Properties

Label 1323.2.h.c.226.2
Level $1323$
Weight $2$
Character 1323.226
Analytic conductor $10.564$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1323,2,Mod(226,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.h (of order \(3\), 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: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.2
Root \(-0.173648 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 1323.226
Dual form 1323.2.h.c.802.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.34730 q^{2} -0.184793 q^{4} +(1.26604 + 2.19285i) q^{5} +2.94356 q^{8} +O(q^{10})\) \(q-1.34730 q^{2} -0.184793 q^{4} +(1.26604 + 2.19285i) q^{5} +2.94356 q^{8} +(-1.70574 - 2.95442i) q^{10} +(0.233956 - 0.405223i) q^{11} +(-2.91147 + 5.04282i) q^{13} -3.59627 q^{16} +(1.93969 + 3.35965i) q^{17} +(1.09240 - 1.89209i) q^{19} +(-0.233956 - 0.405223i) q^{20} +(-0.315207 + 0.545955i) q^{22} +(-0.0530334 - 0.0918566i) q^{23} +(-0.705737 + 1.22237i) q^{25} +(3.92262 - 6.79417i) q^{26} +(4.39053 + 7.60462i) q^{29} -7.68004 q^{31} -1.04189 q^{32} +(-2.61334 - 4.52644i) q^{34} +(3.84002 - 6.65111i) q^{37} +(-1.47178 + 2.54920i) q^{38} +(3.72668 + 6.45480i) q^{40} +(-1.11334 + 1.92836i) q^{41} +(-0.613341 - 1.06234i) q^{43} +(-0.0432332 + 0.0748822i) q^{44} +(0.0714517 + 0.123758i) q^{46} +5.33275 q^{47} +(0.950837 - 1.64690i) q^{50} +(0.538019 - 0.931876i) q^{52} +(-0.358441 - 0.620838i) q^{53} +1.18479 q^{55} +(-5.91534 - 10.2457i) q^{58} -0.736482 q^{59} +0.958111 q^{61} +10.3473 q^{62} +8.59627 q^{64} -14.7442 q^{65} -9.63816 q^{67} +(-0.358441 - 0.620838i) q^{68} -13.2344 q^{71} +(5.13429 + 8.89284i) q^{73} +(-5.17365 + 8.96102i) q^{74} +(-0.201867 + 0.349643i) q^{76} -12.6382 q^{79} +(-4.55303 - 7.88609i) q^{80} +(1.50000 - 2.59808i) q^{82} +(-1.36571 - 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +(0.826352 + 1.43128i) q^{86} +(0.688663 - 1.19280i) q^{88} +(-4.05690 + 7.02676i) q^{89} +(0.00980018 + 0.0169744i) q^{92} -7.18479 q^{94} +5.53209 q^{95} +(6.80200 + 11.7814i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 6 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 3 q^{26} + 9 q^{29} - 6 q^{31} - 9 q^{34} + 3 q^{37} + 6 q^{38} + 9 q^{40} + 3 q^{43} + 15 q^{44} - 6 q^{47} - 6 q^{50} + 21 q^{52} + 6 q^{53} + 9 q^{58} + 6 q^{59} + 12 q^{61} + 60 q^{62} + 24 q^{64} - 30 q^{65} - 24 q^{67} + 6 q^{68} - 18 q^{71} + 21 q^{73} - 30 q^{74} - 15 q^{76} - 42 q^{79} - 15 q^{80} + 9 q^{82} - 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} + 12 q^{89} + 3 q^{92} - 36 q^{94} + 24 q^{95} + 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34730 −0.952682 −0.476341 0.879261i \(-0.658037\pi\)
−0.476341 + 0.879261i \(0.658037\pi\)
\(3\) 0 0
\(4\) −0.184793 −0.0923963
\(5\) 1.26604 + 2.19285i 0.566192 + 0.980674i 0.996938 + 0.0782003i \(0.0249174\pi\)
−0.430745 + 0.902473i \(0.641749\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.94356 1.04071
\(9\) 0 0
\(10\) −1.70574 2.95442i −0.539401 0.934271i
\(11\) 0.233956 0.405223i 0.0705403 0.122179i −0.828598 0.559844i \(-0.810861\pi\)
0.899138 + 0.437665i \(0.144194\pi\)
\(12\) 0 0
\(13\) −2.91147 + 5.04282i −0.807498 + 1.39863i 0.107094 + 0.994249i \(0.465845\pi\)
−0.914592 + 0.404378i \(0.867488\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −3.59627 −0.899067
\(17\) 1.93969 + 3.35965i 0.470445 + 0.814834i 0.999429 0.0337978i \(-0.0107602\pi\)
−0.528984 + 0.848632i \(0.677427\pi\)
\(18\) 0 0
\(19\) 1.09240 1.89209i 0.250613 0.434074i −0.713082 0.701081i \(-0.752701\pi\)
0.963695 + 0.267007i \(0.0860345\pi\)
\(20\) −0.233956 0.405223i −0.0523141 0.0906106i
\(21\) 0 0
\(22\) −0.315207 + 0.545955i −0.0672025 + 0.116398i
\(23\) −0.0530334 0.0918566i −0.0110582 0.0191534i 0.860443 0.509546i \(-0.170187\pi\)
−0.871502 + 0.490393i \(0.836853\pi\)
\(24\) 0 0
\(25\) −0.705737 + 1.22237i −0.141147 + 0.244474i
\(26\) 3.92262 6.79417i 0.769289 1.33245i
\(27\) 0 0
\(28\) 0 0
\(29\) 4.39053 + 7.60462i 0.815301 + 1.41214i 0.909112 + 0.416552i \(0.136762\pi\)
−0.0938108 + 0.995590i \(0.529905\pi\)
\(30\) 0 0
\(31\) −7.68004 −1.37938 −0.689688 0.724106i \(-0.742252\pi\)
−0.689688 + 0.724106i \(0.742252\pi\)
\(32\) −1.04189 −0.184182
\(33\) 0 0
\(34\) −2.61334 4.52644i −0.448184 0.776278i
\(35\) 0 0
\(36\) 0 0
\(37\) 3.84002 6.65111i 0.631296 1.09344i −0.355991 0.934489i \(-0.615857\pi\)
0.987287 0.158947i \(-0.0508099\pi\)
\(38\) −1.47178 + 2.54920i −0.238754 + 0.413535i
\(39\) 0 0
\(40\) 3.72668 + 6.45480i 0.589240 + 1.02059i
\(41\) −1.11334 + 1.92836i −0.173875 + 0.301160i −0.939771 0.341804i \(-0.888962\pi\)
0.765897 + 0.642964i \(0.222295\pi\)
\(42\) 0 0
\(43\) −0.613341 1.06234i −0.0935336 0.162005i 0.815462 0.578811i \(-0.196483\pi\)
−0.908996 + 0.416806i \(0.863150\pi\)
\(44\) −0.0432332 + 0.0748822i −0.00651766 + 0.0112889i
\(45\) 0 0
\(46\) 0.0714517 + 0.123758i 0.0105350 + 0.0182471i
\(47\) 5.33275 0.777861 0.388931 0.921267i \(-0.372845\pi\)
0.388931 + 0.921267i \(0.372845\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.950837 1.64690i 0.134469 0.232907i
\(51\) 0 0
\(52\) 0.538019 0.931876i 0.0746098 0.129228i
\(53\) −0.358441 0.620838i −0.0492356 0.0852786i 0.840357 0.542033i \(-0.182345\pi\)
−0.889593 + 0.456754i \(0.849012\pi\)
\(54\) 0 0
\(55\) 1.18479 0.159757
\(56\) 0 0
\(57\) 0 0
\(58\) −5.91534 10.2457i −0.776723 1.34532i
\(59\) −0.736482 −0.0958818 −0.0479409 0.998850i \(-0.515266\pi\)
−0.0479409 + 0.998850i \(0.515266\pi\)
\(60\) 0 0
\(61\) 0.958111 0.122674 0.0613368 0.998117i \(-0.480464\pi\)
0.0613368 + 0.998117i \(0.480464\pi\)
\(62\) 10.3473 1.31411
\(63\) 0 0
\(64\) 8.59627 1.07453
\(65\) −14.7442 −1.82880
\(66\) 0 0
\(67\) −9.63816 −1.17749 −0.588744 0.808320i \(-0.700377\pi\)
−0.588744 + 0.808320i \(0.700377\pi\)
\(68\) −0.358441 0.620838i −0.0434673 0.0752876i
\(69\) 0 0
\(70\) 0 0
\(71\) −13.2344 −1.57064 −0.785318 0.619092i \(-0.787501\pi\)
−0.785318 + 0.619092i \(0.787501\pi\)
\(72\) 0 0
\(73\) 5.13429 + 8.89284i 0.600923 + 1.04083i 0.992682 + 0.120761i \(0.0385334\pi\)
−0.391759 + 0.920068i \(0.628133\pi\)
\(74\) −5.17365 + 8.96102i −0.601424 + 1.04170i
\(75\) 0 0
\(76\) −0.201867 + 0.349643i −0.0231557 + 0.0401068i
\(77\) 0 0
\(78\) 0 0
\(79\) −12.6382 −1.42190 −0.710952 0.703241i \(-0.751736\pi\)
−0.710952 + 0.703241i \(0.751736\pi\)
\(80\) −4.55303 7.88609i −0.509045 0.881691i
\(81\) 0 0
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) −1.36571 2.36549i −0.149907 0.259646i 0.781286 0.624173i \(-0.214564\pi\)
−0.931193 + 0.364527i \(0.881231\pi\)
\(84\) 0 0
\(85\) −4.91147 + 8.50692i −0.532724 + 0.922705i
\(86\) 0.826352 + 1.43128i 0.0891078 + 0.154339i
\(87\) 0 0
\(88\) 0.688663 1.19280i 0.0734117 0.127153i
\(89\) −4.05690 + 7.02676i −0.430031 + 0.744835i −0.996875 0.0789894i \(-0.974831\pi\)
0.566845 + 0.823825i \(0.308164\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.00980018 + 0.0169744i 0.00102174 + 0.00176970i
\(93\) 0 0
\(94\) −7.18479 −0.741055
\(95\) 5.53209 0.567580
\(96\) 0 0
\(97\) 6.80200 + 11.7814i 0.690639 + 1.19622i 0.971629 + 0.236511i \(0.0760039\pi\)
−0.280990 + 0.959711i \(0.590663\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.130415 0.225885i 0.0130415 0.0225885i
\(101\) −4.78699 + 8.29131i −0.476323 + 0.825016i −0.999632 0.0271271i \(-0.991364\pi\)
0.523309 + 0.852143i \(0.324697\pi\)
\(102\) 0 0
\(103\) −1.52094 2.63435i −0.149863 0.259571i 0.781314 0.624139i \(-0.214550\pi\)
−0.931177 + 0.364568i \(0.881217\pi\)
\(104\) −8.57011 + 14.8439i −0.840368 + 1.45556i
\(105\) 0 0
\(106\) 0.482926 + 0.836452i 0.0469059 + 0.0812434i
\(107\) −3.25877 + 5.64436i −0.315037 + 0.545660i −0.979445 0.201709i \(-0.935350\pi\)
0.664408 + 0.747370i \(0.268684\pi\)
\(108\) 0 0
\(109\) −5.31908 9.21291i −0.509475 0.882437i −0.999940 0.0109759i \(-0.996506\pi\)
0.490465 0.871461i \(-0.336827\pi\)
\(110\) −1.59627 −0.152198
\(111\) 0 0
\(112\) 0 0
\(113\) 2.58853 4.48346i 0.243508 0.421768i −0.718203 0.695834i \(-0.755035\pi\)
0.961711 + 0.274065i \(0.0883684\pi\)
\(114\) 0 0
\(115\) 0.134285 0.232589i 0.0125222 0.0216890i
\(116\) −0.811337 1.40528i −0.0753308 0.130477i
\(117\) 0 0
\(118\) 0.992259 0.0913449
\(119\) 0 0
\(120\) 0 0
\(121\) 5.39053 + 9.33667i 0.490048 + 0.848788i
\(122\) −1.29086 −0.116869
\(123\) 0 0
\(124\) 1.41921 0.127449
\(125\) 9.08647 0.812718
\(126\) 0 0
\(127\) −8.88207 −0.788157 −0.394078 0.919077i \(-0.628936\pi\)
−0.394078 + 0.919077i \(0.628936\pi\)
\(128\) −9.49794 −0.839507
\(129\) 0 0
\(130\) 19.8648 1.74226
\(131\) 5.68139 + 9.84045i 0.496385 + 0.859764i 0.999991 0.00416893i \(-0.00132701\pi\)
−0.503606 + 0.863933i \(0.667994\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.9855 1.12177
\(135\) 0 0
\(136\) 5.70961 + 9.88933i 0.489595 + 0.848003i
\(137\) −2.86231 + 4.95767i −0.244544 + 0.423562i −0.962003 0.273038i \(-0.911972\pi\)
0.717459 + 0.696600i \(0.245305\pi\)
\(138\) 0 0
\(139\) 0.461981 0.800175i 0.0391847 0.0678700i −0.845768 0.533551i \(-0.820857\pi\)
0.884953 + 0.465681i \(0.154191\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 17.8307 1.49632
\(143\) 1.36231 + 2.35959i 0.113922 + 0.197319i
\(144\) 0 0
\(145\) −11.1172 + 19.2556i −0.923234 + 1.59909i
\(146\) −6.91740 11.9813i −0.572488 0.991579i
\(147\) 0 0
\(148\) −0.709607 + 1.22908i −0.0583294 + 0.101029i
\(149\) 4.36231 + 7.55574i 0.357374 + 0.618991i 0.987521 0.157485i \(-0.0503387\pi\)
−0.630147 + 0.776476i \(0.717005\pi\)
\(150\) 0 0
\(151\) −9.21348 + 15.9582i −0.749782 + 1.29866i 0.198145 + 0.980173i \(0.436508\pi\)
−0.947927 + 0.318488i \(0.896825\pi\)
\(152\) 3.21554 5.56947i 0.260815 0.451744i
\(153\) 0 0
\(154\) 0 0
\(155\) −9.72328 16.8412i −0.780992 1.35272i
\(156\) 0 0
\(157\) 4.92396 0.392975 0.196488 0.980506i \(-0.437046\pi\)
0.196488 + 0.980506i \(0.437046\pi\)
\(158\) 17.0273 1.35462
\(159\) 0 0
\(160\) −1.31908 2.28471i −0.104282 0.180622i
\(161\) 0 0
\(162\) 0 0
\(163\) −3.81908 + 6.61484i −0.299133 + 0.518114i −0.975938 0.218049i \(-0.930031\pi\)
0.676805 + 0.736163i \(0.263364\pi\)
\(164\) 0.205737 0.356347i 0.0160654 0.0278260i
\(165\) 0 0
\(166\) 1.84002 + 3.18701i 0.142813 + 0.247360i
\(167\) −2.82770 + 4.89771i −0.218814 + 0.378996i −0.954446 0.298385i \(-0.903552\pi\)
0.735632 + 0.677382i \(0.236885\pi\)
\(168\) 0 0
\(169\) −10.4534 18.1058i −0.804105 1.39275i
\(170\) 6.61721 11.4613i 0.507517 0.879045i
\(171\) 0 0
\(172\) 0.113341 + 0.196312i 0.00864215 + 0.0149687i
\(173\) −21.0692 −1.60186 −0.800932 0.598755i \(-0.795662\pi\)
−0.800932 + 0.598755i \(0.795662\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.841367 + 1.45729i −0.0634204 + 0.109847i
\(177\) 0 0
\(178\) 5.46585 9.46713i 0.409683 0.709592i
\(179\) −2.56031 4.43458i −0.191366 0.331456i 0.754337 0.656487i \(-0.227959\pi\)
−0.945703 + 0.325031i \(0.894625\pi\)
\(180\) 0 0
\(181\) −0.319955 −0.0237821 −0.0118910 0.999929i \(-0.503785\pi\)
−0.0118910 + 0.999929i \(0.503785\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.156107 0.270386i −0.0115084 0.0199331i
\(185\) 19.4466 1.42974
\(186\) 0 0
\(187\) 1.81521 0.132741
\(188\) −0.985452 −0.0718715
\(189\) 0 0
\(190\) −7.45336 −0.540724
\(191\) 15.5672 1.12640 0.563200 0.826320i \(-0.309570\pi\)
0.563200 + 0.826320i \(0.309570\pi\)
\(192\) 0 0
\(193\) 6.04189 0.434905 0.217452 0.976071i \(-0.430225\pi\)
0.217452 + 0.976071i \(0.430225\pi\)
\(194\) −9.16431 15.8731i −0.657959 1.13962i
\(195\) 0 0
\(196\) 0 0
\(197\) −25.2344 −1.79788 −0.898939 0.438074i \(-0.855661\pi\)
−0.898939 + 0.438074i \(0.855661\pi\)
\(198\) 0 0
\(199\) −1.52094 2.63435i −0.107817 0.186744i 0.807069 0.590458i \(-0.201053\pi\)
−0.914886 + 0.403713i \(0.867719\pi\)
\(200\) −2.07738 + 3.59813i −0.146893 + 0.254426i
\(201\) 0 0
\(202\) 6.44949 11.1708i 0.453785 0.785978i
\(203\) 0 0
\(204\) 0 0
\(205\) −5.63816 −0.393786
\(206\) 2.04916 + 3.54925i 0.142772 + 0.247288i
\(207\) 0 0
\(208\) 10.4704 18.1353i 0.725994 1.25746i
\(209\) −0.511144 0.885328i −0.0353566 0.0612394i
\(210\) 0 0
\(211\) 2.72668 4.72275i 0.187713 0.325128i −0.756775 0.653676i \(-0.773226\pi\)
0.944487 + 0.328548i \(0.106559\pi\)
\(212\) 0.0662372 + 0.114726i 0.00454919 + 0.00787942i
\(213\) 0 0
\(214\) 4.39053 7.60462i 0.300130 0.519841i
\(215\) 1.55303 2.68993i 0.105916 0.183452i
\(216\) 0 0
\(217\) 0 0
\(218\) 7.16637 + 12.4125i 0.485368 + 0.840682i
\(219\) 0 0
\(220\) −0.218941 −0.0147610
\(221\) −22.5895 −1.51953
\(222\) 0 0
\(223\) −7.09627 12.2911i −0.475201 0.823073i 0.524395 0.851475i \(-0.324291\pi\)
−0.999597 + 0.0284023i \(0.990958\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.48751 + 6.04055i −0.231986 + 0.401811i
\(227\) −1.44697 + 2.50622i −0.0960385 + 0.166344i −0.910042 0.414517i \(-0.863951\pi\)
0.814003 + 0.580861i \(0.197284\pi\)
\(228\) 0 0
\(229\) −4.58378 7.93934i −0.302905 0.524646i 0.673888 0.738834i \(-0.264623\pi\)
−0.976793 + 0.214187i \(0.931290\pi\)
\(230\) −0.180922 + 0.313366i −0.0119297 + 0.0206628i
\(231\) 0 0
\(232\) 12.9238 + 22.3847i 0.848489 + 1.46963i
\(233\) 6.63563 11.4932i 0.434715 0.752948i −0.562558 0.826758i \(-0.690183\pi\)
0.997272 + 0.0738103i \(0.0235159\pi\)
\(234\) 0 0
\(235\) 6.75150 + 11.6939i 0.440419 + 0.762828i
\(236\) 0.136096 0.00885912
\(237\) 0 0
\(238\) 0 0
\(239\) 4.76857 8.25941i 0.308453 0.534257i −0.669571 0.742748i \(-0.733522\pi\)
0.978024 + 0.208491i \(0.0668553\pi\)
\(240\) 0 0
\(241\) 4.47906 7.75795i 0.288521 0.499734i −0.684936 0.728604i \(-0.740170\pi\)
0.973457 + 0.228870i \(0.0735031\pi\)
\(242\) −7.26264 12.5793i −0.466860 0.808626i
\(243\) 0 0
\(244\) −0.177052 −0.0113346
\(245\) 0 0
\(246\) 0 0
\(247\) 6.36097 + 11.0175i 0.404739 + 0.701028i
\(248\) −22.6067 −1.43553
\(249\) 0 0
\(250\) −12.2422 −0.774262
\(251\) 24.9982 1.57788 0.788938 0.614473i \(-0.210631\pi\)
0.788938 + 0.614473i \(0.210631\pi\)
\(252\) 0 0
\(253\) −0.0496299 −0.00312020
\(254\) 11.9668 0.750863
\(255\) 0 0
\(256\) −4.39599 −0.274750
\(257\) 5.42602 + 9.39815i 0.338466 + 0.586240i 0.984144 0.177369i \(-0.0567587\pi\)
−0.645678 + 0.763609i \(0.723425\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2.72462 0.168974
\(261\) 0 0
\(262\) −7.65451 13.2580i −0.472897 0.819082i
\(263\) 13.0437 22.5924i 0.804309 1.39310i −0.112448 0.993658i \(-0.535869\pi\)
0.916757 0.399446i \(-0.130798\pi\)
\(264\) 0 0
\(265\) 0.907604 1.57202i 0.0557537 0.0965682i
\(266\) 0 0
\(267\) 0 0
\(268\) 1.78106 0.108796
\(269\) −3.81655 6.61046i −0.232699 0.403047i 0.725902 0.687798i \(-0.241422\pi\)
−0.958602 + 0.284751i \(0.908089\pi\)
\(270\) 0 0
\(271\) −1.70187 + 2.94772i −0.103381 + 0.179061i −0.913076 0.407790i \(-0.866299\pi\)
0.809695 + 0.586852i \(0.199633\pi\)
\(272\) −6.97565 12.0822i −0.422961 0.732590i
\(273\) 0 0
\(274\) 3.85638 6.67945i 0.232973 0.403520i
\(275\) 0.330222 + 0.571962i 0.0199131 + 0.0344906i
\(276\) 0 0
\(277\) 2.86097 4.95534i 0.171899 0.297738i −0.767185 0.641426i \(-0.778343\pi\)
0.939084 + 0.343689i \(0.111676\pi\)
\(278\) −0.622426 + 1.07807i −0.0373306 + 0.0646585i
\(279\) 0 0
\(280\) 0 0
\(281\) 14.1887 + 24.5755i 0.846425 + 1.46605i 0.884378 + 0.466771i \(0.154583\pi\)
−0.0379535 + 0.999280i \(0.512084\pi\)
\(282\) 0 0
\(283\) 4.57129 0.271735 0.135867 0.990727i \(-0.456618\pi\)
0.135867 + 0.990727i \(0.456618\pi\)
\(284\) 2.44562 0.145121
\(285\) 0 0
\(286\) −1.83544 3.17907i −0.108532 0.187982i
\(287\) 0 0
\(288\) 0 0
\(289\) 0.975185 1.68907i 0.0573638 0.0993571i
\(290\) 14.9782 25.9430i 0.879549 1.52342i
\(291\) 0 0
\(292\) −0.948778 1.64333i −0.0555230 0.0961687i
\(293\) 2.16385 3.74789i 0.126413 0.218954i −0.795871 0.605466i \(-0.792987\pi\)
0.922285 + 0.386512i \(0.126320\pi\)
\(294\) 0 0
\(295\) −0.932419 1.61500i −0.0542875 0.0940287i
\(296\) 11.3033 19.5780i 0.656994 1.13795i
\(297\) 0 0
\(298\) −5.87733 10.1798i −0.340464 0.589702i
\(299\) 0.617622 0.0357180
\(300\) 0 0
\(301\) 0 0
\(302\) 12.4133 21.5004i 0.714304 1.23721i
\(303\) 0 0
\(304\) −3.92855 + 6.80445i −0.225318 + 0.390262i
\(305\) 1.21301 + 2.10100i 0.0694568 + 0.120303i
\(306\) 0 0
\(307\) 12.3773 0.706411 0.353206 0.935546i \(-0.385092\pi\)
0.353206 + 0.935546i \(0.385092\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 13.1001 + 22.6901i 0.744038 + 1.28871i
\(311\) 21.9855 1.24668 0.623340 0.781951i \(-0.285775\pi\)
0.623340 + 0.781951i \(0.285775\pi\)
\(312\) 0 0
\(313\) −13.8898 −0.785099 −0.392549 0.919731i \(-0.628407\pi\)
−0.392549 + 0.919731i \(0.628407\pi\)
\(314\) −6.63404 −0.374380
\(315\) 0 0
\(316\) 2.33544 0.131379
\(317\) 6.18210 0.347222 0.173611 0.984814i \(-0.444457\pi\)
0.173611 + 0.984814i \(0.444457\pi\)
\(318\) 0 0
\(319\) 4.10876 0.230046
\(320\) 10.8833 + 18.8504i 0.608392 + 1.05377i
\(321\) 0 0
\(322\) 0 0
\(323\) 8.47565 0.471598
\(324\) 0 0
\(325\) −4.10947 7.11781i −0.227952 0.394825i
\(326\) 5.14543 8.91215i 0.284979 0.493598i
\(327\) 0 0
\(328\) −3.27719 + 5.67626i −0.180952 + 0.313419i
\(329\) 0 0
\(330\) 0 0
\(331\) 10.7314 0.589853 0.294926 0.955520i \(-0.404705\pi\)
0.294926 + 0.955520i \(0.404705\pi\)
\(332\) 0.252374 + 0.437124i 0.0138508 + 0.0239903i
\(333\) 0 0
\(334\) 3.80974 6.59867i 0.208460 0.361063i
\(335\) −12.2023 21.1351i −0.666685 1.15473i
\(336\) 0 0
\(337\) 9.29726 16.1033i 0.506454 0.877204i −0.493518 0.869735i \(-0.664289\pi\)
0.999972 0.00746831i \(-0.00237726\pi\)
\(338\) 14.0838 + 24.3938i 0.766057 + 1.32685i
\(339\) 0 0
\(340\) 0.907604 1.57202i 0.0492217 0.0852545i
\(341\) −1.79679 + 3.11213i −0.0973016 + 0.168531i
\(342\) 0 0
\(343\) 0 0
\(344\) −1.80541 3.12706i −0.0973410 0.168600i
\(345\) 0 0
\(346\) 28.3865 1.52607
\(347\) 20.4124 1.09580 0.547898 0.836545i \(-0.315428\pi\)
0.547898 + 0.836545i \(0.315428\pi\)
\(348\) 0 0
\(349\) 1.78106 + 3.08489i 0.0953379 + 0.165130i 0.909750 0.415157i \(-0.136274\pi\)
−0.814412 + 0.580288i \(0.802940\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.243756 + 0.422197i −0.0129922 + 0.0225032i
\(353\) 5.01114 8.67956i 0.266716 0.461966i −0.701296 0.712871i \(-0.747395\pi\)
0.968012 + 0.250904i \(0.0807280\pi\)
\(354\) 0 0
\(355\) −16.7554 29.0211i −0.889283 1.54028i
\(356\) 0.749686 1.29849i 0.0397333 0.0688200i
\(357\) 0 0
\(358\) 3.44949 + 5.97470i 0.182311 + 0.315773i
\(359\) 4.74035 8.21053i 0.250186 0.433335i −0.713391 0.700766i \(-0.752841\pi\)
0.963577 + 0.267431i \(0.0861748\pi\)
\(360\) 0 0
\(361\) 7.11334 + 12.3207i 0.374386 + 0.648456i
\(362\) 0.431074 0.0226568
\(363\) 0 0
\(364\) 0 0
\(365\) −13.0005 + 22.5175i −0.680476 + 1.17862i
\(366\) 0 0
\(367\) −8.06670 + 13.9719i −0.421079 + 0.729329i −0.996045 0.0888474i \(-0.971682\pi\)
0.574967 + 0.818177i \(0.305015\pi\)
\(368\) 0.190722 + 0.330341i 0.00994209 + 0.0172202i
\(369\) 0 0
\(370\) −26.2003 −1.36209
\(371\) 0 0
\(372\) 0 0
\(373\) −7.02481 12.1673i −0.363731 0.630001i 0.624841 0.780752i \(-0.285164\pi\)
−0.988572 + 0.150752i \(0.951831\pi\)
\(374\) −2.44562 −0.126460
\(375\) 0 0
\(376\) 15.6973 0.809525
\(377\) −51.1317 −2.63341
\(378\) 0 0
\(379\) 16.0574 0.824812 0.412406 0.911000i \(-0.364689\pi\)
0.412406 + 0.911000i \(0.364689\pi\)
\(380\) −1.02229 −0.0524423
\(381\) 0 0
\(382\) −20.9736 −1.07310
\(383\) −16.0103 27.7306i −0.818086 1.41697i −0.907090 0.420936i \(-0.861702\pi\)
0.0890039 0.996031i \(-0.471632\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −8.14022 −0.414326
\(387\) 0 0
\(388\) −1.25696 2.17712i −0.0638124 0.110526i
\(389\) −15.0214 + 26.0178i −0.761616 + 1.31916i 0.180402 + 0.983593i \(0.442260\pi\)
−0.942017 + 0.335564i \(0.891073\pi\)
\(390\) 0 0
\(391\) 0.205737 0.356347i 0.0104046 0.0180212i
\(392\) 0 0
\(393\) 0 0
\(394\) 33.9982 1.71281
\(395\) −16.0005 27.7136i −0.805071 1.39442i
\(396\) 0 0
\(397\) 6.15998 10.6694i 0.309160 0.535482i −0.669019 0.743246i \(-0.733285\pi\)
0.978179 + 0.207764i \(0.0666187\pi\)
\(398\) 2.04916 + 3.54925i 0.102715 + 0.177908i
\(399\) 0 0
\(400\) 2.53802 4.39598i 0.126901 0.219799i
\(401\) 10.4880 + 18.1657i 0.523745 + 0.907152i 0.999618 + 0.0276385i \(0.00879873\pi\)
−0.475873 + 0.879514i \(0.657868\pi\)
\(402\) 0 0
\(403\) 22.3603 38.7291i 1.11384 1.92923i
\(404\) 0.884600 1.53217i 0.0440105 0.0762284i
\(405\) 0 0
\(406\) 0 0
\(407\) −1.79679 3.11213i −0.0890635 0.154263i
\(408\) 0 0
\(409\) 25.6614 1.26887 0.634437 0.772975i \(-0.281232\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(410\) 7.59627 0.375153
\(411\) 0 0
\(412\) 0.281059 + 0.486809i 0.0138468 + 0.0239833i
\(413\) 0 0
\(414\) 0 0
\(415\) 3.45811 5.98962i 0.169752 0.294019i
\(416\) 3.03343 5.25406i 0.148726 0.257601i
\(417\) 0 0
\(418\) 0.688663 + 1.19280i 0.0336836 + 0.0583417i
\(419\) −0.739885 + 1.28152i −0.0361458 + 0.0626063i −0.883532 0.468370i \(-0.844841\pi\)
0.847387 + 0.530976i \(0.178175\pi\)
\(420\) 0 0
\(421\) −6.55350 11.3510i −0.319398 0.553214i 0.660965 0.750417i \(-0.270147\pi\)
−0.980363 + 0.197203i \(0.936814\pi\)
\(422\) −3.67365 + 6.36295i −0.178830 + 0.309743i
\(423\) 0 0
\(424\) −1.05509 1.82747i −0.0512398 0.0887500i
\(425\) −5.47565 −0.265608
\(426\) 0 0
\(427\) 0 0
\(428\) 0.602196 1.04303i 0.0291083 0.0504170i
\(429\) 0 0
\(430\) −2.09240 + 3.62414i −0.100904 + 0.174771i
\(431\) 8.86349 + 15.3520i 0.426939 + 0.739481i 0.996599 0.0823997i \(-0.0262584\pi\)
−0.569660 + 0.821881i \(0.692925\pi\)
\(432\) 0 0
\(433\) −5.83843 −0.280577 −0.140289 0.990111i \(-0.544803\pi\)
−0.140289 + 0.990111i \(0.544803\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.982926 + 1.70248i 0.0470736 + 0.0815339i
\(437\) −0.231734 −0.0110853
\(438\) 0 0
\(439\) 29.8553 1.42492 0.712459 0.701714i \(-0.247582\pi\)
0.712459 + 0.701714i \(0.247582\pi\)
\(440\) 3.48751 0.166261
\(441\) 0 0
\(442\) 30.4347 1.44763
\(443\) −10.6655 −0.506733 −0.253367 0.967370i \(-0.581538\pi\)
−0.253367 + 0.967370i \(0.581538\pi\)
\(444\) 0 0
\(445\) −20.5449 −0.973921
\(446\) 9.56077 + 16.5597i 0.452716 + 0.784127i
\(447\) 0 0
\(448\) 0 0
\(449\) −3.55438 −0.167741 −0.0838707 0.996477i \(-0.526728\pi\)
−0.0838707 + 0.996477i \(0.526728\pi\)
\(450\) 0 0
\(451\) 0.520945 + 0.902302i 0.0245303 + 0.0424878i
\(452\) −0.478340 + 0.828510i −0.0224992 + 0.0389698i
\(453\) 0 0
\(454\) 1.94949 3.37662i 0.0914942 0.158473i
\(455\) 0 0
\(456\) 0 0
\(457\) 5.02322 0.234976 0.117488 0.993074i \(-0.462516\pi\)
0.117488 + 0.993074i \(0.462516\pi\)
\(458\) 6.17571 + 10.6966i 0.288572 + 0.499821i
\(459\) 0 0
\(460\) −0.0248149 + 0.0429807i −0.00115700 + 0.00200399i
\(461\) 9.23055 + 15.9878i 0.429910 + 0.744625i 0.996865 0.0791233i \(-0.0252121\pi\)
−0.566955 + 0.823749i \(0.691879\pi\)
\(462\) 0 0
\(463\) 7.11721 12.3274i 0.330765 0.572902i −0.651897 0.758307i \(-0.726027\pi\)
0.982662 + 0.185406i \(0.0593600\pi\)
\(464\) −15.7895 27.3482i −0.733010 1.26961i
\(465\) 0 0
\(466\) −8.94016 + 15.4848i −0.414145 + 0.717320i
\(467\) −1.68433 + 2.91734i −0.0779413 + 0.134998i −0.902362 0.430980i \(-0.858168\pi\)
0.824420 + 0.565978i \(0.191501\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −9.09627 15.7552i −0.419579 0.726733i
\(471\) 0 0
\(472\) −2.16788 −0.0997848
\(473\) −0.573978 −0.0263915
\(474\) 0 0
\(475\) 1.54189 + 2.67063i 0.0707467 + 0.122537i
\(476\) 0 0
\(477\) 0 0
\(478\) −6.42468 + 11.1279i −0.293858 + 0.508977i
\(479\) −18.3833 + 31.8407i −0.839952 + 1.45484i 0.0499812 + 0.998750i \(0.484084\pi\)
−0.889934 + 0.456090i \(0.849249\pi\)
\(480\) 0 0
\(481\) 22.3603 + 38.7291i 1.01954 + 1.76589i
\(482\) −6.03462 + 10.4523i −0.274869 + 0.476087i
\(483\) 0 0
\(484\) −0.996130 1.72535i −0.0452786 0.0784249i
\(485\) −17.2233 + 29.8316i −0.782069 + 1.35458i
\(486\) 0 0
\(487\) 18.7087 + 32.4045i 0.847773 + 1.46839i 0.883191 + 0.469014i \(0.155391\pi\)
−0.0354172 + 0.999373i \(0.511276\pi\)
\(488\) 2.82026 0.127667
\(489\) 0 0
\(490\) 0 0
\(491\) −13.3353 + 23.0974i −0.601813 + 1.04237i 0.390734 + 0.920504i \(0.372221\pi\)
−0.992547 + 0.121866i \(0.961112\pi\)
\(492\) 0 0
\(493\) −17.0326 + 29.5013i −0.767108 + 1.32867i
\(494\) −8.57011 14.8439i −0.385587 0.667857i
\(495\) 0 0
\(496\) 27.6195 1.24015
\(497\) 0 0
\(498\) 0 0
\(499\) −16.8726 29.2242i −0.755320 1.30825i −0.945215 0.326449i \(-0.894148\pi\)
0.189895 0.981804i \(-0.439185\pi\)
\(500\) −1.67911 −0.0750921
\(501\) 0 0
\(502\) −33.6800 −1.50321
\(503\) 32.0401 1.42860 0.714299 0.699840i \(-0.246745\pi\)
0.714299 + 0.699840i \(0.246745\pi\)
\(504\) 0 0
\(505\) −24.2422 −1.07876
\(506\) 0.0668661 0.00297256
\(507\) 0 0
\(508\) 1.64134 0.0728227
\(509\) −3.96926 6.87495i −0.175934 0.304727i 0.764550 0.644564i \(-0.222961\pi\)
−0.940484 + 0.339838i \(0.889628\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 24.9186 1.10126
\(513\) 0 0
\(514\) −7.31046 12.6621i −0.322451 0.558501i
\(515\) 3.85117 6.67042i 0.169703 0.293934i
\(516\) 0 0
\(517\) 1.24763 2.16095i 0.0548705 0.0950386i
\(518\) 0 0
\(519\) 0 0
\(520\) −43.4005 −1.90324
\(521\) −7.33750 12.7089i −0.321462 0.556788i 0.659328 0.751855i \(-0.270841\pi\)
−0.980790 + 0.195067i \(0.937507\pi\)
\(522\) 0 0
\(523\) −14.1716 + 24.5459i −0.619680 + 1.07332i 0.369864 + 0.929086i \(0.379404\pi\)
−0.989544 + 0.144232i \(0.953929\pi\)
\(524\) −1.04988 1.81844i −0.0458641 0.0794390i
\(525\) 0 0
\(526\) −17.5737 + 30.4386i −0.766251 + 1.32719i
\(527\) −14.8969 25.8022i −0.648920 1.12396i
\(528\) 0 0
\(529\) 11.4944 19.9088i 0.499755 0.865602i
\(530\) −1.22281 + 2.11797i −0.0531155 + 0.0919988i
\(531\) 0 0
\(532\) 0 0
\(533\) −6.48293 11.2288i −0.280807 0.486371i
\(534\) 0 0
\(535\) −16.5030 −0.713487
\(536\) −28.3705 −1.22542
\(537\) 0 0
\(538\) 5.14203 + 8.90625i 0.221688 + 0.383976i
\(539\) 0 0
\(540\) 0 0
\(541\) −5.64290 + 9.77380i −0.242607 + 0.420208i −0.961456 0.274958i \(-0.911336\pi\)
0.718849 + 0.695166i \(0.244669\pi\)
\(542\) 2.29292 3.97145i 0.0984893 0.170588i
\(543\) 0 0
\(544\) −2.02094 3.50038i −0.0866473 0.150077i
\(545\) 13.4684 23.3279i 0.576922 0.999258i
\(546\) 0 0
\(547\) 14.6202 + 25.3229i 0.625115 + 1.08273i 0.988519 + 0.151099i \(0.0482812\pi\)
−0.363404 + 0.931632i \(0.618385\pi\)
\(548\) 0.528934 0.916140i 0.0225949 0.0391356i
\(549\) 0 0
\(550\) −0.444907 0.770602i −0.0189709 0.0328586i
\(551\) 19.1848 0.817300
\(552\) 0 0
\(553\) 0 0
\(554\) −3.85457 + 6.67631i −0.163765 + 0.283649i
\(555\) 0 0
\(556\) −0.0853707 + 0.147866i −0.00362052 + 0.00627093i
\(557\) −0.387841 0.671761i −0.0164334 0.0284634i 0.857692 0.514164i \(-0.171898\pi\)
−0.874125 + 0.485701i \(0.838564\pi\)
\(558\) 0 0
\(559\) 7.14290 0.302113
\(560\) 0 0
\(561\) 0 0
\(562\) −19.1163 33.1105i −0.806374 1.39668i
\(563\) −24.9522 −1.05161 −0.525806 0.850605i \(-0.676236\pi\)
−0.525806 + 0.850605i \(0.676236\pi\)
\(564\) 0 0
\(565\) 13.1088 0.551489
\(566\) −6.15888 −0.258877
\(567\) 0 0
\(568\) −38.9564 −1.63457
\(569\) 24.8033 1.03981 0.519905 0.854224i \(-0.325967\pi\)
0.519905 + 0.854224i \(0.325967\pi\)
\(570\) 0 0
\(571\) 8.79654 0.368124 0.184062 0.982915i \(-0.441075\pi\)
0.184062 + 0.982915i \(0.441075\pi\)
\(572\) −0.251745 0.436035i −0.0105260 0.0182315i
\(573\) 0 0
\(574\) 0 0
\(575\) 0.149711 0.00624336
\(576\) 0 0
\(577\) 6.43717 + 11.1495i 0.267983 + 0.464160i 0.968341 0.249632i \(-0.0803096\pi\)
−0.700358 + 0.713792i \(0.746976\pi\)
\(578\) −1.31386 + 2.27568i −0.0546495 + 0.0946557i
\(579\) 0 0
\(580\) 2.05438 3.55829i 0.0853034 0.147750i
\(581\) 0 0
\(582\) 0 0
\(583\) −0.335437 −0.0138924
\(584\) 15.1131 + 26.1766i 0.625384 + 1.08320i
\(585\) 0 0
\(586\) −2.91534 + 5.04952i −0.120432 + 0.208594i
\(587\) 22.4315 + 38.8526i 0.925849 + 1.60362i 0.790190 + 0.612861i \(0.209982\pi\)
0.135658 + 0.990756i \(0.456685\pi\)
\(588\) 0 0
\(589\) −8.38965 + 14.5313i −0.345690 + 0.598752i
\(590\) 1.25624 + 2.17588i 0.0517188 + 0.0895795i
\(591\) 0 0
\(592\) −13.8097 + 23.9192i −0.567577 + 0.983072i
\(593\) 1.88026 3.25671i 0.0772131 0.133737i −0.824833 0.565376i \(-0.808731\pi\)
0.902047 + 0.431639i \(0.142064\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.806123 1.39625i −0.0330201 0.0571924i
\(597\) 0 0
\(598\) −0.832119 −0.0340279
\(599\) 3.69047 0.150789 0.0753943 0.997154i \(-0.475978\pi\)
0.0753943 + 0.997154i \(0.475978\pi\)
\(600\) 0 0
\(601\) 10.9285 + 18.9288i 0.445785 + 0.772122i 0.998107 0.0615091i \(-0.0195913\pi\)
−0.552322 + 0.833631i \(0.686258\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.70258 2.94896i 0.0692771 0.119991i
\(605\) −13.6493 + 23.6413i −0.554923 + 0.961155i
\(606\) 0 0
\(607\) −12.1973 21.1263i −0.495072 0.857490i 0.504911 0.863171i \(-0.331525\pi\)
−0.999984 + 0.00568063i \(0.998192\pi\)
\(608\) −1.13816 + 1.97134i −0.0461583 + 0.0799485i
\(609\) 0 0
\(610\) −1.63429 2.83067i −0.0661703 0.114610i
\(611\) −15.5262 + 26.8921i −0.628121 + 1.08794i
\(612\) 0 0
\(613\) −21.0107 36.3917i −0.848616 1.46985i −0.882444 0.470418i \(-0.844103\pi\)
0.0338284 0.999428i \(-0.489230\pi\)
\(614\) −16.6759 −0.672986
\(615\) 0 0
\(616\) 0 0
\(617\) 23.2049 40.1920i 0.934192 1.61807i 0.158125 0.987419i \(-0.449455\pi\)
0.776068 0.630650i \(-0.217212\pi\)
\(618\) 0 0
\(619\) 13.6047 23.5641i 0.546820 0.947120i −0.451670 0.892185i \(-0.649172\pi\)
0.998490 0.0549349i \(-0.0174951\pi\)
\(620\) 1.79679 + 3.11213i 0.0721608 + 0.124986i
\(621\) 0 0
\(622\) −29.6209 −1.18769
\(623\) 0 0
\(624\) 0 0
\(625\) 15.0326 + 26.0372i 0.601302 + 1.04149i
\(626\) 18.7137 0.747950
\(627\) 0 0
\(628\) −0.909912 −0.0363094
\(629\) 29.7939 1.18796
\(630\) 0 0
\(631\) −29.6023 −1.17845 −0.589224 0.807970i \(-0.700566\pi\)
−0.589224 + 0.807970i \(0.700566\pi\)
\(632\) −37.2012 −1.47978
\(633\) 0 0
\(634\) −8.32913 −0.330792
\(635\) −11.2451 19.4771i −0.446248 0.772925i
\(636\) 0 0
\(637\) 0 0
\(638\) −5.53571 −0.219161
\(639\) 0 0
\(640\) −12.0248 20.8276i −0.475323 0.823283i
\(641\) −0.139500 + 0.241621i −0.00550991 + 0.00954345i −0.868767 0.495221i \(-0.835087\pi\)
0.863257 + 0.504764i \(0.168421\pi\)
\(642\) 0 0
\(643\) 9.12196 15.7997i 0.359735 0.623079i −0.628181 0.778067i \(-0.716200\pi\)
0.987916 + 0.154988i \(0.0495338\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −11.4192 −0.449283
\(647\) 11.2285 + 19.4483i 0.441438 + 0.764592i 0.997796 0.0663498i \(-0.0211353\pi\)
−0.556359 + 0.830942i \(0.687802\pi\)
\(648\) 0 0
\(649\) −0.172304 + 0.298439i −0.00676352 + 0.0117148i
\(650\) 5.53667 + 9.58980i 0.217166 + 0.376143i
\(651\) 0 0
\(652\) 0.705737 1.22237i 0.0276388 0.0478718i
\(653\) −25.2656 43.7614i −0.988721 1.71251i −0.624066 0.781372i \(-0.714520\pi\)
−0.364655 0.931143i \(-0.618813\pi\)
\(654\) 0 0
\(655\) −14.3858 + 24.9169i −0.562099 + 0.973584i
\(656\) 4.00387 6.93491i 0.156325 0.270763i
\(657\) 0 0
\(658\) 0 0
\(659\) −1.33631 2.31456i −0.0520554 0.0901626i 0.838824 0.544403i \(-0.183244\pi\)
−0.890879 + 0.454241i \(0.849911\pi\)
\(660\) 0 0
\(661\) −34.6100 −1.34617 −0.673086 0.739564i \(-0.735032\pi\)
−0.673086 + 0.739564i \(0.735032\pi\)
\(662\) −14.4584 −0.561942
\(663\) 0 0
\(664\) −4.02007 6.96296i −0.156009 0.270215i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.465690 0.806598i 0.0180316 0.0312316i
\(668\) 0.522537 0.905061i 0.0202176 0.0350179i
\(669\) 0 0
\(670\) 16.4402 + 28.4752i 0.635139 + 1.10009i
\(671\) 0.224155 0.388249i 0.00865342 0.0149882i
\(672\) 0 0
\(673\) −8.25624 14.3002i −0.318255 0.551234i 0.661869 0.749619i \(-0.269763\pi\)
−0.980124 + 0.198386i \(0.936430\pi\)
\(674\) −12.5262 + 21.6959i −0.482490 + 0.835697i
\(675\) 0 0
\(676\) 1.93170 + 3.34581i 0.0742963 + 0.128685i
\(677\) 43.7579 1.68175 0.840877 0.541226i \(-0.182040\pi\)
0.840877 + 0.541226i \(0.182040\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −14.4572 + 25.0407i −0.554410 + 0.960266i
\(681\) 0 0
\(682\) 2.42081 4.19296i 0.0926975 0.160557i
\(683\) 14.1206 + 24.4576i 0.540310 + 0.935845i 0.998886 + 0.0471895i \(0.0150265\pi\)
−0.458576 + 0.888655i \(0.651640\pi\)
\(684\) 0 0
\(685\) −14.4953 −0.553835
\(686\) 0 0
\(687\) 0 0
\(688\) 2.20574 + 3.82045i 0.0840929 + 0.145653i
\(689\) 4.17436 0.159031
\(690\) 0 0
\(691\) −29.0651 −1.10569 −0.552844 0.833284i \(-0.686458\pi\)
−0.552844 + 0.833284i \(0.686458\pi\)
\(692\) 3.89344 0.148006
\(693\) 0 0
\(694\) −27.5016 −1.04395
\(695\) 2.33956 0.0887444
\(696\) 0 0
\(697\) −8.63816 −0.327193
\(698\) −2.39961 4.15625i −0.0908268 0.157317i
\(699\) 0 0
\(700\) 0 0
\(701\) 1.10876 0.0418771 0.0209386 0.999781i \(-0.493335\pi\)
0.0209386 + 0.999781i \(0.493335\pi\)
\(702\) 0 0
\(703\) −8.38965 14.5313i −0.316422 0.548059i
\(704\) 2.01114 3.48340i 0.0757979 0.131286i
\(705\) 0 0
\(706\) −6.75150 + 11.6939i −0.254096 + 0.440107i
\(707\) 0 0
\(708\) 0 0
\(709\) −18.4688 −0.693612 −0.346806 0.937937i \(-0.612734\pi\)
−0.346806 + 0.937937i \(0.612734\pi\)
\(710\) 22.5744 + 39.1001i 0.847204 + 1.46740i
\(711\) 0 0
\(712\) −11.9418 + 20.6837i −0.447536 + 0.775155i
\(713\) 0.407299 + 0.705463i 0.0152535 + 0.0264198i
\(714\) 0 0
\(715\) −3.44949 + 5.97470i −0.129004 + 0.223441i
\(716\) 0.473126 + 0.819478i 0.0176815 + 0.0306253i
\(717\) 0 0
\(718\) −6.38666 + 11.0620i −0.238348 + 0.412831i
\(719\) −16.8885 + 29.2517i −0.629834 + 1.09090i 0.357751 + 0.933817i \(0.383544\pi\)
−0.987585 + 0.157087i \(0.949790\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −9.58378 16.5996i −0.356671 0.617773i
\(723\) 0 0
\(724\) 0.0591253 0.00219738
\(725\) −12.3942 −0.460310
\(726\) 0 0
\(727\) −8.40214 14.5529i −0.311618 0.539738i 0.667095 0.744973i \(-0.267538\pi\)
−0.978713 + 0.205234i \(0.934204\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 17.5155 30.3377i 0.648277 1.12285i
\(731\) 2.37939 4.12122i 0.0880047 0.152429i
\(732\) 0 0
\(733\) 6.81820 + 11.8095i 0.251836 + 0.436193i 0.964031 0.265789i \(-0.0856323\pi\)
−0.712195 + 0.701981i \(0.752299\pi\)
\(734\) 10.8682 18.8243i 0.401154 0.694819i
\(735\) 0 0
\(736\) 0.0552549 + 0.0957044i 0.00203672 + 0.00352771i
\(737\) −2.25490 + 3.90560i −0.0830603 + 0.143865i
\(738\) 0 0
\(739\) 16.0209 + 27.7491i 0.589340 + 1.02077i 0.994319 + 0.106441i \(0.0339455\pi\)
−0.404979 + 0.914326i \(0.632721\pi\)
\(740\) −3.59358 −0.132103
\(741\) 0 0
\(742\) 0 0
\(743\) 16.8764 29.2309i 0.619137 1.07238i −0.370507 0.928830i \(-0.620816\pi\)
0.989644 0.143547i \(-0.0458507\pi\)
\(744\) 0 0
\(745\) −11.0458 + 19.1318i −0.404685 + 0.700936i
\(746\) 9.46451 + 16.3930i 0.346520 + 0.600191i
\(747\) 0 0
\(748\) −0.335437 −0.0122648
\(749\) 0 0
\(750\) 0 0
\(751\) −13.0582 22.6175i −0.476502 0.825326i 0.523135 0.852250i \(-0.324762\pi\)
−0.999637 + 0.0269236i \(0.991429\pi\)
\(752\) −19.1780 −0.699349
\(753\) 0 0
\(754\) 68.8895 2.50881
\(755\) −46.6587 −1.69808
\(756\) 0 0
\(757\) 35.6536 1.29585 0.647927 0.761703i \(-0.275636\pi\)
0.647927 + 0.761703i \(0.275636\pi\)
\(758\) −21.6340 −0.785784
\(759\) 0 0
\(760\) 16.2841 0.590685
\(761\) 20.3824 + 35.3033i 0.738861 + 1.27974i 0.953009 + 0.302943i \(0.0979692\pi\)
−0.214148 + 0.976801i \(0.568698\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −2.87670 −0.104075
\(765\) 0 0
\(766\) 21.5706 + 37.3613i 0.779377 + 1.34992i
\(767\) 2.14425 3.71395i 0.0774243 0.134103i
\(768\) 0 0
\(769\) −19.7135 + 34.1447i −0.710886 + 1.23129i 0.253639 + 0.967299i \(0.418373\pi\)
−0.964525 + 0.263992i \(0.914961\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.11650 −0.0401836
\(773\) 12.4513 + 21.5663i 0.447842 + 0.775686i 0.998245 0.0592135i \(-0.0188593\pi\)
−0.550403 + 0.834899i \(0.685526\pi\)
\(774\) 0 0
\(775\) 5.42009 9.38788i 0.194695 0.337222i
\(776\) 20.0221 + 34.6793i 0.718752 + 1.24492i
\(777\) 0 0
\(778\) 20.2383 35.0538i 0.725578 1.25674i
\(779\) 2.43242 + 4.21307i 0.0871504 + 0.150949i
\(780\) 0 0
\(781\) −3.09627 + 5.36289i −0.110793 + 0.191899i
\(782\) −0.277189 + 0.480105i −0.00991225 + 0.0171685i
\(783\) 0 0
\(784\) 0 0
\(785\) 6.23396 + 10.7975i 0.222499 + 0.385380i
\(786\) 0 0
\(787\) −30.7050 −1.09452 −0.547258 0.836964i