Properties

Label 637.2.g.f.263.2
Level $637$
Weight $2$
Character 637.263
Analytic conductor $5.086$
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] = [637,2,Mod(263,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.263");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.08647060876\)
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: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 263.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 637.263
Dual form 637.2.g.f.373.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.20711 - 2.09077i) q^{2} -1.41421 q^{3} +(-1.91421 - 3.31552i) q^{4} +(-1.91421 - 3.31552i) q^{5} +(-1.70711 + 2.95680i) q^{6} -4.41421 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(1.20711 - 2.09077i) q^{2} -1.41421 q^{3} +(-1.91421 - 3.31552i) q^{4} +(-1.91421 - 3.31552i) q^{5} +(-1.70711 + 2.95680i) q^{6} -4.41421 q^{8} -1.00000 q^{9} -9.24264 q^{10} +3.41421 q^{11} +(2.70711 + 4.68885i) q^{12} +(-3.50000 + 0.866025i) q^{13} +(2.70711 + 4.68885i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(0.0857864 + 0.148586i) q^{17} +(-1.20711 + 2.09077i) q^{18} +6.00000 q^{19} +(-7.32843 + 12.6932i) q^{20} +(4.12132 - 7.13834i) q^{22} +(-0.707107 + 1.22474i) q^{23} +6.24264 q^{24} +(-4.82843 + 8.36308i) q^{25} +(-2.41421 + 8.36308i) q^{26} +5.65685 q^{27} +(-4.91421 - 8.51167i) q^{29} +13.0711 q^{30} +(-2.70711 + 4.68885i) q^{31} +(-0.792893 - 1.37333i) q^{32} -4.82843 q^{33} +0.414214 q^{34} +(1.91421 + 3.31552i) q^{36} +(-3.74264 + 6.48244i) q^{37} +(7.24264 - 12.5446i) q^{38} +(4.94975 - 1.22474i) q^{39} +(8.44975 + 14.6354i) q^{40} +(-2.91421 - 5.04757i) q^{41} +(-0.292893 + 0.507306i) q^{43} +(-6.53553 - 11.3199i) q^{44} +(1.91421 + 3.31552i) q^{45} +(1.70711 + 2.95680i) q^{46} +(-3.82843 - 6.63103i) q^{47} +(2.12132 - 3.67423i) q^{48} +(11.6569 + 20.1903i) q^{50} +(-0.121320 - 0.210133i) q^{51} +(9.57107 + 9.94655i) q^{52} +(1.50000 - 2.59808i) q^{53} +(6.82843 - 11.8272i) q^{54} +(-6.53553 - 11.3199i) q^{55} -8.48528 q^{57} -23.7279 q^{58} +(0.878680 + 1.52192i) q^{59} +(10.3640 - 17.9509i) q^{60} +9.82843 q^{61} +(6.53553 + 11.3199i) q^{62} -9.82843 q^{64} +(9.57107 + 9.94655i) q^{65} +(-5.82843 + 10.0951i) q^{66} -4.24264 q^{67} +(0.328427 - 0.568852i) q^{68} +(1.00000 - 1.73205i) q^{69} +(0.171573 - 0.297173i) q^{71} +4.41421 q^{72} +(-0.328427 + 0.568852i) q^{73} +(9.03553 + 15.6500i) q^{74} +(6.82843 - 11.8272i) q^{75} +(-11.4853 - 19.8931i) q^{76} +(3.41421 - 11.8272i) q^{78} +(-5.12132 - 8.87039i) q^{79} +11.4853 q^{80} -5.00000 q^{81} -14.0711 q^{82} -13.0711 q^{83} +(0.328427 - 0.568852i) q^{85} +(0.707107 + 1.22474i) q^{86} +(6.94975 + 12.0373i) q^{87} -15.0711 q^{88} +(3.65685 - 6.33386i) q^{89} +9.24264 q^{90} +5.41421 q^{92} +(3.82843 - 6.63103i) q^{93} -18.4853 q^{94} +(-11.4853 - 19.8931i) q^{95} +(1.12132 + 1.94218i) q^{96} +(2.58579 - 4.47871i) q^{97} -3.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{6} - 12 q^{8} - 4 q^{9} - 20 q^{10} + 8 q^{11} + 8 q^{12} - 14 q^{13} + 8 q^{15} - 6 q^{16} + 6 q^{17} - 2 q^{18} + 24 q^{19} - 18 q^{20} + 8 q^{22} + 8 q^{24} - 8 q^{25} - 4 q^{26} - 14 q^{29} + 24 q^{30} - 8 q^{31} - 6 q^{32} - 8 q^{33} - 4 q^{34} + 2 q^{36} + 2 q^{37} + 12 q^{38} + 14 q^{40} - 6 q^{41} - 4 q^{43} - 12 q^{44} + 2 q^{45} + 4 q^{46} - 4 q^{47} + 24 q^{50} + 8 q^{51} + 10 q^{52} + 6 q^{53} + 16 q^{54} - 12 q^{55} - 44 q^{58} + 12 q^{59} + 16 q^{60} + 28 q^{61} + 12 q^{62} - 28 q^{64} + 10 q^{65} - 12 q^{66} - 10 q^{68} + 4 q^{69} + 12 q^{71} + 12 q^{72} + 10 q^{73} + 22 q^{74} + 16 q^{75} - 12 q^{76} + 8 q^{78} - 12 q^{79} + 12 q^{80} - 20 q^{81} - 28 q^{82} - 24 q^{83} - 10 q^{85} + 8 q^{87} - 32 q^{88} - 8 q^{89} + 20 q^{90} + 16 q^{92} + 4 q^{93} - 40 q^{94} - 12 q^{95} - 4 q^{96} + 16 q^{97} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20711 2.09077i 0.853553 1.47840i −0.0244272 0.999702i \(-0.507776\pi\)
0.877981 0.478696i \(-0.158890\pi\)
\(3\) −1.41421 −0.816497 −0.408248 0.912871i \(-0.633860\pi\)
−0.408248 + 0.912871i \(0.633860\pi\)
\(4\) −1.91421 3.31552i −0.957107 1.65776i
\(5\) −1.91421 3.31552i −0.856062 1.48274i −0.875656 0.482935i \(-0.839571\pi\)
0.0195936 0.999808i \(-0.493763\pi\)
\(6\) −1.70711 + 2.95680i −0.696923 + 1.20711i
\(7\) 0 0
\(8\) −4.41421 −1.56066
\(9\) −1.00000 −0.333333
\(10\) −9.24264 −2.92278
\(11\) 3.41421 1.02942 0.514712 0.857363i \(-0.327899\pi\)
0.514712 + 0.857363i \(0.327899\pi\)
\(12\) 2.70711 + 4.68885i 0.781474 + 1.35355i
\(13\) −3.50000 + 0.866025i −0.970725 + 0.240192i
\(14\) 0 0
\(15\) 2.70711 + 4.68885i 0.698972 + 1.21065i
\(16\) −1.50000 + 2.59808i −0.375000 + 0.649519i
\(17\) 0.0857864 + 0.148586i 0.0208063 + 0.0360375i 0.876241 0.481873i \(-0.160043\pi\)
−0.855435 + 0.517911i \(0.826710\pi\)
\(18\) −1.20711 + 2.09077i −0.284518 + 0.492799i
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) −7.32843 + 12.6932i −1.63869 + 2.83829i
\(21\) 0 0
\(22\) 4.12132 7.13834i 0.878668 1.52190i
\(23\) −0.707107 + 1.22474i −0.147442 + 0.255377i −0.930281 0.366847i \(-0.880437\pi\)
0.782839 + 0.622224i \(0.213771\pi\)
\(24\) 6.24264 1.27427
\(25\) −4.82843 + 8.36308i −0.965685 + 1.67262i
\(26\) −2.41421 + 8.36308i −0.473466 + 1.64014i
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) −4.91421 8.51167i −0.912547 1.58058i −0.810454 0.585802i \(-0.800780\pi\)
−0.102092 0.994775i \(-0.532554\pi\)
\(30\) 13.0711 2.38644
\(31\) −2.70711 + 4.68885i −0.486211 + 0.842142i −0.999874 0.0158500i \(-0.994955\pi\)
0.513664 + 0.857992i \(0.328288\pi\)
\(32\) −0.792893 1.37333i −0.140165 0.242773i
\(33\) −4.82843 −0.840521
\(34\) 0.414214 0.0710370
\(35\) 0 0
\(36\) 1.91421 + 3.31552i 0.319036 + 0.552586i
\(37\) −3.74264 + 6.48244i −0.615286 + 1.06571i 0.375048 + 0.927005i \(0.377626\pi\)
−0.990334 + 0.138702i \(0.955707\pi\)
\(38\) 7.24264 12.5446i 1.17491 2.03501i
\(39\) 4.94975 1.22474i 0.792594 0.196116i
\(40\) 8.44975 + 14.6354i 1.33602 + 2.31406i
\(41\) −2.91421 5.04757i −0.455124 0.788297i 0.543572 0.839363i \(-0.317072\pi\)
−0.998695 + 0.0510654i \(0.983738\pi\)
\(42\) 0 0
\(43\) −0.292893 + 0.507306i −0.0446658 + 0.0773634i −0.887494 0.460819i \(-0.847556\pi\)
0.842828 + 0.538183i \(0.180889\pi\)
\(44\) −6.53553 11.3199i −0.985269 1.70654i
\(45\) 1.91421 + 3.31552i 0.285354 + 0.494248i
\(46\) 1.70711 + 2.95680i 0.251699 + 0.435956i
\(47\) −3.82843 6.63103i −0.558433 0.967235i −0.997628 0.0688429i \(-0.978069\pi\)
0.439194 0.898392i \(-0.355264\pi\)
\(48\) 2.12132 3.67423i 0.306186 0.530330i
\(49\) 0 0
\(50\) 11.6569 + 20.1903i 1.64853 + 2.85533i
\(51\) −0.121320 0.210133i −0.0169882 0.0294245i
\(52\) 9.57107 + 9.94655i 1.32727 + 1.37934i
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 6.82843 11.8272i 0.929231 1.60948i
\(55\) −6.53553 11.3199i −0.881251 1.52637i
\(56\) 0 0
\(57\) −8.48528 −1.12390
\(58\) −23.7279 −3.11563
\(59\) 0.878680 + 1.52192i 0.114394 + 0.198137i 0.917537 0.397649i \(-0.130174\pi\)
−0.803143 + 0.595786i \(0.796841\pi\)
\(60\) 10.3640 17.9509i 1.33798 2.31745i
\(61\) 9.82843 1.25840 0.629201 0.777243i \(-0.283382\pi\)
0.629201 + 0.777243i \(0.283382\pi\)
\(62\) 6.53553 + 11.3199i 0.830014 + 1.43763i
\(63\) 0 0
\(64\) −9.82843 −1.22855
\(65\) 9.57107 + 9.94655i 1.18714 + 1.23372i
\(66\) −5.82843 + 10.0951i −0.717430 + 1.24262i
\(67\) −4.24264 −0.518321 −0.259161 0.965834i \(-0.583446\pi\)
−0.259161 + 0.965834i \(0.583446\pi\)
\(68\) 0.328427 0.568852i 0.0398276 0.0689835i
\(69\) 1.00000 1.73205i 0.120386 0.208514i
\(70\) 0 0
\(71\) 0.171573 0.297173i 0.0203620 0.0352679i −0.855665 0.517530i \(-0.826851\pi\)
0.876027 + 0.482262i \(0.160185\pi\)
\(72\) 4.41421 0.520220
\(73\) −0.328427 + 0.568852i −0.0384395 + 0.0665791i −0.884605 0.466341i \(-0.845572\pi\)
0.846166 + 0.532920i \(0.178905\pi\)
\(74\) 9.03553 + 15.6500i 1.05036 + 1.81928i
\(75\) 6.82843 11.8272i 0.788479 1.36569i
\(76\) −11.4853 19.8931i −1.31745 2.28189i
\(77\) 0 0
\(78\) 3.41421 11.8272i 0.386584 1.33916i
\(79\) −5.12132 8.87039i −0.576194 0.997997i −0.995911 0.0903416i \(-0.971204\pi\)
0.419717 0.907655i \(-0.362129\pi\)
\(80\) 11.4853 1.28409
\(81\) −5.00000 −0.555556
\(82\) −14.0711 −1.55389
\(83\) −13.0711 −1.43474 −0.717368 0.696694i \(-0.754653\pi\)
−0.717368 + 0.696694i \(0.754653\pi\)
\(84\) 0 0
\(85\) 0.328427 0.568852i 0.0356229 0.0617007i
\(86\) 0.707107 + 1.22474i 0.0762493 + 0.132068i
\(87\) 6.94975 + 12.0373i 0.745091 + 1.29054i
\(88\) −15.0711 −1.60658
\(89\) 3.65685 6.33386i 0.387626 0.671388i −0.604504 0.796602i \(-0.706629\pi\)
0.992130 + 0.125215i \(0.0399620\pi\)
\(90\) 9.24264 0.974260
\(91\) 0 0
\(92\) 5.41421 0.564471
\(93\) 3.82843 6.63103i 0.396989 0.687606i
\(94\) −18.4853 −1.90661
\(95\) −11.4853 19.8931i −1.17837 2.04099i
\(96\) 1.12132 + 1.94218i 0.114444 + 0.198223i
\(97\) 2.58579 4.47871i 0.262547 0.454744i −0.704371 0.709832i \(-0.748771\pi\)
0.966918 + 0.255087i \(0.0821042\pi\)
\(98\) 0 0
\(99\) −3.41421 −0.343141
\(100\) 36.9706 3.69706
\(101\) 3.34315 0.332655 0.166328 0.986071i \(-0.446809\pi\)
0.166328 + 0.986071i \(0.446809\pi\)
\(102\) −0.585786 −0.0580015
\(103\) −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i \(-0.924396\pi\)
0.282194 0.959357i \(-0.408938\pi\)
\(104\) 15.4497 3.82282i 1.51497 0.374858i
\(105\) 0 0
\(106\) −3.62132 6.27231i −0.351734 0.609221i
\(107\) 2.65685 4.60181i 0.256848 0.444873i −0.708548 0.705663i \(-0.750649\pi\)
0.965396 + 0.260789i \(0.0839828\pi\)
\(108\) −10.8284 18.7554i −1.04197 1.80474i
\(109\) 1.17157 2.02922i 0.112216 0.194364i −0.804447 0.594024i \(-0.797538\pi\)
0.916664 + 0.399660i \(0.130872\pi\)
\(110\) −31.5563 −3.00878
\(111\) 5.29289 9.16756i 0.502379 0.870146i
\(112\) 0 0
\(113\) 1.15685 2.00373i 0.108828 0.188495i −0.806468 0.591278i \(-0.798624\pi\)
0.915296 + 0.402783i \(0.131957\pi\)
\(114\) −10.2426 + 17.7408i −0.959311 + 1.66158i
\(115\) 5.41421 0.504878
\(116\) −18.8137 + 32.5863i −1.74681 + 3.02556i
\(117\) 3.50000 0.866025i 0.323575 0.0800641i
\(118\) 4.24264 0.390567
\(119\) 0 0
\(120\) −11.9497 20.6976i −1.09086 1.88942i
\(121\) 0.656854 0.0597140
\(122\) 11.8640 20.5490i 1.07411 1.86042i
\(123\) 4.12132 + 7.13834i 0.371607 + 0.643642i
\(124\) 20.7279 1.86142
\(125\) 17.8284 1.59462
\(126\) 0 0
\(127\) 4.65685 + 8.06591i 0.413229 + 0.715734i 0.995241 0.0974468i \(-0.0310676\pi\)
−0.582012 + 0.813180i \(0.697734\pi\)
\(128\) −10.2782 + 17.8023i −0.908471 + 1.57352i
\(129\) 0.414214 0.717439i 0.0364695 0.0631670i
\(130\) 32.3492 8.00436i 2.83722 0.702029i
\(131\) 0.656854 + 1.13770i 0.0573896 + 0.0994017i 0.893293 0.449475i \(-0.148389\pi\)
−0.835903 + 0.548877i \(0.815056\pi\)
\(132\) 9.24264 + 16.0087i 0.804469 + 1.39338i
\(133\) 0 0
\(134\) −5.12132 + 8.87039i −0.442415 + 0.766285i
\(135\) −10.8284 18.7554i −0.931963 1.61421i
\(136\) −0.378680 0.655892i −0.0324715 0.0562423i
\(137\) 2.91421 + 5.04757i 0.248978 + 0.431243i 0.963243 0.268633i \(-0.0865720\pi\)
−0.714264 + 0.699876i \(0.753239\pi\)
\(138\) −2.41421 4.18154i −0.205512 0.355956i
\(139\) −3.94975 + 6.84116i −0.335013 + 0.580260i −0.983487 0.180977i \(-0.942074\pi\)
0.648474 + 0.761237i \(0.275407\pi\)
\(140\) 0 0
\(141\) 5.41421 + 9.37769i 0.455959 + 0.789744i
\(142\) −0.414214 0.717439i −0.0347600 0.0602061i
\(143\) −11.9497 + 2.95680i −0.999288 + 0.247260i
\(144\) 1.50000 2.59808i 0.125000 0.216506i
\(145\) −18.8137 + 32.5863i −1.56239 + 2.70614i
\(146\) 0.792893 + 1.37333i 0.0656203 + 0.113658i
\(147\) 0 0
\(148\) 28.6569 2.35558
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) −16.4853 28.5533i −1.34602 2.33137i
\(151\) 9.48528 16.4290i 0.771901 1.33697i −0.164618 0.986357i \(-0.552639\pi\)
0.936520 0.350615i \(-0.114027\pi\)
\(152\) −26.4853 −2.14824
\(153\) −0.0857864 0.148586i −0.00693542 0.0120125i
\(154\) 0 0
\(155\) 20.7279 1.66491
\(156\) −13.5355 14.0665i −1.08371 1.12622i
\(157\) 5.74264 9.94655i 0.458313 0.793821i −0.540559 0.841306i \(-0.681787\pi\)
0.998872 + 0.0474852i \(0.0151207\pi\)
\(158\) −24.7279 −1.96725
\(159\) −2.12132 + 3.67423i −0.168232 + 0.291386i
\(160\) −3.03553 + 5.25770i −0.239980 + 0.415658i
\(161\) 0 0
\(162\) −6.03553 + 10.4539i −0.474196 + 0.821332i
\(163\) 15.4142 1.20733 0.603667 0.797236i \(-0.293706\pi\)
0.603667 + 0.797236i \(0.293706\pi\)
\(164\) −11.1569 + 19.3242i −0.871204 + 1.50897i
\(165\) 9.24264 + 16.0087i 0.719539 + 1.24628i
\(166\) −15.7782 + 27.3286i −1.22462 + 2.12111i
\(167\) 9.36396 + 16.2189i 0.724605 + 1.25505i 0.959136 + 0.282944i \(0.0913111\pi\)
−0.234531 + 0.972109i \(0.575356\pi\)
\(168\) 0 0
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) −0.792893 1.37333i −0.0608121 0.105330i
\(171\) −6.00000 −0.458831
\(172\) 2.24264 0.171000
\(173\) 18.1421 1.37932 0.689661 0.724133i \(-0.257760\pi\)
0.689661 + 0.724133i \(0.257760\pi\)
\(174\) 33.5563 2.54390
\(175\) 0 0
\(176\) −5.12132 + 8.87039i −0.386034 + 0.668631i
\(177\) −1.24264 2.15232i −0.0934026 0.161778i
\(178\) −8.82843 15.2913i −0.661719 1.14613i
\(179\) 5.65685 0.422813 0.211407 0.977398i \(-0.432196\pi\)
0.211407 + 0.977398i \(0.432196\pi\)
\(180\) 7.32843 12.6932i 0.546229 0.946096i
\(181\) −19.1421 −1.42282 −0.711412 0.702775i \(-0.751944\pi\)
−0.711412 + 0.702775i \(0.751944\pi\)
\(182\) 0 0
\(183\) −13.8995 −1.02748
\(184\) 3.12132 5.40629i 0.230107 0.398557i
\(185\) 28.6569 2.10689
\(186\) −9.24264 16.0087i −0.677703 1.17382i
\(187\) 0.292893 + 0.507306i 0.0214185 + 0.0370979i
\(188\) −14.6569 + 25.3864i −1.06896 + 1.85149i
\(189\) 0 0
\(190\) −55.4558 −4.02319
\(191\) 7.75736 0.561303 0.280651 0.959810i \(-0.409450\pi\)
0.280651 + 0.959810i \(0.409450\pi\)
\(192\) 13.8995 1.00311
\(193\) −21.1421 −1.52184 −0.760922 0.648843i \(-0.775253\pi\)
−0.760922 + 0.648843i \(0.775253\pi\)
\(194\) −6.24264 10.8126i −0.448195 0.776297i
\(195\) −13.5355 14.0665i −0.969300 1.00733i
\(196\) 0 0
\(197\) −4.58579 7.94282i −0.326724 0.565902i 0.655136 0.755511i \(-0.272611\pi\)
−0.981860 + 0.189609i \(0.939278\pi\)
\(198\) −4.12132 + 7.13834i −0.292889 + 0.507299i
\(199\) −9.48528 16.4290i −0.672394 1.16462i −0.977223 0.212213i \(-0.931933\pi\)
0.304830 0.952407i \(-0.401400\pi\)
\(200\) 21.3137 36.9164i 1.50711 2.61039i
\(201\) 6.00000 0.423207
\(202\) 4.03553 6.98975i 0.283939 0.491797i
\(203\) 0 0
\(204\) −0.464466 + 0.804479i −0.0325191 + 0.0563248i
\(205\) −11.1569 + 19.3242i −0.779229 + 1.34966i
\(206\) −33.7990 −2.35489
\(207\) 0.707107 1.22474i 0.0491473 0.0851257i
\(208\) 3.00000 10.3923i 0.208013 0.720577i
\(209\) 20.4853 1.41700
\(210\) 0 0
\(211\) 0.363961 + 0.630399i 0.0250561 + 0.0433985i 0.878282 0.478144i \(-0.158690\pi\)
−0.853225 + 0.521542i \(0.825357\pi\)
\(212\) −11.4853 −0.788812
\(213\) −0.242641 + 0.420266i −0.0166255 + 0.0287962i
\(214\) −6.41421 11.1097i −0.438467 0.759446i
\(215\) 2.24264 0.152947
\(216\) −24.9706 −1.69903
\(217\) 0 0
\(218\) −2.82843 4.89898i −0.191565 0.331801i
\(219\) 0.464466 0.804479i 0.0313857 0.0543616i
\(220\) −25.0208 + 43.3373i −1.68690 + 2.92180i
\(221\) −0.428932 0.445759i −0.0288531 0.0299850i
\(222\) −12.7782 22.1324i −0.857615 1.48543i
\(223\) −1.00000 1.73205i −0.0669650 0.115987i 0.830599 0.556871i \(-0.187998\pi\)
−0.897564 + 0.440884i \(0.854665\pi\)
\(224\) 0 0
\(225\) 4.82843 8.36308i 0.321895 0.557539i
\(226\) −2.79289 4.83743i −0.185780 0.321781i
\(227\) 6.94975 + 12.0373i 0.461271 + 0.798945i 0.999025 0.0441573i \(-0.0140603\pi\)
−0.537754 + 0.843102i \(0.680727\pi\)
\(228\) 16.2426 + 28.1331i 1.07570 + 1.86316i
\(229\) −2.24264 3.88437i −0.148198 0.256686i 0.782364 0.622822i \(-0.214014\pi\)
−0.930561 + 0.366136i \(0.880681\pi\)
\(230\) 6.53553 11.3199i 0.430940 0.746411i
\(231\) 0 0
\(232\) 21.6924 + 37.5723i 1.42418 + 2.46674i
\(233\) 1.41421 + 2.44949i 0.0926482 + 0.160471i 0.908625 0.417614i \(-0.137133\pi\)
−0.815976 + 0.578085i \(0.803800\pi\)
\(234\) 2.41421 8.36308i 0.157822 0.546712i
\(235\) −14.6569 + 25.3864i −0.956108 + 1.65603i
\(236\) 3.36396 5.82655i 0.218975 0.379276i
\(237\) 7.24264 + 12.5446i 0.470460 + 0.814861i
\(238\) 0 0
\(239\) −12.3848 −0.801105 −0.400552 0.916274i \(-0.631182\pi\)
−0.400552 + 0.916274i \(0.631182\pi\)
\(240\) −16.2426 −1.04846
\(241\) 0.742641 + 1.28629i 0.0478377 + 0.0828573i 0.888953 0.457999i \(-0.151434\pi\)
−0.841115 + 0.540856i \(0.818100\pi\)
\(242\) 0.792893 1.37333i 0.0509691 0.0882811i
\(243\) −9.89949 −0.635053
\(244\) −18.8137 32.5863i −1.20442 2.08612i
\(245\) 0 0
\(246\) 19.8995 1.26875
\(247\) −21.0000 + 5.19615i −1.33620 + 0.330623i
\(248\) 11.9497 20.6976i 0.758810 1.31430i
\(249\) 18.4853 1.17146
\(250\) 21.5208 37.2751i 1.36110 2.35749i
\(251\) 5.48528 9.50079i 0.346228 0.599684i −0.639348 0.768917i \(-0.720796\pi\)
0.985576 + 0.169233i \(0.0541291\pi\)
\(252\) 0 0
\(253\) −2.41421 + 4.18154i −0.151780 + 0.262891i
\(254\) 22.4853 1.41085
\(255\) −0.464466 + 0.804479i −0.0290860 + 0.0503784i
\(256\) 14.9853 + 25.9553i 0.936580 + 1.62220i
\(257\) −7.50000 + 12.9904i −0.467837 + 0.810318i −0.999325 0.0367485i \(-0.988300\pi\)
0.531487 + 0.847066i \(0.321633\pi\)
\(258\) −1.00000 1.73205i −0.0622573 0.107833i
\(259\) 0 0
\(260\) 14.6569 50.7728i 0.908980 3.14880i
\(261\) 4.91421 + 8.51167i 0.304182 + 0.526859i
\(262\) 3.17157 0.195940
\(263\) 18.7279 1.15481 0.577407 0.816457i \(-0.304065\pi\)
0.577407 + 0.816457i \(0.304065\pi\)
\(264\) 21.3137 1.31177
\(265\) −11.4853 −0.705535
\(266\) 0 0
\(267\) −5.17157 + 8.95743i −0.316495 + 0.548186i
\(268\) 8.12132 + 14.0665i 0.496089 + 0.859251i
\(269\) 9.00000 + 15.5885i 0.548740 + 0.950445i 0.998361 + 0.0572259i \(0.0182255\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(270\) −52.2843 −3.18192
\(271\) 3.46447 6.00063i 0.210451 0.364512i −0.741405 0.671058i \(-0.765840\pi\)
0.951856 + 0.306546i \(0.0991733\pi\)
\(272\) −0.514719 −0.0312094
\(273\) 0 0
\(274\) 14.0711 0.850064
\(275\) −16.4853 + 28.5533i −0.994100 + 1.72183i
\(276\) −7.65685 −0.460888
\(277\) 15.9853 + 27.6873i 0.960462 + 1.66357i 0.721341 + 0.692580i \(0.243526\pi\)
0.239122 + 0.970990i \(0.423141\pi\)
\(278\) 9.53553 + 16.5160i 0.571903 + 0.990566i
\(279\) 2.70711 4.68885i 0.162070 0.280714i
\(280\) 0 0
\(281\) −0.514719 −0.0307055 −0.0153528 0.999882i \(-0.504887\pi\)
−0.0153528 + 0.999882i \(0.504887\pi\)
\(282\) 26.1421 1.55674
\(283\) −0.100505 −0.00597441 −0.00298720 0.999996i \(-0.500951\pi\)
−0.00298720 + 0.999996i \(0.500951\pi\)
\(284\) −1.31371 −0.0779543
\(285\) 16.2426 + 28.1331i 0.962131 + 1.66646i
\(286\) −8.24264 + 28.5533i −0.487398 + 1.68839i
\(287\) 0 0
\(288\) 0.792893 + 1.37333i 0.0467217 + 0.0809243i
\(289\) 8.48528 14.6969i 0.499134 0.864526i
\(290\) 45.4203 + 78.6703i 2.66717 + 4.61968i
\(291\) −3.65685 + 6.33386i −0.214369 + 0.371297i
\(292\) 2.51472 0.147163
\(293\) 11.2279 19.4473i 0.655942 1.13613i −0.325714 0.945468i \(-0.605605\pi\)
0.981657 0.190657i \(-0.0610618\pi\)
\(294\) 0 0
\(295\) 3.36396 5.82655i 0.195857 0.339235i
\(296\) 16.5208 28.6149i 0.960253 1.66321i
\(297\) 19.3137 1.12070
\(298\) 3.62132 6.27231i 0.209777 0.363345i
\(299\) 1.41421 4.89898i 0.0817861 0.283315i
\(300\) −52.2843 −3.01863
\(301\) 0 0
\(302\) −22.8995 39.6631i −1.31772 2.28235i
\(303\) −4.72792 −0.271612
\(304\) −9.00000 + 15.5885i −0.516185 + 0.894059i
\(305\) −18.8137 32.5863i −1.07727 1.86589i
\(306\) −0.414214 −0.0236790
\(307\) −7.27208 −0.415039 −0.207520 0.978231i \(-0.566539\pi\)
−0.207520 + 0.978231i \(0.566539\pi\)
\(308\) 0 0
\(309\) 9.89949 + 17.1464i 0.563163 + 0.975426i
\(310\) 25.0208 43.3373i 1.42109 2.46139i
\(311\) 13.5355 23.4442i 0.767530 1.32940i −0.171369 0.985207i \(-0.554819\pi\)
0.938899 0.344194i \(-0.111848\pi\)
\(312\) −21.8492 + 5.40629i −1.23697 + 0.306071i
\(313\) 7.00000 + 12.1244i 0.395663 + 0.685309i 0.993186 0.116543i \(-0.0371814\pi\)
−0.597522 + 0.801852i \(0.703848\pi\)
\(314\) −13.8640 24.0131i −0.782389 1.35514i
\(315\) 0 0
\(316\) −19.6066 + 33.9596i −1.10296 + 1.91038i
\(317\) −10.6716 18.4837i −0.599375 1.03815i −0.992913 0.118840i \(-0.962082\pi\)
0.393538 0.919308i \(-0.371251\pi\)
\(318\) 5.12132 + 8.87039i 0.287189 + 0.497427i
\(319\) −16.7782 29.0607i −0.939397 1.62708i
\(320\) 18.8137 + 32.5863i 1.05172 + 1.82163i
\(321\) −3.75736 + 6.50794i −0.209715 + 0.363238i
\(322\) 0 0
\(323\) 0.514719 + 0.891519i 0.0286397 + 0.0496054i
\(324\) 9.57107 + 16.5776i 0.531726 + 0.920976i
\(325\) 9.65685 33.4523i 0.535666 1.85560i
\(326\) 18.6066 32.2276i 1.03052 1.78492i
\(327\) −1.65685 + 2.86976i −0.0916242 + 0.158698i
\(328\) 12.8640 + 22.2810i 0.710293 + 1.23026i
\(329\) 0 0
\(330\) 44.6274 2.45666
\(331\) 28.8701 1.58684 0.793421 0.608673i \(-0.208298\pi\)
0.793421 + 0.608673i \(0.208298\pi\)
\(332\) 25.0208 + 43.3373i 1.37320 + 2.37844i
\(333\) 3.74264 6.48244i 0.205095 0.355236i
\(334\) 45.2132 2.47396
\(335\) 8.12132 + 14.0665i 0.443715 + 0.768537i
\(336\) 0 0
\(337\) 13.4853 0.734590 0.367295 0.930104i \(-0.380284\pi\)
0.367295 + 0.930104i \(0.380284\pi\)
\(338\) 1.20711 31.3616i 0.0656580 1.70584i
\(339\) −1.63604 + 2.83370i −0.0888574 + 0.153906i
\(340\) −2.51472 −0.136380
\(341\) −9.24264 + 16.0087i −0.500517 + 0.866921i
\(342\) −7.24264 + 12.5446i −0.391637 + 0.678335i
\(343\) 0 0
\(344\) 1.29289 2.23936i 0.0697081 0.120738i
\(345\) −7.65685 −0.412231
\(346\) 21.8995 37.9310i 1.17732 2.03919i
\(347\) 12.9497 + 22.4296i 0.695179 + 1.20409i 0.970120 + 0.242624i \(0.0780082\pi\)
−0.274941 + 0.961461i \(0.588658\pi\)
\(348\) 26.6066 46.0840i 1.42626 2.47036i
\(349\) 6.65685 + 11.5300i 0.356333 + 0.617187i 0.987345 0.158586i \(-0.0506935\pi\)
−0.631012 + 0.775773i \(0.717360\pi\)
\(350\) 0 0
\(351\) −19.7990 + 4.89898i −1.05679 + 0.261488i
\(352\) −2.70711 4.68885i −0.144289 0.249916i
\(353\) 0.171573 0.00913190 0.00456595 0.999990i \(-0.498547\pi\)
0.00456595 + 0.999990i \(0.498547\pi\)
\(354\) −6.00000 −0.318896
\(355\) −1.31371 −0.0697244
\(356\) −28.0000 −1.48400
\(357\) 0 0
\(358\) 6.82843 11.8272i 0.360894 0.625086i
\(359\) −8.48528 14.6969i −0.447836 0.775675i 0.550409 0.834895i \(-0.314472\pi\)
−0.998245 + 0.0592205i \(0.981138\pi\)
\(360\) −8.44975 14.6354i −0.445341 0.771353i
\(361\) 17.0000 0.894737
\(362\) −23.1066 + 40.0218i −1.21446 + 2.10350i
\(363\) −0.928932 −0.0487563
\(364\) 0 0
\(365\) 2.51472 0.131626
\(366\) −16.7782 + 29.0607i −0.877009 + 1.51902i
\(367\) −3.27208 −0.170801 −0.0854005 0.996347i \(-0.527217\pi\)
−0.0854005 + 0.996347i \(0.527217\pi\)
\(368\) −2.12132 3.67423i −0.110581 0.191533i
\(369\) 2.91421 + 5.04757i 0.151708 + 0.262766i
\(370\) 34.5919 59.9149i 1.79835 3.11483i
\(371\) 0 0
\(372\) −29.3137 −1.51984
\(373\) −24.4558 −1.26628 −0.633138 0.774039i \(-0.718233\pi\)
−0.633138 + 0.774039i \(0.718233\pi\)
\(374\) 1.41421 0.0731272
\(375\) −25.2132 −1.30200
\(376\) 16.8995 + 29.2708i 0.871525 + 1.50953i
\(377\) 24.5711 + 25.5350i 1.26547 + 1.31512i
\(378\) 0 0
\(379\) −4.12132 7.13834i −0.211698 0.366672i 0.740548 0.672003i \(-0.234566\pi\)
−0.952246 + 0.305332i \(0.901233\pi\)
\(380\) −43.9706 + 76.1592i −2.25564 + 3.90689i
\(381\) −6.58579 11.4069i −0.337400 0.584394i
\(382\) 9.36396 16.2189i 0.479102 0.829829i
\(383\) 14.0416 0.717494 0.358747 0.933435i \(-0.383204\pi\)
0.358747 + 0.933435i \(0.383204\pi\)
\(384\) 14.5355 25.1763i 0.741763 1.28477i
\(385\) 0 0
\(386\) −25.5208 + 44.2033i −1.29898 + 2.24989i
\(387\) 0.292893 0.507306i 0.0148886 0.0257878i
\(388\) −19.7990 −1.00514
\(389\) 0.571068 0.989118i 0.0289543 0.0501503i −0.851185 0.524866i \(-0.824116\pi\)
0.880139 + 0.474715i \(0.157449\pi\)
\(390\) −45.7487 + 11.3199i −2.31658 + 0.573204i
\(391\) −0.242641 −0.0122709
\(392\) 0 0
\(393\) −0.928932 1.60896i −0.0468584 0.0811612i
\(394\) −22.1421 −1.11550
\(395\) −19.6066 + 33.9596i −0.986515 + 1.70869i
\(396\) 6.53553 + 11.3199i 0.328423 + 0.568845i
\(397\) −38.6274 −1.93865 −0.969327 0.245774i \(-0.920958\pi\)
−0.969327 + 0.245774i \(0.920958\pi\)
\(398\) −45.7990 −2.29570
\(399\) 0 0
\(400\) −14.4853 25.0892i −0.724264 1.25446i
\(401\) 15.3995 26.6727i 0.769014 1.33197i −0.169084 0.985602i \(-0.554081\pi\)
0.938098 0.346370i \(-0.112586\pi\)
\(402\) 7.24264 12.5446i 0.361230 0.625669i
\(403\) 5.41421 18.7554i 0.269701 0.934272i
\(404\) −6.39949 11.0843i −0.318387 0.551462i
\(405\) 9.57107 + 16.5776i 0.475590 + 0.823746i
\(406\) 0 0
\(407\) −12.7782 + 22.1324i −0.633391 + 1.09706i
\(408\) 0.535534 + 0.927572i 0.0265129 + 0.0459217i
\(409\) −5.98528 10.3668i −0.295953 0.512606i 0.679253 0.733904i \(-0.262304\pi\)
−0.975206 + 0.221298i \(0.928971\pi\)
\(410\) 26.9350 + 46.6528i 1.33023 + 2.30402i
\(411\) −4.12132 7.13834i −0.203290 0.352108i
\(412\) −26.7990 + 46.4172i −1.32029 + 2.28681i
\(413\) 0 0
\(414\) −1.70711 2.95680i −0.0838997 0.145319i
\(415\) 25.0208 + 43.3373i 1.22822 + 2.12735i
\(416\) 3.96447 + 4.11999i 0.194374 + 0.201999i
\(417\) 5.58579 9.67487i 0.273537 0.473780i
\(418\) 24.7279 42.8300i 1.20948 2.09488i
\(419\) −9.77817 16.9363i −0.477695 0.827392i 0.521978 0.852959i \(-0.325194\pi\)
−0.999673 + 0.0255668i \(0.991861\pi\)
\(420\) 0 0
\(421\) 4.51472 0.220034 0.110017 0.993930i \(-0.464909\pi\)
0.110017 + 0.993930i \(0.464909\pi\)
\(422\) 1.75736 0.0855469
\(423\) 3.82843 + 6.63103i 0.186144 + 0.322412i
\(424\) −6.62132 + 11.4685i −0.321560 + 0.556958i
\(425\) −1.65685 −0.0803692
\(426\) 0.585786 + 1.01461i 0.0283814 + 0.0491581i
\(427\) 0 0
\(428\) −20.3431 −0.983323
\(429\) 16.8995 4.18154i 0.815915 0.201887i
\(430\) 2.70711 4.68885i 0.130548 0.226116i
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) −8.48528 + 14.6969i −0.408248 + 0.707107i
\(433\) −0.257359 + 0.445759i −0.0123679 + 0.0214218i −0.872143 0.489251i \(-0.837270\pi\)
0.859775 + 0.510673i \(0.170604\pi\)
\(434\) 0 0
\(435\) 26.6066 46.0840i 1.27569 2.20956i
\(436\) −8.97056 −0.429612
\(437\) −4.24264 + 7.34847i −0.202953 + 0.351525i
\(438\) −1.12132 1.94218i −0.0535788 0.0928011i
\(439\) 13.3640 23.1471i 0.637827 1.10475i −0.348082 0.937464i \(-0.613167\pi\)
0.985909 0.167285i \(-0.0534999\pi\)
\(440\) 28.8492 + 49.9684i 1.37533 + 2.38215i
\(441\) 0 0
\(442\) −1.44975 + 0.358719i −0.0689575 + 0.0170625i
\(443\) −7.17157 12.4215i −0.340732 0.590165i 0.643837 0.765163i \(-0.277341\pi\)
−0.984569 + 0.174998i \(0.944008\pi\)
\(444\) −40.5269 −1.92332
\(445\) −28.0000 −1.32733
\(446\) −4.82843 −0.228633
\(447\) −4.24264 −0.200670
\(448\) 0 0
\(449\) −7.75736 + 13.4361i −0.366092 + 0.634091i −0.988951 0.148244i \(-0.952638\pi\)
0.622858 + 0.782335i \(0.285971\pi\)
\(450\) −11.6569 20.1903i −0.549509 0.951778i
\(451\) −9.94975 17.2335i −0.468515 0.811492i
\(452\) −8.85786 −0.416639
\(453\) −13.4142 + 23.2341i −0.630255 + 1.09163i
\(454\) 33.5563 1.57488
\(455\) 0 0
\(456\) 37.4558 1.75403
\(457\) 12.5000 21.6506i 0.584725 1.01277i −0.410184 0.912003i \(-0.634536\pi\)
0.994910 0.100771i \(-0.0321310\pi\)
\(458\) −10.8284 −0.505979
\(459\) 0.485281 + 0.840532i 0.0226510 + 0.0392327i
\(460\) −10.3640 17.9509i −0.483222 0.836965i
\(461\) −6.32843 + 10.9612i −0.294744 + 0.510512i −0.974925 0.222532i \(-0.928568\pi\)
0.680181 + 0.733044i \(0.261901\pi\)
\(462\) 0 0
\(463\) −18.7279 −0.870360 −0.435180 0.900343i \(-0.643315\pi\)
−0.435180 + 0.900343i \(0.643315\pi\)
\(464\) 29.4853 1.36882
\(465\) −29.3137 −1.35939
\(466\) 6.82843 0.316321
\(467\) −4.29289 7.43551i −0.198651 0.344074i 0.749440 0.662072i \(-0.230323\pi\)
−0.948091 + 0.317998i \(0.896989\pi\)
\(468\) −9.57107 9.94655i −0.442423 0.459779i
\(469\) 0 0
\(470\) 35.3848 + 61.2882i 1.63218 + 2.82702i
\(471\) −8.12132 + 14.0665i −0.374211 + 0.648152i
\(472\) −3.87868 6.71807i −0.178531 0.309224i
\(473\) −1.00000 + 1.73205i −0.0459800 + 0.0796398i
\(474\) 34.9706 1.60625
\(475\) −28.9706 + 50.1785i −1.32926 + 2.30235i
\(476\) 0 0
\(477\) −1.50000 + 2.59808i −0.0686803 + 0.118958i
\(478\) −14.9497 + 25.8937i −0.683786 + 1.18435i
\(479\) −38.3848 −1.75385 −0.876923 0.480632i \(-0.840407\pi\)
−0.876923 + 0.480632i \(0.840407\pi\)
\(480\) 4.29289 7.43551i 0.195943 0.339383i
\(481\) 7.48528 25.9298i 0.341299 1.18230i
\(482\) 3.58579 0.163328
\(483\) 0 0
\(484\) −1.25736 2.17781i −0.0571527 0.0989914i
\(485\) −19.7990 −0.899026
\(486\) −11.9497 + 20.6976i −0.542052 + 0.938861i
\(487\) −10.4853 18.1610i −0.475133 0.822955i 0.524461 0.851435i \(-0.324267\pi\)
−0.999594 + 0.0284792i \(0.990934\pi\)
\(488\) −43.3848 −1.96394
\(489\) −21.7990 −0.985784
\(490\) 0 0
\(491\) −17.6569 30.5826i −0.796843 1.38017i −0.921662 0.387993i \(-0.873169\pi\)
0.124820 0.992179i \(-0.460165\pi\)
\(492\) 15.7782 27.3286i 0.711335 1.23207i
\(493\) 0.843146 1.46037i 0.0379734 0.0657718i
\(494\) −14.4853 + 50.1785i −0.651724 + 2.25764i
\(495\) 6.53553 + 11.3199i 0.293750 + 0.508791i
\(496\) −8.12132 14.0665i −0.364658 0.631606i
\(497\) 0 0
\(498\) 22.3137 38.6485i 0.999901 1.73188i
\(499\) 14.0208 + 24.2848i 0.627658 + 1.08714i 0.988020 + 0.154323i \(0.0493196\pi\)
−0.360363 + 0.932812i \(0.617347\pi\)
\(500\) −34.1274 59.1104i −1.52622 2.64350i
\(501\) −13.2426 22.9369i −0.591638 1.02475i
\(502\) −13.2426 22.9369i −0.591048 1.02373i
\(503\) 16.7782 29.0607i 0.748102 1.29575i −0.200630 0.979667i \(-0.564299\pi\)
0.948731 0.316083i \(-0.102368\pi\)
\(504\) 0 0
\(505\) −6.39949 11.0843i −0.284774 0.493243i
\(506\) 5.82843 + 10.0951i 0.259105 + 0.448783i
\(507\) −16.2635 + 8.57321i −0.722285 + 0.380750i
\(508\) 17.8284 30.8797i 0.791009 1.37007i
\(509\) 3.32843 5.76500i 0.147530 0.255529i −0.782784 0.622293i \(-0.786201\pi\)
0.930314 + 0.366764i \(0.119534\pi\)
\(510\) 1.12132 + 1.94218i 0.0496529 + 0.0860013i
\(511\) 0 0
\(512\) 31.2426 1.38074
\(513\) 33.9411 1.49854
\(514\) 18.1066 + 31.3616i 0.798648 + 1.38330i
\(515\) −26.7990 + 46.4172i −1.18090 + 2.04539i
\(516\) −3.17157 −0.139621
\(517\) −13.0711 22.6398i −0.574865 0.995695i
\(518\) 0 0
\(519\) −25.6569 −1.12621
\(520\) −42.2487 43.9062i −1.85273 1.92541i
\(521\) 6.67157 11.5555i 0.292287 0.506256i −0.682063 0.731293i \(-0.738917\pi\)
0.974350 + 0.225037i \(0.0722504\pi\)
\(522\) 23.7279 1.03854
\(523\) −8.48528 + 14.6969i −0.371035 + 0.642652i −0.989725 0.142983i \(-0.954331\pi\)
0.618690 + 0.785635i \(0.287664\pi\)
\(524\) 2.51472 4.35562i 0.109856 0.190276i
\(525\) 0 0
\(526\) 22.6066 39.1558i 0.985695 1.70727i
\(527\) −0.928932 −0.0404649
\(528\) 7.24264 12.5446i 0.315195 0.545935i
\(529\) 10.5000 + 18.1865i 0.456522 + 0.790719i
\(530\) −13.8640 + 24.0131i −0.602212 + 1.04306i
\(531\) −0.878680 1.52192i −0.0381314 0.0660456i
\(532\) 0 0
\(533\) 14.5711 + 15.1427i 0.631143 + 0.655903i
\(534\) 12.4853 + 21.6251i 0.540291 + 0.935811i
\(535\) −20.3431 −0.879511
\(536\) 18.7279 0.808923
\(537\) −8.00000 −0.345225
\(538\) 43.4558 1.87351
\(539\) 0 0
\(540\) −41.4558 + 71.8036i −1.78398 + 3.08994i
\(541\) −2.74264 4.75039i −0.117915 0.204235i 0.801026 0.598630i \(-0.204288\pi\)
−0.918941 + 0.394394i \(0.870954\pi\)
\(542\) −8.36396 14.4868i −0.359263 0.622262i
\(543\) 27.0711 1.16173
\(544\) 0.136039 0.235626i 0.00583262 0.0101024i
\(545\) −8.97056 −0.384257
\(546\) 0 0
\(547\) 15.0711 0.644392 0.322196 0.946673i \(-0.395579\pi\)
0.322196 + 0.946673i \(0.395579\pi\)
\(548\) 11.1569 19.3242i 0.476597 0.825491i
\(549\) −9.82843 −0.419467
\(550\) 39.7990 + 68.9339i 1.69703 + 2.93935i
\(551\) −29.4853 51.0700i −1.25612 2.17566i
\(552\) −4.41421 + 7.64564i −0.187881 + 0.325420i
\(553\) 0 0
\(554\) 77.1838 3.27922
\(555\) −40.5269 −1.72027
\(556\) 30.2426 1.28257
\(557\) −10.3137 −0.437006 −0.218503 0.975836i \(-0.570117\pi\)
−0.218503 + 0.975836i \(0.570117\pi\)
\(558\) −6.53553 11.3199i −0.276671 0.479209i
\(559\) 0.585786 2.02922i 0.0247761 0.0858270i
\(560\) 0 0
\(561\) −0.414214 0.717439i −0.0174881 0.0302903i
\(562\) −0.621320 + 1.07616i −0.0262088 + 0.0453950i
\(563\) −9.94975 17.2335i −0.419332 0.726304i 0.576541 0.817069i \(-0.304402\pi\)
−0.995872 + 0.0907645i \(0.971069\pi\)
\(564\) 20.7279 35.9018i 0.872803 1.51174i
\(565\) −8.85786 −0.372653
\(566\) −0.121320 + 0.210133i −0.00509947 + 0.00883255i
\(567\) 0 0
\(568\) −0.757359 + 1.31178i −0.0317781 + 0.0550413i
\(569\) −6.58579 + 11.4069i −0.276091 + 0.478203i −0.970410 0.241464i \(-0.922372\pi\)
0.694319 + 0.719667i \(0.255706\pi\)
\(570\) 78.4264 3.28492
\(571\) 2.48528 4.30463i 0.104006 0.180143i −0.809326 0.587360i \(-0.800167\pi\)
0.913332 + 0.407217i \(0.133501\pi\)
\(572\) 32.6777 + 33.9596i 1.36632 + 1.41992i
\(573\) −10.9706 −0.458302
\(574\) 0 0
\(575\) −6.82843 11.8272i −0.284765 0.493228i
\(576\) 9.82843 0.409518
\(577\) 18.1569 31.4486i 0.755880 1.30922i −0.189056 0.981966i \(-0.560543\pi\)
0.944936 0.327256i \(-0.106124\pi\)
\(578\) −20.4853 35.4815i −0.852075 1.47584i
\(579\) 29.8995 1.24258
\(580\) 144.054 5.98151
\(581\) 0 0
\(582\) 8.82843 + 15.2913i 0.365950 + 0.633844i
\(583\) 5.12132 8.87039i 0.212103 0.367374i
\(584\) 1.44975 2.51104i 0.0599910 0.103907i
\(585\) −9.57107 9.94655i −0.395715 0.411239i
\(586\) −27.1066 46.9500i −1.11976 1.93949i
\(587\) 9.17157 + 15.8856i 0.378551 + 0.655670i 0.990852 0.134955i \(-0.0430890\pi\)
−0.612300 + 0.790625i \(0.709756\pi\)
\(588\) 0 0
\(589\) −16.2426 + 28.1331i −0.669266 + 1.15920i
\(590\) −8.12132 14.0665i −0.334349 0.579110i
\(591\) 6.48528 + 11.2328i 0.266769 + 0.462057i
\(592\) −11.2279 19.4473i −0.461465 0.799280i
\(593\) 15.6421 + 27.0930i 0.642346 + 1.11258i 0.984908 + 0.173080i \(0.0553719\pi\)
−0.342562 + 0.939495i \(0.611295\pi\)
\(594\) 23.3137 40.3805i 0.956573 1.65683i
\(595\) 0 0
\(596\) −5.74264 9.94655i −0.235228 0.407426i
\(597\) 13.4142 + 23.2341i 0.549007 + 0.950908i
\(598\) −8.53553 8.87039i −0.349044 0.362737i
\(599\) −19.8284 + 34.3438i −0.810168 + 1.40325i 0.102579 + 0.994725i \(0.467291\pi\)
−0.912746 + 0.408527i \(0.866043\pi\)
\(600\) −30.1421 + 52.2077i −1.23055 + 2.13137i
\(601\) 18.4706 + 31.9920i 0.753430 + 1.30498i 0.946151 + 0.323725i \(0.104935\pi\)
−0.192721 + 0.981254i \(0.561731\pi\)
\(602\) 0 0
\(603\) 4.24264 0.172774
\(604\) −72.6274 −2.95517
\(605\) −1.25736 2.17781i −0.0511189 0.0885406i
\(606\) −5.70711 + 9.88500i −0.231835 + 0.401551i
\(607\) −43.6569 −1.77198 −0.885989 0.463707i \(-0.846519\pi\)
−0.885989 + 0.463707i \(0.846519\pi\)
\(608\) −4.75736 8.23999i −0.192936 0.334176i
\(609\) 0 0
\(610\) −90.8406 −3.67803
\(611\) 19.1421 + 19.8931i 0.774408 + 0.804788i
\(612\) −0.328427 + 0.568852i −0.0132759 + 0.0229945i
\(613\) 24.7990 1.00162 0.500811 0.865557i \(-0.333035\pi\)
0.500811 + 0.865557i \(0.333035\pi\)
\(614\) −8.77817 + 15.2042i −0.354258 + 0.613593i
\(615\) 15.7782 27.3286i 0.636237 1.10200i
\(616\) 0 0
\(617\) 1.42893 2.47498i 0.0575266 0.0996391i −0.835828 0.548992i \(-0.815012\pi\)
0.893355 + 0.449352i \(0.148345\pi\)
\(618\) 47.7990 1.92276
\(619\) −5.22183 + 9.04447i −0.209883 + 0.363528i −0.951677 0.307099i \(-0.900642\pi\)
0.741795 + 0.670627i \(0.233975\pi\)
\(620\) −39.6777 68.7237i −1.59349 2.76001i
\(621\) −4.00000 + 6.92820i −0.160514 + 0.278019i
\(622\) −32.6777 56.5994i −1.31026 2.26943i
\(623\) 0 0
\(624\) −4.24264 + 14.6969i −0.169842 + 0.588348i
\(625\) −9.98528 17.2950i −0.399411 0.691801i
\(626\) 33.7990 1.35088
\(627\) −28.9706 −1.15697
\(628\) −43.9706 −1.75462
\(629\) −1.28427 −0.0512072
\(630\) 0 0
\(631\) 16.1421 27.9590i 0.642608 1.11303i −0.342240 0.939613i \(-0.611186\pi\)
0.984848 0.173418i \(-0.0554810\pi\)
\(632\) 22.6066 + 39.1558i 0.899242 + 1.55753i
\(633\) −0.514719 0.891519i −0.0204582 0.0354347i
\(634\) −51.5269 −2.04640
\(635\) 17.8284 30.8797i 0.707500 1.22543i
\(636\) 16.2426 0.644063
\(637\) 0 0
\(638\) −81.0122 −3.20730
\(639\) −0.171573 + 0.297173i −0.00678732 + 0.0117560i
\(640\) 78.6985 3.11083
\(641\) −12.3995 21.4766i −0.489751 0.848273i 0.510180 0.860068i \(-0.329579\pi\)
−0.999930 + 0.0117948i \(0.996246\pi\)
\(642\) 9.07107 + 15.7116i 0.358006 + 0.620085i
\(643\) −24.4853 + 42.4098i −0.965605 + 1.67248i −0.257625 + 0.966245i \(0.582940\pi\)
−0.707980 + 0.706232i \(0.750393\pi\)
\(644\) 0 0
\(645\) −3.17157 −0.124881
\(646\) 2.48528 0.0977821
\(647\) 5.31371 0.208903 0.104452 0.994530i \(-0.466691\pi\)
0.104452 + 0.994530i \(0.466691\pi\)
\(648\) 22.0711 0.867033
\(649\) 3.00000 + 5.19615i 0.117760 + 0.203967i
\(650\) −58.2843 60.5708i −2.28610 2.37578i
\(651\) 0 0
\(652\) −29.5061 51.1061i −1.15555 2.00147i
\(653\) 1.07107 1.85514i 0.0419141 0.0725974i −0.844307 0.535859i \(-0.819988\pi\)
0.886221 + 0.463262i \(0.153321\pi\)
\(654\) 4.00000 + 6.92820i 0.156412 + 0.270914i
\(655\) 2.51472 4.35562i 0.0982582 0.170188i
\(656\) 17.4853 0.682686
\(657\) 0.328427 0.568852i 0.0128132 0.0221930i
\(658\) 0 0
\(659\) −3.65685 + 6.33386i −0.142451 + 0.246732i −0.928419 0.371535i \(-0.878832\pi\)
0.785968 + 0.618267i \(0.212165\pi\)
\(660\) 35.3848 61.2882i 1.37735 2.38564i
\(661\) −4.85786 −0.188949 −0.0944745 0.995527i \(-0.530117\pi\)
−0.0944745 + 0.995527i \(0.530117\pi\)
\(662\) 34.8492 60.3607i 1.35445 2.34598i
\(663\) 0.606602 + 0.630399i 0.0235585 + 0.0244827i
\(664\) 57.6985 2.23914
\(665\) 0 0
\(666\) −9.03553 15.6500i −0.350120 0.606425i
\(667\) 13.8995 0.538191
\(668\) 35.8492 62.0927i 1.38705 2.40244i
\(669\) 1.41421 + 2.44949i 0.0546767 + 0.0947027i
\(670\) 39.2132 1.51494
\(671\) 33.5563 1.29543
\(672\) 0 0
\(673\) −15.7426 27.2671i −0.606834 1.05107i −0.991759 0.128120i \(-0.959106\pi\)
0.384925 0.922948i \(-0.374227\pi\)
\(674\) 16.2782 28.1946i 0.627012 1.08602i
\(675\) −27.3137 + 47.3087i −1.05131 + 1.82091i
\(676\) −42.1127 26.5241i −1.61972 1.02016i
\(677\) 3.17157 + 5.49333i 0.121893 + 0.211126i 0.920514 0.390709i \(-0.127770\pi\)
−0.798621 + 0.601834i \(0.794437\pi\)
\(678\) 3.94975 + 6.84116i 0.151689 + 0.262733i
\(679\) 0 0
\(680\) −1.44975 + 2.51104i −0.0555953 + 0.0962938i
\(681\) −9.82843 17.0233i −0.376626 0.652336i
\(682\) 22.3137 + 38.6485i 0.854436 + 1.47993i
\(683\) 8.65685 + 14.9941i 0.331245 + 0.573734i 0.982756 0.184905i \(-0.0591979\pi\)
−0.651511 + 0.758639i \(0.725865\pi\)
\(684\) 11.4853 + 19.8931i 0.439151 + 0.760631i
\(685\) 11.1569 19.3242i 0.426281 0.738341i
\(686\) 0 0
\(687\) 3.17157 + 5.49333i 0.121003 + 0.209583i
\(688\) −0.878680 1.52192i −0.0334993 0.0580226i
\(689\) −3.00000 + 10.3923i −0.114291 + 0.395915i
\(690\) −9.24264 + 16.0087i −0.351861 + 0.609442i
\(691\) 18.9706 32.8580i 0.721674 1.24998i −0.238654 0.971105i \(-0.576706\pi\)
0.960328 0.278872i \(-0.0899604\pi\)
\(692\) −34.7279 60.1505i −1.32016 2.28658i
\(693\) 0 0
\(694\) 62.5269 2.37349
\(695\) 30.2426 1.14717
\(696\) −30.6777 53.1353i −1.16283 2.01409i
\(697\) 0.500000 0.866025i 0.0189389 0.0328031i
\(698\) 32.1421 1.21660
\(699\) −2.00000 3.46410i −0.0756469 0.131024i
\(700\) 0 0
\(701\) 42.1421 1.59169 0.795843 0.605503i \(-0.207028\pi\)
0.795843 + 0.605503i \(0.207028\pi\)
\(702\) −13.6569 + 47.3087i −0.515445 + 1.78555i
\(703\) −22.4558 + 38.8947i −0.846938 + 1.46694i
\(704\) −33.5563 −1.26470
\(705\) 20.7279 35.9018i 0.780659 1.35214i
\(706\) 0.207107 0.358719i 0.00779457 0.0135006i
\(707\) 0 0
\(708\) −4.75736 + 8.23999i −0.178793 + 0.309678i
\(709\) −27.6274 −1.03757 −0.518785 0.854905i \(-0.673615\pi\)
−0.518785 + 0.854905i \(0.673615\pi\)
\(710\) −1.58579 + 2.74666i −0.0595135 + 0.103080i
\(711\) 5.12132 + 8.87039i 0.192065 + 0.332666i
\(712\) −16.1421 + 27.9590i −0.604952 + 1.04781i
\(713\) −3.82843 6.63103i −0.143376 0.248334i
\(714\) 0 0
\(715\) 32.6777 + 33.9596i 1.22208 + 1.27002i
\(716\) −10.8284 18.7554i −0.404677 0.700922i
\(717\) 17.5147 0.654099
\(718\) −40.9706 −1.52901
\(719\) −36.3848 −1.35692 −0.678462 0.734636i \(-0.737353\pi\)
−0.678462 + 0.734636i \(0.737353\pi\)
\(720\) −11.4853 −0.428031
\(721\) 0 0
\(722\) 20.5208 35.5431i 0.763706 1.32278i
\(723\) −1.05025 1.81909i −0.0390593 0.0676527i
\(724\) 36.6421 + 63.4660i 1.36179 + 2.35870i
\(725\) 94.9117 3.52493
\(726\) −1.12132 + 1.94218i −0.0416161 + 0.0720812i
\(727\) −8.97056 −0.332700 −0.166350 0.986067i \(-0.553198\pi\)
−0.166350 + 0.986067i \(0.553198\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) 3.03553 5.25770i 0.112350 0.194596i
\(731\) −0.100505 −0.00371731
\(732\) 26.6066 + 46.0840i 0.983408 + 1.70331i
\(733\) 10.5000 + 18.1865i 0.387826 + 0.671735i 0.992157 0.124999i \(-0.0398927\pi\)
−0.604331 + 0.796734i \(0.706559\pi\)
\(734\) −3.94975 + 6.84116i −0.145788 + 0.252512i
\(735\) 0 0
\(736\) 2.24264 0.0826648
\(737\) −14.4853 −0.533572
\(738\) 14.0711 0.517963
\(739\) 36.2843 1.33474 0.667369 0.744727i \(-0.267420\pi\)
0.667369 + 0.744727i \(0.267420\pi\)
\(740\) −54.8553 95.0122i −2.01652 3.49272i
\(741\) 29.6985 7.34847i 1.09100 0.269953i
\(742\) 0 0
\(743\) 23.7990 + 41.2211i 0.873100 + 1.51225i 0.858773 + 0.512357i \(0.171227\pi\)
0.0143275 + 0.999897i \(0.495439\pi\)
\(744\) −16.8995 + 29.2708i −0.619566 + 1.07312i
\(745\) −5.74264 9.94655i −0.210394 0.364413i
\(746\) −29.5208 + 51.1316i −1.08083 + 1.87206i
\(747\) 13.0711 0.478245
\(748\) 1.12132 1.94218i 0.0409995 0.0710133i
\(749\) 0 0
\(750\) −30.4350 + 52.7150i −1.11133 + 1.92488i
\(751\) −6.77817 + 11.7401i −0.247339 + 0.428404i −0.962787 0.270263i \(-0.912889\pi\)
0.715448 + 0.698666i \(0.246223\pi\)
\(752\) 22.9706 0.837650
\(753\) −7.75736 + 13.4361i −0.282694 + 0.489640i
\(754\) 83.0477 20.5490i 3.02442 0.748350i
\(755\) −72.6274 −2.64318
\(756\) 0 0
\(757\) 10.7279 + 18.5813i 0.389913 + 0.675349i 0.992437 0.122751i \(-0.0391718\pi\)
−0.602525 + 0.798100i \(0.705838\pi\)
\(758\) −19.8995 −0.722782
\(759\) 3.41421 5.91359i 0.123928 0.214650i
\(760\) 50.6985 + 87.8124i 1.83903 + 3.18529i
\(761\) 46.1421 1.67265 0.836326 0.548233i \(-0.184699\pi\)
0.836326 + 0.548233i \(0.184699\pi\)
\(762\) −31.7990 −1.15196
\(763\) 0 0
\(764\) −14.8492 25.7196i −0.537227 0.930504i
\(765\) −0.328427 + 0.568852i −0.0118743 + 0.0205669i
\(766\) 16.9497 29.3578i 0.612419 1.06074i
\(767\) −4.39340 4.56575i −0.158636 0.164860i
\(768\) −21.1924 36.7063i −0.764714 1.32452i
\(769\) −0.727922 1.26080i −0.0262495 0.0454655i 0.852602 0.522560i \(-0.175023\pi\)
−0.878852 + 0.477095i \(0.841690\pi\)
\(770\) 0 0
\(771\) 10.6066 18.3712i 0.381987 0.661622i
\(772\) 40.4706 + 70.0971i 1.45657 + 2.52285i
\(773\) −8.82843 15.2913i −0.317536 0.549989i 0.662437 0.749118i \(-0.269522\pi\)
−0.979973 + 0.199128i \(0.936189\pi\)
\(774\) −0.707107 1.22474i −0.0254164 0.0440225i
\(775\) −26.1421 45.2795i −0.939053 1.62649i
\(776\) −11.4142 + 19.7700i −0.409746 + 0.709702i
\(777\) 0 0
\(778\) −1.37868 2.38794i −0.0494281 0.0856119i
\(779\) −17.4853 30.2854i −0.626475 1.08509i
\(780\) −20.7279 + 71.8036i −0.742179 + 2.57098i
\(781\) 0.585786 1.01461i 0.0209611 0.0363057i
\(782\) −0.292893 + 0.507306i −0.0104738 + 0.0181412i
\(783\) −27.7990 48.1493i −0.993455 1.72071i
\(784\) 0 0
\(785\) −43.9706 −1.56938
\(786\) −4.48528 −0.159985
\(787\) −2.94975 5.10911i −0.105147 0.182120i 0.808651 0.588288i \(-0.200198\pi\)
−0.913798 + 0.406168i \(0.866865\pi\)
\(788\) −17.5563 + 30.4085i −0.625419 + 1.08326i
\(789\) −26.4853 −0.942901
\(790\) 47.3345 + 81.9858i 1.68409 + 2.91692i
\(791\) 0 0
\(792\) 15.0711 0.535527
\(793\) −34.3995 + 8.51167i −1.22156 + 0.302258i
\(794\) −46.6274 + 80.7611i −1.65475 + 2.86610i
\(795\) 16.2426 0.576067
\(796\) −36.3137 + 62.8972i −1.28711 + 2.22933i
\(797\) −5.07107 + 8.78335i −0.179626 + 0.311122i −0.941753 0.336306i \(-0.890822\pi\)
0.762126 + 0.647429i \(0.224156\pi\)
\(798\) 0 0
\(799\) 0.656854 1.13770i 0.0232378 0.0402491i
\(800\) 15.3137 0.541421
\(801\) −3.65685 + 6.33386i −0.129209 + 0.223796i
\(802\) −37.1777 64.3936i −1.31279 2.27382i
\(803\) −1.12132 + 1.94218i −0.0395705 + 0.0685382i
\(804\) −11.4853 19.8931i −0.405055 0.701575i
\(805\) 0 0
\(806\) −32.6777 33.9596i −1.15102 1.19618i
\(807\) −12.7279 22.0454i −0.448044 0.776035i
\(808\) −14.7574 −0.519162
\(809\) 6.85786 0.241110 0.120555 0.992707i \(-0.461533\pi\)
0.120555 + 0.992707i \(0.461533\pi\)
\(810\) 46.2132 1.62377
\(811\) 34.1838 1.20035 0.600177 0.799867i \(-0.295097\pi\)
0.600177 + 0.799867i \(0.295097\pi\)
\(812\) 0 0
\(813\) −4.89949 + 8.48617i −0.171833 + 0.297623i
\(814\) 30.8492 + 53.4325i 1.08127 + 1.87281i
\(815\) −29.5061 51.1061i −1.03355 1.79017i
\(816\) 0.727922 0.0254824
\(817\) −1.75736 + 3.04384i −0.0614822 + 0.106490i
\(818\) −28.8995 −1.01045
\(819\) 0 0
\(820\) 85.4264 2.98322
\(821\) −13.9706 + 24.1977i −0.487576 + 0.844506i −0.999898 0.0142871i \(-0.995452\pi\)
0.512322 + 0.858793i \(0.328785\pi\)
\(822\) −19.8995 −0.694075
\(823\) 1.65685 + 2.86976i 0.0577543 + 0.100033i 0.893457 0.449149i \(-0.148273\pi\)
−0.835703 + 0.549182i \(0.814939\pi\)
\(824\) 30.8995 + 53.5195i 1.07643 + 1.86444i
\(825\) 23.3137 40.3805i 0.811679 1.40587i
\(826\) 0 0
\(827\) 40.6690 1.41420 0.707101 0.707113i \(-0.250003\pi\)
0.707101 + 0.707113i \(0.250003\pi\)
\(828\) −5.41421 −0.188157
\(829\) 23.6863 0.822659 0.411329 0.911487i \(-0.365065\pi\)
0.411329 + 0.911487i \(0.365065\pi\)
\(830\) 120.811 4.19342
\(831\) −22.6066 39.1558i −0.784214 1.35830i
\(832\) 34.3995 8.51167i 1.19259 0.295089i
\(833\) 0 0
\(834\) −13.4853 23.3572i −0.466957 0.808793i
\(835\) 35.8492 62.0927i 1.24061 2.14881i
\(836\) −39.2132 67.9193i −1.35622 2.34904i
\(837\) −15.3137 + 26.5241i −0.529319 + 0.916808i
\(838\) −47.2132 −1.63095
\(839\) −18.7990 + 32.5608i −0.649013 + 1.12412i 0.334346 + 0.942450i \(0.391485\pi\)
−0.983359 + 0.181673i \(0.941849\pi\)
\(840\) 0 0
\(841\) −33.7990 + 58.5416i −1.16548 + 2.01867i
\(842\) 5.44975 9.43924i 0.187811 0.325298i
\(843\) 0.727922 0.0250710
\(844\) 1.39340 2.41344i 0.0479627 0.0830739i
\(845\) −42.1127 26.5241i −1.44872 0.912458i
\(846\) 18.4853 0.635537
\(847\) 0 0
\(848\) 4.50000 + 7.79423i 0.154531 + 0.267655i
\(849\) 0.142136 0.00487808
\(850\) −2.00000 + 3.46410i −0.0685994 + 0.118818i
\(851\) −5.29289 9.16756i −0.181438 0.314260i
\(852\) 1.85786 0.0636494
\(853\) −35.0000 −1.19838 −0.599189 0.800608i \(-0.704510\pi\)
−0.599189 + 0.800608i \(0.704510\pi\)
\(854\) 0 0
\(855\) 11.4853 + 19.8931i 0.392788 + 0.680329i
\(856\) −11.7279 + 20.3134i −0.400852 + 0.694296i
\(857\) −20.3995 + 35.3330i −0.696833 + 1.20695i 0.272725 + 0.962092i \(0.412075\pi\)
−0.969559 + 0.244859i \(0.921258\pi\)
\(858\) 11.6569 40.3805i 0.397958 1.37857i
\(859\) 13.5355 + 23.4442i 0.461826 + 0.799907i 0.999052 0.0435317i \(-0.0138610\pi\)
−0.537226 + 0.843439i \(0.680528\pi\)
\(860\) −4.29289 7.43551i −0.146386 0.253549i
\(861\) 0 0
\(862\) 14.4853 25.0892i 0.493371 0.854543i
\(863\) −28.0919 48.6566i −0.956259 1.65629i −0.731461 0.681883i \(-0.761161\pi\)
−0.224798 0.974405i \(-0.572172\pi\)
\(864\) −4.48528 7.76874i −0.152592 0.264298i
\(865\) −34.7279 60.1505i −1.18078 2.04518i
\(866\) 0.621320 + 1.07616i 0.0211133 + 0.0365694i
\(867\) −12.0000 + 20.7846i −0.407541 + 0.705882i
\(868\) 0 0
\(869\) −17.4853 30.2854i −0.593148 1.02736i
\(870\) −64.2340 111.257i −2.17774 3.77195i
\(871\) 14.8492 3.67423i 0.503147 0.124497i
\(872\) −5.17157 + 8.95743i −0.175132 + 0.303337i
\(873\) −2.58579 + 4.47871i −0.0875156 + 0.151581i
\(874\) 10.2426 + 17.7408i 0.346462 + 0.600091i
\(875\) 0 0
\(876\) −3.55635 −0.120158
\(877\) 17.0000 0.574049 0.287025 0.957923i \(-0.407334\pi\)
0.287025 + 0.957923i \(0.407334\pi\)
\(878\) −32.2635 55.8819i −1.08884 1.88592i
\(879\) −15.8787 + 27.5027i −0.535575 + 0.927642i
\(880\) 39.2132 1.32188
\(881\) 23.2279 + 40.2319i 0.782569 + 1.35545i 0.930441 + 0.366442i \(0.119424\pi\)
−0.147872 + 0.989006i \(0.547242\pi\)
\(882\) 0 0
\(883\) 7.95837 0.267820 0.133910 0.990993i \(-0.457247\pi\)
0.133910 + 0.990993i \(0.457247\pi\)
\(884\) −0.656854 + 2.27541i −0.0220924 + 0.0765303i
\(885\) −4.75736 + 8.23999i −0.159917 + 0.276984i
\(886\) −34.6274 −1.16333
\(887\) −5.31371 + 9.20361i −0.178417 + 0.309027i −0.941338 0.337464i \(-0.890431\pi\)
0.762922 + 0.646491i \(0.223764\pi\)
\(888\) −23.3640 + 40.4676i −0.784043 + 1.35800i
\(889\) 0 0
\(890\) −33.7990 + 58.5416i −1.13294 + 1.96232i
\(891\) −17.0711 −0.571902
\(892\) −3.82843 + 6.63103i −0.128185 + 0.222023i
\(893\) −22.9706 39.7862i −0.768681 1.33139i
\(894\) −5.12132 + 8.87039i −0.171283 + 0.296670i
\(895\) −10.8284 18.7554i −0.361954 0.626923i
\(896\) 0 0
\(897\) −2.00000 + 6.92820i −0.0667781 + 0.231326i
\(898\) 18.7279 + 32.4377i 0.624959 + 1.08246i
\(899\) 53.2132 1.77476
\(900\) −36.9706 −1.23235
\(901\) 0.514719 0.0171478
\(902\) −48.0416 −1.59961
\(903\) 0 0
\(904\) −5.10660 + 8.84489i −0.169843 + 0.294177i
\(905\) 36.6421 + 63.4660i 1.21803 + 2.10968i
\(906\) 32.3848 + 56.0921i 1.07591 + 1.86353i
\(907\) 18.7279 0.621850 0.310925 0.950434i \(-0.399361\pi\)
0.310925 + 0.950434i \(0.399361\pi\)
\(908\) 26.6066 46.0840i 0.882971 1.52935i
\(909\) −3.34315 −0.110885
\(910\) 0 0
\(911\) −18.3431 −0.607736 −0.303868 0.952714i \(-0.598278\pi\)
−0.303868 + 0.952714i \(0.598278\pi\)
\(912\) 12.7279 22.0454i 0.421464 0.729996i
\(913\) −44.6274 −1.47695
\(914\) −30.1777 52.2693i −0.998189 1.72891i
\(915\) 26.6066 + 46.0840i 0.879587 + 1.52349i
\(916\) −8.58579 + 14.8710i −0.283682 + 0.491352i
\(917\) 0 0
\(918\) 2.34315 0.0773353
\(919\) 25.3137 0.835022 0.417511 0.908672i \(-0.362902\pi\)
0.417511 + 0.908672i \(0.362902\pi\)
\(920\) −23.8995 −0.787943
\(921\) 10.2843 0.338878
\(922\) 15.2782 + 26.4626i 0.503160 + 0.871498i
\(923\) −0.343146 + 1.18869i −0.0112948 + 0.0391263i
\(924\) 0 0
\(925\) −36.1421 62.6000i −1.18835 2.05828i
\(926\) −22.6066 + 39.1558i −0.742899 + 1.28674i
\(927\) 7.00000 + 12.1244i 0.229910 + 0.398216i
\(928\) −7.79289 + 13.4977i −0.255814 + 0.443083i
\(929\) −18.9411 −0.621438 −0.310719 0.950502i \(-0.600570\pi\)
−0.310719 + 0.950502i \(0.600570\pi\)
\(930\) −35.3848 + 61.2882i −1.16031 + 2.00972i
\(931\) 0 0
\(932\) 5.41421 9.37769i 0.177348 0.307177i
\(933\) −19.1421 + 33.1552i −0.626685 + 1.08545i
\(934\) −20.7279 −0.678238
\(935\) 1.12132 1.94218i 0.0366711 0.0635162i
\(936\) −15.4497 + 3.82282i −0.504991 + 0.124953i
\(937\) −8.85786 −0.289374 −0.144687 0.989477i \(-0.546217\pi\)
−0.144687 + 0.989477i \(0.546217\pi\)
\(938\) 0 0
\(939\) −9.89949 17.1464i −0.323058 0.559553i
\(940\) 112.225 3.66039
\(941\) −9.51472 + 16.4800i −0.310171 + 0.537232i −0.978399 0.206724i \(-0.933720\pi\)
0.668228 + 0.743956i \(0.267053\pi\)
\(942\) 19.6066 + 33.9596i 0.638818 + 1.10646i
\(943\) 8.24264 0.268417
\(944\) −5.27208 −0.171592
\(945\) 0 0
\(946\) 2.41421 + 4.18154i 0.0784929 + 0.135954i
\(947\) −9.29289 + 16.0958i −0.301978 + 0.523042i −0.976584 0.215136i \(-0.930980\pi\)
0.674606 + 0.738178i \(0.264314\pi\)
\(948\) 27.7279 48.0262i 0.900561 1.55982i
\(949\) 0.656854 2.27541i 0.0213224 0.0738629i
\(950\) 69.9411 + 121.142i 2.26919 + 3.93035i
\(951\) 15.0919 + 26.1399i 0.489388 + 0.847645i
\(952\) 0 0
\(953\) 19.3137 33.4523i 0.625632 1.08363i −0.362786 0.931873i \(-0.618174\pi\)
0.988418 0.151755i \(-0.0484923\pi\)
\(954\) 3.62132 + 6.27231i 0.117245 + 0.203074i
\(955\) −14.8492 25.7196i −0.480510 0.832268i
\(956\) 23.7071 + 41.0619i 0.766743 + 1.32804i
\(957\) 23.7279 + 41.0980i 0.767015 + 1.32851i
\(958\) −46.3345 + 80.2537i −1.49700 + 2.59288i
\(959\) 0 0
\(960\) −26.6066 46.0840i −0.858724 1.48735i
\(961\) 0.843146 + 1.46037i 0.0271983 + 0.0471088i
\(962\) −45.1777 46.9500i −1.45659 1.51373i
\(963\) −2.65685 + 4.60181i −0.0856159 + 0.148291i
\(964\) 2.84315 4.92447i 0.0915716 0.158607i
\(965\) 40.4706 + 70.0971i 1.30279 + 2.25650i
\(966\) 0 0
\(967\) −28.2426 −0.908222 −0.454111 0.890945i \(-0.650043\pi\)
−0.454111 + 0.890945i \(0.650043\pi\)
\(968\) −2.89949 −0.0931933
\(969\) −0.727922 1.26080i −0.0233842 0.0405027i
\(970\) −23.8995 + 41.3951i −0.767367 + 1.32912i
\(971\) 40.3431 1.29467 0.647337 0.762204i \(-0.275883\pi\)
0.647337 + 0.762204i \(0.275883\pi\)
\(972\) 18.9497 + 32.8219i 0.607813 + 1.05276i
\(973\) 0 0
\(974\) −50.6274 −1.62221
\(975\) −13.6569 + 47.3087i −0.437369 + 1.51509i
\(976\) −14.7426 + 25.5350i −0.471900 + 0.817356i
\(977\) −48.5980 −1.55479 −0.777394 0.629015i \(-0.783459\pi\)
−0.777394 + 0.629015i \(0.783459\pi\)
\(978\) −26.3137 + 45.5767i −0.841420 + 1.45738i
\(979\) 12.4853 21.6251i 0.399031 0.691143i
\(980\) 0 0
\(981\) −1.17157 + 2.02922i −0.0374054 + 0.0647881i
\(982\) −85.2548 −2.72059
\(983\) 21.0000 36.3731i 0.669796 1.16012i −0.308165 0.951333i \(-0.599715\pi\)
0.977961 0.208788i \(-0.0669518\pi\)
\(984\) −18.1924 31.5101i −0.579952 1.00451i
\(985\) −17.5563 + 30.4085i −0.559392 + 0.968895i
\(986\) −2.03553 3.52565i −0.0648246 0.112280i
\(987\) 0 0
\(988\) 57.4264 + 59.6793i 1.82698 + 1.89865i
\(989\) −0.414214 0.717439i −0.0131712 0.0228132i
\(990\) 31.5563 1.00293
\(991\) 28.2426 0.897157 0.448579 0.893743i \(-0.351930\pi\)
0.448579 + 0.893743i \(0.351930\pi\)
\(992\) 8.58579 0.272599
\(993\) −40.8284 −1.29565
\(994\) 0 0
\(995\) −36.3137 + 62.8972i −1.15122 + 1.99397i
\(996\) −35.3848 61.2882i −1.12121 1.94199i
\(997\) 9.98528 + 17.2950i 0.316237 + 0.547739i 0.979700 0.200471i \(-0.0642472\pi\)
−0.663463 + 0.748209i \(0.730914\pi\)
\(998\) 67.6985 2.14296
\(999\) −21.1716 + 36.6702i −0.669839 + 1.16020i
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 637.2.g.f.263.2 4
7.2 even 3 637.2.h.b.471.1 4
7.3 odd 6 637.2.f.e.393.2 yes 4
7.4 even 3 637.2.f.f.393.2 yes 4
7.5 odd 6 637.2.h.c.471.1 4
7.6 odd 2 637.2.g.g.263.2 4
13.9 even 3 637.2.h.b.165.1 4
91.3 odd 6 8281.2.a.o.1.1 2
91.9 even 3 inner 637.2.g.f.373.2 4
91.10 odd 6 8281.2.a.y.1.2 2
91.48 odd 6 637.2.h.c.165.1 4
91.61 odd 6 637.2.g.g.373.2 4
91.74 even 3 637.2.f.f.295.2 yes 4
91.81 even 3 8281.2.a.p.1.1 2
91.87 odd 6 637.2.f.e.295.2 4
91.88 even 6 8281.2.a.x.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.f.e.295.2 4 91.87 odd 6
637.2.f.e.393.2 yes 4 7.3 odd 6
637.2.f.f.295.2 yes 4 91.74 even 3
637.2.f.f.393.2 yes 4 7.4 even 3
637.2.g.f.263.2 4 1.1 even 1 trivial
637.2.g.f.373.2 4 91.9 even 3 inner
637.2.g.g.263.2 4 7.6 odd 2
637.2.g.g.373.2 4 91.61 odd 6
637.2.h.b.165.1 4 13.9 even 3
637.2.h.b.471.1 4 7.2 even 3
637.2.h.c.165.1 4 91.48 odd 6
637.2.h.c.471.1 4 7.5 odd 6
8281.2.a.o.1.1 2 91.3 odd 6
8281.2.a.p.1.1 2 91.81 even 3
8281.2.a.x.1.2 2 91.88 even 6
8281.2.a.y.1.2 2 91.10 odd 6