Properties

Label 700.2.t.d.299.5
Level $700$
Weight $2$
Character 700.299
Analytic conductor $5.590$
Analytic rank $0$
Dimension $32$
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] = [700,2,Mod(199,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.199");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.t (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: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 299.5
Character \(\chi\) \(=\) 700.299
Dual form 700.2.t.d.199.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.790498 + 1.17265i) q^{2} +(0.573616 - 0.331177i) q^{3} +(-0.750225 - 1.85396i) q^{4} +(-0.0650866 + 0.934447i) q^{6} +(-2.03775 - 1.68748i) q^{7} +(2.76710 + 0.585797i) q^{8} +(-1.28064 + 2.21814i) q^{9} +O(q^{10})\) \(q+(-0.790498 + 1.17265i) q^{2} +(0.573616 - 0.331177i) q^{3} +(-0.750225 - 1.85396i) q^{4} +(-0.0650866 + 0.934447i) q^{6} +(-2.03775 - 1.68748i) q^{7} +(2.76710 + 0.585797i) q^{8} +(-1.28064 + 2.21814i) q^{9} +(3.12892 - 1.80648i) q^{11} +(-1.04433 - 0.815002i) q^{12} -5.83027 q^{13} +(3.58966 - 1.05561i) q^{14} +(-2.87432 + 2.78177i) q^{16} +(-0.684063 - 1.18483i) q^{17} +(-1.58876 - 3.25518i) q^{18} +(2.04788 - 3.54704i) q^{19} +(-1.72774 - 0.293111i) q^{21} +(-0.355029 + 5.09715i) q^{22} +(-1.62259 + 2.81042i) q^{23} +(1.78126 - 0.580378i) q^{24} +(4.60882 - 6.83688i) q^{26} +3.68354i q^{27} +(-1.59975 + 5.04389i) q^{28} -5.19327 q^{29} +(-4.43405 - 7.67999i) q^{31} +(-0.989905 - 5.56957i) q^{32} +(1.19653 - 2.07245i) q^{33} +(1.93014 + 0.134439i) q^{34} +(5.07311 + 0.710155i) q^{36} +(-9.34942 - 5.39789i) q^{37} +(2.54059 + 5.20538i) q^{38} +(-3.34434 + 1.93085i) q^{39} +0.832730i q^{41} +(1.70949 - 1.79433i) q^{42} -3.10642 q^{43} +(-5.69653 - 4.44561i) q^{44} +(-2.01298 - 4.12437i) q^{46} +(-5.97212 - 3.44801i) q^{47} +(-0.727497 + 2.54758i) q^{48} +(1.30481 + 6.87732i) q^{49} +(-0.784778 - 0.453092i) q^{51} +(4.37402 + 10.8091i) q^{52} +(6.42376 - 3.70876i) q^{53} +(-4.31952 - 2.91183i) q^{54} +(-4.65012 - 5.86314i) q^{56} -2.71285i q^{57} +(4.10527 - 6.08989i) q^{58} +(-3.73928 - 6.47663i) q^{59} +(1.28652 + 0.742772i) q^{61} +(12.5111 + 0.871427i) q^{62} +(6.35269 - 2.35894i) q^{63} +(7.31368 + 3.24192i) q^{64} +(1.48441 + 3.04138i) q^{66} +(1.26880 + 2.19763i) q^{67} +(-1.68343 + 2.15711i) q^{68} +2.14947i q^{69} +3.52502i q^{71} +(-4.84305 + 5.38762i) q^{72} +(2.58492 + 4.47721i) q^{73} +(13.7206 - 6.69660i) q^{74} +(-8.11244 - 1.13561i) q^{76} +(-9.42434 - 1.59884i) q^{77} +(0.379472 - 5.44808i) q^{78} +(9.82082 + 5.67005i) q^{79} +(-2.62202 - 4.54148i) q^{81} +(-0.976503 - 0.658272i) q^{82} -6.49145i q^{83} +(0.752777 + 3.42306i) q^{84} +(2.45562 - 3.64275i) q^{86} +(-2.97894 + 1.71989i) q^{87} +(9.71626 - 3.16580i) q^{88} +(-8.13303 - 4.69560i) q^{89} +(11.8806 + 9.83847i) q^{91} +(6.42771 + 0.899777i) q^{92} +(-5.08688 - 2.93691i) q^{93} +(8.76426 - 4.27758i) q^{94} +(-2.41234 - 2.86696i) q^{96} -0.343189 q^{97} +(-9.09615 - 3.90642i) q^{98} +9.25383i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{4} + 16 q^{9} + 14 q^{12} + 8 q^{13} - 2 q^{14} - 14 q^{16} - 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} - 32 q^{28} + 40 q^{29} - 60 q^{32} + 24 q^{33} + 60 q^{36} + 60 q^{37} + 46 q^{38} - 78 q^{42} + 18 q^{44} + 2 q^{46} + 28 q^{48} + 16 q^{49} + 46 q^{52} + 12 q^{53} - 12 q^{54} - 4 q^{56} - 42 q^{58} + 24 q^{61} - 8 q^{62} - 4 q^{64} + 24 q^{66} + 4 q^{68} - 90 q^{72} + 24 q^{73} - 38 q^{74} - 20 q^{77} - 36 q^{81} - 8 q^{82} + 20 q^{84} + 28 q^{86} + 78 q^{88} + 60 q^{89} - 72 q^{93} - 18 q^{94} - 60 q^{96} + 48 q^{97} + 124 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.790498 + 1.17265i −0.558967 + 0.829190i
\(3\) 0.573616 0.331177i 0.331177 0.191205i −0.325186 0.945650i \(-0.605427\pi\)
0.656364 + 0.754445i \(0.272094\pi\)
\(4\) −0.750225 1.85396i −0.375113 0.926979i
\(5\) 0 0
\(6\) −0.0650866 + 0.934447i −0.0265715 + 0.381486i
\(7\) −2.03775 1.68748i −0.770195 0.637808i
\(8\) 2.76710 + 0.585797i 0.978318 + 0.207111i
\(9\) −1.28064 + 2.21814i −0.426881 + 0.739380i
\(10\) 0 0
\(11\) 3.12892 1.80648i 0.943404 0.544674i 0.0523781 0.998627i \(-0.483320\pi\)
0.891026 + 0.453953i \(0.149987\pi\)
\(12\) −1.04433 0.815002i −0.301472 0.235271i
\(13\) −5.83027 −1.61703 −0.808513 0.588478i \(-0.799727\pi\)
−0.808513 + 0.588478i \(0.799727\pi\)
\(14\) 3.58966 1.05561i 0.959378 0.282125i
\(15\) 0 0
\(16\) −2.87432 + 2.78177i −0.718581 + 0.695443i
\(17\) −0.684063 1.18483i −0.165910 0.287364i 0.771068 0.636752i \(-0.219723\pi\)
−0.936978 + 0.349389i \(0.886389\pi\)
\(18\) −1.58876 3.25518i −0.374474 0.767254i
\(19\) 2.04788 3.54704i 0.469817 0.813747i −0.529588 0.848255i \(-0.677653\pi\)
0.999404 + 0.0345086i \(0.0109866\pi\)
\(20\) 0 0
\(21\) −1.72774 0.293111i −0.377024 0.0639622i
\(22\) −0.355029 + 5.09715i −0.0756925 + 1.08672i
\(23\) −1.62259 + 2.81042i −0.338334 + 0.586012i −0.984120 0.177507i \(-0.943197\pi\)
0.645785 + 0.763519i \(0.276530\pi\)
\(24\) 1.78126 0.580378i 0.363597 0.118469i
\(25\) 0 0
\(26\) 4.60882 6.83688i 0.903863 1.34082i
\(27\) 3.68354i 0.708898i
\(28\) −1.59975 + 5.04389i −0.302325 + 0.953205i
\(29\) −5.19327 −0.964365 −0.482183 0.876071i \(-0.660156\pi\)
−0.482183 + 0.876071i \(0.660156\pi\)
\(30\) 0 0
\(31\) −4.43405 7.67999i −0.796378 1.37937i −0.921960 0.387284i \(-0.873413\pi\)
0.125582 0.992083i \(-0.459920\pi\)
\(32\) −0.989905 5.56957i −0.174992 0.984570i
\(33\) 1.19653 2.07245i 0.208289 0.360768i
\(34\) 1.93014 + 0.134439i 0.331017 + 0.0230562i
\(35\) 0 0
\(36\) 5.07311 + 0.710155i 0.845518 + 0.118359i
\(37\) −9.34942 5.39789i −1.53704 0.887408i −0.999010 0.0444796i \(-0.985837\pi\)
−0.538026 0.842928i \(-0.680830\pi\)
\(38\) 2.54059 + 5.20538i 0.412139 + 0.844425i
\(39\) −3.34434 + 1.93085i −0.535522 + 0.309184i
\(40\) 0 0
\(41\) 0.832730i 0.130051i 0.997884 + 0.0650253i \(0.0207128\pi\)
−0.997884 + 0.0650253i \(0.979287\pi\)
\(42\) 1.70949 1.79433i 0.263780 0.276871i
\(43\) −3.10642 −0.473725 −0.236862 0.971543i \(-0.576119\pi\)
−0.236862 + 0.971543i \(0.576119\pi\)
\(44\) −5.69653 4.44561i −0.858785 0.670201i
\(45\) 0 0
\(46\) −2.01298 4.12437i −0.296798 0.608105i
\(47\) −5.97212 3.44801i −0.871124 0.502943i −0.00340208 0.999994i \(-0.501083\pi\)
−0.867721 + 0.497051i \(0.834416\pi\)
\(48\) −0.727497 + 2.54758i −0.105005 + 0.367712i
\(49\) 1.30481 + 6.87732i 0.186402 + 0.982474i
\(50\) 0 0
\(51\) −0.784778 0.453092i −0.109891 0.0634456i
\(52\) 4.37402 + 10.8091i 0.606567 + 1.49895i
\(53\) 6.42376 3.70876i 0.882371 0.509437i 0.0109318 0.999940i \(-0.496520\pi\)
0.871440 + 0.490503i \(0.163187\pi\)
\(54\) −4.31952 2.91183i −0.587812 0.396250i
\(55\) 0 0
\(56\) −4.65012 5.86314i −0.621399 0.783494i
\(57\) 2.71285i 0.359326i
\(58\) 4.10527 6.08989i 0.539048 0.799642i
\(59\) −3.73928 6.47663i −0.486813 0.843185i 0.513072 0.858346i \(-0.328507\pi\)
−0.999885 + 0.0151606i \(0.995174\pi\)
\(60\) 0 0
\(61\) 1.28652 + 0.742772i 0.164722 + 0.0951022i 0.580095 0.814549i \(-0.303016\pi\)
−0.415373 + 0.909651i \(0.636349\pi\)
\(62\) 12.5111 + 0.871427i 1.58891 + 0.110671i
\(63\) 6.35269 2.35894i 0.800364 0.297199i
\(64\) 7.31368 + 3.24192i 0.914210 + 0.405240i
\(65\) 0 0
\(66\) 1.48441 + 3.04138i 0.182718 + 0.374368i
\(67\) 1.26880 + 2.19763i 0.155009 + 0.268484i 0.933062 0.359715i \(-0.117126\pi\)
−0.778053 + 0.628198i \(0.783793\pi\)
\(68\) −1.68343 + 2.15711i −0.204145 + 0.261589i
\(69\) 2.14947i 0.258765i
\(70\) 0 0
\(71\) 3.52502i 0.418342i 0.977879 + 0.209171i \(0.0670766\pi\)
−0.977879 + 0.209171i \(0.932923\pi\)
\(72\) −4.84305 + 5.38762i −0.570759 + 0.634937i
\(73\) 2.58492 + 4.47721i 0.302542 + 0.524018i 0.976711 0.214559i \(-0.0688314\pi\)
−0.674169 + 0.738577i \(0.735498\pi\)
\(74\) 13.7206 6.69660i 1.59498 0.778464i
\(75\) 0 0
\(76\) −8.11244 1.13561i −0.930561 0.130264i
\(77\) −9.42434 1.59884i −1.07400 0.182205i
\(78\) 0.379472 5.44808i 0.0429668 0.616873i
\(79\) 9.82082 + 5.67005i 1.10493 + 0.637931i 0.937511 0.347955i \(-0.113124\pi\)
0.167417 + 0.985886i \(0.446457\pi\)
\(80\) 0 0
\(81\) −2.62202 4.54148i −0.291336 0.504609i
\(82\) −0.976503 0.658272i −0.107837 0.0726939i
\(83\) 6.49145i 0.712529i −0.934385 0.356264i \(-0.884050\pi\)
0.934385 0.356264i \(-0.115950\pi\)
\(84\) 0.752777 + 3.42306i 0.0821347 + 0.373486i
\(85\) 0 0
\(86\) 2.45562 3.64275i 0.264796 0.392808i
\(87\) −2.97894 + 1.71989i −0.319376 + 0.184392i
\(88\) 9.71626 3.16580i 1.03576 0.337476i
\(89\) −8.13303 4.69560i −0.862099 0.497733i 0.00261566 0.999997i \(-0.499167\pi\)
−0.864715 + 0.502264i \(0.832501\pi\)
\(90\) 0 0
\(91\) 11.8806 + 9.83847i 1.24543 + 1.03135i
\(92\) 6.42771 + 0.899777i 0.670135 + 0.0938083i
\(93\) −5.08688 2.93691i −0.527485 0.304544i
\(94\) 8.76426 4.27758i 0.903965 0.441199i
\(95\) 0 0
\(96\) −2.41234 2.86696i −0.246208 0.292608i
\(97\) −0.343189 −0.0348455 −0.0174228 0.999848i \(-0.505546\pi\)
−0.0174228 + 0.999848i \(0.505546\pi\)
\(98\) −9.09615 3.90642i −0.918850 0.394608i
\(99\) 9.25383i 0.930045i
\(100\) 0 0
\(101\) 3.92859 2.26817i 0.390910 0.225692i −0.291645 0.956527i \(-0.594202\pi\)
0.682554 + 0.730835i \(0.260869\pi\)
\(102\) 1.15169 0.562104i 0.114034 0.0556566i
\(103\) 5.31577 + 3.06906i 0.523778 + 0.302404i 0.738479 0.674276i \(-0.235544\pi\)
−0.214701 + 0.976680i \(0.568878\pi\)
\(104\) −16.1329 3.41536i −1.58196 0.334903i
\(105\) 0 0
\(106\) −0.728886 + 10.4646i −0.0707957 + 1.01641i
\(107\) 3.83398 6.64066i 0.370645 0.641976i −0.619020 0.785375i \(-0.712470\pi\)
0.989665 + 0.143399i \(0.0458032\pi\)
\(108\) 6.82914 2.76349i 0.657134 0.265917i
\(109\) 0.647616 + 1.12170i 0.0620304 + 0.107440i 0.895373 0.445317i \(-0.146909\pi\)
−0.833342 + 0.552757i \(0.813576\pi\)
\(110\) 0 0
\(111\) −7.15064 −0.678709
\(112\) 10.5513 0.818178i 0.997007 0.0773105i
\(113\) 7.10591i 0.668468i −0.942490 0.334234i \(-0.891522\pi\)
0.942490 0.334234i \(-0.108478\pi\)
\(114\) 3.18123 + 2.14450i 0.297950 + 0.200851i
\(115\) 0 0
\(116\) 3.89612 + 9.62810i 0.361746 + 0.893946i
\(117\) 7.46649 12.9323i 0.690278 1.19560i
\(118\) 10.5507 + 0.734884i 0.971273 + 0.0676516i
\(119\) −0.605436 + 3.56873i −0.0555002 + 0.327145i
\(120\) 0 0
\(121\) 1.02675 1.77837i 0.0933405 0.161670i
\(122\) −1.88800 + 0.921479i −0.170932 + 0.0834268i
\(123\) 0.275781 + 0.477667i 0.0248664 + 0.0430698i
\(124\) −10.9119 + 13.9823i −0.979914 + 1.25564i
\(125\) 0 0
\(126\) −2.25558 + 9.31424i −0.200943 + 0.829778i
\(127\) 17.0178 1.51008 0.755041 0.655677i \(-0.227617\pi\)
0.755041 + 0.655677i \(0.227617\pi\)
\(128\) −9.58310 + 6.01367i −0.847034 + 0.531539i
\(129\) −1.78189 + 1.02878i −0.156887 + 0.0905787i
\(130\) 0 0
\(131\) −0.603066 + 1.04454i −0.0526901 + 0.0912619i −0.891167 0.453674i \(-0.850113\pi\)
0.838477 + 0.544936i \(0.183446\pi\)
\(132\) −4.73991 0.663512i −0.412556 0.0577513i
\(133\) −10.1586 + 3.77220i −0.880865 + 0.327091i
\(134\) −3.58005 0.249359i −0.309269 0.0215414i
\(135\) 0 0
\(136\) −1.19880 3.67927i −0.102796 0.315495i
\(137\) 1.85754 1.07245i 0.158701 0.0916258i −0.418547 0.908195i \(-0.637460\pi\)
0.577247 + 0.816570i \(0.304127\pi\)
\(138\) −2.52058 1.69915i −0.214566 0.144641i
\(139\) 3.39555 0.288007 0.144004 0.989577i \(-0.454002\pi\)
0.144004 + 0.989577i \(0.454002\pi\)
\(140\) 0 0
\(141\) −4.56761 −0.384662
\(142\) −4.13362 2.78652i −0.346885 0.233839i
\(143\) −18.2424 + 10.5323i −1.52551 + 0.880753i
\(144\) −2.48938 9.93811i −0.207448 0.828176i
\(145\) 0 0
\(146\) −7.29359 0.508017i −0.603622 0.0420438i
\(147\) 3.02607 + 3.51281i 0.249586 + 0.289732i
\(148\) −2.99329 + 21.3831i −0.246047 + 1.75768i
\(149\) −9.54319 + 16.5293i −0.781808 + 1.35413i 0.149079 + 0.988825i \(0.452369\pi\)
−0.930887 + 0.365307i \(0.880964\pi\)
\(150\) 0 0
\(151\) −8.31900 + 4.80298i −0.676990 + 0.390861i −0.798720 0.601703i \(-0.794489\pi\)
0.121730 + 0.992563i \(0.461156\pi\)
\(152\) 7.74455 8.61537i 0.628166 0.698799i
\(153\) 3.50416 0.283295
\(154\) 9.32481 9.78759i 0.751414 0.788706i
\(155\) 0 0
\(156\) 6.08873 + 4.75168i 0.487488 + 0.380439i
\(157\) 8.23118 + 14.2568i 0.656919 + 1.13782i 0.981409 + 0.191928i \(0.0614742\pi\)
−0.324490 + 0.945889i \(0.605193\pi\)
\(158\) −14.4123 + 7.03424i −1.14658 + 0.559614i
\(159\) 2.45651 4.25481i 0.194814 0.337428i
\(160\) 0 0
\(161\) 8.04896 2.98881i 0.634347 0.235552i
\(162\) 7.39828 + 0.515309i 0.581264 + 0.0404865i
\(163\) 3.57806 6.19738i 0.280255 0.485416i −0.691192 0.722671i \(-0.742914\pi\)
0.971447 + 0.237255i \(0.0762476\pi\)
\(164\) 1.54385 0.624735i 0.120554 0.0487836i
\(165\) 0 0
\(166\) 7.61221 + 5.13148i 0.590822 + 0.398280i
\(167\) 13.7127i 1.06112i 0.847646 + 0.530562i \(0.178019\pi\)
−0.847646 + 0.530562i \(0.821981\pi\)
\(168\) −4.60912 1.82317i −0.355601 0.140661i
\(169\) 20.9920 1.61477
\(170\) 0 0
\(171\) 5.24522 + 9.08498i 0.401112 + 0.694746i
\(172\) 2.33052 + 5.75917i 0.177700 + 0.439133i
\(173\) 1.96219 3.39862i 0.149183 0.258392i −0.781743 0.623601i \(-0.785669\pi\)
0.930926 + 0.365209i \(0.119002\pi\)
\(174\) 0.338012 4.85283i 0.0256246 0.367892i
\(175\) 0 0
\(176\) −3.96830 + 13.8963i −0.299122 + 1.04748i
\(177\) −4.28982 2.47673i −0.322443 0.186162i
\(178\) 11.9355 5.82534i 0.894600 0.436628i
\(179\) −17.8002 + 10.2769i −1.33045 + 0.768134i −0.985368 0.170440i \(-0.945481\pi\)
−0.345079 + 0.938574i \(0.612148\pi\)
\(180\) 0 0
\(181\) 13.0603i 0.970762i 0.874303 + 0.485381i \(0.161319\pi\)
−0.874303 + 0.485381i \(0.838681\pi\)
\(182\) −20.9287 + 6.15452i −1.55134 + 0.456203i
\(183\) 0.983957 0.0727362
\(184\) −6.13622 + 6.82619i −0.452368 + 0.503234i
\(185\) 0 0
\(186\) 7.46514 3.64352i 0.547371 0.267156i
\(187\) −4.28075 2.47149i −0.313039 0.180733i
\(188\) −1.91202 + 13.6588i −0.139449 + 0.996174i
\(189\) 6.21591 7.50612i 0.452141 0.545990i
\(190\) 0 0
\(191\) −10.8038 6.23755i −0.781733 0.451334i 0.0553113 0.998469i \(-0.482385\pi\)
−0.837044 + 0.547136i \(0.815718\pi\)
\(192\) 5.26890 0.562510i 0.380250 0.0405956i
\(193\) −16.5103 + 9.53225i −1.18844 + 0.686147i −0.957952 0.286928i \(-0.907366\pi\)
−0.230489 + 0.973075i \(0.574033\pi\)
\(194\) 0.271290 0.402441i 0.0194775 0.0288936i
\(195\) 0 0
\(196\) 11.7714 7.57860i 0.840811 0.541329i
\(197\) 1.93188i 0.137641i 0.997629 + 0.0688203i \(0.0219235\pi\)
−0.997629 + 0.0688203i \(0.978076\pi\)
\(198\) −10.8515 7.31513i −0.771184 0.519864i
\(199\) −10.2823 17.8094i −0.728892 1.26248i −0.957352 0.288924i \(-0.906702\pi\)
0.228460 0.973553i \(-0.426631\pi\)
\(200\) 0 0
\(201\) 1.45561 + 0.840398i 0.102671 + 0.0592771i
\(202\) −0.445766 + 6.39986i −0.0313640 + 0.450293i
\(203\) 10.5826 + 8.76354i 0.742750 + 0.615080i
\(204\) −0.251253 + 1.79487i −0.0175912 + 0.125666i
\(205\) 0 0
\(206\) −7.80105 + 3.80746i −0.543525 + 0.265278i
\(207\) −4.15593 7.19828i −0.288857 0.500315i
\(208\) 16.7581 16.2185i 1.16196 1.12455i
\(209\) 14.7979i 1.02359i
\(210\) 0 0
\(211\) 9.98398i 0.687326i 0.939093 + 0.343663i \(0.111668\pi\)
−0.939093 + 0.343663i \(0.888332\pi\)
\(212\) −11.6952 9.12698i −0.803227 0.626843i
\(213\) 1.16741 + 2.02200i 0.0799893 + 0.138545i
\(214\) 4.75642 + 9.74536i 0.325142 + 0.666179i
\(215\) 0 0
\(216\) −2.15781 + 10.1927i −0.146820 + 0.693528i
\(217\) −3.92439 + 23.1322i −0.266405 + 1.57032i
\(218\) −1.82731 0.127277i −0.123761 0.00862026i
\(219\) 2.96550 + 1.71213i 0.200390 + 0.115695i
\(220\) 0 0
\(221\) 3.98827 + 6.90789i 0.268280 + 0.464675i
\(222\) 5.65257 8.38521i 0.379375 0.562778i
\(223\) 16.8179i 1.12621i −0.826384 0.563106i \(-0.809606\pi\)
0.826384 0.563106i \(-0.190394\pi\)
\(224\) −7.38137 + 13.0198i −0.493188 + 0.869922i
\(225\) 0 0
\(226\) 8.33276 + 5.61721i 0.554287 + 0.373651i
\(227\) 17.1766 9.91692i 1.14005 0.658209i 0.193608 0.981079i \(-0.437981\pi\)
0.946443 + 0.322870i \(0.104648\pi\)
\(228\) −5.02951 + 2.03525i −0.333088 + 0.134788i
\(229\) −12.0664 6.96655i −0.797371 0.460363i 0.0451798 0.998979i \(-0.485614\pi\)
−0.842551 + 0.538616i \(0.818947\pi\)
\(230\) 0 0
\(231\) −5.93545 + 2.20401i −0.390524 + 0.145013i
\(232\) −14.3703 3.04220i −0.943455 0.199730i
\(233\) 8.85568 + 5.11283i 0.580155 + 0.334953i 0.761195 0.648523i \(-0.224613\pi\)
−0.181040 + 0.983476i \(0.557946\pi\)
\(234\) 9.26289 + 18.9786i 0.605534 + 1.24067i
\(235\) 0 0
\(236\) −9.20209 + 11.7914i −0.599005 + 0.767555i
\(237\) 7.51117 0.487903
\(238\) −3.70628 3.53104i −0.240242 0.228883i
\(239\) 17.0835i 1.10504i −0.833501 0.552518i \(-0.813667\pi\)
0.833501 0.552518i \(-0.186333\pi\)
\(240\) 0 0
\(241\) −16.0074 + 9.24185i −1.03112 + 0.595320i −0.917307 0.398182i \(-0.869641\pi\)
−0.113818 + 0.993502i \(0.536308\pi\)
\(242\) 1.27377 + 2.60982i 0.0818813 + 0.167765i
\(243\) −12.5782 7.26203i −0.806892 0.465859i
\(244\) 0.411889 2.94240i 0.0263685 0.188368i
\(245\) 0 0
\(246\) −0.778142 0.0541995i −0.0496125 0.00345564i
\(247\) −11.9397 + 20.6802i −0.759706 + 1.31585i
\(248\) −7.77053 23.8488i −0.493429 1.51440i
\(249\) −2.14982 3.72360i −0.136239 0.235973i
\(250\) 0 0
\(251\) 16.5313 1.04344 0.521722 0.853116i \(-0.325290\pi\)
0.521722 + 0.853116i \(0.325290\pi\)
\(252\) −9.13933 10.0079i −0.575724 0.630438i
\(253\) 11.7247i 0.737128i
\(254\) −13.4525 + 19.9559i −0.844086 + 1.25215i
\(255\) 0 0
\(256\) 0.523471 15.9914i 0.0327169 0.999465i
\(257\) 3.09749 5.36502i 0.193216 0.334660i −0.753098 0.657908i \(-0.771441\pi\)
0.946314 + 0.323248i \(0.104775\pi\)
\(258\) 0.202186 2.90279i 0.0125876 0.180720i
\(259\) 9.94290 + 26.7765i 0.617822 + 1.66381i
\(260\) 0 0
\(261\) 6.65072 11.5194i 0.411669 0.713032i
\(262\) −0.748160 1.53289i −0.0462215 0.0947025i
\(263\) 10.5768 + 18.3196i 0.652194 + 1.12963i 0.982589 + 0.185790i \(0.0594844\pi\)
−0.330396 + 0.943842i \(0.607182\pi\)
\(264\) 4.52496 5.03376i 0.278492 0.309806i
\(265\) 0 0
\(266\) 3.60691 14.8945i 0.221154 0.913237i
\(267\) −6.22031 −0.380677
\(268\) 3.12243 4.00103i 0.190733 0.244402i
\(269\) 26.8352 15.4933i 1.63617 0.944642i 0.654033 0.756466i \(-0.273076\pi\)
0.982135 0.188177i \(-0.0602578\pi\)
\(270\) 0 0
\(271\) 11.5190 19.9516i 0.699732 1.21197i −0.268827 0.963188i \(-0.586636\pi\)
0.968559 0.248783i \(-0.0800306\pi\)
\(272\) 5.26215 + 1.50268i 0.319065 + 0.0911134i
\(273\) 10.0732 + 1.70892i 0.609657 + 0.103428i
\(274\) −0.210770 + 3.02602i −0.0127331 + 0.182809i
\(275\) 0 0
\(276\) 3.98502 1.61258i 0.239870 0.0970662i
\(277\) 6.01508 3.47281i 0.361411 0.208661i −0.308288 0.951293i \(-0.599756\pi\)
0.669700 + 0.742632i \(0.266423\pi\)
\(278\) −2.68418 + 3.98180i −0.160986 + 0.238813i
\(279\) 22.7137 1.35984
\(280\) 0 0
\(281\) −4.24391 −0.253170 −0.126585 0.991956i \(-0.540402\pi\)
−0.126585 + 0.991956i \(0.540402\pi\)
\(282\) 3.61068 5.35621i 0.215013 0.318958i
\(283\) −7.38891 + 4.26599i −0.439225 + 0.253587i −0.703269 0.710924i \(-0.748277\pi\)
0.264044 + 0.964511i \(0.414944\pi\)
\(284\) 6.53523 2.64456i 0.387795 0.156926i
\(285\) 0 0
\(286\) 2.06992 29.7178i 0.122397 1.75725i
\(287\) 1.40522 1.69689i 0.0829473 0.100164i
\(288\) 13.6218 + 4.93688i 0.802672 + 0.290909i
\(289\) 7.56412 13.1014i 0.444948 0.770673i
\(290\) 0 0
\(291\) −0.196859 + 0.113656i −0.0115401 + 0.00666265i
\(292\) 6.36129 8.15125i 0.372267 0.477016i
\(293\) 25.2319 1.47406 0.737032 0.675857i \(-0.236227\pi\)
0.737032 + 0.675857i \(0.236227\pi\)
\(294\) −6.51141 + 0.771656i −0.379753 + 0.0450039i
\(295\) 0 0
\(296\) −22.7087 20.4134i −1.31992 1.18650i
\(297\) 6.65425 + 11.5255i 0.386119 + 0.668777i
\(298\) −11.8392 24.2572i −0.685828 1.40518i
\(299\) 9.46017 16.3855i 0.547096 0.947597i
\(300\) 0 0
\(301\) 6.33009 + 5.24203i 0.364861 + 0.302145i
\(302\) 0.943933 13.5520i 0.0543172 0.779832i
\(303\) 1.50234 2.60212i 0.0863070 0.149488i
\(304\) 3.98078 + 15.8921i 0.228313 + 0.911474i
\(305\) 0 0
\(306\) −2.77003 + 4.10916i −0.158352 + 0.234905i
\(307\) 29.2635i 1.67016i −0.550132 0.835078i \(-0.685423\pi\)
0.550132 0.835078i \(-0.314577\pi\)
\(308\) 4.10619 + 18.6718i 0.233972 + 1.06393i
\(309\) 4.06561 0.231285
\(310\) 0 0
\(311\) −11.3730 19.6987i −0.644906 1.11701i −0.984323 0.176374i \(-0.943563\pi\)
0.339417 0.940636i \(-0.389770\pi\)
\(312\) −10.3852 + 3.38376i −0.587946 + 0.191568i
\(313\) 3.29240 5.70261i 0.186098 0.322331i −0.757848 0.652431i \(-0.773749\pi\)
0.943946 + 0.330100i \(0.107083\pi\)
\(314\) −23.2250 1.61768i −1.31066 0.0912910i
\(315\) 0 0
\(316\) 3.14421 22.4612i 0.176876 1.26354i
\(317\) 12.2298 + 7.06086i 0.686892 + 0.396577i 0.802447 0.596724i \(-0.203531\pi\)
−0.115555 + 0.993301i \(0.536865\pi\)
\(318\) 3.04754 + 6.24405i 0.170897 + 0.350149i
\(319\) −16.2493 + 9.38153i −0.909786 + 0.525265i
\(320\) 0 0
\(321\) 5.07891i 0.283477i
\(322\) −2.85785 + 11.8013i −0.159262 + 0.657660i
\(323\) −5.60352 −0.311788
\(324\) −6.45260 + 8.26825i −0.358478 + 0.459347i
\(325\) 0 0
\(326\) 4.43892 + 9.09483i 0.245849 + 0.503716i
\(327\) 0.742966 + 0.428952i 0.0410861 + 0.0237211i
\(328\) −0.487811 + 2.30425i −0.0269349 + 0.127231i
\(329\) 6.35122 + 17.1040i 0.350154 + 0.942974i
\(330\) 0 0
\(331\) 17.5997 + 10.1612i 0.967368 + 0.558510i 0.898433 0.439111i \(-0.144707\pi\)
0.0689349 + 0.997621i \(0.478040\pi\)
\(332\) −12.0349 + 4.87005i −0.660499 + 0.267279i
\(333\) 23.9466 13.8255i 1.31226 0.757635i
\(334\) −16.0803 10.8399i −0.879873 0.593133i
\(335\) 0 0
\(336\) 5.78145 3.96368i 0.315404 0.216237i
\(337\) 15.7704i 0.859067i 0.903051 + 0.429533i \(0.141322\pi\)
−0.903051 + 0.429533i \(0.858678\pi\)
\(338\) −16.5942 + 24.6164i −0.902604 + 1.33895i
\(339\) −2.35332 4.07607i −0.127815 0.221381i
\(340\) 0 0
\(341\) −27.7475 16.0200i −1.50261 0.867534i
\(342\) −14.7999 1.03085i −0.800285 0.0557418i
\(343\) 8.94647 16.2161i 0.483064 0.875585i
\(344\) −8.59578 1.81973i −0.463453 0.0981134i
\(345\) 0 0
\(346\) 2.43429 + 4.98757i 0.130868 + 0.268133i
\(347\) −1.52392 2.63950i −0.0818082 0.141696i 0.822218 0.569172i \(-0.192736\pi\)
−0.904027 + 0.427476i \(0.859403\pi\)
\(348\) 5.42348 + 4.23252i 0.290729 + 0.226887i
\(349\) 8.40462i 0.449889i −0.974372 0.224944i \(-0.927780\pi\)
0.974372 0.224944i \(-0.0722201\pi\)
\(350\) 0 0
\(351\) 21.4761i 1.14631i
\(352\) −13.1586 15.6385i −0.701358 0.833533i
\(353\) −0.216411 0.374834i −0.0115184 0.0199504i 0.860209 0.509942i \(-0.170333\pi\)
−0.871727 + 0.489992i \(0.837000\pi\)
\(354\) 6.29544 3.07262i 0.334599 0.163308i
\(355\) 0 0
\(356\) −2.60385 + 18.6011i −0.138004 + 0.985854i
\(357\) 0.834594 + 2.24759i 0.0441714 + 0.118955i
\(358\) 2.01973 28.9973i 0.106746 1.53255i
\(359\) −23.3662 13.4905i −1.23322 0.712002i −0.265522 0.964105i \(-0.585544\pi\)
−0.967700 + 0.252103i \(0.918878\pi\)
\(360\) 0 0
\(361\) 1.11234 + 1.92663i 0.0585442 + 0.101402i
\(362\) −15.3151 10.3241i −0.804946 0.542623i
\(363\) 1.36014i 0.0713888i
\(364\) 9.32699 29.4072i 0.488867 1.54136i
\(365\) 0 0
\(366\) −0.777816 + 1.15384i −0.0406571 + 0.0603121i
\(367\) −18.0317 + 10.4106i −0.941248 + 0.543430i −0.890351 0.455274i \(-0.849541\pi\)
−0.0508965 + 0.998704i \(0.516208\pi\)
\(368\) −3.15408 12.5917i −0.164418 0.656390i
\(369\) −1.84711 1.06643i −0.0961568 0.0555161i
\(370\) 0 0
\(371\) −19.3485 3.28247i −1.00452 0.170417i
\(372\) −1.62860 + 11.6342i −0.0844392 + 0.603206i
\(373\) −15.2953 8.83072i −0.791958 0.457237i 0.0486931 0.998814i \(-0.484494\pi\)
−0.840652 + 0.541576i \(0.817828\pi\)
\(374\) 6.28212 3.06612i 0.324841 0.158545i
\(375\) 0 0
\(376\) −14.5056 13.0394i −0.748071 0.672457i
\(377\) 30.2781 1.55940
\(378\) 3.88840 + 13.2227i 0.199998 + 0.680101i
\(379\) 15.0551i 0.773331i −0.922220 0.386665i \(-0.873627\pi\)
0.922220 0.386665i \(-0.126373\pi\)
\(380\) 0 0
\(381\) 9.76166 5.63590i 0.500105 0.288736i
\(382\) 15.8548 7.73828i 0.811204 0.395925i
\(383\) −26.2843 15.1753i −1.34307 0.775420i −0.355811 0.934558i \(-0.615795\pi\)
−0.987256 + 0.159138i \(0.949129\pi\)
\(384\) −3.50542 + 6.62324i −0.178885 + 0.337991i
\(385\) 0 0
\(386\) 1.87338 26.8961i 0.0953527 1.36898i
\(387\) 3.97822 6.89047i 0.202224 0.350262i
\(388\) 0.257469 + 0.636258i 0.0130710 + 0.0323011i
\(389\) −3.13909 5.43706i −0.159158 0.275670i 0.775407 0.631462i \(-0.217545\pi\)
−0.934565 + 0.355792i \(0.884211\pi\)
\(390\) 0 0
\(391\) 4.43983 0.224532
\(392\) −0.418170 + 19.7946i −0.0211208 + 0.999777i
\(393\) 0.798887i 0.0402985i
\(394\) −2.26542 1.52715i −0.114130 0.0769365i
\(395\) 0 0
\(396\) 17.1562 6.94246i 0.862132 0.348872i
\(397\) 4.86104 8.41956i 0.243968 0.422566i −0.717873 0.696174i \(-0.754884\pi\)
0.961841 + 0.273609i \(0.0882173\pi\)
\(398\) 29.0124 + 2.02079i 1.45426 + 0.101293i
\(399\) −4.57789 + 5.52810i −0.229181 + 0.276751i
\(400\) 0 0
\(401\) −3.49372 + 6.05130i −0.174468 + 0.302188i −0.939977 0.341238i \(-0.889154\pi\)
0.765509 + 0.643425i \(0.222487\pi\)
\(402\) −2.13615 + 1.04259i −0.106542 + 0.0519999i
\(403\) 25.8517 + 44.7764i 1.28776 + 2.23047i
\(404\) −7.15243 5.58181i −0.355847 0.277705i
\(405\) 0 0
\(406\) −18.6421 + 5.48209i −0.925190 + 0.272071i
\(407\) −39.0048 −1.93339
\(408\) −1.90614 1.71347i −0.0943680 0.0848295i
\(409\) −1.94474 + 1.12280i −0.0961611 + 0.0555186i −0.547309 0.836930i \(-0.684348\pi\)
0.451148 + 0.892449i \(0.351015\pi\)
\(410\) 0 0
\(411\) 0.710344 1.23035i 0.0350387 0.0606888i
\(412\) 1.70189 12.1577i 0.0838459 0.598967i
\(413\) −3.30948 + 19.5077i −0.162849 + 0.959910i
\(414\) 11.7263 + 0.816769i 0.576318 + 0.0401420i
\(415\) 0 0
\(416\) 5.77141 + 32.4721i 0.282967 + 1.59207i
\(417\) 1.94774 1.12453i 0.0953814 0.0550685i
\(418\) 17.3527 + 11.6977i 0.848750 + 0.572152i
\(419\) 18.3565 0.896775 0.448388 0.893839i \(-0.351998\pi\)
0.448388 + 0.893839i \(0.351998\pi\)
\(420\) 0 0
\(421\) 2.27310 0.110784 0.0553921 0.998465i \(-0.482359\pi\)
0.0553921 + 0.998465i \(0.482359\pi\)
\(422\) −11.7077 7.89232i −0.569924 0.384192i
\(423\) 15.2963 8.83133i 0.743732 0.429394i
\(424\) 19.9478 6.49949i 0.968749 0.315643i
\(425\) 0 0
\(426\) −3.29394 0.229431i −0.159592 0.0111160i
\(427\) −1.36818 3.68456i −0.0662110 0.178308i
\(428\) −15.1879 2.12606i −0.734133 0.102767i
\(429\) −6.97610 + 12.0830i −0.336809 + 0.583371i
\(430\) 0 0
\(431\) −11.1379 + 6.43048i −0.536494 + 0.309745i −0.743657 0.668561i \(-0.766910\pi\)
0.207163 + 0.978307i \(0.433577\pi\)
\(432\) −10.2468 10.5877i −0.492999 0.509401i
\(433\) −33.6307 −1.61619 −0.808094 0.589054i \(-0.799501\pi\)
−0.808094 + 0.589054i \(0.799501\pi\)
\(434\) −24.0238 22.8879i −1.15318 1.09866i
\(435\) 0 0
\(436\) 1.59373 2.04218i 0.0763260 0.0978029i
\(437\) 6.64577 + 11.5108i 0.317910 + 0.550637i
\(438\) −4.35196 + 2.12406i −0.207945 + 0.101492i
\(439\) −12.4435 + 21.5528i −0.593896 + 1.02866i 0.399806 + 0.916600i \(0.369078\pi\)
−0.993702 + 0.112058i \(0.964256\pi\)
\(440\) 0 0
\(441\) −16.9258 5.91313i −0.805992 0.281578i
\(442\) −11.2533 0.783818i −0.535263 0.0372824i
\(443\) 3.97386 6.88293i 0.188804 0.327018i −0.756048 0.654516i \(-0.772872\pi\)
0.944852 + 0.327498i \(0.106206\pi\)
\(444\) 5.36459 + 13.2570i 0.254592 + 0.629149i
\(445\) 0 0
\(446\) 19.7216 + 13.2946i 0.933845 + 0.629515i
\(447\) 12.6420i 0.597944i
\(448\) −9.43274 18.9479i −0.445655 0.895205i
\(449\) −14.3027 −0.674988 −0.337494 0.941328i \(-0.609579\pi\)
−0.337494 + 0.941328i \(0.609579\pi\)
\(450\) 0 0
\(451\) 1.50431 + 2.60554i 0.0708352 + 0.122690i
\(452\) −13.1741 + 5.33104i −0.619656 + 0.250751i
\(453\) −3.18127 + 5.51013i −0.149469 + 0.258888i
\(454\) −1.94898 + 27.9815i −0.0914702 + 1.31324i
\(455\) 0 0
\(456\) 1.58918 7.50673i 0.0744202 0.351535i
\(457\) −19.2073 11.0893i −0.898478 0.518737i −0.0217719 0.999763i \(-0.506931\pi\)
−0.876706 + 0.481026i \(0.840264\pi\)
\(458\) 17.7078 8.64267i 0.827432 0.403845i
\(459\) 4.36438 2.51977i 0.203712 0.117613i
\(460\) 0 0
\(461\) 32.8587i 1.53038i −0.643803 0.765192i \(-0.722644\pi\)
0.643803 0.765192i \(-0.277356\pi\)
\(462\) 2.10743 8.70248i 0.0980465 0.404876i
\(463\) −3.31392 −0.154011 −0.0770055 0.997031i \(-0.524536\pi\)
−0.0770055 + 0.997031i \(0.524536\pi\)
\(464\) 14.9271 14.4465i 0.692974 0.670661i
\(465\) 0 0
\(466\) −12.9960 + 6.34295i −0.602027 + 0.293832i
\(467\) 30.4264 + 17.5667i 1.40797 + 0.812890i 0.995192 0.0979429i \(-0.0312263\pi\)
0.412775 + 0.910833i \(0.364560\pi\)
\(468\) −29.5776 4.14039i −1.36722 0.191390i
\(469\) 1.12297 6.61930i 0.0518538 0.305651i
\(470\) 0 0
\(471\) 9.44307 + 5.45196i 0.435114 + 0.251213i
\(472\) −6.55298 20.1119i −0.301625 0.925727i
\(473\) −9.71973 + 5.61169i −0.446914 + 0.258026i
\(474\) −5.93757 + 8.80799i −0.272721 + 0.404564i
\(475\) 0 0
\(476\) 7.07049 1.55490i 0.324075 0.0712686i
\(477\) 18.9984i 0.869877i
\(478\) 20.0329 + 13.5044i 0.916285 + 0.617679i
\(479\) −11.1633 19.3354i −0.510065 0.883459i −0.999932 0.0116615i \(-0.996288\pi\)
0.489867 0.871797i \(-0.337045\pi\)
\(480\) 0 0
\(481\) 54.5097 + 31.4712i 2.48543 + 1.43496i
\(482\) 1.81631 26.0767i 0.0827306 1.18776i
\(483\) 3.62719 4.38007i 0.165043 0.199300i
\(484\) −4.06732 0.569361i −0.184878 0.0258800i
\(485\) 0 0
\(486\) 18.4589 9.00923i 0.837311 0.408667i
\(487\) −3.59259 6.22255i −0.162796 0.281971i 0.773074 0.634315i \(-0.218718\pi\)
−0.935870 + 0.352344i \(0.885385\pi\)
\(488\) 3.12481 + 2.80896i 0.141454 + 0.127156i
\(489\) 4.73989i 0.214345i
\(490\) 0 0
\(491\) 5.80059i 0.261777i −0.991397 0.130889i \(-0.958217\pi\)
0.991397 0.130889i \(-0.0417830\pi\)
\(492\) 0.678677 0.869645i 0.0305971 0.0392066i
\(493\) 3.55252 + 6.15314i 0.159997 + 0.277124i
\(494\) −14.8124 30.3488i −0.666439 1.36546i
\(495\) 0 0
\(496\) 34.1089 + 9.74027i 1.53153 + 0.437351i
\(497\) 5.94840 7.18308i 0.266822 0.322205i
\(498\) 6.06591 + 0.422506i 0.271820 + 0.0189329i
\(499\) 34.3466 + 19.8300i 1.53757 + 0.887715i 0.998980 + 0.0451448i \(0.0143749\pi\)
0.538587 + 0.842570i \(0.318958\pi\)
\(500\) 0 0
\(501\) 4.54135 + 7.86585i 0.202892 + 0.351420i
\(502\) −13.0679 + 19.3854i −0.583250 + 0.865213i
\(503\) 8.22384i 0.366683i −0.983049 0.183341i \(-0.941309\pi\)
0.983049 0.183341i \(-0.0586914\pi\)
\(504\) 18.9604 2.80603i 0.844563 0.124991i
\(505\) 0 0
\(506\) −13.7490 9.26839i −0.611220 0.412030i
\(507\) 12.0414 6.95209i 0.534776 0.308753i
\(508\) −12.7672 31.5502i −0.566451 1.39982i
\(509\) 28.2081 + 16.2860i 1.25030 + 0.721863i 0.971170 0.238389i \(-0.0766194\pi\)
0.279134 + 0.960252i \(0.409953\pi\)
\(510\) 0 0
\(511\) 2.28781 13.4854i 0.101207 0.596560i
\(512\) 18.3386 + 13.2550i 0.810459 + 0.585796i
\(513\) 13.0657 + 7.54347i 0.576864 + 0.333052i
\(514\) 3.84273 + 7.87332i 0.169496 + 0.347277i
\(515\) 0 0
\(516\) 3.24413 + 2.53174i 0.142815 + 0.111454i
\(517\) −24.9150 −1.09576
\(518\) −39.2594 9.50722i −1.72496 0.417723i
\(519\) 2.59934i 0.114098i
\(520\) 0 0
\(521\) −4.88783 + 2.82199i −0.214140 + 0.123634i −0.603234 0.797564i \(-0.706121\pi\)
0.389094 + 0.921198i \(0.372788\pi\)
\(522\) 8.25085 + 16.9050i 0.361130 + 0.739913i
\(523\) −2.36780 1.36705i −0.103537 0.0597770i 0.447338 0.894365i \(-0.352372\pi\)
−0.550874 + 0.834588i \(0.685706\pi\)
\(524\) 2.38897 + 0.334418i 0.104363 + 0.0146091i
\(525\) 0 0
\(526\) −29.8434 2.07867i −1.30123 0.0906342i
\(527\) −6.06633 + 10.5072i −0.264254 + 0.457701i
\(528\) 2.32588 + 9.28538i 0.101221 + 0.404094i
\(529\) 6.23437 + 10.7982i 0.271060 + 0.469489i
\(530\) 0 0
\(531\) 19.1547 0.831245
\(532\) 14.6148 + 16.0037i 0.633630 + 0.693848i
\(533\) 4.85504i 0.210295i
\(534\) 4.91714 7.29426i 0.212786 0.315653i
\(535\) 0 0
\(536\) 2.22354 + 6.82433i 0.0960423 + 0.294766i
\(537\) −6.80697 + 11.7900i −0.293743 + 0.508777i
\(538\) −3.04491 + 43.7157i −0.131275 + 1.88472i
\(539\) 16.5064 + 19.1614i 0.710980 + 0.825341i
\(540\) 0 0
\(541\) −14.1500 + 24.5085i −0.608355 + 1.05370i 0.383157 + 0.923683i \(0.374837\pi\)
−0.991512 + 0.130018i \(0.958497\pi\)
\(542\) 14.2905 + 29.2795i 0.613828 + 1.25766i
\(543\) 4.32526 + 7.49157i 0.185615 + 0.321494i
\(544\) −5.92184 + 4.98280i −0.253897 + 0.213636i
\(545\) 0 0
\(546\) −9.96680 + 10.4614i −0.426540 + 0.447708i
\(547\) 20.7596 0.887616 0.443808 0.896122i \(-0.353627\pi\)
0.443808 + 0.896122i \(0.353627\pi\)
\(548\) −3.38186 2.63922i −0.144466 0.112742i
\(549\) −3.29514 + 1.90245i −0.140633 + 0.0811946i
\(550\) 0 0
\(551\) −10.6352 + 18.4207i −0.453075 + 0.784749i
\(552\) −1.25915 + 5.94779i −0.0535930 + 0.253155i
\(553\) −10.4442 28.1266i −0.444133 1.19606i
\(554\) −0.682514 + 9.79885i −0.0289973 + 0.416313i
\(555\) 0 0
\(556\) −2.54743 6.29521i −0.108035 0.266977i
\(557\) −16.2445 + 9.37876i −0.688301 + 0.397391i −0.802975 0.596012i \(-0.796751\pi\)
0.114674 + 0.993403i \(0.463418\pi\)
\(558\) −17.9552 + 26.6353i −0.760102 + 1.12756i
\(559\) 18.1113 0.766025
\(560\) 0 0
\(561\) −3.27401 −0.138229
\(562\) 3.35480 4.97662i 0.141514 0.209926i
\(563\) −28.9028 + 16.6870i −1.21811 + 0.703274i −0.964513 0.264037i \(-0.914946\pi\)
−0.253594 + 0.967311i \(0.581613\pi\)
\(564\) 3.42673 + 8.46815i 0.144292 + 0.356573i
\(565\) 0 0
\(566\) 0.838399 12.0369i 0.0352405 0.505948i
\(567\) −2.32064 + 13.6790i −0.0974579 + 0.574464i
\(568\) −2.06494 + 9.75407i −0.0866431 + 0.409272i
\(569\) 6.51501 11.2843i 0.273124 0.473064i −0.696536 0.717521i \(-0.745277\pi\)
0.969660 + 0.244457i \(0.0786099\pi\)
\(570\) 0 0
\(571\) −28.5406 + 16.4779i −1.19439 + 0.689579i −0.959298 0.282395i \(-0.908871\pi\)
−0.235088 + 0.971974i \(0.575538\pi\)
\(572\) 33.2123 + 25.9191i 1.38868 + 1.08373i
\(573\) −8.26295 −0.345190
\(574\) 0.879042 + 2.98922i 0.0366905 + 0.124768i
\(575\) 0 0
\(576\) −16.5572 + 12.0710i −0.689885 + 0.502959i
\(577\) −18.1937 31.5124i −0.757414 1.31188i −0.944165 0.329473i \(-0.893129\pi\)
0.186751 0.982407i \(-0.440204\pi\)
\(578\) 9.38400 + 19.2267i 0.390323 + 0.799727i
\(579\) −6.31373 + 10.9357i −0.262390 + 0.454472i
\(580\) 0 0
\(581\) −10.9542 + 13.2279i −0.454457 + 0.548786i
\(582\) 0.0223370 0.320692i 0.000925898 0.0132931i
\(583\) 13.3996 23.2088i 0.554955 0.961210i
\(584\) 4.52999 + 13.9031i 0.187452 + 0.575316i
\(585\) 0 0
\(586\) −19.9458 + 29.5883i −0.823953 + 1.22228i
\(587\) 28.4245i 1.17321i −0.809875 0.586603i \(-0.800465\pi\)
0.809875 0.586603i \(-0.199535\pi\)
\(588\) 4.24238 8.24561i 0.174953 0.340043i
\(589\) −36.3217 −1.49661
\(590\) 0 0
\(591\) 0.639794 + 1.10816i 0.0263176 + 0.0455835i
\(592\) 41.8890 10.4927i 1.72163 0.431247i
\(593\) 3.78574 6.55710i 0.155462 0.269268i −0.777765 0.628555i \(-0.783647\pi\)
0.933227 + 0.359287i \(0.116980\pi\)
\(594\) −18.7756 1.30777i −0.770371 0.0536583i
\(595\) 0 0
\(596\) 37.8042 + 5.29198i 1.54852 + 0.216768i
\(597\) −11.7962 6.81052i −0.482785 0.278736i
\(598\) 11.7362 + 24.0462i 0.479930 + 0.983321i
\(599\) −41.0937 + 23.7255i −1.67904 + 0.969397i −0.716772 + 0.697307i \(0.754381\pi\)
−0.962272 + 0.272090i \(0.912285\pi\)
\(600\) 0 0
\(601\) 13.3242i 0.543506i 0.962367 + 0.271753i \(0.0876034\pi\)
−0.962367 + 0.271753i \(0.912397\pi\)
\(602\) −11.1510 + 3.27918i −0.454481 + 0.133650i
\(603\) −6.49954 −0.264682
\(604\) 15.1456 + 11.8198i 0.616267 + 0.480939i
\(605\) 0 0
\(606\) 1.86379 + 3.81869i 0.0757113 + 0.155124i
\(607\) 13.0610 + 7.54080i 0.530132 + 0.306072i 0.741070 0.671428i \(-0.234319\pi\)
−0.210938 + 0.977499i \(0.567652\pi\)
\(608\) −21.7827 7.89460i −0.883405 0.320168i
\(609\) 8.97261 + 1.52221i 0.363588 + 0.0616829i
\(610\) 0 0
\(611\) 34.8191 + 20.1028i 1.40863 + 0.813272i
\(612\) −2.62891 6.49657i −0.106267 0.262608i
\(613\) 4.50739 2.60234i 0.182052 0.105108i −0.406205 0.913782i \(-0.633148\pi\)
0.588256 + 0.808675i \(0.299815\pi\)
\(614\) 34.3159 + 23.1327i 1.38488 + 0.933561i
\(615\) 0 0
\(616\) −25.1415 9.94491i −1.01298 0.400692i
\(617\) 35.7404i 1.43885i −0.694569 0.719426i \(-0.744405\pi\)
0.694569 0.719426i \(-0.255595\pi\)
\(618\) −3.21386 + 4.76755i −0.129280 + 0.191779i
\(619\) −19.1219 33.1200i −0.768573 1.33121i −0.938337 0.345722i \(-0.887634\pi\)
0.169764 0.985485i \(-0.445699\pi\)
\(620\) 0 0
\(621\) −10.3523 5.97690i −0.415423 0.239845i
\(622\) 32.0901 + 2.23515i 1.28670 + 0.0896215i
\(623\) 8.64929 + 23.2928i 0.346526 + 0.933205i
\(624\) 4.24151 14.8531i 0.169796 0.594599i
\(625\) 0 0
\(626\) 4.08454 + 8.36874i 0.163251 + 0.334482i
\(627\) −4.90071 8.48828i −0.195716 0.338989i
\(628\) 20.2563 25.9561i 0.808315 1.03576i
\(629\) 14.7700i 0.588918i
\(630\) 0 0
\(631\) 12.0334i 0.479042i −0.970891 0.239521i \(-0.923010\pi\)
0.970891 0.239521i \(-0.0769904\pi\)
\(632\) 23.8537 + 21.4426i 0.948849 + 0.852941i
\(633\) 3.30647 + 5.72697i 0.131420 + 0.227627i
\(634\) −17.9475 + 8.75966i −0.712788 + 0.347891i
\(635\) 0 0
\(636\) −9.73118 1.36221i −0.385866 0.0540152i
\(637\) −7.60740 40.0966i −0.301416 1.58869i
\(638\) 1.84376 26.4709i 0.0729952 1.04799i
\(639\) −7.81897 4.51429i −0.309314 0.178582i
\(640\) 0 0
\(641\) −11.4676 19.8625i −0.452944 0.784522i 0.545624 0.838030i \(-0.316293\pi\)
−0.998567 + 0.0535086i \(0.982960\pi\)
\(642\) 5.95580 + 4.01487i 0.235057 + 0.158454i
\(643\) 1.23955i 0.0488833i 0.999701 + 0.0244416i \(0.00778079\pi\)
−0.999701 + 0.0244416i \(0.992219\pi\)
\(644\) −11.5797 12.6802i −0.456303 0.499668i
\(645\) 0 0
\(646\) 4.42958 6.57098i 0.174279 0.258532i
\(647\) 12.2469 7.07077i 0.481477 0.277981i −0.239555 0.970883i \(-0.577002\pi\)
0.721032 + 0.692902i \(0.243668\pi\)
\(648\) −4.59502 14.1027i −0.180509 0.554006i
\(649\) −23.3998 13.5099i −0.918523 0.530309i
\(650\) 0 0
\(651\) 5.40978 + 14.5687i 0.212026 + 0.570992i
\(652\) −14.1740 1.98414i −0.555098 0.0777049i
\(653\) −14.8017 8.54579i −0.579237 0.334423i 0.181593 0.983374i \(-0.441875\pi\)
−0.760830 + 0.648951i \(0.775208\pi\)
\(654\) −1.09032 + 0.532155i −0.0426350 + 0.0208089i
\(655\) 0 0
\(656\) −2.31647 2.39354i −0.0904428 0.0934519i
\(657\) −13.2414 −0.516598
\(658\) −25.0777 6.07292i −0.977629 0.236747i
\(659\) 3.45765i 0.134691i −0.997730 0.0673455i \(-0.978547\pi\)
0.997730 0.0673455i \(-0.0214530\pi\)
\(660\) 0 0
\(661\) 13.1317 7.58160i 0.510765 0.294890i −0.222383 0.974959i \(-0.571384\pi\)
0.733148 + 0.680069i \(0.238050\pi\)
\(662\) −25.8281 + 12.6059i −1.00384 + 0.489943i
\(663\) 4.57547 + 2.64165i 0.177697 + 0.102593i
\(664\) 3.80267 17.9625i 0.147572 0.697079i
\(665\) 0 0
\(666\) −2.71715 + 39.0100i −0.105287 + 1.51161i
\(667\) 8.42657 14.5952i 0.326278 0.565130i
\(668\) 25.4229 10.2876i 0.983640 0.398041i
\(669\) −5.56972 9.64704i −0.215338 0.372976i
\(670\) 0 0
\(671\) 5.36721 0.207199
\(672\) 0.0777937 + 9.91291i 0.00300096 + 0.382399i
\(673\) 11.2116i 0.432175i 0.976374 + 0.216087i \(0.0693296\pi\)
−0.976374 + 0.216087i \(0.930670\pi\)
\(674\) −18.4932 12.4664i −0.712330 0.480190i
\(675\) 0 0
\(676\) −15.7488 38.9184i −0.605722 1.49686i
\(677\) −1.83818 + 3.18383i −0.0706471 + 0.122364i −0.899185 0.437568i \(-0.855840\pi\)
0.828538 + 0.559933i \(0.189173\pi\)
\(678\) 6.64010 + 0.462500i 0.255011 + 0.0177622i
\(679\) 0.699331 + 0.579125i 0.0268379 + 0.0222248i
\(680\) 0 0
\(681\) 6.56852 11.3770i 0.251706 0.435968i
\(682\) 40.7203 19.8744i 1.55926 0.761029i
\(683\) −21.0938 36.5356i −0.807133 1.39800i −0.914841 0.403814i \(-0.867684\pi\)
0.107708 0.994183i \(-0.465649\pi\)
\(684\) 12.9081 16.5402i 0.493553 0.632430i
\(685\) 0 0
\(686\) 11.9436 + 23.3099i 0.456010 + 0.889975i
\(687\) −9.22865 −0.352095
\(688\) 8.92886 8.64136i 0.340410 0.329449i
\(689\) −37.4523 + 21.6231i −1.42682 + 0.823773i
\(690\) 0 0
\(691\) −11.5615 + 20.0251i −0.439820 + 0.761790i −0.997675 0.0681478i \(-0.978291\pi\)
0.557855 + 0.829938i \(0.311624\pi\)
\(692\) −7.77298 1.08809i −0.295485 0.0413631i
\(693\) 15.6157 18.8569i 0.593190 0.716316i
\(694\) 4.29987 + 0.299497i 0.163221 + 0.0113688i
\(695\) 0 0
\(696\) −9.25053 + 3.01406i −0.350640 + 0.114248i
\(697\) 0.986645 0.569640i 0.0373718 0.0215766i
\(698\) 9.85569 + 6.64384i 0.373043 + 0.251473i
\(699\) 6.77301 0.256179
\(700\) 0 0
\(701\) 29.3192 1.10737 0.553686 0.832725i \(-0.313221\pi\)
0.553686 + 0.832725i \(0.313221\pi\)
\(702\) 25.1839 + 16.9768i 0.950506 + 0.640747i
\(703\) −38.2931 + 22.1085i −1.44425 + 0.833839i
\(704\) 28.7404 3.06834i 1.08319 0.115642i
\(705\) 0 0
\(706\) 0.610622 + 0.0425314i 0.0229811 + 0.00160069i
\(707\) −11.8330 2.00747i −0.445025 0.0754986i
\(708\) −1.37342 + 9.81126i −0.0516163 + 0.368730i
\(709\) 1.67720 2.90499i 0.0629884 0.109099i −0.832811 0.553557i \(-0.813270\pi\)
0.895800 + 0.444458i \(0.146604\pi\)
\(710\) 0 0
\(711\) −25.1539 + 14.5226i −0.943346 + 0.544641i
\(712\) −19.7542 17.7575i −0.740321 0.665491i
\(713\) 28.7786 1.07777
\(714\) −3.29538 0.798024i −0.123327 0.0298653i
\(715\) 0 0
\(716\) 32.4071 + 25.2908i 1.21111 + 0.945160i
\(717\) −5.65765 9.79934i −0.211289 0.365963i
\(718\) 34.2906 16.7362i 1.27972 0.624591i
\(719\) 15.5142 26.8714i 0.578583 1.00213i −0.417059 0.908879i \(-0.636939\pi\)
0.995642 0.0932556i \(-0.0297274\pi\)
\(720\) 0 0
\(721\) −5.65320 15.2242i −0.210536 0.566980i
\(722\) −3.13857 0.218609i −0.116805 0.00813579i
\(723\) −6.12138 + 10.6025i −0.227657 + 0.394313i
\(724\) 24.2132 9.79814i 0.899876 0.364145i
\(725\) 0 0
\(726\) 1.59497 + 1.07519i 0.0591949 + 0.0399039i
\(727\) 37.9906i 1.40899i 0.709707 + 0.704497i \(0.248827\pi\)
−0.709707 + 0.704497i \(0.751173\pi\)
\(728\) 27.1115 + 34.1837i 1.00482 + 1.26693i
\(729\) 6.11207 0.226373
\(730\) 0 0
\(731\) 2.12499 + 3.68058i 0.0785955 + 0.136131i
\(732\) −0.738189 1.82421i −0.0272843 0.0674249i
\(733\) −15.4876 + 26.8252i −0.572046 + 0.990813i 0.424310 + 0.905517i \(0.360517\pi\)
−0.996356 + 0.0852956i \(0.972817\pi\)
\(734\) 2.04601 29.3745i 0.0755195 1.08423i
\(735\) 0 0
\(736\) 17.2590 + 6.25511i 0.636176 + 0.230566i
\(737\) 7.93996 + 4.58414i 0.292472 + 0.168859i
\(738\) 2.71069 1.32301i 0.0997819 0.0487006i
\(739\) −2.53077 + 1.46114i −0.0930957 + 0.0537488i −0.545825 0.837899i \(-0.683784\pi\)
0.452729 + 0.891648i \(0.350450\pi\)
\(740\) 0 0
\(741\) 15.8167i 0.581039i
\(742\) 19.1441 20.0942i 0.702802 0.737682i
\(743\) 36.6505 1.34457 0.672287 0.740290i \(-0.265312\pi\)
0.672287 + 0.740290i \(0.265312\pi\)
\(744\) −12.3555 11.1066i −0.452974 0.407188i
\(745\) 0 0
\(746\) 22.4462 10.9553i 0.821815 0.401104i
\(747\) 14.3989 + 8.31323i 0.526829 + 0.304165i
\(748\) −1.37052 + 9.79051i −0.0501110 + 0.357976i
\(749\) −19.0187 + 7.06219i −0.694927 + 0.258047i
\(750\) 0 0
\(751\) −31.3355 18.0915i −1.14345 0.660170i −0.196166 0.980571i \(-0.562849\pi\)
−0.947282 + 0.320401i \(0.896182\pi\)
\(752\) 26.7574 6.70241i 0.975741 0.244412i
\(753\) 9.48259 5.47478i 0.345565 0.199512i
\(754\) −23.9348 + 35.5057i −0.871654 + 1.29304i
\(755\) 0 0
\(756\) −18.5794 5.89276i −0.675725 0.214318i
\(757\) 1.44394i 0.0524807i −0.999656 0.0262404i \(-0.991646\pi\)
0.999656 0.0262404i \(-0.00835352\pi\)
\(758\) 17.6544 + 11.9011i 0.641238 + 0.432266i
\(759\) 3.88297 + 6.72550i 0.140943 + 0.244120i
\(760\) 0 0
\(761\) −24.4509 14.1167i −0.886343 0.511730i −0.0135983 0.999908i \(-0.504329\pi\)
−0.872744 + 0.488177i \(0.837662\pi\)
\(762\) −1.10763 + 15.9022i −0.0401251 + 0.576076i
\(763\) 0.573178 3.37859i 0.0207505 0.122313i
\(764\) −3.45891 + 24.7093i −0.125139 + 0.893951i
\(765\) 0 0
\(766\) 38.5730 18.8264i 1.39370 0.680224i
\(767\) 21.8010 + 37.7605i 0.787189 + 1.36345i
\(768\) −4.99573 9.34630i −0.180268 0.337256i
\(769\) 38.3866i 1.38426i 0.721774 + 0.692129i \(0.243327\pi\)
−0.721774 + 0.692129i \(0.756673\pi\)
\(770\) 0 0
\(771\) 4.10328i 0.147776i
\(772\) 30.0589 + 23.4582i 1.08184 + 0.844278i
\(773\) −9.54086 16.5252i −0.343161 0.594372i 0.641857 0.766824i \(-0.278164\pi\)
−0.985018 + 0.172452i \(0.944831\pi\)
\(774\) 4.93535 + 10.1120i 0.177398 + 0.363467i
\(775\) 0 0
\(776\) −0.949638 0.201039i −0.0340900 0.00721688i
\(777\) 14.5712 + 12.0666i 0.522738 + 0.432886i
\(778\) 8.85722 + 0.616928i 0.317547 + 0.0221179i
\(779\) 2.95373 + 1.70533i 0.105828 + 0.0611000i
\(780\) 0 0
\(781\) 6.36787 + 11.0295i 0.227860 + 0.394666i
\(782\) −3.50967 + 5.20637i −0.125506 + 0.186179i
\(783\) 19.1296i 0.683637i
\(784\) −22.8816 16.1379i −0.817199 0.576355i
\(785\) 0 0
\(786\) −0.936816 0.631519i −0.0334151 0.0225255i
\(787\) −4.41858 + 2.55107i −0.157505 + 0.0909358i −0.576681 0.816969i \(-0.695652\pi\)
0.419176 + 0.907905i \(0.362319\pi\)
\(788\) 3.58162 1.44934i 0.127590 0.0516308i
\(789\) 12.1340 + 7.00559i 0.431983 + 0.249406i
\(790\) 0 0
\(791\) −11.9911 + 14.4800i −0.426354 + 0.514851i
\(792\) −5.42087 + 25.6063i −0.192622 + 0.909879i
\(793\) −7.50075 4.33056i −0.266359 0.153783i
\(794\) 6.03058 + 12.3560i 0.214017 + 0.438496i
\(795\) 0 0
\(796\) −25.3039 + 32.4240i −0.896874 + 1.14924i
\(797\) −25.6101 −0.907155 −0.453578 0.891217i \(-0.649852\pi\)
−0.453578 + 0.891217i \(0.649852\pi\)
\(798\) −2.86373 9.73822i −0.101375 0.344729i
\(799\) 9.43461i 0.333772i
\(800\) 0 0
\(801\) 20.8310 12.0268i 0.736027 0.424946i
\(802\) −4.33429 8.88046i −0.153049 0.313580i
\(803\) 16.1760 + 9.33922i 0.570839 + 0.329574i
\(804\) 0.466026 3.32913i 0.0164355 0.117409i
\(805\) 0 0
\(806\) −72.9429 5.08065i −2.56930 0.178958i
\(807\) 10.2621 17.7744i 0.361241 0.625688i
\(808\) 12.1995 3.97491i 0.429177 0.139837i
\(809\) 25.2381 + 43.7136i 0.887323 + 1.53689i 0.843028 + 0.537870i \(0.180771\pi\)
0.0442955 + 0.999018i \(0.485896\pi\)
\(810\) 0 0
\(811\) −3.15050 −0.110629 −0.0553145 0.998469i \(-0.517616\pi\)
−0.0553145 + 0.998469i \(0.517616\pi\)
\(812\) 8.30794 26.1942i 0.291552 0.919238i
\(813\) 15.2594i 0.535170i
\(814\) 30.8332 45.7390i 1.08070 1.60315i
\(815\) 0 0
\(816\) 3.51611 0.880743i 0.123088 0.0308322i
\(817\) −6.36159 + 11.0186i −0.222564 + 0.385492i
\(818\) 0.220664 3.16807i 0.00771533 0.110769i
\(819\) −37.0379 + 13.7533i −1.29421 + 0.480578i
\(820\) 0 0
\(821\) 17.7416 30.7294i 0.619187 1.07246i −0.370448 0.928853i \(-0.620796\pi\)
0.989634 0.143609i \(-0.0458709\pi\)
\(822\) 0.881249 + 1.80558i 0.0307371 + 0.0629767i
\(823\) −4.20565 7.28440i −0.146600 0.253918i 0.783369 0.621557i \(-0.213500\pi\)
−0.929969 + 0.367639i \(0.880166\pi\)
\(824\) 12.9114 + 11.6064i 0.449790 + 0.404327i
\(825\) 0 0
\(826\) −20.2596 19.3017i −0.704921 0.671591i
\(827\) 4.33435 0.150720 0.0753601 0.997156i \(-0.475989\pi\)
0.0753601 + 0.997156i \(0.475989\pi\)
\(828\) −10.2274 + 13.1053i −0.355428 + 0.455439i
\(829\) −20.9404 + 12.0899i −0.727289 + 0.419900i −0.817429 0.576029i \(-0.804602\pi\)
0.0901408 + 0.995929i \(0.471268\pi\)
\(830\) 0 0
\(831\) 2.30023 3.98412i 0.0797942 0.138208i
\(832\) −42.6407 18.9013i −1.47830 0.655283i
\(833\) 7.25589 6.25050i 0.251402 0.216567i
\(834\) −0.221005 + 3.17296i −0.00765277 + 0.109871i
\(835\) 0 0
\(836\) −27.4346 + 11.1017i −0.948846 + 0.383961i
\(837\) 28.2896 16.3330i 0.977831 0.564551i
\(838\) −14.5108 + 21.5258i −0.501267 + 0.743597i
\(839\) 18.3056 0.631979 0.315989 0.948763i \(-0.397664\pi\)
0.315989 + 0.948763i \(0.397664\pi\)
\(840\) 0 0
\(841\) −2.02999 −0.0699998
\(842\) −1.79688 + 2.66556i −0.0619246 + 0.0918611i
\(843\) −2.43437 + 1.40549i −0.0838442 + 0.0484075i
\(844\) 18.5099 7.49024i 0.637137 0.257825i
\(845\) 0 0
\(846\) −1.73563 + 24.9184i −0.0596722 + 0.856712i
\(847\) −5.09322 + 1.89126i −0.175005 + 0.0649845i
\(848\) −8.14704 + 28.5296i −0.279770 + 0.979711i
\(849\) −2.82560 + 4.89408i −0.0969743 + 0.167964i
\(850\) 0 0
\(851\) 30.3407 17.5172i 1.04006 0.600481i
\(852\) 2.87290 3.68128i 0.0984238 0.126119i
\(853\) −16.9533 −0.580469 −0.290234 0.956956i \(-0.593733\pi\)
−0.290234 + 0.956956i \(0.593733\pi\)
\(854\) 5.40225 + 1.30823i 0.184861 + 0.0447668i
\(855\) 0 0
\(856\) 14.4991 16.1294i 0.495569 0.551292i
\(857\) −25.2872 43.7988i −0.863795 1.49614i −0.868238 0.496147i \(-0.834748\pi\)
0.00444284 0.999990i \(-0.498586\pi\)
\(858\) −8.65451 17.7321i −0.295460 0.605364i
\(859\) 2.51925 4.36346i 0.0859555 0.148879i −0.819842 0.572589i \(-0.805939\pi\)
0.905798 + 0.423710i \(0.139272\pi\)
\(860\) 0 0
\(861\) 0.244083 1.43874i 0.00831832 0.0490321i
\(862\) 1.26379 18.1442i 0.0430448 0.617993i
\(863\) −5.87084 + 10.1686i −0.199846 + 0.346143i −0.948478 0.316842i \(-0.897377\pi\)
0.748633 + 0.662985i \(0.230711\pi\)
\(864\) 20.5157 3.64636i 0.697960 0.124052i
\(865\) 0 0
\(866\) 26.5850 39.4371i 0.903395 1.34013i
\(867\) 10.0203i 0.340306i
\(868\) 45.8304 10.0787i 1.55559 0.342095i
\(869\) 40.9714 1.38986
\(870\) 0 0
\(871\) −7.39747 12.8128i −0.250654 0.434145i
\(872\) 1.13493 + 3.48324i 0.0384335 + 0.117957i
\(873\) 0.439502 0.761240i 0.0148749 0.0257641i
\(874\) −18.7517 1.30610i −0.634284 0.0441795i
\(875\) 0 0
\(876\) 0.949429 6.78241i 0.0320782 0.229156i
\(877\) 20.9426 + 12.0912i 0.707180 + 0.408290i 0.810016 0.586408i \(-0.199458\pi\)
−0.102836 + 0.994698i \(0.532792\pi\)
\(878\) −15.4373 31.6293i −0.520985 1.06744i
\(879\) 14.4734 8.35624i 0.488177 0.281849i
\(880\) 0 0
\(881\) 19.6285i 0.661301i −0.943753 0.330651i \(-0.892732\pi\)
0.943753 0.330651i \(-0.107268\pi\)
\(882\) 20.3139 15.1738i 0.684004 0.510928i
\(883\) −11.2418 −0.378315 −0.189158 0.981947i \(-0.560576\pi\)
−0.189158 + 0.981947i \(0.560576\pi\)
\(884\) 9.81483 12.5766i 0.330108 0.422995i
\(885\) 0 0
\(886\) 4.92995 + 10.1009i 0.165625 + 0.339346i
\(887\) −36.2085 20.9050i −1.21576 0.701920i −0.251753 0.967792i \(-0.581007\pi\)
−0.964009 + 0.265871i \(0.914340\pi\)
\(888\) −19.7865 4.18882i −0.663993 0.140568i
\(889\) −34.6779 28.7172i −1.16306 0.963143i
\(890\) 0 0
\(891\) −16.4082 9.47327i −0.549695 0.317366i
\(892\) −31.1798 + 12.6173i −1.04398 + 0.422457i
\(893\) −24.4604 + 14.1222i −0.818537 + 0.472583i
\(894\) −14.8246 9.99344i −0.495809 0.334231i
\(895\) 0 0
\(896\) 29.6759 + 3.91696i 0.991401 + 0.130856i
\(897\) 12.5320i 0.418430i
\(898\) 11.3063 16.7721i 0.377296 0.559693i
\(899\) 23.0272 + 39.8842i 0.768000 + 1.33021i
\(900\) 0 0
\(901\) −8.78851 5.07405i −0.292788 0.169041i
\(902\) −4.24455 0.295644i −0.141328 0.00984385i
\(903\) 5.36708 + 0.910527i 0.178605 + 0.0303005i
\(904\) 4.16262 19.6628i 0.138447 0.653974i
\(905\) 0 0
\(906\) −3.94667 8.08627i −0.131119 0.268648i
\(907\) −10.9044 18.8870i −0.362076 0.627133i 0.626227 0.779641i \(-0.284598\pi\)
−0.988302 + 0.152508i \(0.951265\pi\)
\(908\) −31.2719 24.4048i −1.03779 0.809901i
\(909\) 11.6189i 0.385374i
\(910\) 0 0
\(911\) 2.40991i 0.0798440i 0.999203 + 0.0399220i \(0.0127109\pi\)
−0.999203 + 0.0399220i \(0.987289\pi\)
\(912\) 7.54654 + 7.79761i 0.249891 + 0.258205i
\(913\) −11.7267 20.3112i −0.388096 0.672202i
\(914\) 28.1872 13.7574i 0.932350 0.455053i
\(915\) 0 0
\(916\) −3.86316 + 27.5971i −0.127642 + 0.911835i
\(917\) 2.99154 1.11085i 0.0987893 0.0366833i
\(918\) −0.495214 + 7.10977i −0.0163445 + 0.234657i
\(919\) 13.1661 + 7.60145i 0.434310 + 0.250749i 0.701181 0.712983i \(-0.252657\pi\)
−0.266871 + 0.963732i \(0.585990\pi\)
\(920\) 0 0
\(921\) −9.69140 16.7860i −0.319343 0.553118i
\(922\) 38.5318 + 25.9748i 1.26898 + 0.855433i
\(923\) 20.5518i 0.676470i
\(924\) 8.53906 + 9.35058i 0.280914 + 0.307611i
\(925\) 0 0
\(926\) 2.61965 3.88607i 0.0860870 0.127704i
\(927\) −13.6152 + 7.86074i −0.447182 + 0.258181i
\(928\) 5.14084 + 28.9242i 0.168756 + 0.949485i
\(929\) −18.0735 10.4347i −0.592971 0.342352i 0.173300 0.984869i \(-0.444557\pi\)
−0.766272 + 0.642517i \(0.777890\pi\)
\(930\) 0 0
\(931\) 27.0662 + 9.45573i 0.887059 + 0.309899i
\(932\) 2.83522 20.2538i 0.0928706 0.663437i
\(933\) −13.0475 7.53299i −0.427157 0.246619i
\(934\) −44.6517 + 21.7932i −1.46105 + 0.713094i
\(935\) 0 0
\(936\) 28.2363 31.4112i 0.922931 1.02671i
\(937\) −10.9083 −0.356358 −0.178179 0.983998i \(-0.557021\pi\)
−0.178179 + 0.983998i \(0.557021\pi\)
\(938\) 6.87443 + 6.54939i 0.224458 + 0.213845i
\(939\) 4.36148i 0.142331i
\(940\) 0 0
\(941\) −42.7569 + 24.6857i −1.39383 + 0.804730i −0.993737 0.111743i \(-0.964357\pi\)
−0.400097 + 0.916473i \(0.631023\pi\)
\(942\) −13.8580 + 6.76367i −0.451517 + 0.220372i
\(943\) −2.34032 1.35118i −0.0762113 0.0440006i
\(944\) 28.7644 + 8.21408i 0.936202 + 0.267346i
\(945\) 0 0
\(946\) 1.10287 15.8339i 0.0358574 0.514804i
\(947\) −7.27929 + 12.6081i −0.236545 + 0.409708i −0.959721 0.280956i \(-0.909349\pi\)
0.723175 + 0.690664i \(0.242682\pi\)
\(948\) −5.63507 13.9254i −0.183019 0.452276i
\(949\) −15.0708 26.1034i −0.489218 0.847351i
\(950\) 0 0
\(951\) 9.35358 0.303311
\(952\) −3.76585 + 9.52036i −0.122052 + 0.308557i
\(953\) 9.87954i 0.320030i 0.987115 + 0.160015i \(0.0511542\pi\)
−0.987115 + 0.160015i \(0.948846\pi\)
\(954\) −22.2785 15.0182i −0.721293 0.486232i
\(955\) 0 0
\(956\) −31.6720 + 12.8164i −1.02435 + 0.414513i
\(957\) −6.21390 + 10.7628i −0.200867 + 0.347912i
\(958\) 31.4983 + 2.19394i 1.01766 + 0.0708829i
\(959\) −5.59494 0.949183i −0.180670 0.0306507i
\(960\) 0 0
\(961\) −23.8215 + 41.2601i −0.768437 + 1.33097i
\(962\) −79.9945 + 39.0430i −2.57913 + 1.25880i
\(963\) 9.81993 + 17.0086i 0.316443 + 0.548095i
\(964\) 29.1431 + 22.7435i 0.938637 + 0.732519i
\(965\) 0 0
\(966\) 2.26901 + 7.71586i 0.0730042 + 0.248254i
\(967\) 15.5047 0.498597 0.249298 0.968427i \(-0.419800\pi\)
0.249298 + 0.968427i \(0.419800\pi\)
\(968\) 3.88287 4.31948i 0.124800 0.138833i
\(969\) −3.21427 + 1.85576i −0.103257 + 0.0596156i
\(970\) 0 0
\(971\) 16.5173 28.6089i 0.530067 0.918102i −0.469318 0.883029i \(-0.655500\pi\)
0.999385 0.0350732i \(-0.0111664\pi\)
\(972\) −4.02701 + 28.7676i −0.129166 + 0.922721i
\(973\) −6.91927 5.72993i −0.221822 0.183693i
\(974\) 10.1368 + 0.706056i 0.324805 + 0.0226235i
\(975\) 0 0
\(976\) −5.76409 + 1.44384i −0.184504 + 0.0462161i
\(977\) −44.1430 + 25.4860i −1.41226 + 0.815369i −0.995601 0.0936930i \(-0.970133\pi\)
−0.416660 + 0.909062i \(0.636799\pi\)
\(978\) 5.55824 + 3.74687i 0.177733 + 0.119812i
\(979\) −33.9301 −1.08441
\(980\) 0 0
\(981\) −3.31746 −0.105918
\(982\) 6.80208 + 4.58536i 0.217063 + 0.146325i
\(983\) 21.2423 12.2642i 0.677523 0.391168i −0.121398 0.992604i \(-0.538738\pi\)
0.798921 + 0.601436i \(0.205404\pi\)
\(984\) 0.483298 + 1.48330i 0.0154070 + 0.0472860i
\(985\) 0 0
\(986\) −10.0238 0.698180i −0.319221 0.0222346i
\(987\) 9.30762 + 7.70775i 0.296265 + 0.245340i
\(988\) 47.2977 + 6.62093i 1.50474 + 0.210640i
\(989\) 5.04046 8.73034i 0.160277 0.277609i
\(990\) 0 0
\(991\) 45.8274 26.4585i 1.45576 0.840481i 0.456957 0.889489i \(-0.348939\pi\)
0.998798 + 0.0490078i \(0.0156059\pi\)
\(992\) −38.3850 + 32.2982i −1.21872 + 1.02547i
\(993\) 13.4606 0.427160
\(994\) 3.72106 + 12.6536i 0.118025 + 0.401348i
\(995\) 0 0
\(996\) −5.29054 + 6.77921i −0.167637 + 0.214808i
\(997\) 8.51148 + 14.7423i 0.269561 + 0.466894i 0.968749 0.248045i \(-0.0797880\pi\)
−0.699187 + 0.714939i \(0.746455\pi\)
\(998\) −50.4047 + 24.6011i −1.59553 + 0.778733i
\(999\) 19.8834 34.4390i 0.629082 1.08960i
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 700.2.t.d.299.5 32
4.3 odd 2 inner 700.2.t.d.299.10 32
5.2 odd 4 700.2.p.c.551.3 32
5.3 odd 4 140.2.o.a.131.14 yes 32
5.4 even 2 700.2.t.c.299.12 32
7.3 odd 6 700.2.t.c.199.7 32
20.3 even 4 140.2.o.a.131.2 yes 32
20.7 even 4 700.2.p.c.551.15 32
20.19 odd 2 700.2.t.c.299.7 32
28.3 even 6 700.2.t.c.199.12 32
35.3 even 12 140.2.o.a.31.2 32
35.13 even 4 980.2.o.f.411.14 32
35.17 even 12 700.2.p.c.451.15 32
35.18 odd 12 980.2.o.f.31.2 32
35.23 odd 12 980.2.g.a.391.17 32
35.24 odd 6 inner 700.2.t.d.199.10 32
35.33 even 12 980.2.g.a.391.18 32
140.3 odd 12 140.2.o.a.31.14 yes 32
140.23 even 12 980.2.g.a.391.20 32
140.59 even 6 inner 700.2.t.d.199.5 32
140.83 odd 4 980.2.o.f.411.2 32
140.87 odd 12 700.2.p.c.451.3 32
140.103 odd 12 980.2.g.a.391.19 32
140.123 even 12 980.2.o.f.31.14 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.o.a.31.2 32 35.3 even 12
140.2.o.a.31.14 yes 32 140.3 odd 12
140.2.o.a.131.2 yes 32 20.3 even 4
140.2.o.a.131.14 yes 32 5.3 odd 4
700.2.p.c.451.3 32 140.87 odd 12
700.2.p.c.451.15 32 35.17 even 12
700.2.p.c.551.3 32 5.2 odd 4
700.2.p.c.551.15 32 20.7 even 4
700.2.t.c.199.7 32 7.3 odd 6
700.2.t.c.199.12 32 28.3 even 6
700.2.t.c.299.7 32 20.19 odd 2
700.2.t.c.299.12 32 5.4 even 2
700.2.t.d.199.5 32 140.59 even 6 inner
700.2.t.d.199.10 32 35.24 odd 6 inner
700.2.t.d.299.5 32 1.1 even 1 trivial
700.2.t.d.299.10 32 4.3 odd 2 inner
980.2.g.a.391.17 32 35.23 odd 12
980.2.g.a.391.18 32 35.33 even 12
980.2.g.a.391.19 32 140.103 odd 12
980.2.g.a.391.20 32 140.23 even 12
980.2.o.f.31.2 32 35.18 odd 12
980.2.o.f.31.14 32 140.123 even 12
980.2.o.f.411.2 32 140.83 odd 4
980.2.o.f.411.14 32 35.13 even 4