Properties

Label 225.4.k.c.49.6
Level $225$
Weight $4$
Character 225.49
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 49.6
Root \(2.88506 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 225.49
Dual form 225.4.k.c.124.6

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.96084 2.28679i 1.40037 0.808502i 0.405937 0.913901i \(-0.366945\pi\)
0.994430 + 0.105398i \(0.0336118\pi\)
\(3\) 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 0.0504348 0.998727i \(-0.483939\pi\)
0.890141 + 0.455686i \(0.150606\pi\)
\(8\) 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 −0.815157 0.579240i \(-0.803349\pi\)
−0.0940582 0.995567i \(-0.529984\pi\)
\(12\) 63.2076 22.5870i 1.52054 0.543358i
\(13\) 40.5305 + 23.4003i 0.864703 + 0.499237i 0.865584 0.500763i \(-0.166947\pi\)
−0.000881222 1.00000i \(0.500281\pi\)
\(14\) 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 \(0.110331\pi\)
−0.940528 + 0.339716i \(0.889669\pi\)
\(18\) 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 0.461872 0.886946i \(-0.347178\pi\)
−0.537182 + 0.843466i \(0.680511\pi\)
\(24\) 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 −0.996335 0.0855380i \(-0.972739\pi\)
0.424089 0.905620i \(-0.360594\pi\)
\(30\) 0 0
\(31\) −77.0186 + 133.400i −0.446224 + 0.772883i −0.998137 0.0610190i \(-0.980565\pi\)
0.551912 + 0.833902i \(0.313898\pi\)
\(32\) 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 \(-0.813529\pi\)
0.833262 0.552878i \(-0.186471\pi\)
\(38\) 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 −0.999606 0.0280628i \(-0.991066\pi\)
0.524106 + 0.851653i \(0.324400\pi\)
\(42\) 450.145 160.857i 1.65378 0.590972i
\(43\) −183.809 + 106.122i −0.651876 + 0.376361i −0.789175 0.614169i \(-0.789491\pi\)
0.137299 + 0.990530i \(0.456158\pi\)
\(44\) −856.976 −2.93623
\(45\) 0 0
\(46\) −43.8700 −0.140615
\(47\) −411.963 + 237.847i −1.27853 + 0.738160i −0.976578 0.215163i \(-0.930972\pi\)
−0.301953 + 0.953323i \(0.597638\pi\)
\(48\) −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 \(-0.749623\pi\)
0.706269 0.707944i \(-0.250377\pi\)
\(54\) −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 −0.999090 0.0426512i \(-0.986420\pi\)
0.536482 + 0.843912i \(0.319753\pi\)
\(60\) 0 0
\(61\) 272.605 + 472.165i 0.572188 + 0.991059i 0.996341 + 0.0854682i \(0.0272386\pi\)
−0.424153 + 0.905591i \(0.639428\pi\)
\(62\) 704.502i 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 0.102788 0.994703i \(-0.467224\pi\)
−0.810044 + 0.586369i \(0.800557\pi\)
\(68\) 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 \(-0.907199\pi\)
0.957801 0.287431i \(-0.0928011\pi\)
\(74\) −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 0.535196 0.844728i \(-0.320238\pi\)
−0.999154 + 0.0411297i \(0.986904\pi\)
\(80\) 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 −0.887216 0.461354i \(-0.847364\pi\)
−0.0440636 + 0.999029i \(0.514030\pi\)
\(84\) 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 −0.609915 0.792467i \(-0.708796\pi\)
0.381339 + 0.924435i \(0.375463\pi\)
\(98\) 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 0.855086 0.518485i \(-0.173504\pi\)
−0.876565 + 0.481284i \(0.840171\pi\)
\(102\) −203.060 + 1113.40i −0.197117 + 1.08082i
\(103\) 1247.38 + 720.176i 1.19328 + 0.688942i 0.959050 0.283238i \(-0.0914087\pi\)
0.234233 + 0.972180i \(0.424742\pi\)
\(104\) 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 \(-0.948621\pi\)
0.987002 0.160711i \(-0.0513786\pi\)
\(108\) 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 0.763570 0.645725i \(-0.223445\pi\)
−0.177429 + 0.984134i \(0.556778\pi\)
\(114\) 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 \(0.0976784\pi\)
−0.953285 + 0.302072i \(0.902322\pi\)
\(128\) 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 −0.231879 0.972745i \(-0.574487\pi\)
0.958361 0.285559i \(-0.0921792\pi\)
\(132\) −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 0.272266 0.962222i \(-0.412227\pi\)
0.969442 + 0.245322i \(0.0788937\pi\)
\(138\) −173.762 147.548i −0.107185 0.0910152i
\(139\) −1066.98 + 1848.06i −0.651077 + 1.12770i 0.331785 + 0.943355i \(0.392349\pi\)
−0.982862 + 0.184343i \(0.940984\pi\)
\(140\) 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 −0.518506 0.855074i \(-0.673512\pi\)
0.999769 + 0.0215024i \(0.00684497\pi\)
\(150\) 0 0
\(151\) −437.977 758.598i −0.236040 0.408833i 0.723534 0.690288i \(-0.242516\pi\)
−0.959574 + 0.281455i \(0.909183\pi\)
\(152\) 223.850i 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 0.441815 0.897106i \(-0.354335\pi\)
−0.556009 + 0.831176i \(0.687668\pi\)
\(158\) −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 \(-0.906761\pi\)
0.957405 0.288749i \(-0.0932393\pi\)
\(164\) 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 0.123762 0.992312i \(-0.460504\pi\)
−0.797486 + 0.603337i \(0.793837\pi\)
\(168\) 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 −0.312089 0.950053i \(-0.601029\pi\)
0.666725 + 0.745303i \(0.267695\pi\)
\(174\) −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 0.932713 0.360621i \(-0.117435\pi\)
−0.778663 + 0.627442i \(0.784102\pi\)
\(192\) 3283.80 + 2788.40i 1.23431 + 1.04810i
\(193\) 705.154 + 407.121i 0.262995 + 0.151840i 0.625700 0.780064i \(-0.284813\pi\)
−0.362705 + 0.931904i \(0.618147\pi\)
\(194\) −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 \(-0.736006\pi\)
0.675348 0.737499i \(-0.263994\pi\)
\(198\) 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 −0.517729 0.855545i \(-0.673222\pi\)
0.999788 + 0.0205943i \(0.00655583\pi\)
\(212\) −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 0.0309212 0.999522i \(-0.490156\pi\)
0.881072 + 0.472982i \(0.156823\pi\)
\(224\) 3662.97 1.09260
\(225\) 0 0
\(226\) 3718.31 1.09442
\(227\) −565.364 + 326.413i −0.165306 + 0.0954396i −0.580371 0.814352i \(-0.697092\pi\)
0.415064 + 0.909792i \(0.363759\pi\)
\(228\) 629.090 224.803i 0.182730 0.0652979i
\(229\) 2291.78 3969.47i 0.661331 1.14546i −0.318935 0.947776i \(-0.603325\pi\)
0.980266 0.197682i \(-0.0633414\pi\)
\(230\) 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 \(0.0142138\pi\)
−0.999003 + 0.0446392i \(0.985786\pi\)
\(234\) 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 −0.712521 0.701650i \(-0.752447\pi\)
0.963908 + 0.266236i \(0.0857802\pi\)
\(240\) 0 0
\(241\) 1633.47 + 2829.25i 0.436602 + 0.756217i 0.997425 0.0717190i \(-0.0228485\pi\)
−0.560823 + 0.827936i \(0.689515\pi\)
\(242\) 14041.8i 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 0.371574 0.928404i \(-0.378818\pi\)
−0.618234 + 0.785994i \(0.712152\pi\)
\(258\) −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 −0.764474 0.644655i \(-0.777001\pi\)
0.176051 + 0.984381i \(0.443668\pi\)
\(264\) −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 −0.439402 0.898291i \(-0.644810\pi\)
0.558241 + 0.829679i \(0.311476\pi\)
\(278\) 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 0.991296 0.131653i \(-0.0420286\pi\)
−0.609663 + 0.792661i \(0.708695\pi\)
\(282\) −10645.6 + 3804.16i −2.24800 + 0.803313i
\(283\) −436.796 252.184i −0.0917485 0.0529710i 0.453424 0.891295i \(-0.350202\pi\)
−0.545172 + 0.838324i \(0.683536\pi\)
\(284\) 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 −0.142055 0.989859i \(-0.545371\pi\)
−0.928270 + 0.371906i \(0.878704\pi\)
\(294\) 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 \(0.0585220\pi\)
−0.983147 + 0.182818i \(0.941478\pi\)
\(308\) −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 −0.741552 0.670896i \(-0.765910\pi\)
0.951789 + 0.306755i \(0.0992431\pi\)
\(312\) 5150.51 1840.51i 0.934584 0.333970i
\(313\) 8922.14 5151.20i 1.61121 0.930234i 0.622122 0.782920i \(-0.286271\pi\)
0.989090 0.147314i \(-0.0470627\pi\)
\(314\) −1186.36 −0.213218
\(315\) 0 0
\(316\) −8416.51 −1.49831
\(317\) 1473.83 850.916i 0.261131 0.150764i −0.363719 0.931509i \(-0.618493\pi\)
0.624850 + 0.780745i \(0.285160\pi\)
\(318\) 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 0.970713 + 0.240243i \(0.0772271\pi\)
−0.277300 + 0.960783i \(0.589440\pi\)
\(332\) 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 −0.163729 0.986505i \(-0.552352\pi\)
−0.936203 + 0.351459i \(0.885686\pi\)
\(338\) −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 0.579000 0.815327i \(-0.303443\pi\)
−0.416594 + 0.909093i \(0.636776\pi\)
\(348\) −9144.91 7765.29i −1.40867 1.19616i
\(349\) 699.332 + 1211.28i 0.107262 + 0.185783i 0.914660 0.404224i \(-0.132458\pi\)
−0.807398 + 0.590007i \(0.799125\pi\)
\(350\) 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 −0.318479 0.947930i \(-0.603172\pi\)
0.661692 + 0.749776i \(0.269839\pi\)
\(354\) −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 −0.995185 0.0980185i \(-0.968750\pi\)
−0.412706 + 0.910864i \(0.635416\pi\)
\(368\) 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 0.357971 0.933733i \(-0.383469\pi\)
−0.629650 + 0.776879i \(0.716802\pi\)
\(374\) 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 0.887945 0.459950i \(-0.152133\pi\)
0.0456440 + 0.998958i \(0.485466\pi\)
\(384\) 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 0.949190 0.314703i \(-0.101905\pi\)
−0.747136 + 0.664671i \(0.768572\pi\)
\(390\) 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 \(0.273770\pi\)
−0.652382 + 0.757890i \(0.726230\pi\)
\(398\) 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 0.119076 + 0.992885i \(0.462007\pi\)
−0.919402 + 0.393320i \(0.871327\pi\)
\(402\) −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 −0.790904 0.611940i \(-0.790390\pi\)
0.925408 + 0.378974i \(0.123723\pi\)
\(410\) 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 −0.433007 0.901390i \(-0.642548\pi\)
0.997131 0.0756998i \(-0.0241191\pi\)
\(420\) 0 0
\(421\) 4981.30 + 8627.87i 0.576660 + 0.998804i 0.995859 + 0.0909098i \(0.0289775\pi\)
−0.419199 + 0.907894i \(0.637689\pi\)
\(422\) 13514.8i 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 \(0.142853\pi\)
−0.900975 + 0.433871i \(0.857147\pi\)
\(434\) 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 0.983994 0.178201i \(-0.0570278\pi\)
−0.646324 + 0.763063i \(0.723694\pi\)
\(440\) 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 −0.354962 0.934881i \(-0.615506\pi\)
0.632150 + 0.774846i \(0.282173\pi\)
\(444\) −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 −0.568045 0.822998i \(-0.692300\pi\)
0.428714 + 0.903440i \(0.358967\pi\)
\(458\) 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 0.809213 0.587515i \(-0.199894\pi\)
−0.913410 + 0.407042i \(0.866560\pi\)
\(462\) −24173.5 20526.6i −2.43431 2.06707i
\(463\) −2410.35 1391.62i −0.241940 0.139684i 0.374128 0.927377i \(-0.377942\pi\)
−0.616068 + 0.787693i \(0.711275\pi\)
\(464\) 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 \(-0.817668\pi\)
0.840379 0.541999i \(-0.182332\pi\)
\(468\) 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 0.969342 + 0.245716i \(0.0790230\pi\)
−0.271875 + 0.962333i \(0.587644\pi\)
\(480\) 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 \(-0.722037\pi\)
0.642341 0.766419i \(-0.277963\pi\)
\(488\) 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 −0.184626 + 0.982809i \(0.559107\pi\)
−0.758825 + 0.651295i \(0.774226\pi\)
\(492\) −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 0.337908 + 0.941179i \(0.390281\pi\)
−0.984039 + 0.177953i \(0.943053\pi\)
\(500\) 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 \(-0.958210\pi\)
0.991394 0.130910i \(-0.0417901\pi\)
\(504\) 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 0.188500 + 0.982073i \(0.439637\pi\)
−0.944750 + 0.327790i \(0.893696\pi\)
\(510\) 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 \(-0.939020\pi\)
0.981706 0.190404i \(-0.0609797\pi\)
\(524\) −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 −0.927718 0.373283i \(-0.878232\pi\)
−0.140586 + 0.990068i \(0.544899\pi\)
\(548\) 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 \(0.178096\pi\)
−0.847519 + 0.530766i \(0.821904\pi\)
\(558\) −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 0.871293 0.490762i \(-0.163282\pi\)
0.0106339 + 0.999943i \(0.496615\pi\)
\(564\) −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 0.539950 0.841697i \(-0.318443\pi\)
−0.998906 + 0.0467619i \(0.985110\pi\)
\(570\) 0 0
\(571\) 6728.56 11654.2i 0.493137 0.854139i −0.506831 0.862045i \(-0.669183\pi\)
0.999969 + 0.00790629i \(0.00251668\pi\)
\(572\) −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 \(-0.957123\pi\)
0.990941 0.134296i \(-0.0428774\pi\)
\(578\) 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 0.140437 0.990090i \(-0.455149\pi\)
0.927661 + 0.373423i \(0.121816\pi\)
\(588\) 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 \(-0.718310\pi\)
0.633325 0.773886i \(-0.281690\pi\)
\(594\) 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 −0.906397 0.422427i \(-0.861178\pi\)
0.819031 + 0.573750i \(0.194512\pi\)
\(600\) 0 0
\(601\) −6692.51 11591.8i −0.454232 0.786752i 0.544412 0.838818i \(-0.316753\pi\)
−0.998644 + 0.0520656i \(0.983420\pi\)
\(602\) 19525.6i 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 −0.973700 0.227835i \(-0.926835\pi\)
−0.684161 0.729331i \(-0.739831\pi\)
\(608\) 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 \(0.0761010\pi\)
−0.971557 + 0.236807i \(0.923899\pi\)
\(614\) 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 0.869922 0.493190i \(-0.164169\pi\)
0.00784559 + 0.999969i \(0.497503\pi\)
\(618\) 26092.3 + 22155.9i 1.69836 + 1.44214i
\(619\) −11079.9 19191.0i −0.719450 1.24612i −0.961218 0.275789i \(-0.911061\pi\)
0.241769 0.970334i \(-0.422272\pi\)
\(620\) 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 0.801334 0.598217i \(-0.204124\pi\)
−0.918738 + 0.394867i \(0.870791\pi\)
\(642\) 1516.89 8317.33i 0.0932507 0.511306i
\(643\) −23140.3 13360.0i −1.41923 0.819391i −0.422996 0.906131i \(-0.639022\pi\)
−0.996231 + 0.0867402i \(0.972355\pi\)
\(644\) −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 \(-0.950340\pi\)
0.987855 0.155380i \(-0.0496601\pi\)
\(648\) 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 0.712213 0.701964i \(-0.247693\pi\)
−0.251812 + 0.967776i \(0.581026\pi\)
\(654\) 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 −0.962812 0.270172i \(-0.912920\pi\)
0.247430 0.968906i \(-0.420414\pi\)
\(660\) 0 0
\(661\) −10689.8 + 18515.2i −0.629023 + 1.08950i 0.358726 + 0.933443i \(0.383211\pi\)
−0.987748 + 0.156056i \(0.950122\pi\)
\(662\) 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 0.473730 0.880670i \(-0.342907\pi\)
0.999548 + 0.0300732i \(0.00957403\pi\)
\(674\) −35936.6 −2.05375
\(675\) 0 0
\(676\) −86.5900 −0.00492661
\(677\) −2304.91 + 1330.74i −0.130849 + 0.0755459i −0.563996 0.825778i \(-0.690737\pi\)
0.433147 + 0.901324i \(0.357403\pi\)
\(678\) 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 \(0.297235\pi\)
−0.594789 + 0.803882i \(0.702765\pi\)
\(684\) 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 0.535973 0.844235i \(-0.319945\pi\)
−0.999116 + 0.0420492i \(0.986611\pi\)
\(692\) 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 0.850534 + 0.525921i \(0.176279\pi\)
0.0301937 + 0.999544i \(0.490388\pi\)
\(710\) 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 −0.753170 0.657826i \(-0.771476\pi\)
0.193109 + 0.981177i \(0.438143\pi\)
\(728\) 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 0.270517 0.962715i \(-0.412805\pi\)
−0.698478 + 0.715632i \(0.746139\pi\)
\(734\) −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 −0.0416904 0.999131i \(-0.513274\pi\)
−0.886118 + 0.463460i \(0.846608\pi\)
\(744\) 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 −0.995280 0.0970452i \(-0.969061\pi\)
0.581684 + 0.813415i \(0.302394\pi\)
\(752\) −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 \(-0.735733\pi\)
0.674714 0.738080i \(-0.264267\pi\)
\(758\) 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 0.487911 + 0.872893i \(0.337759\pi\)
−0.999903 + 0.0139035i \(0.995574\pi\)
\(762\) −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 −0.482627 0.875826i \(-0.660317\pi\)
0.999801 0.0199457i \(-0.00634935\pi\)
\(770\) 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 \(0.247517\pi\)
−0.712601 + 0.701570i \(0.752483\pi\)
\(774\) −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