Properties

Label 693.2.i.g.100.2
Level $693$
Weight $2$
Character 693.100
Analytic conductor $5.534$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [693,2,Mod(100,693)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(693, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("693.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.i (of order \(3\), degree \(2\), 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: \(5.53363286007\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1783323.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 100.2
Root \(-0.956115 - 1.65604i\) of defining polynomial
Character \(\chi\) \(=\) 693.100
Dual form 693.2.i.g.298.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.328310 - 0.568650i) q^{2} +(0.784425 + 1.35866i) q^{4} +(-1.78442 + 3.09071i) q^{5} +(1.78442 + 1.95341i) q^{7} +2.34338 q^{8} +O(q^{10})\) \(q+(0.328310 - 0.568650i) q^{2} +(0.784425 + 1.35866i) q^{4} +(-1.78442 + 3.09071i) q^{5} +(1.78442 + 1.95341i) q^{7} +2.34338 q^{8} +(1.17169 + 2.02943i) q^{10} +(-0.500000 - 0.866025i) q^{11} -5.91223 q^{13} +(1.69665 - 0.373387i) q^{14} +(-0.799494 + 1.38476i) q^{16} +(-0.828310 - 1.43468i) q^{17} +(-0.740539 + 1.28265i) q^{19} -5.59899 q^{20} -0.656620 q^{22} +(1.67169 - 2.89545i) q^{23} +(-3.86834 - 6.70017i) q^{25} +(-1.94105 + 3.36199i) q^{26} +(-1.25429 + 3.95674i) q^{28} -3.08007 q^{29} +(3.54003 + 6.13152i) q^{31} +(2.86834 + 4.96812i) q^{32} -1.08777 q^{34} +(-9.22162 + 2.02943i) q^{35} +(2.25561 - 3.90683i) q^{37} +(0.486253 + 0.842215i) q^{38} +(-4.18158 + 7.24272i) q^{40} +1.28575 q^{41} +1.59899 q^{43} +(0.784425 - 1.35866i) q^{44} +(-1.09767 - 1.90121i) q^{46} +(-0.828310 + 1.43468i) q^{47} +(-0.631656 + 6.97144i) q^{49} -5.08007 q^{50} +(-4.63770 - 8.03273i) q^{52} +(4.61274 + 7.98949i) q^{53} +3.56885 q^{55} +(4.18158 + 4.57759i) q^{56} +(-1.01122 + 1.75148i) q^{58} +(4.42598 + 7.66602i) q^{59} +(3.34338 - 5.79090i) q^{61} +4.64892 q^{62} +0.568850 q^{64} +(10.5499 - 18.2730i) q^{65} +(4.91223 + 8.50823i) q^{67} +(1.29949 - 2.25079i) q^{68} +(-1.87352 + 5.91015i) q^{70} +8.61878 q^{71} +(-2.28057 - 3.95007i) q^{73} +(-1.48108 - 2.56530i) q^{74} -2.32359 q^{76} +(0.799494 - 2.52206i) q^{77} +(3.19665 - 5.53677i) q^{79} +(-2.85327 - 4.94202i) q^{80} +(0.422124 - 0.731140i) q^{82} -0.167838 q^{83} +5.91223 q^{85} +(0.524964 - 0.909265i) q^{86} +(-1.17169 - 2.02943i) q^{88} +(-1.28442 + 2.22469i) q^{89} +(-10.5499 - 11.5490i) q^{91} +5.24526 q^{92} +(0.543885 + 0.942037i) q^{94} +(-2.64287 - 4.57759i) q^{95} +9.73669 q^{97} +(3.75693 + 2.64799i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 4 q^{4} - 2 q^{5} + 2 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 4 q^{4} - 2 q^{5} + 2 q^{7} + 18 q^{8} + 9 q^{10} - 3 q^{11} - 22 q^{13} - 12 q^{14} - 2 q^{16} - 3 q^{17} + 11 q^{19} - 28 q^{20} + 12 q^{23} - 3 q^{25} + q^{26} + 13 q^{28} + 18 q^{29} + 3 q^{31} - 3 q^{32} - 20 q^{34} - 9 q^{35} + 4 q^{37} + 8 q^{38} + 3 q^{40} + 10 q^{41} + 4 q^{43} - 4 q^{44} + 10 q^{46} - 3 q^{47} - 24 q^{49} + 6 q^{50} + 7 q^{52} + 17 q^{53} + 4 q^{55} - 3 q^{56} + 13 q^{58} + 8 q^{59} + 24 q^{61} - 26 q^{62} - 14 q^{64} + 15 q^{65} + 16 q^{67} + 5 q^{68} - 27 q^{70} - 14 q^{71} + 20 q^{73} + 22 q^{74} - 78 q^{76} + 2 q^{77} - 3 q^{79} + 9 q^{80} - 41 q^{82} + 22 q^{83} + 22 q^{85} - 21 q^{86} - 9 q^{88} + q^{89} - 15 q^{91} - 50 q^{92} + 10 q^{94} - 17 q^{95} + 18 q^{97} + 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(442\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.328310 0.568650i 0.232150 0.402096i −0.726290 0.687388i \(-0.758757\pi\)
0.958441 + 0.285292i \(0.0920905\pi\)
\(3\) 0 0
\(4\) 0.784425 + 1.35866i 0.392212 + 0.679332i
\(5\) −1.78442 + 3.09071i −0.798019 + 1.38221i 0.122885 + 0.992421i \(0.460785\pi\)
−0.920904 + 0.389789i \(0.872548\pi\)
\(6\) 0 0
\(7\) 1.78442 + 1.95341i 0.674449 + 0.738321i
\(8\) 2.34338 0.828510
\(9\) 0 0
\(10\) 1.17169 + 2.02943i 0.370521 + 0.641761i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) 0 0
\(13\) −5.91223 −1.63976 −0.819879 0.572537i \(-0.805959\pi\)
−0.819879 + 0.572537i \(0.805959\pi\)
\(14\) 1.69665 0.373387i 0.453450 0.0997919i
\(15\) 0 0
\(16\) −0.799494 + 1.38476i −0.199874 + 0.346191i
\(17\) −0.828310 1.43468i −0.200895 0.347960i 0.747922 0.663786i \(-0.231052\pi\)
−0.948817 + 0.315826i \(0.897718\pi\)
\(18\) 0 0
\(19\) −0.740539 + 1.28265i −0.169891 + 0.294261i −0.938382 0.345601i \(-0.887675\pi\)
0.768490 + 0.639862i \(0.221008\pi\)
\(20\) −5.59899 −1.25197
\(21\) 0 0
\(22\) −0.656620 −0.139992
\(23\) 1.67169 2.89545i 0.348571 0.603743i −0.637425 0.770513i \(-0.720000\pi\)
0.985996 + 0.166769i \(0.0533335\pi\)
\(24\) 0 0
\(25\) −3.86834 6.70017i −0.773669 1.34003i
\(26\) −1.94105 + 3.36199i −0.380670 + 0.659340i
\(27\) 0 0
\(28\) −1.25429 + 3.95674i −0.237038 + 0.747754i
\(29\) −3.08007 −0.571954 −0.285977 0.958236i \(-0.592318\pi\)
−0.285977 + 0.958236i \(0.592318\pi\)
\(30\) 0 0
\(31\) 3.54003 + 6.13152i 0.635809 + 1.10125i 0.986343 + 0.164703i \(0.0526667\pi\)
−0.350534 + 0.936550i \(0.614000\pi\)
\(32\) 2.86834 + 4.96812i 0.507056 + 0.878247i
\(33\) 0 0
\(34\) −1.08777 −0.186551
\(35\) −9.22162 + 2.02943i −1.55874 + 0.343036i
\(36\) 0 0
\(37\) 2.25561 3.90683i 0.370820 0.642279i −0.618872 0.785492i \(-0.712410\pi\)
0.989692 + 0.143213i \(0.0457434\pi\)
\(38\) 0.486253 + 0.842215i 0.0788807 + 0.136625i
\(39\) 0 0
\(40\) −4.18158 + 7.24272i −0.661167 + 1.14517i
\(41\) 1.28575 0.200800 0.100400 0.994947i \(-0.467988\pi\)
0.100400 + 0.994947i \(0.467988\pi\)
\(42\) 0 0
\(43\) 1.59899 0.243843 0.121922 0.992540i \(-0.461094\pi\)
0.121922 + 0.992540i \(0.461094\pi\)
\(44\) 0.784425 1.35866i 0.118256 0.204826i
\(45\) 0 0
\(46\) −1.09767 1.90121i −0.161842 0.280319i
\(47\) −0.828310 + 1.43468i −0.120821 + 0.209269i −0.920092 0.391703i \(-0.871886\pi\)
0.799270 + 0.600972i \(0.205220\pi\)
\(48\) 0 0
\(49\) −0.631656 + 6.97144i −0.0902366 + 0.995920i
\(50\) −5.08007 −0.718430
\(51\) 0 0
\(52\) −4.63770 8.03273i −0.643133 1.11394i
\(53\) 4.61274 + 7.98949i 0.633608 + 1.09744i 0.986808 + 0.161893i \(0.0517601\pi\)
−0.353200 + 0.935548i \(0.614907\pi\)
\(54\) 0 0
\(55\) 3.56885 0.481224
\(56\) 4.18158 + 4.57759i 0.558788 + 0.611706i
\(57\) 0 0
\(58\) −1.01122 + 1.75148i −0.132779 + 0.229981i
\(59\) 4.42598 + 7.66602i 0.576213 + 0.998030i 0.995909 + 0.0903653i \(0.0288035\pi\)
−0.419696 + 0.907665i \(0.637863\pi\)
\(60\) 0 0
\(61\) 3.34338 5.79090i 0.428076 0.741449i −0.568626 0.822596i \(-0.692525\pi\)
0.996702 + 0.0811468i \(0.0258583\pi\)
\(62\) 4.64892 0.590413
\(63\) 0 0
\(64\) 0.568850 0.0711062
\(65\) 10.5499 18.2730i 1.30856 2.26649i
\(66\) 0 0
\(67\) 4.91223 + 8.50823i 0.600124 + 1.03945i 0.992802 + 0.119770i \(0.0382156\pi\)
−0.392677 + 0.919676i \(0.628451\pi\)
\(68\) 1.29949 2.25079i 0.157587 0.272948i
\(69\) 0 0
\(70\) −1.87352 + 5.91015i −0.223928 + 0.706399i
\(71\) 8.61878 1.02286 0.511430 0.859325i \(-0.329116\pi\)
0.511430 + 0.859325i \(0.329116\pi\)
\(72\) 0 0
\(73\) −2.28057 3.95007i −0.266921 0.462321i 0.701144 0.713019i \(-0.252673\pi\)
−0.968065 + 0.250699i \(0.919340\pi\)
\(74\) −1.48108 2.56530i −0.172172 0.298210i
\(75\) 0 0
\(76\) −2.32359 −0.266534
\(77\) 0.799494 2.52206i 0.0911108 0.287416i
\(78\) 0 0
\(79\) 3.19665 5.53677i 0.359652 0.622935i −0.628251 0.778011i \(-0.716229\pi\)
0.987903 + 0.155076i \(0.0495622\pi\)
\(80\) −2.85327 4.94202i −0.319006 0.552534i
\(81\) 0 0
\(82\) 0.422124 0.731140i 0.0466158 0.0807409i
\(83\) −0.167838 −0.0184226 −0.00921130 0.999958i \(-0.502932\pi\)
−0.00921130 + 0.999958i \(0.502932\pi\)
\(84\) 0 0
\(85\) 5.91223 0.641271
\(86\) 0.524964 0.909265i 0.0566083 0.0980485i
\(87\) 0 0
\(88\) −1.17169 2.02943i −0.124903 0.216338i
\(89\) −1.28442 + 2.22469i −0.136149 + 0.235817i −0.926036 0.377436i \(-0.876806\pi\)
0.789887 + 0.613252i \(0.210139\pi\)
\(90\) 0 0
\(91\) −10.5499 11.5490i −1.10593 1.21067i
\(92\) 5.24526 0.546856
\(93\) 0 0
\(94\) 0.543885 + 0.942037i 0.0560975 + 0.0971637i
\(95\) −2.64287 4.57759i −0.271153 0.469651i
\(96\) 0 0
\(97\) 9.73669 0.988611 0.494305 0.869288i \(-0.335422\pi\)
0.494305 + 0.869288i \(0.335422\pi\)
\(98\) 3.75693 + 2.64799i 0.379507 + 0.267487i
\(99\) 0 0
\(100\) 6.06885 10.5116i 0.606885 1.05116i
\(101\) 0.927299 + 1.60613i 0.0922697 + 0.159816i 0.908466 0.417959i \(-0.137254\pi\)
−0.816196 + 0.577775i \(0.803921\pi\)
\(102\) 0 0
\(103\) 1.58392 2.74343i 0.156068 0.270318i −0.777379 0.629032i \(-0.783451\pi\)
0.933447 + 0.358714i \(0.116785\pi\)
\(104\) −13.8546 −1.35856
\(105\) 0 0
\(106\) 6.05763 0.588369
\(107\) −2.38341 + 4.12819i −0.230413 + 0.399087i −0.957930 0.287003i \(-0.907341\pi\)
0.727517 + 0.686090i \(0.240674\pi\)
\(108\) 0 0
\(109\) 7.44105 + 12.8883i 0.712723 + 1.23447i 0.963831 + 0.266513i \(0.0858716\pi\)
−0.251108 + 0.967959i \(0.580795\pi\)
\(110\) 1.17169 2.02943i 0.111716 0.193498i
\(111\) 0 0
\(112\) −4.13166 + 0.909265i −0.390405 + 0.0859174i
\(113\) −12.4432 −1.17056 −0.585281 0.810831i \(-0.699016\pi\)
−0.585281 + 0.810831i \(0.699016\pi\)
\(114\) 0 0
\(115\) 5.96601 + 10.3334i 0.556333 + 0.963597i
\(116\) −2.41608 4.18478i −0.224327 0.388547i
\(117\) 0 0
\(118\) 5.81237 0.535072
\(119\) 1.32446 4.17810i 0.121413 0.383006i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −2.19533 3.80243i −0.198756 0.344255i
\(123\) 0 0
\(124\) −5.55378 + 9.61943i −0.498744 + 0.863850i
\(125\) 9.76683 0.873571
\(126\) 0 0
\(127\) −6.62142 −0.587556 −0.293778 0.955874i \(-0.594913\pi\)
−0.293778 + 0.955874i \(0.594913\pi\)
\(128\) −5.54993 + 9.61276i −0.490549 + 0.849656i
\(129\) 0 0
\(130\) −6.92730 11.9984i −0.607564 1.05233i
\(131\) −3.02882 + 5.24606i −0.264629 + 0.458351i −0.967466 0.253000i \(-0.918583\pi\)
0.702837 + 0.711351i \(0.251916\pi\)
\(132\) 0 0
\(133\) −3.82699 + 0.842215i −0.331842 + 0.0730293i
\(134\) 6.45094 0.557276
\(135\) 0 0
\(136\) −1.94105 3.36199i −0.166443 0.288288i
\(137\) −3.71172 6.42889i −0.317114 0.549257i 0.662771 0.748822i \(-0.269380\pi\)
−0.979885 + 0.199565i \(0.936047\pi\)
\(138\) 0 0
\(139\) −10.8245 −0.918119 −0.459059 0.888406i \(-0.651813\pi\)
−0.459059 + 0.888406i \(0.651813\pi\)
\(140\) −9.99097 10.9371i −0.844391 0.924357i
\(141\) 0 0
\(142\) 2.82963 4.90107i 0.237458 0.411288i
\(143\) 2.95611 + 5.12014i 0.247203 + 0.428168i
\(144\) 0 0
\(145\) 5.49615 9.51961i 0.456430 0.790560i
\(146\) −2.99494 −0.247863
\(147\) 0 0
\(148\) 7.07742 0.581760
\(149\) −0.500000 + 0.866025i −0.0409616 + 0.0709476i −0.885779 0.464107i \(-0.846375\pi\)
0.844818 + 0.535054i \(0.179709\pi\)
\(150\) 0 0
\(151\) −8.21172 14.2231i −0.668261 1.15746i −0.978390 0.206767i \(-0.933706\pi\)
0.310130 0.950694i \(-0.399628\pi\)
\(152\) −1.73536 + 3.00574i −0.140757 + 0.243798i
\(153\) 0 0
\(154\) −1.17169 1.28265i −0.0944175 0.103359i
\(155\) −25.2677 −2.02955
\(156\) 0 0
\(157\) 5.72547 + 9.91681i 0.456942 + 0.791447i 0.998798 0.0490246i \(-0.0156113\pi\)
−0.541855 + 0.840472i \(0.682278\pi\)
\(158\) −2.09899 3.63555i −0.166987 0.289229i
\(159\) 0 0
\(160\) −20.4734 −1.61856
\(161\) 8.63902 1.90121i 0.680850 0.149837i
\(162\) 0 0
\(163\) 4.46986 7.74203i 0.350107 0.606402i −0.636161 0.771556i \(-0.719479\pi\)
0.986268 + 0.165154i \(0.0528120\pi\)
\(164\) 1.00857 + 1.74690i 0.0787563 + 0.136410i
\(165\) 0 0
\(166\) −0.0551029 + 0.0954410i −0.00427681 + 0.00740766i
\(167\) 18.2178 1.40973 0.704867 0.709340i \(-0.251007\pi\)
0.704867 + 0.709340i \(0.251007\pi\)
\(168\) 0 0
\(169\) 21.9545 1.68880
\(170\) 1.94105 3.36199i 0.148871 0.257853i
\(171\) 0 0
\(172\) 1.25429 + 2.17249i 0.0956384 + 0.165651i
\(173\) 9.78057 16.9404i 0.743603 1.28796i −0.207241 0.978290i \(-0.566449\pi\)
0.950845 0.309669i \(-0.100218\pi\)
\(174\) 0 0
\(175\) 6.18544 19.5124i 0.467575 1.47500i
\(176\) 1.59899 0.120528
\(177\) 0 0
\(178\) 0.843380 + 1.46078i 0.0632140 + 0.109490i
\(179\) 1.62395 + 2.81277i 0.121380 + 0.210236i 0.920312 0.391185i \(-0.127935\pi\)
−0.798932 + 0.601421i \(0.794601\pi\)
\(180\) 0 0
\(181\) −10.3407 −0.768621 −0.384310 0.923204i \(-0.625561\pi\)
−0.384310 + 0.923204i \(0.625561\pi\)
\(182\) −10.0310 + 2.20755i −0.743548 + 0.163635i
\(183\) 0 0
\(184\) 3.91740 6.78514i 0.288795 0.500207i
\(185\) 8.04993 + 13.9429i 0.591843 + 1.02510i
\(186\) 0 0
\(187\) −0.828310 + 1.43468i −0.0605720 + 0.104914i
\(188\) −2.59899 −0.189551
\(189\) 0 0
\(190\) −3.47073 −0.251793
\(191\) 5.01122 8.67968i 0.362599 0.628040i −0.625789 0.779993i \(-0.715223\pi\)
0.988388 + 0.151953i \(0.0485561\pi\)
\(192\) 0 0
\(193\) −12.6627 21.9324i −0.911478 1.57873i −0.811977 0.583690i \(-0.801609\pi\)
−0.0995016 0.995037i \(-0.531725\pi\)
\(194\) 3.19665 5.53677i 0.229506 0.397517i
\(195\) 0 0
\(196\) −9.96733 + 4.61036i −0.711952 + 0.329312i
\(197\) 24.5809 1.75132 0.875660 0.482929i \(-0.160427\pi\)
0.875660 + 0.482929i \(0.160427\pi\)
\(198\) 0 0
\(199\) −2.79564 4.84219i −0.198178 0.343254i 0.749760 0.661710i \(-0.230169\pi\)
−0.947938 + 0.318456i \(0.896836\pi\)
\(200\) −9.06500 15.7010i −0.640992 1.11023i
\(201\) 0 0
\(202\) 1.21777 0.0856817
\(203\) −5.49615 6.01665i −0.385754 0.422286i
\(204\) 0 0
\(205\) −2.29432 + 3.97388i −0.160242 + 0.277548i
\(206\) −1.04003 1.80139i −0.0724626 0.125509i
\(207\) 0 0
\(208\) 4.72679 8.18705i 0.327744 0.567669i
\(209\) 1.48108 0.102448
\(210\) 0 0
\(211\) 12.0999 0.832988 0.416494 0.909138i \(-0.363259\pi\)
0.416494 + 0.909138i \(0.363259\pi\)
\(212\) −7.23669 + 12.5343i −0.497018 + 0.860860i
\(213\) 0 0
\(214\) 1.56500 + 2.71066i 0.106981 + 0.185297i
\(215\) −2.85327 + 4.94202i −0.194592 + 0.337043i
\(216\) 0 0
\(217\) −5.66047 + 17.8564i −0.384258 + 1.21217i
\(218\) 9.77188 0.661836
\(219\) 0 0
\(220\) 2.79949 + 4.84887i 0.188742 + 0.326910i
\(221\) 4.89716 + 8.48213i 0.329419 + 0.570570i
\(222\) 0 0
\(223\) 15.6265 1.04643 0.523213 0.852202i \(-0.324733\pi\)
0.523213 + 0.852202i \(0.324733\pi\)
\(224\) −4.58645 + 14.4683i −0.306445 + 0.966704i
\(225\) 0 0
\(226\) −4.08524 + 7.07585i −0.271746 + 0.470678i
\(227\) −7.83435 13.5695i −0.519984 0.900639i −0.999730 0.0232317i \(-0.992604\pi\)
0.479746 0.877408i \(-0.340729\pi\)
\(228\) 0 0
\(229\) 2.78575 4.82506i 0.184087 0.318849i −0.759181 0.650879i \(-0.774400\pi\)
0.943269 + 0.332031i \(0.107734\pi\)
\(230\) 7.83481 0.516612
\(231\) 0 0
\(232\) −7.21777 −0.473870
\(233\) −9.63770 + 16.6930i −0.631387 + 1.09359i 0.355882 + 0.934531i \(0.384181\pi\)
−0.987268 + 0.159063i \(0.949153\pi\)
\(234\) 0 0
\(235\) −2.95611 5.12014i −0.192836 0.334001i
\(236\) −6.94369 + 12.0268i −0.451996 + 0.782880i
\(237\) 0 0
\(238\) −1.94105 2.12487i −0.125819 0.137735i
\(239\) 22.1575 1.43325 0.716624 0.697459i \(-0.245686\pi\)
0.716624 + 0.697459i \(0.245686\pi\)
\(240\) 0 0
\(241\) 9.93719 + 17.2117i 0.640111 + 1.10870i 0.985408 + 0.170211i \(0.0544449\pi\)
−0.345297 + 0.938494i \(0.612222\pi\)
\(242\) 0.328310 + 0.568650i 0.0211046 + 0.0365542i
\(243\) 0 0
\(244\) 10.4905 0.671587
\(245\) −20.4196 14.3923i −1.30456 0.919489i
\(246\) 0 0
\(247\) 4.37824 7.58333i 0.278581 0.482516i
\(248\) 8.29564 + 14.3685i 0.526774 + 0.912399i
\(249\) 0 0
\(250\) 3.20655 5.55391i 0.202800 0.351260i
\(251\) −22.1076 −1.39542 −0.697708 0.716382i \(-0.745797\pi\)
−0.697708 + 0.716382i \(0.745797\pi\)
\(252\) 0 0
\(253\) −3.34338 −0.210196
\(254\) −2.17388 + 3.76527i −0.136401 + 0.236254i
\(255\) 0 0
\(256\) 4.21305 + 7.29721i 0.263315 + 0.456076i
\(257\) 14.5598 25.2184i 0.908217 1.57308i 0.0916768 0.995789i \(-0.470777\pi\)
0.816540 0.577289i \(-0.195889\pi\)
\(258\) 0 0
\(259\) 11.6566 2.56530i 0.724307 0.159400i
\(260\) 33.1025 2.05293
\(261\) 0 0
\(262\) 1.98878 + 3.44467i 0.122867 + 0.212813i
\(263\) −7.75176 13.4264i −0.477994 0.827910i 0.521688 0.853136i \(-0.325303\pi\)
−0.999682 + 0.0252268i \(0.991969\pi\)
\(264\) 0 0
\(265\) −32.9243 −2.02252
\(266\) −0.777513 + 2.45272i −0.0476724 + 0.150386i
\(267\) 0 0
\(268\) −7.70655 + 13.3481i −0.470752 + 0.815367i
\(269\) 0.853274 + 1.47791i 0.0520251 + 0.0901100i 0.890865 0.454268i \(-0.150099\pi\)
−0.838840 + 0.544378i \(0.816766\pi\)
\(270\) 0 0
\(271\) 10.2642 17.7781i 0.623505 1.07994i −0.365323 0.930881i \(-0.619042\pi\)
0.988828 0.149061i \(-0.0476251\pi\)
\(272\) 2.64892 0.160614
\(273\) 0 0
\(274\) −4.87439 −0.294472
\(275\) −3.86834 + 6.70017i −0.233270 + 0.404035i
\(276\) 0 0
\(277\) 13.3305 + 23.0891i 0.800952 + 1.38729i 0.918990 + 0.394281i \(0.129006\pi\)
−0.118038 + 0.993009i \(0.537660\pi\)
\(278\) −3.55378 + 6.15533i −0.213142 + 0.369172i
\(279\) 0 0
\(280\) −21.6098 + 4.75572i −1.29143 + 0.284208i
\(281\) −15.7444 −0.939232 −0.469616 0.882871i \(-0.655608\pi\)
−0.469616 + 0.882871i \(0.655608\pi\)
\(282\) 0 0
\(283\) 8.03486 + 13.9168i 0.477623 + 0.827267i 0.999671 0.0256490i \(-0.00816524\pi\)
−0.522048 + 0.852916i \(0.674832\pi\)
\(284\) 6.76078 + 11.7100i 0.401179 + 0.694862i
\(285\) 0 0
\(286\) 3.88209 0.229553
\(287\) 2.29432 + 2.51160i 0.135429 + 0.148255i
\(288\) 0 0
\(289\) 7.12780 12.3457i 0.419283 0.726219i
\(290\) −3.60888 6.25077i −0.211921 0.367058i
\(291\) 0 0
\(292\) 3.57788 6.19706i 0.209379 0.362656i
\(293\) −15.3357 −0.895920 −0.447960 0.894054i \(-0.647849\pi\)
−0.447960 + 0.894054i \(0.647849\pi\)
\(294\) 0 0
\(295\) −31.5913 −1.83932
\(296\) 5.28575 9.15518i 0.307228 0.532134i
\(297\) 0 0
\(298\) 0.328310 + 0.568650i 0.0190185 + 0.0329410i
\(299\) −9.88341 + 17.1186i −0.571573 + 0.989993i
\(300\) 0 0
\(301\) 2.85327 + 3.12349i 0.164460 + 0.180035i
\(302\) −10.7840 −0.620548
\(303\) 0 0
\(304\) −1.18411 2.05095i −0.0679136 0.117630i
\(305\) 11.9320 + 20.6669i 0.683225 + 1.18338i
\(306\) 0 0
\(307\) −16.4707 −0.940034 −0.470017 0.882657i \(-0.655752\pi\)
−0.470017 + 0.882657i \(0.655752\pi\)
\(308\) 4.05378 0.892126i 0.230986 0.0508336i
\(309\) 0 0
\(310\) −8.29564 + 14.3685i −0.471161 + 0.816074i
\(311\) 10.8146 + 18.7314i 0.613238 + 1.06216i 0.990691 + 0.136130i \(0.0434665\pi\)
−0.377453 + 0.926029i \(0.623200\pi\)
\(312\) 0 0
\(313\) −8.19412 + 14.1926i −0.463159 + 0.802215i −0.999116 0.0420298i \(-0.986618\pi\)
0.535957 + 0.844245i \(0.319951\pi\)
\(314\) 7.51892 0.424317
\(315\) 0 0
\(316\) 10.0301 0.564239
\(317\) 2.23064 3.86359i 0.125285 0.217001i −0.796559 0.604561i \(-0.793349\pi\)
0.921844 + 0.387560i \(0.126682\pi\)
\(318\) 0 0
\(319\) 1.54003 + 2.66742i 0.0862253 + 0.149347i
\(320\) −1.01507 + 1.75815i −0.0567441 + 0.0982837i
\(321\) 0 0
\(322\) 1.75515 5.53677i 0.0978109 0.308552i
\(323\) 2.45359 0.136521
\(324\) 0 0
\(325\) 22.8705 + 39.6129i 1.26863 + 2.19733i
\(326\) −2.93500 5.08357i −0.162555 0.281553i
\(327\) 0 0
\(328\) 3.01299 0.166365
\(329\) −4.28057 + 0.942037i −0.235996 + 0.0519362i
\(330\) 0 0
\(331\) −9.51979 + 16.4888i −0.523255 + 0.906304i 0.476379 + 0.879240i \(0.341949\pi\)
−0.999634 + 0.0270640i \(0.991384\pi\)
\(332\) −0.131656 0.228035i −0.00722557 0.0125151i
\(333\) 0 0
\(334\) 5.98108 10.3595i 0.327270 0.566848i
\(335\) −35.0620 −1.91564
\(336\) 0 0
\(337\) 27.0147 1.47159 0.735793 0.677206i \(-0.236810\pi\)
0.735793 + 0.677206i \(0.236810\pi\)
\(338\) 7.20787 12.4844i 0.392057 0.679062i
\(339\) 0 0
\(340\) 4.63770 + 8.03273i 0.251515 + 0.435636i
\(341\) 3.54003 6.13152i 0.191704 0.332040i
\(342\) 0 0
\(343\) −14.7453 + 11.2061i −0.796169 + 0.605074i
\(344\) 3.74704 0.202027
\(345\) 0 0
\(346\) −6.42212 11.1234i −0.345256 0.598000i
\(347\) −10.1089 17.5091i −0.542673 0.939938i −0.998749 0.0499969i \(-0.984079\pi\)
0.456076 0.889941i \(-0.349254\pi\)
\(348\) 0 0
\(349\) −12.0224 −0.643546 −0.321773 0.946817i \(-0.604279\pi\)
−0.321773 + 0.946817i \(0.604279\pi\)
\(350\) −9.06500 9.92348i −0.484545 0.530432i
\(351\) 0 0
\(352\) 2.86834 4.96812i 0.152883 0.264802i
\(353\) −5.37956 9.31767i −0.286325 0.495930i 0.686605 0.727031i \(-0.259100\pi\)
−0.972930 + 0.231101i \(0.925767\pi\)
\(354\) 0 0
\(355\) −15.3796 + 26.6382i −0.816262 + 1.41381i
\(356\) −4.03014 −0.213597
\(357\) 0 0
\(358\) 2.13264 0.112714
\(359\) 12.1451 21.0359i 0.640992 1.11023i −0.344220 0.938889i \(-0.611856\pi\)
0.985212 0.171342i \(-0.0548102\pi\)
\(360\) 0 0
\(361\) 8.40320 + 14.5548i 0.442274 + 0.766041i
\(362\) −3.39497 + 5.88026i −0.178436 + 0.309060i
\(363\) 0 0
\(364\) 7.41563 23.3932i 0.388684 1.22613i
\(365\) 16.2780 0.852032
\(366\) 0 0
\(367\) −5.42212 9.39139i −0.283033 0.490227i 0.689098 0.724669i \(-0.258007\pi\)
−0.972130 + 0.234442i \(0.924674\pi\)
\(368\) 2.67301 + 4.62979i 0.139340 + 0.241345i
\(369\) 0 0
\(370\) 10.5715 0.549586
\(371\) −7.37571 + 23.2672i −0.382928 + 1.20797i
\(372\) 0 0
\(373\) 16.5121 28.5998i 0.854963 1.48084i −0.0217156 0.999764i \(-0.506913\pi\)
0.876679 0.481076i \(-0.159754\pi\)
\(374\) 0.543885 + 0.942037i 0.0281236 + 0.0487116i
\(375\) 0 0
\(376\) −1.94105 + 3.36199i −0.100102 + 0.173381i
\(377\) 18.2101 0.937866
\(378\) 0 0
\(379\) −21.9320 −1.12657 −0.563286 0.826262i \(-0.690463\pi\)
−0.563286 + 0.826262i \(0.690463\pi\)
\(380\) 4.14627 7.18155i 0.212699 0.368406i
\(381\) 0 0
\(382\) −3.29047 5.69926i −0.168355 0.291599i
\(383\) 18.2315 31.5779i 0.931587 1.61356i 0.150977 0.988537i \(-0.451758\pi\)
0.780610 0.625018i \(-0.214909\pi\)
\(384\) 0 0
\(385\) 6.36834 + 6.97144i 0.324561 + 0.355298i
\(386\) −16.6291 −0.846400
\(387\) 0 0
\(388\) 7.63770 + 13.2289i 0.387745 + 0.671595i
\(389\) 9.73801 + 16.8667i 0.493737 + 0.855177i 0.999974 0.00721718i \(-0.00229732\pi\)
−0.506237 + 0.862394i \(0.668964\pi\)
\(390\) 0 0
\(391\) −5.53871 −0.280105
\(392\) −1.48021 + 16.3367i −0.0747619 + 0.825130i
\(393\) 0 0
\(394\) 8.07017 13.9779i 0.406569 0.704199i
\(395\) 11.4084 + 19.7599i 0.574018 + 0.994228i
\(396\) 0 0
\(397\) 3.91993 6.78952i 0.196736 0.340756i −0.750732 0.660606i \(-0.770299\pi\)
0.947468 + 0.319850i \(0.103633\pi\)
\(398\) −3.67135 −0.184028
\(399\) 0 0
\(400\) 12.3709 0.618544
\(401\) −12.2229 + 21.1708i −0.610385 + 1.05722i 0.380791 + 0.924661i \(0.375652\pi\)
−0.991176 + 0.132556i \(0.957682\pi\)
\(402\) 0 0
\(403\) −20.9295 36.2509i −1.04257 1.80579i
\(404\) −1.45479 + 2.51977i −0.0723786 + 0.125363i
\(405\) 0 0
\(406\) −5.22581 + 1.15006i −0.259353 + 0.0570764i
\(407\) −4.51122 −0.223613
\(408\) 0 0
\(409\) 1.17686 + 2.03839i 0.0581922 + 0.100792i 0.893654 0.448757i \(-0.148133\pi\)
−0.835462 + 0.549549i \(0.814800\pi\)
\(410\) 1.50650 + 2.60933i 0.0744006 + 0.128866i
\(411\) 0 0
\(412\) 4.96986 0.244847
\(413\) −7.07708 + 22.3252i −0.348241 + 1.09855i
\(414\) 0 0
\(415\) 0.299494 0.518739i 0.0147016 0.0254639i
\(416\) −16.9583 29.3726i −0.831449 1.44011i
\(417\) 0 0
\(418\) 0.486253 0.842215i 0.0237834 0.0411941i
\(419\) −9.29081 −0.453886 −0.226943 0.973908i \(-0.572873\pi\)
−0.226943 + 0.973908i \(0.572873\pi\)
\(420\) 0 0
\(421\) −39.0319 −1.90230 −0.951149 0.308733i \(-0.900095\pi\)
−0.951149 + 0.308733i \(0.900095\pi\)
\(422\) 3.97251 6.88058i 0.193379 0.334942i
\(423\) 0 0
\(424\) 10.8094 + 18.7224i 0.524950 + 0.909241i
\(425\) −6.40838 + 11.0996i −0.310852 + 0.538411i
\(426\) 0 0
\(427\) 17.2780 3.80243i 0.836143 0.184012i
\(428\) −7.47843 −0.361484
\(429\) 0 0
\(430\) 1.87352 + 3.24503i 0.0903491 + 0.156489i
\(431\) −1.90101 3.29265i −0.0915685 0.158601i 0.816603 0.577200i \(-0.195855\pi\)
−0.908171 + 0.418599i \(0.862521\pi\)
\(432\) 0 0
\(433\) 8.22041 0.395048 0.197524 0.980298i \(-0.436710\pi\)
0.197524 + 0.980298i \(0.436710\pi\)
\(434\) 8.29564 + 9.08126i 0.398204 + 0.435914i
\(435\) 0 0
\(436\) −11.6739 + 20.2198i −0.559077 + 0.968351i
\(437\) 2.47590 + 4.28839i 0.118439 + 0.205142i
\(438\) 0 0
\(439\) −2.27068 + 3.93293i −0.108374 + 0.187708i −0.915112 0.403201i \(-0.867898\pi\)
0.806738 + 0.590909i \(0.201231\pi\)
\(440\) 8.36317 0.398698
\(441\) 0 0
\(442\) 6.43115 0.305899
\(443\) 6.87220 11.9030i 0.326508 0.565528i −0.655309 0.755361i \(-0.727461\pi\)
0.981816 + 0.189833i \(0.0607947\pi\)
\(444\) 0 0
\(445\) −4.58392 7.93958i −0.217299 0.376372i
\(446\) 5.13033 8.88600i 0.242928 0.420764i
\(447\) 0 0
\(448\) 1.01507 + 1.11120i 0.0479575 + 0.0524992i
\(449\) −21.5662 −1.01777 −0.508886 0.860834i \(-0.669943\pi\)
−0.508886 + 0.860834i \(0.669943\pi\)
\(450\) 0 0
\(451\) −0.642874 1.11349i −0.0302717 0.0524322i
\(452\) −9.76078 16.9062i −0.459109 0.795199i
\(453\) 0 0
\(454\) −10.2884 −0.482858
\(455\) 54.5203 11.9984i 2.55595 0.562495i
\(456\) 0 0
\(457\) 1.65277 2.86268i 0.0773133 0.133910i −0.824777 0.565459i \(-0.808699\pi\)
0.902090 + 0.431548i \(0.142033\pi\)
\(458\) −1.82918 3.16823i −0.0854719 0.148042i
\(459\) 0 0
\(460\) −9.35977 + 16.2116i −0.436402 + 0.755870i
\(461\) 32.1524 1.49749 0.748744 0.662859i \(-0.230657\pi\)
0.748744 + 0.662859i \(0.230657\pi\)
\(462\) 0 0
\(463\) 5.82181 0.270563 0.135281 0.990807i \(-0.456806\pi\)
0.135281 + 0.990807i \(0.456806\pi\)
\(464\) 2.46250 4.26517i 0.114318 0.198005i
\(465\) 0 0
\(466\) 6.32831 + 10.9610i 0.293153 + 0.507756i
\(467\) −3.00737 + 5.20891i −0.139164 + 0.241040i −0.927181 0.374615i \(-0.877775\pi\)
0.788016 + 0.615654i \(0.211108\pi\)
\(468\) 0 0
\(469\) −7.85460 + 24.7779i −0.362692 + 1.14414i
\(470\) −3.88209 −0.179067
\(471\) 0 0
\(472\) 10.3717 + 17.9644i 0.477398 + 0.826878i
\(473\) −0.799494 1.38476i −0.0367608 0.0636715i
\(474\) 0 0
\(475\) 11.4586 0.525759
\(476\) 6.71558 1.47791i 0.307808 0.0677401i
\(477\) 0 0
\(478\) 7.27453 12.5999i 0.332729 0.576304i
\(479\) 8.56753 + 14.8394i 0.391460 + 0.678029i 0.992642 0.121083i \(-0.0386367\pi\)
−0.601182 + 0.799112i \(0.705303\pi\)
\(480\) 0 0
\(481\) −13.3357 + 23.0981i −0.608054 + 1.05318i
\(482\) 13.0499 0.594408
\(483\) 0 0
\(484\) −1.56885 −0.0713113
\(485\) −17.3744 + 30.0933i −0.788930 + 1.36647i
\(486\) 0 0
\(487\) −2.85713 4.94869i −0.129469 0.224246i 0.794002 0.607915i \(-0.207994\pi\)
−0.923471 + 0.383669i \(0.874661\pi\)
\(488\) 7.83481 13.5703i 0.354665 0.614298i
\(489\) 0 0
\(490\) −14.8881 + 6.88647i −0.672577 + 0.311099i
\(491\) −24.0673 −1.08614 −0.543071 0.839687i \(-0.682739\pi\)
−0.543071 + 0.839687i \(0.682739\pi\)
\(492\) 0 0
\(493\) 2.55125 + 4.41890i 0.114903 + 0.199017i
\(494\) −2.87484 4.97937i −0.129345 0.224032i
\(495\) 0 0
\(496\) −11.3209 −0.508325
\(497\) 15.3796 + 16.8360i 0.689868 + 0.755200i
\(498\) 0 0
\(499\) −5.39463 + 9.34377i −0.241497 + 0.418285i −0.961141 0.276058i \(-0.910972\pi\)
0.719644 + 0.694343i \(0.244305\pi\)
\(500\) 7.66134 + 13.2698i 0.342626 + 0.593445i
\(501\) 0 0
\(502\) −7.25814 + 12.5715i −0.323947 + 0.561092i
\(503\) −28.0121 −1.24900 −0.624499 0.781026i \(-0.714697\pi\)
−0.624499 + 0.781026i \(0.714697\pi\)
\(504\) 0 0
\(505\) −6.61878 −0.294532
\(506\) −1.09767 + 1.90121i −0.0487972 + 0.0845192i
\(507\) 0 0
\(508\) −5.19401 8.99629i −0.230447 0.399146i
\(509\) −0.957437 + 1.65833i −0.0424377 + 0.0735042i −0.886464 0.462797i \(-0.846846\pi\)
0.844026 + 0.536302i \(0.180179\pi\)
\(510\) 0 0
\(511\) 3.64661 11.5035i 0.161317 0.508885i
\(512\) −16.6670 −0.736583
\(513\) 0 0
\(514\) −9.56028 16.5589i −0.421686 0.730381i
\(515\) 5.65277 + 9.79088i 0.249091 + 0.431438i
\(516\) 0 0
\(517\) 1.65662 0.0728581
\(518\) 2.36823 7.47075i 0.104054 0.328246i
\(519\) 0 0
\(520\) 24.7225 42.8206i 1.08415 1.87781i
\(521\) 0.789599 + 1.36763i 0.0345930 + 0.0599168i 0.882804 0.469742i \(-0.155653\pi\)
−0.848211 + 0.529659i \(0.822320\pi\)
\(522\) 0 0
\(523\) 4.48493 7.76813i 0.196112 0.339677i −0.751152 0.660129i \(-0.770502\pi\)
0.947265 + 0.320452i \(0.103835\pi\)
\(524\) −9.50351 −0.415163
\(525\) 0 0
\(526\) −10.1799 −0.443866
\(527\) 5.86449 10.1576i 0.255461 0.442472i
\(528\) 0 0
\(529\) 5.91091 + 10.2380i 0.256996 + 0.445130i
\(530\) −10.8094 + 18.7224i −0.469530 + 0.813250i
\(531\) 0 0
\(532\) −4.14627 4.53893i −0.179764 0.196788i
\(533\) −7.60163 −0.329263
\(534\) 0 0
\(535\) −8.50604 14.7329i −0.367748 0.636959i
\(536\) 11.5112 + 19.9380i 0.497209 + 0.861191i
\(537\) 0 0
\(538\) 1.12055 0.0483105
\(539\) 6.35327 2.93869i 0.273655 0.126578i
\(540\) 0 0
\(541\) −9.05125 + 15.6772i −0.389144 + 0.674017i −0.992335 0.123580i \(-0.960562\pi\)
0.603191 + 0.797597i \(0.293896\pi\)
\(542\) −6.73967 11.6735i −0.289494 0.501418i
\(543\) 0 0
\(544\) 4.75176 8.23028i 0.203730 0.352871i
\(545\) −53.1119 −2.27507
\(546\) 0 0
\(547\) 22.6885 0.970090 0.485045 0.874489i \(-0.338803\pi\)
0.485045 + 0.874489i \(0.338803\pi\)
\(548\) 5.82314 10.0860i 0.248752 0.430851i
\(549\) 0 0
\(550\) 2.54003 + 4.39947i 0.108307 + 0.187594i
\(551\) 2.28091 3.95065i 0.0971701 0.168304i
\(552\) 0 0
\(553\) 16.5198 3.63555i 0.702493 0.154599i
\(554\) 17.5062 0.743765
\(555\) 0 0
\(556\) −8.49097 14.7068i −0.360097 0.623707i
\(557\) 19.1777 + 33.2168i 0.812587 + 1.40744i 0.911048 + 0.412300i \(0.135275\pi\)
−0.0984613 + 0.995141i \(0.531392\pi\)
\(558\) 0 0
\(559\) −9.45359 −0.399844
\(560\) 4.56235 14.3923i 0.192795 0.608185i
\(561\) 0 0
\(562\) −5.16904 + 8.95305i −0.218043 + 0.377662i
\(563\) −20.8869 36.1772i −0.880279 1.52469i −0.851031 0.525116i \(-0.824022\pi\)
−0.0292482 0.999572i \(-0.509311\pi\)
\(564\) 0 0
\(565\) 22.2040 38.4585i 0.934130 1.61796i
\(566\) 10.5517 0.443521
\(567\) 0 0
\(568\) 20.1971 0.847450
\(569\) −5.93500 + 10.2797i −0.248808 + 0.430949i −0.963195 0.268802i \(-0.913372\pi\)
0.714387 + 0.699751i \(0.246706\pi\)
\(570\) 0 0
\(571\) −9.90067 17.1485i −0.414330 0.717641i 0.581028 0.813884i \(-0.302651\pi\)
−0.995358 + 0.0962427i \(0.969317\pi\)
\(572\) −4.63770 + 8.03273i −0.193912 + 0.335865i
\(573\) 0 0
\(574\) 2.18147 0.480082i 0.0910527 0.0200382i
\(575\) −25.8667 −1.07872
\(576\) 0 0
\(577\) −14.3395 24.8368i −0.596962 1.03397i −0.993267 0.115850i \(-0.963041\pi\)
0.396304 0.918119i \(-0.370293\pi\)
\(578\) −4.68026 8.10645i −0.194673 0.337184i
\(579\) 0 0
\(580\) 17.2453 0.716070
\(581\) −0.299494 0.327857i −0.0124251 0.0136018i
\(582\) 0 0
\(583\) 4.61274 7.98949i 0.191040 0.330891i
\(584\) −5.34425 9.25651i −0.221147 0.383037i
\(585\) 0 0
\(586\) −5.03486 + 8.72063i −0.207988 + 0.360246i
\(587\) −1.01209 −0.0417733 −0.0208866 0.999782i \(-0.506649\pi\)
−0.0208866 + 0.999782i \(0.506649\pi\)
\(588\) 0 0
\(589\) −10.4861 −0.432074
\(590\) −10.3717 + 17.9644i −0.426998 + 0.739582i
\(591\) 0 0
\(592\) 3.60669 + 6.24697i 0.148234 + 0.256749i
\(593\) 7.11659 12.3263i 0.292243 0.506180i −0.682097 0.731262i \(-0.738932\pi\)
0.974340 + 0.225082i \(0.0722650\pi\)
\(594\) 0 0
\(595\) 10.5499 + 11.5490i 0.432505 + 0.473464i
\(596\) −1.56885 −0.0642626
\(597\) 0 0
\(598\) 6.48965 + 11.2404i 0.265382 + 0.459654i
\(599\) −13.2729 22.9893i −0.542315 0.939317i −0.998771 0.0495706i \(-0.984215\pi\)
0.456456 0.889746i \(-0.349119\pi\)
\(600\) 0 0
\(601\) −12.1558 −0.495843 −0.247922 0.968780i \(-0.579748\pi\)
−0.247922 + 0.968780i \(0.579748\pi\)
\(602\) 2.71293 0.597042i 0.110571 0.0243336i
\(603\) 0 0
\(604\) 12.8830 22.3139i 0.524200 0.907941i
\(605\) −1.78442 3.09071i −0.0725472 0.125655i
\(606\) 0 0
\(607\) −6.98361 + 12.0960i −0.283456 + 0.490960i −0.972234 0.234013i \(-0.924814\pi\)
0.688778 + 0.724973i \(0.258148\pi\)
\(608\) −8.49649 −0.344578
\(609\) 0 0
\(610\) 15.6696 0.634444
\(611\) 4.89716 8.48213i 0.198118 0.343150i
\(612\) 0 0
\(613\) −2.32094 4.01999i −0.0937421 0.162366i 0.815341 0.578981i \(-0.196550\pi\)
−0.909083 + 0.416615i \(0.863216\pi\)
\(614\) −5.40751 + 9.36608i −0.218229 + 0.377984i
\(615\) 0 0
\(616\) 1.87352 5.91015i 0.0754862 0.238127i
\(617\) 26.3960 1.06266 0.531331 0.847165i \(-0.321692\pi\)
0.531331 + 0.847165i \(0.321692\pi\)
\(618\) 0 0
\(619\) −7.34073 12.7145i −0.295049 0.511040i 0.679947 0.733261i \(-0.262003\pi\)
−0.974996 + 0.222221i \(0.928669\pi\)
\(620\) −19.8206 34.3303i −0.796015 1.37874i
\(621\) 0 0
\(622\) 14.2021 0.569453
\(623\) −6.63770 + 1.46078i −0.265934 + 0.0585248i
\(624\) 0 0
\(625\) 1.91355 3.31437i 0.0765421 0.132575i
\(626\) 5.38043 + 9.31918i 0.215045 + 0.372469i
\(627\) 0 0
\(628\) −8.98240 + 15.5580i −0.358437 + 0.620831i
\(629\) −7.47338 −0.297983
\(630\) 0 0
\(631\) −30.1498 −1.20024 −0.600122 0.799908i \(-0.704881\pi\)
−0.600122 + 0.799908i \(0.704881\pi\)
\(632\) 7.49097 12.9747i 0.297975 0.516108i
\(633\) 0 0
\(634\) −1.46469 2.53691i −0.0581701 0.100754i
\(635\) 11.8154 20.4649i 0.468881 0.812126i
\(636\) 0 0
\(637\) 3.73450 41.2168i 0.147966 1.63307i
\(638\) 2.02243 0.0800690
\(639\) 0 0
\(640\) −19.8069 34.3065i −0.782935 1.35608i
\(641\) −8.08909 14.0107i −0.319500 0.553390i 0.660884 0.750488i \(-0.270182\pi\)
−0.980384 + 0.197098i \(0.936848\pi\)
\(642\) 0 0
\(643\) −2.33568 −0.0921101 −0.0460550 0.998939i \(-0.514665\pi\)
−0.0460550 + 0.998939i \(0.514665\pi\)
\(644\) 9.35977 + 10.2462i 0.368827 + 0.403756i
\(645\) 0 0
\(646\) 0.805537 1.39523i 0.0316934 0.0548946i
\(647\) 7.48108 + 12.9576i 0.294112 + 0.509416i 0.974778 0.223177i \(-0.0716429\pi\)
−0.680666 + 0.732594i \(0.738310\pi\)
\(648\) 0 0
\(649\) 4.42598 7.66602i 0.173735 0.300917i
\(650\) 30.0345 1.17805
\(651\) 0 0
\(652\) 14.0251 0.549265
\(653\) −11.4449 + 19.8231i −0.447873 + 0.775740i −0.998247 0.0591787i \(-0.981152\pi\)
0.550374 + 0.834918i \(0.314485\pi\)
\(654\) 0 0
\(655\) −10.8094 18.7224i −0.422358 0.731545i
\(656\) −1.02795 + 1.78046i −0.0401346 + 0.0695152i
\(657\) 0 0
\(658\) −0.869666 + 2.74343i −0.0339031 + 0.106950i
\(659\) 2.20568 0.0859211 0.0429606 0.999077i \(-0.486321\pi\)
0.0429606 + 0.999077i \(0.486321\pi\)
\(660\) 0 0
\(661\) 0.341188 + 0.590956i 0.0132707 + 0.0229855i 0.872584 0.488463i \(-0.162442\pi\)
−0.859314 + 0.511449i \(0.829109\pi\)
\(662\) 6.25089 + 10.8269i 0.242948 + 0.420798i
\(663\) 0 0
\(664\) −0.393308 −0.0152633
\(665\) 4.22592 13.3310i 0.163874 0.516954i
\(666\) 0 0
\(667\) −5.14892 + 8.91819i −0.199367 + 0.345314i
\(668\) 14.2905 + 24.7518i 0.552915 + 0.957677i
\(669\) 0 0
\(670\) −11.5112 + 19.9380i −0.444717 + 0.770273i
\(671\) −6.68676 −0.258139
\(672\) 0 0
\(673\) −10.8865 −0.419643 −0.209821 0.977740i \(-0.567288\pi\)
−0.209821 + 0.977740i \(0.567288\pi\)
\(674\) 8.86921 15.3619i 0.341629 0.591719i
\(675\) 0 0
\(676\) 17.2216 + 29.8287i 0.662370 + 1.14726i
\(677\) 22.8327 39.5474i 0.877532 1.51993i 0.0234904 0.999724i \(-0.492522\pi\)
0.854041 0.520205i \(-0.174145\pi\)
\(678\) 0 0
\(679\) 17.3744 + 19.0198i 0.666768 + 0.729912i
\(680\) 13.8546 0.531300
\(681\) 0 0
\(682\) −2.32446 4.02608i −0.0890081 0.154167i
\(683\) 3.24186 + 5.61507i 0.124046 + 0.214855i 0.921360 0.388711i \(-0.127079\pi\)
−0.797313 + 0.603566i \(0.793746\pi\)
\(684\) 0 0
\(685\) 26.4932 1.01225
\(686\) 1.53135 + 12.0640i 0.0584670 + 0.460605i
\(687\) 0 0
\(688\) −1.27838 + 2.21422i −0.0487378 + 0.0844164i
\(689\) −27.2715 47.2357i −1.03896 1.79954i
\(690\) 0 0
\(691\) −5.47338 + 9.48016i −0.208217 + 0.360642i −0.951153 0.308720i \(-0.900099\pi\)
0.742936 + 0.669363i \(0.233433\pi\)
\(692\) 30.6885 1.16660
\(693\) 0 0
\(694\) −13.2754 −0.503927
\(695\) 19.3154 33.4553i 0.732676 1.26903i
\(696\) 0 0
\(697\) −1.06500 1.84463i −0.0403397 0.0698704i
\(698\) −3.94709 + 6.83656i −0.149399 + 0.258768i
\(699\) 0 0
\(700\) 31.3628 6.90210i 1.18540 0.260875i
\(701\) 0.914874 0.0345543 0.0172772 0.999851i \(-0.494500\pi\)
0.0172772 + 0.999851i \(0.494500\pi\)
\(702\) 0 0
\(703\) 3.34073 + 5.78632i 0.125998 + 0.218235i
\(704\) −0.284425 0.492638i −0.0107197 0.0185670i
\(705\) 0 0
\(706\) −7.06466 −0.265882
\(707\) −1.48274 + 4.67741i −0.0557642 + 0.175912i
\(708\) 0 0
\(709\) −22.1562 + 38.3756i −0.832092 + 1.44123i 0.0642838 + 0.997932i \(0.479524\pi\)
−0.896376 + 0.443294i \(0.853810\pi\)
\(710\) 10.0985 + 17.4912i 0.378991 + 0.656432i
\(711\) 0 0
\(712\) −3.00989 + 5.21329i −0.112801 + 0.195376i
\(713\) 23.6714 0.886499
\(714\) 0 0
\(715\) −21.0999 −0.789090
\(716\) −2.54774 + 4.41281i −0.0952134 + 0.164914i
\(717\) 0 0
\(718\) −7.97470 13.8126i −0.297613 0.515481i
\(719\) −2.60118 + 4.50537i −0.0970076 + 0.168022i −0.910445 0.413631i \(-0.864260\pi\)
0.813437 + 0.581653i \(0.197594\pi\)
\(720\) 0 0
\(721\) 8.18544 1.80139i 0.304842 0.0670873i
\(722\) 11.0354 0.410696
\(723\) 0 0
\(724\) −8.11153 14.0496i −0.301463 0.522149i
\(725\) 11.9148 + 20.6370i 0.442503 + 0.766438i
\(726\) 0 0
\(727\) 50.0871 1.85763 0.928814 0.370547i \(-0.120830\pi\)
0.928814 + 0.370547i \(0.120830\pi\)
\(728\) −24.7225 27.0638i −0.916276 1.00305i
\(729\) 0 0
\(730\) 5.34425 9.25651i 0.197799 0.342599i
\(731\) −1.32446 2.29403i −0.0489869 0.0848477i
\(732\) 0 0
\(733\) 23.5349 40.7636i 0.869280 1.50564i 0.00654601 0.999979i \(-0.497916\pi\)
0.862734 0.505658i \(-0.168750\pi\)
\(734\) −7.12055 −0.262824
\(735\) 0 0
\(736\) 19.1799 0.706981
\(737\) 4.91223 8.50823i 0.180944 0.313405i
\(738\) 0 0
\(739\) −23.4957 40.6957i −0.864303 1.49702i −0.867738 0.497023i \(-0.834427\pi\)
0.00343444 0.999994i \(-0.498907\pi\)
\(740\) −12.6291 + 21.8743i −0.464256 + 0.804115i
\(741\) 0 0
\(742\) 10.8094 + 11.8331i 0.396825 + 0.434406i
\(743\) 5.19533 0.190598 0.0952991 0.995449i \(-0.469619\pi\)
0.0952991 + 0.995449i \(0.469619\pi\)
\(744\) 0 0
\(745\) −1.78442 3.09071i −0.0653763 0.113235i
\(746\) −10.8422 18.7792i −0.396960 0.687555i
\(747\) 0 0
\(748\) −2.59899 −0.0950284
\(749\) −12.3171 + 2.71066i −0.450057 + 0.0990452i
\(750\) 0 0
\(751\) −16.7268 + 28.9717i −0.610369 + 1.05719i 0.380809 + 0.924654i \(0.375646\pi\)
−0.991178 + 0.132537i \(0.957688\pi\)
\(752\) −1.32446 2.29403i −0.0482980 0.0836546i
\(753\) 0 0
\(754\) 5.97855 10.3552i 0.217726 0.377112i
\(755\) 58.6128 2.13314
\(756\) 0 0
\(757\) 40.0440 1.45542 0.727711 0.685884i \(-0.240584\pi\)
0.727711 + 0.685884i \(0.240584\pi\)
\(758\) −7.20051 + 12.4716i −0.261534 + 0.452990i
\(759\) 0 0
\(760\) −6.19326 10.7270i −0.224653 0.389110i
\(761\) −3.77925 + 6.54585i −0.136998 + 0.237287i −0.926359 0.376642i \(-0.877079\pi\)
0.789361 + 0.613929i \(0.210412\pi\)
\(762\) 0 0
\(763\) −11.8981 + 37.5336i −0.430742 + 1.35881i
\(764\) 15.7237 0.568863
\(765\) 0 0
\(766\) −11.9712 20.7347i −0.432536 0.749175i
\(767\) −26.1674 45.3232i −0.944849 1.63653i
\(768\) 0 0
\(769\) 51.5407 1.85860 0.929302 0.369320i \(-0.120409\pi\)
0.929302 + 0.369320i \(0.120409\pi\)
\(770\) 6.05510 1.33256i 0.218211 0.0480222i
\(771\) 0 0
\(772\) 19.8658 34.4086i 0.714986 1.23839i
\(773\) −7.73284 13.3937i −0.278131 0.481737i 0.692789 0.721140i \(-0.256382\pi\)
−0.970920 + 0.239403i \(0.923048\pi\)
\(774\) 0 0
\(775\) 27.3881 47.4376i 0.983811 1.70401i
\(776\) 22.8168 0.819074
\(777\) 0 0
\(778\) 12.7884 0.458485
\(779\) −0.952147 + 1.64917i −0.0341142 + 0.0590875i
\(780\) 0 0
\(781\) −4.30939 7.46408i −0.154202 0.267086i
\(782\) −1.81842 + 3.14959i −0.0650264 + 0.112629i
\(783\) 0 0
\(784\) −9.14880 6.44832i −0.326743 0.230297i
\(785\) −40.8667 −1.45859
\(786\) 0 0
\(787\) −10.9759 19.0108i −0.391249 0.677663i 0.601366 0.798974i \(-0.294623\pi\)
−0.992615 + 0.121311i \(0.961290\pi\)
\(788\) 19.2819 + 33.3972i 0.686889 + 1.18973i
\(789\) 0 0
\(790\) 14.9819 0.533034
\(791\) −22.2040 24.3068i −0.789484 0.864250i
\(792\) 0 0
\(793\) −19.7668 + 34.2371i −0.701941 + 1.21580i
\(794\) −2.57391 4.45814i −0.0913446 0.158213i
\(795\) 0 0
\(796\) 4.38594 7.59667i 0.155456 0.269257i
\(797\) −42.6258 −1.50988 −0.754942 0.655792i \(-0.772335\pi\)
−0.754942 + 0.655792i \(0.772335\pi\)
\(798\) 0 0
\(799\) 2.74439 0.0970896
\(800\) 22.1915 38.4368i 0.784587 1.35895i
\(801\) 0 0
\(802\) 8.02583 + 13.9011i 0.283402 + 0.490867i
\(803\) −2.28057 + 3.95007i −0.0804797 + 0.139395i
\(804\) 0 0
\(805\) −9.53958 + 30.0933i −0.336226 + 1.06065i
\(806\) −27.4855 −0.968134
\(807\) 0 0
\(808\) 2.17301 + 3.76377i 0.0764463 + 0.132409i
\(809\) 1.98372 + 3.43591i 0.0697440 + 0.120800i 0.898789 0.438382i \(-0.144448\pi\)
−0.829045 + 0.559183i \(0.811115\pi\)
\(810\) 0 0
\(811\) −46.9217 −1.64764 −0.823821 0.566850i \(-0.808162\pi\)
−0.823821 + 0.566850i \(0.808162\pi\)
\(812\) 3.86329 12.1870i 0.135575 0.427681i
\(813\) 0 0
\(814\) −1.48108 + 2.56530i −0.0519118 + 0.0899138i
\(815\) 15.9523 + 27.6301i 0.558783 + 0.967841i
\(816\) 0 0
\(817\) −1.18411 + 2.05095i −0.0414269 + 0.0717535i
\(818\) 1.54551 0.0540374
\(819\) 0 0
\(820\) −7.19888 −0.251396
\(821\) −25.3000 + 43.8209i −0.882977 + 1.52936i −0.0349620 + 0.999389i \(0.511131\pi\)
−0.848015 + 0.529972i \(0.822202\pi\)
\(822\) 0 0
\(823\) −0.199299 0.345196i −0.00694714 0.0120328i 0.862531 0.506004i \(-0.168878\pi\)
−0.869478 + 0.493972i \(0.835545\pi\)
\(824\) 3.71172 6.42889i 0.129304 0.223961i
\(825\) 0 0
\(826\) 10.3717 + 11.3540i 0.360879 + 0.395055i
\(827\) 20.4234 0.710193 0.355096 0.934830i \(-0.384448\pi\)
0.355096 + 0.934830i \(0.384448\pi\)
\(828\) 0 0
\(829\) 11.6317 + 20.1466i 0.403984 + 0.699721i 0.994203 0.107522i \(-0.0342918\pi\)
−0.590219 + 0.807244i \(0.700958\pi\)
\(830\) −0.196654 0.340615i −0.00682596 0.0118229i
\(831\) 0 0
\(832\) −3.36317 −0.116597
\(833\) 10.5250 4.86830i 0.364668 0.168676i
\(834\) 0 0
\(835\) −32.5082 + 56.3059i −1.12499 + 1.94855i
\(836\) 1.16179 + 2.01229i 0.0401815 + 0.0695964i
\(837\) 0 0
\(838\) −3.05027 + 5.28322i −0.105370 + 0.182506i
\(839\) 16.4861 0.569165 0.284582 0.958652i \(-0.408145\pi\)
0.284582 + 0.958652i \(0.408145\pi\)
\(840\) 0 0
\(841\) −19.5132 −0.672869
\(842\) −12.8146 + 22.1955i −0.441619 + 0.764907i
\(843\) 0 0
\(844\) 9.49143 + 16.4396i 0.326708 + 0.565876i
\(845\) −39.1761 + 67.8549i −1.34770 + 2.33428i
\(846\) 0 0
\(847\) −2.58392 + 0.568650i −0.0887845 + 0.0195390i
\(848\) −14.7514 −0.506566
\(849\) 0 0
\(850\) 4.20787 + 7.28825i 0.144329 + 0.249985i
\(851\) −7.54136 13.0620i −0.258514 0.447760i
\(852\) 0 0
\(853\) −14.8315 −0.507820 −0.253910 0.967228i \(-0.581717\pi\)
−0.253910 + 0.967228i \(0.581717\pi\)
\(854\) 3.51031 11.0735i 0.120120 0.378929i
\(855\) 0 0
\(856\) −5.58524 + 9.67392i −0.190900 + 0.330648i
\(857\) −2.51594 4.35773i −0.0859428 0.148857i 0.819850 0.572579i \(-0.194057\pi\)
−0.905793 + 0.423721i \(0.860724\pi\)
\(858\) 0 0
\(859\) 28.0181 48.5288i 0.955966 1.65578i 0.223825 0.974629i \(-0.428146\pi\)
0.732141 0.681153i \(-0.238521\pi\)
\(860\) −8.95272 −0.305285
\(861\) 0 0
\(862\) −2.49649 −0.0850307
\(863\) −18.2380 + 31.5892i −0.620829 + 1.07531i 0.368503 + 0.929627i \(0.379871\pi\)
−0.989332 + 0.145681i \(0.953463\pi\)
\(864\) 0 0
\(865\) 34.9054 + 60.4579i 1.18682 + 2.05563i
\(866\) 2.69885 4.67454i 0.0917105 0.158847i
\(867\) 0 0
\(868\) −28.7010 + 6.31631i −0.974177 + 0.214390i
\(869\) −6.39331 −0.216878
\(870\) 0 0
\(871\) −29.0422 50.3026i −0.984058 1.70444i
\(872\) 17.4372 + 30.2021i 0.590498 + 1.02277i
\(873\) 0 0
\(874\) 3.25146 0.109982
\(875\) 17.4282 + 19.0787i 0.589180 + 0.644976i
\(876\) 0 0
\(877\) 3.30807 5.72974i 0.111705 0.193480i −0.804753 0.593610i \(-0.797702\pi\)
0.916458 + 0.400131i \(0.131035\pi\)
\(878\) 1.49097 + 2.58244i 0.0503179 + 0.0871532i
\(879\) 0 0
\(880\) −2.85327 + 4.94202i −0.0961839 + 0.166595i
\(881\) 22.5286 0.759008 0.379504 0.925190i \(-0.376095\pi\)
0.379504 + 0.925190i \(0.376095\pi\)
\(882\) 0 0
\(883\) −51.1652 −1.72185 −0.860923 0.508735i \(-0.830113\pi\)
−0.860923 + 0.508735i \(0.830113\pi\)
\(884\) −7.68291 + 13.3072i −0.258404 + 0.447569i
\(885\) 0 0
\(886\) −4.51242 7.81575i −0.151598 0.262575i
\(887\) −3.16904 + 5.48895i −0.106406 + 0.184301i −0.914312 0.405011i \(-0.867268\pi\)
0.807906 + 0.589312i \(0.200601\pi\)
\(888\) 0 0
\(889\) −11.8154 12.9344i −0.396277 0.433805i
\(890\) −6.01979 −0.201784
\(891\) 0 0
\(892\) 12.2578 + 21.2311i 0.410421 + 0.710871i
\(893\) −1.22679 2.12487i −0.0410531 0.0711060i
\(894\) 0 0
\(895\) −11.5913 −0.387454
\(896\) −28.6811 + 6.31193i −0.958169 + 0.210867i
\(897\) 0 0
\(898\) −7.08041 + 12.2636i −0.236276 + 0.409242i
\(899\) −10.9035 18.8855i −0.363653 0.629866i
\(900\) 0 0
\(901\) 7.64155 13.2356i 0.254577 0.440940i
\(902\) −0.844248 −0.0281104
\(903\) 0 0
\(904\) −29.1592 −0.969821
\(905\) 18.4523 31.9603i 0.613374 1.06239i
\(906\) 0 0
\(907\) 3.44237 + 5.96236i 0.114302 + 0.197977i 0.917500 0.397735i \(-0.130204\pi\)
−0.803199 + 0.595711i \(0.796870\pi\)
\(908\) 12.2909 21.2885i 0.407889 0.706484i
\(909\) 0 0
\(910\) 11.0767 34.9422i 0.367188 1.15832i
\(911\) 41.0818 1.36110 0.680550 0.732701i \(-0.261741\pi\)
0.680550 + 0.732701i \(0.261741\pi\)
\(912\) 0 0
\(913\) 0.0839190 + 0.145352i 0.00277731 + 0.00481045i
\(914\) −1.08524 1.87969i −0.0358966 0.0621747i
\(915\) 0 0
\(916\) 8.74084 0.288805
\(917\) −15.6524 + 3.44467i −0.516889 + 0.113753i
\(918\) 0 0
\(919\) 5.81324 10.0688i 0.191761 0.332140i −0.754073 0.656791i \(-0.771913\pi\)
0.945834 + 0.324651i \(0.105247\pi\)
\(920\) 13.9806 + 24.2152i 0.460928 + 0.798350i
\(921\) 0 0
\(922\) 10.5560 18.2835i 0.347642 0.602134i
\(923\) −50.9562 −1.67724
\(924\) 0 0
\(925\) −34.9019 −1.14757
\(926\) 1.91136 3.31057i 0.0628112 0.108792i
\(927\) 0 0
\(928\) −8.83469 15.3021i −0.290013 0.502317i
\(929\) 12.3834 21.4487i 0.406287 0.703709i −0.588184 0.808727i \(-0.700157\pi\)
0.994470 + 0.105018i \(0.0334901\pi\)
\(930\) 0 0
\(931\) −8.47417 5.97282i −0.277730 0.195751i
\(932\) −30.2402 −0.990551
\(933\) 0 0
\(934\) 1.97470 + 3.42028i 0.0646141 + 0.111915i
\(935\) −2.95611 5.12014i −0.0966753 0.167447i
\(936\) 0 0
\(937\) 1.15046 0.0375839 0.0187920 0.999823i \(-0.494018\pi\)
0.0187920 + 0.999823i \(0.494018\pi\)
\(938\) 11.5112 + 12.6014i 0.375855 + 0.411449i
\(939\) 0 0
\(940\) 4.63770 8.03273i 0.151265 0.261999i
\(941\) 5.05510 + 8.75570i 0.164792 + 0.285428i 0.936581 0.350450i \(-0.113971\pi\)
−0.771790 + 0.635878i \(0.780638\pi\)
\(942\) 0 0
\(943\) 2.14937 3.72282i 0.0699931 0.121232i
\(944\) −14.1542 −0.460679
\(945\) 0 0
\(946\) −1.04993 −0.0341361
\(947\) −12.2277 + 21.1789i −0.397346 + 0.688223i −0.993398 0.114723i \(-0.963402\pi\)
0.596052 + 0.802946i \(0.296735\pi\)
\(948\) 0 0
\(949\) 13.4833 + 23.3537i 0.437685 + 0.758093i
\(950\) 3.76199 6.51596i 0.122055 0.211406i
\(951\) 0 0
\(952\) 3.10371 9.79088i 0.100592 0.317324i
\(953\) 16.1696 0.523784 0.261892 0.965097i \(-0.415654\pi\)
0.261892 + 0.965097i \(0.415654\pi\)
\(954\) 0 0
\(955\) 17.8843 + 30.9765i 0.578722 + 1.00238i
\(956\) 17.3809 + 30.1046i 0.562138 + 0.973652i
\(957\) 0 0
\(958\) 11.2512 0.363511
\(959\) 5.93500 18.7224i 0.191651 0.604578i
\(960\) 0 0
\(961\) −9.56368 + 16.5648i −0.308506 + 0.534347i
\(962\) 8.75648 + 15.1667i 0.282320 + 0.488993i
\(963\) 0 0
\(964\) −15.5900 + 27.0026i −0.502119 + 0.869695i
\(965\) 90.3823 2.90951
\(966\) 0 0
\(967\) −1.55941 −0.0501472 −0.0250736 0.999686i \(-0.507982\pi\)
−0.0250736 + 0.999686i \(0.507982\pi\)
\(968\) −1.17169 + 2.02943i −0.0376595 + 0.0652282i
\(969\) 0 0
\(970\) 11.4084 + 19.7599i 0.366301 + 0.634452i
\(971\) −4.52364 + 7.83518i −0.145171 + 0.251443i −0.929437 0.368982i \(-0.879706\pi\)
0.784266 + 0.620425i \(0.213040\pi\)
\(972\) 0 0
\(973\) −19.3154 21.1447i −0.619224 0.677866i
\(974\) −3.75209 −0.120225
\(975\) 0 0
\(976\) 5.34602 + 9.25959i 0.171122 + 0.296392i
\(977\) −3.37824 5.85128i −0.108079 0.187199i 0.806913 0.590671i \(-0.201137\pi\)
−0.914992 + 0.403472i \(0.867803\pi\)
\(978\) 0 0
\(979\) 2.56885 0.0821008
\(980\) 3.53664 39.0330i 0.112974 1.24686i
\(981\) 0 0
\(982\) −7.90154 + 13.6859i −0.252148 + 0.436734i
\(983\) 13.2152 + 22.8895i 0.421501 + 0.730060i 0.996086 0.0883838i \(-0.0281702\pi\)
−0.574586 + 0.818444i \(0.694837\pi\)
\(984\) 0 0
\(985\) −43.8628 + 75.9727i −1.39759 + 2.42069i
\(986\) 3.35041 0.106699
\(987\) 0 0
\(988\) 13.7376 0.437051
\(989\) 2.67301 4.62979i 0.0849969 0.147219i
\(990\) 0 0
\(991\) 0.317093 + 0.549221i 0.0100728 + 0.0174466i 0.871018 0.491251i \(-0.163460\pi\)
−0.860945 + 0.508698i \(0.830127\pi\)
\(992\) −20.3081 + 35.1746i −0.644782 + 1.11679i
\(993\) 0 0
\(994\) 14.6231 3.21814i 0.463816 0.102073i
\(995\) 19.9545 0.632599
\(996\) 0 0
\(997\) −5.06368 8.77054i −0.160368 0.277766i 0.774633 0.632412i \(-0.217935\pi\)
−0.935001 + 0.354646i \(0.884601\pi\)
\(998\) 3.54222 + 6.13531i 0.112127 + 0.194210i
\(999\) 0 0
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 693.2.i.g.100.2 6
3.2 odd 2 77.2.e.b.23.2 6
7.2 even 3 4851.2.a.bo.1.2 3
7.4 even 3 inner 693.2.i.g.298.2 6
7.5 odd 6 4851.2.a.bn.1.2 3
12.11 even 2 1232.2.q.k.177.3 6
21.2 odd 6 539.2.a.h.1.2 3
21.5 even 6 539.2.a.i.1.2 3
21.11 odd 6 77.2.e.b.67.2 yes 6
21.17 even 6 539.2.e.l.67.2 6
21.20 even 2 539.2.e.l.177.2 6
33.2 even 10 847.2.n.d.807.2 24
33.5 odd 10 847.2.n.e.366.2 24
33.8 even 10 847.2.n.d.9.2 24
33.14 odd 10 847.2.n.e.9.2 24
33.17 even 10 847.2.n.d.366.2 24
33.20 odd 10 847.2.n.e.807.2 24
33.26 odd 10 847.2.n.e.632.2 24
33.29 even 10 847.2.n.d.632.2 24
33.32 even 2 847.2.e.d.485.2 6
84.11 even 6 1232.2.q.k.529.3 6
84.23 even 6 8624.2.a.cl.1.1 3
84.47 odd 6 8624.2.a.ck.1.3 3
231.32 even 6 847.2.e.d.606.2 6
231.53 odd 30 847.2.n.e.81.2 24
231.65 even 6 5929.2.a.v.1.2 3
231.74 even 30 847.2.n.d.130.2 24
231.95 even 30 847.2.n.d.753.2 24
231.116 even 30 847.2.n.d.487.2 24
231.131 odd 6 5929.2.a.w.1.2 3
231.137 odd 30 847.2.n.e.487.2 24
231.158 odd 30 847.2.n.e.753.2 24
231.179 odd 30 847.2.n.e.130.2 24
231.200 even 30 847.2.n.d.81.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.e.b.23.2 6 3.2 odd 2
77.2.e.b.67.2 yes 6 21.11 odd 6
539.2.a.h.1.2 3 21.2 odd 6
539.2.a.i.1.2 3 21.5 even 6
539.2.e.l.67.2 6 21.17 even 6
539.2.e.l.177.2 6 21.20 even 2
693.2.i.g.100.2 6 1.1 even 1 trivial
693.2.i.g.298.2 6 7.4 even 3 inner
847.2.e.d.485.2 6 33.32 even 2
847.2.e.d.606.2 6 231.32 even 6
847.2.n.d.9.2 24 33.8 even 10
847.2.n.d.81.2 24 231.200 even 30
847.2.n.d.130.2 24 231.74 even 30
847.2.n.d.366.2 24 33.17 even 10
847.2.n.d.487.2 24 231.116 even 30
847.2.n.d.632.2 24 33.29 even 10
847.2.n.d.753.2 24 231.95 even 30
847.2.n.d.807.2 24 33.2 even 10
847.2.n.e.9.2 24 33.14 odd 10
847.2.n.e.81.2 24 231.53 odd 30
847.2.n.e.130.2 24 231.179 odd 30
847.2.n.e.366.2 24 33.5 odd 10
847.2.n.e.487.2 24 231.137 odd 30
847.2.n.e.632.2 24 33.26 odd 10
847.2.n.e.753.2 24 231.158 odd 30
847.2.n.e.807.2 24 33.20 odd 10
1232.2.q.k.177.3 6 12.11 even 2
1232.2.q.k.529.3 6 84.11 even 6
4851.2.a.bn.1.2 3 7.5 odd 6
4851.2.a.bo.1.2 3 7.2 even 3
5929.2.a.v.1.2 3 231.65 even 6
5929.2.a.w.1.2 3 231.131 odd 6
8624.2.a.ck.1.3 3 84.47 odd 6
8624.2.a.cl.1.1 3 84.23 even 6