Properties

Label 525.2.bf.d.368.2
Level $525$
Weight $2$
Character 525.368
Analytic conductor $4.192$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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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 368.2
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 525.368
Dual form 525.2.bf.d.107.2

$q$-expansion

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 + 1.36603i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) 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 −0.169559 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 \(-0.00612285\pi\)
−0.0192343 + 0.999815i \(0.506123\pi\)
\(14\) 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 \(-0.528472\pi\)
0.420639 + 0.907228i \(0.361806\pi\)
\(18\) −4.22973 0.330749i −0.996957 0.0779583i
\(19\) −6.06218 + 3.50000i −1.39076 + 0.802955i −0.993399 0.114708i \(-0.963407\pi\)
−0.397360 + 0.917663i \(0.630073\pi\)
\(20\) 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 \(-0.270820\pi\)
0.195131 + 0.980777i \(0.437487\pi\)
\(24\) −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 −0.817625 0.575751i \(-0.804710\pi\)
0.907428 + 0.420208i \(0.138043\pi\)
\(32\) 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 \(-0.442861\pi\)
−0.337342 + 0.941382i \(0.609528\pi\)
\(38\) −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 \(-0.813805\pi\)
0.833740 0.552158i \(-0.186195\pi\)
\(42\) −3.12630 + 5.67681i −0.482399 + 0.875951i
\(43\) −3.53553 3.53553i −0.539164 0.539164i 0.384120 0.923283i \(-0.374505\pi\)
−0.923283 + 0.384120i \(0.874505\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) 1.46410 5.46410i 0.213561 0.797021i −0.773107 0.634276i \(-0.781298\pi\)
0.986668 0.162745i \(-0.0520349\pi\)
\(48\) 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 \(-0.0211037\pi\)
−0.897248 + 0.441527i \(0.854437\pi\)
\(54\) −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 −0.816319 0.577601i \(-0.803989\pi\)
0.908377 + 0.418153i \(0.137322\pi\)
\(60\) 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
\(63\) 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 \(-0.102789\pi\)
−0.979932 + 0.199332i \(0.936123\pi\)
\(68\) 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 \(-0.137826\pi\)
\(72\) −6.99536 4.80260i −0.824411 0.565992i
\(73\) 6.76148 1.81173i 0.791371 0.212047i 0.159579 0.987185i \(-0.448986\pi\)
0.631792 + 0.775138i \(0.282320\pi\)
\(74\) 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 −0.800626 0.599164i \(-0.795500\pi\)
0.118578 + 0.992945i \(0.462166\pi\)
\(80\) 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 \(-0.725269\pi\)
0.759856 + 0.650092i \(0.225269\pi\)
\(84\) 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 −0.902312 0.431083i \(-0.858132\pi\)
0.0778275 0.996967i \(-0.475202\pi\)
\(90\) 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 \(-0.580506\pi\)
0.968187 + 0.250229i \(0.0805058\pi\)
\(98\) 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 0.861684 0.507445i \(-0.169410\pi\)
−0.00861771 + 0.999963i \(0.502743\pi\)
\(102\) −2.21441 + 2.66390i −0.219260 + 0.263766i
\(103\) −0.776457 + 2.89778i −0.0765066 + 0.285526i −0.993571 0.113213i \(-0.963886\pi\)
0.917064 + 0.398740i \(0.130552\pi\)
\(104\) −14.1421 −1.38675
\(105\) 0 0
\(106\) −4.00000 −0.388514
\(107\) −4.02628 + 15.0263i −0.389235 + 1.45265i 0.442146 + 0.896943i \(0.354217\pi\)
−0.831381 + 0.555702i \(0.812449\pi\)
\(108\) 0 0
\(109\) 14.7224 + 8.50000i 1.41015 + 0.814152i 0.995402 0.0957826i \(-0.0305354\pi\)
0.414751 + 0.909935i \(0.363869\pi\)
\(110\) 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 −0.400878 + 0.916132i \(0.631295\pi\)
−0.916132 + 0.400878i \(0.868705\pi\)
\(114\) 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 \(-0.518211\pi\)
0.998364 + 0.0571802i \(0.0182109\pi\)
\(128\) 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 0.306486 0.951875i \(-0.400847\pi\)
0.977591 + 0.210513i \(0.0675133\pi\)
\(132\) 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 \(-0.351963\pi\)
0.835295 + 0.549801i \(0.185297\pi\)
\(138\) −9.74907 + 3.59940i −0.829896 + 0.306401i
\(139\) 11.0000i 0.933008i −0.884519 0.466504i \(-0.845513\pi\)
0.884519 0.466504i \(-0.154487\pi\)
\(140\) 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 0.638247 0.769832i \(-0.279660\pi\)
−0.985817 + 0.167822i \(0.946327\pi\)
\(150\) 0 0
\(151\) 3.00000 5.19615i 0.244137 0.422857i −0.717752 0.696299i \(-0.754829\pi\)
0.961888 + 0.273442i \(0.0881622\pi\)
\(152\) 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 \(-0.0323073\pi\)
−0.912230 + 0.409679i \(0.865641\pi\)
\(158\) −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 \(-0.891709\pi\)
0.983231 + 0.182367i \(0.0583758\pi\)
\(164\) 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 \(-0.124883\pi\)
−0.382344 + 0.924020i \(0.624883\pi\)
\(168\) −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 \(-0.450958\pi\)
−0.361176 + 0.932498i \(0.617625\pi\)
\(174\) −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 0.212607 + 0.977138i \(0.431805\pi\)
−0.952529 + 0.304446i \(0.901529\pi\)
\(180\) 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 −0.810674 0.585498i \(-0.800899\pi\)
0.101719 + 0.994813i \(0.467566\pi\)
\(192\) 8.85765 10.6556i 0.639246 0.769002i
\(193\) −22.2163 + 5.95284i −1.59916 + 0.428495i −0.944790 0.327677i \(-0.893734\pi\)
−0.654374 + 0.756171i \(0.727068\pi\)
\(194\) 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 \(-0.298294\pi\)
−0.805855 + 0.592113i \(0.798294\pi\)
\(198\) 14.8394 + 10.1879i 1.05459 + 0.724020i
\(199\) 1.73205 + 1.00000i 0.122782 + 0.0708881i 0.560133 0.828403i \(-0.310750\pi\)
−0.437351 + 0.899291i \(0.644083\pi\)
\(200\) 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 \(-0.358677\pi\)
−0.903050 + 0.429536i \(0.858677\pi\)
\(224\) 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 \(-0.722142\pi\)
−0.173401 + 0.984851i \(0.555476\pi\)
\(228\) 0 0
\(229\) 2.59808 1.50000i 0.171686 0.0991228i −0.411695 0.911322i \(-0.635063\pi\)
0.583380 + 0.812199i \(0.301730\pi\)
\(230\) 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 \(-0.446200\pi\)
−0.347197 + 0.937792i \(0.612867\pi\)
\(234\) −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 0.162930 + 0.986638i \(0.447905\pi\)
−0.935918 + 0.352217i \(0.885428\pi\)
\(242\) −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 \(0.0716375\pi\)
−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
\(257\) 3.29423 12.2942i 0.205488 0.766893i −0.783812 0.620998i \(-0.786727\pi\)
0.989300 0.145894i \(-0.0466060\pi\)
\(258\) 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 0.958577 + 0.284832i \(0.0919379\pi\)
−0.687736 + 0.725961i \(0.741395\pi\)
\(264\) 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 −0.939277 0.343161i \(-0.888502\pi\)
0.766824 + 0.641857i \(0.221836\pi\)
\(270\) 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
\(273\) 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 0.999928 + 0.0119868i \(0.00381560\pi\)
−0.859970 + 0.510345i \(0.829518\pi\)
\(278\) 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 \(0.138610\pi\)
−0.906677 + 0.421825i \(0.861390\pi\)
\(282\) 4.79920 + 12.9988i 0.285788 + 0.774065i
\(283\) −22.2163 + 5.95284i −1.32062 + 0.353859i −0.849211 0.528054i \(-0.822922\pi\)
−0.471411 + 0.881914i \(0.656255\pi\)
\(284\) 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 \(-0.520152\pi\)
0.997997 + 0.0632667i \(0.0201519\pi\)
\(294\) −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 \(-0.890798\pi\)
0.336377 + 0.941727i \(0.390798\pi\)
\(308\) 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 \(-0.706957\pi\)
\(312\) −18.8366 15.6583i −1.06641 0.886475i
\(313\) 4.39992 16.4207i 0.248698 0.928155i −0.722790 0.691068i \(-0.757141\pi\)
0.971488 0.237087i \(-0.0761927\pi\)
\(314\) −5.65685 −0.319235
\(315\) 0 0
\(316\) 0 0
\(317\) −0.366025 + 1.36603i −0.0205580 + 0.0767236i −0.975443 0.220253i \(-0.929312\pi\)
0.954885 + 0.296977i \(0.0959784\pi\)
\(318\) −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 0.879440 0.476011i \(-0.157918\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) 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 \(-0.706516\pi\)
0.796815 + 0.604223i \(0.206516\pi\)
\(338\) −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 \(-0.375565\pi\)
0.792271 + 0.610169i \(0.208899\pi\)
\(348\) 0 0
\(349\) 26.0000i 1.39175i −0.718164 0.695874i \(-0.755017\pi\)
0.718164 0.695874i \(-0.244983\pi\)
\(350\) 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 \(-0.119349\pi\)
−0.988972 + 0.148105i \(0.952683\pi\)
\(354\) 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 0.846762 0.531971i \(-0.178549\pi\)
−0.884082 + 0.467332i \(0.845215\pi\)
\(360\) 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 −0.949773 0.312939i \(-0.898686\pi\)
0.666058 0.745900i \(-0.267980\pi\)
\(368\) −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 0.621906 + 0.783092i \(0.286359\pi\)
−0.930132 + 0.367224i \(0.880308\pi\)
\(374\) 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 \(0.0742486\pi\)
−0.972918 + 0.231149i \(0.925751\pi\)
\(380\) 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 \(-0.559416\pi\)
−0.652030 + 0.758193i \(0.726082\pi\)
\(384\) 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 −0.193532 0.981094i \(-0.561994\pi\)
0.946418 0.322944i \(-0.104672\pi\)
\(390\) 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 \(-0.424655\pi\)
−0.282977 + 0.959127i \(0.591322\pi\)
\(398\) −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 \(0.552581\pi\)
\(402\) 1.88366 + 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 0.994203 + 0.107523i \(0.0342919\pi\)
0.590219 + 0.807243i \(0.299041\pi\)
\(410\) 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 0.557832 0.829954i \(-0.311633\pi\)
−0.439845 + 0.898074i \(0.644967\pi\)
\(432\) 20.7826 0.287721i 0.999904 0.0138430i
\(433\) −10.6066 10.6066i −0.509721 0.509721i 0.404720 0.914441i \(-0.367369\pi\)
−0.914441 + 0.404720i \(0.867369\pi\)
\(434\) 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 0.574571 0.818455i \(-0.305169\pi\)
0.996088 0.0883659i \(-0.0281645\pi\)
\(440\) 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 \(-0.330051\pi\)
0.0103113 + 0.999947i \(0.496718\pi\)
\(444\) 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 \(-0.179392\pi\)
0.464989 + 0.885317i \(0.346058\pi\)
\(458\) 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 \(-0.947345\pi\)
0.986349 0.164666i \(-0.0526547\pi\)
\(462\) 23.5291 14.2261i 1.09467 0.661856i
\(463\) 17.6777 + 17.6777i 0.821551 + 0.821551i 0.986330 0.164779i \(-0.0526912\pi\)
−0.164779 + 0.986330i \(0.552691\pi\)
\(464\) −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 \(-0.874885\pi\)
0.991492 + 0.130168i \(0.0415518\pi\)
\(468\) 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 −0.752672 0.658396i \(-0.771235\pi\)
0.946523 + 0.322635i \(0.104569\pi\)
\(480\) 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 0.898213 + 0.439561i \(0.144866\pi\)
−0.558095 + 0.829777i \(0.688467\pi\)
\(488\) 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 \(-0.896615\pi\)
0.947717 0.319113i \(-0.103385\pi\)
\(492\) 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 −0.921739 0.387812i \(-0.873231\pi\)
−0.125014 + 0.992155i \(0.539898\pi\)
\(500\) 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 −0.0727574 + 0.997350i \(0.523180\pi\)
−0.997350 + 0.0727574i \(0.976820\pi\)
\(504\) −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 0.756549 0.653937i \(-0.226884\pi\)
−0.944601 + 0.328222i \(0.893551\pi\)
\(510\) 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 0.956120 0.292976i \(-0.0946456\pi\)
0.224335 + 0.974512i \(0.427979\pi\)
\(522\) −29.9087 2.33875i −1.30907 0.102364i
\(523\) 1.81173 6.76148i 0.0792216 0.295659i −0.914936 0.403599i \(-0.867759\pi\)
0.994157 + 0.107941i \(0.0344256\pi\)
\(524\) 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 0.959697 0.281037i \(-0.0906783\pi\)
−0.723234 + 0.690604i \(0.757345\pi\)
\(542\) 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 \(-0.818579\pi\)
0.539591 + 0.841928i \(0.318579\pi\)
\(548\) 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 \(-0.721112\pi\)
−0.170213 + 0.985407i \(0.554445\pi\)
\(558\) −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 0.899048 + 0.437851i \(0.144260\pi\)
−0.559673 + 0.828714i \(0.689073\pi\)
\(564\) 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 0.850823 0.525452i \(-0.176104\pi\)
−0.880467 + 0.474108i \(0.842771\pi\)
\(570\) 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
\(573\) −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 \(-0.156868\pi\)
−0.999526 + 0.0307771i \(0.990202\pi\)
\(578\) −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 \(-0.373873\pi\)
−0.922519 + 0.385952i \(0.873873\pi\)
\(588\) 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 \(-0.293455\pi\)
0.124953 + 0.992163i \(0.460122\pi\)
\(594\) 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 −0.994261 0.106981i \(-0.965882\pi\)
0.589779 + 0.807565i \(0.299215\pi\)
\(600\) 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 \(-0.729511\pi\)
−0.947277 + 0.320416i \(0.896177\pi\)
\(608\) 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 \(-0.570473\pi\)
0.297621 + 0.954684i \(0.403807\pi\)
\(614\) −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 \(-0.323132\pi\)
−0.849560 + 0.527492i \(0.823132\pi\)
\(618\) −2.54516 6.89363i −0.102381 0.277303i
\(619\) −2.59808 1.50000i −0.104425 0.0602901i 0.446878 0.894595i \(-0.352536\pi\)
−0.551303 + 0.834305i \(0.685869\pi\)
\(620\) 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 0.659662 0.751562i \(-0.270699\pi\)
−0.321041 + 0.947065i \(0.604033\pi\)
\(642\) −13.1978 35.7466i −0.520876 1.41080i
\(643\) −17.6777 17.6777i −0.697139 0.697139i 0.266653 0.963793i \(-0.414082\pi\)
−0.963793 + 0.266653i \(0.914082\pi\)
\(644\) 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 \(-0.574483\pi\)
0.285571 + 0.958358i \(0.407817\pi\)
\(648\) 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 \(-0.685232\pi\)
−0.893699 + 0.448667i \(0.851899\pi\)
\(654\) −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 −0.989489 0.144611i \(-0.953807\pi\)
0.619981 + 0.784617i \(0.287140\pi\)
\(662\) −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 \(-0.0899688\pi\)
−0.278897 + 0.960321i \(0.589969\pi\)
\(674\) 3.53553 + 6.12372i 0.136184 + 0.235877i
\(675\) 0 0
\(676\) 0 0
\(677\) −11.3468 + 42.3468i −0.436092 + 1.62752i 0.302346 + 0.953198i \(0.402230\pi\)
−0.738438 + 0.674321i \(0.764436\pi\)
\(678\) 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 0.976729 + 0.214476i \(0.0688043\pi\)
−0.738635 + 0.674106i \(0.764529\pi\)
\(684\) 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 −0.998159 0.0606524i \(-0.980682\pi\)
0.446553 0.894757i \(-0.352651\pi\)
\(692\) 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 \(0.131200\pi\)
−0.916250 + 0.400606i \(0.868800\pi\)
\(702\) −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 −0.920053 0.391794i \(-0.871855\pi\)
−0.120723 + 0.992686i \(0.538521\pi\)
\(710\) 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 0.989439 0.144950i \(-0.0463022\pi\)
−0.620250 + 0.784404i \(0.712969\pi\)
\(720\) 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 \(-0.596558\pi\)
0.954343 + 0.298714i \(0.0965577\pi\)
\(728\) −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 0.608081 + 0.793875i \(0.291940\pi\)
−0.923551 + 0.383475i \(0.874727\pi\)
\(734\) 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 0.607339 0.794443i \(-0.292237\pi\)
−0.384338 + 0.923192i \(0.625570\pi\)
\(740\) 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 \(-0.657889\pi\)
0.879482 + 0.475931i \(0.157889\pi\)
\(744\) −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 −0.964269 0.264923i \(-0.914653\pi\)
0.252704 0.967544i \(-0.418680\pi\)
\(752\) −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 \(-0.631597\pi\)
0.915751 + 0.401746i \(0.131597\pi\)
\(758\) −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 −0.0726586 0.997357i \(-0.523148\pi\)
0.827407 + 0.561603i \(0.189815\pi\)
\(762\) −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 \(0.175144\pi\)
−0.852404 + 0.522883i \(0.824856\pi\)
\(770\) 0 0
\(771\) 18.0000 12.7279i 0.648254 0.458385i
\(772\) 0 0
\(773\) −4.75833 17.7583i −0.171145 0.638723i −0.997176 0.0750979i \(-0.976073\pi\)
0.826031 0.563625i \(-0.190594\pi\)
\(774\) 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 −0.975891 0.218258i \(-0.929963\pi\)
0.736018 0.676962i \(-0.236704\pi\)
\(788\) 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 \(-0.109993\pi\)
−0.338717 + 0.940888i \(0.609993\pi\)
\(798\) −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 −0.985903 0.167320i \(-0.946489\pi\)
0.637855 + 0.770157i \(0.279822\pi\)
\(810\) 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 −0.751406 0.659840i \(-0.770624\pi\)
0.195735 + 0.980657i \(0.437291\pi\)
\(822\) −24.3585 + 29.3029i −0.849602 + 1.02206i
\(823\) −27.0459 + 7.24693i −0.942762 + 0.252612i −0.697288 0.716791i \(-0.745610\pi\)
−0.245474 + 0.969403i \(0.578943\pi\)
\(824\) −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 \(-0.395941\pi\)
−0.947039 + 0.321118i \(0.895941\pi\)
\(828\) 0 0
\(829\) 6.06218 + 3.50000i 0.210548 + 0.121560i 0.601566 0.798823i \(-0.294544\pi\)
−0.391018 + 0.920383i \(0.627877\pi\)
\(830\) 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 0.903941 + 0.427657i \(0.140661\pi\)
0.427657 + 0.903941i \(0.359339\pi\)
\(854\) 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 \(-0.413999\pi\)
0.713008 + 0.701156i \(0.247332\pi\)
\(858\) 39.9585 + 33.2162i 1.36416 + 1.13398i
\(859\) −19.0526 + 11.0000i −0.650065 + 0.375315i −0.788481 0.615059i \(-0.789132\pi\)
0.138416 + 0.990374i \(0.455799\pi\)
\(860\) 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 \(-0.181256\pi\)
0.459795 + 0.888025i \(0.347923\pi\)
\(864\) 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 \(-0.283865\pi\)
0.154786 + 0.987948i \(0.450531\pi\)
\(878\) 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 \(-0.168782\pi\)
−0.505743 + 0.862684i \(0.668782\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −8.00000 + 13.8564i −0.268765 + 0.465515i
\(887\) −7.68653 + 28.6865i −0.258089 + 0.963200i 0.708258 + 0.705954i \(0.249482\pi\)
−0.966346 + 0.257245i \(0.917185\pi\)
\(888\) 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 −0.733065 0.680158i \(-0.761911\pi\)
0.294774 0.955567i \(-0.404756\pi\)
\(908\) 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 \(-0.199175\pi\)
\(912\) 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 −0.302682 0.953092i \(-0.597882\pi\)
0.674060 + 0.738676i \(0.264549\pi\)
\(920\) 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 0.709754 0.704449i \(-0.248806\pi\)
−0.964948 + 0.262441i \(0.915473\pi\)
\(930\) 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 \(-0.828793\pi\)
0.512302 + 0.858805i \(0.328793\pi\)
\(938\) 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 0.217506 0.976059i \(-0.430208\pi\)
−0.736539 + 0.676396i \(0.763541\pi\)
\(942\) −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 \(-0.998004\pi\)
0.869144 + 0.494559i \(0.164671\pi\)
\(948\) 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 0.183051 0.983103i \(-0.441403\pi\)
0.983103 0.183051i \(-0.0585973\pi\)
\(954\) −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 \(-0.940261\pi\)
0.186575 + 0.982441i \(0.440261\pi\)
\(968\) −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 0.285094 0.958500i \(-0.407975\pi\)
0.972632 + 0.232351i \(0.0746419\pi\)
\(972\) 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 \(-0.503282\pi\)
0.491044 + 0.871135i \(0.336615\pi\)
\(978\) 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 0.923795 + 0.382887i \(0.125070\pi\)
−0.608586 + 0.793488i \(0.708263\pi\)
\(984\) 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 −0.331627 0.943411i \(-0.607598\pi\)
0.982831 0.184508i \(-0.0590691\pi\)
\(992\) 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 0.919554 + 0.392963i \(0.128550\pi\)
−0.599876 + 0.800093i \(0.704783\pi\)
\(998\) −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.d.368.2 yes 8
3.2 odd 2 525.2.bf.a.368.2 yes 8
5.2 odd 4 525.2.bf.a.32.1 8
5.3 odd 4 inner 525.2.bf.d.32.2 yes 8
5.4 even 2 525.2.bf.a.368.1 yes 8
7.2 even 3 inner 525.2.bf.d.443.1 yes 8
15.2 even 4 inner 525.2.bf.d.32.1 yes 8
15.8 even 4 525.2.bf.a.32.2 yes 8
15.14 odd 2 inner 525.2.bf.d.368.1 yes 8
21.2 odd 6 525.2.bf.a.443.1 yes 8
35.2 odd 12 525.2.bf.a.107.2 yes 8
35.9 even 6 525.2.bf.a.443.2 yes 8
35.23 odd 12 inner 525.2.bf.d.107.1 yes 8
105.2 even 12 inner 525.2.bf.d.107.2 yes 8
105.23 even 12 525.2.bf.a.107.1 yes 8
105.44 odd 6 inner 525.2.bf.d.443.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.bf.a.32.1 8 5.2 odd 4
525.2.bf.a.32.2 yes 8 15.8 even 4
525.2.bf.a.107.1 yes 8 105.23 even 12
525.2.bf.a.107.2 yes 8 35.2 odd 12
525.2.bf.a.368.1 yes 8 5.4 even 2
525.2.bf.a.368.2 yes 8 3.2 odd 2
525.2.bf.a.443.1 yes 8 21.2 odd 6
525.2.bf.a.443.2 yes 8 35.9 even 6
525.2.bf.d.32.1 yes 8 15.2 even 4 inner
525.2.bf.d.32.2 yes 8 5.3 odd 4 inner
525.2.bf.d.107.1 yes 8 35.23 odd 12 inner
525.2.bf.d.107.2 yes 8 105.2 even 12 inner
525.2.bf.d.368.1 yes 8 15.14 odd 2 inner
525.2.bf.d.368.2 yes 8 1.1 even 1 trivial
525.2.bf.d.443.1 yes 8 7.2 even 3 inner
525.2.bf.d.443.2 yes 8 105.44 odd 6 inner