Properties

Label 975.2.bb.i.724.3
Level $975$
Weight $2$
Character 975.724
Analytic conductor $7.785$
Analytic rank $0$
Dimension $8$
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] = [975,2,Mod(724,975)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(975, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("975.724");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 975.bb (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.78541419707\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 724.3
Root \(1.35234 + 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 975.724
Dual form 975.2.bb.i.874.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.35234 + 0.780776i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.219224 + 0.379706i) q^{4} +(0.780776 + 1.35234i) q^{6} +(0.486319 - 0.280776i) q^{7} -2.43845i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(1.35234 + 0.780776i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.219224 + 0.379706i) q^{4} +(0.780776 + 1.35234i) q^{6} +(0.486319 - 0.280776i) q^{7} -2.43845i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +0.438447i q^{12} +(3.57071 - 0.500000i) q^{13} +0.876894 q^{14} +(2.34233 - 4.05703i) q^{16} +(-1.35234 + 0.780776i) q^{17} +1.56155i q^{18} +(3.56155 + 6.16879i) q^{19} +0.561553 q^{21} +(2.70469 - 1.56155i) q^{22} +(1.73205 + 1.00000i) q^{23} +(1.21922 - 2.11176i) q^{24} +(5.21922 + 2.11176i) q^{26} +1.00000i q^{27} +(0.213225 + 0.123106i) q^{28} +(3.34233 - 5.78908i) q^{29} +2.56155 q^{31} +(2.11176 - 1.21922i) q^{32} +(1.73205 - 1.00000i) q^{33} -2.43845 q^{34} +(-0.219224 + 0.379706i) q^{36} +(-6.54850 - 3.78078i) q^{37} +11.1231i q^{38} +(3.34233 + 1.35234i) q^{39} +(0.780776 - 1.35234i) q^{41} +(0.759413 + 0.438447i) q^{42} +(-3.95042 + 2.28078i) q^{43} +0.876894 q^{44} +(1.56155 + 2.70469i) q^{46} +8.24621i q^{47} +(4.05703 - 2.34233i) q^{48} +(-3.34233 + 5.78908i) q^{49} -1.56155 q^{51} +(0.972638 + 1.24621i) q^{52} +0.684658i q^{53} +(-0.780776 + 1.35234i) q^{54} +(-0.684658 - 1.18586i) q^{56} +7.12311i q^{57} +(9.03996 - 5.21922i) q^{58} +(-1.43845 - 2.49146i) q^{59} +(-1.93845 - 3.35749i) q^{61} +(3.46410 + 2.00000i) q^{62} +(0.486319 + 0.280776i) q^{63} -5.56155 q^{64} +3.12311 q^{66} +(-3.95042 - 2.28078i) q^{67} +(-0.592932 - 0.342329i) q^{68} +(1.00000 + 1.73205i) q^{69} +(-7.00000 - 12.1244i) q^{71} +(2.11176 - 1.21922i) q^{72} +10.1231i q^{73} +(-5.90388 - 10.2258i) q^{74} +(-1.56155 + 2.70469i) q^{76} -1.12311i q^{77} +(3.46410 + 4.43845i) q^{78} -5.43845 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.11176 - 1.21922i) q^{82} +0.876894i q^{83} +(0.123106 + 0.213225i) q^{84} -7.12311 q^{86} +(5.78908 - 3.34233i) q^{87} +(-4.22351 - 2.43845i) q^{88} +(2.43845 - 4.22351i) q^{89} +(1.59612 - 1.24573i) q^{91} +0.876894i q^{92} +(2.21837 + 1.28078i) q^{93} +(-6.43845 + 11.1517i) q^{94} +2.43845 q^{96} +(-7.41452 + 4.28078i) q^{97} +(-9.03996 + 5.21922i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 10 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 10 q^{4} - 2 q^{6} + 4 q^{9} + 8 q^{11} + 40 q^{14} - 6 q^{16} + 12 q^{19} - 12 q^{21} + 18 q^{24} + 50 q^{26} + 2 q^{29} + 4 q^{31} - 36 q^{34} - 10 q^{36} + 2 q^{39} - 2 q^{41} + 40 q^{44} - 4 q^{46} - 2 q^{49} + 4 q^{51} + 2 q^{54} + 44 q^{56} - 28 q^{59} - 32 q^{61} - 28 q^{64} - 8 q^{66} + 8 q^{69} - 56 q^{71} - 6 q^{74} + 4 q^{76} - 60 q^{79} - 4 q^{81} - 32 q^{84} - 24 q^{86} + 36 q^{89} + 54 q^{91} - 68 q^{94} + 36 q^{96} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35234 + 0.780776i 0.956252 + 0.552092i 0.895017 0.446031i \(-0.147163\pi\)
0.0612344 + 0.998123i \(0.480496\pi\)
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.219224 + 0.379706i 0.109612 + 0.189853i
\(5\) 0 0
\(6\) 0.780776 + 1.35234i 0.318751 + 0.552092i
\(7\) 0.486319 0.280776i 0.183811 0.106124i −0.405271 0.914197i \(-0.632823\pi\)
0.589082 + 0.808073i \(0.299489\pi\)
\(8\) 2.43845i 0.862121i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 0.438447i 0.126569i
\(13\) 3.57071 0.500000i 0.990338 0.138675i
\(14\) 0.876894 0.234360
\(15\) 0 0
\(16\) 2.34233 4.05703i 0.585582 1.01426i
\(17\) −1.35234 + 0.780776i −0.327992 + 0.189366i −0.654949 0.755673i \(-0.727310\pi\)
0.326957 + 0.945039i \(0.393977\pi\)
\(18\) 1.56155i 0.368062i
\(19\) 3.56155 + 6.16879i 0.817076 + 1.41522i 0.907827 + 0.419344i \(0.137740\pi\)
−0.0907512 + 0.995874i \(0.528927\pi\)
\(20\) 0 0
\(21\) 0.561553 0.122541
\(22\) 2.70469 1.56155i 0.576642 0.332924i
\(23\) 1.73205 + 1.00000i 0.361158 + 0.208514i 0.669588 0.742732i \(-0.266471\pi\)
−0.308431 + 0.951247i \(0.599804\pi\)
\(24\) 1.21922 2.11176i 0.248873 0.431061i
\(25\) 0 0
\(26\) 5.21922 + 2.11176i 1.02357 + 0.414150i
\(27\) 1.00000i 0.192450i
\(28\) 0.213225 + 0.123106i 0.0402958 + 0.0232648i
\(29\) 3.34233 5.78908i 0.620655 1.07501i −0.368709 0.929545i \(-0.620200\pi\)
0.989364 0.145461i \(-0.0464665\pi\)
\(30\) 0 0
\(31\) 2.56155 0.460068 0.230034 0.973183i \(-0.426116\pi\)
0.230034 + 0.973183i \(0.426116\pi\)
\(32\) 2.11176 1.21922i 0.373309 0.215530i
\(33\) 1.73205 1.00000i 0.301511 0.174078i
\(34\) −2.43845 −0.418190
\(35\) 0 0
\(36\) −0.219224 + 0.379706i −0.0365373 + 0.0632844i
\(37\) −6.54850 3.78078i −1.07657 0.621556i −0.146598 0.989196i \(-0.546832\pi\)
−0.929968 + 0.367640i \(0.880166\pi\)
\(38\) 11.1231i 1.80441i
\(39\) 3.34233 + 1.35234i 0.535201 + 0.216548i
\(40\) 0 0
\(41\) 0.780776 1.35234i 0.121937 0.211201i −0.798595 0.601869i \(-0.794423\pi\)
0.920531 + 0.390669i \(0.127756\pi\)
\(42\) 0.759413 + 0.438447i 0.117180 + 0.0676539i
\(43\) −3.95042 + 2.28078i −0.602433 + 0.347815i −0.769998 0.638046i \(-0.779743\pi\)
0.167565 + 0.985861i \(0.446410\pi\)
\(44\) 0.876894 0.132197
\(45\) 0 0
\(46\) 1.56155 + 2.70469i 0.230238 + 0.398785i
\(47\) 8.24621i 1.20283i 0.798935 + 0.601417i \(0.205397\pi\)
−0.798935 + 0.601417i \(0.794603\pi\)
\(48\) 4.05703 2.34233i 0.585582 0.338086i
\(49\) −3.34233 + 5.78908i −0.477476 + 0.827012i
\(50\) 0 0
\(51\) −1.56155 −0.218661
\(52\) 0.972638 + 1.24621i 0.134881 + 0.172818i
\(53\) 0.684658i 0.0940451i 0.998894 + 0.0470225i \(0.0149733\pi\)
−0.998894 + 0.0470225i \(0.985027\pi\)
\(54\) −0.780776 + 1.35234i −0.106250 + 0.184031i
\(55\) 0 0
\(56\) −0.684658 1.18586i −0.0914913 0.158468i
\(57\) 7.12311i 0.943478i
\(58\) 9.03996 5.21922i 1.18700 0.685318i
\(59\) −1.43845 2.49146i −0.187270 0.324361i 0.757069 0.653335i \(-0.226631\pi\)
−0.944339 + 0.328974i \(0.893297\pi\)
\(60\) 0 0
\(61\) −1.93845 3.35749i −0.248193 0.429882i 0.714832 0.699297i \(-0.246503\pi\)
−0.963024 + 0.269414i \(0.913170\pi\)
\(62\) 3.46410 + 2.00000i 0.439941 + 0.254000i
\(63\) 0.486319 + 0.280776i 0.0612704 + 0.0353745i
\(64\) −5.56155 −0.695194
\(65\) 0 0
\(66\) 3.12311 0.384428
\(67\) −3.95042 2.28078i −0.482621 0.278641i 0.238887 0.971047i \(-0.423217\pi\)
−0.721508 + 0.692406i \(0.756551\pi\)
\(68\) −0.592932 0.342329i −0.0719035 0.0415135i
\(69\) 1.00000 + 1.73205i 0.120386 + 0.208514i
\(70\) 0 0
\(71\) −7.00000 12.1244i −0.830747 1.43890i −0.897447 0.441123i \(-0.854580\pi\)
0.0666994 0.997773i \(-0.478753\pi\)
\(72\) 2.11176 1.21922i 0.248873 0.143687i
\(73\) 10.1231i 1.18482i 0.805637 + 0.592410i \(0.201823\pi\)
−0.805637 + 0.592410i \(0.798177\pi\)
\(74\) −5.90388 10.2258i −0.686312 1.18873i
\(75\) 0 0
\(76\) −1.56155 + 2.70469i −0.179122 + 0.310249i
\(77\) 1.12311i 0.127990i
\(78\) 3.46410 + 4.43845i 0.392232 + 0.502555i
\(79\) −5.43845 −0.611873 −0.305937 0.952052i \(-0.598970\pi\)
−0.305937 + 0.952052i \(0.598970\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.11176 1.21922i 0.233205 0.134641i
\(83\) 0.876894i 0.0962517i 0.998841 + 0.0481258i \(0.0153248\pi\)
−0.998841 + 0.0481258i \(0.984675\pi\)
\(84\) 0.123106 + 0.213225i 0.0134319 + 0.0232648i
\(85\) 0 0
\(86\) −7.12311 −0.768104
\(87\) 5.78908 3.34233i 0.620655 0.358335i
\(88\) −4.22351 2.43845i −0.450228 0.259939i
\(89\) 2.43845 4.22351i 0.258475 0.447692i −0.707359 0.706855i \(-0.750113\pi\)
0.965834 + 0.259163i \(0.0834467\pi\)
\(90\) 0 0
\(91\) 1.59612 1.24573i 0.167319 0.130588i
\(92\) 0.876894i 0.0914226i
\(93\) 2.21837 + 1.28078i 0.230034 + 0.132810i
\(94\) −6.43845 + 11.1517i −0.664075 + 1.15021i
\(95\) 0 0
\(96\) 2.43845 0.248873
\(97\) −7.41452 + 4.28078i −0.752831 + 0.434647i −0.826716 0.562620i \(-0.809794\pi\)
0.0738851 + 0.997267i \(0.476460\pi\)
\(98\) −9.03996 + 5.21922i −0.913174 + 0.527221i
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) 3.78078 6.54850i 0.376201 0.651600i −0.614305 0.789069i \(-0.710563\pi\)
0.990506 + 0.137469i \(0.0438968\pi\)
\(102\) −2.11176 1.21922i −0.209095 0.120721i
\(103\) 3.43845i 0.338800i 0.985547 + 0.169400i \(0.0541830\pi\)
−0.985547 + 0.169400i \(0.945817\pi\)
\(104\) −1.21922 8.70700i −0.119555 0.853791i
\(105\) 0 0
\(106\) −0.534565 + 0.925894i −0.0519216 + 0.0899308i
\(107\) 7.14143 + 4.12311i 0.690388 + 0.398596i 0.803757 0.594957i \(-0.202831\pi\)
−0.113369 + 0.993553i \(0.536164\pi\)
\(108\) −0.379706 + 0.219224i −0.0365373 + 0.0210948i
\(109\) 2.80776 0.268935 0.134468 0.990918i \(-0.457068\pi\)
0.134468 + 0.990918i \(0.457068\pi\)
\(110\) 0 0
\(111\) −3.78078 6.54850i −0.358855 0.621556i
\(112\) 2.63068i 0.248576i
\(113\) −5.02967 + 2.90388i −0.473152 + 0.273174i −0.717558 0.696499i \(-0.754740\pi\)
0.244406 + 0.969673i \(0.421407\pi\)
\(114\) −5.56155 + 9.63289i −0.520887 + 0.902203i
\(115\) 0 0
\(116\) 2.93087 0.272124
\(117\) 2.21837 + 2.84233i 0.205088 + 0.262773i
\(118\) 4.49242i 0.413561i
\(119\) −0.438447 + 0.759413i −0.0401924 + 0.0696153i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 6.05398i 0.548101i
\(123\) 1.35234 0.780776i 0.121937 0.0704002i
\(124\) 0.561553 + 0.972638i 0.0504289 + 0.0873455i
\(125\) 0 0
\(126\) 0.438447 + 0.759413i 0.0390600 + 0.0676539i
\(127\) −4.70983 2.71922i −0.417930 0.241292i 0.276261 0.961083i \(-0.410905\pi\)
−0.694191 + 0.719791i \(0.744238\pi\)
\(128\) −11.7446 6.78078i −1.03809 0.599342i
\(129\) −4.56155 −0.401622
\(130\) 0 0
\(131\) 7.36932 0.643860 0.321930 0.946763i \(-0.395668\pi\)
0.321930 + 0.946763i \(0.395668\pi\)
\(132\) 0.759413 + 0.438447i 0.0660984 + 0.0381619i
\(133\) 3.46410 + 2.00000i 0.300376 + 0.173422i
\(134\) −3.56155 6.16879i −0.307671 0.532902i
\(135\) 0 0
\(136\) 1.90388 + 3.29762i 0.163257 + 0.282769i
\(137\) −4.81645 + 2.78078i −0.411497 + 0.237578i −0.691433 0.722441i \(-0.743020\pi\)
0.279936 + 0.960019i \(0.409687\pi\)
\(138\) 3.12311i 0.265856i
\(139\) −8.96543 15.5286i −0.760438 1.31712i −0.942625 0.333854i \(-0.891651\pi\)
0.182187 0.983264i \(-0.441682\pi\)
\(140\) 0 0
\(141\) −4.12311 + 7.14143i −0.347228 + 0.601417i
\(142\) 21.8617i 1.83460i
\(143\) 2.70469 6.68466i 0.226177 0.558999i
\(144\) 4.68466 0.390388
\(145\) 0 0
\(146\) −7.90388 + 13.6899i −0.654130 + 1.13299i
\(147\) −5.78908 + 3.34233i −0.477476 + 0.275671i
\(148\) 3.31534i 0.272519i
\(149\) −1.21922 2.11176i −0.0998827 0.173002i 0.811753 0.584001i \(-0.198513\pi\)
−0.911636 + 0.410999i \(0.865180\pi\)
\(150\) 0 0
\(151\) −9.36932 −0.762464 −0.381232 0.924479i \(-0.624500\pi\)
−0.381232 + 0.924479i \(0.624500\pi\)
\(152\) 15.0423 8.68466i 1.22009 0.704419i
\(153\) −1.35234 0.780776i −0.109331 0.0631220i
\(154\) 0.876894 1.51883i 0.0706622 0.122390i
\(155\) 0 0
\(156\) 0.219224 + 1.56557i 0.0175519 + 0.125346i
\(157\) 20.3693i 1.62565i 0.582509 + 0.812824i \(0.302071\pi\)
−0.582509 + 0.812824i \(0.697929\pi\)
\(158\) −7.35465 4.24621i −0.585105 0.337810i
\(159\) −0.342329 + 0.592932i −0.0271485 + 0.0470225i
\(160\) 0 0
\(161\) 1.12311 0.0885131
\(162\) −1.35234 + 0.780776i −0.106250 + 0.0613436i
\(163\) 4.16365 2.40388i 0.326122 0.188287i −0.327996 0.944679i \(-0.606373\pi\)
0.654118 + 0.756393i \(0.273040\pi\)
\(164\) 0.684658 0.0534628
\(165\) 0 0
\(166\) −0.684658 + 1.18586i −0.0531398 + 0.0920408i
\(167\) −8.87348 5.12311i −0.686650 0.396438i 0.115706 0.993284i \(-0.463087\pi\)
−0.802356 + 0.596846i \(0.796420\pi\)
\(168\) 1.36932i 0.105645i
\(169\) 12.5000 3.57071i 0.961538 0.274670i
\(170\) 0 0
\(171\) −3.56155 + 6.16879i −0.272359 + 0.471739i
\(172\) −1.73205 1.00000i −0.132068 0.0762493i
\(173\) −17.5337 + 10.1231i −1.33307 + 0.769645i −0.985768 0.168110i \(-0.946234\pi\)
−0.347297 + 0.937755i \(0.612900\pi\)
\(174\) 10.4384 0.791337
\(175\) 0 0
\(176\) −4.68466 8.11407i −0.353119 0.611621i
\(177\) 2.87689i 0.216241i
\(178\) 6.59524 3.80776i 0.494334 0.285404i
\(179\) −2.43845 + 4.22351i −0.182258 + 0.315680i −0.942649 0.333785i \(-0.891674\pi\)
0.760391 + 0.649466i \(0.225007\pi\)
\(180\) 0 0
\(181\) −2.68466 −0.199549 −0.0997745 0.995010i \(-0.531812\pi\)
−0.0997745 + 0.995010i \(0.531812\pi\)
\(182\) 3.13114 0.438447i 0.232095 0.0324999i
\(183\) 3.87689i 0.286588i
\(184\) 2.43845 4.22351i 0.179765 0.311362i
\(185\) 0 0
\(186\) 2.00000 + 3.46410i 0.146647 + 0.254000i
\(187\) 3.12311i 0.228384i
\(188\) −3.13114 + 1.80776i −0.228362 + 0.131845i
\(189\) 0.280776 + 0.486319i 0.0204235 + 0.0353745i
\(190\) 0 0
\(191\) 4.56155 + 7.90084i 0.330062 + 0.571685i 0.982524 0.186137i \(-0.0595969\pi\)
−0.652461 + 0.757822i \(0.726264\pi\)
\(192\) −4.81645 2.78078i −0.347597 0.200685i
\(193\) −11.6848 6.74621i −0.841089 0.485603i 0.0165453 0.999863i \(-0.494733\pi\)
−0.857634 + 0.514260i \(0.828067\pi\)
\(194\) −13.3693 −0.959861
\(195\) 0 0
\(196\) −2.93087 −0.209348
\(197\) −11.5782 6.68466i −0.824910 0.476262i 0.0271965 0.999630i \(-0.491342\pi\)
−0.852107 + 0.523368i \(0.824675\pi\)
\(198\) 2.70469 + 1.56155i 0.192214 + 0.110975i
\(199\) 11.0885 + 19.2059i 0.786046 + 1.36147i 0.928372 + 0.371651i \(0.121208\pi\)
−0.142327 + 0.989820i \(0.545458\pi\)
\(200\) 0 0
\(201\) −2.28078 3.95042i −0.160874 0.278641i
\(202\) 10.2258 5.90388i 0.719486 0.415396i
\(203\) 3.75379i 0.263464i
\(204\) −0.342329 0.592932i −0.0239678 0.0415135i
\(205\) 0 0
\(206\) −2.68466 + 4.64996i −0.187049 + 0.323978i
\(207\) 2.00000i 0.139010i
\(208\) 6.33527 15.6577i 0.439272 1.08566i
\(209\) 14.2462 0.985431
\(210\) 0 0
\(211\) −9.84233 + 17.0474i −0.677574 + 1.17359i 0.298136 + 0.954524i \(0.403635\pi\)
−0.975709 + 0.219069i \(0.929698\pi\)
\(212\) −0.259969 + 0.150093i −0.0178548 + 0.0103084i
\(213\) 14.0000i 0.959264i
\(214\) 6.43845 + 11.1517i 0.440123 + 0.762316i
\(215\) 0 0
\(216\) 2.43845 0.165915
\(217\) 1.24573 0.719224i 0.0845658 0.0488241i
\(218\) 3.79706 + 2.19224i 0.257170 + 0.148477i
\(219\) −5.06155 + 8.76687i −0.342028 + 0.592410i
\(220\) 0 0
\(221\) −4.43845 + 3.46410i −0.298562 + 0.233021i
\(222\) 11.8078i 0.792485i
\(223\) 6.92820 + 4.00000i 0.463947 + 0.267860i 0.713702 0.700449i \(-0.247017\pi\)
−0.249756 + 0.968309i \(0.580350\pi\)
\(224\) 0.684658 1.18586i 0.0457457 0.0792338i
\(225\) 0 0
\(226\) −9.06913 −0.603270
\(227\) 6.16879 3.56155i 0.409437 0.236389i −0.281111 0.959675i \(-0.590703\pi\)
0.690548 + 0.723287i \(0.257370\pi\)
\(228\) −2.70469 + 1.56155i −0.179122 + 0.103416i
\(229\) 16.2462 1.07358 0.536790 0.843716i \(-0.319637\pi\)
0.536790 + 0.843716i \(0.319637\pi\)
\(230\) 0 0
\(231\) 0.561553 0.972638i 0.0369475 0.0639949i
\(232\) −14.1164 8.15009i −0.926785 0.535080i
\(233\) 26.0000i 1.70332i −0.524097 0.851658i \(-0.675597\pi\)
0.524097 0.851658i \(-0.324403\pi\)
\(234\) 0.780776 + 5.57586i 0.0510410 + 0.364505i
\(235\) 0 0
\(236\) 0.630683 1.09238i 0.0410540 0.0711076i
\(237\) −4.70983 2.71922i −0.305937 0.176633i
\(238\) −1.18586 + 0.684658i −0.0768681 + 0.0443798i
\(239\) 25.3693 1.64100 0.820502 0.571643i \(-0.193694\pi\)
0.820502 + 0.571643i \(0.193694\pi\)
\(240\) 0 0
\(241\) 8.90388 + 15.4220i 0.573549 + 0.993417i 0.996198 + 0.0871229i \(0.0277673\pi\)
−0.422648 + 0.906294i \(0.638899\pi\)
\(242\) 10.9309i 0.702663i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 0.849907 1.47208i 0.0544097 0.0942404i
\(245\) 0 0
\(246\) 2.43845 0.155470
\(247\) 15.8017 + 20.2462i 1.00544 + 1.28824i
\(248\) 6.24621i 0.396635i
\(249\) −0.438447 + 0.759413i −0.0277855 + 0.0481258i
\(250\) 0 0
\(251\) −9.36932 16.2281i −0.591386 1.02431i −0.994046 0.108961i \(-0.965248\pi\)
0.402660 0.915350i \(-0.368086\pi\)
\(252\) 0.246211i 0.0155099i
\(253\) 3.46410 2.00000i 0.217786 0.125739i
\(254\) −4.24621 7.35465i −0.266431 0.461472i
\(255\) 0 0
\(256\) −5.02699 8.70700i −0.314187 0.544187i
\(257\) −25.2681 14.5885i −1.57618 0.910008i −0.995385 0.0959583i \(-0.969408\pi\)
−0.580795 0.814050i \(-0.697258\pi\)
\(258\) −6.16879 3.56155i −0.384052 0.221733i
\(259\) −4.24621 −0.263847
\(260\) 0 0
\(261\) 6.68466 0.413770
\(262\) 9.96585 + 5.75379i 0.615693 + 0.355470i
\(263\) 8.11407 + 4.68466i 0.500335 + 0.288868i 0.728852 0.684672i \(-0.240054\pi\)
−0.228517 + 0.973540i \(0.573388\pi\)
\(264\) −2.43845 4.22351i −0.150076 0.259939i
\(265\) 0 0
\(266\) 3.12311 + 5.40938i 0.191490 + 0.331670i
\(267\) 4.22351 2.43845i 0.258475 0.149231i
\(268\) 2.00000i 0.122169i
\(269\) −10.6847 18.5064i −0.651455 1.12835i −0.982770 0.184833i \(-0.940826\pi\)
0.331315 0.943520i \(-0.392508\pi\)
\(270\) 0 0
\(271\) 14.9654 25.9209i 0.909085 1.57458i 0.0937481 0.995596i \(-0.470115\pi\)
0.815337 0.578986i \(-0.196551\pi\)
\(272\) 7.31534i 0.443558i
\(273\) 2.00514 0.280776i 0.121357 0.0169934i
\(274\) −8.68466 −0.524659
\(275\) 0 0
\(276\) −0.438447 + 0.759413i −0.0263914 + 0.0457113i
\(277\) 4.60322 2.65767i 0.276581 0.159684i −0.355294 0.934755i \(-0.615619\pi\)
0.631874 + 0.775071i \(0.282286\pi\)
\(278\) 28.0000i 1.67933i
\(279\) 1.28078 + 2.21837i 0.0766781 + 0.132810i
\(280\) 0 0
\(281\) 17.8078 1.06232 0.531161 0.847271i \(-0.321756\pi\)
0.531161 + 0.847271i \(0.321756\pi\)
\(282\) −11.1517 + 6.43845i −0.664075 + 0.383404i
\(283\) −11.8513 6.84233i −0.704484 0.406734i 0.104531 0.994522i \(-0.466666\pi\)
−0.809015 + 0.587787i \(0.799999\pi\)
\(284\) 3.06913 5.31589i 0.182119 0.315440i
\(285\) 0 0
\(286\) 8.87689 6.92820i 0.524902 0.409673i
\(287\) 0.876894i 0.0517614i
\(288\) 2.11176 + 1.21922i 0.124436 + 0.0718434i
\(289\) −7.28078 + 12.6107i −0.428281 + 0.741804i
\(290\) 0 0
\(291\) −8.56155 −0.501887
\(292\) −3.84381 + 2.21922i −0.224942 + 0.129870i
\(293\) −17.7002 + 10.2192i −1.03406 + 0.597013i −0.918144 0.396246i \(-0.870313\pi\)
−0.115913 + 0.993259i \(0.536979\pi\)
\(294\) −10.4384 −0.608783
\(295\) 0 0
\(296\) −9.21922 + 15.9682i −0.535856 + 0.928131i
\(297\) 1.73205 + 1.00000i 0.100504 + 0.0580259i
\(298\) 3.80776i 0.220578i
\(299\) 6.68466 + 2.70469i 0.386584 + 0.156416i
\(300\) 0 0
\(301\) −1.28078 + 2.21837i −0.0738227 + 0.127865i
\(302\) −12.6705 7.31534i −0.729108 0.420951i
\(303\) 6.54850 3.78078i 0.376201 0.217200i
\(304\) 33.3693 1.91386
\(305\) 0 0
\(306\) −1.21922 2.11176i −0.0696984 0.120721i
\(307\) 30.8078i 1.75829i 0.476553 + 0.879146i \(0.341886\pi\)
−0.476553 + 0.879146i \(0.658114\pi\)
\(308\) 0.426450 0.246211i 0.0242993 0.0140292i
\(309\) −1.71922 + 2.97778i −0.0978032 + 0.169400i
\(310\) 0 0
\(311\) −19.1231 −1.08437 −0.542186 0.840259i \(-0.682403\pi\)
−0.542186 + 0.840259i \(0.682403\pi\)
\(312\) 3.29762 8.15009i 0.186691 0.461408i
\(313\) 13.6847i 0.773503i 0.922184 + 0.386751i \(0.126403\pi\)
−0.922184 + 0.386751i \(0.873597\pi\)
\(314\) −15.9039 + 27.5463i −0.897508 + 1.55453i
\(315\) 0 0
\(316\) −1.19224 2.06501i −0.0670685 0.116166i
\(317\) 14.0540i 0.789350i 0.918821 + 0.394675i \(0.129143\pi\)
−0.918821 + 0.394675i \(0.870857\pi\)
\(318\) −0.925894 + 0.534565i −0.0519216 + 0.0299769i
\(319\) −6.68466 11.5782i −0.374269 0.648253i
\(320\) 0 0
\(321\) 4.12311 + 7.14143i 0.230129 + 0.398596i
\(322\) 1.51883 + 0.876894i 0.0846408 + 0.0488674i
\(323\) −9.63289 5.56155i −0.535988 0.309453i
\(324\) −0.438447 −0.0243582
\(325\) 0 0
\(326\) 7.50758 0.415806
\(327\) 2.43160 + 1.40388i 0.134468 + 0.0776349i
\(328\) −3.29762 1.90388i −0.182081 0.105124i
\(329\) 2.31534 + 4.01029i 0.127649 + 0.221094i
\(330\) 0 0
\(331\) 1.59612 + 2.76456i 0.0877306 + 0.151954i 0.906552 0.422095i \(-0.138705\pi\)
−0.818821 + 0.574049i \(0.805372\pi\)
\(332\) −0.332962 + 0.192236i −0.0182737 + 0.0105503i
\(333\) 7.56155i 0.414371i
\(334\) −8.00000 13.8564i −0.437741 0.758189i
\(335\) 0 0
\(336\) 1.31534 2.27824i 0.0717578 0.124288i
\(337\) 6.12311i 0.333547i −0.985995 0.166773i \(-0.946665\pi\)
0.985995 0.166773i \(-0.0533348\pi\)
\(338\) 19.6922 + 4.93087i 1.07112 + 0.268204i
\(339\) −5.80776 −0.315434
\(340\) 0 0
\(341\) 2.56155 4.43674i 0.138716 0.240263i
\(342\) −9.63289 + 5.56155i −0.520887 + 0.300734i
\(343\) 7.68466i 0.414933i
\(344\) 5.56155 + 9.63289i 0.299859 + 0.519371i
\(345\) 0 0
\(346\) −31.6155 −1.69966
\(347\) 23.9157 13.8078i 1.28386 0.741240i 0.306312 0.951931i \(-0.400905\pi\)
0.977553 + 0.210692i \(0.0675716\pi\)
\(348\) 2.53821 + 1.46543i 0.136062 + 0.0785556i
\(349\) 3.40388 5.89570i 0.182206 0.315589i −0.760426 0.649425i \(-0.775010\pi\)
0.942631 + 0.333836i \(0.108343\pi\)
\(350\) 0 0
\(351\) 0.500000 + 3.57071i 0.0266880 + 0.190591i
\(352\) 4.87689i 0.259939i
\(353\) 4.60322 + 2.65767i 0.245005 + 0.141454i 0.617475 0.786591i \(-0.288156\pi\)
−0.372470 + 0.928044i \(0.621489\pi\)
\(354\) 2.24621 3.89055i 0.119385 0.206781i
\(355\) 0 0
\(356\) 2.13826 0.113328
\(357\) −0.759413 + 0.438447i −0.0401924 + 0.0232051i
\(358\) −6.59524 + 3.80776i −0.348569 + 0.201247i
\(359\) 9.36932 0.494494 0.247247 0.968953i \(-0.420474\pi\)
0.247247 + 0.968953i \(0.420474\pi\)
\(360\) 0 0
\(361\) −15.8693 + 27.4865i −0.835227 + 1.44666i
\(362\) −3.63058 2.09612i −0.190819 0.110170i
\(363\) 7.00000i 0.367405i
\(364\) 0.822919 + 0.332962i 0.0431327 + 0.0174520i
\(365\) 0 0
\(366\) 3.02699 5.24290i 0.158223 0.274051i
\(367\) 14.7692 + 8.52699i 0.770945 + 0.445105i 0.833212 0.552954i \(-0.186500\pi\)
−0.0622668 + 0.998060i \(0.519833\pi\)
\(368\) 8.11407 4.68466i 0.422975 0.244205i
\(369\) 1.56155 0.0812912
\(370\) 0 0
\(371\) 0.192236 + 0.332962i 0.00998039 + 0.0172865i
\(372\) 1.12311i 0.0582303i
\(373\) −24.5685 + 14.1847i −1.27211 + 0.734454i −0.975385 0.220509i \(-0.929228\pi\)
−0.296726 + 0.954963i \(0.595895\pi\)
\(374\) −2.43845 + 4.22351i −0.126089 + 0.218393i
\(375\) 0 0
\(376\) 20.1080 1.03699
\(377\) 9.03996 22.3423i 0.465582 1.15069i
\(378\) 0.876894i 0.0451026i
\(379\) 11.8423 20.5115i 0.608300 1.05361i −0.383221 0.923657i \(-0.625185\pi\)
0.991521 0.129949i \(-0.0414814\pi\)
\(380\) 0 0
\(381\) −2.71922 4.70983i −0.139310 0.241292i
\(382\) 14.2462i 0.728900i
\(383\) 19.6922 11.3693i 1.00623 0.580945i 0.0961417 0.995368i \(-0.469350\pi\)
0.910085 + 0.414423i \(0.136016\pi\)
\(384\) −6.78078 11.7446i −0.346030 0.599342i
\(385\) 0 0
\(386\) −10.5346 18.2464i −0.536195 0.928717i
\(387\) −3.95042 2.28078i −0.200811 0.115938i
\(388\) −3.25088 1.87689i −0.165038 0.0952849i
\(389\) −34.0540 −1.72661 −0.863303 0.504687i \(-0.831608\pi\)
−0.863303 + 0.504687i \(0.831608\pi\)
\(390\) 0 0
\(391\) −3.12311 −0.157942
\(392\) 14.1164 + 8.15009i 0.712985 + 0.411642i
\(393\) 6.38202 + 3.68466i 0.321930 + 0.185866i
\(394\) −10.4384 18.0799i −0.525881 0.910853i
\(395\) 0 0
\(396\) 0.438447 + 0.759413i 0.0220328 + 0.0381619i
\(397\) 21.6974 12.5270i 1.08896 0.628711i 0.155661 0.987811i \(-0.450249\pi\)
0.933299 + 0.359099i \(0.116916\pi\)
\(398\) 34.6307i 1.73588i
\(399\) 2.00000 + 3.46410i 0.100125 + 0.173422i
\(400\) 0 0
\(401\) −7.21922 + 12.5041i −0.360511 + 0.624423i −0.988045 0.154166i \(-0.950731\pi\)
0.627534 + 0.778589i \(0.284064\pi\)
\(402\) 7.12311i 0.355268i
\(403\) 9.14657 1.28078i 0.455623 0.0638000i
\(404\) 3.31534 0.164944
\(405\) 0 0
\(406\) 2.93087 5.07642i 0.145457 0.251938i
\(407\) −13.0970 + 7.56155i −0.649194 + 0.374812i
\(408\) 3.80776i 0.188512i
\(409\) 3.18466 + 5.51599i 0.157471 + 0.272748i 0.933956 0.357388i \(-0.116333\pi\)
−0.776485 + 0.630136i \(0.782999\pi\)
\(410\) 0 0
\(411\) −5.56155 −0.274331
\(412\) −1.30560 + 0.753789i −0.0643223 + 0.0371365i
\(413\) −1.39909 0.807764i −0.0688446 0.0397475i
\(414\) −1.56155 + 2.70469i −0.0767461 + 0.132928i
\(415\) 0 0
\(416\) 6.93087 5.40938i 0.339814 0.265217i
\(417\) 17.9309i 0.878078i
\(418\) 19.2658 + 11.1231i 0.942320 + 0.544049i
\(419\) −17.1231 + 29.6581i −0.836518 + 1.44889i 0.0562697 + 0.998416i \(0.482079\pi\)
−0.892788 + 0.450477i \(0.851254\pi\)
\(420\) 0 0
\(421\) 31.2462 1.52285 0.761424 0.648255i \(-0.224501\pi\)
0.761424 + 0.648255i \(0.224501\pi\)
\(422\) −26.6204 + 15.3693i −1.29586 + 0.748167i
\(423\) −7.14143 + 4.12311i −0.347228 + 0.200472i
\(424\) 1.66950 0.0810783
\(425\) 0 0
\(426\) 10.9309 18.9328i 0.529602 0.917298i
\(427\) −1.88541 1.08854i −0.0912413 0.0526782i
\(428\) 3.61553i 0.174763i
\(429\) 5.68466 4.43674i 0.274458 0.214208i
\(430\) 0 0
\(431\) 5.56155 9.63289i 0.267891 0.464000i −0.700426 0.713725i \(-0.747007\pi\)
0.968317 + 0.249725i \(0.0803401\pi\)
\(432\) 4.05703 + 2.34233i 0.195194 + 0.112695i
\(433\) −7.58100 + 4.37689i −0.364320 + 0.210340i −0.670974 0.741481i \(-0.734124\pi\)
0.306654 + 0.951821i \(0.400790\pi\)
\(434\) 2.24621 0.107822
\(435\) 0 0
\(436\) 0.615528 + 1.06613i 0.0294785 + 0.0510582i
\(437\) 14.2462i 0.681489i
\(438\) −13.6899 + 7.90388i −0.654130 + 0.377662i
\(439\) −6.84233 + 11.8513i −0.326567 + 0.565630i −0.981828 0.189772i \(-0.939225\pi\)
0.655262 + 0.755402i \(0.272558\pi\)
\(440\) 0 0
\(441\) −6.68466 −0.318317
\(442\) −8.70700 + 1.21922i −0.414150 + 0.0579926i
\(443\) 34.7386i 1.65048i 0.564781 + 0.825241i \(0.308961\pi\)
−0.564781 + 0.825241i \(0.691039\pi\)
\(444\) 1.65767 2.87117i 0.0786696 0.136260i
\(445\) 0 0
\(446\) 6.24621 + 10.8188i 0.295767 + 0.512283i
\(447\) 2.43845i 0.115335i
\(448\) −2.70469 + 1.56155i −0.127785 + 0.0737764i
\(449\) −4.12311 7.14143i −0.194581 0.337025i 0.752182 0.658956i \(-0.229002\pi\)
−0.946763 + 0.321931i \(0.895668\pi\)
\(450\) 0 0
\(451\) −1.56155 2.70469i −0.0735307 0.127359i
\(452\) −2.20525 1.27320i −0.103726 0.0598862i
\(453\) −8.11407 4.68466i −0.381232 0.220104i
\(454\) 11.1231 0.522033
\(455\) 0 0
\(456\) 17.3693 0.813393
\(457\) −10.9254 6.30776i −0.511067 0.295065i 0.222205 0.975000i \(-0.428675\pi\)
−0.733272 + 0.679935i \(0.762008\pi\)
\(458\) 21.9705 + 12.6847i 1.02661 + 0.592715i
\(459\) −0.780776 1.35234i −0.0364435 0.0631220i
\(460\) 0 0
\(461\) 8.09612 + 14.0229i 0.377074 + 0.653111i 0.990635 0.136536i \(-0.0435970\pi\)
−0.613561 + 0.789647i \(0.710264\pi\)
\(462\) 1.51883 0.876894i 0.0706622 0.0407968i
\(463\) 14.3153i 0.665290i 0.943052 + 0.332645i \(0.107941\pi\)
−0.943052 + 0.332645i \(0.892059\pi\)
\(464\) −15.6577 27.1199i −0.726889 1.25901i
\(465\) 0 0
\(466\) 20.3002 35.1610i 0.940388 1.62880i
\(467\) 26.0000i 1.20314i −0.798821 0.601568i \(-0.794543\pi\)
0.798821 0.601568i \(-0.205457\pi\)
\(468\) −0.592932 + 1.46543i −0.0274083 + 0.0677397i
\(469\) −2.56155 −0.118282
\(470\) 0 0
\(471\) −10.1847 + 17.6403i −0.469284 + 0.812824i
\(472\) −6.07530 + 3.50758i −0.279638 + 0.161449i
\(473\) 9.12311i 0.419481i
\(474\) −4.24621 7.35465i −0.195035 0.337810i
\(475\) 0 0
\(476\) −0.384472 −0.0176222
\(477\) −0.592932 + 0.342329i −0.0271485 + 0.0156742i
\(478\) 34.3081 + 19.8078i 1.56921 + 0.905986i
\(479\) 5.12311 8.87348i 0.234081 0.405440i −0.724924 0.688828i \(-0.758125\pi\)
0.959005 + 0.283389i \(0.0914587\pi\)
\(480\) 0 0
\(481\) −25.2732 10.2258i −1.15236 0.466257i
\(482\) 27.8078i 1.26661i
\(483\) 0.972638 + 0.561553i 0.0442566 + 0.0255515i
\(484\) −1.53457 + 2.65794i −0.0697530 + 0.120816i
\(485\) 0 0
\(486\) −1.56155 −0.0708335
\(487\) 6.16879 3.56155i 0.279535 0.161389i −0.353678 0.935367i \(-0.615069\pi\)
0.633213 + 0.773978i \(0.281736\pi\)
\(488\) −8.18706 + 4.72680i −0.370611 + 0.213972i
\(489\) 4.80776 0.217415
\(490\) 0 0
\(491\) 18.1231 31.3901i 0.817884 1.41662i −0.0893539 0.996000i \(-0.528480\pi\)
0.907238 0.420617i \(-0.138186\pi\)
\(492\) 0.592932 + 0.342329i 0.0267314 + 0.0154334i
\(493\) 10.4384i 0.470124i
\(494\) 5.56155 + 39.7174i 0.250226 + 1.78697i
\(495\) 0 0
\(496\) 6.00000 10.3923i 0.269408 0.466628i
\(497\) −6.80847 3.93087i −0.305401 0.176324i
\(498\) −1.18586 + 0.684658i −0.0531398 + 0.0306803i
\(499\) −4.49242 −0.201108 −0.100554 0.994932i \(-0.532062\pi\)
−0.100554 + 0.994932i \(0.532062\pi\)
\(500\) 0 0
\(501\) −5.12311 8.87348i −0.228883 0.396438i
\(502\) 29.2614i 1.30600i
\(503\) 24.4619 14.1231i 1.09070 0.629718i 0.156940 0.987608i \(-0.449837\pi\)
0.933764 + 0.357890i \(0.116504\pi\)
\(504\) 0.684658 1.18586i 0.0304971 0.0528225i
\(505\) 0 0
\(506\) 6.24621 0.277678
\(507\) 12.6107 + 3.15767i 0.560060 + 0.140237i
\(508\) 2.38447i 0.105794i
\(509\) −6.90388 + 11.9579i −0.306009 + 0.530023i −0.977486 0.211003i \(-0.932327\pi\)
0.671476 + 0.741026i \(0.265660\pi\)
\(510\) 0 0
\(511\) 2.84233 + 4.92306i 0.125737 + 0.217783i
\(512\) 11.4233i 0.504843i
\(513\) −6.16879 + 3.56155i −0.272359 + 0.157246i
\(514\) −22.7808 39.4575i −1.00482 1.74039i
\(515\) 0 0
\(516\) −1.00000 1.73205i −0.0440225 0.0762493i
\(517\) 14.2829 + 8.24621i 0.628159 + 0.362668i
\(518\) −5.74234 3.31534i −0.252304 0.145668i
\(519\) −20.2462 −0.888710
\(520\) 0 0
\(521\) −9.06913 −0.397326 −0.198663 0.980068i \(-0.563660\pi\)
−0.198663 + 0.980068i \(0.563660\pi\)
\(522\) 9.03996 + 5.21922i 0.395668 + 0.228439i
\(523\) 29.3251 + 16.9309i 1.28230 + 0.740335i 0.977268 0.212007i \(-0.0680001\pi\)
0.305030 + 0.952343i \(0.401333\pi\)
\(524\) 1.61553 + 2.79818i 0.0705747 + 0.122239i
\(525\) 0 0
\(526\) 7.31534 + 12.6705i 0.318964 + 0.552462i
\(527\) −3.46410 + 2.00000i −0.150899 + 0.0871214i
\(528\) 9.36932i 0.407747i
\(529\) −9.50000 16.4545i −0.413043 0.715412i
\(530\) 0 0
\(531\) 1.43845 2.49146i 0.0624233 0.108120i
\(532\) 1.75379i 0.0760364i
\(533\) 2.11176 5.21922i 0.0914704 0.226070i
\(534\) 7.61553 0.329556
\(535\) 0 0
\(536\) −5.56155 + 9.63289i −0.240222 + 0.416078i
\(537\) −4.22351 + 2.43845i −0.182258 + 0.105227i
\(538\) 33.3693i 1.43865i
\(539\) 6.68466 + 11.5782i 0.287929 + 0.498707i
\(540\) 0 0
\(541\) 19.7386 0.848630 0.424315 0.905515i \(-0.360515\pi\)
0.424315 + 0.905515i \(0.360515\pi\)
\(542\) 40.4768 23.3693i 1.73863 1.00380i
\(543\) −2.32498 1.34233i −0.0997745 0.0576049i
\(544\) −1.90388 + 3.29762i −0.0816283 + 0.141384i
\(545\) 0 0
\(546\) 2.93087 + 1.18586i 0.125430 + 0.0507503i
\(547\) 3.93087i 0.168072i 0.996463 + 0.0840359i \(0.0267811\pi\)
−0.996463 + 0.0840359i \(0.973219\pi\)
\(548\) −2.11176 1.21922i −0.0902098 0.0520827i
\(549\) 1.93845 3.35749i 0.0827309 0.143294i
\(550\) 0 0
\(551\) 47.6155 2.02849
\(552\) 4.22351 2.43845i 0.179765 0.103787i
\(553\) −2.64482 + 1.52699i −0.112469 + 0.0649341i
\(554\) 8.30019 0.352641
\(555\) 0 0
\(556\) 3.93087 6.80847i 0.166706 0.288743i
\(557\) 37.1792 + 21.4654i 1.57533 + 0.909520i 0.995498 + 0.0947869i \(0.0302170\pi\)
0.579837 + 0.814733i \(0.303116\pi\)
\(558\) 4.00000i 0.169334i
\(559\) −12.9654 + 10.1192i −0.548379 + 0.427997i
\(560\) 0 0
\(561\) −1.56155 + 2.70469i −0.0659288 + 0.114192i
\(562\) 24.0822 + 13.9039i 1.01585 + 0.586500i
\(563\) 20.2384 11.6847i 0.852948 0.492450i −0.00869657 0.999962i \(-0.502768\pi\)
0.861644 + 0.507513i \(0.169435\pi\)
\(564\) −3.61553 −0.152241
\(565\) 0 0
\(566\) −10.6847 18.5064i −0.449110 0.777881i
\(567\) 0.561553i 0.0235830i
\(568\) −29.5646 + 17.0691i −1.24050 + 0.716205i
\(569\) −4.36932 + 7.56788i −0.183171 + 0.317262i −0.942959 0.332910i \(-0.891970\pi\)
0.759787 + 0.650171i \(0.225303\pi\)
\(570\) 0 0
\(571\) −5.36932 −0.224699 −0.112349 0.993669i \(-0.535838\pi\)
−0.112349 + 0.993669i \(0.535838\pi\)
\(572\) 3.13114 0.438447i 0.130920 0.0183324i
\(573\) 9.12311i 0.381123i
\(574\) 0.684658 1.18586i 0.0285771 0.0494970i
\(575\) 0 0
\(576\) −2.78078 4.81645i −0.115866 0.200685i
\(577\) 17.3153i 0.720847i −0.932789 0.360424i \(-0.882632\pi\)
0.932789 0.360424i \(-0.117368\pi\)
\(578\) −19.6922 + 11.3693i −0.819089 + 0.472901i
\(579\) −6.74621 11.6848i −0.280363 0.485603i
\(580\) 0 0
\(581\) 0.246211 + 0.426450i 0.0102146 + 0.0176921i
\(582\) −11.5782 6.68466i −0.479931 0.277088i
\(583\) 1.18586 + 0.684658i 0.0491134 + 0.0283557i
\(584\) 24.6847 1.02146
\(585\) 0 0
\(586\) −31.9157 −1.31843
\(587\) −34.0948 19.6847i −1.40724 0.812473i −0.412123 0.911128i \(-0.635212\pi\)
−0.995122 + 0.0986556i \(0.968546\pi\)
\(588\) −2.53821 1.46543i −0.104674 0.0604335i
\(589\) 9.12311 + 15.8017i 0.375911 + 0.651097i
\(590\) 0 0
\(591\) −6.68466 11.5782i −0.274970 0.476262i
\(592\) −30.6775 + 17.7116i −1.26084 + 0.727944i
\(593\) 17.4233i 0.715489i 0.933820 + 0.357744i \(0.116454\pi\)
−0.933820 + 0.357744i \(0.883546\pi\)
\(594\) 1.56155 + 2.70469i 0.0640713 + 0.110975i
\(595\) 0 0
\(596\) 0.534565 0.925894i 0.0218966 0.0379261i
\(597\) 22.1771i 0.907648i
\(598\) 6.92820 + 8.87689i 0.283315 + 0.363003i
\(599\) 41.6155 1.70036 0.850182 0.526489i \(-0.176492\pi\)
0.850182 + 0.526489i \(0.176492\pi\)
\(600\) 0 0
\(601\) 3.53457 6.12205i 0.144178 0.249723i −0.784888 0.619638i \(-0.787280\pi\)
0.929066 + 0.369914i \(0.120613\pi\)
\(602\) −3.46410 + 2.00000i −0.141186 + 0.0815139i
\(603\) 4.56155i 0.185761i
\(604\) −2.05398 3.55759i −0.0835751 0.144756i
\(605\) 0 0
\(606\) 11.8078 0.479658
\(607\) −13.8564 + 8.00000i −0.562414 + 0.324710i −0.754114 0.656744i \(-0.771933\pi\)
0.191700 + 0.981454i \(0.438600\pi\)
\(608\) 15.0423 + 8.68466i 0.610045 + 0.352209i
\(609\) 1.87689 3.25088i 0.0760556 0.131732i
\(610\) 0 0
\(611\) 4.12311 + 29.4449i 0.166803 + 1.19121i
\(612\) 0.684658i 0.0276757i
\(613\) −30.1912 17.4309i −1.21941 0.704026i −0.254618 0.967042i \(-0.581950\pi\)
−0.964792 + 0.263016i \(0.915283\pi\)
\(614\) −24.0540 + 41.6627i −0.970739 + 1.68137i
\(615\) 0 0
\(616\) −2.73863 −0.110343
\(617\) 8.49377 4.90388i 0.341946 0.197423i −0.319186 0.947692i \(-0.603409\pi\)
0.661132 + 0.750269i \(0.270076\pi\)
\(618\) −4.64996 + 2.68466i −0.187049 + 0.107993i
\(619\) −29.3002 −1.17767 −0.588837 0.808252i \(-0.700414\pi\)
−0.588837 + 0.808252i \(0.700414\pi\)
\(620\) 0 0
\(621\) −1.00000 + 1.73205i −0.0401286 + 0.0695048i
\(622\) −25.8610 14.9309i −1.03693 0.598673i
\(623\) 2.73863i 0.109721i
\(624\) 13.3153 10.3923i 0.533040 0.416025i
\(625\) 0 0
\(626\) −10.6847 + 18.5064i −0.427045 + 0.739663i
\(627\) 12.3376 + 7.12311i 0.492716 + 0.284469i
\(628\) −7.73436 + 4.46543i −0.308635 + 0.178190i
\(629\) 11.8078 0.470806
\(630\) 0 0
\(631\) 9.28078 + 16.0748i 0.369462 + 0.639927i 0.989481 0.144660i \(-0.0462087\pi\)
−0.620020 + 0.784586i \(0.712875\pi\)
\(632\) 13.2614i 0.527509i
\(633\) −17.0474 + 9.84233i −0.677574 + 0.391197i
\(634\) −10.9730 + 19.0058i −0.435794 + 0.754817i
\(635\) 0 0
\(636\) −0.300187 −0.0119032
\(637\) −9.03996 + 22.3423i −0.358176 + 0.885235i
\(638\) 20.8769i 0.826524i
\(639\) 7.00000 12.1244i 0.276916 0.479632i
\(640\) 0 0
\(641\) 9.58854 + 16.6078i 0.378725 + 0.655970i 0.990877 0.134770i \(-0.0430294\pi\)
−0.612152 + 0.790740i \(0.709696\pi\)
\(642\) 12.8769i 0.508210i
\(643\) 27.3200 15.7732i 1.07739 0.622034i 0.147202 0.989106i \(-0.452973\pi\)
0.930192 + 0.367072i \(0.119640\pi\)
\(644\) 0.246211 + 0.426450i 0.00970208 + 0.0168045i
\(645\) 0 0
\(646\) −8.68466 15.0423i −0.341693 0.591830i
\(647\) 5.52911 + 3.19224i 0.217372 + 0.125500i 0.604733 0.796428i \(-0.293280\pi\)
−0.387361 + 0.921928i \(0.626613\pi\)
\(648\) 2.11176 + 1.21922i 0.0829577 + 0.0478956i
\(649\) −5.75379 −0.225856
\(650\) 0 0
\(651\) 1.43845 0.0563772
\(652\) 1.82554 + 1.05398i 0.0714936 + 0.0412769i
\(653\) 20.0252 + 11.5616i 0.783647 + 0.452439i 0.837721 0.546098i \(-0.183888\pi\)
−0.0540745 + 0.998537i \(0.517221\pi\)
\(654\) 2.19224 + 3.79706i 0.0857232 + 0.148477i
\(655\) 0 0
\(656\) −3.65767 6.33527i −0.142808 0.247351i
\(657\) −8.76687 + 5.06155i −0.342028 + 0.197470i
\(658\) 7.23106i 0.281896i
\(659\) −1.12311 1.94528i −0.0437500 0.0757772i 0.843321 0.537410i \(-0.180597\pi\)
−0.887071 + 0.461633i \(0.847264\pi\)
\(660\) 0 0
\(661\) −2.81534 + 4.87631i −0.109504 + 0.189667i −0.915569 0.402160i \(-0.868260\pi\)
0.806065 + 0.591827i \(0.201593\pi\)
\(662\) 4.98485i 0.193742i
\(663\) −5.57586 + 0.780776i −0.216548 + 0.0303228i
\(664\) 2.13826 0.0829806
\(665\) 0 0
\(666\) 5.90388 10.2258i 0.228771 0.396243i
\(667\) 11.5782 6.68466i 0.448308 0.258831i
\(668\) 4.49242i 0.173817i
\(669\) 4.00000 + 6.92820i 0.154649 + 0.267860i
\(670\) 0 0
\(671\) −7.75379 −0.299332
\(672\) 1.18586 0.684658i 0.0457457 0.0264113i
\(673\) −20.1318 11.6231i −0.776024 0.448038i 0.0589952 0.998258i \(-0.481210\pi\)
−0.835019 + 0.550220i \(0.814544\pi\)
\(674\) 4.78078 8.28055i 0.184149 0.318955i
\(675\) 0 0
\(676\) 4.09612 + 3.96355i 0.157543 + 0.152444i
\(677\) 15.6155i 0.600153i −0.953915 0.300077i \(-0.902988\pi\)
0.953915 0.300077i \(-0.0970123\pi\)
\(678\) −7.85410 4.53457i −0.301635 0.174149i
\(679\) −2.40388 + 4.16365i −0.0922525 + 0.159786i
\(680\) 0 0
\(681\) 7.12311 0.272958
\(682\) 6.92820 4.00000i 0.265295 0.153168i
\(683\) 33.0025 19.0540i 1.26280 0.729080i 0.289188 0.957272i \(-0.406615\pi\)
0.973616 + 0.228192i \(0.0732815\pi\)
\(684\) −3.12311 −0.119415
\(685\) 0 0
\(686\) −6.00000 + 10.3923i −0.229081 + 0.396780i
\(687\) 14.0696 + 8.12311i 0.536790 + 0.309916i
\(688\) 21.3693i 0.814698i
\(689\) 0.342329 + 2.44472i 0.0130417 + 0.0931364i
\(690\) 0 0
\(691\) 25.6501 44.4273i 0.975776 1.69009i 0.298424 0.954433i \(-0.403539\pi\)
0.677352 0.735659i \(-0.263128\pi\)
\(692\) −7.68762 4.43845i −0.292239 0.168724i
\(693\) 0.972638 0.561553i 0.0369475 0.0213316i
\(694\) 43.1231 1.63693
\(695\) 0 0
\(696\) −8.15009 14.1164i −0.308928 0.535080i
\(697\) 2.43845i 0.0923628i
\(698\) 9.20644 5.31534i 0.348469 0.201189i
\(699\) 13.0000 22.5167i 0.491705 0.851658i
\(700\) 0 0
\(701\) −5.36932 −0.202796 −0.101398 0.994846i \(-0.532332\pi\)
−0.101398 + 0.994846i \(0.532332\pi\)
\(702\) −2.11176 + 5.21922i −0.0797031 + 0.196987i
\(703\) 53.8617i 2.03143i
\(704\) −5.56155 + 9.63289i −0.209609 + 0.363053i
\(705\) 0 0
\(706\) 4.15009 + 7.18817i 0.156191 + 0.270530i
\(707\) 4.24621i 0.159695i
\(708\) 1.09238 0.630683i 0.0410540 0.0237025i
\(709\) −3.74621 6.48863i −0.140692 0.243686i 0.787065 0.616869i \(-0.211599\pi\)
−0.927757 + 0.373184i \(0.878266\pi\)
\(710\) 0 0
\(711\) −2.71922 4.70983i −0.101979 0.176633i
\(712\) −10.2988 5.94602i −0.385964 0.222837i
\(713\) 4.43674 + 2.56155i 0.166157 + 0.0959309i
\(714\) −1.36932 −0.0512454
\(715\) 0 0
\(716\) −2.13826 −0.0799106
\(717\) 21.9705 + 12.6847i 0.820502 + 0.473717i
\(718\) 12.6705 + 7.31534i 0.472860 + 0.273006i
\(719\) −11.6847 20.2384i −0.435764 0.754766i 0.561593 0.827413i \(-0.310189\pi\)
−0.997358 + 0.0726475i \(0.976855\pi\)
\(720\) 0 0
\(721\) 0.965435 + 1.67218i 0.0359547 + 0.0622753i
\(722\) −42.9216 + 24.7808i −1.59738 + 0.922245i
\(723\) 17.8078i 0.662278i
\(724\) −0.588540 1.01938i −0.0218729 0.0378850i
\(725\) 0 0
\(726\) −5.46543 + 9.46641i −0.202841 + 0.351331i
\(727\) 38.6695i 1.43417i −0.696984 0.717086i \(-0.745475\pi\)
0.696984 0.717086i \(-0.254525\pi\)
\(728\) −3.03765 3.89205i −0.112583 0.144249i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 3.56155 6.16879i 0.131729 0.228161i
\(732\) 1.47208 0.849907i 0.0544097 0.0314135i
\(733\) 20.5076i 0.757465i −0.925506 0.378732i \(-0.876360\pi\)
0.925506 0.378732i \(-0.123640\pi\)
\(734\) 13.3153 + 23.0628i 0.491478 + 0.851265i
\(735\) 0 0
\(736\) 4.87689 0.179765
\(737\) −7.90084 + 4.56155i −0.291031 + 0.168027i
\(738\) 2.11176 + 1.21922i 0.0777349 + 0.0448802i
\(739\) 5.12311 8.87348i 0.188456 0.326416i −0.756279 0.654249i \(-0.772985\pi\)
0.944736 + 0.327833i \(0.106318\pi\)
\(740\) 0 0
\(741\) 3.56155 + 25.4346i 0.130837 + 0.934362i
\(742\) 0.600373i 0.0220404i
\(743\) −10.9385 6.31534i −0.401294 0.231687i 0.285748 0.958305i \(-0.407758\pi\)
−0.687042 + 0.726617i \(0.741091\pi\)
\(744\) 3.12311 5.40938i 0.114499 0.198317i
\(745\) 0 0
\(746\) −44.3002 −1.62195
\(747\) −0.759413 + 0.438447i −0.0277855 + 0.0160419i
\(748\) −1.18586 + 0.684658i −0.0433595 + 0.0250336i
\(749\) 4.63068 0.169201
\(750\) 0 0
\(751\) −22.0540 + 38.1986i −0.804761 + 1.39389i 0.111691 + 0.993743i \(0.464373\pi\)
−0.916452 + 0.400144i \(0.868960\pi\)
\(752\) 33.4552 + 19.3153i 1.21998 + 0.704358i
\(753\) 18.7386i 0.682874i
\(754\) 29.6695 23.1563i 1.08050 0.843304i
\(755\) 0 0
\(756\) −0.123106 + 0.213225i −0.00447731 + 0.00775493i
\(757\) −25.9808 15.0000i −0.944287 0.545184i −0.0529853 0.998595i \(-0.516874\pi\)
−0.891302 + 0.453411i \(0.850207\pi\)
\(758\) 32.0298 18.4924i 1.16338 0.671675i
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) −4.68466 8.11407i −0.169819 0.294135i 0.768537 0.639805i \(-0.220985\pi\)
−0.938356 + 0.345670i \(0.887652\pi\)
\(762\) 8.49242i 0.307648i
\(763\) 1.36547 0.788354i 0.0494333 0.0285403i
\(764\) −2.00000 + 3.46410i −0.0723575 + 0.125327i
\(765\) 0 0
\(766\) 35.5076 1.28294
\(767\) −6.38202 8.17708i −0.230441 0.295257i
\(768\) 10.0540i 0.362792i
\(769\) −9.00000 + 15.5885i −0.324548 + 0.562134i −0.981421 0.191867i \(-0.938546\pi\)
0.656873 + 0.754002i \(0.271879\pi\)
\(770\) 0 0
\(771\) −14.5885 25.2681i −0.525393 0.910008i
\(772\) 5.91571i 0.212911i
\(773\) 20.9978 12.1231i 0.755240 0.436038i −0.0723444 0.997380i \(-0.523048\pi\)
0.827584 + 0.561342i \(0.189715\pi\)
\(774\) −3.56155 6.16879i −0.128017 0.221733i
\(775\) 0 0
\(776\) 10.4384 + 18.0799i 0.374718 + 0.649031i
\(777\) −3.67733 2.12311i −0.131923 0.0761660i
\(778\) −46.0527 26.5885i −1.65107 0.953245i
\(779\) 11.1231 0.398527
\(780\) 0 0
\(781\) −28.0000 −1.00192
\(782\) −4.22351 2.43845i −0.151033 0.0871987i
\(783\) 5.78908 + 3.34233i 0.206885 + 0.119445i
\(784\) 15.6577 + 27.1199i 0.559203 + 0.968567i
\(785\) 0 0
\(786\) 5.75379 + 9.96585i 0.205231 + 0.355470i
\(787\) 38.2585 22.0885i 1.36377 0.787371i 0.373644 0.927572i \(-0.378108\pi\)
0.990123 + 0.140201i \(0.0447748\pi\)
\(788\) 5.86174i 0.208816i
\(789\) 4.68466 + 8.11407i 0.166778 + 0.288868i
\(790\) 0 0
\(791\) −1.63068 + 2.82443i −0.0579804 + 0.100425i
\(792\) 4.87689i 0.173293i
\(793\) −8.60039 11.0194i −0.305409 0.391311i
\(794\) 39.1231 1.38843
\(795\) 0 0
\(796\) −4.86174 + 8.42078i −0.172320 + 0.298467i
\(797\) −0.332962 + 0.192236i −0.0117941 + 0.00680935i −0.505885 0.862601i \(-0.668834\pi\)
0.494091 + 0.869410i \(0.335501\pi\)
\(798\) 6.24621i 0.221113i
\(799\) −6.43845 11.1517i −0.227776 0.394519i
\(800\) 0 0
\(801\) 4.87689 0.172317
\(802\) −19.5258 + 11.2732i −0.689478 + 0.398070i
\(803\) 17.5337 + 10.1231i 0.618752 + 0.357237i
\(804\) 1.00000 1.73205i 0.0352673 0.0610847i
\(805\) 0 0
\(806\) 13.3693 + 5.40938i 0.470914 + 0.190537i
\(807\) 21.3693i 0.752236i
\(808\) −15.9682 9.21922i −0.561758 0.324331i
\(809\) −8.15009 + 14.1164i −0.286542 + 0.496305i −0.972982 0.230881i \(-0.925839\pi\)
0.686440 + 0.727187i \(0.259172\pi\)
\(810\) 0 0
\(811\) 2.56155 0.0899483 0.0449741 0.998988i \(-0.485679\pi\)
0.0449741 + 0.998988i \(0.485679\pi\)
\(812\) 1.42534 0.822919i 0.0500195 0.0288788i
\(813\) 25.9209 14.9654i 0.909085 0.524861i
\(814\) −23.6155 −0.827724
\(815\) 0 0
\(816\) −3.65767 + 6.33527i −0.128044 + 0.221779i
\(817\) −28.1393 16.2462i −0.984468 0.568383i
\(818\) 9.94602i 0.347755i
\(819\) 1.87689 + 0.759413i 0.0655840 + 0.0265360i
\(820\) 0 0
\(821\) −3.24621 + 5.62260i −0.113294 + 0.196230i −0.917096 0.398666i \(-0.869473\pi\)
0.803803 + 0.594896i \(0.202807\pi\)
\(822\) −7.52113 4.34233i −0.262330 0.151456i
\(823\) −6.92820 + 4.00000i −0.241502 + 0.139431i −0.615867 0.787850i \(-0.711194\pi\)
0.374365 + 0.927281i \(0.377861\pi\)
\(824\) 8.38447 0.292087
\(825\) 0 0
\(826\) −1.26137 2.18475i −0.0438885 0.0760172i
\(827\) 14.7386i 0.512513i −0.966609 0.256256i \(-0.917511\pi\)
0.966609 0.256256i \(-0.0824891\pi\)
\(828\) −0.759413 + 0.438447i −0.0263914 + 0.0152371i
\(829\) 6.74621 11.6848i 0.234306 0.405829i −0.724765 0.688996i \(-0.758052\pi\)
0.959071 + 0.283167i \(0.0913850\pi\)
\(830\) 0 0
\(831\) 5.31534 0.184387
\(832\) −19.8587 + 2.78078i −0.688477 + 0.0964061i
\(833\) 10.4384i 0.361671i
\(834\) 14.0000 24.2487i 0.484780 0.839664i
\(835\) 0 0
\(836\) 3.12311 + 5.40938i 0.108015 + 0.187087i
\(837\) 2.56155i 0.0885402i
\(838\) −46.3127 + 26.7386i −1.59984 + 0.923671i
\(839\) 10.8078 + 18.7196i 0.373125 + 0.646272i 0.990045 0.140754i \(-0.0449528\pi\)
−0.616919 + 0.787027i \(0.711619\pi\)
\(840\) 0 0
\(841\) −7.84233 13.5833i −0.270425 0.468390i
\(842\) 42.2556 + 24.3963i 1.45623 + 0.840752i
\(843\) 15.4220 + 8.90388i 0.531161 + 0.306666i
\(844\) −8.63068 −0.297080
\(845\) 0 0
\(846\) −12.8769 −0.442717
\(847\) 3.40423 + 1.96543i 0.116971 + 0.0675331i
\(848\) 2.77768 + 1.60370i 0.0953860 + 0.0550711i
\(849\) −6.84233 11.8513i −0.234828 0.406734i
\(850\) 0 0
\(851\) −7.56155 13.0970i −0.259207 0.448959i
\(852\) 5.31589 3.06913i 0.182119 0.105147i
\(853\) 2.12311i 0.0726938i −0.999339 0.0363469i \(-0.988428\pi\)
0.999339 0.0363469i \(-0.0115721\pi\)
\(854\) −1.69981 2.94416i −0.0581664 0.100747i
\(855\) 0 0
\(856\) 10.0540 17.4140i 0.343638 0.595198i
\(857\) 35.5616i 1.21476i 0.794412 + 0.607380i \(0.207779\pi\)
−0.794412 + 0.607380i \(0.792221\pi\)
\(858\) 11.1517 1.56155i 0.380713 0.0533105i
\(859\) −24.5616 −0.838029 −0.419015 0.907979i \(-0.637624\pi\)
−0.419015 + 0.907979i \(0.637624\pi\)
\(860\) 0 0
\(861\) 0.438447 0.759413i 0.0149422 0.0258807i
\(862\) 15.0423 8.68466i 0.512342 0.295801i
\(863\) 30.4924i 1.03797i −0.854782 0.518987i \(-0.826309\pi\)
0.854782 0.518987i \(-0.173691\pi\)
\(864\) 1.21922 + 2.11176i 0.0414788 + 0.0718434i
\(865\) 0 0
\(866\) −13.6695 −0.464509
\(867\) −12.6107 + 7.28078i −0.428281 + 0.247268i
\(868\) 0.546188 + 0.315342i 0.0185388 + 0.0107034i
\(869\) −5.43845 + 9.41967i −0.184487 + 0.319540i
\(870\) 0 0
\(871\) −15.2462 6.16879i −0.516598 0.209021i
\(872\) 6.84658i 0.231855i
\(873\) −7.41452 4.28078i −0.250944 0.144882i
\(874\) −11.1231 + 19.2658i −0.376245 + 0.651675i
\(875\) 0 0
\(876\) −4.43845 −0.149961
\(877\) 20.4049 11.7808i 0.689025 0.397809i −0.114222 0.993455i \(-0.536437\pi\)
0.803247 + 0.595647i \(0.203104\pi\)
\(878\) −18.5064 + 10.6847i −0.624560 + 0.360590i
\(879\) −20.4384 −0.689372
\(880\) 0 0
\(881\) 4.53457 7.85410i 0.152773 0.264611i −0.779473 0.626436i \(-0.784513\pi\)
0.932246 + 0.361825i \(0.117846\pi\)
\(882\) −9.03996 5.21922i −0.304391 0.175740i
\(883\) 8.80776i 0.296405i −0.988957 0.148202i \(-0.952651\pi\)
0.988957 0.148202i \(-0.0473487\pi\)
\(884\) −2.28835 0.925894i −0.0769657 0.0311412i
\(885\) 0 0
\(886\) −27.1231 + 46.9786i −0.911219 + 1.57828i
\(887\) −21.3308 12.3153i −0.716218 0.413509i 0.0971410 0.995271i \(-0.469030\pi\)
−0.813359 + 0.581762i \(0.802364\pi\)
\(888\) −15.9682 + 9.21922i −0.535856 + 0.309377i
\(889\) −3.05398 −0.102427
\(890\) 0 0
\(891\) 1.00000 + 1.73205i 0.0335013 + 0.0580259i
\(892\) 3.50758i 0.117442i
\(893\) −50.8691 + 29.3693i −1.70227 + 0.982807i
\(894\) 1.90388 3.29762i 0.0636753 0.110289i
\(895\) 0 0
\(896\) −7.61553 −0.254417
\(897\) 4.43674 + 5.68466i 0.148138 + 0.189805i
\(898\) 12.8769i 0.429708i
\(899\) 8.56155 14.8290i 0.285544 0.494576i
\(900\) 0 0
\(901\) −0.534565 0.925894i −0.0178089 0.0308460i
\(902\) 4.87689i 0.162383i
\(903\) −2.21837 + 1.28078i −0.0738227 + 0.0426216i
\(904\) 7.08096 + 12.2646i 0.235509 + 0.407914i
\(905\) 0 0
\(906\) −7.31534 12.6705i −0.243036 0.420951i
\(907\) −24.2487 14.0000i −0.805165 0.464862i 0.0401089 0.999195i \(-0.487230\pi\)
−0.845274 + 0.534333i \(0.820563\pi\)
\(908\) 2.70469 + 1.56155i 0.0897583 + 0.0518220i
\(909\) 7.56155 0.250801
\(910\) 0 0
\(911\) 38.7386 1.28347 0.641734 0.766927i \(-0.278215\pi\)
0.641734 + 0.766927i \(0.278215\pi\)
\(912\) 28.8987 + 16.6847i 0.956931 + 0.552484i
\(913\) 1.51883 + 0.876894i 0.0502658 + 0.0290210i
\(914\) −9.84991 17.0605i −0.325806 0.564312i
\(915\) 0 0
\(916\) 3.56155 + 6.16879i 0.117677 + 0.203823i
\(917\) 3.58384 2.06913i 0.118349 0.0683287i
\(918\) 2.43845i 0.0804807i
\(919\) 5.75379 + 9.96585i 0.189800 + 0.328743i 0.945183 0.326540i \(-0.105883\pi\)
−0.755383 + 0.655283i \(0.772549\pi\)
\(920\) 0 0
\(921\) −15.4039 + 26.6803i −0.507575 + 0.879146i
\(922\) 25.2850i 0.832718i
\(923\) −31.0572 39.7926i −1.02226 1.30979i
\(924\) 0.492423 0.0161995
\(925\) 0 0
\(926\) −11.1771 + 19.3593i −0.367302 + 0.636185i
\(927\) −2.97778 + 1.71922i −0.0978032 + 0.0564667i
\(928\) 16.3002i 0.535080i
\(929\) −3.90388 6.76172i −0.128082 0.221845i 0.794851 0.606804i \(-0.207549\pi\)
−0.922934 + 0.384959i \(0.874215\pi\)
\(930\) 0 0
\(931\) −47.6155 −1.56054
\(932\) 9.87237 5.69981i 0.323380 0.186704i
\(933\) −16.5611 9.56155i −0.542186 0.313031i
\(934\) 20.3002 35.1610i 0.664242 1.15050i
\(935\) 0 0
\(936\) 6.93087 5.40938i 0.226543 0.176811i
\(937\) 7.56155i 0.247025i −0.992343 0.123513i \(-0.960584\pi\)
0.992343 0.123513i \(-0.0394159\pi\)
\(938\) −3.46410 2.00000i −0.113107 0.0653023i
\(939\) −6.84233 + 11.8513i −0.223291 + 0.386751i
\(940\) 0 0
\(941\) 30.4924 0.994025 0.497012 0.867744i \(-0.334430\pi\)
0.497012 + 0.867744i \(0.334430\pi\)
\(942\) −27.5463 + 15.9039i −0.897508 + 0.518176i
\(943\) 2.70469 1.56155i 0.0880768 0.0508512i
\(944\) −13.4773 −0.438648
\(945\) 0 0
\(946\) −7.12311 + 12.3376i −0.231592 + 0.401129i
\(947\) 33.5486 + 19.3693i 1.09018 + 0.629418i 0.933626 0.358250i \(-0.116627\pi\)
0.156559 + 0.987669i \(0.449960\pi\)
\(948\) 2.38447i 0.0774440i
\(949\) 5.06155 + 36.1467i 0.164305 + 1.17337i
\(950\) 0 0
\(951\) −7.02699 + 12.1711i −0.227866 + 0.394675i
\(952\) 1.85179 + 1.06913i 0.0600168 + 0.0346507i
\(953\) −26.8337 + 15.4924i −0.869228 + 0.501849i −0.867091 0.498149i \(-0.834013\pi\)
−0.00213612 + 0.999998i \(0.500680\pi\)
\(954\) −1.06913 −0.0346144
\(955\) 0 0
\(956\) 5.56155 + 9.63289i 0.179873 + 0.311550i
\(957\) 13.3693i 0.432169i
\(958\) 13.8564 8.00000i 0.447680 0.258468i
\(959\) −1.56155 + 2.70469i −0.0504252 + 0.0873390i
\(960\) 0 0
\(961\) −24.4384 −0.788337
\(962\) −26.1940 33.5616i −0.844528 1.08207i
\(963\) 8.24621i 0.265730i
\(964\) −3.90388 + 6.76172i −0.125736 + 0.217780i
\(965\) 0 0
\(966\) 0.876894 + 1.51883i 0.0282136 + 0.0488674i
\(967\) 0.876894i 0.0281990i −0.999901 0.0140995i \(-0.995512\pi\)
0.999901 0.0140995i \(-0.00448816\pi\)
\(968\) 14.7823 8.53457i 0.475121 0.274311i
\(969\) −5.56155 9.63289i −0.178663 0.309453i
\(970\) 0 0
\(971\) 6.49242 + 11.2452i 0.208352 + 0.360876i 0.951195 0.308589i \(-0.0998568\pi\)
−0.742844 + 0.669465i \(0.766523\pi\)
\(972\) −0.379706 0.219224i −0.0121791 0.00703160i
\(973\) −8.72012 5.03457i −0.279554 0.161401i
\(974\) 11.1231 0.356407
\(975\) 0 0
\(976\) −18.1619 −0.581349
\(977\) −52.9809 30.5885i −1.69501 0.978614i −0.950357 0.311162i \(-0.899282\pi\)
−0.744652 0.667453i \(-0.767385\pi\)
\(978\) 6.50175 + 3.75379i 0.207903 + 0.120033i
\(979\) −4.87689 8.44703i −0.155866 0.269968i
\(980\) 0 0
\(981\) 1.40388 + 2.43160i 0.0448225 + 0.0776349i
\(982\) 49.0174 28.3002i 1.56421 0.903095i
\(983\) 13.6155i 0.434268i −0.976142 0.217134i \(-0.930329\pi\)
0.976142 0.217134i \(-0.0696708\pi\)
\(984\) −1.90388 3.29762i −0.0606935 0.105124i
\(985\) 0 0
\(986\) −8.15009 + 14.1164i −0.259552 + 0.449557i
\(987\) 4.63068i 0.147396i
\(988\) −4.22351 + 10.4384i −0.134368 + 0.332091i
\(989\) −9.12311 −0.290098
\(990\) 0 0
\(991\) 25.1771 43.6080i 0.799776 1.38525i −0.119985 0.992776i \(-0.538285\pi\)
0.919762 0.392478i \(-0.128382\pi\)
\(992\) 5.40938 3.12311i 0.171748 0.0991587i
\(993\) 3.19224i 0.101303i
\(994\) −6.13826 10.6318i −0.194694 0.337220i
\(995\) 0 0
\(996\) −0.384472 −0.0121825
\(997\) −17.8536 + 10.3078i −0.565428 + 0.326450i −0.755321 0.655355i \(-0.772519\pi\)
0.189893 + 0.981805i \(0.439186\pi\)
\(998\) −6.07530 3.50758i −0.192310 0.111030i
\(999\) 3.78078 6.54850i 0.119618 0.207185i
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 975.2.bb.i.724.3 8
5.2 odd 4 975.2.i.k.451.1 4
5.3 odd 4 39.2.e.b.22.2 yes 4
5.4 even 2 inner 975.2.bb.i.724.2 8
13.3 even 3 inner 975.2.bb.i.874.2 8
15.8 even 4 117.2.g.c.100.1 4
20.3 even 4 624.2.q.h.529.1 4
60.23 odd 4 1872.2.t.r.1153.2 4
65.3 odd 12 39.2.e.b.16.2 4
65.8 even 4 507.2.j.g.316.3 8
65.18 even 4 507.2.j.g.316.2 8
65.23 odd 12 507.2.e.g.484.1 4
65.28 even 12 507.2.j.g.361.3 8
65.29 even 6 inner 975.2.bb.i.874.3 8
65.33 even 12 507.2.b.d.337.2 4
65.38 odd 4 507.2.e.g.22.1 4
65.42 odd 12 975.2.i.k.601.1 4
65.43 odd 12 507.2.a.d.1.2 2
65.48 odd 12 507.2.a.g.1.1 2
65.58 even 12 507.2.b.d.337.3 4
65.63 even 12 507.2.j.g.361.2 8
195.68 even 12 117.2.g.c.55.1 4
195.98 odd 12 1521.2.b.h.1351.3 4
195.113 even 12 1521.2.a.g.1.2 2
195.173 even 12 1521.2.a.m.1.1 2
195.188 odd 12 1521.2.b.h.1351.2 4
260.3 even 12 624.2.q.h.289.1 4
260.43 even 12 8112.2.a.bo.1.2 2
260.243 even 12 8112.2.a.bk.1.1 2
780.263 odd 12 1872.2.t.r.289.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.e.b.16.2 4 65.3 odd 12
39.2.e.b.22.2 yes 4 5.3 odd 4
117.2.g.c.55.1 4 195.68 even 12
117.2.g.c.100.1 4 15.8 even 4
507.2.a.d.1.2 2 65.43 odd 12
507.2.a.g.1.1 2 65.48 odd 12
507.2.b.d.337.2 4 65.33 even 12
507.2.b.d.337.3 4 65.58 even 12
507.2.e.g.22.1 4 65.38 odd 4
507.2.e.g.484.1 4 65.23 odd 12
507.2.j.g.316.2 8 65.18 even 4
507.2.j.g.316.3 8 65.8 even 4
507.2.j.g.361.2 8 65.63 even 12
507.2.j.g.361.3 8 65.28 even 12
624.2.q.h.289.1 4 260.3 even 12
624.2.q.h.529.1 4 20.3 even 4
975.2.i.k.451.1 4 5.2 odd 4
975.2.i.k.601.1 4 65.42 odd 12
975.2.bb.i.724.2 8 5.4 even 2 inner
975.2.bb.i.724.3 8 1.1 even 1 trivial
975.2.bb.i.874.2 8 13.3 even 3 inner
975.2.bb.i.874.3 8 65.29 even 6 inner
1521.2.a.g.1.2 2 195.113 even 12
1521.2.a.m.1.1 2 195.173 even 12
1521.2.b.h.1351.2 4 195.188 odd 12
1521.2.b.h.1351.3 4 195.98 odd 12
1872.2.t.r.289.2 4 780.263 odd 12
1872.2.t.r.1153.2 4 60.23 odd 4
8112.2.a.bk.1.1 2 260.243 even 12
8112.2.a.bo.1.2 2 260.43 even 12