Properties

Label 230.4.e.a.137.15
Level $230$
Weight $4$
Character 230.137
Analytic conductor $13.570$
Analytic rank $0$
Dimension $72$
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] = [230,4,Mod(137,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("230.137");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 230.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.5704393013\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 137.15
Character \(\chi\) \(=\) 230.137
Dual form 230.4.e.a.183.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41421 - 1.41421i) q^{2} +(5.03526 - 5.03526i) q^{3} +4.00000i q^{4} +(-6.80528 - 8.87064i) q^{5} -14.2419 q^{6} +(11.1481 - 11.1481i) q^{7} +(5.65685 - 5.65685i) q^{8} -23.7076i q^{9} +O(q^{10})\) \(q+(-1.41421 - 1.41421i) q^{2} +(5.03526 - 5.03526i) q^{3} +4.00000i q^{4} +(-6.80528 - 8.87064i) q^{5} -14.2419 q^{6} +(11.1481 - 11.1481i) q^{7} +(5.65685 - 5.65685i) q^{8} -23.7076i q^{9} +(-2.92086 + 22.1691i) q^{10} -8.94113i q^{11} +(20.1410 + 20.1410i) q^{12} +(43.6579 - 43.6579i) q^{13} -31.5316 q^{14} +(-78.9323 - 10.3996i) q^{15} -16.0000 q^{16} +(-33.1397 + 33.1397i) q^{17} +(-33.5277 + 33.5277i) q^{18} -107.253 q^{19} +(35.4826 - 27.2211i) q^{20} -112.267i q^{21} +(-12.6447 + 12.6447i) q^{22} +(33.3466 - 105.143i) q^{23} -56.9674i q^{24} +(-32.3764 + 120.734i) q^{25} -123.483 q^{26} +(16.5779 + 16.5779i) q^{27} +(44.5924 + 44.5924i) q^{28} -25.7005i q^{29} +(96.9198 + 126.334i) q^{30} +81.0455 q^{31} +(22.6274 + 22.6274i) q^{32} +(-45.0209 - 45.0209i) q^{33} +93.7331 q^{34} +(-174.757 - 23.0248i) q^{35} +94.8305 q^{36} +(-109.732 + 109.732i) q^{37} +(151.679 + 151.679i) q^{38} -439.658i q^{39} +(-88.6764 - 11.6834i) q^{40} -276.972 q^{41} +(-158.770 + 158.770i) q^{42} +(91.0717 + 91.0717i) q^{43} +35.7645 q^{44} +(-210.302 + 161.337i) q^{45} +(-195.854 + 101.535i) q^{46} +(147.078 + 147.078i) q^{47} +(-80.5641 + 80.5641i) q^{48} +94.4399i q^{49} +(216.531 - 124.957i) q^{50} +333.733i q^{51} +(174.632 + 174.632i) q^{52} +(-299.388 - 299.388i) q^{53} -46.8894i q^{54} +(-79.3135 + 60.8469i) q^{55} -126.126i q^{56} +(-540.047 + 540.047i) q^{57} +(-36.3460 + 36.3460i) q^{58} -613.321i q^{59} +(41.5985 - 315.729i) q^{60} +40.4771i q^{61} +(-114.616 - 114.616i) q^{62} +(-264.295 - 264.295i) q^{63} -64.0000i q^{64} +(-684.378 - 90.1694i) q^{65} +127.338i q^{66} +(317.182 - 317.182i) q^{67} +(-132.559 - 132.559i) q^{68} +(-361.512 - 697.330i) q^{69} +(214.581 + 279.705i) q^{70} -748.659 q^{71} +(-134.111 - 134.111i) q^{72} +(-142.851 + 142.851i) q^{73} +310.368 q^{74} +(444.905 + 770.952i) q^{75} -429.012i q^{76} +(-99.6766 - 99.6766i) q^{77} +(-621.770 + 621.770i) q^{78} +1335.64 q^{79} +(108.884 + 141.930i) q^{80} +807.054 q^{81} +(391.698 + 391.698i) q^{82} +(30.2308 + 30.2308i) q^{83} +449.068 q^{84} +(519.495 + 68.4454i) q^{85} -257.590i q^{86} +(-129.408 - 129.408i) q^{87} +(-50.5787 - 50.5787i) q^{88} +358.594 q^{89} +(525.577 + 69.2467i) q^{90} -973.406i q^{91} +(420.571 + 133.386i) q^{92} +(408.085 - 408.085i) q^{93} -415.999i q^{94} +(729.887 + 951.403i) q^{95} +227.870 q^{96} +(679.077 - 679.077i) q^{97} +(133.558 - 133.558i) q^{98} -211.973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 16 q^{3} - 16 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 16 q^{3} - 16 q^{6} - 64 q^{12} + 192 q^{13} - 1152 q^{16} + 32 q^{18} + 276 q^{23} + 880 q^{25} + 304 q^{26} + 728 q^{27} + 608 q^{31} + 688 q^{35} + 2816 q^{36} - 2208 q^{41} - 256 q^{46} + 144 q^{47} + 256 q^{48} + 272 q^{50} + 768 q^{52} - 2360 q^{55} - 1376 q^{62} - 1104 q^{70} + 4528 q^{71} + 128 q^{72} - 1296 q^{73} - 2568 q^{75} - 752 q^{77} + 6000 q^{78} - 11560 q^{81} + 80 q^{82} - 904 q^{85} + 6760 q^{87} + 1104 q^{92} - 5288 q^{93} + 9264 q^{95} + 256 q^{96} - 448 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 1.41421i −0.500000 0.500000i
\(3\) 5.03526 5.03526i 0.969036 0.969036i −0.0304990 0.999535i \(-0.509710\pi\)
0.999535 + 0.0304990i \(0.00970965\pi\)
\(4\) 4.00000i 0.500000i
\(5\) −6.80528 8.87064i −0.608682 0.793414i
\(6\) −14.2419 −0.969036
\(7\) 11.1481 11.1481i 0.601941 0.601941i −0.338887 0.940827i \(-0.610050\pi\)
0.940827 + 0.338887i \(0.110050\pi\)
\(8\) 5.65685 5.65685i 0.250000 0.250000i
\(9\) 23.7076i 0.878061i
\(10\) −2.92086 + 22.1691i −0.0923658 + 0.701048i
\(11\) 8.94113i 0.245078i −0.992464 0.122539i \(-0.960896\pi\)
0.992464 0.122539i \(-0.0391036\pi\)
\(12\) 20.1410 + 20.1410i 0.484518 + 0.484518i
\(13\) 43.6579 43.6579i 0.931426 0.931426i −0.0663693 0.997795i \(-0.521142\pi\)
0.997795 + 0.0663693i \(0.0211415\pi\)
\(14\) −31.5316 −0.601941
\(15\) −78.9323 10.3996i −1.35868 0.179011i
\(16\) −16.0000 −0.250000
\(17\) −33.1397 + 33.1397i −0.472797 + 0.472797i −0.902819 0.430022i \(-0.858506\pi\)
0.430022 + 0.902819i \(0.358506\pi\)
\(18\) −33.5277 + 33.5277i −0.439030 + 0.439030i
\(19\) −107.253 −1.29503 −0.647514 0.762053i \(-0.724191\pi\)
−0.647514 + 0.762053i \(0.724191\pi\)
\(20\) 35.4826 27.2211i 0.396707 0.304341i
\(21\) 112.267i 1.16660i
\(22\) −12.6447 + 12.6447i −0.122539 + 0.122539i
\(23\) 33.3466 105.143i 0.302315 0.953208i
\(24\) 56.9674i 0.484518i
\(25\) −32.3764 + 120.734i −0.259011 + 0.965874i
\(26\) −123.483 −0.931426
\(27\) 16.5779 + 16.5779i 0.118164 + 0.118164i
\(28\) 44.5924 + 44.5924i 0.300970 + 0.300970i
\(29\) 25.7005i 0.164568i −0.996609 0.0822838i \(-0.973779\pi\)
0.996609 0.0822838i \(-0.0262214\pi\)
\(30\) 96.9198 + 126.334i 0.589835 + 0.768846i
\(31\) 81.0455 0.469555 0.234777 0.972049i \(-0.424564\pi\)
0.234777 + 0.972049i \(0.424564\pi\)
\(32\) 22.6274 + 22.6274i 0.125000 + 0.125000i
\(33\) −45.0209 45.0209i −0.237489 0.237489i
\(34\) 93.7331 0.472797
\(35\) −174.757 23.0248i −0.843979 0.111197i
\(36\) 94.8305 0.439030
\(37\) −109.732 + 109.732i −0.487561 + 0.487561i −0.907536 0.419975i \(-0.862039\pi\)
0.419975 + 0.907536i \(0.362039\pi\)
\(38\) 151.679 + 151.679i 0.647514 + 0.647514i
\(39\) 439.658i 1.80517i
\(40\) −88.6764 11.6834i −0.350524 0.0461829i
\(41\) −276.972 −1.05502 −0.527510 0.849549i \(-0.676874\pi\)
−0.527510 + 0.849549i \(0.676874\pi\)
\(42\) −158.770 + 158.770i −0.583302 + 0.583302i
\(43\) 91.0717 + 91.0717i 0.322984 + 0.322984i 0.849911 0.526927i \(-0.176656\pi\)
−0.526927 + 0.849911i \(0.676656\pi\)
\(44\) 35.7645 0.122539
\(45\) −210.302 + 161.337i −0.696666 + 0.534460i
\(46\) −195.854 + 101.535i −0.627762 + 0.325446i
\(47\) 147.078 + 147.078i 0.456458 + 0.456458i 0.897491 0.441033i \(-0.145388\pi\)
−0.441033 + 0.897491i \(0.645388\pi\)
\(48\) −80.5641 + 80.5641i −0.242259 + 0.242259i
\(49\) 94.4399i 0.275335i
\(50\) 216.531 124.957i 0.612443 0.353431i
\(51\) 333.733i 0.916314i
\(52\) 174.632 + 174.632i 0.465713 + 0.465713i
\(53\) −299.388 299.388i −0.775928 0.775928i 0.203208 0.979136i \(-0.434863\pi\)
−0.979136 + 0.203208i \(0.934863\pi\)
\(54\) 46.8894i 0.118164i
\(55\) −79.3135 + 60.8469i −0.194448 + 0.149174i
\(56\) 126.126i 0.300970i
\(57\) −540.047 + 540.047i −1.25493 + 1.25493i
\(58\) −36.3460 + 36.3460i −0.0822838 + 0.0822838i
\(59\) 613.321i 1.35335i −0.736283 0.676674i \(-0.763421\pi\)
0.736283 0.676674i \(-0.236579\pi\)
\(60\) 41.5985 315.729i 0.0895057 0.679341i
\(61\) 40.4771i 0.0849600i 0.999097 + 0.0424800i \(0.0135259\pi\)
−0.999097 + 0.0424800i \(0.986474\pi\)
\(62\) −114.616 114.616i −0.234777 0.234777i
\(63\) −264.295 264.295i −0.528540 0.528540i
\(64\) 64.0000i 0.125000i
\(65\) −684.378 90.1694i −1.30595 0.172064i
\(66\) 127.338i 0.237489i
\(67\) 317.182 317.182i 0.578358 0.578358i −0.356093 0.934451i \(-0.615891\pi\)
0.934451 + 0.356093i \(0.115891\pi\)
\(68\) −132.559 132.559i −0.236399 0.236399i
\(69\) −361.512 697.330i −0.630739 1.21665i
\(70\) 214.581 + 279.705i 0.366391 + 0.477588i
\(71\) −748.659 −1.25140 −0.625701 0.780063i \(-0.715187\pi\)
−0.625701 + 0.780063i \(0.715187\pi\)
\(72\) −134.111 134.111i −0.219515 0.219515i
\(73\) −142.851 + 142.851i −0.229033 + 0.229033i −0.812289 0.583256i \(-0.801779\pi\)
0.583256 + 0.812289i \(0.301779\pi\)
\(74\) 310.368 0.487561
\(75\) 444.905 + 770.952i 0.684975 + 1.18696i
\(76\) 429.012i 0.647514i
\(77\) −99.6766 99.6766i −0.147522 0.147522i
\(78\) −621.770 + 621.770i −0.902585 + 0.902585i
\(79\) 1335.64 1.90217 0.951083 0.308935i \(-0.0999724\pi\)
0.951083 + 0.308935i \(0.0999724\pi\)
\(80\) 108.884 + 141.930i 0.152171 + 0.198353i
\(81\) 807.054 1.10707
\(82\) 391.698 + 391.698i 0.527510 + 0.527510i
\(83\) 30.2308 + 30.2308i 0.0399790 + 0.0399790i 0.726814 0.686835i \(-0.241000\pi\)
−0.686835 + 0.726814i \(0.741000\pi\)
\(84\) 449.068 0.583302
\(85\) 519.495 + 68.4454i 0.662907 + 0.0873405i
\(86\) 257.590i 0.322984i
\(87\) −129.408 129.408i −0.159472 0.159472i
\(88\) −50.5787 50.5787i −0.0612694 0.0612694i
\(89\) 358.594 0.427088 0.213544 0.976933i \(-0.431499\pi\)
0.213544 + 0.976933i \(0.431499\pi\)
\(90\) 525.577 + 69.2467i 0.615563 + 0.0811027i
\(91\) 973.406i 1.12133i
\(92\) 420.571 + 133.386i 0.476604 + 0.151158i
\(93\) 408.085 408.085i 0.455015 0.455015i
\(94\) 415.999i 0.456458i
\(95\) 729.887 + 951.403i 0.788261 + 1.02749i
\(96\) 227.870 0.242259
\(97\) 679.077 679.077i 0.710822 0.710822i −0.255885 0.966707i \(-0.582367\pi\)
0.966707 + 0.255885i \(0.0823668\pi\)
\(98\) 133.558 133.558i 0.137668 0.137668i
\(99\) −211.973 −0.215193
\(100\) −482.937 129.506i −0.482937 0.129506i
\(101\) 1031.02 1.01575 0.507873 0.861432i \(-0.330432\pi\)
0.507873 + 0.861432i \(0.330432\pi\)
\(102\) 471.970 471.970i 0.458157 0.458157i
\(103\) 1017.16 + 1017.16i 0.973045 + 0.973045i 0.999646 0.0266009i \(-0.00846832\pi\)
−0.0266009 + 0.999646i \(0.508468\pi\)
\(104\) 493.933i 0.465713i
\(105\) −995.880 + 764.008i −0.925600 + 0.710091i
\(106\) 846.798i 0.775928i
\(107\) 903.362 903.362i 0.816180 0.816180i −0.169372 0.985552i \(-0.554174\pi\)
0.985552 + 0.169372i \(0.0541739\pi\)
\(108\) −66.3116 + 66.3116i −0.0590818 + 0.0590818i
\(109\) 1211.42 1.06453 0.532263 0.846579i \(-0.321342\pi\)
0.532263 + 0.846579i \(0.321342\pi\)
\(110\) 198.217 + 26.1158i 0.171811 + 0.0226368i
\(111\) 1105.05i 0.944928i
\(112\) −178.370 + 178.370i −0.150485 + 0.150485i
\(113\) −1194.23 1194.23i −0.994193 0.994193i 0.00579025 0.999983i \(-0.498157\pi\)
−0.999983 + 0.00579025i \(0.998157\pi\)
\(114\) 1527.48 1.25493
\(115\) −1159.62 + 419.720i −0.940302 + 0.340340i
\(116\) 102.802 0.0822838
\(117\) −1035.03 1035.03i −0.817848 0.817848i
\(118\) −867.366 + 867.366i −0.676674 + 0.676674i
\(119\) 738.888i 0.569191i
\(120\) −505.337 + 387.679i −0.384423 + 0.294918i
\(121\) 1251.06 0.939937
\(122\) 57.2433 57.2433i 0.0424800 0.0424800i
\(123\) −1394.63 + 1394.63i −1.02235 + 1.02235i
\(124\) 324.182i 0.234777i
\(125\) 1291.32 534.431i 0.923994 0.382407i
\(126\) 747.539i 0.528540i
\(127\) −1085.96 1085.96i −0.758764 0.758764i 0.217333 0.976097i \(-0.430264\pi\)
−0.976097 + 0.217333i \(0.930264\pi\)
\(128\) −90.5097 + 90.5097i −0.0625000 + 0.0625000i
\(129\) 917.139 0.625966
\(130\) 840.338 + 1095.38i 0.566943 + 0.739006i
\(131\) 1337.41 0.891984 0.445992 0.895037i \(-0.352851\pi\)
0.445992 + 0.895037i \(0.352851\pi\)
\(132\) 180.084 180.084i 0.118744 0.118744i
\(133\) −1195.67 + 1195.67i −0.779530 + 0.779530i
\(134\) −897.127 −0.578358
\(135\) 34.2394 259.874i 0.0218286 0.165677i
\(136\) 374.932i 0.236399i
\(137\) 1475.55 1475.55i 0.920182 0.920182i −0.0768601 0.997042i \(-0.524489\pi\)
0.997042 + 0.0768601i \(0.0244895\pi\)
\(138\) −474.918 + 1497.43i −0.292954 + 0.923693i
\(139\) 1223.04i 0.746306i −0.927770 0.373153i \(-0.878277\pi\)
0.927770 0.373153i \(-0.121723\pi\)
\(140\) 92.0994 699.026i 0.0555987 0.421989i
\(141\) 1481.15 0.884648
\(142\) 1058.76 + 1058.76i 0.625701 + 0.625701i
\(143\) −390.351 390.351i −0.228272 0.228272i
\(144\) 379.322i 0.219515i
\(145\) −227.980 + 174.899i −0.130570 + 0.100169i
\(146\) 404.043 0.229033
\(147\) 475.529 + 475.529i 0.266809 + 0.266809i
\(148\) −438.926 438.926i −0.243781 0.243781i
\(149\) −3171.57 −1.74379 −0.871895 0.489692i \(-0.837109\pi\)
−0.871895 + 0.489692i \(0.837109\pi\)
\(150\) 461.101 1719.48i 0.250991 0.935967i
\(151\) −240.377 −0.129547 −0.0647735 0.997900i \(-0.520632\pi\)
−0.0647735 + 0.997900i \(0.520632\pi\)
\(152\) −606.715 + 606.715i −0.323757 + 0.323757i
\(153\) 785.663 + 785.663i 0.415144 + 0.415144i
\(154\) 281.928i 0.147522i
\(155\) −551.537 718.925i −0.285810 0.372551i
\(156\) 1758.63 0.902585
\(157\) −1477.32 + 1477.32i −0.750975 + 0.750975i −0.974661 0.223687i \(-0.928191\pi\)
0.223687 + 0.974661i \(0.428191\pi\)
\(158\) −1888.88 1888.88i −0.951083 0.951083i
\(159\) −3015.00 −1.50380
\(160\) 46.7338 354.705i 0.0230914 0.175262i
\(161\) −800.391 1543.89i −0.391799 0.755750i
\(162\) −1141.35 1141.35i −0.553535 0.553535i
\(163\) 502.637 502.637i 0.241531 0.241531i −0.575952 0.817483i \(-0.695369\pi\)
0.817483 + 0.575952i \(0.195369\pi\)
\(164\) 1107.89i 0.527510i
\(165\) −92.9844 + 705.744i −0.0438717 + 0.332982i
\(166\) 85.5055i 0.0399790i
\(167\) −605.669 605.669i −0.280647 0.280647i 0.552720 0.833367i \(-0.313590\pi\)
−0.833367 + 0.552720i \(0.813590\pi\)
\(168\) −635.078 635.078i −0.291651 0.291651i
\(169\) 1615.03i 0.735108i
\(170\) −637.880 831.473i −0.287783 0.375124i
\(171\) 2542.72i 1.13711i
\(172\) −364.287 + 364.287i −0.161492 + 0.161492i
\(173\) 1550.68 1550.68i 0.681479 0.681479i −0.278855 0.960333i \(-0.589955\pi\)
0.960333 + 0.278855i \(0.0899548\pi\)
\(174\) 366.022i 0.159472i
\(175\) 985.022 + 1706.89i 0.425489 + 0.737308i
\(176\) 143.058i 0.0612694i
\(177\) −3088.23 3088.23i −1.31144 1.31144i
\(178\) −507.128 507.128i −0.213544 0.213544i
\(179\) 394.455i 0.164709i −0.996603 0.0823546i \(-0.973756\pi\)
0.996603 0.0823546i \(-0.0262440\pi\)
\(180\) −645.348 841.207i −0.267230 0.348333i
\(181\) 583.628i 0.239673i 0.992794 + 0.119836i \(0.0382370\pi\)
−0.992794 + 0.119836i \(0.961763\pi\)
\(182\) −1376.60 + 1376.60i −0.560663 + 0.560663i
\(183\) 203.813 + 203.813i 0.0823293 + 0.0823293i
\(184\) −406.141 783.414i −0.162723 0.313881i
\(185\) 1720.14 + 226.635i 0.683608 + 0.0900679i
\(186\) −1154.24 −0.455015
\(187\) 296.306 + 296.306i 0.115872 + 0.115872i
\(188\) −588.312 + 588.312i −0.228229 + 0.228229i
\(189\) 369.624 0.142255
\(190\) 313.271 2377.70i 0.119616 0.907877i
\(191\) 3016.41i 1.14272i 0.820700 + 0.571360i \(0.193584\pi\)
−0.820700 + 0.571360i \(0.806416\pi\)
\(192\) −322.256 322.256i −0.121129 0.121129i
\(193\) −467.908 + 467.908i −0.174512 + 0.174512i −0.788958 0.614447i \(-0.789379\pi\)
0.614447 + 0.788958i \(0.289379\pi\)
\(194\) −1920.72 −0.710822
\(195\) −3900.05 + 2991.99i −1.43225 + 1.09878i
\(196\) −377.760 −0.137668
\(197\) 2139.35 + 2139.35i 0.773718 + 0.773718i 0.978754 0.205037i \(-0.0657313\pi\)
−0.205037 + 0.978754i \(0.565731\pi\)
\(198\) 299.775 + 299.775i 0.107596 + 0.107596i
\(199\) 3530.92 1.25779 0.628896 0.777490i \(-0.283507\pi\)
0.628896 + 0.777490i \(0.283507\pi\)
\(200\) 499.828 + 866.125i 0.176716 + 0.306221i
\(201\) 3194.19i 1.12090i
\(202\) −1458.08 1458.08i −0.507873 0.507873i
\(203\) −286.511 286.511i −0.0990599 0.0990599i
\(204\) −1334.93 −0.458157
\(205\) 1884.87 + 2456.92i 0.642172 + 0.837067i
\(206\) 2876.96i 0.973045i
\(207\) −2492.69 790.569i −0.836974 0.265451i
\(208\) −698.527 + 698.527i −0.232856 + 0.232856i
\(209\) 958.964i 0.317382i
\(210\) 2488.86 + 327.917i 0.817846 + 0.107754i
\(211\) −1037.26 −0.338428 −0.169214 0.985579i \(-0.554123\pi\)
−0.169214 + 0.985579i \(0.554123\pi\)
\(212\) 1197.55 1197.55i 0.387964 0.387964i
\(213\) −3769.69 + 3769.69i −1.21265 + 1.21265i
\(214\) −2555.09 −0.816180
\(215\) 188.096 1427.63i 0.0596653 0.452854i
\(216\) 187.558 0.0590818
\(217\) 903.503 903.503i 0.282644 0.282644i
\(218\) −1713.21 1713.21i −0.532263 0.532263i
\(219\) 1438.58i 0.443882i
\(220\) −243.387 317.254i −0.0745872 0.0972240i
\(221\) 2893.62i 0.880751i
\(222\) 1562.78 1562.78i 0.472464 0.472464i
\(223\) −3511.04 + 3511.04i −1.05433 + 1.05433i −0.0558979 + 0.998436i \(0.517802\pi\)
−0.998436 + 0.0558979i \(0.982198\pi\)
\(224\) 504.505 0.150485
\(225\) 2862.32 + 767.569i 0.848096 + 0.227428i
\(226\) 3377.80i 0.994193i
\(227\) −3286.82 + 3286.82i −0.961030 + 0.961030i −0.999269 0.0382385i \(-0.987825\pi\)
0.0382385 + 0.999269i \(0.487825\pi\)
\(228\) −2160.19 2160.19i −0.627464 0.627464i
\(229\) 6525.58 1.88307 0.941534 0.336917i \(-0.109384\pi\)
0.941534 + 0.336917i \(0.109384\pi\)
\(230\) 2233.52 + 1046.37i 0.640321 + 0.299981i
\(231\) −1003.79 −0.285908
\(232\) −145.384 145.384i −0.0411419 0.0411419i
\(233\) −2072.58 + 2072.58i −0.582744 + 0.582744i −0.935656 0.352913i \(-0.885191\pi\)
0.352913 + 0.935656i \(0.385191\pi\)
\(234\) 2927.50i 0.817848i
\(235\) 303.769 2305.58i 0.0843222 0.639998i
\(236\) 2453.28 0.676674
\(237\) 6725.29 6725.29i 1.84327 1.84327i
\(238\) 1044.95 1044.95i 0.284596 0.284596i
\(239\) 62.4305i 0.0168966i −0.999964 0.00844831i \(-0.997311\pi\)
0.999964 0.00844831i \(-0.00268921\pi\)
\(240\) 1262.92 + 166.394i 0.339670 + 0.0447529i
\(241\) 2948.93i 0.788204i 0.919067 + 0.394102i \(0.128944\pi\)
−0.919067 + 0.394102i \(0.871056\pi\)
\(242\) −1769.26 1769.26i −0.469969 0.469969i
\(243\) 3616.12 3616.12i 0.954627 0.954627i
\(244\) −161.908 −0.0424800
\(245\) 837.742 642.690i 0.218455 0.167592i
\(246\) 3944.60 1.02235
\(247\) −4682.45 + 4682.45i −1.20622 + 1.20622i
\(248\) 458.463 458.463i 0.117389 0.117389i
\(249\) 304.439 0.0774822
\(250\) −2582.00 1070.40i −0.653201 0.270793i
\(251\) 713.823i 0.179506i 0.995964 + 0.0897532i \(0.0286078\pi\)
−0.995964 + 0.0897532i \(0.971392\pi\)
\(252\) 1057.18 1057.18i 0.264270 0.264270i
\(253\) −940.095 298.156i −0.233610 0.0740906i
\(254\) 3071.55i 0.758764i
\(255\) 2960.43 2271.15i 0.727017 0.557744i
\(256\) 256.000 0.0625000
\(257\) 386.393 + 386.393i 0.0937841 + 0.0937841i 0.752442 0.658658i \(-0.228876\pi\)
−0.658658 + 0.752442i \(0.728876\pi\)
\(258\) −1297.03 1297.03i −0.312983 0.312983i
\(259\) 2446.60i 0.586966i
\(260\) 360.678 2737.51i 0.0860319 0.652974i
\(261\) −609.297 −0.144500
\(262\) −1891.38 1891.38i −0.445992 0.445992i
\(263\) 5228.19 + 5228.19i 1.22580 + 1.22580i 0.965540 + 0.260256i \(0.0838069\pi\)
0.260256 + 0.965540i \(0.416193\pi\)
\(264\) −509.353 −0.118744
\(265\) −618.345 + 4693.19i −0.143338 + 1.08793i
\(266\) 3381.86 0.779530
\(267\) 1805.61 1805.61i 0.413864 0.413864i
\(268\) 1268.73 + 1268.73i 0.289179 + 0.289179i
\(269\) 7766.80i 1.76041i −0.474593 0.880205i \(-0.657405\pi\)
0.474593 0.880205i \(-0.342595\pi\)
\(270\) −415.939 + 319.095i −0.0937527 + 0.0719241i
\(271\) −7465.38 −1.67339 −0.836696 0.547667i \(-0.815516\pi\)
−0.836696 + 0.547667i \(0.815516\pi\)
\(272\) 530.235 530.235i 0.118199 0.118199i
\(273\) −4901.35 4901.35i −1.08661 1.08661i
\(274\) −4173.49 −0.920182
\(275\) 1079.50 + 289.482i 0.236714 + 0.0634779i
\(276\) 2789.32 1446.05i 0.608323 0.315369i
\(277\) −1302.75 1302.75i −0.282579 0.282579i 0.551558 0.834137i \(-0.314034\pi\)
−0.834137 + 0.551558i \(0.814034\pi\)
\(278\) −1729.63 + 1729.63i −0.373153 + 0.373153i
\(279\) 1921.40i 0.412298i
\(280\) −1118.82 + 858.324i −0.238794 + 0.183195i
\(281\) 7864.44i 1.66958i −0.550565 0.834792i \(-0.685588\pi\)
0.550565 0.834792i \(-0.314412\pi\)
\(282\) −2094.66 2094.66i −0.442324 0.442324i
\(283\) −927.127 927.127i −0.194742 0.194742i 0.603000 0.797742i \(-0.293972\pi\)
−0.797742 + 0.603000i \(0.793972\pi\)
\(284\) 2994.64i 0.625701i
\(285\) 8465.73 + 1115.39i 1.75953 + 0.231825i
\(286\) 1104.08i 0.228272i
\(287\) −3087.71 + 3087.71i −0.635059 + 0.635059i
\(288\) 536.443 536.443i 0.109758 0.109758i
\(289\) 2716.53i 0.552926i
\(290\) 569.756 + 75.0675i 0.115370 + 0.0152004i
\(291\) 6838.65i 1.37762i
\(292\) −571.403 571.403i −0.114516 0.114516i
\(293\) −4777.76 4777.76i −0.952626 0.952626i 0.0463011 0.998928i \(-0.485257\pi\)
−0.998928 + 0.0463011i \(0.985257\pi\)
\(294\) 1345.00i 0.266809i
\(295\) −5440.55 + 4173.82i −1.07377 + 0.823759i
\(296\) 1241.47i 0.243781i
\(297\) 148.225 148.225i 0.0289593 0.0289593i
\(298\) 4485.27 + 4485.27i 0.871895 + 0.871895i
\(299\) −3134.47 6046.16i −0.606259 1.16943i
\(300\) −3083.81 + 1779.62i −0.593479 + 0.342488i
\(301\) 2030.55 0.388834
\(302\) 339.944 + 339.944i 0.0647735 + 0.0647735i
\(303\) 5191.46 5191.46i 0.984295 0.984295i
\(304\) 1716.05 0.323757
\(305\) 359.058 275.458i 0.0674085 0.0517137i
\(306\) 2222.19i 0.415144i
\(307\) 2300.15 + 2300.15i 0.427610 + 0.427610i 0.887813 0.460204i \(-0.152224\pi\)
−0.460204 + 0.887813i \(0.652224\pi\)
\(308\) 398.706 398.706i 0.0737610 0.0737610i
\(309\) 10243.3 1.88583
\(310\) −236.723 + 1796.70i −0.0433708 + 0.329181i
\(311\) −10041.4 −1.83086 −0.915430 0.402477i \(-0.868150\pi\)
−0.915430 + 0.402477i \(0.868150\pi\)
\(312\) −2487.08 2487.08i −0.451292 0.451292i
\(313\) 634.081 + 634.081i 0.114506 + 0.114506i 0.762038 0.647532i \(-0.224199\pi\)
−0.647532 + 0.762038i \(0.724199\pi\)
\(314\) 4178.49 0.750975
\(315\) −545.865 + 4143.07i −0.0976381 + 0.741064i
\(316\) 5342.56i 0.951083i
\(317\) 7828.57 + 7828.57i 1.38705 + 1.38705i 0.831441 + 0.555614i \(0.187517\pi\)
0.555614 + 0.831441i \(0.312483\pi\)
\(318\) 4263.85 + 4263.85i 0.751902 + 0.751902i
\(319\) −229.791 −0.0403318
\(320\) −567.721 + 435.538i −0.0991767 + 0.0760853i
\(321\) 9097.32i 1.58182i
\(322\) −1051.47 + 3315.32i −0.181976 + 0.573775i
\(323\) 3554.33 3554.33i 0.612286 0.612286i
\(324\) 3228.22i 0.553535i
\(325\) 3857.52 + 6684.50i 0.658390 + 1.14089i
\(326\) −1421.67 −0.241531
\(327\) 6099.83 6099.83i 1.03156 1.03156i
\(328\) −1566.79 + 1566.79i −0.263755 + 0.263755i
\(329\) 3279.28 0.549521
\(330\) 1129.57 866.573i 0.188427 0.144555i
\(331\) −9594.36 −1.59321 −0.796607 0.604498i \(-0.793374\pi\)
−0.796607 + 0.604498i \(0.793374\pi\)
\(332\) −120.923 + 120.923i −0.0199895 + 0.0199895i
\(333\) 2601.48 + 2601.48i 0.428108 + 0.428108i
\(334\) 1713.09i 0.280647i
\(335\) −4972.12 655.096i −0.810914 0.106841i
\(336\) 1796.27i 0.291651i
\(337\) 2114.12 2114.12i 0.341731 0.341731i −0.515287 0.857018i \(-0.672314\pi\)
0.857018 + 0.515287i \(0.172314\pi\)
\(338\) −2284.00 + 2284.00i −0.367554 + 0.367554i
\(339\) −12026.5 −1.92682
\(340\) −273.782 + 2077.98i −0.0436703 + 0.331453i
\(341\) 724.638i 0.115077i
\(342\) 3595.94 3595.94i 0.568557 0.568557i
\(343\) 4876.62 + 4876.62i 0.767676 + 0.767676i
\(344\) 1030.36 0.161492
\(345\) −3725.57 + 7952.37i −0.581385 + 1.24099i
\(346\) −4385.98 −0.681479
\(347\) 4685.81 + 4685.81i 0.724921 + 0.724921i 0.969603 0.244682i \(-0.0786836\pi\)
−0.244682 + 0.969603i \(0.578684\pi\)
\(348\) 517.634 517.634i 0.0797359 0.0797359i
\(349\) 7557.11i 1.15909i −0.814940 0.579545i \(-0.803230\pi\)
0.814940 0.579545i \(-0.196770\pi\)
\(350\) 1020.88 3806.94i 0.155909 0.581399i
\(351\) 1447.51 0.220121
\(352\) 202.315 202.315i 0.0306347 0.0306347i
\(353\) −2822.75 + 2822.75i −0.425609 + 0.425609i −0.887130 0.461520i \(-0.847304\pi\)
0.461520 + 0.887130i \(0.347304\pi\)
\(354\) 8734.83i 1.31144i
\(355\) 5094.83 + 6641.09i 0.761706 + 0.992879i
\(356\) 1434.37i 0.213544i
\(357\) 3720.49 + 3720.49i 0.551567 + 0.551567i
\(358\) −557.844 + 557.844i −0.0823546 + 0.0823546i
\(359\) 2400.09 0.352846 0.176423 0.984314i \(-0.443547\pi\)
0.176423 + 0.984314i \(0.443547\pi\)
\(360\) −276.987 + 2102.31i −0.0405514 + 0.307781i
\(361\) 4644.22 0.677098
\(362\) 825.375 825.375i 0.119836 0.119836i
\(363\) 6299.39 6299.39i 0.910833 0.910833i
\(364\) 3893.62 0.560663
\(365\) 2239.31 + 295.038i 0.321126 + 0.0423096i
\(366\) 576.469i 0.0823293i
\(367\) −6417.00 + 6417.00i −0.912710 + 0.912710i −0.996485 0.0837748i \(-0.973302\pi\)
0.0837748 + 0.996485i \(0.473302\pi\)
\(368\) −533.546 + 1682.28i −0.0755788 + 0.238302i
\(369\) 6566.36i 0.926371i
\(370\) −2112.14 2753.16i −0.296770 0.386838i
\(371\) −6675.22 −0.934125
\(372\) 1632.34 + 1632.34i 0.227508 + 0.227508i
\(373\) 7525.86 + 7525.86i 1.04470 + 1.04470i 0.998953 + 0.0457508i \(0.0145680\pi\)
0.0457508 + 0.998953i \(0.485432\pi\)
\(374\) 838.080i 0.115872i
\(375\) 3811.14 9193.13i 0.524817 1.26595i
\(376\) 1664.00 0.228229
\(377\) −1122.03 1122.03i −0.153282 0.153282i
\(378\) −522.727 522.727i −0.0711275 0.0711275i
\(379\) −6482.76 −0.878620 −0.439310 0.898335i \(-0.644777\pi\)
−0.439310 + 0.898335i \(0.644777\pi\)
\(380\) −3805.61 + 2919.55i −0.513747 + 0.394130i
\(381\) −10936.1 −1.47054
\(382\) 4265.84 4265.84i 0.571360 0.571360i
\(383\) 3396.23 + 3396.23i 0.453105 + 0.453105i 0.896384 0.443279i \(-0.146185\pi\)
−0.443279 + 0.896384i \(0.646185\pi\)
\(384\) 911.479i 0.121129i
\(385\) −205.868 + 1562.52i −0.0272520 + 0.206840i
\(386\) 1323.44 0.174512
\(387\) 2159.09 2159.09i 0.283599 0.283599i
\(388\) 2716.31 + 2716.31i 0.355411 + 0.355411i
\(389\) 5629.42 0.733734 0.366867 0.930273i \(-0.380430\pi\)
0.366867 + 0.930273i \(0.380430\pi\)
\(390\) 9746.82 + 1284.18i 1.26551 + 0.166736i
\(391\) 2379.30 + 4589.49i 0.307740 + 0.593608i
\(392\) 534.233 + 534.233i 0.0688338 + 0.0688338i
\(393\) 6734.19 6734.19i 0.864364 0.864364i
\(394\) 6051.00i 0.773718i
\(395\) −9089.39 11848.0i −1.15782 1.50921i
\(396\) 847.892i 0.107596i
\(397\) 382.000 + 382.000i 0.0482923 + 0.0482923i 0.730841 0.682548i \(-0.239128\pi\)
−0.682548 + 0.730841i \(0.739128\pi\)
\(398\) −4993.48 4993.48i −0.628896 0.628896i
\(399\) 12041.0i 1.51079i
\(400\) 518.023 1931.75i 0.0647529 0.241469i
\(401\) 11716.5i 1.45909i 0.683931 + 0.729547i \(0.260269\pi\)
−0.683931 + 0.729547i \(0.739731\pi\)
\(402\) −4517.26 + 4517.26i −0.560449 + 0.560449i
\(403\) 3538.28 3538.28i 0.437356 0.437356i
\(404\) 4124.08i 0.507873i
\(405\) −5492.23 7159.09i −0.673854 0.878365i
\(406\) 810.376i 0.0990599i
\(407\) 981.124 + 981.124i 0.119490 + 0.119490i
\(408\) 1887.88 + 1887.88i 0.229079 + 0.229079i
\(409\) 13931.8i 1.68431i −0.539236 0.842155i \(-0.681287\pi\)
0.539236 0.842155i \(-0.318713\pi\)
\(410\) 808.998 6140.22i 0.0974477 0.739619i
\(411\) 14859.6i 1.78338i
\(412\) −4068.64 + 4068.64i −0.486523 + 0.486523i
\(413\) −6837.36 6837.36i −0.814635 0.814635i
\(414\) 2407.16 + 4643.22i 0.285762 + 0.551213i
\(415\) 62.4375 473.895i 0.00738539 0.0560544i
\(416\) 1975.73 0.232856
\(417\) −6158.30 6158.30i −0.723198 0.723198i
\(418\) 1356.18 1356.18i 0.158691 0.158691i
\(419\) 799.822 0.0932551 0.0466275 0.998912i \(-0.485153\pi\)
0.0466275 + 0.998912i \(0.485153\pi\)
\(420\) −3056.03 3983.52i −0.355046 0.462800i
\(421\) 16334.9i 1.89101i −0.325612 0.945503i \(-0.605570\pi\)
0.325612 0.945503i \(-0.394430\pi\)
\(422\) 1466.91 + 1466.91i 0.169214 + 0.169214i
\(423\) 3486.87 3486.87i 0.400798 0.400798i
\(424\) −3387.19 −0.387964
\(425\) −2928.15 5074.04i −0.334203 0.579122i
\(426\) 10662.3 1.21265
\(427\) 451.243 + 451.243i 0.0511409 + 0.0511409i
\(428\) 3613.45 + 3613.45i 0.408090 + 0.408090i
\(429\) −3931.04 −0.442407
\(430\) −2284.98 + 1752.97i −0.256260 + 0.196595i
\(431\) 6798.48i 0.759795i −0.925029 0.379897i \(-0.875959\pi\)
0.925029 0.379897i \(-0.124041\pi\)
\(432\) −265.246 265.246i −0.0295409 0.0295409i
\(433\) −2823.98 2823.98i −0.313422 0.313422i 0.532812 0.846234i \(-0.321135\pi\)
−0.846234 + 0.532812i \(0.821135\pi\)
\(434\) −2555.49 −0.282644
\(435\) −267.275 + 2028.60i −0.0294595 + 0.223595i
\(436\) 4845.69i 0.532263i
\(437\) −3576.52 + 11276.9i −0.391507 + 1.23443i
\(438\) 2034.46 2034.46i 0.221941 0.221941i
\(439\) 5973.05i 0.649380i 0.945820 + 0.324690i \(0.105260\pi\)
−0.945820 + 0.324690i \(0.894740\pi\)
\(440\) −104.463 + 792.867i −0.0113184 + 0.0859056i
\(441\) 2238.95 0.241761
\(442\) 4092.20 4092.20i 0.440375 0.440375i
\(443\) 3648.17 3648.17i 0.391264 0.391264i −0.483874 0.875138i \(-0.660771\pi\)
0.875138 + 0.483874i \(0.160771\pi\)
\(444\) −4420.21 −0.472464
\(445\) −2440.33 3180.95i −0.259961 0.338858i
\(446\) 9930.72 1.05433
\(447\) −15969.7 + 15969.7i −1.68980 + 1.68980i
\(448\) −713.478 713.478i −0.0752426 0.0752426i
\(449\) 6112.59i 0.642475i 0.946999 + 0.321237i \(0.104099\pi\)
−0.946999 + 0.321237i \(0.895901\pi\)
\(450\) −2962.43 5133.44i −0.310334 0.537762i
\(451\) 2476.44i 0.258561i
\(452\) 4776.92 4776.92i 0.497096 0.497096i
\(453\) −1210.36 + 1210.36i −0.125536 + 0.125536i
\(454\) 9296.53 0.961030
\(455\) −8634.73 + 6624.30i −0.889676 + 0.682531i
\(456\) 6109.93i 0.627464i
\(457\) 626.853 626.853i 0.0641640 0.0641640i −0.674297 0.738461i \(-0.735553\pi\)
0.738461 + 0.674297i \(0.235553\pi\)
\(458\) −9228.57 9228.57i −0.941534 0.941534i
\(459\) −1098.77 −0.111735
\(460\) −1678.88 4638.47i −0.170170 0.470151i
\(461\) 715.928 0.0723299 0.0361650 0.999346i \(-0.488486\pi\)
0.0361650 + 0.999346i \(0.488486\pi\)
\(462\) 1419.58 + 1419.58i 0.142954 + 0.142954i
\(463\) 1427.39 1427.39i 0.143275 0.143275i −0.631831 0.775106i \(-0.717696\pi\)
0.775106 + 0.631831i \(0.217696\pi\)
\(464\) 411.208i 0.0411419i
\(465\) −6397.10 842.843i −0.637975 0.0840557i
\(466\) 5862.14 0.582744
\(467\) 6463.77 6463.77i 0.640488 0.640488i −0.310188 0.950675i \(-0.600392\pi\)
0.950675 + 0.310188i \(0.100392\pi\)
\(468\) 4140.11 4140.11i 0.408924 0.408924i
\(469\) 7071.96i 0.696274i
\(470\) −3690.18 + 2830.99i −0.362160 + 0.277838i
\(471\) 14877.4i 1.45544i
\(472\) −3469.47 3469.47i −0.338337 0.338337i
\(473\) 814.284 814.284i 0.0791561 0.0791561i
\(474\) −19022.0 −1.84327
\(475\) 3472.47 12949.1i 0.335427 1.25083i
\(476\) −2955.55 −0.284596
\(477\) −7097.79 + 7097.79i −0.681311 + 0.681311i
\(478\) −88.2901 + 88.2901i −0.00844831 + 0.00844831i
\(479\) −13521.6 −1.28980 −0.644902 0.764265i \(-0.723102\pi\)
−0.644902 + 0.764265i \(0.723102\pi\)
\(480\) −1550.72 2021.35i −0.147459 0.192212i
\(481\) 9581.31i 0.908254i
\(482\) 4170.42 4170.42i 0.394102 0.394102i
\(483\) −11804.1 3743.73i −1.11202 0.352682i
\(484\) 5004.22i 0.469969i
\(485\) −10645.1 1402.54i −0.996642 0.131311i
\(486\) −10227.9 −0.954627
\(487\) 12591.7 + 12591.7i 1.17163 + 1.17163i 0.981820 + 0.189813i \(0.0607882\pi\)
0.189813 + 0.981820i \(0.439212\pi\)
\(488\) 228.973 + 228.973i 0.0212400 + 0.0212400i
\(489\) 5061.82i 0.468105i
\(490\) −2093.65 275.846i −0.193023 0.0254315i
\(491\) 12457.1 1.14497 0.572486 0.819915i \(-0.305979\pi\)
0.572486 + 0.819915i \(0.305979\pi\)
\(492\) −5578.51 5578.51i −0.511176 0.511176i
\(493\) 851.705 + 851.705i 0.0778070 + 0.0778070i
\(494\) 13244.0 1.20622
\(495\) 1442.54 + 1880.34i 0.130984 + 0.170737i
\(496\) −1296.73 −0.117389
\(497\) −8346.13 + 8346.13i −0.753269 + 0.753269i
\(498\) −430.542 430.542i −0.0387411 0.0387411i
\(499\) 17849.9i 1.60135i 0.599100 + 0.800675i \(0.295525\pi\)
−0.599100 + 0.800675i \(0.704475\pi\)
\(500\) 2137.72 + 5165.28i 0.191204 + 0.461997i
\(501\) −6099.40 −0.543914
\(502\) 1009.50 1009.50i 0.0897532 0.0897532i
\(503\) 4849.45 + 4849.45i 0.429874 + 0.429874i 0.888585 0.458712i \(-0.151689\pi\)
−0.458712 + 0.888585i \(0.651689\pi\)
\(504\) −2990.16 −0.264270
\(505\) −7016.38 9145.81i −0.618267 0.805908i
\(506\) 907.839 + 1751.15i 0.0797596 + 0.153850i
\(507\) −8132.11 8132.11i −0.712346 0.712346i
\(508\) 4343.82 4343.82i 0.379382 0.379382i
\(509\) 11927.2i 1.03863i −0.854582 0.519316i \(-0.826187\pi\)
0.854582 0.519316i \(-0.173813\pi\)
\(510\) −7398.57 974.789i −0.642381 0.0846361i
\(511\) 3185.03i 0.275728i
\(512\) −362.039 362.039i −0.0312500 0.0312500i
\(513\) −1778.03 1778.03i −0.153025 0.153025i
\(514\) 1092.88i 0.0937841i
\(515\) 2100.80 15944.9i 0.179752 1.36430i
\(516\) 3668.56i 0.312983i
\(517\) 1315.04 1315.04i 0.111868 0.111868i
\(518\) 3460.01 3460.01i 0.293483 0.293483i
\(519\) 15616.1i 1.32075i
\(520\) −4381.50 + 3361.35i −0.369503 + 0.283471i
\(521\) 7777.43i 0.654003i 0.945024 + 0.327001i \(0.106038\pi\)
−0.945024 + 0.327001i \(0.893962\pi\)
\(522\) 861.677 + 861.677i 0.0722501 + 0.0722501i
\(523\) −589.813 589.813i −0.0493130 0.0493130i 0.682020 0.731333i \(-0.261102\pi\)
−0.731333 + 0.682020i \(0.761102\pi\)
\(524\) 5349.63i 0.445992i
\(525\) 13554.5 + 3634.81i 1.12679 + 0.302164i
\(526\) 14787.6i 1.22580i
\(527\) −2685.82 + 2685.82i −0.222004 + 0.222004i
\(528\) 720.334 + 720.334i 0.0593722 + 0.0593722i
\(529\) −9943.01 7012.31i −0.817211 0.576338i
\(530\) 7511.64 5762.70i 0.615632 0.472293i
\(531\) −14540.4 −1.18832
\(532\) −4782.67 4782.67i −0.389765 0.389765i
\(533\) −12092.0 + 12092.0i −0.982672 + 0.982672i
\(534\) −5107.04 −0.413864
\(535\) −14161.0 1865.77i −1.14436 0.150774i
\(536\) 3588.51i 0.289179i
\(537\) −1986.18 1986.18i −0.159609 0.159609i
\(538\) −10983.9 + 10983.9i −0.880205 + 0.880205i
\(539\) 844.400 0.0674784
\(540\) 1039.50 + 136.957i 0.0828384 + 0.0109143i
\(541\) 7654.78 0.608326 0.304163 0.952620i \(-0.401623\pi\)
0.304163 + 0.952620i \(0.401623\pi\)
\(542\) 10557.6 + 10557.6i 0.836696 + 0.836696i
\(543\) 2938.72 + 2938.72i 0.232251 + 0.232251i
\(544\) −1499.73 −0.118199
\(545\) −8244.07 10746.1i −0.647958 0.844609i
\(546\) 13863.1i 1.08661i
\(547\) 5952.34 + 5952.34i 0.465272 + 0.465272i 0.900379 0.435107i \(-0.143289\pi\)
−0.435107 + 0.900379i \(0.643289\pi\)
\(548\) 5902.21 + 5902.21i 0.460091 + 0.460091i
\(549\) 959.616 0.0746001
\(550\) −1117.26 1936.03i −0.0866181 0.150096i
\(551\) 2756.45i 0.213120i
\(552\) −5989.71 1899.67i −0.461846 0.146477i
\(553\) 14889.8 14889.8i 1.14499 1.14499i
\(554\) 3684.72i 0.282579i
\(555\) 9802.53 7520.19i 0.749719 0.575161i
\(556\) 4892.15 0.373153
\(557\) −7363.50 + 7363.50i −0.560147 + 0.560147i −0.929349 0.369202i \(-0.879631\pi\)
0.369202 + 0.929349i \(0.379631\pi\)
\(558\) −2717.27 + 2717.27i −0.206149 + 0.206149i
\(559\) 7952.01 0.601671
\(560\) 2796.11 + 368.398i 0.210995 + 0.0277994i
\(561\) 2983.95 0.224568
\(562\) −11122.0 + 11122.0i −0.834792 + 0.834792i
\(563\) 10541.5 + 10541.5i 0.789112 + 0.789112i 0.981349 0.192237i \(-0.0615742\pi\)
−0.192237 + 0.981349i \(0.561574\pi\)
\(564\) 5924.60i 0.442324i
\(565\) −2466.52 + 18720.7i −0.183659 + 1.39395i
\(566\) 2622.31i 0.194742i
\(567\) 8997.12 8997.12i 0.666391 0.666391i
\(568\) −4235.06 + 4235.06i −0.312850 + 0.312850i
\(569\) 2659.83 0.195968 0.0979841 0.995188i \(-0.468761\pi\)
0.0979841 + 0.995188i \(0.468761\pi\)
\(570\) −10394.9 13549.7i −0.763853 0.995678i
\(571\) 2661.99i 0.195098i −0.995231 0.0975490i \(-0.968900\pi\)
0.995231 0.0975490i \(-0.0311003\pi\)
\(572\) 1561.41 1561.41i 0.114136 0.114136i
\(573\) 15188.4 + 15188.4i 1.10734 + 1.10734i
\(574\) 8733.37 0.635059
\(575\) 11614.7 + 7430.23i 0.842376 + 0.538890i
\(576\) −1517.29 −0.109758
\(577\) 3146.05 + 3146.05i 0.226988 + 0.226988i 0.811433 0.584445i \(-0.198688\pi\)
−0.584445 + 0.811433i \(0.698688\pi\)
\(578\) 3841.75 3841.75i 0.276463 0.276463i
\(579\) 4712.07i 0.338216i
\(580\) −699.595 911.918i −0.0500847 0.0652851i
\(581\) 674.031 0.0481300
\(582\) −9671.31 + 9671.31i −0.688812 + 0.688812i
\(583\) −2676.87 + 2676.87i −0.190162 + 0.190162i
\(584\) 1616.17i 0.114516i
\(585\) −2137.70 + 16225.0i −0.151082 + 1.14670i
\(586\) 13513.5i 0.952626i
\(587\) 3610.31 + 3610.31i 0.253856 + 0.253856i 0.822550 0.568693i \(-0.192551\pi\)
−0.568693 + 0.822550i \(0.692551\pi\)
\(588\) −1902.12 + 1902.12i −0.133405 + 0.133405i
\(589\) −8692.38 −0.608087
\(590\) 13596.8 + 1791.43i 0.948762 + 0.125003i
\(591\) 21544.4 1.49952
\(592\) 1755.71 1755.71i 0.121890 0.121890i
\(593\) 927.983 927.983i 0.0642626 0.0642626i −0.674245 0.738508i \(-0.735531\pi\)
0.738508 + 0.674245i \(0.235531\pi\)
\(594\) −419.244 −0.0289593
\(595\) 6554.41 5028.34i 0.451604 0.346457i
\(596\) 12686.3i 0.871895i
\(597\) 17779.1 17779.1i 1.21884 1.21884i
\(598\) −4117.75 + 12983.4i −0.281584 + 0.887843i
\(599\) 28083.7i 1.91564i 0.287370 + 0.957820i \(0.407219\pi\)
−0.287370 + 0.957820i \(0.592781\pi\)
\(600\) 6877.92 + 1844.40i 0.467983 + 0.125496i
\(601\) −8979.33 −0.609442 −0.304721 0.952442i \(-0.598563\pi\)
−0.304721 + 0.952442i \(0.598563\pi\)
\(602\) −2871.63 2871.63i −0.194417 0.194417i
\(603\) −7519.64 7519.64i −0.507833 0.507833i
\(604\) 961.508i 0.0647735i
\(605\) −8513.78 11097.7i −0.572123 0.745759i
\(606\) −14683.7 −0.984295
\(607\) −10379.3 10379.3i −0.694043 0.694043i 0.269076 0.963119i \(-0.413282\pi\)
−0.963119 + 0.269076i \(0.913282\pi\)
\(608\) −2426.86 2426.86i −0.161879 0.161879i
\(609\) −2885.32 −0.191985
\(610\) −897.341 118.228i −0.0595611 0.00784740i
\(611\) 12842.2 0.850314
\(612\) −3142.65 + 3142.65i −0.207572 + 0.207572i
\(613\) −8311.56 8311.56i −0.547636 0.547636i 0.378120 0.925756i \(-0.376571\pi\)
−0.925756 + 0.378120i \(0.876571\pi\)
\(614\) 6505.79i 0.427610i
\(615\) 21862.0 + 2880.41i 1.43344 + 0.188861i
\(616\) −1127.71 −0.0737610
\(617\) 10641.0 10641.0i 0.694315 0.694315i −0.268863 0.963178i \(-0.586648\pi\)
0.963178 + 0.268863i \(0.0866480\pi\)
\(618\) −14486.2 14486.2i −0.942916 0.942916i
\(619\) 26773.6 1.73848 0.869241 0.494388i \(-0.164608\pi\)
0.869241 + 0.494388i \(0.164608\pi\)
\(620\) 2875.70 2206.15i 0.186276 0.142905i
\(621\) 2295.86 1190.23i 0.148357 0.0769119i
\(622\) 14200.7 + 14200.7i 0.915430 + 0.915430i
\(623\) 3997.63 3997.63i 0.257082 0.257082i
\(624\) 7034.53i 0.451292i
\(625\) −13528.5 7817.89i −0.865826 0.500345i
\(626\) 1793.45i 0.114506i
\(627\) 4828.63 + 4828.63i 0.307555 + 0.307555i
\(628\) −5909.28 5909.28i −0.375487 0.375487i
\(629\) 7272.93i 0.461035i
\(630\) 6631.15 5087.21i 0.419351 0.321713i
\(631\) 6798.32i 0.428902i −0.976735 0.214451i \(-0.931204\pi\)
0.976735 0.214451i \(-0.0687962\pi\)
\(632\) 7555.52 7555.52i 0.475542 0.475542i
\(633\) −5222.90 + 5222.90i −0.327949 + 0.327949i
\(634\) 22142.5i 1.38705i
\(635\) −2242.89 + 17023.4i −0.140168 + 1.06386i
\(636\) 12060.0i 0.751902i
\(637\) 4123.05 + 4123.05i 0.256454 + 0.256454i
\(638\) 324.974 + 324.974i 0.0201659 + 0.0201659i
\(639\) 17748.9i 1.09881i
\(640\) 1418.82 + 186.935i 0.0876310 + 0.0115457i
\(641\) 20456.5i 1.26051i −0.776389 0.630253i \(-0.782951\pi\)
0.776389 0.630253i \(-0.217049\pi\)
\(642\) −12865.6 + 12865.6i −0.790908 + 0.790908i
\(643\) −13047.3 13047.3i −0.800213 0.800213i 0.182915 0.983129i \(-0.441447\pi\)
−0.983129 + 0.182915i \(0.941447\pi\)
\(644\) 6175.57 3201.56i 0.377875 0.195899i
\(645\) −6241.38 8135.61i −0.381014 0.496650i
\(646\) −10053.2 −0.612286
\(647\) 4439.60 + 4439.60i 0.269766 + 0.269766i 0.829006 0.559240i \(-0.188907\pi\)
−0.559240 + 0.829006i \(0.688907\pi\)
\(648\) 4565.39 4565.39i 0.276768 0.276768i
\(649\) −5483.78 −0.331675
\(650\) 3997.95 14908.7i 0.241250 0.899640i
\(651\) 9098.74i 0.547785i
\(652\) 2010.55 + 2010.55i 0.120766 + 0.120766i
\(653\) −14019.8 + 14019.8i −0.840180 + 0.840180i −0.988882 0.148702i \(-0.952490\pi\)
0.148702 + 0.988882i \(0.452490\pi\)
\(654\) −17252.9 −1.03156
\(655\) −9101.43 11863.7i −0.542935 0.707712i
\(656\) 4431.56 0.263755
\(657\) 3386.65 + 3386.65i 0.201105 + 0.201105i
\(658\) −4637.60 4637.60i −0.274761 0.274761i
\(659\) 13786.1 0.814917 0.407459 0.913224i \(-0.366415\pi\)
0.407459 + 0.913224i \(0.366415\pi\)
\(660\) −2822.97 371.938i −0.166491 0.0219358i
\(661\) 3702.98i 0.217896i −0.994047 0.108948i \(-0.965252\pi\)
0.994047 0.108948i \(-0.0347482\pi\)
\(662\) 13568.5 + 13568.5i 0.796607 + 0.796607i
\(663\) 14570.1 + 14570.1i 0.853479 + 0.853479i
\(664\) 342.022 0.0199895
\(665\) 18743.2 + 2469.49i 1.09298 + 0.144004i
\(666\) 7358.09i 0.428108i
\(667\) −2702.22 857.023i −0.156867 0.0497512i
\(668\) 2422.68 2422.68i 0.140324 0.140324i
\(669\) 35358.0i 2.04338i
\(670\) 6105.20 + 7958.09i 0.352036 + 0.458877i
\(671\) 361.911 0.0208218
\(672\) 2540.31 2540.31i 0.145825 0.145825i
\(673\) 8639.72 8639.72i 0.494854 0.494854i −0.414978 0.909832i \(-0.636211\pi\)
0.909832 + 0.414978i \(0.136211\pi\)
\(674\) −5979.64 −0.341731
\(675\) −2538.25 + 1464.79i −0.144737 + 0.0835255i
\(676\) 6460.13 0.367554
\(677\) −23219.7 + 23219.7i −1.31818 + 1.31818i −0.402961 + 0.915217i \(0.632019\pi\)
−0.915217 + 0.402961i \(0.867981\pi\)
\(678\) 17008.1 + 17008.1i 0.963409 + 0.963409i
\(679\) 15140.8i 0.855746i
\(680\) 3325.89 2551.52i 0.187562 0.143892i
\(681\) 33100.0i 1.86255i
\(682\) −1024.79 + 1024.79i −0.0575387 + 0.0575387i
\(683\) 10006.5 10006.5i 0.560598 0.560598i −0.368879 0.929477i \(-0.620258\pi\)
0.929477 + 0.368879i \(0.120258\pi\)
\(684\) −10170.9 −0.568557
\(685\) −23130.6 3047.55i −1.29018 0.169987i
\(686\) 13793.2i 0.767676i
\(687\) 32858.0 32858.0i 1.82476 1.82476i
\(688\) −1457.15 1457.15i −0.0807459 0.0807459i
\(689\) −26141.4 −1.44544
\(690\) 16515.1 5977.59i 0.911187 0.329802i
\(691\) −19391.5 −1.06756 −0.533782 0.845622i \(-0.679230\pi\)
−0.533782 + 0.845622i \(0.679230\pi\)
\(692\) 6202.71 + 6202.71i 0.340739 + 0.340739i
\(693\) −2363.10 + 2363.10i −0.129533 + 0.129533i
\(694\) 13253.5i 0.724921i
\(695\) −10849.1 + 8323.10i −0.592130 + 0.454264i
\(696\) −1464.09 −0.0797359
\(697\) 9178.77 9178.77i 0.498810 0.498810i
\(698\) −10687.4 + 10687.4i −0.579545 + 0.579545i
\(699\) 20872.0i 1.12940i
\(700\) −6827.57 + 3940.09i −0.368654 + 0.212745i
\(701\) 21513.0i 1.15911i 0.814933 + 0.579555i \(0.196774\pi\)
−0.814933 + 0.579555i \(0.803226\pi\)
\(702\) −2047.09 2047.09i −0.110061 0.110061i
\(703\) 11769.0 11769.0i 0.631405 0.631405i
\(704\) −572.232 −0.0306347
\(705\) −10079.6 13138.8i −0.538470 0.701892i
\(706\) 7983.95 0.425609
\(707\) 11493.9 11493.9i 0.611419 0.611419i
\(708\) 12352.9 12352.9i 0.655721 0.655721i
\(709\) 23973.3 1.26987 0.634933 0.772567i \(-0.281028\pi\)
0.634933 + 0.772567i \(0.281028\pi\)
\(710\) 2186.73 16597.1i 0.115587 0.877293i
\(711\) 31664.8i 1.67022i
\(712\) 2028.51 2028.51i 0.106772 0.106772i
\(713\) 2702.59 8521.35i 0.141954 0.447583i
\(714\) 10523.1i 0.551567i
\(715\) −806.217 + 6119.12i −0.0421690 + 0.320059i
\(716\) 1577.82 0.0823546
\(717\) −314.354 314.354i −0.0163734 0.0163734i
\(718\) −3394.24 3394.24i −0.176423 0.176423i
\(719\) 20926.9i 1.08545i 0.839909 + 0.542727i \(0.182608\pi\)
−0.839909 + 0.542727i \(0.817392\pi\)
\(720\) 3364.83 2581.39i 0.174166 0.133615i
\(721\) 22678.8 1.17143
\(722\) −6567.92 6567.92i −0.338549 0.338549i
\(723\) 14848.6 + 14848.6i 0.763798 + 0.763798i
\(724\) −2334.51 −0.119836
\(725\) 3102.93 + 832.089i 0.158952 + 0.0426249i
\(726\) −17817.4 −0.910833
\(727\) −5380.89 + 5380.89i −0.274507 + 0.274507i −0.830911 0.556405i \(-0.812180\pi\)
0.556405 + 0.830911i \(0.312180\pi\)
\(728\) −5506.42 5506.42i −0.280332 0.280332i
\(729\) 14625.7i 0.743065i
\(730\) −2749.62 3584.12i −0.139408 0.181718i
\(731\) −6036.17 −0.305412
\(732\) −815.251 + 815.251i −0.0411647 + 0.0411647i
\(733\) 12601.9 + 12601.9i 0.635008 + 0.635008i 0.949320 0.314311i \(-0.101774\pi\)
−0.314311 + 0.949320i \(0.601774\pi\)
\(734\) 18150.0 0.912710
\(735\) 982.140 7454.36i 0.0492881 0.374093i
\(736\) 3133.66 1624.56i 0.156940 0.0813616i
\(737\) −2835.97 2835.97i −0.141743 0.141743i
\(738\) 9286.23 9286.23i 0.463185 0.463185i
\(739\) 12100.4i 0.602326i 0.953573 + 0.301163i \(0.0973749\pi\)
−0.953573 + 0.301163i \(0.902625\pi\)
\(740\) −906.541 + 6880.57i −0.0450340 + 0.341804i
\(741\) 47154.7i 2.33775i
\(742\) 9440.19 + 9440.19i 0.467062 + 0.467062i
\(743\) 6441.47 + 6441.47i 0.318054 + 0.318054i 0.848020 0.529965i \(-0.177795\pi\)
−0.529965 + 0.848020i \(0.677795\pi\)
\(744\) 4616.95i 0.227508i
\(745\) 21583.4 + 28133.8i 1.06141 + 1.38355i
\(746\) 21286.4i 1.04470i
\(747\) 716.700 716.700i 0.0351040 0.0351040i
\(748\) −1185.22 + 1185.22i −0.0579360 + 0.0579360i
\(749\) 20141.5i 0.982584i
\(750\) −18390.8 + 7611.28i −0.895383 + 0.370566i
\(751\) 27627.2i 1.34238i −0.741283 0.671192i \(-0.765782\pi\)
0.741283 0.671192i \(-0.234218\pi\)
\(752\) −2353.25 2353.25i −0.114114 0.114114i
\(753\) 3594.28 + 3594.28i 0.173948 + 0.173948i
\(754\) 3173.58i 0.153282i
\(755\) 1635.83 + 2132.30i 0.0788530 + 0.102784i
\(756\) 1478.50i 0.0711275i
\(757\) 21890.4 21890.4i 1.05102 1.05102i 0.0523915 0.998627i \(-0.483316\pi\)
0.998627 0.0523915i \(-0.0166844\pi\)
\(758\) 9168.01 + 9168.01i 0.439310 + 0.439310i
\(759\) −6234.92 + 3232.33i −0.298173 + 0.154580i
\(760\) 9510.81 + 1253.09i 0.453939 + 0.0598081i
\(761\) −10670.3 −0.508276 −0.254138 0.967168i \(-0.581792\pi\)
−0.254138 + 0.967168i \(0.581792\pi\)
\(762\) 15466.0 + 15466.0i 0.735269 + 0.735269i
\(763\) 13505.1 13505.1i 0.640781 0.640781i
\(764\) −12065.6 −0.571360
\(765\) 1622.68 12316.0i 0.0766903 0.582072i
\(766\) 9605.99i 0.453105i
\(767\) −26776.3 26776.3i −1.26054 1.26054i
\(768\) 1289.03 1289.03i 0.0605647 0.0605647i
\(769\) −10059.6 −0.471725 −0.235863 0.971786i \(-0.575792\pi\)
−0.235863 + 0.971786i \(0.575792\pi\)
\(770\) 2500.88 1918.60i 0.117046 0.0897941i
\(771\) 3891.17 0.181760
\(772\) −1871.63 1871.63i −0.0872558 0.0872558i
\(773\) 20372.3 + 20372.3i 0.947917 + 0.947917i 0.998709 0.0507921i \(-0.0161746\pi\)
−0.0507921 + 0.998709i \(0.516175\pi\)
\(774\) −6106.84 −0.283599
\(775\) −2623.96 + 9784.97i −0.121620 + 0.453531i
\(776\) 7682.87i 0.355411i
\(777\) 12319.2 + 12319.2i 0.568791 + 0.568791i
\(778\) −7961.20 7961.20i −0.366867 0.366867i
\(779\) 29706.1 1.36628
\(780\) −11968.0 15600.2i −0.549388 0.716124i
\(781\) 6693.86i 0.306690i
\(782\) 3125.68 9855.36i 0.142934 0.450674i
\(783\) 426.060 426.060i 0.0194459 0.0194459i
\(784\) 1511.04i 0.0688338i
\(785\) 23158.3 + 3051.20i 1.05294 + 0.138729i
\(786\) −19047.2 −0.864364
\(787\) −22918.0 + 22918.0i −1.03804 + 1.03804i −0.0387932 + 0.999247i \(0.512351\pi\)
−0.999247 + 0.0387932i \(0.987649\pi\)
\(788\) −8557.40 + 8557.40i −0.386859 + 0.386859i
\(789\) 52650.6 2.37568
\(790\) −3901.22 + 29609.9i −0.175695 + 1.33351i
\(791\) −26626.8 −1.19689
\(792\) −1199.10 + 1199.10i −0.0537982 + 0.0537982i
\(793\) 1767.15 + 1767.15i 0.0791340 + 0.0791340i
\(794\) 1080.46i 0.0482923i
\(795\) 20517.9 + 26744.9i 0.915338 + 1.19314i
\(796\) 14123.7i 0.628896i
\(797\) −13843.6 + 13843.6i −0.615264 + 0.615264i −0.944313 0.329049i \(-0.893272\pi\)
0.329049 + 0.944313i \(0.393272\pi\)
\(798\) 17028.5 17028.5i 0.755393 0.755393i
\(799\) −9748.23 −0.431624
\(800\) −3464.50 + 1999.31i −0.153111 + 0.0883579i
\(801\) 8501.40i 0.375009i
\(802\) 16569.7 16569.7i 0.729547 0.729547i
\(803\) 1277.25 + 1277.25i 0.0561308 + 0.0561308i
\(804\) 12776.8 0.560449
\(805\) −8248.43 + 17606.6i −0.361142 + 0.770871i
\(806\) −10007.8 −0.437356
\(807\) −39107.9 39107.9i −1.70590 1.70590i
\(808\) 5832.33 5832.33i 0.253937 0.253937i
\(809\) 13373.0i 0.581174i 0.956849 + 0.290587i \(0.0938506\pi\)
−0.956849 + 0.290587i \(0.906149\pi\)
\(810\) −2357.29 + 17891.7i −0.102255 + 0.776110i
\(811\) −21869.8 −0.946920 −0.473460 0.880815i \(-0.656995\pi\)
−0.473460 + 0.880815i \(0.656995\pi\)
\(812\) 1146.05 1146.05i 0.0495299 0.0495299i
\(813\) −37590.1 + 37590.1i −1.62158 + 1.62158i
\(814\) 2775.04i 0.119490i
\(815\) −7879.30 1038.13i −0.338650 0.0446184i
\(816\) 5339.74i 0.229079i
\(817\) −9767.72 9767.72i −0.418273 0.418273i
\(818\) −19702.5 + 19702.5i −0.842155 + 0.842155i
\(819\) −23077.2 −0.984592
\(820\) −9827.68 + 7539.49i −0.418534 + 0.321086i
\(821\) −19840.0 −0.843385 −0.421693 0.906739i \(-0.638564\pi\)
−0.421693 + 0.906739i \(0.638564\pi\)
\(822\) −21014.6 + 21014.6i −0.891689 + 0.891689i
\(823\) 29859.6 29859.6i 1.26469 1.26469i 0.315897 0.948794i \(-0.397695\pi\)
0.948794 0.315897i \(-0.102305\pi\)
\(824\) 11507.8 0.486523
\(825\) 6893.18 3977.95i 0.290897 0.167872i
\(826\) 19339.0i 0.814635i
\(827\) −32427.4 + 32427.4i −1.36349 + 1.36349i −0.494074 + 0.869420i \(0.664493\pi\)
−0.869420 + 0.494074i \(0.835507\pi\)
\(828\) 3162.28 9970.75i 0.132725 0.418487i
\(829\) 24497.6i 1.02634i 0.858286 + 0.513171i \(0.171529\pi\)
−0.858286 + 0.513171i \(0.828471\pi\)
\(830\) −758.489 + 581.889i −0.0317199 + 0.0243345i
\(831\) −13119.3 −0.547659
\(832\) −2794.11 2794.11i −0.116428 0.116428i
\(833\) −3129.71 3129.71i −0.130178 0.130178i
\(834\) 17418.3i 0.723198i
\(835\) −1250.93 + 9494.42i −0.0518444 + 0.393494i
\(836\) −3835.85 −0.158691
\(837\) 1343.56 + 1343.56i 0.0554843 + 0.0554843i
\(838\) −1131.12 1131.12i −0.0466275 0.0466275i
\(839\) −26598.5 −1.09449 −0.547247 0.836971i \(-0.684324\pi\)
−0.547247 + 0.836971i \(0.684324\pi\)
\(840\) −1311.67 + 9955.43i −0.0538771 + 0.408923i
\(841\) 23728.5 0.972918
\(842\) −23101.0 + 23101.0i −0.945503 + 0.945503i
\(843\) −39599.5 39599.5i −1.61789 1.61789i
\(844\) 4149.06i 0.169214i
\(845\) −14326.4 + 10990.7i −0.583245 + 0.447447i
\(846\) −9862.36 −0.400798
\(847\) 13946.9 13946.9i 0.565786 0.565786i
\(848\) 4790.21 + 4790.21i 0.193982 + 0.193982i
\(849\) −9336.65 −0.377424
\(850\) −3034.74 + 11316.8i −0.122460 + 0.456662i
\(851\) 7878.31 + 15196.7i 0.317350 + 0.612144i
\(852\) −15078.8 15078.8i −0.606326 0.606326i
\(853\) 34394.3 34394.3i 1.38058 1.38058i 0.537003 0.843580i \(-0.319556\pi\)
0.843580 0.537003i \(-0.180444\pi\)
\(854\) 1276.31i 0.0511409i
\(855\) 22555.5 17303.9i 0.902202 0.692141i
\(856\) 10220.4i 0.408090i
\(857\) −537.863 537.863i −0.0214388 0.0214388i 0.696306 0.717745i \(-0.254826\pi\)
−0.717745 + 0.696306i \(0.754826\pi\)
\(858\) 5559.33 + 5559.33i 0.221203 + 0.221203i
\(859\) 42120.1i 1.67301i −0.547957 0.836507i \(-0.684594\pi\)
0.547957 0.836507i \(-0.315406\pi\)
\(860\) 5710.53 + 752.384i 0.226427 + 0.0298326i
\(861\) 31094.9i 1.23079i
\(862\) −9614.51 + 9614.51i −0.379897 + 0.379897i
\(863\) −4664.16 + 4664.16i −0.183974 + 0.183974i −0.793085 0.609111i \(-0.791526\pi\)
0.609111 + 0.793085i \(0.291526\pi\)
\(864\) 750.230i 0.0295409i
\(865\) −24308.3 3202.71i −0.955499 0.125891i
\(866\) 7987.42i 0.313422i
\(867\) 13678.4 + 13678.4i 0.535805 + 0.535805i
\(868\) 3614.01 + 3614.01i 0.141322 + 0.141322i
\(869\) 11942.1i 0.466178i
\(870\) 3246.85 2490.88i 0.126527 0.0970677i
\(871\) 27695.1i 1.07740i
\(872\) 6852.84 6852.84i 0.266131 0.266131i
\(873\) −16099.3 16099.3i −0.624145 0.624145i
\(874\) 21005.9 10890.0i 0.812969 0.421462i
\(875\) 8437.88 20353.6i 0.326003 0.786376i
\(876\) −5754.32 −0.221941
\(877\) 1732.23 + 1732.23i 0.0666968 + 0.0666968i 0.739668 0.672972i \(-0.234982\pi\)
−0.672972 + 0.739668i \(0.734982\pi\)
\(878\) 8447.16 8447.16i 0.324690 0.324690i
\(879\) −48114.5 −1.84626
\(880\) 1269.02 973.550i 0.0486120 0.0372936i
\(881\) 20113.1i 0.769157i −0.923092 0.384579i \(-0.874347\pi\)
0.923092 0.384579i \(-0.125653\pi\)
\(882\) −3166.35 3166.35i −0.120880 0.120880i
\(883\) −8519.50 + 8519.50i −0.324693 + 0.324693i −0.850564 0.525871i \(-0.823739\pi\)
0.525871 + 0.850564i \(0.323739\pi\)
\(884\) −11574.5 −0.440375
\(885\) −6378.31 + 48410.8i −0.242265 + 1.83877i
\(886\) −10318.6 −0.391264
\(887\) −11579.2 11579.2i −0.438322 0.438322i 0.453125 0.891447i \(-0.350309\pi\)
−0.891447 + 0.453125i \(0.850309\pi\)
\(888\) 6251.13 + 6251.13i 0.236232 + 0.236232i
\(889\) −24212.7 −0.913462
\(890\) −1047.40 + 7949.69i −0.0394483 + 0.299409i
\(891\) 7215.98i 0.271318i
\(892\) −14044.2 14044.2i −0.527167 0.527167i
\(893\) −15774.6 15774.6i −0.591126 0.591126i
\(894\) 45169.0 1.68980
\(895\) −3499.07 + 2684.38i −0.130683 + 0.100256i
\(896\) 2018.02i 0.0752426i
\(897\) −46226.9 14661.1i −1.72070 0.545730i
\(898\) 8644.51 8644.51i 0.321237 0.321237i
\(899\) 2082.91i 0.0772735i
\(900\) −3070.27 + 11449.3i −0.113714 + 0.424048i
\(901\) 19843.3 0.733712
\(902\) 3502.22 3502.22i 0.129281 0.129281i
\(903\) 10224.4 10224.4i 0.376794 0.376794i
\(904\) −13511.2 −0.497096
\(905\) 5177.15 3971.75i 0.190160 0.145884i
\(906\) 3423.42 0.125536
\(907\) −2613.75 + 2613.75i −0.0956869 + 0.0956869i −0.753330 0.657643i \(-0.771554\pi\)
0.657643 + 0.753330i \(0.271554\pi\)
\(908\) −13147.3 13147.3i −0.480515 0.480515i
\(909\) 24443.1i 0.891887i
\(910\) 21579.5 + 2843.18i 0.786104 + 0.103572i
\(911\) 30173.3i 1.09735i 0.836036 + 0.548675i \(0.184867\pi\)
−0.836036 + 0.548675i \(0.815133\pi\)
\(912\) 8640.75 8640.75i 0.313732 0.313732i
\(913\) 270.297 270.297i 0.00979796 0.00979796i
\(914\) −1773.01 −0.0641640
\(915\) 420.947 3194.95i 0.0152088 0.115434i
\(916\) 26102.3i 0.941534i
\(917\) 14909.6 14909.6i 0.536921 0.536921i
\(918\) 1553.90 + 1553.90i 0.0558674 + 0.0558674i
\(919\) −26983.4 −0.968553 −0.484276 0.874915i \(-0.660917\pi\)
−0.484276 + 0.874915i \(0.660917\pi\)
\(920\) −4185.49 + 8934.08i −0.149991 + 0.320161i
\(921\) 23163.6 0.828739
\(922\) −1012.48 1012.48i −0.0361650 0.0361650i
\(923\) −32684.9 + 32684.9i −1.16559 + 1.16559i
\(924\) 4015.18i 0.142954i
\(925\) −9695.65 16801.1i −0.344639 0.597207i
\(926\) −4037.27 −0.143275
\(927\) 24114.4 24114.4i 0.854393 0.854393i
\(928\) 581.535 581.535i 0.0205709 0.0205709i
\(929\) 42125.9i 1.48774i −0.668327 0.743868i \(-0.732989\pi\)
0.668327 0.743868i \(-0.267011\pi\)
\(930\) 7854.91 + 10238.8i 0.276960 + 0.361016i
\(931\) 10129.0i 0.356567i
\(932\) −8290.32 8290.32i −0.291372 0.291372i
\(933\) −50561.2 + 50561.2i −1.77417 + 1.77417i
\(934\) −18282.3 −0.640488
\(935\) 611.979 4644.87i 0.0214052 0.162464i
\(936\) −11710.0 −0.408924
\(937\) −14100.5 + 14100.5i −0.491616 + 0.491616i −0.908815 0.417199i \(-0.863012\pi\)
0.417199 + 0.908815i \(0.363012\pi\)
\(938\) −10001.3 + 10001.3i −0.348137 + 0.348137i
\(939\) 6385.52 0.221921
\(940\) 9222.33 + 1215.08i 0.319999 + 0.0421611i
\(941\) 20561.8i 0.712324i −0.934424 0.356162i \(-0.884085\pi\)
0.934424 0.356162i \(-0.115915\pi\)
\(942\) 21039.8 21039.8i 0.727721 0.727721i
\(943\) −9236.08 + 29121.6i −0.318948 + 1.00565i
\(944\) 9813.13i 0.338337i
\(945\) −2515.39 3278.80i −0.0865881 0.112867i
\(946\) −2303.14 −0.0791561
\(947\) 31271.9 + 31271.9i 1.07307 + 1.07307i 0.997111 + 0.0759641i \(0.0242034\pi\)
0.0759641 + 0.997111i \(0.475797\pi\)
\(948\) 26901.2 + 26901.2i 0.921634 + 0.921634i
\(949\) 12473.1i 0.426654i
\(950\) −23223.6 + 13402.0i −0.793131 + 0.457704i
\(951\) 78837.7 2.68821
\(952\) 4179.78 + 4179.78i 0.142298 + 0.142298i
\(953\) −37454.1 37454.1i −1.27309 1.27309i −0.944456 0.328638i \(-0.893410\pi\)
−0.328638 0.944456i \(-0.606590\pi\)
\(954\) 20075.6 0.681311
\(955\) 26757.5 20527.5i 0.906650 0.695554i
\(956\) 249.722 0.00844831
\(957\) −1157.06 + 1157.06i −0.0390830 + 0.0390830i
\(958\) 19122.4 + 19122.4i 0.644902 + 0.644902i
\(959\) 32899.2i 1.10779i
\(960\) −665.576 + 5051.66i −0.0223764 + 0.169835i
\(961\) −23222.6 −0.779518
\(962\) 13550.0 13550.0i 0.454127 0.454127i
\(963\) −21416.6 21416.6i −0.716656 0.716656i
\(964\) −11795.7 −0.394102
\(965\) 7334.88 + 966.399i 0.244682 + 0.0322378i
\(966\) 11399.1 + 21987.9i 0.379667 + 0.732349i
\(967\) −24154.7 24154.7i −0.803272 0.803272i 0.180334 0.983605i \(-0.442282\pi\)
−0.983605 + 0.180334i \(0.942282\pi\)
\(968\) 7077.04 7077.04i 0.234984 0.234984i
\(969\) 35793.9i 1.18665i
\(970\) 13071.0 + 17038.0i 0.432665 + 0.563976i
\(971\) 29666.4i 0.980473i 0.871589 + 0.490237i \(0.163090\pi\)
−0.871589 + 0.490237i \(0.836910\pi\)
\(972\) 14464.5 + 14464.5i 0.477313 + 0.477313i
\(973\) −13634.5 13634.5i −0.449232 0.449232i
\(974\) 35614.8i 1.17163i
\(975\) 53081.8 + 14234.6i 1.74357 + 0.467560i
\(976\) 647.634i 0.0212400i
\(977\) −10267.1 + 10267.1i −0.336207 + 0.336207i −0.854938 0.518731i \(-0.826405\pi\)
0.518731 + 0.854938i \(0.326405\pi\)
\(978\) −7158.49 + 7158.49i −0.234052 + 0.234052i
\(979\) 3206.23i 0.104670i
\(980\) 2570.76 + 3350.97i 0.0837958 + 0.109227i
\(981\) 28720.0i 0.934718i
\(982\) −17617.0 17617.0i −0.572486 0.572486i
\(983\) −15831.6 15831.6i −0.513681 0.513681i 0.401971 0.915652i \(-0.368325\pi\)
−0.915652 + 0.401971i \(0.868325\pi\)
\(984\) 15778.4i 0.511176i
\(985\) 4418.53 33536.3i 0.142930 1.08483i
\(986\) 2408.99i 0.0778070i
\(987\) 16512.0 16512.0i 0.532506 0.532506i
\(988\) −18729.8 18729.8i −0.603111 0.603111i
\(989\) 12612.5 6538.60i 0.405514 0.210228i
\(990\) 619.144 4699.25i 0.0198765 0.150861i
\(991\) 20195.0 0.647342 0.323671 0.946170i \(-0.395083\pi\)
0.323671 + 0.946170i \(0.395083\pi\)
\(992\) 1833.85 + 1833.85i 0.0586944 + 0.0586944i
\(993\) −48310.1 + 48310.1i −1.54388 + 1.54388i
\(994\) 23606.4 0.753269
\(995\) −24028.9 31321.5i −0.765596 0.997949i
\(996\) 1217.76i 0.0387411i
\(997\) −6704.33 6704.33i −0.212967 0.212967i 0.592560 0.805527i \(-0.298117\pi\)
−0.805527 + 0.592560i \(0.798117\pi\)
\(998\) 25243.6 25243.6i 0.800675 0.800675i
\(999\) −3638.24 −0.115224
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 230.4.e.a.137.15 72
5.3 odd 4 inner 230.4.e.a.183.16 yes 72
23.22 odd 2 inner 230.4.e.a.137.16 yes 72
115.68 even 4 inner 230.4.e.a.183.15 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.4.e.a.137.15 72 1.1 even 1 trivial
230.4.e.a.137.16 yes 72 23.22 odd 2 inner
230.4.e.a.183.15 yes 72 115.68 even 4 inner
230.4.e.a.183.16 yes 72 5.3 odd 4 inner