Properties

Label 416.2.i.f.321.2
Level $416$
Weight $2$
Character 416.321
Analytic conductor $3.322$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [416,2,Mod(289,416)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(416, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("416.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 416 = 2^{5} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 416.i (of order \(3\), degree \(2\), 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: \(3.32177672409\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 321.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 416.321
Dual form 416.2.i.f.289.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.20711 - 2.09077i) q^{3} +2.82843 q^{5} +(-2.20711 - 3.82282i) q^{7} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})\) \(q+(1.20711 - 2.09077i) q^{3} +2.82843 q^{5} +(-2.20711 - 3.82282i) q^{7} +(-1.41421 - 2.44949i) q^{9} +(-1.62132 + 2.80821i) q^{11} +(-1.00000 - 3.46410i) q^{13} +(3.41421 - 5.91359i) q^{15} +(2.91421 + 5.04757i) q^{17} +(0.621320 + 1.07616i) q^{19} -10.6569 q^{21} +(-0.621320 + 1.07616i) q^{23} +3.00000 q^{25} +0.414214 q^{27} +(-4.32843 + 7.49706i) q^{29} +5.65685 q^{31} +(3.91421 + 6.77962i) q^{33} +(-6.24264 - 10.8126i) q^{35} +(3.74264 - 6.48244i) q^{37} +(-8.44975 - 2.09077i) q^{39} +(2.91421 - 5.04757i) q^{41} +(-2.03553 - 3.52565i) q^{43} +(-4.00000 - 6.92820i) q^{45} +6.00000 q^{47} +(-6.24264 + 10.8126i) q^{49} +14.0711 q^{51} -2.82843 q^{53} +(-4.58579 + 7.94282i) q^{55} +3.00000 q^{57} +(0.621320 + 1.07616i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(-6.24264 + 10.8126i) q^{63} +(-2.82843 - 9.79796i) q^{65} +(-6.62132 + 11.4685i) q^{67} +(1.50000 + 2.59808i) q^{69} +(3.62132 + 6.27231i) q^{71} +12.4853 q^{73} +(3.62132 - 6.27231i) q^{75} +14.3137 q^{77} -6.00000 q^{79} +(4.74264 - 8.21449i) q^{81} +4.00000 q^{83} +(8.24264 + 14.2767i) q^{85} +(10.4497 + 18.0995i) q^{87} +(1.67157 - 2.89525i) q^{89} +(-11.0355 + 11.4685i) q^{91} +(6.82843 - 11.8272i) q^{93} +(1.75736 + 3.04384i) q^{95} +(4.50000 + 7.79423i) q^{97} +9.17157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} - 6 q^{7} + 2 q^{11} - 4 q^{13} + 8 q^{15} + 6 q^{17} - 6 q^{19} - 20 q^{21} + 6 q^{23} + 12 q^{25} - 4 q^{27} - 6 q^{29} + 10 q^{33} - 8 q^{35} - 2 q^{37} - 14 q^{39} + 6 q^{41} + 6 q^{43} - 16 q^{45} + 24 q^{47} - 8 q^{49} + 28 q^{51} - 24 q^{55} + 12 q^{57} - 6 q^{59} - 14 q^{61} - 8 q^{63} - 18 q^{67} + 6 q^{69} + 6 q^{71} + 16 q^{73} + 6 q^{75} + 12 q^{77} - 24 q^{79} + 2 q^{81} + 16 q^{83} + 16 q^{85} + 22 q^{87} + 18 q^{89} - 30 q^{91} + 16 q^{93} + 24 q^{95} + 18 q^{97} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/416\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(287\) \(353\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.20711 2.09077i 0.696923 1.20711i −0.272605 0.962126i \(-0.587885\pi\)
0.969528 0.244981i \(-0.0787816\pi\)
\(4\) 0 0
\(5\) 2.82843 1.26491 0.632456 0.774597i \(-0.282047\pi\)
0.632456 + 0.774597i \(0.282047\pi\)
\(6\) 0 0
\(7\) −2.20711 3.82282i −0.834208 1.44489i −0.894674 0.446720i \(-0.852592\pi\)
0.0604657 0.998170i \(-0.480741\pi\)
\(8\) 0 0
\(9\) −1.41421 2.44949i −0.471405 0.816497i
\(10\) 0 0
\(11\) −1.62132 + 2.80821i −0.488846 + 0.846707i −0.999918 0.0128314i \(-0.995916\pi\)
0.511071 + 0.859538i \(0.329249\pi\)
\(12\) 0 0
\(13\) −1.00000 3.46410i −0.277350 0.960769i
\(14\) 0 0
\(15\) 3.41421 5.91359i 0.881546 1.52688i
\(16\) 0 0
\(17\) 2.91421 + 5.04757i 0.706801 + 1.22421i 0.966038 + 0.258401i \(0.0831955\pi\)
−0.259237 + 0.965814i \(0.583471\pi\)
\(18\) 0 0
\(19\) 0.621320 + 1.07616i 0.142541 + 0.246888i 0.928453 0.371451i \(-0.121139\pi\)
−0.785912 + 0.618338i \(0.787806\pi\)
\(20\) 0 0
\(21\) −10.6569 −2.32552
\(22\) 0 0
\(23\) −0.621320 + 1.07616i −0.129554 + 0.224395i −0.923504 0.383589i \(-0.874688\pi\)
0.793950 + 0.607983i \(0.208021\pi\)
\(24\) 0 0
\(25\) 3.00000 0.600000
\(26\) 0 0
\(27\) 0.414214 0.0797154
\(28\) 0 0
\(29\) −4.32843 + 7.49706i −0.803769 + 1.39217i 0.113350 + 0.993555i \(0.463842\pi\)
−0.917119 + 0.398613i \(0.869492\pi\)
\(30\) 0 0
\(31\) 5.65685 1.01600 0.508001 0.861357i \(-0.330385\pi\)
0.508001 + 0.861357i \(0.330385\pi\)
\(32\) 0 0
\(33\) 3.91421 + 6.77962i 0.681377 + 1.18018i
\(34\) 0 0
\(35\) −6.24264 10.8126i −1.05520 1.82766i
\(36\) 0 0
\(37\) 3.74264 6.48244i 0.615286 1.06571i −0.375048 0.927005i \(-0.622374\pi\)
0.990334 0.138702i \(-0.0442929\pi\)
\(38\) 0 0
\(39\) −8.44975 2.09077i −1.35304 0.334791i
\(40\) 0 0
\(41\) 2.91421 5.04757i 0.455124 0.788297i −0.543572 0.839363i \(-0.682928\pi\)
0.998695 + 0.0510654i \(0.0162617\pi\)
\(42\) 0 0
\(43\) −2.03553 3.52565i −0.310416 0.537656i 0.668036 0.744129i \(-0.267135\pi\)
−0.978452 + 0.206472i \(0.933802\pi\)
\(44\) 0 0
\(45\) −4.00000 6.92820i −0.596285 1.03280i
\(46\) 0 0
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 0 0
\(49\) −6.24264 + 10.8126i −0.891806 + 1.54465i
\(50\) 0 0
\(51\) 14.0711 1.97034
\(52\) 0 0
\(53\) −2.82843 −0.388514 −0.194257 0.980951i \(-0.562230\pi\)
−0.194257 + 0.980951i \(0.562230\pi\)
\(54\) 0 0
\(55\) −4.58579 + 7.94282i −0.618347 + 1.07101i
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) 0 0
\(59\) 0.621320 + 1.07616i 0.0808890 + 0.140104i 0.903632 0.428310i \(-0.140891\pi\)
−0.822743 + 0.568414i \(0.807557\pi\)
\(60\) 0 0
\(61\) −3.50000 6.06218i −0.448129 0.776182i 0.550135 0.835076i \(-0.314576\pi\)
−0.998264 + 0.0588933i \(0.981243\pi\)
\(62\) 0 0
\(63\) −6.24264 + 10.8126i −0.786499 + 1.36226i
\(64\) 0 0
\(65\) −2.82843 9.79796i −0.350823 1.21529i
\(66\) 0 0
\(67\) −6.62132 + 11.4685i −0.808923 + 1.40110i 0.104687 + 0.994505i \(0.466616\pi\)
−0.913610 + 0.406591i \(0.866718\pi\)
\(68\) 0 0
\(69\) 1.50000 + 2.59808i 0.180579 + 0.312772i
\(70\) 0 0
\(71\) 3.62132 + 6.27231i 0.429772 + 0.744386i 0.996853 0.0792756i \(-0.0252607\pi\)
−0.567081 + 0.823662i \(0.691927\pi\)
\(72\) 0 0
\(73\) 12.4853 1.46129 0.730646 0.682757i \(-0.239219\pi\)
0.730646 + 0.682757i \(0.239219\pi\)
\(74\) 0 0
\(75\) 3.62132 6.27231i 0.418154 0.724264i
\(76\) 0 0
\(77\) 14.3137 1.63120
\(78\) 0 0
\(79\) −6.00000 −0.675053 −0.337526 0.941316i \(-0.609590\pi\)
−0.337526 + 0.941316i \(0.609590\pi\)
\(80\) 0 0
\(81\) 4.74264 8.21449i 0.526960 0.912722i
\(82\) 0 0
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) 8.24264 + 14.2767i 0.894040 + 1.54852i
\(86\) 0 0
\(87\) 10.4497 + 18.0995i 1.12033 + 1.94047i
\(88\) 0 0
\(89\) 1.67157 2.89525i 0.177186 0.306896i −0.763729 0.645537i \(-0.776634\pi\)
0.940916 + 0.338641i \(0.109967\pi\)
\(90\) 0 0
\(91\) −11.0355 + 11.4685i −1.15684 + 1.20222i
\(92\) 0 0
\(93\) 6.82843 11.8272i 0.708075 1.22642i
\(94\) 0 0
\(95\) 1.75736 + 3.04384i 0.180301 + 0.312291i
\(96\) 0 0
\(97\) 4.50000 + 7.79423i 0.456906 + 0.791384i 0.998796 0.0490655i \(-0.0156243\pi\)
−0.541890 + 0.840450i \(0.682291\pi\)
\(98\) 0 0
\(99\) 9.17157 0.921778
\(100\) 0 0
\(101\) −5.91421 + 10.2437i −0.588486 + 1.01929i 0.405945 + 0.913898i \(0.366943\pi\)
−0.994431 + 0.105390i \(0.966391\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) −30.1421 −2.94157
\(106\) 0 0
\(107\) −9.62132 + 16.6646i −0.930128 + 1.61103i −0.147029 + 0.989132i \(0.546971\pi\)
−0.783099 + 0.621897i \(0.786362\pi\)
\(108\) 0 0
\(109\) −8.48528 −0.812743 −0.406371 0.913708i \(-0.633206\pi\)
−0.406371 + 0.913708i \(0.633206\pi\)
\(110\) 0 0
\(111\) −9.03553 15.6500i −0.857615 1.48543i
\(112\) 0 0
\(113\) 0.0857864 + 0.148586i 0.00807011 + 0.0139778i 0.870032 0.492995i \(-0.164098\pi\)
−0.861962 + 0.506973i \(0.830765\pi\)
\(114\) 0 0
\(115\) −1.75736 + 3.04384i −0.163875 + 0.283839i
\(116\) 0 0
\(117\) −7.07107 + 7.34847i −0.653720 + 0.679366i
\(118\) 0 0
\(119\) 12.8640 22.2810i 1.17924 2.04250i
\(120\) 0 0
\(121\) 0.242641 + 0.420266i 0.0220582 + 0.0382060i
\(122\) 0 0
\(123\) −7.03553 12.1859i −0.634373 1.09877i
\(124\) 0 0
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) −0.792893 + 1.37333i −0.0703579 + 0.121863i −0.899058 0.437829i \(-0.855747\pi\)
0.828700 + 0.559693i \(0.189081\pi\)
\(128\) 0 0
\(129\) −9.82843 −0.865345
\(130\) 0 0
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0 0
\(133\) 2.74264 4.75039i 0.237817 0.411911i
\(134\) 0 0
\(135\) 1.17157 0.100833
\(136\) 0 0
\(137\) −4.67157 8.09140i −0.399119 0.691295i 0.594498 0.804097i \(-0.297351\pi\)
−0.993617 + 0.112802i \(0.964017\pi\)
\(138\) 0 0
\(139\) 0.621320 + 1.07616i 0.0526997 + 0.0912786i 0.891172 0.453666i \(-0.149884\pi\)
−0.838472 + 0.544944i \(0.816551\pi\)
\(140\) 0 0
\(141\) 7.24264 12.5446i 0.609940 1.05645i
\(142\) 0 0
\(143\) 11.3492 + 2.80821i 0.949071 + 0.234834i
\(144\) 0 0
\(145\) −12.2426 + 21.2049i −1.01670 + 1.76097i
\(146\) 0 0
\(147\) 15.0711 + 26.1039i 1.24304 + 2.15301i
\(148\) 0 0
\(149\) 1.67157 + 2.89525i 0.136941 + 0.237188i 0.926337 0.376696i \(-0.122940\pi\)
−0.789397 + 0.613884i \(0.789606\pi\)
\(150\) 0 0
\(151\) −16.9706 −1.38104 −0.690522 0.723311i \(-0.742619\pi\)
−0.690522 + 0.723311i \(0.742619\pi\)
\(152\) 0 0
\(153\) 8.24264 14.2767i 0.666378 1.15420i
\(154\) 0 0
\(155\) 16.0000 1.28515
\(156\) 0 0
\(157\) −0.485281 −0.0387297 −0.0193648 0.999812i \(-0.506164\pi\)
−0.0193648 + 0.999812i \(0.506164\pi\)
\(158\) 0 0
\(159\) −3.41421 + 5.91359i −0.270765 + 0.468978i
\(160\) 0 0
\(161\) 5.48528 0.432301
\(162\) 0 0
\(163\) −8.37868 14.5123i −0.656269 1.13669i −0.981574 0.191082i \(-0.938800\pi\)
0.325305 0.945609i \(-0.394533\pi\)
\(164\) 0 0
\(165\) 11.0711 + 19.1757i 0.861881 + 1.49282i
\(166\) 0 0
\(167\) 7.86396 13.6208i 0.608532 1.05401i −0.382951 0.923769i \(-0.625092\pi\)
0.991483 0.130239i \(-0.0415745\pi\)
\(168\) 0 0
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 0 0
\(171\) 1.75736 3.04384i 0.134389 0.232768i
\(172\) 0 0
\(173\) 4.50000 + 7.79423i 0.342129 + 0.592584i 0.984828 0.173534i \(-0.0555188\pi\)
−0.642699 + 0.766119i \(0.722185\pi\)
\(174\) 0 0
\(175\) −6.62132 11.4685i −0.500525 0.866934i
\(176\) 0 0
\(177\) 3.00000 0.225494
\(178\) 0 0
\(179\) 6.37868 11.0482i 0.476765 0.825781i −0.522881 0.852406i \(-0.675143\pi\)
0.999645 + 0.0266249i \(0.00847597\pi\)
\(180\) 0 0
\(181\) −0.485281 −0.0360707 −0.0180353 0.999837i \(-0.505741\pi\)
−0.0180353 + 0.999837i \(0.505741\pi\)
\(182\) 0 0
\(183\) −16.8995 −1.24925
\(184\) 0 0
\(185\) 10.5858 18.3351i 0.778282 1.34802i
\(186\) 0 0
\(187\) −18.8995 −1.38207
\(188\) 0 0
\(189\) −0.914214 1.58346i −0.0664993 0.115180i
\(190\) 0 0
\(191\) −3.37868 5.85204i −0.244473 0.423439i 0.717511 0.696548i \(-0.245282\pi\)
−0.961983 + 0.273109i \(0.911948\pi\)
\(192\) 0 0
\(193\) 9.74264 16.8747i 0.701291 1.21467i −0.266723 0.963773i \(-0.585941\pi\)
0.968014 0.250898i \(-0.0807258\pi\)
\(194\) 0 0
\(195\) −23.8995 5.91359i −1.71148 0.423481i
\(196\) 0 0
\(197\) −1.50000 + 2.59808i −0.106871 + 0.185105i −0.914501 0.404584i \(-0.867416\pi\)
0.807630 + 0.589689i \(0.200750\pi\)
\(198\) 0 0
\(199\) 12.1066 + 20.9692i 0.858214 + 1.48647i 0.873631 + 0.486590i \(0.161759\pi\)
−0.0154165 + 0.999881i \(0.504907\pi\)
\(200\) 0 0
\(201\) 15.9853 + 27.6873i 1.12751 + 1.95291i
\(202\) 0 0
\(203\) 38.2132 2.68204
\(204\) 0 0
\(205\) 8.24264 14.2767i 0.575691 0.997126i
\(206\) 0 0
\(207\) 3.51472 0.244290
\(208\) 0 0
\(209\) −4.02944 −0.278722
\(210\) 0 0
\(211\) −6.79289 + 11.7656i −0.467642 + 0.809980i −0.999316 0.0369691i \(-0.988230\pi\)
0.531674 + 0.846949i \(0.321563\pi\)
\(212\) 0 0
\(213\) 17.4853 1.19807
\(214\) 0 0
\(215\) −5.75736 9.97204i −0.392649 0.680087i
\(216\) 0 0
\(217\) −12.4853 21.6251i −0.847556 1.46801i
\(218\) 0 0
\(219\) 15.0711 26.1039i 1.01841 1.76394i
\(220\) 0 0
\(221\) 14.5711 15.1427i 0.980156 1.01861i
\(222\) 0 0
\(223\) −3.44975 + 5.97514i −0.231012 + 0.400125i −0.958106 0.286413i \(-0.907537\pi\)
0.727094 + 0.686538i \(0.240870\pi\)
\(224\) 0 0
\(225\) −4.24264 7.34847i −0.282843 0.489898i
\(226\) 0 0
\(227\) −7.86396 13.6208i −0.521949 0.904043i −0.999674 0.0255332i \(-0.991872\pi\)
0.477725 0.878510i \(-0.341462\pi\)
\(228\) 0 0
\(229\) 8.48528 0.560723 0.280362 0.959894i \(-0.409546\pi\)
0.280362 + 0.959894i \(0.409546\pi\)
\(230\) 0 0
\(231\) 17.2782 29.9267i 1.13682 1.96903i
\(232\) 0 0
\(233\) −20.4853 −1.34204 −0.671018 0.741441i \(-0.734143\pi\)
−0.671018 + 0.741441i \(0.734143\pi\)
\(234\) 0 0
\(235\) 16.9706 1.10704
\(236\) 0 0
\(237\) −7.24264 + 12.5446i −0.470460 + 0.814861i
\(238\) 0 0
\(239\) −8.97056 −0.580257 −0.290129 0.956988i \(-0.593698\pi\)
−0.290129 + 0.956988i \(0.593698\pi\)
\(240\) 0 0
\(241\) −15.2279 26.3755i −0.980917 1.69900i −0.658838 0.752285i \(-0.728952\pi\)
−0.322078 0.946713i \(-0.604381\pi\)
\(242\) 0 0
\(243\) −10.8284 18.7554i −0.694644 1.20316i
\(244\) 0 0
\(245\) −17.6569 + 30.5826i −1.12806 + 1.95385i
\(246\) 0 0
\(247\) 3.10660 3.22848i 0.197668 0.205423i
\(248\) 0 0
\(249\) 4.82843 8.36308i 0.305989 0.529989i
\(250\) 0 0
\(251\) −8.86396 15.3528i −0.559488 0.969062i −0.997539 0.0701119i \(-0.977664\pi\)
0.438051 0.898950i \(-0.355669\pi\)
\(252\) 0 0
\(253\) −2.01472 3.48960i −0.126664 0.219389i
\(254\) 0 0
\(255\) 39.7990 2.49231
\(256\) 0 0
\(257\) −8.39949 + 14.5484i −0.523946 + 0.907501i 0.475665 + 0.879626i \(0.342207\pi\)
−0.999611 + 0.0278749i \(0.991126\pi\)
\(258\) 0 0
\(259\) −33.0416 −2.05311
\(260\) 0 0
\(261\) 24.4853 1.51560
\(262\) 0 0
\(263\) −4.62132 + 8.00436i −0.284963 + 0.493570i −0.972600 0.232484i \(-0.925315\pi\)
0.687637 + 0.726054i \(0.258648\pi\)
\(264\) 0 0
\(265\) −8.00000 −0.491436
\(266\) 0 0
\(267\) −4.03553 6.98975i −0.246971 0.427766i
\(268\) 0 0
\(269\) −2.74264 4.75039i −0.167222 0.289637i 0.770220 0.637778i \(-0.220146\pi\)
−0.937442 + 0.348141i \(0.886813\pi\)
\(270\) 0 0
\(271\) −12.6213 + 21.8608i −0.766691 + 1.32795i 0.172658 + 0.984982i \(0.444765\pi\)
−0.939348 + 0.342965i \(0.888569\pi\)
\(272\) 0 0
\(273\) 10.6569 + 36.9164i 0.644982 + 2.23428i
\(274\) 0 0
\(275\) −4.86396 + 8.42463i −0.293308 + 0.508024i
\(276\) 0 0
\(277\) −6.74264 11.6786i −0.405126 0.701699i 0.589210 0.807980i \(-0.299439\pi\)
−0.994336 + 0.106281i \(0.966106\pi\)
\(278\) 0 0
\(279\) −8.00000 13.8564i −0.478947 0.829561i
\(280\) 0 0
\(281\) −2.14214 −0.127789 −0.0638945 0.997957i \(-0.520352\pi\)
−0.0638945 + 0.997957i \(0.520352\pi\)
\(282\) 0 0
\(283\) 5.20711 9.01897i 0.309530 0.536122i −0.668729 0.743506i \(-0.733161\pi\)
0.978260 + 0.207384i \(0.0664948\pi\)
\(284\) 0 0
\(285\) 8.48528 0.502625
\(286\) 0 0
\(287\) −25.7279 −1.51867
\(288\) 0 0
\(289\) −8.48528 + 14.6969i −0.499134 + 0.864526i
\(290\) 0 0
\(291\) 21.7279 1.27371
\(292\) 0 0
\(293\) −1.15685 2.00373i −0.0675841 0.117059i 0.830253 0.557386i \(-0.188196\pi\)
−0.897837 + 0.440327i \(0.854862\pi\)
\(294\) 0 0
\(295\) 1.75736 + 3.04384i 0.102317 + 0.177219i
\(296\) 0 0
\(297\) −0.671573 + 1.16320i −0.0389686 + 0.0674956i
\(298\) 0 0
\(299\) 4.34924 + 1.07616i 0.251523 + 0.0622358i
\(300\) 0 0
\(301\) −8.98528 + 15.5630i −0.517903 + 0.897034i
\(302\) 0 0
\(303\) 14.2782 + 24.7305i 0.820260 + 1.42073i
\(304\) 0 0
\(305\) −9.89949 17.1464i −0.566843 0.981802i
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 20.4853 1.15790 0.578948 0.815364i \(-0.303463\pi\)
0.578948 + 0.815364i \(0.303463\pi\)
\(314\) 0 0
\(315\) −17.6569 + 30.5826i −0.994851 + 1.72313i
\(316\) 0 0
\(317\) −17.3137 −0.972435 −0.486217 0.873838i \(-0.661624\pi\)
−0.486217 + 0.873838i \(0.661624\pi\)
\(318\) 0 0
\(319\) −14.0355 24.3103i −0.785839 1.36111i
\(320\) 0 0
\(321\) 23.2279 + 40.2319i 1.29646 + 2.24553i
\(322\) 0 0
\(323\) −3.62132 + 6.27231i −0.201496 + 0.349001i
\(324\) 0 0
\(325\) −3.00000 10.3923i −0.166410 0.576461i
\(326\) 0 0
\(327\) −10.2426 + 17.7408i −0.566419 + 0.981067i
\(328\) 0 0
\(329\) −13.2426 22.9369i −0.730090 1.26455i
\(330\) 0 0
\(331\) 3.62132 + 6.27231i 0.199046 + 0.344757i 0.948219 0.317616i \(-0.102882\pi\)
−0.749174 + 0.662374i \(0.769549\pi\)
\(332\) 0 0
\(333\) −21.1716 −1.16020
\(334\) 0 0
\(335\) −18.7279 + 32.4377i −1.02322 + 1.77226i
\(336\) 0 0
\(337\) 4.48528 0.244329 0.122164 0.992510i \(-0.461016\pi\)
0.122164 + 0.992510i \(0.461016\pi\)
\(338\) 0 0
\(339\) 0.414214 0.0224970
\(340\) 0 0
\(341\) −9.17157 + 15.8856i −0.496669 + 0.860255i
\(342\) 0 0
\(343\) 24.2132 1.30739
\(344\) 0 0
\(345\) 4.24264 + 7.34847i 0.228416 + 0.395628i
\(346\) 0 0
\(347\) 15.6213 + 27.0569i 0.838596 + 1.45249i 0.891068 + 0.453869i \(0.149957\pi\)
−0.0524719 + 0.998622i \(0.516710\pi\)
\(348\) 0 0
\(349\) −17.2279 + 29.8396i −0.922190 + 1.59728i −0.126170 + 0.992009i \(0.540268\pi\)
−0.796020 + 0.605270i \(0.793065\pi\)
\(350\) 0 0
\(351\) −0.414214 1.43488i −0.0221091 0.0765881i
\(352\) 0 0
\(353\) 7.32843 12.6932i 0.390053 0.675591i −0.602403 0.798192i \(-0.705790\pi\)
0.992456 + 0.122601i \(0.0391234\pi\)
\(354\) 0 0
\(355\) 10.2426 + 17.7408i 0.543623 + 0.941583i
\(356\) 0 0
\(357\) −31.0563 53.7912i −1.64368 2.84693i
\(358\) 0 0
\(359\) −8.00000 −0.422224 −0.211112 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 0 0
\(361\) 8.72792 15.1172i 0.459364 0.795642i
\(362\) 0 0
\(363\) 1.17157 0.0614916
\(364\) 0 0
\(365\) 35.3137 1.84840
\(366\) 0 0
\(367\) −4.13604 + 7.16383i −0.215899 + 0.373949i −0.953550 0.301233i \(-0.902602\pi\)
0.737651 + 0.675182i \(0.235935\pi\)
\(368\) 0 0
\(369\) −16.4853 −0.858189
\(370\) 0 0
\(371\) 6.24264 + 10.8126i 0.324102 + 0.561361i
\(372\) 0 0
\(373\) −18.7426 32.4632i −0.970457 1.68088i −0.694178 0.719804i \(-0.744232\pi\)
−0.276280 0.961077i \(-0.589102\pi\)
\(374\) 0 0
\(375\) −6.82843 + 11.8272i −0.352618 + 0.610753i
\(376\) 0 0
\(377\) 30.2990 + 7.49706i 1.56048 + 0.386118i
\(378\) 0 0
\(379\) 13.6924 23.7159i 0.703331 1.21820i −0.263960 0.964534i \(-0.585029\pi\)
0.967291 0.253671i \(-0.0816380\pi\)
\(380\) 0 0
\(381\) 1.91421 + 3.31552i 0.0980681 + 0.169859i
\(382\) 0 0
\(383\) −7.86396 13.6208i −0.401830 0.695989i 0.592117 0.805852i \(-0.298292\pi\)
−0.993947 + 0.109863i \(0.964959\pi\)
\(384\) 0 0
\(385\) 40.4853 2.06332
\(386\) 0 0
\(387\) −5.75736 + 9.97204i −0.292663 + 0.506907i
\(388\) 0 0
\(389\) −16.6274 −0.843044 −0.421522 0.906818i \(-0.638504\pi\)
−0.421522 + 0.906818i \(0.638504\pi\)
\(390\) 0 0
\(391\) −7.24264 −0.366276
\(392\) 0 0
\(393\) −4.82843 + 8.36308i −0.243562 + 0.421862i
\(394\) 0 0
\(395\) −16.9706 −0.853882
\(396\) 0 0
\(397\) 5.74264 + 9.94655i 0.288215 + 0.499203i 0.973384 0.229181i \(-0.0736049\pi\)
−0.685169 + 0.728384i \(0.740272\pi\)
\(398\) 0 0
\(399\) −6.62132 11.4685i −0.331481 0.574141i
\(400\) 0 0
\(401\) −5.57107 + 9.64937i −0.278206 + 0.481867i −0.970939 0.239327i \(-0.923073\pi\)
0.692733 + 0.721194i \(0.256406\pi\)
\(402\) 0 0
\(403\) −5.65685 19.5959i −0.281788 0.976142i
\(404\) 0 0
\(405\) 13.4142 23.2341i 0.666558 1.15451i
\(406\) 0 0
\(407\) 12.1360 + 21.0202i 0.601561 + 1.04193i
\(408\) 0 0
\(409\) 5.25736 + 9.10601i 0.259960 + 0.450263i 0.966231 0.257678i \(-0.0829574\pi\)
−0.706271 + 0.707941i \(0.749624\pi\)
\(410\) 0 0
\(411\) −22.5563 −1.11262
\(412\) 0 0
\(413\) 2.74264 4.75039i 0.134957 0.233752i
\(414\) 0 0
\(415\) 11.3137 0.555368
\(416\) 0 0
\(417\) 3.00000 0.146911
\(418\) 0 0
\(419\) 5.86396 10.1567i 0.286473 0.496186i −0.686492 0.727137i \(-0.740850\pi\)
0.972965 + 0.230951i \(0.0741837\pi\)
\(420\) 0 0
\(421\) 0.485281 0.0236512 0.0118256 0.999930i \(-0.496236\pi\)
0.0118256 + 0.999930i \(0.496236\pi\)
\(422\) 0 0
\(423\) −8.48528 14.6969i −0.412568 0.714590i
\(424\) 0 0
\(425\) 8.74264 + 15.1427i 0.424080 + 0.734529i
\(426\) 0 0
\(427\) −15.4497 + 26.7597i −0.747666 + 1.29499i
\(428\) 0 0
\(429\) 19.5711 20.3389i 0.944900 0.981969i
\(430\) 0 0
\(431\) 17.3492 30.0498i 0.835684 1.44745i −0.0577890 0.998329i \(-0.518405\pi\)
0.893473 0.449118i \(-0.148262\pi\)
\(432\) 0 0
\(433\) 1.25736 + 2.17781i 0.0604248 + 0.104659i 0.894655 0.446757i \(-0.147421\pi\)
−0.834231 + 0.551416i \(0.814088\pi\)
\(434\) 0 0
\(435\) 29.5563 + 51.1931i 1.41712 + 2.45452i
\(436\) 0 0
\(437\) −1.54416 −0.0738670
\(438\) 0 0
\(439\) 14.0355 24.3103i 0.669879 1.16027i −0.308058 0.951368i \(-0.599679\pi\)
0.977937 0.208898i \(-0.0669876\pi\)
\(440\) 0 0
\(441\) 35.3137 1.68161
\(442\) 0 0
\(443\) −28.9706 −1.37643 −0.688216 0.725505i \(-0.741606\pi\)
−0.688216 + 0.725505i \(0.741606\pi\)
\(444\) 0 0
\(445\) 4.72792 8.18900i 0.224125 0.388196i
\(446\) 0 0
\(447\) 8.07107 0.381748
\(448\) 0 0
\(449\) −6.25736 10.8381i −0.295303 0.511480i 0.679752 0.733442i \(-0.262087\pi\)
−0.975055 + 0.221962i \(0.928754\pi\)
\(450\) 0 0
\(451\) 9.44975 + 16.3674i 0.444971 + 0.770713i
\(452\) 0 0
\(453\) −20.4853 + 35.4815i −0.962482 + 1.66707i
\(454\) 0 0
\(455\) −31.2132 + 32.4377i −1.46330 + 1.52070i
\(456\) 0 0
\(457\) −15.5000 + 26.8468i −0.725059 + 1.25584i 0.233890 + 0.972263i \(0.424854\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) 0 0
\(459\) 1.20711 + 2.09077i 0.0563429 + 0.0975888i
\(460\) 0 0
\(461\) −0.600505 1.04011i −0.0279683 0.0484425i 0.851702 0.524026i \(-0.175570\pi\)
−0.879671 + 0.475583i \(0.842237\pi\)
\(462\) 0 0
\(463\) 18.3431 0.852478 0.426239 0.904611i \(-0.359838\pi\)
0.426239 + 0.904611i \(0.359838\pi\)
\(464\) 0 0
\(465\) 19.3137 33.4523i 0.895652 1.55131i
\(466\) 0 0
\(467\) 6.97056 0.322559 0.161280 0.986909i \(-0.448438\pi\)
0.161280 + 0.986909i \(0.448438\pi\)
\(468\) 0 0
\(469\) 58.4558 2.69924
\(470\) 0 0
\(471\) −0.585786 + 1.01461i −0.0269916 + 0.0467508i
\(472\) 0 0
\(473\) 13.2010 0.606983
\(474\) 0 0
\(475\) 1.86396 + 3.22848i 0.0855244 + 0.148133i
\(476\) 0 0
\(477\) 4.00000 + 6.92820i 0.183147 + 0.317221i
\(478\) 0 0
\(479\) 4.37868 7.58410i 0.200067 0.346526i −0.748483 0.663154i \(-0.769217\pi\)
0.948550 + 0.316628i \(0.102551\pi\)
\(480\) 0 0
\(481\) −26.1985 6.48244i −1.19455 0.295574i
\(482\) 0 0
\(483\) 6.62132 11.4685i 0.301281 0.521833i
\(484\) 0 0
\(485\) 12.7279 + 22.0454i 0.577945 + 1.00103i
\(486\) 0 0
\(487\) 6.44975 + 11.1713i 0.292266 + 0.506219i 0.974345 0.225059i \(-0.0722574\pi\)
−0.682079 + 0.731278i \(0.738924\pi\)
\(488\) 0 0
\(489\) −40.4558 −1.82948
\(490\) 0 0
\(491\) −11.1066 + 19.2372i −0.501234 + 0.868163i 0.498765 + 0.866737i \(0.333787\pi\)
−0.999999 + 0.00142539i \(0.999546\pi\)
\(492\) 0 0
\(493\) −50.4558 −2.27242
\(494\) 0 0
\(495\) 25.9411 1.16597
\(496\) 0 0
\(497\) 15.9853 27.6873i 0.717038 1.24195i
\(498\) 0 0
\(499\) −17.6569 −0.790429 −0.395215 0.918589i \(-0.629330\pi\)
−0.395215 + 0.918589i \(0.629330\pi\)
\(500\) 0 0
\(501\) −18.9853 32.8835i −0.848200 1.46913i
\(502\) 0 0
\(503\) −7.37868 12.7802i −0.328999 0.569843i 0.653314 0.757087i \(-0.273378\pi\)
−0.982314 + 0.187244i \(0.940045\pi\)
\(504\) 0 0
\(505\) −16.7279 + 28.9736i −0.744383 + 1.28931i
\(506\) 0 0
\(507\) 1.20711 + 31.3616i 0.0536095 + 1.39282i
\(508\) 0 0
\(509\) 2.57107 4.45322i 0.113961 0.197386i −0.803403 0.595435i \(-0.796980\pi\)
0.917364 + 0.398050i \(0.130313\pi\)
\(510\) 0 0
\(511\) −27.5563 47.7290i −1.21902 2.11141i
\(512\) 0 0
\(513\) 0.257359 + 0.445759i 0.0113627 + 0.0196808i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −9.72792 + 16.8493i −0.427834 + 0.741029i
\(518\) 0 0
\(519\) 21.7279 0.953750
\(520\) 0 0
\(521\) −9.17157 −0.401814 −0.200907 0.979610i \(-0.564389\pi\)
−0.200907 + 0.979610i \(0.564389\pi\)
\(522\) 0 0
\(523\) 8.20711 14.2151i 0.358872 0.621584i −0.628901 0.777485i \(-0.716495\pi\)
0.987773 + 0.155901i \(0.0498282\pi\)
\(524\) 0 0
\(525\) −31.9706 −1.39531
\(526\) 0 0
\(527\) 16.4853 + 28.5533i 0.718110 + 1.24380i
\(528\) 0 0
\(529\) 10.7279 + 18.5813i 0.466431 + 0.807883i
\(530\) 0 0
\(531\) 1.75736 3.04384i 0.0762629 0.132091i
\(532\) 0 0
\(533\) −20.3995 5.04757i −0.883600 0.218634i
\(534\) 0 0
\(535\) −27.2132 + 47.1347i −1.17653 + 2.03781i
\(536\) 0 0
\(537\) −15.3995 26.6727i −0.664537 1.15101i
\(538\) 0 0
\(539\) −20.2426 35.0613i −0.871912 1.51020i
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 0 0
\(543\) −0.585786 + 1.01461i −0.0251385 + 0.0435412i
\(544\) 0 0
\(545\) −24.0000 −1.02805
\(546\) 0 0
\(547\) 36.0000 1.53925 0.769624 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) 0 0
\(549\) −9.89949 + 17.1464i −0.422500 + 0.731792i
\(550\) 0 0
\(551\) −10.7574 −0.458279
\(552\) 0 0
\(553\) 13.2426 + 22.9369i 0.563134 + 0.975377i
\(554\) 0 0
\(555\) −25.5563 44.2649i −1.08481 1.87894i
\(556\) 0 0
\(557\) −4.32843 + 7.49706i −0.183401 + 0.317660i −0.943037 0.332689i \(-0.892044\pi\)
0.759635 + 0.650349i \(0.225377\pi\)
\(558\) 0 0
\(559\) −10.1777 + 10.5769i −0.430470 + 0.447357i
\(560\) 0 0
\(561\) −22.8137 + 39.5145i −0.963196 + 1.66830i
\(562\) 0 0
\(563\) −16.3492 28.3177i −0.689038 1.19345i −0.972149 0.234362i \(-0.924700\pi\)
0.283111 0.959087i \(-0.408634\pi\)
\(564\) 0 0
\(565\) 0.242641 + 0.420266i 0.0102080 + 0.0176807i
\(566\) 0 0
\(567\) −41.8701 −1.75838
\(568\) 0 0
\(569\) 12.9853 22.4912i 0.544371 0.942879i −0.454275 0.890862i \(-0.650102\pi\)
0.998646 0.0520172i \(-0.0165651\pi\)
\(570\) 0 0
\(571\) 40.2843 1.68584 0.842922 0.538036i \(-0.180833\pi\)
0.842922 + 0.538036i \(0.180833\pi\)
\(572\) 0 0
\(573\) −16.3137 −0.681515
\(574\) 0 0
\(575\) −1.86396 + 3.22848i −0.0777325 + 0.134637i
\(576\) 0 0
\(577\) 4.48528 0.186725 0.0933624 0.995632i \(-0.470238\pi\)
0.0933624 + 0.995632i \(0.470238\pi\)
\(578\) 0 0
\(579\) −23.5208 40.7392i −0.977492 1.69307i
\(580\) 0 0
\(581\) −8.82843 15.2913i −0.366265 0.634389i
\(582\) 0 0
\(583\) 4.58579 7.94282i 0.189924 0.328958i
\(584\) 0 0
\(585\) −20.0000 + 20.7846i −0.826898 + 0.859338i
\(586\) 0 0
\(587\) 10.3492 17.9254i 0.427159 0.739861i −0.569460 0.822019i \(-0.692848\pi\)
0.996619 + 0.0821578i \(0.0261811\pi\)
\(588\) 0 0
\(589\) 3.51472 + 6.08767i 0.144821 + 0.250838i
\(590\) 0 0
\(591\) 3.62132 + 6.27231i 0.148961 + 0.258008i
\(592\) 0 0
\(593\) 14.8284 0.608931 0.304465 0.952523i \(-0.401522\pi\)
0.304465 + 0.952523i \(0.401522\pi\)
\(594\) 0 0
\(595\) 36.3848 63.0203i 1.49163 2.58358i
\(596\) 0 0
\(597\) 58.4558 2.39244
\(598\) 0 0
\(599\) 47.9411 1.95882 0.979411 0.201878i \(-0.0647045\pi\)
0.979411 + 0.201878i \(0.0647045\pi\)
\(600\) 0 0
\(601\) 5.25736 9.10601i 0.214452 0.371442i −0.738651 0.674088i \(-0.764537\pi\)
0.953103 + 0.302646i \(0.0978701\pi\)
\(602\) 0 0
\(603\) 37.4558 1.52532
\(604\) 0 0
\(605\) 0.686292 + 1.18869i 0.0279017 + 0.0483272i
\(606\) 0 0
\(607\) 0.792893 + 1.37333i 0.0321825 + 0.0557418i 0.881668 0.471870i \(-0.156421\pi\)
−0.849486 + 0.527612i \(0.823088\pi\)
\(608\) 0 0
\(609\) 46.1274 79.8950i 1.86918 3.23751i
\(610\) 0 0
\(611\) −6.00000 20.7846i −0.242734 0.840855i
\(612\) 0 0
\(613\) 7.25736 12.5701i 0.293122 0.507702i −0.681424 0.731889i \(-0.738639\pi\)
0.974546 + 0.224186i \(0.0719725\pi\)
\(614\) 0 0
\(615\) −19.8995 34.4669i −0.802425 1.38984i
\(616\) 0 0
\(617\) 22.1569 + 38.3768i 0.892001 + 1.54499i 0.837472 + 0.546479i \(0.184032\pi\)
0.0545289 + 0.998512i \(0.482634\pi\)
\(618\) 0 0
\(619\) −4.97056 −0.199784 −0.0998919 0.994998i \(-0.531850\pi\)
−0.0998919 + 0.994998i \(0.531850\pi\)
\(620\) 0 0
\(621\) −0.257359 + 0.445759i −0.0103275 + 0.0178877i
\(622\) 0 0
\(623\) −14.7574 −0.591241
\(624\) 0 0
\(625\) −31.0000 −1.24000
\(626\) 0 0
\(627\) −4.86396 + 8.42463i −0.194248 + 0.336447i
\(628\) 0 0
\(629\) 43.6274 1.73954
\(630\) 0 0
\(631\) 3.62132 + 6.27231i 0.144162 + 0.249697i 0.929060 0.369929i \(-0.120618\pi\)
−0.784898 + 0.619625i \(0.787285\pi\)
\(632\) 0 0
\(633\) 16.3995 + 28.4048i 0.651821 + 1.12899i
\(634\) 0 0
\(635\) −2.24264 + 3.88437i −0.0889965 + 0.154146i
\(636\) 0 0
\(637\) 43.6985 + 10.8126i 1.73140 + 0.428410i
\(638\) 0 0
\(639\) 10.2426 17.7408i 0.405193 0.701814i
\(640\) 0 0
\(641\) 11.3995 + 19.7445i 0.450253 + 0.779861i 0.998401 0.0565200i \(-0.0180005\pi\)
−0.548148 + 0.836381i \(0.684667\pi\)
\(642\) 0 0
\(643\) 0.106602 + 0.184640i 0.00420396 + 0.00728147i 0.868120 0.496355i \(-0.165329\pi\)
−0.863916 + 0.503636i \(0.831995\pi\)
\(644\) 0 0
\(645\) −27.7990 −1.09458
\(646\) 0 0
\(647\) −11.6213 + 20.1287i −0.456881 + 0.791342i −0.998794 0.0490931i \(-0.984367\pi\)
0.541913 + 0.840435i \(0.317700\pi\)
\(648\) 0 0
\(649\) −4.02944 −0.158169
\(650\) 0 0
\(651\) −60.2843 −2.36273
\(652\) 0 0
\(653\) −11.5711 + 20.0417i −0.452811 + 0.784291i −0.998559 0.0536576i \(-0.982912\pi\)
0.545749 + 0.837949i \(0.316245\pi\)
\(654\) 0 0
\(655\) −11.3137 −0.442063
\(656\) 0 0
\(657\) −17.6569 30.5826i −0.688859 1.19314i
\(658\) 0 0
\(659\) 12.1066 + 20.9692i 0.471606 + 0.816846i 0.999472 0.0324816i \(-0.0103410\pi\)
−0.527866 + 0.849328i \(0.677008\pi\)
\(660\) 0 0
\(661\) 12.2279 21.1794i 0.475611 0.823782i −0.523999 0.851719i \(-0.675560\pi\)
0.999610 + 0.0279366i \(0.00889365\pi\)
\(662\) 0 0
\(663\) −14.0711 48.7436i −0.546475 1.89304i
\(664\) 0 0
\(665\) 7.75736 13.4361i 0.300817 0.521031i
\(666\) 0 0
\(667\) −5.37868 9.31615i −0.208263 0.360723i
\(668\) 0 0
\(669\) 8.32843 + 14.4253i 0.321996 + 0.557713i
\(670\) 0 0
\(671\) 22.6985 0.876265
\(672\) 0 0
\(673\) 4.01472 6.95370i 0.154756 0.268045i −0.778214 0.627999i \(-0.783874\pi\)
0.932970 + 0.359954i \(0.117208\pi\)
\(674\) 0 0
\(675\) 1.24264 0.0478293
\(676\) 0 0
\(677\) −25.4558 −0.978348 −0.489174 0.872186i \(-0.662702\pi\)
−0.489174 + 0.872186i \(0.662702\pi\)
\(678\) 0 0
\(679\) 19.8640 34.4054i 0.762309 1.32036i
\(680\) 0 0
\(681\) −37.9706 −1.45504
\(682\) 0 0
\(683\) 4.62132 + 8.00436i 0.176830 + 0.306278i 0.940793 0.338982i \(-0.110082\pi\)
−0.763963 + 0.645260i \(0.776749\pi\)
\(684\) 0 0
\(685\) −13.2132 22.8859i −0.504851 0.874427i
\(686\) 0 0
\(687\) 10.2426 17.7408i 0.390781 0.676853i
\(688\) 0 0
\(689\) 2.82843 + 9.79796i 0.107754 + 0.373273i
\(690\) 0 0
\(691\) 8.03553 13.9180i 0.305686 0.529464i −0.671728 0.740798i \(-0.734448\pi\)
0.977414 + 0.211334i \(0.0677808\pi\)
\(692\) 0 0
\(693\) −20.2426 35.0613i −0.768954 1.33187i
\(694\) 0 0
\(695\) 1.75736 + 3.04384i 0.0666604 + 0.115459i
\(696\) 0 0
\(697\) 33.9706 1.28673
\(698\) 0 0
\(699\) −24.7279 + 42.8300i −0.935296 + 1.61998i
\(700\) 0 0
\(701\) −8.48528 −0.320485 −0.160242 0.987078i \(-0.551228\pi\)
−0.160242 + 0.987078i \(0.551228\pi\)
\(702\) 0 0
\(703\) 9.30152 0.350813
\(704\) 0 0
\(705\) 20.4853 35.4815i 0.771520 1.33631i
\(706\) 0 0
\(707\) 52.2132 1.96368
\(708\) 0 0
\(709\) 9.74264 + 16.8747i 0.365893 + 0.633744i 0.988919 0.148456i \(-0.0474304\pi\)
−0.623026 + 0.782201i \(0.714097\pi\)
\(710\) 0 0
\(711\) 8.48528 + 14.6969i 0.318223 + 0.551178i
\(712\) 0 0
\(713\) −3.51472 + 6.08767i −0.131627 + 0.227985i
\(714\) 0 0
\(715\) 32.1005 + 7.94282i 1.20049 + 0.297044i
\(716\) 0 0
\(717\) −10.8284 + 18.7554i −0.404395 + 0.700433i
\(718\) 0 0
\(719\) −11.3787 19.7085i −0.424353 0.735001i 0.572007 0.820249i \(-0.306165\pi\)
−0.996360 + 0.0852478i \(0.972832\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −73.5269 −2.73450
\(724\) 0 0
\(725\) −12.9853 + 22.4912i −0.482261 + 0.835301i
\(726\) 0 0
\(727\) −35.3137 −1.30971 −0.654856 0.755753i \(-0.727271\pi\)
−0.654856 + 0.755753i \(0.727271\pi\)
\(728\) 0 0
\(729\) −23.8284 −0.882534
\(730\) 0 0
\(731\) 11.8640 20.5490i 0.438804 0.760032i
\(732\) 0 0
\(733\) 43.9411 1.62300 0.811501 0.584351i \(-0.198651\pi\)
0.811501 + 0.584351i \(0.198651\pi\)
\(734\) 0 0
\(735\) 42.6274 + 73.8329i 1.57234 + 2.72337i
\(736\) 0 0
\(737\) −21.4706 37.1881i −0.790878 1.36984i
\(738\) 0 0
\(739\) −15.1066 + 26.1654i −0.555705 + 0.962510i 0.442143 + 0.896945i \(0.354218\pi\)
−0.997848 + 0.0655653i \(0.979115\pi\)
\(740\) 0 0
\(741\) −3.00000 10.3923i −0.110208 0.381771i
\(742\) 0 0
\(743\) −3.62132 + 6.27231i −0.132853 + 0.230109i −0.924775 0.380513i \(-0.875747\pi\)
0.791922 + 0.610622i \(0.209081\pi\)
\(744\) 0 0
\(745\) 4.72792 + 8.18900i 0.173218 + 0.300022i
\(746\) 0 0
\(747\) −5.65685 9.79796i −0.206973 0.358489i
\(748\) 0 0
\(749\) 84.9411 3.10368
\(750\) 0 0
\(751\) 8.55025 14.8095i 0.312003 0.540405i −0.666793 0.745243i \(-0.732333\pi\)
0.978796 + 0.204838i \(0.0656667\pi\)
\(752\) 0 0
\(753\) −42.7990 −1.55968
\(754\) 0 0
\(755\) −48.0000 −1.74690
\(756\) 0 0
\(757\) 11.7426 20.3389i 0.426794 0.739228i −0.569793 0.821789i \(-0.692976\pi\)
0.996586 + 0.0825605i \(0.0263098\pi\)
\(758\) 0 0
\(759\) −9.72792 −0.353101
\(760\) 0 0
\(761\) −14.7426 25.5350i −0.534420 0.925643i −0.999191 0.0402121i \(-0.987197\pi\)
0.464771 0.885431i \(-0.346137\pi\)
\(762\) 0 0
\(763\) 18.7279 + 32.4377i 0.677996 + 1.17432i
\(764\) 0 0
\(765\) 23.3137 40.3805i 0.842909 1.45996i
\(766\) 0 0
\(767\) 3.10660 3.22848i 0.112173 0.116573i
\(768\) 0 0
\(769\) 22.7132 39.3404i 0.819059 1.41865i −0.0873172 0.996181i \(-0.527829\pi\)
0.906376 0.422471i \(-0.138837\pi\)
\(770\) 0 0
\(771\) 20.2782 + 35.1228i 0.730301 + 1.26492i
\(772\) 0 0
\(773\) 5.74264 + 9.94655i 0.206548 + 0.357752i 0.950625 0.310342i \(-0.100444\pi\)
−0.744077 + 0.668094i \(0.767110\pi\)
\(774\) 0 0
\(775\) 16.9706 0.609601
\(776\) 0 0
\(777\) −39.8848 + 69.0825i −1.43086 + 2.47832i
\(778\) 0 0
\(779\) 7.24264 0.259495
\(780\) 0 0
\(781\) −23.4853 −0.840369
\(782\) 0 0
\(783\) −1.79289 + 3.10538i −0.0640728 + 0.110977i
\(784\) 0 0
\(785\) −1.37258 −0.0489896
\(786\) 0 0
\(787\) −19.0061 32.9195i −0.677494 1.17345i −0.975733 0.218963i \(-0.929733\pi\)
0.298239 0.954491i \(-0.403601\pi\)
\(788\) 0 0
\(789\) 11.1569 + 19.3242i 0.397195 + 0.687961i
\(790\) 0 0