Properties

Label 177.3.b.a.119.28
Level $177$
Weight $3$
Character 177.119
Analytic conductor $4.823$
Analytic rank $0$
Dimension $38$
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] = [177,3,Mod(119,177)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(177, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("177.119");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.28
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.90736i q^{2} +(-2.89185 - 0.798268i) q^{3} +0.361959 q^{4} -0.0951742i q^{5} +(1.52259 - 5.51580i) q^{6} -10.1724 q^{7} +8.31985i q^{8} +(7.72554 + 4.61693i) q^{9} +O(q^{10})\) \(q+1.90736i q^{2} +(-2.89185 - 0.798268i) q^{3} +0.361959 q^{4} -0.0951742i q^{5} +(1.52259 - 5.51580i) q^{6} -10.1724 q^{7} +8.31985i q^{8} +(7.72554 + 4.61693i) q^{9} +0.181532 q^{10} -21.4541i q^{11} +(-1.04673 - 0.288940i) q^{12} -18.5391 q^{13} -19.4024i q^{14} +(-0.0759745 + 0.275229i) q^{15} -14.4211 q^{16} -11.7919i q^{17} +(-8.80618 + 14.7354i) q^{18} -16.0947 q^{19} -0.0344492i q^{20} +(29.4169 + 8.12026i) q^{21} +40.9207 q^{22} -4.05406i q^{23} +(6.64147 - 24.0597i) q^{24} +24.9909 q^{25} -35.3609i q^{26} +(-18.6555 - 19.5185i) q^{27} -3.68198 q^{28} -13.2543i q^{29} +(-0.524962 - 0.144911i) q^{30} -10.0374 q^{31} +5.77300i q^{32} +(-17.1261 + 62.0418i) q^{33} +22.4915 q^{34} +0.968146i q^{35} +(2.79633 + 1.67114i) q^{36} -26.6736 q^{37} -30.6984i q^{38} +(53.6123 + 14.7992i) q^{39} +0.791835 q^{40} +42.3187i q^{41} +(-15.4883 + 56.1087i) q^{42} -55.1187 q^{43} -7.76549i q^{44} +(0.439413 - 0.735272i) q^{45} +7.73258 q^{46} +37.5402i q^{47} +(41.7037 + 11.5119i) q^{48} +54.4767 q^{49} +47.6668i q^{50} +(-9.41312 + 34.1005i) q^{51} -6.71041 q^{52} +72.8845i q^{53} +(37.2289 - 35.5829i) q^{54} -2.04187 q^{55} -84.6324i q^{56} +(46.5433 + 12.8478i) q^{57} +25.2809 q^{58} +7.68115i q^{59} +(-0.0274997 + 0.0996217i) q^{60} -69.0450 q^{61} -19.1451i q^{62} +(-78.5869 - 46.9651i) q^{63} -68.6958 q^{64} +1.76445i q^{65} +(-118.336 - 32.6657i) q^{66} +60.8758 q^{67} -4.26820i q^{68} +(-3.23623 + 11.7237i) q^{69} -1.84661 q^{70} -50.2583i q^{71} +(-38.4122 + 64.2753i) q^{72} +29.1706 q^{73} -50.8763i q^{74} +(-72.2699 - 19.9495i) q^{75} -5.82561 q^{76} +218.238i q^{77} +(-28.2275 + 102.258i) q^{78} +59.8769 q^{79} +1.37252i q^{80} +(38.3679 + 71.3366i) q^{81} -80.7172 q^{82} -92.7342i q^{83} +(10.6477 + 2.93920i) q^{84} -1.12229 q^{85} -105.131i q^{86} +(-10.5805 + 38.3295i) q^{87} +178.494 q^{88} -130.792i q^{89} +(1.40243 + 0.838121i) q^{90} +188.587 q^{91} -1.46741i q^{92} +(29.0267 + 8.01257i) q^{93} -71.6028 q^{94} +1.53180i q^{95} +(4.60840 - 16.6946i) q^{96} +68.0654 q^{97} +103.907i q^{98} +(99.0519 - 165.744i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 38 q - 76 q^{4} - 8 q^{6} - 12 q^{7} + 20 q^{9} + 36 q^{10} - 4 q^{13} - 17 q^{15} + 100 q^{16} - 2 q^{18} - 28 q^{19} - 11 q^{21} + 84 q^{22} - 6 q^{24} - 166 q^{25} + 3 q^{27} + 12 q^{28} + 102 q^{30} - 40 q^{31} - 46 q^{33} - 148 q^{34} - 96 q^{36} + 112 q^{37} + 62 q^{39} - 56 q^{40} + 14 q^{42} + 164 q^{43} + 55 q^{45} - 4 q^{46} - 124 q^{48} + 242 q^{49} + 52 q^{51} + 8 q^{52} + 18 q^{54} - 228 q^{55} - 147 q^{57} - 80 q^{58} + 128 q^{60} + 12 q^{61} + 86 q^{63} + 48 q^{64} - 24 q^{66} + 124 q^{67} - 240 q^{69} + 148 q^{70} + 166 q^{72} - 192 q^{73} - 78 q^{75} - 304 q^{76} + 244 q^{78} + 64 q^{79} - 156 q^{81} - 180 q^{82} + 300 q^{84} - 52 q^{85} - 83 q^{87} - 96 q^{88} - 376 q^{90} - 332 q^{91} + 454 q^{93} + 768 q^{94} - 722 q^{96} + 416 q^{97} + 494 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90736i 0.953682i 0.878989 + 0.476841i \(0.158218\pi\)
−0.878989 + 0.476841i \(0.841782\pi\)
\(3\) −2.89185 0.798268i −0.963948 0.266089i
\(4\) 0.361959 0.0904898
\(5\) 0.0951742i 0.0190348i −0.999955 0.00951742i \(-0.996970\pi\)
0.999955 0.00951742i \(-0.00302954\pi\)
\(6\) 1.52259 5.51580i 0.253765 0.919301i
\(7\) −10.1724 −1.45319 −0.726596 0.687064i \(-0.758899\pi\)
−0.726596 + 0.687064i \(0.758899\pi\)
\(8\) 8.31985i 1.03998i
\(9\) 7.72554 + 4.61693i 0.858393 + 0.512993i
\(10\) 0.181532 0.0181532
\(11\) 21.4541i 1.95037i −0.221395 0.975184i \(-0.571061\pi\)
0.221395 0.975184i \(-0.428939\pi\)
\(12\) −1.04673 0.288940i −0.0872275 0.0240784i
\(13\) −18.5391 −1.42609 −0.713043 0.701120i \(-0.752684\pi\)
−0.713043 + 0.701120i \(0.752684\pi\)
\(14\) 19.4024i 1.38588i
\(15\) −0.0759745 + 0.275229i −0.00506497 + 0.0183486i
\(16\) −14.4211 −0.901322
\(17\) 11.7919i 0.693643i −0.937931 0.346822i \(-0.887261\pi\)
0.937931 0.346822i \(-0.112739\pi\)
\(18\) −8.80618 + 14.7354i −0.489232 + 0.818634i
\(19\) −16.0947 −0.847087 −0.423544 0.905876i \(-0.639214\pi\)
−0.423544 + 0.905876i \(0.639214\pi\)
\(20\) 0.0344492i 0.00172246i
\(21\) 29.4169 + 8.12026i 1.40080 + 0.386679i
\(22\) 40.9207 1.86003
\(23\) 4.05406i 0.176264i −0.996109 0.0881318i \(-0.971910\pi\)
0.996109 0.0881318i \(-0.0280897\pi\)
\(24\) 6.64147 24.0597i 0.276728 1.00249i
\(25\) 24.9909 0.999638
\(26\) 35.3609i 1.36003i
\(27\) −18.6555 19.5185i −0.690945 0.722907i
\(28\) −3.68198 −0.131499
\(29\) 13.2543i 0.457046i −0.973538 0.228523i \(-0.926610\pi\)
0.973538 0.228523i \(-0.0733896\pi\)
\(30\) −0.524962 0.144911i −0.0174987 0.00483037i
\(31\) −10.0374 −0.323789 −0.161894 0.986808i \(-0.551760\pi\)
−0.161894 + 0.986808i \(0.551760\pi\)
\(32\) 5.77300i 0.180406i
\(33\) −17.1261 + 62.0418i −0.518972 + 1.88005i
\(34\) 22.4915 0.661516
\(35\) 0.968146i 0.0276613i
\(36\) 2.79633 + 1.67114i 0.0776758 + 0.0464206i
\(37\) −26.6736 −0.720908 −0.360454 0.932777i \(-0.617378\pi\)
−0.360454 + 0.932777i \(0.617378\pi\)
\(38\) 30.6984i 0.807852i
\(39\) 53.6123 + 14.7992i 1.37467 + 0.379466i
\(40\) 0.791835 0.0197959
\(41\) 42.3187i 1.03216i 0.856539 + 0.516082i \(0.172610\pi\)
−0.856539 + 0.516082i \(0.827390\pi\)
\(42\) −15.4883 + 56.1087i −0.368769 + 1.33592i
\(43\) −55.1187 −1.28183 −0.640915 0.767612i \(-0.721445\pi\)
−0.640915 + 0.767612i \(0.721445\pi\)
\(44\) 7.76549i 0.176488i
\(45\) 0.439413 0.735272i 0.00976474 0.0163394i
\(46\) 7.73258 0.168100
\(47\) 37.5402i 0.798727i 0.916793 + 0.399364i \(0.130769\pi\)
−0.916793 + 0.399364i \(0.869231\pi\)
\(48\) 41.7037 + 11.5119i 0.868828 + 0.239832i
\(49\) 54.4767 1.11177
\(50\) 47.6668i 0.953337i
\(51\) −9.41312 + 34.1005i −0.184571 + 0.668637i
\(52\) −6.71041 −0.129046
\(53\) 72.8845i 1.37518i 0.726099 + 0.687590i \(0.241331\pi\)
−0.726099 + 0.687590i \(0.758669\pi\)
\(54\) 37.2289 35.5829i 0.689424 0.658942i
\(55\) −2.04187 −0.0371250
\(56\) 84.6324i 1.51129i
\(57\) 46.5433 + 12.8478i 0.816549 + 0.225401i
\(58\) 25.2809 0.435877
\(59\) 7.68115i 0.130189i
\(60\) −0.0274997 + 0.0996217i −0.000458328 + 0.00166036i
\(61\) −69.0450 −1.13188 −0.565942 0.824445i \(-0.691488\pi\)
−0.565942 + 0.824445i \(0.691488\pi\)
\(62\) 19.1451i 0.308792i
\(63\) −78.5869 46.9651i −1.24741 0.745477i
\(64\) −68.6958 −1.07337
\(65\) 1.76445i 0.0271453i
\(66\) −118.336 32.6657i −1.79298 0.494935i
\(67\) 60.8758 0.908594 0.454297 0.890850i \(-0.349890\pi\)
0.454297 + 0.890850i \(0.349890\pi\)
\(68\) 4.26820i 0.0627676i
\(69\) −3.23623 + 11.7237i −0.0469019 + 0.169909i
\(70\) −1.84661 −0.0263801
\(71\) 50.2583i 0.707864i −0.935271 0.353932i \(-0.884844\pi\)
0.935271 0.353932i \(-0.115156\pi\)
\(72\) −38.4122 + 64.2753i −0.533502 + 0.892712i
\(73\) 29.1706 0.399597 0.199799 0.979837i \(-0.435971\pi\)
0.199799 + 0.979837i \(0.435971\pi\)
\(74\) 50.8763i 0.687518i
\(75\) −72.2699 19.9495i −0.963599 0.265993i
\(76\) −5.82561 −0.0766528
\(77\) 218.238i 2.83426i
\(78\) −28.2275 + 102.258i −0.361890 + 1.31100i
\(79\) 59.8769 0.757936 0.378968 0.925410i \(-0.376279\pi\)
0.378968 + 0.925410i \(0.376279\pi\)
\(80\) 1.37252i 0.0171565i
\(81\) 38.3679 + 71.3366i 0.473677 + 0.880698i
\(82\) −80.7172 −0.984356
\(83\) 92.7342i 1.11728i −0.829411 0.558640i \(-0.811324\pi\)
0.829411 0.558640i \(-0.188676\pi\)
\(84\) 10.6477 + 2.93920i 0.126758 + 0.0349905i
\(85\) −1.12229 −0.0132034
\(86\) 105.131i 1.22246i
\(87\) −10.5805 + 38.3295i −0.121615 + 0.440569i
\(88\) 178.494 2.02835
\(89\) 130.792i 1.46957i −0.678298 0.734787i \(-0.737282\pi\)
0.678298 0.734787i \(-0.262718\pi\)
\(90\) 1.40243 + 0.838121i 0.0155826 + 0.00931246i
\(91\) 188.587 2.07238
\(92\) 1.46741i 0.0159501i
\(93\) 29.0267 + 8.01257i 0.312116 + 0.0861567i
\(94\) −71.6028 −0.761732
\(95\) 1.53180i 0.0161242i
\(96\) 4.60840 16.6946i 0.0480041 0.173902i
\(97\) 68.0654 0.701705 0.350852 0.936431i \(-0.385892\pi\)
0.350852 + 0.936431i \(0.385892\pi\)
\(98\) 103.907i 1.06028i
\(99\) 99.0519 165.744i 1.00052 1.67418i
\(100\) 9.04570 0.0904570
\(101\) 132.603i 1.31290i 0.754371 + 0.656449i \(0.227942\pi\)
−0.754371 + 0.656449i \(0.772058\pi\)
\(102\) −65.0420 17.9543i −0.637667 0.176022i
\(103\) −15.8984 −0.154353 −0.0771767 0.997017i \(-0.524591\pi\)
−0.0771767 + 0.997017i \(0.524591\pi\)
\(104\) 154.243i 1.48310i
\(105\) 0.772839 2.79973i 0.00736038 0.0266641i
\(106\) −139.017 −1.31148
\(107\) 118.559i 1.10803i −0.832508 0.554013i \(-0.813096\pi\)
0.832508 0.554013i \(-0.186904\pi\)
\(108\) −6.75253 7.06490i −0.0625234 0.0654157i
\(109\) 71.1676 0.652914 0.326457 0.945212i \(-0.394145\pi\)
0.326457 + 0.945212i \(0.394145\pi\)
\(110\) 3.89460i 0.0354054i
\(111\) 77.1359 + 21.2927i 0.694918 + 0.191826i
\(112\) 146.697 1.30979
\(113\) 13.6200i 0.120531i 0.998182 + 0.0602654i \(0.0191947\pi\)
−0.998182 + 0.0602654i \(0.980805\pi\)
\(114\) −24.5055 + 88.7750i −0.214961 + 0.778728i
\(115\) −0.385842 −0.00335515
\(116\) 4.79753i 0.0413580i
\(117\) −143.225 85.5939i −1.22414 0.731572i
\(118\) −14.6507 −0.124159
\(119\) 119.952i 1.00800i
\(120\) −2.28986 0.632096i −0.0190822 0.00526747i
\(121\) −339.276 −2.80394
\(122\) 131.694i 1.07946i
\(123\) 33.7817 122.379i 0.274648 0.994953i
\(124\) −3.63315 −0.0292996
\(125\) 4.75785i 0.0380628i
\(126\) 89.5795 149.894i 0.710948 1.18963i
\(127\) −120.467 −0.948557 −0.474279 0.880375i \(-0.657291\pi\)
−0.474279 + 0.880375i \(0.657291\pi\)
\(128\) 107.936i 0.843250i
\(129\) 159.395 + 43.9995i 1.23562 + 0.341081i
\(130\) −3.36545 −0.0258880
\(131\) 210.339i 1.60564i 0.596221 + 0.802820i \(0.296668\pi\)
−0.596221 + 0.802820i \(0.703332\pi\)
\(132\) −6.19894 + 22.4566i −0.0469617 + 0.170126i
\(133\) 163.721 1.23098
\(134\) 116.112i 0.866511i
\(135\) −1.85766 + 1.77552i −0.0137604 + 0.0131520i
\(136\) 98.1071 0.721376
\(137\) 228.804i 1.67010i −0.550170 0.835052i \(-0.685437\pi\)
0.550170 0.835052i \(-0.314563\pi\)
\(138\) −22.3614 6.17267i −0.162039 0.0447295i
\(139\) −235.370 −1.69331 −0.846655 0.532142i \(-0.821387\pi\)
−0.846655 + 0.532142i \(0.821387\pi\)
\(140\) 0.350429i 0.00250307i
\(141\) 29.9671 108.560i 0.212533 0.769932i
\(142\) 95.8609 0.675077
\(143\) 397.739i 2.78140i
\(144\) −111.411 66.5815i −0.773688 0.462371i
\(145\) −1.26147 −0.00869981
\(146\) 55.6390i 0.381089i
\(147\) −157.538 43.4870i −1.07169 0.295830i
\(148\) −9.65476 −0.0652348
\(149\) 52.3287i 0.351200i −0.984462 0.175600i \(-0.943814\pi\)
0.984462 0.175600i \(-0.0561865\pi\)
\(150\) 38.0509 137.845i 0.253673 0.918968i
\(151\) 182.444 1.20824 0.604121 0.796893i \(-0.293525\pi\)
0.604121 + 0.796893i \(0.293525\pi\)
\(152\) 133.905i 0.880955i
\(153\) 54.4426 91.0991i 0.355834 0.595419i
\(154\) −416.260 −2.70299
\(155\) 0.955307i 0.00616327i
\(156\) 19.4055 + 5.35670i 0.124394 + 0.0343378i
\(157\) −274.716 −1.74978 −0.874891 0.484320i \(-0.839067\pi\)
−0.874891 + 0.484320i \(0.839067\pi\)
\(158\) 114.207i 0.722830i
\(159\) 58.1814 210.771i 0.365920 1.32560i
\(160\) 0.549441 0.00343400
\(161\) 41.2394i 0.256145i
\(162\) −136.065 + 73.1815i −0.839907 + 0.451738i
\(163\) 94.9693 0.582634 0.291317 0.956627i \(-0.405907\pi\)
0.291317 + 0.956627i \(0.405907\pi\)
\(164\) 15.3176i 0.0934003i
\(165\) 5.90478 + 1.62996i 0.0357866 + 0.00987855i
\(166\) 176.878 1.06553
\(167\) 195.343i 1.16972i −0.811136 0.584858i \(-0.801150\pi\)
0.811136 0.584858i \(-0.198850\pi\)
\(168\) −67.5593 + 244.744i −0.402139 + 1.45681i
\(169\) 174.699 1.03372
\(170\) 2.14061i 0.0125918i
\(171\) −124.340 74.3080i −0.727134 0.434550i
\(172\) −19.9507 −0.115993
\(173\) 188.675i 1.09061i −0.838238 0.545304i \(-0.816414\pi\)
0.838238 0.545304i \(-0.183586\pi\)
\(174\) −73.1083 20.1809i −0.420163 0.115982i
\(175\) −254.217 −1.45267
\(176\) 309.392i 1.75791i
\(177\) 6.13161 22.2127i 0.0346419 0.125495i
\(178\) 249.468 1.40151
\(179\) 196.729i 1.09904i −0.835479 0.549522i \(-0.814810\pi\)
0.835479 0.549522i \(-0.185190\pi\)
\(180\) 0.159050 0.266138i 0.000883609 0.00147855i
\(181\) 14.7951 0.0817407 0.0408704 0.999164i \(-0.486987\pi\)
0.0408704 + 0.999164i \(0.486987\pi\)
\(182\) 359.703i 1.97639i
\(183\) 199.667 + 55.1164i 1.09108 + 0.301182i
\(184\) 33.7292 0.183311
\(185\) 2.53864i 0.0137224i
\(186\) −15.2829 + 55.3646i −0.0821661 + 0.297659i
\(187\) −252.985 −1.35286
\(188\) 13.5880i 0.0722766i
\(189\) 189.770 + 198.549i 1.00408 + 1.05052i
\(190\) −2.92170 −0.0153773
\(191\) 122.673i 0.642268i −0.947034 0.321134i \(-0.895936\pi\)
0.947034 0.321134i \(-0.104064\pi\)
\(192\) 198.658 + 54.8376i 1.03468 + 0.285613i
\(193\) 201.864 1.04593 0.522963 0.852355i \(-0.324827\pi\)
0.522963 + 0.852355i \(0.324827\pi\)
\(194\) 129.826i 0.669204i
\(195\) 1.40850 5.10251i 0.00722308 0.0261667i
\(196\) 19.7183 0.100604
\(197\) 123.704i 0.627938i 0.949433 + 0.313969i \(0.101659\pi\)
−0.949433 + 0.313969i \(0.898341\pi\)
\(198\) 316.134 + 188.928i 1.59664 + 0.954183i
\(199\) −111.272 −0.559158 −0.279579 0.960123i \(-0.590195\pi\)
−0.279579 + 0.960123i \(0.590195\pi\)
\(200\) 207.921i 1.03960i
\(201\) −176.043 48.5952i −0.875838 0.241767i
\(202\) −252.922 −1.25209
\(203\) 134.828i 0.664176i
\(204\) −3.40717 + 12.3430i −0.0167018 + 0.0605048i
\(205\) 4.02765 0.0196471
\(206\) 30.3241i 0.147204i
\(207\) 18.7173 31.3198i 0.0904219 0.151303i
\(208\) 267.356 1.28536
\(209\) 345.296i 1.65213i
\(210\) 5.34010 + 1.47409i 0.0254291 + 0.00701946i
\(211\) −209.476 −0.992777 −0.496388 0.868101i \(-0.665341\pi\)
−0.496388 + 0.868101i \(0.665341\pi\)
\(212\) 26.3812i 0.124440i
\(213\) −40.1196 + 145.339i −0.188355 + 0.682344i
\(214\) 226.135 1.05671
\(215\) 5.24588i 0.0243994i
\(216\) 162.391 155.211i 0.751810 0.718569i
\(217\) 102.104 0.470527
\(218\) 135.743i 0.622673i
\(219\) −84.3569 23.2860i −0.385191 0.106329i
\(220\) −0.739075 −0.00335943
\(221\) 218.612i 0.989196i
\(222\) −40.6129 + 147.126i −0.182941 + 0.662732i
\(223\) −98.8711 −0.443368 −0.221684 0.975119i \(-0.571155\pi\)
−0.221684 + 0.975119i \(0.571155\pi\)
\(224\) 58.7250i 0.262165i
\(225\) 193.068 + 115.382i 0.858082 + 0.512807i
\(226\) −25.9783 −0.114948
\(227\) 266.082i 1.17217i −0.810251 0.586083i \(-0.800669\pi\)
0.810251 0.586083i \(-0.199331\pi\)
\(228\) 16.8468 + 4.65040i 0.0738893 + 0.0203965i
\(229\) 94.9380 0.414577 0.207288 0.978280i \(-0.433536\pi\)
0.207288 + 0.978280i \(0.433536\pi\)
\(230\) 0.735942i 0.00319975i
\(231\) 174.212 631.111i 0.754167 2.73208i
\(232\) 110.274 0.475319
\(233\) 11.1408i 0.0478147i −0.999714 0.0239073i \(-0.992389\pi\)
0.999714 0.0239073i \(-0.00761067\pi\)
\(234\) 163.259 273.182i 0.697687 1.16744i
\(235\) 3.57286 0.0152036
\(236\) 2.78026i 0.0117808i
\(237\) −173.155 47.7978i −0.730611 0.201679i
\(238\) −228.792 −0.961310
\(239\) 102.629i 0.429410i 0.976679 + 0.214705i \(0.0688791\pi\)
−0.976679 + 0.214705i \(0.931121\pi\)
\(240\) 1.09564 3.96912i 0.00456517 0.0165380i
\(241\) 135.675 0.562968 0.281484 0.959566i \(-0.409173\pi\)
0.281484 + 0.959566i \(0.409173\pi\)
\(242\) 647.124i 2.67407i
\(243\) −54.0082 236.922i −0.222256 0.974988i
\(244\) −24.9915 −0.102424
\(245\) 5.18478i 0.0211624i
\(246\) 233.422 + 64.4339i 0.948869 + 0.261927i
\(247\) 298.381 1.20802
\(248\) 83.5100i 0.336734i
\(249\) −74.0267 + 268.173i −0.297296 + 1.07700i
\(250\) 9.07496 0.0362998
\(251\) 209.115i 0.833129i 0.909106 + 0.416564i \(0.136766\pi\)
−0.909106 + 0.416564i \(0.863234\pi\)
\(252\) −28.4452 16.9994i −0.112878 0.0674581i
\(253\) −86.9761 −0.343779
\(254\) 229.774i 0.904622i
\(255\) 3.24549 + 0.895887i 0.0127274 + 0.00351328i
\(256\) −68.9099 −0.269179
\(257\) 280.472i 1.09133i 0.838003 + 0.545665i \(0.183723\pi\)
−0.838003 + 0.545665i \(0.816277\pi\)
\(258\) −83.9231 + 304.024i −0.325283 + 1.17839i
\(259\) 271.333 1.04762
\(260\) 0.638658i 0.00245638i
\(261\) 61.1944 102.397i 0.234461 0.392325i
\(262\) −401.193 −1.53127
\(263\) 488.477i 1.85733i 0.370925 + 0.928663i \(0.379041\pi\)
−0.370925 + 0.928663i \(0.620959\pi\)
\(264\) −516.178 142.486i −1.95522 0.539721i
\(265\) 6.93673 0.0261763
\(266\) 312.275i 1.17397i
\(267\) −104.407 + 378.231i −0.391038 + 1.41659i
\(268\) 22.0346 0.0822185
\(269\) 289.117i 1.07479i −0.843332 0.537393i \(-0.819409\pi\)
0.843332 0.537393i \(-0.180591\pi\)
\(270\) −3.38657 3.54323i −0.0125429 0.0131231i
\(271\) −173.151 −0.638934 −0.319467 0.947597i \(-0.603504\pi\)
−0.319467 + 0.947597i \(0.603504\pi\)
\(272\) 170.053i 0.625196i
\(273\) −545.363 150.543i −1.99767 0.551438i
\(274\) 436.413 1.59275
\(275\) 536.157i 1.94966i
\(276\) −1.17138 + 4.24351i −0.00424414 + 0.0153750i
\(277\) −27.0948 −0.0978152 −0.0489076 0.998803i \(-0.515574\pi\)
−0.0489076 + 0.998803i \(0.515574\pi\)
\(278\) 448.937i 1.61488i
\(279\) −77.5447 46.3422i −0.277938 0.166101i
\(280\) −8.05483 −0.0287672
\(281\) 39.5691i 0.140815i −0.997518 0.0704076i \(-0.977570\pi\)
0.997518 0.0704076i \(-0.0224300\pi\)
\(282\) 207.064 + 57.1582i 0.734270 + 0.202689i
\(283\) −25.8831 −0.0914599 −0.0457299 0.998954i \(-0.514561\pi\)
−0.0457299 + 0.998954i \(0.514561\pi\)
\(284\) 18.1915i 0.0640544i
\(285\) 1.22278 4.42972i 0.00429047 0.0155429i
\(286\) −758.634 −2.65257
\(287\) 430.481i 1.49993i
\(288\) −26.6535 + 44.5995i −0.0925470 + 0.154859i
\(289\) 149.950 0.518859
\(290\) 2.40609i 0.00829685i
\(291\) −196.835 54.3344i −0.676407 0.186716i
\(292\) 10.5586 0.0361595
\(293\) 344.114i 1.17445i 0.809424 + 0.587225i \(0.199780\pi\)
−0.809424 + 0.587225i \(0.800220\pi\)
\(294\) 82.9456 300.483i 0.282128 1.02205i
\(295\) 0.731047 0.00247813
\(296\) 221.920i 0.749731i
\(297\) −418.751 + 400.236i −1.40994 + 1.34760i
\(298\) 99.8100 0.334933
\(299\) 75.1588i 0.251367i
\(300\) −26.1588 7.22089i −0.0871959 0.0240696i
\(301\) 560.687 1.86275
\(302\) 347.988i 1.15228i
\(303\) 105.852 383.466i 0.349348 1.26557i
\(304\) 232.103 0.763498
\(305\) 6.57130i 0.0215453i
\(306\) 173.759 + 103.842i 0.567840 + 0.339353i
\(307\) 398.833 1.29913 0.649565 0.760306i \(-0.274951\pi\)
0.649565 + 0.760306i \(0.274951\pi\)
\(308\) 78.9933i 0.256472i
\(309\) 45.9757 + 12.6912i 0.148789 + 0.0410718i
\(310\) −1.82212 −0.00587780
\(311\) 369.284i 1.18741i −0.804684 0.593704i \(-0.797665\pi\)
0.804684 0.593704i \(-0.202335\pi\)
\(312\) −123.127 + 446.046i −0.394638 + 1.42964i
\(313\) −132.228 −0.422455 −0.211228 0.977437i \(-0.567746\pi\)
−0.211228 + 0.977437i \(0.567746\pi\)
\(314\) 523.983i 1.66874i
\(315\) −4.46986 + 7.47945i −0.0141900 + 0.0237443i
\(316\) 21.6730 0.0685854
\(317\) 321.344i 1.01370i −0.862033 0.506852i \(-0.830809\pi\)
0.862033 0.506852i \(-0.169191\pi\)
\(318\) 402.017 + 110.973i 1.26420 + 0.348972i
\(319\) −284.359 −0.891409
\(320\) 6.53807i 0.0204315i
\(321\) −94.6417 + 342.854i −0.294834 + 1.06808i
\(322\) −78.6585 −0.244281
\(323\) 189.787i 0.587577i
\(324\) 13.8876 + 25.8209i 0.0428630 + 0.0796942i
\(325\) −463.310 −1.42557
\(326\) 181.141i 0.555647i
\(327\) −205.806 56.8108i −0.629376 0.173733i
\(328\) −352.085 −1.07343
\(329\) 381.872i 1.16070i
\(330\) −3.10893 + 11.2626i −0.00942100 + 0.0341290i
\(331\) 2.24571 0.00678462 0.00339231 0.999994i \(-0.498920\pi\)
0.00339231 + 0.999994i \(0.498920\pi\)
\(332\) 33.5660i 0.101102i
\(333\) −206.068 123.150i −0.618823 0.369821i
\(334\) 372.590 1.11554
\(335\) 5.79381i 0.0172950i
\(336\) −424.225 117.103i −1.26257 0.348522i
\(337\) −336.616 −0.998860 −0.499430 0.866354i \(-0.666457\pi\)
−0.499430 + 0.866354i \(0.666457\pi\)
\(338\) 333.215i 0.985844i
\(339\) 10.8724 39.3869i 0.0320720 0.116186i
\(340\) −0.406223 −0.00119477
\(341\) 215.344i 0.631507i
\(342\) 141.732 237.162i 0.414422 0.693455i
\(343\) −55.7111 −0.162423
\(344\) 458.579i 1.33308i
\(345\) 1.11580 + 0.308006i 0.00323419 + 0.000892770i
\(346\) 359.873 1.04009
\(347\) 84.3858i 0.243187i 0.992580 + 0.121593i \(0.0388004\pi\)
−0.992580 + 0.121593i \(0.961200\pi\)
\(348\) −3.82971 + 13.8737i −0.0110049 + 0.0398670i
\(349\) −300.424 −0.860814 −0.430407 0.902635i \(-0.641630\pi\)
−0.430407 + 0.902635i \(0.641630\pi\)
\(350\) 484.884i 1.38538i
\(351\) 345.857 + 361.856i 0.985347 + 1.03093i
\(352\) 123.854 0.351858
\(353\) 541.944i 1.53525i −0.640898 0.767626i \(-0.721438\pi\)
0.640898 0.767626i \(-0.278562\pi\)
\(354\) 42.3677 + 11.6952i 0.119683 + 0.0330373i
\(355\) −4.78330 −0.0134741
\(356\) 47.3414i 0.132981i
\(357\) 95.7536 346.882i 0.268217 0.971658i
\(358\) 375.234 1.04814
\(359\) 247.949i 0.690666i 0.938480 + 0.345333i \(0.112234\pi\)
−0.938480 + 0.345333i \(0.887766\pi\)
\(360\) 6.11735 + 3.65585i 0.0169926 + 0.0101551i
\(361\) −101.962 −0.282443
\(362\) 28.2196i 0.0779547i
\(363\) 981.135 + 270.833i 2.70285 + 0.746098i
\(364\) 68.2606 0.187529
\(365\) 2.77629i 0.00760628i
\(366\) −105.127 + 380.839i −0.287232 + 1.04054i
\(367\) 368.950 1.00531 0.502656 0.864486i \(-0.332356\pi\)
0.502656 + 0.864486i \(0.332356\pi\)
\(368\) 58.4643i 0.158870i
\(369\) −195.383 + 326.935i −0.529492 + 0.886002i
\(370\) −4.84211 −0.0130868
\(371\) 741.407i 1.99840i
\(372\) 10.5065 + 2.90022i 0.0282433 + 0.00779630i
\(373\) −16.6190 −0.0445549 −0.0222775 0.999752i \(-0.507092\pi\)
−0.0222775 + 0.999752i \(0.507092\pi\)
\(374\) 482.534i 1.29020i
\(375\) −3.79804 + 13.7590i −0.0101281 + 0.0366906i
\(376\) −312.329 −0.830661
\(377\) 245.724i 0.651788i
\(378\) −378.705 + 361.961i −1.00187 + 0.957570i
\(379\) 181.804 0.479694 0.239847 0.970811i \(-0.422903\pi\)
0.239847 + 0.970811i \(0.422903\pi\)
\(380\) 0.554448i 0.00145907i
\(381\) 348.371 + 96.1647i 0.914360 + 0.252401i
\(382\) 233.982 0.612520
\(383\) 254.866i 0.665445i 0.943025 + 0.332723i \(0.107967\pi\)
−0.943025 + 0.332723i \(0.892033\pi\)
\(384\) −86.1618 + 312.134i −0.224380 + 0.812849i
\(385\) 20.7707 0.0539497
\(386\) 385.028i 0.997481i
\(387\) −425.822 254.479i −1.10031 0.657569i
\(388\) 24.6369 0.0634971
\(389\) 613.478i 1.57706i −0.614993 0.788532i \(-0.710841\pi\)
0.614993 0.788532i \(-0.289159\pi\)
\(390\) 9.73235 + 2.68653i 0.0249547 + 0.00688853i
\(391\) −47.8053 −0.122264
\(392\) 453.238i 1.15622i
\(393\) 167.907 608.268i 0.427244 1.54775i
\(394\) −235.948 −0.598854
\(395\) 5.69874i 0.0144272i
\(396\) 35.8527 59.9926i 0.0905372 0.151496i
\(397\) 534.070 1.34526 0.672632 0.739977i \(-0.265164\pi\)
0.672632 + 0.739977i \(0.265164\pi\)
\(398\) 212.237i 0.533259i
\(399\) −473.454 130.693i −1.18660 0.327551i
\(400\) −360.398 −0.900995
\(401\) 674.374i 1.68173i 0.541245 + 0.840865i \(0.317953\pi\)
−0.541245 + 0.840865i \(0.682047\pi\)
\(402\) 92.6888 335.779i 0.230569 0.835272i
\(403\) 186.086 0.461751
\(404\) 47.9967i 0.118804i
\(405\) 6.78940 3.65163i 0.0167640 0.00901637i
\(406\) −257.166 −0.633413
\(407\) 572.257i 1.40604i
\(408\) −283.711 78.3158i −0.695369 0.191950i
\(409\) 592.660 1.44905 0.724523 0.689251i \(-0.242060\pi\)
0.724523 + 0.689251i \(0.242060\pi\)
\(410\) 7.68220i 0.0187371i
\(411\) −182.647 + 661.667i −0.444397 + 1.60989i
\(412\) −5.75457 −0.0139674
\(413\) 78.1353i 0.189190i
\(414\) 59.7383 + 35.7008i 0.144295 + 0.0862338i
\(415\) −8.82590 −0.0212672
\(416\) 107.026i 0.257275i
\(417\) 680.654 + 187.888i 1.63226 + 0.450571i
\(418\) −658.605 −1.57561
\(419\) 218.340i 0.521098i −0.965461 0.260549i \(-0.916096\pi\)
0.965461 0.260549i \(-0.0839036\pi\)
\(420\) 0.279736 1.01339i 0.000666039 0.00241283i
\(421\) 262.667 0.623913 0.311957 0.950096i \(-0.399016\pi\)
0.311957 + 0.950096i \(0.399016\pi\)
\(422\) 399.547i 0.946794i
\(423\) −173.320 + 290.018i −0.409741 + 0.685622i
\(424\) −606.388 −1.43016
\(425\) 294.692i 0.693392i
\(426\) −277.215 76.5227i −0.650739 0.179631i
\(427\) 702.350 1.64485
\(428\) 42.9134i 0.100265i
\(429\) 317.503 1150.20i 0.740099 2.68112i
\(430\) −10.0058 −0.0232693
\(431\) 139.875i 0.324536i 0.986747 + 0.162268i \(0.0518809\pi\)
−0.986747 + 0.162268i \(0.948119\pi\)
\(432\) 269.034 + 281.479i 0.622764 + 0.651572i
\(433\) −41.8624 −0.0966799 −0.0483399 0.998831i \(-0.515393\pi\)
−0.0483399 + 0.998831i \(0.515393\pi\)
\(434\) 194.750i 0.448734i
\(435\) 3.64798 + 1.00699i 0.00838616 + 0.00231492i
\(436\) 25.7598 0.0590821
\(437\) 65.2488i 0.149311i
\(438\) 44.4148 160.899i 0.101404 0.367350i
\(439\) −453.852 −1.03383 −0.516916 0.856036i \(-0.672920\pi\)
−0.516916 + 0.856036i \(0.672920\pi\)
\(440\) 16.9881i 0.0386093i
\(441\) 420.862 + 251.515i 0.954335 + 0.570330i
\(442\) −416.973 −0.943379
\(443\) 247.987i 0.559789i 0.960031 + 0.279895i \(0.0902995\pi\)
−0.960031 + 0.279895i \(0.909700\pi\)
\(444\) 27.9201 + 7.70708i 0.0628830 + 0.0173583i
\(445\) −12.4480 −0.0279731
\(446\) 188.583i 0.422832i
\(447\) −41.7723 + 151.327i −0.0934504 + 0.338538i
\(448\) 698.798 1.55982
\(449\) 682.664i 1.52041i 0.649683 + 0.760205i \(0.274902\pi\)
−0.649683 + 0.760205i \(0.725098\pi\)
\(450\) −220.075 + 368.252i −0.489055 + 0.818338i
\(451\) 907.908 2.01310
\(452\) 4.92988i 0.0109068i
\(453\) −527.601 145.639i −1.16468 0.321500i
\(454\) 507.515 1.11787
\(455\) 17.9486i 0.0394474i
\(456\) −106.892 + 387.233i −0.234413 + 0.849195i
\(457\) −379.628 −0.830696 −0.415348 0.909662i \(-0.636340\pi\)
−0.415348 + 0.909662i \(0.636340\pi\)
\(458\) 181.081i 0.395374i
\(459\) −230.161 + 219.985i −0.501440 + 0.479269i
\(460\) −0.139659 −0.000303607
\(461\) 419.873i 0.910788i −0.890290 0.455394i \(-0.849498\pi\)
0.890290 0.455394i \(-0.150502\pi\)
\(462\) 1203.76 + 332.287i 2.60554 + 0.719235i
\(463\) −885.854 −1.91329 −0.956646 0.291253i \(-0.905928\pi\)
−0.956646 + 0.291253i \(0.905928\pi\)
\(464\) 191.143i 0.411946i
\(465\) 0.762590 2.76260i 0.00163998 0.00594107i
\(466\) 21.2496 0.0456000
\(467\) 393.302i 0.842188i 0.907017 + 0.421094i \(0.138354\pi\)
−0.907017 + 0.421094i \(0.861646\pi\)
\(468\) −51.8415 30.9815i −0.110772 0.0661998i
\(469\) −619.250 −1.32036
\(470\) 6.81474i 0.0144995i
\(471\) 794.435 + 219.297i 1.68670 + 0.465598i
\(472\) −63.9060 −0.135394
\(473\) 1182.52i 2.50004i
\(474\) 91.1679 330.269i 0.192337 0.696771i
\(475\) −402.221 −0.846780
\(476\) 43.4176i 0.0912135i
\(477\) −336.503 + 563.072i −0.705457 + 1.18044i
\(478\) −195.751 −0.409521
\(479\) 32.5927i 0.0680432i −0.999421 0.0340216i \(-0.989168\pi\)
0.999421 0.0340216i \(-0.0108315\pi\)
\(480\) −1.58890 0.438601i −0.00331020 0.000913751i
\(481\) 494.506 1.02808
\(482\) 258.782i 0.536892i
\(483\) 32.9200 119.258i 0.0681574 0.246911i
\(484\) −122.804 −0.253728
\(485\) 6.47807i 0.0133568i
\(486\) 451.897 103.013i 0.929829 0.211962i
\(487\) 12.9619 0.0266157 0.0133079 0.999911i \(-0.495764\pi\)
0.0133079 + 0.999911i \(0.495764\pi\)
\(488\) 574.444i 1.17714i
\(489\) −274.636 75.8109i −0.561629 0.155033i
\(490\) 9.88927 0.0201822
\(491\) 70.7457i 0.144085i 0.997402 + 0.0720425i \(0.0229517\pi\)
−0.997402 + 0.0720425i \(0.977048\pi\)
\(492\) 12.2276 44.2963i 0.0248528 0.0900330i
\(493\) −156.294 −0.317027
\(494\) 569.121i 1.15207i
\(495\) −15.7746 9.42719i −0.0318678 0.0190448i
\(496\) 144.752 0.291838
\(497\) 511.245i 1.02866i
\(498\) −511.504 141.196i −1.02712 0.283526i
\(499\) −497.143 −0.996279 −0.498140 0.867097i \(-0.665983\pi\)
−0.498140 + 0.867097i \(0.665983\pi\)
\(500\) 1.72215i 0.00344429i
\(501\) −155.936 + 564.901i −0.311249 + 1.12755i
\(502\) −398.859 −0.794540
\(503\) 302.588i 0.601567i −0.953692 0.300783i \(-0.902752\pi\)
0.953692 0.300783i \(-0.0972481\pi\)
\(504\) 390.742 653.831i 0.775282 1.29728i
\(505\) 12.6204 0.0249908
\(506\) 165.895i 0.327856i
\(507\) −505.203 139.457i −0.996457 0.275063i
\(508\) −43.6040 −0.0858347
\(509\) 44.8634i 0.0881402i −0.999028 0.0440701i \(-0.985968\pi\)
0.999028 0.0440701i \(-0.0140325\pi\)
\(510\) −1.70878 + 6.19033i −0.00335056 + 0.0121379i
\(511\) −296.734 −0.580692
\(512\) 563.180i 1.09996i
\(513\) 300.254 + 314.144i 0.585291 + 0.612366i
\(514\) −534.963 −1.04078
\(515\) 1.51312i 0.00293809i
\(516\) 57.6944 + 15.9260i 0.111811 + 0.0308644i
\(517\) 805.389 1.55781
\(518\) 517.532i 0.999096i
\(519\) −150.613 + 545.620i −0.290199 + 1.05129i
\(520\) −14.6799 −0.0282306
\(521\) 57.9774i 0.111281i −0.998451 0.0556405i \(-0.982280\pi\)
0.998451 0.0556405i \(-0.0177201\pi\)
\(522\) 195.308 + 116.720i 0.374154 + 0.223602i
\(523\) −681.136 −1.30236 −0.651182 0.758922i \(-0.725726\pi\)
−0.651182 + 0.758922i \(0.725726\pi\)
\(524\) 76.1341i 0.145294i
\(525\) 735.155 + 202.933i 1.40030 + 0.386539i
\(526\) −931.703 −1.77130
\(527\) 118.361i 0.224594i
\(528\) 246.978 894.714i 0.467761 1.69453i
\(529\) 512.565 0.968931
\(530\) 13.2309i 0.0249639i
\(531\) −35.4633 + 59.3410i −0.0667859 + 0.111753i
\(532\) 59.2601 0.111391
\(533\) 784.552i 1.47196i
\(534\) −721.424 199.142i −1.35098 0.372926i
\(535\) −11.2837 −0.0210911
\(536\) 506.478i 0.944921i
\(537\) −157.042 + 568.910i −0.292444 + 1.05942i
\(538\) 551.452 1.02500
\(539\) 1168.75i 2.16836i
\(540\) −0.672396 + 0.642667i −0.00124518 + 0.00119012i
\(541\) −449.122 −0.830170 −0.415085 0.909783i \(-0.636248\pi\)
−0.415085 + 0.909783i \(0.636248\pi\)
\(542\) 330.263i 0.609340i
\(543\) −42.7851 11.8104i −0.0787939 0.0217503i
\(544\) 68.0748 0.125138
\(545\) 6.77333i 0.0124281i
\(546\) 287.140 1040.21i 0.525897 1.90514i
\(547\) −161.571 −0.295377 −0.147689 0.989034i \(-0.547183\pi\)
−0.147689 + 0.989034i \(0.547183\pi\)
\(548\) 82.8178i 0.151127i
\(549\) −533.410 318.776i −0.971602 0.580649i
\(550\) 1022.65 1.85936
\(551\) 213.324i 0.387158i
\(552\) −97.5396 26.9249i −0.176702 0.0487770i
\(553\) −609.089 −1.10143
\(554\) 51.6797i 0.0932846i
\(555\) 2.02651 7.34136i 0.00365138 0.0132277i
\(556\) −85.1943 −0.153227
\(557\) 1097.79i 1.97090i −0.169975 0.985448i \(-0.554369\pi\)
0.169975 0.985448i \(-0.445631\pi\)
\(558\) 88.3915 147.906i 0.158408 0.265065i
\(559\) 1021.85 1.82800
\(560\) 13.9618i 0.0249317i
\(561\) 731.593 + 201.950i 1.30409 + 0.359982i
\(562\) 75.4727 0.134293
\(563\) 310.918i 0.552252i −0.961121 0.276126i \(-0.910949\pi\)
0.961121 0.276126i \(-0.0890507\pi\)
\(564\) 10.8469 39.2944i 0.0192320 0.0696710i
\(565\) 1.29627 0.00229429
\(566\) 49.3686i 0.0872237i
\(567\) −390.291 725.661i −0.688344 1.27982i
\(568\) 418.142 0.736165
\(569\) 465.717i 0.818484i −0.912426 0.409242i \(-0.865793\pi\)
0.912426 0.409242i \(-0.134207\pi\)
\(570\) 8.44909 + 2.33230i 0.0148230 + 0.00409175i
\(571\) 208.273 0.364752 0.182376 0.983229i \(-0.441621\pi\)
0.182376 + 0.983229i \(0.441621\pi\)
\(572\) 143.965i 0.251688i
\(573\) −97.9260 + 354.752i −0.170901 + 0.619113i
\(574\) 821.084 1.43046
\(575\) 101.315i 0.176200i
\(576\) −530.712 317.164i −0.921375 0.550632i
\(577\) −893.615 −1.54873 −0.774363 0.632742i \(-0.781929\pi\)
−0.774363 + 0.632742i \(0.781929\pi\)
\(578\) 286.010i 0.494826i
\(579\) −583.759 161.141i −1.00822 0.278310i
\(580\) −0.456601 −0.000787243
\(581\) 943.325i 1.62362i
\(582\) 103.636 375.435i 0.178068 0.645078i
\(583\) 1563.67 2.68211
\(584\) 242.695i 0.415574i
\(585\) −8.14634 + 13.6313i −0.0139254 + 0.0233014i
\(586\) −656.350 −1.12005
\(587\) 625.531i 1.06564i −0.846228 0.532821i \(-0.821132\pi\)
0.846228 0.532821i \(-0.178868\pi\)
\(588\) −57.0224 15.7405i −0.0969769 0.0267696i
\(589\) 161.549 0.274277
\(590\) 1.39437i 0.00236335i
\(591\) 98.7488 357.732i 0.167088 0.605300i
\(592\) 384.664 0.649770
\(593\) 361.671i 0.609901i −0.952368 0.304951i \(-0.901360\pi\)
0.952368 0.304951i \(-0.0986400\pi\)
\(594\) −763.397 798.711i −1.28518 1.34463i
\(595\) 11.4163 0.0191871
\(596\) 18.9409i 0.0317800i
\(597\) 321.783 + 88.8252i 0.538999 + 0.148786i
\(598\) −143.355 −0.239725
\(599\) 824.494i 1.37645i 0.725497 + 0.688225i \(0.241610\pi\)
−0.725497 + 0.688225i \(0.758390\pi\)
\(600\) 165.976 601.275i 0.276627 1.00212i
\(601\) 98.4169 0.163755 0.0818776 0.996642i \(-0.473908\pi\)
0.0818776 + 0.996642i \(0.473908\pi\)
\(602\) 1069.43i 1.77647i
\(603\) 470.299 + 281.060i 0.779931 + 0.466102i
\(604\) 66.0374 0.109333
\(605\) 32.2904i 0.0533725i
\(606\) 731.410 + 201.899i 1.20695 + 0.333167i
\(607\) −310.874 −0.512149 −0.256074 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(608\) 92.9144i 0.152820i
\(609\) 107.629 389.901i 0.176730 0.640232i
\(610\) −12.5339 −0.0205473
\(611\) 695.962i 1.13905i
\(612\) 19.7060 32.9741i 0.0321993 0.0538793i
\(613\) −925.306 −1.50947 −0.754735 0.656029i \(-0.772235\pi\)
−0.754735 + 0.656029i \(0.772235\pi\)
\(614\) 760.719i 1.23896i
\(615\) −11.6473 3.21514i −0.0189388 0.00522788i
\(616\) −1815.71 −2.94758
\(617\) 88.8400i 0.143987i 0.997405 + 0.0719935i \(0.0229361\pi\)
−0.997405 + 0.0719935i \(0.977064\pi\)
\(618\) −24.2067 + 87.6925i −0.0391694 + 0.141897i
\(619\) −572.406 −0.924727 −0.462364 0.886690i \(-0.652999\pi\)
−0.462364 + 0.886690i \(0.652999\pi\)
\(620\) 0.345782i 0.000557713i
\(621\) −79.1293 + 75.6306i −0.127422 + 0.121788i
\(622\) 704.359 1.13241
\(623\) 1330.46i 2.13557i
\(624\) −773.151 213.421i −1.23902 0.342021i
\(625\) 624.321 0.998913
\(626\) 252.208i 0.402888i
\(627\) 275.638 998.542i 0.439615 1.59257i
\(628\) −99.4359 −0.158337
\(629\) 314.534i 0.500053i
\(630\) −14.2660 8.52566i −0.0226445 0.0135328i
\(631\) 688.994 1.09191 0.545954 0.837815i \(-0.316167\pi\)
0.545954 + 0.837815i \(0.316167\pi\)
\(632\) 498.167i 0.788239i
\(633\) 605.772 + 167.218i 0.956985 + 0.264167i
\(634\) 612.921 0.966752
\(635\) 11.4653i 0.0180556i
\(636\) 21.0593 76.2904i 0.0331121 0.119953i
\(637\) −1009.95 −1.58548
\(638\) 542.377i 0.850121i
\(639\) 232.039 388.272i 0.363129 0.607625i
\(640\) −10.2727 −0.0160511
\(641\) 607.078i 0.947080i −0.880772 0.473540i \(-0.842976\pi\)
0.880772 0.473540i \(-0.157024\pi\)
\(642\) −653.947 180.516i −1.01861 0.281178i
\(643\) 545.922 0.849024 0.424512 0.905422i \(-0.360446\pi\)
0.424512 + 0.905422i \(0.360446\pi\)
\(644\) 14.9270i 0.0231785i
\(645\) 4.18762 15.1703i 0.00649243 0.0235198i
\(646\) −361.994 −0.560362
\(647\) 595.240i 0.920000i 0.887919 + 0.460000i \(0.152151\pi\)
−0.887919 + 0.460000i \(0.847849\pi\)
\(648\) −593.509 + 319.215i −0.915910 + 0.492615i
\(649\) 164.792 0.253916
\(650\) 883.702i 1.35954i
\(651\) −295.270 81.5067i −0.453564 0.125202i
\(652\) 34.3750 0.0527224
\(653\) 572.686i 0.877008i 0.898729 + 0.438504i \(0.144492\pi\)
−0.898729 + 0.438504i \(0.855508\pi\)
\(654\) 108.359 392.547i 0.165687 0.600224i
\(655\) 20.0188 0.0305631
\(656\) 610.284i 0.930312i
\(657\) 225.359 + 134.679i 0.343012 + 0.204991i
\(658\) 728.369 1.10694
\(659\) 601.131i 0.912187i 0.889932 + 0.456094i \(0.150752\pi\)
−0.889932 + 0.456094i \(0.849248\pi\)
\(660\) 2.13729 + 0.589979i 0.00323832 + 0.000893908i
\(661\) 1210.51 1.83132 0.915662 0.401949i \(-0.131667\pi\)
0.915662 + 0.401949i \(0.131667\pi\)
\(662\) 4.28339i 0.00647037i
\(663\) 174.511 632.193i 0.263214 0.953534i
\(664\) 771.534 1.16195
\(665\) 15.5820i 0.0234315i
\(666\) 234.892 393.047i 0.352691 0.590160i
\(667\) −53.7339 −0.0805606
\(668\) 70.7061i 0.105847i
\(669\) 285.920 + 78.9256i 0.427384 + 0.117975i
\(670\) 11.0509 0.0164939
\(671\) 1481.29i 2.20759i
\(672\) −46.8782 + 169.823i −0.0697593 + 0.252713i
\(673\) −1136.89 −1.68928 −0.844641 0.535334i \(-0.820186\pi\)
−0.844641 + 0.535334i \(0.820186\pi\)
\(674\) 642.049i 0.952596i
\(675\) −466.219 487.786i −0.690694 0.722646i
\(676\) 63.2340 0.0935415
\(677\) 250.404i 0.369872i −0.982751 0.184936i \(-0.940792\pi\)
0.982751 0.184936i \(-0.0592078\pi\)
\(678\) 75.1252 + 20.7376i 0.110804 + 0.0305865i
\(679\) −692.385 −1.01971
\(680\) 9.33727i 0.0137313i
\(681\) −212.405 + 769.467i −0.311901 + 1.12991i
\(682\) −410.740 −0.602257
\(683\) 375.307i 0.549497i 0.961516 + 0.274749i \(0.0885946\pi\)
−0.961516 + 0.274749i \(0.911405\pi\)
\(684\) −45.0060 26.8964i −0.0657982 0.0393223i
\(685\) −21.7763 −0.0317902
\(686\) 106.261i 0.154900i
\(687\) −274.546 75.7860i −0.399630 0.110314i
\(688\) 794.875 1.15534
\(689\) 1351.22i 1.96113i
\(690\) −0.587479 + 2.12823i −0.000851419 + 0.00308439i
\(691\) −897.005 −1.29813 −0.649063 0.760734i \(-0.724839\pi\)
−0.649063 + 0.760734i \(0.724839\pi\)
\(692\) 68.2928i 0.0986890i
\(693\) −1007.59 + 1686.01i −1.45396 + 2.43291i
\(694\) −160.954 −0.231923
\(695\) 22.4012i 0.0322319i
\(696\) −318.896 88.0282i −0.458183 0.126477i
\(697\) 499.020 0.715954
\(698\) 573.019i 0.820943i
\(699\) −8.89336 + 32.2175i −0.0127230 + 0.0460909i
\(700\) −92.0160 −0.131451
\(701\) 27.9883i 0.0399263i −0.999801 0.0199631i \(-0.993645\pi\)
0.999801 0.0199631i \(-0.00635489\pi\)
\(702\) −690.192 + 659.675i −0.983179 + 0.939709i
\(703\) 429.303 0.610672
\(704\) 1473.80i 2.09347i
\(705\) −10.3322 2.85210i −0.0146555 0.00404553i
\(706\) 1033.69 1.46414
\(707\) 1348.88i 1.90789i
\(708\) 2.21939 8.04008i 0.00313473 0.0113561i
\(709\) −193.636 −0.273112 −0.136556 0.990632i \(-0.543603\pi\)
−0.136556 + 0.990632i \(0.543603\pi\)
\(710\) 9.12349i 0.0128500i
\(711\) 462.581 + 276.448i 0.650607 + 0.388815i
\(712\) 1088.17 1.52833
\(713\) 40.6925i 0.0570722i
\(714\) 661.630 + 182.637i 0.926653 + 0.255794i
\(715\) 37.8546 0.0529434
\(716\) 71.2079i 0.0994523i
\(717\) 81.9255 296.787i 0.114261 0.413929i
\(718\) −472.929 −0.658676
\(719\) 40.3715i 0.0561495i 0.999606 + 0.0280748i \(0.00893765\pi\)
−0.999606 + 0.0280748i \(0.991062\pi\)
\(720\) −6.33684 + 10.6035i −0.00880117 + 0.0147270i
\(721\) 161.724 0.224305
\(722\) 194.479i 0.269361i
\(723\) −392.352 108.305i −0.542672 0.149800i
\(724\) 5.35521 0.00739670
\(725\) 331.238i 0.456881i
\(726\) −516.578 + 1871.38i −0.711540 + 2.57766i
\(727\) 155.577 0.213998 0.106999 0.994259i \(-0.465876\pi\)
0.106999 + 0.994259i \(0.465876\pi\)
\(728\) 1569.01i 2.15524i
\(729\) −32.9439 + 728.255i −0.0451905 + 0.998978i
\(730\) 5.29540 0.00725397
\(731\) 649.956i 0.889133i
\(732\) 72.2714 + 19.9499i 0.0987315 + 0.0272539i
\(733\) −314.245 −0.428711 −0.214356 0.976756i \(-0.568765\pi\)
−0.214356 + 0.976756i \(0.568765\pi\)
\(734\) 703.722i 0.958749i
\(735\) −4.13884 + 14.9936i −0.00563108 + 0.0203994i
\(736\) 23.4041 0.0317990
\(737\) 1306.03i 1.77209i
\(738\) −623.584 372.666i −0.844965 0.504967i
\(739\) −388.040 −0.525088 −0.262544 0.964920i \(-0.584562\pi\)
−0.262544 + 0.964920i \(0.584562\pi\)
\(740\) 0.918884i 0.00124174i
\(741\) −862.872 238.188i −1.16447 0.321441i
\(742\) 1414.13 1.90584
\(743\) 972.982i 1.30953i 0.755832 + 0.654766i \(0.227233\pi\)
−0.755832 + 0.654766i \(0.772767\pi\)
\(744\) −66.6634 + 241.498i −0.0896013 + 0.324594i
\(745\) −4.98035 −0.00668503
\(746\) 31.6985i 0.0424913i
\(747\) 428.147 716.421i 0.573156 0.959065i
\(748\) −91.5702 −0.122420
\(749\) 1206.02i 1.61018i
\(750\) −26.2434 7.24424i −0.0349912 0.00965899i
\(751\) −1188.98 −1.58319 −0.791596 0.611044i \(-0.790750\pi\)
−0.791596 + 0.611044i \(0.790750\pi\)
\(752\) 541.372i 0.719910i
\(753\) 166.930 604.729i 0.221687 0.803093i
\(754\) −468.685 −0.621598
\(755\) 17.3640i 0.0229987i
\(756\) 68.6891 + 71.8666i 0.0908586 + 0.0950617i
\(757\) 378.178 0.499575 0.249787 0.968301i \(-0.419639\pi\)
0.249787 + 0.968301i \(0.419639\pi\)
\(758\) 346.767i 0.457476i
\(759\) 251.521 + 69.4302i 0.331385 + 0.0914759i
\(760\) −12.7443 −0.0167688
\(761\) 584.274i 0.767771i 0.923381 + 0.383886i \(0.125414\pi\)
−0.923381 + 0.383886i \(0.874586\pi\)
\(762\) −183.421 + 664.471i −0.240710 + 0.872009i
\(763\) −723.942 −0.948810
\(764\) 44.4027i 0.0581187i
\(765\) −8.67028 5.18153i −0.0113337 0.00677324i
\(766\) −486.122 −0.634623
\(767\) 142.402i 0.185661i
\(768\) 199.277 + 55.0086i 0.259475 + 0.0716257i
\(769\) −827.160 −1.07563 −0.537815 0.843063i \(-0.680750\pi\)
−0.537815 + 0.843063i \(0.680750\pi\)
\(770\) 39.6172i 0.0514509i
\(771\) 223.892 811.082i 0.290391 1.05199i
\(772\) 73.0664 0.0946456
\(773\) 39.7974i 0.0514843i −0.999669 0.0257422i \(-0.991805\pi\)
0.999669 0.0257422i \(-0.00819489\pi\)
\(774\) 485.385 812.197i 0.627112 1.04935i
\(775\) −250.845 −0.323671
\(776\) 566.294i 0.729760i
\(777\) −784.654 216.597i −1.00985 0.278760i
\(778\) 1170.13 1.50402
\(779\) 681.105i 0.874333i
\(780\) 0.509820 1.84690i 0.000653615 0.00236782i
\(781\) −1078.24 −1.38059
\(782\) 91.1821i 0.116601i
\(783\) −258.705 + 247.266i −0.330402 + 0.315794i
\(784\) −785.617 −1.00206
\(785\) 26.1459i 0.0333068i
\(786\) 1160.19 + 320.259i 1.47607 + 0.407455i
\(787\) −141.976 −0.180402 −0.0902008 0.995924i \(-0.528751\pi\)
−0.0902008 + 0.995924i \(0.528751\pi\)
\(788\) 44.7757i 0.0568220i
\(789\) 389.935 1412.60i 0.494214 1.79037i
\(790\) 10.8696 0.0137590
\(791\) 138.547i 0.175155i
\(792\) 1378.97 + 824.097i 1.74112 + 1.04053i
\(793\) 1280.03 1.61417
\(794\) 1018.67i 1.28295i
\(795\) −20.0599 5.53737i −0.0252326 0.00696524i
\(796\) −40.2761 −0.0505981
\(797\) 1014.85i 1.27333i −0.771138 0.636667i \(-0.780312\pi\)
0.771138 0.636667i \(-0.219688\pi\)
\(798\) 249.279 903.050i 0.312380 1.13164i
\(799\) 442.671 0.554032
\(800\) 144.273i 0.180341i
\(801\) 603.858 1010.44i 0.753881 1.26147i
\(802\) −1286.28 −1.60384
\(803\) 625.828i 0.779362i
\(804\) −63.7205 17.5895i −0.0792544 0.0218775i
\(805\) 3.92492 0.00487568
\(806\) 354.933i 0.440364i
\(807\) −230.793 + 836.083i −0.285989 + 1.03604i
\(808\) −1103.23 −1.36539
\(809\) 241.557i 0.298588i −0.988793 0.149294i \(-0.952300\pi\)
0.988793 0.149294i \(-0.0477000\pi\)
\(810\) 6.96499 + 12.9499i 0.00859876 + 0.0159875i
\(811\) −811.821 −1.00101 −0.500506 0.865733i \(-0.666853\pi\)
−0.500506 + 0.865733i \(0.666853\pi\)
\(812\) 48.8021i 0.0601012i
\(813\) 500.726 + 138.221i 0.615900 + 0.170014i
\(814\) −1091.50 −1.34091
\(815\) 9.03863i 0.0110903i
\(816\) 135.748 491.768i 0.166358 0.602657i
\(817\) 887.117 1.08582
\(818\) 1130.42i 1.38193i
\(819\) 1456.93 + 870.691i 1.77892 + 1.06312i
\(820\) 1.45785 0.00177786
\(821\) 1518.91i 1.85007i −0.379878 0.925037i \(-0.624034\pi\)
0.379878 0.925037i \(-0.375966\pi\)
\(822\) −1262.04 348.375i −1.53533 0.423813i
\(823\) 31.7446 0.0385718 0.0192859 0.999814i \(-0.493861\pi\)
0.0192859 + 0.999814i \(0.493861\pi\)
\(824\) 132.272i 0.160525i
\(825\) −427.997 + 1550.48i −0.518784 + 1.87937i
\(826\) 149.033 0.180427
\(827\) 20.0349i 0.0242260i 0.999927 + 0.0121130i \(0.00385578\pi\)
−0.999927 + 0.0121130i \(0.996144\pi\)
\(828\) 6.77491 11.3365i 0.00818226 0.0136914i
\(829\) −82.5438 −0.0995704 −0.0497852 0.998760i \(-0.515854\pi\)
−0.0497852 + 0.998760i \(0.515854\pi\)
\(830\) 16.8342i 0.0202822i
\(831\) 78.3540 + 21.6289i 0.0942888 + 0.0260276i
\(832\) 1273.56 1.53072
\(833\) 642.386i 0.771172i
\(834\) −358.372 + 1298.26i −0.429702 + 1.55666i
\(835\) −18.5916 −0.0222654
\(836\) 124.983i 0.149501i
\(837\) 187.254 + 195.916i 0.223720 + 0.234069i
\(838\) 416.454 0.496962
\(839\) 1215.01i 1.44816i 0.689714 + 0.724082i \(0.257736\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(840\) 23.2933 + 6.42991i 0.0277301 + 0.00765465i
\(841\) 665.322 0.791109
\(842\) 501.003i 0.595015i
\(843\) −31.5867 + 114.428i −0.0374694 + 0.135739i
\(844\) −75.8217 −0.0898361
\(845\) 16.6269i 0.0196768i
\(846\) −553.170 330.585i −0.653866 0.390763i
\(847\) 3451.24 4.07466
\(848\) 1051.08i 1.23948i
\(849\) 74.8501 + 20.6617i 0.0881626 + 0.0243365i
\(850\) 562.085 0.661276
\(851\) 108.137i 0.127070i
\(852\) −14.5217 + 52.6069i −0.0170442 + 0.0617452i
\(853\) −197.718 −0.231791 −0.115895 0.993261i \(-0.536974\pi\)
−0.115895 + 0.993261i \(0.536974\pi\)
\(854\) 1339.64i 1.56866i
\(855\) −7.07220 + 11.8340i −0.00827158 + 0.0138409i
\(856\) 986.391 1.15233
\(857\) 970.679i 1.13265i −0.824183 0.566324i \(-0.808365\pi\)
0.824183 0.566324i \(-0.191635\pi\)
\(858\) 2193.85 + 605.593i 2.55694 + 0.705820i
\(859\) 317.154 0.369213 0.184607 0.982813i \(-0.440899\pi\)
0.184607 + 0.982813i \(0.440899\pi\)
\(860\) 1.89879i 0.00220790i
\(861\) −343.639 + 1244.88i −0.399116 + 1.44586i
\(862\) −266.792 −0.309504
\(863\) 471.887i 0.546798i 0.961901 + 0.273399i \(0.0881480\pi\)
−0.961901 + 0.273399i \(0.911852\pi\)
\(864\) 112.680 107.698i 0.130417 0.124651i
\(865\) −17.9570 −0.0207596
\(866\) 79.8469i 0.0922019i
\(867\) −433.633 119.700i −0.500153 0.138063i
\(868\) 36.9576 0.0425779
\(869\) 1284.60i 1.47825i
\(870\) −1.92070 + 6.95803i −0.00220770 + 0.00799774i
\(871\) −1128.58 −1.29573
\(872\) 592.104i 0.679018i
\(873\) 525.842 + 314.253i 0.602339 + 0.359969i
\(874\) −124.453 −0.142395
\(875\) 48.3985i 0.0553126i
\(876\) −30.5338 8.42857i −0.0348559 0.00962165i
\(877\) 235.796 0.268867 0.134433 0.990923i \(-0.457079\pi\)
0.134433 + 0.990923i \(0.457079\pi\)
\(878\) 865.661i 0.985947i
\(879\) 274.695 995.124i 0.312508 1.13211i
\(880\) 29.4462 0.0334615
\(881\) 89.8046i 0.101935i −0.998700 0.0509675i \(-0.983770\pi\)
0.998700 0.0509675i \(-0.0162305\pi\)
\(882\) −479.732 + 802.737i −0.543913 + 0.910133i
\(883\) −231.045 −0.261659 −0.130830 0.991405i \(-0.541764\pi\)
−0.130830 + 0.991405i \(0.541764\pi\)
\(884\) 79.1287i 0.0895121i
\(885\) −2.11408 0.583571i −0.00238879 0.000659403i
\(886\) −473.001 −0.533861
\(887\) 335.627i 0.378385i −0.981940 0.189192i \(-0.939413\pi\)
0.981940 0.189192i \(-0.0605869\pi\)
\(888\) −177.152 + 641.759i −0.199495 + 0.722702i
\(889\) 1225.43 1.37844
\(890\) 23.7430i 0.0266775i
\(891\) 1530.46 823.146i 1.71769 0.923845i
\(892\) −35.7873 −0.0401203
\(893\) 604.196i 0.676592i
\(894\) −288.635 79.6751i −0.322858 0.0891220i
\(895\) −18.7235 −0.0209202
\(896\) 1097.96i 1.22540i
\(897\) 59.9969 217.348i 0.0668861 0.242305i
\(898\) −1302.09 −1.44999
\(899\) 133.040i 0.147986i
\(900\) 69.8829 + 41.7634i 0.0776477 + 0.0464038i
\(901\) 859.450 0.953884
\(902\) 1731.71i 1.91986i
\(903\) −1621.42 447.578i −1.79559 0.495657i
\(904\) −113.316 −0.125350
\(905\) 1.40811i 0.00155592i
\(906\) 277.788 1006.33i 0.306609 1.11074i
\(907\) 823.589 0.908036 0.454018 0.890993i \(-0.349990\pi\)
0.454018 + 0.890993i \(0.349990\pi\)
\(908\) 96.3107i 0.106069i
\(909\) −612.217 + 1024.43i −0.673507 + 1.12698i
\(910\) 34.2345 0.0376203
\(911\) 136.256i 0.149568i −0.997200 0.0747840i \(-0.976173\pi\)
0.997200 0.0747840i \(-0.0238267\pi\)
\(912\) −671.207 185.281i −0.735973 0.203159i
\(913\) −1989.52 −2.17911
\(914\) 724.090i 0.792221i
\(915\) 5.24566 19.0032i 0.00573296 0.0207685i
\(916\) 34.3637 0.0375149
\(917\) 2139.64i 2.33331i
\(918\) −419.591 439.001i −0.457071 0.478215i
\(919\) −784.225 −0.853347 −0.426673 0.904406i \(-0.640315\pi\)
−0.426673 + 0.904406i \(0.640315\pi\)
\(920\) 3.21015i 0.00348929i
\(921\) −1153.36 318.375i −1.25229 0.345684i
\(922\) 800.852 0.868603
\(923\) 931.745i 1.00948i
\(924\) 63.0578 228.436i 0.0682444 0.247226i
\(925\) −666.599 −0.720647
\(926\) 1689.65i 1.82467i
\(927\) −122.824 73.4019i −0.132496 0.0791822i
\(928\) 76.5173 0.0824540
\(929\) 99.4589i 0.107060i −0.998566 0.0535301i \(-0.982953\pi\)
0.998566 0.0535301i \(-0.0170473\pi\)
\(930\) 5.26928 + 1.45454i 0.00566590 + 0.00156402i
\(931\) −876.784 −0.941766
\(932\) 4.03252i 0.00432674i
\(933\) −294.787 + 1067.91i −0.315956 + 1.14460i
\(934\) −750.170 −0.803180
\(935\) 24.0776i 0.0257515i
\(936\) 712.128 1191.61i 0.760821 1.27309i
\(937\) 584.975 0.624307 0.312153 0.950032i \(-0.398950\pi\)
0.312153 + 0.950032i \(0.398950\pi\)
\(938\) 1181.14i 1.25921i
\(939\) 382.384 + 105.554i 0.407225 + 0.112411i
\(940\) 1.29323 0.00137577
\(941\) 31.9566i 0.0339603i −0.999856 0.0169801i \(-0.994595\pi\)
0.999856 0.0169801i \(-0.00540520\pi\)
\(942\) −418.279 + 1515.28i −0.444033 + 1.60858i
\(943\) 171.563 0.181933
\(944\) 110.771i 0.117342i
\(945\) 18.8968 18.0613i 0.0199966 0.0191124i
\(946\) −2255.50 −2.38425
\(947\) 53.3236i 0.0563079i −0.999604 0.0281540i \(-0.991037\pi\)
0.999604 0.0281540i \(-0.00896287\pi\)
\(948\) −62.6750 17.3009i −0.0661128 0.0182498i
\(949\) −540.798 −0.569861
\(950\) 767.182i 0.807560i
\(951\) −256.519 + 929.278i −0.269736 + 0.977159i
\(952\) −997.980 −1.04830
\(953\) 1439.19i 1.51016i −0.655631 0.755082i \(-0.727597\pi\)
0.655631 0.755082i \(-0.272403\pi\)
\(954\) −1073.98 641.834i −1.12577 0.672782i
\(955\) −11.6753 −0.0122255
\(956\) 37.1475i 0.0388572i
\(957\) 822.323 + 226.995i 0.859272 + 0.237194i
\(958\) 62.1662 0.0648916
\(959\) 2327.48i 2.42698i
\(960\) 5.21913 18.9071i 0.00543659 0.0196949i
\(961\) −860.250 −0.895161
\(962\) 943.202i 0.980460i
\(963\) 547.378 915.931i 0.568409 0.951122i
\(964\) 49.1089 0.0509428
\(965\) 19.2122i 0.0199090i
\(966\) 227.468 + 62.7905i 0.235474 + 0.0650006i
\(967\) 1088.89 1.12605 0.563027 0.826438i \(-0.309637\pi\)
0.563027 + 0.826438i \(0.309637\pi\)
\(968\) 2822.73i 2.91604i
\(969\) 151.501 548.835i 0.156348 0.566394i
\(970\) 12.3560 0.0127382
\(971\) 123.265i 0.126946i 0.997984 + 0.0634732i \(0.0202177\pi\)
−0.997984 + 0.0634732i \(0.979782\pi\)
\(972\) −19.5488 85.7561i −0.0201119 0.0882265i
\(973\) 2394.27 2.46071
\(974\) 24.7230i 0.0253829i
\(975\) 1339.82 + 369.846i 1.37418 + 0.379329i
\(976\) 995.708 1.02019
\(977\) 821.807i 0.841154i −0.907257 0.420577i \(-0.861828\pi\)
0.907257 0.420577i \(-0.138172\pi\)
\(978\) 144.599 523.832i 0.147852 0.535615i
\(979\) −2806.02 −2.86621
\(980\) 1.87668i 0.00191498i
\(981\) 549.808 + 328.576i 0.560457 + 0.334940i
\(982\) −134.938 −0.137411
\(983\) 17.3993i 0.0177002i 0.999961 + 0.00885011i \(0.00281712\pi\)
−0.999961 + 0.00885011i \(0.997183\pi\)
\(984\) 1018.18 + 281.058i 1.03473 + 0.285628i
\(985\) 11.7734 0.0119527
\(986\) 298.110i 0.302343i
\(987\) −304.836 + 1104.31i −0.308851 + 1.11886i
\(988\) 108.002 0.109313
\(989\) 223.455i 0.225940i
\(990\) 17.9811 30.0879i 0.0181627 0.0303918i
\(991\) −923.251 −0.931636 −0.465818 0.884881i \(-0.654240\pi\)
−0.465818 + 0.884881i \(0.654240\pi\)
\(992\) 57.9462i 0.0584135i
\(993\) −6.49424 1.79268i −0.00654002 0.00180531i
\(994\) −975.131 −0.981017
\(995\) 10.5903i 0.0106435i
\(996\) −26.7946 + 97.0676i −0.0269022 + 0.0974574i
\(997\) 432.965 0.434267 0.217134 0.976142i \(-0.430329\pi\)
0.217134 + 0.976142i \(0.430329\pi\)
\(998\) 948.234i 0.950134i
\(999\) 497.610 + 520.629i 0.498108 + 0.521150i
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 177.3.b.a.119.28 yes 38
3.2 odd 2 inner 177.3.b.a.119.11 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.3.b.a.119.11 38 3.2 odd 2 inner
177.3.b.a.119.28 yes 38 1.1 even 1 trivial