Properties

Label 775.2.e.e.676.2
Level $775$
Weight $2$
Character 775.676
Analytic conductor $6.188$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [775,2,Mod(501,775)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(775, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("775.501");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 775.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: \(6.18840615665\)
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: no (minimal twist has level 31)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 676.2
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 775.676
Dual form 775.2.e.e.501.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.41421 q^{2} +(-1.20711 - 2.09077i) q^{3} +3.82843 q^{4} +(-2.91421 - 5.04757i) q^{6} +(1.20711 + 2.09077i) q^{7} +4.41421 q^{8} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\) \(q+2.41421 q^{2} +(-1.20711 - 2.09077i) q^{3} +3.82843 q^{4} +(-2.91421 - 5.04757i) q^{6} +(1.20711 + 2.09077i) q^{7} +4.41421 q^{8} +(-1.41421 + 2.44949i) q^{9} +(2.62132 - 4.54026i) q^{11} +(-4.62132 - 8.00436i) q^{12} +(0.914214 - 1.58346i) q^{13} +(2.91421 + 5.04757i) q^{14} +3.00000 q^{16} +(-0.0857864 - 0.148586i) q^{17} +(-3.41421 + 5.91359i) q^{18} +(-0.792893 - 1.37333i) q^{19} +(2.91421 - 5.04757i) q^{21} +(6.32843 - 10.9612i) q^{22} +4.00000 q^{23} +(-5.32843 - 9.22911i) q^{24} +(2.20711 - 3.82282i) q^{26} -0.414214 q^{27} +(4.62132 + 8.00436i) q^{28} -1.17157 q^{29} +(-5.00000 + 2.44949i) q^{31} -1.58579 q^{32} -12.6569 q^{33} +(-0.207107 - 0.358719i) q^{34} +(-5.41421 + 9.37769i) q^{36} +(0.500000 + 0.866025i) q^{37} +(-1.91421 - 3.31552i) q^{38} -4.41421 q^{39} +(-4.74264 + 8.21449i) q^{41} +(7.03553 - 12.1859i) q^{42} +(4.44975 + 7.70719i) q^{43} +(10.0355 - 17.3821i) q^{44} +9.65685 q^{46} +1.65685 q^{47} +(-3.62132 - 6.27231i) q^{48} +(0.585786 - 1.01461i) q^{49} +(-0.207107 + 0.358719i) q^{51} +(3.50000 - 6.06218i) q^{52} +(0.0857864 - 0.148586i) q^{53} -1.00000 q^{54} +(5.32843 + 9.22911i) q^{56} +(-1.91421 + 3.31552i) q^{57} -2.82843 q^{58} +(5.03553 + 8.72180i) q^{59} +2.82843 q^{61} +(-12.0711 + 5.91359i) q^{62} -6.82843 q^{63} -9.82843 q^{64} -30.5563 q^{66} +(-2.62132 + 4.54026i) q^{67} +(-0.328427 - 0.568852i) q^{68} +(-4.82843 - 8.36308i) q^{69} +(7.03553 - 12.1859i) q^{71} +(-6.24264 + 10.8126i) q^{72} +(1.91421 - 3.31552i) q^{73} +(1.20711 + 2.09077i) q^{74} +(-3.03553 - 5.25770i) q^{76} +12.6569 q^{77} -10.6569 q^{78} +(7.62132 + 13.2005i) q^{79} +(4.74264 + 8.21449i) q^{81} +(-11.4497 + 19.8315i) q^{82} +(2.03553 - 3.52565i) q^{83} +(11.1569 - 19.3242i) q^{84} +(10.7426 + 18.6068i) q^{86} +(1.41421 + 2.44949i) q^{87} +(11.5711 - 20.0417i) q^{88} -12.4853 q^{89} +4.41421 q^{91} +15.3137 q^{92} +(11.1569 + 7.49706i) q^{93} +4.00000 q^{94} +(1.91421 + 3.31552i) q^{96} -10.8284 q^{97} +(1.41421 - 2.44949i) q^{98} +(7.41421 + 12.8418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 6 q^{6} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 6 q^{6} + 2 q^{7} + 12 q^{8} + 2 q^{11} - 10 q^{12} - 2 q^{13} + 6 q^{14} + 12 q^{16} - 6 q^{17} - 8 q^{18} - 6 q^{19} + 6 q^{21} + 14 q^{22} + 16 q^{23} - 10 q^{24} + 6 q^{26} + 4 q^{27} + 10 q^{28} - 16 q^{29} - 20 q^{31} - 12 q^{32} - 28 q^{33} + 2 q^{34} - 16 q^{36} + 2 q^{37} - 2 q^{38} - 12 q^{39} - 2 q^{41} + 14 q^{42} - 2 q^{43} + 26 q^{44} + 16 q^{46} - 16 q^{47} - 6 q^{48} + 8 q^{49} + 2 q^{51} + 14 q^{52} + 6 q^{53} - 4 q^{54} + 10 q^{56} - 2 q^{57} + 6 q^{59} - 20 q^{62} - 16 q^{63} - 28 q^{64} - 60 q^{66} - 2 q^{67} + 10 q^{68} - 8 q^{69} + 14 q^{71} - 8 q^{72} + 2 q^{73} + 2 q^{74} + 2 q^{76} + 28 q^{77} - 20 q^{78} + 22 q^{79} + 2 q^{81} - 26 q^{82} - 6 q^{83} + 22 q^{84} + 26 q^{86} + 18 q^{88} - 16 q^{89} + 12 q^{91} + 16 q^{92} + 22 q^{93} + 16 q^{94} + 2 q^{96} - 32 q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/775\mathbb{Z}\right)^\times\).

\(n\) \(251\) \(652\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.41421 1.70711 0.853553 0.521005i \(-0.174443\pi\)
0.853553 + 0.521005i \(0.174443\pi\)
\(3\) −1.20711 2.09077i −0.696923 1.20711i −0.969528 0.244981i \(-0.921218\pi\)
0.272605 0.962126i \(-0.412115\pi\)
\(4\) 3.82843 1.91421
\(5\) 0 0
\(6\) −2.91421 5.04757i −1.18972 2.06066i
\(7\) 1.20711 + 2.09077i 0.456243 + 0.790237i 0.998759 0.0498090i \(-0.0158613\pi\)
−0.542515 + 0.840046i \(0.682528\pi\)
\(8\) 4.41421 1.56066
\(9\) −1.41421 + 2.44949i −0.471405 + 0.816497i
\(10\) 0 0
\(11\) 2.62132 4.54026i 0.790358 1.36894i −0.135388 0.990793i \(-0.543228\pi\)
0.925745 0.378147i \(-0.123439\pi\)
\(12\) −4.62132 8.00436i −1.33406 2.31066i
\(13\) 0.914214 1.58346i 0.253557 0.439174i −0.710945 0.703247i \(-0.751733\pi\)
0.964503 + 0.264073i \(0.0850661\pi\)
\(14\) 2.91421 + 5.04757i 0.778856 + 1.34902i
\(15\) 0 0
\(16\) 3.00000 0.750000
\(17\) −0.0857864 0.148586i −0.0208063 0.0360375i 0.855435 0.517911i \(-0.173290\pi\)
−0.876241 + 0.481873i \(0.839957\pi\)
\(18\) −3.41421 + 5.91359i −0.804738 + 1.39385i
\(19\) −0.792893 1.37333i −0.181902 0.315064i 0.760626 0.649190i \(-0.224892\pi\)
−0.942528 + 0.334126i \(0.891559\pi\)
\(20\) 0 0
\(21\) 2.91421 5.04757i 0.635934 1.10147i
\(22\) 6.32843 10.9612i 1.34923 2.33693i
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) −5.32843 9.22911i −1.08766 1.88388i
\(25\) 0 0
\(26\) 2.20711 3.82282i 0.432849 0.749717i
\(27\) −0.414214 −0.0797154
\(28\) 4.62132 + 8.00436i 0.873347 + 1.51268i
\(29\) −1.17157 −0.217556 −0.108778 0.994066i \(-0.534694\pi\)
−0.108778 + 0.994066i \(0.534694\pi\)
\(30\) 0 0
\(31\) −5.00000 + 2.44949i −0.898027 + 0.439941i
\(32\) −1.58579 −0.280330
\(33\) −12.6569 −2.20328
\(34\) −0.207107 0.358719i −0.0355185 0.0615199i
\(35\) 0 0
\(36\) −5.41421 + 9.37769i −0.902369 + 1.56295i
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −1.91421 3.31552i −0.310526 0.537848i
\(39\) −4.41421 −0.706840
\(40\) 0 0
\(41\) −4.74264 + 8.21449i −0.740676 + 1.28289i 0.211512 + 0.977375i \(0.432161\pi\)
−0.952188 + 0.305513i \(0.901172\pi\)
\(42\) 7.03553 12.1859i 1.08561 1.88033i
\(43\) 4.44975 + 7.70719i 0.678580 + 1.17534i 0.975409 + 0.220404i \(0.0707377\pi\)
−0.296828 + 0.954931i \(0.595929\pi\)
\(44\) 10.0355 17.3821i 1.51291 2.62044i
\(45\) 0 0
\(46\) 9.65685 1.42383
\(47\) 1.65685 0.241677 0.120839 0.992672i \(-0.461442\pi\)
0.120839 + 0.992672i \(0.461442\pi\)
\(48\) −3.62132 6.27231i −0.522693 0.905330i
\(49\) 0.585786 1.01461i 0.0836838 0.144945i
\(50\) 0 0
\(51\) −0.207107 + 0.358719i −0.0290008 + 0.0502308i
\(52\) 3.50000 6.06218i 0.485363 0.840673i
\(53\) 0.0857864 0.148586i 0.0117837 0.0204099i −0.860073 0.510170i \(-0.829582\pi\)
0.871857 + 0.489760i \(0.162916\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 5.32843 + 9.22911i 0.712041 + 1.23329i
\(57\) −1.91421 + 3.31552i −0.253544 + 0.439151i
\(58\) −2.82843 −0.371391
\(59\) 5.03553 + 8.72180i 0.655571 + 1.13548i 0.981750 + 0.190174i \(0.0609052\pi\)
−0.326180 + 0.945308i \(0.605761\pi\)
\(60\) 0 0
\(61\) 2.82843 0.362143 0.181071 0.983470i \(-0.442043\pi\)
0.181071 + 0.983470i \(0.442043\pi\)
\(62\) −12.0711 + 5.91359i −1.53303 + 0.751027i
\(63\) −6.82843 −0.860301
\(64\) −9.82843 −1.22855
\(65\) 0 0
\(66\) −30.5563 −3.76123
\(67\) −2.62132 + 4.54026i −0.320245 + 0.554681i −0.980539 0.196327i \(-0.937099\pi\)
0.660293 + 0.751008i \(0.270432\pi\)
\(68\) −0.328427 0.568852i −0.0398276 0.0689835i
\(69\) −4.82843 8.36308i −0.581274 1.00680i
\(70\) 0 0
\(71\) 7.03553 12.1859i 0.834964 1.44620i −0.0590953 0.998252i \(-0.518822\pi\)
0.894060 0.447948i \(-0.147845\pi\)
\(72\) −6.24264 + 10.8126i −0.735702 + 1.27427i
\(73\) 1.91421 3.31552i 0.224042 0.388052i −0.731990 0.681316i \(-0.761408\pi\)
0.956032 + 0.293264i \(0.0947415\pi\)
\(74\) 1.20711 + 2.09077i 0.140323 + 0.243047i
\(75\) 0 0
\(76\) −3.03553 5.25770i −0.348200 0.603099i
\(77\) 12.6569 1.44238
\(78\) −10.6569 −1.20665
\(79\) 7.62132 + 13.2005i 0.857466 + 1.48517i 0.874339 + 0.485316i \(0.161296\pi\)
−0.0168732 + 0.999858i \(0.505371\pi\)
\(80\) 0 0
\(81\) 4.74264 + 8.21449i 0.526960 + 0.912722i
\(82\) −11.4497 + 19.8315i −1.26441 + 2.19003i
\(83\) 2.03553 3.52565i 0.223429 0.386990i −0.732418 0.680855i \(-0.761608\pi\)
0.955847 + 0.293865i \(0.0949416\pi\)
\(84\) 11.1569 19.3242i 1.21731 2.10845i
\(85\) 0 0
\(86\) 10.7426 + 18.6068i 1.15841 + 2.00642i
\(87\) 1.41421 + 2.44949i 0.151620 + 0.262613i
\(88\) 11.5711 20.0417i 1.23348 2.13645i
\(89\) −12.4853 −1.32344 −0.661719 0.749752i \(-0.730173\pi\)
−0.661719 + 0.749752i \(0.730173\pi\)
\(90\) 0 0
\(91\) 4.41421 0.462735
\(92\) 15.3137 1.59656
\(93\) 11.1569 + 7.49706i 1.15691 + 0.777408i
\(94\) 4.00000 0.412568
\(95\) 0 0
\(96\) 1.91421 + 3.31552i 0.195369 + 0.338388i
\(97\) −10.8284 −1.09946 −0.549730 0.835342i \(-0.685269\pi\)
−0.549730 + 0.835342i \(0.685269\pi\)
\(98\) 1.41421 2.44949i 0.142857 0.247436i
\(99\) 7.41421 + 12.8418i 0.745157 + 1.29065i
\(100\) 0 0
\(101\) 8.48528 0.844317 0.422159 0.906522i \(-0.361273\pi\)
0.422159 + 0.906522i \(0.361273\pi\)
\(102\) −0.500000 + 0.866025i −0.0495074 + 0.0857493i
\(103\) −6.03553 + 10.4539i −0.594699 + 1.03005i 0.398890 + 0.916999i \(0.369395\pi\)
−0.993589 + 0.113050i \(0.963938\pi\)
\(104\) 4.03553 6.98975i 0.395717 0.685401i
\(105\) 0 0
\(106\) 0.207107 0.358719i 0.0201160 0.0348419i
\(107\) 4.79289 + 8.30153i 0.463346 + 0.802540i 0.999125 0.0418188i \(-0.0133152\pi\)
−0.535779 + 0.844358i \(0.679982\pi\)
\(108\) −1.58579 −0.152592
\(109\) −5.17157 −0.495347 −0.247673 0.968844i \(-0.579666\pi\)
−0.247673 + 0.968844i \(0.579666\pi\)
\(110\) 0 0
\(111\) 1.20711 2.09077i 0.114574 0.198447i
\(112\) 3.62132 + 6.27231i 0.342183 + 0.592678i
\(113\) 2.67157 4.62730i 0.251320 0.435300i −0.712569 0.701602i \(-0.752469\pi\)
0.963890 + 0.266302i \(0.0858019\pi\)
\(114\) −4.62132 + 8.00436i −0.432826 + 0.749677i
\(115\) 0 0
\(116\) −4.48528 −0.416448
\(117\) 2.58579 + 4.47871i 0.239056 + 0.414057i
\(118\) 12.1569 + 21.0563i 1.11913 + 1.93839i
\(119\) 0.207107 0.358719i 0.0189854 0.0328838i
\(120\) 0 0
\(121\) −8.24264 14.2767i −0.749331 1.29788i
\(122\) 6.82843 0.618217
\(123\) 22.8995 2.06478
\(124\) −19.1421 + 9.37769i −1.71901 + 0.842142i
\(125\) 0 0
\(126\) −16.4853 −1.46863
\(127\) −5.44975 9.43924i −0.483587 0.837597i 0.516235 0.856447i \(-0.327333\pi\)
−0.999822 + 0.0188496i \(0.994000\pi\)
\(128\) −20.5563 −1.81694
\(129\) 10.7426 18.6068i 0.945837 1.63824i
\(130\) 0 0
\(131\) 2.37868 + 4.11999i 0.207826 + 0.359966i 0.951030 0.309100i \(-0.100028\pi\)
−0.743203 + 0.669066i \(0.766694\pi\)
\(132\) −48.4558 −4.21754
\(133\) 1.91421 3.31552i 0.165983 0.287492i
\(134\) −6.32843 + 10.9612i −0.546693 + 0.946900i
\(135\) 0 0
\(136\) −0.378680 0.655892i −0.0324715 0.0562423i
\(137\) −3.74264 + 6.48244i −0.319755 + 0.553833i −0.980437 0.196834i \(-0.936934\pi\)
0.660681 + 0.750666i \(0.270267\pi\)
\(138\) −11.6569 20.1903i −0.992297 1.71871i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −2.00000 3.46410i −0.168430 0.291730i
\(142\) 16.9853 29.4194i 1.42537 2.46882i
\(143\) −4.79289 8.30153i −0.400802 0.694209i
\(144\) −4.24264 + 7.34847i −0.353553 + 0.612372i
\(145\) 0 0
\(146\) 4.62132 8.00436i 0.382463 0.662446i
\(147\) −2.82843 −0.233285
\(148\) 1.91421 + 3.31552i 0.157347 + 0.272534i
\(149\) −0.500000 0.866025i −0.0409616 0.0709476i 0.844818 0.535054i \(-0.179709\pi\)
−0.885779 + 0.464107i \(0.846375\pi\)
\(150\) 0 0
\(151\) −17.3137 −1.40897 −0.704485 0.709719i \(-0.748822\pi\)
−0.704485 + 0.709719i \(0.748822\pi\)
\(152\) −3.50000 6.06218i −0.283887 0.491708i
\(153\) 0.485281 0.0392327
\(154\) 30.5563 2.46230
\(155\) 0 0
\(156\) −16.8995 −1.35304
\(157\) −14.8284 −1.18344 −0.591719 0.806145i \(-0.701550\pi\)
−0.591719 + 0.806145i \(0.701550\pi\)
\(158\) 18.3995 + 31.8689i 1.46379 + 2.53535i
\(159\) −0.414214 −0.0328493
\(160\) 0 0
\(161\) 4.82843 + 8.36308i 0.380533 + 0.659103i
\(162\) 11.4497 + 19.8315i 0.899577 + 1.55811i
\(163\) 12.9706 1.01593 0.507966 0.861377i \(-0.330397\pi\)
0.507966 + 0.861377i \(0.330397\pi\)
\(164\) −18.1569 + 31.4486i −1.41781 + 2.45572i
\(165\) 0 0
\(166\) 4.91421 8.51167i 0.381417 0.660634i
\(167\) −4.27817 7.41002i −0.331055 0.573404i 0.651664 0.758508i \(-0.274071\pi\)
−0.982719 + 0.185104i \(0.940738\pi\)
\(168\) 12.8640 22.2810i 0.992476 1.71902i
\(169\) 4.82843 + 8.36308i 0.371417 + 0.643314i
\(170\) 0 0
\(171\) 4.48528 0.342998
\(172\) 17.0355 + 29.5064i 1.29895 + 2.24984i
\(173\) −7.15685 + 12.3960i −0.544126 + 0.942453i 0.454536 + 0.890728i \(0.349805\pi\)
−0.998661 + 0.0517246i \(0.983528\pi\)
\(174\) 3.41421 + 5.91359i 0.258831 + 0.448308i
\(175\) 0 0
\(176\) 7.86396 13.6208i 0.592768 1.02670i
\(177\) 12.1569 21.0563i 0.913765 1.58269i
\(178\) −30.1421 −2.25925
\(179\) 3.37868 + 5.85204i 0.252534 + 0.437402i 0.964223 0.265093i \(-0.0854026\pi\)
−0.711689 + 0.702495i \(0.752069\pi\)
\(180\) 0 0
\(181\) 5.15685 8.93193i 0.383306 0.663905i −0.608227 0.793763i \(-0.708119\pi\)
0.991533 + 0.129858i \(0.0414522\pi\)
\(182\) 10.6569 0.789939
\(183\) −3.41421 5.91359i −0.252386 0.437145i
\(184\) 17.6569 1.30168
\(185\) 0 0
\(186\) 26.9350 + 18.0995i 1.97497 + 1.32712i
\(187\) −0.899495 −0.0657776
\(188\) 6.34315 0.462621
\(189\) −0.500000 0.866025i −0.0363696 0.0629941i
\(190\) 0 0
\(191\) 0.550253 0.953065i 0.0398149 0.0689614i −0.845431 0.534084i \(-0.820657\pi\)
0.885246 + 0.465123i \(0.153990\pi\)
\(192\) 11.8640 + 20.5490i 0.856208 + 1.48300i
\(193\) −10.5711 18.3096i −0.760922 1.31796i −0.942376 0.334556i \(-0.891414\pi\)
0.181454 0.983399i \(-0.441920\pi\)
\(194\) −26.1421 −1.87690
\(195\) 0 0
\(196\) 2.24264 3.88437i 0.160189 0.277455i
\(197\) 1.74264 3.01834i 0.124158 0.215048i −0.797245 0.603655i \(-0.793710\pi\)
0.921404 + 0.388607i \(0.127044\pi\)
\(198\) 17.8995 + 31.0028i 1.27206 + 2.20328i
\(199\) −7.79289 + 13.4977i −0.552424 + 0.956826i 0.445675 + 0.895195i \(0.352964\pi\)
−0.998099 + 0.0616310i \(0.980370\pi\)
\(200\) 0 0
\(201\) 12.6569 0.892746
\(202\) 20.4853 1.44134
\(203\) −1.41421 2.44949i −0.0992583 0.171920i
\(204\) −0.792893 + 1.37333i −0.0555136 + 0.0961524i
\(205\) 0 0
\(206\) −14.5711 + 25.2378i −1.01521 + 1.75840i
\(207\) −5.65685 + 9.79796i −0.393179 + 0.681005i
\(208\) 2.74264 4.75039i 0.190168 0.329380i
\(209\) −8.31371 −0.575071
\(210\) 0 0
\(211\) −3.79289 6.56948i −0.261114 0.452262i 0.705425 0.708785i \(-0.250756\pi\)
−0.966538 + 0.256523i \(0.917423\pi\)
\(212\) 0.328427 0.568852i 0.0225565 0.0390689i
\(213\) −33.9706 −2.32762
\(214\) 11.5711 + 20.0417i 0.790982 + 1.37002i
\(215\) 0 0
\(216\) −1.82843 −0.124409
\(217\) −11.1569 7.49706i −0.757377 0.508933i
\(218\) −12.4853 −0.845610
\(219\) −9.24264 −0.624560
\(220\) 0 0
\(221\) −0.313708 −0.0211023
\(222\) 2.91421 5.04757i 0.195589 0.338770i
\(223\) 0.863961 + 1.49642i 0.0578551 + 0.100208i 0.893502 0.449059i \(-0.148241\pi\)
−0.835647 + 0.549266i \(0.814907\pi\)
\(224\) −1.91421 3.31552i −0.127899 0.221527i
\(225\) 0 0
\(226\) 6.44975 11.1713i 0.429031 0.743103i
\(227\) −7.79289 + 13.4977i −0.517232 + 0.895873i 0.482567 + 0.875859i \(0.339704\pi\)
−0.999800 + 0.0200140i \(0.993629\pi\)
\(228\) −7.32843 + 12.6932i −0.485337 + 0.840628i
\(229\) −5.74264 9.94655i −0.379484 0.657286i 0.611503 0.791242i \(-0.290565\pi\)
−0.990987 + 0.133956i \(0.957232\pi\)
\(230\) 0 0
\(231\) −15.2782 26.4626i −1.00523 1.74111i
\(232\) −5.17157 −0.339530
\(233\) 14.8284 0.971443 0.485721 0.874114i \(-0.338557\pi\)
0.485721 + 0.874114i \(0.338557\pi\)
\(234\) 6.24264 + 10.8126i 0.408094 + 0.706840i
\(235\) 0 0
\(236\) 19.2782 + 33.3908i 1.25490 + 2.17355i
\(237\) 18.3995 31.8689i 1.19518 2.07010i
\(238\) 0.500000 0.866025i 0.0324102 0.0561361i
\(239\) 6.37868 11.0482i 0.412602 0.714648i −0.582571 0.812780i \(-0.697953\pi\)
0.995173 + 0.0981314i \(0.0312865\pi\)
\(240\) 0 0
\(241\) −12.3284 21.3535i −0.794144 1.37550i −0.923381 0.383884i \(-0.874586\pi\)
0.129238 0.991614i \(-0.458747\pi\)
\(242\) −19.8995 34.4669i −1.27919 2.21562i
\(243\) 10.8284 18.7554i 0.694644 1.20316i
\(244\) 10.8284 0.693219
\(245\) 0 0
\(246\) 55.2843 3.52480
\(247\) −2.89949 −0.184490
\(248\) −22.0711 + 10.8126i −1.40151 + 0.686599i
\(249\) −9.82843 −0.622851
\(250\) 0 0
\(251\) −1.79289 3.10538i −0.113166 0.196010i 0.803879 0.594793i \(-0.202766\pi\)
−0.917045 + 0.398783i \(0.869433\pi\)
\(252\) −26.1421 −1.64680
\(253\) 10.4853 18.1610i 0.659204 1.14177i
\(254\) −13.1569 22.7883i −0.825534 1.42987i
\(255\) 0 0
\(256\) −29.9706 −1.87316
\(257\) −0.156854 + 0.271680i −0.00978430 + 0.0169469i −0.870876 0.491503i \(-0.836448\pi\)
0.861092 + 0.508450i \(0.169781\pi\)
\(258\) 25.9350 44.9208i 1.61464 2.79665i
\(259\) −1.20711 + 2.09077i −0.0750060 + 0.129914i
\(260\) 0 0
\(261\) 1.65685 2.86976i 0.102557 0.177633i
\(262\) 5.74264 + 9.94655i 0.354782 + 0.614500i
\(263\) 0.686292 0.0423185 0.0211593 0.999776i \(-0.493264\pi\)
0.0211593 + 0.999776i \(0.493264\pi\)
\(264\) −55.8701 −3.43856
\(265\) 0 0
\(266\) 4.62132 8.00436i 0.283351 0.490779i
\(267\) 15.0711 + 26.1039i 0.922334 + 1.59753i
\(268\) −10.0355 + 17.3821i −0.613018 + 1.06178i
\(269\) 15.9142 27.5642i 0.970307 1.68062i 0.275681 0.961249i \(-0.411097\pi\)
0.694626 0.719371i \(-0.255570\pi\)
\(270\) 0 0
\(271\) −23.3137 −1.41621 −0.708103 0.706109i \(-0.750449\pi\)
−0.708103 + 0.706109i \(0.750449\pi\)
\(272\) −0.257359 0.445759i −0.0156047 0.0270281i
\(273\) −5.32843 9.22911i −0.322491 0.558571i
\(274\) −9.03553 + 15.6500i −0.545857 + 0.945451i
\(275\) 0 0
\(276\) −18.4853 32.0174i −1.11268 1.92722i
\(277\) 14.1421 0.849719 0.424859 0.905259i \(-0.360324\pi\)
0.424859 + 0.905259i \(0.360324\pi\)
\(278\) 0 0
\(279\) 1.07107 15.7116i 0.0641232 0.940626i
\(280\) 0 0
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) −4.82843 8.36308i −0.287529 0.498014i
\(283\) 2.34315 0.139286 0.0696428 0.997572i \(-0.477814\pi\)
0.0696428 + 0.997572i \(0.477814\pi\)
\(284\) 26.9350 46.6528i 1.59830 2.76834i
\(285\) 0 0
\(286\) −11.5711 20.0417i −0.684212 1.18509i
\(287\) −22.8995 −1.35171
\(288\) 2.24264 3.88437i 0.132149 0.228889i
\(289\) 8.48528 14.6969i 0.499134 0.864526i
\(290\) 0 0
\(291\) 13.0711 + 22.6398i 0.766240 + 1.32717i
\(292\) 7.32843 12.6932i 0.428864 0.742814i
\(293\) −12.3995 21.4766i −0.724386 1.25467i −0.959226 0.282640i \(-0.908790\pi\)
0.234840 0.972034i \(-0.424543\pi\)
\(294\) −6.82843 −0.398242
\(295\) 0 0
\(296\) 2.20711 + 3.82282i 0.128285 + 0.222197i
\(297\) −1.08579 + 1.88064i −0.0630037 + 0.109126i
\(298\) −1.20711 2.09077i −0.0699258 0.121115i
\(299\) 3.65685 6.33386i 0.211481 0.366296i
\(300\) 0 0
\(301\) −10.7426 + 18.6068i −0.619196 + 1.07248i
\(302\) −41.7990 −2.40526
\(303\) −10.2426 17.7408i −0.588424 1.01918i
\(304\) −2.37868 4.11999i −0.136427 0.236298i
\(305\) 0 0
\(306\) 1.17157 0.0669744
\(307\) −1.37868 2.38794i −0.0786854 0.136287i 0.823998 0.566593i \(-0.191739\pi\)
−0.902683 + 0.430306i \(0.858406\pi\)
\(308\) 48.4558 2.76103
\(309\) 29.1421 1.65784
\(310\) 0 0
\(311\) −11.3137 −0.641542 −0.320771 0.947157i \(-0.603942\pi\)
−0.320771 + 0.947157i \(0.603942\pi\)
\(312\) −19.4853 −1.10314
\(313\) 1.91421 + 3.31552i 0.108198 + 0.187404i 0.915040 0.403363i \(-0.132159\pi\)
−0.806842 + 0.590767i \(0.798825\pi\)
\(314\) −35.7990 −2.02025
\(315\) 0 0
\(316\) 29.1777 + 50.5372i 1.64137 + 2.84294i
\(317\) −1.08579 1.88064i −0.0609838 0.105627i 0.833922 0.551883i \(-0.186090\pi\)
−0.894905 + 0.446256i \(0.852757\pi\)
\(318\) −1.00000 −0.0560772
\(319\) −3.07107 + 5.31925i −0.171947 + 0.297821i
\(320\) 0 0
\(321\) 11.5711 20.0417i 0.645834 1.11862i
\(322\) 11.6569 + 20.1903i 0.649611 + 1.12516i
\(323\) −0.136039 + 0.235626i −0.00756941 + 0.0131106i
\(324\) 18.1569 + 31.4486i 1.00871 + 1.74714i
\(325\) 0 0
\(326\) 31.3137 1.73431
\(327\) 6.24264 + 10.8126i 0.345219 + 0.597937i
\(328\) −20.9350 + 36.2605i −1.15594 + 2.00215i
\(329\) 2.00000 + 3.46410i 0.110264 + 0.190982i
\(330\) 0 0
\(331\) −0.378680 + 0.655892i −0.0208141 + 0.0360511i −0.876245 0.481866i \(-0.839959\pi\)
0.855431 + 0.517917i \(0.173292\pi\)
\(332\) 7.79289 13.4977i 0.427691 0.740782i
\(333\) −2.82843 −0.154997
\(334\) −10.3284 17.8894i −0.565146 0.978862i
\(335\) 0 0
\(336\) 8.74264 15.1427i 0.476950 0.826102i
\(337\) 13.3137 0.725244 0.362622 0.931936i \(-0.381882\pi\)
0.362622 + 0.931936i \(0.381882\pi\)
\(338\) 11.6569 + 20.1903i 0.634049 + 1.09821i
\(339\) −12.8995 −0.700604
\(340\) 0 0
\(341\) −1.98528 + 29.1222i −0.107509 + 1.57706i
\(342\) 10.8284 0.585534
\(343\) 19.7279 1.06521
\(344\) 19.6421 + 34.0212i 1.05903 + 1.83430i
\(345\) 0 0
\(346\) −17.2782 + 29.9267i −0.928880 + 1.60887i
\(347\) 11.2782 + 19.5344i 0.605444 + 1.04866i 0.991981 + 0.126386i \(0.0403378\pi\)
−0.386537 + 0.922274i \(0.626329\pi\)
\(348\) 5.41421 + 9.37769i 0.290232 + 0.502697i
\(349\) 35.1127 1.87954 0.939770 0.341808i \(-0.111039\pi\)
0.939770 + 0.341808i \(0.111039\pi\)
\(350\) 0 0
\(351\) −0.378680 + 0.655892i −0.0202124 + 0.0350089i
\(352\) −4.15685 + 7.19988i −0.221561 + 0.383755i
\(353\) 1.50000 + 2.59808i 0.0798369 + 0.138282i 0.903179 0.429263i \(-0.141227\pi\)
−0.823343 + 0.567545i \(0.807893\pi\)
\(354\) 29.3492 50.8344i 1.55989 2.70182i
\(355\) 0 0
\(356\) −47.7990 −2.53334
\(357\) −1.00000 −0.0529256
\(358\) 8.15685 + 14.1281i 0.431103 + 0.746693i
\(359\) −13.4497 + 23.2956i −0.709851 + 1.22950i 0.255062 + 0.966925i \(0.417904\pi\)
−0.964912 + 0.262572i \(0.915429\pi\)
\(360\) 0 0
\(361\) 8.24264 14.2767i 0.433823 0.751404i
\(362\) 12.4497 21.5636i 0.654344 1.13336i
\(363\) −19.8995 + 34.4669i −1.04445 + 1.80904i
\(364\) 16.8995 0.885774
\(365\) 0 0
\(366\) −8.24264 14.2767i −0.430850 0.746254i
\(367\) 9.10660 15.7731i 0.475361 0.823349i −0.524241 0.851570i \(-0.675651\pi\)
0.999602 + 0.0282210i \(0.00898422\pi\)
\(368\) 12.0000 0.625543
\(369\) −13.4142 23.2341i −0.698316 1.20952i
\(370\) 0 0
\(371\) 0.414214 0.0215049
\(372\) 42.7132 + 28.7019i 2.21458 + 1.48813i
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) −2.17157 −0.112289
\(375\) 0 0
\(376\) 7.31371 0.377176
\(377\) −1.07107 + 1.85514i −0.0551628 + 0.0955448i
\(378\) −1.20711 2.09077i −0.0620869 0.107538i
\(379\) 14.6924 + 25.4480i 0.754697 + 1.30717i 0.945525 + 0.325550i \(0.105550\pi\)
−0.190827 + 0.981624i \(0.561117\pi\)
\(380\) 0 0
\(381\) −13.1569 + 22.7883i −0.674046 + 1.16748i
\(382\) 1.32843 2.30090i 0.0679682 0.117724i
\(383\) 12.4497 21.5636i 0.636152 1.10185i −0.350117 0.936706i \(-0.613858\pi\)
0.986270 0.165142i \(-0.0528084\pi\)
\(384\) 24.8137 + 42.9786i 1.26627 + 2.19324i
\(385\) 0 0
\(386\) −25.5208 44.2033i −1.29898 2.24989i
\(387\) −25.1716 −1.27954
\(388\) −41.4558 −2.10460
\(389\) −8.57107 14.8455i −0.434570 0.752698i 0.562690 0.826668i \(-0.309766\pi\)
−0.997260 + 0.0739699i \(0.976433\pi\)
\(390\) 0 0
\(391\) −0.343146 0.594346i −0.0173536 0.0300574i
\(392\) 2.58579 4.47871i 0.130602 0.226209i
\(393\) 5.74264 9.94655i 0.289678 0.501737i
\(394\) 4.20711 7.28692i 0.211951 0.367110i
\(395\) 0 0
\(396\) 28.3848 + 49.1639i 1.42639 + 2.47058i
\(397\) −8.25736 14.3022i −0.414425 0.717805i 0.580943 0.813944i \(-0.302684\pi\)
−0.995368 + 0.0961392i \(0.969351\pi\)
\(398\) −18.8137 + 32.5863i −0.943046 + 1.63340i
\(399\) −9.24264 −0.462711
\(400\) 0 0
\(401\) −21.1716 −1.05726 −0.528629 0.848853i \(-0.677294\pi\)
−0.528629 + 0.848853i \(0.677294\pi\)
\(402\) 30.5563 1.52401
\(403\) −0.692388 + 10.1567i −0.0344903 + 0.505940i
\(404\) 32.4853 1.61620
\(405\) 0 0
\(406\) −3.41421 5.91359i −0.169445 0.293487i
\(407\) 5.24264 0.259868
\(408\) −0.914214 + 1.58346i −0.0452603 + 0.0783932i
\(409\) −4.67157 8.09140i −0.230994 0.400094i 0.727107 0.686525i \(-0.240865\pi\)
−0.958101 + 0.286431i \(0.907531\pi\)
\(410\) 0 0
\(411\) 18.0711 0.891380
\(412\) −23.1066 + 40.0218i −1.13838 + 1.97173i
\(413\) −12.1569 + 21.0563i −0.598200 + 1.03611i
\(414\) −13.6569 + 23.6544i −0.671198 + 1.16255i
\(415\) 0 0
\(416\) −1.44975 + 2.51104i −0.0710797 + 0.123114i
\(417\) 0 0
\(418\) −20.0711 −0.981708
\(419\) 28.0000 1.36789 0.683945 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 0 0
\(421\) 1.42893 2.47498i 0.0696419 0.120623i −0.829102 0.559098i \(-0.811148\pi\)
0.898744 + 0.438474i \(0.144481\pi\)
\(422\) −9.15685 15.8601i −0.445749 0.772059i
\(423\) −2.34315 + 4.05845i −0.113928 + 0.197328i
\(424\) 0.378680 0.655892i 0.0183903 0.0318530i
\(425\) 0 0
\(426\) −82.0122 −3.97350
\(427\) 3.41421 + 5.91359i 0.165225 + 0.286179i
\(428\) 18.3492 + 31.7818i 0.886944 + 1.53623i
\(429\) −11.5711 + 20.0417i −0.558656 + 0.967621i
\(430\) 0 0
\(431\) 12.6213 + 21.8608i 0.607948 + 1.05300i 0.991578 + 0.129510i \(0.0413403\pi\)
−0.383631 + 0.923487i \(0.625326\pi\)
\(432\) −1.24264 −0.0597866
\(433\) 35.1127 1.68741 0.843704 0.536808i \(-0.180370\pi\)
0.843704 + 0.536808i \(0.180370\pi\)
\(434\) −26.9350 18.0995i −1.29292 0.868803i
\(435\) 0 0
\(436\) −19.7990 −0.948200
\(437\) −3.17157 5.49333i −0.151717 0.262781i
\(438\) −22.3137 −1.06619
\(439\) 6.03553 10.4539i 0.288060 0.498935i −0.685286 0.728274i \(-0.740323\pi\)
0.973347 + 0.229339i \(0.0736563\pi\)
\(440\) 0 0
\(441\) 1.65685 + 2.86976i 0.0788978 + 0.136655i
\(442\) −0.757359 −0.0360239
\(443\) −6.62132 + 11.4685i −0.314588 + 0.544883i −0.979350 0.202173i \(-0.935200\pi\)
0.664761 + 0.747056i \(0.268533\pi\)
\(444\) 4.62132 8.00436i 0.219318 0.379870i
\(445\) 0 0
\(446\) 2.08579 + 3.61269i 0.0987649 + 0.171066i
\(447\) −1.20711 + 2.09077i −0.0570942 + 0.0988900i
\(448\) −11.8640 20.5490i −0.560519 0.970848i
\(449\) 4.62742 0.218381 0.109191 0.994021i \(-0.465174\pi\)
0.109191 + 0.994021i \(0.465174\pi\)
\(450\) 0 0
\(451\) 24.8640 + 43.0656i 1.17080 + 2.02788i
\(452\) 10.2279 17.7153i 0.481081 0.833257i
\(453\) 20.8995 + 36.1990i 0.981944 + 1.70078i
\(454\) −18.8137 + 32.5863i −0.882971 + 1.52935i
\(455\) 0 0
\(456\) −8.44975 + 14.6354i −0.395696 + 0.685365i
\(457\) −31.1127 −1.45539 −0.727695 0.685901i \(-0.759409\pi\)
−0.727695 + 0.685901i \(0.759409\pi\)
\(458\) −13.8640 24.0131i −0.647820 1.12206i
\(459\) 0.0355339 + 0.0615465i 0.00165858 + 0.00287275i
\(460\) 0 0
\(461\) 26.1421 1.21756 0.608780 0.793339i \(-0.291659\pi\)
0.608780 + 0.793339i \(0.291659\pi\)
\(462\) −36.8848 63.8863i −1.71604 2.97226i
\(463\) −24.9706 −1.16048 −0.580240 0.814445i \(-0.697041\pi\)
−0.580240 + 0.814445i \(0.697041\pi\)
\(464\) −3.51472 −0.163167
\(465\) 0 0
\(466\) 35.7990 1.65836
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 9.89949 + 17.1464i 0.457604 + 0.792594i
\(469\) −12.6569 −0.584439
\(470\) 0 0
\(471\) 17.8995 + 31.0028i 0.824765 + 1.42854i
\(472\) 22.2279 + 38.4999i 1.02312 + 1.77210i
\(473\) 46.6569 2.14528
\(474\) 44.4203 76.9382i 2.04029 3.53389i
\(475\) 0 0
\(476\) 0.792893 1.37333i 0.0363422 0.0629465i
\(477\) 0.242641 + 0.420266i 0.0111098 + 0.0192427i
\(478\) 15.3995 26.6727i 0.704357 1.21998i
\(479\) −4.86396 8.42463i −0.222240 0.384931i 0.733248 0.679962i \(-0.238004\pi\)
−0.955488 + 0.295030i \(0.904670\pi\)
\(480\) 0 0
\(481\) 1.82843 0.0833691
\(482\) −29.7635 51.5518i −1.35569 2.34812i
\(483\) 11.6569 20.1903i 0.530405 0.918689i
\(484\) −31.5563 54.6572i −1.43438 2.48442i
\(485\) 0 0
\(486\) 26.1421 45.2795i 1.18583 2.05392i
\(487\) −8.69239 + 15.0557i −0.393890 + 0.682237i −0.992959 0.118460i \(-0.962204\pi\)
0.599069 + 0.800697i \(0.295537\pi\)
\(488\) 12.4853 0.565182
\(489\) −15.6569 27.1185i −0.708027 1.22634i
\(490\) 0 0
\(491\) −2.20711 + 3.82282i −0.0996053 + 0.172522i −0.911521 0.411253i \(-0.865091\pi\)
0.811916 + 0.583774i \(0.198425\pi\)
\(492\) 87.6690 3.95243
\(493\) 0.100505 + 0.174080i 0.00452652 + 0.00784016i
\(494\) −7.00000 −0.314945
\(495\) 0 0
\(496\) −15.0000 + 7.34847i −0.673520 + 0.329956i
\(497\) 33.9706 1.52379
\(498\) −23.7279 −1.06327
\(499\) −20.1066 34.8257i −0.900095 1.55901i −0.827369 0.561659i \(-0.810163\pi\)
−0.0727259 0.997352i \(-0.523170\pi\)
\(500\) 0 0
\(501\) −10.3284 + 17.8894i −0.461440 + 0.799238i
\(502\) −4.32843 7.49706i −0.193187 0.334610i
\(503\) 11.6924 + 20.2518i 0.521338 + 0.902984i 0.999692 + 0.0248166i \(0.00790018\pi\)
−0.478354 + 0.878167i \(0.658766\pi\)
\(504\) −30.1421 −1.34264
\(505\) 0 0
\(506\) 25.3137 43.8446i 1.12533 1.94913i
\(507\) 11.6569 20.1903i 0.517699 0.896681i
\(508\) −20.8640 36.1374i −0.925689 1.60334i
\(509\) −3.39949 + 5.88810i −0.150680 + 0.260985i −0.931478 0.363799i \(-0.881480\pi\)
0.780798 + 0.624784i \(0.214813\pi\)
\(510\) 0 0
\(511\) 9.24264 0.408870
\(512\) −31.2426 −1.38074
\(513\) 0.328427 + 0.568852i 0.0145004 + 0.0251154i
\(514\) −0.378680 + 0.655892i −0.0167028 + 0.0289302i
\(515\) 0 0
\(516\) 41.1274 71.2348i 1.81053 3.13594i
\(517\) 4.34315 7.52255i 0.191011 0.330841i
\(518\) −2.91421 + 5.04757i −0.128043 + 0.221777i
\(519\) 34.5563 1.51686
\(520\) 0 0
\(521\) −15.2279 26.3755i −0.667147 1.15553i −0.978698 0.205304i \(-0.934182\pi\)
0.311551 0.950229i \(-0.399152\pi\)
\(522\) 4.00000 6.92820i 0.175075 0.303239i
\(523\) 8.00000 0.349816 0.174908 0.984585i \(-0.444037\pi\)
0.174908 + 0.984585i \(0.444037\pi\)
\(524\) 9.10660 + 15.7731i 0.397824 + 0.689051i
\(525\) 0 0
\(526\) 1.65685 0.0722423
\(527\) 0.792893 + 0.532799i 0.0345390 + 0.0232091i
\(528\) −37.9706 −1.65246
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) −28.4853 −1.23616
\(532\) 7.32843 12.6932i 0.317728 0.550320i
\(533\) 8.67157 + 15.0196i 0.375608 + 0.650571i
\(534\) 36.3848 + 63.0203i 1.57452 + 2.72715i
\(535\) 0 0
\(536\) −11.5711 + 20.0417i −0.499794 + 0.865669i
\(537\) 8.15685 14.1281i 0.351994 0.609672i
\(538\) 38.4203 66.5459i 1.65642 2.86900i
\(539\) −3.07107 5.31925i −0.132280 0.229116i
\(540\) 0 0
\(541\) −12.6421 21.8968i −0.543528 0.941418i −0.998698 0.0510134i \(-0.983755\pi\)
0.455170 0.890405i \(-0.349578\pi\)
\(542\) −56.2843 −2.41762
\(543\) −24.8995 −1.06854
\(544\) 0.136039 + 0.235626i 0.00583262 + 0.0101024i
\(545\) 0 0
\(546\) −12.8640 22.2810i −0.550527 0.953540i
\(547\) 2.86396 4.96053i 0.122454 0.212097i −0.798281 0.602285i \(-0.794257\pi\)
0.920735 + 0.390189i \(0.127590\pi\)
\(548\) −14.3284 + 24.8176i −0.612080 + 1.06015i
\(549\) −4.00000 + 6.92820i −0.170716 + 0.295689i
\(550\) 0 0
\(551\) 0.928932 + 1.60896i 0.0395738 + 0.0685439i
\(552\) −21.3137 36.9164i −0.907172 1.57127i
\(553\) −18.3995 + 31.8689i −0.782426 + 1.35520i
\(554\) 34.1421 1.45056
\(555\) 0 0
\(556\) 0 0
\(557\) −44.4853 −1.88490 −0.942451 0.334344i \(-0.891485\pi\)
−0.942451 + 0.334344i \(0.891485\pi\)
\(558\) 2.58579 37.9310i 0.109465 1.60575i
\(559\) 16.2721 0.688236
\(560\) 0 0
\(561\) 1.08579 + 1.88064i 0.0458419 + 0.0794006i
\(562\) 4.82843 0.203675
\(563\) 2.37868 4.11999i 0.100249 0.173637i −0.811538 0.584300i \(-0.801369\pi\)
0.911787 + 0.410663i \(0.134703\pi\)
\(564\) −7.65685 13.2621i −0.322412 0.558433i
\(565\) 0 0
\(566\) 5.65685 0.237775
\(567\) −11.4497 + 19.8315i −0.480844 + 0.832847i
\(568\) 31.0563 53.7912i 1.30310 2.25703i
\(569\) −7.57107 + 13.1135i −0.317396 + 0.549745i −0.979944 0.199274i \(-0.936142\pi\)
0.662548 + 0.749019i \(0.269475\pi\)
\(570\) 0 0
\(571\) 20.4497 35.4200i 0.855795 1.48228i −0.0201099 0.999798i \(-0.506402\pi\)
0.875905 0.482483i \(-0.160265\pi\)
\(572\) −18.3492 31.7818i −0.767220 1.32886i
\(573\) −2.65685 −0.110992
\(574\) −55.2843 −2.30752
\(575\) 0 0
\(576\) 13.8995 24.0746i 0.579146 1.00311i
\(577\) −16.9853 29.4194i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(578\) 20.4853 35.4815i 0.852075 1.47584i
\(579\) −25.5208 + 44.2033i −1.06061 + 1.83703i
\(580\) 0 0
\(581\) 9.82843 0.407752
\(582\) 31.5563 + 54.6572i 1.30805 + 2.26561i
\(583\) −0.449747 0.778985i −0.0186266 0.0322623i
\(584\) 8.44975 14.6354i 0.349653 0.605617i
\(585\) 0 0
\(586\) −29.9350 51.8490i −1.23660 2.14186i
\(587\) 20.3431 0.839651 0.419826 0.907605i \(-0.362091\pi\)
0.419826 + 0.907605i \(0.362091\pi\)
\(588\) −10.8284 −0.446557
\(589\) 7.32843 + 4.92447i 0.301963 + 0.202909i
\(590\) 0 0
\(591\) −8.41421 −0.346114
\(592\) 1.50000 + 2.59808i 0.0616496 + 0.106780i
\(593\) −21.3137 −0.875249 −0.437625 0.899158i \(-0.644180\pi\)
−0.437625 + 0.899158i \(0.644180\pi\)
\(594\) −2.62132 + 4.54026i −0.107554 + 0.186289i
\(595\) 0 0
\(596\) −1.91421 3.31552i −0.0784092 0.135809i
\(597\) 37.6274 1.53999
\(598\) 8.82843 15.2913i 0.361021 0.625307i
\(599\) −17.4497 + 30.2238i −0.712977 + 1.23491i 0.250757 + 0.968050i \(0.419320\pi\)
−0.963734 + 0.266863i \(0.914013\pi\)
\(600\) 0 0
\(601\) 11.7426 + 20.3389i 0.478992 + 0.829639i 0.999710 0.0240900i \(-0.00766884\pi\)
−0.520717 + 0.853729i \(0.674336\pi\)
\(602\) −25.9350 + 44.9208i −1.05703 + 1.83083i
\(603\) −7.41421 12.8418i −0.301930 0.522958i
\(604\) −66.2843 −2.69707
\(605\) 0 0
\(606\) −24.7279 42.8300i −1.00450 1.73985i
\(607\) −2.20711 + 3.82282i −0.0895837 + 0.155164i −0.907335 0.420408i \(-0.861887\pi\)
0.817752 + 0.575571i \(0.195220\pi\)
\(608\) 1.25736 + 2.17781i 0.0509927 + 0.0883219i
\(609\) −3.41421 + 5.91359i −0.138351 + 0.239631i
\(610\) 0 0
\(611\) 1.51472 2.62357i 0.0612790 0.106138i
\(612\) 1.85786 0.0750997
\(613\) −5.15685 8.93193i −0.208283 0.360757i 0.742890 0.669413i \(-0.233454\pi\)
−0.951174 + 0.308656i \(0.900121\pi\)
\(614\) −3.32843 5.76500i −0.134324 0.232657i
\(615\) 0 0
\(616\) 55.8701 2.25107
\(617\) 11.6421 + 20.1648i 0.468695 + 0.811803i 0.999360 0.0357786i \(-0.0113911\pi\)
−0.530665 + 0.847582i \(0.678058\pi\)
\(618\) 70.3553 2.83011
\(619\) −31.6569 −1.27240 −0.636198 0.771526i \(-0.719494\pi\)
−0.636198 + 0.771526i \(0.719494\pi\)
\(620\) 0 0
\(621\) −1.65685 −0.0664873
\(622\) −27.3137 −1.09518
\(623\) −15.0711 26.1039i −0.603810 1.04583i
\(624\) −13.2426 −0.530130
\(625\) 0 0
\(626\) 4.62132 + 8.00436i 0.184705 + 0.319919i
\(627\) 10.0355 + 17.3821i 0.400781 + 0.694172i
\(628\) −56.7696 −2.26535
\(629\) 0.0857864 0.148586i 0.00342053 0.00592453i
\(630\) 0 0
\(631\) 16.0061 27.7234i 0.637193 1.10365i −0.348853 0.937177i \(-0.613429\pi\)
0.986046 0.166473i \(-0.0532378\pi\)
\(632\) 33.6421 + 58.2699i 1.33821 + 2.31785i
\(633\) −9.15685 + 15.8601i −0.363952 + 0.630384i
\(634\) −2.62132 4.54026i −0.104106 0.180317i
\(635\) 0 0
\(636\) −1.58579 −0.0628805
\(637\) −1.07107 1.85514i −0.0424373 0.0735035i
\(638\) −7.41421 + 12.8418i −0.293532 + 0.508412i
\(639\) 19.8995 + 34.4669i 0.787212 + 1.36349i
\(640\) 0 0
\(641\) −9.98528 + 17.2950i −0.394395 + 0.683112i −0.993024 0.117915i \(-0.962379\pi\)
0.598629 + 0.801027i \(0.295712\pi\)
\(642\) 27.9350 48.3849i 1.10251 1.90960i
\(643\) −12.6863 −0.500298 −0.250149 0.968207i \(-0.580480\pi\)
−0.250149 + 0.968207i \(0.580480\pi\)
\(644\) 18.4853 + 32.0174i 0.728422 + 1.26166i
\(645\) 0 0
\(646\) −0.328427 + 0.568852i −0.0129218 + 0.0223812i
\(647\) 22.6863 0.891890 0.445945 0.895060i \(-0.352868\pi\)
0.445945 + 0.895060i \(0.352868\pi\)
\(648\) 20.9350 + 36.2605i 0.822406 + 1.42445i
\(649\) 52.7990 2.07254
\(650\) 0 0
\(651\) −2.20711 + 32.3762i −0.0865033 + 1.26892i
\(652\) 49.6569 1.94471
\(653\) −22.1421 −0.866489 −0.433244 0.901276i \(-0.642631\pi\)
−0.433244 + 0.901276i \(0.642631\pi\)
\(654\) 15.0711 + 26.1039i 0.589325 + 1.02074i
\(655\) 0 0
\(656\) −14.2279 + 24.6435i −0.555507 + 0.962166i
\(657\) 5.41421 + 9.37769i 0.211229 + 0.365859i
\(658\) 4.82843 + 8.36308i 0.188232 + 0.326027i
\(659\) 9.65685 0.376178 0.188089 0.982152i \(-0.439771\pi\)
0.188089 + 0.982152i \(0.439771\pi\)
\(660\) 0 0
\(661\) −16.5711 + 28.7019i −0.644540 + 1.11638i 0.339868 + 0.940473i \(0.389618\pi\)
−0.984408 + 0.175903i \(0.943716\pi\)
\(662\) −0.914214 + 1.58346i −0.0355319 + 0.0615431i
\(663\) 0.378680 + 0.655892i 0.0147067 + 0.0254728i
\(664\) 8.98528 15.5630i 0.348697 0.603960i
\(665\) 0 0
\(666\) −6.82843 −0.264596
\(667\) −4.68629 −0.181454
\(668\) −16.3787 28.3687i −0.633710 1.09762i
\(669\) 2.08579 3.61269i 0.0806412 0.139675i
\(670\) 0 0
\(671\) 7.41421 12.8418i 0.286223 0.495752i
\(672\) −4.62132 + 8.00436i −0.178271 + 0.308775i
\(673\) 10.3284 17.8894i 0.398132 0.689584i −0.595364 0.803456i \(-0.702992\pi\)
0.993495 + 0.113872i \(0.0363254\pi\)
\(674\) 32.1421 1.23807
\(675\) 0 0
\(676\) 18.4853 + 32.0174i 0.710972 + 1.23144i
\(677\) 20.2990 35.1589i 0.780154 1.35127i −0.151698 0.988427i \(-0.548474\pi\)
0.931852 0.362839i \(-0.118192\pi\)
\(678\) −31.1421 −1.19601
\(679\) −13.0711 22.6398i −0.501622 0.868834i
\(680\) 0 0
\(681\) 37.6274 1.44189
\(682\) −4.79289 + 70.3072i −0.183529 + 2.69220i
\(683\) 46.6274 1.78415 0.892074 0.451889i \(-0.149250\pi\)
0.892074 + 0.451889i \(0.149250\pi\)
\(684\) 17.1716 0.656571
\(685\) 0 0
\(686\) 47.6274 1.81842
\(687\) −13.8640 + 24.0131i −0.528943 + 0.916156i
\(688\) 13.3492 + 23.1216i 0.508935 + 0.881501i
\(689\) −0.156854 0.271680i −0.00597567 0.0103502i
\(690\) 0 0
\(691\) −7.03553 + 12.1859i −0.267644 + 0.463574i −0.968253 0.249972i \(-0.919579\pi\)
0.700609 + 0.713546i \(0.252912\pi\)
\(692\) −27.3995 + 47.4573i −1.04157 + 1.80406i
\(693\) −17.8995 + 31.0028i −0.679946 + 1.17770i
\(694\) 27.2279 + 47.1601i 1.03356 + 1.79017i
\(695\) 0 0
\(696\) 6.24264 + 10.8126i 0.236627 + 0.409849i
\(697\) 1.62742 0.0616428
\(698\) 84.7696 3.20857
\(699\) −17.8995 31.0028i −0.677021 1.17263i
\(700\) 0 0
\(701\) −1.74264 3.01834i −0.0658186 0.114001i 0.831238 0.555916i \(-0.187633\pi\)
−0.897057 + 0.441915i \(0.854299\pi\)
\(702\) −0.914214 + 1.58346i −0.0345048 + 0.0597640i
\(703\) 0.792893 1.37333i 0.0299045 0.0517962i
\(704\) −25.7635 + 44.6236i −0.970997 + 1.68182i
\(705\) 0 0
\(706\) 3.62132 + 6.27231i 0.136290 + 0.236062i
\(707\) 10.2426 + 17.7408i 0.385214 + 0.667210i
\(708\) 46.5416 80.6125i 1.74914 3.02960i
\(709\) −5.31371 −0.199561 −0.0997803 0.995009i \(-0.531814\pi\)
−0.0997803 + 0.995009i \(0.531814\pi\)
\(710\) 0 0
\(711\) −43.1127 −1.61685
\(712\) −55.1127 −2.06544
\(713\) −20.0000 + 9.79796i −0.749006 + 0.366936i
\(714\) −2.41421 −0.0903497
\(715\) 0 0
\(716\) 12.9350 + 22.4041i 0.483405 + 0.837282i
\(717\) −30.7990 −1.15021
\(718\) −32.4706 + 56.2407i −1.21179 + 2.09888i
\(719\) −3.03553 5.25770i −0.113206 0.196079i 0.803855 0.594825i \(-0.202779\pi\)
−0.917061 + 0.398746i \(0.869445\pi\)
\(720\) 0 0
\(721\) −29.1421 −1.08531
\(722\) 19.8995 34.4669i 0.740583 1.28273i
\(723\) −29.7635 + 51.5518i −1.10691 + 1.91723i
\(724\) 19.7426 34.1953i 0.733729 1.27086i
\(725\) 0 0
\(726\) −48.0416 + 83.2105i −1.78299 + 3.08823i
\(727\) −23.4203 40.5652i −0.868611 1.50448i −0.863416 0.504492i \(-0.831680\pi\)
−0.00519502 0.999987i \(-0.501654\pi\)
\(728\) 19.4853 0.722173
\(729\) −23.8284 −0.882534
\(730\) 0 0
\(731\) 0.763456 1.32234i 0.0282374 0.0489087i
\(732\) −13.0711 22.6398i −0.483121 0.836789i
\(733\) −14.8137 + 25.6581i −0.547157 + 0.947703i 0.451311 + 0.892367i \(0.350957\pi\)
−0.998468 + 0.0553366i \(0.982377\pi\)
\(734\) 21.9853 38.0796i 0.811492 1.40554i
\(735\) 0 0
\(736\) −6.34315 −0.233811
\(737\) 13.7426 + 23.8030i 0.506217 + 0.876793i
\(738\) −32.3848 56.0921i −1.19210 2.06478i
\(739\) 3.93503 6.81567i 0.144752 0.250718i −0.784528 0.620093i \(-0.787095\pi\)
0.929281 + 0.369375i \(0.120428\pi\)
\(740\) 0 0
\(741\) 3.50000 + 6.06218i 0.128576 + 0.222700i
\(742\) 1.00000 0.0367112
\(743\) 5.65685 0.207530 0.103765 0.994602i \(-0.466911\pi\)
0.103765 + 0.994602i \(0.466911\pi\)
\(744\) 49.2487 + 33.0936i 1.80555 + 1.21327i
\(745\) 0 0
\(746\) −24.1421 −0.883906
\(747\) 5.75736 + 9.97204i 0.210651 + 0.364858i
\(748\) −3.44365 −0.125912
\(749\) −11.5711 + 20.0417i −0.422798 + 0.732307i
\(750\) 0 0
\(751\) 0.621320 + 1.07616i 0.0226723 + 0.0392696i 0.877139 0.480237i \(-0.159449\pi\)
−0.854467 + 0.519506i \(0.826116\pi\)
\(752\) 4.97056 0.181258
\(753\) −4.32843 + 7.49706i −0.157737 + 0.273208i
\(754\) −2.58579 + 4.47871i −0.0941688 + 0.163105i
\(755\) 0 0
\(756\) −1.91421 3.31552i −0.0696193 0.120584i
\(757\) 17.3284 30.0137i 0.629812 1.09087i −0.357777 0.933807i \(-0.616465\pi\)
0.987589 0.157060i \(-0.0502016\pi\)
\(758\) 35.4706 + 61.4368i 1.28835 + 2.23149i
\(759\) −50.6274 −1.83766
\(760\) 0 0
\(761\) 10.2279 + 17.7153i 0.370762 + 0.642178i 0.989683 0.143275i \(-0.0457633\pi\)
−0.618921 + 0.785453i \(0.712430\pi\)
\(762\) −31.7635 + 55.0159i −1.15067 + 1.99302i
\(763\) −6.24264 10.8126i −0.225999 0.391441i
\(764\) 2.10660 3.64874i 0.0762142 0.132007i
\(765\) 0 0
\(766\) 30.0563 52.0591i 1.08598 1.88097i
\(767\) 18.4142 0.664899
\(768\) 36.1777 + 62.6616i 1.30545 + 2.26110i
\(769\) 13.0563 + 22.6143i 0.470824 + 0.815491i 0.999443 0.0333680i \(-0.0106233\pi\)
−0.528619 + 0.848859i \(0.677290\pi\)
\(770\) 0 0
\(771\) 0.757359 0.0272756
\(772\) −40.4706 70.0971i −1.45657 2.52285i
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) −60.7696 −2.18432
\(775\) 0 0
\(776\) −47.7990 −1.71588
\(777\) 5.82843 0.209094
\(778\) −20.6924 35.8403i −0.741858 1.28494i
\(779\) 15.0416 0.538922
\(780\) 0 0
\(781\) −36.8848 63.8863i −1.31984 2.28603i
\(782\) −0.828427 1.43488i −0.0296245 0.0513111i
\(783\) 0.485281 0.0173425
\(784\) 1.75736 3.04384i 0.0627628 0.108708i
\(785\) 0 0
\(786\) 13.8640 24.0131i 0.494511 0.856518i
\(787\) 19.7929 + 34.2823i 0.705540 + 1.22203i 0.966496 + 0.256681i \(0.0826290\pi\)
−0.260956 + 0.965351i \(0.584038\pi\)
\(788\) 6.67157 11.5555i 0.237665 0.411648i
\(789\) −0.828427 1.43488i −0.0294928 0.0510830i
\(790\) 0 0
\(791\) 12.8995 0.458653
\(792\) 32.7279 + 56.6864i 1.16294 + 2.01426i
\(793\) 2.58579 4.47871i 0.0918240 0.159044i
\(794\) −19.9350 34.5285i −0.707468 1.22537i
\(795\) 0 0
\(796\) −29.8345 + 51.6749i −1.05746 + 1.83157i
\(797\) −11.2279 + 19.4473i −0.397713 + 0.688860i −0.993443 0.114325i \(-0.963529\pi\)
0.595730 + 0.803185i \(0.296863\pi\)
\(798\) −22.3137 −0.789897
\(799\) −0.142136 0.246186i −0.00502840 0.00870944i
\(800\) 0 0
\(801\) 17.6569 30.5826i 0.623874 1.08058i
\(802\) −51.1127 −1.80485
\(803\) −10.0355 17.3821i −0.354146 0.613399i
\(804\) 48.4558 1.70891
\(805\) 0 0
\(806\) −1.67157 + 24.5204i −0.0588786 + 0.863694i
\(807\) −76.8406 −2.70492
\(808\) 37.4558 1.31769
\(809\) 22.9853 + 39.8117i 0.808119 + 1.39970i 0.914165 + 0.405343i \(0.132848\pi\)
−0.106045 + 0.994361i \(0.533819\pi\)
\(810\) 0 0
\(811\) −5.86396 + 10.1567i −0.205912 + 0.356649i −0.950423 0.310961i \(-0.899349\pi\)
0.744511 + 0.667610i \(0.232683\pi\)
\(812\) −5.41421 9.37769i −0.190002 0.329093i
\(813\) 28.1421 + 48.7436i 0.986988 + 1.70951i
\(814\) 12.6569 0.443623
\(815\) 0 0
\(816\) −0.621320 + 1.07616i −0.0217506 + 0.0376731i
\(817\) 7.05635 12.2220i 0.246870 0.427592i
\(818\) −11.2782 19.5344i −0.394332 0.683003i
\(819\) −6.24264 + 10.8126i −0.218136 + 0.377822i
\(820\) 0 0
\(821\) −8.48528 −0.296138 −0.148069 0.988977i \(-0.547306\pi\)
−0.148069 + 0.988977i \(0.547306\pi\)
\(822\) 43.6274 1.52168
\(823\) −3.10660 5.38079i −0.108289 0.187563i 0.806788 0.590841i \(-0.201204\pi\)
−0.915077 + 0.403278i \(0.867871\pi\)
\(824\) −26.6421 + 46.1455i −0.928123 + 1.60756i
\(825\) 0 0
\(826\) −29.3492 + 50.8344i −1.02119 + 1.76875i
\(827\) 8.55025 14.8095i 0.297321 0.514976i −0.678201 0.734877i \(-0.737240\pi\)
0.975522 + 0.219901i \(0.0705734\pi\)
\(828\) −21.6569 + 37.5108i −0.752628 + 1.30359i
\(829\) −46.4264 −1.61246 −0.806228 0.591605i \(-0.798494\pi\)
−0.806228 + 0.591605i \(0.798494\pi\)
\(830\) 0 0
\(831\) −17.0711 29.5680i −0.592189 1.02570i
\(832\) −8.98528 + 15.5630i −0.311509 + 0.539549i
\(833\) −0.201010 −0.00696459
\(834\) 0 0
\(835\) 0 0
\(836\) −31.8284 −1.10081
\(837\) 2.07107 1.01461i 0.0715866 0.0350701i
\(838\) 67.5980 2.33513
\(839\) 30.6274 1.05738 0.528688 0.848816i \(-0.322684\pi\)
0.528688 + 0.848816i \(0.322684\pi\)
\(840\) 0 0
\(841\) −27.6274 −0.952670
\(842\) 3.44975 5.97514i 0.118886 0.205917i
\(843\) −2.41421 4.18154i −0.0831499 0.144020i
\(844\) −14.5208 25.1508i −0.499827 0.865726i
\(845\) 0 0
\(846\) −5.65685 + 9.79796i −0.194487 + 0.336861i
\(847\) 19.8995 34.4669i 0.683755 1.18430i
\(848\) 0.257359 0.445759i 0.00883776 0.0153074i
\(849\) −2.82843 4.89898i −0.0970714 0.168133i
\(850\) 0 0
\(851\) 2.00000 + 3.46410i 0.0685591 + 0.118748i
\(852\) −130.054 −4.45557
\(853\) 32.4853 1.11227 0.556137 0.831090i \(-0.312283\pi\)
0.556137 + 0.831090i \(0.312283\pi\)
\(854\) 8.24264 + 14.2767i 0.282057 + 0.488538i
\(855\) 0 0
\(856\) 21.1569 + 36.6447i 0.723126 + 1.25249i
\(857\) −1.25736 + 2.17781i −0.0429506 + 0.0743926i −0.886702 0.462342i \(-0.847009\pi\)
0.843751 + 0.536735i \(0.180342\pi\)
\(858\) −27.9350 + 48.3849i −0.953686 + 1.65183i
\(859\) 6.30761 10.9251i 0.215213 0.372760i −0.738125 0.674663i \(-0.764289\pi\)
0.953338 + 0.301904i \(0.0976221\pi\)
\(860\) 0 0
\(861\) 27.6421 + 47.8776i 0.942041 + 1.63166i
\(862\) 30.4706 + 52.7766i 1.03783 + 1.79758i
\(863\) −19.6924 + 34.1082i −0.670337 + 1.16106i 0.307472 + 0.951557i \(0.400517\pi\)
−0.977809 + 0.209500i \(0.932816\pi\)
\(864\) 0.656854 0.0223466
\(865\) 0 0
\(866\) 84.7696 2.88059
\(867\) −40.9706 −1.39143
\(868\) −42.7132 28.7019i −1.44978 0.974207i
\(869\) 79.9117 2.71082
\(870\) 0 0
\(871\) 4.79289 + 8.30153i 0.162401 + 0.281287i
\(872\) −22.8284 −0.773068
\(873\) 15.3137 26.5241i 0.518291 0.897705i
\(874\) −7.65685 13.2621i −0.258997 0.448596i
\(875\) 0 0
\(876\) −35.3848 −1.19554
\(877\) 24.0858 41.7178i 0.813319 1.40871i −0.0972093 0.995264i \(-0.530992\pi\)
0.910529 0.413446i \(-0.135675\pi\)
\(878\) 14.5711 25.2378i 0.491750 0.851735i
\(879\) −29.9350 + 51.8490i −1.00968 + 1.74882i
\(880\) 0 0
\(881\) −17.1569 + 29.7165i −0.578029 + 1.00118i 0.417676 + 0.908596i \(0.362845\pi\)
−0.995705 + 0.0925798i \(0.970489\pi\)
\(882\) 4.00000 + 6.92820i 0.134687 + 0.233285i
\(883\) −26.2843 −0.884536 −0.442268 0.896883i \(-0.645826\pi\)
−0.442268 + 0.896883i \(0.645826\pi\)
\(884\) −1.20101 −0.0403943
\(885\) 0 0
\(886\) −15.9853 + 27.6873i −0.537036 + 0.930174i
\(887\) 26.6630 + 46.1816i 0.895254 + 1.55063i 0.833490 + 0.552535i \(0.186339\pi\)
0.0617647 + 0.998091i \(0.480327\pi\)
\(888\) 5.32843 9.22911i 0.178810 0.309709i
\(889\) 13.1569 22.7883i 0.441267 0.764296i
\(890\) 0 0
\(891\) 49.7279 1.66595
\(892\) 3.30761 + 5.72895i 0.110747 + 0.191819i
\(893\) −1.31371 2.27541i −0.0439616 0.0761437i
\(894\) −2.91421 + 5.04757i −0.0974659 + 0.168816i
\(895\) 0 0
\(896\) −24.8137 42.9786i −0.828968 1.43581i
\(897\) −17.6569 −0.589545
\(898\) 11.1716 0.372800
\(899\) 5.85786 2.86976i 0.195371 0.0957117i
\(900\) 0 0
\(901\) −0.0294373 −0.000980697
\(902\) 60.0269 + 103.970i 1.99868 + 3.46181i
\(903\) 51.8701 1.72613
\(904\) 11.7929 20.4259i 0.392226 0.679355i
\(905\) 0 0
\(906\) 50.4558 + 87.3921i 1.67628 + 2.90341i
\(907\) −55.3137 −1.83666 −0.918331 0.395814i \(-0.870463\pi\)
−0.918331 + 0.395814i \(0.870463\pi\)
\(908\) −29.8345 + 51.6749i −0.990093 + 1.71489i
\(909\) −12.0000 + 20.7846i −0.398015 + 0.689382i
\(910\) 0 0
\(911\) −24.5208 42.4713i −0.812411 1.40714i −0.911172 0.412026i \(-0.864821\pi\)
0.0987614 0.995111i \(-0.468512\pi\)
\(912\) −5.74264 + 9.94655i −0.190158 + 0.329363i
\(913\) −10.6716 18.4837i −0.353178 0.611721i
\(914\) −75.1127 −2.48451
\(915\) 0 0
\(916\) −21.9853 38.0796i −0.726414 1.25819i
\(917\) −5.74264 + 9.94655i −0.189639 + 0.328464i
\(918\) 0.0857864 + 0.148586i 0.00283137 + 0.00490408i
\(919\) 7.55025 13.0774i 0.249060 0.431384i −0.714205 0.699936i \(-0.753212\pi\)
0.963265 + 0.268552i \(0.0865451\pi\)
\(920\) 0 0
\(921\) −3.32843 + 5.76500i −0.109675 + 0.189963i
\(922\) 63.1127 2.07851
\(923\) −12.8640 22.2810i −0.423422 0.733389i
\(924\) −58.4914 101.310i −1.92423 3.33286i
\(925\) 0 0
\(926\) −60.2843 −1.98106
\(927\) −17.0711 29.5680i −0.560687 0.971139i
\(928\) 1.85786 0.0609874
\(929\) 24.4853 0.803336 0.401668 0.915785i \(-0.368431\pi\)
0.401668 + 0.915785i \(0.368431\pi\)
\(930\) 0 0
\(931\) −1.85786 −0.0608890
\(932\) 56.7696 1.85955
\(933\) 13.6569 + 23.6544i 0.447105 + 0.774409i
\(934\) 19.3137 0.631964
\(935\) 0 0
\(936\) 11.4142 + 19.7700i 0.373085 + 0.646203i
\(937\) 19.1569 + 33.1806i 0.625827 + 1.08396i 0.988380 + 0.152001i \(0.0485718\pi\)
−0.362553 + 0.931963i \(0.618095\pi\)
\(938\) −30.5563 −0.997700
\(939\) 4.62132 8.00436i 0.150811 0.261212i
\(940\) 0 0
\(941\) 17.5000 30.3109i 0.570484 0.988107i −0.426033 0.904708i \(-0.640089\pi\)
0.996516 0.0833989i \(-0.0265776\pi\)
\(942\) 43.2132 + 74.8475i 1.40796 + 2.43866i
\(943\) −18.9706 + 32.8580i −0.617767 + 1.07000i
\(944\) 15.1066 + 26.1654i 0.491678 + 0.851611i
\(945\) 0 0
\(946\) 112.640 3.66223
\(947\) 19.4497 + 33.6880i 0.632032 + 1.09471i 0.987136 + 0.159884i \(0.0511122\pi\)
−0.355104 + 0.934827i \(0.615555\pi\)
\(948\) 70.4411 122.008i 2.28782 3.96262i
\(949\) −3.50000 6.06218i −0.113615 0.196787i
\(950\) 0 0
\(951\) −2.62132 + 4.54026i −0.0850021 + 0.147228i
\(952\) 0.914214 1.58346i 0.0296298 0.0513204i
\(953\) −20.4853 −0.663583 −0.331792 0.943353i \(-0.607653\pi\)
−0.331792 + 0.943353i \(0.607653\pi\)
\(954\) 0.585786 + 1.01461i 0.0189655 + 0.0328493i
\(955\) 0 0
\(956\) 24.4203 42.2972i 0.789809 1.36799i
\(957\) 14.8284 0.479335
\(958\) −11.7426 20.3389i −0.379387 0.657118i
\(959\) −18.0711 −0.583545
\(960\) 0 0
\(961\) 19.0000 24.4949i 0.612903 0.790158i
\(962\) 4.41421 0.142320
\(963\) −27.1127 −0.873694
\(964\) −47.1985 81.7502i −1.52016 2.63300i
\(965\) 0 0
\(966\) 28.1421 48.7436i 0.905458 1.56830i
\(967\) −23.2782 40.3190i −0.748576 1.29657i −0.948505 0.316761i \(-0.897405\pi\)
0.199930 0.979810i \(-0.435929\pi\)
\(968\) −36.3848 63.0203i −1.16945 2.02555i
\(969\) 0.656854 0.0211012
\(970\) 0 0
\(971\) −29.3492 + 50.8344i −0.941862 + 1.63135i −0.179947 + 0.983676i \(0.557592\pi\)
−0.761915 + 0.647676i \(0.775741\pi\)
\(972\) 41.4558 71.8036i 1.32970 2.30310i
\(973\) 0 0
\(974\) −20.9853 + 36.3476i −0.672412 + 1.16465i
\(975\) 0 0
\(976\) 8.48528 0.271607
\(977\) −16.4853 −0.527411 −0.263705 0.964603i \(-0.584945\pi\)
−0.263705 + 0.964603i \(0.584945\pi\)
\(978\) −37.7990 65.4698i −1.20868 2.09349i
\(979\) −32.7279 + 56.6864i −1.04599 + 1.81171i
\(980\) 0 0
\(981\) 7.31371 12.6677i 0.233509 0.404449i
\(982\) −5.32843 + 9.22911i −0.170037 + 0.294513i
\(983\) 24.4203 42.2972i 0.778887 1.34907i −0.153697 0.988118i \(-0.549118\pi\)
0.932584 0.360954i \(-0.117549\pi\)
\(984\) 101.083 3.22242
\(985\) 0 0
\(986\) 0.242641 + 0.420266i 0.00772725 + 0.0133840i
\(987\) 4.82843 8.36308i 0.153691 0.266200i
\(988\) −11.1005 −0.353154
\(989\) 17.7990 + 30.8288i 0.565975 + 0.980297i
\(990\) 0 0
\(991\) −19.9411 −0.633451 −0.316725 0.948517i \(-0.602583\pi\)
−0.316725 + 0.948517i \(0.602583\pi\)
\(992\) 7.92893 3.88437i 0.251744 0.123329i
\(993\) 1.82843 0.0580234
\(994\) 82.0122 2.60127
\(995\) 0 0
\(996\) −37.6274 −1.19227
\(997\) −23.2990 + 40.3550i −0.737886 + 1.27806i 0.215559 + 0.976491i \(0.430843\pi\)
−0.953445 + 0.301566i \(0.902491\pi\)
\(998\) −48.5416 84.0766i −1.53656 2.66140i
\(999\) −0.207107 0.358719i −0.00655257 0.0113494i
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 775.2.e.e.676.2 4
5.2 odd 4 775.2.o.d.149.4 8
5.3 odd 4 775.2.o.d.149.1 8
5.4 even 2 31.2.c.a.25.1 yes 4
15.14 odd 2 279.2.h.c.118.2 4
20.19 odd 2 496.2.i.h.273.1 4
31.5 even 3 inner 775.2.e.e.501.2 4
155.4 even 10 961.2.g.o.338.2 16
155.9 even 30 961.2.g.o.816.2 16
155.14 even 30 961.2.d.l.374.2 8
155.19 even 30 961.2.d.l.531.1 8
155.24 odd 30 961.2.d.i.388.2 8
155.29 odd 10 961.2.g.r.844.1 16
155.34 odd 30 961.2.d.i.628.1 8
155.39 even 10 961.2.g.o.732.2 16
155.44 odd 30 961.2.g.r.846.1 16
155.49 even 30 961.2.g.o.846.1 16
155.54 odd 10 961.2.g.r.732.2 16
155.59 even 30 961.2.d.l.628.1 8
155.64 even 10 961.2.g.o.844.1 16
155.67 odd 12 775.2.o.d.749.4 8
155.69 even 30 961.2.d.l.388.2 8
155.74 odd 30 961.2.d.i.531.1 8
155.79 odd 30 961.2.d.i.374.2 8
155.84 odd 30 961.2.g.r.816.2 16
155.89 odd 10 961.2.g.r.338.2 16
155.98 odd 12 775.2.o.d.749.1 8
155.99 odd 6 961.2.a.c.1.1 2
155.104 odd 30 961.2.g.r.235.2 16
155.109 even 10 961.2.g.o.448.1 16
155.114 odd 30 961.2.g.r.547.1 16
155.119 odd 6 961.2.c.a.439.1 4
155.129 even 6 31.2.c.a.5.1 4
155.134 even 30 961.2.g.o.547.1 16
155.139 odd 10 961.2.g.r.448.1 16
155.144 even 30 961.2.g.o.235.2 16
155.149 even 6 961.2.a.a.1.1 2
155.154 odd 2 961.2.c.a.521.1 4
465.149 odd 6 8649.2.a.l.1.2 2
465.254 even 6 8649.2.a.k.1.2 2
465.284 odd 6 279.2.h.c.253.2 4
620.439 odd 6 496.2.i.h.129.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
31.2.c.a.5.1 4 155.129 even 6
31.2.c.a.25.1 yes 4 5.4 even 2
279.2.h.c.118.2 4 15.14 odd 2
279.2.h.c.253.2 4 465.284 odd 6
496.2.i.h.129.1 4 620.439 odd 6
496.2.i.h.273.1 4 20.19 odd 2
775.2.e.e.501.2 4 31.5 even 3 inner
775.2.e.e.676.2 4 1.1 even 1 trivial
775.2.o.d.149.1 8 5.3 odd 4
775.2.o.d.149.4 8 5.2 odd 4
775.2.o.d.749.1 8 155.98 odd 12
775.2.o.d.749.4 8 155.67 odd 12
961.2.a.a.1.1 2 155.149 even 6
961.2.a.c.1.1 2 155.99 odd 6
961.2.c.a.439.1 4 155.119 odd 6
961.2.c.a.521.1 4 155.154 odd 2
961.2.d.i.374.2 8 155.79 odd 30
961.2.d.i.388.2 8 155.24 odd 30
961.2.d.i.531.1 8 155.74 odd 30
961.2.d.i.628.1 8 155.34 odd 30
961.2.d.l.374.2 8 155.14 even 30
961.2.d.l.388.2 8 155.69 even 30
961.2.d.l.531.1 8 155.19 even 30
961.2.d.l.628.1 8 155.59 even 30
961.2.g.o.235.2 16 155.144 even 30
961.2.g.o.338.2 16 155.4 even 10
961.2.g.o.448.1 16 155.109 even 10
961.2.g.o.547.1 16 155.134 even 30
961.2.g.o.732.2 16 155.39 even 10
961.2.g.o.816.2 16 155.9 even 30
961.2.g.o.844.1 16 155.64 even 10
961.2.g.o.846.1 16 155.49 even 30
961.2.g.r.235.2 16 155.104 odd 30
961.2.g.r.338.2 16 155.89 odd 10
961.2.g.r.448.1 16 155.139 odd 10
961.2.g.r.547.1 16 155.114 odd 30
961.2.g.r.732.2 16 155.54 odd 10
961.2.g.r.816.2 16 155.84 odd 30
961.2.g.r.844.1 16 155.29 odd 10
961.2.g.r.846.1 16 155.44 odd 30
8649.2.a.k.1.2 2 465.254 even 6
8649.2.a.l.1.2 2 465.149 odd 6