Properties

Label 225.4.e.f.76.11
Level $225$
Weight $4$
Character 225.76
Analytic conductor $13.275$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 76.11
Character \(\chi\) \(=\) 225.76
Dual form 225.4.e.f.151.11

$q$-expansion

\(f(q)\) \(=\) \(q+(2.39440 + 4.14722i) q^{2} +(-1.75824 + 4.88964i) q^{3} +(-7.46632 + 12.9320i) q^{4} +(-24.4884 + 4.41595i) q^{6} +(15.3349 + 26.5609i) q^{7} -33.1990 q^{8} +(-20.8172 - 17.1943i) q^{9} +O(q^{10})\) \(q+(2.39440 + 4.14722i) q^{2} +(-1.75824 + 4.88964i) q^{3} +(-7.46632 + 12.9320i) q^{4} +(-24.4884 + 4.41595i) q^{6} +(15.3349 + 26.5609i) q^{7} -33.1990 q^{8} +(-20.8172 - 17.1943i) q^{9} +(-21.3952 - 37.0576i) q^{11} +(-50.1055 - 59.2452i) q^{12} +(-26.7209 + 46.2820i) q^{13} +(-73.4359 + 127.195i) q^{14} +(-19.7612 - 34.2274i) q^{16} +0.609730 q^{17} +(21.4640 - 127.504i) q^{18} +94.5419 q^{19} +(-156.836 + 28.2819i) q^{21} +(102.457 - 177.462i) q^{22} +(76.3811 - 132.296i) q^{23} +(58.3718 - 162.331i) q^{24} -255.922 q^{26} +(120.676 - 71.5568i) q^{27} -457.982 q^{28} +(71.6738 + 124.143i) q^{29} +(-18.6894 + 32.3711i) q^{31} +(-38.1634 + 66.1010i) q^{32} +(218.816 - 39.4588i) q^{33} +(1.45994 + 2.52869i) q^{34} +(377.785 - 140.830i) q^{36} -274.029 q^{37} +(226.371 + 392.087i) q^{38} +(-179.321 - 212.031i) q^{39} +(136.746 - 236.851i) q^{41} +(-492.819 - 582.714i) q^{42} +(-92.6811 - 160.528i) q^{43} +638.974 q^{44} +731.548 q^{46} +(219.007 + 379.331i) q^{47} +(202.105 - 36.4453i) q^{48} +(-298.820 + 517.571i) q^{49} +(-1.07205 + 2.98136i) q^{51} +(-399.014 - 691.112i) q^{52} +211.483 q^{53} +(585.708 + 329.133i) q^{54} +(-509.104 - 881.794i) q^{56} +(-166.227 + 462.276i) q^{57} +(-343.232 + 594.494i) q^{58} +(-248.523 + 430.455i) q^{59} +(104.685 + 181.319i) q^{61} -179.000 q^{62} +(137.466 - 816.596i) q^{63} -681.694 q^{64} +(687.578 + 813.000i) q^{66} +(-483.805 + 837.976i) q^{67} +(-4.55244 + 7.88505i) q^{68} +(512.583 + 606.084i) q^{69} -401.080 q^{71} +(691.110 + 570.834i) q^{72} +97.6223 q^{73} +(-656.135 - 1136.46i) q^{74} +(-705.880 + 1222.62i) q^{76} +(656.188 - 1136.55i) q^{77} +(449.973 - 1251.37i) q^{78} +(-566.159 - 980.617i) q^{79} +(137.711 + 715.875i) q^{81} +1309.70 q^{82} +(286.610 + 496.422i) q^{83} +(805.241 - 2239.37i) q^{84} +(443.831 - 768.738i) q^{86} +(-733.033 + 132.187i) q^{87} +(710.300 + 1230.28i) q^{88} -90.6612 q^{89} -1639.05 q^{91} +(1140.57 + 1975.53i) q^{92} +(-125.422 - 148.301i) q^{93} +(-1048.78 + 1816.54i) q^{94} +(-256.110 - 302.827i) q^{96} +(4.62320 + 8.00762i) q^{97} -2861.98 q^{98} +(-191.792 + 1139.31i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} + O(q^{10}) \) \( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} - 29 q^{11} + 77 q^{12} - 24 q^{13} + 69 q^{14} - 192 q^{16} - 158 q^{17} - 125 q^{18} - 150 q^{19} - 60 q^{21} + 18 q^{22} + 318 q^{23} + 342 q^{24} - 308 q^{26} + 394 q^{27} + 192 q^{28} - 106 q^{29} - 60 q^{31} + 914 q^{32} + 80 q^{33} + 108 q^{34} + 1303 q^{36} - 168 q^{37} + 640 q^{38} - 410 q^{39} + 353 q^{41} - 1521 q^{42} + 426 q^{43} + 1142 q^{44} + 540 q^{46} + 1210 q^{47} - 2680 q^{48} - 666 q^{49} - 1369 q^{51} + 75 q^{52} - 896 q^{53} - 2128 q^{54} + 570 q^{56} - 1544 q^{57} - 594 q^{58} - 482 q^{59} - 402 q^{61} - 5088 q^{62} + 1038 q^{63} + 1950 q^{64} + 2041 q^{66} + 201 q^{67} + 3437 q^{68} + 2856 q^{69} - 1888 q^{71} + 5493 q^{72} - 906 q^{73} - 10 q^{74} + 462 q^{76} + 2652 q^{77} + 4589 q^{78} - 258 q^{79} + 3071 q^{81} + 1746 q^{82} + 3012 q^{83} - 2703 q^{84} - 1952 q^{86} - 2708 q^{87} + 216 q^{88} - 1476 q^{89} - 1236 q^{91} + 5232 q^{92} - 3024 q^{93} - 63 q^{94} - 10424 q^{96} + 318 q^{97} - 15022 q^{98} - 1697 q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.39440 + 4.14722i 0.846549 + 1.46627i 0.884269 + 0.466977i \(0.154657\pi\)
−0.0377207 + 0.999288i \(0.512010\pi\)
\(3\) −1.75824 + 4.88964i −0.338373 + 0.941012i
\(4\) −7.46632 + 12.9320i −0.933290 + 1.61650i
\(5\) 0 0
\(6\) −24.4884 + 4.41595i −1.66622 + 0.300467i
\(7\) 15.3349 + 26.5609i 0.828008 + 1.43415i 0.899599 + 0.436718i \(0.143859\pi\)
−0.0715906 + 0.997434i \(0.522808\pi\)
\(8\) −33.1990 −1.46720
\(9\) −20.8172 17.1943i −0.771007 0.636827i
\(10\) 0 0
\(11\) −21.3952 37.0576i −0.586445 1.01575i −0.994694 0.102882i \(-0.967194\pi\)
0.408248 0.912871i \(-0.366140\pi\)
\(12\) −50.1055 59.2452i −1.20535 1.42522i
\(13\) −26.7209 + 46.2820i −0.570081 + 0.987409i 0.426476 + 0.904499i \(0.359755\pi\)
−0.996557 + 0.0829101i \(0.973579\pi\)
\(14\) −73.4359 + 127.195i −1.40190 + 2.42816i
\(15\) 0 0
\(16\) −19.7612 34.2274i −0.308769 0.534804i
\(17\) 0.609730 0.00869890 0.00434945 0.999991i \(-0.498616\pi\)
0.00434945 + 0.999991i \(0.498616\pi\)
\(18\) 21.4640 127.504i 0.281062 1.66961i
\(19\) 94.5419 1.14155 0.570774 0.821107i \(-0.306643\pi\)
0.570774 + 0.821107i \(0.306643\pi\)
\(20\) 0 0
\(21\) −156.836 + 28.2819i −1.62973 + 0.293887i
\(22\) 102.457 177.462i 0.992909 1.71977i
\(23\) 76.3811 132.296i 0.692459 1.19937i −0.278571 0.960416i \(-0.589861\pi\)
0.971030 0.238958i \(-0.0768059\pi\)
\(24\) 58.3718 162.331i 0.496462 1.38066i
\(25\) 0 0
\(26\) −255.922 −1.93040
\(27\) 120.676 71.5568i 0.860150 0.510042i
\(28\) −457.982 −3.09108
\(29\) 71.6738 + 124.143i 0.458948 + 0.794921i 0.998906 0.0467712i \(-0.0148932\pi\)
−0.539958 + 0.841692i \(0.681560\pi\)
\(30\) 0 0
\(31\) −18.6894 + 32.3711i −0.108281 + 0.187549i −0.915074 0.403286i \(-0.867868\pi\)
0.806793 + 0.590835i \(0.201201\pi\)
\(32\) −38.1634 + 66.1010i −0.210825 + 0.365160i
\(33\) 218.816 39.4588i 1.15427 0.208148i
\(34\) 1.45994 + 2.52869i 0.00736404 + 0.0127549i
\(35\) 0 0
\(36\) 377.785 140.830i 1.74901 0.651993i
\(37\) −274.029 −1.21757 −0.608785 0.793335i \(-0.708343\pi\)
−0.608785 + 0.793335i \(0.708343\pi\)
\(38\) 226.371 + 392.087i 0.966375 + 1.67381i
\(39\) −179.321 212.031i −0.736263 0.870566i
\(40\) 0 0
\(41\) 136.746 236.851i 0.520881 0.902193i −0.478824 0.877911i \(-0.658937\pi\)
0.999705 0.0242820i \(-0.00772998\pi\)
\(42\) −492.819 582.714i −1.81056 2.14083i
\(43\) −92.6811 160.528i −0.328691 0.569310i 0.653561 0.756874i \(-0.273274\pi\)
−0.982252 + 0.187564i \(0.939941\pi\)
\(44\) 638.974 2.18929
\(45\) 0 0
\(46\) 731.548 2.34480
\(47\) 219.007 + 379.331i 0.679689 + 1.17726i 0.975074 + 0.221878i \(0.0712188\pi\)
−0.295385 + 0.955378i \(0.595448\pi\)
\(48\) 202.105 36.4453i 0.607736 0.109592i
\(49\) −298.820 + 517.571i −0.871194 + 1.50895i
\(50\) 0 0
\(51\) −1.07205 + 2.98136i −0.00294347 + 0.00818576i
\(52\) −399.014 691.112i −1.06410 1.84308i
\(53\) 211.483 0.548103 0.274051 0.961715i \(-0.411636\pi\)
0.274051 + 0.961715i \(0.411636\pi\)
\(54\) 585.708 + 329.133i 1.47601 + 0.829433i
\(55\) 0 0
\(56\) −509.104 881.794i −1.21486 2.10419i
\(57\) −166.227 + 462.276i −0.386269 + 1.07421i
\(58\) −343.232 + 594.494i −0.777043 + 1.34588i
\(59\) −248.523 + 430.455i −0.548389 + 0.949838i 0.449996 + 0.893031i \(0.351425\pi\)
−0.998385 + 0.0568073i \(0.981908\pi\)
\(60\) 0 0
\(61\) 104.685 + 181.319i 0.219730 + 0.380583i 0.954725 0.297489i \(-0.0961492\pi\)
−0.734996 + 0.678072i \(0.762816\pi\)
\(62\) −179.000 −0.366662
\(63\) 137.466 816.596i 0.274906 1.63304i
\(64\) −681.694 −1.33143
\(65\) 0 0
\(66\) 687.578 + 813.000i 1.28235 + 1.51626i
\(67\) −483.805 + 837.976i −0.882183 + 1.52799i −0.0332735 + 0.999446i \(0.510593\pi\)
−0.848909 + 0.528539i \(0.822740\pi\)
\(68\) −4.55244 + 7.88505i −0.00811859 + 0.0140618i
\(69\) 512.583 + 606.084i 0.894315 + 1.05745i
\(70\) 0 0
\(71\) −401.080 −0.670415 −0.335208 0.942144i \(-0.608806\pi\)
−0.335208 + 0.942144i \(0.608806\pi\)
\(72\) 691.110 + 570.834i 1.13122 + 0.934354i
\(73\) 97.6223 0.156518 0.0782591 0.996933i \(-0.475064\pi\)
0.0782591 + 0.996933i \(0.475064\pi\)
\(74\) −656.135 1136.46i −1.03073 1.78528i
\(75\) 0 0
\(76\) −705.880 + 1222.62i −1.06539 + 1.84532i
\(77\) 656.188 1136.55i 0.971163 1.68210i
\(78\) 449.973 1251.37i 0.653197 1.81653i
\(79\) −566.159 980.617i −0.806302 1.39656i −0.915408 0.402527i \(-0.868132\pi\)
0.109106 0.994030i \(-0.465201\pi\)
\(80\) 0 0
\(81\) 137.711 + 715.875i 0.188903 + 0.981996i
\(82\) 1309.70 1.76381
\(83\) 286.610 + 496.422i 0.379030 + 0.656499i 0.990921 0.134443i \(-0.0429244\pi\)
−0.611891 + 0.790942i \(0.709591\pi\)
\(84\) 805.241 2239.37i 1.04594 2.90875i
\(85\) 0 0
\(86\) 443.831 768.738i 0.556507 0.963898i
\(87\) −733.033 + 132.187i −0.903326 + 0.162895i
\(88\) 710.300 + 1230.28i 0.860434 + 1.49032i
\(89\) −90.6612 −0.107978 −0.0539891 0.998542i \(-0.517194\pi\)
−0.0539891 + 0.998542i \(0.517194\pi\)
\(90\) 0 0
\(91\) −1639.05 −1.88813
\(92\) 1140.57 + 1975.53i 1.29253 + 2.23873i
\(93\) −125.422 148.301i −0.139846 0.165356i
\(94\) −1048.78 + 1816.54i −1.15078 + 1.99321i
\(95\) 0 0
\(96\) −256.110 302.827i −0.272282 0.321949i
\(97\) 4.62320 + 8.00762i 0.00483933 + 0.00838197i 0.868435 0.495803i \(-0.165126\pi\)
−0.863596 + 0.504185i \(0.831793\pi\)
\(98\) −2861.98 −2.95003
\(99\) −191.792 + 1139.31i −0.194705 + 1.15662i
\(100\) 0 0
\(101\) 108.537 + 187.992i 0.106929 + 0.185207i 0.914525 0.404530i \(-0.132565\pi\)
−0.807596 + 0.589737i \(0.799232\pi\)
\(102\) −14.9313 + 2.69254i −0.0144943 + 0.00261373i
\(103\) 217.245 376.279i 0.207823 0.359960i −0.743205 0.669063i \(-0.766696\pi\)
0.951028 + 0.309103i \(0.100029\pi\)
\(104\) 887.108 1536.52i 0.836424 1.44873i
\(105\) 0 0
\(106\) 506.376 + 877.068i 0.463996 + 0.803664i
\(107\) 193.254 0.174604 0.0873018 0.996182i \(-0.472176\pi\)
0.0873018 + 0.996182i \(0.472176\pi\)
\(108\) 24.3733 + 2094.85i 0.0217159 + 1.86645i
\(109\) 1703.14 1.49662 0.748308 0.663351i \(-0.230866\pi\)
0.748308 + 0.663351i \(0.230866\pi\)
\(110\) 0 0
\(111\) 481.809 1339.90i 0.411993 1.14575i
\(112\) 606.074 1049.75i 0.511327 0.885644i
\(113\) 304.784 527.901i 0.253731 0.439476i −0.710819 0.703375i \(-0.751675\pi\)
0.964550 + 0.263899i \(0.0850087\pi\)
\(114\) −2315.18 + 417.492i −1.90207 + 0.342998i
\(115\) 0 0
\(116\) −2140.56 −1.71332
\(117\) 1352.04 504.013i 1.06834 0.398256i
\(118\) −2380.26 −1.85695
\(119\) 9.35016 + 16.1950i 0.00720275 + 0.0124755i
\(120\) 0 0
\(121\) −250.010 + 433.030i −0.187836 + 0.325342i
\(122\) −501.314 + 868.302i −0.372024 + 0.644364i
\(123\) 917.684 + 1085.08i 0.672722 + 0.795434i
\(124\) −279.083 483.385i −0.202116 0.350075i
\(125\) 0 0
\(126\) 3715.76 1385.16i 2.62719 0.979361i
\(127\) 1372.33 0.958857 0.479429 0.877581i \(-0.340844\pi\)
0.479429 + 0.877581i \(0.340844\pi\)
\(128\) −1326.94 2298.33i −0.916298 1.58707i
\(129\) 947.881 170.930i 0.646948 0.116663i
\(130\) 0 0
\(131\) −537.087 + 930.262i −0.358210 + 0.620438i −0.987662 0.156601i \(-0.949946\pi\)
0.629452 + 0.777040i \(0.283280\pi\)
\(132\) −1123.47 + 3124.35i −0.740798 + 2.06015i
\(133\) 1449.79 + 2511.11i 0.945210 + 1.63715i
\(134\) −4633.70 −2.98724
\(135\) 0 0
\(136\) −20.2424 −0.0127630
\(137\) 991.784 + 1717.82i 0.618495 + 1.07127i 0.989760 + 0.142738i \(0.0455908\pi\)
−0.371265 + 0.928527i \(0.621076\pi\)
\(138\) −1286.24 + 3577.01i −0.793418 + 2.20649i
\(139\) 1025.49 1776.20i 0.625761 1.08385i −0.362632 0.931932i \(-0.618122\pi\)
0.988393 0.151918i \(-0.0485448\pi\)
\(140\) 0 0
\(141\) −2239.86 + 403.910i −1.33780 + 0.241244i
\(142\) −960.347 1663.37i −0.567539 0.983007i
\(143\) 2286.80 1.33728
\(144\) −177.145 + 1052.30i −0.102514 + 0.608970i
\(145\) 0 0
\(146\) 233.747 + 404.862i 0.132500 + 0.229497i
\(147\) −2005.34 2371.13i −1.12515 1.33039i
\(148\) 2045.99 3543.75i 1.13635 1.96821i
\(149\) 290.144 502.544i 0.159527 0.276309i −0.775171 0.631751i \(-0.782336\pi\)
0.934698 + 0.355442i \(0.115670\pi\)
\(150\) 0 0
\(151\) 804.674 + 1393.74i 0.433665 + 0.751130i 0.997186 0.0749720i \(-0.0238868\pi\)
−0.563520 + 0.826102i \(0.690553\pi\)
\(152\) −3138.70 −1.67488
\(153\) −12.6929 10.4839i −0.00670691 0.00553969i
\(154\) 6284.71 3.28855
\(155\) 0 0
\(156\) 4080.85 735.893i 2.09442 0.377684i
\(157\) −103.480 + 179.233i −0.0526026 + 0.0911103i −0.891128 0.453753i \(-0.850085\pi\)
0.838525 + 0.544863i \(0.183418\pi\)
\(158\) 2711.23 4695.98i 1.36515 2.36451i
\(159\) −371.838 + 1034.08i −0.185463 + 0.515771i
\(160\) 0 0
\(161\) 4685.19 2.29345
\(162\) −2639.16 + 2285.21i −1.27995 + 1.10829i
\(163\) 2104.04 1.01105 0.505525 0.862812i \(-0.331299\pi\)
0.505525 + 0.862812i \(0.331299\pi\)
\(164\) 2041.98 + 3536.81i 0.972266 + 1.68401i
\(165\) 0 0
\(166\) −1372.52 + 2377.27i −0.641735 + 1.11152i
\(167\) 517.426 896.209i 0.239758 0.415274i −0.720886 0.693053i \(-0.756265\pi\)
0.960645 + 0.277779i \(0.0895984\pi\)
\(168\) 5206.79 938.931i 2.39114 0.431191i
\(169\) −329.515 570.737i −0.149984 0.259780i
\(170\) 0 0
\(171\) −1968.10 1625.58i −0.880141 0.726968i
\(172\) 2767.94 1.22706
\(173\) −1760.62 3049.48i −0.773741 1.34016i −0.935499 0.353329i \(-0.885050\pi\)
0.161758 0.986830i \(-0.448284\pi\)
\(174\) −2303.38 2723.54i −1.00356 1.18662i
\(175\) 0 0
\(176\) −845.591 + 1464.61i −0.362152 + 0.627266i
\(177\) −1667.81 1972.03i −0.708249 0.837441i
\(178\) −217.079 375.992i −0.0914089 0.158325i
\(179\) 961.672 0.401557 0.200779 0.979637i \(-0.435653\pi\)
0.200779 + 0.979637i \(0.435653\pi\)
\(180\) 0 0
\(181\) 1493.35 0.613258 0.306629 0.951829i \(-0.400799\pi\)
0.306629 + 0.951829i \(0.400799\pi\)
\(182\) −3924.55 6797.52i −1.59839 2.76849i
\(183\) −1070.65 + 193.068i −0.432483 + 0.0779891i
\(184\) −2535.78 + 4392.09i −1.01598 + 1.75972i
\(185\) 0 0
\(186\) 314.725 875.246i 0.124069 0.345033i
\(187\) −13.0453 22.5951i −0.00510143 0.00883593i
\(188\) −6540.69 −2.53739
\(189\) 3751.16 + 2107.93i 1.44369 + 0.811267i
\(190\) 0 0
\(191\) −828.719 1435.38i −0.313948 0.543773i 0.665266 0.746607i \(-0.268318\pi\)
−0.979213 + 0.202834i \(0.934985\pi\)
\(192\) 1198.58 3333.24i 0.450522 1.25289i
\(193\) −508.384 + 880.546i −0.189608 + 0.328410i −0.945119 0.326725i \(-0.894055\pi\)
0.755512 + 0.655135i \(0.227388\pi\)
\(194\) −22.1396 + 38.3469i −0.00819346 + 0.0141915i
\(195\) 0 0
\(196\) −4462.16 7728.70i −1.62615 2.81658i
\(197\) 4594.73 1.66173 0.830865 0.556475i \(-0.187846\pi\)
0.830865 + 0.556475i \(0.187846\pi\)
\(198\) −5184.21 + 1932.56i −1.86073 + 0.693643i
\(199\) −832.746 −0.296642 −0.148321 0.988939i \(-0.547387\pi\)
−0.148321 + 0.988939i \(0.547387\pi\)
\(200\) 0 0
\(201\) −3246.75 3839.00i −1.13935 1.34717i
\(202\) −519.763 + 900.255i −0.181041 + 0.313573i
\(203\) −2198.22 + 3807.43i −0.760025 + 1.31640i
\(204\) −30.5508 36.1236i −0.0104852 0.0123978i
\(205\) 0 0
\(206\) 2080.69 0.703729
\(207\) −3864.78 + 1440.71i −1.29768 + 0.483749i
\(208\) 2112.15 0.704093
\(209\) −2022.74 3503.50i −0.669455 1.15953i
\(210\) 0 0
\(211\) −1212.40 + 2099.94i −0.395568 + 0.685145i −0.993174 0.116646i \(-0.962786\pi\)
0.597605 + 0.801791i \(0.296119\pi\)
\(212\) −1579.00 + 2734.91i −0.511539 + 0.886011i
\(213\) 705.195 1961.14i 0.226851 0.630869i
\(214\) 462.728 + 801.468i 0.147810 + 0.256015i
\(215\) 0 0
\(216\) −4006.31 + 2375.62i −1.26201 + 0.748334i
\(217\) −1146.40 −0.358631
\(218\) 4078.00 + 7063.30i 1.26696 + 2.19444i
\(219\) −171.643 + 477.338i −0.0529616 + 0.147286i
\(220\) 0 0
\(221\) −16.2925 + 28.2195i −0.00495907 + 0.00858937i
\(222\) 6710.52 1210.10i 2.02874 0.365840i
\(223\) 1505.39 + 2607.41i 0.452056 + 0.782983i 0.998514 0.0545031i \(-0.0173575\pi\)
−0.546458 + 0.837487i \(0.684024\pi\)
\(224\) −2340.93 −0.698260
\(225\) 0 0
\(226\) 2919.10 0.859184
\(227\) −39.8202 68.9706i −0.0116430 0.0201663i 0.860145 0.510049i \(-0.170373\pi\)
−0.871788 + 0.489883i \(0.837039\pi\)
\(228\) −4737.07 5601.16i −1.37596 1.62695i
\(229\) 1157.98 2005.67i 0.334154 0.578771i −0.649168 0.760645i \(-0.724883\pi\)
0.983322 + 0.181874i \(0.0582162\pi\)
\(230\) 0 0
\(231\) 4403.59 + 5206.85i 1.25426 + 1.48305i
\(232\) −2379.50 4121.41i −0.673369 1.16631i
\(233\) −2055.15 −0.577842 −0.288921 0.957353i \(-0.593297\pi\)
−0.288921 + 0.957353i \(0.593297\pi\)
\(234\) 5327.59 + 4400.41i 1.48836 + 1.22933i
\(235\) 0 0
\(236\) −3711.10 6427.82i −1.02361 1.77295i
\(237\) 5790.31 1044.16i 1.58701 0.286183i
\(238\) −44.7761 + 77.5544i −0.0121950 + 0.0211223i
\(239\) 2279.90 3948.90i 0.617048 1.06876i −0.372974 0.927842i \(-0.621662\pi\)
0.990022 0.140916i \(-0.0450048\pi\)
\(240\) 0 0
\(241\) −1946.62 3371.64i −0.520301 0.901188i −0.999721 0.0236025i \(-0.992486\pi\)
0.479420 0.877585i \(-0.340847\pi\)
\(242\) −2394.50 −0.636050
\(243\) −3742.50 585.324i −0.987990 0.154521i
\(244\) −3126.44 −0.820285
\(245\) 0 0
\(246\) −2302.77 + 6403.96i −0.596825 + 1.65976i
\(247\) −2526.25 + 4375.59i −0.650774 + 1.12717i
\(248\) 620.471 1074.69i 0.158871 0.275172i
\(249\) −2931.26 + 528.589i −0.746027 + 0.134530i
\(250\) 0 0
\(251\) 1560.52 0.392426 0.196213 0.980561i \(-0.437136\pi\)
0.196213 + 0.980561i \(0.437136\pi\)
\(252\) 9533.89 + 7874.68i 2.38325 + 1.96849i
\(253\) −6536.76 −1.62436
\(254\) 3285.92 + 5691.37i 0.811719 + 1.40594i
\(255\) 0 0
\(256\) 3627.68 6283.33i 0.885665 1.53402i
\(257\) 3094.87 5360.47i 0.751177 1.30108i −0.196076 0.980589i \(-0.562820\pi\)
0.947253 0.320488i \(-0.103847\pi\)
\(258\) 2978.49 + 3521.80i 0.718732 + 0.849837i
\(259\) −4202.21 7278.45i −1.00816 1.74618i
\(260\) 0 0
\(261\) 642.502 3816.68i 0.152375 0.905160i
\(262\) −5144.01 −1.21297
\(263\) 2976.03 + 5154.64i 0.697757 + 1.20855i 0.969243 + 0.246108i \(0.0791516\pi\)
−0.271486 + 0.962442i \(0.587515\pi\)
\(264\) −7264.48 + 1309.99i −1.69355 + 0.305396i
\(265\) 0 0
\(266\) −6942.77 + 12025.2i −1.60033 + 2.77186i
\(267\) 159.404 443.301i 0.0365370 0.101609i
\(268\) −7224.49 12513.2i −1.64666 2.85211i
\(269\) 5228.45 1.18507 0.592536 0.805544i \(-0.298127\pi\)
0.592536 + 0.805544i \(0.298127\pi\)
\(270\) 0 0
\(271\) −5868.44 −1.31543 −0.657717 0.753265i \(-0.728478\pi\)
−0.657717 + 0.753265i \(0.728478\pi\)
\(272\) −12.0490 20.8695i −0.00268595 0.00465220i
\(273\) 2881.85 8014.38i 0.638891 1.77675i
\(274\) −4749.46 + 8226.31i −1.04717 + 1.81376i
\(275\) 0 0
\(276\) −11665.0 + 2103.53i −2.54403 + 0.458760i
\(277\) 838.841 + 1452.91i 0.181953 + 0.315152i 0.942546 0.334077i \(-0.108425\pi\)
−0.760592 + 0.649230i \(0.775091\pi\)
\(278\) 9821.72 2.11895
\(279\) 945.660 352.522i 0.202922 0.0756450i
\(280\) 0 0
\(281\) −589.278 1020.66i −0.125101 0.216681i 0.796671 0.604413i \(-0.206592\pi\)
−0.921772 + 0.387731i \(0.873259\pi\)
\(282\) −7038.22 8322.07i −1.48624 1.75735i
\(283\) 1870.28 3239.41i 0.392849 0.680435i −0.599975 0.800019i \(-0.704823\pi\)
0.992824 + 0.119584i \(0.0381560\pi\)
\(284\) 2994.59 5186.79i 0.625692 1.08373i
\(285\) 0 0
\(286\) 5475.51 + 9483.87i 1.13208 + 1.96081i
\(287\) 8387.96 1.72518
\(288\) 1931.02 719.843i 0.395091 0.147282i
\(289\) −4912.63 −0.999924
\(290\) 0 0
\(291\) −47.2831 + 8.52648i −0.00952503 + 0.00171763i
\(292\) −728.879 + 1262.46i −0.146077 + 0.253012i
\(293\) 1358.07 2352.25i 0.270783 0.469009i −0.698280 0.715825i \(-0.746051\pi\)
0.969062 + 0.246816i \(0.0793842\pi\)
\(294\) 5032.04 13994.0i 0.998213 2.77602i
\(295\) 0 0
\(296\) 9097.49 1.78642
\(297\) −5233.61 2940.98i −1.02251 0.574588i
\(298\) 2778.88 0.540189
\(299\) 4081.94 + 7070.13i 0.789515 + 1.36748i
\(300\) 0 0
\(301\) 2842.51 4923.38i 0.544318 0.942787i
\(302\) −3853.42 + 6674.33i −0.734237 + 1.27174i
\(303\) −1110.05 + 200.173i −0.210464 + 0.0379526i
\(304\) −1868.26 3235.93i −0.352475 0.610504i
\(305\) 0 0
\(306\) 13.0873 77.7428i 0.00244493 0.0145237i
\(307\) −4308.59 −0.800992 −0.400496 0.916299i \(-0.631162\pi\)
−0.400496 + 0.916299i \(0.631162\pi\)
\(308\) 9798.61 + 16971.7i 1.81275 + 3.13978i
\(309\) 1457.90 + 1723.84i 0.268405 + 0.317365i
\(310\) 0 0
\(311\) 3153.11 5461.35i 0.574908 0.995770i −0.421143 0.906994i \(-0.638371\pi\)
0.996052 0.0887763i \(-0.0282956\pi\)
\(312\) 5953.26 + 7039.20i 1.08025 + 1.27730i
\(313\) 2381.80 + 4125.40i 0.430120 + 0.744989i 0.996883 0.0788914i \(-0.0251380\pi\)
−0.566764 + 0.823881i \(0.691805\pi\)
\(314\) −991.091 −0.178123
\(315\) 0 0
\(316\) 16908.5 3.01005
\(317\) −731.473 1266.95i −0.129601 0.224476i 0.793921 0.608021i \(-0.208036\pi\)
−0.923522 + 0.383545i \(0.874703\pi\)
\(318\) −5178.88 + 933.899i −0.913261 + 0.164687i
\(319\) 3066.95 5312.11i 0.538296 0.932355i
\(320\) 0 0
\(321\) −339.787 + 944.943i −0.0590812 + 0.164304i
\(322\) 11218.2 + 19430.5i 1.94151 + 3.36280i
\(323\) 57.6450 0.00993020
\(324\) −10285.9 3564.07i −1.76370 0.611123i
\(325\) 0 0
\(326\) 5037.92 + 8725.93i 0.855903 + 1.48247i
\(327\) −2994.53 + 8327.74i −0.506415 + 1.40833i
\(328\) −4539.83 + 7863.22i −0.764239 + 1.32370i
\(329\) −6716.90 + 11634.0i −1.12558 + 1.94956i
\(330\) 0 0
\(331\) 2888.59 + 5003.18i 0.479671 + 0.830814i 0.999728 0.0233171i \(-0.00742273\pi\)
−0.520057 + 0.854131i \(0.674089\pi\)
\(332\) −8559.67 −1.41498
\(333\) 5704.51 + 4711.74i 0.938755 + 0.775381i
\(334\) 4955.71 0.811869
\(335\) 0 0
\(336\) 4067.28 + 4809.20i 0.660382 + 0.780843i
\(337\) −1468.77 + 2543.98i −0.237415 + 0.411214i −0.959972 0.280097i \(-0.909633\pi\)
0.722557 + 0.691311i \(0.242967\pi\)
\(338\) 1577.98 2733.15i 0.253938 0.439833i
\(339\) 2045.36 + 2418.46i 0.327696 + 0.387471i
\(340\) 0 0
\(341\) 1599.46 0.254004
\(342\) 2029.25 12054.4i 0.320846 1.90593i
\(343\) −7809.75 −1.22941
\(344\) 3076.92 + 5329.38i 0.482257 + 0.835293i
\(345\) 0 0
\(346\) 8431.25 14603.3i 1.31002 2.26902i
\(347\) −3495.56 + 6054.49i −0.540783 + 0.936663i 0.458077 + 0.888913i \(0.348539\pi\)
−0.998859 + 0.0477504i \(0.984795\pi\)
\(348\) 3763.61 10466.6i 0.579743 1.61226i
\(349\) 2676.15 + 4635.24i 0.410462 + 0.710941i 0.994940 0.100468i \(-0.0320341\pi\)
−0.584478 + 0.811409i \(0.698701\pi\)
\(350\) 0 0
\(351\) 87.2286 + 7497.17i 0.0132647 + 1.14008i
\(352\) 3266.06 0.494550
\(353\) 517.078 + 895.605i 0.0779639 + 0.135037i 0.902371 0.430959i \(-0.141825\pi\)
−0.824407 + 0.565997i \(0.808491\pi\)
\(354\) 4185.06 11638.6i 0.628343 1.74741i
\(355\) 0 0
\(356\) 676.905 1172.43i 0.100775 0.174547i
\(357\) −95.6273 + 17.2443i −0.0141768 + 0.00255649i
\(358\) 2302.63 + 3988.27i 0.339938 + 0.588789i
\(359\) −7870.36 −1.15705 −0.578526 0.815664i \(-0.696372\pi\)
−0.578526 + 0.815664i \(0.696372\pi\)
\(360\) 0 0
\(361\) 2079.17 0.303130
\(362\) 3575.68 + 6193.25i 0.519153 + 0.899199i
\(363\) −1677.78 1983.83i −0.242592 0.286843i
\(364\) 12237.7 21196.3i 1.76217 3.05216i
\(365\) 0 0
\(366\) −3364.25 3977.93i −0.480471 0.568114i
\(367\) −6625.85 11476.3i −0.942416 1.63231i −0.760845 0.648934i \(-0.775215\pi\)
−0.181571 0.983378i \(-0.558118\pi\)
\(368\) −6037.53 −0.855239
\(369\) −6919.16 + 2579.32i −0.976144 + 0.363886i
\(370\) 0 0
\(371\) 3243.08 + 5617.18i 0.453834 + 0.786063i
\(372\) 2854.27 514.707i 0.397815 0.0717374i
\(373\) −1044.92 + 1809.85i −0.145051 + 0.251235i −0.929392 0.369095i \(-0.879668\pi\)
0.784341 + 0.620330i \(0.213001\pi\)
\(374\) 62.4714 108.204i 0.00863721 0.0149601i
\(375\) 0 0
\(376\) −7270.80 12593.4i −0.997242 1.72727i
\(377\) −7660.76 −1.04655
\(378\) 239.726 + 20604.2i 0.0326196 + 2.80361i
\(379\) −4197.61 −0.568909 −0.284455 0.958690i \(-0.591812\pi\)
−0.284455 + 0.958690i \(0.591812\pi\)
\(380\) 0 0
\(381\) −2412.89 + 6710.22i −0.324452 + 0.902296i
\(382\) 3968.57 6873.77i 0.531544 0.920661i
\(383\) 3856.67 6679.94i 0.514534 0.891199i −0.485324 0.874334i \(-0.661298\pi\)
0.999858 0.0168643i \(-0.00536833\pi\)
\(384\) 13571.1 2447.25i 1.80351 0.325224i
\(385\) 0 0
\(386\) −4869.10 −0.642048
\(387\) −830.816 + 4935.34i −0.109129 + 0.648262i
\(388\) −138.073 −0.0180660
\(389\) −571.797 990.381i −0.0745276 0.129086i 0.826353 0.563152i \(-0.190412\pi\)
−0.900881 + 0.434067i \(0.857078\pi\)
\(390\) 0 0
\(391\) 46.5718 80.6648i 0.00602363 0.0104332i
\(392\) 9920.52 17182.8i 1.27822 2.21394i
\(393\) −3604.32 4261.79i −0.462631 0.547020i
\(394\) 11001.6 + 19055.4i 1.40673 + 2.43654i
\(395\) 0 0
\(396\) −13301.6 10986.7i −1.68796 1.39420i
\(397\) 2122.39 0.268311 0.134156 0.990960i \(-0.457168\pi\)
0.134156 + 0.990960i \(0.457168\pi\)
\(398\) −1993.93 3453.59i −0.251122 0.434956i
\(399\) −14827.5 + 2673.83i −1.86041 + 0.335485i
\(400\) 0 0
\(401\) −164.782 + 285.411i −0.0205208 + 0.0355430i −0.876103 0.482123i \(-0.839866\pi\)
0.855583 + 0.517666i \(0.173199\pi\)
\(402\) 8147.15 22657.1i 1.01080 2.81103i
\(403\) −998.798 1729.97i −0.123458 0.213836i
\(404\) −3241.49 −0.399183
\(405\) 0 0
\(406\) −21053.7 −2.57359
\(407\) 5862.91 + 10154.9i 0.714038 + 1.23675i
\(408\) 35.5910 98.9782i 0.00431867 0.0120102i
\(409\) 593.799 1028.49i 0.0717884 0.124341i −0.827897 0.560881i \(-0.810463\pi\)
0.899685 + 0.436539i \(0.143796\pi\)
\(410\) 0 0
\(411\) −10143.3 + 1829.13i −1.21736 + 0.219524i
\(412\) 3244.04 + 5618.84i 0.387918 + 0.671894i
\(413\) −15244.3 −1.81628
\(414\) −15228.8 12578.5i −1.80786 1.49323i
\(415\) 0 0
\(416\) −2039.52 3532.56i −0.240375 0.416341i
\(417\) 6881.92 + 8137.25i 0.808175 + 0.955595i
\(418\) 9686.52 16777.5i 1.13345 1.96320i
\(419\) 5986.83 10369.5i 0.698032 1.20903i −0.271115 0.962547i \(-0.587392\pi\)
0.969148 0.246481i \(-0.0792742\pi\)
\(420\) 0 0
\(421\) 4318.23 + 7479.40i 0.499900 + 0.865851i 1.00000 0.000115960i \(-3.69112e-5\pi\)
−0.500100 + 0.865967i \(0.666704\pi\)
\(422\) −11611.9 −1.33947
\(423\) 1963.23 11662.3i 0.225663 1.34052i
\(424\) −7021.03 −0.804178
\(425\) 0 0
\(426\) 9821.81 1771.15i 1.11706 0.201438i
\(427\) −3210.66 + 5561.03i −0.363876 + 0.630251i
\(428\) −1442.90 + 2499.17i −0.162956 + 0.282248i
\(429\) −4020.74 + 11181.6i −0.452502 + 1.25840i
\(430\) 0 0
\(431\) −4589.22 −0.512889 −0.256445 0.966559i \(-0.582551\pi\)
−0.256445 + 0.966559i \(0.582551\pi\)
\(432\) −4833.91 2716.37i −0.538360 0.302526i
\(433\) 16279.0 1.80674 0.903369 0.428864i \(-0.141086\pi\)
0.903369 + 0.428864i \(0.141086\pi\)
\(434\) −2744.95 4754.40i −0.303599 0.525849i
\(435\) 0 0
\(436\) −12716.2 + 22025.1i −1.39678 + 2.41929i
\(437\) 7221.21 12507.5i 0.790474 1.36914i
\(438\) −2390.61 + 431.095i −0.260794 + 0.0470286i
\(439\) 5261.48 + 9113.15i 0.572020 + 0.990767i 0.996358 + 0.0852636i \(0.0271732\pi\)
−0.424339 + 0.905503i \(0.639493\pi\)
\(440\) 0 0
\(441\) 15119.9 5636.37i 1.63264 0.608613i
\(442\) −156.044 −0.0167924
\(443\) −7878.97 13646.8i −0.845014 1.46361i −0.885609 0.464432i \(-0.846259\pi\)
0.0405945 0.999176i \(-0.487075\pi\)
\(444\) 13730.3 + 16234.9i 1.46760 + 1.73530i
\(445\) 0 0
\(446\) −7209.02 + 12486.4i −0.765374 + 1.32567i
\(447\) 1947.12 + 2302.29i 0.206030 + 0.243612i
\(448\) −10453.7 18106.4i −1.10244 1.90948i
\(449\) 10964.2 1.15241 0.576206 0.817305i \(-0.304533\pi\)
0.576206 + 0.817305i \(0.304533\pi\)
\(450\) 0 0
\(451\) −11702.8 −1.22187
\(452\) 4551.23 + 7882.95i 0.473610 + 0.820316i
\(453\) −8229.68 + 1484.05i −0.853563 + 0.153922i
\(454\) 190.691 330.287i 0.0197127 0.0341434i
\(455\) 0 0
\(456\) 5518.58 15347.1i 0.566735 1.57608i
\(457\) −6739.14 11672.5i −0.689811 1.19479i −0.971899 0.235400i \(-0.924360\pi\)
0.282087 0.959389i \(-0.408973\pi\)
\(458\) 11090.6 1.13151
\(459\) 73.5796 43.6304i 0.00748235 0.00443680i
\(460\) 0 0
\(461\) 5179.15 + 8970.55i 0.523248 + 0.906291i 0.999634 + 0.0270553i \(0.00861302\pi\)
−0.476386 + 0.879236i \(0.658054\pi\)
\(462\) −11050.0 + 30730.0i −1.11276 + 3.09456i
\(463\) −7199.29 + 12469.5i −0.722634 + 1.25164i 0.237307 + 0.971435i \(0.423735\pi\)
−0.959941 + 0.280203i \(0.909598\pi\)
\(464\) 2832.72 4906.42i 0.283418 0.490894i
\(465\) 0 0
\(466\) −4920.85 8523.16i −0.489172 0.847270i
\(467\) −18838.8 −1.86671 −0.933356 0.358953i \(-0.883134\pi\)
−0.933356 + 0.358953i \(0.883134\pi\)
\(468\) −3576.86 + 21247.8i −0.353291 + 2.09867i
\(469\) −29676.5 −2.92182
\(470\) 0 0
\(471\) −694.441 821.114i −0.0679366 0.0803290i
\(472\) 8250.72 14290.7i 0.804598 1.39360i
\(473\) −3965.86 + 6869.07i −0.385519 + 0.667739i
\(474\) 18194.7 + 21513.6i 1.76310 + 2.08471i
\(475\) 0 0
\(476\) −279.245 −0.0268890
\(477\) −4402.49 3636.31i −0.422591 0.349047i
\(478\) 21836.0 2.08944
\(479\) −3181.96 5511.31i −0.303523 0.525717i 0.673409 0.739271i \(-0.264830\pi\)
−0.976931 + 0.213554i \(0.931496\pi\)
\(480\) 0 0
\(481\) 7322.31 12682.6i 0.694113 1.20224i
\(482\) 9321.96 16146.1i 0.880920 1.52580i
\(483\) −8237.69 + 22908.9i −0.776041 + 2.15816i
\(484\) −3733.31 6466.28i −0.350611 0.607277i
\(485\) 0 0
\(486\) −6533.58 16922.5i −0.609813 1.57946i
\(487\) 1556.53 0.144832 0.0724158 0.997375i \(-0.476929\pi\)
0.0724158 + 0.997375i \(0.476929\pi\)
\(488\) −3475.43 6019.62i −0.322388 0.558392i
\(489\) −3699.41 + 10288.0i −0.342112 + 0.951410i
\(490\) 0 0
\(491\) 6817.36 11808.0i 0.626605 1.08531i −0.361623 0.932324i \(-0.617777\pi\)
0.988228 0.152987i \(-0.0488893\pi\)
\(492\) −20884.0 + 3765.98i −1.91367 + 0.345089i
\(493\) 43.7016 + 75.6935i 0.00399234 + 0.00691493i
\(494\) −24195.4 −2.20365
\(495\) 0 0
\(496\) 1477.30 0.133736
\(497\) −6150.54 10653.0i −0.555109 0.961477i
\(498\) −9210.78 10890.9i −0.828805 0.979988i
\(499\) −1132.45 + 1961.47i −0.101594 + 0.175967i −0.912342 0.409430i \(-0.865728\pi\)
0.810747 + 0.585396i \(0.199061\pi\)
\(500\) 0 0
\(501\) 3472.38 + 4105.78i 0.309650 + 0.366133i
\(502\) 3736.51 + 6471.82i 0.332208 + 0.575401i
\(503\) −20004.6 −1.77329 −0.886643 0.462455i \(-0.846969\pi\)
−0.886643 + 0.462455i \(0.846969\pi\)
\(504\) −4563.74 + 27110.2i −0.403343 + 2.39600i
\(505\) 0 0
\(506\) −15651.6 27109.4i −1.37510 2.38174i
\(507\) 3370.06 607.718i 0.295207 0.0532342i
\(508\) −10246.3 + 17747.1i −0.894891 + 1.55000i
\(509\) 361.966 626.944i 0.0315204 0.0545949i −0.849835 0.527049i \(-0.823298\pi\)
0.881355 + 0.472454i \(0.156632\pi\)
\(510\) 0 0
\(511\) 1497.03 + 2592.93i 0.129598 + 0.224471i
\(512\) 13513.5 1.16644
\(513\) 11408.9 6765.12i 0.981902 0.582237i
\(514\) 29641.4 2.54363
\(515\) 0 0
\(516\) −4866.71 + 13534.3i −0.415203 + 1.15468i
\(517\) 9371.39 16231.7i 0.797201 1.38079i
\(518\) 20123.6 34855.0i 1.70691 2.95645i
\(519\) 18006.4 3247.07i 1.52292 0.274626i
\(520\) 0 0
\(521\) −2150.30 −0.180818 −0.0904090 0.995905i \(-0.528817\pi\)
−0.0904090 + 0.995905i \(0.528817\pi\)
\(522\) 17367.0 6474.07i 1.45620 0.542840i
\(523\) 12696.4 1.06152 0.530760 0.847522i \(-0.321907\pi\)
0.530760 + 0.847522i \(0.321907\pi\)
\(524\) −8020.12 13891.3i −0.668627 1.15810i
\(525\) 0 0
\(526\) −14251.6 + 24684.5i −1.18137 + 2.04619i
\(527\) −11.3955 + 19.7376i −0.000941929 + 0.00163147i
\(528\) −5674.65 6709.77i −0.467722 0.553040i
\(529\) −5584.63 9672.87i −0.458998 0.795008i
\(530\) 0 0
\(531\) 12574.9 4687.67i 1.02769 0.383103i
\(532\) −43298.4 −3.52862
\(533\) 7307.96 + 12657.8i 0.593889 + 1.02865i
\(534\) 2220.14 400.355i 0.179916 0.0324439i
\(535\) 0 0
\(536\) 16061.9 27820.0i 1.29434 2.24186i
\(537\) −1690.85 + 4702.23i −0.135876 + 0.377870i
\(538\) 12519.0 + 21683.6i 1.00322 + 1.73763i
\(539\) 25573.2 2.04363
\(540\) 0 0
\(541\) −12233.1 −0.972167 −0.486083 0.873912i \(-0.661575\pi\)
−0.486083 + 0.873912i \(0.661575\pi\)
\(542\) −14051.4 24337.7i −1.11358 1.92877i
\(543\) −2625.67 + 7301.94i −0.207510 + 0.577083i
\(544\) −23.2694 + 40.3038i −0.00183395 + 0.00317649i
\(545\) 0 0
\(546\) 40137.7 7237.98i 3.14604 0.567320i
\(547\) 9043.15 + 15663.2i 0.706868 + 1.22433i 0.966013 + 0.258493i \(0.0832260\pi\)
−0.259145 + 0.965839i \(0.583441\pi\)
\(548\) −29619.9 −2.30894
\(549\) 938.420 5574.54i 0.0729522 0.433362i
\(550\) 0 0
\(551\) 6776.17 + 11736.7i 0.523911 + 0.907440i
\(552\) −17017.3 20121.4i −1.31214 1.55149i
\(553\) 17364.0 30075.4i 1.33525 2.31272i
\(554\) −4017.04 + 6957.72i −0.308065 + 0.533584i
\(555\) 0 0
\(556\) 15313.2 + 26523.3i 1.16803 + 2.02309i
\(557\) 9106.96 0.692773 0.346386 0.938092i \(-0.387409\pi\)
0.346386 + 0.938092i \(0.387409\pi\)
\(558\) 3726.28 + 3077.79i 0.282699 + 0.233500i
\(559\) 9906.09 0.749523
\(560\) 0 0
\(561\) 133.419 24.0592i 0.0100409 0.00181066i
\(562\) 2821.93 4887.73i 0.211808 0.366862i
\(563\) −7355.90 + 12740.8i −0.550647 + 0.953749i 0.447581 + 0.894243i \(0.352286\pi\)
−0.998228 + 0.0595052i \(0.981048\pi\)
\(564\) 11500.1 31981.6i 0.858584 2.38771i
\(565\) 0 0
\(566\) 17912.8 1.33026
\(567\) −16902.5 + 14635.6i −1.25192 + 1.08402i
\(568\) 13315.5 0.983635
\(569\) −986.825 1709.23i −0.0727062 0.125931i 0.827380 0.561642i \(-0.189830\pi\)
−0.900086 + 0.435711i \(0.856497\pi\)
\(570\) 0 0
\(571\) 13097.0 22684.7i 0.959881 1.66256i 0.237101 0.971485i \(-0.423803\pi\)
0.722780 0.691078i \(-0.242864\pi\)
\(572\) −17074.0 + 29573.0i −1.24807 + 2.16173i
\(573\) 8475.59 1528.39i 0.617928 0.111430i
\(574\) 20084.1 + 34786.7i 1.46045 + 2.52957i
\(575\) 0 0
\(576\) 14190.9 + 11721.3i 1.02654 + 0.847892i
\(577\) 8674.57 0.625870 0.312935 0.949775i \(-0.398688\pi\)
0.312935 + 0.949775i \(0.398688\pi\)
\(578\) −11762.8 20373.8i −0.846485 1.46615i
\(579\) −3411.69 4034.02i −0.244879 0.289548i
\(580\) 0 0
\(581\) −8790.27 + 15225.2i −0.627680 + 1.08717i
\(582\) −148.576 175.678i −0.0105819 0.0125122i
\(583\) −4524.73 7837.06i −0.321432 0.556737i
\(584\) −3240.96 −0.229644
\(585\) 0 0
\(586\) 13007.1 0.916923
\(587\) 12191.9 + 21117.0i 0.857263 + 1.48482i 0.874530 + 0.484972i \(0.161170\pi\)
−0.0172666 + 0.999851i \(0.505496\pi\)
\(588\) 45636.1 8229.49i 3.20068 0.577174i
\(589\) −1766.94 + 3060.42i −0.123608 + 0.214096i
\(590\) 0 0
\(591\) −8078.63 + 22466.6i −0.562285 + 1.56371i
\(592\) 5415.15 + 9379.31i 0.375948 + 0.651161i
\(593\) 12980.5 0.898895 0.449447 0.893307i \(-0.351621\pi\)
0.449447 + 0.893307i \(0.351621\pi\)
\(594\) −334.465 28746.8i −0.0231032 1.98568i
\(595\) 0 0
\(596\) 4332.61 + 7504.30i 0.297770 + 0.515752i
\(597\) 1464.17 4071.83i 0.100376 0.279144i
\(598\) −19547.6 + 33857.5i −1.33673 + 2.31528i
\(599\) 12502.4 21654.7i 0.852808 1.47711i −0.0258550 0.999666i \(-0.508231\pi\)
0.878663 0.477442i \(-0.158436\pi\)
\(600\) 0 0
\(601\) −4154.50 7195.81i −0.281973 0.488391i 0.689898 0.723907i \(-0.257655\pi\)
−0.971871 + 0.235516i \(0.924322\pi\)
\(602\) 27224.5 1.84317
\(603\) 24479.9 9125.59i 1.65323 0.616290i
\(604\) −24031.8 −1.61894
\(605\) 0 0
\(606\) −3488.06 4124.32i −0.233816 0.276467i
\(607\) 11891.8 20597.2i 0.795177 1.37729i −0.127549 0.991832i \(-0.540711\pi\)
0.922726 0.385456i \(-0.125956\pi\)
\(608\) −3608.04 + 6249.31i −0.240667 + 0.416847i
\(609\) −14752.0 17442.9i −0.981577 1.16063i
\(610\) 0 0
\(611\) −23408.2 −1.54991
\(612\) 230.347 85.8685i 0.0152144 0.00567162i
\(613\) −13900.8 −0.915903 −0.457951 0.888977i \(-0.651417\pi\)
−0.457951 + 0.888977i \(0.651417\pi\)
\(614\) −10316.5 17868.7i −0.678078 1.17447i
\(615\) 0 0
\(616\) −21784.8 + 37732.4i −1.42489 + 2.46799i
\(617\) −10100.7 + 17495.0i −0.659061 + 1.14153i 0.321798 + 0.946808i \(0.395713\pi\)
−0.980859 + 0.194719i \(0.937621\pi\)
\(618\) −3658.34 + 10173.8i −0.238123 + 0.662218i
\(619\) −5720.45 9908.11i −0.371445 0.643361i 0.618343 0.785908i \(-0.287804\pi\)
−0.989788 + 0.142547i \(0.954471\pi\)
\(620\) 0 0
\(621\) −249.341 21430.5i −0.0161122 1.38482i
\(622\) 30199.2 1.94675
\(623\) −1390.28 2408.04i −0.0894069 0.154857i
\(624\) −3713.67 + 10327.7i −0.238246 + 0.662560i
\(625\) 0 0
\(626\) −11406.0 + 19755.7i −0.728235 + 1.26134i
\(627\) 20687.3 3730.51i 1.31766 0.237611i
\(628\) −1545.23 2676.42i −0.0981869 0.170065i
\(629\) −167.084 −0.0105915
\(630\) 0 0
\(631\) −7670.95 −0.483955 −0.241978 0.970282i \(-0.577796\pi\)
−0.241978 + 0.970282i \(0.577796\pi\)
\(632\) 18795.9 + 32555.5i 1.18301 + 2.04903i
\(633\) −8136.24 9620.38i −0.510879 0.604069i
\(634\) 3502.88 6067.16i 0.219428 0.380060i
\(635\) 0 0
\(636\) −10596.5 12529.4i −0.660656 0.781166i
\(637\) −15969.5 27659.9i −0.993302 1.72045i
\(638\) 29374.0 1.82277
\(639\) 8349.37 + 6896.31i 0.516895 + 0.426938i
\(640\) 0 0
\(641\) −11992.0 20770.7i −0.738930 1.27986i −0.952978 0.303040i \(-0.901998\pi\)
0.214048 0.976823i \(-0.431335\pi\)
\(642\) −4732.48 + 853.401i −0.290928 + 0.0524627i
\(643\) −14295.2 + 24760.1i −0.876747 + 1.51857i −0.0218578 + 0.999761i \(0.506958\pi\)
−0.854890 + 0.518810i \(0.826375\pi\)
\(644\) −34981.1 + 60589.1i −2.14045 + 3.70737i
\(645\) 0 0
\(646\) 138.025 + 239.067i 0.00840640 + 0.0145603i
\(647\) −25703.8 −1.56186 −0.780928 0.624621i \(-0.785254\pi\)
−0.780928 + 0.624621i \(0.785254\pi\)
\(648\) −4571.86 23766.3i −0.277160 1.44079i
\(649\) 21268.8 1.28640
\(650\) 0 0
\(651\) 2015.65 5605.51i 0.121351 0.337476i
\(652\) −15709.4 + 27209.5i −0.943603 + 1.63437i
\(653\) 1821.61 3155.12i 0.109165 0.189080i −0.806267 0.591552i \(-0.798516\pi\)
0.915432 + 0.402472i \(0.131849\pi\)
\(654\) −41707.1 + 7520.98i −2.49370 + 0.449684i
\(655\) 0 0
\(656\) −10809.1 −0.643328
\(657\) −2032.22 1678.55i −0.120677 0.0996750i
\(658\) −64331.8 −3.81142
\(659\) 9705.17 + 16809.9i 0.573687 + 0.993655i 0.996183 + 0.0872904i \(0.0278208\pi\)
−0.422496 + 0.906365i \(0.638846\pi\)
\(660\) 0 0
\(661\) 10613.7 18383.4i 0.624544 1.08174i −0.364085 0.931366i \(-0.618618\pi\)
0.988629 0.150376i \(-0.0480485\pi\)
\(662\) −13832.9 + 23959.2i −0.812130 + 1.40665i
\(663\) −109.337 129.281i −0.00640468 0.00757296i
\(664\) −9515.15 16480.7i −0.556114 0.963217i
\(665\) 0 0
\(666\) −5881.76 + 34939.7i −0.342213 + 2.03286i
\(667\) 21898.1 1.27121
\(668\) 7726.54 + 13382.8i 0.447528 + 0.775141i
\(669\) −15396.2 + 2776.36i −0.889760 + 0.160449i
\(670\) 0 0
\(671\) 4479.50 7758.73i 0.257719 0.446382i
\(672\) 4115.92 11446.3i 0.236272 0.657071i
\(673\) 7116.80 + 12326.7i 0.407626 + 0.706030i 0.994623 0.103560i \(-0.0330233\pi\)
−0.586997 + 0.809589i \(0.699690\pi\)
\(674\) −14067.3 −0.803932
\(675\) 0 0
\(676\) 9841.05 0.559914
\(677\) −8462.10 14656.8i −0.480391 0.832062i 0.519356 0.854558i \(-0.326172\pi\)
−0.999747 + 0.0224963i \(0.992839\pi\)
\(678\) −5132.48 + 14273.4i −0.290725 + 0.808503i
\(679\) −141.793 + 245.592i −0.00801401 + 0.0138807i
\(680\) 0 0
\(681\) 407.255 73.4397i 0.0229164 0.00413247i
\(682\) 3829.75 + 6633.31i 0.215027 + 0.372438i
\(683\) −3582.98 −0.200730 −0.100365 0.994951i \(-0.532001\pi\)
−0.100365 + 0.994951i \(0.532001\pi\)
\(684\) 35716.5 13314.4i 1.99657 0.744281i
\(685\) 0 0
\(686\) −18699.7 32388.8i −1.04075 1.80264i
\(687\) 7771.03 + 9188.54i 0.431562 + 0.510284i
\(688\) −3662.98 + 6344.47i −0.202979 + 0.351571i
\(689\) −5651.03 + 9787.86i −0.312463 + 0.541202i
\(690\) 0 0
\(691\) 8929.12 + 15465.7i 0.491577 + 0.851436i 0.999953 0.00969887i \(-0.00308730\pi\)
−0.508376 + 0.861135i \(0.669754\pi\)
\(692\) 52581.3 2.88850
\(693\) −33202.2 + 12377.1i −1.81998 + 0.678451i
\(694\) −33479.1 −1.83120
\(695\) 0 0
\(696\) 24336.0 4388.46i 1.32536 0.239000i
\(697\) 83.3781 144.415i 0.00453109 0.00784808i
\(698\) −12815.6 + 22197.2i −0.694952 + 1.20369i
\(699\) 3613.44 10048.9i 0.195526 0.543756i
\(700\) 0 0
\(701\) −19796.1 −1.06660 −0.533302 0.845925i \(-0.679049\pi\)
−0.533302 + 0.845925i \(0.679049\pi\)
\(702\) −30883.6 + 18313.0i −1.66044 + 0.984587i
\(703\) −25907.2 −1.38991
\(704\) 14585.0 + 25261.9i 0.780813 + 1.35241i
\(705\) 0 0
\(706\) −2476.18 + 4288.87i −0.132000 + 0.228632i
\(707\) −3328.81 + 5765.68i −0.177076 + 0.306705i
\(708\) 37954.8 6844.32i 2.01473 0.363313i
\(709\) 8145.36 + 14108.2i 0.431460 + 0.747311i 0.996999 0.0774103i \(-0.0246651\pi\)
−0.565539 + 0.824722i \(0.691332\pi\)
\(710\) 0 0
\(711\) −5075.19 + 30148.4i −0.267700 + 1.59023i
\(712\) 3009.86 0.158426
\(713\) 2855.04 + 4945.07i 0.149961 + 0.259740i
\(714\) −300.486 355.298i −0.0157499 0.0186228i
\(715\) 0 0
\(716\) −7180.15 + 12436.4i −0.374769 + 0.649119i
\(717\) 15300.1 + 18091.0i 0.796922 + 0.942289i
\(718\) −18844.8 32640.1i −0.979501 1.69655i
\(719\) −8647.80 −0.448551 −0.224276 0.974526i \(-0.572002\pi\)
−0.224276 + 0.974526i \(0.572002\pi\)
\(720\) 0 0
\(721\) 13325.7 0.688316
\(722\) 4978.37 + 8622.79i 0.256615 + 0.444470i
\(723\) 19908.7 3590.11i 1.02408 0.184672i
\(724\) −11149.8 + 19312.0i −0.572348 + 0.991335i
\(725\) 0 0
\(726\) 4210.10 11708.2i 0.215222 0.598531i
\(727\) −5290.01 9162.56i −0.269870 0.467429i 0.698958 0.715163i \(-0.253647\pi\)
−0.968828 + 0.247734i \(0.920314\pi\)
\(728\) 54414.9 2.77026
\(729\) 9442.23 17270.3i 0.479715 0.877424i
\(730\) 0 0
\(731\) −56.5104 97.8789i −0.00285925 0.00495237i
\(732\) 5497.02 15287.2i 0.277563 0.771898i
\(733\) 14098.7 24419.7i 0.710435 1.23051i −0.254259 0.967136i \(-0.581832\pi\)
0.964694 0.263373i \(-0.0848349\pi\)
\(734\) 31729.9 54957.8i 1.59560 2.76366i
\(735\) 0 0
\(736\) 5829.93 + 10097.7i 0.291975 + 0.505716i
\(737\) 41404.5 2.06941
\(738\) −27264.3 22519.4i −1.35991 1.12324i
\(739\) −27120.4 −1.34998 −0.674992 0.737825i \(-0.735853\pi\)
−0.674992 + 0.737825i \(0.735853\pi\)
\(740\) 0 0
\(741\) −16953.3 20045.8i −0.840479 0.993792i
\(742\) −15530.5 + 26899.6i −0.768384 + 1.33088i
\(743\) 6332.68 10968.5i 0.312683 0.541583i −0.666259 0.745720i \(-0.732106\pi\)
0.978942 + 0.204137i \(0.0654389\pi\)
\(744\) 4163.90 + 4923.44i 0.205183 + 0.242610i
\(745\) 0 0
\(746\) −10007.8 −0.491169
\(747\) 2569.24 15262.2i 0.125841 0.747542i
\(748\) 389.601 0.0190444
\(749\) 2963.54 + 5133.00i 0.144573 + 0.250408i
\(750\) 0 0
\(751\) −4324.63 + 7490.47i −0.210130 + 0.363956i −0.951755 0.306859i \(-0.900722\pi\)
0.741625 + 0.670815i \(0.234055\pi\)
\(752\) 8655.68 14992.1i 0.419734 0.727001i
\(753\) −2743.76 + 7630.37i −0.132787 + 0.369278i
\(754\) −18342.9 31770.9i −0.885955 1.53452i
\(755\) 0 0
\(756\) −55267.2 + 32771.7i −2.65880 + 1.57658i
\(757\) −11715.6 −0.562496 −0.281248 0.959635i \(-0.590748\pi\)
−0.281248 + 0.959635i \(0.590748\pi\)
\(758\) −10050.8 17408.4i −0.481609 0.834172i
\(759\) 11493.2 31962.4i 0.549639 1.52854i
\(760\) 0 0
\(761\) 18256.8 31621.7i 0.869658 1.50629i 0.00731060 0.999973i \(-0.497673\pi\)
0.862347 0.506318i \(-0.168994\pi\)
\(762\) −33606.2 + 6060.15i −1.59767 + 0.288105i
\(763\) 26117.5 + 45236.9i 1.23921 + 2.14638i
\(764\) 24749.9 1.17202
\(765\) 0 0
\(766\) 36937.6 1.74231
\(767\) −13281.5 23004.3i −0.625252 1.08297i
\(768\) 24344.9 + 28785.7i 1.14384 + 1.35249i
\(769\) 11459.8 19848.9i 0.537386 0.930779i −0.461658 0.887058i \(-0.652745\pi\)
0.999044 0.0437213i \(-0.0139214\pi\)
\(770\) 0 0
\(771\) 20769.2 + 24557.8i 0.970150 + 1.14712i
\(772\) −7591.50 13148.9i −0.353917 0.613003i
\(773\) 5112.86 0.237900 0.118950 0.992900i \(-0.462047\pi\)
0.118950 + 0.992900i \(0.462047\pi\)
\(774\) −22457.3 + 8371.59i −1.04291 + 0.388774i
\(775\) 0 0
\(776\) −153.486 265.845i −0.00710028 0.0122980i
\(777\) 42977.5 7750.06i 1.98431 0.357828i
\(778\) 2738.22 4742.74i 0.126182 0.218554i
\(779\) 12928.2 22392.3i 0.594611 1.02990i
\(780\) 0 0
\(781\) 8581.20 + 14863.1i 0.393162 + 0.680976i