Properties

Label 380.2.u.a.61.3
Level $380$
Weight $2$
Character 380.61
Analytic conductor $3.034$
Analytic rank $0$
Dimension $18$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(61,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(18))
 
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("380.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.u (of order \(9\), degree \(6\), 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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 3 x^{15} + 36 x^{14} + 72 x^{13} - 134 x^{12} - 741 x^{11} + 486 x^{10} + 5700 x^{9} + \cdots + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 61.3
Root \(2.39653 + 2.01093i\) of defining polynomial
Character \(\chi\) \(=\) 380.61
Dual form 380.2.u.a.81.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.543249 + 3.08092i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(0.0481505 - 0.0833990i) q^{7} +(-6.37785 + 2.32135i) q^{9} +O(q^{10})\) \(q+(0.543249 + 3.08092i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(0.0481505 - 0.0833990i) q^{7} +(-6.37785 + 2.32135i) q^{9} +(0.190371 + 0.329733i) q^{11} +(-0.668410 + 3.79074i) q^{13} +(-2.39653 - 2.01093i) q^{15} +(2.49811 + 0.909237i) q^{17} +(-0.788719 - 4.28695i) q^{19} +(0.283103 + 0.103041i) q^{21} +(0.131397 + 0.110255i) q^{23} +(0.173648 - 0.984808i) q^{25} +(-5.92397 - 10.2606i) q^{27} +(-3.67797 + 1.33867i) q^{29} +(-1.23201 + 2.13390i) q^{31} +(-0.912460 + 0.765645i) q^{33} +(0.0167225 + 0.0948379i) q^{35} +6.92274 q^{37} -12.0421 q^{39} +(0.688068 + 3.90223i) q^{41} +(9.81139 - 8.23273i) q^{43} +(3.39358 - 5.87786i) q^{45} +(-10.5733 + 3.84836i) q^{47} +(3.49536 + 6.05415i) q^{49} +(-1.44419 + 8.19040i) q^{51} +(9.54161 + 8.00636i) q^{53} +(-0.357781 - 0.130222i) q^{55} +(12.7793 - 4.75886i) q^{57} +(5.79519 + 2.10928i) q^{59} +(-3.93179 - 3.29916i) q^{61} +(-0.113498 + 0.643680i) q^{63} +(-1.92461 - 3.33352i) q^{65} +(11.4515 - 4.16802i) q^{67} +(-0.268306 + 0.464720i) q^{69} +(1.30881 - 1.09822i) q^{71} +(0.258258 + 1.46465i) q^{73} +3.12844 q^{75} +0.0366658 q^{77} +(2.60810 + 14.7913i) q^{79} +(12.7961 - 10.7372i) q^{81} +(-5.46582 + 9.46708i) q^{83} +(-2.49811 + 0.909237i) q^{85} +(-6.12238 - 10.6043i) q^{87} +(-0.400265 + 2.27002i) q^{89} +(0.283960 + 0.238271i) q^{91} +(-7.24366 - 2.63648i) q^{93} +(3.35979 + 2.77701i) q^{95} +(1.37387 + 0.500047i) q^{97} +(-1.97958 - 1.66107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{3} - 9 q^{9} + 9 q^{13} - 3 q^{15} + 12 q^{17} + 18 q^{19} + 15 q^{21} - 9 q^{23} - 33 q^{29} - 18 q^{31} + 9 q^{33} + 12 q^{35} + 60 q^{37} - 84 q^{39} - 18 q^{41} + 18 q^{43} + 6 q^{45} - 15 q^{47} - 15 q^{49} - 9 q^{51} + 24 q^{53} + 3 q^{55} + 66 q^{57} + 48 q^{59} - 18 q^{61} - 54 q^{63} + 3 q^{65} - 36 q^{67} - 9 q^{69} + 18 q^{73} - 6 q^{75} + 9 q^{79} - 9 q^{81} - 30 q^{83} - 12 q^{85} - 9 q^{87} + 6 q^{89} + 30 q^{91} + 21 q^{95} + 21 q^{97} - 21 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(1\) \(1\)

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
\(3\) 0.543249 + 3.08092i 0.313645 + 1.77877i 0.579720 + 0.814816i \(0.303162\pi\)
−0.266075 + 0.963952i \(0.585727\pi\)
\(4\) 0 0
\(5\) −0.766044 + 0.642788i −0.342585 + 0.287463i
\(6\) 0 0
\(7\) 0.0481505 0.0833990i 0.0181992 0.0315219i −0.856782 0.515678i \(-0.827540\pi\)
0.874982 + 0.484156i \(0.160873\pi\)
\(8\) 0 0
\(9\) −6.37785 + 2.32135i −2.12595 + 0.773782i
\(10\) 0 0
\(11\) 0.190371 + 0.329733i 0.0573991 + 0.0994181i 0.893297 0.449467i \(-0.148386\pi\)
−0.835898 + 0.548885i \(0.815053\pi\)
\(12\) 0 0
\(13\) −0.668410 + 3.79074i −0.185384 + 1.05136i 0.740078 + 0.672521i \(0.234789\pi\)
−0.925461 + 0.378842i \(0.876322\pi\)
\(14\) 0 0
\(15\) −2.39653 2.01093i −0.618781 0.519219i
\(16\) 0 0
\(17\) 2.49811 + 0.909237i 0.605880 + 0.220522i 0.626700 0.779261i \(-0.284405\pi\)
−0.0208196 + 0.999783i \(0.506628\pi\)
\(18\) 0 0
\(19\) −0.788719 4.28695i −0.180945 0.983493i
\(20\) 0 0
\(21\) 0.283103 + 0.103041i 0.0617782 + 0.0224854i
\(22\) 0 0
\(23\) 0.131397 + 0.110255i 0.0273982 + 0.0229898i 0.656384 0.754427i \(-0.272085\pi\)
−0.628986 + 0.777417i \(0.716530\pi\)
\(24\) 0 0
\(25\) 0.173648 0.984808i 0.0347296 0.196962i
\(26\) 0 0
\(27\) −5.92397 10.2606i −1.14007 1.97466i
\(28\) 0 0
\(29\) −3.67797 + 1.33867i −0.682982 + 0.248585i −0.660127 0.751154i \(-0.729498\pi\)
−0.0228544 + 0.999739i \(0.507275\pi\)
\(30\) 0 0
\(31\) −1.23201 + 2.13390i −0.221275 + 0.383260i −0.955195 0.295976i \(-0.904355\pi\)
0.733920 + 0.679236i \(0.237689\pi\)
\(32\) 0 0
\(33\) −0.912460 + 0.765645i −0.158839 + 0.133282i
\(34\) 0 0
\(35\) 0.0167225 + 0.0948379i 0.00282661 + 0.0160305i
\(36\) 0 0
\(37\) 6.92274 1.13809 0.569046 0.822306i \(-0.307313\pi\)
0.569046 + 0.822306i \(0.307313\pi\)
\(38\) 0 0
\(39\) −12.0421 −1.92828
\(40\) 0 0
\(41\) 0.688068 + 3.90223i 0.107458 + 0.609426i 0.990210 + 0.139586i \(0.0445772\pi\)
−0.882752 + 0.469840i \(0.844312\pi\)
\(42\) 0 0
\(43\) 9.81139 8.23273i 1.49622 1.25548i 0.609841 0.792524i \(-0.291233\pi\)
0.886382 0.462956i \(-0.153211\pi\)
\(44\) 0 0
\(45\) 3.39358 5.87786i 0.505885 0.876219i
\(46\) 0 0
\(47\) −10.5733 + 3.84836i −1.54227 + 0.561341i −0.966589 0.256331i \(-0.917486\pi\)
−0.575684 + 0.817672i \(0.695264\pi\)
\(48\) 0 0
\(49\) 3.49536 + 6.05415i 0.499338 + 0.864878i
\(50\) 0 0
\(51\) −1.44419 + 8.19040i −0.202227 + 1.14689i
\(52\) 0 0
\(53\) 9.54161 + 8.00636i 1.31064 + 1.09976i 0.988200 + 0.153169i \(0.0489480\pi\)
0.322442 + 0.946589i \(0.395496\pi\)
\(54\) 0 0
\(55\) −0.357781 0.130222i −0.0482432 0.0175591i
\(56\) 0 0
\(57\) 12.7793 4.75886i 1.69265 0.630326i
\(58\) 0 0
\(59\) 5.79519 + 2.10928i 0.754469 + 0.274604i 0.690485 0.723346i \(-0.257397\pi\)
0.0639842 + 0.997951i \(0.479619\pi\)
\(60\) 0 0
\(61\) −3.93179 3.29916i −0.503414 0.422414i 0.355391 0.934718i \(-0.384348\pi\)
−0.858804 + 0.512304i \(0.828792\pi\)
\(62\) 0 0
\(63\) −0.113498 + 0.643680i −0.0142994 + 0.0810961i
\(64\) 0 0
\(65\) −1.92461 3.33352i −0.238719 0.413473i
\(66\) 0 0
\(67\) 11.4515 4.16802i 1.39903 0.509205i 0.471139 0.882059i \(-0.343843\pi\)
0.927890 + 0.372854i \(0.121621\pi\)
\(68\) 0 0
\(69\) −0.268306 + 0.464720i −0.0323003 + 0.0559457i
\(70\) 0 0
\(71\) 1.30881 1.09822i 0.155327 0.130335i −0.561812 0.827265i \(-0.689896\pi\)
0.717139 + 0.696930i \(0.245451\pi\)
\(72\) 0 0
\(73\) 0.258258 + 1.46465i 0.0302268 + 0.171424i 0.996184 0.0872770i \(-0.0278165\pi\)
−0.965957 + 0.258701i \(0.916705\pi\)
\(74\) 0 0
\(75\) 3.12844 0.361242
\(76\) 0 0
\(77\) 0.0366658 0.00417846
\(78\) 0 0
\(79\) 2.60810 + 14.7913i 0.293434 + 1.66415i 0.673500 + 0.739188i \(0.264790\pi\)
−0.380066 + 0.924960i \(0.624099\pi\)
\(80\) 0 0
\(81\) 12.7961 10.7372i 1.42179 1.19302i
\(82\) 0 0
\(83\) −5.46582 + 9.46708i −0.599952 + 1.03915i 0.392876 + 0.919592i \(0.371480\pi\)
−0.992828 + 0.119555i \(0.961853\pi\)
\(84\) 0 0
\(85\) −2.49811 + 0.909237i −0.270958 + 0.0986206i
\(86\) 0 0
\(87\) −6.12238 10.6043i −0.656389 1.13690i
\(88\) 0 0
\(89\) −0.400265 + 2.27002i −0.0424280 + 0.240621i −0.998645 0.0520369i \(-0.983429\pi\)
0.956217 + 0.292658i \(0.0945398\pi\)
\(90\) 0 0
\(91\) 0.283960 + 0.238271i 0.0297671 + 0.0249776i
\(92\) 0 0
\(93\) −7.24366 2.63648i −0.751132 0.273390i
\(94\) 0 0
\(95\) 3.35979 + 2.77701i 0.344707 + 0.284916i
\(96\) 0 0
\(97\) 1.37387 + 0.500047i 0.139495 + 0.0507721i 0.410824 0.911715i \(-0.365241\pi\)
−0.271329 + 0.962487i \(0.587463\pi\)
\(98\) 0 0
\(99\) −1.97958 1.66107i −0.198956 0.166944i
\(100\) 0 0
\(101\) 1.75107 9.93081i 0.174238 0.988153i −0.764782 0.644290i \(-0.777153\pi\)
0.939020 0.343863i \(-0.111736\pi\)
\(102\) 0 0
\(103\) −6.02829 10.4413i −0.593986 1.02881i −0.993689 0.112169i \(-0.964220\pi\)
0.399704 0.916644i \(-0.369113\pi\)
\(104\) 0 0
\(105\) −0.283103 + 0.103041i −0.0276280 + 0.0100558i
\(106\) 0 0
\(107\) 8.14790 14.1126i 0.787688 1.36431i −0.139693 0.990195i \(-0.544611\pi\)
0.927380 0.374120i \(-0.122055\pi\)
\(108\) 0 0
\(109\) 10.6753 8.95764i 1.02251 0.857986i 0.0325676 0.999470i \(-0.489632\pi\)
0.989941 + 0.141483i \(0.0451871\pi\)
\(110\) 0 0
\(111\) 3.76077 + 21.3284i 0.356957 + 2.02440i
\(112\) 0 0
\(113\) −12.7951 −1.20366 −0.601830 0.798624i \(-0.705562\pi\)
−0.601830 + 0.798624i \(0.705562\pi\)
\(114\) 0 0
\(115\) −0.171527 −0.0159950
\(116\) 0 0
\(117\) −4.53661 25.7284i −0.419410 2.37859i
\(118\) 0 0
\(119\) 0.196114 0.164560i 0.0179778 0.0150851i
\(120\) 0 0
\(121\) 5.42752 9.40074i 0.493411 0.854612i
\(122\) 0 0
\(123\) −11.6486 + 4.23976i −1.05032 + 0.382286i
\(124\) 0 0
\(125\) 0.500000 + 0.866025i 0.0447214 + 0.0774597i
\(126\) 0 0
\(127\) 1.89784 10.7632i 0.168406 0.955076i −0.777077 0.629405i \(-0.783299\pi\)
0.945483 0.325671i \(-0.105590\pi\)
\(128\) 0 0
\(129\) 30.6944 + 25.7556i 2.70249 + 2.26766i
\(130\) 0 0
\(131\) −11.3585 4.13416i −0.992399 0.361204i −0.205750 0.978605i \(-0.565963\pi\)
−0.786649 + 0.617401i \(0.788186\pi\)
\(132\) 0 0
\(133\) −0.395504 0.140640i −0.0342946 0.0121950i
\(134\) 0 0
\(135\) 11.1334 + 4.05223i 0.958212 + 0.348761i
\(136\) 0 0
\(137\) 15.5123 + 13.0164i 1.32530 + 1.11206i 0.985151 + 0.171692i \(0.0549235\pi\)
0.340154 + 0.940370i \(0.389521\pi\)
\(138\) 0 0
\(139\) 3.51481 19.9335i 0.298123 1.69074i −0.356110 0.934444i \(-0.615897\pi\)
0.654233 0.756293i \(-0.272992\pi\)
\(140\) 0 0
\(141\) −17.6004 30.4848i −1.48222 2.56728i
\(142\) 0 0
\(143\) −1.37718 + 0.501252i −0.115165 + 0.0419168i
\(144\) 0 0
\(145\) 1.95701 3.38963i 0.162521 0.281494i
\(146\) 0 0
\(147\) −16.7535 + 14.0578i −1.38180 + 1.15947i
\(148\) 0 0
\(149\) 1.84464 + 10.4615i 0.151119 + 0.857036i 0.962249 + 0.272171i \(0.0877416\pi\)
−0.811130 + 0.584865i \(0.801147\pi\)
\(150\) 0 0
\(151\) −13.5660 −1.10399 −0.551993 0.833849i \(-0.686132\pi\)
−0.551993 + 0.833849i \(0.686132\pi\)
\(152\) 0 0
\(153\) −18.0432 −1.45871
\(154\) 0 0
\(155\) −0.427872 2.42658i −0.0343675 0.194908i
\(156\) 0 0
\(157\) −7.93595 + 6.65905i −0.633358 + 0.531450i −0.901970 0.431798i \(-0.857879\pi\)
0.268613 + 0.963248i \(0.413435\pi\)
\(158\) 0 0
\(159\) −19.4835 + 33.7464i −1.54514 + 2.67626i
\(160\) 0 0
\(161\) 0.0155220 0.00564955i 0.00122331 0.000445247i
\(162\) 0 0
\(163\) 1.38192 + 2.39355i 0.108240 + 0.187477i 0.915057 0.403324i \(-0.132145\pi\)
−0.806817 + 0.590801i \(0.798812\pi\)
\(164\) 0 0
\(165\) 0.206838 1.17304i 0.0161023 0.0913207i
\(166\) 0 0
\(167\) −4.50618 3.78114i −0.348699 0.292593i 0.451568 0.892236i \(-0.350865\pi\)
−0.800267 + 0.599643i \(0.795309\pi\)
\(168\) 0 0
\(169\) −1.70696 0.621281i −0.131304 0.0477908i
\(170\) 0 0
\(171\) 14.9818 + 25.5106i 1.14569 + 1.95085i
\(172\) 0 0
\(173\) 7.18765 + 2.61609i 0.546467 + 0.198898i 0.600476 0.799643i \(-0.294978\pi\)
−0.0540090 + 0.998540i \(0.517200\pi\)
\(174\) 0 0
\(175\) −0.0737708 0.0619010i −0.00557655 0.00467928i
\(176\) 0 0
\(177\) −3.35028 + 19.0004i −0.251822 + 1.42815i
\(178\) 0 0
\(179\) 0.180527 + 0.312681i 0.0134932 + 0.0233709i 0.872693 0.488269i \(-0.162372\pi\)
−0.859200 + 0.511640i \(0.829038\pi\)
\(180\) 0 0
\(181\) −19.5568 + 7.11810i −1.45365 + 0.529084i −0.943607 0.331067i \(-0.892591\pi\)
−0.510039 + 0.860151i \(0.670369\pi\)
\(182\) 0 0
\(183\) 8.02850 13.9058i 0.593484 1.02794i
\(184\) 0 0
\(185\) −5.30313 + 4.44985i −0.389894 + 0.327160i
\(186\) 0 0
\(187\) 0.175763 + 0.996800i 0.0128530 + 0.0728932i
\(188\) 0 0
\(189\) −1.14097 −0.0829932
\(190\) 0 0
\(191\) −22.1534 −1.60296 −0.801481 0.598020i \(-0.795954\pi\)
−0.801481 + 0.598020i \(0.795954\pi\)
\(192\) 0 0
\(193\) −1.32392 7.50831i −0.0952977 0.540460i −0.994656 0.103247i \(-0.967077\pi\)
0.899358 0.437213i \(-0.144034\pi\)
\(194\) 0 0
\(195\) 9.22477 7.74050i 0.660599 0.554308i
\(196\) 0 0
\(197\) 1.99852 3.46154i 0.142389 0.246625i −0.786007 0.618218i \(-0.787855\pi\)
0.928396 + 0.371593i \(0.121188\pi\)
\(198\) 0 0
\(199\) 11.7475 4.27573i 0.832756 0.303099i 0.109767 0.993957i \(-0.464990\pi\)
0.722990 + 0.690859i \(0.242767\pi\)
\(200\) 0 0
\(201\) 19.0624 + 33.0170i 1.34455 + 2.32884i
\(202\) 0 0
\(203\) −0.0654520 + 0.371197i −0.00459383 + 0.0260529i
\(204\) 0 0
\(205\) −3.03539 2.54700i −0.212001 0.177890i
\(206\) 0 0
\(207\) −1.09397 0.398173i −0.0760363 0.0276750i
\(208\) 0 0
\(209\) 1.26340 1.07618i 0.0873910 0.0744408i
\(210\) 0 0
\(211\) 18.7594 + 6.82787i 1.29145 + 0.470050i 0.894203 0.447661i \(-0.147743\pi\)
0.397248 + 0.917711i \(0.369965\pi\)
\(212\) 0 0
\(213\) 4.09454 + 3.43573i 0.280553 + 0.235412i
\(214\) 0 0
\(215\) −2.22406 + 12.6133i −0.151680 + 0.860218i
\(216\) 0 0
\(217\) 0.118643 + 0.205497i 0.00805404 + 0.0139500i
\(218\) 0 0
\(219\) −4.37217 + 1.59134i −0.295444 + 0.107533i
\(220\) 0 0
\(221\) −5.11644 + 8.86194i −0.344169 + 0.596118i
\(222\) 0 0
\(223\) 12.3057 10.3257i 0.824052 0.691462i −0.129865 0.991532i \(-0.541455\pi\)
0.953917 + 0.300070i \(0.0970101\pi\)
\(224\) 0 0
\(225\) 1.17858 + 6.68405i 0.0785719 + 0.445604i
\(226\) 0 0
\(227\) 14.8532 0.985840 0.492920 0.870075i \(-0.335929\pi\)
0.492920 + 0.870075i \(0.335929\pi\)
\(228\) 0 0
\(229\) −9.64786 −0.637548 −0.318774 0.947831i \(-0.603271\pi\)
−0.318774 + 0.947831i \(0.603271\pi\)
\(230\) 0 0
\(231\) 0.0199187 + 0.112964i 0.00131055 + 0.00743251i
\(232\) 0 0
\(233\) −12.7259 + 10.6783i −0.833701 + 0.699558i −0.956138 0.292918i \(-0.905374\pi\)
0.122437 + 0.992476i \(0.460929\pi\)
\(234\) 0 0
\(235\) 5.62593 9.74440i 0.366995 0.635654i
\(236\) 0 0
\(237\) −44.1538 + 16.0707i −2.86810 + 1.04390i
\(238\) 0 0
\(239\) −4.04101 6.99924i −0.261391 0.452743i 0.705221 0.708988i \(-0.250848\pi\)
−0.966612 + 0.256245i \(0.917515\pi\)
\(240\) 0 0
\(241\) 1.91566 10.8643i 0.123399 0.699828i −0.858847 0.512231i \(-0.828819\pi\)
0.982246 0.187597i \(-0.0600699\pi\)
\(242\) 0 0
\(243\) 12.8038 + 10.7436i 0.821361 + 0.689204i
\(244\) 0 0
\(245\) −6.56913 2.39097i −0.419687 0.152753i
\(246\) 0 0
\(247\) 16.7779 0.124393i 1.06755 0.00791493i
\(248\) 0 0
\(249\) −32.1366 11.6968i −2.03657 0.741252i
\(250\) 0 0
\(251\) −21.4319 17.9835i −1.35277 1.13511i −0.978144 0.207930i \(-0.933327\pi\)
−0.374624 0.927177i \(-0.622228\pi\)
\(252\) 0 0
\(253\) −0.0113405 + 0.0643154i −0.000712974 + 0.00404347i
\(254\) 0 0
\(255\) −4.15838 7.20252i −0.260408 0.451039i
\(256\) 0 0
\(257\) 5.77465 2.10180i 0.360213 0.131107i −0.155573 0.987824i \(-0.549722\pi\)
0.515786 + 0.856718i \(0.327500\pi\)
\(258\) 0 0
\(259\) 0.333333 0.577350i 0.0207123 0.0358748i
\(260\) 0 0
\(261\) 20.3500 17.0757i 1.25963 1.05696i
\(262\) 0 0
\(263\) −3.32800 18.8740i −0.205213 1.16382i −0.897104 0.441820i \(-0.854333\pi\)
0.691890 0.722003i \(-0.256778\pi\)
\(264\) 0 0
\(265\) −12.4557 −0.765147
\(266\) 0 0
\(267\) −7.21117 −0.441316
\(268\) 0 0
\(269\) −3.13375 17.7724i −0.191068 1.08360i −0.917908 0.396794i \(-0.870123\pi\)
0.726839 0.686808i \(-0.240988\pi\)
\(270\) 0 0
\(271\) 2.77161 2.32565i 0.168363 0.141273i −0.554713 0.832042i \(-0.687172\pi\)
0.723076 + 0.690768i \(0.242728\pi\)
\(272\) 0 0
\(273\) −0.579831 + 1.00430i −0.0350930 + 0.0607828i
\(274\) 0 0
\(275\) 0.357781 0.130222i 0.0215750 0.00785266i
\(276\) 0 0
\(277\) 2.71265 + 4.69844i 0.162987 + 0.282302i 0.935939 0.352163i \(-0.114554\pi\)
−0.772952 + 0.634465i \(0.781220\pi\)
\(278\) 0 0
\(279\) 2.90404 16.4696i 0.173860 0.986010i
\(280\) 0 0
\(281\) −13.8745 11.6421i −0.827682 0.694507i 0.127076 0.991893i \(-0.459441\pi\)
−0.954757 + 0.297386i \(0.903885\pi\)
\(282\) 0 0
\(283\) 0.741940 + 0.270044i 0.0441037 + 0.0160524i 0.363978 0.931408i \(-0.381418\pi\)
−0.319874 + 0.947460i \(0.603641\pi\)
\(284\) 0 0
\(285\) −6.73054 + 11.8598i −0.398683 + 0.702517i
\(286\) 0 0
\(287\) 0.358573 + 0.130510i 0.0211659 + 0.00770375i
\(288\) 0 0
\(289\) −7.60893 6.38465i −0.447584 0.375568i
\(290\) 0 0
\(291\) −0.794252 + 4.50443i −0.0465599 + 0.264054i
\(292\) 0 0
\(293\) 11.9210 + 20.6478i 0.696433 + 1.20626i 0.969695 + 0.244318i \(0.0785640\pi\)
−0.273262 + 0.961940i \(0.588103\pi\)
\(294\) 0 0
\(295\) −5.79519 + 2.10928i −0.337409 + 0.122807i
\(296\) 0 0
\(297\) 2.25551 3.90665i 0.130878 0.226687i
\(298\) 0 0
\(299\) −0.505777 + 0.424397i −0.0292498 + 0.0245435i
\(300\) 0 0
\(301\) −0.214179 1.21467i −0.0123451 0.0700124i
\(302\) 0 0
\(303\) 31.5473 1.81234
\(304\) 0 0
\(305\) 5.13258 0.293891
\(306\) 0 0
\(307\) −1.00580 5.70416i −0.0574039 0.325554i 0.942560 0.334036i \(-0.108411\pi\)
−0.999964 + 0.00848295i \(0.997300\pi\)
\(308\) 0 0
\(309\) 28.8939 24.2449i 1.64372 1.37924i
\(310\) 0 0
\(311\) 7.43736 12.8819i 0.421734 0.730464i −0.574375 0.818592i \(-0.694755\pi\)
0.996109 + 0.0881277i \(0.0280884\pi\)
\(312\) 0 0
\(313\) −1.57814 + 0.574396i −0.0892017 + 0.0324668i −0.386236 0.922400i \(-0.626225\pi\)
0.297034 + 0.954867i \(0.404003\pi\)
\(314\) 0 0
\(315\) −0.326805 0.566043i −0.0184134 0.0318929i
\(316\) 0 0
\(317\) 1.85471 10.5186i 0.104171 0.590781i −0.887378 0.461043i \(-0.847475\pi\)
0.991548 0.129738i \(-0.0414136\pi\)
\(318\) 0 0
\(319\) −1.14158 0.957902i −0.0639164 0.0536322i
\(320\) 0 0
\(321\) 47.9060 + 17.4364i 2.67385 + 0.973203i
\(322\) 0 0
\(323\) 1.92754 11.4264i 0.107251 0.635781i
\(324\) 0 0
\(325\) 3.61708 + 1.31651i 0.200640 + 0.0730269i
\(326\) 0 0
\(327\) 33.3971 + 28.0235i 1.84686 + 1.54970i
\(328\) 0 0
\(329\) −0.188159 + 1.06710i −0.0103735 + 0.0588313i
\(330\) 0 0
\(331\) −8.30178 14.3791i −0.456307 0.790347i 0.542455 0.840085i \(-0.317495\pi\)
−0.998762 + 0.0497378i \(0.984161\pi\)
\(332\) 0 0
\(333\) −44.1522 + 16.0701i −2.41953 + 0.880635i
\(334\) 0 0
\(335\) −6.09324 + 10.5538i −0.332909 + 0.576616i
\(336\) 0 0
\(337\) −3.48289 + 2.92249i −0.189725 + 0.159198i −0.732703 0.680549i \(-0.761741\pi\)
0.542978 + 0.839747i \(0.317297\pi\)
\(338\) 0 0
\(339\) −6.95092 39.4206i −0.377522 2.14103i
\(340\) 0 0
\(341\) −0.938156 −0.0508040
\(342\) 0 0
\(343\) 1.34732 0.0727484
\(344\) 0 0
\(345\) −0.0931817 0.528460i −0.00501674 0.0284513i
\(346\) 0 0
\(347\) −13.3065 + 11.1655i −0.714332 + 0.599396i −0.925811 0.377986i \(-0.876617\pi\)
0.211479 + 0.977383i \(0.432172\pi\)
\(348\) 0 0
\(349\) −6.05950 + 10.4954i −0.324358 + 0.561804i −0.981382 0.192065i \(-0.938482\pi\)
0.657024 + 0.753869i \(0.271815\pi\)
\(350\) 0 0
\(351\) 42.8550 15.5979i 2.28743 0.832557i
\(352\) 0 0
\(353\) 16.3694 + 28.3526i 0.871255 + 1.50906i 0.860700 + 0.509113i \(0.170027\pi\)
0.0105551 + 0.999944i \(0.496640\pi\)
\(354\) 0 0
\(355\) −0.296683 + 1.68257i −0.0157463 + 0.0893017i
\(356\) 0 0
\(357\) 0.613533 + 0.514815i 0.0324716 + 0.0272469i
\(358\) 0 0
\(359\) 4.48402 + 1.63205i 0.236658 + 0.0861364i 0.457627 0.889145i \(-0.348700\pi\)
−0.220969 + 0.975281i \(0.570922\pi\)
\(360\) 0 0
\(361\) −17.7558 + 6.76240i −0.934518 + 0.355916i
\(362\) 0 0
\(363\) 31.9114 + 11.6148i 1.67491 + 0.609618i
\(364\) 0 0
\(365\) −1.13930 0.955983i −0.0596335 0.0500385i
\(366\) 0 0
\(367\) 1.53048 8.67977i 0.0798903 0.453080i −0.918452 0.395532i \(-0.870560\pi\)
0.998343 0.0575488i \(-0.0183285\pi\)
\(368\) 0 0
\(369\) −13.4468 23.2906i −0.700014 1.21246i
\(370\) 0 0
\(371\) 1.12716 0.410251i 0.0585190 0.0212992i
\(372\) 0 0
\(373\) 11.0167 19.0814i 0.570422 0.987999i −0.426101 0.904676i \(-0.640113\pi\)
0.996523 0.0833236i \(-0.0265535\pi\)
\(374\) 0 0
\(375\) −2.39653 + 2.01093i −0.123756 + 0.103844i
\(376\) 0 0
\(377\) −2.61617 14.8370i −0.134739 0.764145i
\(378\) 0 0
\(379\) 18.1470 0.932150 0.466075 0.884745i \(-0.345668\pi\)
0.466075 + 0.884745i \(0.345668\pi\)
\(380\) 0 0
\(381\) 34.1914 1.75168
\(382\) 0 0
\(383\) 5.44319 + 30.8699i 0.278134 + 1.57738i 0.728828 + 0.684697i \(0.240066\pi\)
−0.450694 + 0.892679i \(0.648823\pi\)
\(384\) 0 0
\(385\) −0.0280877 + 0.0235684i −0.00143148 + 0.00120115i
\(386\) 0 0
\(387\) −43.4645 + 75.2827i −2.20943 + 3.82684i
\(388\) 0 0
\(389\) −23.5340 + 8.56568i −1.19322 + 0.434297i −0.860854 0.508852i \(-0.830070\pi\)
−0.332368 + 0.943150i \(0.607848\pi\)
\(390\) 0 0
\(391\) 0.227996 + 0.394901i 0.0115303 + 0.0199710i
\(392\) 0 0
\(393\) 6.56651 37.2405i 0.331237 1.87854i
\(394\) 0 0
\(395\) −11.5056 9.65431i −0.578908 0.485761i
\(396\) 0 0
\(397\) 23.3194 + 8.48755i 1.17037 + 0.425978i 0.852789 0.522255i \(-0.174909\pi\)
0.317576 + 0.948233i \(0.397131\pi\)
\(398\) 0 0
\(399\) 0.218443 1.29492i 0.0109358 0.0648270i
\(400\) 0 0
\(401\) 4.53343 + 1.65003i 0.226389 + 0.0823988i 0.452724 0.891651i \(-0.350452\pi\)
−0.226335 + 0.974049i \(0.572675\pi\)
\(402\) 0 0
\(403\) −7.26558 6.09655i −0.361924 0.303691i
\(404\) 0 0
\(405\) −2.90064 + 16.4504i −0.144134 + 0.817424i
\(406\) 0 0
\(407\) 1.31789 + 2.28265i 0.0653254 + 0.113147i
\(408\) 0 0
\(409\) −11.7988 + 4.29440i −0.583411 + 0.212344i −0.616829 0.787097i \(-0.711583\pi\)
0.0334179 + 0.999441i \(0.489361\pi\)
\(410\) 0 0
\(411\) −31.6753 + 54.8632i −1.56243 + 2.70620i
\(412\) 0 0
\(413\) 0.454953 0.381751i 0.0223868 0.0187847i
\(414\) 0 0
\(415\) −1.89826 10.7656i −0.0931819 0.528461i
\(416\) 0 0
\(417\) 63.3229 3.10093
\(418\) 0 0
\(419\) 20.7543 1.01391 0.506957 0.861971i \(-0.330770\pi\)
0.506957 + 0.861971i \(0.330770\pi\)
\(420\) 0 0
\(421\) 5.81159 + 32.9592i 0.283240 + 1.60633i 0.711507 + 0.702679i \(0.248013\pi\)
−0.428267 + 0.903652i \(0.640876\pi\)
\(422\) 0 0
\(423\) 58.5015 49.0886i 2.84444 2.38677i
\(424\) 0 0
\(425\) 1.32922 2.30227i 0.0644764 0.111676i
\(426\) 0 0
\(427\) −0.464464 + 0.169051i −0.0224770 + 0.00818095i
\(428\) 0 0
\(429\) −2.29247 3.97067i −0.110681 0.191706i
\(430\) 0 0
\(431\) 4.47549 25.3817i 0.215577 1.22260i −0.664327 0.747442i \(-0.731282\pi\)
0.879903 0.475153i \(-0.157607\pi\)
\(432\) 0 0
\(433\) −8.54685 7.17166i −0.410735 0.344648i 0.413890 0.910327i \(-0.364170\pi\)
−0.824626 + 0.565679i \(0.808614\pi\)
\(434\) 0 0
\(435\) 11.5063 + 4.18796i 0.551686 + 0.200797i
\(436\) 0 0
\(437\) 0.369023 0.650253i 0.0176528 0.0311058i
\(438\) 0 0
\(439\) −1.18318 0.430641i −0.0564699 0.0205534i 0.313631 0.949545i \(-0.398455\pi\)
−0.370101 + 0.928992i \(0.620677\pi\)
\(440\) 0 0
\(441\) −36.3467 30.4985i −1.73079 1.45231i
\(442\) 0 0
\(443\) −1.51072 + 8.56770i −0.0717764 + 0.407064i 0.927658 + 0.373431i \(0.121819\pi\)
−0.999434 + 0.0336328i \(0.989292\pi\)
\(444\) 0 0
\(445\) −1.15252 1.99622i −0.0546345 0.0946298i
\(446\) 0 0
\(447\) −31.2288 + 11.3663i −1.47707 + 0.537610i
\(448\) 0 0
\(449\) 17.5925 30.4710i 0.830240 1.43802i −0.0676084 0.997712i \(-0.521537\pi\)
0.897848 0.440305i \(-0.145130\pi\)
\(450\) 0 0
\(451\) −1.15570 + 0.969751i −0.0544200 + 0.0456638i
\(452\) 0 0
\(453\) −7.36971 41.7957i −0.346259 1.96373i
\(454\) 0 0
\(455\) −0.370683 −0.0173779
\(456\) 0 0
\(457\) −1.11871 −0.0523311 −0.0261655 0.999658i \(-0.508330\pi\)
−0.0261655 + 0.999658i \(0.508330\pi\)
\(458\) 0 0
\(459\) −5.46938 31.0184i −0.255289 1.44782i
\(460\) 0 0
\(461\) −1.43612 + 1.20504i −0.0668866 + 0.0561245i −0.675618 0.737252i \(-0.736123\pi\)
0.608731 + 0.793376i \(0.291679\pi\)
\(462\) 0 0
\(463\) −0.683989 + 1.18470i −0.0317877 + 0.0550578i −0.881482 0.472218i \(-0.843453\pi\)
0.849694 + 0.527276i \(0.176787\pi\)
\(464\) 0 0
\(465\) 7.24366 2.63648i 0.335916 0.122264i
\(466\) 0 0
\(467\) 6.20452 + 10.7465i 0.287111 + 0.497290i 0.973119 0.230303i \(-0.0739719\pi\)
−0.686008 + 0.727594i \(0.740639\pi\)
\(468\) 0 0
\(469\) 0.203788 1.15574i 0.00941006 0.0533671i
\(470\) 0 0
\(471\) −24.8272 20.8325i −1.14398 0.959910i
\(472\) 0 0
\(473\) 4.58241 + 1.66786i 0.210699 + 0.0766883i
\(474\) 0 0
\(475\) −4.35878 + 0.0323164i −0.199995 + 0.00148278i
\(476\) 0 0
\(477\) −79.4405 28.9140i −3.63733 1.32388i
\(478\) 0 0
\(479\) 24.6697 + 20.7003i 1.12719 + 0.945823i 0.998945 0.0459199i \(-0.0146219\pi\)
0.128243 + 0.991743i \(0.459066\pi\)
\(480\) 0 0
\(481\) −4.62723 + 26.2423i −0.210984 + 1.19655i
\(482\) 0 0
\(483\) 0.0258381 + 0.0447529i 0.00117568 + 0.00203633i
\(484\) 0 0
\(485\) −1.37387 + 0.500047i −0.0623842 + 0.0227060i
\(486\) 0 0
\(487\) −14.6132 + 25.3108i −0.662186 + 1.14694i 0.317854 + 0.948140i \(0.397038\pi\)
−0.980040 + 0.198800i \(0.936295\pi\)
\(488\) 0 0
\(489\) −6.62360 + 5.55786i −0.299529 + 0.251335i
\(490\) 0 0
\(491\) 0.782012 + 4.43501i 0.0352917 + 0.200149i 0.997356 0.0726747i \(-0.0231535\pi\)
−0.962064 + 0.272824i \(0.912042\pi\)
\(492\) 0 0
\(493\) −10.4051 −0.468623
\(494\) 0 0
\(495\) 2.58416 0.116149
\(496\) 0 0
\(497\) −0.0285708 0.162033i −0.00128158 0.00726819i
\(498\) 0 0
\(499\) −7.44052 + 6.24334i −0.333083 + 0.279490i −0.793955 0.607977i \(-0.791981\pi\)
0.460871 + 0.887467i \(0.347537\pi\)
\(500\) 0 0
\(501\) 9.20139 15.9373i 0.411088 0.712025i
\(502\) 0 0
\(503\) −2.63383 + 0.958636i −0.117437 + 0.0427435i −0.400070 0.916485i \(-0.631014\pi\)
0.282633 + 0.959228i \(0.408792\pi\)
\(504\) 0 0
\(505\) 5.04201 + 8.73301i 0.224366 + 0.388614i
\(506\) 0 0
\(507\) 0.986813 5.59650i 0.0438259 0.248549i
\(508\) 0 0
\(509\) −19.6233 16.4659i −0.869788 0.729838i 0.0942658 0.995547i \(-0.469950\pi\)
−0.964053 + 0.265709i \(0.914394\pi\)
\(510\) 0 0
\(511\) 0.134586 + 0.0489852i 0.00595372 + 0.00216698i
\(512\) 0 0
\(513\) −39.3144 + 33.4885i −1.73577 + 1.47855i
\(514\) 0 0
\(515\) 11.3295 + 4.12360i 0.499237 + 0.181707i
\(516\) 0 0
\(517\) −3.28178 2.75374i −0.144333 0.121109i
\(518\) 0 0
\(519\) −4.15528 + 23.5657i −0.182396 + 1.03442i
\(520\) 0 0
\(521\) −10.3772 17.9738i −0.454632 0.787445i 0.544035 0.839062i \(-0.316896\pi\)
−0.998667 + 0.0516173i \(0.983562\pi\)
\(522\) 0 0
\(523\) 3.77430 1.37373i 0.165039 0.0600692i −0.258180 0.966097i \(-0.583123\pi\)
0.423218 + 0.906028i \(0.360900\pi\)
\(524\) 0 0
\(525\) 0.150636 0.260909i 0.00657429 0.0113870i
\(526\) 0 0
\(527\) −5.01791 + 4.21052i −0.218584 + 0.183413i
\(528\) 0 0
\(529\) −3.98880 22.6216i −0.173426 0.983548i
\(530\) 0 0
\(531\) −41.8572 −1.81645
\(532\) 0 0
\(533\) −15.2523 −0.660648
\(534\) 0 0
\(535\) 2.82974 + 16.0482i 0.122340 + 0.693826i
\(536\) 0 0
\(537\) −0.865274 + 0.726051i −0.0373393 + 0.0313314i
\(538\) 0 0
\(539\) −1.33083 + 2.30507i −0.0573231 + 0.0992864i
\(540\) 0 0
\(541\) 19.5001 7.09746i 0.838376 0.305144i 0.113084 0.993585i \(-0.463927\pi\)
0.725292 + 0.688442i \(0.241705\pi\)
\(542\) 0 0
\(543\) −32.5545 56.3860i −1.39705 2.41975i
\(544\) 0 0
\(545\) −2.41989 + 13.7239i −0.103657 + 0.587867i
\(546\) 0 0
\(547\) 15.0644 + 12.6405i 0.644105 + 0.540469i 0.905276 0.424824i \(-0.139664\pi\)
−0.261170 + 0.965293i \(0.584108\pi\)
\(548\) 0 0
\(549\) 32.7348 + 11.9145i 1.39709 + 0.508499i
\(550\) 0 0
\(551\) 8.63970 + 14.7114i 0.368063 + 0.626728i
\(552\) 0 0
\(553\) 1.35916 + 0.494693i 0.0577973 + 0.0210365i
\(554\) 0 0
\(555\) −16.5905 13.9211i −0.704229 0.590918i
\(556\) 0 0
\(557\) 3.86522 21.9207i 0.163775 0.928812i −0.786544 0.617534i \(-0.788132\pi\)
0.950319 0.311278i \(-0.100757\pi\)
\(558\) 0 0
\(559\) 24.6501 + 42.6953i 1.04259 + 1.80582i
\(560\) 0 0
\(561\) −2.97558 + 1.08302i −0.125629 + 0.0457252i
\(562\) 0 0
\(563\) −12.3888 + 21.4580i −0.522125 + 0.904348i 0.477543 + 0.878608i \(0.341527\pi\)
−0.999669 + 0.0257394i \(0.991806\pi\)
\(564\) 0 0
\(565\) 9.80161 8.22452i 0.412357 0.346008i
\(566\) 0 0
\(567\) −0.279334 1.58418i −0.0117309 0.0665295i
\(568\) 0 0
\(569\) 41.6154 1.74461 0.872304 0.488963i \(-0.162625\pi\)
0.872304 + 0.488963i \(0.162625\pi\)
\(570\) 0 0
\(571\) −12.1626 −0.508991 −0.254496 0.967074i \(-0.581909\pi\)
−0.254496 + 0.967074i \(0.581909\pi\)
\(572\) 0 0
\(573\) −12.0348 68.2527i −0.502761 2.85130i
\(574\) 0 0
\(575\) 0.131397 0.110255i 0.00547964 0.00459796i
\(576\) 0 0
\(577\) −19.5319 + 33.8302i −0.813122 + 1.40837i 0.0975473 + 0.995231i \(0.468900\pi\)
−0.910669 + 0.413137i \(0.864433\pi\)
\(578\) 0 0
\(579\) 22.4133 8.15776i 0.931463 0.339025i
\(580\) 0 0
\(581\) 0.526363 + 0.911688i 0.0218372 + 0.0378232i
\(582\) 0 0
\(583\) −0.823511 + 4.67036i −0.0341063 + 0.193427i
\(584\) 0 0
\(585\) 20.0131 + 16.7930i 0.827442 + 0.694306i
\(586\) 0 0
\(587\) −5.69284 2.07203i −0.234969 0.0855216i 0.221852 0.975080i \(-0.428790\pi\)
−0.456821 + 0.889559i \(0.651012\pi\)
\(588\) 0 0
\(589\) 10.1196 + 3.59851i 0.416972 + 0.148274i
\(590\) 0 0
\(591\) 11.7504 + 4.27680i 0.483348 + 0.175924i
\(592\) 0 0
\(593\) 22.5998 + 18.9635i 0.928062 + 0.778736i 0.975468 0.220139i \(-0.0706513\pi\)
−0.0474068 + 0.998876i \(0.515096\pi\)
\(594\) 0 0
\(595\) −0.0444555 + 0.252120i −0.00182250 + 0.0103359i
\(596\) 0 0
\(597\) 19.5550 + 33.8702i 0.800332 + 1.38622i
\(598\) 0 0
\(599\) −22.8429 + 8.31415i −0.933337 + 0.339707i −0.763531 0.645771i \(-0.776536\pi\)
−0.169805 + 0.985478i \(0.554314\pi\)
\(600\) 0 0
\(601\) −14.5601 + 25.2188i −0.593917 + 1.02869i 0.399781 + 0.916610i \(0.369086\pi\)
−0.993699 + 0.112084i \(0.964247\pi\)
\(602\) 0 0
\(603\) −63.3608 + 53.1660i −2.58025 + 2.16509i
\(604\) 0 0
\(605\) 1.88496 + 10.6901i 0.0766344 + 0.434615i
\(606\) 0 0
\(607\) 16.5543 0.671920 0.335960 0.941876i \(-0.390939\pi\)
0.335960 + 0.941876i \(0.390939\pi\)
\(608\) 0 0
\(609\) −1.17918 −0.0477829
\(610\) 0 0
\(611\) −7.52086 42.6529i −0.304261 1.72555i
\(612\) 0 0
\(613\) −25.2751 + 21.2083i −1.02085 + 0.856596i −0.989734 0.142920i \(-0.954351\pi\)
−0.0311169 + 0.999516i \(0.509906\pi\)
\(614\) 0 0
\(615\) 6.19812 10.7355i 0.249932 0.432895i
\(616\) 0 0
\(617\) 30.4129 11.0694i 1.22438 0.445637i 0.352708 0.935733i \(-0.385261\pi\)
0.871668 + 0.490097i \(0.163039\pi\)
\(618\) 0 0
\(619\) 20.8433 + 36.1016i 0.837762 + 1.45105i 0.891762 + 0.452505i \(0.149470\pi\)
−0.0539997 + 0.998541i \(0.517197\pi\)
\(620\) 0 0
\(621\) 0.352895 2.00137i 0.0141612 0.0803120i
\(622\) 0 0
\(623\) 0.170044 + 0.142684i 0.00681267 + 0.00571651i
\(624\) 0 0
\(625\) −0.939693 0.342020i −0.0375877 0.0136808i
\(626\) 0 0
\(627\) 4.00195 + 3.30779i 0.159823 + 0.132100i
\(628\) 0 0
\(629\) 17.2937 + 6.29441i 0.689547 + 0.250975i
\(630\) 0 0
\(631\) −4.22290 3.54344i −0.168111 0.141062i 0.554851 0.831950i \(-0.312775\pi\)
−0.722962 + 0.690888i \(0.757220\pi\)
\(632\) 0 0
\(633\) −10.8451 + 61.5054i −0.431053 + 2.44462i
\(634\) 0 0
\(635\) 5.46460 + 9.46497i 0.216856 + 0.375606i
\(636\) 0 0
\(637\) −25.2860 + 9.20337i −1.00187 + 0.364651i
\(638\) 0 0
\(639\) −5.79804 + 10.0425i −0.229367 + 0.397275i
\(640\) 0 0
\(641\) 25.7780 21.6303i 1.01817 0.854346i 0.0287732 0.999586i \(-0.490840\pi\)
0.989396 + 0.145240i \(0.0463955\pi\)
\(642\) 0 0
\(643\) −3.98328 22.5903i −0.157085 0.890874i −0.956855 0.290567i \(-0.906156\pi\)
0.799769 0.600307i \(-0.204955\pi\)
\(644\) 0 0
\(645\) −40.0687 −1.57770
\(646\) 0 0
\(647\) −21.5785 −0.848338 −0.424169 0.905583i \(-0.639434\pi\)
−0.424169 + 0.905583i \(0.639434\pi\)
\(648\) 0 0
\(649\) 0.407740 + 2.31241i 0.0160052 + 0.0907700i
\(650\) 0 0
\(651\) −0.568665 + 0.477166i −0.0222877 + 0.0187016i
\(652\) 0 0
\(653\) −2.26943 + 3.93077i −0.0888097 + 0.153823i −0.907008 0.421113i \(-0.861640\pi\)
0.818199 + 0.574936i \(0.194973\pi\)
\(654\) 0 0
\(655\) 11.3585 4.13416i 0.443814 0.161535i
\(656\) 0 0
\(657\) −5.04709 8.74182i −0.196906 0.341051i
\(658\) 0 0
\(659\) 4.81363 27.2994i 0.187512 1.06343i −0.735173 0.677880i \(-0.762899\pi\)
0.922685 0.385555i \(-0.125990\pi\)
\(660\) 0 0
\(661\) −9.11550 7.64881i −0.354552 0.297504i 0.448063 0.894002i \(-0.352114\pi\)
−0.802615 + 0.596498i \(0.796558\pi\)
\(662\) 0 0
\(663\) −30.0824 10.9491i −1.16830 0.425228i
\(664\) 0 0
\(665\) 0.393376 0.146489i 0.0152545 0.00568059i
\(666\) 0 0
\(667\) −0.630870 0.229618i −0.0244274 0.00889084i
\(668\) 0 0
\(669\) 38.4978 + 32.3035i 1.48841 + 1.24892i
\(670\) 0 0
\(671\) 0.339342 1.92450i 0.0131001 0.0742946i
\(672\) 0 0
\(673\) 12.4259 + 21.5222i 0.478982 + 0.829621i 0.999710 0.0241016i \(-0.00767253\pi\)
−0.520727 + 0.853723i \(0.674339\pi\)
\(674\) 0 0
\(675\) −11.1334 + 4.05223i −0.428526 + 0.155971i
\(676\) 0 0
\(677\) 17.1730 29.7445i 0.660012 1.14317i −0.320600 0.947215i \(-0.603885\pi\)
0.980612 0.195959i \(-0.0627820\pi\)
\(678\) 0 0
\(679\) 0.107856 0.0905018i 0.00413913 0.00347314i
\(680\) 0 0
\(681\) 8.06897 + 45.7614i 0.309204 + 1.75358i
\(682\) 0 0
\(683\) −3.79403 −0.145175 −0.0725873 0.997362i \(-0.523126\pi\)
−0.0725873 + 0.997362i \(0.523126\pi\)
\(684\) 0 0
\(685\) −20.2499 −0.773707
\(686\) 0 0
\(687\) −5.24119 29.7242i −0.199964 1.13405i
\(688\) 0 0
\(689\) −36.7278 + 30.8183i −1.39922 + 1.17408i
\(690\) 0 0
\(691\) −9.26742 + 16.0516i −0.352549 + 0.610633i −0.986695 0.162580i \(-0.948018\pi\)
0.634146 + 0.773213i \(0.281352\pi\)
\(692\) 0 0
\(693\) −0.233849 + 0.0851142i −0.00888320 + 0.00323322i
\(694\) 0 0
\(695\) 10.1205 + 17.5292i 0.383892 + 0.664921i
\(696\) 0 0
\(697\) −1.82918 + 10.3738i −0.0692852 + 0.392936i
\(698\) 0 0
\(699\) −39.8123 33.4064i −1.50584 1.26355i
\(700\) 0 0
\(701\) 44.4694 + 16.1855i 1.67958 + 0.611319i 0.993253 0.115970i \(-0.0369975\pi\)
0.686332 + 0.727288i \(0.259220\pi\)
\(702\) 0 0
\(703\) −5.46010 29.6774i −0.205932 1.11931i
\(704\) 0 0
\(705\) 33.0780 + 12.0394i 1.24579 + 0.453430i
\(706\) 0 0
\(707\) −0.743905 0.624211i −0.0279774 0.0234759i
\(708\) 0 0
\(709\) 3.80759 21.5939i 0.142997 0.810977i −0.825956 0.563734i \(-0.809364\pi\)
0.968953 0.247243i \(-0.0795246\pi\)
\(710\) 0 0
\(711\) −50.9697 88.2821i −1.91151 3.31084i
\(712\) 0 0
\(713\) −0.397156 + 0.144553i −0.0148736 + 0.00541355i
\(714\) 0 0
\(715\) 0.732781 1.26921i 0.0274045 0.0474659i
\(716\) 0 0
\(717\) 19.3688 16.2523i 0.723341 0.606955i
\(718\) 0 0
\(719\) 0.963680 + 5.46530i 0.0359392 + 0.203821i 0.997490 0.0708053i \(-0.0225569\pi\)
−0.961551 + 0.274627i \(0.911446\pi\)
\(720\) 0 0
\(721\) −1.16106 −0.0432401
\(722\) 0 0
\(723\) 34.5126 1.28354
\(724\) 0 0
\(725\) 0.679661 + 3.85455i 0.0252420 + 0.143154i
\(726\) 0 0
\(727\) −1.18242 + 0.992168i −0.0438535 + 0.0367975i −0.664451 0.747332i \(-0.731335\pi\)
0.620597 + 0.784129i \(0.286890\pi\)
\(728\) 0 0
\(729\) −1.08840 + 1.88516i −0.0403110 + 0.0698207i
\(730\) 0 0
\(731\) 31.9954 11.6454i 1.18339 0.430720i
\(732\) 0 0
\(733\) 3.11148 + 5.38924i 0.114925 + 0.199056i 0.917750 0.397159i \(-0.130004\pi\)
−0.802825 + 0.596215i \(0.796671\pi\)
\(734\) 0 0
\(735\) 3.79770 21.5378i 0.140080 0.794435i
\(736\) 0 0
\(737\) 3.55438 + 2.98248i 0.130927 + 0.109861i
\(738\) 0 0
\(739\) −19.5054 7.09939i −0.717518 0.261155i −0.0426465 0.999090i \(-0.513579\pi\)
−0.674872 + 0.737935i \(0.735801\pi\)
\(740\) 0 0
\(741\) 9.49782 + 51.6237i 0.348911 + 1.89645i
\(742\) 0 0
\(743\) 13.4428 + 4.89277i 0.493168 + 0.179498i 0.576618 0.817014i \(-0.304372\pi\)
−0.0834508 + 0.996512i \(0.526594\pi\)
\(744\) 0 0
\(745\) −8.13757 6.82823i −0.298138 0.250167i
\(746\) 0 0
\(747\) 12.8838 73.0677i 0.471394 2.67341i
\(748\) 0 0
\(749\) −0.784651 1.35905i −0.0286705 0.0496588i
\(750\) 0 0
\(751\) −3.00729 + 1.09457i −0.109738 + 0.0399412i −0.396305 0.918119i \(-0.629708\pi\)
0.286568 + 0.958060i \(0.407486\pi\)
\(752\) 0 0
\(753\) 43.7627 75.7993i 1.59480 2.76228i
\(754\) 0 0
\(755\) 10.3922 8.72005i 0.378209 0.317355i
\(756\) 0 0
\(757\) −4.25324 24.1213i −0.154587 0.876704i −0.959163 0.282855i \(-0.908719\pi\)
0.804576 0.593850i \(-0.202393\pi\)
\(758\) 0 0
\(759\) −0.204311 −0.00741602
\(760\) 0 0
\(761\) −9.40561 −0.340953 −0.170477 0.985362i \(-0.554531\pi\)
−0.170477 + 0.985362i \(0.554531\pi\)
\(762\) 0 0
\(763\) −0.233038 1.32162i −0.00843654 0.0478460i
\(764\) 0 0
\(765\) 13.8219 11.5979i 0.499732 0.419325i
\(766\) 0 0
\(767\) −11.8693 + 20.5582i −0.428575 + 0.742314i
\(768\) 0 0
\(769\) −38.8442 + 14.1381i −1.40076 + 0.509834i −0.928403 0.371575i \(-0.878818\pi\)
−0.472354 + 0.881409i \(0.656596\pi\)
\(770\) 0 0
\(771\) 9.61255 + 16.6494i 0.346187 + 0.599614i
\(772\) 0 0
\(773\) 3.57247 20.2605i 0.128493 0.728719i −0.850679 0.525686i \(-0.823809\pi\)
0.979172 0.203034i \(-0.0650801\pi\)
\(774\) 0 0
\(775\) 1.88755 + 1.58384i 0.0678026 + 0.0568932i
\(776\) 0 0
\(777\) 1.95985 + 0.713327i 0.0703092 + 0.0255905i
\(778\) 0 0
\(779\) 16.1860 6.02748i 0.579922 0.215957i
\(780\) 0 0
\(781\) 0.611279 + 0.222487i 0.0218733 + 0.00796123i
\(782\) 0 0
\(783\) 35.5238 + 29.8080i 1.26952 + 1.06525i
\(784\) 0 0
\(785\) 1.79893 10.2023i 0.0642067 0.364134i
\(786\) 0 0
\(787\) 24.2543 + 42.0097i 0.864572 + 1.49748i 0.867471 + 0.497487i </