Properties

Label 1950.2.y.k.49.1
Level $1950$
Weight $2$
Character 1950.49
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1950,2,Mod(49,1950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1950.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), 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: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.17284886784.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Root \(-1.70006 + 1.70006i\) of defining polynomial
Character \(\chi\) \(=\) 1950.49
Dual form 1950.2.y.k.199.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-2.32233 + 4.02239i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-2.32233 + 4.02239i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(3.81062 - 2.20006i) q^{11} -1.00000i q^{12} +(1.32233 + 3.35432i) q^{13} -4.64466 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.46410 + 2.00000i) q^{17} +1.00000 q^{18} +(6.96699 + 4.02239i) q^{19} -4.64466i q^{21} +(3.81062 + 2.20006i) q^{22} +(-0.845746 + 0.488292i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-2.24376 + 2.82233i) q^{26} +1.00000i q^{27} +(-2.32233 - 4.02239i) q^{28} +(-2.15637 - 3.73494i) q^{29} +6.44069i q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.20006 + 3.81062i) q^{33} +4.00000i q^{34} +(0.500000 + 0.866025i) q^{36} +(1.89801 + 3.28745i) q^{37} +8.04479i q^{38} +(-2.82233 - 2.24376i) q^{39} +(-6.31274 + 3.64466i) q^{41} +(4.02239 - 2.32233i) q^{42} +(-0.620469 - 0.358228i) q^{43} +4.40013i q^{44} +(-0.845746 - 0.488292i) q^{46} -9.75342 q^{47} +(0.866025 + 0.500000i) q^{48} +(-7.28643 - 12.6205i) q^{49} -4.00000 q^{51} +(-3.56609 - 0.531987i) q^{52} -13.5089i q^{53} +(-0.866025 + 0.500000i) q^{54} +(2.32233 - 4.02239i) q^{56} -8.04479 q^{57} +(2.15637 - 3.73494i) q^{58} +(1.88842 + 1.09028i) q^{59} +(-3.73205 + 6.46410i) q^{61} +(-5.57780 + 3.22034i) q^{62} +(2.32233 + 4.02239i) q^{63} +1.00000 q^{64} -4.40013 q^{66} +(-0.912609 - 1.58068i) q^{67} +(-3.46410 + 2.00000i) q^{68} +(0.488292 - 0.845746i) q^{69} +(-6.88764 - 3.97658i) q^{71} +(-0.500000 + 0.866025i) q^{72} -4.36112 q^{73} +(-1.89801 + 3.28745i) q^{74} +(-6.96699 + 4.02239i) q^{76} +20.4371i q^{77} +(0.531987 - 3.56609i) q^{78} +14.9340 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-6.31274 - 3.64466i) q^{82} +3.51093 q^{83} +(4.02239 + 2.32233i) q^{84} -0.716456i q^{86} +(3.73494 + 2.15637i) q^{87} +(-3.81062 + 2.20006i) q^{88} +(-7.07780 + 4.08637i) q^{89} +(-16.5633 - 2.47090i) q^{91} -0.976584i q^{92} +(-3.22034 - 5.57780i) q^{93} +(-4.87671 - 8.44671i) q^{94} +1.00000i q^{96} +(-6.91261 + 11.9730i) q^{97} +(7.28643 - 12.6205i) q^{98} -4.40013i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{7} - 8 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{7} - 8 q^{8} + 4 q^{9} + 6 q^{11} - 6 q^{13} - 4 q^{14} - 4 q^{16} + 8 q^{18} + 6 q^{19} + 6 q^{22} - 6 q^{23} - 12 q^{26} - 2 q^{28} + 8 q^{29} + 4 q^{32} - 2 q^{33} + 4 q^{36} + 10 q^{37} - 6 q^{39} + 48 q^{43} - 6 q^{46} + 16 q^{47} - 14 q^{49} - 32 q^{51} - 6 q^{52} + 2 q^{56} - 8 q^{58} - 24 q^{59} - 16 q^{61} - 30 q^{62} + 2 q^{63} + 8 q^{64} - 4 q^{66} + 12 q^{67} - 4 q^{69} - 12 q^{71} - 4 q^{72} - 24 q^{73} - 10 q^{74} - 6 q^{76} + 6 q^{78} + 20 q^{79} - 4 q^{81} + 32 q^{83} - 6 q^{87} - 6 q^{88} - 42 q^{89} - 10 q^{91} - 4 q^{93} + 8 q^{94} - 36 q^{97} + 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) −2.32233 + 4.02239i −0.877758 + 1.52032i −0.0239629 + 0.999713i \(0.507628\pi\)
−0.853795 + 0.520609i \(0.825705\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) 3.81062 2.20006i 1.14895 0.663344i 0.200316 0.979731i \(-0.435803\pi\)
0.948630 + 0.316387i \(0.102470\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.32233 + 3.35432i 0.366748 + 0.930320i
\(14\) −4.64466 −1.24134
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.46410 + 2.00000i 0.840168 + 0.485071i 0.857321 0.514782i \(-0.172127\pi\)
−0.0171533 + 0.999853i \(0.505460\pi\)
\(18\) 1.00000 0.235702
\(19\) 6.96699 + 4.02239i 1.59834 + 0.922800i 0.991808 + 0.127739i \(0.0407720\pi\)
0.606529 + 0.795061i \(0.292561\pi\)
\(20\) 0 0
\(21\) 4.64466i 1.01355i
\(22\) 3.81062 + 2.20006i 0.812427 + 0.469055i
\(23\) −0.845746 + 0.488292i −0.176350 + 0.101816i −0.585577 0.810617i \(-0.699132\pi\)
0.409226 + 0.912433i \(0.365799\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 0 0
\(26\) −2.24376 + 2.82233i −0.440037 + 0.553504i
\(27\) 1.00000i 0.192450i
\(28\) −2.32233 4.02239i −0.438879 0.760161i
\(29\) −2.15637 3.73494i −0.400427 0.693561i 0.593350 0.804945i \(-0.297805\pi\)
−0.993777 + 0.111384i \(0.964472\pi\)
\(30\) 0 0
\(31\) 6.44069i 1.15678i 0.815760 + 0.578391i \(0.196319\pi\)
−0.815760 + 0.578391i \(0.803681\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −2.20006 + 3.81062i −0.382982 + 0.663344i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 1.89801 + 3.28745i 0.312031 + 0.540454i 0.978802 0.204809i \(-0.0656573\pi\)
−0.666771 + 0.745263i \(0.732324\pi\)
\(38\) 8.04479i 1.30504i
\(39\) −2.82233 2.24376i −0.451934 0.359289i
\(40\) 0 0
\(41\) −6.31274 + 3.64466i −0.985884 + 0.569200i −0.904041 0.427445i \(-0.859414\pi\)
−0.0818424 + 0.996645i \(0.526080\pi\)
\(42\) 4.02239 2.32233i 0.620669 0.358343i
\(43\) −0.620469 0.358228i −0.0946207 0.0546293i 0.451943 0.892047i \(-0.350731\pi\)
−0.546564 + 0.837418i \(0.684064\pi\)
\(44\) 4.40013i 0.663344i
\(45\) 0 0
\(46\) −0.845746 0.488292i −0.124698 0.0719947i
\(47\) −9.75342 −1.42268 −0.711341 0.702847i \(-0.751912\pi\)
−0.711341 + 0.702847i \(0.751912\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) −7.28643 12.6205i −1.04092 1.80292i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) −3.56609 0.531987i −0.494528 0.0737734i
\(53\) 13.5089i 1.85559i −0.373092 0.927794i \(-0.621703\pi\)
0.373092 0.927794i \(-0.378297\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) 2.32233 4.02239i 0.310334 0.537515i
\(57\) −8.04479 −1.06556
\(58\) 2.15637 3.73494i 0.283145 0.490421i
\(59\) 1.88842 + 1.09028i 0.245851 + 0.141942i 0.617863 0.786286i \(-0.287999\pi\)
−0.372012 + 0.928228i \(0.621332\pi\)
\(60\) 0 0
\(61\) −3.73205 + 6.46410i −0.477840 + 0.827643i −0.999677 0.0254017i \(-0.991914\pi\)
0.521837 + 0.853045i \(0.325247\pi\)
\(62\) −5.57780 + 3.22034i −0.708381 + 0.408984i
\(63\) 2.32233 + 4.02239i 0.292586 + 0.506774i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −4.40013 −0.541618
\(67\) −0.912609 1.58068i −0.111493 0.193111i 0.804879 0.593438i \(-0.202230\pi\)
−0.916372 + 0.400327i \(0.868897\pi\)
\(68\) −3.46410 + 2.00000i −0.420084 + 0.242536i
\(69\) 0.488292 0.845746i 0.0587834 0.101816i
\(70\) 0 0
\(71\) −6.88764 3.97658i −0.817413 0.471934i 0.0321105 0.999484i \(-0.489777\pi\)
−0.849524 + 0.527551i \(0.823110\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −4.36112 −0.510430 −0.255215 0.966884i \(-0.582146\pi\)
−0.255215 + 0.966884i \(0.582146\pi\)
\(74\) −1.89801 + 3.28745i −0.220640 + 0.382159i
\(75\) 0 0
\(76\) −6.96699 + 4.02239i −0.799168 + 0.461400i
\(77\) 20.4371i 2.32902i
\(78\) 0.531987 3.56609i 0.0602357 0.403780i
\(79\) 14.9340 1.68020 0.840102 0.542429i \(-0.182495\pi\)
0.840102 + 0.542429i \(0.182495\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −6.31274 3.64466i −0.697125 0.402485i
\(83\) 3.51093 0.385375 0.192688 0.981260i \(-0.438280\pi\)
0.192688 + 0.981260i \(0.438280\pi\)
\(84\) 4.02239 + 2.32233i 0.438879 + 0.253387i
\(85\) 0 0
\(86\) 0.716456i 0.0772575i
\(87\) 3.73494 + 2.15637i 0.400427 + 0.231187i
\(88\) −3.81062 + 2.20006i −0.406214 + 0.234528i
\(89\) −7.07780 + 4.08637i −0.750245 + 0.433154i −0.825782 0.563989i \(-0.809266\pi\)
0.0755374 + 0.997143i \(0.475933\pi\)
\(90\) 0 0
\(91\) −16.5633 2.47090i −1.73630 0.259021i
\(92\) 0.976584i 0.101816i
\(93\) −3.22034 5.57780i −0.333934 0.578391i
\(94\) −4.87671 8.44671i −0.502994 0.871212i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −6.91261 + 11.9730i −0.701869 + 1.21567i 0.265941 + 0.963989i \(0.414318\pi\)
−0.967810 + 0.251683i \(0.919016\pi\)
\(98\) 7.28643 12.6205i 0.736041 1.27486i
\(99\) 4.40013i 0.442229i
\(100\) 0 0
\(101\) −3.40013 5.88919i −0.338325 0.585997i 0.645793 0.763513i \(-0.276527\pi\)
−0.984118 + 0.177516i \(0.943194\pi\)
\(102\) −2.00000 3.46410i −0.198030 0.342997i
\(103\) 5.29137i 0.521374i 0.965423 + 0.260687i \(0.0839490\pi\)
−0.965423 + 0.260687i \(0.916051\pi\)
\(104\) −1.32233 3.35432i −0.129665 0.328918i
\(105\) 0 0
\(106\) 11.6990 6.75444i 1.13631 0.656050i
\(107\) 14.6603 8.46410i 1.41726 0.818256i 0.421203 0.906966i \(-0.361608\pi\)
0.996057 + 0.0887109i \(0.0282747\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 12.8003i 1.22604i −0.790067 0.613021i \(-0.789954\pi\)
0.790067 0.613021i \(-0.210046\pi\)
\(110\) 0 0
\(111\) −3.28745 1.89801i −0.312031 0.180151i
\(112\) 4.64466 0.438879
\(113\) 11.3156 + 6.53308i 1.06448 + 0.614580i 0.926669 0.375878i \(-0.122659\pi\)
0.137815 + 0.990458i \(0.455992\pi\)
\(114\) −4.02239 6.96699i −0.376732 0.652518i
\(115\) 0 0
\(116\) 4.31274 0.400427
\(117\) 3.56609 + 0.531987i 0.329685 + 0.0491823i
\(118\) 2.18056i 0.200737i
\(119\) −16.0896 + 9.28932i −1.47493 + 0.851550i
\(120\) 0 0
\(121\) 4.18056 7.24094i 0.380051 0.658267i
\(122\) −7.46410 −0.675768
\(123\) 3.64466 6.31274i 0.328628 0.569200i
\(124\) −5.57780 3.22034i −0.500901 0.289195i
\(125\) 0 0
\(126\) −2.32233 + 4.02239i −0.206890 + 0.358343i
\(127\) −10.5825 + 6.10978i −0.939041 + 0.542156i −0.889660 0.456624i \(-0.849058\pi\)
−0.0493816 + 0.998780i \(0.515725\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0.716456 0.0630805
\(130\) 0 0
\(131\) −0.378757 −0.0330921 −0.0165461 0.999863i \(-0.505267\pi\)
−0.0165461 + 0.999863i \(0.505267\pi\)
\(132\) −2.20006 3.81062i −0.191491 0.331672i
\(133\) −32.3593 + 18.6826i −2.80591 + 1.61999i
\(134\) 0.912609 1.58068i 0.0788374 0.136550i
\(135\) 0 0
\(136\) −3.46410 2.00000i −0.297044 0.171499i
\(137\) 0.626177 1.08457i 0.0534979 0.0926612i −0.838036 0.545615i \(-0.816296\pi\)
0.891534 + 0.452953i \(0.149630\pi\)
\(138\) 0.976584 0.0831323
\(139\) 1.67767 2.90581i 0.142298 0.246468i −0.786064 0.618146i \(-0.787884\pi\)
0.928362 + 0.371678i \(0.121217\pi\)
\(140\) 0 0
\(141\) 8.44671 4.87671i 0.711341 0.410693i
\(142\) 7.95317i 0.667415i
\(143\) 12.4186 + 9.87282i 1.03850 + 0.825607i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −2.18056 3.77684i −0.180464 0.312573i
\(147\) 12.6205 + 7.28643i 1.04092 + 0.600975i
\(148\) −3.79603 −0.312031
\(149\) 4.00077 + 2.30985i 0.327756 + 0.189230i 0.654844 0.755764i \(-0.272734\pi\)
−0.327088 + 0.944994i \(0.606067\pi\)
\(150\) 0 0
\(151\) 11.2425i 0.914901i 0.889235 + 0.457450i \(0.151237\pi\)
−0.889235 + 0.457450i \(0.848763\pi\)
\(152\) −6.96699 4.02239i −0.565097 0.326259i
\(153\) 3.46410 2.00000i 0.280056 0.161690i
\(154\) −17.6990 + 10.2185i −1.42623 + 0.823434i
\(155\) 0 0
\(156\) 3.35432 1.32233i 0.268560 0.105871i
\(157\) 1.50311i 0.119961i −0.998200 0.0599807i \(-0.980896\pi\)
0.998200 0.0599807i \(-0.0191039\pi\)
\(158\) 7.46699 + 12.9332i 0.594042 + 1.02891i
\(159\) 6.75444 + 11.6990i 0.535662 + 0.927794i
\(160\) 0 0
\(161\) 4.53590i 0.357479i
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −0.0881650 + 0.152706i −0.00690561 + 0.0119609i −0.869458 0.494008i \(-0.835531\pi\)
0.862552 + 0.505969i \(0.168865\pi\)
\(164\) 7.28932i 0.569200i
\(165\) 0 0
\(166\) 1.75547 + 3.04056i 0.136251 + 0.235993i
\(167\) 4.34081 + 7.51851i 0.335902 + 0.581800i 0.983658 0.180049i \(-0.0576255\pi\)
−0.647756 + 0.761848i \(0.724292\pi\)
\(168\) 4.64466i 0.358343i
\(169\) −9.50289 + 8.87103i −0.730991 + 0.682387i
\(170\) 0 0
\(171\) 6.96699 4.02239i 0.532779 0.307600i
\(172\) 0.620469 0.358228i 0.0473103 0.0273146i
\(173\) −1.54190 0.890216i −0.117228 0.0676818i 0.440239 0.897880i \(-0.354894\pi\)
−0.557468 + 0.830199i \(0.688227\pi\)
\(174\) 4.31274i 0.326948i
\(175\) 0 0
\(176\) −3.81062 2.20006i −0.287236 0.165836i
\(177\) −2.18056 −0.163901
\(178\) −7.07780 4.08637i −0.530503 0.306286i
\(179\) 8.70786 + 15.0825i 0.650856 + 1.12732i 0.982916 + 0.184057i \(0.0589232\pi\)
−0.332059 + 0.943258i \(0.607743\pi\)
\(180\) 0 0
\(181\) −10.3611 −0.770136 −0.385068 0.922888i \(-0.625822\pi\)
−0.385068 + 0.922888i \(0.625822\pi\)
\(182\) −6.14177 15.5797i −0.455258 1.15484i
\(183\) 7.46410i 0.551762i
\(184\) 0.845746 0.488292i 0.0623492 0.0359973i
\(185\) 0 0
\(186\) 3.22034 5.57780i 0.236127 0.408984i
\(187\) 17.6005 1.28708
\(188\) 4.87671 8.44671i 0.355671 0.616040i
\(189\) −4.02239 2.32233i −0.292586 0.168925i
\(190\) 0 0
\(191\) 0.448507 0.776837i 0.0324528 0.0562100i −0.849343 0.527842i \(-0.823001\pi\)
0.881796 + 0.471632i \(0.156335\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) −10.1322 17.5494i −0.729330 1.26324i −0.957167 0.289537i \(-0.906499\pi\)
0.227837 0.973699i \(-0.426835\pi\)
\(194\) −13.8252 −0.992593
\(195\) 0 0
\(196\) 14.5729 1.04092
\(197\) 4.59028 + 7.95060i 0.327044 + 0.566457i 0.981924 0.189276i \(-0.0606142\pi\)
−0.654880 + 0.755733i \(0.727281\pi\)
\(198\) 3.81062 2.20006i 0.270809 0.156352i
\(199\) 8.10876 14.0448i 0.574815 0.995609i −0.421247 0.906946i \(-0.638407\pi\)
0.996062 0.0886625i \(-0.0282593\pi\)
\(200\) 0 0
\(201\) 1.58068 + 0.912609i 0.111493 + 0.0643705i
\(202\) 3.40013 5.88919i 0.239232 0.414362i
\(203\) 20.0312 1.40591
\(204\) 2.00000 3.46410i 0.140028 0.242536i
\(205\) 0 0
\(206\) −4.58246 + 2.64568i −0.319275 + 0.184333i
\(207\) 0.976584i 0.0678773i
\(208\) 2.24376 2.82233i 0.155577 0.195693i
\(209\) 35.3981 2.44854
\(210\) 0 0
\(211\) 0.809848 + 1.40270i 0.0557522 + 0.0965657i 0.892555 0.450939i \(-0.148911\pi\)
−0.836802 + 0.547505i \(0.815578\pi\)
\(212\) 11.6990 + 6.75444i 0.803493 + 0.463897i
\(213\) 7.95317 0.544942
\(214\) 14.6603 + 8.46410i 1.00215 + 0.578594i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −25.9070 14.9574i −1.75868 1.01537i
\(218\) 11.0853 6.40013i 0.750794 0.433471i
\(219\) 3.77684 2.18056i 0.255215 0.147348i
\(220\) 0 0
\(221\) −2.12795 + 14.2644i −0.143141 + 0.959524i
\(222\) 3.79603i 0.254773i
\(223\) −1.11836 1.93705i −0.0748906 0.129714i 0.826148 0.563453i \(-0.190527\pi\)
−0.901039 + 0.433739i \(0.857194\pi\)
\(224\) 2.32233 + 4.02239i 0.155167 + 0.268757i
\(225\) 0 0
\(226\) 13.0662i 0.869148i
\(227\) 7.66025 13.2679i 0.508429 0.880625i −0.491523 0.870864i \(-0.663560\pi\)
0.999952 0.00976038i \(-0.00310687\pi\)
\(228\) 4.02239 6.96699i 0.266389 0.461400i
\(229\) 10.1279i 0.669274i 0.942347 + 0.334637i \(0.108614\pi\)
−0.942347 + 0.334637i \(0.891386\pi\)
\(230\) 0 0
\(231\) −10.2185 17.6990i −0.672331 1.16451i
\(232\) 2.15637 + 3.73494i 0.141572 + 0.245211i
\(233\) 20.7519i 1.35950i −0.733444 0.679750i \(-0.762088\pi\)
0.733444 0.679750i \(-0.237912\pi\)
\(234\) 1.32233 + 3.35432i 0.0864434 + 0.219279i
\(235\) 0 0
\(236\) −1.88842 + 1.09028i −0.122926 + 0.0709711i
\(237\) −12.9332 + 7.46699i −0.840102 + 0.485033i
\(238\) −16.0896 9.28932i −1.04293 0.602137i
\(239\) 24.3539i 1.57532i 0.616107 + 0.787662i \(0.288709\pi\)
−0.616107 + 0.787662i \(0.711291\pi\)
\(240\) 0 0
\(241\) −17.2066 9.93423i −1.10837 0.639920i −0.169966 0.985450i \(-0.554366\pi\)
−0.938408 + 0.345530i \(0.887699\pi\)
\(242\) 8.36112 0.537473
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −3.73205 6.46410i −0.238920 0.413822i
\(245\) 0 0
\(246\) 7.28932 0.464750
\(247\) −4.27973 + 28.6884i −0.272312 + 1.82540i
\(248\) 6.44069i 0.408984i
\(249\) −3.04056 + 1.75547i −0.192688 + 0.111248i
\(250\) 0 0
\(251\) 6.78566 11.7531i 0.428307 0.741849i −0.568416 0.822741i \(-0.692444\pi\)
0.996723 + 0.0808920i \(0.0257769\pi\)
\(252\) −4.64466 −0.292586
\(253\) −2.14855 + 3.72139i −0.135078 + 0.233962i
\(254\) −10.5825 6.10978i −0.664002 0.383362i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.573569 + 0.331150i −0.0357783 + 0.0206566i −0.517782 0.855512i \(-0.673242\pi\)
0.482004 + 0.876169i \(0.339909\pi\)
\(258\) 0.358228 + 0.620469i 0.0223023 + 0.0386287i
\(259\) −17.6312 −1.09555
\(260\) 0 0
\(261\) −4.31274 −0.266952
\(262\) −0.189378 0.328013i −0.0116998 0.0202647i
\(263\) −26.6301 + 15.3749i −1.64208 + 0.948058i −0.661993 + 0.749510i \(0.730289\pi\)
−0.980091 + 0.198548i \(0.936377\pi\)
\(264\) 2.20006 3.81062i 0.135405 0.234528i
\(265\) 0 0
\(266\) −32.3593 18.6826i −1.98408 1.14551i
\(267\) 4.08637 7.07780i 0.250082 0.433154i
\(268\) 1.82522 0.111493
\(269\) −1.87205 + 3.24249i −0.114141 + 0.197698i −0.917436 0.397883i \(-0.869745\pi\)
0.803295 + 0.595581i \(0.203078\pi\)
\(270\) 0 0
\(271\) 24.0419 13.8806i 1.46044 0.843186i 0.461410 0.887187i \(-0.347344\pi\)
0.999031 + 0.0440009i \(0.0140104\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 15.5797 6.14177i 0.942924 0.371717i
\(274\) 1.25235 0.0756575
\(275\) 0 0
\(276\) 0.488292 + 0.845746i 0.0293917 + 0.0509079i
\(277\) 10.3855 + 5.99609i 0.624006 + 0.360270i 0.778427 0.627735i \(-0.216018\pi\)
−0.154421 + 0.988005i \(0.549351\pi\)
\(278\) 3.35534 0.201240
\(279\) 5.57780 + 3.22034i 0.333934 + 0.192797i
\(280\) 0 0
\(281\) 3.63888i 0.217078i 0.994092 + 0.108539i \(0.0346172\pi\)
−0.994092 + 0.108539i \(0.965383\pi\)
\(282\) 8.44671 + 4.87671i 0.502994 + 0.290404i
\(283\) 4.19538 2.42220i 0.249389 0.143985i −0.370095 0.928994i \(-0.620675\pi\)
0.619485 + 0.785009i \(0.287342\pi\)
\(284\) 6.88764 3.97658i 0.408707 0.235967i
\(285\) 0 0
\(286\) −2.34081 + 15.6912i −0.138415 + 0.927843i
\(287\) 33.8564i 1.99848i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) 13.8252i 0.810449i
\(292\) 2.18056 3.77684i 0.127608 0.221023i
\(293\) 1.85041 3.20500i 0.108102 0.187238i −0.806899 0.590689i \(-0.798856\pi\)
0.915001 + 0.403451i \(0.132189\pi\)
\(294\) 14.5729i 0.849907i
\(295\) 0 0
\(296\) −1.89801 3.28745i −0.110320 0.191079i
\(297\) 2.20006 + 3.81062i 0.127661 + 0.221115i
\(298\) 4.61970i 0.267612i
\(299\) −2.75624 2.19122i −0.159398 0.126721i
\(300\) 0 0
\(301\) 2.88187 1.66385i 0.166108 0.0959026i
\(302\) −9.73628 + 5.62124i −0.560260 + 0.323466i
\(303\) 5.88919 + 3.40013i 0.338325 + 0.195332i
\(304\) 8.04479i 0.461400i
\(305\) 0 0
\(306\) 3.46410 + 2.00000i 0.198030 + 0.114332i
\(307\) 7.11454 0.406048 0.203024 0.979174i \(-0.434923\pi\)
0.203024 + 0.979174i \(0.434923\pi\)
\(308\) −17.6990 10.2185i −1.00850 0.582256i
\(309\) −2.64568 4.58246i −0.150508 0.260687i
\(310\) 0 0
\(311\) −19.9148 −1.12926 −0.564632 0.825343i \(-0.690982\pi\)
−0.564632 + 0.825343i \(0.690982\pi\)
\(312\) 2.82233 + 2.24376i 0.159783 + 0.127028i
\(313\) 6.13950i 0.347025i −0.984832 0.173513i \(-0.944488\pi\)
0.984832 0.173513i \(-0.0555117\pi\)
\(314\) 1.30173 0.751556i 0.0734611 0.0424128i
\(315\) 0 0
\(316\) −7.46699 + 12.9332i −0.420051 + 0.727550i
\(317\) −7.85286 −0.441061 −0.220530 0.975380i \(-0.570779\pi\)
−0.220530 + 0.975380i \(0.570779\pi\)
\(318\) −6.75444 + 11.6990i −0.378770 + 0.656050i
\(319\) −16.4342 9.48829i −0.920139 0.531242i
\(320\) 0 0
\(321\) −8.46410 + 14.6603i −0.472420 + 0.818256i
\(322\) 3.92820 2.26795i 0.218910 0.126388i
\(323\) 16.0896 + 27.8680i 0.895248 + 1.55061i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −0.176330 −0.00976601
\(327\) 6.40013 + 11.0853i 0.353928 + 0.613021i
\(328\) 6.31274 3.64466i 0.348563 0.201243i
\(329\) 22.6507 39.2321i 1.24877 2.16294i
\(330\) 0 0
\(331\) 27.7093 + 15.9980i 1.52304 + 0.879327i 0.999629 + 0.0272463i \(0.00867385\pi\)
0.523410 + 0.852081i \(0.324659\pi\)
\(332\) −1.75547 + 3.04056i −0.0963438 + 0.166872i
\(333\) 3.79603 0.208021
\(334\) −4.34081 + 7.51851i −0.237519 + 0.411394i
\(335\) 0 0
\(336\) −4.02239 + 2.32233i −0.219440 + 0.126693i
\(337\) 35.6432i 1.94161i −0.239867 0.970806i \(-0.577104\pi\)
0.239867 0.970806i \(-0.422896\pi\)
\(338\) −12.4340 3.79423i −0.676319 0.206379i
\(339\) −13.0662 −0.709656
\(340\) 0 0
\(341\) 14.1699 + 24.5430i 0.767344 + 1.32908i
\(342\) 6.96699 + 4.02239i 0.376732 + 0.217506i
\(343\) 35.1734 1.89918
\(344\) 0.620469 + 0.358228i 0.0334535 + 0.0193144i
\(345\) 0 0
\(346\) 1.78043i 0.0957166i
\(347\) 5.97299 + 3.44851i 0.320647 + 0.185126i 0.651681 0.758493i \(-0.274064\pi\)
−0.331034 + 0.943619i \(0.607397\pi\)
\(348\) −3.73494 + 2.15637i −0.200214 + 0.115593i
\(349\) −16.7321 + 9.66025i −0.895646 + 0.517102i −0.875785 0.482701i \(-0.839656\pi\)
−0.0198610 + 0.999803i \(0.506322\pi\)
\(350\) 0 0
\(351\) −3.35432 + 1.32233i −0.179040 + 0.0705807i
\(352\) 4.40013i 0.234528i
\(353\) 13.7086 + 23.7441i 0.729637 + 1.26377i 0.957037 + 0.289967i \(0.0936443\pi\)
−0.227400 + 0.973802i \(0.573022\pi\)
\(354\) −1.09028 1.88842i −0.0579477 0.100368i
\(355\) 0 0
\(356\) 8.17274i 0.433154i
\(357\) 9.28932 16.0896i 0.491643 0.851550i
\(358\) −8.70786 + 15.0825i −0.460225 + 0.797133i
\(359\) 14.3611i 0.757951i −0.925407 0.378975i \(-0.876277\pi\)
0.925407 0.378975i \(-0.123723\pi\)
\(360\) 0 0
\(361\) 22.8593 + 39.5935i 1.20312 + 2.08387i
\(362\) −5.18056 8.97299i −0.272284 0.471610i
\(363\) 8.36112i 0.438845i
\(364\) 10.4215 13.1088i 0.546235 0.687086i
\(365\) 0 0
\(366\) 6.46410 3.73205i 0.337884 0.195077i
\(367\) −11.9298 + 6.88764i −0.622728 + 0.359532i −0.777930 0.628351i \(-0.783730\pi\)
0.155202 + 0.987883i \(0.450397\pi\)
\(368\) 0.845746 + 0.488292i 0.0440876 + 0.0254540i
\(369\) 7.28932i 0.379467i
\(370\) 0 0
\(371\) 54.3381 + 31.3721i 2.82109 + 1.62876i
\(372\) 6.44069 0.333934
\(373\) −28.9795 16.7313i −1.50050 0.866316i −1.00000 0.000581860i \(-0.999815\pi\)
−0.500504 0.865734i \(-0.666852\pi\)
\(374\) 8.80025 + 15.2425i 0.455050 + 0.788170i
\(375\) 0 0
\(376\) 9.75342 0.502994
\(377\) 9.67674 12.1720i 0.498377 0.626888i
\(378\) 4.64466i 0.238896i
\(379\) 28.9052 16.6884i 1.48476 0.857227i 0.484910 0.874564i \(-0.338852\pi\)
0.999850 + 0.0173371i \(0.00551884\pi\)
\(380\) 0 0
\(381\) 6.10978 10.5825i 0.313014 0.542156i
\(382\) 0.897014 0.0458952
\(383\) 3.66519 6.34829i 0.187282 0.324383i −0.757061 0.653344i \(-0.773365\pi\)
0.944343 + 0.328962i \(0.106699\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 0 0
\(386\) 10.1322 17.5494i 0.515714 0.893243i
\(387\) −0.620469 + 0.358228i −0.0315402 + 0.0182098i
\(388\) −6.91261 11.9730i −0.350935 0.607836i
\(389\) 32.6198 1.65389 0.826946 0.562282i \(-0.190076\pi\)
0.826946 + 0.562282i \(0.190076\pi\)
\(390\) 0 0
\(391\) −3.90633 −0.197552
\(392\) 7.28643 + 12.6205i 0.368020 + 0.637430i
\(393\) 0.328013 0.189378i 0.0165461 0.00955288i
\(394\) −4.59028 + 7.95060i −0.231255 + 0.400545i
\(395\) 0 0
\(396\) 3.81062 + 2.20006i 0.191491 + 0.110557i
\(397\) −7.23416 + 12.5299i −0.363072 + 0.628860i −0.988465 0.151451i \(-0.951606\pi\)
0.625392 + 0.780310i \(0.284939\pi\)
\(398\) 16.2175 0.812911
\(399\) 18.6826 32.3593i 0.935302 1.61999i
\(400\) 0 0
\(401\) −6.31096 + 3.64364i −0.315154 + 0.181955i −0.649231 0.760592i \(-0.724909\pi\)
0.334076 + 0.942546i \(0.391576\pi\)
\(402\) 1.82522i 0.0910336i
\(403\) −21.6041 + 8.51671i −1.07618 + 0.424248i
\(404\) 6.80025 0.338325
\(405\) 0 0
\(406\) 10.0156 + 17.3475i 0.497066 + 0.860943i
\(407\) 14.4652 + 8.35150i 0.717014 + 0.413968i
\(408\) 4.00000 0.198030
\(409\) 21.2840 + 12.2883i 1.05242 + 0.607617i 0.923327 0.384015i \(-0.125459\pi\)
0.129097 + 0.991632i \(0.458792\pi\)
\(410\) 0 0
\(411\) 1.25235i 0.0617741i
\(412\) −4.58246 2.64568i −0.225761 0.130343i
\(413\) −8.77106 + 5.06397i −0.431596 + 0.249182i
\(414\) −0.845746 + 0.488292i −0.0415662 + 0.0239982i
\(415\) 0 0
\(416\) 3.56609 + 0.531987i 0.174842 + 0.0260828i
\(417\) 3.35534i 0.164312i
\(418\) 17.6990 + 30.6556i 0.865688 + 1.49942i
\(419\) 7.77684 + 13.4699i 0.379923 + 0.658047i 0.991051 0.133486i \(-0.0426170\pi\)
−0.611127 + 0.791532i \(0.709284\pi\)
\(420\) 0 0
\(421\) 22.3143i 1.08753i −0.839237 0.543766i \(-0.816998\pi\)
0.839237 0.543766i \(-0.183002\pi\)
\(422\) −0.809848 + 1.40270i −0.0394228 + 0.0682822i
\(423\) −4.87671 + 8.44671i −0.237114 + 0.410693i
\(424\) 13.5089i 0.656050i
\(425\) 0 0
\(426\) 3.97658 + 6.88764i 0.192666 + 0.333707i
\(427\) −17.3341 30.0236i −0.838856 1.45294i
\(428\) 16.9282i 0.818256i
\(429\) −15.6912 2.34081i −0.757580 0.113015i
\(430\) 0 0
\(431\) 21.0135 12.1322i 1.01219 0.584386i 0.100356 0.994952i \(-0.468002\pi\)
0.911831 + 0.410565i \(0.134669\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 20.0042 + 11.5494i 0.961342 + 0.555031i 0.896586 0.442870i \(-0.146040\pi\)
0.0647561 + 0.997901i \(0.479373\pi\)
\(434\) 29.9148i 1.43596i
\(435\) 0 0
\(436\) 11.0853 + 6.40013i 0.530892 + 0.306510i
\(437\) −7.85641 −0.375823
\(438\) 3.77684 + 2.18056i 0.180464 + 0.104191i
\(439\) 19.9980 + 34.6375i 0.954450 + 1.65316i 0.735621 + 0.677393i \(0.236890\pi\)
0.218829 + 0.975763i \(0.429776\pi\)
\(440\) 0 0
\(441\) −14.5729 −0.693946
\(442\) −13.4173 + 5.28932i −0.638194 + 0.251587i
\(443\) 15.6036i 0.741350i 0.928763 + 0.370675i \(0.120874\pi\)
−0.928763 + 0.370675i \(0.879126\pi\)
\(444\) 3.28745 1.89801i 0.156016 0.0900757i
\(445\) 0 0
\(446\) 1.11836 1.93705i 0.0529557 0.0917219i
\(447\) −4.61970 −0.218504
\(448\) −2.32233 + 4.02239i −0.109720 + 0.190040i
\(449\) −23.3863 13.5021i −1.10367 0.637203i −0.166486 0.986044i \(-0.553242\pi\)
−0.937182 + 0.348841i \(0.886575\pi\)
\(450\) 0 0
\(451\) −16.0370 + 27.7768i −0.755151 + 1.30796i
\(452\) −11.3156 + 6.53308i −0.532242 + 0.307290i
\(453\) −5.62124 9.73628i −0.264109 0.457450i
\(454\) 15.3205 0.719027
\(455\) 0 0
\(456\) 8.04479 0.376732
\(457\) 8.89342 + 15.4039i 0.416017 + 0.720562i 0.995535 0.0943975i \(-0.0300925\pi\)
−0.579518 + 0.814959i \(0.696759\pi\)
\(458\) −8.77106 + 5.06397i −0.409845 + 0.236624i
\(459\) −2.00000 + 3.46410i −0.0933520 + 0.161690i
\(460\) 0 0
\(461\) 21.6205 + 12.4826i 1.00697 + 0.581372i 0.910302 0.413945i \(-0.135849\pi\)
0.0966638 + 0.995317i \(0.469183\pi\)
\(462\) 10.2185 17.6990i 0.475410 0.823434i
\(463\) 15.6389 0.726801 0.363400 0.931633i \(-0.381616\pi\)
0.363400 + 0.931633i \(0.381616\pi\)
\(464\) −2.15637 + 3.73494i −0.100107 + 0.173390i
\(465\) 0 0
\(466\) 17.9716 10.3759i 0.832521 0.480656i
\(467\) 2.43914i 0.112870i −0.998406 0.0564349i \(-0.982027\pi\)
0.998406 0.0564349i \(-0.0179733\pi\)
\(468\) −2.24376 + 2.82233i −0.103718 + 0.130462i
\(469\) 8.47751 0.391455
\(470\) 0 0
\(471\) 0.751556 + 1.30173i 0.0346299 + 0.0599807i
\(472\) −1.88842 1.09028i −0.0869215 0.0501842i
\(473\) −3.15250 −0.144952
\(474\) −12.9332 7.46699i −0.594042 0.342970i
\(475\) 0 0
\(476\) 18.5786i 0.851550i
\(477\) −11.6990 6.75444i −0.535662 0.309265i
\(478\) −21.0911 + 12.1770i −0.964685 + 0.556961i
\(479\) −12.2857 + 7.09317i −0.561349 + 0.324095i −0.753687 0.657234i \(-0.771726\pi\)
0.192338 + 0.981329i \(0.438393\pi\)
\(480\) 0 0
\(481\) −8.51737 + 10.7136i −0.388358 + 0.488500i
\(482\) 19.8685i 0.904983i
\(483\) 2.26795 + 3.92820i 0.103195 + 0.178739i
\(484\) 4.18056 + 7.24094i 0.190025 + 0.329134i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −2.88164 + 4.99115i −0.130580 + 0.226171i −0.923900 0.382633i \(-0.875017\pi\)
0.793320 + 0.608804i \(0.208351\pi\)
\(488\) 3.73205 6.46410i 0.168942 0.292616i
\(489\) 0.176330i 0.00797392i
\(490\) 0 0
\(491\) −0.537671 0.931273i −0.0242647 0.0420278i 0.853638 0.520867i \(-0.174391\pi\)
−0.877903 + 0.478839i \(0.841058\pi\)
\(492\) 3.64466 + 6.31274i 0.164314 + 0.284600i
\(493\) 17.2509i 0.776943i
\(494\) −26.9848 + 10.6379i −1.21410 + 0.478620i
\(495\) 0 0
\(496\) 5.57780 3.22034i 0.250450 0.144598i
\(497\) 31.9908 18.4699i 1.43498 0.828487i
\(498\) −3.04056 1.75547i −0.136251 0.0786644i
\(499\) 14.7534i 0.660454i −0.943902 0.330227i \(-0.892875\pi\)
0.943902 0.330227i \(-0.107125\pi\)
\(500\) 0 0
\(501\) −7.51851 4.34081i −0.335902 0.193933i
\(502\) 13.5713 0.605717
\(503\) −23.0898 13.3309i −1.02952 0.594395i −0.112675 0.993632i \(-0.535942\pi\)
−0.916848 + 0.399236i \(0.869275\pi\)
\(504\) −2.32233 4.02239i −0.103445 0.179172i
\(505\) 0 0
\(506\) −4.29709 −0.191029
\(507\) 3.79423 12.4340i 0.168508 0.552212i
\(508\) 12.2196i 0.542156i
\(509\) −12.2807 + 7.09028i −0.544333 + 0.314271i −0.746833 0.665011i \(-0.768427\pi\)
0.202500 + 0.979282i \(0.435093\pi\)
\(510\) 0 0
\(511\) 10.1279 17.5421i 0.448034 0.776018i
\(512\) −1.00000 −0.0441942
\(513\) −4.02239 + 6.96699i −0.177593 + 0.307600i
\(514\) −0.573569 0.331150i −0.0252990 0.0146064i
\(515\) 0 0
\(516\) −0.358228 + 0.620469i −0.0157701 + 0.0273146i
\(517\) −37.1666 + 21.4581i −1.63459 + 0.943728i
\(518\) −8.81562 15.2691i −0.387336 0.670886i
\(519\) 1.78043 0.0781523
\(520\) 0 0
\(521\) 23.7476 1.04040 0.520202 0.854043i \(-0.325857\pi\)
0.520202 + 0.854043i \(0.325857\pi\)
\(522\) −2.15637 3.73494i −0.0943817 0.163474i
\(523\) −11.9950 + 6.92532i −0.524505 + 0.302823i −0.738776 0.673951i \(-0.764596\pi\)
0.214271 + 0.976774i \(0.431262\pi\)
\(524\) 0.189378 0.328013i 0.00827303 0.0143293i
\(525\) 0 0
\(526\) −26.6301 15.3749i −1.16113 0.670378i
\(527\) −12.8814 + 22.3112i −0.561121 + 0.971891i
\(528\) 4.40013 0.191491
\(529\) −11.0231 + 19.0926i −0.479267 + 0.830115i
\(530\) 0 0
\(531\) 1.88842 1.09028i 0.0819504 0.0473141i
\(532\) 37.3653i 1.61999i
\(533\) −20.5729 16.3555i −0.891110 0.708434i
\(534\) 8.17274 0.353669
\(535\) 0 0
\(536\) 0.912609 + 1.58068i 0.0394187 + 0.0682752i
\(537\) −15.0825 8.70786i −0.650856 0.375772i
\(538\) −3.74410 −0.161420
\(539\) −55.5317 32.0612i −2.39192 1.38097i
\(540\) 0 0
\(541\) 14.8898i 0.640164i 0.947390 + 0.320082i \(0.103710\pi\)
−0.947390 + 0.320082i \(0.896290\pi\)
\(542\) 24.0419 + 13.8806i 1.03269 + 0.596223i
\(543\) 8.97299 5.18056i 0.385068 0.222319i
\(544\) 3.46410 2.00000i 0.148522 0.0857493i
\(545\) 0 0
\(546\) 13.1088 + 10.4215i 0.561003 + 0.445999i
\(547\) 22.2019i 0.949284i −0.880179 0.474642i \(-0.842578\pi\)
0.880179 0.474642i \(-0.157422\pi\)
\(548\) 0.626177 + 1.08457i 0.0267490 + 0.0463306i
\(549\) 3.73205 + 6.46410i 0.159280 + 0.275881i
\(550\) 0 0
\(551\) 34.6950i 1.47806i
\(552\) −0.488292 + 0.845746i −0.0207831 + 0.0359973i
\(553\) −34.6816 + 60.0703i −1.47481 + 2.55445i
\(554\) 11.9922i 0.509499i
\(555\) 0 0
\(556\) 1.67767 + 2.90581i 0.0711491 + 0.123234i
\(557\) 0.949847 + 1.64518i 0.0402463 + 0.0697087i 0.885447 0.464741i \(-0.153852\pi\)
−0.845201 + 0.534449i \(0.820519\pi\)
\(558\) 6.44069i 0.272656i
\(559\) 0.381146 2.55495i 0.0161207 0.108063i
\(560\) 0 0
\(561\) −15.2425 + 8.80025i −0.643538 + 0.371547i
\(562\) −3.15137 + 1.81944i −0.132932 + 0.0767485i
\(563\) 1.48956 + 0.860000i 0.0627777 + 0.0362447i 0.531060 0.847334i \(-0.321794\pi\)
−0.468283 + 0.883579i \(0.655127\pi\)
\(564\) 9.75342i 0.410693i
\(565\) 0 0
\(566\) 4.19538 + 2.42220i 0.176345 + 0.101813i
\(567\) 4.64466 0.195057
\(568\) 6.88764 + 3.97658i 0.288999 + 0.166854i
\(569\) 0.300960 + 0.521278i 0.0126169 + 0.0218531i 0.872265 0.489034i \(-0.162650\pi\)
−0.859648 + 0.510887i \(0.829317\pi\)
\(570\) 0 0
\(571\) 11.9808 0.501381 0.250691 0.968067i \(-0.419342\pi\)
0.250691 + 0.968067i \(0.419342\pi\)
\(572\) −14.7594 + 5.81842i −0.617122 + 0.243280i
\(573\) 0.897014i 0.0374733i
\(574\) 29.3205 16.9282i 1.22381 0.706570i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 43.0293 1.79133 0.895667 0.444725i \(-0.146699\pi\)
0.895667 + 0.444725i \(0.146699\pi\)
\(578\) 0.500000 0.866025i 0.0207973 0.0360219i
\(579\) 17.5494 + 10.1322i 0.729330 + 0.421079i
\(580\) 0 0
\(581\) −8.15355 + 14.1224i −0.338266 + 0.585894i
\(582\) 11.9730 6.91261i 0.496296 0.286537i
\(583\) −29.7204 51.4773i −1.23089 2.13197i
\(584\) 4.36112 0.180464
\(585\) 0 0
\(586\) 3.70081 0.152879
\(587\) −8.95740 15.5147i −0.369711 0.640359i 0.619809 0.784753i \(-0.287210\pi\)
−0.989520 + 0.144394i \(0.953877\pi\)
\(588\) −12.6205 + 7.28643i −0.520459 + 0.300487i
\(589\) −25.9070 + 44.8722i −1.06748 + 1.84893i
\(590\) 0 0
\(591\) −7.95060 4.59028i −0.327044 0.188819i
\(592\) 1.89801 3.28745i 0.0780078 0.135114i
\(593\) 0.669624 0.0274981 0.0137491 0.999905i \(-0.495623\pi\)
0.0137491 + 0.999905i \(0.495623\pi\)
\(594\) −2.20006 + 3.81062i −0.0902697 + 0.156352i
\(595\) 0 0
\(596\) −4.00077 + 2.30985i −0.163878 + 0.0946151i
\(597\) 16.2175i 0.663739i
\(598\) 0.519530 3.48258i 0.0212452 0.142413i
\(599\) −1.29241 −0.0528066 −0.0264033 0.999651i \(-0.508405\pi\)
−0.0264033 + 0.999651i \(0.508405\pi\)
\(600\) 0 0
\(601\) 5.73671 + 9.93627i 0.234005 + 0.405309i 0.958983 0.283463i \(-0.0914834\pi\)
−0.724978 + 0.688772i \(0.758150\pi\)
\(602\) 2.88187 + 1.66385i 0.117456 + 0.0678134i
\(603\) −1.82522 −0.0743286
\(604\) −9.73628 5.62124i −0.396164 0.228725i
\(605\) 0 0
\(606\) 6.80025i 0.276241i
\(607\) 20.9010 + 12.0672i 0.848344 + 0.489792i 0.860092 0.510139i \(-0.170406\pi\)
−0.0117477 + 0.999931i \(0.503739\pi\)
\(608\) 6.96699 4.02239i 0.282549 0.163130i
\(609\) −17.3475 + 10.0156i −0.702957 + 0.405852i
\(610\) 0 0
\(611\) −12.8972 32.7161i −0.521766 1.32355i
\(612\) 4.00000i 0.161690i
\(613\) −14.4751 25.0716i −0.584644 1.01263i −0.994920 0.100671i \(-0.967901\pi\)
0.410276 0.911961i \(-0.365432\pi\)
\(614\) 3.55727 + 6.16137i 0.143560 + 0.248653i
\(615\) 0 0
\(616\) 20.4371i 0.823434i
\(617\) 0.420655 0.728597i 0.0169349 0.0293322i −0.857434 0.514594i \(-0.827943\pi\)
0.874369 + 0.485262i \(0.161276\pi\)
\(618\) 2.64568 4.58246i 0.106425 0.184333i
\(619\) 6.25076i 0.251239i 0.992078 + 0.125620i \(0.0400919\pi\)
−0.992078 + 0.125620i \(0.959908\pi\)
\(620\) 0 0
\(621\) −0.488292 0.845746i −0.0195945 0.0339386i
\(622\) −9.95740 17.2467i −0.399255 0.691530i
\(623\) 37.9596i 1.52082i
\(624\) −0.531987 + 3.56609i −0.0212965 + 0.142758i
\(625\) 0 0
\(626\) 5.31696 3.06975i 0.212509 0.122692i
\(627\) −30.6556 + 17.6990i −1.22427 + 0.706832i
\(628\) 1.30173 + 0.751556i 0.0519448 + 0.0299904i
\(629\) 15.1841i 0.605430i
\(630\) 0 0
\(631\) 2.61970 + 1.51248i 0.104288 + 0.0602110i 0.551237 0.834349i \(-0.314156\pi\)
−0.446949 + 0.894560i \(0.647489\pi\)
\(632\) −14.9340 −0.594042
\(633\) −1.40270 0.809848i −0.0557522 0.0321886i
\(634\) −3.92643 6.80078i −0.155938 0.270093i
\(635\) 0 0
\(636\) −13.5089 −0.535662
\(637\) 32.6980 41.1294i 1.29554 1.62961i
\(638\) 18.9766i 0.751290i
\(639\) −6.88764 + 3.97658i −0.272471 + 0.157311i
\(640\) 0 0
\(641\) 0.386305 0.669099i 0.0152581 0.0264278i −0.858296 0.513156i \(-0.828476\pi\)
0.873554 + 0.486728i \(0.161810\pi\)
\(642\) −16.9282 −0.668103
\(643\) 9.68726 16.7788i 0.382028 0.661693i −0.609324 0.792922i \(-0.708559\pi\)
0.991352 + 0.131229i \(0.0418923\pi\)
\(644\) 3.92820 + 2.26795i 0.154793 + 0.0893697i
\(645\) 0 0
\(646\) −16.0896 + 27.8680i −0.633036 + 1.09645i
\(647\) 23.5477 13.5953i 0.925755 0.534485i 0.0402882 0.999188i \(-0.487172\pi\)
0.885466 + 0.464703i \(0.153839\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 9.59473 0.376626
\(650\) 0 0
\(651\) 29.9148 1.17245
\(652\) −0.0881650 0.152706i −0.00345281 0.00598044i
\(653\) −13.6797 + 7.89799i −0.535329 + 0.309072i −0.743184 0.669088i \(-0.766685\pi\)
0.207855 + 0.978160i \(0.433352\pi\)
\(654\) −6.40013 + 11.0853i −0.250265 + 0.433471i
\(655\) 0 0
\(656\) 6.31274 + 3.64466i 0.246471 + 0.142300i
\(657\) −2.18056 + 3.77684i −0.0850717 + 0.147348i
\(658\) 45.3013 1.76603
\(659\) 15.2381 26.3932i 0.593593 1.02813i −0.400151 0.916449i \(-0.631042\pi\)
0.993744 0.111684i \(-0.0356243\pi\)
\(660\) 0 0
\(661\) −24.1514 + 13.9438i −0.939379 + 0.542351i −0.889766 0.456418i \(-0.849132\pi\)
−0.0496136 + 0.998768i \(0.515799\pi\)
\(662\) 31.9959i 1.24356i
\(663\) −5.28932 13.4173i −0.205420 0.521084i
\(664\) −3.51093 −0.136251
\(665\) 0 0
\(666\) 1.89801 + 3.28745i 0.0735465 + 0.127386i
\(667\) 3.64748 + 2.10587i 0.141231 + 0.0815397i
\(668\) −8.68162 −0.335902
\(669\) 1.93705 + 1.11836i 0.0748906 + 0.0432381i
\(670\) 0 0
\(671\) 32.8430i 1.26789i
\(672\) −4.02239 2.32233i −0.155167 0.0895858i
\(673\) −0.847086 + 0.489066i −0.0326528 + 0.0188521i −0.516238 0.856445i \(-0.672668\pi\)
0.483585 + 0.875298i \(0.339334\pi\)
\(674\) 30.8680 17.8216i 1.18899 0.686463i
\(675\) 0 0
\(676\) −2.93109 12.6653i −0.112734 0.487125i
\(677\) 19.1926i 0.737630i −0.929503 0.368815i \(-0.879764\pi\)
0.929503 0.368815i \(-0.120236\pi\)
\(678\) −6.53308 11.3156i −0.250901 0.434574i
\(679\) −32.1067 55.6105i −1.23214 2.13413i
\(680\) 0 0
\(681\) 15.3205i 0.587083i
\(682\) −14.1699 + 24.5430i −0.542594 + 0.939801i
\(683\) −0.755467 + 1.30851i −0.0289071 + 0.0500687i −0.880117 0.474757i \(-0.842536\pi\)
0.851210 + 0.524825i \(0.175869\pi\)
\(684\) 8.04479i 0.307600i
\(685\) 0 0
\(686\) 17.5867 + 30.4610i 0.671463 + 1.16301i
\(687\) −5.06397 8.77106i −0.193203 0.334637i
\(688\) 0.716456i 0.0273146i
\(689\) 45.3131 17.8632i 1.72629 0.680534i
\(690\) 0 0
\(691\) 28.6798 16.5583i 1.09103 0.629907i 0.157180 0.987570i \(-0.449760\pi\)
0.933851 + 0.357663i \(0.116426\pi\)
\(692\) 1.54190 0.890216i 0.0586142 0.0338409i
\(693\) 17.6990 + 10.2185i 0.672331 + 0.388170i
\(694\) 6.89701i 0.261807i
\(695\) 0 0
\(696\) −3.73494 2.15637i −0.141572 0.0817369i
\(697\) −29.1573 −1.10441
\(698\) −16.7321 9.66025i −0.633317 0.365646i
\(699\) 10.3759 + 17.9716i 0.392454 + 0.679750i
\(700\) 0 0
\(701\) 27.8695 1.05262 0.526308 0.850294i \(-0.323576\pi\)
0.526308 + 0.850294i \(0.323576\pi\)
\(702\) −2.82233 2.24376i −0.106522 0.0846852i
\(703\) 30.5382i 1.15177i
\(704\) 3.81062 2.20006i 0.143618 0.0829180i
\(705\) 0 0
\(706\) −13.7086 + 23.7441i −0.515931 + 0.893619i
\(707\) 31.5849 1.18787
\(708\) 1.09028 1.88842i 0.0409752 0.0709711i
\(709\) 9.57491 + 5.52808i 0.359593 + 0.207611i 0.668902 0.743350i \(-0.266764\pi\)
−0.309309 + 0.950962i \(0.600098\pi\)
\(710\) 0 0
\(711\) 7.46699 12.9332i 0.280034 0.485033i
\(712\) 7.07780 4.08637i 0.265252 0.153143i
\(713\) −3.14493 5.44719i −0.117779 0.203999i
\(714\) 18.5786 0.695288
\(715\) 0 0
\(716\) −17.4157 −0.650856
\(717\) −12.1770 21.0911i −0.454757 0.787662i
\(718\) 12.4371 7.18056i 0.464148 0.267976i
\(719\) −5.85641 + 10.1436i −0.218407 + 0.378292i −0.954321 0.298783i \(-0.903419\pi\)
0.735914 + 0.677075i \(0.236753\pi\)
\(720\) 0 0
\(721\) −21.2840 12.2883i −0.792656 0.457640i
\(722\) −22.8593 + 39.5935i −0.850735 + 1.47352i
\(723\) 19.8685 0.738916
\(724\) 5.18056 8.97299i 0.192534 0.333479i
\(725\) 0 0
\(726\) −7.24094 + 4.18056i −0.268736 + 0.155155i
\(727\) 19.4152i 0.720071i −0.932939 0.360035i \(-0.882765\pi\)
0.932939 0.360035i \(-0.117235\pi\)
\(728\) 16.5633 + 2.47090i 0.613876 + 0.0915777i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −1.43291 2.48188i −0.0529982 0.0917956i
\(732\) 6.46410 + 3.73205i 0.238920 + 0.137941i
\(733\) 11.9340 0.440792 0.220396 0.975411i \(-0.429265\pi\)
0.220396 + 0.975411i \(0.429265\pi\)
\(734\) −11.9298 6.88764i −0.440335 0.254228i
\(735\) 0 0
\(736\) 0.976584i 0.0359973i
\(737\) −6.95521 4.01559i −0.256199 0.147916i
\(738\) −6.31274 + 3.64466i −0.232375 + 0.134162i
\(739\) −17.2017 + 9.93141i −0.632775 + 0.365333i −0.781826 0.623497i \(-0.785711\pi\)
0.149051 + 0.988830i \(0.452378\pi\)
\(740\) 0 0
\(741\) −10.6379 26.9848i −0.390792 0.991310i
\(742\) 62.7442i 2.30341i
\(743\) −8.24383 14.2787i −0.302437 0.523836i 0.674251 0.738503i \(-0.264467\pi\)
−0.976687 + 0.214667i \(0.931133\pi\)
\(744\) 3.22034 + 5.57780i 0.118063 + 0.204492i
\(745\) 0 0
\(746\) 33.4627i 1.22516i
\(747\) 1.75547 3.04056i 0.0642292 0.111248i
\(748\) −8.80025 + 15.2425i −0.321769 + 0.557320i
\(749\) 78.6257i 2.87292i
\(750\) 0 0
\(751\) −23.3312 40.4109i −0.851368 1.47461i −0.879974 0.475022i \(-0.842440\pi\)
0.0286056 0.999591i \(-0.490893\pi\)
\(752\) 4.87671 + 8.44671i 0.177835 + 0.308020i
\(753\) 13.5713i 0.494566i
\(754\) 15.3796 + 2.29432i 0.560092 + 0.0835542i
\(755\) 0 0
\(756\) 4.02239 2.32233i 0.146293 0.0844623i
\(757\) 2.28282 1.31799i 0.0829705 0.0479030i −0.457941 0.888983i \(-0.651413\pi\)
0.540911 + 0.841080i \(0.318079\pi\)
\(758\) 28.9052 + 16.6884i 1.04988 + 0.606151i
\(759\) 4.29709i 0.155975i
\(760\) 0 0
\(761\) 0.0693410 + 0.0400340i 0.00251361 + 0.00145123i 0.501256 0.865299i \(-0.332871\pi\)
−0.498743 + 0.866750i \(0.666205\pi\)
\(762\) 12.2196 0.442668
\(763\) 51.4877 + 29.7264i 1.86398 + 1.07617i
\(764\) 0.448507 + 0.776837i 0.0162264 + 0.0281050i
\(765\) 0 0
\(766\) 7.33038 0.264857
\(767\) −1.16003 + 7.77606i −0.0418862 + 0.280777i
\(768\) 1.00000i 0.0360844i
\(769\) −4.92177 + 2.84159i −0.177484 + 0.102470i −0.586110 0.810232i \(-0.699341\pi\)
0.408626 + 0.912702i \(0.366008\pi\)
\(770\) 0 0
\(771\) 0.331150 0.573569i 0.0119261 0.0206566i
\(772\) 20.2644 0.729330
\(773\) −3.79425 + 6.57184i −0.136470 + 0.236373i −0.926158 0.377136i \(-0.876909\pi\)
0.789688 + 0.613508i \(0.210242\pi\)
\(774\) −0.620469 0.358228i −0.0223023 0.0128762i
\(775\) 0 0
\(776\) 6.91261 11.9730i 0.248148 0.429805i
\(777\) 15.2691 8.81562i 0.547776 0.316259i
\(778\) 16.3099 + 28.2496i 0.584739 + 1.01280i
\(779\) −58.6410 −2.10103
\(780\) 0 0
\(781\) −34.9949 −1.25222
\(782\) −1.95317 3.38298i −0.0698451 0.120975i
\(783\) 3.73494 2.15637i 0.133476 0.0770623i
\(784\) −7.28643 + 12.6205i −0.260230 + 0.450731i
\(785\) 0 0
\(786\) 0.328013 + 0.189378i 0.0116998 + 0.00675490i
\(787\) 2.36811 4.10169i 0.0844142 0.146210i −0.820727 0.571320i \(-0.806431\pi\)
0.905141 + 0.425111i \(0.139765\pi\)
\(788\) −9.18056 −0.327044
\(789\) 15.3749 26.6301i 0.547361 0.948058i
\(790\) 0 0
\(791\) −52.5572 + 30.3439i −1.86872 + 1.07891i
\(792\) 4.40013i 0.156352i
\(793\) −26.6176 3.97081i −0.945220 0.141008i
\(794\) −14.4683 −0.513462
\(795\) 0 0
\(796\) 8.10876 + 14.0448i 0.287407 + 0.497804i
\(797\) −35.5621 20.5318i −1.25968 0.727274i −0.286664 0.958031i \(-0.592546\pi\)
−0.973011 + 0.230757i \(0.925880\pi\)
\(798\) 37.3653 1.32272
\(799\) −33.7868 19.5068i −1.19529 0.690102i
\(800\) 0 0
\(801\) 8.17274i 0.288769i
\(802\) −6.31096 3.64364i −0.222848 0.128661i
\(803\) −16.6186 + 9.59473i −0.586456 + 0.338591i
\(804\) −1.58068 + 0.912609i −0.0557465 + 0.0321852i
\(805\) 0 0
\(806\) −18.1777 14.4513i −0.640284 0.509027i
\(807\) 3.74410i 0.131799i
\(808\) 3.40013 + 5.88919i 0.119616 + 0.207181i
\(809\) −13.8003 23.9027i −0.485191 0.840376i 0.514664 0.857392i \(-0.327917\pi\)
−0.999855 + 0.0170163i \(0.994583\pi\)
\(810\) 0 0
\(811\) 10.6930i 0.375482i 0.982219 + 0.187741i \(0.0601165\pi\)
−0.982219 + 0.187741i \(0.939883\pi\)
\(812\) −10.0156 + 17.3475i −0.351478 + 0.608779i
\(813\) −13.8806 + 24.0419i −0.486814 + 0.843186i
\(814\) 16.7030i 0.585440i
\(815\) 0 0
\(816\) 2.00000 + 3.46410i 0.0700140 + 0.121268i
\(817\) −2.88187 4.99154i −0.100824 0.174632i
\(818\) 24.5766i 0.859300i
\(819\) −10.4215 + 13.1088i −0.364157 + 0.458057i
\(820\) 0 0
\(821\) 15.2105 8.78177i 0.530849 0.306486i −0.210513 0.977591i \(-0.567513\pi\)
0.741362 + 0.671105i \(0.234180\pi\)
\(822\) −1.08457 + 0.626177i −0.0378288 + 0.0218404i
\(823\) 33.5264 + 19.3565i 1.16866 + 0.674725i 0.953364 0.301824i \(-0.0975955\pi\)
0.215295 + 0.976549i \(0.430929\pi\)
\(824\) 5.29137i 0.184333i
\(825\) 0 0
\(826\) −8.77106 5.06397i −0.305184 0.176198i
\(827\) −28.4703 −0.990010 −0.495005 0.868890i \(-0.664834\pi\)
−0.495005 + 0.868890i \(0.664834\pi\)
\(828\) −0.845746 0.488292i −0.0293917 0.0169693i
\(829\) −4.14354 7.17683i −0.143911 0.249262i 0.785055 0.619426i \(-0.212635\pi\)
−0.928966 + 0.370165i \(0.879301\pi\)
\(830\) 0 0
\(831\) −11.9922 −0.416004
\(832\) 1.32233 + 3.35432i 0.0458435 + 0.116290i
\(833\) 58.2915i 2.01968i
\(834\) −2.90581 + 1.67767i −0.100620 + 0.0580930i
\(835\) 0 0
\(836\) −17.6990 + 30.6556i −0.612134 + 1.06025i
\(837\) −6.44069 −0.222623
\(838\) −7.77684 + 13.4699i −0.268646 + 0.465309i
\(839\) 36.8606 + 21.2815i 1.27257 + 0.734719i 0.975471 0.220128i \(-0.0706474\pi\)
0.297099 + 0.954847i \(0.403981\pi\)
\(840\) 0 0
\(841\) 5.20016 9.00693i 0.179316 0.310584i
\(842\) 19.3247 11.1571i 0.665974 0.384500i
\(843\) −1.81944 3.15137i −0.0626649 0.108539i
\(844\) −1.61970 −0.0557522
\(845\) 0 0
\(846\) −9.75342 −0.335330
\(847\) 19.4173 + 33.6317i 0.667185 + 1.15560i
\(848\) −11.6990 + 6.75444i −0.401747 + 0.231949i
\(849\) −2.42220 + 4.19538i −0.0831298 + 0.143985i
\(850\) 0 0
\(851\) −3.21047 1.85357i −0.110054 0.0635395i
\(852\) −3.97658 + 6.88764i −0.136236 + 0.235967i
\(853\) 28.1380 0.963425 0.481713 0.876329i \(-0.340015\pi\)
0.481713 + 0.876329i \(0.340015\pi\)
\(854\) 17.3341 30.0236i 0.593161 1.02738i
\(855\) 0 0
\(856\) −14.6603 + 8.46410i −0.501077 + 0.289297i
\(857\) 10.3355i 0.353053i −0.984296 0.176526i \(-0.943514\pi\)
0.984296 0.176526i \(-0.0564861\pi\)
\(858\) −5.81842 14.7594i −0.198638 0.503878i
\(859\) −0.380304 −0.0129758 −0.00648791 0.999979i \(-0.502065\pi\)
−0.00648791 + 0.999979i \(0.502065\pi\)
\(860\) 0 0
\(861\) 16.9282 + 29.3205i 0.576912 + 0.999240i
\(862\) 21.0135 + 12.1322i 0.715724 + 0.413224i
\(863\) 47.1484 1.60495 0.802475 0.596685i \(-0.203516\pi\)
0.802475 + 0.596685i \(0.203516\pi\)
\(864\) 0.866025 + 0.500000i 0.0294628 + 0.0170103i
\(865\) 0 0
\(866\) 23.0989i 0.784932i
\(867\) 0.866025 + 0.500000i 0.0294118 + 0.0169809i
\(868\) 25.9070 14.9574i 0.879340 0.507687i
\(869\) 56.9077 32.8557i 1.93046 1.11455i
\(870\) 0 0
\(871\) 4.09535 5.15137i 0.138766 0.174547i
\(872\) 12.8003i 0.433471i
\(873\) 6.91261 + 11.9730i 0.233956 + 0.405224i
\(874\) −3.92820 6.80385i −0.132873 0.230144i
\(875\) 0 0
\(876\) 4.36112i 0.147348i
\(877\) −20.0206 + 34.6767i −0.676047 + 1.17095i 0.300114 + 0.953903i \(0.402975\pi\)
−0.976162 + 0.217045i \(0.930358\pi\)
\(878\) −19.9980 + 34.6375i −0.674898 + 1.16896i
\(879\) 3.70081i 0.124825i
\(880\) 0 0
\(881\) −7.72246 13.3757i −0.260176 0.450638i 0.706112 0.708100i \(-0.250447\pi\)
−0.966289 + 0.257461i \(0.917114\pi\)
\(882\) −7.28643 12.6205i −0.245347 0.424953i
\(883\) 6.02142i 0.202637i 0.994854 + 0.101318i \(0.0323061\pi\)
−0.994854 + 0.101318i \(0.967694\pi\)
\(884\) −11.2893 8.97504i −0.379701 0.301863i
\(885\) 0 0
\(886\) −13.5131 + 7.80180i −0.453982 + 0.262107i
\(887\) −42.5548 + 24.5690i −1.42885 + 0.824947i −0.997030 0.0770129i \(-0.975462\pi\)
−0.431820 + 0.901960i \(0.642128\pi\)
\(888\) 3.28745 + 1.89801i 0.110320 + 0.0636931i
\(889\) 56.7557i 1.90353i
\(890\) 0 0
\(891\) −3.81062 2.20006i −0.127661 0.0737049i
\(892\) 2.23671 0.0748906
\(893\) −67.9520 39.2321i −2.27393 1.31285i
\(894\) −2.30985 4.00077i −0.0772529 0.133806i
\(895\) 0 0
\(896\) −4.64466 −0.155167
\(897\) 3.48258 + 0.519530i 0.116280 + 0.0173466i
\(898\) 27.0042i 0.901141i
\(899\) 24.0556 13.8885i 0.802298 0.463207i
\(900\) 0 0
\(901\) 27.0178 46.7962i 0.900093 1.55901i
\(902\) −32.0739 −1.06795
\(903\) −1.66385 + 2.88187i −0.0553694 + 0.0959026i
\(904\) −11.3156 6.53308i −0.376352 0.217287i
\(905\) 0 0
\(906\) 5.62124 9.73628i 0.186753 0.323466i
\(907\) −14.1741 + 8.18345i −0.470645 + 0.271727i −0.716510 0.697577i \(-0.754261\pi\)
0.245865 + 0.969304i \(0.420928\pi\)
\(908\) 7.66025 + 13.2679i 0.254214 + 0.440312i
\(909\) −6.80025 −0.225550
\(910\) 0 0
\(911\) −10.4819 −0.347280 −0.173640 0.984809i \(-0.555553\pi\)
−0.173640 + 0.984809i \(0.555553\pi\)
\(912\) 4.02239 + 6.96699i 0.133195 + 0.230700i
\(913\) 13.3788 7.72428i 0.442775 0.255636i
\(914\) −8.89342 + 15.4039i −0.294168 + 0.509514i
\(915\) 0 0
\(916\) −8.77106 5.06397i −0.289804 0.167318i
\(917\) 0.879598 1.52351i 0.0290469 0.0503107i
\(918\) −4.00000 −0.132020
\(919\) 1.60565 2.78107i 0.0529655 0.0917389i −0.838327 0.545168i \(-0.816466\pi\)
0.891293 + 0.453429i \(0.149799\pi\)
\(920\) 0 0
\(921\) −6.16137 + 3.55727i −0.203024 + 0.117216i
\(922\) 24.9652i 0.822184i
\(923\) 4.23098 28.3617i 0.139265 0.933537i
\(924\) 20.4371 0.672331
\(925\) 0 0
\(926\) 7.81944 + 13.5437i 0.256963 + 0.445073i
\(927\) 4.58246 + 2.64568i 0.150508 + 0.0868956i
\(928\) −4.31274 −0.141572
\(929\) −40.2518 23.2394i −1.32062 0.762460i −0.336792 0.941579i \(-0.609342\pi\)
−0.983827 + 0.179120i \(0.942675\pi\)
\(930\) 0 0
\(931\) 117.236i 3.84224i
\(932\) 17.9716 + 10.3759i 0.588681 + 0.339875i
\(933\) 17.2467 9.95740i 0.564632 0.325990i
\(934\) 2.11236 1.21957i 0.0691184 0.0399055i
\(935\) 0 0
\(936\) −3.56609 0.531987i −0.116561 0.0173886i
\(937\) 27.7627i 0.906969i −0.891264 0.453485i \(-0.850181\pi\)
0.891264 0.453485i \(-0.149819\pi\)
\(938\) 4.23876 + 7.34174i 0.138400 + 0.239716i
\(939\) 3.06975 + 5.31696i 0.100178 + 0.173513i
\(940\) 0 0
\(941\) 20.7962i 0.677935i −0.940798 0.338968i \(-0.889922\pi\)
0.940798 0.338968i \(-0.110078\pi\)
\(942\) −0.751556 + 1.30173i −0.0244870 + 0.0424128i
\(943\) 3.55931 6.16491i 0.115907 0.200757i
\(944\) 2.18056i 0.0709711i
\(945\) 0 0
\(946\) −1.57625 2.73014i −0.0512483 0.0887646i
\(947\) 4.52962 + 7.84554i 0.147193 + 0.254946i 0.930189 0.367081i \(-0.119643\pi\)
−0.782996 + 0.622027i \(0.786309\pi\)
\(948\) 14.9340i 0.485033i
\(949\) −5.76683 14.6286i −0.187199 0.474863i
\(950\) 0 0
\(951\) 6.80078 3.92643i 0.220530 0.127323i
\(952\) 16.0896 9.28932i 0.521466 0.301069i
\(953\) 13.2296 + 7.63811i 0.428549 + 0.247423i 0.698728 0.715387i \(-0.253750\pi\)
−0.270180 + 0.962810i \(0.587083\pi\)
\(954\) 13.5089i 0.437366i
\(955\) 0 0
\(956\) −21.0911 12.1770i −0.682136 0.393831i
\(957\) 18.9766 0.613426
\(958\) −12.2857 7.09317i −0.396934 0.229170i
\(959\) 2.90838 + 5.03746i 0.0939165 + 0.162668i
\(960\) 0 0
\(961\) −10.4824 −0.338143
\(962\) −13.5370 2.01944i −0.436449 0.0651093i
\(963\) 16.9282i 0.545504i
\(964\) 17.2066 9.93423i 0.554187 0.319960i
\(965\) 0 0
\(966\) −2.26795 + 3.92820i −0.0729701 + 0.126388i
\(967\) −46.3036 −1.48902 −0.744511 0.667610i \(-0.767317\pi\)
−0.744511 + 0.667610i \(0.767317\pi\)
\(968\) −4.18056 + 7.24094i −0.134368 + 0.232733i
\(969\) −27.8680 16.0896i −0.895248 0.516872i
\(970\) 0 0
\(971\) −5.98258 + 10.3621i −0.191990 + 0.332537i −0.945910 0.324430i \(-0.894828\pi\)
0.753919 + 0.656967i \(0.228161\pi\)
\(972\) −0.866025 + 0.500000i −0.0277778 + 0.0160375i
\(973\) 7.79221 + 13.4965i 0.249807 + 0.432678i
\(974\) −5.76329 −0.184668
\(975\) 0 0
\(976\) 7.46410 0.238920
\(977\) 0.882077 + 1.52780i 0.0282201 + 0.0488787i 0.879791 0.475362i \(-0.157683\pi\)
−0.851570 + 0.524240i \(0.824349\pi\)
\(978\) 0.152706 0.0881650i 0.00488301 0.00281921i
\(979\) −17.9805 + 31.1432i −0.574660 + 0.995341i
\(980\) 0 0
\(981\) −11.0853 6.40013i −0.353928 0.204340i
\(982\) 0.537671 0.931273i 0.0171578 0.0297181i
\(983\) 54.2821 1.73133 0.865666 0.500623i \(-0.166896\pi\)
0.865666 + 0.500623i \(0.166896\pi\)
\(984\) −3.64466 + 6.31274i −0.116188 + 0.201243i
\(985\) 0 0
\(986\) 14.9398 8.62547i 0.475779 0.274691i
\(987\) 45.3013i 1.44196i
\(988\) −22.7050 18.0506i −0.722344 0.574265i
\(989\) 0.699680 0.0222485
\(990\) 0 0
\(991\) 8.73917 + 15.1367i 0.277609 + 0.480833i 0.970790 0.239931i \(-0.0771248\pi\)
−0.693181 + 0.720763i \(0.743791\pi\)
\(992\) 5.57780 + 3.22034i 0.177095 + 0.102246i
\(993\) −31.9959 −1.01536
\(994\) 31.9908 + 18.4699i 1.01469 + 0.585829i
\(995\) 0 0
\(996\) 3.51093i 0.111248i
\(997\) 18.4389 + 10.6457i 0.583965 + 0.337152i 0.762707 0.646744i \(-0.223870\pi\)
−0.178743 + 0.983896i \(0.557203\pi\)
\(998\) 12.7768 7.37671i 0.404444 0.233506i
\(999\) −3.28745 + 1.89801i −0.104010 + 0.0600505i
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 1950.2.y.k.49.1 8
5.2 odd 4 1950.2.bc.g.751.1 8
5.3 odd 4 390.2.bb.c.361.4 yes 8
5.4 even 2 1950.2.y.j.49.4 8
13.4 even 6 1950.2.y.j.199.4 8
15.8 even 4 1170.2.bs.f.361.2 8
65.3 odd 12 5070.2.b.ba.1351.5 8
65.4 even 6 inner 1950.2.y.k.199.1 8
65.17 odd 12 1950.2.bc.g.901.1 8
65.23 odd 12 5070.2.b.ba.1351.4 8
65.28 even 12 5070.2.a.ca.1.4 4
65.43 odd 12 390.2.bb.c.121.4 8
65.63 even 12 5070.2.a.bz.1.1 4
195.173 even 12 1170.2.bs.f.901.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.bb.c.121.4 8 65.43 odd 12
390.2.bb.c.361.4 yes 8 5.3 odd 4
1170.2.bs.f.361.2 8 15.8 even 4
1170.2.bs.f.901.2 8 195.173 even 12
1950.2.y.j.49.4 8 5.4 even 2
1950.2.y.j.199.4 8 13.4 even 6
1950.2.y.k.49.1 8 1.1 even 1 trivial
1950.2.y.k.199.1 8 65.4 even 6 inner
1950.2.bc.g.751.1 8 5.2 odd 4
1950.2.bc.g.901.1 8 65.17 odd 12
5070.2.a.bz.1.1 4 65.63 even 12
5070.2.a.ca.1.4 4 65.28 even 12
5070.2.b.ba.1351.4 8 65.23 odd 12
5070.2.b.ba.1351.5 8 65.3 odd 12