Properties

Label 225.4.h.a.46.6
Level $225$
Weight $4$
Character 225.46
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 46.6
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.a.181.6

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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 −0.652260 0.757995i \(-0.726179\pi\)
0.973228 0.229842i \(-0.0738210\pi\)
\(3\) 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 −0.922065 0.387036i \(-0.873499\pi\)
0.973460 + 0.228857i \(0.0734989\pi\)
\(12\) 0 0
\(13\) 24.1805 + 74.4201i 0.515883 + 1.58772i 0.781670 + 0.623692i \(0.214368\pi\)
−0.265787 + 0.964032i \(0.585632\pi\)
\(14\) 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 −0.343689 0.939084i \(-0.611676\pi\)
0.786916 + 0.617060i \(0.211676\pi\)
\(18\) 0 0
\(19\) 75.2030 54.6382i 0.908040 0.659730i −0.0324785 0.999472i \(-0.510340\pi\)
0.940518 + 0.339743i \(0.110340\pi\)
\(20\) 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 −0.771075 0.636744i \(-0.780281\pi\)
0.998082 0.0619104i \(-0.0197193\pi\)
\(24\) 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 0.558525 0.829488i \(-0.311367\pi\)
−0.616296 + 0.787515i \(0.711367\pi\)
\(30\) 0 0
\(31\) 181.125 131.595i 1.04939 0.762425i 0.0772923 0.997008i \(-0.475373\pi\)
0.972096 + 0.234583i \(0.0753725\pi\)
\(32\) −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 0.849425 0.527709i \(-0.176949\pi\)
−0.997379 + 0.0723545i \(0.976949\pi\)
\(38\) −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 0.914179 + 0.405311i \(0.132837\pi\)
−0.501350 + 0.865244i \(0.667163\pi\)
\(42\) 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 0.157861 0.987461i \(-0.449540\pi\)
−0.890350 + 0.455277i \(0.849540\pi\)
\(48\) 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 0.988887 + 0.148669i \(0.0474988\pi\)
0.446975 + 0.894546i \(0.352501\pi\)
\(54\) 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 0.997922 0.0644317i \(-0.0205235\pi\)
−0.845208 + 0.534438i \(0.820523\pi\)
\(60\) 0 0
\(61\) −215.599 + 663.544i −0.452534 + 1.39276i 0.421472 + 0.906842i \(0.361514\pi\)
−0.874006 + 0.485915i \(0.838486\pi\)
\(62\) −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 0.341618 0.939839i \(-0.389025\pi\)
0.999406 0.0344723i \(-0.0109750\pi\)
\(68\) −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 0.715822 0.698283i \(-0.246052\pi\)
−0.442906 + 0.896568i \(0.646052\pi\)
\(72\) 0 0
\(73\) −90.2156 + 277.655i −0.144643 + 0.445165i −0.996965 0.0778521i \(-0.975194\pi\)
0.852322 + 0.523018i \(0.175194\pi\)
\(74\) −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 0.0986978 0.995117i \(-0.468532\pi\)
−0.915914 + 0.401375i \(0.868532\pi\)
\(80\) 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 −0.992866 0.119238i \(-0.961955\pi\)
−0.193410 + 0.981118i \(0.561955\pi\)
\(84\) 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 −0.951750 0.306875i \(-0.900717\pi\)
0.950359 + 0.311157i \(0.100717\pi\)
\(90\) 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 0.579940 0.814659i \(-0.303076\pi\)
−0.595575 + 0.803299i \(0.703076\pi\)
\(98\) 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 −0.299206 0.954188i \(-0.596722\pi\)
−0.999947 + 0.0102985i \(0.996722\pi\)
\(104\) 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 0.993224 0.116218i \(-0.0370772\pi\)
−0.871846 + 0.489780i \(0.837077\pi\)
\(110\) 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 0.998630 0.0523321i \(-0.0166654\pi\)
−0.838668 + 0.544642i \(0.816665\pi\)
\(114\) 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 −0.997752 0.0670095i \(-0.978654\pi\)
0.846586 + 0.532252i \(0.178654\pi\)
\(128\) −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 −0.733600 0.679581i \(-0.762161\pi\)
0.419625 + 0.907697i \(0.362161\pi\)
\(132\) 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 0.876144 0.482050i \(-0.160108\pi\)
−0.992157 + 0.124998i \(0.960108\pi\)
\(138\) 0 0
\(139\) −57.3812 + 176.601i −0.0350145 + 0.107763i −0.967036 0.254639i \(-0.918043\pi\)
0.932022 + 0.362402i \(0.118043\pi\)
\(140\) 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 0.873583 0.486676i \(-0.161791\pi\)
−0.992804 + 0.119750i \(0.961791\pi\)
\(164\) 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 0.0869544 0.996212i \(-0.472287\pi\)
0.974325 + 0.225148i \(0.0722865\pi\)
\(168\) 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 −0.123560 0.992337i \(-0.539431\pi\)
0.683243 0.730191i \(-0.260569\pi\)
\(174\) 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 0.248457 0.968643i \(-0.420076\pi\)
−0.844457 + 0.535624i \(0.820076\pi\)
\(180\) 0 0
\(181\) 1207.80 877.516i 0.495994 0.360361i −0.311491 0.950249i \(-0.600828\pi\)
0.807485 + 0.589888i \(0.200828\pi\)
\(182\) 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 −0.899786 0.436332i \(-0.856277\pi\)
0.471473 0.881881i \(-0.343723\pi\)
\(192\) 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 0.656024 0.754740i \(-0.272237\pi\)
−0.515077 + 0.857144i \(0.672237\pi\)
\(198\) 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 −0.924328 0.381599i \(-0.875373\pi\)
0.972095 + 0.234586i \(0.0753734\pi\)
\(212\) −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 −0.382394 0.923999i \(-0.624900\pi\)
0.852477 0.522766i \(-0.175100\pi\)
\(224\) −538.587 −0.160651
\(225\) 0 0
\(226\) 1826.73 0.537665
\(227\) −1635.48 + 5033.48i −0.478196 + 1.47174i 0.363403 + 0.931632i \(0.381615\pi\)
−0.841599 + 0.540103i \(0.818385\pi\)
\(228\) 0 0
\(229\) −396.216 287.868i −0.114335 0.0830692i 0.529148 0.848529i \(-0.322511\pi\)
−0.643483 + 0.765460i \(0.722511\pi\)
\(230\) 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 −0.807430 0.589964i \(-0.799142\pi\)
0.311579 + 0.950220i \(0.399142\pi\)
\(234\) 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 0.575203 + 0.818011i \(0.304923\pi\)
−0.946163 + 0.323689i \(0.895077\pi\)
\(240\) 0 0
\(241\) 742.522 + 2285.25i 0.198465 + 0.610812i 0.999919 + 0.0127554i \(0.00406027\pi\)
−0.801454 + 0.598057i \(0.795940\pi\)
\(242\) 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 −0.979922 0.199383i \(-0.936106\pi\)
0.675579 0.737288i \(-0.263894\pi\)
\(264\) 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 −0.776069 0.630648i \(-0.782789\pi\)
0.359964 + 0.932966i \(0.382789\pi\)
\(270\) 0 0
\(271\) 630.472 + 458.065i 0.141323 + 0.102677i 0.656200 0.754587i \(-0.272163\pi\)
−0.514878 + 0.857264i \(0.672163\pi\)
\(272\) −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 0.625945 + 0.779867i \(0.284713\pi\)
−0.964795 + 0.263004i \(0.915287\pi\)
\(278\) 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 −0.779281 0.626675i \(-0.784416\pi\)
0.355192 + 0.934793i \(0.384416\pi\)
\(282\) 0 0
\(283\) −1534.87 + 1115.15i −0.322398 + 0.234236i −0.737198 0.675677i \(-0.763851\pi\)
0.414800 + 0.909913i \(0.363851\pi\)
\(284\) −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 −0.927200 0.374567i \(-0.877792\pi\)
0.970285 + 0.241964i \(0.0777915\pi\)
\(312\) 0 0
\(313\) −1734.95 5339.63i −0.313307 0.964261i −0.976446 0.215764i \(-0.930776\pi\)
0.663138 0.748497i \(-0.269224\pi\)
\(314\) −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 −0.995932 0.0901049i \(-0.971280\pi\)
−0.222065 + 0.975032i \(0.571280\pi\)
\(318\) 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 −0.347922 0.937523i \(-0.613113\pi\)
0.784124 + 0.620604i \(0.213113\pi\)
\(332\) 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 −0.946514 0.322664i \(-0.895422\pi\)
0.576089 0.817387i \(-0.304578\pi\)
\(338\) 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 0.626108 0.779736i \(-0.284647\pi\)
−0.548095 + 0.836416i \(0.684647\pi\)
\(348\) 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 0.662146 0.749375i \(-0.269646\pi\)
−0.508084 + 0.861308i \(0.669646\pi\)
\(354\) 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 0.954563 0.298009i \(-0.0963227\pi\)
−0.947423 + 0.319983i \(0.896323\pi\)
\(360\) 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 −0.908835 0.417156i \(-0.863027\pi\)
0.115894 + 0.993262i \(0.463027\pi\)
\(368\) −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 −0.999074 0.0430178i \(-0.986303\pi\)
0.833553 + 0.552439i \(0.186303\pi\)
\(374\) −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 0.827686 0.561192i \(-0.189657\pi\)
−0.277956 + 0.960594i \(0.589657\pi\)
\(380\) 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 0.548218 0.836335i \(-0.315306\pi\)
0.964811 0.262944i \(-0.0846936\pi\)
\(384\) 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 −0.949083 0.315027i \(-0.897987\pi\)
0.952992 + 0.302995i \(0.0979865\pi\)
\(390\) 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 0.822338 0.569000i \(-0.192669\pi\)
−0.287034 + 0.957920i \(0.592669\pi\)
\(398\) 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 −0.939553 0.342403i \(-0.888759\pi\)
0.558855 0.829265i \(-0.311241\pi\)
\(410\) −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 0.0216796 0.999765i \(-0.493099\pi\)
0.957532 + 0.288326i \(0.0930986\pi\)
\(420\) 0 0
\(421\) 7922.06 + 5755.72i 0.917097 + 0.666310i 0.942800 0.333360i \(-0.108182\pi\)
−0.0257029 + 0.999670i \(0.508182\pi\)
\(422\) −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 −0.393951 0.919131i \(-0.628892\pi\)
0.752408 + 0.658697i \(0.228892\pi\)
\(432\) 0 0
\(433\) −3610.83 + 2623.42i −0.400752 + 0.291163i −0.769847 0.638228i \(-0.779668\pi\)
0.369095 + 0.929391i \(0.379668\pi\)
\(434\) −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 0.132997 + 0.991116i \(0.457540\pi\)
−0.690160 + 0.723657i \(0.742460\pi\)
\(440\) 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 −0.973043 0.230624i \(-0.925923\pi\)
0.922766 + 0.385362i \(0.125923\pi\)
\(462\) 0 0
\(463\) 606.515 + 1866.66i 0.0608793 + 0.187367i 0.976871 0.213830i \(-0.0685940\pi\)
−0.915991 + 0.401198i \(0.868594\pi\)
\(464\) −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 −0.522863 0.852417i \(-0.675136\pi\)
0.649123 + 0.760684i \(0.275136\pi\)
\(468\) 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 0.897902 0.440195i \(-0.145091\pi\)
−0.141183 + 0.989983i \(0.545091\pi\)
\(480\) 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 −0.998330 0.0577737i \(-0.981600\pi\)
0.773707 0.633543i \(-0.218400\pi\)
\(488\) 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 0.854142 0.520040i \(-0.174083\pi\)
−0.996687 + 0.0813313i \(0.974083\pi\)
\(492\) 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 0.591740 0.806129i \(-0.298441\pi\)
−0.583816 + 0.811886i \(0.698441\pi\)
\(504\) 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 −0.925067 0.379804i \(-0.875992\pi\)
0.525152 0.851008i \(-0.324008\pi\)
\(510\) 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 0.293213 0.956047i \(-0.405275\pi\)
−0.818647 + 0.574297i \(0.805275\pi\)
\(522\) 0 0
\(523\) −1432.62 + 4409.15i −0.119778 + 0.368640i −0.992914 0.118838i \(-0.962083\pi\)
0.873135 + 0.487478i \(0.162083\pi\)
\(524\) 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 −0.999731 0.0232123i \(-0.992611\pi\)
0.795155 0.606406i \(-0.207389\pi\)
\(542\) 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 0.0274369 0.999624i \(-0.491265\pi\)
−0.942220 + 0.334995i \(0.891265\pi\)
\(548\) −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 0.983365 + 0.181643i \(0.0581414\pi\)
−0.688792 + 0.724959i \(0.741859\pi\)
\(564\) 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 −0.695546 0.718481i \(-0.744838\pi\)
0.468381 + 0.883527i \(0.344838\pi\)
\(570\) 0 0
\(571\) 16776.5 + 12188.9i 1.22955 + 0.893324i 0.996857 0.0792254i \(-0.0252447\pi\)
0.232698 + 0.972549i \(0.425245\pi\)
\(572\) −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 −0.0209185 + 0.999781i \(0.506659\pi\)
−0.570733 + 0.821136i \(0.693341\pi\)
\(578\) 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 0.892012 + 0.452011i \(0.149293\pi\)
−0.455968 + 0.889996i \(0.650707\pi\)
\(588\) 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 0.878454 + 0.477827i \(0.158576\pi\)
−0.429824 + 0.902913i \(0.641424\pi\)
\(614\) 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 −0.406850 0.913495i \(-0.633373\pi\)
0.743062 + 0.669223i \(0.233373\pi\)
\(618\) 0 0
\(619\) −6709.39 + 4874.66i −0.435659 + 0.316525i −0.783908 0.620877i \(-0.786777\pi\)
0.348249 + 0.937402i \(0.386777\pi\)
\(620\) 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 −0.991600 0.129340i \(-0.958714\pi\)
−0.183411 + 0.983036i \(0.558714\pi\)
\(632\) −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 0.885387 + 0.464855i \(0.153894\pi\)
−0.443058 + 0.896493i \(0.646106\pi\)
\(642\) 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 0.912125 0.409911i \(-0.134440\pi\)
−0.107987 + 0.994152i \(0.534440\pi\)
\(648\) 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 0.906781 0.421603i \(-0.138532\pi\)
−0.120758 + 0.992682i \(0.538532\pi\)
\(654\) 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 −0.999942 0.0107834i \(-0.996567\pi\)
0.802632 0.596475i \(-0.203433\pi\)
\(660\) 0 0
\(661\) 4696.20 14453.4i 0.276341 0.850489i −0.712521 0.701651i \(-0.752447\pi\)
0.988862 0.148838i \(-0.0475534\pi\)
\(662\) −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 −0.832462 0.554081i \(-0.813070\pi\)
0.999157 + 0.0410478i \(0.0130696\pi\)
\(674\) −21786.5 −1.24508
\(675\) 0 0
\(676\) 2476.33 0.140892
\(677\) 4739.48 14586.6i 0.269059 0.828079i −0.721671 0.692236i \(-0.756626\pi\)
0.990730 0.135843i \(-0.0433743\pi\)
\(678\) 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 −0.410347 0.911929i \(-0.634592\pi\)
0.740492 + 0.672065i \(0.234592\pi\)
\(684\) 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 0.997829 + 0.0658530i \(0.0209768\pi\)
−0.768553 + 0.639786i \(0.779023\pi\)
\(692\) −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 0.987679 0.156494i \(-0.0500191\pi\)
−0.891034 + 0.453937i \(0.850019\pi\)
\(710\) −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 −0.678156 0.734918i \(-0.737221\pi\)
0.489386 + 0.872067i \(0.337221\pi\)
\(720\) 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 −0.987440 0.157994i \(-0.949497\pi\)
0.891722 + 0.452583i \(0.149497\pi\)
\(728\) 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 −0.974151 0.225897i \(-0.927469\pi\)
−0.0861888 + 0.996279i \(0.527469\pi\)
\(734\) 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 −0.374265 0.927322i \(-0.622105\pi\)
0.847853 0.530232i \(-0.177895\pi\)
\(740\) 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 0.753222 + 0.657767i \(0.228499\pi\)
−0.995995 + 0.0894121i \(0.971501\pi\)
\(762\) 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 −0.632156 0.774841i \(-0.717830\pi\)
0.541571 + 0.840655i \(0.317830\pi\)
\(770\) 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 −0.136068 0.990699i \(-0.543447\pi\)
0.692400 0.721514i \(-0.256553\pi\)
\(774\) 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