Properties

Label 380.2.u.a.61.1
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 61.1
Root \(-1.37827 - 1.15651i\) of defining polynomial
Character \(\chi\) \(=\) 380.61
Dual form 380.2.u.a.81.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.312429 - 1.77187i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(-0.336777 + 0.583316i) q^{7} +(-0.222848 + 0.0811099i) q^{9} +O(q^{10})\) \(q+(-0.312429 - 1.77187i) q^{3} +(-0.766044 + 0.642788i) q^{5} +(-0.336777 + 0.583316i) q^{7} +(-0.222848 + 0.0811099i) q^{9} +(-3.21276 - 5.56466i) q^{11} +(0.791702 - 4.48996i) q^{13} +(1.37827 + 1.15651i) q^{15} +(1.21618 + 0.442652i) q^{17} +(-4.35314 + 0.223964i) q^{19} +(1.13878 + 0.414482i) q^{21} +(-1.04176 - 0.874144i) q^{23} +(0.173648 - 0.984808i) q^{25} +(-2.48547 - 4.30496i) q^{27} +(-6.80288 + 2.47605i) q^{29} +(-2.97241 + 5.14836i) q^{31} +(-8.85612 + 7.43116i) q^{33} +(-0.116962 - 0.663322i) q^{35} +11.5704 q^{37} -8.20300 q^{39} +(-0.463683 - 2.62968i) q^{41} +(7.31756 - 6.14016i) q^{43} +(0.118575 - 0.205377i) q^{45} +(11.0445 - 4.01987i) q^{47} +(3.27316 + 5.66928i) q^{49} +(0.404354 - 2.29321i) q^{51} +(-2.74628 - 2.30440i) q^{53} +(6.03801 + 2.19766i) q^{55} +(1.75689 + 7.64324i) q^{57} +(0.150435 + 0.0547540i) q^{59} +(5.54965 + 4.65671i) q^{61} +(0.0277374 - 0.157306i) q^{63} +(2.27961 + 3.94841i) q^{65} +(-5.13512 + 1.86903i) q^{67} +(-1.22340 + 2.11898i) q^{69} +(9.00684 - 7.55764i) q^{71} +(-0.643012 - 3.64670i) q^{73} -1.79921 q^{75} +4.32794 q^{77} +(-1.11567 - 6.32728i) q^{79} +(-7.39632 + 6.20625i) q^{81} +(-2.52251 + 4.36912i) q^{83} +(-1.21618 + 0.442652i) q^{85} +(6.51266 + 11.2803i) q^{87} +(1.26006 - 7.14615i) q^{89} +(2.35244 + 1.97393i) q^{91} +(10.0509 + 3.65823i) q^{93} +(3.19074 - 2.96971i) q^{95} +(7.40807 + 2.69632i) q^{97} +(1.16730 + 0.979484i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{3} - 9 q^{9}+O(q^{10}) \) 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
\(3\) −0.312429 1.77187i −0.180381 1.02299i −0.931748 0.363107i \(-0.881716\pi\)
0.751366 0.659885i \(-0.229395\pi\)
\(4\) 0 0
\(5\) −0.766044 + 0.642788i −0.342585 + 0.287463i
\(6\) 0 0
\(7\) −0.336777 + 0.583316i −0.127290 + 0.220473i −0.922626 0.385696i \(-0.873961\pi\)
0.795336 + 0.606169i \(0.207295\pi\)
\(8\) 0 0
\(9\) −0.222848 + 0.0811099i −0.0742825 + 0.0270366i
\(10\) 0 0
\(11\) −3.21276 5.56466i −0.968683 1.67781i −0.699376 0.714754i \(-0.746539\pi\)
−0.269307 0.963054i \(-0.586795\pi\)
\(12\) 0 0
\(13\) 0.791702 4.48996i 0.219579 1.24529i −0.653204 0.757182i \(-0.726576\pi\)
0.872782 0.488110i \(-0.162313\pi\)
\(14\) 0 0
\(15\) 1.37827 + 1.15651i 0.355869 + 0.298609i
\(16\) 0 0
\(17\) 1.21618 + 0.442652i 0.294966 + 0.107359i 0.485264 0.874367i \(-0.338723\pi\)
−0.190299 + 0.981726i \(0.560946\pi\)
\(18\) 0 0
\(19\) −4.35314 + 0.223964i −0.998679 + 0.0513810i
\(20\) 0 0
\(21\) 1.13878 + 0.414482i 0.248502 + 0.0904475i
\(22\) 0 0
\(23\) −1.04176 0.874144i −0.217223 0.182272i 0.527683 0.849442i \(-0.323061\pi\)
−0.744906 + 0.667170i \(0.767505\pi\)
\(24\) 0 0
\(25\) 0.173648 0.984808i 0.0347296 0.196962i
\(26\) 0 0
\(27\) −2.48547 4.30496i −0.478329 0.828490i
\(28\) 0 0
\(29\) −6.80288 + 2.47605i −1.26326 + 0.459790i −0.884863 0.465852i \(-0.845748\pi\)
−0.378400 + 0.925642i \(0.623526\pi\)
\(30\) 0 0
\(31\) −2.97241 + 5.14836i −0.533860 + 0.924673i 0.465358 + 0.885123i \(0.345926\pi\)
−0.999218 + 0.0395498i \(0.987408\pi\)
\(32\) 0 0
\(33\) −8.85612 + 7.43116i −1.54165 + 1.29360i
\(34\) 0 0
\(35\) −0.116962 0.663322i −0.0197701 0.112122i
\(36\) 0 0
\(37\) 11.5704 1.90216 0.951079 0.308948i \(-0.0999770\pi\)
0.951079 + 0.308948i \(0.0999770\pi\)
\(38\) 0 0
\(39\) −8.20300 −1.31353
\(40\) 0 0
\(41\) −0.463683 2.62968i −0.0724151 0.410686i −0.999369 0.0355118i \(-0.988694\pi\)
0.926954 0.375175i \(-0.122417\pi\)
\(42\) 0 0
\(43\) 7.31756 6.14016i 1.11592 0.936366i 0.117526 0.993070i \(-0.462504\pi\)
0.998391 + 0.0567043i \(0.0180592\pi\)
\(44\) 0 0
\(45\) 0.118575 0.205377i 0.0176761 0.0306159i
\(46\) 0 0
\(47\) 11.0445 4.01987i 1.61100 0.586358i 0.629366 0.777109i \(-0.283314\pi\)
0.981638 + 0.190751i \(0.0610922\pi\)
\(48\) 0 0
\(49\) 3.27316 + 5.66928i 0.467595 + 0.809898i
\(50\) 0 0
\(51\) 0.404354 2.29321i 0.0566209 0.321113i
\(52\) 0 0
\(53\) −2.74628 2.30440i −0.377230 0.316534i 0.434384 0.900728i \(-0.356966\pi\)
−0.811614 + 0.584194i \(0.801411\pi\)
\(54\) 0 0
\(55\) 6.03801 + 2.19766i 0.814165 + 0.296332i
\(56\) 0 0
\(57\) 1.75689 + 7.64324i 0.232705 + 1.01237i
\(58\) 0 0
\(59\) 0.150435 + 0.0547540i 0.0195850 + 0.00712837i 0.351794 0.936077i \(-0.385572\pi\)
−0.332209 + 0.943206i \(0.607794\pi\)
\(60\) 0 0
\(61\) 5.54965 + 4.65671i 0.710560 + 0.596231i 0.924756 0.380560i \(-0.124269\pi\)
−0.214196 + 0.976791i \(0.568713\pi\)
\(62\) 0 0
\(63\) 0.0277374 0.157306i 0.00349458 0.0198187i
\(64\) 0 0
\(65\) 2.27961 + 3.94841i 0.282751 + 0.489740i
\(66\) 0 0
\(67\) −5.13512 + 1.86903i −0.627354 + 0.228338i −0.636079 0.771624i \(-0.719445\pi\)
0.00872500 + 0.999962i \(0.497223\pi\)
\(68\) 0 0
\(69\) −1.22340 + 2.11898i −0.147280 + 0.255096i
\(70\) 0 0
\(71\) 9.00684 7.55764i 1.06892 0.896927i 0.0739617 0.997261i \(-0.476436\pi\)
0.994954 + 0.100334i \(0.0319913\pi\)
\(72\) 0 0
\(73\) −0.643012 3.64670i −0.0752589 0.426815i −0.999037 0.0438852i \(-0.986026\pi\)
0.923778 0.382929i \(-0.125085\pi\)
\(74\) 0 0
\(75\) −1.79921 −0.207755
\(76\) 0 0
\(77\) 4.32794 0.493214
\(78\) 0 0
\(79\) −1.11567 6.32728i −0.125523 0.711875i −0.980996 0.194028i \(-0.937845\pi\)
0.855473 0.517847i \(-0.173266\pi\)
\(80\) 0 0
\(81\) −7.39632 + 6.20625i −0.821813 + 0.689583i
\(82\) 0 0
\(83\) −2.52251 + 4.36912i −0.276882 + 0.479573i −0.970608 0.240666i \(-0.922634\pi\)
0.693727 + 0.720238i \(0.255968\pi\)
\(84\) 0 0
\(85\) −1.21618 + 0.442652i −0.131913 + 0.0480123i
\(86\) 0 0
\(87\) 6.51266 + 11.2803i 0.698230 + 1.20937i
\(88\) 0 0
\(89\) 1.26006 7.14615i 0.133566 0.757490i −0.842282 0.539038i \(-0.818788\pi\)
0.975848 0.218453i \(-0.0701009\pi\)
\(90\) 0 0
\(91\) 2.35244 + 1.97393i 0.246603 + 0.206924i
\(92\) 0 0
\(93\) 10.0509 + 3.65823i 1.04223 + 0.379341i
\(94\) 0 0
\(95\) 3.19074 2.96971i 0.327363 0.304686i
\(96\) 0 0
\(97\) 7.40807 + 2.69632i 0.752176 + 0.273770i 0.689521 0.724266i \(-0.257821\pi\)
0.0626549 + 0.998035i \(0.480043\pi\)
\(98\) 0 0
\(99\) 1.16730 + 0.979484i 0.117318 + 0.0984419i
\(100\) 0 0
\(101\) −2.35954 + 13.3816i −0.234783 + 1.33152i 0.608289 + 0.793716i \(0.291856\pi\)
−0.843071 + 0.537802i \(0.819255\pi\)
\(102\) 0 0
\(103\) 5.39106 + 9.33758i 0.531197 + 0.920060i 0.999337 + 0.0364055i \(0.0115908\pi\)
−0.468140 + 0.883654i \(0.655076\pi\)
\(104\) 0 0
\(105\) −1.13878 + 0.414482i −0.111134 + 0.0404493i
\(106\) 0 0
\(107\) −0.555176 + 0.961592i −0.0536708 + 0.0929606i −0.891613 0.452799i \(-0.850426\pi\)
0.837942 + 0.545760i \(0.183759\pi\)
\(108\) 0 0
\(109\) 1.91957 1.61071i 0.183862 0.154278i −0.546211 0.837647i \(-0.683930\pi\)
0.730073 + 0.683369i \(0.239486\pi\)
\(110\) 0 0
\(111\) −3.61492 20.5012i −0.343113 1.94589i
\(112\) 0 0
\(113\) −14.8298 −1.39507 −0.697536 0.716550i \(-0.745720\pi\)
−0.697536 + 0.716550i \(0.745720\pi\)
\(114\) 0 0
\(115\) 1.35993 0.126814
\(116\) 0 0
\(117\) 0.187752 + 1.06479i 0.0173576 + 0.0984401i
\(118\) 0 0
\(119\) −0.667786 + 0.560339i −0.0612158 + 0.0513662i
\(120\) 0 0
\(121\) −15.1436 + 26.2295i −1.37669 + 2.38450i
\(122\) 0 0
\(123\) −4.51459 + 1.64317i −0.407067 + 0.148160i
\(124\) 0 0
\(125\) 0.500000 + 0.866025i 0.0447214 + 0.0774597i
\(126\) 0 0
\(127\) −1.01635 + 5.76401i −0.0901865 + 0.511473i 0.905930 + 0.423428i \(0.139173\pi\)
−0.996116 + 0.0880454i \(0.971938\pi\)
\(128\) 0 0
\(129\) −13.1658 11.0474i −1.15918 0.972671i
\(130\) 0 0
\(131\) 7.64603 + 2.78293i 0.668037 + 0.243146i 0.653702 0.756752i \(-0.273215\pi\)
0.0143345 + 0.999897i \(0.495437\pi\)
\(132\) 0 0
\(133\) 1.33540 2.61468i 0.115794 0.226722i
\(134\) 0 0
\(135\) 4.67116 + 1.70016i 0.402029 + 0.146327i
\(136\) 0 0
\(137\) 3.81357 + 3.19997i 0.325816 + 0.273392i 0.790992 0.611826i \(-0.209565\pi\)
−0.465177 + 0.885218i \(0.654009\pi\)
\(138\) 0 0
\(139\) 0.364121 2.06503i 0.0308843 0.175154i −0.965464 0.260537i \(-0.916100\pi\)
0.996348 + 0.0853833i \(0.0272115\pi\)
\(140\) 0 0
\(141\) −10.5733 18.3135i −0.890434 1.54228i
\(142\) 0 0
\(143\) −27.5287 + 10.0196i −2.30206 + 0.837882i
\(144\) 0 0
\(145\) 3.61974 6.26957i 0.300603 0.520659i
\(146\) 0 0
\(147\) 9.02262 7.57088i 0.744173 0.624436i
\(148\) 0 0
\(149\) −1.49492 8.47813i −0.122469 0.694556i −0.982779 0.184785i \(-0.940841\pi\)
0.860310 0.509771i \(-0.170270\pi\)
\(150\) 0 0
\(151\) 18.3265 1.49139 0.745693 0.666289i \(-0.232118\pi\)
0.745693 + 0.666289i \(0.232118\pi\)
\(152\) 0 0
\(153\) −0.306925 −0.0248134
\(154\) 0 0
\(155\) −1.03231 5.85450i −0.0829168 0.470245i
\(156\) 0 0
\(157\) 10.2264 8.58096i 0.816155 0.684835i −0.135913 0.990721i \(-0.543397\pi\)
0.952068 + 0.305885i \(0.0989524\pi\)
\(158\) 0 0
\(159\) −3.22509 + 5.58602i −0.255766 + 0.443000i
\(160\) 0 0
\(161\) 0.860745 0.313285i 0.0678362 0.0246904i
\(162\) 0 0
\(163\) 10.7658 + 18.6469i 0.843240 + 1.46053i 0.887141 + 0.461498i \(0.152688\pi\)
−0.0439014 + 0.999036i \(0.513979\pi\)
\(164\) 0 0
\(165\) 2.00752 11.3852i 0.156285 0.886337i
\(166\) 0 0
\(167\) −9.32714 7.82640i −0.721756 0.605625i 0.206115 0.978528i \(-0.433918\pi\)
−0.927870 + 0.372903i \(0.878362\pi\)
\(168\) 0 0
\(169\) −7.31698 2.66316i −0.562844 0.204859i
\(170\) 0 0
\(171\) 0.951921 0.402993i 0.0727952 0.0308176i
\(172\) 0 0
\(173\) 2.03095 + 0.739205i 0.154410 + 0.0562007i 0.418069 0.908415i \(-0.362707\pi\)
−0.263659 + 0.964616i \(0.584929\pi\)
\(174\) 0 0
\(175\) 0.515973 + 0.432953i 0.0390039 + 0.0327282i
\(176\) 0 0
\(177\) 0.0500168 0.283659i 0.00375949 0.0213212i
\(178\) 0 0
\(179\) −9.07390 15.7164i −0.678215 1.17470i −0.975518 0.219919i \(-0.929421\pi\)
0.297303 0.954783i \(-0.403913\pi\)
\(180\) 0 0
\(181\) 7.02363 2.55639i 0.522062 0.190015i −0.0675283 0.997717i \(-0.521511\pi\)
0.589591 + 0.807702i \(0.299289\pi\)
\(182\) 0 0
\(183\) 6.51723 11.2882i 0.481768 0.834446i
\(184\) 0 0
\(185\) −8.86342 + 7.43729i −0.651652 + 0.546801i
\(186\) 0 0
\(187\) −1.44407 8.18973i −0.105601 0.598893i
\(188\) 0 0
\(189\) 3.34820 0.243546
\(190\) 0 0
\(191\) −21.9662 −1.58942 −0.794710 0.606990i \(-0.792377\pi\)
−0.794710 + 0.606990i \(0.792377\pi\)
\(192\) 0 0
\(193\) −2.07436 11.7643i −0.149315 0.846810i −0.963800 0.266625i \(-0.914091\pi\)
0.814485 0.580185i \(-0.197020\pi\)
\(194\) 0 0
\(195\) 6.28386 5.27279i 0.449997 0.377592i
\(196\) 0 0
\(197\) 3.87650 6.71430i 0.276189 0.478374i −0.694245 0.719739i \(-0.744262\pi\)
0.970435 + 0.241365i \(0.0775950\pi\)
\(198\) 0 0
\(199\) 8.65867 3.15150i 0.613797 0.223404i −0.0163667 0.999866i \(-0.505210\pi\)
0.630164 + 0.776462i \(0.282988\pi\)
\(200\) 0 0
\(201\) 4.91605 + 8.51484i 0.346751 + 0.600591i
\(202\) 0 0
\(203\) 0.846740 4.80210i 0.0594295 0.337042i
\(204\) 0 0
\(205\) 2.04552 + 1.71640i 0.142866 + 0.119879i
\(206\) 0 0
\(207\) 0.303056 + 0.110303i 0.0210639 + 0.00766662i
\(208\) 0 0
\(209\) 15.2319 + 23.5042i 1.05361 + 1.62582i
\(210\) 0 0
\(211\) −19.3970 7.05994i −1.33535 0.486027i −0.427003 0.904250i \(-0.640431\pi\)
−0.908344 + 0.418224i \(0.862653\pi\)
\(212\) 0 0
\(213\) −16.2052 13.5978i −1.11036 0.931703i
\(214\) 0 0
\(215\) −1.65876 + 9.40727i −0.113126 + 0.641570i
\(216\) 0 0
\(217\) −2.00208 3.46770i −0.135910 0.235403i
\(218\) 0 0
\(219\) −6.26061 + 2.27867i −0.423053 + 0.153979i
\(220\) 0 0
\(221\) 2.95034 5.11013i 0.198461 0.343745i
\(222\) 0 0
\(223\) −1.80840 + 1.51742i −0.121099 + 0.101614i −0.701326 0.712841i \(-0.747408\pi\)
0.580227 + 0.814455i \(0.302964\pi\)
\(224\) 0 0
\(225\) 0.0411806 + 0.233547i 0.00274537 + 0.0155698i
\(226\) 0 0
\(227\) −15.3448 −1.01847 −0.509236 0.860627i \(-0.670072\pi\)
−0.509236 + 0.860627i \(0.670072\pi\)
\(228\) 0 0
\(229\) 9.54861 0.630990 0.315495 0.948927i \(-0.397829\pi\)
0.315495 + 0.948927i \(0.397829\pi\)
\(230\) 0 0
\(231\) −1.35217 7.66856i −0.0889665 0.504554i
\(232\) 0 0
\(233\) 19.8464 16.6531i 1.30018 1.09098i 0.310069 0.950714i \(-0.399648\pi\)
0.990113 0.140269i \(-0.0447966\pi\)
\(234\) 0 0
\(235\) −5.87665 + 10.1787i −0.383351 + 0.663983i
\(236\) 0 0
\(237\) −10.8626 + 3.95365i −0.705600 + 0.256817i
\(238\) 0 0
\(239\) −7.42312 12.8572i −0.480162 0.831665i 0.519579 0.854422i \(-0.326089\pi\)
−0.999741 + 0.0227574i \(0.992755\pi\)
\(240\) 0 0
\(241\) 3.35050 19.0016i 0.215825 1.22400i −0.663645 0.748048i \(-0.730992\pi\)
0.879470 0.475955i \(-0.157897\pi\)
\(242\) 0 0
\(243\) 1.88363 + 1.58055i 0.120835 + 0.101392i
\(244\) 0 0
\(245\) −6.15153 2.23897i −0.393007 0.143043i
\(246\) 0 0
\(247\) −2.44080 + 19.7228i −0.155304 + 1.25493i
\(248\) 0 0
\(249\) 8.52963 + 3.10453i 0.540543 + 0.196742i
\(250\) 0 0
\(251\) 14.5731 + 12.2283i 0.919848 + 0.771844i 0.973967 0.226690i \(-0.0727905\pi\)
−0.0541187 + 0.998535i \(0.517235\pi\)
\(252\) 0 0
\(253\) −1.51738 + 8.60548i −0.0953967 + 0.541022i
\(254\) 0 0
\(255\) 1.16429 + 2.01661i 0.0729108 + 0.126285i
\(256\) 0 0
\(257\) −11.1329 + 4.05205i −0.694453 + 0.252760i −0.665041 0.746807i \(-0.731586\pi\)
−0.0294123 + 0.999567i \(0.509364\pi\)
\(258\) 0 0
\(259\) −3.89664 + 6.74918i −0.242125 + 0.419374i
\(260\) 0 0
\(261\) 1.31517 1.10356i 0.0814072 0.0683087i
\(262\) 0 0
\(263\) 0.705433 + 4.00071i 0.0434989 + 0.246694i 0.998802 0.0489336i \(-0.0155823\pi\)
−0.955303 + 0.295628i \(0.904471\pi\)
\(264\) 0 0
\(265\) 3.58501 0.220225
\(266\) 0 0
\(267\) −13.0558 −0.798999
\(268\) 0 0
\(269\) 0.882623 + 5.00561i 0.0538145 + 0.305197i 0.999820 0.0189522i \(-0.00603304\pi\)
−0.946006 + 0.324149i \(0.894922\pi\)
\(270\) 0 0
\(271\) −11.4535 + 9.61062i −0.695750 + 0.583804i −0.920561 0.390599i \(-0.872268\pi\)
0.224811 + 0.974402i \(0.427824\pi\)
\(272\) 0 0
\(273\) 2.76259 4.78494i 0.167199 0.289598i
\(274\) 0 0
\(275\) −6.03801 + 2.19766i −0.364106 + 0.132524i
\(276\) 0 0
\(277\) −6.04752 10.4746i −0.363361 0.629359i 0.625151 0.780504i \(-0.285037\pi\)
−0.988512 + 0.151145i \(0.951704\pi\)
\(278\) 0 0
\(279\) 0.244811 1.38839i 0.0146564 0.0831208i
\(280\) 0 0
\(281\) 16.7076 + 14.0193i 0.996690 + 0.836322i 0.986522 0.163626i \(-0.0523190\pi\)
0.0101678 + 0.999948i \(0.496763\pi\)
\(282\) 0 0
\(283\) 15.0489 + 5.47733i 0.894561 + 0.325594i 0.748071 0.663618i \(-0.230980\pi\)
0.146490 + 0.989212i \(0.453202\pi\)
\(284\) 0 0
\(285\) −6.25884 4.72576i −0.370741 0.279930i
\(286\) 0 0
\(287\) 1.69009 + 0.615142i 0.0997628 + 0.0363107i
\(288\) 0 0
\(289\) −11.7396 9.85071i −0.690566 0.579453i
\(290\) 0 0
\(291\) 2.46304 13.9686i 0.144386 0.818853i
\(292\) 0 0
\(293\) −3.15924 5.47196i −0.184565 0.319675i 0.758865 0.651248i \(-0.225754\pi\)
−0.943430 + 0.331573i \(0.892421\pi\)
\(294\) 0 0
\(295\) −0.150435 + 0.0547540i −0.00875869 + 0.00318790i
\(296\) 0 0
\(297\) −15.9704 + 27.6616i −0.926699 + 1.60509i
\(298\) 0 0
\(299\) −4.74964 + 3.98542i −0.274679 + 0.230483i
\(300\) 0 0
\(301\) 1.11726 + 6.33631i 0.0643980 + 0.365219i
\(302\) 0 0
\(303\) 24.4477 1.40448
\(304\) 0 0
\(305\) −7.24456 −0.414822
\(306\) 0 0
\(307\) −0.139362 0.790360i −0.00795380 0.0451082i 0.980573 0.196157i \(-0.0628461\pi\)
−0.988526 + 0.151049i \(0.951735\pi\)
\(308\) 0 0
\(309\) 14.8607 12.4696i 0.845396 0.709371i
\(310\) 0 0
\(311\) −7.02192 + 12.1623i −0.398176 + 0.689662i −0.993501 0.113824i \(-0.963690\pi\)
0.595325 + 0.803485i \(0.297023\pi\)
\(312\) 0 0
\(313\) −20.5637 + 7.48459i −1.16233 + 0.423054i −0.849930 0.526896i \(-0.823356\pi\)
−0.312402 + 0.949950i \(0.601133\pi\)
\(314\) 0 0
\(315\) 0.0798666 + 0.138333i 0.00449997 + 0.00779418i
\(316\) 0 0
\(317\) 5.41832 30.7288i 0.304323 1.72590i −0.322350 0.946621i \(-0.604473\pi\)
0.626673 0.779282i \(-0.284416\pi\)
\(318\) 0 0
\(319\) 35.6344 + 29.9008i 1.99514 + 1.67412i
\(320\) 0 0
\(321\) 1.87727 + 0.683272i 0.104779 + 0.0381365i
\(322\) 0 0
\(323\) −5.39332 1.65454i −0.300092 0.0920613i
\(324\) 0 0
\(325\) −4.28427 1.55935i −0.237649 0.0864971i
\(326\) 0 0
\(327\) −3.45371 2.89801i −0.190991 0.160260i
\(328\) 0 0
\(329\) −1.37469 + 7.79623i −0.0757888 + 0.429820i
\(330\) 0 0
\(331\) −5.88658 10.1959i −0.323556 0.560415i 0.657663 0.753312i \(-0.271545\pi\)
−0.981219 + 0.192897i \(0.938212\pi\)
\(332\) 0 0
\(333\) −2.57843 + 0.938471i −0.141297 + 0.0514279i
\(334\) 0 0
\(335\) 2.73234 4.73255i 0.149284 0.258567i
\(336\) 0 0
\(337\) 7.27071 6.10085i 0.396061 0.332335i −0.422908 0.906173i \(-0.638991\pi\)
0.818969 + 0.573838i \(0.194546\pi\)
\(338\) 0 0
\(339\) 4.63327 + 26.2766i 0.251645 + 1.42715i
\(340\) 0 0
\(341\) 38.1985 2.06856
\(342\) 0 0
\(343\) −9.12419 −0.492660
\(344\) 0 0
\(345\) −0.424881 2.40962i −0.0228748 0.129730i
\(346\) 0 0
\(347\) 9.01036 7.56059i 0.483701 0.405874i −0.368061 0.929802i \(-0.619978\pi\)
0.851763 + 0.523928i \(0.175534\pi\)
\(348\) 0 0
\(349\) −6.21201 + 10.7595i −0.332521 + 0.575944i −0.983006 0.183576i \(-0.941233\pi\)
0.650484 + 0.759520i \(0.274566\pi\)
\(350\) 0 0
\(351\) −21.2969 + 7.75143i −1.13674 + 0.413741i
\(352\) 0 0
\(353\) −5.73224 9.92852i −0.305096 0.528442i 0.672187 0.740382i \(-0.265355\pi\)
−0.977283 + 0.211940i \(0.932022\pi\)
\(354\) 0 0
\(355\) −2.04169 + 11.5790i −0.108361 + 0.614548i
\(356\) 0 0
\(357\) 1.20149 + 1.00817i 0.0635894 + 0.0533578i
\(358\) 0 0
\(359\) 29.1144 + 10.5968i 1.53660 + 0.559277i 0.965227 0.261413i \(-0.0841885\pi\)
0.571374 + 0.820690i \(0.306411\pi\)
\(360\) 0 0
\(361\) 18.8997 1.94990i 0.994720 0.102626i
\(362\) 0 0
\(363\) 51.2067 + 18.6377i 2.68766 + 0.978227i
\(364\) 0 0
\(365\) 2.83663 + 2.38022i 0.148476 + 0.124586i
\(366\) 0 0
\(367\) −0.782062 + 4.43529i −0.0408233 + 0.231520i −0.998392 0.0566842i \(-0.981947\pi\)
0.957569 + 0.288205i \(0.0930583\pi\)
\(368\) 0 0
\(369\) 0.316623 + 0.548407i 0.0164827 + 0.0285490i
\(370\) 0 0
\(371\) 2.26908 0.825877i 0.117805 0.0428774i
\(372\) 0 0
\(373\) 9.56116 16.5604i 0.495058 0.857466i −0.504926 0.863163i \(-0.668480\pi\)
0.999984 + 0.00569689i \(0.00181339\pi\)
\(374\) 0 0
\(375\) 1.37827 1.15651i 0.0711737 0.0597218i
\(376\) 0 0
\(377\) 5.73150 + 32.5050i 0.295187 + 1.67409i
\(378\) 0 0
\(379\) −1.21152 −0.0622314 −0.0311157 0.999516i \(-0.509906\pi\)
−0.0311157 + 0.999516i \(0.509906\pi\)
\(380\) 0 0
\(381\) 10.5306 0.539501
\(382\) 0 0
\(383\) 1.06603 + 6.04574i 0.0544715 + 0.308923i 0.999855 0.0170375i \(-0.00542347\pi\)
−0.945383 + 0.325960i \(0.894312\pi\)
\(384\) 0 0
\(385\) −3.31539 + 2.78194i −0.168968 + 0.141781i
\(386\) 0 0
\(387\) −1.13267 + 1.96185i −0.0575769 + 0.0997262i
\(388\) 0 0
\(389\) 0.111964 0.0407516i 0.00567680 0.00206619i −0.339180 0.940721i \(-0.610150\pi\)
0.344857 + 0.938655i \(0.387927\pi\)
\(390\) 0 0
\(391\) −0.880027 1.52425i −0.0445049 0.0770847i
\(392\) 0 0
\(393\) 2.54215 14.4173i 0.128235 0.727255i
\(394\) 0 0
\(395\) 4.92175 + 4.12984i 0.247640 + 0.207795i
\(396\) 0 0
\(397\) 2.58876 + 0.942231i 0.129926 + 0.0472892i 0.406165 0.913800i \(-0.366866\pi\)
−0.276239 + 0.961089i \(0.589088\pi\)
\(398\) 0 0
\(399\) −5.05010 1.54925i −0.252821 0.0775597i
\(400\) 0 0
\(401\) −20.4922 7.45853i −1.02333 0.372461i −0.224792 0.974407i \(-0.572170\pi\)
−0.798537 + 0.601945i \(0.794392\pi\)
\(402\) 0 0
\(403\) 20.7627 + 17.4220i 1.03426 + 0.867850i
\(404\) 0 0
\(405\) 1.67661 9.50852i 0.0833114 0.472482i
\(406\) 0 0
\(407\) −37.1728 64.3852i −1.84259 3.19146i
\(408\) 0 0
\(409\) −14.6340 + 5.32635i −0.723605 + 0.263371i −0.677456 0.735564i \(-0.736917\pi\)
−0.0461499 + 0.998935i \(0.514695\pi\)
\(410\) 0 0
\(411\) 4.47847 7.75694i 0.220907 0.382622i
\(412\) 0 0
\(413\) −0.0826022 + 0.0693114i −0.00406459 + 0.00341059i
\(414\) 0 0
\(415\) −0.876059 4.96838i −0.0430040 0.243888i
\(416\) 0 0
\(417\) −3.77274 −0.184752
\(418\) 0 0
\(419\) −15.2596 −0.745479 −0.372739 0.927936i \(-0.621581\pi\)
−0.372739 + 0.927936i \(0.621581\pi\)
\(420\) 0 0
\(421\) 1.42403 + 8.07607i 0.0694029 + 0.393603i 0.999645 + 0.0266562i \(0.00848593\pi\)
−0.930242 + 0.366947i \(0.880403\pi\)
\(422\) 0 0
\(423\) −2.13519 + 1.79163i −0.103816 + 0.0871123i
\(424\) 0 0
\(425\) 0.647113 1.12083i 0.0313896 0.0543684i
\(426\) 0 0
\(427\) −4.58533 + 1.66892i −0.221900 + 0.0807649i
\(428\) 0 0
\(429\) 26.3543 + 45.6469i 1.27240 + 2.20385i
\(430\) 0 0
\(431\) −1.44591 + 8.20017i −0.0696471 + 0.394988i 0.929978 + 0.367615i \(0.119825\pi\)
−0.999625 + 0.0273736i \(0.991286\pi\)
\(432\) 0 0
\(433\) 26.0125 + 21.8271i 1.25008 + 1.04894i 0.996666 + 0.0815863i \(0.0259986\pi\)
0.253416 + 0.967357i \(0.418446\pi\)
\(434\) 0 0
\(435\) −12.2398 4.45492i −0.586853 0.213597i
\(436\) 0 0
\(437\) 4.73072 + 3.57195i 0.226301 + 0.170870i
\(438\) 0 0
\(439\) 11.7612 + 4.28073i 0.561331 + 0.204308i 0.607074 0.794645i \(-0.292343\pi\)
−0.0457426 + 0.998953i \(0.514565\pi\)
\(440\) 0 0
\(441\) −1.18925 0.997900i −0.0566310 0.0475190i
\(442\) 0 0
\(443\) −4.04892 + 22.9625i −0.192370 + 1.09098i 0.723745 + 0.690068i \(0.242419\pi\)
−0.916115 + 0.400916i \(0.868692\pi\)
\(444\) 0 0
\(445\) 3.62820 + 6.28422i 0.171993 + 0.297901i
\(446\) 0 0
\(447\) −14.5551 + 5.29763i −0.688434 + 0.250569i
\(448\) 0 0
\(449\) 10.7619 18.6402i 0.507887 0.879686i −0.492072 0.870555i \(-0.663760\pi\)
0.999958 0.00913096i \(-0.00290651\pi\)
\(450\) 0 0
\(451\) −13.1436 + 11.0287i −0.618906 + 0.519324i
\(452\) 0 0
\(453\) −5.72572 32.4722i −0.269018 1.52568i
\(454\) 0 0
\(455\) −3.07089 −0.143966
\(456\) 0 0
\(457\) −30.0765 −1.40692 −0.703459 0.710735i \(-0.748362\pi\)
−0.703459 + 0.710735i \(0.748362\pi\)
\(458\) 0 0
\(459\) −1.11717 6.33579i −0.0521450 0.295729i
\(460\) 0 0
\(461\) 14.5942 12.2459i 0.679717 0.570351i −0.236206 0.971703i \(-0.575904\pi\)
0.915924 + 0.401352i \(0.131460\pi\)
\(462\) 0 0
\(463\) 10.2775 17.8012i 0.477637 0.827292i −0.522034 0.852925i \(-0.674827\pi\)
0.999671 + 0.0256324i \(0.00815994\pi\)
\(464\) 0 0
\(465\) −10.0509 + 3.65823i −0.466100 + 0.169646i
\(466\) 0 0
\(467\) 20.2855 + 35.1354i 0.938699 + 1.62587i 0.767901 + 0.640568i \(0.221301\pi\)
0.170798 + 0.985306i \(0.445366\pi\)
\(468\) 0 0
\(469\) 0.639157 3.62484i 0.0295135 0.167380i
\(470\) 0 0
\(471\) −18.3994 15.4389i −0.847800 0.711389i
\(472\) 0 0
\(473\) −57.6774 20.9929i −2.65201 0.965253i
\(474\) 0 0
\(475\) −0.535353 + 4.32590i −0.0245637 + 0.198486i
\(476\) 0 0
\(477\) 0.798911 + 0.290780i 0.0365796 + 0.0133139i
\(478\) 0 0
\(479\) 9.78854 + 8.21356i 0.447250 + 0.375287i 0.838414 0.545034i \(-0.183483\pi\)
−0.391164 + 0.920321i \(0.627928\pi\)
\(480\) 0 0
\(481\) 9.16028 51.9506i 0.417673 2.36874i
\(482\) 0 0
\(483\) −0.824024 1.42725i −0.0374944 0.0649422i
\(484\) 0 0
\(485\) −7.40807 + 2.69632i −0.336383 + 0.122434i
\(486\) 0 0
\(487\) 0.754890 1.30751i 0.0342074 0.0592489i −0.848415 0.529332i \(-0.822443\pi\)
0.882622 + 0.470083i \(0.155776\pi\)
\(488\) 0 0
\(489\) 29.6763 24.9014i 1.34201 1.12608i
\(490\) 0 0
\(491\) 5.10731 + 28.9650i 0.230490 + 1.30717i 0.851907 + 0.523693i \(0.175446\pi\)
−0.621417 + 0.783480i \(0.713443\pi\)
\(492\) 0 0
\(493\) −9.36952 −0.421982
\(494\) 0 0
\(495\) −1.52381 −0.0684900
\(496\) 0 0
\(497\) 1.37519 + 7.79907i 0.0616856 + 0.349836i
\(498\) 0 0
\(499\) 13.7504 11.5379i 0.615551 0.516509i −0.280850 0.959752i \(-0.590616\pi\)
0.896402 + 0.443243i \(0.146172\pi\)
\(500\) 0 0
\(501\) −10.9533 + 18.9717i −0.489358 + 0.847594i
\(502\) 0 0
\(503\) −6.63252 + 2.41404i −0.295730 + 0.107637i −0.485624 0.874168i \(-0.661408\pi\)
0.189895 + 0.981804i \(0.439185\pi\)
\(504\) 0 0
\(505\) −6.79401 11.7676i −0.302330 0.523650i
\(506\) 0 0
\(507\) −2.43275 + 13.7968i −0.108042 + 0.612738i
\(508\) 0 0
\(509\) −5.30918 4.45493i −0.235325 0.197461i 0.517497 0.855685i \(-0.326864\pi\)
−0.752823 + 0.658224i \(0.771308\pi\)
\(510\) 0 0
\(511\) 2.34373 + 0.853049i 0.103681 + 0.0377367i
\(512\) 0 0
\(513\) 11.7838 + 18.1835i 0.520266 + 0.802819i
\(514\) 0 0
\(515\) −10.1319 3.68770i −0.446464 0.162499i
\(516\) 0 0
\(517\) −57.8525 48.5440i −2.54435 2.13496i
\(518\) 0 0
\(519\) 0.675251 3.82954i 0.0296402 0.168098i
\(520\) 0 0
\(521\) 18.3552 + 31.7921i 0.804155 + 1.39284i 0.916860 + 0.399208i \(0.130715\pi\)
−0.112705 + 0.993628i \(0.535952\pi\)
\(522\) 0 0
\(523\) 3.83828 1.39702i 0.167836 0.0610874i −0.256736 0.966482i \(-0.582647\pi\)
0.424572 + 0.905394i \(0.360425\pi\)
\(524\) 0 0
\(525\) 0.605933 1.04951i 0.0264451 0.0458042i
\(526\) 0 0
\(527\) −5.89390 + 4.94557i −0.256742 + 0.215432i
\(528\) 0 0
\(529\) −3.67276 20.8293i −0.159685 0.905621i
\(530\) 0 0
\(531\) −0.0379653 −0.00164755
\(532\) 0 0
\(533\) −12.1742 −0.527325
\(534\) 0 0
\(535\) −0.192810 1.09348i −0.00833592 0.0472754i
\(536\) 0 0
\(537\) −25.0126 + 20.9881i −1.07937 + 0.905702i
\(538\) 0 0
\(539\) 21.0318 36.4281i 0.905902 1.56907i
\(540\) 0 0
\(541\) −32.7657 + 11.9257i −1.40871 + 0.512727i −0.930750 0.365657i \(-0.880844\pi\)
−0.477956 + 0.878384i \(0.658622\pi\)
\(542\) 0 0
\(543\) −6.72399 11.6463i −0.288554 0.499790i
\(544\) 0 0
\(545\) −0.435132 + 2.46776i −0.0186390 + 0.105707i
\(546\) 0 0
\(547\) −12.1746 10.2157i −0.520548 0.436792i 0.344275 0.938869i \(-0.388125\pi\)
−0.864823 + 0.502077i \(0.832569\pi\)
\(548\) 0 0
\(549\) −1.61443 0.587605i −0.0689022 0.0250784i
\(550\) 0 0
\(551\) 29.0594 12.3022i 1.23797 0.524090i
\(552\) 0 0
\(553\) 4.06654 + 1.48010i 0.172927 + 0.0629402i
\(554\) 0 0
\(555\) 15.9471 + 13.3812i 0.676918 + 0.568002i
\(556\) 0 0
\(557\) −1.82337 + 10.3409i −0.0772588 + 0.438156i 0.921501 + 0.388375i \(0.126963\pi\)
−0.998760 + 0.0497811i \(0.984148\pi\)
\(558\) 0 0
\(559\) −21.7758 37.7167i −0.921017 1.59525i
\(560\) 0 0
\(561\) −14.0600 + 5.11742i −0.593614 + 0.216058i
\(562\) 0 0
\(563\) −3.48851 + 6.04227i −0.147023 + 0.254651i −0.930126 0.367241i \(-0.880302\pi\)
0.783103 + 0.621892i \(0.213636\pi\)
\(564\) 0 0
\(565\) 11.3603 9.53242i 0.477931 0.401032i
\(566\) 0 0
\(567\) −1.12929 6.40451i −0.0474257 0.268964i
\(568\) 0 0
\(569\) −25.5455 −1.07092 −0.535461 0.844560i \(-0.679862\pi\)
−0.535461 + 0.844560i \(0.679862\pi\)
\(570\) 0 0
\(571\) −1.23193 −0.0515548 −0.0257774 0.999668i \(-0.508206\pi\)
−0.0257774 + 0.999668i \(0.508206\pi\)
\(572\) 0 0
\(573\) 6.86289 + 38.9214i 0.286701 + 1.62596i
\(574\) 0 0
\(575\) −1.04176 + 0.874144i −0.0434446 + 0.0364543i
\(576\) 0 0
\(577\) −2.53389 + 4.38883i −0.105487 + 0.182710i −0.913937 0.405856i \(-0.866974\pi\)
0.808450 + 0.588565i \(0.200307\pi\)
\(578\) 0 0
\(579\) −20.1967 + 7.35100i −0.839346 + 0.305497i
\(580\) 0 0
\(581\) −1.69905 2.94284i −0.0704885 0.122090i
\(582\) 0 0
\(583\) −4.00008 + 22.6856i −0.165666 + 0.939541i
\(584\) 0 0
\(585\) −0.828261 0.694994i −0.0342444 0.0287344i
\(586\) 0 0
\(587\) 23.1177 + 8.41416i 0.954170 + 0.347290i 0.771746 0.635930i \(-0.219384\pi\)
0.182424 + 0.983220i \(0.441606\pi\)
\(588\) 0 0
\(589\) 11.7863 23.0772i 0.485644 0.950881i
\(590\) 0 0
\(591\) −13.1080 4.77093i −0.539192 0.196250i
\(592\) 0 0
\(593\) 16.6285 + 13.9530i 0.682852 + 0.572981i 0.916838 0.399259i \(-0.130733\pi\)
−0.233986 + 0.972240i \(0.575177\pi\)
\(594\) 0 0
\(595\) 0.151375 0.858489i 0.00620576 0.0351946i
\(596\) 0 0
\(597\) −8.28928 14.3575i −0.339258 0.587612i
\(598\) 0 0
\(599\) 35.2847 12.8426i 1.44169 0.524734i 0.501435 0.865195i \(-0.332806\pi\)
0.940258 + 0.340461i \(0.110583\pi\)
\(600\) 0 0
\(601\) −9.31628 + 16.1363i −0.380019 + 0.658212i −0.991065 0.133383i \(-0.957416\pi\)
0.611046 + 0.791595i \(0.290749\pi\)
\(602\) 0 0
\(603\) 0.992751 0.833017i 0.0404280 0.0339231i
\(604\) 0 0
\(605\) −5.25933 29.8271i −0.213822 1.21264i
\(606\) 0 0
\(607\) −43.4925 −1.76531 −0.882653 0.470025i \(-0.844245\pi\)
−0.882653 + 0.470025i \(0.844245\pi\)
\(608\) 0 0
\(609\) −8.77327 −0.355511
\(610\) 0 0
\(611\) −9.30511 52.7719i −0.376444 2.13492i
\(612\) 0 0
\(613\) 37.0997 31.1304i 1.49844 1.25734i 0.615253 0.788330i \(-0.289054\pi\)
0.883191 0.469014i \(-0.155391\pi\)
\(614\) 0 0
\(615\) 2.40216 4.16066i 0.0968645 0.167774i
\(616\) 0 0
\(617\) 21.8080 7.93747i 0.877957 0.319550i 0.136572 0.990630i \(-0.456391\pi\)
0.741385 + 0.671080i \(0.234169\pi\)
\(618\) 0 0
\(619\) 2.33161 + 4.03847i 0.0937154 + 0.162320i 0.909072 0.416640i \(-0.136792\pi\)
−0.815356 + 0.578959i \(0.803459\pi\)
\(620\) 0 0
\(621\) −1.17388 + 6.65742i −0.0471063 + 0.267153i
\(622\) 0 0
\(623\) 3.74410 + 3.14167i 0.150004 + 0.125869i
\(624\) 0 0
\(625\) −0.939693 0.342020i −0.0375877 0.0136808i
\(626\) 0 0
\(627\) 36.8876 34.3324i 1.47315 1.37110i
\(628\) 0 0
\(629\) 14.0716 + 5.12164i 0.561071 + 0.204213i
\(630\) 0 0
\(631\) 6.92604 + 5.81163i 0.275721 + 0.231357i 0.770153 0.637859i \(-0.220180\pi\)
−0.494432 + 0.869216i \(0.664624\pi\)
\(632\) 0 0
\(633\) −6.44913 + 36.5748i −0.256330 + 1.45372i
\(634\) 0 0
\(635\) −2.92646 5.06878i −0.116133 0.201149i
\(636\) 0 0
\(637\) 28.0462 10.2080i 1.11123 0.404456i
\(638\) 0 0
\(639\) −1.39415 + 2.41474i −0.0551519 + 0.0955258i
\(640\) 0 0
\(641\) 4.88738 4.10100i 0.193040 0.161980i −0.541145 0.840929i \(-0.682009\pi\)
0.734185 + 0.678950i \(0.237565\pi\)
\(642\) 0 0
\(643\) −7.28320 41.3051i −0.287221 1.62891i −0.697241 0.716837i \(-0.745589\pi\)
0.410020 0.912077i \(-0.365522\pi\)
\(644\) 0 0
\(645\) 17.1867 0.676727
\(646\) 0 0
\(647\) 28.4481 1.11841 0.559205 0.829030i \(-0.311107\pi\)
0.559205 + 0.829030i \(0.311107\pi\)
\(648\) 0 0
\(649\) −0.178625 1.01303i −0.00701165 0.0397651i
\(650\) 0 0
\(651\) −5.51882 + 4.63084i −0.216300 + 0.181497i
\(652\) 0 0
\(653\) −14.5691 + 25.2345i −0.570134 + 0.987501i 0.426418 + 0.904526i \(0.359775\pi\)
−0.996552 + 0.0829744i \(0.973558\pi\)
\(654\) 0 0
\(655\) −7.64603 + 2.78293i −0.298755 + 0.108738i
\(656\) 0 0
\(657\) 0.439077 + 0.760504i 0.0171300 + 0.0296701i
\(658\) 0 0
\(659\) −1.78347 + 10.1145i −0.0694740 + 0.394006i 0.930165 + 0.367141i \(0.119664\pi\)
−0.999639 + 0.0268649i \(0.991448\pi\)
\(660\) 0 0
\(661\) 13.4375 + 11.2754i 0.522658 + 0.438562i 0.865557 0.500810i \(-0.166965\pi\)
−0.342899 + 0.939372i \(0.611409\pi\)
\(662\) 0 0
\(663\) −9.97628 3.63107i −0.387447 0.141019i
\(664\) 0 0
\(665\) 0.657711 + 2.86134i 0.0255049 + 0.110958i
\(666\) 0 0
\(667\) 9.25142 + 3.36724i 0.358216 + 0.130380i
\(668\) 0 0
\(669\) 3.25368 + 2.73016i 0.125795 + 0.105554i
\(670\) 0 0
\(671\) 8.08332 45.8428i 0.312053 1.76974i
\(672\) 0 0
\(673\) −18.8057 32.5724i −0.724906 1.25557i −0.959012 0.283364i \(-0.908550\pi\)
0.234106 0.972211i \(-0.424784\pi\)
\(674\) 0 0
\(675\) −4.67116 + 1.70016i −0.179793 + 0.0654393i
\(676\) 0 0
\(677\) 2.73960 4.74513i 0.105291 0.182370i −0.808566 0.588406i \(-0.799756\pi\)
0.913857 + 0.406036i \(0.133089\pi\)
\(678\) 0 0
\(679\) −4.06768 + 3.41319i −0.156103 + 0.130986i
\(680\) 0 0
\(681\) 4.79417 + 27.1891i 0.183713 + 1.04189i
\(682\) 0 0
\(683\) −7.75347 −0.296678 −0.148339 0.988937i \(-0.547393\pi\)
−0.148339 + 0.988937i \(0.547393\pi\)
\(684\) 0 0
\(685\) −4.97827 −0.190210
\(686\) 0 0
\(687\) −2.98326 16.9189i −0.113819 0.645498i
\(688\) 0 0
\(689\) −12.5209 + 10.5063i −0.477009 + 0.400258i
\(690\) 0 0
\(691\) −22.8718 + 39.6151i −0.870084 + 1.50703i −0.00817434 + 0.999967i \(0.502602\pi\)
−0.861909 + 0.507062i \(0.830731\pi\)
\(692\) 0 0
\(693\) −0.964470 + 0.351038i −0.0366372 + 0.0133348i
\(694\) 0 0
\(695\) 1.04844 + 1.81596i 0.0397698 + 0.0688833i
\(696\) 0 0
\(697\) 0.600111 3.40340i 0.0227308 0.128913i
\(698\) 0 0
\(699\) −35.7078 29.9624i −1.35059 1.13328i
\(700\) 0 0
\(701\) 9.17535 + 3.33956i 0.346548 + 0.126133i 0.509429 0.860512i \(-0.329856\pi\)
−0.162881 + 0.986646i \(0.552079\pi\)
\(702\) 0 0
\(703\) −50.3675 + 2.59135i −1.89965 + 0.0977347i
\(704\) 0 0
\(705\) 19.8713 + 7.23258i 0.748398 + 0.272395i
\(706\) 0 0
\(707\) −7.01105 5.88297i −0.263678 0.221252i
\(708\) 0 0
\(709\) −5.49893 + 31.1860i −0.206517 + 1.17121i 0.688518 + 0.725219i \(0.258261\pi\)
−0.895035 + 0.445996i \(0.852850\pi\)
\(710\) 0 0
\(711\) 0.761829 + 1.31953i 0.0285708 + 0.0494861i
\(712\) 0 0
\(713\) 7.59695 2.76507i 0.284508 0.103553i
\(714\) 0 0
\(715\) 14.6477 25.3706i 0.547793 0.948805i
\(716\) 0 0
\(717\) −20.4622 + 17.1698i −0.764174 + 0.641218i
\(718\) 0 0
\(719\) 5.66644 + 32.1360i 0.211322 + 1.19847i 0.887175 + 0.461433i \(0.152664\pi\)
−0.675853 + 0.737037i \(0.736225\pi\)
\(720\) 0 0
\(721\) −7.26235 −0.270464
\(722\) 0 0
\(723\) −34.7153 −1.29108
\(724\) 0 0
\(725\) 1.25712 + 7.12949i 0.0466883 + 0.264783i
\(726\) 0 0
\(727\) 25.4241 21.3333i 0.942927 0.791210i −0.0351651 0.999382i \(-0.511196\pi\)
0.978092 + 0.208172i \(0.0667513\pi\)
\(728\) 0 0
\(729\) −12.2708 + 21.2536i −0.454473 + 0.787171i
\(730\) 0 0
\(731\) 11.6174 4.22838i 0.429684 0.156392i
\(732\) 0 0
\(733\) 3.60440 + 6.24300i 0.133132 + 0.230591i 0.924882 0.380254i \(-0.124163\pi\)
−0.791751 + 0.610845i \(0.790830\pi\)
\(734\) 0 0
\(735\) −2.04526 + 11.5993i −0.0754406 + 0.427845i
\(736\) 0 0
\(737\) 26.8984 + 22.5704i 0.990815 + 0.831393i
\(738\) 0 0
\(739\) −23.3257 8.48987i −0.858051 0.312305i −0.124733 0.992190i \(-0.539807\pi\)
−0.733318 + 0.679885i \(0.762030\pi\)
\(740\) 0 0
\(741\) 35.7088 1.83718i 1.31180 0.0674905i
\(742\) 0 0
\(743\) 27.6624 + 10.0683i 1.01483 + 0.369370i 0.795288 0.606232i \(-0.207320\pi\)
0.219547 + 0.975602i \(0.429542\pi\)
\(744\) 0 0
\(745\) 6.59482 + 5.53371i 0.241615 + 0.202739i
\(746\) 0 0
\(747\) 0.207757 1.17825i 0.00760142 0.0431098i
\(748\) 0 0
\(749\) −0.373941 0.647685i −0.0136635 0.0236659i
\(750\) 0 0
\(751\) −30.6975 + 11.1730i −1.12017 + 0.407707i −0.834713 0.550685i \(-0.814366\pi\)
−0.285453 + 0.958393i \(0.592144\pi\)
\(752\) 0 0
\(753\) 17.1140 29.6422i 0.623667 1.08022i
\(754\) 0 0
\(755\) −14.0389 + 11.7800i −0.510927 + 0.428719i
\(756\) 0 0
\(757\) 9.00156 + 51.0504i 0.327167 + 1.85546i 0.493986 + 0.869470i \(0.335539\pi\)
−0.166819 + 0.985988i \(0.553349\pi\)
\(758\) 0 0
\(759\) 15.7219 0.570669
\(760\) 0 0
\(761\) 29.7963 1.08011 0.540057 0.841628i \(-0.318403\pi\)
0.540057 + 0.841628i \(0.318403\pi\)
\(762\) 0 0
\(763\) 0.293085 + 1.66217i 0.0106104 + 0.0601746i
\(764\) 0 0
\(765\) 0.235118 0.197288i 0.00850072 0.00713295i
\(766\) 0 0
\(767\) 0.364944 0.632101i 0.0131774 0.0228238i
\(768\) 0 0
\(769\) 11.7119 4.26278i 0.422342 0.153720i −0.122101 0.992518i \(-0.538963\pi\)
0.544443 + 0.838798i \(0.316741\pi\)
\(770\) 0 0
\(771\) 10.6580 + 18.4602i 0.383838 + 0.664827i
\(772\) 0 0
\(773\) −5.08078 + 28.8145i −0.182743 + 1.03639i 0.746078 + 0.665858i \(0.231934\pi\)
−0.928821 + 0.370528i \(0.879177\pi\)
\(774\) 0 0
\(775\) 4.55399 + 3.82125i 0.163584 + 0.137263i
\(776\) 0 0
\(777\) 13.1761 + 4.79572i 0.472691 + 0.172045i
\(778\) 0 0
\(779\) 2.60743 + 11.3435i 0.0934209 + 0.406423i
\(780\) 0 0
\(781\) −70.9925 25.8392i −2.54031 0.924598i
\(782\) 0 0
\(783\) 27.5676 + 23.1320i 0.985187 + 0.826670i
\(784\) 0 0
\(785\) −2.31814 + 13.1468i −0.0827378 + 0.469229i
\(786\) 0 0
\(787\) 16.1220 + 27.9240i 0.574686 + 0.995385i 0.996076 + 0.0885051i \(0.0282090\pi\)