928.71i −1.09993 + 0.635046i −0.936203 0.351459i \(-0.885686\pi\)
−0.163729 + 0.986505i \(0.552352\pi\)
\(338\) −26.5504 + 15.3289i −0.00427264 + 0.00246681i
\(339\) 1421.56 3978.10i 0.227753 0.637347i
\(340\) 0 0
\(341\) 10219.1 1.62286
\(342\) 778.916 950.691i 0.123155 0.150314i
\(343\) 5660.34i 0.891048i
\(344\) 2386.82 4134.10i 0.374095 0.647952i
\(345\) 0 0
\(346\) 2130.83 + 3690.70i 0.331081 + 0.573449i
\(347\) 1049.78 606.088i 0.162406 0.0937652i −0.416594 0.909093i \(-0.636776\pi\)
0.579000 + 0.815327i \(0.303443\pi\)
\(348\) −9144.91 + 7765.29i −1.40867 + 1.19616i
\(349\) 699.332 1211.28i 0.107262 0.185783i −0.807398 0.590007i \(-0.799125\pi\)
0.914660 + 0.404224i \(0.132458\pi\)
\(350\) 0 0
\(351\) −5743.12 3182.47i −0.873348 0.483954i
\(352\) 12081.2i 1.82934i
\(353\) 2276.28 + 1314.21i 0.343214 + 0.198154i 0.661692 0.749776i \(-0.269839\pi\)
−0.318479 + 0.947930i \(0.603172\pi\)
\(354\) −6449.75 7595.64i −0.968362 1.14041i
\(355\) 0 0
\(356\) 1298.22 + 2248.59i 0.193274 + 0.334761i
\(357\) −893.053 4896.73i −0.132396 0.725946i
\(358\) −4053.53 2340.31i −0.598424 0.345500i
\(359\) −3677.48 −0.540640 −0.270320 0.962770i \(-0.587130\pi\)
−0.270320 + 0.962770i \(0.587130\pi\)
\(360\) 0 0
\(361\) −6759.94 −0.985558
\(362\) 10456.3 + 6036.96i 1.51815 + 0.876507i
\(363\) −15022.9 5368.36i −2.17217 0.776215i
\(364\) 6080.16 + 10531.1i 0.875513 + 1.51643i
\(365\) 0 0
\(366\) 4360.08 12201.3i 0.622692 1.74255i
\(367\) −9898.47 5714.88i −1.40789 0.812846i −0.412706 0.910864i \(-0.635416\pi\)
−0.995185 + 0.0980185i \(0.968750\pi\)
\(368\) 4.56301i 0.000646368i
\(369\) −6306.94 + 2379.64i −0.889773 + 0.335715i
\(370\) 0 0
\(371\) −5494.43 + 9516.63i −0.768886 + 1.33175i
\(372\) −1855.05 10171.5i −0.258549 1.41766i
\(373\) −1957.13 + 1129.95i −0.271679 + 0.156854i −0.629650 0.776879i \(-0.716802\pi\)
0.357971 + 0.933733i \(0.383469\pi\)
\(374\) 7224.90 + 12513.9i 0.998905 + 1.73015i
\(375\) 0 0
\(376\) 5349.47 9265.55i 0.733717 1.27084i
\(377\) 8364.90i 1.14274i
\(378\) 6255.76 11289.2i 0.851221 1.53612i
\(379\) 11815.8 1.60142 0.800709 0.599053i \(-0.204456\pi\)
0.800709 + 0.599053i \(0.204456\pi\)
\(380\) 0 0
\(381\) −2908.12 3424.78i −0.391043 0.460517i
\(382\) 3221.27 1859.80i 0.431452 0.249099i
\(383\) 6997.68 4040.11i 0.933589 0.539008i 0.0456440 0.998958i \(-0.485466\pi\)
0.887945 + 0.459950i \(0.152133\pi\)
\(384\) 11936.0 2176.85i 1.58621 0.289289i
\(385\) 0 0
\(386\) 3724.00 0.491054
\(387\) −3631.85 + 4432.78i −0.477047 + 0.582251i
\(388\) 3257.17i 0.426180i
\(389\) 1550.22 2685.05i 0.202054 0.349968i −0.747136 0.664671i \(-0.768572\pi\)
0.949190 + 0.314703i \(0.101905\pi\)
\(390\) 0 0
\(391\) 228.402 + 395.604i 0.0295417 + 0.0511677i
\(392\) −1199.74 + 692.669i −0.154581 + 0.0892476i
\(393\) 10659.8 + 3809.22i 1.36823 + 0.488931i
\(394\) −9326.47 + 16153.9i −1.19254 + 2.06554i
\(395\) 0 0
\(396\) −3750.52 + 22832.4i −0.475936 + 2.89740i
\(397\) 11990.1i 1.51578i −0.652382 0.757890i \(-0.726230\pi\)
0.652382 0.757890i \(-0.273770\pi\)
\(398\) 5317.38 + 3069.99i 0.669689 + 0.386645i
\(399\) 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 \(-0.462007\pi\)
\(402\) −8113.38 + 6889.38i −1.00661 + 0.854753i
\(403\) −6243.21 3604.52i −0.771703 0.445543i
\(404\) −563.243 −0.0693623
\(405\) 0 0
\(406\) −16442.8 −2.00996
\(407\) −14298.1 8255.02i −1.74135 1.00537i
\(408\) 4242.48 3602.45i 0.514789 0.437127i
\(409\) 1112.54 + 1926.98i 0.134503 + 0.232966i 0.925408 0.378974i \(-0.123723\pi\)
−0.790904 + 0.611940i \(0.790390\pi\)
\(410\) 0 0
\(411\) 11752.9 2143.47i 1.41053 0.257249i
\(412\) 16113.2 + 9302.97i 1.92680 + 1.11244i
\(413\) 8433.95i 1.00486i
\(414\) −191.995 + 1168.82i −0.0227924 + 0.138755i
\(415\) 0 0
\(416\) 4261.32 7380.83i 0.502232 0.869891i
\(417\) −10441.7 3731.29i −1.22621 0.438183i
\(418\) −2615.27 + 1509.93i −0.306021 + 0.176682i
\(419\) 4838.33 + 8380.23i 0.564123 + 0.977090i 0.997131 + 0.0756998i \(0.0241191\pi\)
−0.433007 + 0.901390i \(0.642548\pi\)
\(420\) 0 0
\(421\) 4981.30 8627.87i 0.576660 0.998804i −0.419199 0.907894i \(-0.637689\pi\)
0.995859 0.0909098i \(-0.0289775\pi\)
\(422\) 13514.8i 1.55898i
\(423\) −8139.88 + 9934.98i −0.935637 + 1.14197i
\(424\) −12287.3 −1.40737
\(425\) 0 0
\(426\) 9574.84 1746.23i 1.08897 0.198604i
\(427\) 9497.39 5483.32i 1.07637 0.621444i
\(428\) −3979.83 + 2297.76i −0.449468 + 0.259500i
\(429\) 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 \(0.543922\pi\)
\(432\) −66.7297 + 1.17358i −0.00743179 + 0.000130704i
\(433\) 7818.49i 0.867743i −0.900975 0.433871i \(-0.857147\pi\)
0.900975 0.433871i \(-0.142853\pi\)
\(434\) 7085.36 12272.2i 0.783660 1.35734i
\(435\) 0 0
\(436\) 9833.63 + 17032.3i 1.08015 + 1.87087i
\(437\) −82.6770 + 47.7336i −0.00905030 + 0.00522519i
\(438\) 1528.80 + 8382.64i 0.166779 + 0.914470i
\(439\) 3105.91 5379.60i 0.337670 0.584862i −0.646324 0.763063i \(-0.723694\pi\)
0.983994 + 0.178201i \(0.0570278\pi\)
\(440\) 0 0
\(441\) 1555.98 587.080i 0.168015 0.0633927i
\(442\) 10193.6i 1.09697i
\(443\) 2584.52 + 1492.17i 0.277188 + 0.160034i 0.632150 0.774846i \(-0.282173\pi\)
−0.354962 + 0.934881i \(0.615506\pi\)
\(444\) −5621.08 + 15730.1i −0.600822 + 1.68134i
\(445\) 0 0
\(446\) 8019.45 + 13890.1i 0.851417 + 1.47470i
\(447\) 8565.99 + 3061.02i 0.906392 + 0.323896i
\(448\) 14442.1 + 8338.16i 1.52305 + 0.879333i
\(449\) 810.476 0.0851865 0.0425932 0.999092i \(-0.486438\pi\)
0.0425932 + 0.999092i \(0.486438\pi\)
\(450\) 0 0
\(451\) 16563.1 1.72933
\(452\) 9095.01 + 5251.01i 0.946446 + 0.546431i
\(453\) 816.637 + 4477.73i 0.0846996 + 0.464420i
\(454\) −1492.88 2585.74i −0.154326 0.267301i
\(455\) 0 0
\(456\) 752.873 + 886.632i 0.0773169 + 0.0910534i
\(457\) −1361.20 785.887i −0.139331 0.0804425i 0.428714 0.903440i \(-0.358967\pi\)
−0.568045 + 0.822998i \(0.692300\pi\)
\(458\) 20963.2i 2.13875i
\(459\) −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 \(0.199894\pi\)
\(462\) −24173.5 + 20526.6i −2.43431 + 2.06707i
\(463\) −2410.35 + 1391.62i −0.241940 + 0.139684i −0.616068 0.787693i \(-0.711275\pi\)
0.374128 + 0.927377i \(0.377942\pi\)
\(464\) 42.5128 + 73.6344i 0.00425347 + 0.00736722i
\(465\) 0 0
\(466\) 726.118 1257.67i 0.0721819 0.125023i
\(467\) 10939.7i 1.08400i 0.840379 + 0.541999i \(0.182332\pi\)
−0.840379 + 0.541999i \(0.817668\pi\)
\(468\) 10344.9 12626.2i 1.02178 1.24711i
\(469\) −9008.83 −0.886970
\(470\) 0 0
\(471\) −453.561 + 1269.25i −0.0443716 + 0.124170i
\(472\) 8167.04 4715.24i 0.796438 0.459823i
\(473\) 12194.2 7040.33i 1.18539 0.684386i
\(474\) −5210.51 + 14581.1i −0.504908 + 1.41294i
\(475\) 0 0
\(476\) 12374.1 1.19152
\(477\) 14555.4 + 2390.92i 1.39716 + 0.229503i
\(478\) 8496.21i 0.812986i
\(479\) 7311.85 12664.5i 0.697467 1.20805i −0.271875 0.962333i \(-0.587644\pi\)
0.969342 0.245716i \(-0.0790230\pi\)
\(480\) 0 0
\(481\) 5823.49 + 10086.6i 0.552034 + 0.956151i
\(482\) 12939.8 7470.81i 1.22281 0.705987i
\(483\) −764.201 + 648.913i −0.0719925 + 0.0611316i
\(484\) 19829.9 34346.4i 1.86231 3.22562i
\(485\) 0 0
\(486\) −17142.3 2507.13i −1.59998 0.234003i
\(487\) 16473.6i 1.53284i 0.642341 + 0.766419i \(0.277963\pi\)
−0.642341 + 0.766419i \(0.722037\pi\)
\(488\) 10619.6 + 6131.22i 0.985093 + 0.568744i
\(489\) 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 \(-0.559107\pi\)
\(492\) −3006.68 16486.0i −0.275511 1.51067i
\(493\) 7371.56 + 4255.97i 0.673425 + 0.388802i
\(494\) 2130.35 0.194026
\(495\) 0 0
\(496\) −73.2768 −0.00663352
\(497\) 7134.10 + 4118.87i 0.643879 + 0.371744i
\(498\) −18197.4 6502.76i −1.63744 0.585132i
\(499\) −7202.31 12474.8i −0.646131 1.11913i −0.984039 0.177953i \(-0.943053\pi\)
0.337908 0.941179i \(-0.390281\pi\)
\(500\) 0 0
\(501\) −2935.63 + 8215.08i −0.261785 + 0.732580i
\(502\) −22344.5 12900.6i −1.98663 1.14698i
\(503\) 2953.63i 0.261821i 0.991394 + 0.130910i \(0.0417901\pi\)
−0.991394 + 0.130910i \(0.958210\pi\)
\(504\) 9448.49 + 7741.30i 0.835058 + 0.684176i
\(505\) 0 0
\(506\) 1455.20 2520.48i 0.127849 0.221441i
\(507\) 6.24932 + 34.2659i 0.000547420 + 0.00300158i
\(508\) 9672.98 5584.69i 0.844821 0.487757i
\(509\) −8684.44 15041.9i −0.756250 1.30986i −0.944750 0.327790i \(-0.893696\pi\)
0.188500 0.982073i \(-0.439637\pi\)
\(510\) 0 0
\(511\) −3606.02 + 6245.80i −0.312174 + 0.540701i
\(512\) 172.223i 0.0148657i
\(513\) −719.323 1196.80i −0.0619082 0.103002i
\(514\) −5366.92 −0.460554
\(515\) 0 0
\(516\) −9221.16 10859.4i −0.786703 0.926473i
\(517\) 27330.3 15779.1i 2.32492 1.34229i
\(518\) −19827.1 + 11447.2i −1.68176 + 0.970966i
\(519\) 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 \(0.583202\pi\)
\(522\) 7791.48 + 20650.4i 0.653303 + 1.73150i
\(523\) 4554.68i 0.380807i 0.981706 + 0.190404i \(0.0609797\pi\)
−0.981706 + 0.190404i \(0.939020\pi\)
\(524\) −14070.7 + 24371.1i −1.17305 + 2.03179i
\(525\) 0 0
\(526\) −6627.03 11478.4i −0.549339 0.951483i
\(527\) −6352.96 + 3667.88i −0.525122 + 0.303179i
\(528\) 154.423 + 55.1824i 0.0127280 + 0.00454831i
\(529\) −6037.50 + 10457.3i −0.496219 + 0.859476i
\(530\) 0 0
\(531\) −10592.1 + 3996.46i −0.865649 + 0.326613i
\(532\) 2586.05i 0.210751i
\(533\) −10119.0 5842.22i −0.822333 0.474774i
\(534\) 4699.25 857.037i 0.380817 0.0694525i
\(535\) 0 0
\(536\) −5036.64 8723.72i −0.405877 0.702999i
\(537\) −4053.53 + 3442.01i −0.325741 + 0.276599i
\(538\) −11605.8 6700.59i −0.930037 0.536957i
\(539\) −4086.28 −0.326547
\(540\) 0 0
\(541\) 18091.8 1.43776 0.718879 0.695135i \(-0.244655\pi\)
0.718879 + 0.695135i \(0.244655\pi\)
\(542\) −2649.33 1529.59i −0.209960 0.121221i
\(543\) 10456.3 8878.86i 0.826379 0.701710i
\(544\) −4336.23 7510.58i −0.341754 0.591936i
\(545\) 0 0
\(546\) 22008.7 4013.89i 1.72507 0.314613i
\(547\) −13667.1 7890.69i −1.06830 0.616786i −0.140586 0.990068i \(-0.544899\pi\)
−0.927718 + 0.373283i \(0.878232\pi\)
\(548\) 29699.7i 2.31516i
\(549\) −11386.8 9329.41i −0.885206 0.725263i
\(550\) 0 0
\(551\) −889.453 + 1540.58i −0.0687694 + 0.119112i
\(552\) −1055.62 377.223i −0.0813956 0.0290864i
\(553\) −11349.8 + 6552.83i −0.872774 + 0.503896i
\(554\) 1446.69 + 2505.75i 0.110946 + 0.192164i
\(555\) 0 0
\(556\) 13782.8 23872.5i 1.05130 1.82090i
\(557\) 13954.5i 1.06153i −0.847519 0.530766i \(-0.821904\pi\)
0.847519 0.530766i \(-0.178096\pi\)
\(558\) −18770.0 3083.22i −1.42401 0.233913i
\(559\) −9933.18 −0.751572
\(560\) 0 0
\(561\) 16150.4 2945.46i 1.21545 0.221671i
\(562\) 14240.4 8221.69i 1.06885 0.617102i
\(563\) 11781.4 6801.97i 0.881927 0.509181i 0.0106339 0.999943i \(-0.496615\pi\)
0.871293 + 0.490762i \(0.163282\pi\)
\(564\) −20666.9 24338.7i −1.54297 1.81710i
\(565\) 0 0
\(566\) −2306.77 −0.171309
\(567\) −9686.28 11008.8i −0.717435 0.815392i
\(568\) 9211.10i 0.680438i
\(569\) −6229.30 + 10789.5i −0.458956 + 0.794935i −0.998906 0.0467619i \(-0.985110\pi\)
0.539950 + 0.841697i \(0.318443\pi\)
\(570\) 0 0
\(571\) 6728.56 + 11654.2i 0.493137 + 0.854139i 0.999969 0.00790629i \(-0.00251668\pi\)
−0.506831 + 0.862045i \(0.669183\pi\)
\(572\) −34733.7 + 20053.5i −2.53897 + 1.46587i
\(573\) −758.207 4157.36i −0.0552785 0.303100i
\(574\) 11484.0 19890.8i 0.835074 1.44639i
\(575\) 0 0
\(576\) 3628.38 22088.8i 0.262470 1.59786i
\(577\) 3722.70i 0.268592i 0.990941 + 0.134296i \(0.0428774\pi\)
−0.990941 + 0.134296i \(0.957123\pi\)
\(578\) 10476.5 + 6048.61i 0.753918 + 0.435275i
\(579\) 1423.73 3984.18i 0.102190 0.285971i
\(580\) 0 0
\(581\) −8177.99 14164.7i −0.583959 1.01145i
\(582\) −5642.86 2016.45i −0.401897 0.143616i
\(583\) −31387.7 18121.7i −2.22975 1.28735i
\(584\) −8064.19 −0.571401
\(585\) 0 0
\(586\) −28349.3 −1.99847
\(587\) 15190.4 + 8770.16i 1.06810 + 0.616667i 0.927661 0.373423i \(-0.121816\pi\)
0.140437 + 0.990090i \(0.455149\pi\)
\(588\) 741.777 + 4067.27i 0.0520244 + 0.285257i
\(589\) −766.548 1327.70i −0.0536249 0.0928810i
\(590\) 0 0
\(591\) 13716.9 + 16153.9i 0.954718 + 1.12434i
\(592\) 102.526 + 59.1933i 0.00711788 + 0.00410951i
\(593\) 22350.6i 1.54777i 0.633325 + 0.773886i \(0.281690\pi\)
−0.633325 + 0.773886i \(0.718310\pi\)
\(594\) 37233.9 + 20632.7i 2.57193 + 1.42520i
\(595\) 0 0
\(596\) −11306.9 + 19584.2i −0.777097 + 1.34597i
\(597\) 5317.38 4515.19i 0.364533 0.309539i
\(598\) −1778.07 + 1026.57i −0.121590 + 0.0702000i
\(599\) −1280.81 2218.43i −0.0873665 0.151323i 0.819031 0.573750i \(-0.194512\pi\)
−0.906397 + 0.422427i \(0.861178\pi\)
\(600\) 0 0
\(601\) −6692.51 + 11591.8i −0.454232 + 0.786752i −0.998644 0.0520656i \(-0.983420\pi\)
0.544412 + 0.838818i \(0.316753\pi\)
\(602\) 19525.6i 1.32193i
\(603\) 4268.87 + 11314.1i 0.288295 + 0.764091i
\(604\) −11315.3 −0.762270
\(605\) 0 0
\(606\) −348.693 + 975.786i −0.0233741 + 0.0654103i
\(607\) −24793.1 + 14314.3i −1.65786 + 0.957166i −0.684161 + 0.729331i \(0.739831\pi\)
−0.973700 + 0.227835i \(0.926835\pi\)
\(608\) 1569.63 906.226i 0.104699 0.0604479i
\(609\) −6286.29 + 17591.6i −0.418281 + 1.17052i
\(610\) 0 0
\(611\) −22262.8 −1.47407
\(612\) −5863.50 15540.5i −0.387284 1.02645i
\(613\) 7188.12i 0.473614i −0.971557 0.236807i \(-0.923899\pi\)
0.971557 0.236807i \(-0.0761010\pi\)
\(614\) 4497.63 7790.12i 0.295618 0.512025i
\(615\) 0 0
\(616\) −15006.5 25992.0i −0.981539 1.70008i
\(617\) 13452.6 7766.88i 0.877767 0.506779i 0.00784559 0.999969i \(-0.497503\pi\)
0.869922 + 0.493190i \(0.164169\pi\)
\(618\) 26092.3 22155.9i 1.69836 1.44214i
\(619\) −11079.9 + 19191.0i −0.719450 + 1.24612i 0.241769 + 0.970334i \(0.422272\pi\)
−0.961218 + 0.275789i \(0.911061\pi\)
\(620\) 0 0
\(621\) 1177.08 + 652.265i 0.0760624 + 0.0421490i
\(622\) 10547.2i 0.679908i
\(623\) 3501.36 + 2021.51i 0.225167 + 0.130000i
\(624\) −74.8785 88.1818i −0.00480375 0.00565721i
\(625\) 0 0
\(626\) 23559.4 + 40806.1i 1.50419 + 2.60534i
\(627\) 615.569 + 3375.25i 0.0392081 + 0.214983i
\(628\) −2901.85 1675.38i −0.184389 0.106457i
\(629\) 11851.7 0.751287
\(630\) 0 0
\(631\) −25582.8 −1.61400 −0.807002 0.590549i \(-0.798911\pi\)
−0.807002 + 0.590549i \(0.798911\pi\)
\(632\) −12690.9 7327.10i −0.798761 0.461165i
\(633\) 14459.0 + 5166.88i 0.907891 + 0.324431i
\(634\) 3891.73 + 6740.68i 0.243786 + 0.422250i
\(635\) 0 0
\(636\) −12339.6 + 34531.2i −0.769334 + 2.15291i
\(637\) 2496.46 + 1441.33i 0.155280 + 0.0896510i
\(638\) 54231.5i 3.36527i
\(639\) 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 \(0.204124\pi\)
\(642\) 1516.89 + 8317.33i 0.0932507 + 0.511306i
\(643\) −23140.3 + 13360.0i −1.41923 + 0.819391i −0.996231 0.0867402i \(-0.972355\pi\)
−0.422996 + 0.906131i \(0.639022\pi\)
\(644\) −1246.16 2158.41i −0.0762509 0.132071i
\(645\) 0 0
\(646\) 1083.90 1877.37i 0.0660147 0.114341i
\(647\) 5114.23i 0.310759i 0.987855 + 0.155380i \(0.0496601\pi\)
−0.987855 + 0.155380i \(0.950340\pi\)
\(648\) 5245.03 15534.5i 0.317970 0.941750i
\(649\) 27816.8 1.68244
\(650\) 0 0
\(651\) −10420.8 12272.2i −0.627378 0.738842i
\(652\) −13444.5 + 7762.20i −0.807559 + 0.466244i
\(653\) 7682.56 4435.53i 0.460401 0.265813i −0.251812 0.967776i \(-0.581026\pi\)
0.712213 + 0.701964i \(0.247693\pi\)
\(654\) 35595.4 6491.79i 2.12827 0.388148i
\(655\) 0 0
\(656\) −118.767 −0.00706872
\(657\) 9552.78 + 1569.17i 0.567259 + 0.0931799i
\(658\) 43761.7i 2.59272i
\(659\) −12102.2 + 20961.7i −0.715382 + 1.23908i 0.247430 + 0.968906i \(0.420414\pi\)
−0.962812 + 0.270172i \(0.912920\pi\)
\(660\) 0 0
\(661\) −10689.8 18515.2i −0.629023 1.08950i −0.987748 0.156056i \(-0.950122\pi\)
0.358726 0.933443i \(-0.383211\pi\)
\(662\) 33078.9 19098.1i 1.94207 1.12125i
\(663\) −10905.8 3897.14i −0.638832 0.228284i
\(664\) 9144.28 15838.4i 0.534438 0.925674i
\(665\) 0 0
\(666\) 23771.6 + 19476.4i 1.38308 + 1.13318i
\(667\) 1714.43i 0.0995248i
\(668\) −18781.9 10843.7i −1.08787 0.628079i
\(669\) 17926.5 3269.38i 1.03599 0.188941i
\(670\) 0 0
\(671\) 18085.0 + 31324.2i 1.04048 + 1.80217i
\(672\) 14508.4 12319.6i 0.832849 0.707203i
\(673\) 25722.1 + 14850.7i 1.47328 + 0.850597i 0.999548 0.0300732i \(-0.00957403\pi\)
0.473730 + 0.880670i \(0.342907\pi\)
\(674\) −35936.6 −2.05375
\(675\) 0 0
\(676\) −86.5900 −0.00492661
\(677\) −2304.91 1330.74i −0.130849 0.0755459i 0.433147 0.901324i \(-0.357403\pi\)
−0.563996 + 0.825778i \(0.690737\pi\)
\(678\) 14727.6 12505.8i 0.834235 0.708381i
\(679\) −2535.93 4392.36i −0.143328 0.248252i
\(680\) 0 0
\(681\) −3337.14 + 608.618i −0.187782 + 0.0342471i
\(682\) 40476.1 + 23368.9i 2.27259 + 1.31208i
\(683\) 28698.1i 1.60776i −0.594789 0.803882i \(-0.702765\pi\)
0.594789 0.803882i \(-0.297235\pi\)
\(684\) 3247.80 1225.41i 0.181554 0.0685010i
\(685\) 0 0
\(686\) 12944.0 22419.7i 0.720415 1.24780i
\(687\) 22427.9 + 8014.51i 1.24553 + 0.445084i
\(688\) −87.4396 + 50.4833i −0.00484535 + 0.00279747i
\(689\) 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 \(0.319945\pi\)
\(692\) 12036.6i 0.661220i
\(693\) 12718.9 + 33710.0i 0.697189 + 1.84781i
\(694\) 5543.99 0.303238
\(695\) 0 0
\(696\) −20549.4 + 3747.74i −1.11914 + 0.204106i
\(697\) −10296.9 + 5944.92i −0.559574 + 0.323070i
\(698\) 5539.88 3198.45i 0.300412 0.173443i
\(699\) −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 \(0.508566\pi\)
\(702\) −15469.9 25738.6i −0.831730 1.38382i
\(703\) 2476.88i 0.132884i
\(704\) −27500.8 + 47632.9i −1.47227 + 2.55004i
\(705\) 0 0
\(706\) 6010.66 + 10410.8i 0.320417 + 0.554978i
\(707\) −759.545 + 438.523i −0.0404040 + 0.0233272i
\(708\) −5049.54 27687.3i −0.268041 1.46971i
\(709\) 16626.9 28798.6i 0.880727 1.52546i 0.0301937 0.999544i \(-0.490388\pi\)
0.850534 0.525921i \(-0.176279\pi\)
\(710\) 0 0
\(711\) 13607.8 + 11149.1i 0.717768 + 0.588078i
\(712\) 4520.73i 0.237952i
\(713\) 1279.58 + 738.765i 0.0672099 + 0.0388036i
\(714\) 7660.56 21437.4i 0.401526 1.12363i
\(715\) 0 0
\(716\) −6609.97 11448.8i −0.345009 0.597573i
\(717\) 9089.81 + 3248.21i 0.473452 + 0.169186i
\(718\) −14565.9 8409.62i −0.757095 0.437109i
\(719\) −1178.94 −0.0611503 −0.0305752 0.999532i \(-0.509734\pi\)
−0.0305752 + 0.999532i \(0.509734\pi\)
\(720\) 0 0
\(721\) 28972.0 1.49650
\(722\) −26775.0 15458.6i −1.38014 0.796826i
\(723\) −3045.71 16700.1i −0.156668 0.859034i
\(724\) 17050.8 + 29532.9i 0.875260 + 1.51600i
\(725\) 0 0
\(726\) −47226.8 55617.4i −2.41426 2.84319i
\(727\) −10978.3 6338.35i −0.560061 0.323351i 0.193109 0.981177i \(-0.438143\pi\)
−0.753170 + 0.657826i \(0.771476\pi\)
\(728\) 21172.6i 1.07790i
\(729\) −9236.02 + 17381.5i −0.469238 + 0.883072i
\(730\) 0 0
\(731\) −5053.90 + 8753.61i −0.255712 + 0.442906i
\(732\) 27895.5 23687.1i 1.40853 1.19604i
\(733\) −8492.98 + 4903.42i −0.427961 + 0.247083i −0.698478 0.715632i \(-0.746139\pi\)
0.270517 + 0.962715i \(0.412805\pi\)
\(734\) −26137.5 45271.4i −1.31438 2.27657i
\(735\) 0 0
\(736\) −873.381 + 1512.74i −0.0437408 + 0.0757613i
\(737\) 29712.8i 1.48506i
\(738\) −30422.5 4997.30i −1.51744 0.249259i
\(739\) 29970.4 1.49185 0.745927 0.666028i \(-0.232007\pi\)
0.745927 + 0.666028i \(0.232007\pi\)
\(740\) 0 0
\(741\) 814.460 2279.19i 0.0403778 0.112994i
\(742\) −43525.1 + 25129.2i −2.15345 + 1.24329i
\(743\) −18790.6 + 10848.8i −0.927808 + 0.535670i −0.886118 0.463460i \(-0.846608\pi\)
−0.0416904 + 0.999131i \(0.513274\pi\)
\(744\) 6057.78 16952.1i 0.298507 0.835344i
\(745\) 0 0
\(746\) −10335.8 −0.507267
\(747\) −13914.2 + 16982.7i −0.681516 + 0.831812i
\(748\) 40812.1i 1.99497i
\(749\) −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 \(0.969061\pi\)
\(752\) −195.974 + 113.146i −0.00950324 + 0.00548670i
\(753\) −22344.5 + 18973.6i −1.08138 + 0.918243i
\(754\) −19128.8 + 33132.0i −0.923911 + 1.60026i
\(755\) 0 0
\(756\) 31244.2 18779.0i 1.50310 0.903422i
\(757\) 30745.2i 1.47616i 0.674714 + 0.738080i \(0.264267\pi\)
−0.674714 + 0.738080i \(0.735733\pi\)
\(758\) 46800.5 + 27020.3i 2.24257 + 1.29475i
\(759\) −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 \(-0.337759\pi\)
\(762\) −3686.81 20215.3i −0.175274 0.961052i
\(763\) 26521.7 + 15312.3i 1.25839 + 0.726530i
\(764\) 10505.7 0.497489
\(765\) 0 0
\(766\) 36955.5 1.74316
\(767\) −16994.3 9811.66i −0.800037 0.461902i
\(768\) 19800.6 + 7075.65i 0.930327 + 0.332449i
\(769\) 11028.7 + 19102.4i 0.517174 + 0.895772i 0.999801 + 0.0199457i \(0.00634935\pi\)
−0.482627 + 0.875826i \(0.660317\pi\)
\(770\) 0 0
\(771\) −2051.84 + 5741.89i −0.0958434 + 0.268209i
\(772\) 9108.93 + 5259.04i 0.424660 + 0.245178i
\(773\) 30155.8i 1.40314i −0.712601 0.701570i \(-0.752483\pi\)
0.712601 0.701570i \(-0.247517\pi\)
\(774\) −24522.0 + 9252.26i −1.13879 + 0.429671i
\(775\) 0 0
\(776\) 2835.57 4911.35i 0.131174 0.227200i
\(777\) 4666.81 + 25588.7i 0.215471 + 1.18146i
\(778\)