Properties

Label 950.2.u.f.549.3
Level $950$
Weight $2$
Character 950.549
Analytic conductor $7.586$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(99,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), not 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 549.3
Character \(\chi\) \(=\) 950.549
Dual form 950.2.u.f.199.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.984808 + 0.173648i) q^{2} +(-1.90555 + 2.27095i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.27095 + 1.90555i) q^{6} +(2.51922 - 1.45447i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-1.00513 - 5.70040i) q^{9} +O(q^{10})\) \(q+(0.984808 + 0.173648i) q^{2} +(-1.90555 + 2.27095i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.27095 + 1.90555i) q^{6} +(2.51922 - 1.45447i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-1.00513 - 5.70040i) q^{9} +(-0.688430 + 1.19240i) q^{11} +(-2.56734 + 1.48226i) q^{12} +(3.44902 + 4.11038i) q^{13} +(2.73352 - 0.994919i) q^{14} +(0.766044 + 0.642788i) q^{16} +(5.22100 + 0.920603i) q^{17} -5.78833i q^{18} +(-2.17069 + 3.77996i) q^{19} +(-1.49748 + 8.49261i) q^{21} +(-0.885029 + 1.05474i) q^{22} +(-0.546254 + 1.50082i) q^{23} +(-2.78573 + 1.01392i) q^{24} +(2.68286 + 4.64685i) q^{26} +(7.15861 + 4.13303i) q^{27} +(2.86476 - 0.505134i) q^{28} +(0.411474 + 2.33359i) q^{29} +(-3.50252 - 6.06655i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-1.39603 - 3.83556i) q^{33} +(4.98182 + 1.81323i) q^{34} +(1.00513 - 5.70040i) q^{36} +8.31135i q^{37} +(-2.79409 + 3.34560i) q^{38} -15.9067 q^{39} +(-7.13497 - 5.98695i) q^{41} +(-2.94945 + 8.10355i) q^{42} +(-1.99787 - 5.48910i) q^{43} +(-1.05474 + 0.885029i) q^{44} +(-0.798570 + 1.38316i) q^{46} +(2.41402 - 0.425657i) q^{47} +(-2.91947 + 0.514782i) q^{48} +(0.730994 - 1.26612i) q^{49} +(-12.0395 + 10.1024i) q^{51} +(1.83518 + 5.04213i) q^{52} +(-3.63506 + 9.98725i) q^{53} +(6.33216 + 5.31332i) q^{54} +2.90895 q^{56} +(-4.44774 - 12.1324i) q^{57} +2.36959i q^{58} +(1.39863 - 7.93202i) q^{59} +(14.5150 + 5.28304i) q^{61} +(-2.39587 - 6.58259i) q^{62} +(-10.8232 - 12.8986i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.708783 - 4.01971i) q^{66} +(-10.0911 + 1.77933i) q^{67} +(4.59127 + 2.65077i) q^{68} +(-2.36737 - 4.10041i) q^{69} +(-2.36737 + 0.861653i) q^{71} +(1.97973 - 5.43926i) q^{72} +(4.37520 - 5.21416i) q^{73} +(-1.44325 + 8.18508i) q^{74} +(-3.33260 + 2.80958i) q^{76} +4.00522i q^{77} +(-15.6651 - 2.76218i) q^{78} +(6.31181 + 5.29624i) q^{79} +(-6.70923 + 2.44196i) q^{81} +(-5.98695 - 7.13497i) q^{82} +(-0.419755 + 0.242346i) q^{83} +(-4.31181 + 7.46827i) q^{84} +(-1.01435 - 5.75264i) q^{86} +(-6.08354 - 3.51233i) q^{87} +(-1.19240 + 0.688430i) q^{88} +(-9.24921 + 7.76101i) q^{89} +(14.6673 + 5.33846i) q^{91} +(-1.02662 + 1.22348i) q^{92} +(20.4511 + 3.60607i) q^{93} +2.45126 q^{94} -2.96451 q^{96} +(9.01879 + 1.59026i) q^{97} +(0.939748 - 1.11995i) q^{98} +(7.48910 + 2.72581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.984808 + 0.173648i 0.696364 + 0.122788i
\(3\) −1.90555 + 2.27095i −1.10017 + 1.31113i −0.153781 + 0.988105i \(0.549145\pi\)
−0.946389 + 0.323028i \(0.895299\pi\)
\(4\) 0.939693 + 0.342020i 0.469846 + 0.171010i
\(5\) 0 0
\(6\) −2.27095 + 1.90555i −0.927111 + 0.777938i
\(7\) 2.51922 1.45447i 0.952177 0.549740i 0.0584207 0.998292i \(-0.481394\pi\)
0.893757 + 0.448552i \(0.148060\pi\)
\(8\) 0.866025 + 0.500000i 0.306186 + 0.176777i
\(9\) −1.00513 5.70040i −0.335045 1.90013i
\(10\) 0 0
\(11\) −0.688430 + 1.19240i −0.207570 + 0.359521i −0.950948 0.309350i \(-0.899889\pi\)
0.743379 + 0.668871i \(0.233222\pi\)
\(12\) −2.56734 + 1.48226i −0.741128 + 0.427891i
\(13\) 3.44902 + 4.11038i 0.956585 + 1.14001i 0.990070 + 0.140575i \(0.0448951\pi\)
−0.0334846 + 0.999439i \(0.510660\pi\)
\(14\) 2.73352 0.994919i 0.730564 0.265903i
\(15\) 0 0
\(16\) 0.766044 + 0.642788i 0.191511 + 0.160697i
\(17\) 5.22100 + 0.920603i 1.26628 + 0.223279i 0.766144 0.642669i \(-0.222173\pi\)
0.500134 + 0.865948i \(0.333284\pi\)
\(18\) 5.78833i 1.36432i
\(19\) −2.17069 + 3.77996i −0.497990 + 0.867183i
\(20\) 0 0
\(21\) −1.49748 + 8.49261i −0.326776 + 1.85324i
\(22\) −0.885029 + 1.05474i −0.188689 + 0.224871i
\(23\) −0.546254 + 1.50082i −0.113902 + 0.312943i −0.983525 0.180774i \(-0.942140\pi\)
0.869623 + 0.493717i \(0.164362\pi\)
\(24\) −2.78573 + 1.01392i −0.568635 + 0.206966i
\(25\) 0 0
\(26\) 2.68286 + 4.64685i 0.526152 + 0.911322i
\(27\) 7.15861 + 4.13303i 1.37768 + 0.795401i
\(28\) 2.86476 0.505134i 0.541388 0.0954613i
\(29\) 0.411474 + 2.33359i 0.0764088 + 0.433336i 0.998882 + 0.0472746i \(0.0150536\pi\)
−0.922473 + 0.386061i \(0.873835\pi\)
\(30\) 0 0
\(31\) −3.50252 6.06655i −0.629072 1.08958i −0.987738 0.156119i \(-0.950102\pi\)
0.358666 0.933466i \(-0.383232\pi\)
\(32\) 0.642788 + 0.766044i 0.113630 + 0.135419i
\(33\) −1.39603 3.83556i −0.243018 0.667686i
\(34\) 4.98182 + 1.81323i 0.854375 + 0.310967i
\(35\) 0 0
\(36\) 1.00513 5.70040i 0.167522 0.950066i
\(37\) 8.31135i 1.36638i 0.730242 + 0.683189i \(0.239407\pi\)
−0.730242 + 0.683189i \(0.760593\pi\)
\(38\) −2.79409 + 3.34560i −0.453262 + 0.542728i
\(39\) −15.9067 −2.54712
\(40\) 0 0
\(41\) −7.13497 5.98695i −1.11430 0.935005i −0.115993 0.993250i \(-0.537005\pi\)
−0.998302 + 0.0582455i \(0.981449\pi\)
\(42\) −2.94945 + 8.10355i −0.455110 + 1.25040i
\(43\) −1.99787 5.48910i −0.304672 0.837080i −0.993672 0.112319i \(-0.964172\pi\)
0.689000 0.724761i \(-0.258050\pi\)
\(44\) −1.05474 + 0.885029i −0.159008 + 0.133423i
\(45\) 0 0
\(46\) −0.798570 + 1.38316i −0.117743 + 0.203936i
\(47\) 2.41402 0.425657i 0.352121 0.0620885i 0.00520990 0.999986i \(-0.498342\pi\)
0.346911 + 0.937898i \(0.387231\pi\)
\(48\) −2.91947 + 0.514782i −0.421390 + 0.0743024i
\(49\) 0.730994 1.26612i 0.104428 0.180874i
\(50\) 0 0
\(51\) −12.0395 + 10.1024i −1.68587 + 1.41461i
\(52\) 1.83518 + 5.04213i 0.254494 + 0.699217i
\(53\) −3.63506 + 9.98725i −0.499314 + 1.37185i 0.392625 + 0.919699i \(0.371567\pi\)
−0.891939 + 0.452155i \(0.850655\pi\)
\(54\) 6.33216 + 5.31332i 0.861698 + 0.723051i
\(55\) 0 0
\(56\) 2.90895 0.388725
\(57\) −4.44774 12.1324i −0.589118 1.60698i
\(58\) 2.36959i 0.311142i
\(59\) 1.39863 7.93202i 0.182086 1.03266i −0.747556 0.664199i \(-0.768773\pi\)
0.929642 0.368463i \(-0.120116\pi\)
\(60\) 0 0
\(61\) 14.5150 + 5.28304i 1.85846 + 0.676424i 0.980127 + 0.198371i \(0.0635652\pi\)
0.878332 + 0.478052i \(0.158657\pi\)
\(62\) −2.39587 6.58259i −0.304276 0.835990i
\(63\) −10.8232 12.8986i −1.36360 1.62508i
\(64\) 0.500000 + 0.866025i 0.0625000 + 0.108253i
\(65\) 0 0
\(66\) −0.708783 4.01971i −0.0872452 0.494792i
\(67\) −10.0911 + 1.77933i −1.23282 + 0.217380i −0.751837 0.659349i \(-0.770832\pi\)
−0.480985 + 0.876729i \(0.659721\pi\)
\(68\) 4.59127 + 2.65077i 0.556773 + 0.321453i
\(69\) −2.36737 4.10041i −0.284998 0.493631i
\(70\) 0 0
\(71\) −2.36737 + 0.861653i −0.280955 + 0.102259i −0.478654 0.878003i \(-0.658875\pi\)
0.197699 + 0.980263i \(0.436653\pi\)
\(72\) 1.97973 5.43926i 0.233313 0.641022i
\(73\) 4.37520 5.21416i 0.512079 0.610272i −0.446610 0.894729i \(-0.647369\pi\)
0.958689 + 0.284457i \(0.0918133\pi\)
\(74\) −1.44325 + 8.18508i −0.167774 + 0.951496i
\(75\) 0 0
\(76\) −3.33260 + 2.80958i −0.382276 + 0.322281i
\(77\) 4.00522i 0.456437i
\(78\) −15.6651 2.76218i −1.77372 0.312755i
\(79\) 6.31181 + 5.29624i 0.710134 + 0.595873i 0.924637 0.380850i \(-0.124369\pi\)
−0.214503 + 0.976723i \(0.568813\pi\)
\(80\) 0 0
\(81\) −6.70923 + 2.44196i −0.745470 + 0.271329i
\(82\) −5.98695 7.13497i −0.661148 0.787926i
\(83\) −0.419755 + 0.242346i −0.0460741 + 0.0266009i −0.522860 0.852419i \(-0.675135\pi\)
0.476786 + 0.879019i \(0.341802\pi\)
\(84\) −4.31181 + 7.46827i −0.470457 + 0.814855i
\(85\) 0 0
\(86\) −1.01435 5.75264i −0.109380 0.620323i
\(87\) −6.08354 3.51233i −0.652224 0.376562i
\(88\) −1.19240 + 0.688430i −0.127110 + 0.0733869i
\(89\) −9.24921 + 7.76101i −0.980414 + 0.822665i −0.984152 0.177328i \(-0.943255\pi\)
0.00373759 + 0.999993i \(0.498810\pi\)
\(90\) 0 0
\(91\) 14.6673 + 5.33846i 1.53755 + 0.559622i
\(92\) −1.02662 + 1.22348i −0.107033 + 0.127557i
\(93\) 20.4511 + 3.60607i 2.12068 + 0.373933i
\(94\) 2.45126 0.252828
\(95\) 0 0
\(96\) −2.96451 −0.302564
\(97\) 9.01879 + 1.59026i 0.915719 + 0.161466i 0.611599 0.791168i \(-0.290526\pi\)
0.304120 + 0.952634i \(0.401638\pi\)
\(98\) 0.939748 1.11995i 0.0949289 0.113132i
\(99\) 7.48910 + 2.72581i 0.752683 + 0.273954i
\(100\) 0 0
\(101\) 3.78879 3.17918i 0.376999 0.316340i −0.434524 0.900660i \(-0.643083\pi\)
0.811523 + 0.584320i \(0.198639\pi\)
\(102\) −13.6109 + 7.85824i −1.34768 + 0.778082i
\(103\) 4.77000 + 2.75396i 0.470002 + 0.271356i 0.716240 0.697854i \(-0.245861\pi\)
−0.246239 + 0.969209i \(0.579195\pi\)
\(104\) 0.931747 + 5.28420i 0.0913653 + 0.518159i
\(105\) 0 0
\(106\) −5.31410 + 9.20430i −0.516151 + 0.894000i
\(107\) −5.43798 + 3.13962i −0.525710 + 0.303519i −0.739268 0.673412i \(-0.764828\pi\)
0.213558 + 0.976930i \(0.431495\pi\)
\(108\) 5.31332 + 6.33216i 0.511274 + 0.609313i
\(109\) 5.14544 1.87279i 0.492844 0.179380i −0.0836288 0.996497i \(-0.526651\pi\)
0.576473 + 0.817117i \(0.304429\pi\)
\(110\) 0 0
\(111\) −18.8746 15.8377i −1.79150 1.50325i
\(112\) 2.86476 + 0.505134i 0.270694 + 0.0477307i
\(113\) 3.38326i 0.318271i −0.987257 0.159135i \(-0.949129\pi\)
0.987257 0.159135i \(-0.0508706\pi\)
\(114\) −2.27340 12.7205i −0.212923 1.19138i
\(115\) 0 0
\(116\) −0.411474 + 2.33359i −0.0382044 + 0.216668i
\(117\) 19.9641 23.7923i 1.84568 2.19959i
\(118\) 2.75476 7.56865i 0.253597 0.696751i
\(119\) 14.4919 5.27461i 1.32847 0.483522i
\(120\) 0 0
\(121\) 4.55213 + 7.88452i 0.413830 + 0.716774i
\(122\) 13.3771 + 7.72328i 1.21111 + 0.699233i
\(123\) 27.1921 4.79470i 2.45183 0.432324i
\(124\) −1.21641 6.89863i −0.109237 0.619515i
\(125\) 0 0
\(126\) −8.41899 14.5821i −0.750023 1.29908i
\(127\) 5.27100 + 6.28174i 0.467726 + 0.557414i 0.947408 0.320028i \(-0.103692\pi\)
−0.479682 + 0.877442i \(0.659248\pi\)
\(128\) 0.342020 + 0.939693i 0.0302306 + 0.0830579i
\(129\) 16.2725 + 5.92271i 1.43271 + 0.521466i
\(130\) 0 0
\(131\) 3.31008 18.7724i 0.289203 1.64015i −0.400671 0.916222i \(-0.631223\pi\)
0.689874 0.723929i \(-0.257666\pi\)
\(132\) 4.08172i 0.355268i
\(133\) 0.0294142 + 12.6798i 0.00255054 + 1.09948i
\(134\) −10.2467 −0.885184
\(135\) 0 0
\(136\) 4.06122 + 3.40777i 0.348246 + 0.292213i
\(137\) 4.30123 11.8175i 0.367479 1.00964i −0.608838 0.793294i \(-0.708364\pi\)
0.976317 0.216345i \(-0.0694136\pi\)
\(138\) −1.61938 4.44920i −0.137851 0.378741i
\(139\) −6.64986 + 5.57990i −0.564034 + 0.473281i −0.879660 0.475603i \(-0.842230\pi\)
0.315626 + 0.948884i \(0.397785\pi\)
\(140\) 0 0
\(141\) −3.63340 + 6.29323i −0.305987 + 0.529985i
\(142\) −2.48103 + 0.437473i −0.208203 + 0.0367119i
\(143\) −7.27561 + 1.28289i −0.608417 + 0.107280i
\(144\) 2.89417 5.01285i 0.241181 0.417737i
\(145\) 0 0
\(146\) 5.21416 4.37520i 0.431527 0.362094i
\(147\) 1.48234 + 4.07271i 0.122262 + 0.335911i
\(148\) −2.84265 + 7.81011i −0.233664 + 0.641987i
\(149\) −12.5465 10.5278i −1.02785 0.862467i −0.0372549 0.999306i \(-0.511861\pi\)
−0.990593 + 0.136839i \(0.956306\pi\)
\(150\) 0 0
\(151\) 12.8845 1.04852 0.524261 0.851557i \(-0.324341\pi\)
0.524261 + 0.851557i \(0.324341\pi\)
\(152\) −3.76985 + 2.18820i −0.305775 + 0.177487i
\(153\) 30.6871i 2.48090i
\(154\) −0.695499 + 3.94437i −0.0560449 + 0.317846i
\(155\) 0 0
\(156\) −14.9474 5.44043i −1.19675 0.435583i
\(157\) −5.60574 15.4017i −0.447387 1.22919i −0.934537 0.355867i \(-0.884186\pi\)
0.487150 0.873318i \(-0.338037\pi\)
\(158\) 5.29624 + 6.31181i 0.421346 + 0.502141i
\(159\) −15.7537 27.2863i −1.24935 2.16394i
\(160\) 0 0
\(161\) 0.806770 + 4.57542i 0.0635824 + 0.360594i
\(162\) −7.03135 + 1.23982i −0.552435 + 0.0974092i
\(163\) −3.53398 2.04034i −0.276803 0.159812i 0.355172 0.934801i \(-0.384422\pi\)
−0.631975 + 0.774989i \(0.717755\pi\)
\(164\) −4.65702 8.06620i −0.363652 0.629864i
\(165\) 0 0
\(166\) −0.455461 + 0.165774i −0.0353506 + 0.0128666i
\(167\) −5.42127 + 14.8948i −0.419510 + 1.15260i 0.532473 + 0.846447i \(0.321263\pi\)
−0.951984 + 0.306149i \(0.900960\pi\)
\(168\) −5.54315 + 6.60607i −0.427664 + 0.509670i
\(169\) −2.74207 + 15.5510i −0.210928 + 1.19623i
\(170\) 0 0
\(171\) 23.7291 + 8.57441i 1.81461 + 0.655701i
\(172\) 5.84138i 0.445401i
\(173\) −2.38705 0.420901i −0.181484 0.0320005i 0.0821676 0.996619i \(-0.473816\pi\)
−0.263651 + 0.964618i \(0.584927\pi\)
\(174\) −5.38121 4.51537i −0.407948 0.342309i
\(175\) 0 0
\(176\) −1.29383 + 0.470914i −0.0975258 + 0.0354965i
\(177\) 15.3481 + 18.2911i 1.15363 + 1.37484i
\(178\) −10.4564 + 6.03699i −0.783739 + 0.452492i
\(179\) 9.04557 15.6674i 0.676098 1.17104i −0.300049 0.953924i \(-0.597003\pi\)
0.976147 0.217112i \(-0.0696636\pi\)
\(180\) 0 0
\(181\) −3.48949 19.7899i −0.259371 1.47097i −0.784597 0.620006i \(-0.787130\pi\)
0.525226 0.850963i \(-0.323981\pi\)
\(182\) 13.5174 + 7.80430i 1.00198 + 0.578493i
\(183\) −39.6566 + 22.8958i −2.93150 + 1.69250i
\(184\) −1.22348 + 1.02662i −0.0901962 + 0.0756836i
\(185\) 0 0
\(186\) 19.5142 + 7.10258i 1.43085 + 0.520786i
\(187\) −4.69202 + 5.59173i −0.343114 + 0.408908i
\(188\) 2.41402 + 0.425657i 0.176061 + 0.0310442i
\(189\) 24.0455 1.74906
\(190\) 0 0
\(191\) −7.33371 −0.530649 −0.265324 0.964159i \(-0.585479\pi\)
−0.265324 + 0.964159i \(0.585479\pi\)
\(192\) −2.91947 0.514782i −0.210695 0.0371512i
\(193\) 16.5147 19.6814i 1.18875 1.41670i 0.302720 0.953079i \(-0.402105\pi\)
0.886033 0.463622i \(-0.153450\pi\)
\(194\) 8.60563 + 3.13219i 0.617848 + 0.224878i
\(195\) 0 0
\(196\) 1.11995 0.939748i 0.0799963 0.0671248i
\(197\) 11.4157 6.59085i 0.813334 0.469579i −0.0347781 0.999395i \(-0.511072\pi\)
0.848112 + 0.529816i \(0.177739\pi\)
\(198\) 6.90199 + 3.98487i 0.490503 + 0.283192i
\(199\) −1.78833 10.1421i −0.126771 0.718957i −0.980240 0.197812i \(-0.936616\pi\)
0.853468 0.521144i \(-0.174495\pi\)
\(200\) 0 0
\(201\) 15.1883 26.3069i 1.07130 1.85555i
\(202\) 4.28329 2.47296i 0.301371 0.173997i
\(203\) 4.43074 + 5.28035i 0.310977 + 0.370608i
\(204\) −14.7687 + 5.37535i −1.03401 + 0.376350i
\(205\) 0 0
\(206\) 4.21931 + 3.54042i 0.293973 + 0.246673i
\(207\) 9.10434 + 1.60534i 0.632795 + 0.111579i
\(208\) 5.36572i 0.372046i
\(209\) −3.01285 5.19056i −0.208403 0.359039i
\(210\) 0 0
\(211\) −2.74895 + 15.5901i −0.189245 + 1.07326i 0.731133 + 0.682235i \(0.238992\pi\)
−0.920379 + 0.391029i \(0.872119\pi\)
\(212\) −6.83168 + 8.14168i −0.469202 + 0.559173i
\(213\) 2.55438 7.01810i 0.175023 0.480873i
\(214\) −5.90056 + 2.14763i −0.403354 + 0.146809i
\(215\) 0 0
\(216\) 4.13303 + 7.15861i 0.281217 + 0.487082i
\(217\) −17.6473 10.1887i −1.19798 0.691652i
\(218\) 5.39247 0.950839i 0.365224 0.0643989i
\(219\) 3.50392 + 19.8717i 0.236773 + 1.34281i
\(220\) 0 0
\(221\) 14.2233 + 24.6355i 0.956762 + 1.65716i
\(222\) −15.8377 18.8746i −1.06296 1.26678i
\(223\) −1.12396 3.08806i −0.0752660 0.206792i 0.896354 0.443339i \(-0.146206\pi\)
−0.971620 + 0.236548i \(0.923984\pi\)
\(224\) 2.73352 + 0.994919i 0.182641 + 0.0664758i
\(225\) 0 0
\(226\) 0.587497 3.33186i 0.0390797 0.221632i
\(227\) 11.8147i 0.784172i −0.919928 0.392086i \(-0.871754\pi\)
0.919928 0.392086i \(-0.128246\pi\)
\(228\) −0.0299760 12.9220i −0.00198521 0.855779i
\(229\) 11.9186 0.787604 0.393802 0.919195i \(-0.371160\pi\)
0.393802 + 0.919195i \(0.371160\pi\)
\(230\) 0 0
\(231\) −9.09564 7.63215i −0.598450 0.502159i
\(232\) −0.810446 + 2.22668i −0.0532084 + 0.146189i
\(233\) 3.14124 + 8.63049i 0.205790 + 0.565402i 0.999055 0.0434743i \(-0.0138427\pi\)
−0.793265 + 0.608877i \(0.791620\pi\)
\(234\) 23.7923 19.9641i 1.55535 1.30509i
\(235\) 0 0
\(236\) 4.02719 6.97531i 0.262148 0.454054i
\(237\) −24.0550 + 4.24154i −1.56254 + 0.275518i
\(238\) 15.1876 2.67799i 0.984467 0.173588i
\(239\) 2.70456 4.68443i 0.174943 0.303011i −0.765198 0.643795i \(-0.777359\pi\)
0.940142 + 0.340784i \(0.110692\pi\)
\(240\) 0 0
\(241\) 20.3709 17.0932i 1.31221 1.10107i 0.324311 0.945951i \(-0.394868\pi\)
0.987895 0.155121i \(-0.0495768\pi\)
\(242\) 3.11384 + 8.55520i 0.200165 + 0.549949i
\(243\) −1.24225 + 3.41305i −0.0796902 + 0.218947i
\(244\) 11.8328 + 9.92886i 0.757515 + 0.635630i
\(245\) 0 0
\(246\) 27.6116 1.76045
\(247\) −23.0238 + 4.11481i −1.46497 + 0.261819i
\(248\) 7.00505i 0.444821i
\(249\) 0.249510 1.41504i 0.0158121 0.0896748i
\(250\) 0 0
\(251\) 1.42144 + 0.517363i 0.0897206 + 0.0326556i 0.386490 0.922293i \(-0.373687\pi\)
−0.296770 + 0.954949i \(0.595909\pi\)
\(252\) −5.75893 15.8225i −0.362778 0.996725i
\(253\) −1.41352 1.68456i −0.0888670 0.105908i
\(254\) 4.10011 + 7.10160i 0.257264 + 0.445594i
\(255\) 0 0
\(256\) 0.173648 + 0.984808i 0.0108530 + 0.0615505i
\(257\) 6.75923 1.19184i 0.421629 0.0743446i 0.0411918 0.999151i \(-0.486885\pi\)
0.380438 + 0.924807i \(0.375773\pi\)
\(258\) 14.9968 + 8.65842i 0.933662 + 0.539050i
\(259\) 12.0886 + 20.9382i 0.751152 + 1.30103i
\(260\) 0 0
\(261\) 12.8888 4.69113i 0.797795 0.290374i
\(262\) 6.51958 17.9124i 0.402781 1.10663i
\(263\) −13.1920 + 15.7216i −0.813454 + 0.969437i −0.999915 0.0130252i \(-0.995854\pi\)
0.186461 + 0.982462i \(0.440298\pi\)
\(264\) 0.708783 4.01971i 0.0436226 0.247396i
\(265\) 0 0
\(266\) −2.17285 + 12.4923i −0.133226 + 0.765949i
\(267\) 35.7935i 2.19053i
\(268\) −10.0911 1.77933i −0.616411 0.108690i
\(269\) −13.4461 11.2826i −0.819824 0.687914i 0.133107 0.991102i \(-0.457505\pi\)
−0.952931 + 0.303188i \(0.901949\pi\)
\(270\) 0 0
\(271\) −8.16550 + 2.97200i −0.496019 + 0.180536i −0.577902 0.816106i \(-0.696129\pi\)
0.0818838 + 0.996642i \(0.473906\pi\)
\(272\) 3.40777 + 4.06122i 0.206626 + 0.246247i
\(273\) −40.0727 + 23.1360i −2.42531 + 1.40025i
\(274\) 6.28797 10.8911i 0.379870 0.657955i
\(275\) 0 0
\(276\) −0.822180 4.66281i −0.0494894 0.280668i
\(277\) −7.11964 4.11052i −0.427778 0.246977i 0.270622 0.962686i \(-0.412771\pi\)
−0.698399 + 0.715708i \(0.746104\pi\)
\(278\) −7.51777 + 4.34039i −0.450886 + 0.260319i
\(279\) −31.0612 + 26.0635i −1.85959 + 1.56038i
\(280\) 0 0
\(281\) −15.2981 5.56805i −0.912608 0.332162i −0.157314 0.987549i \(-0.550284\pi\)
−0.755294 + 0.655387i \(0.772506\pi\)
\(282\) −4.67100 + 5.56669i −0.278154 + 0.331491i
\(283\) 6.15584 + 1.08544i 0.365927 + 0.0645228i 0.353588 0.935401i \(-0.384961\pi\)
0.0123385 + 0.999924i \(0.496072\pi\)
\(284\) −2.51930 −0.149493
\(285\) 0 0
\(286\) −7.38785 −0.436853
\(287\) −26.6825 4.70484i −1.57502 0.277718i
\(288\) 3.72067 4.43412i 0.219243 0.261283i
\(289\) 10.4365 + 3.79859i 0.613914 + 0.223447i
\(290\) 0 0
\(291\) −20.7972 + 17.4509i −1.21915 + 1.02299i
\(292\) 5.89470 3.40330i 0.344961 0.199163i
\(293\) 13.1722 + 7.60497i 0.769528 + 0.444287i 0.832706 0.553715i \(-0.186790\pi\)
−0.0631781 + 0.998002i \(0.520124\pi\)
\(294\) 0.752605 + 4.26824i 0.0438928 + 0.248929i
\(295\) 0 0
\(296\) −4.15567 + 7.19784i −0.241544 + 0.418366i
\(297\) −9.85641 + 5.69060i −0.571927 + 0.330202i
\(298\) −10.5278 12.5465i −0.609856 0.726798i
\(299\) −8.05299 + 2.93105i −0.465716 + 0.169507i
\(300\) 0 0
\(301\) −13.0168 10.9224i −0.750278 0.629558i
\(302\) 12.6887 + 2.23736i 0.730154 + 0.128746i
\(303\) 14.6622i 0.842324i
\(304\) −4.09256 + 1.50033i −0.234724 + 0.0860498i
\(305\) 0 0
\(306\) 5.32876 30.2209i 0.304625 1.72761i
\(307\) 0.417451 0.497498i 0.0238252 0.0283937i −0.754000 0.656874i \(-0.771878\pi\)
0.777825 + 0.628480i \(0.216323\pi\)
\(308\) −1.36987 + 3.76367i −0.0780553 + 0.214455i
\(309\) −15.3436 + 5.58461i −0.872866 + 0.317697i
\(310\) 0 0
\(311\) −5.79261 10.0331i −0.328469 0.568924i 0.653740 0.756720i \(-0.273199\pi\)
−0.982208 + 0.187795i \(0.939866\pi\)
\(312\) −13.7756 7.95337i −0.779892 0.450271i
\(313\) −0.620641 + 0.109436i −0.0350807 + 0.00618568i −0.191161 0.981559i \(-0.561225\pi\)
0.156080 + 0.987744i \(0.450114\pi\)
\(314\) −2.84611 16.1411i −0.160615 0.910894i
\(315\) 0 0
\(316\) 4.11974 + 7.13560i 0.231754 + 0.401409i
\(317\) 5.98705 + 7.13509i 0.336266 + 0.400746i 0.907508 0.420036i \(-0.137982\pi\)
−0.571241 + 0.820782i \(0.693538\pi\)
\(318\) −10.7762 29.6073i −0.604298 1.66030i
\(319\) −3.06583 1.11587i −0.171654 0.0624768i
\(320\) 0 0
\(321\) 3.23244 18.3321i 0.180417 1.02320i
\(322\) 4.64600i 0.258912i
\(323\) −14.8130 + 17.7368i −0.824217 + 0.986904i
\(324\) −7.13982 −0.396656
\(325\) 0 0
\(326\) −3.12599 2.62302i −0.173132 0.145275i
\(327\) −5.55190 + 15.2537i −0.307021 + 0.843533i
\(328\) −3.18559 8.75234i −0.175895 0.483267i
\(329\) 5.46235 4.58346i 0.301149 0.252694i
\(330\) 0 0
\(331\) 6.03292 10.4493i 0.331599 0.574347i −0.651226 0.758884i \(-0.725745\pi\)
0.982826 + 0.184537i \(0.0590784\pi\)
\(332\) −0.477328 + 0.0841657i −0.0261968 + 0.00461920i
\(333\) 47.3780 8.35402i 2.59630 0.457797i
\(334\) −7.92536 + 13.7271i −0.433657 + 0.751115i
\(335\) 0 0
\(336\) −6.60607 + 5.54315i −0.360391 + 0.302404i
\(337\) 0.385456 + 1.05903i 0.0209971 + 0.0576891i 0.949748 0.313014i \(-0.101339\pi\)
−0.928751 + 0.370704i \(0.879117\pi\)
\(338\) −5.40082 + 14.8386i −0.293766 + 0.807115i
\(339\) 7.68321 + 6.44698i 0.417295 + 0.350152i
\(340\) 0 0
\(341\) 9.64498 0.522305
\(342\) 21.8797 + 12.5647i 1.18312 + 0.679419i
\(343\) 16.1098i 0.869847i
\(344\) 1.01435 5.75264i 0.0546898 0.310161i
\(345\) 0 0
\(346\) −2.27769 0.829012i −0.122450 0.0445680i
\(347\) 4.40192 + 12.0942i 0.236308 + 0.649250i 0.999993 + 0.00366167i \(0.00116555\pi\)
−0.763686 + 0.645588i \(0.776612\pi\)
\(348\) −4.51537 5.38121i −0.242049 0.288463i
\(349\) −4.18866 7.25497i −0.224214 0.388350i 0.731870 0.681445i \(-0.238648\pi\)
−0.956083 + 0.293095i \(0.905315\pi\)
\(350\) 0 0
\(351\) 7.70187 + 43.6795i 0.411096 + 2.33144i
\(352\) −1.35594 + 0.239089i −0.0722720 + 0.0127435i
\(353\) −13.0798 7.55163i −0.696168 0.401933i 0.109751 0.993959i \(-0.464995\pi\)
−0.805918 + 0.592027i \(0.798328\pi\)
\(354\) 11.9387 + 20.6784i 0.634533 + 1.09904i
\(355\) 0 0
\(356\) −11.3458 + 4.12955i −0.601328 + 0.218866i
\(357\) −15.6366 + 42.9613i −0.827579 + 2.27375i
\(358\) 11.6288 13.8586i 0.614599 0.732451i
\(359\) 5.84746 33.1626i 0.308617 1.75025i −0.297353 0.954768i \(-0.596104\pi\)
0.605970 0.795487i \(-0.292785\pi\)
\(360\) 0 0
\(361\) −9.57624 16.4102i −0.504013 0.863696i
\(362\) 20.0951i 1.05618i
\(363\) −26.5796 4.68671i −1.39507 0.245988i
\(364\) 11.9569 + 10.0330i 0.626711 + 0.525873i
\(365\) 0 0
\(366\) −43.0300 + 15.6616i −2.24921 + 0.818646i
\(367\) −2.70290 3.22119i −0.141090 0.168145i 0.690872 0.722977i \(-0.257227\pi\)
−0.831962 + 0.554832i \(0.812782\pi\)
\(368\) −1.38316 + 0.798570i −0.0721024 + 0.0416284i
\(369\) −26.9564 + 46.6898i −1.40329 + 2.43058i
\(370\) 0 0
\(371\) 5.36867 + 30.4472i 0.278727 + 1.58074i
\(372\) 17.9844 + 10.3833i 0.932446 + 0.538348i
\(373\) −4.63852 + 2.67805i −0.240173 + 0.138664i −0.615256 0.788327i \(-0.710948\pi\)
0.375083 + 0.926991i \(0.377614\pi\)
\(374\) −5.59173 + 4.69202i −0.289141 + 0.242618i
\(375\) 0 0
\(376\) 2.30343 + 0.838381i 0.118790 + 0.0432362i
\(377\) −8.17274 + 9.73989i −0.420918 + 0.501630i
\(378\) 23.6802 + 4.17546i 1.21798 + 0.214763i
\(379\) 5.86331 0.301178 0.150589 0.988596i \(-0.451883\pi\)
0.150589 + 0.988596i \(0.451883\pi\)
\(380\) 0 0
\(381\) −24.3097 −1.24542
\(382\) −7.22230 1.27349i −0.369525 0.0651572i
\(383\) 18.6249 22.1962i 0.951686 1.13418i −0.0391675 0.999233i \(-0.512471\pi\)
0.990853 0.134942i \(-0.0430850\pi\)
\(384\) −2.78573 1.01392i −0.142159 0.0517415i
\(385\) 0 0
\(386\) 19.6814 16.5147i 1.00176 0.840576i
\(387\) −29.2819 + 16.9059i −1.48848 + 0.859377i
\(388\) 7.93099 + 4.57896i 0.402635 + 0.232461i
\(389\) 0.653743 + 3.70756i 0.0331461 + 0.187981i 0.996885 0.0788651i \(-0.0251297\pi\)
−0.963739 + 0.266846i \(0.914019\pi\)
\(390\) 0 0
\(391\) −4.23365 + 7.33290i −0.214105 + 0.370841i
\(392\) 1.26612 0.730994i 0.0639487 0.0369208i
\(393\) 36.3236 + 43.2888i 1.83228 + 2.18363i
\(394\) 12.3868 4.50841i 0.624036 0.227130i
\(395\) 0 0
\(396\) 6.10517 + 5.12284i 0.306796 + 0.257433i
\(397\) 18.6157 + 3.28244i 0.934293 + 0.164741i 0.620015 0.784590i \(-0.287126\pi\)
0.314278 + 0.949331i \(0.398238\pi\)
\(398\) 10.2986i 0.516222i
\(399\) −28.8512 24.0952i −1.44437 1.20627i
\(400\) 0 0
\(401\) 2.11371 11.9874i 0.105554 0.598624i −0.885444 0.464746i \(-0.846146\pi\)
0.990998 0.133878i \(-0.0427431\pi\)
\(402\) 19.5257 23.2698i 0.973854 1.16059i
\(403\) 12.8556 35.3203i 0.640381 1.75943i
\(404\) 4.64764 1.69160i 0.231229 0.0841605i
\(405\) 0 0
\(406\) 3.44650 + 5.96952i 0.171047 + 0.296262i
\(407\) −9.91042 5.72179i −0.491241 0.283618i
\(408\) −15.4777 + 2.72914i −0.766261 + 0.135113i
\(409\) 4.90892 + 27.8399i 0.242731 + 1.37659i 0.825705 + 0.564103i \(0.190778\pi\)
−0.582974 + 0.812491i \(0.698111\pi\)
\(410\) 0 0
\(411\) 18.6408 + 32.2868i 0.919482 + 1.59259i
\(412\) 3.54042 + 4.21931i 0.174424 + 0.207870i
\(413\) −8.01347 22.0168i −0.394317 1.08338i
\(414\) 8.68726 + 3.16190i 0.426955 + 0.155399i
\(415\) 0 0
\(416\) −0.931747 + 5.28420i −0.0456827 + 0.259079i
\(417\) 25.7343i 1.26021i
\(418\) −2.06574 5.63488i −0.101039 0.275611i
\(419\) 11.5301 0.563284 0.281642 0.959520i \(-0.409121\pi\)
0.281642 + 0.959520i \(0.409121\pi\)
\(420\) 0 0
\(421\) −15.9361 13.3719i −0.776676 0.651709i 0.165733 0.986171i \(-0.447001\pi\)
−0.942409 + 0.334462i \(0.891445\pi\)
\(422\) −5.41437 + 14.8759i −0.263567 + 0.724145i
\(423\) −4.85283 13.3330i −0.235953 0.648274i
\(424\) −8.14168 + 6.83168i −0.395395 + 0.331776i
\(425\) 0 0
\(426\) 3.73426 6.46792i 0.180925 0.313372i
\(427\) 44.2506 7.80258i 2.14144 0.377593i
\(428\) −6.18385 + 1.09038i −0.298908 + 0.0527055i
\(429\) 10.9507 18.9671i 0.528704 0.915742i
\(430\) 0 0
\(431\) 2.06480 1.73257i 0.0994578 0.0834550i −0.591703 0.806156i \(-0.701544\pi\)
0.691161 + 0.722701i \(0.257100\pi\)
\(432\) 2.82716 + 7.76755i 0.136022 + 0.373716i
\(433\) 10.4904 28.8221i 0.504135 1.38510i −0.383068 0.923720i \(-0.625132\pi\)
0.887203 0.461380i \(-0.152645\pi\)
\(434\) −15.6099 13.0983i −0.749301 0.628738i
\(435\) 0 0
\(436\) 5.47566 0.262237
\(437\) −4.48730 5.32263i −0.214657 0.254616i
\(438\) 20.1783i 0.964155i
\(439\) 4.34601 24.6474i 0.207424 1.17636i −0.686156 0.727454i \(-0.740703\pi\)
0.893580 0.448904i \(-0.148185\pi\)
\(440\) 0 0
\(441\) −7.95213 2.89434i −0.378673 0.137826i
\(442\) 9.72930 + 26.7310i 0.462776 + 1.27147i
\(443\) −22.5689 26.8966i −1.07228 1.27790i −0.958716 0.284367i \(-0.908217\pi\)
−0.113567 0.993530i \(-0.536228\pi\)
\(444\) −12.3195 21.3381i −0.584660 1.01266i
\(445\) 0 0
\(446\) −0.570650 3.23631i −0.0270210 0.153244i
\(447\) 47.8160 8.43124i 2.26162 0.398784i
\(448\) 2.51922 + 1.45447i 0.119022 + 0.0687175i
\(449\) −1.27642 2.21082i −0.0602380 0.104335i 0.834334 0.551260i \(-0.185853\pi\)
−0.894572 + 0.446924i \(0.852519\pi\)
\(450\) 0 0
\(451\) 12.0507 4.38611i 0.567448 0.206534i
\(452\) 1.15714 3.17923i 0.0544275 0.149538i
\(453\) −24.5520 + 29.2600i −1.15355 + 1.37475i
\(454\) 2.05161 11.6353i 0.0962868 0.546070i
\(455\) 0 0
\(456\) 2.21436 12.7309i 0.103697 0.596177i
\(457\) 29.0079i 1.35693i 0.734631 + 0.678467i \(0.237355\pi\)
−0.734631 + 0.678467i \(0.762645\pi\)
\(458\) 11.7375 + 2.06964i 0.548459 + 0.0967081i
\(459\) 33.5702 + 28.1688i 1.56692 + 1.31481i
\(460\) 0 0
\(461\) −35.2153 + 12.8173i −1.64014 + 0.596962i −0.987064 0.160329i \(-0.948745\pi\)
−0.653077 + 0.757291i \(0.726522\pi\)
\(462\) −7.63215 9.09564i −0.355080 0.423168i
\(463\) 3.83218 2.21251i 0.178096 0.102824i −0.408302 0.912847i \(-0.633879\pi\)
0.586398 + 0.810023i \(0.300545\pi\)
\(464\) −1.18479 + 2.05212i −0.0550026 + 0.0952673i
\(465\) 0 0
\(466\) 1.59485 + 9.04485i 0.0738800 + 0.418994i
\(467\) 3.74952 + 2.16478i 0.173507 + 0.100174i 0.584238 0.811582i \(-0.301393\pi\)
−0.410732 + 0.911756i \(0.634727\pi\)
\(468\) 26.8975 15.5293i 1.24334 0.717842i
\(469\) −22.8337 + 19.1597i −1.05436 + 0.884715i
\(470\) 0 0
\(471\) 45.6584 + 16.6183i 2.10383 + 0.765731i
\(472\) 5.17726 6.17002i 0.238303 0.283998i
\(473\) 7.92058 + 1.39661i 0.364189 + 0.0642163i
\(474\) −24.4260 −1.12193
\(475\) 0 0
\(476\) 15.4219 0.706862
\(477\) 60.5850 + 10.6828i 2.77400 + 0.489130i
\(478\) 3.47691 4.14362i 0.159030 0.189525i
\(479\) −7.03629 2.56100i −0.321496 0.117015i 0.176231 0.984349i \(-0.443610\pi\)
−0.497727 + 0.867334i \(0.665832\pi\)
\(480\) 0 0
\(481\) −34.1628 + 28.6660i −1.55769 + 1.30706i
\(482\) 23.0296 13.2962i 1.04897 0.605624i
\(483\) −11.9279 6.88657i −0.542737 0.313350i
\(484\) 1.58094 + 8.96594i 0.0718608 + 0.407543i
\(485\) 0 0
\(486\) −1.81604 + 3.14548i −0.0823774 + 0.142682i
\(487\) 15.4397 8.91410i 0.699638 0.403936i −0.107575 0.994197i \(-0.534308\pi\)
0.807213 + 0.590261i \(0.200975\pi\)
\(488\) 9.92886 + 11.8328i 0.449458 + 0.535644i
\(489\) 11.3677 4.13750i 0.514065 0.187104i
\(490\) 0 0
\(491\) −9.18783 7.70951i −0.414641 0.347925i 0.411479 0.911419i \(-0.365012\pi\)
−0.826120 + 0.563494i \(0.809457\pi\)
\(492\) 27.1921 + 4.79470i 1.22591 + 0.216162i
\(493\) 12.5625i 0.565784i
\(494\) −23.3886 + 0.0542561i −1.05230 + 0.00244110i
\(495\) 0 0
\(496\) 1.21641 6.89863i 0.0546186 0.309757i
\(497\) −4.71069 + 5.61398i −0.211303 + 0.251821i
\(498\) 0.491440 1.35022i 0.0220219 0.0605048i
\(499\) −6.32111 + 2.30070i −0.282972 + 0.102993i −0.479607 0.877483i \(-0.659221\pi\)
0.196635 + 0.980477i \(0.436999\pi\)
\(500\) 0 0
\(501\) −23.4948 40.6943i −1.04967 1.81809i
\(502\) 1.31001 + 0.756334i 0.0584685 + 0.0337568i
\(503\) −4.86312 + 0.857499i −0.216836 + 0.0382340i −0.281011 0.959705i \(-0.590670\pi\)
0.0641748 + 0.997939i \(0.479558\pi\)
\(504\) −2.92388 16.5822i −0.130240 0.738628i
\(505\) 0 0
\(506\) −1.09952 1.90442i −0.0488796 0.0846620i
\(507\) −30.0905 35.8604i −1.33636 1.59262i
\(508\) 2.80464 + 7.70569i 0.124436 + 0.341885i
\(509\) 18.1920 + 6.62133i 0.806345 + 0.293485i 0.712113 0.702065i \(-0.247738\pi\)
0.0942316 + 0.995550i \(0.469961\pi\)
\(510\) 0 0
\(511\) 3.43825 19.4993i 0.152099 0.862597i
\(512\) 1.00000i 0.0441942i
\(513\) −31.1618 + 18.0878i −1.37583 + 0.798595i
\(514\) 6.86350 0.302736
\(515\) 0 0
\(516\) 13.2655 + 11.1311i 0.583980 + 0.490017i
\(517\) −1.15433 + 3.17150i −0.0507675 + 0.139483i
\(518\) 8.26912 + 22.7192i 0.363324 + 0.998226i
\(519\) 5.50448 4.61881i 0.241620 0.202743i
\(520\) 0 0
\(521\) 3.76749 6.52549i 0.165057 0.285887i −0.771619 0.636085i \(-0.780553\pi\)
0.936675 + 0.350199i \(0.113886\pi\)
\(522\) 13.5076 2.38175i 0.591211 0.104246i
\(523\) −25.8798 + 4.56331i −1.13164 + 0.199539i −0.707948 0.706265i \(-0.750379\pi\)
−0.423697 + 0.905804i \(0.639268\pi\)
\(524\) 9.53099 16.5082i 0.416363 0.721162i
\(525\) 0 0
\(526\) −15.7216 + 13.1920i −0.685496 + 0.575199i
\(527\) −12.7018 34.8979i −0.553299 1.52018i
\(528\) 1.39603 3.83556i 0.0607544 0.166921i
\(529\) 15.6650 + 13.1445i 0.681085 + 0.571498i
\(530\) 0 0
\(531\) −46.6215 −2.02320
\(532\) −4.30910 + 11.9252i −0.186823 + 0.517021i
\(533\) 49.9765i 2.16472i
\(534\) 6.21547 35.2497i 0.268970 1.52540i
\(535\) 0 0
\(536\) −9.62879 3.50459i −0.415900 0.151375i
\(537\) 18.3430 + 50.3970i 0.791560 + 2.17479i
\(538\) −11.2826 13.4461i −0.486429 0.579703i
\(539\) 1.00648 + 1.74327i 0.0433520 + 0.0750879i
\(540\) 0 0
\(541\) 2.24024 + 12.7051i 0.0963156 + 0.546233i 0.994336 + 0.106280i \(0.0338939\pi\)
−0.898021 + 0.439953i \(0.854995\pi\)
\(542\) −8.55753 + 1.50892i −0.367577 + 0.0648138i
\(543\) 51.5911 + 29.7862i 2.21399 + 1.27825i
\(544\) 2.65077 + 4.59127i 0.113651 + 0.196849i
\(545\) 0 0
\(546\) −43.4814 + 15.8259i −1.86083 + 0.677287i
\(547\) −14.5722 + 40.0367i −0.623061 + 1.71185i 0.0763080 + 0.997084i \(0.475687\pi\)
−0.699369 + 0.714761i \(0.746535\pi\)
\(548\) 8.08366 9.63374i 0.345317 0.411533i
\(549\) 15.5259 88.0516i 0.662628 3.75795i
\(550\) 0 0
\(551\) −9.71405 3.51013i −0.413832 0.149536i
\(552\) 4.73474i 0.201524i
\(553\) 23.6041 + 4.16204i 1.00375 + 0.176988i
\(554\) −6.29769 5.28439i −0.267563 0.224512i
\(555\) 0 0
\(556\) −8.15726 + 2.96900i −0.345945 + 0.125914i
\(557\) −7.74009 9.22427i −0.327958 0.390845i 0.576719 0.816942i \(-0.304333\pi\)
−0.904677 + 0.426097i \(0.859888\pi\)
\(558\) −35.1152 + 20.2738i −1.48655 + 0.858258i
\(559\) 15.6716 27.1440i 0.662838 1.14807i
\(560\) 0 0
\(561\) −3.75764 21.3107i −0.158648 0.899737i
\(562\) −14.0988 8.13995i −0.594722 0.343363i
\(563\) 38.8377 22.4230i 1.63681 0.945015i 0.654893 0.755721i \(-0.272714\pi\)
0.981921 0.189293i \(-0.0606198\pi\)
\(564\) −5.56669 + 4.67100i −0.234400 + 0.196685i
\(565\) 0 0
\(566\) 5.87384 + 2.13790i 0.246896 + 0.0898627i
\(567\) −13.3503 + 15.9103i −0.560660 + 0.668168i
\(568\) −2.48103 0.437473i −0.104102 0.0183559i
\(569\) −30.1492 −1.26392 −0.631959 0.775002i \(-0.717749\pi\)
−0.631959 + 0.775002i \(0.717749\pi\)
\(570\) 0 0
\(571\) 3.87066 0.161982 0.0809910 0.996715i \(-0.474192\pi\)
0.0809910 + 0.996715i \(0.474192\pi\)
\(572\) −7.27561 1.28289i −0.304209 0.0536402i
\(573\) 13.9748 16.6545i 0.583804 0.695751i
\(574\) −25.4601 9.26672i −1.06268 0.386785i
\(575\) 0 0
\(576\) 4.43412 3.72067i 0.184755 0.155028i
\(577\) −13.2589 + 7.65505i −0.551976 + 0.318684i −0.749919 0.661530i \(-0.769907\pi\)
0.197942 + 0.980214i \(0.436574\pi\)
\(578\) 9.61837 + 5.55317i 0.400072 + 0.230981i
\(579\) 13.2259 + 75.0080i 0.549651 + 3.11723i
\(580\) 0 0
\(581\) −0.704971 + 1.22105i −0.0292471 + 0.0506575i
\(582\) −23.5115 + 13.5744i −0.974584 + 0.562676i
\(583\) −9.40627 11.2100i −0.389568 0.464269i
\(584\) 6.39612 2.32800i 0.264673 0.0963332i
\(585\) 0 0
\(586\) 11.6515 + 9.77676i 0.481319 + 0.403874i
\(587\) 17.8491 + 3.14728i 0.736713 + 0.129902i 0.529400 0.848372i \(-0.322417\pi\)
0.207313 + 0.978275i \(0.433528\pi\)
\(588\) 4.33408i 0.178735i
\(589\) 30.5342 0.0708324i 1.25814 0.00291860i
\(590\) 0 0
\(591\) −6.78571 + 38.4837i −0.279127 + 1.58301i
\(592\) −5.34243 + 6.36686i −0.219573 + 0.261676i
\(593\) −9.01955 + 24.7810i −0.370389 + 1.01763i 0.604823 + 0.796360i \(0.293244\pi\)
−0.975212 + 0.221275i \(0.928978\pi\)
\(594\) −10.6948 + 3.89260i −0.438814 + 0.159715i
\(595\) 0 0
\(596\) −8.18914 14.1840i −0.335440 0.580999i
\(597\) 26.4400 + 15.2651i 1.08212 + 0.624761i
\(598\) −8.43961 + 1.48813i −0.345121 + 0.0608542i
\(599\) 5.45740 + 30.9505i 0.222983 + 1.26460i 0.866503 + 0.499172i \(0.166363\pi\)
−0.643519 + 0.765430i \(0.722526\pi\)
\(600\) 0 0
\(601\) 8.30819 + 14.3902i 0.338898 + 0.586989i 0.984226 0.176917i \(-0.0566125\pi\)
−0.645328 + 0.763906i \(0.723279\pi\)
\(602\) −10.9224 13.0168i −0.445165 0.530527i
\(603\) 20.2858 + 55.7347i 0.826100 + 2.26969i
\(604\) 12.1074 + 4.40675i 0.492645 + 0.179308i
\(605\) 0 0
\(606\) −2.54607 + 14.4395i −0.103427 + 0.586564i
\(607\) 4.44153i 0.180276i −0.995929 0.0901381i \(-0.971269\pi\)
0.995929 0.0901381i \(-0.0287308\pi\)
\(608\) −4.29091 + 0.766871i −0.174019 + 0.0311007i
\(609\) −20.4344 −0.828044
\(610\) 0 0
\(611\) 10.0756 + 8.45444i 0.407616 + 0.342030i
\(612\) 10.4956 28.8364i 0.424260 1.16564i
\(613\) 1.85677 + 5.10144i 0.0749943 + 0.206045i 0.971525 0.236936i \(-0.0761431\pi\)
−0.896531 + 0.442981i \(0.853921\pi\)
\(614\) 0.497498 0.417451i 0.0200774 0.0168469i
\(615\) 0 0
\(616\) −2.00261 + 3.46862i −0.0806874 + 0.139755i
\(617\) −30.2620 + 5.33600i −1.21830 + 0.214819i −0.745594 0.666401i \(-0.767834\pi\)
−0.472707 + 0.881220i \(0.656723\pi\)
\(618\) −16.0802 + 2.83538i −0.646842 + 0.114056i
\(619\) −13.0502 + 22.6035i −0.524530 + 0.908512i 0.475062 + 0.879952i \(0.342426\pi\)
−0.999592 + 0.0285602i \(0.990908\pi\)
\(620\) 0 0
\(621\) −10.1134 + 8.48611i −0.405835 + 0.340536i
\(622\) −3.96238 10.8865i −0.158877 0.436510i
\(623\) −12.0126 + 33.0045i −0.481276 + 1.32230i
\(624\) −12.1853 10.2247i −0.487801 0.409314i
\(625\) 0 0
\(626\) −0.630216 −0.0251885
\(627\) 17.5286 + 3.04886i 0.700026 + 0.121760i
\(628\) 16.3901i 0.654036i
\(629\) −7.65145 + 43.3935i −0.305083 + 1.73021i
\(630\) 0 0
\(631\) 39.5529 + 14.3961i 1.57458 + 0.573099i 0.974016 0.226479i \(-0.0727215\pi\)
0.600562 + 0.799579i \(0.294944\pi\)
\(632\) 2.81807 + 7.74258i 0.112097 + 0.307983i
\(633\) −30.1659 35.9504i −1.19899 1.42890i
\(634\) 4.65710 + 8.06633i 0.184957 + 0.320355i
\(635\) 0 0
\(636\) −5.47121 31.0288i −0.216948 1.23037i
\(637\) 7.72544 1.36220i 0.306093 0.0539725i
\(638\) −2.82548 1.63129i −0.111862 0.0645836i
\(639\) 7.29129 + 12.6289i 0.288439 + 0.499591i
\(640\) 0 0
\(641\) −13.5601 + 4.93548i −0.535592 + 0.194940i −0.595634 0.803256i \(-0.703099\pi\)
0.0600414 + 0.998196i \(0.480877\pi\)
\(642\) 6.36667 17.4923i 0.251272 0.690365i
\(643\) 16.1189 19.2098i 0.635667 0.757559i −0.348012 0.937490i \(-0.613143\pi\)
0.983679 + 0.179931i \(0.0575875\pi\)
\(644\) −0.806770 + 4.57542i −0.0317912 + 0.180297i
\(645\) 0 0
\(646\) −17.6679 + 14.8951i −0.695135 + 0.586041i
\(647\) 25.9344i 1.01959i 0.860297 + 0.509793i \(0.170278\pi\)
−0.860297 + 0.509793i \(0.829722\pi\)
\(648\) −7.03135 1.23982i −0.276217 0.0487046i
\(649\) 8.49526 + 7.12837i 0.333468 + 0.279813i
\(650\) 0 0
\(651\) 56.7658 20.6610i 2.22483 0.809770i
\(652\) −2.62302 3.12599i −0.102725 0.122423i
\(653\) 10.2190 5.89996i 0.399901 0.230883i −0.286540 0.958068i \(-0.592505\pi\)
0.686441 + 0.727185i \(0.259172\pi\)
\(654\) −8.11633 + 14.0579i −0.317374 + 0.549708i
\(655\) 0 0
\(656\) −1.61737 9.17254i −0.0631475 0.358128i
\(657\) −34.1205 19.6995i −1.33117 0.768549i
\(658\) 6.17528 3.56530i 0.240737 0.138990i
\(659\) −16.7858 + 14.0849i −0.653880 + 0.548671i −0.908246 0.418438i \(-0.862578\pi\)
0.254365 + 0.967108i \(0.418133\pi\)
\(660\) 0 0
\(661\) −36.0396 13.1173i −1.40178 0.510205i −0.473072 0.881024i \(-0.656855\pi\)
−0.928705 + 0.370819i \(0.879077\pi\)
\(662\) 7.75578 9.24297i 0.301437 0.359238i
\(663\) −83.0491 14.6438i −3.22536 0.568718i
\(664\) −0.484691 −0.0188097
\(665\) 0 0
\(666\) 48.1089 1.86418
\(667\) −3.72706 0.657182i −0.144313 0.0254462i
\(668\) −10.1887 + 12.1424i −0.394211 + 0.469802i
\(669\) 9.15458 + 3.33199i 0.353937 + 0.128822i
\(670\) 0 0
\(671\) −16.2921 + 13.6707i −0.628948 + 0.527750i
\(672\) −7.46827 + 4.31181i −0.288095 + 0.166332i
\(673\) −1.17684 0.679451i −0.0453640 0.0261909i 0.477146 0.878824i \(-0.341671\pi\)
−0.522510 + 0.852633i \(0.675004\pi\)
\(674\) 0.195701 + 1.10988i 0.00753812 + 0.0427508i
\(675\) 0 0
\(676\) −7.89547 + 13.6754i −0.303672 + 0.525975i
\(677\) −17.1281 + 9.88891i −0.658286 + 0.380062i −0.791624 0.611009i \(-0.790764\pi\)
0.133338 + 0.991071i \(0.457431\pi\)
\(678\) 6.44698 + 7.68321i 0.247595 + 0.295072i
\(679\) 25.0333 9.11139i 0.960692 0.349663i
\(680\) 0 0
\(681\) 26.8307 + 22.5136i 1.02815 + 0.862724i
\(682\) 9.49845 + 1.67483i 0.363714 + 0.0641327i
\(683\) 38.4380i 1.47079i −0.677640 0.735394i \(-0.736997\pi\)
0.677640 0.735394i \(-0.263003\pi\)
\(684\) 19.3655 + 16.1731i 0.740457 + 0.618396i
\(685\) 0 0
\(686\) −2.79744 + 15.8651i −0.106807 + 0.605731i
\(687\) −22.7115 + 27.0665i −0.866499 + 1.03265i
\(688\) 1.99787 5.48910i 0.0761681 0.209270i
\(689\) −53.5888 + 19.5047i −2.04157 + 0.743070i
\(690\) 0 0
\(691\) 4.00672 + 6.93985i 0.152423 + 0.264004i 0.932118 0.362156i \(-0.117959\pi\)
−0.779695 + 0.626160i \(0.784626\pi\)
\(692\) −2.09913 1.21193i −0.0797971 0.0460708i
\(693\) 22.8313 4.02578i 0.867291 0.152927i
\(694\) 2.23492 + 12.6748i 0.0848362 + 0.481130i
\(695\) 0 0
\(696\) −3.51233 6.08354i −0.133135 0.230596i
\(697\) −31.7401 37.8263i −1.20224 1.43277i
\(698\) −2.86521 7.87210i −0.108450 0.297963i
\(699\) −25.5852 9.31225i −0.967721 0.352222i
\(700\) 0 0
\(701\) −4.88207 + 27.6876i −0.184393 + 1.04575i 0.742339 + 0.670025i \(0.233716\pi\)
−0.926732 + 0.375722i \(0.877395\pi\)
\(702\) 44.3533i 1.67401i
\(703\) −31.4166 18.0413i −1.18490 0.680442i
\(704\) −1.37686 −0.0518924
\(705\) 0 0
\(706\) −11.5698 9.70819i −0.435434 0.365372i
\(707\) 4.92079 13.5198i 0.185065 0.508463i
\(708\) 8.16653 + 22.4374i 0.306917 + 0.843248i
\(709\) 25.7736 21.6266i 0.967946 0.812204i −0.0142810 0.999898i \(-0.504546\pi\)
0.982227 + 0.187694i \(0.0601015\pi\)
\(710\) 0 0
\(711\) 23.8464 41.3032i 0.894311 1.54899i
\(712\) −11.8906 + 2.09663i −0.445617 + 0.0785744i
\(713\) 11.0181 1.94278i 0.412630 0.0727578i
\(714\) −22.8592 + 39.5934i −0.855485 + 1.48174i
\(715\) 0 0
\(716\) 13.8586 11.6288i 0.517921 0.434587i
\(717\) 5.48442 + 15.0683i 0.204820 + 0.562737i
\(718\) 11.5172 31.6434i 0.429820 1.18092i
\(719\) 0.633806 + 0.531826i 0.0236370 + 0.0198338i 0.654530 0.756036i \(-0.272867\pi\)
−0.630893 + 0.775870i \(0.717311\pi\)
\(720\) 0 0
\(721\) 16.0223 0.596700
\(722\) −6.58115 17.8238i −0.244925 0.663334i
\(723\) 78.8333i 2.93184i
\(724\) 3.48949 19.7899i 0.129686 0.735484i
\(725\) 0 0
\(726\) −25.3620 9.23101i −0.941272 0.342595i
\(727\) −16.1735 44.4363i −0.599842 1.64805i −0.751588 0.659633i \(-0.770712\pi\)
0.151745 0.988420i \(-0.451511\pi\)
\(728\) 10.0330 + 11.9569i 0.371848 + 0.443152i
\(729\) −16.0934 27.8746i −0.596052 1.03239i
\(730\) 0 0
\(731\) −5.37759 30.4978i −0.198897 1.12800i
\(732\) −45.0959 + 7.95162i −1.66679 + 0.293900i
\(733\) 9.72810 + 5.61652i 0.359315 + 0.207451i 0.668780 0.743460i \(-0.266817\pi\)
−0.309465 + 0.950911i \(0.600150\pi\)
\(734\) −2.10248 3.64161i −0.0776041 0.134414i
\(735\) 0 0
\(736\) −1.50082 + 0.546254i −0.0553210 + 0.0201352i
\(737\) 4.82534 13.2575i 0.177744 0.488347i
\(738\) −34.6545 + 41.2996i −1.27565 + 1.52026i
\(739\) −4.49255 + 25.4785i −0.165261 + 0.937242i 0.783534 + 0.621349i \(0.213415\pi\)
−0.948795 + 0.315893i \(0.897696\pi\)
\(740\) 0 0
\(741\) 34.5286 60.1269i 1.26844 2.20882i
\(742\) 30.9169i 1.13500i
\(743\) −42.9858 7.57956i −1.57700 0.278067i −0.684463 0.729047i \(-0.739963\pi\)
−0.892534 + 0.450980i \(0.851075\pi\)
\(744\) 15.9081 + 13.3485i 0.583219 + 0.489379i
\(745\) 0 0
\(746\) −5.03309 + 1.83189i −0.184274 + 0.0670704i
\(747\) 1.80338 + 2.14918i 0.0659821 + 0.0786344i
\(748\) −6.32154 + 3.64974i −0.231138 + 0.133448i
\(749\) −9.13300 + 15.8188i −0.333713 + 0.578007i
\(750\) 0 0
\(751\) 3.63508 + 20.6156i 0.132646 + 0.752273i 0.976470 + 0.215653i \(0.0691881\pi\)
−0.843824 + 0.536620i \(0.819701\pi\)
\(752\) 2.12285 + 1.22563i 0.0774125 + 0.0446941i
\(753\) −3.88354 + 2.24216i −0.141524 + 0.0817089i
\(754\) −9.73989 + 8.17274i −0.354706 + 0.297634i
\(755\) 0 0
\(756\) 22.5954 + 8.22406i 0.821787 + 0.299106i
\(757\) −12.7499 + 15.1947i −0.463403 + 0.552262i −0.946247 0.323444i \(-0.895159\pi\)
0.482844 + 0.875706i \(0.339604\pi\)
\(758\) 5.77423 + 1.01815i 0.209730 + 0.0369810i
\(759\) 6.51908 0.236628
\(760\) 0 0
\(761\) −10.8607 −0.393700 −0.196850 0.980434i \(-0.563071\pi\)
−0.196850 + 0.980434i \(0.563071\pi\)
\(762\) −23.9403 4.22133i −0.867267 0.152923i
\(763\) 10.2386 12.2019i 0.370662 0.441738i
\(764\) −6.89144 2.50828i −0.249323 0.0907463i
\(765\) 0 0
\(766\) 22.1962 18.6249i 0.801983 0.672944i
\(767\) 37.4275 21.6088i 1.35143 0.780248i
\(768\) −2.56734 1.48226i −0.0926410 0.0534863i
\(769\) −2.51395 14.2573i −0.0906553 0.514132i −0.995992 0.0894380i \(-0.971493\pi\)
0.905337 0.424694i \(-0.139618\pi\)
\(770\) 0 0
\(771\) −10.1735 + 17.6210i −0.366389 + 0.634604i
\(772\) 22.2502 12.8461i 0.800802 0.462343i
\(773\) −23.0096 27.4218i −0.827597 0.986292i −0.999999 0.00126532i \(-0.999597\pi\)
0.172402 0.985027i \(-0.444847\pi\)
\(774\) −31.7728 + 11.5643i −1.14205 + 0.415672i
\(775\) 0 0
\(776\) 7.01537 + 5.88660i 0.251837 + 0.211317i
\(777\) −70.5850 12.4460i −2.53222 0.446499i
\(778\) 3.76475i 0.134973i
\(779\) 38.1182 13.9741i 1.36573 0.500675i
\(780\) 0 0
\(781\) 0.602339 3.41603i 0.0215534 0.122235i
\(782\) −5.44268 + 6.48633i −0.194630 + 0.231951i
\(783\) −6.69919 + 18.4059i −0.239409 + 0.657772i
\(784\) 1.37382 0.500029i 0.0490650 0.0178582i
\(785\) 0 0
\(786\) 28.2547 + 48.9386i 1.00781 + 1.74558i
\(787\) −12.4112 7.16560i −0.442411 0.255426i 0.262209 0.965011i \(-0.415549\pi\)
−0.704620 + 0.709585i \(0.748882\pi\)
\(788\) 12.9814 2.28898i 0.462445 0.0815415i
\(789\) −10.5649 59.9168i −0.376122 2.13309i
\(790\) 0 0
\(791\) −4.92087 8.52320i −0.174966 0.303050i
\(792\) 5.12284 + 6.10517i 0.182032 + 0.216938i
\(793\) 28.3473 + 77.8835i 1.00664 + 2.76573i
\(794\) 17.7629 + 6.46515i 0.630380 + 0.229440i
\(795\) 0 0
\(796\) 1.78833 10.1421i 0.0633857 0.359478i
\(797\) 17.7667i 0.629330i −0.949203 0.314665i \(-0.898108\pi\)
0.949203 0.314665i \(-0.101892\pi\)
\(798\) −24.2288 28.7391i −0.857690 1.01735i
\(799\) 12.9955 0.459746
\(800\) 0 0
\(801\) 53.5375 + 44.9233i 1.89166 + 1.58729i
\(802\) 4.16319 11.4383i 0.147007 0.403900i
\(803\) 3.20533 + 8.80657i 0.113114 + 0.310777i
\(804\) 23.2698 19.5257i 0.820664 0.688619i
\(805\) 0 0
\(806\) 18.7936 32.5514i 0.661975 1.14657i
\(807\) 51.2445 9.03580i 1.80389 0.318075i
\(808\) 4.87078 0.858850i 0.171353 0.0302142i
\(809\) −5.86927 + 10.1659i −0.206353 + 0.357413i −0.950563 0.310532i \(-0.899493\pi\)
0.744210 + 0.667946i \(0.232826\pi\)
\(810\) 0 0
\(811\) −8.28725 + 6.95383i −0.291005 + 0.244182i −0.776588 0.630008i \(-0.783052\pi\)
0.485584 + 0.874190i \(0.338607\pi\)
\(812\) 2.35755 + 6.47730i 0.0827336 + 0.227309i
\(813\) 8.81052 24.2067i 0.308999 0.848967i
\(814\) −8.76628 7.35579i −0.307258 0.257820i
\(815\) 0 0
\(816\) −15.7165 −0.550187
\(817\) 25.0854 + 4.36325i 0.877625 + 0.152651i
\(818\) 28.2694i 0.988415i
\(819\) 15.6887 88.9753i 0.548209 3.10905i
\(820\) 0 0
\(821\) 12.0721 + 4.39387i 0.421318 + 0.153347i 0.543974 0.839102i \(-0.316919\pi\)
−0.122656 + 0.992449i \(0.539141\pi\)
\(822\) 12.7510 + 35.0332i 0.444744 + 1.22192i
\(823\) 7.30126 + 8.70130i 0.254506 + 0.303308i 0.878136 0.478411i \(-0.158787\pi\)
−0.623630 + 0.781720i \(0.714343\pi\)
\(824\) 2.75396 + 4.77000i 0.0959387 + 0.166171i
\(825\) 0 0
\(826\) −4.06854 23.0739i −0.141563 0.802842i
\(827\) 25.7071 4.53285i 0.893923 0.157623i 0.292228 0.956349i \(-0.405603\pi\)
0.601695 + 0.798726i \(0.294492\pi\)
\(828\) 8.00622 + 4.62239i 0.278235 + 0.160639i
\(829\) −12.3906 21.4611i −0.430342 0.745374i 0.566561 0.824020i \(-0.308274\pi\)
−0.996903 + 0.0786462i \(0.974940\pi\)
\(830\) 0 0
\(831\) 22.9016 8.33551i 0.794449 0.289156i
\(832\) −1.83518 + 5.04213i −0.0636236 + 0.174804i
\(833\) 4.98211 5.93745i 0.172620 0.205720i
\(834\) 4.46871 25.3433i 0.154739 0.877567i
\(835\) 0 0
\(836\) −1.05587 5.90799i −0.0365182 0.204332i
\(837\) 57.9041i 2.00146i
\(838\) 11.3550 + 2.00219i 0.392251 + 0.0691644i
\(839\) 24.0765 + 20.2026i 0.831214 + 0.697472i 0.955569 0.294766i \(-0.0952417\pi\)
−0.124355 + 0.992238i \(0.539686\pi\)
\(840\) 0 0
\(841\) 21.9748 7.99816i 0.757751 0.275799i
\(842\) −13.3719 15.9361i −0.460828 0.549193i
\(843\) 41.7961 24.1310i 1.43953 0.831115i
\(844\) −7.91528 + 13.7097i −0.272455 + 0.471906i
\(845\) 0 0
\(846\) −2.46385 13.9732i −0.0847087 0.480407i
\(847\) 22.9357 + 13.2419i 0.788079 + 0.454997i
\(848\) −9.20430 + 5.31410i −0.316077 + 0.182487i
\(849\) −14.1953 + 11.9112i −0.487180 + 0.408793i
\(850\) 0 0
\(851\) −12.4739 4.54011i −0.427598 0.155633i
\(852\) 4.80067 5.72121i 0.164468 0.196005i
\(853\) 39.5963 + 6.98190i 1.35575 + 0.239056i 0.803840 0.594846i \(-0.202787\pi\)
0.551913 + 0.833902i \(0.313898\pi\)
\(854\) 44.9333 1.53759
\(855\) 0 0
\(856\) −6.27924 −0.214620
\(857\) −4.70367 0.829384i −0.160674 0.0283312i 0.0927323 0.995691i \(-0.470440\pi\)
−0.253407 + 0.967360i \(0.581551\pi\)
\(858\) 14.0779 16.7774i 0.480613 0.572772i
\(859\) −9.73955 3.54491i −0.332309 0.120951i 0.170476 0.985362i \(-0.445469\pi\)
−0.502786 + 0.864411i \(0.667692\pi\)
\(860\) 0 0
\(861\) 61.5292 51.6292i 2.09691 1.75952i
\(862\) 2.33429 1.34770i 0.0795061 0.0459029i
\(863\) −27.4609 15.8545i −0.934779 0.539695i −0.0464590 0.998920i \(-0.514794\pi\)
−0.888320 + 0.459225i \(0.848127\pi\)
\(864\) 1.43539 + 8.14047i 0.0488328 + 0.276945i
\(865\) 0 0
\(866\) 15.3359 26.5626i 0.521135 0.902632i
\(867\) −28.5138 + 16.4624i −0.968379 + 0.559094i
\(868\) −13.0983 15.6099i −0.444585 0.529836i
\(869\) −10.6605 + 3.88009i −0.361631 + 0.131623i
\(870\) 0 0
\(871\) −42.1180 35.3412i −1.42711 1.19749i
\(872\) 5.39247 + 0.950839i 0.182612 + 0.0321995i
\(873\) 53.0091i 1.79409i
\(874\) −3.49486 6.02098i −0.118216 0.203663i
\(875\) 0 0
\(876\) −3.50392 + 19.8717i −0.118387 + 0.671403i
\(877\) 4.04949 4.82600i 0.136742 0.162962i −0.693328 0.720622i \(-0.743856\pi\)
0.830070 + 0.557660i \(0.188301\pi\)
\(878\) 8.55996 23.5183i 0.288885 0.793705i
\(879\) −42.3708 + 15.4217i −1.42913 + 0.520162i
\(880\) 0 0
\(881\) −26.9351 46.6530i −0.907468 1.57178i −0.817570 0.575830i \(-0.804679\pi\)
−0.0898984 0.995951i \(-0.528654\pi\)
\(882\) −7.32872 4.23124i −0.246771 0.142473i
\(883\) −1.94292 + 0.342590i −0.0653846 + 0.0115291i −0.206245 0.978500i \(-0.566124\pi\)
0.140860 + 0.990030i \(0.455013\pi\)
\(884\) 4.93970 + 28.0144i 0.166140 + 0.942227i
\(885\) 0 0
\(886\) −17.5555 30.4071i −0.589789 1.02155i
\(887\) 17.3589 + 20.6876i 0.582856 + 0.694621i 0.974216 0.225617i \(-0.0724397\pi\)
−0.391360 + 0.920238i \(0.627995\pi\)
\(888\) −8.42707 23.1532i −0.282794 0.776970i
\(889\) 22.4155 + 8.15856i 0.751790 + 0.273629i
\(890\) 0 0
\(891\) 1.70705 9.68119i 0.0571885 0.324332i
\(892\) 3.28624i 0.110031i
\(893\) −3.63111 + 10.0489i −0.121511 + 0.336273i
\(894\) 48.5536 1.62388
\(895\) 0 0
\(896\) 2.22838 + 1.86984i 0.0744451 + 0.0624669i
\(897\) 8.68913 23.8732i 0.290121 0.797102i
\(898\) −0.873122 2.39888i −0.0291365 0.0800518i
\(899\) 12.7156 10.6697i 0.424090 0.355853i
\(900\) 0 0
\(901\) −28.1729 + 48.7970i −0.938577 + 1.62566i
\(902\) 12.6293 2.22689i 0.420510 0.0741473i
\(903\) 49.6085 8.74733i 1.65087 0.291093i
\(904\) 1.69163 2.92999i 0.0562628 0.0974501i
\(905\) 0 0
\(906\) −29.2600 + 24.5520i −0.972097 + 0.815686i
\(907\) 8.43355 + 23.1710i 0.280031 + 0.769380i 0.997358 + 0.0726427i \(0.0231433\pi\)
−0.717327 + 0.696737i \(0.754635\pi\)
\(908\) 4.04088 11.1022i 0.134101 0.368440i
\(909\) −21.9308 18.4021i −0.727399 0.610360i
\(910\) 0 0
\(911\) −10.4670 −0.346787 −0.173394 0.984853i \(-0.555473\pi\)
−0.173394 + 0.984853i \(0.555473\pi\)
\(912\) 4.39141 12.1529i 0.145414 0.402424i
\(913\) 0.667352i 0.0220861i
\(914\) −5.03718 + 28.5672i −0.166615 + 0.944920i
\(915\) 0 0
\(916\) 11.1998 + 4.07640i 0.370053 + 0.134688i
\(917\) −18.9651 52.1063i −0.626284 1.72070i
\(918\) 28.1688 + 33.5702i 0.929708 + 1.10798i
\(919\) −12.5834 21.7950i −0.415087 0.718952i 0.580351 0.814367i \(-0.302916\pi\)
−0.995438 + 0.0954150i \(0.969582\pi\)
\(920\) 0 0
\(921\) 0.334319 + 1.89602i 0.0110162 + 0.0624759i
\(922\) −36.9060 + 6.50753i −1.21544 + 0.214314i
\(923\) −11.7068 6.75894i −0.385335 0.222473i
\(924\) −5.93676 10.2828i −0.195305 0.338278i
\(925\) 0 0
\(926\) 4.15816 1.51345i 0.136645 0.0497349i
\(927\) 10.9042 29.9590i 0.358140 0.983982i
\(928\) −1.52314 + 1.81521i −0.0499995 + 0.0595871i
\(929\) 3.26147 18.4967i 0.107005 0.606857i −0.883395 0.468629i \(-0.844748\pi\)
0.990400 0.138228i \(-0.0441408\pi\)
\(930\) 0 0
\(931\) 3.19912 + 5.51148i 0.104847 + 0.180631i
\(932\) 9.18438i 0.300844i
\(933\) 33.8227 + 5.96386i 1.10731 + 0.195248i
\(934\) 3.31664 + 2.78299i 0.108524 + 0.0910623i
\(935\) 0 0
\(936\) 29.1855 10.6227i 0.953958 0.347212i
\(937\) −9.00408 10.7306i −0.294150 0.350555i 0.598647 0.801013i \(-0.295705\pi\)
−0.892798 + 0.450458i \(0.851261\pi\)
\(938\) −25.8139 + 14.9036i −0.842852 + 0.486621i
\(939\) 0.934141 1.61798i 0.0304845 0.0528008i
\(940\) 0 0
\(941\) 10.1772 + 57.7176i 0.331766 + 1.88154i 0.457082 + 0.889424i \(0.348894\pi\)
−0.125316 + 0.992117i \(0.539994\pi\)
\(942\) 42.0790 + 24.2943i 1.37101 + 0.791552i
\(943\) 12.8829 7.43792i 0.419523 0.242212i
\(944\) 6.17002 5.17726i 0.200817 0.168506i
\(945\) 0 0
\(946\) 7.55773 + 2.75079i 0.245723 + 0.0894359i
\(947\) −0.912031 + 1.08692i −0.0296370 + 0.0353200i −0.780659 0.624957i \(-0.785117\pi\)
0.751022 + 0.660277i \(0.229561\pi\)
\(948\) −24.0550 4.24154i −0.781269 0.137759i
\(949\) 36.5223 1.18557
\(950\) 0 0
\(951\) −27.6120 −0.895382
\(952\) 15.1876 + 2.67799i 0.492234 + 0.0867941i
\(953\) −23.7773 + 28.3367i −0.770223 + 0.917916i −0.998448 0.0556922i \(-0.982263\pi\)
0.228225 + 0.973608i \(0.426708\pi\)
\(954\) 57.8095 + 21.0410i 1.87165 + 0.681226i
\(955\) 0 0
\(956\) 4.14362 3.47691i 0.134014 0.112451i
\(957\) 8.37619 4.83599i 0.270764 0.156325i
\(958\) −6.48468 3.74393i −0.209510 0.120961i
\(959\) −6.35254 36.0270i −0.205134 1.16337i
\(960\) 0 0
\(961\) −9.03536 + 15.6497i −0.291463 + 0.504829i
\(962\) −38.6216 + 22.2982i −1.24521 + 0.718922i
\(963\) 23.3630 + 27.8429i 0.752862 + 0.897226i
\(964\) 24.9886 9.09512i 0.804830 0.292934i
\(965\) 0 0
\(966\) −10.5508 8.85320i −0.339467 0.284847i
\(967\) 3.64316 + 0.642387i 0.117156 + 0.0206578i 0.231919 0.972735i \(-0.425500\pi\)
−0.114763 + 0.993393i \(0.536611\pi\)
\(968\) 9.10425i 0.292622i
\(969\) −12.0525 67.4380i −0.387183 2.16642i
\(970\) 0 0
\(971\) 1.26262 7.16068i 0.0405194 0.229797i −0.957822 0.287361i \(-0.907222\pi\)
0.998342 + 0.0575637i \(0.0183332\pi\)
\(972\) −2.33466 + 2.78234i −0.0748843 + 0.0892436i
\(973\) −8.63667 + 23.7291i −0.276879 + 0.760719i
\(974\) 16.7530 6.09760i 0.536801 0.195380i
\(975\) 0 0
\(976\) 7.72328 + 13.3771i 0.247216 + 0.428191i
\(977\) −9.69861 5.59949i −0.310286 0.179144i 0.336768 0.941587i \(-0.390666\pi\)
−0.647054 + 0.762444i \(0.723999\pi\)
\(978\) 11.9135 2.10067i 0.380951 0.0671719i
\(979\) −2.88676 16.3716i −0.0922613 0.523240i
\(980\) 0 0
\(981\) −15.8475 27.4486i −0.505971 0.876368i
\(982\) −7.70951 9.18783i −0.246020 0.293196i
\(983\) 12.0730 + 33.1702i 0.385068 + 1.05797i 0.969193 + 0.246302i \(0.0792154\pi\)
−0.584125 + 0.811663i \(0.698562\pi\)
\(984\) 25.9464 + 9.44372i 0.827141 + 0.301055i
\(985\) 0 0
\(986\) −2.18145 + 12.3716i −0.0694714 + 0.393992i
\(987\) 21.1387i 0.672853i
\(988\) −23.0427 4.00795i −0.733085 0.127510i
\(989\) 9.32951 0.296661
\(990\) 0 0
\(991\) 15.8273 + 13.2807i 0.502771 + 0.421875i 0.858577 0.512685i \(-0.171349\pi\)
−0.355806 + 0.934560i \(0.615794\pi\)
\(992\) 2.39587 6.58259i 0.0760689 0.208998i
\(993\) 12.2338 + 33.6122i 0.388229 + 1.06665i
\(994\) −5.61398 + 4.71069i −0.178065 + 0.149414i
\(995\) 0 0
\(996\) 0.718437 1.24437i 0.0227645 0.0394293i
\(997\) 44.3241 7.81553i 1.40376 0.247520i 0.580071 0.814566i \(-0.303025\pi\)
0.823687 + 0.567045i \(0.191913\pi\)
\(998\) −6.62459 + 1.16809i −0.209698 + 0.0369754i
\(999\) −34.3510 + 59.4977i −1.08682 + 1.88242i
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 950.2.u.f.549.3 24
5.2 odd 4 950.2.l.g.701.2 12
5.3 odd 4 190.2.k.c.131.1 12
5.4 even 2 inner 950.2.u.f.549.2 24
19.9 even 9 inner 950.2.u.f.199.2 24
95.3 even 36 3610.2.a.bd.1.6 6
95.9 even 18 inner 950.2.u.f.199.3 24
95.28 odd 36 190.2.k.c.161.1 yes 12
95.47 odd 36 950.2.l.g.351.2 12
95.73 odd 36 3610.2.a.bf.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.k.c.131.1 12 5.3 odd 4
190.2.k.c.161.1 yes 12 95.28 odd 36
950.2.l.g.351.2 12 95.47 odd 36
950.2.l.g.701.2 12 5.2 odd 4
950.2.u.f.199.2 24 19.9 even 9 inner
950.2.u.f.199.3 24 95.9 even 18 inner
950.2.u.f.549.2 24 5.4 even 2 inner
950.2.u.f.549.3 24 1.1 even 1 trivial
3610.2.a.bd.1.6 6 95.3 even 36
3610.2.a.bf.1.1 6 95.73 odd 36