Properties

Label 210.4.g.a.169.3
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 169.3
Root \(1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 210.169
Dual form 210.4.g.a.169.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +(-10.7980 + 2.89898i) q^{5} -6.00000 q^{6} +7.00000i q^{7} -8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q+2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +(-10.7980 + 2.89898i) q^{5} -6.00000 q^{6} +7.00000i q^{7} -8.00000i q^{8} -9.00000 q^{9} +(-5.79796 - 21.5959i) q^{10} -13.5959 q^{11} -12.0000i q^{12} +10.8082i q^{13} -14.0000 q^{14} +(-8.69694 - 32.3939i) q^{15} +16.0000 q^{16} -98.7878i q^{17} -18.0000i q^{18} -7.79796 q^{19} +(43.1918 - 11.5959i) q^{20} -21.0000 q^{21} -27.1918i q^{22} -95.3735i q^{23} +24.0000 q^{24} +(108.192 - 62.6061i) q^{25} -21.6163 q^{26} -27.0000i q^{27} -28.0000i q^{28} -0.202041 q^{29} +(64.7878 - 17.3939i) q^{30} -165.596 q^{31} +32.0000i q^{32} -40.7878i q^{33} +197.576 q^{34} +(-20.2929 - 75.5857i) q^{35} +36.0000 q^{36} -10.9694i q^{37} -15.5959i q^{38} -32.4245 q^{39} +(23.1918 + 86.3837i) q^{40} +12.3837 q^{41} -42.0000i q^{42} +358.929i q^{43} +54.3837 q^{44} +(97.1816 - 26.0908i) q^{45} +190.747 q^{46} -450.565i q^{47} +48.0000i q^{48} -49.0000 q^{49} +(125.212 + 216.384i) q^{50} +296.363 q^{51} -43.2327i q^{52} -286.504i q^{53} +54.0000 q^{54} +(146.808 - 39.4143i) q^{55} +56.0000 q^{56} -23.3939i q^{57} -0.404082i q^{58} -739.069 q^{59} +(34.7878 + 129.576i) q^{60} -407.716 q^{61} -331.192i q^{62} -63.0000i q^{63} -64.0000 q^{64} +(-31.3326 - 116.706i) q^{65} +81.5755 q^{66} -77.8796i q^{67} +395.151i q^{68} +286.120 q^{69} +(151.171 - 40.5857i) q^{70} -558.100 q^{71} +72.0000i q^{72} +28.8286i q^{73} +21.9388 q^{74} +(187.818 + 324.576i) q^{75} +31.1918 q^{76} -95.1714i q^{77} -64.8490i q^{78} -109.616 q^{79} +(-172.767 + 46.3837i) q^{80} +81.0000 q^{81} +24.7673i q^{82} +1262.75i q^{83} +84.0000 q^{84} +(286.384 + 1066.71i) q^{85} -717.857 q^{86} -0.606123i q^{87} +108.767i q^{88} -1390.97 q^{89} +(52.1816 + 194.363i) q^{90} -75.6571 q^{91} +381.494i q^{92} -496.788i q^{93} +901.131 q^{94} +(84.2020 - 22.6061i) q^{95} -96.0000 q^{96} -418.082i q^{97} -98.0000i q^{98} +122.363 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 16 q^{4} - 4 q^{5} - 24 q^{6} - 36 q^{9}+O(q^{10}) \) 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
\(5\) −10.7980 + 2.89898i −0.965799 + 0.259293i
\(6\) −6.00000 −0.408248
\(7\) 7.00000i 0.377964i
\(8\) 8.00000i 0.353553i
\(9\) −9.00000 −0.333333
\(10\) −5.79796 21.5959i −0.183348 0.682923i
\(11\) −13.5959 −0.372666 −0.186333 0.982487i \(-0.559660\pi\)
−0.186333 + 0.982487i \(0.559660\pi\)
\(12\) 12.0000i 0.288675i
\(13\) 10.8082i 0.230588i 0.993331 + 0.115294i \(0.0367810\pi\)
−0.993331 + 0.115294i \(0.963219\pi\)
\(14\) −14.0000 −0.267261
\(15\) −8.69694 32.3939i −0.149703 0.557604i
\(16\) 16.0000 0.250000
\(17\) 98.7878i 1.40939i −0.709513 0.704693i \(-0.751085\pi\)
0.709513 0.704693i \(-0.248915\pi\)
\(18\) 18.0000i 0.235702i
\(19\) −7.79796 −0.0941566 −0.0470783 0.998891i \(-0.514991\pi\)
−0.0470783 + 0.998891i \(0.514991\pi\)
\(20\) 43.1918 11.5959i 0.482899 0.129646i
\(21\) −21.0000 −0.218218
\(22\) 27.1918i 0.263514i
\(23\) 95.3735i 0.864641i −0.901720 0.432320i \(-0.857695\pi\)
0.901720 0.432320i \(-0.142305\pi\)
\(24\) 24.0000 0.204124
\(25\) 108.192 62.6061i 0.865535 0.500849i
\(26\) −21.6163 −0.163050
\(27\) 27.0000i 0.192450i
\(28\) 28.0000i 0.188982i
\(29\) −0.202041 −0.00129373 −0.000646863 1.00000i \(-0.500206\pi\)
−0.000646863 1.00000i \(0.500206\pi\)
\(30\) 64.7878 17.3939i 0.394286 0.105856i
\(31\) −165.596 −0.959416 −0.479708 0.877428i \(-0.659257\pi\)
−0.479708 + 0.877428i \(0.659257\pi\)
\(32\) 32.0000i 0.176777i
\(33\) 40.7878i 0.215159i
\(34\) 197.576 0.996586
\(35\) −20.2929 75.5857i −0.0980034 0.365038i
\(36\) 36.0000 0.166667
\(37\) 10.9694i 0.0487393i −0.999703 0.0243697i \(-0.992242\pi\)
0.999703 0.0243697i \(-0.00775788\pi\)
\(38\) 15.5959i 0.0665787i
\(39\) −32.4245 −0.133130
\(40\) 23.1918 + 86.3837i 0.0916738 + 0.341461i
\(41\) 12.3837 0.0471708 0.0235854 0.999722i \(-0.492492\pi\)
0.0235854 + 0.999722i \(0.492492\pi\)
\(42\) 42.0000i 0.154303i
\(43\) 358.929i 1.27293i 0.771305 + 0.636466i \(0.219605\pi\)
−0.771305 + 0.636466i \(0.780395\pi\)
\(44\) 54.3837 0.186333
\(45\) 97.1816 26.0908i 0.321933 0.0864309i
\(46\) 190.747 0.611393
\(47\) 450.565i 1.39833i −0.714958 0.699167i \(-0.753554\pi\)
0.714958 0.699167i \(-0.246446\pi\)
\(48\) 48.0000i 0.144338i
\(49\) −49.0000 −0.142857
\(50\) 125.212 + 216.384i 0.354154 + 0.612025i
\(51\) 296.363 0.813709
\(52\) 43.2327i 0.115294i
\(53\) 286.504i 0.742535i −0.928526 0.371268i \(-0.878923\pi\)
0.928526 0.371268i \(-0.121077\pi\)
\(54\) 54.0000 0.136083
\(55\) 146.808 39.4143i 0.359920 0.0966295i
\(56\) 56.0000 0.133631
\(57\) 23.3939i 0.0543613i
\(58\) 0.404082i 0.000914803i
\(59\) −739.069 −1.63082 −0.815412 0.578881i \(-0.803490\pi\)
−0.815412 + 0.578881i \(0.803490\pi\)
\(60\) 34.7878 + 129.576i 0.0748513 + 0.278802i
\(61\) −407.716 −0.855782 −0.427891 0.903830i \(-0.640743\pi\)
−0.427891 + 0.903830i \(0.640743\pi\)
\(62\) 331.192i 0.678410i
\(63\) 63.0000i 0.125988i
\(64\) −64.0000 −0.125000
\(65\) −31.3326 116.706i −0.0597898 0.222702i
\(66\) 81.5755 0.152140
\(67\) 77.8796i 0.142008i −0.997476 0.0710038i \(-0.977380\pi\)
0.997476 0.0710038i \(-0.0226202\pi\)
\(68\) 395.151i 0.704693i
\(69\) 286.120 0.499201
\(70\) 151.171 40.5857i 0.258121 0.0692989i
\(71\) −558.100 −0.932877 −0.466439 0.884554i \(-0.654463\pi\)
−0.466439 + 0.884554i \(0.654463\pi\)
\(72\) 72.0000i 0.117851i
\(73\) 28.8286i 0.0462210i 0.999733 + 0.0231105i \(0.00735695\pi\)
−0.999733 + 0.0231105i \(0.992643\pi\)
\(74\) 21.9388 0.0344639
\(75\) 187.818 + 324.576i 0.289165 + 0.499717i
\(76\) 31.1918 0.0470783
\(77\) 95.1714i 0.140854i
\(78\) 64.8490i 0.0941372i
\(79\) −109.616 −0.156111 −0.0780557 0.996949i \(-0.524871\pi\)
−0.0780557 + 0.996949i \(0.524871\pi\)
\(80\) −172.767 + 46.3837i −0.241450 + 0.0648232i
\(81\) 81.0000 0.111111
\(82\) 24.7673i 0.0333548i
\(83\) 1262.75i 1.66993i 0.550300 + 0.834967i \(0.314513\pi\)
−0.550300 + 0.834967i \(0.685487\pi\)
\(84\) 84.0000 0.109109
\(85\) 286.384 + 1066.71i 0.365443 + 1.36118i
\(86\) −717.857 −0.900099
\(87\) 0.606123i 0.000746934i
\(88\) 108.767i 0.131757i
\(89\) −1390.97 −1.65665 −0.828327 0.560245i \(-0.810707\pi\)
−0.828327 + 0.560245i \(0.810707\pi\)
\(90\) 52.1816 + 194.363i 0.0611159 + 0.227641i
\(91\) −75.6571 −0.0871541
\(92\) 381.494i 0.432320i
\(93\) 496.788i 0.553919i
\(94\) 901.131 0.988772
\(95\) 84.2020 22.6061i 0.0909363 0.0244141i
\(96\) −96.0000 −0.102062
\(97\) 418.082i 0.437626i −0.975767 0.218813i \(-0.929781\pi\)
0.975767 0.218813i \(-0.0702185\pi\)
\(98\) 98.0000i 0.101015i
\(99\) 122.363 0.124222
\(100\) −432.767 + 250.424i −0.432767 + 0.250424i
\(101\) −1619.37 −1.59538 −0.797690 0.603067i \(-0.793945\pi\)
−0.797690 + 0.603067i \(0.793945\pi\)
\(102\) 592.727i 0.575379i
\(103\) 1470.22i 1.40646i 0.710964 + 0.703229i \(0.248259\pi\)
−0.710964 + 0.703229i \(0.751741\pi\)
\(104\) 86.4653 0.0815252
\(105\) 226.757 60.8786i 0.210755 0.0565823i
\(106\) 573.008 0.525052
\(107\) 1201.39i 1.08545i −0.839911 0.542725i \(-0.817393\pi\)
0.839911 0.542725i \(-0.182607\pi\)
\(108\) 108.000i 0.0962250i
\(109\) 917.718 0.806436 0.403218 0.915104i \(-0.367892\pi\)
0.403218 + 0.915104i \(0.367892\pi\)
\(110\) 78.8286 + 293.616i 0.0683274 + 0.254502i
\(111\) 32.9082 0.0281397
\(112\) 112.000i 0.0944911i
\(113\) 774.827i 0.645040i 0.946563 + 0.322520i \(0.104530\pi\)
−0.946563 + 0.322520i \(0.895470\pi\)
\(114\) 46.7878 0.0384393
\(115\) 276.486 + 1029.84i 0.224195 + 0.835069i
\(116\) 0.808164 0.000646863
\(117\) 97.2735i 0.0768627i
\(118\) 1478.14i 1.15317i
\(119\) 691.514 0.532698
\(120\) −259.151 + 69.5755i −0.197143 + 0.0529279i
\(121\) −1146.15 −0.861120
\(122\) 815.433i 0.605130i
\(123\) 37.1510i 0.0272341i
\(124\) 662.384 0.479708
\(125\) −986.757 + 989.664i −0.706066 + 0.708146i
\(126\) 126.000 0.0890871
\(127\) 8.15916i 0.00570085i 0.999996 + 0.00285043i \(0.000907320\pi\)
−0.999996 + 0.00285043i \(0.999093\pi\)
\(128\) 128.000i 0.0883883i
\(129\) −1076.79 −0.734928
\(130\) 233.412 62.6653i 0.157474 0.0422778i
\(131\) 876.808 0.584787 0.292393 0.956298i \(-0.405548\pi\)
0.292393 + 0.956298i \(0.405548\pi\)
\(132\) 163.151i 0.107579i
\(133\) 54.5857i 0.0355878i
\(134\) 155.759 0.100415
\(135\) 78.2724 + 291.545i 0.0499009 + 0.185868i
\(136\) −790.302 −0.498293
\(137\) 1077.53i 0.671970i −0.941867 0.335985i \(-0.890931\pi\)
0.941867 0.335985i \(-0.109069\pi\)
\(138\) 572.241i 0.352988i
\(139\) 1555.72 0.949310 0.474655 0.880172i \(-0.342573\pi\)
0.474655 + 0.880172i \(0.342573\pi\)
\(140\) 81.1714 + 302.343i 0.0490017 + 0.182519i
\(141\) 1351.70 0.807329
\(142\) 1116.20i 0.659644i
\(143\) 146.947i 0.0859323i
\(144\) −144.000 −0.0833333
\(145\) 2.18163 0.585713i 0.00124948 0.000335454i
\(146\) −57.6571 −0.0326831
\(147\) 147.000i 0.0824786i
\(148\) 43.8775i 0.0243697i
\(149\) −1806.99 −0.993519 −0.496760 0.867888i \(-0.665477\pi\)
−0.496760 + 0.867888i \(0.665477\pi\)
\(150\) −649.151 + 375.637i −0.353353 + 0.204471i
\(151\) 949.612 0.511777 0.255889 0.966706i \(-0.417632\pi\)
0.255889 + 0.966706i \(0.417632\pi\)
\(152\) 62.3837i 0.0332894i
\(153\) 889.090i 0.469795i
\(154\) 190.343 0.0995991
\(155\) 1788.10 480.059i 0.926603 0.248770i
\(156\) 129.698 0.0665651
\(157\) 3018.52i 1.53442i −0.641395 0.767211i \(-0.721644\pi\)
0.641395 0.767211i \(-0.278356\pi\)
\(158\) 219.233i 0.110387i
\(159\) 859.512 0.428703
\(160\) −92.7673 345.535i −0.0458369 0.170731i
\(161\) 667.614 0.326804
\(162\) 162.000i 0.0785674i
\(163\) 741.231i 0.356182i −0.984014 0.178091i \(-0.943008\pi\)
0.984014 0.178091i \(-0.0569921\pi\)
\(164\) −49.5347 −0.0235854
\(165\) 118.243 + 440.424i 0.0557891 + 0.207800i
\(166\) −2525.49 −1.18082
\(167\) 52.2591i 0.0242152i 0.999927 + 0.0121076i \(0.00385406\pi\)
−0.999927 + 0.0121076i \(0.996146\pi\)
\(168\) 168.000i 0.0771517i
\(169\) 2080.18 0.946829
\(170\) −2133.41 + 572.767i −0.962501 + 0.258407i
\(171\) 70.1816 0.0313855
\(172\) 1435.71i 0.636466i
\(173\) 155.378i 0.0682840i 0.999417 + 0.0341420i \(0.0108699\pi\)
−0.999417 + 0.0341420i \(0.989130\pi\)
\(174\) 1.21225 0.000528162
\(175\) 438.243 + 757.343i 0.189303 + 0.327141i
\(176\) −217.535 −0.0931664
\(177\) 2217.21i 0.941557i
\(178\) 2781.93i 1.17143i
\(179\) 2442.07 1.01972 0.509858 0.860259i \(-0.329698\pi\)
0.509858 + 0.860259i \(0.329698\pi\)
\(180\) −388.727 + 104.363i −0.160966 + 0.0432154i
\(181\) −1153.49 −0.473693 −0.236846 0.971547i \(-0.576114\pi\)
−0.236846 + 0.971547i \(0.576114\pi\)
\(182\) 151.314i 0.0616273i
\(183\) 1223.15i 0.494086i
\(184\) −762.988 −0.305697
\(185\) 31.8000 + 118.447i 0.0126378 + 0.0470724i
\(186\) 993.576 0.391680
\(187\) 1343.11i 0.525230i
\(188\) 1802.26i 0.699167i
\(189\) 189.000 0.0727393
\(190\) 45.2122 + 168.404i 0.0172634 + 0.0643017i
\(191\) 4828.85 1.82934 0.914668 0.404206i \(-0.132452\pi\)
0.914668 + 0.404206i \(0.132452\pi\)
\(192\) 192.000i 0.0721688i
\(193\) 527.437i 0.196714i −0.995151 0.0983568i \(-0.968641\pi\)
0.995151 0.0983568i \(-0.0313586\pi\)
\(194\) 836.163 0.309449
\(195\) 350.118 93.9979i 0.128577 0.0345197i
\(196\) 196.000 0.0714286
\(197\) 2527.48i 0.914087i −0.889444 0.457044i \(-0.848908\pi\)
0.889444 0.457044i \(-0.151092\pi\)
\(198\) 244.727i 0.0878382i
\(199\) −5137.31 −1.83002 −0.915010 0.403431i \(-0.867817\pi\)
−0.915010 + 0.403431i \(0.867817\pi\)
\(200\) −500.849 865.535i −0.177077 0.306013i
\(201\) 233.639 0.0819881
\(202\) 3238.74i 1.12810i
\(203\) 1.41429i 0.000488983i
\(204\) −1185.45 −0.406854
\(205\) −133.718 + 35.9000i −0.0455575 + 0.0122311i
\(206\) −2940.44 −0.994516
\(207\) 858.361i 0.288214i
\(208\) 172.931i 0.0576470i
\(209\) 106.020 0.0350889
\(210\) 121.757 + 453.514i 0.0400097 + 0.149026i
\(211\) 5766.29 1.88137 0.940683 0.339288i \(-0.110186\pi\)
0.940683 + 0.339288i \(0.110186\pi\)
\(212\) 1146.02i 0.371268i
\(213\) 1674.30i 0.538597i
\(214\) 2402.79 0.767529
\(215\) −1040.53 3875.70i −0.330062 1.22940i
\(216\) −216.000 −0.0680414
\(217\) 1159.17i 0.362625i
\(218\) 1835.44i 0.570236i
\(219\) −86.4857 −0.0266857
\(220\) −587.233 + 157.657i −0.179960 + 0.0483147i
\(221\) 1067.71 0.324987
\(222\) 65.8163i 0.0198978i
\(223\) 1194.30i 0.358637i 0.983791 + 0.179319i \(0.0573893\pi\)
−0.983791 + 0.179319i \(0.942611\pi\)
\(224\) −224.000 −0.0668153
\(225\) −973.727 + 563.455i −0.288512 + 0.166950i
\(226\) −1549.65 −0.456112
\(227\) 3101.45i 0.906830i −0.891300 0.453415i \(-0.850206\pi\)
0.891300 0.453415i \(-0.149794\pi\)
\(228\) 93.5755i 0.0271807i
\(229\) −2161.00 −0.623594 −0.311797 0.950149i \(-0.600931\pi\)
−0.311797 + 0.950149i \(0.600931\pi\)
\(230\) −2059.68 + 552.971i −0.590483 + 0.158530i
\(231\) 285.514 0.0813223
\(232\) 1.61633i 0.000457401i
\(233\) 3124.28i 0.878449i 0.898377 + 0.439225i \(0.144747\pi\)
−0.898377 + 0.439225i \(0.855253\pi\)
\(234\) 194.547 0.0543501
\(235\) 1306.18 + 4865.19i 0.362578 + 1.35051i
\(236\) 2956.28 0.815412
\(237\) 328.849i 0.0901310i
\(238\) 1383.03i 0.376674i
\(239\) −1632.89 −0.441937 −0.220969 0.975281i \(-0.570922\pi\)
−0.220969 + 0.975281i \(0.570922\pi\)
\(240\) −139.151 518.302i −0.0374257 0.139401i
\(241\) −4947.81 −1.32247 −0.661237 0.750177i \(-0.729968\pi\)
−0.661237 + 0.750177i \(0.729968\pi\)
\(242\) 2292.30i 0.608904i
\(243\) 243.000i 0.0641500i
\(244\) 1630.87 0.427891
\(245\) 529.100 142.050i 0.137971 0.0370418i
\(246\) −74.3020 −0.0192574
\(247\) 84.2816i 0.0217114i
\(248\) 1324.77i 0.339205i
\(249\) −3788.24 −0.964137
\(250\) −1979.33 1973.51i −0.500735 0.499264i
\(251\) 6977.04 1.75453 0.877265 0.480006i \(-0.159365\pi\)
0.877265 + 0.480006i \(0.159365\pi\)
\(252\) 252.000i 0.0629941i
\(253\) 1296.69i 0.322222i
\(254\) −16.3183 −0.00403111
\(255\) −3200.12 + 859.151i −0.785879 + 0.210989i
\(256\) 256.000 0.0625000
\(257\) 3164.36i 0.768045i −0.923324 0.384022i \(-0.874539\pi\)
0.923324 0.384022i \(-0.125461\pi\)
\(258\) 2153.57i 0.519672i
\(259\) 76.7857 0.0184217
\(260\) 125.331 + 466.824i 0.0298949 + 0.111351i
\(261\) 1.81837 0.000431242
\(262\) 1753.62i 0.413507i
\(263\) 496.871i 0.116496i −0.998302 0.0582479i \(-0.981449\pi\)
0.998302 0.0582479i \(-0.0185514\pi\)
\(264\) −326.302 −0.0760701
\(265\) 830.569 + 3093.66i 0.192534 + 0.717140i
\(266\) 109.171 0.0251644
\(267\) 4172.90i 0.956470i
\(268\) 311.518i 0.0710038i
\(269\) −3897.19 −0.883330 −0.441665 0.897180i \(-0.645612\pi\)
−0.441665 + 0.897180i \(0.645612\pi\)
\(270\) −583.090 + 156.545i −0.131429 + 0.0352853i
\(271\) −7309.63 −1.63848 −0.819240 0.573450i \(-0.805605\pi\)
−0.819240 + 0.573450i \(0.805605\pi\)
\(272\) 1580.60i 0.352346i
\(273\) 226.971i 0.0503185i
\(274\) 2155.07 0.475154
\(275\) −1470.97 + 851.188i −0.322555 + 0.186649i
\(276\) −1144.48 −0.249600
\(277\) 8351.24i 1.81147i 0.423844 + 0.905735i \(0.360680\pi\)
−0.423844 + 0.905735i \(0.639320\pi\)
\(278\) 3111.43i 0.671264i
\(279\) 1490.36 0.319805
\(280\) −604.686 + 162.343i −0.129060 + 0.0346494i
\(281\) 3816.91 0.810311 0.405156 0.914248i \(-0.367217\pi\)
0.405156 + 0.914248i \(0.367217\pi\)
\(282\) 2703.39i 0.570868i
\(283\) 3683.58i 0.773733i 0.922136 + 0.386866i \(0.126443\pi\)
−0.922136 + 0.386866i \(0.873557\pi\)
\(284\) 2232.40 0.466439
\(285\) 67.8184 + 252.606i 0.0140955 + 0.0525021i
\(286\) 293.894 0.0607633
\(287\) 86.6857i 0.0178289i
\(288\) 288.000i 0.0589256i
\(289\) −4846.02 −0.986367
\(290\) 1.17143 + 4.36326i 0.000237202 + 0.000883516i
\(291\) 1254.24 0.252664
\(292\) 115.314i 0.0231105i
\(293\) 8450.79i 1.68498i 0.538709 + 0.842492i \(0.318912\pi\)
−0.538709 + 0.842492i \(0.681088\pi\)
\(294\) 294.000 0.0583212
\(295\) 7980.44 2142.55i 1.57505 0.422861i
\(296\) −87.7551 −0.0172320
\(297\) 367.090i 0.0717196i
\(298\) 3613.98i 0.702524i
\(299\) 1030.81 0.199376
\(300\) −751.273 1298.30i −0.144583 0.249858i
\(301\) −2512.50 −0.481123
\(302\) 1899.22i 0.361881i
\(303\) 4858.11i 0.921094i
\(304\) −124.767 −0.0235391
\(305\) 4402.50 1181.96i 0.826514 0.221898i
\(306\) −1778.18 −0.332195
\(307\) 3323.79i 0.617911i 0.951076 + 0.308956i \(0.0999795\pi\)
−0.951076 + 0.308956i \(0.900021\pi\)
\(308\) 380.686i 0.0704272i
\(309\) −4410.66 −0.812019
\(310\) 960.118 + 3576.20i 0.175907 + 0.655207i
\(311\) 1760.61 0.321013 0.160506 0.987035i \(-0.448687\pi\)
0.160506 + 0.987035i \(0.448687\pi\)
\(312\) 259.396i 0.0470686i
\(313\) 1717.91i 0.310230i −0.987896 0.155115i \(-0.950425\pi\)
0.987896 0.155115i \(-0.0495748\pi\)
\(314\) 6037.04 1.08500
\(315\) 182.636 + 680.271i 0.0326678 + 0.121679i
\(316\) 438.465 0.0780557
\(317\) 9539.06i 1.69012i 0.534674 + 0.845059i \(0.320435\pi\)
−0.534674 + 0.845059i \(0.679565\pi\)
\(318\) 1719.02i 0.303139i
\(319\) 2.74693 0.000482128
\(320\) 691.069 185.535i 0.120725 0.0324116i
\(321\) 3604.18 0.626685
\(322\) 1335.23i 0.231085i
\(323\) 770.343i 0.132703i
\(324\) −324.000 −0.0555556
\(325\) 676.657 + 1169.36i 0.115490 + 0.199582i
\(326\) 1482.46 0.251859
\(327\) 2753.16i 0.465596i
\(328\) 99.0694i 0.0166774i
\(329\) 3153.96 0.528521
\(330\) −880.849 + 236.486i −0.146937 + 0.0394488i
\(331\) −452.359 −0.0751175 −0.0375588 0.999294i \(-0.511958\pi\)
−0.0375588 + 0.999294i \(0.511958\pi\)
\(332\) 5050.99i 0.834967i
\(333\) 98.7245i 0.0162464i
\(334\) −104.518 −0.0171227
\(335\) 225.771 + 840.941i 0.0368215 + 0.137151i
\(336\) −336.000 −0.0545545
\(337\) 5637.61i 0.911277i −0.890165 0.455638i \(-0.849411\pi\)
0.890165 0.455638i \(-0.150589\pi\)
\(338\) 4160.37i 0.669509i
\(339\) −2324.48 −0.372414
\(340\) −1145.53 4266.82i −0.182722 0.680591i
\(341\) 2251.43 0.357542
\(342\) 140.363i 0.0221929i
\(343\) 343.000i 0.0539949i
\(344\) 2871.43 0.450050
\(345\) −3089.52 + 829.457i −0.482127 + 0.129439i
\(346\) −310.755 −0.0482841
\(347\) 12313.1i 1.90490i 0.304696 + 0.952450i \(0.401445\pi\)
−0.304696 + 0.952450i \(0.598555\pi\)
\(348\) 2.42449i 0.000373467i
\(349\) −7203.55 −1.10486 −0.552432 0.833558i \(-0.686300\pi\)
−0.552432 + 0.833558i \(0.686300\pi\)
\(350\) −1514.69 + 876.486i −0.231324 + 0.133858i
\(351\) 291.820 0.0443767
\(352\) 435.069i 0.0658786i
\(353\) 7030.58i 1.06006i −0.847980 0.530028i \(-0.822181\pi\)
0.847980 0.530028i \(-0.177819\pi\)
\(354\) 4434.42 0.665781
\(355\) 6026.34 1617.92i 0.900972 0.241888i
\(356\) 5563.87 0.828327
\(357\) 2074.54i 0.307553i
\(358\) 4884.15i 0.721048i
\(359\) −5999.06 −0.881946 −0.440973 0.897520i \(-0.645366\pi\)
−0.440973 + 0.897520i \(0.645366\pi\)
\(360\) −208.727 777.453i −0.0305579 0.113820i
\(361\) −6798.19 −0.991135
\(362\) 2306.98i 0.334951i
\(363\) 3438.45i 0.497168i
\(364\) 302.629 0.0435771
\(365\) −83.5734 311.290i −0.0119848 0.0446401i
\(366\) 2446.30 0.349372
\(367\) 9039.02i 1.28565i 0.766014 + 0.642824i \(0.222237\pi\)
−0.766014 + 0.642824i \(0.777763\pi\)
\(368\) 1525.98i 0.216160i
\(369\) −111.453 −0.0157236
\(370\) −236.894 + 63.6000i −0.0332852 + 0.00893624i
\(371\) 2005.53 0.280652
\(372\) 1987.15i 0.276960i
\(373\) 12415.4i 1.72345i −0.507375 0.861726i \(-0.669384\pi\)
0.507375 0.861726i \(-0.330616\pi\)
\(374\) −2686.22 −0.371393
\(375\) −2968.99 2960.27i −0.408848 0.407647i
\(376\) −3604.52 −0.494386
\(377\) 2.18369i 0.000298318i
\(378\) 378.000i 0.0514344i
\(379\) −7339.39 −0.994721 −0.497360 0.867544i \(-0.665697\pi\)
−0.497360 + 0.867544i \(0.665697\pi\)
\(380\) −336.808 + 90.4245i −0.0454681 + 0.0122070i
\(381\) −24.4775 −0.00329139
\(382\) 9657.69i 1.29354i
\(383\) 8054.27i 1.07455i −0.843406 0.537277i \(-0.819453\pi\)
0.843406 0.537277i \(-0.180547\pi\)
\(384\) 384.000 0.0510310
\(385\) 275.900 + 1027.66i 0.0365225 + 0.136037i
\(386\) 1054.87 0.139098
\(387\) 3230.36i 0.424311i
\(388\) 1672.33i 0.218813i
\(389\) −4405.48 −0.574208 −0.287104 0.957899i \(-0.592693\pi\)
−0.287104 + 0.957899i \(0.592693\pi\)
\(390\) 187.996 + 700.237i 0.0244091 + 0.0909176i
\(391\) −9421.73 −1.21861
\(392\) 392.000i 0.0505076i
\(393\) 2630.42i 0.337627i
\(394\) 5054.95 0.646357
\(395\) 1183.63 317.775i 0.150772 0.0404785i
\(396\) −489.453 −0.0621110
\(397\) 10950.6i 1.38437i −0.721721 0.692184i \(-0.756649\pi\)
0.721721 0.692184i \(-0.243351\pi\)
\(398\) 10274.6i 1.29402i
\(399\) 163.757 0.0205466
\(400\) 1731.07 1001.70i 0.216384 0.125212i
\(401\) −7942.59 −0.989112 −0.494556 0.869146i \(-0.664669\pi\)
−0.494556 + 0.869146i \(0.664669\pi\)
\(402\) 467.278i 0.0579743i
\(403\) 1789.79i 0.221230i
\(404\) 6477.49 0.797690
\(405\) −874.635 + 234.817i −0.107311 + 0.0288103i
\(406\) 2.82857 0.000345763
\(407\) 149.139i 0.0181635i
\(408\) 2370.91i 0.287690i
\(409\) 7094.02 0.857645 0.428822 0.903389i \(-0.358929\pi\)
0.428822 + 0.903389i \(0.358929\pi\)
\(410\) −71.8000 267.437i −0.00864866 0.0322140i
\(411\) 3232.60 0.387962
\(412\) 5880.88i 0.703229i
\(413\) 5173.49i 0.616394i
\(414\) −1716.72 −0.203798
\(415\) −3660.68 13635.1i −0.433001 1.61282i
\(416\) −345.861 −0.0407626
\(417\) 4667.15i 0.548085i
\(418\) 212.041i 0.0248116i
\(419\) 2491.00 0.290438 0.145219 0.989400i \(-0.453611\pi\)
0.145219 + 0.989400i \(0.453611\pi\)
\(420\) −907.029 + 243.514i −0.105377 + 0.0282911i
\(421\) −1567.51 −0.181462 −0.0907311 0.995875i \(-0.528920\pi\)
−0.0907311 + 0.995875i \(0.528920\pi\)
\(422\) 11532.6i 1.33033i
\(423\) 4055.09i 0.466111i
\(424\) −2292.03 −0.262526
\(425\) −6184.72 10688.0i −0.705889 1.21987i
\(426\) 3348.60 0.380846
\(427\) 2854.01i 0.323455i
\(428\) 4805.58i 0.542725i
\(429\) 440.841 0.0496130
\(430\) 7751.39 2081.05i 0.869315 0.233389i
\(431\) 715.843 0.0800022 0.0400011 0.999200i \(-0.487264\pi\)
0.0400011 + 0.999200i \(0.487264\pi\)
\(432\) 432.000i 0.0481125i
\(433\) 3583.72i 0.397743i −0.980026 0.198871i \(-0.936272\pi\)
0.980026 0.198871i \(-0.0637276\pi\)
\(434\) 2318.34 0.256415
\(435\) 1.75714 + 6.54489i 0.000193674 + 0.000721388i
\(436\) −3670.87 −0.403218
\(437\) 743.718i 0.0814116i
\(438\) 172.971i 0.0188696i
\(439\) 10290.4 1.11875 0.559376 0.828914i \(-0.311041\pi\)
0.559376 + 0.828914i \(0.311041\pi\)
\(440\) −315.314 1174.47i −0.0341637 0.127251i
\(441\) 441.000 0.0476190
\(442\) 2135.43i 0.229801i
\(443\) 3716.40i 0.398581i −0.979940 0.199291i \(-0.936136\pi\)
0.979940 0.199291i \(-0.0638637\pi\)
\(444\) −131.633 −0.0140698
\(445\) 15019.6 4032.39i 1.59999 0.429558i
\(446\) −2388.60 −0.253595
\(447\) 5420.97i 0.573609i
\(448\) 448.000i 0.0472456i
\(449\) −10608.7 −1.11504 −0.557521 0.830163i \(-0.688247\pi\)
−0.557521 + 0.830163i \(0.688247\pi\)
\(450\) −1126.91 1947.45i −0.118051 0.204008i
\(451\) −168.367 −0.0175790
\(452\) 3099.31i 0.322520i
\(453\) 2848.84i 0.295475i
\(454\) 6202.90 0.641226
\(455\) 816.943 219.329i 0.0841733 0.0225984i
\(456\) −187.151 −0.0192196
\(457\) 8241.22i 0.843563i −0.906698 0.421781i \(-0.861405\pi\)
0.906698 0.421781i \(-0.138595\pi\)
\(458\) 4322.00i 0.440948i
\(459\) −2667.27 −0.271236
\(460\) −1105.94 4119.36i −0.112098 0.417535i
\(461\) −15252.5 −1.54096 −0.770478 0.637467i \(-0.779982\pi\)
−0.770478 + 0.637467i \(0.779982\pi\)
\(462\) 571.029i 0.0575036i
\(463\) 3541.52i 0.355482i −0.984077 0.177741i \(-0.943121\pi\)
0.984077 0.177741i \(-0.0568790\pi\)
\(464\) −3.23266 −0.000323432
\(465\) 1440.18 + 5364.29i 0.143627 + 0.534975i
\(466\) −6248.57 −0.621157
\(467\) 4220.46i 0.418200i 0.977894 + 0.209100i \(0.0670534\pi\)
−0.977894 + 0.209100i \(0.932947\pi\)
\(468\) 389.094i 0.0384314i
\(469\) 545.157 0.0536738
\(470\) −9730.37 + 2612.36i −0.954954 + 0.256381i
\(471\) 9055.57 0.885899
\(472\) 5912.55i 0.576583i
\(473\) 4879.96i 0.474378i
\(474\) 657.698 0.0637322
\(475\) −843.675 + 488.200i −0.0814958 + 0.0471582i
\(476\) −2766.06 −0.266349
\(477\) 2578.54i 0.247512i
\(478\) 3265.78i 0.312497i
\(479\) −6685.70 −0.637740 −0.318870 0.947798i \(-0.603303\pi\)
−0.318870 + 0.947798i \(0.603303\pi\)
\(480\) 1036.60 278.302i 0.0985714 0.0264639i
\(481\) 118.559 0.0112387
\(482\) 9895.62i 0.935131i
\(483\) 2002.84i 0.188680i
\(484\) 4584.60 0.430560
\(485\) 1212.01 + 4514.43i 0.113473 + 0.422659i
\(486\) −486.000 −0.0453609
\(487\) 5921.10i 0.550946i 0.961309 + 0.275473i \(0.0888345\pi\)
−0.961309 + 0.275473i \(0.911166\pi\)
\(488\) 3261.73i 0.302565i
\(489\) 2223.69 0.205642
\(490\) 284.100 + 1058.20i 0.0261925 + 0.0975604i
\(491\) −1625.67 −0.149420 −0.0747100 0.997205i \(-0.523803\pi\)
−0.0747100 + 0.997205i \(0.523803\pi\)
\(492\) 148.604i 0.0136170i
\(493\) 19.9592i 0.00182336i
\(494\) 168.563 0.0153523
\(495\) −1321.27 + 354.729i −0.119973 + 0.0322098i
\(496\) −2649.53 −0.239854
\(497\) 3906.70i 0.352594i
\(498\) 7576.48i 0.681748i
\(499\) 20263.3 1.81786 0.908929 0.416952i \(-0.136902\pi\)
0.908929 + 0.416952i \(0.136902\pi\)
\(500\) 3947.03 3958.66i 0.353033 0.354073i
\(501\) −156.777 −0.0139806
\(502\) 13954.1i 1.24064i
\(503\) 13300.9i 1.17904i 0.807753 + 0.589521i \(0.200684\pi\)
−0.807753 + 0.589521i \(0.799316\pi\)
\(504\) −504.000 −0.0445435
\(505\) 17485.9 4694.52i 1.54082 0.413670i
\(506\) −2593.38 −0.227845
\(507\) 6240.55i 0.546652i
\(508\) 32.6366i 0.00285043i
\(509\) 12280.6 1.06941 0.534704 0.845039i \(-0.320423\pi\)
0.534704 + 0.845039i \(0.320423\pi\)
\(510\) −1718.30 6400.24i −0.149192 0.555700i
\(511\) −201.800 −0.0174699
\(512\) 512.000i 0.0441942i
\(513\) 210.545i 0.0181204i
\(514\) 6328.73 0.543090
\(515\) −4262.14 15875.4i −0.364684 1.35835i
\(516\) 4307.14 0.367464
\(517\) 6125.85i 0.521111i
\(518\) 153.571i 0.0130261i
\(519\) −466.133 −0.0394238
\(520\) −933.649 + 250.661i −0.0787369 + 0.0211389i
\(521\) 18174.1 1.52826 0.764128 0.645064i \(-0.223169\pi\)
0.764128 + 0.645064i \(0.223169\pi\)
\(522\) 3.63674i 0.000304934i
\(523\) 8750.68i 0.731626i 0.930688 + 0.365813i \(0.119209\pi\)
−0.930688 + 0.365813i \(0.880791\pi\)
\(524\) −3507.23 −0.292393
\(525\) −2272.03 + 1314.73i −0.188875 + 0.109294i
\(526\) 993.743 0.0823750
\(527\) 16358.8i 1.35219i
\(528\) 652.604i 0.0537897i
\(529\) 3070.90 0.252396
\(530\) −6187.32 + 1661.14i −0.507094 + 0.136142i
\(531\) 6651.62 0.543608
\(532\) 218.343i 0.0177939i
\(533\) 133.845i 0.0108770i
\(534\) 8345.80 0.676326
\(535\) 3482.82 + 12972.6i 0.281449 + 1.04833i
\(536\) −623.037 −0.0502073
\(537\) 7326.22i 0.588733i
\(538\) 7794.38i 0.624609i
\(539\) 666.200 0.0532380
\(540\) −313.090 1166.18i −0.0249504 0.0929340i
\(541\) −656.045 −0.0521360 −0.0260680 0.999660i \(-0.508299\pi\)
−0.0260680 + 0.999660i \(0.508299\pi\)
\(542\) 14619.3i 1.15858i
\(543\) 3460.48i 0.273487i
\(544\) 3161.21 0.249146
\(545\) −9909.49 + 2660.45i −0.778855 + 0.209103i
\(546\) 453.943 0.0355805
\(547\) 5798.36i 0.453236i −0.973984 0.226618i \(-0.927233\pi\)
0.973984 0.226618i \(-0.0727669\pi\)
\(548\) 4310.13i 0.335985i
\(549\) 3669.45 0.285261
\(550\) −1702.38 2941.93i −0.131981 0.228081i
\(551\) 1.57551 0.000121813
\(552\) 2288.96i 0.176494i
\(553\) 767.314i 0.0590046i
\(554\) −16702.5 −1.28090
\(555\) −355.341 + 95.4001i −0.0271773 + 0.00729641i
\(556\) −6222.87 −0.474655
\(557\) 10841.0i 0.824680i 0.911030 + 0.412340i \(0.135288\pi\)
−0.911030 + 0.412340i \(0.864712\pi\)
\(558\) 2980.73i 0.226137i
\(559\) −3879.36 −0.293523
\(560\) −324.686 1209.37i −0.0245008 0.0912594i
\(561\) −4029.33 −0.303241
\(562\) 7633.81i 0.572977i
\(563\) 844.473i 0.0632155i 0.999500 + 0.0316077i \(0.0100627\pi\)
−0.999500 + 0.0316077i \(0.989937\pi\)
\(564\) −5406.78 −0.403664
\(565\) −2246.21 8366.54i −0.167254 0.622979i
\(566\) −7367.17 −0.547112
\(567\) 567.000i 0.0419961i
\(568\) 4464.80i 0.329822i
\(569\) 12991.7 0.957187 0.478593 0.878037i \(-0.341147\pi\)
0.478593 + 0.878037i \(0.341147\pi\)
\(570\) −505.212 + 135.637i −0.0371246 + 0.00996701i
\(571\) 5989.62 0.438980 0.219490 0.975615i \(-0.429561\pi\)
0.219490 + 0.975615i \(0.429561\pi\)
\(572\) 587.788i 0.0429661i
\(573\) 14486.5i 1.05617i
\(574\) −173.371 −0.0126069
\(575\) −5970.96 10318.6i −0.433055 0.748377i
\(576\) 576.000 0.0416667
\(577\) 7876.11i 0.568261i −0.958786 0.284130i \(-0.908295\pi\)
0.958786 0.284130i \(-0.0917049\pi\)
\(578\) 9692.04i 0.697467i
\(579\) 1582.31 0.113573
\(580\) −8.72652 + 2.34285i −0.000624740 + 0.000167727i
\(581\) −8839.23 −0.631176
\(582\) 2508.49i 0.178660i
\(583\) 3895.29i 0.276717i
\(584\) 230.629 0.0163416
\(585\) 281.994 + 1050.36i 0.0199299 + 0.0742339i
\(586\) −16901.6 −1.19146
\(587\) 18207.9i 1.28028i 0.768260 + 0.640138i \(0.221123\pi\)
−0.768260 + 0.640138i \(0.778877\pi\)
\(588\) 588.000i 0.0412393i
\(589\) 1291.31 0.0903353
\(590\) 4285.09 + 15960.9i 0.299008 + 1.11373i
\(591\) 7582.43 0.527748
\(592\) 175.510i 0.0121848i
\(593\) 11709.0i 0.810848i −0.914129 0.405424i \(-0.867124\pi\)
0.914129 0.405424i \(-0.132876\pi\)
\(594\) −734.180 −0.0507134
\(595\) −7466.94 + 2004.69i −0.514479 + 0.138125i
\(596\) 7227.96 0.496760
\(597\) 15411.9i 1.05656i
\(598\) 2061.62i 0.140980i
\(599\) −20376.3 −1.38990 −0.694952 0.719056i \(-0.744574\pi\)
−0.694952 + 0.719056i \(0.744574\pi\)
\(600\) 2596.60 1502.55i 0.176677 0.102235i
\(601\) −13509.9 −0.916937 −0.458469 0.888711i \(-0.651602\pi\)
−0.458469 + 0.888711i \(0.651602\pi\)
\(602\) 5025.00i 0.340205i
\(603\) 700.916i 0.0473359i
\(604\) −3798.45 −0.255889
\(605\) 12376.1 3322.67i 0.831669 0.223282i
\(606\) 9716.23 0.651312
\(607\) 24253.6i 1.62179i 0.585193 + 0.810894i \(0.301019\pi\)
−0.585193 + 0.810894i \(0.698981\pi\)
\(608\) 249.535i 0.0166447i
\(609\) 4.24286 0.000282314
\(610\) 2363.92 + 8805.01i 0.156906 + 0.584433i
\(611\) 4869.78 0.322439
\(612\) 3556.36i 0.234898i
\(613\) 696.145i 0.0458679i −0.999737 0.0229340i \(-0.992699\pi\)
0.999737 0.0229340i \(-0.00730074\pi\)
\(614\) −6647.58 −0.436929
\(615\) −107.700 401.155i −0.00706160 0.0263027i
\(616\) −761.371 −0.0497996
\(617\) 19894.8i 1.29811i 0.760740 + 0.649056i \(0.224836\pi\)
−0.760740 + 0.649056i \(0.775164\pi\)
\(618\) 8821.32i 0.574184i
\(619\) −5616.19 −0.364675 −0.182337 0.983236i \(-0.558366\pi\)
−0.182337 + 0.983236i \(0.558366\pi\)
\(620\) −7152.39 + 1920.24i −0.463302 + 0.124385i
\(621\) −2575.08 −0.166400
\(622\) 3521.22i 0.226990i
\(623\) 9736.77i 0.626157i
\(624\) −518.792 −0.0332825
\(625\) 7785.95 13546.9i 0.498301 0.867004i
\(626\) 3435.82 0.219366
\(627\) 318.061i 0.0202586i
\(628\) 12074.1i 0.767211i
\(629\) −1083.64 −0.0686925
\(630\) −1360.54 + 365.271i −0.0860402 + 0.0230996i
\(631\) −27234.6 −1.71821 −0.859106 0.511798i \(-0.828980\pi\)
−0.859106 + 0.511798i \(0.828980\pi\)
\(632\) 876.931i 0.0551937i
\(633\) 17298.9i 1.08621i
\(634\) −19078.1 −1.19509
\(635\) −23.6532 88.1023i −0.00147819 0.00550588i
\(636\) −3438.05 −0.214351
\(637\) 529.600i 0.0329412i
\(638\) 5.49387i 0.000340916i
\(639\) 5022.90 0.310959
\(640\) 371.069 + 1382.14i 0.0229184 + 0.0853654i
\(641\) −18064.7 −1.11313 −0.556563 0.830806i \(-0.687880\pi\)
−0.556563 + 0.830806i \(0.687880\pi\)
\(642\) 7208.36i 0.443133i
\(643\) 2169.88i 0.133082i 0.997784 + 0.0665409i \(0.0211963\pi\)
−0.997784 + 0.0665409i \(0.978804\pi\)
\(644\) −2670.46 −0.163402
\(645\) 11627.1 3121.58i 0.709792 0.190561i
\(646\) −1540.69 −0.0938351
\(647\) 10954.9i 0.665657i −0.942987 0.332829i \(-0.891997\pi\)
0.942987 0.332829i \(-0.108003\pi\)
\(648\) 648.000i 0.0392837i
\(649\) 10048.3 0.607752
\(650\) −2338.71 + 1353.31i −0.141126 + 0.0816636i
\(651\) 3477.51 0.209362
\(652\) 2964.92i 0.178091i
\(653\) 23846.3i 1.42906i 0.699603 + 0.714532i \(0.253360\pi\)
−0.699603 + 0.714532i \(0.746640\pi\)
\(654\) −5506.31 −0.329226
\(655\) −9467.74 + 2541.85i −0.564787 + 0.151631i
\(656\) 198.139 0.0117927
\(657\) 259.457i 0.0154070i
\(658\) 6307.91i 0.373721i
\(659\) −29345.7 −1.73467 −0.867334 0.497726i \(-0.834168\pi\)
−0.867334 + 0.497726i \(0.834168\pi\)
\(660\) −472.971 1761.70i −0.0278945 0.103900i
\(661\) 19909.3 1.17153 0.585764 0.810482i \(-0.300794\pi\)
0.585764 + 0.810482i \(0.300794\pi\)
\(662\) 904.718i 0.0531161i
\(663\) 3203.14i 0.187632i
\(664\) 10102.0 0.590411
\(665\) 158.243 + 589.414i 0.00922766 + 0.0343707i
\(666\) −197.449 −0.0114880
\(667\) 19.2694i 0.00111861i
\(668\) 209.037i 0.0121076i
\(669\) −3582.89 −0.207059
\(670\) −1681.88 + 451.543i −0.0969802 + 0.0260367i
\(671\) 5543.28 0.318921
\(672\) 672.000i 0.0385758i
\(673\) 14940.2i 0.855722i 0.903845 + 0.427861i \(0.140733\pi\)
−0.903845 + 0.427861i \(0.859267\pi\)
\(674\) 11275.2 0.644370
\(675\) −1690.37 2921.18i −0.0963884 0.166572i
\(676\) −8320.73 −0.473415
\(677\) 22193.1i 1.25989i 0.776638 + 0.629947i \(0.216924\pi\)
−0.776638 + 0.629947i \(0.783076\pi\)
\(678\) 4648.96i 0.263337i
\(679\) 2926.57 0.165407
\(680\) 8533.65 2291.07i 0.481251 0.129204i
\(681\) 9304.35 0.523559
\(682\) 4502.86i 0.252820i
\(683\) 31363.3i 1.75708i −0.477670 0.878539i \(-0.658518\pi\)
0.477670 0.878539i \(-0.341482\pi\)
\(684\) −280.727 −0.0156928
\(685\) 3123.74 + 11635.2i 0.174237 + 0.648987i
\(686\) 686.000 0.0381802
\(687\) 6483.01i 0.360032i
\(688\) 5742.86i 0.318233i
\(689\) 3096.58 0.171220
\(690\) −1658.91 6179.03i −0.0915272 0.340916i
\(691\) 3043.95 0.167579 0.0837897 0.996483i \(-0.473298\pi\)
0.0837897 + 0.996483i \(0.473298\pi\)
\(692\) 621.510i 0.0341420i
\(693\) 856.543i 0.0469515i
\(694\) −24626.1 −1.34697
\(695\) −16798.6 + 4509.99i −0.916843 + 0.246149i
\(696\) −4.84898 −0.000264081
\(697\) 1223.36i 0.0664819i
\(698\) 14407.1i 0.781256i
\(699\) −9372.85 −0.507173
\(700\) −1752.97 3029.37i −0.0946516 0.163571i
\(701\) 24625.6 1.32681 0.663405 0.748260i \(-0.269110\pi\)
0.663405 + 0.748260i \(0.269110\pi\)
\(702\) 583.641i 0.0313791i
\(703\) 85.5388i 0.00458913i
\(704\) 870.139 0.0465832
\(705\) −14595.6 + 3918.54i −0.779717 + 0.209334i
\(706\) 14061.2 0.749573
\(707\) 11335.6i 0.602997i
\(708\) 8868.83i 0.470778i
\(709\) 29005.6 1.53643 0.768215 0.640192i \(-0.221145\pi\)
0.768215 + 0.640192i \(0.221145\pi\)
\(710\) 3235.84 + 12052.7i 0.171041 + 0.637083i
\(711\) 986.547 0.0520371
\(712\) 11127.7i 0.585716i
\(713\) 15793.5i 0.829551i
\(714\) −4149.09 −0.217473
\(715\) 425.996 + 1586.73i 0.0222816 + 0.0829933i
\(716\) −9768.29 −0.509858
\(717\) 4898.68i 0.255153i
\(718\) 11998.1i 0.623630i
\(719\) −2287.47 −0.118648 −0.0593242 0.998239i \(-0.518895\pi\)
−0.0593242 + 0.998239i \(0.518895\pi\)
\(720\) 1554.91 417.453i 0.0804832 0.0216077i
\(721\) −10291.5 −0.531591
\(722\) 13596.4i 0.700838i
\(723\) 14843.4i 0.763531i
\(724\) 4613.97 0.236846
\(725\) −21.8592 + 12.6490i −0.00111977 + 0.000647962i
\(726\) 6876.91 0.351551
\(727\) 36915.8i 1.88326i −0.336645 0.941632i \(-0.609292\pi\)
0.336645 0.941632i \(-0.390708\pi\)
\(728\) 605.257i 0.0308136i
\(729\) −729.000 −0.0370370
\(730\) 622.580 167.147i 0.0315653 0.00847450i
\(731\) 35457.7 1.79405
\(732\) 4892.60i 0.247043i
\(733\) 7943.12i 0.400254i 0.979770 + 0.200127i \(0.0641354\pi\)
−0.979770 + 0.200127i \(0.935865\pi\)
\(734\) −18078.0 −0.909091
\(735\) 426.150 + 1587.30i 0.0213861 + 0.0796577i
\(736\) 3051.95 0.152848
\(737\) 1058.84i 0.0529214i
\(738\) 222.906i 0.0111183i
\(739\) 3388.38 0.168665 0.0843327 0.996438i \(-0.473124\pi\)
0.0843327 + 0.996438i \(0.473124\pi\)
\(740\) −127.200 473.788i −0.00631888 0.0235362i
\(741\) 252.845 0.0125351
\(742\) 4011.06i 0.198451i
\(743\) 26530.0i 1.30995i −0.755652 0.654973i \(-0.772680\pi\)
0.755652 0.654973i \(-0.227320\pi\)
\(744\) −3974.30 −0.195840
\(745\) 19511.8 5238.43i 0.959540 0.257612i
\(746\) 24830.9 1.21866
\(747\) 11364.7i 0.556645i
\(748\) 5372.44i 0.262615i
\(749\) 8409.76 0.410261
\(750\) 5920.54 5937.99i 0.288250 0.289099i
\(751\) 11544.9 0.560956 0.280478 0.959860i \(-0.409507\pi\)
0.280478 + 0.959860i \(0.409507\pi\)
\(752\) 7209.04i 0.349584i
\(753\) 20931.1i 1.01298i
\(754\) 4.36739 0.000210943
\(755\) −10253.9 + 2752.91i −0.494274 + 0.132700i
\(756\) −756.000 −0.0363696
\(757\) 38521.4i 1.84952i −0.380555 0.924758i \(-0.624267\pi\)
0.380555 0.924758i \(-0.375733\pi\)
\(758\) 14678.8i 0.703374i
\(759\) −3890.07 −0.186035
\(760\) −180.849 673.616i −0.00863169 0.0321508i
\(761\) 23725.7 1.13017 0.565083 0.825034i \(-0.308844\pi\)
0.565083 + 0.825034i \(0.308844\pi\)
\(762\) 48.9550i 0.00232736i
\(763\) 6424.03i 0.304804i
\(764\) −19315.4 −0.914668
\(765\) −2577.45 9600.36i −0.121814 0.453728i
\(766\) 16108.5 0.759824
\(767\) 7987.98i 0.376049i
\(768\) 768.000i 0.0360844i
\(769\) 39110.5 1.83402 0.917009 0.398866i \(-0.130596\pi\)
0.917009 + 0.398866i \(0.130596\pi\)
\(770\) −2055.31 + 551.800i −0.0961927 + 0.0258253i
\(771\) 9493.09 0.443431
\(772\) 2109.75i 0.0983568i
\(773\) 35966.5i 1.67351i −0.547577 0.836755i \(-0.684450\pi\)
0.547577 0.836755i \(-0.315550\pi\)
\(774\) 6460.71 0.300033
\(775\) −17916.1 + 10367.3i −0.830408 + 0.480523i
\(776\) −3344.65 −0.154724
\(777\) 230.357i 0.0106358i
\(778\) 8810.97i 0.406026i
\(779\) −96.5674 −0.00444144
\(780\) −1400.47 + 375.992i −0.0642884 + 0.0172598i
\(781\) 7587.88 0.347651
\(782\) 18843.5i 0.861689i
\(783\) 5.45511i 0.000248978i
\(784\) −784.000 −0.0357143
\(785\) 8750.63 + 32593.9i 0.397864 + 1.48194i
\(786\) −5260.85 −0.238738
\(787\) 13194.2i 0.597614i 0.954313 + 0.298807i \(0.0965888\pi\)
−0.954313 + 0.298807i \(0.903411\pi\)
\(788\) 10109.9i 0.457044i
\(789\) 1490.61 0.0672589
\(790\) 635.551 + 2367.27i 0.0286226 + 0.106612i
\(791\) −5423.79 −0.243802
\(792\) 978.906i 0.0439191i
\(793\) 4406.66i 0.197333i
\(794\) 21901.2 0.978896
\(795\) −9280.98 + 2491.71i −0.414041 + 0.111159i
\(796\) 20549.2 0.915010
\(797\) 10384.7i 0.461537i 0.973009 + 0.230769i \(0.0741240\pi\)
−0.973009 + 0.230769i \(0.925876\pi\)
\(798\) 327.514i 0.0145287i
\(799\) −44510.3 −1.97079
\(800\) 2003.40 + 3462.14i 0.0885384 + 0.153006i
\(801\) 12518.7 0.552218
\(802\) 15885.2i 0.699408i
\(803\) 391.951i 0.0172250i
\(804\) −934.555 −0.0409941
\(805\) −7208.87 + 1935.40i −0.315627 + 0.0847378i
\(806\) 3579.58 0.156433
\(807\) 11691.6i 0.509991i
\(808\) 12955.0i 0.564052i
\(809\) −1318.94 −0.0573196 −0.0286598 0.999589i \(-0.509124\pi\)
−0.0286598 + 0.999589i \(0.509124\pi\)
\(810\) −469.635 1749.27i −0.0203720 0.0758803i
\(811\) −23639.6 −1.02355 −0.511774 0.859120i \(-0.671012\pi\)
−0.511774 + 0.859120i \(0.671012\pi\)
\(812\) 5.65715i 0.000244491i
\(813\) 21928.9i 0.945977i
\(814\) −298.278 −0.0128435
\(815\) 2148.81 + 8003.78i 0.0923554 + 0.344000i
\(816\) 4741.81 0.203427
\(817\) 2798.91i 0.119855i
\(818\) 14188.0i 0.606446i
\(819\) 680.914 0.0290514
\(820\) 534.874 143.600i 0.0227788 0.00611553i
\(821\) −23351.9 −0.992677 −0.496338 0.868129i \(-0.665322\pi\)
−0.496338 + 0.868129i \(0.665322\pi\)
\(822\) 6465.20i 0.274330i
\(823\) 5675.84i 0.240398i −0.992750 0.120199i \(-0.961647\pi\)
0.992750 0.120199i \(-0.0383533\pi\)
\(824\) 11761.8 0.497258
\(825\) −2553.56 4412.90i −0.107762 0.186227i
\(826\) 10347.0 0.435856
\(827\) 8698.65i 0.365758i −0.983135 0.182879i \(-0.941458\pi\)
0.983135 0.182879i \(-0.0585416\pi\)
\(828\) 3433.44i 0.144107i
\(829\) −19561.7 −0.819551 −0.409775 0.912186i \(-0.634393\pi\)
−0.409775 + 0.912186i \(0.634393\pi\)
\(830\) 27270.2 7321.35i 1.14044 0.306178i
\(831\) −25053.7 −1.04585
\(832\) 691.723i 0.0288235i
\(833\) 4840.60i 0.201341i
\(834\) −9334.30 −0.387554
\(835\) −151.498 564.292i −0.00627882 0.0233870i
\(836\) −424.082 −0.0175445
\(837\) 4471.09i 0.184640i
\(838\) 4982.00i 0.205370i
\(839\) 32967.7 1.35658 0.678290 0.734794i \(-0.262721\pi\)
0.678290 + 0.734794i \(0.262721\pi\)
\(840\) −487.029 1814.06i −0.0200049 0.0745130i
\(841\) −24389.0 −0.999998
\(842\) 3135.01i 0.128313i
\(843\) 11450.7i 0.467834i
\(844\) −23065.2 −0.940683
\(845\) −22461.7 + 6030.41i −0.914446 + 0.245506i
\(846\) −8110.18 −0.329591
\(847\) 8023.06i 0.325473i
\(848\) 4584.07i 0.185634i
\(849\) −11050.8 −0.446715
\(850\) 21376.1 12369.4i 0.862580 0.499139i
\(851\) −1046.19 −0.0421420
\(852\) 6697.20i 0.269298i
\(853\) 22005.6i 0.883302i −0.897187 0.441651i \(-0.854393\pi\)
0.897187 0.441651i \(-0.145607\pi\)
\(854\) 5708.03 0.228717
\(855\) −757.818 + 203.455i −0.0303121 + 0.00813803i
\(856\) −9611.15 −0.383764
\(857\) 8008.58i 0.319216i −0.987181 0.159608i \(-0.948977\pi\)
0.987181 0.159608i \(-0.0510229\pi\)
\(858\) 881.681i 0.0350817i
\(859\) 21100.9 0.838130 0.419065 0.907956i \(-0.362358\pi\)
0.419065 + 0.907956i \(0.362358\pi\)
\(860\) 4162.11 + 15502.8i 0.165031 + 0.614698i
\(861\) −260.057 −0.0102935
\(862\) 1431.69i 0.0565701i
\(863\) 30473.1i 1.20199i 0.799253 + 0.600994i \(0.205229\pi\)
−0.799253 + 0.600994i \(0.794771\pi\)
\(864\) 864.000 0.0340207
\(865\) −450.436 1677.76i −0.0177055 0.0659486i
\(866\) 7167.44 0.281246
\(867\) 14538.1i 0.569479i
\(868\) 4636.69i 0.181313i
\(869\) 1490.33 0.0581774
\(870\) −13.0898 + 3.51428i −0.000510098 + 0.000136948i
\(871\) 841.735 0.0327453
\(872\) 7341.75i 0.285118i
\(873\) 3762.73i 0.145875i
\(874\) −1487.44 −0.0575667
\(875\) −6927.65 6907.30i −0.267654 0.266868i
\(876\) 345.943 0.0133428
\(877\) 19268.9i 0.741921i −0.928649 0.370961i \(-0.879028\pi\)
0.928649 0.370961i \(-0.120972\pi\)
\(878\) 20580.7i 0.791077i
\(879\) −25352.4 −0.972826
\(880\) 2348.93 630.629i 0.0899800 0.0241574i
\(881\) −25810.9 −0.987049 −0.493525 0.869732i \(-0.664292\pi\)
−0.493525 + 0.869732i \(0.664292\pi\)
\(882\) 882.000i 0.0336718i
\(883\) 2908.02i 0.110830i 0.998463 + 0.0554149i \(0.0176482\pi\)
−0.998463 + 0.0554149i \(0.982352\pi\)
\(884\) −4270.86 −0.162494
\(885\) 6427.64 + 23941.3i 0.244139 + 0.909355i
\(886\) 7432.80 0.281839
\(887\) 50742.2i 1.92081i −0.278615 0.960403i \(-0.589875\pi\)
0.278615 0.960403i \(-0.410125\pi\)
\(888\) 263.265i 0.00994888i
\(889\) −57.1141 −0.00215472
\(890\) 8064.77 + 30039.2i 0.303744 + 1.13137i
\(891\) −1101.27 −0.0414073
\(892\) 4777.19i 0.179319i
\(893\) 3513.49i 0.131662i
\(894\) 10841.9 0.405603
\(895\) −26369.4 + 7079.52i −0.984840 + 0.264405i
\(896\) 896.000 0.0334077
\(897\) 3092.44i 0.115110i
\(898\) 21217.3i 0.788453i
\(899\) 33.4572 0.00124122
\(900\) 3894.91 2253.82i 0.144256 0.0834748i
\(901\) −28303.1 −1.04652
\(902\) 336.735i 0.0124302i
\(903\) 7537.50i 0.277777i
\(904\) 6198.61 0.228056
\(905\) 12455.4 3343.95i 0.457492 0.122825i
\(906\) −5697.67 −0.208932
\(907\) 14210.5i 0.520235i 0.965577 + 0.260117i \(0.0837612\pi\)
−0.965577 + 0.260117i \(0.916239\pi\)
\(908\) 12405.8i 0.453415i
\(909\) 14574.3 0.531794
\(910\) 438.657 + 1633.89i 0.0159795 + 0.0595195i
\(911\) 14523.3 0.528188 0.264094 0.964497i \(-0.414927\pi\)
0.264094 + 0.964497i \(0.414927\pi\)
\(912\) 374.302i 0.0135903i
\(913\) 17168.2i 0.622327i
\(914\) 16482.4 0.596489
\(915\) 3545.88 + 13207.5i 0.128113 + 0.477188i
\(916\) 8644.01 0.311797
\(917\) 6137.66i 0.221029i
\(918\) 5334.54i 0.191793i
\(919\) −24513.7 −0.879905 −0.439953 0.898021i \(-0.645005\pi\)
−0.439953 + 0.898021i \(0.645005\pi\)
\(920\) 8238.71 2211.89i 0.295242 0.0792649i
\(921\) −9971.38 −0.356751
\(922\) 30505.0i 1.08962i
\(923\) 6032.04i 0.215110i
\(924\) −1142.06 −0.0406612
\(925\) −686.751 1186.80i −0.0244111 0.0421856i
\(926\) 7083.04 0.251364
\(927\) 13232.0i 0.468819i
\(928\) 6.46531i 0.000228701i
\(929\) 27502.6 0.971291 0.485646 0.874156i \(-0.338585\pi\)
0.485646 + 0.874156i \(0.338585\pi\)
\(930\) −10728.6 + 2880.36i −0.378284 + 0.101560i
\(931\) 382.100 0.0134509
\(932\) 12497.1i 0.439225i
\(933\) 5281.82i 0.185337i
\(934\) −8440.91 −0.295712
\(935\) −3893.65 14502.8i −0.136188 0.507266i
\(936\) −778.188 −0.0271751
\(937\) 52359.0i 1.82550i −0.408520 0.912749i \(-0.633955\pi\)
0.408520 0.912749i \(-0.366045\pi\)
\(938\) 1090.31i 0.0379531i
\(939\) 5153.73 0.179111
\(940\) −5224.72 19460.7i −0.181289 0.675255i
\(941\) −873.156 −0.0302487 −0.0151244 0.999886i \(-0.504814\pi\)
−0.0151244 + 0.999886i \(0.504814\pi\)
\(942\) 18111.1i 0.626425i
\(943\) 1181.07i 0.0407858i
\(944\) −11825.1 −0.407706
\(945\) −2040.81 + 547.907i −0.0702515 + 0.0188608i
\(946\) 9759.93 0.335436
\(947\) 25333.0i 0.869283i 0.900604 + 0.434641i \(0.143125\pi\)
−0.900604 + 0.434641i \(0.856875\pi\)
\(948\) 1315.40i 0.0450655i
\(949\) −311.584 −0.0106580
\(950\) −976.400 1687.35i −0.0333459 0.0576262i
\(951\) −28617.2 −0.975790
\(952\) 5532.11i 0.188337i
\(953\) 28335.5i 0.963145i 0.876406 + 0.481573i \(0.159934\pi\)
−0.876406 + 0.481573i \(0.840066\pi\)
\(954\) −5157.07 −0.175017
\(955\) −52141.7 + 13998.7i −1.76677 + 0.474333i
\(956\) 6531.57 0.220969
\(957\) 8.24080i 0.000278357i
\(958\) 13371.4i 0.450950i
\(959\) 7542.73 0.253981
\(960\) 556.604 + 2073.21i 0.0187128 + 0.0697005i
\(961\) −2368.99 −0.0795204
\(962\) 237.118i 0.00794697i
\(963\) 10812.5i 0.361817i
\(964\) 19791.2 0.661237
\(965\) 1529.03 + 5695.24i 0.0510064 + 0.189986i
\(966\) −4005.69 −0.133417
\(967\) 12644.3i 0.420490i −0.977649 0.210245i \(-0.932574\pi\)
0.977649 0.210245i \(-0.0674262\pi\)
\(968\) 9169.21i 0.304452i
\(969\) −2311.03 −0.0766160
\(970\) −9028.86 + 2424.02i −0.298865 + 0.0802377i
\(971\) 41862.8 1.38357 0.691783 0.722106i \(-0.256826\pi\)
0.691783 + 0.722106i \(0.256826\pi\)
\(972\) 972.000i 0.0320750i
\(973\) 10890.0i 0.358806i
\(974\) −11842.2 −0.389578
\(975\) −3508.07 + 2029.97i −0.115229 + 0.0666781i
\(976\) −6523.46 −0.213946
\(977\) 12362.4i 0.404818i 0.979301 + 0.202409i \(0.0648770\pi\)
−0.979301 + 0.202409i \(0.935123\pi\)
\(978\) 4447.38i 0.145411i
\(979\) 18911.5 0.617378
\(980\) −2116.40 + 568.200i −0.0689856 + 0.0185209i
\(981\) −8259.47 −0.268812
\(982\) 3251.33i 0.105656i
\(983\) 25887.9i 0.839976i 0.907530 + 0.419988i \(0.137966\pi\)
−0.907530 + 0.419988i \(0.862034\pi\)
\(984\) 297.208 0.00962871
\(985\) 7327.10 + 27291.6i 0.237016 + 0.882824i
\(986\) −39.9184 −0.00128931
\(987\) 9461.87i 0.305142i
\(988\) 337.126i 0.0108557i
\(989\) 34232.3 1.10063
\(990\) −709.457 2642.55i −0.0227758 0.0848340i
\(991\) 9414.31 0.301771 0.150886 0.988551i \(-0.451787\pi\)
0.150886 + 0.988551i \(0.451787\pi\)
\(992\) 5299.07i 0.169602i
\(993\) 1357.08i 0.0433691i
\(994\) 7813.40 0.249322
\(995\) 55472.4 14892.9i 1.76743 0.474511i
\(996\) 15153.0 0.482068
\(997\) 12125.8i 0.385183i 0.981279 + 0.192592i \(0.0616892\pi\)
−0.981279 + 0.192592i \(0.938311\pi\)
\(998\) 40526.6i 1.28542i
\(999\) −296.173 −0.00937989
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.169.3 yes 4
3.2 odd 2 630.4.g.e.379.2 4
5.2 odd 4 1050.4.a.bc.1.1 2
5.3 odd 4 1050.4.a.bg.1.1 2
5.4 even 2 inner 210.4.g.a.169.1 4
15.14 odd 2 630.4.g.e.379.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.4.g.a.169.1 4 5.4 even 2 inner
210.4.g.a.169.3 yes 4 1.1 even 1 trivial
630.4.g.e.379.2 4 3.2 odd 2
630.4.g.e.379.4 4 15.14 odd 2
1050.4.a.bc.1.1 2 5.2 odd 4
1050.4.a.bg.1.1 2 5.3 odd 4