Properties

Label 225.4.h.d.181.13
Level $225$
Weight $4$
Character 225.181
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,4,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
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 181.13
Character \(\chi\) \(=\) 225.181
Dual form 225.4.h.d.46.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.20400 + 3.70554i) q^{2} +(-5.80928 + 4.22069i) q^{4} +(-3.34114 - 10.6694i) q^{5} +6.27975 q^{7} +(2.58263 + 1.87639i) q^{8} +O(q^{10})\) \(q+(1.20400 + 3.70554i) q^{2} +(-5.80928 + 4.22069i) q^{4} +(-3.34114 - 10.6694i) q^{5} +6.27975 q^{7} +(2.58263 + 1.87639i) q^{8} +(35.5133 - 25.2268i) q^{10} +(13.6357 + 41.9663i) q^{11} +(-13.2560 + 40.7979i) q^{13} +(7.56084 + 23.2699i) q^{14} +(-21.5951 + 66.4630i) q^{16} +(81.6862 + 59.3485i) q^{17} +(-65.1304 - 47.3200i) q^{19} +(64.4420 + 47.8798i) q^{20} +(-139.090 + 101.055i) q^{22} +(48.5949 + 149.560i) q^{23} +(-102.674 + 71.2962i) q^{25} -167.138 q^{26} +(-36.4808 + 26.5049i) q^{28} +(199.754 - 145.129i) q^{29} +(69.6687 + 50.6173i) q^{31} -246.744 q^{32} +(-121.568 + 374.147i) q^{34} +(-20.9815 - 67.0014i) q^{35} +(61.0938 - 188.027i) q^{37} +(96.9290 - 298.317i) q^{38} +(11.3911 - 33.8245i) q^{40} +(-17.2714 + 53.1560i) q^{41} +211.713 q^{43} +(-256.340 - 186.242i) q^{44} +(-495.692 + 360.141i) q^{46} +(-85.9089 + 62.4165i) q^{47} -303.565 q^{49} +(-387.810 - 294.620i) q^{50} +(-95.1871 - 292.956i) q^{52} +(153.468 - 111.501i) q^{53} +(402.198 - 285.700i) q^{55} +(16.2183 + 11.7833i) q^{56} +(778.288 + 565.459i) q^{58} +(140.608 - 432.747i) q^{59} +(171.878 + 528.986i) q^{61} +(-103.683 + 319.104i) q^{62} +(-124.319 - 382.615i) q^{64} +(479.580 + 5.12286i) q^{65} +(-773.054 - 561.657i) q^{67} -725.030 q^{68} +(223.015 - 158.418i) q^{70} +(-454.325 + 330.086i) q^{71} +(-54.7181 - 168.405i) q^{73} +770.300 q^{74} +578.084 q^{76} +(85.6286 + 263.538i) q^{77} +(-769.301 + 558.930i) q^{79} +(781.275 + 8.34556i) q^{80} -217.767 q^{82} +(-11.3373 - 8.23700i) q^{83} +(360.290 - 1069.84i) q^{85} +(254.903 + 784.511i) q^{86} +(-43.5293 + 133.970i) q^{88} +(143.004 + 440.120i) q^{89} +(-83.2445 + 256.200i) q^{91} +(-913.547 - 663.731i) q^{92} +(-334.722 - 243.189i) q^{94} +(-287.268 + 853.007i) q^{95} +(1052.46 - 764.659i) q^{97} +(-365.493 - 1124.87i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20400 + 3.70554i 0.425680 + 1.31011i 0.902342 + 0.431021i \(0.141846\pi\)
−0.476662 + 0.879086i \(0.658154\pi\)
\(3\) 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 0.944314 + 0.329045i \(0.106727\pi\)
−0.570559 + 0.821257i \(0.693273\pi\)
\(12\) 0 0
\(13\) −13.2560 + 40.7979i −0.282812 + 0.870407i 0.704233 + 0.709968i \(0.251291\pi\)
−0.987046 + 0.160438i \(0.948709\pi\)
\(14\) 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 \(-0.0440238\pi\)
0.174949 + 0.984577i \(0.444024\pi\)
\(18\) 0 0
\(19\) −65.1304 47.3200i −0.786417 0.571366i 0.120481 0.992716i \(-0.461556\pi\)
−0.906898 + 0.421350i \(0.861556\pi\)
\(20\) 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 0.887287 + 0.461218i \(0.152587\pi\)
−0.446733 + 0.894667i \(0.647413\pi\)
\(24\) 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 \(-0.409813\pi\)
0.999525 + 0.0308238i \(0.00981308\pi\)
\(30\) 0 0
\(31\) 69.6687 + 50.6173i 0.403641 + 0.293262i 0.771022 0.636808i \(-0.219746\pi\)
−0.367381 + 0.930070i \(0.619746\pi\)
\(32\) −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 −0.718683 0.695338i \(-0.755255\pi\)
0.990136 0.140108i \(-0.0447451\pi\)
\(38\) 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 \(-0.933948\pi\)
0.912758 + 0.408500i \(0.133948\pi\)
\(42\) 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 \(-0.752691\pi\)
0.446441 + 0.894813i \(0.352691\pi\)
\(48\) 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 \(-0.620943\pi\)
0.768621 + 0.639704i \(0.220943\pi\)
\(54\) 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 −0.667395 0.744703i \(-0.732591\pi\)
0.977660 0.210193i \(-0.0674091\pi\)
\(60\) 0 0
\(61\) 171.878 + 528.986i 0.360766 + 1.11032i 0.952590 + 0.304256i \(0.0984079\pi\)
−0.591824 + 0.806067i \(0.701592\pi\)
\(62\) −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 −0.993380 0.114878i \(-0.963352\pi\)
−0.416227 0.909261i \(-0.636648\pi\)
\(68\) −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 \(-0.855510\pi\)
0.139316 + 0.990248i \(0.455510\pi\)
\(72\) 0 0
\(73\) −54.7181 168.405i −0.0877298 0.270004i 0.897561 0.440890i \(-0.145337\pi\)
−0.985291 + 0.170886i \(0.945337\pi\)
\(74\) 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 −0.980338 0.197327i \(-0.936774\pi\)
−0.115272 + 0.993334i \(0.536774\pi\)
\(80\) 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 \(-0.302950\pi\)
−0.595257 + 0.803536i \(0.702950\pi\)
\(84\) 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 \(-0.0111297\pi\)
−0.829070 + 0.559145i \(0.811130\pi\)
\(90\) 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 0.120333 0.992734i \(-0.461604\pi\)
0.981331 + 0.192328i \(0.0616038\pi\)
\(98\) −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 \(-0.283406\pi\)
0.629143 + 0.777289i \(0.283406\pi\)
\(102\) 0 0
\(103\) 895.730 650.786i 0.856883 0.622562i −0.0701525 0.997536i \(-0.522349\pi\)
0.927035 + 0.374975i \(0.122349\pi\)
\(104\) −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 \(-0.526550\pi\)
−0.0833134 + 0.996523i \(0.526550\pi\)
\(108\) 0 0
\(109\) 251.160 772.991i 0.220704 0.679258i −0.777995 0.628270i \(-0.783763\pi\)
0.998699 0.0509874i \(-0.0162368\pi\)
\(110\) 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 −0.782029 0.623242i \(-0.785815\pi\)
0.999007 0.0445486i \(-0.0141850\pi\)
\(114\) 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 −0.941609 0.336709i \(-0.890686\pi\)
0.563865 0.825867i \(-0.309314\pi\)
\(128\) −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 \(-0.246556\pi\)
−0.444322 + 0.895867i \(0.646556\pi\)
\(132\) 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 −0.722453 0.691420i \(-0.756985\pi\)
0.990883 0.134723i \(-0.0430145\pi\)
\(138\) 0 0
\(139\) 287.901 + 886.067i 0.175679 + 0.540685i 0.999664 0.0259271i \(-0.00825378\pi\)
−0.823985 + 0.566612i \(0.808254\pi\)
\(140\) 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 \(-0.794803\pi\)
−0.799313 + 0.600914i \(0.794803\pi\)
\(150\) 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 −0.938362 0.345655i \(-0.887657\pi\)
0.962321 + 0.271914i \(0.0876568\pi\)
\(164\) −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 \(-0.537303\pi\)
−0.980665 + 0.195696i \(0.937303\pi\)
\(168\) 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 −0.968687 0.248284i \(-0.920133\pi\)
0.637747 0.770246i \(-0.279867\pi\)
\(174\) 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 \(-0.442734\pi\)
0.991002 + 0.133849i \(0.0427336\pi\)
\(180\) 0 0
\(181\) −3051.24 2216.86i −1.25302 0.910374i −0.254629 0.967039i \(-0.581953\pi\)
−0.998393 + 0.0566644i \(0.981953\pi\)
\(182\) −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 0.748687 + 0.662923i \(0.230685\pi\)
−0.995357 + 0.0962491i \(0.969315\pi\)
\(192\) 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 \(-0.939864\pi\)
−0.124911 + 0.992168i \(0.539864\pi\)
\(198\) 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 0.939396 + 0.342834i \(0.111387\pi\)
−0.558475 + 0.829522i \(0.688613\pi\)
\(212\) −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 −0.976872 0.213823i \(-0.931408\pi\)
0.664624 0.747178i \(-0.268592\pi\)
\(224\) −1549.49 −0.462185
\(225\) 0 0
\(226\) 3286.23 0.967241
\(227\) 1868.95 + 5752.02i 0.546459 + 1.68183i 0.717494 + 0.696564i \(0.245289\pi\)
−0.171035 + 0.985265i \(0.554711\pi\)
\(228\) 0 0
\(229\) 1649.37 1198.34i 0.475953 0.345800i −0.323804 0.946124i \(-0.604962\pi\)
0.799757 + 0.600324i \(0.204962\pi\)
\(230\) 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 \(-0.299421\pi\)
−0.586313 + 0.810085i \(0.699421\pi\)
\(234\) 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 \(-0.100544\pi\)
−0.951583 + 0.307393i \(0.900544\pi\)
\(240\) 0 0
\(241\) 2084.79 6416.33i 0.557233 1.71499i −0.132738 0.991151i \(-0.542377\pi\)
0.689972 0.723836i \(-0.257623\pi\)
\(242\) −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 \(-0.462962\pi\)
0.116096 + 0.993238i \(0.462962\pi\)
\(252\) 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 \(-0.332470\pi\)
0.502348 + 0.864666i \(0.332470\pi\)
\(258\) 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 \(-0.970616\pi\)
0.859756 + 0.510705i \(0.170616\pi\)
\(264\) 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 \(-0.371791\pi\)
−0.753821 + 0.657080i \(0.771791\pi\)
\(270\) 0 0
\(271\) −4209.83 + 3058.62i −0.943650 + 0.685602i −0.949296 0.314382i \(-0.898203\pi\)
0.00564662 + 0.999984i \(0.498203\pi\)
\(272\) −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 0.988749 0.149581i \(-0.0477924\pi\)
−0.887837 + 0.460159i \(0.847792\pi\)
\(278\) −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 \(-0.495632\pi\)
−0.946727 + 0.322037i \(0.895632\pi\)
\(282\) 0 0
\(283\) −1837.68 1335.15i −0.386003 0.280448i 0.377813 0.925882i \(-0.376676\pi\)
−0.763816 + 0.645435i \(0.776676\pi\)
\(284\) 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 \(-0.319911\pi\)
0.536062 + 0.844178i \(0.319911\pi\)
\(294\) 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 \(-0.0781003\pi\)
−0.927563 + 0.373667i \(0.878100\pi\)
\(312\) 0 0
\(313\) 1329.80 4092.70i 0.240143 0.739084i −0.756254 0.654278i \(-0.772973\pi\)
0.996397 0.0848065i \(-0.0270272\pi\)
\(314\) 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 \(-0.404367\pi\)
−0.817004 + 0.576632i \(0.804367\pi\)
\(318\) 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 0.806921 0.590659i \(-0.201132\pi\)
−0.312398 + 0.949951i \(0.601132\pi\)
\(332\) 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 −0.957709 0.287740i \(-0.907096\pi\)
0.943932 + 0.330141i \(0.107096\pi\)
\(338\) −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 0.400607 0.916250i \(-0.368799\pi\)
0.995200 0.0978631i \(-0.0312007\pi\)
\(348\) 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 \(-0.653039\pi\)
0.700324 + 0.713825i \(0.253039\pi\)
\(354\) 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 −0.281598 0.959533i \(-0.590864\pi\)
0.791816 0.610759i \(-0.209136\pi\)
\(360\) 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 0.897158 0.441710i \(-0.145628\pi\)
−0.142854 + 0.989744i \(0.545628\pi\)
\(368\) −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 0.813099 0.582126i \(-0.197779\pi\)
−0.999976 + 0.00697762i \(0.997779\pi\)
\(374\) −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 −0.838973 0.544173i \(-0.816844\pi\)
0.258282 + 0.966069i \(0.416844\pi\)
\(380\) −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 \(-0.125759\pi\)
−0.0808353 + 0.996727i \(0.525759\pi\)
\(384\) 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 0.769079 + 0.639153i \(0.220715\pi\)
−0.246514 + 0.969139i \(0.579285\pi\)
\(390\) 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 0.0694198 0.997588i \(-0.477885\pi\)
0.970214 + 0.242249i \(0.0778852\pi\)
\(398\) 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 \(-0.329110\pi\)
0.511447 + 0.859315i \(0.329110\pi\)
\(402\) 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 −0.997496 0.0707261i \(-0.977468\pi\)
0.848563 + 0.529095i \(0.177468\pi\)
\(410\) 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 \(-0.119737\pi\)
−0.0619658 + 0.998078i \(0.519737\pi\)
\(420\) 0 0
\(421\) −11708.9 + 8506.99i −1.35548 + 0.984810i −0.356757 + 0.934197i \(0.616118\pi\)
−0.998718 + 0.0506132i \(0.983882\pi\)
\(422\) −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 0.966925 + 0.255063i \(0.0820961\pi\)
0.541375 + 0.840781i \(0.317904\pi\)
\(432\) 0 0
\(433\) −6033.95 4383.92i −0.669684 0.486554i 0.200235 0.979748i \(-0.435829\pi\)
−0.869919 + 0.493194i \(0.835829\pi\)
\(434\) −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 0.964534 + 0.263957i \(0.0850278\pi\)
−0.625174 + 0.780485i \(0.714972\pi\)
\(440\) 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 \(-0.553603\pi\)
−0.167603 + 0.985855i \(0.553603\pi\)
\(444\) 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 \(-0.777565\pi\)
−0.765614 + 0.643300i \(0.777565\pi\)
\(450\) 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 \(-0.0403258\pi\)
−0.876799 + 0.480856i \(0.840326\pi\)
\(462\) 0 0
\(463\) −4273.76 + 13153.3i −0.428981 + 1.32027i 0.470149 + 0.882587i \(0.344200\pi\)
−0.899130 + 0.437681i \(0.855800\pi\)
\(464\) 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 \(-0.295678\pi\)
−0.576747 + 0.816923i \(0.695678\pi\)
\(468\) 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 \(-0.949819\pi\)
−0.155872 + 0.987777i \(0.549819\pi\)
\(480\) 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 −0.316765 0.948504i \(-0.602597\pi\)
0.813785 0.581166i \(-0.197403\pi\)
\(488\) −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 −0.707924 0.706288i \(-0.750368\pi\)
0.987869 0.155292i \(-0.0496317\pi\)
\(492\) 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 \(-0.613956\pi\)
0.782477 + 0.622679i \(0.213956\pi\)
\(504\) 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 −0.343001 0.939335i \(-0.611443\pi\)
0.829621 0.558327i \(-0.188557\pi\)
\(510\) 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 \(-0.819588\pi\)
0.249943 + 0.968260i \(0.419588\pi\)
\(522\) 0 0
\(523\) 2270.43 + 6987.67i 0.189826 + 0.584225i 0.999998 0.00196745i \(-0.000626259\pi\)
−0.810172 + 0.586192i \(0.800626\pi\)
\(524\) −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 0.351900 + 0.936038i \(0.385536\pi\)
−0.834882 + 0.550429i \(0.814464\pi\)
\(542\) −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 −0.587987 + 0.808870i \(0.700079\pi\)
−0.950979 + 0.309254i \(0.899921\pi\)
\(548\) 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 \(-0.305592\pi\)
0.573481 + 0.819219i \(0.305592\pi\)
\(558\) 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 −0.636575 0.771215i \(-0.719649\pi\)
0.968309 0.249757i \(-0.0803507\pi\)
\(564\) 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 \(-0.347421\pi\)
−0.701355 + 0.712812i \(0.747421\pi\)
\(570\) 0 0
\(571\) 9126.02 6630.45i 0.668848 0.485947i −0.200791 0.979634i \(-0.564351\pi\)
0.869639 + 0.493687i \(0.164351\pi\)
\(572\) 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 −0.988188 0.153245i \(-0.951028\pi\)
0.709386 0.704820i \(-0.248972\pi\)
\(578\) −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 0.561693 + 0.827346i \(0.310150\pi\)
−0.940721 + 0.339182i \(0.889850\pi\)
\(588\) 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 \(-0.288643\pi\)
0.616269 + 0.787536i \(0.288643\pi\)
\(594\) 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 \(-0.791305\pi\)
−0.792661 + 0.609662i \(0.791305\pi\)
\(600\) 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 −0.969171 0.246390i \(-0.920756\pi\)
0.928900 + 0.370331i \(0.120756\pi\)
\(614\) 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 \(-0.211822\pi\)
−0.344119 + 0.938926i \(0.611822\pi\)
\(618\) 0 0
\(619\) −15968.8 11602.0i −1.03690 0.753350i −0.0672201 0.997738i \(-0.521413\pi\)
−0.969678 + 0.244388i \(0.921413\pi\)
\(620\) 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 0.718936 0.695076i \(-0.244629\pi\)
−0.438893 + 0.898539i \(0.644629\pi\)
\(632\) −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 \(-0.969788\pi\)
0.861082 + 0.508467i \(0.169788\pi\)
\(642\) 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 \(-0.740282\pi\)
0.480978 + 0.876732i \(0.340282\pi\)
\(648\) 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 \(-0.517092\pi\)
0.933101 + 0.359616i \(0.117092\pi\)
\(654\) 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 \(-0.850809\pi\)
0.987287 + 0.158946i \(0.0508094\pi\)
\(660\) 0 0
\(661\) −5473.66 16846.2i −0.322089 0.991287i −0.972738 0.231908i \(-0.925503\pi\)
0.650649 0.759379i \(-0.274497\pi\)
\(662\) −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 −0.762855 0.646570i \(-0.776203\pi\)
0.237118 0.971481i \(-0.423797\pi\)
\(674\) −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 \(-0.163533\pi\)
−0.993445 + 0.114315i \(0.963533\pi\)
\(678\) 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 \(-0.259859\pi\)
−0.481366 + 0.876520i \(0.659859\pi\)
\(684\) 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 −0.138016 0.990430i \(-0.544072\pi\)
0.693817 0.720151i \(-0.255928\pi\)
\(692\) 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 \(-0.483605\pi\)
0.0514852 + 0.998674i \(0.483605\pi\)
\(702\) 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 −0.146329 0.989236i \(-0.546746\pi\)
0.699841 0.714298i \(-0.253254\pi\)
\(710\) −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 \(-0.374497\pi\)
−0.759379 + 0.650649i \(0.774497\pi\)
\(720\) 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 0.995847 0.0910429i \(-0.0290201\pi\)
−0.859171 + 0.511689i \(0.829020\pi\)
\(728\) −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 −0.0190713 0.999818i \(-0.506071\pi\)
−0.956777 + 0.290823i \(0.906071\pi\)
\(734\) −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 0.980485 0.196595i \(-0.0629884\pi\)
−0.908784 + 0.417266i \(0.862988\pi\)
\(740\) 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 \(-0.726350\pi\)
−0.652666 + 0.757646i \(0.726350\pi\)
\(744\) 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 \(-0.0791435\pi\)
−0.928783 + 0.370625i \(0.879144\pi\)
\(762\) 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 0.678954 0.734181i \(-0.262434\pi\)
−0.488440 + 0.872598i \(0.662434\pi\)
\(770\) 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 −0.997801 0.0662830i \(-0.978886\pi\)
0.768278 0.640117i \(-0.221114\pi\)
\(774\) 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