Properties

Label 210.3.c.a.29.4
Level $210$
Weight $3$
Character 210.29
Analytic conductor $5.722$
Analytic rank $0$
Dimension $24$
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] = [210,3,Mod(29,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 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("210.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.c (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: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.4
Character \(\chi\) \(=\) 210.29
Dual form 210.3.c.a.29.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-2.01468 + 2.22285i) q^{3} +2.00000 q^{4} +(3.91845 - 3.10576i) q^{5} +(2.84919 - 3.14358i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(-0.882103 - 8.95667i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-2.01468 + 2.22285i) q^{3} +2.00000 q^{4} +(3.91845 - 3.10576i) q^{5} +(2.84919 - 3.14358i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(-0.882103 - 8.95667i) q^{9} +(-5.54153 + 4.39221i) q^{10} -6.10339i q^{11} +(-4.02937 + 4.44570i) q^{12} -6.09265i q^{13} -3.74166i q^{14} +(-0.990810 + 14.9672i) q^{15} +4.00000 q^{16} -7.30179 q^{17} +(1.24748 + 12.6666i) q^{18} +31.7506 q^{19} +(7.83690 - 6.21152i) q^{20} +(-5.88110 - 5.33035i) q^{21} +8.63149i q^{22} +33.8856 q^{23} +(5.69838 - 6.28716i) q^{24} +(5.70852 - 24.3395i) q^{25} +8.61631i q^{26} +(21.6865 + 16.0841i) q^{27} +5.29150i q^{28} +41.0122i q^{29} +(1.40122 - 21.1669i) q^{30} +42.9120 q^{31} -5.65685 q^{32} +(13.5669 + 12.2964i) q^{33} +10.3263 q^{34} +(8.21707 + 10.3672i) q^{35} +(-1.76421 - 17.9133i) q^{36} -18.1246i q^{37} -44.9022 q^{38} +(13.5430 + 12.2748i) q^{39} +(-11.0831 + 8.78441i) q^{40} -36.4331i q^{41} +(8.31713 + 7.53825i) q^{42} -17.7024i q^{43} -12.2068i q^{44} +(-31.2737 - 32.3567i) q^{45} -47.9215 q^{46} -45.3150 q^{47} +(-8.05873 + 8.89139i) q^{48} -7.00000 q^{49} +(-8.07307 + 34.4213i) q^{50} +(14.7108 - 16.2308i) q^{51} -12.1853i q^{52} +18.1388 q^{53} +(-30.6693 - 22.7463i) q^{54} +(-18.9557 - 23.9158i) q^{55} -7.48331i q^{56} +(-63.9675 + 70.5769i) q^{57} -58.0000i q^{58} -4.22725i q^{59} +(-1.98162 + 29.9345i) q^{60} +16.8936 q^{61} -60.6867 q^{62} +(23.6971 - 2.33383i) q^{63} +8.00000 q^{64} +(-18.9223 - 23.8738i) q^{65} +(-19.1865 - 17.3897i) q^{66} +17.1392i q^{67} -14.6036 q^{68} +(-68.2688 + 75.3226i) q^{69} +(-11.6207 - 14.6615i) q^{70} +113.824i q^{71} +(2.49497 + 25.3333i) q^{72} -105.073i q^{73} +25.6320i q^{74} +(42.6022 + 61.7256i) q^{75} +63.5013 q^{76} +16.1480 q^{77} +(-19.1527 - 17.3591i) q^{78} -74.8132 q^{79} +(15.6738 - 12.4230i) q^{80} +(-79.4438 + 15.8014i) q^{81} +51.5242i q^{82} +76.5950 q^{83} +(-11.7622 - 10.6607i) q^{84} +(-28.6117 + 22.6776i) q^{85} +25.0350i q^{86} +(-91.1639 - 82.6266i) q^{87} +17.2630i q^{88} -26.8568i q^{89} +(44.2277 + 45.7592i) q^{90} +16.1196 q^{91} +67.7713 q^{92} +(-86.4541 + 95.3868i) q^{93} +64.0851 q^{94} +(124.413 - 98.6099i) q^{95} +(11.3968 - 12.5743i) q^{96} +120.087i q^{97} +9.89949 q^{98} +(-54.6660 + 5.38382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 48 q^{4} + 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 48 q^{4} + 44 q^{9} + 16 q^{10} + 4 q^{15} + 96 q^{16} - 80 q^{19} - 28 q^{21} + 48 q^{25} - 56 q^{30} + 224 q^{31} + 128 q^{34} + 88 q^{36} - 92 q^{39} + 32 q^{40} - 72 q^{45} - 144 q^{46} - 168 q^{49} - 284 q^{51} - 144 q^{54} - 320 q^{55} + 8 q^{60} + 192 q^{64} + 224 q^{66} - 152 q^{69} - 56 q^{70} + 48 q^{75} - 160 q^{76} - 72 q^{79} - 212 q^{81} - 56 q^{84} - 64 q^{85} - 240 q^{90} + 168 q^{91} - 128 q^{94} - 876 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −2.01468 + 2.22285i −0.671561 + 0.740949i
\(4\) 2.00000 0.500000
\(5\) 3.91845 3.10576i 0.783690 0.621152i
\(6\) 2.84919 3.14358i 0.474865 0.523930i
\(7\) 2.64575i 0.377964i
\(8\) −2.82843 −0.353553
\(9\) −0.882103 8.95667i −0.0980115 0.995185i
\(10\) −5.54153 + 4.39221i −0.554153 + 0.439221i
\(11\) 6.10339i 0.554853i −0.960747 0.277427i \(-0.910518\pi\)
0.960747 0.277427i \(-0.0894816\pi\)
\(12\) −4.02937 + 4.44570i −0.335781 + 0.370475i
\(13\) 6.09265i 0.468666i −0.972156 0.234333i \(-0.924709\pi\)
0.972156 0.234333i \(-0.0752905\pi\)
\(14\) 3.74166i 0.267261i
\(15\) −0.990810 + 14.9672i −0.0660540 + 0.997816i
\(16\) 4.00000 0.250000
\(17\) −7.30179 −0.429517 −0.214758 0.976667i \(-0.568896\pi\)
−0.214758 + 0.976667i \(0.568896\pi\)
\(18\) 1.24748 + 12.6666i 0.0693046 + 0.703702i
\(19\) 31.7506 1.67109 0.835543 0.549424i \(-0.185153\pi\)
0.835543 + 0.549424i \(0.185153\pi\)
\(20\) 7.83690 6.21152i 0.391845 0.310576i
\(21\) −5.88110 5.33035i −0.280052 0.253826i
\(22\) 8.63149i 0.392341i
\(23\) 33.8856 1.47329 0.736644 0.676280i \(-0.236409\pi\)
0.736644 + 0.676280i \(0.236409\pi\)
\(24\) 5.69838 6.28716i 0.237433 0.261965i
\(25\) 5.70852 24.3395i 0.228341 0.973581i
\(26\) 8.61631i 0.331397i
\(27\) 21.6865 + 16.0841i 0.803202 + 0.595706i
\(28\) 5.29150i 0.188982i
\(29\) 41.0122i 1.41421i 0.707106 + 0.707107i \(0.250000\pi\)
−0.707106 + 0.707107i \(0.750000\pi\)
\(30\) 1.40122 21.1669i 0.0467072 0.705562i
\(31\) 42.9120 1.38426 0.692129 0.721774i \(-0.256673\pi\)
0.692129 + 0.721774i \(0.256673\pi\)
\(32\) −5.65685 −0.176777
\(33\) 13.5669 + 12.2964i 0.411118 + 0.372618i
\(34\) 10.3263 0.303714
\(35\) 8.21707 + 10.3672i 0.234773 + 0.296207i
\(36\) −1.76421 17.9133i −0.0490057 0.497593i
\(37\) 18.1246i 0.489854i −0.969542 0.244927i \(-0.921236\pi\)
0.969542 0.244927i \(-0.0787640\pi\)
\(38\) −44.9022 −1.18164
\(39\) 13.5430 + 12.2748i 0.347257 + 0.314738i
\(40\) −11.0831 + 8.78441i −0.277076 + 0.219610i
\(41\) 36.4331i 0.888612i −0.895875 0.444306i \(-0.853450\pi\)
0.895875 0.444306i \(-0.146550\pi\)
\(42\) 8.31713 + 7.53825i 0.198027 + 0.179482i
\(43\) 17.7024i 0.411684i −0.978585 0.205842i \(-0.934007\pi\)
0.978585 0.205842i \(-0.0659932\pi\)
\(44\) 12.2068i 0.277427i
\(45\) −31.2737 32.3567i −0.694972 0.719037i
\(46\) −47.9215 −1.04177
\(47\) −45.3150 −0.964149 −0.482074 0.876130i \(-0.660116\pi\)
−0.482074 + 0.876130i \(0.660116\pi\)
\(48\) −8.05873 + 8.89139i −0.167890 + 0.185237i
\(49\) −7.00000 −0.142857
\(50\) −8.07307 + 34.4213i −0.161461 + 0.688426i
\(51\) 14.7108 16.2308i 0.288447 0.318250i
\(52\) 12.1853i 0.234333i
\(53\) 18.1388 0.342242 0.171121 0.985250i \(-0.445261\pi\)
0.171121 + 0.985250i \(0.445261\pi\)
\(54\) −30.6693 22.7463i −0.567950 0.421228i
\(55\) −18.9557 23.9158i −0.344648 0.434833i
\(56\) 7.48331i 0.133631i
\(57\) −63.9675 + 70.5769i −1.12224 + 1.23819i
\(58\) 58.0000i 1.00000i
\(59\) 4.22725i 0.0716482i −0.999358 0.0358241i \(-0.988594\pi\)
0.999358 0.0358241i \(-0.0114056\pi\)
\(60\) −1.98162 + 29.9345i −0.0330270 + 0.498908i
\(61\) 16.8936 0.276944 0.138472 0.990366i \(-0.455781\pi\)
0.138472 + 0.990366i \(0.455781\pi\)
\(62\) −60.6867 −0.978818
\(63\) 23.6971 2.33383i 0.376145 0.0370449i
\(64\) 8.00000 0.125000
\(65\) −18.9223 23.8738i −0.291112 0.367289i
\(66\) −19.1865 17.3897i −0.290704 0.263481i
\(67\) 17.1392i 0.255810i 0.991786 + 0.127905i \(0.0408252\pi\)
−0.991786 + 0.127905i \(0.959175\pi\)
\(68\) −14.6036 −0.214758
\(69\) −68.2688 + 75.3226i −0.989404 + 1.09163i
\(70\) −11.6207 14.6615i −0.166010 0.209450i
\(71\) 113.824i 1.60316i 0.597890 + 0.801578i \(0.296006\pi\)
−0.597890 + 0.801578i \(0.703994\pi\)
\(72\) 2.49497 + 25.3333i 0.0346523 + 0.351851i
\(73\) 105.073i 1.43935i −0.694311 0.719675i \(-0.744291\pi\)
0.694311 0.719675i \(-0.255709\pi\)
\(74\) 25.6320i 0.346379i
\(75\) 42.6022 + 61.7256i 0.568029 + 0.823008i
\(76\) 63.5013 0.835543
\(77\) 16.1480 0.209715
\(78\) −19.1527 17.3591i −0.245548 0.222553i
\(79\) −74.8132 −0.947003 −0.473501 0.880793i \(-0.657010\pi\)
−0.473501 + 0.880793i \(0.657010\pi\)
\(80\) 15.6738 12.4230i 0.195923 0.155288i
\(81\) −79.4438 + 15.8014i −0.980787 + 0.195079i
\(82\) 51.5242i 0.628344i
\(83\) 76.5950 0.922831 0.461416 0.887184i \(-0.347342\pi\)
0.461416 + 0.887184i \(0.347342\pi\)
\(84\) −11.7622 10.6607i −0.140026 0.126913i
\(85\) −28.6117 + 22.6776i −0.336608 + 0.266795i
\(86\) 25.0350i 0.291104i
\(87\) −91.1639 82.6266i −1.04786 0.949732i
\(88\) 17.2630i 0.196170i
\(89\) 26.8568i 0.301762i −0.988552 0.150881i \(-0.951789\pi\)
0.988552 0.150881i \(-0.0482110\pi\)
\(90\) 44.2277 + 45.7592i 0.491419 + 0.508436i
\(91\) 16.1196 0.177139
\(92\) 67.7713 0.736644
\(93\) −86.4541 + 95.3868i −0.929614 + 1.02566i
\(94\) 64.0851 0.681756
\(95\) 124.413 98.6099i 1.30961 1.03800i
\(96\) 11.3968 12.5743i 0.118716 0.130983i
\(97\) 120.087i 1.23801i 0.785387 + 0.619005i \(0.212464\pi\)
−0.785387 + 0.619005i \(0.787536\pi\)
\(98\) 9.89949 0.101015
\(99\) −54.6660 + 5.38382i −0.552182 + 0.0543820i
\(100\) 11.4170 48.6791i 0.114170 0.486791i
\(101\) 162.983i 1.61369i −0.590764 0.806844i \(-0.701174\pi\)
0.590764 0.806844i \(-0.298826\pi\)
\(102\) −20.8042 + 22.9538i −0.203963 + 0.225037i
\(103\) 186.379i 1.80951i −0.425937 0.904753i \(-0.640056\pi\)
0.425937 0.904753i \(-0.359944\pi\)
\(104\) 17.2326i 0.165698i
\(105\) −39.5996 2.62144i −0.377139 0.0249661i
\(106\) −25.6522 −0.242002
\(107\) −164.926 −1.54136 −0.770681 0.637221i \(-0.780084\pi\)
−0.770681 + 0.637221i \(0.780084\pi\)
\(108\) 43.3729 + 32.1681i 0.401601 + 0.297853i
\(109\) −96.6905 −0.887069 −0.443535 0.896257i \(-0.646276\pi\)
−0.443535 + 0.896257i \(0.646276\pi\)
\(110\) 26.8073 + 33.8221i 0.243703 + 0.307474i
\(111\) 40.2882 + 36.5153i 0.362957 + 0.328967i
\(112\) 10.5830i 0.0944911i
\(113\) 112.284 0.993660 0.496830 0.867848i \(-0.334497\pi\)
0.496830 + 0.867848i \(0.334497\pi\)
\(114\) 90.4637 99.8107i 0.793541 0.875533i
\(115\) 132.779 105.241i 1.15460 0.915136i
\(116\) 82.0245i 0.707107i
\(117\) −54.5699 + 5.37435i −0.466409 + 0.0459346i
\(118\) 5.97823i 0.0506629i
\(119\) 19.3187i 0.162342i
\(120\) 2.80243 42.3337i 0.0233536 0.352781i
\(121\) 83.7487 0.692138
\(122\) −23.8911 −0.195829
\(123\) 80.9852 + 73.4012i 0.658417 + 0.596757i
\(124\) 85.8240 0.692129
\(125\) −53.2241 113.103i −0.425793 0.904821i
\(126\) −33.5128 + 3.30053i −0.265974 + 0.0261947i
\(127\) 197.632i 1.55616i 0.628167 + 0.778078i \(0.283805\pi\)
−0.628167 + 0.778078i \(0.716195\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 39.3497 + 35.6647i 0.305037 + 0.276471i
\(130\) 26.7602 + 33.7626i 0.205848 + 0.259712i
\(131\) 38.0418i 0.290396i 0.989403 + 0.145198i \(0.0463819\pi\)
−0.989403 + 0.145198i \(0.953618\pi\)
\(132\) 27.1338 + 24.5928i 0.205559 + 0.186309i
\(133\) 84.0043i 0.631611i
\(134\) 24.2385i 0.180885i
\(135\) 134.931 4.32830i 0.999486 0.0320615i
\(136\) 20.6526 0.151857
\(137\) −43.7923 −0.319652 −0.159826 0.987145i \(-0.551093\pi\)
−0.159826 + 0.987145i \(0.551093\pi\)
\(138\) 96.5467 106.522i 0.699614 0.771901i
\(139\) −175.928 −1.26567 −0.632836 0.774286i \(-0.718109\pi\)
−0.632836 + 0.774286i \(0.718109\pi\)
\(140\) 16.4341 + 20.7345i 0.117387 + 0.148104i
\(141\) 91.2953 100.728i 0.647485 0.714385i
\(142\) 160.972i 1.13360i
\(143\) −37.1858 −0.260041
\(144\) −3.52841 35.8267i −0.0245029 0.248796i
\(145\) 127.374 + 160.704i 0.878442 + 1.10831i
\(146\) 148.595i 1.01777i
\(147\) 14.1028 15.5599i 0.0959373 0.105850i
\(148\) 36.2492i 0.244927i
\(149\) 150.593i 1.01069i −0.862917 0.505345i \(-0.831365\pi\)
0.862917 0.505345i \(-0.168635\pi\)
\(150\) −60.2486 87.2932i −0.401657 0.581955i
\(151\) −5.63028 −0.0372866 −0.0186433 0.999826i \(-0.505935\pi\)
−0.0186433 + 0.999826i \(0.505935\pi\)
\(152\) −89.8044 −0.590818
\(153\) 6.44093 + 65.3997i 0.0420976 + 0.427449i
\(154\) −22.8368 −0.148291
\(155\) 168.149 133.274i 1.08483 0.859834i
\(156\) 27.0861 + 24.5495i 0.173629 + 0.157369i
\(157\) 119.059i 0.758341i 0.925327 + 0.379170i \(0.123791\pi\)
−0.925327 + 0.379170i \(0.876209\pi\)
\(158\) 105.802 0.669632
\(159\) −36.5440 + 40.3199i −0.229837 + 0.253584i
\(160\) −22.1661 + 17.5688i −0.138538 + 0.109805i
\(161\) 89.6530i 0.556851i
\(162\) 112.350 22.3466i 0.693521 0.137942i
\(163\) 74.5829i 0.457564i 0.973478 + 0.228782i \(0.0734743\pi\)
−0.973478 + 0.228782i \(0.926526\pi\)
\(164\) 72.8662i 0.444306i
\(165\) 91.3509 + 6.04729i 0.553642 + 0.0366503i
\(166\) −108.322 −0.652540
\(167\) 114.419 0.685144 0.342572 0.939492i \(-0.388702\pi\)
0.342572 + 0.939492i \(0.388702\pi\)
\(168\) 16.6343 + 15.0765i 0.0990135 + 0.0897411i
\(169\) 131.880 0.780353
\(170\) 40.4630 32.0710i 0.238018 0.188653i
\(171\) −28.0074 284.380i −0.163786 1.66304i
\(172\) 35.4048i 0.205842i
\(173\) −173.820 −1.00474 −0.502370 0.864653i \(-0.667538\pi\)
−0.502370 + 0.864653i \(0.667538\pi\)
\(174\) 128.925 + 116.852i 0.740950 + 0.671562i
\(175\) 64.3963 + 15.1033i 0.367979 + 0.0863048i
\(176\) 24.4136i 0.138713i
\(177\) 9.39652 + 8.51656i 0.0530877 + 0.0481162i
\(178\) 37.9812i 0.213378i
\(179\) 134.192i 0.749677i 0.927090 + 0.374838i \(0.122302\pi\)
−0.927090 + 0.374838i \(0.877698\pi\)
\(180\) −62.5475 64.7133i −0.347486 0.359519i
\(181\) −199.113 −1.10007 −0.550036 0.835141i \(-0.685386\pi\)
−0.550036 + 0.835141i \(0.685386\pi\)
\(182\) −22.7966 −0.125256
\(183\) −34.0352 + 37.5518i −0.185985 + 0.205201i
\(184\) −95.8431 −0.520886
\(185\) −56.2906 71.0203i −0.304274 0.383894i
\(186\) 122.265 134.897i 0.657336 0.725255i
\(187\) 44.5656i 0.238319i
\(188\) −90.6300 −0.482074
\(189\) −42.5544 + 57.3770i −0.225156 + 0.303582i
\(190\) −175.947 + 139.455i −0.926037 + 0.733976i
\(191\) 224.206i 1.17385i 0.809640 + 0.586927i \(0.199662\pi\)
−0.809640 + 0.586927i \(0.800338\pi\)
\(192\) −16.1175 + 17.7828i −0.0839451 + 0.0926187i
\(193\) 340.124i 1.76230i 0.472838 + 0.881149i \(0.343230\pi\)
−0.472838 + 0.881149i \(0.656770\pi\)
\(194\) 169.829i 0.875405i
\(195\) 91.1902 + 6.03666i 0.467642 + 0.0309572i
\(196\) −14.0000 −0.0714286
\(197\) 115.404 0.585805 0.292903 0.956142i \(-0.405379\pi\)
0.292903 + 0.956142i \(0.405379\pi\)
\(198\) 77.3094 7.61387i 0.390452 0.0384539i
\(199\) 186.569 0.937534 0.468767 0.883322i \(-0.344698\pi\)
0.468767 + 0.883322i \(0.344698\pi\)
\(200\) −16.1461 + 68.8426i −0.0807307 + 0.344213i
\(201\) −38.0979 34.5301i −0.189542 0.171792i
\(202\) 230.492i 1.14105i
\(203\) −108.508 −0.534523
\(204\) 29.4216 32.4615i 0.144223 0.159125i
\(205\) −113.152 142.761i −0.551963 0.696397i
\(206\) 263.580i 1.27951i
\(207\) −29.8906 303.502i −0.144399 1.46620i
\(208\) 24.3706i 0.117166i
\(209\) 193.787i 0.927208i
\(210\) 56.0023 + 3.70727i 0.266678 + 0.0176537i
\(211\) −348.892 −1.65352 −0.826759 0.562556i \(-0.809818\pi\)
−0.826759 + 0.562556i \(0.809818\pi\)
\(212\) 36.2777 0.171121
\(213\) −253.014 229.320i −1.18786 1.07662i
\(214\) 233.240 1.08991
\(215\) −54.9794 69.3660i −0.255718 0.322633i
\(216\) −61.3386 45.4926i −0.283975 0.210614i
\(217\) 113.534i 0.523200i
\(218\) 136.741 0.627253
\(219\) 233.560 + 211.688i 1.06649 + 0.966611i
\(220\) −37.9113 47.8317i −0.172324 0.217417i
\(221\) 44.4872i 0.201300i
\(222\) −56.9761 51.6404i −0.256649 0.232615i
\(223\) 442.370i 1.98372i −0.127331 0.991860i \(-0.540641\pi\)
0.127331 0.991860i \(-0.459359\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) −223.037 29.6594i −0.991274 0.131819i
\(226\) −158.793 −0.702624
\(227\) 105.606 0.465225 0.232613 0.972569i \(-0.425273\pi\)
0.232613 + 0.972569i \(0.425273\pi\)
\(228\) −127.935 + 141.154i −0.561118 + 0.619095i
\(229\) −300.234 −1.31107 −0.655534 0.755166i \(-0.727556\pi\)
−0.655534 + 0.755166i \(0.727556\pi\)
\(230\) −187.778 + 148.833i −0.816427 + 0.647099i
\(231\) −32.5332 + 35.8946i −0.140836 + 0.155388i
\(232\) 116.000i 0.500000i
\(233\) −224.338 −0.962823 −0.481411 0.876495i \(-0.659876\pi\)
−0.481411 + 0.876495i \(0.659876\pi\)
\(234\) 77.1734 7.60048i 0.329801 0.0324807i
\(235\) −177.565 + 140.737i −0.755594 + 0.598883i
\(236\) 8.45449i 0.0358241i
\(237\) 150.725 166.298i 0.635970 0.701681i
\(238\) 27.3208i 0.114793i
\(239\) 298.399i 1.24853i 0.781212 + 0.624266i \(0.214602\pi\)
−0.781212 + 0.624266i \(0.785398\pi\)
\(240\) −3.96324 + 59.8690i −0.0165135 + 0.249454i
\(241\) 37.2693 0.154645 0.0773223 0.997006i \(-0.475363\pi\)
0.0773223 + 0.997006i \(0.475363\pi\)
\(242\) −118.438 −0.489415
\(243\) 124.930 208.426i 0.514115 0.857721i
\(244\) 33.7872 0.138472
\(245\) −27.4292 + 21.7403i −0.111956 + 0.0887360i
\(246\) −114.530 103.805i −0.465571 0.421971i
\(247\) 193.446i 0.783181i
\(248\) −121.373 −0.489409
\(249\) −154.315 + 170.259i −0.619738 + 0.683771i
\(250\) 75.2703 + 159.951i 0.301081 + 0.639805i
\(251\) 247.604i 0.986471i 0.869896 + 0.493235i \(0.164186\pi\)
−0.869896 + 0.493235i \(0.835814\pi\)
\(252\) 47.3942 4.66765i 0.188072 0.0185224i
\(253\) 206.817i 0.817459i
\(254\) 279.494i 1.10037i
\(255\) 7.23468 109.288i 0.0283713 0.428579i
\(256\) 16.0000 0.0625000
\(257\) 75.6252 0.294262 0.147131 0.989117i \(-0.452996\pi\)
0.147131 + 0.989117i \(0.452996\pi\)
\(258\) −55.6489 50.4375i −0.215694 0.195494i
\(259\) 47.9532 0.185147
\(260\) −37.8446 47.7475i −0.145556 0.183644i
\(261\) 367.333 36.1770i 1.40741 0.138609i
\(262\) 53.7993i 0.205341i
\(263\) 56.5685 0.215089 0.107545 0.994200i \(-0.465701\pi\)
0.107545 + 0.994200i \(0.465701\pi\)
\(264\) −38.3730 34.7795i −0.145352 0.131740i
\(265\) 71.0762 56.3349i 0.268212 0.212584i
\(266\) 118.800i 0.446617i
\(267\) 59.6985 + 54.1079i 0.223590 + 0.202651i
\(268\) 34.2785i 0.127905i
\(269\) 253.707i 0.943149i 0.881826 + 0.471574i \(0.156314\pi\)
−0.881826 + 0.471574i \(0.843686\pi\)
\(270\) −190.821 + 6.12114i −0.706743 + 0.0226709i
\(271\) 256.392 0.946096 0.473048 0.881037i \(-0.343154\pi\)
0.473048 + 0.881037i \(0.343154\pi\)
\(272\) −29.2071 −0.107379
\(273\) −32.4760 + 35.8315i −0.118960 + 0.131251i
\(274\) 61.9317 0.226028
\(275\) −148.554 34.8413i −0.540195 0.126696i
\(276\) −136.538 + 150.645i −0.494702 + 0.545816i
\(277\) 185.677i 0.670312i −0.942163 0.335156i \(-0.891211\pi\)
0.942163 0.335156i \(-0.108789\pi\)
\(278\) 248.800 0.894966
\(279\) −37.8528 384.349i −0.135673 1.37759i
\(280\) −23.2414 29.3230i −0.0830049 0.104725i
\(281\) 260.250i 0.926157i 0.886317 + 0.463078i \(0.153255\pi\)
−0.886317 + 0.463078i \(0.846745\pi\)
\(282\) −129.111 + 142.451i −0.457841 + 0.505147i
\(283\) 445.523i 1.57429i 0.616770 + 0.787143i \(0.288441\pi\)
−0.616770 + 0.787143i \(0.711559\pi\)
\(284\) 227.648i 0.801578i
\(285\) −31.4588 + 475.220i −0.110382 + 1.66744i
\(286\) 52.5887 0.183877
\(287\) 96.3929 0.335864
\(288\) 4.98993 + 50.6666i 0.0173261 + 0.175926i
\(289\) −235.684 −0.815515
\(290\) −180.134 227.270i −0.621152 0.783691i
\(291\) −266.935 241.937i −0.917302 0.831399i
\(292\) 210.145i 0.719675i
\(293\) 173.565 0.592371 0.296186 0.955130i \(-0.404285\pi\)
0.296186 + 0.955130i \(0.404285\pi\)
\(294\) −19.9443 + 22.0051i −0.0678379 + 0.0748472i
\(295\) −13.1288 16.5643i −0.0445044 0.0561500i
\(296\) 51.2641i 0.173189i
\(297\) 98.1673 132.361i 0.330530 0.445660i
\(298\) 212.971i 0.714666i
\(299\) 206.453i 0.690480i
\(300\) 85.2044 + 123.451i 0.284015 + 0.411504i
\(301\) 46.8361 0.155602
\(302\) 7.96241 0.0263656
\(303\) 362.285 + 328.358i 1.19566 + 1.08369i
\(304\) 127.003 0.417772
\(305\) 66.1967 52.4674i 0.217038 0.172024i
\(306\) −9.10885 92.4891i −0.0297675 0.302252i
\(307\) 243.521i 0.793227i −0.917986 0.396613i \(-0.870185\pi\)
0.917986 0.396613i \(-0.129815\pi\)
\(308\) 32.2961 0.104857
\(309\) 414.292 + 375.495i 1.34075 + 1.21519i
\(310\) −237.798 + 188.478i −0.767090 + 0.607995i
\(311\) 257.759i 0.828809i 0.910093 + 0.414404i \(0.136010\pi\)
−0.910093 + 0.414404i \(0.863990\pi\)
\(312\) −38.3055 34.7183i −0.122774 0.111277i
\(313\) 156.412i 0.499718i −0.968282 0.249859i \(-0.919616\pi\)
0.968282 0.249859i \(-0.0803842\pi\)
\(314\) 168.376i 0.536228i
\(315\) 85.6077 82.7425i 0.271770 0.262675i
\(316\) −149.626 −0.473501
\(317\) 269.689 0.850754 0.425377 0.905016i \(-0.360142\pi\)
0.425377 + 0.905016i \(0.360142\pi\)
\(318\) 51.6811 57.0209i 0.162519 0.179311i
\(319\) 250.314 0.784682
\(320\) 31.3476 24.8461i 0.0979613 0.0776440i
\(321\) 332.273 366.605i 1.03512 1.14207i
\(322\) 126.788i 0.393753i
\(323\) −231.836 −0.717760
\(324\) −158.888 + 31.6028i −0.490394 + 0.0975396i
\(325\) −148.292 34.7801i −0.456284 0.107016i
\(326\) 105.476i 0.323547i
\(327\) 194.801 214.928i 0.595721 0.657273i
\(328\) 103.048i 0.314172i
\(329\) 119.892i 0.364414i
\(330\) −129.190 8.55217i −0.391484 0.0259157i
\(331\) 100.748 0.304374 0.152187 0.988352i \(-0.451368\pi\)
0.152187 + 0.988352i \(0.451368\pi\)
\(332\) 153.190 0.461416
\(333\) −162.336 + 15.9878i −0.487495 + 0.0480113i
\(334\) −161.813 −0.484470
\(335\) 53.2304 + 67.1593i 0.158897 + 0.200475i
\(336\) −23.5244 21.3214i −0.0700131 0.0634566i
\(337\) 172.052i 0.510541i −0.966870 0.255270i \(-0.917835\pi\)
0.966870 0.255270i \(-0.0821645\pi\)
\(338\) −186.506 −0.551793
\(339\) −226.216 + 249.589i −0.667303 + 0.736252i
\(340\) −57.2234 + 45.3552i −0.168304 + 0.133398i
\(341\) 261.909i 0.768060i
\(342\) 39.6084 + 402.174i 0.115814 + 1.17595i
\(343\) 18.5203i 0.0539949i
\(344\) 50.0699i 0.145552i
\(345\) −33.5742 + 507.175i −0.0973166 + 1.47007i
\(346\) 245.818 0.710458
\(347\) −376.866 −1.08607 −0.543034 0.839711i \(-0.682725\pi\)
−0.543034 + 0.839711i \(0.682725\pi\)
\(348\) −182.328 165.253i −0.523931 0.474866i
\(349\) −334.570 −0.958652 −0.479326 0.877637i \(-0.659119\pi\)
−0.479326 + 0.877637i \(0.659119\pi\)
\(350\) −91.0702 21.3593i −0.260201 0.0610267i
\(351\) 97.9946 132.128i 0.279187 0.376433i
\(352\) 34.5260i 0.0980852i
\(353\) 291.223 0.824995 0.412497 0.910959i \(-0.364657\pi\)
0.412497 + 0.910959i \(0.364657\pi\)
\(354\) −13.2887 12.0442i −0.0375387 0.0340233i
\(355\) 353.510 + 446.014i 0.995804 + 1.25638i
\(356\) 53.7136i 0.150881i
\(357\) 42.9426 + 38.9211i 0.120287 + 0.109023i
\(358\) 189.776i 0.530102i
\(359\) 204.579i 0.569858i 0.958549 + 0.284929i \(0.0919701\pi\)
−0.958549 + 0.284929i \(0.908030\pi\)
\(360\) 88.4555 + 91.5185i 0.245710 + 0.254218i
\(361\) 647.104 1.79253
\(362\) 281.589 0.777869
\(363\) −168.727 + 186.161i −0.464813 + 0.512839i
\(364\) 32.2393 0.0885695
\(365\) −326.330 411.722i −0.894055 1.12800i
\(366\) 48.1331 53.1063i 0.131511 0.145099i
\(367\) 242.592i 0.661015i 0.943803 + 0.330507i \(0.107220\pi\)
−0.943803 + 0.330507i \(0.892780\pi\)
\(368\) 135.543 0.368322
\(369\) −326.319 + 32.1378i −0.884334 + 0.0870942i
\(370\) 79.6069 + 100.438i 0.215154 + 0.271454i
\(371\) 47.9909i 0.129355i
\(372\) −172.908 + 190.774i −0.464807 + 0.512832i
\(373\) 101.784i 0.272880i 0.990648 + 0.136440i \(0.0435660\pi\)
−0.990648 + 0.136440i \(0.956434\pi\)
\(374\) 63.0253i 0.168517i
\(375\) 358.640 + 109.557i 0.956372 + 0.292151i
\(376\) 128.170 0.340878
\(377\) 249.873 0.662794
\(378\) 60.1811 81.1433i 0.159209 0.214665i
\(379\) 247.028 0.651789 0.325894 0.945406i \(-0.394335\pi\)
0.325894 + 0.945406i \(0.394335\pi\)
\(380\) 248.827 197.220i 0.654807 0.518999i
\(381\) −439.306 398.166i −1.15303 1.04505i
\(382\) 317.075i 0.830040i
\(383\) 18.9699 0.0495297 0.0247649 0.999693i \(-0.492116\pi\)
0.0247649 + 0.999693i \(0.492116\pi\)
\(384\) 22.7935 25.1487i 0.0593582 0.0654913i
\(385\) 63.2753 50.1519i 0.164352 0.130265i
\(386\) 481.008i 1.24613i
\(387\) −158.554 + 15.6153i −0.409702 + 0.0403497i
\(388\) 240.174i 0.619005i
\(389\) 623.289i 1.60229i −0.598473 0.801143i \(-0.704226\pi\)
0.598473 0.801143i \(-0.295774\pi\)
\(390\) −128.962 8.53712i −0.330673 0.0218901i
\(391\) −247.426 −0.632802
\(392\) 19.7990 0.0505076
\(393\) −84.5612 76.6422i −0.215168 0.195018i
\(394\) −163.205 −0.414227
\(395\) −293.152 + 232.352i −0.742157 + 0.588232i
\(396\) −109.332 + 10.7676i −0.276091 + 0.0271910i
\(397\) 368.913i 0.929253i 0.885507 + 0.464626i \(0.153811\pi\)
−0.885507 + 0.464626i \(0.846189\pi\)
\(398\) −263.849 −0.662937
\(399\) −186.729 169.242i −0.467992 0.424166i
\(400\) 22.8341 97.3581i 0.0570852 0.243395i
\(401\) 291.137i 0.726027i −0.931784 0.363014i \(-0.881748\pi\)
0.931784 0.363014i \(-0.118252\pi\)
\(402\) 53.8786 + 48.8330i 0.134026 + 0.121475i
\(403\) 261.448i 0.648754i
\(404\) 325.965i 0.806844i
\(405\) −262.221 + 308.650i −0.647460 + 0.762100i
\(406\) 153.454 0.377965
\(407\) −110.621 −0.271797
\(408\) −41.6084 + 45.9075i −0.101981 + 0.112518i
\(409\) −131.054 −0.320425 −0.160212 0.987083i \(-0.551218\pi\)
−0.160212 + 0.987083i \(0.551218\pi\)
\(410\) 160.022 + 201.895i 0.390297 + 0.492427i
\(411\) 88.2277 97.3437i 0.214666 0.236846i
\(412\) 372.758i 0.904753i
\(413\) 11.1842 0.0270805
\(414\) 42.2718 + 429.217i 0.102106 + 1.03676i
\(415\) 300.134 237.886i 0.723214 0.573218i
\(416\) 34.4652i 0.0828492i
\(417\) 354.440 391.062i 0.849976 0.937799i
\(418\) 274.056i 0.655635i
\(419\) 639.030i 1.52513i −0.646911 0.762566i \(-0.723939\pi\)
0.646911 0.762566i \(-0.276061\pi\)
\(420\) −79.1992 5.24287i −0.188570 0.0124830i
\(421\) 496.330 1.17893 0.589466 0.807793i \(-0.299338\pi\)
0.589466 + 0.807793i \(0.299338\pi\)
\(422\) 493.408 1.16921
\(423\) 39.9725 + 405.871i 0.0944976 + 0.959506i
\(424\) −51.3044 −0.121001
\(425\) −41.6824 + 177.722i −0.0980763 + 0.418170i
\(426\) 357.815 + 324.307i 0.839942 + 0.761284i
\(427\) 44.6962i 0.104675i
\(428\) −329.851 −0.770681
\(429\) 74.9177 82.6584i 0.174633 0.192677i
\(430\) 77.7526 + 98.0983i 0.180820 + 0.228136i
\(431\) 242.169i 0.561877i 0.959726 + 0.280939i \(0.0906457\pi\)
−0.959726 + 0.280939i \(0.909354\pi\)
\(432\) 86.7459 + 64.3363i 0.200801 + 0.148927i
\(433\) 123.653i 0.285574i 0.989753 + 0.142787i \(0.0456063\pi\)
−0.989753 + 0.142787i \(0.954394\pi\)
\(434\) 160.562i 0.369959i
\(435\) −613.840 40.6353i −1.41113 0.0934145i
\(436\) −193.381 −0.443535
\(437\) 1075.89 2.46199
\(438\) −330.304 299.372i −0.754119 0.683497i
\(439\) 419.828 0.956328 0.478164 0.878271i \(-0.341302\pi\)
0.478164 + 0.878271i \(0.341302\pi\)
\(440\) 53.6147 + 67.6442i 0.121852 + 0.153737i
\(441\) 6.17472 + 62.6967i 0.0140016 + 0.142169i
\(442\) 62.9145i 0.142340i
\(443\) −95.9458 −0.216582 −0.108291 0.994119i \(-0.534538\pi\)
−0.108291 + 0.994119i \(0.534538\pi\)
\(444\) 80.5764 + 73.0306i 0.181478 + 0.164483i
\(445\) −83.4107 105.237i −0.187440 0.236488i
\(446\) 625.605i 1.40270i
\(447\) 334.745 + 303.397i 0.748871 + 0.678741i
\(448\) 21.1660i 0.0472456i
\(449\) 780.855i 1.73910i 0.493847 + 0.869549i \(0.335590\pi\)
−0.493847 + 0.869549i \(0.664410\pi\)
\(450\) 315.421 + 41.9447i 0.700936 + 0.0932104i
\(451\) −222.365 −0.493050
\(452\) 224.567 0.496830
\(453\) 11.3432 12.5152i 0.0250402 0.0276275i
\(454\) −149.350 −0.328964
\(455\) 63.1640 50.0637i 0.138822 0.110030i
\(456\) 180.927 199.621i 0.396771 0.437766i
\(457\) 615.383i 1.34657i −0.739383 0.673286i \(-0.764882\pi\)
0.739383 0.673286i \(-0.235118\pi\)
\(458\) 424.596 0.927064
\(459\) −158.350 117.442i −0.344989 0.255866i
\(460\) 265.559 210.481i 0.577301 0.457568i
\(461\) 463.592i 1.00562i 0.864396 + 0.502811i \(0.167701\pi\)
−0.864396 + 0.502811i \(0.832299\pi\)
\(462\) 46.0089 50.7627i 0.0995863 0.109876i
\(463\) 249.784i 0.539491i 0.962932 + 0.269746i \(0.0869396\pi\)
−0.962932 + 0.269746i \(0.913060\pi\)
\(464\) 164.049i 0.353554i
\(465\) −42.5176 + 642.274i −0.0914357 + 1.38123i
\(466\) 317.261 0.680819
\(467\) −629.113 −1.34714 −0.673569 0.739124i \(-0.735240\pi\)
−0.673569 + 0.739124i \(0.735240\pi\)
\(468\) −109.140 + 10.7487i −0.233205 + 0.0229673i
\(469\) −45.3462 −0.0966869
\(470\) 251.114 199.033i 0.534286 0.423474i
\(471\) −264.651 239.867i −0.561892 0.509272i
\(472\) 11.9565i 0.0253315i
\(473\) −108.045 −0.228424
\(474\) −213.157 + 235.181i −0.449699 + 0.496163i
\(475\) 181.249 772.796i 0.381578 1.62694i
\(476\) 38.6374i 0.0811711i
\(477\) −16.0003 162.464i −0.0335437 0.340595i
\(478\) 422.000i 0.882845i
\(479\) 554.807i 1.15826i 0.815235 + 0.579131i \(0.196608\pi\)
−0.815235 + 0.579131i \(0.803392\pi\)
\(480\) 5.60487 84.6675i 0.0116768 0.176391i
\(481\) −110.427 −0.229578
\(482\) −52.7068 −0.109350
\(483\) −199.285 180.622i −0.412598 0.373959i
\(484\) 167.497 0.346069
\(485\) 372.961 + 470.555i 0.768992 + 0.970216i
\(486\) −176.678 + 294.759i −0.363534 + 0.606501i
\(487\) 244.109i 0.501251i −0.968084 0.250626i \(-0.919364\pi\)
0.968084 0.250626i \(-0.0806363\pi\)
\(488\) −47.7823 −0.0979145
\(489\) −165.786 150.261i −0.339032 0.307282i
\(490\) 38.7907 30.7454i 0.0791647 0.0627458i
\(491\) 170.600i 0.347454i −0.984794 0.173727i \(-0.944419\pi\)
0.984794 0.173727i \(-0.0555810\pi\)
\(492\) 161.970 + 146.802i 0.329208 + 0.298379i
\(493\) 299.463i 0.607429i
\(494\) 273.573i 0.553793i
\(495\) −197.485 + 190.876i −0.398960 + 0.385607i
\(496\) 171.648 0.346065
\(497\) −301.150 −0.605936
\(498\) 218.234 240.783i 0.438221 0.483499i
\(499\) −965.312 −1.93449 −0.967247 0.253837i \(-0.918307\pi\)
−0.967247 + 0.253837i \(0.918307\pi\)
\(500\) −106.448 226.205i −0.212897 0.452410i
\(501\) −230.518 + 254.336i −0.460116 + 0.507657i
\(502\) 350.165i 0.697540i
\(503\) 86.1692 0.171311 0.0856553 0.996325i \(-0.472702\pi\)
0.0856553 + 0.996325i \(0.472702\pi\)
\(504\) −67.0256 + 6.60106i −0.132987 + 0.0130973i
\(505\) −506.184 638.639i −1.00235 1.26463i
\(506\) 292.484i 0.578031i
\(507\) −265.696 + 293.148i −0.524054 + 0.578202i
\(508\) 395.264i 0.778078i
\(509\) 115.697i 0.227303i 0.993521 + 0.113651i \(0.0362547\pi\)
−0.993521 + 0.113651i \(0.963745\pi\)
\(510\) −10.2314 + 154.556i −0.0200615 + 0.303051i
\(511\) 277.996 0.544023
\(512\) −22.6274 −0.0441942
\(513\) 688.559 + 510.680i 1.34222 + 0.995477i
\(514\) −106.950 −0.208074
\(515\) −578.848 730.317i −1.12398 1.41809i
\(516\) 78.6995 + 71.3294i 0.152518 + 0.138235i
\(517\) 276.575i 0.534961i
\(518\) −67.8160 −0.130919
\(519\) 350.192 386.375i 0.674744 0.744461i
\(520\) 53.5204 + 67.5252i 0.102924 + 0.129856i
\(521\) 527.925i 1.01329i −0.862154 0.506646i \(-0.830885\pi\)
0.862154 0.506646i \(-0.169115\pi\)
\(522\) −519.487 + 51.1620i −0.995186 + 0.0980116i
\(523\) 637.700i 1.21931i 0.792666 + 0.609656i \(0.208693\pi\)
−0.792666 + 0.609656i \(0.791307\pi\)
\(524\) 76.0837i 0.145198i
\(525\) −163.311 + 112.715i −0.311068 + 0.214695i
\(526\) −79.9999 −0.152091
\(527\) −313.334 −0.594562
\(528\) 54.2676 + 49.1856i 0.102780 + 0.0931545i
\(529\) 619.237 1.17058
\(530\) −100.517 + 79.6696i −0.189655 + 0.150320i
\(531\) −37.8620 + 3.72887i −0.0713033 + 0.00702235i
\(532\) 168.009i 0.315806i
\(533\) −221.974 −0.416462
\(534\) −84.4265 76.5202i −0.158102 0.143296i
\(535\) −646.253 + 512.220i −1.20795 + 0.957420i
\(536\) 48.4771i 0.0904423i
\(537\) −298.289 270.355i −0.555472 0.503454i
\(538\) 358.796i 0.666907i
\(539\) 42.7237i 0.0792648i
\(540\) 269.861 8.65660i 0.499743 0.0160307i
\(541\) −749.392 −1.38520 −0.692599 0.721323i \(-0.743534\pi\)
−0.692599 + 0.721323i \(0.743534\pi\)
\(542\) −362.593 −0.668991
\(543\) 401.150 442.598i 0.738766 0.815098i
\(544\) 41.3051 0.0759286
\(545\) −378.877 + 300.297i −0.695187 + 0.551005i
\(546\) 45.9280 50.6734i 0.0841172 0.0928084i
\(547\) 129.416i 0.236592i −0.992978 0.118296i \(-0.962257\pi\)
0.992978 0.118296i \(-0.0377432\pi\)
\(548\) −87.5847 −0.159826
\(549\) −14.9019 151.310i −0.0271437 0.275610i
\(550\) 210.087 + 49.2731i 0.381975 + 0.0895874i
\(551\) 1302.16i 2.36328i
\(552\) 193.093 213.045i 0.349807 0.385950i
\(553\) 197.937i 0.357933i
\(554\) 262.586i 0.473982i
\(555\) 271.275 + 17.9580i 0.488784 + 0.0323568i
\(556\) −351.857 −0.632836
\(557\) −926.902 −1.66410 −0.832049 0.554703i \(-0.812832\pi\)
−0.832049 + 0.554703i \(0.812832\pi\)
\(558\) 53.5320 + 543.551i 0.0959354 + 0.974106i
\(559\) −107.855 −0.192942
\(560\) 32.8683 + 41.4690i 0.0586933 + 0.0740518i
\(561\) −99.0626 89.7856i −0.176582 0.160046i
\(562\) 368.049i 0.654892i
\(563\) −690.211 −1.22595 −0.612976 0.790101i \(-0.710028\pi\)
−0.612976 + 0.790101i \(0.710028\pi\)
\(564\) 182.591 201.457i 0.323742 0.357193i
\(565\) 439.978 348.726i 0.778722 0.617214i
\(566\) 630.065i 1.11319i
\(567\) −41.8066 210.189i −0.0737330 0.370703i
\(568\) 321.943i 0.566801i
\(569\) 155.630i 0.273515i −0.990605 0.136757i \(-0.956332\pi\)
0.990605 0.136757i \(-0.0436680\pi\)
\(570\) 44.4895 672.062i 0.0780518 1.17906i
\(571\) −961.721 −1.68427 −0.842137 0.539263i \(-0.818703\pi\)
−0.842137 + 0.539263i \(0.818703\pi\)
\(572\) −74.3716 −0.130020
\(573\) −498.376 451.704i −0.869766 0.788315i
\(574\) −136.320 −0.237492
\(575\) 193.437 824.761i 0.336412 1.43437i
\(576\) −7.05683 71.6533i −0.0122514 0.124398i
\(577\) 670.111i 1.16137i 0.814128 + 0.580685i \(0.197215\pi\)
−0.814128 + 0.580685i \(0.802785\pi\)
\(578\) 333.307 0.576656
\(579\) −756.043 685.241i −1.30577 1.18349i
\(580\) 254.748 + 321.409i 0.439221 + 0.554153i
\(581\) 202.651i 0.348797i
\(582\) 377.503 + 342.151i 0.648631 + 0.587888i
\(583\) 110.708i 0.189894i
\(584\) 297.190i 0.508887i
\(585\) −197.138 + 190.540i −0.336988 + 0.325709i
\(586\) −245.458 −0.418870
\(587\) −671.384 −1.14376 −0.571878 0.820339i \(-0.693785\pi\)
−0.571878 + 0.820339i \(0.693785\pi\)
\(588\) 28.2056 31.1199i 0.0479686 0.0529249i
\(589\) 1362.48 2.31322
\(590\) 18.5669 + 23.4254i 0.0314694 + 0.0397041i
\(591\) −232.502 + 256.525i −0.393404 + 0.434052i
\(592\) 72.4984i 0.122463i
\(593\) −173.594 −0.292738 −0.146369 0.989230i \(-0.546759\pi\)
−0.146369 + 0.989230i \(0.546759\pi\)
\(594\) −138.830 + 187.187i −0.233720 + 0.315129i
\(595\) −59.9993 75.6994i −0.100839 0.127226i
\(596\) 301.186i 0.505345i
\(597\) −375.878 + 414.715i −0.629612 + 0.694665i
\(598\) 291.969i 0.488243i
\(599\) 561.565i 0.937504i −0.883330 0.468752i \(-0.844704\pi\)
0.883330 0.468752i \(-0.155296\pi\)
\(600\) −120.497 174.586i −0.200829 0.290977i
\(601\) 382.578 0.636568 0.318284 0.947995i \(-0.396893\pi\)
0.318284 + 0.947995i \(0.396893\pi\)
\(602\) −66.2363 −0.110027
\(603\) 153.510 15.1186i 0.254578 0.0250723i
\(604\) −11.2606 −0.0186433
\(605\) 328.165 260.103i 0.542422 0.429923i
\(606\) −512.349 464.369i −0.845460 0.766285i
\(607\) 489.748i 0.806833i 0.915016 + 0.403417i \(0.132177\pi\)
−0.915016 + 0.403417i \(0.867823\pi\)
\(608\) −179.609 −0.295409
\(609\) 218.610 241.197i 0.358965 0.396054i
\(610\) −93.6162 + 74.2001i −0.153469 + 0.121639i
\(611\) 276.088i 0.451863i
\(612\) 12.8819 + 130.799i 0.0210488 + 0.213724i
\(613\) 103.287i 0.168494i −0.996445 0.0842472i \(-0.973151\pi\)
0.996445 0.0842472i \(-0.0268486\pi\)
\(614\) 344.390i 0.560896i
\(615\) 545.303 + 36.0983i 0.886672 + 0.0586964i
\(616\) −45.6736 −0.0741454
\(617\) −103.427 −0.167629 −0.0838144 0.996481i \(-0.526710\pi\)
−0.0838144 + 0.996481i \(0.526710\pi\)
\(618\) −585.898 531.030i −0.948054 0.859271i
\(619\) 1040.92 1.68162 0.840809 0.541332i \(-0.182080\pi\)
0.840809 + 0.541332i \(0.182080\pi\)
\(620\) 336.297 266.549i 0.542415 0.429917i
\(621\) 734.860 + 545.019i 1.18335 + 0.877647i
\(622\) 364.527i 0.586056i
\(623\) 71.0564 0.114055
\(624\) 54.1722 + 49.0991i 0.0868144 + 0.0786844i
\(625\) −559.826 277.886i −0.895721 0.444617i
\(626\) 221.199i 0.353354i
\(627\) 430.758 + 390.418i 0.687014 + 0.622677i
\(628\) 238.119i 0.379170i
\(629\) 132.342i 0.210400i
\(630\) −121.068 + 117.016i −0.192171 + 0.185739i
\(631\) −1243.34 −1.97043 −0.985216 0.171315i \(-0.945198\pi\)
−0.985216 + 0.171315i \(0.945198\pi\)
\(632\) 211.604 0.334816
\(633\) 702.907 775.534i 1.11044 1.22517i
\(634\) −381.398 −0.601574
\(635\) 613.797 + 774.411i 0.966609 + 1.21954i
\(636\) −73.0881 + 80.6398i −0.114918 + 0.126792i
\(637\) 42.6486i 0.0669522i
\(638\) −353.997 −0.554854
\(639\) 1019.48 100.405i 1.59544 0.157128i
\(640\) −44.3322 + 35.1377i −0.0692691 + 0.0549026i
\(641\) 168.859i 0.263431i −0.991288 0.131715i \(-0.957951\pi\)
0.991288 0.131715i \(-0.0420485\pi\)
\(642\) −469.905 + 518.457i −0.731939 + 0.807566i
\(643\) 290.872i 0.452366i 0.974085 + 0.226183i \(0.0726248\pi\)
−0.974085 + 0.226183i \(0.927375\pi\)
\(644\) 179.306i 0.278425i
\(645\) 264.956 + 17.5397i 0.410785 + 0.0271933i
\(646\) 327.866 0.507533
\(647\) 725.855 1.12188 0.560939 0.827857i \(-0.310440\pi\)
0.560939 + 0.827857i \(0.310440\pi\)
\(648\) 224.701 44.6931i 0.346761 0.0689709i
\(649\) −25.8005 −0.0397543
\(650\) 209.717 + 49.1864i 0.322642 + 0.0756714i
\(651\) −252.370 228.736i −0.387665 0.351361i
\(652\) 149.166i 0.228782i
\(653\) 977.062 1.49627 0.748133 0.663548i \(-0.230950\pi\)
0.748133 + 0.663548i \(0.230950\pi\)
\(654\) −275.490 + 303.955i −0.421238 + 0.464762i
\(655\) 118.149 + 149.065i 0.180380 + 0.227580i
\(656\) 145.732i 0.222153i
\(657\) −941.100 + 92.6848i −1.43242 + 0.141073i
\(658\) 169.553i 0.257680i
\(659\) 157.771i 0.239409i 0.992810 + 0.119705i \(0.0381948\pi\)
−0.992810 + 0.119705i \(0.961805\pi\)
\(660\) 182.702 + 12.0946i 0.276821 + 0.0183251i
\(661\) 1072.89 1.62314 0.811568 0.584258i \(-0.198614\pi\)
0.811568 + 0.584258i \(0.198614\pi\)
\(662\) −142.479 −0.215225
\(663\) −98.8884 89.6277i −0.149153 0.135185i
\(664\) −216.643 −0.326270
\(665\) 260.897 + 329.167i 0.392327 + 0.494988i
\(666\) 229.578 22.6101i 0.344711 0.0339491i
\(667\) 1389.73i 2.08355i
\(668\) 228.838 0.342572
\(669\) 983.320 + 891.235i 1.46984 + 1.33219i
\(670\) −75.2791 94.9776i −0.112357 0.141758i
\(671\) 103.108i 0.153663i
\(672\) 33.2685 + 30.1530i 0.0495068 + 0.0448706i
\(673\) 293.836i 0.436606i 0.975881 + 0.218303i \(0.0700521\pi\)
−0.975881 + 0.218303i \(0.929948\pi\)
\(674\) 243.319i 0.361007i
\(675\) 515.276 436.022i 0.763372 0.645959i
\(676\) 263.759 0.390176
\(677\) 569.262 0.840859 0.420429 0.907325i \(-0.361879\pi\)
0.420429 + 0.907325i \(0.361879\pi\)
\(678\) 319.918 352.973i 0.471855 0.520609i
\(679\) −317.720 −0.467924
\(680\) 80.9261 64.1419i 0.119009 0.0943263i
\(681\) −212.763 + 234.746i −0.312427 + 0.344708i
\(682\) 370.395i 0.543101i
\(683\) 21.2129 0.0310585 0.0155292 0.999879i \(-0.495057\pi\)
0.0155292 + 0.999879i \(0.495057\pi\)
\(684\) −56.0147 568.760i −0.0818928 0.831520i
\(685\) −171.598 + 136.008i −0.250508 + 0.198552i
\(686\) 26.1916i 0.0381802i
\(687\) 604.877 667.375i 0.880462 0.971434i
\(688\) 70.8096i 0.102921i
\(689\) 110.514i 0.160397i
\(690\) 47.4811 717.253i 0.0688132 1.03950i
\(691\) −698.350 −1.01064 −0.505318 0.862933i \(-0.668625\pi\)
−0.505318 + 0.862933i \(0.668625\pi\)
\(692\) −347.640 −0.502370
\(693\) −14.2442 144.633i −0.0205545 0.208705i
\(694\) 532.969 0.767966
\(695\) −689.367 + 546.391i −0.991895 + 0.786175i
\(696\) 257.851 + 233.703i 0.370475 + 0.335781i
\(697\) 266.027i 0.381674i
\(698\) 473.153 0.677869
\(699\) 451.969 498.669i 0.646594 0.713403i
\(700\) 128.793 + 30.2067i 0.183990 + 0.0431524i
\(701\) 1019.57i 1.45445i −0.686399 0.727225i \(-0.740810\pi\)
0.686399 0.727225i \(-0.259190\pi\)
\(702\) −138.585 + 186.857i −0.197415 + 0.266179i
\(703\) 575.468i 0.818588i
\(704\) 48.8271i 0.0693567i
\(705\) 44.8985 678.240i 0.0636858 0.962043i
\(706\) −411.852 −0.583359
\(707\) 431.211 0.609917
\(708\) 18.7930 + 17.0331i 0.0265438 + 0.0240581i
\(709\) −482.736 −0.680869 −0.340435 0.940268i \(-0.610574\pi\)
−0.340435 + 0.940268i \(0.610574\pi\)
\(710\) −499.939 630.759i −0.704139 0.888394i
\(711\) 65.9930 + 670.077i 0.0928171 + 0.942443i
\(712\) 75.9625i 0.106689i
\(713\) 1454.10 2.03941
\(714\) −60.7299 55.0427i −0.0850559 0.0770906i
\(715\) −145.711 + 115.490i −0.203791 + 0.161525i
\(716\) 268.384i 0.374838i
\(717\) −663.296 601.180i −0.925099 0.838466i
\(718\) 289.319i 0.402951i
\(719\) 1275.40i 1.77385i −0.461915 0.886924i \(-0.652838\pi\)
0.461915 0.886924i \(-0.347162\pi\)
\(720\) −125.095 129.427i −0.173743 0.179759i
\(721\) 493.113 0.683929
\(722\) −915.143 −1.26751
\(723\) −75.0859 + 82.8441i −0.103853 + 0.114584i
\(724\) −398.226 −0.550036
\(725\) 998.218 + 234.119i 1.37685 + 0.322923i
\(726\) 238.616 263.271i 0.328672 0.362632i
\(727\) 90.3245i 0.124243i 0.998069 + 0.0621214i \(0.0197866\pi\)
−0.998069 + 0.0621214i \(0.980213\pi\)
\(728\) −45.5932 −0.0626281
\(729\) 211.606 + 697.613i 0.290268 + 0.956945i
\(730\) 461.500 + 582.262i 0.632192 + 0.797620i
\(731\) 129.259i 0.176825i
\(732\) −68.0704 + 75.1037i −0.0929924 + 0.102601i
\(733\) 515.475i 0.703240i 0.936143 + 0.351620i \(0.114369\pi\)
−0.936143 + 0.351620i \(0.885631\pi\)
\(734\) 343.077i 0.467408i
\(735\) 6.93567 104.771i 0.00943628 0.142545i
\(736\) −191.686 −0.260443
\(737\) 104.607 0.141937
\(738\) 461.485 45.4497i 0.625318 0.0615849i
\(739\) −91.7703 −0.124182 −0.0620909 0.998071i \(-0.519777\pi\)
−0.0620909 + 0.998071i \(0.519777\pi\)
\(740\) −112.581 142.041i −0.152137 0.191947i
\(741\) 430.000 + 389.732i 0.580297 + 0.525954i
\(742\) 67.8694i 0.0914681i
\(743\) 680.829 0.916324 0.458162 0.888869i \(-0.348508\pi\)
0.458162 + 0.888869i \(0.348508\pi\)
\(744\) 244.529 269.795i 0.328668 0.362627i
\(745\) −467.705 590.091i −0.627792 0.792069i
\(746\) 143.944i 0.192955i
\(747\) −67.5647 686.036i −0.0904481 0.918388i
\(748\) 89.1313i 0.119159i
\(749\) 436.352i 0.582580i
\(750\) −507.193 154.937i −0.676257 0.206582i
\(751\) 275.733 0.367155 0.183577 0.983005i \(-0.441232\pi\)
0.183577 + 0.983005i \(0.441232\pi\)
\(752\) −181.260 −0.241037
\(753\) −550.386 498.844i −0.730925 0.662475i
\(754\) −353.374 −0.468666
\(755\) −22.0620 + 17.4863i −0.0292211 + 0.0231606i
\(756\) −85.1089 + 114.754i −0.112578 + 0.151791i
\(757\) 622.898i 0.822851i 0.911443 + 0.411425i \(0.134969\pi\)
−0.911443 + 0.411425i \(0.865031\pi\)
\(758\) −349.350 −0.460884
\(759\) 459.723 + 416.671i 0.605696 + 0.548974i
\(760\) −351.894 + 278.911i −0.463019 + 0.366988i
\(761\) 1122.56i 1.47511i −0.675288 0.737554i \(-0.735981\pi\)
0.675288 0.737554i \(-0.264019\pi\)
\(762\) 621.272 + 563.091i 0.815317 + 0.738965i
\(763\) 255.819i 0.335281i
\(764\) 448.412i 0.586927i
\(765\) 228.354 + 236.261i 0.298502 + 0.308839i
\(766\) −26.8275 −0.0350228
\(767\) −25.7551 −0.0335791
\(768\) −32.2349 + 35.5656i −0.0419726 + 0.0463093i
\(769\) 344.788 0.448359 0.224179 0.974548i \(-0.428030\pi\)
0.224179 + 0.974548i \(0.428030\pi\)
\(770\) −89.4848 + 70.9256i −0.116214 + 0.0921111i
\(771\) −152.361 + 168.103i −0.197615 + 0.218033i
\(772\) 680.247i 0.881149i
\(773\) −235.375 −0.304495 −0.152248 0.988342i \(-0.548651\pi\)
−0.152248 + 0.988342i \(0.548651\pi\)
\(774\) 224.230 22.0834i 0.289703 0.0285316i
\(775\) 244.964 1044.46i 0.316083 1.34769i
\(776\) 339.657i 0.437702i
\(777\) −96.6104 + 106.593i −0.124338 + 0.137185i
\(778\) 881.464i 1.13299i
\(779\) 1156.77i 1.48495i
\(780\) 182.380 + 12.0733i 0.233821 + 0.0154786i
\(781\) 694.713 0.889517
\(782\) 349.913 0.447459
\(783\) −659.643 + 889.410i −0.842456 + 1.13590i
\(784\) −28.0000 −0.0357143
\(785\) 369.770 + 466.529i 0.471045 + 0.594304i
\(786\) 119.588 + 108.388i 0.152147 + 0.137899i
\(787\) 579.779i 0.736695i 0.929688 + 0.368348i \(0.120076\pi\)
−0.929688 + 0.368348i \(0.879924\pi\)
\(788\) 230.807 0.292903
\(789\) −113.968 + 125.743i −0.144446 + 0.159370i
\(790\) 414.580 328.595i 0.524784 0.415943i
\(791\) 297.074i 0.375568i
\(792\) 154.619 15.2277i 0.195226 0.0192269i
\(793\) 102.927i 0.129794i
\(794\) 521.722i 0.657081i
\(795\) −17.9721 + 271.489i −0.0226065 + 0.341495i
\(796\) 373.139 0.468767
\(797\) −391.482 −0.491195 −0.245597 0.969372i \(-0.578984\pi\)
−0.245597 + 0.969372i \(0.578984\pi\)
\(798\) 264.074 + 239.344i 0.330920 + 0.299930i
\(799\) 330.880 0.414118
\(800\) −32.2923 + 137.685i −0.0403654 + 0.172106i
\(801\) −240.547 + 23.6905i −0.300309 + 0.0295761i
\(802\) 411.730i 0.513379i
\(803\) −641.299 −0.798628
\(804\) −76.1958 69.0603i −0.0947710 0.0858959i
\(805\) 278.441 + 351.301i 0.345889 + 0.436399i
\(806\) 369.743i 0.458738i
\(807\) −563.952 511.139i −0.698826 0.633382i
\(808\) 460.984i 0.570525i
\(809\) 1062.72i 1.31362i 0.754054 + 0.656812i \(0.228096\pi\)
−0.754054 + 0.656812i \(0.771904\pi\)
\(810\) 370.837 436.497i 0.457823 0.538886i
\(811\) −243.505 −0.300253 −0.150126 0.988667i \(-0.547968\pi\)
−0.150126 + 0.988667i \(0.547968\pi\)
\(812\) −217.016 −0.267261
\(813\) −516.549 + 569.921i −0.635361 + 0.701009i
\(814\) 156.442 0.192190
\(815\) 231.637 + 292.250i 0.284217 + 0.358588i
\(816\) 58.8431 64.9230i 0.0721117 0.0795625i
\(817\) 562.063i 0.687959i
\(818\) 185.338 0.226574
\(819\) −14.2192 144.378i −0.0173617 0.176286i
\(820\) −226.305 285.523i −0.275982 0.348198i
\(821\) 570.152i 0.694460i −0.937780 0.347230i \(-0.887122\pi\)
0.937780 0.347230i \(-0.112878\pi\)
\(822\) −124.773 + 137.665i −0.151792 + 0.167475i
\(823\) 1588.27i 1.92985i −0.262527 0.964925i \(-0.584556\pi\)
0.262527 0.964925i \(-0.415444\pi\)
\(824\) 527.160i 0.639757i
\(825\) 376.735 260.018i 0.456649 0.315173i
\(826\) −15.8169 −0.0191488
\(827\) −1084.80 −1.31173 −0.655865 0.754878i \(-0.727696\pi\)
−0.655865 + 0.754878i \(0.727696\pi\)
\(828\) −59.7813 607.005i −0.0721996 0.733098i
\(829\) −330.609 −0.398805 −0.199402 0.979918i \(-0.563900\pi\)
−0.199402 + 0.979918i \(0.563900\pi\)
\(830\) −424.453 + 336.421i −0.511390 + 0.405327i
\(831\) 412.731 + 374.079i 0.496667 + 0.450156i
\(832\) 48.7412i 0.0585832i
\(833\) 51.1125 0.0613595
\(834\) −501.254 + 553.046i −0.601024 + 0.663124i
\(835\) 448.345 355.358i 0.536940 0.425578i
\(836\) 387.573i 0.463604i
\(837\) 930.610 + 690.199i 1.11184 + 0.824611i
\(838\) 903.725i 1.07843i
\(839\) 150.651i 0.179560i 0.995962 + 0.0897802i \(0.0286165\pi\)
−0.995962 + 0.0897802i \(0.971384\pi\)
\(840\) 112.005 + 7.41454i 0.133339 + 0.00882683i
\(841\) −841.003 −1.00000
\(842\) −701.917 −0.833631
\(843\) −578.496 524.321i −0.686235 0.621971i
\(844\) −697.785 −0.826759
\(845\) 516.764 409.586i 0.611555 0.484717i
\(846\) −56.5296 573.989i −0.0668199 0.678474i
\(847\) 221.578i 0.261603i
\(848\) 72.5554 0.0855606
\(849\) −990.330 897.588i −1.16647 1.05723i
\(850\) 58.9478 251.337i 0.0693504 0.295691i
\(851\) 614.164i 0.721696i
\(852\) −506.027 458.639i −0.593929 0.538309i
\(853\) 1239.94i 1.45362i 0.686836 + 0.726812i \(0.258999\pi\)
−0.686836 + 0.726812i \(0.741001\pi\)
\(854\) 63.2100i 0.0740164i
\(855\) −992.961 1027.35i −1.16136 1.20157i
\(856\) 466.480 0.544954
\(857\) −1016.43 −1.18604 −0.593018 0.805189i \(-0.702064\pi\)
−0.593018 + 0.805189i \(0.702064\pi\)
\(858\) −105.950 + 116.897i −0.123484 + 0.136243i
\(859\) −810.174 −0.943160 −0.471580 0.881823i \(-0.656316\pi\)
−0.471580 + 0.881823i \(0.656316\pi\)
\(860\) −109.959 138.732i −0.127859 0.161316i
\(861\) −194.201 + 214.267i −0.225553 + 0.248858i
\(862\) 342.479i 0.397307i
\(863\) −23.4880 −0.0272167 −0.0136083 0.999907i \(-0.504332\pi\)
−0.0136083 + 0.999907i \(0.504332\pi\)
\(864\) −122.677 90.9852i −0.141987 0.105307i
\(865\) −681.105 + 539.843i −0.787404 + 0.624096i
\(866\) 174.872i 0.201931i
\(867\) 474.828 523.889i 0.547668 0.604255i
\(868\) 227.069i 0.261600i
\(869\) 456.614i 0.525448i
\(870\) 868.101 + 57.4670i 0.997817 + 0.0660540i
\(871\) 104.423 0.119889
\(872\) 273.482 0.313626
\(873\) 1075.58 105.929i 1.23205 0.121339i
\(874\) −1521.54 −1.74089
\(875\) 299.241 140.818i 0.341990 0.160935i
\(876\) 467.121 + 423.376i 0.533243 + 0.483306i
\(877\) 580.082i 0.661439i −0.943729 0.330719i \(-0.892709\pi\)
0.943729 0.330719i \(-0.107291\pi\)
\(878\) −593.727 −0.676226
\(879\) −349.678 + 385.808i −0.397813 + 0.438917i
\(880\) −75.8226 95.6633i −0.0861620 0.108708i
\(881\) 444.274i 0.504284i 0.967690 + 0.252142i \(0.0811350\pi\)
−0.967690 + 0.252142i \(0.918865\pi\)
\(882\) −8.73238 88.6665i −0.00990065 0.100529i
\(883\) 192.468i 0.217970i −0.994043 0.108985i \(-0.965240\pi\)
0.994043 0.108985i \(-0.0347601\pi\)
\(884\) 88.9745i 0.100650i
\(885\) 63.2702 + 4.18840i 0.0714918 + 0.00473265i
\(886\) 135.688 0.153147
\(887\) 1294.72 1.45966 0.729829 0.683630i \(-0.239600\pi\)
0.729829 + 0.683630i \(0.239600\pi\)
\(888\) −113.952 103.281i −0.128325 0.116307i
\(889\) −522.885 −0.588172
\(890\) 117.961 + 148.828i 0.132540 + 0.167222i
\(891\) 96.4422 + 484.876i 0.108240 + 0.544193i
\(892\) 884.739i 0.991860i
\(893\) −1438.78 −1.61118
\(894\) −473.401 429.068i −0.529532 0.479942i
\(895\) 416.768 + 525.825i 0.465663 + 0.587514i
\(896\) 29.9333i 0.0334077i
\(897\) 458.915 + 415.938i 0.511611 + 0.463699i
\(898\) 1104.30i 1.22973i
\(899\) 1759.92i 1.95764i
\(900\) −446.073 59.3187i −0.495637 0.0659097i
\(901\) −132.446 −0.146999
\(902\) 314.472 0.348639
\(903\) −94.3600 + 104.110i −0.104496 + 0.115293i
\(904\) −317.586 −0.351312
\(905\) −780.215 + 618.398i −0.862116 + 0.683312i
\(906\) −16.0417 + 17.6992i −0.0177061 + 0.0195356i
\(907\) 1622.83i 1.78922i 0.446844 + 0.894612i \(0.352548\pi\)
−0.446844 + 0.894612i \(0.647452\pi\)
\(908\) 211.212 0.232613
\(909\) −1459.78 + 143.767i −1.60592 + 0.158160i
\(910\) −89.3274 + 70.8008i −0.0981620 + 0.0778031i
\(911\) 181.811i 0.199573i 0.995009 + 0.0997865i \(0.0318160\pi\)
−0.995009 + 0.0997865i \(0.968184\pi\)
\(912\) −255.870 + 282.307i −0.280559 + 0.309548i
\(913\) 467.489i 0.512036i
\(914\) 870.283i 0.952170i
\(915\) −16.7383 + 252.850i −0.0182932 + 0.276339i
\(916\) −600.469 −0.655534
\(917\) −100.649 −0.109759
\(918\) 223.941 + 166.089i 0.243944 + 0.180924i
\(919\) 690.193 0.751026 0.375513 0.926817i \(-0.377467\pi\)
0.375513 + 0.926817i \(0.377467\pi\)
\(920\) −375.556 + 297.666i −0.408214 + 0.323549i
\(921\) 541.309 + 490.617i 0.587741 + 0.532700i
\(922\) 655.618i 0.711082i
\(923\) 693.491 0.751344
\(924\) −65.0664 + 71.7893i −0.0704182 + 0.0776940i
\(925\) −441.144 103.465i −0.476912 0.111854i
\(926\) 353.248i 0.381478i
\(927\) −1669.34 + 164.406i −1.80079 + 0.177352i
\(928\) 232.000i 0.250000i
\(929\) 1269.52i 1.36654i −0.730165 0.683271i \(-0.760557\pi\)
0.730165 0.683271i \(-0.239443\pi\)
\(930\) 60.1290 908.313i 0.0646548 0.976681i
\(931\) −222.255 −0.238727
\(932\) −448.675 −0.481411
\(933\) −572.960 519.304i −0.614105 0.556596i
\(934\) 889.701 0.952570
\(935\) 138.410 + 174.628i 0.148032 + 0.186768i
\(936\) 154.347 15.2010i 0.164901 0.0162403i
\(937\) 65.8708i 0.0702997i −0.999382 0.0351499i \(-0.988809\pi\)
0.999382 0.0351499i \(-0.0111909\pi\)
\(938\) 64.1292 0.0683680
\(939\) 347.679 + 315.120i 0.370265 + 0.335591i
\(940\) −355.129 + 281.475i −0.377797 + 0.299441i
\(941\) 1456.21i 1.54751i −0.633485 0.773755i \(-0.718376\pi\)
0.633485 0.773755i \(-0.281624\pi\)
\(942\) 374.273 + 339.223i 0.397318 + 0.360110i
\(943\) 1234.56i 1.30918i
\(944\) 16.9090i 0.0179121i
\(945\) 11.4516 + 356.993i 0.0121181 + 0.377770i
\(946\) 152.798 0.161520
\(947\) 1143.90 1.20792 0.603959 0.797015i \(-0.293589\pi\)
0.603959 + 0.797015i \(0.293589\pi\)
\(948\) 301.450 332.597i 0.317985 0.350840i
\(949\) −640.171 −0.674574
\(950\) −256.325 + 1092.90i −0.269816 + 1.15042i
\(951\) −543.338 + 599.477i −0.571333 + 0.630365i
\(952\) 54.6416i 0.0573966i
\(953\) 675.499 0.708814 0.354407 0.935091i \(-0.384683\pi\)
0.354407 + 0.935091i \(0.384683\pi\)
\(954\) 22.6279 + 229.758i 0.0237190 + 0.240837i
\(955\) 696.330 + 878.541i 0.729141 + 0.919938i
\(956\) 596.798i 0.624266i
\(957\) −504.302 + 556.409i −0.526962 + 0.581409i
\(958\) 784.616i 0.819014i
\(959\) 115.864i 0.120817i
\(960\) −7.92648 + 119.738i −0.00825675 + 0.124727i
\(961\) 880.440 0.916171
\(962\) 156.167 0.162336
\(963\) 145.482 + 1477.18i 0.151071 + 1.53394i
\(964\) 74.5387 0.0773223
\(965\) 1056.34 + 1332.76i 1.09466 + 1.38110i
\(966\) 281.831 + 255.439i 0.291751 + 0.264429i
\(967\) 451.801i 0.467220i −0.972330 0.233610i \(-0.924946\pi\)
0.972330 0.233610i \(-0.0750538\pi\)
\(968\) −236.877 −0.244708
\(969\) 467.077 515.337i 0.482020 0.531824i
\(970\) −527.447 665.465i −0.543759 0.686046i
\(971\) 587.257i 0.604796i −0.953182 0.302398i \(-0.902213\pi\)
0.953182 0.302398i \(-0.0977872\pi\)
\(972\) 249.860 416.853i 0.257057 0.428861i
\(973\) 465.463i 0.478379i
\(974\) 345.223i 0.354438i
\(975\) 376.073 259.560i 0.385716 0.266216i
\(976\) 67.5743 0.0692360
\(977\) −1077.86 −1.10324 −0.551620 0.834096i \(-0.685990\pi\)
−0.551620 + 0.834096i \(0.685990\pi\)
\(978\) 234.457 + 212.501i 0.239732 + 0.217281i
\(979\) −163.917 −0.167434
\(980\) −54.8583 + 43.4806i −0.0559779 + 0.0443680i
\(981\) 85.2910 + 866.025i 0.0869430 + 0.882798i
\(982\) 241.265i 0.245687i
\(983\) −1663.72 −1.69249 −0.846245 0.532794i \(-0.821142\pi\)
−0.846245 + 0.532794i \(0.821142\pi\)
\(984\) −229.061 207.610i −0.232785 0.210986i
\(985\) 452.204 358.416i 0.459090 0.363874i
\(986\) 423.504i 0.429517i
\(987\) 266.502 + 241.545i 0.270012 + 0.244726i
\(988\) 386.891i 0.391590i
\(989\) 599.857i 0.606529i
\(990\) 279.286 269.939i 0.282107 0.272666i
\(991\) 873.134 0.881064 0.440532 0.897737i \(-0.354790\pi\)
0.440532 + 0.897737i \(0.354790\pi\)
\(992\) −242.747 −0.244705
\(993\) −202.975 + 223.947i −0.204405 + 0.225525i
\(994\) 425.891 0.428462
\(995\) 731.063 579.439i 0.734737 0.582351i
\(996\) −308.629 + 340.518i −0.309869 + 0.341886i
\(997\) 1548.17i 1.55283i −0.630224 0.776413i \(-0.717037\pi\)
0.630224 0.776413i \(-0.282963\pi\)
\(998\) 1365.16 1.36789
\(999\) 291.517 393.058i 0.291809 0.393452i
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 210.3.c.a.29.4 yes 24
3.2 odd 2 inner 210.3.c.a.29.22 yes 24
5.2 odd 4 1050.3.e.e.701.6 24
5.3 odd 4 1050.3.e.e.701.7 24
5.4 even 2 inner 210.3.c.a.29.21 yes 24
15.2 even 4 1050.3.e.e.701.8 24
15.8 even 4 1050.3.e.e.701.5 24
15.14 odd 2 inner 210.3.c.a.29.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.c.a.29.3 24 15.14 odd 2 inner
210.3.c.a.29.4 yes 24 1.1 even 1 trivial
210.3.c.a.29.21 yes 24 5.4 even 2 inner
210.3.c.a.29.22 yes 24 3.2 odd 2 inner
1050.3.e.e.701.5 24 15.8 even 4
1050.3.e.e.701.6 24 5.2 odd 4
1050.3.e.e.701.7 24 5.3 odd 4
1050.3.e.e.701.8 24 15.2 even 4