Properties

Label 784.2.x.o.165.7
Level $784$
Weight $2$
Character 784.165
Analytic conductor $6.260$
Analytic rank $0$
Dimension $48$
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] = [784,2,Mod(165,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.x (of order \(12\), degree \(4\), 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: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 165.7
Character \(\chi\) \(=\) 784.165
Dual form 784.2.x.o.765.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0582062 - 1.41302i) q^{2} +(0.523249 + 1.95279i) q^{3} +(-1.99322 - 0.164492i) q^{4} +(0.256983 - 0.959072i) q^{5} +(2.78978 - 0.625694i) q^{6} +(-0.348448 + 2.80688i) q^{8} +(-0.941530 + 0.543593i) q^{9} +O(q^{10})\) \(q+(0.0582062 - 1.41302i) q^{2} +(0.523249 + 1.95279i) q^{3} +(-1.99322 - 0.164492i) q^{4} +(0.256983 - 0.959072i) q^{5} +(2.78978 - 0.625694i) q^{6} +(-0.348448 + 2.80688i) q^{8} +(-0.941530 + 0.543593i) q^{9} +(-1.34023 - 0.418944i) q^{10} +(1.88773 - 0.505816i) q^{11} +(-0.721733 - 3.97842i) q^{12} +(2.10314 - 2.10314i) q^{13} +2.00733 q^{15} +(3.94588 + 0.655741i) q^{16} +(-2.83885 + 4.91704i) q^{17} +(0.713302 + 1.36204i) q^{18} +(-0.616573 - 0.165210i) q^{19} +(-0.669984 + 1.86937i) q^{20} +(-0.604848 - 2.69683i) q^{22} +(5.92691 - 3.42190i) q^{23} +(-5.66358 + 0.788251i) q^{24} +(3.47635 + 2.00707i) q^{25} +(-2.84936 - 3.09419i) q^{26} +(2.73445 + 2.73445i) q^{27} +(-0.207295 + 0.207295i) q^{29} +(0.116839 - 2.83639i) q^{30} +(3.94693 - 6.83628i) q^{31} +(1.15625 - 5.53743i) q^{32} +(1.97551 + 3.42168i) q^{33} +(6.78261 + 4.29755i) q^{34} +(1.96610 - 0.928627i) q^{36} +(-2.57374 + 9.60533i) q^{37} +(-0.269333 + 0.861610i) q^{38} +(5.20747 + 3.00653i) q^{39} +(2.60246 + 1.05551i) q^{40} -2.40202i q^{41} +(3.65586 + 3.65586i) q^{43} +(-3.84587 + 0.697687i) q^{44} +(0.279388 + 1.04269i) q^{45} +(-4.49022 - 8.57399i) q^{46} +(0.144593 + 0.250442i) q^{47} +(0.784155 + 8.04861i) q^{48} +(3.03837 - 4.79531i) q^{50} +(-11.0874 - 2.97086i) q^{51} +(-4.53798 + 3.84608i) q^{52} +(7.62740 - 2.04376i) q^{53} +(4.02298 - 3.70466i) q^{54} -1.94045i q^{55} -1.29048i q^{57} +(0.280845 + 0.304976i) q^{58} +(13.4543 - 3.60507i) q^{59} +(-4.00107 - 0.330191i) q^{60} +(-3.61701 - 0.969174i) q^{61} +(-9.43003 - 5.97498i) q^{62} +(-7.75717 - 1.95611i) q^{64} +(-1.47659 - 2.55754i) q^{65} +(4.94987 - 2.59226i) q^{66} +(-2.69202 - 10.0468i) q^{67} +(6.46729 - 9.33379i) q^{68} +(9.78352 + 9.78352i) q^{69} +11.5947i q^{71} +(-1.19773 - 2.83218i) q^{72} +(-0.310772 - 0.179424i) q^{73} +(13.4227 + 4.19582i) q^{74} +(-2.10040 + 7.83878i) q^{75} +(1.20179 + 0.430722i) q^{76} +(4.55138 - 7.18323i) q^{78} +(-3.84953 - 6.66758i) q^{79} +(1.64293 - 3.61587i) q^{80} +(-5.53979 + 9.59520i) q^{81} +(-3.39409 - 0.139812i) q^{82} +(0.424001 - 0.424001i) q^{83} +(3.98626 + 3.98626i) q^{85} +(5.37858 - 4.95300i) q^{86} +(-0.513270 - 0.296337i) q^{87} +(0.761988 + 5.47488i) q^{88} +(-15.2323 + 8.79437i) q^{89} +(1.48960 - 0.334088i) q^{90} +(-12.3765 + 5.84569i) q^{92} +(15.4150 + 4.13045i) q^{93} +(0.362294 - 0.189734i) q^{94} +(-0.316897 + 0.548881i) q^{95} +(11.4184 - 0.639544i) q^{96} -12.2678 q^{97} +(-1.50240 + 1.50240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0582062 1.41302i 0.0411580 0.999153i
\(3\) 0.523249 + 1.95279i 0.302098 + 1.12744i 0.935415 + 0.353552i \(0.115026\pi\)
−0.633317 + 0.773893i \(0.718307\pi\)
\(4\) −1.99322 0.164492i −0.996612 0.0822462i
\(5\) 0.256983 0.959072i 0.114926 0.428910i −0.884355 0.466814i \(-0.845402\pi\)
0.999281 + 0.0379045i \(0.0120683\pi\)
\(6\) 2.78978 0.625694i 1.13892 0.255439i
\(7\) 0 0
\(8\) −0.348448 + 2.80688i −0.123195 + 0.992382i
\(9\) −0.941530 + 0.543593i −0.313843 + 0.181198i
\(10\) −1.34023 0.418944i −0.423816 0.132482i
\(11\) 1.88773 0.505816i 0.569172 0.152509i 0.0372551 0.999306i \(-0.488139\pi\)
0.531917 + 0.846797i \(0.321472\pi\)
\(12\) −0.721733 3.97842i −0.208346 1.14847i
\(13\) 2.10314 2.10314i 0.583307 0.583307i −0.352504 0.935810i \(-0.614670\pi\)
0.935810 + 0.352504i \(0.114670\pi\)
\(14\) 0 0
\(15\) 2.00733 0.518291
\(16\) 3.94588 + 0.655741i 0.986471 + 0.163935i
\(17\) −2.83885 + 4.91704i −0.688523 + 1.19256i 0.283792 + 0.958886i \(0.408407\pi\)
−0.972316 + 0.233672i \(0.924926\pi\)
\(18\) 0.713302 + 1.36204i 0.168127 + 0.321035i
\(19\) −0.616573 0.165210i −0.141451 0.0379018i 0.187399 0.982284i \(-0.439994\pi\)
−0.328850 + 0.944382i \(0.606661\pi\)
\(20\) −0.669984 + 1.86937i −0.149813 + 0.418005i
\(21\) 0 0
\(22\) −0.604848 2.69683i −0.128954 0.574967i
\(23\) 5.92691 3.42190i 1.23585 0.713516i 0.267604 0.963529i \(-0.413768\pi\)
0.968243 + 0.250013i \(0.0804348\pi\)
\(24\) −5.66358 + 0.788251i −1.15607 + 0.160901i
\(25\) 3.47635 + 2.00707i 0.695270 + 0.401414i
\(26\) −2.84936 3.09419i −0.558805 0.606820i
\(27\) 2.73445 + 2.73445i 0.526245 + 0.526245i
\(28\) 0 0
\(29\) −0.207295 + 0.207295i −0.0384937 + 0.0384937i −0.726092 0.687598i \(-0.758665\pi\)
0.687598 + 0.726092i \(0.258665\pi\)
\(30\) 0.116839 2.83639i 0.0213318 0.517852i
\(31\) 3.94693 6.83628i 0.708889 1.22783i −0.256381 0.966576i \(-0.582530\pi\)
0.965270 0.261255i \(-0.0841365\pi\)
\(32\) 1.15625 5.53743i 0.204397 0.978888i
\(33\) 1.97551 + 3.42168i 0.343891 + 0.595637i
\(34\) 6.78261 + 4.29755i 1.16321 + 0.737023i
\(35\) 0 0
\(36\) 1.96610 0.928627i 0.327683 0.154771i
\(37\) −2.57374 + 9.60533i −0.423120 + 1.57911i 0.344873 + 0.938649i \(0.387922\pi\)
−0.767994 + 0.640457i \(0.778745\pi\)
\(38\) −0.269333 + 0.861610i −0.0436916 + 0.139772i
\(39\) 5.20747 + 3.00653i 0.833862 + 0.481430i
\(40\) 2.60246 + 1.05551i 0.411484 + 0.166890i
\(41\) 2.40202i 0.375132i −0.982252 0.187566i \(-0.939940\pi\)
0.982252 0.187566i \(-0.0600599\pi\)
\(42\) 0 0
\(43\) 3.65586 + 3.65586i 0.557514 + 0.557514i 0.928599 0.371085i \(-0.121014\pi\)
−0.371085 + 0.928599i \(0.621014\pi\)
\(44\) −3.84587 + 0.697687i −0.579787 + 0.105180i
\(45\) 0.279388 + 1.04269i 0.0416486 + 0.155435i
\(46\) −4.49022 8.57399i −0.662047 1.26417i
\(47\) 0.144593 + 0.250442i 0.0210910 + 0.0365307i 0.876378 0.481623i \(-0.159953\pi\)
−0.855287 + 0.518154i \(0.826619\pi\)
\(48\) 0.784155 + 8.04861i 0.113183 + 1.16172i
\(49\) 0 0
\(50\) 3.03837 4.79531i 0.429690 0.678159i
\(51\) −11.0874 2.97086i −1.55254 0.416003i
\(52\) −4.53798 + 3.84608i −0.629305 + 0.533356i
\(53\) 7.62740 2.04376i 1.04770 0.280732i 0.306402 0.951902i \(-0.400875\pi\)
0.741303 + 0.671171i \(0.234208\pi\)
\(54\) 4.02298 3.70466i 0.547459 0.504140i
\(55\) 1.94045i 0.261651i
\(56\) 0 0
\(57\) 1.29048i 0.170929i
\(58\) 0.280845 + 0.304976i 0.0368767 + 0.0400454i
\(59\) 13.4543 3.60507i 1.75160 0.469340i 0.766634 0.642084i \(-0.221930\pi\)
0.984967 + 0.172744i \(0.0552633\pi\)
\(60\) −4.00107 0.330191i −0.516535 0.0426275i
\(61\) −3.61701 0.969174i −0.463110 0.124090i 0.0197171 0.999806i \(-0.493723\pi\)
−0.482827 + 0.875716i \(0.660390\pi\)
\(62\) −9.43003 5.97498i −1.19761 0.758823i
\(63\) 0 0
\(64\) −7.75717 1.95611i −0.969646 0.244513i
\(65\) −1.47659 2.55754i −0.183149 0.317223i
\(66\) 4.94987 2.59226i 0.609286 0.319085i
\(67\) −2.69202 10.0468i −0.328883 1.22741i −0.910350 0.413838i \(-0.864188\pi\)
0.581467 0.813570i \(-0.302479\pi\)
\(68\) 6.46729 9.33379i 0.784274 1.13189i
\(69\) 9.78352 + 9.78352i 1.17780 + 1.17780i
\(70\) 0 0
\(71\) 11.5947i 1.37603i 0.725695 + 0.688017i \(0.241518\pi\)
−0.725695 + 0.688017i \(0.758482\pi\)
\(72\) −1.19773 2.83218i −0.141153 0.333775i
\(73\) −0.310772 0.179424i −0.0363731 0.0210000i 0.481703 0.876334i \(-0.340018\pi\)
−0.518076 + 0.855334i \(0.673352\pi\)
\(74\) 13.4227 + 4.19582i 1.56035 + 0.487755i
\(75\) −2.10040 + 7.83878i −0.242533 + 0.905145i
\(76\) 1.20179 + 0.430722i 0.137855 + 0.0494073i
\(77\) 0 0
\(78\) 4.55138 7.18323i 0.515342 0.813341i
\(79\) −3.84953 6.66758i −0.433106 0.750161i 0.564033 0.825752i \(-0.309249\pi\)
−0.997139 + 0.0755910i \(0.975916\pi\)
\(80\) 1.64293 3.61587i 0.183685 0.404267i
\(81\) −5.53979 + 9.59520i −0.615532 + 1.06613i
\(82\) −3.39409 0.139812i −0.374814 0.0154397i
\(83\) 0.424001 0.424001i 0.0465402 0.0465402i −0.683454 0.729994i \(-0.739523\pi\)
0.729994 + 0.683454i \(0.239523\pi\)
\(84\) 0 0
\(85\) 3.98626 + 3.98626i 0.432371 + 0.432371i
\(86\) 5.37858 4.95300i 0.579988 0.534095i
\(87\) −0.513270 0.296337i −0.0550283 0.0317706i
\(88\) 0.761988 + 5.47488i 0.0812282 + 0.583625i
\(89\) −15.2323 + 8.79437i −1.61462 + 0.932201i −0.626340 + 0.779550i \(0.715448\pi\)
−0.988280 + 0.152652i \(0.951219\pi\)
\(90\) 1.48960 0.334088i 0.157017 0.0352160i
\(91\) 0 0
\(92\) −12.3765 + 5.84569i −1.29034 + 0.609455i
\(93\) 15.4150 + 4.13045i 1.59847 + 0.428308i
\(94\) 0.362294 0.189734i 0.0373678 0.0195696i
\(95\) −0.316897 + 0.548881i −0.0325129 + 0.0563140i
\(96\) 11.4184 0.639544i 1.16539 0.0652732i
\(97\) −12.2678 −1.24560 −0.622802 0.782379i \(-0.714006\pi\)
−0.622802 + 0.782379i \(0.714006\pi\)
\(98\) 0 0
\(99\) −1.50240 + 1.50240i −0.150997 + 0.150997i
\(100\) −6.59899 4.57237i −0.659899 0.457237i
\(101\) −1.16857 + 0.313118i −0.116277 + 0.0311564i −0.316488 0.948596i \(-0.602504\pi\)
0.200211 + 0.979753i \(0.435837\pi\)
\(102\) −4.84322 + 15.4937i −0.479550 + 1.53411i
\(103\) 5.06181 2.92244i 0.498755 0.287956i −0.229444 0.973322i \(-0.573691\pi\)
0.728199 + 0.685365i \(0.240357\pi\)
\(104\) 5.17043 + 6.63611i 0.507003 + 0.650724i
\(105\) 0 0
\(106\) −2.44390 10.8966i −0.237372 1.05837i
\(107\) −0.971295 + 3.62492i −0.0938987 + 0.350435i −0.996850 0.0793079i \(-0.974729\pi\)
0.902952 + 0.429742i \(0.141396\pi\)
\(108\) −5.00058 5.90017i −0.481181 0.567744i
\(109\) −2.59283 9.67656i −0.248348 0.926846i −0.971671 0.236337i \(-0.924053\pi\)
0.723323 0.690509i \(-0.242614\pi\)
\(110\) −2.74189 0.112946i −0.261429 0.0107690i
\(111\) −20.1039 −1.90818
\(112\) 0 0
\(113\) 5.07461 0.477379 0.238689 0.971096i \(-0.423282\pi\)
0.238689 + 0.971096i \(0.423282\pi\)
\(114\) −1.82347 0.0751142i −0.170784 0.00703509i
\(115\) −1.75874 6.56370i −0.164003 0.612069i
\(116\) 0.447283 0.379086i 0.0415292 0.0351973i
\(117\) −0.836919 + 3.12342i −0.0773732 + 0.288761i
\(118\) −4.31089 19.2210i −0.396850 1.76943i
\(119\) 0 0
\(120\) −0.699452 + 5.63435i −0.0638509 + 0.514343i
\(121\) −6.21861 + 3.59031i −0.565328 + 0.326392i
\(122\) −1.57999 + 5.05447i −0.143046 + 0.457611i
\(123\) 4.69064 1.25685i 0.422941 0.113327i
\(124\) −8.99162 + 12.9770i −0.807472 + 1.16537i
\(125\) 6.32873 6.32873i 0.566059 0.566059i
\(126\) 0 0
\(127\) −11.1710 −0.991270 −0.495635 0.868531i \(-0.665065\pi\)
−0.495635 + 0.868531i \(0.665065\pi\)
\(128\) −3.21552 + 10.8471i −0.284215 + 0.958761i
\(129\) −5.22621 + 9.05207i −0.460142 + 0.796990i
\(130\) −3.69978 + 1.93758i −0.324492 + 0.169937i
\(131\) −12.1789 3.26332i −1.06407 0.285118i −0.316017 0.948753i \(-0.602346\pi\)
−0.748056 + 0.663636i \(0.769012\pi\)
\(132\) −3.37478 7.14512i −0.293737 0.621903i
\(133\) 0 0
\(134\) −14.3529 + 3.21909i −1.23990 + 0.278087i
\(135\) 3.32524 1.91983i 0.286191 0.165233i
\(136\) −12.8124 9.68166i −1.09865 0.830196i
\(137\) −14.0325 8.10166i −1.19888 0.692172i −0.238572 0.971125i \(-0.576679\pi\)
−0.960305 + 0.278953i \(0.910013\pi\)
\(138\) 14.3937 13.2548i 1.22527 1.12832i
\(139\) −10.5018 10.5018i −0.890748 0.890748i 0.103846 0.994593i \(-0.466885\pi\)
−0.994593 + 0.103846i \(0.966885\pi\)
\(140\) 0 0
\(141\) −0.413403 + 0.413403i −0.0348148 + 0.0348148i
\(142\) 16.3834 + 0.674881i 1.37487 + 0.0566348i
\(143\) 2.90636 5.03397i 0.243042 0.420961i
\(144\) −4.07162 + 1.52755i −0.339302 + 0.127296i
\(145\) 0.145539 + 0.252082i 0.0120864 + 0.0209342i
\(146\) −0.271618 + 0.428682i −0.0224793 + 0.0354780i
\(147\) 0 0
\(148\) 6.71005 18.7222i 0.551562 1.53896i
\(149\) 2.57749 9.61931i 0.211156 0.788045i −0.776328 0.630329i \(-0.782920\pi\)
0.987484 0.157716i \(-0.0504132\pi\)
\(150\) 10.9541 + 3.42416i 0.894395 + 0.279581i
\(151\) −8.97638 5.18252i −0.730487 0.421747i 0.0881130 0.996110i \(-0.471916\pi\)
−0.818600 + 0.574363i \(0.805250\pi\)
\(152\) 0.678569 1.67308i 0.0550392 0.135705i
\(153\) 6.17272i 0.499035i
\(154\) 0 0
\(155\) −5.54219 5.54219i −0.445159 0.445159i
\(156\) −9.88509 6.84928i −0.791441 0.548381i
\(157\) 1.06781 + 3.98512i 0.0852205 + 0.318047i 0.995356 0.0962637i \(-0.0306892\pi\)
−0.910135 + 0.414311i \(0.864023\pi\)
\(158\) −9.64546 + 5.05135i −0.767351 + 0.401864i
\(159\) 7.98206 + 13.8253i 0.633019 + 1.09642i
\(160\) −5.01366 2.53195i −0.396364 0.200168i
\(161\) 0 0
\(162\) 13.2357 + 8.38631i 1.03990 + 0.658891i
\(163\) −7.98280 2.13899i −0.625261 0.167538i −0.0677429 0.997703i \(-0.521580\pi\)
−0.557518 + 0.830165i \(0.688246\pi\)
\(164\) −0.395114 + 4.78776i −0.0308532 + 0.373861i
\(165\) 3.78930 1.01534i 0.294997 0.0790442i
\(166\) −0.574440 0.623799i −0.0445852 0.0484162i
\(167\) 8.92669i 0.690768i 0.938462 + 0.345384i \(0.112251\pi\)
−0.938462 + 0.345384i \(0.887749\pi\)
\(168\) 0 0
\(169\) 4.15359i 0.319507i
\(170\) 5.86467 5.40062i 0.449800 0.414209i
\(171\) 0.670329 0.179614i 0.0512613 0.0137354i
\(172\) −6.68559 7.88832i −0.509772 0.601478i
\(173\) 5.26383 + 1.41044i 0.400202 + 0.107234i 0.453305 0.891355i \(-0.350245\pi\)
−0.0531037 + 0.998589i \(0.516911\pi\)
\(174\) −0.448604 + 0.708010i −0.0340086 + 0.0536741i
\(175\) 0 0
\(176\) 7.78045 0.758029i 0.586473 0.0571386i
\(177\) 14.0799 + 24.3871i 1.05831 + 1.83305i
\(178\) 11.5400 + 22.0354i 0.864957 + 1.65162i
\(179\) 2.52526 + 9.42440i 0.188747 + 0.704413i 0.993797 + 0.111207i \(0.0354715\pi\)
−0.805050 + 0.593206i \(0.797862\pi\)
\(180\) −0.385368 2.12427i −0.0287236 0.158334i
\(181\) 8.42976 + 8.42976i 0.626579 + 0.626579i 0.947206 0.320627i \(-0.103894\pi\)
−0.320627 + 0.947206i \(0.603894\pi\)
\(182\) 0 0
\(183\) 7.57038i 0.559619i
\(184\) 7.53966 + 17.8285i 0.555831 + 1.31433i
\(185\) 8.55080 + 4.93680i 0.628667 + 0.362961i
\(186\) 6.73364 21.5413i 0.493734 1.57948i
\(187\) −2.87187 + 10.7180i −0.210012 + 0.783776i
\(188\) −0.247010 0.522971i −0.0180150 0.0381416i
\(189\) 0 0
\(190\) 0.757132 + 0.479728i 0.0549282 + 0.0348032i
\(191\) 2.46522 + 4.26989i 0.178377 + 0.308958i 0.941325 0.337502i \(-0.109582\pi\)
−0.762948 + 0.646460i \(0.776249\pi\)
\(192\) −0.239061 16.1717i −0.0172527 1.16709i
\(193\) −10.9543 + 18.9735i −0.788510 + 1.36574i 0.138370 + 0.990381i \(0.455814\pi\)
−0.926880 + 0.375358i \(0.877520\pi\)
\(194\) −0.714061 + 17.3346i −0.0512666 + 1.24455i
\(195\) 4.22171 4.22171i 0.302323 0.302323i
\(196\) 0 0
\(197\) 7.61984 + 7.61984i 0.542891 + 0.542891i 0.924375 0.381484i \(-0.124587\pi\)
−0.381484 + 0.924375i \(0.624587\pi\)
\(198\) 2.03546 + 2.21036i 0.144654 + 0.157083i
\(199\) −3.09710 1.78811i −0.219547 0.126756i 0.386193 0.922418i \(-0.373790\pi\)
−0.605741 + 0.795662i \(0.707123\pi\)
\(200\) −6.84494 + 9.05834i −0.484010 + 0.640521i
\(201\) 18.2106 10.5139i 1.28448 0.741595i
\(202\) 0.374422 + 1.66944i 0.0263443 + 0.117461i
\(203\) 0 0
\(204\) 21.6110 + 7.74537i 1.51307 + 0.542285i
\(205\) −2.30371 0.617276i −0.160898 0.0431125i
\(206\) −3.83482 7.32252i −0.267185 0.510184i
\(207\) −3.72024 + 6.44365i −0.258575 + 0.447865i
\(208\) 9.67787 6.91964i 0.671040 0.479791i
\(209\) −1.24749 −0.0862906
\(210\) 0 0
\(211\) 7.33737 7.33737i 0.505126 0.505126i −0.407901 0.913026i \(-0.633739\pi\)
0.913026 + 0.407901i \(0.133739\pi\)
\(212\) −15.5393 + 2.81901i −1.06724 + 0.193611i
\(213\) −22.6420 + 6.06690i −1.55140 + 0.415697i
\(214\) 5.06554 + 1.58345i 0.346273 + 0.108242i
\(215\) 4.44573 2.56674i 0.303196 0.175050i
\(216\) −8.62809 + 6.72246i −0.587067 + 0.457406i
\(217\) 0 0
\(218\) −13.8240 + 3.10047i −0.936283 + 0.209990i
\(219\) 0.187767 0.700757i 0.0126881 0.0473528i
\(220\) −0.319190 + 3.86776i −0.0215198 + 0.260764i
\(221\) 4.37072 + 16.3117i 0.294006 + 1.09725i
\(222\) −1.17017 + 28.4071i −0.0785368 + 1.90656i
\(223\) −4.26037 −0.285295 −0.142648 0.989774i \(-0.545562\pi\)
−0.142648 + 0.989774i \(0.545562\pi\)
\(224\) 0 0
\(225\) −4.36411 −0.290941
\(226\) 0.295373 7.17049i 0.0196479 0.476974i
\(227\) −1.25223 4.67340i −0.0831136 0.310184i 0.911837 0.410553i \(-0.134664\pi\)
−0.994950 + 0.100369i \(0.967998\pi\)
\(228\) −0.212275 + 2.57222i −0.0140583 + 0.170350i
\(229\) 5.07737 18.9490i 0.335522 1.25218i −0.567781 0.823180i \(-0.692198\pi\)
0.903302 0.429005i \(-0.141136\pi\)
\(230\) −9.37698 + 2.10308i −0.618300 + 0.138673i
\(231\) 0 0
\(232\) −0.509620 0.654083i −0.0334582 0.0429427i
\(233\) −4.38681 + 2.53273i −0.287390 + 0.165925i −0.636764 0.771059i \(-0.719727\pi\)
0.349374 + 0.936983i \(0.386394\pi\)
\(234\) 4.36473 + 1.36438i 0.285331 + 0.0891924i
\(235\) 0.277349 0.0743155i 0.0180923 0.00484781i
\(236\) −27.4104 + 4.97258i −1.78427 + 0.323687i
\(237\) 11.0061 11.0061i 0.714925 0.714925i
\(238\) 0 0
\(239\) −9.32494 −0.603181 −0.301590 0.953438i \(-0.597517\pi\)
−0.301590 + 0.953438i \(0.597517\pi\)
\(240\) 7.92071 + 1.31629i 0.511279 + 0.0849662i
\(241\) 12.8663 22.2850i 0.828789 1.43550i −0.0702006 0.997533i \(-0.522364\pi\)
0.898989 0.437971i \(-0.144303\pi\)
\(242\) 4.71121 + 8.99596i 0.302848 + 0.578282i
\(243\) −10.4301 2.79475i −0.669093 0.179283i
\(244\) 7.05008 + 2.52675i 0.451335 + 0.161759i
\(245\) 0 0
\(246\) −1.50293 6.70110i −0.0958232 0.427247i
\(247\) −1.64420 + 0.949280i −0.104618 + 0.0604012i
\(248\) 17.8133 + 13.4606i 1.13115 + 0.854752i
\(249\) 1.04984 + 0.606128i 0.0665312 + 0.0384118i
\(250\) −8.57422 9.31097i −0.542282 0.588877i
\(251\) 3.64372 + 3.64372i 0.229990 + 0.229990i 0.812688 0.582699i \(-0.198003\pi\)
−0.582699 + 0.812688i \(0.698003\pi\)
\(252\) 0 0
\(253\) 9.45755 9.45755i 0.594591 0.594591i
\(254\) −0.650224 + 15.7849i −0.0407987 + 0.990430i
\(255\) −5.69853 + 9.87014i −0.356856 + 0.618092i
\(256\) 15.1400 + 5.17495i 0.946251 + 0.323435i
\(257\) −1.87774 3.25234i −0.117130 0.202875i 0.801499 0.597996i \(-0.204036\pi\)
−0.918629 + 0.395121i \(0.870703\pi\)
\(258\) 12.4865 + 7.91160i 0.777376 + 0.492555i
\(259\) 0 0
\(260\) 2.52249 + 5.34063i 0.156438 + 0.331212i
\(261\) 0.0824903 0.307858i 0.00510602 0.0190559i
\(262\) −5.32001 + 17.0190i −0.328671 + 1.05144i
\(263\) 16.3252 + 9.42534i 1.00665 + 0.581191i 0.910210 0.414147i \(-0.135920\pi\)
0.0964430 + 0.995339i \(0.469253\pi\)
\(264\) −10.2926 + 4.35273i −0.633466 + 0.267892i
\(265\) 7.84044i 0.481634i
\(266\) 0 0
\(267\) −25.1439 25.1439i −1.53878 1.53878i
\(268\) 3.71319 + 20.4683i 0.226819 + 1.25030i
\(269\) 4.43839 + 16.5643i 0.270614 + 1.00994i 0.958724 + 0.284338i \(0.0917737\pi\)
−0.688111 + 0.725606i \(0.741560\pi\)
\(270\) −2.51920 4.81036i −0.153313 0.292749i
\(271\) 2.65608 + 4.60046i 0.161345 + 0.279458i 0.935351 0.353720i \(-0.115083\pi\)
−0.774006 + 0.633178i \(0.781750\pi\)
\(272\) −14.4261 + 17.5405i −0.874711 + 1.06355i
\(273\) 0 0
\(274\) −12.2646 + 19.3566i −0.740929 + 1.16937i
\(275\) 7.57761 + 2.03042i 0.456947 + 0.122439i
\(276\) −17.8914 21.1101i −1.07694 1.27068i
\(277\) 14.6832 3.93434i 0.882226 0.236392i 0.210859 0.977517i \(-0.432374\pi\)
0.671367 + 0.741125i \(0.265707\pi\)
\(278\) −15.4504 + 14.2279i −0.926654 + 0.853331i
\(279\) 8.58208i 0.513795i
\(280\) 0 0
\(281\) 3.15786i 0.188382i −0.995554 0.0941910i \(-0.969974\pi\)
0.995554 0.0941910i \(-0.0300264\pi\)
\(282\) 0.560082 + 0.608207i 0.0333524 + 0.0362182i
\(283\) −13.6357 + 3.65368i −0.810559 + 0.217189i −0.640215 0.768196i \(-0.721155\pi\)
−0.170344 + 0.985385i \(0.554488\pi\)
\(284\) 1.90723 23.1108i 0.113174 1.37137i
\(285\) −1.23767 0.331632i −0.0733131 0.0196442i
\(286\) −6.94390 4.39974i −0.410602 0.260162i
\(287\) 0 0
\(288\) 1.92146 + 5.84218i 0.113223 + 0.344254i
\(289\) −7.61819 13.1951i −0.448129 0.776182i
\(290\) 0.364666 0.190977i 0.0214140 0.0112145i
\(291\) −6.41911 23.9564i −0.376295 1.40435i
\(292\) 0.589925 + 0.408753i 0.0345227 + 0.0239204i
\(293\) 10.9335 + 10.9335i 0.638743 + 0.638743i 0.950245 0.311502i \(-0.100832\pi\)
−0.311502 + 0.950245i \(0.600832\pi\)
\(294\) 0 0
\(295\) 13.8301i 0.805219i
\(296\) −26.0642 10.5711i −1.51495 0.614435i
\(297\) 6.54503 + 3.77878i 0.379781 + 0.219267i
\(298\) −13.4422 4.20193i −0.778686 0.243411i
\(299\) 5.26839 19.6619i 0.304679 1.13708i
\(300\) 5.47598 15.2789i 0.316156 0.882131i
\(301\) 0 0
\(302\) −7.84545 + 12.3821i −0.451455 + 0.712510i
\(303\) −1.22291 2.11814i −0.0702543 0.121684i
\(304\) −2.32459 1.05621i −0.133324 0.0605779i
\(305\) −1.85902 + 3.21991i −0.106447 + 0.184371i
\(306\) −8.72215 0.359291i −0.498612 0.0205393i
\(307\) 14.7735 14.7735i 0.843170 0.843170i −0.146100 0.989270i \(-0.546672\pi\)
0.989270 + 0.146100i \(0.0466721\pi\)
\(308\) 0 0
\(309\) 8.35550 + 8.35550i 0.475328 + 0.475328i
\(310\) −8.15379 + 7.50861i −0.463104 + 0.426460i
\(311\) −7.56549 4.36794i −0.429000 0.247683i 0.269921 0.962883i \(-0.413002\pi\)
−0.698920 + 0.715199i \(0.746336\pi\)
\(312\) −10.2535 + 13.5691i −0.580491 + 0.768200i
\(313\) 3.56615 2.05892i 0.201571 0.116377i −0.395817 0.918329i \(-0.629539\pi\)
0.597388 + 0.801952i \(0.296205\pi\)
\(314\) 5.69319 1.27687i 0.321285 0.0720581i
\(315\) 0 0
\(316\) 6.57621 + 13.9232i 0.369940 + 0.783241i
\(317\) −23.5962 6.32257i −1.32529 0.355111i −0.474335 0.880345i \(-0.657311\pi\)
−0.850958 + 0.525234i \(0.823978\pi\)
\(318\) 20.0000 10.4741i 1.12155 0.587356i
\(319\) −0.286463 + 0.496169i −0.0160389 + 0.0277801i
\(320\) −3.86950 + 6.93700i −0.216312 + 0.387790i
\(321\) −7.58695 −0.423462
\(322\) 0 0
\(323\) 2.56271 2.56271i 0.142593 0.142593i
\(324\) 12.6204 18.2141i 0.701133 1.01190i
\(325\) 11.5324 3.09010i 0.639703 0.171408i
\(326\) −3.48707 + 11.1553i −0.193131 + 0.617836i
\(327\) 17.5396 10.1265i 0.969943 0.559997i
\(328\) 6.74218 + 0.836979i 0.372274 + 0.0462144i
\(329\) 0 0
\(330\) −1.21413 5.41344i −0.0668357 0.298000i
\(331\) 1.89039 7.05503i 0.103905 0.387780i −0.894313 0.447441i \(-0.852335\pi\)
0.998219 + 0.0596615i \(0.0190021\pi\)
\(332\) −0.914874 + 0.775384i −0.0502102 + 0.0425547i
\(333\) −2.79813 10.4428i −0.153337 0.572260i
\(334\) 12.6135 + 0.519588i 0.690182 + 0.0284306i
\(335\) −10.3274 −0.564245
\(336\) 0 0
\(337\) −9.53985 −0.519669 −0.259834 0.965653i \(-0.583668\pi\)
−0.259834 + 0.965653i \(0.583668\pi\)
\(338\) 5.86908 + 0.241765i 0.319236 + 0.0131503i
\(339\) 2.65528 + 9.90965i 0.144215 + 0.538218i
\(340\) −7.28980 8.60122i −0.395345 0.466467i
\(341\) 3.99283 14.9015i 0.216224 0.806959i
\(342\) −0.214780 0.957639i −0.0116140 0.0517832i
\(343\) 0 0
\(344\) −11.5355 + 8.98769i −0.621950 + 0.484584i
\(345\) 11.8973 6.86890i 0.640528 0.369809i
\(346\) 2.29936 7.35578i 0.123614 0.395449i
\(347\) −8.82567 + 2.36483i −0.473787 + 0.126951i −0.487808 0.872951i \(-0.662203\pi\)
0.0140212 + 0.999902i \(0.495537\pi\)
\(348\) 0.974317 + 0.675094i 0.0522289 + 0.0361889i
\(349\) −24.4862 + 24.4862i −1.31072 + 1.31072i −0.389831 + 0.920887i \(0.627467\pi\)
−0.920887 + 0.389831i \(0.872533\pi\)
\(350\) 0 0
\(351\) 11.5019 0.613925
\(352\) −0.618236 11.0380i −0.0329521 0.588328i
\(353\) −13.0352 + 22.5776i −0.693793 + 1.20168i 0.276793 + 0.960930i \(0.410728\pi\)
−0.970586 + 0.240755i \(0.922605\pi\)
\(354\) 35.2789 18.4756i 1.87505 0.981969i
\(355\) 11.1201 + 2.97963i 0.590194 + 0.158142i
\(356\) 31.8080 15.0236i 1.68582 0.796247i
\(357\) 0 0
\(358\) 13.4638 3.01967i 0.711584 0.159595i
\(359\) 3.01740 1.74210i 0.159252 0.0919443i −0.418256 0.908329i \(-0.637358\pi\)
0.577508 + 0.816385i \(0.304025\pi\)
\(360\) −3.02406 + 0.420885i −0.159382 + 0.0221826i
\(361\) −16.1016 9.29627i −0.847453 0.489277i
\(362\) 12.4020 11.4207i 0.651837 0.600259i
\(363\) −10.2650 10.2650i −0.538773 0.538773i
\(364\) 0 0
\(365\) −0.251944 + 0.251944i −0.0131873 + 0.0131873i
\(366\) −10.6971 0.440643i −0.559144 0.0230328i
\(367\) 12.2280 21.1796i 0.638298 1.10556i −0.347508 0.937677i \(-0.612972\pi\)
0.985806 0.167888i \(-0.0536946\pi\)
\(368\) 25.6308 9.61592i 1.33610 0.501264i
\(369\) 1.30572 + 2.26157i 0.0679730 + 0.117733i
\(370\) 7.47349 11.7951i 0.388528 0.613196i
\(371\) 0 0
\(372\) −30.0462 10.7686i −1.55782 0.558324i
\(373\) 9.51200 35.4993i 0.492513 1.83808i −0.0510246 0.998697i \(-0.516249\pi\)
0.543537 0.839385i \(-0.317085\pi\)
\(374\) 14.9775 + 4.68185i 0.774469 + 0.242093i
\(375\) 15.6702 + 9.04719i 0.809206 + 0.467195i
\(376\) −0.753343 + 0.318588i −0.0388507 + 0.0164299i
\(377\) 0.871940i 0.0449072i
\(378\) 0 0
\(379\) 18.5183 + 18.5183i 0.951222 + 0.951222i 0.998864 0.0476420i \(-0.0151707\pi\)
−0.0476420 + 0.998864i \(0.515171\pi\)
\(380\) 0.721933 1.04192i 0.0370344 0.0534492i
\(381\) −5.84524 21.8147i −0.299461 1.11760i
\(382\) 6.17690 3.23486i 0.316038 0.165510i
\(383\) −7.89785 13.6795i −0.403562 0.698989i 0.590591 0.806971i \(-0.298895\pi\)
−0.994153 + 0.107982i \(0.965561\pi\)
\(384\) −22.8647 0.603494i −1.16681 0.0307969i
\(385\) 0 0
\(386\) 26.1722 + 16.5830i 1.33213 + 0.844053i
\(387\) −5.42940 1.45480i −0.275992 0.0739519i
\(388\) 24.4524 + 2.01796i 1.24138 + 0.102446i
\(389\) −5.50707 + 1.47562i −0.279220 + 0.0748167i −0.395711 0.918375i \(-0.629502\pi\)
0.116492 + 0.993192i \(0.462835\pi\)
\(390\) −5.71961 6.21107i −0.289624 0.314510i
\(391\) 38.8572i 1.96509i
\(392\) 0 0
\(393\) 25.4903i 1.28582i
\(394\) 11.2105 10.3234i 0.564776 0.520087i
\(395\) −7.38395 + 1.97852i −0.371527 + 0.0995503i
\(396\) 3.24175 2.74748i 0.162904 0.138066i
\(397\) 0.971927 + 0.260427i 0.0487796 + 0.0130705i 0.283126 0.959083i \(-0.408628\pi\)
−0.234347 + 0.972153i \(0.575295\pi\)
\(398\) −2.70690 + 4.27216i −0.135684 + 0.214144i
\(399\) 0 0
\(400\) 12.4012 + 10.1993i 0.620058 + 0.509963i
\(401\) 8.70318 + 15.0744i 0.434616 + 0.752777i 0.997264 0.0739192i \(-0.0235507\pi\)
−0.562648 + 0.826697i \(0.690217\pi\)
\(402\) −13.7964 26.3439i −0.688100 1.31391i
\(403\) −6.07671 22.6786i −0.302703 1.12970i
\(404\) 2.38073 0.431893i 0.118446 0.0214875i
\(405\) 7.77886 + 7.77886i 0.386535 + 0.386535i
\(406\) 0 0
\(407\) 19.4341i 0.963313i
\(408\) 12.2022 30.0858i 0.604100 1.48947i
\(409\) −33.0605 19.0875i −1.63474 0.943815i −0.982605 0.185709i \(-0.940542\pi\)
−0.652131 0.758106i \(-0.726125\pi\)
\(410\) −1.00631 + 3.21924i −0.0496982 + 0.158987i
\(411\) 8.47837 31.6417i 0.418207 1.56077i
\(412\) −10.5700 + 4.99245i −0.520749 + 0.245960i
\(413\) 0 0
\(414\) 8.88843 + 5.63182i 0.436843 + 0.276789i
\(415\) −0.297687 0.515608i −0.0146129 0.0253102i
\(416\) −9.21424 14.0777i −0.451765 0.690218i
\(417\) 15.0127 26.0028i 0.735176 1.27336i
\(418\) −0.0726116 + 1.76272i −0.00355155 + 0.0862175i
\(419\) 27.0004 27.0004i 1.31905 1.31905i 0.404529 0.914525i \(-0.367435\pi\)
0.914525 0.404529i \(-0.132565\pi\)
\(420\) 0 0
\(421\) −19.1472 19.1472i −0.933175 0.933175i 0.0647277 0.997903i \(-0.479382\pi\)
−0.997903 + 0.0647277i \(0.979382\pi\)
\(422\) −9.94074 10.7949i −0.483908 0.525488i
\(423\) −0.272276 0.157199i −0.0132385 0.00764327i
\(424\) 3.07883 + 22.1214i 0.149521 + 1.07431i
\(425\) −19.7377 + 11.3956i −0.957419 + 0.552766i
\(426\) 7.25471 + 32.3466i 0.351492 + 1.56720i
\(427\) 0 0
\(428\) 2.53228 7.06551i 0.122402 0.341524i
\(429\) 11.3510 + 3.04150i 0.548033 + 0.146845i
\(430\) −3.36808 6.43128i −0.162423 0.310144i
\(431\) −0.628555 + 1.08869i −0.0302764 + 0.0524403i −0.880767 0.473551i \(-0.842972\pi\)
0.850490 + 0.525991i \(0.176305\pi\)
\(432\) 8.99674 + 12.5829i 0.432856 + 0.605396i
\(433\) 9.16885 0.440627 0.220313 0.975429i \(-0.429292\pi\)
0.220313 + 0.975429i \(0.429292\pi\)
\(434\) 0 0
\(435\) −0.416110 + 0.416110i −0.0199509 + 0.0199509i
\(436\) 3.57636 + 19.7141i 0.171277 + 0.944132i
\(437\) −4.21971 + 1.13067i −0.201856 + 0.0540871i
\(438\) −0.979251 0.306106i −0.0467904 0.0146263i
\(439\) −6.89864 + 3.98293i −0.329254 + 0.190095i −0.655510 0.755187i \(-0.727546\pi\)
0.326256 + 0.945282i \(0.394213\pi\)
\(440\) 5.44663 + 0.676148i 0.259658 + 0.0322341i
\(441\) 0 0
\(442\) 23.3032 5.22645i 1.10842 0.248597i
\(443\) 6.47610 24.1691i 0.307689 1.14831i −0.622918 0.782288i \(-0.714053\pi\)
0.930606 0.366022i \(-0.119281\pi\)
\(444\) 40.0716 + 3.30694i 1.90171 + 0.156941i
\(445\) 4.52000 + 16.8689i 0.214269 + 0.799661i
\(446\) −0.247980 + 6.01996i −0.0117422 + 0.285053i
\(447\) 20.1332 0.952267
\(448\) 0 0
\(449\) −8.33038 −0.393135 −0.196567 0.980490i \(-0.562979\pi\)
−0.196567 + 0.980490i \(0.562979\pi\)
\(450\) −0.254018 + 6.16656i −0.0119745 + 0.290694i
\(451\) −1.21498 4.53436i −0.0572111 0.213515i
\(452\) −10.1148 0.834734i −0.475761 0.0392626i
\(453\) 5.42349 20.2407i 0.254818 0.950993i
\(454\) −6.67647 + 1.49740i −0.313342 + 0.0702766i
\(455\) 0 0
\(456\) 3.62224 + 0.449667i 0.169627 + 0.0210576i
\(457\) 12.5338 7.23641i 0.586308 0.338505i −0.177328 0.984152i \(-0.556745\pi\)
0.763636 + 0.645647i \(0.223412\pi\)
\(458\) −26.4797 8.27734i −1.23731 0.386775i
\(459\) −21.2081 + 5.68270i −0.989910 + 0.265246i
\(460\) 2.42588 + 13.3722i 0.113107 + 0.623483i
\(461\) 4.23021 4.23021i 0.197020 0.197020i −0.601701 0.798721i \(-0.705510\pi\)
0.798721 + 0.601701i \(0.205510\pi\)
\(462\) 0 0
\(463\) −25.1987 −1.17108 −0.585542 0.810642i \(-0.699118\pi\)
−0.585542 + 0.810642i \(0.699118\pi\)
\(464\) −0.953892 + 0.682029i −0.0442833 + 0.0316624i
\(465\) 7.92280 13.7227i 0.367411 0.636374i
\(466\) 3.32344 + 6.34605i 0.153956 + 0.293975i
\(467\) 14.8411 + 3.97667i 0.686766 + 0.184018i 0.585295 0.810820i \(-0.300979\pi\)
0.101470 + 0.994839i \(0.467645\pi\)
\(468\) 2.18195 6.08802i 0.100860 0.281419i
\(469\) 0 0
\(470\) −0.0888655 0.396224i −0.00409906 0.0182765i
\(471\) −7.22338 + 4.17042i −0.332836 + 0.192163i
\(472\) 5.43087 + 39.0208i 0.249976 + 1.79608i
\(473\) 8.75047 + 5.05209i 0.402347 + 0.232295i
\(474\) −14.9112 16.1925i −0.684894 0.743744i
\(475\) −1.81183 1.81183i −0.0831326 0.0831326i
\(476\) 0 0
\(477\) −6.07046 + 6.07046i −0.277947 + 0.277947i
\(478\) −0.542770 + 13.1763i −0.0248257 + 0.602669i
\(479\) −10.4147 + 18.0387i −0.475859 + 0.824211i −0.999618 0.0276553i \(-0.991196\pi\)
0.523759 + 0.851867i \(0.324529\pi\)
\(480\) 2.32097 11.1155i 0.105937 0.507349i
\(481\) 14.7884 + 25.6143i 0.674294 + 1.16791i
\(482\) −30.7402 19.4773i −1.40018 0.887169i
\(483\) 0 0
\(484\) 12.9857 6.13339i 0.590257 0.278790i
\(485\) −3.15261 + 11.7657i −0.143152 + 0.534252i
\(486\) −4.55612 + 14.5753i −0.206670 + 0.661147i
\(487\) 0.192631 + 0.111216i 0.00872895 + 0.00503966i 0.504358 0.863495i \(-0.331729\pi\)
−0.495629 + 0.868534i \(0.665062\pi\)
\(488\) 3.98070 9.81480i 0.180198 0.444295i
\(489\) 16.7080i 0.755561i
\(490\) 0 0
\(491\) 18.1586 + 18.1586i 0.819486 + 0.819486i 0.986033 0.166547i \(-0.0532618\pi\)
−0.166547 + 0.986033i \(0.553262\pi\)
\(492\) −9.55624 + 1.73361i −0.430828 + 0.0781574i
\(493\) −0.430797 1.60776i −0.0194021 0.0724097i
\(494\) 1.24564 + 2.37853i 0.0560442 + 0.107015i
\(495\) 1.05482 + 1.82700i 0.0474105 + 0.0821173i
\(496\) 20.0569 24.3870i 0.900583 1.09501i
\(497\) 0 0
\(498\) 0.917575 1.44816i 0.0411175 0.0648938i
\(499\) −3.39149 0.908747i −0.151824 0.0406811i 0.182107 0.983279i \(-0.441708\pi\)
−0.333930 + 0.942598i \(0.608375\pi\)
\(500\) −13.6556 + 11.5736i −0.610697 + 0.517585i
\(501\) −17.4320 + 4.67088i −0.778802 + 0.208680i
\(502\) 5.36072 4.93654i 0.239261 0.220329i
\(503\) 7.65278i 0.341220i 0.985339 + 0.170610i \(0.0545739\pi\)
−0.985339 + 0.170610i \(0.945426\pi\)
\(504\) 0 0
\(505\) 1.20121i 0.0534532i
\(506\) −12.8132 13.9142i −0.569615 0.618560i
\(507\) −8.11109 + 2.17336i −0.360226 + 0.0965223i
\(508\) 22.2664 + 1.83755i 0.987912 + 0.0815282i
\(509\) −30.8730 8.27238i −1.36842 0.366667i −0.501519 0.865147i \(-0.667225\pi\)
−0.866901 + 0.498480i \(0.833892\pi\)
\(510\) 13.6150 + 8.62661i 0.602881 + 0.381993i
\(511\) 0 0
\(512\) 8.19353 21.0918i 0.362106 0.932137i
\(513\) −1.23423 2.13775i −0.0544925 0.0943838i
\(514\) −4.70490 + 2.46397i −0.207524 + 0.108681i
\(515\) −1.50203 5.60566i −0.0661874 0.247015i
\(516\) 11.9060 17.1831i 0.524133 0.756445i
\(517\) 0.399629 + 0.399629i 0.0175757 + 0.0175757i
\(518\) 0 0
\(519\) 11.0172i 0.483600i
\(520\) 7.69321 3.25345i 0.337370 0.142673i
\(521\) 2.39816 + 1.38458i 0.105065 + 0.0606595i 0.551612 0.834101i \(-0.314013\pi\)
−0.446547 + 0.894760i \(0.647346\pi\)
\(522\) −0.430207 0.134479i −0.0188296 0.00588600i
\(523\) −5.72293 + 21.3583i −0.250246 + 0.933932i 0.720427 + 0.693530i \(0.243946\pi\)
−0.970674 + 0.240401i \(0.922721\pi\)
\(524\) 23.7384 + 8.50786i 1.03702 + 0.371668i
\(525\) 0 0
\(526\) 14.2684 22.5191i 0.622131 0.981879i
\(527\) 22.4095 + 38.8144i 0.976173 + 1.69078i
\(528\) 5.55138 + 14.7970i 0.241593 + 0.643955i
\(529\) 11.9189 20.6441i 0.518211 0.897568i
\(530\) −11.0787 0.456362i −0.481226 0.0198231i
\(531\) −10.7079 + 10.7079i −0.464685 + 0.464685i
\(532\) 0 0
\(533\) −5.05178 5.05178i −0.218817 0.218817i
\(534\) −36.9922 + 34.0651i −1.60081 + 1.47414i
\(535\) 3.22696 + 1.86308i 0.139513 + 0.0805481i
\(536\) 29.1381 4.05541i 1.25857 0.175167i
\(537\) −17.0826 + 9.86262i −0.737167 + 0.425603i
\(538\) 23.6640 5.30737i 1.02023 0.228817i
\(539\) 0 0
\(540\) −6.94375 + 3.27967i −0.298811 + 0.141135i
\(541\) −32.2635 8.64497i −1.38711 0.371676i −0.513414 0.858141i \(-0.671619\pi\)
−0.873700 + 0.486465i \(0.838286\pi\)
\(542\) 6.65512 3.48530i 0.285862 0.149706i
\(543\) −12.0507 + 20.8724i −0.517145 + 0.895721i
\(544\) 23.9453 + 21.4053i 1.02665 + 0.917743i
\(545\) −9.94683 −0.426075
\(546\) 0 0
\(547\) 3.45137 3.45137i 0.147570 0.147570i −0.629462 0.777032i \(-0.716724\pi\)
0.777032 + 0.629462i \(0.216724\pi\)
\(548\) 26.6372 + 18.4567i 1.13789 + 0.788430i
\(549\) 3.93236 1.05367i 0.167829 0.0449696i
\(550\) 3.31007 10.5891i 0.141142 0.451521i
\(551\) 0.162059 0.0935651i 0.00690396 0.00398601i
\(552\) −30.8702 + 24.0521i −1.31392 + 1.02373i
\(553\) 0 0
\(554\) −4.70464 20.9765i −0.199881 0.891208i
\(555\) −5.16636 + 19.2811i −0.219300 + 0.818437i
\(556\) 19.2049 + 22.6598i 0.814469 + 0.960990i
\(557\) −5.70879 21.3055i −0.241889 0.902742i −0.974922 0.222549i \(-0.928562\pi\)
0.733032 0.680194i \(-0.238104\pi\)
\(558\) 12.1266 + 0.499530i 0.513360 + 0.0211468i
\(559\) 15.3776 0.650403
\(560\) 0 0
\(561\) −22.4327 −0.947109
\(562\) −4.46210 0.183807i −0.188222 0.00775342i
\(563\) 7.14593 + 26.6690i 0.301165 + 1.12396i 0.936196 + 0.351477i \(0.114321\pi\)
−0.635031 + 0.772486i \(0.719013\pi\)
\(564\) 0.892006 0.756002i 0.0375602 0.0318334i
\(565\) 1.30408 4.86691i 0.0548633 0.204752i
\(566\) 4.36902 + 19.4801i 0.183644 + 0.818811i
\(567\) 0 0
\(568\) −32.5448 4.04014i −1.36555 0.169521i
\(569\) −30.3657 + 17.5317i −1.27300 + 0.734965i −0.975551 0.219773i \(-0.929468\pi\)
−0.297446 + 0.954739i \(0.596135\pi\)
\(570\) −0.540641 + 1.72954i −0.0226450 + 0.0724424i
\(571\) 1.24755 0.334280i 0.0522083 0.0139892i −0.232620 0.972568i \(-0.574730\pi\)
0.284829 + 0.958578i \(0.408063\pi\)
\(572\) −6.62108 + 9.55575i −0.276841 + 0.399546i
\(573\) −7.04827 + 7.04827i −0.294446 + 0.294446i
\(574\) 0 0
\(575\) 27.4720 1.14566
\(576\) 8.36693 2.37501i 0.348622 0.0989586i
\(577\) 7.66470 13.2757i 0.319086 0.552673i −0.661212 0.750199i \(-0.729958\pi\)
0.980298 + 0.197527i \(0.0632909\pi\)
\(578\) −19.0883 + 9.99658i −0.793968 + 0.415803i
\(579\) −42.7830 11.4637i −1.77800 0.476414i
\(580\) −0.248627 0.526395i −0.0103237 0.0218574i
\(581\) 0 0
\(582\) −34.2244 + 7.67588i −1.41865 + 0.318176i
\(583\) 13.3647 7.71612i 0.553510 0.319569i
\(584\) 0.611911 0.809780i 0.0253211 0.0335090i
\(585\) 2.78051 + 1.60533i 0.114960 + 0.0663722i
\(586\) 16.0856 14.8128i 0.664491 0.611913i
\(587\) 27.8270 + 27.8270i 1.14854 + 1.14854i 0.986840 + 0.161702i \(0.0516982\pi\)
0.161702 + 0.986840i \(0.448302\pi\)
\(588\) 0 0
\(589\) −3.56299 + 3.56299i −0.146810 + 0.146810i
\(590\) −19.5421 0.804997i −0.804536 0.0331412i
\(591\) −10.8929 + 18.8670i −0.448074 + 0.776087i
\(592\) −16.4543 + 36.2138i −0.676267 + 1.48838i
\(593\) 8.89810 + 15.4120i 0.365401 + 0.632894i 0.988840 0.148978i \(-0.0475984\pi\)
−0.623439 + 0.781872i \(0.714265\pi\)
\(594\) 5.72043 9.02828i 0.234712 0.370435i
\(595\) 0 0
\(596\) −6.71981 + 18.7495i −0.275254 + 0.768008i
\(597\) 1.87125 6.98361i 0.0765853 0.285820i
\(598\) −27.4759 8.58875i −1.12357 0.351220i
\(599\) 16.6221 + 9.59676i 0.679159 + 0.392113i 0.799538 0.600615i \(-0.205078\pi\)
−0.120379 + 0.992728i \(0.538411\pi\)
\(600\) −21.2707 8.62697i −0.868371 0.352195i
\(601\) 26.9530i 1.09944i 0.835351 + 0.549718i \(0.185265\pi\)
−0.835351 + 0.549718i \(0.814735\pi\)
\(602\) 0 0
\(603\) 7.99597 + 7.99597i 0.325621 + 0.325621i
\(604\) 17.0395 + 11.8065i 0.693325 + 0.480398i
\(605\) 1.84530 + 6.88674i 0.0750219 + 0.279986i
\(606\) −3.06415 + 1.60470i −0.124472 + 0.0651865i
\(607\) −14.7276 25.5089i −0.597773 1.03537i −0.993149 0.116854i \(-0.962719\pi\)
0.395376 0.918519i \(-0.370614\pi\)
\(608\) −1.62775 + 3.22320i −0.0660140 + 0.130718i
\(609\) 0 0
\(610\) 4.44157 + 2.81424i 0.179834 + 0.113945i
\(611\) 0.830813 + 0.222616i 0.0336111 + 0.00900607i
\(612\) −1.01537 + 12.3036i −0.0410437 + 0.497344i
\(613\) 24.1091 6.46001i 0.973756 0.260917i 0.263343 0.964702i \(-0.415175\pi\)
0.710413 + 0.703785i \(0.248508\pi\)
\(614\) −20.0153 21.7351i −0.807752 0.877159i
\(615\) 4.82165i 0.194428i
\(616\) 0 0
\(617\) 10.8407i 0.436431i 0.975901 + 0.218216i \(0.0700236\pi\)
−0.975901 + 0.218216i \(0.929976\pi\)
\(618\) 12.2928 11.3201i 0.494489 0.455362i
\(619\) 19.3962 5.19721i 0.779601 0.208893i 0.152992 0.988227i \(-0.451109\pi\)
0.626609 + 0.779334i \(0.284442\pi\)
\(620\) 10.1352 + 11.9585i 0.407038 + 0.480264i
\(621\) 25.5639 + 6.84982i 1.02584 + 0.274874i
\(622\) −6.61232 + 10.4359i −0.265130 + 0.418442i
\(623\) 0 0
\(624\) 18.5766 + 15.2782i 0.743657 + 0.611616i
\(625\) 5.59202 + 9.68566i 0.223681 + 0.387426i
\(626\) −2.70171 5.15887i −0.107982 0.206190i
\(627\) −0.652747 2.43609i −0.0260682 0.0972879i
\(628\) −1.47286 8.11889i −0.0587736 0.323979i
\(629\) −39.9233 39.9233i −1.59185 1.59185i
\(630\) 0 0
\(631\) 5.71697i 0.227589i −0.993504 0.113794i \(-0.963699\pi\)
0.993504 0.113794i \(-0.0363005\pi\)
\(632\) 20.0565 8.48186i 0.797803 0.337390i
\(633\) 18.1676 + 10.4891i 0.722099 + 0.416904i
\(634\) −10.3073 + 32.9737i −0.409357 + 1.30955i
\(635\) −2.87076 + 10.7138i −0.113923 + 0.425166i
\(636\) −13.6359 28.8700i −0.540698 1.14477i
\(637\) 0 0
\(638\) 0.684421 + 0.433657i 0.0270965 + 0.0171687i
\(639\) −6.30277 10.9167i −0.249334 0.431859i
\(640\) 9.57685 + 5.87144i 0.378558 + 0.232089i
\(641\) −14.8475 + 25.7166i −0.586441 + 1.01575i 0.408253 + 0.912869i \(0.366138\pi\)
−0.994694 + 0.102877i \(0.967195\pi\)
\(642\) −0.441607 + 10.7205i −0.0174289 + 0.423103i
\(643\) −3.53512 + 3.53512i −0.139412 + 0.139412i −0.773368 0.633957i \(-0.781430\pi\)
0.633957 + 0.773368i \(0.281430\pi\)
\(644\) 0 0
\(645\) 7.33854 + 7.33854i 0.288955 + 0.288955i
\(646\) −3.47198 3.77031i −0.136603 0.148341i
\(647\) 12.7788 + 7.37782i 0.502385 + 0.290052i 0.729698 0.683770i \(-0.239661\pi\)
−0.227313 + 0.973822i \(0.572994\pi\)
\(648\) −25.0023 18.8930i −0.982182 0.742186i
\(649\) 23.5746 13.6108i 0.925384 0.534270i
\(650\) −3.69510 16.4753i −0.144934 0.646216i
\(651\) 0 0
\(652\) 15.5597 + 5.57659i 0.609364 + 0.218396i
\(653\) 9.56710 + 2.56350i 0.374390 + 0.100317i 0.441107 0.897455i \(-0.354586\pi\)
−0.0667174 + 0.997772i \(0.521253\pi\)
\(654\) −13.2880 25.3732i −0.519601 0.992169i
\(655\) −6.25952 + 10.8418i −0.244580 + 0.423624i
\(656\) 1.57510 9.47808i 0.0614973 0.370057i
\(657\) 0.390135 0.0152206
\(658\) 0 0
\(659\) 5.68205 5.68205i 0.221341 0.221341i −0.587722 0.809063i \(-0.699975\pi\)
0.809063 + 0.587722i \(0.199975\pi\)
\(660\) −7.71995 + 1.40049i −0.300498 + 0.0545140i
\(661\) −9.26542 + 2.48266i −0.360383 + 0.0965643i −0.434467 0.900688i \(-0.643063\pi\)
0.0740843 + 0.997252i \(0.476397\pi\)
\(662\) −9.85883 3.08180i −0.383174 0.119777i
\(663\) −29.5665 + 17.0702i −1.14827 + 0.662952i
\(664\) 1.04238 + 1.33786i 0.0404521 + 0.0519192i
\(665\) 0 0
\(666\) −14.9187 + 3.34597i −0.578086 + 0.129654i
\(667\) −0.519275 + 1.93796i −0.0201064 + 0.0750381i
\(668\) 1.46837 17.7929i 0.0568130 0.688427i
\(669\) −2.22923 8.31961i −0.0861871 0.321655i
\(670\) −0.601117 + 14.5927i −0.0232232 + 0.563767i
\(671\) −7.31815 −0.282514
\(672\) 0 0
\(673\) 3.24280 0.125001 0.0625004 0.998045i \(-0.480093\pi\)
0.0625004 + 0.998045i \(0.480093\pi\)
\(674\) −0.555278 + 13.4800i −0.0213885 + 0.519228i
\(675\) 4.01767 + 14.9941i 0.154640 + 0.577125i
\(676\) 0.683234 8.27903i 0.0262782 0.318424i
\(677\) −8.67832 + 32.3879i −0.333535 + 1.24477i 0.571914 + 0.820314i \(0.306201\pi\)
−0.905449 + 0.424455i \(0.860466\pi\)
\(678\) 14.1570 3.17515i 0.543698 0.121941i
\(679\) 0 0
\(680\) −12.5780 + 9.79995i −0.482343 + 0.375811i
\(681\) 8.47094 4.89070i 0.324607 0.187412i
\(682\) −20.8236 6.50929i −0.797376 0.249254i
\(683\) −17.9673 + 4.81432i −0.687499 + 0.184215i −0.585624 0.810583i \(-0.699151\pi\)
−0.101874 + 0.994797i \(0.532484\pi\)
\(684\) −1.36566 + 0.247747i −0.0522173 + 0.00947284i
\(685\) −11.3762 + 11.3762i −0.434662 + 0.434662i
\(686\) 0 0
\(687\) 39.6602 1.51313
\(688\) 12.0283 + 16.8229i 0.458575 + 0.641367i
\(689\) 11.7432 20.3398i 0.447380 0.774886i
\(690\) −9.01337 17.2109i −0.343133 0.655206i
\(691\) 20.9303 + 5.60826i 0.796227 + 0.213348i 0.633927 0.773393i \(-0.281442\pi\)
0.162300 + 0.986741i \(0.448109\pi\)
\(692\) −10.2600 3.67718i −0.390026 0.139786i
\(693\) 0 0
\(694\) 2.82783 + 12.6085i 0.107343 + 0.478611i
\(695\) −12.7707 + 7.37317i −0.484421 + 0.279680i
\(696\) 1.01063 1.33743i 0.0383078 0.0506952i
\(697\) 11.8108 + 6.81898i 0.447367 + 0.258287i
\(698\) 33.1742 + 36.0247i 1.25566 + 1.36355i
\(699\) −7.24128 7.24128i −0.273891 0.273891i
\(700\) 0 0
\(701\) 4.96023 4.96023i 0.187345 0.187345i −0.607202 0.794547i \(-0.707708\pi\)
0.794547 + 0.607202i \(0.207708\pi\)
\(702\) 0.669481 16.2523i 0.0252679 0.613405i
\(703\) 3.17380 5.49718i 0.119702 0.207330i
\(704\) −15.6329 + 0.231096i −0.589186 + 0.00870976i
\(705\) 0.290246 + 0.502720i 0.0109313 + 0.0189335i
\(706\) 31.1438 + 19.7331i 1.17211 + 0.742664i
\(707\) 0 0
\(708\) −24.0529 50.9250i −0.903963 1.91388i
\(709\) −3.74523 + 13.9774i −0.140655 + 0.524932i 0.859255 + 0.511547i \(0.170927\pi\)
−0.999910 + 0.0133851i \(0.995739\pi\)
\(710\) 4.85752 15.5395i 0.182299 0.583185i
\(711\) 7.24889 + 4.18515i 0.271855 + 0.156955i
\(712\) −19.3771 45.8196i −0.726187 1.71716i
\(713\) 54.0240i 2.02321i
\(714\) 0 0
\(715\) −4.08105 4.08105i −0.152623 0.152623i
\(716\) −3.48317 19.2003i −0.130172 0.717550i
\(717\) −4.87927 18.2097i −0.182220 0.680053i
\(718\) −2.28598 4.36503i −0.0853119 0.162902i
\(719\) 16.5646 + 28.6908i 0.617756 + 1.06998i 0.989894 + 0.141808i \(0.0452914\pi\)
−0.372138 + 0.928177i \(0.621375\pi\)
\(720\) 0.418698 + 4.29753i 0.0156039 + 0.160160i
\(721\) 0 0
\(722\) −14.0730 + 22.2107i −0.523742 + 0.826598i
\(723\) 50.2502 + 13.4645i 1.86883 + 0.500751i
\(724\) −15.4158 18.1890i −0.572922 0.675990i
\(725\) −1.13668 + 0.304573i −0.0422154 + 0.0113116i
\(726\) −15.1021 + 13.9071i −0.560492 + 0.516142i
\(727\) 23.5496i 0.873406i −0.899606 0.436703i \(-0.856146\pi\)
0.899606 0.436703i \(-0.143854\pi\)
\(728\) 0 0
\(729\) 11.4085i 0.422538i
\(730\) 0.341336 + 0.370665i 0.0126334 + 0.0137189i
\(731\) −28.3545 + 7.59756i −1.04873 + 0.281006i
\(732\) −1.24527 + 15.0895i −0.0460265 + 0.557723i
\(733\) 1.72774 + 0.462947i 0.0638156 + 0.0170993i 0.290586 0.956849i \(-0.406150\pi\)
−0.226770 + 0.973948i \(0.572817\pi\)
\(734\) −29.2153 18.5112i −1.07836 0.683260i
\(735\) 0 0
\(736\) −12.0956 36.7764i −0.445849 1.35560i
\(737\) −10.1636 17.6039i −0.374382 0.648448i
\(738\) 3.27163 1.71336i 0.120431 0.0630698i
\(739\) 6.06175 + 22.6228i 0.222985 + 0.832192i 0.983202 + 0.182522i \(0.0584261\pi\)
−0.760217 + 0.649670i \(0.774907\pi\)
\(740\) −16.2316 11.2467i −0.596685 0.413437i
\(741\) −2.71407 2.71407i −0.0997039 0.0997039i
\(742\) 0 0
\(743\) 13.9219i 0.510747i −0.966843 0.255373i \(-0.917802\pi\)
0.966843 0.255373i \(-0.0821984\pi\)
\(744\) −16.9650 + 41.8290i −0.621968 + 1.53352i
\(745\) −8.56324 4.94399i −0.313733 0.181134i
\(746\) −49.6073 15.5069i −1.81625 0.567747i
\(747\) −0.168726 + 0.629693i −0.00617336 + 0.0230393i
\(748\) 7.48732 20.8909i 0.273763 0.763848i
\(749\) 0 0
\(750\) 13.6959 21.6156i 0.500104 0.789291i
\(751\) 4.53854 + 7.86098i 0.165614 + 0.286851i 0.936873 0.349670i \(-0.113706\pi\)
−0.771259 + 0.636521i \(0.780373\pi\)
\(752\) 0.406321 + 1.08303i 0.0148170 + 0.0394940i
\(753\) −5.20885 + 9.02200i −0.189821 + 0.328780i
\(754\) 1.23207 + 0.0507523i 0.0448692 + 0.00184829i
\(755\) −7.27718 + 7.27718i −0.264844 + 0.264844i
\(756\) 0 0
\(757\) −1.14043 1.14043i −0.0414496 0.0414496i 0.686078 0.727528i \(-0.259331\pi\)
−0.727528 + 0.686078i \(0.759331\pi\)
\(758\) 27.2446 25.0888i 0.989567 0.911266i
\(759\) 23.4173 + 13.5200i 0.849994 + 0.490744i
\(760\) −1.43022 1.08075i −0.0518796 0.0392029i
\(761\) −7.60476 + 4.39061i −0.275672 + 0.159159i −0.631463 0.775406i \(-0.717545\pi\)
0.355790 + 0.934566i \(0.384212\pi\)
\(762\) −31.1648 + 6.98966i −1.12898 + 0.253209i
\(763\) 0 0
\(764\) −4.21137 8.91635i −0.152362 0.322582i
\(765\) −5.92008 1.58628i −0.214041 0.0573521i
\(766\) −19.7890 + 10.3636i −0.715007 + 0.374451i
\(767\) 20.7143 35.8783i 0.747951 1.29549i
\(768\) −2.18361 + 32.2731i −0.0787944 + 1.16455i
\(769\) −29.8204 −1.07535 −0.537676 0.843152i \(-0.680697\pi\)
−0.537676 + 0.843152i \(0.680697\pi\)
\(770\) 0 0
\(771\) 5.36862 5.36862i 0.193346 0.193346i
\(772\) 24.9554 36.0164i 0.898165 1.29626i
\(773\) 44.5476 11.9365i 1.60227 0.429326i 0.656540 0.754291i \(-0.272019\pi\)
0.945726 + 0.324965i \(0.105352\pi\)
\(774\) −2.37169 + 7.58715i −0.0852485 + 0.272715i
\(775\) 27.4418 15.8435i 0.985738 0.569116i
\(776\) 4.27469 34.4342i 0.153452 1.23612i
\(777\) 0 0
\(778\) 1.76452 + 7.86746i 0.0632611 + 0.282062i
\(779\) −0.396838 + 1.48102i −0.0142182 + 0.0530630i
\(780\) −9.10925 + 7.72037i −0.326163 + 0.276434i
\(781\) 5.86476 + 21.8876i 0.209858 + 0.783199i
\(782\) 54.9057 + 2.26173i 1.96343 + 0.0808792i
\(783\) −1.13367 −0.0405142
\(784\) 0 0
\(785\) 4.09643 0.146208
\(786\) −36.0182 1.48370i −1.28473 0.0529217i
\(787\) −6.78154 25.3091i −0.241736 0.902170i −0.974996 0.222222i \(-0.928669\pi\)
0.733260 0.679948i \(-0.237998\pi\)
\(788\) −13.9347 16.4415i −0.496401 0.585703i
\(789\) −9.86360 + 36.8115i −0.351153 + 1.31052i
\(790\) 2.36589 + 10.5488i 0.0841746 + 0.375309i
\(791\) 0 0
\(792\) −3.69354 4.74056i −0.131244 0.168448i
\(793\) −9.64539 + 5.56877i −0.342518 + 0.197753i
\(794\) 0.424560 1.35819i 0.0150671 0.0482003i
\(795\) 15.3107 4.10250i 0.543016 0.145501i
\(796\) 5.87908 + 4.07355i 0.208378 + 0.144383i
\(797\) 16.7419 16.7419i 0.593028 0.593028i −0.345420 0.938448i \(-0.612264\pi\)
0.938448 + 0.345420i \(0.112264\pi\)
\(798\) 0 0
\(799\) −1.64191 −0.0580866
\(800\) 15.1335 16.9294i 0.535051 0.598543i
\(801\) 9.56111 16.5603i 0.337825 0.585130i
\(802\) 21.8069 11.4203i 0.770027 0.403265i
\(803\) −0.677409 0.181511i −0.0239053 0.00640540i
\(804\) −38.0274 + 17.9611i −1.34112 + 0.633439i
\(805\) 0 0
\(806\) −32.3989 + 7.26645i −1.14120 + 0.255950i
\(807\) −30.0243 + 17.3345i −1.05690 + 0.610204i
\(808\) −0.471698 3.38915i −0.0165943 0.119230i
\(809\) −30.7720 17.7662i −1.08189 0.624628i −0.150482 0.988613i \(-0.548083\pi\)
−0.931405 + 0.363985i \(0.881416\pi\)
\(810\) 11.4444 10.5389i 0.402116 0.370298i
\(811\) −29.5602 29.5602i −1.03800 1.03800i −0.999249 0.0387507i \(-0.987662\pi\)
−0.0387507 0.999249i \(-0.512338\pi\)
\(812\) 0 0
\(813\) −7.59395 + 7.59395i −0.266331 + 0.266331i
\(814\) 27.4607 + 1.13119i 0.962497 + 0.0396480i
\(815\) −4.10288 + 7.10640i −0.143718 + 0.248926i
\(816\) −41.8014 18.9931i −1.46334 0.664892i
\(817\) −1.65012 2.85809i −0.0577304 0.0999920i
\(818\) −28.8952 + 45.6040i −1.01030 + 1.59451i
\(819\) 0 0
\(820\) 4.49027 + 1.60931i 0.156807 + 0.0561996i
\(821\) 2.04620 7.63653i 0.0714129 0.266517i −0.920983 0.389602i \(-0.872612\pi\)
0.992396 + 0.123086i \(0.0392791\pi\)
\(822\) −44.2167 13.8218i −1.54224 0.482091i
\(823\) −43.2107 24.9477i −1.50623 0.869623i −0.999974 0.00724096i \(-0.997695\pi\)
−0.506258 0.862382i \(-0.668972\pi\)
\(824\) 6.43916 + 15.2262i 0.224319 + 0.530431i
\(825\) 15.8599i 0.552171i
\(826\) 0 0
\(827\) −8.11672 8.11672i −0.282246 0.282246i 0.551758 0.834004i \(-0.313957\pi\)
−0.834004 + 0.551758i \(0.813957\pi\)
\(828\) 8.47521 12.2317i 0.294534 0.425080i
\(829\) 1.84091 + 6.87035i 0.0639373 + 0.238617i 0.990498 0.137528i \(-0.0439159\pi\)
−0.926561 + 0.376146i \(0.877249\pi\)
\(830\) −0.745890 + 0.390624i −0.0258902 + 0.0135588i
\(831\) 15.3659 + 26.6145i 0.533037 + 0.923248i
\(832\) −20.4284 + 12.2005i −0.708227 + 0.422975i
\(833\) 0 0
\(834\) −35.8685 22.7267i −1.24202 0.786962i
\(835\) 8.56133 + 2.29400i 0.296277 + 0.0793872i
\(836\) 2.48652 + 0.205202i 0.0859982 + 0.00709708i
\(837\) 29.4861 7.90079i 1.01919 0.273091i
\(838\) −36.5803 39.7235i −1.26365 1.37223i
\(839\) 3.57060i 0.123271i 0.998099 + 0.0616354i \(0.0196316\pi\)
−0.998099 + 0.0616354i \(0.980368\pi\)
\(840\) 0 0
\(841\) 28.9141i 0.997036i
\(842\) −28.1697 + 25.9407i −0.970792 + 0.893977i
\(843\) 6.16664 1.65235i 0.212390 0.0569098i
\(844\) −15.8320 + 13.4181i −0.544959 + 0.461870i
\(845\) 3.98359 + 1.06740i 0.137040 + 0.0367197i
\(846\) −0.237973 + 0.375581i −0.00818167 + 0.0129127i
\(847\) 0 0
\(848\) 31.4370 3.06283i 1.07955 0.105178i
\(849\) −14.2697 24.7159i −0.489736 0.848248i
\(850\) 14.9532 + 28.5530i 0.512892 + 0.979358i
\(851\) 17.6142 + 65.7370i 0.603806 + 2.25344i
\(852\) 46.1285 8.36825i 1.58034 0.286691i
\(853\) −13.8958 13.8958i −0.475784 0.475784i 0.427996 0.903780i \(-0.359220\pi\)
−0.903780 + 0.427996i \(0.859220\pi\)
\(854\) 0 0
\(855\) 0.689051i 0.0235650i
\(856\) −9.83628 3.98941i −0.336197 0.136355i
\(857\) 34.8241 + 20.1057i 1.18957 + 0.686798i 0.958209 0.286070i \(-0.0923490\pi\)
0.231360 + 0.972868i \(0.425682\pi\)
\(858\) 4.95839 15.8622i 0.169277 0.541525i
\(859\) −6.71022 + 25.0429i −0.228950 + 0.854452i 0.751834 + 0.659353i \(0.229170\pi\)
−0.980784 + 0.195099i \(0.937497\pi\)
\(860\) −9.28354 + 4.38480i −0.316566 + 0.149521i
\(861\) 0 0
\(862\) 1.50175 + 0.951526i 0.0511497 + 0.0324091i
\(863\) −8.22908 14.2532i −0.280121 0.485184i 0.691293 0.722574i \(-0.257041\pi\)
−0.971414 + 0.237390i \(0.923708\pi\)
\(864\) 18.3035 11.9801i 0.622698 0.407572i
\(865\) 2.70543 4.68593i 0.0919872 0.159327i
\(866\) 0.533684 12.9557i 0.0181353 0.440253i
\(867\) 21.7811 21.7811i 0.739724 0.739724i
\(868\) 0 0
\(869\) −10.6394 10.6394i −0.360918 0.360918i
\(870\) 0.563749 + 0.612189i 0.0191129 + 0.0207552i
\(871\) −26.7915 15.4681i −0.907795 0.524116i
\(872\) 28.0644 3.90598i 0.950381 0.132273i
\(873\) 11.5505 6.66868i 0.390925 0.225700i
\(874\) 1.35204 + 6.02832i 0.0457333 + 0.203911i
\(875\) 0 0
\(876\) −0.489531 + 1.36588i −0.0165397 + 0.0461488i
\(877\) −22.0521 5.90884i −0.744646 0.199527i −0.133504 0.991048i \(-0.542623\pi\)
−0.611142 + 0.791521i \(0.709290\pi\)
\(878\) 5.22640 + 9.97971i 0.176382 + 0.336799i
\(879\) −15.6299 + 27.0718i −0.527185 + 0.913111i
\(880\) 1.27243 7.65681i 0.0428938 0.258111i
\(881\) −5.29761 −0.178481 −0.0892405 0.996010i \(-0.528444\pi\)
−0.0892405 + 0.996010i \(0.528444\pi\)
\(882\) 0 0
\(883\) −30.7426 + 30.7426i −1.03457 + 1.03457i −0.0351900 + 0.999381i \(0.511204\pi\)
−0.999381 + 0.0351900i \(0.988796\pi\)
\(884\) −6.02866 33.2319i −0.202766 1.11771i
\(885\) 27.0073 7.23658i 0.907840 0.243255i
\(886\) −33.7744 10.5576i −1.13467 0.354690i
\(887\) 5.04199 2.91100i 0.169294 0.0977417i −0.412959 0.910750i \(-0.635505\pi\)
0.582253 + 0.813008i \(0.302171\pi\)
\(888\) 7.00518 56.4293i 0.235078 1.89364i
\(889\) 0 0
\(890\) 24.0991 5.40496i 0.807802 0.181175i
\(891\) −5.60423 + 20.9153i −0.187749 + 0.700688i
\(892\) 8.49186 + 0.700798i 0.284329 + 0.0234645i
\(893\) −0.0477763 0.178304i −0.00159877 0.00596671i
\(894\) 1.17188 28.4485i 0.0391934 0.951460i
\(895\) 9.68763 0.323822
\(896\) 0 0
\(897\) 41.1522 1.37403
\(898\) −0.484880 + 11.7710i −0.0161806 + 0.392802i
\(899\) 0.598947 + 2.23530i 0.0199760 + 0.0745514i
\(900\) 8.69866 + 0.717864i 0.289955 + 0.0239288i
\(901\) −11.6039 + 43.3062i −0.386581 + 1.44274i
\(902\) −6.47784 + 1.45285i −0.215688 + 0.0483748i
\(903\) 0 0
\(904\) −1.76824 + 14.2438i −0.0588107 + 0.473742i
\(905\) 10.2510 5.91844i 0.340756 0.196736i
\(906\) −28.2848 8.84161i −0.939700 0.293743i
\(907\) 20.3319 5.44791i 0.675108 0.180895i 0.0950536 0.995472i \(-0.469698\pi\)
0.580055 + 0.814577i \(0.303031\pi\)
\(908\) 1.72724 + 9.52111i 0.0573205 + 0.315969i
\(909\) 0.930037 0.930037i 0.0308474 0.0308474i
\(910\) 0 0
\(911\) −46.3231 −1.53475 −0.767376 0.641197i \(-0.778438\pi\)
−0.767376 + 0.641197i \(0.778438\pi\)
\(912\) 0.846223 5.09210i 0.0280212 0.168616i
\(913\) 0.585933 1.01487i 0.0193916 0.0335872i
\(914\) −9.49561 18.1317i −0.314087 0.599743i
\(915\) −7.26054 1.94546i −0.240026 0.0643148i
\(916\) −13.2373 + 36.9344i −0.437373 + 1.22035i
\(917\) 0 0
\(918\) 6.79529 + 30.2982i 0.224278 + 0.999988i
\(919\) −12.8775 + 7.43484i −0.424790 + 0.245253i −0.697125 0.716950i \(-0.745538\pi\)
0.272335 + 0.962203i \(0.412204\pi\)
\(920\) 19.0364 2.64946i 0.627610 0.0873501i
\(921\) 36.5799 + 21.1194i 1.20535 + 0.695908i
\(922\) −5.73112 6.22357i −0.188744 0.204962i
\(923\) 24.3852 + 24.3852i 0.802649 + 0.802649i
\(924\) 0 0
\(925\) −28.2258 + 28.2258i −0.928058 + 0.928058i
\(926\) −1.46672 + 35.6062i −0.0481995 + 1.17009i
\(927\) −3.17723 + 5.50313i −0.104354 + 0.180746i
\(928\) 0.908195 + 1.38756i 0.0298130 + 0.0455490i
\(929\) −25.8504 44.7742i −0.848124 1.46899i −0.882881 0.469598i \(-0.844399\pi\)
0.0347569 0.999396i \(-0.488934\pi\)
\(930\) −18.9292 11.9938i −0.620713 0.393291i
\(931\) 0 0
\(932\) 9.16052 4.32670i 0.300063 0.141726i
\(933\) 4.57104 17.0593i 0.149649 0.558498i
\(934\) 6.48294 20.7393i 0.212128 0.678610i
\(935\) 9.54129 + 5.50867i 0.312034 + 0.180153i
\(936\) −8.47546 3.43748i −0.277029 0.112358i
\(937\) 50.1408i 1.63803i 0.573773 + 0.819014i \(0.305479\pi\)
−0.573773 + 0.819014i \(0.694521\pi\)
\(938\) 0 0
\(939\) 5.88663 + 5.88663i 0.192103 + 0.192103i
\(940\) −0.565044 + 0.102506i −0.0184297 + 0.00334337i
\(941\) −11.6055 43.3123i −0.378328 1.41194i −0.848421 0.529322i \(-0.822446\pi\)
0.470093 0.882617i \(-0.344220\pi\)
\(942\) 5.47243 + 10.4495i 0.178301 + 0.340463i
\(943\) −8.21947 14.2365i −0.267663 0.463606i
\(944\) 55.4531 5.40265i 1.80485 0.175841i
\(945\) 0 0
\(946\) 7.64801 12.0705i 0.248658 0.392445i
\(947\) −1.59414 0.427149i −0.0518027 0.0138805i 0.232825 0.972519i \(-0.425203\pi\)
−0.284627 + 0.958638i \(0.591870\pi\)
\(948\) −23.7481 + 20.1273i −0.771303 + 0.653703i
\(949\) −1.03095 + 0.276243i −0.0334661 + 0.00896723i
\(950\) −2.66561 + 2.45469i −0.0864837 + 0.0796406i
\(951\) 49.3867i 1.60147i
\(952\) 0 0
\(953\) 40.9510i 1.32653i −0.748384 0.663266i \(-0.769170\pi\)
0.748384 0.663266i \(-0.230830\pi\)
\(954\) 8.22431 + 8.93099i 0.266272 + 0.289151i
\(955\) 4.72865 1.26704i 0.153015 0.0410003i
\(956\) 18.5867 + 1.53388i 0.601137 + 0.0496093i
\(957\) −1.11881 0.299783i −0.0361659 0.00969062i
\(958\) 24.8828 + 15.7661i 0.803927 + 0.509378i
\(959\) 0 0
\(960\) −15.5712 3.92656i −0.502559 0.126729i
\(961\) −15.6564 27.1177i −0.505046 0.874766i
\(962\) 37.0542 19.4054i 1.19468 0.625654i
\(963\) −1.05598 3.94096i −0.0340284 0.126996i
\(964\) −29.3111 + 42.3026i −0.944045 + 1.36248i
\(965\) 15.3818 + 15.3818i 0.495159 + 0.495159i
\(966\) 0 0
\(967\) 14.6315i 0.470518i 0.971933 + 0.235259i \(0.0755938\pi\)
−0.971933 + 0.235259i \(0.924406\pi\)
\(968\) −7.91072 18.7059i −0.254260 0.601231i
\(969\) 6.34536 + 3.66350i 0.203842 + 0.117688i
\(970\) 16.4416 + 5.13952i 0.527908 + 0.165020i
\(971\) −6.32211 + 23.5944i −0.202886 + 0.757181i 0.787197 + 0.616701i \(0.211531\pi\)
−0.990084 + 0.140480i \(0.955135\pi\)
\(972\) 20.3299 + 7.28623i 0.652081 + 0.233706i
\(973\) 0 0
\(974\) 0.168362 0.265717i 0.00539466 0.00851413i
\(975\) 12.0686 + 20.9035i 0.386506 + 0.669448i
\(976\) −13.6368 6.19607i −0.436502 0.198331i
\(977\) 2.85781 4.94988i 0.0914295 0.158361i −0.816683 0.577086i \(-0.804190\pi\)
0.908113 + 0.418725i \(0.137523\pi\)
\(978\) −23.6086 0.972507i −0.754920 0.0310974i
\(979\) −24.3061 + 24.3061i −0.776827 + 0.776827i
\(980\) 0 0
\(981\) 7.70133 + 7.70133i 0.245885 + 0.245885i
\(982\) 26.7153 24.6014i 0.852520 0.785063i
\(983\) 18.6714 + 10.7799i 0.595525 + 0.343827i 0.767279 0.641313i \(-0.221610\pi\)
−0.171754 + 0.985140i \(0.554943\pi\)
\(984\) 1.89339 + 13.6040i 0.0603591 + 0.433680i
\(985\) 9.26615 5.34981i 0.295244 0.170459i
\(986\) −2.29686 + 0.515141i −0.0731469 + 0.0164054i
\(987\) 0 0
\(988\) 3.43341 1.62167i 0.109231 0.0515921i
\(989\) 34.1780 + 9.15796i 1.08680 + 0.291206i
\(990\) 2.64297 1.38413i 0.0839991 0.0439905i
\(991\) 17.3811 30.1049i 0.552128 0.956314i −0.445993 0.895037i \(-0.647149\pi\)
0.998121 0.0612772i \(-0.0195174\pi\)
\(992\) −33.2918 29.7602i −1.05701 0.944888i
\(993\) 14.7661 0.468590
\(994\) 0 0
\(995\) −2.51082 + 2.51082i −0.0795985 + 0.0795985i
\(996\) −1.99287 1.38084i −0.0631465 0.0437536i
\(997\) 4.95586 1.32792i 0.156954 0.0420556i −0.179487 0.983760i \(-0.557444\pi\)
0.336440 + 0.941705i \(0.390777\pi\)
\(998\) −1.48148 + 4.73933i −0.0468954 + 0.150021i
\(999\) −33.3031 + 19.2275i −1.05366 + 0.608332i
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 784.2.x.o.165.7 48
7.2 even 3 inner 784.2.x.o.373.3 48
7.3 odd 6 784.2.m.j.197.10 24
7.4 even 3 784.2.m.k.197.10 24
7.5 odd 6 112.2.w.c.37.3 48
7.6 odd 2 112.2.w.c.53.7 yes 48
16.13 even 4 inner 784.2.x.o.557.3 48
28.19 even 6 448.2.ba.c.177.3 48
28.27 even 2 448.2.ba.c.305.10 48
56.5 odd 6 896.2.ba.f.737.3 48
56.13 odd 2 896.2.ba.f.865.10 48
56.19 even 6 896.2.ba.e.737.10 48
56.27 even 2 896.2.ba.e.865.3 48
112.5 odd 12 896.2.ba.f.289.10 48
112.13 odd 4 112.2.w.c.109.3 yes 48
112.19 even 12 448.2.ba.c.401.10 48
112.27 even 4 896.2.ba.e.417.10 48
112.45 odd 12 784.2.m.j.589.10 24
112.61 odd 12 112.2.w.c.93.7 yes 48
112.69 odd 4 896.2.ba.f.417.3 48
112.75 even 12 896.2.ba.e.289.3 48
112.83 even 4 448.2.ba.c.81.3 48
112.93 even 12 inner 784.2.x.o.765.7 48
112.109 even 12 784.2.m.k.589.10 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.w.c.37.3 48 7.5 odd 6
112.2.w.c.53.7 yes 48 7.6 odd 2
112.2.w.c.93.7 yes 48 112.61 odd 12
112.2.w.c.109.3 yes 48 112.13 odd 4
448.2.ba.c.81.3 48 112.83 even 4
448.2.ba.c.177.3 48 28.19 even 6
448.2.ba.c.305.10 48 28.27 even 2
448.2.ba.c.401.10 48 112.19 even 12
784.2.m.j.197.10 24 7.3 odd 6
784.2.m.j.589.10 24 112.45 odd 12
784.2.m.k.197.10 24 7.4 even 3
784.2.m.k.589.10 24 112.109 even 12
784.2.x.o.165.7 48 1.1 even 1 trivial
784.2.x.o.373.3 48 7.2 even 3 inner
784.2.x.o.557.3 48 16.13 even 4 inner
784.2.x.o.765.7 48 112.93 even 12 inner
896.2.ba.e.289.3 48 112.75 even 12
896.2.ba.e.417.10 48 112.27 even 4
896.2.ba.e.737.10 48 56.19 even 6
896.2.ba.e.865.3 48 56.27 even 2
896.2.ba.f.289.10 48 112.5 odd 12
896.2.ba.f.417.3 48 112.69 odd 4
896.2.ba.f.737.3 48 56.5 odd 6
896.2.ba.f.865.10 48 56.13 odd 2