Properties

Label 225.4.h.a.181.6
Level $225$
Weight $4$
Character 225.181
Analytic conductor $13.275$
Analytic rank $0$
Dimension $28$
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.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.6
Character \(\chi\) \(=\) 225.181
Dual form 225.4.h.a.46.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.907834 + 2.79403i) q^{2} +(-0.510282 + 0.370741i) q^{4} +(-10.7234 - 3.16365i) q^{5} +18.9115 q^{7} +(17.5148 + 12.7253i) q^{8} +O(q^{10})\) \(q+(0.907834 + 2.79403i) q^{2} +(-0.510282 + 0.370741i) q^{4} +(-10.7234 - 3.16365i) q^{5} +18.9115 q^{7} +(17.5148 + 12.7253i) q^{8} +(-0.895733 - 32.8335i) q^{10} +(1.87505 + 5.77082i) q^{11} +(24.1805 - 74.4201i) q^{13} +(17.1685 + 52.8393i) q^{14} +(-21.2134 + 65.2882i) q^{16} +(31.0670 + 22.5715i) q^{17} +(75.2030 + 54.6382i) q^{19} +(6.64485 - 2.36125i) q^{20} +(-14.4216 + 10.4779i) q^{22} +(25.0398 + 77.0645i) q^{23} +(104.983 + 67.8503i) q^{25} +229.884 q^{26} +(-9.65021 + 7.01128i) q^{28} +(-9.02201 + 6.55487i) q^{29} +(181.125 + 131.595i) q^{31} -28.4793 q^{32} +(-34.8617 + 107.293i) q^{34} +(-202.796 - 59.8295i) q^{35} +(-33.2987 + 102.483i) q^{37} +(-84.3887 + 259.722i) q^{38} +(-147.560 - 191.869i) q^{40} +(108.379 - 333.556i) q^{41} -356.550 q^{43} +(-3.09629 - 2.24959i) q^{44} +(-192.588 + 139.924i) q^{46} +(-236.019 + 171.478i) q^{47} +14.6457 q^{49} +(-94.2687 + 354.921i) q^{50} +(15.2517 + 46.9399i) q^{52} +(554.021 - 402.520i) q^{53} +(-1.85006 - 67.8149i) q^{55} +(331.232 + 240.654i) q^{56} +(-26.5050 - 19.2570i) q^{58} +(69.2082 - 213.001i) q^{59} +(-215.599 - 663.544i) q^{61} +(-203.249 + 625.535i) q^{62} +(143.853 + 442.734i) q^{64} +(-494.737 + 721.537i) q^{65} +(735.443 + 534.330i) q^{67} -24.2211 q^{68} +(-16.9397 - 620.932i) q^{70} +(163.274 - 118.625i) q^{71} +(-90.2156 - 277.655i) q^{73} -316.570 q^{74} -58.6314 q^{76} +(35.4601 + 109.135i) q^{77} +(-573.822 + 416.906i) q^{79} +(434.030 - 633.000i) q^{80} +1030.36 q^{82} +(-897.021 - 651.724i) q^{83} +(-261.736 - 340.329i) q^{85} +(-323.688 - 996.211i) q^{86} +(-40.5940 + 124.935i) q^{88} +(-1.16808 - 3.59497i) q^{89} +(457.291 - 1407.40i) q^{91} +(-41.3483 - 30.0413i) q^{92} +(-693.380 - 503.770i) q^{94} +(-633.576 - 823.824i) q^{95} +(-14.9369 + 10.8523i) q^{97} +(13.2959 + 40.9205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.907834 + 2.79403i 0.320968 + 0.987837i 0.973228 + 0.229842i \(0.0738210\pi\)
−0.652260 + 0.757995i \(0.726179\pi\)
\(3\) 0 0
\(4\) −0.510282 + 0.370741i −0.0637852 + 0.0463427i
\(5\) −10.7234 3.16365i −0.959130 0.282966i
\(6\) 0 0
\(7\) 18.9115 1.02113 0.510563 0.859840i \(-0.329437\pi\)
0.510563 + 0.859840i \(0.329437\pi\)
\(8\) 17.5148 + 12.7253i 0.774053 + 0.562382i
\(9\) 0 0
\(10\) −0.895733 32.8335i −0.0283256 1.03829i
\(11\) 1.87505 + 5.77082i 0.0513955 + 0.158179i 0.973460 0.228857i \(-0.0734989\pi\)
−0.922065 + 0.387036i \(0.873499\pi\)
\(12\) 0 0
\(13\) 24.1805 74.4201i 0.515883 1.58772i −0.265787 0.964032i \(-0.585632\pi\)
0.781670 0.623692i \(-0.214368\pi\)
\(14\) 17.1685 + 52.8393i 0.327749 + 1.00871i
\(15\) 0 0
\(16\) −21.2134 + 65.2882i −0.331460 + 1.02013i
\(17\) 31.0670 + 22.5715i 0.443227 + 0.322023i 0.786916 0.617060i \(-0.211676\pi\)
−0.343689 + 0.939084i \(0.611676\pi\)
\(18\) 0 0
\(19\) 75.2030 + 54.6382i 0.908040 + 0.659730i 0.940518 0.339743i \(-0.110340\pi\)
−0.0324785 + 0.999472i \(0.510340\pi\)
\(20\) 6.64485 2.36125i 0.0742917 0.0263996i
\(21\) 0 0
\(22\) −14.4216 + 10.4779i −0.139759 + 0.101541i
\(23\) 25.0398 + 77.0645i 0.227007 + 0.698655i 0.998082 + 0.0619104i \(0.0197193\pi\)
−0.771075 + 0.636744i \(0.780281\pi\)
\(24\) 0 0
\(25\) 104.983 + 67.8503i 0.839861 + 0.542802i
\(26\) 229.884 1.73399
\(27\) 0 0
\(28\) −9.65021 + 7.01128i −0.0651328 + 0.0473217i
\(29\) −9.02201 + 6.55487i −0.0577705 + 0.0419727i −0.616296 0.787515i \(-0.711367\pi\)
0.558525 + 0.829488i \(0.311367\pi\)
\(30\) 0 0
\(31\) 181.125 + 131.595i 1.04939 + 0.762425i 0.972096 0.234583i \(-0.0753725\pi\)
0.0772923 + 0.997008i \(0.475373\pi\)
\(32\) −28.4793 −0.157327
\(33\) 0 0
\(34\) −34.8617 + 107.293i −0.175845 + 0.541196i
\(35\) −202.796 59.8295i −0.979393 0.288944i
\(36\) 0 0
\(37\) −33.2987 + 102.483i −0.147954 + 0.455354i −0.997379 0.0723545i \(-0.976949\pi\)
0.849425 + 0.527709i \(0.176949\pi\)
\(38\) −84.3887 + 259.722i −0.360254 + 1.10875i
\(39\) 0 0
\(40\) −147.560 191.869i −0.583282 0.758428i
\(41\) 108.379 333.556i 0.412828 1.27056i −0.501350 0.865244i \(-0.667163\pi\)
0.914179 0.405311i \(-0.132837\pi\)
\(42\) 0 0
\(43\) −356.550 −1.26450 −0.632249 0.774765i \(-0.717868\pi\)
−0.632249 + 0.774765i \(0.717868\pi\)
\(44\) −3.09629 2.24959i −0.0106087 0.00770768i
\(45\) 0 0
\(46\) −192.588 + 139.924i −0.617295 + 0.448491i
\(47\) −236.019 + 171.478i −0.732488 + 0.532184i −0.890350 0.455277i \(-0.849540\pi\)
0.157861 + 0.987461i \(0.449540\pi\)
\(48\) 0 0
\(49\) 14.6457 0.0426989
\(50\) −94.2687 + 354.921i −0.266632 + 1.00387i
\(51\) 0 0
\(52\) 15.2517 + 46.9399i 0.0406737 + 0.125181i
\(53\) 554.021 402.520i 1.43586 1.04322i 0.446975 0.894546i \(-0.352501\pi\)
0.988887 0.148669i \(-0.0474988\pi\)
\(54\) 0 0
\(55\) −1.85006 67.8149i −0.00453568 0.166257i
\(56\) 331.232 + 240.654i 0.790405 + 0.574263i
\(57\) 0 0
\(58\) −26.5050 19.2570i −0.0600047 0.0435960i
\(59\) 69.2082 213.001i 0.152714 0.470006i −0.845208 0.534438i \(-0.820523\pi\)
0.997922 + 0.0644317i \(0.0205235\pi\)
\(60\) 0 0
\(61\) −215.599 663.544i −0.452534 1.39276i −0.874006 0.485915i \(-0.838486\pi\)
0.421472 0.906842i \(-0.361514\pi\)
\(62\) −203.249 + 625.535i −0.416332 + 1.28134i
\(63\) 0 0
\(64\) 143.853 + 442.734i 0.280963 + 0.864715i
\(65\) −494.737 + 721.537i −0.944070 + 1.37686i
\(66\) 0 0
\(67\) 735.443 + 534.330i 1.34102 + 0.974311i 0.999406 + 0.0344723i \(0.0109750\pi\)
0.341618 + 0.939839i \(0.389025\pi\)
\(68\) −24.2211 −0.0431948
\(69\) 0 0
\(70\) −16.9397 620.932i −0.0289240 1.06022i
\(71\) 163.274 118.625i 0.272916 0.198285i −0.442906 0.896568i \(-0.646052\pi\)
0.715822 + 0.698283i \(0.246052\pi\)
\(72\) 0 0
\(73\) −90.2156 277.655i −0.144643 0.445165i 0.852322 0.523018i \(-0.175194\pi\)
−0.996965 + 0.0778521i \(0.975194\pi\)
\(74\) −316.570 −0.497304
\(75\) 0 0
\(76\) −58.6314 −0.0884932
\(77\) 35.4601 + 109.135i 0.0524813 + 0.161521i
\(78\) 0 0
\(79\) −573.822 + 416.906i −0.817216 + 0.593742i −0.915914 0.401375i \(-0.868532\pi\)
0.0986978 + 0.995117i \(0.468532\pi\)
\(80\) 434.030 633.000i 0.606575 0.884644i
\(81\) 0 0
\(82\) 1030.36 1.38761
\(83\) −897.021 651.724i −1.18628 0.861880i −0.193410 0.981118i \(-0.561955\pi\)
−0.992866 + 0.119238i \(0.961955\pi\)
\(84\) 0 0
\(85\) −261.736 340.329i −0.333991 0.434281i
\(86\) −323.688 996.211i −0.405863 1.24912i
\(87\) 0 0
\(88\) −40.5940 + 124.935i −0.0491742 + 0.151343i
\(89\) −1.16808 3.59497i −0.00139119 0.00428165i 0.950359 0.311157i \(-0.100717\pi\)
−0.951750 + 0.306875i \(0.900717\pi\)
\(90\) 0 0
\(91\) 457.291 1407.40i 0.526782 1.62127i
\(92\) −41.3483 30.0413i −0.0468572 0.0340438i
\(93\) 0 0
\(94\) −693.380 503.770i −0.760816 0.552765i
\(95\) −633.576 823.824i −0.684247 0.889711i
\(96\) 0 0
\(97\) −14.9369 + 10.8523i −0.0156351 + 0.0113596i −0.595575 0.803299i \(-0.703076\pi\)
0.579940 + 0.814659i \(0.303076\pi\)
\(98\) 13.2959 + 40.9205i 0.0137050 + 0.0421795i
\(99\) 0 0
\(100\) −78.7256 + 4.29863i −0.0787256 + 0.00429863i
\(101\) 1332.50 1.31276 0.656381 0.754430i \(-0.272087\pi\)
0.656381 + 0.754430i \(0.272087\pi\)
\(102\) 0 0
\(103\) −1358.05 + 986.682i −1.29915 + 0.943890i −0.999947 0.0102985i \(-0.996722\pi\)
−0.299206 + 0.954188i \(0.596722\pi\)
\(104\) 1370.53 995.750i 1.29223 0.938859i
\(105\) 0 0
\(106\) 1627.61 + 1182.53i 1.49139 + 1.08356i
\(107\) −1550.64 −1.40099 −0.700496 0.713657i \(-0.747038\pi\)
−0.700496 + 0.713657i \(0.747038\pi\)
\(108\) 0 0
\(109\) 138.127 425.111i 0.121378 0.373562i −0.871846 0.489780i \(-0.837077\pi\)
0.993224 + 0.116218i \(0.0370772\pi\)
\(110\) 187.797 66.7338i 0.162779 0.0578438i
\(111\) 0 0
\(112\) −401.178 + 1234.70i −0.338462 + 1.04168i
\(113\) 192.146 591.366i 0.159961 0.492310i −0.838668 0.544642i \(-0.816665\pi\)
0.998630 + 0.0523321i \(0.0166654\pi\)
\(114\) 0 0
\(115\) −24.7060 905.611i −0.0200334 0.734336i
\(116\) 2.17360 6.68966i 0.00173978 0.00535448i
\(117\) 0 0
\(118\) 657.959 0.513306
\(119\) 587.525 + 426.862i 0.452591 + 0.328827i
\(120\) 0 0
\(121\) 1047.02 760.701i 0.786638 0.571526i
\(122\) 1658.23 1204.78i 1.23057 0.894060i
\(123\) 0 0
\(124\) −141.213 −0.102268
\(125\) −911.115 1059.71i −0.651941 0.758270i
\(126\) 0 0
\(127\) −216.352 665.864i −0.151167 0.465243i 0.846586 0.532252i \(-0.178654\pi\)
−0.997752 + 0.0670095i \(0.978654\pi\)
\(128\) −1290.74 + 937.776i −0.891298 + 0.647566i
\(129\) 0 0
\(130\) −2465.13 727.272i −1.66313 0.490661i
\(131\) −470.763 342.029i −0.313975 0.228116i 0.419625 0.907697i \(-0.362161\pi\)
−0.733600 + 0.679581i \(0.762161\pi\)
\(132\) 0 0
\(133\) 1422.20 + 1033.29i 0.927223 + 0.673667i
\(134\) −825.273 + 2539.93i −0.532035 + 1.63744i
\(135\) 0 0
\(136\) 256.905 + 790.672i 0.161981 + 0.498526i
\(137\) −186.032 + 572.548i −0.116013 + 0.357051i −0.992157 0.124998i \(-0.960108\pi\)
0.876144 + 0.482050i \(0.160108\pi\)
\(138\) 0 0
\(139\) −57.3812 176.601i −0.0350145 0.107763i 0.932022 0.362402i \(-0.118043\pi\)
−0.967036 + 0.254639i \(0.918043\pi\)
\(140\) 125.664 44.6549i 0.0758612 0.0269573i
\(141\) 0 0
\(142\) 479.668 + 348.499i 0.283471 + 0.205953i
\(143\) 474.805 0.277659
\(144\) 0 0
\(145\) 117.484 41.7480i 0.0672863 0.0239102i
\(146\) 693.875 504.130i 0.393325 0.285768i
\(147\) 0 0
\(148\) −21.0029 64.6404i −0.0116651 0.0359014i
\(149\) −2586.71 −1.42223 −0.711113 0.703078i \(-0.751808\pi\)
−0.711113 + 0.703078i \(0.751808\pi\)
\(150\) 0 0
\(151\) −276.537 −0.149035 −0.0745175 0.997220i \(-0.523742\pi\)
−0.0745175 + 0.997220i \(0.523742\pi\)
\(152\) 621.882 + 1913.96i 0.331850 + 1.02133i
\(153\) 0 0
\(154\) −272.734 + 198.153i −0.142711 + 0.103686i
\(155\) −1525.96 1984.16i −0.790759 1.02821i
\(156\) 0 0
\(157\) −3052.85 −1.55187 −0.775937 0.630810i \(-0.782723\pi\)
−0.775937 + 0.630810i \(0.782723\pi\)
\(158\) −1685.78 1224.79i −0.848821 0.616704i
\(159\) 0 0
\(160\) 305.395 + 90.0987i 0.150897 + 0.0445183i
\(161\) 473.540 + 1457.41i 0.231802 + 0.713415i
\(162\) 0 0
\(163\) −248.105 + 763.589i −0.119221 + 0.366926i −0.992804 0.119750i \(-0.961791\pi\)
0.873583 + 0.486676i \(0.161791\pi\)
\(164\) 68.3593 + 210.388i 0.0325486 + 0.100174i
\(165\) 0 0
\(166\) 1006.59 3097.96i 0.470641 1.44848i
\(167\) 2290.36 + 1664.05i 1.06128 + 0.771064i 0.974325 0.225148i \(-0.0722865\pi\)
0.0869544 + 0.996212i \(0.472287\pi\)
\(168\) 0 0
\(169\) −3176.24 2307.67i −1.44572 1.05037i
\(170\) 713.275 1040.26i 0.321798 0.469319i
\(171\) 0 0
\(172\) 181.941 132.188i 0.0806563 0.0586002i
\(173\) 1273.54 + 3919.54i 0.559683 + 1.72253i 0.683243 + 0.730191i \(0.260569\pi\)
−0.123560 + 0.992337i \(0.539431\pi\)
\(174\) 0 0
\(175\) 1985.38 + 1283.15i 0.857604 + 0.554270i
\(176\) −416.543 −0.178398
\(177\) 0 0
\(178\) 8.98403 6.52728i 0.00378304 0.00274854i
\(179\) −1427.33 + 1037.02i −0.595999 + 0.433019i −0.844457 0.535624i \(-0.820076\pi\)
0.248457 + 0.968643i \(0.420076\pi\)
\(180\) 0 0
\(181\) 1207.80 + 877.516i 0.495994 + 0.360361i 0.807485 0.589888i \(-0.200828\pi\)
−0.311491 + 0.950249i \(0.600828\pi\)
\(182\) 4347.45 1.77063
\(183\) 0 0
\(184\) −542.099 + 1668.41i −0.217196 + 0.668460i
\(185\) 681.297 993.620i 0.270756 0.394878i
\(186\) 0 0
\(187\) −72.0039 + 221.605i −0.0281575 + 0.0866598i
\(188\) 56.8623 175.004i 0.0220591 0.0678909i
\(189\) 0 0
\(190\) 1726.60 2518.12i 0.659268 0.961493i
\(191\) −1130.61 + 3479.65i −0.428313 + 1.31821i 0.471473 + 0.881881i \(0.343723\pi\)
−0.899786 + 0.436332i \(0.856277\pi\)
\(192\) 0 0
\(193\) −4695.92 −1.75140 −0.875699 0.482858i \(-0.839599\pi\)
−0.875699 + 0.482858i \(0.839599\pi\)
\(194\) −43.8817 31.8819i −0.0162398 0.0117989i
\(195\) 0 0
\(196\) −7.47344 + 5.42977i −0.00272356 + 0.00197878i
\(197\) 389.722 283.150i 0.140947 0.102404i −0.515077 0.857144i \(-0.672237\pi\)
0.656024 + 0.754740i \(0.272237\pi\)
\(198\) 0 0
\(199\) 494.959 0.176315 0.0881575 0.996107i \(-0.471902\pi\)
0.0881575 + 0.996107i \(0.471902\pi\)
\(200\) 975.338 + 2524.31i 0.344834 + 0.892480i
\(201\) 0 0
\(202\) 1209.69 + 3723.05i 0.421354 + 1.29679i
\(203\) −170.620 + 123.963i −0.0589910 + 0.0428595i
\(204\) 0 0
\(205\) −2217.45 + 3233.99i −0.755480 + 1.10181i
\(206\) −3989.70 2898.69i −1.34940 0.980394i
\(207\) 0 0
\(208\) 4345.80 + 3157.41i 1.44869 + 1.05253i
\(209\) −174.298 + 536.433i −0.0576862 + 0.177540i
\(210\) 0 0
\(211\) 146.406 + 450.590i 0.0477676 + 0.147014i 0.972095 0.234586i \(-0.0753734\pi\)
−0.924328 + 0.381599i \(0.875373\pi\)
\(212\) −133.476 + 410.797i −0.0432414 + 0.133083i
\(213\) 0 0
\(214\) −1407.72 4332.53i −0.449673 1.38395i
\(215\) 3823.43 + 1128.00i 1.21282 + 0.357810i
\(216\) 0 0
\(217\) 3425.35 + 2488.66i 1.07156 + 0.778532i
\(218\) 1313.17 0.407976
\(219\) 0 0
\(220\) 26.0858 + 33.9188i 0.00799412 + 0.0103946i
\(221\) 2430.99 1766.22i 0.739938 0.537596i
\(222\) 0 0
\(223\) 1565.42 + 4817.87i 0.470082 + 1.44676i 0.852477 + 0.522766i \(0.175100\pi\)
−0.382394 + 0.923999i \(0.624900\pi\)
\(224\) −538.587 −0.160651
\(225\) 0 0
\(226\) 1826.73 0.537665
\(227\) −1635.48 5033.48i −0.478196 1.47174i −0.841599 0.540103i \(-0.818385\pi\)
0.363403 0.931632i \(-0.381615\pi\)
\(228\) 0 0
\(229\) −396.216 + 287.868i −0.114335 + 0.0830692i −0.643483 0.765460i \(-0.722511\pi\)
0.529148 + 0.848529i \(0.322511\pi\)
\(230\) 2507.87 891.173i 0.718974 0.255488i
\(231\) 0 0
\(232\) −241.431 −0.0683221
\(233\) −1763.54 1281.28i −0.495850 0.360256i 0.311579 0.950220i \(-0.399142\pi\)
−0.807430 + 0.589964i \(0.799142\pi\)
\(234\) 0 0
\(235\) 3073.43 1092.14i 0.853141 0.303164i
\(236\) 43.6526 + 134.349i 0.0120404 + 0.0370566i
\(237\) 0 0
\(238\) −659.288 + 2029.08i −0.179560 + 0.552629i
\(239\) −1370.65 4218.41i −0.370961 1.14170i −0.946163 0.323689i \(-0.895077\pi\)
0.575203 0.818011i \(-0.304923\pi\)
\(240\) 0 0
\(241\) 742.522 2285.25i 0.198465 0.610812i −0.801454 0.598057i \(-0.795940\pi\)
0.999919 0.0127554i \(-0.00406027\pi\)
\(242\) 3075.93 + 2234.80i 0.817060 + 0.593629i
\(243\) 0 0
\(244\) 356.019 + 258.663i 0.0934091 + 0.0678657i
\(245\) −157.052 46.3340i −0.0409538 0.0120823i
\(246\) 0 0
\(247\) 5884.63 4275.43i 1.51591 1.10137i
\(248\) 1497.79 + 4609.73i 0.383507 + 1.18031i
\(249\) 0 0
\(250\) 2133.73 3507.72i 0.539795 0.887392i
\(251\) 3459.69 0.870014 0.435007 0.900427i \(-0.356746\pi\)
0.435007 + 0.900427i \(0.356746\pi\)
\(252\) 0 0
\(253\) −397.775 + 289.000i −0.0988454 + 0.0718154i
\(254\) 1664.03 1208.99i 0.411065 0.298656i
\(255\) 0 0
\(256\) −779.049 566.012i −0.190197 0.138187i
\(257\) −4772.57 −1.15838 −0.579192 0.815191i \(-0.696632\pi\)
−0.579192 + 0.815191i \(0.696632\pi\)
\(258\) 0 0
\(259\) −629.730 + 1938.11i −0.151079 + 0.464974i
\(260\) −15.0484 551.607i −0.00358947 0.131574i
\(261\) 0 0
\(262\) 528.264 1625.83i 0.124566 0.383374i
\(263\) −1298.07 + 3995.04i −0.304343 + 0.936671i 0.675579 + 0.737288i \(0.263894\pi\)
−0.979922 + 0.199383i \(0.936106\pi\)
\(264\) 0 0
\(265\) −7214.43 + 2563.65i −1.67237 + 0.594279i
\(266\) −1595.92 + 4911.73i −0.367865 + 1.13217i
\(267\) 0 0
\(268\) −573.381 −0.130690
\(269\) −1835.82 1333.80i −0.416105 0.302318i 0.359964 0.932966i \(-0.382789\pi\)
−0.776069 + 0.630648i \(0.782789\pi\)
\(270\) 0 0
\(271\) 630.472 458.065i 0.141323 0.102677i −0.514878 0.857264i \(-0.672163\pi\)
0.656200 + 0.754587i \(0.272163\pi\)
\(272\) −2132.69 + 1549.49i −0.475417 + 0.345411i
\(273\) 0 0
\(274\) −1768.60 −0.389945
\(275\) −194.704 + 733.059i −0.0426949 + 0.160746i
\(276\) 0 0
\(277\) −1562.16 4807.84i −0.338849 1.04287i −0.964795 0.263004i \(-0.915287\pi\)
0.625945 0.779867i \(-0.284713\pi\)
\(278\) 441.336 320.649i 0.0952142 0.0691772i
\(279\) 0 0
\(280\) −2790.58 3628.53i −0.595605 0.774451i
\(281\) −1997.64 1451.37i −0.424089 0.308119i 0.355192 0.934793i \(-0.384416\pi\)
−0.779281 + 0.626675i \(0.784416\pi\)
\(282\) 0 0
\(283\) −1534.87 1115.15i −0.322398 0.234236i 0.414800 0.909913i \(-0.363851\pi\)
−0.737198 + 0.675677i \(0.763851\pi\)
\(284\) −39.3363 + 121.065i −0.00821895 + 0.0252953i
\(285\) 0 0
\(286\) 431.044 + 1326.62i 0.0891195 + 0.274282i
\(287\) 2049.61 6308.06i 0.421550 1.29740i
\(288\) 0 0
\(289\) −1062.51 3270.08i −0.216266 0.665597i
\(290\) 223.301 + 290.353i 0.0452161 + 0.0587935i
\(291\) 0 0
\(292\) 148.974 + 108.236i 0.0298562 + 0.0216918i
\(293\) −1090.95 −0.217522 −0.108761 0.994068i \(-0.534688\pi\)
−0.108761 + 0.994068i \(0.534688\pi\)
\(294\) 0 0
\(295\) −1416.01 + 2065.14i −0.279468 + 0.407584i
\(296\) −1887.34 + 1371.24i −0.370607 + 0.269262i
\(297\) 0 0
\(298\) −2348.30 7227.34i −0.456489 1.40493i
\(299\) 6340.62 1.22638
\(300\) 0 0
\(301\) −6742.91 −1.29121
\(302\) −251.050 772.652i −0.0478354 0.147222i
\(303\) 0 0
\(304\) −5162.55 + 3750.81i −0.973988 + 0.707644i
\(305\) 212.725 + 7797.53i 0.0399364 + 1.46389i
\(306\) 0 0
\(307\) 8283.37 1.53992 0.769962 0.638090i \(-0.220275\pi\)
0.769962 + 0.638090i \(0.220275\pi\)
\(308\) −58.5556 42.5431i −0.0108328 0.00787051i
\(309\) 0 0
\(310\) 4158.49 6064.85i 0.761892 1.11116i
\(311\) 236.303 + 727.265i 0.0430852 + 0.132603i 0.970285 0.241964i \(-0.0777915\pi\)
−0.927200 + 0.374567i \(0.877792\pi\)
\(312\) 0 0
\(313\) −1734.95 + 5339.63i −0.313307 + 0.964261i 0.663138 + 0.748497i \(0.269224\pi\)
−0.976446 + 0.215764i \(0.930776\pi\)
\(314\) −2771.48 8529.75i −0.498102 1.53300i
\(315\) 0 0
\(316\) 138.247 425.479i 0.0246107 0.0757439i
\(317\) −6874.41 4994.55i −1.21800 0.884927i −0.222065 0.975032i \(-0.571280\pi\)
−0.995932 + 0.0901049i \(0.971280\pi\)
\(318\) 0 0
\(319\) −54.7438 39.7737i −0.00960835 0.00698087i
\(320\) −141.935 5202.71i −0.0247951 0.908877i
\(321\) 0 0
\(322\) −3642.14 + 2646.17i −0.630337 + 0.457966i
\(323\) 1103.07 + 3394.89i 0.190020 + 0.584820i
\(324\) 0 0
\(325\) 7587.96 6172.15i 1.29509 1.05344i
\(326\) −2358.72 −0.400729
\(327\) 0 0
\(328\) 6142.83 4463.03i 1.03409 0.751309i
\(329\) −4463.48 + 3242.91i −0.747963 + 0.543427i
\(330\) 0 0
\(331\) 2626.81 + 1908.49i 0.436202 + 0.316919i 0.784124 0.620604i \(-0.213113\pi\)
−0.347922 + 0.937523i \(0.613113\pi\)
\(332\) 699.355 0.115609
\(333\) 0 0
\(334\) −2570.12 + 7910.01i −0.421050 + 1.29586i
\(335\) −6196.01 8056.52i −1.01052 1.31396i
\(336\) 0 0
\(337\) −2291.63 + 7052.92i −0.370425 + 1.14005i 0.576089 + 0.817387i \(0.304578\pi\)
−0.946514 + 0.322664i \(0.895422\pi\)
\(338\) 3564.20 10969.5i 0.573570 1.76527i
\(339\) 0 0
\(340\) 259.733 + 76.6273i 0.0414294 + 0.0122226i
\(341\) −419.793 + 1291.99i −0.0666659 + 0.205176i
\(342\) 0 0
\(343\) −6209.68 −0.977525
\(344\) −6244.91 4537.19i −0.978788 0.711131i
\(345\) 0 0
\(346\) −9795.14 + 7116.59i −1.52194 + 1.10575i
\(347\) 504.270 366.374i 0.0780133 0.0566800i −0.548095 0.836416i \(-0.684647\pi\)
0.626108 + 0.779736i \(0.284647\pi\)
\(348\) 0 0
\(349\) 12079.4 1.85271 0.926356 0.376649i \(-0.122924\pi\)
0.926356 + 0.376649i \(0.122924\pi\)
\(350\) −1782.76 + 6712.09i −0.272265 + 1.02508i
\(351\) 0 0
\(352\) −53.4003 164.349i −0.00808592 0.0248859i
\(353\) 1021.78 742.368i 0.154062 0.111933i −0.508084 0.861308i \(-0.669646\pi\)
0.662146 + 0.749375i \(0.269646\pi\)
\(354\) 0 0
\(355\) −2126.14 + 755.525i −0.317870 + 0.112955i
\(356\) 1.92886 + 1.40140i 0.000287160 + 0.000208634i
\(357\) 0 0
\(358\) −4193.24 3046.56i −0.619049 0.449765i
\(359\) 48.5654 149.469i 0.00713979 0.0219740i −0.947423 0.319983i \(-0.896323\pi\)
0.954563 + 0.298009i \(0.0963227\pi\)
\(360\) 0 0
\(361\) 550.615 + 1694.62i 0.0802763 + 0.247065i
\(362\) −1355.32 + 4171.26i −0.196780 + 0.605625i
\(363\) 0 0
\(364\) 288.433 + 887.706i 0.0415330 + 0.127825i
\(365\) 89.0131 + 3262.82i 0.0127648 + 0.467901i
\(366\) 0 0
\(367\) −5574.94 4050.43i −0.792941 0.576106i 0.115894 0.993262i \(-0.463027\pi\)
−0.908835 + 0.417156i \(0.863027\pi\)
\(368\) −5562.58 −0.787961
\(369\) 0 0
\(370\) 3394.71 + 1001.52i 0.476979 + 0.140720i
\(371\) 10477.4 7612.27i 1.46620 1.06525i
\(372\) 0 0
\(373\) −1192.38 3669.78i −0.165521 0.509421i 0.833553 0.552439i \(-0.186303\pi\)
−0.999074 + 0.0430178i \(0.986303\pi\)
\(374\) −684.538 −0.0946434
\(375\) 0 0
\(376\) −6315.93 −0.866275
\(377\) 269.657 + 829.919i 0.0368383 + 0.113377i
\(378\) 0 0
\(379\) 4056.09 2946.92i 0.549730 0.399402i −0.277956 0.960594i \(-0.589657\pi\)
0.827686 + 0.561192i \(0.189657\pi\)
\(380\) 628.728 + 185.489i 0.0848764 + 0.0250405i
\(381\) 0 0
\(382\) −10748.6 −1.43965
\(383\) 11340.8 + 8239.61i 1.51303 + 1.09928i 0.964811 + 0.262944i \(0.0846936\pi\)
0.548218 + 0.836335i \(0.315306\pi\)
\(384\) 0 0
\(385\) −34.9875 1282.48i −0.00463150 0.169770i
\(386\) −4263.12 13120.5i −0.562142 1.73010i
\(387\) 0 0
\(388\) 3.59863 11.0754i 0.000470857 0.00144915i
\(389\) 29.9938 + 92.3116i 0.00390938 + 0.0120318i 0.952992 0.302995i \(-0.0979865\pi\)
−0.949083 + 0.315027i \(0.897987\pi\)
\(390\) 0 0
\(391\) −961.552 + 2959.35i −0.124368 + 0.382764i
\(392\) 256.517 + 186.370i 0.0330512 + 0.0240131i
\(393\) 0 0
\(394\) 1144.93 + 831.841i 0.146398 + 0.106364i
\(395\) 7472.27 2655.28i 0.951825 0.338232i
\(396\) 0 0
\(397\) 4234.34 3076.43i 0.535303 0.388921i −0.287034 0.957920i \(-0.592669\pi\)
0.822338 + 0.569000i \(0.192669\pi\)
\(398\) 449.340 + 1382.93i 0.0565915 + 0.174171i
\(399\) 0 0
\(400\) −6656.86 + 5414.79i −0.832108 + 0.676849i
\(401\) 10349.0 1.28879 0.644396 0.764692i \(-0.277109\pi\)
0.644396 + 0.764692i \(0.277109\pi\)
\(402\) 0 0
\(403\) 14173.0 10297.3i 1.75188 1.27282i
\(404\) −679.951 + 494.014i −0.0837348 + 0.0608369i
\(405\) 0 0
\(406\) −501.249 364.179i −0.0612724 0.0445170i
\(407\) −653.848 −0.0796316
\(408\) 0 0
\(409\) −3148.95 + 9691.47i −0.380698 + 1.17167i 0.558855 + 0.829265i \(0.311241\pi\)
−0.939553 + 0.342403i \(0.888759\pi\)
\(410\) −11048.9 3259.69i −1.33090 0.392645i
\(411\) 0 0
\(412\) 327.185 1006.97i 0.0391244 0.120412i
\(413\) 1308.83 4028.17i 0.155940 0.479935i
\(414\) 0 0
\(415\) 7557.29 + 9826.56i 0.893910 + 1.16233i
\(416\) −688.645 + 2119.43i −0.0811625 + 0.249793i
\(417\) 0 0
\(418\) −1657.04 −0.193896
\(419\) 8398.42 + 6101.81i 0.979212 + 0.711439i 0.957532 0.288326i \(-0.0930986\pi\)
0.0216796 + 0.999765i \(0.493099\pi\)
\(420\) 0 0
\(421\) 7922.06 5755.72i 0.917097 0.666310i −0.0257029 0.999670i \(-0.508182\pi\)
0.942800 + 0.333360i \(0.108182\pi\)
\(422\) −1126.05 + 818.122i −0.129894 + 0.0943733i
\(423\) 0 0
\(424\) 14825.8 1.69812
\(425\) 1730.01 + 4477.52i 0.197454 + 0.511040i
\(426\) 0 0
\(427\) −4077.30 12548.6i −0.462094 1.42218i
\(428\) 791.264 574.887i 0.0893625 0.0649257i
\(429\) 0 0
\(430\) 319.374 + 11706.8i 0.0358176 + 1.31291i
\(431\) 3207.40 + 2330.31i 0.358457 + 0.260434i 0.752408 0.658697i \(-0.228892\pi\)
−0.393951 + 0.919131i \(0.628892\pi\)
\(432\) 0 0
\(433\) −3610.83 2623.42i −0.400752 0.291163i 0.369095 0.929391i \(-0.379668\pi\)
−0.769847 + 0.638228i \(0.779668\pi\)
\(434\) −3843.74 + 11829.8i −0.425128 + 1.30841i
\(435\) 0 0
\(436\) 87.1225 + 268.136i 0.00956975 + 0.0294527i
\(437\) −2327.60 + 7163.61i −0.254792 + 0.784169i
\(438\) 0 0
\(439\) −5124.83 15772.6i −0.557164 1.71477i −0.690160 0.723657i \(-0.742460\pi\)
0.132997 0.991116i \(-0.457540\pi\)
\(440\) 830.558 1211.31i 0.0899893 0.131243i
\(441\) 0 0
\(442\) 7141.80 + 5188.82i 0.768554 + 0.558387i
\(443\) −5664.63 −0.607528 −0.303764 0.952747i \(-0.598243\pi\)
−0.303764 + 0.952747i \(0.598243\pi\)
\(444\) 0 0
\(445\) 1.15251 + 42.2457i 0.000122773 + 0.00450032i
\(446\) −12040.1 + 8747.66i −1.27829 + 0.928730i
\(447\) 0 0
\(448\) 2720.48 + 8372.77i 0.286899 + 0.882983i
\(449\) 14047.7 1.47651 0.738253 0.674524i \(-0.235651\pi\)
0.738253 + 0.674524i \(0.235651\pi\)
\(450\) 0 0
\(451\) 2128.11 0.222193
\(452\) 121.195 + 373.000i 0.0126118 + 0.0388151i
\(453\) 0 0
\(454\) 12578.9 9139.13i 1.30035 0.944759i
\(455\) −9356.23 + 13645.4i −0.964015 + 1.40594i
\(456\) 0 0
\(457\) −11501.1 −1.17724 −0.588622 0.808409i \(-0.700329\pi\)
−0.588622 + 0.808409i \(0.700329\pi\)
\(458\) −1164.01 845.702i −0.118757 0.0862817i
\(459\) 0 0
\(460\) 348.354 + 452.957i 0.0353089 + 0.0459114i
\(461\) −497.651 1531.61i −0.0502775 0.154738i 0.922766 0.385362i \(-0.125923\pi\)
−0.973043 + 0.230624i \(0.925923\pi\)
\(462\) 0 0
\(463\) 606.515 1866.66i 0.0608793 0.187367i −0.915991 0.401198i \(-0.868594\pi\)
0.976871 + 0.213830i \(0.0685940\pi\)
\(464\) −236.568 728.082i −0.0236690 0.0728456i
\(465\) 0 0
\(466\) 1978.94 6090.56i 0.196723 0.605450i
\(467\) 1274.21 + 925.764i 0.126260 + 0.0917329i 0.649123 0.760684i \(-0.275136\pi\)
−0.522863 + 0.852417i \(0.675136\pi\)
\(468\) 0 0
\(469\) 13908.3 + 10105.0i 1.36935 + 0.994895i
\(470\) 5841.64 + 7595.75i 0.573308 + 0.745459i
\(471\) 0 0
\(472\) 3922.66 2849.98i 0.382532 0.277926i
\(473\) −668.551 2057.59i −0.0649895 0.200017i
\(474\) 0 0
\(475\) 4187.79 + 10838.6i 0.404524 + 1.04697i
\(476\) −458.059 −0.0441073
\(477\) 0 0
\(478\) 10542.0 7659.24i 1.00875 0.732898i
\(479\) 7933.01 5763.67i 0.756719 0.549789i −0.141183 0.989983i \(-0.545091\pi\)
0.897902 + 0.440195i \(0.145091\pi\)
\(480\) 0 0
\(481\) 6821.61 + 4956.19i 0.646650 + 0.469819i
\(482\) 7059.13 0.667084
\(483\) 0 0
\(484\) −252.249 + 776.344i −0.0236898 + 0.0729098i
\(485\) 194.507 69.1181i 0.0182105 0.00647112i
\(486\) 0 0
\(487\) −2414.05 + 7429.69i −0.224623 + 0.691317i 0.773707 + 0.633543i \(0.218400\pi\)
−0.998330 + 0.0577737i \(0.981600\pi\)
\(488\) 4667.60 14365.4i 0.432976 1.33256i
\(489\) 0 0
\(490\) −13.1186 480.870i −0.00120947 0.0443337i
\(491\) −1550.87 + 4773.07i −0.142545 + 0.438708i −0.996687 0.0813313i \(-0.974083\pi\)
0.854142 + 0.520040i \(0.174083\pi\)
\(492\) 0 0
\(493\) −428.241 −0.0391217
\(494\) 17287.9 + 12560.4i 1.57454 + 1.14397i
\(495\) 0 0
\(496\) −12433.9 + 9033.76i −1.12560 + 0.817798i
\(497\) 3087.76 2243.39i 0.278682 0.202474i
\(498\) 0 0
\(499\) −16251.9 −1.45798 −0.728991 0.684523i \(-0.760011\pi\)
−0.728991 + 0.684523i \(0.760011\pi\)
\(500\) 857.805 + 202.965i 0.0767244 + 0.0181537i
\(501\) 0 0
\(502\) 3140.82 + 9666.45i 0.279246 + 0.859432i
\(503\) 89.3910 64.9464i 0.00792395 0.00575709i −0.583816 0.811886i \(-0.698441\pi\)
0.591740 + 0.806129i \(0.298441\pi\)
\(504\) 0 0
\(505\) −14289.0 4215.58i −1.25911 0.371467i
\(506\) −1168.59 849.029i −0.102668 0.0745927i
\(507\) 0 0
\(508\) 357.264 + 259.567i 0.0312028 + 0.0226702i
\(509\) −4592.45 + 14134.1i −0.399915 + 1.23081i 0.525152 + 0.851008i \(0.324008\pi\)
−0.925067 + 0.379804i \(0.875992\pi\)
\(510\) 0 0
\(511\) −1706.11 5250.88i −0.147699 0.454570i
\(512\) −3069.94 + 9448.29i −0.264987 + 0.815546i
\(513\) 0 0
\(514\) −4332.70 13334.7i −0.371804 1.14429i
\(515\) 17684.4 6284.18i 1.51315 0.537697i
\(516\) 0 0
\(517\) −1432.12 1040.50i −0.121827 0.0885124i
\(518\) −5986.82 −0.507810
\(519\) 0 0
\(520\) −17847.0 + 6341.93i −1.50508 + 0.534831i
\(521\) −6248.48 + 4539.79i −0.525433 + 0.381750i −0.818647 0.574297i \(-0.805275\pi\)
0.293213 + 0.956047i \(0.405275\pi\)
\(522\) 0 0
\(523\) −1432.62 4409.15i −0.119778 0.368640i 0.873135 0.487478i \(-0.162083\pi\)
−0.992914 + 0.118838i \(0.962083\pi\)
\(524\) 367.026 0.0305985
\(525\) 0 0
\(526\) −12340.7 −1.02296
\(527\) 2656.72 + 8176.54i 0.219599 + 0.675855i
\(528\) 0 0
\(529\) 4531.36 3292.23i 0.372431 0.270587i
\(530\) −13712.4 17829.9i −1.12383 1.46129i
\(531\) 0 0
\(532\) −1108.81 −0.0903627
\(533\) −22202.6 16131.2i −1.80432 1.31092i
\(534\) 0 0
\(535\) 16628.1 + 4905.69i 1.34373 + 0.396433i
\(536\) 6081.65 + 18717.4i 0.490088 + 1.50834i
\(537\) 0 0
\(538\) 2060.06 6340.21i 0.165085 0.508078i
\(539\) 27.4615 + 84.5179i 0.00219453 + 0.00675407i
\(540\) 0 0
\(541\) −2574.24 + 7922.70i −0.204575 + 0.629618i 0.795155 + 0.606406i \(0.207389\pi\)
−0.999731 + 0.0232123i \(0.992611\pi\)
\(542\) 1852.21 + 1345.71i 0.146788 + 0.106648i
\(543\) 0 0
\(544\) −884.768 642.821i −0.0697318 0.0506631i
\(545\) −2826.09 + 4121.65i −0.222122 + 0.323948i
\(546\) 0 0
\(547\) −11703.1 + 8502.77i −0.914783 + 0.664629i −0.942220 0.334995i \(-0.891265\pi\)
0.0274369 + 0.999624i \(0.491265\pi\)
\(548\) −117.338 361.130i −0.00914680 0.0281510i
\(549\) 0 0
\(550\) −2224.94 + 121.488i −0.172494 + 0.00941867i
\(551\) −1036.63 −0.0801486
\(552\) 0 0
\(553\) −10851.9 + 7884.33i −0.834481 + 0.606286i
\(554\) 12015.1 8729.45i 0.921427 0.669456i
\(555\) 0 0
\(556\) 94.7539 + 68.8428i 0.00722745 + 0.00525105i
\(557\) −21991.8 −1.67293 −0.836467 0.548017i \(-0.815383\pi\)
−0.836467 + 0.548017i \(0.815383\pi\)
\(558\) 0 0
\(559\) −8621.58 + 26534.5i −0.652333 + 2.00767i
\(560\) 8208.16 11971.0i 0.619389 0.903333i
\(561\) 0 0
\(562\) 2241.64 6899.05i 0.168252 0.517827i
\(563\) 3935.09 12111.0i 0.294573 0.906602i −0.688792 0.724959i \(-0.741859\pi\)
0.983365 0.181643i \(-0.0581414\pi\)
\(564\) 0 0
\(565\) −3931.34 + 5733.57i −0.292731 + 0.426926i
\(566\) 1722.35 5300.84i 0.127907 0.393659i
\(567\) 0 0
\(568\) 4369.25 0.322763
\(569\) −3083.27 2240.13i −0.227166 0.165046i 0.468381 0.883527i \(-0.344838\pi\)
−0.695546 + 0.718481i \(0.744838\pi\)
\(570\) 0 0
\(571\) 16776.5 12188.9i 1.22955 0.893324i 0.232698 0.972549i \(-0.425245\pi\)
0.996857 + 0.0792254i \(0.0252447\pi\)
\(572\) −242.284 + 176.030i −0.0177105 + 0.0128674i
\(573\) 0 0
\(574\) 19485.6 1.41692
\(575\) −2600.11 + 9789.39i −0.188577 + 0.709992i
\(576\) 0 0
\(577\) −8200.30 25237.9i −0.591652 1.82092i −0.570733 0.821136i \(-0.693341\pi\)
−0.0209185 0.999781i \(-0.506659\pi\)
\(578\) 8172.10 5937.38i 0.588088 0.427271i
\(579\) 0 0
\(580\) −44.4722 + 64.8594i −0.00318381 + 0.00464335i
\(581\) −16964.0 12325.1i −1.21134 0.880088i
\(582\) 0 0
\(583\) 3361.69 + 2442.41i 0.238812 + 0.173507i
\(584\) 1953.12 6011.09i 0.138392 0.425926i
\(585\) 0 0
\(586\) −990.402 3048.14i −0.0698177 0.214877i
\(587\) 6201.38 19085.9i 0.436045 1.34201i −0.455968 0.889996i \(-0.650707\pi\)
0.892012 0.452011i \(-0.149293\pi\)
\(588\) 0 0
\(589\) 6431.04 + 19792.7i 0.449892 + 1.38462i
\(590\) −7055.56 2081.56i −0.492327 0.145248i
\(591\) 0 0
\(592\) −5984.55 4348.03i −0.415479 0.301863i
\(593\) −5902.00 −0.408712 −0.204356 0.978897i \(-0.565510\pi\)
−0.204356 + 0.978897i \(0.565510\pi\)
\(594\) 0 0
\(595\) −4949.82 6436.14i −0.341047 0.443455i
\(596\) 1319.95 959.001i 0.0907170 0.0659097i
\(597\) 0 0
\(598\) 5756.23 + 17715.9i 0.393628 + 1.21146i
\(599\) 1759.46 0.120016 0.0600079 0.998198i \(-0.480887\pi\)
0.0600079 + 0.998198i \(0.480887\pi\)
\(600\) 0 0
\(601\) 22974.1 1.55929 0.779646 0.626220i \(-0.215399\pi\)
0.779646 + 0.626220i \(0.215399\pi\)
\(602\) −6121.44 18839.9i −0.414437 1.27551i
\(603\) 0 0
\(604\) 141.112 102.524i 0.00950623 0.00690668i
\(605\) −13634.2 + 4844.91i −0.916210 + 0.325576i
\(606\) 0 0
\(607\) −18961.8 −1.26794 −0.633968 0.773359i \(-0.718575\pi\)
−0.633968 + 0.773359i \(0.718575\pi\)
\(608\) −2141.73 1556.06i −0.142860 0.103794i
\(609\) 0 0
\(610\) −21593.4 + 7673.22i −1.43326 + 0.509311i
\(611\) 7054.33 + 21711.0i 0.467083 + 1.43753i
\(612\) 0 0
\(613\) 6808.93 20955.7i 0.448630 1.38074i −0.429824 0.902913i \(-0.641424\pi\)
0.878454 0.477827i \(-0.158576\pi\)
\(614\) 7519.92 + 23143.9i 0.494266 + 1.52119i
\(615\) 0 0
\(616\) −767.694 + 2362.72i −0.0502131 + 0.154540i
\(617\) 5152.77 + 3743.71i 0.336212 + 0.244272i 0.743062 0.669223i \(-0.233373\pi\)
−0.406850 + 0.913495i \(0.633373\pi\)
\(618\) 0 0
\(619\) −6709.39 4874.66i −0.435659 0.316525i 0.348249 0.937402i \(-0.386777\pi\)
−0.783908 + 0.620877i \(0.786777\pi\)
\(620\) 1514.28 + 446.748i 0.0980886 + 0.0289384i
\(621\) 0 0
\(622\) −1817.47 + 1320.47i −0.117161 + 0.0851224i
\(623\) −22.0901 67.9865i −0.00142058 0.00437210i
\(624\) 0 0
\(625\) 6417.68 + 14246.2i 0.410732 + 0.911756i
\(626\) −16494.1 −1.05309
\(627\) 0 0
\(628\) 1557.82 1131.82i 0.0989867 0.0719180i
\(629\) −3347.69 + 2432.24i −0.212212 + 0.154181i
\(630\) 0 0
\(631\) −18624.6 13531.5i −1.17501 0.853696i −0.183411 0.983036i \(-0.558714\pi\)
−0.991600 + 0.129340i \(0.958714\pi\)
\(632\) −15355.6 −0.966478
\(633\) 0 0
\(634\) 7714.08 23741.5i 0.483226 1.48722i
\(635\) 213.468 + 7824.78i 0.0133405 + 0.489003i
\(636\) 0 0
\(637\) 354.141 1089.94i 0.0220276 0.0677940i
\(638\) 61.4304 189.063i 0.00381200 0.0117321i
\(639\) 0 0
\(640\) 16807.9 5972.69i 1.03811 0.368893i
\(641\) 7178.47 22093.1i 0.442329 1.36135i −0.443058 0.896493i \(-0.646106\pi\)
0.885387 0.464855i \(-0.153894\pi\)
\(642\) 0 0
\(643\) 17439.0 1.06956 0.534780 0.844991i \(-0.320395\pi\)
0.534780 + 0.844991i \(0.320395\pi\)
\(644\) −781.960 568.127i −0.0478471 0.0347630i
\(645\) 0 0
\(646\) −8484.02 + 6164.00i −0.516717 + 0.375417i
\(647\) 13233.9 9614.98i 0.804139 0.584241i −0.107987 0.994152i \(-0.534440\pi\)
0.912125 + 0.409911i \(0.134440\pi\)
\(648\) 0 0
\(649\) 1358.96 0.0821939
\(650\) 24133.8 + 15597.7i 1.45631 + 0.941216i
\(651\) 0 0
\(652\) −156.490 481.628i −0.00939975 0.0289295i
\(653\) 13116.1 9529.41i 0.786023 0.571079i −0.120758 0.992682i \(-0.538532\pi\)
0.906781 + 0.421603i \(0.138532\pi\)
\(654\) 0 0
\(655\) 3966.11 + 5157.04i 0.236594 + 0.307637i
\(656\) 19478.2 + 14151.8i 1.15929 + 0.842276i
\(657\) 0 0
\(658\) −13112.9 9527.06i −0.776889 0.564443i
\(659\) −3337.93 + 10273.1i −0.197310 + 0.607258i 0.802632 + 0.596475i \(0.203433\pi\)
−0.999942 + 0.0107834i \(0.996567\pi\)
\(660\) 0 0
\(661\) 4696.20 + 14453.4i 0.276341 + 0.850489i 0.988862 + 0.148838i \(0.0475534\pi\)
−0.712521 + 0.701651i \(0.752447\pi\)
\(662\) −2947.66 + 9071.98i −0.173058 + 0.532617i
\(663\) 0 0
\(664\) −7417.80 22829.6i −0.433534 1.33428i
\(665\) −11981.9 15579.8i −0.698703 0.908507i
\(666\) 0 0
\(667\) −731.057 531.144i −0.0424387 0.0308336i
\(668\) −1785.66 −0.103427
\(669\) 0 0
\(670\) 16885.2 24625.8i 0.973630 1.41997i
\(671\) 3424.94 2488.36i 0.197047 0.143163i
\(672\) 0 0
\(673\) 2910.35 + 8957.12i 0.166695 + 0.513034i 0.999157 0.0410478i \(-0.0130696\pi\)
−0.832462 + 0.554081i \(0.813070\pi\)
\(674\) −21786.5 −1.24508
\(675\) 0 0
\(676\) 2476.33 0.140892
\(677\) 4739.48 + 14586.6i 0.269059 + 0.828079i 0.990730 + 0.135843i \(0.0433743\pi\)
−0.721671 + 0.692236i \(0.756626\pi\)
\(678\) 0 0
\(679\) −282.479 + 205.233i −0.0159655 + 0.0115996i
\(680\) −253.480 9291.45i −0.0142949 0.523986i
\(681\) 0 0
\(682\) −3990.95 −0.224079
\(683\) 5893.00 + 4281.51i 0.330145 + 0.239865i 0.740492 0.672065i \(-0.234592\pi\)
−0.410347 + 0.911929i \(0.634592\pi\)
\(684\) 0 0
\(685\) 3806.24 5551.12i 0.212305 0.309631i
\(686\) −5637.36 17350.0i −0.313754 0.965636i
\(687\) 0 0
\(688\) 7563.65 23278.5i 0.419130 1.28995i
\(689\) −16559.0 50963.5i −0.915601 2.81793i
\(690\) 0 0
\(691\) 4164.62 12817.4i 0.229276 0.705639i −0.768553 0.639786i \(-0.779023\pi\)
0.997829 0.0658530i \(-0.0209768\pi\)
\(692\) −2103.00 1527.92i −0.115526 0.0839346i
\(693\) 0 0
\(694\) 1481.45 + 1076.34i 0.0810304 + 0.0588720i
\(695\) 56.6163 + 2075.30i 0.00309004 + 0.113267i
\(696\) 0 0
\(697\) 10895.9 7916.33i 0.592125 0.430204i
\(698\) 10966.1 + 33750.2i 0.594661 + 1.83018i
\(699\) 0 0
\(700\) −1488.82 + 81.2937i −0.0803888 + 0.00438945i
\(701\) −16099.1 −0.867413 −0.433706 0.901054i \(-0.642794\pi\)
−0.433706 + 0.901054i \(0.642794\pi\)
\(702\) 0 0
\(703\) −8103.65 + 5887.65i −0.434758 + 0.315870i
\(704\) −2285.21 + 1660.30i −0.122339 + 0.0888848i
\(705\) 0 0
\(706\) 3001.81 + 2180.94i 0.160020 + 0.116262i
\(707\) 25199.6 1.34050
\(708\) 0 0
\(709\) 1824.52 5615.31i 0.0966452 0.297443i −0.891034 0.453937i \(-0.850019\pi\)
0.987679 + 0.156494i \(0.0500191\pi\)
\(710\) −4041.14 5254.60i −0.213607 0.277749i
\(711\) 0 0
\(712\) 25.2883 77.8294i 0.00133107 0.00409660i
\(713\) −5605.98 + 17253.4i −0.294454 + 0.906236i
\(714\) 0 0
\(715\) −5091.52 1502.12i −0.266311 0.0785679i
\(716\) 343.876 1058.34i 0.0179487 0.0552404i
\(717\) 0 0
\(718\) 461.710 0.0239984
\(719\) −3639.38 2644.16i −0.188770 0.137150i 0.489386 0.872067i \(-0.337221\pi\)
−0.678156 + 0.734918i \(0.737221\pi\)
\(720\) 0 0
\(721\) −25682.8 + 18659.7i −1.32660 + 0.963831i
\(722\) −4234.94 + 3076.86i −0.218294 + 0.158600i
\(723\) 0 0
\(724\) −941.649 −0.0483372
\(725\) −1391.90 + 76.0017i −0.0713021 + 0.00389329i
\(726\) 0 0
\(727\) −1876.26 5774.55i −0.0957177 0.294589i 0.891722 0.452583i \(-0.149497\pi\)
−0.987440 + 0.157994i \(0.949497\pi\)
\(728\) 25918.8 18831.1i 1.31953 0.958693i
\(729\) 0 0
\(730\) −9035.59 + 3210.80i −0.458113 + 0.162791i
\(731\) −11077.0 8047.88i −0.560460 0.407198i
\(732\) 0 0
\(733\) −21042.7 15288.4i −1.06034 0.770382i −0.0861888 0.996279i \(-0.527469\pi\)
−0.974151 + 0.225897i \(0.927469\pi\)
\(734\) 6255.89 19253.6i 0.314590 0.968208i
\(735\) 0 0
\(736\) −713.115 2194.74i −0.0357144 0.109918i
\(737\) −1704.53 + 5246.01i −0.0851930 + 0.262197i
\(738\) 0 0
\(739\) 9514.09 + 29281.4i 0.473588 + 1.45755i 0.847853 + 0.530232i \(0.177895\pi\)
−0.374265 + 0.927322i \(0.622105\pi\)
\(740\) 20.7230 + 759.611i 0.00102945 + 0.0377350i
\(741\) 0 0
\(742\) 30780.6 + 22363.4i 1.52290 + 1.10645i
\(743\) −29872.6 −1.47499 −0.737496 0.675352i \(-0.763992\pi\)
−0.737496 + 0.675352i \(0.763992\pi\)
\(744\) 0 0
\(745\) 27738.3 + 8183.46i 1.36410 + 0.402441i
\(746\) 9170.98 6663.11i 0.450098 0.327016i
\(747\) 0 0
\(748\) −45.4160 139.776i −0.00222002 0.00683251i
\(749\) −29325.0 −1.43059
\(750\) 0 0
\(751\) −22462.4 −1.09143 −0.545716 0.837970i \(-0.683742\pi\)
−0.545716 + 0.837970i \(0.683742\pi\)
\(752\) −6188.72 19046.9i −0.300106 0.923630i
\(753\) 0 0
\(754\) −2074.01 + 1506.86i −0.100174 + 0.0727805i
\(755\) 2965.42 + 874.869i 0.142944 + 0.0421718i
\(756\) 0 0
\(757\) 22613.9 1.08575 0.542876 0.839813i \(-0.317335\pi\)
0.542876 + 0.839813i \(0.317335\pi\)
\(758\) 11916.0 + 8657.51i 0.570990 + 0.414848i
\(759\) 0 0
\(760\) −613.592 22491.5i −0.0292860 1.07349i
\(761\) −5096.57 15685.6i −0.242773 0.747179i −0.995995 0.0894121i \(-0.971501\pi\)
0.753222 0.657767i \(-0.228499\pi\)
\(762\) 0 0
\(763\) 2612.19 8039.49i 0.123942 0.381454i
\(764\) −713.122 2194.76i −0.0337694 0.103932i
\(765\) 0 0
\(766\) −12726.1 + 39166.8i −0.600276 + 1.84746i
\(767\) −14178.0 10301.0i −0.667457 0.484936i
\(768\) 0 0
\(769\) −1931.73 1403.49i −0.0905853 0.0658140i 0.541571 0.840655i \(-0.317830\pi\)
−0.632156 + 0.774841i \(0.717830\pi\)
\(770\) 3551.53 1262.04i 0.166218 0.0590658i
\(771\) 0 0
\(772\) 2396.24 1740.97i 0.111713 0.0811644i
\(773\) 11956.5 + 36798.2i 0.556332 + 1.71221i 0.692400 + 0.721514i \(0.256553\pi\)
−0.136068 + 0.990699i \(0.543447\pi\)
\(774\) 0 0
\(775\) 10086.2 + 26104.6i 0.467494 + 1.20994i
\(776\) −399.714 −0.0184909
\(777\) 0 0
\(778\) −230.691 + 167.607i −0.0106307 + 0.00772366i
\(779\) 26375.4 19162.8i 1.21309 0.881360i
\(780\) 0 0
\(781\) 990.713 + 719.795i 0.0453912 + 0.0329786i
\(782\) −9141.43 −0.418027
\(783\) 0 0
\(784\) −310.686 + 956.193i −0.0141530 + 0.0435583i