Properties

Label 324.3.j.a.19.4
Level $324$
Weight $3$
Character 324.19
Analytic conductor $8.828$
Analytic rank $0$
Dimension $204$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [324,3,Mod(19,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 16]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.j (of order \(18\), degree \(6\), 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: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(34\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 19.4
Character \(\chi\) \(=\) 324.19
Dual form 324.3.j.a.307.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.91833 - 0.565700i) q^{2} +(3.35997 + 2.17040i) q^{4} +(1.66005 + 9.41462i) q^{5} +(4.14643 - 4.94152i) q^{7} +(-5.21773 - 6.06427i) q^{8} +O(q^{10})\) \(q+(-1.91833 - 0.565700i) q^{2} +(3.35997 + 2.17040i) q^{4} +(1.66005 + 9.41462i) q^{5} +(4.14643 - 4.94152i) q^{7} +(-5.21773 - 6.06427i) q^{8} +(2.14133 - 18.9994i) q^{10} +(9.17297 + 1.61744i) q^{11} +(13.9635 + 5.08231i) q^{13} +(-10.7496 + 7.13382i) q^{14} +(6.57875 + 14.5849i) q^{16} +(-2.55788 - 4.43037i) q^{17} +(-10.2181 - 5.89945i) q^{19} +(-14.8557 + 35.2358i) q^{20} +(-16.6818 - 8.29194i) q^{22} +(0.496108 + 0.591239i) q^{23} +(-62.3870 + 22.7070i) q^{25} +(-23.9116 - 17.6487i) q^{26} +(24.6569 - 7.60395i) q^{28} +(-11.5797 + 4.21465i) q^{29} +(34.5346 + 41.1567i) q^{31} +(-4.36951 - 31.7003i) q^{32} +(2.40058 + 9.94590i) q^{34} +(53.4058 + 30.8339i) q^{35} +(11.8651 + 20.5510i) q^{37} +(16.2644 + 17.0975i) q^{38} +(48.4311 - 59.1899i) q^{40} +(-14.0864 - 5.12705i) q^{41} +(37.1520 + 6.55091i) q^{43} +(27.3104 + 25.3436i) q^{44} +(-0.617234 - 1.41484i) q^{46} +(-8.14341 + 9.70494i) q^{47} +(1.28300 + 7.27625i) q^{49} +(132.524 - 8.26716i) q^{50} +(35.8863 + 47.3828i) q^{52} +44.1869 q^{53} +89.0451i q^{55} +(-51.6016 + 0.638447i) q^{56} +(24.5978 - 1.53447i) q^{58} +(-24.6079 + 4.33904i) q^{59} +(-50.4986 - 42.3734i) q^{61} +(-42.9663 - 98.4884i) q^{62} +(-9.55069 + 63.2834i) q^{64} +(-24.6678 + 139.898i) q^{65} +(-0.545347 + 1.49833i) q^{67} +(1.02129 - 20.4375i) q^{68} +(-85.0072 - 89.3612i) q^{70} +(6.96921 - 4.02368i) q^{71} +(-11.0385 + 19.1193i) q^{73} +(-11.1355 - 46.1356i) q^{74} +(-21.5285 - 41.9994i) q^{76} +(46.0277 - 38.6218i) q^{77} +(-35.5509 - 97.6752i) q^{79} +(-126.390 + 86.1482i) q^{80} +(24.1221 + 17.8041i) q^{82} +(3.74244 + 10.2823i) q^{83} +(37.4640 - 31.4361i) q^{85} +(-67.5639 - 33.5837i) q^{86} +(-38.0535 - 64.0667i) q^{88} +(-59.2666 + 102.653i) q^{89} +(83.0131 - 47.9276i) q^{91} +(0.383684 + 3.06329i) q^{92} +(21.1118 - 14.0105i) q^{94} +(38.5784 - 105.993i) q^{95} +(-6.45300 + 36.5968i) q^{97} +(1.65496 - 14.6840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.91833 0.565700i −0.959164 0.282850i
\(3\) 0 0
\(4\) 3.35997 + 2.17040i 0.839992 + 0.542599i
\(5\) 1.66005 + 9.41462i 0.332010 + 1.88292i 0.454962 + 0.890511i \(0.349653\pi\)
−0.122952 + 0.992413i \(0.539236\pi\)
\(6\) 0 0
\(7\) 4.14643 4.94152i 0.592347 0.705932i −0.383708 0.923454i \(-0.625353\pi\)
0.976055 + 0.217523i \(0.0697976\pi\)
\(8\) −5.21773 6.06427i −0.652216 0.758033i
\(9\) 0 0
\(10\) 2.14133 18.9994i 0.214133 1.89994i
\(11\) 9.17297 + 1.61744i 0.833907 + 0.147040i 0.574270 0.818666i \(-0.305286\pi\)
0.259637 + 0.965706i \(0.416397\pi\)
\(12\) 0 0
\(13\) 13.9635 + 5.08231i 1.07412 + 0.390947i 0.817715 0.575624i \(-0.195241\pi\)
0.256402 + 0.966570i \(0.417463\pi\)
\(14\) −10.7496 + 7.13382i −0.767831 + 0.509559i
\(15\) 0 0
\(16\) 6.57875 + 14.5849i 0.411172 + 0.911558i
\(17\) −2.55788 4.43037i −0.150463 0.260610i 0.780935 0.624613i \(-0.214743\pi\)
−0.931398 + 0.364003i \(0.881410\pi\)
\(18\) 0 0
\(19\) −10.2181 5.89945i −0.537797 0.310497i 0.206389 0.978470i \(-0.433829\pi\)
−0.744186 + 0.667973i \(0.767162\pi\)
\(20\) −14.8557 + 35.2358i −0.742787 + 1.76179i
\(21\) 0 0
\(22\) −16.6818 8.29194i −0.758263 0.376906i
\(23\) 0.496108 + 0.591239i 0.0215699 + 0.0257060i 0.776722 0.629844i \(-0.216881\pi\)
−0.755152 + 0.655550i \(0.772437\pi\)
\(24\) 0 0
\(25\) −62.3870 + 22.7070i −2.49548 + 0.908280i
\(26\) −23.9116 17.6487i −0.919675 0.678796i
\(27\) 0 0
\(28\) 24.6569 7.60395i 0.880605 0.271570i
\(29\) −11.5797 + 4.21465i −0.399298 + 0.145333i −0.533861 0.845572i \(-0.679259\pi\)
0.134562 + 0.990905i \(0.457037\pi\)
\(30\) 0 0
\(31\) 34.5346 + 41.1567i 1.11402 + 1.32764i 0.939331 + 0.343013i \(0.111448\pi\)
0.174689 + 0.984624i \(0.444108\pi\)
\(32\) −4.36951 31.7003i −0.136547 0.990634i
\(33\) 0 0
\(34\) 2.40058 + 9.94590i 0.0706054 + 0.292526i
\(35\) 53.4058 + 30.8339i 1.52588 + 0.880968i
\(36\) 0 0
\(37\) 11.8651 + 20.5510i 0.320678 + 0.555431i 0.980628 0.195878i \(-0.0627558\pi\)
−0.659950 + 0.751310i \(0.729422\pi\)
\(38\) 16.2644 + 17.0975i 0.428011 + 0.449934i
\(39\) 0 0
\(40\) 48.4311 59.1899i 1.21078 1.47975i
\(41\) −14.0864 5.12705i −0.343572 0.125050i 0.164471 0.986382i \(-0.447408\pi\)
−0.508042 + 0.861332i \(0.669631\pi\)
\(42\) 0 0
\(43\) 37.1520 + 6.55091i 0.864001 + 0.152347i 0.588049 0.808825i \(-0.299896\pi\)
0.275951 + 0.961172i \(0.411007\pi\)
\(44\) 27.3104 + 25.3436i 0.620691 + 0.575990i
\(45\) 0 0
\(46\) −0.617234 1.41484i −0.0134181 0.0307574i
\(47\) −8.14341 + 9.70494i −0.173264 + 0.206488i −0.845687 0.533679i \(-0.820809\pi\)
0.672423 + 0.740167i \(0.265254\pi\)
\(48\) 0 0
\(49\) 1.28300 + 7.27625i 0.0261836 + 0.148495i
\(50\) 132.524 8.26716i 2.65048 0.165343i
\(51\) 0 0
\(52\) 35.8863 + 47.3828i 0.690122 + 0.911207i
\(53\) 44.1869 0.833715 0.416858 0.908972i \(-0.363131\pi\)
0.416858 + 0.908972i \(0.363131\pi\)
\(54\) 0 0
\(55\) 89.0451i 1.61900i
\(56\) −51.6016 + 0.638447i −0.921458 + 0.0114008i
\(57\) 0 0
\(58\) 24.5978 1.53447i 0.424100 0.0264564i
\(59\) −24.6079 + 4.33904i −0.417083 + 0.0735430i −0.378252 0.925703i \(-0.623475\pi\)
−0.0388313 + 0.999246i \(0.512363\pi\)
\(60\) 0 0
\(61\) −50.4986 42.3734i −0.827847 0.694646i 0.126949 0.991909i \(-0.459482\pi\)
−0.954795 + 0.297263i \(0.903926\pi\)
\(62\) −42.9663 98.4884i −0.693005 1.58852i
\(63\) 0 0
\(64\) −9.55069 + 63.2834i −0.149229 + 0.988803i
\(65\) −24.6678 + 139.898i −0.379505 + 2.15228i
\(66\) 0 0
\(67\) −0.545347 + 1.49833i −0.00813951 + 0.0223631i −0.943696 0.330814i \(-0.892677\pi\)
0.935556 + 0.353177i \(0.114899\pi\)
\(68\) 1.02129 20.4375i 0.0150189 0.300552i
\(69\) 0 0
\(70\) −85.0072 89.3612i −1.21439 1.27659i
\(71\) 6.96921 4.02368i 0.0981579 0.0566715i −0.450117 0.892969i \(-0.648618\pi\)
0.548275 + 0.836298i \(0.315285\pi\)
\(72\) 0 0
\(73\) −11.0385 + 19.1193i −0.151213 + 0.261908i −0.931674 0.363296i \(-0.881651\pi\)
0.780461 + 0.625205i \(0.214985\pi\)
\(74\) −11.1355 46.1356i −0.150479 0.623454i
\(75\) 0 0
\(76\) −21.5285 41.9994i −0.283269 0.552623i
\(77\) 46.0277 38.6218i 0.597762 0.501582i
\(78\) 0 0
\(79\) −35.5509 97.6752i −0.450011 1.23639i −0.932716 0.360612i \(-0.882568\pi\)
0.482705 0.875783i \(-0.339654\pi\)
\(80\) −126.390 + 86.1482i −1.57988 + 1.07685i
\(81\) 0 0
\(82\) 24.1221 + 17.8041i 0.294171 + 0.217123i
\(83\) 3.74244 + 10.2823i 0.0450896 + 0.123883i 0.960194 0.279335i \(-0.0901140\pi\)
−0.915104 + 0.403218i \(0.867892\pi\)
\(84\) 0 0
\(85\) 37.4640 31.4361i 0.440754 0.369836i
\(86\) −67.5639 33.5837i −0.785627 0.390508i
\(87\) 0 0
\(88\) −38.0535 64.0667i −0.432426 0.728031i
\(89\) −59.2666 + 102.653i −0.665916 + 1.15340i 0.313119 + 0.949714i \(0.398626\pi\)
−0.979036 + 0.203687i \(0.934707\pi\)
\(90\) 0 0
\(91\) 83.0131 47.9276i 0.912232 0.526677i
\(92\) 0.383684 + 3.06329i 0.00417048 + 0.0332967i
\(93\) 0 0
\(94\) 21.1118 14.0105i 0.224594 0.149048i
\(95\) 38.5784 105.993i 0.406088 1.11572i
\(96\) 0 0
\(97\) −6.45300 + 36.5968i −0.0665257 + 0.377286i 0.933308 + 0.359076i \(0.116908\pi\)
−0.999834 + 0.0182105i \(0.994203\pi\)
\(98\) 1.65496 14.6840i 0.0168874 0.149837i
\(99\) 0 0
\(100\) −258.901 59.1097i −2.58901 0.591097i
\(101\) 116.941 + 98.1248i 1.15783 + 0.971533i 0.999873 0.0159135i \(-0.00506564\pi\)
0.157954 + 0.987446i \(0.449510\pi\)
\(102\) 0 0
\(103\) −111.688 + 19.6935i −1.08435 + 0.191199i −0.687136 0.726528i \(-0.741133\pi\)
−0.397210 + 0.917728i \(0.630021\pi\)
\(104\) −42.0374 111.197i −0.404205 1.06920i
\(105\) 0 0
\(106\) −84.7650 24.9965i −0.799670 0.235816i
\(107\) 187.221i 1.74973i −0.484368 0.874864i \(-0.660951\pi\)
0.484368 0.874864i \(-0.339049\pi\)
\(108\) 0 0
\(109\) 73.3509 0.672944 0.336472 0.941693i \(-0.390766\pi\)
0.336472 + 0.941693i \(0.390766\pi\)
\(110\) 50.3728 170.818i 0.457935 1.55289i
\(111\) 0 0
\(112\) 99.3500 + 27.9663i 0.887054 + 0.249699i
\(113\) −0.634025 3.59573i −0.00561084 0.0318207i 0.981874 0.189536i \(-0.0606983\pi\)
−0.987485 + 0.157715i \(0.949587\pi\)
\(114\) 0 0
\(115\) −4.74272 + 5.65216i −0.0412411 + 0.0491492i
\(116\) −48.0547 10.9714i −0.414265 0.0945807i
\(117\) 0 0
\(118\) 49.6606 + 5.59699i 0.420853 + 0.0474321i
\(119\) −32.4988 5.73042i −0.273099 0.0481548i
\(120\) 0 0
\(121\) −32.1755 11.7109i −0.265913 0.0967844i
\(122\) 72.9023 + 109.853i 0.597560 + 0.900436i
\(123\) 0 0
\(124\) 26.7087 + 213.239i 0.215392 + 1.71967i
\(125\) −197.845 342.678i −1.58276 2.74142i
\(126\) 0 0
\(127\) 74.4569 + 42.9877i 0.586274 + 0.338486i 0.763623 0.645662i \(-0.223419\pi\)
−0.177349 + 0.984148i \(0.556752\pi\)
\(128\) 54.1208 115.995i 0.422818 0.906214i
\(129\) 0 0
\(130\) 126.461 254.416i 0.972780 1.95705i
\(131\) −26.9506 32.1185i −0.205730 0.245179i 0.653307 0.757093i \(-0.273381\pi\)
−0.859037 + 0.511914i \(0.828937\pi\)
\(132\) 0 0
\(133\) −71.5210 + 26.0315i −0.537752 + 0.195726i
\(134\) 1.89376 2.56578i 0.0141325 0.0191476i
\(135\) 0 0
\(136\) −13.5207 + 38.6281i −0.0994166 + 0.284030i
\(137\) 164.469 59.8617i 1.20050 0.436947i 0.337102 0.941468i \(-0.390553\pi\)
0.863399 + 0.504521i \(0.168331\pi\)
\(138\) 0 0
\(139\) −162.043 193.116i −1.16578 1.38932i −0.905799 0.423707i \(-0.860729\pi\)
−0.259980 0.965614i \(-0.583716\pi\)
\(140\) 112.520 + 219.513i 0.803715 + 1.56795i
\(141\) 0 0
\(142\) −15.6454 + 3.77625i −0.110179 + 0.0265933i
\(143\) 119.867 + 69.2051i 0.838229 + 0.483951i
\(144\) 0 0
\(145\) −58.9021 102.021i −0.406222 0.703596i
\(146\) 31.9914 30.4326i 0.219119 0.208443i
\(147\) 0 0
\(148\) −4.73739 + 94.8025i −0.0320094 + 0.640557i
\(149\) −22.1608 8.06587i −0.148730 0.0541333i 0.266582 0.963812i \(-0.414106\pi\)
−0.415313 + 0.909679i \(0.636328\pi\)
\(150\) 0 0
\(151\) −137.784 24.2951i −0.912480 0.160895i −0.302351 0.953197i \(-0.597771\pi\)
−0.610129 + 0.792302i \(0.708882\pi\)
\(152\) 17.5396 + 92.7472i 0.115392 + 0.610179i
\(153\) 0 0
\(154\) −110.145 + 48.0515i −0.715225 + 0.312023i
\(155\) −330.146 + 393.452i −2.12997 + 2.53840i
\(156\) 0 0
\(157\) 27.2412 + 154.492i 0.173511 + 0.984028i 0.939849 + 0.341591i \(0.110966\pi\)
−0.766338 + 0.642437i \(0.777923\pi\)
\(158\) 12.9434 + 207.484i 0.0819200 + 1.31319i
\(159\) 0 0
\(160\) 291.192 93.7614i 1.81995 0.586009i
\(161\) 4.97870 0.0309236
\(162\) 0 0
\(163\) 61.6254i 0.378070i 0.981970 + 0.189035i \(0.0605359\pi\)
−0.981970 + 0.189035i \(0.939464\pi\)
\(164\) −36.2023 47.7999i −0.220746 0.291463i
\(165\) 0 0
\(166\) −1.36255 21.8418i −0.00820811 0.131577i
\(167\) 164.986 29.0915i 0.987940 0.174200i 0.343746 0.939063i \(-0.388304\pi\)
0.644194 + 0.764862i \(0.277193\pi\)
\(168\) 0 0
\(169\) 39.6886 + 33.3027i 0.234844 + 0.197057i
\(170\) −89.6517 + 39.1113i −0.527363 + 0.230066i
\(171\) 0 0
\(172\) 110.612 + 102.645i 0.643090 + 0.596776i
\(173\) 25.9331 147.074i 0.149902 0.850138i −0.813397 0.581709i \(-0.802384\pi\)
0.963299 0.268429i \(-0.0865046\pi\)
\(174\) 0 0
\(175\) −146.476 + 402.439i −0.837005 + 2.29965i
\(176\) 36.7564 + 144.428i 0.208843 + 0.820613i
\(177\) 0 0
\(178\) 171.763 163.394i 0.964963 0.917947i
\(179\) 30.5538 17.6403i 0.170692 0.0985490i −0.412220 0.911084i \(-0.635247\pi\)
0.582912 + 0.812535i \(0.301913\pi\)
\(180\) 0 0
\(181\) 35.0639 60.7325i 0.193723 0.335539i −0.752758 0.658298i \(-0.771277\pi\)
0.946481 + 0.322759i \(0.104610\pi\)
\(182\) −186.359 + 44.9804i −1.02395 + 0.247145i
\(183\) 0 0
\(184\) 0.996874 6.09345i 0.00541779 0.0331166i
\(185\) −173.783 + 145.821i −0.939366 + 0.788222i
\(186\) 0 0
\(187\) −16.2975 44.7769i −0.0871522 0.239449i
\(188\) −48.4252 + 14.9338i −0.257581 + 0.0794353i
\(189\) 0 0
\(190\) −133.966 + 181.506i −0.705086 + 0.955295i
\(191\) −105.068 288.671i −0.550092 1.51137i −0.833585 0.552391i \(-0.813716\pi\)
0.283493 0.958974i \(-0.408507\pi\)
\(192\) 0 0
\(193\) 129.962 109.051i 0.673379 0.565032i −0.240685 0.970603i \(-0.577372\pi\)
0.914063 + 0.405572i \(0.132928\pi\)
\(194\) 33.0818 66.5541i 0.170525 0.343063i
\(195\) 0 0
\(196\) −11.4815 + 27.2326i −0.0585791 + 0.138942i
\(197\) 77.3014 133.890i 0.392393 0.679644i −0.600372 0.799721i \(-0.704981\pi\)
0.992765 + 0.120077i \(0.0383141\pi\)
\(198\) 0 0
\(199\) 183.949 106.203i 0.924364 0.533682i 0.0393397 0.999226i \(-0.487475\pi\)
0.885025 + 0.465544i \(0.154141\pi\)
\(200\) 463.219 + 259.852i 2.31610 + 1.29926i
\(201\) 0 0
\(202\) −168.821 254.389i −0.835749 1.25935i
\(203\) −27.1874 + 74.6969i −0.133928 + 0.367965i
\(204\) 0 0
\(205\) 24.8850 141.130i 0.121390 0.688437i
\(206\) 225.394 + 25.4030i 1.09415 + 0.123316i
\(207\) 0 0
\(208\) 17.7375 + 237.092i 0.0852765 + 1.13987i
\(209\) −84.1887 70.6427i −0.402817 0.338003i
\(210\) 0 0
\(211\) 302.621 53.3602i 1.43422 0.252892i 0.598094 0.801426i \(-0.295925\pi\)
0.836128 + 0.548534i \(0.184814\pi\)
\(212\) 148.467 + 95.9031i 0.700314 + 0.452373i
\(213\) 0 0
\(214\) −105.911 + 359.151i −0.494911 + 1.67828i
\(215\) 360.647i 1.67743i
\(216\) 0 0
\(217\) 346.572 1.59711
\(218\) −140.711 41.4946i −0.645464 0.190342i
\(219\) 0 0
\(220\) −193.263 + 299.189i −0.878469 + 1.35995i
\(221\) −13.2005 74.8635i −0.0597306 0.338749i
\(222\) 0 0
\(223\) 266.463 317.558i 1.19490 1.42403i 0.314851 0.949141i \(-0.398045\pi\)
0.880048 0.474884i \(-0.157510\pi\)
\(224\) −174.765 109.851i −0.780203 0.490406i
\(225\) 0 0
\(226\) −0.817839 + 7.25647i −0.00361876 + 0.0321083i
\(227\) 342.743 + 60.4349i 1.50988 + 0.266233i 0.866448 0.499268i \(-0.166398\pi\)
0.643435 + 0.765501i \(0.277509\pi\)
\(228\) 0 0
\(229\) −155.459 56.5825i −0.678861 0.247085i −0.0205025 0.999790i \(-0.506527\pi\)
−0.658358 + 0.752705i \(0.728749\pi\)
\(230\) 12.2955 8.15973i 0.0534588 0.0354771i
\(231\) 0 0
\(232\) 85.9782 + 48.2312i 0.370596 + 0.207893i
\(233\) 141.020 + 244.253i 0.605234 + 1.04830i 0.992014 + 0.126125i \(0.0402539\pi\)
−0.386780 + 0.922172i \(0.626413\pi\)
\(234\) 0 0
\(235\) −104.887 60.5564i −0.446327 0.257687i
\(236\) −92.0991 38.8299i −0.390251 0.164533i
\(237\) 0 0
\(238\) 59.1017 + 29.3774i 0.248327 + 0.123435i
\(239\) −229.840 273.912i −0.961672 1.14608i −0.989217 0.146455i \(-0.953214\pi\)
0.0275453 0.999621i \(-0.491231\pi\)
\(240\) 0 0
\(241\) 213.563 77.7307i 0.886154 0.322534i 0.141464 0.989943i \(-0.454819\pi\)
0.744691 + 0.667410i \(0.232597\pi\)
\(242\) 55.0983 + 40.6671i 0.227679 + 0.168046i
\(243\) 0 0
\(244\) −77.7067 251.975i −0.318470 1.03269i
\(245\) −66.3732 + 24.1579i −0.270911 + 0.0986036i
\(246\) 0 0
\(247\) −112.698 134.309i −0.456269 0.543760i
\(248\) 69.3934 424.172i 0.279812 1.71037i
\(249\) 0 0
\(250\) 185.679 + 769.289i 0.742716 + 3.07716i
\(251\) 102.959 + 59.4435i 0.410196 + 0.236827i 0.690874 0.722975i \(-0.257226\pi\)
−0.280678 + 0.959802i \(0.590559\pi\)
\(252\) 0 0
\(253\) 3.59449 + 6.22584i 0.0142075 + 0.0246081i
\(254\) −118.515 124.585i −0.466593 0.490491i
\(255\) 0 0
\(256\) −169.440 + 191.901i −0.661875 + 0.749614i
\(257\) −73.6502 26.8065i −0.286577 0.104305i 0.194732 0.980856i \(-0.437616\pi\)
−0.481309 + 0.876551i \(0.659838\pi\)
\(258\) 0 0
\(259\) 150.751 + 26.5814i 0.582049 + 0.102631i
\(260\) −386.517 + 416.514i −1.48661 + 1.60198i
\(261\) 0 0
\(262\) 33.5307 + 76.8598i 0.127980 + 0.293358i
\(263\) −27.2928 + 32.5263i −0.103775 + 0.123674i −0.815432 0.578853i \(-0.803501\pi\)
0.711657 + 0.702527i \(0.247945\pi\)
\(264\) 0 0
\(265\) 73.3525 + 416.003i 0.276802 + 1.56982i
\(266\) 151.927 9.47756i 0.571154 0.0356299i
\(267\) 0 0
\(268\) −5.08432 + 3.85072i −0.0189713 + 0.0143683i
\(269\) 120.901 0.449446 0.224723 0.974423i \(-0.427852\pi\)
0.224723 + 0.974423i \(0.427852\pi\)
\(270\) 0 0
\(271\) 167.365i 0.617583i 0.951130 + 0.308791i \(0.0999245\pi\)
−0.951130 + 0.308791i \(0.900076\pi\)
\(272\) 47.7890 66.4527i 0.175695 0.244312i
\(273\) 0 0
\(274\) −349.369 + 21.7944i −1.27507 + 0.0795418i
\(275\) −609.001 + 107.383i −2.21455 + 0.390485i
\(276\) 0 0
\(277\) −263.128 220.791i −0.949921 0.797079i 0.0293630 0.999569i \(-0.490652\pi\)
−0.979284 + 0.202490i \(0.935097\pi\)
\(278\) 201.607 + 462.127i 0.725204 + 1.66233i
\(279\) 0 0
\(280\) −91.6721 484.750i −0.327400 1.73125i
\(281\) −14.0638 + 79.7600i −0.0500493 + 0.283843i −0.999552 0.0299138i \(-0.990477\pi\)
0.949503 + 0.313757i \(0.101588\pi\)
\(282\) 0 0
\(283\) 4.57602 12.5725i 0.0161697 0.0444259i −0.931345 0.364138i \(-0.881364\pi\)
0.947515 + 0.319712i \(0.103586\pi\)
\(284\) 32.1493 + 1.60654i 0.113202 + 0.00565683i
\(285\) 0 0
\(286\) −190.794 200.567i −0.667113 0.701282i
\(287\) −83.7439 + 48.3495i −0.291790 + 0.168465i
\(288\) 0 0
\(289\) 131.415 227.617i 0.454722 0.787601i
\(290\) 55.2801 + 229.032i 0.190621 + 0.789764i
\(291\) 0 0
\(292\) −78.5857 + 40.2823i −0.269129 + 0.137953i
\(293\) −200.462 + 168.207i −0.684169 + 0.574086i −0.917221 0.398378i \(-0.869573\pi\)
0.233052 + 0.972464i \(0.425129\pi\)
\(294\) 0 0
\(295\) −81.7007 224.471i −0.276952 0.760918i
\(296\) 62.7177 179.182i 0.211884 0.605346i
\(297\) 0 0
\(298\) 37.9488 + 28.0093i 0.127345 + 0.0939911i
\(299\) 3.92256 + 10.7771i 0.0131189 + 0.0360440i
\(300\) 0 0
\(301\) 186.420 156.425i 0.619334 0.519683i
\(302\) 250.572 + 124.551i 0.829709 + 0.412420i
\(303\) 0 0
\(304\) 18.8204 187.842i 0.0619091 0.617901i
\(305\) 315.099 545.767i 1.03311 1.78940i
\(306\) 0 0
\(307\) −219.994 + 127.014i −0.716594 + 0.413726i −0.813498 0.581568i \(-0.802439\pi\)
0.0969039 + 0.995294i \(0.469106\pi\)
\(308\) 238.476 29.8697i 0.774274 0.0969795i
\(309\) 0 0
\(310\) 855.904 568.007i 2.76098 1.83228i
\(311\) 55.4547 152.361i 0.178311 0.489905i −0.818049 0.575148i \(-0.804944\pi\)
0.996360 + 0.0852429i \(0.0271666\pi\)
\(312\) 0 0
\(313\) −40.4452 + 229.376i −0.129218 + 0.732832i 0.849495 + 0.527597i \(0.176907\pi\)
−0.978713 + 0.205235i \(0.934204\pi\)
\(314\) 35.1388 311.777i 0.111907 0.992922i
\(315\) 0 0
\(316\) 92.5442 405.345i 0.292862 1.28274i
\(317\) −333.357 279.720i −1.05160 0.882397i −0.0583393 0.998297i \(-0.518581\pi\)
−0.993261 + 0.115899i \(0.963025\pi\)
\(318\) 0 0
\(319\) −113.037 + 19.9314i −0.354347 + 0.0624810i
\(320\) −611.643 + 15.1376i −1.91139 + 0.0473049i
\(321\) 0 0
\(322\) −9.55077 2.81645i −0.0296608 0.00874674i
\(323\) 60.3602i 0.186874i
\(324\) 0 0
\(325\) −986.545 −3.03552
\(326\) 34.8615 118.218i 0.106937 0.362631i
\(327\) 0 0
\(328\) 42.4074 + 112.176i 0.129291 + 0.341999i
\(329\) 14.1911 + 80.4817i 0.0431340 + 0.244625i
\(330\) 0 0
\(331\) −158.081 + 188.393i −0.477585 + 0.569164i −0.950015 0.312204i \(-0.898933\pi\)
0.472430 + 0.881368i \(0.343377\pi\)
\(332\) −9.74212 + 42.6706i −0.0293437 + 0.128526i
\(333\) 0 0
\(334\) −332.954 37.5256i −0.996869 0.112352i
\(335\) −15.0115 2.64693i −0.0448104 0.00790129i
\(336\) 0 0
\(337\) 155.225 + 56.4972i 0.460607 + 0.167647i 0.561893 0.827210i \(-0.310073\pi\)
−0.101285 + 0.994857i \(0.532296\pi\)
\(338\) −57.2964 86.3373i −0.169516 0.255436i
\(339\) 0 0
\(340\) 194.107 24.3123i 0.570902 0.0715067i
\(341\) 250.216 + 433.387i 0.733772 + 1.27093i
\(342\) 0 0
\(343\) 315.013 + 181.873i 0.918404 + 0.530241i
\(344\) −154.123 259.481i −0.448031 0.754304i
\(345\) 0 0
\(346\) −132.948 + 267.466i −0.384243 + 0.773022i
\(347\) −94.9627 113.172i −0.273668 0.326145i 0.611652 0.791127i \(-0.290505\pi\)
−0.885320 + 0.464982i \(0.846061\pi\)
\(348\) 0 0
\(349\) −195.978 + 71.3303i −0.561542 + 0.204385i −0.607167 0.794574i \(-0.707694\pi\)
0.0456250 + 0.998959i \(0.485472\pi\)
\(350\) 508.649 689.149i 1.45328 1.96900i
\(351\) 0 0
\(352\) 11.1919 297.853i 0.0317953 0.846174i
\(353\) 192.471 70.0538i 0.545244 0.198453i −0.0546879 0.998503i \(-0.517416\pi\)
0.599932 + 0.800051i \(0.295194\pi\)
\(354\) 0 0
\(355\) 49.4506 + 58.9330i 0.139298 + 0.166008i
\(356\) −421.931 + 216.278i −1.18520 + 0.607522i
\(357\) 0 0
\(358\) −68.5914 + 16.5555i −0.191596 + 0.0462445i
\(359\) −311.659 179.936i −0.868130 0.501215i −0.00140384 0.999999i \(-0.500447\pi\)
−0.866726 + 0.498784i \(0.833780\pi\)
\(360\) 0 0
\(361\) −110.893 192.072i −0.307183 0.532057i
\(362\) −101.621 + 96.6693i −0.280720 + 0.267042i
\(363\) 0 0
\(364\) 382.943 + 19.1361i 1.05204 + 0.0525718i
\(365\) −198.326 72.1846i −0.543358 0.197766i
\(366\) 0 0
\(367\) −519.619 91.6229i −1.41586 0.249654i −0.587214 0.809432i \(-0.699775\pi\)
−0.828642 + 0.559778i \(0.810886\pi\)
\(368\) −5.35940 + 11.1253i −0.0145636 + 0.0302318i
\(369\) 0 0
\(370\) 415.863 181.424i 1.12395 0.490334i
\(371\) 183.218 218.351i 0.493849 0.588546i
\(372\) 0 0
\(373\) 58.2221 + 330.194i 0.156091 + 0.885238i 0.957781 + 0.287498i \(0.0928234\pi\)
−0.801690 + 0.597740i \(0.796065\pi\)
\(374\) 5.93358 + 95.1163i 0.0158652 + 0.254322i
\(375\) 0 0
\(376\) 101.343 1.25388i 0.269530 0.00333479i
\(377\) −183.113 −0.485711
\(378\) 0 0
\(379\) 471.750i 1.24472i −0.782730 0.622362i \(-0.786173\pi\)
0.782730 0.622362i \(-0.213827\pi\)
\(380\) 359.670 272.403i 0.946499 0.716851i
\(381\) 0 0
\(382\) 38.2530 + 613.202i 0.100139 + 1.60524i
\(383\) 692.255 122.063i 1.80745 0.318703i 0.834728 0.550662i \(-0.185625\pi\)
0.972725 + 0.231959i \(0.0745136\pi\)
\(384\) 0 0
\(385\) 440.018 + 369.219i 1.14290 + 0.959011i
\(386\) −311.000 + 135.676i −0.805700 + 0.351493i
\(387\) 0 0
\(388\) −101.111 + 108.958i −0.260596 + 0.280820i
\(389\) −34.0255 + 192.968i −0.0874691 + 0.496062i 0.909327 + 0.416082i \(0.136597\pi\)
−0.996796 + 0.0799805i \(0.974514\pi\)
\(390\) 0 0
\(391\) 1.35042 3.71026i 0.00345377 0.00948915i
\(392\) 37.4308 45.7459i 0.0954867 0.116699i
\(393\) 0 0
\(394\) −224.031 + 213.115i −0.568606 + 0.540902i
\(395\) 860.558 496.844i 2.17863 1.25783i
\(396\) 0 0
\(397\) 213.100 369.100i 0.536775 0.929722i −0.462300 0.886724i \(-0.652976\pi\)
0.999075 0.0429986i \(-0.0136911\pi\)
\(398\) −412.953 + 99.6720i −1.03757 + 0.250432i
\(399\) 0 0
\(400\) −741.608 760.525i −1.85402 1.90131i
\(401\) 29.6819 24.9061i 0.0740198 0.0621100i −0.605027 0.796205i \(-0.706838\pi\)
0.679047 + 0.734095i \(0.262393\pi\)
\(402\) 0 0
\(403\) 273.054 + 750.208i 0.677552 + 1.86156i
\(404\) 179.947 + 583.504i 0.445413 + 1.44432i
\(405\) 0 0
\(406\) 94.4104 127.913i 0.232538 0.315057i
\(407\) 75.5983 + 207.704i 0.185745 + 0.510330i
\(408\) 0 0
\(409\) −155.781 + 130.715i −0.380882 + 0.319598i −0.813048 0.582196i \(-0.802194\pi\)
0.432167 + 0.901794i \(0.357749\pi\)
\(410\) −127.575 + 256.656i −0.311158 + 0.625989i
\(411\) 0 0
\(412\) −418.010 176.237i −1.01459 0.427759i
\(413\) −80.5934 + 139.592i −0.195141 + 0.337995i
\(414\) 0 0
\(415\) −90.5909 + 52.3027i −0.218291 + 0.126031i
\(416\) 100.097 464.855i 0.240617 1.11744i
\(417\) 0 0
\(418\) 121.539 + 183.141i 0.290763 + 0.438138i
\(419\) −44.1415 + 121.278i −0.105350 + 0.289445i −0.981156 0.193217i \(-0.938108\pi\)
0.875807 + 0.482662i \(0.160330\pi\)
\(420\) 0 0
\(421\) −29.2736 + 166.019i −0.0695335 + 0.394344i 0.930101 + 0.367304i \(0.119719\pi\)
−0.999634 + 0.0270398i \(0.991392\pi\)
\(422\) −610.712 68.8302i −1.44718 0.163105i
\(423\) 0 0
\(424\) −230.555 267.961i −0.543762 0.631984i
\(425\) 260.178 + 218.316i 0.612185 + 0.513684i
\(426\) 0 0
\(427\) −418.778 + 73.8419i −0.980745 + 0.172932i
\(428\) 406.344 629.056i 0.949401 1.46976i
\(429\) 0 0
\(430\) 204.018 691.839i 0.474461 1.60893i
\(431\) 80.4167i 0.186582i −0.995639 0.0932909i \(-0.970261\pi\)
0.995639 0.0932909i \(-0.0297387\pi\)
\(432\) 0 0
\(433\) 794.373 1.83458 0.917289 0.398221i \(-0.130372\pi\)
0.917289 + 0.398221i \(0.130372\pi\)
\(434\) −664.839 196.056i −1.53189 0.451742i
\(435\) 0 0
\(436\) 246.457 + 159.201i 0.565267 + 0.365139i
\(437\) −1.58132 8.96812i −0.00361859 0.0205220i
\(438\) 0 0
\(439\) −102.084 + 121.659i −0.232537 + 0.277127i −0.869677 0.493621i \(-0.835673\pi\)
0.637140 + 0.770748i \(0.280117\pi\)
\(440\) 539.993 464.613i 1.22726 1.05594i
\(441\) 0 0
\(442\) −17.0275 + 151.080i −0.0385237 + 0.341811i
\(443\) 293.648 + 51.7781i 0.662863 + 0.116881i 0.494950 0.868921i \(-0.335186\pi\)
0.167913 + 0.985802i \(0.446297\pi\)
\(444\) 0 0
\(445\) −1064.82 387.563i −2.39286 0.870929i
\(446\) −690.805 + 458.442i −1.54889 + 1.02790i
\(447\) 0 0
\(448\) 273.115 + 309.595i 0.609631 + 0.691060i
\(449\) 357.658 + 619.482i 0.796566 + 1.37969i 0.921840 + 0.387571i \(0.126686\pi\)
−0.125274 + 0.992122i \(0.539981\pi\)
\(450\) 0 0
\(451\) −120.922 69.8143i −0.268120 0.154799i
\(452\) 5.67387 13.4576i 0.0125528 0.0297735i
\(453\) 0 0
\(454\) −623.306 309.824i −1.37292 0.682431i
\(455\) 589.026 + 701.974i 1.29456 + 1.54280i
\(456\) 0 0
\(457\) 325.010 118.294i 0.711182 0.258849i 0.0390042 0.999239i \(-0.487581\pi\)
0.672177 + 0.740390i \(0.265359\pi\)
\(458\) 266.213 + 196.487i 0.581251 + 0.429011i
\(459\) 0 0
\(460\) −28.2028 + 8.69746i −0.0613105 + 0.0189075i
\(461\) 97.9219 35.6407i 0.212412 0.0773116i −0.233623 0.972327i \(-0.575058\pi\)
0.446035 + 0.895016i \(0.352836\pi\)
\(462\) 0 0
\(463\) −124.607 148.501i −0.269130 0.320736i 0.614505 0.788913i \(-0.289356\pi\)
−0.883635 + 0.468176i \(0.844911\pi\)
\(464\) −137.650 141.161i −0.296660 0.304227i
\(465\) 0 0
\(466\) −132.348 548.332i −0.284008 1.17668i
\(467\) −486.781 281.043i −1.04236 0.601806i −0.121858 0.992548i \(-0.538885\pi\)
−0.920500 + 0.390742i \(0.872218\pi\)
\(468\) 0 0
\(469\) 5.14278 + 8.90756i 0.0109654 + 0.0189927i
\(470\) 166.951 + 175.502i 0.355214 + 0.373408i
\(471\) 0 0
\(472\) 154.710 + 126.589i 0.327776 + 0.268197i
\(473\) 330.199 + 120.183i 0.698095 + 0.254086i
\(474\) 0 0
\(475\) 771.437 + 136.025i 1.62408 + 0.286369i
\(476\) −96.7577 89.7894i −0.203272 0.188633i
\(477\) 0 0
\(478\) 285.956 + 655.474i 0.598234 + 1.37128i
\(479\) −256.804 + 306.047i −0.536125 + 0.638929i −0.964314 0.264760i \(-0.914707\pi\)
0.428189 + 0.903689i \(0.359152\pi\)
\(480\) 0 0
\(481\) 61.2323 + 347.266i 0.127302 + 0.721966i
\(482\) −453.657 + 28.3002i −0.941196 + 0.0587141i
\(483\) 0 0
\(484\) −82.6912 109.182i −0.170850 0.225582i
\(485\) −355.257 −0.732488
\(486\) 0 0
\(487\) 213.387i 0.438167i −0.975706 0.219083i \(-0.929693\pi\)
0.975706 0.219083i \(-0.0703067\pi\)
\(488\) 6.52445 + 527.330i 0.0133698 + 1.08059i
\(489\) 0 0
\(490\) 140.992 8.79540i 0.287738 0.0179498i
\(491\) 279.504 49.2840i 0.569254 0.100375i 0.118389 0.992967i \(-0.462227\pi\)
0.450865 + 0.892592i \(0.351116\pi\)
\(492\) 0 0
\(493\) 48.2918 + 40.5216i 0.0979549 + 0.0821939i
\(494\) 140.214 + 321.402i 0.283834 + 0.650611i
\(495\) 0 0
\(496\) −373.073 + 774.445i −0.752164 + 1.56138i
\(497\) 9.01426 51.1224i 0.0181373 0.102862i
\(498\) 0 0
\(499\) 54.6097 150.039i 0.109438 0.300679i −0.872869 0.487954i \(-0.837743\pi\)
0.982308 + 0.187275i \(0.0599655\pi\)
\(500\) 78.9938 1580.79i 0.157988 3.16158i
\(501\) 0 0
\(502\) −163.882 172.276i −0.326459 0.343180i
\(503\) −793.165 + 457.934i −1.57687 + 0.910405i −0.581575 + 0.813493i \(0.697563\pi\)
−0.995293 + 0.0969126i \(0.969103\pi\)
\(504\) 0 0
\(505\) −729.680 + 1263.84i −1.44491 + 2.50266i
\(506\) −3.37346 13.9766i −0.00666691 0.0276218i
\(507\) 0 0
\(508\) 156.872 + 306.038i 0.308804 + 0.602437i
\(509\) 664.450 557.540i 1.30540 1.09536i 0.316218 0.948687i \(-0.397587\pi\)
0.989185 0.146676i \(-0.0468575\pi\)
\(510\) 0 0
\(511\) 48.7080 + 133.824i 0.0953190 + 0.261887i
\(512\) 433.600 272.277i 0.846875 0.531792i
\(513\) 0 0
\(514\) 126.121 + 93.0876i 0.245371 + 0.181104i
\(515\) −370.814 1018.80i −0.720028 1.97826i
\(516\) 0 0
\(517\) −90.3965 + 75.8517i −0.174848 + 0.146715i
\(518\) −274.152 136.272i −0.529252 0.263073i
\(519\) 0 0
\(520\) 977.089 580.358i 1.87902 1.11607i
\(521\) −467.837 + 810.317i −0.897959 + 1.55531i −0.0678599 + 0.997695i \(0.521617\pi\)
−0.830099 + 0.557616i \(0.811716\pi\)
\(522\) 0 0
\(523\) −74.4213 + 42.9672i −0.142297 + 0.0821552i −0.569458 0.822020i \(-0.692847\pi\)
0.427161 + 0.904175i \(0.359514\pi\)
\(524\) −20.8433 166.411i −0.0397773 0.317577i
\(525\) 0 0
\(526\) 70.7566 46.9565i 0.134518 0.0892710i
\(527\) 94.0044 258.275i 0.178376 0.490085i
\(528\) 0 0
\(529\) 91.7564 520.377i 0.173453 0.983699i
\(530\) 94.6186 839.526i 0.178526 1.58401i
\(531\) 0 0
\(532\) −296.807 67.7640i −0.557908 0.127376i
\(533\) −170.639 143.183i −0.320149 0.268637i
\(534\) 0 0
\(535\) 1762.61 310.796i 3.29460 0.580928i
\(536\) 11.9317 4.51074i 0.0222607 0.00841555i
\(537\) 0 0
\(538\) −231.928 68.3938i −0.431093 0.127126i
\(539\) 68.8200i 0.127681i
\(540\) 0 0
\(541\) −579.648 −1.07144 −0.535719 0.844396i \(-0.679959\pi\)
−0.535719 + 0.844396i \(0.679959\pi\)
\(542\) 94.6784 321.061i 0.174683 0.592363i
\(543\) 0 0
\(544\) −129.267 + 100.444i −0.237624 + 0.184640i
\(545\) 121.766 + 690.571i 0.223424 + 1.26710i
\(546\) 0 0
\(547\) −565.910 + 674.425i −1.03457 + 1.23295i −0.0625529 + 0.998042i \(0.519924\pi\)
−0.972017 + 0.234911i \(0.924520\pi\)
\(548\) 682.533 + 155.829i 1.24550 + 0.284360i
\(549\) 0 0
\(550\) 1229.01 + 138.516i 2.23457 + 0.251846i
\(551\) 143.187 + 25.2477i 0.259867 + 0.0458215i
\(552\) 0 0
\(553\) −630.073 229.328i −1.13937 0.414698i
\(554\) 379.865 + 572.401i 0.685677 + 1.03321i
\(555\) 0 0
\(556\) −125.322 1000.56i −0.225400 1.79957i
\(557\) −429.760 744.366i −0.771562 1.33638i −0.936707 0.350115i \(-0.886143\pi\)
0.165145 0.986269i \(-0.447191\pi\)
\(558\) 0 0
\(559\) 485.479 + 280.292i 0.868478 + 0.501416i
\(560\) −98.3659 + 981.768i −0.175653 + 1.75316i
\(561\) 0 0
\(562\) 72.0993 145.050i 0.128291 0.258096i
\(563\) 411.363 + 490.243i 0.730663 + 0.870770i 0.995620 0.0934901i \(-0.0298024\pi\)
−0.264957 + 0.964260i \(0.585358\pi\)
\(564\) 0 0
\(565\) 32.8000 11.9382i 0.0580530 0.0211296i
\(566\) −15.8906 + 21.5296i −0.0280753 + 0.0380381i
\(567\) 0 0
\(568\) −60.7641 21.2687i −0.106979 0.0374449i
\(569\) −774.636 + 281.944i −1.36140 + 0.495509i −0.916487 0.400066i \(-0.868987\pi\)
−0.444912 + 0.895574i \(0.646765\pi\)
\(570\) 0 0
\(571\) −272.247 324.452i −0.476791 0.568217i 0.473016 0.881054i \(-0.343165\pi\)
−0.949807 + 0.312837i \(0.898721\pi\)
\(572\) 252.546 + 492.685i 0.441513 + 0.861337i
\(573\) 0 0
\(574\) 188.000 45.3764i 0.327525 0.0790529i
\(575\) −44.3759 25.6205i −0.0771755 0.0445573i
\(576\) 0 0
\(577\) 239.288 + 414.459i 0.414711 + 0.718301i 0.995398 0.0958263i \(-0.0305493\pi\)
−0.580687 + 0.814127i \(0.697216\pi\)
\(578\) −380.859 + 362.302i −0.658926 + 0.626821i
\(579\) 0 0
\(580\) 23.5179 470.630i 0.0405482 0.811431i
\(581\) 66.3277 + 24.1413i 0.114161 + 0.0415513i
\(582\) 0 0
\(583\) 405.325 + 71.4698i 0.695241 + 0.122590i
\(584\) 173.541 32.8187i 0.297159 0.0561964i
\(585\) 0 0
\(586\) 479.706 209.276i 0.818611 0.357126i
\(587\) −52.1927 + 62.2008i −0.0889143 + 0.105964i −0.808667 0.588266i \(-0.799811\pi\)
0.719753 + 0.694230i \(0.244255\pi\)
\(588\) 0 0
\(589\) −110.077 624.280i −0.186889 1.05990i
\(590\) 29.7456 + 476.827i 0.0504163 + 0.808181i
\(591\) 0 0
\(592\) −221.677 + 308.251i −0.374454 + 0.520695i
\(593\) −656.393 −1.10690 −0.553451 0.832881i \(-0.686690\pi\)
−0.553451 + 0.832881i \(0.686690\pi\)
\(594\) 0 0
\(595\) 315.477i 0.530213i
\(596\) −56.9534 75.1988i −0.0955594 0.126172i
\(597\) 0 0
\(598\) −1.42813 22.8931i −0.00238817 0.0382828i
\(599\) −1106.16 + 195.046i −1.84668 + 0.325619i −0.983727 0.179672i \(-0.942496\pi\)
−0.862949 + 0.505291i \(0.831385\pi\)
\(600\) 0 0
\(601\) −354.566 297.517i −0.589961 0.495036i 0.298240 0.954491i \(-0.403600\pi\)
−0.888201 + 0.459455i \(0.848045\pi\)
\(602\) −446.104 + 194.616i −0.741036 + 0.323283i
\(603\) 0 0
\(604\) −410.221 380.678i −0.679174 0.630261i
\(605\) 56.8409 322.361i 0.0939518 0.532827i
\(606\) 0 0
\(607\) −167.587 + 460.442i −0.276091 + 0.758554i 0.721705 + 0.692201i \(0.243359\pi\)
−0.997796 + 0.0663532i \(0.978864\pi\)
\(608\) −142.366 + 349.696i −0.234154 + 0.575157i
\(609\) 0 0
\(610\) −913.204 + 868.710i −1.49706 + 1.42411i
\(611\) −163.034 + 94.1278i −0.266832 + 0.154055i
\(612\) 0 0
\(613\) 175.664 304.259i 0.286564 0.496344i −0.686423 0.727202i \(-0.740820\pi\)
0.972987 + 0.230859i \(0.0741535\pi\)
\(614\) 493.873 119.203i 0.804353 0.194142i
\(615\) 0 0
\(616\) −474.373 77.6062i −0.770086 0.125984i
\(617\) −108.589 + 91.1174i −0.175996 + 0.147678i −0.726530 0.687134i \(-0.758868\pi\)
0.550535 + 0.834812i \(0.314424\pi\)
\(618\) 0 0
\(619\) −244.984 673.088i −0.395774 1.08738i −0.964323 0.264730i \(-0.914717\pi\)
0.568549 0.822650i \(-0.307505\pi\)
\(620\) −1963.23 + 605.440i −3.16650 + 0.976516i
\(621\) 0 0
\(622\) −192.571 + 260.907i −0.309599 + 0.419464i
\(623\) 261.516 + 718.509i 0.419769 + 1.15331i
\(624\) 0 0
\(625\) 1626.29 1364.62i 2.60206 2.18339i
\(626\) 207.345 417.139i 0.331223 0.666356i
\(627\) 0 0
\(628\) −243.780 + 578.213i −0.388185 + 0.920722i
\(629\) 60.6989 105.134i 0.0965006 0.167144i
\(630\) 0 0
\(631\) −912.443 + 526.799i −1.44603 + 0.834864i −0.998242 0.0592769i \(-0.981121\pi\)
−0.447785 + 0.894141i \(0.647787\pi\)
\(632\) −406.834 + 725.232i −0.643725 + 1.14752i
\(633\) 0 0
\(634\) 481.251 + 725.175i 0.759071 + 1.14381i
\(635\) −281.110 + 772.345i −0.442694 + 1.21629i
\(636\) 0 0
\(637\) −19.0649 + 108.123i −0.0299293 + 0.169737i
\(638\) 228.117 + 25.7099i 0.357550 + 0.0402976i
\(639\) 0 0
\(640\) 1181.90 + 316.968i 1.84671 + 0.495262i
\(641\) 496.119 + 416.293i 0.773977 + 0.649444i 0.941724 0.336386i \(-0.109205\pi\)
−0.167747 + 0.985830i \(0.553649\pi\)
\(642\) 0 0
\(643\) 876.872 154.616i 1.36372 0.240461i 0.556567 0.830802i \(-0.312118\pi\)
0.807153 + 0.590342i \(0.201007\pi\)
\(644\) 16.7283 + 10.8057i 0.0259755 + 0.0167791i
\(645\) 0 0
\(646\) 34.1458 115.791i 0.0528572 0.179243i
\(647\) 337.800i 0.522102i 0.965325 + 0.261051i \(0.0840691\pi\)
−0.965325 + 0.261051i \(0.915931\pi\)
\(648\) 0 0
\(649\) −232.746 −0.358622
\(650\) 1892.52 + 558.089i 2.91157 + 0.858598i
\(651\) 0 0
\(652\) −133.752 + 207.059i −0.205140 + 0.317575i
\(653\) −77.4104 439.016i −0.118546 0.672307i −0.984933 0.172935i \(-0.944675\pi\)
0.866387 0.499372i \(-0.166436\pi\)
\(654\) 0 0
\(655\) 257.644 307.048i 0.393349 0.468776i
\(656\) −17.8937 239.179i −0.0272769 0.364603i
\(657\) 0 0
\(658\) 18.3053 162.418i 0.0278196 0.246836i
\(659\) −18.1969 3.20861i −0.0276129 0.00486890i 0.159825 0.987145i \(-0.448907\pi\)
−0.187438 + 0.982277i \(0.560018\pi\)
\(660\) 0 0
\(661\) 218.906 + 79.6751i 0.331173 + 0.120537i 0.502255 0.864720i \(-0.332504\pi\)
−0.171082 + 0.985257i \(0.554726\pi\)
\(662\) 409.825 271.974i 0.619071 0.410837i
\(663\) 0 0
\(664\) 42.8274 76.3451i 0.0644990 0.114978i
\(665\) −363.805 630.129i −0.547076 0.947563i
\(666\) 0 0
\(667\) −8.23662 4.75542i −0.0123488 0.00712956i
\(668\) 617.487 + 260.339i 0.924382 + 0.389728i
\(669\) 0 0
\(670\) 27.2996 + 13.5697i 0.0407457 + 0.0202533i
\(671\) −394.686 470.369i −0.588206 0.700997i
\(672\) 0 0
\(673\) −502.586 + 182.927i −0.746785 + 0.271808i −0.687252 0.726419i \(-0.741183\pi\)
−0.0595329 + 0.998226i \(0.518961\pi\)
\(674\) −265.811 196.191i −0.394379 0.291084i
\(675\) 0 0
\(676\) 61.0723 + 198.036i 0.0903436 + 0.292952i
\(677\) 747.713 272.145i 1.10445 0.401987i 0.275495 0.961302i \(-0.411158\pi\)
0.828955 + 0.559315i \(0.188936\pi\)
\(678\) 0 0
\(679\) 154.087 + 183.633i 0.226932 + 0.270447i
\(680\) −386.114 63.1672i −0.567814 0.0928930i
\(681\) 0 0
\(682\) −234.830 972.927i −0.344325 1.42658i
\(683\) 510.054 + 294.480i 0.746785 + 0.431156i 0.824531 0.565817i \(-0.191439\pi\)
−0.0777464 + 0.996973i \(0.524772\pi\)
\(684\) 0 0
\(685\) 836.602 + 1449.04i 1.22132 + 2.11538i
\(686\) −501.412 527.094i −0.730921 0.768359i
\(687\) 0 0
\(688\) 148.870 + 584.956i 0.216380 + 0.850227i
\(689\) 617.005 + 224.571i 0.895508 + 0.325938i
\(690\) 0 0
\(691\) −761.202 134.220i −1.10159 0.194241i −0.406848 0.913496i \(-0.633372\pi\)
−0.694746 + 0.719255i \(0.744483\pi\)
\(692\) 406.343 437.878i 0.587201 0.632772i
\(693\) 0 0
\(694\) 118.148 + 270.822i 0.170242 + 0.390233i
\(695\) 1549.11 1846.16i 2.22894 2.65634i
\(696\) 0 0
\(697\) 13.3167 + 75.5225i 0.0191057 + 0.108354i
\(698\) 416.302 25.9699i 0.596422 0.0372062i
\(699\) 0 0
\(700\) −1365.61 + 1034.27i −1.95087 + 1.47753i
\(701\) 766.488 1.09342 0.546710 0.837322i \(-0.315880\pi\)
0.546710 + 0.837322i \(0.315880\pi\)
\(702\) 0 0
\(703\) 279.990i 0.398279i
\(704\) −189.965 + 565.049i −0.269837 + 0.802626i
\(705\) 0 0
\(706\) −408.853 + 25.5052i −0.579111 + 0.0361263i
\(707\) 969.772 170.997i 1.37167 0.241863i
\(708\) 0 0
\(709\) 850.957 + 714.038i 1.20022 + 1.00711i 0.999624 + 0.0274323i \(0.00873306\pi\)
0.200598 + 0.979674i \(0.435711\pi\)
\(710\) −61.5241 141.027i −0.0866537 0.198630i
\(711\) 0 0
\(712\) 931.750 176.205i 1.30864 0.247479i
\(713\) −7.20056 + 40.8364i −0.0100990 + 0.0572740i
\(714\) 0 0
\(715\) −452.554 + 1243.38i −0.632943 + 1.73900i
\(716\) 140.946 + 7.04325i 0.196852 + 0.00983695i
\(717\) 0 0
\(718\) 496.074 + 521.482i 0.690911 + 0.726298i
\(719\) −540.075 + 311.812i −0.751148 + 0.433675i −0.826108 0.563511i \(-0.809450\pi\)
0.0749608 + 0.997186i \(0.476117\pi\)
\(720\) 0 0
\(721\) −365.789 + 633.565i −0.507335 + 0.878731i
\(722\) 104.074 + 431.190i 0.144147 + 0.597216i
\(723\) 0 0
\(724\) 249.627 127.957i 0.344789 0.176736i
\(725\) 626.717 525.878i 0.864438 0.725349i
\(726\) 0 0
\(727\) −133.681 367.285i −0.183880 0.505206i 0.813165 0.582034i \(-0.197743\pi\)
−0.997044 + 0.0768283i \(0.975521\pi\)
\(728\) −723.785 253.340i −0.994211 0.347995i
\(729\) 0 0
\(730\) 339.619 + 250.667i 0.465231 + 0.343379i
\(731\) −66.0073 181.354i −0.0902973 0.248090i
\(732\) 0 0
\(733\) 874.224 733.561i 1.19267 1.00077i 0.192856 0.981227i \(-0.438225\pi\)
0.999809 0.0195380i \(-0.00621954\pi\)
\(734\) 944.969 + 469.711i 1.28742 + 0.639934i
\(735\) 0 0
\(736\) 16.5747 18.3102i 0.0225199 0.0248780i
\(737\) −7.42592 + 12.8621i −0.0100759 + 0.0174519i
\(738\) 0 0
\(739\) 97.0676 56.0420i 0.131350 0.0758349i −0.432885 0.901449i \(-0.642504\pi\)
0.564235 + 0.825614i \(0.309171\pi\)
\(740\) −900.394 + 112.776i −1.21675 + 0.152400i
\(741\) 0 0
\(742\) −474.993 + 315.222i −0.640152 + 0.424827i
\(743\) −242.050 + 665.027i −0.325774 + 0.895056i 0.663394 + 0.748270i \(0.269115\pi\)
−0.989168 + 0.146786i \(0.953107\pi\)
\(744\) 0 0
\(745\) 39.1490 222.025i 0.0525490 0.298020i
\(746\) 75.1016 666.356i 0.100672 0.893239i
\(747\) 0 0
\(748\) 42.4247 185.821i 0.0567176 0.248424i
\(749\) −925.156 776.298i −1.23519 1.03645i
\(750\) 0 0
\(751\) 251.989 44.4325i 0.335538 0.0591645i −0.00334065 0.999994i \(-0.501063\pi\)
0.338879 + 0.940830i \(0.389952\pi\)
\(752\) −195.119 54.9246i −0.259467 0.0730381i
\(753\) 0 0
\(754\) 351.271 + 103.587i 0.465876 + 0.137383i
\(755\) 1337.52i 1.77155i
\(756\) 0 0
\(757\) 384.164 0.507483 0.253741 0.967272i \(-0.418339\pi\)
0.253741 + 0.967272i \(0.418339\pi\)
\(758\) −266.869 + 904.972i −0.352070 + 1.19389i
\(759\) 0 0
\(760\) −844.063 + 319.094i −1.11061 + 0.419861i
\(761\) −146.561 831.191i −0.192591 1.09224i −0.915808 0.401615i \(-0.868449\pi\)
0.723218 0.690620i \(-0.242662\pi\)
\(762\) 0 0
\(763\) 304.144 362.465i 0.398616 0.475052i
\(764\) 273.507 1197.96i 0.357993 1.56801i
\(765\) 0 0
\(766\) −1397.02 157.451i −1.82379 0.205550i
\(767\) −365.665 64.4766i −0.476747 0.0840634i
\(768\) 0 0
\(769\) −371.992 135.394i −0.483735 0.176065i 0.0886291 0.996065i \(-0.471751\pi\)
−0.572364 + 0.820000i \(0.693974\pi\)
\(770\) −635.232 957.202i −0.824977 1.24312i
\(771\) 0 0
\(772\) 673.352 84.3388i 0.872218 0.109247i
\(773\) 74.6477 + 129.294i 0.0965688 + 0.167262i 0.910262 0.414032i \(-0.135880\pi\)
−0.813693 + 0.581294i \(0.802547\pi\)
\(774\) 0 0
\(775\) −3089.05 1783.47i −3.98588 2.30125i
\(776\) 255.603 151.819i 0.329385 0.195643i
\(777\) 0 0
\(778\) 174.434 350.928i 0.224208 0.451064i
\(779\) 113.691 + 135.491i 0.145944 + 0.173930i
\(780\) 0 0
\(781\) 70.4365 25.6368i 0.0901875 0.0328256i
\(782\) −4.68945 + 6.35356i −0.00599674 + 0.00812476i
\(783\) 0 0
\(784\) −97.6830 + 66.5811i −0.124596 + 0.0849248i
\(785\) −1409.26 + 512.931i −1.79524 + 0.653415i
\(786\) 0 0
\(787\) −883.158 1052.51i −1.12218 1.33737i −0.934839 0.355071i \(-0.884457\pi\)
−0.187343 0.982295i \(-0.559988\pi\)
\(788\) 550.324 282.091i 0.698381 0.357983i
\(789\) 0 0
\(790\) −1931.90 + 466.291i −2.44544 + 0.590242i
\(791\) −20.3973 11.7764i −0.0257868 0.0148880i
\(792\) 0 0
\(793\) −489.784 848.331i −0.617635 1.06977i
\(794\) −617.595 + 587.504i −0.777828 + 0.739929i
\(795\) 0 0
\(796\) 848.563 + 42.4037i 1.06603 + 0.0532710i
\(797\) −264.891 96.4123i −0.332360 0.120969i 0.170450 0.985366i \(-0.445478\pi\)
−0.502809 + 0.864397i \(0.667700\pi\)
\(798\) 0 0
\(799\) 63.8263 + 11.2543i 0.0798828 + 0.0140855i
\(800\) 992.419 + 1878.46i 1.24052 + 2.34808i
\(801\) 0 0
\(802\) −71.0291 + 30.9870i −0.0885649 + 0.0386371i
\(803\) −132.181 + 157.527i −0.164609 + 0.196173i
\(804\) 0 0
\(805\) 8.26489 + 46.8725i 0.0102669 + 0.0582267i
\(806\) −99.4133 1593.61i −0.123342 1.97719i
\(807\) 0 0
\(808\) −15.1088 1221.15i −0.0186990 1.51132i
\(809\) 1048.06 1.29550 0.647749 0.761854i \(-0.275711\pi\)
0.647749 + 0.761854i \(0.275711\pi\)
\(810\) 0 0
\(811\) 750.843i 0.925824i 0.886404 + 0.462912i \(0.153195\pi\)
−0.886404 + 0.462912i \(0.846805\pi\)
\(812\) −253.471 + 191.971i −0.312156 + 0.236418i
\(813\) 0 0
\(814\) −27.5238 441.211i −0.0338130 0.542029i
\(815\) −580.179 + 102.301i −0.711876 + 0.125523i
\(816\) 0 0
\(817\) −340.978 286.114i −0.417354 0.350201i
\(818\) 372.784 162.630i 0.455726 0.198814i
\(819\) 0 0
\(820\) 389.920 420.181i 0.475512 0.512416i
\(821\) 102.983 584.044i 0.125436 0.711382i −0.855612 0.517617i \(-0.826819\pi\)
0.981048 0.193764i \(-0.0620697\pi\)
\(822\) 0 0
\(823\) 461.497 1267.95i 0.560750 1.54065i −0.257791 0.966201i \(-0.582995\pi\)
0.818541 0.574448i \(-0.194783\pi\)
\(824\) 702.182 + 574.548i 0.852163 + 0.697267i
\(825\) 0 0
\(826\) 233.572 222.191i 0.282775 0.268997i
\(827\) −771.784 + 445.590i −0.933233 + 0.538803i −0.887833 0.460166i \(-0.847790\pi\)
−0.0454007 + 0.998969i \(0.514456\pi\)
\(828\) 0 0
\(829\) 440.587 763.119i 0.531468 0.920529i −0.467857 0.883804i \(-0.654974\pi\)
0.999325 0.0367255i \(-0.0116927\pi\)
\(830\) 203.371 49.0864i 0.245025 0.0591403i
\(831\) 0 0
\(832\) −454.987 + 835.119i −0.546859 + 1.00375i
\(833\) 28.9547 24.2959i 0.0347596 0.0291667i
\(834\) 0 0
\(835\) 547.770 + 1504.99i 0.656012 + 1.80238i
\(836\) −129.549 420.080i −0.154962 0.502488i
\(837\) 0 0
\(838\) 153.285 207.680i 0.182917 0.247828i
\(839\) 381.014 + 1046.83i 0.454129 + 1.24771i 0.929793 + 0.368082i \(0.119985\pi\)
−0.475665 + 0.879627i \(0.657792\pi\)
\(840\) 0 0
\(841\) −527.918 + 442.976i −0.627727 + 0.526725i
\(842\) 150.073 301.919i 0.178234 0.358573i
\(843\) 0 0
\(844\) 1132.61 + 477.519i 1.34195 + 0.565780i
\(845\) −247.647 + 428.937i −0.293073 + 0.507618i
\(846\) 0 0
\(847\) −191.283 + 110.437i −0.225836 + 0.130386i
\(848\) 290.695 + 644.463i 0.342800 + 0.759980i
\(849\) 0 0
\(850\) −375.607 565.984i −0.441890 0.665864i
\(851\) −6.26415 + 17.2106i −0.00736092 + 0.0202240i
\(852\) 0 0
\(853\) 143.568 814.212i 0.168309 0.954528i −0.777278 0.629158i \(-0.783400\pi\)
0.945587 0.325370i \(-0.105489\pi\)
\(854\) 845.126 + 95.2499i 0.989609 + 0.111534i
\(855\) 0 0
\(856\) −1135.36 + 976.867i −1.32635 + 1.14120i
\(857\) −178.468 149.753i −0.208248 0.174741i 0.532698 0.846305i \(-0.321178\pi\)
−0.740946 + 0.671565i \(0.765623\pi\)
\(858\) 0 0
\(859\) −573.273 + 101.083i −0.667372 + 0.117676i −0.497062 0.867715i \(-0.665588\pi\)
−0.170310 + 0.985391i \(0.554477\pi\)
\(860\) −782.747 + 1211.76i −0.910171 + 1.40903i
\(861\) 0 0
\(862\) −45.4918 + 154.266i −0.0527747 + 0.178963i
\(863\) 972.167i 1.12650i −0.826288 0.563248i \(-0.809551\pi\)
0.826288 0.563248i \(-0.190449\pi\)
\(864\) 0 0
\(865\) 1427.70 1.65051
\(866\) −1523.87 449.377i −1.75966 0.518911i
\(867\) 0 0
\(868\) 1164.47 + 752.199i 1.34156 + 0.866589i
\(869\) −168.123 953.474i −0.193467 1.09721i
\(870\) 0 0
\(871\) −15.2299 + 18.1503i −0.0174856 + 0.0208385i
\(872\) −382.725 444.819i −0.438905 0.510114i
\(873\) 0 0
\(874\) −2.03977 + 18.0984i −0.00233384 + 0.0207075i
\(875\) −2513.70 443.233i −2.87280 0.506552i
\(876\) 0 0
\(877\) −929.589 338.343i −1.05996 0.385795i −0.247549 0.968875i \(-0.579625\pi\)
−0.812415 + 0.583080i \(0.801847\pi\)
\(878\) 264.653 175.633i 0.301427 0.200037i
\(879\) 0 0
\(880\) −1298.72 + 585.806i −1.47581 + 0.665688i
\(881\) −162.043 280.667i −0.183931 0.318578i 0.759285 0.650759i \(-0.225549\pi\)
−0.943216 + 0.332181i \(0.892216\pi\)
\(882\) 0 0
\(883\) 638.603 + 368.697i 0.723219 + 0.417551i 0.815936 0.578142i \(-0.196222\pi\)
−0.0927172 + 0.995692i \(0.529555\pi\)
\(884\) 118.130 280.189i 0.133632 0.316956i
\(885\) 0 0
\(886\) −534.023 265.444i −0.602735 0.299599i
\(887\) −539.552 643.013i −0.608289 0.724930i 0.370721 0.928744i \(-0.379111\pi\)
−0.979010 + 0.203814i \(0.934666\pi\)
\(888\) 0 0
\(889\) 521.155 189.685i 0.586226 0.213369i
\(890\) 1823.43 + 1345.84i 2.04880 + 1.51218i
\(891\) 0 0
\(892\) 1584.53 488.654i 1.77638 0.547818i
\(893\) 140.464 51.1248i 0.157295 0.0572506i
\(894\) 0 0
\(895\) 216.797 + 258.369i 0.242232 + 0.288680i
\(896\) −348.786 748.406i −0.389270 0.835274i
\(897\) 0 0
\(898\) −335.665 1390.70i −0.373791 1.54866i
\(899\) −573.360 331.030i −0.637775 0.368220i
\(900\) 0 0
\(901\) −113.025 195.764i −0.125444 0.217275i
\(902\) 192.474 + 202.332i 0.213386 + 0.224315i
\(903\) 0 0
\(904\) −18.4973 + 22.6065i −0.0204616 + 0.0250071i
\(905\) 629.982 + 229.295i 0.696112 + 0.253364i
\(906\) 0 0
\(907\) −61.5751 10.8574i −0.0678888 0.0119706i 0.139601 0.990208i \(-0.455418\pi\)
−0.207489 + 0.978237i \(0.566529\pi\)
\(908\) 1020.44 + 946.948i 1.12383 + 1.04289i
\(909\) 0 0
\(910\) −732.839 1679.83i −0.805317 1.84597i
\(911\) −142.414 + 169.723i −0.156327 + 0.186304i −0.838523 0.544866i \(-0.816581\pi\)
0.682196 + 0.731169i \(0.261025\pi\)
\(912\) 0 0
\(913\) 17.6983 + 100.372i 0.0193848 + 0.109937i
\(914\) −690.395 + 43.0685i −0.755355 + 0.0471209i
\(915\) 0 0
\(916\) −399.531 527.523i −0.436169 0.575899i
\(917\) −270.463 −0.294943
\(918\) 0 0
\(919\) 610.515i 0.664326i 0.943222 + 0.332163i \(0.107778\pi\)
−0.943222 + 0.332163i \(0.892222\pi\)
\(920\) 59.0224 0.730261i 0.0641548 0.000793762i
\(921\) 0 0
\(922\) −208.008 + 12.9760i −0.225605 + 0.0140738i
\(923\) 117.764 20.7650i 0.127589 0.0224973i
\(924\) 0 0
\(925\) −1206.88 1012.69i −1.30473 1.09480i
\(926\) 155.030 + 355.364i 0.167419 + 0.383762i
\(927\) 0 0
\(928\) 184.203 + 348.662i 0.198495 + 0.375714i
\(929\) −101.641 + 576.432i −0.109409 + 0.620487i 0.879959 + 0.475050i \(0.157570\pi\)
−0.989368 + 0.145437i \(0.953541\pi\)
\(930\) 0 0
\(931\) 29.8160 81.9187i 0.0320257 0.0879900i
\(932\) −56.3051 + 1126.75i −0.0604132 + 1.20896i
\(933\) 0 0
\(934\) 774.820 + 814.505i 0.829572 + 0.872061i
\(935\) 394.503 227.766i 0.421928 0.243600i
\(936\) 0 0
\(937\) 106.276 184.075i 0.113422 0.196452i −0.803726 0.594999i \(-0.797152\pi\)
0.917148 + 0.398548i \(0.130486\pi\)
\(938\) −4.82654 19.9969i −0.00514556 0.0213186i
\(939\) 0 0
\(940\) −220.985 431.114i −0.235090 0.458631i
\(941\) −277.591 + 232.926i −0.294995 + 0.247530i −0.778258 0.627945i \(-0.783896\pi\)
0.483262 + 0.875476i \(0.339452\pi\)
\(942\) 0 0
\(943\) −3.95709 10.8720i −0.00419628 0.0115292i
\(944\) −225.174 330.359i −0.238531 0.349956i
\(945\) 0 0
\(946\) −565.443 417.343i −0.597719 0.441166i
\(947\) −262.181 720.335i −0.276854 0.760650i −0.997715 0.0675697i \(-0.978475\pi\)
0.720861 0.693080i \(-0.243747\pi\)
\(948\) 0 0
\(949\) −251.307 + 210.872i −0.264813 + 0.222204i
\(950\) −1402.92 697.343i −1.47676 0.734045i
\(951\) 0 0
\(952\) 134.819 + 226.981i 0.141617 + 0.238426i
\(953\) −649.243 + 1124.52i −0.681262 + 1.17998i 0.293333 + 0.956010i \(0.405235\pi\)
−0.974596 + 0.223971i \(0.928098\pi\)
\(954\) 0 0
\(955\) 2543.31 1468.38i 2.66315 1.53757i
\(956\) −177.755 1419.18i −0.185936 1.48450i
\(957\) 0 0
\(958\) 665.765 441.825i 0.694953 0.461195i
\(959\) 386.150 1060.94i 0.402659 1.10630i
\(960\) 0 0
\(961\) −334.362 + 1896.26i −0.347932 + 1.97322i
\(962\) 78.9846 700.809i 0.0821046 0.728492i
\(963\) 0 0
\(964\) 886.272 + 202.345i 0.919369 + 0.209901i
\(965\) 1242.42 + 1042.51i 1.28748 + 1.08032i
\(966\) 0 0
\(967\) 589.937 104.022i 0.610069 0.107572i 0.139926 0.990162i \(-0.455314\pi\)
0.470143 + 0.882590i \(0.344202\pi\)
\(968\) 96.8647 + 256.225i 0.100067 + 0.264695i
\(969\) 0 0
\(970\) 681.499 + 200.969i 0.702577 + 0.207184i
\(971\) 642.416i 0.661603i 0.943700 + 0.330801i \(0.107319\pi\)
−0.943700 + 0.330801i \(0.892681\pi\)
\(972\) 0 0
\(973\) −1626.19 −1.67131
\(974\) −120.713 + 409.347i −0.123935 + 0.420274i
\(975\) 0 0
\(976\) 285.795 1015.28i 0.292822 1.04025i
\(977\) −70.1942 398.091i −0.0718466 0.407462i −0.999427 0.0338395i \(-0.989227\pi\)
0.927581 0.373623i \(-0.121885\pi\)
\(978\) 0 0
\(979\) −709.686 + 845.770i −0.724909 + 0.863912i
\(980\) −275.444 62.8866i −0.281065 0.0641700i
\(981\) 0 0
\(982\) −564.060 63.5723i −0.574399 0.0647376i
\(983\) 1233.41 + 217.483i 1.25474 + 0.221245i 0.761222 0.648491i \(-0.224600\pi\)
0.493518 + 0.869736i \(0.335711\pi\)
\(984\) 0 0
\(985\) 1388.85 + 505.499i 1.41000 + 0.513197i
\(986\) −69.7164 105.052i −0.0707063 0.106544i
\(987\) 0 0
\(988\) −87.1596 695.873i −0.0882182 0.704325i
\(989\) 14.5583 + 25.2157i 0.0147202 + 0.0254961i
\(990\) 0 0
\(991\) 1340.40 + 773.883i 1.35258 + 0.780911i 0.988610 0.150501i \(-0.0480885\pi\)
0.363968 + 0.931412i \(0.381422\pi\)
\(992\) 1153.78 1274.59i 1.16309 1.28487i
\(993\) 0 0
\(994\) −46.2122 + 92.9702i −0.0464912 + 0.0935314i
\(995\) 1305.22 + 1555.50i 1.31178 + 1.56332i
\(996\) 0 0
\(997\) 690.289 251.245i 0.692366 0.252001i 0.0282179 0.999602i \(-0.491017\pi\)
0.664148 + 0.747601i \(0.268795\pi\)
\(998\) −189.637 + 256.931i −0.190017 + 0.257446i
\(999\) 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 324.3.j.a.19.4 204
3.2 odd 2 108.3.j.a.7.31 yes 204
4.3 odd 2 inner 324.3.j.a.19.11 204
12.11 even 2 108.3.j.a.7.24 204
27.4 even 9 inner 324.3.j.a.307.11 204
27.23 odd 18 108.3.j.a.31.24 yes 204
108.23 even 18 108.3.j.a.31.31 yes 204
108.31 odd 18 inner 324.3.j.a.307.4 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.j.a.7.24 204 12.11 even 2
108.3.j.a.7.31 yes 204 3.2 odd 2
108.3.j.a.31.24 yes 204 27.23 odd 18
108.3.j.a.31.31 yes 204 108.23 even 18
324.3.j.a.19.4 204 1.1 even 1 trivial
324.3.j.a.19.11 204 4.3 odd 2 inner
324.3.j.a.307.4 204 108.31 odd 18 inner
324.3.j.a.307.11 204 27.4 even 9 inner