Properties

Label 210.2.d.a.209.2
Level $210$
Weight $2$
Character 210.209
Analytic conductor $1.677$
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] = [210,2,Mod(209,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.209");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.10070523904.11
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 10x^{4} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 209.2
Root \(-1.68014 - 0.420861i\) of defining polynomial
Character \(\chi\) \(=\) 210.209
Dual form 210.2.d.a.209.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-1.68014 + 0.420861i) q^{3} +1.00000 q^{4} +(-1.08495 - 1.95522i) q^{5} +(1.68014 - 0.420861i) q^{6} +(0.595188 + 2.57794i) q^{7} -1.00000 q^{8} +(2.64575 - 1.41421i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-1.68014 + 0.420861i) q^{3} +1.00000 q^{4} +(-1.08495 - 1.95522i) q^{5} +(1.68014 - 0.420861i) q^{6} +(0.595188 + 2.57794i) q^{7} -1.00000 q^{8} +(2.64575 - 1.41421i) q^{9} +(1.08495 + 1.95522i) q^{10} +2.82843i q^{11} +(-1.68014 + 0.420861i) q^{12} +3.36028 q^{13} +(-0.595188 - 2.57794i) q^{14} +(2.64575 + 2.82843i) q^{15} +1.00000 q^{16} +4.75216i q^{17} +(-2.64575 + 1.41421i) q^{18} +5.59388i q^{19} +(-1.08495 - 1.95522i) q^{20} +(-2.08495 - 4.08080i) q^{21} -2.82843i q^{22} +7.29150 q^{23} +(1.68014 - 0.420861i) q^{24} +(-2.64575 + 4.24264i) q^{25} -3.36028 q^{26} +(-3.85005 + 3.48957i) q^{27} +(0.595188 + 2.57794i) q^{28} -0.500983i q^{29} +(-2.64575 - 2.82843i) q^{30} -3.06871i q^{31} -1.00000 q^{32} +(-1.19038 - 4.75216i) q^{33} -4.75216i q^{34} +(4.39467 - 3.96066i) q^{35} +(2.64575 - 1.41421i) q^{36} -3.32941i q^{37} -5.59388i q^{38} +(-5.64575 + 1.41421i) q^{39} +(1.08495 + 1.95522i) q^{40} +4.33981 q^{41} +(2.08495 + 4.08080i) q^{42} -10.3117i q^{43} +2.82843i q^{44} +(-5.63561 - 3.63866i) q^{45} -7.29150 q^{46} +7.82087i q^{47} +(-1.68014 + 0.420861i) q^{48} +(-6.29150 + 3.06871i) q^{49} +(2.64575 - 4.24264i) q^{50} +(-2.00000 - 7.98430i) q^{51} +3.36028 q^{52} -8.58301 q^{53} +(3.85005 - 3.48957i) q^{54} +(5.53019 - 3.06871i) q^{55} +(-0.595188 - 2.57794i) q^{56} +(-2.35425 - 9.39851i) q^{57} +0.500983i q^{58} -2.16991 q^{59} +(2.64575 + 2.82843i) q^{60} -2.52517i q^{61} +3.06871i q^{62} +(5.22047 + 5.97885i) q^{63} +1.00000 q^{64} +(-3.64575 - 6.57008i) q^{65} +(1.19038 + 4.75216i) q^{66} +10.3117i q^{67} +4.75216i q^{68} +(-12.2508 + 3.06871i) q^{69} +(-4.39467 + 3.96066i) q^{70} +9.81076i q^{71} +(-2.64575 + 1.41421i) q^{72} +5.53019 q^{73} +3.32941i q^{74} +(2.65967 - 8.24173i) q^{75} +5.59388i q^{76} +(-7.29150 + 1.68345i) q^{77} +(5.64575 - 1.41421i) q^{78} +3.29150 q^{79} +(-1.08495 - 1.95522i) q^{80} +(5.00000 - 7.48331i) q^{81} -4.33981 q^{82} -6.97915i q^{83} +(-2.08495 - 4.08080i) q^{84} +(9.29150 - 5.15587i) q^{85} +10.3117i q^{86} +(0.210845 + 0.841723i) q^{87} -2.82843i q^{88} +15.8219 q^{89} +(5.63561 + 3.63866i) q^{90} +(2.00000 + 8.66259i) q^{91} +7.29150 q^{92} +(1.29150 + 5.15587i) q^{93} -7.82087i q^{94} +(10.9373 - 6.06910i) q^{95} +(1.68014 - 0.420861i) q^{96} -14.6315 q^{97} +(6.29150 - 3.06871i) q^{98} +(4.00000 + 7.48331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 8 q^{16} - 8 q^{21} + 16 q^{23} - 8 q^{32} + 16 q^{35} - 24 q^{39} + 8 q^{42} - 16 q^{46} - 8 q^{49} - 16 q^{51} + 16 q^{53} - 40 q^{57} + 8 q^{63} + 8 q^{64} - 8 q^{65} - 16 q^{70} - 16 q^{77} + 24 q^{78} - 16 q^{79} + 40 q^{81} - 8 q^{84} + 32 q^{85} + 16 q^{91} + 16 q^{92} - 32 q^{93} + 24 q^{95} + 8 q^{98} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.68014 + 0.420861i −0.970030 + 0.242984i
\(4\) 1.00000 0.500000
\(5\) −1.08495 1.95522i −0.485206 0.874400i
\(6\) 1.68014 0.420861i 0.685915 0.171816i
\(7\) 0.595188 + 2.57794i 0.224960 + 0.974368i
\(8\) −1.00000 −0.353553
\(9\) 2.64575 1.41421i 0.881917 0.471405i
\(10\) 1.08495 + 1.95522i 0.343092 + 0.618294i
\(11\) 2.82843i 0.852803i 0.904534 + 0.426401i \(0.140219\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) −1.68014 + 0.420861i −0.485015 + 0.121492i
\(13\) 3.36028 0.931975 0.465987 0.884791i \(-0.345699\pi\)
0.465987 + 0.884791i \(0.345699\pi\)
\(14\) −0.595188 2.57794i −0.159071 0.688982i
\(15\) 2.64575 + 2.82843i 0.683130 + 0.730297i
\(16\) 1.00000 0.250000
\(17\) 4.75216i 1.15257i 0.817250 + 0.576284i \(0.195498\pi\)
−0.817250 + 0.576284i \(0.804502\pi\)
\(18\) −2.64575 + 1.41421i −0.623610 + 0.333333i
\(19\) 5.59388i 1.28332i 0.766987 + 0.641662i \(0.221755\pi\)
−0.766987 + 0.641662i \(0.778245\pi\)
\(20\) −1.08495 1.95522i −0.242603 0.437200i
\(21\) −2.08495 4.08080i −0.454974 0.890505i
\(22\) 2.82843i 0.603023i
\(23\) 7.29150 1.52038 0.760192 0.649699i \(-0.225105\pi\)
0.760192 + 0.649699i \(0.225105\pi\)
\(24\) 1.68014 0.420861i 0.342957 0.0859080i
\(25\) −2.64575 + 4.24264i −0.529150 + 0.848528i
\(26\) −3.36028 −0.659006
\(27\) −3.85005 + 3.48957i −0.740942 + 0.671569i
\(28\) 0.595188 + 2.57794i 0.112480 + 0.487184i
\(29\) 0.500983i 0.0930303i −0.998918 0.0465151i \(-0.985188\pi\)
0.998918 0.0465151i \(-0.0148116\pi\)
\(30\) −2.64575 2.82843i −0.483046 0.516398i
\(31\) 3.06871i 0.551157i −0.961279 0.275578i \(-0.911131\pi\)
0.961279 0.275578i \(-0.0888694\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.19038 4.75216i −0.207218 0.827245i
\(34\) 4.75216i 0.814988i
\(35\) 4.39467 3.96066i 0.742835 0.669474i
\(36\) 2.64575 1.41421i 0.440959 0.235702i
\(37\) 3.32941i 0.547352i −0.961822 0.273676i \(-0.911760\pi\)
0.961822 0.273676i \(-0.0882396\pi\)
\(38\) 5.59388i 0.907447i
\(39\) −5.64575 + 1.41421i −0.904044 + 0.226455i
\(40\) 1.08495 + 1.95522i 0.171546 + 0.309147i
\(41\) 4.33981 0.677765 0.338883 0.940829i \(-0.389951\pi\)
0.338883 + 0.940829i \(0.389951\pi\)
\(42\) 2.08495 + 4.08080i 0.321715 + 0.629682i
\(43\) 10.3117i 1.57253i −0.617892 0.786263i \(-0.712013\pi\)
0.617892 0.786263i \(-0.287987\pi\)
\(44\) 2.82843i 0.426401i
\(45\) −5.63561 3.63866i −0.840108 0.542420i
\(46\) −7.29150 −1.07507
\(47\) 7.82087i 1.14079i 0.821370 + 0.570396i \(0.193210\pi\)
−0.821370 + 0.570396i \(0.806790\pi\)
\(48\) −1.68014 + 0.420861i −0.242508 + 0.0607461i
\(49\) −6.29150 + 3.06871i −0.898786 + 0.438387i
\(50\) 2.64575 4.24264i 0.374166 0.600000i
\(51\) −2.00000 7.98430i −0.280056 1.11803i
\(52\) 3.36028 0.465987
\(53\) −8.58301 −1.17897 −0.589483 0.807781i \(-0.700669\pi\)
−0.589483 + 0.807781i \(0.700669\pi\)
\(54\) 3.85005 3.48957i 0.523925 0.474871i
\(55\) 5.53019 3.06871i 0.745691 0.413785i
\(56\) −0.595188 2.57794i −0.0795353 0.344491i
\(57\) −2.35425 9.39851i −0.311828 1.24486i
\(58\) 0.500983i 0.0657823i
\(59\) −2.16991 −0.282498 −0.141249 0.989974i \(-0.545112\pi\)
−0.141249 + 0.989974i \(0.545112\pi\)
\(60\) 2.64575 + 2.82843i 0.341565 + 0.365148i
\(61\) 2.52517i 0.323315i −0.986847 0.161657i \(-0.948316\pi\)
0.986847 0.161657i \(-0.0516839\pi\)
\(62\) 3.06871i 0.389727i
\(63\) 5.22047 + 5.97885i 0.657717 + 0.753265i
\(64\) 1.00000 0.125000
\(65\) −3.64575 6.57008i −0.452200 0.814919i
\(66\) 1.19038 + 4.75216i 0.146525 + 0.584950i
\(67\) 10.3117i 1.25978i 0.776684 + 0.629890i \(0.216900\pi\)
−0.776684 + 0.629890i \(0.783100\pi\)
\(68\) 4.75216i 0.576284i
\(69\) −12.2508 + 3.06871i −1.47482 + 0.369430i
\(70\) −4.39467 + 3.96066i −0.525264 + 0.473390i
\(71\) 9.81076i 1.16432i 0.813073 + 0.582161i \(0.197793\pi\)
−0.813073 + 0.582161i \(0.802207\pi\)
\(72\) −2.64575 + 1.41421i −0.311805 + 0.166667i
\(73\) 5.53019 0.647260 0.323630 0.946184i \(-0.395097\pi\)
0.323630 + 0.946184i \(0.395097\pi\)
\(74\) 3.32941i 0.387036i
\(75\) 2.65967 8.24173i 0.307113 0.951673i
\(76\) 5.59388i 0.641662i
\(77\) −7.29150 + 1.68345i −0.830944 + 0.191846i
\(78\) 5.64575 1.41421i 0.639255 0.160128i
\(79\) 3.29150 0.370323 0.185161 0.982708i \(-0.440719\pi\)
0.185161 + 0.982708i \(0.440719\pi\)
\(80\) −1.08495 1.95522i −0.121302 0.218600i
\(81\) 5.00000 7.48331i 0.555556 0.831479i
\(82\) −4.33981 −0.479252
\(83\) 6.97915i 0.766061i −0.923736 0.383030i \(-0.874880\pi\)
0.923736 0.383030i \(-0.125120\pi\)
\(84\) −2.08495 4.08080i −0.227487 0.445252i
\(85\) 9.29150 5.15587i 1.00780 0.559233i
\(86\) 10.3117i 1.11194i
\(87\) 0.210845 + 0.841723i 0.0226049 + 0.0902422i
\(88\) 2.82843i 0.301511i
\(89\) 15.8219 1.67712 0.838558 0.544812i \(-0.183399\pi\)
0.838558 + 0.544812i \(0.183399\pi\)
\(90\) 5.63561 + 3.63866i 0.594046 + 0.383549i
\(91\) 2.00000 + 8.66259i 0.209657 + 0.908086i
\(92\) 7.29150 0.760192
\(93\) 1.29150 + 5.15587i 0.133923 + 0.534639i
\(94\) 7.82087i 0.806661i
\(95\) 10.9373 6.06910i 1.12214 0.622677i
\(96\) 1.68014 0.420861i 0.171479 0.0429540i
\(97\) −14.6315 −1.48560 −0.742802 0.669511i \(-0.766504\pi\)
−0.742802 + 0.669511i \(0.766504\pi\)
\(98\) 6.29150 3.06871i 0.635538 0.309987i
\(99\) 4.00000 + 7.48331i 0.402015 + 0.752101i
\(100\) −2.64575 + 4.24264i −0.264575 + 0.424264i
\(101\) 2.16991 0.215914 0.107957 0.994156i \(-0.465569\pi\)
0.107957 + 0.994156i \(0.465569\pi\)
\(102\) 2.00000 + 7.98430i 0.198030 + 0.790563i
\(103\) −3.14944 −0.310323 −0.155162 0.987889i \(-0.549590\pi\)
−0.155162 + 0.987889i \(0.549590\pi\)
\(104\) −3.36028 −0.329503
\(105\) −5.71678 + 8.50402i −0.557901 + 0.829908i
\(106\) 8.58301 0.833655
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −3.85005 + 3.48957i −0.370471 + 0.335784i
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) −5.53019 + 3.06871i −0.527283 + 0.292590i
\(111\) 1.40122 + 5.59388i 0.132998 + 0.530948i
\(112\) 0.595188 + 2.57794i 0.0562400 + 0.243592i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 2.35425 + 9.39851i 0.220496 + 0.880251i
\(115\) −7.91094 14.2565i −0.737699 1.32942i
\(116\) 0.500983i 0.0465151i
\(117\) 8.89047 4.75216i 0.821925 0.439337i
\(118\) 2.16991 0.199756
\(119\) −12.2508 + 2.82843i −1.12303 + 0.259281i
\(120\) −2.64575 2.82843i −0.241523 0.258199i
\(121\) 3.00000 0.272727
\(122\) 2.52517i 0.228618i
\(123\) −7.29150 + 1.82646i −0.657453 + 0.164686i
\(124\) 3.06871i 0.275578i
\(125\) 11.1658 + 0.569951i 0.998700 + 0.0509780i
\(126\) −5.22047 5.97885i −0.465076 0.532639i
\(127\) 3.32941i 0.295437i 0.989029 + 0.147719i \(0.0471930\pi\)
−0.989029 + 0.147719i \(0.952807\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.33981 + 17.3252i 0.382099 + 1.52540i
\(130\) 3.64575 + 6.57008i 0.319754 + 0.576235i
\(131\) −17.9918 −1.57195 −0.785975 0.618258i \(-0.787839\pi\)
−0.785975 + 0.618258i \(0.787839\pi\)
\(132\) −1.19038 4.75216i −0.103609 0.413622i
\(133\) −14.4207 + 3.32941i −1.25043 + 0.288696i
\(134\) 10.3117i 0.890799i
\(135\) 11.0000 + 3.74166i 0.946729 + 0.322031i
\(136\) 4.75216i 0.407494i
\(137\) 1.29150 0.110341 0.0551703 0.998477i \(-0.482430\pi\)
0.0551703 + 0.998477i \(0.482430\pi\)
\(138\) 12.2508 3.06871i 1.04285 0.261226i
\(139\) 0.543544i 0.0461028i 0.999734 + 0.0230514i \(0.00733813\pi\)
−0.999734 + 0.0230514i \(0.992662\pi\)
\(140\) 4.39467 3.96066i 0.371418 0.334737i
\(141\) −3.29150 13.1402i −0.277195 1.10660i
\(142\) 9.81076i 0.823301i
\(143\) 9.50432i 0.794791i
\(144\) 2.64575 1.41421i 0.220479 0.117851i
\(145\) −0.979531 + 0.543544i −0.0813457 + 0.0451388i
\(146\) −5.53019 −0.457682
\(147\) 9.27911 7.80372i 0.765328 0.643640i
\(148\) 3.32941i 0.273676i
\(149\) 10.8127i 0.885813i −0.896568 0.442906i \(-0.853947\pi\)
0.896568 0.442906i \(-0.146053\pi\)
\(150\) −2.65967 + 8.24173i −0.217161 + 0.672935i
\(151\) −1.41699 −0.115313 −0.0576567 0.998336i \(-0.518363\pi\)
−0.0576567 + 0.998336i \(0.518363\pi\)
\(152\) 5.59388i 0.453724i
\(153\) 6.72057 + 12.5730i 0.543326 + 1.01647i
\(154\) 7.29150 1.68345i 0.587566 0.135656i
\(155\) −6.00000 + 3.32941i −0.481932 + 0.267425i
\(156\) −5.64575 + 1.41421i −0.452022 + 0.113228i
\(157\) 16.3797 1.30724 0.653622 0.756821i \(-0.273249\pi\)
0.653622 + 0.756821i \(0.273249\pi\)
\(158\) −3.29150 −0.261858
\(159\) 14.4207 3.61226i 1.14363 0.286471i
\(160\) 1.08495 + 1.95522i 0.0857731 + 0.154574i
\(161\) 4.33981 + 18.7970i 0.342025 + 1.48141i
\(162\) −5.00000 + 7.48331i −0.392837 + 0.587945i
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 4.33981 0.338883
\(165\) −8.00000 + 7.48331i −0.622799 + 0.582575i
\(166\) 6.97915i 0.541687i
\(167\) 20.6921i 1.60120i −0.599198 0.800601i \(-0.704514\pi\)
0.599198 0.800601i \(-0.295486\pi\)
\(168\) 2.08495 + 4.08080i 0.160858 + 0.314841i
\(169\) −1.70850 −0.131423
\(170\) −9.29150 + 5.15587i −0.712626 + 0.395437i
\(171\) 7.91094 + 14.8000i 0.604965 + 1.13179i
\(172\) 10.3117i 0.786263i
\(173\) 2.22699i 0.169315i 0.996410 + 0.0846574i \(0.0269796\pi\)
−0.996410 + 0.0846574i \(0.973020\pi\)
\(174\) −0.210845 0.841723i −0.0159841 0.0638108i
\(175\) −12.5120 4.29541i −0.945816 0.324702i
\(176\) 2.82843i 0.213201i
\(177\) 3.64575 0.913230i 0.274031 0.0686426i
\(178\) −15.8219 −1.18590
\(179\) 24.4539i 1.82777i −0.405975 0.913884i \(-0.633068\pi\)
0.405975 0.913884i \(-0.366932\pi\)
\(180\) −5.63561 3.63866i −0.420054 0.271210i
\(181\) 14.8000i 1.10008i −0.835139 0.550038i \(-0.814613\pi\)
0.835139 0.550038i \(-0.185387\pi\)
\(182\) −2.00000 8.66259i −0.148250 0.642114i
\(183\) 1.06275 + 4.24264i 0.0785604 + 0.313625i
\(184\) −7.29150 −0.537537
\(185\) −6.50972 + 3.61226i −0.478604 + 0.265578i
\(186\) −1.29150 5.15587i −0.0946976 0.378047i
\(187\) −13.4411 −0.982913
\(188\) 7.82087i 0.570396i
\(189\) −11.2874 7.84823i −0.821037 0.570874i
\(190\) −10.9373 + 6.06910i −0.793472 + 0.440299i
\(191\) 0.500983i 0.0362499i −0.999836 0.0181249i \(-0.994230\pi\)
0.999836 0.0181249i \(-0.00576966\pi\)
\(192\) −1.68014 + 0.420861i −0.121254 + 0.0303731i
\(193\) 8.48528i 0.610784i −0.952227 0.305392i \(-0.901213\pi\)
0.952227 0.305392i \(-0.0987875\pi\)
\(194\) 14.6315 1.05048
\(195\) 8.89047 + 9.50432i 0.636660 + 0.680618i
\(196\) −6.29150 + 3.06871i −0.449393 + 0.219194i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) −4.00000 7.48331i −0.284268 0.531816i
\(199\) 9.20614i 0.652606i −0.945265 0.326303i \(-0.894197\pi\)
0.945265 0.326303i \(-0.105803\pi\)
\(200\) 2.64575 4.24264i 0.187083 0.300000i
\(201\) −4.33981 17.3252i −0.306107 1.22202i
\(202\) −2.16991 −0.152674
\(203\) 1.29150 0.298179i 0.0906457 0.0209281i
\(204\) −2.00000 7.98430i −0.140028 0.559013i
\(205\) −4.70850 8.48528i −0.328856 0.592638i
\(206\) 3.14944 0.219432
\(207\) 19.2915 10.3117i 1.34085 0.716716i
\(208\) 3.36028 0.232994
\(209\) −15.8219 −1.09442
\(210\) 5.71678 8.50402i 0.394496 0.586833i
\(211\) −21.1660 −1.45713 −0.728564 0.684978i \(-0.759812\pi\)
−0.728564 + 0.684978i \(0.759812\pi\)
\(212\) −8.58301 −0.589483
\(213\) −4.12897 16.4835i −0.282912 1.12943i
\(214\) 0 0
\(215\) −20.1617 + 11.1878i −1.37502 + 0.762999i
\(216\) 3.85005 3.48957i 0.261963 0.237435i
\(217\) 7.91094 1.82646i 0.537030 0.123988i
\(218\) −2.00000 −0.135457
\(219\) −9.29150 + 2.32744i −0.627862 + 0.157274i
\(220\) 5.53019 3.06871i 0.372845 0.206893i
\(221\) 15.9686i 1.07416i
\(222\) −1.40122 5.59388i −0.0940438 0.375437i
\(223\) 1.19038 0.0797135 0.0398567 0.999205i \(-0.487310\pi\)
0.0398567 + 0.999205i \(0.487310\pi\)
\(224\) −0.595188 2.57794i −0.0397677 0.172246i
\(225\) −1.00000 + 14.9666i −0.0666667 + 0.997775i
\(226\) 6.00000 0.399114
\(227\) 18.1669i 1.20578i −0.797824 0.602890i \(-0.794016\pi\)
0.797824 0.602890i \(-0.205984\pi\)
\(228\) −2.35425 9.39851i −0.155914 0.622432i
\(229\) 24.9007i 1.64548i 0.568415 + 0.822742i \(0.307557\pi\)
−0.568415 + 0.822742i \(0.692443\pi\)
\(230\) 7.91094 + 14.2565i 0.521632 + 0.940044i
\(231\) 11.5423 5.89714i 0.759425 0.388003i
\(232\) 0.500983i 0.0328912i
\(233\) 13.2915 0.870755 0.435378 0.900248i \(-0.356615\pi\)
0.435378 + 0.900248i \(0.356615\pi\)
\(234\) −8.89047 + 4.75216i −0.581188 + 0.310658i
\(235\) 15.2915 8.48528i 0.997508 0.553519i
\(236\) −2.16991 −0.141249
\(237\) −5.53019 + 1.38527i −0.359224 + 0.0899827i
\(238\) 12.2508 2.82843i 0.794099 0.183340i
\(239\) 14.6431i 0.947185i 0.880744 + 0.473592i \(0.157043\pi\)
−0.880744 + 0.473592i \(0.842957\pi\)
\(240\) 2.64575 + 2.82843i 0.170783 + 0.182574i
\(241\) 17.3252i 1.11601i −0.829836 0.558007i \(-0.811566\pi\)
0.829836 0.558007i \(-0.188434\pi\)
\(242\) −3.00000 −0.192847
\(243\) −5.25127 + 14.6773i −0.336869 + 0.941551i
\(244\) 2.52517i 0.161657i
\(245\) 12.8260 + 8.97185i 0.819422 + 0.573190i
\(246\) 7.29150 1.82646i 0.464889 0.116451i
\(247\) 18.7970i 1.19603i
\(248\) 3.06871i 0.194863i
\(249\) 2.93725 + 11.7260i 0.186141 + 0.743102i
\(250\) −11.1658 0.569951i −0.706187 0.0360469i
\(251\) 6.50972 0.410890 0.205445 0.978669i \(-0.434136\pi\)
0.205445 + 0.978669i \(0.434136\pi\)
\(252\) 5.22047 + 5.97885i 0.328859 + 0.376632i
\(253\) 20.6235i 1.29659i
\(254\) 3.32941i 0.208906i
\(255\) −13.4411 + 12.5730i −0.841716 + 0.787354i
\(256\) 1.00000 0.0625000
\(257\) 18.7105i 1.16713i −0.812068 0.583563i \(-0.801658\pi\)
0.812068 0.583563i \(-0.198342\pi\)
\(258\) −4.33981 17.3252i −0.270185 1.07862i
\(259\) 8.58301 1.98162i 0.533322 0.123132i
\(260\) −3.64575 6.57008i −0.226100 0.407459i
\(261\) −0.708497 1.32548i −0.0438549 0.0820450i
\(262\) 17.9918 1.11154
\(263\) 14.5830 0.899227 0.449613 0.893223i \(-0.351562\pi\)
0.449613 + 0.893223i \(0.351562\pi\)
\(264\) 1.19038 + 4.75216i 0.0732626 + 0.292475i
\(265\) 9.31216 + 16.7816i 0.572042 + 1.03089i
\(266\) 14.4207 3.32941i 0.884188 0.204139i
\(267\) −26.5830 + 6.65882i −1.62685 + 0.407513i
\(268\) 10.3117i 0.629890i
\(269\) 9.31216 0.567773 0.283886 0.958858i \(-0.408376\pi\)
0.283886 + 0.958858i \(0.408376\pi\)
\(270\) −11.0000 3.74166i −0.669439 0.227710i
\(271\) 20.3939i 1.23884i 0.785059 + 0.619421i \(0.212632\pi\)
−0.785059 + 0.619421i \(0.787368\pi\)
\(272\) 4.75216i 0.288142i
\(273\) −7.00603 13.7127i −0.424024 0.829928i
\(274\) −1.29150 −0.0780225
\(275\) −12.0000 7.48331i −0.723627 0.451261i
\(276\) −12.2508 + 3.06871i −0.737409 + 0.184715i
\(277\) 6.98233i 0.419528i −0.977752 0.209764i \(-0.932730\pi\)
0.977752 0.209764i \(-0.0672695\pi\)
\(278\) 0.543544i 0.0325996i
\(279\) −4.33981 8.11905i −0.259818 0.486075i
\(280\) −4.39467 + 3.96066i −0.262632 + 0.236695i
\(281\) 9.30978i 0.555375i −0.960672 0.277687i \(-0.910432\pi\)
0.960672 0.277687i \(-0.0895679\pi\)
\(282\) 3.29150 + 13.1402i 0.196006 + 0.782486i
\(283\) 32.2016 1.91419 0.957094 0.289779i \(-0.0935819\pi\)
0.957094 + 0.289779i \(0.0935819\pi\)
\(284\) 9.81076i 0.582161i
\(285\) −15.8219 + 14.8000i −0.937208 + 0.876677i
\(286\) 9.50432i 0.562002i
\(287\) 2.58301 + 11.1878i 0.152470 + 0.660393i
\(288\) −2.64575 + 1.41421i −0.155902 + 0.0833333i
\(289\) −5.58301 −0.328412
\(290\) 0.979531 0.543544i 0.0575201 0.0319180i
\(291\) 24.5830 6.15784i 1.44108 0.360979i
\(292\) 5.53019 0.323630
\(293\) 7.27733i 0.425146i 0.977145 + 0.212573i \(0.0681843\pi\)
−0.977145 + 0.212573i \(0.931816\pi\)
\(294\) −9.27911 + 7.80372i −0.541169 + 0.455122i
\(295\) 2.35425 + 4.24264i 0.137070 + 0.247016i
\(296\) 3.32941i 0.193518i
\(297\) −9.87000 10.8896i −0.572716 0.631878i
\(298\) 10.8127i 0.626364i
\(299\) 24.5015 1.41696
\(300\) 2.65967 8.24173i 0.153556 0.475837i
\(301\) 26.5830 6.13742i 1.53222 0.353755i
\(302\) 1.41699 0.0815389
\(303\) −3.64575 + 0.913230i −0.209443 + 0.0524637i
\(304\) 5.59388i 0.320831i
\(305\) −4.93725 + 2.73969i −0.282706 + 0.156874i
\(306\) −6.72057 12.5730i −0.384189 0.718752i
\(307\) 12.0399 0.687154 0.343577 0.939124i \(-0.388361\pi\)
0.343577 + 0.939124i \(0.388361\pi\)
\(308\) −7.29150 + 1.68345i −0.415472 + 0.0959232i
\(309\) 5.29150 1.32548i 0.301023 0.0754038i
\(310\) 6.00000 3.32941i 0.340777 0.189098i
\(311\) −24.5015 −1.38935 −0.694677 0.719322i \(-0.744453\pi\)
−0.694677 + 0.719322i \(0.744453\pi\)
\(312\) 5.64575 1.41421i 0.319628 0.0800641i
\(313\) −14.6315 −0.827022 −0.413511 0.910499i \(-0.635698\pi\)
−0.413511 + 0.910499i \(0.635698\pi\)
\(314\) −16.3797 −0.924361
\(315\) 6.02599 16.6939i 0.339526 0.940597i
\(316\) 3.29150 0.185161
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) −14.4207 + 3.61226i −0.808671 + 0.202565i
\(319\) 1.41699 0.0793365
\(320\) −1.08495 1.95522i −0.0606508 0.109300i
\(321\) 0 0
\(322\) −4.33981 18.7970i −0.241848 1.04752i
\(323\) −26.5830 −1.47912
\(324\) 5.00000 7.48331i 0.277778 0.415740i
\(325\) −8.89047 + 14.2565i −0.493155 + 0.790807i
\(326\) 0 0
\(327\) −3.36028 + 0.841723i −0.185824 + 0.0465474i
\(328\) −4.33981 −0.239626
\(329\) −20.1617 + 4.65489i −1.11155 + 0.256632i
\(330\) 8.00000 7.48331i 0.440386 0.411943i
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 6.97915i 0.383030i
\(333\) −4.70850 8.80879i −0.258024 0.482719i
\(334\) 20.6921i 1.13222i
\(335\) 20.1617 11.1878i 1.10155 0.611253i
\(336\) −2.08495 4.08080i −0.113744 0.222626i
\(337\) 22.4499i 1.22293i 0.791273 + 0.611463i \(0.209419\pi\)
−0.791273 + 0.611463i \(0.790581\pi\)
\(338\) 1.70850 0.0929300
\(339\) 10.0808 2.52517i 0.547517 0.137148i
\(340\) 9.29150 5.15587i 0.503902 0.279616i
\(341\) 8.67963 0.470028
\(342\) −7.91094 14.8000i −0.427775 0.800293i
\(343\) −11.6556 14.3926i −0.629342 0.777129i
\(344\) 10.3117i 0.555972i
\(345\) 19.2915 + 20.6235i 1.03862 + 1.11033i
\(346\) 2.22699i 0.119724i
\(347\) −24.0000 −1.28839 −0.644194 0.764862i \(-0.722807\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(348\) 0.210845 + 0.841723i 0.0113025 + 0.0451211i
\(349\) 13.7129i 0.734036i −0.930214 0.367018i \(-0.880379\pi\)
0.930214 0.367018i \(-0.119621\pi\)
\(350\) 12.5120 + 4.29541i 0.668793 + 0.229599i
\(351\) −12.9373 + 11.7260i −0.690540 + 0.625885i
\(352\) 2.82843i 0.150756i
\(353\) 9.80250i 0.521734i 0.965375 + 0.260867i \(0.0840084\pi\)
−0.965375 + 0.260867i \(0.915992\pi\)
\(354\) −3.64575 + 0.913230i −0.193769 + 0.0485376i
\(355\) 19.1822 10.6442i 1.01808 0.564936i
\(356\) 15.8219 0.838558
\(357\) 19.3926 9.90803i 1.02637 0.524388i
\(358\) 24.4539i 1.29243i
\(359\) 4.33138i 0.228601i 0.993446 + 0.114301i \(0.0364627\pi\)
−0.993446 + 0.114301i \(0.963537\pi\)
\(360\) 5.63561 + 3.63866i 0.297023 + 0.191774i
\(361\) −12.2915 −0.646921
\(362\) 14.8000i 0.777872i
\(363\) −5.04042 + 1.26258i −0.264554 + 0.0662685i
\(364\) 2.00000 + 8.66259i 0.104828 + 0.454043i
\(365\) −6.00000 10.8127i −0.314054 0.565964i
\(366\) −1.06275 4.24264i −0.0555506 0.221766i
\(367\) −14.6315 −0.763759 −0.381879 0.924212i \(-0.624723\pi\)
−0.381879 + 0.924212i \(0.624723\pi\)
\(368\) 7.29150 0.380096
\(369\) 11.4821 6.13742i 0.597733 0.319502i
\(370\) 6.50972 3.61226i 0.338424 0.187792i
\(371\) −5.10850 22.1264i −0.265220 1.14875i
\(372\) 1.29150 + 5.15587i 0.0669613 + 0.267319i
\(373\) 6.98233i 0.361531i 0.983526 + 0.180766i \(0.0578576\pi\)
−0.983526 + 0.180766i \(0.942142\pi\)
\(374\) 13.4411 0.695024
\(375\) −19.0000 + 3.74166i −0.981156 + 0.193218i
\(376\) 7.82087i 0.403331i
\(377\) 1.68345i 0.0867019i
\(378\) 11.2874 + 7.84823i 0.580561 + 0.403669i
\(379\) −6.58301 −0.338146 −0.169073 0.985604i \(-0.554077\pi\)
−0.169073 + 0.985604i \(0.554077\pi\)
\(380\) 10.9373 6.06910i 0.561069 0.311338i
\(381\) −1.40122 5.59388i −0.0717867 0.286583i
\(382\) 0.500983i 0.0256325i
\(383\) 20.6921i 1.05732i −0.848835 0.528658i \(-0.822695\pi\)
0.848835 0.528658i \(-0.177305\pi\)
\(384\) 1.68014 0.420861i 0.0857394 0.0214770i
\(385\) 11.2024 + 12.4300i 0.570929 + 0.633492i
\(386\) 8.48528i 0.431889i
\(387\) −14.5830 27.2823i −0.741296 1.38684i
\(388\) −14.6315 −0.742802
\(389\) 37.0931i 1.88069i 0.340218 + 0.940346i \(0.389499\pi\)
−0.340218 + 0.940346i \(0.610501\pi\)
\(390\) −8.89047 9.50432i −0.450187 0.481270i
\(391\) 34.6504i 1.75234i
\(392\) 6.29150 3.06871i 0.317769 0.154993i
\(393\) 30.2288 7.57205i 1.52484 0.381959i
\(394\) −18.0000 −0.906827
\(395\) −3.57113 6.43560i −0.179683 0.323810i
\(396\) 4.00000 + 7.48331i 0.201008 + 0.376051i
\(397\) 14.8424 0.744916 0.372458 0.928049i \(-0.378515\pi\)
0.372458 + 0.928049i \(0.378515\pi\)
\(398\) 9.20614i 0.461462i
\(399\) 22.8275 11.6630i 1.14281 0.583879i
\(400\) −2.64575 + 4.24264i −0.132288 + 0.212132i
\(401\) 7.48331i 0.373699i −0.982389 0.186849i \(-0.940172\pi\)
0.982389 0.186849i \(-0.0598277\pi\)
\(402\) 4.33981 + 17.3252i 0.216450 + 0.864102i
\(403\) 10.3117i 0.513664i
\(404\) 2.16991 0.107957
\(405\) −20.0563 1.65704i −0.996604 0.0823389i
\(406\) −1.29150 + 0.298179i −0.0640962 + 0.0147984i
\(407\) 9.41699 0.466783
\(408\) 2.00000 + 7.98430i 0.0990148 + 0.395282i
\(409\) 23.4626i 1.16015i −0.814563 0.580076i \(-0.803023\pi\)
0.814563 0.580076i \(-0.196977\pi\)
\(410\) 4.70850 + 8.48528i 0.232536 + 0.419058i
\(411\) −2.16991 + 0.543544i −0.107034 + 0.0268110i
\(412\) −3.14944 −0.155162
\(413\) −1.29150 5.59388i −0.0635507 0.275257i
\(414\) −19.2915 + 10.3117i −0.948126 + 0.506794i
\(415\) −13.6458 + 7.57205i −0.669844 + 0.371697i
\(416\) −3.36028 −0.164751
\(417\) −0.228757 0.913230i −0.0112023 0.0447211i
\(418\) 15.8219 0.773874
\(419\) −33.8137 −1.65191 −0.825953 0.563739i \(-0.809362\pi\)
−0.825953 + 0.563739i \(0.809362\pi\)
\(420\) −5.71678 + 8.50402i −0.278950 + 0.414954i
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 21.1660 1.03035
\(423\) 11.0604 + 20.6921i 0.537774 + 1.00608i
\(424\) 8.58301 0.416828
\(425\) −20.1617 12.5730i −0.977986 0.609881i
\(426\) 4.12897 + 16.4835i 0.200049 + 0.798626i
\(427\) 6.50972 1.50295i 0.315028 0.0727328i
\(428\) 0 0
\(429\) −4.00000 15.9686i −0.193122 0.770971i
\(430\) 20.1617 11.1878i 0.972283 0.539522i
\(431\) 8.98626i 0.432853i −0.976299 0.216427i \(-0.930560\pi\)
0.976299 0.216427i \(-0.0694402\pi\)
\(432\) −3.85005 + 3.48957i −0.185236 + 0.167892i
\(433\) 18.5496 0.891439 0.445719 0.895173i \(-0.352948\pi\)
0.445719 + 0.895173i \(0.352948\pi\)
\(434\) −7.91094 + 1.82646i −0.379737 + 0.0876729i
\(435\) 1.41699 1.32548i 0.0679397 0.0635518i
\(436\) 2.00000 0.0957826
\(437\) 40.7878i 1.95114i
\(438\) 9.29150 2.32744i 0.443965 0.111210i
\(439\) 26.5313i 1.26627i −0.774041 0.633135i \(-0.781768\pi\)
0.774041 0.633135i \(-0.218232\pi\)
\(440\) −5.53019 + 3.06871i −0.263641 + 0.146295i
\(441\) −12.3059 + 17.0166i −0.585997 + 0.810313i
\(442\) 15.9686i 0.759549i
\(443\) −29.1660 −1.38572 −0.692859 0.721073i \(-0.743649\pi\)
−0.692859 + 0.721073i \(0.743649\pi\)
\(444\) 1.40122 + 5.59388i 0.0664990 + 0.265474i
\(445\) −17.1660 30.9352i −0.813747 1.46647i
\(446\) −1.19038 −0.0563659
\(447\) 4.55066 + 18.1669i 0.215239 + 0.859265i
\(448\) 0.595188 + 2.57794i 0.0281200 + 0.121796i
\(449\) 36.5921i 1.72689i −0.504446 0.863444i \(-0.668303\pi\)
0.504446 0.863444i \(-0.331697\pi\)
\(450\) 1.00000 14.9666i 0.0471405 0.705534i
\(451\) 12.2748i 0.578000i
\(452\) −6.00000 −0.282216
\(453\) 2.38075 0.596358i 0.111857 0.0280194i
\(454\) 18.1669i 0.852615i
\(455\) 14.7673 13.3089i 0.692304 0.623933i
\(456\) 2.35425 + 9.39851i 0.110248 + 0.440126i
\(457\) 8.48528i 0.396925i 0.980109 + 0.198462i \(0.0635948\pi\)
−0.980109 + 0.198462i \(0.936405\pi\)
\(458\) 24.9007i 1.16353i
\(459\) −16.5830 18.2960i −0.774028 0.853986i
\(460\) −7.91094 14.2565i −0.368850 0.664712i
\(461\) 17.9918 0.837961 0.418981 0.907995i \(-0.362388\pi\)
0.418981 + 0.907995i \(0.362388\pi\)
\(462\) −11.5423 + 5.89714i −0.536994 + 0.274360i
\(463\) 1.50295i 0.0698480i 0.999390 + 0.0349240i \(0.0111189\pi\)
−0.999390 + 0.0349240i \(0.988881\pi\)
\(464\) 0.500983i 0.0232576i
\(465\) 8.67963 8.11905i 0.402508 0.376512i
\(466\) −13.2915 −0.615717
\(467\) 0.841723i 0.0389503i −0.999810 0.0194751i \(-0.993800\pi\)
0.999810 0.0194751i \(-0.00619952\pi\)
\(468\) 8.89047 4.75216i 0.410962 0.219669i
\(469\) −26.5830 + 6.13742i −1.22749 + 0.283400i
\(470\) −15.2915 + 8.48528i −0.705344 + 0.391397i
\(471\) −27.5203 + 6.89360i −1.26807 + 0.317640i
\(472\) 2.16991 0.0998781
\(473\) 29.1660 1.34105
\(474\) 5.53019 1.38527i 0.254010 0.0636274i
\(475\) −23.7328 14.8000i −1.08894 0.679071i
\(476\) −12.2508 + 2.82843i −0.561513 + 0.129641i
\(477\) −22.7085 + 12.1382i −1.03975 + 0.555770i
\(478\) 14.6431i 0.669761i
\(479\) 21.6991 0.991456 0.495728 0.868478i \(-0.334901\pi\)
0.495728 + 0.868478i \(0.334901\pi\)
\(480\) −2.64575 2.82843i −0.120761 0.129099i
\(481\) 11.1878i 0.510118i
\(482\) 17.3252i 0.789141i
\(483\) −15.2024 29.7552i −0.691735 1.35391i
\(484\) 3.00000 0.136364
\(485\) 15.8745 + 28.6078i 0.720824 + 1.29901i
\(486\) 5.25127 14.6773i 0.238202 0.665777i
\(487\) 9.98823i 0.452610i −0.974056 0.226305i \(-0.927335\pi\)
0.974056 0.226305i \(-0.0726646\pi\)
\(488\) 2.52517i 0.114309i
\(489\) 0 0
\(490\) −12.8260 8.97185i −0.579419 0.405307i
\(491\) 14.1421i 0.638226i −0.947717 0.319113i \(-0.896615\pi\)
0.947717 0.319113i \(-0.103385\pi\)
\(492\) −7.29150 + 1.82646i −0.328726 + 0.0823432i
\(493\) 2.38075 0.107224
\(494\) 18.7970i 0.845718i
\(495\) 10.2917 15.9399i 0.462577 0.716446i
\(496\) 3.06871i 0.137789i
\(497\) −25.2915 + 5.83925i −1.13448 + 0.261926i
\(498\) −2.93725 11.7260i −0.131621 0.525453i
\(499\) 22.5830 1.01095 0.505477 0.862840i \(-0.331317\pi\)
0.505477 + 0.862840i \(0.331317\pi\)
\(500\) 11.1658 + 0.569951i 0.499350 + 0.0254890i
\(501\) 8.70850 + 34.7656i 0.389067 + 1.55321i
\(502\) −6.50972 −0.290543
\(503\) 15.6417i 0.697431i −0.937229 0.348715i \(-0.886618\pi\)
0.937229 0.348715i \(-0.113382\pi\)
\(504\) −5.22047 5.97885i −0.232538 0.266319i
\(505\) −2.35425 4.24264i −0.104763 0.188795i
\(506\) 20.6235i 0.916826i
\(507\) 2.87052 0.719041i 0.127484 0.0319337i
\(508\) 3.32941i 0.147719i
\(509\) 39.6909 1.75927 0.879633 0.475652i \(-0.157788\pi\)
0.879633 + 0.475652i \(0.157788\pi\)
\(510\) 13.4411 12.5730i 0.595183 0.556743i
\(511\) 3.29150 + 14.2565i 0.145608 + 0.630669i
\(512\) −1.00000 −0.0441942
\(513\) −19.5203 21.5367i −0.861840 0.950869i
\(514\) 18.7105i 0.825283i
\(515\) 3.41699 + 6.15784i 0.150571 + 0.271347i
\(516\) 4.33981 + 17.3252i 0.191050 + 0.762699i
\(517\) −22.1208 −0.972870
\(518\) −8.58301 + 1.98162i −0.377116 + 0.0870676i
\(519\) −0.937254 3.74166i −0.0411409 0.164241i
\(520\) 3.64575 + 6.57008i 0.159877 + 0.288117i
\(521\) −13.0194 −0.570392 −0.285196 0.958469i \(-0.592059\pi\)
−0.285196 + 0.958469i \(0.592059\pi\)
\(522\) 0.708497 + 1.32548i 0.0310101 + 0.0580146i
\(523\) −16.8014 −0.734675 −0.367337 0.930088i \(-0.619731\pi\)
−0.367337 + 0.930088i \(0.619731\pi\)
\(524\) −17.9918 −0.785975
\(525\) 22.8297 + 1.95109i 0.996368 + 0.0851524i
\(526\) −14.5830 −0.635849
\(527\) 14.5830 0.635246
\(528\) −1.19038 4.75216i −0.0518045 0.206811i
\(529\) 30.1660 1.31157
\(530\) −9.31216 16.7816i −0.404494 0.728948i
\(531\) −5.74103 + 3.06871i −0.249140 + 0.133171i
\(532\) −14.4207 + 3.32941i −0.625215 + 0.144348i
\(533\) 14.5830 0.631660
\(534\) 26.5830 6.65882i 1.15036 0.288155i
\(535\) 0 0
\(536\) 10.3117i 0.445399i
\(537\) 10.2917 + 41.0860i 0.444119 + 1.77299i
\(538\) −9.31216 −0.401476
\(539\) −8.67963 17.7951i −0.373858 0.766487i
\(540\) 11.0000 + 3.74166i 0.473365 + 0.161015i
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 20.3939i 0.875993i
\(543\) 6.22876 + 24.8661i 0.267302 + 1.06711i
\(544\) 4.75216i 0.203747i
\(545\) −2.16991 3.91044i −0.0929486 0.167505i
\(546\) 7.00603 + 13.7127i 0.299831 + 0.586848i
\(547\) 16.9706i 0.725609i −0.931865 0.362804i \(-0.881819\pi\)
0.931865 0.362804i \(-0.118181\pi\)
\(548\) 1.29150 0.0551703
\(549\) −3.57113 6.68097i −0.152412 0.285137i
\(550\) 12.0000 + 7.48331i 0.511682 + 0.319090i
\(551\) 2.80244 0.119388
\(552\) 12.2508 3.06871i 0.521427 0.130613i
\(553\) 1.95906 + 8.48528i 0.0833078 + 0.360831i
\(554\) 6.98233i 0.296651i
\(555\) 9.41699 8.80879i 0.399729 0.373912i
\(556\) 0.543544i 0.0230514i
\(557\) −35.1660 −1.49003 −0.745016 0.667047i \(-0.767558\pi\)
−0.745016 + 0.667047i \(0.767558\pi\)
\(558\) 4.33981 + 8.11905i 0.183719 + 0.343707i
\(559\) 34.6504i 1.46555i
\(560\) 4.39467 3.96066i 0.185709 0.167369i
\(561\) 22.5830 5.65685i 0.953455 0.238833i
\(562\) 9.30978i 0.392709i
\(563\) 13.1166i 0.552798i −0.961043 0.276399i \(-0.910859\pi\)
0.961043 0.276399i \(-0.0891411\pi\)
\(564\) −3.29150 13.1402i −0.138597 0.553301i
\(565\) 6.50972 + 11.7313i 0.273866 + 0.493540i
\(566\) −32.2016 −1.35353
\(567\) 22.2674 + 8.43570i 0.935145 + 0.354266i
\(568\) 9.81076i 0.411650i
\(569\) 33.7637i 1.41545i 0.706490 + 0.707723i \(0.250278\pi\)
−0.706490 + 0.707723i \(0.749722\pi\)
\(570\) 15.8219 14.8000i 0.662706 0.619905i
\(571\) −13.4170 −0.561484 −0.280742 0.959783i \(-0.590580\pi\)
−0.280742 + 0.959783i \(0.590580\pi\)
\(572\) 9.50432i 0.397395i
\(573\) 0.210845 + 0.841723i 0.00880816 + 0.0351635i
\(574\) −2.58301 11.1878i −0.107813 0.466968i
\(575\) −19.2915 + 30.9352i −0.804511 + 1.29009i
\(576\) 2.64575 1.41421i 0.110240 0.0589256i
\(577\) −36.3306 −1.51246 −0.756231 0.654305i \(-0.772961\pi\)
−0.756231 + 0.654305i \(0.772961\pi\)
\(578\) 5.58301 0.232222
\(579\) 3.57113 + 14.2565i 0.148411 + 0.592479i
\(580\) −0.979531 + 0.543544i −0.0406728 + 0.0225694i
\(581\) 17.9918 4.15390i 0.746425 0.172333i
\(582\) −24.5830 + 6.15784i −1.01900 + 0.255251i
\(583\) 24.2764i 1.00543i
\(584\) −5.53019 −0.228841
\(585\) −18.9373 12.2269i −0.782959 0.505522i
\(586\) 7.27733i 0.300624i
\(587\) 37.7719i 1.55901i 0.626394 + 0.779507i \(0.284530\pi\)
−0.626394 + 0.779507i \(0.715470\pi\)
\(588\) 9.27911 7.80372i 0.382664 0.321820i
\(589\) 17.1660 0.707313
\(590\) −2.35425 4.24264i −0.0969229 0.174667i
\(591\) −30.2425 + 7.57551i −1.24401 + 0.311615i
\(592\) 3.32941i 0.136838i
\(593\) 6.43560i 0.264279i −0.991231 0.132139i \(-0.957815\pi\)
0.991231 0.132139i \(-0.0421846\pi\)
\(594\) 9.87000 + 10.8896i 0.404971 + 0.446805i
\(595\) 18.8217 + 20.8842i 0.771614 + 0.856168i
\(596\) 10.8127i 0.442906i
\(597\) 3.87451 + 15.4676i 0.158573 + 0.633047i
\(598\) −24.5015 −1.00194
\(599\) 4.15390i 0.169724i −0.996393 0.0848620i \(-0.972955\pi\)
0.996393 0.0848620i \(-0.0270449\pi\)
\(600\) −2.65967 + 8.24173i −0.108581 + 0.336467i
\(601\) 6.13742i 0.250351i −0.992135 0.125175i \(-0.960051\pi\)
0.992135 0.125175i \(-0.0399494\pi\)
\(602\) −26.5830 + 6.13742i −1.08344 + 0.250143i
\(603\) 14.5830 + 27.2823i 0.593866 + 1.11102i
\(604\) −1.41699 −0.0576567
\(605\) −3.25486 5.86565i −0.132329 0.238473i
\(606\) 3.64575 0.913230i 0.148099 0.0370974i
\(607\) −5.95188 −0.241579 −0.120790 0.992678i \(-0.538543\pi\)
−0.120790 + 0.992678i \(0.538543\pi\)
\(608\) 5.59388i 0.226862i
\(609\) −2.04442 + 1.04453i −0.0828439 + 0.0423264i
\(610\) 4.93725 2.73969i 0.199904 0.110927i
\(611\) 26.2803i 1.06319i
\(612\) 6.72057 + 12.5730i 0.271663 + 0.508235i
\(613\) 47.5823i 1.92183i 0.276843 + 0.960915i \(0.410712\pi\)
−0.276843 + 0.960915i \(0.589288\pi\)
\(614\) −12.0399 −0.485891
\(615\) 11.4821 + 12.2748i 0.463002 + 0.494970i
\(616\) 7.29150 1.68345i 0.293783 0.0678280i
\(617\) 47.1660 1.89883 0.949416 0.314021i \(-0.101676\pi\)
0.949416 + 0.314021i \(0.101676\pi\)
\(618\) −5.29150 + 1.32548i −0.212855 + 0.0533185i
\(619\) 40.2443i 1.61755i 0.588116 + 0.808777i \(0.299870\pi\)
−0.588116 + 0.808777i \(0.700130\pi\)
\(620\) −6.00000 + 3.32941i −0.240966 + 0.133712i
\(621\) −28.0726 + 25.4442i −1.12652 + 1.02104i
\(622\) 24.5015 0.982421
\(623\) 9.41699 + 40.7878i 0.377284 + 1.63413i
\(624\) −5.64575 + 1.41421i −0.226011 + 0.0566139i
\(625\) −11.0000 22.4499i −0.440000 0.897998i
\(626\) 14.6315 0.584793
\(627\) 26.5830 6.65882i 1.06162 0.265928i
\(628\) 16.3797 0.653622
\(629\) 15.8219 0.630860
\(630\) −6.02599 + 16.6939i −0.240081 + 0.665102i
\(631\) 32.4575 1.29211 0.646057 0.763290i \(-0.276417\pi\)
0.646057 + 0.763290i \(0.276417\pi\)
\(632\) −3.29150 −0.130929
\(633\) 35.5619 8.90796i 1.41346 0.354060i
\(634\) −6.00000 −0.238290
\(635\) 6.50972 3.61226i 0.258330 0.143348i
\(636\) 14.4207 3.61226i 0.571817 0.143235i
\(637\) −21.1412 + 10.3117i −0.837646 + 0.408566i
\(638\) −1.41699 −0.0560994
\(639\) 13.8745 + 25.9568i 0.548867 + 1.02684i
\(640\) 1.08495 + 1.95522i 0.0428866 + 0.0772868i
\(641\) 28.1068i 1.11015i −0.831800 0.555076i \(-0.812689\pi\)
0.831800 0.555076i \(-0.187311\pi\)
\(642\) 0 0
\(643\) −22.6786 −0.894357 −0.447178 0.894445i \(-0.647571\pi\)
−0.447178 + 0.894445i \(0.647571\pi\)
\(644\) 4.33981 + 18.7970i 0.171013 + 0.740706i
\(645\) 29.1660 27.2823i 1.14841 1.07424i
\(646\) 26.5830 1.04589
\(647\) 13.9583i 0.548757i 0.961622 + 0.274379i \(0.0884721\pi\)
−0.961622 + 0.274379i \(0.911528\pi\)
\(648\) −5.00000 + 7.48331i −0.196419 + 0.293972i
\(649\) 6.13742i 0.240915i
\(650\) 8.89047 14.2565i 0.348713 0.559185i
\(651\) −12.5228 + 6.39812i −0.490808 + 0.250762i
\(652\) 0 0
\(653\) −23.1660 −0.906556 −0.453278 0.891369i \(-0.649746\pi\)
−0.453278 + 0.891369i \(0.649746\pi\)
\(654\) 3.36028 0.841723i 0.131397 0.0329140i
\(655\) 19.5203 + 35.1779i 0.762720 + 1.37451i
\(656\) 4.33981 0.169441
\(657\) 14.6315 7.82087i 0.570830 0.305121i
\(658\) 20.1617 4.65489i 0.785985 0.181466i
\(659\) 27.1048i 1.05585i 0.849290 + 0.527927i \(0.177031\pi\)
−0.849290 + 0.527927i \(0.822969\pi\)
\(660\) −8.00000 + 7.48331i −0.311400 + 0.291288i
\(661\) 8.66259i 0.336936i −0.985707 0.168468i \(-0.946118\pi\)
0.985707 0.168468i \(-0.0538820\pi\)
\(662\) −8.00000 −0.310929
\(663\) −6.72057 26.8295i −0.261005 1.04197i
\(664\) 6.97915i 0.270843i
\(665\) 22.1555 + 24.5833i 0.859152 + 0.953299i
\(666\) 4.70850 + 8.80879i 0.182451 + 0.341334i
\(667\) 3.65292i 0.141442i
\(668\) 20.6921i 0.800601i
\(669\) −2.00000 + 0.500983i −0.0773245 + 0.0193691i
\(670\) −20.1617 + 11.1878i −0.778914 + 0.432221i
\(671\) 7.14226 0.275724
\(672\) 2.08495 + 4.08080i 0.0804288 + 0.157420i
\(673\) 23.6294i 0.910846i −0.890275 0.455423i \(-0.849488\pi\)
0.890275 0.455423i \(-0.150512\pi\)
\(674\) 22.4499i 0.864740i
\(675\) −4.61874 25.5669i −0.177775 0.984071i
\(676\) −1.70850 −0.0657114
\(677\) 6.19024i 0.237910i 0.992900 + 0.118955i \(0.0379545\pi\)
−0.992900 + 0.118955i \(0.962046\pi\)
\(678\) −10.0808 + 2.52517i −0.387153 + 0.0969785i
\(679\) −8.70850 37.7191i −0.334201 1.44753i
\(680\) −9.29150 + 5.15587i −0.356313 + 0.197719i
\(681\) 7.64575 + 30.5230i 0.292986 + 1.16964i
\(682\) −8.67963 −0.332360
\(683\) 26.5830 1.01717 0.508585 0.861012i \(-0.330169\pi\)
0.508585 + 0.861012i \(0.330169\pi\)
\(684\) 7.91094 + 14.8000i 0.302482 + 0.565893i
\(685\) −1.40122 2.52517i −0.0535379 0.0964817i
\(686\) 11.6556 + 14.3926i 0.445012 + 0.549513i
\(687\) −10.4797 41.8367i −0.399827 1.59617i
\(688\) 10.3117i 0.393131i
\(689\) −28.8413 −1.09877
\(690\) −19.2915 20.6235i −0.734415 0.785123i
\(691\) 11.7313i 0.446280i −0.974786 0.223140i \(-0.928369\pi\)
0.974786 0.223140i \(-0.0716307\pi\)
\(692\) 2.22699i 0.0846574i
\(693\) −16.9108 + 14.7657i −0.642386 + 0.560903i
\(694\) 24.0000 0.911028
\(695\) 1.06275 0.589720i 0.0403123 0.0223693i
\(696\) −0.210845 0.841723i −0.00799204 0.0319054i
\(697\) 20.6235i 0.781170i
\(698\) 13.7129i 0.519042i
\(699\) −22.3316 + 5.59388i −0.844659 + 0.211580i
\(700\) −12.5120 4.29541i −0.472908 0.162351i
\(701\) 21.1245i 0.797860i −0.916981 0.398930i \(-0.869382\pi\)
0.916981 0.398930i \(-0.130618\pi\)
\(702\) 12.9373 11.7260i 0.488285 0.442568i
\(703\) 18.6243 0.702430
\(704\) 2.82843i 0.106600i
\(705\) −22.1208 + 20.6921i −0.833116 + 0.779309i
\(706\) 9.80250i 0.368922i
\(707\) 1.29150 + 5.59388i 0.0485720 + 0.210380i
\(708\) 3.64575 0.913230i 0.137016 0.0343213i
\(709\) −0.583005 −0.0218952 −0.0109476 0.999940i \(-0.503485\pi\)
−0.0109476 + 0.999940i \(0.503485\pi\)
\(710\) −19.1822 + 10.6442i −0.719894 + 0.399470i
\(711\) 8.70850 4.65489i 0.326594 0.174572i
\(712\) −15.8219 −0.592950
\(713\) 22.3755i 0.837970i
\(714\) −19.3926 + 9.90803i −0.725751 + 0.370799i
\(715\) 18.5830 10.3117i 0.694965 0.385637i
\(716\) 24.4539i 0.913884i
\(717\) −6.16272 24.6025i −0.230151 0.918798i
\(718\) 4.33138i 0.161646i
\(719\) 2.80244 0.104513 0.0522567 0.998634i \(-0.483359\pi\)
0.0522567 + 0.998634i \(0.483359\pi\)
\(720\) −5.63561 3.63866i −0.210027 0.135605i
\(721\) −1.87451 8.11905i −0.0698103 0.302369i
\(722\) 12.2915 0.457442
\(723\) 7.29150 + 29.1088i 0.271174 + 1.08257i
\(724\) 14.8000i 0.550038i
\(725\) 2.12549 + 1.32548i 0.0789388 + 0.0492270i
\(726\) 5.04042 1.26258i 0.187068 0.0468589i
\(727\) 45.8536 1.70062 0.850308 0.526286i \(-0.176416\pi\)
0.850308 + 0.526286i \(0.176416\pi\)
\(728\) −2.00000 8.66259i −0.0741249 0.321057i
\(729\) 2.64575 26.8701i 0.0979908 0.995187i
\(730\) 6.00000 + 10.8127i 0.222070 + 0.400197i
\(731\) 49.0030 1.81244
\(732\) 1.06275 + 4.24264i 0.0392802 + 0.156813i
\(733\) −28.2835 −1.04467 −0.522337 0.852739i \(-0.674940\pi\)
−0.522337 + 0.852739i \(0.674940\pi\)
\(734\) 14.6315 0.540059
\(735\) −25.3254 9.67601i −0.934141 0.356905i
\(736\) −7.29150 −0.268768
\(737\) −29.1660 −1.07434
\(738\) −11.4821 + 6.13742i −0.422661 + 0.225922i
\(739\) −33.1660 −1.22003 −0.610016 0.792389i \(-0.708837\pi\)
−0.610016 + 0.792389i \(0.708837\pi\)
\(740\) −6.50972 + 3.61226i −0.239302 + 0.132789i
\(741\) −7.91094 31.5817i −0.290616 1.16018i
\(742\) 5.10850 + 22.1264i 0.187539 + 0.812287i
\(743\) −2.12549 −0.0779767 −0.0389884 0.999240i \(-0.512414\pi\)
−0.0389884 + 0.999240i \(0.512414\pi\)
\(744\) −1.29150 5.15587i −0.0473488 0.189023i
\(745\) −21.1412 + 11.7313i −0.774555 + 0.429802i
\(746\) 6.98233i 0.255641i
\(747\) −9.87000 18.4651i −0.361125 0.675602i
\(748\) −13.4411 −0.491456
\(749\) 0 0
\(750\) 19.0000 3.74166i 0.693782 0.136626i
\(751\) −21.1660 −0.772359 −0.386179 0.922424i \(-0.626205\pi\)
−0.386179 + 0.922424i \(0.626205\pi\)
\(752\) 7.82087i 0.285198i
\(753\) −10.9373 + 2.73969i −0.398576 + 0.0998399i
\(754\) 1.68345i 0.0613075i
\(755\) 1.53737 + 2.77053i 0.0559508 + 0.100830i
\(756\) −11.2874 7.84823i −0.410519 0.285437i
\(757\) 34.2646i 1.24537i −0.782473 0.622685i \(-0.786042\pi\)
0.782473 0.622685i \(-0.213958\pi\)
\(758\) 6.58301 0.239106
\(759\) −8.67963 34.6504i −0.315051 1.25773i
\(760\) −10.9373 + 6.06910i −0.396736 + 0.220149i
\(761\) −11.4821 −0.416225 −0.208112 0.978105i \(-0.566732\pi\)
−0.208112 + 0.978105i \(0.566732\pi\)
\(762\) 1.40122 + 5.59388i 0.0507609 + 0.202645i
\(763\) 1.19038 + 5.15587i 0.0430945 + 0.186655i
\(764\) 0.500983i 0.0181249i
\(765\) 17.2915 26.7813i 0.625176 0.968281i
\(766\) 20.6921i 0.747635i
\(767\) −7.29150 −0.263281
\(768\) −1.68014 + 0.420861i −0.0606269 + 0.0151865i
\(769\) 35.7375i 1.28873i 0.764720 + 0.644363i \(0.222877\pi\)
−0.764720 + 0.644363i \(0.777123\pi\)
\(770\) −11.2024 12.4300i −0.403708 0.447947i
\(771\) 7.87451 + 31.4362i 0.283593 + 1.13215i
\(772\) 8.48528i 0.305392i
\(773\) 41.9277i 1.50803i 0.656855 + 0.754017i \(0.271887\pi\)
−0.656855 + 0.754017i \(0.728113\pi\)
\(774\) 14.5830 + 27.2823i 0.524175 + 0.980642i
\(775\) 13.0194 + 8.11905i 0.467672 + 0.291645i
\(776\) 14.6315 0.525241
\(777\) −13.5867 + 6.94167i −0.487419 + 0.249031i
\(778\) 37.0931i 1.32985i
\(779\) 24.2764i 0.869792i
\(780\) 8.89047 + 9.50432i 0.318330 + 0.340309i
\(781\) −27.7490 −0.992938
\(782\) 34.6504i 1.23909i
\(783\) 1.74822 + 1.92881i 0.0624762 + 0.0689301i
\(784\) −6.29150 + 3.06871i −0.224697 + 0.109597i
\(785\) −17.7712 32.0259i −0.634283 1.14305i
\(786\) −30.2288 + 7.57205i −1.07822 + 0.270086i
\(787\) −28.2835 −1.00820 −0.504099 0.863646i \(-0.668175\pi\)
−0.504099 + 0.863646i \(0.668175\pi\)
\(788\) 18.0000 0.641223
\(789\) −24.5015 + 6.13742i −0.872277 + 0.218498i
\(790\) 3.57113 + 6.43560i 0.127055 + 0.228969i
\(791\) −3.57113 15.4676i −0.126975 0.549965i
\(792\) −4.00000 7.48331i −0.142134 0.265908i
\(793\) 8.48528i 0.301321i
\(794\) −14.8424 −0.526735
\(795\) −22.7085 24.2764i −0.805387 0.860995i
\(796\) 9.20614i 0.326303i
\(797\) 15.0982i 0.534806i −0.963585 0.267403i \(-0.913835\pi\)
0.963585 0.267403i \(-0.0861654\pi\)
\(798\) −22.8275 + 11.6630i −0.808086 + 0.412865i
\(799\) −37.1660 −1.31484
\(800\) 2.64575 4.24264i 0.0935414 0.150000i
\(801\) 41.8608 22.3755i 1.47908 0.790600i
\(802\) 7.48331i 0.264245i
\(803\) 15.6417i 0.551985i
\(804\) −4.33981 17.3252i −0.153053 0.611012i
\(805\) 32.0438 28.8792i 1.12939 1.01786i
\(806\) 10.3117i 0.363216i
\(807\) −15.6458 + 3.91913i −0.550757 + 0.137960i
\(808\) −2.16991 −0.0763371
\(809\) 11.1362i 0.391529i −0.980651 0.195765i \(-0.937281\pi\)
0.980651 0.195765i \(-0.0627188\pi\)
\(810\) 20.0563 + 1.65704i 0.704706 + 0.0582224i
\(811\) 24.0062i 0.842970i −0.906835 0.421485i \(-0.861509\pi\)
0.906835 0.421485i \(-0.138491\pi\)
\(812\) 1.29150 0.298179i 0.0453229 0.0104640i
\(813\) −8.58301 34.2646i −0.301019 1.20171i
\(814\) −9.41699 −0.330065
\(815\) 0 0
\(816\) −2.00000 7.98430i −0.0700140 0.279506i
\(817\) 57.6827 2.01806
\(818\) 23.4626i 0.820351i
\(819\) 17.5423 + 20.0906i 0.612976 + 0.702024i
\(820\) −4.70850 8.48528i −0.164428 0.296319i
\(821\) 31.4362i 1.09713i −0.836107 0.548566i \(-0.815174\pi\)
0.836107 0.548566i \(-0.184826\pi\)
\(822\) 2.16991 0.543544i 0.0756842 0.0189583i
\(823\) 11.8147i 0.411834i −0.978569 0.205917i \(-0.933982\pi\)
0.978569 0.205917i \(-0.0660177\pi\)
\(824\) 3.14944 0.109716
\(825\) 23.3111 + 7.52269i 0.811590 + 0.261906i
\(826\) 1.29150 + 5.59388i 0.0449371 + 0.194636i
\(827\) 36.0000 1.25184 0.625921 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 19.2915 10.3117i 0.670426 0.358358i
\(829\) 33.2123i 1.15351i 0.816917 + 0.576755i \(0.195681\pi\)
−0.816917 + 0.576755i \(0.804319\pi\)
\(830\) 13.6458 7.57205i 0.473651 0.262830i
\(831\) 2.93859 + 11.7313i 0.101939 + 0.406954i
\(832\) 3.36028 0.116497
\(833\) −14.5830 29.8982i −0.505271 1.03591i
\(834\) 0.228757 + 0.913230i 0.00792119 + 0.0316226i
\(835\) −40.4575 + 22.4499i −1.40009 + 0.776912i
\(836\) −15.8219 −0.547211
\(837\) 10.7085 + 11.8147i 0.370140 + 0.408375i
\(838\) 33.8137 1.16807
\(839\) 37.5210 1.29537 0.647684 0.761909i \(-0.275738\pi\)
0.647684 + 0.761909i \(0.275738\pi\)
\(840\) 5.71678 8.50402i 0.197248 0.293417i
\(841\) 28.7490 0.991345
\(842\) 10.0000 0.344623
\(843\) 3.91813 + 15.6417i 0.134947 + 0.538730i
\(844\) −21.1660 −0.728564
\(845\) 1.85364 + 3.34048i 0.0637672 + 0.114916i
\(846\) −11.0604 20.6921i −0.380264 0.711408i
\(847\) 1.78556 + 7.73381i 0.0613527 + 0.265737i
\(848\) −8.58301 −0.294742
\(849\) −54.1033 + 13.5524i −1.85682 + 0.465118i
\(850\) 20.1617 + 12.5730i 0.691541 + 0.431251i
\(851\) 24.2764i 0.832184i
\(852\) −4.12897 16.4835i −0.141456 0.564714i
\(853\) 23.5220 0.805377 0.402689 0.915337i \(-0.368076\pi\)
0.402689 + 0.915337i \(0.368076\pi\)
\(854\) −6.50972 + 1.50295i −0.222758 + 0.0514299i
\(855\) 20.3542 31.5249i 0.696101 1.07813i
\(856\) 0 0
\(857\) 46.1363i 1.57599i −0.615684 0.787993i \(-0.711120\pi\)
0.615684 0.787993i \(-0.288880\pi\)
\(858\) 4.00000 + 15.9686i 0.136558 + 0.545159i
\(859\) 22.9191i 0.781988i 0.920393 + 0.390994i \(0.127869\pi\)
−0.920393 + 0.390994i \(0.872131\pi\)
\(860\) −20.1617 + 11.1878i −0.687508 + 0.381500i
\(861\) −9.04831 17.7099i −0.308366 0.603553i
\(862\) 8.98626i 0.306073i
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 3.85005 3.48957i 0.130981 0.118718i
\(865\) 4.35425 2.41618i 0.148049 0.0821526i
\(866\) −18.5496 −0.630342
\(867\) 9.38024 2.34967i 0.318570 0.0797990i
\(868\) 7.91094 1.82646i 0.268515 0.0619941i
\(869\) 9.30978i 0.315812i
\(870\) −1.41699 + 1.32548i −0.0480406 + 0.0449379i
\(871\) 34.6504i 1.17408i
\(872\) −2.00000 −0.0677285
\(873\) −38.7113 + 20.6921i −1.31018 + 0.700321i
\(874\) 40.7878i 1.37967i
\(875\) 5.17645 + 29.1239i 0.174996 + 0.984569i
\(876\) −9.29150 + 2.32744i −0.313931 + 0.0786370i
\(877\) 23.9529i 0.808832i −0.914575 0.404416i \(-0.867475\pi\)
0.914575 0.404416i \(-0.132525\pi\)
\(878\) 26.5313i 0.895389i
\(879\) −3.06275 12.2269i −0.103304 0.412404i
\(880\) 5.53019 3.06871i 0.186423 0.103446i
\(881\) −15.8219 −0.533053 −0.266526 0.963828i \(-0.585876\pi\)
−0.266526 + 0.963828i \(0.585876\pi\)
\(882\) 12.3059 17.0166i 0.414362 0.572978i
\(883\) 30.9352i 1.04105i −0.853845 0.520527i \(-0.825736\pi\)
0.853845 0.520527i \(-0.174264\pi\)
\(884\) 15.9686i 0.537082i
\(885\) −5.74103 6.13742i −0.192983 0.206307i
\(886\) 29.1660 0.979851
\(887\) 2.27980i 0.0765483i −0.999267 0.0382742i \(-0.987814\pi\)
0.999267 0.0382742i \(-0.0121860\pi\)
\(888\) −1.40122 5.59388i −0.0470219 0.187718i
\(889\) −8.58301 + 1.98162i −0.287865 + 0.0664616i
\(890\) 17.1660 + 30.9352i 0.575406 + 1.03695i
\(891\) 21.1660 + 14.1421i 0.709088 + 0.473779i
\(892\) 1.19038 0.0398567
\(893\) −43.7490 −1.46400
\(894\) −4.55066 18.1669i −0.152197 0.607592i
\(895\) −47.8127 + 26.5313i −1.59820 + 0.886844i
\(896\) −0.595188 2.57794i −0.0198838 0.0861228i
\(897\) −41.1660 + 10.3117i −1.37449 + 0.344299i
\(898\) 36.5921i 1.22109i
\(899\) −1.53737 −0.0512743
\(900\) −1.00000 + 14.9666i −0.0333333 + 0.498888i
\(901\) 40.7878i 1.35884i
\(902\) 12.2748i 0.408708i
\(903\) −42.0802 + 21.4995i −1.40034 + 0.715459i
\(904\) 6.00000 0.199557
\(905\) −28.9373 + 16.0573i −0.961907 + 0.533764i
\(906\) −2.38075 + 0.596358i −0.0790952 + 0.0198127i
\(907\) 33.9411i 1.12700i 0.826117 + 0.563498i \(0.190545\pi\)
−0.826117 + 0.563498i \(0.809455\pi\)
\(908\) 18.1669i 0.602890i
\(909\) 5.74103 3.06871i 0.190418 0.101783i
\(910\) −14.7673 + 13.3089i −0.489533 + 0.441187i
\(911\) 18.2960i 0.606175i 0.952963 + 0.303087i \(0.0980174\pi\)
−0.952963 + 0.303087i \(0.901983\pi\)
\(912\) −2.35425 9.39851i −0.0779570 0.311216i
\(913\) 19.7400 0.653299
\(914\) 8.48528i 0.280668i
\(915\) 7.14226 6.68097i 0.236116 0.220866i
\(916\) 24.9007i 0.822742i
\(917\) −10.7085 46.3817i −0.353626 1.53166i
\(918\) 16.5830 + 18.2960i 0.547321 + 0.603859i
\(919\) 41.8745 1.38131 0.690656 0.723183i \(-0.257322\pi\)
0.690656 + 0.723183i \(0.257322\pi\)
\(920\) 7.91094 + 14.2565i 0.260816 + 0.470022i
\(921\) −20.2288 + 5.06713i −0.666560 + 0.166968i
\(922\) −17.9918 −0.592528
\(923\) 32.9669i 1.08512i
\(924\) 11.5423 5.89714i 0.379712 0.194002i
\(925\) 14.1255 + 8.80879i 0.464443 + 0.289631i
\(926\) 1.50295i 0.0493900i
\(927\) −8.33263 + 4.45398i −0.273680 + 0.146288i
\(928\) 0.500983i 0.0164456i
\(929\) −51.8055 −1.69968 −0.849841 0.527039i \(-0.823302\pi\)
−0.849841 + 0.527039i \(0.823302\pi\)
\(930\) −8.67963 + 8.11905i −0.284616 + 0.266234i
\(931\) −17.1660 35.1939i −0.562593 1.15343i
\(932\) 13.2915 0.435378
\(933\) 41.1660 10.3117i 1.34771 0.337591i
\(934\) 0.841723i 0.0275420i
\(935\) 14.5830 + 26.2803i 0.476915 + 0.859459i
\(936\) −8.89047 + 4.75216i −0.290594 + 0.155329i
\(937\) 5.53019 0.180663 0.0903317 0.995912i \(-0.471207\pi\)
0.0903317 + 0.995912i \(0.471207\pi\)
\(938\) 26.5830 6.13742i 0.867966 0.200394i
\(939\) 24.5830 6.15784i 0.802236 0.200953i
\(940\) 15.2915 8.48528i 0.498754 0.276759i
\(941\) 0.632534 0.0206200 0.0103100 0.999947i \(-0.496718\pi\)
0.0103100 + 0.999947i \(0.496718\pi\)
\(942\) 27.5203 6.89360i 0.896658 0.224605i
\(943\) 31.6438 1.03046
\(944\) −2.16991 −0.0706245
\(945\) −3.09868 + 30.5843i −0.100800 + 0.994907i
\(946\) −29.1660 −0.948269
\(947\) 24.0000 0.779895 0.389948 0.920837i \(-0.372493\pi\)
0.389948 + 0.920837i \(0.372493\pi\)
\(948\) −5.53019 + 1.38527i −0.179612 + 0.0449914i
\(949\) 18.5830 0.603230
\(950\) 23.7328 + 14.8000i 0.769995 + 0.480176i
\(951\) −10.0808 + 2.52517i −0.326894 + 0.0818842i
\(952\) 12.2508 2.82843i 0.397049 0.0916698i
\(953\) 3.87451 0.125508 0.0627538 0.998029i \(-0.480012\pi\)
0.0627538 + 0.998029i \(0.480012\pi\)
\(954\) 22.7085 12.1382i 0.735215 0.392989i
\(955\) −0.979531 + 0.543544i −0.0316969 + 0.0175887i
\(956\) 14.6431i 0.473592i
\(957\) −2.38075 + 0.596358i −0.0769588 + 0.0192775i
\(958\) −21.6991 −0.701065
\(959\) 0.768687 + 3.32941i 0.0248222 + 0.107512i
\(960\) 2.64575 + 2.82843i 0.0853913 + 0.0912871i
\(961\) 21.5830 0.696226
\(962\) 11.1878i 0.360708i
\(963\) 0 0
\(964\) 17.3252i 0.558007i
\(965\) −16.5906 + 9.20614i −0.534069 + 0.296356i
\(966\) 15.2024 + 29.7552i 0.489131 + 0.957358i
\(967\) 26.9588i 0.866936i 0.901169 + 0.433468i \(0.142710\pi\)
−0.901169 + 0.433468i \(0.857290\pi\)
\(968\) −3.00000 −0.0964237
\(969\) 44.6632 11.1878i 1.43479 0.359403i
\(970\) −15.8745 28.6078i −0.509700 0.918541i
\(971\) 9.31216 0.298842 0.149421 0.988774i \(-0.452259\pi\)
0.149421 + 0.988774i \(0.452259\pi\)
\(972\) −5.25127 + 14.6773i −0.168435 + 0.470776i
\(973\) −1.40122 + 0.323511i −0.0449211 + 0.0103713i
\(974\) 9.98823i 0.320044i
\(975\) 8.93725 27.6946i 0.286221 0.886935i
\(976\) 2.52517i 0.0808287i
\(977\) −20.1255 −0.643872 −0.321936 0.946762i \(-0.604334\pi\)
−0.321936 + 0.946762i \(0.604334\pi\)
\(978\) 0 0
\(979\) 44.7510i 1.43025i
\(980\) 12.8260 + 8.97185i 0.409711 + 0.286595i
\(981\) 5.29150 2.82843i 0.168945 0.0903047i
\(982\) 14.1421i 0.451294i
\(983\) 29.0037i 0.925074i −0.886600 0.462537i \(-0.846939\pi\)
0.886600 0.462537i \(-0.153061\pi\)
\(984\) 7.29150 1.82646i 0.232445 0.0582254i
\(985\) −19.5292 35.1939i −0.622251 1.12137i
\(986\) −2.38075 −0.0758186
\(987\) 31.9154 16.3062i 1.01588 0.519031i
\(988\) 18.7970i 0.598013i
\(989\) 75.1881i 2.39084i
\(990\) −10.2917 + 15.9399i −0.327092 + 0.506604i
\(991\) −11.2915 −0.358686 −0.179343 0.983787i \(-0.557397\pi\)
−0.179343 + 0.983787i \(0.557397\pi\)
\(992\) 3.06871i 0.0974317i
\(993\) −13.4411 + 3.36689i −0.426541 + 0.106845i
\(994\) 25.2915 5.83925i 0.802198 0.185210i
\(995\) −18.0000 + 9.98823i −0.570638 + 0.316648i
\(996\) 2.93725 + 11.7260i 0.0930705 + 0.371551i
\(997\) 26.3244 0.833703 0.416851 0.908975i \(-0.363134\pi\)
0.416851 + 0.908975i \(0.363134\pi\)
\(998\) −22.5830 −0.714853
\(999\) 11.6182 + 12.8184i 0.367584 + 0.405556i
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 210.2.d.a.209.2 yes 8
3.2 odd 2 210.2.d.b.209.1 yes 8
4.3 odd 2 1680.2.k.e.209.7 8
5.2 odd 4 1050.2.b.f.251.6 16
5.3 odd 4 1050.2.b.f.251.11 16
5.4 even 2 210.2.d.b.209.7 yes 8
7.6 odd 2 inner 210.2.d.a.209.7 yes 8
12.11 even 2 1680.2.k.f.209.8 8
15.2 even 4 1050.2.b.f.251.12 16
15.8 even 4 1050.2.b.f.251.5 16
15.14 odd 2 inner 210.2.d.a.209.8 yes 8
20.19 odd 2 1680.2.k.f.209.2 8
21.20 even 2 210.2.d.b.209.8 yes 8
28.27 even 2 1680.2.k.e.209.2 8
35.13 even 4 1050.2.b.f.251.14 16
35.27 even 4 1050.2.b.f.251.3 16
35.34 odd 2 210.2.d.b.209.2 yes 8
60.59 even 2 1680.2.k.e.209.1 8
84.83 odd 2 1680.2.k.f.209.1 8
105.62 odd 4 1050.2.b.f.251.13 16
105.83 odd 4 1050.2.b.f.251.4 16
105.104 even 2 inner 210.2.d.a.209.1 8
140.139 even 2 1680.2.k.f.209.7 8
420.419 odd 2 1680.2.k.e.209.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.d.a.209.1 8 105.104 even 2 inner
210.2.d.a.209.2 yes 8 1.1 even 1 trivial
210.2.d.a.209.7 yes 8 7.6 odd 2 inner
210.2.d.a.209.8 yes 8 15.14 odd 2 inner
210.2.d.b.209.1 yes 8 3.2 odd 2
210.2.d.b.209.2 yes 8 35.34 odd 2
210.2.d.b.209.7 yes 8 5.4 even 2
210.2.d.b.209.8 yes 8 21.20 even 2
1050.2.b.f.251.3 16 35.27 even 4
1050.2.b.f.251.4 16 105.83 odd 4
1050.2.b.f.251.5 16 15.8 even 4
1050.2.b.f.251.6 16 5.2 odd 4
1050.2.b.f.251.11 16 5.3 odd 4
1050.2.b.f.251.12 16 15.2 even 4
1050.2.b.f.251.13 16 105.62 odd 4
1050.2.b.f.251.14 16 35.13 even 4
1680.2.k.e.209.1 8 60.59 even 2
1680.2.k.e.209.2 8 28.27 even 2
1680.2.k.e.209.7 8 4.3 odd 2
1680.2.k.e.209.8 8 420.419 odd 2
1680.2.k.f.209.1 8 84.83 odd 2
1680.2.k.f.209.2 8 20.19 odd 2
1680.2.k.f.209.7 8 140.139 even 2
1680.2.k.f.209.8 8 12.11 even 2