Properties

Label 450.2.l.d.289.2
Level $450$
Weight $2$
Character 450.289
Analytic conductor $3.593$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [450,2,Mod(19,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.l (of order \(10\), degree \(4\), 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: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 289.2
Root \(0.644389 - 0.983224i\) of defining polynomial
Character \(\chi\) \(=\) 450.289
Dual form 450.2.l.d.109.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(2.23347 + 0.107666i) q^{5} +0.992398i q^{7} +(0.951057 - 0.309017i) q^{8} +O(q^{10})\) \(q+(-0.587785 - 0.809017i) q^{2} +(-0.309017 + 0.951057i) q^{4} +(2.23347 + 0.107666i) q^{5} +0.992398i q^{7} +(0.951057 - 0.309017i) q^{8} +(-1.22570 - 1.87020i) q^{10} +(2.58148 - 1.87556i) q^{11} +(-2.26510 + 3.11764i) q^{13} +(0.802867 - 0.583317i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(2.15854 - 0.701351i) q^{17} +(1.45140 + 4.46695i) q^{19} +(-0.792578 + 2.09089i) q^{20} +(-3.03472 - 0.986039i) q^{22} +(3.29138 + 4.53019i) q^{23} +(4.97682 + 0.480938i) q^{25} +3.85361 q^{26} +(-0.943827 - 0.306668i) q^{28} +(2.25903 - 6.95256i) q^{29} +(-1.80729 - 5.56226i) q^{31} +1.00000i q^{32} +(-1.83616 - 1.33405i) q^{34} +(-0.106847 + 2.21650i) q^{35} +(3.07223 - 4.22856i) q^{37} +(2.76073 - 3.79981i) q^{38} +(2.15743 - 0.587785i) q^{40} +(-0.919147 - 0.667799i) q^{41} +6.88806i q^{43} +(0.986039 + 3.03472i) q^{44} +(1.73038 - 5.32556i) q^{46} +(-6.88191 - 2.23607i) q^{47} +6.01515 q^{49} +(-2.53621 - 4.30902i) q^{50} +(-2.26510 - 3.11764i) q^{52} +(4.00902 + 1.30261i) q^{53} +(5.96761 - 3.91107i) q^{55} +(0.306668 + 0.943827i) q^{56} +(-6.95256 + 2.25903i) q^{58} +(-5.55591 - 4.03660i) q^{59} +(8.95256 - 6.50442i) q^{61} +(-3.43767 + 4.73154i) q^{62} +(0.809017 - 0.587785i) q^{64} +(-5.39470 + 6.71929i) q^{65} +(-12.4631 + 4.04950i) q^{67} +2.26962i q^{68} +(1.85599 - 1.21638i) q^{70} +(0.675441 - 2.07879i) q^{71} +(1.67716 + 2.30841i) q^{73} -5.22679 q^{74} -4.69683 q^{76} +(1.86130 + 2.56186i) q^{77} +(-3.44678 + 10.6081i) q^{79} +(-1.74363 - 1.39991i) q^{80} +1.13613i q^{82} +(-9.87934 + 3.20999i) q^{83} +(4.89655 - 1.33405i) q^{85} +(5.57255 - 4.04870i) q^{86} +(1.87556 - 2.58148i) q^{88} +(1.56046 - 1.13374i) q^{89} +(-3.09394 - 2.24788i) q^{91} +(-5.32556 + 1.73038i) q^{92} +(2.23607 + 6.88191i) q^{94} +(2.76073 + 10.1331i) q^{95} +(-15.7543 - 5.11887i) q^{97} +(-3.53561 - 4.86635i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{4} - 4 q^{16} - 16 q^{19} - 20 q^{22} + 20 q^{25} - 10 q^{28} + 6 q^{31} - 26 q^{34} + 10 q^{37} + 20 q^{46} + 28 q^{49} - 20 q^{55} + 32 q^{61} + 4 q^{64} - 40 q^{67} - 30 q^{70} - 24 q^{76} - 36 q^{79} - 70 q^{85} + 10 q^{88} + 52 q^{91} - 70 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.587785 0.809017i −0.415627 0.572061i
\(3\) 0 0
\(4\) −0.309017 + 0.951057i −0.154508 + 0.475528i
\(5\) 2.23347 + 0.107666i 0.998840 + 0.0481496i
\(6\) 0 0
\(7\) 0.992398i 0.375091i 0.982256 + 0.187546i \(0.0600533\pi\)
−0.982256 + 0.187546i \(0.939947\pi\)
\(8\) 0.951057 0.309017i 0.336249 0.109254i
\(9\) 0 0
\(10\) −1.22570 1.87020i −0.387600 0.591410i
\(11\) 2.58148 1.87556i 0.778347 0.565502i −0.126136 0.992013i \(-0.540257\pi\)
0.904482 + 0.426511i \(0.140257\pi\)
\(12\) 0 0
\(13\) −2.26510 + 3.11764i −0.628225 + 0.864677i −0.997919 0.0644761i \(-0.979462\pi\)
0.369694 + 0.929153i \(0.379462\pi\)
\(14\) 0.802867 0.583317i 0.214575 0.155898i
\(15\) 0 0
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) 2.15854 0.701351i 0.523522 0.170103i −0.0353211 0.999376i \(-0.511245\pi\)
0.558843 + 0.829273i \(0.311245\pi\)
\(18\) 0 0
\(19\) 1.45140 + 4.46695i 0.332974 + 1.02479i 0.967711 + 0.252061i \(0.0811082\pi\)
−0.634738 + 0.772728i \(0.718892\pi\)
\(20\) −0.792578 + 2.09089i −0.177226 + 0.467537i
\(21\) 0 0
\(22\) −3.03472 0.986039i −0.647004 0.210224i
\(23\) 3.29138 + 4.53019i 0.686300 + 0.944611i 0.999988 0.00491540i \(-0.00156463\pi\)
−0.313688 + 0.949526i \(0.601565\pi\)
\(24\) 0 0
\(25\) 4.97682 + 0.480938i 0.995363 + 0.0961876i
\(26\) 3.85361 0.755756
\(27\) 0 0
\(28\) −0.943827 0.306668i −0.178367 0.0579548i
\(29\) 2.25903 6.95256i 0.419490 1.29106i −0.488682 0.872462i \(-0.662522\pi\)
0.908172 0.418597i \(-0.137478\pi\)
\(30\) 0 0
\(31\) −1.80729 5.56226i −0.324599 0.999012i −0.971621 0.236541i \(-0.923986\pi\)
0.647023 0.762471i \(-0.276014\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −1.83616 1.33405i −0.314899 0.228788i
\(35\) −0.106847 + 2.21650i −0.0180605 + 0.374656i
\(36\) 0 0
\(37\) 3.07223 4.22856i 0.505071 0.695171i −0.478007 0.878356i \(-0.658641\pi\)
0.983078 + 0.183185i \(0.0586407\pi\)
\(38\) 2.76073 3.79981i 0.447849 0.616411i
\(39\) 0 0
\(40\) 2.15743 0.587785i 0.341120 0.0929370i
\(41\) −0.919147 0.667799i −0.143547 0.104293i 0.513694 0.857973i \(-0.328277\pi\)
−0.657241 + 0.753681i \(0.728277\pi\)
\(42\) 0 0
\(43\) 6.88806i 1.05042i 0.850973 + 0.525209i \(0.176013\pi\)
−0.850973 + 0.525209i \(0.823987\pi\)
\(44\) 0.986039 + 3.03472i 0.148651 + 0.457501i
\(45\) 0 0
\(46\) 1.73038 5.32556i 0.255131 0.785211i
\(47\) −6.88191 2.23607i −1.00383 0.326164i −0.239435 0.970912i \(-0.576962\pi\)
−0.764395 + 0.644748i \(0.776962\pi\)
\(48\) 0 0
\(49\) 6.01515 0.859306
\(50\) −2.53621 4.30902i −0.358675 0.609387i
\(51\) 0 0
\(52\) −2.26510 3.11764i −0.314112 0.432339i
\(53\) 4.00902 + 1.30261i 0.550681 + 0.178927i 0.571124 0.820864i \(-0.306508\pi\)
−0.0204428 + 0.999791i \(0.506508\pi\)
\(54\) 0 0
\(55\) 5.96761 3.91107i 0.804673 0.527369i
\(56\) 0.306668 + 0.943827i 0.0409802 + 0.126124i
\(57\) 0 0
\(58\) −6.95256 + 2.25903i −0.912916 + 0.296625i
\(59\) −5.55591 4.03660i −0.723317 0.525521i 0.164125 0.986440i \(-0.447520\pi\)
−0.887442 + 0.460919i \(0.847520\pi\)
\(60\) 0 0
\(61\) 8.95256 6.50442i 1.14626 0.832805i 0.158280 0.987394i \(-0.449405\pi\)
0.987979 + 0.154589i \(0.0494053\pi\)
\(62\) −3.43767 + 4.73154i −0.436584 + 0.600907i
\(63\) 0 0
\(64\) 0.809017 0.587785i 0.101127 0.0734732i
\(65\) −5.39470 + 6.71929i −0.669130 + 0.833426i
\(66\) 0 0
\(67\) −12.4631 + 4.04950i −1.52261 + 0.494726i −0.946515 0.322658i \(-0.895423\pi\)
−0.576093 + 0.817384i \(0.695423\pi\)
\(68\) 2.26962i 0.275232i
\(69\) 0 0
\(70\) 1.85599 1.21638i 0.221833 0.145386i
\(71\) 0.675441 2.07879i 0.0801601 0.246707i −0.902943 0.429760i \(-0.858598\pi\)
0.983103 + 0.183053i \(0.0585980\pi\)
\(72\) 0 0
\(73\) 1.67716 + 2.30841i 0.196297 + 0.270179i 0.895807 0.444443i \(-0.146598\pi\)
−0.699510 + 0.714623i \(0.746598\pi\)
\(74\) −5.22679 −0.607602
\(75\) 0 0
\(76\) −4.69683 −0.538763
\(77\) 1.86130 + 2.56186i 0.212115 + 0.291951i
\(78\) 0 0
\(79\) −3.44678 + 10.6081i −0.387793 + 1.19350i 0.546641 + 0.837367i \(0.315906\pi\)
−0.934434 + 0.356137i \(0.884094\pi\)
\(80\) −1.74363 1.39991i −0.194944 0.156514i
\(81\) 0 0
\(82\) 1.13613i 0.125464i
\(83\) −9.87934 + 3.20999i −1.08440 + 0.352342i −0.796079 0.605192i \(-0.793096\pi\)
−0.288319 + 0.957534i \(0.593096\pi\)
\(84\) 0 0
\(85\) 4.89655 1.33405i 0.531105 0.144698i
\(86\) 5.57255 4.04870i 0.600904 0.436582i
\(87\) 0 0
\(88\) 1.87556 2.58148i 0.199935 0.275187i
\(89\) 1.56046 1.13374i 0.165409 0.120176i −0.502001 0.864867i \(-0.667403\pi\)
0.667410 + 0.744690i \(0.267403\pi\)
\(90\) 0 0
\(91\) −3.09394 2.24788i −0.324333 0.235642i
\(92\) −5.32556 + 1.73038i −0.555228 + 0.180405i
\(93\) 0 0
\(94\) 2.23607 + 6.88191i 0.230633 + 0.709815i
\(95\) 2.76073 + 10.1331i 0.283245 + 1.03963i
\(96\) 0 0
\(97\) −15.7543 5.11887i −1.59960 0.519743i −0.632594 0.774484i \(-0.718010\pi\)
−0.967009 + 0.254741i \(0.918010\pi\)
\(98\) −3.53561 4.86635i −0.357151 0.491576i
\(99\) 0 0
\(100\) −1.99532 + 4.58462i −0.199532 + 0.458462i
\(101\) −16.4535 −1.63719 −0.818593 0.574374i \(-0.805246\pi\)
−0.818593 + 0.574374i \(0.805246\pi\)
\(102\) 0 0
\(103\) −8.91260 2.89588i −0.878185 0.285340i −0.164982 0.986297i \(-0.552756\pi\)
−0.713203 + 0.700957i \(0.752756\pi\)
\(104\) −1.19083 + 3.66500i −0.116771 + 0.359383i
\(105\) 0 0
\(106\) −1.30261 4.00902i −0.126521 0.389390i
\(107\) 8.47591i 0.819397i −0.912221 0.409698i \(-0.865634\pi\)
0.912221 0.409698i \(-0.134366\pi\)
\(108\) 0 0
\(109\) 12.2467 + 8.89774i 1.17302 + 0.852249i 0.991367 0.131114i \(-0.0418553\pi\)
0.181653 + 0.983363i \(0.441855\pi\)
\(110\) −6.67180 2.52903i −0.636131 0.241133i
\(111\) 0 0
\(112\) 0.583317 0.802867i 0.0551183 0.0758638i
\(113\) −3.00083 + 4.13029i −0.282294 + 0.388545i −0.926492 0.376314i \(-0.877191\pi\)
0.644198 + 0.764859i \(0.277191\pi\)
\(114\) 0 0
\(115\) 6.86346 + 10.4724i 0.640021 + 0.976560i
\(116\) 5.91420 + 4.29692i 0.549120 + 0.398959i
\(117\) 0 0
\(118\) 6.86748i 0.632202i
\(119\) 0.696020 + 2.14213i 0.0638040 + 0.196369i
\(120\) 0 0
\(121\) −0.252844 + 0.778174i −0.0229858 + 0.0707431i
\(122\) −10.5244 3.41958i −0.952832 0.309594i
\(123\) 0 0
\(124\) 5.84851 0.525212
\(125\) 11.0638 + 1.61000i 0.989577 + 0.144002i
\(126\) 0 0
\(127\) −2.57239 3.54059i −0.228262 0.314176i 0.679488 0.733686i \(-0.262202\pi\)
−0.907751 + 0.419510i \(0.862202\pi\)
\(128\) −0.951057 0.309017i −0.0840623 0.0273135i
\(129\) 0 0
\(130\) 8.60695 + 0.414902i 0.754879 + 0.0363894i
\(131\) 1.56629 + 4.82055i 0.136848 + 0.421173i 0.995873 0.0907598i \(-0.0289295\pi\)
−0.859025 + 0.511933i \(0.828930\pi\)
\(132\) 0 0
\(133\) −4.43299 + 1.44037i −0.384389 + 0.124896i
\(134\) 10.6017 + 7.70261i 0.915851 + 0.665404i
\(135\) 0 0
\(136\) 1.83616 1.33405i 0.157450 0.114394i
\(137\) −1.37475 + 1.89218i −0.117453 + 0.161660i −0.863695 0.504014i \(-0.831856\pi\)
0.746243 + 0.665674i \(0.231856\pi\)
\(138\) 0 0
\(139\) 1.47591 1.07231i 0.125185 0.0909520i −0.523431 0.852068i \(-0.675348\pi\)
0.648616 + 0.761116i \(0.275348\pi\)
\(140\) −2.07500 0.786553i −0.175369 0.0664759i
\(141\) 0 0
\(142\) −2.07879 + 0.675441i −0.174449 + 0.0566818i
\(143\) 12.2965i 1.02828i
\(144\) 0 0
\(145\) 5.79403 15.2852i 0.481168 1.26936i
\(146\) 0.881735 2.71370i 0.0729729 0.224587i
\(147\) 0 0
\(148\) 3.07223 + 4.22856i 0.252536 + 0.347586i
\(149\) −23.8922 −1.95732 −0.978661 0.205483i \(-0.934123\pi\)
−0.978661 + 0.205483i \(0.934123\pi\)
\(150\) 0 0
\(151\) −7.99856 −0.650914 −0.325457 0.945557i \(-0.605518\pi\)
−0.325457 + 0.945557i \(0.605518\pi\)
\(152\) 2.76073 + 3.79981i 0.223924 + 0.308206i
\(153\) 0 0
\(154\) 0.978544 3.01165i 0.0788533 0.242686i
\(155\) −3.43767 12.6178i −0.276120 1.01348i
\(156\) 0 0
\(157\) 5.20135i 0.415113i −0.978223 0.207557i \(-0.933449\pi\)
0.978223 0.207557i \(-0.0665511\pi\)
\(158\) 10.6081 3.44678i 0.843935 0.274211i
\(159\) 0 0
\(160\) −0.107666 + 2.23347i −0.00851173 + 0.176572i
\(161\) −4.49576 + 3.26636i −0.354315 + 0.257425i
\(162\) 0 0
\(163\) −10.7791 + 14.8361i −0.844283 + 1.16206i 0.140811 + 0.990036i \(0.455029\pi\)
−0.985094 + 0.172019i \(0.944971\pi\)
\(164\) 0.919147 0.667799i 0.0717733 0.0521464i
\(165\) 0 0
\(166\) 8.40387 + 6.10577i 0.652267 + 0.473899i
\(167\) 22.8298 7.41785i 1.76662 0.574010i 0.768770 0.639525i \(-0.220869\pi\)
0.997852 + 0.0655146i \(0.0208689\pi\)
\(168\) 0 0
\(169\) −0.571784 1.75977i −0.0439834 0.135367i
\(170\) −3.95739 3.17726i −0.303518 0.243684i
\(171\) 0 0
\(172\) −6.55093 2.12853i −0.499504 0.162299i
\(173\) −8.99653 12.3827i −0.683994 0.941437i 0.315979 0.948766i \(-0.397667\pi\)
−0.999973 + 0.00732946i \(0.997667\pi\)
\(174\) 0 0
\(175\) −0.477282 + 4.93898i −0.0360791 + 0.373352i
\(176\) −3.19089 −0.240522
\(177\) 0 0
\(178\) −1.83443 0.596044i −0.137497 0.0446754i
\(179\) 7.23182 22.2572i 0.540532 1.66358i −0.190852 0.981619i \(-0.561125\pi\)
0.731384 0.681966i \(-0.238875\pi\)
\(180\) 0 0
\(181\) −7.36808 22.6766i −0.547665 1.68554i −0.714567 0.699567i \(-0.753376\pi\)
0.166902 0.985974i \(-0.446624\pi\)
\(182\) 3.82432i 0.283477i
\(183\) 0 0
\(184\) 4.53019 + 3.29138i 0.333970 + 0.242644i
\(185\) 7.31702 9.11361i 0.537958 0.670046i
\(186\) 0 0
\(187\) 4.25680 5.85899i 0.311288 0.428452i
\(188\) 4.25325 5.85410i 0.310200 0.426954i
\(189\) 0 0
\(190\) 6.57512 8.18955i 0.477009 0.594132i
\(191\) −10.1616 7.38286i −0.735270 0.534205i 0.155956 0.987764i \(-0.450154\pi\)
−0.891226 + 0.453559i \(0.850154\pi\)
\(192\) 0 0
\(193\) 5.70634i 0.410751i −0.978683 0.205376i \(-0.934158\pi\)
0.978683 0.205376i \(-0.0658416\pi\)
\(194\) 5.11887 + 15.7543i 0.367513 + 1.13109i
\(195\) 0 0
\(196\) −1.85878 + 5.72074i −0.132770 + 0.408625i
\(197\) 15.8269 + 5.14248i 1.12762 + 0.366387i 0.812672 0.582722i \(-0.198012\pi\)
0.314950 + 0.949108i \(0.398012\pi\)
\(198\) 0 0
\(199\) −10.6260 −0.753254 −0.376627 0.926365i \(-0.622916\pi\)
−0.376627 + 0.926365i \(0.622916\pi\)
\(200\) 4.88185 1.08052i 0.345199 0.0764044i
\(201\) 0 0
\(202\) 9.67114 + 13.3112i 0.680459 + 0.936571i
\(203\) 6.89971 + 2.24185i 0.484265 + 0.157347i
\(204\) 0 0
\(205\) −1.98099 1.59047i −0.138358 0.111083i
\(206\) 2.89588 + 8.91260i 0.201766 + 0.620971i
\(207\) 0 0
\(208\) 3.66500 1.19083i 0.254122 0.0825693i
\(209\) 12.1248 + 8.80917i 0.838689 + 0.609343i
\(210\) 0 0
\(211\) 0.651586 0.473405i 0.0448570 0.0325905i −0.565131 0.825001i \(-0.691174\pi\)
0.609988 + 0.792411i \(0.291174\pi\)
\(212\) −2.47771 + 3.41027i −0.170170 + 0.234219i
\(213\) 0 0
\(214\) −6.85715 + 4.98201i −0.468745 + 0.340563i
\(215\) −0.741608 + 15.3843i −0.0505773 + 1.04920i
\(216\) 0 0
\(217\) 5.51998 1.79355i 0.374721 0.121754i
\(218\) 15.1377i 1.02526i
\(219\) 0 0
\(220\) 1.87556 + 6.88413i 0.126450 + 0.464128i
\(221\) −2.70274 + 8.31817i −0.181806 + 0.559540i
\(222\) 0 0
\(223\) −9.46004 13.0206i −0.633491 0.871926i 0.364756 0.931103i \(-0.381152\pi\)
−0.998247 + 0.0591772i \(0.981152\pi\)
\(224\) −0.992398 −0.0663074
\(225\) 0 0
\(226\) 5.10532 0.339601
\(227\) 8.08813 + 11.1324i 0.536828 + 0.738881i 0.988152 0.153480i \(-0.0490479\pi\)
−0.451323 + 0.892360i \(0.649048\pi\)
\(228\) 0 0
\(229\) 4.58275 14.1043i 0.302837 0.932036i −0.677639 0.735395i \(-0.736997\pi\)
0.980476 0.196641i \(-0.0630034\pi\)
\(230\) 4.43814 11.7082i 0.292642 0.772016i
\(231\) 0 0
\(232\) 7.31036i 0.479949i
\(233\) −0.842292 + 0.273677i −0.0551804 + 0.0179292i −0.336477 0.941692i \(-0.609235\pi\)
0.281297 + 0.959621i \(0.409235\pi\)
\(234\) 0 0
\(235\) −15.1298 5.73515i −0.986961 0.374120i
\(236\) 5.55591 4.03660i 0.361659 0.262760i
\(237\) 0 0
\(238\) 1.32391 1.82220i 0.0858162 0.118116i
\(239\) 17.6874 12.8506i 1.14410 0.831239i 0.156417 0.987691i \(-0.450006\pi\)
0.987686 + 0.156452i \(0.0500056\pi\)
\(240\) 0 0
\(241\) 9.21929 + 6.69821i 0.593867 + 0.431469i 0.843697 0.536820i \(-0.180375\pi\)
−0.249830 + 0.968290i \(0.580375\pi\)
\(242\) 0.778174 0.252844i 0.0500229 0.0162534i
\(243\) 0 0
\(244\) 3.41958 + 10.5244i 0.218916 + 0.673754i
\(245\) 13.4347 + 0.647626i 0.858310 + 0.0413753i
\(246\) 0 0
\(247\) −17.2139 5.59313i −1.09529 0.355883i
\(248\) −3.43767 4.73154i −0.218292 0.300453i
\(249\) 0 0
\(250\) −5.20063 9.89714i −0.328917 0.625950i
\(251\) 10.3970 0.656250 0.328125 0.944634i \(-0.393583\pi\)
0.328125 + 0.944634i \(0.393583\pi\)
\(252\) 0 0
\(253\) 16.9933 + 5.52145i 1.06836 + 0.347131i
\(254\) −1.35238 + 4.16221i −0.0848561 + 0.261160i
\(255\) 0 0
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) 19.6467i 1.22553i −0.790266 0.612763i \(-0.790058\pi\)
0.790266 0.612763i \(-0.209942\pi\)
\(258\) 0 0
\(259\) 4.19642 + 3.04888i 0.260753 + 0.189448i
\(260\) −4.72337 7.20704i −0.292931 0.446962i
\(261\) 0 0
\(262\) 2.97926 4.10060i 0.184060 0.253336i
\(263\) −5.32150 + 7.32442i −0.328138 + 0.451643i −0.940930 0.338601i \(-0.890046\pi\)
0.612792 + 0.790244i \(0.290046\pi\)
\(264\) 0 0
\(265\) 8.81379 + 3.34098i 0.541427 + 0.205235i
\(266\) 3.77093 + 2.73974i 0.231210 + 0.167984i
\(267\) 0 0
\(268\) 13.1045i 0.800483i
\(269\) 9.18078 + 28.2555i 0.559762 + 1.72277i 0.683024 + 0.730395i \(0.260664\pi\)
−0.123263 + 0.992374i \(0.539336\pi\)
\(270\) 0 0
\(271\) 1.29803 3.99491i 0.0788495 0.242674i −0.903860 0.427829i \(-0.859279\pi\)
0.982709 + 0.185155i \(0.0592787\pi\)
\(272\) −2.15854 0.701351i −0.130881 0.0425257i
\(273\) 0 0
\(274\) 2.33886 0.141296
\(275\) 13.7496 8.09277i 0.829132 0.488013i
\(276\) 0 0
\(277\) 13.2634 + 18.2555i 0.796919 + 1.09686i 0.993212 + 0.116319i \(0.0371095\pi\)
−0.196293 + 0.980545i \(0.562890\pi\)
\(278\) −1.73503 0.563746i −0.104060 0.0338112i
\(279\) 0 0
\(280\) 0.583317 + 2.14103i 0.0348599 + 0.127951i
\(281\) −2.08103 6.40474i −0.124144 0.382075i 0.869600 0.493756i \(-0.164376\pi\)
−0.993744 + 0.111681i \(0.964376\pi\)
\(282\) 0 0
\(283\) 8.89142 2.88900i 0.528540 0.171733i −0.0325774 0.999469i \(-0.510372\pi\)
0.561118 + 0.827736i \(0.310372\pi\)
\(284\) 1.76833 + 1.28477i 0.104931 + 0.0762368i
\(285\) 0 0
\(286\) 9.94804 7.22768i 0.588240 0.427381i
\(287\) 0.662723 0.912160i 0.0391193 0.0538431i
\(288\) 0 0
\(289\) −9.58590 + 6.96456i −0.563877 + 0.409680i
\(290\) −15.7716 + 4.29692i −0.926140 + 0.252324i
\(291\) 0 0
\(292\) −2.71370 + 0.881735i −0.158807 + 0.0515996i
\(293\) 5.03444i 0.294115i −0.989128 0.147058i \(-0.953020\pi\)
0.989128 0.147058i \(-0.0469803\pi\)
\(294\) 0 0
\(295\) −11.9744 9.61383i −0.697175 0.559739i
\(296\) 1.61517 4.97097i 0.0938796 0.288932i
\(297\) 0 0
\(298\) 14.0435 + 19.3292i 0.813515 + 1.11971i
\(299\) −21.5788 −1.24793
\(300\) 0 0
\(301\) −6.83570 −0.394003
\(302\) 4.70144 + 6.47097i 0.270537 + 0.372363i
\(303\) 0 0
\(304\) 1.45140 4.46695i 0.0832435 0.256197i
\(305\) 20.6956 13.5636i 1.18503 0.776648i
\(306\) 0 0
\(307\) 24.3696i 1.39085i 0.718600 + 0.695424i \(0.244783\pi\)
−0.718600 + 0.695424i \(0.755217\pi\)
\(308\) −3.01165 + 0.978544i −0.171605 + 0.0557577i
\(309\) 0 0
\(310\) −8.18737 + 10.1977i −0.465011 + 0.579188i
\(311\) −13.9864 + 10.1617i −0.793098 + 0.576219i −0.908881 0.417055i \(-0.863062\pi\)
0.115783 + 0.993275i \(0.463062\pi\)
\(312\) 0 0
\(313\) −0.0734148 + 0.101047i −0.00414965 + 0.00571151i −0.811087 0.584926i \(-0.801124\pi\)
0.806937 + 0.590637i \(0.201124\pi\)
\(314\) −4.20798 + 3.05728i −0.237470 + 0.172532i
\(315\) 0 0
\(316\) −9.02379 6.55616i −0.507628 0.368813i
\(317\) 20.3368 6.60782i 1.14223 0.371132i 0.324017 0.946051i \(-0.394966\pi\)
0.818210 + 0.574919i \(0.194966\pi\)
\(318\) 0 0
\(319\) −7.20830 22.1849i −0.403587 1.24211i
\(320\) 1.87020 1.22570i 0.104548 0.0685187i
\(321\) 0 0
\(322\) 5.28508 + 1.71723i 0.294526 + 0.0956973i
\(323\) 6.26580 + 8.62413i 0.348638 + 0.479860i
\(324\) 0 0
\(325\) −12.7724 + 14.4265i −0.708483 + 0.800241i
\(326\) 18.3385 1.01567
\(327\) 0 0
\(328\) −1.08052 0.351083i −0.0596618 0.0193853i
\(329\) 2.21907 6.82960i 0.122341 0.376528i
\(330\) 0 0
\(331\) 9.25913 + 28.4967i 0.508928 + 1.56632i 0.794065 + 0.607833i \(0.207961\pi\)
−0.285137 + 0.958487i \(0.592039\pi\)
\(332\) 10.3878i 0.570102i
\(333\) 0 0
\(334\) −19.4202 14.1096i −1.06262 0.772042i
\(335\) −28.2720 + 7.70261i −1.54466 + 0.420839i
\(336\) 0 0
\(337\) 9.17918 12.6341i 0.500022 0.688221i −0.482175 0.876075i \(-0.660153\pi\)
0.982197 + 0.187854i \(0.0601532\pi\)
\(338\) −1.08760 + 1.49695i −0.0591575 + 0.0814234i
\(339\) 0 0
\(340\) −0.244361 + 5.06914i −0.0132523 + 0.274913i
\(341\) −15.0978 10.9692i −0.817594 0.594017i
\(342\) 0 0
\(343\) 12.9162i 0.697410i
\(344\) 2.12853 + 6.55093i 0.114762 + 0.353202i
\(345\) 0 0
\(346\) −4.72976 + 14.5567i −0.254273 + 0.782573i
\(347\) −32.8612 10.6773i −1.76408 0.573185i −0.766472 0.642277i \(-0.777990\pi\)
−0.997610 + 0.0690922i \(0.977990\pi\)
\(348\) 0 0
\(349\) −18.9109 −1.01228 −0.506139 0.862452i \(-0.668928\pi\)
−0.506139 + 0.862452i \(0.668928\pi\)
\(350\) 4.27626 2.51693i 0.228576 0.134536i
\(351\) 0 0
\(352\) 1.87556 + 2.58148i 0.0999676 + 0.137594i
\(353\) −29.1745 9.47936i −1.55280 0.504535i −0.597928 0.801550i \(-0.704009\pi\)
−0.954873 + 0.297015i \(0.904009\pi\)
\(354\) 0 0
\(355\) 1.73240 4.57021i 0.0919460 0.242562i
\(356\) 0.596044 + 1.83443i 0.0315902 + 0.0972248i
\(357\) 0 0
\(358\) −22.2572 + 7.23182i −1.17633 + 0.382213i
\(359\) −3.02381 2.19693i −0.159590 0.115949i 0.505124 0.863047i \(-0.331447\pi\)
−0.664714 + 0.747098i \(0.731447\pi\)
\(360\) 0 0
\(361\) −2.47575 + 1.79874i −0.130303 + 0.0946703i
\(362\) −14.0149 + 19.2899i −0.736608 + 1.01385i
\(363\) 0 0
\(364\) 3.09394 2.24788i 0.162166 0.117821i
\(365\) 3.49736 + 5.33635i 0.183060 + 0.279317i
\(366\) 0 0
\(367\) 16.3640 5.31699i 0.854194 0.277544i 0.150992 0.988535i \(-0.451753\pi\)
0.703202 + 0.710990i \(0.251753\pi\)
\(368\) 5.59963i 0.291901i
\(369\) 0 0
\(370\) −11.6739 0.562747i −0.606897 0.0292558i
\(371\) −1.29271 + 3.97854i −0.0671140 + 0.206556i
\(372\) 0 0
\(373\) −15.4109 21.2113i −0.797948 1.09828i −0.993073 0.117503i \(-0.962511\pi\)
0.195124 0.980778i \(-0.437489\pi\)
\(374\) −7.24211 −0.374480
\(375\) 0 0
\(376\) −7.23607 −0.373172
\(377\) 16.5587 + 22.7911i 0.852815 + 1.17380i
\(378\) 0 0
\(379\) −5.77908 + 17.7862i −0.296851 + 0.913614i 0.685742 + 0.727845i \(0.259478\pi\)
−0.982593 + 0.185770i \(0.940522\pi\)
\(380\) −10.4902 0.505688i −0.538138 0.0259412i
\(381\) 0 0
\(382\) 12.5605i 0.642649i
\(383\) 0.620541 0.201626i 0.0317082 0.0103026i −0.293120 0.956076i \(-0.594694\pi\)
0.324828 + 0.945773i \(0.394694\pi\)
\(384\) 0 0
\(385\) 3.88134 + 5.92225i 0.197812 + 0.301826i
\(386\) −4.61653 + 3.35410i −0.234975 + 0.170719i
\(387\) 0 0
\(388\) 9.73667 13.4014i 0.494305 0.680352i
\(389\) 2.20848 1.60456i 0.111974 0.0813542i −0.530389 0.847755i \(-0.677954\pi\)
0.642363 + 0.766400i \(0.277954\pi\)
\(390\) 0 0
\(391\) 10.2818 + 7.47018i 0.519974 + 0.377783i
\(392\) 5.72074 1.85878i 0.288941 0.0938827i
\(393\) 0 0
\(394\) −5.14248 15.8269i −0.259074 0.797349i
\(395\) −8.84042 + 23.3218i −0.444810 + 1.17345i
\(396\) 0 0
\(397\) 21.5908 + 7.01527i 1.08361 + 0.352086i 0.795774 0.605594i \(-0.207064\pi\)
0.287836 + 0.957680i \(0.407064\pi\)
\(398\) 6.24578 + 8.59658i 0.313073 + 0.430908i
\(399\) 0 0
\(400\) −3.74364 3.31439i −0.187182 0.165719i
\(401\) −26.1671 −1.30672 −0.653362 0.757045i \(-0.726642\pi\)
−0.653362 + 0.757045i \(0.726642\pi\)
\(402\) 0 0
\(403\) 21.4348 + 6.96459i 1.06774 + 0.346931i
\(404\) 5.08442 15.6482i 0.252959 0.778528i
\(405\) 0 0
\(406\) −2.24185 6.89971i −0.111261 0.342427i
\(407\) 16.6781i 0.826703i
\(408\) 0 0
\(409\) −7.05454 5.12543i −0.348825 0.253436i 0.399551 0.916711i \(-0.369166\pi\)
−0.748376 + 0.663275i \(0.769166\pi\)
\(410\) −0.122322 + 2.53751i −0.00604106 + 0.125319i
\(411\) 0 0
\(412\) 5.50829 7.58151i 0.271374 0.373514i
\(413\) 4.00592 5.51367i 0.197118 0.271310i
\(414\) 0 0
\(415\) −22.4109 + 6.10577i −1.10011 + 0.299720i
\(416\) −3.11764 2.26510i −0.152855 0.111056i
\(417\) 0 0
\(418\) 14.9871i 0.733041i
\(419\) 3.24062 + 9.97361i 0.158315 + 0.487243i 0.998482 0.0550852i \(-0.0175430\pi\)
−0.840167 + 0.542328i \(0.817543\pi\)
\(420\) 0 0
\(421\) −7.49324 + 23.0618i −0.365198 + 1.12397i 0.584658 + 0.811280i \(0.301229\pi\)
−0.949857 + 0.312685i \(0.898771\pi\)
\(422\) −0.765985 0.248884i −0.0372876 0.0121155i
\(423\) 0 0
\(424\) 4.21533 0.204715
\(425\) 11.0799 2.45237i 0.537456 0.118958i
\(426\) 0 0
\(427\) 6.45498 + 8.88451i 0.312378 + 0.429952i
\(428\) 8.06107 + 2.61920i 0.389646 + 0.126604i
\(429\) 0 0
\(430\) 12.8821 8.44269i 0.621228 0.407143i
\(431\) −0.741608 2.28244i −0.0357220 0.109941i 0.931606 0.363471i \(-0.118408\pi\)
−0.967328 + 0.253530i \(0.918408\pi\)
\(432\) 0 0
\(433\) 37.4703 12.1748i 1.80071 0.585086i 0.800805 0.598925i \(-0.204405\pi\)
0.999904 + 0.0138396i \(0.00440543\pi\)
\(434\) −4.69558 3.41154i −0.225395 0.163759i
\(435\) 0 0
\(436\) −12.2467 + 8.89774i −0.586510 + 0.426125i
\(437\) −15.4590 + 21.2775i −0.739506 + 1.01784i
\(438\) 0 0
\(439\) 32.2528 23.4330i 1.53934 1.11840i 0.588598 0.808426i \(-0.299680\pi\)
0.950746 0.309972i \(-0.100320\pi\)
\(440\) 4.46695 5.56375i 0.212953 0.265241i
\(441\) 0 0
\(442\) 8.31817 2.70274i 0.395655 0.128556i
\(443\) 20.2834i 0.963696i 0.876255 + 0.481848i \(0.160034\pi\)
−0.876255 + 0.481848i \(0.839966\pi\)
\(444\) 0 0
\(445\) 3.60732 2.36418i 0.171003 0.112073i
\(446\) −4.97344 + 15.3067i −0.235499 + 0.724792i
\(447\) 0 0
\(448\) 0.583317 + 0.802867i 0.0275591 + 0.0379319i
\(449\) −41.6650 −1.96629 −0.983147 0.182819i \(-0.941478\pi\)
−0.983147 + 0.182819i \(0.941478\pi\)
\(450\) 0 0
\(451\) −3.62526 −0.170707
\(452\) −3.00083 4.13029i −0.141147 0.194272i
\(453\) 0 0
\(454\) 4.25218 13.0869i 0.199565 0.614198i
\(455\) −6.66821 5.35369i −0.312611 0.250985i
\(456\) 0 0
\(457\) 2.32297i 0.108664i 0.998523 + 0.0543319i \(0.0173029\pi\)
−0.998523 + 0.0543319i \(0.982697\pi\)
\(458\) −14.1043 + 4.58275i −0.659049 + 0.214138i
\(459\) 0 0
\(460\) −12.0808 + 3.29138i −0.563271 + 0.153461i
\(461\) 4.25272 3.08979i 0.198069 0.143906i −0.484330 0.874885i \(-0.660937\pi\)
0.682399 + 0.730980i \(0.260937\pi\)
\(462\) 0 0
\(463\) 16.6900 22.9718i 0.775650 1.06759i −0.220099 0.975478i \(-0.570638\pi\)
0.995749 0.0921126i \(-0.0293620\pi\)
\(464\) −5.91420 + 4.29692i −0.274560 + 0.199480i
\(465\) 0 0
\(466\) 0.716497 + 0.520565i 0.0331911 + 0.0241147i
\(467\) −21.5655 + 7.00707i −0.997934 + 0.324249i −0.762040 0.647530i \(-0.775802\pi\)
−0.235895 + 0.971779i \(0.575802\pi\)
\(468\) 0 0
\(469\) −4.01872 12.3684i −0.185567 0.571117i
\(470\) 4.25325 + 15.6113i 0.196188 + 0.720096i
\(471\) 0 0
\(472\) −6.53136 2.12217i −0.300630 0.0976807i
\(473\) 12.9189 + 17.7814i 0.594014 + 0.817590i
\(474\) 0 0
\(475\) 5.07502 + 22.9292i 0.232858 + 1.05206i
\(476\) −2.25237 −0.103237
\(477\) 0 0
\(478\) −20.7928 6.75598i −0.951040 0.309012i
\(479\) 12.8774 39.6326i 0.588383 1.81086i 0.00314730 0.999995i \(-0.498998\pi\)
0.585236 0.810863i \(-0.301002\pi\)
\(480\) 0 0
\(481\) 6.22423 + 19.1562i 0.283800 + 0.873447i
\(482\) 11.3957i 0.519059i
\(483\) 0 0
\(484\) −0.661954 0.480938i −0.0300888 0.0218608i
\(485\) −34.6356 13.1291i −1.57272 0.596160i
\(486\) 0 0
\(487\) 13.5877 18.7019i 0.615719 0.847464i −0.381314 0.924446i \(-0.624528\pi\)
0.997033 + 0.0769816i \(0.0245283\pi\)
\(488\) 6.50442 8.95256i 0.294441 0.405264i
\(489\) 0 0
\(490\) −7.37276 11.2495i −0.333067 0.508203i
\(491\) 33.1199 + 24.0630i 1.49468 + 1.08595i 0.972441 + 0.233147i \(0.0749025\pi\)
0.522237 + 0.852800i \(0.325098\pi\)
\(492\) 0 0
\(493\) 16.5917i 0.747254i
\(494\) 5.59313 + 17.2139i 0.251647 + 0.774490i
\(495\) 0 0
\(496\) −1.80729 + 5.56226i −0.0811497 + 0.249753i
\(497\) 2.06299 + 0.670307i 0.0925378 + 0.0300674i
\(498\) 0 0
\(499\) 7.87697 0.352622 0.176311 0.984335i \(-0.443584\pi\)
0.176311 + 0.984335i \(0.443584\pi\)
\(500\) −4.95010 + 10.0248i −0.221375 + 0.448322i
\(501\) 0 0
\(502\) −6.11118 8.41132i −0.272755 0.375416i
\(503\) 6.58276 + 2.13887i 0.293511 + 0.0953674i 0.452071 0.891982i \(-0.350685\pi\)
−0.158561 + 0.987349i \(0.550685\pi\)
\(504\) 0 0
\(505\) −36.7485 1.77148i −1.63529 0.0788299i
\(506\) −5.52145 16.9933i −0.245459 0.755444i
\(507\) 0 0
\(508\) 4.16221 1.35238i 0.184668 0.0600023i
\(509\) −8.20925 5.96437i −0.363869 0.264366i 0.390795 0.920478i \(-0.372200\pi\)
−0.754664 + 0.656112i \(0.772200\pi\)
\(510\) 0 0
\(511\) −2.29086 + 1.66441i −0.101342 + 0.0736292i
\(512\) 0.587785 0.809017i 0.0259767 0.0357538i
\(513\) 0 0
\(514\) −15.8945 + 11.5480i −0.701077 + 0.509362i
\(515\) −19.5943 7.42746i −0.863427 0.327293i
\(516\) 0 0
\(517\) −21.9594 + 7.13505i −0.965774 + 0.313799i
\(518\) 5.18706i 0.227906i
\(519\) 0 0
\(520\) −3.05429 + 8.05748i −0.133939 + 0.353344i
\(521\) 4.12922 12.7084i 0.180904 0.556766i −0.818949 0.573866i \(-0.805443\pi\)
0.999854 + 0.0170994i \(0.00544318\pi\)
\(522\) 0 0
\(523\) −4.34954 5.98663i −0.190192 0.261777i 0.703263 0.710930i \(-0.251726\pi\)
−0.893455 + 0.449153i \(0.851726\pi\)
\(524\) −5.06863 −0.221424
\(525\) 0 0
\(526\) 9.05348 0.394750
\(527\) −7.80220 10.7388i −0.339869 0.467790i
\(528\) 0 0
\(529\) −2.58209 + 7.94686i −0.112265 + 0.345516i
\(530\) −2.47771 9.09429i −0.107625 0.395031i
\(531\) 0 0
\(532\) 4.66112i 0.202085i
\(533\) 4.16391 1.35294i 0.180359 0.0586022i
\(534\) 0 0
\(535\) 0.912566 18.9307i 0.0394536 0.818446i
\(536\) −10.6017 + 7.70261i −0.457925 + 0.332702i
\(537\) 0 0
\(538\) 17.4629 24.0356i 0.752878 1.03625i
\(539\) 15.5280 11.2818i 0.668838 0.485940i
\(540\) 0 0
\(541\) 20.6625 + 15.0122i 0.888350 + 0.645424i 0.935447 0.353466i \(-0.114997\pi\)
−0.0470972 + 0.998890i \(0.514997\pi\)
\(542\) −3.99491 + 1.29803i −0.171596 + 0.0557550i
\(543\) 0 0
\(544\) 0.701351 + 2.15854i 0.0300702 + 0.0925465i
\(545\) 26.3947 + 21.1914i 1.13062 + 0.907741i
\(546\) 0 0
\(547\) 24.9282 + 8.09966i 1.06585 + 0.346317i 0.788871 0.614559i \(-0.210666\pi\)
0.276982 + 0.960875i \(0.410666\pi\)
\(548\) −1.37475 1.89218i −0.0587263 0.0808298i
\(549\) 0 0
\(550\) −14.6290 6.36685i −0.623783 0.271483i
\(551\) 34.3355 1.46274
\(552\) 0 0
\(553\) −10.5275 3.42058i −0.447673 0.145458i
\(554\) 6.97297 21.4606i 0.296253 0.911773i
\(555\) 0 0
\(556\) 0.563746 + 1.73503i 0.0239081 + 0.0735817i
\(557\) 5.75884i 0.244010i −0.992529 0.122005i \(-0.961068\pi\)
0.992529 0.122005i \(-0.0389324\pi\)
\(558\) 0 0
\(559\) −21.4745 15.6021i −0.908273 0.659899i
\(560\) 1.38927 1.73038i 0.0587072 0.0731219i
\(561\) 0 0
\(562\) −3.95835 + 5.44820i −0.166973 + 0.229818i
\(563\) −3.71075 + 5.10741i −0.156390 + 0.215252i −0.880021 0.474935i \(-0.842472\pi\)
0.723631 + 0.690187i \(0.242472\pi\)
\(564\) 0 0
\(565\) −7.14697 + 8.90180i −0.300675 + 0.374502i
\(566\) −7.56350 5.49520i −0.317917 0.230981i
\(567\) 0 0
\(568\) 2.18577i 0.0917130i
\(569\) 9.21364 + 28.3567i 0.386256 + 1.18877i 0.935565 + 0.353154i \(0.114891\pi\)
−0.549309 + 0.835619i \(0.685109\pi\)
\(570\) 0 0
\(571\) −9.34861 + 28.7721i −0.391227 + 1.20407i 0.540634 + 0.841258i \(0.318184\pi\)
−0.931861 + 0.362815i \(0.881816\pi\)
\(572\) −11.6946 3.79981i −0.488977 0.158878i
\(573\) 0 0
\(574\) −1.12749 −0.0470606
\(575\) 14.2018 + 24.1289i 0.592258 + 1.00624i
\(576\) 0 0
\(577\) 18.2932 + 25.1784i 0.761554 + 1.04819i 0.997083 + 0.0763219i \(0.0243177\pi\)
−0.235529 + 0.971867i \(0.575682\pi\)
\(578\) 11.2689 + 3.66149i 0.468725 + 0.152298i
\(579\) 0 0
\(580\) 12.7466 + 10.2338i 0.529273 + 0.424936i
\(581\) −3.18559 9.80424i −0.132161 0.406748i
\(582\) 0 0
\(583\) 12.7923 4.15648i 0.529805 0.172144i
\(584\) 2.30841 + 1.67716i 0.0955228 + 0.0694014i
\(585\) 0 0
\(586\) −4.07295 + 2.95917i −0.168252 + 0.122242i
\(587\) −4.55905 + 6.27500i −0.188172 + 0.258997i −0.892672 0.450708i \(-0.851172\pi\)
0.704499 + 0.709705i \(0.251172\pi\)
\(588\) 0 0
\(589\) 22.2233 16.1461i 0.915693 0.665290i
\(590\) −0.739393 + 15.3383i −0.0304403 + 0.631469i
\(591\) 0 0
\(592\) −4.97097 + 1.61517i −0.204306 + 0.0663829i
\(593\) 24.6122i 1.01070i −0.862914 0.505351i \(-0.831363\pi\)
0.862914 0.505351i \(-0.168637\pi\)
\(594\) 0 0
\(595\) 1.32391 + 4.85933i 0.0542749 + 0.199213i
\(596\) 7.38308 22.7228i 0.302423 0.930762i
\(597\) 0 0
\(598\) 12.6837 + 17.4576i 0.518675 + 0.713895i
\(599\) −18.4703 −0.754675 −0.377337 0.926076i \(-0.623160\pi\)
−0.377337 + 0.926076i \(0.623160\pi\)
\(600\) 0 0
\(601\) −14.2568 −0.581547 −0.290774 0.956792i \(-0.593913\pi\)
−0.290774 + 0.956792i \(0.593913\pi\)
\(602\) 4.01792 + 5.53019i 0.163758 + 0.225394i
\(603\) 0 0
\(604\) 2.47169 7.60708i 0.100572 0.309528i
\(605\) −0.648503 + 1.71081i −0.0263654 + 0.0695543i
\(606\) 0 0
\(607\) 1.70894i 0.0693637i 0.999398 + 0.0346819i \(0.0110418\pi\)
−0.999398 + 0.0346819i \(0.988958\pi\)
\(608\) −4.46695 + 1.45140i −0.181159 + 0.0588620i
\(609\) 0 0
\(610\) −23.1377 8.77065i −0.936820 0.355113i
\(611\) 22.5594 16.3904i 0.912657 0.663084i
\(612\) 0 0
\(613\) −17.1588 + 23.6171i −0.693038 + 0.953885i 0.306959 + 0.951723i \(0.400688\pi\)
−0.999998 + 0.00216283i \(0.999312\pi\)
\(614\) 19.7154 14.3241i 0.795650 0.578074i
\(615\) 0 0
\(616\) 2.56186 + 1.86130i 0.103220 + 0.0749940i
\(617\) 20.1736 6.55479i 0.812158 0.263886i 0.126646 0.991948i \(-0.459579\pi\)
0.685511 + 0.728062i \(0.259579\pi\)
\(618\) 0 0
\(619\) −2.59372 7.98266i −0.104251 0.320850i 0.885303 0.465014i \(-0.153951\pi\)
−0.989554 + 0.144164i \(0.953951\pi\)
\(620\) 13.0625 + 0.629685i 0.524603 + 0.0252888i
\(621\) 0 0
\(622\) 16.4420 + 5.34234i 0.659266 + 0.214208i
\(623\) 1.12512 + 1.54860i 0.0450771 + 0.0620434i
\(624\) 0 0
\(625\) 24.5374 + 4.78708i 0.981496 + 0.191483i
\(626\) 0.124901 0.00499204
\(627\) 0 0
\(628\) 4.94678 + 1.60731i 0.197398 + 0.0641385i
\(629\) 3.66581 11.2822i 0.146166 0.449851i
\(630\) 0 0
\(631\) −6.42507 19.7743i −0.255778 0.787204i −0.993675 0.112291i \(-0.964181\pi\)
0.737897 0.674913i \(-0.235819\pi\)
\(632\) 11.1540i 0.443683i
\(633\) 0 0
\(634\) −17.2995 12.5688i −0.687051 0.499172i
\(635\) −5.36416 8.18477i −0.212870 0.324803i
\(636\) 0 0
\(637\) −13.6249 + 18.7530i −0.539838 + 0.743023i
\(638\) −13.7110 + 18.8716i −0.542824 + 0.747133i
\(639\) 0 0
\(640\) −2.09089 0.792578i −0.0826497 0.0313294i
\(641\) 6.22913 + 4.52573i 0.246036 + 0.178756i 0.703968 0.710232i \(-0.251410\pi\)
−0.457932 + 0.888987i \(0.651410\pi\)
\(642\) 0 0
\(643\) 18.3706i 0.724467i −0.932087 0.362234i \(-0.882014\pi\)
0.932087 0.362234i \(-0.117986\pi\)
\(644\) −1.71723 5.28508i −0.0676682 0.208261i
\(645\) 0 0
\(646\) 3.29413 10.1383i 0.129606 0.398885i
\(647\) −40.8863 13.2848i −1.60741 0.522278i −0.638482 0.769636i \(-0.720437\pi\)
−0.968924 + 0.247358i \(0.920437\pi\)
\(648\) 0 0
\(649\) −21.9134 −0.860175
\(650\) 19.1787 + 1.85335i 0.752251 + 0.0726943i
\(651\) 0 0
\(652\) −10.7791 14.8361i −0.422141 0.581028i
\(653\) 9.30596 + 3.02369i 0.364170 + 0.118326i 0.485386 0.874300i \(-0.338679\pi\)
−0.121215 + 0.992626i \(0.538679\pi\)
\(654\) 0 0
\(655\) 2.97926 + 10.9352i 0.116409 + 0.427274i
\(656\) 0.351083 + 1.08052i 0.0137075 + 0.0421873i
\(657\) 0 0
\(658\) −6.82960 + 2.21907i −0.266245 + 0.0865084i
\(659\) 35.4038 + 25.7224i 1.37914 + 1.00200i 0.996960 + 0.0779123i \(0.0248254\pi\)
0.382177 + 0.924089i \(0.375175\pi\)
\(660\) 0 0
\(661\) −20.8527 + 15.1503i −0.811075 + 0.589280i −0.914142 0.405394i \(-0.867134\pi\)
0.103067 + 0.994674i \(0.467134\pi\)
\(662\) 17.6119 24.2407i 0.684507 0.942143i
\(663\) 0 0
\(664\) −8.40387 + 6.10577i −0.326133 + 0.236950i
\(665\) −10.0561 + 2.73974i −0.389957 + 0.106243i
\(666\) 0 0
\(667\) 38.9318 12.6497i 1.50744 0.489798i
\(668\) 24.0047i 0.928768i
\(669\) 0 0
\(670\) 22.8494 + 18.3450i 0.882749 + 0.708731i
\(671\) 10.9115 33.5821i 0.421233 1.29642i
\(672\) 0 0
\(673\) −1.83966 2.53207i −0.0709135 0.0976041i 0.772087 0.635517i \(-0.219213\pi\)
−0.843000 + 0.537913i \(0.819213\pi\)
\(674\) −15.6165 −0.601527
\(675\) 0 0
\(676\) 1.85033 0.0711666
\(677\) 20.4250 + 28.1126i 0.784996 + 1.08045i 0.994713 + 0.102692i \(0.0327456\pi\)
−0.209717 + 0.977762i \(0.567254\pi\)
\(678\) 0 0
\(679\) 5.07996 15.6345i 0.194951 0.599997i
\(680\) 4.24465 2.78187i 0.162775 0.106680i
\(681\) 0 0
\(682\) 18.6620i 0.714603i
\(683\) 39.7609 12.9191i 1.52141 0.494336i 0.575234 0.817989i \(-0.304911\pi\)
0.946176 + 0.323653i \(0.104911\pi\)
\(684\) 0 0
\(685\) −3.27419 + 4.07812i −0.125100 + 0.155817i
\(686\) 10.4494 7.59196i 0.398961 0.289862i
\(687\) 0 0
\(688\) 4.04870 5.57255i 0.154355 0.212452i
\(689\) −13.1419 + 9.54813i −0.500666 + 0.363755i
\(690\) 0 0
\(691\) −10.5080 7.63452i −0.399744 0.290431i 0.369693 0.929154i \(-0.379463\pi\)
−0.769437 + 0.638723i \(0.779463\pi\)
\(692\) 14.5567 4.72976i 0.553363 0.179798i
\(693\) 0 0
\(694\) 10.6773 + 32.8612i 0.405303 + 1.24739i
\(695\) 3.41185 2.23607i 0.129419 0.0848189i
\(696\) 0 0
\(697\) −2.45237 0.796825i −0.0928903 0.0301819i
\(698\) 11.1156 + 15.2993i 0.420730 + 0.579085i
\(699\) 0 0
\(700\) −4.54977 1.98015i −0.171965 0.0748427i
\(701\) 19.9966 0.755261 0.377630 0.925956i \(-0.376739\pi\)
0.377630 + 0.925956i \(0.376739\pi\)
\(702\) 0 0
\(703\) 23.3478 + 7.58616i 0.880579 + 0.286117i
\(704\) 0.986039 3.03472i 0.0371628 0.114375i
\(705\) 0 0
\(706\) 9.47936 + 29.1745i 0.356760 + 1.09800i
\(707\) 16.3284i 0.614094i
\(708\) 0 0
\(709\) 3.75564 + 2.72863i 0.141046 + 0.102476i 0.656071 0.754699i \(-0.272217\pi\)
−0.515025 + 0.857175i \(0.672217\pi\)
\(710\) −4.71566 + 1.28477i −0.176975 + 0.0482164i
\(711\) 0 0
\(712\) 1.13374 1.56046i 0.0424888 0.0584808i
\(713\) 19.2497 26.4949i 0.720906 0.992241i
\(714\) 0 0
\(715\) −1.32391 + 27.4638i −0.0495114 + 1.02709i
\(716\) 18.9331 + 13.7557i 0.707565 + 0.514076i
\(717\) 0 0
\(718\) 3.73763i 0.139487i
\(719\) −3.34562 10.2968i −0.124771 0.384005i 0.869089 0.494657i \(-0.164706\pi\)
−0.993859 + 0.110652i \(0.964706\pi\)
\(720\) 0 0
\(721\) 2.87387 8.84485i 0.107028 0.329400i
\(722\) 2.91042 + 0.945652i 0.108314 + 0.0351935i
\(723\) 0 0
\(724\) 23.8436 0.886141
\(725\) 14.5865 33.5152i 0.541729 1.24472i
\(726\) 0 0
\(727\) −16.3513 22.5057i −0.606437 0.834689i 0.389842 0.920882i \(-0.372530\pi\)
−0.996278 + 0.0861932i \(0.972530\pi\)
\(728\) −3.63714 1.18178i −0.134802 0.0437997i
\(729\) 0 0
\(730\) 2.26151 5.96605i 0.0837021 0.220813i
\(731\) 4.83095 + 14.8681i 0.178679 + 0.549917i
\(732\) 0 0
\(733\) 10.1351 3.29309i 0.374348 0.121633i −0.115799 0.993273i \(-0.536943\pi\)
0.490148 + 0.871639i \(0.336943\pi\)
\(734\) −13.9201 10.1135i −0.513799 0.373296i
\(735\) 0 0
\(736\) −4.53019 + 3.29138i −0.166985 + 0.121322i
\(737\) −24.5782 + 33.8290i −0.905349 + 1.24611i
\(738\) 0 0
\(739\) −21.4485 + 15.5832i −0.788994 + 0.573238i −0.907665 0.419696i \(-0.862137\pi\)
0.118671 + 0.992934i \(0.462137\pi\)
\(740\) 6.40647 + 9.77516i 0.235507 + 0.359342i
\(741\) 0 0
\(742\) 3.97854 1.29271i 0.146057 0.0474568i
\(743\) 4.29218i 0.157465i 0.996896 + 0.0787325i \(0.0250873\pi\)
−0.996896 + 0.0787325i \(0.974913\pi\)
\(744\) 0 0
\(745\) −53.3625 2.57237i −1.95505 0.0942443i
\(746\) −8.10201 + 24.9354i −0.296636 + 0.912951i
\(747\) 0 0
\(748\) 4.25680 + 5.85899i 0.155644 + 0.214226i
\(749\) 8.41148 0.307349
\(750\) 0 0
\(751\) 24.1035 0.879549 0.439774 0.898108i \(-0.355058\pi\)
0.439774 + 0.898108i \(0.355058\pi\)
\(752\) 4.25325 + 5.85410i 0.155100 + 0.213477i
\(753\) 0 0
\(754\) 8.70541 26.7925i 0.317032 0.975725i
\(755\) −17.8646 0.861172i −0.650159 0.0313412i
\(756\) 0 0
\(757\) 37.3911i 1.35900i −0.733674 0.679502i \(-0.762196\pi\)
0.733674 0.679502i \(-0.237804\pi\)
\(758\) 17.7862 5.77908i 0.646023 0.209906i
\(759\) 0 0
\(760\) 5.75690 + 8.78402i 0.208825 + 0.318630i
\(761\) −28.5644 + 20.7533i −1.03546 + 0.752305i −0.969394 0.245510i \(-0.921045\pi\)
−0.0660654 + 0.997815i \(0.521045\pi\)
\(762\) 0 0
\(763\) −8.83010 + 12.1536i −0.319671 + 0.439990i
\(764\) 10.1616 7.38286i 0.367635 0.267102i
\(765\) 0 0
\(766\) −0.527864 0.383516i −0.0190725 0.0138570i
\(767\) 25.1693 8.17801i 0.908812 0.295291i
\(768\) 0 0
\(769\) −4.66718 14.3641i −0.168303 0.517982i 0.830962 0.556329i \(-0.187791\pi\)
−0.999264 + 0.0383471i \(0.987791\pi\)
\(770\) 2.50980 6.62108i 0.0904471 0.238607i
\(771\) 0 0
\(772\) 5.42705 + 1.76336i 0.195324 + 0.0634646i
\(773\) −20.9839 28.8818i −0.754737 1.03881i −0.997634 0.0687538i \(-0.978098\pi\)
0.242897 0.970052i \(-0.421902\pi\)
\(774\) 0 0
\(775\) −6.31944 28.5516i −0.227001 1.02560i
\(776\) −16.5650 −0.594649
\(777\) 0 0
\(778\) −2.59623 0.843565i −0.0930792 0.0302433i
\(779\) 1.64898 5.07502i 0.0590807 0.181832i
\(780\) 0 0
\(781\) −2.15526 6.63320i −0.0771212 0.237355i
\(782\) 12.7090i 0.454474i
\(783\) 0 0
\(784\) −4.86635 3.53561i −0.173798 0.126272i
\(785\) 0.560008 11.6171i 0.0199875 0.414632i
\(786\) 0 0
\(787\) −19.7169 + 27.1379i −0.702830 + 0.967363i 0.297091 + 0.954849i \(0.403983\pi\)
−0.999922 + 0.0125140i \(0.996017\pi\)
\(788\) −9.78158 + 13.4632i −0.348454 + 0.479606i
\(789\) 0 0
\(790\) 24.0640 6.55616i 0.856159 0.233258i
\(791\) −4.09889 2.97802i −0.145740 0.105886i
\(792\) 0 0
\(793\) 42.6440i 1.51433i
\(794\) −7.01527 21.5908i −0.248963 0.766228i
\(795\) 0 0
\(796\) 3.28360 10.1059i 0.116384 0.358194i
\(797\) −4.41143 1.43336i −0.156261 0.0507723i 0.229842 0.973228i \(-0.426179\pi\)
−0.386103 + 0.922456i \(0.626179\pi\)
\(798\) 0 0
\(799\) −16.4231 −0.581008
\(800\) −0.480938 + 4.97682i −0.0170037 + 0.175957i
\(801\) 0 0
\(802\) 15.3807 + 21.1697i 0.543110 + 0.747527i
\(803\) 8.65912 + 2.81352i 0.305574 + 0.0992869i
\(804\) 0 0
\(805\) −10.3928 + 6.81129i −0.366299 + 0.240066i
\(806\) −6.96459 21.4348i −0.245317 0.755009i
\(807\) 0 0
\(808\) −15.6482 + 5.08442i −0.550503 + 0.178869i
\(809\) 9.20558 + 6.68825i 0.323651 + 0.235146i 0.737732 0.675094i \(-0.235897\pi\)
−0.414081 + 0.910240i \(0.635897\pi\)
\(810\) 0 0
\(811\) 25.9772 18.8735i 0.912183 0.662740i −0.0293830 0.999568i \(-0.509354\pi\)
0.941566 + 0.336828i \(0.109354\pi\)
\(812\) −4.26426 + 5.86925i −0.149646 + 0.205970i
\(813\) 0 0
\(814\) −13.4929 + 9.80315i −0.472925 + 0.343600i
\(815\) −25.6721 + 31.9756i −0.899256 + 1.12006i
\(816\) 0 0
\(817\) −30.7686 + 9.99732i −1.07646 + 0.349762i
\(818\) 8.71989i 0.304884i
\(819\) 0 0
\(820\) 2.12479 1.39255i 0.0742009 0.0486300i
\(821\) −16.0525 + 49.4045i −0.560236 + 1.72423i 0.121461 + 0.992596i \(0.461242\pi\)
−0.681697 + 0.731634i \(0.738758\pi\)
\(822\) 0 0
\(823\) −32.1554 44.2582i −1.12087 1.54274i −0.804350 0.594155i \(-0.797486\pi\)
−0.316518 0.948587i \(-0.602514\pi\)
\(824\) −9.37127 −0.326464
\(825\) 0 0
\(826\) −6.81527 −0.237134
\(827\) −20.9773 28.8727i −0.729451 1.00400i −0.999157 0.0410607i \(-0.986926\pi\)
0.269705 0.962943i \(-0.413074\pi\)
\(828\) 0 0
\(829\) −10.8942 + 33.5288i −0.378370 + 1.16450i 0.562807 + 0.826588i \(0.309721\pi\)
−0.941177 + 0.337914i \(0.890279\pi\)
\(830\) 18.1124 + 14.5419i 0.628692 + 0.504756i
\(831\) 0 0
\(832\) 3.85361i 0.133600i
\(833\) 12.9839 4.21873i 0.449866 0.146170i
\(834\) 0 0
\(835\) 51.7884 14.1096i 1.79221 0.488282i
\(836\) −12.1248 + 8.80917i −0.419345 + 0.304672i
\(837\) 0 0
\(838\) 6.16403 8.48406i 0.212933 0.293077i
\(839\) 30.1946 21.9377i 1.04243 0.757373i 0.0716748 0.997428i \(-0.477166\pi\)
0.970759 + 0.240055i \(0.0771656\pi\)
\(840\) 0 0
\(841\) −19.7735 14.3663i −0.681844 0.495388i
\(842\) 23.0618 7.49324i 0.794763 0.258234i
\(843\) 0 0
\(844\) 0.248884 + 0.765985i 0.00856693 + 0.0263663i
\(845\) −1.08760 3.99196i −0.0374145 0.137328i
\(846\) 0 0
\(847\) −0.772258 0.250922i −0.0265351 0.00862178i
\(848\) −2.47771 3.41027i −0.0850849 0.117109i
\(849\) 0 0
\(850\) −8.49664 7.52240i −0.291432 0.258016i
\(851\) 29.2681 1.00330
\(852\) 0 0
\(853\) −20.7438 6.74007i −0.710254 0.230776i −0.0684615 0.997654i \(-0.521809\pi\)
−0.641793 + 0.766878i \(0.721809\pi\)
\(854\) 3.39358 10.4444i 0.116126 0.357399i
\(855\) 0 0
\(856\) −2.61920 8.06107i −0.0895224 0.275522i
\(857\) 19.1130i 0.652889i 0.945216 + 0.326445i \(0.105851\pi\)
−0.945216 + 0.326445i \(0.894149\pi\)
\(858\) 0 0
\(859\) 24.5197 + 17.8146i 0.836602 + 0.607827i 0.921419 0.388570i \(-0.127031\pi\)
−0.0848177 + 0.996396i \(0.527031\pi\)
\(860\) −14.4022 5.45932i −0.491110 0.186161i
\(861\) 0 0
\(862\) −1.41062 + 1.94156i −0.0480460 + 0.0661297i
\(863\) −25.6283 + 35.2743i −0.872396 + 1.20075i 0.106073 + 0.994358i \(0.466172\pi\)
−0.978469 + 0.206392i \(0.933828\pi\)
\(864\) 0 0
\(865\) −18.7603 28.6250i −0.637871 0.973279i
\(866\) −31.8742 23.1579i −1.08313 0.786939i
\(867\) 0 0
\(868\) 5.80405i 0.197002i
\(869\) 10.9983 + 33.8493i 0.373092 + 1.14826i
\(870\) 0 0
\(871\) 15.6052 48.0279i 0.528763 1.62736i
\(872\) 14.3968 + 4.67782i 0.487539 + 0.158411i
\(873\) 0 0
\(874\) 26.3005 0.889627
\(875\) −1.59776 + 10.9797i −0.0540140 + 0.371182i
\(876\) 0 0
\(877\) −10.8557 14.9416i −0.366570 0.504541i 0.585394 0.810749i \(-0.300940\pi\)
−0.951965 + 0.306208i \(0.900940\pi\)
\(878\) −37.9155 12.3195i −1.27959 0.415762i
\(879\) 0 0
\(880\) −7.12677 0.343550i −0.240243 0.0115811i
\(881\) −9.98946 30.7444i −0.336553 1.03581i −0.965952 0.258722i \(-0.916699\pi\)
0.629398 0.777083i \(-0.283301\pi\)
\(882\) 0 0
\(883\) 22.7220 7.38283i 0.764657 0.248452i 0.0993809 0.995049i \(-0.468314\pi\)
0.665276 + 0.746597i \(0.268314\pi\)
\(884\) −7.07585 5.14091i −0.237987 0.172907i
\(885\) 0 0
\(886\) 16.4097 11.9223i 0.551293 0.400538i
\(887\) −13.4359 + 18.4929i −0.451132 + 0.620930i −0.972640 0.232316i \(-0.925370\pi\)
0.521508 + 0.853246i \(0.325370\pi\)
\(888\) 0 0
\(889\) 3.51367 2.55283i 0.117845 0.0856192i
\(890\) −4.03299 1.52875i −0.135186 0.0512439i
\(891\) 0 0
\(892\) 15.3067 4.97344i 0.512505 0.166523i
\(893\) 33.9866i 1.13732i
\(894\) 0 0
\(895\) 18.5484 48.9324i 0.620006 1.63563i
\(896\) 0.306668 0.943827i 0.0102451 0.0315310i
\(897\) 0 0
\(898\) 24.4901 + 33.7077i 0.817244 + 1.12484i
\(899\) −42.7547 −1.42595
\(900\) 0 0
\(901\) 9.56720 0.318730
\(902\) 2.13087 + 2.93290i 0.0709503 + 0.0976548i
\(903\) 0 0
\(904\) −1.57763 + 4.85544i −0.0524712 + 0.161490i
\(905\) −14.0149 51.4410i −0.465872 1.70996i
\(906\) 0 0
\(907\) 7.20307i 0.239174i 0.992824 + 0.119587i \(0.0381570\pi\)
−0.992824 + 0.119587i \(0.961843\pi\)
\(908\) −13.0869 + 4.25218i −0.434303 + 0.141114i
\(909\) 0 0
\(910\) −0.411749 + 8.54152i −0.0136493 + 0.283149i
\(911\) 20.3748 14.8031i 0.675047 0.490450i −0.196664 0.980471i \(-0.563011\pi\)
0.871711 + 0.490021i \(0.163011\pi\)
\(912\) 0 0
\(913\) −19.4828 + 26.8158i −0.644788 + 0.887474i
\(914\) 1.87932 1.36541i 0.0621623 0.0451636i
\(915\) 0 0
\(916\) 11.9978 + 8.71692i 0.396419 + 0.288015i
\(917\) −4.78391 + 1.55439i −0.157979 + 0.0513303i
\(918\) 0 0
\(919\) 4.59171 + 14.1318i 0.151466 + 0.466166i 0.997786 0.0665102i \(-0.0211865\pi\)
−0.846319 + 0.532676i \(0.821186\pi\)
\(920\) 9.76370 + 7.83896i 0.321900 + 0.258443i
\(921\) 0 0
\(922\) −4.99938 1.62440i −0.164646 0.0534966i
\(923\) 4.95099 + 6.81445i 0.162964 + 0.224300i
\(924\) 0 0
\(925\) 17.3236 19.5672i 0.569596 0.643366i
\(926\) −28.3947 −0.933108
\(927\) 0 0
\(928\) 6.95256 + 2.25903i 0.228229 + 0.0741561i
\(929\) −18.3634 + 56.5166i −0.602482 + 1.85425i −0.0892298 + 0.996011i \(0.528441\pi\)
−0.513252 + 0.858238i \(0.671559\pi\)
\(930\) 0 0
\(931\) 8.73038 + 26.8693i 0.286127 + 0.880607i
\(932\) 0.885638i 0.0290101i
\(933\) 0 0
\(934\) 18.3447 + 13.3282i 0.600258 + 0.436113i
\(935\) 10.1383 12.6276i 0.331557 0.412966i
\(936\) 0 0
\(937\) 8.76118 12.0587i 0.286215 0.393941i −0.641565 0.767069i \(-0.721715\pi\)
0.927780 + 0.373127i \(0.121715\pi\)
\(938\) −7.64406 + 10.5211i −0.249587 + 0.343528i
\(939\) 0 0
\(940\) 10.1298 12.6171i 0.330398 0.411523i
\(941\) −5.12951 3.72681i −0.167217 0.121490i 0.501029 0.865430i \(-0.332955\pi\)
−0.668247 + 0.743940i \(0.732955\pi\)
\(942\) 0 0
\(943\) 6.36189i 0.207172i
\(944\) 2.12217 + 6.53136i 0.0690707 + 0.212578i
\(945\) 0 0
\(946\) 6.79189 20.9033i 0.220823 0.679625i
\(947\) −17.0473 5.53899i −0.553961 0.179993i 0.0186409 0.999826i \(-0.494066\pi\)
−0.572602 + 0.819833i \(0.694066\pi\)
\(948\) 0 0
\(949\) −10.9957 −0.356936
\(950\) 15.5671 17.5832i 0.505063 0.570476i
\(951\) 0 0
\(952\) 1.32391 + 1.82220i 0.0429081 + 0.0590580i
\(953\) −6.52939 2.12153i −0.211508 0.0687230i 0.201347 0.979520i \(-0.435468\pi\)
−0.412855 + 0.910797i \(0.635468\pi\)
\(954\) 0 0
\(955\) −21.9009 17.5835i −0.708695 0.568988i
\(956\) 6.75598 + 20.7928i 0.218504 + 0.672487i
\(957\) 0 0
\(958\) −39.6326 + 12.8774i −1.28047 + 0.416050i
\(959\) −1.87779 1.36430i −0.0606371 0.0440554i
\(960\) 0 0
\(961\) −2.59297 + 1.88390i −0.0836440 + 0.0607710i
\(962\) 11.8392 16.2952i 0.381711 0.525379i
\(963\) 0 0
\(964\) −9.21929 + 6.69821i −0.296933 + 0.215735i
\(965\) 0.614378 12.7450i 0.0197775 0.410275i
\(966\) 0 0
\(967\) 8.38555 2.72463i 0.269661 0.0876182i −0.171065 0.985260i \(-0.554721\pi\)
0.440726 + 0.897641i \(0.354721\pi\)
\(968\) 0.818220i 0.0262986i
\(969\) 0 0
\(970\) 9.73667 + 35.7379i 0.312626 + 1.14747i
\(971\) −8.37280 + 25.7688i −0.268696 + 0.826961i 0.722123 + 0.691765i \(0.243167\pi\)
−0.990819 + 0.135197i \(0.956833\pi\)
\(972\) 0 0
\(973\) 1.06416 + 1.46469i 0.0341153 + 0.0469557i
\(974\) −23.1168 −0.740711
\(975\) 0 0
\(976\) −11.0660 −0.354213
\(977\) 12.3606 + 17.0130i 0.395452 + 0.544293i 0.959595 0.281384i \(-0.0907935\pi\)
−0.564144 + 0.825677i \(0.690794\pi\)
\(978\) 0 0
\(979\) 1.90191 5.85348i 0.0607853 0.187078i
\(980\) −4.76747 + 12.5770i −0.152291 + 0.401758i
\(981\) 0 0
\(982\) 40.9384i 1.30640i
\(983\) −44.7399 + 14.5369i −1.42698 + 0.463654i −0.917813 0.397013i \(-0.870047\pi\)
−0.509168 + 0.860667i \(0.670047\pi\)
\(984\) 0 0
\(985\) 34.7954 + 13.1896i 1.10867 + 0.420256i
\(986\) −13.4230 + 9.75238i −0.427475 + 0.310579i
\(987\) 0 0
\(988\) 10.6388 14.6430i 0.338464 0.465856i
\(989\) −31.2042 + 22.6712i −0.992237 + 0.720902i
\(990\) 0 0
\(991\) −40.2778 29.2635i −1.27947 0.929586i −0.279929 0.960021i \(-0.590311\pi\)
−0.999537 + 0.0304345i \(0.990311\pi\)
\(992\) 5.56226 1.80729i 0.176602 0.0573815i
\(993\) 0 0
\(994\) −0.670307 2.06299i −0.0212608 0.0654341i
\(995\) −23.7328 1.14405i −0.752380 0.0362689i
\(996\) 0 0
\(997\) −21.5340 6.99681i −0.681987 0.221591i −0.0525222 0.998620i \(-0.516726\pi\)
−0.629465 + 0.777029i \(0.716726\pi\)
\(998\) −4.62997 6.37261i −0.146559 0.201721i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 450.2.l.d.289.2 yes 16
3.2 odd 2 inner 450.2.l.d.289.3 yes 16
25.9 even 10 inner 450.2.l.d.109.2 16
75.59 odd 10 inner 450.2.l.d.109.3 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.l.d.109.2 16 25.9 even 10 inner
450.2.l.d.109.3 yes 16 75.59 odd 10 inner
450.2.l.d.289.2 yes 16 1.1 even 1 trivial
450.2.l.d.289.3 yes 16 3.2 odd 2 inner