Properties

Label 225.4.p.b.68.2
Level $225$
Weight $4$
Character 225.68
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
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.p (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 68.2
Character \(\chi\) \(=\) 225.68
Dual form 225.4.p.b.182.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.15194 + 4.29910i) q^{2} +(2.52446 + 4.54171i) q^{3} +(-10.2271 - 5.90461i) q^{4} +(-22.4333 + 5.62113i) q^{6} +(7.13532 + 1.91190i) q^{7} +(11.9883 - 11.9883i) q^{8} +(-14.2542 + 22.9307i) q^{9} +O(q^{10})\) \(q+(-1.15194 + 4.29910i) q^{2} +(2.52446 + 4.54171i) q^{3} +(-10.2271 - 5.90461i) q^{4} +(-22.4333 + 5.62113i) q^{6} +(7.13532 + 1.91190i) q^{7} +(11.9883 - 11.9883i) q^{8} +(-14.2542 + 22.9307i) q^{9} +(-7.55654 + 4.36277i) q^{11} +(0.999152 - 61.3544i) q^{12} +(-73.7842 + 19.7704i) q^{13} +(-16.4389 + 28.4731i) q^{14} +(-9.50797 - 16.4683i) q^{16} +(5.92131 + 5.92131i) q^{17} +(-82.1614 - 87.6951i) q^{18} -106.718i q^{19} +(9.32953 + 37.2331i) q^{21} +(-10.0513 - 37.5120i) q^{22} +(-27.4553 - 102.465i) q^{23} +(84.7110 + 24.1833i) q^{24} -339.980i q^{26} +(-140.129 - 6.85080i) q^{27} +(-61.6846 - 61.6846i) q^{28} +(85.3380 + 147.810i) q^{29} +(-157.999 + 273.662i) q^{31} +(212.761 - 57.0093i) q^{32} +(-38.8906 - 23.3059i) q^{33} +(-32.2773 + 18.6353i) q^{34} +(281.176 - 150.349i) q^{36} +(31.7091 - 31.7091i) q^{37} +(458.791 + 122.933i) q^{38} +(-276.057 - 285.197i) q^{39} +(298.272 + 172.207i) q^{41} +(-170.816 - 2.78172i) q^{42} +(-115.545 + 431.220i) q^{43} +103.042 q^{44} +472.133 q^{46} +(60.9929 - 227.629i) q^{47} +(50.7917 - 84.7559i) q^{48} +(-249.789 - 144.216i) q^{49} +(-11.9448 + 41.8410i) q^{51} +(871.335 + 233.473i) q^{52} +(60.5508 - 60.5508i) q^{53} +(190.872 - 594.536i) q^{54} +(108.460 - 62.6197i) q^{56} +(484.682 - 269.405i) q^{57} +(-733.754 + 196.609i) q^{58} +(-25.4427 + 44.0680i) q^{59} +(-36.1174 - 62.5572i) q^{61} +(-994.494 - 994.494i) q^{62} +(-145.550 + 136.365i) q^{63} +828.227i q^{64} +(144.994 - 140.347i) q^{66} +(-4.59668 - 17.1550i) q^{67} +(-25.5947 - 95.5208i) q^{68} +(396.055 - 383.362i) q^{69} +109.592i q^{71} +(104.016 + 445.782i) q^{72} +(144.319 + 144.319i) q^{73} +(99.7935 + 172.847i) q^{74} +(-630.128 + 1091.41i) q^{76} +(-62.2595 + 16.6824i) q^{77} +(1544.09 - 858.266i) q^{78} +(-140.624 + 81.1891i) q^{79} +(-322.635 - 653.718i) q^{81} +(-1083.93 + 1083.93i) q^{82} +(-279.860 - 74.9883i) q^{83} +(124.433 - 435.873i) q^{84} +(-1720.76 - 993.479i) q^{86} +(-455.877 + 760.720i) q^{87} +(-38.2877 + 142.892i) q^{88} -1107.89 q^{89} -564.273 q^{91} +(-324.227 + 1210.03i) q^{92} +(-1641.75 - 26.7358i) q^{93} +(908.339 + 524.430i) q^{94} +(796.027 + 822.383i) q^{96} +(197.725 + 52.9802i) q^{97} +(907.741 - 907.741i) q^{98} +(7.67108 - 235.465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} + O(q^{10}) \) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15194 + 4.29910i −0.407272 + 1.51996i 0.392553 + 0.919729i \(0.371592\pi\)
−0.799826 + 0.600232i \(0.795075\pi\)
\(3\) 2.52446 + 4.54171i 0.485832 + 0.874052i
\(4\) −10.2271 5.90461i −1.27839 0.738077i
\(5\) 0 0
\(6\) −22.4333 + 5.62113i −1.52639 + 0.382469i
\(7\) 7.13532 + 1.91190i 0.385271 + 0.103233i 0.446255 0.894906i \(-0.352757\pi\)
−0.0609842 + 0.998139i \(0.519424\pi\)
\(8\) 11.9883 11.9883i 0.529811 0.529811i
\(9\) −14.2542 + 22.9307i −0.527934 + 0.849286i
\(10\) 0 0
\(11\) −7.55654 + 4.36277i −0.207126 + 0.119584i −0.599975 0.800019i \(-0.704823\pi\)
0.392849 + 0.919603i \(0.371489\pi\)
\(12\) 0.999152 61.3544i 0.0240359 1.47596i
\(13\) −73.7842 + 19.7704i −1.57416 + 0.421794i −0.937111 0.349030i \(-0.886511\pi\)
−0.637047 + 0.770825i \(0.719844\pi\)
\(14\) −16.4389 + 28.4731i −0.313821 + 0.543553i
\(15\) 0 0
\(16\) −9.50797 16.4683i −0.148562 0.257317i
\(17\) 5.92131 + 5.92131i 0.0844782 + 0.0844782i 0.748083 0.663605i \(-0.230974\pi\)
−0.663605 + 0.748083i \(0.730974\pi\)
\(18\) −82.1614 87.6951i −1.07587 1.14833i
\(19\) 106.718i 1.28857i −0.764787 0.644284i \(-0.777156\pi\)
0.764787 0.644284i \(-0.222844\pi\)
\(20\) 0 0
\(21\) 9.32953 + 37.2331i 0.0969462 + 0.386901i
\(22\) −10.0513 37.5120i −0.0974066 0.363526i
\(23\) −27.4553 102.465i −0.248906 0.928930i −0.971380 0.237531i \(-0.923662\pi\)
0.722474 0.691398i \(-0.243005\pi\)
\(24\) 84.7110 + 24.1833i 0.720482 + 0.205683i
\(25\) 0 0
\(26\) 339.980i 2.56445i
\(27\) −140.129 6.85080i −0.998807 0.0488310i
\(28\) −61.6846 61.6846i −0.416332 0.416332i
\(29\) 85.3380 + 147.810i 0.546444 + 0.946469i 0.998515 + 0.0544866i \(0.0173522\pi\)
−0.452070 + 0.891982i \(0.649314\pi\)
\(30\) 0 0
\(31\) −157.999 + 273.662i −0.915400 + 1.58552i −0.109085 + 0.994032i \(0.534792\pi\)
−0.806315 + 0.591487i \(0.798541\pi\)
\(32\) 212.761 57.0093i 1.17535 0.314935i
\(33\) −38.8906 23.3059i −0.205151 0.122941i
\(34\) −32.2773 + 18.6353i −0.162809 + 0.0939979i
\(35\) 0 0
\(36\) 281.176 150.349i 1.30174 0.696060i
\(37\) 31.7091 31.7091i 0.140890 0.140890i −0.633144 0.774034i \(-0.718236\pi\)
0.774034 + 0.633144i \(0.218236\pi\)
\(38\) 458.791 + 122.933i 1.95857 + 0.524798i
\(39\) −276.057 285.197i −1.13345 1.17097i
\(40\) 0 0
\(41\) 298.272 + 172.207i 1.13615 + 0.655958i 0.945475 0.325695i \(-0.105598\pi\)
0.190677 + 0.981653i \(0.438932\pi\)
\(42\) −170.816 2.78172i −0.627558 0.0102197i
\(43\) −115.545 + 431.220i −0.409778 + 1.52931i 0.385292 + 0.922795i \(0.374101\pi\)
−0.795070 + 0.606517i \(0.792566\pi\)
\(44\) 103.042 0.353049
\(45\) 0 0
\(46\) 472.133 1.51331
\(47\) 60.9929 227.629i 0.189292 0.706448i −0.804379 0.594117i \(-0.797502\pi\)
0.993671 0.112331i \(-0.0358317\pi\)
\(48\) 50.7917 84.7559i 0.152732 0.254864i
\(49\) −249.789 144.216i −0.728249 0.420454i
\(50\) 0 0
\(51\) −11.9448 + 41.8410i −0.0327961 + 0.114881i
\(52\) 871.335 + 233.473i 2.32370 + 0.622633i
\(53\) 60.5508 60.5508i 0.156930 0.156930i −0.624275 0.781205i \(-0.714605\pi\)
0.781205 + 0.624275i \(0.214605\pi\)
\(54\) 190.872 594.536i 0.481008 1.49826i
\(55\) 0 0
\(56\) 108.460 62.6197i 0.258815 0.149427i
\(57\) 484.682 269.405i 1.12627 0.626028i
\(58\) −733.754 + 196.609i −1.66115 + 0.445103i
\(59\) −25.4427 + 44.0680i −0.0561416 + 0.0972401i −0.892730 0.450591i \(-0.851213\pi\)
0.836589 + 0.547831i \(0.184546\pi\)
\(60\) 0 0
\(61\) −36.1174 62.5572i −0.0758092 0.131305i 0.825629 0.564214i \(-0.190821\pi\)
−0.901438 + 0.432909i \(0.857487\pi\)
\(62\) −994.494 994.494i −2.03711 2.03711i
\(63\) −145.550 + 136.365i −0.291072 + 0.272705i
\(64\) 828.227i 1.61763i
\(65\) 0 0
\(66\) 144.994 140.347i 0.270418 0.261751i
\(67\) −4.59668 17.1550i −0.00838169 0.0312809i 0.961608 0.274426i \(-0.0884877\pi\)
−0.969990 + 0.243145i \(0.921821\pi\)
\(68\) −25.5947 95.5208i −0.0456444 0.170347i
\(69\) 396.055 383.362i 0.691006 0.668861i
\(70\) 0 0
\(71\) 109.592i 0.183185i 0.995797 + 0.0915927i \(0.0291958\pi\)
−0.995797 + 0.0915927i \(0.970804\pi\)
\(72\) 104.016 + 445.782i 0.170256 + 0.729666i
\(73\) 144.319 + 144.319i 0.231387 + 0.231387i 0.813271 0.581885i \(-0.197685\pi\)
−0.581885 + 0.813271i \(0.697685\pi\)
\(74\) 99.7935 + 172.847i 0.156767 + 0.271529i
\(75\) 0 0
\(76\) −630.128 + 1091.41i −0.951062 + 1.64729i
\(77\) −62.2595 + 16.6824i −0.0921446 + 0.0246901i
\(78\) 1544.09 858.266i 2.24146 1.24589i
\(79\) −140.624 + 81.1891i −0.200271 + 0.115626i −0.596782 0.802404i \(-0.703554\pi\)
0.396511 + 0.918030i \(0.370221\pi\)
\(80\) 0 0
\(81\) −322.635 653.718i −0.442572 0.896733i
\(82\) −1083.93 + 1083.93i −1.45975 + 1.45975i
\(83\) −279.860 74.9883i −0.370104 0.0991691i 0.0689728 0.997619i \(-0.478028\pi\)
−0.439077 + 0.898449i \(0.644694\pi\)
\(84\) 124.433 435.873i 0.161628 0.566163i
\(85\) 0 0
\(86\) −1720.76 993.479i −2.15760 1.24569i
\(87\) −455.877 + 760.720i −0.561783 + 0.937446i
\(88\) −38.2877 + 142.892i −0.0463805 + 0.173094i
\(89\) −1107.89 −1.31950 −0.659751 0.751484i \(-0.729338\pi\)
−0.659751 + 0.751484i \(0.729338\pi\)
\(90\) 0 0
\(91\) −564.273 −0.650021
\(92\) −324.227 + 1210.03i −0.367423 + 1.37124i
\(93\) −1641.75 26.7358i −1.83056 0.0298105i
\(94\) 908.339 + 524.430i 0.996681 + 0.575434i
\(95\) 0 0
\(96\) 796.027 + 822.383i 0.846294 + 0.874314i
\(97\) 197.725 + 52.9802i 0.206968 + 0.0554569i 0.360813 0.932638i \(-0.382499\pi\)
−0.153845 + 0.988095i \(0.549166\pi\)
\(98\) 907.741 907.741i 0.935670 0.935670i
\(99\) 7.67108 235.465i 0.00778760 0.239041i
\(100\) 0 0
\(101\) −960.085 + 554.305i −0.945862 + 0.546093i −0.891793 0.452444i \(-0.850552\pi\)
−0.0540686 + 0.998537i \(0.517219\pi\)
\(102\) −166.119 99.5500i −0.161257 0.0966364i
\(103\) 276.457 74.0766i 0.264468 0.0708639i −0.124148 0.992264i \(-0.539620\pi\)
0.388616 + 0.921400i \(0.372953\pi\)
\(104\) −647.531 + 1121.56i −0.610535 + 1.05748i
\(105\) 0 0
\(106\) 190.563 + 330.065i 0.174614 + 0.302441i
\(107\) 864.028 + 864.028i 0.780643 + 0.780643i 0.979939 0.199296i \(-0.0638656\pi\)
−0.199296 + 0.979939i \(0.563866\pi\)
\(108\) 1392.66 + 897.470i 1.24082 + 0.799621i
\(109\) 990.712i 0.870578i 0.900291 + 0.435289i \(0.143354\pi\)
−0.900291 + 0.435289i \(0.856646\pi\)
\(110\) 0 0
\(111\) 224.062 + 63.9651i 0.191595 + 0.0546964i
\(112\) −36.3567 135.685i −0.0306730 0.114473i
\(113\) −19.6119 73.1927i −0.0163269 0.0609327i 0.957282 0.289157i \(-0.0933748\pi\)
−0.973609 + 0.228224i \(0.926708\pi\)
\(114\) 599.875 + 2394.03i 0.492837 + 1.96686i
\(115\) 0 0
\(116\) 2015.55i 1.61327i
\(117\) 598.386 1973.74i 0.472827 1.55959i
\(118\) −160.144 160.144i −0.124936 0.124936i
\(119\) 30.9295 + 53.5714i 0.0238261 + 0.0412679i
\(120\) 0 0
\(121\) −627.432 + 1086.74i −0.471399 + 0.816488i
\(122\) 310.545 83.2102i 0.230454 0.0617500i
\(123\) −29.1401 + 1789.39i −0.0213616 + 1.31174i
\(124\) 3231.73 1865.84i 2.34047 1.35127i
\(125\) 0 0
\(126\) −418.584 782.818i −0.295956 0.553484i
\(127\) −1084.18 + 1084.18i −0.757521 + 0.757521i −0.975871 0.218350i \(-0.929933\pi\)
0.218350 + 0.975871i \(0.429933\pi\)
\(128\) −1858.54 497.994i −1.28338 0.343882i
\(129\) −2250.16 + 563.825i −1.53578 + 0.384822i
\(130\) 0 0
\(131\) 1415.36 + 817.157i 0.943972 + 0.545003i 0.891203 0.453604i \(-0.149862\pi\)
0.0527689 + 0.998607i \(0.483195\pi\)
\(132\) 260.125 + 467.986i 0.171523 + 0.308583i
\(133\) 204.035 761.467i 0.133023 0.496448i
\(134\) 79.0463 0.0509594
\(135\) 0 0
\(136\) 141.972 0.0895149
\(137\) −591.988 + 2209.33i −0.369175 + 1.37778i 0.492497 + 0.870314i \(0.336084\pi\)
−0.861672 + 0.507465i \(0.830583\pi\)
\(138\) 1191.88 + 2144.29i 0.735215 + 1.32271i
\(139\) −1895.18 1094.18i −1.15645 0.667678i −0.206001 0.978552i \(-0.566045\pi\)
−0.950451 + 0.310874i \(0.899378\pi\)
\(140\) 0 0
\(141\) 1187.80 297.627i 0.709437 0.177764i
\(142\) −471.146 126.243i −0.278435 0.0746063i
\(143\) 471.299 471.299i 0.275609 0.275609i
\(144\) 513.158 + 16.7179i 0.296967 + 0.00967471i
\(145\) 0 0
\(146\) −786.687 + 454.194i −0.445936 + 0.257461i
\(147\) 24.4035 1498.54i 0.0136923 0.840797i
\(148\) −511.522 + 137.062i −0.284100 + 0.0761244i
\(149\) 311.430 539.412i 0.171230 0.296580i −0.767620 0.640905i \(-0.778559\pi\)
0.938850 + 0.344326i \(0.111892\pi\)
\(150\) 0 0
\(151\) −1009.02 1747.68i −0.543795 0.941881i −0.998682 0.0513314i \(-0.983654\pi\)
0.454887 0.890549i \(-0.349680\pi\)
\(152\) −1279.36 1279.36i −0.682697 0.682697i
\(153\) −220.183 + 51.3763i −0.116345 + 0.0271472i
\(154\) 286.877i 0.150112i
\(155\) 0 0
\(156\) 1139.28 + 4546.74i 0.584715 + 2.33353i
\(157\) −182.444 680.891i −0.0927428 0.346121i 0.903925 0.427692i \(-0.140673\pi\)
−0.996668 + 0.0815706i \(0.974006\pi\)
\(158\) −187.050 698.080i −0.0941829 0.351495i
\(159\) 427.862 + 122.146i 0.213407 + 0.0609233i
\(160\) 0 0
\(161\) 783.611i 0.383585i
\(162\) 3182.06 633.996i 1.54325 0.307478i
\(163\) 426.426 + 426.426i 0.204909 + 0.204909i 0.802100 0.597190i \(-0.203716\pi\)
−0.597190 + 0.802100i \(0.703716\pi\)
\(164\) −2033.64 3522.36i −0.968294 1.67714i
\(165\) 0 0
\(166\) 644.765 1116.77i 0.301467 0.522155i
\(167\) −613.477 + 164.381i −0.284265 + 0.0761686i −0.398134 0.917327i \(-0.630342\pi\)
0.113869 + 0.993496i \(0.463676\pi\)
\(168\) 558.204 + 334.515i 0.256348 + 0.153621i
\(169\) 3150.58 1818.99i 1.43404 0.827943i
\(170\) 0 0
\(171\) 2447.12 + 1521.18i 1.09436 + 0.680278i
\(172\) 3727.88 3727.88i 1.65260 1.65260i
\(173\) −686.713 184.004i −0.301791 0.0808646i 0.104746 0.994499i \(-0.466597\pi\)
−0.406537 + 0.913634i \(0.633264\pi\)
\(174\) −2745.27 2836.16i −1.19608 1.23568i
\(175\) 0 0
\(176\) 143.695 + 82.9622i 0.0615420 + 0.0355313i
\(177\) −264.373 4.30529i −0.112268 0.00182828i
\(178\) 1276.22 4762.91i 0.537397 2.00559i
\(179\) 2690.52 1.12346 0.561730 0.827321i \(-0.310136\pi\)
0.561730 + 0.827321i \(0.310136\pi\)
\(180\) 0 0
\(181\) 197.441 0.0810810 0.0405405 0.999178i \(-0.487092\pi\)
0.0405405 + 0.999178i \(0.487092\pi\)
\(182\) 650.009 2425.87i 0.264736 0.988007i
\(183\) 192.939 321.958i 0.0779371 0.130054i
\(184\) −1557.52 899.232i −0.624030 0.360284i
\(185\) 0 0
\(186\) 2006.14 7027.26i 0.790846 2.77023i
\(187\) −70.5779 18.9113i −0.0275998 0.00739535i
\(188\) −1967.84 + 1967.84i −0.763402 + 0.763402i
\(189\) −986.766 316.795i −0.379771 0.121923i
\(190\) 0 0
\(191\) 306.085 176.718i 0.115956 0.0669470i −0.440900 0.897556i \(-0.645341\pi\)
0.556856 + 0.830609i \(0.312007\pi\)
\(192\) −3761.56 + 2090.82i −1.41389 + 0.785897i
\(193\) −1387.59 + 371.803i −0.517517 + 0.138668i −0.508118 0.861287i \(-0.669659\pi\)
−0.00939936 + 0.999956i \(0.502992\pi\)
\(194\) −455.534 + 789.008i −0.168585 + 0.291997i
\(195\) 0 0
\(196\) 1703.08 + 2949.82i 0.620655 + 1.07501i
\(197\) 2647.40 + 2647.40i 0.957458 + 0.957458i 0.999131 0.0416736i \(-0.0132690\pi\)
−0.0416736 + 0.999131i \(0.513269\pi\)
\(198\) 1003.45 + 304.220i 0.360162 + 0.109192i
\(199\) 3785.65i 1.34853i 0.738488 + 0.674266i \(0.235540\pi\)
−0.738488 + 0.674266i \(0.764460\pi\)
\(200\) 0 0
\(201\) 66.3090 64.1839i 0.0232690 0.0225233i
\(202\) −1277.05 4766.03i −0.444818 1.66008i
\(203\) 326.316 + 1217.83i 0.112822 + 0.421058i
\(204\) 369.215 357.382i 0.126717 0.122656i
\(205\) 0 0
\(206\) 1273.85i 0.430842i
\(207\) 2740.94 + 830.983i 0.920332 + 0.279021i
\(208\) 1027.12 + 1027.12i 0.342395 + 0.342395i
\(209\) 465.586 + 806.418i 0.154092 + 0.266895i
\(210\) 0 0
\(211\) 676.890 1172.41i 0.220849 0.382521i −0.734217 0.678915i \(-0.762451\pi\)
0.955066 + 0.296394i \(0.0957840\pi\)
\(212\) −976.788 + 261.730i −0.316444 + 0.0847908i
\(213\) −497.734 + 276.660i −0.160114 + 0.0889974i
\(214\) −4709.85 + 2719.24i −1.50448 + 0.868613i
\(215\) 0 0
\(216\) −1762.03 + 1597.77i −0.555050 + 0.503308i
\(217\) −1650.59 + 1650.59i −0.516355 + 0.516355i
\(218\) −4259.17 1141.24i −1.32325 0.354563i
\(219\) −291.126 + 1019.78i −0.0898288 + 0.314659i
\(220\) 0 0
\(221\) −553.966 319.832i −0.168614 0.0973496i
\(222\) −533.098 + 889.579i −0.161168 + 0.268940i
\(223\) −508.185 + 1896.57i −0.152604 + 0.569525i 0.846695 + 0.532079i \(0.178589\pi\)
−0.999299 + 0.0374461i \(0.988078\pi\)
\(224\) 1627.12 0.485341
\(225\) 0 0
\(226\) 337.255 0.0992648
\(227\) 816.800 3048.34i 0.238823 0.891301i −0.737564 0.675277i \(-0.764024\pi\)
0.976388 0.216025i \(-0.0693092\pi\)
\(228\) −6547.62 106.627i −1.90187 0.0309718i
\(229\) 3455.23 + 1994.88i 0.997066 + 0.575656i 0.907379 0.420314i \(-0.138080\pi\)
0.0896872 + 0.995970i \(0.471413\pi\)
\(230\) 0 0
\(231\) −232.938 240.651i −0.0663472 0.0685439i
\(232\) 2795.04 + 748.928i 0.790962 + 0.211937i
\(233\) 2166.38 2166.38i 0.609118 0.609118i −0.333598 0.942715i \(-0.608263\pi\)
0.942715 + 0.333598i \(0.108263\pi\)
\(234\) 7795.98 + 4846.15i 2.17795 + 1.35386i
\(235\) 0 0
\(236\) 520.409 300.458i 0.143541 0.0828736i
\(237\) −723.736 433.713i −0.198362 0.118872i
\(238\) −265.938 + 71.2579i −0.0724294 + 0.0194074i
\(239\) −1946.01 + 3370.59i −0.526682 + 0.912239i 0.472835 + 0.881151i \(0.343231\pi\)
−0.999517 + 0.0310884i \(0.990103\pi\)
\(240\) 0 0
\(241\) −3291.66 5701.33i −0.879812 1.52388i −0.851547 0.524278i \(-0.824335\pi\)
−0.0282647 0.999600i \(-0.508998\pi\)
\(242\) −3949.26 3949.26i −1.04904 1.04904i
\(243\) 2154.52 3115.60i 0.568775 0.822493i
\(244\) 853.037i 0.223812i
\(245\) 0 0
\(246\) −7659.22 2186.55i −1.98510 0.566705i
\(247\) 2109.86 + 7874.10i 0.543511 + 2.02841i
\(248\) 1386.60 + 5174.85i 0.355036 + 1.32501i
\(249\) −365.921 1460.35i −0.0931297 0.371670i
\(250\) 0 0
\(251\) 6323.18i 1.59010i 0.606543 + 0.795051i \(0.292556\pi\)
−0.606543 + 0.795051i \(0.707444\pi\)
\(252\) 2293.74 535.206i 0.573380 0.133789i
\(253\) 654.497 + 654.497i 0.162640 + 0.162640i
\(254\) −3412.08 5909.89i −0.842885 1.45992i
\(255\) 0 0
\(256\) 968.943 1678.26i 0.236558 0.409731i
\(257\) 1363.16 365.257i 0.330861 0.0886541i −0.0895642 0.995981i \(-0.528547\pi\)
0.420426 + 0.907327i \(0.361881\pi\)
\(258\) 168.112 10323.2i 0.0405666 2.49106i
\(259\) 286.879 165.630i 0.0688255 0.0397364i
\(260\) 0 0
\(261\) −4605.81 150.050i −1.09231 0.0355857i
\(262\) −5143.45 + 5143.45i −1.21284 + 1.21284i
\(263\) −317.317 85.0248i −0.0743977 0.0199348i 0.221428 0.975177i \(-0.428928\pi\)
−0.295826 + 0.955242i \(0.595595\pi\)
\(264\) −745.628 + 186.833i −0.173827 + 0.0435559i
\(265\) 0 0
\(266\) 3038.59 + 1754.33i 0.700405 + 0.404379i
\(267\) −2796.81 5031.70i −0.641057 1.15331i
\(268\) −54.2832 + 202.588i −0.0123727 + 0.0461754i
\(269\) 764.226 0.173218 0.0866091 0.996242i \(-0.472397\pi\)
0.0866091 + 0.996242i \(0.472397\pi\)
\(270\) 0 0
\(271\) 4645.09 1.04121 0.520607 0.853797i \(-0.325706\pi\)
0.520607 + 0.853797i \(0.325706\pi\)
\(272\) 41.2142 153.813i 0.00918742 0.0342879i
\(273\) −1424.49 2562.76i −0.315801 0.568152i
\(274\) −8816.19 5090.03i −1.94382 1.12226i
\(275\) 0 0
\(276\) −6314.10 + 1582.13i −1.37704 + 0.345047i
\(277\) −5783.77 1549.76i −1.25456 0.336158i −0.430463 0.902608i \(-0.641650\pi\)
−0.824096 + 0.566450i \(0.808316\pi\)
\(278\) 6887.13 6887.13i 1.48584 1.48584i
\(279\) −4023.11 7523.85i −0.863288 1.61448i
\(280\) 0 0
\(281\) 4201.11 2425.51i 0.891877 0.514925i 0.0173209 0.999850i \(-0.494486\pi\)
0.874556 + 0.484925i \(0.161153\pi\)
\(282\) −88.7415 + 5449.31i −0.0187393 + 1.15071i
\(283\) 345.530 92.5845i 0.0725782 0.0194473i −0.222347 0.974968i \(-0.571372\pi\)
0.294925 + 0.955520i \(0.404705\pi\)
\(284\) 647.098 1120.81i 0.135205 0.234182i
\(285\) 0 0
\(286\) 1483.25 + 2569.07i 0.306667 + 0.531162i
\(287\) 1799.02 + 1799.02i 0.370010 + 0.370010i
\(288\) −1725.48 + 5691.39i −0.353039 + 1.16447i
\(289\) 4842.88i 0.985727i
\(290\) 0 0
\(291\) 258.528 + 1031.75i 0.0520796 + 0.207844i
\(292\) −623.814 2328.11i −0.125020 0.466582i
\(293\) 2206.15 + 8233.45i 0.439879 + 1.64165i 0.729114 + 0.684392i \(0.239932\pi\)
−0.289236 + 0.957258i \(0.593401\pi\)
\(294\) 6414.25 + 1831.14i 1.27240 + 0.363245i
\(295\) 0 0
\(296\) 760.273i 0.149290i
\(297\) 1088.78 559.581i 0.212718 0.109327i
\(298\) 1960.24 + 1960.24i 0.381052 + 0.381052i
\(299\) 4051.54 + 7017.48i 0.783635 + 1.35730i
\(300\) 0 0
\(301\) −1648.90 + 2855.98i −0.315751 + 0.546897i
\(302\) 8675.77 2324.67i 1.65310 0.442946i
\(303\) −4941.19 2961.10i −0.936844 0.561422i
\(304\) −1757.46 + 1014.67i −0.331570 + 0.191432i
\(305\) 0 0
\(306\) 32.7665 1005.77i 0.00612137 0.187896i
\(307\) 6239.03 6239.03i 1.15987 1.15987i 0.175367 0.984503i \(-0.443889\pi\)
0.984503 0.175367i \(-0.0561111\pi\)
\(308\) 735.237 + 197.006i 0.136020 + 0.0364463i
\(309\) 1034.34 + 1068.59i 0.190426 + 0.196730i
\(310\) 0 0
\(311\) −1983.11 1144.95i −0.361582 0.208760i 0.308192 0.951324i \(-0.400276\pi\)
−0.669775 + 0.742565i \(0.733609\pi\)
\(312\) −6728.45 109.572i −1.22091 0.0198824i
\(313\) −1583.94 + 5911.34i −0.286037 + 1.06750i 0.662042 + 0.749467i \(0.269690\pi\)
−0.948079 + 0.318036i \(0.896977\pi\)
\(314\) 3137.38 0.563862
\(315\) 0 0
\(316\) 1917.56 0.341365
\(317\) −2327.37 + 8685.87i −0.412361 + 1.53895i 0.377704 + 0.925927i \(0.376714\pi\)
−0.790064 + 0.613024i \(0.789953\pi\)
\(318\) −1017.99 + 1698.72i −0.179516 + 0.299558i
\(319\) −1289.72 744.620i −0.226365 0.130692i
\(320\) 0 0
\(321\) −1742.96 + 6105.37i −0.303061 + 1.06158i
\(322\) 3368.82 + 902.673i 0.583035 + 0.156224i
\(323\) 631.910 631.910i 0.108856 0.108856i
\(324\) −560.337 + 8590.67i −0.0960797 + 1.47302i
\(325\) 0 0
\(326\) −2324.46 + 1342.03i −0.394909 + 0.228001i
\(327\) −4499.53 + 2501.01i −0.760931 + 0.422955i
\(328\) 5640.22 1511.29i 0.949479 0.254412i
\(329\) 870.409 1507.59i 0.145858 0.252633i
\(330\) 0 0
\(331\) 368.018 + 637.425i 0.0611120 + 0.105849i 0.894963 0.446141i \(-0.147202\pi\)
−0.833851 + 0.551990i \(0.813869\pi\)
\(332\) 2419.38 + 2419.38i 0.399942 + 0.399942i
\(333\) 275.124 + 1179.10i 0.0452754 + 0.194037i
\(334\) 2826.75i 0.463093i
\(335\) 0 0
\(336\) 524.460 507.652i 0.0851537 0.0824247i
\(337\) −1168.46 4360.75i −0.188873 0.704883i −0.993768 0.111466i \(-0.964445\pi\)
0.804896 0.593417i \(-0.202221\pi\)
\(338\) 4190.74 + 15640.0i 0.674396 + 2.51688i
\(339\) 282.910 273.844i 0.0453262 0.0438736i
\(340\) 0 0
\(341\) 2757.25i 0.437869i
\(342\) −9358.64 + 8768.10i −1.47970 + 1.38633i
\(343\) −3298.23 3298.23i −0.519207 0.519207i
\(344\) 3784.39 + 6554.76i 0.593141 + 1.02735i
\(345\) 0 0
\(346\) 1582.11 2740.29i 0.245822 0.425777i
\(347\) 3929.82 1052.99i 0.607964 0.162904i 0.0583140 0.998298i \(-0.481428\pi\)
0.549651 + 0.835395i \(0.314761\pi\)
\(348\) 9154.05 5088.18i 1.41008 0.783779i
\(349\) −2120.49 + 1224.26i −0.325235 + 0.187775i −0.653724 0.756733i \(-0.726794\pi\)
0.328489 + 0.944508i \(0.393461\pi\)
\(350\) 0 0
\(351\) 10474.7 2264.92i 1.59288 0.344424i
\(352\) −1359.02 + 1359.02i −0.205784 + 0.205784i
\(353\) 10497.9 + 2812.90i 1.58285 + 0.424123i 0.939807 0.341707i \(-0.111005\pi\)
0.643043 + 0.765830i \(0.277672\pi\)
\(354\) 323.051 1131.61i 0.0485027 0.169899i
\(355\) 0 0
\(356\) 11330.5 + 6541.64i 1.68683 + 0.973894i
\(357\) −165.226 + 275.712i −0.0244949 + 0.0408745i
\(358\) −3099.32 + 11566.8i −0.457554 + 1.70762i
\(359\) 6928.63 1.01861 0.509303 0.860587i \(-0.329903\pi\)
0.509303 + 0.860587i \(0.329903\pi\)
\(360\) 0 0
\(361\) −4529.72 −0.660406
\(362\) −227.440 + 848.818i −0.0330221 + 0.123240i
\(363\) −6519.61 106.171i −0.942674 0.0153514i
\(364\) 5770.88 + 3331.82i 0.830978 + 0.479766i
\(365\) 0 0
\(366\) 1161.87 + 1200.34i 0.165935 + 0.171429i
\(367\) 9084.65 + 2434.22i 1.29214 + 0.346227i 0.838472 0.544944i \(-0.183449\pi\)
0.453666 + 0.891172i \(0.350116\pi\)
\(368\) −1426.37 + 1426.37i −0.202051 + 0.202051i
\(369\) −8200.47 + 4384.91i −1.15691 + 0.618615i
\(370\) 0 0
\(371\) 547.817 316.282i 0.0766610 0.0442603i
\(372\) 16632.5 + 9967.34i 2.31816 + 1.38920i
\(373\) 5601.71 1500.97i 0.777602 0.208358i 0.151875 0.988400i \(-0.451469\pi\)
0.625727 + 0.780042i \(0.284802\pi\)
\(374\) 162.603 281.637i 0.0224813 0.0389388i
\(375\) 0 0
\(376\) −1997.67 3460.07i −0.273995 0.474573i
\(377\) −9218.86 9218.86i −1.25940 1.25940i
\(378\) 2498.63 3877.28i 0.339989 0.527581i
\(379\) 6617.31i 0.896856i −0.893819 0.448428i \(-0.851984\pi\)
0.893819 0.448428i \(-0.148016\pi\)
\(380\) 0 0
\(381\) −7660.97 2187.05i −1.03014 0.294084i
\(382\) 407.137 + 1519.46i 0.0545313 + 0.203514i
\(383\) −3218.73 12012.4i −0.429423 1.60263i −0.754070 0.656795i \(-0.771912\pi\)
0.324646 0.945836i \(-0.394755\pi\)
\(384\) −2430.06 9698.10i −0.322939 1.28881i
\(385\) 0 0
\(386\) 6393.68i 0.843082i
\(387\) −8241.18 8796.23i −1.08249 1.15539i
\(388\) −1709.32 1709.32i −0.223654 0.223654i
\(389\) −4995.39 8652.28i −0.651096 1.12773i −0.982857 0.184369i \(-0.940976\pi\)
0.331761 0.943364i \(-0.392357\pi\)
\(390\) 0 0
\(391\) 444.154 769.297i 0.0574471 0.0995014i
\(392\) −4723.43 + 1265.64i −0.608595 + 0.163073i
\(393\) −138.276 + 8491.02i −0.0177483 + 1.08986i
\(394\) −14431.1 + 8331.78i −1.84524 + 1.06535i
\(395\) 0 0
\(396\) −1468.78 + 2362.82i −0.186386 + 0.299839i
\(397\) −1248.70 + 1248.70i −0.157860 + 0.157860i −0.781618 0.623758i \(-0.785605\pi\)
0.623758 + 0.781618i \(0.285605\pi\)
\(398\) −16274.9 4360.85i −2.04972 0.549220i
\(399\) 3973.44 995.628i 0.498548 0.124922i
\(400\) 0 0
\(401\) 7999.65 + 4618.60i 0.996218 + 0.575166i 0.907127 0.420857i \(-0.138271\pi\)
0.0890905 + 0.996024i \(0.471604\pi\)
\(402\) 199.549 + 359.005i 0.0247577 + 0.0445412i
\(403\) 6247.40 23315.6i 0.772221 2.88197i
\(404\) 13091.8 1.61224
\(405\) 0 0
\(406\) −5611.47 −0.685942
\(407\) −101.271 + 377.950i −0.0123338 + 0.0460302i
\(408\) 358.403 + 644.797i 0.0434892 + 0.0782407i
\(409\) 2817.50 + 1626.68i 0.340626 + 0.196661i 0.660549 0.750783i \(-0.270324\pi\)
−0.319923 + 0.947444i \(0.603657\pi\)
\(410\) 0 0
\(411\) −11528.6 + 2888.73i −1.38361 + 0.346692i
\(412\) −3264.75 874.787i −0.390395 0.104606i
\(413\) −265.796 + 265.796i −0.0316681 + 0.0316681i
\(414\) −6729.89 + 10826.3i −0.798927 + 1.28523i
\(415\) 0 0
\(416\) −14571.3 + 8412.77i −1.71735 + 0.991514i
\(417\) 185.152 11369.6i 0.0217433 1.33518i
\(418\) −4003.20 + 1072.65i −0.468428 + 0.125515i
\(419\) −1840.03 + 3187.02i −0.214537 + 0.371590i −0.953129 0.302563i \(-0.902158\pi\)
0.738592 + 0.674153i \(0.235491\pi\)
\(420\) 0 0
\(421\) −3430.26 5941.39i −0.397104 0.687804i 0.596263 0.802789i \(-0.296651\pi\)
−0.993367 + 0.114985i \(0.963318\pi\)
\(422\) 4260.56 + 4260.56i 0.491472 + 0.491472i
\(423\) 4350.28 + 4643.28i 0.500043 + 0.533721i
\(424\) 1451.80i 0.166287i
\(425\) 0 0
\(426\) −616.030 2458.50i −0.0700628 0.279613i
\(427\) −138.106 515.419i −0.0156520 0.0584142i
\(428\) −3734.74 13938.3i −0.421789 1.57414i
\(429\) 3330.28 + 950.728i 0.374796 + 0.106997i
\(430\) 0 0
\(431\) 3116.28i 0.348273i 0.984722 + 0.174137i \(0.0557134\pi\)
−0.984722 + 0.174137i \(0.944287\pi\)
\(432\) 1219.52 + 2372.82i 0.135820 + 0.264264i
\(433\) −526.507 526.507i −0.0584349 0.0584349i 0.677285 0.735720i \(-0.263156\pi\)
−0.735720 + 0.677285i \(0.763156\pi\)
\(434\) −5194.66 8997.41i −0.574543 0.995137i
\(435\) 0 0
\(436\) 5849.77 10132.1i 0.642554 1.11294i
\(437\) −10934.8 + 2929.98i −1.19699 + 0.320732i
\(438\) −4048.77 2426.31i −0.441685 0.264688i
\(439\) 3213.40 1855.26i 0.349356 0.201701i −0.315046 0.949076i \(-0.602020\pi\)
0.664401 + 0.747376i \(0.268687\pi\)
\(440\) 0 0
\(441\) 6867.52 3672.16i 0.741553 0.396519i
\(442\) 2013.13 2013.13i 0.216640 0.216640i
\(443\) 1898.77 + 508.773i 0.203641 + 0.0545655i 0.359198 0.933261i \(-0.383050\pi\)
−0.155556 + 0.987827i \(0.549717\pi\)
\(444\) −1913.81 1977.17i −0.204562 0.211335i
\(445\) 0 0
\(446\) −7568.16 4369.48i −0.803504 0.463903i
\(447\) 3236.05 + 52.6987i 0.342415 + 0.00557621i
\(448\) −1583.49 + 5909.67i −0.166993 + 0.623226i
\(449\) −6556.48 −0.689131 −0.344565 0.938762i \(-0.611974\pi\)
−0.344565 + 0.938762i \(0.611974\pi\)
\(450\) 0 0
\(451\) −3005.20 −0.313768
\(452\) −231.602 + 864.350i −0.0241010 + 0.0899460i
\(453\) 5390.20 8994.62i 0.559059 0.932901i
\(454\) 12164.2 + 7023.01i 1.25748 + 0.726005i
\(455\) 0 0
\(456\) 2580.79 9040.18i 0.265036 0.928389i
\(457\) −12355.7 3310.69i −1.26471 0.338879i −0.436710 0.899603i \(-0.643856\pi\)
−0.828003 + 0.560724i \(0.810523\pi\)
\(458\) −12556.4 + 12556.4i −1.28105 + 1.28105i
\(459\) −789.180 870.311i −0.0802522 0.0885025i
\(460\) 0 0
\(461\) −1996.02 + 1152.40i −0.201657 + 0.116427i −0.597428 0.801922i \(-0.703811\pi\)
0.395771 + 0.918349i \(0.370477\pi\)
\(462\) 1302.91 724.210i 0.131206 0.0729292i
\(463\) 1195.40 320.306i 0.119989 0.0321509i −0.198325 0.980136i \(-0.563550\pi\)
0.318314 + 0.947985i \(0.396883\pi\)
\(464\) 1622.78 2810.74i 0.162362 0.281219i
\(465\) 0 0
\(466\) 6817.95 + 11809.0i 0.677759 + 1.17391i
\(467\) −3769.54 3769.54i −0.373519 0.373519i 0.495238 0.868757i \(-0.335081\pi\)
−0.868757 + 0.495238i \(0.835081\pi\)
\(468\) −17773.9 + 16652.3i −1.75555 + 1.64478i
\(469\) 131.195i 0.0129169i
\(470\) 0 0
\(471\) 2631.83 2547.49i 0.257470 0.249219i
\(472\) 223.285 + 833.312i 0.0217744 + 0.0812633i
\(473\) −1008.19 3762.63i −0.0980058 0.365763i
\(474\) 2698.28 2611.80i 0.261468 0.253089i
\(475\) 0 0
\(476\) 730.507i 0.0703419i
\(477\) 525.369 + 2251.58i 0.0504298 + 0.216127i
\(478\) −12248.8 12248.8i −1.17207 1.17207i
\(479\) −1205.53 2088.04i −0.114994 0.199175i 0.802783 0.596271i \(-0.203352\pi\)
−0.917777 + 0.397096i \(0.870018\pi\)
\(480\) 0 0
\(481\) −1712.73 + 2966.53i −0.162357 + 0.281210i
\(482\) 28302.4 7583.60i 2.67456 0.716646i
\(483\) 3558.93 1978.19i 0.335273 0.186358i
\(484\) 12833.6 7409.49i 1.20526 0.695858i
\(485\) 0 0
\(486\) 10912.4 + 12851.5i 1.01851 + 1.19950i
\(487\) 13278.0 13278.0i 1.23549 1.23549i 0.273666 0.961825i \(-0.411764\pi\)
0.961825 0.273666i \(-0.0882362\pi\)
\(488\) −1182.94 316.967i −0.109732 0.0294025i
\(489\) −860.207 + 3013.20i −0.0795499 + 0.278653i
\(490\) 0 0
\(491\) −4882.30 2818.80i −0.448748 0.259085i 0.258553 0.965997i \(-0.416754\pi\)
−0.707301 + 0.706912i \(0.750088\pi\)
\(492\) 10863.7 18128.2i 0.995474 1.66115i
\(493\) −369.915 + 1380.54i −0.0337934 + 0.126119i
\(494\) −36282.0 −3.30446
\(495\) 0 0
\(496\) 6008.99 0.543975
\(497\) −209.529 + 781.973i −0.0189108 + 0.0705760i
\(498\) 6699.70 + 109.104i 0.602853 + 0.00981741i
\(499\) 5518.24 + 3185.96i 0.495051 + 0.285818i 0.726667 0.686990i \(-0.241068\pi\)
−0.231617 + 0.972807i \(0.574402\pi\)
\(500\) 0 0
\(501\) −2295.27 2371.26i −0.204680 0.211457i
\(502\) −27184.0 7283.92i −2.41689 0.647604i
\(503\) −5861.56 + 5861.56i −0.519591 + 0.519591i −0.917448 0.397857i \(-0.869754\pi\)
0.397857 + 0.917448i \(0.369754\pi\)
\(504\) −110.104 + 3379.67i −0.00973104 + 0.298695i
\(505\) 0 0
\(506\) −3567.69 + 2059.81i −0.313445 + 0.180968i
\(507\) 16214.8 + 9717.06i 1.42037 + 0.851183i
\(508\) 17489.6 4686.33i 1.52751 0.409296i
\(509\) −10716.8 + 18562.0i −0.933228 + 1.61640i −0.155465 + 0.987841i \(0.549688\pi\)
−0.777763 + 0.628557i \(0.783646\pi\)
\(510\) 0 0
\(511\) 753.837 + 1305.68i 0.0652598 + 0.113033i
\(512\) −4785.52 4785.52i −0.413070 0.413070i
\(513\) −731.103 + 14954.3i −0.0629220 + 1.28703i
\(514\) 6281.10i 0.539003i
\(515\) 0 0
\(516\) 26341.8 + 7520.05i 2.24735 + 0.641573i
\(517\) 532.196 + 1986.18i 0.0452727 + 0.168960i
\(518\) 381.591 + 1424.12i 0.0323671 + 0.120796i
\(519\) −897.886 3583.36i −0.0759399 0.303068i
\(520\) 0 0
\(521\) 18398.8i 1.54715i −0.633703 0.773577i \(-0.718466\pi\)
0.633703 0.773577i \(-0.281534\pi\)
\(522\) 5950.70 19628.0i 0.498956 1.64577i
\(523\) 12039.3 + 12039.3i 1.00658 + 1.00658i 0.999978 + 0.00659910i \(0.00210057\pi\)
0.00659910 + 0.999978i \(0.497899\pi\)
\(524\) −9649.99 16714.3i −0.804508 1.39345i
\(525\) 0 0
\(526\) 731.060 1266.23i 0.0606003 0.104963i
\(527\) −2555.99 + 684.877i −0.211273 + 0.0566104i
\(528\) −14.0385 + 862.054i −0.00115709 + 0.0710532i
\(529\) 791.700 457.088i 0.0650695 0.0375679i
\(530\) 0 0
\(531\) −647.846 1211.57i −0.0529456 0.0990166i
\(532\) −6582.85 + 6582.85i −0.536471 + 0.536471i
\(533\) −25412.4 6809.22i −2.06516 0.553359i
\(534\) 24853.5 6227.57i 2.01408 0.504669i
\(535\) 0 0
\(536\) −260.765 150.553i −0.0210137 0.0121322i
\(537\) 6792.12 + 12219.6i 0.545813 + 0.981962i
\(538\) −880.343 + 3285.49i −0.0705470 + 0.263285i
\(539\) 2516.72 0.201119
\(540\) 0 0
\(541\) 11737.9 0.932811 0.466405 0.884571i \(-0.345549\pi\)
0.466405 + 0.884571i \(0.345549\pi\)
\(542\) −5350.86 + 19969.7i −0.424058 + 1.58260i
\(543\) 498.431 + 896.719i 0.0393918 + 0.0708690i
\(544\) 1597.40 + 922.257i 0.125897 + 0.0726865i
\(545\) 0 0
\(546\) 12658.5 3171.85i 0.992187 0.248613i
\(547\) 8392.40 + 2248.74i 0.656002 + 0.175775i 0.571441 0.820643i \(-0.306385\pi\)
0.0845610 + 0.996418i \(0.473051\pi\)
\(548\) 19099.6 19099.6i 1.48886 1.48886i
\(549\) 1949.31 + 63.5054i 0.151538 + 0.00493687i
\(550\) 0 0
\(551\) 15774.0 9107.10i 1.21959 0.704130i
\(552\) 152.164 9343.85i 0.0117328 0.720472i
\(553\) −1158.62 + 310.452i −0.0890951 + 0.0238730i
\(554\) 13325.1 23079.8i 1.02189 1.76997i
\(555\) 0 0
\(556\) 12921.4 + 22380.6i 0.985595 + 1.70710i
\(557\) 3736.22 + 3736.22i 0.284217 + 0.284217i 0.834788 0.550571i \(-0.185590\pi\)
−0.550571 + 0.834788i \(0.685590\pi\)
\(558\) 36980.2 8628.73i 2.80555 0.654629i
\(559\) 34101.6i 2.58022i
\(560\) 0 0
\(561\) −92.2815 368.285i −0.00694497 0.0277166i
\(562\) 5588.10 + 20855.1i 0.419430 + 1.56533i
\(563\) 2537.76 + 9471.07i 0.189972 + 0.708984i 0.993511 + 0.113733i \(0.0362807\pi\)
−0.803540 + 0.595251i \(0.797053\pi\)
\(564\) −13905.1 3969.62i −1.03814 0.296367i
\(565\) 0 0
\(566\) 1592.12i 0.118236i
\(567\) −1052.26 5281.34i −0.0779377 0.391174i
\(568\) 1313.81 + 1313.81i 0.0970536 + 0.0970536i
\(569\) 5188.49 + 8986.72i 0.382272 + 0.662114i 0.991387 0.130968i \(-0.0418084\pi\)
−0.609115 + 0.793082i \(0.708475\pi\)
\(570\) 0 0
\(571\) 2372.48 4109.26i 0.173880 0.301168i −0.765893 0.642968i \(-0.777703\pi\)
0.939773 + 0.341799i \(0.111036\pi\)
\(572\) −7602.86 + 2037.18i −0.555755 + 0.148914i
\(573\) 1575.30 + 944.030i 0.114850 + 0.0688262i
\(574\) −9806.54 + 5661.81i −0.713096 + 0.411706i
\(575\) 0 0
\(576\) −18991.8 11805.7i −1.37383 0.854002i
\(577\) −2575.02 + 2575.02i −0.185788 + 0.185788i −0.793872 0.608085i \(-0.791938\pi\)
0.608085 + 0.793872i \(0.291938\pi\)
\(578\) 20820.0 + 5578.70i 1.49827 + 0.401459i
\(579\) −5191.53 5363.42i −0.372630 0.384967i
\(580\) 0 0
\(581\) −1853.52 1070.13i −0.132353 0.0764140i
\(582\) −4733.42 77.0834i −0.337125 0.00549005i
\(583\) −193.385 + 721.724i −0.0137379 + 0.0512706i
\(584\) 3460.26 0.245182
\(585\) 0 0
\(586\) −37937.8 −2.67439
\(587\) 2355.29 8790.07i 0.165610 0.618067i −0.832351 0.554249i \(-0.813006\pi\)
0.997962 0.0638179i \(-0.0203277\pi\)
\(588\) −9097.86 + 15181.6i −0.638077 + 1.06476i
\(589\) 29204.6 + 16861.3i 2.04305 + 1.17955i
\(590\) 0 0
\(591\) −5340.45 + 18706.9i −0.371704 + 1.30203i
\(592\) −823.683 220.705i −0.0571844 0.0153225i
\(593\) 9619.29 9619.29i 0.666133 0.666133i −0.290686 0.956819i \(-0.593883\pi\)
0.956819 + 0.290686i \(0.0938833\pi\)
\(594\) 1151.49 + 5325.36i 0.0795390 + 0.367849i
\(595\) 0 0
\(596\) −6370.05 + 3677.75i −0.437797 + 0.252762i
\(597\) −17193.3 + 9556.73i −1.17869 + 0.655161i
\(598\) −34836.0 + 9334.27i −2.38219 + 0.638306i
\(599\) 339.119 587.372i 0.0231320 0.0400657i −0.854228 0.519899i \(-0.825970\pi\)
0.877360 + 0.479833i \(0.159303\pi\)
\(600\) 0 0
\(601\) −4560.19 7898.48i −0.309508 0.536083i 0.668747 0.743490i \(-0.266831\pi\)
−0.978255 + 0.207407i \(0.933498\pi\)
\(602\) −10378.7 10378.7i −0.702666 0.702666i
\(603\) 458.899 + 139.126i 0.0309914 + 0.00939579i
\(604\) 23831.5i 1.60545i
\(605\) 0 0
\(606\) 18422.0 17831.6i 1.23489 1.19532i
\(607\) 3566.69 + 13311.1i 0.238497 + 0.890082i 0.976541 + 0.215330i \(0.0690827\pi\)
−0.738045 + 0.674752i \(0.764251\pi\)
\(608\) −6083.91 22705.5i −0.405815 1.51452i
\(609\) −4707.25 + 4556.39i −0.313214 + 0.303176i
\(610\) 0 0
\(611\) 18001.3i 1.19190i
\(612\) 2555.19 + 774.669i 0.168771 + 0.0511669i
\(613\) −7501.39 7501.39i −0.494255 0.494255i 0.415389 0.909644i \(-0.363645\pi\)
−0.909644 + 0.415389i \(0.863645\pi\)
\(614\) 19635.2 + 34009.2i 1.29057 + 2.23534i
\(615\) 0 0
\(616\) −546.390 + 946.376i −0.0357381 + 0.0619003i
\(617\) −21447.4 + 5746.81i −1.39942 + 0.374972i −0.878135 0.478413i \(-0.841212\pi\)
−0.521281 + 0.853385i \(0.674546\pi\)
\(618\) −5785.46 + 3215.78i −0.376578 + 0.209317i
\(619\) 6003.77 3466.28i 0.389841 0.225075i −0.292250 0.956342i \(-0.594404\pi\)
0.682091 + 0.731267i \(0.261071\pi\)
\(620\) 0 0
\(621\) 3145.32 + 14546.3i 0.203248 + 0.939976i
\(622\) 7206.69 7206.69i 0.464569 0.464569i
\(623\) −7905.13 2118.17i −0.508366 0.136216i
\(624\) −2071.96 + 7257.82i −0.132924 + 0.465618i
\(625\) 0 0
\(626\) −23588.8 13619.0i −1.50607 0.869529i
\(627\) −2487.16 + 4150.33i −0.158417 + 0.264351i
\(628\) −2154.52 + 8040.79i −0.136903 + 0.510928i
\(629\) 375.519 0.0238043
\(630\) 0 0
\(631\) 5174.87 0.326479 0.163239 0.986586i \(-0.447806\pi\)
0.163239 + 0.986586i \(0.447806\pi\)
\(632\) −712.516 + 2659.15i −0.0448455 + 0.167366i
\(633\) 7033.52 + 114.540i 0.441639 + 0.00719205i
\(634\) −34660.5 20011.2i −2.17120 1.25354i
\(635\) 0 0
\(636\) −3654.56 3775.56i −0.227850 0.235394i
\(637\) 21281.7 + 5702.42i 1.32372 + 0.354691i
\(638\) 4686.88 4686.88i 0.290839 0.290839i
\(639\) −2513.02 1562.15i −0.155577 0.0967097i
\(640\) 0 0
\(641\) 1800.01 1039.24i 0.110914 0.0640365i −0.443517 0.896266i \(-0.646269\pi\)
0.554431 + 0.832230i \(0.312936\pi\)
\(642\) −24239.8 14526.2i −1.49014 0.892995i
\(643\) −8982.29 + 2406.80i −0.550898 + 0.147613i −0.523521 0.852013i \(-0.675382\pi\)
−0.0273763 + 0.999625i \(0.508715\pi\)
\(644\) −4626.92 + 8014.06i −0.283115 + 0.490370i
\(645\) 0 0
\(646\) 1988.72 + 3444.57i 0.121123 + 0.209791i
\(647\) 12361.4 + 12361.4i 0.751125 + 0.751125i 0.974689 0.223564i \(-0.0717691\pi\)
−0.223564 + 0.974689i \(0.571769\pi\)
\(648\) −11704.8 3969.11i −0.709578 0.240619i
\(649\) 444.002i 0.0268546i
\(650\) 0 0
\(651\) −11663.3 3329.64i −0.702184 0.200459i
\(652\) −1843.22 6878.98i −0.110715 0.413192i
\(653\) 7383.03 + 27553.8i 0.442450 + 1.65125i 0.722581 + 0.691286i \(0.242955\pi\)
−0.280131 + 0.959962i \(0.590378\pi\)
\(654\) −5568.92 22224.9i −0.332969 1.32884i
\(655\) 0 0
\(656\) 6549.37i 0.389802i
\(657\) −5366.48 + 1252.18i −0.318670 + 0.0743565i
\(658\) 5478.63 + 5478.63i 0.324589 + 0.324589i
\(659\) 5594.17 + 9689.39i 0.330680 + 0.572754i 0.982645 0.185494i \(-0.0593887\pi\)
−0.651966 + 0.758249i \(0.726055\pi\)
\(660\) 0 0
\(661\) −12520.6 + 21686.4i −0.736757 + 1.27610i 0.217190 + 0.976129i \(0.430311\pi\)
−0.953948 + 0.299972i \(0.903023\pi\)
\(662\) −3164.29 + 847.869i −0.185776 + 0.0497785i
\(663\) 54.1206 3323.36i 0.00317024 0.194673i
\(664\) −4254.01 + 2456.06i −0.248626 + 0.143544i
\(665\) 0 0
\(666\) −5385.99 175.467i −0.313368 0.0102090i
\(667\) 12802.3 12802.3i 0.743190 0.743190i
\(668\) 7244.69 + 1941.21i 0.419619 + 0.112437i
\(669\) −9896.58 + 2479.79i −0.571934 + 0.143310i
\(670\) 0 0
\(671\) 545.845 + 315.144i 0.0314040 + 0.0181311i
\(672\) 4107.59 + 7389.90i 0.235794 + 0.424213i
\(673\) 4660.65 17393.8i 0.266946 0.996257i −0.694102 0.719877i \(-0.744198\pi\)
0.961048 0.276381i \(-0.0891350\pi\)
\(674\) 20093.3 1.14832
\(675\) 0 0
\(676\) −42961.7 −2.44434
\(677\) 5566.38 20774.0i 0.316002 1.17934i −0.607051 0.794663i \(-0.707648\pi\)
0.923053 0.384673i \(-0.125686\pi\)
\(678\) 851.386 + 1531.71i 0.0482261 + 0.0867626i
\(679\) 1309.54 + 756.062i 0.0740139 + 0.0427319i
\(680\) 0 0
\(681\) 15906.6 3985.74i 0.895072 0.224279i
\(682\) 11853.7 + 3176.18i 0.665544 + 0.178332i
\(683\) 4348.95 4348.95i 0.243643 0.243643i −0.574713 0.818355i \(-0.694886\pi\)
0.818355 + 0.574713i \(0.194886\pi\)
\(684\) −16044.9 30006.5i −0.896920 1.67738i
\(685\) 0 0
\(686\) 17978.8 10380.1i 1.00063 0.577715i
\(687\) −337.564 + 20728.6i −0.0187465 + 1.15116i
\(688\) 8200.05 2197.20i 0.454395 0.121755i
\(689\) −3270.58 + 5664.81i −0.180841 + 0.313225i
\(690\) 0 0
\(691\) 7927.92 + 13731.6i 0.436458 + 0.755967i 0.997413 0.0718787i \(-0.0228994\pi\)
−0.560955 + 0.827846i \(0.689566\pi\)
\(692\) 5936.61 + 5936.61i 0.326121 + 0.326121i
\(693\) 504.921 1665.45i 0.0276773 0.0912918i
\(694\) 18107.7i 0.990429i
\(695\) 0 0
\(696\) 3654.54 + 14584.9i 0.199030 + 0.794308i
\(697\) 746.467 + 2785.85i 0.0405659 + 0.151394i
\(698\) −2820.56 10526.5i −0.152951 0.570820i
\(699\) 15308.0 + 4370.13i 0.828330 + 0.236471i
\(700\) 0 0
\(701\) 21918.5i 1.18096i −0.807054 0.590478i \(-0.798939\pi\)
0.807054 0.590478i \(-0.201061\pi\)
\(702\) −2329.14 + 47641.0i −0.125224 + 2.56139i
\(703\) −3383.93 3383.93i −0.181547 0.181547i
\(704\) −3613.36 6258.53i −0.193443 0.335053i
\(705\) 0 0
\(706\) −24185.9 + 41891.2i −1.28930 + 2.23314i
\(707\) −7910.29 + 2119.56i −0.420788 + 0.112750i
\(708\) 2678.35 + 1605.05i 0.142173 + 0.0851999i
\(709\) −25661.5 + 14815.7i −1.35929 + 0.784787i −0.989528 0.144338i \(-0.953895\pi\)
−0.369763 + 0.929126i \(0.620561\pi\)
\(710\) 0 0
\(711\) 142.755 4381.89i 0.00752987 0.231130i
\(712\) −13281.6 + 13281.6i −0.699087 + 0.699087i
\(713\) 32378.6 + 8675.82i 1.70068 + 0.455697i
\(714\) −994.982 1027.92i −0.0521516 0.0538783i
\(715\) 0 0
\(716\) −27516.2 15886.5i −1.43622 0.829199i
\(717\) −20220.8 329.295i −1.05322 0.0171517i
\(718\) −7981.37 + 29786.9i −0.414850 + 1.54824i
\(719\) 5855.14 0.303700 0.151850 0.988404i \(-0.451477\pi\)
0.151850 + 0.988404i \(0.451477\pi\)
\(720\) 0 0
\(721\) 2114.24 0.109207
\(722\) 5217.97 19473.7i 0.268965 1.00379i
\(723\) 17584.1 29342.5i 0.904508 1.50935i
\(724\) −2019.25 1165.81i −0.103653 0.0598440i
\(725\) 0 0
\(726\) 7966.64 27906.1i 0.407258 1.42658i
\(727\) −17456.9 4677.55i −0.890563 0.238626i −0.215604 0.976481i \(-0.569172\pi\)
−0.674959 + 0.737855i \(0.735839\pi\)
\(728\) −6764.65 + 6764.65i −0.344388 + 0.344388i
\(729\) 19589.1 + 1919.99i 0.995231 + 0.0975455i
\(730\) 0 0
\(731\) −3237.56 + 1869.21i −0.163811 + 0.0945762i
\(732\) −3874.25 + 2153.46i −0.195623 + 0.108735i
\(733\) −35884.0 + 9615.09i −1.80819 + 0.484504i −0.995208 0.0977795i \(-0.968826\pi\)
−0.812986 + 0.582284i \(0.802159\pi\)
\(734\) −20929.9 + 36251.7i −1.05250 + 1.82299i
\(735\) 0 0
\(736\) −11682.9 20235.3i −0.585104 1.01343i
\(737\) 109.578 + 109.578i 0.00547676 + 0.00547676i
\(738\) −9404.70 40305.8i −0.469095 2.01040i
\(739\) 16862.4i 0.839371i 0.907670 + 0.419686i \(0.137860\pi\)
−0.907670 + 0.419686i \(0.862140\pi\)
\(740\) 0 0
\(741\) −30435.6 + 29460.2i −1.50888 + 1.46052i
\(742\) 728.677 + 2719.46i 0.0360520 + 0.134548i
\(743\) 2026.03 + 7561.26i 0.100038 + 0.373345i 0.997735 0.0672671i \(-0.0214280\pi\)
−0.897697 + 0.440613i \(0.854761\pi\)
\(744\) −20002.3 + 19361.2i −0.985643 + 0.954055i
\(745\) 0 0
\(746\) 25811.4i 1.26678i
\(747\) 5708.72 5348.49i 0.279613 0.261969i
\(748\) 610.143 + 610.143i 0.0298249 + 0.0298249i
\(749\) 4513.18 + 7817.06i 0.220171 + 0.381347i
\(750\) 0 0
\(751\) 9768.62 16919.7i 0.474650 0.822117i −0.524929 0.851146i \(-0.675908\pi\)
0.999579 + 0.0290288i \(0.00924145\pi\)
\(752\) −4328.57 + 1159.84i −0.209903 + 0.0562433i
\(753\) −28718.0 + 15962.6i −1.38983 + 0.772523i
\(754\) 50252.4 29013.2i 2.42717 1.40133i
\(755\) 0 0
\(756\) 8221.19 + 9066.37i 0.395505 + 0.436165i
\(757\) −10039.5 + 10039.5i −0.482024 + 0.482024i −0.905777 0.423754i \(-0.860712\pi\)
0.423754 + 0.905777i \(0.360712\pi\)
\(758\) 28448.5 + 7622.74i 1.36319 + 0.365265i
\(759\) −1320.28 + 4624.79i −0.0631400 + 0.221172i
\(760\) 0 0
\(761\) −20084.8 11595.9i −0.956731 0.552369i −0.0615654 0.998103i \(-0.519609\pi\)
−0.895165 + 0.445734i \(0.852943\pi\)
\(762\) 18227.3 30415.9i 0.866545 1.44600i
\(763\) −1894.15 + 7069.05i −0.0898725 + 0.335409i
\(764\) −4173.81 −0.197648
\(765\) 0 0
\(766\) 55350.5 2.61083
\(767\) 1006.02 3754.54i 0.0473604 0.176752i
\(768\) 10068.2 + 163.960i 0.473054 + 0.00770364i
\(769\) −30950.8 17869.4i −1.45138 0.837956i −0.452822 0.891601i \(-0.649583\pi\)
−0.998560 + 0.0536450i \(0.982916\pi\)
\(770\) 0 0
\(771\) 5100.12 + 5268.98i 0.238231 + 0.246119i
\(772\) 16386.4 + 4390.71i 0.763935 + 0.204696i
\(773\) −7858.61 + 7858.61i −0.365659 + 0.365659i −0.865891 0.500232i \(-0.833248\pi\)
0.500232 + 0.865891i \(0.333248\pi\)
\(774\) 47309.2 25296.9i 2.19702 1.17478i
\(775\) 0 0
\(776\) 3005.51 1735.23i 0.139036 0.0802723i
\(777\) 1476.46 + 884.796i 0.0681694 + 0.0408518i
\(778\) 42951.4 11508.8i 1.97928 0.530347i
\(779\) 18377.6 31831.0i 0.845246 1.46401i
\(780\) 0 0