Properties

Label 225.4.h.d.46.4
Level $225$
Weight $4$
Character 225.46
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.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 46.4
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.d.181.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.20400 + 3.70554i) q^{2} +(-5.80928 - 4.22069i) q^{4} +(3.34114 - 10.6694i) q^{5} +6.27975 q^{7} +(-2.58263 + 1.87639i) q^{8} +O(q^{10})\) \(q+(-1.20400 + 3.70554i) q^{2} +(-5.80928 - 4.22069i) q^{4} +(3.34114 - 10.6694i) q^{5} +6.27975 q^{7} +(-2.58263 + 1.87639i) q^{8} +(35.5133 + 25.2268i) q^{10} +(-13.6357 + 41.9663i) q^{11} +(-13.2560 - 40.7979i) q^{13} +(-7.56084 + 23.2699i) q^{14} +(-21.5951 - 66.4630i) q^{16} +(-81.6862 + 59.3485i) q^{17} +(-65.1304 + 47.3200i) q^{19} +(-64.4420 + 47.8798i) q^{20} +(-139.090 - 101.055i) q^{22} +(-48.5949 + 149.560i) q^{23} +(-102.674 - 71.2962i) q^{25} +167.138 q^{26} +(-36.4808 - 26.5049i) q^{28} +(-199.754 - 145.129i) q^{29} +(69.6687 - 50.6173i) q^{31} +246.744 q^{32} +(-121.568 - 374.147i) q^{34} +(20.9815 - 67.0014i) q^{35} +(61.0938 + 188.027i) q^{37} +(-96.9290 - 298.317i) q^{38} +(11.3911 + 33.8245i) q^{40} +(17.2714 + 53.1560i) q^{41} +211.713 q^{43} +(256.340 - 186.242i) q^{44} +(-495.692 - 360.141i) q^{46} +(85.9089 + 62.4165i) q^{47} -303.565 q^{49} +(387.810 - 294.620i) q^{50} +(-95.1871 + 292.956i) q^{52} +(-153.468 - 111.501i) q^{53} +(402.198 + 285.700i) q^{55} +(-16.2183 + 11.7833i) q^{56} +(778.288 - 565.459i) q^{58} +(-140.608 - 432.747i) q^{59} +(171.878 - 528.986i) q^{61} +(103.683 + 319.104i) q^{62} +(-124.319 + 382.615i) q^{64} +(-479.580 + 5.12286i) q^{65} +(-773.054 + 561.657i) q^{67} +725.030 q^{68} +(223.015 + 158.418i) q^{70} +(454.325 + 330.086i) q^{71} +(-54.7181 + 168.405i) q^{73} -770.300 q^{74} +578.084 q^{76} +(-85.6286 + 263.538i) q^{77} +(-769.301 - 558.930i) q^{79} +(-781.275 + 8.34556i) q^{80} -217.767 q^{82} +(11.3373 - 8.23700i) q^{83} +(360.290 + 1069.84i) q^{85} +(-254.903 + 784.511i) q^{86} +(-43.5293 - 133.970i) q^{88} +(-143.004 + 440.120i) q^{89} +(-83.2445 - 256.200i) q^{91} +(913.547 - 663.731i) q^{92} +(-334.722 + 243.189i) q^{94} +(287.268 + 853.007i) q^{95} +(1052.46 + 764.659i) q^{97} +(365.493 - 1124.87i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7} + O(q^{10}) \) \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20400 + 3.70554i −0.425680 + 1.31011i 0.476662 + 0.879086i \(0.341846\pi\)
−0.902342 + 0.431021i \(0.858154\pi\)
\(3\) 0 0
\(4\) −5.80928 4.22069i −0.726160 0.527586i
\(5\) 3.34114 10.6694i 0.298841 0.954303i
\(6\) 0 0
\(7\) 6.27975 0.339075 0.169537 0.985524i \(-0.445773\pi\)
0.169537 + 0.985524i \(0.445773\pi\)
\(8\) −2.58263 + 1.87639i −0.114137 + 0.0829257i
\(9\) 0 0
\(10\) 35.5133 + 25.2268i 1.12303 + 0.797741i
\(11\) −13.6357 + 41.9663i −0.373756 + 1.15030i 0.570559 + 0.821257i \(0.306727\pi\)
−0.944314 + 0.329045i \(0.893273\pi\)
\(12\) 0 0
\(13\) −13.2560 40.7979i −0.282812 0.870407i −0.987046 0.160438i \(-0.948709\pi\)
0.704233 0.709968i \(-0.251291\pi\)
\(14\) −7.56084 + 23.2699i −0.144337 + 0.444224i
\(15\) 0 0
\(16\) −21.5951 66.4630i −0.337424 1.03848i
\(17\) −81.6862 + 59.3485i −1.16540 + 0.846713i −0.990451 0.137864i \(-0.955976\pi\)
−0.174949 + 0.984577i \(0.555976\pi\)
\(18\) 0 0
\(19\) −65.1304 + 47.3200i −0.786417 + 0.571366i −0.906898 0.421350i \(-0.861556\pi\)
0.120481 + 0.992716i \(0.461556\pi\)
\(20\) −64.4420 + 47.8798i −0.720484 + 0.535313i
\(21\) 0 0
\(22\) −139.090 101.055i −1.34792 0.979320i
\(23\) −48.5949 + 149.560i −0.440554 + 1.35589i 0.446733 + 0.894667i \(0.352587\pi\)
−0.887287 + 0.461218i \(0.847413\pi\)
\(24\) 0 0
\(25\) −102.674 71.2962i −0.821388 0.570369i
\(26\) 167.138 1.26071
\(27\) 0 0
\(28\) −36.4808 26.5049i −0.246223 0.178891i
\(29\) −199.754 145.129i −1.27908 0.929306i −0.279555 0.960130i \(-0.590187\pi\)
−0.999525 + 0.0308238i \(0.990187\pi\)
\(30\) 0 0
\(31\) 69.6687 50.6173i 0.403641 0.293262i −0.367381 0.930070i \(-0.619746\pi\)
0.771022 + 0.636808i \(0.219746\pi\)
\(32\) 246.744 1.36308
\(33\) 0 0
\(34\) −121.568 374.147i −0.613197 1.88723i
\(35\) 20.9815 67.0014i 0.101329 0.323580i
\(36\) 0 0
\(37\) 61.0938 + 188.027i 0.271453 + 0.835446i 0.990136 + 0.140108i \(0.0447451\pi\)
−0.718683 + 0.695338i \(0.755255\pi\)
\(38\) −96.9290 298.317i −0.413788 1.27351i
\(39\) 0 0
\(40\) 11.3911 + 33.8245i 0.0450273 + 0.133703i
\(41\) 17.2714 + 53.1560i 0.0657889 + 0.202477i 0.978547 0.206023i \(-0.0660520\pi\)
−0.912758 + 0.408500i \(0.866052\pi\)
\(42\) 0 0
\(43\) 211.713 0.750835 0.375418 0.926856i \(-0.377499\pi\)
0.375418 + 0.926856i \(0.377499\pi\)
\(44\) 256.340 186.242i 0.878290 0.638115i
\(45\) 0 0
\(46\) −495.692 360.141i −1.58882 1.15435i
\(47\) 85.9089 + 62.4165i 0.266619 + 0.193710i 0.713060 0.701103i \(-0.247309\pi\)
−0.446441 + 0.894813i \(0.647309\pi\)
\(48\) 0 0
\(49\) −303.565 −0.885028
\(50\) 387.810 294.620i 1.09689 0.833312i
\(51\) 0 0
\(52\) −95.1871 + 292.956i −0.253848 + 0.781263i
\(53\) −153.468 111.501i −0.397743 0.288978i 0.370878 0.928682i \(-0.379057\pi\)
−0.768621 + 0.639704i \(0.779057\pi\)
\(54\) 0 0
\(55\) 402.198 + 285.700i 0.986043 + 0.700433i
\(56\) −16.2183 + 11.7833i −0.0387011 + 0.0281180i
\(57\) 0 0
\(58\) 778.288 565.459i 1.76197 1.28014i
\(59\) −140.608 432.747i −0.310265 0.954896i −0.977660 0.210193i \(-0.932591\pi\)
0.667395 0.744703i \(-0.267409\pi\)
\(60\) 0 0
\(61\) 171.878 528.986i 0.360766 1.11032i −0.591824 0.806067i \(-0.701592\pi\)
0.952590 0.304256i \(-0.0984079\pi\)
\(62\) 103.683 + 319.104i 0.212383 + 0.653649i
\(63\) 0 0
\(64\) −124.319 + 382.615i −0.242811 + 0.747295i
\(65\) −479.580 + 5.12286i −0.915148 + 0.00977558i
\(66\) 0 0
\(67\) −773.054 + 561.657i −1.40961 + 1.02414i −0.416227 + 0.909261i \(0.636648\pi\)
−0.993380 + 0.114878i \(0.963352\pi\)
\(68\) 725.030 1.29298
\(69\) 0 0
\(70\) 223.015 + 158.418i 0.380790 + 0.270494i
\(71\) 454.325 + 330.086i 0.759415 + 0.551747i 0.898731 0.438501i \(-0.144490\pi\)
−0.139316 + 0.990248i \(0.544490\pi\)
\(72\) 0 0
\(73\) −54.7181 + 168.405i −0.0877298 + 0.270004i −0.985291 0.170886i \(-0.945337\pi\)
0.897561 + 0.440890i \(0.145337\pi\)
\(74\) −770.300 −1.21008
\(75\) 0 0
\(76\) 578.084 0.872510
\(77\) −85.6286 + 263.538i −0.126731 + 0.390038i
\(78\) 0 0
\(79\) −769.301 558.930i −1.09561 0.796007i −0.115272 0.993334i \(-0.536774\pi\)
−0.980338 + 0.197327i \(0.936774\pi\)
\(80\) −781.275 + 8.34556i −1.09187 + 0.0116633i
\(81\) 0 0
\(82\) −217.767 −0.293272
\(83\) 11.3373 8.23700i 0.0149931 0.0108931i −0.580263 0.814429i \(-0.697050\pi\)
0.595257 + 0.803536i \(0.297050\pi\)
\(84\) 0 0
\(85\) 360.290 + 1069.84i 0.459752 + 1.36518i
\(86\) −254.903 + 784.511i −0.319615 + 0.983675i
\(87\) 0 0
\(88\) −43.5293 133.970i −0.0527300 0.162286i
\(89\) −143.004 + 440.120i −0.170319 + 0.524187i −0.999389 0.0349577i \(-0.988870\pi\)
0.829070 + 0.559145i \(0.188870\pi\)
\(90\) 0 0
\(91\) −83.2445 256.200i −0.0958945 0.295133i
\(92\) 913.547 663.731i 1.03526 0.752160i
\(93\) 0 0
\(94\) −334.722 + 243.189i −0.367275 + 0.266841i
\(95\) 287.268 + 853.007i 0.310242 + 0.921228i
\(96\) 0 0
\(97\) 1052.46 + 764.659i 1.10166 + 0.800406i 0.981331 0.192328i \(-0.0616038\pi\)
0.120333 + 0.992734i \(0.461604\pi\)
\(98\) 365.493 1124.87i 0.376739 1.15948i
\(99\) 0 0
\(100\) 295.541 + 847.533i 0.295541 + 0.847533i
\(101\) −1277.21 −1.25829 −0.629143 0.777289i \(-0.716594\pi\)
−0.629143 + 0.777289i \(0.716594\pi\)
\(102\) 0 0
\(103\) 895.730 + 650.786i 0.856883 + 0.622562i 0.927035 0.374975i \(-0.122349\pi\)
−0.0701525 + 0.997536i \(0.522349\pi\)
\(104\) 110.788 + 80.4924i 0.104459 + 0.0758936i
\(105\) 0 0
\(106\) 597.946 434.433i 0.547903 0.398075i
\(107\) 184.425 0.166627 0.0833134 0.996523i \(-0.473450\pi\)
0.0833134 + 0.996523i \(0.473450\pi\)
\(108\) 0 0
\(109\) 251.160 + 772.991i 0.220704 + 0.679258i 0.998699 + 0.0509874i \(0.0162368\pi\)
−0.777995 + 0.628270i \(0.783763\pi\)
\(110\) −1542.92 + 1146.38i −1.33738 + 0.993661i
\(111\) 0 0
\(112\) −135.612 417.371i −0.114412 0.352124i
\(113\) −260.636 802.155i −0.216978 0.667791i −0.999007 0.0445486i \(-0.985815\pi\)
0.782029 0.623242i \(-0.214185\pi\)
\(114\) 0 0
\(115\) 1433.36 + 1018.18i 1.16227 + 0.825616i
\(116\) 547.878 + 1686.20i 0.438528 + 1.34965i
\(117\) 0 0
\(118\) 1772.86 1.38309
\(119\) −512.969 + 372.694i −0.395158 + 0.287099i
\(120\) 0 0
\(121\) −498.437 362.135i −0.374483 0.272078i
\(122\) 1753.24 + 1273.80i 1.30107 + 0.945284i
\(123\) 0 0
\(124\) −618.365 −0.447829
\(125\) −1103.74 + 857.258i −0.789769 + 0.613404i
\(126\) 0 0
\(127\) −540.633 + 1663.90i −0.377744 + 1.16258i 0.563865 + 0.825867i \(0.309314\pi\)
−0.941609 + 0.336709i \(0.890686\pi\)
\(128\) 328.843 + 238.919i 0.227078 + 0.164982i
\(129\) 0 0
\(130\) 558.433 1783.27i 0.376753 1.20310i
\(131\) −405.420 + 294.555i −0.270395 + 0.196453i −0.714717 0.699414i \(-0.753444\pi\)
0.444322 + 0.895867i \(0.353444\pi\)
\(132\) 0 0
\(133\) −409.002 + 297.158i −0.266654 + 0.193736i
\(134\) −1150.48 3540.82i −0.741691 2.28269i
\(135\) 0 0
\(136\) 99.6044 306.551i 0.0628015 0.193283i
\(137\) −430.440 1324.76i −0.268430 0.826143i −0.990883 0.134723i \(-0.956985\pi\)
0.722453 0.691420i \(-0.243015\pi\)
\(138\) 0 0
\(139\) 287.901 886.067i 0.175679 0.540685i −0.823985 0.566612i \(-0.808254\pi\)
0.999664 + 0.0259271i \(0.00825378\pi\)
\(140\) −404.680 + 300.673i −0.244298 + 0.181511i
\(141\) 0 0
\(142\) −1770.16 + 1286.10i −1.04612 + 0.760047i
\(143\) 1892.89 1.10693
\(144\) 0 0
\(145\) −2215.85 + 1646.36i −1.26908 + 0.942915i
\(146\) −558.151 405.521i −0.316390 0.229871i
\(147\) 0 0
\(148\) 438.694 1350.16i 0.243652 0.749883i
\(149\) 2907.55 1.59863 0.799313 0.600914i \(-0.205197\pi\)
0.799313 + 0.600914i \(0.205197\pi\)
\(150\) 0 0
\(151\) −760.111 −0.409648 −0.204824 0.978799i \(-0.565662\pi\)
−0.204824 + 0.978799i \(0.565662\pi\)
\(152\) 79.4170 244.420i 0.0423788 0.130428i
\(153\) 0 0
\(154\) −873.453 634.601i −0.457045 0.332062i
\(155\) −307.285 912.445i −0.159237 0.472834i
\(156\) 0 0
\(157\) 2824.97 1.43603 0.718016 0.696027i \(-0.245051\pi\)
0.718016 + 0.696027i \(0.245051\pi\)
\(158\) 2997.38 2177.72i 1.50923 1.09652i
\(159\) 0 0
\(160\) 824.405 2632.61i 0.407344 1.30079i
\(161\) −305.164 + 939.198i −0.149381 + 0.459746i
\(162\) 0 0
\(163\) 49.8613 + 153.457i 0.0239598 + 0.0737406i 0.962321 0.271914i \(-0.0876568\pi\)
−0.938362 + 0.345655i \(0.887657\pi\)
\(164\) 124.020 381.696i 0.0590510 0.181740i
\(165\) 0 0
\(166\) 16.8725 + 51.9281i 0.00788890 + 0.0242795i
\(167\) 2368.72 1720.98i 1.09759 0.797444i 0.116924 0.993141i \(-0.462697\pi\)
0.980665 + 0.195696i \(0.0626967\pi\)
\(168\) 0 0
\(169\) 288.667 209.729i 0.131392 0.0954616i
\(170\) −4398.12 + 46.9806i −1.98424 + 0.0211956i
\(171\) 0 0
\(172\) −1229.90 893.575i −0.545227 0.396131i
\(173\) 753.042 2317.62i 0.330940 1.01853i −0.637747 0.770246i \(-0.720133\pi\)
0.968687 0.248284i \(-0.0798666\pi\)
\(174\) 0 0
\(175\) −644.764 447.722i −0.278512 0.193398i
\(176\) 3083.67 1.32068
\(177\) 0 0
\(178\) −1458.71 1059.81i −0.614240 0.446271i
\(179\) −2801.84 2035.66i −1.16994 0.850012i −0.178939 0.983860i \(-0.557266\pi\)
−0.991002 + 0.133849i \(0.957266\pi\)
\(180\) 0 0
\(181\) −3051.24 + 2216.86i −1.25302 + 0.910374i −0.998393 0.0566644i \(-0.981953\pi\)
−0.254629 + 0.967039i \(0.581953\pi\)
\(182\) 1049.59 0.427476
\(183\) 0 0
\(184\) −155.130 477.441i −0.0621540 0.191290i
\(185\) 2210.27 23.6100i 0.878390 0.00938294i
\(186\) 0 0
\(187\) −1376.79 4237.32i −0.538400 1.65703i
\(188\) −235.629 725.190i −0.0914094 0.281329i
\(189\) 0 0
\(190\) −3506.72 + 37.4587i −1.33897 + 0.0143029i
\(191\) 651.128 + 2003.97i 0.246670 + 0.759173i 0.995357 + 0.0962491i \(0.0306845\pi\)
−0.748687 + 0.662923i \(0.769315\pi\)
\(192\) 0 0
\(193\) −3761.96 −1.40307 −0.701533 0.712637i \(-0.747501\pi\)
−0.701533 + 0.712637i \(0.747501\pi\)
\(194\) −4100.64 + 2979.29i −1.51757 + 1.10258i
\(195\) 0 0
\(196\) 1763.49 + 1281.25i 0.642673 + 0.466929i
\(197\) 3061.21 + 2224.10i 1.10712 + 0.804368i 0.982207 0.187800i \(-0.0601355\pi\)
0.124911 + 0.992168i \(0.460136\pi\)
\(198\) 0 0
\(199\) 4606.97 1.64110 0.820552 0.571572i \(-0.193666\pi\)
0.820552 + 0.571572i \(0.193666\pi\)
\(200\) 398.948 8.52407i 0.141049 0.00301372i
\(201\) 0 0
\(202\) 1537.76 4732.75i 0.535627 1.64849i
\(203\) −1254.40 911.377i −0.433703 0.315104i
\(204\) 0 0
\(205\) 624.851 6.67464i 0.212885 0.00227403i
\(206\) −3489.98 + 2535.62i −1.18038 + 0.857596i
\(207\) 0 0
\(208\) −2425.28 + 1762.07i −0.808476 + 0.587393i
\(209\) −1097.75 3378.52i −0.363315 1.11817i
\(210\) 0 0
\(211\) 1167.51 3593.21i 0.380921 1.17236i −0.558475 0.829522i \(-0.688613\pi\)
0.939396 0.342834i \(-0.111387\pi\)
\(212\) 420.927 + 1295.48i 0.136365 + 0.419688i
\(213\) 0 0
\(214\) −222.049 + 683.396i −0.0709296 + 0.218299i
\(215\) 707.363 2258.86i 0.224380 0.716525i
\(216\) 0 0
\(217\) 437.502 317.864i 0.136864 0.0994378i
\(218\) −3166.75 −0.983850
\(219\) 0 0
\(220\) −1130.63 3357.27i −0.346486 1.02885i
\(221\) 3504.13 + 2545.90i 1.06657 + 0.774912i
\(222\) 0 0
\(223\) −1039.82 + 3200.23i −0.312248 + 0.961001i 0.664624 + 0.747178i \(0.268592\pi\)
−0.976872 + 0.213823i \(0.931408\pi\)
\(224\) 1549.49 0.462185
\(225\) 0 0
\(226\) 3286.23 0.967241
\(227\) −1868.95 + 5752.02i −0.546459 + 1.68183i 0.171035 + 0.985265i \(0.445289\pi\)
−0.717494 + 0.696564i \(0.754711\pi\)
\(228\) 0 0
\(229\) 1649.37 + 1198.34i 0.475953 + 0.345800i 0.799757 0.600324i \(-0.204962\pi\)
−0.323804 + 0.946124i \(0.604962\pi\)
\(230\) −5498.68 + 4085.46i −1.57640 + 1.17125i
\(231\) 0 0
\(232\) 788.211 0.223054
\(233\) −10.4656 + 7.60373i −0.00294260 + 0.00213793i −0.589256 0.807947i \(-0.700579\pi\)
0.586313 + 0.810085i \(0.300579\pi\)
\(234\) 0 0
\(235\) 952.982 708.057i 0.264535 0.196547i
\(236\) −1009.66 + 3107.41i −0.278488 + 0.857099i
\(237\) 0 0
\(238\) −763.416 2349.55i −0.207920 0.639911i
\(239\) 3.89930 12.0008i 0.00105533 0.00324798i −0.950527 0.310641i \(-0.899456\pi\)
0.951583 + 0.307393i \(0.0994565\pi\)
\(240\) 0 0
\(241\) 2084.79 + 6416.33i 0.557233 + 1.71499i 0.689972 + 0.723836i \(0.257623\pi\)
−0.132738 + 0.991151i \(0.542377\pi\)
\(242\) 1942.03 1410.97i 0.515861 0.374795i
\(243\) 0 0
\(244\) −3231.17 + 2347.59i −0.847765 + 0.615937i
\(245\) −1014.25 + 3238.86i −0.264483 + 0.844585i
\(246\) 0 0
\(247\) 2793.92 + 2029.90i 0.719729 + 0.522914i
\(248\) −84.9509 + 261.452i −0.0217516 + 0.0669444i
\(249\) 0 0
\(250\) −1847.70 5122.08i −0.467436 1.29580i
\(251\) −923.332 −0.232192 −0.116096 0.993238i \(-0.537038\pi\)
−0.116096 + 0.993238i \(0.537038\pi\)
\(252\) 0 0
\(253\) −5613.84 4078.70i −1.39502 1.01354i
\(254\) −5514.72 4006.68i −1.36230 0.989769i
\(255\) 0 0
\(256\) −3885.03 + 2822.64i −0.948493 + 0.689120i
\(257\) −4139.37 −1.00470 −0.502348 0.864666i \(-0.667530\pi\)
−0.502348 + 0.864666i \(0.667530\pi\)
\(258\) 0 0
\(259\) 383.654 + 1180.76i 0.0920428 + 0.283279i
\(260\) 2807.64 + 1994.40i 0.669701 + 0.475721i
\(261\) 0 0
\(262\) −603.358 1856.95i −0.142273 0.437872i
\(263\) 580.001 + 1785.06i 0.135986 + 0.418522i 0.995742 0.0921827i \(-0.0293844\pi\)
−0.859756 + 0.510705i \(0.829384\pi\)
\(264\) 0 0
\(265\) −1702.41 + 1264.87i −0.394634 + 0.293209i
\(266\) −608.690 1873.35i −0.140305 0.431815i
\(267\) 0 0
\(268\) 6861.47 1.56392
\(269\) 1596.43 1159.87i 0.361843 0.262895i −0.391977 0.919975i \(-0.628209\pi\)
0.753821 + 0.657080i \(0.228209\pi\)
\(270\) 0 0
\(271\) −4209.83 3058.62i −0.943650 0.685602i 0.00564662 0.999984i \(-0.498203\pi\)
−0.949296 + 0.314382i \(0.898203\pi\)
\(272\) 5708.50 + 4147.47i 1.27253 + 0.924549i
\(273\) 0 0
\(274\) 5427.19 1.19660
\(275\) 4392.06 3336.66i 0.963095 0.731665i
\(276\) 0 0
\(277\) 465.229 1431.83i 0.100913 0.310578i −0.887837 0.460159i \(-0.847792\pi\)
0.988749 + 0.149581i \(0.0477924\pi\)
\(278\) 2936.73 + 2133.66i 0.633572 + 0.460317i
\(279\) 0 0
\(280\) 71.5333 + 212.410i 0.0152676 + 0.0453354i
\(281\) 4394.85 3193.05i 0.933007 0.677869i −0.0137206 0.999906i \(-0.504368\pi\)
0.946727 + 0.322037i \(0.104368\pi\)
\(282\) 0 0
\(283\) −1837.68 + 1335.15i −0.386003 + 0.280448i −0.763816 0.645435i \(-0.776676\pi\)
0.377813 + 0.925882i \(0.376676\pi\)
\(284\) −1246.11 3835.13i −0.260363 0.801314i
\(285\) 0 0
\(286\) −2279.05 + 7014.18i −0.471199 + 1.45020i
\(287\) 108.460 + 333.806i 0.0223073 + 0.0686549i
\(288\) 0 0
\(289\) 1632.19 5023.36i 0.332218 1.02246i
\(290\) −3432.76 10193.2i −0.695098 2.06401i
\(291\) 0 0
\(292\) 1028.66 747.364i 0.206157 0.149781i
\(293\) −5377.08 −1.07212 −0.536062 0.844178i \(-0.680089\pi\)
−0.536062 + 0.844178i \(0.680089\pi\)
\(294\) 0 0
\(295\) −5086.96 + 54.3387i −1.00398 + 0.0107245i
\(296\) −510.596 370.970i −0.100263 0.0728452i
\(297\) 0 0
\(298\) −3500.69 + 10774.0i −0.680503 + 2.09437i
\(299\) 6745.89 1.30477
\(300\) 0 0
\(301\) 1329.50 0.254589
\(302\) 915.176 2816.62i 0.174379 0.536683i
\(303\) 0 0
\(304\) 4551.53 + 3306.88i 0.858711 + 0.623890i
\(305\) −5069.71 3601.26i −0.951773 0.676090i
\(306\) 0 0
\(307\) 8104.37 1.50665 0.753324 0.657649i \(-0.228449\pi\)
0.753324 + 0.657649i \(0.228449\pi\)
\(308\) 1609.75 1169.55i 0.297806 0.216369i
\(309\) 0 0
\(310\) 3751.08 40.0689i 0.687248 0.00734116i
\(311\) −233.023 + 717.171i −0.0424872 + 0.130762i −0.970050 0.242905i \(-0.921900\pi\)
0.927563 + 0.373667i \(0.121900\pi\)
\(312\) 0 0
\(313\) 1329.80 + 4092.70i 0.240143 + 0.739084i 0.996397 + 0.0848065i \(0.0270272\pi\)
−0.756254 + 0.654278i \(0.772973\pi\)
\(314\) −3401.27 + 10468.0i −0.611289 + 1.88136i
\(315\) 0 0
\(316\) 2110.02 + 6493.97i 0.375626 + 1.15606i
\(317\) 2940.89 2136.68i 0.521062 0.378574i −0.295942 0.955206i \(-0.595633\pi\)
0.817004 + 0.576632i \(0.195633\pi\)
\(318\) 0 0
\(319\) 8814.32 6403.98i 1.54704 1.12399i
\(320\) 3666.92 + 2604.78i 0.640584 + 0.455037i
\(321\) 0 0
\(322\) −3112.82 2261.59i −0.538729 0.391409i
\(323\) 2511.88 7730.78i 0.432708 1.33174i
\(324\) 0 0
\(325\) −1547.69 + 5133.96i −0.264155 + 0.876250i
\(326\) −628.676 −0.106807
\(327\) 0 0
\(328\) −144.347 104.875i −0.0242995 0.0176547i
\(329\) 539.486 + 391.960i 0.0904038 + 0.0656822i
\(330\) 0 0
\(331\) 2978.03 2163.66i 0.494524 0.359292i −0.312398 0.949951i \(-0.601132\pi\)
0.806921 + 0.590659i \(0.201132\pi\)
\(332\) −100.627 −0.0166344
\(333\) 0 0
\(334\) 3525.20 + 10849.5i 0.577517 + 1.77741i
\(335\) 3409.68 + 10124.6i 0.556091 + 1.65125i
\(336\) 0 0
\(337\) −85.2315 262.316i −0.0137770 0.0424013i 0.943932 0.330141i \(-0.107096\pi\)
−0.957709 + 0.287740i \(0.907096\pi\)
\(338\) 429.604 + 1322.18i 0.0691342 + 0.212773i
\(339\) 0 0
\(340\) 2422.43 7735.65i 0.386396 1.23390i
\(341\) 1174.24 + 3613.94i 0.186477 + 0.573917i
\(342\) 0 0
\(343\) −4060.26 −0.639165
\(344\) −546.777 + 397.257i −0.0856984 + 0.0622635i
\(345\) 0 0
\(346\) 7681.39 + 5580.85i 1.19351 + 0.867135i
\(347\) −9022.35 6555.12i −1.39581 1.01411i −0.995200 0.0978631i \(-0.968799\pi\)
−0.400607 0.916250i \(-0.631201\pi\)
\(348\) 0 0
\(349\) −8219.29 −1.26065 −0.630327 0.776330i \(-0.717079\pi\)
−0.630327 + 0.776330i \(0.717079\pi\)
\(350\) 2435.35 1850.14i 0.371929 0.282555i
\(351\) 0 0
\(352\) −3364.52 + 10354.9i −0.509458 + 1.56795i
\(353\) −1577.47 1146.10i −0.237848 0.172806i 0.462476 0.886632i \(-0.346961\pi\)
−0.700324 + 0.713825i \(0.746961\pi\)
\(354\) 0 0
\(355\) 5039.80 3744.52i 0.753478 0.559827i
\(356\) 2688.36 1953.21i 0.400232 0.290786i
\(357\) 0 0
\(358\) 10916.6 7931.40i 1.61163 1.17091i
\(359\) −3470.55 10681.2i −0.510219 1.57029i −0.791816 0.610759i \(-0.790864\pi\)
0.281598 0.959533i \(-0.409136\pi\)
\(360\) 0 0
\(361\) −116.764 + 359.361i −0.0170234 + 0.0523927i
\(362\) −4540.95 13975.6i −0.659302 2.02912i
\(363\) 0 0
\(364\) −597.751 + 1839.69i −0.0860733 + 0.264906i
\(365\) 1613.97 + 1146.48i 0.231449 + 0.164409i
\(366\) 0 0
\(367\) 5303.29 3853.06i 0.754304 0.548034i −0.142854 0.989744i \(-0.545628\pi\)
0.897158 + 0.441710i \(0.145628\pi\)
\(368\) 10989.6 1.55672
\(369\) 0 0
\(370\) −2573.68 + 8218.67i −0.361620 + 1.15478i
\(371\) −963.738 700.197i −0.134865 0.0979849i
\(372\) 0 0
\(373\) −1346.23 + 4143.27i −0.186877 + 0.575148i −0.999976 0.00697762i \(-0.997779\pi\)
0.813099 + 0.582126i \(0.197779\pi\)
\(374\) 17359.2 2.40007
\(375\) 0 0
\(376\) −338.989 −0.0464948
\(377\) −3273.03 + 10073.4i −0.447135 + 1.37614i
\(378\) 0 0
\(379\) −4284.53 3112.90i −0.580691 0.421896i 0.258282 0.966069i \(-0.416844\pi\)
−0.838973 + 0.544173i \(0.816844\pi\)
\(380\) 1931.46 6167.82i 0.260742 0.832639i
\(381\) 0 0
\(382\) −8209.74 −1.09960
\(383\) −6312.15 + 4586.04i −0.842129 + 0.611843i −0.922965 0.384885i \(-0.874241\pi\)
0.0808353 + 0.996727i \(0.474241\pi\)
\(384\) 0 0
\(385\) 2525.70 + 1794.13i 0.334342 + 0.237499i
\(386\) 4529.41 13940.1i 0.597257 1.83817i
\(387\) 0 0
\(388\) −2886.66 8884.24i −0.377701 1.16245i
\(389\) −4009.27 + 12339.3i −0.522566 + 1.60829i 0.246514 + 0.969139i \(0.420715\pi\)
−0.769079 + 0.639153i \(0.779285\pi\)
\(390\) 0 0
\(391\) −4906.61 15101.0i −0.634624 1.95317i
\(392\) 783.997 569.607i 0.101015 0.0733916i
\(393\) 0 0
\(394\) −11927.2 + 8665.62i −1.52509 + 1.10804i
\(395\) −8533.81 + 6340.54i −1.08704 + 0.807664i
\(396\) 0 0
\(397\) 8223.68 + 5974.85i 1.03963 + 0.755338i 0.970214 0.242249i \(-0.0778852\pi\)
0.0694198 + 0.997588i \(0.477885\pi\)
\(398\) −5546.81 + 17071.3i −0.698585 + 2.15002i
\(399\) 0 0
\(400\) −2521.31 + 8363.64i −0.315164 + 1.04546i
\(401\) −8213.85 −1.02289 −0.511447 0.859315i \(-0.670890\pi\)
−0.511447 + 0.859315i \(0.670890\pi\)
\(402\) 0 0
\(403\) −2988.61 2171.35i −0.369412 0.268394i
\(404\) 7419.66 + 5390.70i 0.913718 + 0.663855i
\(405\) 0 0
\(406\) 4887.45 3550.94i 0.597439 0.434065i
\(407\) −8723.87 −1.06247
\(408\) 0 0
\(409\) −1231.90 3791.40i −0.148933 0.458369i 0.848563 0.529095i \(-0.177468\pi\)
−0.997496 + 0.0707261i \(0.977468\pi\)
\(410\) −727.589 + 2323.45i −0.0876416 + 0.279870i
\(411\) 0 0
\(412\) −2456.78 7561.20i −0.293779 0.904159i
\(413\) −882.983 2717.54i −0.105203 0.323781i
\(414\) 0 0
\(415\) −50.0047 148.483i −0.00591479 0.0175633i
\(416\) −3270.84 10066.6i −0.385496 1.18643i
\(417\) 0 0
\(418\) 13840.9 1.61958
\(419\) −7445.57 + 5409.52i −0.868115 + 0.630722i −0.930080 0.367356i \(-0.880263\pi\)
0.0619658 + 0.998078i \(0.480263\pi\)
\(420\) 0 0
\(421\) −11708.9 8506.99i −1.35548 0.984810i −0.998718 0.0506132i \(-0.983882\pi\)
−0.356757 0.934197i \(-0.616118\pi\)
\(422\) 11909.1 + 8652.48i 1.37376 + 0.998095i
\(423\) 0 0
\(424\) 605.570 0.0693611
\(425\) 12618.3 269.608i 1.44019 0.0307716i
\(426\) 0 0
\(427\) 1079.35 3321.90i 0.122327 0.376482i
\(428\) −1071.38 778.402i −0.120998 0.0879100i
\(429\) 0 0
\(430\) 7518.62 + 5340.84i 0.843210 + 0.598972i
\(431\) −13496.0 + 9805.38i −1.50830 + 1.09584i −0.541375 + 0.840781i \(0.682096\pi\)
−0.966925 + 0.255063i \(0.917904\pi\)
\(432\) 0 0
\(433\) −6033.95 + 4383.92i −0.669684 + 0.486554i −0.869919 0.493194i \(-0.835829\pi\)
0.200235 + 0.979748i \(0.435829\pi\)
\(434\) 651.104 + 2003.89i 0.0720138 + 0.221636i
\(435\) 0 0
\(436\) 1803.50 5550.59i 0.198100 0.609691i
\(437\) −3912.16 12040.4i −0.428247 1.31801i
\(438\) 0 0
\(439\) 3121.46 9606.85i 0.339360 1.04444i −0.625174 0.780485i \(-0.714972\pi\)
0.964534 0.263957i \(-0.0850278\pi\)
\(440\) −1574.82 + 16.8221i −0.170628 + 0.00182265i
\(441\) 0 0
\(442\) −13652.9 + 9919.42i −1.46924 + 1.06746i
\(443\) 3125.48 0.335205 0.167603 0.985855i \(-0.446397\pi\)
0.167603 + 0.985855i \(0.446397\pi\)
\(444\) 0 0
\(445\) 4218.04 + 2996.27i 0.449335 + 0.319184i
\(446\) −10606.6 7706.18i −1.12610 0.818157i
\(447\) 0 0
\(448\) −780.693 + 2402.73i −0.0823310 + 0.253389i
\(449\) 14568.3 1.53123 0.765614 0.643300i \(-0.222435\pi\)
0.765614 + 0.643300i \(0.222435\pi\)
\(450\) 0 0
\(451\) −2466.27 −0.257499
\(452\) −1871.54 + 5760.01i −0.194756 + 0.599398i
\(453\) 0 0
\(454\) −19064.1 13850.9i −1.97076 1.43184i
\(455\) −3011.64 + 32.1703i −0.310303 + 0.00331465i
\(456\) 0 0
\(457\) −14908.3 −1.52600 −0.763000 0.646399i \(-0.776274\pi\)
−0.763000 + 0.646399i \(0.776274\pi\)
\(458\) −6426.33 + 4669.00i −0.655639 + 0.476349i
\(459\) 0 0
\(460\) −4029.34 11964.6i −0.408411 1.21273i
\(461\) −1140.13 + 3508.95i −0.115187 + 0.354508i −0.991986 0.126349i \(-0.959674\pi\)
0.876799 + 0.480856i \(0.159674\pi\)
\(462\) 0 0
\(463\) −4273.76 13153.3i −0.428981 1.32027i −0.899130 0.437681i \(-0.855800\pi\)
0.470149 0.882587i \(-0.344200\pi\)
\(464\) −5332.04 + 16410.3i −0.533477 + 1.64187i
\(465\) 0 0
\(466\) −15.5753 47.9358i −0.00154831 0.00476520i
\(467\) −221.710 + 161.082i −0.0219690 + 0.0159614i −0.598716 0.800962i \(-0.704322\pi\)
0.576747 + 0.816923i \(0.304322\pi\)
\(468\) 0 0
\(469\) −4854.59 + 3527.06i −0.477962 + 0.347260i
\(470\) 1476.34 + 4383.82i 0.144891 + 0.430235i
\(471\) 0 0
\(472\) 1175.14 + 853.791i 0.114598 + 0.0832605i
\(473\) −2886.85 + 8884.81i −0.280629 + 0.863687i
\(474\) 0 0
\(475\) 10060.9 214.965i 0.971844 0.0207648i
\(476\) 4553.00 0.438417
\(477\) 0 0
\(478\) 39.7747 + 28.8980i 0.00380597 + 0.00276520i
\(479\) 11987.5 + 8709.43i 1.14347 + 0.830781i 0.987599 0.156997i \(-0.0501812\pi\)
0.155872 + 0.987777i \(0.450181\pi\)
\(480\) 0 0
\(481\) 6861.25 4984.99i 0.650408 0.472549i
\(482\) −26286.1 −2.48402
\(483\) 0 0
\(484\) 1367.10 + 4207.49i 0.128390 + 0.395144i
\(485\) 11674.9 8674.34i 1.09305 0.812127i
\(486\) 0 0
\(487\) 5341.55 + 16439.6i 0.497020 + 1.52967i 0.813785 + 0.581166i \(0.197403\pi\)
−0.316765 + 0.948504i \(0.602597\pi\)
\(488\) 548.688 + 1688.69i 0.0508974 + 0.156646i
\(489\) 0 0
\(490\) −10780.6 7657.96i −0.993912 0.706023i
\(491\) −3045.75 9373.84i −0.279944 0.861580i −0.987869 0.155292i \(-0.950368\pi\)
0.707924 0.706288i \(-0.249632\pi\)
\(492\) 0 0
\(493\) 24930.3 2.27750
\(494\) −10885.8 + 7908.99i −0.991447 + 0.720329i
\(495\) 0 0
\(496\) −4868.68 3537.30i −0.440747 0.320221i
\(497\) 2853.05 + 2072.86i 0.257498 + 0.187083i
\(498\) 0 0
\(499\) 10126.4 0.908458 0.454229 0.890885i \(-0.349915\pi\)
0.454229 + 0.890885i \(0.349915\pi\)
\(500\) 10030.1 321.523i 0.897123 0.0287579i
\(501\) 0 0
\(502\) 1111.69 3421.44i 0.0988394 0.304196i
\(503\) −4874.27 3541.36i −0.432073 0.313920i 0.350404 0.936599i \(-0.386044\pi\)
−0.782477 + 0.622679i \(0.786044\pi\)
\(504\) 0 0
\(505\) −4267.33 + 13627.1i −0.376027 + 1.20079i
\(506\) 21872.9 15891.6i 1.92168 1.39618i
\(507\) 0 0
\(508\) 10163.5 7384.21i 0.887662 0.644924i
\(509\) −5588.13 17198.5i −0.486620 1.49766i −0.829621 0.558327i \(-0.811443\pi\)
0.343001 0.939335i \(-0.388557\pi\)
\(510\) 0 0
\(511\) −343.616 + 1057.54i −0.0297469 + 0.0915516i
\(512\) −4776.96 14702.0i −0.412331 1.26903i
\(513\) 0 0
\(514\) 4983.81 15338.6i 0.427678 1.31626i
\(515\) 9936.28 7382.56i 0.850184 0.631679i
\(516\) 0 0
\(517\) −3790.81 + 2754.19i −0.322476 + 0.234292i
\(518\) −4837.29 −0.410306
\(519\) 0 0
\(520\) 1228.97 913.112i 0.103642 0.0770050i
\(521\) 7060.19 + 5129.53i 0.593690 + 0.431341i 0.843634 0.536919i \(-0.180412\pi\)
−0.249943 + 0.968260i \(0.580412\pi\)
\(522\) 0 0
\(523\) 2270.43 6987.67i 0.189826 0.584225i −0.810172 0.586192i \(-0.800626\pi\)
0.999998 + 0.00196745i \(0.000626259\pi\)
\(524\) 3598.42 0.299996
\(525\) 0 0
\(526\) −7312.93 −0.606196
\(527\) −2686.91 + 8269.46i −0.222094 + 0.683536i
\(528\) 0 0
\(529\) −10163.3 7384.10i −0.835321 0.606896i
\(530\) −2637.33 7831.25i −0.216148 0.641826i
\(531\) 0 0
\(532\) 3630.22 0.295846
\(533\) 1939.70 1409.27i 0.157632 0.114526i
\(534\) 0 0
\(535\) 616.191 1967.71i 0.0497949 0.159012i
\(536\) 942.627 2901.11i 0.0759614 0.233785i
\(537\) 0 0
\(538\) 2375.85 + 7312.12i 0.190391 + 0.585962i
\(539\) 4139.31 12739.5i 0.330784 1.01805i
\(540\) 0 0
\(541\) −6077.53 18704.7i −0.482982 1.48647i −0.834882 0.550429i \(-0.814464\pi\)
0.351900 0.936038i \(-0.385536\pi\)
\(542\) 16402.5 11917.1i 1.29990 0.944436i
\(543\) 0 0
\(544\) −20155.5 + 14643.9i −1.58853 + 1.15414i
\(545\) 9086.53 97.0621i 0.714173 0.00762878i
\(546\) 0 0
\(547\) −19688.4 14304.5i −1.53897 1.11812i −0.950979 0.309254i \(-0.899921\pi\)
−0.587987 0.808870i \(-0.700079\pi\)
\(548\) −3090.84 + 9512.64i −0.240939 + 0.741533i
\(549\) 0 0
\(550\) 7076.07 + 20292.3i 0.548590 + 1.57321i
\(551\) 19877.6 1.53686
\(552\) 0 0
\(553\) −4831.02 3509.94i −0.371493 0.269906i
\(554\) 4745.56 + 3447.85i 0.363934 + 0.264413i
\(555\) 0 0
\(556\) −5412.31 + 3932.27i −0.412829 + 0.299938i
\(557\) −15077.6 −1.14696 −0.573481 0.819219i \(-0.694408\pi\)
−0.573481 + 0.819219i \(0.694408\pi\)
\(558\) 0 0
\(559\) −2806.47 8637.44i −0.212346 0.653532i
\(560\) −4906.21 + 52.4080i −0.370224 + 0.00395472i
\(561\) 0 0
\(562\) 6540.55 + 20129.7i 0.490919 + 1.51089i
\(563\) −4431.52 13638.8i −0.331734 1.02097i −0.968309 0.249757i \(-0.919649\pi\)
0.636575 0.771215i \(-0.280351\pi\)
\(564\) 0 0
\(565\) −9429.36 + 100.724i −0.702117 + 0.00749999i
\(566\) −2734.89 8417.14i −0.203103 0.625086i
\(567\) 0 0
\(568\) −1792.73 −0.132432
\(569\) 3259.66 2368.28i 0.240162 0.174488i −0.461194 0.887300i \(-0.652579\pi\)
0.701355 + 0.712812i \(0.252579\pi\)
\(570\) 0 0
\(571\) 9126.02 + 6630.45i 0.668848 + 0.485947i 0.869639 0.493687i \(-0.164351\pi\)
−0.200791 + 0.979634i \(0.564351\pi\)
\(572\) −10996.3 7989.30i −0.803811 0.584003i
\(573\) 0 0
\(574\) −1367.52 −0.0994411
\(575\) 15652.4 11891.2i 1.13522 0.862430i
\(576\) 0 0
\(577\) −3864.21 + 11892.8i −0.278802 + 0.858066i 0.709386 + 0.704820i \(0.248972\pi\)
−0.988188 + 0.153245i \(0.951028\pi\)
\(578\) 16649.1 + 12096.3i 1.19812 + 0.870483i
\(579\) 0 0
\(580\) 19821.3 211.731i 1.41903 0.0151580i
\(581\) 71.1952 51.7263i 0.00508377 0.00369358i
\(582\) 0 0
\(583\) 6771.91 4920.08i 0.481070 0.349518i
\(584\) −174.677 537.602i −0.0123771 0.0380927i
\(585\) 0 0
\(586\) 6474.03 19925.0i 0.456382 1.40460i
\(587\) 5390.49 + 16590.2i 0.379028 + 1.16653i 0.940721 + 0.339182i \(0.110150\pi\)
−0.561693 + 0.827346i \(0.689850\pi\)
\(588\) 0 0
\(589\) −2142.34 + 6593.44i −0.149870 + 0.461253i
\(590\) 5923.36 18915.4i 0.413323 1.31989i
\(591\) 0 0
\(592\) 11177.5 8120.95i 0.776003 0.563799i
\(593\) −17798.5 −1.23254 −0.616269 0.787536i \(-0.711357\pi\)
−0.616269 + 0.787536i \(0.711357\pi\)
\(594\) 0 0
\(595\) 2262.53 + 6718.31i 0.155890 + 0.462897i
\(596\) −16890.8 12271.8i −1.16086 0.843414i
\(597\) 0 0
\(598\) −8122.08 + 24997.2i −0.555412 + 1.70938i
\(599\) 23241.2 1.58532 0.792661 0.609662i \(-0.208695\pi\)
0.792661 + 0.609662i \(0.208695\pi\)
\(600\) 0 0
\(601\) −2735.11 −0.185637 −0.0928183 0.995683i \(-0.529588\pi\)
−0.0928183 + 0.995683i \(0.529588\pi\)
\(602\) −1600.73 + 4926.53i −0.108373 + 0.333539i
\(603\) 0 0
\(604\) 4415.70 + 3208.19i 0.297470 + 0.216125i
\(605\) −5529.13 + 4108.09i −0.371555 + 0.276062i
\(606\) 0 0
\(607\) 1676.42 0.112098 0.0560492 0.998428i \(-0.482150\pi\)
0.0560492 + 0.998428i \(0.482150\pi\)
\(608\) −16070.5 + 11675.9i −1.07195 + 0.778817i
\(609\) 0 0
\(610\) 19448.6 14450.1i 1.29090 0.959127i
\(611\) 1407.65 4332.29i 0.0932035 0.286851i
\(612\) 0 0
\(613\) −611.200 1881.08i −0.0402710 0.123941i 0.928900 0.370331i \(-0.120756\pi\)
−0.969171 + 0.246390i \(0.920756\pi\)
\(614\) −9757.70 + 30031.1i −0.641349 + 1.97387i
\(615\) 0 0
\(616\) −273.353 841.295i −0.0178794 0.0550272i
\(617\) −6781.95 + 4927.38i −0.442514 + 0.321505i −0.786633 0.617421i \(-0.788178\pi\)
0.344119 + 0.938926i \(0.388178\pi\)
\(618\) 0 0
\(619\) −15968.8 + 11602.0i −1.03690 + 0.753350i −0.969678 0.244388i \(-0.921413\pi\)
−0.0672201 + 0.997738i \(0.521413\pi\)
\(620\) −2066.05 + 6597.60i −0.133830 + 0.427365i
\(621\) 0 0
\(622\) −2376.95 1726.95i −0.153227 0.111326i
\(623\) −898.027 + 2763.84i −0.0577507 + 0.177738i
\(624\) 0 0
\(625\) 5458.71 + 14640.5i 0.349358 + 0.936989i
\(626\) −16766.8 −1.07050
\(627\) 0 0
\(628\) −16411.0 11923.3i −1.04279 0.757631i
\(629\) −16149.7 11733.4i −1.02373 0.743787i
\(630\) 0 0
\(631\) 4438.84 3225.00i 0.280043 0.203463i −0.438893 0.898539i \(-0.644629\pi\)
0.718936 + 0.695076i \(0.244629\pi\)
\(632\) 3035.60 0.191059
\(633\) 0 0
\(634\) 4376.72 + 13470.2i 0.274167 + 0.843798i
\(635\) 15946.5 + 11327.6i 0.996564 + 0.707907i
\(636\) 0 0
\(637\) 4024.06 + 12384.8i 0.250297 + 0.770335i
\(638\) 13117.7 + 40372.3i 0.814007 + 2.50526i
\(639\) 0 0
\(640\) 3647.84 2710.31i 0.225302 0.167398i
\(641\) 2181.43 + 6713.77i 0.134417 + 0.413694i 0.995499 0.0947728i \(-0.0302125\pi\)
−0.861082 + 0.508467i \(0.830212\pi\)
\(642\) 0 0
\(643\) 21740.4 1.33337 0.666687 0.745338i \(-0.267712\pi\)
0.666687 + 0.745338i \(0.267712\pi\)
\(644\) 5736.85 4168.06i 0.351030 0.255038i
\(645\) 0 0
\(646\) 25622.4 + 18615.8i 1.56053 + 1.13379i
\(647\) 3360.78 + 2441.75i 0.204213 + 0.148370i 0.685192 0.728363i \(-0.259718\pi\)
−0.480978 + 0.876732i \(0.659718\pi\)
\(648\) 0 0
\(649\) 20078.1 1.21438
\(650\) −17160.7 11916.3i −1.03554 0.719072i
\(651\) 0 0
\(652\) 358.038 1101.93i 0.0215059 0.0661883i
\(653\) −14674.8 10661.8i −0.879430 0.638943i 0.0536708 0.998559i \(-0.482908\pi\)
−0.933101 + 0.359616i \(0.882908\pi\)
\(654\) 0 0
\(655\) 1788.17 + 5309.75i 0.106671 + 0.316747i
\(656\) 3159.93 2295.82i 0.188071 0.136641i
\(657\) 0 0
\(658\) −2101.97 + 1527.17i −0.124534 + 0.0904791i
\(659\) −1609.32 4952.97i −0.0951292 0.292778i 0.892158 0.451723i \(-0.149191\pi\)
−0.987287 + 0.158946i \(0.949191\pi\)
\(660\) 0 0
\(661\) −5473.66 + 16846.2i −0.322089 + 0.991287i 0.650649 + 0.759379i \(0.274497\pi\)
−0.972738 + 0.231908i \(0.925503\pi\)
\(662\) 4431.99 + 13640.3i 0.260203 + 0.800822i
\(663\) 0 0
\(664\) −13.8241 + 42.5463i −0.000807953 + 0.00248662i
\(665\) 1803.97 + 5356.67i 0.105195 + 0.312365i
\(666\) 0 0
\(667\) 31412.5 22822.5i 1.82354 1.32488i
\(668\) −21024.3 −1.21775
\(669\) 0 0
\(670\) −41622.5 + 444.610i −2.40003 + 0.0256370i
\(671\) 19855.9 + 14426.2i 1.14237 + 0.829979i
\(672\) 0 0
\(673\) −9178.90 + 28249.8i −0.525737 + 1.61805i 0.237118 + 0.971481i \(0.423797\pi\)
−0.762855 + 0.646570i \(0.776203\pi\)
\(674\) 1074.64 0.0614149
\(675\) 0 0
\(676\) −2562.15 −0.145776
\(677\) 2158.52 6643.23i 0.122538 0.377134i −0.870906 0.491449i \(-0.836467\pi\)
0.993445 + 0.114315i \(0.0364673\pi\)
\(678\) 0 0
\(679\) 6609.20 + 4801.87i 0.373546 + 0.271397i
\(680\) −2937.93 2086.95i −0.165683 0.117693i
\(681\) 0 0
\(682\) −14805.4 −0.831272
\(683\) −3632.47 + 2639.14i −0.203503 + 0.147854i −0.684869 0.728666i \(-0.740141\pi\)
0.481366 + 0.876520i \(0.340141\pi\)
\(684\) 0 0
\(685\) −15572.6 + 166.346i −0.868609 + 0.00927846i
\(686\) 4888.57 15045.5i 0.272080 0.837375i
\(687\) 0 0
\(688\) −4571.97 14071.1i −0.253350 0.779731i
\(689\) −2514.62 + 7739.21i −0.139041 + 0.427925i
\(690\) 0 0
\(691\) 10095.7 + 31071.4i 0.555802 + 1.71058i 0.693817 + 0.720151i \(0.255928\pi\)
−0.138016 + 0.990430i \(0.544072\pi\)
\(692\) −14156.6 + 10285.4i −0.777678 + 0.565016i
\(693\) 0 0
\(694\) 35153.2 25540.3i 1.92276 1.39697i
\(695\) −8491.92 6032.21i −0.463477 0.329230i
\(696\) 0 0
\(697\) −4565.56 3317.08i −0.248111 0.180263i
\(698\) 9896.05 30456.9i 0.536635 1.65159i
\(699\) 0 0
\(700\) 1855.92 + 5322.29i 0.100210 + 0.287377i
\(701\) −1911.12 −0.102970 −0.0514852 0.998674i \(-0.516395\pi\)
−0.0514852 + 0.998674i \(0.516395\pi\)
\(702\) 0 0
\(703\) −12876.5 9355.33i −0.690820 0.501910i
\(704\) −14361.8 10434.4i −0.768862 0.558611i
\(705\) 0 0
\(706\) 6146.19 4465.47i 0.327642 0.238046i
\(707\) −8020.54 −0.426653
\(708\) 0 0
\(709\) 10449.5 + 32160.3i 0.553512 + 1.70353i 0.699841 + 0.714298i \(0.253254\pi\)
−0.146329 + 0.989236i \(0.546746\pi\)
\(710\) 7807.56 + 23183.6i 0.412694 + 1.22544i
\(711\) 0 0
\(712\) −456.512 1405.00i −0.0240288 0.0739531i
\(713\) 4184.76 + 12879.4i 0.219805 + 0.676489i
\(714\) 0 0
\(715\) 6324.41 20196.1i 0.330797 1.05635i
\(716\) 7684.81 + 23651.4i 0.401110 + 1.23449i
\(717\) 0 0
\(718\) 43758.4 2.27444
\(719\) 7234.32 5256.04i 0.375236 0.272625i −0.384143 0.923274i \(-0.625503\pi\)
0.759379 + 0.650649i \(0.225503\pi\)
\(720\) 0 0
\(721\) 5624.96 + 4086.77i 0.290547 + 0.211095i
\(722\) −1191.04 865.345i −0.0613935 0.0446050i
\(723\) 0 0
\(724\) 27082.2 1.39020
\(725\) 10162.2 + 29142.6i 0.520574 + 1.49287i
\(726\) 0 0
\(727\) 2679.13 8245.53i 0.136676 0.420646i −0.859171 0.511689i \(-0.829020\pi\)
0.995847 + 0.0910429i \(0.0290201\pi\)
\(728\) 695.723 + 505.472i 0.0354192 + 0.0257336i
\(729\) 0 0
\(730\) −6191.54 + 4600.26i −0.313917 + 0.233237i
\(731\) −17294.0 + 12564.8i −0.875024 + 0.635742i
\(732\) 0 0
\(733\) −19365.9 + 14070.2i −0.975848 + 0.708995i −0.956777 0.290823i \(-0.906071\pi\)
−0.0190713 + 0.999818i \(0.506071\pi\)
\(734\) 7892.52 + 24290.7i 0.396891 + 1.22151i
\(735\) 0 0
\(736\) −11990.5 + 36902.9i −0.600510 + 1.84818i
\(737\) −13029.5 40100.8i −0.651220 2.00425i
\(738\) 0 0
\(739\) 1440.41 4433.14i 0.0717003 0.220671i −0.908784 0.417266i \(-0.862988\pi\)
0.980485 + 0.196595i \(0.0629884\pi\)
\(740\) −12939.7 9191.70i −0.642802 0.456613i
\(741\) 0 0
\(742\) 3754.95 2728.13i 0.185780 0.134977i
\(743\) 26436.5 1.30533 0.652666 0.757646i \(-0.273650\pi\)
0.652666 + 0.757646i \(0.273650\pi\)
\(744\) 0 0
\(745\) 9714.52 31021.9i 0.477735 1.52557i
\(746\) −13732.2 9977.02i −0.673956 0.489658i
\(747\) 0 0
\(748\) −9886.27 + 30426.8i −0.483259 + 1.48732i
\(749\) 1158.14 0.0564989
\(750\) 0 0
\(751\) −11047.7 −0.536802 −0.268401 0.963307i \(-0.586495\pi\)
−0.268401 + 0.963307i \(0.586495\pi\)
\(752\) 2293.17 7057.66i 0.111201 0.342242i
\(753\) 0 0
\(754\) −33386.5 24256.7i −1.61255 1.17159i
\(755\) −2539.64 + 8109.95i −0.122420 + 0.390929i
\(756\) 0 0
\(757\) −1908.68 −0.0916411 −0.0458205 0.998950i \(-0.514590\pi\)
−0.0458205 + 0.998950i \(0.514590\pi\)
\(758\) 16693.6 12128.6i 0.799918 0.581174i
\(759\) 0 0
\(760\) −2342.48 1663.98i −0.111804 0.0794195i
\(761\) −849.513 + 2614.53i −0.0404662 + 0.124542i −0.969249 0.246083i \(-0.920856\pi\)
0.928783 + 0.370625i \(0.120856\pi\)
\(762\) 0 0
\(763\) 1577.22 + 4854.19i 0.0748352 + 0.230319i
\(764\) 4675.54 14389.8i 0.221407 0.681421i
\(765\) 0 0
\(766\) −9393.93 28911.5i −0.443102 1.36373i
\(767\) −15791.2 + 11473.0i −0.743401 + 0.540113i
\(768\) 0 0
\(769\) 4062.71 2951.73i 0.190514 0.138416i −0.488440 0.872598i \(-0.662434\pi\)
0.678954 + 0.734181i \(0.262434\pi\)
\(770\) −9689.16 + 7198.96i −0.453472 + 0.336925i
\(771\) 0 0
\(772\) 21854.3 + 15878.1i 1.01885 + 0.740239i
\(773\) 4932.83 15181.7i 0.229523 0.706400i −0.768278 0.640117i \(-0.778886\pi\)
0.997801 0.0662830i \(-0.0211140\pi\)
\(774\) 0 0
\(775\) −10762.0 + 229.944i −0.498814 + 0.0106578i
\(776\) −4152.93 −0.192115
\(777\) 0 0
\(778\) −40896.5 29713.1i −1.88459 1.36923i
\(779\) −3640.24 2644.79i −0.167426 0.121642i
\(780\) 0 0
\(781\) −20047.5 + 14565.4i −0.918511 + 0.667337i
\(782\) 61865.0 2.82901
\(783\) 0 0
\(784\) 6555.52 + 20175.8i 0.298630 + 0.919088i
\(785\) 9438.62 30140.8i 0.429145 1.37041i
\(786\) 0 0
\(787\) −837.844 2578.62i −0.0379491 0.116795i 0.930287 0.366832i \(-0.119557\pi\)
−0.968236 + 0.250036i \(0.919557\pi\)
\(