Properties

Label 210.4.g.a.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: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 169.2
Root \(-1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 210.169
Dual form 210.4.g.a.169.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(8.79796 + 6.89898i) q^{5} -6.00000 q^{6} -7.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q-2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(8.79796 + 6.89898i) q^{5} -6.00000 q^{6} -7.00000i q^{7} +8.00000i q^{8} -9.00000 q^{9} +(13.7980 - 17.5959i) q^{10} +25.5959 q^{11} +12.0000i q^{12} -89.1918i q^{13} -14.0000 q^{14} +(20.6969 - 26.3939i) q^{15} +16.0000 q^{16} -18.7878i q^{17} +18.0000i q^{18} +11.7980 q^{19} +(-35.1918 - 27.5959i) q^{20} -21.0000 q^{21} -51.1918i q^{22} -159.373i q^{23} +24.0000 q^{24} +(29.8082 + 121.394i) q^{25} -178.384 q^{26} +27.0000i q^{27} +28.0000i q^{28} -19.7980 q^{29} +(-52.7878 - 41.3939i) q^{30} -126.404 q^{31} -32.0000i q^{32} -76.7878i q^{33} -37.5755 q^{34} +(48.2929 - 61.5857i) q^{35} +36.0000 q^{36} -282.969i q^{37} -23.5959i q^{38} -267.576 q^{39} +(-55.1918 + 70.3837i) q^{40} -144.384 q^{41} +42.0000i q^{42} +326.929i q^{43} -102.384 q^{44} +(-79.1816 - 62.0908i) q^{45} -318.747 q^{46} +117.435i q^{47} -48.0000i q^{48} -49.0000 q^{49} +(242.788 - 59.6163i) q^{50} -56.3633 q^{51} +356.767i q^{52} -634.504i q^{53} +54.0000 q^{54} +(225.192 + 176.586i) q^{55} +56.0000 q^{56} -35.3939i q^{57} +39.5959i q^{58} +515.069 q^{59} +(-82.7878 + 105.576i) q^{60} +395.716 q^{61} +252.808i q^{62} +63.0000i q^{63} -64.0000 q^{64} +(615.333 - 784.706i) q^{65} -153.576 q^{66} +842.120i q^{67} +75.1510i q^{68} -478.120 q^{69} +(-123.171 - 96.5857i) q^{70} +402.100 q^{71} -72.0000i q^{72} -303.171i q^{73} -565.939 q^{74} +(364.182 - 89.4245i) q^{75} -47.1918 q^{76} -179.171i q^{77} +535.151i q^{78} -266.384 q^{79} +(140.767 + 110.384i) q^{80} +81.0000 q^{81} +288.767i q^{82} -753.253i q^{83} +84.0000 q^{84} +(129.616 - 165.294i) q^{85} +653.857 q^{86} +59.3939i q^{87} +204.767i q^{88} +842.967 q^{89} +(-124.182 + 158.363i) q^{90} -624.343 q^{91} +637.494i q^{92} +379.212i q^{93} +234.869 q^{94} +(103.798 + 81.3939i) q^{95} -96.0000 q^{96} +1201.92i q^{97} +98.0000i q^{98} -230.363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 16 q^{4} - 4 q^{5} - 24 q^{6} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 16 q^{4} - 4 q^{5} - 24 q^{6} - 36 q^{9} + 16 q^{10} + 24 q^{11} - 56 q^{14} + 24 q^{15} + 64 q^{16} + 8 q^{19} + 16 q^{20} - 84 q^{21} + 96 q^{24} + 276 q^{25} - 400 q^{26} - 40 q^{29} + 24 q^{30} - 584 q^{31} + 320 q^{34} + 56 q^{35} + 144 q^{36} - 600 q^{39} - 64 q^{40} - 264 q^{41} - 96 q^{44} + 36 q^{45} - 256 q^{46} - 196 q^{49} + 736 q^{50} + 480 q^{51} + 216 q^{54} + 744 q^{55} + 224 q^{56} - 448 q^{59} - 96 q^{60} - 24 q^{61} - 256 q^{64} + 1168 q^{65} - 144 q^{66} - 384 q^{69} + 56 q^{70} - 312 q^{71} - 1088 q^{74} + 1104 q^{75} - 32 q^{76} - 752 q^{79} - 64 q^{80} + 324 q^{81} + 336 q^{84} + 832 q^{85} - 128 q^{86} - 1096 q^{89} - 144 q^{90} - 1400 q^{91} + 2272 q^{94} + 376 q^{95} - 384 q^{96} - 216 q^{99}+O(q^{100}) \) 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
\(5\) 8.79796 + 6.89898i 0.786913 + 0.617063i
\(6\) −6.00000 −0.408248
\(7\) 7.00000i 0.377964i
\(8\) 8.00000i 0.353553i
\(9\) −9.00000 −0.333333
\(10\) 13.7980 17.5959i 0.436330 0.556432i
\(11\) 25.5959 0.701587 0.350794 0.936453i \(-0.385912\pi\)
0.350794 + 0.936453i \(0.385912\pi\)
\(12\) 12.0000i 0.288675i
\(13\) 89.1918i 1.90287i −0.307843 0.951437i \(-0.599607\pi\)
0.307843 0.951437i \(-0.400393\pi\)
\(14\) −14.0000 −0.267261
\(15\) 20.6969 26.3939i 0.356262 0.454325i
\(16\) 16.0000 0.250000
\(17\) 18.7878i 0.268041i −0.990979 0.134021i \(-0.957211\pi\)
0.990979 0.134021i \(-0.0427888\pi\)
\(18\) 18.0000i 0.235702i
\(19\) 11.7980 0.142455 0.0712273 0.997460i \(-0.477308\pi\)
0.0712273 + 0.997460i \(0.477308\pi\)
\(20\) −35.1918 27.5959i −0.393457 0.308532i
\(21\) −21.0000 −0.218218
\(22\) 51.1918i 0.496097i
\(23\) 159.373i 1.44486i −0.691447 0.722428i \(-0.743026\pi\)
0.691447 0.722428i \(-0.256974\pi\)
\(24\) 24.0000 0.204124
\(25\) 29.8082 + 121.394i 0.238465 + 0.971151i
\(26\) −178.384 −1.34554
\(27\) 27.0000i 0.192450i
\(28\) 28.0000i 0.188982i
\(29\) −19.7980 −0.126772 −0.0633860 0.997989i \(-0.520190\pi\)
−0.0633860 + 0.997989i \(0.520190\pi\)
\(30\) −52.7878 41.3939i −0.321256 0.251915i
\(31\) −126.404 −0.732350 −0.366175 0.930546i \(-0.619333\pi\)
−0.366175 + 0.930546i \(0.619333\pi\)
\(32\) 32.0000i 0.176777i
\(33\) 76.7878i 0.405062i
\(34\) −37.5755 −0.189534
\(35\) 48.2929 61.5857i 0.233228 0.297425i
\(36\) 36.0000 0.166667
\(37\) 282.969i 1.25729i −0.777691 0.628647i \(-0.783609\pi\)
0.777691 0.628647i \(-0.216391\pi\)
\(38\) 23.5959i 0.100731i
\(39\) −267.576 −1.09862
\(40\) −55.1918 + 70.3837i −0.218165 + 0.278216i
\(41\) −144.384 −0.549974 −0.274987 0.961448i \(-0.588674\pi\)
−0.274987 + 0.961448i \(0.588674\pi\)
\(42\) 42.0000i 0.154303i
\(43\) 326.929i 1.15945i 0.814814 + 0.579723i \(0.196839\pi\)
−0.814814 + 0.579723i \(0.803161\pi\)
\(44\) −102.384 −0.350794
\(45\) −79.1816 62.0908i −0.262304 0.205688i
\(46\) −318.747 −1.02167
\(47\) 117.435i 0.364460i 0.983256 + 0.182230i \(0.0583315\pi\)
−0.983256 + 0.182230i \(0.941668\pi\)
\(48\) 48.0000i 0.144338i
\(49\) −49.0000 −0.142857
\(50\) 242.788 59.6163i 0.686707 0.168620i
\(51\) −56.3633 −0.154754
\(52\) 356.767i 0.951437i
\(53\) 634.504i 1.64445i −0.569163 0.822225i \(-0.692733\pi\)
0.569163 0.822225i \(-0.307267\pi\)
\(54\) 54.0000 0.136083
\(55\) 225.192 + 176.586i 0.552088 + 0.432924i
\(56\) 56.0000 0.133631
\(57\) 35.3939i 0.0822462i
\(58\) 39.5959i 0.0896414i
\(59\) 515.069 1.13655 0.568274 0.822839i \(-0.307611\pi\)
0.568274 + 0.822839i \(0.307611\pi\)
\(60\) −82.7878 + 105.576i −0.178131 + 0.227162i
\(61\) 395.716 0.830595 0.415297 0.909686i \(-0.363678\pi\)
0.415297 + 0.909686i \(0.363678\pi\)
\(62\) 252.808i 0.517849i
\(63\) 63.0000i 0.125988i
\(64\) −64.0000 −0.125000
\(65\) 615.333 784.706i 1.17419 1.49740i
\(66\) −153.576 −0.286422
\(67\) 842.120i 1.53554i 0.640724 + 0.767772i \(0.278634\pi\)
−0.640724 + 0.767772i \(0.721366\pi\)
\(68\) 75.1510i 0.134021i
\(69\) −478.120 −0.834187
\(70\) −123.171 96.5857i −0.210311 0.164917i
\(71\) 402.100 0.672120 0.336060 0.941841i \(-0.390906\pi\)
0.336060 + 0.941841i \(0.390906\pi\)
\(72\) 72.0000i 0.117851i
\(73\) 303.171i 0.486076i −0.970017 0.243038i \(-0.921856\pi\)
0.970017 0.243038i \(-0.0781439\pi\)
\(74\) −565.939 −0.889041
\(75\) 364.182 89.4245i 0.560694 0.137678i
\(76\) −47.1918 −0.0712273
\(77\) 179.171i 0.265175i
\(78\) 535.151i 0.776845i
\(79\) −266.384 −0.379373 −0.189687 0.981845i \(-0.560747\pi\)
−0.189687 + 0.981845i \(0.560747\pi\)
\(80\) 140.767 + 110.384i 0.196728 + 0.154266i
\(81\) 81.0000 0.111111
\(82\) 288.767i 0.388890i
\(83\) 753.253i 0.996148i −0.867135 0.498074i \(-0.834041\pi\)
0.867135 0.498074i \(-0.165959\pi\)
\(84\) 84.0000 0.109109
\(85\) 129.616 165.294i 0.165398 0.210925i
\(86\) 653.857 0.819851
\(87\) 59.3939i 0.0731919i
\(88\) 204.767i 0.248049i
\(89\) 842.967 1.00398 0.501991 0.864873i \(-0.332601\pi\)
0.501991 + 0.864873i \(0.332601\pi\)
\(90\) −124.182 + 158.363i −0.145443 + 0.185477i
\(91\) −624.343 −0.719219
\(92\) 637.494i 0.722428i
\(93\) 379.212i 0.422822i
\(94\) 234.869 0.257712
\(95\) 103.798 + 81.3939i 0.112099 + 0.0879035i
\(96\) −96.0000 −0.102062
\(97\) 1201.92i 1.25811i 0.777362 + 0.629053i \(0.216557\pi\)
−0.777362 + 0.629053i \(0.783443\pi\)
\(98\) 98.0000i 0.101015i
\(99\) −230.363 −0.233862
\(100\) −119.233 485.576i −0.119233 0.485576i
\(101\) 575.371 0.566847 0.283424 0.958995i \(-0.408530\pi\)
0.283424 + 0.958995i \(0.408530\pi\)
\(102\) 112.727i 0.109427i
\(103\) 254.220i 0.243195i 0.992579 + 0.121597i \(0.0388017\pi\)
−0.992579 + 0.121597i \(0.961198\pi\)
\(104\) 713.535 0.672768
\(105\) −184.757 144.879i −0.171719 0.134654i
\(106\) −1269.01 −1.16280
\(107\) 1142.61i 1.03234i 0.856487 + 0.516168i \(0.172642\pi\)
−0.856487 + 0.516168i \(0.827358\pi\)
\(108\) 108.000i 0.0962250i
\(109\) 2054.28 1.80518 0.902589 0.430502i \(-0.141664\pi\)
0.902589 + 0.430502i \(0.141664\pi\)
\(110\) 353.171 450.384i 0.306123 0.390385i
\(111\) −848.908 −0.725899
\(112\) 112.000i 0.0944911i
\(113\) 890.827i 0.741610i 0.928711 + 0.370805i \(0.120918\pi\)
−0.928711 + 0.370805i \(0.879082\pi\)
\(114\) −70.7878 −0.0581568
\(115\) 1099.51 1402.16i 0.891567 1.13698i
\(116\) 79.1918 0.0633860
\(117\) 802.727i 0.634291i
\(118\) 1030.14i 0.803661i
\(119\) −131.514 −0.101310
\(120\) 211.151 + 165.576i 0.160628 + 0.125958i
\(121\) −675.849 −0.507775
\(122\) 791.433i 0.587319i
\(123\) 433.151i 0.317528i
\(124\) 505.616 0.366175
\(125\) −575.243 + 1273.66i −0.411610 + 0.911360i
\(126\) 126.000 0.0890871
\(127\) 2304.16i 1.60993i 0.593323 + 0.804965i \(0.297816\pi\)
−0.593323 + 0.804965i \(0.702184\pi\)
\(128\) 128.000i 0.0883883i
\(129\) 980.786 0.669406
\(130\) −1569.41 1230.67i −1.05882 0.830281i
\(131\) 955.192 0.637065 0.318532 0.947912i \(-0.396810\pi\)
0.318532 + 0.947912i \(0.396810\pi\)
\(132\) 307.151i 0.202531i
\(133\) 82.5857i 0.0538428i
\(134\) 1684.24 1.08579
\(135\) −186.272 + 237.545i −0.118754 + 0.151442i
\(136\) 150.302 0.0947669
\(137\) 1489.53i 0.928900i −0.885599 0.464450i \(-0.846252\pi\)
0.885599 0.464450i \(-0.153748\pi\)
\(138\) 956.241i 0.589860i
\(139\) 752.284 0.459049 0.229525 0.973303i \(-0.426283\pi\)
0.229525 + 0.973303i \(0.426283\pi\)
\(140\) −193.171 + 246.343i −0.116614 + 0.148713i
\(141\) 352.304 0.210421
\(142\) 804.200i 0.475260i
\(143\) 2282.95i 1.33503i
\(144\) −144.000 −0.0833333
\(145\) −174.182 136.586i −0.0997586 0.0782264i
\(146\) −606.343 −0.343707
\(147\) 147.000i 0.0824786i
\(148\) 1131.88i 0.628647i
\(149\) −1709.01 −0.939648 −0.469824 0.882760i \(-0.655683\pi\)
−0.469824 + 0.882760i \(0.655683\pi\)
\(150\) −178.849 728.363i −0.0973531 0.396471i
\(151\) −2773.61 −1.49479 −0.747395 0.664380i \(-0.768696\pi\)
−0.747395 + 0.664380i \(0.768696\pi\)
\(152\) 94.3837i 0.0503653i
\(153\) 169.090i 0.0893471i
\(154\) −358.343 −0.187507
\(155\) −1112.10 872.059i −0.576296 0.451906i
\(156\) 1070.30 0.549312
\(157\) 353.478i 0.179685i 0.995956 + 0.0898426i \(0.0286364\pi\)
−0.995956 + 0.0898426i \(0.971364\pi\)
\(158\) 532.767i 0.268258i
\(159\) −1903.51 −0.949424
\(160\) 220.767 281.535i 0.109082 0.139108i
\(161\) −1115.61 −0.546104
\(162\) 162.000i 0.0785674i
\(163\) 885.231i 0.425378i −0.977120 0.212689i \(-0.931778\pi\)
0.977120 0.212689i \(-0.0682221\pi\)
\(164\) 577.535 0.274987
\(165\) 529.757 675.576i 0.249949 0.318748i
\(166\) −1506.51 −0.704383
\(167\) 3220.26i 1.49216i 0.665855 + 0.746081i \(0.268067\pi\)
−0.665855 + 0.746081i \(0.731933\pi\)
\(168\) 168.000i 0.0771517i
\(169\) −5758.18 −2.62093
\(170\) −330.588 259.233i −0.149147 0.116954i
\(171\) −106.182 −0.0474849
\(172\) 1307.71i 0.579723i
\(173\) 3780.62i 1.66148i −0.556663 0.830738i \(-0.687919\pi\)
0.556663 0.830738i \(-0.312081\pi\)
\(174\) 118.788 0.0517545
\(175\) 849.757 208.657i 0.367061 0.0901314i
\(176\) 409.535 0.175397
\(177\) 1545.21i 0.656186i
\(178\) 1685.93i 0.709922i
\(179\) −4534.07 −1.89325 −0.946627 0.322330i \(-0.895534\pi\)
−0.946627 + 0.322330i \(0.895534\pi\)
\(180\) 316.727 + 248.363i 0.131152 + 0.102844i
\(181\) 1805.49 0.741443 0.370721 0.928744i \(-0.379110\pi\)
0.370721 + 0.928744i \(0.379110\pi\)
\(182\) 1248.69i 0.508565i
\(183\) 1187.15i 0.479544i
\(184\) 1274.99 0.510833
\(185\) 1952.20 2489.55i 0.775830 0.989382i
\(186\) 758.424 0.298981
\(187\) 480.890i 0.188054i
\(188\) 469.739i 0.182230i
\(189\) 189.000 0.0727393
\(190\) 162.788 207.596i 0.0621572 0.0792663i
\(191\) 3359.15 1.27256 0.636282 0.771456i \(-0.280471\pi\)
0.636282 + 0.771456i \(0.280471\pi\)
\(192\) 192.000i 0.0721688i
\(193\) 2800.56i 1.04450i 0.852792 + 0.522251i \(0.174908\pi\)
−0.852792 + 0.522251i \(0.825092\pi\)
\(194\) 2403.84 0.889616
\(195\) −2354.12 1846.00i −0.864523 0.677921i
\(196\) 196.000 0.0714286
\(197\) 3252.52i 1.17631i 0.808749 + 0.588154i \(0.200145\pi\)
−0.808749 + 0.588154i \(0.799855\pi\)
\(198\) 460.727i 0.165366i
\(199\) 1525.31 0.543347 0.271674 0.962389i \(-0.412423\pi\)
0.271674 + 0.962389i \(0.412423\pi\)
\(200\) −971.151 + 238.465i −0.343354 + 0.0843102i
\(201\) 2526.36 0.886546
\(202\) 1150.74i 0.400822i
\(203\) 138.586i 0.0479153i
\(204\) 225.453 0.0773768
\(205\) −1270.28 996.100i −0.432782 0.339369i
\(206\) 508.441 0.171965
\(207\) 1434.36i 0.481618i
\(208\) 1427.07i 0.475719i
\(209\) 301.980 0.0999443
\(210\) −289.757 + 369.514i −0.0952150 + 0.121423i
\(211\) −2934.29 −0.957370 −0.478685 0.877987i \(-0.658886\pi\)
−0.478685 + 0.877987i \(0.658886\pi\)
\(212\) 2538.02i 0.822225i
\(213\) 1206.30i 0.388048i
\(214\) 2285.21 0.729971
\(215\) −2255.47 + 2876.30i −0.715451 + 0.912383i
\(216\) −216.000 −0.0680414
\(217\) 884.829i 0.276802i
\(218\) 4108.56i 1.27645i
\(219\) −909.514 −0.280636
\(220\) −900.767 706.343i −0.276044 0.216462i
\(221\) −1675.71 −0.510049
\(222\) 1697.82i 0.513288i
\(223\) 3626.30i 1.08895i 0.838778 + 0.544473i \(0.183270\pi\)
−0.838778 + 0.544473i \(0.816730\pi\)
\(224\) −224.000 −0.0668153
\(225\) −268.273 1092.54i −0.0794884 0.323717i
\(226\) 1781.65 0.524397
\(227\) 2189.45i 0.640171i −0.947389 0.320086i \(-0.896288\pi\)
0.947389 0.320086i \(-0.103712\pi\)
\(228\) 141.576i 0.0411231i
\(229\) 5501.00 1.58741 0.793704 0.608304i \(-0.208150\pi\)
0.793704 + 0.608304i \(0.208150\pi\)
\(230\) −2804.32 2199.03i −0.803963 0.630433i
\(231\) −537.514 −0.153099
\(232\) 158.384i 0.0448207i
\(233\) 3927.72i 1.10435i −0.833729 0.552174i \(-0.813798\pi\)
0.833729 0.552174i \(-0.186202\pi\)
\(234\) 1605.45 0.448512
\(235\) −810.180 + 1033.19i −0.224895 + 0.286798i
\(236\) −2060.28 −0.568274
\(237\) 799.151i 0.219031i
\(238\) 263.029i 0.0716370i
\(239\) −4435.11 −1.20035 −0.600174 0.799869i \(-0.704902\pi\)
−0.600174 + 0.799869i \(0.704902\pi\)
\(240\) 331.151 422.302i 0.0890654 0.113581i
\(241\) 4575.81 1.22304 0.611522 0.791227i \(-0.290557\pi\)
0.611522 + 0.791227i \(0.290557\pi\)
\(242\) 1351.70i 0.359051i
\(243\) 243.000i 0.0641500i
\(244\) −1582.87 −0.415297
\(245\) −431.100 338.050i −0.112416 0.0881519i
\(246\) 866.302 0.224526
\(247\) 1052.28i 0.271073i
\(248\) 1011.23i 0.258925i
\(249\) −2259.76 −0.575126
\(250\) 2547.33 + 1150.49i 0.644429 + 0.291052i
\(251\) 1646.96 0.414163 0.207081 0.978324i \(-0.433603\pi\)
0.207081 + 0.978324i \(0.433603\pi\)
\(252\) 252.000i 0.0629941i
\(253\) 4079.31i 1.01369i
\(254\) 4608.32 1.13839
\(255\) −495.882 388.849i −0.121778 0.0954928i
\(256\) 256.000 0.0625000
\(257\) 2811.64i 0.682432i 0.939985 + 0.341216i \(0.110839\pi\)
−0.939985 + 0.341216i \(0.889161\pi\)
\(258\) 1961.57i 0.473341i
\(259\) −1980.79 −0.475212
\(260\) −2461.33 + 3138.82i −0.587097 + 0.748699i
\(261\) 178.182 0.0422573
\(262\) 1910.38i 0.450473i
\(263\) 3103.13i 0.727556i 0.931486 + 0.363778i \(0.118513\pi\)
−0.931486 + 0.363778i \(0.881487\pi\)
\(264\) 614.302 0.143211
\(265\) 4377.43 5582.34i 1.01473 1.29404i
\(266\) −165.171 −0.0380726
\(267\) 2528.90i 0.579649i
\(268\) 3368.48i 0.767772i
\(269\) 61.1877 0.0138687 0.00693435 0.999976i \(-0.497793\pi\)
0.00693435 + 0.999976i \(0.497793\pi\)
\(270\) 475.090 + 372.545i 0.107085 + 0.0839717i
\(271\) 97.6285 0.0218838 0.0109419 0.999940i \(-0.496517\pi\)
0.0109419 + 0.999940i \(0.496517\pi\)
\(272\) 300.604i 0.0670103i
\(273\) 1873.03i 0.415241i
\(274\) −2979.07 −0.656832
\(275\) 762.967 + 3107.19i 0.167304 + 0.681347i
\(276\) 1912.48 0.417094
\(277\) 4719.24i 1.02365i 0.859089 + 0.511826i \(0.171031\pi\)
−0.859089 + 0.511826i \(0.828969\pi\)
\(278\) 1504.57i 0.324597i
\(279\) 1137.64 0.244117
\(280\) 492.686 + 386.343i 0.105156 + 0.0824586i
\(281\) 995.094 0.211254 0.105627 0.994406i \(-0.466315\pi\)
0.105627 + 0.994406i \(0.466315\pi\)
\(282\) 704.608i 0.148790i
\(283\) 7995.58i 1.67946i 0.543002 + 0.839732i \(0.317288\pi\)
−0.543002 + 0.839732i \(0.682712\pi\)
\(284\) −1608.40 −0.336060
\(285\) 244.182 311.394i 0.0507511 0.0647206i
\(286\) −4565.89 −0.944010
\(287\) 1010.69i 0.207871i
\(288\) 288.000i 0.0589256i
\(289\) 4560.02 0.928154
\(290\) −273.171 + 348.363i −0.0553144 + 0.0705400i
\(291\) 3605.76 0.726368
\(292\) 1212.69i 0.243038i
\(293\) 8930.79i 1.78069i 0.455286 + 0.890345i \(0.349537\pi\)
−0.455286 + 0.890345i \(0.650463\pi\)
\(294\) 294.000 0.0583212
\(295\) 4531.56 + 3553.45i 0.894365 + 0.701322i
\(296\) 2263.76 0.444521
\(297\) 691.090i 0.135021i
\(298\) 3418.02i 0.664432i
\(299\) −14214.8 −2.74938
\(300\) −1456.73 + 357.698i −0.280347 + 0.0688390i
\(301\) 2288.50 0.438229
\(302\) 5547.22i 1.05698i
\(303\) 1726.11i 0.327270i
\(304\) 188.767 0.0356137
\(305\) 3481.50 + 2730.04i 0.653606 + 0.512530i
\(306\) 338.180 0.0631779
\(307\) 2515.79i 0.467700i 0.972273 + 0.233850i \(0.0751324\pi\)
−0.972273 + 0.233850i \(0.924868\pi\)
\(308\) 716.686i 0.132588i
\(309\) 762.661 0.140409
\(310\) −1744.12 + 2224.20i −0.319546 + 0.407503i
\(311\) 3759.39 0.685452 0.342726 0.939435i \(-0.388650\pi\)
0.342726 + 0.939435i \(0.388650\pi\)
\(312\) 2140.60i 0.388423i
\(313\) 6825.91i 1.23266i −0.787487 0.616331i \(-0.788618\pi\)
0.787487 0.616331i \(-0.211382\pi\)
\(314\) 706.955 0.127057
\(315\) −434.636 + 554.271i −0.0777427 + 0.0991418i
\(316\) 1065.53 0.189687
\(317\) 2464.94i 0.436734i −0.975867 0.218367i \(-0.929927\pi\)
0.975867 0.218367i \(-0.0700730\pi\)
\(318\) 3807.02i 0.671344i
\(319\) −506.747 −0.0889416
\(320\) −563.069 441.535i −0.0983642 0.0771329i
\(321\) 3427.82 0.596019
\(322\) 2231.23i 0.386154i
\(323\) 221.657i 0.0381837i
\(324\) −324.000 −0.0555556
\(325\) 10827.3 2658.64i 1.84798 0.453769i
\(326\) −1770.46 −0.300788
\(327\) 6162.84i 1.04222i
\(328\) 1155.07i 0.194445i
\(329\) 822.043 0.137753
\(330\) −1351.15 1059.51i −0.225389 0.176740i
\(331\) 3780.36 0.627756 0.313878 0.949463i \(-0.398372\pi\)
0.313878 + 0.949463i \(0.398372\pi\)
\(332\) 3013.01i 0.498074i
\(333\) 2546.72i 0.419098i
\(334\) 6440.52 1.05512
\(335\) −5809.77 + 7408.94i −0.947528 + 1.20834i
\(336\) −336.000 −0.0545545
\(337\) 1914.39i 0.309446i 0.987958 + 0.154723i \(0.0494485\pi\)
−0.987958 + 0.154723i \(0.950551\pi\)
\(338\) 11516.4i 1.85328i
\(339\) 2672.48 0.428169
\(340\) −518.465 + 661.176i −0.0826992 + 0.105463i
\(341\) −3235.43 −0.513807
\(342\) 212.363i 0.0335769i
\(343\) 343.000i 0.0539949i
\(344\) −2615.43 −0.409926
\(345\) −4206.48 3298.54i −0.656433 0.514747i
\(346\) −7561.24 −1.17484
\(347\) 9118.93i 1.41075i −0.708835 0.705375i \(-0.750779\pi\)
0.708835 0.705375i \(-0.249221\pi\)
\(348\) 237.576i 0.0365959i
\(349\) −4832.45 −0.741189 −0.370594 0.928795i \(-0.620846\pi\)
−0.370594 + 0.928795i \(0.620846\pi\)
\(350\) −417.314 1699.51i −0.0637325 0.259551i
\(351\) 2408.18 0.366208
\(352\) 819.069i 0.124024i
\(353\) 2806.58i 0.423170i −0.977360 0.211585i \(-0.932138\pi\)
0.977360 0.211585i \(-0.0678625\pi\)
\(354\) −3090.42 −0.463994
\(355\) 3537.66 + 2774.08i 0.528900 + 0.414740i
\(356\) −3371.87 −0.501991
\(357\) 394.543i 0.0584914i
\(358\) 9068.15i 1.33873i
\(359\) 1075.06 0.158049 0.0790246 0.996873i \(-0.474819\pi\)
0.0790246 + 0.996873i \(0.474819\pi\)
\(360\) 496.727 633.453i 0.0727216 0.0927386i
\(361\) −6719.81 −0.979707
\(362\) 3610.98i 0.524279i
\(363\) 2027.55i 0.293164i
\(364\) 2497.37 0.359609
\(365\) 2091.57 2667.29i 0.299940 0.382500i
\(366\) −2374.30 −0.339089
\(367\) 367.020i 0.0522025i 0.999659 + 0.0261012i \(0.00830922\pi\)
−0.999659 + 0.0261012i \(0.991691\pi\)
\(368\) 2549.98i 0.361214i
\(369\) 1299.45 0.183325
\(370\) −4979.11 3904.40i −0.699598 0.548595i
\(371\) −4441.53 −0.621544
\(372\) 1516.85i 0.211411i
\(373\) 1304.56i 0.181092i 0.995892 + 0.0905461i \(0.0288613\pi\)
−0.995892 + 0.0905461i \(0.971139\pi\)
\(374\) −961.780 −0.132974
\(375\) 3820.99 + 1725.73i 0.526174 + 0.237643i
\(376\) −939.478 −0.128856
\(377\) 1765.82i 0.241231i
\(378\) 378.000i 0.0514344i
\(379\) −5340.61 −0.723822 −0.361911 0.932213i \(-0.617876\pi\)
−0.361911 + 0.932213i \(0.617876\pi\)
\(380\) −415.192 325.576i −0.0560497 0.0439518i
\(381\) 6912.48 0.929493
\(382\) 6718.31i 0.899839i
\(383\) 6662.27i 0.888841i −0.895818 0.444420i \(-0.853410\pi\)
0.895818 0.444420i \(-0.146590\pi\)
\(384\) 384.000 0.0510310
\(385\) 1236.10 1576.34i 0.163630 0.208670i
\(386\) 5601.13 0.738575
\(387\) 2942.36i 0.386482i
\(388\) 4807.67i 0.629053i
\(389\) 6313.48 0.822895 0.411448 0.911433i \(-0.365023\pi\)
0.411448 + 0.911433i \(0.365023\pi\)
\(390\) −3692.00 + 4708.24i −0.479363 + 0.611310i
\(391\) −2994.27 −0.387281
\(392\) 392.000i 0.0505076i
\(393\) 2865.58i 0.367810i
\(394\) 6505.05 0.831776
\(395\) −2343.63 1837.78i −0.298534 0.234098i
\(396\) 921.453 0.116931
\(397\) 14210.6i 1.79650i −0.439490 0.898248i \(-0.644841\pi\)
0.439490 0.898248i \(-0.355159\pi\)
\(398\) 3050.61i 0.384204i
\(399\) −247.757 −0.0310861
\(400\) 476.931 + 1942.30i 0.0596163 + 0.242788i
\(401\) 5578.59 0.694717 0.347359 0.937732i \(-0.387079\pi\)
0.347359 + 0.937732i \(0.387079\pi\)
\(402\) 5052.72i 0.626883i
\(403\) 11274.2i 1.39357i
\(404\) −2301.49 −0.283424
\(405\) 712.635 + 558.817i 0.0874348 + 0.0685626i
\(406\) 277.171 0.0338812
\(407\) 7242.86i 0.882101i
\(408\) 450.906i 0.0547137i
\(409\) −11914.0 −1.44037 −0.720184 0.693783i \(-0.755943\pi\)
−0.720184 + 0.693783i \(0.755943\pi\)
\(410\) −1992.20 + 2540.56i −0.239970 + 0.306023i
\(411\) −4468.60 −0.536301
\(412\) 1016.88i 0.121597i
\(413\) 3605.49i 0.429575i
\(414\) 2868.72 0.340556
\(415\) 5196.68 6627.09i 0.614686 0.783882i
\(416\) −2854.14 −0.336384
\(417\) 2256.85i 0.265032i
\(418\) 603.959i 0.0706713i
\(419\) 12093.0 1.40998 0.704990 0.709217i \(-0.250951\pi\)
0.704990 + 0.709217i \(0.250951\pi\)
\(420\) 739.029 + 579.514i 0.0858593 + 0.0673271i
\(421\) −12188.5 −1.41100 −0.705500 0.708710i \(-0.749277\pi\)
−0.705500 + 0.708710i \(0.749277\pi\)
\(422\) 5868.59i 0.676963i
\(423\) 1056.91i 0.121487i
\(424\) 5076.03 0.581401
\(425\) 2280.72 560.028i 0.260308 0.0639185i
\(426\) −2412.60 −0.274392
\(427\) 2770.01i 0.313935i
\(428\) 4570.42i 0.516168i
\(429\) −6848.84 −0.770781
\(430\) 5752.61 + 4510.95i 0.645152 + 0.505900i
\(431\) 4968.16 0.555238 0.277619 0.960691i \(-0.410455\pi\)
0.277619 + 0.960691i \(0.410455\pi\)
\(432\) 432.000i 0.0481125i
\(433\) 14483.7i 1.60749i −0.594974 0.803745i \(-0.702838\pi\)
0.594974 0.803745i \(-0.297162\pi\)
\(434\) 1769.66 0.195729
\(435\) −409.757 + 522.545i −0.0451640 + 0.0575957i
\(436\) −8217.13 −0.902589
\(437\) 1880.28i 0.205826i
\(438\) 1819.03i 0.198440i
\(439\) 9937.64 1.08040 0.540202 0.841535i \(-0.318348\pi\)
0.540202 + 0.841535i \(0.318348\pi\)
\(440\) −1412.69 + 1801.53i −0.153062 + 0.195193i
\(441\) 441.000 0.0476190
\(442\) 3351.43i 0.360659i
\(443\) 17139.6i 1.83821i 0.394013 + 0.919105i \(0.371087\pi\)
−0.394013 + 0.919105i \(0.628913\pi\)
\(444\) 3395.63 0.362950
\(445\) 7416.39 + 5815.61i 0.790047 + 0.619520i
\(446\) 7252.60 0.770001
\(447\) 5127.03i 0.542506i
\(448\) 448.000i 0.0472456i
\(449\) −1555.34 −0.163477 −0.0817385 0.996654i \(-0.526047\pi\)
−0.0817385 + 0.996654i \(0.526047\pi\)
\(450\) −2185.09 + 536.547i −0.228902 + 0.0562068i
\(451\) −3695.63 −0.385855
\(452\) 3563.31i 0.370805i
\(453\) 8320.84i 0.863018i
\(454\) −4378.90 −0.452669
\(455\) −5492.94 4307.33i −0.565963 0.443804i
\(456\) 283.151 0.0290784
\(457\) 18409.2i 1.88435i −0.335124 0.942174i \(-0.608778\pi\)
0.335124 0.942174i \(-0.391222\pi\)
\(458\) 11002.0i 1.12247i
\(459\) 507.269 0.0515845
\(460\) −4398.06 + 5608.64i −0.445784 + 0.568488i
\(461\) 6616.52 0.668465 0.334232 0.942491i \(-0.391523\pi\)
0.334232 + 0.942491i \(0.391523\pi\)
\(462\) 1075.03i 0.108257i
\(463\) 12605.5i 1.26529i −0.774443 0.632644i \(-0.781970\pi\)
0.774443 0.632644i \(-0.218030\pi\)
\(464\) −316.767 −0.0316930
\(465\) −2616.18 + 3336.29i −0.260908 + 0.332725i
\(466\) −7855.43 −0.780892
\(467\) 16291.5i 1.61431i −0.590340 0.807155i \(-0.701006\pi\)
0.590340 0.807155i \(-0.298994\pi\)
\(468\) 3210.91i 0.317146i
\(469\) 5894.84 0.580381
\(470\) 2066.37 + 1620.36i 0.202797 + 0.159025i
\(471\) 1060.43 0.103741
\(472\) 4120.55i 0.401830i
\(473\) 8368.04i 0.813452i
\(474\) 1598.30 0.154879
\(475\) 351.675 + 1432.20i 0.0339705 + 0.138345i
\(476\) 526.057 0.0506550
\(477\) 5710.54i 0.548150i
\(478\) 8870.22i 0.848775i
\(479\) −11506.3 −1.09757 −0.548785 0.835963i \(-0.684909\pi\)
−0.548785 + 0.835963i \(0.684909\pi\)
\(480\) −844.604 662.302i −0.0803140 0.0629788i
\(481\) −25238.6 −2.39247
\(482\) 9151.62i 0.864823i
\(483\) 3346.84i 0.315293i
\(484\) 2703.40 0.253888
\(485\) −8292.01 + 10574.4i −0.776332 + 0.990021i
\(486\) −486.000 −0.0453609
\(487\) 16502.9i 1.53556i −0.640714 0.767780i \(-0.721361\pi\)
0.640714 0.767780i \(-0.278639\pi\)
\(488\) 3165.73i 0.293660i
\(489\) −2655.69 −0.245592
\(490\) −676.100 + 862.200i −0.0623328 + 0.0794903i
\(491\) 9269.67 0.852004 0.426002 0.904722i \(-0.359922\pi\)
0.426002 + 0.904722i \(0.359922\pi\)
\(492\) 1732.60i 0.158764i
\(493\) 371.959i 0.0339801i
\(494\) −2104.56 −0.191678
\(495\) −2026.73 1589.27i −0.184029 0.144308i
\(496\) −2022.47 −0.183087
\(497\) 2814.70i 0.254037i
\(498\) 4519.52i 0.406676i
\(499\) −13167.3 −1.18126 −0.590631 0.806941i \(-0.701121\pi\)
−0.590631 + 0.806941i \(0.701121\pi\)
\(500\) 2300.97 5094.66i 0.205805 0.455680i
\(501\) 9660.78 0.861500
\(502\) 3293.91i 0.292857i
\(503\) 16299.1i 1.44481i −0.691469 0.722406i \(-0.743036\pi\)
0.691469 0.722406i \(-0.256964\pi\)
\(504\) −504.000 −0.0445435
\(505\) 5062.09 + 3969.48i 0.446060 + 0.349781i
\(506\) −8158.62 −0.716788
\(507\) 17274.6i 1.51319i
\(508\) 9216.64i 0.804965i
\(509\) 10595.4 0.922656 0.461328 0.887230i \(-0.347373\pi\)
0.461328 + 0.887230i \(0.347373\pi\)
\(510\) −777.698 + 991.763i −0.0675236 + 0.0861098i
\(511\) −2122.20 −0.183719
\(512\) 512.000i 0.0441942i
\(513\) 318.545i 0.0274154i
\(514\) 5623.27 0.482552
\(515\) −1753.86 + 2236.62i −0.150067 + 0.191373i
\(516\) −3923.14 −0.334703
\(517\) 3005.85i 0.255700i
\(518\) 3961.57i 0.336026i
\(519\) −11341.9 −0.959254
\(520\) 6277.65 + 4922.66i 0.529410 + 0.415140i
\(521\) −3930.10 −0.330481 −0.165241 0.986253i \(-0.552840\pi\)
−0.165241 + 0.986253i \(0.552840\pi\)
\(522\) 356.363i 0.0298805i
\(523\) 15430.7i 1.29013i 0.764129 + 0.645064i \(0.223169\pi\)
−0.764129 + 0.645064i \(0.776831\pi\)
\(524\) −3820.77 −0.318532
\(525\) −625.971 2549.27i −0.0520374 0.211923i
\(526\) 6206.26 0.514459
\(527\) 2374.85i 0.196300i
\(528\) 1228.60i 0.101265i
\(529\) −13232.9 −1.08761
\(530\) −11164.7 8754.86i −0.915024 0.717522i
\(531\) −4635.62 −0.378849
\(532\) 330.343i 0.0269214i
\(533\) 12877.8i 1.04653i
\(534\) −5057.80 −0.409874
\(535\) −7882.82 + 10052.6i −0.637017 + 0.812359i
\(536\) −6736.96 −0.542896
\(537\) 13602.2i 1.09307i
\(538\) 122.375i 0.00980665i
\(539\) −1254.20 −0.100227
\(540\) 745.090 950.180i 0.0593770 0.0757208i
\(541\) −24132.0 −1.91777 −0.958885 0.283794i \(-0.908407\pi\)
−0.958885 + 0.283794i \(0.908407\pi\)
\(542\) 195.257i 0.0154742i
\(543\) 5416.48i 0.428072i
\(544\) −601.208 −0.0473834
\(545\) 18073.5 + 14172.4i 1.42052 + 1.11391i
\(546\) 3746.06 0.293620
\(547\) 3505.64i 0.274022i 0.990569 + 0.137011i \(0.0437496\pi\)
−0.990569 + 0.137011i \(0.956250\pi\)
\(548\) 5958.13i 0.464450i
\(549\) −3561.45 −0.276865
\(550\) 6214.38 1525.93i 0.481785 0.118302i
\(551\) −233.576 −0.0180593
\(552\) 3824.96i 0.294930i
\(553\) 1864.69i 0.143390i
\(554\) 9438.48 0.723831
\(555\) −7468.66 5856.60i −0.571220 0.447926i
\(556\) −3009.13 −0.229525
\(557\) 14427.0i 1.09747i −0.835995 0.548737i \(-0.815109\pi\)
0.835995 0.548737i \(-0.184891\pi\)
\(558\) 2275.27i 0.172616i
\(559\) 29159.4 2.20628
\(560\) 772.686 985.371i 0.0583070 0.0743563i
\(561\) −1442.67 −0.108573
\(562\) 1990.19i 0.149379i
\(563\) 9972.47i 0.746518i 0.927727 + 0.373259i \(0.121760\pi\)
−0.927727 + 0.373259i \(0.878240\pi\)
\(564\) −1409.22 −0.105210
\(565\) −6145.79 + 7837.46i −0.457620 + 0.583583i
\(566\) 15991.2 1.18756
\(567\) 567.000i 0.0419961i
\(568\) 3216.80i 0.237630i
\(569\) 25180.3 1.85521 0.927605 0.373563i \(-0.121864\pi\)
0.927605 + 0.373563i \(0.121864\pi\)
\(570\) −622.788 488.363i −0.0457644 0.0358865i
\(571\) 6146.38 0.450470 0.225235 0.974305i \(-0.427685\pi\)
0.225235 + 0.974305i \(0.427685\pi\)
\(572\) 9131.79i 0.667516i
\(573\) 10077.5i 0.734715i
\(574\) 2021.37 0.146987
\(575\) 19347.0 4750.63i 1.40317 0.344548i
\(576\) 576.000 0.0416667
\(577\) 12735.9i 0.918895i 0.888205 + 0.459447i \(0.151952\pi\)
−0.888205 + 0.459447i \(0.848048\pi\)
\(578\) 9120.04i 0.656304i
\(579\) 8401.69 0.603044
\(580\) 696.727 + 546.343i 0.0498793 + 0.0391132i
\(581\) −5272.77 −0.376508
\(582\) 7211.51i 0.513620i
\(583\) 16240.7i 1.15372i
\(584\) 2425.37 0.171854
\(585\) −5537.99 + 7062.36i −0.391398 + 0.499132i
\(586\) 17861.6 1.25914
\(587\) 13223.9i 0.929829i 0.885355 + 0.464915i \(0.153915\pi\)
−0.885355 + 0.464915i \(0.846085\pi\)
\(588\) 588.000i 0.0412393i
\(589\) −1491.31 −0.104327
\(590\) 7106.91 9063.12i 0.495910 0.632411i
\(591\) 9757.57 0.679142
\(592\) 4527.51i 0.314324i
\(593\) 2498.96i 0.173052i 0.996250 + 0.0865261i \(0.0275766\pi\)
−0.996250 + 0.0865261i \(0.972423\pi\)
\(594\) 1382.18 0.0954739
\(595\) −1157.06 907.314i −0.0797222 0.0625147i
\(596\) 6836.04 0.469824
\(597\) 4575.92i 0.313702i
\(598\) 28429.6i 1.94410i
\(599\) 9468.29 0.645850 0.322925 0.946425i \(-0.395334\pi\)
0.322925 + 0.946425i \(0.395334\pi\)
\(600\) 715.396 + 2913.45i 0.0486765 + 0.198235i
\(601\) −12334.1 −0.837137 −0.418569 0.908185i \(-0.637468\pi\)
−0.418569 + 0.908185i \(0.637468\pi\)
\(602\) 4577.00i 0.309875i
\(603\) 7579.08i 0.511848i
\(604\) 11094.4 0.747395
\(605\) −5946.09 4662.67i −0.399575 0.313330i
\(606\) −3452.23 −0.231415
\(607\) 25245.6i 1.68812i 0.536248 + 0.844060i \(0.319841\pi\)
−0.536248 + 0.844060i \(0.680159\pi\)
\(608\) 377.535i 0.0251827i
\(609\) 415.757 0.0276639
\(610\) 5460.08 6962.99i 0.362413 0.462169i
\(611\) 10474.2 0.693521
\(612\) 676.359i 0.0446735i
\(613\) 4007.86i 0.264071i 0.991245 + 0.132036i \(0.0421513\pi\)
−0.991245 + 0.132036i \(0.957849\pi\)
\(614\) 5031.58 0.330714
\(615\) −2988.30 + 3810.84i −0.195935 + 0.249867i
\(616\) 1433.37 0.0937535
\(617\) 14349.2i 0.936266i −0.883658 0.468133i \(-0.844927\pi\)
0.883658 0.468133i \(-0.155073\pi\)
\(618\) 1525.32i 0.0992839i
\(619\) 6004.19 0.389869 0.194934 0.980816i \(-0.437551\pi\)
0.194934 + 0.980816i \(0.437551\pi\)
\(620\) 4448.39 + 3488.24i 0.288148 + 0.225953i
\(621\) 4303.08 0.278062
\(622\) 7518.78i 0.484688i
\(623\) 5900.77i 0.379469i
\(624\) −4281.21 −0.274656
\(625\) −13847.9 + 7237.06i −0.886269 + 0.463172i
\(626\) −13651.8 −0.871624
\(627\) 905.939i 0.0577029i
\(628\) 1413.91i 0.0898426i
\(629\) −5316.36 −0.337007
\(630\) 1108.54 + 869.271i 0.0701038 + 0.0549724i
\(631\) 17130.6 1.08076 0.540378 0.841422i \(-0.318281\pi\)
0.540378 + 0.841422i \(0.318281\pi\)
\(632\) 2131.07i 0.134129i
\(633\) 8802.88i 0.552738i
\(634\) −4929.87 −0.308817
\(635\) −15896.3 + 20271.9i −0.993429 + 1.26688i
\(636\) 7614.05 0.474712
\(637\) 4370.40i 0.271839i
\(638\) 1013.49i 0.0628912i
\(639\) −3618.90 −0.224040
\(640\) −883.069 + 1126.14i −0.0545412 + 0.0695540i
\(641\) 13484.7 0.830911 0.415456 0.909613i \(-0.363622\pi\)
0.415456 + 0.909613i \(0.363622\pi\)
\(642\) 6855.64i 0.421449i
\(643\) 18209.9i 1.11684i 0.829559 + 0.558419i \(0.188592\pi\)
−0.829559 + 0.558419i \(0.811408\pi\)
\(644\) 4462.46 0.273052
\(645\) 8628.91 + 6766.42i 0.526764 + 0.413066i
\(646\) −443.314 −0.0270000
\(647\) 13402.9i 0.814406i −0.913338 0.407203i \(-0.866504\pi\)
0.913338 0.407203i \(-0.133496\pi\)
\(648\) 648.000i 0.0392837i
\(649\) 13183.7 0.797387
\(650\) −5317.29 21654.7i −0.320863 1.30672i
\(651\) 2654.49 0.159812
\(652\) 3540.92i 0.212689i
\(653\) 1922.32i 0.115201i 0.998340 + 0.0576003i \(0.0183449\pi\)
−0.998340 + 0.0576003i \(0.981655\pi\)
\(654\) −12325.7 −0.736961
\(655\) 8403.74 + 6589.85i 0.501315 + 0.393109i
\(656\) −2310.14 −0.137494
\(657\) 2728.54i 0.162025i
\(658\) 1644.09i 0.0974060i
\(659\) −22722.3 −1.34315 −0.671574 0.740937i \(-0.734382\pi\)
−0.671574 + 0.740937i \(0.734382\pi\)
\(660\) −2119.03 + 2702.30i −0.124974 + 0.159374i
\(661\) −16049.3 −0.944393 −0.472196 0.881493i \(-0.656539\pi\)
−0.472196 + 0.881493i \(0.656539\pi\)
\(662\) 7560.72i 0.443891i
\(663\) 5027.14i 0.294477i
\(664\) 6026.02 0.352191
\(665\) 569.757 726.586i 0.0332244 0.0423696i
\(666\) 5093.45 0.296347
\(667\) 3155.27i 0.183167i
\(668\) 12881.0i 0.746081i
\(669\) 10878.9 0.628703
\(670\) 14817.9 + 11619.5i 0.854425 + 0.670003i
\(671\) 10128.7 0.582735
\(672\) 672.000i 0.0385758i
\(673\) 16507.8i 0.945513i −0.881193 0.472757i \(-0.843259\pi\)
0.881193 0.472757i \(-0.156741\pi\)
\(674\) 3828.78 0.218811
\(675\) −3277.63 + 804.820i −0.186898 + 0.0458927i
\(676\) 23032.7 1.31047
\(677\) 15118.9i 0.858298i −0.903234 0.429149i \(-0.858813\pi\)
0.903234 0.429149i \(-0.141187\pi\)
\(678\) 5344.96i 0.302761i
\(679\) 8413.43 0.475520
\(680\) 1322.35 + 1036.93i 0.0745733 + 0.0584772i
\(681\) −6568.35 −0.369603
\(682\) 6470.86i 0.363317i
\(683\) 68.6595i 0.00384654i 0.999998 + 0.00192327i \(0.000612195\pi\)
−0.999998 + 0.00192327i \(0.999388\pi\)
\(684\) 424.727 0.0237424
\(685\) 10276.3 13104.8i 0.573191 0.730964i
\(686\) 686.000 0.0381802
\(687\) 16503.0i 0.916490i
\(688\) 5230.86i 0.289861i
\(689\) −56592.6 −3.12918
\(690\) −6597.09 + 8412.97i −0.363981 + 0.464168i
\(691\) −3167.95 −0.174406 −0.0872030 0.996191i \(-0.527793\pi\)
−0.0872030 + 0.996191i \(0.527793\pi\)
\(692\) 15122.5i 0.830738i
\(693\) 1612.54i 0.0883917i
\(694\) −18237.9 −0.997550
\(695\) 6618.56 + 5189.99i 0.361232 + 0.283263i
\(696\) −475.151 −0.0258772
\(697\) 2712.64i 0.147416i
\(698\) 9664.89i 0.524100i
\(699\) −11783.1 −0.637596
\(700\) −3399.03 + 834.629i −0.183530 + 0.0450657i
\(701\) 6930.44 0.373408 0.186704 0.982416i \(-0.440219\pi\)
0.186704 + 0.982416i \(0.440219\pi\)
\(702\) 4816.36i 0.258948i
\(703\) 3338.46i 0.179107i
\(704\) −1638.14 −0.0876984
\(705\) 3099.56 + 2430.54i 0.165583 + 0.129843i
\(706\) −5613.15 −0.299226
\(707\) 4027.60i 0.214248i
\(708\) 6180.83i 0.328093i
\(709\) −20689.6 −1.09593 −0.547966 0.836501i \(-0.684598\pi\)
−0.547966 + 0.836501i \(0.684598\pi\)
\(710\) 5548.16 7075.32i 0.293266 0.373989i
\(711\) 2397.45 0.126458
\(712\) 6743.74i 0.354961i
\(713\) 20145.5i 1.05814i
\(714\) 789.086 0.0413596
\(715\) 15750.0 20085.3i 0.823800 1.05055i
\(716\) 18136.3 0.946627
\(717\) 13305.3i 0.693022i
\(718\) 2150.13i 0.111758i
\(719\) 2807.47 0.145620 0.0728101 0.997346i \(-0.476803\pi\)
0.0728101 + 0.997346i \(0.476803\pi\)
\(720\) −1266.91 993.453i −0.0655761 0.0514220i
\(721\) 1779.54 0.0919190
\(722\) 13439.6i 0.692757i
\(723\) 13727.4i 0.706125i
\(724\) −7221.97 −0.370721
\(725\) −590.141 2403.35i −0.0302307 0.123115i
\(726\) 4055.09 0.207298
\(727\) 3059.84i 0.156098i −0.996950 0.0780489i \(-0.975131\pi\)
0.996950 0.0780489i \(-0.0248690\pi\)
\(728\) 4994.74i 0.254282i
\(729\) −729.000 −0.0370370
\(730\) −5334.58 4183.15i −0.270468 0.212089i
\(731\) 6142.25 0.310779
\(732\) 4748.60i 0.239772i
\(733\) 483.122i 0.0243445i 0.999926 + 0.0121723i \(0.00387465\pi\)
−0.999926 + 0.0121723i \(0.996125\pi\)
\(734\) 734.041 0.0369127
\(735\) −1014.15 + 1293.30i −0.0508945 + 0.0649035i
\(736\) −5099.95 −0.255417
\(737\) 21554.8i 1.07732i
\(738\) 2598.91i 0.129630i
\(739\) −15972.4 −0.795066 −0.397533 0.917588i \(-0.630134\pi\)
−0.397533 + 0.917588i \(0.630134\pi\)
\(740\) −7808.80 + 9958.21i −0.387915 + 0.494691i
\(741\) −3156.84 −0.156504
\(742\) 8883.06i 0.439498i
\(743\) 1310.03i 0.0646840i 0.999477 + 0.0323420i \(0.0102966\pi\)
−0.999477 + 0.0323420i \(0.989703\pi\)
\(744\) −3033.70 −0.149490
\(745\) −15035.8 11790.4i −0.739422 0.579823i
\(746\) 2609.11 0.128052
\(747\) 6779.28i 0.332049i
\(748\) 1923.56i 0.0940271i
\(749\) 7998.24 0.390186
\(750\) 3451.46 7641.99i 0.168039 0.372061i
\(751\) −14752.9 −0.716830 −0.358415 0.933562i \(-0.616683\pi\)
−0.358415 + 0.933562i \(0.616683\pi\)
\(752\) 1878.96i 0.0911150i
\(753\) 4940.87i 0.239117i
\(754\) 3531.63 0.170576
\(755\) −24402.1 19135.1i −1.17627 0.922381i
\(756\) −756.000 −0.0363696
\(757\) 3934.60i 0.188911i 0.995529 + 0.0944555i \(0.0301110\pi\)
−0.995529 + 0.0944555i \(0.969889\pi\)
\(758\) 10681.2i 0.511820i
\(759\) −12237.9 −0.585255
\(760\) −651.151 + 830.384i −0.0310786 + 0.0396331i
\(761\) 17102.3 0.814662 0.407331 0.913281i \(-0.366460\pi\)
0.407331 + 0.913281i \(0.366460\pi\)
\(762\) 13825.0i 0.657251i
\(763\) 14380.0i 0.682293i
\(764\) −13436.6 −0.636282
\(765\) −1166.55 + 1487.64i −0.0551328 + 0.0703084i
\(766\) −13324.5 −0.628505
\(767\) 45940.0i 2.16271i
\(768\) 768.000i 0.0360844i
\(769\) 32173.5 1.50872 0.754361 0.656460i \(-0.227947\pi\)
0.754361 + 0.656460i \(0.227947\pi\)
\(770\) −3152.69 2472.20i −0.147552 0.115704i
\(771\) 8434.91 0.394002
\(772\) 11202.3i 0.522251i
\(773\) 19329.5i 0.899398i 0.893180 + 0.449699i \(0.148469\pi\)
−0.893180 + 0.449699i \(0.851531\pi\)
\(774\) −5884.71 −0.273284
\(775\) −3767.87 15344.7i −0.174640 0.711222i
\(776\) −9615.35 −0.444808
\(777\) 5942.36i 0.274364i
\(778\) 12627.0i 0.581875i
\(779\) −1703.43 −0.0783464
\(780\) 9416.47 + 7383.99i 0.432261 + 0.338961i
\(781\) 10292.1 0.471551
\(782\) 5988.54i 0.273849i
\(783\) 534.545i 0.0243973i
\(784\) −784.000 −0.0357143
\(785\) −2438.63 + 3109.88i −0.110877 + 0.141397i
\(786\) −5731.15 −0.260081
\(787\) 4050.20i 0.183449i 0.995784 + 0.0917244i \(0.0292379\pi\)
−0.995784 + 0.0917244i \(0.970762\pi\)
\(788\) 13010.1i 0.588154i
\(789\) 9309.39 0.420054
\(790\) −3675.55 + 4687.27i −0.165532 + 0.211095i
\(791\) 6235.79 0.280302
\(792\) 1842.91i 0.0826828i
\(793\) 35294.7i 1.58052i
\(794\) −28421.2 −1.27031
\(795\) −16747.0 13132.3i −0.747114 0.585855i
\(796\) −6101.22 −0.271674
\(797\) 30864.7i 1.37175i 0.727720 + 0.685874i \(0.240580\pi\)
−0.727720 + 0.685874i \(0.759420\pi\)
\(798\) 495.514i 0.0219812i
\(799\) 2206.33 0.0976902
\(800\) 3884.60 953.861i 0.171677 0.0421551i
\(801\) −7586.71 −0.334661
\(802\) 11157.2i 0.491239i
\(803\) 7759.95i 0.341025i
\(804\) −10105.4 −0.443273
\(805\) −9815.13 7696.60i −0.429736 0.336981i
\(806\) 22548.4 0.985402
\(807\) 183.563i 0.00800710i
\(808\) 4602.97i 0.200411i
\(809\) −14213.1 −0.617682 −0.308841 0.951114i \(-0.599941\pi\)
−0.308841 + 0.951114i \(0.599941\pi\)
\(810\) 1117.63 1425.27i 0.0484811 0.0618258i
\(811\) 1619.57 0.0701242 0.0350621 0.999385i \(-0.488837\pi\)
0.0350621 + 0.999385i \(0.488837\pi\)
\(812\) 554.343i 0.0239577i
\(813\) 292.885i 0.0126346i
\(814\) −14485.7 −0.623740
\(815\) 6107.19 7788.22i 0.262485 0.334736i
\(816\) −901.812 −0.0386884
\(817\) 3857.09i 0.165168i
\(818\) 23828.0i 1.01849i
\(819\) 5619.09 0.239740
\(820\) 5081.13 + 3984.40i 0.216391 + 0.169684i
\(821\) −20628.1 −0.876888 −0.438444 0.898758i \(-0.644470\pi\)
−0.438444 + 0.898758i \(0.644470\pi\)
\(822\) 8937.20i 0.379222i
\(823\) 11868.2i 0.502671i 0.967900 + 0.251335i \(0.0808697\pi\)
−0.967900 + 0.251335i \(0.919130\pi\)
\(824\) −2033.76 −0.0859824
\(825\) 9321.56 2288.90i 0.393376 0.0965931i
\(826\) −7210.97 −0.303755
\(827\) 9149.35i 0.384709i 0.981326 + 0.192354i \(0.0616123\pi\)
−0.981326 + 0.192354i \(0.938388\pi\)
\(828\) 5737.44i 0.240809i
\(829\) 11693.7 0.489916 0.244958 0.969534i \(-0.421226\pi\)
0.244958 + 0.969534i \(0.421226\pi\)
\(830\) −13254.2 10393.4i −0.554288 0.434649i
\(831\) 14157.7 0.591006
\(832\) 5708.28i 0.237859i
\(833\) 920.600i 0.0382916i
\(834\) −4513.70 −0.187406
\(835\) −22216.5 + 28331.7i −0.920759 + 1.17420i
\(836\) −1207.92 −0.0499722
\(837\) 3412.91i 0.140941i
\(838\) 24186.0i 0.997007i
\(839\) 41472.3 1.70654 0.853268 0.521473i \(-0.174617\pi\)
0.853268 + 0.521473i \(0.174617\pi\)
\(840\) 1159.03 1478.06i 0.0476075 0.0607117i
\(841\) −23997.0 −0.983929
\(842\) 24377.0i 0.997727i
\(843\) 2985.28i 0.121967i
\(844\) 11737.2 0.478685
\(845\) −50660.3 39725.6i −2.06245 1.61728i
\(846\) −2113.82 −0.0859040
\(847\) 4730.94i 0.191921i
\(848\) 10152.1i 0.411112i
\(849\) 23986.8 0.969639
\(850\) −1120.06 4561.44i −0.0451972 0.184066i
\(851\) −45097.8 −1.81661
\(852\) 4825.20i 0.194024i
\(853\) 10326.4i 0.414501i 0.978288 + 0.207251i \(0.0664516\pi\)
−0.978288 + 0.207251i \(0.933548\pi\)
\(854\) −5540.03 −0.221986
\(855\) −934.182 732.545i −0.0373665 0.0293012i
\(856\) −9140.85 −0.364986
\(857\) 17375.4i 0.692571i 0.938129 + 0.346285i \(0.112557\pi\)
−0.938129 + 0.346285i \(0.887443\pi\)
\(858\) 13697.7i 0.545025i
\(859\) −10624.9 −0.422022 −0.211011 0.977484i \(-0.567676\pi\)
−0.211011 + 0.977484i \(0.567676\pi\)
\(860\) 9021.89 11505.2i 0.357726 0.456191i
\(861\) 3032.06 0.120014
\(862\) 9936.31i 0.392613i
\(863\) 22377.1i 0.882648i 0.897348 + 0.441324i \(0.145491\pi\)
−0.897348 + 0.441324i \(0.854509\pi\)
\(864\) 864.000 0.0340207
\(865\) 26082.4 33261.8i 1.02524 1.30744i
\(866\) −28967.4 −1.13667
\(867\) 13680.1i 0.535870i
\(868\) 3539.31i 0.138401i
\(869\) −6818.33 −0.266164
\(870\) 1045.09 + 819.514i 0.0407263 + 0.0319358i
\(871\) 75110.3 2.92195
\(872\) 16434.3i 0.638227i
\(873\) 10817.3i 0.419369i
\(874\) −3760.56 −0.145541
\(875\) 8915.65 + 4026.70i 0.344462 + 0.155574i
\(876\) 3638.06 0.140318
\(877\) 22267.1i 0.857362i 0.903456 + 0.428681i \(0.141021\pi\)
−0.903456 + 0.428681i \(0.858979\pi\)
\(878\) 19875.3i 0.763961i
\(879\) 26792.4 1.02808
\(880\) 3603.07 + 2825.37i 0.138022 + 0.108231i
\(881\) −7273.13 −0.278136 −0.139068 0.990283i \(-0.544411\pi\)
−0.139068 + 0.990283i \(0.544411\pi\)
\(882\) 882.000i 0.0336718i
\(883\) 43452.0i 1.65603i −0.560705 0.828016i \(-0.689470\pi\)
0.560705 0.828016i \(-0.310530\pi\)
\(884\) 6702.86 0.255024
\(885\) 10660.4 13594.7i 0.404909 0.516362i
\(886\) 34279.2 1.29981
\(887\) 34206.2i 1.29485i −0.762130 0.647424i \(-0.775846\pi\)
0.762130 0.647424i \(-0.224154\pi\)
\(888\) 6791.27i 0.256644i
\(889\) 16129.1 0.608496
\(890\) 11631.2 14832.8i 0.438067 0.558647i
\(891\) 2073.27 0.0779541
\(892\) 14505.2i 0.544473i
\(893\) 1385.49i 0.0519190i
\(894\) 10254.1 0.383610
\(895\) −39890.6 31280.5i −1.48983 1.16826i
\(896\) 896.000 0.0334077
\(897\) 42644.4i 1.58735i
\(898\) 3110.69i 0.115596i
\(899\) 2502.54 0.0928415
\(900\) 1073.09 + 4370.18i 0.0397442 + 0.161859i
\(901\) −11920.9 −0.440780
\(902\) 7391.27i 0.272841i
\(903\) 6865.50i 0.253012i
\(904\) −7126.61 −0.262199
\(905\) 15884.6 + 12456.1i 0.583451 + 0.457517i
\(906\) 16641.7 0.610246
\(907\) 24922.5i 0.912391i 0.889880 + 0.456196i \(0.150788\pi\)
−0.889880 + 0.456196i \(0.849212\pi\)
\(908\) 8757.80i 0.320086i
\(909\) −5178.34 −0.188949
\(910\) −8614.66 + 10985.9i −0.313817 + 0.400196i
\(911\) 29200.7 1.06198 0.530989 0.847379i \(-0.321821\pi\)
0.530989 + 0.847379i \(0.321821\pi\)
\(912\) 566.302i 0.0205616i
\(913\) 19280.2i 0.698885i
\(914\) −36818.4 −1.33244
\(915\) 8190.12 10444.5i 0.295909 0.377360i
\(916\) −22004.0 −0.793704
\(917\) 6686.34i 0.240788i
\(918\) 1014.54i 0.0364758i
\(919\) 31961.7 1.14725 0.573623 0.819119i \(-0.305537\pi\)
0.573623 + 0.819119i \(0.305537\pi\)
\(920\) 11217.3 + 8796.11i 0.401982 + 0.315217i
\(921\) 7547.38 0.270027
\(922\) 13233.0i 0.472676i
\(923\) 35864.0i 1.27896i
\(924\) 2150.06 0.0765494
\(925\) 34350.8 8434.80i 1.22102 0.299821i
\(926\) −25211.0 −0.894693
\(927\) 2287.98i 0.0810650i
\(928\) 633.535i 0.0224103i
\(929\) 21349.4 0.753985 0.376993 0.926216i \(-0.376958\pi\)
0.376993 + 0.926216i \(0.376958\pi\)
\(930\) 6672.59 + 5232.36i 0.235272 + 0.184490i
\(931\) −578.100 −0.0203507
\(932\) 15710.9i 0.552174i
\(933\) 11278.2i 0.395746i
\(934\) −32583.1 −1.14149
\(935\) 3317.65 4230.85i 0.116041 0.147982i
\(936\) −6421.81 −0.224256
\(937\) 3802.95i 0.132590i −0.997800 0.0662951i \(-0.978882\pi\)
0.997800 0.0662951i \(-0.0211179\pi\)
\(938\) 11789.7i 0.410391i
\(939\) −20477.7 −0.711678
\(940\) 3240.72 4132.74i 0.112447 0.143399i
\(941\) −42690.8 −1.47894 −0.739470 0.673190i \(-0.764924\pi\)
−0.739470 + 0.673190i \(0.764924\pi\)
\(942\) 2120.87i 0.0733562i
\(943\) 23010.9i 0.794633i
\(944\) 8241.11 0.284137
\(945\) 1662.81 + 1303.91i 0.0572395 + 0.0448848i
\(946\) 16736.1 0.575197
\(947\) 40333.0i 1.38400i 0.721899 + 0.691998i \(0.243270\pi\)
−0.721899 + 0.691998i \(0.756730\pi\)
\(948\) 3196.60i 0.109516i
\(949\) −27040.4 −0.924941
\(950\) 2864.40 703.351i 0.0978246 0.0240208i
\(951\) −7394.81 −0.252148
\(952\) 1052.11i 0.0358185i
\(953\) 39603.5i 1.34615i 0.739573 + 0.673077i \(0.235028\pi\)
−0.739573 + 0.673077i \(0.764972\pi\)
\(954\) 11421.1 0.387601
\(955\) 29553.7 + 23174.7i 1.00140 + 0.785253i
\(956\) 17740.4 0.600174
\(957\) 1520.24i 0.0513505i
\(958\) 23012.6i 0.776099i
\(959\) −10426.7 −0.351091
\(960\) −1324.60 + 1689.21i −0.0445327 + 0.0567906i
\(961\) −13813.0 −0.463664
\(962\) 50477.1i 1.69173i
\(963\) 10283.5i 0.344112i
\(964\) −18303.2 −0.611522
\(965\) −19321.0 + 24639.2i −0.644524 + 0.821933i
\(966\) 6693.69 0.222946
\(967\) 4139.69i 0.137666i 0.997628 + 0.0688332i \(0.0219276\pi\)
−0.997628 + 0.0688332i \(0.978072\pi\)
\(968\) 5406.79i 0.179526i
\(969\) −664.971 −0.0220454
\(970\) 21148.9 + 16584.0i 0.700050 + 0.548949i
\(971\) 42137.2 1.39263 0.696316 0.717735i \(-0.254821\pi\)
0.696316 + 0.717735i \(0.254821\pi\)
\(972\) 972.000i 0.0320750i
\(973\) 5265.99i 0.173504i
\(974\) −33005.8 −1.08580
\(975\) −7975.93 32482.0i −0.261984 1.06693i
\(976\) 6331.46 0.207649
\(977\) 39782.4i 1.30271i 0.758772 + 0.651357i \(0.225800\pi\)
−0.758772 + 0.651357i \(0.774200\pi\)
\(978\) 5311.38i 0.173660i
\(979\) 21576.5 0.704381
\(980\) 1724.40 + 1352.20i 0.0562081 + 0.0440760i
\(981\) −18488.5 −0.601726
\(982\) 18539.3i 0.602458i
\(983\) 3799.91i 0.123294i 0.998098 + 0.0616471i \(0.0196353\pi\)
−0.998098 + 0.0616471i \(0.980365\pi\)
\(984\) −3465.21 −0.112263
\(985\) −22439.1 + 28615.6i −0.725857 + 0.925653i
\(986\) 743.918 0.0240276
\(987\) 2466.13i 0.0795317i
\(988\) 4209.13i 0.135537i
\(989\) 52103.7 1.67523
\(990\) −3178.54 + 4053.45i −0.102041 + 0.130128i
\(991\) 20113.7 0.644735 0.322367 0.946615i \(-0.395521\pi\)
0.322367 + 0.946615i \(0.395521\pi\)
\(992\) 4044.93i 0.129462i
\(993\) 11341.1i 0.362435i
\(994\) −5629.40 −0.179632
\(995\) 13419.6 + 10523.1i 0.427567 + 0.335280i
\(996\) 9039.04 0.287563
\(997\) 40814.2i 1.29649i −0.761432 0.648244i \(-0.775504\pi\)
0.761432 0.648244i \(-0.224496\pi\)
\(998\) 26334.6i 0.835279i
\(999\) 7640.17 0.241966
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.a.169.2 4
3.2 odd 2 630.4.g.e.379.3 4
5.2 odd 4 1050.4.a.bg.1.2 2
5.3 odd 4 1050.4.a.bc.1.2 2
5.4 even 2 inner 210.4.g.a.169.4 yes 4
15.14 odd 2 630.4.g.e.379.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.4.g.a.169.2 4 1.1 even 1 trivial
210.4.g.a.169.4 yes 4 5.4 even 2 inner
630.4.g.e.379.1 4 15.14 odd 2
630.4.g.e.379.3 4 3.2 odd 2
1050.4.a.bc.1.2 2 5.3 odd 4
1050.4.a.bg.1.2 2 5.2 odd 4