Properties

Label 124.4.d.c.123.2
Level $124$
Weight $4$
Character 124.123
Analytic conductor $7.316$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [124,4,Mod(123,124)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(124, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("124.123");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 124.d (of order \(2\), degree \(1\), 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: \(7.31623684071\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 123.2
Character \(\chi\) \(=\) 124.123
Dual form 124.4.d.c.123.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.73824 - 0.708563i) q^{2} +3.81956 q^{3} +(6.99588 + 3.88043i) q^{4} -9.46257 q^{5} +(-10.4589 - 2.70640i) q^{6} +9.26693i q^{7} +(-16.4068 - 15.5825i) q^{8} -12.4110 q^{9} +O(q^{10})\) \(q+(-2.73824 - 0.708563i) q^{2} +3.81956 q^{3} +(6.99588 + 3.88043i) q^{4} -9.46257 q^{5} +(-10.4589 - 2.70640i) q^{6} +9.26693i q^{7} +(-16.4068 - 15.5825i) q^{8} -12.4110 q^{9} +(25.9108 + 6.70483i) q^{10} -30.4376 q^{11} +(26.7212 + 14.8215i) q^{12} -64.5589i q^{13} +(6.56620 - 25.3750i) q^{14} -36.1429 q^{15} +(33.8846 + 54.2940i) q^{16} +109.086i q^{17} +(33.9841 + 8.79395i) q^{18} -151.848i q^{19} +(-66.1990 - 36.7188i) q^{20} +35.3956i q^{21} +(83.3454 + 21.5670i) q^{22} -188.023 q^{23} +(-62.6669 - 59.5185i) q^{24} -35.4597 q^{25} +(-45.7440 + 176.777i) q^{26} -150.533 q^{27} +(-35.9596 + 64.8303i) q^{28} +186.328i q^{29} +(98.9677 + 25.6095i) q^{30} +(-157.033 + 71.6352i) q^{31} +(-54.3133 - 172.679i) q^{32} -116.258 q^{33} +(77.2945 - 298.704i) q^{34} -87.6890i q^{35} +(-86.8255 - 48.1598i) q^{36} -17.4257i q^{37} +(-107.594 + 415.797i) q^{38} -246.587i q^{39} +(155.251 + 147.451i) q^{40} +130.136 q^{41} +(25.0800 - 96.9215i) q^{42} +227.289 q^{43} +(-212.938 - 118.111i) q^{44} +117.440 q^{45} +(514.850 + 133.226i) q^{46} +4.18830i q^{47} +(129.424 + 207.379i) q^{48} +257.124 q^{49} +(97.0970 + 25.1254i) q^{50} +416.662i q^{51} +(250.516 - 451.646i) q^{52} -575.583i q^{53} +(412.194 + 106.662i) q^{54} +288.018 q^{55} +(144.402 - 152.041i) q^{56} -579.994i q^{57} +(132.025 - 510.211i) q^{58} +130.150i q^{59} +(-252.851 - 140.250i) q^{60} +479.687i q^{61} +(480.752 - 84.8863i) q^{62} -115.011i q^{63} +(26.3686 + 511.321i) q^{64} +610.893i q^{65} +(318.343 + 82.3763i) q^{66} +508.558i q^{67} +(-423.301 + 763.154i) q^{68} -718.164 q^{69} +(-62.1332 + 240.113i) q^{70} -1125.13i q^{71} +(203.625 + 193.394i) q^{72} +155.093i q^{73} +(-12.3472 + 47.7157i) q^{74} -135.440 q^{75} +(589.236 - 1062.31i) q^{76} -282.063i q^{77} +(-174.722 + 675.212i) q^{78} -936.657 q^{79} +(-320.635 - 513.761i) q^{80} -239.872 q^{81} +(-356.343 - 92.2095i) q^{82} +635.990 q^{83} +(-137.350 + 247.623i) q^{84} -1032.24i q^{85} +(-622.372 - 161.049i) q^{86} +711.693i q^{87} +(499.385 + 474.295i) q^{88} +757.874i q^{89} +(-321.577 - 83.2134i) q^{90} +598.263 q^{91} +(-1315.38 - 729.608i) q^{92} +(-599.797 + 273.615i) q^{93} +(2.96768 - 11.4686i) q^{94} +1436.88i q^{95} +(-207.453 - 659.558i) q^{96} +1784.88 q^{97} +(-704.066 - 182.189i) q^{98} +377.760 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9} + 228 q^{10} - 104 q^{14} - 78 q^{16} + 114 q^{18} - 44 q^{20} + 28 q^{25} + 48 q^{28} - 602 q^{32} - 136 q^{33} - 482 q^{36} + 420 q^{38} - 516 q^{40} - 4 q^{41} - 1596 q^{45} + 1876 q^{49} - 662 q^{50} + 1576 q^{56} - 838 q^{62} - 302 q^{64} - 3900 q^{66} - 872 q^{69} - 912 q^{70} - 2166 q^{72} + 3220 q^{76} - 476 q^{78} + 572 q^{80} - 2056 q^{81} + 3096 q^{82} - 6220 q^{90} - 2904 q^{93} + 6408 q^{94} - 1836 q^{97} - 1358 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73824 0.708563i −0.968113 0.250515i
\(3\) 3.81956 0.735075 0.367537 0.930009i \(-0.380201\pi\)
0.367537 + 0.930009i \(0.380201\pi\)
\(4\) 6.99588 + 3.88043i 0.874485 + 0.485053i
\(5\) −9.46257 −0.846358 −0.423179 0.906046i \(-0.639086\pi\)
−0.423179 + 0.906046i \(0.639086\pi\)
\(6\) −10.4589 2.70640i −0.711635 0.184147i
\(7\) 9.26693i 0.500367i 0.968198 + 0.250184i \(0.0804910\pi\)
−0.968198 + 0.250184i \(0.919509\pi\)
\(8\) −16.4068 15.5825i −0.725087 0.688658i
\(9\) −12.4110 −0.459665
\(10\) 25.9108 + 6.70483i 0.819370 + 0.212025i
\(11\) −30.4376 −0.834299 −0.417149 0.908838i \(-0.636971\pi\)
−0.417149 + 0.908838i \(0.636971\pi\)
\(12\) 26.7212 + 14.8215i 0.642812 + 0.356550i
\(13\) 64.5589i 1.37734i −0.725075 0.688670i \(-0.758195\pi\)
0.725075 0.688670i \(-0.241805\pi\)
\(14\) 6.56620 25.3750i 0.125349 0.484412i
\(15\) −36.1429 −0.622137
\(16\) 33.8846 + 54.2940i 0.529447 + 0.848343i
\(17\) 109.086i 1.55631i 0.628071 + 0.778156i \(0.283845\pi\)
−0.628071 + 0.778156i \(0.716155\pi\)
\(18\) 33.9841 + 8.79395i 0.445008 + 0.115153i
\(19\) 151.848i 1.83349i −0.399468 0.916747i \(-0.630805\pi\)
0.399468 0.916747i \(-0.369195\pi\)
\(20\) −66.1990 36.7188i −0.740127 0.410529i
\(21\) 35.3956i 0.367807i
\(22\) 83.3454 + 21.5670i 0.807695 + 0.209004i
\(23\) −188.023 −1.70458 −0.852292 0.523067i \(-0.824788\pi\)
−0.852292 + 0.523067i \(0.824788\pi\)
\(24\) −62.6669 59.5185i −0.532993 0.506215i
\(25\) −35.4597 −0.283678
\(26\) −45.7440 + 176.777i −0.345044 + 1.33342i
\(27\) −150.533 −1.07296
\(28\) −35.9596 + 64.8303i −0.242705 + 0.437563i
\(29\) 186.328i 1.19311i 0.802570 + 0.596557i \(0.203465\pi\)
−0.802570 + 0.596557i \(0.796535\pi\)
\(30\) 98.9677 + 25.6095i 0.602298 + 0.155854i
\(31\) −157.033 + 71.6352i −0.909806 + 0.415034i
\(32\) −54.3133 172.679i −0.300041 0.953926i
\(33\) −116.258 −0.613272
\(34\) 77.2945 298.704i 0.389880 1.50669i
\(35\) 87.6890i 0.423490i
\(36\) −86.8255 48.1598i −0.401970 0.222962i
\(37\) 17.4257i 0.0774262i −0.999250 0.0387131i \(-0.987674\pi\)
0.999250 0.0387131i \(-0.0123258\pi\)
\(38\) −107.594 + 415.797i −0.459318 + 1.77503i
\(39\) 246.587i 1.01245i
\(40\) 155.251 + 147.451i 0.613683 + 0.582851i
\(41\) 130.136 0.495703 0.247851 0.968798i \(-0.420276\pi\)
0.247851 + 0.968798i \(0.420276\pi\)
\(42\) 25.0800 96.9215i 0.0921412 0.356079i
\(43\) 227.289 0.806077 0.403038 0.915183i \(-0.367954\pi\)
0.403038 + 0.915183i \(0.367954\pi\)
\(44\) −212.938 118.111i −0.729581 0.404679i
\(45\) 117.440 0.389041
\(46\) 514.850 + 133.226i 1.65023 + 0.427024i
\(47\) 4.18830i 0.0129984i 0.999979 + 0.00649922i \(0.00206878\pi\)
−0.999979 + 0.00649922i \(0.997931\pi\)
\(48\) 129.424 + 207.379i 0.389183 + 0.623596i
\(49\) 257.124 0.749633
\(50\) 97.0970 + 25.1254i 0.274632 + 0.0710655i
\(51\) 416.662i 1.14401i
\(52\) 250.516 451.646i 0.668083 1.20446i
\(53\) 575.583i 1.49174i −0.666089 0.745872i \(-0.732033\pi\)
0.666089 0.745872i \(-0.267967\pi\)
\(54\) 412.194 + 106.662i 1.03875 + 0.268793i
\(55\) 288.018 0.706116
\(56\) 144.402 152.041i 0.344582 0.362810i
\(57\) 579.994i 1.34776i
\(58\) 132.025 510.211i 0.298893 1.15507i
\(59\) 130.150i 0.287189i 0.989637 + 0.143595i \(0.0458661\pi\)
−0.989637 + 0.143595i \(0.954134\pi\)
\(60\) −252.851 140.250i −0.544049 0.301769i
\(61\) 479.687i 1.00685i 0.864040 + 0.503424i \(0.167926\pi\)
−0.864040 + 0.503424i \(0.832074\pi\)
\(62\) 480.752 84.8863i 0.984767 0.173880i
\(63\) 115.011i 0.230001i
\(64\) 26.3686 + 511.321i 0.0515012 + 0.998673i
\(65\) 610.893i 1.16572i
\(66\) 318.343 + 82.3763i 0.593716 + 0.153634i
\(67\) 508.558i 0.927316i 0.886014 + 0.463658i \(0.153463\pi\)
−0.886014 + 0.463658i \(0.846537\pi\)
\(68\) −423.301 + 763.154i −0.754895 + 1.36097i
\(69\) −718.164 −1.25300
\(70\) −62.1332 + 240.113i −0.106091 + 0.409986i
\(71\) 1125.13i 1.88068i −0.340236 0.940340i \(-0.610507\pi\)
0.340236 0.940340i \(-0.389493\pi\)
\(72\) 203.625 + 193.394i 0.333297 + 0.316552i
\(73\) 155.093i 0.248661i 0.992241 + 0.124330i \(0.0396782\pi\)
−0.992241 + 0.124330i \(0.960322\pi\)
\(74\) −12.3472 + 47.7157i −0.0193964 + 0.0749573i
\(75\) −135.440 −0.208524
\(76\) 589.236 1062.31i 0.889342 1.60336i
\(77\) 282.063i 0.417456i
\(78\) −174.722 + 675.212i −0.253633 + 0.980163i
\(79\) −936.657 −1.33395 −0.666975 0.745080i \(-0.732411\pi\)
−0.666975 + 0.745080i \(0.732411\pi\)
\(80\) −320.635 513.761i −0.448102 0.718002i
\(81\) −239.872 −0.329043
\(82\) −356.343 92.2095i −0.479896 0.124181i
\(83\) 635.990 0.841072 0.420536 0.907276i \(-0.361842\pi\)
0.420536 + 0.907276i \(0.361842\pi\)
\(84\) −137.350 + 247.623i −0.178406 + 0.321642i
\(85\) 1032.24i 1.31720i
\(86\) −622.372 161.049i −0.780373 0.201934i
\(87\) 711.693i 0.877029i
\(88\) 499.385 + 474.295i 0.604939 + 0.574546i
\(89\) 757.874i 0.902635i 0.892363 + 0.451317i \(0.149046\pi\)
−0.892363 + 0.451317i \(0.850954\pi\)
\(90\) −321.577 83.2134i −0.376636 0.0974607i
\(91\) 598.263 0.689175
\(92\) −1315.38 729.608i −1.49063 0.826814i
\(93\) −599.797 + 273.615i −0.668775 + 0.305081i
\(94\) 2.96768 11.4686i 0.00325630 0.0125840i
\(95\) 1436.88i 1.55179i
\(96\) −207.453 659.558i −0.220553 0.701207i
\(97\) 1784.88 1.86832 0.934158 0.356860i \(-0.116153\pi\)
0.934158 + 0.356860i \(0.116153\pi\)
\(98\) −704.066 182.189i −0.725729 0.187794i
\(99\) 377.760 0.383498
\(100\) −248.072 137.599i −0.248072 0.137599i
\(101\) −169.443 −0.166933 −0.0834663 0.996511i \(-0.526599\pi\)
−0.0834663 + 0.996511i \(0.526599\pi\)
\(102\) 295.231 1140.92i 0.286591 1.10753i
\(103\) 936.624i 0.896003i −0.894033 0.448001i \(-0.852136\pi\)
0.894033 0.448001i \(-0.147864\pi\)
\(104\) −1005.99 + 1059.21i −0.948515 + 0.998690i
\(105\) 334.933i 0.311297i
\(106\) −407.837 + 1576.08i −0.373704 + 1.44418i
\(107\) 640.208i 0.578423i −0.957265 0.289212i \(-0.906607\pi\)
0.957265 0.289212i \(-0.0933931\pi\)
\(108\) −1053.11 584.130i −0.938290 0.520444i
\(109\) −794.543 −0.698197 −0.349098 0.937086i \(-0.613512\pi\)
−0.349098 + 0.937086i \(0.613512\pi\)
\(110\) −788.662 204.079i −0.683600 0.176892i
\(111\) 66.5586i 0.0569141i
\(112\) −503.138 + 314.006i −0.424483 + 0.264918i
\(113\) −80.4600 −0.0669826 −0.0334913 0.999439i \(-0.510663\pi\)
−0.0334913 + 0.999439i \(0.510663\pi\)
\(114\) −410.962 + 1588.16i −0.337633 + 1.30478i
\(115\) 1779.18 1.44269
\(116\) −723.034 + 1303.53i −0.578724 + 1.04336i
\(117\) 801.238i 0.633115i
\(118\) 92.2198 356.383i 0.0719451 0.278031i
\(119\) −1010.90 −0.778728
\(120\) 592.990 + 563.198i 0.451103 + 0.428439i
\(121\) −404.552 −0.303946
\(122\) 339.889 1313.50i 0.252230 0.974742i
\(123\) 497.062 0.364379
\(124\) −1376.56 108.204i −0.996925 0.0783631i
\(125\) 1518.36 1.08645
\(126\) −81.4929 + 314.929i −0.0576187 + 0.222667i
\(127\) −42.8766 −0.0299581 −0.0149791 0.999888i \(-0.504768\pi\)
−0.0149791 + 0.999888i \(0.504768\pi\)
\(128\) 290.099 1418.80i 0.200323 0.979730i
\(129\) 868.145 0.592527
\(130\) 432.856 1672.77i 0.292031 1.12855i
\(131\) 293.978i 0.196068i 0.995183 + 0.0980342i \(0.0312555\pi\)
−0.995183 + 0.0980342i \(0.968745\pi\)
\(132\) −813.329 451.132i −0.536297 0.297470i
\(133\) 1407.17 0.917420
\(134\) 360.345 1392.55i 0.232307 0.897747i
\(135\) 1424.43 0.908111
\(136\) 1699.84 1789.76i 1.07177 1.12846i
\(137\) 1051.10i 0.655484i 0.944767 + 0.327742i \(0.106288\pi\)
−0.944767 + 0.327742i \(0.893712\pi\)
\(138\) 1966.50 + 508.864i 1.21304 + 0.313894i
\(139\) −1797.90 −1.09709 −0.548547 0.836120i \(-0.684819\pi\)
−0.548547 + 0.836120i \(0.684819\pi\)
\(140\) 340.271 613.461i 0.205415 0.370335i
\(141\) 15.9975i 0.00955482i
\(142\) −797.225 + 3080.87i −0.471138 + 1.82071i
\(143\) 1965.02i 1.14911i
\(144\) −420.540 673.840i −0.243368 0.389954i
\(145\) 1763.15i 1.00980i
\(146\) 109.893 424.680i 0.0622932 0.240731i
\(147\) 982.101 0.551036
\(148\) 67.6192 121.908i 0.0375558 0.0677080i
\(149\) −2424.79 −1.33320 −0.666598 0.745418i \(-0.732250\pi\)
−0.666598 + 0.745418i \(0.732250\pi\)
\(150\) 370.868 + 95.9681i 0.201875 + 0.0522384i
\(151\) 467.016 0.251690 0.125845 0.992050i \(-0.459836\pi\)
0.125845 + 0.992050i \(0.459836\pi\)
\(152\) −2366.18 + 2491.35i −1.26265 + 1.32944i
\(153\) 1353.87i 0.715383i
\(154\) −199.860 + 772.356i −0.104579 + 0.404144i
\(155\) 1485.94 677.854i 0.770022 0.351268i
\(156\) 956.861 1725.09i 0.491091 0.885370i
\(157\) −1373.35 −0.698125 −0.349063 0.937099i \(-0.613500\pi\)
−0.349063 + 0.937099i \(0.613500\pi\)
\(158\) 2564.79 + 663.680i 1.29141 + 0.334174i
\(159\) 2198.47i 1.09654i
\(160\) 513.944 + 1633.99i 0.253943 + 0.807363i
\(161\) 1742.39i 0.852918i
\(162\) 656.827 + 169.965i 0.318551 + 0.0824301i
\(163\) 2019.82i 0.970580i 0.874353 + 0.485290i \(0.161286\pi\)
−0.874353 + 0.485290i \(0.838714\pi\)
\(164\) 910.415 + 504.983i 0.433484 + 0.240442i
\(165\) 1100.10 0.519048
\(166\) −1741.49 450.639i −0.814252 0.210701i
\(167\) −1328.55 −0.615606 −0.307803 0.951450i \(-0.599594\pi\)
−0.307803 + 0.951450i \(0.599594\pi\)
\(168\) 551.553 580.730i 0.253293 0.266692i
\(169\) −1970.85 −0.897064
\(170\) −731.405 + 2826.51i −0.329978 + 1.27520i
\(171\) 1884.58i 0.842793i
\(172\) 1590.09 + 881.979i 0.704902 + 0.390990i
\(173\) 142.896 0.0627985 0.0313993 0.999507i \(-0.490004\pi\)
0.0313993 + 0.999507i \(0.490004\pi\)
\(174\) 504.279 1948.78i 0.219709 0.849062i
\(175\) 328.603i 0.141943i
\(176\) −1031.37 1652.58i −0.441717 0.707772i
\(177\) 497.118i 0.211105i
\(178\) 537.002 2075.24i 0.226123 0.873852i
\(179\) −1070.32 −0.446924 −0.223462 0.974713i \(-0.571736\pi\)
−0.223462 + 0.974713i \(0.571736\pi\)
\(180\) 821.593 + 455.716i 0.340211 + 0.188706i
\(181\) 2749.35i 1.12905i 0.825417 + 0.564523i \(0.190940\pi\)
−0.825417 + 0.564523i \(0.809060\pi\)
\(182\) −1638.18 423.907i −0.667199 0.172649i
\(183\) 1832.20i 0.740108i
\(184\) 3084.86 + 2929.87i 1.23597 + 1.17387i
\(185\) 164.892i 0.0655303i
\(186\) 1836.26 324.228i 0.723877 0.127815i
\(187\) 3320.33i 1.29843i
\(188\) −16.2524 + 29.3008i −0.00630493 + 0.0113669i
\(189\) 1394.97i 0.536875i
\(190\) 1018.12 3934.51i 0.388747 1.50231i
\(191\) 4316.68i 1.63531i −0.575708 0.817655i \(-0.695274\pi\)
0.575708 0.817655i \(-0.304726\pi\)
\(192\) 100.717 + 1953.02i 0.0378572 + 0.734099i
\(193\) 1237.75 0.461634 0.230817 0.972997i \(-0.425860\pi\)
0.230817 + 0.972997i \(0.425860\pi\)
\(194\) −4887.41 1264.70i −1.80874 0.468041i
\(195\) 2333.34i 0.856893i
\(196\) 1798.81 + 997.751i 0.655542 + 0.363612i
\(197\) 332.728i 0.120335i −0.998188 0.0601673i \(-0.980837\pi\)
0.998188 0.0601673i \(-0.0191634\pi\)
\(198\) −1034.40 267.667i −0.371269 0.0960720i
\(199\) −2698.95 −0.961423 −0.480711 0.876879i \(-0.659622\pi\)
−0.480711 + 0.876879i \(0.659622\pi\)
\(200\) 581.781 + 552.552i 0.205691 + 0.195357i
\(201\) 1942.47i 0.681647i
\(202\) 463.975 + 120.061i 0.161610 + 0.0418191i
\(203\) −1726.69 −0.596995
\(204\) −1616.83 + 2914.91i −0.554904 + 1.00042i
\(205\) −1231.42 −0.419542
\(206\) −663.657 + 2564.70i −0.224462 + 0.867432i
\(207\) 2333.54 0.783538
\(208\) 3505.16 2187.55i 1.16846 0.729228i
\(209\) 4621.90i 1.52968i
\(210\) −237.321 + 917.127i −0.0779845 + 0.301370i
\(211\) 1290.39i 0.421015i 0.977592 + 0.210507i \(0.0675116\pi\)
−0.977592 + 0.210507i \(0.932488\pi\)
\(212\) 2233.51 4026.71i 0.723575 1.30451i
\(213\) 4297.50i 1.38244i
\(214\) −453.628 + 1753.04i −0.144904 + 0.559979i
\(215\) −2150.74 −0.682230
\(216\) 2469.76 + 2345.68i 0.777991 + 0.738904i
\(217\) −663.839 1455.21i −0.207670 0.455237i
\(218\) 2175.65 + 562.984i 0.675933 + 0.174909i
\(219\) 592.386i 0.182784i
\(220\) 2014.94 + 1117.63i 0.617487 + 0.342504i
\(221\) 7042.49 2.14357
\(222\) −47.1609 + 182.253i −0.0142578 + 0.0550992i
\(223\) 906.580 0.272238 0.136119 0.990692i \(-0.456537\pi\)
0.136119 + 0.990692i \(0.456537\pi\)
\(224\) 1600.20 503.317i 0.477313 0.150131i
\(225\) 440.089 0.130397
\(226\) 220.318 + 57.0110i 0.0648468 + 0.0167802i
\(227\) 3703.09i 1.08274i −0.840784 0.541371i \(-0.817905\pi\)
0.840784 0.541371i \(-0.182095\pi\)
\(228\) 2250.62 4057.57i 0.653733 1.17859i
\(229\) 2450.12i 0.707024i 0.935430 + 0.353512i \(0.115013\pi\)
−0.935430 + 0.353512i \(0.884987\pi\)
\(230\) −4871.81 1260.66i −1.39669 0.361415i
\(231\) 1077.36i 0.306861i
\(232\) 2903.47 3057.06i 0.821648 0.865112i
\(233\) −4653.13 −1.30831 −0.654156 0.756359i \(-0.726976\pi\)
−0.654156 + 0.756359i \(0.726976\pi\)
\(234\) 567.727 2193.98i 0.158605 0.612927i
\(235\) 39.6321i 0.0110013i
\(236\) −505.039 + 910.517i −0.139302 + 0.251142i
\(237\) −3577.62 −0.980553
\(238\) 2768.07 + 716.283i 0.753896 + 0.195083i
\(239\) −2406.38 −0.651280 −0.325640 0.945494i \(-0.605580\pi\)
−0.325640 + 0.945494i \(0.605580\pi\)
\(240\) −1224.69 1962.34i −0.329388 0.527785i
\(241\) 1415.16i 0.378251i −0.981953 0.189126i \(-0.939435\pi\)
0.981953 0.189126i \(-0.0605653\pi\)
\(242\) 1107.76 + 286.650i 0.294254 + 0.0761429i
\(243\) 3148.17 0.831092
\(244\) −1861.39 + 3355.83i −0.488375 + 0.880472i
\(245\) −2433.06 −0.634458
\(246\) −1361.07 352.200i −0.352760 0.0912822i
\(247\) −9803.16 −2.52534
\(248\) 3692.68 + 1271.67i 0.945505 + 0.325609i
\(249\) 2429.20 0.618251
\(250\) −4157.63 1075.86i −1.05181 0.272172i
\(251\) −2537.00 −0.637985 −0.318993 0.947757i \(-0.603345\pi\)
−0.318993 + 0.947757i \(0.603345\pi\)
\(252\) 446.294 804.606i 0.111563 0.201133i
\(253\) 5722.96 1.42213
\(254\) 117.406 + 30.3807i 0.0290028 + 0.00750495i
\(255\) 3942.69i 0.968239i
\(256\) −1799.67 + 3679.46i −0.439373 + 0.898305i
\(257\) 178.609 0.0433515 0.0216758 0.999765i \(-0.493100\pi\)
0.0216758 + 0.999765i \(0.493100\pi\)
\(258\) −2377.19 615.136i −0.573633 0.148437i
\(259\) 161.483 0.0387415
\(260\) −2370.53 + 4273.73i −0.565438 + 1.01941i
\(261\) 2312.51i 0.548433i
\(262\) 208.302 804.981i 0.0491181 0.189816i
\(263\) 327.884 0.0768753 0.0384376 0.999261i \(-0.487762\pi\)
0.0384376 + 0.999261i \(0.487762\pi\)
\(264\) 1907.43 + 1811.60i 0.444675 + 0.422334i
\(265\) 5446.50i 1.26255i
\(266\) −3853.16 997.067i −0.888166 0.229827i
\(267\) 2894.75i 0.663504i
\(268\) −1973.42 + 3557.81i −0.449798 + 0.810924i
\(269\) 1387.76i 0.314548i 0.987555 + 0.157274i \(0.0502706\pi\)
−0.987555 + 0.157274i \(0.949729\pi\)
\(270\) −3900.41 1009.30i −0.879154 0.227495i
\(271\) −7466.85 −1.67372 −0.836861 0.547415i \(-0.815612\pi\)
−0.836861 + 0.547415i \(0.815612\pi\)
\(272\) −5922.73 + 3696.34i −1.32029 + 0.823984i
\(273\) 2285.10 0.506595
\(274\) 744.769 2878.15i 0.164208 0.634582i
\(275\) 1079.31 0.236672
\(276\) −5024.19 2786.78i −1.09573 0.607770i
\(277\) 1078.25i 0.233884i 0.993139 + 0.116942i \(0.0373092\pi\)
−0.993139 + 0.116942i \(0.962691\pi\)
\(278\) 4923.08 + 1273.93i 1.06211 + 0.274838i
\(279\) 1948.93 889.062i 0.418206 0.190777i
\(280\) −1366.42 + 1438.70i −0.291640 + 0.307067i
\(281\) −3150.77 −0.668894 −0.334447 0.942415i \(-0.608550\pi\)
−0.334447 + 0.942415i \(0.608550\pi\)
\(282\) 11.3352 43.8049i 0.00239363 0.00925015i
\(283\) 6582.92i 1.38274i −0.722503 0.691368i \(-0.757009\pi\)
0.722503 0.691368i \(-0.242991\pi\)
\(284\) 4365.98 7871.27i 0.912230 1.64463i
\(285\) 5488.23i 1.14068i
\(286\) 1392.34 5380.68i 0.287870 1.11247i
\(287\) 1205.96i 0.248033i
\(288\) 674.080 + 2143.11i 0.137919 + 0.438487i
\(289\) −6986.82 −1.42211
\(290\) −1249.30 + 4827.91i −0.252971 + 0.977603i
\(291\) 6817.44 1.37335
\(292\) −601.825 + 1085.01i −0.120614 + 0.217450i
\(293\) −5147.06 −1.02626 −0.513131 0.858310i \(-0.671514\pi\)
−0.513131 + 0.858310i \(0.671514\pi\)
\(294\) −2689.22 695.880i −0.533465 0.138043i
\(295\) 1231.56i 0.243065i
\(296\) −271.537 + 285.901i −0.0533202 + 0.0561407i
\(297\) 4581.85 0.895172
\(298\) 6639.64 + 1718.11i 1.29068 + 0.333985i
\(299\) 12138.5i 2.34779i
\(300\) −947.525 525.567i −0.182351 0.101145i
\(301\) 2106.27i 0.403334i
\(302\) −1278.80 330.911i −0.243665 0.0630522i
\(303\) −647.197 −0.122708
\(304\) 8244.45 5145.32i 1.55543 0.970737i
\(305\) 4539.08i 0.852154i
\(306\) −959.299 + 3707.20i −0.179214 + 0.692571i
\(307\) 2143.54i 0.398496i −0.979949 0.199248i \(-0.936150\pi\)
0.979949 0.199248i \(-0.0638500\pi\)
\(308\) 1094.53 1973.28i 0.202488 0.365059i
\(309\) 3577.49i 0.658629i
\(310\) −4549.15 + 803.243i −0.833466 + 0.147165i
\(311\) 3855.76i 0.703023i 0.936184 + 0.351511i \(0.114332\pi\)
−0.936184 + 0.351511i \(0.885668\pi\)
\(312\) −3842.45 + 4045.71i −0.697230 + 0.734112i
\(313\) 8238.66i 1.48779i −0.668299 0.743893i \(-0.732977\pi\)
0.668299 0.743893i \(-0.267023\pi\)
\(314\) 3760.57 + 973.109i 0.675864 + 0.174891i
\(315\) 1088.30i 0.194664i
\(316\) −6552.73 3634.63i −1.16652 0.647037i
\(317\) 2461.44 0.436114 0.218057 0.975936i \(-0.430028\pi\)
0.218057 + 0.975936i \(0.430028\pi\)
\(318\) −1557.76 + 6019.94i −0.274700 + 1.06158i
\(319\) 5671.39i 0.995414i
\(320\) −249.515 4838.41i −0.0435885 0.845235i
\(321\) 2445.31i 0.425184i
\(322\) −1234.59 + 4771.08i −0.213669 + 0.825720i
\(323\) 16564.6 2.85349
\(324\) −1678.12 930.807i −0.287743 0.159603i
\(325\) 2289.24i 0.390720i
\(326\) 1431.17 5530.74i 0.243145 0.939631i
\(327\) −3034.81 −0.513227
\(328\) −2135.12 2027.85i −0.359427 0.341369i
\(329\) −38.8127 −0.00650399
\(330\) −3012.34 779.492i −0.502497 0.130029i
\(331\) 4230.78 0.702553 0.351276 0.936272i \(-0.385748\pi\)
0.351276 + 0.936272i \(0.385748\pi\)
\(332\) 4449.31 + 2467.91i 0.735504 + 0.407965i
\(333\) 216.270i 0.0355901i
\(334\) 3637.88 + 941.361i 0.595976 + 0.154219i
\(335\) 4812.26i 0.784842i
\(336\) −1921.77 + 1199.37i −0.312027 + 0.194734i
\(337\) 7430.42i 1.20107i 0.799598 + 0.600535i \(0.205046\pi\)
−0.799598 + 0.600535i \(0.794954\pi\)
\(338\) 5396.65 + 1396.47i 0.868459 + 0.224728i
\(339\) −307.322 −0.0492373
\(340\) 4005.52 7221.40i 0.638911 1.15187i
\(341\) 4779.71 2180.41i 0.759050 0.346263i
\(342\) 1335.35 5160.43i 0.211132 0.815919i
\(343\) 5561.31i 0.875459i
\(344\) −3729.10 3541.75i −0.584475 0.555111i
\(345\) 6795.68 1.06048
\(346\) −391.282 101.251i −0.0607961 0.0157320i
\(347\) 8501.37 1.31521 0.657604 0.753363i \(-0.271570\pi\)
0.657604 + 0.753363i \(0.271570\pi\)
\(348\) −2761.67 + 4978.92i −0.425406 + 0.766948i
\(349\) −2706.83 −0.415168 −0.207584 0.978217i \(-0.566560\pi\)
−0.207584 + 0.978217i \(0.566560\pi\)
\(350\) −232.836 + 899.791i −0.0355588 + 0.137417i
\(351\) 9718.21i 1.47783i
\(352\) 1653.17 + 5255.94i 0.250324 + 0.795859i
\(353\) 9655.40i 1.45582i −0.685672 0.727911i \(-0.740492\pi\)
0.685672 0.727911i \(-0.259508\pi\)
\(354\) 352.239 1361.23i 0.0528850 0.204374i
\(355\) 10646.6i 1.59173i
\(356\) −2940.87 + 5301.99i −0.437826 + 0.789340i
\(357\) −3861.18 −0.572423
\(358\) 2930.78 + 758.388i 0.432673 + 0.111961i
\(359\) 476.929i 0.0701151i 0.999385 + 0.0350576i \(0.0111615\pi\)
−0.999385 + 0.0350576i \(0.988839\pi\)
\(360\) −1926.81 1830.01i −0.282089 0.267916i
\(361\) −16198.9 −2.36170
\(362\) 1948.08 7528.36i 0.282843 1.09304i
\(363\) −1545.21 −0.223423
\(364\) 4185.37 + 2321.51i 0.602673 + 0.334287i
\(365\) 1467.58i 0.210456i
\(366\) 1298.23 5016.98i 0.185408 0.716508i
\(367\) −8768.34 −1.24715 −0.623575 0.781764i \(-0.714320\pi\)
−0.623575 + 0.781764i \(0.714320\pi\)
\(368\) −6371.07 10208.5i −0.902486 1.44607i
\(369\) −1615.11 −0.227857
\(370\) 116.836 451.514i 0.0164163 0.0634407i
\(371\) 5333.89 0.746420
\(372\) −5257.85 413.293i −0.732814 0.0576027i
\(373\) 7522.64 1.04426 0.522128 0.852867i \(-0.325138\pi\)
0.522128 + 0.852867i \(0.325138\pi\)
\(374\) −2352.66 + 9091.84i −0.325276 + 1.25703i
\(375\) 5799.47 0.798623
\(376\) 65.2644 68.7168i 0.00895147 0.00942499i
\(377\) 12029.2 1.64332
\(378\) −988.427 + 3819.77i −0.134495 + 0.519756i
\(379\) 1738.11i 0.235569i −0.993039 0.117785i \(-0.962421\pi\)
0.993039 0.117785i \(-0.0375792\pi\)
\(380\) −5575.69 + 10052.2i −0.752702 + 1.35702i
\(381\) −163.770 −0.0220214
\(382\) −3058.64 + 11820.1i −0.409670 + 1.58316i
\(383\) 9366.09 1.24957 0.624784 0.780798i \(-0.285187\pi\)
0.624784 + 0.780798i \(0.285187\pi\)
\(384\) 1108.05 5419.19i 0.147253 0.720175i
\(385\) 2669.04i 0.353317i
\(386\) −3389.26 877.026i −0.446914 0.115646i
\(387\) −2820.88 −0.370525
\(388\) 12486.8 + 6926.08i 1.63381 + 0.906233i
\(389\) 15028.2i 1.95877i −0.202004 0.979385i \(-0.564745\pi\)
0.202004 0.979385i \(-0.435255\pi\)
\(390\) 1653.32 6389.25i 0.214665 0.829569i
\(391\) 20510.7i 2.65287i
\(392\) −4218.59 4006.65i −0.543549 0.516240i
\(393\) 1122.87i 0.144125i
\(394\) −235.759 + 911.089i −0.0301456 + 0.116497i
\(395\) 8863.18 1.12900
\(396\) 2642.76 + 1465.87i 0.335363 + 0.186017i
\(397\) 9159.27 1.15791 0.578955 0.815359i \(-0.303461\pi\)
0.578955 + 0.815359i \(0.303461\pi\)
\(398\) 7390.35 + 1912.37i 0.930766 + 0.240851i
\(399\) 5374.76 0.674373
\(400\) −1201.54 1925.25i −0.150192 0.240656i
\(401\) 5548.22i 0.690935i 0.938431 + 0.345467i \(0.112280\pi\)
−0.938431 + 0.345467i \(0.887720\pi\)
\(402\) 1376.36 5318.93i 0.170763 0.659911i
\(403\) 4624.69 + 10137.9i 0.571643 + 1.25311i
\(404\) −1185.40 657.511i −0.145980 0.0809712i
\(405\) 2269.81 0.278488
\(406\) 4728.09 + 1223.47i 0.577959 + 0.149556i
\(407\) 530.397i 0.0645966i
\(408\) 6492.65 6836.10i 0.787829 0.829504i
\(409\) 5925.82i 0.716413i −0.933642 0.358207i \(-0.883388\pi\)
0.933642 0.358207i \(-0.116612\pi\)
\(410\) 3371.92 + 872.539i 0.406164 + 0.105102i
\(411\) 4014.73i 0.481830i
\(412\) 3634.50 6552.50i 0.434609 0.783540i
\(413\) −1206.10 −0.143700
\(414\) −6389.79 1653.46i −0.758553 0.196288i
\(415\) −6018.10 −0.711848
\(416\) −11148.0 + 3506.41i −1.31388 + 0.413259i
\(417\) −6867.19 −0.806446
\(418\) 3274.91 12655.9i 0.383208 1.48090i
\(419\) 5094.04i 0.593938i 0.954887 + 0.296969i \(0.0959758\pi\)
−0.954887 + 0.296969i \(0.904024\pi\)
\(420\) 1299.68 2343.15i 0.150996 0.272224i
\(421\) 6347.20 0.734782 0.367391 0.930066i \(-0.380251\pi\)
0.367391 + 0.930066i \(0.380251\pi\)
\(422\) 914.323 3533.39i 0.105470 0.407590i
\(423\) 51.9808i 0.00597493i
\(424\) −8969.05 + 9443.50i −1.02730 + 1.08164i
\(425\) 3868.17i 0.441491i
\(426\) −3045.05 + 11767.6i −0.346322 + 1.33836i
\(427\) −4445.23 −0.503793
\(428\) 2484.28 4478.82i 0.280566 0.505822i
\(429\) 7505.51i 0.844684i
\(430\) 5889.24 + 1523.94i 0.660475 + 0.170909i
\(431\) 12542.6i 1.40175i 0.713284 + 0.700875i \(0.247207\pi\)
−0.713284 + 0.700875i \(0.752793\pi\)
\(432\) −5100.73 8173.01i −0.568077 0.910241i
\(433\) 13001.1i 1.44293i 0.692448 + 0.721467i \(0.256532\pi\)
−0.692448 + 0.721467i \(0.743468\pi\)
\(434\) 786.635 + 4455.09i 0.0870039 + 0.492745i
\(435\) 6734.45i 0.742280i
\(436\) −5558.53 3083.17i −0.610562 0.338663i
\(437\) 28550.9i 3.12534i
\(438\) 419.743 1622.09i 0.0457901 0.176956i
\(439\) 10070.5i 1.09485i −0.836855 0.547424i \(-0.815609\pi\)
0.836855 0.547424i \(-0.184391\pi\)
\(440\) −4725.47 4488.06i −0.511995 0.486272i
\(441\) −3191.16 −0.344580
\(442\) −19284.0 4990.05i −2.07522 0.536996i
\(443\) 2712.26i 0.290888i 0.989366 + 0.145444i \(0.0464611\pi\)
−0.989366 + 0.145444i \(0.953539\pi\)
\(444\) 258.276 465.636i 0.0276064 0.0497705i
\(445\) 7171.44i 0.763952i
\(446\) −2482.43 642.369i −0.263557 0.0681997i
\(447\) −9261.61 −0.979998
\(448\) −4738.37 + 244.356i −0.499703 + 0.0257695i
\(449\) 2188.99i 0.230077i −0.993361 0.115039i \(-0.963301\pi\)
0.993361 0.115039i \(-0.0366992\pi\)
\(450\) −1205.07 311.831i −0.126239 0.0326663i
\(451\) −3961.03 −0.413564
\(452\) −562.888 312.219i −0.0585753 0.0324902i
\(453\) 1783.80 0.185011
\(454\) −2623.87 + 10139.9i −0.271243 + 1.04822i
\(455\) −5661.10 −0.583289
\(456\) −9037.78 + 9515.86i −0.928142 + 0.977239i
\(457\) 12887.0i 1.31910i −0.751662 0.659549i \(-0.770747\pi\)
0.751662 0.659549i \(-0.229253\pi\)
\(458\) 1736.06 6709.00i 0.177120 0.684479i
\(459\) 16421.0i 1.66987i
\(460\) 12446.9 + 6903.97i 1.26161 + 0.699781i
\(461\) 3884.09i 0.392408i −0.980563 0.196204i \(-0.937139\pi\)
0.980563 0.196204i \(-0.0628614\pi\)
\(462\) −763.376 + 2950.06i −0.0768733 + 0.297076i
\(463\) −10637.9 −1.06778 −0.533892 0.845553i \(-0.679271\pi\)
−0.533892 + 0.845553i \(0.679271\pi\)
\(464\) −10116.5 + 6313.66i −1.01217 + 0.631691i
\(465\) 5675.63 2589.10i 0.566023 0.258208i
\(466\) 12741.4 + 3297.04i 1.26659 + 0.327752i
\(467\) 12794.4i 1.26778i −0.773421 0.633892i \(-0.781456\pi\)
0.773421 0.633892i \(-0.218544\pi\)
\(468\) −3109.14 + 5605.36i −0.307094 + 0.553649i
\(469\) −4712.77 −0.463999
\(470\) −28.0818 + 108.522i −0.00275600 + 0.0106505i
\(471\) −5245.61 −0.513174
\(472\) 2028.08 2135.36i 0.197775 0.208237i
\(473\) −6918.15 −0.672509
\(474\) 9796.36 + 2534.97i 0.949286 + 0.245643i
\(475\) 5384.50i 0.520121i
\(476\) −7072.10 3922.70i −0.680985 0.377724i
\(477\) 7143.54i 0.685703i
\(478\) 6589.24 + 1705.07i 0.630512 + 0.163155i
\(479\) 81.3581i 0.00776064i −0.999992 0.00388032i \(-0.998765\pi\)
0.999992 0.00388032i \(-0.00123515\pi\)
\(480\) 1963.04 + 6241.12i 0.186667 + 0.593472i
\(481\) −1124.98 −0.106642
\(482\) −1002.73 + 3875.04i −0.0947575 + 0.366190i
\(483\) 6655.17i 0.626958i
\(484\) −2830.19 1569.83i −0.265796 0.147430i
\(485\) −16889.5 −1.58126
\(486\) −8620.44 2230.68i −0.804591 0.208201i
\(487\) 2758.76 0.256696 0.128348 0.991729i \(-0.459032\pi\)
0.128348 + 0.991729i \(0.459032\pi\)
\(488\) 7474.75 7870.15i 0.693373 0.730051i
\(489\) 7714.82i 0.713449i
\(490\) 6662.28 + 1723.97i 0.614227 + 0.158941i
\(491\) −16607.5 −1.52645 −0.763224 0.646134i \(-0.776385\pi\)
−0.763224 + 0.646134i \(0.776385\pi\)
\(492\) 3477.38 + 1928.81i 0.318643 + 0.176743i
\(493\) −20325.9 −1.85686
\(494\) 26843.4 + 6946.16i 2.44482 + 0.632636i
\(495\) −3574.58 −0.324577
\(496\) −9210.36 6098.62i −0.833785 0.552089i
\(497\) 10426.5 0.941031
\(498\) −6651.73 1721.24i −0.598536 0.154881i
\(499\) −18736.1 −1.68084 −0.840422 0.541932i \(-0.817693\pi\)
−0.840422 + 0.541932i \(0.817693\pi\)
\(500\) 10622.3 + 5891.89i 0.950085 + 0.526987i
\(501\) −5074.48 −0.452517
\(502\) 6946.92 + 1797.63i 0.617642 + 0.159825i
\(503\) 3947.37i 0.349910i 0.984576 + 0.174955i \(0.0559780\pi\)
−0.984576 + 0.174955i \(0.944022\pi\)
\(504\) −1792.17 + 1886.97i −0.158392 + 0.166771i
\(505\) 1603.37 0.141285
\(506\) −15670.8 4055.08i −1.37678 0.356265i
\(507\) −7527.78 −0.659409
\(508\) −299.959 166.379i −0.0261979 0.0145313i
\(509\) 10379.7i 0.903873i −0.892050 0.451937i \(-0.850733\pi\)
0.892050 0.451937i \(-0.149267\pi\)
\(510\) −2793.65 + 10796.0i −0.242558 + 0.937365i
\(511\) −1437.23 −0.124422
\(512\) 7535.05 8800.04i 0.650401 0.759591i
\(513\) 22858.1i 1.96727i
\(514\) −489.074 126.556i −0.0419692 0.0108602i
\(515\) 8862.87i 0.758339i
\(516\) 6073.44 + 3368.77i 0.518155 + 0.287407i
\(517\) 127.482i 0.0108446i
\(518\) −442.178 114.421i −0.0375062 0.00970533i
\(519\) 545.798 0.0461616
\(520\) 9519.27 10022.8i 0.802784 0.845250i
\(521\) −3140.11 −0.264051 −0.132025 0.991246i \(-0.542148\pi\)
−0.132025 + 0.991246i \(0.542148\pi\)
\(522\) −1638.56 + 6332.21i −0.137391 + 0.530945i
\(523\) 3358.50 0.280797 0.140398 0.990095i \(-0.455162\pi\)
0.140398 + 0.990095i \(0.455162\pi\)
\(524\) −1140.76 + 2056.63i −0.0951036 + 0.171459i
\(525\) 1255.12i 0.104339i
\(526\) −897.824 232.327i −0.0744240 0.0192584i
\(527\) −7814.42 17130.2i −0.645923 1.41594i
\(528\) −3939.36 6312.13i −0.324695 0.520265i
\(529\) 23185.5 1.90561
\(530\) 3859.19 14913.8i 0.316288 1.22229i
\(531\) 1615.29i 0.132011i
\(532\) 9844.37 + 5460.41i 0.802270 + 0.444998i
\(533\) 8401.43i 0.682751i
\(534\) 2051.11 7926.50i 0.166218 0.642347i
\(535\) 6058.02i 0.489553i
\(536\) 7924.62 8343.82i 0.638603 0.672385i
\(537\) −4088.15 −0.328522
\(538\) 983.318 3800.02i 0.0787989 0.304518i
\(539\) −7826.24 −0.625418
\(540\) 9965.10 + 5527.38i 0.794129 + 0.440482i
\(541\) −10801.4 −0.858387 −0.429193 0.903213i \(-0.641202\pi\)
−0.429193 + 0.903213i \(0.641202\pi\)
\(542\) 20446.0 + 5290.73i 1.62035 + 0.419292i
\(543\) 10501.3i 0.829933i
\(544\) 18836.9 5924.84i 1.48461 0.466958i
\(545\) 7518.42 0.590925
\(546\) −6257.14 1619.14i −0.490441 0.126910i
\(547\) 1639.49i 0.128152i 0.997945 + 0.0640762i \(0.0204101\pi\)
−0.997945 + 0.0640762i \(0.979590\pi\)
\(548\) −4078.70 + 7353.35i −0.317945 + 0.573210i
\(549\) 5953.38i 0.462813i
\(550\) −2955.40 764.758i −0.229125 0.0592898i
\(551\) 28293.7 2.18757
\(552\) 11782.8 + 11190.8i 0.908531 + 0.862886i
\(553\) 8679.93i 0.667465i
\(554\) 764.010 2952.51i 0.0585914 0.226426i
\(555\) 629.815i 0.0481697i
\(556\) −12577.9 6976.62i −0.959392 0.532149i
\(557\) 5127.94i 0.390086i −0.980795 0.195043i \(-0.937515\pi\)
0.980795 0.195043i \(-0.0624846\pi\)
\(558\) −5966.59 + 1053.52i −0.452663 + 0.0799267i
\(559\) 14673.5i 1.11024i
\(560\) 4760.98 2971.31i 0.359265 0.224215i
\(561\) 12682.2i 0.954443i
\(562\) 8627.56 + 2232.52i 0.647565 + 0.167568i
\(563\) 8497.74i 0.636123i −0.948070 0.318061i \(-0.896968\pi\)
0.948070 0.318061i \(-0.103032\pi\)
\(564\) −62.0770 + 111.916i −0.00463460 + 0.00835555i
\(565\) 761.359 0.0566913
\(566\) −4664.41 + 18025.6i −0.346396 + 1.33864i
\(567\) 2222.88i 0.164642i
\(568\) −17532.4 + 18459.8i −1.29514 + 1.36366i
\(569\) 19751.4i 1.45522i 0.685989 + 0.727612i \(0.259370\pi\)
−0.685989 + 0.727612i \(0.740630\pi\)
\(570\) 3888.76 15028.1i 0.285758 1.10431i
\(571\) 4844.86 0.355081 0.177540 0.984113i \(-0.443186\pi\)
0.177540 + 0.984113i \(0.443186\pi\)
\(572\) −7625.11 + 13747.0i −0.557381 + 1.00488i
\(573\) 16487.8i 1.20208i
\(574\) 854.499 3302.20i 0.0621360 0.240124i
\(575\) 6667.23 0.483552
\(576\) −327.260 6345.98i −0.0236733 0.459055i
\(577\) 13906.9 1.00339 0.501693 0.865046i \(-0.332711\pi\)
0.501693 + 0.865046i \(0.332711\pi\)
\(578\) 19131.6 + 4950.61i 1.37676 + 0.356260i
\(579\) 4727.67 0.339336
\(580\) 6841.76 12334.8i 0.489808 0.883057i
\(581\) 5893.67i 0.420845i
\(582\) −18667.8 4830.59i −1.32956 0.344045i
\(583\) 17519.4i 1.24456i
\(584\) 2416.74 2544.58i 0.171242 0.180300i
\(585\) 7581.77i 0.535842i
\(586\) 14093.9 + 3647.02i 0.993537 + 0.257094i
\(587\) −115.159 −0.00809731 −0.00404865 0.999992i \(-0.501289\pi\)
−0.00404865 + 0.999992i \(0.501289\pi\)
\(588\) 6870.66 + 3810.97i 0.481873 + 0.267282i
\(589\) 10877.7 + 23845.2i 0.760963 + 1.66812i
\(590\) −872.637 + 3372.30i −0.0608914 + 0.235314i
\(591\) 1270.88i 0.0884549i
\(592\) 946.111 590.463i 0.0656840 0.0409930i
\(593\) 17027.7 1.17916 0.589581 0.807710i \(-0.299293\pi\)
0.589581 + 0.807710i \(0.299293\pi\)
\(594\) −12546.2 3246.53i −0.866627 0.224254i
\(595\) 9565.67 0.659083
\(596\) −16963.5 9409.20i −1.16586 0.646671i
\(597\) −10308.8 −0.706718
\(598\) 8600.91 33238.2i 0.588156 2.27293i
\(599\) 10657.5i 0.726965i 0.931601 + 0.363483i \(0.118412\pi\)
−0.931601 + 0.363483i \(0.881588\pi\)
\(600\) 2222.15 + 2110.51i 0.151198 + 0.143602i
\(601\) 15474.3i 1.05027i 0.851020 + 0.525134i \(0.175985\pi\)
−0.851020 + 0.525134i \(0.824015\pi\)
\(602\) 1492.43 5767.48i 0.101041 0.390473i
\(603\) 6311.69i 0.426255i
\(604\) 3267.19 + 1812.22i 0.220099 + 0.122083i
\(605\) 3828.10 0.257247
\(606\) 1772.18 + 458.580i 0.118795 + 0.0307402i
\(607\) 9398.38i 0.628449i −0.949349 0.314224i \(-0.898256\pi\)
0.949349 0.314224i \(-0.101744\pi\)
\(608\) −26221.0 + 8247.38i −1.74902 + 0.550124i
\(609\) −6595.21 −0.438836
\(610\) −3216.22 + 12429.1i −0.213477 + 0.824981i
\(611\) 270.392 0.0179033
\(612\) 5253.58 9471.48i 0.346999 0.625591i
\(613\) 7795.68i 0.513645i −0.966459 0.256823i \(-0.917324\pi\)
0.966459 0.256823i \(-0.0826756\pi\)
\(614\) −1518.83 + 5869.52i −0.0998293 + 0.385789i
\(615\) −4703.48 −0.308395
\(616\) −4395.26 + 4627.77i −0.287484 + 0.302692i
\(617\) −26366.1 −1.72035 −0.860177 0.509996i \(-0.829647\pi\)
−0.860177 + 0.509996i \(0.829647\pi\)
\(618\) −2534.88 + 9796.02i −0.164996 + 0.637627i
\(619\) 3059.01 0.198630 0.0993151 0.995056i \(-0.468335\pi\)
0.0993151 + 0.995056i \(0.468335\pi\)
\(620\) 13025.8 + 1023.89i 0.843756 + 0.0663233i
\(621\) 28303.5 1.82896
\(622\) 2732.05 10558.0i 0.176118 0.680605i
\(623\) −7023.17 −0.451649
\(624\) 13388.2 8355.48i 0.858903 0.536037i
\(625\) −9935.15 −0.635849
\(626\) −5837.61 + 22559.4i −0.372712 + 1.44034i
\(627\) 17653.6i 1.12443i
\(628\) −9607.82 5329.20i −0.610500 0.338628i
\(629\) 1900.91 0.120499
\(630\) 771.132 2980.03i 0.0487661 0.188456i
\(631\) 19286.1 1.21675 0.608374 0.793651i \(-0.291822\pi\)
0.608374 + 0.793651i \(0.291822\pi\)
\(632\) 15367.6 + 14595.5i 0.967230 + 0.918635i
\(633\) 4928.72i 0.309477i
\(634\) −6739.99 1744.08i −0.422207 0.109253i
\(635\) 405.723 0.0253553
\(636\) 8531.02 15380.3i 0.531882 0.958910i
\(637\) 16599.6i 1.03250i
\(638\) −4018.54 + 15529.6i −0.249366 + 0.963673i
\(639\) 13963.9i 0.864483i
\(640\) −2745.09 + 13425.5i −0.169545 + 0.829202i
\(641\) 12489.2i 0.769572i −0.923006 0.384786i \(-0.874275\pi\)
0.923006 0.384786i \(-0.125725\pi\)
\(642\) −1732.66 + 6695.85i −0.106515 + 0.411626i
\(643\) −11132.3 −0.682763 −0.341381 0.939925i \(-0.610895\pi\)
−0.341381 + 0.939925i \(0.610895\pi\)
\(644\) 6761.22 12189.6i 0.413711 0.745863i
\(645\) −8214.89 −0.501490
\(646\) −45357.7 11737.0i −2.76250 0.714842i
\(647\) −9983.67 −0.606644 −0.303322 0.952888i \(-0.598096\pi\)
−0.303322 + 0.952888i \(0.598096\pi\)
\(648\) 3935.55 + 3737.82i 0.238585 + 0.226598i
\(649\) 3961.47i 0.239601i
\(650\) 1622.07 6268.48i 0.0978812 0.378261i
\(651\) −2535.57 5558.28i −0.152653 0.334633i
\(652\) −7837.76 + 14130.4i −0.470783 + 0.848757i
\(653\) 24074.4 1.44273 0.721367 0.692553i \(-0.243514\pi\)
0.721367 + 0.692553i \(0.243514\pi\)
\(654\) 8310.02 + 2150.35i 0.496861 + 0.128571i
\(655\) 2781.79i 0.165944i
\(656\) 4409.60 + 7065.59i 0.262448 + 0.420526i
\(657\) 1924.85i 0.114301i
\(658\) 106.278 + 27.5012i 0.00629660 + 0.00162935i
\(659\) 16509.4i 0.975894i 0.872873 + 0.487947i \(0.162254\pi\)
−0.872873 + 0.487947i \(0.837746\pi\)
\(660\) 7696.18 + 4268.87i 0.453899 + 0.251766i
\(661\) −7485.67 −0.440483 −0.220241 0.975445i \(-0.570684\pi\)
−0.220241 + 0.975445i \(0.570684\pi\)
\(662\) −11584.9 2997.78i −0.680150 0.176000i
\(663\) 26899.2 1.57568
\(664\) −10434.6 9910.34i −0.609850 0.579210i
\(665\) −13315.4 −0.776466
\(666\) 153.241 592.198i 0.00891586 0.0344553i
\(667\) 35034.0i 2.03376i
\(668\) −9294.37 5155.34i −0.538338 0.298602i
\(669\) 3462.74 0.200115
\(670\) −3409.79 + 13177.1i −0.196615 + 0.759815i
\(671\) 14600.5i 0.840011i
\(672\) 6112.08 1922.45i 0.350861 0.110357i
\(673\) 16211.6i 0.928548i 0.885692 + 0.464274i \(0.153685\pi\)
−0.885692 + 0.464274i \(0.846315\pi\)
\(674\) 5264.92 20346.2i 0.300886 1.16277i
\(675\) 5337.84 0.304376
\(676\) −13787.8 7647.73i −0.784468 0.435124i
\(677\) 20444.8i 1.16065i 0.814386 + 0.580324i \(0.197074\pi\)
−0.814386 + 0.580324i \(0.802926\pi\)
\(678\) 841.520 + 217.757i 0.0476672 + 0.0123347i
\(679\) 16540.3i 0.934844i
\(680\) −16084.9 + 16935.7i −0.907099 + 0.955083i
\(681\) 14144.2i 0.795897i
\(682\) −14632.9 + 2583.74i −0.821590 + 0.145068i
\(683\) 3374.87i 0.189072i −0.995521 0.0945358i \(-0.969863\pi\)
0.995521 0.0945358i \(-0.0301367\pi\)
\(684\) −7312.99 + 13184.3i −0.408800 + 0.737010i
\(685\) 9946.08i 0.554774i
\(686\) 3940.54 15228.2i 0.219315 0.847543i
\(687\) 9358.38i 0.519715i
\(688\) 7701.60 + 12340.4i 0.426775 + 0.683830i
\(689\) −37159.0 −2.05464
\(690\) −18608.2 4815.17i −1.02667 0.265667i
\(691\) 13420.2i 0.738825i 0.929266 + 0.369412i \(0.120441\pi\)
−0.929266 + 0.369412i \(0.879559\pi\)
\(692\) 999.680 + 554.496i 0.0549163 + 0.0304606i
\(693\) 3500.67i 0.191890i
\(694\) −23278.8 6023.76i −1.27327 0.329479i
\(695\) 17012.8 0.928534
\(696\) 11090.0 11676.6i 0.603972 0.635922i
\(697\) 14196.0i 0.771468i
\(698\) 7411.95 + 1917.96i 0.401929 + 0.104006i
\(699\) −17772.9 −0.961708
\(700\) 1275.12 2298.86i 0.0688499 0.124127i
\(701\) 14116.8 0.760607 0.380303 0.924862i \(-0.375820\pi\)
0.380303 + 0.924862i \(0.375820\pi\)
\(702\) 6885.97 26610.8i 0.370219 1.43071i
\(703\) −2646.07 −0.141961
\(704\) −802.598 15563.4i −0.0429674 0.833192i
\(705\) 151.377i 0.00808680i
\(706\) −6841.46 + 26438.8i −0.364705 + 1.40940i
\(707\) 1570.22i 0.0835276i
\(708\) −1929.03 + 3477.77i −0.102397 + 0.184608i
\(709\) 3483.75i 0.184535i −0.995734 0.0922673i \(-0.970589\pi\)
0.995734 0.0922673i \(-0.0294114\pi\)
\(710\) 7543.80 29153.0i 0.398752 1.54097i
\(711\) 11624.8 0.613171
\(712\) 11809.6 12434.3i 0.621606 0.654488i
\(713\) 29525.8 13469.0i 1.55084 0.707461i
\(714\) 10572.8 + 2735.89i 0.554170 + 0.143401i
\(715\) 18594.1i 0.972561i
\(716\) −7487.82 4153.29i −0.390828 0.216782i
\(717\) −9191.32 −0.478739
\(718\) 337.934 1305.94i 0.0175649 0.0678793i
\(719\) −10584.3 −0.548996 −0.274498 0.961588i \(-0.588512\pi\)
−0.274498 + 0.961588i \(0.588512\pi\)
\(720\) 3979.39 + 6376.26i 0.205977 + 0.330041i
\(721\) 8679.62 0.448330
\(722\) 44356.4 + 11477.9i 2.28639 + 0.591641i
\(723\) 5405.29i 0.278043i
\(724\) −10668.6 + 19234.1i −0.547647 + 0.987333i
\(725\) 6607.15i 0.338460i
\(726\) 4231.15 + 1094.88i 0.216298 + 0.0559707i
\(727\) 27393.4i 1.39748i 0.715377 + 0.698739i \(0.246255\pi\)
−0.715377 + 0.698739i \(0.753745\pi\)
\(728\) −9815.60 9322.45i −0.499712 0.474606i
\(729\) 18501.2 0.939958
\(730\) −1039.87 + 4018.57i −0.0527223 + 0.203745i
\(731\) 24794.2i 1.25451i
\(732\) −7109.70 + 12817.8i −0.358992 + 0.647213i
\(733\) −23289.0 −1.17353 −0.586766 0.809756i \(-0.699599\pi\)
−0.586766 + 0.809756i \(0.699599\pi\)
\(734\) 24009.8 + 6212.92i 1.20738 + 0.312429i
\(735\) −9293.20 −0.466374
\(736\) 10212.1 + 32467.6i 0.511446 + 1.62605i
\(737\) 15479.3i 0.773659i
\(738\) 4422.56 + 1144.41i 0.220591 + 0.0570816i
\(739\) 39175.7 1.95007 0.975034 0.222054i \(-0.0712760\pi\)
0.975034 + 0.222054i \(0.0712760\pi\)
\(740\) −639.852 + 1153.56i −0.0317857 + 0.0573053i
\(741\) −37443.8 −1.85632
\(742\) −14605.4 3779.40i −0.722618 0.186989i
\(743\) 8911.68 0.440024 0.220012 0.975497i \(-0.429390\pi\)
0.220012 + 0.975497i \(0.429390\pi\)
\(744\) 14104.4 + 4857.21i 0.695017 + 0.239347i
\(745\) 22944.7 1.12836
\(746\) −20598.8 5330.26i −1.01096 0.261602i
\(747\) −7893.24 −0.386611
\(748\) 12884.3 23228.6i 0.629808 1.13546i
\(749\) 5932.76 0.289424
\(750\) −15880.3 4109.29i −0.773157 0.200067i
\(751\) 9463.00i 0.459800i 0.973214 + 0.229900i \(0.0738399\pi\)
−0.973214 + 0.229900i \(0.926160\pi\)
\(752\) −227.399 + 141.919i −0.0110271 + 0.00688198i
\(753\) −9690.24 −0.468967
\(754\) −32938.7 8523.42i −1.59092 0.411677i
\(755\) −4419.18 −0.213020
\(756\) 5413.10 9759.07i 0.260413 0.469489i
\(757\) 18574.5i 0.891811i −0.895080 0.445905i \(-0.852882\pi\)
0.895080 0.445905i \(-0.147118\pi\)
\(758\) −1231.56 + 4759.36i −0.0590136 + 0.228057i
\(759\) 21859.2 1.04537
\(760\) 22390.2 23574.6i 1.06865 1.12518i
\(761\) 11022.0i 0.525030i 0.964928 + 0.262515i \(0.0845519\pi\)
−0.964928 + 0.262515i \(0.915448\pi\)
\(762\) 448.440 + 116.041i 0.0213192 + 0.00551670i
\(763\) 7362.98i 0.349355i
\(764\) 16750.6 30199.0i 0.793213 1.43005i
\(765\) 12811.1i 0.605470i
\(766\) −25646.6 6636.46i −1.20972 0.313035i
\(767\) 8402.37 0.395557
\(768\) −6873.95 + 14053.9i −0.322972 + 0.660321i
\(769\) −23335.5 −1.09428 −0.547139 0.837041i \(-0.684283\pi\)
−0.547139 + 0.837041i \(0.684283\pi\)
\(770\) 1891.19 7308.47i 0.0885112 0.342051i
\(771\) 682.209 0.0318666
\(772\) 8659.17 + 4803.01i 0.403692 + 0.223917i
\(773\) 19348.4i 0.900275i −0.892959 0.450137i \(-0.851375\pi\)
0.892959 0.450137i \(-0.148625\pi\)
\(774\) 7724.23 + 1998.77i 0.358710 + 0.0928221i
\(775\) 5568.35 2540.16i 0.258091 0.117736i
\(776\) −29284.2 27812.9i −1.35469 1.28663i
\(777\) 616.794 0.0284779
\(778\) −10648.4 + 41150.8i −0.490701 + 1.89631i
\(779\) 19760.9i 0.908868i
\(780\) −9054.37 + 16323.8i −0.415639 + 0.749340i
\(781\) 34246.3i 1.56905i
\(782\) −14533.1 + 56163.1i −0.664582 + 2.56827i
\(783\) 28048.5i 1.28017i
\(784\) 8712.54 + 13960.3i 0.396890 + 0.635946i
\(785\) 12995.5 0.590864
\(786\) 795.621 3074.67i 0.0361054 0.139529i
\(787\) −31328.1 −1.41896 −0.709482 0.704723i \(-0.751071\pi\)
−0.709482 + 0.704723i \(0.751071\pi\)
\(788\) 1291.13 2327.73i 0.0583687 0.105231i
\(789\) 1252.37 0.0565091
\(790\) −24269.5 6280.12i −1.09300 0.282831i
\(791\) 745.617i 0.0335159i
\(792\) −6197.85 5886.46i −0.278069 0.264099i
\(793\) 30968.1 1.38677
\(794\) −25080.2 6489.92i −1.12099 0.290074i
\(795\) 20803.2i 0.928069i
\(796\) −18881.5 10473.1i −0.840750 0.466341i
\(797\) 12772.5i 0.567659i 0.958875 + 0.283830i \(0.0916051\pi\)
−0.958875 + 0.283830i \(0.908395\pi\)
\(798\) −14717.4 3808.36i −0.652869 0.168940i
\(799\) −456.886 −0.0202296
\(800\) 1925.93 + 6123.15i 0.0851150 + 0.270607i
\(801\) 9405.94i 0.414910i
\(802\) 3931.26 15192.3i 0.173089 0.668903i
\(803\) 4720.65i 0.207457i
\(804\) −7537.60 + 13589.3i −0.330635 + 0.596090i
\(805\) 16487.5i 0.721874i
\(806\) −5480.17 31036.8i −0.239492 1.35636i
\(807\) 5300.64i 0.231216i
\(808\) 2780.02 + 2640.35i 0.121041 + 0.114959i
\(809\) 5227.08i 0.227162i −0.993529 0.113581i \(-0.963768\pi\)
0.993529 0.113581i \(-0.0362322\pi\)
\(810\) −6215.27 1608.30i −0.269608 0.0697654i
\(811\) 37006.1i 1.60229i 0.598467 + 0.801147i \(0.295777\pi\)
−0.598467 + 0.801147i \(0.704223\pi\)
\(812\) −12079.7 6700.30i −0.522063 0.289575i
\(813\) −28520.1 −1.23031
\(814\) 375.820 1452.35i 0.0161824 0.0625368i
\(815\) 19112.7i 0.821458i
\(816\) −22622.2 + 14118.4i −0.970510 + 0.605690i
\(817\) 34513.5i 1.47794i
\(818\) −4198.82 + 16226.3i −0.179472 + 0.693569i
\(819\) −7425.01 −0.316790
\(820\) −8614.87 4778.44i −0.366883 0.203500i
\(821\) 2790.80i 0.118635i −0.998239 0.0593177i \(-0.981107\pi\)
0.998239 0.0593177i \(-0.0188925\pi\)
\(822\) 2844.69 10993.3i 0.120705 0.466465i
\(823\) 9068.64 0.384098 0.192049 0.981385i \(-0.438487\pi\)
0.192049 + 0.981385i \(0.438487\pi\)
\(824\) −14595.0 + 15367.0i −0.617039 + 0.649680i
\(825\) 4122.48 0.173972
\(826\) 3302.57 + 854.595i 0.139118 + 0.0359990i
\(827\) −14541.0 −0.611415 −0.305708 0.952125i \(-0.598893\pi\)
−0.305708 + 0.952125i \(0.598893\pi\)
\(828\) 16325.2 + 9055.13i 0.685192 + 0.380058i
\(829\) 10893.8i 0.456401i 0.973614 + 0.228200i \(0.0732841\pi\)
−0.973614 + 0.228200i \(0.926716\pi\)
\(830\) 16479.0 + 4264.20i 0.689149 + 0.178329i
\(831\) 4118.45i 0.171922i
\(832\) 33010.3 1702.33i 1.37551 0.0709346i
\(833\) 28048.7i 1.16666i
\(834\) 18804.0 + 4865.84i 0.780731 + 0.202027i
\(835\) 12571.5 0.521024
\(836\) −17934.9 + 32334.2i −0.741977 + 1.33768i
\(837\) 23638.6 10783.4i 0.976188 0.445317i
\(838\) 3609.45 13948.7i 0.148790 0.574999i
\(839\) 3041.54i 0.125156i −0.998040 0.0625779i \(-0.980068\pi\)
0.998040 0.0625779i \(-0.0199322\pi\)
\(840\) −5219.12 + 5495.20i −0.214377 + 0.225717i
\(841\) −10329.3 −0.423523
\(842\) −17380.1 4497.39i −0.711352 0.184074i
\(843\) −12034.6 −0.491687
\(844\) −5007.26 + 9027.41i −0.204215 + 0.368171i
\(845\) 18649.3 0.759237
\(846\) −36.8317 + 142.336i −0.00149681 + 0.00578440i
\(847\) 3748.95i 0.152084i
\(848\) 31250.7 19503.4i 1.26551 0.789799i
\(849\) 25143.9i 1.01641i
\(850\) −2740.84 + 10592.0i −0.110600 + 0.427413i
\(851\) 3276.43i 0.131979i
\(852\) 16676.1 30064.8i 0.670557 1.20892i
\(853\) 2781.25 0.111639 0.0558196 0.998441i \(-0.482223\pi\)
0.0558196 + 0.998441i \(0.482223\pi\)
\(854\) 12172.1 + 3149.73i 0.487729 + 0.126208i
\(855\) 17833.0i 0.713305i
\(856\) −9976.07 + 10503.8i −0.398335 + 0.419407i
\(857\) −22771.0 −0.907635 −0.453817 0.891095i \(-0.649938\pi\)
−0.453817 + 0.891095i \(0.649938\pi\)
\(858\) 5318.12 20551.9i 0.211606 0.817749i
\(859\) −11358.4 −0.451157 −0.225579 0.974225i \(-0.572427\pi\)
−0.225579 + 0.974225i \(0.572427\pi\)
\(860\) −15046.3 8345.80i −0.596599 0.330918i
\(861\) 4606.24i 0.182323i
\(862\) 8887.20 34344.5i 0.351159 1.35705i
\(863\) −10371.7 −0.409106 −0.204553 0.978856i \(-0.565574\pi\)
−0.204553 + 0.978856i \(0.565574\pi\)
\(864\) 8175.92 + 25993.8i 0.321933 + 1.02353i
\(865\) −1352.16 −0.0531501
\(866\) 9212.07 35600.0i 0.361477 1.39692i
\(867\) −26686.6 −1.04536
\(868\) 1002.72 12756.5i 0.0392103 0.498828i
\(869\) 28509.6 1.11291
\(870\) −4771.78 + 18440.5i −0.185952 + 0.718611i
\(871\) 32831.9 1.27723
\(872\) 13035.9 + 12381.0i 0.506253 + 0.480818i
\(873\) −22152.0 −0.858800
\(874\) 20230.1 78179.2i 0.782945 3.02569i
\(875\) 14070.6i 0.543624i
\(876\) −2298.71 + 4144.26i −0.0886600 + 0.159842i
\(877\) −21745.3 −0.837270 −0.418635 0.908155i \(-0.637491\pi\)
−0.418635 + 0.908155i \(0.637491\pi\)
\(878\) −7135.58 + 27575.4i −0.274276 + 1.05994i
\(879\) −19659.5 −0.754379
\(880\) 9759.38 + 15637.7i 0.373851 + 0.599029i
\(881\) 49333.2i 1.88658i 0.331967 + 0.943291i \(0.392288\pi\)
−0.331967 + 0.943291i \(0.607712\pi\)
\(882\) 8738.14 + 2261.13i 0.333592 + 0.0863224i
\(883\) 18511.0 0.705488 0.352744 0.935720i \(-0.385249\pi\)
0.352744 + 0.935720i \(0.385249\pi\)
\(884\) 49268.4 + 27327.9i 1.87452 + 1.03975i
\(885\) 4704.01i 0.178671i
\(886\) 1921.81 7426.81i 0.0728718 0.281612i
\(887\) 9356.28i 0.354175i −0.984195 0.177087i \(-0.943332\pi\)
0.984195 0.177087i \(-0.0566675\pi\)
\(888\) −1037.15 + 1092.02i −0.0391943 + 0.0412676i
\(889\) 397.334i 0.0149900i
\(890\) −5081.42 + 19637.1i −0.191381 + 0.739592i
\(891\) 7301.14 0.274520
\(892\) 6342.32 + 3517.92i 0.238068 + 0.132050i
\(893\) 635.986 0.0238326
\(894\) 25360.5 + 6562.44i 0.948749 + 0.245504i
\(895\) 10128.0 0.378258
\(896\) 13147.9 + 2688.33i 0.490225 + 0.100235i
\(897\) 46363.8i 1.72580i
\(898\) −1551.04 + 5993.97i −0.0576378 + 0.222741i
\(899\) −13347.7 29259.7i −0.495184 1.08550i
\(900\) 3078.81 + 1707.73i 0.114030 + 0.0632493i
\(901\) 62788.2 2.32162
\(902\) 10846.2 + 2806.64i 0.400377 + 0.103604i
\(903\) 8045.04i 0.296481i
\(904\) 1320.09 + 1253.77i 0.0485682 + 0.0461281i
\(905\) 26015.9i 0.955577i
\(906\) −4884.46 1263.93i −0.179112 0.0463481i
\(907\) 40031.7i 1.46552i −0.680486 0.732761i \(-0.738231\pi\)
0.680486 0.732761i \(-0.261769\pi\)
\(908\) 14369.6 25906.4i 0.525188 0.946842i
\(909\) 2102.95 0.0767331
\(910\) 15501.4 + 4011.25i 0.564690 + 0.146123i
\(911\) 89.8672 0.00326831 0.00163416 0.999999i \(-0.499480\pi\)
0.00163416 + 0.999999i \(0.499480\pi\)
\(912\) 31490.2 19652.8i 1.14336 0.713565i
\(913\) −19358.0 −0.701705
\(914\) −9131.24 + 35287.6i −0.330454 + 1.27704i
\(915\) 17337.3i 0.626397i
\(916\) −9507.50 + 17140.7i −0.342944 + 0.618281i
\(917\) −2724.27 −0.0981062
\(918\) −11635.3 + 44964.7i −0.418326 + 1.61662i
\(919\) 49107.0i 1.76267i 0.472496 + 0.881333i \(0.343353\pi\)
−0.472496 + 0.881333i \(0.656647\pi\)
\(920\) −29190.7 27724.1i −1.04607 0.993519i
\(921\) 8187.39i 0.292925i
\(922\) −2752.12 + 10635.5i −0.0983039 + 0.379895i
\(923\) −72637.1 −2.59033
\(924\) 4180.61 7537.06i 0.148844 0.268345i
\(925\) 617.911i 0.0219641i
\(926\) 29129.0 + 7537.61i 1.03374 + 0.267496i
\(927\) 11624.4i 0.411861i
\(928\) 32175.0 10120.1i 1.13814 0.357984i
\(929\) 32104.1i 1.13380i −0.823786 0.566901i \(-0.808142\pi\)
0.823786 0.566901i \(-0.191858\pi\)
\(930\) −17375.8 + 3068.04i −0.612660 + 0.108177i
\(931\) 39043.8i 1.37445i
\(932\) −32552.7 18056.1i −1.14410 0.634601i
\(933\) 14727.3i 0.516774i
\(934\) −9065.66 + 35034.2i −0.317599 + 1.22736i
\(935\) 31418.8i 1.09894i
\(936\) 12485.3 13145.8i 0.435999 0.459063i
\(937\) −32113.0 −1.11962 −0.559811 0.828620i \(-0.689126\pi\)
−0.559811 + 0.828620i \(0.689126\pi\)
\(938\) 12904.7 + 3339.29i 0.449203 + 0.116239i
\(939\) 31468.1i 1.09363i
\(940\) 153.789 277.261i 0.00533623 0.00962050i
\(941\) 12035.2i 0.416936i −0.978029 0.208468i \(-0.933152\pi\)
0.978029 0.208468i \(-0.0668476\pi\)
\(942\) 14363.7 + 3716.85i 0.496810 + 0.128558i
\(943\) −24468.5 −0.844967
\(944\) −7066.39 + 4410.10i −0.243635 + 0.152051i
\(945\) 13200.0i 0.454389i
\(946\) 18943.5 + 4901.94i 0.651064 + 0.168473i
\(947\) 39152.4 1.34349 0.671744 0.740783i \(-0.265546\pi\)
0.671744 + 0.740783i \(0.265546\pi\)
\(948\) −25028.6 13882.7i −0.857479 0.475621i
\(949\) 10012.6 0.342490
\(950\) 3815.25 14744.0i 0.130298 0.503536i
\(951\) 9401.60 0.320576
\(952\) 16585.6 + 15752.3i 0.564645 + 0.536277i
\(953\) 12593.2i 0.428053i 0.976828 + 0.214027i \(0.0686579\pi\)
−0.976828 + 0.214027i \(0.931342\pi\)
\(954\) 5061.65 19560.7i 0.171779 0.663837i
\(955\) 40846.9i 1.38406i
\(956\) −16834.7 9337.78i −0.569534 0.315905i
\(957\) 21662.2i 0.731704i
\(958\) −57.6473 + 222.778i −0.00194416 + 0.00751317i
\(959\) −9740.44 −0.327983
\(960\) −953.037 18480.6i −0.0320408 0.621311i
\(961\) 19527.8 22498.2i 0.655493 0.755201i
\(962\) 3080.47 + 797.123i 0.103242 + 0.0267155i
\(963\) 7945.60i 0.265881i
\(964\) 5491.43 9900.29i 0.183472 0.330775i
\(965\) −11712.3 −0.390708
\(966\) −4715.61 + 18223.4i −0.157062 + 0.606966i
\(967\) 2721.79 0.0905139 0.0452570 0.998975i \(-0.485589\pi\)
0.0452570 + 0.998975i \(0.485589\pi\)
\(968\) 6637.41 + 6303.94i 0.220387 + 0.209314i
\(969\) 63269.4 2.09753
\(970\) 46247.5 + 11967.3i 1.53084 + 0.396130i
\(971\) 17284.8i 0.571263i −0.958339 0.285632i \(-0.907797\pi\)
0.958339 0.285632i \(-0.0922034\pi\)
\(972\) 22024.2 + 12216.2i 0.726777 + 0.403124i
\(973\) 16661.0i 0.548950i
\(974\) −7554.13 1954.75i −0.248511 0.0643063i
\(975\) 8743.88i 0.287209i
\(976\) −26044.1 + 16254.0i −0.854152 + 0.533072i
\(977\) −60227.2 −1.97220 −0.986099 0.166158i \(-0.946864\pi\)
−0.986099 + 0.166158i \(0.946864\pi\)
\(978\) 5466.44 21125.0i 0.178730 0.690699i
\(979\) 23067.9i 0.753067i
\(980\) −17021.4 9441.29i −0.554824 0.307746i
\(981\) 9861.04 0.320937
\(982\) 45475.2 + 11767.5i 1.47777 + 0.382398i
\(983\) 29092.5 0.943953 0.471977 0.881611i \(-0.343541\pi\)
0.471977 + 0.881611i \(0.343541\pi\)
\(984\) −8155.21 7745.49i −0.264206 0.250932i
\(985\) 3148.47i 0.101846i
\(986\) 55657.1 + 14402.2i 1.79765 + 0.465171i
\(987\) −148.247 −0.00478092
\(988\) −68581.7 38040.4i −2.20837 1.22493i
\(989\) −42735.5 −1.37403
\(990\) 9788.05 + 2532.82i 0.314227 + 0.0813113i
\(991\) 48237.2 1.54622 0.773110 0.634271i \(-0.218700\pi\)
0.773110 + 0.634271i \(0.218700\pi\)
\(992\) 20898.9 + 23225.6i 0.668892 + 0.743360i
\(993\) 16159.7 0.516429
\(994\) −28550.2 7387.83i −0.911024 0.235742i
\(995\) 25539.0 0.813708
\(996\) 16994.4 + 9426.34i 0.540651 + 0.299884i
\(997\) 5979.31 0.189937 0.0949683 0.995480i \(-0.469725\pi\)
0.0949683 + 0.995480i \(0.469725\pi\)
\(998\) 51303.8 + 13275.7i 1.62725 + 0.421077i
\(999\) 2623.14i 0.0830755i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 124.4.d.c.123.2 yes 40
4.3 odd 2 inner 124.4.d.c.123.3 yes 40
31.30 odd 2 inner 124.4.d.c.123.1 40
124.123 even 2 inner 124.4.d.c.123.4 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
124.4.d.c.123.1 40 31.30 odd 2 inner
124.4.d.c.123.2 yes 40 1.1 even 1 trivial
124.4.d.c.123.3 yes 40 4.3 odd 2 inner
124.4.d.c.123.4 yes 40 124.123 even 2 inner