Properties

Label 143.4.o.a.32.17
Level $143$
Weight $4$
Character 143.32
Analytic conductor $8.437$
Analytic rank $0$
Dimension $160$
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] = [143,4,Mod(32,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.32");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.o (of order \(12\), 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: \(8.43727313082\)
Analytic rank: \(0\)
Dimension: \(160\)
Relative dimension: \(40\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.17
Character \(\chi\) \(=\) 143.32
Dual form 143.4.o.a.76.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.15192 + 0.308657i) q^{2} +(-3.89437 + 6.74525i) q^{3} +(-5.69654 + 3.28890i) q^{4} +(12.2876 - 12.2876i) q^{5} +(2.40405 - 8.97204i) q^{6} +(32.4067 + 8.68335i) q^{7} +(12.2930 - 12.2930i) q^{8} +(-16.8323 - 29.1543i) q^{9} +O(q^{10})\) \(q+(-1.15192 + 0.308657i) q^{2} +(-3.89437 + 6.74525i) q^{3} +(-5.69654 + 3.28890i) q^{4} +(12.2876 - 12.2876i) q^{5} +(2.40405 - 8.97204i) q^{6} +(32.4067 + 8.68335i) q^{7} +(12.2930 - 12.2930i) q^{8} +(-16.8323 - 29.1543i) q^{9} +(-10.3617 + 17.9470i) q^{10} +(35.8108 - 6.97037i) q^{11} -51.2328i q^{12} +(-45.6796 + 10.5059i) q^{13} -40.0102 q^{14} +(35.0304 + 130.735i) q^{15} +(15.9450 - 27.6175i) q^{16} +(57.2173 + 99.1033i) q^{17} +(28.3882 + 28.3882i) q^{18} +(8.10390 - 30.2442i) q^{19} +(-29.5841 + 110.409i) q^{20} +(-184.775 + 184.775i) q^{21} +(-39.0999 + 19.0826i) q^{22} +(-44.1676 - 25.5002i) q^{23} +(35.0458 + 130.793i) q^{24} -176.970i q^{25} +(49.3767 - 26.2014i) q^{26} +51.9082 q^{27} +(-213.165 + 57.1174i) q^{28} +(136.585 + 78.8575i) q^{29} +(-80.7047 - 139.785i) q^{30} +(29.9915 - 29.9915i) q^{31} +(-45.8394 + 171.075i) q^{32} +(-92.4437 + 268.698i) q^{33} +(-96.4989 - 96.4989i) q^{34} +(504.898 - 291.503i) q^{35} +(191.771 + 110.719i) q^{36} +(-75.7423 + 20.2951i) q^{37} +37.3403i q^{38} +(107.028 - 349.034i) q^{39} -302.102i q^{40} +(210.469 - 56.3950i) q^{41} +(155.815 - 269.879i) q^{42} +(128.947 + 223.342i) q^{43} +(-181.073 + 157.485i) q^{44} +(-565.064 - 151.408i) q^{45} +(58.7485 + 15.7416i) q^{46} +(106.213 + 106.213i) q^{47} +(124.191 + 215.106i) q^{48} +(677.747 + 391.297i) q^{49} +(54.6229 + 203.855i) q^{50} -891.302 q^{51} +(225.663 - 210.083i) q^{52} -724.401 q^{53} +(-59.7943 + 16.0218i) q^{54} +(354.379 - 525.677i) q^{55} +(505.119 - 291.631i) q^{56} +(172.445 + 172.445i) q^{57} +(-181.676 - 48.6798i) q^{58} +(50.1583 - 187.193i) q^{59} +(-629.528 - 629.528i) q^{60} +(-106.436 + 61.4511i) q^{61} +(-25.2909 + 43.8051i) q^{62} +(-292.321 - 1090.96i) q^{63} +43.9057i q^{64} +(-432.199 + 690.385i) q^{65} +(23.5525 - 338.053i) q^{66} +(143.932 + 537.163i) q^{67} +(-651.882 - 376.364i) q^{68} +(344.010 - 198.614i) q^{69} +(-491.629 + 491.629i) q^{70} +(-330.104 - 88.4511i) q^{71} +(-565.312 - 151.475i) q^{72} +(-310.252 + 310.252i) q^{73} +(80.9851 - 46.7568i) q^{74} +(1193.70 + 689.185i) q^{75} +(53.3059 + 198.940i) q^{76} +(1221.04 + 85.0710i) q^{77} +(-15.5563 + 435.096i) q^{78} -784.587i q^{79} +(-143.427 - 535.277i) q^{80} +(252.321 - 437.033i) q^{81} +(-225.037 + 129.925i) q^{82} +(326.241 + 326.241i) q^{83} +(444.873 - 1660.29i) q^{84} +(1920.80 + 514.678i) q^{85} +(-217.473 - 217.473i) q^{86} +(-1063.83 + 614.201i) q^{87} +(354.535 - 525.908i) q^{88} +(285.539 - 76.5098i) q^{89} +697.644 q^{90} +(-1571.55 - 56.1887i) q^{91} +335.470 q^{92} +(85.5022 + 319.099i) q^{93} +(-155.133 - 89.5662i) q^{94} +(-272.050 - 471.205i) q^{95} +(-975.427 - 975.427i) q^{96} +(33.1914 + 8.89361i) q^{97} +(-901.489 - 241.553i) q^{98} +(-805.993 - 926.713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 160 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 652 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 160 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 652 q^{9} - 80 q^{11} - 64 q^{14} - 76 q^{15} + 940 q^{16} + 68 q^{20} + 28 q^{22} - 240 q^{23} + 496 q^{26} + 824 q^{27} - 280 q^{31} - 266 q^{33} + 2212 q^{34} - 2760 q^{36} + 328 q^{37} + 1164 q^{42} + 104 q^{44} + 896 q^{45} + 4 q^{47} + 2080 q^{48} - 12 q^{49} - 6528 q^{53} + 682 q^{55} - 1356 q^{56} + 1096 q^{58} - 1392 q^{59} + 4 q^{60} - 1880 q^{66} + 304 q^{67} - 12 q^{69} - 1932 q^{70} - 5076 q^{71} + 8832 q^{75} - 10876 q^{78} + 4588 q^{80} - 4624 q^{81} - 7716 q^{82} + 5608 q^{86} + 10152 q^{88} + 7268 q^{89} - 1008 q^{91} + 8120 q^{92} + 2740 q^{93} + 2728 q^{97} - 6996 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15192 + 0.308657i −0.407266 + 0.109127i −0.456635 0.889654i \(-0.650946\pi\)
0.0493690 + 0.998781i \(0.484279\pi\)
\(3\) −3.89437 + 6.74525i −0.749472 + 1.29812i 0.198604 + 0.980080i \(0.436359\pi\)
−0.948076 + 0.318044i \(0.896974\pi\)
\(4\) −5.69654 + 3.28890i −0.712068 + 0.411113i
\(5\) 12.2876 12.2876i 1.09904 1.09904i 0.104511 0.994524i \(-0.466672\pi\)
0.994524 0.104511i \(-0.0333279\pi\)
\(6\) 2.40405 8.97204i 0.163575 0.610470i
\(7\) 32.4067 + 8.68335i 1.74980 + 0.468857i 0.984583 0.174918i \(-0.0559662\pi\)
0.765215 + 0.643775i \(0.222633\pi\)
\(8\) 12.2930 12.2930i 0.543278 0.543278i
\(9\) −16.8323 29.1543i −0.623417 1.07979i
\(10\) −10.3617 + 17.9470i −0.327666 + 0.567534i
\(11\) 35.8108 6.97037i 0.981579 0.191059i
\(12\) 51.2328i 1.23247i
\(13\) −45.6796 + 10.5059i −0.974557 + 0.224140i
\(14\) −40.0102 −0.763799
\(15\) 35.0304 + 130.735i 0.602987 + 2.25038i
\(16\) 15.9450 27.6175i 0.249140 0.431523i
\(17\) 57.2173 + 99.1033i 0.816308 + 1.41389i 0.908385 + 0.418136i \(0.137316\pi\)
−0.0920763 + 0.995752i \(0.529350\pi\)
\(18\) 28.3882 + 28.3882i 0.371731 + 0.371731i
\(19\) 8.10390 30.2442i 0.0978506 0.365184i −0.899586 0.436744i \(-0.856131\pi\)
0.997436 + 0.0715610i \(0.0227980\pi\)
\(20\) −29.5841 + 110.409i −0.330761 + 1.23442i
\(21\) −184.775 + 184.775i −1.92006 + 1.92006i
\(22\) −39.0999 + 19.0826i −0.378914 + 0.184928i
\(23\) −44.1676 25.5002i −0.400416 0.231180i 0.286247 0.958156i \(-0.407592\pi\)
−0.686664 + 0.726975i \(0.740925\pi\)
\(24\) 35.0458 + 130.793i 0.298070 + 1.11241i
\(25\) 176.970i 1.41576i
\(26\) 49.3767 26.2014i 0.372445 0.197635i
\(27\) 51.9082 0.369991
\(28\) −213.165 + 57.1174i −1.43873 + 0.385506i
\(29\) 136.585 + 78.8575i 0.874594 + 0.504947i 0.868872 0.495036i \(-0.164845\pi\)
0.00572198 + 0.999984i \(0.498179\pi\)
\(30\) −80.7047 139.785i −0.491153 0.850702i
\(31\) 29.9915 29.9915i 0.173763 0.173763i −0.614868 0.788630i \(-0.710791\pi\)
0.788630 + 0.614868i \(0.210791\pi\)
\(32\) −45.8394 + 171.075i −0.253229 + 0.945064i
\(33\) −92.4437 + 268.698i −0.487648 + 1.41740i
\(34\) −96.4989 96.4989i −0.486748 0.486748i
\(35\) 504.898 291.503i 2.43838 1.40780i
\(36\) 191.771 + 110.719i 0.887831 + 0.512589i
\(37\) −75.7423 + 20.2951i −0.336539 + 0.0901755i −0.423131 0.906068i \(-0.639069\pi\)
0.0865918 + 0.996244i \(0.472402\pi\)
\(38\) 37.3403i 0.159405i
\(39\) 107.028 349.034i 0.439441 1.43308i
\(40\) 302.102i 1.19416i
\(41\) 210.469 56.3950i 0.801701 0.214815i 0.165370 0.986232i \(-0.447118\pi\)
0.636331 + 0.771416i \(0.280451\pi\)
\(42\) 155.815 269.879i 0.572446 0.991505i
\(43\) 128.947 + 223.342i 0.457307 + 0.792079i 0.998818 0.0486148i \(-0.0154807\pi\)
−0.541510 + 0.840694i \(0.682147\pi\)
\(44\) −181.073 + 157.485i −0.620404 + 0.539586i
\(45\) −565.064 151.408i −1.87188 0.501570i
\(46\) 58.7485 + 15.7416i 0.188304 + 0.0504559i
\(47\) 106.213 + 106.213i 0.329635 + 0.329635i 0.852447 0.522813i \(-0.175117\pi\)
−0.522813 + 0.852447i \(0.675117\pi\)
\(48\) 124.191 + 215.106i 0.373447 + 0.646829i
\(49\) 677.747 + 391.297i 1.97594 + 1.14081i
\(50\) 54.6229 + 203.855i 0.154497 + 0.576590i
\(51\) −891.302 −2.44720
\(52\) 225.663 210.083i 0.601804 0.560256i
\(53\) −724.401 −1.87744 −0.938718 0.344687i \(-0.887985\pi\)
−0.938718 + 0.344687i \(0.887985\pi\)
\(54\) −59.7943 + 16.0218i −0.150685 + 0.0403759i
\(55\) 354.379 525.677i 0.868809 1.28877i
\(56\) 505.119 291.631i 1.20535 0.695907i
\(57\) 172.445 + 172.445i 0.400717 + 0.400717i
\(58\) −181.676 48.6798i −0.411296 0.110206i
\(59\) 50.1583 187.193i 0.110679 0.413059i −0.888249 0.459363i \(-0.848078\pi\)
0.998927 + 0.0463042i \(0.0147444\pi\)
\(60\) −629.528 629.528i −1.35453 1.35453i
\(61\) −106.436 + 61.4511i −0.223406 + 0.128984i −0.607527 0.794299i \(-0.707838\pi\)
0.384120 + 0.923283i \(0.374505\pi\)
\(62\) −25.2909 + 43.8051i −0.0518055 + 0.0897298i
\(63\) −292.321 1090.96i −0.584587 2.18171i
\(64\) 43.9057i 0.0857532i
\(65\) −432.199 + 690.385i −0.824734 + 1.31741i
\(66\) 23.5525 338.053i 0.0439260 0.630476i
\(67\) 143.932 + 537.163i 0.262450 + 0.979477i 0.963793 + 0.266652i \(0.0859176\pi\)
−0.701343 + 0.712824i \(0.747416\pi\)
\(68\) −651.882 376.364i −1.16253 0.671189i
\(69\) 344.010 198.614i 0.600202 0.346527i
\(70\) −491.629 + 491.629i −0.839441 + 0.839441i
\(71\) −330.104 88.4511i −0.551776 0.147848i −0.0278508 0.999612i \(-0.508866\pi\)
−0.523926 + 0.851764i \(0.675533\pi\)
\(72\) −565.312 151.475i −0.925315 0.247937i
\(73\) −310.252 + 310.252i −0.497428 + 0.497428i −0.910637 0.413208i \(-0.864408\pi\)
0.413208 + 0.910637i \(0.364408\pi\)
\(74\) 80.9851 46.7568i 0.127221 0.0734509i
\(75\) 1193.70 + 689.185i 1.83783 + 1.06107i
\(76\) 53.3059 + 198.940i 0.0804553 + 0.300263i
\(77\) 1221.04 + 85.0710i 1.80714 + 0.125906i
\(78\) −15.5563 + 435.096i −0.0225820 + 0.631601i
\(79\) 784.587i 1.11738i −0.829377 0.558690i \(-0.811304\pi\)
0.829377 0.558690i \(-0.188696\pi\)
\(80\) −143.427 535.277i −0.200446 0.748073i
\(81\) 252.321 437.033i 0.346119 0.599496i
\(82\) −225.037 + 129.925i −0.303064 + 0.174974i
\(83\) 326.241 + 326.241i 0.431441 + 0.431441i 0.889118 0.457677i \(-0.151318\pi\)
−0.457677 + 0.889118i \(0.651318\pi\)
\(84\) 444.873 1660.29i 0.577852 2.15657i
\(85\) 1920.80 + 514.678i 2.45106 + 0.656760i
\(86\) −217.473 217.473i −0.272683 0.272683i
\(87\) −1063.83 + 614.201i −1.31097 + 0.756888i
\(88\) 354.535 525.908i 0.429472 0.637068i
\(89\) 285.539 76.5098i 0.340079 0.0911239i −0.0847377 0.996403i \(-0.527005\pi\)
0.424817 + 0.905279i \(0.360339\pi\)
\(90\) 697.644 0.817090
\(91\) −1571.55 56.1887i −1.81037 0.0647272i
\(92\) 335.470 0.380165
\(93\) 85.5022 + 319.099i 0.0953352 + 0.355796i
\(94\) −155.133 89.5662i −0.170221 0.0982771i
\(95\) −272.050 471.205i −0.293808 0.508891i
\(96\) −975.427 975.427i −1.03702 1.03702i
\(97\) 33.1914 + 8.89361i 0.0347431 + 0.00930938i 0.276149 0.961115i \(-0.410942\pi\)
−0.241406 + 0.970424i \(0.577608\pi\)
\(98\) −901.489 241.553i −0.929226 0.248985i
\(99\) −805.993 926.713i −0.818236 0.940790i
\(100\) 582.035 + 1008.11i 0.582035 + 1.00811i
\(101\) −365.816 + 633.612i −0.360397 + 0.624225i −0.988026 0.154287i \(-0.950692\pi\)
0.627629 + 0.778512i \(0.284025\pi\)
\(102\) 1026.71 275.107i 0.996663 0.267055i
\(103\) 953.318i 0.911973i −0.889987 0.455987i \(-0.849286\pi\)
0.889987 0.455987i \(-0.150714\pi\)
\(104\) −432.389 + 690.687i −0.407685 + 0.651226i
\(105\) 4540.88i 4.22042i
\(106\) 834.454 223.591i 0.764616 0.204878i
\(107\) −20.2988 11.7195i −0.0183398 0.0105885i 0.490802 0.871271i \(-0.336704\pi\)
−0.509142 + 0.860683i \(0.670037\pi\)
\(108\) −295.698 + 170.721i −0.263459 + 0.152108i
\(109\) 13.0285 + 13.0285i 0.0114486 + 0.0114486i 0.712808 0.701359i \(-0.247423\pi\)
−0.701359 + 0.712808i \(0.747423\pi\)
\(110\) −245.964 + 714.922i −0.213198 + 0.619683i
\(111\) 158.073 589.937i 0.135168 0.504454i
\(112\) 756.536 756.536i 0.638267 0.638267i
\(113\) 106.843 + 185.058i 0.0889464 + 0.154060i 0.907066 0.420988i \(-0.138317\pi\)
−0.818120 + 0.575048i \(0.804983\pi\)
\(114\) −251.870 145.417i −0.206928 0.119470i
\(115\) −856.048 + 229.377i −0.694147 + 0.185996i
\(116\) −1037.42 −0.830361
\(117\) 1075.18 + 1154.92i 0.849580 + 0.912584i
\(118\) 231.114i 0.180303i
\(119\) 993.676 + 3708.45i 0.765463 + 2.85675i
\(120\) 2037.75 + 1176.50i 1.55017 + 0.894992i
\(121\) 1233.83 499.229i 0.926993 0.375078i
\(122\) 103.639 103.639i 0.0769103 0.0769103i
\(123\) −439.246 + 1639.29i −0.321996 + 1.20170i
\(124\) −72.2089 + 269.487i −0.0522948 + 0.195167i
\(125\) −638.580 638.580i −0.456931 0.456931i
\(126\) 673.462 + 1166.47i 0.476165 + 0.824742i
\(127\) −40.4032 + 69.9805i −0.0282300 + 0.0488958i −0.879795 0.475353i \(-0.842320\pi\)
0.851565 + 0.524249i \(0.175654\pi\)
\(128\) −380.267 1419.17i −0.262587 0.979988i
\(129\) −2008.67 −1.37096
\(130\) 284.768 928.671i 0.192122 0.626537i
\(131\) 2610.19i 1.74086i −0.492289 0.870432i \(-0.663840\pi\)
0.492289 0.870432i \(-0.336160\pi\)
\(132\) −357.112 1834.69i −0.235474 1.20977i
\(133\) 525.241 909.745i 0.342438 0.593119i
\(134\) −331.598 574.345i −0.213774 0.370268i
\(135\) 637.827 637.827i 0.406633 0.406633i
\(136\) 1921.65 + 514.903i 1.21162 + 0.324651i
\(137\) 315.984 1179.27i 0.197054 0.735414i −0.794672 0.607039i \(-0.792357\pi\)
0.991726 0.128375i \(-0.0409762\pi\)
\(138\) −334.969 + 334.969i −0.206627 + 0.206627i
\(139\) −206.534 + 119.243i −0.126029 + 0.0727628i −0.561689 0.827348i \(-0.689848\pi\)
0.435660 + 0.900111i \(0.356515\pi\)
\(140\) −1917.45 + 3321.12i −1.15753 + 2.00490i
\(141\) −1130.07 + 302.802i −0.674958 + 0.180855i
\(142\) 407.555 0.240854
\(143\) −1562.59 + 694.630i −0.913780 + 0.406209i
\(144\) −1073.56 −0.621273
\(145\) 2647.27 709.334i 1.51616 0.406255i
\(146\) 261.625 453.148i 0.148303 0.256869i
\(147\) −5278.80 + 3047.72i −2.96182 + 1.71001i
\(148\) 364.721 364.721i 0.202567 0.202567i
\(149\) −498.770 + 1861.43i −0.274234 + 1.02345i 0.682120 + 0.731241i \(0.261058\pi\)
−0.956353 + 0.292213i \(0.905608\pi\)
\(150\) −1587.78 425.444i −0.864276 0.231582i
\(151\) 1525.17 1525.17i 0.821966 0.821966i −0.164424 0.986390i \(-0.552576\pi\)
0.986390 + 0.164424i \(0.0525765\pi\)
\(152\) −272.170 471.412i −0.145236 0.251556i
\(153\) 1926.19 3336.27i 1.01780 1.76288i
\(154\) −1432.80 + 278.886i −0.749728 + 0.145930i
\(155\) 737.047i 0.381942i
\(156\) 538.249 + 2340.29i 0.276246 + 1.20111i
\(157\) 49.1073 0.0249630 0.0124815 0.999922i \(-0.496027\pi\)
0.0124815 + 0.999922i \(0.496027\pi\)
\(158\) 242.168 + 903.785i 0.121936 + 0.455071i
\(159\) 2821.09 4886.26i 1.40709 2.43714i
\(160\) 1538.84 + 2665.35i 0.760351 + 1.31697i
\(161\) −1209.90 1209.90i −0.592257 0.592257i
\(162\) −155.761 + 581.309i −0.0755417 + 0.281926i
\(163\) 901.439 3364.22i 0.433167 1.61660i −0.312249 0.950000i \(-0.601082\pi\)
0.745416 0.666600i \(-0.232251\pi\)
\(164\) −1013.47 + 1013.47i −0.482552 + 0.482552i
\(165\) 2165.74 + 4437.56i 1.02183 + 2.09372i
\(166\) −476.502 275.108i −0.222793 0.128630i
\(167\) 710.575 + 2651.90i 0.329257 + 1.22880i 0.909963 + 0.414690i \(0.136110\pi\)
−0.580706 + 0.814114i \(0.697223\pi\)
\(168\) 4542.87i 2.08625i
\(169\) 1976.25 959.815i 0.899522 0.436875i
\(170\) −2371.48 −1.06991
\(171\) −1018.16 + 272.814i −0.455323 + 0.122004i
\(172\) −1469.10 848.187i −0.651268 0.376010i
\(173\) −899.519 1558.01i −0.395313 0.684702i 0.597828 0.801624i \(-0.296031\pi\)
−0.993141 + 0.116922i \(0.962697\pi\)
\(174\) 1035.87 1035.87i 0.451317 0.451317i
\(175\) 1536.69 5735.00i 0.663787 2.47729i
\(176\) 378.498 1100.15i 0.162104 0.471174i
\(177\) 1067.33 + 1067.33i 0.453251 + 0.453251i
\(178\) −305.303 + 176.267i −0.128559 + 0.0742234i
\(179\) −3362.58 1941.39i −1.40408 0.810648i −0.409276 0.912411i \(-0.634219\pi\)
−0.994809 + 0.101762i \(0.967552\pi\)
\(180\) 3716.88 995.935i 1.53911 0.412404i
\(181\) 2223.00i 0.912898i 0.889750 + 0.456449i \(0.150879\pi\)
−0.889750 + 0.456449i \(0.849121\pi\)
\(182\) 1827.65 420.345i 0.744365 0.171198i
\(183\) 957.253i 0.386679i
\(184\) −856.424 + 229.478i −0.343133 + 0.0919421i
\(185\) −681.312 + 1180.07i −0.270763 + 0.468975i
\(186\) −196.984 341.186i −0.0776536 0.134500i
\(187\) 2739.79 + 3150.14i 1.07141 + 1.23188i
\(188\) −954.375 255.724i −0.370239 0.0992053i
\(189\) 1682.18 + 450.737i 0.647409 + 0.173473i
\(190\) 458.822 + 458.822i 0.175192 + 0.175192i
\(191\) 1314.47 + 2276.74i 0.497969 + 0.862507i 0.999997 0.00234388i \(-0.000746082\pi\)
−0.502028 + 0.864851i \(0.667413\pi\)
\(192\) −296.155 170.985i −0.111318 0.0642697i
\(193\) −673.943 2515.19i −0.251355 0.938069i −0.970082 0.242777i \(-0.921942\pi\)
0.718727 0.695292i \(-0.244725\pi\)
\(194\) −40.9790 −0.0151656
\(195\) −2973.67 5603.91i −1.09205 2.05797i
\(196\) −5147.76 −1.87600
\(197\) −1073.76 + 287.714i −0.388337 + 0.104055i −0.447704 0.894182i \(-0.647758\pi\)
0.0593674 + 0.998236i \(0.481092\pi\)
\(198\) 1214.48 + 818.727i 0.435905 + 0.293861i
\(199\) −308.655 + 178.202i −0.109950 + 0.0634794i −0.553966 0.832539i \(-0.686886\pi\)
0.444017 + 0.896018i \(0.353553\pi\)
\(200\) −2175.48 2175.48i −0.769149 0.769149i
\(201\) −4183.83 1121.05i −1.46818 0.393398i
\(202\) 225.823 842.784i 0.0786578 0.293555i
\(203\) 3741.53 + 3741.53i 1.29361 + 1.29361i
\(204\) 5077.34 2931.41i 1.74257 1.00608i
\(205\) 1893.20 3279.11i 0.645008 1.11719i
\(206\) 294.248 + 1098.15i 0.0995206 + 0.371416i
\(207\) 1716.90i 0.576487i
\(208\) −438.211 + 1429.07i −0.146079 + 0.476386i
\(209\) 79.3941 1139.56i 0.0262766 0.377152i
\(210\) −1401.57 5230.75i −0.460561 1.71884i
\(211\) −3743.98 2161.59i −1.22154 0.705259i −0.256298 0.966598i \(-0.582503\pi\)
−0.965247 + 0.261339i \(0.915836\pi\)
\(212\) 4126.58 2382.48i 1.33686 0.771838i
\(213\) 1882.17 1882.17i 0.605466 0.605466i
\(214\) 27.0000 + 7.23463i 0.00862468 + 0.00231098i
\(215\) 4328.78 + 1159.89i 1.37312 + 0.367926i
\(216\) 638.107 638.107i 0.201008 0.201008i
\(217\) 1232.35 711.500i 0.385519 0.222580i
\(218\) −19.0291 10.9865i −0.00591199 0.00341329i
\(219\) −884.491 3300.96i −0.272915 1.01853i
\(220\) −289.837 + 4160.06i −0.0888217 + 1.27487i
\(221\) −3654.84 3925.88i −1.11245 1.19495i
\(222\) 728.353i 0.220198i
\(223\) −506.903 1891.79i −0.152219 0.568088i −0.999327 0.0366682i \(-0.988326\pi\)
0.847109 0.531419i \(-0.178341\pi\)
\(224\) −2971.01 + 5145.93i −0.886199 + 1.53494i
\(225\) −5159.43 + 2978.80i −1.52872 + 0.882607i
\(226\) −180.194 180.194i −0.0530369 0.0530369i
\(227\) −32.3987 + 120.914i −0.00947303 + 0.0353538i −0.970501 0.241099i \(-0.922492\pi\)
0.961028 + 0.276453i \(0.0891589\pi\)
\(228\) −1549.49 415.186i −0.450078 0.120598i
\(229\) −836.611 836.611i −0.241418 0.241418i 0.576018 0.817437i \(-0.304606\pi\)
−0.817437 + 0.576018i \(0.804606\pi\)
\(230\) 915.303 528.450i 0.262406 0.151500i
\(231\) −5328.99 + 7904.90i −1.51784 + 2.25153i
\(232\) 2648.43 709.645i 0.749474 0.200821i
\(233\) −2243.51 −0.630804 −0.315402 0.948958i \(-0.602139\pi\)
−0.315402 + 0.948958i \(0.602139\pi\)
\(234\) −1595.00 998.515i −0.445593 0.278953i
\(235\) 2610.21 0.724560
\(236\) 329.931 + 1231.32i 0.0910029 + 0.339628i
\(237\) 5292.24 + 3055.47i 1.45050 + 0.837445i
\(238\) −2289.28 3965.15i −0.623495 1.07993i
\(239\) −966.176 966.176i −0.261493 0.261493i 0.564168 0.825660i \(-0.309197\pi\)
−0.825660 + 0.564168i \(0.809197\pi\)
\(240\) 4169.14 + 1117.12i 1.12132 + 0.300457i
\(241\) −6404.47 1716.07i −1.71182 0.458680i −0.735949 0.677037i \(-0.763264\pi\)
−0.975869 + 0.218357i \(0.929930\pi\)
\(242\) −1267.18 + 955.903i −0.336602 + 0.253916i
\(243\) 2666.03 + 4617.69i 0.703809 + 1.21903i
\(244\) 404.213 700.118i 0.106054 0.183690i
\(245\) 13136.0 3519.77i 3.42542 0.917837i
\(246\) 2023.91i 0.524552i
\(247\) −52.4392 + 1466.68i −0.0135086 + 0.377824i
\(248\) 737.371i 0.188803i
\(249\) −3471.08 + 930.074i −0.883418 + 0.236711i
\(250\) 932.697 + 538.493i 0.235956 + 0.136229i
\(251\) −3005.39 + 1735.16i −0.755770 + 0.436344i −0.827775 0.561060i \(-0.810394\pi\)
0.0720047 + 0.997404i \(0.477060\pi\)
\(252\) 5253.27 + 5253.27i 1.31319 + 1.31319i
\(253\) −1759.42 605.317i −0.437209 0.150419i
\(254\) 24.9415 93.0829i 0.00616129 0.0229943i
\(255\) −10952.0 + 10952.0i −2.68956 + 2.68956i
\(256\) 700.454 + 1213.22i 0.171009 + 0.296197i
\(257\) −4216.84 2434.59i −1.02350 0.590917i −0.108383 0.994109i \(-0.534567\pi\)
−0.915115 + 0.403192i \(0.867901\pi\)
\(258\) 2313.83 619.989i 0.558344 0.149608i
\(259\) −2630.79 −0.631155
\(260\) 191.435 5354.27i 0.0456626 1.27714i
\(261\) 5309.40i 1.25917i
\(262\) 805.652 + 3006.74i 0.189975 + 0.708995i
\(263\) 3216.01 + 1856.76i 0.754020 + 0.435334i 0.827145 0.561989i \(-0.189964\pi\)
−0.0731243 + 0.997323i \(0.523297\pi\)
\(264\) 2166.69 + 4439.51i 0.505116 + 1.03497i
\(265\) −8901.14 + 8901.14i −2.06337 + 2.06337i
\(266\) −324.239 + 1210.08i −0.0747382 + 0.278927i
\(267\) −595.915 + 2223.99i −0.136590 + 0.509759i
\(268\) −2586.59 2586.59i −0.589558 0.589558i
\(269\) −2370.92 4106.55i −0.537389 0.930785i −0.999044 0.0437249i \(-0.986077\pi\)
0.461655 0.887060i \(-0.347256\pi\)
\(270\) −537.858 + 931.598i −0.121233 + 0.209982i
\(271\) 841.508 + 3140.55i 0.188627 + 0.703966i 0.993825 + 0.110960i \(0.0353925\pi\)
−0.805198 + 0.593006i \(0.797941\pi\)
\(272\) 3649.31 0.813500
\(273\) 6499.21 10381.7i 1.44084 2.30157i
\(274\) 1455.96i 0.321013i
\(275\) −1233.54 6337.42i −0.270493 1.38968i
\(276\) −1306.45 + 2262.83i −0.284923 + 0.493501i
\(277\) 2638.05 + 4569.23i 0.572220 + 0.991114i 0.996338 + 0.0855072i \(0.0272511\pi\)
−0.424117 + 0.905607i \(0.639416\pi\)
\(278\) 201.107 201.107i 0.0433870 0.0433870i
\(279\) −1379.21 369.558i −0.295954 0.0793006i
\(280\) 2623.26 9790.13i 0.559891 2.08954i
\(281\) 1096.49 1096.49i 0.232780 0.232780i −0.581072 0.813852i \(-0.697367\pi\)
0.813852 + 0.581072i \(0.197367\pi\)
\(282\) 1208.29 697.608i 0.255152 0.147312i
\(283\) 1514.66 2623.47i 0.318153 0.551057i −0.661950 0.749548i \(-0.730271\pi\)
0.980103 + 0.198491i \(0.0636041\pi\)
\(284\) 2171.36 581.814i 0.453685 0.121564i
\(285\) 4237.86 0.880804
\(286\) 1585.58 1282.47i 0.327824 0.265153i
\(287\) 7310.30 1.50353
\(288\) 5759.15 1543.16i 1.17834 0.315735i
\(289\) −4091.15 + 7086.07i −0.832719 + 1.44231i
\(290\) −2830.51 + 1634.20i −0.573150 + 0.330908i
\(291\) −189.249 + 189.249i −0.0381237 + 0.0381237i
\(292\) 746.976 2787.75i 0.149704 0.558702i
\(293\) 5133.39 + 1375.49i 1.02353 + 0.274255i 0.731274 0.682083i \(-0.238926\pi\)
0.292261 + 0.956339i \(0.405593\pi\)
\(294\) 5140.07 5140.07i 1.01964 1.01964i
\(295\) −1683.83 2916.48i −0.332326 0.575606i
\(296\) −681.611 + 1180.58i −0.133844 + 0.231825i
\(297\) 1858.88 361.820i 0.363175 0.0706899i
\(298\) 2298.18i 0.446744i
\(299\) 2285.46 + 700.815i 0.442045 + 0.135549i
\(300\) −9066.65 −1.74488
\(301\) 2239.38 + 8357.48i 0.428823 + 1.60039i
\(302\) −1286.13 + 2227.64i −0.245061 + 0.424458i
\(303\) −2849.25 4935.04i −0.540215 0.935679i
\(304\) −706.051 706.051i −0.133207 0.133207i
\(305\) −552.761 + 2062.93i −0.103774 + 0.387289i
\(306\) −1189.07 + 4437.66i −0.222139 + 0.829032i
\(307\) 5400.28 5400.28i 1.00394 1.00394i 0.00394949 0.999992i \(-0.498743\pi\)
0.999992 0.00394949i \(-0.00125717\pi\)
\(308\) −7235.48 + 3531.26i −1.33857 + 0.653286i
\(309\) 6430.37 + 3712.58i 1.18385 + 0.683499i
\(310\) 227.495 + 849.022i 0.0416801 + 0.155552i
\(311\) 361.172i 0.0658527i −0.999458 0.0329263i \(-0.989517\pi\)
0.999458 0.0329263i \(-0.0104827\pi\)
\(312\) −2974.98 5606.36i −0.539823 1.01730i
\(313\) 3887.77 0.702076 0.351038 0.936361i \(-0.385829\pi\)
0.351038 + 0.936361i \(0.385829\pi\)
\(314\) −56.5679 + 15.1573i −0.0101666 + 0.00272413i
\(315\) −16997.1 9813.30i −3.04025 1.75529i
\(316\) 2580.43 + 4469.44i 0.459369 + 0.795650i
\(317\) −838.885 + 838.885i −0.148632 + 0.148632i −0.777507 0.628874i \(-0.783516\pi\)
0.628874 + 0.777507i \(0.283516\pi\)
\(318\) −1741.50 + 6499.35i −0.307101 + 1.14612i
\(319\) 5440.89 + 1871.90i 0.954958 + 0.328547i
\(320\) 539.494 + 539.494i 0.0942458 + 0.0942458i
\(321\) 158.102 91.2804i 0.0274904 0.0158716i
\(322\) 1767.15 + 1020.27i 0.305837 + 0.176575i
\(323\) 3460.98 927.367i 0.596205 0.159753i
\(324\) 3319.44i 0.569176i
\(325\) 1859.23 + 8083.90i 0.317328 + 1.37973i
\(326\) 4153.56i 0.705657i
\(327\) −138.618 + 37.1425i −0.0234422 + 0.00628131i
\(328\) 1894.03 3280.55i 0.318842 0.552250i
\(329\) 2519.74 + 4364.32i 0.422242 + 0.731345i
\(330\) −3864.45 4443.26i −0.644639 0.741192i
\(331\) −6472.83 1734.39i −1.07486 0.288008i −0.322372 0.946613i \(-0.604480\pi\)
−0.752489 + 0.658605i \(0.771147\pi\)
\(332\) −2931.42 785.473i −0.484587 0.129845i
\(333\) 1866.60 + 1866.60i 0.307175 + 0.307175i
\(334\) −1637.05 2835.46i −0.268191 0.464520i
\(335\) 8369.02 + 4831.86i 1.36492 + 0.788037i
\(336\) 2156.79 + 8049.26i 0.350186 + 1.30691i
\(337\) 2113.11 0.341569 0.170784 0.985308i \(-0.445370\pi\)
0.170784 + 0.985308i \(0.445370\pi\)
\(338\) −1980.24 + 1715.62i −0.318670 + 0.276086i
\(339\) −1664.35 −0.266652
\(340\) −12634.7 + 3385.45i −2.01533 + 0.540005i
\(341\) 864.969 1283.07i 0.137363 0.203761i
\(342\) 1088.63 628.521i 0.172124 0.0993759i
\(343\) 10428.7 + 10428.7i 1.64168 + 1.64168i
\(344\) 4330.68 + 1160.40i 0.678764 + 0.181874i
\(345\) 1786.56 6667.54i 0.278798 1.04049i
\(346\) 1517.07 + 1517.07i 0.235717 + 0.235717i
\(347\) 169.434 97.8226i 0.0262123 0.0151337i −0.486837 0.873493i \(-0.661849\pi\)
0.513049 + 0.858359i \(0.328516\pi\)
\(348\) 4040.09 6997.64i 0.622332 1.07791i
\(349\) −2774.29 10353.8i −0.425515 1.58804i −0.762797 0.646638i \(-0.776174\pi\)
0.337282 0.941404i \(-0.390492\pi\)
\(350\) 7080.59i 1.08135i
\(351\) −2371.15 + 545.345i −0.360577 + 0.0829299i
\(352\) −449.090 + 6445.85i −0.0680016 + 0.976036i
\(353\) 2024.58 + 7555.84i 0.305262 + 1.13925i 0.932719 + 0.360603i \(0.117429\pi\)
−0.627457 + 0.778651i \(0.715904\pi\)
\(354\) −1558.92 900.043i −0.234056 0.135132i
\(355\) −5143.03 + 2969.33i −0.768912 + 0.443931i
\(356\) −1374.95 + 1374.95i −0.204697 + 0.204697i
\(357\) −28884.2 7739.49i −4.28211 1.14739i
\(358\) 4472.66 + 1198.45i 0.660300 + 0.176927i
\(359\) −2909.86 + 2909.86i −0.427790 + 0.427790i −0.887875 0.460085i \(-0.847819\pi\)
0.460085 + 0.887875i \(0.347819\pi\)
\(360\) −8807.58 + 5085.06i −1.28944 + 0.744461i
\(361\) 5091.03 + 2939.31i 0.742241 + 0.428533i
\(362\) −686.145 2560.73i −0.0996215 0.371793i
\(363\) −1437.56 + 10266.7i −0.207857 + 1.48446i
\(364\) 9137.21 4848.60i 1.31571 0.698175i
\(365\) 7624.50i 1.09338i
\(366\) 295.463 + 1102.68i 0.0421970 + 0.157481i
\(367\) 5853.11 10137.9i 0.832507 1.44194i −0.0635379 0.997979i \(-0.520238\pi\)
0.896044 0.443964i \(-0.146428\pi\)
\(368\) −1408.50 + 813.198i −0.199519 + 0.115193i
\(369\) −5186.83 5186.83i −0.731749 0.731749i
\(370\) 420.584 1569.64i 0.0590949 0.220545i
\(371\) −23475.4 6290.22i −3.28513 0.880249i
\(372\) −1536.55 1536.55i −0.214157 0.214157i
\(373\) −8305.49 + 4795.18i −1.15293 + 0.665643i −0.949599 0.313467i \(-0.898509\pi\)
−0.203329 + 0.979111i \(0.565176\pi\)
\(374\) −4128.34 2783.07i −0.570779 0.384784i
\(375\) 6794.25 1820.51i 0.935609 0.250696i
\(376\) 2611.36 0.358166
\(377\) −7067.63 2167.22i −0.965521 0.296068i
\(378\) −2076.86 −0.282598
\(379\) −1219.85 4552.54i −0.165328 0.617014i −0.997998 0.0632439i \(-0.979855\pi\)
0.832670 0.553770i \(-0.186811\pi\)
\(380\) 3099.49 + 1789.49i 0.418423 + 0.241577i
\(381\) −314.691 545.060i −0.0423152 0.0732920i
\(382\) −2216.90 2216.90i −0.296929 0.296929i
\(383\) −7233.47 1938.20i −0.965047 0.258583i −0.258311 0.966062i \(-0.583166\pi\)
−0.706735 + 0.707478i \(0.749833\pi\)
\(384\) 11053.6 + 2961.80i 1.46895 + 0.393603i
\(385\) 16048.9 13958.3i 2.12449 1.84774i
\(386\) 1552.66 + 2689.29i 0.204737 + 0.354614i
\(387\) 4340.93 7518.72i 0.570186 0.987591i
\(388\) −218.327 + 58.5004i −0.0285666 + 0.00765441i
\(389\) 6533.95i 0.851631i −0.904810 0.425815i \(-0.859987\pi\)
0.904810 0.425815i \(-0.140013\pi\)
\(390\) 5155.13 + 5537.42i 0.669333 + 0.718970i
\(391\) 5836.20i 0.754858i
\(392\) 13141.7 3521.32i 1.69326 0.453708i
\(393\) 17606.4 + 10165.0i 2.25986 + 1.30473i
\(394\) 1148.09 662.848i 0.146801 0.0847559i
\(395\) −9640.68 9640.68i −1.22804 1.22804i
\(396\) 7639.25 + 2628.23i 0.969410 + 0.333519i
\(397\) −1034.02 + 3859.03i −0.130721 + 0.487856i −0.999979 0.00650216i \(-0.997930\pi\)
0.869258 + 0.494358i \(0.164597\pi\)
\(398\) 300.543 300.543i 0.0378514 0.0378514i
\(399\) 4090.97 + 7085.77i 0.513295 + 0.889053i
\(400\) −4887.45 2821.77i −0.610932 0.352722i
\(401\) 5500.89 1473.96i 0.685041 0.183556i 0.100520 0.994935i \(-0.467949\pi\)
0.584521 + 0.811379i \(0.301283\pi\)
\(402\) 5165.47 0.640871
\(403\) −1054.91 + 1685.09i −0.130394 + 0.208289i
\(404\) 4812.53i 0.592655i
\(405\) −2269.66 8470.49i −0.278470 1.03926i
\(406\) −5464.80 3155.11i −0.668014 0.385678i
\(407\) −2570.93 + 1254.74i −0.313111 + 0.152813i
\(408\) −10956.8 + 10956.8i −1.32951 + 1.32951i
\(409\) 3195.03 11924.0i 0.386269 1.44158i −0.449887 0.893085i \(-0.648536\pi\)
0.836156 0.548491i \(-0.184798\pi\)
\(410\) −1168.70 + 4361.64i −0.140775 + 0.525380i
\(411\) 6723.90 + 6723.90i 0.806973 + 0.806973i
\(412\) 3135.37 + 5430.62i 0.374924 + 0.649387i
\(413\) 3250.93 5630.77i 0.387331 0.670877i
\(414\) −529.934 1977.74i −0.0629102 0.234784i
\(415\) 8017.44 0.948338
\(416\) 296.620 8296.22i 0.0349591 0.977777i
\(417\) 1857.50i 0.218135i
\(418\) 260.276 + 1337.19i 0.0304557 + 0.156469i
\(419\) 4713.81 8164.56i 0.549605 0.951945i −0.448696 0.893684i \(-0.648111\pi\)
0.998301 0.0582601i \(-0.0185553\pi\)
\(420\) −14934.5 25867.3i −1.73507 3.00523i
\(421\) 5496.82 5496.82i 0.636338 0.636338i −0.313312 0.949650i \(-0.601439\pi\)
0.949650 + 0.313312i \(0.101439\pi\)
\(422\) 4979.96 + 1334.38i 0.574457 + 0.153925i
\(423\) 1308.77 4884.39i 0.150436 0.561436i
\(424\) −8905.04 + 8905.04i −1.01997 + 1.01997i
\(425\) 17538.3 10125.7i 2.00172 1.15569i
\(426\) −1587.17 + 2749.06i −0.180513 + 0.312659i
\(427\) −3982.85 + 1067.20i −0.451391 + 0.120950i
\(428\) 154.178 0.0174123
\(429\) 1399.86 13245.2i 0.157543 1.49064i
\(430\) −5344.44 −0.599376
\(431\) 6317.37 1692.73i 0.706025 0.189179i 0.112098 0.993697i \(-0.464243\pi\)
0.593928 + 0.804518i \(0.297576\pi\)
\(432\) 827.675 1433.58i 0.0921795 0.159660i
\(433\) −3295.04 + 1902.39i −0.365703 + 0.211139i −0.671580 0.740932i \(-0.734384\pi\)
0.305877 + 0.952071i \(0.401050\pi\)
\(434\) −1199.97 + 1199.97i −0.132720 + 0.132720i
\(435\) −5524.82 + 20618.9i −0.608954 + 2.27265i
\(436\) −117.066 31.3679i −0.0128589 0.00344552i
\(437\) −1129.16 + 1129.16i −0.123604 + 0.123604i
\(438\) 2037.73 + 3529.45i 0.222298 + 0.385032i
\(439\) −4171.70 + 7225.59i −0.453541 + 0.785555i −0.998603 0.0528402i \(-0.983173\pi\)
0.545062 + 0.838395i \(0.316506\pi\)
\(440\) −2105.76 10818.5i −0.228155 1.17216i
\(441\) 26345.7i 2.84480i
\(442\) 5421.84 + 3394.22i 0.583463 + 0.365264i
\(443\) −2814.79 −0.301884 −0.150942 0.988543i \(-0.548231\pi\)
−0.150942 + 0.988543i \(0.548231\pi\)
\(444\) 1039.77 + 3880.49i 0.111139 + 0.414775i
\(445\) 2568.46 4448.70i 0.273610 0.473907i
\(446\) 1167.83 + 2022.74i 0.123987 + 0.214752i
\(447\) −10613.4 10613.4i −1.12304 1.12304i
\(448\) −381.248 + 1422.84i −0.0402060 + 0.150051i
\(449\) −2343.16 + 8744.80i −0.246282 + 0.919137i 0.726453 + 0.687217i \(0.241168\pi\)
−0.972735 + 0.231921i \(0.925499\pi\)
\(450\) 5023.84 5023.84i 0.526280 0.526280i
\(451\) 7143.97 3486.60i 0.745890 0.364030i
\(452\) −1217.27 702.793i −0.126672 0.0731340i
\(453\) 4348.08 + 16227.3i 0.450973 + 1.68305i
\(454\) 149.283i 0.0154322i
\(455\) −20001.0 + 18620.2i −2.06079 + 1.91852i
\(456\) 4239.72 0.435401
\(457\) −12699.2 + 3402.74i −1.29988 + 0.348301i −0.841404 0.540407i \(-0.818270\pi\)
−0.458473 + 0.888708i \(0.651604\pi\)
\(458\) 1221.94 + 705.486i 0.124667 + 0.0719764i
\(459\) 2970.05 + 5144.28i 0.302026 + 0.523125i
\(460\) 4122.12 4122.12i 0.417815 0.417815i
\(461\) 304.789 1137.49i 0.0307927 0.114920i −0.948819 0.315821i \(-0.897720\pi\)
0.979612 + 0.200901i \(0.0643869\pi\)
\(462\) 3698.69 10750.7i 0.372465 1.08261i
\(463\) −9517.49 9517.49i −0.955324 0.955324i 0.0437198 0.999044i \(-0.486079\pi\)
−0.999044 + 0.0437198i \(0.986079\pi\)
\(464\) 4355.69 2514.76i 0.435793 0.251605i
\(465\) 4971.57 + 2870.34i 0.495809 + 0.286255i
\(466\) 2584.35 692.475i 0.256905 0.0688375i
\(467\) 15212.1i 1.50735i −0.657249 0.753674i \(-0.728280\pi\)
0.657249 0.753674i \(-0.271720\pi\)
\(468\) −9923.25 3042.87i −0.980134 0.300549i
\(469\) 18657.5i 1.83694i
\(470\) −3006.77 + 805.661i −0.295089 + 0.0790688i
\(471\) −191.242 + 331.241i −0.0187091 + 0.0324051i
\(472\) −1684.57 2917.75i −0.164276 0.284535i
\(473\) 6174.47 + 7099.27i 0.600217 + 0.690115i
\(474\) −7039.35 1886.19i −0.682126 0.182775i
\(475\) −5352.30 1434.14i −0.517011 0.138533i
\(476\) −17857.2 17857.2i −1.71951 1.71951i
\(477\) 12193.3 + 21119.4i 1.17043 + 2.02724i
\(478\) 1411.18 + 814.744i 0.135033 + 0.0779613i
\(479\) 5054.35 + 18863.1i 0.482128 + 1.79933i 0.592659 + 0.805453i \(0.298078\pi\)
−0.110532 + 0.993873i \(0.535255\pi\)
\(480\) −23971.3 −2.27945
\(481\) 3246.66 1722.82i 0.307765 0.163313i
\(482\) 7907.14 0.747220
\(483\) 12872.9 3449.27i 1.21270 0.324943i
\(484\) −5386.64 + 6901.82i −0.505883 + 0.648180i
\(485\) 517.123 298.561i 0.0484152 0.0279525i
\(486\) −4496.34 4496.34i −0.419667 0.419667i
\(487\) 13990.8 + 3748.82i 1.30181 + 0.348820i 0.842136 0.539265i \(-0.181298\pi\)
0.459678 + 0.888086i \(0.347965\pi\)
\(488\) −553.003 + 2063.84i −0.0512977 + 0.191446i
\(489\) 19181.9 + 19181.9i 1.77390 + 1.77390i
\(490\) −14045.2 + 8109.02i −1.29490 + 0.747609i
\(491\) −5780.40 + 10012.0i −0.531295 + 0.920230i 0.468038 + 0.883709i \(0.344961\pi\)
−0.999333 + 0.0365217i \(0.988372\pi\)
\(492\) −2889.27 10782.9i −0.264753 0.988072i
\(493\) 18048.1i 1.64877i
\(494\) −392.295 1705.69i −0.0357291 0.155349i
\(495\) −21290.8 1483.35i −1.93323 0.134690i
\(496\) −350.077 1306.51i −0.0316914 0.118274i
\(497\) −9929.53 5732.81i −0.896177 0.517408i
\(498\) 3711.35 2142.75i 0.333955 0.192809i
\(499\) 11348.7 11348.7i 1.01811 1.01811i 0.0182769 0.999833i \(-0.494182\pi\)
0.999833 0.0182769i \(-0.00581805\pi\)
\(500\) 5737.93 + 1537.47i 0.513216 + 0.137516i
\(501\) −20655.0 5534.48i −1.84191 0.493538i
\(502\) 2926.41 2926.41i 0.260183 0.260183i
\(503\) −3956.37 + 2284.21i −0.350708 + 0.202481i −0.664997 0.746846i \(-0.731567\pi\)
0.314289 + 0.949327i \(0.398234\pi\)
\(504\) −17004.6 9817.60i −1.50287 0.867680i
\(505\) 3290.57 + 12280.6i 0.289957 + 1.08213i
\(506\) 2213.55 + 154.221i 0.194475 + 0.0135493i
\(507\) −1222.06 + 17068.2i −0.107049 + 1.49512i
\(508\) 531.529i 0.0464228i
\(509\) 862.832 + 3220.13i 0.0751363 + 0.280412i 0.993264 0.115872i \(-0.0369662\pi\)
−0.918128 + 0.396284i \(0.870299\pi\)
\(510\) 9235.41 15996.2i 0.801865 1.38887i
\(511\) −12748.3 + 7360.22i −1.10362 + 0.637176i
\(512\) 7129.93 + 7129.93i 0.615432 + 0.615432i
\(513\) 420.659 1569.92i 0.0362038 0.135114i
\(514\) 5608.92 + 1502.91i 0.481321 + 0.128970i
\(515\) −11714.0 11714.0i −1.00229 1.00229i
\(516\) 11442.5 6606.31i 0.976214 0.563617i
\(517\) 4543.94 + 3063.24i 0.386542 + 0.260583i
\(518\) 3030.47 812.011i 0.257048 0.0688759i
\(519\) 14012.2 1.18510
\(520\) 3173.87 + 13799.9i 0.267660 + 1.16378i
\(521\) 11760.2 0.988916 0.494458 0.869202i \(-0.335367\pi\)
0.494458 + 0.869202i \(0.335367\pi\)
\(522\) 1638.78 + 6116.02i 0.137409 + 0.512818i
\(523\) −14480.8 8360.50i −1.21071 0.699004i −0.247796 0.968812i \(-0.579706\pi\)
−0.962914 + 0.269808i \(0.913040\pi\)
\(524\) 8584.65 + 14869.0i 0.715691 + 1.23961i
\(525\) 32699.6 + 32699.6i 2.71833 + 2.71833i
\(526\) −4277.69 1146.20i −0.354594 0.0950131i
\(527\) 4688.30 + 1256.23i 0.387525 + 0.103837i
\(528\) 5946.75 + 6837.44i 0.490150 + 0.563563i
\(529\) −4782.98 8284.37i −0.393111 0.680889i
\(530\) 7506.03 13000.8i 0.615172 1.06551i
\(531\) −6301.77 + 1688.55i −0.515016 + 0.137998i
\(532\) 6909.87i 0.563122i
\(533\) −9021.65 + 4787.28i −0.733154 + 0.389043i
\(534\) 2745.80i 0.222513i
\(535\) −393.428 + 105.419i −0.0317932 + 0.00851897i
\(536\) 8372.69 + 4833.98i 0.674711 + 0.389545i
\(537\) 26190.3 15121.0i 2.10464 1.21512i
\(538\) 3998.63 + 3998.63i 0.320434 + 0.320434i
\(539\) 26998.2 + 9288.53i 2.15750 + 0.742273i
\(540\) −1535.66 + 5731.16i −0.122378 + 0.456722i
\(541\) −13461.1 + 13461.1i −1.06976 + 1.06976i −0.0723785 + 0.997377i \(0.523059\pi\)
−0.997377 + 0.0723785i \(0.976941\pi\)
\(542\) −1938.71 3357.94i −0.153643 0.266118i
\(543\) −14994.7 8657.20i −1.18505 0.684192i
\(544\) −19576.9 + 5245.61i −1.54293 + 0.413426i
\(545\) 320.177 0.0251649
\(546\) −4282.22 + 13964.9i −0.335645 + 1.09459i
\(547\) 18210.8i 1.42347i −0.702448 0.711735i \(-0.747910\pi\)
0.702448 0.711735i \(-0.252090\pi\)
\(548\) 2078.48 + 7757.00i 0.162023 + 0.604676i
\(549\) 3583.13 + 2068.72i 0.278551 + 0.160821i
\(550\) 3377.04 + 6919.48i 0.261813 + 0.536450i
\(551\) 3491.85 3491.85i 0.269978 0.269978i
\(552\) 1787.35 6670.46i 0.137816 0.514337i
\(553\) 6812.85 25425.9i 0.523891 1.95519i
\(554\) −4449.16 4449.16i −0.341203 0.341203i
\(555\) −5306.57 9191.24i −0.405858 0.702967i
\(556\) 784.355 1358.54i 0.0598274 0.103624i
\(557\) 1380.70 + 5152.83i 0.105031 + 0.391979i 0.998349 0.0574456i \(-0.0182956\pi\)
−0.893318 + 0.449425i \(0.851629\pi\)
\(558\) 1702.81 0.129186
\(559\) −8236.66 8847.48i −0.623209 0.669425i
\(560\) 18592.0i 1.40296i
\(561\) −31918.3 + 6212.71i −2.40212 + 0.467559i
\(562\) −924.634 + 1601.51i −0.0694009 + 0.120206i
\(563\) −1476.57 2557.49i −0.110533 0.191448i 0.805452 0.592660i \(-0.201922\pi\)
−0.915985 + 0.401212i \(0.868589\pi\)
\(564\) 5441.61 5441.61i 0.406265 0.406265i
\(565\) 3586.75 + 961.068i 0.267072 + 0.0715618i
\(566\) −935.022 + 3489.55i −0.0694380 + 0.259146i
\(567\) 11971.8 11971.8i 0.886717 0.886717i
\(568\) −5145.28 + 2970.63i −0.380090 + 0.219445i
\(569\) −7913.05 + 13705.8i −0.583009 + 1.00980i 0.412111 + 0.911134i \(0.364792\pi\)
−0.995120 + 0.0986683i \(0.968542\pi\)
\(570\) −4881.69 + 1308.05i −0.358722 + 0.0961193i
\(571\) −22151.5 −1.62349 −0.811744 0.584014i \(-0.801481\pi\)
−0.811744 + 0.584014i \(0.801481\pi\)
\(572\) 6616.81 9096.21i 0.483676 0.664915i
\(573\) −20476.2 −1.49285
\(574\) −8420.91 + 2256.38i −0.612338 + 0.164075i
\(575\) −4512.75 + 7816.31i −0.327295 + 0.566892i
\(576\) 1280.04 739.031i 0.0925955 0.0534600i
\(577\) −14453.6 + 14453.6i −1.04283 + 1.04283i −0.0437881 + 0.999041i \(0.513943\pi\)
−0.999041 + 0.0437881i \(0.986057\pi\)
\(578\) 2525.52 9425.37i 0.181744 0.678277i
\(579\) 19590.2 + 5249.17i 1.40611 + 0.376767i
\(580\) −12747.4 + 12747.4i −0.912596 + 0.912596i
\(581\) 7739.54 + 13405.3i 0.552651 + 0.957219i
\(582\) 159.588 276.414i 0.0113662 0.0196868i
\(583\) −25941.4 + 5049.34i −1.84285 + 0.358700i
\(584\) 7627.84i 0.540483i
\(585\) 27402.6 + 979.743i 1.93668 + 0.0692434i
\(586\) −6337.82 −0.446780
\(587\) −563.998 2104.87i −0.0396570 0.148002i 0.943258 0.332059i \(-0.107743\pi\)
−0.982916 + 0.184057i \(0.941077\pi\)
\(588\) 20047.3 34722.9i 1.40601 2.43529i
\(589\) −664.021 1150.12i −0.0464525 0.0804580i
\(590\) 2839.83 + 2839.83i 0.198159 + 0.198159i
\(591\) 2240.93 8363.26i 0.155972 0.582095i
\(592\) −647.209 + 2415.42i −0.0449326 + 0.167691i
\(593\) −2579.51 + 2579.51i −0.178630 + 0.178630i −0.790759 0.612128i \(-0.790314\pi\)
0.612128 + 0.790759i \(0.290314\pi\)
\(594\) −2029.60 + 990.544i −0.140195 + 0.0684217i
\(595\) 57777.8 + 33358.0i 3.98094 + 2.29840i
\(596\) −3280.81 12244.1i −0.225482 0.841510i
\(597\) 2775.94i 0.190304i
\(598\) −2848.99 101.862i −0.194822 0.00696561i
\(599\) 21207.6 1.44661 0.723305 0.690529i \(-0.242622\pi\)
0.723305 + 0.690529i \(0.242622\pi\)
\(600\) 23146.3 6202.03i 1.57491 0.421995i
\(601\) 9221.87 + 5324.25i 0.625904 + 0.361366i 0.779164 0.626820i \(-0.215644\pi\)
−0.153260 + 0.988186i \(0.548977\pi\)
\(602\) −5159.19 8935.98i −0.349291 0.604989i
\(603\) 13237.9 13237.9i 0.894013 0.894013i
\(604\) −3672.07 + 13704.4i −0.247375 + 0.923216i
\(605\) 9026.44 21295.1i 0.606574 1.43102i
\(606\) 4805.35 + 4805.35i 0.322119 + 0.322119i
\(607\) 10740.3 6200.91i 0.718180 0.414641i −0.0959025 0.995391i \(-0.530574\pi\)
0.814082 + 0.580749i \(0.197240\pi\)
\(608\) 4802.54 + 2772.75i 0.320343 + 0.184950i
\(609\) −39808.4 + 10666.6i −2.64880 + 0.709744i
\(610\) 2546.95i 0.169054i
\(611\) −5967.66 3735.91i −0.395132 0.247363i
\(612\) 25340.3i 1.67372i
\(613\) 3185.06 853.434i 0.209858 0.0562314i −0.152358 0.988325i \(-0.548687\pi\)
0.362217 + 0.932094i \(0.382020\pi\)
\(614\) −4553.87 + 7887.54i −0.299315 + 0.518429i
\(615\) 14745.6 + 25540.2i 0.966831 + 1.67460i
\(616\) 16055.9 13964.4i 1.05018 0.913379i
\(617\) −20360.0 5455.43i −1.32846 0.355960i −0.476320 0.879272i \(-0.658030\pi\)
−0.852141 + 0.523311i \(0.824696\pi\)
\(618\) −8553.21 2291.82i −0.556732 0.149176i
\(619\) −18909.2 18909.2i −1.22783 1.22783i −0.964784 0.263042i \(-0.915274\pi\)
−0.263042 0.964784i \(-0.584726\pi\)
\(620\) 2424.08 + 4198.62i 0.157021 + 0.271969i
\(621\) −2292.66 1323.67i −0.148150 0.0855346i
\(622\) 111.478 + 416.042i 0.00718628 + 0.0268196i
\(623\) 9917.72 0.637793
\(624\) −7932.89 8521.18i −0.508926 0.546667i
\(625\) 6427.98 0.411391
\(626\) −4478.41 + 1199.99i −0.285932 + 0.0766153i
\(627\) 7377.39 + 4973.38i 0.469896 + 0.316775i
\(628\) −279.742 + 161.509i −0.0177754 + 0.0102626i
\(629\) −6345.08 6345.08i −0.402218 0.402218i
\(630\) 22608.3 + 6057.89i 1.42974 + 0.383098i
\(631\) 1138.23 4247.95i 0.0718104 0.268000i −0.920681 0.390316i \(-0.872366\pi\)
0.992491 + 0.122316i \(0.0390323\pi\)
\(632\) −9644.91 9644.91i −0.607047 0.607047i
\(633\) 29160.9 16836.0i 1.83103 1.05714i
\(634\) 707.404 1225.26i 0.0443132 0.0767528i
\(635\) 363.433 + 1356.35i 0.0227124 + 0.0847639i
\(636\) 37113.1i 2.31388i
\(637\) −35070.2 10753.9i −2.18137 0.668895i
\(638\) −6845.27 476.918i −0.424775 0.0295946i
\(639\) 2977.66 + 11112.8i 0.184342 + 0.687974i
\(640\) −22110.8 12765.7i −1.36563 0.788449i
\(641\) −18464.0 + 10660.2i −1.13773 + 0.656869i −0.945868 0.324553i \(-0.894786\pi\)
−0.191863 + 0.981422i \(0.561453\pi\)
\(642\) −153.947 + 153.947i −0.00946389 + 0.00946389i
\(643\) 10531.1 + 2821.80i 0.645888 + 0.173065i 0.566869 0.823808i \(-0.308154\pi\)
0.0790193 + 0.996873i \(0.474821\pi\)
\(644\) 10871.5 + 2913.00i 0.665212 + 0.178243i
\(645\) −24681.7 + 24681.7i −1.50673 + 1.50673i
\(646\) −3700.55 + 2136.51i −0.225381 + 0.130124i
\(647\) −10586.0 6111.81i −0.643241 0.371375i 0.142621 0.989777i \(-0.454447\pi\)
−0.785862 + 0.618402i \(0.787780\pi\)
\(648\) −2270.66 8474.21i −0.137654 0.513732i
\(649\) 491.402 7053.16i 0.0297214 0.426596i
\(650\) −4636.84 8738.16i −0.279803 0.527291i
\(651\) 11083.4i 0.667269i
\(652\) 5929.49 + 22129.2i 0.356161 + 1.32921i
\(653\) −4053.54 + 7020.93i −0.242921 + 0.420751i −0.961545 0.274648i \(-0.911439\pi\)
0.718624 + 0.695399i \(0.244772\pi\)
\(654\) 148.213 85.5707i 0.00886174 0.00511633i
\(655\) −32072.9 32072.9i −1.91327 1.91327i
\(656\) 1798.43 6711.84i 0.107038 0.399472i
\(657\) 14267.4 + 3822.95i 0.847223 + 0.227013i
\(658\) −4249.62 4249.62i −0.251774 0.251774i
\(659\) −16003.9 + 9239.86i −0.946015 + 0.546182i −0.891841 0.452350i \(-0.850586\pi\)
−0.0541741 + 0.998532i \(0.517253\pi\)
\(660\) −26931.9 18155.9i −1.58837 1.07078i
\(661\) 10415.1 2790.71i 0.612858 0.164215i 0.0609792 0.998139i \(-0.480578\pi\)
0.551879 + 0.833924i \(0.313911\pi\)
\(662\) 7991.54 0.469184
\(663\) 40714.3 9363.98i 2.38494 0.548517i
\(664\) 8020.95 0.468785
\(665\) −4724.62 17632.5i −0.275508 1.02821i
\(666\) −2726.32 1574.04i −0.158623 0.0915811i
\(667\) −4021.76 6965.89i −0.233468 0.404378i
\(668\) −12769.7 12769.7i −0.739630 0.739630i
\(669\) 14734.7 + 3948.14i 0.851532 + 0.228167i
\(670\) −11131.9 2982.77i −0.641882 0.171992i
\(671\) −3383.24 + 2942.51i −0.194647 + 0.169291i
\(672\) −23140.4 40080.3i −1.32836 2.30079i
\(673\) −12205.9 + 21141.2i −0.699110 + 1.21089i 0.269665 + 0.962954i \(0.413087\pi\)
−0.968775 + 0.247940i \(0.920246\pi\)
\(674\) −2434.15 + 652.227i −0.139110 + 0.0372743i
\(675\) 9186.18i 0.523816i
\(676\) −8101.06 + 11967.3i −0.460916 + 0.680890i
\(677\) 27057.0i 1.53602i −0.640439 0.768009i \(-0.721247\pi\)
0.640439 0.768009i \(-0.278753\pi\)
\(678\) 1917.20 513.712i 0.108598 0.0290988i
\(679\) 998.398 + 576.425i 0.0564286 + 0.0325791i
\(680\) 29939.3 17285.5i 1.68841 0.974805i
\(681\) −689.420 689.420i −0.0387939 0.0387939i
\(682\) −600.349 + 1744.98i −0.0337075 + 0.0979748i
\(683\) −6217.96 + 23205.7i −0.348351 + 1.30006i 0.540298 + 0.841474i \(0.318311\pi\)
−0.888649 + 0.458589i \(0.848355\pi\)
\(684\) 4902.71 4902.71i 0.274064 0.274064i
\(685\) −10607.7 18373.1i −0.591677 1.02481i
\(686\) −15231.9 8794.14i −0.847750 0.489449i
\(687\) 8901.22 2385.07i 0.494327 0.132455i
\(688\) 8224.21 0.455734
\(689\) 33090.3 7610.52i 1.82967 0.420809i
\(690\) 8231.93i 0.454180i
\(691\) −1275.89 4761.70i −0.0702421 0.262147i 0.921870 0.387499i \(-0.126661\pi\)
−0.992112 + 0.125352i \(0.959994\pi\)
\(692\) 10248.3 + 5916.86i 0.562980 + 0.325036i
\(693\) −18072.6 37030.4i −0.990652 2.02983i
\(694\) −164.981 + 164.981i −0.00902391 + 0.00902391i
\(695\) −1072.60 + 4003.01i −0.0585413 + 0.218479i
\(696\) −5527.24 + 20627.9i −0.301019 + 1.12342i
\(697\) 17631.4 + 17631.4i 0.958159 + 0.958159i
\(698\) 6391.55 + 11070.5i 0.346596 + 0.600321i
\(699\) 8737.06 15133.0i 0.472770 0.818861i
\(700\) 10108.0 + 37723.7i 0.545782 + 2.03689i
\(701\) −27102.5 −1.46027 −0.730133 0.683305i \(-0.760542\pi\)
−0.730133 + 0.683305i \(0.760542\pi\)
\(702\) 2563.06 1360.07i 0.137801 0.0731231i
\(703\) 2455.23i 0.131722i
\(704\) 306.039 + 1572.30i 0.0163839 + 0.0841735i
\(705\) −10165.1 + 17606.5i −0.543037 + 0.940568i
\(706\) −4664.33 8078.85i −0.248646 0.430668i
\(707\) −17356.8 + 17356.8i −0.923293 + 0.923293i
\(708\) −9590.43 2569.75i −0.509083 0.136408i
\(709\) 3112.16 11614.7i 0.164851 0.615234i −0.833208 0.552960i \(-0.813498\pi\)
0.998059 0.0622738i \(-0.0198352\pi\)
\(710\) 5007.87 5007.87i 0.264707 0.264707i
\(711\) −22874.1 + 13206.4i −1.20654 + 0.696593i
\(712\) 2569.58 4450.65i 0.135252 0.234263i
\(713\) −2089.44 + 559.865i −0.109748 + 0.0294069i
\(714\) 35661.2 1.86917
\(715\) −10665.2 + 27735.8i −0.557838 + 1.45071i
\(716\) 25540.1 1.33307
\(717\) 10279.7 2754.45i 0.535431 0.143468i
\(718\) 2453.79 4250.08i 0.127541 0.220908i
\(719\) 23787.8 13733.9i 1.23384 0.712360i 0.266014 0.963969i \(-0.414293\pi\)
0.967829 + 0.251609i \(0.0809598\pi\)
\(720\) −13191.4 + 13191.4i −0.682800 + 0.682800i
\(721\) 8278.00 30893.9i 0.427585 1.59577i
\(722\) −6771.72 1814.48i −0.349054 0.0935288i
\(723\) 36516.7 36516.7i 1.87838 1.87838i
\(724\) −7311.24 12663.4i −0.375304 0.650045i
\(725\) 13955.4 24171.4i 0.714882 1.23821i
\(726\) −1512.92 12270.1i −0.0773412 0.627255i
\(727\) 19509.5i 0.995278i −0.867384 0.497639i \(-0.834200\pi\)
0.867384 0.497639i \(-0.165800\pi\)
\(728\) −20009.8 + 18628.3i −1.01870 + 0.948367i
\(729\) −27904.6 −1.41770
\(730\) −2353.35 8782.84i −0.119317 0.445298i
\(731\) −14756.0 + 25558.1i −0.746607 + 1.29316i
\(732\) 3148.31 + 5453.04i 0.158969 + 0.275342i
\(733\) 5125.21 + 5125.21i 0.258259 + 0.258259i 0.824346 0.566087i \(-0.191543\pi\)
−0.566087 + 0.824346i \(0.691543\pi\)
\(734\) −3613.21 + 13484.7i −0.181697 + 0.678104i
\(735\) −27414.6 + 102313.i −1.37579 + 5.13451i
\(736\) 6387.05 6387.05i 0.319877 0.319877i
\(737\) 8898.56 + 18233.0i 0.444753 + 0.911290i
\(738\) 7575.78 + 4373.88i 0.377870 + 0.218163i
\(739\) −7764.62 28978.0i −0.386504 1.44245i −0.835783 0.549060i \(-0.814986\pi\)
0.449279 0.893392i \(-0.351681\pi\)
\(740\) 8963.08i 0.445256i
\(741\) −9688.91 6065.51i −0.480339 0.300705i
\(742\) 28983.4 1.43398
\(743\) −4201.36 + 1125.75i −0.207447 + 0.0555852i −0.361046 0.932548i \(-0.617580\pi\)
0.153599 + 0.988133i \(0.450914\pi\)
\(744\) 4973.75 + 2871.59i 0.245089 + 0.141502i
\(745\) 16743.9 + 29001.2i 0.823419 + 1.42620i
\(746\) 8087.23 8087.23i 0.396909 0.396909i
\(747\) 4019.97 15002.7i 0.196898 0.734834i
\(748\) −25967.8 8934.05i −1.26936 0.436713i
\(749\) −556.053 556.053i −0.0271265 0.0271265i
\(750\) −7264.54 + 4194.18i −0.353685 + 0.204200i
\(751\) 944.877 + 545.525i 0.0459109 + 0.0265066i 0.522780 0.852468i \(-0.324895\pi\)
−0.476869 + 0.878974i \(0.658228\pi\)
\(752\) 4626.92 1239.78i 0.224370 0.0601198i
\(753\) 27029.4i 1.30811i
\(754\) 8810.29 + 315.000i 0.425533 + 0.0152144i
\(755\) 37481.4i 1.80674i
\(756\) −11065.0 + 2964.86i −0.532316 + 0.142634i
\(757\) −8144.20 + 14106.2i −0.391025 + 0.677275i −0.992585 0.121552i \(-0.961213\pi\)
0.601560 + 0.798828i \(0.294546\pi\)
\(758\) 2810.35 + 4867.66i 0.134665 + 0.233247i
\(759\) 10934.9 9510.41i 0.522938 0.454817i
\(760\) −9136.82 2448.20i −0.436089 0.116850i
\(761\) 10766.3 + 2884.82i 0.512848 + 0.137417i 0.505956 0.862559i \(-0.331140\pi\)
0.00689156 + 0.999976i \(0.497806\pi\)
\(762\) 530.736 + 530.736i 0.0252317 + 0.0252317i
\(763\) 309.079 + 535.340i 0.0146650 + 0.0254005i
\(764\) −14975.9 8646.35i −0.709175 0.409443i
\(765\) −17326.4 64662.9i −0.818871 3.05607i
\(766\) 8930.64 0.421249
\(767\) −324.567 + 9077.87i −0.0152796 + 0.427357i
\(768\) −10911.3 −0.512667
\(769\) 22166.8 5939.59i 1.03948 0.278527i 0.301579 0.953441i \(-0.402486\pi\)
0.737896 + 0.674914i \(0.235819\pi\)
\(770\) −14178.8 + 21032.5i −0.663595 + 0.984360i
\(771\) 32843.8 18962.4i 1.53417 0.885751i
\(772\) 12111.4 + 12111.4i 0.564634 + 0.564634i
\(773\) 25182.7 + 6747.68i 1.17174 + 0.313968i 0.791647 0.610979i \(-0.209224\pi\)
0.380097 + 0.924947i \(0.375891\pi\)
\(774\) −2679.72 + 10000.8i −0.124445 + 0.464435i
\(775\) −5307.59 5307.59i −0.246005 0.246005i
\(776\) 517.350 298.692i 0.0239327 0.0138176i
\(777\) 10245.3 17745.3i 0.473033 0.819318i
\(778\) 2016.75 + 7526.61i 0.0929357 + 0.346841i
\(779\) 6822.48i 0.313788i
\(780\) 35370.4 + 22142.8i 1.62367 + 1.01646i
\(781\) −12437.8 866.558i −0.569860 0.0397028i
\(782\) 1801.39 + 6722.86i 0.0823752 + 0.307428i
\(783\) 7089.90 + 4093.35i 0.323592 + 0.186826i
\(784\) 21613.3 12478.4i 0.984571 0.568442i
\(785\) 603.410 603.410i 0.0274352 0.0274352i
\(786\) −23418.7 6275.02i −1.06274 0.284762i
\(787\) 39254.0 + 10518.1i 1.77796 + 0.476402i 0.990209 0.139594i \(-0.0445796\pi\)
0.787749 + 0.615996i \(0.211246\pi\)
\(788\) 5170.47 5170.47i 0.233744 0.233744i
\(789\) −25048.6 + 14461.8i −1.13023 + 0.652541i
\(790\) 14081.0 + 8129.67i 0.634151 + 0.366127i
\(791\) 1855.51 + 6924.86i 0.0834063 + 0.311277i
\(792\) −21300.1 1484.00i −0.955640 0.0665805i
\(793\) 4216.37 3925.28i 0.188812 0.175776i
\(794\) 4764.46i 0.212953i
\(795\) −25376.1 94704.7i −1.13207 4.22494i
\(796\) 1172.18 2030.27i 0.0521944 0.0904033i
\(797\) −17065.6 + 9852.83i −0.758463 + 0.437899i −0.828744 0.559629i \(-0.810944\pi\)
0.0702807 + 0.997527i \(0.477610\pi\)
\(798\) −6899.55 6899.55i −0.306067 0.306067i
\(799\) −4448.86 + 16603.4i −0.196983 + 0.735150i
\(800\) 30275.0 + 8112.17i 1.33798 + 0.358511i
\(801\) −7036.85 7036.85i −0.310406 0.310406i
\(802\) −5881.66 + 3395.78i −0.258963 + 0.149512i
\(803\) −8947.81 + 13272.9i −0.393227 + 0.583303i
\(804\) 27520.4 7374.07i 1.20718 0.323462i
\(805\) −29733.5 −1.30182
\(806\) 695.063 2266.70i 0.0303754 0.0990585i
\(807\) 36933.0 1.61103
\(808\) 3292.01 + 12285.9i 0.143332 + 0.534923i
\(809\) −23765.1 13720.8i −1.03280 0.596287i −0.115015 0.993364i \(-0.536691\pi\)
−0.917786 + 0.397076i \(0.870025\pi\)
\(810\) 5228.95 + 9056.81i 0.226823 + 0.392869i
\(811\) −7822.39 7822.39i −0.338695 0.338695i 0.517181 0.855876i \(-0.326981\pi\)
−0.855876 + 0.517181i \(0.826981\pi\)
\(812\) −33619.3 9008.26i −1.45296 0.389320i
\(813\) −24460.9 6554.29i −1.05521 0.282742i
\(814\) 2574.23 2238.89i 0.110844 0.0964044i
\(815\) −30261.6 52414.6i −1.30064 2.25277i
\(816\) −14211.8 + 24615.5i −0.609696 + 1.05602i
\(817\) 7799.78 2089.94i 0.334002 0.0894956i
\(818\) 14721.7i 0.629258i
\(819\) 24814.6 + 46763.3i 1.05872 + 1.99517i
\(820\) 24906.2i 1.06068i
\(821\) −7316.24 + 1960.38i −0.311009 + 0.0833347i −0.410948 0.911659i \(-0.634802\pi\)
0.0999384 + 0.994994i \(0.468135\pi\)
\(822\) −9820.80 5670.04i −0.416715 0.240591i
\(823\) −2511.34 + 1449.92i −0.106367 + 0.0614108i −0.552240 0.833685i \(-0.686227\pi\)
0.445873 + 0.895096i \(0.352893\pi\)
\(824\) −11719.1 11719.1i −0.495455 0.495455i
\(825\) 47551.4 + 16359.7i 2.00670 + 0.690391i
\(826\) −2006.84 + 7489.64i −0.0845363 + 0.315494i
\(827\) −14963.2 + 14963.2i −0.629167 + 0.629167i −0.947858 0.318692i \(-0.896757\pi\)
0.318692 + 0.947858i \(0.396757\pi\)
\(828\) −5646.72 9780.41i −0.237001 0.410498i
\(829\) −22331.0 12892.8i −0.935571 0.540152i −0.0470019 0.998895i \(-0.514967\pi\)
−0.888569 + 0.458743i \(0.848300\pi\)
\(830\) −9235.47 + 2474.64i −0.386226 + 0.103489i
\(831\) −41094.2 −1.71545
\(832\) −461.271 2005.59i −0.0192208 0.0835714i
\(833\) 89556.0i 3.72501i
\(834\) 573.331 + 2139.70i 0.0238043 + 0.0888390i
\(835\) 41316.7 + 23854.2i 1.71236 + 0.988633i
\(836\) 3295.61 + 6752.65i 0.136341 + 0.279360i
\(837\) 1556.81 1556.81i 0.0642905 0.0642905i
\(838\) −2909.90 + 10859.9i −0.119953 + 0.447672i
\(839\) −7377.92 + 27534.8i −0.303593 + 1.13302i 0.630557 + 0.776143i \(0.282826\pi\)
−0.934150 + 0.356881i \(0.883840\pi\)
\(840\) 55820.9 + 55820.9i 2.29286 + 2.29286i
\(841\) 242.508 + 420.037i 0.00994334 + 0.0172224i
\(842\) −4635.28 + 8028.54i −0.189718 + 0.328601i
\(843\) 3125.96 + 11666.2i 0.127715 + 0.476639i
\(844\) 28437.0 1.15976
\(845\) 12489.5 36077.1i 0.508465 1.46875i
\(846\) 6030.41i 0.245071i
\(847\) 44319.3 5464.61i 1.79791 0.221684i
\(848\) −11550.5 + 20006.1i −0.467744 + 0.810157i
\(849\) 11797.3 + 20433.6i 0.476894 + 0.826004i
\(850\) −17077.4 + 17077.4i −0.689116 + 0.689116i
\(851\) 3862.88 + 1035.06i 0.155603 + 0.0416936i
\(852\) −4531.60 + 16912.2i −0.182218 + 0.680048i
\(853\) 4472.37 4472.37i 0.179520 0.179520i −0.611626 0.791147i \(-0.709484\pi\)
0.791147 + 0.611626i \(0.209484\pi\)
\(854\) 4258.54 2458.67i 0.170637 0.0985176i
\(855\) −9158.45 + 15862.9i −0.366330 + 0.634502i
\(856\) −393.601 + 105.465i −0.0157161 + 0.00421112i
\(857\) −13917.4 −0.554735 −0.277368 0.960764i \(-0.589462\pi\)
−0.277368 + 0.960764i \(0.589462\pi\)
\(858\) 2475.70 + 15689.6i 0.0985069 + 0.624281i
\(859\) −45799.0 −1.81914 −0.909570 0.415551i \(-0.863589\pi\)
−0.909570 + 0.415551i \(0.863589\pi\)
\(860\) −28473.9 + 7629.56i −1.12901 + 0.302518i
\(861\) −28469.0 + 49309.8i −1.12686 + 1.95177i
\(862\) −6754.65 + 3899.80i −0.266896 + 0.154092i
\(863\) 21600.1 21600.1i 0.852001 0.852001i −0.138379 0.990379i \(-0.544189\pi\)
0.990379 + 0.138379i \(0.0441891\pi\)
\(864\) −2379.44 + 8880.20i −0.0936924 + 0.349665i
\(865\) −30197.1 8091.30i −1.18697 0.318049i
\(866\) 3208.44 3208.44i 0.125898 0.125898i
\(867\) −31864.9 55191.6i −1.24820 2.16194i
\(868\) −4680.11 + 8106.18i −0.183011 + 0.316984i
\(869\) −5468.86 28096.7i −0.213485 1.09680i
\(870\) 25456.7i 0.992025i
\(871\) −12218.2 23025.3i −0.475313 0.895730i
\(872\) 320.317 0.0124396
\(873\) −299.399 1117.37i −0.0116073 0.0433188i
\(874\) 952.183 1649.23i 0.0368513 0.0638284i
\(875\) −15149.3 26239.3i −0.585301 1.01377i
\(876\) 15895.1 + 15895.1i 0.613065 + 0.613065i
\(877\) −8620.48 + 32172.1i −0.331919 + 1.23874i 0.575252 + 0.817976i \(0.304904\pi\)
−0.907171 + 0.420762i \(0.861763\pi\)
\(878\) 2575.25 9610.95i 0.0989868 0.369424i
\(879\) −29269.3 + 29269.3i −1.12313 + 1.12313i
\(880\) −8867.32 18169.0i −0.339679 0.695995i
\(881\) 29194.1 + 16855.2i 1.11643 + 0.644571i 0.940487 0.339830i \(-0.110369\pi\)
0.175942 + 0.984400i \(0.443703\pi\)
\(882\) 8131.78 + 30348.2i 0.310444 + 1.15859i
\(883\) 20495.2i 0.781107i 0.920580 + 0.390554i \(0.127716\pi\)
−0.920580 + 0.390554i \(0.872284\pi\)
\(884\) 33731.8 + 10343.5i 1.28340 + 0.393541i
\(885\) 26229.8 0.996277
\(886\) 3242.42 868.804i 0.122947 0.0329436i
\(887\) 9942.13 + 5740.09i 0.376352 + 0.217287i 0.676230 0.736691i \(-0.263613\pi\)
−0.299878 + 0.953978i \(0.596946\pi\)
\(888\) −5308.89 9195.27i −0.200625 0.347492i
\(889\) −1917.00 + 1917.00i −0.0723219 + 0.0723219i
\(890\) −1585.54 + 5917.33i −0.0597164 + 0.222865i
\(891\) 5989.54 17409.3i 0.225204 0.654582i
\(892\) 9109.50 + 9109.50i 0.341938 + 0.341938i
\(893\) 4073.08 2351.59i 0.152632 0.0881222i
\(894\) 15501.8 + 8949.96i 0.579930 + 0.334823i
\(895\) −65173.0 + 17463.0i −2.43407 + 0.652207i
\(896\) 49292.8i 1.83790i
\(897\) −13627.6 + 12686.8i −0.507260 + 0.472239i
\(898\) 10796.6i 0.401210i
\(899\) 6461.46 1731.34i 0.239713 0.0642308i
\(900\) 19593.9 33937.7i 0.725702 1.25695i
\(901\) −41448.3 71790.5i −1.53257 2.65448i
\(902\) −7153.14 + 6221.33i −0.264051 + 0.229654i
\(903\) −65094.3 17442.0i −2.39890 0.642782i
\(904\) 3588.33 + 961.489i 0.132020 + 0.0353746i
\(905\) 27315.3 + 27315.3i 1.00331 + 1.00331i
\(906\) −10017.3 17350.5i −0.367332 0.636238i
\(907\) 10629.2 + 6136.76i 0.389125 + 0.224661i 0.681781 0.731557i \(-0.261206\pi\)
−0.292656 + 0.956218i \(0.594539\pi\)
\(908\) −213.112 795.346i −0.00778897 0.0290688i
\(909\) 24630.0 0.898710
\(910\) 17292.4 27622.4i 0.629931 1.00624i
\(911\) 46216.2 1.68080 0.840402 0.541964i \(-0.182319\pi\)
0.840402 + 0.541964i \(0.182319\pi\)
\(912\) 7512.12 2012.87i 0.272753 0.0730841i
\(913\) 13957.0 + 9408.94i 0.505924 + 0.341063i
\(914\) 13578.2 7839.40i 0.491387 0.283703i
\(915\) −11762.3 11762.3i −0.424973 0.424973i
\(916\) 7517.32 + 2014.26i 0.271156 + 0.0726561i
\(917\) 22665.2 84587.6i 0.816216 3.04616i
\(918\) −5009.09 5009.09i −0.180092 0.180092i
\(919\) 19805.7 11434.8i 0.710913 0.410446i −0.100486 0.994938i \(-0.532040\pi\)
0.811399 + 0.584493i \(0.198706\pi\)
\(920\) −7703.65 + 13343.1i −0.276067 + 0.478162i
\(921\) 15395.5 + 57456.9i 0.550814 + 2.05567i
\(922\) 1404.37i 0.0501633i
\(923\) 16008.3 + 572.354i 0.570876 + 0.0204109i
\(924\) 4358.43 62557.1i 0.155175 2.22725i
\(925\) 3591.61 + 13404.1i 0.127666 + 0.476458i
\(926\) 13901.1 + 8025.78i 0.493323 + 0.284820i
\(927\) −27793.4 + 16046.5i −0.984740 + 0.568540i
\(928\) −19751.5 + 19751.5i −0.698680 + 0.698680i
\(929\) 6541.13 + 1752.69i 0.231009 + 0.0618987i 0.372467 0.928046i \(-0.378512\pi\)
−0.141457 + 0.989944i \(0.545179\pi\)
\(930\) −6612.82 1771.90i −0.233164 0.0624762i
\(931\) 17326.9 17326.9i 0.609952 0.609952i
\(932\) 12780.3 7378.69i 0.449175 0.259331i
\(933\) 2436.19 + 1406.54i 0.0854849 + 0.0493547i
\(934\) 4695.32 + 17523.2i 0.164492 + 0.613892i
\(935\) 72373.0 + 5042.31i 2.53139 + 0.176365i
\(936\) 27414.6 + 980.172i 0.957344 + 0.0342286i
\(937\) 26407.2i 0.920690i −0.887740 0.460345i \(-0.847726\pi\)
0.887740 0.460345i \(-0.152274\pi\)
\(938\) −5758.77 21492.0i −0.200459 0.748123i
\(939\) −15140.4 + 26224.0i −0.526187 + 0.911382i
\(940\) −14869.2 + 8584.74i −0.515936 + 0.297876i
\(941\) 38502.5 + 38502.5i 1.33384 + 1.33384i 0.901903 + 0.431938i \(0.142170\pi\)
0.431938 + 0.901903i \(0.357830\pi\)
\(942\) 118.056 440.592i 0.00408332 0.0152391i
\(943\) −10734.0 2876.16i −0.370675 0.0993221i
\(944\) −4370.03 4370.03i −0.150670 0.150670i
\(945\) 26208.3 15131.4i 0.902177 0.520872i
\(946\) −9303.75 6272.02i −0.319758 0.215561i
\(947\) −1802.86 + 483.075i −0.0618638 + 0.0165764i −0.289618 0.957142i \(-0.593528\pi\)
0.227754 + 0.973719i \(0.426862\pi\)
\(948\) −40196.6 −1.37714
\(949\) 10912.7 17431.7i 0.373278 0.596266i
\(950\) 6608.09 0.225679
\(951\) −2391.56 8925.42i −0.0815474 0.304339i
\(952\) 57803.1 + 33372.6i 1.96787 + 1.13615i
\(953\) 10911.4 + 18899.1i 0.370887 + 0.642396i 0.989702 0.143141i \(-0.0457202\pi\)
−0.618815 + 0.785537i \(0.712387\pi\)
\(954\) −20564.4 20564.4i −0.697901 0.697901i
\(955\) 44127.3 + 11823.9i 1.49521 + 0.400641i
\(956\) 8681.52 + 2326.21i 0.293703 + 0.0786976i
\(957\) −33815.3 + 29410.3i −1.14221 + 0.993417i
\(958\) −11644.5 20168.8i −0.392709 0.680192i
\(959\) 20480.0 35472.4i 0.689608 1.19444i
\(960\) −5740.02 + 1538.03i −0.192977 + 0.0517081i
\(961\) 27992.0i 0.939613i
\(962\) −3208.14 + 2986.66i −0.107520 + 0.100097i
\(963\) 789.065i 0.0264042i
\(964\) 42127.3 11288.0i 1.40750 0.377139i
\(965\) −39186.7 22624.5i −1.30722 0.754723i
\(966\) −13763.9 + 7946.60i −0.458433 + 0.264677i
\(967\) 24046.4 + 24046.4i 0.799668 + 0.799668i 0.983043 0.183375i \(-0.0587022\pi\)
−0.183375 + 0.983043i \(0.558702\pi\)
\(968\) 9030.40 21304.4i 0.299843 0.707386i
\(969\) −7223.02 + 26956.7i −0.239460 + 0.893678i
\(970\) −503.534 + 503.534i −0.0166675 + 0.0166675i
\(971\) 4616.86 + 7996.64i 0.152587 + 0.264289i 0.932178 0.362001i \(-0.117906\pi\)
−0.779591 + 0.626289i \(0.784573\pi\)
\(972\) −30374.3 17536.6i −1.00232 0.578690i
\(973\) −7728.52 + 2070.85i −0.254640 + 0.0682307i
\(974\) −17273.4 −0.568251
\(975\) −61768.4 18940.7i −2.02890 0.622142i
\(976\) 3919.34i 0.128540i
\(977\) 702.487 + 2621.72i 0.0230036 + 0.0858507i 0.976473 0.215638i \(-0.0691831\pi\)
−0.953470 + 0.301489i \(0.902516\pi\)
\(978\) −28016.8 16175.5i −0.916030 0.528870i
\(979\) 9692.06 4730.19i 0.316404 0.154420i
\(980\) −63253.5 + 63253.5i −2.06179 + 2.06179i
\(981\) 160.538 599.134i 0.00522484 0.0194994i
\(982\) 3568.32 13317.2i 0.115957 0.432757i
\(983\) 17226.3 + 17226.3i 0.558934 + 0.558934i 0.929004 0.370070i \(-0.120666\pi\)
−0.370070 + 0.929004i \(0.620666\pi\)
\(984\) 14752.1 + 25551.4i 0.477926 + 0.827793i
\(985\) −9658.64 + 16729.2i −0.312436 + 0.541156i
\(986\) −5570.66 20790.0i −0.179925 0.671489i
\(987\) −39251.2 −1.26584
\(988\) −4525.04 8527.48i −0.145709 0.274590i
\(989\) 13152.7i 0.422882i
\(990\) 24983.2 4862.84i 0.802038 0.156112i
\(991\) −1432.54 + 2481.24i −0.0459195 + 0.0795349i −0.888072 0.459705i \(-0.847955\pi\)
0.842152 + 0.539240i \(0.181288\pi\)
\(992\) 3756.01 + 6505.59i 0.120215 + 0.208219i
\(993\) 36906.5 36906.5i 1.17945 1.17945i
\(994\) 13207.5 + 3538.95i 0.421446 + 0.112926i
\(995\) −1602.95 + 5982.29i −0.0510723 + 0.190604i
\(996\) 16714.3 16714.3i 0.531739 0.531739i
\(997\) −17716.5 + 10228.6i −0.562776 + 0.324919i −0.754259 0.656577i \(-0.772004\pi\)
0.191483 + 0.981496i \(0.438670\pi\)
\(998\) −9569.96 + 16575.7i −0.303539 + 0.525745i
\(999\) −3931.65 + 1053.48i −0.124516 + 0.0333641i
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 143.4.o.a.32.17 160
11.10 odd 2 inner 143.4.o.a.32.24 yes 160
13.11 odd 12 inner 143.4.o.a.76.24 yes 160
143.76 even 12 inner 143.4.o.a.76.17 yes 160
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.o.a.32.17 160 1.1 even 1 trivial
143.4.o.a.32.24 yes 160 11.10 odd 2 inner
143.4.o.a.76.17 yes 160 143.76 even 12 inner
143.4.o.a.76.24 yes 160 13.11 odd 12 inner