Properties

Label 441.2.u.c.127.3
Level $441$
Weight $2$
Character 441.127
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(64,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.u (of order \(7\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{7})\)
Twist minimal: no (minimal twist has level 147)
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 127.3
Character \(\chi\) \(=\) 441.127
Dual form 441.2.u.c.316.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0441061 + 0.0212404i) q^{2} +(-1.24549 - 1.56179i) q^{4} +(0.763028 + 3.34304i) q^{5} +(1.92953 - 1.81022i) q^{7} +(-0.0435471 - 0.190792i) q^{8} +O(q^{10})\) \(q+(0.0441061 + 0.0212404i) q^{2} +(-1.24549 - 1.56179i) q^{4} +(0.763028 + 3.34304i) q^{5} +(1.92953 - 1.81022i) q^{7} +(-0.0435471 - 0.190792i) q^{8} +(-0.0373533 + 0.163656i) q^{10} +(-0.156245 - 0.0752435i) q^{11} +(2.72757 + 1.31353i) q^{13} +(0.123554 - 0.0388579i) q^{14} +(-0.886885 + 3.88570i) q^{16} +(1.10733 - 1.38855i) q^{17} +2.19549 q^{19} +(4.27079 - 5.35540i) q^{20} +(-0.00529315 - 0.00663740i) q^{22} +(4.46206 + 5.59525i) q^{23} +(-6.08889 + 2.93225i) q^{25} +(0.0924026 + 0.115869i) q^{26} +(-5.23039 - 0.758915i) q^{28} +(1.71227 - 2.14711i) q^{29} +10.3306 q^{31} +(-0.365683 + 0.458552i) q^{32} +(0.0783332 - 0.0377233i) q^{34} +(7.52394 + 5.06926i) q^{35} +(1.42405 - 1.78570i) q^{37} +(0.0968344 + 0.0466330i) q^{38} +(0.604600 - 0.291160i) q^{40} +(-2.16786 - 9.49800i) q^{41} +(-2.03116 + 8.89909i) q^{43} +(0.0770861 + 0.337736i) q^{44} +(0.0779589 + 0.341560i) q^{46} +(-5.51726 - 2.65697i) q^{47} +(0.446185 - 6.98577i) q^{49} -0.330839 q^{50} +(-1.34569 - 5.89587i) q^{52} +(-7.52725 - 9.43887i) q^{53} +(0.132323 - 0.579746i) q^{55} +(-0.429402 - 0.289310i) q^{56} +(0.121127 - 0.0583316i) q^{58} +(-2.75873 + 12.0868i) q^{59} +(-1.52035 + 1.90646i) q^{61} +(0.455640 + 0.219425i) q^{62} +(7.15598 - 3.44614i) q^{64} +(-2.30997 + 10.1206i) q^{65} -7.55109 q^{67} -3.54778 q^{68} +(0.224179 + 0.383396i) q^{70} +(3.70495 + 4.64586i) q^{71} +(-3.12362 + 1.50426i) q^{73} +(0.100738 - 0.0485131i) q^{74} +(-2.73445 - 3.42889i) q^{76} +(-0.437687 + 0.137653i) q^{77} -13.8888 q^{79} -13.6668 q^{80} +(0.106125 - 0.464966i) q^{82} +(-4.19369 + 2.01957i) q^{83} +(5.48689 + 2.64235i) q^{85} +(-0.278606 + 0.349361i) q^{86} +(-0.00755188 + 0.0330870i) q^{88} +(-5.43329 + 2.61654i) q^{89} +(7.64071 - 2.40302i) q^{91} +(3.18117 - 13.9376i) q^{92} +(-0.186910 - 0.234377i) q^{94} +(1.67522 + 7.33961i) q^{95} -4.03179 q^{97} +(0.168060 - 0.298638i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{3}{7}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0441061 + 0.0212404i 0.0311877 + 0.0150192i 0.449413 0.893324i \(-0.351633\pi\)
−0.418225 + 0.908344i \(0.637348\pi\)
\(3\) 0 0
\(4\) −1.24549 1.56179i −0.622743 0.780895i
\(5\) 0.763028 + 3.34304i 0.341236 + 1.49505i 0.796467 + 0.604681i \(0.206700\pi\)
−0.455231 + 0.890373i \(0.650443\pi\)
\(6\) 0 0
\(7\) 1.92953 1.81022i 0.729294 0.684200i
\(8\) −0.0435471 0.190792i −0.0153962 0.0674553i
\(9\) 0 0
\(10\) −0.0373533 + 0.163656i −0.0118122 + 0.0517524i
\(11\) −0.156245 0.0752435i −0.0471096 0.0226868i 0.410181 0.912004i \(-0.365466\pi\)
−0.457290 + 0.889318i \(0.651180\pi\)
\(12\) 0 0
\(13\) 2.72757 + 1.31353i 0.756492 + 0.364307i 0.772042 0.635572i \(-0.219236\pi\)
−0.0155499 + 0.999879i \(0.504950\pi\)
\(14\) 0.123554 0.0388579i 0.0330212 0.0103852i
\(15\) 0 0
\(16\) −0.886885 + 3.88570i −0.221721 + 0.971425i
\(17\) 1.10733 1.38855i 0.268567 0.336772i −0.629200 0.777244i \(-0.716617\pi\)
0.897767 + 0.440472i \(0.145189\pi\)
\(18\) 0 0
\(19\) 2.19549 0.503679 0.251840 0.967769i \(-0.418964\pi\)
0.251840 + 0.967769i \(0.418964\pi\)
\(20\) 4.27079 5.35540i 0.954978 1.19750i
\(21\) 0 0
\(22\) −0.00529315 0.00663740i −0.00112850 0.00141510i
\(23\) 4.46206 + 5.59525i 0.930404 + 1.16669i 0.985749 + 0.168222i \(0.0538026\pi\)
−0.0553453 + 0.998467i \(0.517626\pi\)
\(24\) 0 0
\(25\) −6.08889 + 2.93225i −1.21778 + 0.586451i
\(26\) 0.0924026 + 0.115869i 0.0181216 + 0.0227238i
\(27\) 0 0
\(28\) −5.23039 0.758915i −0.988451 0.143422i
\(29\) 1.71227 2.14711i 0.317960 0.398709i −0.597008 0.802235i \(-0.703644\pi\)
0.914968 + 0.403526i \(0.132215\pi\)
\(30\) 0 0
\(31\) 10.3306 1.85542 0.927711 0.373299i \(-0.121773\pi\)
0.927711 + 0.373299i \(0.121773\pi\)
\(32\) −0.365683 + 0.458552i −0.0646443 + 0.0810614i
\(33\) 0 0
\(34\) 0.0783332 0.0377233i 0.0134340 0.00646949i
\(35\) 7.52394 + 5.06926i 1.27178 + 0.856861i
\(36\) 0 0
\(37\) 1.42405 1.78570i 0.234113 0.293568i −0.650873 0.759187i \(-0.725597\pi\)
0.884985 + 0.465619i \(0.154168\pi\)
\(38\) 0.0968344 + 0.0466330i 0.0157086 + 0.00756487i
\(39\) 0 0
\(40\) 0.604600 0.291160i 0.0955956 0.0460364i
\(41\) −2.16786 9.49800i −0.338562 1.48334i −0.802061 0.597242i \(-0.796263\pi\)
0.463499 0.886097i \(-0.346594\pi\)
\(42\) 0 0
\(43\) −2.03116 + 8.89909i −0.309749 + 1.35710i 0.545165 + 0.838328i \(0.316467\pi\)
−0.854914 + 0.518769i \(0.826390\pi\)
\(44\) 0.0770861 + 0.337736i 0.0116212 + 0.0509156i
\(45\) 0 0
\(46\) 0.0779589 + 0.341560i 0.0114944 + 0.0503603i
\(47\) −5.51726 2.65697i −0.804775 0.387559i −0.0141806 0.999899i \(-0.504514\pi\)
−0.790594 + 0.612340i \(0.790228\pi\)
\(48\) 0 0
\(49\) 0.446185 6.98577i 0.0637407 0.997966i
\(50\) −0.330839 −0.0467877
\(51\) 0 0
\(52\) −1.34569 5.89587i −0.186614 0.817610i
\(53\) −7.52725 9.43887i −1.03395 1.29653i −0.954025 0.299728i \(-0.903104\pi\)
−0.0799225 0.996801i \(-0.525467\pi\)
\(54\) 0 0
\(55\) 0.132323 0.579746i 0.0178425 0.0781730i
\(56\) −0.429402 0.289310i −0.0573813 0.0386607i
\(57\) 0 0
\(58\) 0.121127 0.0583316i 0.0159047 0.00765932i
\(59\) −2.75873 + 12.0868i −0.359156 + 1.57356i 0.396146 + 0.918188i \(0.370347\pi\)
−0.755302 + 0.655377i \(0.772510\pi\)
\(60\) 0 0
\(61\) −1.52035 + 1.90646i −0.194661 + 0.244097i −0.869577 0.493798i \(-0.835608\pi\)
0.674916 + 0.737894i \(0.264180\pi\)
\(62\) 0.455640 + 0.219425i 0.0578664 + 0.0278670i
\(63\) 0 0
\(64\) 7.15598 3.44614i 0.894498 0.430767i
\(65\) −2.30997 + 10.1206i −0.286517 + 1.25531i
\(66\) 0 0
\(67\) −7.55109 −0.922513 −0.461256 0.887267i \(-0.652601\pi\)
−0.461256 + 0.887267i \(0.652601\pi\)
\(68\) −3.54778 −0.430231
\(69\) 0 0
\(70\) 0.224179 + 0.383396i 0.0267945 + 0.0458246i
\(71\) 3.70495 + 4.64586i 0.439696 + 0.551362i 0.951463 0.307763i \(-0.0995803\pi\)
−0.511767 + 0.859124i \(0.671009\pi\)
\(72\) 0 0
\(73\) −3.12362 + 1.50426i −0.365592 + 0.176060i −0.607656 0.794200i \(-0.707890\pi\)
0.242064 + 0.970260i \(0.422176\pi\)
\(74\) 0.100738 0.0485131i 0.0117106 0.00563953i
\(75\) 0 0
\(76\) −2.73445 3.42889i −0.313663 0.393321i
\(77\) −0.437687 + 0.137653i −0.0498791 + 0.0156870i
\(78\) 0 0
\(79\) −13.8888 −1.56261 −0.781307 0.624147i \(-0.785447\pi\)
−0.781307 + 0.624147i \(0.785447\pi\)
\(80\) −13.6668 −1.52799
\(81\) 0 0
\(82\) 0.106125 0.464966i 0.0117196 0.0513469i
\(83\) −4.19369 + 2.01957i −0.460317 + 0.221677i −0.649646 0.760237i \(-0.725083\pi\)
0.189329 + 0.981914i \(0.439369\pi\)
\(84\) 0 0
\(85\) 5.48689 + 2.64235i 0.595137 + 0.286603i
\(86\) −0.278606 + 0.349361i −0.0300429 + 0.0376726i
\(87\) 0 0
\(88\) −0.00755188 + 0.0330870i −0.000805033 + 0.00352708i
\(89\) −5.43329 + 2.61654i −0.575928 + 0.277352i −0.699089 0.715034i \(-0.746411\pi\)
0.123161 + 0.992387i \(0.460697\pi\)
\(90\) 0 0
\(91\) 7.64071 2.40302i 0.800964 0.251904i
\(92\) 3.18117 13.9376i 0.331659 1.45309i
\(93\) 0 0
\(94\) −0.186910 0.234377i −0.0192783 0.0241742i
\(95\) 1.67522 + 7.33961i 0.171874 + 0.753028i
\(96\) 0 0
\(97\) −4.03179 −0.409366 −0.204683 0.978828i \(-0.565616\pi\)
−0.204683 + 0.978828i \(0.565616\pi\)
\(98\) 0.168060 0.298638i 0.0169766 0.0301670i
\(99\) 0 0
\(100\) 12.1632 + 5.85748i 1.21632 + 0.585748i
\(101\) −0.404077 1.77038i −0.0402072 0.176159i 0.950837 0.309690i \(-0.100225\pi\)
−0.991045 + 0.133531i \(0.957368\pi\)
\(102\) 0 0
\(103\) −2.44367 10.7064i −0.240782 1.05493i −0.940308 0.340326i \(-0.889463\pi\)
0.699526 0.714607i \(-0.253395\pi\)
\(104\) 0.131833 0.577600i 0.0129273 0.0566383i
\(105\) 0 0
\(106\) −0.131512 0.576193i −0.0127736 0.0559648i
\(107\) 9.38522 4.51969i 0.907304 0.436934i 0.0787824 0.996892i \(-0.474897\pi\)
0.828521 + 0.559957i \(0.189182\pi\)
\(108\) 0 0
\(109\) 6.24606 + 3.00794i 0.598264 + 0.288109i 0.708404 0.705807i \(-0.249416\pi\)
−0.110140 + 0.993916i \(0.535130\pi\)
\(110\) 0.0181503 0.0227597i 0.00173056 0.00217006i
\(111\) 0 0
\(112\) 5.32271 + 9.10304i 0.502949 + 0.860156i
\(113\) −2.07851 + 1.00096i −0.195530 + 0.0941621i −0.529087 0.848568i \(-0.677465\pi\)
0.333557 + 0.942730i \(0.391751\pi\)
\(114\) 0 0
\(115\) −15.3005 + 19.1862i −1.42678 + 1.78912i
\(116\) −5.48594 −0.509357
\(117\) 0 0
\(118\) −0.378404 + 0.474504i −0.0348350 + 0.0436816i
\(119\) −0.376953 4.68376i −0.0345552 0.429359i
\(120\) 0 0
\(121\) −6.83964 8.57663i −0.621785 0.779694i
\(122\) −0.107550 + 0.0517935i −0.00973715 + 0.00468917i
\(123\) 0 0
\(124\) −12.8666 16.1342i −1.15545 1.44889i
\(125\) −3.75886 4.71346i −0.336203 0.421585i
\(126\) 0 0
\(127\) 5.11411 6.41289i 0.453804 0.569052i −0.501319 0.865263i \(-0.667152\pi\)
0.955123 + 0.296210i \(0.0957230\pi\)
\(128\) 1.56184 0.138049
\(129\) 0 0
\(130\) −0.316850 + 0.397317i −0.0277896 + 0.0348470i
\(131\) 5.02370 22.0103i 0.438922 1.92304i 0.0583427 0.998297i \(-0.481418\pi\)
0.380580 0.924748i \(-0.375724\pi\)
\(132\) 0 0
\(133\) 4.23626 3.97432i 0.367331 0.344618i
\(134\) −0.333049 0.160388i −0.0287711 0.0138554i
\(135\) 0 0
\(136\) −0.313145 0.150803i −0.0268520 0.0129312i
\(137\) −1.23748 + 5.42174i −0.105725 + 0.463210i 0.894156 + 0.447756i \(0.147777\pi\)
−0.999881 + 0.0154544i \(0.995081\pi\)
\(138\) 0 0
\(139\) −1.32002 5.78338i −0.111963 0.490540i −0.999553 0.0299059i \(-0.990479\pi\)
0.887590 0.460634i \(-0.152378\pi\)
\(140\) −1.45385 18.0645i −0.122872 1.52673i
\(141\) 0 0
\(142\) 0.0647310 + 0.283605i 0.00543210 + 0.0237996i
\(143\) −0.327334 0.410464i −0.0273731 0.0343247i
\(144\) 0 0
\(145\) 8.48440 + 4.08587i 0.704591 + 0.339313i
\(146\) −0.169722 −0.0140463
\(147\) 0 0
\(148\) −4.56253 −0.375038
\(149\) −10.5171 5.06479i −0.861597 0.414923i −0.0497281 0.998763i \(-0.515835\pi\)
−0.811869 + 0.583839i \(0.801550\pi\)
\(150\) 0 0
\(151\) 0.0429142 + 0.0538127i 0.00349231 + 0.00437922i 0.783575 0.621298i \(-0.213394\pi\)
−0.780082 + 0.625677i \(0.784823\pi\)
\(152\) −0.0956072 0.418882i −0.00775476 0.0339758i
\(153\) 0 0
\(154\) −0.0222285 0.00322529i −0.00179122 0.000259901i
\(155\) 7.88250 + 34.5355i 0.633138 + 2.77396i
\(156\) 0 0
\(157\) −3.31802 + 14.5372i −0.264806 + 1.16019i 0.651161 + 0.758940i \(0.274282\pi\)
−0.915967 + 0.401253i \(0.868575\pi\)
\(158\) −0.612581 0.295004i −0.0487344 0.0234692i
\(159\) 0 0
\(160\) −1.81199 0.872607i −0.143250 0.0689857i
\(161\) 18.7383 + 2.71888i 1.47679 + 0.214278i
\(162\) 0 0
\(163\) −3.24351 + 14.2107i −0.254051 + 1.11307i 0.673445 + 0.739237i \(0.264814\pi\)
−0.927496 + 0.373833i \(0.878043\pi\)
\(164\) −12.1338 + 15.2154i −0.947494 + 1.18812i
\(165\) 0 0
\(166\) −0.227864 −0.0176856
\(167\) 9.87406 12.3817i 0.764077 0.958123i −0.235829 0.971795i \(-0.575781\pi\)
0.999907 + 0.0136718i \(0.00435200\pi\)
\(168\) 0 0
\(169\) −2.39109 2.99833i −0.183930 0.230641i
\(170\) 0.185881 + 0.233087i 0.0142564 + 0.0178770i
\(171\) 0 0
\(172\) 16.4283 7.91144i 1.25264 0.603242i
\(173\) −7.71405 9.67311i −0.586488 0.735433i 0.396716 0.917941i \(-0.370150\pi\)
−0.983204 + 0.182509i \(0.941578\pi\)
\(174\) 0 0
\(175\) −6.44067 + 16.6801i −0.486869 + 1.26090i
\(176\) 0.430945 0.540388i 0.0324837 0.0407333i
\(177\) 0 0
\(178\) −0.295217 −0.0221275
\(179\) −8.89583 + 11.1550i −0.664906 + 0.833766i −0.993867 0.110578i \(-0.964730\pi\)
0.328962 + 0.944343i \(0.393301\pi\)
\(180\) 0 0
\(181\) −2.26203 + 1.08934i −0.168135 + 0.0809696i −0.516058 0.856553i \(-0.672601\pi\)
0.347923 + 0.937523i \(0.386887\pi\)
\(182\) 0.388043 + 0.0563040i 0.0287637 + 0.00417353i
\(183\) 0 0
\(184\) 0.873220 1.09498i 0.0643747 0.0807233i
\(185\) 7.05628 + 3.39813i 0.518788 + 0.249835i
\(186\) 0 0
\(187\) −0.277494 + 0.133634i −0.0202923 + 0.00977227i
\(188\) 2.72204 + 11.9260i 0.198525 + 0.869794i
\(189\) 0 0
\(190\) −0.0820088 + 0.359304i −0.00594954 + 0.0260666i
\(191\) 0.626443 + 2.74463i 0.0453278 + 0.198594i 0.992522 0.122067i \(-0.0389522\pi\)
−0.947194 + 0.320661i \(0.896095\pi\)
\(192\) 0 0
\(193\) 2.92073 + 12.7966i 0.210239 + 0.921116i 0.964404 + 0.264432i \(0.0851845\pi\)
−0.754166 + 0.656684i \(0.771958\pi\)
\(194\) −0.177826 0.0856367i −0.0127672 0.00614836i
\(195\) 0 0
\(196\) −11.4660 + 8.00382i −0.819001 + 0.571702i
\(197\) 25.8402 1.84104 0.920520 0.390695i \(-0.127765\pi\)
0.920520 + 0.390695i \(0.127765\pi\)
\(198\) 0 0
\(199\) −3.22207 14.1168i −0.228406 1.00071i −0.950940 0.309377i \(-0.899880\pi\)
0.722533 0.691336i \(-0.242978\pi\)
\(200\) 0.824605 + 1.03402i 0.0583084 + 0.0731164i
\(201\) 0 0
\(202\) 0.0197812 0.0866672i 0.00139180 0.00609788i
\(203\) −0.582883 7.24251i −0.0409104 0.508324i
\(204\) 0 0
\(205\) 30.0981 14.4945i 2.10214 1.01234i
\(206\) 0.119627 0.524122i 0.00833483 0.0365173i
\(207\) 0 0
\(208\) −7.52302 + 9.43357i −0.521627 + 0.654100i
\(209\) −0.343034 0.165196i −0.0237281 0.0114269i
\(210\) 0 0
\(211\) 7.22051 3.47721i 0.497080 0.239381i −0.168508 0.985700i \(-0.553895\pi\)
0.665588 + 0.746319i \(0.268181\pi\)
\(212\) −5.36645 + 23.5120i −0.368569 + 1.61481i
\(213\) 0 0
\(214\) 0.509945 0.0348591
\(215\) −31.2999 −2.13463
\(216\) 0 0
\(217\) 19.9331 18.7006i 1.35315 1.26948i
\(218\) 0.211599 + 0.265337i 0.0143313 + 0.0179709i
\(219\) 0 0
\(220\) −1.07025 + 0.515404i −0.0721561 + 0.0347486i
\(221\) 4.84421 2.33285i 0.325857 0.156924i
\(222\) 0 0
\(223\) 3.07653 + 3.85784i 0.206019 + 0.258340i 0.874097 0.485751i \(-0.161454\pi\)
−0.668078 + 0.744092i \(0.732883\pi\)
\(224\) 0.124485 + 1.54676i 0.00831748 + 0.103347i
\(225\) 0 0
\(226\) −0.112936 −0.00751236
\(227\) 13.5643 0.900293 0.450146 0.892955i \(-0.351372\pi\)
0.450146 + 0.892955i \(0.351372\pi\)
\(228\) 0 0
\(229\) −3.19641 + 14.0044i −0.211225 + 0.925436i 0.752512 + 0.658579i \(0.228842\pi\)
−0.963736 + 0.266857i \(0.914015\pi\)
\(230\) −1.08237 + 0.521240i −0.0713691 + 0.0343695i
\(231\) 0 0
\(232\) −0.484217 0.233187i −0.0317904 0.0153095i
\(233\) 8.86914 11.1216i 0.581037 0.728597i −0.401253 0.915967i \(-0.631425\pi\)
0.982289 + 0.187370i \(0.0599965\pi\)
\(234\) 0 0
\(235\) 4.67255 20.4718i 0.304804 1.33543i
\(236\) 22.3130 10.7454i 1.45245 0.699463i
\(237\) 0 0
\(238\) 0.0828588 0.214589i 0.00537094 0.0139097i
\(239\) −3.87374 + 16.9719i −0.250571 + 1.09782i 0.680432 + 0.732812i \(0.261792\pi\)
−0.931003 + 0.365012i \(0.881065\pi\)
\(240\) 0 0
\(241\) −13.9013 17.4317i −0.895462 1.12287i −0.991835 0.127528i \(-0.959296\pi\)
0.0963734 0.995345i \(-0.469276\pi\)
\(242\) −0.119499 0.523558i −0.00768167 0.0336556i
\(243\) 0 0
\(244\) 4.87105 0.311837
\(245\) 23.6942 3.83872i 1.51377 0.245247i
\(246\) 0 0
\(247\) 5.98835 + 2.88384i 0.381029 + 0.183494i
\(248\) −0.449866 1.97099i −0.0285665 0.125158i
\(249\) 0 0
\(250\) −0.0656729 0.287732i −0.00415352 0.0181978i
\(251\) −4.55597 + 19.9610i −0.287570 + 1.25993i 0.600279 + 0.799791i \(0.295056\pi\)
−0.887849 + 0.460136i \(0.847801\pi\)
\(252\) 0 0
\(253\) −0.276168 1.20997i −0.0173625 0.0760701i
\(254\) 0.361776 0.174222i 0.0226998 0.0109317i
\(255\) 0 0
\(256\) −14.2431 6.85911i −0.890192 0.428694i
\(257\) 12.7043 15.9307i 0.792472 0.993729i −0.207408 0.978255i \(-0.566503\pi\)
0.999880 0.0154744i \(-0.00492584\pi\)
\(258\) 0 0
\(259\) −0.484771 6.02343i −0.0301222 0.374278i
\(260\) 18.6834 8.99743i 1.15869 0.557997i
\(261\) 0 0
\(262\) 0.689082 0.864081i 0.0425716 0.0533831i
\(263\) −12.5861 −0.776090 −0.388045 0.921640i \(-0.626850\pi\)
−0.388045 + 0.921640i \(0.626850\pi\)
\(264\) 0 0
\(265\) 25.8111 32.3661i 1.58556 1.98823i
\(266\) 0.271261 0.0853120i 0.0166321 0.00523082i
\(267\) 0 0
\(268\) 9.40477 + 11.7932i 0.574488 + 0.720385i
\(269\) 15.1678 7.30444i 0.924799 0.445360i 0.0900168 0.995940i \(-0.471308\pi\)
0.834782 + 0.550581i \(0.185594\pi\)
\(270\) 0 0
\(271\) −0.0705992 0.0885286i −0.00428860 0.00537773i 0.779683 0.626175i \(-0.215380\pi\)
−0.783971 + 0.620797i \(0.786809\pi\)
\(272\) 4.41340 + 5.53423i 0.267602 + 0.335562i
\(273\) 0 0
\(274\) −0.169740 + 0.212847i −0.0102544 + 0.0128586i
\(275\) 1.17199 0.0706737
\(276\) 0 0
\(277\) −12.4437 + 15.6039i −0.747667 + 0.937545i −0.999543 0.0302148i \(-0.990381\pi\)
0.251877 + 0.967759i \(0.418952\pi\)
\(278\) 0.0646203 0.283120i 0.00387567 0.0169804i
\(279\) 0 0
\(280\) 0.639530 1.65626i 0.0382192 0.0989806i
\(281\) −27.8157 13.3953i −1.65935 0.799099i −0.998834 0.0482844i \(-0.984625\pi\)
−0.660513 0.750815i \(-0.729661\pi\)
\(282\) 0 0
\(283\) 20.6131 + 9.92675i 1.22532 + 0.590084i 0.930789 0.365557i \(-0.119122\pi\)
0.294533 + 0.955641i \(0.404836\pi\)
\(284\) 2.64139 11.5727i 0.156738 0.686713i
\(285\) 0 0
\(286\) −0.00571902 0.0250567i −0.000338173 0.00148163i
\(287\) −21.3765 14.4024i −1.26181 0.850146i
\(288\) 0 0
\(289\) 3.08097 + 13.4986i 0.181234 + 0.794036i
\(290\) 0.287428 + 0.360424i 0.0168784 + 0.0211648i
\(291\) 0 0
\(292\) 6.23976 + 3.00491i 0.365154 + 0.175849i
\(293\) 0.681514 0.0398145 0.0199072 0.999802i \(-0.493663\pi\)
0.0199072 + 0.999802i \(0.493663\pi\)
\(294\) 0 0
\(295\) −42.5116 −2.47512
\(296\) −0.402712 0.193936i −0.0234072 0.0112723i
\(297\) 0 0
\(298\) −0.356292 0.446776i −0.0206394 0.0258810i
\(299\) 4.82107 + 21.1225i 0.278809 + 1.22154i
\(300\) 0 0
\(301\) 12.1901 + 20.8479i 0.702628 + 1.20165i
\(302\) 0.000749776 0.00328498i 4.31447e−5 0.000189029i
\(303\) 0 0
\(304\) −1.94715 + 8.53100i −0.111676 + 0.489287i
\(305\) −7.53343 3.62791i −0.431363 0.207733i
\(306\) 0 0
\(307\) −7.44934 3.58741i −0.425156 0.204744i 0.209056 0.977904i \(-0.432961\pi\)
−0.634212 + 0.773159i \(0.718675\pi\)
\(308\) 0.760118 + 0.512130i 0.0433117 + 0.0291813i
\(309\) 0 0
\(310\) −0.385881 + 1.69065i −0.0219165 + 0.0960226i
\(311\) −7.73302 + 9.69689i −0.438499 + 0.549860i −0.951147 0.308738i \(-0.900093\pi\)
0.512648 + 0.858599i \(0.328665\pi\)
\(312\) 0 0
\(313\) −1.96289 −0.110949 −0.0554745 0.998460i \(-0.517667\pi\)
−0.0554745 + 0.998460i \(0.517667\pi\)
\(314\) −0.455120 + 0.570702i −0.0256839 + 0.0322066i
\(315\) 0 0
\(316\) 17.2983 + 21.6914i 0.973106 + 1.22024i
\(317\) −2.87381 3.60364i −0.161409 0.202401i 0.694550 0.719445i \(-0.255604\pi\)
−0.855959 + 0.517044i \(0.827032\pi\)
\(318\) 0 0
\(319\) −0.429089 + 0.206638i −0.0240244 + 0.0115695i
\(320\) 16.9808 + 21.2933i 0.949256 + 1.19033i
\(321\) 0 0
\(322\) 0.768724 + 0.517928i 0.0428393 + 0.0288630i
\(323\) 2.43113 3.04854i 0.135272 0.169625i
\(324\) 0 0
\(325\) −20.4595 −1.13489
\(326\) −0.444899 + 0.557886i −0.0246407 + 0.0308985i
\(327\) 0 0
\(328\) −1.71774 + 0.827221i −0.0948465 + 0.0456757i
\(329\) −15.4554 + 4.86076i −0.852086 + 0.267982i
\(330\) 0 0
\(331\) −9.50841 + 11.9232i −0.522630 + 0.655357i −0.971165 0.238408i \(-0.923374\pi\)
0.448535 + 0.893765i \(0.351946\pi\)
\(332\) 8.37732 + 4.03431i 0.459765 + 0.221411i
\(333\) 0 0
\(334\) 0.698497 0.336379i 0.0382201 0.0184058i
\(335\) −5.76169 25.2436i −0.314795 1.37921i
\(336\) 0 0
\(337\) −1.41355 + 6.19318i −0.0770011 + 0.337364i −0.998725 0.0504829i \(-0.983924\pi\)
0.921724 + 0.387847i \(0.126781\pi\)
\(338\) −0.0417759 0.183032i −0.00227231 0.00995563i
\(339\) 0 0
\(340\) −2.70705 11.8604i −0.146811 0.643219i
\(341\) −1.61410 0.777308i −0.0874082 0.0420936i
\(342\) 0 0
\(343\) −11.7849 14.2869i −0.636323 0.771423i
\(344\) 1.78633 0.0963124
\(345\) 0 0
\(346\) −0.134776 0.590492i −0.00724560 0.0317451i
\(347\) 9.62174 + 12.0653i 0.516522 + 0.647698i 0.969866 0.243637i \(-0.0783407\pi\)
−0.453344 + 0.891335i \(0.649769\pi\)
\(348\) 0 0
\(349\) −1.98224 + 8.68474i −0.106107 + 0.464884i 0.893760 + 0.448546i \(0.148058\pi\)
−0.999867 + 0.0163379i \(0.994799\pi\)
\(350\) −0.638365 + 0.598893i −0.0341220 + 0.0320122i
\(351\) 0 0
\(352\) 0.0916392 0.0441311i 0.00488439 0.00235220i
\(353\) 0.320591 1.40460i 0.0170634 0.0747594i −0.965679 0.259737i \(-0.916364\pi\)
0.982743 + 0.184978i \(0.0592213\pi\)
\(354\) 0 0
\(355\) −12.7043 + 15.9307i −0.674275 + 0.845515i
\(356\) 10.8536 + 5.22680i 0.575238 + 0.277020i
\(357\) 0 0
\(358\) −0.629297 + 0.303054i −0.0332594 + 0.0160169i
\(359\) −2.03265 + 8.90562i −0.107279 + 0.470021i 0.892539 + 0.450970i \(0.148922\pi\)
−0.999819 + 0.0190512i \(0.993935\pi\)
\(360\) 0 0
\(361\) −14.1798 −0.746307
\(362\) −0.122907 −0.00645985
\(363\) 0 0
\(364\) −13.2694 8.94026i −0.695506 0.468597i
\(365\) −7.41221 9.29461i −0.387973 0.486502i
\(366\) 0 0
\(367\) 24.5186 11.8075i 1.27986 0.616348i 0.334506 0.942393i \(-0.391430\pi\)
0.945354 + 0.326045i \(0.105716\pi\)
\(368\) −25.6988 + 12.3759i −1.33964 + 0.645137i
\(369\) 0 0
\(370\) 0.239048 + 0.299756i 0.0124275 + 0.0155836i
\(371\) −31.6105 4.58660i −1.64114 0.238125i
\(372\) 0 0
\(373\) −26.4804 −1.37110 −0.685551 0.728025i \(-0.740439\pi\)
−0.685551 + 0.728025i \(0.740439\pi\)
\(374\) −0.0150776 −0.000779643
\(375\) 0 0
\(376\) −0.266669 + 1.16835i −0.0137524 + 0.0602533i
\(377\) 7.49062 3.60729i 0.385787 0.185785i
\(378\) 0 0
\(379\) 6.81277 + 3.28086i 0.349948 + 0.168526i 0.600597 0.799552i \(-0.294930\pi\)
−0.250649 + 0.968078i \(0.580644\pi\)
\(380\) 9.37647 11.7577i 0.481003 0.603158i
\(381\) 0 0
\(382\) −0.0306669 + 0.134361i −0.00156906 + 0.00687449i
\(383\) −10.0694 + 4.84916i −0.514521 + 0.247780i −0.673081 0.739569i \(-0.735029\pi\)
0.158560 + 0.987349i \(0.449315\pi\)
\(384\) 0 0
\(385\) −0.794148 1.35817i −0.0404735 0.0692189i
\(386\) −0.142982 + 0.626443i −0.00727757 + 0.0318851i
\(387\) 0 0
\(388\) 5.02153 + 6.29680i 0.254930 + 0.319672i
\(389\) −4.51022 19.7606i −0.228677 1.00190i −0.950720 0.310052i \(-0.899654\pi\)
0.722043 0.691849i \(-0.243203\pi\)
\(390\) 0 0
\(391\) 12.7102 0.642784
\(392\) −1.35226 + 0.219081i −0.0682995 + 0.0110653i
\(393\) 0 0
\(394\) 1.13971 + 0.548856i 0.0574179 + 0.0276510i
\(395\) −10.5976 46.4309i −0.533221 2.33619i
\(396\) 0 0
\(397\) −0.449116 1.96770i −0.0225405 0.0987563i 0.962406 0.271613i \(-0.0875572\pi\)
−0.984947 + 0.172857i \(0.944700\pi\)
\(398\) 0.157733 0.691074i 0.00790645 0.0346404i
\(399\) 0 0
\(400\) −5.99371 26.2602i −0.299685 1.31301i
\(401\) −23.0932 + 11.1211i −1.15322 + 0.555361i −0.909999 0.414611i \(-0.863918\pi\)
−0.243219 + 0.969971i \(0.578203\pi\)
\(402\) 0 0
\(403\) 28.1773 + 13.5695i 1.40361 + 0.675944i
\(404\) −2.26168 + 2.83606i −0.112523 + 0.141099i
\(405\) 0 0
\(406\) 0.128125 0.331819i 0.00635873 0.0164679i
\(407\) −0.356864 + 0.171856i −0.0176891 + 0.00851861i
\(408\) 0 0
\(409\) 19.5306 24.4906i 0.965725 1.21098i −0.0117503 0.999931i \(-0.503740\pi\)
0.977475 0.211050i \(-0.0676882\pi\)
\(410\) 1.63538 0.0807656
\(411\) 0 0
\(412\) −13.6776 + 17.1512i −0.673847 + 0.844977i
\(413\) 16.5567 + 28.3157i 0.814703 + 1.39333i
\(414\) 0 0
\(415\) −9.95142 12.4787i −0.488496 0.612555i
\(416\) −1.59975 + 0.770398i −0.0784341 + 0.0377719i
\(417\) 0 0
\(418\) −0.0116210 0.0145723i −0.000568404 0.000712756i
\(419\) −13.6567 17.1249i −0.667172 0.836607i 0.326931 0.945048i \(-0.393986\pi\)
−0.994103 + 0.108441i \(0.965414\pi\)
\(420\) 0 0
\(421\) 15.7154 19.7065i 0.765920 0.960434i −0.234010 0.972234i \(-0.575185\pi\)
0.999930 + 0.0118004i \(0.00375629\pi\)
\(422\) 0.392326 0.0190981
\(423\) 0 0
\(424\) −1.47307 + 1.84718i −0.0715388 + 0.0897069i
\(425\) −2.67083 + 11.7017i −0.129554 + 0.567614i
\(426\) 0 0
\(427\) 0.517551 + 6.43073i 0.0250461 + 0.311205i
\(428\) −18.7480 9.02854i −0.906217 0.436411i
\(429\) 0 0
\(430\) −1.38051 0.664821i −0.0665743 0.0320605i
\(431\) 1.62140 7.10380i 0.0780999 0.342178i −0.920748 0.390157i \(-0.872421\pi\)
0.998848 + 0.0479786i \(0.0152779\pi\)
\(432\) 0 0
\(433\) −2.01722 8.83801i −0.0969413 0.424728i 0.903047 0.429542i \(-0.141325\pi\)
−0.999988 + 0.00481386i \(0.998468\pi\)
\(434\) 1.27638 0.401424i 0.0612682 0.0192689i
\(435\) 0 0
\(436\) −3.08160 13.5014i −0.147582 0.646599i
\(437\) 9.79640 + 12.2843i 0.468625 + 0.587638i
\(438\) 0 0
\(439\) −12.9362 6.22974i −0.617410 0.297329i 0.0989147 0.995096i \(-0.468463\pi\)
−0.716325 + 0.697767i \(0.754177\pi\)
\(440\) −0.116373 −0.00554789
\(441\) 0 0
\(442\) 0.263210 0.0125196
\(443\) −8.93121 4.30104i −0.424335 0.204349i 0.209514 0.977806i \(-0.432812\pi\)
−0.633849 + 0.773457i \(0.718526\pi\)
\(444\) 0 0
\(445\) −12.8929 16.1672i −0.611184 0.766401i
\(446\) 0.0537515 + 0.235501i 0.00254521 + 0.0111513i
\(447\) 0 0
\(448\) 7.56941 19.6034i 0.357621 0.926172i
\(449\) 1.87386 + 8.20992i 0.0884330 + 0.387450i 0.999703 0.0243585i \(-0.00775432\pi\)
−0.911270 + 0.411809i \(0.864897\pi\)
\(450\) 0 0
\(451\) −0.375947 + 1.64713i −0.0177026 + 0.0775604i
\(452\) 4.15204 + 1.99951i 0.195295 + 0.0940493i
\(453\) 0 0
\(454\) 0.598267 + 0.288110i 0.0280781 + 0.0135217i
\(455\) 13.8635 + 23.7097i 0.649929 + 1.11153i
\(456\) 0 0
\(457\) 6.67062 29.2259i 0.312038 1.36713i −0.539124 0.842227i \(-0.681244\pi\)
0.851162 0.524903i \(-0.175898\pi\)
\(458\) −0.438439 + 0.549786i −0.0204869 + 0.0256898i
\(459\) 0 0
\(460\) 49.0213 2.28563
\(461\) 6.92950 8.68931i 0.322739 0.404702i −0.593822 0.804596i \(-0.702382\pi\)
0.916561 + 0.399894i \(0.130953\pi\)
\(462\) 0 0
\(463\) −9.95467 12.4828i −0.462633 0.580123i 0.494717 0.869054i \(-0.335272\pi\)
−0.957350 + 0.288931i \(0.906700\pi\)
\(464\) 6.82445 + 8.55760i 0.316817 + 0.397276i
\(465\) 0 0
\(466\) 0.627409 0.302144i 0.0290642 0.0139966i
\(467\) 7.38867 + 9.26510i 0.341907 + 0.428738i 0.922822 0.385226i \(-0.125877\pi\)
−0.580915 + 0.813964i \(0.697305\pi\)
\(468\) 0 0
\(469\) −14.5701 + 13.6692i −0.672783 + 0.631183i
\(470\) 0.640916 0.803684i 0.0295633 0.0370712i
\(471\) 0 0
\(472\) 2.42620 0.111675
\(473\) 0.986957 1.23760i 0.0453803 0.0569051i
\(474\) 0 0
\(475\) −13.3681 + 6.43773i −0.613370 + 0.295383i
\(476\) −6.84555 + 6.42227i −0.313765 + 0.294364i
\(477\) 0 0
\(478\) −0.531346 + 0.666286i −0.0243032 + 0.0304752i
\(479\) −6.93808 3.34120i −0.317009 0.152663i 0.268612 0.963248i \(-0.413435\pi\)
−0.585621 + 0.810585i \(0.699149\pi\)
\(480\) 0 0
\(481\) 6.22978 3.00010i 0.284053 0.136793i
\(482\) −0.242877 1.06411i −0.0110627 0.0484690i
\(483\) 0 0
\(484\) −4.87623 + 21.3641i −0.221647 + 0.971097i
\(485\) −3.07637 13.4784i −0.139691 0.612025i
\(486\) 0 0
\(487\) 1.59077 + 6.96962i 0.0720847 + 0.315824i 0.998097 0.0616708i \(-0.0196429\pi\)
−0.926012 + 0.377494i \(0.876786\pi\)
\(488\) 0.429944 + 0.207050i 0.0194626 + 0.00937271i
\(489\) 0 0
\(490\) 1.12659 + 0.333962i 0.0508943 + 0.0150869i
\(491\) −16.5694 −0.747765 −0.373882 0.927476i \(-0.621974\pi\)
−0.373882 + 0.927476i \(0.621974\pi\)
\(492\) 0 0
\(493\) −1.08533 4.75512i −0.0488806 0.214160i
\(494\) 0.202869 + 0.254389i 0.00912750 + 0.0114455i
\(495\) 0 0
\(496\) −9.16202 + 40.1414i −0.411387 + 1.80240i
\(497\) 15.5588 + 2.25755i 0.697910 + 0.101265i
\(498\) 0 0
\(499\) −4.85575 + 2.33840i −0.217373 + 0.104681i −0.539402 0.842049i \(-0.681350\pi\)
0.322029 + 0.946730i \(0.395635\pi\)
\(500\) −2.67983 + 11.7411i −0.119846 + 0.525078i
\(501\) 0 0
\(502\) −0.624925 + 0.783631i −0.0278918 + 0.0349752i
\(503\) −6.28116 3.02485i −0.280063 0.134871i 0.288580 0.957456i \(-0.406817\pi\)
−0.568643 + 0.822585i \(0.692531\pi\)
\(504\) 0 0
\(505\) 5.61013 2.70169i 0.249647 0.120224i
\(506\) 0.0135195 0.0592329i 0.000601016 0.00263322i
\(507\) 0 0
\(508\) −16.3851 −0.726973
\(509\) −21.5845 −0.956718 −0.478359 0.878164i \(-0.658768\pi\)
−0.478359 + 0.878164i \(0.658768\pi\)
\(510\) 0 0
\(511\) −3.30409 + 8.55696i −0.146164 + 0.378538i
\(512\) −2.43010 3.04725i −0.107396 0.134671i
\(513\) 0 0
\(514\) 0.898711 0.432796i 0.0396404 0.0190898i
\(515\) 33.9274 16.3386i 1.49502 0.719963i
\(516\) 0 0
\(517\) 0.662123 + 0.830276i 0.0291201 + 0.0365155i
\(518\) 0.106558 0.275966i 0.00468191 0.0121253i
\(519\) 0 0
\(520\) 2.03153 0.0890887
\(521\) −19.5369 −0.855925 −0.427963 0.903796i \(-0.640769\pi\)
−0.427963 + 0.903796i \(0.640769\pi\)
\(522\) 0 0
\(523\) 6.26070 27.4299i 0.273761 1.19943i −0.631773 0.775154i \(-0.717672\pi\)
0.905534 0.424273i \(-0.139470\pi\)
\(524\) −40.6323 + 19.5675i −1.77503 + 0.854810i
\(525\) 0 0
\(526\) −0.555122 0.267333i −0.0242045 0.0116563i
\(527\) 11.4393 14.3445i 0.498305 0.624854i
\(528\) 0 0
\(529\) −6.27882 + 27.5093i −0.272992 + 1.19606i
\(530\) 1.82589 0.879303i 0.0793117 0.0381945i
\(531\) 0 0
\(532\) −11.4833 1.66619i −0.497862 0.0722385i
\(533\) 6.56292 28.7540i 0.284271 1.24547i
\(534\) 0 0
\(535\) 22.2707 + 27.9266i 0.962846 + 1.20737i
\(536\) 0.328828 + 1.44069i 0.0142032 + 0.0622284i
\(537\) 0 0
\(538\) 0.824143 0.0355313
\(539\) −0.595348 + 1.05792i −0.0256434 + 0.0455677i
\(540\) 0 0
\(541\) −17.9803 8.65887i −0.773034 0.372274i 0.00541156 0.999985i \(-0.498277\pi\)
−0.778446 + 0.627712i \(0.783992\pi\)
\(542\) −0.00123347 0.00540421i −5.29823e−5 0.000232131i
\(543\) 0 0
\(544\) 0.231790 + 1.01554i 0.00993790 + 0.0435408i
\(545\) −5.28977 + 23.1760i −0.226589 + 0.992750i
\(546\) 0 0
\(547\) 6.73345 + 29.5012i 0.287902 + 1.26138i 0.887399 + 0.461002i \(0.152510\pi\)
−0.599497 + 0.800377i \(0.704633\pi\)
\(548\) 10.0089 4.82002i 0.427558 0.205901i
\(549\) 0 0
\(550\) 0.0516919 + 0.0248935i 0.00220415 + 0.00106146i
\(551\) 3.75926 4.71396i 0.160150 0.200822i
\(552\) 0 0
\(553\) −26.7989 + 25.1419i −1.13961 + 1.06914i
\(554\) −0.880273 + 0.423917i −0.0373992 + 0.0180105i
\(555\) 0 0
\(556\) −7.38836 + 9.26471i −0.313336 + 0.392911i
\(557\) 33.2445 1.40861 0.704307 0.709895i \(-0.251258\pi\)
0.704307 + 0.709895i \(0.251258\pi\)
\(558\) 0 0
\(559\) −17.2293 + 21.6049i −0.728723 + 0.913790i
\(560\) −26.3705 + 24.7399i −1.11436 + 1.04545i
\(561\) 0 0
\(562\) −0.942320 1.18163i −0.0397494 0.0498442i
\(563\) 23.9867 11.5514i 1.01092 0.486833i 0.146289 0.989242i \(-0.453267\pi\)
0.864630 + 0.502409i \(0.167553\pi\)
\(564\) 0 0
\(565\) −4.93220 6.18479i −0.207499 0.260196i
\(566\) 0.698316 + 0.875660i 0.0293524 + 0.0368067i
\(567\) 0 0
\(568\) 0.725054 0.909189i 0.0304226 0.0381487i
\(569\) −5.01248 −0.210134 −0.105067 0.994465i \(-0.533506\pi\)
−0.105067 + 0.994465i \(0.533506\pi\)
\(570\) 0 0
\(571\) 14.7139 18.4506i 0.615756 0.772134i −0.371984 0.928239i \(-0.621322\pi\)
0.987740 + 0.156105i \(0.0498938\pi\)
\(572\) −0.233368 + 1.02245i −0.00975762 + 0.0427509i
\(573\) 0 0
\(574\) −0.636920 1.08928i −0.0265845 0.0454655i
\(575\) −43.5757 20.9849i −1.81723 0.875132i
\(576\) 0 0
\(577\) −15.3017 7.36890i −0.637017 0.306771i 0.0873582 0.996177i \(-0.472158\pi\)
−0.724376 + 0.689406i \(0.757872\pi\)
\(578\) −0.150826 + 0.660812i −0.00627354 + 0.0274862i
\(579\) 0 0
\(580\) −4.18593 18.3397i −0.173811 0.761517i
\(581\) −4.43597 + 11.4883i −0.184035 + 0.476617i
\(582\) 0 0
\(583\) 0.465880 + 2.04115i 0.0192948 + 0.0845359i
\(584\) 0.423025 + 0.530457i 0.0175049 + 0.0219505i
\(585\) 0 0
\(586\) 0.0300589 + 0.0144756i 0.00124172 + 0.000597982i
\(587\) 25.9448 1.07086 0.535429 0.844580i \(-0.320150\pi\)
0.535429 + 0.844580i \(0.320150\pi\)
\(588\) 0 0
\(589\) 22.6806 0.934538
\(590\) −1.87502 0.902963i −0.0771934 0.0371744i
\(591\) 0 0
\(592\) 5.67574 + 7.11715i 0.233272 + 0.292513i
\(593\) 5.15607 + 22.5902i 0.211734 + 0.927669i 0.963388 + 0.268111i \(0.0863994\pi\)
−0.751654 + 0.659558i \(0.770744\pi\)
\(594\) 0 0
\(595\) 15.3704 4.83401i 0.630124 0.198175i
\(596\) 5.18881 + 22.7337i 0.212542 + 0.931207i
\(597\) 0 0
\(598\) −0.236011 + 1.03403i −0.00965120 + 0.0422847i
\(599\) 28.8256 + 13.8817i 1.17778 + 0.567191i 0.917265 0.398278i \(-0.130392\pi\)
0.260519 + 0.965469i \(0.416106\pi\)
\(600\) 0 0
\(601\) 18.9261 + 9.11434i 0.772012 + 0.371782i 0.778052 0.628200i \(-0.216208\pi\)
−0.00603931 + 0.999982i \(0.501922\pi\)
\(602\) 0.0948422 + 1.17844i 0.00386548 + 0.0480298i
\(603\) 0 0
\(604\) 0.0305951 0.134046i 0.00124490 0.00545425i
\(605\) 23.4532 29.4094i 0.953509 1.19566i
\(606\) 0 0
\(607\) −0.999958 −0.0405870 −0.0202935 0.999794i \(-0.506460\pi\)
−0.0202935 + 0.999794i \(0.506460\pi\)
\(608\) −0.802853 + 1.00675i −0.0325600 + 0.0408290i
\(609\) 0 0
\(610\) −0.255212 0.320026i −0.0103332 0.0129575i
\(611\) −11.5587 14.4942i −0.467615 0.586371i
\(612\) 0 0
\(613\) −10.9895 + 5.29227i −0.443862 + 0.213753i −0.642446 0.766331i \(-0.722080\pi\)
0.198584 + 0.980084i \(0.436366\pi\)
\(614\) −0.252363 0.316453i −0.0101845 0.0127710i
\(615\) 0 0
\(616\) 0.0453232 + 0.0775129i 0.00182612 + 0.00312308i
\(617\) 26.0055 32.6098i 1.04694 1.31282i 0.0987523 0.995112i \(-0.468515\pi\)
0.948188 0.317710i \(-0.102914\pi\)
\(618\) 0 0
\(619\) −19.9752 −0.802870 −0.401435 0.915888i \(-0.631488\pi\)
−0.401435 + 0.915888i \(0.631488\pi\)
\(620\) 44.1196 55.3243i 1.77189 2.22188i
\(621\) 0 0
\(622\) −0.547039 + 0.263440i −0.0219343 + 0.0105630i
\(623\) −5.74720 + 14.8842i −0.230257 + 0.596321i
\(624\) 0 0
\(625\) −8.17901 + 10.2562i −0.327160 + 0.410246i
\(626\) −0.0865753 0.0416925i −0.00346025 0.00166637i
\(627\) 0 0
\(628\) 26.8365 12.9238i 1.07089 0.515716i
\(629\) −0.902640 3.95473i −0.0359906 0.157685i
\(630\) 0 0
\(631\) −4.05987 + 17.7875i −0.161621 + 0.708108i 0.827556 + 0.561383i \(0.189730\pi\)
−0.989177 + 0.146725i \(0.953127\pi\)
\(632\) 0.604818 + 2.64988i 0.0240584 + 0.105407i
\(633\) 0 0
\(634\) −0.0502097 0.219983i −0.00199408 0.00873665i
\(635\) 25.3408 + 12.2035i 1.00562 + 0.484281i
\(636\) 0 0
\(637\) 10.3930 18.4681i 0.411786 0.731732i
\(638\) −0.0233145 −0.000923031
\(639\) 0 0
\(640\) 1.19173 + 5.22130i 0.0471072 + 0.206390i
\(641\) 26.0385 + 32.6513i 1.02846 + 1.28965i 0.956341 + 0.292252i \(0.0944046\pi\)
0.0721187 + 0.997396i \(0.477024\pi\)
\(642\) 0 0
\(643\) 5.14418 22.5381i 0.202867 0.888817i −0.766314 0.642466i \(-0.777911\pi\)
0.969181 0.246351i \(-0.0792316\pi\)
\(644\) −19.0920 32.6516i −0.752330 1.28666i
\(645\) 0 0
\(646\) 0.171980 0.0828210i 0.00676645 0.00325855i
\(647\) −8.47312 + 37.1232i −0.333113 + 1.45946i 0.479955 + 0.877293i \(0.340653\pi\)
−0.813067 + 0.582170i \(0.802204\pi\)
\(648\) 0 0
\(649\) 1.34049 1.68092i 0.0526188 0.0659819i
\(650\) −0.902387 0.434567i −0.0353945 0.0170451i
\(651\) 0 0
\(652\) 26.2339 12.6336i 1.02740 0.494769i
\(653\) 8.16520 35.7741i 0.319529 1.39995i −0.518852 0.854864i \(-0.673641\pi\)
0.838381 0.545084i \(-0.183502\pi\)
\(654\) 0 0
\(655\) 77.4145 3.02483
\(656\) 38.8290 1.51602
\(657\) 0 0
\(658\) −0.784923 0.113890i −0.0305995 0.00443990i
\(659\) −0.117004 0.146718i −0.00455782 0.00571532i 0.779547 0.626343i \(-0.215449\pi\)
−0.784105 + 0.620628i \(0.786878\pi\)
\(660\) 0 0
\(661\) 18.5623 8.93915i 0.721991 0.347693i −0.0365374 0.999332i \(-0.511633\pi\)
0.758529 + 0.651640i \(0.225919\pi\)
\(662\) −0.672631 + 0.323922i −0.0261426 + 0.0125896i
\(663\) 0 0
\(664\) 0.567942 + 0.712177i 0.0220404 + 0.0276378i
\(665\) 16.5187 + 11.1295i 0.640569 + 0.431583i
\(666\) 0 0
\(667\) 19.6539 0.761001
\(668\) −31.6356 −1.22402
\(669\) 0 0
\(670\) 0.282058 1.23578i 0.0108969 0.0477423i
\(671\) 0.380995 0.183477i 0.0147081 0.00708307i
\(672\) 0 0
\(673\) −13.3526 6.43029i −0.514706 0.247870i 0.158454 0.987366i \(-0.449349\pi\)
−0.673160 + 0.739497i \(0.735063\pi\)
\(674\) −0.193892 + 0.243133i −0.00746843 + 0.00936512i
\(675\) 0 0
\(676\) −1.70469 + 7.46874i −0.0655651 + 0.287259i
\(677\) −17.5002 + 8.42766i −0.672588 + 0.323901i −0.738820 0.673903i \(-0.764617\pi\)
0.0662319 + 0.997804i \(0.478902\pi\)
\(678\) 0 0
\(679\) −7.77946 + 7.29844i −0.298548 + 0.280088i
\(680\) 0.265202 1.16192i 0.0101700 0.0445578i
\(681\) 0 0
\(682\) −0.0546811 0.0685680i −0.00209385 0.00262560i
\(683\) 4.96725 + 21.7629i 0.190067 + 0.832736i 0.976579 + 0.215161i \(0.0690276\pi\)
−0.786512 + 0.617575i \(0.788115\pi\)
\(684\) 0 0
\(685\) −19.0693 −0.728602
\(686\) −0.216324 0.880456i −0.00825930 0.0336160i
\(687\) 0 0
\(688\) −32.7778 15.7849i −1.24964 0.601795i
\(689\) −8.13287 35.6324i −0.309838 1.35749i
\(690\) 0 0
\(691\) −4.10034 17.9648i −0.155984 0.683412i −0.991076 0.133301i \(-0.957442\pi\)
0.835091 0.550111i \(-0.185415\pi\)
\(692\) −5.49962 + 24.0954i −0.209064 + 0.915971i
\(693\) 0 0
\(694\) 0.168106 + 0.736521i 0.00638122 + 0.0279580i
\(695\) 18.3269 8.82576i 0.695178 0.334780i
\(696\) 0 0
\(697\) −15.5889 7.50724i −0.590474 0.284357i
\(698\) −0.271896 + 0.340947i −0.0102914 + 0.0129050i
\(699\) 0 0
\(700\) 34.0726 10.7159i 1.28782 0.405022i
\(701\) −36.2625 + 17.4631i −1.36961 + 0.659572i −0.966758 0.255692i \(-0.917697\pi\)
−0.402856 + 0.915263i \(0.631982\pi\)
\(702\) 0 0
\(703\) 3.12649 3.92049i 0.117918 0.147864i
\(704\) −1.37738 −0.0519121
\(705\) 0 0
\(706\) 0.0439743 0.0551420i 0.00165499 0.00207530i
\(707\) −3.98446 2.68453i −0.149851 0.100962i
\(708\) 0 0
\(709\) −12.8009 16.0518i −0.480747 0.602838i 0.481019 0.876710i \(-0.340267\pi\)
−0.961766 + 0.273872i \(0.911696\pi\)
\(710\) −0.898712 + 0.432797i −0.0337281 + 0.0162426i
\(711\) 0 0
\(712\) 0.735819 + 0.922688i 0.0275760 + 0.0345792i
\(713\) 46.0956 + 57.8020i 1.72629 + 2.16470i
\(714\) 0 0
\(715\) 1.12243 1.40749i 0.0419767 0.0526371i
\(716\) 28.5014 1.06515
\(717\) 0 0
\(718\) −0.278811 + 0.349618i −0.0104051 + 0.0130476i
\(719\) −0.332603 + 1.45723i −0.0124040 + 0.0543455i −0.980751 0.195262i \(-0.937444\pi\)
0.968347 + 0.249607i \(0.0803015\pi\)
\(720\) 0 0
\(721\) −24.0961 16.2348i −0.897386 0.604614i
\(722\) −0.625417 0.301185i −0.0232756 0.0112089i
\(723\) 0 0
\(724\) 4.51863 + 2.17606i 0.167934 + 0.0808726i
\(725\) −4.12991 + 18.0943i −0.153381 + 0.672007i
\(726\) 0 0
\(727\) 10.4250 + 45.6749i 0.386642 + 1.69399i 0.676109 + 0.736802i \(0.263665\pi\)
−0.289466 + 0.957188i \(0.593478\pi\)
\(728\) −0.791208 1.35315i −0.0293241 0.0501509i
\(729\) 0 0
\(730\) −0.129502 0.567387i −0.00479310 0.0209999i
\(731\) 10.1076 + 12.6746i 0.373844 + 0.468786i
\(732\) 0 0
\(733\) 29.9367 + 14.4168i 1.10574 + 0.532495i 0.895458 0.445146i \(-0.146848\pi\)
0.210280 + 0.977641i \(0.432562\pi\)
\(734\) 1.33222 0.0491730
\(735\) 0 0
\(736\) −4.19741 −0.154719
\(737\) 1.17982 + 0.568171i 0.0434592 + 0.0209288i
\(738\) 0 0
\(739\) 14.0533 + 17.6223i 0.516959 + 0.648246i 0.969960 0.243264i \(-0.0782181\pi\)
−0.453001 + 0.891510i \(0.649647\pi\)
\(740\) −3.48134 15.2527i −0.127977 0.560702i
\(741\) 0 0
\(742\) −1.29680 0.873717i −0.0476069 0.0320751i
\(743\) 7.45239 + 32.6511i 0.273402 + 1.19785i 0.905968 + 0.423345i \(0.139144\pi\)
−0.632567 + 0.774506i \(0.717999\pi\)
\(744\) 0 0
\(745\) 8.90693 39.0238i 0.326325 1.42972i
\(746\) −1.16795 0.562453i −0.0427615 0.0205929i
\(747\) 0 0
\(748\) 0.554322 + 0.266947i 0.0202680 + 0.00976056i
\(749\) 9.92745 25.7102i 0.362741 0.939431i
\(750\) 0 0
\(751\) 6.25892 27.4221i 0.228391 1.00065i −0.722561 0.691308i \(-0.757035\pi\)
0.950952 0.309339i \(-0.100108\pi\)
\(752\) 15.2174 19.0820i 0.554920 0.695848i
\(753\) 0 0
\(754\) 0.407002 0.0148221
\(755\) −0.147154 + 0.184525i −0.00535546 + 0.00671554i
\(756\) 0 0
\(757\) −16.5086 20.7011i −0.600014 0.752394i 0.385366 0.922764i \(-0.374075\pi\)
−0.985380 + 0.170370i \(0.945504\pi\)
\(758\) 0.230798 + 0.289411i 0.00838296 + 0.0105119i
\(759\) 0 0
\(760\) 1.32739 0.639238i 0.0481495 0.0231876i
\(761\) 1.34817 + 1.69055i 0.0488711 + 0.0612824i 0.805666 0.592370i \(-0.201807\pi\)
−0.756795 + 0.653652i \(0.773236\pi\)
\(762\) 0 0
\(763\) 17.4970 5.50284i 0.633434 0.199216i
\(764\) 3.50630 4.39676i 0.126854 0.159069i
\(765\) 0 0
\(766\) −0.547119 −0.0197682
\(767\) −23.4010 + 29.3439i −0.844960 + 1.05955i
\(768\) 0 0
\(769\) −19.5570 + 9.41817i −0.705244 + 0.339628i −0.751894 0.659284i \(-0.770860\pi\)
0.0466502 + 0.998911i \(0.485145\pi\)
\(770\) −0.00617866 0.0767717i −0.000222663 0.00276666i
\(771\) 0 0
\(772\) 16.3478 20.4995i 0.588370 0.737793i
\(773\) 18.0076 + 8.67202i 0.647690 + 0.311911i 0.728731 0.684800i \(-0.240110\pi\)
−0.0810414 + 0.996711i \(0.525825\pi\)
\(774\) 0 0
\(775\) −62.9016 + 30.2918i −2.25949 + 1.08811i
\(776\) 0.175573 + 0.769234i 0.00630269 + 0.0276139i
\(777\) 0 0
\(778\) 0.220794 0.967360i 0.00791583 0.0346815i
\(779\) −4.75950 20.8528i −0.170527 0.747127i
\(780\) 0 0
\(781\) −0.229308 1.00466i −0.00820529 0.0359497i
\(782\) 0.560598 + 0.269970i 0.0200470 + 0.00965411i
\(783\) 0 0
\(784\) 26.7489 + 7.92931i 0.955317 + 0.283190i
\(785\) −51.1302 −1.82491
\(786\) 0 0
\(787\) 0.861751 + 3.77558i 0.0307181 + 0.134585i 0.987962 0.154698i \(-0.0494404\pi\)
−0.957244 + 0.289283i \(0.906583\pi\)
\(788\) −32.1836 40.3570i −1.14649 1.43766i
\(789\) 0 0
\(790\) 0.518793 2.27298i 0.0184578 0.0808691i
\(791\) −2.19859 + 5.69394i −0.0781729 + 0.202453i
\(792\) 0 0
\(793\) −6.65104 + 3.20297i −0.236185 + 0.113741i
\(794\) 0.0219860 0.0963271i 0.000780255 0.00341852i
\(795\) 0 0
\(796\) −18.0344 + 22.6144i −0.639213 + 0.801548i
\(797\) −47.4329 22.8425i −1.68016 0.809123i −0.996877 0.0789694i \(-0.974837\pi\)
−0.683283 0.730153i \(-0.739449\pi\)
\(798\) 0 0
\(799\) −9.79875 + 4.71883i −0.346655 + 0.166940i
\(800\) 0.882013 3.86435i 0.0311839 0.136625i
\(801\) 0 0
\(802\) −1.25477 −0.0443073
\(803\) 0.601235 0.0212171
\(804\) 0 0
\(805\) 5.20853 + 64.7176i 0.183577 + 2.28100i
\(806\) 0.954570 + 1.19699i 0.0336233 + 0.0421623i
\(807\) 0 0
\(808\) −0.320178 + 0.154190i −0.0112638 + 0.00542437i
\(809\) −13.8665 + 6.67773i −0.487518 + 0.234777i −0.661461 0.749979i \(-0.730063\pi\)
0.173943 + 0.984756i \(0.444349\pi\)
\(810\) 0 0
\(811\) 16.2455 + 20.3712i 0.570457 + 0.715330i 0.980452 0.196757i \(-0.0630411\pi\)
−0.409995 + 0.912088i \(0.634470\pi\)
\(812\) −10.5853 + 9.93078i −0.371471 + 0.348502i
\(813\) 0 0
\(814\) −0.0193901 −0.000679624
\(815\) −49.9820 −1.75079
\(816\) 0 0
\(817\) −4.45938 + 19.5378i −0.156014 + 0.683542i
\(818\) 1.38161 0.665347i 0.0483067 0.0232633i
\(819\) 0 0
\(820\) −60.1241 28.9542i −2.09962 1.01113i
\(821\) −33.2476 + 41.6911i −1.16035 + 1.45503i −0.293849 + 0.955852i \(0.594936\pi\)
−0.866499 + 0.499179i \(0.833635\pi\)
\(822\) 0 0
\(823\) −0.150512 + 0.659437i −0.00524653 + 0.0229865i −0.977483 0.211012i \(-0.932324\pi\)
0.972237 + 0.233999i \(0.0751812\pi\)
\(824\) −1.93628 + 0.932466i −0.0674537 + 0.0324840i
\(825\) 0 0
\(826\) 0.128815 + 1.60057i 0.00448205 + 0.0556909i
\(827\) −7.11633 + 31.1787i −0.247459 + 1.08419i 0.686591 + 0.727044i \(0.259107\pi\)
−0.934049 + 0.357144i \(0.883751\pi\)
\(828\) 0 0
\(829\) 5.93326 + 7.44007i 0.206071 + 0.258404i 0.874117 0.485715i \(-0.161441\pi\)
−0.668047 + 0.744119i \(0.732869\pi\)
\(830\) −0.173866 0.761758i −0.00603499 0.0264410i
\(831\) 0 0
\(832\) 24.0450 0.833612
\(833\) −9.20599 8.35509i −0.318969 0.289487i
\(834\) 0 0
\(835\) 48.9267 + 23.5618i 1.69318 + 0.815391i
\(836\) 0.169242 + 0.741496i 0.00585334 + 0.0256452i
\(837\) 0 0
\(838\) −0.238603 1.04539i −0.00824239 0.0361123i
\(839\) 3.06395 13.4241i 0.105779 0.463450i −0.894099 0.447869i \(-0.852183\pi\)
0.999879 0.0155810i \(-0.00495979\pi\)
\(840\) 0 0
\(841\) 4.77486 + 20.9200i 0.164650 + 0.721381i
\(842\) 1.11172 0.535374i 0.0383123 0.0184502i
\(843\) 0 0
\(844\) −14.4237 6.94610i −0.496485 0.239094i
\(845\) 8.19907 10.2813i 0.282057 0.353688i
\(846\) 0 0
\(847\) −28.7229 4.16762i −0.986931 0.143201i
\(848\) 43.3524 20.8774i 1.48873 0.716934i
\(849\) 0 0
\(850\) −0.366348 + 0.459386i −0.0125656 + 0.0157568i
\(851\) 16.3457 0.560322
\(852\) 0 0
\(853\) 15.4792 19.4103i 0.529997 0.664595i −0.442701 0.896669i \(-0.645980\pi\)
0.972698 + 0.232074i \(0.0745511\pi\)
\(854\) −0.113764 + 0.294627i −0.00389292 + 0.0100819i
\(855\) 0 0
\(856\) −1.27102 1.59381i −0.0434426 0.0544753i
\(857\) 40.1913 19.3551i 1.37291 0.661158i 0.405434 0.914124i \(-0.367120\pi\)
0.967475 + 0.252966i \(0.0814060\pi\)
\(858\) 0 0
\(859\) 9.17315 + 11.5028i 0.312984 + 0.392469i 0.913296 0.407297i \(-0.133528\pi\)
−0.600312 + 0.799766i \(0.704957\pi\)
\(860\) 38.9835 + 48.8838i 1.32933 + 1.66692i
\(861\) 0 0
\(862\) 0.222401 0.278882i 0.00757501 0.00949876i
\(863\) 0.0760250 0.00258792 0.00129396 0.999999i \(-0.499588\pi\)
0.00129396 + 0.999999i \(0.499588\pi\)
\(864\) 0 0
\(865\) 26.4516 33.1693i 0.899381 1.12779i
\(866\) 0.0987510 0.432657i 0.00335570 0.0147023i
\(867\) 0 0
\(868\) −54.0328 7.84002i −1.83399 0.266108i
\(869\) 2.17006 + 1.04504i 0.0736141 + 0.0354507i
\(870\) 0 0
\(871\) −20.5961 9.91857i −0.697873 0.336078i
\(872\) 0.301895 1.32269i 0.0102234 0.0447918i
\(873\) 0 0
\(874\) 0.171158 + 0.749891i 0.00578950 + 0.0253655i
\(875\) −15.7853 2.29040i −0.533639 0.0774296i
\(876\) 0 0
\(877\) 7.16816 + 31.4058i 0.242051 + 1.06050i 0.939146 + 0.343518i \(0.111619\pi\)
−0.697095 + 0.716979i \(0.745524\pi\)
\(878\) −0.438242 0.549539i −0.0147900 0.0185460i
\(879\) 0 0
\(880\) 2.13536 + 1.02834i 0.0719831 + 0.0346652i
\(881\) 40.0778 1.35026 0.675128 0.737701i \(-0.264089\pi\)
0.675128 + 0.737701i \(0.264089\pi\)
\(882\) 0 0
\(883\) −29.5726 −0.995198 −0.497599 0.867407i \(-0.665785\pi\)
−0.497599 + 0.867407i \(0.665785\pi\)
\(884\) −9.67682 4.66011i −0.325467 0.156736i
\(885\) 0 0
\(886\) −0.302565 0.379404i −0.0101649 0.0127463i
\(887\) 0.347965 + 1.52454i 0.0116835 + 0.0511889i 0.980434 0.196850i \(-0.0630711\pi\)
−0.968750 + 0.248039i \(0.920214\pi\)
\(888\) 0 0
\(889\) −1.74093 21.6316i −0.0583888 0.725499i
\(890\) −0.225259 0.986925i −0.00755070 0.0330818i
\(891\) 0 0
\(892\) 2.19337 9.60977i 0.0734394 0.321759i
\(893\) −12.1131 5.83335i −0.405349 0.195206i
\(894\) 0 0
\(895\) −44.0795 21.2276i −1.47342 0.709559i
\(896\) 3.01362 2.82728i 0.100678 0.0944528i
\(897\) 0 0
\(898\) −0.0917331 + 0.401909i −0.00306117 + 0.0134119i
\(899\) 17.6887 22.1809i 0.589950 0.739774i
\(900\) 0 0
\(901\) −21.4415 −0.714318
\(902\) −0.0515672 + 0.0646633i −0.00171700 + 0.00215305i
\(903\) 0 0
\(904\) 0.281488 + 0.352975i 0.00936215 + 0.0117398i
\(905\) −5.36769 6.73086i −0.178428 0.223742i
\(906\) 0 0
\(907\) 5.37282 2.58741i 0.178402 0.0859137i −0.342551 0.939499i \(-0.611291\pi\)
0.520953 + 0.853585i \(0.325577\pi\)
\(908\) −16.8941 21.1845i −0.560651 0.703034i
\(909\) 0 0
\(910\) 0.107861 + 1.34021i 0.00357556 + 0.0444274i
\(911\) −10.4648 + 13.1224i −0.346713 + 0.434764i −0.924359 0.381523i \(-0.875400\pi\)
0.577646 + 0.816287i \(0.303971\pi\)
\(912\) 0 0
\(913\) 0.807202 0.0267145
\(914\) 0.914984 1.14735i 0.0302650 0.0379511i
\(915\) 0 0
\(916\) 25.8530 12.4501i 0.854206 0.411364i
\(917\) −30.1501 51.5635i −0.995644 1.70278i
\(918\) 0 0
\(919\) −5.62680 + 7.05579i −0.185611 + 0.232749i −0.865927 0.500170i \(-0.833271\pi\)
0.680316 + 0.732919i \(0.261842\pi\)
\(920\) 4.32687 + 2.08371i 0.142653 + 0.0686979i
\(921\) 0 0
\(922\) 0.490197 0.236067i 0.0161438 0.00777444i
\(923\) 4.00304 + 17.5384i 0.131762 + 0.577285i
\(924\) 0 0
\(925\) −3.43475 + 15.0486i −0.112934 + 0.494796i
\(926\) −0.173923 0.762007i −0.00571547 0.0250411i
\(927\) 0 0
\(928\) 0.358417 + 1.57033i 0.0117656 + 0.0515485i
\(929\) 8.13724 + 3.91869i 0.266974 + 0.128568i 0.562582 0.826741i \(-0.309808\pi\)
−0.295608 + 0.955309i \(0.595522\pi\)
\(930\) 0 0
\(931\) 0.979593 15.3372i 0.0321049 0.502655i
\(932\) −28.4159 −0.930794
\(933\) 0 0
\(934\) 0.129091 + 0.565585i 0.00422399 + 0.0185065i
\(935\) −0.658479 0.825707i −0.0215346 0.0270035i
\(936\) 0 0
\(937\) 8.70141 38.1234i 0.284263 1.24544i −0.608007 0.793932i \(-0.708031\pi\)
0.892269 0.451504i \(-0.149112\pi\)
\(938\) −0.932967 + 0.293419i −0.0304624 + 0.00958049i
\(939\) 0 0
\(940\) −37.7922 + 18.1998i −1.23265 + 0.593611i
\(941\) 2.42878 10.6412i 0.0791761 0.346893i −0.919787 0.392418i \(-0.871639\pi\)
0.998963 + 0.0455246i \(0.0144959\pi\)
\(942\) 0 0
\(943\) 43.4706 54.5104i 1.41560 1.77510i
\(944\) −44.5189 21.4392i −1.44897 0.697786i
\(945\) 0 0
\(946\) 0.0698180 0.0336226i 0.00226998 0.00109316i
\(947\) 12.4930 54.7355i 0.405969 1.77866i −0.196481 0.980508i \(-0.562951\pi\)
0.602450 0.798157i \(-0.294191\pi\)
\(948\) 0 0
\(949\) −10.4958 −0.340707
\(950\) −0.726353 −0.0235660
\(951\) 0 0
\(952\) −0.877210 + 0.275884i −0.0284305 + 0.00894144i
\(953\) 1.70562 + 2.13878i 0.0552504 + 0.0692818i 0.808689 0.588237i \(-0.200178\pi\)
−0.753438 + 0.657518i \(0.771606\pi\)
\(954\) 0 0
\(955\) −8.69741 + 4.18845i −0.281442 + 0.135535i
\(956\) 31.3313 15.0883i 1.01333 0.487992i
\(957\) 0 0
\(958\) −0.235043 0.294735i −0.00759390 0.00952245i
\(959\) 7.42681 + 12.7015i 0.239824 + 0.410154i
\(960\) 0 0
\(961\) 75.7204 2.44259
\(962\) 0.338494 0.0109135
\(963\) 0 0
\(964\) −9.91074 + 43.4218i −0.319204 + 1.39852i
\(965\) −40.5509 + 19.5283i −1.30538 + 0.628637i
\(966\) 0 0
\(967\) 18.5668 + 8.94129i 0.597068 + 0.287533i 0.707907 0.706306i \(-0.249640\pi\)
−0.110839 + 0.993838i \(0.535354\pi\)
\(968\) −1.33851 + 1.67844i −0.0430213 + 0.0539470i
\(969\) 0 0
\(970\) 0.150601 0.659825i 0.00483550 0.0211857i
\(971\) 16.0534 7.73093i 0.515179 0.248097i −0.158183 0.987410i \(-0.550564\pi\)
0.673362 + 0.739312i \(0.264849\pi\)
\(972\) 0 0
\(973\) −13.0162 8.76969i −0.417281 0.281143i
\(974\) −0.0778746 + 0.341191i −0.00249526 + 0.0109325i
\(975\) 0 0
\(976\) −6.05954 7.59842i −0.193961 0.243219i
\(977\) −2.55259 11.1836i −0.0816645 0.357796i 0.917541 0.397640i \(-0.130171\pi\)
−0.999206 + 0.0398447i \(0.987314\pi\)
\(978\) 0 0
\(979\) 1.04580 0.0334239
\(980\) −35.5060 32.2242i −1.13420 1.02937i
\(981\) 0 0
\(982\) −0.730810 0.351939i −0.0233211 0.0112308i
\(983\) −2.86970 12.5730i −0.0915291 0.401015i 0.908322 0.418272i \(-0.137364\pi\)
−0.999851 + 0.0172563i \(0.994507\pi\)
\(984\) 0 0
\(985\) 19.7168 + 86.3851i 0.628230 + 2.75246i
\(986\) 0.0531311 0.232783i 0.00169204 0.00741331i
\(987\) 0 0
\(988\) −2.95445 12.9443i −0.0939937 0.411813i
\(989\) −58.8557 + 28.3434i −1.87150 + 0.901268i
\(990\) 0 0
\(991\) −39.7079 19.1223i −1.26136 0.607440i −0.320827 0.947138i \(-0.603961\pi\)
−0.940535 + 0.339698i \(0.889675\pi\)
\(992\) −3.77771 + 4.73710i −0.119942 + 0.150403i
\(993\) 0 0
\(994\) 0.638289 + 0.430047i 0.0202453 + 0.0136403i
\(995\) 44.7345 21.5430i 1.41818 0.682959i
\(996\) 0 0
\(997\) 11.7042 14.6765i 0.370674 0.464811i −0.561154 0.827712i \(-0.689642\pi\)
0.931828 + 0.362901i \(0.118214\pi\)
\(998\) −0.263836 −0.00835160
\(999\) 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 441.2.u.c.127.3 24
3.2 odd 2 147.2.i.a.127.2 yes 24
49.22 even 7 inner 441.2.u.c.316.3 24
147.62 even 14 7203.2.a.b.1.7 12
147.71 odd 14 147.2.i.a.22.2 24
147.134 odd 14 7203.2.a.a.1.7 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.2.i.a.22.2 24 147.71 odd 14
147.2.i.a.127.2 yes 24 3.2 odd 2
441.2.u.c.127.3 24 1.1 even 1 trivial
441.2.u.c.316.3 24 49.22 even 7 inner
7203.2.a.a.1.7 12 147.134 odd 14
7203.2.a.b.1.7 12 147.62 even 14