Properties

Label 189.4.s.a.17.13
Level $189$
Weight $4$
Character 189.17
Analytic conductor $11.151$
Analytic rank $0$
Dimension $44$
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] = [189,4,Mod(17,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.17");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 189.s (of order \(6\), degree \(2\), not 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: \(11.1513609911\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.13
Character \(\chi\) \(=\) 189.17
Dual form 189.4.s.a.89.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.998155 + 0.576285i) q^{2} +(-3.33579 - 5.77776i) q^{4} -0.274718 q^{5} +(-9.15344 + 16.1001i) q^{7} -16.9100i q^{8} +O(q^{10})\) \(q+(0.998155 + 0.576285i) q^{2} +(-3.33579 - 5.77776i) q^{4} -0.274718 q^{5} +(-9.15344 + 16.1001i) q^{7} -16.9100i q^{8} +(-0.274212 - 0.158316i) q^{10} +26.2387i q^{11} +(-39.6128 - 22.8704i) q^{13} +(-18.4148 + 10.7954i) q^{14} +(-16.9413 + 29.3432i) q^{16} +(-30.2340 + 52.3669i) q^{17} +(-38.8827 + 22.4489i) q^{19} +(0.916403 + 1.58726i) q^{20} +(-15.1209 + 26.1902i) q^{22} +127.767i q^{23} -124.925 q^{25} +(-26.3598 - 45.6565i) q^{26} +(123.557 - 0.820329i) q^{28} +(-58.2779 + 33.6468i) q^{29} +(85.6986 - 49.4781i) q^{31} +(-150.976 + 87.1662i) q^{32} +(-60.3565 + 34.8469i) q^{34} +(2.51462 - 4.42301i) q^{35} +(-123.714 - 214.278i) q^{37} -51.7480 q^{38} +4.64550i q^{40} +(-134.234 + 232.500i) q^{41} +(-72.4990 - 125.572i) q^{43} +(151.601 - 87.5267i) q^{44} +(-73.6304 + 127.532i) q^{46} +(250.874 - 434.526i) q^{47} +(-175.429 - 294.743i) q^{49} +(-124.694 - 71.9922i) q^{50} +305.164i q^{52} +(333.839 + 192.742i) q^{53} -7.20824i q^{55} +(272.254 + 154.785i) q^{56} -77.5605 q^{58} +(-274.307 - 475.113i) q^{59} +(189.637 + 109.487i) q^{61} +114.054 q^{62} +70.1309 q^{64} +(10.8824 + 6.28293i) q^{65} +(378.858 + 656.202i) q^{67} +403.418 q^{68} +(5.05889 - 2.96571i) q^{70} +1109.53i q^{71} +(-125.762 - 72.6086i) q^{73} -285.177i q^{74} +(259.409 + 149.770i) q^{76} +(-422.446 - 240.174i) q^{77} +(445.950 - 772.407i) q^{79} +(4.65409 - 8.06113i) q^{80} +(-267.972 + 154.714i) q^{82} +(-745.760 - 1291.69i) q^{83} +(8.30585 - 14.3862i) q^{85} -167.120i q^{86} +443.696 q^{88} +(145.205 + 251.503i) q^{89} +(730.810 - 428.428i) q^{91} +(738.209 - 426.205i) q^{92} +(500.822 - 289.150i) q^{94} +(10.6818 - 6.16714i) q^{95} +(144.917 - 83.6676i) q^{97} +(-5.24921 - 395.297i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} - 6 q^{10} + 36 q^{13} - 129 q^{14} - 263 q^{16} - 72 q^{17} - 6 q^{19} + 24 q^{20} + 14 q^{22} + 698 q^{25} - 96 q^{26} - 156 q^{28} + 132 q^{29} + 177 q^{31} + 501 q^{32} - 24 q^{34} + 765 q^{35} + 82 q^{37} + 1746 q^{38} + 618 q^{41} + 82 q^{43} + 603 q^{44} + 266 q^{46} + 201 q^{47} + 515 q^{49} + 1845 q^{50} + 564 q^{53} - 3600 q^{56} - 538 q^{58} - 747 q^{59} - 1209 q^{61} - 2904 q^{62} - 1144 q^{64} + 831 q^{65} + 295 q^{67} - 7008 q^{68} - 390 q^{70} - 6 q^{73} + 144 q^{76} + 1203 q^{77} - 551 q^{79} - 4239 q^{80} + 18 q^{82} + 1830 q^{83} - 237 q^{85} + 1246 q^{88} + 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 3 q^{94} + 1053 q^{95} + 792 q^{97} + 5667 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.998155 + 0.576285i 0.352901 + 0.203748i 0.665962 0.745985i \(-0.268021\pi\)
−0.313061 + 0.949733i \(0.601354\pi\)
\(3\) 0 0
\(4\) −3.33579 5.77776i −0.416974 0.722220i
\(5\) −0.274718 −0.0245716 −0.0122858 0.999925i \(-0.503911\pi\)
−0.0122858 + 0.999925i \(0.503911\pi\)
\(6\) 0 0
\(7\) −9.15344 + 16.1001i −0.494239 + 0.869326i
\(8\) 16.9100i 0.747325i
\(9\) 0 0
\(10\) −0.274212 0.158316i −0.00867133 0.00500640i
\(11\) 26.2387i 0.719205i 0.933106 + 0.359602i \(0.117088\pi\)
−0.933106 + 0.359602i \(0.882912\pi\)
\(12\) 0 0
\(13\) −39.6128 22.8704i −0.845123 0.487932i 0.0138792 0.999904i \(-0.495582\pi\)
−0.859002 + 0.511972i \(0.828915\pi\)
\(14\) −18.4148 + 10.7954i −0.351541 + 0.206086i
\(15\) 0 0
\(16\) −16.9413 + 29.3432i −0.264708 + 0.458488i
\(17\) −30.2340 + 52.3669i −0.431343 + 0.747108i −0.996989 0.0775399i \(-0.975293\pi\)
0.565646 + 0.824648i \(0.308627\pi\)
\(18\) 0 0
\(19\) −38.8827 + 22.4489i −0.469490 + 0.271060i −0.716026 0.698074i \(-0.754041\pi\)
0.246536 + 0.969134i \(0.420708\pi\)
\(20\) 0.916403 + 1.58726i 0.0102457 + 0.0177461i
\(21\) 0 0
\(22\) −15.1209 + 26.1902i −0.146536 + 0.253808i
\(23\) 127.767i 1.15832i 0.815214 + 0.579159i \(0.196619\pi\)
−0.815214 + 0.579159i \(0.803381\pi\)
\(24\) 0 0
\(25\) −124.925 −0.999396
\(26\) −26.3598 45.6565i −0.198830 0.344384i
\(27\) 0 0
\(28\) 123.557 0.820329i 0.833929 0.00553670i
\(29\) −58.2779 + 33.6468i −0.373170 + 0.215450i −0.674843 0.737962i \(-0.735788\pi\)
0.301672 + 0.953412i \(0.402455\pi\)
\(30\) 0 0
\(31\) 85.6986 49.4781i 0.496513 0.286662i −0.230759 0.973011i \(-0.574121\pi\)
0.727273 + 0.686349i \(0.240788\pi\)
\(32\) −150.976 + 87.1662i −0.834034 + 0.481530i
\(33\) 0 0
\(34\) −60.3565 + 34.8469i −0.304443 + 0.175770i
\(35\) 2.51462 4.42301i 0.0121442 0.0213607i
\(36\) 0 0
\(37\) −123.714 214.278i −0.549686 0.952085i −0.998296 0.0583567i \(-0.981414\pi\)
0.448610 0.893728i \(-0.351919\pi\)
\(38\) −51.7480 −0.220911
\(39\) 0 0
\(40\) 4.64550i 0.0183629i
\(41\) −134.234 + 232.500i −0.511312 + 0.885618i 0.488602 + 0.872507i \(0.337507\pi\)
−0.999914 + 0.0131112i \(0.995826\pi\)
\(42\) 0 0
\(43\) −72.4990 125.572i −0.257116 0.445338i 0.708352 0.705859i \(-0.249439\pi\)
−0.965468 + 0.260521i \(0.916106\pi\)
\(44\) 151.601 87.5267i 0.519424 0.299890i
\(45\) 0 0
\(46\) −73.6304 + 127.532i −0.236005 + 0.408772i
\(47\) 250.874 434.526i 0.778589 1.34856i −0.154166 0.988045i \(-0.549269\pi\)
0.932755 0.360511i \(-0.117398\pi\)
\(48\) 0 0
\(49\) −175.429 294.743i −0.511455 0.859310i
\(50\) −124.694 71.9922i −0.352688 0.203625i
\(51\) 0 0
\(52\) 305.164i 0.813820i
\(53\) 333.839 + 192.742i 0.865213 + 0.499531i 0.865755 0.500469i \(-0.166839\pi\)
−0.000541270 1.00000i \(0.500172\pi\)
\(54\) 0 0
\(55\) 7.20824i 0.0176720i
\(56\) 272.254 + 154.785i 0.649669 + 0.369357i
\(57\) 0 0
\(58\) −77.5605 −0.175590
\(59\) −274.307 475.113i −0.605283 1.04838i −0.992007 0.126185i \(-0.959727\pi\)
0.386724 0.922195i \(-0.373607\pi\)
\(60\) 0 0
\(61\) 189.637 + 109.487i 0.398041 + 0.229809i 0.685638 0.727942i \(-0.259523\pi\)
−0.287597 + 0.957751i \(0.592857\pi\)
\(62\) 114.054 0.233627
\(63\) 0 0
\(64\) 70.1309 0.136974
\(65\) 10.8824 + 6.28293i 0.0207660 + 0.0119893i
\(66\) 0 0
\(67\) 378.858 + 656.202i 0.690819 + 1.19653i 0.971570 + 0.236753i \(0.0760834\pi\)
−0.280750 + 0.959781i \(0.590583\pi\)
\(68\) 403.418 0.719435
\(69\) 0 0
\(70\) 5.05889 2.96571i 0.00863790 0.00506386i
\(71\) 1109.53i 1.85461i 0.374306 + 0.927305i \(0.377881\pi\)
−0.374306 + 0.927305i \(0.622119\pi\)
\(72\) 0 0
\(73\) −125.762 72.6086i −0.201634 0.116414i 0.395783 0.918344i \(-0.370473\pi\)
−0.597418 + 0.801930i \(0.703806\pi\)
\(74\) 285.177i 0.447989i
\(75\) 0 0
\(76\) 259.409 + 149.770i 0.391530 + 0.226050i
\(77\) −422.446 240.174i −0.625223 0.355459i
\(78\) 0 0
\(79\) 445.950 772.407i 0.635104 1.10003i −0.351389 0.936230i \(-0.614290\pi\)
0.986493 0.163803i \(-0.0523763\pi\)
\(80\) 4.65409 8.06113i 0.00650429 0.0112658i
\(81\) 0 0
\(82\) −267.972 + 154.714i −0.360885 + 0.208357i
\(83\) −745.760 1291.69i −0.986238 1.70821i −0.636299 0.771442i \(-0.719536\pi\)
−0.349939 0.936772i \(-0.613798\pi\)
\(84\) 0 0
\(85\) 8.30585 14.3862i 0.0105988 0.0183576i
\(86\) 167.120i 0.209547i
\(87\) 0 0
\(88\) 443.696 0.537480
\(89\) 145.205 + 251.503i 0.172941 + 0.299542i 0.939447 0.342695i \(-0.111340\pi\)
−0.766506 + 0.642237i \(0.778006\pi\)
\(90\) 0 0
\(91\) 730.810 428.428i 0.841865 0.493532i
\(92\) 738.209 426.205i 0.836561 0.482989i
\(93\) 0 0
\(94\) 500.822 289.150i 0.549530 0.317271i
\(95\) 10.6818 6.16714i 0.0115361 0.00666037i
\(96\) 0 0
\(97\) 144.917 83.6676i 0.151691 0.0875789i −0.422233 0.906487i \(-0.638754\pi\)
0.573924 + 0.818908i \(0.305420\pi\)
\(98\) −5.24921 395.297i −0.00541072 0.407459i
\(99\) 0 0
\(100\) 416.722 + 721.784i 0.416722 + 0.721784i
\(101\) −945.019 −0.931019 −0.465510 0.885043i \(-0.654129\pi\)
−0.465510 + 0.885043i \(0.654129\pi\)
\(102\) 0 0
\(103\) 836.645i 0.800360i 0.916437 + 0.400180i \(0.131052\pi\)
−0.916437 + 0.400180i \(0.868948\pi\)
\(104\) −386.740 + 669.853i −0.364644 + 0.631582i
\(105\) 0 0
\(106\) 222.149 + 384.773i 0.203557 + 0.352570i
\(107\) 1220.83 704.848i 1.10301 0.636825i 0.166002 0.986125i \(-0.446914\pi\)
0.937011 + 0.349301i \(0.113581\pi\)
\(108\) 0 0
\(109\) 7.79612 13.5033i 0.00685076 0.0118659i −0.862580 0.505921i \(-0.831153\pi\)
0.869430 + 0.494055i \(0.164486\pi\)
\(110\) 4.15400 7.19494i 0.00360062 0.00623646i
\(111\) 0 0
\(112\) −317.359 541.349i −0.267746 0.456721i
\(113\) 382.754 + 220.983i 0.318641 + 0.183968i 0.650787 0.759261i \(-0.274439\pi\)
−0.332146 + 0.943228i \(0.607773\pi\)
\(114\) 0 0
\(115\) 35.1000i 0.0284617i
\(116\) 388.806 + 224.477i 0.311204 + 0.179674i
\(117\) 0 0
\(118\) 632.315i 0.493299i
\(119\) −566.369 966.110i −0.436294 0.744228i
\(120\) 0 0
\(121\) 642.533 0.482745
\(122\) 126.191 + 218.570i 0.0936461 + 0.162200i
\(123\) 0 0
\(124\) −571.745 330.097i −0.414066 0.239061i
\(125\) 68.6589 0.0491283
\(126\) 0 0
\(127\) −2019.56 −1.41108 −0.705539 0.708671i \(-0.749295\pi\)
−0.705539 + 0.708671i \(0.749295\pi\)
\(128\) 1277.81 + 737.745i 0.882372 + 0.509438i
\(129\) 0 0
\(130\) 7.24152 + 12.5427i 0.00488556 + 0.00846204i
\(131\) −954.174 −0.636386 −0.318193 0.948026i \(-0.603076\pi\)
−0.318193 + 0.948026i \(0.603076\pi\)
\(132\) 0 0
\(133\) −5.52058 831.502i −0.00359921 0.542108i
\(134\) 873.322i 0.563011i
\(135\) 0 0
\(136\) 885.526 + 511.259i 0.558333 + 0.322353i
\(137\) 1382.02i 0.861857i 0.902386 + 0.430928i \(0.141814\pi\)
−0.902386 + 0.430928i \(0.858186\pi\)
\(138\) 0 0
\(139\) −2724.54 1573.02i −1.66254 0.959867i −0.971497 0.237052i \(-0.923819\pi\)
−0.691041 0.722815i \(-0.742848\pi\)
\(140\) −33.9433 + 0.225359i −0.0204909 + 0.000136045i
\(141\) 0 0
\(142\) −639.407 + 1107.49i −0.377872 + 0.654494i
\(143\) 600.089 1039.39i 0.350923 0.607817i
\(144\) 0 0
\(145\) 16.0100 9.24339i 0.00916938 0.00529394i
\(146\) −83.6865 144.949i −0.0474380 0.0821650i
\(147\) 0 0
\(148\) −825.365 + 1429.57i −0.458410 + 0.793989i
\(149\) 363.709i 0.199975i 0.994989 + 0.0999873i \(0.0318802\pi\)
−0.994989 + 0.0999873i \(0.968120\pi\)
\(150\) 0 0
\(151\) −516.508 −0.278363 −0.139181 0.990267i \(-0.544447\pi\)
−0.139181 + 0.990267i \(0.544447\pi\)
\(152\) 379.612 + 657.508i 0.202570 + 0.350861i
\(153\) 0 0
\(154\) −283.258 483.180i −0.148218 0.252830i
\(155\) −23.5430 + 13.5925i −0.0122001 + 0.00704374i
\(156\) 0 0
\(157\) −1002.39 + 578.732i −0.509552 + 0.294190i −0.732650 0.680606i \(-0.761717\pi\)
0.223097 + 0.974796i \(0.428383\pi\)
\(158\) 890.254 513.988i 0.448258 0.258802i
\(159\) 0 0
\(160\) 41.4760 23.9462i 0.0204935 0.0118319i
\(161\) −2057.07 1169.51i −1.00696 0.572487i
\(162\) 0 0
\(163\) 1783.72 + 3089.49i 0.857126 + 1.48459i 0.874658 + 0.484740i \(0.161086\pi\)
−0.0175321 + 0.999846i \(0.505581\pi\)
\(164\) 1791.10 0.852814
\(165\) 0 0
\(166\) 1719.08i 0.803775i
\(167\) −1874.87 + 3247.37i −0.868754 + 1.50473i −0.00548318 + 0.999985i \(0.501745\pi\)
−0.863271 + 0.504741i \(0.831588\pi\)
\(168\) 0 0
\(169\) −52.3864 90.7359i −0.0238445 0.0412999i
\(170\) 16.5811 9.57308i 0.00748064 0.00431895i
\(171\) 0 0
\(172\) −483.683 + 837.763i −0.214421 + 0.371389i
\(173\) −1176.24 + 2037.30i −0.516922 + 0.895335i 0.482885 + 0.875684i \(0.339589\pi\)
−0.999807 + 0.0196514i \(0.993744\pi\)
\(174\) 0 0
\(175\) 1143.49 2011.30i 0.493941 0.868801i
\(176\) −769.927 444.518i −0.329747 0.190379i
\(177\) 0 0
\(178\) 334.718i 0.140945i
\(179\) −1977.18 1141.53i −0.825595 0.476657i 0.0267473 0.999642i \(-0.491485\pi\)
−0.852342 + 0.522985i \(0.824818\pi\)
\(180\) 0 0
\(181\) 3446.80i 1.41546i −0.706482 0.707731i \(-0.749719\pi\)
0.706482 0.707731i \(-0.250281\pi\)
\(182\) 976.359 6.48233i 0.397651 0.00264012i
\(183\) 0 0
\(184\) 2160.55 0.865640
\(185\) 33.9864 + 58.8662i 0.0135067 + 0.0233942i
\(186\) 0 0
\(187\) −1374.04 793.301i −0.537324 0.310224i
\(188\) −3347.45 −1.29861
\(189\) 0 0
\(190\) 14.2161 0.00542814
\(191\) −1540.99 889.689i −0.583780 0.337045i 0.178854 0.983876i \(-0.442761\pi\)
−0.762634 + 0.646830i \(0.776094\pi\)
\(192\) 0 0
\(193\) 249.570 + 432.268i 0.0930800 + 0.161219i 0.908806 0.417220i \(-0.136995\pi\)
−0.815726 + 0.578439i \(0.803662\pi\)
\(194\) 192.866 0.0713760
\(195\) 0 0
\(196\) −1117.76 + 1996.79i −0.407347 + 0.727693i
\(197\) 4333.51i 1.56726i 0.621229 + 0.783629i \(0.286634\pi\)
−0.621229 + 0.783629i \(0.713366\pi\)
\(198\) 0 0
\(199\) −1426.57 823.632i −0.508176 0.293396i 0.223907 0.974610i \(-0.428119\pi\)
−0.732084 + 0.681215i \(0.761452\pi\)
\(200\) 2112.48i 0.746874i
\(201\) 0 0
\(202\) −943.276 544.601i −0.328558 0.189693i
\(203\) −8.27433 1246.27i −0.00286081 0.430890i
\(204\) 0 0
\(205\) 36.8765 63.8719i 0.0125637 0.0217610i
\(206\) −482.146 + 835.102i −0.163071 + 0.282448i
\(207\) 0 0
\(208\) 1342.19 774.911i 0.447422 0.258319i
\(209\) −589.030 1020.23i −0.194948 0.337659i
\(210\) 0 0
\(211\) −1023.38 + 1772.54i −0.333897 + 0.578327i −0.983272 0.182141i \(-0.941697\pi\)
0.649375 + 0.760468i \(0.275031\pi\)
\(212\) 2571.79i 0.833166i
\(213\) 0 0
\(214\) 1624.77 0.519006
\(215\) 19.9168 + 34.4969i 0.00631775 + 0.0109427i
\(216\) 0 0
\(217\) 12.1675 + 1832.65i 0.00380638 + 0.573312i
\(218\) 15.5635 8.98558i 0.00483528 0.00279165i
\(219\) 0 0
\(220\) −41.6475 + 24.0452i −0.0127631 + 0.00736876i
\(221\) 2395.31 1382.93i 0.729076 0.420932i
\(222\) 0 0
\(223\) −1682.84 + 971.590i −0.505343 + 0.291760i −0.730917 0.682466i \(-0.760908\pi\)
0.225574 + 0.974226i \(0.427574\pi\)
\(224\) −21.4357 3228.61i −0.00639389 0.963038i
\(225\) 0 0
\(226\) 254.699 + 441.151i 0.0749659 + 0.129845i
\(227\) 3979.61 1.16359 0.581797 0.813334i \(-0.302350\pi\)
0.581797 + 0.813334i \(0.302350\pi\)
\(228\) 0 0
\(229\) 3742.04i 1.07983i 0.841720 + 0.539915i \(0.181544\pi\)
−0.841720 + 0.539915i \(0.818456\pi\)
\(230\) 20.2276 35.0353i 0.00579900 0.0100442i
\(231\) 0 0
\(232\) 568.968 + 985.481i 0.161011 + 0.278879i
\(233\) 4212.14 2431.88i 1.18432 0.683767i 0.227309 0.973823i \(-0.427007\pi\)
0.957010 + 0.290056i \(0.0936739\pi\)
\(234\) 0 0
\(235\) −68.9196 + 119.372i −0.0191311 + 0.0331361i
\(236\) −1830.06 + 3169.75i −0.504774 + 0.874294i
\(237\) 0 0
\(238\) −8.56945 1290.72i −0.00233393 0.351533i
\(239\) 3994.45 + 2306.19i 1.08108 + 0.624165i 0.931189 0.364537i \(-0.118773\pi\)
0.149896 + 0.988702i \(0.452106\pi\)
\(240\) 0 0
\(241\) 945.401i 0.252691i −0.991986 0.126346i \(-0.959675\pi\)
0.991986 0.126346i \(-0.0403248\pi\)
\(242\) 641.348 + 370.282i 0.170361 + 0.0983580i
\(243\) 0 0
\(244\) 1460.90i 0.383297i
\(245\) 48.1936 + 80.9714i 0.0125672 + 0.0211146i
\(246\) 0 0
\(247\) 2053.67 0.529036
\(248\) −836.676 1449.17i −0.214230 0.371057i
\(249\) 0 0
\(250\) 68.5322 + 39.5671i 0.0173374 + 0.0100098i
\(251\) 478.897 0.120429 0.0602146 0.998185i \(-0.480822\pi\)
0.0602146 + 0.998185i \(0.480822\pi\)
\(252\) 0 0
\(253\) −3352.44 −0.833068
\(254\) −2015.83 1163.84i −0.497971 0.287504i
\(255\) 0 0
\(256\) 569.780 + 986.887i 0.139106 + 0.240939i
\(257\) 4135.57 1.00377 0.501887 0.864933i \(-0.332639\pi\)
0.501887 + 0.864933i \(0.332639\pi\)
\(258\) 0 0
\(259\) 4582.31 30.4233i 1.09935 0.00729889i
\(260\) 83.8342i 0.0199968i
\(261\) 0 0
\(262\) −952.414 549.876i −0.224581 0.129662i
\(263\) 1336.33i 0.313315i 0.987653 + 0.156658i \(0.0500719\pi\)
−0.987653 + 0.156658i \(0.949928\pi\)
\(264\) 0 0
\(265\) −91.7117 52.9498i −0.0212596 0.0122743i
\(266\) 473.672 833.150i 0.109183 0.192044i
\(267\) 0 0
\(268\) 2527.58 4377.90i 0.576107 0.997847i
\(269\) 1094.02 1894.90i 0.247969 0.429494i −0.714993 0.699131i \(-0.753570\pi\)
0.962962 + 0.269637i \(0.0869037\pi\)
\(270\) 0 0
\(271\) 3642.53 2103.02i 0.816488 0.471400i −0.0327159 0.999465i \(-0.510416\pi\)
0.849204 + 0.528065i \(0.177082\pi\)
\(272\) −1024.41 1774.33i −0.228360 0.395531i
\(273\) 0 0
\(274\) −796.440 + 1379.48i −0.175601 + 0.304150i
\(275\) 3277.85i 0.718770i
\(276\) 0 0
\(277\) −2108.80 −0.457421 −0.228710 0.973495i \(-0.573451\pi\)
−0.228710 + 0.973495i \(0.573451\pi\)
\(278\) −1813.01 3140.23i −0.391141 0.677476i
\(279\) 0 0
\(280\) −74.7932 42.5223i −0.0159634 0.00907569i
\(281\) −5062.18 + 2922.65i −1.07468 + 0.620465i −0.929455 0.368934i \(-0.879723\pi\)
−0.145221 + 0.989399i \(0.546389\pi\)
\(282\) 0 0
\(283\) 6556.08 3785.15i 1.37710 0.795067i 0.385288 0.922796i \(-0.374102\pi\)
0.991809 + 0.127729i \(0.0407688\pi\)
\(284\) 6410.61 3701.17i 1.33944 0.773324i
\(285\) 0 0
\(286\) 1197.96 691.645i 0.247682 0.142999i
\(287\) −2514.58 4289.35i −0.517180 0.882204i
\(288\) 0 0
\(289\) 628.305 + 1088.26i 0.127886 + 0.221505i
\(290\) 21.3073 0.00431451
\(291\) 0 0
\(292\) 968.828i 0.194166i
\(293\) −92.9288 + 160.957i −0.0185289 + 0.0320930i −0.875141 0.483868i \(-0.839232\pi\)
0.856612 + 0.515961i \(0.172565\pi\)
\(294\) 0 0
\(295\) 75.3571 + 130.522i 0.0148727 + 0.0257603i
\(296\) −3623.45 + 2092.00i −0.711516 + 0.410794i
\(297\) 0 0
\(298\) −209.600 + 363.038i −0.0407444 + 0.0705713i
\(299\) 2922.09 5061.22i 0.565181 0.978922i
\(300\) 0 0
\(301\) 2685.34 17.8288i 0.514221 0.00341406i
\(302\) −515.555 297.656i −0.0982346 0.0567158i
\(303\) 0 0
\(304\) 1521.26i 0.287007i
\(305\) −52.0967 30.0780i −0.00978049 0.00564677i
\(306\) 0 0
\(307\) 2608.06i 0.484853i −0.970170 0.242427i \(-0.922057\pi\)
0.970170 0.242427i \(-0.0779434\pi\)
\(308\) 21.5243 + 3241.96i 0.00398202 + 0.599766i
\(309\) 0 0
\(310\) −31.3327 −0.00574058
\(311\) −1846.85 3198.84i −0.336738 0.583247i 0.647079 0.762423i \(-0.275990\pi\)
−0.983817 + 0.179176i \(0.942657\pi\)
\(312\) 0 0
\(313\) 5911.47 + 3412.99i 1.06753 + 0.616337i 0.927505 0.373811i \(-0.121949\pi\)
0.140023 + 0.990148i \(0.455282\pi\)
\(314\) −1334.06 −0.239762
\(315\) 0 0
\(316\) −5950.38 −1.05929
\(317\) 2657.16 + 1534.11i 0.470791 + 0.271811i 0.716571 0.697514i \(-0.245711\pi\)
−0.245780 + 0.969326i \(0.579044\pi\)
\(318\) 0 0
\(319\) −882.846 1529.13i −0.154953 0.268386i
\(320\) −19.2662 −0.00336567
\(321\) 0 0
\(322\) −1379.31 2352.81i −0.238713 0.407196i
\(323\) 2714.89i 0.467680i
\(324\) 0 0
\(325\) 4948.60 + 2857.08i 0.844613 + 0.487638i
\(326\) 4111.72i 0.698550i
\(327\) 0 0
\(328\) 3931.57 + 2269.90i 0.661844 + 0.382116i
\(329\) 4699.57 + 8016.51i 0.787525 + 1.34336i
\(330\) 0 0
\(331\) −455.469 + 788.896i −0.0756340 + 0.131002i −0.901362 0.433067i \(-0.857431\pi\)
0.825728 + 0.564069i \(0.190765\pi\)
\(332\) −4975.40 + 8617.64i −0.822471 + 1.42456i
\(333\) 0 0
\(334\) −3742.83 + 2160.92i −0.613169 + 0.354013i
\(335\) −104.079 180.271i −0.0169745 0.0294007i
\(336\) 0 0
\(337\) −2379.71 + 4121.79i −0.384663 + 0.666255i −0.991722 0.128401i \(-0.959016\pi\)
0.607060 + 0.794656i \(0.292349\pi\)
\(338\) 120.758i 0.0194330i
\(339\) 0 0
\(340\) −110.826 −0.0176776
\(341\) 1298.24 + 2248.61i 0.206169 + 0.357095i
\(342\) 0 0
\(343\) 6351.19 126.517i 0.999802 0.0199163i
\(344\) −2123.43 + 1225.96i −0.332812 + 0.192149i
\(345\) 0 0
\(346\) −2348.13 + 1355.69i −0.364845 + 0.210643i
\(347\) −2185.79 + 1261.97i −0.338154 + 0.195233i −0.659455 0.751744i \(-0.729213\pi\)
0.321302 + 0.946977i \(0.395880\pi\)
\(348\) 0 0
\(349\) −6370.82 + 3678.20i −0.977142 + 0.564153i −0.901406 0.432975i \(-0.857464\pi\)
−0.0757357 + 0.997128i \(0.524131\pi\)
\(350\) 2300.46 1348.62i 0.351328 0.205962i
\(351\) 0 0
\(352\) −2287.12 3961.41i −0.346318 0.599841i
\(353\) 192.834 0.0290752 0.0145376 0.999894i \(-0.495372\pi\)
0.0145376 + 0.999894i \(0.495372\pi\)
\(354\) 0 0
\(355\) 304.809i 0.0455707i
\(356\) 968.748 1677.92i 0.144223 0.249802i
\(357\) 0 0
\(358\) −1315.69 2278.84i −0.194236 0.336426i
\(359\) 3707.83 2140.72i 0.545103 0.314715i −0.202042 0.979377i \(-0.564758\pi\)
0.747144 + 0.664662i \(0.231424\pi\)
\(360\) 0 0
\(361\) −2421.59 + 4194.32i −0.353053 + 0.611506i
\(362\) 1986.34 3440.44i 0.288397 0.499518i
\(363\) 0 0
\(364\) −4913.18 2793.30i −0.707475 0.402222i
\(365\) 34.5491 + 19.9469i 0.00495447 + 0.00286046i
\(366\) 0 0
\(367\) 5775.69i 0.821495i 0.911749 + 0.410747i \(0.134732\pi\)
−0.911749 + 0.410747i \(0.865268\pi\)
\(368\) −3749.11 2164.55i −0.531075 0.306616i
\(369\) 0 0
\(370\) 78.3435i 0.0110078i
\(371\) −6158.95 + 3610.60i −0.861878 + 0.505264i
\(372\) 0 0
\(373\) −12373.8 −1.71767 −0.858834 0.512255i \(-0.828810\pi\)
−0.858834 + 0.512255i \(0.828810\pi\)
\(374\) −914.335 1583.67i −0.126415 0.218957i
\(375\) 0 0
\(376\) −7347.85 4242.28i −1.00781 0.581859i
\(377\) 3078.07 0.420500
\(378\) 0 0
\(379\) 9640.94 1.30665 0.653327 0.757076i \(-0.273373\pi\)
0.653327 + 0.757076i \(0.273373\pi\)
\(380\) −71.2645 41.1446i −0.00962050 0.00555440i
\(381\) 0 0
\(382\) −1025.43 1776.10i −0.137344 0.237887i
\(383\) −10541.8 −1.40642 −0.703212 0.710980i \(-0.748252\pi\)
−0.703212 + 0.710980i \(0.748252\pi\)
\(384\) 0 0
\(385\) 116.054 + 65.9802i 0.0153627 + 0.00873419i
\(386\) 575.294i 0.0758593i
\(387\) 0 0
\(388\) −966.822 558.195i −0.126503 0.0730363i
\(389\) 1429.20i 0.186281i 0.995653 + 0.0931406i \(0.0296906\pi\)
−0.995653 + 0.0931406i \(0.970309\pi\)
\(390\) 0 0
\(391\) −6690.78 3862.92i −0.865389 0.499633i
\(392\) −4984.12 + 2966.51i −0.642184 + 0.382223i
\(393\) 0 0
\(394\) −2497.34 + 4325.52i −0.319325 + 0.553087i
\(395\) −122.511 + 212.195i −0.0156055 + 0.0270295i
\(396\) 0 0
\(397\) −5532.85 + 3194.39i −0.699460 + 0.403834i −0.807146 0.590351i \(-0.798989\pi\)
0.107686 + 0.994185i \(0.465656\pi\)
\(398\) −949.294 1644.23i −0.119557 0.207079i
\(399\) 0 0
\(400\) 2116.39 3665.69i 0.264548 0.458211i
\(401\) 15077.6i 1.87765i 0.344396 + 0.938825i \(0.388084\pi\)
−0.344396 + 0.938825i \(0.611916\pi\)
\(402\) 0 0
\(403\) −4526.34 −0.559487
\(404\) 3152.39 + 5460.09i 0.388211 + 0.672401i
\(405\) 0 0
\(406\) 709.946 1248.74i 0.0867833 0.152645i
\(407\) 5622.37 3246.08i 0.684744 0.395337i
\(408\) 0 0
\(409\) 5666.97 3271.83i 0.685119 0.395554i −0.116662 0.993172i \(-0.537219\pi\)
0.801781 + 0.597618i \(0.203886\pi\)
\(410\) 73.6169 42.5027i 0.00886751 0.00511966i
\(411\) 0 0
\(412\) 4833.93 2790.87i 0.578036 0.333729i
\(413\) 10160.2 67.4567i 1.21054 0.00803712i
\(414\) 0 0
\(415\) 204.874 + 354.852i 0.0242334 + 0.0419735i
\(416\) 7974.12 0.939815
\(417\) 0 0
\(418\) 1357.80i 0.158880i
\(419\) −3808.29 + 6596.15i −0.444027 + 0.769077i −0.997984 0.0634684i \(-0.979784\pi\)
0.553957 + 0.832545i \(0.313117\pi\)
\(420\) 0 0
\(421\) 2874.27 + 4978.38i 0.332739 + 0.576321i 0.983048 0.183349i \(-0.0586938\pi\)
−0.650309 + 0.759670i \(0.725360\pi\)
\(422\) −2042.98 + 1179.52i −0.235665 + 0.136061i
\(423\) 0 0
\(424\) 3259.27 5645.23i 0.373312 0.646595i
\(425\) 3776.97 6541.91i 0.431083 0.746657i
\(426\) 0 0
\(427\) −3498.58 + 2051.00i −0.396506 + 0.232447i
\(428\) −8144.89 4702.45i −0.919855 0.531079i
\(429\) 0 0
\(430\) 45.9111i 0.00514890i
\(431\) −11353.0 6554.64i −1.26880 0.732543i −0.294040 0.955793i \(-0.595000\pi\)
−0.974761 + 0.223251i \(0.928333\pi\)
\(432\) 0 0
\(433\) 12018.7i 1.33390i 0.745102 + 0.666951i \(0.232401\pi\)
−0.745102 + 0.666951i \(0.767599\pi\)
\(434\) −1043.99 + 1836.28i −0.115468 + 0.203098i
\(435\) 0 0
\(436\) −104.025 −0.0114263
\(437\) −2868.24 4967.94i −0.313974 0.543819i
\(438\) 0 0
\(439\) −3519.12 2031.76i −0.382593 0.220890i 0.296353 0.955079i \(-0.404230\pi\)
−0.678946 + 0.734188i \(0.737563\pi\)
\(440\) −121.892 −0.0132067
\(441\) 0 0
\(442\) 3187.85 0.343056
\(443\) 5733.91 + 3310.47i 0.614958 + 0.355046i 0.774903 0.632080i \(-0.217799\pi\)
−0.159946 + 0.987126i \(0.551132\pi\)
\(444\) 0 0
\(445\) −39.8905 69.0924i −0.00424942 0.00736021i
\(446\) −2239.65 −0.237782
\(447\) 0 0
\(448\) −641.939 + 1129.12i −0.0676981 + 0.119075i
\(449\) 3211.25i 0.337524i 0.985657 + 0.168762i \(0.0539769\pi\)
−0.985657 + 0.168762i \(0.946023\pi\)
\(450\) 0 0
\(451\) −6100.48 3522.11i −0.636940 0.367738i
\(452\) 2948.61i 0.306839i
\(453\) 0 0
\(454\) 3972.26 + 2293.39i 0.410634 + 0.237079i
\(455\) −200.767 + 117.697i −0.0206859 + 0.0121269i
\(456\) 0 0
\(457\) 3926.69 6801.23i 0.401932 0.696166i −0.592027 0.805918i \(-0.701672\pi\)
0.993959 + 0.109752i \(0.0350056\pi\)
\(458\) −2156.48 + 3735.14i −0.220013 + 0.381073i
\(459\) 0 0
\(460\) −202.800 + 117.086i −0.0205556 + 0.0118678i
\(461\) −2992.54 5183.22i −0.302335 0.523659i 0.674330 0.738430i \(-0.264433\pi\)
−0.976664 + 0.214771i \(0.931099\pi\)
\(462\) 0 0
\(463\) 9378.59 16244.2i 0.941383 1.63052i 0.178546 0.983932i \(-0.442861\pi\)
0.762837 0.646591i \(-0.223806\pi\)
\(464\) 2280.08i 0.228125i
\(465\) 0 0
\(466\) 5605.82 0.557263
\(467\) 4572.53 + 7919.86i 0.453087 + 0.784770i 0.998576 0.0533484i \(-0.0169894\pi\)
−0.545489 + 0.838118i \(0.683656\pi\)
\(468\) 0 0
\(469\) −14032.8 + 93.1678i −1.38161 + 0.00917290i
\(470\) −137.585 + 79.4347i −0.0135028 + 0.00779585i
\(471\) 0 0
\(472\) −8034.17 + 4638.53i −0.783480 + 0.452343i
\(473\) 3294.84 1902.28i 0.320289 0.184919i
\(474\) 0 0
\(475\) 4857.40 2804.42i 0.469206 0.270896i
\(476\) −3692.66 + 6495.08i −0.355573 + 0.625424i
\(477\) 0 0
\(478\) 2658.05 + 4603.88i 0.254344 + 0.440537i
\(479\) 40.6827 0.00388067 0.00194033 0.999998i \(-0.499382\pi\)
0.00194033 + 0.999998i \(0.499382\pi\)
\(480\) 0 0
\(481\) 11317.5i 1.07284i
\(482\) 544.820 943.657i 0.0514852 0.0891751i
\(483\) 0 0
\(484\) −2143.36 3712.40i −0.201292 0.348648i
\(485\) −39.8112 + 22.9850i −0.00372729 + 0.00215195i
\(486\) 0 0
\(487\) 5493.67 9515.32i 0.511174 0.885380i −0.488742 0.872429i \(-0.662544\pi\)
0.999916 0.0129516i \(-0.00412273\pi\)
\(488\) 1851.43 3206.76i 0.171742 0.297466i
\(489\) 0 0
\(490\) 1.44206 + 108.595i 0.000132950 + 0.0100119i
\(491\) 2232.83 + 1289.12i 0.205226 + 0.118488i 0.599091 0.800681i \(-0.295529\pi\)
−0.393865 + 0.919168i \(0.628862\pi\)
\(492\) 0 0
\(493\) 4069.11i 0.371731i
\(494\) 2049.88 + 1183.50i 0.186697 + 0.107790i
\(495\) 0 0
\(496\) 3352.90i 0.303527i
\(497\) −17863.6 10156.0i −1.61226 0.916621i
\(498\) 0 0
\(499\) −1096.63 −0.0983809 −0.0491904 0.998789i \(-0.515664\pi\)
−0.0491904 + 0.998789i \(0.515664\pi\)
\(500\) −229.032 396.694i −0.0204852 0.0354814i
\(501\) 0 0
\(502\) 478.014 + 275.981i 0.0424996 + 0.0245372i
\(503\) 22314.6 1.97805 0.989024 0.147755i \(-0.0472046\pi\)
0.989024 + 0.147755i \(0.0472046\pi\)
\(504\) 0 0
\(505\) 259.614 0.0228766
\(506\) −3346.26 1931.96i −0.293991 0.169736i
\(507\) 0 0
\(508\) 6736.82 + 11668.5i 0.588382 + 1.01911i
\(509\) −5432.23 −0.473044 −0.236522 0.971626i \(-0.576007\pi\)
−0.236522 + 0.971626i \(0.576007\pi\)
\(510\) 0 0
\(511\) 2320.16 1360.16i 0.200857 0.117750i
\(512\) 10490.5i 0.905506i
\(513\) 0 0
\(514\) 4127.94 + 2383.27i 0.354233 + 0.204516i
\(515\) 229.842i 0.0196661i
\(516\) 0 0
\(517\) 11401.4 + 6582.59i 0.969888 + 0.559965i
\(518\) 4591.39 + 2610.35i 0.389448 + 0.221414i
\(519\) 0 0
\(520\) 106.245 184.021i 0.00895987 0.0155189i
\(521\) −5784.74 + 10019.5i −0.486438 + 0.842535i −0.999878 0.0155903i \(-0.995037\pi\)
0.513441 + 0.858125i \(0.328371\pi\)
\(522\) 0 0
\(523\) 9256.60 5344.30i 0.773925 0.446826i −0.0603481 0.998177i \(-0.519221\pi\)
0.834273 + 0.551352i \(0.185888\pi\)
\(524\) 3182.93 + 5512.99i 0.265356 + 0.459611i
\(525\) 0 0
\(526\) −770.110 + 1333.87i −0.0638372 + 0.110569i
\(527\) 5983.69i 0.494599i
\(528\) 0 0
\(529\) −4157.49 −0.341702
\(530\) −61.0284 105.704i −0.00500170 0.00866320i
\(531\) 0 0
\(532\) −4785.80 + 2805.61i −0.390020 + 0.228644i
\(533\) 10634.7 6139.97i 0.864243 0.498971i
\(534\) 0 0
\(535\) −335.385 + 193.635i −0.0271028 + 0.0156478i
\(536\) 11096.4 6406.50i 0.894200 0.516266i
\(537\) 0 0
\(538\) 2184.00 1260.94i 0.175017 0.101046i
\(539\) 7733.67 4603.02i 0.618020 0.367841i
\(540\) 0 0
\(541\) −6142.32 10638.8i −0.488131 0.845468i 0.511776 0.859119i \(-0.328988\pi\)
−0.999907 + 0.0136513i \(0.995655\pi\)
\(542\) 4847.75 0.384186
\(543\) 0 0
\(544\) 10541.5i 0.830818i
\(545\) −2.14174 + 3.70960i −0.000168334 + 0.000291563i
\(546\) 0 0
\(547\) 2319.96 + 4018.29i 0.181342 + 0.314094i 0.942338 0.334663i \(-0.108622\pi\)
−0.760996 + 0.648757i \(0.775289\pi\)
\(548\) 7985.01 4610.15i 0.622450 0.359372i
\(549\) 0 0
\(550\) 1888.98 3271.80i 0.146448 0.253655i
\(551\) 1510.67 2616.56i 0.116800 0.202303i
\(552\) 0 0
\(553\) 8353.89 + 14250.0i 0.642394 + 1.09579i
\(554\) −2104.91 1215.27i −0.161424 0.0931983i
\(555\) 0 0
\(556\) 20989.0i 1.60096i
\(557\) 918.666 + 530.392i 0.0698835 + 0.0403473i 0.534535 0.845147i \(-0.320487\pi\)
−0.464651 + 0.885494i \(0.653820\pi\)
\(558\) 0 0
\(559\) 6632.33i 0.501821i
\(560\) 87.1843 + 148.719i 0.00657895 + 0.0112223i
\(561\) 0 0
\(562\) −6737.12 −0.505673
\(563\) −9805.04 16982.8i −0.733984 1.27130i −0.955168 0.296066i \(-0.904325\pi\)
0.221183 0.975232i \(-0.429008\pi\)
\(564\) 0 0
\(565\) −105.150 60.7081i −0.00782951 0.00452037i
\(566\) 8725.31 0.647972
\(567\) 0 0
\(568\) 18762.2 1.38600
\(569\) −18029.9 10409.6i −1.32839 0.766945i −0.343337 0.939212i \(-0.611557\pi\)
−0.985050 + 0.172267i \(0.944891\pi\)
\(570\) 0 0
\(571\) −7362.92 12753.0i −0.539630 0.934667i −0.998924 0.0463823i \(-0.985231\pi\)
0.459294 0.888285i \(-0.348103\pi\)
\(572\) −8007.09 −0.585303
\(573\) 0 0
\(574\) −38.0468 5730.55i −0.00276663 0.416705i
\(575\) 15961.3i 1.15762i
\(576\) 0 0
\(577\) −14296.1 8253.86i −1.03146 0.595516i −0.114060 0.993474i \(-0.536386\pi\)
−0.917404 + 0.397958i \(0.869719\pi\)
\(578\) 1448.33i 0.104226i
\(579\) 0 0
\(580\) −106.812 61.6680i −0.00764678 0.00441487i
\(581\) 27622.7 183.395i 1.97243 0.0130956i
\(582\) 0 0
\(583\) −5057.29 + 8759.48i −0.359265 + 0.622266i
\(584\) −1227.81 + 2126.64i −0.0869988 + 0.150686i
\(585\) 0 0
\(586\) −185.515 + 107.107i −0.0130777 + 0.00755043i
\(587\) −6104.52 10573.3i −0.429234 0.743456i 0.567571 0.823324i \(-0.307883\pi\)
−0.996805 + 0.0798686i \(0.974550\pi\)
\(588\) 0 0
\(589\) −2221.46 + 3847.68i −0.155405 + 0.269170i
\(590\) 173.709i 0.0121211i
\(591\) 0 0
\(592\) 8383.49 0.582026
\(593\) 4385.09 + 7595.19i 0.303666 + 0.525965i 0.976963 0.213407i \(-0.0684560\pi\)
−0.673298 + 0.739372i \(0.735123\pi\)
\(594\) 0 0
\(595\) 155.592 + 265.408i 0.0107204 + 0.0182868i
\(596\) 2101.42 1213.26i 0.144426 0.0833842i
\(597\) 0 0
\(598\) 5833.41 3367.92i 0.398906 0.230308i
\(599\) −19136.2 + 11048.3i −1.30531 + 0.753623i −0.981310 0.192433i \(-0.938362\pi\)
−0.324003 + 0.946056i \(0.605029\pi\)
\(600\) 0 0
\(601\) 10189.4 5882.86i 0.691572 0.399279i −0.112629 0.993637i \(-0.535927\pi\)
0.804201 + 0.594358i \(0.202594\pi\)
\(602\) 2690.66 + 1529.73i 0.182165 + 0.103566i
\(603\) 0 0
\(604\) 1722.96 + 2984.26i 0.116070 + 0.201039i
\(605\) −176.516 −0.0118618
\(606\) 0 0
\(607\) 8352.53i 0.558515i −0.960216 0.279258i \(-0.909912\pi\)
0.960216 0.279258i \(-0.0900884\pi\)
\(608\) 3913.58 6778.52i 0.261047 0.452147i
\(609\) 0 0
\(610\) −34.6671 60.0451i −0.00230103 0.00398550i
\(611\) −19875.6 + 11475.2i −1.31601 + 0.759797i
\(612\) 0 0
\(613\) −6844.06 + 11854.3i −0.450945 + 0.781059i −0.998445 0.0557466i \(-0.982246\pi\)
0.547500 + 0.836805i \(0.315579\pi\)
\(614\) 1502.99 2603.25i 0.0987877 0.171105i
\(615\) 0 0
\(616\) −4061.35 + 7143.58i −0.265644 + 0.467245i
\(617\) −2227.88 1286.27i −0.145366 0.0839274i 0.425553 0.904934i \(-0.360080\pi\)
−0.570919 + 0.821006i \(0.693413\pi\)
\(618\) 0 0
\(619\) 27393.3i 1.77872i −0.457206 0.889361i \(-0.651150\pi\)
0.457206 0.889361i \(-0.348850\pi\)
\(620\) 157.069 + 90.6838i 0.0101743 + 0.00587411i
\(621\) 0 0
\(622\) 4257.26i 0.274438i
\(623\) −5378.36 + 35.7085i −0.345874 + 0.00229636i
\(624\) 0 0
\(625\) 15596.7 0.998189
\(626\) 3933.71 + 6813.39i 0.251154 + 0.435012i
\(627\) 0 0
\(628\) 6687.55 + 3861.06i 0.424940 + 0.245339i
\(629\) 14961.5 0.948414
\(630\) 0 0
\(631\) −15166.2 −0.956822 −0.478411 0.878136i \(-0.658787\pi\)
−0.478411 + 0.878136i \(0.658787\pi\)
\(632\) −13061.4 7541.02i −0.822082 0.474629i
\(633\) 0 0
\(634\) 1768.17 + 3062.56i 0.110762 + 0.191845i
\(635\) 554.810 0.0346724
\(636\) 0 0
\(637\) 208.320 + 15687.7i 0.0129575 + 0.975778i
\(638\) 2035.08i 0.126285i
\(639\) 0 0
\(640\) −351.038 202.672i −0.0216813 0.0125177i
\(641\) 22415.6i 1.38122i 0.723226 + 0.690612i \(0.242659\pi\)
−0.723226 + 0.690612i \(0.757341\pi\)
\(642\) 0 0
\(643\) 14768.9 + 8526.82i 0.905798 + 0.522963i 0.879077 0.476680i \(-0.158160\pi\)
0.0267213 + 0.999643i \(0.491493\pi\)
\(644\) 104.811 + 15786.5i 0.00641326 + 0.965956i
\(645\) 0 0
\(646\) 1564.55 2709.88i 0.0952886 0.165045i
\(647\) −13132.8 + 22746.6i −0.797995 + 1.38217i 0.122925 + 0.992416i \(0.460773\pi\)
−0.920920 + 0.389752i \(0.872561\pi\)
\(648\) 0 0
\(649\) 12466.3 7197.43i 0.754000 0.435322i
\(650\) 3292.98 + 5703.62i 0.198710 + 0.344176i
\(651\) 0 0
\(652\) 11900.2 20611.8i 0.714798 1.23807i
\(653\) 153.742i 0.00921345i 0.999989 + 0.00460672i \(0.00146637\pi\)
−0.999989 + 0.00460672i \(0.998534\pi\)
\(654\) 0 0
\(655\) 262.129 0.0156370
\(656\) −4548.19 7877.70i −0.270697 0.468861i
\(657\) 0 0
\(658\) 71.1069 + 10710.0i 0.00421282 + 0.634529i
\(659\) 9292.80 5365.20i 0.549311 0.317145i −0.199533 0.979891i \(-0.563942\pi\)
0.748844 + 0.662746i \(0.230609\pi\)
\(660\) 0 0
\(661\) −27734.8 + 16012.7i −1.63201 + 0.942243i −0.648541 + 0.761180i \(0.724621\pi\)
−0.983471 + 0.181063i \(0.942046\pi\)
\(662\) −909.258 + 524.960i −0.0533826 + 0.0308205i
\(663\) 0 0
\(664\) −21842.6 + 12610.8i −1.27659 + 0.737040i
\(665\) 1.51661 + 228.429i 8.84383e−5 + 0.0133204i
\(666\) 0 0
\(667\) −4298.96 7446.01i −0.249560 0.432250i
\(668\) 25016.7 1.44899
\(669\) 0 0
\(670\) 239.918i 0.0138341i
\(671\) −2872.79 + 4975.81i −0.165280 + 0.286273i
\(672\) 0 0
\(673\) −6229.97 10790.6i −0.356831 0.618050i 0.630598 0.776110i \(-0.282810\pi\)
−0.987430 + 0.158059i \(0.949476\pi\)
\(674\) −4750.65 + 2742.79i −0.271496 + 0.156748i
\(675\) 0 0
\(676\) −349.500 + 605.352i −0.0198851 + 0.0344420i
\(677\) −4805.25 + 8322.94i −0.272793 + 0.472491i −0.969576 0.244791i \(-0.921281\pi\)
0.696783 + 0.717282i \(0.254614\pi\)
\(678\) 0 0
\(679\) 20.5753 + 3099.02i 0.00116290 + 0.175154i
\(680\) −243.270 140.452i −0.0137191 0.00792073i
\(681\) 0 0
\(682\) 2992.62i 0.168026i
\(683\) −24434.5 14107.2i −1.36890 0.790335i −0.378113 0.925760i \(-0.623427\pi\)
−0.990788 + 0.135425i \(0.956760\pi\)
\(684\) 0 0
\(685\) 379.668i 0.0211772i
\(686\) 6412.38 + 3533.81i 0.356889 + 0.196679i
\(687\) 0 0
\(688\) 4912.92 0.272243
\(689\) −8816.19 15270.1i −0.487475 0.844331i
\(690\) 0 0
\(691\) 2458.51 + 1419.42i 0.135349 + 0.0781439i 0.566146 0.824305i \(-0.308434\pi\)
−0.430796 + 0.902449i \(0.641767\pi\)
\(692\) 15694.7 0.862172
\(693\) 0 0
\(694\) −2909.01 −0.159113
\(695\) 748.483 + 432.137i 0.0408512 + 0.0235854i
\(696\) 0 0
\(697\) −8116.85 14058.8i −0.441102 0.764010i
\(698\) −8478.76 −0.459779
\(699\) 0 0
\(700\) −15435.3 + 102.479i −0.833426 + 0.00553336i
\(701\) 5765.47i 0.310640i −0.987864 0.155320i \(-0.950359\pi\)
0.987864 0.155320i \(-0.0496409\pi\)
\(702\) 0 0
\(703\) 9620.64 + 5554.48i 0.516144 + 0.297996i
\(704\) 1840.14i 0.0985126i
\(705\) 0 0
\(706\) 192.479 + 111.128i 0.0102607 + 0.00592399i
\(707\) 8650.18 15214.9i 0.460146 0.809359i
\(708\) 0 0
\(709\) −2400.73 + 4158.18i −0.127167 + 0.220259i −0.922578 0.385811i \(-0.873922\pi\)
0.795411 + 0.606070i \(0.207255\pi\)
\(710\) 175.657 304.247i 0.00928492 0.0160819i
\(711\) 0 0
\(712\) 4252.92 2455.42i 0.223855 0.129243i
\(713\) 6321.68 + 10949.5i 0.332046 + 0.575121i
\(714\) 0 0
\(715\) −164.856 + 285.538i −0.00862273 + 0.0149350i
\(716\) 15231.6i 0.795014i
\(717\) 0 0
\(718\) 4934.65 0.256490
\(719\) −2528.38 4379.29i −0.131144 0.227149i 0.792974 0.609256i \(-0.208532\pi\)
−0.924118 + 0.382107i \(0.875198\pi\)
\(720\) 0 0
\(721\) −13470.1 7658.18i −0.695774 0.395569i
\(722\) −4834.25 + 2791.05i −0.249186 + 0.143867i
\(723\) 0 0
\(724\) −19914.8 + 11497.8i −1.02228 + 0.590211i
\(725\) 7280.34 4203.31i 0.372945 0.215320i
\(726\) 0 0
\(727\) −8680.56 + 5011.72i −0.442839 + 0.255673i −0.704801 0.709405i \(-0.748964\pi\)
0.261962 + 0.965078i \(0.415630\pi\)
\(728\) −7244.73 12358.0i −0.368829 0.629147i
\(729\) 0 0
\(730\) 22.9902 + 39.8202i 0.00116563 + 0.00201892i
\(731\) 8767.75 0.443621
\(732\) 0 0
\(733\) 31917.2i 1.60831i −0.594422 0.804153i \(-0.702619\pi\)
0.594422 0.804153i \(-0.297381\pi\)
\(734\) −3328.44 + 5765.03i −0.167378 + 0.289906i
\(735\) 0 0
\(736\) −11137.0 19289.8i −0.557765 0.966077i
\(737\) −17217.8 + 9940.73i −0.860553 + 0.496841i
\(738\) 0 0
\(739\) 4191.82 7260.45i 0.208659 0.361407i −0.742634 0.669698i \(-0.766424\pi\)
0.951292 + 0.308291i \(0.0997569\pi\)
\(740\) 226.743 392.731i 0.0112638 0.0195095i
\(741\) 0 0
\(742\) −8228.32 + 54.6302i −0.407104 + 0.00270288i
\(743\) −14035.0 8103.09i −0.692992 0.400099i 0.111740 0.993737i \(-0.464358\pi\)
−0.804732 + 0.593638i \(0.797691\pi\)
\(744\) 0 0
\(745\) 99.9176i 0.00491369i
\(746\) −12351.0 7130.82i −0.606167 0.349971i
\(747\) 0 0
\(748\) 10585.1i 0.517421i
\(749\) 173.334 + 26107.4i 0.00845594 + 1.27362i
\(750\) 0 0
\(751\) −29812.4 −1.44856 −0.724281 0.689505i \(-0.757828\pi\)
−0.724281 + 0.689505i \(0.757828\pi\)
\(752\) 8500.26 + 14722.9i 0.412198 + 0.713948i
\(753\) 0 0
\(754\) 3072.39 + 1773.84i 0.148395 + 0.0856758i
\(755\) 141.894 0.00683981
\(756\) 0 0
\(757\) 29462.2 1.41456 0.707281 0.706933i \(-0.249922\pi\)
0.707281 + 0.706933i \(0.249922\pi\)
\(758\) 9623.15 + 5555.93i 0.461120 + 0.266227i
\(759\) 0 0
\(760\) −104.286 180.630i −0.00497746 0.00862121i
\(761\) 1305.63 0.0621931 0.0310965 0.999516i \(-0.490100\pi\)
0.0310965 + 0.999516i \(0.490100\pi\)
\(762\) 0 0
\(763\) 146.043 + 249.120i 0.00692939 + 0.0118201i
\(764\) 11871.3i 0.562156i
\(765\) 0 0
\(766\) −10522.3 6075.08i −0.496329 0.286556i
\(767\) 25094.0i 1.18135i
\(768\) 0 0
\(769\) −1387.38 801.002i −0.0650586 0.0375616i 0.467118 0.884195i \(-0.345292\pi\)
−0.532176 + 0.846633i \(0.678626\pi\)
\(770\) 77.8162 + 132.739i 0.00364195 + 0.00621242i
\(771\) 0 0
\(772\) 1665.03 2883.91i 0.0776239 0.134449i
\(773\) 9429.57 16332.5i 0.438755 0.759947i −0.558838 0.829277i \(-0.688753\pi\)
0.997594 + 0.0693300i \(0.0220861\pi\)
\(774\) 0 0
\(775\) −10705.9 + 6181.03i −0.496214 + 0.286489i
\(776\) −1414.82 2450.54i −0.0654499 0.113363i
\(777\) 0 0
\(778\) −823.627 + 1426.56i −0.0379543 + 0.0657388i
\(779\) 12053.6i 0.554385i
\(780\) 0 0
\(781\) −29112.7 −1.33384
\(782\) −4452.29 7711.59i −0.203598 0.352642i
\(783\) 0 0
\(784\) 11620.7 154.314i 0.529370 0.00702959i
\(785\) 275.376 158.988i 0.0125205 0.00722872i
\(786\) 0 0
\(787\) 20329.8 11737.4i 0.920810 0.531630i 0.0369165 0.999318i \(-0.488246\pi\)
0.883893 + 0.467689i \(0.154913\pi\)
\(788\) 25038.0 14455.7i 1.13190 0.653506i
\(789\) 0 0
\(790\) −244.569 + 141.202i −0.0110144 + 0.00635917i
\(791\) −7061.37 + 4139.64i −0.317413 + 0.186079i
\(792\) 0 0
\(793\) −5008.02 8674.15i −0.224262 0.388434i
\(794\) −7363.52 −0.329120
\(795\) 0 0
\(796\) 10989.9i 0.489353i
\(797\) −15759.6 + 27296.5i −0.700420 + 1.21316i 0.267900 + 0.963447i \(0.413670\pi\)
−0.968319 + 0.249715i \(0.919663\pi\)
\(798\) 0 0
\(799\) 15169.9 + 26275.0i 0.671678 + 1.16338i
\(800\) 18860.6 10889.2i 0.833530 0.481239i
\(801\) 0 0
\(802\) −8688.97 + 15049.7i −0.382566 + 0.662625i
\(803\) 1905.15 3299.82i 0.0837252 0.145016i
\(804\) 0 0
\(805\) 565.116 + 321.286i 0.0247425 + 0.0140669i
\(806\) −4517.99 2608.46i −0.197444 0.113994i
\(807\) 0 0
\(808\) 15980.3i 0.695774i
\(809\) −14756.8 8519.85i −0.641312 0.370262i 0.143807 0.989606i \(-0.454065\pi\)
−0.785120 + 0.619344i \(0.787399\pi\)
\(810\) 0 0
\(811\) 9916.81i 0.429379i 0.976682 + 0.214689i \(0.0688739\pi\)
−0.976682 + 0.214689i \(0.931126\pi\)
\(812\) −7173.03 + 4205.09i −0.310005 + 0.181736i
\(813\) 0 0
\(814\) 7482.67 0.322196
\(815\) −490.020 848.740i −0.0210609 0.0364786i
\(816\) 0 0
\(817\) 5637.91 + 3255.05i 0.241427 + 0.139388i
\(818\) 7542.02 0.322372
\(819\) 0 0
\(820\) −492.049 −0.0209550
\(821\) −1740.83 1005.07i −0.0740018 0.0427250i 0.462543 0.886597i \(-0.346937\pi\)
−0.536544 + 0.843872i \(0.680271\pi\)
\(822\) 0 0
\(823\) −5316.32 9208.13i −0.225170 0.390006i 0.731200 0.682163i \(-0.238961\pi\)
−0.956371 + 0.292157i \(0.905627\pi\)
\(824\) 14147.7 0.598129
\(825\) 0 0
\(826\) 10180.4 + 5787.86i 0.428838 + 0.243808i
\(827\) 5725.20i 0.240731i 0.992730 + 0.120366i \(0.0384067\pi\)
−0.992730 + 0.120366i \(0.961593\pi\)
\(828\) 0 0
\(829\) 16983.1 + 9805.21i 0.711517 + 0.410795i 0.811623 0.584182i \(-0.198585\pi\)
−0.100105 + 0.994977i \(0.531918\pi\)
\(830\) 472.263i 0.0197500i
\(831\) 0 0
\(832\) −2778.08 1603.92i −0.115760 0.0668342i
\(833\) 20738.7 275.393i 0.862610 0.0114547i
\(834\) 0 0
\(835\) 515.062 892.113i 0.0213466 0.0369735i
\(836\) −3929.76 + 6806.55i −0.162576 + 0.281590i
\(837\) 0 0
\(838\) −7602.53 + 4389.32i −0.313395 + 0.180939i
\(839\) −14243.5 24670.5i −0.586104 1.01516i −0.994737 0.102462i \(-0.967328\pi\)
0.408633 0.912699i \(-0.366005\pi\)
\(840\) 0 0
\(841\) −9930.29 + 17199.8i −0.407163 + 0.705226i
\(842\) 6625.59i 0.271179i
\(843\) 0 0
\(844\) 13655.1 0.556906
\(845\) 14.3915 + 24.9268i 0.000585897 + 0.00101480i
\(846\) 0 0
\(847\) −5881.39 + 10344.9i −0.238591 + 0.419662i
\(848\) −11311.3 + 6530.61i −0.458058 + 0.264460i
\(849\) 0 0
\(850\) 7540.01 4353.23i 0.304259 0.175664i
\(851\) 27377.8 15806.6i 1.10282 0.636712i
\(852\) 0 0
\(853\) 20170.8 11645.6i 0.809652 0.467453i −0.0371829 0.999308i \(-0.511838\pi\)
0.846835 + 0.531856i \(0.178505\pi\)
\(854\) −4674.09 + 31.0326i −0.187288 + 0.00124346i
\(855\) 0 0
\(856\) −11919.0 20644.3i −0.475915 0.824309i
\(857\) −34729.8 −1.38430 −0.692152 0.721752i \(-0.743337\pi\)
−0.692152 + 0.721752i \(0.743337\pi\)
\(858\) 0 0
\(859\) 38761.1i 1.53960i 0.638288 + 0.769798i \(0.279643\pi\)
−0.638288 + 0.769798i \(0.720357\pi\)
\(860\) 132.877 230.149i 0.00526867 0.00912560i
\(861\) 0 0
\(862\) −7554.68 13085.1i −0.298508 0.517030i
\(863\) 6375.08 3680.65i 0.251460 0.145181i −0.368972 0.929440i \(-0.620290\pi\)
0.620433 + 0.784260i \(0.286957\pi\)
\(864\) 0 0
\(865\) 323.134 559.684i 0.0127016 0.0219998i
\(866\) −6926.17 + 11996.5i −0.271779 + 0.470736i
\(867\) 0 0
\(868\) 10548.0 6183.65i 0.412470 0.241805i
\(869\) 20266.9 + 11701.1i 0.791149 + 0.456770i
\(870\) 0 0
\(871\) 34658.6i 1.34829i
\(872\) −228.341 131.833i −0.00886765 0.00511974i
\(873\) 0 0
\(874\) 6611.70i 0.255886i
\(875\) −628.465 + 1105.42i −0.0242811 + 0.0427085i
\(876\) 0 0
\(877\) −1980.37 −0.0762512 −0.0381256 0.999273i \(-0.512139\pi\)
−0.0381256 + 0.999273i \(0.512139\pi\)
\(878\) −2341.75 4056.03i −0.0900117 0.155905i
\(879\) 0 0
\(880\) 211.513 + 122.117i 0.00810239 + 0.00467792i
\(881\) −30117.5 −1.15174 −0.575870 0.817541i \(-0.695337\pi\)
−0.575870 + 0.817541i \(0.695337\pi\)
\(882\) 0 0
\(883\) 3739.43 0.142516 0.0712580 0.997458i \(-0.477299\pi\)
0.0712580 + 0.997458i \(0.477299\pi\)
\(884\) −15980.5 9226.34i −0.608011 0.351036i
\(885\) 0 0
\(886\) 3815.55 + 6608.73i 0.144680 + 0.250592i
\(887\) 35778.8 1.35438 0.677190 0.735809i \(-0.263198\pi\)
0.677190 + 0.735809i \(0.263198\pi\)
\(888\) 0 0
\(889\) 18485.9 32515.2i 0.697410 1.22669i
\(890\) 91.9533i 0.00346324i
\(891\) 0 0
\(892\) 11227.2 + 6482.04i 0.421430 + 0.243313i
\(893\) 22527.4i 0.844177i
\(894\) 0 0
\(895\) 543.168 + 313.598i 0.0202861 + 0.0117122i
\(896\) −23574.2 + 13820.0i −0.878971 + 0.515285i
\(897\) 0 0
\(898\) −1850.60 + 3205.33i −0.0687697 + 0.119113i
\(899\) −3329.56 + 5766.96i −0.123523 + 0.213948i
\(900\) 0 0
\(901\) −20186.6 + 11654.7i −0.746408 + 0.430939i
\(902\) −4059.48 7031.23i −0.149851 0.259550i
\(903\) 0 0
\(904\) 3736.83 6472.38i 0.137484 0.238128i
\(905\) 946.900i 0.0347801i
\(906\) 0 0
\(907\) 30813.7 1.12806 0.564031 0.825753i \(-0.309250\pi\)
0.564031 + 0.825753i \(0.309250\pi\)
\(908\) −13275.1 22993.2i −0.485188 0.840370i
\(909\) 0 0
\(910\) −268.224 + 1.78082i −0.00977091 + 6.48719e-5i
\(911\) 10135.1 5851.50i 0.368595 0.212809i −0.304249 0.952592i \(-0.598406\pi\)
0.672845 + 0.739784i \(0.265072\pi\)
\(912\) 0 0
\(913\) 33892.3 19567.7i 1.22856 0.709307i
\(914\) 7838.89 4525.79i 0.283684 0.163785i
\(915\) 0 0
\(916\) 21620.6 12482.7i 0.779875 0.450261i
\(917\) 8733.98 15362.3i 0.314527 0.553227i
\(918\) 0 0
\(919\) 9866.32 + 17089.0i 0.354146 + 0.613398i 0.986971 0.160896i \(-0.0514384\pi\)
−0.632826 + 0.774294i \(0.718105\pi\)
\(920\) −593.543 −0.0212701
\(921\) 0 0
\(922\) 6898.22i 0.246400i
\(923\) 25375.5 43951.7i 0.904924 1.56737i
\(924\) 0 0
\(925\) 15454.9 + 26768.6i 0.549354 + 0.951510i
\(926\) 18722.6 10809.5i 0.664430 0.383609i
\(927\) 0 0
\(928\) 5865.72 10159.7i 0.207491 0.359385i
\(929\) 8592.29 14882.3i 0.303449 0.525589i −0.673466 0.739218i \(-0.735195\pi\)
0.976915 + 0.213629i \(0.0685285\pi\)
\(930\) 0 0
\(931\) 13437.8 + 7522.22i 0.473047 + 0.264802i
\(932\) −28101.6 16224.5i −0.987660 0.570226i
\(933\) 0 0
\(934\) 10540.3i 0.369261i
\(935\) 377.473 + 217.934i 0.0132029 + 0.00762269i
\(936\) 0 0
\(937\) 16777.3i 0.584940i −0.956275 0.292470i \(-0.905523\pi\)
0.956275 0.292470i \(-0.0944772\pi\)
\(938\) −14060.6 7993.90i −0.489440 0.278262i
\(939\) 0 0
\(940\) 919.606 0.0319088
\(941\) −4512.78 7816.36i −0.156336 0.270782i 0.777209 0.629243i \(-0.216635\pi\)
−0.933545 + 0.358461i \(0.883302\pi\)
\(942\) 0 0
\(943\) −29705.8 17150.7i −1.02583 0.592262i
\(944\) 18588.5 0.640893
\(945\) 0 0
\(946\) 4385.01 0.150707
\(947\) 49093.6 + 28344.2i 1.68461 + 0.972611i 0.958525 + 0.285009i \(0.0919967\pi\)
0.726088 + 0.687602i \(0.241337\pi\)
\(948\) 0 0
\(949\) 3321.18 + 5752.45i 0.113604 + 0.196768i
\(950\) 6464.59 0.220778
\(951\) 0 0
\(952\) −16336.9 + 9577.32i −0.556180 + 0.326053i
\(953\) 2869.91i 0.0975503i −0.998810 0.0487751i \(-0.984468\pi\)
0.998810 0.0487751i \(-0.0155318\pi\)
\(954\) 0 0
\(955\) 423.338 + 244.414i 0.0143444 + 0.00828173i
\(956\) 30771.9i 1.04104i
\(957\) 0 0
\(958\) 40.6077 + 23.4448i 0.00136949 + 0.000790677i
\(959\) −22250.8 12650.3i −0.749234 0.425963i
\(960\) 0 0
\(961\) −9999.34 + 17319.4i −0.335650 + 0.581362i
\(962\) −6522.13 + 11296.7i −0.218588 + 0.378606i
\(963\) 0 0
\(964\) −5462.30 + 3153.66i −0.182499 + 0.105366i
\(965\) −68.5615 118.752i −0.00228712 0.00396141i
\(966\) 0 0
\(967\) −20201.6 + 34990.2i −0.671810 + 1.16361i 0.305580 + 0.952166i \(0.401150\pi\)
−0.977390 + 0.211443i \(0.932184\pi\)
\(968\) 10865.3i 0.360767i
\(969\) 0 0
\(970\) −52.9837 −0.00175382
\(971\) 15681.9 + 27161.9i 0.518288 + 0.897701i 0.999774 + 0.0212472i \(0.00676372\pi\)
−0.481486 + 0.876454i \(0.659903\pi\)
\(972\) 0 0
\(973\) 50264.7 29467.0i 1.65613 0.970884i
\(974\) 10967.1 6331.84i 0.360788 0.208301i
\(975\) 0 0
\(976\) −6425.39 + 3709.70i −0.210729 + 0.121665i
\(977\) 20718.0 11961.5i 0.678430 0.391692i −0.120833 0.992673i \(-0.538557\pi\)
0.799263 + 0.600981i \(0.205223\pi\)
\(978\) 0 0
\(979\) −6599.09 + 3809.99i −0.215432 + 0.124380i
\(980\) 307.070 548.555i 0.0100092 0.0178805i
\(981\) 0 0
\(982\) 1485.81 + 2573.49i 0.0482831 + 0.0836288i
\(983\) 39291.6 1.27488 0.637440 0.770500i \(-0.279993\pi\)
0.637440 + 0.770500i \(0.279993\pi\)
\(984\) 0 0
\(985\) 1190.50i 0.0385100i
\(986\) 2344.97 4061.61i 0.0757394 0.131184i
\(987\) 0 0
\(988\) −6850.61 11865.6i −0.220594 0.382080i
\(989\) 16044.0 9263.00i 0.515844 0.297822i
\(990\) 0 0
\(991\) 12281.2 21271.6i 0.393667 0.681852i −0.599263 0.800552i \(-0.704539\pi\)
0.992930 + 0.118700i \(0.0378728\pi\)
\(992\) −8625.63 + 14940.0i −0.276073 + 0.478172i
\(993\) 0 0
\(994\) −11977.9 20431.9i −0.382209 0.651971i
\(995\) 391.906 + 226.267i 0.0124867 + 0.00720919i
\(996\) 0 0
\(997\) 10337.6i 0.328379i −0.986429 0.164190i \(-0.947499\pi\)
0.986429 0.164190i \(-0.0525009\pi\)
\(998\) −1094.61 631.974i −0.0347187 0.0200449i
\(999\) 0 0
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 189.4.s.a.17.13 44
3.2 odd 2 63.4.s.a.59.10 yes 44
7.5 odd 6 189.4.i.a.152.10 44
9.2 odd 6 189.4.i.a.143.13 44
9.7 even 3 63.4.i.a.38.10 yes 44
21.5 even 6 63.4.i.a.5.13 44
63.47 even 6 inner 189.4.s.a.89.13 44
63.61 odd 6 63.4.s.a.47.10 yes 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.i.a.5.13 44 21.5 even 6
63.4.i.a.38.10 yes 44 9.7 even 3
63.4.s.a.47.10 yes 44 63.61 odd 6
63.4.s.a.59.10 yes 44 3.2 odd 2
189.4.i.a.143.13 44 9.2 odd 6
189.4.i.a.152.10 44 7.5 odd 6
189.4.s.a.17.13 44 1.1 even 1 trivial
189.4.s.a.89.13 44 63.47 even 6 inner