Properties

Label 294.3.h.b.275.2
Level $294$
Weight $3$
Character 294.275
Analytic conductor $8.011$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [294,3,Mod(263,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.263");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 294.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.01091977219\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 275.2
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 294.275
Dual form 294.3.h.b.263.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(-2.94949 + 0.548188i) q^{3} +(1.00000 + 1.73205i) q^{4} +(7.34847 + 4.24264i) q^{5} +(-4.00000 - 1.41421i) q^{6} +2.82843i q^{8} +(8.39898 - 3.23375i) q^{9} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(-2.94949 + 0.548188i) q^{3} +(1.00000 + 1.73205i) q^{4} +(7.34847 + 4.24264i) q^{5} +(-4.00000 - 1.41421i) q^{6} +2.82843i q^{8} +(8.39898 - 3.23375i) q^{9} +(6.00000 + 10.3923i) q^{10} +(-3.89898 - 4.56048i) q^{12} +1.00000 q^{13} +(-24.0000 - 8.48528i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(7.34847 - 4.24264i) q^{17} +(12.5732 + 1.97846i) q^{18} +(-15.5000 + 26.8468i) q^{19} +16.9706i q^{20} +(7.34847 + 4.24264i) q^{23} +(-1.55051 - 8.34242i) q^{24} +(23.5000 + 40.7032i) q^{25} +(1.22474 + 0.707107i) q^{26} +(-23.0000 + 14.1421i) q^{27} +16.9706i q^{29} +(-23.3939 - 27.3629i) q^{30} +(-3.50000 - 6.06218i) q^{31} +(-4.89898 + 2.82843i) q^{32} +12.0000 q^{34} +(14.0000 + 11.3137i) q^{36} +(0.500000 - 0.866025i) q^{37} +(-37.9671 + 21.9203i) q^{38} +(-2.94949 + 0.548188i) q^{39} +(-12.0000 + 20.7846i) q^{40} -33.9411i q^{41} -31.0000 q^{43} +(75.4393 + 11.8707i) q^{45} +(6.00000 + 10.3923i) q^{46} +(36.7423 + 21.2132i) q^{47} +(4.00000 - 11.3137i) q^{48} +66.4680i q^{50} +(-19.3485 + 16.5420i) q^{51} +(1.00000 + 1.73205i) q^{52} +(22.0454 - 12.7279i) q^{53} +(-38.1691 + 1.05705i) q^{54} +(31.0000 - 87.6812i) q^{57} +(-12.0000 + 20.7846i) q^{58} +(7.34847 - 4.24264i) q^{59} +(-9.30306 - 50.0545i) q^{60} +(25.0000 - 43.3013i) q^{61} -9.89949i q^{62} -8.00000 q^{64} +(7.34847 + 4.24264i) q^{65} +(-32.5000 - 56.2917i) q^{67} +(14.6969 + 8.48528i) q^{68} +(-24.0000 - 8.48528i) q^{69} -59.3970i q^{71} +(9.14643 + 23.7559i) q^{72} +(-48.5000 - 84.0045i) q^{73} +(1.22474 - 0.707107i) q^{74} +(-91.6260 - 107.171i) q^{75} -62.0000 q^{76} +(-4.00000 - 1.41421i) q^{78} +(51.5000 - 89.2006i) q^{79} +(-29.3939 + 16.9706i) q^{80} +(60.0857 - 54.3204i) q^{81} +(24.0000 - 41.5692i) q^{82} -42.4264i q^{83} +72.0000 q^{85} +(-37.9671 - 21.9203i) q^{86} +(-9.30306 - 50.0545i) q^{87} +(102.879 + 59.3970i) q^{89} +(84.0000 + 67.8823i) q^{90} +16.9706i q^{92} +(13.6464 + 15.9617i) q^{93} +(30.0000 + 51.9615i) q^{94} +(-227.803 + 131.522i) q^{95} +(12.8990 - 11.0280i) q^{96} +166.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 4 q^{4} - 16 q^{6} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} + 4 q^{4} - 16 q^{6} + 14 q^{9} + 24 q^{10} + 4 q^{12} + 4 q^{13} - 96 q^{15} - 8 q^{16} + 16 q^{18} - 62 q^{19} - 16 q^{24} + 94 q^{25} - 92 q^{27} + 24 q^{30} - 14 q^{31} + 48 q^{34} + 56 q^{36} + 2 q^{37} - 2 q^{39} - 48 q^{40} - 124 q^{43} + 96 q^{45} + 24 q^{46} + 16 q^{48} - 48 q^{51} + 4 q^{52} - 40 q^{54} + 124 q^{57} - 48 q^{58} - 96 q^{60} + 100 q^{61} - 32 q^{64} - 130 q^{67} - 96 q^{69} - 32 q^{72} - 194 q^{73} + 94 q^{75} - 248 q^{76} - 16 q^{78} + 206 q^{79} - 34 q^{81} + 96 q^{82} + 288 q^{85} - 96 q^{87} + 336 q^{90} - 14 q^{93} + 120 q^{94} + 32 q^{96} + 664 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.612372 + 0.353553i
\(3\) −2.94949 + 0.548188i −0.983163 + 0.182729i
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) 7.34847 + 4.24264i 1.46969 + 0.848528i 0.999422 0.0339935i \(-0.0108226\pi\)
0.470272 + 0.882522i \(0.344156\pi\)
\(6\) −4.00000 1.41421i −0.666667 0.235702i
\(7\) 0 0
\(8\) 2.82843i 0.353553i
\(9\) 8.39898 3.23375i 0.933220 0.359306i
\(10\) 6.00000 + 10.3923i 0.600000 + 1.03923i
\(11\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) −3.89898 4.56048i −0.324915 0.380040i
\(13\) 1.00000 0.0769231 0.0384615 0.999260i \(-0.487754\pi\)
0.0384615 + 0.999260i \(0.487754\pi\)
\(14\) 0 0
\(15\) −24.0000 8.48528i −1.60000 0.565685i
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 7.34847 4.24264i 0.432263 0.249567i −0.268047 0.963406i \(-0.586378\pi\)
0.700310 + 0.713839i \(0.253045\pi\)
\(18\) 12.5732 + 1.97846i 0.698512 + 0.109914i
\(19\) −15.5000 + 26.8468i −0.815789 + 1.41299i 0.0929702 + 0.995669i \(0.470364\pi\)
−0.908760 + 0.417320i \(0.862969\pi\)
\(20\) 16.9706i 0.848528i
\(21\) 0 0
\(22\) 0 0
\(23\) 7.34847 + 4.24264i 0.319499 + 0.184463i 0.651169 0.758933i \(-0.274279\pi\)
−0.331670 + 0.943395i \(0.607612\pi\)
\(24\) −1.55051 8.34242i −0.0646046 0.347601i
\(25\) 23.5000 + 40.7032i 0.940000 + 1.62813i
\(26\) 1.22474 + 0.707107i 0.0471056 + 0.0271964i
\(27\) −23.0000 + 14.1421i −0.851852 + 0.523783i
\(28\) 0 0
\(29\) 16.9706i 0.585192i 0.956236 + 0.292596i \(0.0945191\pi\)
−0.956236 + 0.292596i \(0.905481\pi\)
\(30\) −23.3939 27.3629i −0.779796 0.912096i
\(31\) −3.50000 6.06218i −0.112903 0.195554i 0.804036 0.594580i \(-0.202682\pi\)
−0.916940 + 0.399026i \(0.869348\pi\)
\(32\) −4.89898 + 2.82843i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 12.0000 0.352941
\(35\) 0 0
\(36\) 14.0000 + 11.3137i 0.388889 + 0.314270i
\(37\) 0.500000 0.866025i 0.0135135 0.0234061i −0.859190 0.511657i \(-0.829032\pi\)
0.872703 + 0.488251i \(0.162365\pi\)
\(38\) −37.9671 + 21.9203i −0.999134 + 0.576850i
\(39\) −2.94949 + 0.548188i −0.0756279 + 0.0140561i
\(40\) −12.0000 + 20.7846i −0.300000 + 0.519615i
\(41\) 33.9411i 0.827832i −0.910315 0.413916i \(-0.864161\pi\)
0.910315 0.413916i \(-0.135839\pi\)
\(42\) 0 0
\(43\) −31.0000 −0.720930 −0.360465 0.932773i \(-0.617382\pi\)
−0.360465 + 0.932773i \(0.617382\pi\)
\(44\) 0 0
\(45\) 75.4393 + 11.8707i 1.67643 + 0.263794i
\(46\) 6.00000 + 10.3923i 0.130435 + 0.225920i
\(47\) 36.7423 + 21.2132i 0.781752 + 0.451345i 0.837051 0.547125i \(-0.184278\pi\)
−0.0552988 + 0.998470i \(0.517611\pi\)
\(48\) 4.00000 11.3137i 0.0833333 0.235702i
\(49\) 0 0
\(50\) 66.4680i 1.32936i
\(51\) −19.3485 + 16.5420i −0.379382 + 0.324352i
\(52\) 1.00000 + 1.73205i 0.0192308 + 0.0333087i
\(53\) 22.0454 12.7279i 0.415951 0.240149i −0.277392 0.960757i \(-0.589470\pi\)
0.693344 + 0.720607i \(0.256137\pi\)
\(54\) −38.1691 + 1.05705i −0.706836 + 0.0195750i
\(55\) 0 0
\(56\) 0 0
\(57\) 31.0000 87.6812i 0.543860 1.53827i
\(58\) −12.0000 + 20.7846i −0.206897 + 0.358355i
\(59\) 7.34847 4.24264i 0.124550 0.0719092i −0.436430 0.899738i \(-0.643757\pi\)
0.560981 + 0.827829i \(0.310424\pi\)
\(60\) −9.30306 50.0545i −0.155051 0.834242i
\(61\) 25.0000 43.3013i 0.409836 0.709857i −0.585035 0.811008i \(-0.698919\pi\)
0.994871 + 0.101151i \(0.0322526\pi\)
\(62\) 9.89949i 0.159669i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) 7.34847 + 4.24264i 0.113053 + 0.0652714i
\(66\) 0 0
\(67\) −32.5000 56.2917i −0.485075 0.840174i 0.514778 0.857323i \(-0.327874\pi\)
−0.999853 + 0.0171494i \(0.994541\pi\)
\(68\) 14.6969 + 8.48528i 0.216131 + 0.124784i
\(69\) −24.0000 8.48528i −0.347826 0.122975i
\(70\) 0 0
\(71\) 59.3970i 0.836577i −0.908314 0.418289i \(-0.862630\pi\)
0.908314 0.418289i \(-0.137370\pi\)
\(72\) 9.14643 + 23.7559i 0.127034 + 0.329943i
\(73\) −48.5000 84.0045i −0.664384 1.15075i −0.979452 0.201677i \(-0.935361\pi\)
0.315068 0.949069i \(-0.397973\pi\)
\(74\) 1.22474 0.707107i 0.0165506 0.00955550i
\(75\) −91.6260 107.171i −1.22168 1.42895i
\(76\) −62.0000 −0.815789
\(77\) 0 0
\(78\) −4.00000 1.41421i −0.0512821 0.0181309i
\(79\) 51.5000 89.2006i 0.651899 1.12912i −0.330763 0.943714i \(-0.607306\pi\)
0.982662 0.185408i \(-0.0593606\pi\)
\(80\) −29.3939 + 16.9706i −0.367423 + 0.212132i
\(81\) 60.0857 54.3204i 0.741799 0.670622i
\(82\) 24.0000 41.5692i 0.292683 0.506942i
\(83\) 42.4264i 0.511162i −0.966788 0.255581i \(-0.917733\pi\)
0.966788 0.255581i \(-0.0822667\pi\)
\(84\) 0 0
\(85\) 72.0000 0.847059
\(86\) −37.9671 21.9203i −0.441478 0.254887i
\(87\) −9.30306 50.0545i −0.106932 0.575339i
\(88\) 0 0
\(89\) 102.879 + 59.3970i 1.15594 + 0.667382i 0.950327 0.311252i \(-0.100748\pi\)
0.205612 + 0.978634i \(0.434082\pi\)
\(90\) 84.0000 + 67.8823i 0.933333 + 0.754247i
\(91\) 0 0
\(92\) 16.9706i 0.184463i
\(93\) 13.6464 + 15.9617i 0.146736 + 0.171631i
\(94\) 30.0000 + 51.9615i 0.319149 + 0.552782i
\(95\) −227.803 + 131.522i −2.39792 + 1.38444i
\(96\) 12.8990 11.0280i 0.134364 0.114875i
\(97\) 166.000 1.71134 0.855670 0.517522i \(-0.173145\pi\)
0.855670 + 0.517522i \(0.173145\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −47.0000 + 81.4064i −0.470000 + 0.814064i
\(101\) −117.576 + 67.8823i −1.16411 + 0.672101i −0.952286 0.305206i \(-0.901275\pi\)
−0.211827 + 0.977307i \(0.567941\pi\)
\(102\) −35.3939 + 6.57826i −0.346999 + 0.0644927i
\(103\) 32.5000 56.2917i 0.315534 0.546521i −0.664017 0.747718i \(-0.731150\pi\)
0.979551 + 0.201197i \(0.0644830\pi\)
\(104\) 2.82843i 0.0271964i
\(105\) 0 0
\(106\) 36.0000 0.339623
\(107\) 139.621 + 80.6102i 1.30487 + 0.753366i 0.981235 0.192816i \(-0.0617622\pi\)
0.323634 + 0.946183i \(0.395096\pi\)
\(108\) −47.4949 25.6950i −0.439768 0.237917i
\(109\) −83.5000 144.626i −0.766055 1.32685i −0.939687 0.342036i \(-0.888884\pi\)
0.173632 0.984811i \(-0.444450\pi\)
\(110\) 0 0
\(111\) −1.00000 + 2.82843i −0.00900901 + 0.0254813i
\(112\) 0 0
\(113\) 161.220i 1.42673i 0.700793 + 0.713364i \(0.252830\pi\)
−0.700793 + 0.713364i \(0.747170\pi\)
\(114\) 99.9671 85.4668i 0.876904 0.749709i
\(115\) 36.0000 + 62.3538i 0.313043 + 0.542207i
\(116\) −29.3939 + 16.9706i −0.253395 + 0.146298i
\(117\) 8.39898 3.23375i 0.0717861 0.0276389i
\(118\) 12.0000 0.101695
\(119\) 0 0
\(120\) 24.0000 67.8823i 0.200000 0.565685i
\(121\) −60.5000 + 104.789i −0.500000 + 0.866025i
\(122\) 61.2372 35.3553i 0.501945 0.289798i
\(123\) 18.6061 + 100.109i 0.151269 + 0.813894i
\(124\) 7.00000 12.1244i 0.0564516 0.0977771i
\(125\) 186.676i 1.49341i
\(126\) 0 0
\(127\) 113.000 0.889764 0.444882 0.895589i \(-0.353246\pi\)
0.444882 + 0.895589i \(0.353246\pi\)
\(128\) −9.79796 5.65685i −0.0765466 0.0441942i
\(129\) 91.4342 16.9938i 0.708792 0.131735i
\(130\) 6.00000 + 10.3923i 0.0461538 + 0.0799408i
\(131\) −73.4847 42.4264i −0.560952 0.323866i 0.192576 0.981282i \(-0.438316\pi\)
−0.753527 + 0.657416i \(0.771649\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 91.9239i 0.685999i
\(135\) −229.015 + 6.34231i −1.69641 + 0.0469801i
\(136\) 12.0000 + 20.7846i 0.0882353 + 0.152828i
\(137\) 161.666 93.3381i 1.18005 0.681300i 0.224021 0.974584i \(-0.428082\pi\)
0.956025 + 0.293284i \(0.0947483\pi\)
\(138\) −23.3939 27.3629i −0.169521 0.198282i
\(139\) −113.000 −0.812950 −0.406475 0.913662i \(-0.633242\pi\)
−0.406475 + 0.913662i \(0.633242\pi\)
\(140\) 0 0
\(141\) −120.000 42.4264i −0.851064 0.300897i
\(142\) 42.0000 72.7461i 0.295775 0.512297i
\(143\) 0 0
\(144\) −5.59592 + 35.5624i −0.0388605 + 0.246961i
\(145\) −72.0000 + 124.708i −0.496552 + 0.860053i
\(146\) 137.179i 0.939580i
\(147\) 0 0
\(148\) 2.00000 0.0135135
\(149\) −58.7878 33.9411i −0.394549 0.227793i 0.289580 0.957154i \(-0.406484\pi\)
−0.684129 + 0.729361i \(0.739818\pi\)
\(150\) −36.4370 196.047i −0.242913 1.30698i
\(151\) 29.0000 + 50.2295i 0.192053 + 0.332646i 0.945930 0.324370i \(-0.105152\pi\)
−0.753877 + 0.657015i \(0.771819\pi\)
\(152\) −75.9342 43.8406i −0.499567 0.288425i
\(153\) 48.0000 59.3970i 0.313725 0.388215i
\(154\) 0 0
\(155\) 59.3970i 0.383206i
\(156\) −3.89898 4.56048i −0.0249935 0.0292338i
\(157\) −59.0000 102.191i −0.375796 0.650898i 0.614650 0.788800i \(-0.289297\pi\)
−0.990446 + 0.137902i \(0.955964\pi\)
\(158\) 126.149 72.8320i 0.798410 0.460962i
\(159\) −58.0454 + 49.6259i −0.365065 + 0.312113i
\(160\) −48.0000 −0.300000
\(161\) 0 0
\(162\) 112.000 24.0416i 0.691358 0.148405i
\(163\) 53.0000 91.7987i 0.325153 0.563182i −0.656390 0.754422i \(-0.727917\pi\)
0.981543 + 0.191240i \(0.0612507\pi\)
\(164\) 58.7878 33.9411i 0.358462 0.206958i
\(165\) 0 0
\(166\) 30.0000 51.9615i 0.180723 0.313021i
\(167\) 144.250i 0.863771i −0.901928 0.431886i \(-0.857848\pi\)
0.901928 0.431886i \(-0.142152\pi\)
\(168\) 0 0
\(169\) −168.000 −0.994083
\(170\) 88.1816 + 50.9117i 0.518715 + 0.299481i
\(171\) −43.3684 + 275.609i −0.253616 + 1.61175i
\(172\) −31.0000 53.6936i −0.180233 0.312172i
\(173\) 66.1362 + 38.1838i 0.382290 + 0.220715i 0.678814 0.734310i \(-0.262494\pi\)
−0.296524 + 0.955025i \(0.595827\pi\)
\(174\) 24.0000 67.8823i 0.137931 0.390128i
\(175\) 0 0
\(176\) 0 0
\(177\) −19.3485 + 16.5420i −0.109313 + 0.0934575i
\(178\) 84.0000 + 145.492i 0.471910 + 0.817372i
\(179\) 139.621 80.6102i 0.780005 0.450336i −0.0564270 0.998407i \(-0.517971\pi\)
0.836432 + 0.548071i \(0.184637\pi\)
\(180\) 54.8786 + 142.535i 0.304881 + 0.791863i
\(181\) −215.000 −1.18785 −0.593923 0.804522i \(-0.702421\pi\)
−0.593923 + 0.804522i \(0.702421\pi\)
\(182\) 0 0
\(183\) −50.0000 + 141.421i −0.273224 + 0.772794i
\(184\) −12.0000 + 20.7846i −0.0652174 + 0.112960i
\(185\) 7.34847 4.24264i 0.0397215 0.0229332i
\(186\) 5.42679 + 29.1985i 0.0291763 + 0.156981i
\(187\) 0 0
\(188\) 84.8528i 0.451345i
\(189\) 0 0
\(190\) −372.000 −1.95789
\(191\) −154.318 89.0955i −0.807947 0.466468i 0.0382955 0.999266i \(-0.487807\pi\)
−0.846242 + 0.532798i \(0.821141\pi\)
\(192\) 23.5959 4.38551i 0.122895 0.0228412i
\(193\) 48.5000 + 84.0045i 0.251295 + 0.435256i 0.963883 0.266327i \(-0.0858101\pi\)
−0.712587 + 0.701583i \(0.752477\pi\)
\(194\) 203.308 + 117.380i 1.04798 + 0.605050i
\(195\) −24.0000 8.48528i −0.123077 0.0435143i
\(196\) 0 0
\(197\) 364.867i 1.85212i 0.377380 + 0.926059i \(0.376825\pi\)
−0.377380 + 0.926059i \(0.623175\pi\)
\(198\) 0 0
\(199\) −53.0000 91.7987i −0.266332 0.461300i 0.701580 0.712591i \(-0.252478\pi\)
−0.967912 + 0.251291i \(0.919145\pi\)
\(200\) −115.126 + 66.4680i −0.575630 + 0.332340i
\(201\) 126.717 + 148.216i 0.630432 + 0.737391i
\(202\) −192.000 −0.950495
\(203\) 0 0
\(204\) −48.0000 16.9706i −0.235294 0.0831890i
\(205\) 144.000 249.415i 0.702439 1.21666i
\(206\) 79.6084 45.9619i 0.386449 0.223116i
\(207\) 75.4393 + 11.8707i 0.364441 + 0.0573465i
\(208\) −2.00000 + 3.46410i −0.00961538 + 0.0166543i
\(209\) 0 0
\(210\) 0 0
\(211\) 62.0000 0.293839 0.146919 0.989148i \(-0.453064\pi\)
0.146919 + 0.989148i \(0.453064\pi\)
\(212\) 44.0908 + 25.4558i 0.207976 + 0.120075i
\(213\) 32.5607 + 175.191i 0.152867 + 0.822492i
\(214\) 114.000 + 197.454i 0.532710 + 0.922681i
\(215\) −227.803 131.522i −1.05955 0.611730i
\(216\) −40.0000 65.0538i −0.185185 0.301175i
\(217\) 0 0
\(218\) 236.174i 1.08337i
\(219\) 189.101 + 221.183i 0.863473 + 1.00997i
\(220\) 0 0
\(221\) 7.34847 4.24264i 0.0332510 0.0191975i
\(222\) −3.22474 + 2.75699i −0.0145259 + 0.0124189i
\(223\) 202.000 0.905830 0.452915 0.891554i \(-0.350384\pi\)
0.452915 + 0.891554i \(0.350384\pi\)
\(224\) 0 0
\(225\) 329.000 + 265.872i 1.46222 + 1.18165i
\(226\) −114.000 + 197.454i −0.504425 + 0.873689i
\(227\) 14.6969 8.48528i 0.0647442 0.0373801i −0.467278 0.884110i \(-0.654765\pi\)
0.532023 + 0.846730i \(0.321432\pi\)
\(228\) 182.868 33.9877i 0.802054 0.149069i
\(229\) −0.500000 + 0.866025i −0.00218341 + 0.00378177i −0.867115 0.498108i \(-0.834028\pi\)
0.864932 + 0.501890i \(0.167362\pi\)
\(230\) 101.823i 0.442710i
\(231\) 0 0
\(232\) −48.0000 −0.206897
\(233\) −286.590 165.463i −1.23000 0.710142i −0.262971 0.964804i \(-0.584702\pi\)
−0.967030 + 0.254662i \(0.918036\pi\)
\(234\) 12.5732 + 1.97846i 0.0537317 + 0.00845494i
\(235\) 180.000 + 311.769i 0.765957 + 1.32668i
\(236\) 14.6969 + 8.48528i 0.0622752 + 0.0359546i
\(237\) −103.000 + 291.328i −0.434599 + 1.22923i
\(238\) 0 0
\(239\) 458.205i 1.91718i −0.284796 0.958588i \(-0.591926\pi\)
0.284796 0.958588i \(-0.408074\pi\)
\(240\) 77.3939 66.1679i 0.322474 0.275699i
\(241\) −11.0000 19.0526i −0.0456432 0.0790563i 0.842301 0.539007i \(-0.181200\pi\)
−0.887944 + 0.459951i \(0.847867\pi\)
\(242\) −148.194 + 85.5599i −0.612372 + 0.353553i
\(243\) −147.444 + 193.156i −0.606767 + 0.794880i
\(244\) 100.000 0.409836
\(245\) 0 0
\(246\) −48.0000 + 135.765i −0.195122 + 0.551888i
\(247\) −15.5000 + 26.8468i −0.0627530 + 0.108691i
\(248\) 17.1464 9.89949i 0.0691388 0.0399173i
\(249\) 23.2577 + 125.136i 0.0934042 + 0.502555i
\(250\) −132.000 + 228.631i −0.528000 + 0.914523i
\(251\) 178.191i 0.709924i 0.934881 + 0.354962i \(0.115506\pi\)
−0.934881 + 0.354962i \(0.884494\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 138.396 + 79.9031i 0.544867 + 0.314579i
\(255\) −212.363 + 39.4695i −0.832797 + 0.154783i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −242.499 140.007i −0.943578 0.544775i −0.0524977 0.998621i \(-0.516718\pi\)
−0.891080 + 0.453846i \(0.850052\pi\)
\(258\) 124.000 + 43.8406i 0.480620 + 0.169925i
\(259\) 0 0
\(260\) 16.9706i 0.0652714i
\(261\) 54.8786 + 142.535i 0.210263 + 0.546113i
\(262\) −60.0000 103.923i −0.229008 0.396653i
\(263\) −88.1816 + 50.9117i −0.335291 + 0.193581i −0.658188 0.752854i \(-0.728677\pi\)
0.322897 + 0.946434i \(0.395343\pi\)
\(264\) 0 0
\(265\) 216.000 0.815094
\(266\) 0 0
\(267\) −336.000 118.794i −1.25843 0.444921i
\(268\) 65.0000 112.583i 0.242537 0.420087i
\(269\) 367.423 212.132i 1.36589 0.788595i 0.375487 0.926828i \(-0.377476\pi\)
0.990400 + 0.138233i \(0.0441422\pi\)
\(270\) −284.969 154.170i −1.05544 0.571001i
\(271\) −125.000 + 216.506i −0.461255 + 0.798916i −0.999024 0.0441757i \(-0.985934\pi\)
0.537769 + 0.843092i \(0.319267\pi\)
\(272\) 33.9411i 0.124784i
\(273\) 0 0
\(274\) 264.000 0.963504
\(275\) 0 0
\(276\) −9.30306 50.0545i −0.0337067 0.181357i
\(277\) −191.500 331.688i −0.691336 1.19743i −0.971400 0.237447i \(-0.923689\pi\)
0.280065 0.959981i \(-0.409644\pi\)
\(278\) −138.396 79.9031i −0.497828 0.287421i
\(279\) −49.0000 39.5980i −0.175627 0.141928i
\(280\) 0 0
\(281\) 178.191i 0.634131i −0.948404 0.317066i \(-0.897302\pi\)
0.948404 0.317066i \(-0.102698\pi\)
\(282\) −116.969 136.814i −0.414785 0.485157i
\(283\) 152.500 + 264.138i 0.538869 + 0.933349i 0.998965 + 0.0454798i \(0.0144817\pi\)
−0.460096 + 0.887869i \(0.652185\pi\)
\(284\) 102.879 59.3970i 0.362248 0.209144i
\(285\) 599.803 512.801i 2.10457 1.79930i
\(286\) 0 0
\(287\) 0 0
\(288\) −32.0000 + 39.5980i −0.111111 + 0.137493i
\(289\) −108.500 + 187.928i −0.375433 + 0.650268i
\(290\) −176.363 + 101.823i −0.608149 + 0.351115i
\(291\) −489.615 + 90.9992i −1.68253 + 0.312712i
\(292\) 97.0000 168.009i 0.332192 0.575373i
\(293\) 135.765i 0.463360i 0.972792 + 0.231680i \(0.0744222\pi\)
−0.972792 + 0.231680i \(0.925578\pi\)
\(294\) 0 0
\(295\) 72.0000 0.244068
\(296\) 2.44949 + 1.41421i 0.00827530 + 0.00477775i
\(297\) 0 0
\(298\) −48.0000 83.1384i −0.161074 0.278988i
\(299\) 7.34847 + 4.24264i 0.0245768 + 0.0141894i
\(300\) 94.0000 265.872i 0.313333 0.886240i
\(301\) 0 0
\(302\) 82.0244i 0.271604i
\(303\) 309.576 264.672i 1.02170 0.873503i
\(304\) −62.0000 107.387i −0.203947 0.353247i
\(305\) 367.423 212.132i 1.20467 0.695515i
\(306\) 100.788 38.8050i 0.329372 0.126814i
\(307\) 199.000 0.648208 0.324104 0.946021i \(-0.394937\pi\)
0.324104 + 0.946021i \(0.394937\pi\)
\(308\) 0 0
\(309\) −65.0000 + 183.848i −0.210356 + 0.594977i
\(310\) 42.0000 72.7461i 0.135484 0.234665i
\(311\) −382.120 + 220.617i −1.22868 + 0.709380i −0.966754 0.255707i \(-0.917692\pi\)
−0.261929 + 0.965087i \(0.584358\pi\)
\(312\) −1.55051 8.34242i −0.00496958 0.0267385i
\(313\) 59.5000 103.057i 0.190096 0.329256i −0.755186 0.655511i \(-0.772453\pi\)
0.945282 + 0.326255i \(0.105787\pi\)
\(314\) 166.877i 0.531456i
\(315\) 0 0
\(316\) 206.000 0.651899
\(317\) 176.363 + 101.823i 0.556351 + 0.321209i 0.751680 0.659528i \(-0.229244\pi\)
−0.195329 + 0.980738i \(0.562577\pi\)
\(318\) −106.182 + 19.7348i −0.333904 + 0.0620590i
\(319\) 0 0
\(320\) −58.7878 33.9411i −0.183712 0.106066i
\(321\) −456.000 161.220i −1.42056 0.502244i
\(322\) 0 0
\(323\) 263.044i 0.814377i
\(324\) 154.171 + 49.7511i 0.475838 + 0.153553i
\(325\) 23.5000 + 40.7032i 0.0723077 + 0.125241i
\(326\) 129.823 74.9533i 0.398230 0.229918i
\(327\) 325.565 + 380.800i 0.995611 + 1.16453i
\(328\) 96.0000 0.292683
\(329\) 0 0
\(330\) 0 0
\(331\) −260.500 + 451.199i −0.787009 + 1.36314i 0.140782 + 0.990041i \(0.455038\pi\)
−0.927791 + 0.373099i \(0.878295\pi\)
\(332\) 73.4847 42.4264i 0.221339 0.127790i
\(333\) 1.39898 8.89060i 0.00420114 0.0266985i
\(334\) 102.000 176.669i 0.305389 0.528950i
\(335\) 551.543i 1.64640i
\(336\) 0 0
\(337\) 311.000 0.922849 0.461424 0.887180i \(-0.347339\pi\)
0.461424 + 0.887180i \(0.347339\pi\)
\(338\) −205.757 118.794i −0.608749 0.351461i
\(339\) −88.3791 475.518i −0.260705 1.40271i
\(340\) 72.0000 + 124.708i 0.211765 + 0.366787i
\(341\) 0 0
\(342\) −248.000 + 306.884i −0.725146 + 0.897323i
\(343\) 0 0
\(344\) 87.6812i 0.254887i
\(345\) −140.363 164.177i −0.406850 0.475876i
\(346\) 54.0000 + 93.5307i 0.156069 + 0.270320i
\(347\) −95.5301 + 55.1543i −0.275303 + 0.158946i −0.631295 0.775543i \(-0.717476\pi\)
0.355992 + 0.934489i \(0.384143\pi\)
\(348\) 77.3939 66.1679i 0.222396 0.190138i
\(349\) −50.0000 −0.143266 −0.0716332 0.997431i \(-0.522821\pi\)
−0.0716332 + 0.997431i \(0.522821\pi\)
\(350\) 0 0
\(351\) −23.0000 + 14.1421i −0.0655271 + 0.0402910i
\(352\) 0 0
\(353\) 139.621 80.6102i 0.395527 0.228357i −0.289025 0.957321i \(-0.593331\pi\)
0.684552 + 0.728964i \(0.259998\pi\)
\(354\) −35.3939 + 6.57826i −0.0999827 + 0.0185826i
\(355\) 252.000 436.477i 0.709859 1.22951i
\(356\) 237.588i 0.667382i
\(357\) 0 0
\(358\) 228.000 0.636872
\(359\) 352.727 + 203.647i 0.982525 + 0.567261i 0.903032 0.429574i \(-0.141336\pi\)
0.0794936 + 0.996835i \(0.474670\pi\)
\(360\) −33.5755 + 213.375i −0.0932653 + 0.592707i
\(361\) −300.000 519.615i −0.831025 1.43938i
\(362\) −263.320 152.028i −0.727404 0.419967i
\(363\) 121.000 342.240i 0.333333 0.942809i
\(364\) 0 0
\(365\) 823.072i 2.25499i
\(366\) −161.237 + 137.850i −0.440539 + 0.376639i
\(367\) −267.500 463.324i −0.728883 1.26246i −0.957356 0.288912i \(-0.906707\pi\)
0.228473 0.973550i \(-0.426627\pi\)
\(368\) −29.3939 + 16.9706i −0.0798747 + 0.0461157i
\(369\) −109.757 285.071i −0.297445 0.772550i
\(370\) 12.0000 0.0324324
\(371\) 0 0
\(372\) −14.0000 + 39.5980i −0.0376344 + 0.106446i
\(373\) 192.500 333.420i 0.516086 0.893887i −0.483740 0.875212i \(-0.660722\pi\)
0.999826 0.0186750i \(-0.00594477\pi\)
\(374\) 0 0
\(375\) −102.334 550.600i −0.272890 1.46827i
\(376\) −60.0000 + 103.923i −0.159574 + 0.276391i
\(377\) 16.9706i 0.0450148i
\(378\) 0 0
\(379\) −55.0000 −0.145119 −0.0725594 0.997364i \(-0.523117\pi\)
−0.0725594 + 0.997364i \(0.523117\pi\)
\(380\) −455.605 263.044i −1.19896 0.692220i
\(381\) −333.292 + 61.9453i −0.874783 + 0.162586i
\(382\) −126.000 218.238i −0.329843 0.571305i
\(383\) −360.075 207.889i −0.940144 0.542792i −0.0501383 0.998742i \(-0.515966\pi\)
−0.890005 + 0.455950i \(0.849300\pi\)
\(384\) 32.0000 + 11.3137i 0.0833333 + 0.0294628i
\(385\) 0 0
\(386\) 137.179i 0.355385i
\(387\) −260.368 + 100.246i −0.672786 + 0.259034i
\(388\) 166.000 + 287.520i 0.427835 + 0.741032i
\(389\) −330.681 + 190.919i −0.850080 + 0.490794i −0.860678 0.509150i \(-0.829960\pi\)
0.0105979 + 0.999944i \(0.496627\pi\)
\(390\) −23.3939 27.3629i −0.0599843 0.0701612i
\(391\) 72.0000 0.184143
\(392\) 0 0
\(393\) 240.000 + 84.8528i 0.610687 + 0.215910i
\(394\) −258.000 + 446.869i −0.654822 + 1.13419i
\(395\) 756.892 436.992i 1.91618 1.10631i
\(396\) 0 0
\(397\) −240.500 + 416.558i −0.605793 + 1.04927i 0.386132 + 0.922443i \(0.373811\pi\)
−0.991926 + 0.126822i \(0.959522\pi\)
\(398\) 149.907i 0.376650i
\(399\) 0 0
\(400\) −188.000 −0.470000
\(401\) −66.1362 38.1838i −0.164928 0.0952214i 0.415264 0.909701i \(-0.363689\pi\)
−0.580192 + 0.814480i \(0.697023\pi\)
\(402\) 50.3916 + 271.129i 0.125352 + 0.674449i
\(403\) −3.50000 6.06218i −0.00868486 0.0150426i
\(404\) −235.151 135.765i −0.582057 0.336051i
\(405\) 672.000 144.250i 1.65926 0.356172i
\(406\) 0 0
\(407\) 0 0
\(408\) −46.7878 54.7257i −0.114676 0.134132i
\(409\) −24.5000 42.4352i −0.0599022 0.103754i 0.834519 0.550979i \(-0.185746\pi\)
−0.894421 + 0.447225i \(0.852412\pi\)
\(410\) 352.727 203.647i 0.860309 0.496699i
\(411\) −425.666 + 363.923i −1.03568 + 0.885458i
\(412\) 130.000 0.315534
\(413\) 0 0
\(414\) 84.0000 + 67.8823i 0.202899 + 0.163967i
\(415\) 180.000 311.769i 0.433735 0.751251i
\(416\) −4.89898 + 2.82843i −0.0117764 + 0.00679910i
\(417\) 333.292 61.9453i 0.799262 0.148550i
\(418\) 0 0
\(419\) 322.441i 0.769548i 0.923011 + 0.384774i \(0.125721\pi\)
−0.923011 + 0.384774i \(0.874279\pi\)
\(420\) 0 0
\(421\) −313.000 −0.743468 −0.371734 0.928339i \(-0.621237\pi\)
−0.371734 + 0.928339i \(0.621237\pi\)
\(422\) 75.9342 + 43.8406i 0.179939 + 0.103888i
\(423\) 377.196 + 59.3537i 0.891717 + 0.140316i
\(424\) 36.0000 + 62.3538i 0.0849057 + 0.147061i
\(425\) 345.378 + 199.404i 0.812654 + 0.469186i
\(426\) −84.0000 + 237.588i −0.197183 + 0.557718i
\(427\) 0 0
\(428\) 322.441i 0.753366i
\(429\) 0 0
\(430\) −186.000 322.161i −0.432558 0.749213i
\(431\) −301.287 + 173.948i −0.699042 + 0.403592i −0.806991 0.590564i \(-0.798905\pi\)
0.107948 + 0.994157i \(0.465572\pi\)
\(432\) −2.98979 107.959i −0.00692082 0.249904i
\(433\) 97.0000 0.224018 0.112009 0.993707i \(-0.464271\pi\)
0.112009 + 0.993707i \(0.464271\pi\)
\(434\) 0 0
\(435\) 144.000 407.294i 0.331034 0.936307i
\(436\) 167.000 289.252i 0.383028 0.663423i
\(437\) −227.803 + 131.522i −0.521287 + 0.300965i
\(438\) 75.1997 + 404.607i 0.171689 + 0.923761i
\(439\) 187.000 323.894i 0.425968 0.737798i −0.570542 0.821268i \(-0.693267\pi\)
0.996510 + 0.0834699i \(0.0266002\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.0000 0.0271493
\(443\) −521.741 301.227i −1.17775 0.679972i −0.222254 0.974989i \(-0.571341\pi\)
−0.955492 + 0.295017i \(0.904675\pi\)
\(444\) −5.89898 + 1.09638i −0.0132860 + 0.00246932i
\(445\) 504.000 + 872.954i 1.13258 + 1.96169i
\(446\) 247.398 + 142.836i 0.554705 + 0.320259i
\(447\) 192.000 + 67.8823i 0.429530 + 0.151862i
\(448\) 0 0
\(449\) 42.4264i 0.0944909i 0.998883 + 0.0472454i \(0.0150443\pi\)
−0.998883 + 0.0472454i \(0.984956\pi\)
\(450\) 214.941 + 558.264i 0.477647 + 1.24059i
\(451\) 0 0
\(452\) −279.242 + 161.220i −0.617792 + 0.356682i
\(453\) −113.070 132.254i −0.249604 0.291951i
\(454\) 24.0000 0.0528634
\(455\) 0 0
\(456\) 248.000 + 87.6812i 0.543860 + 0.192283i
\(457\) −227.500 + 394.042i −0.497812 + 0.862235i −0.999997 0.00252486i \(-0.999196\pi\)
0.502185 + 0.864760i \(0.332530\pi\)
\(458\) −1.22474 + 0.707107i −0.00267412 + 0.00154390i
\(459\) −109.015 + 201.504i −0.237505 + 0.439006i
\(460\) −72.0000 + 124.708i −0.156522 + 0.271104i
\(461\) 220.617i 0.478563i 0.970950 + 0.239281i \(0.0769118\pi\)
−0.970950 + 0.239281i \(0.923088\pi\)
\(462\) 0 0
\(463\) −7.00000 −0.0151188 −0.00755940 0.999971i \(-0.502406\pi\)
−0.00755940 + 0.999971i \(0.502406\pi\)
\(464\) −58.7878 33.9411i −0.126698 0.0731490i
\(465\) 32.5607 + 175.191i 0.0700230 + 0.376754i
\(466\) −234.000 405.300i −0.502146 0.869742i
\(467\) 536.438 + 309.713i 1.14869 + 0.663197i 0.948568 0.316574i \(-0.102533\pi\)
0.200122 + 0.979771i \(0.435866\pi\)
\(468\) 14.0000 + 11.3137i 0.0299145 + 0.0241746i
\(469\) 0 0
\(470\) 509.117i 1.08323i
\(471\) 230.040 + 269.068i 0.488407 + 0.571270i
\(472\) 12.0000 + 20.7846i 0.0254237 + 0.0440352i
\(473\) 0 0
\(474\) −332.149 + 283.970i −0.700736 + 0.599094i
\(475\) −1457.00 −3.06737
\(476\) 0 0
\(477\) 144.000 178.191i 0.301887 0.373566i
\(478\) 324.000 561.184i 0.677824 1.17403i
\(479\) −580.529 + 335.169i −1.21196 + 0.699726i −0.963186 0.268836i \(-0.913361\pi\)
−0.248774 + 0.968561i \(0.580028\pi\)
\(480\) 141.576 26.3130i 0.294949 0.0548188i
\(481\) 0.500000 0.866025i 0.00103950 0.00180047i
\(482\) 31.1127i 0.0645492i
\(483\) 0 0
\(484\) −242.000 −0.500000
\(485\) 1219.85 + 704.278i 2.51515 + 1.45212i
\(486\) −317.164 + 132.308i −0.652600 + 0.272238i
\(487\) 231.500 + 400.970i 0.475359 + 0.823347i 0.999602 0.0282226i \(-0.00898473\pi\)
−0.524242 + 0.851569i \(0.675651\pi\)
\(488\) 122.474 + 70.7107i 0.250972 + 0.144899i
\(489\) −106.000 + 299.813i −0.216769 + 0.613115i
\(490\) 0 0
\(491\) 356.382i 0.725829i 0.931823 + 0.362914i \(0.118218\pi\)
−0.931823 + 0.362914i \(0.881782\pi\)
\(492\) −154.788 + 132.336i −0.314609 + 0.268975i
\(493\) 72.0000 + 124.708i 0.146045 + 0.252957i
\(494\) −37.9671 + 21.9203i −0.0768565 + 0.0443731i
\(495\) 0 0
\(496\) 28.0000 0.0564516
\(497\) 0 0
\(498\) −60.0000 + 169.706i −0.120482 + 0.340774i
\(499\) 267.500 463.324i 0.536072 0.928504i −0.463038 0.886338i \(-0.653241\pi\)
0.999111 0.0421660i \(-0.0134258\pi\)
\(500\) −323.333 + 186.676i −0.646665 + 0.373352i
\(501\) 79.0760 + 425.463i 0.157836 + 0.849228i
\(502\) −126.000 + 218.238i −0.250996 + 0.434738i
\(503\) 627.911i 1.24833i 0.781292 + 0.624166i \(0.214561\pi\)
−0.781292 + 0.624166i \(0.785439\pi\)
\(504\) 0 0
\(505\) −1152.00 −2.28119
\(506\) 0 0
\(507\) 495.514 92.0956i 0.977346 0.181648i
\(508\) 113.000 + 195.722i 0.222441 + 0.385279i
\(509\) 551.135 + 318.198i 1.08278 + 0.625144i 0.931645 0.363370i \(-0.118374\pi\)
0.151135 + 0.988513i \(0.451707\pi\)
\(510\) −288.000 101.823i −0.564706 0.199654i
\(511\) 0 0
\(512\) 22.6274i 0.0441942i
\(513\) −23.1709 836.679i −0.0451675 1.63095i
\(514\) −198.000 342.946i −0.385214 0.667210i
\(515\) 477.650 275.772i 0.927477 0.535479i
\(516\) 120.868 + 141.375i 0.234241 + 0.273982i
\(517\) 0 0
\(518\) 0 0
\(519\) −216.000 76.3675i −0.416185 0.147144i
\(520\) −12.0000 + 20.7846i −0.0230769 + 0.0399704i
\(521\) 558.484 322.441i 1.07195 0.618888i 0.143233 0.989689i \(-0.454250\pi\)
0.928712 + 0.370801i \(0.120917\pi\)
\(522\) −33.5755 + 213.375i −0.0643209 + 0.408763i
\(523\) 344.500 596.692i 0.658700 1.14090i −0.322253 0.946654i \(-0.604440\pi\)
0.980952 0.194248i \(-0.0622266\pi\)
\(524\) 169.706i 0.323866i
\(525\) 0 0
\(526\) −144.000 −0.273764
\(527\) −51.4393 29.6985i −0.0976078 0.0563539i
\(528\) 0 0
\(529\) −228.500 395.774i −0.431947 0.748154i
\(530\) 264.545 + 152.735i 0.499141 + 0.288179i
\(531\) 48.0000 59.3970i 0.0903955 0.111859i
\(532\) 0 0
\(533\) 33.9411i 0.0636794i
\(534\) −327.514 383.080i −0.613323 0.717379i
\(535\) 684.000 + 1184.72i 1.27850 + 2.21444i
\(536\) 159.217 91.9239i 0.297046 0.171500i
\(537\) −367.621 + 314.297i −0.684583 + 0.585284i
\(538\) 600.000 1.11524
\(539\) 0 0
\(540\) −240.000 390.323i −0.444444 0.722820i
\(541\) −287.500 + 497.965i −0.531423 + 0.920452i 0.467904 + 0.883779i \(0.345009\pi\)
−0.999327 + 0.0366729i \(0.988324\pi\)
\(542\) −306.186 + 176.777i −0.564919 + 0.326156i
\(543\) 634.140 117.860i 1.16785 0.217054i
\(544\) −24.0000 + 41.5692i −0.0441176 + 0.0764140i
\(545\) 1417.04i 2.60008i
\(546\) 0 0
\(547\) 302.000 0.552102 0.276051 0.961143i \(-0.410974\pi\)
0.276051 + 0.961143i \(0.410974\pi\)
\(548\) 323.333 + 186.676i 0.590023 + 0.340650i
\(549\) 69.9490 444.530i 0.127412 0.809709i
\(550\) 0 0
\(551\) −455.605 263.044i −0.826869 0.477393i
\(552\) 24.0000 67.8823i 0.0434783 0.122975i
\(553\) 0 0
\(554\) 541.644i 0.977696i
\(555\) −19.3485 + 16.5420i −0.0348621 + 0.0298053i
\(556\) −113.000 195.722i −0.203237 0.352018i
\(557\) 117.576 67.8823i 0.211087 0.121871i −0.390729 0.920506i \(-0.627777\pi\)
0.601817 + 0.798634i \(0.294444\pi\)
\(558\) −32.0125 83.1457i −0.0573701 0.149007i
\(559\) −31.0000 −0.0554562
\(560\) 0 0
\(561\) 0 0
\(562\) 126.000 218.238i 0.224199 0.388325i
\(563\) −521.741 + 301.227i −0.926716 + 0.535040i −0.885772 0.464121i \(-0.846370\pi\)
−0.0409448 + 0.999161i \(0.513037\pi\)
\(564\) −46.5153 250.273i −0.0824739 0.443746i
\(565\) −684.000 + 1184.72i −1.21062 + 2.09685i
\(566\) 431.335i 0.762076i
\(567\) 0 0
\(568\) 168.000 0.295775
\(569\) −573.181 330.926i −1.00735 0.581592i −0.0969334 0.995291i \(-0.530903\pi\)
−0.910414 + 0.413699i \(0.864237\pi\)
\(570\) 1097.21 203.926i 1.92493 0.357765i
\(571\) −56.5000 97.8609i −0.0989492 0.171385i 0.812301 0.583239i \(-0.198215\pi\)
−0.911250 + 0.411854i \(0.864881\pi\)
\(572\) 0 0
\(573\) 504.000 + 178.191i 0.879581 + 0.310979i
\(574\) 0 0
\(575\) 398.808i 0.693580i
\(576\) −67.1918 + 25.8700i −0.116652 + 0.0449132i
\(577\) −60.5000 104.789i −0.104853 0.181610i 0.808825 0.588049i \(-0.200104\pi\)
−0.913678 + 0.406439i \(0.866770\pi\)
\(578\) −265.770 + 153.442i −0.459809 + 0.265471i
\(579\) −189.101 221.183i −0.326598 0.382009i
\(580\) −288.000 −0.496552
\(581\) 0 0
\(582\) −664.000 234.759i −1.14089 0.403367i
\(583\) 0 0
\(584\) 237.601 137.179i 0.406850 0.234895i
\(585\) 75.4393 + 11.8707i 0.128956 + 0.0202919i
\(586\) −96.0000 + 166.277i −0.163823 + 0.283749i
\(587\) 67.8823i 0.115643i 0.998327 + 0.0578213i \(0.0184154\pi\)
−0.998327 + 0.0578213i \(0.981585\pi\)
\(588\) 0 0
\(589\) 217.000 0.368421
\(590\) 88.1816 + 50.9117i 0.149460 + 0.0862910i
\(591\) −200.016 1076.17i −0.338436 1.82093i
\(592\) 2.00000 + 3.46410i 0.00337838 + 0.00585152i
\(593\) −426.211 246.073i −0.718737 0.414963i 0.0955505 0.995425i \(-0.469539\pi\)
−0.814288 + 0.580461i \(0.802872\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 135.765i 0.227793i
\(597\) 206.646 + 241.705i 0.346141 + 0.404867i
\(598\) 6.00000 + 10.3923i 0.0100334 + 0.0173784i
\(599\) 88.1816 50.9117i 0.147215 0.0849945i −0.424583 0.905389i \(-0.639579\pi\)
0.571798 + 0.820394i \(0.306246\pi\)
\(600\) 303.126 259.158i 0.505210 0.431929i
\(601\) −791.000 −1.31614 −0.658070 0.752957i \(-0.728627\pi\)
−0.658070 + 0.752957i \(0.728627\pi\)
\(602\) 0 0
\(603\) −455.000 367.696i −0.754561 0.609777i
\(604\) −58.0000 + 100.459i −0.0960265 + 0.166323i
\(605\) −889.165 + 513.360i −1.46969 + 0.848528i
\(606\) 566.302 105.252i 0.934492 0.173683i
\(607\) 56.5000 97.8609i 0.0930807 0.161221i −0.815725 0.578440i \(-0.803662\pi\)
0.908806 + 0.417219i \(0.136995\pi\)
\(608\) 175.362i 0.288425i
\(609\) 0 0
\(610\) 600.000 0.983607
\(611\) 36.7423 + 21.2132i 0.0601348 + 0.0347188i
\(612\) 150.879 + 23.7415i 0.246534 + 0.0387933i
\(613\) 287.000 + 497.099i 0.468189 + 0.810928i 0.999339 0.0363503i \(-0.0115732\pi\)
−0.531150 + 0.847278i \(0.678240\pi\)
\(614\) 243.724 + 140.714i 0.396945 + 0.229176i
\(615\) −288.000 + 814.587i −0.468293 + 1.32453i
\(616\) 0 0
\(617\) 661.852i 1.07269i 0.843998 + 0.536347i \(0.180196\pi\)
−0.843998 + 0.536347i \(0.819804\pi\)
\(618\) −209.608 + 179.205i −0.339172 + 0.289975i
\(619\) 476.500 + 825.322i 0.769790 + 1.33332i 0.937677 + 0.347509i \(0.112972\pi\)
−0.167887 + 0.985806i \(0.553694\pi\)
\(620\) 102.879 59.3970i 0.165933 0.0958016i
\(621\) −229.015 + 6.34231i −0.368784 + 0.0102131i
\(622\) −624.000 −1.00322
\(623\) 0 0
\(624\) 4.00000 11.3137i 0.00641026 0.0181309i
\(625\) −204.500 + 354.204i −0.327200 + 0.566727i
\(626\) 145.745 84.1457i 0.232819 0.134418i
\(627\) 0 0
\(628\) 118.000 204.382i 0.187898 0.325449i
\(629\) 8.48528i 0.0134901i
\(630\) 0 0
\(631\) 758.000 1.20127 0.600634 0.799524i \(-0.294915\pi\)
0.600634 + 0.799524i \(0.294915\pi\)
\(632\) 252.297 + 145.664i 0.399205 + 0.230481i
\(633\) −182.868 + 33.9877i −0.288892 + 0.0536930i
\(634\) 144.000 + 249.415i 0.227129 + 0.393400i
\(635\) 830.377 + 479.418i 1.30768 + 0.754990i
\(636\) −144.000 50.9117i −0.226415 0.0800498i
\(637\) 0 0
\(638\) 0 0
\(639\) −192.075 498.874i −0.300587 0.780710i
\(640\) −48.0000 83.1384i −0.0750000 0.129904i
\(641\) −933.256 + 538.815i −1.45594 + 0.840586i −0.998808 0.0488147i \(-0.984456\pi\)
−0.457129 + 0.889400i \(0.651122\pi\)
\(642\) −444.484 519.894i −0.692342 0.809804i
\(643\) 1111.00 1.72784 0.863919 0.503631i \(-0.168003\pi\)
0.863919 + 0.503631i \(0.168003\pi\)
\(644\) 0 0
\(645\) 744.000 + 263.044i 1.15349 + 0.407820i
\(646\) −186.000 + 322.161i −0.287926 + 0.498702i
\(647\) 293.939 169.706i 0.454310 0.262296i −0.255339 0.966852i \(-0.582187\pi\)
0.709649 + 0.704556i \(0.248854\pi\)
\(648\) 153.641 + 169.948i 0.237101 + 0.262266i
\(649\) 0 0
\(650\) 66.4680i 0.102259i
\(651\) 0 0
\(652\) 212.000 0.325153
\(653\) −558.484 322.441i −0.855258 0.493784i 0.00716327 0.999974i \(-0.497720\pi\)
−0.862422 + 0.506191i \(0.831053\pi\)
\(654\) 129.468 + 696.592i 0.197963 + 1.06513i
\(655\) −360.000 623.538i −0.549618 0.951967i
\(656\) 117.576 + 67.8823i 0.179231 + 0.103479i
\(657\) −679.000 548.715i −1.03349 0.835182i
\(658\) 0 0
\(659\) 873.984i 1.32623i 0.748519 + 0.663114i \(0.230765\pi\)
−0.748519 + 0.663114i \(0.769235\pi\)
\(660\) 0 0
\(661\) −432.500 749.112i −0.654312 1.13330i −0.982066 0.188538i \(-0.939625\pi\)
0.327754 0.944763i \(-0.393708\pi\)
\(662\) −638.092 + 368.403i −0.963885 + 0.556499i
\(663\) −19.3485 + 16.5420i −0.0291832 + 0.0249502i
\(664\) 120.000 0.180723
\(665\) 0 0
\(666\) 8.00000 9.89949i 0.0120120 0.0148641i
\(667\) −72.0000 + 124.708i −0.107946 + 0.186968i
\(668\) 249.848 144.250i 0.374024 0.215943i
\(669\) −595.797 + 110.734i −0.890578 + 0.165522i
\(670\) 390.000 675.500i 0.582090 1.00821i
\(671\) 0 0
\(672\) 0 0
\(673\) −505.000 −0.750371 −0.375186 0.926950i \(-0.622421\pi\)
−0.375186 + 0.926950i \(0.622421\pi\)
\(674\) 380.896 + 219.910i 0.565127 + 0.326276i
\(675\) −1116.13 603.833i −1.65353 0.894568i
\(676\) −168.000 290.985i −0.248521 0.430450i
\(677\) 279.242 + 161.220i 0.412469 + 0.238139i 0.691850 0.722041i \(-0.256796\pi\)
−0.279381 + 0.960180i \(0.590129\pi\)
\(678\) 228.000 644.881i 0.336283 0.951152i
\(679\) 0 0
\(680\) 203.647i 0.299481i
\(681\) −38.6969 + 33.0839i −0.0568237 + 0.0485814i
\(682\) 0 0
\(683\) 683.408 394.566i 1.00060 0.577695i 0.0921720 0.995743i \(-0.470619\pi\)
0.908425 + 0.418048i \(0.137286\pi\)
\(684\) −520.737 + 200.493i −0.761311 + 0.293118i
\(685\) 1584.00 2.31241
\(686\) 0 0
\(687\) 1.00000 2.82843i 0.00145560 0.00411707i
\(688\) 62.0000 107.387i 0.0901163 0.156086i
\(689\) 22.0454 12.7279i 0.0319962 0.0184730i
\(690\) −55.8184 300.327i −0.0808962 0.435257i
\(691\) 92.5000 160.215i 0.133864 0.231859i −0.791299 0.611429i \(-0.790595\pi\)
0.925163 + 0.379570i \(0.123928\pi\)
\(692\) 152.735i 0.220715i
\(693\) 0 0
\(694\) −156.000 −0.224784
\(695\) −830.377 479.418i −1.19479 0.689811i
\(696\) 141.576 26.3130i 0.203413 0.0378061i
\(697\) −144.000 249.415i −0.206600 0.357841i
\(698\) −61.2372 35.3553i −0.0877324 0.0506523i
\(699\) 936.000 + 330.926i 1.33906 + 0.473428i
\(700\) 0 0
\(701\) 93.3381i 0.133150i 0.997781 + 0.0665750i \(0.0212072\pi\)
−0.997781 + 0.0665750i \(0.978793\pi\)
\(702\) −38.1691 + 1.05705i −0.0543720 + 0.00150577i
\(703\) 15.5000 + 26.8468i 0.0220484 + 0.0381889i
\(704\) 0 0
\(705\) −701.816 820.886i −0.995484 1.16438i
\(706\) 228.000 0.322946
\(707\) 0 0
\(708\) −48.0000 16.9706i −0.0677966 0.0239697i
\(709\) −97.0000 + 168.009i −0.136812 + 0.236966i −0.926288 0.376815i \(-0.877019\pi\)
0.789476 + 0.613782i \(0.210352\pi\)
\(710\) 617.271 356.382i 0.869396 0.501946i
\(711\) 144.095 915.732i 0.202665 1.28795i
\(712\) −168.000 + 290.985i −0.235955 + 0.408686i
\(713\) 59.3970i 0.0833057i
\(714\) 0 0
\(715\) 0 0
\(716\) 279.242 + 161.220i 0.390003 + 0.225168i
\(717\) 251.183 + 1351.47i 0.350324 + 1.88490i
\(718\) 288.000 + 498.831i 0.401114 + 0.694750i
\(719\) 338.030 + 195.161i 0.470139 + 0.271435i 0.716298 0.697795i \(-0.245835\pi\)
−0.246159 + 0.969229i \(0.579169\pi\)
\(720\) −192.000 + 237.588i −0.266667 + 0.329983i
\(721\) 0 0
\(722\) 848.528i 1.17525i
\(723\) 42.8888 + 50.1653i 0.0593206 + 0.0693849i
\(724\) −215.000 372.391i −0.296961 0.514352i
\(725\) −690.756 + 398.808i −0.952767 + 0.550080i
\(726\) 390.194 333.596i 0.537457 0.459499i
\(727\) −425.000 −0.584594 −0.292297 0.956328i \(-0.594420\pi\)
−0.292297 + 0.956328i \(0.594420\pi\)
\(728\) 0 0
\(729\) 329.000 650.538i 0.451303 0.892371i
\(730\) 582.000 1008.05i 0.797260 1.38090i
\(731\) −227.803 + 131.522i −0.311631 + 0.179920i
\(732\) −294.949 + 54.8188i −0.402936 + 0.0748891i
\(733\) 203.500 352.472i 0.277626 0.480863i −0.693168 0.720776i \(-0.743786\pi\)
0.970794 + 0.239913i \(0.0771190\pi\)
\(734\) 756.604i 1.03080i
\(735\) 0 0
\(736\) −48.0000 −0.0652174
\(737\) 0 0
\(738\) 67.1510 426.749i 0.0909905 0.578251i
\(739\) −380.500 659.045i −0.514885 0.891807i −0.999851 0.0172738i \(-0.994501\pi\)
0.484966 0.874533i \(-0.338832\pi\)
\(740\) 14.6969 + 8.48528i 0.0198607 + 0.0114666i
\(741\) 31.0000 87.6812i 0.0418354 0.118328i
\(742\) 0 0
\(743\) 576.999i 0.776580i 0.921537 + 0.388290i \(0.126934\pi\)
−0.921537 + 0.388290i \(0.873066\pi\)
\(744\) −45.1464 + 38.5979i −0.0606807 + 0.0518789i
\(745\) −288.000 498.831i −0.386577 0.669571i
\(746\) 471.527 272.236i 0.632073 0.364928i
\(747\) −137.196 356.339i −0.183663 0.477026i
\(748\) 0 0
\(749\) 0 0
\(750\) 264.000 746.705i 0.352000 0.995606i
\(751\) −344.500 + 596.692i −0.458722 + 0.794529i −0.998894 0.0470253i \(-0.985026\pi\)
0.540172 + 0.841555i \(0.318359\pi\)
\(752\) −146.969 + 84.8528i −0.195438 + 0.112836i
\(753\) −97.6821 525.572i −0.129724 0.697971i
\(754\) −12.0000 + 20.7846i −0.0159151 + 0.0275658i
\(755\) 492.146i 0.651849i
\(756\) 0 0
\(757\) −142.000 −0.187583 −0.0937913 0.995592i \(-0.529899\pi\)
−0.0937913 + 0.995592i \(0.529899\pi\)
\(758\) −67.3610 38.8909i −0.0888667 0.0513072i
\(759\) 0 0
\(760\) −372.000 644.323i −0.489474 0.847793i
\(761\) −962.649 555.786i −1.26498 0.730336i −0.290946 0.956740i \(-0.593970\pi\)
−0.974034 + 0.226403i \(0.927303\pi\)
\(762\) −452.000 159.806i −0.593176 0.209719i
\(763\) 0 0
\(764\) 356.382i 0.466468i
\(765\) 604.727 232.830i 0.790492 0.304353i
\(766\) −294.000 509.223i −0.383812 0.664782i
\(767\) 7.34847 4.24264i 0.00958079 0.00553147i
\(768\) 31.1918 + 36.4838i 0.0406144 + 0.0475050i
\(769\) −1127.00 −1.46554 −0.732770 0.680477i \(-0.761773\pi\)
−0.732770 + 0.680477i \(0.761773\pi\)
\(770\) 0 0
\(771\) 792.000 + 280.014i 1.02724 + 0.363183i
\(772\) −97.0000 + 168.009i −0.125648 + 0.217628i
\(773\) −396.817 + 229.103i −0.513347 + 0.296381i −0.734208 0.678924i \(-0.762447\pi\)
0.220861 + 0.975305i \(0.429113\pi\)
\(774\) −389.770 61.3321i −0.503578 0.0792405i
\(775\) 164.500 284.922i 0.212258 0.367642i
\(776\) 469.519i 0.605050i
\(777\) 0 0
\(778\) −540.000 −0.694087
\(779\) 911.210 + 526.087i 1.16972 + 0.675337i
\(780\) −9.30306 50.0545i −0.0119270 0.0641724i
\(781\) 0 0
\(782\) 88.1816 + 50.9117i 0.112764 + 0.0651045i
\(783\) −240.000 390.323i −0.306513 0.498497i
\(784\) 0 0
\(785\) 1001.26i 1.27549i
\(786\) 233.939 + 273.629i 0.297632 + 0.348128i
\(787\) −293.000 507.491i −0.372300 0.644842i 0.617619 0.786477i \(-0.288097\pi\)
−0.989919 + 0.141635i \(0.954764\pi\)
\(788\) −631.968 + 364.867i −0.801990 + 0.463029i
\(789\) 232.182 198.504i 0.294273 0.251589i
\(790\) 1236.00 1.56456
\(791\) 0 0
\(792\) 0 0
\(793\) 25.0000 43.3013i 0.0315259 0.0546044i
\(794\) −589.102 + 340.118i −0.741942 + 0.428361i
\(795\) −637.090 + 118.409i −0.801371 + 0.148942i
\(796\) 106.000 183.597i 0.133166 0.230650i
\(797\) 483.661i 0.606852i 0.952855 + 0.303426i \(0.0981305\pi\)
−0.952855 + 0.303426i \(0.901869\pi\)
\(798\) 0 0
\(799\) 360.000 0.450563
\(800\) −230.252 132.936i −0.287815 0.166170i
\(801\) 1056.15 + 166.190i 1.31854 + 0.207479i
\(802\) −54.0000 93.5307i −0.0673317 0.116622i
\(803\) 0 0
\(804\) −130.000 + 367.696i −0.161692 + 0.457333i
\(805\) 0 0
\(806\) 9.89949i 0.0122823i
\(807\) −967.423 + 827.098i −1.19879 + 1.02491i
\(808\) −192.000 332.554i −0.237624 0.411576i
\(809\) 698.105 403.051i 0.862923 0.498209i −0.00206714 0.999998i \(-0.500658\pi\)
0.864990 + 0.501789i \(0.167325\pi\)
\(810\) 925.029 + 298.507i 1.14201 + 0.368527i
\(811\) −398.000 −0.490752 −0.245376 0.969428i \(-0.578911\pi\)
−0.245376 + 0.969428i \(0.578911\pi\)
\(812\) 0 0
\(813\) 250.000 707.107i 0.307503 0.869750i
\(814\) 0 0
\(815\) 778.938 449.720i 0.955752 0.551804i
\(816\) −18.6061 100.109i −0.0228016 0.122683i
\(817\) 480.500 832.250i 0.588127 1.01867i
\(818\) 69.2965i 0.0847145i
\(819\) 0 0
\(820\) 576.000 0.702439
\(821\) 1403.56 + 810.344i 1.70957 + 0.987021i 0.935081 + 0.354435i \(0.115327\pi\)
0.774490 + 0.632586i \(0.218006\pi\)
\(822\) −778.665 + 144.722i −0.947281 + 0.176060i
\(823\) 581.000 + 1006.32i 0.705954 + 1.22275i 0.966346 + 0.257245i \(0.0828147\pi\)
−0.260392 + 0.965503i \(0.583852\pi\)
\(824\) 159.217 + 91.9239i 0.193224 + 0.111558i
\(825\) 0 0
\(826\) 0 0
\(827\) 144.250i 0.174425i −0.996190 0.0872127i \(-0.972204\pi\)
0.996190 0.0872127i \(-0.0277960\pi\)
\(828\) 54.8786 + 142.535i 0.0662785 + 0.172144i
\(829\) 623.500 + 1079.93i 0.752111 + 1.30269i 0.946798 + 0.321829i \(0.104298\pi\)
−0.194687 + 0.980865i \(0.562369\pi\)
\(830\) 440.908 254.558i 0.531215 0.306697i
\(831\) 746.655 + 873.332i 0.898501 + 1.05094i
\(832\) −8.00000 −0.00961538
\(833\) 0 0
\(834\) 452.000 + 159.806i 0.541966 + 0.191614i
\(835\) 612.000 1060.02i 0.732934 1.26948i
\(836\) 0 0
\(837\) 166.232 + 89.9326i 0.198605 + 0.107446i
\(838\) −228.000 + 394.908i −0.272076 + 0.471250i
\(839\) 1001.26i 1.19340i −0.802464 0.596700i \(-0.796478\pi\)
0.802464 0.596700i \(-0.203522\pi\)
\(840\) 0 0
\(841\) 553.000 0.657551
\(842\) −383.345 221.324i −0.455279 0.262856i
\(843\) 97.6821 + 525.572i 0.115874 + 0.623455i
\(844\) 62.0000 + 107.387i 0.0734597 + 0.127236i
\(845\) −1234.54 712.764i −1.46100 0.843507i
\(846\) 420.000 + 339.411i 0.496454 + 0.401195i
\(847\) 0 0
\(848\) 101.823i 0.120075i
\(849\) −594.594 695.473i −0.700347 0.819167i
\(850\) 282.000 + 488.438i 0.331765 + 0.574633i
\(851\) 7.34847 4.24264i 0.00863510 0.00498548i
\(852\) −270.879 + 231.588i −0.317933 + 0.271816i
\(853\) 337.000 0.395076 0.197538 0.980295i \(-0.436705\pi\)
0.197538 + 0.980295i \(0.436705\pi\)
\(854\) 0 0
\(855\) −1488.00 + 1841.31i −1.74035 + 2.15357i
\(856\) −228.000 + 394.908i −0.266355 + 0.461341i
\(857\) −969.998 + 560.029i −1.13185 + 0.653476i −0.944400 0.328798i \(-0.893356\pi\)
−0.187453 + 0.982274i \(0.560023\pi\)
\(858\) 0 0
\(859\) −545.000 + 943.968i −0.634459 + 1.09891i 0.352171 + 0.935936i \(0.385444\pi\)
−0.986630 + 0.162979i \(0.947890\pi\)
\(860\) 526.087i 0.611730i
\(861\) 0 0
\(862\) −492.000 −0.570766
\(863\) 999.392 + 576.999i 1.15804 + 0.668597i 0.950834 0.309700i \(-0.100229\pi\)
0.207209 + 0.978297i \(0.433562\pi\)
\(864\) 72.6765 134.336i 0.0841164 0.155481i
\(865\) 324.000 + 561.184i 0.374566 + 0.648768i
\(866\) 118.800 + 68.5894i 0.137183 + 0.0792025i
\(867\) 217.000 613.769i 0.250288 0.707922i
\(868\) 0 0
\(869\) 0 0
\(870\) 464.363 397.007i 0.533751 0.456330i
\(871\) −32.5000 56.2917i −0.0373134 0.0646288i
\(872\) 409.065 236.174i 0.469111 0.270841i
\(873\) 1394.23 536.803i 1.59706 0.614894i
\(874\) −372.000 −0.425629
\(875\) 0 0
\(876\) −194.000 + 548.715i −0.221461 + 0.626387i
\(877\) 23.0000 39.8372i 0.0262258 0.0454244i −0.852615 0.522540i \(-0.824984\pi\)
0.878840 + 0.477116i \(0.158318\pi\)
\(878\) 458.055 264.458i 0.521702 0.301205i
\(879\) −74.4245 400.436i −0.0846695 0.455559i
\(880\) 0 0
\(881\) 924.896i 1.04982i 0.851156 + 0.524912i \(0.175902\pi\)
−0.851156 + 0.524912i \(0.824098\pi\)
\(882\) 0 0
\(883\) 329.000 0.372593 0.186297 0.982494i \(-0.440351\pi\)
0.186297 + 0.982494i \(0.440351\pi\)
\(884\) 14.6969 + 8.48528i 0.0166255 + 0.00959873i
\(885\) −212.363 + 39.4695i −0.239958 + 0.0445984i
\(886\) −426.000 737.854i −0.480813 0.832792i
\(887\) 1219.85 + 704.278i 1.37525 + 0.794000i 0.991583 0.129472i \(-0.0413281\pi\)
0.383666 + 0.923472i \(0.374661\pi\)
\(888\) −8.00000 2.82843i −0.00900901 0.00318517i
\(889\) 0 0
\(890\) 1425.53i 1.60172i
\(891\) 0 0
\(892\) 202.000 + 349.874i 0.226457 + 0.392236i
\(893\) −1139.01 + 657.609i −1.27549 + 0.736405i
\(894\) 187.151 + 218.903i 0.209341 + 0.244858i
\(895\) 1368.00 1.52849
\(896\) 0 0
\(897\) −24.0000 8.48528i −0.0267559 0.00945962i
\(898\) −30.0000 + 51.9615i −0.0334076 + 0.0578636i
\(899\) 102.879 59.3970i 0.114437 0.0660700i
\(900\) −131.504 + 835.717i −0.146116 + 0.928574i
\(901\) 108.000 187.061i 0.119867 0.207615i
\(902\) 0 0
\(903\) 0 0
\(904\) −456.000 −0.504425
\(905\) −1579.92 912.168i −1.74577 1.00792i
\(906\) −44.9648 241.930i −0.0496300 0.267031i
\(907\) 87.5000 + 151.554i 0.0964719 + 0.167094i 0.910222 0.414121i \(-0.135911\pi\)
−0.813750 + 0.581215i \(0.802578\pi\)
\(908\) 29.3939 + 16.9706i 0.0323721 + 0.0186900i
\(909\) −768.000 + 950.352i −0.844884 + 1.04549i
\(910\) 0 0
\(911\) 1450.98i 1.59274i −0.604812 0.796368i \(-0.706752\pi\)
0.604812 0.796368i \(-0.293248\pi\)
\(912\) 241.737 + 282.750i 0.265062 + 0.310032i
\(913\) 0 0
\(914\) −557.259 + 321.734i −0.609692 + 0.352006i
\(915\) −967.423 + 827.098i −1.05729 + 0.903933i
\(916\) −2.00000 −0.00218341
\(917\) 0 0
\(918\) −276.000 + 169.706i −0.300654 + 0.184865i
\(919\) −548.500 + 950.030i −0.596844 + 1.03376i 0.396439 + 0.918061i \(0.370246\pi\)
−0.993284 + 0.115704i \(0.963088\pi\)
\(920\) −176.363 + 101.823i −0.191699 + 0.110678i
\(921\) −586.948 + 109.089i −0.637295 + 0.118447i
\(922\) −156.000 + 270.200i −0.169197 + 0.293058i
\(923\) 59.3970i 0.0643521i
\(924\) 0 0
\(925\) 47.0000 0.0508108
\(926\) −8.57321 4.94975i −0.00925833 0.00534530i
\(927\) 90.9337 577.889i 0.0980946 0.623397i
\(928\) −48.0000 83.1384i −0.0517241 0.0895888i
\(929\) −492.347 284.257i −0.529976 0.305982i 0.211031 0.977479i \(-0.432318\pi\)
−0.741007 + 0.671498i \(0.765651\pi\)
\(930\) −84.0000 + 237.588i −0.0903226 + 0.255471i
\(931\) 0 0
\(932\) 661.852i 0.710142i
\(933\) 1006.12 860.182i 1.07837 0.921953i
\(934\) 438.000 + 758.638i 0.468951 + 0.812247i
\(935\) 0 0
\(936\) 9.14643 + 23.7559i 0.00977182 + 0.0253802i
\(937\) 1.00000 0.00106724 0.000533618 1.00000i \(-0.499830\pi\)
0.000533618 1.00000i \(0.499830\pi\)
\(938\) 0 0
\(939\) −119.000 + 336.583i −0.126731 + 0.358448i
\(940\) −360.000 + 623.538i −0.382979 + 0.663339i
\(941\) 330.681 190.919i 0.351415 0.202889i −0.313894 0.949458i \(-0.601634\pi\)
0.665308 + 0.746569i \(0.268300\pi\)
\(942\) 91.4801 + 492.203i 0.0971126 + 0.522508i
\(943\) 144.000 249.415i 0.152704 0.264491i
\(944\) 33.9411i 0.0359546i
\(945\) 0 0
\(946\) 0 0
\(947\) −1455.00 840.043i −1.53643 0.887057i −0.999044 0.0437190i \(-0.986079\pi\)
−0.537384 0.843338i \(-0.680587\pi\)
\(948\) −607.595 + 112.927i −0.640923 + 0.119121i
\(949\) −48.5000 84.0045i −0.0511064 0.0885189i
\(950\) −1784.45 1030.25i −1.87837 1.08448i
\(951\) −576.000 203.647i −0.605678 0.214140i
\(952\) 0 0
\(953\) 195.161i 0.204786i 0.994744 + 0.102393i \(0.0326500\pi\)
−0.994744 + 0.102393i \(0.967350\pi\)
\(954\) 302.363 116.415i 0.316943 0.122028i
\(955\) −756.000 1309.43i −0.791623 1.37113i
\(956\) 793.635 458.205i 0.830162 0.479294i
\(957\) 0 0
\(958\) −948.000 −0.989562
\(959\) 0 0
\(960\) 192.000 + 67.8823i 0.200000 + 0.0707107i
\(961\) 456.000 789.815i 0.474506 0.821868i
\(962\) 1.22474 0.707107i 0.00127312 0.000735038i
\(963\) 1433.35 + 225.544i 1.48842 + 0.234210i
\(964\) 22.0000 38.1051i 0.0228216 0.0395281i
\(965\) 823.072i 0.852925i
\(966\) 0 0
\(967\) −223.000 −0.230610 −0.115305 0.993330i \(-0.536785\pi\)
−0.115305 + 0.993330i \(0.536785\pi\)
\(968\) −296.388 171.120i −0.306186 0.176777i
\(969\) −144.197 775.845i −0.148811 0.800665i
\(970\) 996.000 + 1725.12i 1.02680 + 1.77848i
\(971\) −492.347 284.257i −0.507052 0.292747i 0.224569 0.974458i \(-0.427903\pi\)
−0.731621 + 0.681712i \(0.761236\pi\)
\(972\) −482.000 62.2254i −0.495885 0.0640179i
\(973\) 0 0
\(974\) 654.781i 0.672260i
\(975\) −91.6260 107.171i −0.0939754 0.109919i
\(976\) 100.000 + 173.205i 0.102459 + 0.177464i
\(977\) 1396.21 806.102i 1.42908 0.825079i 0.432030 0.901859i \(-0.357797\pi\)
0.997048 + 0.0767807i \(0.0244641\pi\)
\(978\) −341.823 + 292.241i −0.349512 + 0.298815i
\(979\) 0 0
\(980\) 0 0
\(981\) −1169.00 944.695i −1.19164 0.962991i
\(982\) −252.000 + 436.477i −0.256619 + 0.444477i
\(983\) 1491.74 861.256i 1.51754 0.876151i 0.517750 0.855532i \(-0.326770\pi\)
0.999787 0.0206186i \(-0.00656358\pi\)
\(984\) −283.151 + 52.6261i −0.287755 + 0.0534818i
\(985\) −1548.00 + 2681.21i −1.57157 + 2.72205i
\(986\) 203.647i 0.206538i
\(987\) 0 0
\(988\) −62.0000 −0.0627530
\(989\) −227.803 131.522i −0.230336 0.132985i
\(990\) 0 0
\(991\) 447.500 + 775.093i 0.451564 + 0.782132i 0.998483 0.0550534i \(-0.0175329\pi\)
−0.546919 + 0.837185i \(0.684200\pi\)
\(992\) 34.2929 + 19.7990i 0.0345694 + 0.0199587i
\(993\) 521.000 1473.61i 0.524673 1.48400i
\(994\) 0 0
\(995\) 899.440i 0.903960i
\(996\) −193.485 + 165.420i −0.194262 + 0.166084i
\(997\) 203.500 + 352.472i 0.204112 + 0.353533i 0.949850 0.312707i \(-0.101236\pi\)
−0.745737 + 0.666240i \(0.767903\pi\)
\(998\) 655.239 378.302i 0.656552 0.379060i
\(999\) 0.747449 + 26.9897i 0.000748197 + 0.0270167i
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 294.3.h.b.275.2 4
3.2 odd 2 inner 294.3.h.b.275.1 4
7.2 even 3 294.3.b.c.197.1 2
7.3 odd 6 42.3.h.a.11.1 4
7.4 even 3 inner 294.3.h.b.263.1 4
7.5 odd 6 294.3.b.b.197.1 2
7.6 odd 2 42.3.h.a.23.2 yes 4
21.2 odd 6 294.3.b.c.197.2 2
21.5 even 6 294.3.b.b.197.2 2
21.11 odd 6 inner 294.3.h.b.263.2 4
21.17 even 6 42.3.h.a.11.2 yes 4
21.20 even 2 42.3.h.a.23.1 yes 4
28.3 even 6 336.3.bn.c.305.2 4
28.27 even 2 336.3.bn.c.65.1 4
84.59 odd 6 336.3.bn.c.305.1 4
84.83 odd 2 336.3.bn.c.65.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.3.h.a.11.1 4 7.3 odd 6
42.3.h.a.11.2 yes 4 21.17 even 6
42.3.h.a.23.1 yes 4 21.20 even 2
42.3.h.a.23.2 yes 4 7.6 odd 2
294.3.b.b.197.1 2 7.5 odd 6
294.3.b.b.197.2 2 21.5 even 6
294.3.b.c.197.1 2 7.2 even 3
294.3.b.c.197.2 2 21.2 odd 6
294.3.h.b.263.1 4 7.4 even 3 inner
294.3.h.b.263.2 4 21.11 odd 6 inner
294.3.h.b.275.1 4 3.2 odd 2 inner
294.3.h.b.275.2 4 1.1 even 1 trivial
336.3.bn.c.65.1 4 28.27 even 2
336.3.bn.c.65.2 4 84.83 odd 2
336.3.bn.c.305.1 4 84.59 odd 6
336.3.bn.c.305.2 4 28.3 even 6