Properties

Label 144.3.m.a.19.3
Level $144$
Weight $3$
Character 144.19
Analytic conductor $3.924$
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] = [144,3,Mod(19,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.m (of order \(4\), 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: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(i)\)
Coefficient field: 6.0.399424.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 19.3
Root \(1.40680 - 0.144584i\) of defining polynomial
Character \(\chi\) \(=\) 144.19
Dual form 144.3.m.a.91.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.55139 + 1.26222i) q^{2} +(0.813607 + 3.91638i) q^{4} +(4.62721 - 4.62721i) q^{5} +3.04888 q^{7} +(-3.68111 + 7.10278i) q^{8} +O(q^{10})\) \(q+(1.55139 + 1.26222i) q^{2} +(0.813607 + 3.91638i) q^{4} +(4.62721 - 4.62721i) q^{5} +3.04888 q^{7} +(-3.68111 + 7.10278i) q^{8} +(13.0192 - 1.33804i) q^{10} +(9.15165 + 9.15165i) q^{11} +(-5.78389 - 5.78389i) q^{13} +(4.72999 + 3.84835i) q^{14} +(-14.6761 + 6.37279i) q^{16} -17.6655 q^{17} +(-1.15165 + 1.15165i) q^{19} +(21.8867 + 14.3572i) q^{20} +(2.64637 + 25.7491i) q^{22} +3.45998 q^{23} -17.8222i q^{25} +(-1.67252 - 16.2736i) q^{26} +(2.48059 + 11.9406i) q^{28} +(-12.1950 - 12.1950i) q^{29} -38.5089i q^{31} +(-30.8122 - 8.63778i) q^{32} +(-27.4061 - 22.2978i) q^{34} +(14.1078 - 14.1078i) q^{35} +(-0.0972356 + 0.0972356i) q^{37} +(-3.24029 + 0.333021i) q^{38} +(15.8328 + 49.8993i) q^{40} -51.5266i q^{41} +(-1.70172 - 1.70172i) q^{43} +(-28.3955 + 43.2872i) q^{44} +(5.36776 + 4.36725i) q^{46} +24.1533i q^{47} -39.7044 q^{49} +(22.4955 - 27.6491i) q^{50} +(17.9461 - 27.3577i) q^{52} +(-27.0383 + 27.0383i) q^{53} +84.6933 q^{55} +(-11.2233 + 21.6555i) q^{56} +(-3.52641 - 34.3119i) q^{58} +(-19.5939 - 19.5939i) q^{59} +(16.7250 + 16.7250i) q^{61} +(48.6066 - 59.7422i) q^{62} +(-36.8988 - 52.2922i) q^{64} -53.5266 q^{65} +(-75.8560 + 75.8560i) q^{67} +(-14.3728 - 69.1849i) q^{68} +(39.6938 - 4.07953i) q^{70} +134.749 q^{71} -112.210i q^{73} +(-0.273583 + 0.0281175i) q^{74} +(-5.44730 - 3.57331i) q^{76} +(27.9022 + 27.9022i) q^{77} +135.915i q^{79} +(-38.4211 + 97.3976i) q^{80} +(65.0378 - 79.9377i) q^{82} +(-74.9250 + 74.9250i) q^{83} +(-81.7422 + 81.7422i) q^{85} +(-0.492084 - 4.78797i) q^{86} +(-98.6904 + 31.3139i) q^{88} -31.4278i q^{89} +(-17.6344 - 17.6344i) q^{91} +(2.81506 + 13.5506i) q^{92} +(-30.4867 + 37.4711i) q^{94} +10.6579i q^{95} +31.5456 q^{97} +(-61.5968 - 50.1156i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8} + 36 q^{10} + 18 q^{11} - 2 q^{13} - 12 q^{14} - 40 q^{16} + 4 q^{17} + 30 q^{19} + 84 q^{20} - 52 q^{22} - 60 q^{23} - 96 q^{26} + 56 q^{28} + 18 q^{29} - 8 q^{32} - 76 q^{34} + 100 q^{35} + 46 q^{37} - 40 q^{38} + 40 q^{40} - 114 q^{43} - 20 q^{44} + 28 q^{46} - 46 q^{49} - 46 q^{50} + 100 q^{52} - 78 q^{53} + 252 q^{55} + 168 q^{56} - 176 q^{58} - 206 q^{59} + 30 q^{61} + 144 q^{62} + 64 q^{64} - 12 q^{65} - 226 q^{67} - 112 q^{68} - 16 q^{70} + 260 q^{71} + 92 q^{74} - 188 q^{76} + 212 q^{77} - 232 q^{80} + 304 q^{82} - 318 q^{83} - 212 q^{85} - 268 q^{86} - 8 q^{88} + 188 q^{91} + 168 q^{92} + 48 q^{94} - 4 q^{97} - 10 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.55139 + 1.26222i 0.775694 + 0.631109i
\(3\) 0 0
\(4\) 0.813607 + 3.91638i 0.203402 + 0.979095i
\(5\) 4.62721 4.62721i 0.925443 0.925443i −0.0719646 0.997407i \(-0.522927\pi\)
0.997407 + 0.0719646i \(0.0229269\pi\)
\(6\) 0 0
\(7\) 3.04888 0.435554 0.217777 0.975999i \(-0.430119\pi\)
0.217777 + 0.975999i \(0.430119\pi\)
\(8\) −3.68111 + 7.10278i −0.460139 + 0.887847i
\(9\) 0 0
\(10\) 13.0192 1.33804i 1.30192 0.133804i
\(11\) 9.15165 + 9.15165i 0.831968 + 0.831968i 0.987786 0.155818i \(-0.0498012\pi\)
−0.155818 + 0.987786i \(0.549801\pi\)
\(12\) 0 0
\(13\) −5.78389 5.78389i −0.444914 0.444914i 0.448745 0.893660i \(-0.351871\pi\)
−0.893660 + 0.448745i \(0.851871\pi\)
\(14\) 4.72999 + 3.84835i 0.337856 + 0.274882i
\(15\) 0 0
\(16\) −14.6761 + 6.37279i −0.917256 + 0.398299i
\(17\) −17.6655 −1.03915 −0.519574 0.854425i \(-0.673909\pi\)
−0.519574 + 0.854425i \(0.673909\pi\)
\(18\) 0 0
\(19\) −1.15165 + 1.15165i −0.0606132 + 0.0606132i −0.736764 0.676150i \(-0.763647\pi\)
0.676150 + 0.736764i \(0.263647\pi\)
\(20\) 21.8867 + 14.3572i 1.09433 + 0.717860i
\(21\) 0 0
\(22\) 2.64637 + 25.7491i 0.120290 + 1.17042i
\(23\) 3.45998 0.150434 0.0752169 0.997167i \(-0.476035\pi\)
0.0752169 + 0.997167i \(0.476035\pi\)
\(24\) 0 0
\(25\) 17.8222i 0.712888i
\(26\) −1.67252 16.2736i −0.0643276 0.625907i
\(27\) 0 0
\(28\) 2.48059 + 11.9406i 0.0885923 + 0.426449i
\(29\) −12.1950 12.1950i −0.420517 0.420517i 0.464865 0.885382i \(-0.346103\pi\)
−0.885382 + 0.464865i \(0.846103\pi\)
\(30\) 0 0
\(31\) 38.5089i 1.24222i −0.783723 0.621111i \(-0.786682\pi\)
0.783723 0.621111i \(-0.213318\pi\)
\(32\) −30.8122 8.63778i −0.962880 0.269930i
\(33\) 0 0
\(34\) −27.4061 22.2978i −0.806061 0.655817i
\(35\) 14.1078 14.1078i 0.403080 0.403080i
\(36\) 0 0
\(37\) −0.0972356 + 0.0972356i −0.00262799 + 0.00262799i −0.708420 0.705792i \(-0.750592\pi\)
0.705792 + 0.708420i \(0.250592\pi\)
\(38\) −3.24029 + 0.333021i −0.0852709 + 0.00876372i
\(39\) 0 0
\(40\) 15.8328 + 49.8993i 0.395819 + 1.24748i
\(41\) 51.5266i 1.25675i −0.777912 0.628373i \(-0.783721\pi\)
0.777912 0.628373i \(-0.216279\pi\)
\(42\) 0 0
\(43\) −1.70172 1.70172i −0.0395749 0.0395749i 0.687042 0.726617i \(-0.258909\pi\)
−0.726617 + 0.687042i \(0.758909\pi\)
\(44\) −28.3955 + 43.2872i −0.645353 + 0.983800i
\(45\) 0 0
\(46\) 5.36776 + 4.36725i 0.116691 + 0.0949402i
\(47\) 24.1533i 0.513899i 0.966425 + 0.256949i \(0.0827174\pi\)
−0.966425 + 0.256949i \(0.917283\pi\)
\(48\) 0 0
\(49\) −39.7044 −0.810293
\(50\) 22.4955 27.6491i 0.449910 0.552983i
\(51\) 0 0
\(52\) 17.9461 27.3577i 0.345117 0.526110i
\(53\) −27.0383 + 27.0383i −0.510157 + 0.510157i −0.914574 0.404418i \(-0.867474\pi\)
0.404418 + 0.914574i \(0.367474\pi\)
\(54\) 0 0
\(55\) 84.6933 1.53988
\(56\) −11.2233 + 21.6555i −0.200415 + 0.386705i
\(57\) 0 0
\(58\) −3.52641 34.3119i −0.0608001 0.591584i
\(59\) −19.5939 19.5939i −0.332100 0.332100i 0.521283 0.853384i \(-0.325453\pi\)
−0.853384 + 0.521283i \(0.825453\pi\)
\(60\) 0 0
\(61\) 16.7250 + 16.7250i 0.274180 + 0.274180i 0.830780 0.556601i \(-0.187895\pi\)
−0.556601 + 0.830780i \(0.687895\pi\)
\(62\) 48.6066 59.7422i 0.783977 0.963583i
\(63\) 0 0
\(64\) −36.8988 52.2922i −0.576544 0.817066i
\(65\) −53.5266 −0.823485
\(66\) 0 0
\(67\) −75.8560 + 75.8560i −1.13218 + 1.13218i −0.142365 + 0.989814i \(0.545471\pi\)
−0.989814 + 0.142365i \(0.954529\pi\)
\(68\) −14.3728 69.1849i −0.211365 1.01743i
\(69\) 0 0
\(70\) 39.6938 4.07953i 0.567054 0.0582790i
\(71\) 134.749 1.89787 0.948935 0.315471i \(-0.102163\pi\)
0.948935 + 0.315471i \(0.102163\pi\)
\(72\) 0 0
\(73\) 112.210i 1.53712i −0.639777 0.768560i \(-0.720974\pi\)
0.639777 0.768560i \(-0.279026\pi\)
\(74\) −0.273583 + 0.0281175i −0.00369706 + 0.000379966i
\(75\) 0 0
\(76\) −5.44730 3.57331i −0.0716749 0.0470173i
\(77\) 27.9022 + 27.9022i 0.362367 + 0.362367i
\(78\) 0 0
\(79\) 135.915i 1.72045i 0.509915 + 0.860225i \(0.329677\pi\)
−0.509915 + 0.860225i \(0.670323\pi\)
\(80\) −38.4211 + 97.3976i −0.480264 + 1.21747i
\(81\) 0 0
\(82\) 65.0378 79.9377i 0.793144 0.974849i
\(83\) −74.9250 + 74.9250i −0.902711 + 0.902711i −0.995670 0.0929594i \(-0.970367\pi\)
0.0929594 + 0.995670i \(0.470367\pi\)
\(84\) 0 0
\(85\) −81.7422 + 81.7422i −0.961672 + 0.961672i
\(86\) −0.492084 4.78797i −0.00572191 0.0556741i
\(87\) 0 0
\(88\) −98.6904 + 31.3139i −1.12148 + 0.355839i
\(89\) 31.4278i 0.353121i −0.984290 0.176561i \(-0.943503\pi\)
0.984290 0.176561i \(-0.0564971\pi\)
\(90\) 0 0
\(91\) −17.6344 17.6344i −0.193784 0.193784i
\(92\) 2.81506 + 13.5506i 0.0305985 + 0.147289i
\(93\) 0 0
\(94\) −30.4867 + 37.4711i −0.324327 + 0.398628i
\(95\) 10.6579i 0.112188i
\(96\) 0 0
\(97\) 31.5456 0.325213 0.162606 0.986691i \(-0.448010\pi\)
0.162606 + 0.986691i \(0.448010\pi\)
\(98\) −61.5968 50.1156i −0.628539 0.511384i
\(99\) 0 0
\(100\) 69.7985 14.5003i 0.697985 0.145003i
\(101\) −27.4695 + 27.4695i −0.271975 + 0.271975i −0.829895 0.557920i \(-0.811600\pi\)
0.557920 + 0.829895i \(0.311600\pi\)
\(102\) 0 0
\(103\) 102.882 0.998854 0.499427 0.866356i \(-0.333544\pi\)
0.499427 + 0.866356i \(0.333544\pi\)
\(104\) 62.3728 19.7905i 0.599738 0.190293i
\(105\) 0 0
\(106\) −76.0752 + 7.81863i −0.717690 + 0.0737607i
\(107\) 79.6605 + 79.6605i 0.744491 + 0.744491i 0.973439 0.228948i \(-0.0735286\pi\)
−0.228948 + 0.973439i \(0.573529\pi\)
\(108\) 0 0
\(109\) 125.408 + 125.408i 1.15053 + 1.15053i 0.986446 + 0.164088i \(0.0524682\pi\)
0.164088 + 0.986446i \(0.447532\pi\)
\(110\) 131.392 + 106.901i 1.19447 + 0.971831i
\(111\) 0 0
\(112\) −44.7456 + 19.4298i −0.399514 + 0.173481i
\(113\) 96.6199 0.855043 0.427521 0.904005i \(-0.359387\pi\)
0.427521 + 0.904005i \(0.359387\pi\)
\(114\) 0 0
\(115\) 16.0100 16.0100i 0.139218 0.139218i
\(116\) 37.8383 57.6821i 0.326192 0.497260i
\(117\) 0 0
\(118\) −5.66595 55.1296i −0.0480165 0.467200i
\(119\) −53.8600 −0.452605
\(120\) 0 0
\(121\) 46.5054i 0.384342i
\(122\) 4.83633 + 47.0575i 0.0396421 + 0.385717i
\(123\) 0 0
\(124\) 150.815 31.3311i 1.21625 0.252670i
\(125\) 33.2132 + 33.2132i 0.265706 + 0.265706i
\(126\) 0 0
\(127\) 196.309i 1.54574i −0.634566 0.772868i \(-0.718821\pi\)
0.634566 0.772868i \(-0.281179\pi\)
\(128\) 8.75986 127.700i 0.0684364 0.997655i
\(129\) 0 0
\(130\) −83.0404 67.5622i −0.638773 0.519709i
\(131\) −17.9437 + 17.9437i −0.136975 + 0.136975i −0.772270 0.635295i \(-0.780879\pi\)
0.635295 + 0.772270i \(0.280879\pi\)
\(132\) 0 0
\(133\) −3.51124 + 3.51124i −0.0264003 + 0.0264003i
\(134\) −213.429 + 21.9352i −1.59275 + 0.163695i
\(135\) 0 0
\(136\) 65.0288 125.474i 0.478153 0.922605i
\(137\) 51.7200i 0.377518i 0.982023 + 0.188759i \(0.0604465\pi\)
−0.982023 + 0.188759i \(0.939553\pi\)
\(138\) 0 0
\(139\) −17.4640 17.4640i −0.125640 0.125640i 0.641491 0.767131i \(-0.278316\pi\)
−0.767131 + 0.641491i \(0.778316\pi\)
\(140\) 66.7297 + 43.7733i 0.476641 + 0.312667i
\(141\) 0 0
\(142\) 209.048 + 170.082i 1.47217 + 1.19776i
\(143\) 105.864i 0.740309i
\(144\) 0 0
\(145\) −112.858 −0.778328
\(146\) 141.633 174.081i 0.970091 1.19233i
\(147\) 0 0
\(148\) −0.459923 0.301700i −0.00310759 0.00203851i
\(149\) −11.9170 + 11.9170i −0.0799802 + 0.0799802i −0.745965 0.665985i \(-0.768011\pi\)
0.665985 + 0.745965i \(0.268011\pi\)
\(150\) 0 0
\(151\) −132.548 −0.877805 −0.438902 0.898535i \(-0.644633\pi\)
−0.438902 + 0.898535i \(0.644633\pi\)
\(152\) −3.94056 12.4193i −0.0259247 0.0817058i
\(153\) 0 0
\(154\) 8.06845 + 78.5059i 0.0523925 + 0.509779i
\(155\) −178.189 178.189i −1.14960 1.14960i
\(156\) 0 0
\(157\) 106.091 + 106.091i 0.675742 + 0.675742i 0.959034 0.283292i \(-0.0914266\pi\)
−0.283292 + 0.959034i \(0.591427\pi\)
\(158\) −171.555 + 210.858i −1.08579 + 1.33454i
\(159\) 0 0
\(160\) −182.543 + 102.606i −1.14090 + 0.641285i
\(161\) 10.5490 0.0655220
\(162\) 0 0
\(163\) −105.577 + 105.577i −0.647712 + 0.647712i −0.952440 0.304728i \(-0.901435\pi\)
0.304728 + 0.952440i \(0.401435\pi\)
\(164\) 201.798 41.9223i 1.23047 0.255624i
\(165\) 0 0
\(166\) −210.809 + 21.6659i −1.26994 + 0.130518i
\(167\) −111.591 −0.668210 −0.334105 0.942536i \(-0.608434\pi\)
−0.334105 + 0.942536i \(0.608434\pi\)
\(168\) 0 0
\(169\) 102.093i 0.604102i
\(170\) −229.990 + 23.6373i −1.35288 + 0.139043i
\(171\) 0 0
\(172\) 5.28006 8.04912i 0.0306980 0.0467972i
\(173\) −14.5363 14.5363i −0.0840249 0.0840249i 0.663845 0.747870i \(-0.268923\pi\)
−0.747870 + 0.663845i \(0.768923\pi\)
\(174\) 0 0
\(175\) 54.3377i 0.310501i
\(176\) −192.632 75.9889i −1.09450 0.431755i
\(177\) 0 0
\(178\) 39.6687 48.7567i 0.222858 0.273914i
\(179\) 19.7371 19.7371i 0.110263 0.110263i −0.649823 0.760086i \(-0.725157\pi\)
0.760086 + 0.649823i \(0.225157\pi\)
\(180\) 0 0
\(181\) 168.153 168.153i 0.929021 0.929021i −0.0686221 0.997643i \(-0.521860\pi\)
0.997643 + 0.0686221i \(0.0218603\pi\)
\(182\) −5.09930 49.6161i −0.0280181 0.272616i
\(183\) 0 0
\(184\) −12.7366 + 24.5754i −0.0692204 + 0.133562i
\(185\) 0.899859i 0.00486410i
\(186\) 0 0
\(187\) −161.669 161.669i −0.864539 0.864539i
\(188\) −94.5934 + 19.6512i −0.503156 + 0.104528i
\(189\) 0 0
\(190\) −13.4526 + 16.5345i −0.0708030 + 0.0870236i
\(191\) 196.309i 1.02779i −0.857852 0.513897i \(-0.828201\pi\)
0.857852 0.513897i \(-0.171799\pi\)
\(192\) 0 0
\(193\) −40.3699 −0.209170 −0.104585 0.994516i \(-0.533351\pi\)
−0.104585 + 0.994516i \(0.533351\pi\)
\(194\) 48.9395 + 39.8175i 0.252265 + 0.205245i
\(195\) 0 0
\(196\) −32.3037 155.497i −0.164815 0.793354i
\(197\) 230.578 230.578i 1.17045 1.17045i 0.188344 0.982103i \(-0.439688\pi\)
0.982103 0.188344i \(-0.0603121\pi\)
\(198\) 0 0
\(199\) 61.5598 0.309346 0.154673 0.987966i \(-0.450568\pi\)
0.154673 + 0.987966i \(0.450568\pi\)
\(200\) 126.587 + 65.6055i 0.632935 + 0.328028i
\(201\) 0 0
\(202\) −77.2884 + 7.94332i −0.382616 + 0.0393234i
\(203\) −37.1810 37.1810i −0.183158 0.183158i
\(204\) 0 0
\(205\) −238.424 238.424i −1.16305 1.16305i
\(206\) 159.610 + 129.860i 0.774805 + 0.630386i
\(207\) 0 0
\(208\) 121.744 + 48.0254i 0.585309 + 0.230891i
\(209\) −21.0790 −0.100857
\(210\) 0 0
\(211\) 151.149 151.149i 0.716346 0.716346i −0.251509 0.967855i \(-0.580927\pi\)
0.967855 + 0.251509i \(0.0809267\pi\)
\(212\) −127.891 83.8938i −0.603259 0.395725i
\(213\) 0 0
\(214\) 23.0353 + 224.133i 0.107642 + 1.04735i
\(215\) −15.7485 −0.0732486
\(216\) 0 0
\(217\) 117.409i 0.541054i
\(218\) 36.2641 + 352.849i 0.166349 + 1.61857i
\(219\) 0 0
\(220\) 68.9070 + 331.691i 0.313214 + 1.50769i
\(221\) 102.175 + 102.175i 0.462332 + 0.462332i
\(222\) 0 0
\(223\) 115.527i 0.518056i 0.965870 + 0.259028i \(0.0834022\pi\)
−0.965870 + 0.259028i \(0.916598\pi\)
\(224\) −93.9424 26.3355i −0.419386 0.117569i
\(225\) 0 0
\(226\) 149.895 + 121.955i 0.663251 + 0.539626i
\(227\) −25.2363 + 25.2363i −0.111173 + 0.111173i −0.760505 0.649332i \(-0.775049\pi\)
0.649332 + 0.760505i \(0.275049\pi\)
\(228\) 0 0
\(229\) −155.318 + 155.318i −0.678244 + 0.678244i −0.959603 0.281359i \(-0.909215\pi\)
0.281359 + 0.959603i \(0.409215\pi\)
\(230\) 45.0460 4.62960i 0.195852 0.0201287i
\(231\) 0 0
\(232\) 131.509 41.7271i 0.566851 0.179858i
\(233\) 119.738i 0.513899i 0.966425 + 0.256949i \(0.0827174\pi\)
−0.966425 + 0.256949i \(0.917283\pi\)
\(234\) 0 0
\(235\) 111.762 + 111.762i 0.475584 + 0.475584i
\(236\) 60.7955 92.6790i 0.257608 0.392708i
\(237\) 0 0
\(238\) −83.5577 67.9831i −0.351083 0.285643i
\(239\) 245.409i 1.02681i 0.858145 + 0.513407i \(0.171617\pi\)
−0.858145 + 0.513407i \(0.828383\pi\)
\(240\) 0 0
\(241\) 431.216 1.78928 0.894639 0.446790i \(-0.147433\pi\)
0.894639 + 0.446790i \(0.147433\pi\)
\(242\) −58.7000 + 72.1479i −0.242562 + 0.298132i
\(243\) 0 0
\(244\) −51.8938 + 79.1089i −0.212680 + 0.324217i
\(245\) −183.721 + 183.721i −0.749880 + 0.749880i
\(246\) 0 0
\(247\) 13.3220 0.0539354
\(248\) 273.520 + 141.755i 1.10290 + 0.571594i
\(249\) 0 0
\(250\) 9.60421 + 93.4489i 0.0384169 + 0.373796i
\(251\) 24.0171 + 24.0171i 0.0956858 + 0.0956858i 0.753329 0.657643i \(-0.228447\pi\)
−0.657643 + 0.753329i \(0.728447\pi\)
\(252\) 0 0
\(253\) 31.6645 + 31.6645i 0.125156 + 0.125156i
\(254\) 247.784 304.551i 0.975529 1.19902i
\(255\) 0 0
\(256\) 174.775 187.055i 0.682716 0.730684i
\(257\) 100.860 0.392450 0.196225 0.980559i \(-0.437132\pi\)
0.196225 + 0.980559i \(0.437132\pi\)
\(258\) 0 0
\(259\) −0.296459 + 0.296459i −0.00114463 + 0.00114463i
\(260\) −43.5496 209.630i −0.167498 0.806271i
\(261\) 0 0
\(262\) −50.4865 + 5.18876i −0.192697 + 0.0198044i
\(263\) −216.776 −0.824242 −0.412121 0.911129i \(-0.635212\pi\)
−0.412121 + 0.911129i \(0.635212\pi\)
\(264\) 0 0
\(265\) 250.224i 0.944242i
\(266\) −9.87925 + 1.01534i −0.0371400 + 0.00381707i
\(267\) 0 0
\(268\) −358.798 235.364i −1.33880 0.878224i
\(269\) 256.778 + 256.778i 0.954567 + 0.954567i 0.999012 0.0444453i \(-0.0141520\pi\)
−0.0444453 + 0.999012i \(0.514152\pi\)
\(270\) 0 0
\(271\) 12.8603i 0.0474551i −0.999718 0.0237275i \(-0.992447\pi\)
0.999718 0.0237275i \(-0.00755342\pi\)
\(272\) 259.261 112.579i 0.953165 0.413892i
\(273\) 0 0
\(274\) −65.2820 + 80.2378i −0.238255 + 0.292839i
\(275\) 163.103 163.103i 0.593100 0.593100i
\(276\) 0 0
\(277\) 77.1023 77.1023i 0.278348 0.278348i −0.554102 0.832449i \(-0.686938\pi\)
0.832449 + 0.554102i \(0.186938\pi\)
\(278\) −5.05003 49.1367i −0.0181656 0.176751i
\(279\) 0 0
\(280\) 48.2721 + 152.137i 0.172400 + 0.543346i
\(281\) 189.034i 0.672719i −0.941734 0.336360i \(-0.890804\pi\)
0.941734 0.336360i \(-0.109196\pi\)
\(282\) 0 0
\(283\) −69.4317 69.4317i −0.245342 0.245342i 0.573714 0.819056i \(-0.305502\pi\)
−0.819056 + 0.573714i \(0.805502\pi\)
\(284\) 109.632 + 527.728i 0.386030 + 1.85820i
\(285\) 0 0
\(286\) 133.624 164.236i 0.467216 0.574253i
\(287\) 157.098i 0.547380i
\(288\) 0 0
\(289\) 23.0708 0.0798298
\(290\) −175.086 142.451i −0.603744 0.491210i
\(291\) 0 0
\(292\) 439.456 91.2946i 1.50499 0.312653i
\(293\) −239.919 + 239.919i −0.818837 + 0.818837i −0.985939 0.167103i \(-0.946559\pi\)
0.167103 + 0.985939i \(0.446559\pi\)
\(294\) 0 0
\(295\) −181.331 −0.614680
\(296\) −0.332707 1.04858i −0.00112401 0.00354249i
\(297\) 0 0
\(298\) −33.5299 + 3.44604i −0.112516 + 0.0115639i
\(299\) −20.0121 20.0121i −0.0669301 0.0669301i
\(300\) 0 0
\(301\) −5.18834 5.18834i −0.0172370 0.0172370i
\(302\) −205.634 167.305i −0.680908 0.553991i
\(303\) 0 0
\(304\) 9.56251 24.2410i 0.0314556 0.0797400i
\(305\) 154.780 0.507475
\(306\) 0 0
\(307\) −231.185 + 231.185i −0.753046 + 0.753046i −0.975046 0.222001i \(-0.928741\pi\)
0.222001 + 0.975046i \(0.428741\pi\)
\(308\) −86.5744 + 131.977i −0.281086 + 0.428498i
\(309\) 0 0
\(310\) −51.5266 501.353i −0.166215 1.61727i
\(311\) 513.328 1.65057 0.825287 0.564714i \(-0.191013\pi\)
0.825287 + 0.564714i \(0.191013\pi\)
\(312\) 0 0
\(313\) 345.242i 1.10301i 0.834172 + 0.551504i \(0.185946\pi\)
−0.834172 + 0.551504i \(0.814054\pi\)
\(314\) 30.6783 + 298.500i 0.0977016 + 0.950635i
\(315\) 0 0
\(316\) −532.297 + 110.582i −1.68448 + 0.349942i
\(317\) −345.632 345.632i −1.09032 1.09032i −0.995494 0.0948290i \(-0.969770\pi\)
−0.0948290 0.995494i \(-0.530230\pi\)
\(318\) 0 0
\(319\) 223.209i 0.699713i
\(320\) −412.706 71.2285i −1.28971 0.222589i
\(321\) 0 0
\(322\) 16.3656 + 13.3152i 0.0508250 + 0.0413515i
\(323\) 20.3445 20.3445i 0.0629861 0.0629861i
\(324\) 0 0
\(325\) −103.082 + 103.082i −0.317174 + 0.317174i
\(326\) −297.052 + 30.5296i −0.911203 + 0.0936489i
\(327\) 0 0
\(328\) 365.982 + 189.675i 1.11580 + 0.578278i
\(329\) 73.6403i 0.223831i
\(330\) 0 0
\(331\) 425.968 + 425.968i 1.28691 + 1.28691i 0.936652 + 0.350261i \(0.113907\pi\)
0.350261 + 0.936652i \(0.386093\pi\)
\(332\) −354.394 232.475i −1.06745 0.700227i
\(333\) 0 0
\(334\) −173.121 140.852i −0.518326 0.421714i
\(335\) 702.004i 2.09553i
\(336\) 0 0
\(337\) −467.297 −1.38664 −0.693319 0.720631i \(-0.743852\pi\)
−0.693319 + 0.720631i \(0.743852\pi\)
\(338\) 128.864 158.386i 0.381255 0.468598i
\(339\) 0 0
\(340\) −386.639 253.628i −1.13717 0.745963i
\(341\) 352.420 352.420i 1.03349 1.03349i
\(342\) 0 0
\(343\) −270.449 −0.788480
\(344\) 18.3512 5.82272i 0.0533464 0.0169265i
\(345\) 0 0
\(346\) −4.20344 40.8994i −0.0121487 0.118206i
\(347\) 22.0463 + 22.0463i 0.0635341 + 0.0635341i 0.738160 0.674626i \(-0.235695\pi\)
−0.674626 + 0.738160i \(0.735695\pi\)
\(348\) 0 0
\(349\) −158.622 158.622i −0.454506 0.454506i 0.442341 0.896847i \(-0.354148\pi\)
−0.896847 + 0.442341i \(0.854148\pi\)
\(350\) 68.5860 84.2988i 0.195960 0.240854i
\(351\) 0 0
\(352\) −202.932 361.032i −0.576512 1.02566i
\(353\) −404.451 −1.14575 −0.572877 0.819642i \(-0.694173\pi\)
−0.572877 + 0.819642i \(0.694173\pi\)
\(354\) 0 0
\(355\) 623.511 623.511i 1.75637 1.75637i
\(356\) 123.083 25.5698i 0.345739 0.0718254i
\(357\) 0 0
\(358\) 55.5325 5.70736i 0.155119 0.0159423i
\(359\) −423.833 −1.18059 −0.590297 0.807186i \(-0.700989\pi\)
−0.590297 + 0.807186i \(0.700989\pi\)
\(360\) 0 0
\(361\) 358.347i 0.992652i
\(362\) 473.116 48.6245i 1.30695 0.134322i
\(363\) 0 0
\(364\) 54.7154 83.4103i 0.150317 0.229149i
\(365\) −519.219 519.219i −1.42252 1.42252i
\(366\) 0 0
\(367\) 477.144i 1.30012i 0.759883 + 0.650059i \(0.225256\pi\)
−0.759883 + 0.650059i \(0.774744\pi\)
\(368\) −50.7789 + 22.0497i −0.137986 + 0.0599176i
\(369\) 0 0
\(370\) −1.13582 + 1.39603i −0.00306978 + 0.00377306i
\(371\) −82.4365 + 82.4365i −0.222201 + 0.222201i
\(372\) 0 0
\(373\) 112.221 112.221i 0.300860 0.300860i −0.540490 0.841350i \(-0.681761\pi\)
0.841350 + 0.540490i \(0.181761\pi\)
\(374\) −46.7495 454.872i −0.124999 1.21624i
\(375\) 0 0
\(376\) −171.555 88.9108i −0.456264 0.236465i
\(377\) 141.069i 0.374188i
\(378\) 0 0
\(379\) 52.2069 + 52.2069i 0.137749 + 0.137749i 0.772619 0.634870i \(-0.218946\pi\)
−0.634870 + 0.772619i \(0.718946\pi\)
\(380\) −41.7403 + 8.67131i −0.109843 + 0.0228192i
\(381\) 0 0
\(382\) 247.784 304.551i 0.648650 0.797253i
\(383\) 74.8407i 0.195406i −0.995216 0.0977032i \(-0.968850\pi\)
0.995216 0.0977032i \(-0.0311496\pi\)
\(384\) 0 0
\(385\) 258.219 0.670699
\(386\) −62.6293 50.9556i −0.162252 0.132009i
\(387\) 0 0
\(388\) 25.6657 + 123.545i 0.0661488 + 0.318414i
\(389\) 57.0441 57.0441i 0.146643 0.146643i −0.629974 0.776617i \(-0.716934\pi\)
0.776617 + 0.629974i \(0.216934\pi\)
\(390\) 0 0
\(391\) −61.1223 −0.156323
\(392\) 146.156 282.011i 0.372847 0.719416i
\(393\) 0 0
\(394\) 648.756 66.6759i 1.64659 0.169228i
\(395\) 628.910 + 628.910i 1.59218 + 1.59218i
\(396\) 0 0
\(397\) −355.874 355.874i −0.896407 0.896407i 0.0987089 0.995116i \(-0.468529\pi\)
−0.995116 + 0.0987089i \(0.968529\pi\)
\(398\) 95.5031 + 77.7019i 0.239958 + 0.195231i
\(399\) 0 0
\(400\) 113.577 + 261.560i 0.283943 + 0.653900i
\(401\) −113.892 −0.284019 −0.142010 0.989865i \(-0.545356\pi\)
−0.142010 + 0.989865i \(0.545356\pi\)
\(402\) 0 0
\(403\) −222.731 + 222.731i −0.552682 + 0.552682i
\(404\) −129.930 85.2317i −0.321610 0.210970i
\(405\) 0 0
\(406\) −10.7516 104.613i −0.0264817 0.257667i
\(407\) −1.77973 −0.00437281
\(408\) 0 0
\(409\) 139.909i 0.342077i 0.985264 + 0.171038i \(0.0547122\pi\)
−0.985264 + 0.171038i \(0.945288\pi\)
\(410\) −68.9448 670.832i −0.168158 1.63618i
\(411\) 0 0
\(412\) 83.7054 + 402.925i 0.203168 + 0.977973i
\(413\) −59.7394 59.7394i −0.144648 0.144648i
\(414\) 0 0
\(415\) 693.388i 1.67081i
\(416\) 128.254 + 228.174i 0.308303 + 0.548495i
\(417\) 0 0
\(418\) −32.7017 26.6063i −0.0782338 0.0636515i
\(419\) 370.978 370.978i 0.885389 0.885389i −0.108687 0.994076i \(-0.534665\pi\)
0.994076 + 0.108687i \(0.0346647\pi\)
\(420\) 0 0
\(421\) 465.112 465.112i 1.10478 1.10478i 0.110955 0.993825i \(-0.464609\pi\)
0.993825 0.110955i \(-0.0353908\pi\)
\(422\) 425.274 43.7075i 1.00776 0.103572i
\(423\) 0 0
\(424\) −92.5160 291.578i −0.218198 0.687684i
\(425\) 314.839i 0.740797i
\(426\) 0 0
\(427\) 50.9923 + 50.9923i 0.119420 + 0.119420i
\(428\) −247.169 + 376.793i −0.577497 + 0.880358i
\(429\) 0 0
\(430\) −24.4320 19.8780i −0.0568185 0.0462279i
\(431\) 409.924i 0.951099i −0.879689 0.475549i \(-0.842249\pi\)
0.879689 0.475549i \(-0.157751\pi\)
\(432\) 0 0
\(433\) −20.6859 −0.0477735 −0.0238868 0.999715i \(-0.507604\pi\)
−0.0238868 + 0.999715i \(0.507604\pi\)
\(434\) 148.196 182.146i 0.341464 0.419692i
\(435\) 0 0
\(436\) −389.113 + 593.179i −0.892462 + 1.36050i
\(437\) −3.98468 + 3.98468i −0.00911827 + 0.00911827i
\(438\) 0 0
\(439\) −63.2889 −0.144166 −0.0720830 0.997399i \(-0.522965\pi\)
−0.0720830 + 0.997399i \(0.522965\pi\)
\(440\) −311.765 + 601.557i −0.708558 + 1.36718i
\(441\) 0 0
\(442\) 29.5459 + 287.481i 0.0668460 + 0.650410i
\(443\) 297.084 + 297.084i 0.670619 + 0.670619i 0.957859 0.287240i \(-0.0927377\pi\)
−0.287240 + 0.957859i \(0.592738\pi\)
\(444\) 0 0
\(445\) −145.423 145.423i −0.326793 0.326793i
\(446\) −145.820 + 179.226i −0.326950 + 0.401853i
\(447\) 0 0
\(448\) −112.500 159.432i −0.251116 0.355876i
\(449\) −364.701 −0.812251 −0.406126 0.913817i \(-0.633120\pi\)
−0.406126 + 0.913817i \(0.633120\pi\)
\(450\) 0 0
\(451\) 471.553 471.553i 1.04557 1.04557i
\(452\) 78.6105 + 378.400i 0.173917 + 0.837169i
\(453\) 0 0
\(454\) −71.0049 + 7.29753i −0.156398 + 0.0160739i
\(455\) −163.196 −0.358672
\(456\) 0 0
\(457\) 640.046i 1.40054i −0.713879 0.700269i \(-0.753064\pi\)
0.713879 0.700269i \(-0.246936\pi\)
\(458\) −437.003 + 44.9130i −0.954156 + 0.0980634i
\(459\) 0 0
\(460\) 75.7273 + 49.6756i 0.164625 + 0.107990i
\(461\) 239.416 + 239.416i 0.519341 + 0.519341i 0.917372 0.398031i \(-0.130306\pi\)
−0.398031 + 0.917372i \(0.630306\pi\)
\(462\) 0 0
\(463\) 479.413i 1.03545i −0.855548 0.517724i \(-0.826779\pi\)
0.855548 0.517724i \(-0.173221\pi\)
\(464\) 256.691 + 101.259i 0.553213 + 0.218230i
\(465\) 0 0
\(466\) −151.136 + 185.761i −0.324326 + 0.398628i
\(467\) −403.375 + 403.375i −0.863758 + 0.863758i −0.991772 0.128015i \(-0.959140\pi\)
0.128015 + 0.991772i \(0.459140\pi\)
\(468\) 0 0
\(469\) −231.276 + 231.276i −0.493125 + 0.493125i
\(470\) 32.3181 + 314.455i 0.0687620 + 0.669053i
\(471\) 0 0
\(472\) 211.299 67.0438i 0.447667 0.142042i
\(473\) 31.1471i 0.0658501i
\(474\) 0 0
\(475\) 20.5250 + 20.5250i 0.0432104 + 0.0432104i
\(476\) −43.8208 210.936i −0.0920606 0.443143i
\(477\) 0 0
\(478\) −309.760 + 380.724i −0.648032 + 0.796494i
\(479\) 460.611i 0.961609i −0.876828 0.480805i \(-0.840345\pi\)
0.876828 0.480805i \(-0.159655\pi\)
\(480\) 0 0
\(481\) 1.12480 0.00233846
\(482\) 668.983 + 544.289i 1.38793 + 1.12923i
\(483\) 0 0
\(484\) −182.133 + 37.8371i −0.376308 + 0.0781759i
\(485\) 145.968 145.968i 0.300966 0.300966i
\(486\) 0 0
\(487\) −575.128 −1.18096 −0.590481 0.807052i \(-0.701062\pi\)
−0.590481 + 0.807052i \(0.701062\pi\)
\(488\) −180.360 + 57.2272i −0.369590 + 0.117269i
\(489\) 0 0
\(490\) −516.917 + 53.1262i −1.05493 + 0.108421i
\(491\) −271.375 271.375i −0.552699 0.552699i 0.374520 0.927219i \(-0.377808\pi\)
−0.927219 + 0.374520i \(0.877808\pi\)
\(492\) 0 0
\(493\) 215.431 + 215.431i 0.436979 + 0.436979i
\(494\) 20.6676 + 16.8153i 0.0418373 + 0.0340391i
\(495\) 0 0
\(496\) 245.409 + 565.159i 0.494776 + 1.13943i
\(497\) 410.832 0.826624
\(498\) 0 0
\(499\) 268.082 268.082i 0.537239 0.537239i −0.385478 0.922717i \(-0.625963\pi\)
0.922717 + 0.385478i \(0.125963\pi\)
\(500\) −103.053 + 157.098i −0.206106 + 0.314196i
\(501\) 0 0
\(502\) 6.94500 + 67.5748i 0.0138347 + 0.134611i
\(503\) 368.002 0.731615 0.365807 0.930691i \(-0.380793\pi\)
0.365807 + 0.930691i \(0.380793\pi\)
\(504\) 0 0
\(505\) 254.215i 0.503395i
\(506\) 9.15638 + 89.0914i 0.0180956 + 0.176070i
\(507\) 0 0
\(508\) 768.819 159.718i 1.51342 0.314405i
\(509\) −297.809 297.809i −0.585087 0.585087i 0.351210 0.936297i \(-0.385770\pi\)
−0.936297 + 0.351210i \(0.885770\pi\)
\(510\) 0 0
\(511\) 342.114i 0.669498i
\(512\) 507.249 69.5905i 0.990720 0.135919i
\(513\) 0 0
\(514\) 156.472 + 127.307i 0.304421 + 0.247679i
\(515\) 476.057 476.057i 0.924382 0.924382i
\(516\) 0 0
\(517\) −221.042 + 221.042i −0.427548 + 0.427548i
\(518\) −0.834119 + 0.0857267i −0.00161027 + 0.000165495i
\(519\) 0 0
\(520\) 197.037 380.187i 0.378918 0.731129i
\(521\) 95.5605i 0.183418i −0.995786 0.0917088i \(-0.970767\pi\)
0.995786 0.0917088i \(-0.0292329\pi\)
\(522\) 0 0
\(523\) −250.389 250.389i −0.478756 0.478756i 0.425978 0.904734i \(-0.359930\pi\)
−0.904734 + 0.425978i \(0.859930\pi\)
\(524\) −84.8735 55.6753i −0.161972 0.106251i
\(525\) 0 0
\(526\) −336.303 273.618i −0.639360 0.520187i
\(527\) 680.279i 1.29085i
\(528\) 0 0
\(529\) −517.029 −0.977370
\(530\) −315.838 + 388.194i −0.595920 + 0.732442i
\(531\) 0 0
\(532\) −16.6081 10.8946i −0.0312183 0.0204786i
\(533\) −298.024 + 298.024i −0.559144 + 0.559144i
\(534\) 0 0
\(535\) 737.212 1.37797
\(536\) −259.554 818.023i −0.484242 1.52616i
\(537\) 0 0
\(538\) 74.2522 + 722.473i 0.138015 + 1.34289i
\(539\) −363.360 363.360i −0.674138 0.674138i
\(540\) 0 0
\(541\) −81.7015 81.7015i −0.151019 0.151019i 0.627554 0.778573i \(-0.284056\pi\)
−0.778573 + 0.627554i \(0.784056\pi\)
\(542\) 16.2325 19.9513i 0.0299493 0.0368106i
\(543\) 0 0
\(544\) 544.313 + 152.591i 1.00058 + 0.280498i
\(545\) 1160.58 2.12951
\(546\) 0 0
\(547\) −381.162 + 381.162i −0.696823 + 0.696823i −0.963724 0.266901i \(-0.914000\pi\)
0.266901 + 0.963724i \(0.414000\pi\)
\(548\) −202.555 + 42.0797i −0.369626 + 0.0767878i
\(549\) 0 0
\(550\) 458.906 47.1641i 0.834375 0.0857530i
\(551\) 28.0887 0.0509777
\(552\) 0 0
\(553\) 414.389i 0.749348i
\(554\) 216.935 22.2956i 0.391580 0.0402447i
\(555\) 0 0
\(556\) 54.1868 82.6044i 0.0974582 0.148569i
\(557\) 63.7634 + 63.7634i 0.114476 + 0.114476i 0.762025 0.647548i \(-0.224206\pi\)
−0.647548 + 0.762025i \(0.724206\pi\)
\(558\) 0 0
\(559\) 19.6851i 0.0352149i
\(560\) −117.141 + 296.953i −0.209181 + 0.530274i
\(561\) 0 0
\(562\) 238.602 293.265i 0.424559 0.521824i
\(563\) −333.679 + 333.679i −0.592681 + 0.592681i −0.938355 0.345674i \(-0.887650\pi\)
0.345674 + 0.938355i \(0.387650\pi\)
\(564\) 0 0
\(565\) 447.081 447.081i 0.791293 0.791293i
\(566\) −20.0775 195.353i −0.0354725 0.345147i
\(567\) 0 0
\(568\) −496.025 + 957.090i −0.873284 + 1.68502i
\(569\) 93.3114i 0.163992i −0.996633 0.0819960i \(-0.973871\pi\)
0.996633 0.0819960i \(-0.0261295\pi\)
\(570\) 0 0
\(571\) 196.999 + 196.999i 0.345007 + 0.345007i 0.858246 0.513239i \(-0.171555\pi\)
−0.513239 + 0.858246i \(0.671555\pi\)
\(572\) 414.605 86.1318i 0.724833 0.150580i
\(573\) 0 0
\(574\) 198.292 243.720i 0.345457 0.424599i
\(575\) 61.6644i 0.107242i
\(576\) 0 0
\(577\) 370.057 0.641347 0.320673 0.947190i \(-0.396091\pi\)
0.320673 + 0.947190i \(0.396091\pi\)
\(578\) 35.7918 + 29.1204i 0.0619235 + 0.0503814i
\(579\) 0 0
\(580\) −91.8217 441.993i −0.158313 0.762058i
\(581\) −228.437 + 228.437i −0.393179 + 0.393179i
\(582\) 0 0
\(583\) −494.890 −0.848869
\(584\) 797.001 + 413.057i 1.36473 + 0.707289i
\(585\) 0 0
\(586\) −675.038 + 69.3771i −1.15194 + 0.118391i
\(587\) −328.063 328.063i −0.558880 0.558880i 0.370108 0.928989i \(-0.379321\pi\)
−0.928989 + 0.370108i \(0.879321\pi\)
\(588\) 0 0
\(589\) 44.3488 + 44.3488i 0.0752950 + 0.0752950i
\(590\) −281.314 228.879i −0.476803 0.387930i
\(591\) 0 0
\(592\) 0.807376 2.04670i 0.00136381 0.00345726i
\(593\) −1088.78 −1.83605 −0.918024 0.396525i \(-0.870216\pi\)
−0.918024 + 0.396525i \(0.870216\pi\)
\(594\) 0 0
\(595\) −249.222 + 249.222i −0.418860 + 0.418860i
\(596\) −56.3675 36.9759i −0.0945763 0.0620401i
\(597\) 0 0
\(598\) −5.78687 56.3062i −0.00967705 0.0941575i
\(599\) 350.354 0.584899 0.292449 0.956281i \(-0.405530\pi\)
0.292449 + 0.956281i \(0.405530\pi\)
\(600\) 0 0
\(601\) 1021.45i 1.69958i −0.527123 0.849789i \(-0.676729\pi\)
0.527123 0.849789i \(-0.323271\pi\)
\(602\) −1.50030 14.5979i −0.00249220 0.0242491i
\(603\) 0 0
\(604\) −107.842 519.110i −0.178547 0.859454i
\(605\) 215.191 + 215.191i 0.355687 + 0.355687i
\(606\) 0 0
\(607\) 394.204i 0.649431i −0.945812 0.324715i \(-0.894732\pi\)
0.945812 0.324715i \(-0.105268\pi\)
\(608\) 45.4325 25.5371i 0.0747246 0.0420019i
\(609\) 0 0
\(610\) 240.124 + 195.366i 0.393645 + 0.320272i
\(611\) 139.700 139.700i 0.228641 0.228641i
\(612\) 0 0
\(613\) 157.606 157.606i 0.257106 0.257106i −0.566770 0.823876i \(-0.691807\pi\)
0.823876 + 0.566770i \(0.191807\pi\)
\(614\) −650.464 + 66.8514i −1.05939 + 0.108879i
\(615\) 0 0
\(616\) −300.895 + 95.4721i −0.488465 + 0.154987i
\(617\) 609.080i 0.987164i −0.869699 0.493582i \(-0.835687\pi\)
0.869699 0.493582i \(-0.164313\pi\)
\(618\) 0 0
\(619\) −497.519 497.519i −0.803747 0.803747i 0.179932 0.983679i \(-0.442412\pi\)
−0.983679 + 0.179932i \(0.942412\pi\)
\(620\) 552.879 842.830i 0.891741 1.35940i
\(621\) 0 0
\(622\) 796.371 + 647.933i 1.28034 + 1.04169i
\(623\) 95.8194i 0.153803i
\(624\) 0 0
\(625\) 752.924 1.20468
\(626\) −435.771 + 535.604i −0.696119 + 0.855597i
\(627\) 0 0
\(628\) −329.178 + 501.811i −0.524169 + 0.799062i
\(629\) 1.71772 1.71772i 0.00273087 0.00273087i
\(630\) 0 0
\(631\) 668.065 1.05874 0.529370 0.848391i \(-0.322428\pi\)
0.529370 + 0.848391i \(0.322428\pi\)
\(632\) −965.377 500.320i −1.52750 0.791646i
\(633\) 0 0
\(634\) −99.9460 972.473i −0.157644 1.53387i
\(635\) −908.362 908.362i −1.43049 1.43049i
\(636\) 0 0
\(637\) 229.646 + 229.646i 0.360511 + 0.360511i
\(638\) 281.738 346.283i 0.441596 0.542763i
\(639\) 0 0
\(640\) −550.361 631.428i −0.859939 0.986607i
\(641\) 419.792 0.654902 0.327451 0.944868i \(-0.393810\pi\)
0.327451 + 0.944868i \(0.393810\pi\)
\(642\) 0 0
\(643\) −138.767 + 138.767i −0.215813 + 0.215813i −0.806731 0.590919i \(-0.798765\pi\)
0.590919 + 0.806731i \(0.298765\pi\)
\(644\) 8.58277 + 41.3141i 0.0133273 + 0.0641523i
\(645\) 0 0
\(646\) 57.2415 5.88300i 0.0886091 0.00910680i
\(647\) −647.036 −1.00006 −0.500028 0.866009i \(-0.666677\pi\)
−0.500028 + 0.866009i \(0.666677\pi\)
\(648\) 0 0
\(649\) 358.633i 0.552594i
\(650\) −290.031 + 29.8080i −0.446202 + 0.0458584i
\(651\) 0 0
\(652\) −499.378 327.582i −0.765917 0.502426i
\(653\) 452.293 + 452.293i 0.692639 + 0.692639i 0.962812 0.270173i \(-0.0870808\pi\)
−0.270173 + 0.962812i \(0.587081\pi\)
\(654\) 0 0
\(655\) 166.059i 0.253525i
\(656\) 328.368 + 756.208i 0.500561 + 1.15276i
\(657\) 0 0
\(658\) −92.9501 + 114.245i −0.141262 + 0.173624i
\(659\) −382.858 + 382.858i −0.580969 + 0.580969i −0.935169 0.354201i \(-0.884753\pi\)
0.354201 + 0.935169i \(0.384753\pi\)
\(660\) 0 0
\(661\) −841.606 + 841.606i −1.27323 + 1.27323i −0.328849 + 0.944383i \(0.606661\pi\)
−0.944383 + 0.328849i \(0.893339\pi\)
\(662\) 123.177 + 1198.51i 0.186067 + 1.81043i
\(663\) 0 0
\(664\) −256.368 807.982i −0.386096 1.21684i
\(665\) 32.4945i 0.0488639i
\(666\) 0 0
\(667\) −42.1944 42.1944i −0.0632599 0.0632599i
\(668\) −90.7912 437.033i −0.135915 0.654241i
\(669\) 0 0
\(670\) −886.083 + 1089.08i −1.32251 + 1.62549i
\(671\) 306.122i 0.456218i
\(672\) 0 0
\(673\) −506.103 −0.752010 −0.376005 0.926618i \(-0.622703\pi\)
−0.376005 + 0.926618i \(0.622703\pi\)
\(674\) −724.958 589.831i −1.07561 0.875120i
\(675\) 0 0
\(676\) 399.836 83.0638i 0.591474 0.122875i
\(677\) 430.816 430.816i 0.636361 0.636361i −0.313295 0.949656i \(-0.601433\pi\)
0.949656 + 0.313295i \(0.101433\pi\)
\(678\) 0 0
\(679\) 96.1787 0.141648
\(680\) −279.694 881.498i −0.411315 1.29632i
\(681\) 0 0
\(682\) 991.570 101.909i 1.45391 0.149426i
\(683\) 910.083 + 910.083i 1.33248 + 1.33248i 0.903146 + 0.429333i \(0.141251\pi\)
0.429333 + 0.903146i \(0.358749\pi\)
\(684\) 0 0
\(685\) 239.319 + 239.319i 0.349371 + 0.349371i
\(686\) −419.571 341.365i −0.611619 0.497617i
\(687\) 0 0
\(688\) 35.8193 + 14.1299i 0.0520630 + 0.0205377i
\(689\) 312.773 0.453952
\(690\) 0 0
\(691\) −601.836 + 601.836i −0.870964 + 0.870964i −0.992577 0.121614i \(-0.961193\pi\)
0.121614 + 0.992577i \(0.461193\pi\)
\(692\) 45.1029 68.7565i 0.0651776 0.0993592i
\(693\) 0 0
\(694\) 6.37511 + 62.0297i 0.00918604 + 0.0893800i
\(695\) −161.619 −0.232545
\(696\) 0 0
\(697\) 910.244i 1.30595i
\(698\) −45.8686 446.301i −0.0657144 0.639400i
\(699\) 0 0
\(700\) 212.807 44.2095i 0.304010 0.0631564i
\(701\) 555.343 + 555.343i 0.792215 + 0.792215i 0.981854 0.189639i \(-0.0607317\pi\)
−0.189639 + 0.981854i \(0.560732\pi\)
\(702\) 0 0
\(703\) 0.223963i 0.000318582i
\(704\) 140.875 816.245i 0.200107 1.15944i
\(705\) 0 0
\(706\) −627.460 510.506i −0.888754 0.723096i
\(707\) −83.7511 + 83.7511i −0.118460 + 0.118460i
\(708\) 0 0
\(709\) −412.979 + 412.979i −0.582480 + 0.582480i −0.935584 0.353104i \(-0.885126\pi\)
0.353104 + 0.935584i \(0.385126\pi\)
\(710\) 1754.32 180.300i 2.47087 0.253943i
\(711\) 0 0
\(712\) 223.224 + 115.689i 0.313517 + 0.162485i
\(713\) 133.240i 0.186872i
\(714\) 0 0
\(715\) −489.856 489.856i −0.685114 0.685114i
\(716\) 93.3564 + 61.2399i 0.130386 + 0.0855305i
\(717\) 0 0
\(718\) −657.529 534.970i −0.915779 0.745084i
\(719\) 1173.98i 1.63279i −0.577495 0.816394i \(-0.695970\pi\)
0.577495 0.816394i \(-0.304030\pi\)
\(720\) 0 0
\(721\) 313.674 0.435054
\(722\) −452.313 + 555.936i −0.626472 + 0.769994i
\(723\) 0 0
\(724\) 795.360 + 521.740i 1.09856 + 0.720636i
\(725\) −217.342 + 217.342i −0.299781 + 0.299781i
\(726\) 0 0
\(727\) 678.813 0.933718 0.466859 0.884332i \(-0.345386\pi\)
0.466859 + 0.884332i \(0.345386\pi\)
\(728\) 190.167 60.3388i 0.261218 0.0828830i
\(729\) 0 0
\(730\) −150.142 1460.88i −0.205674 2.00120i
\(731\) 30.0618 + 30.0618i 0.0411242 + 0.0411242i
\(732\) 0 0
\(733\) 336.854 + 336.854i 0.459556 + 0.459556i 0.898510 0.438954i \(-0.144651\pi\)
−0.438954 + 0.898510i \(0.644651\pi\)
\(734\) −602.260 + 740.235i −0.820517 + 1.00849i
\(735\) 0 0
\(736\) −106.609 29.8865i −0.144850 0.0406067i
\(737\) −1388.42 −1.88387
\(738\) 0 0
\(739\) 178.478 178.478i 0.241513 0.241513i −0.575963 0.817476i \(-0.695373\pi\)
0.817476 + 0.575963i \(0.195373\pi\)
\(740\) −3.52419 + 0.732131i −0.00476242 + 0.000989367i
\(741\) 0 0
\(742\) −231.944 + 23.8380i −0.312593 + 0.0321267i
\(743\) −795.320 −1.07042 −0.535208 0.844720i \(-0.679767\pi\)
−0.535208 + 0.844720i \(0.679767\pi\)
\(744\) 0 0
\(745\) 110.285i 0.148034i
\(746\) 315.745 32.4508i 0.423251 0.0434997i
\(747\) 0 0
\(748\) 501.622 764.691i 0.670617 1.02231i
\(749\) 242.875 + 242.875i 0.324266 + 0.324266i
\(750\) 0 0
\(751\) 102.850i 0.136951i 0.997653 + 0.0684755i \(0.0218135\pi\)
−0.997653 + 0.0684755i \(0.978186\pi\)
\(752\) −153.924 354.475i −0.204686 0.471377i
\(753\) 0 0
\(754\) −178.060 + 218.852i −0.236154 + 0.290255i
\(755\) −613.330 + 613.330i −0.812358 + 0.812358i
\(756\) 0 0
\(757\) 48.6324 48.6324i 0.0642436 0.0642436i −0.674255 0.738499i \(-0.735535\pi\)
0.738499 + 0.674255i \(0.235535\pi\)
\(758\) 15.0966 + 146.890i 0.0199164 + 0.193786i
\(759\) 0 0
\(760\) −75.7004 39.2328i −0.0996058 0.0516221i
\(761\) 947.802i 1.24547i 0.782433 + 0.622734i \(0.213978\pi\)
−0.782433 + 0.622734i \(0.786022\pi\)
\(762\) 0 0
\(763\) 382.354 + 382.354i 0.501119 + 0.501119i
\(764\) 768.819 159.718i 1.00631 0.209055i
\(765\) 0 0
\(766\) 94.4653 116.107i 0.123323 0.151576i
\(767\) 226.658i 0.295512i
\(768\) 0 0
\(769\) −183.427 −0.238527 −0.119263 0.992863i \(-0.538053\pi\)
−0.119263 + 0.992863i \(0.538053\pi\)
\(770\) 400.598 + 325.929i 0.520257 + 0.423285i
\(771\) 0 0
\(772\) −32.8452 158.104i −0.0425456 0.204798i
\(773\) 178.338 178.338i 0.230710 0.230710i −0.582279 0.812989i \(-0.697839\pi\)
0.812989 + 0.582279i \(0.197839\pi\)
\(774\) 0 0
\(775\) −686.312 −0.885564
\(776\) −116.123 + 224.061i −0.149643 + 0.288739i
\(777\) 0 0
\(778\) 160.500 16.4954i 0.206298 0.0212023i
\(779\) 59.3406 + 59.3406i 0.0761754 + 0.0761754i
\(780\) 0 0
\(781\) 1233.17 + 1233.17i 1.57897 + 1.57897i
\(782\) −94.8244 77.1497i −0.121259 0.0986569i
\(783\) 0 0
\(784\) 582.705 253.027i 0.743246 0.322739i
\(785\) 981.815 1.25072
\(786\) 0 0
\(787\) −480.981 + 480.981i −0.611158 + 0.611158i −0.943248 0.332090i \(-0.892246\pi\)
0.332090 + 0.943248i \(0.392246\pi\)
\(788\) 1090.63 + 715.432i 1.38405 + 0.907909i
\(789\) 0 0
\(790\) 181.861 + 1769.51i 0.230204 + 2.23988i
\(791\) 294.582 0.372417
\(792\) 0 0
\(793\) 193.471i 0.243973i
\(794\) −102.907 1001.29i −0.129606 1.26107i
\(795\) 0 0
\(796\) 50.0854 + 241.092i 0.0629214 + 0.302879i
\(797\) 558.478 + 558.478i 0.700725 + 0.700725i 0.964566 0.263841i \(-0.0849894\pi\)
−0.263841 + 0.964566i \(0.584989\pi\)
\(798\) 0 0
\(799\) 426.680i 0.534017i
\(800\) −153.944 + 549.140i −0.192430 + 0.686425i
\(801\) 0 0
\(802\) −176.690 143.756i −0.220312 0.179247i
\(803\) 1026.90 1026.90i 1.27884 1.27884i
\(804\) 0 0
\(805\) 48.8126 48.8126i 0.0606368 0.0606368i
\(806\) −626.677 + 64.4068i −0.777515 + 0.0799091i
\(807\) 0 0
\(808\) −93.9914 296.228i −0.116326 0.366619i
\(809\) 1152.43i 1.42451i 0.701918 + 0.712257i \(0.252327\pi\)
−0.701918 + 0.712257i \(0.747673\pi\)
\(810\) 0 0
\(811\) 364.890 + 364.890i 0.449926 + 0.449926i 0.895330 0.445404i \(-0.146940\pi\)
−0.445404 + 0.895330i \(0.646940\pi\)
\(812\) 115.364 175.866i 0.142074 0.216583i
\(813\) 0 0
\(814\) −2.76105 2.24641i −0.00339196 0.00275972i
\(815\) 977.055i 1.19884i
\(816\) 0 0
\(817\) 3.91958 0.00479753
\(818\) −176.596 + 217.054i −0.215888 + 0.265347i
\(819\) 0 0
\(820\) 739.777 1127.74i 0.902167 1.37530i
\(821\) 618.975 618.975i 0.753928 0.753928i −0.221282 0.975210i \(-0.571024\pi\)
0.975210 + 0.221282i \(0.0710240\pi\)
\(822\) 0 0
\(823\) 626.066 0.760712 0.380356 0.924840i \(-0.375801\pi\)
0.380356 + 0.924840i \(0.375801\pi\)
\(824\) −378.720 + 730.747i −0.459612 + 0.886829i
\(825\) 0 0
\(826\) −17.2748 168.083i −0.0209138 0.203491i
\(827\) −375.666 375.666i −0.454252 0.454252i 0.442511 0.896763i \(-0.354088\pi\)
−0.896763 + 0.442511i \(0.854088\pi\)
\(828\) 0 0
\(829\) −299.648 299.648i −0.361457 0.361457i 0.502892 0.864349i \(-0.332269\pi\)
−0.864349 + 0.502892i \(0.832269\pi\)
\(830\) −875.207 + 1075.71i −1.05447 + 1.29604i
\(831\) 0 0
\(832\) −89.0337 + 515.871i −0.107012 + 0.620037i
\(833\) 701.398 0.842015
\(834\) 0 0
\(835\) −516.356 + 516.356i −0.618390 + 0.618390i
\(836\) −17.1500 82.5535i −0.0205144 0.0987482i
\(837\) 0 0
\(838\) 1043.79 107.275i 1.24557 0.128013i
\(839\) 1477.80 1.76138 0.880689 0.473694i \(-0.157080\pi\)
0.880689 + 0.473694i \(0.157080\pi\)
\(840\) 0 0
\(841\) 543.565i 0.646331i
\(842\) 1308.64 134.496i 1.55421 0.159734i
\(843\) 0 0
\(844\) 714.933 + 468.981i 0.847077 + 0.555665i
\(845\) −472.407 472.407i −0.559062 0.559062i
\(846\) 0 0
\(847\) 141.789i 0.167402i
\(848\) 224.507 569.126i 0.264749 0.671139i
\(849\) 0 0
\(850\) −397.395 + 488.437i −0.467524 + 0.574631i
\(851\) −0.336433 + 0.336433i −0.000395338 + 0.000395338i
\(852\) 0 0
\(853\) 404.051 404.051i 0.473682 0.473682i −0.429422 0.903104i \(-0.641283\pi\)
0.903104 + 0.429422i \(0.141283\pi\)
\(854\) 14.7454 + 143.472i 0.0172663 + 0.168000i
\(855\) 0 0
\(856\) −859.050 + 272.571i −1.00356 + 0.318425i
\(857\) 892.363i 1.04126i −0.853781 0.520632i \(-0.825696\pi\)
0.853781 0.520632i \(-0.174304\pi\)
\(858\) 0 0
\(859\) −378.424 378.424i −0.440540 0.440540i 0.451654 0.892193i \(-0.350834\pi\)
−0.892193 + 0.451654i \(0.850834\pi\)
\(860\) −12.8130 61.6770i −0.0148989 0.0717174i
\(861\) 0 0
\(862\) 517.413 635.950i 0.600247 0.737761i
\(863\) 1457.30i 1.68865i −0.535833 0.844324i \(-0.680002\pi\)
0.535833 0.844324i \(-0.319998\pi\)
\(864\) 0 0
\(865\) −134.525 −0.155520
\(866\) −32.0919 26.1102i −0.0370576 0.0301503i
\(867\) 0 0
\(868\) 459.817 95.5245i 0.529743 0.110051i
\(869\) −1243.85 + 1243.85i −1.43136 + 1.43136i
\(870\) 0 0
\(871\) 877.485 1.00745
\(872\) −1352.39 + 429.105i −1.55090 + 0.492092i
\(873\) 0 0
\(874\) −11.2113 + 1.15225i −0.0128276 + 0.00131836i
\(875\) 101.263 + 101.263i 0.115729 + 0.115729i
\(876\) 0 0
\(877\) −571.322 571.322i −0.651450 0.651450i 0.301892 0.953342i \(-0.402382\pi\)
−0.953342 + 0.301892i \(0.902382\pi\)
\(878\) −98.1856 79.8845i −0.111829 0.0909846i
\(879\) 0 0
\(880\) −1242.97 + 539.732i −1.41246 + 0.613332i
\(881\) −994.662 −1.12901 −0.564507 0.825428i \(-0.690934\pi\)
−0.564507 + 0.825428i \(0.690934\pi\)
\(882\) 0 0
\(883\) 74.0725 74.0725i 0.0838873 0.0838873i −0.663918 0.747805i \(-0.731108\pi\)
0.747805 + 0.663918i \(0.231108\pi\)
\(884\) −317.027 + 483.288i −0.358628 + 0.546706i
\(885\) 0 0
\(886\) 85.9074 + 835.878i 0.0969609 + 0.943429i
\(887\) 522.759 0.589356 0.294678 0.955597i \(-0.404788\pi\)
0.294678 + 0.955597i \(0.404788\pi\)
\(888\) 0 0
\(889\) 598.520i 0.673251i
\(890\) −42.0518 409.163i −0.0472492 0.459734i
\(891\) 0 0
\(892\) −452.446 + 93.9932i −0.507227 + 0.105373i
\(893\) −27.8161 27.8161i −0.0311491 0.0311491i
\(894\) 0 0
\(895\) 182.656i 0.204085i
\(896\) 26.7077 389.341i 0.0298077 0.434533i
\(897\) 0 0
\(898\) −565.792 460.332i −0.630058 0.512619i
\(899\) −469.615 + 469.615i −0.522375 + 0.522375i
\(900\) 0 0
\(901\) 477.646 477.646i 0.530129 0.530129i
\(902\) 1326.76 136.358i 1.47091 0.151173i
\(903\) 0 0
\(904\) −355.669 + 686.269i −0.393439 + 0.759147i
\(905\) 1556.16i 1.71951i
\(906\) 0 0
\(907\) 442.760 + 442.760i 0.488159 + 0.488159i 0.907725 0.419566i \(-0.137818\pi\)
−0.419566 + 0.907725i \(0.637818\pi\)
\(908\) −119.367 78.3024i −0.131462 0.0862362i
\(909\) 0 0
\(910\) −253.180 205.989i −0.278220 0.226361i
\(911\) 835.738i 0.917385i 0.888595 + 0.458692i \(0.151682\pi\)
−0.888595 + 0.458692i \(0.848318\pi\)
\(912\) 0 0
\(913\) −1371.37 −1.50205
\(914\) 807.878 992.959i 0.883892 1.08639i
\(915\) 0 0
\(916\) −734.652 481.916i −0.802022 0.526110i
\(917\) −54.7082 + 54.7082i −0.0596599 + 0.0596599i
\(918\) 0 0
\(919\) 776.423 0.844856 0.422428 0.906396i \(-0.361178\pi\)
0.422428 + 0.906396i \(0.361178\pi\)
\(920\) 54.7810 + 172.651i 0.0595445 + 0.187664i
\(921\) 0 0
\(922\) 69.2316 + 673.623i 0.0750885 + 0.730610i
\(923\) −779.372 779.372i −0.844390 0.844390i
\(924\) 0 0
\(925\) 1.73295 + 1.73295i 0.00187346 + 0.00187346i
\(926\) 605.124 743.755i 0.653481 0.803191i
\(927\) 0 0
\(928\) 270.416 + 481.091i 0.291397 + 0.518417i
\(929\) 144.945 0.156022 0.0780112 0.996952i \(-0.475143\pi\)
0.0780112 + 0.996952i \(0.475143\pi\)
\(930\) 0 0
\(931\) 45.7256 45.7256i 0.0491145 0.0491145i
\(932\) −468.941 + 97.4199i −0.503156 + 0.104528i
\(933\) 0 0
\(934\) −1134.94 + 116.643i −1.21514 + 0.124886i
\(935\) −1496.15 −1.60016
\(936\) 0 0
\(937\) 851.499i 0.908750i −0.890811 0.454375i \(-0.849863\pi\)
0.890811 0.454375i \(-0.150137\pi\)
\(938\) −650.718 + 66.8776i −0.693730 + 0.0712981i
\(939\) 0 0
\(940\) −346.773 + 528.634i −0.368908 + 0.562377i
\(941\) −1251.60 1251.60i −1.33008 1.33008i −0.905297 0.424778i \(-0.860352\pi\)
−0.424778 0.905297i \(-0.639648\pi\)
\(942\) 0 0
\(943\) 178.281i 0.189057i
\(944\) 412.430 + 162.694i 0.436896 + 0.172346i
\(945\) 0 0
\(946\) 39.3145 48.3213i 0.0415587 0.0510795i
\(947\) −919.818 + 919.818i −0.971296 + 0.971296i −0.999599 0.0283032i \(-0.990990\pi\)
0.0283032 + 0.999599i \(0.490990\pi\)
\(948\) 0 0
\(949\) −649.009 + 649.009i −0.683887 + 0.683887i
\(950\) 5.93517 + 57.7491i 0.00624755 + 0.0607886i
\(951\) 0 0
\(952\) 198.265 382.555i 0.208261 0.401844i
\(953\) 489.450i 0.513589i −0.966466 0.256794i \(-0.917334\pi\)
0.966466 0.256794i \(-0.0826663\pi\)
\(954\) 0 0
\(955\) −908.362 908.362i −0.951164 0.951164i
\(956\) −961.114 + 199.666i −1.00535 + 0.208856i
\(957\) 0 0
\(958\) 581.392 714.586i 0.606881 0.745914i
\(959\) 157.688i 0.164429i
\(960\) 0 0
\(961\) −521.932 −0.543113
\(962\) 1.74500 + 1.41974i 0.00181393 + 0.00147582i
\(963\) 0 0
\(964\) 350.840 + 1688.81i 0.363942 + 1.75187i
\(965\) −186.800 + 186.800i −0.193575 + 0.193575i
\(966\) 0 0
\(967\) −1368.49 −1.41519 −0.707594 0.706619i \(-0.750220\pi\)
−0.707594 + 0.706619i \(0.750220\pi\)
\(968\) −330.318 171.192i −0.341237 0.176851i
\(969\) 0 0
\(970\) 410.697 42.2094i 0.423399 0.0435149i
\(971\) 1013.79 + 1013.79i 1.04407 + 1.04407i 0.998983 + 0.0450900i \(0.0143575\pi\)
0.0450900 + 0.998983i \(0.485643\pi\)
\(972\) 0 0
\(973\) −53.2455 53.2455i −0.0547230 0.0547230i
\(974\) −892.247 725.938i −0.916064 0.745316i
\(975\) 0 0
\(976\) −352.042 138.872i −0.360698 0.142287i
\(977\) 5.19534 0.00531765 0.00265882 0.999996i \(-0.499154\pi\)
0.00265882 + 0.999996i \(0.499154\pi\)
\(978\) 0 0
\(979\) 287.616 287.616i 0.293785 0.293785i
\(980\) −868.996 570.043i −0.886730 0.581677i
\(981\) 0 0
\(982\) −78.4732 763.543i −0.0799116 0.777539i
\(983\) 1591.90 1.61943 0.809714 0.586825i \(-0.199622\pi\)
0.809714 + 0.586825i \(0.199622\pi\)
\(984\) 0 0
\(985\) 2133.87i 2.16636i
\(986\) 62.2958 + 606.138i 0.0631804 + 0.614744i
\(987\) 0 0
\(988\) 10.8389 + 52.1742i 0.0109705 + 0.0528079i
\(989\) −5.88792 5.88792i −0.00595340 0.00595340i
\(990\) 0 0
\(991\) 622.896i 0.628553i −0.949331 0.314277i \(-0.898238\pi\)
0.949331 0.314277i \(-0.101762\pi\)
\(992\) −332.631 + 1186.54i −0.335313 + 1.19611i
\(993\) 0 0
\(994\) 637.360 + 518.560i 0.641207 + 0.521690i
\(995\) 284.850 284.850i 0.286282 0.286282i
\(996\) 0 0
\(997\) −635.503 + 635.503i −0.637415 + 0.637415i −0.949917 0.312502i \(-0.898833\pi\)
0.312502 + 0.949917i \(0.398833\pi\)
\(998\) 754.278 77.5210i 0.755790 0.0776763i
\(999\) 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 144.3.m.a.19.3 6
3.2 odd 2 16.3.f.a.3.1 6
4.3 odd 2 576.3.m.a.559.3 6
8.3 odd 2 1152.3.m.b.991.1 6
8.5 even 2 1152.3.m.a.991.1 6
12.11 even 2 64.3.f.a.47.1 6
15.2 even 4 400.3.k.d.99.2 6
15.8 even 4 400.3.k.c.99.2 6
15.14 odd 2 400.3.r.c.51.3 6
16.3 odd 4 1152.3.m.a.415.1 6
16.5 even 4 576.3.m.a.271.3 6
16.11 odd 4 inner 144.3.m.a.91.3 6
16.13 even 4 1152.3.m.b.415.1 6
24.5 odd 2 128.3.f.b.95.1 6
24.11 even 2 128.3.f.a.95.3 6
48.5 odd 4 64.3.f.a.15.1 6
48.11 even 4 16.3.f.a.11.1 yes 6
48.29 odd 4 128.3.f.a.31.3 6
48.35 even 4 128.3.f.b.31.1 6
96.5 odd 8 1024.3.c.j.1023.9 12
96.11 even 8 1024.3.c.j.1023.10 12
96.29 odd 8 1024.3.d.k.511.9 12
96.35 even 8 1024.3.d.k.511.3 12
96.53 odd 8 1024.3.c.j.1023.4 12
96.59 even 8 1024.3.c.j.1023.3 12
96.77 odd 8 1024.3.d.k.511.4 12
96.83 even 8 1024.3.d.k.511.10 12
240.59 even 4 400.3.r.c.251.3 6
240.107 odd 4 400.3.k.c.299.2 6
240.203 odd 4 400.3.k.d.299.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.3.f.a.3.1 6 3.2 odd 2
16.3.f.a.11.1 yes 6 48.11 even 4
64.3.f.a.15.1 6 48.5 odd 4
64.3.f.a.47.1 6 12.11 even 2
128.3.f.a.31.3 6 48.29 odd 4
128.3.f.a.95.3 6 24.11 even 2
128.3.f.b.31.1 6 48.35 even 4
128.3.f.b.95.1 6 24.5 odd 2
144.3.m.a.19.3 6 1.1 even 1 trivial
144.3.m.a.91.3 6 16.11 odd 4 inner
400.3.k.c.99.2 6 15.8 even 4
400.3.k.c.299.2 6 240.107 odd 4
400.3.k.d.99.2 6 15.2 even 4
400.3.k.d.299.2 6 240.203 odd 4
400.3.r.c.51.3 6 15.14 odd 2
400.3.r.c.251.3 6 240.59 even 4
576.3.m.a.271.3 6 16.5 even 4
576.3.m.a.559.3 6 4.3 odd 2
1024.3.c.j.1023.3 12 96.59 even 8
1024.3.c.j.1023.4 12 96.53 odd 8
1024.3.c.j.1023.9 12 96.5 odd 8
1024.3.c.j.1023.10 12 96.11 even 8
1024.3.d.k.511.3 12 96.35 even 8
1024.3.d.k.511.4 12 96.77 odd 8
1024.3.d.k.511.9 12 96.29 odd 8
1024.3.d.k.511.10 12 96.83 even 8
1152.3.m.a.415.1 6 16.3 odd 4
1152.3.m.a.991.1 6 8.5 even 2
1152.3.m.b.415.1 6 16.13 even 4
1152.3.m.b.991.1 6 8.3 odd 2