Properties

Label 144.3.m.b.91.8
Level $144$
Weight $3$
Character 144.91
Analytic conductor $3.924$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6x^{14} + 10x^{12} + 88x^{10} - 752x^{8} + 1408x^{6} + 2560x^{4} - 24576x^{2} + 65536 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 91.8
Root \(-0.136762 - 1.99532i\) of defining polynomial
Character \(\chi\) \(=\) 144.91
Dual form 144.3.m.b.19.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.99532 - 0.136762i) q^{2} +(3.96259 - 0.545766i) q^{4} +(0.227650 + 0.227650i) q^{5} +3.90219 q^{7} +(7.83199 - 1.63091i) q^{8} +O(q^{10})\) \(q+(1.99532 - 0.136762i) q^{2} +(3.96259 - 0.545766i) q^{4} +(0.227650 + 0.227650i) q^{5} +3.90219 q^{7} +(7.83199 - 1.63091i) q^{8} +(0.485368 + 0.423100i) q^{10} +(-2.21045 + 2.21045i) q^{11} +(5.08526 - 5.08526i) q^{13} +(7.78612 - 0.533670i) q^{14} +(15.4043 - 4.32530i) q^{16} -18.8341 q^{17} +(11.7651 + 11.7651i) q^{19} +(1.02633 + 0.777840i) q^{20} +(-4.10825 + 4.71286i) q^{22} -35.4354 q^{23} -24.8964i q^{25} +(9.45124 - 10.8422i) q^{26} +(15.4628 - 2.12968i) q^{28} +(-21.2499 + 21.2499i) q^{29} +35.9691i q^{31} +(30.1449 - 10.7371i) q^{32} +(-37.5799 + 2.57578i) q^{34} +(0.888334 + 0.888334i) q^{35} +(-34.4199 - 34.4199i) q^{37} +(25.0842 + 21.8661i) q^{38} +(2.15423 + 1.41168i) q^{40} -44.1055i q^{41} +(-28.3018 + 28.3018i) q^{43} +(-7.55273 + 9.96550i) q^{44} +(-70.7049 + 4.84620i) q^{46} +32.8802i q^{47} -33.7729 q^{49} +(-3.40486 - 49.6762i) q^{50} +(17.3754 - 22.9262i) q^{52} +(42.1450 + 42.1450i) q^{53} -1.00642 q^{55} +(30.5620 - 6.36412i) q^{56} +(-39.4941 + 45.3065i) q^{58} +(66.9935 - 66.9935i) q^{59} +(17.3728 - 17.3728i) q^{61} +(4.91919 + 71.7697i) q^{62} +(58.6803 - 25.5465i) q^{64} +2.31532 q^{65} +(39.6756 + 39.6756i) q^{67} +(-74.6317 + 10.2790i) q^{68} +(1.89400 + 1.65102i) q^{70} -63.0272 q^{71} -75.4549i q^{73} +(-73.3859 - 63.9713i) q^{74} +(53.0413 + 40.1993i) q^{76} +(-8.62561 + 8.62561i) q^{77} +59.1583i q^{79} +(4.49144 + 2.52213i) q^{80} +(-6.03194 - 88.0046i) q^{82} +(71.2155 + 71.2155i) q^{83} +(-4.28757 - 4.28757i) q^{85} +(-52.6004 + 60.3416i) q^{86} +(-13.7072 + 20.9173i) q^{88} -150.671i q^{89} +(19.8437 - 19.8437i) q^{91} +(-140.416 + 19.3394i) q^{92} +(4.49675 + 65.6065i) q^{94} +5.35665i q^{95} +51.5586 q^{97} +(-67.3876 + 4.61883i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 12 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 12 q^{4} + 16 q^{10} + 32 q^{16} - 32 q^{19} + 104 q^{22} - 24 q^{34} + 96 q^{37} - 312 q^{40} - 32 q^{43} - 224 q^{46} + 112 q^{49} - 264 q^{52} - 256 q^{55} + 312 q^{58} - 32 q^{61} + 456 q^{64} - 256 q^{67} + 744 q^{70} + 264 q^{76} - 280 q^{82} + 160 q^{85} - 912 q^{88} + 288 q^{91} - 1104 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.99532 0.136762i 0.997659 0.0683808i
\(3\) 0 0
\(4\) 3.96259 0.545766i 0.990648 0.136441i
\(5\) 0.227650 + 0.227650i 0.0455300 + 0.0455300i 0.729505 0.683975i \(-0.239750\pi\)
−0.683975 + 0.729505i \(0.739750\pi\)
\(6\) 0 0
\(7\) 3.90219 0.557456 0.278728 0.960370i \(-0.410087\pi\)
0.278728 + 0.960370i \(0.410087\pi\)
\(8\) 7.83199 1.63091i 0.978999 0.203863i
\(9\) 0 0
\(10\) 0.485368 + 0.423100i 0.0485368 + 0.0423100i
\(11\) −2.21045 + 2.21045i −0.200950 + 0.200950i −0.800407 0.599457i \(-0.795383\pi\)
0.599457 + 0.800407i \(0.295383\pi\)
\(12\) 0 0
\(13\) 5.08526 5.08526i 0.391174 0.391174i −0.483932 0.875106i \(-0.660792\pi\)
0.875106 + 0.483932i \(0.160792\pi\)
\(14\) 7.78612 0.533670i 0.556152 0.0381193i
\(15\) 0 0
\(16\) 15.4043 4.32530i 0.962767 0.270331i
\(17\) −18.8341 −1.10789 −0.553943 0.832555i \(-0.686877\pi\)
−0.553943 + 0.832555i \(0.686877\pi\)
\(18\) 0 0
\(19\) 11.7651 + 11.7651i 0.619216 + 0.619216i 0.945330 0.326114i \(-0.105739\pi\)
−0.326114 + 0.945330i \(0.605739\pi\)
\(20\) 1.02633 + 0.777840i 0.0513164 + 0.0388920i
\(21\) 0 0
\(22\) −4.10825 + 4.71286i −0.186739 + 0.214221i
\(23\) −35.4354 −1.54067 −0.770335 0.637640i \(-0.779911\pi\)
−0.770335 + 0.637640i \(0.779911\pi\)
\(24\) 0 0
\(25\) 24.8964i 0.995854i
\(26\) 9.45124 10.8422i 0.363509 0.417007i
\(27\) 0 0
\(28\) 15.4628 2.12968i 0.552243 0.0760602i
\(29\) −21.2499 + 21.2499i −0.732755 + 0.732755i −0.971165 0.238410i \(-0.923374\pi\)
0.238410 + 0.971165i \(0.423374\pi\)
\(30\) 0 0
\(31\) 35.9691i 1.16029i 0.814512 + 0.580146i \(0.197005\pi\)
−0.814512 + 0.580146i \(0.802995\pi\)
\(32\) 30.1449 10.7371i 0.942028 0.335533i
\(33\) 0 0
\(34\) −37.5799 + 2.57578i −1.10529 + 0.0757581i
\(35\) 0.888334 + 0.888334i 0.0253810 + 0.0253810i
\(36\) 0 0
\(37\) −34.4199 34.4199i −0.930267 0.930267i 0.0674555 0.997722i \(-0.478512\pi\)
−0.997722 + 0.0674555i \(0.978512\pi\)
\(38\) 25.0842 + 21.8661i 0.660110 + 0.575425i
\(39\) 0 0
\(40\) 2.15423 + 1.41168i 0.0538557 + 0.0352919i
\(41\) 44.1055i 1.07574i −0.843026 0.537872i \(-0.819228\pi\)
0.843026 0.537872i \(-0.180772\pi\)
\(42\) 0 0
\(43\) −28.3018 + 28.3018i −0.658180 + 0.658180i −0.954949 0.296769i \(-0.904091\pi\)
0.296769 + 0.954949i \(0.404091\pi\)
\(44\) −7.55273 + 9.96550i −0.171653 + 0.226489i
\(45\) 0 0
\(46\) −70.7049 + 4.84620i −1.53706 + 0.105352i
\(47\) 32.8802i 0.699579i 0.936828 + 0.349790i \(0.113747\pi\)
−0.936828 + 0.349790i \(0.886253\pi\)
\(48\) 0 0
\(49\) −33.7729 −0.689242
\(50\) −3.40486 49.6762i −0.0680973 0.993523i
\(51\) 0 0
\(52\) 17.3754 22.9262i 0.334143 0.440888i
\(53\) 42.1450 + 42.1450i 0.795189 + 0.795189i 0.982333 0.187144i \(-0.0599230\pi\)
−0.187144 + 0.982333i \(0.559923\pi\)
\(54\) 0 0
\(55\) −1.00642 −0.0182985
\(56\) 30.5620 6.36412i 0.545749 0.113645i
\(57\) 0 0
\(58\) −39.4941 + 45.3065i −0.680933 + 0.781146i
\(59\) 66.9935 66.9935i 1.13548 1.13548i 0.146233 0.989250i \(-0.453285\pi\)
0.989250 0.146233i \(-0.0467149\pi\)
\(60\) 0 0
\(61\) 17.3728 17.3728i 0.284800 0.284800i −0.550220 0.835020i \(-0.685456\pi\)
0.835020 + 0.550220i \(0.185456\pi\)
\(62\) 4.91919 + 71.7697i 0.0793417 + 1.15758i
\(63\) 0 0
\(64\) 58.6803 25.5465i 0.916879 0.399164i
\(65\) 2.31532 0.0356203
\(66\) 0 0
\(67\) 39.6756 + 39.6756i 0.592174 + 0.592174i 0.938218 0.346044i \(-0.112475\pi\)
−0.346044 + 0.938218i \(0.612475\pi\)
\(68\) −74.6317 + 10.2790i −1.09752 + 0.151162i
\(69\) 0 0
\(70\) 1.89400 + 1.65102i 0.0270571 + 0.0235860i
\(71\) −63.0272 −0.887707 −0.443853 0.896099i \(-0.646389\pi\)
−0.443853 + 0.896099i \(0.646389\pi\)
\(72\) 0 0
\(73\) 75.4549i 1.03363i −0.856097 0.516815i \(-0.827118\pi\)
0.856097 0.516815i \(-0.172882\pi\)
\(74\) −73.3859 63.9713i −0.991702 0.864477i
\(75\) 0 0
\(76\) 53.0413 + 40.1993i 0.697912 + 0.528939i
\(77\) −8.62561 + 8.62561i −0.112021 + 0.112021i
\(78\) 0 0
\(79\) 59.1583i 0.748839i 0.927259 + 0.374419i \(0.122158\pi\)
−0.927259 + 0.374419i \(0.877842\pi\)
\(80\) 4.49144 + 2.52213i 0.0561430 + 0.0315266i
\(81\) 0 0
\(82\) −6.03194 88.0046i −0.0735603 1.07323i
\(83\) 71.2155 + 71.2155i 0.858018 + 0.858018i 0.991104 0.133086i \(-0.0424887\pi\)
−0.133086 + 0.991104i \(0.542489\pi\)
\(84\) 0 0
\(85\) −4.28757 4.28757i −0.0504420 0.0504420i
\(86\) −52.6004 + 60.3416i −0.611633 + 0.701647i
\(87\) 0 0
\(88\) −13.7072 + 20.9173i −0.155764 + 0.237696i
\(89\) 150.671i 1.69293i −0.532443 0.846466i \(-0.678726\pi\)
0.532443 0.846466i \(-0.321274\pi\)
\(90\) 0 0
\(91\) 19.8437 19.8437i 0.218062 0.218062i
\(92\) −140.416 + 19.3394i −1.52626 + 0.210211i
\(93\) 0 0
\(94\) 4.49675 + 65.6065i 0.0478378 + 0.697942i
\(95\) 5.35665i 0.0563858i
\(96\) 0 0
\(97\) 51.5586 0.531532 0.265766 0.964038i \(-0.414375\pi\)
0.265766 + 0.964038i \(0.414375\pi\)
\(98\) −67.3876 + 4.61883i −0.687629 + 0.0471309i
\(99\) 0 0
\(100\) −13.5876 98.6541i −0.135876 0.986541i
\(101\) 139.414 + 139.414i 1.38034 + 1.38034i 0.844010 + 0.536327i \(0.180189\pi\)
0.536327 + 0.844010i \(0.319811\pi\)
\(102\) 0 0
\(103\) 67.9691 0.659894 0.329947 0.943999i \(-0.392969\pi\)
0.329947 + 0.943999i \(0.392969\pi\)
\(104\) 31.5341 48.1213i 0.303213 0.462705i
\(105\) 0 0
\(106\) 89.8565 + 78.3289i 0.847703 + 0.738952i
\(107\) 129.801 129.801i 1.21309 1.21309i 0.243090 0.970004i \(-0.421839\pi\)
0.970004 0.243090i \(-0.0781609\pi\)
\(108\) 0 0
\(109\) 30.1323 30.1323i 0.276443 0.276443i −0.555244 0.831687i \(-0.687375\pi\)
0.831687 + 0.555244i \(0.187375\pi\)
\(110\) −2.00812 + 0.137639i −0.0182557 + 0.00125127i
\(111\) 0 0
\(112\) 60.1105 16.8781i 0.536701 0.150698i
\(113\) 5.11034 0.0452243 0.0226121 0.999744i \(-0.492802\pi\)
0.0226121 + 0.999744i \(0.492802\pi\)
\(114\) 0 0
\(115\) −8.06687 8.06687i −0.0701467 0.0701467i
\(116\) −72.6072 + 95.8021i −0.625924 + 0.825880i
\(117\) 0 0
\(118\) 124.511 142.836i 1.05518 1.21047i
\(119\) −73.4942 −0.617598
\(120\) 0 0
\(121\) 111.228i 0.919238i
\(122\) 32.2884 37.0403i 0.264659 0.303609i
\(123\) 0 0
\(124\) 19.6307 + 142.531i 0.158312 + 1.14944i
\(125\) 11.3589 11.3589i 0.0908712 0.0908712i
\(126\) 0 0
\(127\) 123.225i 0.970277i −0.874437 0.485138i \(-0.838769\pi\)
0.874437 0.485138i \(-0.161231\pi\)
\(128\) 113.592 58.9986i 0.887438 0.460927i
\(129\) 0 0
\(130\) 4.61980 0.316646i 0.0355369 0.00243574i
\(131\) 76.2899 + 76.2899i 0.582365 + 0.582365i 0.935553 0.353187i \(-0.114902\pi\)
−0.353187 + 0.935553i \(0.614902\pi\)
\(132\) 0 0
\(133\) 45.9098 + 45.9098i 0.345186 + 0.345186i
\(134\) 84.5917 + 73.7394i 0.631281 + 0.550294i
\(135\) 0 0
\(136\) −147.508 + 30.7166i −1.08462 + 0.225857i
\(137\) 73.0194i 0.532988i −0.963837 0.266494i \(-0.914135\pi\)
0.963837 0.266494i \(-0.0858653\pi\)
\(138\) 0 0
\(139\) 16.5250 16.5250i 0.118885 0.118885i −0.645162 0.764046i \(-0.723210\pi\)
0.764046 + 0.645162i \(0.223210\pi\)
\(140\) 4.00493 + 3.03528i 0.0286066 + 0.0216806i
\(141\) 0 0
\(142\) −125.759 + 8.61969i −0.885629 + 0.0607021i
\(143\) 22.4814i 0.157213i
\(144\) 0 0
\(145\) −9.67507 −0.0667246
\(146\) −10.3193 150.557i −0.0706804 1.03121i
\(147\) 0 0
\(148\) −155.177 117.607i −1.04849 0.794640i
\(149\) 22.0334 + 22.0334i 0.147875 + 0.147875i 0.777168 0.629293i \(-0.216656\pi\)
−0.629293 + 0.777168i \(0.716656\pi\)
\(150\) 0 0
\(151\) −161.017 −1.06634 −0.533168 0.846010i \(-0.678999\pi\)
−0.533168 + 0.846010i \(0.678999\pi\)
\(152\) 111.332 + 72.9565i 0.732448 + 0.479977i
\(153\) 0 0
\(154\) −16.0312 + 18.3905i −0.104099 + 0.119419i
\(155\) −8.18836 + 8.18836i −0.0528281 + 0.0528281i
\(156\) 0 0
\(157\) −151.888 + 151.888i −0.967441 + 0.967441i −0.999486 0.0320455i \(-0.989798\pi\)
0.0320455 + 0.999486i \(0.489798\pi\)
\(158\) 8.09058 + 118.040i 0.0512062 + 0.747086i
\(159\) 0 0
\(160\) 9.30678 + 4.41820i 0.0581674 + 0.0276137i
\(161\) −138.276 −0.858856
\(162\) 0 0
\(163\) −186.334 186.334i −1.14315 1.14315i −0.987870 0.155283i \(-0.950371\pi\)
−0.155283 0.987870i \(-0.549629\pi\)
\(164\) −24.0713 174.772i −0.146776 1.06568i
\(165\) 0 0
\(166\) 151.837 + 132.358i 0.914682 + 0.797338i
\(167\) −199.590 −1.19515 −0.597576 0.801813i \(-0.703869\pi\)
−0.597576 + 0.801813i \(0.703869\pi\)
\(168\) 0 0
\(169\) 117.280i 0.693966i
\(170\) −9.14145 7.96870i −0.0537732 0.0468747i
\(171\) 0 0
\(172\) −96.7022 + 127.594i −0.562222 + 0.741828i
\(173\) −138.631 + 138.631i −0.801333 + 0.801333i −0.983304 0.181971i \(-0.941752\pi\)
0.181971 + 0.983304i \(0.441752\pi\)
\(174\) 0 0
\(175\) 97.1504i 0.555145i
\(176\) −24.4895 + 43.6112i −0.139145 + 0.247791i
\(177\) 0 0
\(178\) −20.6060 300.637i −0.115764 1.68897i
\(179\) −148.572 148.572i −0.830010 0.830010i 0.157508 0.987518i \(-0.449654\pi\)
−0.987518 + 0.157508i \(0.949654\pi\)
\(180\) 0 0
\(181\) 99.6006 + 99.6006i 0.550280 + 0.550280i 0.926522 0.376242i \(-0.122784\pi\)
−0.376242 + 0.926522i \(0.622784\pi\)
\(182\) 36.8806 42.3083i 0.202641 0.232463i
\(183\) 0 0
\(184\) −277.530 + 57.7918i −1.50831 + 0.314086i
\(185\) 15.6714i 0.0847101i
\(186\) 0 0
\(187\) 41.6318 41.6318i 0.222630 0.222630i
\(188\) 17.9449 + 130.291i 0.0954516 + 0.693037i
\(189\) 0 0
\(190\) 0.732584 + 10.6882i 0.00385571 + 0.0562539i
\(191\) 149.517i 0.782812i 0.920218 + 0.391406i \(0.128011\pi\)
−0.920218 + 0.391406i \(0.871989\pi\)
\(192\) 0 0
\(193\) −52.8254 −0.273707 −0.136853 0.990591i \(-0.543699\pi\)
−0.136853 + 0.990591i \(0.543699\pi\)
\(194\) 102.876 7.05123i 0.530288 0.0363466i
\(195\) 0 0
\(196\) −133.828 + 18.4321i −0.682797 + 0.0940412i
\(197\) −108.072 108.072i −0.548590 0.548590i 0.377443 0.926033i \(-0.376803\pi\)
−0.926033 + 0.377443i \(0.876803\pi\)
\(198\) 0 0
\(199\) −2.24707 −0.0112918 −0.00564590 0.999984i \(-0.501797\pi\)
−0.00564590 + 0.999984i \(0.501797\pi\)
\(200\) −40.6036 194.988i −0.203018 0.974940i
\(201\) 0 0
\(202\) 297.242 + 259.109i 1.47149 + 1.28272i
\(203\) −82.9212 + 82.9212i −0.408479 + 0.408479i
\(204\) 0 0
\(205\) 10.0406 10.0406i 0.0489787 0.0489787i
\(206\) 135.620 9.29556i 0.658349 0.0451241i
\(207\) 0 0
\(208\) 56.3395 100.330i 0.270863 0.482356i
\(209\) −52.0124 −0.248863
\(210\) 0 0
\(211\) 50.4041 + 50.4041i 0.238882 + 0.238882i 0.816387 0.577505i \(-0.195974\pi\)
−0.577505 + 0.816387i \(0.695974\pi\)
\(212\) 190.005 + 144.002i 0.896249 + 0.679256i
\(213\) 0 0
\(214\) 241.243 276.746i 1.12730 1.29321i
\(215\) −12.8858 −0.0599339
\(216\) 0 0
\(217\) 140.358i 0.646812i
\(218\) 56.0026 64.2445i 0.256893 0.294699i
\(219\) 0 0
\(220\) −3.98802 + 0.549268i −0.0181274 + 0.00249667i
\(221\) −95.7760 + 95.7760i −0.433376 + 0.433376i
\(222\) 0 0
\(223\) 230.340i 1.03291i −0.856313 0.516457i \(-0.827251\pi\)
0.856313 0.516457i \(-0.172749\pi\)
\(224\) 117.631 41.8981i 0.525140 0.187045i
\(225\) 0 0
\(226\) 10.1968 0.698898i 0.0451184 0.00309247i
\(227\) 12.1395 + 12.1395i 0.0534779 + 0.0534779i 0.733340 0.679862i \(-0.237960\pi\)
−0.679862 + 0.733340i \(0.737960\pi\)
\(228\) 0 0
\(229\) 39.1259 + 39.1259i 0.170855 + 0.170855i 0.787355 0.616500i \(-0.211450\pi\)
−0.616500 + 0.787355i \(0.711450\pi\)
\(230\) −17.1992 14.9927i −0.0747792 0.0651858i
\(231\) 0 0
\(232\) −131.772 + 201.086i −0.567985 + 0.866748i
\(233\) 36.6784i 0.157418i 0.996898 + 0.0787090i \(0.0250798\pi\)
−0.996898 + 0.0787090i \(0.974920\pi\)
\(234\) 0 0
\(235\) −7.48518 + 7.48518i −0.0318518 + 0.0318518i
\(236\) 228.905 302.031i 0.969937 1.27979i
\(237\) 0 0
\(238\) −146.644 + 10.0512i −0.616152 + 0.0422318i
\(239\) 147.098i 0.615474i −0.951471 0.307737i \(-0.900428\pi\)
0.951471 0.307737i \(-0.0995717\pi\)
\(240\) 0 0
\(241\) 205.488 0.852649 0.426324 0.904570i \(-0.359808\pi\)
0.426324 + 0.904570i \(0.359808\pi\)
\(242\) 15.2117 + 221.935i 0.0628582 + 0.917086i
\(243\) 0 0
\(244\) 59.3600 78.3229i 0.243278 0.320996i
\(245\) −7.68839 7.68839i −0.0313812 0.0313812i
\(246\) 0 0
\(247\) 119.657 0.484442
\(248\) 58.6622 + 281.710i 0.236541 + 1.13593i
\(249\) 0 0
\(250\) 21.1112 24.2181i 0.0844447 0.0968724i
\(251\) −55.4867 + 55.4867i −0.221063 + 0.221063i −0.808946 0.587883i \(-0.799961\pi\)
0.587883 + 0.808946i \(0.299961\pi\)
\(252\) 0 0
\(253\) 78.3282 78.3282i 0.309598 0.309598i
\(254\) −16.8525 245.873i −0.0663483 0.968005i
\(255\) 0 0
\(256\) 218.584 133.256i 0.853842 0.520532i
\(257\) 142.878 0.555944 0.277972 0.960589i \(-0.410338\pi\)
0.277972 + 0.960589i \(0.410338\pi\)
\(258\) 0 0
\(259\) −134.313 134.313i −0.518583 0.518583i
\(260\) 9.17466 1.26362i 0.0352872 0.00486008i
\(261\) 0 0
\(262\) 162.656 + 141.789i 0.620825 + 0.541180i
\(263\) 242.691 0.922780 0.461390 0.887197i \(-0.347351\pi\)
0.461390 + 0.887197i \(0.347351\pi\)
\(264\) 0 0
\(265\) 19.1886i 0.0724099i
\(266\) 97.8833 + 85.3259i 0.367982 + 0.320774i
\(267\) 0 0
\(268\) 178.872 + 135.565i 0.667433 + 0.505839i
\(269\) 292.665 292.665i 1.08797 1.08797i 0.0922353 0.995737i \(-0.470599\pi\)
0.995737 0.0922353i \(-0.0294012\pi\)
\(270\) 0 0
\(271\) 258.180i 0.952694i 0.879257 + 0.476347i \(0.158039\pi\)
−0.879257 + 0.476347i \(0.841961\pi\)
\(272\) −290.125 + 81.4629i −1.06664 + 0.299496i
\(273\) 0 0
\(274\) −9.98625 145.697i −0.0364462 0.531741i
\(275\) 55.0322 + 55.0322i 0.200117 + 0.200117i
\(276\) 0 0
\(277\) 63.2023 + 63.2023i 0.228167 + 0.228167i 0.811927 0.583759i \(-0.198419\pi\)
−0.583759 + 0.811927i \(0.698419\pi\)
\(278\) 30.7126 35.2325i 0.110477 0.126736i
\(279\) 0 0
\(280\) 8.40622 + 5.50864i 0.0300222 + 0.0196737i
\(281\) 421.406i 1.49966i 0.661628 + 0.749832i \(0.269866\pi\)
−0.661628 + 0.749832i \(0.730134\pi\)
\(282\) 0 0
\(283\) 275.707 275.707i 0.974229 0.974229i −0.0254475 0.999676i \(-0.508101\pi\)
0.999676 + 0.0254475i \(0.00810107\pi\)
\(284\) −249.751 + 34.3981i −0.879405 + 0.121120i
\(285\) 0 0
\(286\) 3.07459 + 44.8576i 0.0107503 + 0.156845i
\(287\) 172.108i 0.599681i
\(288\) 0 0
\(289\) 65.7217 0.227411
\(290\) −19.3049 + 1.32318i −0.0665685 + 0.00456268i
\(291\) 0 0
\(292\) −41.1807 298.997i −0.141030 1.02396i
\(293\) −181.330 181.330i −0.618873 0.618873i 0.326369 0.945242i \(-0.394175\pi\)
−0.945242 + 0.326369i \(0.894175\pi\)
\(294\) 0 0
\(295\) 30.5021 0.103397
\(296\) −325.712 213.441i −1.10038 0.721083i
\(297\) 0 0
\(298\) 46.9769 + 40.9503i 0.157641 + 0.137417i
\(299\) −180.198 + 180.198i −0.602669 + 0.602669i
\(300\) 0 0
\(301\) −110.439 + 110.439i −0.366907 + 0.366907i
\(302\) −321.280 + 22.0209i −1.06384 + 0.0729169i
\(303\) 0 0
\(304\) 232.121 + 130.345i 0.763555 + 0.428768i
\(305\) 7.90985 0.0259339
\(306\) 0 0
\(307\) 279.027 + 279.027i 0.908883 + 0.908883i 0.996182 0.0872996i \(-0.0278237\pi\)
−0.0872996 + 0.996182i \(0.527824\pi\)
\(308\) −29.4722 + 38.8873i −0.0956890 + 0.126258i
\(309\) 0 0
\(310\) −15.2185 + 17.4582i −0.0490920 + 0.0563169i
\(311\) 414.511 1.33283 0.666417 0.745579i \(-0.267827\pi\)
0.666417 + 0.745579i \(0.267827\pi\)
\(312\) 0 0
\(313\) 331.008i 1.05753i −0.848767 0.528767i \(-0.822654\pi\)
0.848767 0.528767i \(-0.177346\pi\)
\(314\) −282.293 + 323.838i −0.899022 + 1.03133i
\(315\) 0 0
\(316\) 32.2866 + 234.420i 0.102173 + 0.741836i
\(317\) 194.563 194.563i 0.613764 0.613764i −0.330161 0.943925i \(-0.607103\pi\)
0.943925 + 0.330161i \(0.107103\pi\)
\(318\) 0 0
\(319\) 93.9437i 0.294494i
\(320\) 19.1742 + 7.54290i 0.0599195 + 0.0235716i
\(321\) 0 0
\(322\) −275.904 + 18.9108i −0.856846 + 0.0587293i
\(323\) −221.585 221.585i −0.686021 0.686021i
\(324\) 0 0
\(325\) −126.604 126.604i −0.389552 0.389552i
\(326\) −397.279 346.312i −1.21865 1.06231i
\(327\) 0 0
\(328\) −71.9320 345.434i −0.219305 1.05315i
\(329\) 128.305i 0.389985i
\(330\) 0 0
\(331\) −462.054 + 462.054i −1.39593 + 1.39593i −0.584641 + 0.811292i \(0.698765\pi\)
−0.811292 + 0.584641i \(0.801235\pi\)
\(332\) 321.065 + 243.331i 0.967063 + 0.732925i
\(333\) 0 0
\(334\) −398.246 + 27.2963i −1.19235 + 0.0817254i
\(335\) 18.0643i 0.0539233i
\(336\) 0 0
\(337\) −472.439 −1.40190 −0.700948 0.713212i \(-0.747240\pi\)
−0.700948 + 0.713212i \(0.747240\pi\)
\(338\) 16.0394 + 234.012i 0.0474540 + 0.692342i
\(339\) 0 0
\(340\) −19.3299 14.6499i −0.0568527 0.0430879i
\(341\) −79.5078 79.5078i −0.233161 0.233161i
\(342\) 0 0
\(343\) −322.996 −0.941679
\(344\) −175.502 + 267.817i −0.510179 + 0.778537i
\(345\) 0 0
\(346\) −257.653 + 295.572i −0.744662 + 0.854253i
\(347\) −92.8976 + 92.8976i −0.267716 + 0.267716i −0.828179 0.560463i \(-0.810623\pi\)
0.560463 + 0.828179i \(0.310623\pi\)
\(348\) 0 0
\(349\) 264.708 264.708i 0.758475 0.758475i −0.217570 0.976045i \(-0.569813\pi\)
0.976045 + 0.217570i \(0.0698129\pi\)
\(350\) −13.2864 193.846i −0.0379613 0.553846i
\(351\) 0 0
\(352\) −42.9001 + 90.3676i −0.121875 + 0.256726i
\(353\) 413.360 1.17099 0.585495 0.810676i \(-0.300900\pi\)
0.585495 + 0.810676i \(0.300900\pi\)
\(354\) 0 0
\(355\) −14.3481 14.3481i −0.0404173 0.0404173i
\(356\) −82.2311 597.048i −0.230986 1.67710i
\(357\) 0 0
\(358\) −316.767 276.129i −0.884824 0.771311i
\(359\) 625.198 1.74150 0.870749 0.491728i \(-0.163635\pi\)
0.870749 + 0.491728i \(0.163635\pi\)
\(360\) 0 0
\(361\) 84.1643i 0.233142i
\(362\) 212.357 + 185.113i 0.586620 + 0.511363i
\(363\) 0 0
\(364\) 67.8024 89.4624i 0.186270 0.245776i
\(365\) 17.1773 17.1773i 0.0470611 0.0470611i
\(366\) 0 0
\(367\) 601.904i 1.64007i 0.572316 + 0.820033i \(0.306045\pi\)
−0.572316 + 0.820033i \(0.693955\pi\)
\(368\) −545.857 + 153.269i −1.48331 + 0.416491i
\(369\) 0 0
\(370\) −2.14324 31.2694i −0.00579254 0.0845118i
\(371\) 164.458 + 164.458i 0.443283 + 0.443283i
\(372\) 0 0
\(373\) −493.026 493.026i −1.32179 1.32179i −0.912330 0.409455i \(-0.865719\pi\)
−0.409455 0.912330i \(-0.634281\pi\)
\(374\) 77.3750 88.7622i 0.206885 0.237332i
\(375\) 0 0
\(376\) 53.6246 + 257.518i 0.142619 + 0.684888i
\(377\) 216.122i 0.573269i
\(378\) 0 0
\(379\) −144.970 + 144.970i −0.382506 + 0.382506i −0.872004 0.489498i \(-0.837180\pi\)
0.489498 + 0.872004i \(0.337180\pi\)
\(380\) 2.92348 + 21.2262i 0.00769337 + 0.0558585i
\(381\) 0 0
\(382\) 20.4482 + 298.334i 0.0535293 + 0.780979i
\(383\) 417.764i 1.09077i −0.838187 0.545384i \(-0.816384\pi\)
0.838187 0.545384i \(-0.183616\pi\)
\(384\) 0 0
\(385\) −3.92724 −0.0102006
\(386\) −105.403 + 7.22448i −0.273066 + 0.0187163i
\(387\) 0 0
\(388\) 204.306 28.1389i 0.526561 0.0725230i
\(389\) −144.751 144.751i −0.372109 0.372109i 0.496136 0.868245i \(-0.334752\pi\)
−0.868245 + 0.496136i \(0.834752\pi\)
\(390\) 0 0
\(391\) 667.392 1.70689
\(392\) −264.509 + 55.0804i −0.674768 + 0.140511i
\(393\) 0 0
\(394\) −230.418 200.858i −0.584819 0.509793i
\(395\) −13.4674 + 13.4674i −0.0340946 + 0.0340946i
\(396\) 0 0
\(397\) −105.531 + 105.531i −0.265822 + 0.265822i −0.827414 0.561592i \(-0.810189\pi\)
0.561592 + 0.827414i \(0.310189\pi\)
\(398\) −4.48362 + 0.307313i −0.0112654 + 0.000772142i
\(399\) 0 0
\(400\) −107.684 383.510i −0.269210 0.958776i
\(401\) 529.383 1.32016 0.660078 0.751197i \(-0.270523\pi\)
0.660078 + 0.751197i \(0.270523\pi\)
\(402\) 0 0
\(403\) 182.912 + 182.912i 0.453876 + 0.453876i
\(404\) 628.529 + 476.354i 1.55576 + 1.17909i
\(405\) 0 0
\(406\) −154.114 + 176.795i −0.379591 + 0.435455i
\(407\) 152.167 0.373874
\(408\) 0 0
\(409\) 371.204i 0.907590i −0.891106 0.453795i \(-0.850070\pi\)
0.891106 0.453795i \(-0.149930\pi\)
\(410\) 18.6611 21.4074i 0.0455148 0.0522132i
\(411\) 0 0
\(412\) 269.334 37.0952i 0.653723 0.0900369i
\(413\) 261.422 261.422i 0.632982 0.632982i
\(414\) 0 0
\(415\) 32.4244i 0.0781311i
\(416\) 98.6940 207.895i 0.237245 0.499748i
\(417\) 0 0
\(418\) −103.781 + 7.11330i −0.248281 + 0.0170175i
\(419\) −124.486 124.486i −0.297103 0.297103i 0.542775 0.839878i \(-0.317374\pi\)
−0.839878 + 0.542775i \(0.817374\pi\)
\(420\) 0 0
\(421\) 51.7267 + 51.7267i 0.122866 + 0.122866i 0.765866 0.643000i \(-0.222310\pi\)
−0.643000 + 0.765866i \(0.722310\pi\)
\(422\) 107.465 + 93.6788i 0.254658 + 0.221988i
\(423\) 0 0
\(424\) 398.814 + 261.345i 0.940599 + 0.616379i
\(425\) 468.899i 1.10329i
\(426\) 0 0
\(427\) 67.7922 67.7922i 0.158764 0.158764i
\(428\) 443.508 585.189i 1.03623 1.36727i
\(429\) 0 0
\(430\) −25.7112 + 1.76228i −0.0597936 + 0.00409833i
\(431\) 424.978i 0.986029i 0.870021 + 0.493014i \(0.164105\pi\)
−0.870021 + 0.493014i \(0.835895\pi\)
\(432\) 0 0
\(433\) 283.151 0.653927 0.326964 0.945037i \(-0.393975\pi\)
0.326964 + 0.945037i \(0.393975\pi\)
\(434\) 19.1956 + 280.059i 0.0442295 + 0.645298i
\(435\) 0 0
\(436\) 102.957 135.847i 0.236140 0.311576i
\(437\) −416.901 416.901i −0.954008 0.954008i
\(438\) 0 0
\(439\) −701.459 −1.59786 −0.798928 0.601427i \(-0.794599\pi\)
−0.798928 + 0.601427i \(0.794599\pi\)
\(440\) −7.88226 + 1.64137i −0.0179142 + 0.00373040i
\(441\) 0 0
\(442\) −178.005 + 204.202i −0.402727 + 0.461996i
\(443\) −272.651 + 272.651i −0.615464 + 0.615464i −0.944365 0.328900i \(-0.893322\pi\)
0.328900 + 0.944365i \(0.393322\pi\)
\(444\) 0 0
\(445\) 34.3002 34.3002i 0.0770792 0.0770792i
\(446\) −31.5016 459.601i −0.0706314 1.03050i
\(447\) 0 0
\(448\) 228.982 99.6875i 0.511120 0.222517i
\(449\) −614.711 −1.36907 −0.684534 0.728981i \(-0.739994\pi\)
−0.684534 + 0.728981i \(0.739994\pi\)
\(450\) 0 0
\(451\) 97.4931 + 97.4931i 0.216171 + 0.216171i
\(452\) 20.2502 2.78905i 0.0448013 0.00617046i
\(453\) 0 0
\(454\) 25.8823 + 22.5619i 0.0570096 + 0.0496959i
\(455\) 9.03482 0.0198567
\(456\) 0 0
\(457\) 117.859i 0.257898i −0.991651 0.128949i \(-0.958840\pi\)
0.991651 0.128949i \(-0.0411603\pi\)
\(458\) 83.4195 + 72.7177i 0.182139 + 0.158772i
\(459\) 0 0
\(460\) −36.3683 27.5631i −0.0790616 0.0599198i
\(461\) −262.235 + 262.235i −0.568839 + 0.568839i −0.931803 0.362964i \(-0.881765\pi\)
0.362964 + 0.931803i \(0.381765\pi\)
\(462\) 0 0
\(463\) 192.234i 0.415192i 0.978215 + 0.207596i \(0.0665640\pi\)
−0.978215 + 0.207596i \(0.933436\pi\)
\(464\) −235.427 + 419.251i −0.507386 + 0.903559i
\(465\) 0 0
\(466\) 5.01619 + 73.1851i 0.0107644 + 0.157049i
\(467\) −529.169 529.169i −1.13312 1.13312i −0.989655 0.143470i \(-0.954174\pi\)
−0.143470 0.989655i \(-0.545826\pi\)
\(468\) 0 0
\(469\) 154.822 + 154.822i 0.330111 + 0.330111i
\(470\) −13.9116 + 15.9590i −0.0295992 + 0.0339553i
\(471\) 0 0
\(472\) 415.433 633.953i 0.880154 1.34312i
\(473\) 125.119i 0.264523i
\(474\) 0 0
\(475\) 292.908 292.908i 0.616649 0.616649i
\(476\) −291.227 + 40.1106i −0.611822 + 0.0842660i
\(477\) 0 0
\(478\) −20.1174 293.508i −0.0420866 0.614033i
\(479\) 1.43750i 0.00300104i 0.999999 + 0.00150052i \(0.000477630\pi\)
−0.999999 + 0.00150052i \(0.999522\pi\)
\(480\) 0 0
\(481\) −350.068 −0.727792
\(482\) 410.015 28.1029i 0.850653 0.0583048i
\(483\) 0 0
\(484\) 60.7043 + 440.751i 0.125422 + 0.910642i
\(485\) 11.7373 + 11.7373i 0.0242006 + 0.0242006i
\(486\) 0 0
\(487\) 701.238 1.43991 0.719957 0.694019i \(-0.244162\pi\)
0.719957 + 0.694019i \(0.244162\pi\)
\(488\) 107.730 164.397i 0.220759 0.336880i
\(489\) 0 0
\(490\) −16.3923 14.2893i −0.0334536 0.0291619i
\(491\) −519.668 + 519.668i −1.05839 + 1.05839i −0.0602007 + 0.998186i \(0.519174\pi\)
−0.998186 + 0.0602007i \(0.980826\pi\)
\(492\) 0 0
\(493\) 400.222 400.222i 0.811809 0.811809i
\(494\) 238.754 16.3645i 0.483308 0.0331265i
\(495\) 0 0
\(496\) 155.577 + 554.077i 0.313663 + 1.11709i
\(497\) −245.944 −0.494858
\(498\) 0 0
\(499\) 359.284 + 359.284i 0.720009 + 0.720009i 0.968607 0.248598i \(-0.0799698\pi\)
−0.248598 + 0.968607i \(0.579970\pi\)
\(500\) 38.8114 51.2100i 0.0776228 0.102420i
\(501\) 0 0
\(502\) −103.125 + 118.302i −0.205429 + 0.235662i
\(503\) −174.376 −0.346671 −0.173335 0.984863i \(-0.555454\pi\)
−0.173335 + 0.984863i \(0.555454\pi\)
\(504\) 0 0
\(505\) 63.4752i 0.125693i
\(506\) 145.577 167.002i 0.287702 0.330043i
\(507\) 0 0
\(508\) −67.2521 488.291i −0.132386 0.961203i
\(509\) −314.247 + 314.247i −0.617381 + 0.617381i −0.944859 0.327478i \(-0.893801\pi\)
0.327478 + 0.944859i \(0.393801\pi\)
\(510\) 0 0
\(511\) 294.440i 0.576203i
\(512\) 417.920 295.782i 0.816249 0.577700i
\(513\) 0 0
\(514\) 285.086 19.5402i 0.554643 0.0380159i
\(515\) 15.4732 + 15.4732i 0.0300450 + 0.0300450i
\(516\) 0 0
\(517\) −72.6801 72.6801i −0.140580 0.140580i
\(518\) −286.366 249.628i −0.552830 0.481908i
\(519\) 0 0
\(520\) 18.1336 3.77607i 0.0348722 0.00726167i
\(521\) 468.678i 0.899575i 0.893136 + 0.449787i \(0.148500\pi\)
−0.893136 + 0.449787i \(0.851500\pi\)
\(522\) 0 0
\(523\) −417.239 + 417.239i −0.797780 + 0.797780i −0.982745 0.184965i \(-0.940783\pi\)
0.184965 + 0.982745i \(0.440783\pi\)
\(524\) 343.942 + 260.669i 0.656378 + 0.497460i
\(525\) 0 0
\(526\) 484.246 33.1908i 0.920620 0.0631004i
\(527\) 677.443i 1.28547i
\(528\) 0 0
\(529\) 726.667 1.37366
\(530\) 2.62427 + 38.2874i 0.00495144 + 0.0722404i
\(531\) 0 0
\(532\) 206.978 + 156.866i 0.389056 + 0.294860i
\(533\) −224.288 224.288i −0.420803 0.420803i
\(534\) 0 0
\(535\) 59.0984 0.110464
\(536\) 375.447 + 246.032i 0.700460 + 0.459015i
\(537\) 0 0
\(538\) 543.934 623.984i 1.01103 1.15982i
\(539\) 74.6533 74.6533i 0.138503 0.138503i
\(540\) 0 0
\(541\) −163.152 + 163.152i −0.301574 + 0.301574i −0.841629 0.540055i \(-0.818403\pi\)
0.540055 + 0.841629i \(0.318403\pi\)
\(542\) 35.3091 + 515.152i 0.0651460 + 0.950464i
\(543\) 0 0
\(544\) −567.751 + 202.222i −1.04366 + 0.371732i
\(545\) 13.7192 0.0251729
\(546\) 0 0
\(547\) −595.267 595.267i −1.08824 1.08824i −0.995710 0.0925300i \(-0.970505\pi\)
−0.0925300 0.995710i \(-0.529495\pi\)
\(548\) −39.8515 289.346i −0.0727217 0.528004i
\(549\) 0 0
\(550\) 117.333 + 102.280i 0.213333 + 0.185964i
\(551\) −500.015 −0.907468
\(552\) 0 0
\(553\) 230.847i 0.417445i
\(554\) 134.752 + 117.465i 0.243235 + 0.212031i
\(555\) 0 0
\(556\) 56.4629 74.5004i 0.101552 0.133994i
\(557\) 370.177 370.177i 0.664590 0.664590i −0.291868 0.956459i \(-0.594277\pi\)
0.956459 + 0.291868i \(0.0942769\pi\)
\(558\) 0 0
\(559\) 287.843i 0.514926i
\(560\) 17.5265 + 9.84184i 0.0312973 + 0.0175747i
\(561\) 0 0
\(562\) 57.6321 + 840.839i 0.102548 + 1.49615i
\(563\) 426.543 + 426.543i 0.757625 + 0.757625i 0.975890 0.218264i \(-0.0700395\pi\)
−0.218264 + 0.975890i \(0.570040\pi\)
\(564\) 0 0
\(565\) 1.16337 + 1.16337i 0.00205906 + 0.00205906i
\(566\) 512.417 587.829i 0.905330 1.03857i
\(567\) 0 0
\(568\) −493.628 + 102.791i −0.869064 + 0.180971i
\(569\) 291.547i 0.512385i −0.966626 0.256192i \(-0.917532\pi\)
0.966626 0.256192i \(-0.0824680\pi\)
\(570\) 0 0
\(571\) 569.328 569.328i 0.997071 0.997071i −0.00292477 0.999996i \(-0.500931\pi\)
0.999996 + 0.00292477i \(0.000930984\pi\)
\(572\) 12.2696 + 89.0847i 0.0214503 + 0.155743i
\(573\) 0 0
\(574\) −23.5378 343.411i −0.0410066 0.598277i
\(575\) 882.212i 1.53428i
\(576\) 0 0
\(577\) −360.847 −0.625385 −0.312692 0.949854i \(-0.601231\pi\)
−0.312692 + 0.949854i \(0.601231\pi\)
\(578\) 131.136 8.98820i 0.226878 0.0155505i
\(579\) 0 0
\(580\) −38.3384 + 5.28032i −0.0661006 + 0.00910401i
\(581\) 277.897 + 277.897i 0.478308 + 0.478308i
\(582\) 0 0
\(583\) −186.319 −0.319586
\(584\) −123.060 590.963i −0.210719 1.01192i
\(585\) 0 0
\(586\) −386.610 337.012i −0.659744 0.575106i
\(587\) 373.439 373.439i 0.636183 0.636183i −0.313429 0.949612i \(-0.601478\pi\)
0.949612 + 0.313429i \(0.101478\pi\)
\(588\) 0 0
\(589\) −423.180 + 423.180i −0.718472 + 0.718472i
\(590\) 60.8615 4.17152i 0.103155 0.00707037i
\(591\) 0 0
\(592\) −679.089 381.337i −1.14711 0.644151i
\(593\) −608.053 −1.02538 −0.512692 0.858572i \(-0.671352\pi\)
−0.512692 + 0.858572i \(0.671352\pi\)
\(594\) 0 0
\(595\) −16.7309 16.7309i −0.0281192 0.0281192i
\(596\) 99.3343 + 75.2842i 0.166668 + 0.126316i
\(597\) 0 0
\(598\) −334.909 + 384.197i −0.560048 + 0.642470i
\(599\) −211.563 −0.353194 −0.176597 0.984283i \(-0.556509\pi\)
−0.176597 + 0.984283i \(0.556509\pi\)
\(600\) 0 0
\(601\) 343.381i 0.571349i 0.958327 + 0.285674i \(0.0922176\pi\)
−0.958327 + 0.285674i \(0.907782\pi\)
\(602\) −205.257 + 235.465i −0.340959 + 0.391137i
\(603\) 0 0
\(604\) −638.043 + 87.8774i −1.05636 + 0.145492i
\(605\) −25.3210 + 25.3210i −0.0418529 + 0.0418529i
\(606\) 0 0
\(607\) 1006.23i 1.65771i −0.559461 0.828856i \(-0.688992\pi\)
0.559461 0.828856i \(-0.311008\pi\)
\(608\) 480.981 + 228.336i 0.791087 + 0.375552i
\(609\) 0 0
\(610\) 15.7827 1.08176i 0.0258732 0.00177338i
\(611\) 167.204 + 167.204i 0.273657 + 0.273657i
\(612\) 0 0
\(613\) 380.705 + 380.705i 0.621052 + 0.621052i 0.945801 0.324748i \(-0.105280\pi\)
−0.324748 + 0.945801i \(0.605280\pi\)
\(614\) 594.908 + 518.587i 0.968905 + 0.844605i
\(615\) 0 0
\(616\) −53.4882 + 81.6233i −0.0868314 + 0.132505i
\(617\) 693.808i 1.12449i −0.826972 0.562243i \(-0.809939\pi\)
0.826972 0.562243i \(-0.190061\pi\)
\(618\) 0 0
\(619\) −619.279 + 619.279i −1.00045 + 1.00045i −0.000450619 1.00000i \(0.500143\pi\)
−1.00000 0.000450619i \(0.999857\pi\)
\(620\) −27.9782 + 36.9160i −0.0451261 + 0.0595420i
\(621\) 0 0
\(622\) 827.082 56.6892i 1.32971 0.0911403i
\(623\) 587.947i 0.943736i
\(624\) 0 0
\(625\) −617.237 −0.987579
\(626\) −45.2692 660.467i −0.0723151 1.05506i
\(627\) 0 0
\(628\) −518.976 + 684.767i −0.826394 + 1.09039i
\(629\) 648.266 + 648.266i 1.03063 + 1.03063i
\(630\) 0 0
\(631\) −1007.91 −1.59732 −0.798661 0.601781i \(-0.794458\pi\)
−0.798661 + 0.601781i \(0.794458\pi\)
\(632\) 96.4816 + 463.327i 0.152661 + 0.733113i
\(633\) 0 0
\(634\) 361.607 414.824i 0.570358 0.654297i
\(635\) 28.0522 28.0522i 0.0441767 0.0441767i
\(636\) 0 0
\(637\) −171.744 + 171.744i −0.269613 + 0.269613i
\(638\) −12.8479 187.448i −0.0201377 0.293805i
\(639\) 0 0
\(640\) 39.2903 + 12.4282i 0.0613910 + 0.0194191i
\(641\) 511.481 0.797943 0.398971 0.916963i \(-0.369367\pi\)
0.398971 + 0.916963i \(0.369367\pi\)
\(642\) 0 0
\(643\) −497.727 497.727i −0.774071 0.774071i 0.204745 0.978815i \(-0.434364\pi\)
−0.978815 + 0.204745i \(0.934364\pi\)
\(644\) −547.931 + 75.4662i −0.850824 + 0.117184i
\(645\) 0 0
\(646\) −472.437 411.828i −0.731326 0.637505i
\(647\) −59.8694 −0.0925339 −0.0462669 0.998929i \(-0.514732\pi\)
−0.0462669 + 0.998929i \(0.514732\pi\)
\(648\) 0 0
\(649\) 296.172i 0.456351i
\(650\) −269.931 235.301i −0.415278 0.362002i
\(651\) 0 0
\(652\) −840.060 636.671i −1.28844 0.976489i
\(653\) −489.952 + 489.952i −0.750310 + 0.750310i −0.974537 0.224227i \(-0.928014\pi\)
0.224227 + 0.974537i \(0.428014\pi\)
\(654\) 0 0
\(655\) 34.7348i 0.0530302i
\(656\) −190.769 679.414i −0.290807 1.03569i
\(657\) 0 0
\(658\) 17.5472 + 256.009i 0.0266675 + 0.389072i
\(659\) −234.984 234.984i −0.356577 0.356577i 0.505973 0.862549i \(-0.331134\pi\)
−0.862549 + 0.505973i \(0.831134\pi\)
\(660\) 0 0
\(661\) 305.060 + 305.060i 0.461512 + 0.461512i 0.899151 0.437639i \(-0.144185\pi\)
−0.437639 + 0.899151i \(0.644185\pi\)
\(662\) −858.753 + 985.136i −1.29721 + 1.48812i
\(663\) 0 0
\(664\) 673.905 + 441.614i 1.01492 + 0.665081i
\(665\) 20.9027i 0.0314326i
\(666\) 0 0
\(667\) 752.998 752.998i 1.12893 1.12893i
\(668\) −790.895 + 108.930i −1.18397 + 0.163068i
\(669\) 0 0
\(670\) 2.47050 + 36.0441i 0.00368732 + 0.0537971i
\(671\) 76.8036i 0.114461i
\(672\) 0 0
\(673\) 458.738 0.681632 0.340816 0.940130i \(-0.389297\pi\)
0.340816 + 0.940130i \(0.389297\pi\)
\(674\) −942.666 + 64.6115i −1.39861 + 0.0958628i
\(675\) 0 0
\(676\) 64.0076 + 464.734i 0.0946858 + 0.687476i
\(677\) −171.344 171.344i −0.253094 0.253094i 0.569144 0.822238i \(-0.307275\pi\)
−0.822238 + 0.569144i \(0.807275\pi\)
\(678\) 0 0
\(679\) 201.192 0.296306
\(680\) −40.5729 26.5876i −0.0596660 0.0390994i
\(681\) 0 0
\(682\) −169.517 147.770i −0.248559 0.216671i
\(683\) 769.447 769.447i 1.12657 1.12657i 0.135838 0.990731i \(-0.456627\pi\)
0.990731 0.135838i \(-0.0433728\pi\)
\(684\) 0 0
\(685\) 16.6229 16.6229i 0.0242670 0.0242670i
\(686\) −644.480 + 44.1734i −0.939475 + 0.0643927i
\(687\) 0 0
\(688\) −313.555 + 558.382i −0.455748 + 0.811601i
\(689\) 428.636 0.622114
\(690\) 0 0
\(691\) 44.7951 + 44.7951i 0.0648264 + 0.0648264i 0.738777 0.673950i \(-0.235404\pi\)
−0.673950 + 0.738777i \(0.735404\pi\)
\(692\) −473.677 + 624.996i −0.684504 + 0.903174i
\(693\) 0 0
\(694\) −172.655 + 198.065i −0.248783 + 0.285396i
\(695\) 7.52381 0.0108256
\(696\) 0 0
\(697\) 830.686i 1.19180i
\(698\) 491.975 564.378i 0.704835 0.808565i
\(699\) 0 0
\(700\) −53.0214 384.967i −0.0757448 0.549954i
\(701\) −31.7012 + 31.7012i −0.0452229 + 0.0452229i −0.729357 0.684134i \(-0.760180\pi\)
0.684134 + 0.729357i \(0.260180\pi\)
\(702\) 0 0
\(703\) 809.907i 1.15207i
\(704\) −73.2406 + 186.179i −0.104035 + 0.264459i
\(705\) 0 0
\(706\) 824.784 56.5317i 1.16825 0.0800732i
\(707\) 544.021 + 544.021i 0.769478 + 0.769478i
\(708\) 0 0
\(709\) 256.706 + 256.706i 0.362068 + 0.362068i 0.864574 0.502506i \(-0.167589\pi\)
−0.502506 + 0.864574i \(0.667589\pi\)
\(710\) −30.5914 26.6668i −0.0430864 0.0375589i
\(711\) 0 0
\(712\) −245.730 1180.05i −0.345127 1.65738i
\(713\) 1274.58i 1.78763i
\(714\) 0 0
\(715\) −5.11789 + 5.11789i −0.00715789 + 0.00715789i
\(716\) −669.815 507.644i −0.935496 0.709000i
\(717\) 0 0
\(718\) 1247.47 85.5030i 1.73742 0.119085i
\(719\) 1368.29i 1.90305i 0.307574 + 0.951524i \(0.400483\pi\)
−0.307574 + 0.951524i \(0.599517\pi\)
\(720\) 0 0
\(721\) 265.229 0.367862
\(722\) −11.5104 167.935i −0.0159424 0.232596i
\(723\) 0 0
\(724\) 449.035 + 340.318i 0.620215 + 0.470053i
\(725\) 529.045 + 529.045i 0.729717 + 0.729717i
\(726\) 0 0
\(727\) 37.5336 0.0516281 0.0258141 0.999667i \(-0.491782\pi\)
0.0258141 + 0.999667i \(0.491782\pi\)
\(728\) 123.052 187.779i 0.169028 0.257938i
\(729\) 0 0
\(730\) 31.9250 36.6234i 0.0437329 0.0501691i
\(731\) 533.037 533.037i 0.729189 0.729189i
\(732\) 0 0
\(733\) −385.216 + 385.216i −0.525534 + 0.525534i −0.919237 0.393704i \(-0.871194\pi\)
0.393704 + 0.919237i \(0.371194\pi\)
\(734\) 82.3174 + 1200.99i 0.112149 + 1.63623i
\(735\) 0 0
\(736\) −1068.20 + 380.472i −1.45135 + 0.516945i
\(737\) −175.402 −0.237995
\(738\) 0 0
\(739\) −889.039 889.039i −1.20303 1.20303i −0.973240 0.229790i \(-0.926196\pi\)
−0.229790 0.973240i \(-0.573804\pi\)
\(740\) −8.55289 62.0992i −0.0115580 0.0839179i
\(741\) 0 0
\(742\) 350.638 + 305.655i 0.472557 + 0.411933i
\(743\) −506.252 −0.681362 −0.340681 0.940179i \(-0.610658\pi\)
−0.340681 + 0.940179i \(0.610658\pi\)
\(744\) 0 0
\(745\) 10.0318i 0.0134655i
\(746\) −1051.17 916.317i −1.40908 1.22831i
\(747\) 0 0
\(748\) 142.248 187.691i 0.190172 0.250924i
\(749\) 506.509 506.509i 0.676247 0.676247i
\(750\) 0 0
\(751\) 456.844i 0.608314i 0.952622 + 0.304157i \(0.0983748\pi\)
−0.952622 + 0.304157i \(0.901625\pi\)
\(752\) 142.217 + 506.496i 0.189118 + 0.673532i
\(753\) 0 0
\(754\) 29.5572 + 431.233i 0.0392006 + 0.571927i
\(755\) −36.6554 36.6554i −0.0485502 0.0485502i
\(756\) 0 0
\(757\) −221.708 221.708i −0.292877 0.292877i 0.545339 0.838216i \(-0.316401\pi\)
−0.838216 + 0.545339i \(0.816401\pi\)
\(758\) −269.434 + 309.087i −0.355454 + 0.407766i
\(759\) 0 0
\(760\) 8.73621 + 41.9533i 0.0114950 + 0.0552017i
\(761\) 205.900i 0.270566i −0.990807 0.135283i \(-0.956806\pi\)
0.990807 0.135283i \(-0.0431943\pi\)
\(762\) 0 0
\(763\) 117.582 117.582i 0.154105 0.154105i
\(764\) 81.6013 + 592.475i 0.106808 + 0.775491i
\(765\) 0 0
\(766\) −57.1340 833.572i −0.0745875 1.08821i
\(767\) 681.359i 0.888342i
\(768\) 0 0
\(769\) 900.133 1.17052 0.585262 0.810844i \(-0.300992\pi\)
0.585262 + 0.810844i \(0.300992\pi\)
\(770\) −7.83609 + 0.537095i −0.0101767 + 0.000697526i
\(771\) 0 0
\(772\) −209.325 + 28.8303i −0.271147 + 0.0373449i
\(773\) 870.407 + 870.407i 1.12601 + 1.12601i 0.990819 + 0.135193i \(0.0431654\pi\)
0.135193 + 0.990819i \(0.456835\pi\)
\(774\) 0 0
\(775\) 895.498 1.15548
\(776\) 403.807 84.0873i 0.520369 0.108360i
\(777\) 0 0
\(778\) −308.620 269.027i −0.396683 0.345793i
\(779\) 518.907 518.907i 0.666119 0.666119i
\(780\) 0 0
\(781\) 139.318 139.318i 0.178385 0.178385i
\(782\) 1331.66 91.2736i 1.70289 0.116718i
\(783\) 0 0
\(784\) −520.247 + 146.078i −0.663580 + 0.186324i
\(785\) −69.1547 −0.0880951
\(786\) 0 0
\(787\) 1005.24 + 1005.24i 1.27730 + 1.27730i 0.942171 + 0.335133i \(0.108781\pi\)
0.335133 + 0.942171i \(0.391219\pi\)
\(788\) −487.228 369.264i −0.618310 0.468609i
\(789\) 0 0
\(790\) −25.0299 + 28.7135i −0.0316834 + 0.0363462i
\(791\) 19.9415 0.0252106
\(792\) 0 0
\(793\) 176.691i 0.222813i
\(794\) −196.136 + 225.002i −0.247023 + 0.283377i
\(795\) 0 0
\(796\) −8.90421 + 1.22637i −0.0111862 + 0.00154067i
\(797\) −434.779 + 434.779i −0.545520 + 0.545520i −0.925142 0.379622i \(-0.876054\pi\)
0.379622 + 0.925142i \(0.376054\pi\)
\(798\) 0 0
\(799\) 619.268i 0.775054i
\(800\) −267.313 750.498i −0.334142 0.938123i
\(801\) 0 0
\(802\) 1056.29 72.3992i 1.31707 0.0902733i
\(803\) 166.789 + 166.789i 0.207708 + 0.207708i
\(804\) 0 0
\(805\) −31.4785 31.4785i −0.0391037 0.0391037i
\(806\) 389.983 + 339.952i 0.483850 + 0.421777i
\(807\) 0 0
\(808\) 1319.26 + 864.519i 1.63275 + 1.06995i
\(809\) 50.0002i 0.0618049i −0.999522 0.0309024i \(-0.990162\pi\)
0.999522 0.0309024i \(-0.00983812\pi\)
\(810\) 0 0
\(811\) −36.9957 + 36.9957i −0.0456173 + 0.0456173i −0.729547 0.683930i \(-0.760269\pi\)
0.683930 + 0.729547i \(0.260269\pi\)
\(812\) −283.327 + 373.839i −0.348925 + 0.460392i
\(813\) 0 0
\(814\) 303.621 20.8106i 0.372999 0.0255658i
\(815\) 84.8378i 0.104096i
\(816\) 0 0
\(817\) −665.947 −0.815112
\(818\) −50.7665 740.671i −0.0620617 0.905465i
\(819\) 0 0
\(820\) 34.3071 45.2667i 0.0418379 0.0552033i
\(821\) 297.373 + 297.373i 0.362208 + 0.362208i 0.864625 0.502417i \(-0.167556\pi\)
−0.502417 + 0.864625i \(0.667556\pi\)
\(822\) 0 0
\(823\) −345.052 −0.419262 −0.209631 0.977781i \(-0.567226\pi\)
−0.209631 + 0.977781i \(0.567226\pi\)
\(824\) 532.333 110.851i 0.646036 0.134528i
\(825\) 0 0
\(826\) 485.867 557.372i 0.588217 0.674785i
\(827\) 426.416 426.416i 0.515618 0.515618i −0.400624 0.916242i \(-0.631207\pi\)
0.916242 + 0.400624i \(0.131207\pi\)
\(828\) 0 0
\(829\) 897.159 897.159i 1.08222 1.08222i 0.0859157 0.996302i \(-0.472618\pi\)
0.996302 0.0859157i \(-0.0273816\pi\)
\(830\) 4.43441 + 64.6970i 0.00534267 + 0.0779482i
\(831\) 0 0
\(832\) 168.494 428.315i 0.202517 0.514802i
\(833\) 636.080 0.763602
\(834\) 0 0
\(835\) −45.4367 45.4367i −0.0544152 0.0544152i
\(836\) −206.104 + 28.3866i −0.246536 + 0.0339552i
\(837\) 0 0
\(838\) −265.414 231.364i −0.316723 0.276091i
\(839\) −708.037 −0.843906 −0.421953 0.906618i \(-0.638655\pi\)
−0.421953 + 0.906618i \(0.638655\pi\)
\(840\) 0 0
\(841\) 62.1159i 0.0738595i
\(842\) 110.285 + 96.1370i 0.130980 + 0.114177i
\(843\) 0 0
\(844\) 227.240 + 172.222i 0.269241 + 0.204054i
\(845\) −26.6989 + 26.6989i −0.0315963 + 0.0315963i
\(846\) 0 0
\(847\) 434.033i 0.512435i
\(848\) 831.503 + 466.924i 0.980546 + 0.550618i
\(849\) 0 0
\(850\) 64.1274 + 935.603i 0.0754440 + 1.10071i
\(851\) 1219.68 + 1219.68i 1.43323 + 1.43323i
\(852\) 0 0
\(853\) 795.484 + 795.484i 0.932572 + 0.932572i 0.997866 0.0652942i \(-0.0207986\pi\)
−0.0652942 + 0.997866i \(0.520799\pi\)
\(854\) 125.996 144.538i 0.147536 0.169249i
\(855\) 0 0
\(856\) 804.907 1228.29i 0.940312 1.43492i
\(857\) 1447.28i 1.68877i −0.535735 0.844386i \(-0.679966\pi\)
0.535735 0.844386i \(-0.320034\pi\)
\(858\) 0 0
\(859\) −99.6061 + 99.6061i −0.115956 + 0.115956i −0.762704 0.646748i \(-0.776129\pi\)
0.646748 + 0.762704i \(0.276129\pi\)
\(860\) −51.0611 + 7.03262i −0.0593734 + 0.00817747i
\(861\) 0 0
\(862\) 58.1207 + 847.967i 0.0674254 + 0.983721i
\(863\) 549.773i 0.637049i 0.947915 + 0.318525i \(0.103187\pi\)
−0.947915 + 0.318525i \(0.896813\pi\)
\(864\) 0 0
\(865\) −63.1185 −0.0729694
\(866\) 564.976 38.7241i 0.652397 0.0447161i
\(867\) 0 0
\(868\) 76.6028 + 556.183i 0.0882520 + 0.640763i
\(869\) −130.766 130.766i −0.150479 0.150479i
\(870\) 0 0
\(871\) 403.522 0.463286
\(872\) 186.853 285.139i 0.214281 0.326994i
\(873\) 0 0
\(874\) −888.867 774.835i −1.01701 0.886539i
\(875\) 44.3246 44.3246i 0.0506567 0.0506567i
\(876\) 0 0
\(877\) −165.469 + 165.469i −0.188677 + 0.188677i −0.795124 0.606447i \(-0.792594\pi\)
0.606447 + 0.795124i \(0.292594\pi\)
\(878\) −1399.63 + 95.9326i −1.59412 + 0.109263i
\(879\) 0 0
\(880\) −15.5031 + 4.35305i −0.0176172 + 0.00494665i
\(881\) −1046.60 −1.18796 −0.593982 0.804479i \(-0.702445\pi\)
−0.593982 + 0.804479i \(0.702445\pi\)
\(882\) 0 0
\(883\) 338.581 + 338.581i 0.383444 + 0.383444i 0.872341 0.488897i \(-0.162601\pi\)
−0.488897 + 0.872341i \(0.662601\pi\)
\(884\) −327.250 + 431.793i −0.370192 + 0.488453i
\(885\) 0 0
\(886\) −506.737 + 581.313i −0.571938 + 0.656109i
\(887\) −1486.13 −1.67546 −0.837728 0.546088i \(-0.816117\pi\)
−0.837728 + 0.546088i \(0.816117\pi\)
\(888\) 0 0
\(889\) 480.848i 0.540887i
\(890\) 63.7489 73.1309i 0.0716280 0.0821695i
\(891\) 0 0
\(892\) −125.711 912.742i −0.140932 1.02325i
\(893\) −386.840 + 386.840i −0.433191 + 0.433191i
\(894\) 0 0
\(895\) 67.6447i 0.0755807i
\(896\) 443.258 230.224i 0.494708 0.256947i
\(897\) 0 0
\(898\) −1226.54 + 84.0689i −1.36586 + 0.0936179i
\(899\) −764.339 764.339i −0.850210 0.850210i
\(900\) 0 0
\(901\) −793.761 793.761i −0.880978 0.880978i
\(902\) 207.863 + 181.197i 0.230447 + 0.200883i
\(903\) 0 0
\(904\) 40.0242 8.33449i 0.0442745 0.00921957i
\(905\) 45.3482i 0.0501085i
\(906\) 0 0
\(907\) −66.8336 + 66.8336i −0.0736864 + 0.0736864i −0.742989 0.669303i \(-0.766593\pi\)
0.669303 + 0.742989i \(0.266593\pi\)
\(908\) 54.7291 + 41.4785i 0.0602744 + 0.0456812i
\(909\) 0 0
\(910\) 18.0273 1.23562i 0.0198103 0.00135782i
\(911\) 227.208i 0.249406i −0.992194 0.124703i \(-0.960202\pi\)
0.992194 0.124703i \(-0.0397977\pi\)
\(912\) 0 0
\(913\) −314.837 −0.344838
\(914\) −16.1186 235.167i −0.0176352 0.257294i
\(915\) 0 0
\(916\) 176.393 + 133.686i 0.192569 + 0.145946i
\(917\) 297.698 + 297.698i 0.324643 + 0.324643i
\(918\) 0 0
\(919\) −1375.00 −1.49619 −0.748097 0.663589i \(-0.769032\pi\)
−0.748097 + 0.663589i \(0.769032\pi\)
\(920\) −76.3360 50.0233i −0.0829739 0.0543732i
\(921\) 0 0
\(922\) −487.378 + 559.106i −0.528610 + 0.606405i
\(923\) −320.509 + 320.509i −0.347247 + 0.347247i
\(924\) 0 0
\(925\) −856.929 + 856.929i −0.926410 + 0.926410i
\(926\) 26.2902 + 383.568i 0.0283912 + 0.414220i
\(927\) 0 0
\(928\) −412.415 + 868.737i −0.444413 + 0.936139i
\(929\) −1788.04 −1.92470 −0.962348 0.271822i \(-0.912374\pi\)
−0.962348 + 0.271822i \(0.912374\pi\)
\(930\) 0 0
\(931\) −397.342 397.342i −0.426790 0.426790i
\(932\) 20.0178 + 145.341i 0.0214783 + 0.155946i
\(933\) 0 0
\(934\) −1128.23 983.491i −1.20796 1.05299i
\(935\) 18.9549 0.0202727
\(936\) 0 0
\(937\) 768.834i 0.820527i −0.911967 0.410263i \(-0.865437\pi\)
0.911967 0.410263i \(-0.134563\pi\)
\(938\) 330.093 + 287.746i 0.351912 + 0.306765i
\(939\) 0 0
\(940\) −25.5756 + 33.7459i −0.0272081 + 0.0358999i
\(941\) −1016.85 + 1016.85i −1.08061 + 1.08061i −0.0841571 + 0.996453i \(0.526820\pi\)
−0.996453 + 0.0841571i \(0.973180\pi\)
\(942\) 0 0
\(943\) 1562.90i 1.65737i
\(944\) 742.220 1321.75i 0.786250 1.40016i
\(945\) 0 0
\(946\) −17.1115 249.653i −0.0180883 0.263904i
\(947\) −476.431 476.431i −0.503095 0.503095i 0.409304 0.912398i \(-0.365772\pi\)
−0.912398 + 0.409304i \(0.865772\pi\)
\(948\) 0 0
\(949\) −383.708 383.708i −0.404329 0.404329i
\(950\) 544.387 624.504i 0.573039 0.657373i
\(951\) 0 0
\(952\) −575.606 + 119.862i −0.604628 + 0.125906i
\(953\) 577.529i 0.606011i 0.952989 + 0.303006i \(0.0979901\pi\)
−0.952989 + 0.303006i \(0.902010\pi\)
\(954\) 0 0
\(955\) −34.0375 + 34.0375i −0.0356414 + 0.0356414i
\(956\) −80.2812 582.890i −0.0839761 0.609718i
\(957\) 0 0
\(958\) 0.196594 + 2.86827i 0.000205213 + 0.00299401i
\(959\) 284.936i 0.297118i
\(960\) 0 0
\(961\) −332.773 −0.346278
\(962\) −698.497 + 47.8758i −0.726088 + 0.0497670i
\(963\) 0 0
\(964\) 814.266 112.148i 0.844675 0.116337i
\(965\) −12.0257 12.0257i −0.0124619 0.0124619i
\(966\) 0 0
\(967\) 864.047 0.893534 0.446767 0.894650i \(-0.352575\pi\)
0.446767 + 0.894650i \(0.352575\pi\)
\(968\) 181.402 + 871.136i 0.187399 + 0.899934i
\(969\) 0 0
\(970\) 25.0249 + 21.8145i 0.0257989 + 0.0224891i
\(971\) −898.515 + 898.515i −0.925350 + 0.925350i −0.997401 0.0720505i \(-0.977046\pi\)
0.0720505 + 0.997401i \(0.477046\pi\)
\(972\) 0 0
\(973\) 64.4836 64.4836i 0.0662730 0.0662730i
\(974\) 1399.19 95.9024i 1.43654 0.0984624i
\(975\) 0 0
\(976\) 192.473 342.759i 0.197206 0.351187i
\(977\) 538.131 0.550799 0.275400 0.961330i \(-0.411190\pi\)
0.275400 + 0.961330i \(0.411190\pi\)
\(978\) 0 0
\(979\) 333.051 + 333.051i 0.340195 + 0.340195i
\(980\) −34.6620 26.2699i −0.0353694 0.0268060i
\(981\) 0 0
\(982\) −965.833 + 1107.97i −0.983536 + 1.12828i
\(983\) −759.452 −0.772586 −0.386293 0.922376i \(-0.626245\pi\)
−0.386293 + 0.922376i \(0.626245\pi\)
\(984\) 0 0
\(985\) 49.2052i 0.0499546i
\(986\) 743.835 853.305i 0.754396 0.865421i
\(987\) 0 0
\(988\) 474.153 65.3048i 0.479912 0.0660980i
\(989\) 1002.88 1002.88i 1.01404 1.01404i
\(990\) 0 0
\(991\) 514.565i 0.519238i −0.965711 0.259619i \(-0.916403\pi\)
0.965711 0.259619i \(-0.0835969\pi\)
\(992\) 386.202 + 1084.28i 0.389316 + 1.09303i
\(993\) 0 0
\(994\) −490.737 + 33.6357i −0.493699 + 0.0338388i
\(995\) −0.511545 0.511545i −0.000514115 0.000514115i
\(996\) 0 0
\(997\) −1249.59 1249.59i −1.25335 1.25335i −0.954208 0.299145i \(-0.903299\pi\)
−0.299145 0.954208i \(-0.596701\pi\)
\(998\) 766.023 + 667.751i 0.767558 + 0.669089i
\(999\) 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.b.91.8 yes 16
3.2 odd 2 inner 144.3.m.b.91.1 yes 16
4.3 odd 2 576.3.m.b.271.5 16
8.3 odd 2 1152.3.m.d.415.4 16
8.5 even 2 1152.3.m.e.415.4 16
12.11 even 2 576.3.m.b.271.4 16
16.3 odd 4 inner 144.3.m.b.19.8 yes 16
16.5 even 4 1152.3.m.d.991.4 16
16.11 odd 4 1152.3.m.e.991.4 16
16.13 even 4 576.3.m.b.559.5 16
24.5 odd 2 1152.3.m.e.415.5 16
24.11 even 2 1152.3.m.d.415.5 16
48.5 odd 4 1152.3.m.d.991.5 16
48.11 even 4 1152.3.m.e.991.5 16
48.29 odd 4 576.3.m.b.559.4 16
48.35 even 4 inner 144.3.m.b.19.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.3.m.b.19.1 16 48.35 even 4 inner
144.3.m.b.19.8 yes 16 16.3 odd 4 inner
144.3.m.b.91.1 yes 16 3.2 odd 2 inner
144.3.m.b.91.8 yes 16 1.1 even 1 trivial
576.3.m.b.271.4 16 12.11 even 2
576.3.m.b.271.5 16 4.3 odd 2
576.3.m.b.559.4 16 48.29 odd 4
576.3.m.b.559.5 16 16.13 even 4
1152.3.m.d.415.4 16 8.3 odd 2
1152.3.m.d.415.5 16 24.11 even 2
1152.3.m.d.991.4 16 16.5 even 4
1152.3.m.d.991.5 16 48.5 odd 4
1152.3.m.e.415.4 16 8.5 even 2
1152.3.m.e.415.5 16 24.5 odd 2
1152.3.m.e.991.4 16 16.11 odd 4
1152.3.m.e.991.5 16 48.11 even 4