Properties

Label 1089.2.e.p.364.10
Level $1089$
Weight $2$
Character 1089.364
Analytic conductor $8.696$
Analytic rank $0$
Dimension $36$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1089,2,Mod(364,1089)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1089, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1089.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1089.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.69570878012\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 364.10
Character \(\chi\) \(=\) 1089.364
Dual form 1089.2.e.p.727.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.245247 + 0.424780i) q^{2} +(-0.361332 - 1.69394i) q^{3} +(0.879708 - 1.52370i) q^{4} +(-0.854089 + 1.47932i) q^{5} +(0.630937 - 0.568921i) q^{6} +(-1.70526 - 2.95360i) q^{7} +1.84397 q^{8} +(-2.73888 + 1.22415i) q^{9} -0.837851 q^{10} +(-2.89892 - 0.939612i) q^{12} +(1.99896 - 3.46230i) q^{13} +(0.836420 - 1.44872i) q^{14} +(2.81450 + 0.912248i) q^{15} +(-1.30719 - 2.26411i) q^{16} -3.30458 q^{17} +(-1.19170 - 0.863202i) q^{18} -4.41765 q^{19} +(1.50270 + 2.60275i) q^{20} +(-4.38706 + 3.95584i) q^{21} +(-3.74601 + 6.48827i) q^{23} +(-0.666286 - 3.12358i) q^{24} +(1.04107 + 1.80318i) q^{25} +1.96096 q^{26} +(3.06329 + 4.19717i) q^{27} -6.00053 q^{28} +(-0.845644 - 1.46470i) q^{29} +(0.302743 + 1.41927i) q^{30} +(1.94926 - 3.37621i) q^{31} +(2.48514 - 4.30439i) q^{32} +(-0.810437 - 1.40372i) q^{34} +5.82578 q^{35} +(-0.544173 + 5.25012i) q^{36} +3.06553 q^{37} +(-1.08342 - 1.87653i) q^{38} +(-6.58723 - 2.13508i) q^{39} +(-1.57491 + 2.72783i) q^{40} +(-0.195437 + 0.338507i) q^{41} +(-2.75628 - 0.893377i) q^{42} +(-4.80634 - 8.32483i) q^{43} +(0.528325 - 5.09722i) q^{45} -3.67479 q^{46} +(0.540129 + 0.935531i) q^{47} +(-3.36295 + 3.03240i) q^{48} +(-2.31583 + 4.01114i) q^{49} +(-0.510636 + 0.884448i) q^{50} +(1.19405 + 5.59776i) q^{51} +(-3.51700 - 6.09163i) q^{52} -12.5638 q^{53} +(-1.03161 + 2.33057i) q^{54} +(-3.14445 - 5.44635i) q^{56} +(1.59624 + 7.48324i) q^{57} +(0.414783 - 0.718426i) q^{58} +(1.82827 - 3.16666i) q^{59} +(3.86593 - 3.48594i) q^{60} +(1.92659 + 3.33695i) q^{61} +1.91220 q^{62} +(8.28616 + 6.00205i) q^{63} -2.79086 q^{64} +(3.41458 + 5.91423i) q^{65} +(-1.55060 + 2.68572i) q^{67} +(-2.90706 + 5.03518i) q^{68} +(12.3443 + 4.00109i) q^{69} +(1.42875 + 2.47467i) q^{70} +7.01715 q^{71} +(-5.05041 + 2.25730i) q^{72} -15.0426 q^{73} +(0.751812 + 1.30218i) q^{74} +(2.67831 - 2.41505i) q^{75} +(-3.88624 + 6.73117i) q^{76} +(-0.708557 - 3.32175i) q^{78} +(1.99957 + 3.46335i) q^{79} +4.46581 q^{80} +(6.00290 - 6.70561i) q^{81} -0.191722 q^{82} +(0.0624829 + 0.108224i) q^{83} +(2.16818 + 10.1645i) q^{84} +(2.82240 - 4.88854i) q^{85} +(2.35748 - 4.08328i) q^{86} +(-2.17556 + 1.96172i) q^{87} -7.93327 q^{89} +(2.29477 - 1.02566i) q^{90} -13.6350 q^{91} +(6.59078 + 11.4156i) q^{92} +(-6.42344 - 2.08199i) q^{93} +(-0.264930 + 0.458872i) q^{94} +(3.77307 - 6.53514i) q^{95} +(-8.18934 - 2.65437i) q^{96} +(-0.171580 - 0.297185i) q^{97} -2.27180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} - q^{6} - q^{7} - 12 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} - 3 q^{13} - 5 q^{15} + 8 q^{16} - 40 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20} - 8 q^{21} + 10 q^{23}+ \cdots - 164 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(848\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.245247 + 0.424780i 0.173416 + 0.300365i 0.939612 0.342242i \(-0.111186\pi\)
−0.766196 + 0.642607i \(0.777853\pi\)
\(3\) −0.361332 1.69394i −0.208615 0.977998i
\(4\) 0.879708 1.52370i 0.439854 0.761849i
\(5\) −0.854089 + 1.47932i −0.381960 + 0.661574i −0.991342 0.131302i \(-0.958084\pi\)
0.609382 + 0.792876i \(0.291417\pi\)
\(6\) 0.630937 0.568921i 0.257579 0.232261i
\(7\) −1.70526 2.95360i −0.644528 1.11636i −0.984410 0.175888i \(-0.943720\pi\)
0.339882 0.940468i \(-0.389613\pi\)
\(8\) 1.84397 0.651942
\(9\) −2.73888 + 1.22415i −0.912959 + 0.408051i
\(10\) −0.837851 −0.264952
\(11\) 0 0
\(12\) −2.89892 0.939612i −0.836847 0.271243i
\(13\) 1.99896 3.46230i 0.554412 0.960270i −0.443537 0.896256i \(-0.646276\pi\)
0.997949 0.0640140i \(-0.0203902\pi\)
\(14\) 0.836420 1.44872i 0.223543 0.387187i
\(15\) 2.81450 + 0.912248i 0.726701 + 0.235541i
\(16\) −1.30719 2.26411i −0.326797 0.566029i
\(17\) −3.30458 −0.801477 −0.400739 0.916192i \(-0.631246\pi\)
−0.400739 + 0.916192i \(0.631246\pi\)
\(18\) −1.19170 0.863202i −0.280886 0.203459i
\(19\) −4.41765 −1.01348 −0.506739 0.862099i \(-0.669149\pi\)
−0.506739 + 0.862099i \(0.669149\pi\)
\(20\) 1.50270 + 2.60275i 0.336013 + 0.581992i
\(21\) −4.38706 + 3.95584i −0.957335 + 0.863236i
\(22\) 0 0
\(23\) −3.74601 + 6.48827i −0.781096 + 1.35290i 0.150208 + 0.988654i \(0.452006\pi\)
−0.931304 + 0.364244i \(0.881328\pi\)
\(24\) −0.666286 3.12358i −0.136005 0.637598i
\(25\) 1.04107 + 1.80318i 0.208213 + 0.360636i
\(26\) 1.96096 0.384575
\(27\) 3.06329 + 4.19717i 0.589530 + 0.807746i
\(28\) −6.00053 −1.13399
\(29\) −0.845644 1.46470i −0.157032 0.271988i 0.776765 0.629791i \(-0.216859\pi\)
−0.933797 + 0.357803i \(0.883526\pi\)
\(30\) 0.302743 + 1.41927i 0.0552730 + 0.259122i
\(31\) 1.94926 3.37621i 0.350097 0.606386i −0.636169 0.771550i \(-0.719482\pi\)
0.986266 + 0.165164i \(0.0528153\pi\)
\(32\) 2.48514 4.30439i 0.439315 0.760915i
\(33\) 0 0
\(34\) −0.810437 1.40372i −0.138989 0.240736i
\(35\) 5.82578 0.984736
\(36\) −0.544173 + 5.25012i −0.0906955 + 0.875020i
\(37\) 3.06553 0.503970 0.251985 0.967731i \(-0.418917\pi\)
0.251985 + 0.967731i \(0.418917\pi\)
\(38\) −1.08342 1.87653i −0.175753 0.304414i
\(39\) −6.58723 2.13508i −1.05480 0.341887i
\(40\) −1.57491 + 2.72783i −0.249016 + 0.431308i
\(41\) −0.195437 + 0.338507i −0.0305222 + 0.0528660i −0.880883 0.473334i \(-0.843050\pi\)
0.850361 + 0.526200i \(0.176384\pi\)
\(42\) −2.75628 0.893377i −0.425303 0.137851i
\(43\) −4.80634 8.32483i −0.732960 1.26952i −0.955613 0.294626i \(-0.904805\pi\)
0.222652 0.974898i \(-0.428529\pi\)
\(44\) 0 0
\(45\) 0.528325 5.09722i 0.0787581 0.759849i
\(46\) −3.67479 −0.541818
\(47\) 0.540129 + 0.935531i 0.0787859 + 0.136461i 0.902726 0.430215i \(-0.141562\pi\)
−0.823940 + 0.566676i \(0.808229\pi\)
\(48\) −3.36295 + 3.03240i −0.485400 + 0.437689i
\(49\) −2.31583 + 4.01114i −0.330833 + 0.573020i
\(50\) −0.510636 + 0.884448i −0.0722149 + 0.125080i
\(51\) 1.19405 + 5.59776i 0.167200 + 0.783843i
\(52\) −3.51700 6.09163i −0.487721 0.844757i
\(53\) −12.5638 −1.72577 −0.862884 0.505402i \(-0.831344\pi\)
−0.862884 + 0.505402i \(0.831344\pi\)
\(54\) −1.03161 + 2.33057i −0.140385 + 0.317150i
\(55\) 0 0
\(56\) −3.14445 5.44635i −0.420195 0.727799i
\(57\) 1.59624 + 7.48324i 0.211427 + 0.991180i
\(58\) 0.414783 0.718426i 0.0544637 0.0943339i
\(59\) 1.82827 3.16666i 0.238021 0.412264i −0.722126 0.691762i \(-0.756835\pi\)
0.960146 + 0.279498i \(0.0901681\pi\)
\(60\) 3.86593 3.48594i 0.499089 0.450033i
\(61\) 1.92659 + 3.33695i 0.246674 + 0.427252i 0.962601 0.270923i \(-0.0873289\pi\)
−0.715927 + 0.698175i \(0.753996\pi\)
\(62\) 1.91220 0.242849
\(63\) 8.28616 + 6.00205i 1.04396 + 0.756187i
\(64\) −2.79086 −0.348857
\(65\) 3.41458 + 5.91423i 0.423527 + 0.733570i
\(66\) 0 0
\(67\) −1.55060 + 2.68572i −0.189436 + 0.328113i −0.945062 0.326890i \(-0.893999\pi\)
0.755626 + 0.655003i \(0.227333\pi\)
\(68\) −2.90706 + 5.03518i −0.352533 + 0.610605i
\(69\) 12.3443 + 4.00109i 1.48608 + 0.481675i
\(70\) 1.42875 + 2.47467i 0.170769 + 0.295780i
\(71\) 7.01715 0.832783 0.416391 0.909186i \(-0.363295\pi\)
0.416391 + 0.909186i \(0.363295\pi\)
\(72\) −5.05041 + 2.25730i −0.595197 + 0.266025i
\(73\) −15.0426 −1.76060 −0.880302 0.474413i \(-0.842660\pi\)
−0.880302 + 0.474413i \(0.842660\pi\)
\(74\) 0.751812 + 1.30218i 0.0873963 + 0.151375i
\(75\) 2.67831 2.41505i 0.309264 0.278866i
\(76\) −3.88624 + 6.73117i −0.445783 + 0.772118i
\(77\) 0 0
\(78\) −0.708557 3.32175i −0.0802283 0.376114i
\(79\) 1.99957 + 3.46335i 0.224969 + 0.389657i 0.956310 0.292354i \(-0.0944387\pi\)
−0.731341 + 0.682012i \(0.761105\pi\)
\(80\) 4.46581 0.499293
\(81\) 6.00290 6.70561i 0.666989 0.745067i
\(82\) −0.191722 −0.0211721
\(83\) 0.0624829 + 0.108224i 0.00685839 + 0.0118791i 0.869434 0.494049i \(-0.164484\pi\)
−0.862576 + 0.505928i \(0.831150\pi\)
\(84\) 2.16818 + 10.1645i 0.236568 + 1.10904i
\(85\) 2.82240 4.88854i 0.306132 0.530237i
\(86\) 2.35748 4.08328i 0.254214 0.440311i
\(87\) −2.17556 + 1.96172i −0.233244 + 0.210318i
\(88\) 0 0
\(89\) −7.93327 −0.840925 −0.420462 0.907310i \(-0.638132\pi\)
−0.420462 + 0.907310i \(0.638132\pi\)
\(90\) 2.29477 1.02566i 0.241890 0.108114i
\(91\) −13.6350 −1.42934
\(92\) 6.59078 + 11.4156i 0.687136 + 1.19016i
\(93\) −6.42344 2.08199i −0.666080 0.215893i
\(94\) −0.264930 + 0.458872i −0.0273255 + 0.0473291i
\(95\) 3.77307 6.53514i 0.387108 0.670491i
\(96\) −8.18934 2.65437i −0.835821 0.270910i
\(97\) −0.171580 0.297185i −0.0174213 0.0301746i 0.857183 0.515011i \(-0.172212\pi\)
−0.874605 + 0.484837i \(0.838879\pi\)
\(98\) −2.27180 −0.229487
\(99\) 0 0
\(100\) 3.66333 0.366333
\(101\) −3.55779 6.16228i −0.354014 0.613169i 0.632935 0.774205i \(-0.281850\pi\)
−0.986949 + 0.161035i \(0.948517\pi\)
\(102\) −2.08498 + 1.88004i −0.206444 + 0.186152i
\(103\) 0.827144 1.43266i 0.0815009 0.141164i −0.822394 0.568918i \(-0.807362\pi\)
0.903895 + 0.427755i \(0.140695\pi\)
\(104\) 3.68603 6.38439i 0.361445 0.626041i
\(105\) −2.10504 9.86853i −0.205431 0.963070i
\(106\) −3.08123 5.33685i −0.299275 0.518360i
\(107\) 3.30683 0.319683 0.159842 0.987143i \(-0.448902\pi\)
0.159842 + 0.987143i \(0.448902\pi\)
\(108\) 9.09003 0.975241i 0.874688 0.0938426i
\(109\) −5.50709 −0.527484 −0.263742 0.964593i \(-0.584957\pi\)
−0.263742 + 0.964593i \(0.584957\pi\)
\(110\) 0 0
\(111\) −1.10767 5.19283i −0.105136 0.492881i
\(112\) −4.45819 + 7.72182i −0.421260 + 0.729643i
\(113\) 8.20461 14.2108i 0.771825 1.33684i −0.164737 0.986338i \(-0.552677\pi\)
0.936562 0.350503i \(-0.113989\pi\)
\(114\) −2.78726 + 2.51329i −0.261051 + 0.235392i
\(115\) −6.39884 11.0831i −0.596695 1.03351i
\(116\) −2.97568 −0.276285
\(117\) −1.23653 + 11.9299i −0.114317 + 1.10292i
\(118\) 1.79351 0.165106
\(119\) 5.63516 + 9.76039i 0.516575 + 0.894734i
\(120\) 5.18986 + 1.68216i 0.473767 + 0.153559i
\(121\) 0 0
\(122\) −0.944980 + 1.63675i −0.0855545 + 0.148185i
\(123\) 0.644030 + 0.208746i 0.0580702 + 0.0188220i
\(124\) −3.42956 5.94016i −0.307983 0.533442i
\(125\) −12.0975 −1.08204
\(126\) −0.517396 + 4.99178i −0.0460933 + 0.444703i
\(127\) 10.7949 0.957894 0.478947 0.877844i \(-0.341019\pi\)
0.478947 + 0.877844i \(0.341019\pi\)
\(128\) −5.65473 9.79427i −0.499812 0.865700i
\(129\) −12.3651 + 11.1497i −1.08869 + 0.981676i
\(130\) −1.67483 + 2.90089i −0.146892 + 0.254425i
\(131\) 10.5778 18.3213i 0.924189 1.60074i 0.131329 0.991339i \(-0.458075\pi\)
0.792860 0.609404i \(-0.208591\pi\)
\(132\) 0 0
\(133\) 7.53325 + 13.0480i 0.653216 + 1.13140i
\(134\) −1.52112 −0.131405
\(135\) −8.82530 + 0.946840i −0.759561 + 0.0814910i
\(136\) −6.09354 −0.522517
\(137\) −1.60026 2.77173i −0.136720 0.236805i 0.789533 0.613708i \(-0.210323\pi\)
−0.926253 + 0.376902i \(0.876989\pi\)
\(138\) 1.32782 + 6.22487i 0.113031 + 0.529896i
\(139\) 7.49682 12.9849i 0.635872 1.10136i −0.350457 0.936579i \(-0.613974\pi\)
0.986330 0.164784i \(-0.0526928\pi\)
\(140\) 5.12498 8.87673i 0.433140 0.750220i
\(141\) 1.38957 1.25299i 0.117023 0.105520i
\(142\) 1.72094 + 2.98075i 0.144418 + 0.250139i
\(143\) 0 0
\(144\) 6.35185 + 4.60094i 0.529321 + 0.383411i
\(145\) 2.88902 0.239920
\(146\) −3.68916 6.38980i −0.305317 0.528824i
\(147\) 7.63142 + 2.47353i 0.629429 + 0.204013i
\(148\) 2.69677 4.67094i 0.221673 0.383949i
\(149\) −2.02556 + 3.50838i −0.165940 + 0.287417i −0.936989 0.349359i \(-0.886399\pi\)
0.771048 + 0.636777i \(0.219733\pi\)
\(150\) 1.68271 + 0.545409i 0.137393 + 0.0445324i
\(151\) 3.89699 + 6.74979i 0.317133 + 0.549290i 0.979889 0.199546i \(-0.0639466\pi\)
−0.662756 + 0.748836i \(0.730613\pi\)
\(152\) −8.14602 −0.660729
\(153\) 9.05083 4.04530i 0.731716 0.327043i
\(154\) 0 0
\(155\) 3.32968 + 5.76717i 0.267446 + 0.463230i
\(156\) −9.04806 + 8.15870i −0.724425 + 0.653219i
\(157\) −0.154576 + 0.267734i −0.0123365 + 0.0213675i −0.872128 0.489278i \(-0.837260\pi\)
0.859791 + 0.510646i \(0.170594\pi\)
\(158\) −0.980775 + 1.69875i −0.0780262 + 0.135145i
\(159\) 4.53970 + 21.2823i 0.360022 + 1.68780i
\(160\) 4.24506 + 7.35265i 0.335601 + 0.581278i
\(161\) 25.5517 2.01375
\(162\) 4.32060 + 0.905385i 0.339459 + 0.0711337i
\(163\) 10.9941 0.861125 0.430563 0.902561i \(-0.358315\pi\)
0.430563 + 0.902561i \(0.358315\pi\)
\(164\) 0.343855 + 0.595575i 0.0268506 + 0.0465066i
\(165\) 0 0
\(166\) −0.0306475 + 0.0530830i −0.00237871 + 0.00412004i
\(167\) 8.78693 15.2194i 0.679953 1.17771i −0.295041 0.955485i \(-0.595333\pi\)
0.974994 0.222229i \(-0.0713333\pi\)
\(168\) −8.08961 + 7.29446i −0.624127 + 0.562780i
\(169\) −1.49170 2.58369i −0.114746 0.198746i
\(170\) 2.76874 0.212353
\(171\) 12.0994 5.40788i 0.925265 0.413551i
\(172\) −16.9127 −1.28958
\(173\) −6.18287 10.7090i −0.470075 0.814193i 0.529340 0.848410i \(-0.322440\pi\)
−0.999414 + 0.0342165i \(0.989106\pi\)
\(174\) −1.36685 0.443028i −0.103620 0.0335859i
\(175\) 3.55058 6.14978i 0.268398 0.464880i
\(176\) 0 0
\(177\) −6.02475 1.95277i −0.452848 0.146779i
\(178\) −1.94561 3.36990i −0.145830 0.252584i
\(179\) 21.8823 1.63556 0.817780 0.575531i \(-0.195205\pi\)
0.817780 + 0.575531i \(0.195205\pi\)
\(180\) −7.30186 5.28908i −0.544249 0.394224i
\(181\) −4.38018 −0.325576 −0.162788 0.986661i \(-0.552049\pi\)
−0.162788 + 0.986661i \(0.552049\pi\)
\(182\) −3.34394 5.79188i −0.247870 0.429323i
\(183\) 4.95646 4.46928i 0.366392 0.330378i
\(184\) −6.90752 + 11.9642i −0.509229 + 0.882011i
\(185\) −2.61823 + 4.53491i −0.192496 + 0.333413i
\(186\) −0.690939 3.23915i −0.0506621 0.237506i
\(187\) 0 0
\(188\) 1.90062 0.138617
\(189\) 7.17306 16.2050i 0.521764 1.17874i
\(190\) 3.70133 0.268523
\(191\) −6.25737 10.8381i −0.452767 0.784216i 0.545790 0.837922i \(-0.316230\pi\)
−0.998557 + 0.0537064i \(0.982896\pi\)
\(192\) 1.00843 + 4.72755i 0.0727770 + 0.341182i
\(193\) 6.28286 10.8822i 0.452250 0.783320i −0.546276 0.837606i \(-0.683955\pi\)
0.998525 + 0.0542857i \(0.0172882\pi\)
\(194\) 0.0841588 0.145767i 0.00604225 0.0104655i
\(195\) 8.78456 7.92110i 0.629075 0.567242i
\(196\) 4.07451 + 7.05726i 0.291037 + 0.504090i
\(197\) −10.3453 −0.737075 −0.368538 0.929613i \(-0.620141\pi\)
−0.368538 + 0.929613i \(0.620141\pi\)
\(198\) 0 0
\(199\) 26.4773 1.87693 0.938464 0.345376i \(-0.112249\pi\)
0.938464 + 0.345376i \(0.112249\pi\)
\(200\) 1.91969 + 3.32501i 0.135743 + 0.235114i
\(201\) 5.10973 + 1.65619i 0.360413 + 0.116819i
\(202\) 1.74508 3.02256i 0.122783 0.212667i
\(203\) −2.88409 + 4.99539i −0.202423 + 0.350608i
\(204\) 9.57971 + 3.10502i 0.670714 + 0.217395i
\(205\) −0.333842 0.578231i −0.0233165 0.0403854i
\(206\) 0.811418 0.0565342
\(207\) 2.31722 22.3563i 0.161058 1.55387i
\(208\) −10.4521 −0.724721
\(209\) 0 0
\(210\) 3.67570 3.31441i 0.253647 0.228716i
\(211\) 3.64195 6.30804i 0.250722 0.434264i −0.713003 0.701161i \(-0.752665\pi\)
0.963725 + 0.266898i \(0.0859986\pi\)
\(212\) −11.0525 + 19.1434i −0.759086 + 1.31478i
\(213\) −2.53552 11.8866i −0.173731 0.814459i
\(214\) 0.810990 + 1.40468i 0.0554382 + 0.0960217i
\(215\) 16.4202 1.11985
\(216\) 5.64861 + 7.73947i 0.384339 + 0.526604i
\(217\) −13.2960 −0.902590
\(218\) −1.35060 2.33930i −0.0914741 0.158438i
\(219\) 5.43538 + 25.4813i 0.367289 + 1.72187i
\(220\) 0 0
\(221\) −6.60572 + 11.4414i −0.444349 + 0.769635i
\(222\) 1.93416 1.74404i 0.129812 0.117053i
\(223\) −11.7550 20.3603i −0.787175 1.36343i −0.927691 0.373349i \(-0.878209\pi\)
0.140516 0.990078i \(-0.455124\pi\)
\(224\) −16.9512 −1.13260
\(225\) −5.05872 3.66426i −0.337248 0.244284i
\(226\) 8.04863 0.535387
\(227\) 5.96109 + 10.3249i 0.395652 + 0.685289i 0.993184 0.116556i \(-0.0371854\pi\)
−0.597532 + 0.801845i \(0.703852\pi\)
\(228\) 12.8064 + 4.15088i 0.848127 + 0.274899i
\(229\) −1.52879 + 2.64793i −0.101025 + 0.174980i −0.912107 0.409952i \(-0.865546\pi\)
0.811082 + 0.584932i \(0.198879\pi\)
\(230\) 3.13859 5.43620i 0.206953 0.358453i
\(231\) 0 0
\(232\) −1.55934 2.70086i −0.102376 0.177320i
\(233\) −24.5314 −1.60710 −0.803552 0.595235i \(-0.797059\pi\)
−0.803552 + 0.595235i \(0.797059\pi\)
\(234\) −5.37082 + 2.40051i −0.351102 + 0.156926i
\(235\) −1.84527 −0.120372
\(236\) −3.21669 5.57147i −0.209389 0.362672i
\(237\) 5.14420 4.63857i 0.334152 0.301307i
\(238\) −2.76401 + 4.78741i −0.179164 + 0.310322i
\(239\) 3.47531 6.01942i 0.224799 0.389364i −0.731460 0.681885i \(-0.761161\pi\)
0.956259 + 0.292521i \(0.0944940\pi\)
\(240\) −1.61364 7.56483i −0.104160 0.488308i
\(241\) 3.88529 + 6.72952i 0.250274 + 0.433487i 0.963601 0.267344i \(-0.0861461\pi\)
−0.713327 + 0.700831i \(0.752813\pi\)
\(242\) 0 0
\(243\) −13.5280 7.74562i −0.867818 0.496881i
\(244\) 6.77934 0.434003
\(245\) −3.95585 6.85174i −0.252730 0.437741i
\(246\) 0.0692753 + 0.324765i 0.00441683 + 0.0207063i
\(247\) −8.83072 + 15.2952i −0.561885 + 0.973213i
\(248\) 3.59438 6.22564i 0.228243 0.395329i
\(249\) 0.160747 0.144947i 0.0101870 0.00918565i
\(250\) −2.96688 5.13879i −0.187642 0.325006i
\(251\) 0.327168 0.0206506 0.0103253 0.999947i \(-0.496713\pi\)
0.0103253 + 0.999947i \(0.496713\pi\)
\(252\) 16.4347 7.34556i 1.03529 0.462727i
\(253\) 0 0
\(254\) 2.64742 + 4.58547i 0.166114 + 0.287718i
\(255\) −9.30073 3.01459i −0.582434 0.188781i
\(256\) −0.0172493 + 0.0298766i −0.00107808 + 0.00186729i
\(257\) 6.86458 11.8898i 0.428201 0.741666i −0.568512 0.822675i \(-0.692481\pi\)
0.996713 + 0.0810088i \(0.0258142\pi\)
\(258\) −7.76867 2.51802i −0.483656 0.156765i
\(259\) −5.22753 9.05434i −0.324823 0.562609i
\(260\) 12.0153 0.745159
\(261\) 4.10913 + 2.97643i 0.254349 + 0.184237i
\(262\) 10.3767 0.641076
\(263\) 8.42709 + 14.5961i 0.519637 + 0.900037i 0.999739 + 0.0228249i \(0.00726603\pi\)
−0.480103 + 0.877212i \(0.659401\pi\)
\(264\) 0 0
\(265\) 10.7306 18.5859i 0.659174 1.14172i
\(266\) −3.69501 + 6.39995i −0.226556 + 0.392406i
\(267\) 2.86655 + 13.4385i 0.175430 + 0.822422i
\(268\) 2.72815 + 4.72529i 0.166648 + 0.288643i
\(269\) 12.3974 0.755882 0.377941 0.925830i \(-0.376632\pi\)
0.377941 + 0.925830i \(0.376632\pi\)
\(270\) −2.56658 3.51660i −0.156197 0.214014i
\(271\) 19.2695 1.17054 0.585269 0.810839i \(-0.300989\pi\)
0.585269 + 0.810839i \(0.300989\pi\)
\(272\) 4.31970 + 7.48194i 0.261920 + 0.453659i
\(273\) 4.92677 + 23.0969i 0.298182 + 1.39789i
\(274\) 0.784919 1.35952i 0.0474187 0.0821316i
\(275\) 0 0
\(276\) 16.9558 15.2892i 1.02062 0.920302i
\(277\) −5.17554 8.96430i −0.310968 0.538613i 0.667604 0.744516i \(-0.267320\pi\)
−0.978572 + 0.205904i \(0.933987\pi\)
\(278\) 7.35429 0.441081
\(279\) −1.20578 + 11.6332i −0.0721882 + 0.696463i
\(280\) 10.7426 0.641991
\(281\) 8.21790 + 14.2338i 0.490239 + 0.849119i 0.999937 0.0112348i \(-0.00357623\pi\)
−0.509698 + 0.860353i \(0.670243\pi\)
\(282\) 0.873031 + 0.282971i 0.0519882 + 0.0168507i
\(283\) 0.632477 1.09548i 0.0375968 0.0651197i −0.846615 0.532206i \(-0.821363\pi\)
0.884212 + 0.467087i \(0.154696\pi\)
\(284\) 6.17304 10.6920i 0.366303 0.634455i
\(285\) −12.4335 4.02999i −0.736496 0.238716i
\(286\) 0 0
\(287\) 1.33309 0.0786896
\(288\) −1.53727 + 14.8314i −0.0905843 + 0.873947i
\(289\) −6.07978 −0.357634
\(290\) 0.708523 + 1.22720i 0.0416059 + 0.0720636i
\(291\) −0.441417 + 0.398029i −0.0258763 + 0.0233329i
\(292\) −13.2331 + 22.9204i −0.774409 + 1.34132i
\(293\) 12.0437 20.8603i 0.703601 1.21867i −0.263593 0.964634i \(-0.584908\pi\)
0.967194 0.254038i \(-0.0817589\pi\)
\(294\) 0.820876 + 3.84830i 0.0478745 + 0.224438i
\(295\) 3.12301 + 5.40921i 0.181829 + 0.314937i
\(296\) 5.65274 0.328559
\(297\) 0 0
\(298\) −1.98705 −0.115107
\(299\) 14.9762 + 25.9396i 0.866098 + 1.50013i
\(300\) −1.32368 6.20548i −0.0764228 0.358273i
\(301\) −16.3921 + 28.3920i −0.944827 + 1.63649i
\(302\) −1.91145 + 3.31073i −0.109992 + 0.190511i
\(303\) −9.15299 + 8.25332i −0.525826 + 0.474141i
\(304\) 5.77470 + 10.0021i 0.331202 + 0.573658i
\(305\) −6.58191 −0.376879
\(306\) 3.93805 + 2.85251i 0.225124 + 0.163067i
\(307\) 16.2949 0.930001 0.465001 0.885310i \(-0.346054\pi\)
0.465001 + 0.885310i \(0.346054\pi\)
\(308\) 0 0
\(309\) −2.72571 0.883469i −0.155060 0.0502588i
\(310\) −1.63319 + 2.82876i −0.0927588 + 0.160663i
\(311\) −10.6856 + 18.5080i −0.605926 + 1.04950i 0.385978 + 0.922508i \(0.373864\pi\)
−0.991904 + 0.126987i \(0.959469\pi\)
\(312\) −12.1467 3.93703i −0.687669 0.222890i
\(313\) −1.55806 2.69864i −0.0880669 0.152536i 0.818627 0.574325i \(-0.194736\pi\)
−0.906694 + 0.421789i \(0.861402\pi\)
\(314\) −0.151637 −0.00855738
\(315\) −15.9561 + 7.13164i −0.899024 + 0.401822i
\(316\) 7.03613 0.395813
\(317\) 9.13242 + 15.8178i 0.512928 + 0.888417i 0.999888 + 0.0149929i \(0.00477258\pi\)
−0.486960 + 0.873425i \(0.661894\pi\)
\(318\) −7.92696 + 7.14780i −0.444522 + 0.400829i
\(319\) 0 0
\(320\) 2.38364 4.12859i 0.133250 0.230795i
\(321\) −1.19487 5.60158i −0.0666909 0.312650i
\(322\) 6.26647 + 10.8538i 0.349217 + 0.604861i
\(323\) 14.5985 0.812280
\(324\) −4.93652 15.0456i −0.274251 0.835866i
\(325\) 8.32420 0.461744
\(326\) 2.69627 + 4.67008i 0.149333 + 0.258652i
\(327\) 1.98989 + 9.32870i 0.110041 + 0.515878i
\(328\) −0.360381 + 0.624198i −0.0198987 + 0.0344656i
\(329\) 1.84212 3.19065i 0.101560 0.175906i
\(330\) 0 0
\(331\) −1.88308 3.26159i −0.103503 0.179273i 0.809622 0.586951i \(-0.199672\pi\)
−0.913126 + 0.407678i \(0.866339\pi\)
\(332\) 0.219867 0.0120668
\(333\) −8.39611 + 3.75267i −0.460104 + 0.205645i
\(334\) 8.61988 0.471659
\(335\) −2.64870 4.58768i −0.144714 0.250652i
\(336\) 14.6912 + 4.76178i 0.801470 + 0.259776i
\(337\) −2.98309 + 5.16686i −0.162499 + 0.281457i −0.935764 0.352626i \(-0.885289\pi\)
0.773265 + 0.634083i \(0.218622\pi\)
\(338\) 0.731668 1.26729i 0.0397975 0.0689313i
\(339\) −27.0369 8.76331i −1.46844 0.475958i
\(340\) −4.96577 8.60097i −0.269307 0.466453i
\(341\) 0 0
\(342\) 5.26450 + 3.81332i 0.284672 + 0.206201i
\(343\) −8.07726 −0.436131
\(344\) −8.86275 15.3507i −0.477848 0.827656i
\(345\) −16.4620 + 14.8440i −0.886287 + 0.799172i
\(346\) 3.03266 5.25272i 0.163037 0.282388i
\(347\) −12.1747 + 21.0871i −0.653570 + 1.13202i 0.328680 + 0.944441i \(0.393396\pi\)
−0.982250 + 0.187575i \(0.939937\pi\)
\(348\) 1.07521 + 5.04063i 0.0576373 + 0.270206i
\(349\) −8.37089 14.4988i −0.448083 0.776103i 0.550178 0.835047i \(-0.314560\pi\)
−0.998261 + 0.0589445i \(0.981227\pi\)
\(350\) 3.48307 0.186178
\(351\) 20.6553 2.21604i 1.10250 0.118284i
\(352\) 0 0
\(353\) 4.01566 + 6.95533i 0.213732 + 0.370195i 0.952880 0.303349i \(-0.0981047\pi\)
−0.739148 + 0.673544i \(0.764771\pi\)
\(354\) −0.648054 3.03811i −0.0344437 0.161473i
\(355\) −5.99327 + 10.3806i −0.318090 + 0.550947i
\(356\) −6.97896 + 12.0879i −0.369884 + 0.640658i
\(357\) 14.4974 13.0724i 0.767282 0.691864i
\(358\) 5.36657 + 9.29517i 0.283632 + 0.491265i
\(359\) −28.8250 −1.52133 −0.760663 0.649147i \(-0.775126\pi\)
−0.760663 + 0.649147i \(0.775126\pi\)
\(360\) 0.974217 9.39913i 0.0513457 0.495378i
\(361\) 0.515640 0.0271390
\(362\) −1.07422 1.86061i −0.0564600 0.0977916i
\(363\) 0 0
\(364\) −11.9948 + 20.7756i −0.628700 + 1.08894i
\(365\) 12.8477 22.2529i 0.672481 1.16477i
\(366\) 3.11402 + 1.00933i 0.162772 + 0.0527585i
\(367\) −11.1717 19.3499i −0.583158 1.01006i −0.995102 0.0988500i \(-0.968484\pi\)
0.411945 0.911209i \(-0.364850\pi\)
\(368\) 19.5869 1.02104
\(369\) 0.120894 1.16638i 0.00629351 0.0607191i
\(370\) −2.56845 −0.133528
\(371\) 21.4245 + 37.1084i 1.11231 + 1.92657i
\(372\) −8.82308 + 7.95584i −0.457456 + 0.412491i
\(373\) −3.53936 + 6.13036i −0.183261 + 0.317418i −0.942989 0.332823i \(-0.891999\pi\)
0.759728 + 0.650241i \(0.225332\pi\)
\(374\) 0 0
\(375\) 4.37123 + 20.4925i 0.225729 + 1.05823i
\(376\) 0.995982 + 1.72509i 0.0513639 + 0.0889648i
\(377\) −6.76164 −0.348242
\(378\) 8.64274 0.927253i 0.444534 0.0476927i
\(379\) −24.3461 −1.25057 −0.625287 0.780394i \(-0.715018\pi\)
−0.625287 + 0.780394i \(0.715018\pi\)
\(380\) −6.63839 11.4980i −0.340542 0.589836i
\(381\) −3.90055 18.2860i −0.199831 0.936818i
\(382\) 3.06920 5.31601i 0.157034 0.271991i
\(383\) 8.81894 15.2749i 0.450627 0.780509i −0.547798 0.836611i \(-0.684534\pi\)
0.998425 + 0.0561017i \(0.0178671\pi\)
\(384\) −14.5477 + 13.1178i −0.742384 + 0.669413i
\(385\) 0 0
\(386\) 6.16341 0.313709
\(387\) 23.3548 + 16.9170i 1.18719 + 0.859939i
\(388\) −0.603760 −0.0306513
\(389\) 8.94149 + 15.4871i 0.453352 + 0.785228i 0.998592 0.0530517i \(-0.0168948\pi\)
−0.545240 + 0.838280i \(0.683561\pi\)
\(390\) 5.51911 + 1.78888i 0.279471 + 0.0905835i
\(391\) 12.3790 21.4410i 0.626031 1.08432i
\(392\) −4.27033 + 7.39642i −0.215684 + 0.373576i
\(393\) −34.8574 11.2981i −1.75832 0.569915i
\(394\) −2.53717 4.39450i −0.127821 0.221392i
\(395\) −6.83122 −0.343716
\(396\) 0 0
\(397\) −21.9395 −1.10111 −0.550556 0.834798i \(-0.685584\pi\)
−0.550556 + 0.834798i \(0.685584\pi\)
\(398\) 6.49349 + 11.2471i 0.325489 + 0.563764i
\(399\) 19.3805 17.4755i 0.970238 0.874871i
\(400\) 2.72174 4.71418i 0.136087 0.235709i
\(401\) −2.70378 + 4.68308i −0.135020 + 0.233862i −0.925605 0.378490i \(-0.876443\pi\)
0.790585 + 0.612352i \(0.209777\pi\)
\(402\) 0.549630 + 2.57669i 0.0274131 + 0.128514i
\(403\) −7.79298 13.4978i −0.388196 0.672376i
\(404\) −12.5193 −0.622857
\(405\) 4.79276 + 14.6074i 0.238154 + 0.725849i
\(406\) −2.82926 −0.140414
\(407\) 0 0
\(408\) 2.20179 + 10.3221i 0.109005 + 0.511020i
\(409\) −11.8101 + 20.4556i −0.583970 + 1.01147i 0.411033 + 0.911621i \(0.365168\pi\)
−0.995003 + 0.0998457i \(0.968165\pi\)
\(410\) 0.163747 0.283619i 0.00808690 0.0140069i
\(411\) −4.11693 + 3.71227i −0.203073 + 0.183113i
\(412\) −1.45529 2.52064i −0.0716970 0.124183i
\(413\) −12.4707 −0.613644
\(414\) 10.0648 4.49850i 0.494657 0.221089i
\(415\) −0.213464 −0.0104785
\(416\) −9.93539 17.2086i −0.487123 0.843721i
\(417\) −24.7045 8.00733i −1.20978 0.392120i
\(418\) 0 0
\(419\) 9.06566 15.7022i 0.442886 0.767102i −0.555016 0.831840i \(-0.687288\pi\)
0.997902 + 0.0647380i \(0.0206212\pi\)
\(420\) −16.8885 5.47397i −0.824074 0.267102i
\(421\) 6.40610 + 11.0957i 0.312214 + 0.540771i 0.978841 0.204620i \(-0.0655960\pi\)
−0.666627 + 0.745391i \(0.732263\pi\)
\(422\) 3.57271 0.173917
\(423\) −2.62458 1.90111i −0.127611 0.0924349i
\(424\) −23.1672 −1.12510
\(425\) −3.44028 5.95874i −0.166878 0.289041i
\(426\) 4.42738 3.99220i 0.214507 0.193423i
\(427\) 6.57067 11.3807i 0.317977 0.550753i
\(428\) 2.90904 5.03861i 0.140614 0.243551i
\(429\) 0 0
\(430\) 4.02700 + 6.97496i 0.194199 + 0.336362i
\(431\) −6.57916 −0.316907 −0.158453 0.987366i \(-0.550651\pi\)
−0.158453 + 0.987366i \(0.550651\pi\)
\(432\) 5.49859 12.4221i 0.264551 0.597660i
\(433\) 13.9978 0.672690 0.336345 0.941739i \(-0.390809\pi\)
0.336345 + 0.941739i \(0.390809\pi\)
\(434\) −3.26080 5.64787i −0.156523 0.271106i
\(435\) −1.04390 4.89383i −0.0500510 0.234641i
\(436\) −4.84463 + 8.39115i −0.232016 + 0.401863i
\(437\) 16.5485 28.6629i 0.791624 1.37113i
\(438\) −9.49095 + 8.55806i −0.453495 + 0.408920i
\(439\) −12.5891 21.8050i −0.600846 1.04070i −0.992693 0.120665i \(-0.961497\pi\)
0.391848 0.920030i \(-0.371836\pi\)
\(440\) 0 0
\(441\) 1.43254 13.8210i 0.0682160 0.658141i
\(442\) −6.48013 −0.308228
\(443\) −13.4112 23.2289i −0.637187 1.10364i −0.986047 0.166466i \(-0.946765\pi\)
0.348860 0.937175i \(-0.386569\pi\)
\(444\) −8.88673 2.88041i −0.421746 0.136698i
\(445\) 6.77571 11.7359i 0.321200 0.556334i
\(446\) 5.76577 9.98661i 0.273017 0.472880i
\(447\) 6.67488 + 2.16349i 0.315711 + 0.102330i
\(448\) 4.75914 + 8.24308i 0.224848 + 0.389449i
\(449\) 14.1758 0.668999 0.334499 0.942396i \(-0.391433\pi\)
0.334499 + 0.942396i \(0.391433\pi\)
\(450\) 0.315872 3.04749i 0.0148903 0.143660i
\(451\) 0 0
\(452\) −14.4353 25.0027i −0.678981 1.17603i
\(453\) 10.0256 9.04020i 0.471046 0.424745i
\(454\) −2.92388 + 5.06431i −0.137225 + 0.237680i
\(455\) 11.6455 20.1706i 0.545950 0.945613i
\(456\) 2.94342 + 13.7989i 0.137838 + 0.646192i
\(457\) −12.3206 21.3400i −0.576335 0.998242i −0.995895 0.0905145i \(-0.971149\pi\)
0.419560 0.907728i \(-0.362184\pi\)
\(458\) −1.49972 −0.0700773
\(459\) −10.1229 13.8699i −0.472495 0.647390i
\(460\) −22.5164 −1.04983
\(461\) 13.1227 + 22.7292i 0.611185 + 1.05860i 0.991041 + 0.133558i \(0.0426401\pi\)
−0.379856 + 0.925046i \(0.624027\pi\)
\(462\) 0 0
\(463\) −6.34609 + 10.9917i −0.294928 + 0.510830i −0.974968 0.222345i \(-0.928629\pi\)
0.680040 + 0.733175i \(0.261962\pi\)
\(464\) −2.21083 + 3.82927i −0.102635 + 0.177769i
\(465\) 8.56613 7.72415i 0.397245 0.358199i
\(466\) −6.01624 10.4204i −0.278697 0.482718i
\(467\) −27.7040 −1.28199 −0.640994 0.767546i \(-0.721478\pi\)
−0.640994 + 0.767546i \(0.721478\pi\)
\(468\) 17.0897 + 12.3789i 0.789973 + 0.572214i
\(469\) 10.5767 0.488387
\(470\) −0.452548 0.783835i −0.0208745 0.0361556i
\(471\) 0.509378 + 0.165102i 0.0234709 + 0.00760750i
\(472\) 3.37128 5.83923i 0.155176 0.268772i
\(473\) 0 0
\(474\) 3.23197 + 1.04756i 0.148449 + 0.0481161i
\(475\) −4.59906 7.96581i −0.211020 0.365497i
\(476\) 19.8292 0.908870
\(477\) 34.4107 15.3800i 1.57556 0.704201i
\(478\) 3.40924 0.155935
\(479\) 7.81110 + 13.5292i 0.356898 + 0.618166i 0.987441 0.157989i \(-0.0505009\pi\)
−0.630543 + 0.776155i \(0.717168\pi\)
\(480\) 10.9211 9.84763i 0.498477 0.449481i
\(481\) 6.12787 10.6138i 0.279407 0.483947i
\(482\) −1.90571 + 3.30079i −0.0868028 + 0.150347i
\(483\) −9.23265 43.2830i −0.420100 1.96945i
\(484\) 0 0
\(485\) 0.586177 0.0266169
\(486\) −0.0275048 7.64600i −0.00124764 0.346829i
\(487\) 26.9270 1.22018 0.610090 0.792332i \(-0.291133\pi\)
0.610090 + 0.792332i \(0.291133\pi\)
\(488\) 3.55257 + 6.15324i 0.160817 + 0.278544i
\(489\) −3.97253 18.6234i −0.179644 0.842178i
\(490\) 1.94032 3.36074i 0.0876548 0.151823i
\(491\) −19.4999 + 33.7748i −0.880017 + 1.52423i −0.0286964 + 0.999588i \(0.509136\pi\)
−0.851321 + 0.524646i \(0.824198\pi\)
\(492\) 0.884624 0.797672i 0.0398819 0.0359618i
\(493\) 2.79450 + 4.84021i 0.125858 + 0.217992i
\(494\) −8.66283 −0.389759
\(495\) 0 0
\(496\) −10.1922 −0.457642
\(497\) −11.9661 20.7259i −0.536752 0.929681i
\(498\) 0.100993 + 0.0327345i 0.00452563 + 0.00146687i
\(499\) 12.0176 20.8150i 0.537980 0.931809i −0.461033 0.887383i \(-0.652521\pi\)
0.999013 0.0444256i \(-0.0141457\pi\)
\(500\) −10.6423 + 18.4330i −0.475938 + 0.824349i
\(501\) −28.9558 9.38528i −1.29365 0.419304i
\(502\) 0.0802369 + 0.138974i 0.00358115 + 0.00620273i
\(503\) −23.9865 −1.06950 −0.534752 0.845009i \(-0.679595\pi\)
−0.534752 + 0.845009i \(0.679595\pi\)
\(504\) 15.2794 + 11.0676i 0.680600 + 0.492990i
\(505\) 12.1547 0.540876
\(506\) 0 0
\(507\) −3.83763 + 3.46042i −0.170435 + 0.153683i
\(508\) 9.49637 16.4482i 0.421333 0.729771i
\(509\) −1.84943 + 3.20331i −0.0819746 + 0.141984i −0.904098 0.427325i \(-0.859456\pi\)
0.822123 + 0.569309i \(0.192789\pi\)
\(510\) −1.00044 4.69009i −0.0443000 0.207680i
\(511\) 25.6516 + 44.4298i 1.13476 + 1.96546i
\(512\) −22.6358 −1.00037
\(513\) −13.5325 18.5416i −0.597476 0.818634i
\(514\) 6.73407 0.297027
\(515\) 1.41291 + 2.44723i 0.0622602 + 0.107838i
\(516\) 6.11111 + 28.6491i 0.269027 + 1.26121i
\(517\) 0 0
\(518\) 2.56407 4.44110i 0.112659 0.195131i
\(519\) −15.9064 + 14.3429i −0.698215 + 0.629585i
\(520\) 6.29639 + 10.9057i 0.276115 + 0.478245i
\(521\) −6.41318 −0.280966 −0.140483 0.990083i \(-0.544866\pi\)
−0.140483 + 0.990083i \(0.544866\pi\)
\(522\) −0.256578 + 2.47544i −0.0112301 + 0.108347i
\(523\) −2.73856 −0.119749 −0.0598745 0.998206i \(-0.519070\pi\)
−0.0598745 + 0.998206i \(0.519070\pi\)
\(524\) −18.6108 32.2348i −0.813016 1.40819i
\(525\) −11.7003 3.79236i −0.510643 0.165512i
\(526\) −4.13344 + 7.15932i −0.180226 + 0.312161i
\(527\) −6.44147 + 11.1570i −0.280595 + 0.486005i
\(528\) 0 0
\(529\) −16.5651 28.6916i −0.720222 1.24746i
\(530\) 10.5266 0.457245
\(531\) −1.13094 + 10.9112i −0.0490786 + 0.473505i
\(532\) 26.5082 1.14928
\(533\) 0.781343 + 1.35333i 0.0338437 + 0.0586191i
\(534\) −5.00539 + 4.51340i −0.216605 + 0.195314i
\(535\) −2.82433 + 4.89188i −0.122106 + 0.211494i
\(536\) −2.85926 + 4.95239i −0.123501 + 0.213910i
\(537\) −7.90678 37.0673i −0.341203 1.59957i
\(538\) 3.04042 + 5.26617i 0.131082 + 0.227041i
\(539\) 0 0
\(540\) −6.32099 + 14.2800i −0.272012 + 0.614515i
\(541\) 20.9037 0.898719 0.449359 0.893351i \(-0.351652\pi\)
0.449359 + 0.893351i \(0.351652\pi\)
\(542\) 4.72579 + 8.18530i 0.202990 + 0.351589i
\(543\) 1.58270 + 7.41976i 0.0679201 + 0.318412i
\(544\) −8.21233 + 14.2242i −0.352101 + 0.609856i
\(545\) 4.70355 8.14678i 0.201478 0.348970i
\(546\) −8.60284 + 7.75724i −0.368167 + 0.331979i
\(547\) 20.9382 + 36.2660i 0.895252 + 1.55062i 0.833493 + 0.552531i \(0.186338\pi\)
0.0617594 + 0.998091i \(0.480329\pi\)
\(548\) −5.63105 −0.240547
\(549\) −9.36162 6.78106i −0.399544 0.289408i
\(550\) 0 0
\(551\) 3.73576 + 6.47053i 0.159149 + 0.275654i
\(552\) 22.7625 + 7.37790i 0.968838 + 0.314024i
\(553\) 6.81956 11.8118i 0.289997 0.502290i
\(554\) 2.53857 4.39693i 0.107854 0.186808i
\(555\) 8.62793 + 2.79652i 0.366235 + 0.118706i
\(556\) −13.1900 22.8458i −0.559382 0.968878i
\(557\) −12.5244 −0.530675 −0.265337 0.964156i \(-0.585483\pi\)
−0.265337 + 0.964156i \(0.585483\pi\)
\(558\) −5.23728 + 2.34082i −0.221712 + 0.0990949i
\(559\) −38.4308 −1.62545
\(560\) −7.61538 13.1902i −0.321809 0.557389i
\(561\) 0 0
\(562\) −4.03083 + 6.98160i −0.170030 + 0.294501i
\(563\) 7.25437 12.5649i 0.305735 0.529549i −0.671690 0.740833i \(-0.734431\pi\)
0.977425 + 0.211284i \(0.0677644\pi\)
\(564\) −0.686757 3.21955i −0.0289177 0.135567i
\(565\) 14.0149 + 24.2746i 0.589613 + 1.02124i
\(566\) 0.620452 0.0260796
\(567\) −30.0422 6.29536i −1.26165 0.264380i
\(568\) 12.9394 0.542926
\(569\) 13.9862 + 24.2248i 0.586332 + 1.01556i 0.994708 + 0.102743i \(0.0327621\pi\)
−0.408375 + 0.912814i \(0.633905\pi\)
\(570\) −1.33741 6.26984i −0.0560180 0.262615i
\(571\) −4.52443 + 7.83654i −0.189341 + 0.327949i −0.945031 0.326981i \(-0.893969\pi\)
0.755689 + 0.654930i \(0.227302\pi\)
\(572\) 0 0
\(573\) −16.0981 + 14.5158i −0.672507 + 0.606405i
\(574\) 0.326936 + 0.566269i 0.0136460 + 0.0236356i
\(575\) −15.5993 −0.650538
\(576\) 7.64382 3.41644i 0.318493 0.142351i
\(577\) 38.3471 1.59641 0.798204 0.602387i \(-0.205783\pi\)
0.798204 + 0.602387i \(0.205783\pi\)
\(578\) −1.49105 2.58257i −0.0620194 0.107421i
\(579\) −20.7041 6.71069i −0.860431 0.278887i
\(580\) 2.54149 4.40200i 0.105530 0.182783i
\(581\) 0.213099 0.369099i 0.00884085 0.0153128i
\(582\) −0.277331 0.0898897i −0.0114957 0.00372605i
\(583\) 0 0
\(584\) −27.7381 −1.14781
\(585\) −16.5920 12.0184i −0.685996 0.496899i
\(586\) 11.8147 0.488062
\(587\) 0.361309 + 0.625805i 0.0149128 + 0.0258297i 0.873385 0.487030i \(-0.161920\pi\)
−0.858473 + 0.512859i \(0.828586\pi\)
\(588\) 10.4823 9.45200i 0.432284 0.389794i
\(589\) −8.61114 + 14.9149i −0.354816 + 0.614559i
\(590\) −1.53182 + 2.65319i −0.0630640 + 0.109230i
\(591\) 3.73811 + 17.5244i 0.153765 + 0.720858i
\(592\) −4.00722 6.94071i −0.164696 0.285261i
\(593\) −39.6596 −1.62863 −0.814313 0.580426i \(-0.802886\pi\)
−0.814313 + 0.580426i \(0.802886\pi\)
\(594\) 0 0
\(595\) −19.2517 −0.789244
\(596\) 3.56380 + 6.17269i 0.145979 + 0.252843i
\(597\) −9.56712 44.8511i −0.391556 1.83563i
\(598\) −7.34576 + 12.7232i −0.300390 + 0.520291i
\(599\) 10.1884 17.6468i 0.416287 0.721030i −0.579276 0.815132i \(-0.696665\pi\)
0.995563 + 0.0941018i \(0.0299979\pi\)
\(600\) 4.93872 4.45328i 0.201623 0.181805i
\(601\) 24.1859 + 41.8911i 0.986562 + 1.70878i 0.634780 + 0.772693i \(0.281091\pi\)
0.351782 + 0.936082i \(0.385576\pi\)
\(602\) −16.0805 −0.655392
\(603\) 0.959176 9.25402i 0.0390607 0.376853i
\(604\) 13.7129 0.557968
\(605\) 0 0
\(606\) −5.75059 1.86391i −0.233602 0.0757161i
\(607\) 9.85114 17.0627i 0.399845 0.692553i −0.593861 0.804568i \(-0.702397\pi\)
0.993707 + 0.112015i \(0.0357304\pi\)
\(608\) −10.9785 + 19.0153i −0.445236 + 0.771171i
\(609\) 9.50401 + 3.08048i 0.385122 + 0.124827i
\(610\) −1.61419 2.79586i −0.0653568 0.113201i
\(611\) 4.31879 0.174720
\(612\) 1.79826 17.3494i 0.0726904 0.701309i
\(613\) 5.71781 0.230940 0.115470 0.993311i \(-0.463163\pi\)
0.115470 + 0.993311i \(0.463163\pi\)
\(614\) 3.99629 + 6.92177i 0.161277 + 0.279340i
\(615\) −0.858861 + 0.774442i −0.0346326 + 0.0312285i
\(616\) 0 0
\(617\) −3.05346 + 5.28875i −0.122928 + 0.212917i −0.920921 0.389749i \(-0.872562\pi\)
0.797993 + 0.602666i \(0.205895\pi\)
\(618\) −0.293192 1.37450i −0.0117939 0.0552903i
\(619\) 0.889867 + 1.54129i 0.0357668 + 0.0619499i 0.883355 0.468705i \(-0.155279\pi\)
−0.847588 + 0.530655i \(0.821946\pi\)
\(620\) 11.7166 0.470549
\(621\) −38.7075 + 4.15281i −1.55328 + 0.166646i
\(622\) −10.4825 −0.420309
\(623\) 13.5283 + 23.4317i 0.542000 + 0.938771i
\(624\) 3.77667 + 17.7052i 0.151188 + 0.708775i
\(625\) 5.12704 8.88029i 0.205081 0.355212i
\(626\) 0.764220 1.32367i 0.0305444 0.0529044i
\(627\) 0 0
\(628\) 0.271963 + 0.471055i 0.0108525 + 0.0187971i
\(629\) −10.1303 −0.403920
\(630\) −6.94256 5.02882i −0.276598 0.200353i
\(631\) −44.8407 −1.78508 −0.892541 0.450966i \(-0.851079\pi\)
−0.892541 + 0.450966i \(0.851079\pi\)
\(632\) 3.68714 + 6.38631i 0.146667 + 0.254034i
\(633\) −12.0014 3.88995i −0.477013 0.154612i
\(634\) −4.47940 + 7.75855i −0.177900 + 0.308131i
\(635\) −9.21981 + 15.9692i −0.365877 + 0.633718i
\(636\) 36.4214 + 11.8051i 1.44420 + 0.468102i
\(637\) 9.25852 + 16.0362i 0.366836 + 0.635379i
\(638\) 0 0
\(639\) −19.2191 + 8.59006i −0.760297 + 0.339818i
\(640\) 19.3185 0.763633
\(641\) 13.5048 + 23.3910i 0.533407 + 0.923888i 0.999239 + 0.0390143i \(0.0124218\pi\)
−0.465832 + 0.884873i \(0.654245\pi\)
\(642\) 2.08640 1.88133i 0.0823438 0.0742500i
\(643\) 16.2787 28.1955i 0.641969 1.11192i −0.343024 0.939327i \(-0.611451\pi\)
0.984993 0.172596i \(-0.0552155\pi\)
\(644\) 22.4780 38.9330i 0.885758 1.53418i
\(645\) −5.93314 27.8148i −0.233617 1.09521i
\(646\) 3.58023 + 6.20114i 0.140862 + 0.243981i
\(647\) −31.4833 −1.23774 −0.618868 0.785495i \(-0.712408\pi\)
−0.618868 + 0.785495i \(0.712408\pi\)
\(648\) 11.0692 12.3649i 0.434838 0.485741i
\(649\) 0 0
\(650\) 2.04149 + 3.53596i 0.0800736 + 0.138692i
\(651\) 4.80427 + 22.5226i 0.188294 + 0.882731i
\(652\) 9.67160 16.7517i 0.378769 0.656048i
\(653\) 2.32989 4.03548i 0.0911755 0.157921i −0.816831 0.576878i \(-0.804271\pi\)
0.908006 + 0.418957i \(0.137604\pi\)
\(654\) −3.47463 + 3.13310i −0.135869 + 0.122514i
\(655\) 18.0688 + 31.2961i 0.706007 + 1.22284i
\(656\) 1.02189 0.0398982
\(657\) 41.1999 18.4144i 1.60736 0.718416i
\(658\) 1.80710 0.0704481
\(659\) 16.0209 + 27.7490i 0.624086 + 1.08095i 0.988717 + 0.149797i \(0.0478619\pi\)
−0.364631 + 0.931152i \(0.618805\pi\)
\(660\) 0 0
\(661\) 20.3527 35.2519i 0.791627 1.37114i −0.133331 0.991072i \(-0.542567\pi\)
0.924959 0.380067i \(-0.124099\pi\)
\(662\) 0.923639 1.59979i 0.0358982 0.0621776i
\(663\) 21.7680 + 7.05554i 0.845399 + 0.274015i
\(664\) 0.115217 + 0.199561i 0.00447127 + 0.00774448i
\(665\) −25.7362 −0.998009
\(666\) −3.65318 2.64617i −0.141558 0.102537i
\(667\) 12.6712 0.490629
\(668\) −15.4599 26.7773i −0.598160 1.03604i
\(669\) −30.2417 + 27.2692i −1.16921 + 1.05429i
\(670\) 1.29917 2.25023i 0.0501914 0.0869340i
\(671\) 0 0
\(672\) 6.12503 + 28.7144i 0.236278 + 1.10768i
\(673\) 18.8818 + 32.7042i 0.727838 + 1.26065i 0.957795 + 0.287452i \(0.0928083\pi\)
−0.229957 + 0.973201i \(0.573858\pi\)
\(674\) −2.92637 −0.112720
\(675\) −4.37917 + 9.89319i −0.168554 + 0.380789i
\(676\) −5.24903 −0.201886
\(677\) −9.45033 16.3685i −0.363206 0.629091i 0.625281 0.780400i \(-0.284984\pi\)
−0.988487 + 0.151309i \(0.951651\pi\)
\(678\) −2.90823 13.6339i −0.111690 0.523607i
\(679\) −0.585177 + 1.01356i −0.0224570 + 0.0388967i
\(680\) 5.20442 9.01433i 0.199581 0.345684i
\(681\) 15.3359 13.8285i 0.587672 0.529908i
\(682\) 0 0
\(683\) 31.1053 1.19021 0.595105 0.803648i \(-0.297110\pi\)
0.595105 + 0.803648i \(0.297110\pi\)
\(684\) 2.40397 23.1932i 0.0919180 0.886814i
\(685\) 5.46706 0.208886
\(686\) −1.98092 3.43106i −0.0756320 0.130998i
\(687\) 5.03785 + 1.63289i 0.192206 + 0.0622986i
\(688\) −12.5656 + 21.7642i −0.479058 + 0.829753i
\(689\) −25.1145 + 43.4996i −0.956787 + 1.65720i
\(690\) −10.3427 3.35232i −0.393739 0.127621i
\(691\) −11.1057 19.2356i −0.422481 0.731758i 0.573701 0.819065i \(-0.305507\pi\)
−0.996181 + 0.0873068i \(0.972174\pi\)
\(692\) −21.7565 −0.827057
\(693\) 0 0
\(694\) −11.9432 −0.453358
\(695\) 12.8059 + 22.1805i 0.485756 + 0.841353i
\(696\) −4.01166 + 3.61735i −0.152062 + 0.137115i
\(697\) 0.645837 1.11862i 0.0244628 0.0423709i
\(698\) 4.10587 7.11157i 0.155409 0.269177i
\(699\) 8.86398 + 41.5547i 0.335266 + 1.57174i
\(700\) −6.24694 10.8200i −0.236112 0.408958i
\(701\) −29.9457 −1.13103 −0.565517 0.824736i \(-0.691323\pi\)
−0.565517 + 0.824736i \(0.691323\pi\)
\(702\) 6.00698 + 8.23048i 0.226719 + 0.310639i
\(703\) −13.5424 −0.510763
\(704\) 0 0
\(705\) 0.666757 + 3.12578i 0.0251115 + 0.117724i
\(706\) −1.96966 + 3.41155i −0.0741290 + 0.128395i
\(707\) −12.1339 + 21.0166i −0.456343 + 0.790410i
\(708\) −8.27545 + 7.46204i −0.311010 + 0.280441i
\(709\) −8.60286 14.9006i −0.323087 0.559604i 0.658036 0.752986i \(-0.271387\pi\)
−0.981123 + 0.193383i \(0.938054\pi\)
\(710\) −5.87932 −0.220647
\(711\) −9.71623 7.03792i −0.364387 0.263942i
\(712\) −14.6287 −0.548234
\(713\) 14.6039 + 25.2946i 0.546919 + 0.947291i
\(714\) 9.10833 + 2.95223i 0.340871 + 0.110485i
\(715\) 0 0
\(716\) 19.2500 33.3420i 0.719407 1.24605i
\(717\) −11.4523 3.71197i −0.427694 0.138626i
\(718\) −7.06925 12.2443i −0.263822 0.456953i
\(719\) 4.72508 0.176216 0.0881079 0.996111i \(-0.471918\pi\)
0.0881079 + 0.996111i \(0.471918\pi\)
\(720\) −12.2313 + 5.46684i −0.455834 + 0.203737i
\(721\) −5.64199 −0.210119
\(722\) 0.126459 + 0.219034i 0.00470633 + 0.00815160i
\(723\) 9.99554 9.01306i 0.371738 0.335199i
\(724\) −3.85327 + 6.67407i −0.143206 + 0.248040i
\(725\) 1.76074 3.04969i 0.0653923 0.113263i
\(726\) 0 0
\(727\) −2.60044 4.50410i −0.0964450 0.167048i 0.813766 0.581193i \(-0.197414\pi\)
−0.910211 + 0.414145i \(0.864081\pi\)
\(728\) −25.1426 −0.931845
\(729\) −8.23253 + 25.7143i −0.304909 + 0.952382i
\(730\) 12.6035 0.466475
\(731\) 15.8829 + 27.5100i 0.587451 + 1.01749i
\(732\) −2.44959 11.4838i −0.0905396 0.424454i
\(733\) 24.5316 42.4900i 0.906095 1.56940i 0.0866539 0.996238i \(-0.472383\pi\)
0.819441 0.573164i \(-0.194284\pi\)
\(734\) 5.47965 9.49103i 0.202258 0.350320i
\(735\) −10.1771 + 9.17674i −0.375387 + 0.338489i
\(736\) 18.6187 + 32.2485i 0.686294 + 1.18870i
\(737\) 0 0
\(738\) 0.525102 0.234697i 0.0193293 0.00863930i
\(739\) −15.5942 −0.573641 −0.286821 0.957984i \(-0.592598\pi\)
−0.286821 + 0.957984i \(0.592598\pi\)
\(740\) 4.60656 + 7.97879i 0.169340 + 0.293306i
\(741\) 29.1001 + 9.43205i 1.06902 + 0.346495i
\(742\) −10.5086 + 18.2014i −0.385783 + 0.668196i
\(743\) −5.56722 + 9.64271i −0.204242 + 0.353757i −0.949891 0.312582i \(-0.898806\pi\)
0.745649 + 0.666339i \(0.232139\pi\)
\(744\) −11.8446 3.83914i −0.434245 0.140750i
\(745\) −3.46002 5.99293i −0.126765 0.219564i
\(746\) −3.47207 −0.127122
\(747\) −0.303615 0.219923i −0.0111087 0.00804655i
\(748\) 0 0
\(749\) −5.63901 9.76705i −0.206045 0.356880i
\(750\) −7.63279 + 6.88254i −0.278710 + 0.251315i
\(751\) 4.04260 7.00199i 0.147517 0.255506i −0.782792 0.622283i \(-0.786205\pi\)
0.930309 + 0.366777i \(0.119539\pi\)
\(752\) 1.41210 2.44583i 0.0514940 0.0891902i
\(753\) −0.118216 0.554203i −0.00430804 0.0201963i
\(754\) −1.65827 2.87221i −0.0603907 0.104600i
\(755\) −13.3135 −0.484528
\(756\) −18.3813 25.1853i −0.668523 0.915979i
\(757\) 29.8616 1.08534 0.542669 0.839947i \(-0.317414\pi\)
0.542669 + 0.839947i \(0.317414\pi\)
\(758\) −5.97081 10.3417i −0.216869 0.375629i
\(759\) 0 0
\(760\) 6.95742 12.0506i 0.252372 0.437121i
\(761\) −17.4463 + 30.2179i −0.632428 + 1.09540i 0.354626 + 0.935008i \(0.384608\pi\)
−0.987054 + 0.160389i \(0.948725\pi\)
\(762\) 6.81091 6.14145i 0.246733 0.222481i
\(763\) 9.39103 + 16.2657i 0.339978 + 0.588860i
\(764\) −22.0186 −0.796606
\(765\) −1.74589 + 16.8442i −0.0631228 + 0.609002i
\(766\) 8.65128 0.312583
\(767\) −7.30929 12.6601i −0.263923 0.457128i
\(768\) 0.0568420 + 0.0184239i 0.00205111 + 0.000664815i
\(769\) 2.80362 4.85600i 0.101101 0.175112i −0.811038 0.584994i \(-0.801097\pi\)
0.912139 + 0.409882i \(0.134430\pi\)
\(770\) 0 0
\(771\) −22.6210 7.33203i −0.814677 0.264057i
\(772\) −11.0542 19.1464i −0.397848 0.689093i
\(773\) −10.8401 −0.389893 −0.194946 0.980814i \(-0.562453\pi\)
−0.194946 + 0.980814i \(0.562453\pi\)
\(774\) −1.45830 + 14.0695i −0.0524175 + 0.505718i
\(775\) 8.11722 0.291579
\(776\) −0.316388 0.548000i −0.0113577 0.0196721i
\(777\) −13.4487 + 12.1268i −0.482468 + 0.435045i
\(778\) −4.38575 + 7.59634i −0.157237 + 0.272342i
\(779\) 0.863374 1.49541i 0.0309336 0.0535785i
\(780\) −4.34153 20.3533i −0.155452 0.728764i
\(781\) 0 0
\(782\) 12.1436 0.434255
\(783\) 3.55714 8.03611i 0.127122 0.287187i
\(784\) 12.1089 0.432461
\(785\) −0.264043 0.457336i −0.00942411 0.0163230i
\(786\) −3.74945 17.5776i −0.133738 0.626971i
\(787\) 1.23822 2.14465i 0.0441376 0.0764486i −0.843113 0.537737i \(-0.819279\pi\)
0.887250 + 0.461288i \(0.152613\pi\)
\(788\) −9.10088 + 15.7632i −0.324206 + 0.561540i
\(789\) 21.6800 19.5491i 0.771830 0.695965i
\(790\) −1.67534 2.90177i −0.0596058 0.103240i
\(791\) −55.9640 −1.98985
\(792\) 0 0
\(793\) 15.4047 0.547037
\(794\) −5.38060 9.31947i −0.190950 0.330735i
\(795\) −35.3608 11.4613i −1.25412 0.406490i
\(796\) 23.2923 40.3435i 0.825574 1.42994i
\(797\) 4.83984 8.38286i 0.171436 0.296936i −0.767486 0.641066i \(-0.778493\pi\)
0.938922 + 0.344130i \(0.111826\pi\)
\(798\) 12.1763 + 3.94663i 0.431035 + 0.139709i
\(799\) −1.78490 3.09153i −0.0631451 0.109371i
\(800\) 10.3488 0.365884
\(801\) 21.7282 9.71153i 0.767730 0.343140i
\(802\) −2.65237 −0.0936586
\(803\) 0 0
\(804\) 7.01861 6.32873i 0.247527 0.223197i
\(805\) −21.8234 + 37.7992i −0.769173 + 1.33225i
\(806\) 3.82241 6.62061i 0.134639 0.233201i
\(807\) −4.47958 21.0005i −0.157689 0.739251i
\(808\) −6.56046 11.3631i −0.230796 0.399751i
\(809\) −7.86532 −0.276530 −0.138265 0.990395i \(-0.544153\pi\)
−0.138265 + 0.990395i \(0.544153\pi\)
\(810\) −5.02954 + 5.61830i −0.176720 + 0.197407i
\(811\) 39.5047 1.38720 0.693599 0.720361i \(-0.256024\pi\)
0.693599 + 0.720361i \(0.256024\pi\)
\(812\) 5.07431 + 8.78896i 0.178073 + 0.308432i
\(813\) −6.96269 32.6414i −0.244192 1.14478i
\(814\) 0 0
\(815\) −9.38994 + 16.2639i −0.328915 + 0.569698i
\(816\) 11.1131 10.0208i 0.389037 0.350798i
\(817\) 21.2327 + 36.7762i 0.742839 + 1.28664i
\(818\) −11.5855 −0.405079
\(819\) 37.3446 16.6913i 1.30493 0.583242i
\(820\) −1.17473 −0.0410234
\(821\) 1.67681 + 2.90432i 0.0585211 + 0.101361i 0.893802 0.448462i \(-0.148028\pi\)
−0.835281 + 0.549824i \(0.814695\pi\)
\(822\) −2.58656 0.838368i −0.0902167 0.0292415i
\(823\) −8.05091 + 13.9446i −0.280637 + 0.486078i −0.971542 0.236868i \(-0.923879\pi\)
0.690905 + 0.722946i \(0.257212\pi\)
\(824\) 1.52523 2.64177i 0.0531339 0.0920306i
\(825\) 0 0
\(826\) −3.05841 5.29732i −0.106416 0.184317i
\(827\) 15.2905 0.531702 0.265851 0.964014i \(-0.414347\pi\)
0.265851 + 0.964014i \(0.414347\pi\)
\(828\) −32.0257 23.1977i −1.11297 0.806177i
\(829\) −42.1463 −1.46380 −0.731901 0.681411i \(-0.761367\pi\)
−0.731901 + 0.681411i \(0.761367\pi\)
\(830\) −0.0523514 0.0906752i −0.00181714 0.00314738i
\(831\) −13.3149 + 12.0062i −0.461889 + 0.416489i
\(832\) −5.57882 + 9.66280i −0.193411 + 0.334997i
\(833\) 7.65284 13.2551i 0.265155 0.459262i
\(834\) −2.65734 12.4577i −0.0920163 0.431376i
\(835\) 15.0096 + 25.9975i 0.519430 + 0.899679i
\(836\) 0 0
\(837\) 20.1417 2.16094i 0.696199 0.0746930i
\(838\) 8.89330 0.307214
\(839\) −1.32370 2.29271i −0.0456990 0.0791531i 0.842271 0.539054i \(-0.181218\pi\)
−0.887970 + 0.459901i \(0.847885\pi\)
\(840\) −3.88164 18.1973i −0.133929 0.627866i
\(841\) 13.0698 22.6375i 0.450682 0.780604i
\(842\) −3.14215 + 5.44237i −0.108286 + 0.187556i
\(843\) 21.1419 19.0638i 0.728165 0.656592i
\(844\) −6.40771 11.0985i −0.220562 0.382025i
\(845\) 5.09616 0.175313
\(846\) 0.163882 1.58111i 0.00563436 0.0543597i
\(847\) 0 0
\(848\) 16.4232 + 28.4458i 0.563976 + 0.976834i
\(849\) −2.08422 0.675546i −0.0715302 0.0231847i
\(850\) 1.68744 2.92273i 0.0578786 0.100249i
\(851\) −11.4835 + 19.8900i −0.393649 + 0.681820i
\(852\) −20.3422 6.59340i −0.696912 0.225886i
\(853\) −4.63519 8.02838i −0.158706 0.274886i 0.775696 0.631106i \(-0.217399\pi\)
−0.934402 + 0.356220i \(0.884065\pi\)
\(854\) 6.44575 0.220569
\(855\) −2.33396 + 22.5178i −0.0798197 + 0.770091i
\(856\) 6.09770 0.208415
\(857\) 10.2678 + 17.7844i 0.350742 + 0.607502i 0.986380 0.164485i \(-0.0525962\pi\)
−0.635638 + 0.771987i \(0.719263\pi\)
\(858\) 0 0
\(859\) −18.0139 + 31.2010i −0.614626 + 1.06456i 0.375824 + 0.926691i \(0.377360\pi\)
−0.990450 + 0.137872i \(0.955974\pi\)
\(860\) 14.4449 25.0194i 0.492569 0.853154i
\(861\) −0.481688 2.25817i −0.0164159 0.0769583i
\(862\) −1.61352 2.79470i −0.0549566 0.0951877i
\(863\) 4.31646 0.146934 0.0734670 0.997298i \(-0.476594\pi\)
0.0734670 + 0.997298i \(0.476594\pi\)
\(864\) 25.6789 2.75502i 0.873616 0.0937275i
\(865\) 21.1229 0.718199
\(866\) 3.43291 + 5.94598i 0.116655 + 0.202053i
\(867\) 2.19682 + 10.2988i 0.0746080 + 0.349765i
\(868\) −11.6966 + 20.2591i −0.397008 + 0.687637i
\(869\) 0 0
\(870\) 1.82279 1.64362i 0.0617984 0.0557241i
\(871\) 6.19918 + 10.7373i 0.210051 + 0.363819i
\(872\) −10.1549 −0.343889
\(873\) 0.833736 + 0.603913i 0.0282177 + 0.0204394i
\(874\) 16.2339 0.549121
\(875\) 20.6295 + 35.7313i 0.697403 + 1.20794i
\(876\) 43.6074 + 14.1342i 1.47336 + 0.477551i
\(877\) −15.5580 + 26.9473i −0.525356 + 0.909944i 0.474207 + 0.880413i \(0.342735\pi\)
−0.999564 + 0.0295309i \(0.990599\pi\)
\(878\) 6.17488 10.6952i 0.208392 0.360946i
\(879\) −39.6879 12.8638i −1.33864 0.433886i
\(880\) 0 0
\(881\) 43.9267 1.47993 0.739964 0.672647i \(-0.234843\pi\)
0.739964 + 0.672647i \(0.234843\pi\)
\(882\) 6.22219 2.78103i 0.209512 0.0936423i
\(883\) −5.87946 −0.197860 −0.0989298 0.995094i \(-0.531542\pi\)
−0.0989298 + 0.995094i \(0.531542\pi\)
\(884\) 11.6222 + 20.1303i 0.390897 + 0.677054i
\(885\) 8.03445 7.24472i 0.270075 0.243529i
\(886\) 6.57813 11.3937i 0.220997 0.382777i
\(887\) 3.84755 6.66416i 0.129188 0.223760i −0.794174 0.607690i \(-0.792096\pi\)
0.923362 + 0.383930i \(0.125430\pi\)
\(888\) −2.04252 9.57542i −0.0685425 0.321330i
\(889\) −18.4082 31.8839i −0.617390 1.06935i
\(890\) 6.64689 0.222804
\(891\) 0 0
\(892\) −41.3640 −1.38497
\(893\) −2.38610 4.13285i −0.0798479 0.138301i
\(894\) 0.717986 + 3.36595i 0.0240130 + 0.112574i
\(895\) −18.6894 + 32.3710i −0.624718 + 1.08204i
\(896\) −19.2856 + 33.4036i −0.644286 + 1.11594i
\(897\) 38.5288 34.7417i 1.28644 1.15999i
\(898\) 3.47658 + 6.02161i 0.116015 + 0.200944i
\(899\) −6.59352 −0.219906
\(900\) −10.0334 + 4.48448i −0.334447 + 0.149483i
\(901\) 41.5180 1.38316
\(902\) 0 0
\(903\) 54.0174 + 17.5084i 1.79759 + 0.582642i
\(904\) 15.1291 26.2043i 0.503185 0.871542i
\(905\) 3.74106 6.47970i 0.124357 0.215393i
\(906\) 6.29886 + 2.04161i 0.209265 + 0.0678281i
\(907\) 9.49528 + 16.4463i 0.315285 + 0.546091i 0.979498 0.201453i \(-0.0645664\pi\)
−0.664213 + 0.747544i \(0.731233\pi\)
\(908\) 20.9761 0.696116
\(909\) 17.2879 + 12.5224i 0.573404 + 0.415343i
\(910\) 11.4241 0.378705
\(911\) −25.0176 43.3318i −0.828871 1.43565i −0.898924 0.438104i \(-0.855650\pi\)
0.0700530 0.997543i \(-0.477683\pi\)
\(912\) 14.8563 13.3961i 0.491943 0.443588i
\(913\) 0 0
\(914\) 6.04320 10.4671i 0.199891 0.346222i
\(915\) 2.37826 + 11.1494i 0.0786227 + 0.368587i
\(916\) 2.68977 + 4.65882i 0.0888725 + 0.153932i
\(917\) −72.1519 −2.38266
\(918\) 3.40905 7.70154i 0.112515 0.254189i
\(919\) 3.07419 0.101408 0.0507042 0.998714i \(-0.483853\pi\)
0.0507042 + 0.998714i \(0.483853\pi\)
\(920\) −11.7993 20.4369i −0.389011 0.673786i
\(921\) −5.88789 27.6027i −0.194013 0.909539i
\(922\) −6.43660 + 11.1485i −0.211978 + 0.367157i
\(923\) 14.0270 24.2955i 0.461705 0.799696i
\(924\) 0 0
\(925\) 3.19142 + 5.52769i 0.104933 + 0.181749i
\(926\) −6.22544 −0.204581
\(927\) −0.511658 + 4.93642i −0.0168051 + 0.162133i
\(928\) −8.40617 −0.275946
\(929\) 0.452787 + 0.784250i 0.0148555 + 0.0257304i 0.873358 0.487080i \(-0.161938\pi\)
−0.858502 + 0.512810i \(0.828605\pi\)
\(930\) 5.38188 + 1.74440i 0.176479 + 0.0572011i
\(931\) 10.2305 17.7198i 0.335292 0.580743i
\(932\) −21.5804 + 37.3784i −0.706891 + 1.22437i
\(933\) 35.2126 + 11.4133i 1.15281 + 0.373654i
\(934\) −6.79433 11.7681i −0.222317 0.385065i
\(935\) 0 0
\(936\) −2.28012 + 21.9983i −0.0745280 + 0.719037i
\(937\) −22.0542 −0.720481 −0.360240 0.932860i \(-0.617305\pi\)
−0.360240 + 0.932860i \(0.617305\pi\)
\(938\) 2.59391 + 4.49278i 0.0846941 + 0.146694i
\(939\) −4.00837 + 3.61437i −0.130808 + 0.117951i
\(940\) −1.62330 + 2.81164i −0.0529462 + 0.0917056i
\(941\) −2.73046 + 4.72930i −0.0890105 + 0.154171i −0.907093 0.420930i \(-0.861704\pi\)
0.818083 + 0.575101i \(0.195037\pi\)
\(942\) 0.0547914 + 0.256865i 0.00178520 + 0.00836910i
\(943\) −1.46422 2.53610i −0.0476815 0.0825868i
\(944\) −9.55957 −0.311138
\(945\) 17.8460 + 24.4518i 0.580531 + 0.795417i
\(946\) 0 0
\(947\) −16.2203 28.0944i −0.527089 0.912945i −0.999502 0.0315677i \(-0.989950\pi\)
0.472412 0.881378i \(-0.343383\pi\)
\(948\) −2.54238 11.9188i −0.0825728 0.387105i
\(949\) −30.0696 + 52.0821i −0.976101 + 1.69066i
\(950\) 2.25581 3.90718i 0.0731883 0.126766i
\(951\) 23.4946 21.1853i 0.761866 0.686980i
\(952\) 10.3911 + 17.9979i 0.336777 + 0.583315i
\(953\) −53.8088 −1.74304 −0.871518 0.490363i \(-0.836864\pi\)
−0.871518 + 0.490363i \(0.836864\pi\)
\(954\) 14.9722 + 10.8451i 0.484744 + 0.351122i
\(955\) 21.3774 0.691756
\(956\) −6.11452 10.5907i −0.197758 0.342527i
\(957\) 0 0
\(958\) −3.83130 + 6.63600i −0.123784 + 0.214400i
\(959\) −5.45773 + 9.45306i −0.176239 + 0.305255i
\(960\) −7.85487 2.54596i −0.253515 0.0821704i
\(961\) 7.90079 + 13.6846i 0.254864 + 0.441437i
\(962\) 6.01137 0.193814
\(963\) −9.05701 + 4.04806i −0.291858 + 0.130447i
\(964\) 13.6717 0.440335
\(965\) 10.7322 + 18.5888i 0.345483 + 0.598394i
\(966\) 16.1215 14.5369i 0.518701 0.467717i
\(967\) 14.4075 24.9546i 0.463315 0.802486i −0.535809 0.844340i \(-0.679993\pi\)
0.999124 + 0.0418540i \(0.0133264\pi\)
\(968\) 0 0
\(969\) −5.27490 24.7289i −0.169454 0.794408i
\(970\) 0.143758 + 0.248997i 0.00461580 + 0.00799480i
\(971\) 5.39405 0.173103 0.0865517 0.996247i \(-0.472415\pi\)
0.0865517 + 0.996247i \(0.472415\pi\)
\(972\) −23.7026 + 13.7986i −0.760262 + 0.442592i
\(973\) −51.1362 −1.63935
\(974\) 6.60377 + 11.4381i 0.211598 + 0.366499i
\(975\) −3.00780 14.1007i −0.0963268 0.451584i
\(976\) 5.03682 8.72403i 0.161225 0.279250i
\(977\) 1.65618 2.86859i 0.0529859 0.0917742i −0.838316 0.545185i \(-0.816460\pi\)
0.891302 + 0.453411i \(0.149793\pi\)
\(978\) 6.93659 6.25478i 0.221808 0.200006i
\(979\) 0 0
\(980\) −13.9200 −0.444657
\(981\) 15.0833 6.74152i 0.481571 0.215240i
\(982\) −19.1291 −0.610435
\(983\) −16.9361 29.3341i −0.540176 0.935613i −0.998893 0.0470306i \(-0.985024\pi\)
0.458717 0.888582i \(-0.348309\pi\)
\(984\) 1.18757 + 0.384921i 0.0378584 + 0.0122708i
\(985\) 8.83584 15.3041i 0.281533 0.487630i
\(986\) −1.37068 + 2.37409i −0.0436514 + 0.0756065i
\(987\) −6.07039 1.96756i −0.193223 0.0626282i
\(988\) 15.5369 + 26.9107i 0.494295 + 0.856143i
\(989\) 72.0183 2.29005
\(990\) 0 0
\(991\) 8.66640 0.275297 0.137649 0.990481i \(-0.456046\pi\)
0.137649 + 0.990481i \(0.456046\pi\)
\(992\) −9.68835 16.7807i −0.307605 0.532788i
\(993\) −4.84452 + 4.36834i −0.153736 + 0.138625i
\(994\) 5.86929 10.1659i 0.186163 0.322443i
\(995\) −22.6140 + 39.1686i −0.716912 + 1.24173i
\(996\) −0.0794450 0.372442i −0.00251731 0.0118013i
\(997\) 15.1327 + 26.2106i 0.479258 + 0.830098i 0.999717 0.0237880i \(-0.00757266\pi\)
−0.520459 + 0.853886i \(0.674239\pi\)
\(998\) 11.7891 0.373177
\(999\) 9.39060 + 12.8666i 0.297105 + 0.407080i
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 1089.2.e.p.364.10 36
9.4 even 3 9801.2.a.cm.1.9 18
9.5 odd 6 9801.2.a.cp.1.10 18
9.7 even 3 inner 1089.2.e.p.727.10 36
11.5 even 5 99.2.m.b.58.5 yes 72
11.9 even 5 99.2.m.b.4.5 72
11.10 odd 2 1089.2.e.o.364.9 36
33.5 odd 10 297.2.n.b.91.5 72
33.20 odd 10 297.2.n.b.37.5 72
99.5 odd 30 891.2.f.e.487.5 36
99.16 even 15 99.2.m.b.25.5 yes 72
99.20 odd 30 297.2.n.b.235.5 72
99.31 even 15 891.2.f.f.730.5 36
99.32 even 6 9801.2.a.cn.1.9 18
99.38 odd 30 297.2.n.b.289.5 72
99.43 odd 6 1089.2.e.o.727.9 36
99.49 even 15 891.2.f.f.487.5 36
99.76 odd 6 9801.2.a.co.1.10 18
99.86 odd 30 891.2.f.e.730.5 36
99.97 even 15 99.2.m.b.70.5 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.5 72 11.9 even 5
99.2.m.b.25.5 yes 72 99.16 even 15
99.2.m.b.58.5 yes 72 11.5 even 5
99.2.m.b.70.5 yes 72 99.97 even 15
297.2.n.b.37.5 72 33.20 odd 10
297.2.n.b.91.5 72 33.5 odd 10
297.2.n.b.235.5 72 99.20 odd 30
297.2.n.b.289.5 72 99.38 odd 30
891.2.f.e.487.5 36 99.5 odd 30
891.2.f.e.730.5 36 99.86 odd 30
891.2.f.f.487.5 36 99.49 even 15
891.2.f.f.730.5 36 99.31 even 15
1089.2.e.o.364.9 36 11.10 odd 2
1089.2.e.o.727.9 36 99.43 odd 6
1089.2.e.p.364.10 36 1.1 even 1 trivial
1089.2.e.p.727.10 36 9.7 even 3 inner
9801.2.a.cm.1.9 18 9.4 even 3
9801.2.a.cn.1.9 18 99.32 even 6
9801.2.a.co.1.10 18 99.76 odd 6
9801.2.a.cp.1.10 18 9.5 odd 6