Properties

Label 855.2.k.h.406.1
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 406.1
Root \(1.07988 + 1.87040i\) of defining polynomial
Character \(\chi\) \(=\) 855.406
Dual form 855.2.k.h.676.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.832272 - 1.44154i) q^{2} +(-0.385355 + 0.667454i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.43525 q^{7} -2.04621 q^{8} +O(q^{10})\) \(q+(-0.832272 - 1.44154i) q^{2} +(-0.385355 + 0.667454i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.43525 q^{7} -2.04621 q^{8} +(0.832272 - 1.44154i) q^{10} +5.75477 q^{11} +(0.797505 - 1.38132i) q^{13} +(2.02680 + 3.51051i) q^{14} +(2.47371 + 4.28460i) q^{16} +(-2.99203 - 5.18234i) q^{17} +(0.149412 - 4.35634i) q^{19} -0.770710 q^{20} +(-4.78953 - 8.29572i) q^{22} +(-0.470022 + 0.814102i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.65497 q^{26} +(0.938437 - 1.62542i) q^{28} +(1.30917 - 2.26755i) q^{29} -5.26913 q^{31} +(2.07140 - 3.58777i) q^{32} +(-4.98037 + 8.62625i) q^{34} +(-1.21763 - 2.10899i) q^{35} -2.89384 q^{37} +(-6.40418 + 3.41028i) q^{38} +(-1.02310 - 1.77207i) q^{40} +(-3.15767 - 5.46925i) q^{41} +(-2.26961 - 3.93108i) q^{43} +(-2.21763 + 3.84104i) q^{44} +1.56475 q^{46} +(4.47718 - 7.75471i) q^{47} -1.06953 q^{49} +1.66454 q^{50} +(0.614645 + 1.06460i) q^{52} +(-1.09819 + 1.90213i) q^{53} +(2.87738 + 4.98377i) q^{55} +4.98304 q^{56} -4.35834 q^{58} +(-5.39939 - 9.35202i) q^{59} +(5.26434 - 9.11811i) q^{61} +(4.38535 + 7.59566i) q^{62} +2.99898 q^{64} +1.59501 q^{65} +(-0.504789 + 0.874320i) q^{67} +4.61197 q^{68} +(-2.02680 + 3.51051i) q^{70} +(4.41694 + 7.65036i) q^{71} +(5.12499 + 8.87674i) q^{73} +(2.40846 + 4.17157i) q^{74} +(2.85008 + 1.77846i) q^{76} -14.0143 q^{77} +(-3.80229 - 6.58577i) q^{79} +(-2.47371 + 4.28460i) q^{80} +(-5.25609 + 9.10381i) q^{82} -3.11355 q^{83} +(2.99203 - 5.18234i) q^{85} +(-3.77787 + 6.54346i) q^{86} -11.7755 q^{88} +(-5.55706 + 9.62511i) q^{89} +(-1.94213 + 3.36387i) q^{91} +(-0.362251 - 0.627436i) q^{92} -14.9049 q^{94} +(3.84741 - 2.04877i) q^{95} +(-2.02888 - 3.51412i) q^{97} +(0.890144 + 1.54177i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.832272 1.44154i −0.588506 1.01932i −0.994428 0.105414i \(-0.966383\pi\)
0.405923 0.913907i \(-0.366950\pi\)
\(3\) 0 0
\(4\) −0.385355 + 0.667454i −0.192677 + 0.333727i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −2.43525 −0.920440 −0.460220 0.887805i \(-0.652229\pi\)
−0.460220 + 0.887805i \(0.652229\pi\)
\(8\) −2.04621 −0.723444
\(9\) 0 0
\(10\) 0.832272 1.44154i 0.263188 0.455854i
\(11\) 5.75477 1.73513 0.867564 0.497326i \(-0.165685\pi\)
0.867564 + 0.497326i \(0.165685\pi\)
\(12\) 0 0
\(13\) 0.797505 1.38132i 0.221188 0.383109i −0.733981 0.679170i \(-0.762340\pi\)
0.955169 + 0.296061i \(0.0956732\pi\)
\(14\) 2.02680 + 3.51051i 0.541684 + 0.938224i
\(15\) 0 0
\(16\) 2.47371 + 4.28460i 0.618428 + 1.07115i
\(17\) −2.99203 5.18234i −0.725673 1.25690i −0.958696 0.284432i \(-0.908195\pi\)
0.233023 0.972471i \(-0.425138\pi\)
\(18\) 0 0
\(19\) 0.149412 4.35634i 0.0342775 0.999412i
\(20\) −0.770710 −0.172336
\(21\) 0 0
\(22\) −4.78953 8.29572i −1.02113 1.76865i
\(23\) −0.470022 + 0.814102i −0.0980064 + 0.169752i −0.910859 0.412717i \(-0.864580\pi\)
0.812853 + 0.582469i \(0.197913\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −2.65497 −0.520682
\(27\) 0 0
\(28\) 0.938437 1.62542i 0.177348 0.307176i
\(29\) 1.30917 2.26755i 0.243106 0.421073i −0.718491 0.695536i \(-0.755167\pi\)
0.961598 + 0.274463i \(0.0885002\pi\)
\(30\) 0 0
\(31\) −5.26913 −0.946364 −0.473182 0.880965i \(-0.656895\pi\)
−0.473182 + 0.880965i \(0.656895\pi\)
\(32\) 2.07140 3.58777i 0.366175 0.634233i
\(33\) 0 0
\(34\) −4.98037 + 8.62625i −0.854126 + 1.47939i
\(35\) −1.21763 2.10899i −0.205817 0.356485i
\(36\) 0 0
\(37\) −2.89384 −0.475744 −0.237872 0.971297i \(-0.576450\pi\)
−0.237872 + 0.971297i \(0.576450\pi\)
\(38\) −6.40418 + 3.41028i −1.03889 + 0.553220i
\(39\) 0 0
\(40\) −1.02310 1.77207i −0.161767 0.280189i
\(41\) −3.15767 5.46925i −0.493145 0.854153i 0.506823 0.862050i \(-0.330820\pi\)
−0.999969 + 0.00789701i \(0.997486\pi\)
\(42\) 0 0
\(43\) −2.26961 3.93108i −0.346113 0.599485i 0.639443 0.768839i \(-0.279165\pi\)
−0.985555 + 0.169354i \(0.945832\pi\)
\(44\) −2.21763 + 3.84104i −0.334320 + 0.579059i
\(45\) 0 0
\(46\) 1.56475 0.230709
\(47\) 4.47718 7.75471i 0.653064 1.13114i −0.329311 0.944221i \(-0.606816\pi\)
0.982375 0.186919i \(-0.0598502\pi\)
\(48\) 0 0
\(49\) −1.06953 −0.152791
\(50\) 1.66454 0.235402
\(51\) 0 0
\(52\) 0.614645 + 1.06460i 0.0852359 + 0.147633i
\(53\) −1.09819 + 1.90213i −0.150848 + 0.261277i −0.931540 0.363640i \(-0.881534\pi\)
0.780691 + 0.624917i \(0.214867\pi\)
\(54\) 0 0
\(55\) 2.87738 + 4.98377i 0.387986 + 0.672012i
\(56\) 4.98304 0.665887
\(57\) 0 0
\(58\) −4.35834 −0.572278
\(59\) −5.39939 9.35202i −0.702941 1.21753i −0.967430 0.253140i \(-0.918537\pi\)
0.264489 0.964389i \(-0.414797\pi\)
\(60\) 0 0
\(61\) 5.26434 9.11811i 0.674030 1.16745i −0.302721 0.953079i \(-0.597895\pi\)
0.976751 0.214375i \(-0.0687716\pi\)
\(62\) 4.38535 + 7.59566i 0.556941 + 0.964649i
\(63\) 0 0
\(64\) 2.99898 0.374873
\(65\) 1.59501 0.197837
\(66\) 0 0
\(67\) −0.504789 + 0.874320i −0.0616698 + 0.106815i −0.895212 0.445641i \(-0.852976\pi\)
0.833542 + 0.552456i \(0.186309\pi\)
\(68\) 4.61197 0.559284
\(69\) 0 0
\(70\) −2.02680 + 3.51051i −0.242248 + 0.419587i
\(71\) 4.41694 + 7.65036i 0.524194 + 0.907931i 0.999603 + 0.0281662i \(0.00896677\pi\)
−0.475409 + 0.879765i \(0.657700\pi\)
\(72\) 0 0
\(73\) 5.12499 + 8.87674i 0.599835 + 1.03894i 0.992845 + 0.119410i \(0.0381003\pi\)
−0.393011 + 0.919534i \(0.628566\pi\)
\(74\) 2.40846 + 4.17157i 0.279978 + 0.484936i
\(75\) 0 0
\(76\) 2.85008 + 1.77846i 0.326927 + 0.204004i
\(77\) −14.0143 −1.59708
\(78\) 0 0
\(79\) −3.80229 6.58577i −0.427792 0.740957i 0.568885 0.822417i \(-0.307375\pi\)
−0.996677 + 0.0814604i \(0.974042\pi\)
\(80\) −2.47371 + 4.28460i −0.276570 + 0.479032i
\(81\) 0 0
\(82\) −5.25609 + 9.10381i −0.580438 + 1.00535i
\(83\) −3.11355 −0.341756 −0.170878 0.985292i \(-0.554660\pi\)
−0.170878 + 0.985292i \(0.554660\pi\)
\(84\) 0 0
\(85\) 2.99203 5.18234i 0.324531 0.562104i
\(86\) −3.77787 + 6.54346i −0.407378 + 0.705600i
\(87\) 0 0
\(88\) −11.7755 −1.25527
\(89\) −5.55706 + 9.62511i −0.589047 + 1.02026i 0.405310 + 0.914179i \(0.367163\pi\)
−0.994358 + 0.106081i \(0.966170\pi\)
\(90\) 0 0
\(91\) −1.94213 + 3.36387i −0.203590 + 0.352629i
\(92\) −0.362251 0.627436i −0.0377672 0.0654148i
\(93\) 0 0
\(94\) −14.9049 −1.53733
\(95\) 3.84741 2.04877i 0.394735 0.210200i
\(96\) 0 0
\(97\) −2.02888 3.51412i −0.206002 0.356805i 0.744450 0.667678i \(-0.232712\pi\)
−0.950451 + 0.310873i \(0.899379\pi\)
\(98\) 0.890144 + 1.54177i 0.0899181 + 0.155743i
\(99\) 0 0
\(100\) −0.385355 0.667454i −0.0385355 0.0667454i
\(101\) −5.56503 + 9.63892i −0.553741 + 0.959108i 0.444259 + 0.895898i \(0.353467\pi\)
−0.998000 + 0.0632098i \(0.979866\pi\)
\(102\) 0 0
\(103\) 11.5791 1.14092 0.570460 0.821326i \(-0.306765\pi\)
0.570460 + 0.821326i \(0.306765\pi\)
\(104\) −1.63186 + 2.82647i −0.160017 + 0.277158i
\(105\) 0 0
\(106\) 3.65598 0.355101
\(107\) −17.9177 −1.73217 −0.866086 0.499894i \(-0.833372\pi\)
−0.866086 + 0.499894i \(0.833372\pi\)
\(108\) 0 0
\(109\) −2.81235 4.87113i −0.269374 0.466570i 0.699326 0.714803i \(-0.253484\pi\)
−0.968700 + 0.248233i \(0.920150\pi\)
\(110\) 4.78953 8.29572i 0.456664 0.790965i
\(111\) 0 0
\(112\) −6.02412 10.4341i −0.569226 0.985928i
\(113\) 15.6789 1.47494 0.737472 0.675378i \(-0.236019\pi\)
0.737472 + 0.675378i \(0.236019\pi\)
\(114\) 0 0
\(115\) −0.940044 −0.0876595
\(116\) 1.00899 + 1.74762i 0.0936822 + 0.162262i
\(117\) 0 0
\(118\) −8.98753 + 15.5669i −0.827369 + 1.43304i
\(119\) 7.28635 + 12.6203i 0.667939 + 1.15690i
\(120\) 0 0
\(121\) 22.1173 2.01067
\(122\) −17.5255 −1.58668
\(123\) 0 0
\(124\) 2.03049 3.51691i 0.182343 0.315827i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −3.05996 + 5.30000i −0.271527 + 0.470299i −0.969253 0.246066i \(-0.920862\pi\)
0.697726 + 0.716365i \(0.254195\pi\)
\(128\) −6.63877 11.4987i −0.586790 1.01635i
\(129\) 0 0
\(130\) −1.32748 2.29927i −0.116428 0.201659i
\(131\) −7.44055 12.8874i −0.650084 1.12598i −0.983102 0.183058i \(-0.941400\pi\)
0.333018 0.942920i \(-0.391933\pi\)
\(132\) 0 0
\(133\) −0.363857 + 10.6088i −0.0315504 + 0.919899i
\(134\) 1.68049 0.145172
\(135\) 0 0
\(136\) 6.12231 + 10.6042i 0.524984 + 0.909299i
\(137\) 8.67518 15.0258i 0.741170 1.28374i −0.210793 0.977531i \(-0.567604\pi\)
0.951963 0.306214i \(-0.0990622\pi\)
\(138\) 0 0
\(139\) 3.35267 5.80700i 0.284370 0.492543i −0.688086 0.725629i \(-0.741549\pi\)
0.972456 + 0.233086i \(0.0748823\pi\)
\(140\) 1.87687 0.158625
\(141\) 0 0
\(142\) 7.35219 12.7344i 0.616982 1.06864i
\(143\) 4.58946 7.94917i 0.383790 0.664743i
\(144\) 0 0
\(145\) 2.61834 0.217441
\(146\) 8.53077 14.7757i 0.706012 1.22285i
\(147\) 0 0
\(148\) 1.11515 1.93150i 0.0916651 0.158769i
\(149\) 7.19642 + 12.4646i 0.589553 + 1.02114i 0.994291 + 0.106704i \(0.0340296\pi\)
−0.404737 + 0.914433i \(0.632637\pi\)
\(150\) 0 0
\(151\) 12.7219 1.03529 0.517645 0.855595i \(-0.326809\pi\)
0.517645 + 0.855595i \(0.326809\pi\)
\(152\) −0.305729 + 8.91398i −0.0247979 + 0.723019i
\(153\) 0 0
\(154\) 11.6637 + 20.2022i 0.939890 + 1.62794i
\(155\) −2.63457 4.56320i −0.211614 0.366525i
\(156\) 0 0
\(157\) 1.68765 + 2.92309i 0.134689 + 0.233288i 0.925479 0.378800i \(-0.123663\pi\)
−0.790790 + 0.612088i \(0.790330\pi\)
\(158\) −6.32909 + 10.9623i −0.503515 + 0.872114i
\(159\) 0 0
\(160\) 4.14280 0.327517
\(161\) 1.14462 1.98255i 0.0902089 0.156246i
\(162\) 0 0
\(163\) 0.307960 0.0241213 0.0120607 0.999927i \(-0.496161\pi\)
0.0120607 + 0.999927i \(0.496161\pi\)
\(164\) 4.86730 0.380072
\(165\) 0 0
\(166\) 2.59132 + 4.48830i 0.201125 + 0.348359i
\(167\) 7.13215 12.3532i 0.551902 0.955923i −0.446235 0.894916i \(-0.647235\pi\)
0.998137 0.0610070i \(-0.0194312\pi\)
\(168\) 0 0
\(169\) 5.22797 + 9.05511i 0.402152 + 0.696547i
\(170\) −9.96073 −0.763953
\(171\) 0 0
\(172\) 3.49842 0.266752
\(173\) 6.67357 + 11.5590i 0.507382 + 0.878811i 0.999963 + 0.00854514i \(0.00272003\pi\)
−0.492581 + 0.870266i \(0.663947\pi\)
\(174\) 0 0
\(175\) 1.21763 2.10899i 0.0920440 0.159425i
\(176\) 14.2356 + 24.6569i 1.07305 + 1.85858i
\(177\) 0 0
\(178\) 18.5000 1.38663
\(179\) 14.2207 1.06291 0.531454 0.847087i \(-0.321646\pi\)
0.531454 + 0.847087i \(0.321646\pi\)
\(180\) 0 0
\(181\) −4.94132 + 8.55861i −0.367285 + 0.636157i −0.989140 0.146976i \(-0.953046\pi\)
0.621855 + 0.783133i \(0.286379\pi\)
\(182\) 6.46552 0.479256
\(183\) 0 0
\(184\) 0.961763 1.66582i 0.0709021 0.122806i
\(185\) −1.44692 2.50613i −0.106379 0.184255i
\(186\) 0 0
\(187\) −17.2184 29.8232i −1.25914 2.18089i
\(188\) 3.45061 + 5.97663i 0.251661 + 0.435891i
\(189\) 0 0
\(190\) −6.15548 3.84104i −0.446565 0.278659i
\(191\) 12.9942 0.940228 0.470114 0.882606i \(-0.344213\pi\)
0.470114 + 0.882606i \(0.344213\pi\)
\(192\) 0 0
\(193\) −7.25795 12.5711i −0.522439 0.904890i −0.999659 0.0261066i \(-0.991689\pi\)
0.477221 0.878784i \(-0.341644\pi\)
\(194\) −3.37716 + 5.84942i −0.242466 + 0.419964i
\(195\) 0 0
\(196\) 0.412150 0.713865i 0.0294393 0.0509904i
\(197\) 25.0010 1.78125 0.890624 0.454740i \(-0.150268\pi\)
0.890624 + 0.454740i \(0.150268\pi\)
\(198\) 0 0
\(199\) 1.12769 1.95322i 0.0799401 0.138460i −0.823284 0.567630i \(-0.807860\pi\)
0.903224 + 0.429170i \(0.141194\pi\)
\(200\) 1.02310 1.77207i 0.0723444 0.125304i
\(201\) 0 0
\(202\) 18.5265 1.30352
\(203\) −3.18816 + 5.52205i −0.223765 + 0.387572i
\(204\) 0 0
\(205\) 3.15767 5.46925i 0.220541 0.381989i
\(206\) −9.63694 16.6917i −0.671437 1.16296i
\(207\) 0 0
\(208\) 7.89120 0.547156
\(209\) 0.859833 25.0697i 0.0594759 1.73411i
\(210\) 0 0
\(211\) −11.1081 19.2397i −0.764710 1.32452i −0.940400 0.340071i \(-0.889549\pi\)
0.175689 0.984446i \(-0.443785\pi\)
\(212\) −0.846388 1.46599i −0.0581302 0.100684i
\(213\) 0 0
\(214\) 14.9124 + 25.8291i 1.01939 + 1.76564i
\(215\) 2.26961 3.93108i 0.154786 0.268098i
\(216\) 0 0
\(217\) 12.8317 0.871071
\(218\) −4.68128 + 8.10822i −0.317057 + 0.549158i
\(219\) 0 0
\(220\) −4.43525 −0.299025
\(221\) −9.54463 −0.642041
\(222\) 0 0
\(223\) −5.10799 8.84730i −0.342056 0.592459i 0.642758 0.766069i \(-0.277790\pi\)
−0.984814 + 0.173610i \(0.944457\pi\)
\(224\) −5.04438 + 8.73712i −0.337042 + 0.583774i
\(225\) 0 0
\(226\) −13.0491 22.6017i −0.868012 1.50344i
\(227\) −4.15180 −0.275565 −0.137782 0.990463i \(-0.543997\pi\)
−0.137782 + 0.990463i \(0.543997\pi\)
\(228\) 0 0
\(229\) 6.53286 0.431703 0.215852 0.976426i \(-0.430747\pi\)
0.215852 + 0.976426i \(0.430747\pi\)
\(230\) 0.782373 + 1.35511i 0.0515881 + 0.0893533i
\(231\) 0 0
\(232\) −2.67883 + 4.63987i −0.175874 + 0.304623i
\(233\) 2.57410 + 4.45848i 0.168635 + 0.292084i 0.937940 0.346797i \(-0.112731\pi\)
−0.769305 + 0.638882i \(0.779397\pi\)
\(234\) 0 0
\(235\) 8.95437 0.584118
\(236\) 8.32272 0.541763
\(237\) 0 0
\(238\) 12.1285 21.0071i 0.786171 1.36169i
\(239\) −13.9962 −0.905338 −0.452669 0.891679i \(-0.649528\pi\)
−0.452669 + 0.891679i \(0.649528\pi\)
\(240\) 0 0
\(241\) −7.61285 + 13.1858i −0.490387 + 0.849375i −0.999939 0.0110652i \(-0.996478\pi\)
0.509552 + 0.860440i \(0.329811\pi\)
\(242\) −18.4076 31.8830i −1.18329 2.04952i
\(243\) 0 0
\(244\) 4.05728 + 7.02742i 0.259741 + 0.449884i
\(245\) −0.534767 0.926244i −0.0341650 0.0591756i
\(246\) 0 0
\(247\) −5.89834 3.68059i −0.375302 0.234190i
\(248\) 10.7817 0.684642
\(249\) 0 0
\(250\) 0.832272 + 1.44154i 0.0526375 + 0.0911709i
\(251\) −3.05630 + 5.29366i −0.192912 + 0.334133i −0.946214 0.323542i \(-0.895126\pi\)
0.753302 + 0.657674i \(0.228460\pi\)
\(252\) 0 0
\(253\) −2.70487 + 4.68497i −0.170053 + 0.294541i
\(254\) 10.1869 0.639181
\(255\) 0 0
\(256\) −8.05154 + 13.9457i −0.503221 + 0.871605i
\(257\) 0.0613414 0.106246i 0.00382637 0.00662747i −0.864106 0.503310i \(-0.832115\pi\)
0.867932 + 0.496683i \(0.165449\pi\)
\(258\) 0 0
\(259\) 7.04723 0.437893
\(260\) −0.614645 + 1.06460i −0.0381187 + 0.0660235i
\(261\) 0 0
\(262\) −12.3851 + 21.4517i −0.765156 + 1.32529i
\(263\) −5.03027 8.71267i −0.310179 0.537247i 0.668222 0.743962i \(-0.267056\pi\)
−0.978401 + 0.206716i \(0.933722\pi\)
\(264\) 0 0
\(265\) −2.19639 −0.134923
\(266\) 15.5958 8.30489i 0.956240 0.509206i
\(267\) 0 0
\(268\) −0.389046 0.673847i −0.0237648 0.0411618i
\(269\) 2.85614 + 4.94698i 0.174142 + 0.301623i 0.939864 0.341549i \(-0.110951\pi\)
−0.765722 + 0.643172i \(0.777618\pi\)
\(270\) 0 0
\(271\) 6.35560 + 11.0082i 0.386075 + 0.668702i 0.991918 0.126883i \(-0.0404972\pi\)
−0.605843 + 0.795585i \(0.707164\pi\)
\(272\) 14.8028 25.6393i 0.897554 1.55461i
\(273\) 0 0
\(274\) −28.8804 −1.74473
\(275\) −2.87738 + 4.98377i −0.173513 + 0.300533i
\(276\) 0 0
\(277\) 17.6019 1.05760 0.528799 0.848747i \(-0.322642\pi\)
0.528799 + 0.848747i \(0.322642\pi\)
\(278\) −11.1613 −0.669413
\(279\) 0 0
\(280\) 2.49152 + 4.31544i 0.148897 + 0.257897i
\(281\) −10.2502 + 17.7539i −0.611476 + 1.05911i 0.379516 + 0.925185i \(0.376090\pi\)
−0.990992 + 0.133922i \(0.957243\pi\)
\(282\) 0 0
\(283\) 5.92805 + 10.2677i 0.352386 + 0.610350i 0.986667 0.162752i \(-0.0520371\pi\)
−0.634281 + 0.773103i \(0.718704\pi\)
\(284\) −6.80836 −0.404002
\(285\) 0 0
\(286\) −15.2787 −0.903449
\(287\) 7.68973 + 13.3190i 0.453911 + 0.786196i
\(288\) 0 0
\(289\) −9.40447 + 16.2890i −0.553204 + 0.958177i
\(290\) −2.17917 3.77443i −0.127965 0.221642i
\(291\) 0 0
\(292\) −7.89976 −0.462298
\(293\) 24.9814 1.45943 0.729715 0.683751i \(-0.239653\pi\)
0.729715 + 0.683751i \(0.239653\pi\)
\(294\) 0 0
\(295\) 5.39939 9.35202i 0.314365 0.544495i
\(296\) 5.92139 0.344174
\(297\) 0 0
\(298\) 11.9788 20.7478i 0.693911 1.20189i
\(299\) 0.749690 + 1.29850i 0.0433557 + 0.0750943i
\(300\) 0 0
\(301\) 5.52708 + 9.57319i 0.318576 + 0.551789i
\(302\) −10.5881 18.3391i −0.609274 1.05529i
\(303\) 0 0
\(304\) 19.0348 10.1362i 1.09172 0.581348i
\(305\) 10.5287 0.602871
\(306\) 0 0
\(307\) −8.45997 14.6531i −0.482836 0.836296i 0.516970 0.856003i \(-0.327060\pi\)
−0.999806 + 0.0197074i \(0.993727\pi\)
\(308\) 5.40049 9.35392i 0.307721 0.532989i
\(309\) 0 0
\(310\) −4.38535 + 7.59566i −0.249071 + 0.431404i
\(311\) 15.2133 0.862670 0.431335 0.902192i \(-0.358043\pi\)
0.431335 + 0.902192i \(0.358043\pi\)
\(312\) 0 0
\(313\) −12.4637 + 21.5877i −0.704488 + 1.22021i 0.262389 + 0.964962i \(0.415490\pi\)
−0.966876 + 0.255246i \(0.917844\pi\)
\(314\) 2.80917 4.86562i 0.158531 0.274583i
\(315\) 0 0
\(316\) 5.86093 0.329703
\(317\) −12.6152 + 21.8502i −0.708541 + 1.22723i 0.256857 + 0.966449i \(0.417313\pi\)
−0.965398 + 0.260780i \(0.916020\pi\)
\(318\) 0 0
\(319\) 7.53396 13.0492i 0.421821 0.730615i
\(320\) 1.49949 + 2.59720i 0.0838241 + 0.145188i
\(321\) 0 0
\(322\) −3.81055 −0.212354
\(323\) −23.0231 + 12.2600i −1.28104 + 0.682163i
\(324\) 0 0
\(325\) 0.797505 + 1.38132i 0.0442376 + 0.0766218i
\(326\) −0.256307 0.443937i −0.0141955 0.0245874i
\(327\) 0 0
\(328\) 6.46125 + 11.1912i 0.356763 + 0.617932i
\(329\) −10.9031 + 18.8847i −0.601106 + 1.04115i
\(330\) 0 0
\(331\) −20.2063 −1.11064 −0.555320 0.831637i \(-0.687404\pi\)
−0.555320 + 0.831637i \(0.687404\pi\)
\(332\) 1.19982 2.07815i 0.0658487 0.114053i
\(333\) 0 0
\(334\) −23.7436 −1.29919
\(335\) −1.00958 −0.0551592
\(336\) 0 0
\(337\) 15.9123 + 27.5610i 0.866800 + 1.50134i 0.865249 + 0.501342i \(0.167160\pi\)
0.00155051 + 0.999999i \(0.499506\pi\)
\(338\) 8.70219 15.0726i 0.473337 0.819843i
\(339\) 0 0
\(340\) 2.30599 + 3.99408i 0.125060 + 0.216610i
\(341\) −30.3226 −1.64206
\(342\) 0 0
\(343\) 19.6514 1.06107
\(344\) 4.64410 + 8.04382i 0.250393 + 0.433693i
\(345\) 0 0
\(346\) 11.1085 19.2404i 0.597194 1.03437i
\(347\) −1.65128 2.86009i −0.0886451 0.153538i 0.818294 0.574801i \(-0.194920\pi\)
−0.906939 + 0.421263i \(0.861587\pi\)
\(348\) 0 0
\(349\) 17.8486 0.955416 0.477708 0.878519i \(-0.341468\pi\)
0.477708 + 0.878519i \(0.341468\pi\)
\(350\) −4.05359 −0.216674
\(351\) 0 0
\(352\) 11.9204 20.6468i 0.635360 1.10048i
\(353\) 8.29523 0.441511 0.220755 0.975329i \(-0.429148\pi\)
0.220755 + 0.975329i \(0.429148\pi\)
\(354\) 0 0
\(355\) −4.41694 + 7.65036i −0.234427 + 0.406039i
\(356\) −4.28288 7.41817i −0.226992 0.393162i
\(357\) 0 0
\(358\) −11.8355 20.4997i −0.625527 1.08344i
\(359\) 4.17511 + 7.23150i 0.220354 + 0.381664i 0.954915 0.296878i \(-0.0959455\pi\)
−0.734562 + 0.678542i \(0.762612\pi\)
\(360\) 0 0
\(361\) −18.9554 1.30178i −0.997650 0.0685148i
\(362\) 16.4501 0.864598
\(363\) 0 0
\(364\) −1.49682 2.59256i −0.0784545 0.135887i
\(365\) −5.12499 + 8.87674i −0.268254 + 0.464630i
\(366\) 0 0
\(367\) −7.20988 + 12.4879i −0.376353 + 0.651862i −0.990528 0.137307i \(-0.956155\pi\)
0.614176 + 0.789169i \(0.289489\pi\)
\(368\) −4.65080 −0.242440
\(369\) 0 0
\(370\) −2.40846 + 4.17157i −0.125210 + 0.216870i
\(371\) 2.67438 4.63216i 0.138847 0.240490i
\(372\) 0 0
\(373\) −24.1157 −1.24866 −0.624332 0.781159i \(-0.714629\pi\)
−0.624332 + 0.781159i \(0.714629\pi\)
\(374\) −28.6608 + 49.6420i −1.48202 + 2.56693i
\(375\) 0 0
\(376\) −9.16125 + 15.8678i −0.472455 + 0.818317i
\(377\) −2.08814 3.61676i −0.107545 0.186273i
\(378\) 0 0
\(379\) 16.6757 0.856571 0.428285 0.903644i \(-0.359118\pi\)
0.428285 + 0.903644i \(0.359118\pi\)
\(380\) −0.115154 + 3.35747i −0.00590725 + 0.172235i
\(381\) 0 0
\(382\) −10.8147 18.7316i −0.553329 0.958395i
\(383\) −5.43895 9.42053i −0.277917 0.481367i 0.692950 0.720986i \(-0.256311\pi\)
−0.970867 + 0.239619i \(0.922977\pi\)
\(384\) 0 0
\(385\) −7.00716 12.1368i −0.357118 0.618546i
\(386\) −12.0812 + 20.9252i −0.614916 + 1.06507i
\(387\) 0 0
\(388\) 3.12736 0.158767
\(389\) 18.2272 31.5704i 0.924154 1.60068i 0.131237 0.991351i \(-0.458105\pi\)
0.792917 0.609330i \(-0.208562\pi\)
\(390\) 0 0
\(391\) 5.62528 0.284482
\(392\) 2.18849 0.110535
\(393\) 0 0
\(394\) −20.8077 36.0399i −1.04827 1.81566i
\(395\) 3.80229 6.58577i 0.191314 0.331366i
\(396\) 0 0
\(397\) −4.29191 7.43380i −0.215405 0.373092i 0.737993 0.674808i \(-0.235774\pi\)
−0.953398 + 0.301717i \(0.902440\pi\)
\(398\) −3.75419 −0.188181
\(399\) 0 0
\(400\) −4.94743 −0.247371
\(401\) −8.52785 14.7707i −0.425860 0.737612i 0.570640 0.821200i \(-0.306695\pi\)
−0.996500 + 0.0835885i \(0.973362\pi\)
\(402\) 0 0
\(403\) −4.20216 + 7.27836i −0.209325 + 0.362561i
\(404\) −4.28903 7.42881i −0.213387 0.369597i
\(405\) 0 0
\(406\) 10.6137 0.526747
\(407\) −16.6533 −0.825476
\(408\) 0 0
\(409\) 5.89702 10.2139i 0.291589 0.505047i −0.682597 0.730795i \(-0.739149\pi\)
0.974186 + 0.225749i \(0.0724828\pi\)
\(410\) −10.5122 −0.519159
\(411\) 0 0
\(412\) −4.46205 + 7.72850i −0.219829 + 0.380756i
\(413\) 13.1489 + 22.7745i 0.647015 + 1.12066i
\(414\) 0 0
\(415\) −1.55677 2.69641i −0.0764190 0.132362i
\(416\) −3.30390 5.72252i −0.161987 0.280570i
\(417\) 0 0
\(418\) −36.8546 + 19.6253i −1.80261 + 0.959907i
\(419\) −1.14280 −0.0558292 −0.0279146 0.999610i \(-0.508887\pi\)
−0.0279146 + 0.999610i \(0.508887\pi\)
\(420\) 0 0
\(421\) −9.75944 16.9039i −0.475646 0.823843i 0.523965 0.851740i \(-0.324452\pi\)
−0.999611 + 0.0278967i \(0.991119\pi\)
\(422\) −18.4899 + 32.0254i −0.900072 + 1.55897i
\(423\) 0 0
\(424\) 2.24713 3.89215i 0.109130 0.189019i
\(425\) 5.98406 0.290269
\(426\) 0 0
\(427\) −12.8200 + 22.2049i −0.620404 + 1.07457i
\(428\) 6.90469 11.9593i 0.333751 0.578073i
\(429\) 0 0
\(430\) −7.55574 −0.364370
\(431\) −18.4392 + 31.9377i −0.888187 + 1.53838i −0.0461694 + 0.998934i \(0.514701\pi\)
−0.842017 + 0.539451i \(0.818632\pi\)
\(432\) 0 0
\(433\) −0.184467 + 0.319506i −0.00886490 + 0.0153545i −0.870424 0.492303i \(-0.836155\pi\)
0.861559 + 0.507658i \(0.169488\pi\)
\(434\) −10.6795 18.4974i −0.512630 0.887902i
\(435\) 0 0
\(436\) 4.33501 0.207609
\(437\) 3.47628 + 2.16921i 0.166293 + 0.103767i
\(438\) 0 0
\(439\) 1.13220 + 1.96102i 0.0540367 + 0.0935944i 0.891778 0.452472i \(-0.149458\pi\)
−0.837742 + 0.546067i \(0.816125\pi\)
\(440\) −5.88773 10.1978i −0.280686 0.486163i
\(441\) 0 0
\(442\) 7.94373 + 13.7590i 0.377845 + 0.654447i
\(443\) −8.23137 + 14.2572i −0.391084 + 0.677378i −0.992593 0.121488i \(-0.961233\pi\)
0.601508 + 0.798866i \(0.294567\pi\)
\(444\) 0 0
\(445\) −11.1141 −0.526860
\(446\) −8.50248 + 14.7267i −0.402604 + 0.697331i
\(447\) 0 0
\(448\) −7.30329 −0.345048
\(449\) −14.1613 −0.668315 −0.334158 0.942517i \(-0.608452\pi\)
−0.334158 + 0.942517i \(0.608452\pi\)
\(450\) 0 0
\(451\) −18.1717 31.4742i −0.855670 1.48206i
\(452\) −6.04193 + 10.4649i −0.284188 + 0.492229i
\(453\) 0 0
\(454\) 3.45543 + 5.98498i 0.162171 + 0.280889i
\(455\) −3.88426 −0.182097
\(456\) 0 0
\(457\) 1.22073 0.0571033 0.0285516 0.999592i \(-0.490910\pi\)
0.0285516 + 0.999592i \(0.490910\pi\)
\(458\) −5.43712 9.41736i −0.254060 0.440045i
\(459\) 0 0
\(460\) 0.362251 0.627436i 0.0168900 0.0292544i
\(461\) −4.34580 7.52714i −0.202404 0.350574i 0.746898 0.664938i \(-0.231542\pi\)
−0.949303 + 0.314364i \(0.898209\pi\)
\(462\) 0 0
\(463\) −19.7149 −0.916229 −0.458114 0.888893i \(-0.651475\pi\)
−0.458114 + 0.888893i \(0.651475\pi\)
\(464\) 12.9540 0.601375
\(465\) 0 0
\(466\) 4.28471 7.42133i 0.198485 0.343787i
\(467\) 11.4795 0.531207 0.265604 0.964082i \(-0.414429\pi\)
0.265604 + 0.964082i \(0.414429\pi\)
\(468\) 0 0
\(469\) 1.22929 2.12919i 0.0567633 0.0983170i
\(470\) −7.45247 12.9081i −0.343757 0.595404i
\(471\) 0 0
\(472\) 11.0483 + 19.1362i 0.508538 + 0.880814i
\(473\) −13.0611 22.6225i −0.600549 1.04018i
\(474\) 0 0
\(475\) 3.69799 + 2.30756i 0.169676 + 0.105878i
\(476\) −11.2313 −0.514787
\(477\) 0 0
\(478\) 11.6486 + 20.1760i 0.532796 + 0.922830i
\(479\) 19.6316 34.0029i 0.896989 1.55363i 0.0656652 0.997842i \(-0.479083\pi\)
0.831324 0.555789i \(-0.187584\pi\)
\(480\) 0 0
\(481\) −2.30785 + 3.99731i −0.105229 + 0.182262i
\(482\) 25.3439 1.15438
\(483\) 0 0
\(484\) −8.52302 + 14.7623i −0.387410 + 0.671014i
\(485\) 2.02888 3.51412i 0.0921267 0.159568i
\(486\) 0 0
\(487\) 31.5943 1.43168 0.715838 0.698266i \(-0.246045\pi\)
0.715838 + 0.698266i \(0.246045\pi\)
\(488\) −10.7719 + 18.6576i −0.487623 + 0.844588i
\(489\) 0 0
\(490\) −0.890144 + 1.54177i −0.0402126 + 0.0696503i
\(491\) −5.53187 9.58148i −0.249650 0.432406i 0.713779 0.700371i \(-0.246982\pi\)
−0.963429 + 0.267965i \(0.913649\pi\)
\(492\) 0 0
\(493\) −15.6683 −0.705663
\(494\) −0.396685 + 11.5659i −0.0178477 + 0.520376i
\(495\) 0 0
\(496\) −13.0343 22.5761i −0.585258 1.01370i
\(497\) −10.7564 18.6306i −0.482489 0.835696i
\(498\) 0 0
\(499\) 10.1868 + 17.6440i 0.456023 + 0.789854i 0.998746 0.0500570i \(-0.0159403\pi\)
−0.542724 + 0.839911i \(0.682607\pi\)
\(500\) 0.385355 0.667454i 0.0172336 0.0298495i
\(501\) 0 0
\(502\) 10.1747 0.454118
\(503\) −6.83622 + 11.8407i −0.304812 + 0.527950i −0.977219 0.212231i \(-0.931927\pi\)
0.672407 + 0.740181i \(0.265260\pi\)
\(504\) 0 0
\(505\) −11.1301 −0.495281
\(506\) 9.00474 0.400310
\(507\) 0 0
\(508\) −2.35834 4.08476i −0.104634 0.181232i
\(509\) −3.86196 + 6.68912i −0.171179 + 0.296490i −0.938832 0.344375i \(-0.888091\pi\)
0.767654 + 0.640865i \(0.221424\pi\)
\(510\) 0 0
\(511\) −12.4807 21.6171i −0.552112 0.956285i
\(512\) 0.249240 0.0110150
\(513\) 0 0
\(514\) −0.204211 −0.00900736
\(515\) 5.78953 + 10.0278i 0.255117 + 0.441876i
\(516\) 0 0
\(517\) 25.7651 44.6265i 1.13315 1.96267i
\(518\) −5.86521 10.1588i −0.257703 0.446354i
\(519\) 0 0
\(520\) −3.26372 −0.143124
\(521\) 2.16876 0.0950151 0.0475075 0.998871i \(-0.484872\pi\)
0.0475075 + 0.998871i \(0.484872\pi\)
\(522\) 0 0
\(523\) 11.9466 20.6921i 0.522389 0.904804i −0.477272 0.878756i \(-0.658374\pi\)
0.999661 0.0260485i \(-0.00829243\pi\)
\(524\) 11.4690 0.501026
\(525\) 0 0
\(526\) −8.37310 + 14.5026i −0.365085 + 0.632345i
\(527\) 15.7654 + 27.3065i 0.686751 + 1.18949i
\(528\) 0 0
\(529\) 11.0582 + 19.1533i 0.480790 + 0.832752i
\(530\) 1.82799 + 3.16617i 0.0794029 + 0.137530i
\(531\) 0 0
\(532\) −6.94067 4.33101i −0.300916 0.187773i
\(533\) −10.0730 −0.436312
\(534\) 0 0
\(535\) −8.95887 15.5172i −0.387326 0.670868i
\(536\) 1.03290 1.78904i 0.0446147 0.0772749i
\(537\) 0 0
\(538\) 4.75418 8.23448i 0.204967 0.355013i
\(539\) −6.15492 −0.265111
\(540\) 0 0
\(541\) −21.2275 + 36.7671i −0.912641 + 1.58074i −0.102323 + 0.994751i \(0.532627\pi\)
−0.810319 + 0.585990i \(0.800706\pi\)
\(542\) 10.5792 18.3237i 0.454415 0.787069i
\(543\) 0 0
\(544\) −24.7907 −1.06289
\(545\) 2.81235 4.87113i 0.120468 0.208656i
\(546\) 0 0
\(547\) −6.01535 + 10.4189i −0.257198 + 0.445480i −0.965490 0.260439i \(-0.916133\pi\)
0.708292 + 0.705919i \(0.249466\pi\)
\(548\) 6.68604 + 11.5806i 0.285614 + 0.494697i
\(549\) 0 0
\(550\) 9.57907 0.408453
\(551\) −9.68259 6.04198i −0.412492 0.257397i
\(552\) 0 0
\(553\) 9.25956 + 16.0380i 0.393756 + 0.682006i
\(554\) −14.6496 25.3739i −0.622403 1.07803i
\(555\) 0 0
\(556\) 2.58394 + 4.47551i 0.109583 + 0.189804i
\(557\) −4.37635 + 7.58006i −0.185432 + 0.321178i −0.943722 0.330740i \(-0.892702\pi\)
0.758290 + 0.651917i \(0.226035\pi\)
\(558\) 0 0
\(559\) −7.24011 −0.306224
\(560\) 6.02412 10.4341i 0.254566 0.440921i
\(561\) 0 0
\(562\) 34.1238 1.43943
\(563\) 35.9707 1.51598 0.757991 0.652265i \(-0.226181\pi\)
0.757991 + 0.652265i \(0.226181\pi\)
\(564\) 0 0
\(565\) 7.83943 + 13.5783i 0.329807 + 0.571243i
\(566\) 9.86750 17.0910i 0.414762 0.718389i
\(567\) 0 0
\(568\) −9.03798 15.6542i −0.379225 0.656837i
\(569\) 20.3125 0.851543 0.425772 0.904831i \(-0.360003\pi\)
0.425772 + 0.904831i \(0.360003\pi\)
\(570\) 0 0
\(571\) 10.1773 0.425906 0.212953 0.977062i \(-0.431692\pi\)
0.212953 + 0.977062i \(0.431692\pi\)
\(572\) 3.53714 + 6.12650i 0.147895 + 0.256162i
\(573\) 0 0
\(574\) 12.7999 22.1701i 0.534258 0.925362i
\(575\) −0.470022 0.814102i −0.0196013 0.0339504i
\(576\) 0 0
\(577\) −32.7441 −1.36316 −0.681578 0.731745i \(-0.738706\pi\)
−0.681578 + 0.731745i \(0.738706\pi\)
\(578\) 31.3083 1.30225
\(579\) 0 0
\(580\) −1.00899 + 1.74762i −0.0418960 + 0.0725660i
\(581\) 7.58228 0.314566
\(582\) 0 0
\(583\) −6.31984 + 10.9463i −0.261741 + 0.453349i
\(584\) −10.4868 18.1637i −0.433947 0.751618i
\(585\) 0 0
\(586\) −20.7913 36.0117i −0.858883 1.48763i
\(587\) 4.38663 + 7.59786i 0.181056 + 0.313597i 0.942240 0.334938i \(-0.108715\pi\)
−0.761185 + 0.648535i \(0.775382\pi\)
\(588\) 0 0
\(589\) −0.787274 + 22.9541i −0.0324390 + 0.945808i
\(590\) −17.9751 −0.740021
\(591\) 0 0
\(592\) −7.15852 12.3989i −0.294213 0.509592i
\(593\) −16.1603 + 27.9905i −0.663625 + 1.14943i 0.316031 + 0.948749i \(0.397650\pi\)
−0.979656 + 0.200684i \(0.935684\pi\)
\(594\) 0 0
\(595\) −7.28635 + 12.6203i −0.298711 + 0.517383i
\(596\) −11.0927 −0.454375
\(597\) 0 0
\(598\) 1.24789 2.16141i 0.0510301 0.0883868i
\(599\) −9.77520 + 16.9311i −0.399404 + 0.691787i −0.993652 0.112494i \(-0.964116\pi\)
0.594249 + 0.804281i \(0.297449\pi\)
\(600\) 0 0
\(601\) −0.401837 −0.0163913 −0.00819564 0.999966i \(-0.502609\pi\)
−0.00819564 + 0.999966i \(0.502609\pi\)
\(602\) 9.20008 15.9350i 0.374967 0.649462i
\(603\) 0 0
\(604\) −4.90243 + 8.49126i −0.199477 + 0.345505i
\(605\) 11.0587 + 19.1542i 0.449599 + 0.778728i
\(606\) 0 0
\(607\) 13.4453 0.545727 0.272863 0.962053i \(-0.412029\pi\)
0.272863 + 0.962053i \(0.412029\pi\)
\(608\) −15.3200 9.55976i −0.621309 0.387700i
\(609\) 0 0
\(610\) −8.76274 15.1775i −0.354793 0.614519i
\(611\) −7.14115 12.3688i −0.288900 0.500390i
\(612\) 0 0
\(613\) 10.3527 + 17.9313i 0.418140 + 0.724239i 0.995752 0.0920716i \(-0.0293489\pi\)
−0.577613 + 0.816311i \(0.696016\pi\)
\(614\) −14.0820 + 24.3907i −0.568303 + 0.984330i
\(615\) 0 0
\(616\) 28.6762 1.15540
\(617\) −4.63936 + 8.03560i −0.186773 + 0.323501i −0.944173 0.329451i \(-0.893136\pi\)
0.757399 + 0.652952i \(0.226470\pi\)
\(618\) 0 0
\(619\) −2.89129 −0.116211 −0.0581053 0.998310i \(-0.518506\pi\)
−0.0581053 + 0.998310i \(0.518506\pi\)
\(620\) 4.06097 0.163093
\(621\) 0 0
\(622\) −12.6616 21.9306i −0.507686 0.879338i
\(623\) 13.5329 23.4396i 0.542183 0.939088i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 41.4926 1.65838
\(627\) 0 0
\(628\) −2.60138 −0.103806
\(629\) 8.65844 + 14.9969i 0.345234 + 0.597964i
\(630\) 0 0
\(631\) −15.2270 + 26.3740i −0.606178 + 1.04993i 0.385686 + 0.922630i \(0.373965\pi\)
−0.991864 + 0.127301i \(0.959369\pi\)
\(632\) 7.78029 + 13.4759i 0.309483 + 0.536041i
\(633\) 0 0
\(634\) 41.9972 1.66792
\(635\) −6.11991 −0.242861
\(636\) 0 0
\(637\) −0.852959 + 1.47737i −0.0337955 + 0.0585355i
\(638\) −25.0812 −0.992975
\(639\) 0 0
\(640\) 6.63877 11.4987i 0.262420 0.454525i
\(641\) −10.0369 17.3845i −0.396434 0.686645i 0.596849 0.802354i \(-0.296419\pi\)
−0.993283 + 0.115709i \(0.963086\pi\)
\(642\) 0 0
\(643\) 1.04457 + 1.80924i 0.0411937 + 0.0713496i 0.885887 0.463901i \(-0.153551\pi\)
−0.844693 + 0.535250i \(0.820217\pi\)
\(644\) 0.882172 + 1.52797i 0.0347625 + 0.0602103i
\(645\) 0 0
\(646\) 36.8347 + 22.9850i 1.44924 + 0.904334i
\(647\) 2.10623 0.0828043 0.0414021 0.999143i \(-0.486818\pi\)
0.0414021 + 0.999143i \(0.486818\pi\)
\(648\) 0 0
\(649\) −31.0722 53.8187i −1.21969 2.11257i
\(650\) 1.32748 2.29927i 0.0520682 0.0901847i
\(651\) 0 0
\(652\) −0.118674 + 0.205549i −0.00464763 + 0.00804994i
\(653\) −1.83067 −0.0716395 −0.0358197 0.999358i \(-0.511404\pi\)
−0.0358197 + 0.999358i \(0.511404\pi\)
\(654\) 0 0
\(655\) 7.44055 12.8874i 0.290726 0.503553i
\(656\) 15.6223 27.0587i 0.609950 1.05646i
\(657\) 0 0
\(658\) 36.2973 1.41502
\(659\) 12.0268 20.8310i 0.468497 0.811460i −0.530855 0.847463i \(-0.678129\pi\)
0.999352 + 0.0360024i \(0.0114624\pi\)
\(660\) 0 0
\(661\) 8.72110 15.1054i 0.339211 0.587531i −0.645073 0.764121i \(-0.723173\pi\)
0.984285 + 0.176589i \(0.0565065\pi\)
\(662\) 16.8172 + 29.1282i 0.653617 + 1.13210i
\(663\) 0 0
\(664\) 6.37097 0.247241
\(665\) −9.36941 + 4.98929i −0.363330 + 0.193476i
\(666\) 0 0
\(667\) 1.23068 + 2.13159i 0.0476519 + 0.0825356i
\(668\) 5.49682 + 9.52077i 0.212678 + 0.368370i
\(669\) 0 0
\(670\) 0.840244 + 1.45535i 0.0324615 + 0.0562249i
\(671\) 30.2951 52.4726i 1.16953 2.02568i
\(672\) 0 0
\(673\) 47.5187 1.83171 0.915856 0.401506i \(-0.131513\pi\)
0.915856 + 0.401506i \(0.131513\pi\)
\(674\) 26.4868 45.8765i 1.02023 1.76709i
\(675\) 0 0
\(676\) −8.05850 −0.309942
\(677\) −14.5531 −0.559321 −0.279661 0.960099i \(-0.590222\pi\)
−0.279661 + 0.960099i \(0.590222\pi\)
\(678\) 0 0
\(679\) 4.94084 + 8.55778i 0.189612 + 0.328418i
\(680\) −6.12231 + 10.6042i −0.234780 + 0.406651i
\(681\) 0 0
\(682\) 25.2367 + 43.7112i 0.966363 + 1.67379i
\(683\) −3.33714 −0.127692 −0.0638460 0.997960i \(-0.520337\pi\)
−0.0638460 + 0.997960i \(0.520337\pi\)
\(684\) 0 0
\(685\) 17.3504 0.662923
\(686\) −16.3553 28.3282i −0.624448 1.08158i
\(687\) 0 0
\(688\) 11.2287 19.4487i 0.428092 0.741476i
\(689\) 1.75163 + 3.03391i 0.0667318 + 0.115583i
\(690\) 0 0
\(691\) −19.3318 −0.735415 −0.367708 0.929941i \(-0.619857\pi\)
−0.367708 + 0.929941i \(0.619857\pi\)
\(692\) −10.2868 −0.391044
\(693\) 0 0
\(694\) −2.74862 + 4.76075i −0.104336 + 0.180716i
\(695\) 6.70534 0.254348
\(696\) 0 0
\(697\) −18.8957 + 32.7283i −0.715725 + 1.23967i
\(698\) −14.8549 25.7295i −0.562268 0.973876i
\(699\) 0 0
\(700\) 0.938437 + 1.62542i 0.0354696 + 0.0614351i
\(701\) 4.96892 + 8.60643i 0.187674 + 0.325060i 0.944474 0.328586i \(-0.106572\pi\)
−0.756801 + 0.653646i \(0.773239\pi\)
\(702\) 0 0
\(703\) −0.432375 + 12.6065i −0.0163073 + 0.475464i
\(704\) 17.2584 0.650452
\(705\) 0 0
\(706\) −6.90389 11.9579i −0.259831 0.450041i
\(707\) 13.5523 23.4732i 0.509686 0.882801i
\(708\) 0 0
\(709\) −18.6059 + 32.2264i −0.698760 + 1.21029i 0.270136 + 0.962822i \(0.412931\pi\)
−0.968897 + 0.247466i \(0.920402\pi\)
\(710\) 14.7044 0.551846
\(711\) 0 0
\(712\) 11.3709 19.6950i 0.426143 0.738101i
\(713\) 2.47661 4.28961i 0.0927497 0.160647i
\(714\) 0 0
\(715\) 9.17891 0.343272
\(716\) −5.48003 + 9.49169i −0.204798 + 0.354721i
\(717\) 0 0
\(718\) 6.94966 12.0372i 0.259359 0.449223i
\(719\) −1.32109 2.28819i −0.0492683 0.0853351i 0.840340 0.542060i \(-0.182356\pi\)
−0.889608 + 0.456725i \(0.849022\pi\)
\(720\) 0 0
\(721\) −28.1980 −1.05015
\(722\) 13.8995 + 28.4083i 0.517284 + 1.05725i
\(723\) 0 0
\(724\) −3.80832 6.59621i −0.141535 0.245146i
\(725\) 1.30917 + 2.26755i 0.0486213 + 0.0842145i
\(726\) 0 0
\(727\) 5.08653 + 8.81013i 0.188649 + 0.326750i 0.944800 0.327647i \(-0.106256\pi\)
−0.756151 + 0.654397i \(0.772923\pi\)
\(728\) 3.97400 6.88317i 0.147286 0.255107i
\(729\) 0 0
\(730\) 17.0615 0.631476
\(731\) −13.5815 + 23.5238i −0.502329 + 0.870060i
\(732\) 0 0
\(733\) 14.8222 0.547472 0.273736 0.961805i \(-0.411741\pi\)
0.273736 + 0.961805i \(0.411741\pi\)
\(734\) 24.0023 0.885942
\(735\) 0 0
\(736\) 1.94720 + 3.37266i 0.0717749 + 0.124318i
\(737\) −2.90494 + 5.03151i −0.107005 + 0.185338i
\(738\) 0 0
\(739\) −17.7433 30.7323i −0.652697 1.13050i −0.982466 0.186443i \(-0.940304\pi\)
0.329769 0.944062i \(-0.393029\pi\)
\(740\) 2.23031 0.0819877
\(741\) 0 0
\(742\) −8.90325 −0.326849
\(743\) −4.36941 7.56804i −0.160298 0.277645i 0.774677 0.632357i \(-0.217912\pi\)
−0.934976 + 0.354712i \(0.884579\pi\)
\(744\) 0 0
\(745\) −7.19642 + 12.4646i −0.263656 + 0.456666i
\(746\) 20.0708 + 34.7637i 0.734846 + 1.27279i
\(747\) 0 0
\(748\) 26.5408 0.970428
\(749\) 43.6342 1.59436
\(750\) 0 0
\(751\) −6.54957 + 11.3442i −0.238997 + 0.413955i −0.960427 0.278533i \(-0.910152\pi\)
0.721430 + 0.692488i \(0.243485\pi\)
\(752\) 44.3011 1.61549
\(753\) 0 0
\(754\) −3.47580 + 6.02026i −0.126581 + 0.219245i
\(755\) 6.36093 + 11.0175i 0.231498 + 0.400966i
\(756\) 0 0
\(757\) 8.21901 + 14.2357i 0.298725 + 0.517407i 0.975845 0.218466i \(-0.0701053\pi\)
−0.677119 + 0.735873i \(0.736772\pi\)
\(758\) −13.8787 24.0386i −0.504097 0.873121i
\(759\) 0 0
\(760\) −7.87259 + 4.19222i −0.285569 + 0.152068i
\(761\) −16.3918 −0.594203 −0.297101 0.954846i \(-0.596020\pi\)
−0.297101 + 0.954846i \(0.596020\pi\)
\(762\) 0 0
\(763\) 6.84879 + 11.8625i 0.247943 + 0.429450i
\(764\) −5.00738 + 8.67304i −0.181161 + 0.313780i
\(765\) 0 0
\(766\) −9.05337 + 15.6809i −0.327112 + 0.566574i
\(767\) −17.2242 −0.621929
\(768\) 0 0
\(769\) 25.0210 43.3377i 0.902282 1.56280i 0.0777564 0.996972i \(-0.475224\pi\)
0.824525 0.565825i \(-0.191442\pi\)
\(770\) −11.6637 + 20.2022i −0.420332 + 0.728036i
\(771\) 0 0
\(772\) 11.1875 0.402649
\(773\) 24.3436 42.1644i 0.875580 1.51655i 0.0194356 0.999811i \(-0.493813\pi\)
0.856144 0.516737i \(-0.172854\pi\)
\(774\) 0 0
\(775\) 2.63457 4.56320i 0.0946364 0.163915i
\(776\) 4.15151 + 7.19063i 0.149031 + 0.258129i
\(777\) 0 0
\(778\) −60.6799 −2.17548
\(779\) −24.2977 + 12.9387i −0.870555 + 0.463577i
\(780\) 0 0
\(781\) 25.4185 + 44.0261i 0.909544 + 1.57538i
\(782\) −4.68176 8.10905i −0.167419 0.289979i
\(783\) 0 0