Properties

Label 156.3.f.a.79.20
Level $156$
Weight $3$
Character 156.79
Analytic conductor $4.251$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [156,3,Mod(79,156)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(156, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("156.79");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 156.f (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.25069212402\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 79.20
Character \(\chi\) \(=\) 156.79
Dual form 156.3.f.a.79.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.69411 + 1.06301i) q^{2} -1.73205i q^{3} +(1.74001 + 3.60171i) q^{4} +5.51671 q^{5} +(1.84119 - 2.93428i) q^{6} -1.01261i q^{7} +(-0.880886 + 7.95135i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(1.69411 + 1.06301i) q^{2} -1.73205i q^{3} +(1.74001 + 3.60171i) q^{4} +5.51671 q^{5} +(1.84119 - 2.93428i) q^{6} -1.01261i q^{7} +(-0.880886 + 7.95135i) q^{8} -3.00000 q^{9} +(9.34592 + 5.86433i) q^{10} -5.63101i q^{11} +(6.23835 - 3.01379i) q^{12} +3.60555 q^{13} +(1.07642 - 1.71548i) q^{14} -9.55523i q^{15} +(-9.94470 + 12.5341i) q^{16} +8.22149 q^{17} +(-5.08233 - 3.18903i) q^{18} +11.5444i q^{19} +(9.59916 + 19.8696i) q^{20} -1.75390 q^{21} +(5.98583 - 9.53955i) q^{22} +5.25666i q^{23} +(13.7722 + 1.52574i) q^{24} +5.43413 q^{25} +(6.10820 + 3.83274i) q^{26} +5.19615i q^{27} +(3.64714 - 1.76196i) q^{28} -48.7699 q^{29} +(10.1573 - 16.1876i) q^{30} -59.3391i q^{31} +(-30.1713 + 10.6628i) q^{32} -9.75320 q^{33} +(13.9281 + 8.73953i) q^{34} -5.58630i q^{35} +(-5.22004 - 10.8051i) q^{36} -19.4001 q^{37} +(-12.2718 + 19.5575i) q^{38} -6.24500i q^{39} +(-4.85960 + 43.8653i) q^{40} -65.6042 q^{41} +(-2.97129 - 1.86441i) q^{42} -14.0189i q^{43} +(20.2813 - 9.79804i) q^{44} -16.5501 q^{45} +(-5.58788 + 8.90535i) q^{46} +9.34635i q^{47} +(21.7097 + 17.2247i) q^{48} +47.9746 q^{49} +(9.20601 + 5.77654i) q^{50} -14.2400i q^{51} +(6.27371 + 12.9862i) q^{52} -25.9791 q^{53} +(-5.52357 + 8.80285i) q^{54} -31.0647i q^{55} +(8.05165 + 0.891997i) q^{56} +19.9955 q^{57} +(-82.6216 - 51.8429i) q^{58} +38.4414i q^{59} +(34.4152 - 16.6262i) q^{60} +72.1566 q^{61} +(63.0781 - 100.527i) q^{62} +3.03784i q^{63} +(-62.4481 - 14.0085i) q^{64} +19.8908 q^{65} +(-16.5230 - 10.3678i) q^{66} -101.440i q^{67} +(14.3055 + 29.6115i) q^{68} +9.10480 q^{69} +(5.93829 - 9.46380i) q^{70} +80.3131i q^{71} +(2.64266 - 23.8541i) q^{72} +5.60676 q^{73} +(-32.8659 - 20.6225i) q^{74} -9.41219i q^{75} +(-41.5797 + 20.0875i) q^{76} -5.70204 q^{77} +(6.63850 - 10.5797i) q^{78} +28.5754i q^{79} +(-54.8620 + 69.1469i) q^{80} +9.00000 q^{81} +(-111.141 - 69.7380i) q^{82} +103.937i q^{83} +(-3.05181 - 6.31704i) q^{84} +45.3556 q^{85} +(14.9022 - 23.7495i) q^{86} +84.4720i q^{87} +(44.7742 + 4.96028i) q^{88} +69.8749 q^{89} +(-28.0378 - 17.5930i) q^{90} -3.65103i q^{91} +(-18.9330 + 9.14666i) q^{92} -102.778 q^{93} +(-9.93528 + 15.8337i) q^{94} +63.6872i q^{95} +(18.4685 + 52.2582i) q^{96} -27.6984 q^{97} +(81.2743 + 50.9975i) q^{98} +16.8930i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{2} + 8 q^{4} - 12 q^{6} - 32 q^{8} - 72 q^{9} - 12 q^{10} + 12 q^{12} + 32 q^{14} + 4 q^{16} - 12 q^{18} + 84 q^{20} + 28 q^{22} - 36 q^{24} + 104 q^{25} - 96 q^{28} + 64 q^{29} - 12 q^{30} + 44 q^{32} + 48 q^{33} + 40 q^{34} - 24 q^{36} - 192 q^{37} - 104 q^{38} + 220 q^{40} - 220 q^{44} - 104 q^{46} - 144 q^{48} - 248 q^{49} + 100 q^{50} - 52 q^{52} + 336 q^{53} + 36 q^{54} + 168 q^{56} - 16 q^{58} + 60 q^{60} + 16 q^{61} + 152 q^{62} - 16 q^{64} - 132 q^{66} + 400 q^{68} - 192 q^{69} + 208 q^{70} + 96 q^{72} + 112 q^{73} - 104 q^{74} - 264 q^{76} - 272 q^{77} - 300 q^{80} + 216 q^{81} - 4 q^{82} + 96 q^{84} + 64 q^{85} + 288 q^{86} - 492 q^{88} + 36 q^{90} + 328 q^{92} - 96 q^{93} - 884 q^{94} + 72 q^{96} - 80 q^{97} - 572 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(79\) \(145\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.69411 + 1.06301i 0.847055 + 0.531506i
\(3\) 1.73205i 0.577350i
\(4\) 1.74001 + 3.60171i 0.435004 + 0.900429i
\(5\) 5.51671 1.10334 0.551671 0.834062i \(-0.313990\pi\)
0.551671 + 0.834062i \(0.313990\pi\)
\(6\) 1.84119 2.93428i 0.306865 0.489047i
\(7\) 1.01261i 0.144659i −0.997381 0.0723295i \(-0.976957\pi\)
0.997381 0.0723295i \(-0.0230433\pi\)
\(8\) −0.880886 + 7.95135i −0.110111 + 0.993919i
\(9\) −3.00000 −0.333333
\(10\) 9.34592 + 5.86433i 0.934592 + 0.586433i
\(11\) 5.63101i 0.511910i −0.966689 0.255955i \(-0.917610\pi\)
0.966689 0.255955i \(-0.0823899\pi\)
\(12\) 6.23835 3.01379i 0.519863 0.251150i
\(13\) 3.60555 0.277350
\(14\) 1.07642 1.71548i 0.0768871 0.122534i
\(15\) 9.55523i 0.637015i
\(16\) −9.94470 + 12.5341i −0.621543 + 0.783380i
\(17\) 8.22149 0.483617 0.241808 0.970324i \(-0.422259\pi\)
0.241808 + 0.970324i \(0.422259\pi\)
\(18\) −5.08233 3.18903i −0.282352 0.177169i
\(19\) 11.5444i 0.607601i 0.952736 + 0.303800i \(0.0982556\pi\)
−0.952736 + 0.303800i \(0.901744\pi\)
\(20\) 9.59916 + 19.8696i 0.479958 + 0.993481i
\(21\) −1.75390 −0.0835189
\(22\) 5.98583 9.53955i 0.272083 0.433616i
\(23\) 5.25666i 0.228550i 0.993449 + 0.114275i \(0.0364545\pi\)
−0.993449 + 0.114275i \(0.963545\pi\)
\(24\) 13.7722 + 1.52574i 0.573840 + 0.0635725i
\(25\) 5.43413 0.217365
\(26\) 6.10820 + 3.83274i 0.234931 + 0.147413i
\(27\) 5.19615i 0.192450i
\(28\) 3.64714 1.76196i 0.130255 0.0629272i
\(29\) −48.7699 −1.68172 −0.840860 0.541252i \(-0.817951\pi\)
−0.840860 + 0.541252i \(0.817951\pi\)
\(30\) 10.1573 16.1876i 0.338577 0.539587i
\(31\) 59.3391i 1.91417i −0.289815 0.957083i \(-0.593594\pi\)
0.289815 0.957083i \(-0.406406\pi\)
\(32\) −30.1713 + 10.6628i −0.942852 + 0.333212i
\(33\) −9.75320 −0.295551
\(34\) 13.9281 + 8.73953i 0.409650 + 0.257045i
\(35\) 5.58630i 0.159608i
\(36\) −5.22004 10.8051i −0.145001 0.300143i
\(37\) −19.4001 −0.524327 −0.262164 0.965023i \(-0.584436\pi\)
−0.262164 + 0.965023i \(0.584436\pi\)
\(38\) −12.2718 + 19.5575i −0.322943 + 0.514671i
\(39\) 6.24500i 0.160128i
\(40\) −4.85960 + 43.8653i −0.121490 + 1.09663i
\(41\) −65.6042 −1.60010 −0.800052 0.599931i \(-0.795195\pi\)
−0.800052 + 0.599931i \(0.795195\pi\)
\(42\) −2.97129 1.86441i −0.0707451 0.0443908i
\(43\) 14.0189i 0.326021i −0.986624 0.163010i \(-0.947880\pi\)
0.986624 0.163010i \(-0.0521204\pi\)
\(44\) 20.2813 9.79804i 0.460939 0.222683i
\(45\) −16.5501 −0.367781
\(46\) −5.58788 + 8.90535i −0.121476 + 0.193595i
\(47\) 9.34635i 0.198859i 0.995045 + 0.0994293i \(0.0317017\pi\)
−0.995045 + 0.0994293i \(0.968298\pi\)
\(48\) 21.7097 + 17.2247i 0.452284 + 0.358848i
\(49\) 47.9746 0.979074
\(50\) 9.20601 + 5.77654i 0.184120 + 0.115531i
\(51\) 14.2400i 0.279216i
\(52\) 6.27371 + 12.9862i 0.120648 + 0.249734i
\(53\) −25.9791 −0.490172 −0.245086 0.969501i \(-0.578816\pi\)
−0.245086 + 0.969501i \(0.578816\pi\)
\(54\) −5.52357 + 8.80285i −0.102288 + 0.163016i
\(55\) 31.0647i 0.564812i
\(56\) 8.05165 + 0.891997i 0.143779 + 0.0159285i
\(57\) 19.9955 0.350798
\(58\) −82.6216 51.8429i −1.42451 0.893844i
\(59\) 38.4414i 0.651548i 0.945448 + 0.325774i \(0.105625\pi\)
−0.945448 + 0.325774i \(0.894375\pi\)
\(60\) 34.4152 16.6262i 0.573587 0.277104i
\(61\) 72.1566 1.18289 0.591447 0.806344i \(-0.298557\pi\)
0.591447 + 0.806344i \(0.298557\pi\)
\(62\) 63.0781 100.527i 1.01739 1.62140i
\(63\) 3.03784i 0.0482197i
\(64\) −62.4481 14.0085i −0.975751 0.218882i
\(65\) 19.8908 0.306012
\(66\) −16.5230 10.3678i −0.250348 0.157087i
\(67\) 101.440i 1.51403i −0.653399 0.757013i \(-0.726658\pi\)
0.653399 0.757013i \(-0.273342\pi\)
\(68\) 14.3055 + 29.6115i 0.210375 + 0.435463i
\(69\) 9.10480 0.131954
\(70\) 5.93829 9.46380i 0.0848328 0.135197i
\(71\) 80.3131i 1.13117i 0.824690 + 0.565585i \(0.191350\pi\)
−0.824690 + 0.565585i \(0.808650\pi\)
\(72\) 2.64266 23.8541i 0.0367036 0.331306i
\(73\) 5.60676 0.0768049 0.0384025 0.999262i \(-0.487773\pi\)
0.0384025 + 0.999262i \(0.487773\pi\)
\(74\) −32.8659 20.6225i −0.444134 0.278683i
\(75\) 9.41219i 0.125496i
\(76\) −41.5797 + 20.0875i −0.547101 + 0.264309i
\(77\) −5.70204 −0.0740524
\(78\) 6.63850 10.5797i 0.0851090 0.135637i
\(79\) 28.5754i 0.361715i 0.983509 + 0.180857i \(0.0578872\pi\)
−0.983509 + 0.180857i \(0.942113\pi\)
\(80\) −54.8620 + 69.1469i −0.685775 + 0.864336i
\(81\) 9.00000 0.111111
\(82\) −111.141 69.7380i −1.35538 0.850464i
\(83\) 103.937i 1.25226i 0.779720 + 0.626128i \(0.215361\pi\)
−0.779720 + 0.626128i \(0.784639\pi\)
\(84\) −3.05181 6.31704i −0.0363310 0.0752028i
\(85\) 45.3556 0.533595
\(86\) 14.9022 23.7495i 0.173282 0.276157i
\(87\) 84.4720i 0.970942i
\(88\) 44.7742 + 4.96028i 0.508797 + 0.0563668i
\(89\) 69.8749 0.785111 0.392555 0.919728i \(-0.371591\pi\)
0.392555 + 0.919728i \(0.371591\pi\)
\(90\) −28.0378 17.5930i −0.311531 0.195478i
\(91\) 3.65103i 0.0401212i
\(92\) −18.9330 + 9.14666i −0.205793 + 0.0994202i
\(93\) −102.778 −1.10514
\(94\) −9.93528 + 15.8337i −0.105694 + 0.168444i
\(95\) 63.6872i 0.670392i
\(96\) 18.4685 + 52.2582i 0.192380 + 0.544356i
\(97\) −27.6984 −0.285550 −0.142775 0.989755i \(-0.545603\pi\)
−0.142775 + 0.989755i \(0.545603\pi\)
\(98\) 81.2743 + 50.9975i 0.829329 + 0.520383i
\(99\) 16.8930i 0.170637i
\(100\) 9.45547 + 19.5722i 0.0945547 + 0.195722i
\(101\) −39.6436 −0.392511 −0.196255 0.980553i \(-0.562878\pi\)
−0.196255 + 0.980553i \(0.562878\pi\)
\(102\) 15.1373 24.1242i 0.148405 0.236512i
\(103\) 80.8239i 0.784698i 0.919816 + 0.392349i \(0.128338\pi\)
−0.919816 + 0.392349i \(0.871662\pi\)
\(104\) −3.17608 + 28.6690i −0.0305392 + 0.275664i
\(105\) −9.67575 −0.0921500
\(106\) −44.0114 27.6161i −0.415202 0.260529i
\(107\) 97.0127i 0.906661i −0.891342 0.453331i \(-0.850236\pi\)
0.891342 0.453331i \(-0.149764\pi\)
\(108\) −18.7151 + 9.04138i −0.173288 + 0.0837165i
\(109\) 211.083 1.93654 0.968271 0.249904i \(-0.0803992\pi\)
0.968271 + 0.249904i \(0.0803992\pi\)
\(110\) 33.0221 52.6270i 0.300201 0.478427i
\(111\) 33.6020i 0.302721i
\(112\) 12.6922 + 10.0701i 0.113323 + 0.0899119i
\(113\) 68.4234 0.605517 0.302759 0.953067i \(-0.402092\pi\)
0.302759 + 0.953067i \(0.402092\pi\)
\(114\) 33.8746 + 21.2555i 0.297146 + 0.186451i
\(115\) 28.9995i 0.252169i
\(116\) −84.8604 175.655i −0.731555 1.51427i
\(117\) −10.8167 −0.0924500
\(118\) −40.8636 + 65.1239i −0.346302 + 0.551897i
\(119\) 8.32519i 0.0699596i
\(120\) 75.9770 + 8.41707i 0.633142 + 0.0701422i
\(121\) 89.2917 0.737948
\(122\) 122.241 + 76.7032i 1.00198 + 0.628715i
\(123\) 113.630i 0.923820i
\(124\) 213.723 103.251i 1.72357 0.832669i
\(125\) −107.939 −0.863514
\(126\) −3.22926 + 5.14643i −0.0256290 + 0.0408447i
\(127\) 47.0102i 0.370159i 0.982724 + 0.185080i \(0.0592543\pi\)
−0.982724 + 0.185080i \(0.940746\pi\)
\(128\) −90.9027 90.1149i −0.710178 0.704023i
\(129\) −24.2814 −0.188228
\(130\) 33.6972 + 21.1441i 0.259209 + 0.162647i
\(131\) 85.1555i 0.650042i −0.945707 0.325021i \(-0.894629\pi\)
0.945707 0.325021i \(-0.105371\pi\)
\(132\) −16.9707 35.1282i −0.128566 0.266123i
\(133\) 11.6900 0.0878949
\(134\) 107.832 171.850i 0.804714 1.28246i
\(135\) 28.6657i 0.212338i
\(136\) −7.24220 + 65.3720i −0.0532514 + 0.480676i
\(137\) 199.295 1.45471 0.727354 0.686263i \(-0.240750\pi\)
0.727354 + 0.686263i \(0.240750\pi\)
\(138\) 15.4245 + 9.67850i 0.111772 + 0.0701341i
\(139\) 68.3395i 0.491651i −0.969314 0.245825i \(-0.920941\pi\)
0.969314 0.245825i \(-0.0790590\pi\)
\(140\) 20.1202 9.72024i 0.143716 0.0694303i
\(141\) 16.1884 0.114811
\(142\) −85.3737 + 136.059i −0.601223 + 0.958163i
\(143\) 20.3029i 0.141978i
\(144\) 29.8341 37.6022i 0.207181 0.261127i
\(145\) −269.050 −1.85551
\(146\) 9.49847 + 5.96005i 0.0650580 + 0.0408223i
\(147\) 83.0945i 0.565269i
\(148\) −33.7565 69.8737i −0.228084 0.472119i
\(149\) 158.760 1.06550 0.532751 0.846272i \(-0.321158\pi\)
0.532751 + 0.846272i \(0.321158\pi\)
\(150\) 10.0053 15.9453i 0.0667017 0.106302i
\(151\) 262.554i 1.73877i 0.494135 + 0.869385i \(0.335485\pi\)
−0.494135 + 0.869385i \(0.664515\pi\)
\(152\) −91.7937 10.1693i −0.603906 0.0669034i
\(153\) −24.6645 −0.161206
\(154\) −9.65987 6.06133i −0.0627265 0.0393593i
\(155\) 327.357i 2.11198i
\(156\) 22.4927 10.8664i 0.144184 0.0696563i
\(157\) 112.088 0.713935 0.356967 0.934117i \(-0.383811\pi\)
0.356967 + 0.934117i \(0.383811\pi\)
\(158\) −30.3760 + 48.4099i −0.192253 + 0.306392i
\(159\) 44.9971i 0.283001i
\(160\) −166.446 + 58.8235i −1.04029 + 0.367647i
\(161\) 5.32296 0.0330619
\(162\) 15.2470 + 9.56710i 0.0941172 + 0.0590562i
\(163\) 7.91246i 0.0485427i 0.999705 + 0.0242714i \(0.00772657\pi\)
−0.999705 + 0.0242714i \(0.992273\pi\)
\(164\) −114.152 236.288i −0.696051 1.44078i
\(165\) −53.8056 −0.326095
\(166\) −110.486 + 176.081i −0.665581 + 1.06073i
\(167\) 244.909i 1.46652i 0.679949 + 0.733260i \(0.262002\pi\)
−0.679949 + 0.733260i \(0.737998\pi\)
\(168\) 1.54498 13.9459i 0.00919633 0.0830111i
\(169\) 13.0000 0.0769231
\(170\) 76.8374 + 48.2135i 0.451984 + 0.283609i
\(171\) 34.6332i 0.202534i
\(172\) 50.4920 24.3931i 0.293558 0.141820i
\(173\) −168.979 −0.976759 −0.488379 0.872631i \(-0.662412\pi\)
−0.488379 + 0.872631i \(0.662412\pi\)
\(174\) −89.7946 + 143.105i −0.516061 + 0.822441i
\(175\) 5.50267i 0.0314438i
\(176\) 70.5795 + 55.9987i 0.401020 + 0.318174i
\(177\) 66.5824 0.376172
\(178\) 118.376 + 74.2778i 0.665032 + 0.417291i
\(179\) 124.469i 0.695355i −0.937614 0.347678i \(-0.886970\pi\)
0.937614 0.347678i \(-0.113030\pi\)
\(180\) −28.7975 59.6089i −0.159986 0.331160i
\(181\) −232.729 −1.28579 −0.642897 0.765952i \(-0.722268\pi\)
−0.642897 + 0.765952i \(0.722268\pi\)
\(182\) 3.88108 6.18524i 0.0213246 0.0339848i
\(183\) 124.979i 0.682944i
\(184\) −41.7975 4.63052i −0.227161 0.0251659i
\(185\) −107.025 −0.578513
\(186\) −174.118 109.255i −0.936117 0.587390i
\(187\) 46.2953i 0.247568i
\(188\) −33.6629 + 16.2628i −0.179058 + 0.0865042i
\(189\) 5.26169 0.0278396
\(190\) −67.7002 + 107.893i −0.356317 + 0.567859i
\(191\) 278.249i 1.45680i −0.685150 0.728402i \(-0.740264\pi\)
0.685150 0.728402i \(-0.259736\pi\)
\(192\) −24.2634 + 108.163i −0.126372 + 0.563350i
\(193\) −6.91306 −0.0358190 −0.0179095 0.999840i \(-0.505701\pi\)
−0.0179095 + 0.999840i \(0.505701\pi\)
\(194\) −46.9241 29.4437i −0.241877 0.151772i
\(195\) 34.4519i 0.176676i
\(196\) 83.4765 + 172.791i 0.425901 + 0.881586i
\(197\) −278.468 −1.41354 −0.706771 0.707443i \(-0.749849\pi\)
−0.706771 + 0.707443i \(0.749849\pi\)
\(198\) −17.9575 + 28.6187i −0.0906944 + 0.144539i
\(199\) 148.075i 0.744097i 0.928213 + 0.372049i \(0.121345\pi\)
−0.928213 + 0.372049i \(0.878655\pi\)
\(200\) −4.78685 + 43.2087i −0.0239343 + 0.216043i
\(201\) −175.699 −0.874124
\(202\) −67.1606 42.1416i −0.332478 0.208622i
\(203\) 49.3850i 0.243276i
\(204\) 51.2885 24.7779i 0.251414 0.121460i
\(205\) −361.920 −1.76546
\(206\) −85.9167 + 136.925i −0.417072 + 0.664683i
\(207\) 15.7700i 0.0761834i
\(208\) −35.8561 + 45.1922i −0.172385 + 0.217270i
\(209\) 65.0067 0.311037
\(210\) −16.3918 10.2854i −0.0780561 0.0489782i
\(211\) 390.419i 1.85033i −0.379568 0.925164i \(-0.623927\pi\)
0.379568 0.925164i \(-0.376073\pi\)
\(212\) −45.2040 93.5693i −0.213227 0.441365i
\(213\) 139.106 0.653081
\(214\) 103.126 164.350i 0.481895 0.767992i
\(215\) 77.3382i 0.359712i
\(216\) −41.3165 4.57722i −0.191280 0.0211908i
\(217\) −60.0876 −0.276901
\(218\) 357.598 + 224.384i 1.64036 + 1.02928i
\(219\) 9.71120i 0.0443434i
\(220\) 111.886 54.0530i 0.508573 0.245695i
\(221\) 29.6430 0.134131
\(222\) −35.7193 + 56.9254i −0.160898 + 0.256421i
\(223\) 317.454i 1.42356i −0.702403 0.711779i \(-0.747890\pi\)
0.702403 0.711779i \(-0.252110\pi\)
\(224\) 10.7973 + 30.5518i 0.0482021 + 0.136392i
\(225\) −16.3024 −0.0724551
\(226\) 115.917 + 72.7349i 0.512906 + 0.321836i
\(227\) 428.142i 1.88609i −0.332668 0.943044i \(-0.607949\pi\)
0.332668 0.943044i \(-0.392051\pi\)
\(228\) 34.7925 + 72.0181i 0.152599 + 0.315869i
\(229\) 409.617 1.78872 0.894361 0.447345i \(-0.147631\pi\)
0.894361 + 0.447345i \(0.147631\pi\)
\(230\) −30.8268 + 49.1283i −0.134029 + 0.213601i
\(231\) 9.87622i 0.0427542i
\(232\) 42.9607 387.787i 0.185176 1.67149i
\(233\) −84.1548 −0.361180 −0.180590 0.983559i \(-0.557801\pi\)
−0.180590 + 0.983559i \(0.557801\pi\)
\(234\) −18.3246 11.4982i −0.0783102 0.0491377i
\(235\) 51.5611i 0.219409i
\(236\) −138.455 + 66.8885i −0.586673 + 0.283426i
\(237\) 49.4941 0.208836
\(238\) 8.84977 14.1038i 0.0371839 0.0592596i
\(239\) 243.858i 1.02033i 0.860078 + 0.510163i \(0.170415\pi\)
−0.860078 + 0.510163i \(0.829585\pi\)
\(240\) 119.766 + 95.0238i 0.499025 + 0.395933i
\(241\) −222.925 −0.925002 −0.462501 0.886619i \(-0.653048\pi\)
−0.462501 + 0.886619i \(0.653048\pi\)
\(242\) 151.270 + 94.9181i 0.625082 + 0.392223i
\(243\) 15.5885i 0.0641500i
\(244\) 125.553 + 259.887i 0.514563 + 1.06511i
\(245\) 264.662 1.08025
\(246\) −120.790 + 192.501i −0.491015 + 0.782526i
\(247\) 41.6240i 0.168518i
\(248\) 471.826 + 52.2710i 1.90253 + 0.210770i
\(249\) 180.025 0.722990
\(250\) −182.861 114.741i −0.731444 0.458963i
\(251\) 441.458i 1.75880i 0.476085 + 0.879399i \(0.342055\pi\)
−0.476085 + 0.879399i \(0.657945\pi\)
\(252\) −10.9414 + 5.28589i −0.0434184 + 0.0209757i
\(253\) 29.6003 0.116997
\(254\) −49.9724 + 79.6405i −0.196742 + 0.313545i
\(255\) 78.5582i 0.308071i
\(256\) −58.2061 249.295i −0.227367 0.973809i
\(257\) −289.124 −1.12500 −0.562498 0.826799i \(-0.690160\pi\)
−0.562498 + 0.826799i \(0.690160\pi\)
\(258\) −41.1354 25.8114i −0.159439 0.100044i
\(259\) 19.6448i 0.0758487i
\(260\) 34.6103 + 71.6410i 0.133116 + 0.275542i
\(261\) 146.310 0.560574
\(262\) 90.5213 144.263i 0.345501 0.550621i
\(263\) 411.852i 1.56598i 0.622037 + 0.782988i \(0.286305\pi\)
−0.622037 + 0.782988i \(0.713695\pi\)
\(264\) 8.59146 77.5511i 0.0325434 0.293754i
\(265\) −143.319 −0.540827
\(266\) 19.8042 + 12.4266i 0.0744518 + 0.0467166i
\(267\) 121.027i 0.453284i
\(268\) 365.357 176.507i 1.36327 0.658607i
\(269\) −17.9467 −0.0667165 −0.0333583 0.999443i \(-0.510620\pi\)
−0.0333583 + 0.999443i \(0.510620\pi\)
\(270\) −30.4719 + 48.5628i −0.112859 + 0.179862i
\(271\) 323.464i 1.19359i 0.802392 + 0.596797i \(0.203560\pi\)
−0.802392 + 0.596797i \(0.796440\pi\)
\(272\) −81.7602 + 103.049i −0.300589 + 0.378856i
\(273\) −6.32377 −0.0231640
\(274\) 337.627 + 211.853i 1.23222 + 0.773185i
\(275\) 30.5997i 0.111271i
\(276\) 15.8425 + 32.7929i 0.0574003 + 0.118815i
\(277\) 179.377 0.647571 0.323786 0.946130i \(-0.395044\pi\)
0.323786 + 0.946130i \(0.395044\pi\)
\(278\) 72.6456 115.775i 0.261315 0.416455i
\(279\) 178.017i 0.638055i
\(280\) 44.4186 + 4.92089i 0.158638 + 0.0175746i
\(281\) 437.349 1.55640 0.778201 0.628016i \(-0.216133\pi\)
0.778201 + 0.628016i \(0.216133\pi\)
\(282\) 27.4249 + 17.2084i 0.0972512 + 0.0610227i
\(283\) 492.934i 1.74182i −0.491447 0.870908i \(-0.663532\pi\)
0.491447 0.870908i \(-0.336468\pi\)
\(284\) −289.265 + 139.746i −1.01854 + 0.492063i
\(285\) 110.310 0.387051
\(286\) 21.5822 34.3953i 0.0754623 0.120263i
\(287\) 66.4317i 0.231469i
\(288\) 90.5138 31.9883i 0.314284 0.111071i
\(289\) −221.407 −0.766115
\(290\) −455.800 286.003i −1.57172 0.986216i
\(291\) 47.9750i 0.164863i
\(292\) 9.75585 + 20.1940i 0.0334104 + 0.0691574i
\(293\) 61.8712 0.211164 0.105582 0.994411i \(-0.466329\pi\)
0.105582 + 0.994411i \(0.466329\pi\)
\(294\) 88.3303 140.771i 0.300443 0.478813i
\(295\) 212.070i 0.718881i
\(296\) 17.0893 154.257i 0.0577341 0.521139i
\(297\) 29.2596 0.0985171
\(298\) 268.956 + 168.763i 0.902538 + 0.566320i
\(299\) 18.9531i 0.0633885i
\(300\) 33.9000 16.3774i 0.113000 0.0545912i
\(301\) −14.1957 −0.0471618
\(302\) −279.098 + 444.796i −0.924166 + 1.47283i
\(303\) 68.6647i 0.226616i
\(304\) −144.699 114.806i −0.475982 0.377650i
\(305\) 398.067 1.30514
\(306\) −41.7843 26.2186i −0.136550 0.0856817i
\(307\) 446.721i 1.45512i 0.686045 + 0.727559i \(0.259345\pi\)
−0.686045 + 0.727559i \(0.740655\pi\)
\(308\) −9.92163 20.5371i −0.0322131 0.0666789i
\(309\) 139.991 0.453046
\(310\) 347.984 554.579i 1.12253 1.78896i
\(311\) 248.932i 0.800423i −0.916423 0.400211i \(-0.868937\pi\)
0.916423 0.400211i \(-0.131063\pi\)
\(312\) 49.6562 + 5.50113i 0.159154 + 0.0176318i
\(313\) −56.7003 −0.181151 −0.0905756 0.995890i \(-0.528871\pi\)
−0.0905756 + 0.995890i \(0.528871\pi\)
\(314\) 189.889 + 119.151i 0.604742 + 0.379460i
\(315\) 16.7589i 0.0532028i
\(316\) −102.921 + 49.7217i −0.325698 + 0.157347i
\(317\) −57.8199 −0.182397 −0.0911986 0.995833i \(-0.529070\pi\)
−0.0911986 + 0.995833i \(0.529070\pi\)
\(318\) −47.8324 + 76.2301i −0.150416 + 0.239717i
\(319\) 274.624i 0.860890i
\(320\) −344.508 77.2808i −1.07659 0.241502i
\(321\) −168.031 −0.523461
\(322\) 9.01768 + 5.65836i 0.0280052 + 0.0175726i
\(323\) 94.9123i 0.293846i
\(324\) 15.6601 + 32.4154i 0.0483337 + 0.100048i
\(325\) 19.5930 0.0602863
\(326\) −8.41103 + 13.4046i −0.0258007 + 0.0411183i
\(327\) 365.606i 1.11806i
\(328\) 57.7899 521.642i 0.176189 1.59037i
\(329\) 9.46424 0.0287667
\(330\) −91.1526 57.1959i −0.276220 0.173321i
\(331\) 49.0850i 0.148293i −0.997247 0.0741465i \(-0.976377\pi\)
0.997247 0.0741465i \(-0.0236232\pi\)
\(332\) −374.352 + 180.852i −1.12757 + 0.544736i
\(333\) 58.2003 0.174776
\(334\) −260.341 + 414.902i −0.779463 + 1.24222i
\(335\) 559.614i 1.67049i
\(336\) 17.4420 21.9835i 0.0519106 0.0654270i
\(337\) −402.253 −1.19363 −0.596815 0.802379i \(-0.703567\pi\)
−0.596815 + 0.802379i \(0.703567\pi\)
\(338\) 22.0234 + 13.8191i 0.0651581 + 0.0408850i
\(339\) 118.513i 0.349596i
\(340\) 78.9194 + 163.358i 0.232116 + 0.480464i
\(341\) −334.139 −0.979881
\(342\) 36.8155 58.6725i 0.107648 0.171557i
\(343\) 98.1978i 0.286291i
\(344\) 111.469 + 12.3490i 0.324038 + 0.0358984i
\(345\) 50.2286 0.145590
\(346\) −286.269 179.627i −0.827368 0.519153i
\(347\) 81.1956i 0.233993i 0.993132 + 0.116997i \(0.0373266\pi\)
−0.993132 + 0.116997i \(0.962673\pi\)
\(348\) −304.244 + 146.982i −0.874264 + 0.422363i
\(349\) 230.981 0.661835 0.330918 0.943660i \(-0.392642\pi\)
0.330918 + 0.943660i \(0.392642\pi\)
\(350\) 5.84940 9.32213i 0.0167126 0.0266347i
\(351\) 18.7350i 0.0533761i
\(352\) 60.0422 + 169.895i 0.170574 + 0.482655i
\(353\) 274.410 0.777366 0.388683 0.921372i \(-0.372930\pi\)
0.388683 + 0.921372i \(0.372930\pi\)
\(354\) 112.798 + 70.7778i 0.318638 + 0.199937i
\(355\) 443.064i 1.24807i
\(356\) 121.583 + 251.669i 0.341526 + 0.706936i
\(357\) −14.4196 −0.0403912
\(358\) 132.311 210.863i 0.369585 0.589004i
\(359\) 537.223i 1.49644i 0.663450 + 0.748221i \(0.269092\pi\)
−0.663450 + 0.748221i \(0.730908\pi\)
\(360\) 14.5788 131.596i 0.0404966 0.365545i
\(361\) 227.726 0.630821
\(362\) −394.268 247.393i −1.08914 0.683407i
\(363\) 154.658i 0.426054i
\(364\) 13.1500 6.35284i 0.0361263 0.0174529i
\(365\) 30.9309 0.0847422
\(366\) 132.854 211.728i 0.362989 0.578491i
\(367\) 567.303i 1.54578i −0.634537 0.772892i \(-0.718809\pi\)
0.634537 0.772892i \(-0.281191\pi\)
\(368\) −65.8873 52.2759i −0.179042 0.142054i
\(369\) 196.813 0.533368
\(370\) −181.312 113.769i −0.490032 0.307483i
\(371\) 26.3068i 0.0709077i
\(372\) −178.836 370.178i −0.480742 0.995103i
\(373\) −511.015 −1.37001 −0.685007 0.728537i \(-0.740201\pi\)
−0.685007 + 0.728537i \(0.740201\pi\)
\(374\) 49.2124 78.4293i 0.131584 0.209704i
\(375\) 186.956i 0.498550i
\(376\) −74.3162 8.23307i −0.197649 0.0218965i
\(377\) −175.842 −0.466425
\(378\) 8.91388 + 5.59324i 0.0235817 + 0.0147969i
\(379\) 245.900i 0.648813i 0.945918 + 0.324406i \(0.105164\pi\)
−0.945918 + 0.324406i \(0.894836\pi\)
\(380\) −229.383 + 110.817i −0.603640 + 0.291623i
\(381\) 81.4241 0.213712
\(382\) 295.782 471.385i 0.774299 1.23399i
\(383\) 277.986i 0.725812i 0.931826 + 0.362906i \(0.118215\pi\)
−0.931826 + 0.362906i \(0.881785\pi\)
\(384\) −156.084 + 157.448i −0.406468 + 0.410021i
\(385\) −31.4565 −0.0817052
\(386\) −11.7115 7.34866i −0.0303406 0.0190380i
\(387\) 42.0566i 0.108674i
\(388\) −48.1956 99.7617i −0.124215 0.257118i
\(389\) 132.554 0.340756 0.170378 0.985379i \(-0.445501\pi\)
0.170378 + 0.985379i \(0.445501\pi\)
\(390\) 36.6227 58.3652i 0.0939044 0.149654i
\(391\) 43.2175i 0.110531i
\(392\) −42.2602 + 381.463i −0.107807 + 0.973120i
\(393\) −147.494 −0.375302
\(394\) −471.755 296.014i −1.19735 0.751305i
\(395\) 157.643i 0.399095i
\(396\) −60.8439 + 29.3941i −0.153646 + 0.0742276i
\(397\) −469.545 −1.18273 −0.591366 0.806403i \(-0.701411\pi\)
−0.591366 + 0.806403i \(0.701411\pi\)
\(398\) −157.406 + 250.856i −0.395492 + 0.630291i
\(399\) 20.2477i 0.0507462i
\(400\) −54.0408 + 68.1118i −0.135102 + 0.170279i
\(401\) 169.002 0.421451 0.210726 0.977545i \(-0.432417\pi\)
0.210726 + 0.977545i \(0.432417\pi\)
\(402\) −297.653 186.770i −0.740431 0.464602i
\(403\) 213.950i 0.530894i
\(404\) −68.9804 142.785i −0.170744 0.353428i
\(405\) 49.6504 0.122594
\(406\) −52.4968 + 83.6637i −0.129303 + 0.206068i
\(407\) 109.242i 0.268409i
\(408\) 113.228 + 12.5439i 0.277519 + 0.0307447i
\(409\) 330.022 0.806900 0.403450 0.915002i \(-0.367811\pi\)
0.403450 + 0.915002i \(0.367811\pi\)
\(410\) −613.132 384.725i −1.49544 0.938353i
\(411\) 345.189i 0.839876i
\(412\) −291.105 + 140.635i −0.706565 + 0.341347i
\(413\) 38.9262 0.0942523
\(414\) 16.7637 26.7161i 0.0404919 0.0645315i
\(415\) 573.392i 1.38167i
\(416\) −108.784 + 38.4452i −0.261500 + 0.0924163i
\(417\) −118.367 −0.283855
\(418\) 110.129 + 69.1029i 0.263465 + 0.165318i
\(419\) 459.934i 1.09769i 0.835923 + 0.548847i \(0.184933\pi\)
−0.835923 + 0.548847i \(0.815067\pi\)
\(420\) −16.8359 34.8493i −0.0400856 0.0829745i
\(421\) −62.9112 −0.149433 −0.0747163 0.997205i \(-0.523805\pi\)
−0.0747163 + 0.997205i \(0.523805\pi\)
\(422\) 415.020 661.413i 0.983460 1.56733i
\(423\) 28.0391i 0.0662862i
\(424\) 22.8846 206.569i 0.0539732 0.487191i
\(425\) 44.6766 0.105122
\(426\) 235.661 + 147.872i 0.553196 + 0.347116i
\(427\) 73.0667i 0.171116i
\(428\) 349.412 168.804i 0.816384 0.394401i
\(429\) −35.1657 −0.0819712
\(430\) 82.2113 131.019i 0.191189 0.304696i
\(431\) 383.771i 0.890421i −0.895426 0.445210i \(-0.853129\pi\)
0.895426 0.445210i \(-0.146871\pi\)
\(432\) −65.1290 51.6742i −0.150761 0.119616i
\(433\) 536.435 1.23888 0.619439 0.785044i \(-0.287360\pi\)
0.619439 + 0.785044i \(0.287360\pi\)
\(434\) −101.795 63.8738i −0.234551 0.147175i
\(435\) 466.008i 1.07128i
\(436\) 367.288 + 760.261i 0.842403 + 1.74372i
\(437\) −60.6850 −0.138867
\(438\) 10.3231 16.4518i 0.0235687 0.0375613i
\(439\) 263.036i 0.599170i 0.954070 + 0.299585i \(0.0968482\pi\)
−0.954070 + 0.299585i \(0.903152\pi\)
\(440\) 247.006 + 27.3644i 0.561378 + 0.0621919i
\(441\) −143.924 −0.326358
\(442\) 50.2185 + 31.5108i 0.113616 + 0.0712915i
\(443\) 696.607i 1.57248i −0.617924 0.786238i \(-0.712026\pi\)
0.617924 0.786238i \(-0.287974\pi\)
\(444\) −121.025 + 58.4680i −0.272578 + 0.131685i
\(445\) 385.480 0.866246
\(446\) 337.457 537.801i 0.756629 1.20583i
\(447\) 274.980i 0.615167i
\(448\) −14.1852 + 63.2357i −0.0316633 + 0.141151i
\(449\) −189.583 −0.422233 −0.211117 0.977461i \(-0.567710\pi\)
−0.211117 + 0.977461i \(0.567710\pi\)
\(450\) −27.6180 17.3296i −0.0613734 0.0385103i
\(451\) 369.418i 0.819109i
\(452\) 119.058 + 246.442i 0.263402 + 0.545225i
\(453\) 454.758 1.00388
\(454\) 455.120 725.319i 1.00247 1.59762i
\(455\) 20.1417i 0.0442674i
\(456\) −17.6138 + 158.991i −0.0386267 + 0.348665i
\(457\) 149.051 0.326150 0.163075 0.986614i \(-0.447859\pi\)
0.163075 + 0.986614i \(0.447859\pi\)
\(458\) 693.937 + 435.428i 1.51515 + 0.950716i
\(459\) 42.7201i 0.0930721i
\(460\) −104.448 + 50.4595i −0.227060 + 0.109695i
\(461\) −34.1785 −0.0741400 −0.0370700 0.999313i \(-0.511802\pi\)
−0.0370700 + 0.999313i \(0.511802\pi\)
\(462\) −10.4985 + 16.7314i −0.0227241 + 0.0362151i
\(463\) 553.129i 1.19466i −0.801994 0.597332i \(-0.796228\pi\)
0.801994 0.597332i \(-0.203772\pi\)
\(464\) 485.002 611.286i 1.04526 1.31743i
\(465\) −566.999 −1.21935
\(466\) −142.568 89.4575i −0.305939 0.191969i
\(467\) 8.93243i 0.0191273i −0.999954 0.00956363i \(-0.996956\pi\)
0.999954 0.00956363i \(-0.00304424\pi\)
\(468\) −18.8211 38.9585i −0.0402161 0.0832447i
\(469\) −102.719 −0.219018
\(470\) −54.8101 + 87.3502i −0.116617 + 0.185852i
\(471\) 194.142i 0.412190i
\(472\) −305.661 33.8625i −0.647587 0.0717425i
\(473\) −78.9405 −0.166893
\(474\) 83.8485 + 52.6128i 0.176896 + 0.110997i
\(475\) 62.7339i 0.132071i
\(476\) 29.9849 14.4859i 0.0629936 0.0304327i
\(477\) 77.9373 0.163391
\(478\) −259.224 + 413.122i −0.542309 + 0.864272i
\(479\) 569.142i 1.18819i 0.804396 + 0.594094i \(0.202489\pi\)
−0.804396 + 0.594094i \(0.797511\pi\)
\(480\) 101.885 + 288.293i 0.212261 + 0.600611i
\(481\) −69.9481 −0.145422
\(482\) −377.660 236.972i −0.783527 0.491644i
\(483\) 9.21964i 0.0190883i
\(484\) 155.369 + 321.603i 0.321010 + 0.664470i
\(485\) −152.804 −0.315060
\(486\) 16.5707 26.4086i 0.0340961 0.0543386i
\(487\) 225.936i 0.463935i 0.972724 + 0.231968i \(0.0745163\pi\)
−0.972724 + 0.231968i \(0.925484\pi\)
\(488\) −63.5617 + 573.742i −0.130249 + 1.17570i
\(489\) 13.7048 0.0280261
\(490\) 448.367 + 281.339i 0.915034 + 0.574161i
\(491\) 876.858i 1.78586i −0.450194 0.892931i \(-0.648645\pi\)
0.450194 0.892931i \(-0.351355\pi\)
\(492\) −409.262 + 197.718i −0.831834 + 0.401865i
\(493\) −400.961 −0.813309
\(494\) −44.2468 + 70.5156i −0.0895683 + 0.142744i
\(495\) 93.1940i 0.188271i
\(496\) 743.761 + 590.110i 1.49952 + 1.18974i
\(497\) 81.3261 0.163634
\(498\) 304.981 + 191.368i 0.612412 + 0.384273i
\(499\) 259.904i 0.520851i 0.965494 + 0.260425i \(0.0838628\pi\)
−0.965494 + 0.260425i \(0.916137\pi\)
\(500\) −187.816 388.767i −0.375632 0.777533i
\(501\) 424.194 0.846695
\(502\) −469.275 + 747.879i −0.934811 + 1.48980i
\(503\) 172.379i 0.342702i −0.985210 0.171351i \(-0.945187\pi\)
0.985210 0.171351i \(-0.0548132\pi\)
\(504\) −24.1549 2.67599i −0.0479265 0.00530951i
\(505\) −218.702 −0.433074
\(506\) 50.1461 + 31.4654i 0.0991031 + 0.0621847i
\(507\) 22.5167i 0.0444116i
\(508\) −169.317 + 81.7985i −0.333302 + 0.161021i
\(509\) −713.109 −1.40100 −0.700500 0.713653i \(-0.747039\pi\)
−0.700500 + 0.713653i \(0.747039\pi\)
\(510\) 83.5082 133.086i 0.163742 0.260953i
\(511\) 5.67748i 0.0111105i
\(512\) 166.396 484.207i 0.324992 0.945717i
\(513\) −59.9865 −0.116933
\(514\) −489.808 307.342i −0.952933 0.597942i
\(515\) 445.882i 0.865791i
\(516\) −42.2500 87.4547i −0.0818799 0.169486i
\(517\) 52.6294 0.101798
\(518\) −20.8827 + 33.2805i −0.0403140 + 0.0642480i
\(519\) 292.681i 0.563932i
\(520\) −17.5215 + 158.159i −0.0336952 + 0.304151i
\(521\) −475.193 −0.912078 −0.456039 0.889960i \(-0.650732\pi\)
−0.456039 + 0.889960i \(0.650732\pi\)
\(522\) 247.865 + 155.529i 0.474837 + 0.297948i
\(523\) 807.769i 1.54449i −0.635324 0.772246i \(-0.719133\pi\)
0.635324 0.772246i \(-0.280867\pi\)
\(524\) 306.706 148.172i 0.585317 0.282771i
\(525\) −9.53091 −0.0181541
\(526\) −437.803 + 697.722i −0.832325 + 1.32647i
\(527\) 487.856i 0.925723i
\(528\) 96.9926 122.247i 0.183698 0.231529i
\(529\) 501.368 0.947765
\(530\) −242.799 152.350i −0.458110 0.287453i
\(531\) 115.324i 0.217183i
\(532\) 20.3408 + 42.1041i 0.0382346 + 0.0791431i
\(533\) −236.539 −0.443789
\(534\) 128.653 205.033i 0.240923 0.383956i
\(535\) 535.191i 1.00036i
\(536\) 806.584 + 89.3569i 1.50482 + 0.166711i
\(537\) −215.586 −0.401464
\(538\) −30.4038 19.0776i −0.0565126 0.0354602i
\(539\) 270.146i 0.501198i
\(540\) −103.246 + 49.8787i −0.191196 + 0.0923680i
\(541\) −38.9119 −0.0719258 −0.0359629 0.999353i \(-0.511450\pi\)
−0.0359629 + 0.999353i \(0.511450\pi\)
\(542\) −343.846 + 547.984i −0.634402 + 1.01104i
\(543\) 403.098i 0.742354i
\(544\) −248.053 + 87.6639i −0.455979 + 0.161147i
\(545\) 1164.48 2.13667
\(546\) −10.7132 6.72223i −0.0196212 0.0123118i
\(547\) 329.904i 0.603116i −0.953448 0.301558i \(-0.902493\pi\)
0.953448 0.301558i \(-0.0975066\pi\)
\(548\) 346.776 + 717.803i 0.632803 + 1.30986i
\(549\) −216.470 −0.394298
\(550\) 32.5278 51.8392i 0.0591414 0.0942530i
\(551\) 563.020i 1.02181i
\(552\) −8.02029 + 72.3955i −0.0145295 + 0.131151i
\(553\) 28.9359 0.0523253
\(554\) 303.885 + 190.680i 0.548529 + 0.344188i
\(555\) 185.373i 0.334005i
\(556\) 246.139 118.912i 0.442696 0.213870i
\(557\) −499.645 −0.897028 −0.448514 0.893776i \(-0.648047\pi\)
−0.448514 + 0.893776i \(0.648047\pi\)
\(558\) −189.234 + 301.581i −0.339130 + 0.540468i
\(559\) 50.5458i 0.0904218i
\(560\) 70.0191 + 55.5540i 0.125034 + 0.0992036i
\(561\) −80.1858 −0.142934
\(562\) 740.917 + 464.907i 1.31836 + 0.827236i
\(563\) 79.9277i 0.141967i −0.997477 0.0709837i \(-0.977386\pi\)
0.997477 0.0709837i \(-0.0226138\pi\)
\(564\) 28.1680 + 58.3058i 0.0499432 + 0.103379i
\(565\) 377.473 0.668093
\(566\) 523.994 835.084i 0.925784 1.47541i
\(567\) 9.11352i 0.0160732i
\(568\) −638.598 70.7467i −1.12429 0.124554i
\(569\) 822.992 1.44638 0.723192 0.690647i \(-0.242674\pi\)
0.723192 + 0.690647i \(0.242674\pi\)
\(570\) 186.876 + 117.260i 0.327853 + 0.205720i
\(571\) 237.913i 0.416660i 0.978059 + 0.208330i \(0.0668028\pi\)
−0.978059 + 0.208330i \(0.933197\pi\)
\(572\) 73.1253 35.3274i 0.127841 0.0617611i
\(573\) −481.942 −0.841086
\(574\) −70.6176 + 112.543i −0.123027 + 0.196067i
\(575\) 28.5654i 0.0496789i
\(576\) 187.344 + 42.0254i 0.325250 + 0.0729608i
\(577\) −764.467 −1.32490 −0.662450 0.749106i \(-0.730483\pi\)
−0.662450 + 0.749106i \(0.730483\pi\)
\(578\) −375.088 235.358i −0.648941 0.407194i
\(579\) 11.9738i 0.0206801i
\(580\) −468.150 969.040i −0.807156 1.67076i
\(581\) 105.248 0.181150
\(582\) −50.9980 + 81.2749i −0.0876254 + 0.139648i
\(583\) 146.289i 0.250924i
\(584\) −4.93892 + 44.5813i −0.00845705 + 0.0763379i
\(585\) −59.6724 −0.102004
\(586\) 104.817 + 65.7697i 0.178868 + 0.112235i
\(587\) 349.212i 0.594910i 0.954736 + 0.297455i \(0.0961379\pi\)
−0.954736 + 0.297455i \(0.903862\pi\)
\(588\) 299.283 144.586i 0.508984 0.245894i
\(589\) 685.036 1.16305
\(590\) −225.433 + 359.270i −0.382089 + 0.608932i
\(591\) 482.320i 0.816109i
\(592\) 192.928 243.162i 0.325892 0.410747i
\(593\) −240.972 −0.406360 −0.203180 0.979141i \(-0.565128\pi\)
−0.203180 + 0.979141i \(0.565128\pi\)
\(594\) 49.5690 + 31.1033i 0.0834494 + 0.0523624i
\(595\) 45.9277i 0.0771894i
\(596\) 276.244 + 571.807i 0.463497 + 0.959408i
\(597\) 256.474 0.429605
\(598\) −20.1474 + 32.1087i −0.0336913 + 0.0536935i
\(599\) 429.935i 0.717755i −0.933385 0.358878i \(-0.883160\pi\)
0.933385 0.358878i \(-0.116840\pi\)
\(600\) 74.8397 + 8.29107i 0.124733 + 0.0138184i
\(601\) 812.327 1.35163 0.675813 0.737073i \(-0.263793\pi\)
0.675813 + 0.737073i \(0.263793\pi\)
\(602\) −24.0491 15.0902i −0.0399486 0.0250668i
\(603\) 304.319i 0.504676i
\(604\) −945.646 + 456.849i −1.56564 + 0.756372i
\(605\) 492.597 0.814210
\(606\) −72.9914 + 116.326i −0.120448 + 0.191956i
\(607\) 772.664i 1.27292i −0.771308 0.636462i \(-0.780397\pi\)
0.771308 0.636462i \(-0.219603\pi\)
\(608\) −123.096 348.310i −0.202460 0.572878i
\(609\) 85.5374 0.140456
\(610\) 674.369 + 423.150i 1.10552 + 0.693688i
\(611\) 33.6988i 0.0551534i
\(612\) −42.9165 88.8344i −0.0701251 0.145154i
\(613\) 323.297 0.527402 0.263701 0.964605i \(-0.415057\pi\)
0.263701 + 0.964605i \(0.415057\pi\)
\(614\) −474.869 + 756.794i −0.773403 + 1.23256i
\(615\) 626.863i 1.01929i
\(616\) 5.02284 45.3389i 0.00815397 0.0736021i
\(617\) −440.441 −0.713842 −0.356921 0.934135i \(-0.616173\pi\)
−0.356921 + 0.934135i \(0.616173\pi\)
\(618\) 237.160 + 148.812i 0.383755 + 0.240796i
\(619\) 444.566i 0.718200i −0.933299 0.359100i \(-0.883084\pi\)
0.933299 0.359100i \(-0.116916\pi\)
\(620\) 1179.05 569.606i 1.90169 0.918719i
\(621\) −27.3144 −0.0439845
\(622\) 264.617 421.717i 0.425429 0.678002i
\(623\) 70.7562i 0.113573i
\(624\) 78.2753 + 62.1046i 0.125441 + 0.0995266i
\(625\) −731.323 −1.17012
\(626\) −96.0566 60.2731i −0.153445 0.0962829i
\(627\) 112.595i 0.179577i
\(628\) 195.034 + 403.708i 0.310564 + 0.642847i
\(629\) −159.498 −0.253574
\(630\) −17.8149 + 28.3914i −0.0282776 + 0.0450657i
\(631\) 394.541i 0.625263i −0.949874 0.312632i \(-0.898789\pi\)
0.949874 0.312632i \(-0.101211\pi\)
\(632\) −227.214 25.1717i −0.359515 0.0398287i
\(633\) −676.226 −1.06829
\(634\) −97.9533 61.4632i −0.154500 0.0969452i
\(635\) 259.342i 0.408413i
\(636\) −162.067 + 78.2957i −0.254822 + 0.123106i
\(637\) 172.975 0.271546
\(638\) −291.928 + 465.243i −0.457568 + 0.729221i
\(639\) 240.939i 0.377057i
\(640\) −501.484 497.138i −0.783569 0.776778i
\(641\) 941.707 1.46912 0.734561 0.678543i \(-0.237388\pi\)
0.734561 + 0.678543i \(0.237388\pi\)
\(642\) −284.663 178.619i −0.443400 0.278222i
\(643\) 187.307i 0.291301i 0.989336 + 0.145651i \(0.0465275\pi\)
−0.989336 + 0.145651i \(0.953472\pi\)
\(644\) 9.26203 + 19.1718i 0.0143820 + 0.0297698i
\(645\) −133.954 −0.207680
\(646\) −100.893 + 160.792i −0.156181 + 0.248904i
\(647\) 324.114i 0.500949i 0.968123 + 0.250474i \(0.0805866\pi\)
−0.968123 + 0.250474i \(0.919413\pi\)
\(648\) −7.92798 + 71.5622i −0.0122345 + 0.110435i
\(649\) 216.464 0.333534
\(650\) 33.1928 + 20.8276i 0.0510658 + 0.0320425i
\(651\) 104.075i 0.159869i
\(652\) −28.4984 + 13.7678i −0.0437092 + 0.0211163i
\(653\) −746.434 −1.14308 −0.571542 0.820573i \(-0.693654\pi\)
−0.571542 + 0.820573i \(0.693654\pi\)
\(654\) 388.644 619.377i 0.594256 0.947060i
\(655\) 469.779i 0.717219i
\(656\) 652.414 822.288i 0.994534 1.25349i
\(657\) −16.8203 −0.0256016
\(658\) 16.0335 + 10.0606i 0.0243670 + 0.0152896i
\(659\) 797.604i 1.21032i 0.796102 + 0.605162i \(0.206892\pi\)
−0.796102 + 0.605162i \(0.793108\pi\)
\(660\) −93.6226 193.792i −0.141852 0.293625i
\(661\) −606.767 −0.917952 −0.458976 0.888449i \(-0.651784\pi\)
−0.458976 + 0.888449i \(0.651784\pi\)
\(662\) 52.1779 83.1553i 0.0788185 0.125612i
\(663\) 51.3432i 0.0774407i
\(664\) −826.442 91.5569i −1.24464 0.137887i
\(665\) 64.4905 0.0969782
\(666\) 98.5978 + 61.8676i 0.148045 + 0.0928943i
\(667\) 256.367i 0.384358i
\(668\) −882.091 + 426.145i −1.32050 + 0.637942i
\(669\) −549.846 −0.821892
\(670\) 594.876 948.048i 0.887875 1.41500i
\(671\) 406.314i 0.605536i
\(672\) 52.9173 18.7014i 0.0787460 0.0278295i
\(673\) −402.160 −0.597563 −0.298782 0.954322i \(-0.596580\pi\)
−0.298782 + 0.954322i \(0.596580\pi\)
\(674\) −681.461 427.600i −1.01107 0.634421i
\(675\) 28.2366i 0.0418320i
\(676\) 22.6202 + 46.8223i 0.0334618 + 0.0692637i
\(677\) −673.548 −0.994901 −0.497450 0.867492i \(-0.665730\pi\)
−0.497450 + 0.867492i \(0.665730\pi\)
\(678\) 125.980 200.774i 0.185812 0.296127i
\(679\) 28.0477i 0.0413074i
\(680\) −39.9531 + 360.638i −0.0587546 + 0.530351i
\(681\) −741.564 −1.08893
\(682\) −566.069 355.194i −0.830013 0.520812i
\(683\) 562.406i 0.823435i −0.911312 0.411717i \(-0.864929\pi\)
0.911312 0.411717i \(-0.135071\pi\)
\(684\) 124.739 60.2624i 0.182367 0.0881029i
\(685\) 1099.45 1.60504
\(686\) 104.385 166.358i 0.152165 0.242504i
\(687\) 709.478i 1.03272i
\(688\) 175.714 + 139.414i 0.255398 + 0.202636i
\(689\) −93.6690 −0.135949
\(690\) 85.0927 + 53.3935i 0.123323 + 0.0773819i
\(691\) 206.103i 0.298268i −0.988817 0.149134i \(-0.952351\pi\)
0.988817 0.149134i \(-0.0476486\pi\)
\(692\) −294.026 608.615i −0.424894 0.879502i
\(693\) 17.1061 0.0246841
\(694\) −86.3118 + 137.554i −0.124369 + 0.198205i
\(695\) 377.009i 0.542459i
\(696\) −671.666 74.4102i −0.965038 0.106911i
\(697\) −539.364 −0.773837
\(698\) 391.306 + 245.535i 0.560611 + 0.351769i
\(699\) 145.760i 0.208527i
\(700\) 19.8191 9.57473i 0.0283129 0.0136782i
\(701\) 42.7330 0.0609601 0.0304801 0.999535i \(-0.490296\pi\)
0.0304801 + 0.999535i \(0.490296\pi\)
\(702\) −19.9155 + 31.7391i −0.0283697 + 0.0452124i
\(703\) 223.963i 0.318582i
\(704\) −78.8819 + 351.646i −0.112048 + 0.499497i
\(705\) 89.3065 0.126676
\(706\) 464.881 + 291.701i 0.658472 + 0.413174i
\(707\) 40.1436i 0.0567802i
\(708\) 115.854 + 239.811i 0.163636 + 0.338716i
\(709\) −89.9432 −0.126859 −0.0634296 0.997986i \(-0.520204\pi\)
−0.0634296 + 0.997986i \(0.520204\pi\)
\(710\) −470.982 + 750.599i −0.663355 + 1.05718i
\(711\) 85.7263i 0.120572i
\(712\) −61.5518 + 555.600i −0.0864492 + 0.780337i
\(713\) 311.925 0.437483
\(714\) −24.4285 15.3282i −0.0342135 0.0214681i
\(715\) 112.005i 0.156651i
\(716\) 448.300 216.577i 0.626118 0.302482i
\(717\) 422.374 0.589085
\(718\) −571.074 + 910.114i −0.795367 + 1.26757i
\(719\) 699.403i 0.972744i 0.873752 + 0.486372i \(0.161680\pi\)
−0.873752 + 0.486372i \(0.838320\pi\)
\(720\) 164.586 207.441i 0.228592 0.288112i
\(721\) 81.8434 0.113514
\(722\) 385.794 + 242.076i 0.534340 + 0.335285i
\(723\) 386.118i 0.534050i
\(724\) −404.952 838.223i −0.559325 1.15777i
\(725\) −265.022 −0.365548
\(726\) 164.403 262.007i 0.226450 0.360892i
\(727\) 1083.55i 1.49044i 0.666817 + 0.745221i \(0.267656\pi\)
−0.666817 + 0.745221i \(0.732344\pi\)
\(728\) 29.0306 + 3.21614i 0.0398772 + 0.00441778i
\(729\) −27.0000 −0.0370370
\(730\) 52.4003 + 32.8799i 0.0717813 + 0.0450409i
\(731\) 115.256i 0.157669i
\(732\) 450.138 217.465i 0.614943 0.297083i
\(733\) −459.669 −0.627107 −0.313553 0.949571i \(-0.601519\pi\)
−0.313553 + 0.949571i \(0.601519\pi\)
\(734\) 603.049 961.073i 0.821593 1.30936i
\(735\) 458.408i 0.623685i
\(736\) −56.0506 158.600i −0.0761556 0.215489i
\(737\) −571.209 −0.775046
\(738\) 333.422 + 209.214i 0.451792 + 0.283488i
\(739\) 779.296i 1.05453i 0.849702 + 0.527264i \(0.176782\pi\)
−0.849702 + 0.527264i \(0.823218\pi\)
\(740\) −186.225 385.473i −0.251655 0.520910i
\(741\) 72.0948 0.0972940
\(742\) −27.9644 + 44.5666i −0.0376879 + 0.0600628i
\(743\) 696.785i 0.937799i 0.883251 + 0.468900i \(0.155349\pi\)
−0.883251 + 0.468900i \(0.844651\pi\)
\(744\) 90.5361 817.227i 0.121688 1.09842i
\(745\) 875.832 1.17561
\(746\) −865.716 543.215i −1.16048 0.728170i
\(747\) 311.812i 0.417419i
\(748\) 166.742 80.5545i 0.222918 0.107693i
\(749\) −98.2364 −0.131157
\(750\) −198.737 + 316.725i −0.264982 + 0.422299i
\(751\) 237.983i 0.316889i 0.987368 + 0.158444i \(0.0506478\pi\)
−0.987368 + 0.158444i \(0.949352\pi\)
\(752\) −117.148 92.9466i −0.155782 0.123599i
\(753\) 764.628 1.01544
\(754\) −297.896 186.922i −0.395088 0.247908i
\(755\) 1448.44i 1.91846i
\(756\) 9.15542 + 18.9511i 0.0121103 + 0.0250676i
\(757\) −62.2735 −0.0822635 −0.0411318 0.999154i \(-0.513096\pi\)
−0.0411318 + 0.999154i \(0.513096\pi\)
\(758\) −261.394 + 416.581i −0.344847 + 0.549580i
\(759\) 51.2692i 0.0675484i
\(760\) −506.400 56.1012i −0.666315 0.0738174i
\(761\) −734.114 −0.964670 −0.482335 0.875987i \(-0.660211\pi\)
−0.482335 + 0.875987i \(0.660211\pi\)
\(762\) 137.941 + 86.5547i 0.181025 + 0.113589i
\(763\) 213.745i 0.280138i
\(764\) 1002.18 484.158i 1.31175 0.633715i
\(765\) −136.067 −0.177865
\(766\) −295.502 + 470.939i −0.385773 + 0.614803i
\(767\) 138.602i 0.180707i
\(768\) −431.792 + 100.816i −0.562229 + 0.131271i
\(769\) 378.181 0.491783 0.245891 0.969297i \(-0.420919\pi\)
0.245891 + 0.969297i \(0.420919\pi\)
\(770\) −53.2908 33.4386i −0.0692088 0.0434268i
\(771\) 500.777i 0.649517i
\(772\) −12.0288 24.8989i −0.0155814 0.0322524i
\(773\) −1276.10 −1.65084 −0.825421 0.564517i \(-0.809062\pi\)
−0.825421 + 0.564517i \(0.809062\pi\)
\(774\) −44.7067 + 71.2486i −0.0577606 + 0.0920524i
\(775\) 322.457i 0.416073i
\(776\) 24.3991 220.240i 0.0314422 0.283814i
\(777\) 34.0258 0.0437913
\(778\) 224.561 + 140.907i 0.288639 + 0.181114i
\(779\) 757.362i 0.972224i
\(780\) 124.086 59.9468i 0.159084 0.0768548i
\(781\) 452.244 0.579057
\(782\) −45.9407 + 73.2153i −0.0587477 + 0.0936257i
\(783\) 253.416i 0.323647i
\(784\) −477.093 + 601.317i −0.608537 + 0.766986i
\(785\) 618.356 0.787715
\(786\) −249.871 156.787i −0.317901 0.199475i
\(787\) 1247.47i 1.58509i 0.609811 + 0.792547i \(0.291245\pi\)
−0.609811 + 0.792547i \(0.708755\pi\)
\(788\) −484.538 1002.96i −0.614896 1.27279i
\(789\) 713.348 0.904117
\(790\) −167.576 + 267.064i −0.212121 + 0.338055i
\(791\) 69.2865i 0.0875935i
\(792\) −134.323 14.8808i −0.169599 0.0187889i
\(793\) 260.164 0.328076
\(794\) −795.460 499.131i −1.00184 0.628629i
\(795\) 248.236i 0.312247i
\(796\) −533.325 + 257.653i −0.670007 + 0.323685i
\(797\) 252.682 0.317042 0.158521 0.987356i \(-0.449328\pi\)
0.158521 + 0.987356i \(0.449328\pi\)
\(798\) 21.5235 34.3019i 0.0269719 0.0429848i
\(799\) 76.8409i 0.0961714i
\(800\) −163.955 + 57.9429i −0.204943 + 0.0724286i
\(801\) −209.625 −0.261704
\(802\) 286.308 + 179.651i 0.356992 + 0.224004i
\(803\) 31.5717i 0.0393172i
\(804\) −305.719 632.817i −0.380247 0.787086i
\(805\) 29.3652 0.0364786
\(806\) 227.431 362.455i 0.282173 0.449696i
\(807\) 31.0847i 0.0385188i
\(808\) 34.9215 315.220i 0.0432197 0.390124i
\(809\) 412.690 0.510124 0.255062 0.966925i \(-0.417904\pi\)
0.255062 + 0.966925i \(0.417904\pi\)
\(810\) 84.1133 + 52.7789i 0.103844 + 0.0651592i
\(811\) 1013.28i 1.24942i 0.780857 + 0.624710i \(0.214783\pi\)
−0.780857 + 0.624710i \(0.785217\pi\)
\(812\) −177.871 + 85.9307i −0.219053 + 0.105826i
\(813\) 560.256 0.689122
\(814\) −116.126 + 185.068i −0.142661 + 0.227357i
\(815\) 43.6508i 0.0535592i
\(816\) 178.486 + 141.613i 0.218732 + 0.173545i
\(817\) 161.840 0.198090
\(818\) 559.093 + 350.817i 0.683488 + 0.428872i
\(819\) 10.9531i 0.0133737i
\(820\) −629.746 1303.53i −0.767983 1.58967i
\(821\) 13.0550 0.0159014 0.00795070 0.999968i \(-0.497469\pi\)
0.00795070 + 0.999968i \(0.497469\pi\)
\(822\) 366.940 584.788i 0.446399 0.711421i
\(823\) 724.939i 0.880850i −0.897789 0.440425i \(-0.854828\pi\)
0.897789 0.440425i \(-0.145172\pi\)
\(824\) −642.660 71.1967i −0.779927 0.0864037i
\(825\) −53.0002 −0.0642426
\(826\) 65.9453 + 41.3790i 0.0798369 + 0.0500956i
\(827\) 1270.08i 1.53576i 0.640592 + 0.767882i \(0.278689\pi\)
−0.640592 + 0.767882i \(0.721311\pi\)
\(828\) 56.7989 27.4400i 0.0685977 0.0331401i
\(829\) 524.786 0.633035 0.316517 0.948587i \(-0.397486\pi\)
0.316517 + 0.948587i \(0.397486\pi\)
\(830\) −609.522 + 971.389i −0.734364 + 1.17035i
\(831\) 310.691i 0.373876i
\(832\) −225.160 50.5083i −0.270625 0.0607071i
\(833\) 394.423 0.473497
\(834\) −200.527 125.826i −0.240441 0.150870i
\(835\) 1351.09i 1.61807i
\(836\) 113.113 + 234.136i 0.135302 + 0.280067i
\(837\) 308.335 0.368381
\(838\) −488.915 + 779.179i −0.583431 + 0.929808i
\(839\) 566.375i 0.675060i 0.941315 + 0.337530i \(0.109591\pi\)
−0.941315 + 0.337530i \(0.890409\pi\)
\(840\) 8.52323 76.9353i 0.0101467 0.0915897i
\(841\) 1537.50 1.82819
\(842\) −106.578 66.8753i −0.126578 0.0794243i
\(843\) 757.510i 0.898589i
\(844\) 1406.18 679.335i 1.66609 0.804900i
\(845\) 71.7173 0.0848725
\(846\) 29.8058 47.5012i 0.0352315 0.0561480i
\(847\) 90.4180i 0.106751i
\(848\) 258.354 325.624i 0.304663 0.383991i
\(849\) −853.786 −1.00564
\(850\) 75.6871 + 47.4918i 0.0890437 + 0.0558727i
\(851\) 101.980i 0.119835i
\(852\) 242.047 + 501.021i 0.284093 + 0.588053i
\(853\) 918.949 1.07731 0.538657 0.842525i \(-0.318932\pi\)
0.538657 + 0.842525i \(0.318932\pi\)
\(854\) 77.6707 123.783i 0.0909493 0.144945i
\(855\) 191.062i 0.223464i
\(856\) 771.383 + 85.4572i 0.901148 + 0.0998332i
\(857\) 1131.98 1.32086 0.660429 0.750888i \(-0.270374\pi\)
0.660429 + 0.750888i \(0.270374\pi\)
\(858\) −59.5745 37.3815i −0.0694341 0.0435682i
\(859\) 275.908i 0.321197i −0.987020 0.160598i \(-0.948658\pi\)
0.987020 0.160598i \(-0.0513424\pi\)
\(860\) 278.550 134.570i 0.323895 0.156476i
\(861\) 115.063 0.133639
\(862\) 407.953 650.151i 0.473263 0.754235i
\(863\) 976.882i 1.13196i −0.824419 0.565980i \(-0.808498\pi\)
0.824419 0.565980i \(-0.191502\pi\)
\(864\) −55.4054 156.774i −0.0641266 0.181452i
\(865\) −932.210 −1.07770
\(866\) 908.779 + 570.236i 1.04940 + 0.658471i
\(867\) 383.488i 0.442316i
\(868\) −104.553 216.418i −0.120453 0.249330i
\(869\) 160.909 0.185165
\(870\) −495.371 + 789.468i −0.569392 + 0.907434i
\(871\) 365.746i 0.419916i
\(872\) −185.940 + 1678.40i −0.213234 + 1.92477i
\(873\) 83.0951 0.0951834
\(874\) −102.807 64.5089i −0.117628 0.0738088i
\(875\) 109.301i 0.124915i
\(876\) 34.9770 16.8976i 0.0399280 0.0192895i
\(877\) 1188.18 1.35482 0.677410 0.735606i \(-0.263102\pi\)
0.677410 + 0.735606i \(0.263102\pi\)
\(878\) −279.610 + 445.611i −0.318462 + 0.507530i
\(879\) 107.164i 0.121916i
\(880\) 389.367 + 308.929i 0.442462 + 0.351055i
\(881\) 450.708 0.511587 0.255793 0.966731i \(-0.417663\pi\)
0.255793 + 0.966731i \(0.417663\pi\)
\(882\) −243.823 152.993i −0.276443 0.173461i
\(883\) 607.667i 0.688184i −0.938936 0.344092i \(-0.888187\pi\)
0.938936 0.344092i \(-0.111813\pi\)
\(884\) 51.5793 + 106.766i 0.0583476 + 0.120776i
\(885\) 367.316 0.415046
\(886\) 740.501 1180.13i 0.835780 1.33197i
\(887\) 653.859i 0.737158i 0.929596 + 0.368579i \(0.120156\pi\)
−0.929596 + 0.368579i \(0.879844\pi\)
\(888\) −267.181 29.5995i −0.300880 0.0333328i
\(889\) 47.6032 0.0535469
\(890\) 653.045 + 409.769i 0.733758 + 0.460415i
\(891\) 50.6791i 0.0568789i
\(892\) 1143.38 552.374i 1.28181 0.619253i
\(893\) −107.898 −0.120827
\(894\) 292.307 465.846i 0.326965 0.521081i
\(895\) 686.658i 0.767215i
\(896\) −91.2515 + 92.0493i −0.101843 + 0.102734i
\(897\) 32.8278 0.0365973
\(898\) −321.174 201.529i −0.357655 0.224419i
\(899\) 2893.96i 3.21909i
\(900\) −28.3664 58.7166i −0.0315182 0.0652406i
\(901\) −213.587 −0.237055
\(902\) −392.696 + 625.835i −0.435361 + 0.693830i
\(903\) 24.5877i 0.0272289i
\(904\) −60.2733 + 544.059i −0.0666740 + 0.601835i
\(905\) −1283.90 −1.41867
\(906\) 770.409 + 483.412i 0.850341 + 0.533568i
\(907\) 183.685i 0.202519i 0.994860 + 0.101260i \(0.0322873\pi\)
−0.994860 + 0.101260i \(0.967713\pi\)
\(908\) 1542.04 744.973i 1.69829 0.820455i
\(909\) 118.931 0.130837
\(910\) 21.4108 34.1222i 0.0235284 0.0374969i
\(911\) 1057.82i 1.16116i −0.814203 0.580581i \(-0.802826\pi\)
0.814203 0.580581i \(-0.197174\pi\)
\(912\) −198.849 + 250.625i −0.218037 + 0.274808i
\(913\) 585.272 0.641043
\(914\) 252.508 + 158.442i 0.276267 + 0.173351i
\(915\) 689.472i 0.753522i
\(916\) 712.741 + 1475.33i 0.778101 + 1.61062i
\(917\) −86.2296 −0.0940345
\(918\) −45.4119 + 72.3725i −0.0494684 + 0.0788372i
\(919\) 1464.17i 1.59322i −0.604494 0.796609i \(-0.706625\pi\)
0.604494 0.796609i \(-0.293375\pi\)
\(920\) −230.585 25.5452i −0.250636 0.0277666i
\(921\) 773.744 0.840112
\(922\) −57.9022 36.3321i −0.0628006 0.0394058i
\(923\) 289.573i 0.313730i
\(924\) −35.5713 + 17.1848i −0.0384971 + 0.0185982i
\(925\) −105.423 −0.113971
\(926\) 587.982 937.061i 0.634970 1.01195i
\(927\) 242.472i 0.261566i
\(928\) 1471.45 520.023i 1.58561 0.560369i
\(929\) 431.688 0.464680 0.232340 0.972635i \(-0.425362\pi\)
0.232340 + 0.972635i \(0.425362\pi\)
\(930\) −960.558 602.726i −1.03286 0.648093i
\(931\) 553.839i 0.594886i
\(932\) −146.431 303.102i −0.157114 0.325216i
\(933\) −431.162 −0.462124
\(934\) 9.49527 15.1325i 0.0101662 0.0162018i
\(935\) 255.398i 0.273153i
\(936\) 9.52824 86.0070i 0.0101797 0.0918879i
\(937\) −1476.62 −1.57590 −0.787952 0.615736i \(-0.788859\pi\)
−0.787952 + 0.615736i \(0.788859\pi\)
\(938\) −174.018 109.192i −0.185520 0.116409i
\(939\) 98.2079i 0.104588i
\(940\) −185.709 + 89.7172i −0.197562 + 0.0954438i
\(941\) 540.724 0.574627 0.287314 0.957837i \(-0.407238\pi\)
0.287314 + 0.957837i \(0.407238\pi\)
\(942\) 206.375 328.897i 0.219081 0.349148i
\(943\) 344.859i 0.365704i
\(944\) −481.827 382.288i −0.510410 0.404966i
\(945\) 29.0272 0.0307167
\(946\) −133.734 83.9146i −0.141368 0.0887047i
\(947\) 857.512i 0.905504i −0.891636 0.452752i \(-0.850442\pi\)
0.891636 0.452752i \(-0.149558\pi\)
\(948\) 86.1205 + 178.264i 0.0908444 + 0.188042i
\(949\) 20.2155 0.0213019
\(950\) −66.6868 + 106.278i −0.0701966 + 0.111872i
\(951\) 100.147i 0.105307i
\(952\) 66.1965 + 7.33354i 0.0695341 + 0.00770330i
\(953\) −1044.61 −1.09613 −0.548064 0.836436i \(-0.684635\pi\)
−0.548064 + 0.836436i \(0.684635\pi\)
\(954\) 132.034 + 82.8482i 0.138401 + 0.0868430i
\(955\) 1535.02i 1.60735i
\(956\) −878.306 + 424.316i −0.918731 + 0.443846i
\(957\) 475.663 0.497035
\(958\) −605.004 + 964.188i −0.631528 + 1.00646i
\(959\) 201.809i 0.210437i
\(960\) −133.854 + 596.706i −0.139431 + 0.621568i
\(961\) −2560.13 −2.66403
\(962\) −118.500 74.3556i −0.123181 0.0772927i
\(963\) 291.038i 0.302220i
\(964\) −387.894 802.914i −0.402379 0.832898i
\(965\) −38.1374 −0.0395206
\(966\) 9.80058 15.6191i 0.0101455 0.0161688i
\(967\) 523.468i 0.541332i 0.962673 + 0.270666i \(0.0872440\pi\)
−0.962673 + 0.270666i \(0.912756\pi\)
\(968\) −78.6558 + 709.990i −0.0812560 + 0.733461i
\(969\) 164.393 0.169652
\(970\) −258.867 162.432i −0.266873 0.167456i
\(971\) 533.084i 0.549005i −0.961586 0.274503i \(-0.911487\pi\)
0.961586 0.274503i \(-0.0885132\pi\)
\(972\) 56.1452 27.1241i 0.0577625 0.0279055i
\(973\) −69.2014 −0.0711217
\(974\) −240.173 + 382.761i −0.246584 + 0.392979i
\(975\) 33.9361i 0.0348063i
\(976\) −717.575 + 904.416i −0.735220 + 0.926655i
\(977\) 1316.34 1.34733 0.673667 0.739035i \(-0.264718\pi\)
0.673667 + 0.739035i \(0.264718\pi\)
\(978\) 23.2174 + 14.5683i 0.0237397 + 0.0148960i
\(979\) 393.466i 0.401906i
\(980\) 460.516 + 953.238i 0.469915 + 0.972692i
\(981\) −633.249 −0.645514
\(982\) 932.110 1485.49i 0.949195 1.51272i
\(983\) 761.922i 0.775098i −0.921849 0.387549i \(-0.873322\pi\)
0.921849 0.387549i \(-0.126678\pi\)
\(984\) −903.511 100.095i −0.918203 0.101723i
\(985\) −1536.23 −1.55962
\(986\) −679.272 426.226i −0.688917 0.432278i
\(987\) 16.3925i 0.0166085i
\(988\) −149.918 + 72.4263i −0.151739 + 0.0733060i
\(989\) 73.6925 0.0745121
\(990\) −99.0663 + 157.881i −0.100067 + 0.159476i
\(991\) 1048.30i 1.05782i 0.848679 + 0.528908i \(0.177398\pi\)
−0.848679 + 0.528908i \(0.822602\pi\)
\(992\) 632.720 + 1790.34i 0.637822 + 1.80477i
\(993\) −85.0177 −0.0856170
\(994\) 137.775 + 86.4505i 0.138607 + 0.0869723i
\(995\) 816.890i 0.820994i
\(996\) 313.245 + 648.397i 0.314504 + 0.651001i
\(997\) −1347.16 −1.35121 −0.675607 0.737262i \(-0.736118\pi\)
−0.675607 + 0.737262i \(0.736118\pi\)
\(998\) −276.281 + 440.307i −0.276835 + 0.441189i
\(999\) 100.806i 0.100907i
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 156.3.f.a.79.20 yes 24
3.2 odd 2 468.3.f.b.235.5 24
4.3 odd 2 inner 156.3.f.a.79.19 24
8.3 odd 2 2496.3.k.e.703.17 24
8.5 even 2 2496.3.k.e.703.18 24
12.11 even 2 468.3.f.b.235.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
156.3.f.a.79.19 24 4.3 odd 2 inner
156.3.f.a.79.20 yes 24 1.1 even 1 trivial
468.3.f.b.235.5 24 3.2 odd 2
468.3.f.b.235.6 24 12.11 even 2
2496.3.k.e.703.17 24 8.3 odd 2
2496.3.k.e.703.18 24 8.5 even 2