Properties

Label 418.2.e.g.45.2
Level $418$
Weight $2$
Character 418.45
Analytic conductor $3.338$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [418,2,Mod(45,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.45");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 45.2
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 418.45
Dual form 418.2.e.g.353.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(1.22474 + 2.12132i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 + 2.12132i) q^{6} -2.44949 q^{7} -1.00000 q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(1.22474 + 2.12132i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 + 2.12132i) q^{6} -2.44949 q^{7} -1.00000 q^{8} +(-1.50000 + 2.59808i) q^{9} -1.00000 q^{11} -2.44949 q^{12} +(-1.94949 + 3.37662i) q^{13} +(-1.22474 - 2.12132i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.22474 + 3.85337i) q^{17} -3.00000 q^{18} +(4.17423 + 1.25529i) q^{19} +(-3.00000 - 5.19615i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(-0.449490 + 0.778539i) q^{23} +(-1.22474 - 2.12132i) q^{24} +(2.50000 - 4.33013i) q^{25} -3.89898 q^{26} +(1.22474 - 2.12132i) q^{28} +(0.949490 - 1.64456i) q^{29} +2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.22474 - 2.12132i) q^{33} +(-2.22474 + 3.85337i) q^{34} +(-1.50000 - 2.59808i) q^{36} +8.44949 q^{37} +(1.00000 + 4.24264i) q^{38} -9.55051 q^{39} +(3.77526 + 6.53893i) q^{41} +(3.00000 - 5.19615i) q^{42} +(-4.72474 - 8.18350i) q^{43} +(0.500000 - 0.866025i) q^{44} -0.898979 q^{46} +(3.27526 - 5.67291i) q^{47} +(1.22474 - 2.12132i) q^{48} -1.00000 q^{49} +5.00000 q^{50} +(-5.44949 + 9.43879i) q^{51} +(-1.94949 - 3.37662i) q^{52} +(3.89898 - 6.75323i) q^{53} +2.44949 q^{56} +(2.44949 + 10.3923i) q^{57} +1.89898 q^{58} +(-1.44949 - 2.51059i) q^{59} +(-3.94949 + 6.84072i) q^{61} +(1.00000 + 1.73205i) q^{62} +(3.67423 - 6.36396i) q^{63} +1.00000 q^{64} +(1.22474 - 2.12132i) q^{66} +(-4.77526 + 8.27098i) q^{67} -4.44949 q^{68} -2.20204 q^{69} +(-3.72474 - 6.45145i) q^{71} +(1.50000 - 2.59808i) q^{72} +(7.22474 + 12.5136i) q^{73} +(4.22474 + 7.31747i) q^{74} +12.2474 q^{75} +(-3.17423 + 2.98735i) q^{76} +2.44949 q^{77} +(-4.77526 - 8.27098i) q^{78} +(-2.22474 - 3.85337i) q^{79} +(4.50000 + 7.79423i) q^{81} +(-3.77526 + 6.53893i) q^{82} -5.44949 q^{83} +6.00000 q^{84} +(4.72474 - 8.18350i) q^{86} +4.65153 q^{87} +1.00000 q^{88} +(4.50000 - 7.79423i) q^{89} +(4.77526 - 8.27098i) q^{91} +(-0.449490 - 0.778539i) q^{92} +(2.44949 + 4.24264i) q^{93} +6.55051 q^{94} +2.44949 q^{96} +(-1.94949 - 3.37662i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 6 q^{9} - 4 q^{11} + 2 q^{13} - 2 q^{16} + 4 q^{17} - 12 q^{18} + 2 q^{19} - 12 q^{21} - 2 q^{22} + 8 q^{23} + 10 q^{25} + 4 q^{26} - 6 q^{29} + 8 q^{31} + 2 q^{32} - 4 q^{34} - 6 q^{36} + 24 q^{37} + 4 q^{38} - 48 q^{39} + 20 q^{41} + 12 q^{42} - 14 q^{43} + 2 q^{44} + 16 q^{46} + 18 q^{47} - 4 q^{49} + 20 q^{50} - 12 q^{51} + 2 q^{52} - 4 q^{53} - 12 q^{58} + 4 q^{59} - 6 q^{61} + 4 q^{62} + 4 q^{64} - 24 q^{67} - 8 q^{68} - 48 q^{69} - 10 q^{71} + 6 q^{72} + 24 q^{73} + 12 q^{74} + 2 q^{76} - 24 q^{78} - 4 q^{79} + 18 q^{81} - 20 q^{82} - 12 q^{83} + 24 q^{84} + 14 q^{86} + 48 q^{87} + 4 q^{88} + 18 q^{89} + 24 q^{91} + 8 q^{92} + 36 q^{94} + 2 q^{97} - 2 q^{98} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 1.22474 + 2.12132i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) −1.22474 + 2.12132i −0.500000 + 0.866025i
\(7\) −2.44949 −0.925820 −0.462910 0.886405i \(-0.653195\pi\)
−0.462910 + 0.886405i \(0.653195\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.50000 + 2.59808i −0.500000 + 0.866025i
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) −2.44949 −0.707107
\(13\) −1.94949 + 3.37662i −0.540691 + 0.936505i 0.458173 + 0.888863i \(0.348504\pi\)
−0.998864 + 0.0476417i \(0.984829\pi\)
\(14\) −1.22474 2.12132i −0.327327 0.566947i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.22474 + 3.85337i 0.539580 + 0.934580i 0.998927 + 0.0463227i \(0.0147502\pi\)
−0.459347 + 0.888257i \(0.651916\pi\)
\(18\) −3.00000 −0.707107
\(19\) 4.17423 + 1.25529i 0.957635 + 0.287984i
\(20\) 0 0
\(21\) −3.00000 5.19615i −0.654654 1.13389i
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) −0.449490 + 0.778539i −0.0937251 + 0.162337i −0.909076 0.416631i \(-0.863211\pi\)
0.815351 + 0.578967i \(0.196544\pi\)
\(24\) −1.22474 2.12132i −0.250000 0.433013i
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) −3.89898 −0.764653
\(27\) 0 0
\(28\) 1.22474 2.12132i 0.231455 0.400892i
\(29\) 0.949490 1.64456i 0.176316 0.305388i −0.764300 0.644861i \(-0.776915\pi\)
0.940616 + 0.339473i \(0.110249\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −1.22474 2.12132i −0.213201 0.369274i
\(34\) −2.22474 + 3.85337i −0.381541 + 0.660848i
\(35\) 0 0
\(36\) −1.50000 2.59808i −0.250000 0.433013i
\(37\) 8.44949 1.38909 0.694544 0.719450i \(-0.255606\pi\)
0.694544 + 0.719450i \(0.255606\pi\)
\(38\) 1.00000 + 4.24264i 0.162221 + 0.688247i
\(39\) −9.55051 −1.52931
\(40\) 0 0
\(41\) 3.77526 + 6.53893i 0.589596 + 1.02121i 0.994285 + 0.106756i \(0.0340463\pi\)
−0.404689 + 0.914454i \(0.632620\pi\)
\(42\) 3.00000 5.19615i 0.462910 0.801784i
\(43\) −4.72474 8.18350i −0.720517 1.24797i −0.960793 0.277267i \(-0.910571\pi\)
0.240276 0.970705i \(-0.422762\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) −0.898979 −0.132547
\(47\) 3.27526 5.67291i 0.477745 0.827479i −0.521930 0.852989i \(-0.674788\pi\)
0.999675 + 0.0255099i \(0.00812093\pi\)
\(48\) 1.22474 2.12132i 0.176777 0.306186i
\(49\) −1.00000 −0.142857
\(50\) 5.00000 0.707107
\(51\) −5.44949 + 9.43879i −0.763081 + 1.32170i
\(52\) −1.94949 3.37662i −0.270346 0.468252i
\(53\) 3.89898 6.75323i 0.535566 0.927628i −0.463570 0.886060i \(-0.653432\pi\)
0.999136 0.0415671i \(-0.0132350\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.44949 0.327327
\(57\) 2.44949 + 10.3923i 0.324443 + 1.37649i
\(58\) 1.89898 0.249348
\(59\) −1.44949 2.51059i −0.188707 0.326851i 0.756112 0.654442i \(-0.227096\pi\)
−0.944820 + 0.327591i \(0.893763\pi\)
\(60\) 0 0
\(61\) −3.94949 + 6.84072i −0.505680 + 0.875864i 0.494298 + 0.869292i \(0.335425\pi\)
−0.999978 + 0.00657156i \(0.997908\pi\)
\(62\) 1.00000 + 1.73205i 0.127000 + 0.219971i
\(63\) 3.67423 6.36396i 0.462910 0.801784i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.22474 2.12132i 0.150756 0.261116i
\(67\) −4.77526 + 8.27098i −0.583390 + 1.01046i 0.411684 + 0.911327i \(0.364941\pi\)
−0.995074 + 0.0991348i \(0.968392\pi\)
\(68\) −4.44949 −0.539580
\(69\) −2.20204 −0.265095
\(70\) 0 0
\(71\) −3.72474 6.45145i −0.442046 0.765646i 0.555795 0.831319i \(-0.312414\pi\)
−0.997841 + 0.0656732i \(0.979080\pi\)
\(72\) 1.50000 2.59808i 0.176777 0.306186i
\(73\) 7.22474 + 12.5136i 0.845592 + 1.46461i 0.885106 + 0.465390i \(0.154086\pi\)
−0.0395133 + 0.999219i \(0.512581\pi\)
\(74\) 4.22474 + 7.31747i 0.491117 + 0.850639i
\(75\) 12.2474 1.41421
\(76\) −3.17423 + 2.98735i −0.364110 + 0.342672i
\(77\) 2.44949 0.279145
\(78\) −4.77526 8.27098i −0.540691 0.936505i
\(79\) −2.22474 3.85337i −0.250303 0.433538i 0.713306 0.700853i \(-0.247197\pi\)
−0.963609 + 0.267315i \(0.913864\pi\)
\(80\) 0 0
\(81\) 4.50000 + 7.79423i 0.500000 + 0.866025i
\(82\) −3.77526 + 6.53893i −0.416907 + 0.722104i
\(83\) −5.44949 −0.598159 −0.299080 0.954228i \(-0.596680\pi\)
−0.299080 + 0.954228i \(0.596680\pi\)
\(84\) 6.00000 0.654654
\(85\) 0 0
\(86\) 4.72474 8.18350i 0.509482 0.882449i
\(87\) 4.65153 0.498696
\(88\) 1.00000 0.106600
\(89\) 4.50000 7.79423i 0.476999 0.826187i −0.522654 0.852545i \(-0.675058\pi\)
0.999653 + 0.0263586i \(0.00839118\pi\)
\(90\) 0 0
\(91\) 4.77526 8.27098i 0.500583 0.867035i
\(92\) −0.449490 0.778539i −0.0468625 0.0811683i
\(93\) 2.44949 + 4.24264i 0.254000 + 0.439941i
\(94\) 6.55051 0.675634
\(95\) 0 0
\(96\) 2.44949 0.250000
\(97\) −1.94949 3.37662i −0.197941 0.342843i 0.749920 0.661529i \(-0.230092\pi\)
−0.947861 + 0.318685i \(0.896759\pi\)
\(98\) −0.500000 0.866025i −0.0505076 0.0874818i
\(99\) 1.50000 2.59808i 0.150756 0.261116i
\(100\) 2.50000 + 4.33013i 0.250000 + 0.433013i
\(101\) −2.50000 + 4.33013i −0.248759 + 0.430864i −0.963182 0.268851i \(-0.913356\pi\)
0.714423 + 0.699715i \(0.246689\pi\)
\(102\) −10.8990 −1.07916
\(103\) −8.34847 −0.822599 −0.411300 0.911500i \(-0.634925\pi\)
−0.411300 + 0.911500i \(0.634925\pi\)
\(104\) 1.94949 3.37662i 0.191163 0.331104i
\(105\) 0 0
\(106\) 7.79796 0.757405
\(107\) 10.3485 1.00042 0.500212 0.865903i \(-0.333255\pi\)
0.500212 + 0.865903i \(0.333255\pi\)
\(108\) 0 0
\(109\) −7.94949 13.7689i −0.761423 1.31882i −0.942117 0.335284i \(-0.891168\pi\)
0.180694 0.983539i \(-0.442166\pi\)
\(110\) 0 0
\(111\) 10.3485 + 17.9241i 0.982233 + 1.70128i
\(112\) 1.22474 + 2.12132i 0.115728 + 0.200446i
\(113\) 15.6969 1.47664 0.738322 0.674449i \(-0.235619\pi\)
0.738322 + 0.674449i \(0.235619\pi\)
\(114\) −7.77526 + 7.31747i −0.728219 + 0.685344i
\(115\) 0 0
\(116\) 0.949490 + 1.64456i 0.0881579 + 0.152694i
\(117\) −5.84847 10.1298i −0.540691 0.936505i
\(118\) 1.44949 2.51059i 0.133436 0.231119i
\(119\) −5.44949 9.43879i −0.499554 0.865253i
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −7.89898 −0.715140
\(123\) −9.24745 + 16.0171i −0.833814 + 1.44421i
\(124\) −1.00000 + 1.73205i −0.0898027 + 0.155543i
\(125\) 0 0
\(126\) 7.34847 0.654654
\(127\) −6.34847 + 10.9959i −0.563336 + 0.975726i 0.433867 + 0.900977i \(0.357149\pi\)
−0.997202 + 0.0747488i \(0.976185\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 11.5732 20.0454i 1.01896 1.76490i
\(130\) 0 0
\(131\) −2.17423 3.76588i −0.189964 0.329027i 0.755274 0.655409i \(-0.227504\pi\)
−0.945238 + 0.326382i \(0.894170\pi\)
\(132\) 2.44949 0.213201
\(133\) −10.2247 3.07483i −0.886598 0.266622i
\(134\) −9.55051 −0.825038
\(135\) 0 0
\(136\) −2.22474 3.85337i −0.190770 0.330424i
\(137\) 3.94949 6.84072i 0.337428 0.584442i −0.646520 0.762897i \(-0.723776\pi\)
0.983948 + 0.178455i \(0.0571098\pi\)
\(138\) −1.10102 1.90702i −0.0937251 0.162337i
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 0 0
\(141\) 16.0454 1.35127
\(142\) 3.72474 6.45145i 0.312574 0.541393i
\(143\) 1.94949 3.37662i 0.163025 0.282367i
\(144\) 3.00000 0.250000
\(145\) 0 0
\(146\) −7.22474 + 12.5136i −0.597924 + 1.03563i
\(147\) −1.22474 2.12132i −0.101015 0.174964i
\(148\) −4.22474 + 7.31747i −0.347272 + 0.601493i
\(149\) −9.34847 16.1920i −0.765856 1.32650i −0.939793 0.341745i \(-0.888982\pi\)
0.173936 0.984757i \(-0.444351\pi\)
\(150\) 6.12372 + 10.6066i 0.500000 + 0.866025i
\(151\) −8.44949 −0.687610 −0.343805 0.939041i \(-0.611716\pi\)
−0.343805 + 0.939041i \(0.611716\pi\)
\(152\) −4.17423 1.25529i −0.338575 0.101818i
\(153\) −13.3485 −1.07916
\(154\) 1.22474 + 2.12132i 0.0986928 + 0.170941i
\(155\) 0 0
\(156\) 4.77526 8.27098i 0.382326 0.662209i
\(157\) 3.00000 + 5.19615i 0.239426 + 0.414698i 0.960550 0.278108i \(-0.0897074\pi\)
−0.721124 + 0.692806i \(0.756374\pi\)
\(158\) 2.22474 3.85337i 0.176991 0.306558i
\(159\) 19.1010 1.51481
\(160\) 0 0
\(161\) 1.10102 1.90702i 0.0867726 0.150295i
\(162\) −4.50000 + 7.79423i −0.353553 + 0.612372i
\(163\) 2.89898 0.227066 0.113533 0.993534i \(-0.463783\pi\)
0.113533 + 0.993534i \(0.463783\pi\)
\(164\) −7.55051 −0.589596
\(165\) 0 0
\(166\) −2.72474 4.71940i −0.211481 0.366296i
\(167\) 6.57321 11.3851i 0.508651 0.881009i −0.491299 0.870991i \(-0.663478\pi\)
0.999950 0.0100178i \(-0.00318882\pi\)
\(168\) 3.00000 + 5.19615i 0.231455 + 0.400892i
\(169\) −1.10102 1.90702i −0.0846939 0.146694i
\(170\) 0 0
\(171\) −9.52270 + 8.96204i −0.728219 + 0.685344i
\(172\) 9.44949 0.720517
\(173\) −4.89898 8.48528i −0.372463 0.645124i 0.617481 0.786586i \(-0.288153\pi\)
−0.989944 + 0.141462i \(0.954820\pi\)
\(174\) 2.32577 + 4.02834i 0.176316 + 0.305388i
\(175\) −6.12372 + 10.6066i −0.462910 + 0.801784i
\(176\) 0.500000 + 0.866025i 0.0376889 + 0.0652791i
\(177\) 3.55051 6.14966i 0.266873 0.462237i
\(178\) 9.00000 0.674579
\(179\) −9.79796 −0.732334 −0.366167 0.930549i \(-0.619330\pi\)
−0.366167 + 0.930549i \(0.619330\pi\)
\(180\) 0 0
\(181\) −2.12372 + 3.67840i −0.157855 + 0.273413i −0.934095 0.357025i \(-0.883791\pi\)
0.776240 + 0.630438i \(0.217125\pi\)
\(182\) 9.55051 0.707931
\(183\) −19.3485 −1.43028
\(184\) 0.449490 0.778539i 0.0331368 0.0573947i
\(185\) 0 0
\(186\) −2.44949 + 4.24264i −0.179605 + 0.311086i
\(187\) −2.22474 3.85337i −0.162689 0.281786i
\(188\) 3.27526 + 5.67291i 0.238873 + 0.413739i
\(189\) 0 0
\(190\) 0 0
\(191\) −7.65153 −0.553645 −0.276823 0.960921i \(-0.589281\pi\)
−0.276823 + 0.960921i \(0.589281\pi\)
\(192\) 1.22474 + 2.12132i 0.0883883 + 0.153093i
\(193\) 11.6742 + 20.2204i 0.840330 + 1.45549i 0.889616 + 0.456709i \(0.150972\pi\)
−0.0492862 + 0.998785i \(0.515695\pi\)
\(194\) 1.94949 3.37662i 0.139965 0.242427i
\(195\) 0 0
\(196\) 0.500000 0.866025i 0.0357143 0.0618590i
\(197\) 6.10102 0.434680 0.217340 0.976096i \(-0.430262\pi\)
0.217340 + 0.976096i \(0.430262\pi\)
\(198\) 3.00000 0.213201
\(199\) −10.1742 + 17.6223i −0.721232 + 1.24921i 0.239274 + 0.970952i \(0.423091\pi\)
−0.960506 + 0.278259i \(0.910243\pi\)
\(200\) −2.50000 + 4.33013i −0.176777 + 0.306186i
\(201\) −23.3939 −1.65008
\(202\) −5.00000 −0.351799
\(203\) −2.32577 + 4.02834i −0.163237 + 0.282734i
\(204\) −5.44949 9.43879i −0.381541 0.660848i
\(205\) 0 0
\(206\) −4.17423 7.22999i −0.290833 0.503737i
\(207\) −1.34847 2.33562i −0.0937251 0.162337i
\(208\) 3.89898 0.270346
\(209\) −4.17423 1.25529i −0.288738 0.0868306i
\(210\) 0 0
\(211\) −10.0000 17.3205i −0.688428 1.19239i −0.972346 0.233544i \(-0.924968\pi\)
0.283918 0.958849i \(-0.408366\pi\)
\(212\) 3.89898 + 6.75323i 0.267783 + 0.463814i
\(213\) 9.12372 15.8028i 0.625147 1.08279i
\(214\) 5.17423 + 8.96204i 0.353703 + 0.612632i
\(215\) 0 0
\(216\) 0 0
\(217\) −4.89898 −0.332564
\(218\) 7.94949 13.7689i 0.538407 0.932549i
\(219\) −17.6969 + 30.6520i −1.19585 + 2.07127i
\(220\) 0 0
\(221\) −17.3485 −1.16698
\(222\) −10.3485 + 17.9241i −0.694544 + 1.20299i
\(223\) −0.623724 1.08032i −0.0417677 0.0723437i 0.844386 0.535736i \(-0.179966\pi\)
−0.886154 + 0.463392i \(0.846632\pi\)
\(224\) −1.22474 + 2.12132i −0.0818317 + 0.141737i
\(225\) 7.50000 + 12.9904i 0.500000 + 0.866025i
\(226\) 7.84847 + 13.5939i 0.522072 + 0.904256i
\(227\) 4.20204 0.278899 0.139450 0.990229i \(-0.455467\pi\)
0.139450 + 0.990229i \(0.455467\pi\)
\(228\) −10.2247 3.07483i −0.677150 0.203636i
\(229\) −0.651531 −0.0430544 −0.0215272 0.999768i \(-0.506853\pi\)
−0.0215272 + 0.999768i \(0.506853\pi\)
\(230\) 0 0
\(231\) 3.00000 + 5.19615i 0.197386 + 0.341882i
\(232\) −0.949490 + 1.64456i −0.0623371 + 0.107971i
\(233\) 5.22474 + 9.04952i 0.342284 + 0.592854i 0.984857 0.173371i \(-0.0554660\pi\)
−0.642572 + 0.766225i \(0.722133\pi\)
\(234\) 5.84847 10.1298i 0.382326 0.662209i
\(235\) 0 0
\(236\) 2.89898 0.188707
\(237\) 5.44949 9.43879i 0.353982 0.613115i
\(238\) 5.44949 9.43879i 0.353238 0.611826i
\(239\) 21.7980 1.40999 0.704996 0.709211i \(-0.250949\pi\)
0.704996 + 0.709211i \(0.250949\pi\)
\(240\) 0 0
\(241\) −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i \(-0.937715\pi\)
0.658838 + 0.752285i \(0.271048\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) −11.0227 + 19.0919i −0.707107 + 1.22474i
\(244\) −3.94949 6.84072i −0.252840 0.437932i
\(245\) 0 0
\(246\) −18.4949 −1.17919
\(247\) −12.3763 + 11.6476i −0.787484 + 0.741119i
\(248\) −2.00000 −0.127000
\(249\) −6.67423 11.5601i −0.422962 0.732592i
\(250\) 0 0
\(251\) −12.1237 + 20.9989i −0.765243 + 1.32544i 0.174875 + 0.984591i \(0.444048\pi\)
−0.940118 + 0.340849i \(0.889286\pi\)
\(252\) 3.67423 + 6.36396i 0.231455 + 0.400892i
\(253\) 0.449490 0.778539i 0.0282592 0.0489463i
\(254\) −12.6969 −0.796677
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 11.0000 19.0526i 0.686161 1.18847i −0.286909 0.957958i \(-0.592628\pi\)
0.973070 0.230508i \(-0.0740389\pi\)
\(258\) 23.1464 1.44103
\(259\) −20.6969 −1.28605
\(260\) 0 0
\(261\) 2.84847 + 4.93369i 0.176316 + 0.305388i
\(262\) 2.17423 3.76588i 0.134325 0.232657i
\(263\) −0.898979 1.55708i −0.0554334 0.0960136i 0.836977 0.547238i \(-0.184321\pi\)
−0.892411 + 0.451224i \(0.850987\pi\)
\(264\) 1.22474 + 2.12132i 0.0753778 + 0.130558i
\(265\) 0 0
\(266\) −2.44949 10.3923i −0.150188 0.637193i
\(267\) 22.0454 1.34916
\(268\) −4.77526 8.27098i −0.291695 0.505231i
\(269\) −10.2247 17.7098i −0.623414 1.07978i −0.988845 0.148946i \(-0.952412\pi\)
0.365432 0.930838i \(-0.380921\pi\)
\(270\) 0 0
\(271\) −12.3485 21.3882i −0.750116 1.29924i −0.947766 0.318966i \(-0.896664\pi\)
0.197650 0.980273i \(-0.436669\pi\)
\(272\) 2.22474 3.85337i 0.134895 0.233645i
\(273\) 23.3939 1.41586
\(274\) 7.89898 0.477195
\(275\) −2.50000 + 4.33013i −0.150756 + 0.261116i
\(276\) 1.10102 1.90702i 0.0662736 0.114789i
\(277\) −31.4949 −1.89234 −0.946172 0.323663i \(-0.895086\pi\)
−0.946172 + 0.323663i \(0.895086\pi\)
\(278\) 4.00000 0.239904
\(279\) −3.00000 + 5.19615i −0.179605 + 0.311086i
\(280\) 0 0
\(281\) 8.57321 14.8492i 0.511435 0.885832i −0.488477 0.872577i \(-0.662447\pi\)
0.999912 0.0132548i \(-0.00421926\pi\)
\(282\) 8.02270 + 13.8957i 0.477745 + 0.827479i
\(283\) −1.55051 2.68556i −0.0921683 0.159640i 0.816255 0.577692i \(-0.196046\pi\)
−0.908423 + 0.418052i \(0.862713\pi\)
\(284\) 7.44949 0.442046
\(285\) 0 0
\(286\) 3.89898 0.230551
\(287\) −9.24745 16.0171i −0.545860 0.945457i
\(288\) 1.50000 + 2.59808i 0.0883883 + 0.153093i
\(289\) −1.39898 + 2.42310i −0.0822929 + 0.142536i
\(290\) 0 0
\(291\) 4.77526 8.27098i 0.279930 0.484854i
\(292\) −14.4495 −0.845592
\(293\) −7.89898 −0.461463 −0.230732 0.973017i \(-0.574112\pi\)
−0.230732 + 0.973017i \(0.574112\pi\)
\(294\) 1.22474 2.12132i 0.0714286 0.123718i
\(295\) 0 0
\(296\) −8.44949 −0.491117
\(297\) 0 0
\(298\) 9.34847 16.1920i 0.541542 0.937979i
\(299\) −1.75255 3.03551i −0.101353 0.175548i
\(300\) −6.12372 + 10.6066i −0.353553 + 0.612372i
\(301\) 11.5732 + 20.0454i 0.667069 + 1.15540i
\(302\) −4.22474 7.31747i −0.243107 0.421073i
\(303\) −12.2474 −0.703598
\(304\) −1.00000 4.24264i −0.0573539 0.243332i
\(305\) 0 0
\(306\) −6.67423 11.5601i −0.381541 0.660848i
\(307\) 9.62372 + 16.6688i 0.549255 + 0.951337i 0.998326 + 0.0578413i \(0.0184218\pi\)
−0.449071 + 0.893496i \(0.648245\pi\)
\(308\) −1.22474 + 2.12132i −0.0697863 + 0.120873i
\(309\) −10.2247 17.7098i −0.581665 1.00747i
\(310\) 0 0
\(311\) 7.24745 0.410965 0.205483 0.978661i \(-0.434124\pi\)
0.205483 + 0.978661i \(0.434124\pi\)
\(312\) 9.55051 0.540691
\(313\) 9.84847 17.0580i 0.556668 0.964178i −0.441103 0.897456i \(-0.645413\pi\)
0.997772 0.0667216i \(-0.0212539\pi\)
\(314\) −3.00000 + 5.19615i −0.169300 + 0.293236i
\(315\) 0 0
\(316\) 4.44949 0.250303
\(317\) 12.0227 20.8239i 0.675262 1.16959i −0.301130 0.953583i \(-0.597364\pi\)
0.976392 0.216005i \(-0.0693029\pi\)
\(318\) 9.55051 + 16.5420i 0.535566 + 0.927628i
\(319\) −0.949490 + 1.64456i −0.0531612 + 0.0920779i
\(320\) 0 0
\(321\) 12.6742 + 21.9524i 0.707407 + 1.22526i
\(322\) 2.20204 0.122715
\(323\) 4.44949 + 18.8776i 0.247576 + 1.05038i
\(324\) −9.00000 −0.500000
\(325\) 9.74745 + 16.8831i 0.540691 + 0.936505i
\(326\) 1.44949 + 2.51059i 0.0802798 + 0.139049i
\(327\) 19.4722 33.7268i 1.07681 1.86510i
\(328\) −3.77526 6.53893i −0.208454 0.361052i
\(329\) −8.02270 + 13.8957i −0.442306 + 0.766096i
\(330\) 0 0
\(331\) 5.34847 0.293978 0.146989 0.989138i \(-0.453042\pi\)
0.146989 + 0.989138i \(0.453042\pi\)
\(332\) 2.72474 4.71940i 0.149540 0.259011i
\(333\) −12.6742 + 21.9524i −0.694544 + 1.20299i
\(334\) 13.1464 0.719341
\(335\) 0 0
\(336\) −3.00000 + 5.19615i −0.163663 + 0.283473i
\(337\) −6.10102 10.5673i −0.332344 0.575636i 0.650627 0.759397i \(-0.274506\pi\)
−0.982971 + 0.183761i \(0.941173\pi\)
\(338\) 1.10102 1.90702i 0.0598876 0.103728i
\(339\) 19.2247 + 33.2982i 1.04414 + 1.80851i
\(340\) 0 0
\(341\) −2.00000 −0.108306
\(342\) −12.5227 3.76588i −0.677150 0.203636i
\(343\) 19.5959 1.05808
\(344\) 4.72474 + 8.18350i 0.254741 + 0.441225i
\(345\) 0 0
\(346\) 4.89898 8.48528i 0.263371 0.456172i
\(347\) 3.72474 + 6.45145i 0.199955 + 0.346332i 0.948514 0.316737i \(-0.102587\pi\)
−0.748559 + 0.663068i \(0.769254\pi\)
\(348\) −2.32577 + 4.02834i −0.124674 + 0.215942i
\(349\) 31.0000 1.65939 0.829696 0.558216i \(-0.188514\pi\)
0.829696 + 0.558216i \(0.188514\pi\)
\(350\) −12.2474 −0.654654
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 27.4949 1.46341 0.731703 0.681624i \(-0.238726\pi\)
0.731703 + 0.681624i \(0.238726\pi\)
\(354\) 7.10102 0.377415
\(355\) 0 0
\(356\) 4.50000 + 7.79423i 0.238500 + 0.413093i
\(357\) 13.3485 23.1202i 0.706476 1.22365i
\(358\) −4.89898 8.48528i −0.258919 0.448461i
\(359\) −12.3485 21.3882i −0.651727 1.12882i −0.982704 0.185186i \(-0.940711\pi\)
0.330976 0.943639i \(-0.392622\pi\)
\(360\) 0 0
\(361\) 15.8485 + 10.4798i 0.834130 + 0.551568i
\(362\) −4.24745 −0.223241
\(363\) 1.22474 + 2.12132i 0.0642824 + 0.111340i
\(364\) 4.77526 + 8.27098i 0.250291 + 0.433517i
\(365\) 0 0
\(366\) −9.67423 16.7563i −0.505680 0.875864i
\(367\) 12.7247 22.0399i 0.664226 1.15047i −0.315268 0.949003i \(-0.602094\pi\)
0.979494 0.201471i \(-0.0645722\pi\)
\(368\) 0.898979 0.0468625
\(369\) −22.6515 −1.17919
\(370\) 0 0
\(371\) −9.55051 + 16.5420i −0.495838 + 0.858816i
\(372\) −4.89898 −0.254000
\(373\) −17.7980 −0.921543 −0.460772 0.887519i \(-0.652427\pi\)
−0.460772 + 0.887519i \(0.652427\pi\)
\(374\) 2.22474 3.85337i 0.115039 0.199253i
\(375\) 0 0
\(376\) −3.27526 + 5.67291i −0.168908 + 0.292558i
\(377\) 3.70204 + 6.41212i 0.190665 + 0.330241i
\(378\) 0 0
\(379\) −3.34847 −0.171999 −0.0859997 0.996295i \(-0.527408\pi\)
−0.0859997 + 0.996295i \(0.527408\pi\)
\(380\) 0 0
\(381\) −31.1010 −1.59335
\(382\) −3.82577 6.62642i −0.195743 0.339037i
\(383\) 13.3485 + 23.1202i 0.682075 + 1.18139i 0.974347 + 0.225053i \(0.0722555\pi\)
−0.292272 + 0.956335i \(0.594411\pi\)
\(384\) −1.22474 + 2.12132i −0.0625000 + 0.108253i
\(385\) 0 0
\(386\) −11.6742 + 20.2204i −0.594203 + 1.02919i
\(387\) 28.3485 1.44103
\(388\) 3.89898 0.197941
\(389\) 4.12372 7.14250i 0.209081 0.362139i −0.742344 0.670019i \(-0.766286\pi\)
0.951425 + 0.307880i \(0.0996194\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 1.00000 0.0505076
\(393\) 5.32577 9.22450i 0.268649 0.465314i
\(394\) 3.05051 + 5.28364i 0.153682 + 0.266186i
\(395\) 0 0
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) 12.6742 + 21.9524i 0.636102 + 1.10176i 0.986281 + 0.165077i \(0.0527874\pi\)
−0.350179 + 0.936683i \(0.613879\pi\)
\(398\) −20.3485 −1.01998
\(399\) −6.00000 25.4558i −0.300376 1.27439i
\(400\) −5.00000 −0.250000
\(401\) −19.3485 33.5125i −0.966216 1.67354i −0.706311 0.707902i \(-0.749642\pi\)
−0.259906 0.965634i \(-0.583692\pi\)
\(402\) −11.6969 20.2597i −0.583390 1.01046i
\(403\) −3.89898 + 6.75323i −0.194222 + 0.336402i
\(404\) −2.50000 4.33013i −0.124380 0.215432i
\(405\) 0 0
\(406\) −4.65153 −0.230852
\(407\) −8.44949 −0.418826
\(408\) 5.44949 9.43879i 0.269790 0.467290i
\(409\) 11.4722 19.8704i 0.567263 0.982529i −0.429572 0.903033i \(-0.641335\pi\)
0.996835 0.0794964i \(-0.0253312\pi\)
\(410\) 0 0
\(411\) 19.3485 0.954390
\(412\) 4.17423 7.22999i 0.205650 0.356196i
\(413\) 3.55051 + 6.14966i 0.174709 + 0.302605i
\(414\) 1.34847 2.33562i 0.0662736 0.114789i
\(415\) 0 0
\(416\) 1.94949 + 3.37662i 0.0955816 + 0.165552i
\(417\) 9.79796 0.479808
\(418\) −1.00000 4.24264i −0.0489116 0.207514i
\(419\) −17.3485 −0.847528 −0.423764 0.905773i \(-0.639291\pi\)
−0.423764 + 0.905773i \(0.639291\pi\)
\(420\) 0 0
\(421\) 17.6742 + 30.6127i 0.861389 + 1.49197i 0.870588 + 0.492013i \(0.163739\pi\)
−0.00919855 + 0.999958i \(0.502928\pi\)
\(422\) 10.0000 17.3205i 0.486792 0.843149i
\(423\) 9.82577 + 17.0187i 0.477745 + 0.827479i
\(424\) −3.89898 + 6.75323i −0.189351 + 0.327966i
\(425\) 22.2474 1.07916
\(426\) 18.2474 0.884092
\(427\) 9.67423 16.7563i 0.468169 0.810893i
\(428\) −5.17423 + 8.96204i −0.250106 + 0.433196i
\(429\) 9.55051 0.461103
\(430\) 0 0
\(431\) −8.02270 + 13.8957i −0.386440 + 0.669334i −0.991968 0.126490i \(-0.959629\pi\)
0.605528 + 0.795824i \(0.292962\pi\)
\(432\) 0 0
\(433\) −15.8485 + 27.4504i −0.761629 + 1.31918i 0.180382 + 0.983597i \(0.442267\pi\)
−0.942011 + 0.335583i \(0.891067\pi\)
\(434\) −2.44949 4.24264i −0.117579 0.203653i
\(435\) 0 0
\(436\) 15.8990 0.761423
\(437\) −2.85357 + 2.68556i −0.136505 + 0.128468i
\(438\) −35.3939 −1.69118
\(439\) −5.79796 10.0424i −0.276721 0.479296i 0.693847 0.720123i \(-0.255915\pi\)
−0.970568 + 0.240827i \(0.922581\pi\)
\(440\) 0 0
\(441\) 1.50000 2.59808i 0.0714286 0.123718i
\(442\) −8.67423 15.0242i −0.412591 0.714629i
\(443\) 10.6742 18.4883i 0.507148 0.878406i −0.492818 0.870133i \(-0.664033\pi\)
0.999966 0.00827378i \(-0.00263366\pi\)
\(444\) −20.6969 −0.982233
\(445\) 0 0
\(446\) 0.623724 1.08032i 0.0295342 0.0511547i
\(447\) 22.8990 39.6622i 1.08308 1.87596i
\(448\) −2.44949 −0.115728
\(449\) 10.2020 0.481464 0.240732 0.970592i \(-0.422612\pi\)
0.240732 + 0.970592i \(0.422612\pi\)
\(450\) −7.50000 + 12.9904i −0.353553 + 0.612372i
\(451\) −3.77526 6.53893i −0.177770 0.307906i
\(452\) −7.84847 + 13.5939i −0.369161 + 0.639406i
\(453\) −10.3485 17.9241i −0.486213 0.842146i
\(454\) 2.10102 + 3.63907i 0.0986058 + 0.170790i
\(455\) 0 0
\(456\) −2.44949 10.3923i −0.114708 0.486664i
\(457\) −22.9444 −1.07329 −0.536647 0.843807i \(-0.680309\pi\)
−0.536647 + 0.843807i \(0.680309\pi\)
\(458\) −0.325765 0.564242i −0.0152220 0.0263653i
\(459\) 0 0
\(460\) 0 0
\(461\) 6.39898 + 11.0834i 0.298030 + 0.516203i 0.975685 0.219177i \(-0.0703371\pi\)
−0.677655 + 0.735380i \(0.737004\pi\)
\(462\) −3.00000 + 5.19615i −0.139573 + 0.241747i
\(463\) 40.1464 1.86576 0.932881 0.360184i \(-0.117286\pi\)
0.932881 + 0.360184i \(0.117286\pi\)
\(464\) −1.89898 −0.0881579
\(465\) 0 0
\(466\) −5.22474 + 9.04952i −0.242032 + 0.419211i
\(467\) −6.65153 −0.307796 −0.153898 0.988087i \(-0.549183\pi\)
−0.153898 + 0.988087i \(0.549183\pi\)
\(468\) 11.6969 0.540691
\(469\) 11.6969 20.2597i 0.540114 0.935506i
\(470\) 0 0
\(471\) −7.34847 + 12.7279i −0.338600 + 0.586472i
\(472\) 1.44949 + 2.51059i 0.0667182 + 0.115559i
\(473\) 4.72474 + 8.18350i 0.217244 + 0.376278i
\(474\) 10.8990 0.500607
\(475\) 15.8712 14.9367i 0.728219 0.685344i
\(476\) 10.8990 0.499554
\(477\) 11.6969 + 20.2597i 0.535566 + 0.927628i
\(478\) 10.8990 + 18.8776i 0.498508 + 0.863441i
\(479\) 21.5732 37.3659i 0.985705 1.70729i 0.346946 0.937885i \(-0.387219\pi\)
0.638759 0.769407i \(-0.279448\pi\)
\(480\) 0 0
\(481\) −16.4722 + 28.5307i −0.751067 + 1.30089i
\(482\) −10.0000 −0.455488
\(483\) 5.39388 0.245430
\(484\) −0.500000 + 0.866025i −0.0227273 + 0.0393648i
\(485\) 0 0
\(486\) −22.0454 −1.00000
\(487\) −7.65153 −0.346724 −0.173362 0.984858i \(-0.555463\pi\)
−0.173362 + 0.984858i \(0.555463\pi\)
\(488\) 3.94949 6.84072i 0.178785 0.309665i
\(489\) 3.55051 + 6.14966i 0.160560 + 0.278097i
\(490\) 0 0
\(491\) 6.89898 + 11.9494i 0.311347 + 0.539268i 0.978654 0.205514i \(-0.0658867\pi\)
−0.667308 + 0.744782i \(0.732553\pi\)
\(492\) −9.24745 16.0171i −0.416907 0.722104i
\(493\) 8.44949 0.380546
\(494\) −16.2753 4.89437i −0.732258 0.220208i
\(495\) 0 0
\(496\) −1.00000 1.73205i −0.0449013 0.0777714i
\(497\) 9.12372 + 15.8028i 0.409255 + 0.708850i
\(498\) 6.67423 11.5601i 0.299080 0.518021i
\(499\) 0.348469 + 0.603566i 0.0155996 + 0.0270193i 0.873720 0.486429i \(-0.161701\pi\)
−0.858120 + 0.513449i \(0.828368\pi\)
\(500\) 0 0
\(501\) 32.2020 1.43868
\(502\) −24.2474 −1.08222
\(503\) 5.44949 9.43879i 0.242981 0.420855i −0.718581 0.695443i \(-0.755208\pi\)
0.961562 + 0.274588i \(0.0885415\pi\)
\(504\) −3.67423 + 6.36396i −0.163663 + 0.283473i
\(505\) 0 0
\(506\) 0.898979 0.0399645
\(507\) 2.69694 4.67123i 0.119775 0.207457i
\(508\) −6.34847 10.9959i −0.281668 0.487863i
\(509\) −11.7980 + 20.4347i −0.522935 + 0.905751i 0.476708 + 0.879061i \(0.341830\pi\)
−0.999644 + 0.0266891i \(0.991504\pi\)
\(510\) 0 0
\(511\) −17.6969 30.6520i −0.782866 1.35596i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 22.0000 0.970378
\(515\) 0 0
\(516\) 11.5732 + 20.0454i 0.509482 + 0.882449i
\(517\) −3.27526 + 5.67291i −0.144046 + 0.249494i
\(518\) −10.3485 17.9241i −0.454686 0.787539i
\(519\) 12.0000 20.7846i 0.526742 0.912343i
\(520\) 0 0
\(521\) −41.6969 −1.82678 −0.913388 0.407090i \(-0.866544\pi\)
−0.913388 + 0.407090i \(0.866544\pi\)
\(522\) −2.84847 + 4.93369i −0.124674 + 0.215942i
\(523\) 14.1742 24.5505i 0.619796 1.07352i −0.369727 0.929141i \(-0.620549\pi\)
0.989523 0.144378i \(-0.0461180\pi\)
\(524\) 4.34847 0.189964
\(525\) −30.0000 −1.30931
\(526\) 0.898979 1.55708i 0.0391974 0.0678918i
\(527\) 4.44949 + 7.70674i 0.193823 + 0.335711i
\(528\) −1.22474 + 2.12132i −0.0533002 + 0.0923186i
\(529\) 11.0959 + 19.2187i 0.482431 + 0.835595i
\(530\) 0 0
\(531\) 8.69694 0.377415
\(532\) 7.77526 7.31747i 0.337100 0.317253i
\(533\) −29.4393 −1.27516
\(534\) 11.0227 + 19.0919i 0.476999 + 0.826187i
\(535\) 0 0
\(536\) 4.77526 8.27098i 0.206260 0.357252i
\(537\) −12.0000 20.7846i −0.517838 0.896922i
\(538\) 10.2247 17.7098i 0.440820 0.763523i
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −18.8990 + 32.7340i −0.812531 + 1.40734i 0.0985570 + 0.995131i \(0.468577\pi\)
−0.911088 + 0.412213i \(0.864756\pi\)
\(542\) 12.3485 21.3882i 0.530412 0.918701i
\(543\) −10.4041 −0.446482
\(544\) 4.44949 0.190770
\(545\) 0 0
\(546\) 11.6969 + 20.2597i 0.500583 + 0.867035i
\(547\) −7.82577 + 13.5546i −0.334606 + 0.579554i −0.983409 0.181402i \(-0.941936\pi\)
0.648803 + 0.760956i \(0.275270\pi\)
\(548\) 3.94949 + 6.84072i 0.168714 + 0.292221i
\(549\) −11.8485 20.5222i −0.505680 0.875864i
\(550\) −5.00000 −0.213201
\(551\) 6.02781 5.67291i 0.256793 0.241674i
\(552\) 2.20204 0.0937251
\(553\) 5.44949 + 9.43879i 0.231736 + 0.401378i
\(554\) −15.7474 27.2754i −0.669045 1.15882i
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −8.29796 + 14.3725i −0.351596 + 0.608982i −0.986529 0.163585i \(-0.947694\pi\)
0.634933 + 0.772567i \(0.281028\pi\)
\(558\) −6.00000 −0.254000
\(559\) 36.8434 1.55831
\(560\) 0 0
\(561\) 5.44949 9.43879i 0.230078 0.398506i
\(562\) 17.1464 0.723278
\(563\) 0.898979 0.0378875 0.0189437 0.999821i \(-0.493970\pi\)
0.0189437 + 0.999821i \(0.493970\pi\)
\(564\) −8.02270 + 13.8957i −0.337817 + 0.585116i
\(565\) 0 0
\(566\) 1.55051 2.68556i 0.0651728 0.112883i
\(567\) −11.0227 19.0919i −0.462910 0.801784i
\(568\) 3.72474 + 6.45145i 0.156287 + 0.270697i
\(569\) −33.5959 −1.40841 −0.704207 0.709995i \(-0.748697\pi\)
−0.704207 + 0.709995i \(0.748697\pi\)
\(570\) 0 0
\(571\) −19.9444 −0.834647 −0.417323 0.908758i \(-0.637032\pi\)
−0.417323 + 0.908758i \(0.637032\pi\)
\(572\) 1.94949 + 3.37662i 0.0815123 + 0.141183i
\(573\) −9.37117 16.2313i −0.391486 0.678074i
\(574\) 9.24745 16.0171i 0.385981 0.668539i
\(575\) 2.24745 + 3.89270i 0.0937251 + 0.162337i
\(576\) −1.50000 + 2.59808i −0.0625000 + 0.108253i
\(577\) −37.7980 −1.57355 −0.786775 0.617240i \(-0.788251\pi\)
−0.786775 + 0.617240i \(0.788251\pi\)
\(578\) −2.79796 −0.116380
\(579\) −28.5959 + 49.5296i −1.18841 + 2.05838i
\(580\) 0 0
\(581\) 13.3485 0.553788
\(582\) 9.55051 0.395881
\(583\) −3.89898 + 6.75323i −0.161479 + 0.279690i
\(584\) −7.22474 12.5136i −0.298962 0.517817i
\(585\) 0 0
\(586\) −3.94949 6.84072i −0.163152 0.282587i
\(587\) 13.6742 + 23.6845i 0.564396 + 0.977563i 0.997106 + 0.0760293i \(0.0242242\pi\)
−0.432710 + 0.901533i \(0.642442\pi\)
\(588\) 2.44949 0.101015
\(589\) 8.34847 + 2.51059i 0.343993 + 0.103447i
\(590\) 0 0
\(591\) 7.47219 + 12.9422i 0.307365 + 0.532372i
\(592\) −4.22474 7.31747i −0.173636 0.300746i
\(593\) −12.6969 + 21.9917i −0.521401 + 0.903093i 0.478289 + 0.878202i \(0.341257\pi\)
−0.999690 + 0.0248904i \(0.992076\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 18.6969 0.765856
\(597\) −49.8434 −2.03995
\(598\) 1.75255 3.03551i 0.0716672 0.124131i
\(599\) −17.1742 + 29.7466i −0.701720 + 1.21542i 0.266142 + 0.963934i \(0.414251\pi\)
−0.967862 + 0.251481i \(0.919082\pi\)
\(600\) −12.2474 −0.500000
\(601\) 4.40408 0.179646 0.0898231 0.995958i \(-0.471370\pi\)
0.0898231 + 0.995958i \(0.471370\pi\)
\(602\) −11.5732 + 20.0454i −0.471689 + 0.816989i
\(603\) −14.3258 24.8130i −0.583390 1.01046i
\(604\) 4.22474 7.31747i 0.171902 0.297744i
\(605\) 0 0
\(606\) −6.12372 10.6066i −0.248759 0.430864i
\(607\) −19.1464 −0.777130 −0.388565 0.921421i \(-0.627029\pi\)
−0.388565 + 0.921421i \(0.627029\pi\)
\(608\) 3.17423 2.98735i 0.128732 0.121153i
\(609\) −11.3939 −0.461703
\(610\) 0 0
\(611\) 12.7702 + 22.1186i 0.516625 + 0.894821i
\(612\) 6.67423 11.5601i 0.269790 0.467290i
\(613\) 13.3990 + 23.2077i 0.541180 + 0.937351i 0.998837 + 0.0482219i \(0.0153555\pi\)
−0.457657 + 0.889129i \(0.651311\pi\)
\(614\) −9.62372 + 16.6688i −0.388382 + 0.672697i
\(615\) 0 0
\(616\) −2.44949 −0.0986928
\(617\) 19.1969 33.2501i 0.772840 1.33860i −0.163161 0.986599i \(-0.552169\pi\)
0.936001 0.351998i \(-0.114498\pi\)
\(618\) 10.2247 17.7098i 0.411300 0.712392i
\(619\) −24.6969 −0.992654 −0.496327 0.868136i \(-0.665318\pi\)
−0.496327 + 0.868136i \(0.665318\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 3.62372 + 6.27647i 0.145298 + 0.251664i
\(623\) −11.0227 + 19.0919i −0.441615 + 0.764900i
\(624\) 4.77526 + 8.27098i 0.191163 + 0.331104i
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) 19.6969 0.787248
\(627\) −2.44949 10.3923i −0.0978232 0.415029i
\(628\) −6.00000 −0.239426
\(629\) 18.7980 + 32.5590i 0.749524 + 1.29821i
\(630\) 0 0
\(631\) −0.477296 + 0.826701i −0.0190009 + 0.0329105i −0.875369 0.483455i \(-0.839382\pi\)
0.856369 + 0.516365i \(0.172715\pi\)
\(632\) 2.22474 + 3.85337i 0.0884956 + 0.153279i
\(633\) 24.4949 42.4264i 0.973585 1.68630i
\(634\) 24.0454 0.954965
\(635\) 0 0
\(636\) −9.55051 + 16.5420i −0.378702 + 0.655932i
\(637\) 1.94949 3.37662i 0.0772416 0.133786i
\(638\) −1.89898 −0.0751813
\(639\) 22.3485 0.884092
\(640\) 0 0
\(641\) 21.7474 + 37.6677i 0.858973 + 1.48778i 0.872910 + 0.487881i \(0.162230\pi\)
−0.0139374 + 0.999903i \(0.504437\pi\)
\(642\) −12.6742 + 21.9524i −0.500212 + 0.866393i
\(643\) 1.67423 + 2.89986i 0.0660254 + 0.114359i 0.897148 0.441729i \(-0.145635\pi\)
−0.831123 + 0.556089i \(0.812302\pi\)
\(644\) 1.10102 + 1.90702i 0.0433863 + 0.0751473i
\(645\) 0 0
\(646\) −14.1237 + 13.2922i −0.555691 + 0.522973i
\(647\) −39.2474 −1.54298 −0.771488 0.636244i \(-0.780487\pi\)
−0.771488 + 0.636244i \(0.780487\pi\)
\(648\) −4.50000 7.79423i −0.176777 0.306186i
\(649\) 1.44949 + 2.51059i 0.0568974 + 0.0985493i
\(650\) −9.74745 + 16.8831i −0.382326 + 0.662209i
\(651\) −6.00000 10.3923i −0.235159 0.407307i
\(652\) −1.44949 + 2.51059i −0.0567664 + 0.0983223i
\(653\) 3.34847 0.131036 0.0655179 0.997851i \(-0.479130\pi\)
0.0655179 + 0.997851i \(0.479130\pi\)
\(654\) 38.9444 1.52285
\(655\) 0 0
\(656\) 3.77526 6.53893i 0.147399 0.255302i
\(657\) −43.3485 −1.69118
\(658\) −16.0454 −0.625515
\(659\) 10.9722 19.0044i 0.427416 0.740306i −0.569227 0.822181i \(-0.692757\pi\)
0.996643 + 0.0818744i \(0.0260906\pi\)
\(660\) 0 0
\(661\) −4.57321 + 7.92104i −0.177877 + 0.308093i −0.941153 0.337980i \(-0.890256\pi\)
0.763276 + 0.646073i \(0.223590\pi\)
\(662\) 2.67423 + 4.63191i 0.103937 + 0.180024i
\(663\) −21.2474 36.8017i −0.825183 1.42926i
\(664\) 5.44949 0.211481
\(665\) 0 0
\(666\) −25.3485 −0.982233
\(667\) 0.853572 + 1.47843i 0.0330504 + 0.0572450i
\(668\) 6.57321 + 11.3851i 0.254325 + 0.440504i
\(669\) 1.52781 2.64624i 0.0590684 0.102309i
\(670\) 0 0
\(671\) 3.94949 6.84072i 0.152468 0.264083i
\(672\) −6.00000 −0.231455
\(673\) −42.7423 −1.64760 −0.823798 0.566883i \(-0.808149\pi\)
−0.823798 + 0.566883i \(0.808149\pi\)
\(674\) 6.10102 10.5673i 0.235003 0.407036i
\(675\) 0 0
\(676\) 2.20204 0.0846939
\(677\) 13.6969 0.526416 0.263208 0.964739i \(-0.415219\pi\)
0.263208 + 0.964739i \(0.415219\pi\)
\(678\) −19.2247 + 33.2982i −0.738322 + 1.27881i
\(679\) 4.77526 + 8.27098i 0.183257 + 0.317411i
\(680\) 0 0
\(681\) 5.14643 + 8.91388i 0.197212 + 0.341580i
\(682\) −1.00000 1.73205i −0.0382920 0.0663237i
\(683\) −35.1464 −1.34484 −0.672420 0.740169i \(-0.734745\pi\)
−0.672420 + 0.740169i \(0.734745\pi\)
\(684\) −3.00000 12.7279i −0.114708 0.486664i
\(685\) 0 0
\(686\) 9.79796 + 16.9706i 0.374088 + 0.647939i
\(687\) −0.797959 1.38211i −0.0304440 0.0527306i
\(688\) −4.72474 + 8.18350i −0.180129 + 0.311993i
\(689\) 15.2020 + 26.3307i 0.579152 + 1.00312i
\(690\) 0 0
\(691\) −39.6413 −1.50803 −0.754014 0.656859i \(-0.771885\pi\)
−0.754014 + 0.656859i \(0.771885\pi\)
\(692\) 9.79796 0.372463
\(693\) −3.67423 + 6.36396i −0.139573 + 0.241747i
\(694\) −3.72474 + 6.45145i −0.141389 + 0.244894i
\(695\) 0 0
\(696\) −4.65153 −0.176316
\(697\) −16.7980 + 29.0949i −0.636268 + 1.10205i
\(698\) 15.5000 + 26.8468i 0.586684 + 1.01617i
\(699\) −12.7980 + 22.1667i −0.484063 + 0.838422i
\(700\) −6.12372 10.6066i −0.231455 0.400892i
\(701\) 23.2980 + 40.3532i 0.879952 + 1.52412i 0.851393 + 0.524529i \(0.175759\pi\)
0.0285592 + 0.999592i \(0.490908\pi\)
\(702\) 0 0
\(703\) 35.2702 + 10.6066i 1.33024 + 0.400036i
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 13.7474 + 23.8113i 0.517392 + 0.896149i
\(707\) 6.12372 10.6066i 0.230306 0.398902i
\(708\) 3.55051 + 6.14966i 0.133436 + 0.231119i
\(709\) −7.69694 + 13.3315i −0.289065 + 0.500675i −0.973587 0.228318i \(-0.926678\pi\)
0.684522 + 0.728992i \(0.260011\pi\)
\(710\) 0 0
\(711\) 13.3485 0.500607
\(712\) −4.50000 + 7.79423i −0.168645 + 0.292101i
\(713\) −0.898979 + 1.55708i −0.0336670 + 0.0583130i
\(714\) 26.6969 0.999108
\(715\) 0 0
\(716\) 4.89898 8.48528i 0.183083 0.317110i
\(717\) 26.6969 + 46.2405i 0.997015 + 1.72688i
\(718\) 12.3485 21.3882i 0.460841 0.798200i
\(719\) 2.92679 + 5.06934i 0.109151 + 0.189055i 0.915426 0.402485i \(-0.131854\pi\)
−0.806276 + 0.591540i \(0.798520\pi\)
\(720\) 0 0
\(721\) 20.4495 0.761579
\(722\) −1.15153 + 18.9651i −0.0428555 + 0.705807i
\(723\) −24.4949 −0.910975
\(724\) −2.12372 3.67840i −0.0789276 0.136707i
\(725\) −4.74745 8.22282i −0.176316 0.305388i
\(726\) −1.22474 + 2.12132i −0.0454545 + 0.0787296i
\(727\) −4.97219 8.61209i −0.184408 0.319405i 0.758969 0.651127i \(-0.225704\pi\)
−0.943377 + 0.331722i \(0.892370\pi\)
\(728\) −4.77526 + 8.27098i −0.176983 + 0.306543i
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 21.0227 36.4124i 0.777553 1.34676i
\(732\) 9.67423 16.7563i 0.357570 0.619329i
\(733\) 31.1010 1.14874 0.574371 0.818595i \(-0.305247\pi\)
0.574371 + 0.818595i \(0.305247\pi\)
\(734\) 25.4495 0.939358
\(735\) 0 0
\(736\) 0.449490 + 0.778539i 0.0165684 + 0.0286973i
\(737\) 4.77526 8.27098i 0.175899 0.304666i
\(738\) −11.3258 19.6168i −0.416907 0.722104i
\(739\) −15.8712 27.4897i −0.583831 1.01122i −0.995020 0.0996743i \(-0.968220\pi\)
0.411190 0.911550i \(-0.365113\pi\)
\(740\) 0 0
\(741\) −39.8661 11.9887i −1.46452 0.440416i
\(742\) −19.1010 −0.701221
\(743\) 18.5732 + 32.1698i 0.681385 + 1.18019i 0.974558 + 0.224134i \(0.0719554\pi\)
−0.293173 + 0.956059i \(0.594711\pi\)
\(744\) −2.44949 4.24264i −0.0898027 0.155543i
\(745\) 0 0
\(746\) −8.89898 15.4135i −0.325815 0.564328i
\(747\) 8.17423 14.1582i 0.299080 0.518021i
\(748\) 4.44949 0.162689
\(749\) −25.3485 −0.926213
\(750\) 0 0
\(751\) 23.7702 41.1711i 0.867385 1.50236i 0.00272600 0.999996i \(-0.499132\pi\)
0.864659 0.502359i \(-0.167534\pi\)
\(752\) −6.55051 −0.238873
\(753\) −59.3939 −2.16443
\(754\) −3.70204 + 6.41212i −0.134820 + 0.233516i
\(755\) 0 0
\(756\) 0 0
\(757\) −8.10102 14.0314i −0.294437 0.509979i 0.680417 0.732825i \(-0.261799\pi\)
−0.974854 + 0.222846i \(0.928465\pi\)
\(758\) −1.67423 2.89986i −0.0608109 0.105328i
\(759\) 2.20204 0.0799290
\(760\) 0 0
\(761\) 31.1918 1.13070 0.565352 0.824850i \(-0.308741\pi\)
0.565352 + 0.824850i \(0.308741\pi\)
\(762\) −15.5505 26.9343i −0.563336 0.975726i
\(763\) 19.4722 + 33.7268i 0.704941 + 1.22099i
\(764\) 3.82577 6.62642i 0.138411 0.239735i
\(765\) 0 0
\(766\) −13.3485 + 23.1202i −0.482300 + 0.835368i
\(767\) 11.3031 0.408130
\(768\) −2.44949 −0.0883883
\(769\) 19.6969 34.1161i 0.710290 1.23026i −0.254459 0.967084i \(-0.581897\pi\)
0.964748 0.263174i \(-0.0847694\pi\)
\(770\) 0 0
\(771\) 53.8888 1.94076
\(772\) −23.3485 −0.840330
\(773\) −5.57321 + 9.65309i −0.200455 + 0.347198i −0.948675 0.316253i \(-0.897575\pi\)
0.748220 + 0.663450i \(0.230909\pi\)
\(774\) 14.1742 + 24.5505i 0.509482 + 0.882449i
\(775\) 5.00000 8.66025i 0.179605 0.311086i
\(776\) 1.94949 + 3.37662i 0.0699826 + 0.121213i
\(777\) −25.3485 43.9048i −0.909371 1.57508i
\(778\) 8.24745 0.295685
\(779\) 7.55051 + 32.0341i 0.270525 + 1.14774i
\(780\) 0 0
\(781\) 3.72474 + 6.45145i 0.133282 + 0.230851i
\(782\) −2.00000 3.46410i −0.0715199 0.123876i
\(783\) 0 0
\(784\) 0.500000 + 0.866025i 0.0178571 + 0.0309295i
\(785\) 0 0
\(786\) 10.6515 0.379928
\(787\) 25.2474 0.899974 0.449987 0.893035i \(-0.351429\pi\)
0.449987 + 0.893035i \(0.351429\pi\)
\(788\) −3.05051 + 5.28364i −0.108670 + 0.188222i
\(789\) 2.20204 3.81405i 0.0783947 0.135784i
\(790\) 0 0
\(791\) −38.4495 −1.36711
\(792\) −1.50000 + 2.59808i −0.0533002 + 0.0923186i
\(793\) −15.3990 26.6718i −0.546834 0.947144i
\(794\) −12.6742 + 21.9524i −0.449792 + 0.779062i
\(795\) 0 0
\(796\) −10.1742 17.6223i −0.360616 0.624606i
\(797\) 2.04541 0.0724521 0.0362260 0.999344i \(-0.488466\pi\)
0.0362260 + 0.999344i \(0.488466\pi\)
\(798\) 19.0454 17.9241i 0.674200 0.634505i
\(799\) 29.1464 1.03113
\(800\) −2.50000 4.33013i −0.0883883 0.153093i
\(801\) 13.5000 + 23.3827i 0.476999 + 0.826187i
\(802\) 19.3485 33.5125i 0.683218 1.18337i
\(803\) −7.22474 12.5136i −0.254956 0.441596i
\(804\) 11.6969 20.2597i 0.412519 0.714504i
\(805\) 0 0
\(806\) −7.79796 −0.274671
\(807\) 25.0454 43.3799i 0.881640 1.52705i
\(808\) 2.50000 4.33013i 0.0879497 0.152333i
\(809\) 0.853572 0.0300100 0.0150050 0.999887i \(-0.495224\pi\)
0.0150050 + 0.999887i \(0.495224\pi\)
\(810\) 0 0
\(811\) 1.27526 2.20881i 0.0447803 0.0775617i −0.842767 0.538279i \(-0.819075\pi\)
0.887547 + 0.460718i \(0.152408\pi\)
\(812\) −2.32577 4.02834i −0.0816184 0.141367i
\(813\) 30.2474 52.3901i 1.06082 1.83740i
\(814\) −4.22474 7.31747i −0.148077 0.256477i
\(815\) 0 0
\(816\) 10.8990 0.381541
\(817\) −9.44949 40.0908i −0.330596 1.40260i
\(818\) 22.9444 0.802232
\(819\) 14.3258 + 24.8130i 0.500583 + 0.867035i
\(820\) 0 0
\(821\) −23.1464 + 40.0908i −0.807816 + 1.39918i 0.106558 + 0.994307i \(0.466017\pi\)
−0.914374 + 0.404872i \(0.867316\pi\)
\(822\) 9.67423 + 16.7563i 0.337428 + 0.584442i
\(823\) 4.72474 8.18350i 0.164694 0.285259i −0.771852 0.635802i \(-0.780670\pi\)
0.936547 + 0.350543i \(0.114003\pi\)
\(824\) 8.34847 0.290833
\(825\) −12.2474 −0.426401
\(826\) −3.55051 + 6.14966i −0.123538 + 0.213974i
\(827\) 14.4217 24.9791i 0.501491 0.868608i −0.498507 0.866885i \(-0.666118\pi\)
0.999999 0.00172259i \(-0.000548318\pi\)
\(828\) 2.69694 0.0937251
\(829\) 3.14643 0.109280 0.0546400 0.998506i \(-0.482599\pi\)
0.0546400 + 0.998506i \(0.482599\pi\)
\(830\) 0 0
\(831\) −38.5732 66.8108i −1.33809 2.31764i
\(832\) −1.94949 + 3.37662i −0.0675864 + 0.117063i
\(833\) −2.22474 3.85337i −0.0770828 0.133511i
\(834\) 4.89898 + 8.48528i 0.169638 + 0.293821i
\(835\) 0 0
\(836\) 3.17423 2.98735i 0.109783 0.103320i
\(837\) 0 0
\(838\) −8.67423 15.0242i −0.299646 0.519003i
\(839\) −10.3763 17.9722i −0.358229 0.620471i 0.629436 0.777052i \(-0.283286\pi\)
−0.987665 + 0.156582i \(0.949953\pi\)
\(840\) 0 0
\(841\) 12.6969 + 21.9917i 0.437825 + 0.758336i
\(842\) −17.6742 + 30.6127i −0.609094 + 1.05498i
\(843\) 42.0000 1.44656
\(844\) 20.0000 0.688428
\(845\) 0 0
\(846\) −9.82577 + 17.0187i −0.337817 + 0.585116i
\(847\) −2.44949 −0.0841655
\(848\) −7.79796 −0.267783
\(849\) 3.79796 6.57826i 0.130346 0.225765i
\(850\) 11.1237 + 19.2669i 0.381541 + 0.660848i
\(851\) −3.79796 + 6.57826i −0.130192 + 0.225500i
\(852\) 9.12372 + 15.8028i 0.312574 + 0.541393i
\(853\) 1.34847 + 2.33562i 0.0461707 + 0.0799700i 0.888187 0.459482i \(-0.151965\pi\)
−0.842016 + 0.539452i \(0.818632\pi\)
\(854\) 19.3485 0.662091
\(855\) 0 0
\(856\) −10.3485 −0.353703
\(857\) −5.57321 9.65309i −0.190377 0.329743i 0.754998 0.655727i \(-0.227638\pi\)
−0.945375 + 0.325984i \(0.894304\pi\)
\(858\) 4.77526 + 8.27098i 0.163025 + 0.282367i
\(859\) 0.550510 0.953512i 0.0187832 0.0325334i −0.856481 0.516178i \(-0.827354\pi\)
0.875264 + 0.483645i \(0.160687\pi\)
\(860\) 0 0
\(861\) 22.6515 39.2336i 0.771962 1.33708i
\(862\) −16.0454 −0.546509
\(863\) −11.6515 −0.396623 −0.198311 0.980139i \(-0.563546\pi\)
−0.198311 + 0.980139i \(0.563546\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −31.6969 −1.07711
\(867\) −6.85357 −0.232760
\(868\) 2.44949 4.24264i 0.0831411 0.144005i
\(869\) 2.22474 + 3.85337i 0.0754693 + 0.130717i
\(870\) 0 0
\(871\) −18.6186 32.2484i −0.630868 1.09270i
\(872\) 7.94949 + 13.7689i 0.269204 + 0.466274i
\(873\) 11.6969 0.395881
\(874\) −3.75255 1.12848i −0.126932 0.0381716i
\(875\) 0 0
\(876\) −17.6969 30.6520i −0.597924 1.03563i
\(877\) −18.7980 32.5590i −0.634762 1.09944i −0.986566 0.163366i \(-0.947765\pi\)
0.351804 0.936074i \(-0.385569\pi\)
\(878\) 5.79796 10.0424i 0.195672 0.338913i
\(879\) −9.67423 16.7563i −0.326304 0.565175i
\(880\) 0 0
\(881\) 12.8990 0.434578 0.217289 0.976107i \(-0.430279\pi\)
0.217289 + 0.976107i \(0.430279\pi\)
\(882\) 3.00000 0.101015
\(883\) 6.22474 10.7816i 0.209479 0.362829i −0.742071 0.670321i \(-0.766156\pi\)
0.951551 + 0.307492i \(0.0994898\pi\)
\(884\) 8.67423 15.0242i 0.291746 0.505319i
\(885\) 0 0
\(886\) 21.3485 0.717216
\(887\) −6.67423 + 11.5601i −0.224099 + 0.388151i −0.956049 0.293208i \(-0.905277\pi\)
0.731950 + 0.681359i \(0.238611\pi\)
\(888\) −10.3485 17.9241i −0.347272 0.601493i
\(889\) 15.5505 26.9343i 0.521547 0.903347i
\(890\) 0 0
\(891\) −4.50000 7.79423i −0.150756 0.261116i
\(892\) 1.24745 0.0417677
\(893\) 20.7929 19.5686i 0.695806 0.654840i
\(894\) 45.7980 1.53171
\(895\) 0 0
\(896\) −1.22474 2.12132i −0.0409159 0.0708683i
\(897\) 4.29286 7.43545i 0.143334 0.248262i
\(898\) 5.10102 + 8.83523i 0.170223 + 0.294835i
\(899\) 1.89898 3.28913i 0.0633345 0.109699i
\(900\) −15.0000 −0.500000
\(901\) 34.6969 1.15592
\(902\) 3.77526 6.53893i 0.125702 0.217723i
\(903\) −28.3485 + 49.1010i −0.943378 + 1.63398i
\(904\) −15.6969 −0.522072
\(905\) 0 0
\(906\) 10.3485 17.9241i 0.343805 0.595487i
\(907\) −19.4495 33.6875i −0.645810 1.11858i −0.984114 0.177538i \(-0.943187\pi\)
0.338304 0.941037i \(-0.390147\pi\)
\(908\) −2.10102 + 3.63907i −0.0697248 + 0.120767i
\(909\) −7.50000 12.9904i −0.248759 0.430864i
\(910\) 0 0
\(911\) −24.4949 −0.811552 −0.405776 0.913973i \(-0.632999\pi\)
−0.405776 + 0.913973i \(0.632999\pi\)
\(912\) 7.77526 7.31747i 0.257464 0.242306i
\(913\) 5.44949 0.180352
\(914\) −11.4722 19.8704i −0.379466 0.657255i
\(915\) 0 0
\(916\) 0.325765 0.564242i 0.0107636 0.0186431i
\(917\) 5.32577 + 9.22450i 0.175872 + 0.304620i
\(918\) 0 0
\(919\) −25.3485 −0.836169 −0.418084 0.908408i \(-0.637298\pi\)
−0.418084 + 0.908408i \(0.637298\pi\)
\(920\) 0 0
\(921\) −23.5732 + 40.8300i −0.776764 + 1.34539i
\(922\) −6.39898 + 11.0834i −0.210739 + 0.365011i
\(923\) 29.0454 0.956041
\(924\) −6.00000 −0.197386
\(925\) 21.1237 36.5874i 0.694544 1.20299i
\(926\) 20.0732 + 34.7678i 0.659647 + 1.14254i
\(927\) 12.5227 21.6900i 0.411300 0.712392i
\(928\) −0.949490 1.64456i −0.0311685 0.0539855i
\(929\) 18.7474 + 32.4715i 0.615084 + 1.06536i 0.990370 + 0.138447i \(0.0442112\pi\)
−0.375286 + 0.926909i \(0.622455\pi\)
\(930\) 0 0
\(931\) −4.17423 1.25529i −0.136805 0.0411406i
\(932\) −10.4495 −0.342284
\(933\) 8.87628 + 15.3742i 0.290596 + 0.503327i
\(934\) −3.32577 5.76039i −0.108822 0.188486i
\(935\) 0 0
\(936\) 5.84847 + 10.1298i 0.191163 + 0.331104i
\(937\) 6.89898 11.9494i 0.225380 0.390369i −0.731053 0.682320i \(-0.760971\pi\)
0.956433 + 0.291951i \(0.0943044\pi\)
\(938\) 23.3939 0.763837
\(939\) 48.2474 1.57450
\(940\) 0 0
\(941\) 22.8990 39.6622i 0.746485 1.29295i −0.203012 0.979176i \(-0.565073\pi\)
0.949498 0.313774i \(-0.101594\pi\)
\(942\) −14.6969 −0.478852
\(943\) −6.78775 −0.221040
\(944\) −1.44949 + 2.51059i −0.0471769 + 0.0817127i
\(945\) 0 0
\(946\) −4.72474 + 8.18350i −0.153615 + 0.266068i
\(947\) 24.1464 + 41.8228i 0.784653 + 1.35906i 0.929206 + 0.369563i \(0.120492\pi\)
−0.144552 + 0.989497i \(0.546174\pi\)
\(948\) 5.44949 + 9.43879i 0.176991 + 0.306558i
\(949\) −56.3383 −1.82882
\(950\) 20.8712 + 6.27647i 0.677150 + 0.203636i
\(951\) 58.8990 1.90993
\(952\) 5.44949 + 9.43879i 0.176619 + 0.305913i
\(953\) −20.0000 34.6410i −0.647864 1.12213i −0.983632 0.180188i \(-0.942329\pi\)
0.335769 0.941944i \(-0.391004\pi\)
\(954\) −11.6969 + 20.2597i −0.378702 + 0.655932i
\(955\) 0 0
\(956\) −10.8990 + 18.8776i −0.352498 + 0.610545i
\(957\) −4.65153 −0.150363
\(958\) 43.1464 1.39400
\(959\) −9.67423 + 16.7563i −0.312397 + 0.541088i
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) −32.9444 −1.06217
\(963\) −15.5227 + 26.8861i −0.500212 + 0.866393i
\(964\) −5.00000 8.66025i −0.161039 0.278928i
\(965\) 0 0
\(966\) 2.69694 + 4.67123i 0.0867726 + 0.150295i
\(967\) 18.8990 + 32.7340i 0.607750 + 1.05265i 0.991610 + 0.129263i \(0.0412611\pi\)
−0.383860 + 0.923391i \(0.625406\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −34.5959 + 32.5590i −1.11138 + 1.04595i
\(970\) 0 0
\(971\) 21.9217 + 37.9695i 0.703500 + 1.21850i 0.967230 + 0.253902i \(0.0817140\pi\)
−0.263730 + 0.964597i \(0.584953\pi\)
\(972\) −11.0227 19.0919i −0.353553 0.612372i
\(973\) −4.89898 + 8.48528i −0.157054 + 0.272026i
\(974\) −3.82577 6.62642i −0.122585 0.212324i
\(975\) −23.8763 + 41.3549i −0.764653 + 1.32442i
\(976\) 7.89898 0.252840
\(977\) −57.0000 −1.82359 −0.911796 0.410644i \(-0.865304\pi\)
−0.911796 + 0.410644i \(0.865304\pi\)
\(978\) −3.55051 + 6.14966i −0.113533 + 0.196645i
\(979\) −4.50000 + 7.79423i −0.143821 + 0.249105i
\(980\) 0 0
\(981\) 47.6969 1.52285
\(982\) −6.89898 + 11.9494i −0.220155 + 0.381320i
\(983\) −22.8712 39.6140i −0.729477 1.26349i −0.957104 0.289743i \(-0.906430\pi\)
0.227627 0.973748i \(-0.426903\pi\)
\(984\) 9.24745 16.0171i 0.294798 0.510605i
\(985\) 0 0
\(986\) 4.22474 + 7.31747i 0.134543 + 0.233036i
\(987\) −39.3031 −1.25103
\(988\) −3.89898 16.5420i −0.124043 0.526270i
\(989\) 8.49490 0.270122
\(990\) 0 0
\(991\) −0.724745 1.25529i −0.0230223 0.0398758i 0.854285 0.519805i \(-0.173996\pi\)
−0.877307 + 0.479930i \(0.840662\pi\)
\(992\) 1.00000 1.73205i 0.0317500 0.0549927i
\(993\) 6.55051 + 11.3458i 0.207874 + 0.360049i
\(994\) −9.12372 + 15.8028i −0.289387 + 0.501233i
\(995\) 0 0
\(996\) 13.3485 0.422962
\(997\) 14.5959 25.2809i 0.462257 0.800653i −0.536816 0.843700i \(-0.680373\pi\)
0.999073 + 0.0430463i \(0.0137063\pi\)
\(998\) −0.348469 + 0.603566i −0.0110306 + 0.0191056i
\(999\) 0 0
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 418.2.e.g.45.2 4
19.7 even 3 7942.2.a.v.1.1 2
19.11 even 3 inner 418.2.e.g.353.2 yes 4
19.12 odd 6 7942.2.a.y.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.e.g.45.2 4 1.1 even 1 trivial
418.2.e.g.353.2 yes 4 19.11 even 3 inner
7942.2.a.v.1.1 2 19.7 even 3
7942.2.a.y.1.2 2 19.12 odd 6