Properties

Label 855.2.k.h.406.4
Level $855$
Weight $2$
Character 855.406
Analytic conductor $6.827$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(406,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, 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("855.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.k (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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.4601315889.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 406.4
Root \(-0.245959 - 0.426014i\) of defining polynomial
Character \(\chi\) \(=\) 855.406
Dual form 855.2.k.h.676.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.37901 + 2.38851i) q^{2} +(-2.80333 + 4.85550i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.84864 q^{7} -9.94721 q^{8} +O(q^{10})\) \(q+(1.37901 + 2.38851i) q^{2} +(-2.80333 + 4.85550i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.84864 q^{7} -9.94721 q^{8} +(-1.37901 + 2.38851i) q^{10} +0.864801 q^{11} +(-0.321640 + 0.557098i) q^{13} +(-3.92829 - 6.80401i) q^{14} +(-8.11063 - 14.0480i) q^{16} +(1.87093 + 3.24054i) q^{17} +(-3.36069 - 2.77592i) q^{19} -5.60665 q^{20} +(1.19257 + 2.06559i) q^{22} +(0.208730 - 0.361531i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.77418 q^{26} +(7.98566 - 13.8316i) q^{28} +(-4.85261 + 8.40497i) q^{29} +4.93349 q^{31} +(12.4220 - 21.5156i) q^{32} +(-5.16005 + 8.93746i) q^{34} +(-1.42432 - 2.46699i) q^{35} +6.36467 q^{37} +(1.99589 - 11.8551i) q^{38} +(-4.97360 - 8.61454i) q^{40} +(-2.00686 - 3.47598i) q^{41} +(1.02915 + 1.78254i) q^{43} +(-2.42432 + 4.19904i) q^{44} +1.15136 q^{46} +(-1.97698 + 3.42423i) q^{47} +1.11474 q^{49} -2.75802 q^{50} +(-1.80333 - 3.12345i) q^{52} +(-5.49374 + 9.51544i) q^{53} +(0.432400 + 0.748939i) q^{55} +28.3360 q^{56} -26.7672 q^{58} +(1.22980 + 2.13007i) q^{59} +(-3.16740 + 5.48609i) q^{61} +(6.80333 + 11.7837i) q^{62} +36.0778 q^{64} -0.643281 q^{65} +(1.26610 - 2.19295i) q^{67} -20.9793 q^{68} +(3.92829 - 6.80401i) q^{70} +(-0.891065 - 1.54337i) q^{71} +(3.56545 + 6.17554i) q^{73} +(8.77693 + 15.2021i) q^{74} +(22.8996 - 8.53606i) q^{76} -2.46350 q^{77} +(-0.912262 - 1.58008i) q^{79} +(8.11063 - 14.0480i) q^{80} +(5.53495 - 9.58681i) q^{82} +7.43913 q^{83} +(-1.87093 + 3.24054i) q^{85} +(-2.83841 + 4.91626i) q^{86} -8.60235 q^{88} +(2.22294 - 3.85024i) q^{89} +(0.916237 - 1.58697i) q^{91} +(1.17028 + 2.02698i) q^{92} -10.9051 q^{94} +(0.723670 - 4.29841i) q^{95} +(5.42707 + 9.39996i) q^{97} +(1.53723 + 2.66256i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8} - q^{10} + 4 q^{11} - 7 q^{13} - q^{14} - 7 q^{16} - q^{17} + 5 q^{19} - 10 q^{20} - 2 q^{22} + 2 q^{23} - 4 q^{25} - 6 q^{26} + 19 q^{28} - q^{29} + 30 q^{32} - 15 q^{34} - 4 q^{35} - 4 q^{37} - 13 q^{38} - 12 q^{40} - 8 q^{41} - q^{43} - 12 q^{44} + 24 q^{46} - 12 q^{47} - 20 q^{49} - 2 q^{50} + 3 q^{52} - 5 q^{53} + 2 q^{55} + 82 q^{56} - 54 q^{58} - 5 q^{59} + 37 q^{62} + 112 q^{64} - 14 q^{65} - 4 q^{67} - 32 q^{68} + q^{70} + 20 q^{71} + 20 q^{73} + 25 q^{74} + 63 q^{76} - 28 q^{77} - 17 q^{79} + 7 q^{80} - 21 q^{82} - 2 q^{83} + q^{85} + 8 q^{86} - 14 q^{88} + 11 q^{89} - 6 q^{91} - q^{92} - 62 q^{94} + 4 q^{95} - q^{97} + 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37901 + 2.38851i 0.975106 + 1.68893i 0.679585 + 0.733597i \(0.262160\pi\)
0.295521 + 0.955336i \(0.404507\pi\)
\(3\) 0 0
\(4\) −2.80333 + 4.85550i −1.40166 + 2.42775i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −2.84864 −1.07668 −0.538342 0.842727i \(-0.680949\pi\)
−0.538342 + 0.842727i \(0.680949\pi\)
\(8\) −9.94721 −3.51687
\(9\) 0 0
\(10\) −1.37901 + 2.38851i −0.436081 + 0.755314i
\(11\) 0.864801 0.260747 0.130374 0.991465i \(-0.458382\pi\)
0.130374 + 0.991465i \(0.458382\pi\)
\(12\) 0 0
\(13\) −0.321640 + 0.557098i −0.0892070 + 0.154511i −0.907176 0.420751i \(-0.861767\pi\)
0.817969 + 0.575262i \(0.195100\pi\)
\(14\) −3.92829 6.80401i −1.04988 1.81845i
\(15\) 0 0
\(16\) −8.11063 14.0480i −2.02766 3.51201i
\(17\) 1.87093 + 3.24054i 0.453766 + 0.785946i 0.998616 0.0525872i \(-0.0167467\pi\)
−0.544850 + 0.838534i \(0.683413\pi\)
\(18\) 0 0
\(19\) −3.36069 2.77592i −0.770996 0.636840i
\(20\) −5.60665 −1.25369
\(21\) 0 0
\(22\) 1.19257 + 2.06559i 0.254256 + 0.440385i
\(23\) 0.208730 0.361531i 0.0435233 0.0753845i −0.843443 0.537218i \(-0.819475\pi\)
0.886966 + 0.461834i \(0.152808\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −1.77418 −0.347945
\(27\) 0 0
\(28\) 7.98566 13.8316i 1.50915 2.61392i
\(29\) −4.85261 + 8.40497i −0.901108 + 1.56076i −0.0750490 + 0.997180i \(0.523911\pi\)
−0.826059 + 0.563584i \(0.809422\pi\)
\(30\) 0 0
\(31\) 4.93349 0.886081 0.443041 0.896501i \(-0.353900\pi\)
0.443041 + 0.896501i \(0.353900\pi\)
\(32\) 12.4220 21.5156i 2.19593 3.80346i
\(33\) 0 0
\(34\) −5.16005 + 8.93746i −0.884941 + 1.53276i
\(35\) −1.42432 2.46699i −0.240754 0.416998i
\(36\) 0 0
\(37\) 6.36467 1.04635 0.523173 0.852227i \(-0.324748\pi\)
0.523173 + 0.852227i \(0.324748\pi\)
\(38\) 1.99589 11.8551i 0.323777 1.92315i
\(39\) 0 0
\(40\) −4.97360 8.61454i −0.786396 1.36208i
\(41\) −2.00686 3.47598i −0.313419 0.542857i 0.665681 0.746236i \(-0.268141\pi\)
−0.979100 + 0.203379i \(0.934808\pi\)
\(42\) 0 0
\(43\) 1.02915 + 1.78254i 0.156944 + 0.271834i 0.933765 0.357887i \(-0.116503\pi\)
−0.776821 + 0.629721i \(0.783169\pi\)
\(44\) −2.42432 + 4.19904i −0.365480 + 0.633030i
\(45\) 0 0
\(46\) 1.15136 0.169759
\(47\) −1.97698 + 3.42423i −0.288372 + 0.499475i −0.973421 0.229022i \(-0.926447\pi\)
0.685049 + 0.728497i \(0.259781\pi\)
\(48\) 0 0
\(49\) 1.11474 0.159248
\(50\) −2.75802 −0.390042
\(51\) 0 0
\(52\) −1.80333 3.12345i −0.250076 0.433145i
\(53\) −5.49374 + 9.51544i −0.754624 + 1.30705i 0.190937 + 0.981602i \(0.438847\pi\)
−0.945561 + 0.325444i \(0.894486\pi\)
\(54\) 0 0
\(55\) 0.432400 + 0.748939i 0.0583048 + 0.100987i
\(56\) 28.3360 3.78656
\(57\) 0 0
\(58\) −26.7672 −3.51470
\(59\) 1.22980 + 2.13007i 0.160106 + 0.277311i 0.934906 0.354894i \(-0.115483\pi\)
−0.774801 + 0.632206i \(0.782150\pi\)
\(60\) 0 0
\(61\) −3.16740 + 5.48609i −0.405543 + 0.702422i −0.994385 0.105827i \(-0.966251\pi\)
0.588841 + 0.808249i \(0.299584\pi\)
\(62\) 6.80333 + 11.7837i 0.864023 + 1.49653i
\(63\) 0 0
\(64\) 36.0778 4.50973
\(65\) −0.643281 −0.0797892
\(66\) 0 0
\(67\) 1.26610 2.19295i 0.154678 0.267911i −0.778263 0.627938i \(-0.783899\pi\)
0.932942 + 0.360027i \(0.117233\pi\)
\(68\) −20.9793 −2.54411
\(69\) 0 0
\(70\) 3.92829 6.80401i 0.469521 0.813234i
\(71\) −0.891065 1.54337i −0.105750 0.183164i 0.808294 0.588779i \(-0.200391\pi\)
−0.914044 + 0.405614i \(0.867058\pi\)
\(72\) 0 0
\(73\) 3.56545 + 6.17554i 0.417304 + 0.722792i 0.995667 0.0929873i \(-0.0296416\pi\)
−0.578363 + 0.815780i \(0.696308\pi\)
\(74\) 8.77693 + 15.2021i 1.02030 + 1.76721i
\(75\) 0 0
\(76\) 22.8996 8.53606i 2.62677 0.979153i
\(77\) −2.46350 −0.280742
\(78\) 0 0
\(79\) −0.912262 1.58008i −0.102637 0.177773i 0.810133 0.586246i \(-0.199395\pi\)
−0.912771 + 0.408473i \(0.866061\pi\)
\(80\) 8.11063 14.0480i 0.906796 1.57062i
\(81\) 0 0
\(82\) 5.53495 9.58681i 0.611233 1.05869i
\(83\) 7.43913 0.816550 0.408275 0.912859i \(-0.366130\pi\)
0.408275 + 0.912859i \(0.366130\pi\)
\(84\) 0 0
\(85\) −1.87093 + 3.24054i −0.202930 + 0.351486i
\(86\) −2.83841 + 4.91626i −0.306073 + 0.530134i
\(87\) 0 0
\(88\) −8.60235 −0.917014
\(89\) 2.22294 3.85024i 0.235631 0.408125i −0.723825 0.689984i \(-0.757618\pi\)
0.959456 + 0.281859i \(0.0909510\pi\)
\(90\) 0 0
\(91\) 0.916237 1.58697i 0.0960478 0.166360i
\(92\) 1.17028 + 2.02698i 0.122010 + 0.211327i
\(93\) 0 0
\(94\) −10.9051 −1.12477
\(95\) 0.723670 4.29841i 0.0742470 0.441007i
\(96\) 0 0
\(97\) 5.42707 + 9.39996i 0.551036 + 0.954422i 0.998200 + 0.0599699i \(0.0191005\pi\)
−0.447165 + 0.894452i \(0.647566\pi\)
\(98\) 1.53723 + 2.66256i 0.155284 + 0.268959i
\(99\) 0 0
\(100\) −2.80333 4.85550i −0.280333 0.485550i
\(101\) −2.64799 + 4.58645i −0.263485 + 0.456369i −0.967166 0.254147i \(-0.918205\pi\)
0.703681 + 0.710516i \(0.251539\pi\)
\(102\) 0 0
\(103\) −0.385134 −0.0379484 −0.0189742 0.999820i \(-0.506040\pi\)
−0.0189742 + 0.999820i \(0.506040\pi\)
\(104\) 3.19943 5.54157i 0.313729 0.543395i
\(105\) 0 0
\(106\) −30.3037 −2.94335
\(107\) 6.43336 0.621937 0.310968 0.950420i \(-0.399347\pi\)
0.310968 + 0.950420i \(0.399347\pi\)
\(108\) 0 0
\(109\) −3.28441 5.68877i −0.314590 0.544885i 0.664761 0.747056i \(-0.268534\pi\)
−0.979350 + 0.202171i \(0.935200\pi\)
\(110\) −1.19257 + 2.06559i −0.113707 + 0.196946i
\(111\) 0 0
\(112\) 23.1042 + 40.0177i 2.18315 + 3.78132i
\(113\) −0.294513 −0.0277054 −0.0138527 0.999904i \(-0.504410\pi\)
−0.0138527 + 0.999904i \(0.504410\pi\)
\(114\) 0 0
\(115\) 0.417460 0.0389284
\(116\) −27.2069 47.1238i −2.52610 4.37533i
\(117\) 0 0
\(118\) −3.39180 + 5.87477i −0.312240 + 0.540816i
\(119\) −5.32959 9.23112i −0.488563 0.846216i
\(120\) 0 0
\(121\) −10.2521 −0.932011
\(122\) −17.4715 −1.58179
\(123\) 0 0
\(124\) −13.8302 + 23.9546i −1.24199 + 2.15119i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −4.41746 + 7.65127i −0.391986 + 0.678940i −0.992711 0.120516i \(-0.961545\pi\)
0.600725 + 0.799456i \(0.294879\pi\)
\(128\) 24.9076 + 43.1412i 2.20154 + 3.81318i
\(129\) 0 0
\(130\) −0.887090 1.53648i −0.0778029 0.134759i
\(131\) 10.4564 + 18.1110i 0.913578 + 1.58236i 0.808969 + 0.587851i \(0.200026\pi\)
0.104609 + 0.994513i \(0.466641\pi\)
\(132\) 0 0
\(133\) 9.57340 + 7.90759i 0.830119 + 0.685675i
\(134\) 6.98384 0.603312
\(135\) 0 0
\(136\) −18.6105 32.2343i −1.59584 2.76407i
\(137\) 2.60739 4.51613i 0.222764 0.385839i −0.732882 0.680356i \(-0.761825\pi\)
0.955646 + 0.294517i \(0.0951587\pi\)
\(138\) 0 0
\(139\) 5.36192 9.28711i 0.454792 0.787723i −0.543884 0.839160i \(-0.683047\pi\)
0.998676 + 0.0514375i \(0.0163803\pi\)
\(140\) 15.9713 1.34982
\(141\) 0 0
\(142\) 2.45757 4.25664i 0.206235 0.357209i
\(143\) −0.278155 + 0.481778i −0.0232605 + 0.0402883i
\(144\) 0 0
\(145\) −9.70523 −0.805975
\(146\) −9.83357 + 17.0322i −0.813832 + 1.40960i
\(147\) 0 0
\(148\) −17.8423 + 30.9037i −1.46662 + 2.54027i
\(149\) −7.45578 12.9138i −0.610801 1.05794i −0.991106 0.133078i \(-0.957514\pi\)
0.380304 0.924861i \(-0.375819\pi\)
\(150\) 0 0
\(151\) 21.4589 1.74630 0.873152 0.487448i \(-0.162072\pi\)
0.873152 + 0.487448i \(0.162072\pi\)
\(152\) 33.4295 + 27.6127i 2.71149 + 2.23968i
\(153\) 0 0
\(154\) −3.39719 5.88411i −0.273753 0.474155i
\(155\) 2.46675 + 4.27253i 0.198134 + 0.343178i
\(156\) 0 0
\(157\) 1.21559 + 2.10546i 0.0970145 + 0.168034i 0.910448 0.413624i \(-0.135737\pi\)
−0.813433 + 0.581659i \(0.802404\pi\)
\(158\) 2.51603 4.35790i 0.200165 0.346696i
\(159\) 0 0
\(160\) 24.8441 1.96410
\(161\) −0.594597 + 1.02987i −0.0468608 + 0.0811653i
\(162\) 0 0
\(163\) 17.8175 1.39558 0.697788 0.716305i \(-0.254168\pi\)
0.697788 + 0.716305i \(0.254168\pi\)
\(164\) 22.5035 1.75723
\(165\) 0 0
\(166\) 10.2586 + 17.7684i 0.796223 + 1.37910i
\(167\) −0.202799 + 0.351258i −0.0156931 + 0.0271812i −0.873765 0.486348i \(-0.838329\pi\)
0.858072 + 0.513529i \(0.171662\pi\)
\(168\) 0 0
\(169\) 6.29309 + 10.9000i 0.484084 + 0.838458i
\(170\) −10.3201 −0.791515
\(171\) 0 0
\(172\) −11.5401 −0.879928
\(173\) 9.01051 + 15.6067i 0.685056 + 1.18655i 0.973419 + 0.229031i \(0.0735557\pi\)
−0.288363 + 0.957521i \(0.593111\pi\)
\(174\) 0 0
\(175\) 1.42432 2.46699i 0.107668 0.186487i
\(176\) −7.01408 12.1487i −0.528706 0.915746i
\(177\) 0 0
\(178\) 12.2618 0.919061
\(179\) −20.1523 −1.50625 −0.753127 0.657875i \(-0.771455\pi\)
−0.753127 + 0.657875i \(0.771455\pi\)
\(180\) 0 0
\(181\) 8.55541 14.8184i 0.635919 1.10144i −0.350401 0.936600i \(-0.613955\pi\)
0.986320 0.164844i \(-0.0527120\pi\)
\(182\) 5.05399 0.374627
\(183\) 0 0
\(184\) −2.07628 + 3.59623i −0.153066 + 0.265117i
\(185\) 3.18233 + 5.51197i 0.233970 + 0.405248i
\(186\) 0 0
\(187\) 1.61798 + 2.80242i 0.118318 + 0.204933i
\(188\) −11.0842 19.1985i −0.808401 1.40019i
\(189\) 0 0
\(190\) 11.2647 4.19904i 0.817230 0.304631i
\(191\) −5.28080 −0.382105 −0.191053 0.981580i \(-0.561190\pi\)
−0.191053 + 0.981580i \(0.561190\pi\)
\(192\) 0 0
\(193\) −9.00182 15.5916i −0.647966 1.12231i −0.983608 0.180320i \(-0.942287\pi\)
0.335642 0.941989i \(-0.391047\pi\)
\(194\) −14.9679 + 25.9252i −1.07464 + 1.86132i
\(195\) 0 0
\(196\) −3.12497 + 5.41260i −0.223212 + 0.386614i
\(197\) −8.07785 −0.575523 −0.287761 0.957702i \(-0.592911\pi\)
−0.287761 + 0.957702i \(0.592911\pi\)
\(198\) 0 0
\(199\) −0.701872 + 1.21568i −0.0497544 + 0.0861771i −0.889830 0.456292i \(-0.849177\pi\)
0.840076 + 0.542469i \(0.182511\pi\)
\(200\) 4.97360 8.61454i 0.351687 0.609140i
\(201\) 0 0
\(202\) −14.6064 −1.02770
\(203\) 13.8233 23.9427i 0.970208 1.68045i
\(204\) 0 0
\(205\) 2.00686 3.47598i 0.140165 0.242773i
\(206\) −0.531103 0.919897i −0.0370037 0.0640923i
\(207\) 0 0
\(208\) 10.4348 0.723525
\(209\) −2.90633 2.40062i −0.201035 0.166054i
\(210\) 0 0
\(211\) −9.45817 16.3820i −0.651128 1.12779i −0.982850 0.184409i \(-0.940963\pi\)
0.331722 0.943377i \(-0.392370\pi\)
\(212\) −30.8015 53.3498i −2.11546 3.66408i
\(213\) 0 0
\(214\) 8.87166 + 15.3662i 0.606454 + 1.05041i
\(215\) −1.02915 + 1.78254i −0.0701873 + 0.121568i
\(216\) 0 0
\(217\) −14.0537 −0.954030
\(218\) 9.05846 15.6897i 0.613516 1.06264i
\(219\) 0 0
\(220\) −4.84864 −0.326895
\(221\) −2.40706 −0.161917
\(222\) 0 0
\(223\) 8.07400 + 13.9846i 0.540675 + 0.936477i 0.998865 + 0.0476227i \(0.0151645\pi\)
−0.458190 + 0.888854i \(0.651502\pi\)
\(224\) −35.3859 + 61.2901i −2.36432 + 4.09512i
\(225\) 0 0
\(226\) −0.406136 0.703448i −0.0270157 0.0467926i
\(227\) −26.3186 −1.74683 −0.873414 0.486978i \(-0.838099\pi\)
−0.873414 + 0.486978i \(0.838099\pi\)
\(228\) 0 0
\(229\) −13.3323 −0.881026 −0.440513 0.897746i \(-0.645203\pi\)
−0.440513 + 0.897746i \(0.645203\pi\)
\(230\) 0.575681 + 0.997109i 0.0379593 + 0.0657474i
\(231\) 0 0
\(232\) 48.2700 83.6060i 3.16908 5.48900i
\(233\) 12.6547 + 21.9186i 0.829038 + 1.43594i 0.898794 + 0.438372i \(0.144445\pi\)
−0.0697556 + 0.997564i \(0.522222\pi\)
\(234\) 0 0
\(235\) −3.95396 −0.257928
\(236\) −13.7901 −0.897658
\(237\) 0 0
\(238\) 14.6991 25.4596i 0.952801 1.65030i
\(239\) 23.5500 1.52332 0.761660 0.647977i \(-0.224385\pi\)
0.761660 + 0.647977i \(0.224385\pi\)
\(240\) 0 0
\(241\) −4.19208 + 7.26089i −0.270035 + 0.467715i −0.968871 0.247568i \(-0.920369\pi\)
0.698835 + 0.715283i \(0.253702\pi\)
\(242\) −14.1378 24.4873i −0.908809 1.57410i
\(243\) 0 0
\(244\) −17.7585 30.7586i −1.13687 1.96912i
\(245\) 0.557368 + 0.965389i 0.0356089 + 0.0616764i
\(246\) 0 0
\(247\) 2.62739 0.979387i 0.167177 0.0623169i
\(248\) −49.0745 −3.11623
\(249\) 0 0
\(250\) −1.37901 2.38851i −0.0872161 0.151063i
\(251\) 9.12391 15.8031i 0.575896 0.997481i −0.420048 0.907502i \(-0.637987\pi\)
0.995944 0.0899792i \(-0.0286800\pi\)
\(252\) 0 0
\(253\) 0.180510 0.312652i 0.0113486 0.0196563i
\(254\) −24.3669 −1.52891
\(255\) 0 0
\(256\) −32.6176 + 56.4954i −2.03860 + 3.53096i
\(257\) 7.04989 12.2108i 0.439760 0.761687i −0.557911 0.829901i \(-0.688397\pi\)
0.997671 + 0.0682144i \(0.0217302\pi\)
\(258\) 0 0
\(259\) −18.1306 −1.12658
\(260\) 1.80333 3.12345i 0.111838 0.193708i
\(261\) 0 0
\(262\) −28.8389 + 49.9504i −1.78167 + 3.08595i
\(263\) −3.20536 5.55184i −0.197651 0.342341i 0.750116 0.661307i \(-0.229998\pi\)
−0.947766 + 0.318966i \(0.896665\pi\)
\(264\) 0 0
\(265\) −10.9875 −0.674956
\(266\) −5.68558 + 33.7708i −0.348605 + 2.07062i
\(267\) 0 0
\(268\) 7.09857 + 12.2951i 0.433614 + 0.751042i
\(269\) 8.99557 + 15.5808i 0.548469 + 0.949977i 0.998380 + 0.0569032i \(0.0181226\pi\)
−0.449910 + 0.893074i \(0.648544\pi\)
\(270\) 0 0
\(271\) −5.94095 10.2900i −0.360887 0.625075i 0.627220 0.778842i \(-0.284193\pi\)
−0.988107 + 0.153767i \(0.950859\pi\)
\(272\) 30.3488 52.5656i 1.84017 3.18726i
\(273\) 0 0
\(274\) 14.3824 0.868874
\(275\) −0.432400 + 0.748939i −0.0260747 + 0.0451627i
\(276\) 0 0
\(277\) 23.6240 1.41943 0.709715 0.704489i \(-0.248824\pi\)
0.709715 + 0.704489i \(0.248824\pi\)
\(278\) 29.5765 1.77388
\(279\) 0 0
\(280\) 14.1680 + 24.5397i 0.846700 + 1.46653i
\(281\) 6.90465 11.9592i 0.411897 0.713426i −0.583200 0.812328i \(-0.698200\pi\)
0.995097 + 0.0989020i \(0.0315330\pi\)
\(282\) 0 0
\(283\) 5.87868 + 10.1822i 0.349451 + 0.605268i 0.986152 0.165843i \(-0.0530346\pi\)
−0.636701 + 0.771111i \(0.719701\pi\)
\(284\) 9.99179 0.592904
\(285\) 0 0
\(286\) −1.53431 −0.0907257
\(287\) 5.71681 + 9.90181i 0.337453 + 0.584485i
\(288\) 0 0
\(289\) 1.49927 2.59681i 0.0881922 0.152753i
\(290\) −13.3836 23.1810i −0.785911 1.36124i
\(291\) 0 0
\(292\) −39.9805 −2.33968
\(293\) 27.0576 1.58072 0.790362 0.612640i \(-0.209892\pi\)
0.790362 + 0.612640i \(0.209892\pi\)
\(294\) 0 0
\(295\) −1.22980 + 2.13007i −0.0716015 + 0.124017i
\(296\) −63.3107 −3.67986
\(297\) 0 0
\(298\) 20.5632 35.6165i 1.19119 2.06321i
\(299\) 0.134272 + 0.232566i 0.00776516 + 0.0134497i
\(300\) 0 0
\(301\) −2.93167 5.07780i −0.168979 0.292679i
\(302\) 29.5921 + 51.2549i 1.70283 + 2.94939i
\(303\) 0 0
\(304\) −11.7388 + 69.7256i −0.673269 + 3.99904i
\(305\) −6.33479 −0.362729
\(306\) 0 0
\(307\) −4.41912 7.65414i −0.252212 0.436845i 0.711922 0.702258i \(-0.247825\pi\)
−0.964135 + 0.265414i \(0.914492\pi\)
\(308\) 6.90601 11.9616i 0.393506 0.681573i
\(309\) 0 0
\(310\) −6.80333 + 11.7837i −0.386403 + 0.669270i
\(311\) 0.651493 0.0369428 0.0184714 0.999829i \(-0.494120\pi\)
0.0184714 + 0.999829i \(0.494120\pi\)
\(312\) 0 0
\(313\) 1.48278 2.56825i 0.0838116 0.145166i −0.821073 0.570824i \(-0.806624\pi\)
0.904884 + 0.425658i \(0.139957\pi\)
\(314\) −3.35261 + 5.80690i −0.189199 + 0.327702i
\(315\) 0 0
\(316\) 10.2295 0.575453
\(317\) −5.18993 + 8.98921i −0.291495 + 0.504885i −0.974164 0.225844i \(-0.927486\pi\)
0.682668 + 0.730728i \(0.260819\pi\)
\(318\) 0 0
\(319\) −4.19654 + 7.26862i −0.234961 + 0.406965i
\(320\) 18.0389 + 31.2443i 1.00841 + 1.74661i
\(321\) 0 0
\(322\) −3.27981 −0.182777
\(323\) 2.70787 16.0840i 0.150670 0.894938i
\(324\) 0 0
\(325\) −0.321640 0.557098i −0.0178414 0.0309022i
\(326\) 24.5705 + 42.5574i 1.36083 + 2.35703i
\(327\) 0 0
\(328\) 19.9626 + 34.5763i 1.10225 + 1.90916i
\(329\) 5.63170 9.75438i 0.310485 0.537776i
\(330\) 0 0
\(331\) 15.0922 0.829543 0.414772 0.909926i \(-0.363861\pi\)
0.414772 + 0.909926i \(0.363861\pi\)
\(332\) −20.8543 + 36.1207i −1.14453 + 1.98238i
\(333\) 0 0
\(334\) −1.11865 −0.0612096
\(335\) 2.53220 0.138349
\(336\) 0 0
\(337\) −7.89872 13.6810i −0.430271 0.745251i 0.566626 0.823975i \(-0.308249\pi\)
−0.996896 + 0.0787246i \(0.974915\pi\)
\(338\) −17.3565 + 30.0623i −0.944067 + 1.63517i
\(339\) 0 0
\(340\) −10.4896 18.1686i −0.568880 0.985330i
\(341\) 4.26649 0.231043
\(342\) 0 0
\(343\) 16.7650 0.905224
\(344\) −10.2371 17.7313i −0.551950 0.956005i
\(345\) 0 0
\(346\) −24.8511 + 43.0434i −1.33600 + 2.31403i
\(347\) −10.6761 18.4915i −0.573122 0.992676i −0.996243 0.0866031i \(-0.972399\pi\)
0.423121 0.906073i \(-0.360935\pi\)
\(348\) 0 0
\(349\) −32.3897 −1.73378 −0.866891 0.498497i \(-0.833885\pi\)
−0.866891 + 0.498497i \(0.833885\pi\)
\(350\) 7.85659 0.419952
\(351\) 0 0
\(352\) 10.7426 18.6067i 0.572582 0.991741i
\(353\) −0.730583 −0.0388850 −0.0194425 0.999811i \(-0.506189\pi\)
−0.0194425 + 0.999811i \(0.506189\pi\)
\(354\) 0 0
\(355\) 0.891065 1.54337i 0.0472928 0.0819136i
\(356\) 12.4632 + 21.5870i 0.660551 + 1.14411i
\(357\) 0 0
\(358\) −27.7902 48.1340i −1.46876 2.54396i
\(359\) −13.4248 23.2524i −0.708533 1.22722i −0.965401 0.260769i \(-0.916024\pi\)
0.256868 0.966447i \(-0.417309\pi\)
\(360\) 0 0
\(361\) 3.58853 + 18.6580i 0.188870 + 0.982002i
\(362\) 47.1919 2.48035
\(363\) 0 0
\(364\) 5.13702 + 8.89759i 0.269253 + 0.466360i
\(365\) −3.56545 + 6.17554i −0.186624 + 0.323242i
\(366\) 0 0
\(367\) 11.4822 19.8877i 0.599364 1.03813i −0.393551 0.919303i \(-0.628754\pi\)
0.992915 0.118826i \(-0.0379130\pi\)
\(368\) −6.77173 −0.353001
\(369\) 0 0
\(370\) −8.77693 + 15.2021i −0.456291 + 0.790319i
\(371\) 15.6497 27.1060i 0.812491 1.40728i
\(372\) 0 0
\(373\) 29.5305 1.52903 0.764515 0.644606i \(-0.222979\pi\)
0.764515 + 0.644606i \(0.222979\pi\)
\(374\) −4.46241 + 7.72912i −0.230746 + 0.399663i
\(375\) 0 0
\(376\) 19.6654 34.0615i 1.01417 1.75659i
\(377\) −3.12159 5.40676i −0.160770 0.278462i
\(378\) 0 0
\(379\) 17.5117 0.899517 0.449759 0.893150i \(-0.351510\pi\)
0.449759 + 0.893150i \(0.351510\pi\)
\(380\) 18.8423 + 15.5636i 0.966587 + 0.798397i
\(381\) 0 0
\(382\) −7.28226 12.6132i −0.372593 0.645350i
\(383\) 4.05326 + 7.02045i 0.207112 + 0.358728i 0.950804 0.309794i \(-0.100260\pi\)
−0.743692 + 0.668523i \(0.766927\pi\)
\(384\) 0 0
\(385\) −1.23175 2.13346i −0.0627759 0.108731i
\(386\) 24.8272 43.0019i 1.26367 2.18874i
\(387\) 0 0
\(388\) −60.8554 −3.08947
\(389\) 8.65392 14.9890i 0.438771 0.759974i −0.558824 0.829286i \(-0.688747\pi\)
0.997595 + 0.0693125i \(0.0220805\pi\)
\(390\) 0 0
\(391\) 1.56208 0.0789976
\(392\) −11.0885 −0.560054
\(393\) 0 0
\(394\) −11.1394 19.2940i −0.561196 0.972019i
\(395\) 0.912262 1.58008i 0.0459009 0.0795026i
\(396\) 0 0
\(397\) 5.69472 + 9.86354i 0.285810 + 0.495037i 0.972805 0.231625i \(-0.0744041\pi\)
−0.686996 + 0.726662i \(0.741071\pi\)
\(398\) −3.87155 −0.194063
\(399\) 0 0
\(400\) 16.2213 0.811063
\(401\) −4.46930 7.74106i −0.223186 0.386570i 0.732587 0.680673i \(-0.238313\pi\)
−0.955774 + 0.294103i \(0.904979\pi\)
\(402\) 0 0
\(403\) −1.58681 + 2.74844i −0.0790447 + 0.136909i
\(404\) −14.8464 25.7146i −0.738634 1.27935i
\(405\) 0 0
\(406\) 76.2500 3.78422
\(407\) 5.50417 0.272832
\(408\) 0 0
\(409\) 3.27235 5.66788i 0.161808 0.280259i −0.773709 0.633541i \(-0.781601\pi\)
0.935517 + 0.353282i \(0.114934\pi\)
\(410\) 11.0699 0.546703
\(411\) 0 0
\(412\) 1.07966 1.87002i 0.0531909 0.0921293i
\(413\) −3.50324 6.06780i −0.172383 0.298577i
\(414\) 0 0
\(415\) 3.71956 + 6.44247i 0.182586 + 0.316249i
\(416\) 7.99086 + 13.8406i 0.391784 + 0.678590i
\(417\) 0 0
\(418\) 1.72605 10.2523i 0.0844239 0.501455i
\(419\) −21.8441 −1.06715 −0.533576 0.845752i \(-0.679152\pi\)
−0.533576 + 0.845752i \(0.679152\pi\)
\(420\) 0 0
\(421\) 14.6717 + 25.4121i 0.715054 + 1.23851i 0.962939 + 0.269720i \(0.0869311\pi\)
−0.247885 + 0.968789i \(0.579736\pi\)
\(422\) 26.0858 45.1819i 1.26984 2.19942i
\(423\) 0 0
\(424\) 54.6474 94.6521i 2.65391 4.59671i
\(425\) −3.74185 −0.181507
\(426\) 0 0
\(427\) 9.02276 15.6279i 0.436642 0.756286i
\(428\) −18.0348 + 31.2372i −0.871746 + 1.50991i
\(429\) 0 0
\(430\) −5.67681 −0.273760
\(431\) −6.44336 + 11.1602i −0.310366 + 0.537570i −0.978442 0.206524i \(-0.933785\pi\)
0.668076 + 0.744093i \(0.267118\pi\)
\(432\) 0 0
\(433\) 6.92144 11.9883i 0.332623 0.576120i −0.650402 0.759590i \(-0.725400\pi\)
0.983025 + 0.183470i \(0.0587330\pi\)
\(434\) −19.3802 33.5675i −0.930280 1.61129i
\(435\) 0 0
\(436\) 36.8291 1.76379
\(437\) −1.70506 + 0.635578i −0.0815641 + 0.0304038i
\(438\) 0 0
\(439\) 0.0354040 + 0.0613216i 0.00168974 + 0.00292672i 0.866869 0.498536i \(-0.166129\pi\)
−0.865179 + 0.501463i \(0.832795\pi\)
\(440\) −4.30118 7.44986i −0.205051 0.355158i
\(441\) 0 0
\(442\) −3.31936 5.74930i −0.157886 0.273466i
\(443\) −1.89457 + 3.28149i −0.0900137 + 0.155908i −0.907517 0.420016i \(-0.862024\pi\)
0.817503 + 0.575924i \(0.195358\pi\)
\(444\) 0 0
\(445\) 4.44588 0.210755
\(446\) −22.2682 + 38.5697i −1.05443 + 1.82633i
\(447\) 0 0
\(448\) −102.773 −4.85555
\(449\) 26.5765 1.25422 0.627112 0.778929i \(-0.284237\pi\)
0.627112 + 0.778929i \(0.284237\pi\)
\(450\) 0 0
\(451\) −1.73553 3.00603i −0.0817230 0.141548i
\(452\) 0.825616 1.43001i 0.0388337 0.0672620i
\(453\) 0 0
\(454\) −36.2936 62.8624i −1.70334 2.95028i
\(455\) 1.83247 0.0859077
\(456\) 0 0
\(457\) −33.1523 −1.55080 −0.775400 0.631471i \(-0.782452\pi\)
−0.775400 + 0.631471i \(0.782452\pi\)
\(458\) −18.3854 31.8445i −0.859094 1.48799i
\(459\) 0 0
\(460\) −1.17028 + 2.02698i −0.0545645 + 0.0945085i
\(461\) −9.62679 16.6741i −0.448364 0.776590i 0.549915 0.835220i \(-0.314660\pi\)
−0.998280 + 0.0586304i \(0.981327\pi\)
\(462\) 0 0
\(463\) 39.1713 1.82044 0.910222 0.414120i \(-0.135911\pi\)
0.910222 + 0.414120i \(0.135911\pi\)
\(464\) 157.431 7.30855
\(465\) 0 0
\(466\) −34.9019 + 60.4519i −1.61680 + 2.80038i
\(467\) 39.0650 1.80771 0.903856 0.427836i \(-0.140724\pi\)
0.903856 + 0.427836i \(0.140724\pi\)
\(468\) 0 0
\(469\) −3.60665 + 6.24691i −0.166540 + 0.288455i
\(470\) −5.45254 9.44407i −0.251507 0.435623i
\(471\) 0 0
\(472\) −12.2330 21.1882i −0.563071 0.975268i
\(473\) 0.890007 + 1.54154i 0.0409226 + 0.0708800i
\(474\) 0 0
\(475\) 4.08436 1.52249i 0.187404 0.0698565i
\(476\) 59.7623 2.73920
\(477\) 0 0
\(478\) 32.4756 + 56.2493i 1.48540 + 2.57279i
\(479\) −12.3775 + 21.4385i −0.565543 + 0.979550i 0.431455 + 0.902134i \(0.358000\pi\)
−0.996999 + 0.0774158i \(0.975333\pi\)
\(480\) 0 0
\(481\) −2.04714 + 3.54574i −0.0933413 + 0.161672i
\(482\) −23.1236 −1.05325
\(483\) 0 0
\(484\) 28.7400 49.7792i 1.30637 2.26269i
\(485\) −5.42707 + 9.39996i −0.246431 + 0.426830i
\(486\) 0 0
\(487\) 21.8871 0.991797 0.495899 0.868380i \(-0.334839\pi\)
0.495899 + 0.868380i \(0.334839\pi\)
\(488\) 31.5067 54.5713i 1.42624 2.47033i
\(489\) 0 0
\(490\) −1.53723 + 2.66256i −0.0694449 + 0.120282i
\(491\) 4.69777 + 8.13677i 0.212007 + 0.367207i 0.952343 0.305030i \(-0.0986666\pi\)
−0.740335 + 0.672238i \(0.765333\pi\)
\(492\) 0 0
\(493\) −36.3155 −1.63557
\(494\) 5.96247 + 4.92498i 0.268264 + 0.221585i
\(495\) 0 0
\(496\) −40.0137 69.3058i −1.79667 3.11192i
\(497\) 2.53832 + 4.39650i 0.113859 + 0.197210i
\(498\) 0 0
\(499\) −12.4558 21.5740i −0.557596 0.965785i −0.997696 0.0678367i \(-0.978390\pi\)
0.440100 0.897949i \(-0.354943\pi\)
\(500\) 2.80333 4.85550i 0.125369 0.217145i
\(501\) 0 0
\(502\) 50.3278 2.24624
\(503\) −15.6590 + 27.1222i −0.698200 + 1.20932i 0.270890 + 0.962610i \(0.412682\pi\)
−0.969090 + 0.246707i \(0.920651\pi\)
\(504\) 0 0
\(505\) −5.29598 −0.235668
\(506\) 0.995699 0.0442642
\(507\) 0 0
\(508\) −24.7672 42.8980i −1.09887 1.90329i
\(509\) −4.83310 + 8.37117i −0.214223 + 0.371045i −0.953032 0.302870i \(-0.902055\pi\)
0.738809 + 0.673915i \(0.235389\pi\)
\(510\) 0 0
\(511\) −10.1567 17.5919i −0.449305 0.778219i
\(512\) −80.2896 −3.54833
\(513\) 0 0
\(514\) 38.8874 1.71525
\(515\) −0.192567 0.333536i −0.00848552 0.0146973i
\(516\) 0 0
\(517\) −1.70969 + 2.96127i −0.0751922 + 0.130237i
\(518\) −25.0023 43.3052i −1.09854 1.90272i
\(519\) 0 0
\(520\) 6.39885 0.280608
\(521\) 0.982633 0.0430499 0.0215250 0.999768i \(-0.493148\pi\)
0.0215250 + 0.999768i \(0.493148\pi\)
\(522\) 0 0
\(523\) −19.8604 + 34.3993i −0.868436 + 1.50418i −0.00484172 + 0.999988i \(0.501541\pi\)
−0.863594 + 0.504187i \(0.831792\pi\)
\(524\) −117.251 −5.12212
\(525\) 0 0
\(526\) 8.84043 15.3121i 0.385461 0.667638i
\(527\) 9.23020 + 15.9872i 0.402074 + 0.696413i
\(528\) 0 0
\(529\) 11.4129 + 19.7677i 0.496211 + 0.859463i
\(530\) −15.1518 26.2437i −0.658154 1.13996i
\(531\) 0 0
\(532\) −65.2327 + 24.3161i −2.82820 + 1.05424i
\(533\) 2.58195 0.111837
\(534\) 0 0
\(535\) 3.21668 + 5.57146i 0.139069 + 0.240875i
\(536\) −12.5941 + 21.8137i −0.543984 + 0.942208i
\(537\) 0 0
\(538\) −24.8099 + 42.9720i −1.06963 + 1.85266i
\(539\) 0.964024 0.0415234
\(540\) 0 0
\(541\) −15.3887 + 26.6541i −0.661614 + 1.14595i 0.318577 + 0.947897i \(0.396795\pi\)
−0.980191 + 0.198052i \(0.936538\pi\)
\(542\) 16.3852 28.3801i 0.703807 1.21903i
\(543\) 0 0
\(544\) 92.9629 3.98575
\(545\) 3.28441 5.68877i 0.140689 0.243680i
\(546\) 0 0
\(547\) 8.93287 15.4722i 0.381942 0.661543i −0.609398 0.792865i \(-0.708589\pi\)
0.991340 + 0.131322i \(0.0419221\pi\)
\(548\) 14.6187 + 25.3203i 0.624480 + 1.08163i
\(549\) 0 0
\(550\) −2.38513 −0.101702
\(551\) 39.6397 14.7761i 1.68871 0.629482i
\(552\) 0 0
\(553\) 2.59870 + 4.50109i 0.110508 + 0.191406i
\(554\) 32.5777 + 56.4263i 1.38409 + 2.39732i
\(555\) 0 0
\(556\) 30.0624 + 52.0696i 1.27493 + 2.20824i
\(557\) −5.32878 + 9.22971i −0.225787 + 0.391075i −0.956555 0.291551i \(-0.905829\pi\)
0.730768 + 0.682626i \(0.239162\pi\)
\(558\) 0 0
\(559\) −1.32406 −0.0560019
\(560\) −23.1042 + 40.0177i −0.976332 + 1.69106i
\(561\) 0 0
\(562\) 38.0863 1.60657
\(563\) −7.75961 −0.327029 −0.163514 0.986541i \(-0.552283\pi\)
−0.163514 + 0.986541i \(0.552283\pi\)
\(564\) 0 0
\(565\) −0.147256 0.255056i −0.00619513 0.0107303i
\(566\) −16.2135 + 28.0826i −0.681504 + 1.18040i
\(567\) 0 0
\(568\) 8.86361 + 15.3522i 0.371909 + 0.644165i
\(569\) −5.72754 −0.240111 −0.120056 0.992767i \(-0.538307\pi\)
−0.120056 + 0.992767i \(0.538307\pi\)
\(570\) 0 0
\(571\) −20.8347 −0.871903 −0.435952 0.899970i \(-0.643588\pi\)
−0.435952 + 0.899970i \(0.643588\pi\)
\(572\) −1.55952 2.70116i −0.0652067 0.112941i
\(573\) 0 0
\(574\) −15.7671 + 27.3093i −0.658104 + 1.13987i
\(575\) 0.208730 + 0.361531i 0.00870465 + 0.0150769i
\(576\) 0 0
\(577\) −5.11190 −0.212811 −0.106406 0.994323i \(-0.533934\pi\)
−0.106406 + 0.994323i \(0.533934\pi\)
\(578\) 8.27001 0.343987
\(579\) 0 0
\(580\) 27.2069 47.1238i 1.12971 1.95671i
\(581\) −21.1914 −0.879167
\(582\) 0 0
\(583\) −4.75099 + 8.22896i −0.196766 + 0.340809i
\(584\) −35.4663 61.4294i −1.46760 2.54197i
\(585\) 0 0
\(586\) 37.3127 + 64.6275i 1.54137 + 2.66974i
\(587\) −5.33462 9.23984i −0.220184 0.381369i 0.734680 0.678414i \(-0.237332\pi\)
−0.954864 + 0.297045i \(0.903999\pi\)
\(588\) 0 0
\(589\) −16.5800 13.6950i −0.683165 0.564292i
\(590\) −6.78360 −0.279276
\(591\) 0 0
\(592\) −51.6215 89.4110i −2.12163 3.67477i
\(593\) −8.50133 + 14.7247i −0.349108 + 0.604673i −0.986091 0.166205i \(-0.946849\pi\)
0.636983 + 0.770878i \(0.280182\pi\)
\(594\) 0 0
\(595\) 5.32959 9.23112i 0.218492 0.378439i
\(596\) 83.6040 3.42455
\(597\) 0 0
\(598\) −0.370325 + 0.641421i −0.0151437 + 0.0262297i
\(599\) 14.3375 24.8334i 0.585816 1.01466i −0.408957 0.912554i \(-0.634107\pi\)
0.994773 0.102110i \(-0.0325592\pi\)
\(600\) 0 0
\(601\) 27.4370 1.11918 0.559590 0.828770i \(-0.310959\pi\)
0.559590 + 0.828770i \(0.310959\pi\)
\(602\) 8.08559 14.0046i 0.329544 0.570787i
\(603\) 0 0
\(604\) −60.1564 + 104.194i −2.44773 + 4.23959i
\(605\) −5.12606 8.87860i −0.208404 0.360966i
\(606\) 0 0
\(607\) −17.7547 −0.720639 −0.360320 0.932829i \(-0.617332\pi\)
−0.360320 + 0.932829i \(0.617332\pi\)
\(608\) −101.472 + 37.8248i −4.11524 + 1.53400i
\(609\) 0 0
\(610\) −8.73573 15.1307i −0.353699 0.612625i
\(611\) −1.27175 2.20274i −0.0514496 0.0891133i
\(612\) 0 0
\(613\) −17.3196 29.9983i −0.699530 1.21162i −0.968629 0.248509i \(-0.920059\pi\)
0.269099 0.963112i \(-0.413274\pi\)
\(614\) 12.1880 21.1102i 0.491868 0.851940i
\(615\) 0 0
\(616\) 24.5050 0.987334
\(617\) 2.23284 3.86740i 0.0898909 0.155696i −0.817574 0.575824i \(-0.804681\pi\)
0.907465 + 0.420128i \(0.138015\pi\)
\(618\) 0 0
\(619\) −17.9112 −0.719913 −0.359957 0.932969i \(-0.617209\pi\)
−0.359957 + 0.932969i \(0.617209\pi\)
\(620\) −27.6604 −1.11087
\(621\) 0 0
\(622\) 0.898414 + 1.55610i 0.0360231 + 0.0623939i
\(623\) −6.33234 + 10.9679i −0.253700 + 0.439421i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 8.17906 0.326901
\(627\) 0 0
\(628\) −13.6308 −0.543927
\(629\) 11.9078 + 20.6250i 0.474796 + 0.822371i
\(630\) 0 0
\(631\) −2.48440 + 4.30311i −0.0989026 + 0.171304i −0.911231 0.411896i \(-0.864867\pi\)
0.812328 + 0.583201i \(0.198200\pi\)
\(632\) 9.07446 + 15.7174i 0.360963 + 0.625205i
\(633\) 0 0
\(634\) −28.6278 −1.13696
\(635\) −8.83492 −0.350603
\(636\) 0 0
\(637\) −0.358544 + 0.621016i −0.0142060 + 0.0246056i
\(638\) −23.1483 −0.916449
\(639\) 0 0
\(640\) −24.9076 + 43.1412i −0.984558 + 1.70530i
\(641\) −18.9760 32.8675i −0.749508 1.29819i −0.948059 0.318096i \(-0.896957\pi\)
0.198550 0.980091i \(-0.436377\pi\)
\(642\) 0 0
\(643\) −17.6251 30.5276i −0.695067 1.20389i −0.970158 0.242473i \(-0.922042\pi\)
0.275092 0.961418i \(-0.411292\pi\)
\(644\) −3.33370 5.77413i −0.131366 0.227533i
\(645\) 0 0
\(646\) 42.1510 15.7122i 1.65841 0.618188i
\(647\) −35.5219 −1.39651 −0.698254 0.715850i \(-0.746040\pi\)
−0.698254 + 0.715850i \(0.746040\pi\)
\(648\) 0 0
\(649\) 1.06353 + 1.84209i 0.0417471 + 0.0723082i
\(650\) 0.887090 1.53648i 0.0347945 0.0602659i
\(651\) 0 0
\(652\) −49.9483 + 86.5130i −1.95613 + 3.38811i
\(653\) −8.02411 −0.314008 −0.157004 0.987598i \(-0.550184\pi\)
−0.157004 + 0.987598i \(0.550184\pi\)
\(654\) 0 0
\(655\) −10.4564 + 18.1110i −0.408565 + 0.707655i
\(656\) −32.5538 + 56.3848i −1.27101 + 2.20146i
\(657\) 0 0
\(658\) 31.0646 1.21102
\(659\) −23.6098 + 40.8933i −0.919706 + 1.59298i −0.119844 + 0.992793i \(0.538240\pi\)
−0.799861 + 0.600185i \(0.795094\pi\)
\(660\) 0 0
\(661\) 13.0580 22.6171i 0.507896 0.879702i −0.492062 0.870560i \(-0.663757\pi\)
0.999958 0.00914181i \(-0.00290997\pi\)
\(662\) 20.8123 + 36.0479i 0.808892 + 1.40104i
\(663\) 0 0
\(664\) −73.9986 −2.87170
\(665\) −2.06147 + 12.2446i −0.0799405 + 0.474825i
\(666\) 0 0
\(667\) 2.02577 + 3.50874i 0.0784383 + 0.135859i
\(668\) −1.13702 1.96938i −0.0439928 0.0761978i
\(669\) 0 0
\(670\) 3.49192 + 6.04818i 0.134905 + 0.233662i
\(671\) −2.73917 + 4.74437i −0.105744 + 0.183154i
\(672\) 0 0
\(673\) 15.3820 0.592931 0.296466 0.955044i \(-0.404192\pi\)
0.296466 + 0.955044i \(0.404192\pi\)
\(674\) 21.7848 37.7324i 0.839119 1.45340i
\(675\) 0 0
\(676\) −70.5664 −2.71409
\(677\) −24.4763 −0.940701 −0.470350 0.882480i \(-0.655872\pi\)
−0.470350 + 0.882480i \(0.655872\pi\)
\(678\) 0 0
\(679\) −15.4598 26.7771i −0.593291 1.02761i
\(680\) 18.6105 32.2343i 0.713680 1.23613i
\(681\) 0 0
\(682\) 5.88352 + 10.1906i 0.225292 + 0.390217i
\(683\) 17.8502 0.683018 0.341509 0.939879i \(-0.389062\pi\)
0.341509 + 0.939879i \(0.389062\pi\)
\(684\) 0 0
\(685\) 5.21477 0.199246
\(686\) 23.1191 + 40.0434i 0.882689 + 1.52886i
\(687\) 0 0
\(688\) 16.6941 28.9150i 0.636455 1.10237i
\(689\) −3.53402 6.12110i −0.134635 0.233195i
\(690\) 0 0
\(691\) −9.27242 −0.352739 −0.176370 0.984324i \(-0.556435\pi\)
−0.176370 + 0.984324i \(0.556435\pi\)
\(692\) −101.038 −3.84087
\(693\) 0 0
\(694\) 29.4448 50.9999i 1.11771 1.93593i
\(695\) 10.7238 0.406778
\(696\) 0 0
\(697\) 7.50937 13.0066i 0.284438 0.492660i
\(698\) −44.6657 77.3633i −1.69062 2.92824i
\(699\) 0 0
\(700\) 7.98566 + 13.8316i 0.301830 + 0.522784i
\(701\) −3.84453 6.65892i −0.145206 0.251504i 0.784244 0.620453i \(-0.213051\pi\)
−0.929450 + 0.368949i \(0.879718\pi\)
\(702\) 0 0
\(703\) −21.3897 17.6678i −0.806728 0.666354i
\(704\) 31.2001 1.17590
\(705\) 0 0
\(706\) −1.00748 1.74501i −0.0379170 0.0656742i
\(707\) 7.54316 13.0651i 0.283690 0.491365i
\(708\) 0 0
\(709\) −12.2187 + 21.1635i −0.458885 + 0.794812i −0.998902 0.0468421i \(-0.985084\pi\)
0.540018 + 0.841654i \(0.318418\pi\)
\(710\) 4.91514 0.184462
\(711\) 0 0
\(712\) −22.1120 + 38.2992i −0.828683 + 1.43532i
\(713\) 1.02977 1.78361i 0.0385652 0.0667968i
\(714\) 0 0
\(715\) −0.556310 −0.0208048
\(716\) 56.4935 97.8496i 2.11126 3.65681i
\(717\) 0 0
\(718\) 37.0258 64.1305i 1.38179 2.39333i
\(719\) −11.0563 19.1501i −0.412331 0.714178i 0.582813 0.812606i \(-0.301952\pi\)
−0.995144 + 0.0984282i \(0.968619\pi\)
\(720\) 0 0
\(721\) 1.09711 0.0408584
\(722\) −39.6163 + 34.3008i −1.47437 + 1.27655i
\(723\) 0 0
\(724\) 47.9672 + 83.0817i 1.78269 + 3.08771i
\(725\) −4.85261 8.40497i −0.180222 0.312153i
\(726\) 0 0
\(727\) 14.5247 + 25.1575i 0.538692 + 0.933042i 0.998975 + 0.0452694i \(0.0144146\pi\)
−0.460283 + 0.887772i \(0.652252\pi\)
\(728\) −9.11400 + 15.7859i −0.337787 + 0.585065i
\(729\) 0 0
\(730\) −19.6671 −0.727913
\(731\) −3.85092 + 6.66999i −0.142431 + 0.246698i
\(732\) 0 0
\(733\) 14.5428 0.537151 0.268576 0.963259i \(-0.413447\pi\)
0.268576 + 0.963259i \(0.413447\pi\)
\(734\) 63.3360 2.33777
\(735\) 0 0
\(736\) −5.18571 8.98191i −0.191148 0.331078i
\(737\) 1.09492 1.89646i 0.0403320 0.0698570i
\(738\) 0 0
\(739\) 2.37798 + 4.11878i 0.0874754 + 0.151512i 0.906443 0.422327i \(-0.138787\pi\)
−0.818968 + 0.573839i \(0.805453\pi\)
\(740\) −35.6845 −1.31179
\(741\) 0 0
\(742\) 86.3242 3.16906
\(743\) 2.93853 + 5.08968i 0.107804 + 0.186722i 0.914880 0.403725i \(-0.132285\pi\)
−0.807076 + 0.590447i \(0.798951\pi\)
\(744\) 0 0
\(745\) 7.45578 12.9138i 0.273159 0.473125i
\(746\) 40.7228 + 70.5339i 1.49097 + 2.58243i
\(747\) 0 0
\(748\) −18.1429 −0.663370
\(749\) −18.3263 −0.669629
\(750\) 0 0
\(751\) −0.810481 + 1.40379i −0.0295749 + 0.0512252i −0.880434 0.474169i \(-0.842749\pi\)
0.850859 + 0.525394i \(0.176082\pi\)
\(752\) 64.1382 2.33888
\(753\) 0 0
\(754\) 8.60941 14.9119i 0.313536 0.543060i
\(755\) 10.7295 + 18.5840i 0.390485 + 0.676341i
\(756\) 0 0
\(757\) 14.0567 + 24.3470i 0.510901 + 0.884907i 0.999920 + 0.0126336i \(0.00402151\pi\)
−0.489019 + 0.872273i \(0.662645\pi\)
\(758\) 24.1488 + 41.8270i 0.877125 + 1.51922i
\(759\) 0 0
\(760\) −7.19850 + 42.7572i −0.261117 + 1.55096i
\(761\) −20.1663 −0.731027 −0.365514 0.930806i \(-0.619107\pi\)
−0.365514 + 0.930806i \(0.619107\pi\)
\(762\) 0 0
\(763\) 9.35610 + 16.2052i 0.338713 + 0.586669i
\(764\) 14.8038 25.6409i 0.535583 0.927656i
\(765\) 0 0
\(766\) −11.1790 + 19.3625i −0.403912 + 0.699597i
\(767\) −1.58221 −0.0571303
\(768\) 0 0
\(769\) −22.6524 + 39.2350i −0.816865 + 1.41485i 0.0911160 + 0.995840i \(0.470957\pi\)
−0.907981 + 0.419011i \(0.862377\pi\)
\(770\) 3.39719 5.88411i 0.122426 0.212049i
\(771\) 0 0
\(772\) 100.940 3.63292
\(773\) −10.0881 + 17.4731i −0.362843 + 0.628462i −0.988428 0.151694i \(-0.951527\pi\)
0.625585 + 0.780156i \(0.284861\pi\)
\(774\) 0 0
\(775\) −2.46675 + 4.27253i −0.0886081 + 0.153474i
\(776\) −53.9842 93.5034i −1.93792 3.35658i
\(777\) 0 0
\(778\) 47.7353 1.71139
\(779\) −2.90461 + 17.2526i −0.104068 + 0.618138i
\(780\) 0 0
\(781\) −0.770594 1.33471i −0.0275740 0.0477596i
\(782\) 2.15411 + 3.73104i 0.0770310 + 0.133422i
\(783\) 0 0