Properties

Label 210.4.g.b.169.2
Level $210$
Weight $4$
Character 210.169
Analytic conductor $12.390$
Analytic rank $0$
Dimension $4$
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] = [210,4,Mod(169,210)]
 
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([0, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.169");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 210.g (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: \(12.3904011012\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{21})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 11x^{2} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 169.2
Root \(-1.79129i\) of defining polynomial
Character \(\chi\) \(=\) 210.169
Dual form 210.4.g.b.169.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +(8.58258 - 7.16515i) q^{5} +6.00000 q^{6} +7.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q-2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +(8.58258 - 7.16515i) q^{5} +6.00000 q^{6} +7.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +(-14.3303 - 17.1652i) q^{10} +30.6606 q^{11} -12.0000i q^{12} -54.8348i q^{13} +14.0000 q^{14} +(21.4955 + 25.7477i) q^{15} +16.0000 q^{16} +116.486i q^{17} +18.0000i q^{18} +105.652 q^{19} +(-34.3303 + 28.6606i) q^{20} -21.0000 q^{21} -61.3212i q^{22} -195.652i q^{23} -24.0000 q^{24} +(22.3212 - 122.991i) q^{25} -109.670 q^{26} -27.0000i q^{27} -28.0000i q^{28} +176.156 q^{29} +(51.4955 - 42.9909i) q^{30} +159.808 q^{31} -32.0000i q^{32} +91.9818i q^{33} +232.973 q^{34} +(50.1561 + 60.0780i) q^{35} +36.0000 q^{36} +47.5136i q^{37} -211.303i q^{38} +164.505 q^{39} +(57.3212 + 68.6606i) q^{40} +83.8076 q^{41} +42.0000i q^{42} -280.835i q^{43} -122.642 q^{44} +(-77.2432 + 64.4864i) q^{45} -391.303 q^{46} -538.744i q^{47} +48.0000i q^{48} -49.0000 q^{49} +(-245.982 - 44.6424i) q^{50} -349.459 q^{51} +219.339i q^{52} +555.633i q^{53} -54.0000 q^{54} +(263.147 - 219.688i) q^{55} -56.0000 q^{56} +316.955i q^{57} -352.312i q^{58} -494.606 q^{59} +(-85.9818 - 102.991i) q^{60} +312.744 q^{61} -319.615i q^{62} -63.0000i q^{63} -64.0000 q^{64} +(-392.900 - 470.624i) q^{65} +183.964 q^{66} +1061.39i q^{67} -465.945i q^{68} +586.955 q^{69} +(120.156 - 100.312i) q^{70} -1106.07 q^{71} -72.0000i q^{72} +279.808i q^{73} +95.0273 q^{74} +(368.973 + 66.9636i) q^{75} -422.606 q^{76} +214.624i q^{77} -329.009i q^{78} +643.579 q^{79} +(137.321 - 114.642i) q^{80} +81.0000 q^{81} -167.615i q^{82} +578.367i q^{83} +84.0000 q^{84} +(834.642 + 999.753i) q^{85} -561.670 q^{86} +528.468i q^{87} +245.285i q^{88} +117.477 q^{89} +(128.973 + 154.486i) q^{90} +383.844 q^{91} +782.606i q^{92} +479.423i q^{93} -1077.49 q^{94} +(906.762 - 757.009i) q^{95} +96.0000 q^{96} +648.635i q^{97} +98.0000i q^{98} -275.945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 16 q^{4} + 16 q^{5} + 24 q^{6} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 16 q^{4} + 16 q^{5} + 24 q^{6} - 36 q^{9} + 16 q^{10} - 24 q^{11} + 56 q^{14} - 24 q^{15} + 64 q^{16} + 56 q^{19} - 64 q^{20} - 84 q^{21} - 96 q^{24} - 204 q^{25} - 512 q^{26} + 448 q^{29} + 96 q^{30} + 16 q^{31} + 272 q^{34} - 56 q^{35} + 144 q^{36} + 768 q^{39} - 64 q^{40} - 288 q^{41} + 96 q^{44} - 144 q^{45} - 832 q^{46} - 196 q^{49} - 544 q^{50} - 408 q^{51} - 216 q^{54} + 576 q^{55} - 224 q^{56} - 512 q^{59} + 96 q^{60} - 912 q^{61} - 256 q^{64} + 848 q^{65} - 144 q^{66} + 1248 q^{69} + 224 q^{70} - 1968 q^{71} + 1040 q^{74} + 816 q^{75} - 224 q^{76} + 448 q^{79} + 256 q^{80} + 324 q^{81} + 336 q^{84} + 2752 q^{85} - 2320 q^{86} - 80 q^{89} - 144 q^{90} + 1792 q^{91} + 16 q^{94} + 1904 q^{95} + 384 q^{96} + 216 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 0.707107i
\(3\) 3.00000i 0.577350i
\(4\) −4.00000 −0.500000
\(5\) 8.58258 7.16515i 0.767649 0.640871i
\(6\) 6.00000 0.408248
\(7\) 7.00000i 0.377964i
\(8\) 8.00000i 0.353553i
\(9\) −9.00000 −0.333333
\(10\) −14.3303 17.1652i −0.453164 0.542810i
\(11\) 30.6606 0.840411 0.420205 0.907429i \(-0.361958\pi\)
0.420205 + 0.907429i \(0.361958\pi\)
\(12\) 12.0000i 0.288675i
\(13\) 54.8348i 1.16988i −0.811076 0.584940i \(-0.801118\pi\)
0.811076 0.584940i \(-0.198882\pi\)
\(14\) 14.0000 0.267261
\(15\) 21.4955 + 25.7477i 0.370007 + 0.443202i
\(16\) 16.0000 0.250000
\(17\) 116.486i 1.66189i 0.556356 + 0.830944i \(0.312199\pi\)
−0.556356 + 0.830944i \(0.687801\pi\)
\(18\) 18.0000i 0.235702i
\(19\) 105.652 1.27569 0.637845 0.770165i \(-0.279826\pi\)
0.637845 + 0.770165i \(0.279826\pi\)
\(20\) −34.3303 + 28.6606i −0.383824 + 0.320435i
\(21\) −21.0000 −0.218218
\(22\) 61.3212i 0.594260i
\(23\) 195.652i 1.77375i −0.462013 0.886873i \(-0.652873\pi\)
0.462013 0.886873i \(-0.347127\pi\)
\(24\) −24.0000 −0.204124
\(25\) 22.3212 122.991i 0.178570 0.983927i
\(26\) −109.670 −0.827231
\(27\) 27.0000i 0.192450i
\(28\) 28.0000i 0.188982i
\(29\) 176.156 1.12798 0.563989 0.825782i \(-0.309266\pi\)
0.563989 + 0.825782i \(0.309266\pi\)
\(30\) 51.4955 42.9909i 0.313391 0.261634i
\(31\) 159.808 0.925880 0.462940 0.886390i \(-0.346794\pi\)
0.462940 + 0.886390i \(0.346794\pi\)
\(32\) 32.0000i 0.176777i
\(33\) 91.9818i 0.485211i
\(34\) 232.973 1.17513
\(35\) 50.1561 + 60.0780i 0.242226 + 0.290144i
\(36\) 36.0000 0.166667
\(37\) 47.5136i 0.211113i 0.994413 + 0.105557i \(0.0336624\pi\)
−0.994413 + 0.105557i \(0.966338\pi\)
\(38\) 211.303i 0.902049i
\(39\) 164.505 0.675431
\(40\) 57.3212 + 68.6606i 0.226582 + 0.271405i
\(41\) 83.8076 0.319233 0.159616 0.987179i \(-0.448974\pi\)
0.159616 + 0.987179i \(0.448974\pi\)
\(42\) 42.0000i 0.154303i
\(43\) 280.835i 0.995975i −0.867184 0.497987i \(-0.834073\pi\)
0.867184 0.497987i \(-0.165927\pi\)
\(44\) −122.642 −0.420205
\(45\) −77.2432 + 64.4864i −0.255883 + 0.213624i
\(46\) −391.303 −1.25423
\(47\) 538.744i 1.67200i −0.548731 0.835999i \(-0.684889\pi\)
0.548731 0.835999i \(-0.315111\pi\)
\(48\) 48.0000i 0.144338i
\(49\) −49.0000 −0.142857
\(50\) −245.982 44.6424i −0.695742 0.126268i
\(51\) −349.459 −0.959491
\(52\) 219.339i 0.584940i
\(53\) 555.633i 1.44004i 0.693953 + 0.720020i \(0.255867\pi\)
−0.693953 + 0.720020i \(0.744133\pi\)
\(54\) −54.0000 −0.136083
\(55\) 263.147 219.688i 0.645141 0.538595i
\(56\) −56.0000 −0.133631
\(57\) 316.955i 0.736520i
\(58\) 352.312i 0.797601i
\(59\) −494.606 −1.09139 −0.545697 0.837983i \(-0.683735\pi\)
−0.545697 + 0.837983i \(0.683735\pi\)
\(60\) −85.9818 102.991i −0.185003 0.221601i
\(61\) 312.744 0.656439 0.328219 0.944602i \(-0.393551\pi\)
0.328219 + 0.944602i \(0.393551\pi\)
\(62\) 319.615i 0.654696i
\(63\) 63.0000i 0.125988i
\(64\) −64.0000 −0.125000
\(65\) −392.900 470.624i −0.749742 0.898058i
\(66\) 183.964 0.343096
\(67\) 1061.39i 1.93536i 0.252185 + 0.967679i \(0.418851\pi\)
−0.252185 + 0.967679i \(0.581149\pi\)
\(68\) 465.945i 0.830944i
\(69\) 586.955 1.02407
\(70\) 120.156 100.312i 0.205163 0.171280i
\(71\) −1106.07 −1.84881 −0.924407 0.381408i \(-0.875439\pi\)
−0.924407 + 0.381408i \(0.875439\pi\)
\(72\) 72.0000i 0.117851i
\(73\) 279.808i 0.448616i 0.974518 + 0.224308i \(0.0720122\pi\)
−0.974518 + 0.224308i \(0.927988\pi\)
\(74\) 95.0273 0.149280
\(75\) 368.973 + 66.9636i 0.568071 + 0.103097i
\(76\) −422.606 −0.637845
\(77\) 214.624i 0.317645i
\(78\) 329.009i 0.477602i
\(79\) 643.579 0.916560 0.458280 0.888808i \(-0.348466\pi\)
0.458280 + 0.888808i \(0.348466\pi\)
\(80\) 137.321 114.642i 0.191912 0.160218i
\(81\) 81.0000 0.111111
\(82\) 167.615i 0.225732i
\(83\) 578.367i 0.764867i 0.923983 + 0.382434i \(0.124914\pi\)
−0.923983 + 0.382434i \(0.875086\pi\)
\(84\) 84.0000 0.109109
\(85\) 834.642 + 999.753i 1.06506 + 1.27575i
\(86\) −561.670 −0.704260
\(87\) 528.468i 0.651238i
\(88\) 245.285i 0.297130i
\(89\) 117.477 0.139916 0.0699582 0.997550i \(-0.477713\pi\)
0.0699582 + 0.997550i \(0.477713\pi\)
\(90\) 128.973 + 154.486i 0.151055 + 0.180937i
\(91\) 383.844 0.442173
\(92\) 782.606i 0.886873i
\(93\) 479.423i 0.534557i
\(94\) −1077.49 −1.18228
\(95\) 906.762 757.009i 0.979282 0.817553i
\(96\) 96.0000 0.102062
\(97\) 648.635i 0.678958i 0.940614 + 0.339479i \(0.110251\pi\)
−0.940614 + 0.339479i \(0.889749\pi\)
\(98\) 98.0000i 0.101015i
\(99\) −275.945 −0.280137
\(100\) −89.2848 + 491.964i −0.0892848 + 0.491964i
\(101\) −1465.96 −1.44424 −0.722119 0.691769i \(-0.756832\pi\)
−0.722119 + 0.691769i \(0.756832\pi\)
\(102\) 698.918i 0.678463i
\(103\) 681.670i 0.652106i −0.945352 0.326053i \(-0.894281\pi\)
0.945352 0.326053i \(-0.105719\pi\)
\(104\) 438.679 0.413615
\(105\) −180.234 + 150.468i −0.167515 + 0.139849i
\(106\) 1111.27 1.01826
\(107\) 1401.05i 1.26583i 0.774220 + 0.632917i \(0.218142\pi\)
−0.774220 + 0.632917i \(0.781858\pi\)
\(108\) 108.000i 0.0962250i
\(109\) 161.761 0.142145 0.0710727 0.997471i \(-0.477358\pi\)
0.0710727 + 0.997471i \(0.477358\pi\)
\(110\) −439.376 526.294i −0.380844 0.456183i
\(111\) −142.541 −0.121886
\(112\) 112.000i 0.0944911i
\(113\) 382.552i 0.318473i 0.987240 + 0.159236i \(0.0509032\pi\)
−0.987240 + 0.159236i \(0.949097\pi\)
\(114\) 633.909 0.520798
\(115\) −1401.87 1679.19i −1.13674 1.36161i
\(116\) −704.624 −0.563989
\(117\) 493.514i 0.389960i
\(118\) 989.212i 0.771732i
\(119\) −815.405 −0.628135
\(120\) −205.982 + 171.964i −0.156696 + 0.130817i
\(121\) −390.927 −0.293709
\(122\) 625.488i 0.464172i
\(123\) 251.423i 0.184309i
\(124\) −639.230 −0.462940
\(125\) −689.675 1215.51i −0.493491 0.869751i
\(126\) −126.000 −0.0890871
\(127\) 144.515i 0.100974i −0.998725 0.0504868i \(-0.983923\pi\)
0.998725 0.0504868i \(-0.0160773\pi\)
\(128\) 128.000i 0.0883883i
\(129\) 842.505 0.575026
\(130\) −941.248 + 785.800i −0.635023 + 0.530148i
\(131\) 767.194 0.511680 0.255840 0.966719i \(-0.417648\pi\)
0.255840 + 0.966719i \(0.417648\pi\)
\(132\) 367.927i 0.242606i
\(133\) 739.561i 0.482166i
\(134\) 2122.77 1.36850
\(135\) −193.459 231.730i −0.123336 0.147734i
\(136\) −931.891 −0.587566
\(137\) 17.7606i 0.0110759i 0.999985 + 0.00553793i \(0.00176279\pi\)
−0.999985 + 0.00553793i \(0.998237\pi\)
\(138\) 1173.91i 0.724129i
\(139\) −1217.48 −0.742919 −0.371459 0.928449i \(-0.621143\pi\)
−0.371459 + 0.928449i \(0.621143\pi\)
\(140\) −200.624 240.312i −0.121113 0.145072i
\(141\) 1616.23 0.965328
\(142\) 2212.13i 1.30731i
\(143\) 1681.27i 0.983181i
\(144\) −144.000 −0.0833333
\(145\) 1511.87 1262.18i 0.865891 0.722888i
\(146\) 559.615 0.317220
\(147\) 147.000i 0.0824786i
\(148\) 190.055i 0.105557i
\(149\) −3485.64 −1.91648 −0.958239 0.285970i \(-0.907684\pi\)
−0.958239 + 0.285970i \(0.907684\pi\)
\(150\) 133.927 737.945i 0.0729008 0.401687i
\(151\) 665.394 0.358603 0.179301 0.983794i \(-0.442616\pi\)
0.179301 + 0.983794i \(0.442616\pi\)
\(152\) 845.212i 0.451025i
\(153\) 1048.38i 0.553963i
\(154\) 429.248 0.224609
\(155\) 1371.56 1145.05i 0.710751 0.593369i
\(156\) −658.018 −0.337716
\(157\) 1905.39i 0.968577i −0.874908 0.484289i \(-0.839078\pi\)
0.874908 0.484289i \(-0.160922\pi\)
\(158\) 1287.16i 0.648106i
\(159\) −1666.90 −0.831407
\(160\) −229.285 274.642i −0.113291 0.135702i
\(161\) 1369.56 0.670413
\(162\) 162.000i 0.0785674i
\(163\) 1389.83i 0.667851i −0.942599 0.333926i \(-0.891627\pi\)
0.942599 0.333926i \(-0.108373\pi\)
\(164\) −335.230 −0.159616
\(165\) 659.064 + 789.441i 0.310958 + 0.372472i
\(166\) 1156.73 0.540843
\(167\) 216.080i 0.100125i 0.998746 + 0.0500623i \(0.0159420\pi\)
−0.998746 + 0.0500623i \(0.984058\pi\)
\(168\) 168.000i 0.0771517i
\(169\) −809.861 −0.368621
\(170\) 1999.51 1669.28i 0.902089 0.753108i
\(171\) −950.864 −0.425230
\(172\) 1123.34i 0.497987i
\(173\) 3128.09i 1.37471i −0.726322 0.687354i \(-0.758772\pi\)
0.726322 0.687354i \(-0.241228\pi\)
\(174\) 1056.94 0.460495
\(175\) 860.936 + 156.248i 0.371890 + 0.0674930i
\(176\) 490.570 0.210103
\(177\) 1483.82i 0.630116i
\(178\) 234.955i 0.0989359i
\(179\) −449.870 −0.187848 −0.0939241 0.995579i \(-0.529941\pi\)
−0.0939241 + 0.995579i \(0.529941\pi\)
\(180\) 308.973 257.945i 0.127941 0.106812i
\(181\) 2647.87 1.08737 0.543686 0.839289i \(-0.317028\pi\)
0.543686 + 0.839289i \(0.317028\pi\)
\(182\) 767.688i 0.312664i
\(183\) 938.232i 0.378995i
\(184\) 1565.21 0.627114
\(185\) 340.442 + 407.789i 0.135296 + 0.162061i
\(186\) 958.845 0.377989
\(187\) 3571.54i 1.39667i
\(188\) 2154.98i 0.835999i
\(189\) 189.000 0.0727393
\(190\) −1514.02 1813.52i −0.578097 0.692457i
\(191\) −2809.04 −1.06416 −0.532081 0.846693i \(-0.678590\pi\)
−0.532081 + 0.846693i \(0.678590\pi\)
\(192\) 192.000i 0.0721688i
\(193\) 342.621i 0.127785i −0.997957 0.0638923i \(-0.979649\pi\)
0.997957 0.0638923i \(-0.0203514\pi\)
\(194\) 1297.27 0.480096
\(195\) 1411.87 1178.70i 0.518494 0.432864i
\(196\) 196.000 0.0714286
\(197\) 3653.00i 1.32114i 0.750763 + 0.660572i \(0.229686\pi\)
−0.750763 + 0.660572i \(0.770314\pi\)
\(198\) 551.891i 0.198087i
\(199\) −5024.78 −1.78994 −0.894968 0.446131i \(-0.852802\pi\)
−0.894968 + 0.446131i \(0.852802\pi\)
\(200\) 983.927 + 178.570i 0.347871 + 0.0631339i
\(201\) −3184.16 −1.11738
\(202\) 2931.91i 1.02123i
\(203\) 1233.09i 0.426336i
\(204\) 1397.84 0.479746
\(205\) 719.285 600.494i 0.245059 0.204587i
\(206\) −1363.34 −0.461109
\(207\) 1760.86i 0.591249i
\(208\) 877.358i 0.292470i
\(209\) 3239.34 1.07210
\(210\) 300.936 + 360.468i 0.0988885 + 0.118451i
\(211\) 4033.65 1.31606 0.658029 0.752993i \(-0.271390\pi\)
0.658029 + 0.752993i \(0.271390\pi\)
\(212\) 2222.53i 0.720020i
\(213\) 3318.20i 1.06741i
\(214\) 2802.09 0.895079
\(215\) −2012.22 2410.29i −0.638291 0.764559i
\(216\) 216.000 0.0680414
\(217\) 1118.65i 0.349950i
\(218\) 323.521i 0.100512i
\(219\) −839.423 −0.259009
\(220\) −1052.59 + 878.752i −0.322570 + 0.269297i
\(221\) 6387.51 1.94421
\(222\) 285.082i 0.0861867i
\(223\) 4000.83i 1.20141i −0.799469 0.600707i \(-0.794886\pi\)
0.799469 0.600707i \(-0.205114\pi\)
\(224\) 224.000 0.0668153
\(225\) −200.891 + 1106.92i −0.0595232 + 0.327976i
\(226\) 765.103 0.225194
\(227\) 2755.60i 0.805707i −0.915264 0.402854i \(-0.868018\pi\)
0.915264 0.402854i \(-0.131982\pi\)
\(228\) 1267.82i 0.368260i
\(229\) −333.971 −0.0963731 −0.0481865 0.998838i \(-0.515344\pi\)
−0.0481865 + 0.998838i \(0.515344\pi\)
\(230\) −3358.39 + 2803.75i −0.962807 + 0.803798i
\(231\) −643.873 −0.183393
\(232\) 1409.25i 0.398800i
\(233\) 5518.48i 1.55162i 0.630966 + 0.775810i \(0.282659\pi\)
−0.630966 + 0.775810i \(0.717341\pi\)
\(234\) 987.027 0.275744
\(235\) −3860.18 4623.81i −1.07153 1.28351i
\(236\) 1978.42 0.545697
\(237\) 1930.74i 0.529176i
\(238\) 1630.81i 0.444158i
\(239\) 3933.97 1.06472 0.532359 0.846519i \(-0.321306\pi\)
0.532359 + 0.846519i \(0.321306\pi\)
\(240\) 343.927 + 411.964i 0.0925017 + 0.110801i
\(241\) 3910.07 1.04510 0.522552 0.852608i \(-0.324980\pi\)
0.522552 + 0.852608i \(0.324980\pi\)
\(242\) 781.855i 0.207684i
\(243\) 243.000i 0.0641500i
\(244\) −1250.98 −0.328219
\(245\) −420.546 + 351.092i −0.109664 + 0.0915529i
\(246\) 502.845 0.130326
\(247\) 5793.38i 1.49241i
\(248\) 1278.46i 0.327348i
\(249\) −1735.10 −0.441596
\(250\) −2431.03 + 1379.35i −0.615007 + 0.348951i
\(251\) −1950.53 −0.490504 −0.245252 0.969459i \(-0.578871\pi\)
−0.245252 + 0.969459i \(0.578871\pi\)
\(252\) 252.000i 0.0629941i
\(253\) 5998.79i 1.49068i
\(254\) −289.030 −0.0713991
\(255\) −2999.26 + 2503.93i −0.736553 + 0.614910i
\(256\) 256.000 0.0625000
\(257\) 4481.31i 1.08769i 0.839185 + 0.543846i \(0.183032\pi\)
−0.839185 + 0.543846i \(0.816968\pi\)
\(258\) 1685.01i 0.406605i
\(259\) −332.595 −0.0797933
\(260\) 1571.60 + 1882.50i 0.374871 + 0.449029i
\(261\) −1585.40 −0.375993
\(262\) 1534.39i 0.361812i
\(263\) 4266.78i 1.00038i 0.865915 + 0.500192i \(0.166737\pi\)
−0.865915 + 0.500192i \(0.833263\pi\)
\(264\) −735.855 −0.171548
\(265\) 3981.20 + 4768.77i 0.922879 + 1.10544i
\(266\) 1479.12 0.340943
\(267\) 352.432i 0.0807808i
\(268\) 4245.55i 0.967679i
\(269\) 500.380 0.113415 0.0567077 0.998391i \(-0.481940\pi\)
0.0567077 + 0.998391i \(0.481940\pi\)
\(270\) −463.459 + 386.918i −0.104464 + 0.0872114i
\(271\) −1133.76 −0.254136 −0.127068 0.991894i \(-0.540557\pi\)
−0.127068 + 0.991894i \(0.540557\pi\)
\(272\) 1863.78i 0.415472i
\(273\) 1151.53i 0.255289i
\(274\) 35.5212 0.00783181
\(275\) 684.382 3770.98i 0.150072 0.826903i
\(276\) −2347.82 −0.512036
\(277\) 2315.90i 0.502342i 0.967943 + 0.251171i \(0.0808157\pi\)
−0.967943 + 0.251171i \(0.919184\pi\)
\(278\) 2434.97i 0.525323i
\(279\) −1438.27 −0.308627
\(280\) −480.624 + 401.248i −0.102581 + 0.0856399i
\(281\) −3792.45 −0.805119 −0.402559 0.915394i \(-0.631879\pi\)
−0.402559 + 0.915394i \(0.631879\pi\)
\(282\) 3232.46i 0.682590i
\(283\) 4375.29i 0.919026i −0.888171 0.459513i \(-0.848024\pi\)
0.888171 0.459513i \(-0.151976\pi\)
\(284\) 4424.26 0.924407
\(285\) 2271.03 + 2720.29i 0.472014 + 0.565389i
\(286\) −3362.54 −0.695214
\(287\) 586.653i 0.120659i
\(288\) 288.000i 0.0589256i
\(289\) −8656.07 −1.76187
\(290\) −2524.37 3023.75i −0.511159 0.612277i
\(291\) −1945.90 −0.391996
\(292\) 1119.23i 0.224308i
\(293\) 1703.22i 0.339602i −0.985478 0.169801i \(-0.945687\pi\)
0.985478 0.169801i \(-0.0543125\pi\)
\(294\) −294.000 −0.0583212
\(295\) −4244.99 + 3543.93i −0.837807 + 0.699442i
\(296\) −380.109 −0.0746398
\(297\) 827.836i 0.161737i
\(298\) 6971.29i 1.35515i
\(299\) −10728.5 −2.07507
\(300\) −1475.89 267.855i −0.284035 0.0515486i
\(301\) 1965.84 0.376443
\(302\) 1330.79i 0.253570i
\(303\) 4397.87i 0.833831i
\(304\) 1690.42 0.318923
\(305\) 2684.15 2240.86i 0.503914 0.420692i
\(306\) −2096.75 −0.391711
\(307\) 4284.48i 0.796509i −0.917275 0.398254i \(-0.869616\pi\)
0.917275 0.398254i \(-0.130384\pi\)
\(308\) 858.497i 0.158823i
\(309\) 2045.01 0.376494
\(310\) −2290.09 2743.12i −0.419576 0.502577i
\(311\) 2637.47 0.480892 0.240446 0.970663i \(-0.422706\pi\)
0.240446 + 0.970663i \(0.422706\pi\)
\(312\) 1316.04i 0.238801i
\(313\) 6610.92i 1.19384i 0.802302 + 0.596919i \(0.203609\pi\)
−0.802302 + 0.596919i \(0.796391\pi\)
\(314\) −3810.78 −0.684888
\(315\) −451.405 540.702i −0.0807421 0.0967147i
\(316\) −2574.32 −0.458280
\(317\) 8959.15i 1.58737i 0.608329 + 0.793685i \(0.291840\pi\)
−0.608329 + 0.793685i \(0.708160\pi\)
\(318\) 3333.80i 0.587894i
\(319\) 5401.05 0.947965
\(320\) −549.285 + 458.570i −0.0959561 + 0.0801088i
\(321\) −4203.14 −0.730829
\(322\) 2739.12i 0.474054i
\(323\) 12307.0i 2.12005i
\(324\) −324.000 −0.0555556
\(325\) −6744.19 1223.98i −1.15108 0.208905i
\(326\) −2779.66 −0.472242
\(327\) 485.282i 0.0820677i
\(328\) 670.461i 0.112866i
\(329\) 3771.21 0.631956
\(330\) 1578.88 1318.13i 0.263378 0.219880i
\(331\) 3741.55 0.621311 0.310655 0.950523i \(-0.399451\pi\)
0.310655 + 0.950523i \(0.399451\pi\)
\(332\) 2313.47i 0.382434i
\(333\) 427.623i 0.0703711i
\(334\) 432.161 0.0707987
\(335\) 7604.99 + 9109.43i 1.24031 + 1.48568i
\(336\) −336.000 −0.0545545
\(337\) 738.512i 0.119375i −0.998217 0.0596874i \(-0.980990\pi\)
0.998217 0.0596874i \(-0.0190104\pi\)
\(338\) 1619.72i 0.260655i
\(339\) −1147.65 −0.183870
\(340\) −3338.57 3999.01i −0.532528 0.637873i
\(341\) 4899.80 0.778120
\(342\) 1901.73i 0.300683i
\(343\) 343.000i 0.0539949i
\(344\) 2246.68 0.352130
\(345\) 5037.58 4205.62i 0.786128 0.656298i
\(346\) −6256.19 −0.972066
\(347\) 3194.42i 0.494195i 0.968991 + 0.247098i \(0.0794768\pi\)
−0.968991 + 0.247098i \(0.920523\pi\)
\(348\) 2113.87i 0.325619i
\(349\) 7646.63 1.17282 0.586411 0.810014i \(-0.300540\pi\)
0.586411 + 0.810014i \(0.300540\pi\)
\(350\) 312.497 1721.87i 0.0477248 0.262966i
\(351\) −1480.54 −0.225144
\(352\) 981.139i 0.148565i
\(353\) 4009.84i 0.604596i 0.953213 + 0.302298i \(0.0977538\pi\)
−0.953213 + 0.302298i \(0.902246\pi\)
\(354\) −2967.64 −0.445560
\(355\) −9492.89 + 7925.12i −1.41924 + 1.18485i
\(356\) −469.909 −0.0699582
\(357\) 2446.21i 0.362654i
\(358\) 899.739i 0.132829i
\(359\) −3743.25 −0.550309 −0.275155 0.961400i \(-0.588729\pi\)
−0.275155 + 0.961400i \(0.588729\pi\)
\(360\) −515.891 617.945i −0.0755273 0.0904683i
\(361\) 4303.24 0.627386
\(362\) 5295.73i 0.768888i
\(363\) 1172.78i 0.169573i
\(364\) −1535.38 −0.221087
\(365\) 2004.86 + 2401.47i 0.287505 + 0.344380i
\(366\) 1876.46 0.267990
\(367\) 3886.64i 0.552809i −0.961041 0.276404i \(-0.910857\pi\)
0.961041 0.276404i \(-0.0891429\pi\)
\(368\) 3130.42i 0.443437i
\(369\) −754.268 −0.106411
\(370\) 815.579 680.885i 0.114594 0.0956690i
\(371\) −3889.43 −0.544284
\(372\) 1917.69i 0.267279i
\(373\) 5980.37i 0.830165i 0.909784 + 0.415083i \(0.136247\pi\)
−0.909784 + 0.415083i \(0.863753\pi\)
\(374\) 7143.08 0.987594
\(375\) 3646.54 2069.02i 0.502151 0.284917i
\(376\) 4309.95 0.591140
\(377\) 9659.49i 1.31960i
\(378\) 378.000i 0.0514344i
\(379\) −3455.16 −0.468285 −0.234142 0.972202i \(-0.575228\pi\)
−0.234142 + 0.972202i \(0.575228\pi\)
\(380\) −3627.05 + 3028.04i −0.489641 + 0.408776i
\(381\) 433.545 0.0582971
\(382\) 5618.08i 0.752477i
\(383\) 11859.9i 1.58228i −0.611638 0.791138i \(-0.709489\pi\)
0.611638 0.791138i \(-0.290511\pi\)
\(384\) −384.000 −0.0510310
\(385\) 1537.82 + 1842.03i 0.203570 + 0.243840i
\(386\) −685.242 −0.0903573
\(387\) 2527.51i 0.331992i
\(388\) 2594.54i 0.339479i
\(389\) 11427.4 1.48944 0.744720 0.667377i \(-0.232583\pi\)
0.744720 + 0.667377i \(0.232583\pi\)
\(390\) −2357.40 2823.75i −0.306081 0.366631i
\(391\) 22790.7 2.94777
\(392\) 392.000i 0.0505076i
\(393\) 2301.58i 0.295418i
\(394\) 7305.99 0.934189
\(395\) 5523.56 4611.34i 0.703597 0.587397i
\(396\) 1103.78 0.140068
\(397\) 794.377i 0.100425i 0.998739 + 0.0502124i \(0.0159898\pi\)
−0.998739 + 0.0502124i \(0.984010\pi\)
\(398\) 10049.6i 1.26568i
\(399\) −2218.68 −0.278378
\(400\) 357.139 1967.85i 0.0446424 0.245982i
\(401\) −4513.82 −0.562118 −0.281059 0.959690i \(-0.590686\pi\)
−0.281059 + 0.959690i \(0.590686\pi\)
\(402\) 6368.32i 0.790107i
\(403\) 8763.02i 1.08317i
\(404\) 5863.82 0.722119
\(405\) 695.189 580.377i 0.0852943 0.0712078i
\(406\) 2466.18 0.301465
\(407\) 1456.80i 0.177422i
\(408\) 2795.67i 0.339231i
\(409\) −4671.30 −0.564745 −0.282373 0.959305i \(-0.591121\pi\)
−0.282373 + 0.959305i \(0.591121\pi\)
\(410\) −1200.99 1438.57i −0.144665 0.173283i
\(411\) −53.2818 −0.00639465
\(412\) 2726.68i 0.326053i
\(413\) 3462.24i 0.412508i
\(414\) 3521.73 0.418076
\(415\) 4144.08 + 4963.88i 0.490181 + 0.587150i
\(416\) −1754.72 −0.206808
\(417\) 3652.45i 0.428924i
\(418\) 6478.68i 0.758092i
\(419\) −11816.9 −1.37779 −0.688893 0.724863i \(-0.741903\pi\)
−0.688893 + 0.724863i \(0.741903\pi\)
\(420\) 720.936 601.873i 0.0837574 0.0699247i
\(421\) −14992.7 −1.73563 −0.867815 0.496888i \(-0.834476\pi\)
−0.867815 + 0.496888i \(0.834476\pi\)
\(422\) 8067.31i 0.930594i
\(423\) 4848.70i 0.557332i
\(424\) −4445.07 −0.509131
\(425\) 14326.8 + 2600.12i 1.63518 + 0.296763i
\(426\) −6636.39 −0.754775
\(427\) 2189.21i 0.248110i
\(428\) 5604.18i 0.632917i
\(429\) 5043.81 0.567640
\(430\) −4820.57 + 4024.45i −0.540625 + 0.451340i
\(431\) −8068.52 −0.901733 −0.450866 0.892591i \(-0.648885\pi\)
−0.450866 + 0.892591i \(0.648885\pi\)
\(432\) 432.000i 0.0481125i
\(433\) 12399.1i 1.37612i 0.725652 + 0.688062i \(0.241538\pi\)
−0.725652 + 0.688062i \(0.758462\pi\)
\(434\) 2237.31 0.247452
\(435\) 3786.55 + 4535.62i 0.417360 + 0.499922i
\(436\) −647.042 −0.0710727
\(437\) 20670.9i 2.26275i
\(438\) 1678.85i 0.183147i
\(439\) −4110.70 −0.446909 −0.223455 0.974714i \(-0.571733\pi\)
−0.223455 + 0.974714i \(0.571733\pi\)
\(440\) 1757.50 + 2105.18i 0.190422 + 0.228092i
\(441\) 441.000 0.0476190
\(442\) 12775.0i 1.37476i
\(443\) 2734.90i 0.293316i 0.989187 + 0.146658i \(0.0468516\pi\)
−0.989187 + 0.146658i \(0.953148\pi\)
\(444\) 570.164 0.0609432
\(445\) 1008.26 841.742i 0.107407 0.0896684i
\(446\) −8001.65 −0.849528
\(447\) 10456.9i 1.10648i
\(448\) 448.000i 0.0472456i
\(449\) 5943.34 0.624685 0.312342 0.949970i \(-0.398886\pi\)
0.312342 + 0.949970i \(0.398886\pi\)
\(450\) 2213.84 + 401.782i 0.231914 + 0.0420893i
\(451\) 2569.59 0.268287
\(452\) 1530.21i 0.159236i
\(453\) 1996.18i 0.207039i
\(454\) −5511.20 −0.569721
\(455\) 3294.37 2750.30i 0.339434 0.283376i
\(456\) −2535.64 −0.260399
\(457\) 287.312i 0.0294090i −0.999892 0.0147045i \(-0.995319\pi\)
0.999892 0.0147045i \(-0.00468075\pi\)
\(458\) 667.942i 0.0681461i
\(459\) 3145.13 0.319830
\(460\) 5607.49 + 6716.78i 0.568371 + 0.680807i
\(461\) −12184.2 −1.23096 −0.615481 0.788152i \(-0.711038\pi\)
−0.615481 + 0.788152i \(0.711038\pi\)
\(462\) 1287.75i 0.129678i
\(463\) 6900.69i 0.692662i 0.938112 + 0.346331i \(0.112573\pi\)
−0.938112 + 0.346331i \(0.887427\pi\)
\(464\) 2818.50 0.281994
\(465\) 3435.14 + 4114.68i 0.342582 + 0.410352i
\(466\) 11037.0 1.09716
\(467\) 4294.71i 0.425557i −0.977100 0.212779i \(-0.931749\pi\)
0.977100 0.212779i \(-0.0682513\pi\)
\(468\) 1974.05i 0.194980i
\(469\) −7429.70 −0.731497
\(470\) −9247.62 + 7720.36i −0.907577 + 0.757689i
\(471\) 5716.17 0.559208
\(472\) 3956.85i 0.385866i
\(473\) 8610.57i 0.837028i
\(474\) 3861.47 0.374184
\(475\) 2358.27 12994.2i 0.227800 1.25519i
\(476\) 3261.62 0.314067
\(477\) 5000.70i 0.480013i
\(478\) 7867.94i 0.752869i
\(479\) 6568.42 0.626553 0.313276 0.949662i \(-0.398573\pi\)
0.313276 + 0.949662i \(0.398573\pi\)
\(480\) 823.927 687.855i 0.0783478 0.0654086i
\(481\) 2605.40 0.246977
\(482\) 7820.15i 0.739000i
\(483\) 4108.68i 0.387063i
\(484\) 1563.71 0.146855
\(485\) 4647.57 + 5566.96i 0.435124 + 0.521201i
\(486\) 486.000 0.0453609
\(487\) 3832.82i 0.356636i −0.983973 0.178318i \(-0.942934\pi\)
0.983973 0.178318i \(-0.0570655\pi\)
\(488\) 2501.95i 0.232086i
\(489\) 4169.49 0.385584
\(490\) 702.185 + 841.092i 0.0647377 + 0.0775442i
\(491\) −179.779 −0.0165240 −0.00826202 0.999966i \(-0.502630\pi\)
−0.00826202 + 0.999966i \(0.502630\pi\)
\(492\) 1005.69i 0.0921546i
\(493\) 20519.8i 1.87457i
\(494\) −11586.8 −1.05529
\(495\) −2368.32 + 1977.19i −0.215047 + 0.179532i
\(496\) 2556.92 0.231470
\(497\) 7742.46i 0.698786i
\(498\) 3470.20i 0.312256i
\(499\) 9992.79 0.896470 0.448235 0.893916i \(-0.352053\pi\)
0.448235 + 0.893916i \(0.352053\pi\)
\(500\) 2758.70 + 4862.05i 0.246746 + 0.434875i
\(501\) −648.241 −0.0578069
\(502\) 3901.07i 0.346839i
\(503\) 3949.67i 0.350113i −0.984558 0.175057i \(-0.943989\pi\)
0.984558 0.175057i \(-0.0560109\pi\)
\(504\) 504.000 0.0445435
\(505\) −12581.7 + 10503.8i −1.10867 + 0.925570i
\(506\) −11997.6 −1.05407
\(507\) 2429.58i 0.212824i
\(508\) 578.061i 0.0504868i
\(509\) −10074.5 −0.877301 −0.438650 0.898658i \(-0.644543\pi\)
−0.438650 + 0.898658i \(0.644543\pi\)
\(510\) 5007.85 + 5998.52i 0.434807 + 0.520821i
\(511\) −1958.65 −0.169561
\(512\) 512.000i 0.0441942i
\(513\) 2852.59i 0.245507i
\(514\) 8962.63 0.769114
\(515\) −4884.27 5850.48i −0.417916 0.500588i
\(516\) −3370.02 −0.287513
\(517\) 16518.2i 1.40516i
\(518\) 665.191i 0.0564224i
\(519\) 9384.28 0.793688
\(520\) 3764.99 3143.20i 0.317511 0.265074i
\(521\) 414.977 0.0348954 0.0174477 0.999848i \(-0.494446\pi\)
0.0174477 + 0.999848i \(0.494446\pi\)
\(522\) 3170.81i 0.265867i
\(523\) 22461.1i 1.87793i −0.344013 0.938965i \(-0.611787\pi\)
0.344013 0.938965i \(-0.388213\pi\)
\(524\) −3068.78 −0.255840
\(525\) −468.745 + 2582.81i −0.0389671 + 0.214711i
\(526\) 8533.56 0.707378
\(527\) 18615.4i 1.53871i
\(528\) 1471.71i 0.121303i
\(529\) −26112.5 −2.14618
\(530\) 9537.53 7962.39i 0.781668 0.652574i
\(531\) 4451.45 0.363798
\(532\) 2958.24i 0.241083i
\(533\) 4595.58i 0.373464i
\(534\) 704.864 0.0571207
\(535\) 10038.7 + 12024.6i 0.811235 + 0.971716i
\(536\) −8491.09 −0.684252
\(537\) 1349.61i 0.108454i
\(538\) 1000.76i 0.0801967i
\(539\) −1502.37 −0.120059
\(540\) 773.836 + 926.918i 0.0616678 + 0.0738671i
\(541\) 12212.8 0.970551 0.485275 0.874361i \(-0.338719\pi\)
0.485275 + 0.874361i \(0.338719\pi\)
\(542\) 2267.52i 0.179702i
\(543\) 7943.60i 0.627794i
\(544\) 3727.56 0.293783
\(545\) 1388.32 1159.04i 0.109118 0.0910969i
\(546\) 2303.06 0.180517
\(547\) 3849.74i 0.300920i −0.988616 0.150460i \(-0.951925\pi\)
0.988616 0.150460i \(-0.0480754\pi\)
\(548\) 71.0425i 0.00553793i
\(549\) −2814.70 −0.218813
\(550\) −7541.95 1368.76i −0.584709 0.106117i
\(551\) 18611.2 1.43895
\(552\) 4695.64i 0.362064i
\(553\) 4505.05i 0.346427i
\(554\) 4631.80 0.355210
\(555\) −1223.37 + 1021.33i −0.0935659 + 0.0781134i
\(556\) 4869.94 0.371459
\(557\) 5257.65i 0.399953i −0.979801 0.199977i \(-0.935913\pi\)
0.979801 0.199977i \(-0.0640866\pi\)
\(558\) 2876.54i 0.218232i
\(559\) −15399.5 −1.16517
\(560\) 802.497 + 961.248i 0.0605566 + 0.0725360i
\(561\) −10714.6 −0.806367
\(562\) 7584.89i 0.569305i
\(563\) 11261.0i 0.842972i −0.906835 0.421486i \(-0.861509\pi\)
0.906835 0.421486i \(-0.138491\pi\)
\(564\) −6464.93 −0.482664
\(565\) 2741.04 + 3283.28i 0.204100 + 0.244475i
\(566\) −8750.59 −0.649849
\(567\) 567.000i 0.0419961i
\(568\) 8848.52i 0.653654i
\(569\) −16824.1 −1.23955 −0.619773 0.784781i \(-0.712775\pi\)
−0.619773 + 0.784781i \(0.712775\pi\)
\(570\) 5440.57 4542.05i 0.399790 0.333764i
\(571\) −3359.28 −0.246202 −0.123101 0.992394i \(-0.539284\pi\)
−0.123101 + 0.992394i \(0.539284\pi\)
\(572\) 6725.08i 0.491590i
\(573\) 8427.12i 0.614395i
\(574\) 1173.31 0.0853185
\(575\) −24063.4 4367.18i −1.74524 0.316737i
\(576\) 576.000 0.0416667
\(577\) 5889.04i 0.424894i 0.977173 + 0.212447i \(0.0681433\pi\)
−0.977173 + 0.212447i \(0.931857\pi\)
\(578\) 17312.1i 1.24583i
\(579\) 1027.86 0.0737764
\(580\) −6047.49 + 5048.74i −0.432946 + 0.361444i
\(581\) −4048.57 −0.289093
\(582\) 3891.81i 0.277183i
\(583\) 17036.1i 1.21023i
\(584\) −2238.46 −0.158610
\(585\) 3536.10 + 4235.62i 0.249914 + 0.299353i
\(586\) −3406.45 −0.240135
\(587\) 4350.31i 0.305888i −0.988235 0.152944i \(-0.951125\pi\)
0.988235 0.152944i \(-0.0488754\pi\)
\(588\) 588.000i 0.0412393i
\(589\) 16883.9 1.18114
\(590\) 7087.85 + 8489.99i 0.494580 + 0.592419i
\(591\) −10959.0 −0.762763
\(592\) 760.218i 0.0527783i
\(593\) 8538.13i 0.591263i −0.955302 0.295632i \(-0.904470\pi\)
0.955302 0.295632i \(-0.0955301\pi\)
\(594\) −1655.67 −0.114365
\(595\) −6998.27 + 5842.50i −0.482187 + 0.402553i
\(596\) 13942.6 0.958239
\(597\) 15074.3i 1.03342i
\(598\) 21457.0i 1.46730i
\(599\) 7492.48 0.511076 0.255538 0.966799i \(-0.417747\pi\)
0.255538 + 0.966799i \(0.417747\pi\)
\(600\) −535.709 + 2951.78i −0.0364504 + 0.200843i
\(601\) −6589.31 −0.447227 −0.223614 0.974678i \(-0.571785\pi\)
−0.223614 + 0.974678i \(0.571785\pi\)
\(602\) 3931.69i 0.266185i
\(603\) 9552.48i 0.645119i
\(604\) −2661.58 −0.179301
\(605\) −3355.16 + 2801.05i −0.225466 + 0.188230i
\(606\) −8795.74 −0.589608
\(607\) 28667.8i 1.91695i 0.285169 + 0.958477i \(0.407950\pi\)
−0.285169 + 0.958477i \(0.592050\pi\)
\(608\) 3380.85i 0.225512i
\(609\) −3699.28 −0.246145
\(610\) −4481.72 5368.30i −0.297474 0.356321i
\(611\) −29541.9 −1.95604
\(612\) 4193.51i 0.276981i
\(613\) 55.7559i 0.00367367i −0.999998 0.00183683i \(-0.999415\pi\)
0.999998 0.00183683i \(-0.000584683\pi\)
\(614\) −8568.96 −0.563217
\(615\) 1801.48 + 2157.85i 0.118118 + 0.141485i
\(616\) −1716.99 −0.112305
\(617\) 18958.2i 1.23700i −0.785786 0.618499i \(-0.787741\pi\)
0.785786 0.618499i \(-0.212259\pi\)
\(618\) 4090.02i 0.266221i
\(619\) 12269.4 0.796684 0.398342 0.917237i \(-0.369586\pi\)
0.398342 + 0.917237i \(0.369586\pi\)
\(620\) −5486.24 + 4580.18i −0.355375 + 0.296685i
\(621\) −5282.59 −0.341358
\(622\) 5274.95i 0.340042i
\(623\) 822.341i 0.0528835i
\(624\) 2632.07 0.168858
\(625\) −14628.5 5490.61i −0.936226 0.351399i
\(626\) 13221.8 0.844171
\(627\) 9718.02i 0.618980i
\(628\) 7621.56i 0.484289i
\(629\) −5534.69 −0.350847
\(630\) −1081.40 + 902.809i −0.0683876 + 0.0570933i
\(631\) −33.4151 −0.00210814 −0.00105407 0.999999i \(-0.500336\pi\)
−0.00105407 + 0.999999i \(0.500336\pi\)
\(632\) 5148.63i 0.324053i
\(633\) 12101.0i 0.759826i
\(634\) 17918.3 1.12244
\(635\) −1035.47 1240.31i −0.0647110 0.0775123i
\(636\) 6667.60 0.415704
\(637\) 2686.91i 0.167126i
\(638\) 10802.1i 0.670312i
\(639\) 9954.59 0.616271
\(640\) 917.139 + 1098.57i 0.0566455 + 0.0678512i
\(641\) −12210.4 −0.752389 −0.376195 0.926541i \(-0.622768\pi\)
−0.376195 + 0.926541i \(0.622768\pi\)
\(642\) 8406.27i 0.516774i
\(643\) 22026.2i 1.35090i 0.737406 + 0.675450i \(0.236050\pi\)
−0.737406 + 0.675450i \(0.763950\pi\)
\(644\) −5478.24 −0.335207
\(645\) 7230.86 6036.67i 0.441418 0.368517i
\(646\) 24613.9 1.49910
\(647\) 27688.0i 1.68242i 0.540706 + 0.841212i \(0.318157\pi\)
−0.540706 + 0.841212i \(0.681843\pi\)
\(648\) 648.000i 0.0392837i
\(649\) −15164.9 −0.917219
\(650\) −2447.96 + 13488.4i −0.147718 + 0.813935i
\(651\) −3355.96 −0.202044
\(652\) 5559.32i 0.333926i
\(653\) 23235.6i 1.39246i 0.717816 + 0.696232i \(0.245142\pi\)
−0.717816 + 0.696232i \(0.754858\pi\)
\(654\) 970.564 0.0580306
\(655\) 6584.50 5497.06i 0.392790 0.327921i
\(656\) 1340.92 0.0798082
\(657\) 2518.27i 0.149539i
\(658\) 7542.42i 0.446860i
\(659\) −7260.41 −0.429174 −0.214587 0.976705i \(-0.568841\pi\)
−0.214587 + 0.976705i \(0.568841\pi\)
\(660\) −2636.25 3157.76i −0.155479 0.186236i
\(661\) 2442.72 0.143738 0.0718690 0.997414i \(-0.477104\pi\)
0.0718690 + 0.997414i \(0.477104\pi\)
\(662\) 7483.09i 0.439333i
\(663\) 19162.5i 1.12249i
\(664\) −4626.93 −0.270421
\(665\) 5299.06 + 6347.33i 0.309006 + 0.370134i
\(666\) −855.245 −0.0497599
\(667\) 34465.2i 2.00075i
\(668\) 864.321i 0.0500623i
\(669\) 12002.5 0.693636
\(670\) 18218.9 15210.0i 1.05053 0.877034i
\(671\) 9588.92 0.551678
\(672\) 672.000i 0.0385758i
\(673\) 12046.6i 0.689986i −0.938605 0.344993i \(-0.887881\pi\)
0.938605 0.344993i \(-0.112119\pi\)
\(674\) −1477.02 −0.0844108
\(675\) −3320.75 602.673i −0.189357 0.0343658i
\(676\) 3239.44 0.184311
\(677\) 8308.82i 0.471689i 0.971791 + 0.235845i \(0.0757857\pi\)
−0.971791 + 0.235845i \(0.924214\pi\)
\(678\) 2295.31i 0.130016i
\(679\) −4540.44 −0.256622
\(680\) −7998.02 + 6677.14i −0.451044 + 0.376554i
\(681\) 8266.80 0.465175
\(682\) 9799.59i 0.550214i
\(683\) 18537.2i 1.03852i −0.854617 0.519259i \(-0.826208\pi\)
0.854617 0.519259i \(-0.173792\pi\)
\(684\) 3803.45 0.212615
\(685\) 127.257 + 152.432i 0.00709819 + 0.00850237i
\(686\) −686.000 −0.0381802
\(687\) 1001.91i 0.0556410i
\(688\) 4493.36i 0.248994i
\(689\) 30468.1 1.68467
\(690\) −8411.24 10075.2i −0.464073 0.555877i
\(691\) 28357.0 1.56114 0.780572 0.625066i \(-0.214928\pi\)
0.780572 + 0.625066i \(0.214928\pi\)
\(692\) 12512.4i 0.687354i
\(693\) 1931.62i 0.105882i
\(694\) 6388.85 0.349449
\(695\) −10449.2 + 8723.46i −0.570301 + 0.476115i
\(696\) −4227.75 −0.230248
\(697\) 9762.44i 0.530529i
\(698\) 15293.3i 0.829310i
\(699\) −16555.4 −0.895828
\(700\) −3443.75 624.994i −0.185945 0.0337465i
\(701\) −28949.5 −1.55978 −0.779892 0.625915i \(-0.784726\pi\)
−0.779892 + 0.625915i \(0.784726\pi\)
\(702\) 2961.08i 0.159201i
\(703\) 5019.89i 0.269315i
\(704\) −1962.28 −0.105051
\(705\) 13871.4 11580.5i 0.741033 0.618650i
\(706\) 8019.69 0.427514
\(707\) 10261.7i 0.545871i
\(708\) 5935.27i 0.315058i
\(709\) −15702.9 −0.831783 −0.415891 0.909414i \(-0.636530\pi\)
−0.415891 + 0.909414i \(0.636530\pi\)
\(710\) 15850.2 + 18985.8i 0.837816 + 1.00355i
\(711\) −5792.21 −0.305520
\(712\) 939.818i 0.0494679i
\(713\) 31266.6i 1.64228i
\(714\) −4892.43 −0.256435
\(715\) −12046.6 14429.6i −0.630092 0.754738i
\(716\) 1799.48 0.0939241
\(717\) 11801.9i 0.614715i
\(718\) 7486.49i 0.389127i
\(719\) 19148.5 0.993210 0.496605 0.867977i \(-0.334580\pi\)
0.496605 + 0.867977i \(0.334580\pi\)
\(720\) −1235.89 + 1031.78i −0.0639707 + 0.0534059i
\(721\) 4771.69 0.246473
\(722\) 8606.48i 0.443629i
\(723\) 11730.2i 0.603391i
\(724\) −10591.5 −0.543686
\(725\) 3932.02 21665.6i 0.201423 1.10985i
\(726\) −2345.56 −0.119906
\(727\) 18535.5i 0.945591i −0.881172 0.472795i \(-0.843245\pi\)
0.881172 0.472795i \(-0.156755\pi\)
\(728\) 3070.75i 0.156332i
\(729\) −729.000 −0.0370370
\(730\) 4802.94 4009.73i 0.243513 0.203297i
\(731\) 32713.4 1.65520
\(732\) 3752.93i 0.189498i
\(733\) 13310.0i 0.670690i 0.942095 + 0.335345i \(0.108853\pi\)
−0.942095 + 0.335345i \(0.891147\pi\)
\(734\) −7773.27 −0.390895
\(735\) −1053.28 1261.64i −0.0528581 0.0633146i
\(736\) −6260.85 −0.313557
\(737\) 32542.7i 1.62650i
\(738\) 1508.54i 0.0752439i
\(739\) −23801.7 −1.18479 −0.592394 0.805648i \(-0.701817\pi\)
−0.592394 + 0.805648i \(0.701817\pi\)
\(740\) −1361.77 1631.16i −0.0676482 0.0810305i
\(741\) 17380.2 0.861641
\(742\) 7778.87i 0.384867i
\(743\) 4631.89i 0.228705i 0.993440 + 0.114352i \(0.0364793\pi\)
−0.993440 + 0.114352i \(0.963521\pi\)
\(744\) −3835.38 −0.188995
\(745\) −29915.8 + 24975.2i −1.47118 + 1.22821i
\(746\) 11960.7 0.587016
\(747\) 5205.30i 0.254956i
\(748\) 14286.2i 0.698334i
\(749\) −9807.32 −0.478440
\(750\) −4138.05 7293.08i −0.201467 0.355074i
\(751\) 39632.9 1.92573 0.962867 0.269976i \(-0.0870159\pi\)
0.962867 + 0.269976i \(0.0870159\pi\)
\(752\) 8619.90i 0.417999i
\(753\) 5851.60i 0.283193i
\(754\) −19319.0 −0.933098
\(755\) 5710.79 4767.65i 0.275281 0.229818i
\(756\) −756.000 −0.0363696
\(757\) 9018.43i 0.432999i −0.976283 0.216500i \(-0.930536\pi\)
0.976283 0.216500i \(-0.0694640\pi\)
\(758\) 6910.33i 0.331127i
\(759\) 17996.4 0.860642
\(760\) 6056.07 + 7254.10i 0.289048 + 0.346229i
\(761\) −8028.09 −0.382415 −0.191208 0.981550i \(-0.561240\pi\)
−0.191208 + 0.981550i \(0.561240\pi\)
\(762\) 867.091i 0.0412223i
\(763\) 1132.32i 0.0537259i
\(764\) 11236.2 0.532081
\(765\) −7511.78 8997.78i −0.355018 0.425249i
\(766\) −23719.8 −1.11884
\(767\) 27121.6i 1.27680i
\(768\) 768.000i 0.0360844i
\(769\) 2437.28 0.114292 0.0571461 0.998366i \(-0.481800\pi\)
0.0571461 + 0.998366i \(0.481800\pi\)
\(770\) 3684.06 3075.63i 0.172421 0.143945i
\(771\) −13443.9 −0.627979
\(772\) 1370.48i 0.0638923i
\(773\) 20074.6i 0.934065i −0.884240 0.467032i \(-0.845323\pi\)
0.884240 0.467032i \(-0.154677\pi\)
\(774\) 5055.03 0.234753
\(775\) 3567.10 19654.9i 0.165334 0.910999i
\(776\) −5189.08 −0.240048
\(777\) 997.786i 0.0460687i
\(778\) 22854.8i 1.05319i
\(779\) 8854.40 0.407242
\(780\) −5647.49 + 4714.80i −0.259247 + 0.216432i
\(781\) −33912.6 −1.55376
\(782\) 45581.5i 2.08439i
\(783\) 4756.21i 0.217079i
\(784\) −784.000 −0.0357143
\(785\) −13652.4 16353.1i −0.620733 0.743527i
\(786\) 4603.16 0.208892
\(787\) 8697.12i 0.393925i −0.980411 0.196962i \(-0.936892\pi\)
0.980411 0.196962i \(-0.0631077\pi\)
\(788\) 14612.0i 0.660572i
\(789\) −12800.3 −0.577572
\(790\) −9222.68 11047.1i −0.415352 0.497518i
\(791\) −2677.86 −0.120371
\(792\) 2207.56i 0.0990434i
\(793\) 17149.3i 0.767955i
\(794\) 1588.75 0.0710111
\(795\) −14306.3 + 11943.6i −0.638229 + 0.532825i
\(796\) 20099.1 0.894968
\(797\) 35253.0i 1.56678i 0.621528 + 0.783392i \(0.286512\pi\)
−0.621528 + 0.783392i \(0.713488\pi\)
\(798\) 4437.36i 0.196843i
\(799\) 62756.3 2.77867
\(800\) −3935.71 714.279i −0.173935 0.0315670i
\(801\) −1057.30 −0.0466388
\(802\) 9027.64i 0.397477i
\(803\) 8579.07i 0.377022i
\(804\) 12736.6 0.558690
\(805\) 11754.4 9813.11i 0.514642 0.429648i
\(806\) −17526.0 −0.765917
\(807\) 1501.14i 0.0654804i
\(808\) 11727.6i 0.510615i
\(809\) 31944.9 1.38828 0.694142 0.719838i \(-0.255784\pi\)
0.694142 + 0.719838i \(0.255784\pi\)
\(810\) −1160.75 1390.38i −0.0503516 0.0603122i
\(811\) −1254.44 −0.0543150 −0.0271575 0.999631i \(-0.508646\pi\)
−0.0271575 + 0.999631i \(0.508646\pi\)
\(812\) 4932.37i 0.213168i
\(813\) 3401.28i 0.146726i
\(814\) 2913.59 0.125456
\(815\) −9958.33 11928.3i −0.428006 0.512675i
\(816\) −5591.35 −0.239873
\(817\) 29670.6i 1.27056i
\(818\) 9342.59i 0.399335i
\(819\) −3454.60 −0.147391
\(820\) −2877.14 + 2401.98i −0.122529 + 0.102293i
\(821\) 10557.8 0.448807 0.224404 0.974496i \(-0.427957\pi\)
0.224404 + 0.974496i \(0.427957\pi\)
\(822\) 106.564i 0.00452170i
\(823\) 3302.12i 0.139860i −0.997552 0.0699300i \(-0.977722\pi\)
0.997552 0.0699300i \(-0.0222776\pi\)
\(824\) 5453.36 0.230554
\(825\) 11312.9 + 2053.15i 0.477413 + 0.0866441i
\(826\) −6924.48 −0.291687
\(827\) 14906.3i 0.626773i 0.949626 + 0.313387i \(0.101464\pi\)
−0.949626 + 0.313387i \(0.898536\pi\)
\(828\) 7043.45i 0.295624i
\(829\) 44271.0 1.85476 0.927380 0.374121i \(-0.122055\pi\)
0.927380 + 0.374121i \(0.122055\pi\)
\(830\) 9927.75 8288.17i 0.415177 0.346610i
\(831\) −6947.70 −0.290028
\(832\) 3509.43i 0.146235i
\(833\) 5707.83i 0.237413i
\(834\) −7304.91 −0.303295
\(835\) 1548.25 + 1854.53i 0.0641669 + 0.0768605i
\(836\) −12957.4 −0.536052
\(837\) 4314.80i 0.178186i
\(838\) 23633.8i 0.974242i
\(839\) −20275.1 −0.834294 −0.417147 0.908839i \(-0.636970\pi\)
−0.417147 + 0.908839i \(0.636970\pi\)
\(840\) −1203.75 1441.87i −0.0494442 0.0592254i
\(841\) 6641.96 0.272334
\(842\) 29985.4i 1.22728i
\(843\) 11377.3i 0.464835i
\(844\) −16134.6 −0.658029
\(845\) −6950.69 + 5802.77i −0.282972 + 0.236238i
\(846\) 9697.39 0.394094
\(847\) 2736.49i 0.111012i
\(848\) 8890.13i 0.360010i
\(849\) 13125.9 0.530600
\(850\) 5200.23 28653.5i 0.209843 1.15624i
\(851\) 9296.12 0.374461
\(852\) 13272.8i 0.533707i
\(853\) 5641.20i 0.226437i −0.993570 0.113219i \(-0.963884\pi\)
0.993570 0.113219i \(-0.0361161\pi\)
\(854\) 4378.42 0.175441
\(855\) −8160.86 + 6813.08i −0.326427 + 0.272518i
\(856\) −11208.4 −0.447540
\(857\) 10407.2i 0.414823i −0.978254 0.207412i \(-0.933496\pi\)
0.978254 0.207412i \(-0.0665039\pi\)
\(858\) 10087.6i 0.401382i
\(859\) −32492.8 −1.29062 −0.645308 0.763923i \(-0.723271\pi\)
−0.645308 + 0.763923i \(0.723271\pi\)
\(860\) 8048.90 + 9641.15i 0.319145 + 0.382279i
\(861\) −1759.96 −0.0696623
\(862\) 16137.0i 0.637622i
\(863\) 13052.9i 0.514862i 0.966297 + 0.257431i \(0.0828761\pi\)
−0.966297 + 0.257431i \(0.917124\pi\)
\(864\) −864.000 −0.0340207
\(865\) −22413.3 26847.1i −0.881010 1.05529i
\(866\) 24798.1 0.973066
\(867\) 25968.2i 1.01722i
\(868\) 4474.61i 0.174975i
\(869\) 19732.5 0.770287
\(870\) 9071.24 7573.11i 0.353499 0.295118i
\(871\) 58201.0 2.26414
\(872\) 1294.08i 0.0502560i
\(873\) 5837.71i 0.226319i
\(874\) −41341.8 −1.60001
\(875\) 8508.60 4827.72i 0.328735 0.186522i
\(876\) 3357.69 0.129504
\(877\) 40123.2i 1.54488i 0.635085 + 0.772442i \(0.280965\pi\)
−0.635085 + 0.772442i \(0.719035\pi\)
\(878\) 8221.41i 0.316013i
\(879\) 5109.67 0.196069
\(880\) 4210.35 3515.01i 0.161285 0.134649i
\(881\) 24173.9 0.924450 0.462225 0.886763i \(-0.347051\pi\)
0.462225 + 0.886763i \(0.347051\pi\)
\(882\) 882.000i 0.0336718i
\(883\) 17236.7i 0.656921i 0.944518 + 0.328460i \(0.106530\pi\)
−0.944518 + 0.328460i \(0.893470\pi\)
\(884\) −25550.0 −0.972105
\(885\) −10631.8 12735.0i −0.403823 0.483708i
\(886\) 5469.79 0.207406
\(887\) 20394.9i 0.772033i 0.922492 + 0.386017i \(0.126149\pi\)
−0.922492 + 0.386017i \(0.873851\pi\)
\(888\) 1140.33i 0.0430933i
\(889\) 1011.61 0.0381644
\(890\) −1683.48 2016.52i −0.0634051 0.0759480i
\(891\) 2483.51 0.0933790
\(892\) 16003.3i 0.600707i
\(893\) 56919.1i 2.13295i
\(894\) −20913.9 −0.782398
\(895\) −3861.04 + 3223.38i −0.144202 + 0.120386i
\(896\) −896.000 −0.0334077
\(897\) 32185.6i 1.19804i
\(898\) 11886.7i 0.441719i
\(899\) 28151.1 1.04437
\(900\) 803.564 4427.67i 0.0297616 0.163988i
\(901\) −64723.7 −2.39318
\(902\) 5139.18i 0.189707i
\(903\) 5897.53i 0.217340i
\(904\) −3060.41 −0.112597
\(905\) 22725.5 18972.4i 0.834720 0.696865i
\(906\) 3992.36 0.146399
\(907\) 34733.2i 1.27155i 0.771875 + 0.635775i \(0.219319\pi\)
−0.771875 + 0.635775i \(0.780681\pi\)
\(908\) 11022.4i 0.402854i
\(909\) 13193.6 0.481413
\(910\) −5500.60 6588.74i −0.200377 0.240016i
\(911\) 26713.5 0.971524 0.485762 0.874091i \(-0.338542\pi\)
0.485762 + 0.874091i \(0.338542\pi\)
\(912\) 5071.27i 0.184130i
\(913\) 17733.1i 0.642803i
\(914\) −574.624 −0.0207953
\(915\) 6722.57 + 8052.45i 0.242887 + 0.290935i
\(916\) 1335.88 0.0481865
\(917\) 5370.36i 0.193397i
\(918\) 6290.26i 0.226154i
\(919\) −38603.5 −1.38565 −0.692825 0.721106i \(-0.743634\pi\)
−0.692825 + 0.721106i \(0.743634\pi\)
\(920\) 13433.6 11215.0i 0.481403 0.401899i
\(921\) 12853.4 0.459864
\(922\) 24368.4i 0.870422i
\(923\) 60650.9i 2.16289i
\(924\) 2575.49 0.0916964
\(925\) 5843.75 + 1060.56i 0.207720 + 0.0376984i
\(926\) 13801.4 0.489786
\(927\) 6135.03i 0.217369i
\(928\) 5636.99i 0.199400i
\(929\) 54066.0 1.90942 0.954709 0.297541i \(-0.0961665\pi\)
0.954709 + 0.297541i \(0.0961665\pi\)
\(930\) 8229.36 6870.27i 0.290163 0.242242i
\(931\) −5176.92 −0.182242
\(932\) 22073.9i 0.775810i
\(933\) 7912.42i 0.277643i
\(934\) −8589.41 −0.300915
\(935\) 25590.6 + 30653.0i 0.895084 + 1.07215i
\(936\) −3948.11 −0.137872
\(937\) 1515.57i 0.0528403i 0.999651 + 0.0264202i \(0.00841077\pi\)
−0.999651 + 0.0264202i \(0.991589\pi\)
\(938\) 14859.4i 0.517246i
\(939\) −19832.8 −0.689263
\(940\) 15440.7 + 18495.2i 0.535767 + 0.641753i
\(941\) −37134.9 −1.28647 −0.643233 0.765671i \(-0.722407\pi\)
−0.643233 + 0.765671i \(0.722407\pi\)
\(942\) 11432.3i 0.395420i
\(943\) 16397.1i 0.566238i
\(944\) −7913.70 −0.272848
\(945\) 1622.11 1354.21i 0.0558382 0.0466165i
\(946\) −17221.1 −0.591868
\(947\) 18402.2i 0.631460i −0.948849 0.315730i \(-0.897751\pi\)
0.948849 0.315730i \(-0.102249\pi\)
\(948\) 7722.95i 0.264588i
\(949\) 15343.2 0.524828
\(950\) −25988.4 4716.54i −0.887551 0.161079i
\(951\) −26877.5 −0.916468
\(952\) 6523.24i 0.222079i
\(953\) 22868.7i 0.777325i 0.921380 + 0.388663i \(0.127063\pi\)
−0.921380 + 0.388663i \(0.872937\pi\)
\(954\) −10001.4 −0.339421
\(955\) −24108.8 + 20127.2i −0.816903 + 0.681991i
\(956\) −15735.9 −0.532359
\(957\) 16203.2i 0.547308i
\(958\) 13136.8i 0.443040i
\(959\) −124.324 −0.00418628
\(960\) −1375.71 1647.85i −0.0462509 0.0554003i
\(961\) −4252.54 −0.142746
\(962\) 5210.81i 0.174639i
\(963\) 12609.4i 0.421944i
\(964\) −15640.3 −0.522552
\(965\) −2454.93 2940.57i −0.0818934 0.0980937i
\(966\) 8217.36 0.273695
\(967\) 40859.1i 1.35878i 0.733777 + 0.679391i \(0.237756\pi\)
−0.733777 + 0.679391i \(0.762244\pi\)
\(968\) 3127.42i 0.103842i
\(969\) −36920.9 −1.22401
\(970\) 11133.9 9295.13i 0.368545 0.307679i
\(971\) 45438.0 1.50172 0.750862 0.660460i \(-0.229639\pi\)
0.750862 + 0.660460i \(0.229639\pi\)
\(972\) 972.000i 0.0320750i
\(973\) 8522.39i 0.280797i
\(974\) −7665.64 −0.252179
\(975\) 3671.94 20232.6i 0.120612 0.664575i
\(976\) 5003.90 0.164110
\(977\) 28110.1i 0.920493i 0.887791 + 0.460247i \(0.152239\pi\)
−0.887791 + 0.460247i \(0.847761\pi\)
\(978\) 8338.97i 0.272649i
\(979\) 3601.92 0.117587
\(980\) 1682.18 1404.37i 0.0548321 0.0457765i
\(981\) −1455.85 −0.0473818
\(982\) 359.558i 0.0116843i
\(983\) 22370.7i 0.725853i −0.931818 0.362927i \(-0.881778\pi\)
0.931818 0.362927i \(-0.118222\pi\)
\(984\) −2011.38 −0.0651631
\(985\) 26174.3 + 31352.1i 0.846682 + 1.01417i
\(986\) 41039.6 1.32552
\(987\) 11313.6i 0.364860i
\(988\) 23173.5i 0.746203i
\(989\) −54945.8 −1.76661
\(990\) 3954.38 + 4736.65i 0.126948 + 0.152061i
\(991\) 3410.74 0.109330 0.0546648 0.998505i \(-0.482591\pi\)
0.0546648 + 0.998505i \(0.482591\pi\)
\(992\) 5113.84i 0.163674i
\(993\) 11224.6i 0.358714i
\(994\) −15484.9 −0.494116
\(995\) −43125.6 + 36003.3i −1.37404 + 1.14712i
\(996\) 6940.40 0.220798
\(997\) 45250.9i 1.43742i 0.695309 + 0.718711i \(0.255267\pi\)
−0.695309 + 0.718711i \(0.744733\pi\)
\(998\) 19985.6i 0.633900i
\(999\) 1282.87 0.0406288
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 210.4.g.b.169.2 4
3.2 odd 2 630.4.g.d.379.3 4
5.2 odd 4 1050.4.a.bh.1.2 2
5.3 odd 4 1050.4.a.ba.1.2 2
5.4 even 2 inner 210.4.g.b.169.4 yes 4
15.14 odd 2 630.4.g.d.379.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.4.g.b.169.2 4 1.1 even 1 trivial
210.4.g.b.169.4 yes 4 5.4 even 2 inner
630.4.g.d.379.1 4 15.14 odd 2
630.4.g.d.379.3 4 3.2 odd 2
1050.4.a.ba.1.2 2 5.3 odd 4
1050.4.a.bh.1.2 2 5.2 odd 4