Properties

Label 525.2.bf.d.32.2
Level $525$
Weight $2$
Character 525.32
Analytic conductor $4.192$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(32,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 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("525.32");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.bf (of order \(12\), degree \(4\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.2
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 525.32
Dual form 525.2.bf.d.443.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.36603 + 0.366025i) q^{2} +(-1.10721 + 1.33195i) q^{3} +(-2.00000 + 1.41421i) q^{6} +(-1.15539 - 2.38014i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.548188 - 2.94949i) q^{9} +O(q^{10})\) \(q+(1.36603 + 0.366025i) q^{2} +(-1.10721 + 1.33195i) q^{3} +(-2.00000 + 1.41421i) q^{6} +(-1.15539 - 2.38014i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.548188 - 2.94949i) q^{9} +(-3.67423 - 2.12132i) q^{11} +(-3.53553 + 3.53553i) q^{13} +(-0.707107 - 3.67423i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-0.366025 - 1.36603i) q^{17} +(0.330749 - 4.22973i) q^{18} +(6.06218 - 3.50000i) q^{19} +(4.44949 + 1.09638i) q^{21} +(-4.24264 - 4.24264i) q^{22} +(-1.09808 + 4.09808i) q^{23} +(4.87832 - 0.449490i) q^{24} +(-6.12372 + 3.53553i) q^{26} +(4.53553 + 2.53553i) q^{27} -7.07107 q^{29} +(0.500000 - 0.866025i) q^{31} +(6.89363 - 2.54516i) q^{33} -2.00000i q^{34} +(-0.258819 + 0.965926i) q^{37} +(9.56218 - 2.56218i) q^{38} +(-0.794593 - 8.62372i) q^{39} -7.07107i q^{41} +(5.67681 + 3.12630i) q^{42} +(3.53553 - 3.53553i) q^{43} +(-3.00000 + 5.19615i) q^{46} +(-5.46410 - 1.46410i) q^{47} +(6.82843 + 1.17157i) q^{48} +(-4.33013 + 5.50000i) q^{49} +(2.22474 + 1.02494i) q^{51} +(-2.73205 + 0.732051i) q^{53} +(5.26758 + 5.12372i) q^{54} +(-2.44949 + 7.07107i) q^{56} +(-2.05025 + 11.9497i) q^{57} +(-9.65926 - 2.58819i) q^{58} +(-0.707107 + 1.22474i) q^{59} +(-2.00000 - 3.46410i) q^{61} +(1.00000 - 1.00000i) q^{62} +(-6.38682 + 4.71259i) q^{63} +8.00000i q^{64} +(10.3485 - 0.953512i) q^{66} +(-0.965926 + 0.258819i) q^{67} +(-4.24264 - 6.00000i) q^{69} -7.07107i q^{71} +(-4.80260 + 6.99536i) q^{72} +(1.81173 + 6.76148i) q^{73} +(-0.707107 + 1.22474i) q^{74} +(-0.803848 + 11.1962i) q^{77} +(2.07107 - 12.0711i) q^{78} +(6.06218 - 3.50000i) q^{79} +(-8.39898 + 3.23375i) q^{81} +(2.58819 - 9.65926i) q^{82} +(1.00000 + 1.00000i) q^{83} +(6.12372 - 3.53553i) q^{86} +(7.82913 - 9.41832i) q^{87} +(3.10583 + 11.5911i) q^{88} +(7.77817 + 13.4722i) q^{89} +(12.5000 + 4.33013i) q^{91} +(0.599900 + 1.62484i) q^{93} +(-6.92820 - 4.00000i) q^{94} +(-7.07107 - 7.07107i) q^{97} +(-7.92820 + 5.92820i) q^{98} +(-4.24264 + 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{3} - 16 q^{6} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 4 q^{3} - 16 q^{6} - 16 q^{8} - 16 q^{16} + 4 q^{17} + 4 q^{18} + 16 q^{21} + 12 q^{23} + 8 q^{27} + 4 q^{31} - 12 q^{33} + 28 q^{38} + 20 q^{42} - 24 q^{46} - 16 q^{47} + 32 q^{48} + 8 q^{51} - 8 q^{53} - 56 q^{57} - 16 q^{61} + 8 q^{62} + 8 q^{63} + 24 q^{66} - 8 q^{72} - 48 q^{77} - 40 q^{78} - 28 q^{81} + 8 q^{83} + 20 q^{87} + 100 q^{91} + 4 q^{93} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 + 0.366025i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(3\) −1.10721 + 1.33195i −0.639246 + 0.769002i
\(4\) 0 0
\(5\) 0 0
\(6\) −2.00000 + 1.41421i −0.816497 + 0.577350i
\(7\) −1.15539 2.38014i −0.436698 0.899608i
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) −0.548188 2.94949i −0.182729 0.983163i
\(10\) 0 0
\(11\) −3.67423 2.12132i −1.10782 0.639602i −0.169559 0.985520i \(-0.554234\pi\)
−0.938265 + 0.345918i \(0.887568\pi\)
\(12\) 0 0
\(13\) −3.53553 + 3.53553i −0.980581 + 0.980581i −0.999815 0.0192343i \(-0.993877\pi\)
0.0192343 + 0.999815i \(0.493877\pi\)
\(14\) −0.707107 3.67423i −0.188982 0.981981i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) −0.366025 1.36603i −0.0887742 0.331310i 0.907228 0.420639i \(-0.138194\pi\)
−0.996002 + 0.0893296i \(0.971528\pi\)
\(18\) 0.330749 4.22973i 0.0779583 0.996957i
\(19\) 6.06218 3.50000i 1.39076 0.802955i 0.397360 0.917663i \(-0.369927\pi\)
0.993399 + 0.114708i \(0.0365932\pi\)
\(20\) 0 0
\(21\) 4.44949 + 1.09638i 0.970958 + 0.239249i
\(22\) −4.24264 4.24264i −0.904534 0.904534i
\(23\) −1.09808 + 4.09808i −0.228965 + 0.854508i 0.751812 + 0.659377i \(0.229180\pi\)
−0.980777 + 0.195131i \(0.937487\pi\)
\(24\) 4.87832 0.449490i 0.995782 0.0917517i
\(25\) 0 0
\(26\) −6.12372 + 3.53553i −1.20096 + 0.693375i
\(27\) 4.53553 + 2.53553i 0.872864 + 0.487964i
\(28\) 0 0
\(29\) −7.07107 −1.31306 −0.656532 0.754298i \(-0.727977\pi\)
−0.656532 + 0.754298i \(0.727977\pi\)
\(30\) 0 0
\(31\) 0.500000 0.866025i 0.0898027 0.155543i −0.817625 0.575751i \(-0.804710\pi\)
0.907428 + 0.420208i \(0.138043\pi\)
\(32\) 0 0
\(33\) 6.89363 2.54516i 1.20003 0.443056i
\(34\) 2.00000i 0.342997i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.258819 + 0.965926i −0.0425496 + 0.158797i −0.983932 0.178545i \(-0.942861\pi\)
0.941382 + 0.337342i \(0.109528\pi\)
\(38\) 9.56218 2.56218i 1.55119 0.415640i
\(39\) −0.794593 8.62372i −0.127237 1.38090i
\(40\) 0 0
\(41\) 7.07107i 1.10432i −0.833740 0.552158i \(-0.813805\pi\)
0.833740 0.552158i \(-0.186195\pi\)
\(42\) 5.67681 + 3.12630i 0.875951 + 0.482399i
\(43\) 3.53553 3.53553i 0.539164 0.539164i −0.384120 0.923283i \(-0.625495\pi\)
0.923283 + 0.384120i \(0.125495\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) −5.46410 1.46410i −0.797021 0.213561i −0.162745 0.986668i \(-0.552035\pi\)
−0.634276 + 0.773107i \(0.718702\pi\)
\(48\) 6.82843 + 1.17157i 0.985599 + 0.169102i
\(49\) −4.33013 + 5.50000i −0.618590 + 0.785714i
\(50\) 0 0
\(51\) 2.22474 + 1.02494i 0.311527 + 0.143521i
\(52\) 0 0
\(53\) −2.73205 + 0.732051i −0.375276 + 0.100555i −0.441527 0.897248i \(-0.645563\pi\)
0.0662507 + 0.997803i \(0.478896\pi\)
\(54\) 5.26758 + 5.12372i 0.716827 + 0.697251i
\(55\) 0 0
\(56\) −2.44949 + 7.07107i −0.327327 + 0.944911i
\(57\) −2.05025 + 11.9497i −0.271563 + 1.58278i
\(58\) −9.65926 2.58819i −1.26832 0.339846i
\(59\) −0.707107 + 1.22474i −0.0920575 + 0.159448i −0.908377 0.418153i \(-0.862678\pi\)
0.816319 + 0.577601i \(0.196011\pi\)
\(60\) 0 0
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 1.00000 1.00000i 0.127000 0.127000i
\(63\) −6.38682 + 4.71259i −0.804664 + 0.593730i
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 10.3485 0.953512i 1.27381 0.117369i
\(67\) −0.965926 + 0.258819i −0.118007 + 0.0316198i −0.317339 0.948312i \(-0.602789\pi\)
0.199332 + 0.979932i \(0.436123\pi\)
\(68\) 0 0
\(69\) −4.24264 6.00000i −0.510754 0.722315i
\(70\) 0 0
\(71\) 7.07107i 0.839181i −0.907713 0.419591i \(-0.862174\pi\)
0.907713 0.419591i \(-0.137826\pi\)
\(72\) −4.80260 + 6.99536i −0.565992 + 0.824411i
\(73\) 1.81173 + 6.76148i 0.212047 + 0.791371i 0.987185 + 0.159579i \(0.0510137\pi\)
−0.775138 + 0.631792i \(0.782320\pi\)
\(74\) −0.707107 + 1.22474i −0.0821995 + 0.142374i
\(75\) 0 0
\(76\) 0 0
\(77\) −0.803848 + 11.1962i −0.0916069 + 1.27592i
\(78\) 2.07107 12.0711i 0.234502 1.36678i
\(79\) 6.06218 3.50000i 0.682048 0.393781i −0.118578 0.992945i \(-0.537834\pi\)
0.800626 + 0.599164i \(0.204500\pi\)
\(80\) 0 0
\(81\) −8.39898 + 3.23375i −0.933220 + 0.359306i
\(82\) 2.58819 9.65926i 0.285818 1.06669i
\(83\) 1.00000 + 1.00000i 0.109764 + 0.109764i 0.759856 0.650092i \(-0.225269\pi\)
−0.650092 + 0.759856i \(0.725269\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.12372 3.53553i 0.660338 0.381246i
\(87\) 7.82913 9.41832i 0.839371 1.00975i
\(88\) 3.10583 + 11.5911i 0.331082 + 1.23562i
\(89\) 7.77817 + 13.4722i 0.824485 + 1.42805i 0.902312 + 0.431083i \(0.141868\pi\)
−0.0778275 + 0.996967i \(0.524798\pi\)
\(90\) 0 0
\(91\) 12.5000 + 4.33013i 1.31036 + 0.453921i
\(92\) 0 0
\(93\) 0.599900 + 1.62484i 0.0622068 + 0.168489i
\(94\) −6.92820 4.00000i −0.714590 0.412568i
\(95\) 0 0
\(96\) 0 0
\(97\) −7.07107 7.07107i −0.717958 0.717958i 0.250229 0.968187i \(-0.419494\pi\)
−0.968187 + 0.250229i \(0.919494\pi\)
\(98\) −7.92820 + 5.92820i −0.800869 + 0.598839i
\(99\) −4.24264 + 12.0000i −0.426401 + 1.20605i
\(100\) 0 0
\(101\) 8.57321 + 4.94975i 0.853067 + 0.492518i 0.861684 0.507445i \(-0.169410\pi\)
−0.00861771 + 0.999963i \(0.502743\pi\)
\(102\) 2.66390 + 2.21441i 0.263766 + 0.219260i
\(103\) −2.89778 0.776457i −0.285526 0.0765066i 0.113213 0.993571i \(-0.463886\pi\)
−0.398740 + 0.917064i \(0.630552\pi\)
\(104\) 14.1421 1.38675
\(105\) 0 0
\(106\) −4.00000 −0.388514
\(107\) 15.0263 + 4.02628i 1.45265 + 0.389235i 0.896943 0.442146i \(-0.145783\pi\)
0.555702 + 0.831381i \(0.312449\pi\)
\(108\) 0 0
\(109\) −14.7224 8.50000i −1.41015 0.814152i −0.414751 0.909935i \(-0.636131\pi\)
−0.995402 + 0.0957826i \(0.969465\pi\)
\(110\) 0 0
\(111\) −1.00000 1.41421i −0.0949158 0.134231i
\(112\) −5.93426 + 8.76268i −0.560734 + 0.827996i
\(113\) −14.0000 14.0000i −1.31701 1.31701i −0.916132 0.400878i \(-0.868705\pi\)
−0.400878 0.916132i \(-0.631295\pi\)
\(114\) −7.17461 + 15.5732i −0.671964 + 1.45857i
\(115\) 0 0
\(116\) 0 0
\(117\) 12.3662 + 8.48988i 1.14325 + 0.784890i
\(118\) −1.41421 + 1.41421i −0.130189 + 0.130189i
\(119\) −2.82843 + 2.44949i −0.259281 + 0.224544i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −1.46410 5.46410i −0.132554 0.494697i
\(123\) 9.41832 + 7.82913i 0.849221 + 0.705929i
\(124\) 0 0
\(125\) 0 0
\(126\) −10.4495 + 4.09978i −0.930915 + 0.365237i
\(127\) −10.6066 10.6066i −0.941184 0.941184i 0.0571802 0.998364i \(-0.481789\pi\)
−0.998364 + 0.0571802i \(0.981789\pi\)
\(128\) −2.92820 + 10.9282i −0.258819 + 0.965926i
\(129\) 0.794593 + 8.62372i 0.0699600 + 0.759277i
\(130\) 0 0
\(131\) 14.6969 8.48528i 1.28408 0.741362i 0.306486 0.951875i \(-0.400847\pi\)
0.977591 + 0.210513i \(0.0675133\pi\)
\(132\) 0 0
\(133\) −15.3347 10.3849i −1.32969 0.900489i
\(134\) −1.41421 −0.122169
\(135\) 0 0
\(136\) −2.00000 + 3.46410i −0.171499 + 0.297044i
\(137\) −4.02628 15.0263i −0.343988 1.28378i −0.893790 0.448486i \(-0.851963\pi\)
0.549801 0.835295i \(-0.314703\pi\)
\(138\) −3.59940 9.74907i −0.306401 0.829896i
\(139\) 11.0000i 0.933008i 0.884519 + 0.466504i \(0.154487\pi\)
−0.884519 + 0.466504i \(0.845513\pi\)
\(140\) 0 0
\(141\) 8.00000 5.65685i 0.673722 0.476393i
\(142\) 2.58819 9.65926i 0.217196 0.810587i
\(143\) 20.4904 5.49038i 1.71349 0.459129i
\(144\) −9.12096 + 7.79796i −0.760080 + 0.649830i
\(145\) 0 0
\(146\) 9.89949i 0.819288i
\(147\) −2.53139 11.8572i −0.208785 0.977961i
\(148\) 0 0
\(149\) 4.24264 + 7.34847i 0.347571 + 0.602010i 0.985817 0.167822i \(-0.0536733\pi\)
−0.638247 + 0.769832i \(0.720340\pi\)
\(150\) 0 0
\(151\) 3.00000 5.19615i 0.244137 0.422857i −0.717752 0.696299i \(-0.754829\pi\)
0.961888 + 0.273442i \(0.0881622\pi\)
\(152\) −19.1244 5.12436i −1.55119 0.415640i
\(153\) −3.82843 + 1.82843i −0.309510 + 0.147820i
\(154\) −5.19615 + 15.0000i −0.418718 + 1.20873i
\(155\) 0 0
\(156\) 0 0
\(157\) 3.86370 1.03528i 0.308357 0.0826240i −0.101322 0.994854i \(-0.532307\pi\)
0.409679 + 0.912230i \(0.365641\pi\)
\(158\) 9.56218 2.56218i 0.760726 0.203836i
\(159\) 2.04989 4.44949i 0.162567 0.352867i
\(160\) 0 0
\(161\) 11.0227 2.12132i 0.868711 0.167183i
\(162\) −12.6569 + 1.34315i −0.994416 + 0.105527i
\(163\) 1.93185 + 0.517638i 0.151314 + 0.0405445i 0.333681 0.942686i \(-0.391709\pi\)
−0.182367 + 0.983231i \(0.558376\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.00000 + 1.73205i 0.0776151 + 0.134433i
\(167\) 7.00000 7.00000i 0.541676 0.541676i −0.382344 0.924020i \(-0.624883\pi\)
0.924020 + 0.382344i \(0.124883\pi\)
\(168\) −6.70623 11.0917i −0.517397 0.855746i
\(169\) 12.0000i 0.923077i
\(170\) 0 0
\(171\) −13.6464 15.9617i −1.04357 1.22062i
\(172\) 0 0
\(173\) 0.732051 2.73205i 0.0556568 0.207714i −0.932498 0.361176i \(-0.882375\pi\)
0.988155 + 0.153462i \(0.0490422\pi\)
\(174\) 14.1421 10.0000i 1.07211 0.758098i
\(175\) 0 0
\(176\) 16.9706i 1.27920i
\(177\) −0.848387 2.29788i −0.0637687 0.172719i
\(178\) 5.69402 + 21.2504i 0.426785 + 1.59278i
\(179\) 9.89949 17.1464i 0.739923 1.28158i −0.212607 0.977138i \(-0.568195\pi\)
0.952529 0.304446i \(-0.0984714\pi\)
\(180\) 0 0
\(181\) −3.00000 −0.222988 −0.111494 0.993765i \(-0.535564\pi\)
−0.111494 + 0.993765i \(0.535564\pi\)
\(182\) 15.4904 + 10.4904i 1.14822 + 0.777599i
\(183\) 6.82843 + 1.17157i 0.504772 + 0.0866052i
\(184\) 10.3923 6.00000i 0.766131 0.442326i
\(185\) 0 0
\(186\) 0.224745 + 2.43916i 0.0164791 + 0.178848i
\(187\) −1.55291 + 5.79555i −0.113560 + 0.423813i
\(188\) 0 0
\(189\) 0.794593 13.7247i 0.0577981 0.998328i
\(190\) 0 0
\(191\) −9.79796 + 5.65685i −0.708955 + 0.409316i −0.810674 0.585498i \(-0.800899\pi\)
0.101719 + 0.994813i \(0.467566\pi\)
\(192\) −10.6556 8.85765i −0.769002 0.639246i
\(193\) −5.95284 22.2163i −0.428495 1.59916i −0.756171 0.654374i \(-0.772932\pi\)
0.327677 0.944790i \(-0.393734\pi\)
\(194\) −7.07107 12.2474i −0.507673 0.879316i
\(195\) 0 0
\(196\) 0 0
\(197\) −3.00000 + 3.00000i −0.213741 + 0.213741i −0.805855 0.592113i \(-0.798294\pi\)
0.592113 + 0.805855i \(0.298294\pi\)
\(198\) −10.1879 + 14.8394i −0.724020 + 1.05459i
\(199\) −1.73205 1.00000i −0.122782 0.0708881i 0.437351 0.899291i \(-0.355917\pi\)
−0.560133 + 0.828403i \(0.689250\pi\)
\(200\) 0 0
\(201\) 0.724745 1.57313i 0.0511196 0.110960i
\(202\) 9.89949 + 9.89949i 0.696526 + 0.696526i
\(203\) 8.16987 + 16.8301i 0.573413 + 1.18124i
\(204\) 0 0
\(205\) 0 0
\(206\) −3.67423 2.12132i −0.255996 0.147799i
\(207\) 12.6892 + 0.992248i 0.881959 + 0.0689660i
\(208\) 19.3185 + 5.17638i 1.33950 + 0.358917i
\(209\) −29.6985 −2.05429
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) 0 0
\(213\) 9.41832 + 7.82913i 0.645332 + 0.536443i
\(214\) 19.0526 + 11.0000i 1.30241 + 0.751945i
\(215\) 0 0
\(216\) −4.00000 14.1421i −0.272166 0.962250i
\(217\) −2.63896 0.189469i −0.179144 0.0128620i
\(218\) −17.0000 17.0000i −1.15139 1.15139i
\(219\) −11.0119 5.07321i −0.744117 0.342816i
\(220\) 0 0
\(221\) 6.12372 + 3.53553i 0.411926 + 0.237826i
\(222\) −0.848387 2.29788i −0.0569400 0.154223i
\(223\) 7.07107 7.07107i 0.473514 0.473514i −0.429536 0.903050i \(-0.641323\pi\)
0.903050 + 0.429536i \(0.141323\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −14.0000 24.2487i −0.931266 1.61300i
\(227\) 3.29423 + 12.2942i 0.218646 + 0.815997i 0.984851 + 0.173401i \(0.0554757\pi\)
−0.766206 + 0.642595i \(0.777858\pi\)
\(228\) 0 0
\(229\) −2.59808 + 1.50000i −0.171686 + 0.0991228i −0.583380 0.812199i \(-0.698270\pi\)
0.411695 + 0.911322i \(0.364937\pi\)
\(230\) 0 0
\(231\) −14.0227 13.4671i −0.922626 0.886073i
\(232\) 14.1421 + 14.1421i 0.928477 + 0.928477i
\(233\) 0.732051 2.73205i 0.0479582 0.178983i −0.937792 0.347197i \(-0.887133\pi\)
0.985750 + 0.168215i \(0.0538001\pi\)
\(234\) 13.7850 + 16.1237i 0.901152 + 1.05404i
\(235\) 0 0
\(236\) 0 0
\(237\) −2.05025 + 11.9497i −0.133178 + 0.776220i
\(238\) −4.76028 + 2.31079i −0.308563 + 0.149786i
\(239\) 28.2843 1.82956 0.914779 0.403955i \(-0.132365\pi\)
0.914779 + 0.403955i \(0.132365\pi\)
\(240\) 0 0
\(241\) −12.0000 + 20.7846i −0.772988 + 1.33885i 0.162930 + 0.986638i \(0.447905\pi\)
−0.935918 + 0.352217i \(0.885428\pi\)
\(242\) 2.56218 + 9.56218i 0.164703 + 0.614680i
\(243\) 4.99221 14.7675i 0.320250 0.947333i
\(244\) 0 0
\(245\) 0 0
\(246\) 10.0000 + 14.1421i 0.637577 + 0.901670i
\(247\) −9.05867 + 33.8074i −0.576389 + 2.15111i
\(248\) −2.73205 + 0.732051i −0.173485 + 0.0464853i
\(249\) −2.43916 + 0.224745i −0.154575 + 0.0142426i
\(250\) 0 0
\(251\) 7.07107i 0.446322i 0.974782 + 0.223161i \(0.0716375\pi\)
−0.974782 + 0.223161i \(0.928362\pi\)
\(252\) 0 0
\(253\) 12.7279 12.7279i 0.800198 0.800198i
\(254\) −10.6066 18.3712i −0.665517 1.15271i
\(255\) 0 0
\(256\) 0 0
\(257\) −12.2942 3.29423i −0.766893 0.205488i −0.145894 0.989300i \(-0.546606\pi\)
−0.620998 + 0.783812i \(0.713273\pi\)
\(258\) −2.07107 + 12.0711i −0.128939 + 0.751512i
\(259\) 2.59808 0.500000i 0.161437 0.0310685i
\(260\) 0 0
\(261\) 3.87628 + 20.8560i 0.239935 + 1.29096i
\(262\) 23.1822 6.21166i 1.43220 0.383757i
\(263\) −16.3923 + 4.39230i −1.01079 + 0.270841i −0.725961 0.687736i \(-0.758605\pi\)
−0.284832 + 0.958577i \(0.591938\pi\)
\(264\) −18.8776 8.69694i −1.16184 0.535260i
\(265\) 0 0
\(266\) −17.1464 19.7990i −1.05131 1.21395i
\(267\) −26.5563 4.55635i −1.62522 0.278844i
\(268\) 0 0
\(269\) 2.82843 4.89898i 0.172452 0.298696i −0.766824 0.641857i \(-0.778164\pi\)
0.939277 + 0.343161i \(0.111498\pi\)
\(270\) 0 0
\(271\) −7.00000 12.1244i −0.425220 0.736502i 0.571221 0.820796i \(-0.306470\pi\)
−0.996441 + 0.0842940i \(0.973137\pi\)
\(272\) −4.00000 + 4.00000i −0.242536 + 0.242536i
\(273\) −19.6076 + 11.8550i −1.18671 + 0.717500i
\(274\) 22.0000i 1.32907i
\(275\) 0 0
\(276\) 0 0
\(277\) 8.69333 2.32937i 0.522332 0.139958i 0.0119868 0.999928i \(-0.496184\pi\)
0.510345 + 0.859970i \(0.329518\pi\)
\(278\) −4.02628 + 15.0263i −0.241480 + 0.901216i
\(279\) −2.82843 1.00000i −0.169334 0.0598684i
\(280\) 0 0
\(281\) 14.1421i 0.843649i 0.906677 + 0.421825i \(0.138610\pi\)
−0.906677 + 0.421825i \(0.861390\pi\)
\(282\) 12.9988 4.79920i 0.774065 0.285788i
\(283\) −5.95284 22.2163i −0.353859 1.32062i −0.881914 0.471411i \(-0.843745\pi\)
0.528054 0.849211i \(-0.322922\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 30.0000 1.77394
\(287\) −16.8301 + 8.16987i −0.993451 + 0.482252i
\(288\) 0 0
\(289\) 12.9904 7.50000i 0.764140 0.441176i
\(290\) 0 0
\(291\) 17.2474 1.58919i 1.01106 0.0931597i
\(292\) 0 0
\(293\) 16.0000 + 16.0000i 0.934730 + 0.934730i 0.997997 0.0632667i \(-0.0201519\pi\)
−0.0632667 + 0.997997i \(0.520152\pi\)
\(294\) 0.882079 17.1237i 0.0514439 0.998676i
\(295\) 0 0
\(296\) 2.44949 1.41421i 0.142374 0.0821995i
\(297\) −11.2859 18.9375i −0.654876 1.09886i
\(298\) 3.10583 + 11.5911i 0.179916 + 0.671455i
\(299\) −10.6066 18.3712i −0.613396 1.06243i
\(300\) 0 0
\(301\) −12.5000 4.33013i −0.720488 0.249584i
\(302\) 6.00000 6.00000i 0.345261 0.345261i
\(303\) −16.0851 + 5.93871i −0.924067 + 0.341170i
\(304\) −24.2487 14.0000i −1.39076 0.802955i
\(305\) 0 0
\(306\) −5.89898 + 1.09638i −0.337222 + 0.0626757i
\(307\) 10.6066 + 10.6066i 0.605351 + 0.605351i 0.941727 0.336377i \(-0.109202\pi\)
−0.336377 + 0.941727i \(0.609202\pi\)
\(308\) 0 0
\(309\) 4.24264 3.00000i 0.241355 0.170664i
\(310\) 0 0
\(311\) −28.1691 16.2635i −1.59732 0.922216i −0.992000 0.126237i \(-0.959710\pi\)
−0.605325 0.795979i \(-0.706957\pi\)
\(312\) −15.6583 + 18.8366i −0.886475 + 1.06641i
\(313\) 16.4207 + 4.39992i 0.928155 + 0.248698i 0.691068 0.722790i \(-0.257141\pi\)
0.237087 + 0.971488i \(0.423807\pi\)
\(314\) 5.65685 0.319235
\(315\) 0 0
\(316\) 0 0
\(317\) 1.36603 + 0.366025i 0.0767236 + 0.0205580i 0.296977 0.954885i \(-0.404022\pi\)
−0.220253 + 0.975443i \(0.570688\pi\)
\(318\) 4.42883 5.32780i 0.248356 0.298768i
\(319\) 25.9808 + 15.0000i 1.45464 + 0.839839i
\(320\) 0 0
\(321\) −22.0000 + 15.5563i −1.22792 + 0.868271i
\(322\) 15.8338 + 1.13681i 0.882380 + 0.0633521i
\(323\) −7.00000 7.00000i −0.389490 0.389490i
\(324\) 0 0
\(325\) 0 0
\(326\) 2.44949 + 1.41421i 0.135665 + 0.0783260i
\(327\) 27.6224 10.1983i 1.52752 0.563968i
\(328\) −14.1421 + 14.1421i −0.780869 + 0.780869i
\(329\) 2.82843 + 14.6969i 0.155936 + 0.810268i
\(330\) 0 0
\(331\) 0.500000 + 0.866025i 0.0274825 + 0.0476011i 0.879440 0.476011i \(-0.157918\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) 0 0
\(333\) 2.99087 + 0.233875i 0.163899 + 0.0128163i
\(334\) 12.1244 7.00000i 0.663415 0.383023i
\(335\) 0 0
\(336\) −5.10102 17.6062i −0.278283 0.960499i
\(337\) −3.53553 3.53553i −0.192593 0.192593i 0.604223 0.796815i \(-0.293484\pi\)
−0.796815 + 0.604223i \(0.793484\pi\)
\(338\) 4.39230 16.3923i 0.238910 0.891624i
\(339\) 34.1482 3.14643i 1.85468 0.170891i
\(340\) 0 0
\(341\) −3.67423 + 2.12132i −0.198971 + 0.114876i
\(342\) −12.7990 26.7990i −0.692090 1.44912i
\(343\) 18.0938 + 3.95164i 0.976972 + 0.213368i
\(344\) −14.1421 −0.762493
\(345\) 0 0
\(346\) 2.00000 3.46410i 0.107521 0.186231i
\(347\) −5.85641 21.8564i −0.314388 1.17331i −0.924558 0.381042i \(-0.875565\pi\)
0.610169 0.792271i \(-0.291101\pi\)
\(348\) 0 0
\(349\) 26.0000i 1.39175i 0.718164 + 0.695874i \(0.244983\pi\)
−0.718164 + 0.695874i \(0.755017\pi\)
\(350\) 0 0
\(351\) −25.0000 + 7.07107i −1.33440 + 0.377426i
\(352\) 0 0
\(353\) 4.09808 1.09808i 0.218119 0.0584447i −0.148105 0.988972i \(-0.547317\pi\)
0.366223 + 0.930527i \(0.380651\pi\)
\(354\) −0.317837 3.44949i −0.0168929 0.183338i
\(355\) 0 0
\(356\) 0 0
\(357\) −0.130948 6.47942i −0.00693052 0.342927i
\(358\) 19.7990 19.7990i 1.04641 1.04641i
\(359\) 0.707107 + 1.22474i 0.0373197 + 0.0646396i 0.884082 0.467332i \(-0.154785\pi\)
−0.846762 + 0.531971i \(0.821451\pi\)
\(360\) 0 0
\(361\) 15.0000 25.9808i 0.789474 1.36741i
\(362\) −4.09808 1.09808i −0.215390 0.0577136i
\(363\) −11.9497 2.05025i −0.627199 0.107610i
\(364\) 0 0
\(365\) 0 0
\(366\) 8.89898 + 4.09978i 0.465157 + 0.214299i
\(367\) −20.2844 + 5.43520i −1.05884 + 0.283715i −0.745900 0.666058i \(-0.767980\pi\)
−0.312939 + 0.949773i \(0.601314\pi\)
\(368\) 16.3923 4.39230i 0.854508 0.228965i
\(369\) −20.8560 + 3.87628i −1.08572 + 0.201791i
\(370\) 0 0
\(371\) 4.89898 + 5.65685i 0.254342 + 0.293689i
\(372\) 0 0
\(373\) −22.2163 5.95284i −1.15032 0.308226i −0.367224 0.930132i \(-0.619692\pi\)
−0.783092 + 0.621906i \(0.786359\pi\)
\(374\) −4.24264 + 7.34847i −0.219382 + 0.379980i
\(375\) 0 0
\(376\) 8.00000 + 13.8564i 0.412568 + 0.714590i
\(377\) 25.0000 25.0000i 1.28757 1.28757i
\(378\) 6.10904 18.4575i 0.314215 0.949352i
\(379\) 9.00000i 0.462299i −0.972918 0.231149i \(-0.925751\pi\)
0.972918 0.231149i \(-0.0742486\pi\)
\(380\) 0 0
\(381\) 25.8712 2.38378i 1.32542 0.122125i
\(382\) −15.4548 + 4.14110i −0.790737 + 0.211877i
\(383\) 4.39230 16.3923i 0.224436 0.837608i −0.758193 0.652030i \(-0.773918\pi\)
0.982630 0.185578i \(-0.0594157\pi\)
\(384\) −11.3137 16.0000i −0.577350 0.816497i
\(385\) 0 0
\(386\) 32.5269i 1.65558i
\(387\) −12.3662 8.48988i −0.628607 0.431565i
\(388\) 0 0
\(389\) −14.8492 + 25.7196i −0.752886 + 1.30404i 0.193532 + 0.981094i \(0.438006\pi\)
−0.946418 + 0.322944i \(0.895328\pi\)
\(390\) 0 0
\(391\) 6.00000 0.303433
\(392\) 19.6603 2.33975i 0.992993 0.118175i
\(393\) −4.97056 + 28.9706i −0.250732 + 1.46137i
\(394\) −5.19615 + 3.00000i −0.261778 + 0.151138i
\(395\) 0 0
\(396\) 0 0
\(397\) −0.258819 + 0.965926i −0.0129898 + 0.0484784i −0.972117 0.234498i \(-0.924655\pi\)
0.959127 + 0.282977i \(0.0913219\pi\)
\(398\) −2.00000 2.00000i −0.100251 0.100251i
\(399\) 30.8109 8.92679i 1.54248 0.446898i
\(400\) 0 0
\(401\) −22.0454 + 12.7279i −1.10090 + 0.635602i −0.936456 0.350785i \(-0.885915\pi\)
−0.164439 + 0.986387i \(0.552581\pi\)
\(402\) 1.56583 1.88366i 0.0780963 0.0939486i
\(403\) 1.29410 + 4.82963i 0.0644635 + 0.240581i
\(404\) 0 0
\(405\) 0 0
\(406\) 5.00000 + 25.9808i 0.248146 + 1.28940i
\(407\) 3.00000 3.00000i 0.148704 0.148704i
\(408\) −2.39960 6.49938i −0.118798 0.321767i
\(409\) −32.0429 18.5000i −1.58442 0.914766i −0.994203 0.107523i \(-0.965708\pi\)
−0.590219 0.807243i \(-0.700959\pi\)
\(410\) 0 0
\(411\) 24.4722 + 11.2744i 1.20712 + 0.556124i
\(412\) 0 0
\(413\) 3.73205 + 0.267949i 0.183642 + 0.0131849i
\(414\) 16.9706 + 6.00000i 0.834058 + 0.294884i
\(415\) 0 0
\(416\) 0 0
\(417\) −14.6515 12.1793i −0.717485 0.596421i
\(418\) −40.5689 10.8704i −1.98429 0.531689i
\(419\) 14.1421 0.690889 0.345444 0.938439i \(-0.387728\pi\)
0.345444 + 0.938439i \(0.387728\pi\)
\(420\) 0 0
\(421\) −23.0000 −1.12095 −0.560476 0.828171i \(-0.689382\pi\)
−0.560476 + 0.828171i \(0.689382\pi\)
\(422\) 2.73205 + 0.732051i 0.132994 + 0.0356357i
\(423\) −1.32300 + 16.9189i −0.0643263 + 0.822626i
\(424\) 6.92820 + 4.00000i 0.336463 + 0.194257i
\(425\) 0 0
\(426\) 10.0000 + 14.1421i 0.484502 + 0.685189i
\(427\) −5.93426 + 8.76268i −0.287179 + 0.424056i
\(428\) 0 0
\(429\) −15.3742 + 33.3712i −0.742271 + 1.61118i
\(430\) 0 0
\(431\) 2.44949 + 1.41421i 0.117988 + 0.0681203i 0.557832 0.829954i \(-0.311633\pi\)
−0.439845 + 0.898074i \(0.644967\pi\)
\(432\) −0.287721 20.7826i −0.0138430 0.999904i
\(433\) 10.6066 10.6066i 0.509721 0.509721i −0.404720 0.914441i \(-0.632631\pi\)
0.914441 + 0.404720i \(0.132631\pi\)
\(434\) −3.53553 1.22474i −0.169711 0.0587896i
\(435\) 0 0
\(436\) 0 0
\(437\) 7.68653 + 28.6865i 0.367697 + 1.37226i
\(438\) −13.1856 10.9608i −0.630034 0.523727i
\(439\) −32.9090 + 19.0000i −1.57066 + 0.906821i −0.574571 + 0.818455i \(0.694831\pi\)
−0.996088 + 0.0883659i \(0.971836\pi\)
\(440\) 0 0
\(441\) 18.5959 + 9.75663i 0.885520 + 0.464601i
\(442\) 7.07107 + 7.07107i 0.336336 + 0.336336i
\(443\) −2.92820 + 10.9282i −0.139123 + 0.519215i 0.860824 + 0.508903i \(0.169949\pi\)
−0.999947 + 0.0103113i \(0.996718\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 12.2474 7.07107i 0.579934 0.334825i
\(447\) −14.4853 2.48528i −0.685130 0.117550i
\(448\) 19.0411 9.24316i 0.899608 0.436698i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) −15.0000 + 25.9808i −0.706322 + 1.22339i
\(452\) 0 0
\(453\) 3.59940 + 9.74907i 0.169115 + 0.458051i
\(454\) 18.0000i 0.844782i
\(455\) 0 0
\(456\) 28.0000 19.7990i 1.31122 0.927173i
\(457\) 7.50575 28.0118i 0.351104 1.31034i −0.534212 0.845350i \(-0.679392\pi\)
0.885317 0.464989i \(-0.153942\pi\)
\(458\) −4.09808 + 1.09808i −0.191491 + 0.0513097i
\(459\) 1.80348 7.12372i 0.0841794 0.332507i
\(460\) 0 0
\(461\) 7.07107i 0.329332i −0.986349 0.164666i \(-0.947345\pi\)
0.986349 0.164666i \(-0.0526547\pi\)
\(462\) −14.2261 23.5291i −0.661856 1.09467i
\(463\) −17.6777 + 17.6777i −0.821551 + 0.821551i −0.986330 0.164779i \(-0.947309\pi\)
0.164779 + 0.986330i \(0.447309\pi\)
\(464\) 14.1421 + 24.4949i 0.656532 + 1.13715i
\(465\) 0 0
\(466\) 2.00000 3.46410i 0.0926482 0.160471i
\(467\) −5.46410 1.46410i −0.252848 0.0677505i 0.130168 0.991492i \(-0.458448\pi\)
−0.383017 + 0.923741i \(0.625115\pi\)
\(468\) 0 0
\(469\) 1.73205 + 2.00000i 0.0799787 + 0.0923514i
\(470\) 0 0
\(471\) −2.89898 + 6.29253i −0.133578 + 0.289944i
\(472\) 3.86370 1.03528i 0.177841 0.0476524i
\(473\) −20.4904 + 5.49038i −0.942149 + 0.252448i
\(474\) −7.17461 + 15.5732i −0.329541 + 0.715301i
\(475\) 0 0
\(476\) 0 0
\(477\) 3.65685 + 7.65685i 0.167436 + 0.350583i
\(478\) 38.6370 + 10.3528i 1.76722 + 0.473524i
\(479\) −4.24264 + 7.34847i −0.193851 + 0.335760i −0.946523 0.322635i \(-0.895431\pi\)
0.752672 + 0.658396i \(0.228765\pi\)
\(480\) 0 0
\(481\) −2.50000 4.33013i −0.113990 0.197437i
\(482\) −24.0000 + 24.0000i −1.09317 + 1.09317i
\(483\) −9.37891 + 17.0304i −0.426755 + 0.774912i
\(484\) 0 0
\(485\) 0 0
\(486\) 12.2247 18.3455i 0.554526 0.832167i
\(487\) 28.0118 7.50575i 1.26934 0.340118i 0.439561 0.898213i \(-0.355134\pi\)
0.829777 + 0.558095i \(0.188467\pi\)
\(488\) −2.92820 + 10.9282i −0.132554 + 0.494697i
\(489\) −2.82843 + 2.00000i −0.127906 + 0.0904431i
\(490\) 0 0
\(491\) 14.1421i 0.638226i −0.947717 0.319113i \(-0.896615\pi\)
0.947717 0.319113i \(-0.103385\pi\)
\(492\) 0 0
\(493\) 2.58819 + 9.65926i 0.116566 + 0.435031i
\(494\) −24.7487 + 42.8661i −1.11350 + 1.92864i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) −16.8301 + 8.16987i −0.754934 + 0.366469i
\(498\) −3.41421 0.585786i −0.152995 0.0262497i
\(499\) 23.3827 13.5000i 1.04675 0.604343i 0.125014 0.992155i \(-0.460102\pi\)
0.921739 + 0.387812i \(0.126769\pi\)
\(500\) 0 0
\(501\) 1.57321 + 17.0741i 0.0702860 + 0.762815i
\(502\) −2.58819 + 9.65926i −0.115517 + 0.431114i
\(503\) −24.0000 24.0000i −1.07011 1.07011i −0.997350 0.0727574i \(-0.976820\pi\)
−0.0727574 0.997350i \(-0.523180\pi\)
\(504\) 22.1988 + 3.34847i 0.988814 + 0.149153i
\(505\) 0 0
\(506\) 22.0454 12.7279i 0.980038 0.565825i
\(507\) 15.9834 + 13.2865i 0.709848 + 0.590073i
\(508\) 0 0
\(509\) 4.24264 + 7.34847i 0.188052 + 0.325715i 0.944601 0.328222i \(-0.106449\pi\)
−0.756549 + 0.653937i \(0.773116\pi\)
\(510\) 0 0
\(511\) 14.0000 12.1244i 0.619324 0.536350i
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) 36.3696 0.503511i 1.60576 0.0222306i
\(514\) −15.5885 9.00000i −0.687577 0.396973i
\(515\) 0 0
\(516\) 0 0
\(517\) 16.9706 + 16.9706i 0.746364 + 0.746364i
\(518\) 3.73205 + 0.267949i 0.163977 + 0.0117730i
\(519\) 2.82843 + 4.00000i 0.124154 + 0.175581i
\(520\) 0 0
\(521\) 26.9444 + 15.5563i 1.18046 + 0.681536i 0.956120 0.292976i \(-0.0946456\pi\)
0.224335 + 0.974512i \(0.427979\pi\)
\(522\) −2.33875 + 29.9087i −0.102364 + 1.30907i
\(523\) 6.76148 + 1.81173i 0.295659 + 0.0792216i 0.403599 0.914936i \(-0.367759\pi\)
−0.107941 + 0.994157i \(0.534426\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) −1.36603 0.366025i −0.0595050 0.0159443i
\(528\) −22.6040 18.7899i −0.983711 0.817726i
\(529\) 4.33013 + 2.50000i 0.188266 + 0.108696i
\(530\) 0 0
\(531\) 4.00000 + 1.41421i 0.173585 + 0.0613716i
\(532\) 0 0
\(533\) 25.0000 + 25.0000i 1.08287 + 1.08287i
\(534\) −34.6089 15.9444i −1.49767 0.689981i
\(535\) 0 0
\(536\) 2.44949 + 1.41421i 0.105802 + 0.0610847i
\(537\) 11.8774 + 32.1703i 0.512549 + 1.38825i
\(538\) 5.65685 5.65685i 0.243884 0.243884i
\(539\) 27.5772 11.0227i 1.18783 0.474781i
\(540\) 0 0
\(541\) 5.50000 + 9.52628i 0.236463 + 0.409567i 0.959697 0.281037i \(-0.0906783\pi\)
−0.723234 + 0.690604i \(0.757345\pi\)
\(542\) −5.12436 19.1244i −0.220110 0.821461i
\(543\) 3.32162 3.99585i 0.142544 0.171478i
\(544\) 0 0
\(545\) 0 0
\(546\) −31.1237 + 9.01742i −1.33197 + 0.385910i
\(547\) 7.07107 + 7.07107i 0.302337 + 0.302337i 0.841928 0.539591i \(-0.181421\pi\)
−0.539591 + 0.841928i \(0.681421\pi\)
\(548\) 0 0
\(549\) −9.12096 + 7.79796i −0.389273 + 0.332809i
\(550\) 0 0
\(551\) −42.8661 + 24.7487i −1.82616 + 1.05433i
\(552\) −3.51472 + 20.4853i −0.149596 + 0.871911i
\(553\) −15.3347 10.3849i −0.652098 0.441613i
\(554\) 12.7279 0.540758
\(555\) 0 0
\(556\) 0 0
\(557\) 5.12436 + 19.1244i 0.217126 + 0.810325i 0.985407 + 0.170213i \(0.0544455\pi\)
−0.768281 + 0.640112i \(0.778888\pi\)
\(558\) −3.49768 2.40130i −0.148069 0.101655i
\(559\) 25.0000i 1.05739i
\(560\) 0 0
\(561\) −6.00000 8.48528i −0.253320 0.358249i
\(562\) −5.17638 + 19.3185i −0.218352 + 0.814902i
\(563\) −30.0526 + 8.05256i −1.26656 + 0.339375i −0.828714 0.559673i \(-0.810927\pi\)
−0.437851 + 0.899048i \(0.644260\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 32.5269i 1.36721i
\(567\) 17.4009 + 16.2545i 0.730770 + 0.682624i
\(568\) −14.1421 + 14.1421i −0.593391 + 0.593391i
\(569\) 0.707107 + 1.22474i 0.0296435 + 0.0513440i 0.880467 0.474108i \(-0.157229\pi\)
−0.850823 + 0.525452i \(0.823896\pi\)
\(570\) 0 0
\(571\) 0.500000 0.866025i 0.0209243 0.0362420i −0.855374 0.518012i \(-0.826672\pi\)
0.876298 + 0.481770i \(0.160006\pi\)
\(572\) 0 0
\(573\) 3.31371 19.3137i 0.138432 0.806842i
\(574\) −25.9808 + 5.00000i −1.08442 + 0.208696i
\(575\) 0 0
\(576\) 23.5959 4.38551i 0.983163 0.182729i
\(577\) −10.6252 + 2.84701i −0.442332 + 0.118523i −0.473109 0.881004i \(-0.656868\pi\)
0.0307771 + 0.999526i \(0.490202\pi\)
\(578\) 20.4904 5.49038i 0.852287 0.228370i
\(579\) 36.1820 + 16.6691i 1.50367 + 0.692745i
\(580\) 0 0
\(581\) 1.22474 3.53553i 0.0508110 0.146679i
\(582\) 24.1421 + 4.14214i 1.00072 + 0.171697i
\(583\) 11.5911 + 3.10583i 0.480055 + 0.128630i
\(584\) 9.89949 17.1464i 0.409644 0.709524i
\(585\) 0 0
\(586\) 16.0000 + 27.7128i 0.660954 + 1.14481i
\(587\) −13.0000 + 13.0000i −0.536567 + 0.536567i −0.922519 0.385952i \(-0.873873\pi\)
0.385952 + 0.922519i \(0.373873\pi\)
\(588\) 0 0
\(589\) 7.00000i 0.288430i
\(590\) 0 0
\(591\) −0.674235 7.31747i −0.0277343 0.301001i
\(592\) 3.86370 1.03528i 0.158797 0.0425496i
\(593\) −4.75833 + 17.7583i −0.195401 + 0.729247i 0.796761 + 0.604294i \(0.206545\pi\)
−0.992163 + 0.124953i \(0.960122\pi\)
\(594\) −8.48528 30.0000i −0.348155 1.23091i
\(595\) 0 0
\(596\) 0 0
\(597\) 3.24969 1.19980i 0.133001 0.0491046i
\(598\) −7.76457 28.9778i −0.317517 1.18499i
\(599\) 9.89949 17.1464i 0.404482 0.700584i −0.589779 0.807565i \(-0.700785\pi\)
0.994261 + 0.106981i \(0.0341184\pi\)
\(600\) 0 0
\(601\) 7.00000 0.285536 0.142768 0.989756i \(-0.454400\pi\)
0.142768 + 0.989756i \(0.454400\pi\)
\(602\) −15.4904 10.4904i −0.631341 0.427556i
\(603\) 1.29289 + 2.70711i 0.0526507 + 0.110242i
\(604\) 0 0
\(605\) 0 0
\(606\) −24.1464 + 2.22486i −0.980882 + 0.0903788i
\(607\) −10.6116 + 39.6030i −0.430711 + 1.60743i 0.320416 + 0.947277i \(0.396177\pi\)
−0.751127 + 0.660158i \(0.770489\pi\)
\(608\) 0 0
\(609\) −31.4626 7.75255i −1.27493 0.314149i
\(610\) 0 0
\(611\) 24.4949 14.1421i 0.990957 0.572130i
\(612\) 0 0
\(613\) 0.517638 + 1.93185i 0.0209072 + 0.0780268i 0.975591 0.219594i \(-0.0704734\pi\)
−0.954684 + 0.297621i \(0.903807\pi\)
\(614\) 10.6066 + 18.3712i 0.428048 + 0.741400i
\(615\) 0 0
\(616\) 24.0000 20.7846i 0.966988 0.837436i
\(617\) −8.00000 + 8.00000i −0.322068 + 0.322068i −0.849560 0.527492i \(-0.823132\pi\)
0.527492 + 0.849560i \(0.323132\pi\)
\(618\) 6.89363 2.54516i 0.277303 0.102381i
\(619\) 2.59808 + 1.50000i 0.104425 + 0.0602901i 0.551303 0.834305i \(-0.314131\pi\)
−0.446878 + 0.894595i \(0.647464\pi\)
\(620\) 0 0
\(621\) −15.3712 + 15.8028i −0.616824 + 0.634143i
\(622\) −32.5269 32.5269i −1.30421 1.30421i
\(623\) 23.0788 34.0788i 0.924634 1.36534i
\(624\) −28.2843 + 20.0000i −1.13228 + 0.800641i
\(625\) 0 0
\(626\) 20.8207 + 12.0208i 0.832161 + 0.480448i
\(627\) 32.8824 39.5569i 1.31319 1.57975i
\(628\) 0 0
\(629\) 1.41421 0.0563884
\(630\) 0 0
\(631\) 12.0000 0.477712 0.238856 0.971055i \(-0.423228\pi\)
0.238856 + 0.971055i \(0.423228\pi\)
\(632\) −19.1244 5.12436i −0.760726 0.203836i
\(633\) −2.21441 + 2.66390i −0.0880150 + 0.105881i
\(634\) 1.73205 + 1.00000i 0.0687885 + 0.0397151i
\(635\) 0 0
\(636\) 0 0
\(637\) −4.13613 34.7547i −0.163879 1.37703i
\(638\) 30.0000 + 30.0000i 1.18771 + 1.18771i
\(639\) −20.8560 + 3.87628i −0.825052 + 0.153343i
\(640\) 0 0
\(641\) 8.57321 + 4.94975i 0.338622 + 0.195503i 0.659662 0.751562i \(-0.270699\pi\)
−0.321041 + 0.947065i \(0.604033\pi\)
\(642\) −35.7466 + 13.1978i −1.41080 + 0.520876i
\(643\) 17.6777 17.6777i 0.697139 0.697139i −0.266653 0.963793i \(-0.585918\pi\)
0.963793 + 0.266653i \(0.0859179\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −7.00000 12.1244i −0.275411 0.477026i
\(647\) −0.366025 1.36603i −0.0143899 0.0537040i 0.958358 0.285571i \(-0.0921832\pi\)
−0.972747 + 0.231867i \(0.925517\pi\)
\(648\) 23.2655 + 10.3305i 0.913954 + 0.405819i
\(649\) 5.19615 3.00000i 0.203967 0.117760i
\(650\) 0 0
\(651\) 3.17423 3.30518i 0.124408 0.129540i
\(652\) 0 0
\(653\) 9.88269 36.8827i 0.386739 1.44333i −0.448667 0.893699i \(-0.648101\pi\)
0.835407 0.549632i \(-0.185232\pi\)
\(654\) 41.4657 3.82066i 1.62144 0.149400i
\(655\) 0 0
\(656\) −24.4949 + 14.1421i −0.956365 + 0.552158i
\(657\) 18.9497 9.05025i 0.739300 0.353084i
\(658\) −1.51575 + 21.1117i −0.0590901 + 0.823018i
\(659\) −28.2843 −1.10180 −0.550899 0.834572i \(-0.685715\pi\)
−0.550899 + 0.834572i \(0.685715\pi\)
\(660\) 0 0
\(661\) −9.50000 + 16.4545i −0.369507 + 0.640005i −0.989489 0.144611i \(-0.953807\pi\)
0.619981 + 0.784617i \(0.287140\pi\)
\(662\) 0.366025 + 1.36603i 0.0142260 + 0.0530921i
\(663\) −11.4894 + 4.24194i −0.446211 + 0.164743i
\(664\) 4.00000i 0.155230i
\(665\) 0 0
\(666\) 4.00000 + 1.41421i 0.154997 + 0.0547997i
\(667\) 7.76457 28.9778i 0.300645 1.12202i
\(668\) 0 0
\(669\) 1.58919 + 17.2474i 0.0614415 + 0.666825i
\(670\) 0 0
\(671\) 16.9706i 0.655141i
\(672\) 0 0
\(673\) −17.6777 + 17.6777i −0.681424 + 0.681424i −0.960321 0.278897i \(-0.910031\pi\)
0.278897 + 0.960321i \(0.410031\pi\)
\(674\) −3.53553 6.12372i −0.136184 0.235877i
\(675\) 0 0
\(676\) 0 0
\(677\) 42.3468 + 11.3468i 1.62752 + 0.436092i 0.953198 0.302346i \(-0.0977698\pi\)
0.674321 + 0.738438i \(0.264436\pi\)
\(678\) 47.7990 + 8.20101i 1.83571 + 0.314958i
\(679\) −8.66025 + 25.0000i −0.332350 + 0.959412i
\(680\) 0 0
\(681\) −20.0227 9.22450i −0.767272 0.353483i
\(682\) −5.79555 + 1.55291i −0.221923 + 0.0594642i
\(683\) −23.2224 + 6.22243i −0.888582 + 0.238095i −0.674106 0.738635i \(-0.735471\pi\)
−0.214476 + 0.976729i \(0.568804\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 23.2702 + 12.0208i 0.888459 + 0.458957i
\(687\) 0.878680 5.12132i 0.0335237 0.195391i
\(688\) −19.3185 5.17638i −0.736512 0.197348i
\(689\) 7.07107 12.2474i 0.269386 0.466591i
\(690\) 0 0
\(691\) −14.5000 25.1147i −0.551606 0.955410i −0.998159 0.0606524i \(-0.980682\pi\)
0.446553 0.894757i \(-0.352651\pi\)
\(692\) 0 0
\(693\) 33.4636 3.76666i 1.27118 0.143084i
\(694\) 32.0000i 1.21470i
\(695\) 0 0
\(696\) −34.4949 + 3.17837i −1.30753 + 0.120476i
\(697\) −9.65926 + 2.58819i −0.365870 + 0.0980347i
\(698\) −9.51666 + 35.5167i −0.360211 + 1.34433i
\(699\) 2.82843 + 4.00000i 0.106981 + 0.151294i
\(700\) 0 0
\(701\) 21.2132i 0.801212i 0.916250 + 0.400606i \(0.131200\pi\)
−0.916250 + 0.400606i \(0.868800\pi\)
\(702\) −36.7388 + 0.508623i −1.38662 + 0.0191967i
\(703\) 1.81173 + 6.76148i 0.0683308 + 0.255014i
\(704\) 16.9706 29.3939i 0.639602 1.10782i
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 1.87564 26.1244i 0.0705409 0.982508i
\(708\) 0 0
\(709\) 27.7128 16.0000i 1.04078 0.600893i 0.120723 0.992686i \(-0.461479\pi\)
0.920053 + 0.391794i \(0.128145\pi\)
\(710\) 0 0
\(711\) −13.6464 15.9617i −0.511781 0.598609i
\(712\) 11.3880 42.5007i 0.426785 1.59278i
\(713\) 3.00000 + 3.00000i 0.112351 + 0.112351i
\(714\) 2.19275 8.89898i 0.0820617 0.333036i
\(715\) 0 0
\(716\) 0 0
\(717\) −31.3165 + 37.6733i −1.16954 + 1.40693i
\(718\) 0.517638 + 1.93185i 0.0193181 + 0.0720961i
\(719\) −9.89949 17.1464i −0.369189 0.639454i 0.620250 0.784404i \(-0.287031\pi\)
−0.989439 + 0.144950i \(0.953698\pi\)
\(720\) 0 0
\(721\) 1.50000 + 7.79423i 0.0558629 + 0.290272i
\(722\) 30.0000 30.0000i 1.11648 1.11648i
\(723\) −14.3976 38.9963i −0.535453 1.45029i
\(724\) 0 0
\(725\) 0 0
\(726\) −15.5732 7.17461i −0.577976 0.266275i
\(727\) −17.6777 17.6777i −0.655628 0.655628i 0.298714 0.954343i \(-0.403442\pi\)
−0.954343 + 0.298714i \(0.903442\pi\)
\(728\) −16.3397 33.6603i −0.605591 1.24753i
\(729\) 14.1421 + 23.0000i 0.523783 + 0.851852i
\(730\) 0 0
\(731\) −6.12372 3.53553i −0.226494 0.130766i
\(732\) 0 0
\(733\) −31.8756 8.54103i −1.17735 0.315470i −0.383475 0.923551i \(-0.625273\pi\)
−0.793875 + 0.608081i \(0.791940\pi\)
\(734\) −29.6985 −1.09619
\(735\) 0 0
\(736\) 0 0
\(737\) 4.09808 + 1.09808i 0.150955 + 0.0404482i
\(738\) −29.9087 2.33875i −1.10095 0.0860906i
\(739\) −6.06218 3.50000i −0.223001 0.128750i 0.384338 0.923192i \(-0.374430\pi\)
−0.607339 + 0.794443i \(0.707763\pi\)
\(740\) 0 0
\(741\) −35.0000 49.4975i −1.28576 1.81834i
\(742\) 4.62158 + 9.52056i 0.169663 + 0.349511i
\(743\) 11.0000 + 11.0000i 0.403551 + 0.403551i 0.879482 0.475931i \(-0.157889\pi\)
−0.475931 + 0.879482i \(0.657889\pi\)
\(744\) 2.04989 4.44949i 0.0751525 0.163126i
\(745\) 0 0
\(746\) −28.1691 16.2635i −1.03135 0.595447i
\(747\) 2.40130 3.49768i 0.0878590 0.127973i
\(748\) 0 0
\(749\) −7.77817 40.4166i −0.284208 1.47679i
\(750\) 0 0
\(751\) −19.5000 33.7750i −0.711565 1.23247i −0.964269 0.264923i \(-0.914653\pi\)
0.252704 0.967544i \(-0.418680\pi\)
\(752\) 5.85641 + 21.8564i 0.213561 + 0.797021i
\(753\) −9.41832 7.82913i −0.343223 0.285309i
\(754\) 43.3013 25.0000i 1.57694 0.910446i
\(755\) 0 0
\(756\) 0 0
\(757\) −14.1421 14.1421i −0.514005 0.514005i 0.401746 0.915751i \(-0.368403\pi\)
−0.915751 + 0.401746i \(0.868403\pi\)
\(758\) 3.29423 12.2942i 0.119652 0.446546i
\(759\) 2.86054 + 31.0454i 0.103831 + 1.12688i
\(760\) 0 0
\(761\) 20.8207 12.0208i 0.754748 0.435754i −0.0726586 0.997357i \(-0.523148\pi\)
0.827407 + 0.561603i \(0.189815\pi\)
\(762\) 36.2132 + 6.21320i 1.31187 + 0.225081i
\(763\) −3.22097 + 44.8623i −0.116607 + 1.62412i
\(764\) 0 0
\(765\) 0 0
\(766\) 12.0000 20.7846i 0.433578 0.750978i
\(767\) −1.83013 6.83013i −0.0660821 0.246622i
\(768\) 0 0
\(769\) 29.0000i 1.04577i −0.852404 0.522883i \(-0.824856\pi\)
0.852404 0.522883i \(-0.175144\pi\)
\(770\) 0 0
\(771\) 18.0000 12.7279i 0.648254 0.458385i
\(772\) 0 0
\(773\) 17.7583 4.75833i 0.638723 0.171145i 0.0750979 0.997176i \(-0.476073\pi\)
0.563625 + 0.826031i \(0.309406\pi\)
\(774\) −13.7850 16.1237i −0.495491 0.579555i
\(775\) 0 0
\(776\) 28.2843i 1.01535i
\(777\) −2.21063 + 4.01411i −0.0793059 + 0.144006i
\(778\) −29.6985 + 29.6985i −1.06474 + 1.06474i
\(779\) −24.7487 42.8661i −0.886716 1.53584i
\(780\) 0 0
\(781\) −15.0000 + 25.9808i −0.536742 + 0.929665i
\(782\) 8.19615 + 2.19615i 0.293094 + 0.0785343i
\(783\) −32.0711 17.9289i −1.14613 0.640728i
\(784\) 27.7128 + 4.00000i 0.989743 + 0.142857i
\(785\) 0 0
\(786\) −17.3939 + 37.7552i −0.620419 + 1.34668i
\(787\) −25.1141 + 6.72930i −0.895220 + 0.239873i −0.676962 0.736018i \(-0.736704\pi\)
−0.218258 + 0.975891i \(0.570037\pi\)
\(788\) 0 0
\(789\) 12.2993 26.6969i 0.437868 0.950436i
\(790\) 0 0
\(791\) −17.1464 + 49.4975i −0.609657 + 1.75993i
\(792\) 32.4853 15.5147i 1.15431 0.551292i
\(793\) 19.3185 + 5.17638i 0.686021 + 0.183819i
\(794\) −0.707107 + 1.22474i −0.0250943 + 0.0434646i
\(795\) 0 0
\(796\) 0 0
\(797\) 17.0000 17.0000i 0.602171 0.602171i −0.338717 0.940888i \(-0.609993\pi\)
0.940888 + 0.338717i \(0.109993\pi\)
\(798\) 45.3559 0.916639i 1.60558 0.0324487i
\(799\) 8.00000i 0.283020i
\(800\) 0 0
\(801\) 35.4722 30.3269i 1.25335 1.07155i
\(802\) −34.7733 + 9.31749i −1.22789 + 0.329012i
\(803\) 7.68653 28.6865i 0.271252 1.01233i
\(804\) 0 0
\(805\) 0 0
\(806\) 7.07107i 0.249068i
\(807\) 3.39355 + 9.19151i 0.119459 + 0.323556i
\(808\) −7.24693 27.0459i −0.254946 0.951472i
\(809\) 9.89949 17.1464i 0.348048 0.602836i −0.637855 0.770157i \(-0.720178\pi\)
0.985903 + 0.167320i \(0.0535114\pi\)
\(810\) 0 0
\(811\) −18.0000 −0.632065 −0.316033 0.948748i \(-0.602351\pi\)
−0.316033 + 0.948748i \(0.602351\pi\)
\(812\) 0 0
\(813\) 23.8995 + 4.10051i 0.838192 + 0.143811i
\(814\) 5.19615 3.00000i 0.182125 0.105150i
\(815\) 0 0
\(816\) −0.898979 9.75663i −0.0314706 0.341550i
\(817\) 9.05867 33.8074i 0.316923 1.18277i
\(818\) −37.0000 37.0000i −1.29367 1.29367i
\(819\) 5.91931 39.2423i 0.206838 1.37124i
\(820\) 0 0
\(821\) −15.9217 + 9.19239i −0.555671 + 0.320817i −0.751406 0.659840i \(-0.770624\pi\)
0.195735 + 0.980657i \(0.437291\pi\)
\(822\) 29.3029 + 24.3585i 1.02206 + 0.849602i
\(823\) −7.24693 27.0459i −0.252612 0.942762i −0.969403 0.245474i \(-0.921057\pi\)
0.716791 0.697288i \(-0.245610\pi\)
\(824\) 4.24264 + 7.34847i 0.147799 + 0.255996i
\(825\) 0 0
\(826\) 5.00000 + 1.73205i 0.173972 + 0.0602658i
\(827\) −18.0000 + 18.0000i −0.625921 + 0.625921i −0.947039 0.321118i \(-0.895941\pi\)
0.321118 + 0.947039i \(0.395941\pi\)
\(828\) 0 0
\(829\) −6.06218 3.50000i −0.210548 0.121560i 0.391018 0.920383i \(-0.372123\pi\)
−0.601566 + 0.798823i \(0.705456\pi\)
\(830\) 0 0
\(831\) −6.52270 + 14.1582i −0.226270 + 0.491142i
\(832\) −28.2843 28.2843i −0.980581 0.980581i
\(833\) 9.09808 + 3.90192i 0.315230 + 0.135194i
\(834\) −15.5563 22.0000i −0.538672 0.761798i
\(835\) 0 0
\(836\) 0 0
\(837\) 4.46360 2.66012i 0.154285 0.0919472i
\(838\) 19.3185 + 5.17638i 0.667347 + 0.178815i
\(839\) 35.3553 1.22060 0.610301 0.792170i \(-0.291049\pi\)
0.610301 + 0.792170i \(0.291049\pi\)
\(840\) 0 0
\(841\) 21.0000 0.724138
\(842\) −31.4186 8.41858i −1.08276 0.290124i
\(843\) −18.8366 15.6583i −0.648768 0.539299i
\(844\) 0 0
\(845\) 0 0
\(846\) −8.00000 + 22.6274i −0.275046 + 0.777947i
\(847\) 10.3849 15.3347i 0.356831 0.526906i
\(848\) 8.00000 + 8.00000i 0.274721 + 0.274721i
\(849\) 36.1820 + 16.6691i 1.24176 + 0.572083i
\(850\) 0 0
\(851\) −3.67423 2.12132i −0.125951 0.0727179i
\(852\) 0 0
\(853\) −38.8909 + 38.8909i −1.33160 + 1.33160i −0.427657 + 0.903941i \(0.640661\pi\)
−0.903941 + 0.427657i \(0.859339\pi\)
\(854\) −11.3137 + 9.79796i −0.387147 + 0.335279i
\(855\) 0 0
\(856\) −22.0000 38.1051i −0.751945 1.30241i
\(857\) −7.68653 28.6865i −0.262567 0.979913i −0.963723 0.266905i \(-0.913999\pi\)
0.701156 0.713008i \(-0.252668\pi\)
\(858\) −33.2162 + 39.9585i −1.13398 + 1.36416i
\(859\) 19.0526 11.0000i 0.650065 0.375315i −0.138416 0.990374i \(-0.544201\pi\)
0.788481 + 0.615059i \(0.210868\pi\)
\(860\) 0 0
\(861\) 7.75255 31.4626i 0.264206 1.07224i
\(862\) 2.82843 + 2.82843i 0.0963366 + 0.0963366i
\(863\) −10.2487 + 38.2487i −0.348870 + 1.30200i 0.539155 + 0.842207i \(0.318744\pi\)
−0.888025 + 0.459795i \(0.847923\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 18.3712 10.6066i 0.624278 0.360427i
\(867\) −4.39340 + 25.6066i −0.149208 + 0.869646i
\(868\) 0 0
\(869\) −29.6985 −1.00745
\(870\) 0 0
\(871\) 2.50000 4.33013i 0.0847093 0.146721i
\(872\) 12.4449 + 46.4449i 0.421436 + 1.57282i
\(873\) −16.9798 + 24.7323i −0.574678 + 0.837062i
\(874\) 42.0000i 1.42067i
\(875\) 0 0
\(876\) 0 0
\(877\) 6.21166 23.1822i 0.209753 0.782808i −0.778195 0.628022i \(-0.783865\pi\)
0.987948 0.154786i \(-0.0494687\pi\)
\(878\) −51.9090 + 13.9090i −1.75184 + 0.469405i
\(879\) −39.0265 + 3.59592i −1.31633 + 0.121287i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 21.8313 + 20.1344i 0.735099 + 0.677960i
\(883\) −10.6066 + 10.6066i −0.356941 + 0.356941i −0.862684 0.505743i \(-0.831218\pi\)
0.505743 + 0.862684i \(0.331218\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −8.00000 + 13.8564i −0.268765 + 0.465515i
\(887\) 28.6865 + 7.68653i 0.963200 + 0.258089i 0.705954 0.708258i \(-0.250518\pi\)
0.257245 + 0.966346i \(0.417185\pi\)
\(888\) −0.828427 + 4.82843i −0.0278002 + 0.162031i
\(889\) −12.9904 + 37.5000i −0.435683 + 1.25771i
\(890\) 0 0
\(891\) 37.7196 + 5.93537i 1.26366 + 0.198842i
\(892\) 0 0
\(893\) −38.2487 + 10.2487i −1.27994 + 0.342960i
\(894\) −18.8776 8.69694i −0.631361 0.290869i
\(895\) 0 0
\(896\) 29.3939 5.65685i 0.981981 0.188982i
\(897\) 36.2132 + 6.21320i 1.20912 + 0.207453i
\(898\) 0 0
\(899\) −3.53553 + 6.12372i −0.117917 + 0.204238i
\(900\) 0 0
\(901\) 2.00000 + 3.46410i 0.0666297 + 0.115406i
\(902\) −30.0000 + 30.0000i −0.998891 + 0.998891i
\(903\) 19.6076 11.8550i 0.652500 0.394511i
\(904\) 56.0000i 1.86253i
\(905\) 0 0
\(906\) 1.34847 + 14.6349i 0.0447999 + 0.486213i
\(907\) −49.2622 + 13.1998i −1.63573 + 0.438291i −0.955567 0.294774i \(-0.904756\pi\)
−0.680158 + 0.733065i \(0.738089\pi\)
\(908\) 0 0
\(909\) 9.89949 28.0000i 0.328346 0.928701i
\(910\) 0 0
\(911\) 35.3553i 1.17137i −0.810537 0.585687i \(-0.800825\pi\)
0.810537 0.585687i \(-0.199175\pi\)
\(912\) 45.4956 16.7972i 1.50651 0.556211i
\(913\) −1.55291 5.79555i −0.0513940 0.191805i
\(914\) 20.5061 35.5176i 0.678281 1.17482i
\(915\) 0 0
\(916\) 0 0
\(917\) −37.1769 25.1769i −1.22769 0.831415i
\(918\) 5.07107 9.07107i 0.167370 0.299390i
\(919\) −11.2583 + 6.50000i −0.371378 + 0.214415i −0.674060 0.738676i \(-0.735451\pi\)
0.302682 + 0.953092i \(0.402118\pi\)
\(920\) 0 0
\(921\) −25.8712 + 2.38378i −0.852484 + 0.0785482i
\(922\) 2.58819 9.65926i 0.0852375 0.318111i
\(923\) 25.0000 + 25.0000i 0.822885 + 0.822885i
\(924\) 0 0
\(925\) 0 0
\(926\) −30.6186 + 17.6777i −1.00619 + 0.580924i
\(927\) −0.701625 + 8.97261i −0.0230444 + 0.294699i
\(928\) 0 0
\(929\) 7.77817 + 13.4722i 0.255194 + 0.442008i 0.964948 0.262441i \(-0.0845275\pi\)
−0.709754 + 0.704449i \(0.751194\pi\)
\(930\) 0 0
\(931\) −7.00000 + 48.4974i −0.229416 + 1.58944i
\(932\) 0 0
\(933\) 52.8512 19.5129i 1.73027 0.638824i
\(934\) −6.92820 4.00000i −0.226698 0.130884i
\(935\) 0 0
\(936\) −7.75255 41.7121i −0.253400 1.36340i
\(937\) 10.6066 + 10.6066i 0.346503 + 0.346503i 0.858805 0.512302i \(-0.171207\pi\)
−0.512302 + 0.858805i \(0.671207\pi\)
\(938\) 1.63397 + 3.36603i 0.0533512 + 0.109905i
\(939\) −24.0416 + 17.0000i −0.784569 + 0.554774i
\(940\) 0 0
\(941\) −15.9217 9.19239i −0.519032 0.299663i 0.217506 0.976059i \(-0.430208\pi\)
−0.736539 + 0.676396i \(0.763541\pi\)
\(942\) −6.26330 + 7.53465i −0.204070 + 0.245492i
\(943\) 28.9778 + 7.76457i 0.943646 + 0.252849i
\(944\) 5.65685 0.184115
\(945\) 0 0
\(946\) −30.0000 −0.975384
\(947\) 15.0263 + 4.02628i 0.488288 + 0.130837i 0.494559 0.869144i \(-0.335329\pi\)
−0.00627092 + 0.999980i \(0.501996\pi\)
\(948\) 0 0
\(949\) −30.3109 17.5000i −0.983933 0.568074i
\(950\) 0 0
\(951\) −2.00000 + 1.41421i −0.0648544 + 0.0458590i
\(952\) 10.5558 + 0.757875i 0.342117 + 0.0245629i
\(953\) 36.0000 + 36.0000i 1.16615 + 1.16615i 0.983103 + 0.183051i \(0.0585973\pi\)
0.183051 + 0.983103i \(0.441403\pi\)
\(954\) 2.19275 + 11.7980i 0.0709930 + 0.381973i
\(955\) 0 0
\(956\) 0 0
\(957\) −48.7453 + 17.9970i −1.57571 + 0.581761i
\(958\) −8.48528 + 8.48528i −0.274147 + 0.274147i
\(959\) −31.1127 + 26.9444i −1.00468 + 0.870080i
\(960\) 0 0
\(961\) 15.0000 + 25.9808i 0.483871 + 0.838089i
\(962\) −1.83013 6.83013i −0.0590057 0.220212i
\(963\) 3.63824 46.5270i 0.117241 1.49931i
\(964\) 0 0
\(965\) 0 0
\(966\) −19.0454 + 19.8311i −0.612776 + 0.638055i
\(967\) 24.7487 + 24.7487i 0.795866 + 0.795866i 0.982441 0.186575i \(-0.0597387\pi\)
−0.186575 + 0.982441i \(0.559739\pi\)
\(968\) 5.12436 19.1244i 0.164703 0.614680i
\(969\) 17.0741 1.57321i 0.548499 0.0505389i
\(970\) 0 0
\(971\) 39.1918 22.6274i 1.25773 0.726148i 0.285094 0.958500i \(-0.407975\pi\)
0.972632 + 0.232351i \(0.0746419\pi\)
\(972\) 0 0
\(973\) 26.1815 12.7093i 0.839341 0.407443i
\(974\) 41.0122 1.31412
\(975\) 0 0
\(976\) −8.00000 + 13.8564i −0.256074 + 0.443533i
\(977\) −4.02628 15.0263i −0.128812 0.480733i 0.871135 0.491044i \(-0.163385\pi\)
−0.999947 + 0.0103108i \(0.996718\pi\)
\(978\) −4.59575 + 1.69677i −0.146956 + 0.0542569i
\(979\) 66.0000i 2.10937i
\(980\) 0 0
\(981\) −17.0000 + 48.0833i −0.542768 + 1.53518i
\(982\) 5.17638 19.3185i 0.165185 0.616479i
\(983\) −36.8827 + 9.88269i −1.17637 + 0.315209i −0.793488 0.608586i \(-0.791737\pi\)
−0.382887 + 0.923795i \(0.625070\pi\)
\(984\) −3.17837 34.4949i −0.101323 1.09966i
\(985\) 0 0
\(986\) 14.1421i 0.450377i
\(987\) −22.7073 12.5052i −0.722780 0.398045i
\(988\) 0 0
\(989\) 10.6066 + 18.3712i 0.337270 + 0.584169i
\(990\) 0 0
\(991\) 20.5000 35.5070i 0.651204 1.12792i −0.331627 0.943411i \(-0.607598\pi\)
0.982831 0.184508i \(-0.0590691\pi\)
\(992\) 0 0
\(993\) −1.70711 0.292893i −0.0541734 0.00929469i
\(994\) −25.9808 + 5.00000i −0.824060 + 0.158590i
\(995\) 0 0
\(996\) 0 0
\(997\) 37.6711 10.0939i 1.19306 0.319678i 0.392963 0.919554i \(-0.371450\pi\)
0.800093 + 0.599876i \(0.204783\pi\)
\(998\) 36.8827 9.88269i 1.16750 0.312831i
\(999\) −3.62302 + 3.72474i −0.114627 + 0.117846i
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 525.2.bf.d.32.2 yes 8
3.2 odd 2 525.2.bf.a.32.2 yes 8
5.2 odd 4 inner 525.2.bf.d.368.2 yes 8
5.3 odd 4 525.2.bf.a.368.1 yes 8
5.4 even 2 525.2.bf.a.32.1 8
7.2 even 3 inner 525.2.bf.d.107.1 yes 8
15.2 even 4 525.2.bf.a.368.2 yes 8
15.8 even 4 inner 525.2.bf.d.368.1 yes 8
15.14 odd 2 inner 525.2.bf.d.32.1 yes 8
21.2 odd 6 525.2.bf.a.107.1 yes 8
35.2 odd 12 inner 525.2.bf.d.443.1 yes 8
35.9 even 6 525.2.bf.a.107.2 yes 8
35.23 odd 12 525.2.bf.a.443.2 yes 8
105.2 even 12 525.2.bf.a.443.1 yes 8
105.23 even 12 inner 525.2.bf.d.443.2 yes 8
105.44 odd 6 inner 525.2.bf.d.107.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.bf.a.32.1 8 5.4 even 2
525.2.bf.a.32.2 yes 8 3.2 odd 2
525.2.bf.a.107.1 yes 8 21.2 odd 6
525.2.bf.a.107.2 yes 8 35.9 even 6
525.2.bf.a.368.1 yes 8 5.3 odd 4
525.2.bf.a.368.2 yes 8 15.2 even 4
525.2.bf.a.443.1 yes 8 105.2 even 12
525.2.bf.a.443.2 yes 8 35.23 odd 12
525.2.bf.d.32.1 yes 8 15.14 odd 2 inner
525.2.bf.d.32.2 yes 8 1.1 even 1 trivial
525.2.bf.d.107.1 yes 8 7.2 even 3 inner
525.2.bf.d.107.2 yes 8 105.44 odd 6 inner
525.2.bf.d.368.1 yes 8 15.8 even 4 inner
525.2.bf.d.368.2 yes 8 5.2 odd 4 inner
525.2.bf.d.443.1 yes 8 35.2 odd 12 inner
525.2.bf.d.443.2 yes 8 105.23 even 12 inner