Properties

Label 525.2.bf.a.107.1
Level $525$
Weight $2$
Character 525.107
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 107.1
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 525.107
Dual form 525.2.bf.a.368.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.366025 + 1.36603i) q^{2} +(-1.33195 + 1.10721i) q^{3} +(-2.00000 - 1.41421i) q^{6} +(-2.38014 - 1.15539i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.548188 - 2.94949i) q^{9} +O(q^{10})\) \(q+(0.366025 + 1.36603i) q^{2} +(-1.33195 + 1.10721i) q^{3} +(-2.00000 - 1.41421i) q^{6} +(-2.38014 - 1.15539i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.548188 - 2.94949i) q^{9} +(-3.67423 + 2.12132i) q^{11} +(-3.53553 + 3.53553i) q^{13} +(0.707107 - 3.67423i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-1.36603 - 0.366025i) q^{17} +(4.22973 - 0.330749i) q^{18} +(-6.06218 - 3.50000i) q^{19} +(4.44949 - 1.09638i) q^{21} +(-4.24264 - 4.24264i) q^{22} +(-4.09808 + 1.09808i) q^{23} +(-4.87832 - 0.449490i) q^{24} +(-6.12372 - 3.53553i) q^{26} +(2.53553 + 4.53553i) q^{27} +7.07107 q^{29} +(0.500000 + 0.866025i) q^{31} +(2.54516 - 6.89363i) q^{33} -2.00000i q^{34} +(0.965926 - 0.258819i) q^{37} +(2.56218 - 9.56218i) q^{38} +(0.794593 - 8.62372i) q^{39} +7.07107i q^{41} +(3.12630 + 5.67681i) q^{42} +(3.53553 - 3.53553i) q^{43} +(-3.00000 - 5.19615i) q^{46} +(-1.46410 - 5.46410i) q^{47} +(-1.17157 - 6.82843i) q^{48} +(4.33013 + 5.50000i) q^{49} +(2.22474 - 1.02494i) q^{51} +(-0.732051 + 2.73205i) q^{53} +(-5.26758 + 5.12372i) q^{54} +(-2.44949 - 7.07107i) q^{56} +(11.9497 - 2.05025i) q^{57} +(2.58819 + 9.65926i) q^{58} +(0.707107 + 1.22474i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(-1.00000 + 1.00000i) q^{62} +(-4.71259 + 6.38682i) q^{63} +8.00000i q^{64} +(10.3485 + 0.953512i) q^{66} +(0.258819 - 0.965926i) q^{67} +(4.24264 - 6.00000i) q^{69} +7.07107i q^{71} +(6.99536 - 4.80260i) q^{72} +(-6.76148 - 1.81173i) q^{73} +(0.707107 + 1.22474i) q^{74} +(11.1962 - 0.803848i) q^{77} +(12.0711 - 2.07107i) q^{78} +(-6.06218 - 3.50000i) q^{79} +(-8.39898 - 3.23375i) q^{81} +(-9.65926 + 2.58819i) q^{82} +(-1.00000 - 1.00000i) q^{83} +(6.12372 + 3.53553i) q^{86} +(-9.41832 + 7.82913i) q^{87} +(-11.5911 - 3.10583i) q^{88} +(-7.77817 + 13.4722i) q^{89} +(12.5000 - 4.33013i) q^{91} +(-1.62484 - 0.599900i) q^{93} +(6.92820 - 4.00000i) q^{94} +(-7.07107 - 7.07107i) q^{97} +(-5.92820 + 7.92820i) q^{98} +(4.24264 + 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} + 4 q^{3} - 16 q^{6} + 16 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 + 1.36603i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) −1.33195 + 1.10721i −0.769002 + 0.639246i
\(4\) 0 0
\(5\) 0 0
\(6\) −2.00000 1.41421i −0.816497 0.577350i
\(7\) −2.38014 1.15539i −0.899608 0.436698i
\(8\) 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 −0.938265 0.345918i \(-0.887568\pi\)
−0.169559 + 0.985520i \(0.554234\pi\)
\(12\) 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
\(17\) −1.36603 0.366025i −0.331310 0.0887742i 0.0893296 0.996002i \(-0.471528\pi\)
−0.420639 + 0.907228i \(0.638194\pi\)
\(18\) 4.22973 0.330749i 0.996957 0.0779583i
\(19\) −6.06218 3.50000i −1.39076 0.802955i −0.397360 0.917663i \(-0.630073\pi\)
−0.993399 + 0.114708i \(0.963407\pi\)
\(20\) 0 0
\(21\) 4.44949 1.09638i 0.970958 0.239249i
\(22\) −4.24264 4.24264i −0.904534 0.904534i
\(23\) −4.09808 + 1.09808i −0.854508 + 0.228965i −0.659377 0.751812i \(-0.729180\pi\)
−0.195131 + 0.980777i \(0.562513\pi\)
\(24\) −4.87832 0.449490i −0.995782 0.0917517i
\(25\) 0 0
\(26\) −6.12372 3.53553i −1.20096 0.693375i
\(27\) 2.53553 + 4.53553i 0.487964 + 0.872864i
\(28\) 0 0
\(29\) 7.07107 1.31306 0.656532 0.754298i \(-0.272023\pi\)
0.656532 + 0.754298i \(0.272023\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) 0 0
\(33\) 2.54516 6.89363i 0.443056 1.20003i
\(34\) 2.00000i 0.342997i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.965926 0.258819i 0.158797 0.0425496i −0.178545 0.983932i \(-0.557139\pi\)
0.337342 + 0.941382i \(0.390472\pi\)
\(38\) 2.56218 9.56218i 0.415640 1.55119i
\(39\) 0.794593 8.62372i 0.127237 1.38090i
\(40\) 0 0
\(41\) 7.07107i 1.10432i 0.833740 + 0.552158i \(0.186195\pi\)
−0.833740 + 0.552158i \(0.813805\pi\)
\(42\) 3.12630 + 5.67681i 0.482399 + 0.875951i
\(43\) 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
\(47\) −1.46410 5.46410i −0.213561 0.797021i −0.986668 0.162745i \(-0.947965\pi\)
0.773107 0.634276i \(-0.218702\pi\)
\(48\) −1.17157 6.82843i −0.169102 0.985599i
\(49\) 4.33013 + 5.50000i 0.618590 + 0.785714i
\(50\) 0 0
\(51\) 2.22474 1.02494i 0.311527 0.143521i
\(52\) 0 0
\(53\) −0.732051 + 2.73205i −0.100555 + 0.375276i −0.997803 0.0662507i \(-0.978896\pi\)
0.897248 + 0.441527i \(0.145563\pi\)
\(54\) −5.26758 + 5.12372i −0.716827 + 0.697251i
\(55\) 0 0
\(56\) −2.44949 7.07107i −0.327327 0.944911i
\(57\) 11.9497 2.05025i 1.58278 0.271563i
\(58\) 2.58819 + 9.65926i 0.339846 + 1.26832i
\(59\) 0.707107 + 1.22474i 0.0920575 + 0.159448i 0.908377 0.418153i \(-0.137322\pi\)
−0.816319 + 0.577601i \(0.803989\pi\)
\(60\) 0 0
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) −1.00000 + 1.00000i −0.127000 + 0.127000i
\(63\) −4.71259 + 6.38682i −0.593730 + 0.804664i
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 10.3485 + 0.953512i 1.27381 + 0.117369i
\(67\) 0.258819 0.965926i 0.0316198 0.118007i −0.948312 0.317339i \(-0.897211\pi\)
0.979932 + 0.199332i \(0.0638774\pi\)
\(68\) 0 0
\(69\) 4.24264 6.00000i 0.510754 0.722315i
\(70\) 0 0
\(71\) 7.07107i 0.839181i 0.907713 + 0.419591i \(0.137826\pi\)
−0.907713 + 0.419591i \(0.862174\pi\)
\(72\) 6.99536 4.80260i 0.824411 0.565992i
\(73\) −6.76148 1.81173i −0.791371 0.212047i −0.159579 0.987185i \(-0.551014\pi\)
−0.631792 + 0.775138i \(0.717680\pi\)
\(74\) 0.707107 + 1.22474i 0.0821995 + 0.142374i
\(75\) 0 0
\(76\) 0 0
\(77\) 11.1962 0.803848i 1.27592 0.0916069i
\(78\) 12.0711 2.07107i 1.36678 0.234502i
\(79\) −6.06218 3.50000i −0.682048 0.393781i 0.118578 0.992945i \(-0.462166\pi\)
−0.800626 + 0.599164i \(0.795500\pi\)
\(80\) 0 0
\(81\) −8.39898 3.23375i −0.933220 0.359306i
\(82\) −9.65926 + 2.58819i −1.06669 + 0.285818i
\(83\) −1.00000 1.00000i −0.109764 0.109764i 0.650092 0.759856i \(-0.274731\pi\)
−0.759856 + 0.650092i \(0.774731\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.12372 + 3.53553i 0.660338 + 0.381246i
\(87\) −9.41832 + 7.82913i −1.00975 + 0.839371i
\(88\) −11.5911 3.10583i −1.23562 0.331082i
\(89\) −7.77817 + 13.4722i −0.824485 + 1.42805i 0.0778275 + 0.996967i \(0.475202\pi\)
−0.902312 + 0.431083i \(0.858132\pi\)
\(90\) 0 0
\(91\) 12.5000 4.33013i 1.31036 0.453921i
\(92\) 0 0
\(93\) −1.62484 0.599900i −0.168489 0.0622068i
\(94\) 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 \(0.919494\pi\)
\(98\) −5.92820 + 7.92820i −0.598839 + 0.800869i
\(99\) 4.24264 + 12.0000i 0.426401 + 1.20605i
\(100\) 0 0
\(101\) 8.57321 4.94975i 0.853067 0.492518i −0.00861771 0.999963i \(-0.502743\pi\)
0.861684 + 0.507445i \(0.169410\pi\)
\(102\) 2.21441 + 2.66390i 0.219260 + 0.263766i
\(103\) 0.776457 + 2.89778i 0.0765066 + 0.285526i 0.993571 0.113213i \(-0.0361143\pi\)
−0.917064 + 0.398740i \(0.869448\pi\)
\(104\) −14.1421 −1.38675
\(105\) 0 0
\(106\) −4.00000 −0.388514
\(107\) 4.02628 + 15.0263i 0.389235 + 1.45265i 0.831381 + 0.555702i \(0.187551\pi\)
−0.442146 + 0.896943i \(0.645783\pi\)
\(108\) 0 0
\(109\) 14.7224 8.50000i 1.41015 0.814152i 0.414751 0.909935i \(-0.363869\pi\)
0.995402 + 0.0957826i \(0.0305354\pi\)
\(110\) 0 0
\(111\) −1.00000 + 1.41421i −0.0949158 + 0.134231i
\(112\) 8.76268 5.93426i 0.827996 0.560734i
\(113\) 14.0000 + 14.0000i 1.31701 + 1.31701i 0.916132 + 0.400878i \(0.131295\pi\)
0.400878 + 0.916132i \(0.368705\pi\)
\(114\) 7.17461 + 15.5732i 0.671964 + 1.45857i
\(115\) 0 0
\(116\) 0 0
\(117\) 8.48988 + 12.3662i 0.784890 + 1.14325i
\(118\) −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
\(122\) −5.46410 1.46410i −0.494697 0.132554i
\(123\) −7.82913 9.41832i −0.705929 0.849221i
\(124\) 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 \(0.981789\pi\)
\(128\) −10.9282 + 2.92820i −0.965926 + 0.258819i
\(129\) −0.794593 + 8.62372i −0.0699600 + 0.759277i
\(130\) 0 0
\(131\) 14.6969 + 8.48528i 1.28408 + 0.741362i 0.977591 0.210513i \(-0.0675133\pi\)
0.306486 + 0.951875i \(0.400847\pi\)
\(132\) 0 0
\(133\) 10.3849 + 15.3347i 0.900489 + 1.32969i
\(134\) 1.41421 0.122169
\(135\) 0 0
\(136\) −2.00000 3.46410i −0.171499 0.297044i
\(137\) −15.0263 4.02628i −1.28378 0.343988i −0.448486 0.893790i \(-0.648037\pi\)
−0.835295 + 0.549801i \(0.814703\pi\)
\(138\) 9.74907 + 3.59940i 0.829896 + 0.306401i
\(139\) 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
\(142\) −9.65926 + 2.58819i −0.810587 + 0.217196i
\(143\) 5.49038 20.4904i 0.459129 1.71349i
\(144\) 9.12096 + 7.79796i 0.760080 + 0.649830i
\(145\) 0 0
\(146\) 9.89949i 0.819288i
\(147\) −11.8572 2.53139i −0.977961 0.208785i
\(148\) 0 0
\(149\) −4.24264 + 7.34847i −0.347571 + 0.602010i −0.985817 0.167822i \(-0.946327\pi\)
0.638247 + 0.769832i \(0.279660\pi\)
\(150\) 0 0
\(151\) 3.00000 + 5.19615i 0.244137 + 0.422857i 0.961888 0.273442i \(-0.0881622\pi\)
−0.717752 + 0.696299i \(0.754829\pi\)
\(152\) −5.12436 19.1244i −0.415640 1.55119i
\(153\) −1.82843 + 3.82843i −0.147820 + 0.309510i
\(154\) 5.19615 + 15.0000i 0.418718 + 1.20873i
\(155\) 0 0
\(156\) 0 0
\(157\) −1.03528 + 3.86370i −0.0826240 + 0.308357i −0.994854 0.101322i \(-0.967693\pi\)
0.912230 + 0.409679i \(0.134359\pi\)
\(158\) 2.56218 9.56218i 0.203836 0.760726i
\(159\) −2.04989 4.44949i −0.162567 0.352867i
\(160\) 0 0
\(161\) 11.0227 + 2.12132i 0.868711 + 0.167183i
\(162\) 1.34315 12.6569i 0.105527 0.994416i
\(163\) −0.517638 1.93185i −0.0405445 0.151314i 0.942686 0.333681i \(-0.108291\pi\)
−0.983231 + 0.182367i \(0.941624\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.00000 1.73205i 0.0776151 0.134433i
\(167\) −7.00000 + 7.00000i −0.541676 + 0.541676i −0.924020 0.382344i \(-0.875117\pi\)
0.382344 + 0.924020i \(0.375117\pi\)
\(168\) 11.0917 + 6.70623i 0.855746 + 0.517397i
\(169\) 12.0000i 0.923077i
\(170\) 0 0
\(171\) −13.6464 + 15.9617i −1.04357 + 1.22062i
\(172\) 0 0
\(173\) 2.73205 0.732051i 0.207714 0.0556568i −0.153462 0.988155i \(-0.549042\pi\)
0.361176 + 0.932498i \(0.382375\pi\)
\(174\) −14.1421 10.0000i −1.07211 0.758098i
\(175\) 0 0
\(176\) 16.9706i 1.27920i
\(177\) −2.29788 0.848387i −0.172719 0.0637687i
\(178\) −21.2504 5.69402i −1.59278 0.426785i
\(179\) −9.89949 17.1464i −0.739923 1.28158i −0.952529 0.304446i \(-0.901529\pi\)
0.212607 0.977138i \(-0.431805\pi\)
\(180\) 0 0
\(181\) −3.00000 −0.222988 −0.111494 0.993765i \(-0.535564\pi\)
−0.111494 + 0.993765i \(0.535564\pi\)
\(182\) 10.4904 + 15.4904i 0.777599 + 1.14822i
\(183\) −1.17157 6.82843i −0.0866052 0.504772i
\(184\) −10.3923 6.00000i −0.766131 0.442326i
\(185\) 0 0
\(186\) 0.224745 2.43916i 0.0164791 0.178848i
\(187\) 5.79555 1.55291i 0.423813 0.113560i
\(188\) 0 0
\(189\) −0.794593 13.7247i −0.0577981 0.998328i
\(190\) 0 0
\(191\) −9.79796 5.65685i −0.708955 0.409316i 0.101719 0.994813i \(-0.467566\pi\)
−0.810674 + 0.585498i \(0.800899\pi\)
\(192\) −8.85765 10.6556i −0.639246 0.769002i
\(193\) 22.2163 + 5.95284i 1.59916 + 0.428495i 0.944790 0.327677i \(-0.106266\pi\)
0.654374 + 0.756171i \(0.272932\pi\)
\(194\) 7.07107 12.2474i 0.507673 0.879316i
\(195\) 0 0
\(196\) 0 0
\(197\) 3.00000 3.00000i 0.213741 0.213741i −0.592113 0.805855i \(-0.701706\pi\)
0.805855 + 0.592113i \(0.201706\pi\)
\(198\) −14.8394 + 10.1879i −1.05459 + 0.724020i
\(199\) 1.73205 1.00000i 0.122782 0.0708881i −0.437351 0.899291i \(-0.644083\pi\)
0.560133 + 0.828403i \(0.310750\pi\)
\(200\) 0 0
\(201\) 0.724745 + 1.57313i 0.0511196 + 0.110960i
\(202\) 9.89949 + 9.89949i 0.696526 + 0.696526i
\(203\) −16.8301 8.16987i −1.18124 0.573413i
\(204\) 0 0
\(205\) 0 0
\(206\) −3.67423 + 2.12132i −0.255996 + 0.147799i
\(207\) 0.992248 + 12.6892i 0.0689660 + 0.881959i
\(208\) −5.17638 19.3185i −0.358917 1.33950i
\(209\) 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
\(213\) −7.82913 9.41832i −0.536443 0.645332i
\(214\) −19.0526 + 11.0000i −1.30241 + 0.751945i
\(215\) 0 0
\(216\) −4.00000 + 14.1421i −0.272166 + 0.962250i
\(217\) −0.189469 2.63896i −0.0128620 0.179144i
\(218\) 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
\(222\) −2.29788 0.848387i −0.154223 0.0569400i
\(223\) 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
\(227\) 12.2942 + 3.29423i 0.815997 + 0.218646i 0.642595 0.766206i \(-0.277858\pi\)
0.173401 + 0.984851i \(0.444524\pi\)
\(228\) 0 0
\(229\) 2.59808 + 1.50000i 0.171686 + 0.0991228i 0.583380 0.812199i \(-0.301730\pi\)
−0.411695 + 0.911322i \(0.635063\pi\)
\(230\) 0 0
\(231\) −14.0227 + 13.4671i −0.922626 + 0.886073i
\(232\) 14.1421 + 14.1421i 0.928477 + 0.928477i
\(233\) 2.73205 0.732051i 0.178983 0.0479582i −0.168215 0.985750i \(-0.553800\pi\)
0.347197 + 0.937792i \(0.387133\pi\)
\(234\) −13.7850 + 16.1237i −0.901152 + 1.05404i
\(235\) 0 0
\(236\) 0 0
\(237\) 11.9497 2.05025i 0.776220 0.133178i
\(238\) −2.31079 + 4.76028i −0.149786 + 0.308563i
\(239\) −28.2843 −1.82956 −0.914779 0.403955i \(-0.867635\pi\)
−0.914779 + 0.403955i \(0.867635\pi\)
\(240\) 0 0
\(241\) −12.0000 20.7846i −0.772988 1.33885i −0.935918 0.352217i \(-0.885428\pi\)
0.162930 0.986638i \(-0.447905\pi\)
\(242\) 9.56218 + 2.56218i 0.614680 + 0.164703i
\(243\) 14.7675 4.99221i 0.947333 0.320250i
\(244\) 0 0
\(245\) 0 0
\(246\) 10.0000 14.1421i 0.637577 0.901670i
\(247\) 33.8074 9.05867i 2.15111 0.576389i
\(248\) −0.732051 + 2.73205i −0.0464853 + 0.173485i
\(249\) 2.43916 + 0.224745i 0.154575 + 0.0142426i
\(250\) 0 0
\(251\) 7.07107i 0.446322i −0.974782 0.223161i \(-0.928362\pi\)
0.974782 0.223161i \(-0.0716375\pi\)
\(252\) 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
\(257\) −3.29423 12.2942i −0.205488 0.766893i −0.989300 0.145894i \(-0.953394\pi\)
0.783812 0.620998i \(-0.213273\pi\)
\(258\) −12.0711 + 2.07107i −0.751512 + 0.128939i
\(259\) −2.59808 0.500000i −0.161437 0.0310685i
\(260\) 0 0
\(261\) 3.87628 20.8560i 0.239935 1.29096i
\(262\) −6.21166 + 23.1822i −0.383757 + 1.43220i
\(263\) −4.39230 + 16.3923i −0.270841 + 1.01079i 0.687736 + 0.725961i \(0.258605\pi\)
−0.958577 + 0.284832i \(0.908062\pi\)
\(264\) 18.8776 8.69694i 1.16184 0.535260i
\(265\) 0 0
\(266\) −17.1464 + 19.7990i −1.05131 + 1.21395i
\(267\) −4.55635 26.5563i −0.278844 1.62522i
\(268\) 0 0
\(269\) −2.82843 4.89898i −0.172452 0.298696i 0.766824 0.641857i \(-0.221836\pi\)
−0.939277 + 0.343161i \(0.888502\pi\)
\(270\) 0 0
\(271\) −7.00000 + 12.1244i −0.425220 + 0.736502i −0.996441 0.0842940i \(-0.973137\pi\)
0.571221 + 0.820796i \(0.306470\pi\)
\(272\) 4.00000 4.00000i 0.242536 0.242536i
\(273\) −11.8550 + 19.6076i −0.717500 + 1.18671i
\(274\) 22.0000i 1.32907i
\(275\) 0 0
\(276\) 0 0
\(277\) −2.32937 + 8.69333i −0.139958 + 0.522332i 0.859970 + 0.510345i \(0.170482\pi\)
−0.999928 + 0.0119868i \(0.996184\pi\)
\(278\) −15.0263 + 4.02628i −0.901216 + 0.241480i
\(279\) 2.82843 1.00000i 0.169334 0.0598684i
\(280\) 0 0
\(281\) 14.1421i 0.843649i −0.906677 0.421825i \(-0.861390\pi\)
0.906677 0.421825i \(-0.138610\pi\)
\(282\) −4.79920 + 12.9988i −0.285788 + 0.774065i
\(283\) 22.2163 + 5.95284i 1.32062 + 0.353859i 0.849211 0.528054i \(-0.177078\pi\)
0.471411 + 0.881914i \(0.343745\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 30.0000 1.77394
\(287\) 8.16987 16.8301i 0.482252 0.993451i
\(288\) 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 0.0632667 0.997997i \(-0.479848\pi\)
−0.997997 + 0.0632667i \(0.979848\pi\)
\(294\) −0.882079 17.1237i −0.0514439 0.998676i
\(295\) 0 0
\(296\) 2.44949 + 1.41421i 0.142374 + 0.0821995i
\(297\) −18.9375 11.2859i −1.09886 0.654876i
\(298\) −11.5911 3.10583i −0.671455 0.179916i
\(299\) 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
\(303\) −5.93871 + 16.0851i −0.341170 + 0.924067i
\(304\) 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 −0.605325 + 0.795979i \(0.706957\pi\)
−0.992000 + 0.126237i \(0.959710\pi\)
\(312\) 18.8366 15.6583i 1.06641 0.886475i
\(313\) −4.39992 16.4207i −0.248698 0.928155i −0.971488 0.237087i \(-0.923807\pi\)
0.722790 0.691068i \(-0.242859\pi\)
\(314\) −5.65685 −0.319235
\(315\) 0 0
\(316\) 0 0
\(317\) 0.366025 + 1.36603i 0.0205580 + 0.0767236i 0.975443 0.220253i \(-0.0706883\pi\)
−0.954885 + 0.296977i \(0.904022\pi\)
\(318\) 5.32780 4.42883i 0.298768 0.248356i
\(319\) −25.9808 + 15.0000i −1.45464 + 0.839839i
\(320\) 0 0
\(321\) −22.0000 15.5563i −1.22792 0.868271i
\(322\) 1.13681 + 15.8338i 0.0633521 + 0.882380i
\(323\) 7.00000 + 7.00000i 0.389490 + 0.389490i
\(324\) 0 0
\(325\) 0 0
\(326\) 2.44949 1.41421i 0.135665 0.0783260i
\(327\) −10.1983 + 27.6224i −0.563968 + 1.52752i
\(328\) −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 −0.851957 0.523612i \(-0.824584\pi\)
0.879440 + 0.476011i \(0.157918\pi\)
\(332\) 0 0
\(333\) −0.233875 2.99087i −0.0128163 0.163899i
\(334\) −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 \(0.793484\pi\)
\(338\) 16.3923 4.39230i 0.891624 0.238910i
\(339\) −34.1482 3.14643i −1.85468 0.170891i
\(340\) 0 0
\(341\) −3.67423 2.12132i −0.198971 0.114876i
\(342\) −26.7990 12.7990i −1.44912 0.692090i
\(343\) −3.95164 18.0938i −0.213368 0.976972i
\(344\) 14.1421 0.762493
\(345\) 0 0
\(346\) 2.00000 + 3.46410i 0.107521 + 0.186231i
\(347\) −21.8564 5.85641i −1.17331 0.314388i −0.381042 0.924558i \(-0.624435\pi\)
−0.792271 + 0.610169i \(0.791101\pi\)
\(348\) 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
\(353\) 1.09808 4.09808i 0.0584447 0.218119i −0.930527 0.366223i \(-0.880651\pi\)
0.988972 + 0.148105i \(0.0473173\pi\)
\(354\) 0.317837 3.44949i 0.0168929 0.183338i
\(355\) 0 0
\(356\) 0 0
\(357\) −6.47942 0.130948i −0.342927 0.00693052i
\(358\) 19.7990 19.7990i 1.04641 1.04641i
\(359\) −0.707107 + 1.22474i −0.0373197 + 0.0646396i −0.884082 0.467332i \(-0.845215\pi\)
0.846762 + 0.531971i \(0.178549\pi\)
\(360\) 0 0
\(361\) 15.0000 + 25.9808i 0.789474 + 1.36741i
\(362\) −1.09808 4.09808i −0.0577136 0.215390i
\(363\) 2.05025 + 11.9497i 0.107610 + 0.627199i
\(364\) 0 0
\(365\) 0 0
\(366\) 8.89898 4.09978i 0.465157 0.214299i
\(367\) 5.43520 20.2844i 0.283715 1.05884i −0.666058 0.745900i \(-0.732020\pi\)
0.949773 0.312939i \(-0.101314\pi\)
\(368\) 4.39230 16.3923i 0.228965 0.854508i
\(369\) 20.8560 + 3.87628i 1.08572 + 0.201791i
\(370\) 0 0
\(371\) 4.89898 5.65685i 0.254342 0.293689i
\(372\) 0 0
\(373\) 5.95284 + 22.2163i 0.308226 + 1.15032i 0.930132 + 0.367224i \(0.119692\pi\)
−0.621906 + 0.783092i \(0.713641\pi\)
\(374\) 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
\(378\) 18.4575 6.10904i 0.949352 0.314215i
\(379\) 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
\(382\) 4.14110 15.4548i 0.211877 0.790737i
\(383\) 16.3923 4.39230i 0.837608 0.224436i 0.185578 0.982630i \(-0.440584\pi\)
0.652030 + 0.758193i \(0.273918\pi\)
\(384\) 11.3137 16.0000i 0.577350 0.816497i
\(385\) 0 0
\(386\) 32.5269i 1.65558i
\(387\) −8.48988 12.3662i −0.431565 0.628607i
\(388\) 0 0
\(389\) 14.8492 + 25.7196i 0.752886 + 1.30404i 0.946418 + 0.322944i \(0.104672\pi\)
−0.193532 + 0.981094i \(0.561994\pi\)
\(390\) 0 0
\(391\) 6.00000 0.303433
\(392\) −2.33975 + 19.6603i −0.118175 + 0.992993i
\(393\) −28.9706 + 4.97056i −1.46137 + 0.250732i
\(394\) 5.19615 + 3.00000i 0.261778 + 0.151138i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.965926 0.258819i 0.0484784 0.0129898i −0.234498 0.972117i \(-0.575345\pi\)
0.282977 + 0.959127i \(0.408678\pi\)
\(398\) 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 −0.164439 0.986387i \(-0.552581\pi\)
−0.936456 + 0.350785i \(0.885915\pi\)
\(402\) −1.88366 + 1.56583i −0.0939486 + 0.0780963i
\(403\) −4.82963 1.29410i −0.240581 0.0644635i
\(404\) 0 0
\(405\) 0 0
\(406\) 5.00000 25.9808i 0.248146 1.28940i
\(407\) −3.00000 + 3.00000i −0.148704 + 0.148704i
\(408\) 6.49938 + 2.39960i 0.321767 + 0.118798i
\(409\) 32.0429 18.5000i 1.58442 0.914766i 0.590219 0.807243i \(-0.299041\pi\)
0.994203 0.107523i \(-0.0342919\pi\)
\(410\) 0 0
\(411\) 24.4722 11.2744i 1.20712 0.556124i
\(412\) 0 0
\(413\) −0.267949 3.73205i −0.0131849 0.183642i
\(414\) −16.9706 + 6.00000i −0.834058 + 0.294884i
\(415\) 0 0
\(416\) 0 0
\(417\) −12.1793 14.6515i −0.596421 0.717485i
\(418\) 10.8704 + 40.5689i 0.531689 + 1.98429i
\(419\) −14.1421 −0.690889 −0.345444 0.938439i \(-0.612272\pi\)
−0.345444 + 0.938439i \(0.612272\pi\)
\(420\) 0 0
\(421\) −23.0000 −1.12095 −0.560476 0.828171i \(-0.689382\pi\)
−0.560476 + 0.828171i \(0.689382\pi\)
\(422\) 0.732051 + 2.73205i 0.0356357 + 0.132994i
\(423\) −16.9189 + 1.32300i −0.822626 + 0.0643263i
\(424\) −6.92820 + 4.00000i −0.336463 + 0.194257i
\(425\) 0 0
\(426\) 10.0000 14.1421i 0.484502 0.685189i
\(427\) 8.76268 5.93426i 0.424056 0.287179i
\(428\) 0 0
\(429\) 15.3742 + 33.3712i 0.742271 + 1.61118i
\(430\) 0 0
\(431\) 2.44949 1.41421i 0.117988 0.0681203i −0.439845 0.898074i \(-0.644967\pi\)
0.557832 + 0.829954i \(0.311633\pi\)
\(432\) −20.7826 0.287721i −0.999904 0.0138430i
\(433\) 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
\(437\) 28.6865 + 7.68653i 1.37226 + 0.367697i
\(438\) 10.9608 + 13.1856i 0.523727 + 0.630034i
\(439\) 32.9090 + 19.0000i 1.57066 + 0.906821i 0.996088 + 0.0883659i \(0.0281645\pi\)
0.574571 + 0.818455i \(0.305169\pi\)
\(440\) 0 0
\(441\) 18.5959 9.75663i 0.885520 0.464601i
\(442\) 7.07107 + 7.07107i 0.336336 + 0.336336i
\(443\) −10.9282 + 2.92820i −0.519215 + 0.139123i −0.508903 0.860824i \(-0.669949\pi\)
−0.0103113 + 0.999947i \(0.503282\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 12.2474 + 7.07107i 0.579934 + 0.334825i
\(447\) −2.48528 14.4853i −0.117550 0.685130i
\(448\) 9.24316 19.0411i 0.436698 0.899608i
\(449\) 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
\(453\) −9.74907 3.59940i −0.458051 0.169115i
\(454\) 18.0000i 0.844782i
\(455\) 0 0
\(456\) 28.0000 + 19.7990i 1.31122 + 0.927173i
\(457\) −28.0118 + 7.50575i −1.31034 + 0.351104i −0.845350 0.534212i \(-0.820608\pi\)
−0.464989 + 0.885317i \(0.653942\pi\)
\(458\) −1.09808 + 4.09808i −0.0513097 + 0.191491i
\(459\) −1.80348 7.12372i −0.0841794 0.332507i
\(460\) 0 0
\(461\) 7.07107i 0.329332i 0.986349 + 0.164666i \(0.0526547\pi\)
−0.986349 + 0.164666i \(0.947345\pi\)
\(462\) −23.5291 14.2261i −1.09467 0.661856i
\(463\) −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
\(467\) −1.46410 5.46410i −0.0677505 0.252848i 0.923741 0.383017i \(-0.125115\pi\)
−0.991492 + 0.130168i \(0.958448\pi\)
\(468\) 0 0
\(469\) −1.73205 + 2.00000i −0.0799787 + 0.0923514i
\(470\) 0 0
\(471\) −2.89898 6.29253i −0.133578 0.289944i
\(472\) −1.03528 + 3.86370i −0.0476524 + 0.177841i
\(473\) −5.49038 + 20.4904i −0.252448 + 0.942149i
\(474\) 7.17461 + 15.5732i 0.329541 + 0.715301i
\(475\) 0 0
\(476\) 0 0
\(477\) 7.65685 + 3.65685i 0.350583 + 0.167436i
\(478\) −10.3528 38.6370i −0.473524 1.76722i
\(479\) 4.24264 + 7.34847i 0.193851 + 0.335760i 0.946523 0.322635i \(-0.104569\pi\)
−0.752672 + 0.658396i \(0.771235\pi\)
\(480\) 0 0
\(481\) −2.50000 + 4.33013i −0.113990 + 0.197437i
\(482\) 24.0000 24.0000i 1.09317 1.09317i
\(483\) −17.0304 + 9.37891i −0.774912 + 0.426755i
\(484\) 0 0
\(485\) 0 0
\(486\) 12.2247 + 18.3455i 0.554526 + 0.832167i
\(487\) −7.50575 + 28.0118i −0.340118 + 1.26934i 0.558095 + 0.829777i \(0.311533\pi\)
−0.898213 + 0.439561i \(0.855134\pi\)
\(488\) −10.9282 + 2.92820i −0.494697 + 0.132554i
\(489\) 2.82843 + 2.00000i 0.127906 + 0.0904431i
\(490\) 0 0
\(491\) 14.1421i 0.638226i 0.947717 + 0.319113i \(0.103385\pi\)
−0.947717 + 0.319113i \(0.896615\pi\)
\(492\) 0 0
\(493\) −9.65926 2.58819i −0.435031 0.116566i
\(494\) 24.7487 + 42.8661i 1.11350 + 1.92864i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 8.16987 16.8301i 0.366469 0.754934i
\(498\) 0.585786 + 3.41421i 0.0262497 + 0.152995i
\(499\) −23.3827 13.5000i −1.04675 0.604343i −0.125014 0.992155i \(-0.539898\pi\)
−0.921739 + 0.387812i \(0.873231\pi\)
\(500\) 0 0
\(501\) 1.57321 17.0741i 0.0702860 0.762815i
\(502\) 9.65926 2.58819i 0.431114 0.115517i
\(503\) 24.0000 + 24.0000i 1.07011 + 1.07011i 0.997350 + 0.0727574i \(0.0231799\pi\)
0.0727574 + 0.997350i \(0.476820\pi\)
\(504\) −22.1988 + 3.34847i −0.988814 + 0.149153i
\(505\) 0 0
\(506\) 22.0454 + 12.7279i 0.980038 + 0.565825i
\(507\) 13.2865 + 15.9834i 0.590073 + 0.709848i
\(508\) 0 0
\(509\) −4.24264 + 7.34847i −0.188052 + 0.325715i −0.944601 0.328222i \(-0.893551\pi\)
0.756549 + 0.653937i \(0.226884\pi\)
\(510\) 0 0
\(511\) 14.0000 + 12.1244i 0.619324 + 0.536350i
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) 0.503511 36.3696i 0.0222306 1.60576i
\(514\) 15.5885 9.00000i 0.687577 0.396973i
\(515\) 0 0
\(516\) 0 0
\(517\) 16.9706 + 16.9706i 0.746364 + 0.746364i
\(518\) −0.267949 3.73205i −0.0117730 0.163977i
\(519\) −2.82843 + 4.00000i −0.124154 + 0.175581i
\(520\) 0 0
\(521\) 26.9444 15.5563i 1.18046 0.681536i 0.224335 0.974512i \(-0.427979\pi\)
0.956120 + 0.292976i \(0.0946456\pi\)
\(522\) 29.9087 2.33875i 1.30907 0.102364i
\(523\) −1.81173 6.76148i −0.0792216 0.295659i 0.914936 0.403599i \(-0.132241\pi\)
−0.994157 + 0.107941i \(0.965574\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) −0.366025 1.36603i −0.0159443 0.0595050i
\(528\) 18.7899 + 22.6040i 0.817726 + 0.983711i
\(529\) −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
\(537\) 32.1703 + 11.8774i 1.38825 + 0.512549i
\(538\) 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 −0.723234 0.690604i \(-0.757345\pi\)
0.959697 + 0.281037i \(0.0906783\pi\)
\(542\) −19.1244 5.12436i −0.821461 0.220110i
\(543\) 3.99585 3.32162i 0.171478 0.142544i
\(544\) 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
\(552\) 20.4853 3.51472i 0.871911 0.149596i
\(553\) 10.3849 + 15.3347i 0.441613 + 0.652098i
\(554\) −12.7279 −0.540758
\(555\) 0 0
\(556\) 0 0
\(557\) 19.1244 + 5.12436i 0.810325 + 0.217126i 0.640112 0.768281i \(-0.278888\pi\)
0.170213 + 0.985407i \(0.445555\pi\)
\(558\) 2.40130 + 3.49768i 0.101655 + 0.148069i
\(559\) 25.0000i 1.05739i
\(560\) 0 0
\(561\) −6.00000 + 8.48528i −0.253320 + 0.358249i
\(562\) 19.3185 5.17638i 0.814902 0.218352i
\(563\) −8.05256 + 30.0526i −0.339375 + 1.26656i 0.559673 + 0.828714i \(0.310927\pi\)
−0.899048 + 0.437851i \(0.855740\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 32.5269i 1.36721i
\(567\) 16.2545 + 17.4009i 0.682624 + 0.730770i
\(568\) −14.1421 + 14.1421i −0.593391 + 0.593391i
\(569\) −0.707107 + 1.22474i −0.0296435 + 0.0513440i −0.880467 0.474108i \(-0.842771\pi\)
0.850823 + 0.525452i \(0.176104\pi\)
\(570\) 0 0
\(571\) 0.500000 + 0.866025i 0.0209243 + 0.0362420i 0.876298 0.481770i \(-0.160006\pi\)
−0.855374 + 0.518012i \(0.826672\pi\)
\(572\) 0 0
\(573\) 19.3137 3.31371i 0.806842 0.138432i
\(574\) 25.9808 + 5.00000i 1.08442 + 0.208696i
\(575\) 0 0
\(576\) 23.5959 + 4.38551i 0.983163 + 0.182729i
\(577\) 2.84701 10.6252i 0.118523 0.442332i −0.881004 0.473109i \(-0.843132\pi\)
0.999526 + 0.0307771i \(0.00979822\pi\)
\(578\) 5.49038 20.4904i 0.228370 0.852287i
\(579\) −36.1820 + 16.6691i −1.50367 + 0.692745i
\(580\) 0 0
\(581\) 1.22474 + 3.53553i 0.0508110 + 0.146679i
\(582\) 4.14214 + 24.1421i 0.171697 + 1.00072i
\(583\) −3.10583 11.5911i −0.128630 0.480055i
\(584\) −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 −0.385952 0.922519i \(-0.626127\pi\)
0.922519 + 0.385952i \(0.126127\pi\)
\(588\) 0 0
\(589\) 7.00000i 0.288430i
\(590\) 0 0
\(591\) −0.674235 + 7.31747i −0.0277343 + 0.301001i
\(592\) −1.03528 + 3.86370i −0.0425496 + 0.158797i
\(593\) −17.7583 + 4.75833i −0.729247 + 0.195401i −0.604294 0.796761i \(-0.706545\pi\)
−0.124953 + 0.992163i \(0.539878\pi\)
\(594\) 8.48528 30.0000i 0.348155 1.23091i
\(595\) 0 0
\(596\) 0 0
\(597\) −1.19980 + 3.24969i −0.0491046 + 0.133001i
\(598\) 28.9778 + 7.76457i 1.18499 + 0.317517i
\(599\) −9.89949 17.1464i −0.404482 0.700584i 0.589779 0.807565i \(-0.299215\pi\)
−0.994261 + 0.106981i \(0.965882\pi\)
\(600\) 0 0
\(601\) 7.00000 0.285536 0.142768 0.989756i \(-0.454400\pi\)
0.142768 + 0.989756i \(0.454400\pi\)
\(602\) −10.4904 15.4904i −0.427556 0.631341i
\(603\) −2.70711 1.29289i −0.110242 0.0526507i
\(604\) 0 0
\(605\) 0 0
\(606\) −24.1464 2.22486i −0.980882 0.0903788i
\(607\) 39.6030 10.6116i 1.60743 0.430711i 0.660158 0.751127i \(-0.270489\pi\)
0.947277 + 0.320416i \(0.103823\pi\)
\(608\) 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
\(613\) −1.93185 0.517638i −0.0780268 0.0209072i 0.219594 0.975591i \(-0.429527\pi\)
−0.297621 + 0.954684i \(0.596193\pi\)
\(614\) −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 −0.527492 0.849560i \(-0.676868\pi\)
0.849560 + 0.527492i \(0.176868\pi\)
\(618\) 2.54516 6.89363i 0.102381 0.277303i
\(619\) −2.59808 + 1.50000i −0.104425 + 0.0602901i −0.551303 0.834305i \(-0.685869\pi\)
0.446878 + 0.894595i \(0.352536\pi\)
\(620\) 0 0
\(621\) −15.3712 15.8028i −0.616824 0.634143i
\(622\) −32.5269 32.5269i −1.30421 1.30421i
\(623\) 34.0788 23.0788i 1.36534 0.924634i
\(624\) 28.2843 + 20.0000i 1.13228 + 0.800641i
\(625\) 0 0
\(626\) 20.8207 12.0208i 0.832161 0.480448i
\(627\) −39.5569 + 32.8824i −1.57975 + 1.31319i
\(628\) 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 \(0.423228\pi\)
\(632\) −5.12436 19.1244i −0.203836 0.760726i
\(633\) −2.66390 + 2.21441i −0.105881 + 0.0880150i
\(634\) −1.73205 + 1.00000i −0.0687885 + 0.0397151i
\(635\) 0 0
\(636\) 0 0
\(637\) −34.7547 4.13613i −1.37703 0.163879i
\(638\) −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 −0.321041 0.947065i \(-0.604033\pi\)
0.659662 + 0.751562i \(0.270699\pi\)
\(642\) 13.1978 35.7466i 0.520876 1.41080i
\(643\) 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
\(647\) −1.36603 0.366025i −0.0537040 0.0143899i 0.231867 0.972747i \(-0.425517\pi\)
−0.285571 + 0.958358i \(0.592183\pi\)
\(648\) −10.3305 23.2655i −0.405819 0.913954i
\(649\) −5.19615 3.00000i −0.203967 0.117760i
\(650\) 0 0
\(651\) 3.17423 + 3.30518i 0.124408 + 0.129540i
\(652\) 0 0
\(653\) 36.8827 9.88269i 1.44333 0.386739i 0.549632 0.835407i \(-0.314768\pi\)
0.893699 + 0.448667i \(0.148101\pi\)
\(654\) −41.4657 3.82066i −1.62144 0.149400i
\(655\) 0 0
\(656\) −24.4949 14.1421i −0.956365 0.552158i
\(657\) −9.05025 + 18.9497i −0.353084 + 0.739300i
\(658\) −21.1117 + 1.51575i −0.823018 + 0.0590901i
\(659\) 28.2843 1.10180 0.550899 0.834572i \(-0.314285\pi\)
0.550899 + 0.834572i \(0.314285\pi\)
\(660\) 0 0
\(661\) −9.50000 16.4545i −0.369507 0.640005i 0.619981 0.784617i \(-0.287140\pi\)
−0.989489 + 0.144611i \(0.953807\pi\)
\(662\) 1.36603 + 0.366025i 0.0530921 + 0.0142260i
\(663\) −4.24194 + 11.4894i −0.164743 + 0.446211i
\(664\) 4.00000i 0.155230i
\(665\) 0 0
\(666\) 4.00000 1.41421i 0.154997 0.0547997i
\(667\) −28.9778 + 7.76457i −1.12202 + 0.300645i
\(668\) 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
\(677\) 11.3468 + 42.3468i 0.436092 + 1.62752i 0.738438 + 0.674321i \(0.235564\pi\)
−0.302346 + 0.953198i \(0.597770\pi\)
\(678\) −8.20101 47.7990i −0.314958 1.83571i
\(679\) 8.66025 + 25.0000i 0.332350 + 0.959412i
\(680\) 0 0
\(681\) −20.0227 + 9.22450i −0.767272 + 0.353483i
\(682\) 1.55291 5.79555i 0.0594642 0.221923i
\(683\) −6.22243 + 23.2224i −0.238095 + 0.888582i 0.738635 + 0.674106i \(0.235471\pi\)
−0.976729 + 0.214476i \(0.931196\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 23.2702 12.0208i 0.888459 0.458957i
\(687\) −5.12132 + 0.878680i −0.195391 + 0.0335237i
\(688\) 5.17638 + 19.3185i 0.197348 + 0.736512i
\(689\) −7.07107 12.2474i −0.269386 0.466591i
\(690\) 0 0
\(691\) −14.5000 + 25.1147i −0.551606 + 0.955410i 0.446553 + 0.894757i \(0.352651\pi\)
−0.998159 + 0.0606524i \(0.980682\pi\)
\(692\) 0 0
\(693\) 3.76666 33.4636i 0.143084 1.27118i
\(694\) 32.0000i 1.21470i
\(695\) 0 0
\(696\) −34.4949 3.17837i −1.30753 0.120476i
\(697\) 2.58819 9.65926i 0.0980347 0.365870i
\(698\) −35.5167 + 9.51666i −1.34433 + 0.360211i
\(699\) −2.82843 + 4.00000i −0.106981 + 0.151294i
\(700\) 0 0
\(701\) 21.2132i 0.801212i −0.916250 0.400606i \(-0.868800\pi\)
0.916250 0.400606i \(-0.131200\pi\)
\(702\) 0.508623 36.7388i 0.0191967 1.38662i
\(703\) −6.76148 1.81173i −0.255014 0.0683308i
\(704\) −16.9706 29.3939i −0.639602 1.10782i
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) −26.1244 + 1.87564i −0.982508 + 0.0705409i
\(708\) 0 0
\(709\) −27.7128 16.0000i −1.04078 0.600893i −0.120723 0.992686i \(-0.538521\pi\)
−0.920053 + 0.391794i \(0.871855\pi\)
\(710\) 0 0
\(711\) −13.6464 + 15.9617i −0.511781 + 0.598609i
\(712\) −42.5007 + 11.3880i −1.59278 + 0.426785i
\(713\) −3.00000 3.00000i −0.112351 0.112351i
\(714\) −2.19275 8.89898i −0.0820617 0.333036i
\(715\) 0 0
\(716\) 0 0
\(717\) 37.6733 31.3165i 1.40693 1.16954i
\(718\) −1.93185 0.517638i −0.0720961 0.0193181i
\(719\) 9.89949 17.1464i 0.369189 0.639454i −0.620250 0.784404i \(-0.712969\pi\)
0.989439 + 0.144950i \(0.0463022\pi\)
\(720\) 0 0
\(721\) 1.50000 7.79423i 0.0558629 0.290272i
\(722\) −30.0000 + 30.0000i −1.11648 + 1.11648i
\(723\) 38.9963 + 14.3976i 1.45029 + 0.535453i
\(724\) 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 \(0.903442\pi\)
\(728\) 33.6603 + 16.3397i 1.24753 + 0.605591i
\(729\) −14.1421 + 23.0000i −0.523783 + 0.851852i
\(730\) 0 0
\(731\) −6.12372 + 3.53553i −0.226494 + 0.130766i
\(732\) 0 0
\(733\) 8.54103 + 31.8756i 0.315470 + 1.17735i 0.923551 + 0.383475i \(0.125273\pi\)
−0.608081 + 0.793875i \(0.708060\pi\)
\(734\) 29.6985 1.09619
\(735\) 0 0
\(736\) 0 0
\(737\) 1.09808 + 4.09808i 0.0404482 + 0.150955i
\(738\) 2.33875 + 29.9087i 0.0860906 + 1.10095i
\(739\) 6.06218 3.50000i 0.223001 0.128750i −0.384338 0.923192i \(-0.625570\pi\)
0.607339 + 0.794443i \(0.292237\pi\)
\(740\) 0 0
\(741\) −35.0000 + 49.4975i −1.28576 + 1.81834i
\(742\) 9.52056 + 4.62158i 0.349511 + 0.169663i
\(743\) −11.0000 11.0000i −0.403551 0.403551i 0.475931 0.879482i \(-0.342111\pi\)
−0.879482 + 0.475931i \(0.842111\pi\)
\(744\) −2.04989 4.44949i −0.0751525 0.163126i
\(745\) 0 0
\(746\) −28.1691 + 16.2635i −1.03135 + 0.595447i
\(747\) −3.49768 + 2.40130i −0.127973 + 0.0878590i
\(748\) 0 0
\(749\) 7.77817 40.4166i 0.284208 1.47679i
\(750\) 0 0
\(751\) −19.5000 + 33.7750i −0.711565 + 1.23247i 0.252704 + 0.967544i \(0.418680\pi\)
−0.964269 + 0.264923i \(0.914653\pi\)
\(752\) 21.8564 + 5.85641i 0.797021 + 0.213561i
\(753\) 7.82913 + 9.41832i 0.285309 + 0.343223i
\(754\) −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 \(0.868403\pi\)
\(758\) 12.2942 3.29423i 0.446546 0.119652i
\(759\) −2.86054 + 31.0454i −0.103831 + 1.12688i
\(760\) 0 0
\(761\) 20.8207 + 12.0208i 0.754748 + 0.435754i 0.827407 0.561603i \(-0.189815\pi\)
−0.0726586 + 0.997357i \(0.523148\pi\)
\(762\) 6.21320 + 36.2132i 0.225081 + 1.31187i
\(763\) −44.8623 + 3.22097i −1.62412 + 0.116607i
\(764\) 0 0
\(765\) 0 0
\(766\) 12.0000 + 20.7846i 0.433578 + 0.750978i
\(767\) −6.83013 1.83013i −0.246622 0.0660821i
\(768\) 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
\(773\) 4.75833 17.7583i 0.171145 0.638723i −0.826031 0.563625i \(-0.809406\pi\)
0.997176 0.0750979i \(-0.0239269\pi\)
\(774\) 13.7850 16.1237i 0.495491 0.579555i
\(775\) 0 0
\(776\) 28.2843i 1.01535i
\(777\) 4.01411 2.21063i 0.144006 0.0793059i
\(778\) −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
\(782\) 2.19615 + 8.19615i 0.0785343 + 0.293094i
\(783\) 17.9289 + 32.0711i 0.640728 + 1.14613i
\(784\) −27.7128 + 4.00000i −0.989743 + 0.142857i
\(785\) 0 0
\(786\) −17.3939 37.7552i −0.620419 1.34668i
\(787\) 6.72930 25.1141i 0.239873 0.895220i −0.736018 0.676962i \(-0.763296\pi\)
0.975891 0.218258i \(-0.0700373\pi\)
\(788\) 0 0
\(789\) −12.2993 26.6969i −0.437868 0.950436i
\(790\) 0 0
\(791\) −17.1464 49.4975i −0.609657 1.75993i
\(792\) −15.5147 + 32.4853i −0.551292 + 1.15431i
\(793\) −5.17638 19.3185i −0.183819 0.686021i
\(794\) 0.707107 + 1.22474i 0.0250943 + 0.0434646i
\(795\) 0 0
\(796\) 0 0
\(797\) −17.0000 + 17.0000i −0.602171 + 0.602171i −0.940888 0.338717i \(-0.890007\pi\)
0.338717 + 0.940888i \(0.390007\pi\)
\(798\) 0.916639 45.3559i 0.0324487 1.60558i
\(799\) 8.00000i 0.283020i
\(800\) 0 0
\(801\) 35.4722 + 30.3269i 1.25335 + 1.07155i
\(802\) 9.31749 34.7733i 0.329012 1.22789i
\(803\) 28.6865 7.68653i 1.01233 0.271252i
\(804\) 0 0
\(805\) 0 0
\(806\) 7.07107i 0.249068i
\(807\) 9.19151 + 3.39355i 0.323556 + 0.119459i
\(808\) 27.0459 + 7.24693i 0.951472 + 0.254946i
\(809\) −9.89949 17.1464i −0.348048 0.602836i 0.637855 0.770157i \(-0.279822\pi\)
−0.985903 + 0.167320i \(0.946489\pi\)
\(810\) 0 0
\(811\) −18.0000 −0.632065 −0.316033 0.948748i \(-0.602351\pi\)
−0.316033 + 0.948748i \(0.602351\pi\)
\(812\) 0 0
\(813\) −4.10051 23.8995i −0.143811 0.838192i
\(814\) −5.19615 3.00000i −0.182125 0.105150i
\(815\) 0 0
\(816\) −0.898979 + 9.75663i −0.0314706 + 0.341550i
\(817\) −33.8074 + 9.05867i −1.18277 + 0.316923i
\(818\) 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 0.195735 0.980657i \(-0.437291\pi\)
−0.751406 + 0.659840i \(0.770624\pi\)
\(822\) 24.3585 + 29.3029i 0.849602 + 1.02206i
\(823\) 27.0459 + 7.24693i 0.942762 + 0.252612i 0.697288 0.716791i \(-0.254390\pi\)
0.245474 + 0.969403i \(0.421057\pi\)
\(824\) −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 −0.321118 0.947039i \(-0.604059\pi\)
0.947039 + 0.321118i \(0.104059\pi\)
\(828\) 0 0
\(829\) 6.06218 3.50000i 0.210548 0.121560i −0.391018 0.920383i \(-0.627877\pi\)
0.601566 + 0.798823i \(0.294544\pi\)
\(830\) 0 0
\(831\) −6.52270 14.1582i −0.226270 0.491142i
\(832\) −28.2843 28.2843i −0.980581 0.980581i
\(833\) −3.90192 9.09808i −0.135194 0.315230i
\(834\) 15.5563 22.0000i 0.538672 0.761798i
\(835\) 0 0
\(836\) 0 0
\(837\) −2.66012 + 4.46360i −0.0919472 + 0.154285i
\(838\) −5.17638 19.3185i −0.178815 0.667347i
\(839\) −35.3553 −1.22060 −0.610301 0.792170i \(-0.708951\pi\)
−0.610301 + 0.792170i \(0.708951\pi\)
\(840\) 0 0
\(841\) 21.0000 0.724138
\(842\) −8.41858 31.4186i −0.290124 1.08276i
\(843\) 15.6583 + 18.8366i 0.539299 + 0.648768i
\(844\) 0 0
\(845\) 0 0
\(846\) −8.00000 22.6274i −0.275046 0.777947i
\(847\) −15.3347 + 10.3849i −0.526906 + 0.356831i
\(848\) −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
\(857\) −28.6865 7.68653i −0.979913 0.262567i −0.266905 0.963723i \(-0.586001\pi\)
−0.713008 + 0.701156i \(0.752668\pi\)
\(858\) −39.9585 + 33.2162i −1.36416 + 1.13398i
\(859\) −19.0526 11.0000i −0.650065 0.375315i 0.138416 0.990374i \(-0.455799\pi\)
−0.788481 + 0.615059i \(0.789132\pi\)
\(860\) 0 0
\(861\) 7.75255 + 31.4626i 0.264206 + 1.07224i
\(862\) 2.82843 + 2.82843i 0.0963366 + 0.0963366i
\(863\) −38.2487 + 10.2487i −1.30200 + 0.348870i −0.842207 0.539155i \(-0.818744\pi\)
−0.459795 + 0.888025i \(0.652077\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 18.3712 + 10.6066i 0.624278 + 0.360427i
\(867\) 25.6066 4.39340i 0.869646 0.149208i
\(868\) 0 0
\(869\) 29.6985 1.00745
\(870\) 0 0
\(871\) 2.50000 + 4.33013i 0.0847093 + 0.146721i
\(872\) 46.4449 + 12.4449i 1.57282 + 0.421436i
\(873\) −24.7323 + 16.9798i −0.837062 + 0.574678i
\(874\) 42.0000i 1.42067i
\(875\) 0 0
\(876\) 0 0
\(877\) −23.1822 + 6.21166i −0.782808 + 0.209753i −0.628022 0.778195i \(-0.716135\pi\)
−0.154786 + 0.987948i \(0.549469\pi\)
\(878\) −13.9090 + 51.9090i −0.469405 + 1.75184i
\(879\) 39.0265 + 3.59592i 1.31633 + 0.121287i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 20.1344 + 21.8313i 0.677960 + 0.735099i
\(883\) −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
\(887\) 7.68653 + 28.6865i 0.258089 + 0.963200i 0.966346 + 0.257245i \(0.0828149\pi\)
−0.708258 + 0.705954i \(0.750518\pi\)
\(888\) −4.82843 + 0.828427i −0.162031 + 0.0278002i
\(889\) 12.9904 + 37.5000i 0.435683 + 1.25771i
\(890\) 0 0
\(891\) 37.7196 5.93537i 1.26366 0.198842i
\(892\) 0 0
\(893\) −10.2487 + 38.2487i −0.342960 + 1.27994i
\(894\) 18.8776 8.69694i 0.631361 0.290869i
\(895\) 0 0
\(896\) 29.3939 + 5.65685i 0.981981 + 0.188982i
\(897\) 6.21320 + 36.2132i 0.207453 + 1.20912i
\(898\) 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
\(903\) 11.8550 19.6076i 0.394511 0.652500i
\(904\) 56.0000i 1.86253i
\(905\) 0 0
\(906\) 1.34847 14.6349i 0.0447999 0.486213i
\(907\) 13.1998 49.2622i 0.438291 1.63573i −0.294774 0.955567i \(-0.595244\pi\)
0.733065 0.680158i \(-0.238089\pi\)
\(908\) 0 0
\(909\) −9.89949 28.0000i −0.328346 0.928701i
\(910\) 0 0
\(911\) 35.3553i 1.17137i 0.810537 + 0.585687i \(0.199175\pi\)
−0.810537 + 0.585687i \(0.800825\pi\)
\(912\) −16.7972 + 45.4956i −0.556211 + 1.50651i
\(913\) 5.79555 + 1.55291i 0.191805 + 0.0513940i
\(914\) −20.5061 35.5176i −0.678281 1.17482i
\(915\) 0 0
\(916\) 0 0
\(917\) −25.1769 37.1769i −0.831415 1.22769i
\(918\) 9.07107 5.07107i 0.299390 0.167370i
\(919\) 11.2583 + 6.50000i 0.371378 + 0.214415i 0.674060 0.738676i \(-0.264549\pi\)
−0.302682 + 0.953092i \(0.597882\pi\)
\(920\) 0 0
\(921\) −25.8712 2.38378i −0.852484 0.0785482i
\(922\) −9.65926 + 2.58819i −0.318111 + 0.0852375i
\(923\) −25.0000 25.0000i −0.822885 0.822885i
\(924\) 0 0
\(925\) 0 0
\(926\) −30.6186 17.6777i −1.00619 0.580924i
\(927\) 8.97261 0.701625i 0.294699 0.0230444i
\(928\) 0 0
\(929\) −7.77817 + 13.4722i −0.255194 + 0.442008i −0.964948 0.262441i \(-0.915473\pi\)
0.709754 + 0.704449i \(0.248806\pi\)
\(930\) 0 0
\(931\) −7.00000 48.4974i −0.229416 1.58944i
\(932\) 0 0
\(933\) 19.5129 52.8512i 0.638824 1.73027i
\(934\) 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 \(0.671207\pi\)
\(938\) −3.36603 1.63397i −0.109905 0.0533512i
\(939\) 24.0416 + 17.0000i 0.784569 + 0.554774i
\(940\) 0 0
\(941\) −15.9217 + 9.19239i −0.519032 + 0.299663i −0.736539 0.676396i \(-0.763541\pi\)
0.217506 + 0.976059i \(0.430208\pi\)
\(942\) 7.53465 6.26330i 0.245492 0.204070i
\(943\) −7.76457 28.9778i −0.252849 0.943646i
\(944\) −5.65685 −0.184115
\(945\) 0 0
\(946\) −30.0000 −0.975384
\(947\) 4.02628 + 15.0263i 0.130837 + 0.488288i 0.999980 0.00627092i \(-0.00199611\pi\)
−0.869144 + 0.494559i \(0.835329\pi\)
\(948\) 0 0
\(949\) 30.3109 17.5000i 0.983933 0.568074i
\(950\) 0 0
\(951\) −2.00000 1.41421i −0.0648544 0.0458590i
\(952\) 0.757875 + 10.5558i 0.0245629 + 0.342117i
\(953\) −36.0000 36.0000i −1.16615 1.16615i −0.983103 0.183051i \(-0.941403\pi\)
−0.183051 0.983103i \(-0.558597\pi\)
\(954\) −2.19275 + 11.7980i −0.0709930 + 0.381973i
\(955\) 0 0
\(956\) 0 0
\(957\) 17.9970 48.7453i 0.581761 1.57571i
\(958\) −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
\(962\) −6.83013 1.83013i −0.220212 0.0590057i
\(963\) 46.5270 3.63824i 1.49931 0.117241i
\(964\) 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 \(0.559739\pi\)
\(968\) 19.1244 5.12436i 0.614680 0.164703i
\(969\) −17.0741 1.57321i −0.548499 0.0505389i
\(970\) 0 0
\(971\) 39.1918 + 22.6274i 1.25773 + 0.726148i 0.972632 0.232351i \(-0.0746419\pi\)
0.285094 + 0.958500i \(0.407975\pi\)
\(972\) 0 0
\(973\) 12.7093 26.1815i 0.407443 0.839341i
\(974\) −41.0122 −1.31412
\(975\) 0 0
\(976\) −8.00000 13.8564i −0.256074 0.443533i
\(977\) −15.0263 4.02628i −0.480733 0.128812i 0.0103108 0.999947i \(-0.496718\pi\)
−0.491044 + 0.871135i \(0.663385\pi\)
\(978\) −1.69677 + 4.59575i −0.0542569 + 0.146956i
\(979\) 66.0000i 2.10937i
\(980\) 0 0
\(981\) −17.0000 48.0833i −0.542768 1.53518i
\(982\) −19.3185 + 5.17638i −0.616479 + 0.165185i
\(983\) −9.88269 + 36.8827i −0.315209 + 1.17637i 0.608586 + 0.793488i \(0.291737\pi\)
−0.923795 + 0.382887i \(0.874930\pi\)
\(984\) 3.17837 34.4949i 0.101323 1.09966i
\(985\) 0 0
\(986\) 14.1421i 0.450377i
\(987\) −12.5052 22.7073i −0.398045 0.722780i
\(988\) 0 0
\(989\) −10.6066 + 18.3712i −0.337270 + 0.584169i
\(990\) 0 0
\(991\) 20.5000 + 35.5070i 0.651204 + 1.12792i 0.982831 + 0.184508i \(0.0590691\pi\)
−0.331627 + 0.943411i \(0.607598\pi\)
\(992\) 0 0
\(993\) 0.292893 + 1.70711i 0.00929469 + 0.0541734i
\(994\) 25.9808 + 5.00000i 0.824060 + 0.158590i
\(995\) 0 0
\(996\) 0 0
\(997\) −10.0939 + 37.6711i −0.319678 + 1.19306i 0.599876 + 0.800093i \(0.295217\pi\)
−0.919554 + 0.392963i \(0.871450\pi\)
\(998\) 9.88269 36.8827i 0.312831 1.16750i
\(999\) 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.a.107.1 yes 8
3.2 odd 2 525.2.bf.d.107.1 yes 8
5.2 odd 4 inner 525.2.bf.a.443.1 yes 8
5.3 odd 4 525.2.bf.d.443.2 yes 8
5.4 even 2 525.2.bf.d.107.2 yes 8
7.4 even 3 inner 525.2.bf.a.32.2 yes 8
15.2 even 4 525.2.bf.d.443.1 yes 8
15.8 even 4 inner 525.2.bf.a.443.2 yes 8
15.14 odd 2 inner 525.2.bf.a.107.2 yes 8
21.11 odd 6 525.2.bf.d.32.2 yes 8
35.4 even 6 525.2.bf.d.32.1 yes 8
35.18 odd 12 525.2.bf.d.368.1 yes 8
35.32 odd 12 inner 525.2.bf.a.368.2 yes 8
105.32 even 12 525.2.bf.d.368.2 yes 8
105.53 even 12 inner 525.2.bf.a.368.1 yes 8
105.74 odd 6 inner 525.2.bf.a.32.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.bf.a.32.1 8 105.74 odd 6 inner
525.2.bf.a.32.2 yes 8 7.4 even 3 inner
525.2.bf.a.107.1 yes 8 1.1 even 1 trivial
525.2.bf.a.107.2 yes 8 15.14 odd 2 inner
525.2.bf.a.368.1 yes 8 105.53 even 12 inner
525.2.bf.a.368.2 yes 8 35.32 odd 12 inner
525.2.bf.a.443.1 yes 8 5.2 odd 4 inner
525.2.bf.a.443.2 yes 8 15.8 even 4 inner
525.2.bf.d.32.1 yes 8 35.4 even 6
525.2.bf.d.32.2 yes 8 21.11 odd 6
525.2.bf.d.107.1 yes 8 3.2 odd 2
525.2.bf.d.107.2 yes 8 5.4 even 2
525.2.bf.d.368.1 yes 8 35.18 odd 12
525.2.bf.d.368.2 yes 8 105.32 even 12
525.2.bf.d.443.1 yes 8 15.2 even 4
525.2.bf.d.443.2 yes 8 5.3 odd 4