Properties

Label 1078.2.i.c.901.2
Level $1078$
Weight $2$
Character 1078.901
Analytic conductor $8.608$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1078,2,Mod(901,1078)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1078.901");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} - 102 x^{7} + 144 x^{6} - 432 x^{5} + 502 x^{4} + 288 x^{3} + 72 x^{2} + 12 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.2
Root \(-1.29724 - 0.347596i\) of defining polynomial
Character \(\chi\) \(=\) 1078.901
Dual form 1078.2.i.c.1011.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-1.35034 + 0.779618i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.882559 - 0.509546i) q^{5} +1.55924 q^{6} -1.00000i q^{8} +(-0.284392 + 0.492581i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-1.35034 + 0.779618i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.882559 - 0.509546i) q^{5} +1.55924 q^{6} -1.00000i q^{8} +(-0.284392 + 0.492581i) q^{9} +(0.509546 + 0.882559i) q^{10} +(-0.510616 - 3.27708i) q^{11} +(-1.35034 - 0.779618i) q^{12} +0.167247 q^{13} +1.58900 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.47616 + 2.55678i) q^{17} +(0.492581 - 0.284392i) q^{18} +(0.155850 - 0.269940i) q^{19} -1.01909i q^{20} +(-1.19633 + 3.09335i) q^{22} +(0.237719 - 0.411742i) q^{23} +(0.779618 + 1.35034i) q^{24} +(-1.98073 - 3.43072i) q^{25} +(-0.144840 - 0.0836233i) q^{26} -5.56458i q^{27} +1.89701i q^{29} +(-1.37612 - 0.794502i) q^{30} +(2.20834 - 1.27498i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.24438 + 4.02708i) q^{33} -2.95232i q^{34} -0.568783 q^{36} +(-3.04667 + 5.27699i) q^{37} +(-0.269940 + 0.155850i) q^{38} +(-0.225839 + 0.130388i) q^{39} +(-0.509546 + 0.882559i) q^{40} +10.2084 q^{41} +10.1222i q^{43} +(2.58273 - 2.08075i) q^{44} +(0.501985 - 0.289821i) q^{45} +(-0.411742 + 0.237719i) q^{46} +(3.28968 + 1.89930i) q^{47} -1.55924i q^{48} +3.96145i q^{50} +(-3.98663 - 2.30168i) q^{51} +(0.0836233 + 0.144840i) q^{52} +(-4.21079 - 7.29330i) q^{53} +(-2.78229 + 4.81906i) q^{54} +(-1.21917 + 3.15240i) q^{55} +0.486014i q^{57} +(0.948505 - 1.64286i) q^{58} +(-5.40617 + 3.12126i) q^{59} +(0.794502 + 1.37612i) q^{60} +(-5.93960 + 10.2877i) q^{61} -2.54997 q^{62} -1.00000 q^{64} +(-0.147605 - 0.0852198i) q^{65} +(-0.796171 - 5.10974i) q^{66} +(5.19151 + 8.99196i) q^{67} +(-1.47616 + 2.55678i) q^{68} +0.741321i q^{69} +14.5206 q^{71} +(0.492581 + 0.284392i) q^{72} +(4.85385 + 8.40712i) q^{73} +(5.27699 - 3.04667i) q^{74} +(5.34930 + 3.08842i) q^{75} +0.311700 q^{76} +0.260777 q^{78} +(6.06709 + 3.50284i) q^{79} +(0.882559 - 0.509546i) q^{80} +(3.48507 + 6.03631i) q^{81} +(-8.84069 - 5.10418i) q^{82} +14.6915 q^{83} -3.00868i q^{85} +(5.06112 - 8.76612i) q^{86} +(-1.47894 - 2.56161i) q^{87} +(-3.27708 + 0.510616i) q^{88} +(-5.97639 - 3.45047i) q^{89} -0.579642 q^{90} +0.475438 q^{92} +(-1.98800 + 3.44332i) q^{93} +(-1.89930 - 3.28968i) q^{94} +(-0.275094 + 0.158826i) q^{95} +(-0.779618 + 1.35034i) q^{96} +11.0218i q^{97} +(1.75944 + 0.680455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 36 q^{26} + 12 q^{31} + 24 q^{33} + 32 q^{36} - 16 q^{37} - 12 q^{38} - 8 q^{44} + 108 q^{45} - 24 q^{47} - 28 q^{53} - 12 q^{58} - 60 q^{59} - 4 q^{60} - 16 q^{64} - 48 q^{66} + 12 q^{67} + 8 q^{71} - 60 q^{75} - 16 q^{78} - 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} - 96 q^{89} + 32 q^{92} - 44 q^{93} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −1.35034 + 0.779618i −0.779618 + 0.450113i −0.836295 0.548280i \(-0.815283\pi\)
0.0566769 + 0.998393i \(0.481950\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.882559 0.509546i −0.394692 0.227876i 0.289499 0.957178i \(-0.406511\pi\)
−0.684191 + 0.729303i \(0.739845\pi\)
\(6\) 1.55924 0.636555
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −0.284392 + 0.492581i −0.0947972 + 0.164194i
\(10\) 0.509546 + 0.882559i 0.161132 + 0.279090i
\(11\) −0.510616 3.27708i −0.153957 0.988078i
\(12\) −1.35034 0.779618i −0.389809 0.225056i
\(13\) 0.167247 0.0463859 0.0231929 0.999731i \(-0.492617\pi\)
0.0231929 + 0.999731i \(0.492617\pi\)
\(14\) 0 0
\(15\) 1.58900 0.410279
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.47616 + 2.55678i 0.358021 + 0.620111i 0.987630 0.156801i \(-0.0501182\pi\)
−0.629609 + 0.776912i \(0.716785\pi\)
\(18\) 0.492581 0.284392i 0.116102 0.0670318i
\(19\) 0.155850 0.269940i 0.0357545 0.0619286i −0.847594 0.530645i \(-0.821950\pi\)
0.883349 + 0.468716i \(0.155283\pi\)
\(20\) 1.01909i 0.227876i
\(21\) 0 0
\(22\) −1.19633 + 3.09335i −0.255059 + 0.659503i
\(23\) 0.237719 0.411742i 0.0495679 0.0858541i −0.840177 0.542312i \(-0.817549\pi\)
0.889745 + 0.456458i \(0.150882\pi\)
\(24\) 0.779618 + 1.35034i 0.159139 + 0.275637i
\(25\) −1.98073 3.43072i −0.396145 0.686144i
\(26\) −0.144840 0.0836233i −0.0284054 0.0163999i
\(27\) 5.56458i 1.07090i
\(28\) 0 0
\(29\) 1.89701i 0.352266i 0.984366 + 0.176133i \(0.0563589\pi\)
−0.984366 + 0.176133i \(0.943641\pi\)
\(30\) −1.37612 0.794502i −0.251244 0.145056i
\(31\) 2.20834 1.27498i 0.396629 0.228994i −0.288400 0.957510i \(-0.593123\pi\)
0.685028 + 0.728516i \(0.259790\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 3.24438 + 4.02708i 0.564774 + 0.701025i
\(34\) 2.95232i 0.506318i
\(35\) 0 0
\(36\) −0.568783 −0.0947972
\(37\) −3.04667 + 5.27699i −0.500870 + 0.867532i 0.499130 + 0.866527i \(0.333653\pi\)
−0.999999 + 0.00100474i \(0.999680\pi\)
\(38\) −0.269940 + 0.155850i −0.0437901 + 0.0252822i
\(39\) −0.225839 + 0.130388i −0.0361633 + 0.0208789i
\(40\) −0.509546 + 0.882559i −0.0805662 + 0.139545i
\(41\) 10.2084 1.59428 0.797138 0.603797i \(-0.206346\pi\)
0.797138 + 0.603797i \(0.206346\pi\)
\(42\) 0 0
\(43\) 10.1222i 1.54363i 0.635848 + 0.771814i \(0.280650\pi\)
−0.635848 + 0.771814i \(0.719350\pi\)
\(44\) 2.58273 2.08075i 0.389361 0.313685i
\(45\) 0.501985 0.289821i 0.0748315 0.0432040i
\(46\) −0.411742 + 0.237719i −0.0607080 + 0.0350498i
\(47\) 3.28968 + 1.89930i 0.479849 + 0.277041i 0.720354 0.693607i \(-0.243980\pi\)
−0.240505 + 0.970648i \(0.577313\pi\)
\(48\) 1.55924i 0.225056i
\(49\) 0 0
\(50\) 3.96145i 0.560234i
\(51\) −3.98663 2.30168i −0.558239 0.322300i
\(52\) 0.0836233 + 0.144840i 0.0115965 + 0.0200857i
\(53\) −4.21079 7.29330i −0.578396 1.00181i −0.995664 0.0930275i \(-0.970346\pi\)
0.417268 0.908784i \(-0.362988\pi\)
\(54\) −2.78229 + 4.81906i −0.378621 + 0.655791i
\(55\) −1.21917 + 3.15240i −0.164393 + 0.425070i
\(56\) 0 0
\(57\) 0.486014i 0.0643742i
\(58\) 0.948505 1.64286i 0.124545 0.215718i
\(59\) −5.40617 + 3.12126i −0.703824 + 0.406353i −0.808770 0.588125i \(-0.799866\pi\)
0.104946 + 0.994478i \(0.466533\pi\)
\(60\) 0.794502 + 1.37612i 0.102570 + 0.177656i
\(61\) −5.93960 + 10.2877i −0.760488 + 1.31720i 0.182111 + 0.983278i \(0.441707\pi\)
−0.942599 + 0.333926i \(0.891626\pi\)
\(62\) −2.54997 −0.323846
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −0.147605 0.0852198i −0.0183081 0.0105702i
\(66\) −0.796171 5.10974i −0.0980019 0.628966i
\(67\) 5.19151 + 8.99196i 0.634244 + 1.09854i 0.986675 + 0.162705i \(0.0520219\pi\)
−0.352431 + 0.935838i \(0.614645\pi\)
\(68\) −1.47616 + 2.55678i −0.179011 + 0.310055i
\(69\) 0.741321i 0.0892445i
\(70\) 0 0
\(71\) 14.5206 1.72328 0.861639 0.507522i \(-0.169439\pi\)
0.861639 + 0.507522i \(0.169439\pi\)
\(72\) 0.492581 + 0.284392i 0.0580512 + 0.0335159i
\(73\) 4.85385 + 8.40712i 0.568101 + 0.983979i 0.996754 + 0.0805099i \(0.0256549\pi\)
−0.428653 + 0.903469i \(0.641012\pi\)
\(74\) 5.27699 3.04667i 0.613438 0.354168i
\(75\) 5.34930 + 3.08842i 0.617684 + 0.356620i
\(76\) 0.311700 0.0357545
\(77\) 0 0
\(78\) 0.260777 0.0295272
\(79\) 6.06709 + 3.50284i 0.682601 + 0.394100i 0.800834 0.598886i \(-0.204390\pi\)
−0.118233 + 0.992986i \(0.537723\pi\)
\(80\) 0.882559 0.509546i 0.0986731 0.0569689i
\(81\) 3.48507 + 6.03631i 0.387230 + 0.670702i
\(82\) −8.84069 5.10418i −0.976291 0.563662i
\(83\) 14.6915 1.61261 0.806303 0.591502i \(-0.201465\pi\)
0.806303 + 0.591502i \(0.201465\pi\)
\(84\) 0 0
\(85\) 3.00868i 0.326337i
\(86\) 5.06112 8.76612i 0.545755 0.945275i
\(87\) −1.47894 2.56161i −0.158559 0.274633i
\(88\) −3.27708 + 0.510616i −0.349338 + 0.0544319i
\(89\) −5.97639 3.45047i −0.633496 0.365749i 0.148609 0.988896i \(-0.452520\pi\)
−0.782105 + 0.623147i \(0.785854\pi\)
\(90\) −0.579642 −0.0610997
\(91\) 0 0
\(92\) 0.475438 0.0495679
\(93\) −1.98800 + 3.44332i −0.206146 + 0.357055i
\(94\) −1.89930 3.28968i −0.195898 0.339305i
\(95\) −0.275094 + 0.158826i −0.0282240 + 0.0162952i
\(96\) −0.779618 + 1.35034i −0.0795694 + 0.137818i
\(97\) 11.0218i 1.11909i 0.828799 + 0.559547i \(0.189025\pi\)
−0.828799 + 0.559547i \(0.810975\pi\)
\(98\) 0 0
\(99\) 1.75944 + 0.680455i 0.176831 + 0.0683883i
\(100\) 1.98073 3.43072i 0.198073 0.343072i
\(101\) 2.66752 + 4.62028i 0.265428 + 0.459735i 0.967676 0.252198i \(-0.0811534\pi\)
−0.702248 + 0.711933i \(0.747820\pi\)
\(102\) 2.30168 + 3.98663i 0.227900 + 0.394735i
\(103\) 10.7849 + 6.22664i 1.06266 + 0.613529i 0.926168 0.377112i \(-0.123083\pi\)
0.136496 + 0.990641i \(0.456416\pi\)
\(104\) 0.167247i 0.0163999i
\(105\) 0 0
\(106\) 8.42157i 0.817975i
\(107\) 6.28227 + 3.62707i 0.607330 + 0.350642i 0.771920 0.635720i \(-0.219297\pi\)
−0.164590 + 0.986362i \(0.552630\pi\)
\(108\) 4.81906 2.78229i 0.463715 0.267726i
\(109\) 1.01103 0.583716i 0.0968387 0.0559098i −0.450799 0.892626i \(-0.648861\pi\)
0.547637 + 0.836716i \(0.315527\pi\)
\(110\) 2.63204 2.12047i 0.250955 0.202179i
\(111\) 9.50096i 0.901791i
\(112\) 0 0
\(113\) −8.40135 −0.790333 −0.395166 0.918610i \(-0.629313\pi\)
−0.395166 + 0.918610i \(0.629313\pi\)
\(114\) 0.243007 0.420901i 0.0227597 0.0394210i
\(115\) −0.419602 + 0.242258i −0.0391281 + 0.0225906i
\(116\) −1.64286 + 0.948505i −0.152536 + 0.0880665i
\(117\) −0.0475636 + 0.0823825i −0.00439725 + 0.00761626i
\(118\) 6.24251 0.574670
\(119\) 0 0
\(120\) 1.58900i 0.145056i
\(121\) −10.4785 + 3.34666i −0.952595 + 0.304242i
\(122\) 10.2877 5.93960i 0.931404 0.537746i
\(123\) −13.7847 + 7.95862i −1.24293 + 0.717604i
\(124\) 2.20834 + 1.27498i 0.198314 + 0.114497i
\(125\) 9.13254i 0.816839i
\(126\) 0 0
\(127\) 3.53324i 0.313525i −0.987636 0.156762i \(-0.949894\pi\)
0.987636 0.156762i \(-0.0501057\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −7.89149 13.6685i −0.694807 1.20344i
\(130\) 0.0852198 + 0.147605i 0.00747427 + 0.0129458i
\(131\) 6.98984 12.1068i 0.610705 1.05777i −0.380417 0.924815i \(-0.624219\pi\)
0.991122 0.132957i \(-0.0424473\pi\)
\(132\) −1.86537 + 4.82325i −0.162359 + 0.419810i
\(133\) 0 0
\(134\) 10.3830i 0.896957i
\(135\) −2.83541 + 4.91107i −0.244033 + 0.422677i
\(136\) 2.55678 1.47616i 0.219242 0.126580i
\(137\) 3.50529 + 6.07134i 0.299477 + 0.518709i 0.976016 0.217697i \(-0.0698545\pi\)
−0.676539 + 0.736406i \(0.736521\pi\)
\(138\) 0.370660 0.642003i 0.0315527 0.0546509i
\(139\) −11.4615 −0.972148 −0.486074 0.873918i \(-0.661571\pi\)
−0.486074 + 0.873918i \(0.661571\pi\)
\(140\) 0 0
\(141\) −5.92291 −0.498799
\(142\) −12.5752 7.26030i −1.05529 0.609270i
\(143\) −0.0853989 0.548081i −0.00714141 0.0458328i
\(144\) −0.284392 0.492581i −0.0236993 0.0410484i
\(145\) 0.966613 1.67422i 0.0802729 0.139037i
\(146\) 9.70771i 0.803416i
\(147\) 0 0
\(148\) −6.09335 −0.500870
\(149\) 12.2602 + 7.07841i 1.00439 + 0.579886i 0.909545 0.415606i \(-0.136430\pi\)
0.0948474 + 0.995492i \(0.469764\pi\)
\(150\) −3.08842 5.34930i −0.252168 0.436768i
\(151\) 20.1819 11.6520i 1.64238 0.948228i 0.662394 0.749156i \(-0.269541\pi\)
0.979985 0.199072i \(-0.0637928\pi\)
\(152\) −0.269940 0.155850i −0.0218951 0.0126411i
\(153\) −1.67923 −0.135758
\(154\) 0 0
\(155\) −2.59865 −0.208728
\(156\) −0.225839 0.130388i −0.0180816 0.0104394i
\(157\) −3.49234 + 2.01630i −0.278719 + 0.160919i −0.632843 0.774280i \(-0.718112\pi\)
0.354124 + 0.935198i \(0.384779\pi\)
\(158\) −3.50284 6.06709i −0.278671 0.482672i
\(159\) 11.3720 + 6.56561i 0.901856 + 0.520687i
\(160\) −1.01909 −0.0805662
\(161\) 0 0
\(162\) 6.97014i 0.547626i
\(163\) 2.76994 4.79768i 0.216958 0.375783i −0.736918 0.675982i \(-0.763720\pi\)
0.953877 + 0.300199i \(0.0970530\pi\)
\(164\) 5.10418 + 8.84069i 0.398569 + 0.690342i
\(165\) −0.811371 5.20730i −0.0631652 0.405388i
\(166\) −12.7233 7.34577i −0.987516 0.570143i
\(167\) −21.2252 −1.64245 −0.821226 0.570603i \(-0.806709\pi\)
−0.821226 + 0.570603i \(0.806709\pi\)
\(168\) 0 0
\(169\) −12.9720 −0.997848
\(170\) −1.50434 + 2.60560i −0.115378 + 0.199840i
\(171\) 0.0886450 + 0.153538i 0.00677885 + 0.0117413i
\(172\) −8.76612 + 5.06112i −0.668411 + 0.385907i
\(173\) 7.53277 13.0471i 0.572706 0.991956i −0.423581 0.905858i \(-0.639227\pi\)
0.996287 0.0860973i \(-0.0274396\pi\)
\(174\) 2.95789i 0.224237i
\(175\) 0 0
\(176\) 3.09335 + 1.19633i 0.233170 + 0.0901771i
\(177\) 4.86677 8.42950i 0.365809 0.633600i
\(178\) 3.45047 + 5.97639i 0.258623 + 0.447949i
\(179\) 1.08088 + 1.87214i 0.0807887 + 0.139930i 0.903589 0.428401i \(-0.140923\pi\)
−0.822800 + 0.568331i \(0.807589\pi\)
\(180\) 0.501985 + 0.289821i 0.0374158 + 0.0216020i
\(181\) 5.39285i 0.400848i 0.979709 + 0.200424i \(0.0642319\pi\)
−0.979709 + 0.200424i \(0.935768\pi\)
\(182\) 0 0
\(183\) 18.5225i 1.36922i
\(184\) −0.411742 0.237719i −0.0303540 0.0175249i
\(185\) 5.37774 3.10484i 0.395379 0.228272i
\(186\) 3.44332 1.98800i 0.252476 0.145767i
\(187\) 7.62504 6.14303i 0.557598 0.449223i
\(188\) 3.79859i 0.277041i
\(189\) 0 0
\(190\) 0.317651 0.0230448
\(191\) −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i \(-0.902984\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(192\) 1.35034 0.779618i 0.0974522 0.0562641i
\(193\) 8.31348 4.79979i 0.598417 0.345496i −0.170001 0.985444i \(-0.554377\pi\)
0.768419 + 0.639947i \(0.221044\pi\)
\(194\) 5.51090 9.54515i 0.395659 0.685302i
\(195\) 0.265756 0.0190311
\(196\) 0 0
\(197\) 14.8180i 1.05574i 0.849325 + 0.527870i \(0.177009\pi\)
−0.849325 + 0.527870i \(0.822991\pi\)
\(198\) −1.18350 1.46901i −0.0841073 0.104398i
\(199\) −3.55962 + 2.05515i −0.252335 + 0.145686i −0.620833 0.783943i \(-0.713205\pi\)
0.368498 + 0.929629i \(0.379872\pi\)
\(200\) −3.43072 + 1.98073i −0.242588 + 0.140059i
\(201\) −14.0206 8.09479i −0.988936 0.570963i
\(202\) 5.33504i 0.375372i
\(203\) 0 0
\(204\) 4.60336i 0.322300i
\(205\) −9.00947 5.20162i −0.629249 0.363297i
\(206\) −6.22664 10.7849i −0.433831 0.751417i
\(207\) 0.135211 + 0.234192i 0.00939780 + 0.0162775i
\(208\) −0.0836233 + 0.144840i −0.00579823 + 0.0100428i
\(209\) −0.964197 0.372898i −0.0666949 0.0257939i
\(210\) 0 0
\(211\) 7.52456i 0.518012i −0.965876 0.259006i \(-0.916605\pi\)
0.965876 0.259006i \(-0.0833950\pi\)
\(212\) 4.21079 7.29330i 0.289198 0.500906i
\(213\) −19.6077 + 11.3205i −1.34350 + 0.775669i
\(214\) −3.62707 6.28227i −0.247941 0.429447i
\(215\) 5.15775 8.93348i 0.351755 0.609258i
\(216\) −5.56458 −0.378621
\(217\) 0 0
\(218\) −1.16743 −0.0790685
\(219\) −13.1087 7.56830i −0.885803 0.511418i
\(220\) −3.33965 + 0.520365i −0.225159 + 0.0350830i
\(221\) 0.246883 + 0.427613i 0.0166071 + 0.0287644i
\(222\) −4.75048 + 8.22807i −0.318831 + 0.552232i
\(223\) 13.5885i 0.909951i 0.890504 + 0.454975i \(0.150352\pi\)
−0.890504 + 0.454975i \(0.849648\pi\)
\(224\) 0 0
\(225\) 2.25321 0.150214
\(226\) 7.27578 + 4.20068i 0.483978 + 0.279425i
\(227\) 10.8318 + 18.7611i 0.718929 + 1.24522i 0.961425 + 0.275069i \(0.0887006\pi\)
−0.242496 + 0.970152i \(0.577966\pi\)
\(228\) −0.420901 + 0.243007i −0.0278748 + 0.0160935i
\(229\) −26.0355 15.0316i −1.72047 0.993317i −0.917948 0.396700i \(-0.870155\pi\)
−0.802527 0.596616i \(-0.796511\pi\)
\(230\) 0.484515 0.0319480
\(231\) 0 0
\(232\) 1.89701 0.124545
\(233\) 14.0223 + 8.09580i 0.918633 + 0.530373i 0.883199 0.468999i \(-0.155385\pi\)
0.0354345 + 0.999372i \(0.488718\pi\)
\(234\) 0.0823825 0.0475636i 0.00538551 0.00310933i
\(235\) −1.93556 3.35248i −0.126262 0.218692i
\(236\) −5.40617 3.12126i −0.351912 0.203176i
\(237\) −10.9235 −0.709558
\(238\) 0 0
\(239\) 26.0701i 1.68633i −0.537652 0.843167i \(-0.680689\pi\)
0.537652 0.843167i \(-0.319311\pi\)
\(240\) −0.794502 + 1.37612i −0.0512849 + 0.0888280i
\(241\) −6.60221 11.4354i −0.425286 0.736617i 0.571161 0.820838i \(-0.306493\pi\)
−0.996447 + 0.0842210i \(0.973160\pi\)
\(242\) 10.7480 + 2.34098i 0.690909 + 0.150484i
\(243\) 5.04515 + 2.91282i 0.323647 + 0.186858i
\(244\) −11.8792 −0.760488
\(245\) 0 0
\(246\) 15.9172 1.01485
\(247\) 0.0260654 0.0451466i 0.00165850 0.00287261i
\(248\) −1.27498 2.20834i −0.0809615 0.140229i
\(249\) −19.8386 + 11.4538i −1.25722 + 0.725855i
\(250\) 4.56627 7.90901i 0.288796 0.500210i
\(251\) 28.9829i 1.82939i −0.404149 0.914693i \(-0.632432\pi\)
0.404149 0.914693i \(-0.367568\pi\)
\(252\) 0 0
\(253\) −1.47070 0.568783i −0.0924618 0.0357591i
\(254\) −1.76662 + 3.05988i −0.110848 + 0.191994i
\(255\) 2.34562 + 4.06274i 0.146889 + 0.254419i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.05007 3.49301i −0.377393 0.217888i 0.299290 0.954162i \(-0.403250\pi\)
−0.676683 + 0.736274i \(0.736583\pi\)
\(258\) 15.7830i 0.982605i
\(259\) 0 0
\(260\) 0.170440i 0.0105702i
\(261\) −0.934431 0.539494i −0.0578398 0.0333938i
\(262\) −12.1068 + 6.98984i −0.747958 + 0.431834i
\(263\) −3.87174 + 2.23535i −0.238741 + 0.137837i −0.614598 0.788840i \(-0.710682\pi\)
0.375857 + 0.926678i \(0.377348\pi\)
\(264\) 4.02708 3.24438i 0.247850 0.199678i
\(265\) 8.58235i 0.527210i
\(266\) 0 0
\(267\) 10.7602 0.658513
\(268\) −5.19151 + 8.99196i −0.317122 + 0.549272i
\(269\) −1.92024 + 1.10865i −0.117079 + 0.0675956i −0.557396 0.830247i \(-0.688199\pi\)
0.440317 + 0.897842i \(0.354866\pi\)
\(270\) 4.91107 2.83541i 0.298878 0.172557i
\(271\) −11.2561 + 19.4961i −0.683759 + 1.18431i 0.290066 + 0.957007i \(0.406323\pi\)
−0.973825 + 0.227299i \(0.927011\pi\)
\(272\) −2.95232 −0.179011
\(273\) 0 0
\(274\) 7.01058i 0.423524i
\(275\) −10.2314 + 8.24279i −0.616974 + 0.497059i
\(276\) −0.642003 + 0.370660i −0.0386440 + 0.0223111i
\(277\) −21.1880 + 12.2329i −1.27306 + 0.735004i −0.975563 0.219718i \(-0.929486\pi\)
−0.297500 + 0.954722i \(0.596153\pi\)
\(278\) 9.92591 + 5.73073i 0.595317 + 0.343706i
\(279\) 1.45038i 0.0868319i
\(280\) 0 0
\(281\) 11.3532i 0.677273i −0.940917 0.338636i \(-0.890034\pi\)
0.940917 0.338636i \(-0.109966\pi\)
\(282\) 5.12939 + 2.96145i 0.305451 + 0.176352i
\(283\) −10.8268 18.7526i −0.643589 1.11473i −0.984626 0.174679i \(-0.944111\pi\)
0.341037 0.940050i \(-0.389222\pi\)
\(284\) 7.26030 + 12.5752i 0.430819 + 0.746201i
\(285\) 0.247646 0.428936i 0.0146693 0.0254080i
\(286\) −0.200083 + 0.517352i −0.0118312 + 0.0305916i
\(287\) 0 0
\(288\) 0.568783i 0.0335159i
\(289\) 4.14191 7.17400i 0.243642 0.422000i
\(290\) −1.67422 + 0.966613i −0.0983138 + 0.0567615i
\(291\) −8.59279 14.8831i −0.503718 0.872465i
\(292\) −4.85385 + 8.40712i −0.284050 + 0.491990i
\(293\) −12.1233 −0.708249 −0.354124 0.935198i \(-0.615221\pi\)
−0.354124 + 0.935198i \(0.615221\pi\)
\(294\) 0 0
\(295\) 6.36169 0.370392
\(296\) 5.27699 + 3.04667i 0.306719 + 0.177084i
\(297\) −18.2356 + 2.84136i −1.05814 + 0.164873i
\(298\) −7.07841 12.2602i −0.410041 0.710213i
\(299\) 0.0397577 0.0688624i 0.00229925 0.00398242i
\(300\) 6.17684i 0.356620i
\(301\) 0 0
\(302\) −23.3040 −1.34100
\(303\) −7.20410 4.15929i −0.413865 0.238945i
\(304\) 0.155850 + 0.269940i 0.00893862 + 0.0154821i
\(305\) 10.4841 6.05300i 0.600318 0.346594i
\(306\) 1.45426 + 0.839615i 0.0831343 + 0.0479976i
\(307\) −9.65817 −0.551221 −0.275610 0.961269i \(-0.588880\pi\)
−0.275610 + 0.961269i \(0.588880\pi\)
\(308\) 0 0
\(309\) −19.4176 −1.10463
\(310\) 2.25050 + 1.29932i 0.127820 + 0.0737967i
\(311\) 15.3094 8.83890i 0.868118 0.501208i 0.00139530 0.999999i \(-0.499556\pi\)
0.866722 + 0.498791i \(0.166223\pi\)
\(312\) 0.130388 + 0.225839i 0.00738179 + 0.0127856i
\(313\) 24.9505 + 14.4052i 1.41028 + 0.814228i 0.995415 0.0956530i \(-0.0304939\pi\)
0.414869 + 0.909881i \(0.363827\pi\)
\(314\) 4.03261 0.227573
\(315\) 0 0
\(316\) 7.00567i 0.394100i
\(317\) −5.17280 + 8.95955i −0.290533 + 0.503218i −0.973936 0.226823i \(-0.927166\pi\)
0.683403 + 0.730042i \(0.260499\pi\)
\(318\) −6.56561 11.3720i −0.368181 0.637708i
\(319\) 6.21666 0.968644i 0.348066 0.0542337i
\(320\) 0.882559 + 0.509546i 0.0493366 + 0.0284845i
\(321\) −11.3109 −0.631314
\(322\) 0 0
\(323\) 0.920239 0.0512034
\(324\) −3.48507 + 6.03631i −0.193615 + 0.335351i
\(325\) −0.331270 0.573776i −0.0183755 0.0318274i
\(326\) −4.79768 + 2.76994i −0.265719 + 0.153413i
\(327\) −0.910151 + 1.57643i −0.0503315 + 0.0871766i
\(328\) 10.2084i 0.563662i
\(329\) 0 0
\(330\) −1.90098 + 4.91534i −0.104646 + 0.270580i
\(331\) 13.4224 23.2483i 0.737763 1.27784i −0.215737 0.976451i \(-0.569215\pi\)
0.953500 0.301392i \(-0.0974512\pi\)
\(332\) 7.34577 + 12.7233i 0.403152 + 0.698279i
\(333\) −1.73290 3.00147i −0.0949622 0.164479i
\(334\) 18.3815 + 10.6126i 1.00579 + 0.580694i
\(335\) 10.5813i 0.578116i
\(336\) 0 0
\(337\) 14.5505i 0.792614i 0.918118 + 0.396307i \(0.129708\pi\)
−0.918118 + 0.396307i \(0.870292\pi\)
\(338\) 11.2341 + 6.48601i 0.611055 + 0.352793i
\(339\) 11.3447 6.54984i 0.616158 0.355739i
\(340\) 2.60560 1.50434i 0.141308 0.0815844i
\(341\) −5.30584 6.58587i −0.287327 0.356645i
\(342\) 0.177290i 0.00958674i
\(343\) 0 0
\(344\) 10.1222 0.545755
\(345\) 0.377737 0.654259i 0.0203367 0.0352241i
\(346\) −13.0471 + 7.53277i −0.701418 + 0.404964i
\(347\) −24.7179 + 14.2709i −1.32693 + 0.766101i −0.984823 0.173562i \(-0.944472\pi\)
−0.342102 + 0.939663i \(0.611139\pi\)
\(348\) 1.47894 2.56161i 0.0792797 0.137316i
\(349\) 34.6026 1.85224 0.926118 0.377235i \(-0.123125\pi\)
0.926118 + 0.377235i \(0.123125\pi\)
\(350\) 0 0
\(351\) 0.930656i 0.0496748i
\(352\) −2.08075 2.58273i −0.110904 0.137660i
\(353\) 14.6534 8.46017i 0.779924 0.450289i −0.0564792 0.998404i \(-0.517987\pi\)
0.836403 + 0.548114i \(0.184654\pi\)
\(354\) −8.42950 + 4.86677i −0.448023 + 0.258666i
\(355\) −12.8153 7.39891i −0.680164 0.392693i
\(356\) 6.90094i 0.365749i
\(357\) 0 0
\(358\) 2.16176i 0.114252i
\(359\) 26.2848 + 15.1755i 1.38726 + 0.800934i 0.993006 0.118067i \(-0.0376698\pi\)
0.394254 + 0.919002i \(0.371003\pi\)
\(360\) −0.289821 0.501985i −0.0152749 0.0264569i
\(361\) 9.45142 + 16.3703i 0.497443 + 0.861597i
\(362\) 2.69643 4.67035i 0.141721 0.245468i
\(363\) 11.5405 12.6884i 0.605717 0.665968i
\(364\) 0 0
\(365\) 9.89304i 0.517825i
\(366\) −9.26124 + 16.0409i −0.484093 + 0.838474i
\(367\) 15.0875 8.71075i 0.787559 0.454698i −0.0515432 0.998671i \(-0.516414\pi\)
0.839103 + 0.543973i \(0.183081\pi\)
\(368\) 0.237719 + 0.411742i 0.0123920 + 0.0214635i
\(369\) −2.90317 + 5.02844i −0.151133 + 0.261770i
\(370\) −6.20968 −0.322826
\(371\) 0 0
\(372\) −3.97600 −0.206146
\(373\) 7.92596 + 4.57606i 0.410391 + 0.236939i 0.690958 0.722895i \(-0.257189\pi\)
−0.280567 + 0.959834i \(0.590522\pi\)
\(374\) −9.67499 + 1.50750i −0.500282 + 0.0779511i
\(375\) −7.11989 12.3320i −0.367670 0.636822i
\(376\) 1.89930 3.28968i 0.0979488 0.169652i
\(377\) 0.317269i 0.0163402i
\(378\) 0 0
\(379\) −6.15382 −0.316100 −0.158050 0.987431i \(-0.550521\pi\)
−0.158050 + 0.987431i \(0.550521\pi\)
\(380\) −0.275094 0.158826i −0.0141120 0.00814758i
\(381\) 2.75458 + 4.77107i 0.141121 + 0.244429i
\(382\) 5.19615 3.00000i 0.265858 0.153493i
\(383\) −11.2281 6.48253i −0.573728 0.331242i 0.184909 0.982756i \(-0.440801\pi\)
−0.758637 + 0.651514i \(0.774134\pi\)
\(384\) −1.55924 −0.0795694
\(385\) 0 0
\(386\) −9.59958 −0.488606
\(387\) −4.98603 2.87868i −0.253454 0.146332i
\(388\) −9.54515 + 5.51090i −0.484582 + 0.279773i
\(389\) −2.58323 4.47429i −0.130975 0.226856i 0.793078 0.609121i \(-0.208477\pi\)
−0.924053 + 0.382265i \(0.875144\pi\)
\(390\) −0.230151 0.132878i −0.0116542 0.00672853i
\(391\) 1.40365 0.0709854
\(392\) 0 0
\(393\) 21.7976i 1.09954i
\(394\) 7.40901 12.8328i 0.373261 0.646506i
\(395\) −3.56971 6.18292i −0.179612 0.311097i
\(396\) 0.290430 + 1.86395i 0.0145947 + 0.0936670i
\(397\) −8.01690 4.62856i −0.402357 0.232301i 0.285144 0.958485i \(-0.407959\pi\)
−0.687500 + 0.726184i \(0.741292\pi\)
\(398\) 4.11030 0.206030
\(399\) 0 0
\(400\) 3.96145 0.198073
\(401\) 15.4624 26.7816i 0.772155 1.33741i −0.164225 0.986423i \(-0.552512\pi\)
0.936380 0.350988i \(-0.114154\pi\)
\(402\) 8.09479 + 14.0206i 0.403732 + 0.699284i
\(403\) 0.369337 0.213237i 0.0183980 0.0106221i
\(404\) −2.66752 + 4.62028i −0.132714 + 0.229867i
\(405\) 7.10320i 0.352961i
\(406\) 0 0
\(407\) 18.8488 + 7.28968i 0.934301 + 0.361336i
\(408\) −2.30168 + 3.98663i −0.113950 + 0.197367i
\(409\) 11.9198 + 20.6458i 0.589399 + 1.02087i 0.994311 + 0.106513i \(0.0339686\pi\)
−0.404913 + 0.914355i \(0.632698\pi\)
\(410\) 5.20162 + 9.00947i 0.256890 + 0.444946i
\(411\) −9.46665 5.46557i −0.466955 0.269597i
\(412\) 12.4533i 0.613529i
\(413\) 0 0
\(414\) 0.270422i 0.0132905i
\(415\) −12.9662 7.48601i −0.636484 0.367474i
\(416\) 0.144840 0.0836233i 0.00710136 0.00409997i
\(417\) 15.4768 8.93556i 0.757904 0.437576i
\(418\) 0.648570 + 0.805037i 0.0317226 + 0.0393757i
\(419\) 5.03426i 0.245940i −0.992410 0.122970i \(-0.960758\pi\)
0.992410 0.122970i \(-0.0392418\pi\)
\(420\) 0 0
\(421\) −16.9250 −0.824872 −0.412436 0.910987i \(-0.635322\pi\)
−0.412436 + 0.910987i \(0.635322\pi\)
\(422\) −3.76228 + 6.51646i −0.183145 + 0.317216i
\(423\) −1.87112 + 1.08029i −0.0909767 + 0.0525254i
\(424\) −7.29330 + 4.21079i −0.354194 + 0.204494i
\(425\) 5.84773 10.1286i 0.283657 0.491308i
\(426\) 22.6410 1.09696
\(427\) 0 0
\(428\) 7.25414i 0.350642i
\(429\) 0.542611 + 0.673516i 0.0261975 + 0.0325177i
\(430\) −8.93348 + 5.15775i −0.430811 + 0.248729i
\(431\) −5.19535 + 2.99953i −0.250251 + 0.144482i −0.619879 0.784697i \(-0.712818\pi\)
0.369628 + 0.929180i \(0.379485\pi\)
\(432\) 4.81906 + 2.78229i 0.231857 + 0.133863i
\(433\) 36.1175i 1.73570i 0.496829 + 0.867849i \(0.334498\pi\)
−0.496829 + 0.867849i \(0.665502\pi\)
\(434\) 0 0
\(435\) 3.01436i 0.144527i
\(436\) 1.01103 + 0.583716i 0.0484193 + 0.0279549i
\(437\) −0.0740971 0.128340i −0.00354455 0.00613934i
\(438\) 7.56830 + 13.1087i 0.361627 + 0.626357i
\(439\) −5.67481 + 9.82906i −0.270844 + 0.469116i −0.969078 0.246754i \(-0.920636\pi\)
0.698234 + 0.715869i \(0.253969\pi\)
\(440\) 3.15240 + 1.21917i 0.150285 + 0.0581219i
\(441\) 0 0
\(442\) 0.493765i 0.0234860i
\(443\) 2.37538 4.11428i 0.112858 0.195475i −0.804064 0.594543i \(-0.797333\pi\)
0.916921 + 0.399068i \(0.130666\pi\)
\(444\) 8.22807 4.75048i 0.390487 0.225448i
\(445\) 3.51634 + 6.09048i 0.166691 + 0.288717i
\(446\) 6.79423 11.7680i 0.321716 0.557229i
\(447\) −22.0738 −1.04406
\(448\) 0 0
\(449\) 7.33297 0.346064 0.173032 0.984916i \(-0.444644\pi\)
0.173032 + 0.984916i \(0.444644\pi\)
\(450\) −1.95134 1.12660i −0.0919869 0.0531086i
\(451\) −5.21255 33.4536i −0.245449 1.57527i
\(452\) −4.20068 7.27578i −0.197583 0.342224i
\(453\) −18.1682 + 31.4683i −0.853619 + 1.47851i
\(454\) 21.6635i 1.01672i
\(455\) 0 0
\(456\) 0.486014 0.0227597
\(457\) −11.7066 6.75879i −0.547610 0.316163i 0.200547 0.979684i \(-0.435728\pi\)
−0.748158 + 0.663521i \(0.769061\pi\)
\(458\) 15.0316 + 26.0355i 0.702381 + 1.21656i
\(459\) 14.2274 8.21420i 0.664079 0.383406i
\(460\) −0.419602 0.242258i −0.0195641 0.0112953i
\(461\) 18.5730 0.865033 0.432516 0.901626i \(-0.357626\pi\)
0.432516 + 0.901626i \(0.357626\pi\)
\(462\) 0 0
\(463\) 28.2849 1.31451 0.657256 0.753667i \(-0.271717\pi\)
0.657256 + 0.753667i \(0.271717\pi\)
\(464\) −1.64286 0.948505i −0.0762678 0.0440332i
\(465\) 3.50905 2.02595i 0.162728 0.0939513i
\(466\) −8.09580 14.0223i −0.375030 0.649572i
\(467\) 18.6881 + 10.7896i 0.864782 + 0.499282i 0.865611 0.500717i \(-0.166930\pi\)
−0.000828665 1.00000i \(0.500264\pi\)
\(468\) −0.0951271 −0.00439725
\(469\) 0 0
\(470\) 3.87112i 0.178561i
\(471\) 3.14389 5.44538i 0.144863 0.250910i
\(472\) 3.12126 + 5.40617i 0.143667 + 0.248839i
\(473\) 33.1714 5.16859i 1.52522 0.237652i
\(474\) 9.46003 + 5.46175i 0.434513 + 0.250866i
\(475\) −1.23479 −0.0566559
\(476\) 0 0
\(477\) 4.79005 0.219321
\(478\) −13.0350 + 22.5774i −0.596209 + 1.03266i
\(479\) 3.46780 + 6.00641i 0.158448 + 0.274440i 0.934309 0.356464i \(-0.116018\pi\)
−0.775861 + 0.630904i \(0.782684\pi\)
\(480\) 1.37612 0.794502i 0.0628109 0.0362639i
\(481\) −0.509546 + 0.882559i −0.0232333 + 0.0402412i
\(482\) 13.2044i 0.601445i
\(483\) 0 0
\(484\) −8.13757 7.40135i −0.369889 0.336425i
\(485\) 5.61611 9.72738i 0.255014 0.441698i
\(486\) −2.91282 5.04515i −0.132128 0.228853i
\(487\) 6.08702 + 10.5430i 0.275829 + 0.477750i 0.970344 0.241728i \(-0.0777143\pi\)
−0.694515 + 0.719478i \(0.744381\pi\)
\(488\) 10.2877 + 5.93960i 0.465702 + 0.268873i
\(489\) 8.63798i 0.390623i
\(490\) 0 0
\(491\) 2.37152i 0.107025i −0.998567 0.0535125i \(-0.982958\pi\)
0.998567 0.0535125i \(-0.0170417\pi\)
\(492\) −13.7847 7.95862i −0.621463 0.358802i
\(493\) −4.85024 + 2.80029i −0.218444 + 0.126119i
\(494\) −0.0451466 + 0.0260654i −0.00203124 + 0.00117274i
\(495\) −1.20609 1.49706i −0.0542097 0.0672878i
\(496\) 2.54997i 0.114497i
\(497\) 0 0
\(498\) 22.9076 1.02651
\(499\) 1.96446 3.40255i 0.0879413 0.152319i −0.818699 0.574222i \(-0.805305\pi\)
0.906641 + 0.421903i \(0.138638\pi\)
\(500\) −7.90901 + 4.56627i −0.353702 + 0.204210i
\(501\) 28.6611 16.5475i 1.28048 0.739288i
\(502\) −14.4915 + 25.1000i −0.646786 + 1.12027i
\(503\) 19.8703 0.885971 0.442986 0.896529i \(-0.353919\pi\)
0.442986 + 0.896529i \(0.353919\pi\)
\(504\) 0 0
\(505\) 5.43689i 0.241938i
\(506\) 0.989268 + 1.22793i 0.0439783 + 0.0545881i
\(507\) 17.5166 10.1132i 0.777940 0.449144i
\(508\) 3.05988 1.76662i 0.135760 0.0783812i
\(509\) −13.2438 7.64634i −0.587023 0.338918i 0.176896 0.984229i \(-0.443394\pi\)
−0.763920 + 0.645312i \(0.776728\pi\)
\(510\) 4.69125i 0.207732i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) −1.50210 0.867240i −0.0663195 0.0382896i
\(514\) 3.49301 + 6.05007i 0.154070 + 0.266857i
\(515\) −6.34552 10.9908i −0.279617 0.484311i
\(516\) 7.89149 13.6685i 0.347403 0.601720i
\(517\) 4.54439 11.7504i 0.199862 0.516780i
\(518\) 0 0
\(519\) 23.4907i 1.03113i
\(520\) −0.0852198 + 0.147605i −0.00373714 + 0.00647291i
\(521\) 0.121861 0.0703565i 0.00533883 0.00308237i −0.497328 0.867562i \(-0.665686\pi\)
0.502667 + 0.864480i \(0.332352\pi\)
\(522\) 0.539494 + 0.934431i 0.0236130 + 0.0408989i
\(523\) 4.56153 7.90081i 0.199462 0.345478i −0.748892 0.662692i \(-0.769414\pi\)
0.948354 + 0.317214i \(0.102747\pi\)
\(524\) 13.9797 0.610705
\(525\) 0 0
\(526\) 4.47070 0.194932
\(527\) 6.51971 + 3.76416i 0.284003 + 0.163969i
\(528\) −5.10974 + 0.796171i −0.222373 + 0.0346489i
\(529\) 11.3870 + 19.7228i 0.495086 + 0.857514i
\(530\) 4.29118 7.43253i 0.186397 0.322849i
\(531\) 3.55064i 0.154085i
\(532\) 0 0
\(533\) 1.70731 0.0739519
\(534\) −9.31859 5.38009i −0.403255 0.232819i
\(535\) −3.69632 6.40221i −0.159806 0.276792i
\(536\) 8.99196 5.19151i 0.388394 0.224239i
\(537\) −2.91910 1.68534i −0.125969 0.0727280i
\(538\) 2.21730 0.0955946
\(539\) 0 0
\(540\) −5.67081 −0.244033
\(541\) −21.6730 12.5129i −0.931797 0.537973i −0.0444172 0.999013i \(-0.514143\pi\)
−0.887379 + 0.461040i \(0.847476\pi\)
\(542\) 19.4961 11.2561i 0.837430 0.483491i
\(543\) −4.20437 7.28217i −0.180427 0.312508i
\(544\) 2.55678 + 1.47616i 0.109621 + 0.0632898i
\(545\) −1.18972 −0.0509620
\(546\) 0 0
\(547\) 36.7246i 1.57023i 0.619348 + 0.785116i \(0.287397\pi\)
−0.619348 + 0.785116i \(0.712603\pi\)
\(548\) −3.50529 + 6.07134i −0.149738 + 0.259355i
\(549\) −3.37835 5.85147i −0.144184 0.249735i
\(550\) 12.9820 2.02278i 0.553555 0.0862517i
\(551\) 0.512080 + 0.295649i 0.0218153 + 0.0125951i
\(552\) 0.741321 0.0315527
\(553\) 0 0
\(554\) 24.4658 1.03945
\(555\) −4.84117 + 8.38516i −0.205496 + 0.355930i
\(556\) −5.73073 9.92591i −0.243037 0.420952i
\(557\) −33.5815 + 19.3883i −1.42290 + 0.821509i −0.996545 0.0830490i \(-0.973534\pi\)
−0.426350 + 0.904558i \(0.640201\pi\)
\(558\) 0.725189 1.25606i 0.0306997 0.0531735i
\(559\) 1.69291i 0.0716025i
\(560\) 0 0
\(561\) −5.50716 + 14.2398i −0.232512 + 0.601204i
\(562\) −5.67658 + 9.83212i −0.239452 + 0.414743i
\(563\) 21.6247 + 37.4550i 0.911371 + 1.57854i 0.812129 + 0.583477i \(0.198308\pi\)
0.0992415 + 0.995063i \(0.468358\pi\)
\(564\) −2.96145 5.12939i −0.124700 0.215986i
\(565\) 7.41469 + 4.28087i 0.311938 + 0.180098i
\(566\) 21.6537i 0.910172i
\(567\) 0 0
\(568\) 14.5206i 0.609270i
\(569\) −18.4783 10.6685i −0.774651 0.447245i 0.0598803 0.998206i \(-0.480928\pi\)
−0.834531 + 0.550961i \(0.814261\pi\)
\(570\) −0.428936 + 0.247646i −0.0179662 + 0.0103728i
\(571\) 19.5677 11.2974i 0.818883 0.472782i −0.0311482 0.999515i \(-0.509916\pi\)
0.850031 + 0.526733i \(0.176583\pi\)
\(572\) 0.431953 0.347998i 0.0180608 0.0145505i
\(573\) 9.35542i 0.390828i
\(574\) 0 0
\(575\) −1.88343 −0.0785443
\(576\) 0.284392 0.492581i 0.0118497 0.0205242i
\(577\) 29.3358 16.9370i 1.22126 0.705097i 0.256077 0.966656i \(-0.417570\pi\)
0.965187 + 0.261559i \(0.0842366\pi\)
\(578\) −7.17400 + 4.14191i −0.298399 + 0.172281i
\(579\) −7.48400 + 12.9627i −0.311025 + 0.538710i
\(580\) 1.93323 0.0802729
\(581\) 0 0
\(582\) 17.1856i 0.712365i
\(583\) −21.7506 + 17.5232i −0.900819 + 0.725736i
\(584\) 8.40712 4.85385i 0.347889 0.200854i
\(585\) 0.0839553 0.0484716i 0.00347112 0.00200405i
\(586\) 10.4991 + 6.06163i 0.433712 + 0.250404i
\(587\) 6.07819i 0.250874i −0.992102 0.125437i \(-0.959967\pi\)
0.992102 0.125437i \(-0.0400332\pi\)
\(588\) 0 0
\(589\) 0.794825i 0.0327502i
\(590\) −5.50939 3.18085i −0.226818 0.130953i
\(591\) −11.5524 20.0093i −0.475202 0.823074i
\(592\) −3.04667 5.27699i −0.125217 0.216883i
\(593\) 0.809196 1.40157i 0.0332297 0.0575555i −0.848932 0.528502i \(-0.822754\pi\)
0.882162 + 0.470946i \(0.156087\pi\)
\(594\) 17.2132 + 6.65709i 0.706264 + 0.273144i
\(595\) 0 0
\(596\) 14.1568i 0.579886i
\(597\) 3.20446 5.55029i 0.131150 0.227158i
\(598\) −0.0688624 + 0.0397577i −0.00281599 + 0.00162581i
\(599\) −2.63955 4.57184i −0.107849 0.186800i 0.807050 0.590484i \(-0.201063\pi\)
−0.914899 + 0.403684i \(0.867730\pi\)
\(600\) 3.08842 5.34930i 0.126084 0.218384i
\(601\) 32.7945 1.33771 0.668857 0.743391i \(-0.266784\pi\)
0.668857 + 0.743391i \(0.266784\pi\)
\(602\) 0 0
\(603\) −5.90569 −0.240498
\(604\) 20.1819 + 11.6520i 0.821189 + 0.474114i
\(605\) 10.9532 + 2.38567i 0.445311 + 0.0969912i
\(606\) 4.15929 + 7.20410i 0.168960 + 0.292647i
\(607\) −0.332910 + 0.576616i −0.0135124 + 0.0234041i −0.872703 0.488252i \(-0.837635\pi\)
0.859190 + 0.511656i \(0.170968\pi\)
\(608\) 0.311700i 0.0126411i
\(609\) 0 0
\(610\) −12.1060 −0.490158
\(611\) 0.550188 + 0.317651i 0.0222582 + 0.0128508i
\(612\) −0.839615 1.45426i −0.0339394 0.0587848i
\(613\) 3.71908 2.14721i 0.150212 0.0867251i −0.423010 0.906125i \(-0.639027\pi\)
0.573222 + 0.819400i \(0.305693\pi\)
\(614\) 8.36422 + 4.82908i 0.337552 + 0.194886i
\(615\) 16.2211 0.654098
\(616\) 0 0
\(617\) −30.9913 −1.24766 −0.623831 0.781559i \(-0.714425\pi\)
−0.623831 + 0.781559i \(0.714425\pi\)
\(618\) 16.8161 + 9.70880i 0.676444 + 0.390545i
\(619\) 0.685357 0.395691i 0.0275468 0.0159042i −0.486163 0.873868i \(-0.661604\pi\)
0.513710 + 0.857964i \(0.328271\pi\)
\(620\) −1.29932 2.25050i −0.0521821 0.0903821i
\(621\) −2.29117 1.32281i −0.0919414 0.0530824i
\(622\) −17.6778 −0.708815
\(623\) 0 0
\(624\) 0.260777i 0.0104394i
\(625\) −5.25019 + 9.09359i −0.210007 + 0.363744i
\(626\) −14.4052 24.9505i −0.575746 0.997222i
\(627\) 1.59271 0.248167i 0.0636067 0.00991083i
\(628\) −3.49234 2.01630i −0.139360 0.0804593i
\(629\) −17.9895 −0.717288
\(630\) 0 0
\(631\) −34.3677 −1.36816 −0.684078 0.729409i \(-0.739795\pi\)
−0.684078 + 0.729409i \(0.739795\pi\)
\(632\) 3.50284 6.06709i 0.139335 0.241336i
\(633\) 5.86628 + 10.1607i 0.233164 + 0.403852i
\(634\) 8.95955 5.17280i 0.355829 0.205438i
\(635\) −1.80035 + 3.11830i −0.0714447 + 0.123746i
\(636\) 13.1312i 0.520687i
\(637\) 0 0
\(638\) −5.86811 2.26946i −0.232321 0.0898488i
\(639\) −4.12954 + 7.15257i −0.163362 + 0.282951i
\(640\) −0.509546 0.882559i −0.0201416 0.0348862i
\(641\) −2.47939 4.29443i −0.0979301 0.169620i 0.812898 0.582407i \(-0.197889\pi\)
−0.910828 + 0.412787i \(0.864556\pi\)
\(642\) 9.79554 + 5.65546i 0.386599 + 0.223203i
\(643\) 48.1404i 1.89847i −0.314562 0.949237i \(-0.601858\pi\)
0.314562 0.949237i \(-0.398142\pi\)
\(644\) 0 0
\(645\) 16.0843i 0.633318i
\(646\) −0.796950 0.460119i −0.0313556 0.0181031i
\(647\) 2.74160 1.58286i 0.107783 0.0622287i −0.445139 0.895461i \(-0.646846\pi\)
0.552923 + 0.833233i \(0.313513\pi\)
\(648\) 6.03631 3.48507i 0.237129 0.136906i
\(649\) 12.9891 + 16.1227i 0.509867 + 0.632872i
\(650\) 0.662540i 0.0259869i
\(651\) 0 0
\(652\) 5.53988 0.216958
\(653\) 11.0606 19.1575i 0.432833 0.749689i −0.564283 0.825582i \(-0.690847\pi\)
0.997116 + 0.0758922i \(0.0241805\pi\)
\(654\) 1.57643 0.910151i 0.0616432 0.0355897i
\(655\) −12.3379 + 7.12329i −0.482081 + 0.278330i
\(656\) −5.10418 + 8.84069i −0.199285 + 0.345171i
\(657\) −5.52158 −0.215417
\(658\) 0 0
\(659\) 24.6258i 0.959286i −0.877464 0.479643i \(-0.840766\pi\)
0.877464 0.479643i \(-0.159234\pi\)
\(660\) 4.10397 3.30632i 0.159747 0.128698i
\(661\) −24.0205 + 13.8682i −0.934289 + 0.539412i −0.888166 0.459524i \(-0.848020\pi\)
−0.0461236 + 0.998936i \(0.514687\pi\)
\(662\) −23.2483 + 13.4224i −0.903572 + 0.521677i
\(663\) −0.666750 0.384948i −0.0258944 0.0149502i
\(664\) 14.6915i 0.570143i
\(665\) 0 0
\(666\) 3.46579i 0.134297i
\(667\) 0.781078 + 0.450956i 0.0302435 + 0.0174611i
\(668\) −10.6126 18.3815i −0.410613 0.711202i
\(669\) −10.5938 18.3490i −0.409580 0.709414i
\(670\) −5.29063 + 9.16363i −0.204395 + 0.354022i
\(671\) 36.7465 + 14.2115i 1.41858 + 0.548629i
\(672\) 0 0
\(673\) 15.9518i 0.614897i −0.951565 0.307449i \(-0.900525\pi\)
0.951565 0.307449i \(-0.0994752\pi\)
\(674\) 7.27523 12.6011i 0.280231 0.485375i
\(675\) −19.0905 + 11.0219i −0.734793 + 0.424233i
\(676\) −6.48601 11.2341i −0.249462 0.432081i
\(677\) −7.52574 + 13.0350i −0.289238 + 0.500974i −0.973628 0.228141i \(-0.926735\pi\)
0.684390 + 0.729116i \(0.260068\pi\)
\(678\) −13.0997 −0.503091
\(679\) 0 0
\(680\) −3.00868 −0.115378
\(681\) −29.2531 16.8893i −1.12098 0.647198i
\(682\) 1.30205 + 8.35645i 0.0498582 + 0.319985i
\(683\) 2.64673 + 4.58427i 0.101274 + 0.175412i 0.912210 0.409723i \(-0.134375\pi\)
−0.810936 + 0.585135i \(0.801041\pi\)
\(684\) −0.0886450 + 0.153538i −0.00338943 + 0.00587066i
\(685\) 7.14442i 0.272974i
\(686\) 0 0
\(687\) 46.8756 1.78842
\(688\) −8.76612 5.06112i −0.334205 0.192954i
\(689\) −0.704240 1.21978i −0.0268294 0.0464699i
\(690\) −0.654259 + 0.377737i −0.0249072 + 0.0143802i
\(691\) 23.4089 + 13.5151i 0.890517 + 0.514140i 0.874112 0.485725i \(-0.161444\pi\)
0.0164055 + 0.999865i \(0.494778\pi\)
\(692\) 15.0655 0.572706
\(693\) 0 0
\(694\) 28.5417 1.08343
\(695\) 10.1154 + 5.84014i 0.383699 + 0.221529i
\(696\) −2.56161 + 1.47894i −0.0970974 + 0.0560592i
\(697\) 15.0692 + 26.1005i 0.570785 + 0.988629i
\(698\) −29.9667 17.3013i −1.13426 0.654864i
\(699\) −25.2465 −0.954911
\(700\) 0 0
\(701\) 19.9250i 0.752555i 0.926507 + 0.376278i \(0.122796\pi\)
−0.926507 + 0.376278i \(0.877204\pi\)
\(702\) −0.465328 + 0.805972i −0.0175627 + 0.0304195i
\(703\) 0.949649 + 1.64484i 0.0358167 + 0.0620363i
\(704\) 0.510616 + 3.27708i 0.0192446 + 0.123510i
\(705\) 5.22731 + 3.01799i 0.196872 + 0.113664i
\(706\) −16.9203 −0.636805
\(707\) 0 0
\(708\) 9.73355 0.365809
\(709\) −4.98412 + 8.63276i −0.187183 + 0.324210i −0.944310 0.329058i \(-0.893269\pi\)
0.757127 + 0.653268i \(0.226602\pi\)
\(710\) 7.39891 + 12.8153i 0.277676 + 0.480949i
\(711\) −3.45086 + 1.99236i −0.129417 + 0.0747192i
\(712\) −3.45047 + 5.97639i −0.129312 + 0.223975i
\(713\) 1.21235i 0.0454029i
\(714\) 0 0
\(715\) −0.203903 + 0.527228i −0.00762553 + 0.0197172i
\(716\) −1.08088 + 1.87214i −0.0403943 + 0.0699650i
\(717\) 20.3247 + 35.2034i 0.759040 + 1.31470i
\(718\) −15.1755 26.2848i −0.566346 0.980940i
\(719\) −35.6817 20.6008i −1.33070 0.768282i −0.345295 0.938494i \(-0.612221\pi\)
−0.985407 + 0.170212i \(0.945555\pi\)
\(720\) 0.579642i 0.0216020i
\(721\) 0 0
\(722\) 18.9028i 0.703491i
\(723\) 17.8304 + 10.2944i 0.663121 + 0.382853i
\(724\) −4.67035 + 2.69643i −0.173572 + 0.100212i
\(725\) 6.50811 3.75746i 0.241705 0.139549i
\(726\) −16.3385 + 5.21824i −0.606379 + 0.193667i
\(727\) 0.0415718i 0.00154181i 1.00000 0.000770906i \(0.000245387\pi\)
−1.00000 0.000770906i \(0.999755\pi\)
\(728\) 0 0
\(729\) −29.9940 −1.11089
\(730\) −4.94652 + 8.56762i −0.183079 + 0.317102i
\(731\) −25.8804 + 14.9420i −0.957221 + 0.552652i
\(732\) 16.0409 9.26124i 0.592890 0.342305i
\(733\) −4.40404 + 7.62803i −0.162667 + 0.281748i −0.935824 0.352467i \(-0.885343\pi\)
0.773157 + 0.634214i \(0.218676\pi\)
\(734\) −17.4215 −0.643040
\(735\) 0 0
\(736\) 0.475438i 0.0175249i
\(737\) 26.8165 21.6045i 0.987800 0.795810i
\(738\) 5.02844 2.90317i 0.185099 0.106867i
\(739\) −28.4003 + 16.3969i −1.04472 + 0.603170i −0.921167 0.389167i \(-0.872763\pi\)
−0.123555 + 0.992338i \(0.539429\pi\)
\(740\) 5.37774 + 3.10484i 0.197690 + 0.114136i
\(741\) 0.0812842i 0.00298605i
\(742\) 0 0
\(743\) 25.7575i 0.944952i 0.881344 + 0.472476i \(0.156640\pi\)
−0.881344 + 0.472476i \(0.843360\pi\)
\(744\) 3.44332 + 1.98800i 0.126238 + 0.0728836i
\(745\) −7.21355 12.4942i −0.264284 0.457753i
\(746\) −4.57606 7.92596i −0.167541 0.290190i
\(747\) −4.17815 + 7.23678i −0.152871 + 0.264780i
\(748\) 9.13254 + 3.53196i 0.333919 + 0.129141i
\(749\) 0 0
\(750\) 14.2398i 0.519963i
\(751\) −5.73290 + 9.92967i −0.209196 + 0.362339i −0.951462 0.307767i \(-0.900418\pi\)
0.742265 + 0.670106i \(0.233751\pi\)
\(752\) −3.28968 + 1.89930i −0.119962 + 0.0692603i
\(753\) 22.5956 + 39.1367i 0.823430 + 1.42622i
\(754\) 0.158634 0.274763i 0.00577712 0.0100063i
\(755\) −23.7489 −0.864313
\(756\) 0 0
\(757\) 21.9741 0.798661 0.399331 0.916807i \(-0.369243\pi\)
0.399331 + 0.916807i \(0.369243\pi\)
\(758\) 5.32936 + 3.07691i 0.193571 + 0.111758i
\(759\) 2.42937 0.378530i 0.0881805 0.0137398i
\(760\) 0.158826 + 0.275094i 0.00576121 + 0.00997871i
\(761\) −13.0047 + 22.5249i −0.471421 + 0.816526i −0.999466 0.0326910i \(-0.989592\pi\)
0.528044 + 0.849217i \(0.322926\pi\)
\(762\) 5.50916i 0.199576i
\(763\) 0 0
\(764\) −6.00000 −0.217072
\(765\) 1.48202 + 0.855644i 0.0535825 + 0.0309359i
\(766\) 6.48253 + 11.2281i 0.234223 + 0.405687i
\(767\) −0.904164 + 0.522020i −0.0326475 + 0.0188490i
\(768\) 1.35034 + 0.779618i 0.0487261 + 0.0281320i
\(769\) 40.8753 1.47400 0.737001 0.675891i \(-0.236241\pi\)
0.737001 + 0.675891i \(0.236241\pi\)
\(770\) 0 0
\(771\) 10.8929 0.392296
\(772\) 8.31348 + 4.79979i 0.299209 + 0.172748i
\(773\) −40.8229 + 23.5691i −1.46830 + 0.847722i −0.999369 0.0355144i \(-0.988693\pi\)
−0.468928 + 0.883236i \(0.655360\pi\)
\(774\) 2.87868 + 4.98603i 0.103472 + 0.179219i
\(775\) −8.74822 5.05078i −0.314245 0.181430i
\(776\) 11.0218 0.395659
\(777\) 0 0
\(778\) 5.16647i 0.185227i
\(779\) 1.59097 2.75565i 0.0570025 0.0987313i
\(780\) 0.132878 + 0.230151i 0.00475779 + 0.00824073i
\(781\) −7.41445 47.5852i −0.265310 1.70273i
\(782\) −1.21559 0.701823i −0.0434695 0.0250971i
\(783\) 10.5561 0.377243
\(784\) 0 0
\(785\) 4.10960 0.146678
\(786\) 10.8988 18.8773i 0.388748 0.673331i
\(787\) −12.0746 20.9137i −0.430411 0.745494i 0.566497 0.824064i \(-0.308298\pi\)
−0.996909 + 0.0785692i \(0.974965\pi\)
\(788\) −12.8328 + 7.40901i −0.457149 + 0.263935i
\(789\) 3.48543 6.03695i 0.124085 0.214921i
\(790\) 7.13942i 0.254009i
\(791\) 0 0
\(792\) 0.680455 1.75944i 0.0241789 0.0625191i
\(793\) −0.993379 + 1.72058i −0.0352759 + 0.0610997i
\(794\) 4.62856 + 8.01690i 0.164261 + 0.284509i
\(795\) −6.69096 11.5891i −0.237304 0.411022i
\(796\) −3.55962 2.05515i −0.126167 0.0728428i
\(797\) 20.3073i 0.719321i −0.933083 0.359660i \(-0.882893\pi\)
0.933083 0.359660i \(-0.117107\pi\)
\(798\) 0 0
\(799\) 11.2147i 0.396746i
\(800\) −3.43072 1.98073i −0.121294 0.0700293i
\(801\) 3.39927 1.96257i 0.120107 0.0693440i
\(802\) −26.7816 + 15.4624i −0.945692 + 0.545996i
\(803\) 25.0724 20.1993i 0.884785 0.712818i
\(804\) 16.1896i 0.570963i
\(805\) 0 0
\(806\) −0.426473 −0.0150219
\(807\) 1.72865 2.99410i 0.0608513 0.105397i
\(808\) 4.62028 2.66752i 0.162541 0.0938430i
\(809\) −23.4501 + 13.5389i −0.824461 + 0.476003i −0.851953 0.523619i \(-0.824582\pi\)
0.0274911 + 0.999622i \(0.491248\pi\)
\(810\) −3.55160 + 6.15156i −0.124791 + 0.216144i
\(811\) −23.5808 −0.828033 −0.414016 0.910269i \(-0.635874\pi\)
−0.414016 + 0.910269i \(0.635874\pi\)
\(812\) 0 0
\(813\) 35.1018i 1.23107i
\(814\) −12.6787 15.7375i −0.444389 0.551598i
\(815\) −4.88927 + 2.82282i −0.171264 + 0.0988792i
\(816\) 3.98663 2.30168i 0.139560 0.0805749i
\(817\) 2.73240 + 1.57755i 0.0955947 + 0.0551916i
\(818\) 23.8397i 0.833535i
\(819\) 0 0
\(820\) 10.4032i 0.363297i
\(821\) 29.4247 + 16.9884i 1.02693 + 0.592898i 0.916104 0.400942i \(-0.131317\pi\)
0.110826 + 0.993840i \(0.464650\pi\)
\(822\) 5.46557 + 9.46665i 0.190634 + 0.330187i
\(823\) 5.90033 + 10.2197i 0.205673 + 0.356235i 0.950347 0.311193i \(-0.100728\pi\)
−0.744674 + 0.667428i \(0.767395\pi\)
\(824\) 6.22664 10.7849i 0.216915 0.375708i
\(825\) 7.38957 19.1071i 0.257272 0.665224i
\(826\) 0 0
\(827\) 17.0595i 0.593217i −0.954999 0.296609i \(-0.904144\pi\)
0.954999 0.296609i \(-0.0958557\pi\)
\(828\) −0.135211 + 0.234192i −0.00469890 + 0.00813873i
\(829\) 21.7387 12.5508i 0.755015 0.435908i −0.0724880 0.997369i \(-0.523094\pi\)
0.827503 + 0.561461i \(0.189761\pi\)
\(830\) 7.48601 + 12.9662i 0.259843 + 0.450062i
\(831\) 19.0740 33.0371i 0.661669 1.14604i
\(832\) −0.167247 −0.00579823
\(833\) 0 0
\(834\) −17.8711 −0.618826
\(835\) 18.7324 + 10.8152i 0.648263 + 0.374275i
\(836\) −0.159159 1.02147i −0.00550464 0.0353282i
\(837\) −7.09474 12.2884i −0.245230 0.424751i
\(838\) −2.51713 + 4.35980i −0.0869528 + 0.150607i
\(839\) 41.1030i 1.41903i 0.704688 + 0.709517i \(0.251087\pi\)
−0.704688 + 0.709517i \(0.748913\pi\)
\(840\) 0 0
\(841\) 25.4014 0.875909
\(842\) 14.6574 + 8.46248i 0.505129 + 0.291636i
\(843\) 8.85113 + 15.3306i 0.304849 + 0.528014i
\(844\) 6.51646 3.76228i 0.224306 0.129503i
\(845\) 11.4486 + 6.60984i 0.393843 + 0.227385i
\(846\) 2.16058 0.0742822
\(847\) 0 0
\(848\) 8.42157 0.289198
\(849\) 29.2398 + 16.8816i 1.00351 + 0.579375i
\(850\) −10.1286 + 5.84773i −0.347407 + 0.200576i
\(851\) 1.44851 + 2.50888i 0.0496541 + 0.0860035i
\(852\) −19.6077 11.3205i −0.671749 0.387834i
\(853\) −52.7195 −1.80508 −0.902541 0.430605i \(-0.858300\pi\)
−0.902541 + 0.430605i \(0.858300\pi\)
\(854\) 0 0
\(855\) 0.180675i 0.00617894i
\(856\) 3.62707 6.28227i 0.123971 0.214724i
\(857\) 10.9387 + 18.9464i 0.373659 + 0.647197i 0.990125 0.140184i \(-0.0447695\pi\)
−0.616466 + 0.787382i \(0.711436\pi\)
\(858\) −0.133157 0.854588i −0.00454590 0.0291751i
\(859\) −11.8529 6.84326i −0.404415 0.233489i 0.283972 0.958832i \(-0.408348\pi\)
−0.688387 + 0.725344i \(0.741681\pi\)
\(860\) 10.3155 0.351755
\(861\) 0 0
\(862\) 5.99907 0.204329
\(863\) −15.0240 + 26.0223i −0.511423 + 0.885810i 0.488490 + 0.872570i \(0.337548\pi\)
−0.999912 + 0.0132402i \(0.995785\pi\)
\(864\) −2.78229 4.81906i −0.0946553 0.163948i
\(865\) −13.2962 + 7.67658i −0.452085 + 0.261012i
\(866\) 18.0588 31.2787i 0.613662 1.06289i
\(867\) 12.9164i 0.438665i
\(868\) 0 0
\(869\) 8.38113 21.6710i 0.284310 0.735137i
\(870\) 1.50718 2.61051i 0.0510981 0.0885046i
\(871\) 0.868263 + 1.50388i 0.0294200 + 0.0509569i
\(872\) −0.583716 1.01103i −0.0197671 0.0342377i
\(873\) −5.42913 3.13451i −0.183748 0.106087i
\(874\) 0.148194i 0.00501275i
\(875\) 0 0
\(876\) 15.1366i 0.511418i
\(877\) −12.2786 7.08908i −0.414620 0.239381i 0.278153 0.960537i \(-0.410278\pi\)
−0.692773 + 0.721156i \(0.743611\pi\)
\(878\) 9.82906 5.67481i 0.331715 0.191516i
\(879\) 16.3705 9.45151i 0.552163 0.318792i
\(880\) −2.12047 2.63204i −0.0714811 0.0887259i
\(881\) 22.3264i 0.752196i 0.926580 + 0.376098i \(0.122734\pi\)
−0.926580 + 0.376098i \(0.877266\pi\)
\(882\) 0 0
\(883\) −4.45618 −0.149962 −0.0749812 0.997185i \(-0.523890\pi\)
−0.0749812 + 0.997185i \(0.523890\pi\)
\(884\) −0.246883 + 0.427613i −0.00830356 + 0.0143822i
\(885\) −8.59043 + 4.95969i −0.288764 + 0.166718i
\(886\) −4.11428 + 2.37538i −0.138222 + 0.0798025i
\(887\) 4.50070 7.79545i 0.151119 0.261746i −0.780520 0.625131i \(-0.785046\pi\)
0.931639 + 0.363385i \(0.118379\pi\)
\(888\) −9.50096 −0.318831
\(889\) 0 0
\(890\) 7.03268i 0.235736i
\(891\) 18.0020 14.5031i 0.603089 0.485872i
\(892\) −11.7680 + 6.79423i −0.394020 + 0.227488i
\(893\) 1.02539 0.592012i 0.0343135 0.0198109i
\(894\) 19.1165 + 11.0369i 0.639351 + 0.369130i
\(895\) 2.20303i 0.0736391i
\(896\) 0 0
\(897\) 0.123983i 0.00413968i
\(898\) −6.35054 3.66649i −0.211920 0.122352i
\(899\) 2.41866 + 4.18924i 0.0806667 + 0.139719i
\(900\) 1.12660 + 1.95134i 0.0375535 + 0.0650445i
\(901\) 12.4316 21.5321i 0.414156 0.717339i
\(902\) −12.2126 + 31.5780i −0.406635 + 1.05143i
\(903\) 0 0
\(904\) 8.40135i 0.279425i
\(905\) 2.74791 4.75951i 0.0913435 0.158212i
\(906\) 31.4683 18.1682i 1.04547 0.603600i
\(907\) −10.6872 18.5107i −0.354862 0.614638i 0.632233 0.774779i \(-0.282139\pi\)
−0.987094 + 0.160140i \(0.948805\pi\)
\(908\) −10.8318 + 18.7611i −0.359464 + 0.622611i
\(909\) −3.03448 −0.100647
\(910\) 0 0
\(911\) −28.4299 −0.941924 −0.470962 0.882153i \(-0.656093\pi\)
−0.470962 + 0.882153i \(0.656093\pi\)
\(912\) −0.420901 0.243007i −0.0139374 0.00804677i
\(913\) −7.50174 48.1454i −0.248271 1.59338i
\(914\) 6.75879 + 11.7066i 0.223561 + 0.387219i
\(915\) −9.43805 + 16.3472i −0.312012 + 0.540421i
\(916\) 30.0632i 0.993317i
\(917\) 0 0
\(918\) −16.4284 −0.542218
\(919\) 18.2320 + 10.5263i 0.601419 + 0.347229i 0.769600 0.638527i \(-0.220456\pi\)
−0.168181 + 0.985756i \(0.553789\pi\)
\(920\) 0.242258 + 0.419602i 0.00798700 + 0.0138339i
\(921\) 13.0418 7.52968i 0.429741 0.248111i
\(922\) −16.0847 9.28652i −0.529722 0.305835i
\(923\) 2.42852 0.0799357
\(924\) 0 0
\(925\) 24.1385 0.793669
\(926\) −24.4955 14.1425i −0.804971 0.464750i
\(927\) −6.13425 + 3.54161i −0.201475 + 0.116322i
\(928\) 0.948505 + 1.64286i 0.0311362 + 0.0539295i
\(929\) −10.8055 6.23858i −0.354518 0.204681i 0.312155 0.950031i \(-0.398949\pi\)
−0.666674 + 0.745350i \(0.732282\pi\)
\(930\) −4.05191 −0.132867
\(931\) 0 0
\(932\) 16.1916i 0.530373i
\(933\) −13.7819 + 23.8710i −0.451200 + 0.781501i
\(934\) −10.7896 18.6881i −0.353046 0.611493i
\(935\) −9.85970 + 1.53628i −0.322447 + 0.0502418i
\(936\) 0.0823825 + 0.0475636i 0.00269276 + 0.00155466i
\(937\) −43.2128 −1.41170 −0.705850 0.708362i \(-0.749435\pi\)
−0.705850 + 0.708362i \(0.749435\pi\)
\(938\) 0 0
\(939\) −44.9221 −1.46598
\(940\) 1.93556 3.35248i 0.0631309 0.109346i
\(941\) −7.73754 13.4018i −0.252236 0.436886i 0.711905 0.702276i \(-0.247833\pi\)
−0.964141 + 0.265390i \(0.914499\pi\)
\(942\) −5.44538 + 3.14389i −0.177420 + 0.102434i
\(943\) 2.42672 4.20321i 0.0790249 0.136875i
\(944\) 6.24251i 0.203176i
\(945\) 0 0
\(946\) −31.3116 12.1096i −1.01803 0.393717i
\(947\) −16.7488 + 29.0098i −0.544264 + 0.942693i 0.454389 + 0.890803i \(0.349858\pi\)
−0.998653 + 0.0518895i \(0.983476\pi\)
\(948\) −5.46175 9.46003i −0.177389 0.307247i
\(949\) 0.811791 + 1.40606i 0.0263518 + 0.0456427i
\(950\) 1.06936 + 0.617393i 0.0346945 + 0.0200309i
\(951\) 16.1312i 0.523091i
\(952\) 0 0
\(953\) 25.4820i 0.825444i −0.910857 0.412722i \(-0.864578\pi\)
0.910857 0.412722i \(-0.135422\pi\)
\(954\) −4.14831 2.39503i −0.134306 0.0775418i
\(955\) 5.29535 3.05727i 0.171354 0.0989311i
\(956\) 22.5774 13.0350i 0.730204 0.421583i
\(957\) −7.63942 + 6.15462i −0.246947 + 0.198951i
\(958\) 6.93560i 0.224079i
\(959\) 0 0
\(960\) −1.58900 −0.0512849
\(961\) −12.2488 + 21.2156i −0.395124 + 0.684374i
\(962\) 0.882559 0.509546i 0.0284548 0.0164284i
\(963\) −3.57325 + 2.06302i −0.115146 + 0.0664798i
\(964\) 6.60221 11.4354i 0.212643 0.368309i
\(965\) −9.78285 −0.314921
\(966\) 0 0
\(967\) 39.6417i 1.27479i −0.770537 0.637395i \(-0.780012\pi\)
0.770537 0.637395i \(-0.219988\pi\)
\(968\) 3.34666 + 10.4785i 0.107566 + 0.336793i
\(969\) −1.24263 + 0.717434i −0.0399191 + 0.0230473i
\(970\) −9.72738 + 5.61611i −0.312327 + 0.180322i
\(971\) 16.5082 + 9.53101i 0.529773 + 0.305865i 0.740924 0.671589i \(-0.234388\pi\)
−0.211151 + 0.977454i \(0.567721\pi\)
\(972\) 5.82564i 0.186858i
\(973\) 0 0
\(974\) 12.1740i 0.390081i
\(975\) 0.894652 + 0.516528i 0.0286518 + 0.0165421i
\(976\) −5.93960 10.2877i −0.190122 0.329301i
\(977\) −23.8348 41.2832i −0.762544 1.32077i −0.941535 0.336915i \(-0.890617\pi\)
0.178991 0.983851i \(-0.442717\pi\)
\(978\) 4.31899 7.48071i 0.138106 0.239207i
\(979\) −8.25583 + 21.3470i −0.263857 + 0.682252i
\(980\) 0 0
\(981\) 0.664016i 0.0212004i
\(982\) −1.18576 + 2.05379i −0.0378391 + 0.0655392i
\(983\) −40.2377 + 23.2312i −1.28338 + 0.740961i −0.977465 0.211097i \(-0.932296\pi\)
−0.305917 + 0.952058i \(0.598963\pi\)
\(984\) 7.95862 + 13.7847i 0.253711 + 0.439441i
\(985\) 7.55046 13.0778i 0.240578 0.416693i
\(986\) 5.60058 0.178359
\(987\) 0 0
\(988\) 0.0521308 0.00165850
\(989\) 4.16775 + 2.40625i 0.132527 + 0.0765144i
\(990\) 0.295975 + 1.89954i 0.00940670 + 0.0603712i
\(991\) 7.28588 + 12.6195i 0.231444 + 0.400872i 0.958233 0.285988i \(-0.0923218\pi\)
−0.726790 + 0.686860i \(0.758988\pi\)
\(992\) 1.27498 2.20834i 0.0404808 0.0701147i
\(993\) 41.8575i 1.32831i
\(994\) 0 0
\(995\) 4.18877 0.132793
\(996\) −19.8386 11.4538i −0.628609 0.362927i
\(997\) 2.05848 + 3.56539i 0.0651927 + 0.112917i 0.896779 0.442478i \(-0.145900\pi\)
−0.831587 + 0.555395i \(0.812567\pi\)
\(998\) −3.40255 + 1.96446i −0.107706 + 0.0621839i
\(999\) 29.3642 + 16.9534i 0.929043 + 0.536383i
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 1078.2.i.c.901.2 16
7.2 even 3 1078.2.c.b.1077.11 16
7.3 odd 6 inner 1078.2.i.c.1011.6 16
7.4 even 3 154.2.i.a.87.7 yes 16
7.5 odd 6 1078.2.c.b.1077.14 16
7.6 odd 2 154.2.i.a.131.3 yes 16
11.10 odd 2 inner 1078.2.i.c.901.6 16
21.11 odd 6 1386.2.bk.c.703.2 16
21.20 even 2 1386.2.bk.c.901.6 16
28.11 odd 6 1232.2.bn.b.241.4 16
28.27 even 2 1232.2.bn.b.593.3 16
77.10 even 6 inner 1078.2.i.c.1011.2 16
77.32 odd 6 154.2.i.a.87.3 16
77.54 even 6 1078.2.c.b.1077.6 16
77.65 odd 6 1078.2.c.b.1077.3 16
77.76 even 2 154.2.i.a.131.7 yes 16
231.32 even 6 1386.2.bk.c.703.6 16
231.230 odd 2 1386.2.bk.c.901.2 16
308.263 even 6 1232.2.bn.b.241.3 16
308.307 odd 2 1232.2.bn.b.593.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.2.i.a.87.3 16 77.32 odd 6
154.2.i.a.87.7 yes 16 7.4 even 3
154.2.i.a.131.3 yes 16 7.6 odd 2
154.2.i.a.131.7 yes 16 77.76 even 2
1078.2.c.b.1077.3 16 77.65 odd 6
1078.2.c.b.1077.6 16 77.54 even 6
1078.2.c.b.1077.11 16 7.2 even 3
1078.2.c.b.1077.14 16 7.5 odd 6
1078.2.i.c.901.2 16 1.1 even 1 trivial
1078.2.i.c.901.6 16 11.10 odd 2 inner
1078.2.i.c.1011.2 16 77.10 even 6 inner
1078.2.i.c.1011.6 16 7.3 odd 6 inner
1232.2.bn.b.241.3 16 308.263 even 6
1232.2.bn.b.241.4 16 28.11 odd 6
1232.2.bn.b.593.3 16 28.27 even 2
1232.2.bn.b.593.4 16 308.307 odd 2
1386.2.bk.c.703.2 16 21.11 odd 6
1386.2.bk.c.703.6 16 231.32 even 6
1386.2.bk.c.901.2 16 231.230 odd 2
1386.2.bk.c.901.6 16 21.20 even 2