Properties

Label 775.2.e.e.676.1
Level $775$
Weight $2$
Character 775.676
Analytic conductor $6.188$
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] = [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 676.1
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 775.676
Dual form 775.2.e.e.501.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.414214 q^{2} +(0.207107 + 0.358719i) q^{3} -1.82843 q^{4} +(-0.0857864 - 0.148586i) q^{6} +(-0.207107 - 0.358719i) q^{7} +1.58579 q^{8} +(1.41421 - 2.44949i) q^{9} +O(q^{10})\) \(q-0.414214 q^{2} +(0.207107 + 0.358719i) q^{3} -1.82843 q^{4} +(-0.0857864 - 0.148586i) q^{6} +(-0.207107 - 0.358719i) q^{7} +1.58579 q^{8} +(1.41421 - 2.44949i) q^{9} +(-1.62132 + 2.80821i) q^{11} +(-0.378680 - 0.655892i) q^{12} +(-1.91421 + 3.31552i) q^{13} +(0.0857864 + 0.148586i) q^{14} +3.00000 q^{16} +(-2.91421 - 5.04757i) q^{17} +(-0.585786 + 1.01461i) q^{18} +(-2.20711 - 3.82282i) q^{19} +(0.0857864 - 0.148586i) q^{21} +(0.671573 - 1.16320i) q^{22} +4.00000 q^{23} +(0.328427 + 0.568852i) q^{24} +(0.792893 - 1.37333i) q^{26} +2.41421 q^{27} +(0.378680 + 0.655892i) q^{28} -6.82843 q^{29} +(-5.00000 - 2.44949i) q^{31} -4.41421 q^{32} -1.34315 q^{33} +(1.20711 + 2.09077i) q^{34} +(-2.58579 + 4.47871i) q^{36} +(0.500000 + 0.866025i) q^{37} +(0.914214 + 1.58346i) q^{38} -1.58579 q^{39} +(3.74264 - 6.48244i) q^{41} +(-0.0355339 + 0.0615465i) q^{42} +(-5.44975 - 9.43924i) q^{43} +(2.96447 - 5.13461i) q^{44} -1.65685 q^{46} -9.65685 q^{47} +(0.621320 + 1.07616i) q^{48} +(3.41421 - 5.91359i) q^{49} +(1.20711 - 2.09077i) q^{51} +(3.50000 - 6.06218i) q^{52} +(2.91421 - 5.04757i) q^{53} -1.00000 q^{54} +(-0.328427 - 0.568852i) q^{56} +(0.914214 - 1.58346i) q^{57} +2.82843 q^{58} +(-2.03553 - 3.52565i) q^{59} -2.82843 q^{61} +(2.07107 + 1.01461i) q^{62} -1.17157 q^{63} -4.17157 q^{64} +0.556349 q^{66} +(1.62132 - 2.80821i) q^{67} +(5.32843 + 9.22911i) q^{68} +(0.828427 + 1.43488i) q^{69} +(-0.0355339 + 0.0615465i) q^{71} +(2.24264 - 3.88437i) q^{72} +(-0.914214 + 1.58346i) q^{73} +(-0.207107 - 0.358719i) q^{74} +(4.03553 + 6.98975i) q^{76} +1.34315 q^{77} +0.656854 q^{78} +(3.37868 + 5.85204i) q^{79} +(-3.74264 - 6.48244i) q^{81} +(-1.55025 + 2.68512i) q^{82} +(-5.03553 + 8.72180i) q^{83} +(-0.156854 + 0.271680i) q^{84} +(2.25736 + 3.90986i) q^{86} +(-1.41421 - 2.44949i) q^{87} +(-2.57107 + 4.45322i) q^{88} +4.48528 q^{89} +1.58579 q^{91} -7.31371 q^{92} +(-0.156854 - 2.30090i) q^{93} +4.00000 q^{94} +(-0.914214 - 1.58346i) q^{96} -5.17157 q^{97} +(-1.41421 + 2.44949i) q^{98} +(4.58579 + 7.94282i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.414214 −0.292893 −0.146447 0.989219i \(-0.546784\pi\)
−0.146447 + 0.989219i \(0.546784\pi\)
\(3\) 0.207107 + 0.358719i 0.119573 + 0.207107i 0.919599 0.392859i \(-0.128514\pi\)
−0.800025 + 0.599966i \(0.795181\pi\)
\(4\) −1.82843 −0.914214
\(5\) 0 0
\(6\) −0.0857864 0.148586i −0.0350222 0.0606602i
\(7\) −0.207107 0.358719i −0.0782790 0.135583i 0.824228 0.566257i \(-0.191609\pi\)
−0.902507 + 0.430674i \(0.858276\pi\)
\(8\) 1.58579 0.560660
\(9\) 1.41421 2.44949i 0.471405 0.816497i
\(10\) 0 0
\(11\) −1.62132 + 2.80821i −0.488846 + 0.846707i −0.999918 0.0128314i \(-0.995916\pi\)
0.511071 + 0.859538i \(0.329249\pi\)
\(12\) −0.378680 0.655892i −0.109315 0.189340i
\(13\) −1.91421 + 3.31552i −0.530907 + 0.919558i 0.468442 + 0.883494i \(0.344815\pi\)
−0.999349 + 0.0360643i \(0.988518\pi\)
\(14\) 0.0857864 + 0.148586i 0.0229274 + 0.0397114i
\(15\) 0 0
\(16\) 3.00000 0.750000
\(17\) −2.91421 5.04757i −0.706801 1.22421i −0.966038 0.258401i \(-0.916804\pi\)
0.259237 0.965814i \(-0.416529\pi\)
\(18\) −0.585786 + 1.01461i −0.138071 + 0.239146i
\(19\) −2.20711 3.82282i −0.506345 0.877015i −0.999973 0.00734216i \(-0.997663\pi\)
0.493628 0.869673i \(-0.335670\pi\)
\(20\) 0 0
\(21\) 0.0857864 0.148586i 0.0187201 0.0324242i
\(22\) 0.671573 1.16320i 0.143180 0.247995i
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0.328427 + 0.568852i 0.0670399 + 0.116117i
\(25\) 0 0
\(26\) 0.792893 1.37333i 0.155499 0.269332i
\(27\) 2.41421 0.464616
\(28\) 0.378680 + 0.655892i 0.0715637 + 0.123952i
\(29\) −6.82843 −1.26801 −0.634004 0.773330i \(-0.718590\pi\)
−0.634004 + 0.773330i \(0.718590\pi\)
\(30\) 0 0
\(31\) −5.00000 2.44949i −0.898027 0.439941i
\(32\) −4.41421 −0.780330
\(33\) −1.34315 −0.233812
\(34\) 1.20711 + 2.09077i 0.207017 + 0.358564i
\(35\) 0 0
\(36\) −2.58579 + 4.47871i −0.430964 + 0.746452i
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0.914214 + 1.58346i 0.148305 + 0.256872i
\(39\) −1.58579 −0.253929
\(40\) 0 0
\(41\) 3.74264 6.48244i 0.584502 1.01239i −0.410435 0.911890i \(-0.634623\pi\)
0.994937 0.100498i \(-0.0320435\pi\)
\(42\) −0.0355339 + 0.0615465i −0.00548300 + 0.00949684i
\(43\) −5.44975 9.43924i −0.831079 1.43947i −0.897184 0.441658i \(-0.854391\pi\)
0.0661049 0.997813i \(-0.478943\pi\)
\(44\) 2.96447 5.13461i 0.446910 0.774071i
\(45\) 0 0
\(46\) −1.65685 −0.244290
\(47\) −9.65685 −1.40860 −0.704298 0.709904i \(-0.748738\pi\)
−0.704298 + 0.709904i \(0.748738\pi\)
\(48\) 0.621320 + 1.07616i 0.0896799 + 0.155330i
\(49\) 3.41421 5.91359i 0.487745 0.844799i
\(50\) 0 0
\(51\) 1.20711 2.09077i 0.169029 0.292766i
\(52\) 3.50000 6.06218i 0.485363 0.840673i
\(53\) 2.91421 5.04757i 0.400298 0.693337i −0.593464 0.804861i \(-0.702240\pi\)
0.993762 + 0.111524i \(0.0355733\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −0.328427 0.568852i −0.0438879 0.0760161i
\(57\) 0.914214 1.58346i 0.121091 0.209735i
\(58\) 2.82843 0.371391
\(59\) −2.03553 3.52565i −0.265004 0.459000i 0.702561 0.711624i \(-0.252040\pi\)
−0.967565 + 0.252624i \(0.918707\pi\)
\(60\) 0 0
\(61\) −2.82843 −0.362143 −0.181071 0.983470i \(-0.557957\pi\)
−0.181071 + 0.983470i \(0.557957\pi\)
\(62\) 2.07107 + 1.01461i 0.263026 + 0.128856i
\(63\) −1.17157 −0.147604
\(64\) −4.17157 −0.521447
\(65\) 0 0
\(66\) 0.556349 0.0684819
\(67\) 1.62132 2.80821i 0.198076 0.343077i −0.749829 0.661632i \(-0.769864\pi\)
0.947904 + 0.318555i \(0.103197\pi\)
\(68\) 5.32843 + 9.22911i 0.646167 + 1.11919i
\(69\) 0.828427 + 1.43488i 0.0997309 + 0.172739i
\(70\) 0 0
\(71\) −0.0355339 + 0.0615465i −0.00421710 + 0.00730423i −0.868126 0.496343i \(-0.834676\pi\)
0.863909 + 0.503648i \(0.168009\pi\)
\(72\) 2.24264 3.88437i 0.264298 0.457777i
\(73\) −0.914214 + 1.58346i −0.107001 + 0.185330i −0.914554 0.404464i \(-0.867458\pi\)
0.807553 + 0.589795i \(0.200791\pi\)
\(74\) −0.207107 0.358719i −0.0240757 0.0417003i
\(75\) 0 0
\(76\) 4.03553 + 6.98975i 0.462907 + 0.801779i
\(77\) 1.34315 0.153066
\(78\) 0.656854 0.0743741
\(79\) 3.37868 + 5.85204i 0.380131 + 0.658406i 0.991081 0.133263i \(-0.0425455\pi\)
−0.610950 + 0.791670i \(0.709212\pi\)
\(80\) 0 0
\(81\) −3.74264 6.48244i −0.415849 0.720272i
\(82\) −1.55025 + 2.68512i −0.171197 + 0.296521i
\(83\) −5.03553 + 8.72180i −0.552722 + 0.957342i 0.445355 + 0.895354i \(0.353077\pi\)
−0.998077 + 0.0619880i \(0.980256\pi\)
\(84\) −0.156854 + 0.271680i −0.0171142 + 0.0296427i
\(85\) 0 0
\(86\) 2.25736 + 3.90986i 0.243417 + 0.421611i
\(87\) −1.41421 2.44949i −0.151620 0.262613i
\(88\) −2.57107 + 4.45322i −0.274077 + 0.474715i
\(89\) 4.48528 0.475439 0.237719 0.971334i \(-0.423600\pi\)
0.237719 + 0.971334i \(0.423600\pi\)
\(90\) 0 0
\(91\) 1.58579 0.166236
\(92\) −7.31371 −0.762507
\(93\) −0.156854 2.30090i −0.0162650 0.238593i
\(94\) 4.00000 0.412568
\(95\) 0 0
\(96\) −0.914214 1.58346i −0.0933065 0.161612i
\(97\) −5.17157 −0.525094 −0.262547 0.964919i \(-0.584562\pi\)
−0.262547 + 0.964919i \(0.584562\pi\)
\(98\) −1.41421 + 2.44949i −0.142857 + 0.247436i
\(99\) 4.58579 + 7.94282i 0.460889 + 0.798283i
\(100\) 0 0
\(101\) −8.48528 −0.844317 −0.422159 0.906522i \(-0.638727\pi\)
−0.422159 + 0.906522i \(0.638727\pi\)
\(102\) −0.500000 + 0.866025i −0.0495074 + 0.0857493i
\(103\) 1.03553 1.79360i 0.102034 0.176728i −0.810488 0.585755i \(-0.800798\pi\)
0.912523 + 0.409026i \(0.134132\pi\)
\(104\) −3.03553 + 5.25770i −0.297659 + 0.515560i
\(105\) 0 0
\(106\) −1.20711 + 2.09077i −0.117245 + 0.203074i
\(107\) 6.20711 + 10.7510i 0.600064 + 1.03934i 0.992811 + 0.119694i \(0.0381914\pi\)
−0.392747 + 0.919646i \(0.628475\pi\)
\(108\) −4.41421 −0.424758
\(109\) −10.8284 −1.03718 −0.518588 0.855024i \(-0.673542\pi\)
−0.518588 + 0.855024i \(0.673542\pi\)
\(110\) 0 0
\(111\) −0.207107 + 0.358719i −0.0196577 + 0.0340481i
\(112\) −0.621320 1.07616i −0.0587093 0.101687i
\(113\) 8.32843 14.4253i 0.783473 1.35701i −0.146435 0.989220i \(-0.546780\pi\)
0.929907 0.367794i \(-0.119887\pi\)
\(114\) −0.378680 + 0.655892i −0.0354666 + 0.0614300i
\(115\) 0 0
\(116\) 12.4853 1.15923
\(117\) 5.41421 + 9.37769i 0.500544 + 0.866968i
\(118\) 0.843146 + 1.46037i 0.0776179 + 0.134438i
\(119\) −1.20711 + 2.09077i −0.110655 + 0.191661i
\(120\) 0 0
\(121\) 0.242641 + 0.420266i 0.0220582 + 0.0382060i
\(122\) 1.17157 0.106069
\(123\) 3.10051 0.279563
\(124\) 9.14214 + 4.47871i 0.820988 + 0.402200i
\(125\) 0 0
\(126\) 0.485281 0.0432323
\(127\) 4.44975 + 7.70719i 0.394851 + 0.683902i 0.993082 0.117421i \(-0.0374628\pi\)
−0.598231 + 0.801324i \(0.704129\pi\)
\(128\) 10.5563 0.933058
\(129\) 2.25736 3.90986i 0.198749 0.344244i
\(130\) 0 0
\(131\) 6.62132 + 11.4685i 0.578507 + 1.00200i 0.995651 + 0.0931636i \(0.0296980\pi\)
−0.417143 + 0.908841i \(0.636969\pi\)
\(132\) 2.45584 0.213754
\(133\) −0.914214 + 1.58346i −0.0792724 + 0.137304i
\(134\) −0.671573 + 1.16320i −0.0580151 + 0.100485i
\(135\) 0 0
\(136\) −4.62132 8.00436i −0.396275 0.686368i
\(137\) 4.74264 8.21449i 0.405191 0.701812i −0.589153 0.808022i \(-0.700538\pi\)
0.994344 + 0.106210i \(0.0338716\pi\)
\(138\) −0.343146 0.594346i −0.0292105 0.0505941i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −2.00000 3.46410i −0.168430 0.291730i
\(142\) 0.0147186 0.0254934i 0.00123516 0.00213936i
\(143\) −6.20711 10.7510i −0.519064 0.899046i
\(144\) 4.24264 7.34847i 0.353553 0.612372i
\(145\) 0 0
\(146\) 0.378680 0.655892i 0.0313398 0.0542820i
\(147\) 2.82843 0.233285
\(148\) −0.914214 1.58346i −0.0751479 0.130160i
\(149\) −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
\(151\) 5.31371 0.432423 0.216212 0.976346i \(-0.430630\pi\)
0.216212 + 0.976346i \(0.430630\pi\)
\(152\) −3.50000 6.06218i −0.283887 0.491708i
\(153\) −16.4853 −1.33276
\(154\) −0.556349 −0.0448319
\(155\) 0 0
\(156\) 2.89949 0.232145
\(157\) −9.17157 −0.731971 −0.365986 0.930621i \(-0.619268\pi\)
−0.365986 + 0.930621i \(0.619268\pi\)
\(158\) −1.39949 2.42400i −0.111338 0.192843i
\(159\) 2.41421 0.191460
\(160\) 0 0
\(161\) −0.828427 1.43488i −0.0652892 0.113084i
\(162\) 1.55025 + 2.68512i 0.121799 + 0.210963i
\(163\) −20.9706 −1.64254 −0.821271 0.570539i \(-0.806734\pi\)
−0.821271 + 0.570539i \(0.806734\pi\)
\(164\) −6.84315 + 11.8527i −0.534360 + 0.925539i
\(165\) 0 0
\(166\) 2.08579 3.61269i 0.161888 0.280399i
\(167\) 11.2782 + 19.5344i 0.872731 + 1.51162i 0.859160 + 0.511707i \(0.170987\pi\)
0.0135714 + 0.999908i \(0.495680\pi\)
\(168\) 0.136039 0.235626i 0.0104956 0.0181790i
\(169\) −0.828427 1.43488i −0.0637252 0.110375i
\(170\) 0 0
\(171\) −12.4853 −0.954773
\(172\) 9.96447 + 17.2590i 0.759783 + 1.31598i
\(173\) 4.15685 7.19988i 0.316040 0.547397i −0.663618 0.748071i \(-0.730980\pi\)
0.979658 + 0.200674i \(0.0643134\pi\)
\(174\) 0.585786 + 1.01461i 0.0444084 + 0.0769175i
\(175\) 0 0
\(176\) −4.86396 + 8.42463i −0.366635 + 0.635030i
\(177\) 0.843146 1.46037i 0.0633747 0.109768i
\(178\) −1.85786 −0.139253
\(179\) 7.62132 + 13.2005i 0.569644 + 0.986653i 0.996601 + 0.0823807i \(0.0262523\pi\)
−0.426957 + 0.904272i \(0.640414\pi\)
\(180\) 0 0
\(181\) −6.15685 + 10.6640i −0.457635 + 0.792648i −0.998835 0.0482461i \(-0.984637\pi\)
0.541200 + 0.840894i \(0.317970\pi\)
\(182\) −0.656854 −0.0486893
\(183\) −0.585786 1.01461i −0.0433026 0.0750023i
\(184\) 6.34315 0.467623
\(185\) 0 0
\(186\) 0.0649712 + 0.953065i 0.00476392 + 0.0698821i
\(187\) 18.8995 1.38207
\(188\) 17.6569 1.28776
\(189\) −0.500000 0.866025i −0.0363696 0.0629941i
\(190\) 0 0
\(191\) 10.4497 18.0995i 0.756117 1.30963i −0.188700 0.982035i \(-0.560427\pi\)
0.944817 0.327599i \(-0.106239\pi\)
\(192\) −0.863961 1.49642i −0.0623510 0.107995i
\(193\) 3.57107 + 6.18527i 0.257051 + 0.445226i 0.965451 0.260586i \(-0.0839158\pi\)
−0.708400 + 0.705812i \(0.750582\pi\)
\(194\) 2.14214 0.153796
\(195\) 0 0
\(196\) −6.24264 + 10.8126i −0.445903 + 0.772326i
\(197\) −6.74264 + 11.6786i −0.480393 + 0.832066i −0.999747 0.0224938i \(-0.992839\pi\)
0.519354 + 0.854559i \(0.326173\pi\)
\(198\) −1.89949 3.29002i −0.134991 0.233812i
\(199\) −9.20711 + 15.9472i −0.652674 + 1.13047i 0.329797 + 0.944052i \(0.393020\pi\)
−0.982471 + 0.186413i \(0.940314\pi\)
\(200\) 0 0
\(201\) 1.34315 0.0947382
\(202\) 3.51472 0.247295
\(203\) 1.41421 + 2.44949i 0.0992583 + 0.171920i
\(204\) −2.20711 + 3.82282i −0.154528 + 0.267651i
\(205\) 0 0
\(206\) −0.428932 + 0.742932i −0.0298851 + 0.0517625i
\(207\) 5.65685 9.79796i 0.393179 0.681005i
\(208\) −5.74264 + 9.94655i −0.398180 + 0.689669i
\(209\) 14.3137 0.990100
\(210\) 0 0
\(211\) −5.20711 9.01897i −0.358472 0.620892i 0.629234 0.777216i \(-0.283369\pi\)
−0.987706 + 0.156324i \(0.950035\pi\)
\(212\) −5.32843 + 9.22911i −0.365958 + 0.633858i
\(213\) −0.0294373 −0.00201701
\(214\) −2.57107 4.45322i −0.175755 0.304416i
\(215\) 0 0
\(216\) 3.82843 0.260491
\(217\) 0.156854 + 2.30090i 0.0106480 + 0.156195i
\(218\) 4.48528 0.303782
\(219\) −0.757359 −0.0511776
\(220\) 0 0
\(221\) 22.3137 1.50098
\(222\) 0.0857864 0.148586i 0.00575761 0.00997247i
\(223\) −11.8640 20.5490i −0.794470 1.37606i −0.923175 0.384379i \(-0.874416\pi\)
0.128706 0.991683i \(-0.458918\pi\)
\(224\) 0.914214 + 1.58346i 0.0610835 + 0.105800i
\(225\) 0 0
\(226\) −3.44975 + 5.97514i −0.229474 + 0.397460i
\(227\) −9.20711 + 15.9472i −0.611097 + 1.05845i 0.379959 + 0.925003i \(0.375938\pi\)
−0.991056 + 0.133448i \(0.957395\pi\)
\(228\) −1.67157 + 2.89525i −0.110703 + 0.191743i
\(229\) 2.74264 + 4.75039i 0.181239 + 0.313915i 0.942303 0.334762i \(-0.108656\pi\)
−0.761064 + 0.648677i \(0.775323\pi\)
\(230\) 0 0
\(231\) 0.278175 + 0.481813i 0.0183025 + 0.0317009i
\(232\) −10.8284 −0.710921
\(233\) 9.17157 0.600850 0.300425 0.953805i \(-0.402872\pi\)
0.300425 + 0.953805i \(0.402872\pi\)
\(234\) −2.24264 3.88437i −0.146606 0.253929i
\(235\) 0 0
\(236\) 3.72183 + 6.44639i 0.242270 + 0.419624i
\(237\) −1.39949 + 2.42400i −0.0909070 + 0.157455i
\(238\) 0.500000 0.866025i 0.0324102 0.0561361i
\(239\) 10.6213 18.3967i 0.687036 1.18998i −0.285756 0.958302i \(-0.592245\pi\)
0.972792 0.231679i \(-0.0744219\pi\)
\(240\) 0 0
\(241\) −6.67157 11.5555i −0.429754 0.744355i 0.567097 0.823651i \(-0.308066\pi\)
−0.996851 + 0.0792954i \(0.974733\pi\)
\(242\) −0.100505 0.174080i −0.00646071 0.0111903i
\(243\) 5.17157 8.95743i 0.331757 0.574619i
\(244\) 5.17157 0.331076
\(245\) 0 0
\(246\) −1.28427 −0.0818821
\(247\) 16.8995 1.07529
\(248\) −7.92893 3.88437i −0.503488 0.246658i
\(249\) −4.17157 −0.264363
\(250\) 0 0
\(251\) −3.20711 5.55487i −0.202431 0.350620i 0.746880 0.664958i \(-0.231551\pi\)
−0.949311 + 0.314338i \(0.898217\pi\)
\(252\) 2.14214 0.134942
\(253\) −6.48528 + 11.2328i −0.407726 + 0.706202i
\(254\) −1.84315 3.19242i −0.115649 0.200310i
\(255\) 0 0
\(256\) 3.97056 0.248160
\(257\) 11.1569 19.3242i 0.695945 1.20541i −0.273915 0.961754i \(-0.588319\pi\)
0.969861 0.243659i \(-0.0783478\pi\)
\(258\) −0.935029 + 1.61952i −0.0582124 + 0.100827i
\(259\) 0.207107 0.358719i 0.0128690 0.0222897i
\(260\) 0 0
\(261\) −9.65685 + 16.7262i −0.597744 + 1.03532i
\(262\) −2.74264 4.75039i −0.169441 0.293480i
\(263\) 23.3137 1.43758 0.718792 0.695225i \(-0.244695\pi\)
0.718792 + 0.695225i \(0.244695\pi\)
\(264\) −2.12994 −0.131089
\(265\) 0 0
\(266\) 0.378680 0.655892i 0.0232183 0.0402153i
\(267\) 0.928932 + 1.60896i 0.0568497 + 0.0984666i
\(268\) −2.96447 + 5.13461i −0.181084 + 0.313646i
\(269\) 13.0858 22.6652i 0.797854 1.38192i −0.123156 0.992387i \(-0.539302\pi\)
0.921011 0.389537i \(-0.127365\pi\)
\(270\) 0 0
\(271\) −0.686292 −0.0416892 −0.0208446 0.999783i \(-0.506636\pi\)
−0.0208446 + 0.999783i \(0.506636\pi\)
\(272\) −8.74264 15.1427i −0.530100 0.918161i
\(273\) 0.328427 + 0.568852i 0.0198773 + 0.0344285i
\(274\) −1.96447 + 3.40256i −0.118678 + 0.205556i
\(275\) 0 0
\(276\) −1.51472 2.62357i −0.0911753 0.157920i
\(277\) −14.1421 −0.849719 −0.424859 0.905259i \(-0.639676\pi\)
−0.424859 + 0.905259i \(0.639676\pi\)
\(278\) 0 0
\(279\) −13.0711 + 8.78335i −0.782544 + 0.525845i
\(280\) 0 0
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) 0.828427 + 1.43488i 0.0493321 + 0.0854457i
\(283\) 13.6569 0.811816 0.405908 0.913914i \(-0.366955\pi\)
0.405908 + 0.913914i \(0.366955\pi\)
\(284\) 0.0649712 0.112533i 0.00385533 0.00667763i
\(285\) 0 0
\(286\) 2.57107 + 4.45322i 0.152030 + 0.263324i
\(287\) −3.10051 −0.183017
\(288\) −6.24264 + 10.8126i −0.367851 + 0.637137i
\(289\) −8.48528 + 14.6969i −0.499134 + 0.864526i
\(290\) 0 0
\(291\) −1.07107 1.85514i −0.0627871 0.108750i
\(292\) 1.67157 2.89525i 0.0978214 0.169432i
\(293\) 7.39949 + 12.8163i 0.432283 + 0.748736i 0.997070 0.0765008i \(-0.0243748\pi\)
−0.564786 + 0.825237i \(0.691041\pi\)
\(294\) −1.17157 −0.0683275
\(295\) 0 0
\(296\) 0.792893 + 1.37333i 0.0460860 + 0.0798233i
\(297\) −3.91421 + 6.77962i −0.227126 + 0.393393i
\(298\) 0.207107 + 0.358719i 0.0119974 + 0.0207801i
\(299\) −7.65685 + 13.2621i −0.442807 + 0.766965i
\(300\) 0 0
\(301\) −2.25736 + 3.90986i −0.130112 + 0.225361i
\(302\) −2.20101 −0.126654
\(303\) −1.75736 3.04384i −0.100958 0.174864i
\(304\) −6.62132 11.4685i −0.379759 0.657761i
\(305\) 0 0
\(306\) 6.82843 0.390355
\(307\) −5.62132 9.73641i −0.320826 0.555686i 0.659833 0.751412i \(-0.270627\pi\)
−0.980659 + 0.195726i \(0.937294\pi\)
\(308\) −2.45584 −0.139935
\(309\) 0.857864 0.0488022
\(310\) 0 0
\(311\) 11.3137 0.641542 0.320771 0.947157i \(-0.396058\pi\)
0.320771 + 0.947157i \(0.396058\pi\)
\(312\) −2.51472 −0.142368
\(313\) −0.914214 1.58346i −0.0516744 0.0895027i 0.839031 0.544083i \(-0.183122\pi\)
−0.890706 + 0.454581i \(0.849789\pi\)
\(314\) 3.79899 0.214389
\(315\) 0 0
\(316\) −6.17767 10.7000i −0.347521 0.601924i
\(317\) −3.91421 6.77962i −0.219844 0.380781i 0.734916 0.678158i \(-0.237222\pi\)
−0.954760 + 0.297377i \(0.903888\pi\)
\(318\) −1.00000 −0.0560772
\(319\) 11.0711 19.1757i 0.619861 1.07363i
\(320\) 0 0
\(321\) −2.57107 + 4.45322i −0.143503 + 0.248555i
\(322\) 0.343146 + 0.594346i 0.0191228 + 0.0331216i
\(323\) −12.8640 + 22.2810i −0.715770 + 1.23975i
\(324\) 6.84315 + 11.8527i 0.380175 + 0.658482i
\(325\) 0 0
\(326\) 8.68629 0.481089
\(327\) −2.24264 3.88437i −0.124018 0.214806i
\(328\) 5.93503 10.2798i 0.327707 0.567605i
\(329\) 2.00000 + 3.46410i 0.110264 + 0.190982i
\(330\) 0 0
\(331\) −4.62132 + 8.00436i −0.254011 + 0.439960i −0.964626 0.263621i \(-0.915083\pi\)
0.710616 + 0.703580i \(0.248417\pi\)
\(332\) 9.20711 15.9472i 0.505306 0.875215i
\(333\) 2.82843 0.154997
\(334\) −4.67157 8.09140i −0.255617 0.442742i
\(335\) 0 0
\(336\) 0.257359 0.445759i 0.0140401 0.0243182i
\(337\) −9.31371 −0.507350 −0.253675 0.967290i \(-0.581639\pi\)
−0.253675 + 0.967290i \(0.581639\pi\)
\(338\) 0.343146 + 0.594346i 0.0186647 + 0.0323282i
\(339\) 6.89949 0.374729
\(340\) 0 0
\(341\) 14.9853 10.0696i 0.811498 0.545301i
\(342\) 5.17157 0.279647
\(343\) −5.72792 −0.309279
\(344\) −8.64214 14.9686i −0.465953 0.807054i
\(345\) 0 0
\(346\) −1.72183 + 2.98229i −0.0925659 + 0.160329i
\(347\) −4.27817 7.41002i −0.229664 0.397790i 0.728044 0.685530i \(-0.240430\pi\)
−0.957709 + 0.287740i \(0.907096\pi\)
\(348\) 2.58579 + 4.47871i 0.138613 + 0.240084i
\(349\) −27.1127 −1.45131 −0.725655 0.688059i \(-0.758463\pi\)
−0.725655 + 0.688059i \(0.758463\pi\)
\(350\) 0 0
\(351\) −4.62132 + 8.00436i −0.246668 + 0.427241i
\(352\) 7.15685 12.3960i 0.381462 0.660711i
\(353\) 1.50000 + 2.59808i 0.0798369 + 0.138282i 0.903179 0.429263i \(-0.141227\pi\)
−0.823343 + 0.567545i \(0.807893\pi\)
\(354\) −0.349242 + 0.604906i −0.0185620 + 0.0321504i
\(355\) 0 0
\(356\) −8.20101 −0.434653
\(357\) −1.00000 −0.0529256
\(358\) −3.15685 5.46783i −0.166845 0.288984i
\(359\) −3.55025 + 6.14922i −0.187375 + 0.324543i −0.944374 0.328873i \(-0.893331\pi\)
0.756999 + 0.653416i \(0.226665\pi\)
\(360\) 0 0
\(361\) −0.242641 + 0.420266i −0.0127706 + 0.0221193i
\(362\) 2.55025 4.41717i 0.134038 0.232161i
\(363\) −0.100505 + 0.174080i −0.00527515 + 0.00913682i
\(364\) −2.89949 −0.151975
\(365\) 0 0
\(366\) 0.242641 + 0.420266i 0.0126830 + 0.0219677i
\(367\) −12.1066 + 20.9692i −0.631959 + 1.09459i 0.355191 + 0.934794i \(0.384416\pi\)
−0.987151 + 0.159792i \(0.948918\pi\)
\(368\) 12.0000 0.625543
\(369\) −10.5858 18.3351i −0.551074 0.954488i
\(370\) 0 0
\(371\) −2.41421 −0.125340
\(372\) 0.286797 + 4.20703i 0.0148697 + 0.218125i
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) −7.82843 −0.404798
\(375\) 0 0
\(376\) −15.3137 −0.789744
\(377\) 13.0711 22.6398i 0.673194 1.16601i
\(378\) 0.207107 + 0.358719i 0.0106524 + 0.0184505i
\(379\) −3.69239 6.39540i −0.189665 0.328510i 0.755473 0.655179i \(-0.227407\pi\)
−0.945139 + 0.326669i \(0.894074\pi\)
\(380\) 0 0
\(381\) −1.84315 + 3.19242i −0.0944272 + 0.163553i
\(382\) −4.32843 + 7.49706i −0.221462 + 0.383583i
\(383\) 2.55025 4.41717i 0.130312 0.225707i −0.793485 0.608590i \(-0.791735\pi\)
0.923797 + 0.382883i \(0.125069\pi\)
\(384\) 2.18629 + 3.78677i 0.111569 + 0.193243i
\(385\) 0 0
\(386\) −1.47918 2.56202i −0.0752885 0.130404i
\(387\) −30.8284 −1.56710
\(388\) 9.45584 0.480048
\(389\) 5.57107 + 9.64937i 0.282464 + 0.489243i 0.971991 0.235018i \(-0.0755148\pi\)
−0.689527 + 0.724260i \(0.742181\pi\)
\(390\) 0 0
\(391\) −11.6569 20.1903i −0.589512 1.02107i
\(392\) 5.41421 9.37769i 0.273459 0.473645i
\(393\) −2.74264 + 4.75039i −0.138348 + 0.239626i
\(394\) 2.79289 4.83743i 0.140704 0.243706i
\(395\) 0 0
\(396\) −8.38478 14.5229i −0.421351 0.729801i
\(397\) −16.7426 28.9991i −0.840289 1.45542i −0.889650 0.456642i \(-0.849052\pi\)
0.0493613 0.998781i \(-0.484281\pi\)
\(398\) 3.81371 6.60554i 0.191164 0.331106i
\(399\) −0.757359 −0.0379154
\(400\) 0 0
\(401\) −26.8284 −1.33975 −0.669874 0.742475i \(-0.733652\pi\)
−0.669874 + 0.742475i \(0.733652\pi\)
\(402\) −0.556349 −0.0277482
\(403\) 17.6924 11.8887i 0.881321 0.592220i
\(404\) 15.5147 0.771886
\(405\) 0 0
\(406\) −0.585786 1.01461i −0.0290721 0.0503543i
\(407\) −3.24264 −0.160732
\(408\) 1.91421 3.31552i 0.0947677 0.164142i
\(409\) −10.3284 17.8894i −0.510708 0.884572i −0.999923 0.0124088i \(-0.996050\pi\)
0.489215 0.872163i \(-0.337283\pi\)
\(410\) 0 0
\(411\) 3.92893 0.193800
\(412\) −1.89340 + 3.27946i −0.0932810 + 0.161567i
\(413\) −0.843146 + 1.46037i −0.0414885 + 0.0718602i
\(414\) −2.34315 + 4.05845i −0.115159 + 0.199462i
\(415\) 0 0
\(416\) 8.44975 14.6354i 0.414283 0.717559i
\(417\) 0 0
\(418\) −5.92893 −0.289994
\(419\) 28.0000 1.36789 0.683945 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 0 0
\(421\) 15.5711 26.9699i 0.758887 1.31443i −0.184531 0.982827i \(-0.559077\pi\)
0.943418 0.331605i \(-0.107590\pi\)
\(422\) 2.15685 + 3.73578i 0.104994 + 0.181855i
\(423\) −13.6569 + 23.6544i −0.664019 + 1.15011i
\(424\) 4.62132 8.00436i 0.224431 0.388726i
\(425\) 0 0
\(426\) 0.0121933 0.000590768
\(427\) 0.585786 + 1.01461i 0.0283482 + 0.0491005i
\(428\) −11.3492 19.6575i −0.548586 0.950179i
\(429\) 2.57107 4.45322i 0.124132 0.215003i
\(430\) 0 0
\(431\) 8.37868 + 14.5123i 0.403587 + 0.699033i 0.994156 0.107954i \(-0.0344300\pi\)
−0.590569 + 0.806987i \(0.701097\pi\)
\(432\) 7.24264 0.348462
\(433\) −27.1127 −1.30295 −0.651477 0.758669i \(-0.725850\pi\)
−0.651477 + 0.758669i \(0.725850\pi\)
\(434\) −0.0649712 0.953065i −0.00311872 0.0457486i
\(435\) 0 0
\(436\) 19.7990 0.948200
\(437\) −8.82843 15.2913i −0.422321 0.731481i
\(438\) 0.313708 0.0149896
\(439\) −1.03553 + 1.79360i −0.0494233 + 0.0856037i −0.889679 0.456587i \(-0.849072\pi\)
0.840255 + 0.542191i \(0.182405\pi\)
\(440\) 0 0
\(441\) −9.65685 16.7262i −0.459850 0.796484i
\(442\) −9.24264 −0.439628
\(443\) −2.37868 + 4.11999i −0.113014 + 0.195747i −0.916984 0.398923i \(-0.869384\pi\)
0.803970 + 0.594670i \(0.202717\pi\)
\(444\) 0.378680 0.655892i 0.0179713 0.0311273i
\(445\) 0 0
\(446\) 4.91421 + 8.51167i 0.232695 + 0.403039i
\(447\) 0.207107 0.358719i 0.00979581 0.0169668i
\(448\) 0.863961 + 1.49642i 0.0408183 + 0.0706994i
\(449\) −40.6274 −1.91733 −0.958663 0.284543i \(-0.908158\pi\)
−0.958663 + 0.284543i \(0.908158\pi\)
\(450\) 0 0
\(451\) 12.1360 + 21.0202i 0.571464 + 0.989804i
\(452\) −15.2279 + 26.3755i −0.716261 + 1.24060i
\(453\) 1.10051 + 1.90613i 0.0517062 + 0.0895578i
\(454\) 3.81371 6.60554i 0.178986 0.310013i
\(455\) 0 0
\(456\) 1.44975 2.51104i 0.0678906 0.117590i
\(457\) 31.1127 1.45539 0.727695 0.685901i \(-0.240591\pi\)
0.727695 + 0.685901i \(0.240591\pi\)
\(458\) −1.13604 1.96768i −0.0530836 0.0919435i
\(459\) −7.03553 12.1859i −0.328391 0.568789i
\(460\) 0 0
\(461\) −2.14214 −0.0997692 −0.0498846 0.998755i \(-0.515885\pi\)
−0.0498846 + 0.998755i \(0.515885\pi\)
\(462\) −0.115224 0.199573i −0.00536069 0.00928499i
\(463\) 8.97056 0.416897 0.208449 0.978033i \(-0.433159\pi\)
0.208449 + 0.978033i \(0.433159\pi\)
\(464\) −20.4853 −0.951005
\(465\) 0 0
\(466\) −3.79899 −0.175985
\(467\) 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
\(469\) −1.34315 −0.0620207
\(470\) 0 0
\(471\) −1.89949 3.29002i −0.0875241 0.151596i
\(472\) −3.22792 5.59093i −0.148577 0.257343i
\(473\) 35.3431 1.62508
\(474\) 0.579690 1.00405i 0.0266260 0.0461176i
\(475\) 0 0
\(476\) 2.20711 3.82282i 0.101163 0.175219i
\(477\) −8.24264 14.2767i −0.377405 0.653684i
\(478\) −4.39949 + 7.62015i −0.201228 + 0.348537i
\(479\) 7.86396 + 13.6208i 0.359314 + 0.622349i 0.987846 0.155434i \(-0.0496775\pi\)
−0.628533 + 0.777783i \(0.716344\pi\)
\(480\) 0 0
\(481\) −3.82843 −0.174561
\(482\) 2.76346 + 4.78645i 0.125872 + 0.218017i
\(483\) 0.343146 0.594346i 0.0156137 0.0270437i
\(484\) −0.443651 0.768426i −0.0201659 0.0349284i
\(485\) 0 0
\(486\) −2.14214 + 3.71029i −0.0971692 + 0.168302i
\(487\) 9.69239 16.7877i 0.439204 0.760724i −0.558424 0.829556i \(-0.688594\pi\)
0.997628 + 0.0688318i \(0.0219272\pi\)
\(488\) −4.48528 −0.203039
\(489\) −4.34315 7.52255i −0.196404 0.340181i
\(490\) 0 0
\(491\) −0.792893 + 1.37333i −0.0357828 + 0.0619776i −0.883362 0.468691i \(-0.844726\pi\)
0.847579 + 0.530669i \(0.178059\pi\)
\(492\) −5.66905 −0.255580
\(493\) 19.8995 + 34.4669i 0.896228 + 1.55231i
\(494\) −7.00000 −0.314945
\(495\) 0 0
\(496\) −15.0000 7.34847i −0.673520 0.329956i
\(497\) 0.0294373 0.00132044
\(498\) 1.72792 0.0774300
\(499\) 1.10660 + 1.91669i 0.0495383 + 0.0858028i 0.889731 0.456485i \(-0.150892\pi\)
−0.840193 + 0.542288i \(0.817558\pi\)
\(500\) 0 0
\(501\) −4.67157 + 8.09140i −0.208710 + 0.361497i
\(502\) 1.32843 + 2.30090i 0.0592906 + 0.102694i
\(503\) −6.69239 11.5916i −0.298399 0.516842i 0.677371 0.735642i \(-0.263119\pi\)
−0.975770 + 0.218800i \(0.929786\pi\)
\(504\) −1.85786 −0.0827559
\(505\) 0 0
\(506\) 2.68629 4.65279i 0.119420 0.206842i
\(507\) 0.343146 0.594346i 0.0152396 0.0263958i
\(508\) −8.13604 14.0920i −0.360978 0.625233i
\(509\) 16.3995 28.4048i 0.726895 1.25902i −0.231294 0.972884i \(-0.574296\pi\)
0.958189 0.286135i \(-0.0923706\pi\)
\(510\) 0 0
\(511\) 0.757359 0.0335036
\(512\) −22.7574 −1.00574
\(513\) −5.32843 9.22911i −0.235256 0.407475i
\(514\) −4.62132 + 8.00436i −0.203838 + 0.353057i
\(515\) 0 0
\(516\) −4.12742 + 7.14890i −0.181699 + 0.314713i
\(517\) 15.6569 27.1185i 0.688588 1.19267i
\(518\) −0.0857864 + 0.148586i −0.00376924 + 0.00652851i
\(519\) 3.44365 0.151159
\(520\) 0 0
\(521\) 10.2279 + 17.7153i 0.448093 + 0.776121i 0.998262 0.0589331i \(-0.0187699\pi\)
−0.550169 + 0.835054i \(0.685437\pi\)
\(522\) 4.00000 6.92820i 0.175075 0.303239i
\(523\) 8.00000 0.349816 0.174908 0.984585i \(-0.444037\pi\)
0.174908 + 0.984585i \(0.444037\pi\)
\(524\) −12.1066 20.9692i −0.528879 0.916046i
\(525\) 0 0
\(526\) −9.65685 −0.421059
\(527\) 2.20711 + 32.3762i 0.0961431 + 1.41033i
\(528\) −4.02944 −0.175359
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) −11.5147 −0.499696
\(532\) 1.67157 2.89525i 0.0724719 0.125525i
\(533\) 14.3284 + 24.8176i 0.620633 + 1.07497i
\(534\) −0.384776 0.666452i −0.0166509 0.0288402i
\(535\) 0 0
\(536\) 2.57107 4.45322i 0.111053 0.192350i
\(537\) −3.15685 + 5.46783i −0.136228 + 0.235954i
\(538\) −5.42031 + 9.38825i −0.233686 + 0.404756i
\(539\) 11.0711 + 19.1757i 0.476865 + 0.825954i
\(540\) 0 0
\(541\) 15.6421 + 27.0930i 0.672508 + 1.16482i 0.977191 + 0.212364i \(0.0681162\pi\)
−0.304683 + 0.952454i \(0.598550\pi\)
\(542\) 0.284271 0.0122105
\(543\) −5.10051 −0.218884
\(544\) 12.8640 + 22.2810i 0.551538 + 0.955291i
\(545\) 0 0
\(546\) −0.136039 0.235626i −0.00582193 0.0100839i
\(547\) −9.86396 + 17.0849i −0.421753 + 0.730497i −0.996111 0.0881071i \(-0.971918\pi\)
0.574358 + 0.818604i \(0.305252\pi\)
\(548\) −8.67157 + 15.0196i −0.370431 + 0.641606i
\(549\) −4.00000 + 6.92820i −0.170716 + 0.295689i
\(550\) 0 0
\(551\) 15.0711 + 26.1039i 0.642049 + 1.11206i
\(552\) 1.31371 + 2.27541i 0.0559151 + 0.0968479i
\(553\) 1.39949 2.42400i 0.0595126 0.103079i
\(554\) 5.85786 0.248877
\(555\) 0 0
\(556\) 0 0
\(557\) −27.5147 −1.16584 −0.582918 0.812531i \(-0.698089\pi\)
−0.582918 + 0.812531i \(0.698089\pi\)
\(558\) 5.41421 3.63818i 0.229202 0.154017i
\(559\) 41.7279 1.76490
\(560\) 0 0
\(561\) 3.91421 + 6.77962i 0.165258 + 0.286236i
\(562\) −0.828427 −0.0349451
\(563\) 6.62132 11.4685i 0.279055 0.483338i −0.692095 0.721807i \(-0.743312\pi\)
0.971150 + 0.238468i \(0.0766454\pi\)
\(564\) 3.65685 + 6.33386i 0.153981 + 0.266704i
\(565\) 0 0
\(566\) −5.65685 −0.237775
\(567\) −1.55025 + 2.68512i −0.0651045 + 0.112764i
\(568\) −0.0563492 + 0.0975997i −0.00236436 + 0.00409519i
\(569\) 6.57107 11.3814i 0.275473 0.477134i −0.694781 0.719221i \(-0.744499\pi\)
0.970254 + 0.242087i \(0.0778320\pi\)
\(570\) 0 0
\(571\) 10.5503 18.2736i 0.441514 0.764725i −0.556288 0.830990i \(-0.687775\pi\)
0.997802 + 0.0662645i \(0.0211081\pi\)
\(572\) 11.3492 + 19.6575i 0.474536 + 0.821920i
\(573\) 8.65685 0.361645
\(574\) 1.28427 0.0536044
\(575\) 0 0
\(576\) −5.89949 + 10.2182i −0.245812 + 0.425759i
\(577\) −0.0147186 0.0254934i −0.000612744 0.00106130i 0.865719 0.500531i \(-0.166862\pi\)
−0.866332 + 0.499469i \(0.833528\pi\)
\(578\) 3.51472 6.08767i 0.146193 0.253214i
\(579\) −1.47918 + 2.56202i −0.0614728 + 0.106474i
\(580\) 0 0
\(581\) 4.17157 0.173066
\(582\) 0.443651 + 0.768426i 0.0183899 + 0.0318523i
\(583\) 9.44975 + 16.3674i 0.391369 + 0.677870i
\(584\) −1.44975 + 2.51104i −0.0599910 + 0.103907i
\(585\) 0 0
\(586\) −3.06497 5.30869i −0.126613 0.219300i
\(587\) 31.6569 1.30662 0.653309 0.757091i \(-0.273380\pi\)
0.653309 + 0.757091i \(0.273380\pi\)
\(588\) −5.17157 −0.213272
\(589\) 1.67157 + 24.5204i 0.0688760 + 1.01035i
\(590\) 0 0
\(591\) −5.58579 −0.229769
\(592\) 1.50000 + 2.59808i 0.0616496 + 0.106780i
\(593\) 1.31371 0.0539475 0.0269738 0.999636i \(-0.491413\pi\)
0.0269738 + 0.999636i \(0.491413\pi\)
\(594\) 1.62132 2.80821i 0.0665236 0.115222i
\(595\) 0 0
\(596\) 0.914214 + 1.58346i 0.0374476 + 0.0648612i
\(597\) −7.62742 −0.312169
\(598\) 3.17157 5.49333i 0.129695 0.224639i
\(599\) −7.55025 + 13.0774i −0.308495 + 0.534329i −0.978033 0.208449i \(-0.933159\pi\)
0.669538 + 0.742777i \(0.266492\pi\)
\(600\) 0 0
\(601\) 3.25736 + 5.64191i 0.132870 + 0.230138i 0.924782 0.380498i \(-0.124247\pi\)
−0.791911 + 0.610636i \(0.790914\pi\)
\(602\) 0.935029 1.61952i 0.0381089 0.0660066i
\(603\) −4.58579 7.94282i −0.186748 0.323456i
\(604\) −9.71573 −0.395327
\(605\) 0 0
\(606\) 0.727922 + 1.26080i 0.0295698 + 0.0512164i
\(607\) −0.792893 + 1.37333i −0.0321825 + 0.0557418i −0.881668 0.471870i \(-0.843579\pi\)
0.849486 + 0.527612i \(0.176912\pi\)
\(608\) 9.74264 + 16.8747i 0.395116 + 0.684361i
\(609\) −0.585786 + 1.01461i −0.0237373 + 0.0411141i
\(610\) 0 0
\(611\) 18.4853 32.0174i 0.747834 1.29529i
\(612\) 30.1421 1.21842
\(613\) 6.15685 + 10.6640i 0.248673 + 0.430714i 0.963158 0.268937i \(-0.0866722\pi\)
−0.714485 + 0.699651i \(0.753339\pi\)
\(614\) 2.32843 + 4.03295i 0.0939677 + 0.162757i
\(615\) 0 0
\(616\) 2.12994 0.0858178
\(617\) −16.6421 28.8250i −0.669987 1.16045i −0.977907 0.209040i \(-0.932966\pi\)
0.307920 0.951412i \(-0.400367\pi\)
\(618\) −0.355339 −0.0142938
\(619\) −20.3431 −0.817660 −0.408830 0.912611i \(-0.634063\pi\)
−0.408830 + 0.912611i \(0.634063\pi\)
\(620\) 0 0
\(621\) 9.65685 0.387516
\(622\) −4.68629 −0.187903
\(623\) −0.928932 1.60896i −0.0372169 0.0644615i
\(624\) −4.75736 −0.190447
\(625\) 0 0
\(626\) 0.378680 + 0.655892i 0.0151351 + 0.0262147i
\(627\) 2.96447 + 5.13461i 0.118389 + 0.205056i
\(628\) 16.7696 0.669178
\(629\) 2.91421 5.04757i 0.116197 0.201260i
\(630\) 0 0
\(631\) −25.0061 + 43.3118i −0.995477 + 1.72422i −0.415464 + 0.909610i \(0.636381\pi\)
−0.580013 + 0.814607i \(0.696953\pi\)
\(632\) 5.35786 + 9.28009i 0.213124 + 0.369142i
\(633\) 2.15685 3.73578i 0.0857273 0.148484i
\(634\) 1.62132 + 2.80821i 0.0643909 + 0.111528i
\(635\) 0 0
\(636\) −4.41421 −0.175035
\(637\) 13.0711 + 22.6398i 0.517895 + 0.897020i
\(638\) −4.58579 + 7.94282i −0.181553 + 0.314459i
\(639\) 0.100505 + 0.174080i 0.00397592 + 0.00688649i
\(640\) 0 0
\(641\) 6.98528 12.0989i 0.275902 0.477876i −0.694460 0.719531i \(-0.744357\pi\)
0.970362 + 0.241655i \(0.0776901\pi\)
\(642\) 1.06497 1.84458i 0.0420311 0.0727999i
\(643\) −35.3137 −1.39264 −0.696318 0.717733i \(-0.745180\pi\)
−0.696318 + 0.717733i \(0.745180\pi\)
\(644\) 1.51472 + 2.62357i 0.0596883 + 0.103383i
\(645\) 0 0
\(646\) 5.32843 9.22911i 0.209644 0.363114i
\(647\) 45.3137 1.78147 0.890733 0.454527i \(-0.150192\pi\)
0.890733 + 0.454527i \(0.150192\pi\)
\(648\) −5.93503 10.2798i −0.233150 0.403828i
\(649\) 13.2010 0.518185
\(650\) 0 0
\(651\) −0.792893 + 0.532799i −0.0310759 + 0.0208821i
\(652\) 38.3431 1.50163
\(653\) 6.14214 0.240360 0.120180 0.992752i \(-0.461653\pi\)
0.120180 + 0.992752i \(0.461653\pi\)
\(654\) 0.928932 + 1.60896i 0.0363241 + 0.0629152i
\(655\) 0 0
\(656\) 11.2279 19.4473i 0.438377 0.759291i
\(657\) 2.58579 + 4.47871i 0.100881 + 0.174731i
\(658\) −0.828427 1.43488i −0.0322955 0.0559374i
\(659\) −1.65685 −0.0645419 −0.0322709 0.999479i \(-0.510274\pi\)
−0.0322709 + 0.999479i \(0.510274\pi\)
\(660\) 0 0
\(661\) −2.42893 + 4.20703i −0.0944745 + 0.163635i −0.909389 0.415946i \(-0.863450\pi\)
0.814915 + 0.579581i \(0.196784\pi\)
\(662\) 1.91421 3.31552i 0.0743980 0.128861i
\(663\) 4.62132 + 8.00436i 0.179477 + 0.310864i
\(664\) −7.98528 + 13.8309i −0.309889 + 0.536744i
\(665\) 0 0
\(666\) −1.17157 −0.0453975
\(667\) −27.3137 −1.05759
\(668\) −20.6213 35.7172i −0.797863 1.38194i
\(669\) 4.91421 8.51167i 0.189994 0.329080i
\(670\) 0 0
\(671\) 4.58579 7.94282i 0.177032 0.306629i
\(672\) −0.378680 + 0.655892i −0.0146079 + 0.0253016i
\(673\) 4.67157 8.09140i 0.180076 0.311901i −0.761830 0.647777i \(-0.775699\pi\)
0.941906 + 0.335876i \(0.109032\pi\)
\(674\) 3.85786 0.148599
\(675\) 0 0
\(676\) 1.51472 + 2.62357i 0.0582584 + 0.100907i
\(677\) −19.2990 + 33.4268i −0.741720 + 1.28470i 0.209991 + 0.977703i \(0.432657\pi\)
−0.951711 + 0.306994i \(0.900677\pi\)
\(678\) −2.85786 −0.109756
\(679\) 1.07107 + 1.85514i 0.0411038 + 0.0711939i
\(680\) 0 0
\(681\) −7.62742 −0.292283
\(682\) −6.20711 + 4.17098i −0.237682 + 0.159715i
\(683\) 1.37258 0.0525204 0.0262602 0.999655i \(-0.491640\pi\)
0.0262602 + 0.999655i \(0.491640\pi\)
\(684\) 22.8284 0.872867
\(685\) 0 0
\(686\) 2.37258 0.0905856
\(687\) −1.13604 + 1.96768i −0.0433426 + 0.0750716i
\(688\) −16.3492 28.3177i −0.623309 1.07960i
\(689\) 11.1569 + 19.3242i 0.425042 + 0.736195i
\(690\) 0 0
\(691\) 0.0355339 0.0615465i 0.00135177 0.00234134i −0.865349 0.501170i \(-0.832903\pi\)
0.866700 + 0.498829i \(0.166236\pi\)
\(692\) −7.60051 + 13.1645i −0.288928 + 0.500438i
\(693\) 1.89949 3.29002i 0.0721558 0.124978i
\(694\) 1.77208 + 3.06933i 0.0672672 + 0.116510i
\(695\) 0 0
\(696\) −2.24264 3.88437i −0.0850071 0.147237i
\(697\) −43.6274 −1.65251
\(698\) 11.2304 0.425079
\(699\) 1.89949 + 3.29002i 0.0718455 + 0.124440i
\(700\) 0 0
\(701\) 6.74264 + 11.6786i 0.254666 + 0.441094i 0.964805 0.262967i \(-0.0847011\pi\)
−0.710139 + 0.704062i \(0.751368\pi\)
\(702\) 1.91421 3.31552i 0.0722473 0.125136i
\(703\) 2.20711 3.82282i 0.0832426 0.144180i
\(704\) 6.76346 11.7146i 0.254907 0.441512i
\(705\) 0 0
\(706\) −0.621320 1.07616i −0.0233837 0.0405018i
\(707\) 1.75736 + 3.04384i 0.0660923 + 0.114475i
\(708\) −1.54163 + 2.67018i −0.0579380 + 0.100352i
\(709\) 17.3137 0.650230 0.325115 0.945674i \(-0.394597\pi\)
0.325115 + 0.945674i \(0.394597\pi\)
\(710\) 0 0
\(711\) 19.1127 0.716782
\(712\) 7.11270 0.266560
\(713\) −20.0000 9.79796i −0.749006 0.366936i
\(714\) 0.414214 0.0155016
\(715\) 0 0
\(716\) −13.9350 24.1362i −0.520776 0.902011i
\(717\) 8.79899 0.328604
\(718\) 1.47056 2.54709i 0.0548809 0.0950565i
\(719\) 4.03553 + 6.98975i 0.150500 + 0.260674i 0.931411 0.363968i \(-0.118578\pi\)
−0.780911 + 0.624642i \(0.785245\pi\)
\(720\) 0 0
\(721\) −0.857864 −0.0319485
\(722\) 0.100505 0.174080i 0.00374041 0.00647858i
\(723\) 2.76346 4.78645i 0.102774 0.178010i
\(724\) 11.2574 19.4983i 0.418376 0.724649i
\(725\) 0 0
\(726\) 0.0416306 0.0721062i 0.00154506 0.00267611i
\(727\) 20.4203 + 35.3690i 0.757347 + 1.31176i 0.944199 + 0.329376i \(0.106838\pi\)
−0.186851 + 0.982388i \(0.559828\pi\)
\(728\) 2.51472 0.0932017
\(729\) −18.1716 −0.673021
\(730\) 0 0
\(731\) −31.7635 + 55.0159i −1.17481 + 2.03484i
\(732\) 1.07107 + 1.85514i 0.0395878 + 0.0685681i
\(733\) 7.81371 13.5337i 0.288606 0.499880i −0.684871 0.728664i \(-0.740142\pi\)
0.973477 + 0.228784i \(0.0734749\pi\)
\(734\) 5.01472 8.68575i 0.185097 0.320597i
\(735\) 0 0
\(736\) −17.6569 −0.650840
\(737\) 5.25736 + 9.10601i 0.193657 + 0.335424i
\(738\) 4.38478 + 7.59466i 0.161406 + 0.279563i
\(739\) −22.9350 + 39.7246i −0.843679 + 1.46129i 0.0430851 + 0.999071i \(0.486281\pi\)
−0.886764 + 0.462223i \(0.847052\pi\)
\(740\) 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 \(-0.533089\pi\)
−0.103765 + 0.994602i \(0.533089\pi\)
\(744\) −0.248737 3.64874i −0.00911915 0.133769i
\(745\) 0 0
\(746\) 4.14214 0.151654
\(747\) 14.2426 + 24.6690i 0.521111 + 0.902591i
\(748\) −34.5563 −1.26351
\(749\) 2.57107 4.45322i 0.0939448 0.162717i
\(750\) 0 0
\(751\) −3.62132 6.27231i −0.132144 0.228880i 0.792359 0.610055i \(-0.208853\pi\)
−0.924503 + 0.381175i \(0.875519\pi\)
\(752\) −28.9706 −1.05645
\(753\) 1.32843 2.30090i 0.0484106 0.0838496i
\(754\) −5.41421 + 9.37769i −0.197174 + 0.341515i
\(755\) 0 0
\(756\) 0.914214 + 1.58346i 0.0332496 + 0.0575900i
\(757\) 11.6716 20.2158i 0.424211 0.734754i −0.572136 0.820159i \(-0.693885\pi\)
0.996346 + 0.0854047i \(0.0272183\pi\)
\(758\) 1.52944 + 2.64906i 0.0555517 + 0.0962183i
\(759\) −5.37258 −0.195012
\(760\) 0 0
\(761\) −15.2279 26.3755i −0.552012 0.956112i −0.998129 0.0611380i \(-0.980527\pi\)
0.446118 0.894974i \(-0.352806\pi\)
\(762\) 0.763456 1.32234i 0.0276571 0.0479035i
\(763\) 2.24264 + 3.88437i 0.0811890 + 0.140624i
\(764\) −19.1066 + 33.0936i −0.691253 + 1.19728i
\(765\) 0 0
\(766\) −1.05635 + 1.82965i −0.0381674 + 0.0661080i
\(767\) 15.5858 0.562770
\(768\) 0.822330 + 1.42432i 0.0296733 + 0.0513957i
\(769\) −18.0563 31.2745i −0.651129 1.12779i −0.982849 0.184410i \(-0.940963\pi\)
0.331721 0.943378i \(-0.392371\pi\)
\(770\) 0 0
\(771\) 9.24264 0.332866
\(772\) −6.52944 11.3093i −0.235000 0.407031i
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 12.7696 0.458992
\(775\) 0 0
\(776\) −8.20101 −0.294399
\(777\) 0.171573 0.00615514
\(778\) −2.30761 3.99690i −0.0827319 0.143296i
\(779\) −33.0416 −1.18384
\(780\) 0 0
\(781\) −0.115224 0.199573i −0.00412303 0.00714129i
\(782\) 4.82843 + 8.36308i 0.172664 + 0.299063i
\(783\) −16.4853 −0.589136
\(784\) 10.2426 17.7408i 0.365809 0.633599i
\(785\) 0 0
\(786\) 1.13604 1.96768i 0.0405212 0.0701847i
\(787\) 21.2071 + 36.7318i 0.755952 + 1.30935i 0.944900 + 0.327360i \(0.106159\pi\)
−0.188948 + 0.981987i \(0.560508\pi\)
\(788\) 12.3284 21.3535i 0.439182 0.760686i
\(789\) 4.82843 + 8.36308i 0.171897 + 0.297734i
\(790\) 0 0
\(791\) −6.89949 −0.245318
\(792\) 7.27208 + 12.5956i 0.258402 + 0.447565i
\(793\) 5.41421 9.37769i 0.192264 0.333012i
\(794\) 6.93503 + 12.0118i 0.246115 + 0.426284i
\(795\) 0 0
\(796\) 16.8345 29.1583i 0.596684 1.03349i
\(797\) 14.2279 24.6435i 0.503979 0.872917i −0.496011 0.868316i \(-0.665202\pi\)
0.999989 0.00460050i \(-0.00146439\pi\)
\(798\) 0.313708 0.0111052
\(799\) 28.1421 + 48.7436i 0.995597 + 1.72442i
\(800\) 0 0
\(801\) 6.34315 10.9867i 0.224124 0.388194i
\(802\) 11.1127 0.392403
\(803\) −2.96447 5.13461i −0.104614 0.181196i
\(804\) −2.45584 −0.0866109
\(805\) 0 0
\(806\) −7.32843 + 4.92447i −0.258133 + 0.173457i
\(807\) 10.8406 0.381608
\(808\) −13.4558 −0.473375
\(809\) 6.01472 + 10.4178i 0.211466 + 0.366270i 0.952174 0.305558i \(-0.0988428\pi\)
−0.740707 + 0.671828i \(0.765509\pi\)
\(810\) 0 0
\(811\) 6.86396 11.8887i 0.241026 0.417470i −0.719981 0.693994i \(-0.755849\pi\)
0.961007 + 0.276524i \(0.0891827\pi\)
\(812\) −2.58579 4.47871i −0.0907433 0.157172i
\(813\) −0.142136 0.246186i −0.00498491 0.00863412i
\(814\) 1.34315 0.0470772
\(815\) 0 0
\(816\) 3.62132 6.27231i 0.126772 0.219575i
\(817\) −24.0563 + 41.6668i −0.841625 + 1.45774i
\(818\) 4.27817 + 7.41002i 0.149583 + 0.259085i
\(819\) 2.24264 3.88437i 0.0783642 0.135731i
\(820\) 0 0
\(821\) 8.48528 0.296138 0.148069 0.988977i \(-0.452694\pi\)
0.148069 + 0.988977i \(0.452694\pi\)
\(822\) −1.62742 −0.0567627
\(823\) 18.1066 + 31.3616i 0.631156 + 1.09320i 0.987316 + 0.158770i \(0.0507528\pi\)
−0.356159 + 0.934425i \(0.615914\pi\)
\(824\) 1.64214 2.84426i 0.0572065 0.0990846i
\(825\) 0 0
\(826\) 0.349242 0.604906i 0.0121517 0.0210474i
\(827\) 18.4497 31.9559i 0.641561 1.11122i −0.343524 0.939144i \(-0.611621\pi\)
0.985084 0.172072i \(-0.0550460\pi\)
\(828\) −10.3431 + 17.9149i −0.359449 + 0.622584i
\(829\) 38.4264 1.33460 0.667302 0.744787i \(-0.267449\pi\)
0.667302 + 0.744787i \(0.267449\pi\)
\(830\) 0 0
\(831\) −2.92893 5.07306i −0.101604 0.175982i
\(832\) 7.98528 13.8309i 0.276840 0.479501i
\(833\) −39.7990 −1.37895
\(834\) 0 0
\(835\) 0 0
\(836\) −26.1716 −0.905163
\(837\) −12.0711 5.91359i −0.417237 0.204404i
\(838\) −11.5980 −0.400646
\(839\) −14.6274 −0.504995 −0.252497 0.967598i \(-0.581252\pi\)
−0.252497 + 0.967598i \(0.581252\pi\)
\(840\) 0 0
\(841\) 17.6274 0.607842
\(842\) −6.44975 + 11.1713i −0.222273 + 0.384988i
\(843\) 0.414214 + 0.717439i 0.0142663 + 0.0247099i
\(844\) 9.52082 + 16.4905i 0.327720 + 0.567628i
\(845\) 0 0
\(846\) 5.65685 9.79796i 0.194487 0.336861i
\(847\) 0.100505 0.174080i 0.00345339 0.00598146i
\(848\) 8.74264 15.1427i 0.300224 0.520002i
\(849\) 2.82843 + 4.89898i 0.0970714 + 0.168133i
\(850\) 0 0
\(851\) 2.00000 + 3.46410i 0.0685591 + 0.118748i
\(852\) 0.0538239 0.00184398
\(853\) 15.5147 0.531214 0.265607 0.964081i \(-0.414428\pi\)
0.265607 + 0.964081i \(0.414428\pi\)
\(854\) −0.242641 0.420266i −0.00830299 0.0143812i
\(855\) 0 0
\(856\) 9.84315 + 17.0488i 0.336432 + 0.582717i
\(857\) −9.74264 + 16.8747i −0.332802 + 0.576430i −0.983060 0.183283i \(-0.941328\pi\)
0.650258 + 0.759714i \(0.274661\pi\)
\(858\) −1.06497 + 1.84458i −0.0363575 + 0.0629731i
\(859\) 24.6924 42.7685i 0.842493 1.45924i −0.0452869 0.998974i \(-0.514420\pi\)
0.887780 0.460267i \(-0.152246\pi\)
\(860\) 0 0
\(861\) −0.642136 1.11221i −0.0218839 0.0379041i
\(862\) −3.47056 6.01119i −0.118208 0.204742i
\(863\) −1.30761 + 2.26485i −0.0445116 + 0.0770964i −0.887423 0.460956i \(-0.847507\pi\)
0.842911 + 0.538053i \(0.180840\pi\)
\(864\) −10.6569 −0.362554
\(865\) 0 0
\(866\) 11.2304 0.381626
\(867\) −7.02944 −0.238732
\(868\) −0.286797 4.20703i −0.00973451 0.142796i
\(869\) −21.9117 −0.743303
\(870\) 0 0
\(871\) 6.20711 + 10.7510i 0.210320 + 0.364285i
\(872\) −17.1716 −0.581503
\(873\) −7.31371 + 12.6677i −0.247532 + 0.428737i
\(874\) 3.65685 + 6.33386i 0.123695 + 0.214246i
\(875\) 0 0
\(876\) 1.38478 0.0467873
\(877\) 26.9142 46.6168i 0.908828 1.57414i 0.0931343 0.995654i \(-0.470311\pi\)
0.815694 0.578483i \(-0.196355\pi\)
\(878\) 0.428932 0.742932i 0.0144758 0.0250728i
\(879\) −3.06497 + 5.30869i −0.103379 + 0.179058i
\(880\) 0 0
\(881\) −5.84315 + 10.1206i −0.196861 + 0.340973i −0.947509 0.319729i \(-0.896408\pi\)
0.750648 + 0.660702i \(0.229741\pi\)
\(882\) 4.00000 + 6.92820i 0.134687 + 0.233285i
\(883\) 30.2843 1.01915 0.509573 0.860427i \(-0.329803\pi\)
0.509573 + 0.860427i \(0.329803\pi\)
\(884\) −40.7990 −1.37222
\(885\) 0 0
\(886\) 0.985281 1.70656i 0.0331012 0.0573329i
\(887\) −25.6630 44.4495i −0.861678 1.49247i −0.870309 0.492507i \(-0.836081\pi\)
0.00863117 0.999963i \(-0.497253\pi\)
\(888\) −0.328427 + 0.568852i −0.0110213 + 0.0190894i
\(889\) 1.84315 3.19242i 0.0618171 0.107070i
\(890\) 0 0
\(891\) 24.2721 0.813145
\(892\) 21.6924 + 37.5723i 0.726315 + 1.25801i
\(893\) 21.3137 + 36.9164i 0.713236 + 1.23536i
\(894\) −0.0857864 + 0.148586i −0.00286913 + 0.00496947i
\(895\) 0 0
\(896\) −2.18629 3.78677i −0.0730389 0.126507i
\(897\) −6.34315 −0.211791
\(898\) 16.8284 0.561572
\(899\) 34.1421 + 16.7262i 1.13870 + 0.557849i
\(900\) 0 0
\(901\) −33.9706 −1.13172
\(902\) −5.02691 8.70687i −0.167378 0.289907i
\(903\) −1.87006 −0.0622316
\(904\) 13.2071 22.8754i 0.439262 0.760824i
\(905\) 0 0
\(906\) −0.455844 0.789545i −0.0151444 0.0262309i
\(907\) −32.6863 −1.08533 −0.542665 0.839949i \(-0.682585\pi\)
−0.542665 + 0.839949i \(0.682585\pi\)
\(908\) 16.8345 29.1583i 0.558673 0.967651i
\(909\) −12.0000 + 20.7846i −0.398015 + 0.689382i
\(910\) 0 0
\(911\) −0.479185 0.829972i −0.0158761 0.0274982i 0.857978 0.513686i \(-0.171720\pi\)
−0.873854 + 0.486188i \(0.838387\pi\)
\(912\) 2.74264 4.75039i 0.0908179 0.157301i
\(913\) −16.3284 28.2817i −0.540392 0.935987i
\(914\) −12.8873 −0.426274
\(915\) 0 0
\(916\) −5.01472 8.68575i −0.165691 0.286985i
\(917\) 2.74264 4.75039i 0.0905700 0.156872i
\(918\) 2.91421 + 5.04757i 0.0961834 + 0.166595i
\(919\) 17.4497 30.2238i 0.575614 0.996993i −0.420361 0.907357i \(-0.638096\pi\)
0.995975 0.0896356i \(-0.0285703\pi\)
\(920\) 0 0
\(921\) 2.32843 4.03295i 0.0767243 0.132890i
\(922\) 0.887302 0.0292217
\(923\) −0.136039 0.235626i −0.00447778 0.00775574i
\(924\) −0.508622 0.880959i −0.0167324 0.0289814i
\(925\) 0 0
\(926\) −3.71573 −0.122106
\(927\) −2.92893 5.07306i −0.0961988 0.166621i
\(928\) 30.1421 0.989464
\(929\) 7.51472 0.246550 0.123275 0.992373i \(-0.460660\pi\)
0.123275 + 0.992373i \(0.460660\pi\)
\(930\) 0 0
\(931\) −30.1421 −0.987869
\(932\) −16.7696 −0.549305
\(933\) 2.34315 + 4.05845i 0.0767111 + 0.132868i
\(934\) −3.31371 −0.108428
\(935\) 0 0
\(936\) 8.58579 + 14.8710i 0.280635 + 0.486074i
\(937\) 7.84315 + 13.5847i 0.256224 + 0.443794i 0.965227 0.261412i \(-0.0841881\pi\)
−0.709003 + 0.705206i \(0.750855\pi\)
\(938\) 0.556349 0.0181654
\(939\) 0.378680 0.655892i 0.0123577 0.0214042i
\(940\) 0 0
\(941\) 17.5000 30.3109i 0.570484 0.988107i −0.426033 0.904708i \(-0.640089\pi\)
0.996516 0.0833989i \(-0.0265776\pi\)
\(942\) 0.786797 + 1.36277i 0.0256352 + 0.0444015i
\(943\) 14.9706 25.9298i 0.487509 0.844390i
\(944\) −6.10660 10.5769i −0.198753 0.344250i
\(945\) 0 0
\(946\) −14.6396 −0.475975
\(947\) 9.55025 + 16.5415i 0.310342 + 0.537527i 0.978436 0.206549i \(-0.0662233\pi\)
−0.668095 + 0.744076i \(0.732890\pi\)
\(948\) 2.55887 4.43210i 0.0831084 0.143948i
\(949\) −3.50000 6.06218i −0.113615 0.196787i
\(950\) 0 0
\(951\) 1.62132 2.80821i 0.0525749 0.0910624i
\(952\) −1.91421 + 3.31552i −0.0620400 + 0.107456i
\(953\) −3.51472 −0.113853 −0.0569265 0.998378i \(-0.518130\pi\)
−0.0569265 + 0.998378i \(0.518130\pi\)
\(954\) 3.41421 + 5.91359i 0.110539 + 0.191460i
\(955\) 0 0
\(956\) −19.4203 + 33.6370i −0.628098 + 1.08790i
\(957\) 9.17157 0.296475
\(958\) −3.25736 5.64191i −0.105241 0.182282i
\(959\) −3.92893 −0.126872
\(960\) 0 0
\(961\) 19.0000 + 24.4949i 0.612903 + 0.790158i
\(962\) 1.58579 0.0511278
\(963\) 35.1127 1.13149
\(964\) 12.1985 + 21.1284i 0.392887 + 0.680500i
\(965\) 0 0
\(966\) −0.142136 + 0.246186i −0.00457314 + 0.00792091i
\(967\) −7.72183 13.3746i −0.248317 0.430098i 0.714742 0.699388i \(-0.246544\pi\)
−0.963059 + 0.269290i \(0.913211\pi\)
\(968\) 0.384776 + 0.666452i 0.0123672 + 0.0214206i
\(969\) −10.6569 −0.342347
\(970\) 0 0
\(971\) 0.349242 0.604906i 0.0112077 0.0194123i −0.860367 0.509675i \(-0.829766\pi\)
0.871575 + 0.490262i \(0.163099\pi\)
\(972\) −9.45584 + 16.3780i −0.303296 + 0.525325i
\(973\) 0 0
\(974\) −4.01472 + 6.95370i −0.128640 + 0.222811i
\(975\) 0 0
\(976\) −8.48528 −0.271607
\(977\) 0.485281 0.0155255 0.00776276 0.999970i \(-0.497529\pi\)
0.00776276 + 0.999970i \(0.497529\pi\)
\(978\) 1.79899 + 3.11594i 0.0575254 + 0.0996368i
\(979\) −7.27208 + 12.5956i −0.232417 + 0.402557i
\(980\) 0 0
\(981\) −15.3137 + 26.5241i −0.488929 + 0.846850i
\(982\) 0.328427 0.568852i 0.0104805 0.0181528i
\(983\) −19.4203 + 33.6370i −0.619412 + 1.07285i 0.370182 + 0.928959i \(0.379295\pi\)
−0.989593 + 0.143893i \(0.954038\pi\)
\(984\) 4.91674 0.156740
\(985\) 0 0
\(986\) −8.24264 14.2767i −0.262499 0.454662i
\(987\) −0.828427 + 1.43488i −0.0263691 + 0.0456727i
\(988\) −30.8995 −0.983044
\(989\) −21.7990 37.7570i −0.693168 1.20060i
\(990\) 0 0
\(991\) 47.9411 1.52290 0.761450 0.648224i \(-0.224488\pi\)
0.761450 + 0.648224i \(0.224488\pi\)
\(992\) 22.0711 + 10.8126i 0.700757 + 0.343299i
\(993\) −3.82843 −0.121491
\(994\) −0.0121933 −0.000386748
\(995\) 0 0
\(996\) 7.62742 0.241684
\(997\) 16.2990 28.2307i 0.516194 0.894075i −0.483629 0.875273i \(-0.660682\pi\)
0.999823 0.0188015i \(-0.00598505\pi\)
\(998\) −0.458369 0.793919i −0.0145094 0.0251311i
\(999\) 1.20711 + 2.09077i 0.0381912 + 0.0661490i
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.676.1 4
5.2 odd 4 775.2.o.d.149.2 8
5.3 odd 4 775.2.o.d.149.3 8
5.4 even 2 31.2.c.a.25.2 yes 4
15.14 odd 2 279.2.h.c.118.1 4
20.19 odd 2 496.2.i.h.273.2 4
31.5 even 3 inner 775.2.e.e.501.1 4
155.4 even 10 961.2.g.o.338.1 16
155.9 even 30 961.2.g.o.816.1 16
155.14 even 30 961.2.d.l.374.1 8
155.19 even 30 961.2.d.l.531.2 8
155.24 odd 30 961.2.d.i.388.1 8
155.29 odd 10 961.2.g.r.844.2 16
155.34 odd 30 961.2.d.i.628.2 8
155.39 even 10 961.2.g.o.732.1 16
155.44 odd 30 961.2.g.r.846.2 16
155.49 even 30 961.2.g.o.846.2 16
155.54 odd 10 961.2.g.r.732.1 16
155.59 even 30 961.2.d.l.628.2 8
155.64 even 10 961.2.g.o.844.2 16
155.67 odd 12 775.2.o.d.749.2 8
155.69 even 30 961.2.d.l.388.1 8
155.74 odd 30 961.2.d.i.531.2 8
155.79 odd 30 961.2.d.i.374.1 8
155.84 odd 30 961.2.g.r.816.1 16
155.89 odd 10 961.2.g.r.338.1 16
155.98 odd 12 775.2.o.d.749.3 8
155.99 odd 6 961.2.a.c.1.2 2
155.104 odd 30 961.2.g.r.235.1 16
155.109 even 10 961.2.g.o.448.2 16
155.114 odd 30 961.2.g.r.547.2 16
155.119 odd 6 961.2.c.a.439.2 4
155.129 even 6 31.2.c.a.5.2 4
155.134 even 30 961.2.g.o.547.2 16
155.139 odd 10 961.2.g.r.448.2 16
155.144 even 30 961.2.g.o.235.1 16
155.149 even 6 961.2.a.a.1.2 2
155.154 odd 2 961.2.c.a.521.2 4
465.149 odd 6 8649.2.a.l.1.1 2
465.254 even 6 8649.2.a.k.1.1 2
465.284 odd 6 279.2.h.c.253.1 4
620.439 odd 6 496.2.i.h.129.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
31.2.c.a.5.2 4 155.129 even 6
31.2.c.a.25.2 yes 4 5.4 even 2
279.2.h.c.118.1 4 15.14 odd 2
279.2.h.c.253.1 4 465.284 odd 6
496.2.i.h.129.2 4 620.439 odd 6
496.2.i.h.273.2 4 20.19 odd 2
775.2.e.e.501.1 4 31.5 even 3 inner
775.2.e.e.676.1 4 1.1 even 1 trivial
775.2.o.d.149.2 8 5.2 odd 4
775.2.o.d.149.3 8 5.3 odd 4
775.2.o.d.749.2 8 155.67 odd 12
775.2.o.d.749.3 8 155.98 odd 12
961.2.a.a.1.2 2 155.149 even 6
961.2.a.c.1.2 2 155.99 odd 6
961.2.c.a.439.2 4 155.119 odd 6
961.2.c.a.521.2 4 155.154 odd 2
961.2.d.i.374.1 8 155.79 odd 30
961.2.d.i.388.1 8 155.24 odd 30
961.2.d.i.531.2 8 155.74 odd 30
961.2.d.i.628.2 8 155.34 odd 30
961.2.d.l.374.1 8 155.14 even 30
961.2.d.l.388.1 8 155.69 even 30
961.2.d.l.531.2 8 155.19 even 30
961.2.d.l.628.2 8 155.59 even 30
961.2.g.o.235.1 16 155.144 even 30
961.2.g.o.338.1 16 155.4 even 10
961.2.g.o.448.2 16 155.109 even 10
961.2.g.o.547.2 16 155.134 even 30
961.2.g.o.732.1 16 155.39 even 10
961.2.g.o.816.1 16 155.9 even 30
961.2.g.o.844.2 16 155.64 even 10
961.2.g.o.846.2 16 155.49 even 30
961.2.g.r.235.1 16 155.104 odd 30
961.2.g.r.338.1 16 155.89 odd 10
961.2.g.r.448.2 16 155.139 odd 10
961.2.g.r.547.2 16 155.114 odd 30
961.2.g.r.732.1 16 155.54 odd 10
961.2.g.r.816.1 16 155.84 odd 30
961.2.g.r.844.2 16 155.29 odd 10
961.2.g.r.846.2 16 155.44 odd 30
8649.2.a.k.1.1 2 465.254 even 6
8649.2.a.l.1.1 2 465.149 odd 6