Properties

Label 930.2.e.a.929.1
Level $930$
Weight $2$
Character 930.929
Analytic conductor $7.426$
Analytic rank $0$
Dimension $32$
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] = [930,2,Mod(929,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.929");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.e (of order \(2\), degree \(1\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 929.1
Character \(\chi\) \(=\) 930.929
Dual form 930.2.e.a.929.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-1.70787 - 0.288390i) q^{3} +1.00000 q^{4} +(2.10277 - 0.760496i) q^{5} +(1.70787 + 0.288390i) q^{6} +4.63015i q^{7} -1.00000 q^{8} +(2.83366 + 0.985067i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-1.70787 - 0.288390i) q^{3} +1.00000 q^{4} +(2.10277 - 0.760496i) q^{5} +(1.70787 + 0.288390i) q^{6} +4.63015i q^{7} -1.00000 q^{8} +(2.83366 + 0.985067i) q^{9} +(-2.10277 + 0.760496i) q^{10} -1.87069 q^{11} +(-1.70787 - 0.288390i) q^{12} -3.74423 q^{13} -4.63015i q^{14} +(-3.81059 + 0.692413i) q^{15} +1.00000 q^{16} +7.48978i q^{17} +(-2.83366 - 0.985067i) q^{18} -5.69026 q^{19} +(2.10277 - 0.760496i) q^{20} +(1.33529 - 7.90771i) q^{21} +1.87069 q^{22} -7.09305i q^{23} +(1.70787 + 0.288390i) q^{24} +(3.84329 - 3.19830i) q^{25} +3.74423 q^{26} +(-4.55545 - 2.49957i) q^{27} +4.63015i q^{28} +6.19127 q^{29} +(3.81059 - 0.692413i) q^{30} +(-4.94030 - 2.56778i) q^{31} -1.00000 q^{32} +(3.19490 + 0.539487i) q^{33} -7.48978i q^{34} +(3.52121 + 9.73615i) q^{35} +(2.83366 + 0.985067i) q^{36} -1.89952 q^{37} +5.69026 q^{38} +(6.39467 + 1.07980i) q^{39} +(-2.10277 + 0.760496i) q^{40} -3.77682i q^{41} +(-1.33529 + 7.90771i) q^{42} -5.39424 q^{43} -1.87069 q^{44} +(6.70768 - 0.0836188i) q^{45} +7.09305i q^{46} -6.33921 q^{47} +(-1.70787 - 0.288390i) q^{48} -14.4383 q^{49} +(-3.84329 + 3.19830i) q^{50} +(2.15998 - 12.7916i) q^{51} -3.74423 q^{52} -2.24609i q^{53} +(4.55545 + 2.49957i) q^{54} +(-3.93363 + 1.42265i) q^{55} -4.63015i q^{56} +(9.71824 + 1.64101i) q^{57} -6.19127 q^{58} -4.58001i q^{59} +(-3.81059 + 0.692413i) q^{60} +7.47286i q^{61} +(4.94030 + 2.56778i) q^{62} +(-4.56101 + 13.1203i) q^{63} +1.00000 q^{64} +(-7.87326 + 2.84747i) q^{65} +(-3.19490 - 0.539487i) q^{66} -8.18959i q^{67} +7.48978i q^{68} +(-2.04556 + 12.1140i) q^{69} +(-3.52121 - 9.73615i) q^{70} +14.8896i q^{71} +(-2.83366 - 0.985067i) q^{72} -11.5855 q^{73} +1.89952 q^{74} +(-7.48621 + 4.35392i) q^{75} -5.69026 q^{76} -8.66156i q^{77} +(-6.39467 - 1.07980i) q^{78} +10.6362i q^{79} +(2.10277 - 0.760496i) q^{80} +(7.05929 + 5.58269i) q^{81} +3.77682i q^{82} -1.01351i q^{83} +(1.33529 - 7.90771i) q^{84} +(5.69595 + 15.7493i) q^{85} +5.39424 q^{86} +(-10.5739 - 1.78550i) q^{87} +1.87069 q^{88} -11.8892 q^{89} +(-6.70768 + 0.0836188i) q^{90} -17.3364i q^{91} -7.09305i q^{92} +(7.69688 + 5.81017i) q^{93} +6.33921 q^{94} +(-11.9653 + 4.32742i) q^{95} +(1.70787 + 0.288390i) q^{96} +1.87390i q^{97} +14.4383 q^{98} +(-5.30089 - 1.84275i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} - 4 q^{18} + 8 q^{19} + 2 q^{20} + 10 q^{25} - 12 q^{31} - 32 q^{32} - 8 q^{33} + 16 q^{35} + 4 q^{36} - 8 q^{38} - 4 q^{39} - 2 q^{40} + 10 q^{45} - 4 q^{47} - 36 q^{49} - 10 q^{50} - 4 q^{51} + 12 q^{62} - 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} - 4 q^{72} + 8 q^{76} + 4 q^{78} + 2 q^{80} + 24 q^{81} - 4 q^{87} - 10 q^{90} + 24 q^{93} + 4 q^{94} - 26 q^{95} + 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.70787 0.288390i −0.986041 0.166502i
\(4\) 1.00000 0.500000
\(5\) 2.10277 0.760496i 0.940388 0.340104i
\(6\) 1.70787 + 0.288390i 0.697236 + 0.117735i
\(7\) 4.63015i 1.75003i 0.484093 + 0.875016i \(0.339149\pi\)
−0.484093 + 0.875016i \(0.660851\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.83366 + 0.985067i 0.944554 + 0.328356i
\(10\) −2.10277 + 0.760496i −0.664955 + 0.240490i
\(11\) −1.87069 −0.564033 −0.282017 0.959410i \(-0.591003\pi\)
−0.282017 + 0.959410i \(0.591003\pi\)
\(12\) −1.70787 0.288390i −0.493021 0.0832510i
\(13\) −3.74423 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(14\) 4.63015i 1.23746i
\(15\) −3.81059 + 0.692413i −0.983889 + 0.178780i
\(16\) 1.00000 0.250000
\(17\) 7.48978i 1.81654i 0.418386 + 0.908269i \(0.362596\pi\)
−0.418386 + 0.908269i \(0.637404\pi\)
\(18\) −2.83366 0.985067i −0.667901 0.232182i
\(19\) −5.69026 −1.30543 −0.652717 0.757602i \(-0.726371\pi\)
−0.652717 + 0.757602i \(0.726371\pi\)
\(20\) 2.10277 0.760496i 0.470194 0.170052i
\(21\) 1.33529 7.90771i 0.291384 1.72560i
\(22\) 1.87069 0.398832
\(23\) 7.09305i 1.47900i −0.673155 0.739502i \(-0.735061\pi\)
0.673155 0.739502i \(-0.264939\pi\)
\(24\) 1.70787 + 0.288390i 0.348618 + 0.0588673i
\(25\) 3.84329 3.19830i 0.768658 0.639659i
\(26\) 3.74423 0.734304
\(27\) −4.55545 2.49957i −0.876697 0.481042i
\(28\) 4.63015i 0.875016i
\(29\) 6.19127 1.14969 0.574845 0.818262i \(-0.305062\pi\)
0.574845 + 0.818262i \(0.305062\pi\)
\(30\) 3.81059 0.692413i 0.695715 0.126417i
\(31\) −4.94030 2.56778i −0.887303 0.461186i
\(32\) −1.00000 −0.176777
\(33\) 3.19490 + 0.539487i 0.556160 + 0.0939127i
\(34\) 7.48978i 1.28449i
\(35\) 3.52121 + 9.73615i 0.595193 + 1.64571i
\(36\) 2.83366 + 0.985067i 0.472277 + 0.164178i
\(37\) −1.89952 −0.312279 −0.156139 0.987735i \(-0.549905\pi\)
−0.156139 + 0.987735i \(0.549905\pi\)
\(38\) 5.69026 0.923082
\(39\) 6.39467 + 1.07980i 1.02397 + 0.172906i
\(40\) −2.10277 + 0.760496i −0.332477 + 0.120245i
\(41\) 3.77682i 0.589840i −0.955522 0.294920i \(-0.904707\pi\)
0.955522 0.294920i \(-0.0952930\pi\)
\(42\) −1.33529 + 7.90771i −0.206040 + 1.22019i
\(43\) −5.39424 −0.822613 −0.411307 0.911497i \(-0.634927\pi\)
−0.411307 + 0.911497i \(0.634927\pi\)
\(44\) −1.87069 −0.282017
\(45\) 6.70768 0.0836188i 0.999922 0.0124651i
\(46\) 7.09305i 1.04581i
\(47\) −6.33921 −0.924669 −0.462335 0.886705i \(-0.652988\pi\)
−0.462335 + 0.886705i \(0.652988\pi\)
\(48\) −1.70787 0.288390i −0.246510 0.0416255i
\(49\) −14.4383 −2.06261
\(50\) −3.84329 + 3.19830i −0.543524 + 0.452308i
\(51\) 2.15998 12.7916i 0.302457 1.79118i
\(52\) −3.74423 −0.519231
\(53\) 2.24609i 0.308525i −0.988030 0.154262i \(-0.950700\pi\)
0.988030 0.154262i \(-0.0493001\pi\)
\(54\) 4.55545 + 2.49957i 0.619919 + 0.340148i
\(55\) −3.93363 + 1.42265i −0.530410 + 0.191830i
\(56\) 4.63015i 0.618730i
\(57\) 9.71824 + 1.64101i 1.28721 + 0.217357i
\(58\) −6.19127 −0.812954
\(59\) 4.58001i 0.596266i −0.954524 0.298133i \(-0.903636\pi\)
0.954524 0.298133i \(-0.0963639\pi\)
\(60\) −3.81059 + 0.692413i −0.491945 + 0.0893901i
\(61\) 7.47286i 0.956802i 0.878141 + 0.478401i \(0.158783\pi\)
−0.878141 + 0.478401i \(0.841217\pi\)
\(62\) 4.94030 + 2.56778i 0.627418 + 0.326108i
\(63\) −4.56101 + 13.1203i −0.574633 + 1.65300i
\(64\) 1.00000 0.125000
\(65\) −7.87326 + 2.84747i −0.976558 + 0.353185i
\(66\) −3.19490 0.539487i −0.393264 0.0664063i
\(67\) 8.18959i 1.00052i −0.865876 0.500259i \(-0.833238\pi\)
0.865876 0.500259i \(-0.166762\pi\)
\(68\) 7.48978i 0.908269i
\(69\) −2.04556 + 12.1140i −0.246257 + 1.45836i
\(70\) −3.52121 9.73615i −0.420865 1.16369i
\(71\) 14.8896i 1.76706i 0.468370 + 0.883532i \(0.344841\pi\)
−0.468370 + 0.883532i \(0.655159\pi\)
\(72\) −2.83366 0.985067i −0.333950 0.116091i
\(73\) −11.5855 −1.35598 −0.677991 0.735071i \(-0.737149\pi\)
−0.677991 + 0.735071i \(0.737149\pi\)
\(74\) 1.89952 0.220814
\(75\) −7.48621 + 4.35392i −0.864433 + 0.502747i
\(76\) −5.69026 −0.652717
\(77\) 8.66156i 0.987077i
\(78\) −6.39467 1.07980i −0.724054 0.122263i
\(79\) 10.6362i 1.19667i 0.801246 + 0.598335i \(0.204171\pi\)
−0.801246 + 0.598335i \(0.795829\pi\)
\(80\) 2.10277 0.760496i 0.235097 0.0850260i
\(81\) 7.05929 + 5.58269i 0.784365 + 0.620299i
\(82\) 3.77682i 0.417080i
\(83\) 1.01351i 0.111247i −0.998452 0.0556234i \(-0.982285\pi\)
0.998452 0.0556234i \(-0.0177146\pi\)
\(84\) 1.33529 7.90771i 0.145692 0.862802i
\(85\) 5.69595 + 15.7493i 0.617812 + 1.70825i
\(86\) 5.39424 0.581676
\(87\) −10.5739 1.78550i −1.13364 0.191426i
\(88\) 1.87069 0.199416
\(89\) −11.8892 −1.26025 −0.630126 0.776493i \(-0.716997\pi\)
−0.630126 + 0.776493i \(0.716997\pi\)
\(90\) −6.70768 + 0.0836188i −0.707052 + 0.00881419i
\(91\) 17.3364i 1.81734i
\(92\) 7.09305i 0.739502i
\(93\) 7.69688 + 5.81017i 0.798129 + 0.602486i
\(94\) 6.33921 0.653840
\(95\) −11.9653 + 4.32742i −1.22761 + 0.443984i
\(96\) 1.70787 + 0.288390i 0.174309 + 0.0294337i
\(97\) 1.87390i 0.190266i 0.995465 + 0.0951331i \(0.0303277\pi\)
−0.995465 + 0.0951331i \(0.969672\pi\)
\(98\) 14.4383 1.45849
\(99\) −5.30089 1.84275i −0.532760 0.185203i
\(100\) 3.84329 3.19830i 0.384329 0.319830i
\(101\) 0.0683091i 0.00679701i −0.999994 0.00339851i \(-0.998918\pi\)
0.999994 0.00339851i \(-0.00108178\pi\)
\(102\) −2.15998 + 12.7916i −0.213870 + 1.26656i
\(103\) 4.29810i 0.423504i −0.977323 0.211752i \(-0.932083\pi\)
0.977323 0.211752i \(-0.0679170\pi\)
\(104\) 3.74423 0.367152
\(105\) −3.20598 17.6436i −0.312871 1.72184i
\(106\) 2.24609i 0.218160i
\(107\) −3.57584 −0.345690 −0.172845 0.984949i \(-0.555296\pi\)
−0.172845 + 0.984949i \(0.555296\pi\)
\(108\) −4.55545 2.49957i −0.438349 0.240521i
\(109\) 0.722467 0.0691998 0.0345999 0.999401i \(-0.488984\pi\)
0.0345999 + 0.999401i \(0.488984\pi\)
\(110\) 3.93363 1.42265i 0.375057 0.135644i
\(111\) 3.24413 + 0.547801i 0.307920 + 0.0519950i
\(112\) 4.63015i 0.437508i
\(113\) 5.66365 0.532792 0.266396 0.963864i \(-0.414167\pi\)
0.266396 + 0.963864i \(0.414167\pi\)
\(114\) −9.71824 1.64101i −0.910196 0.153695i
\(115\) −5.39424 14.9151i −0.503015 1.39084i
\(116\) 6.19127 0.574845
\(117\) −10.6099 3.68832i −0.980884 0.340985i
\(118\) 4.58001i 0.421624i
\(119\) −34.6788 −3.17900
\(120\) 3.81059 0.692413i 0.347857 0.0632083i
\(121\) −7.50053 −0.681866
\(122\) 7.47286i 0.676561i
\(123\) −1.08920 + 6.45033i −0.0982095 + 0.581606i
\(124\) −4.94030 2.56778i −0.443652 0.230593i
\(125\) 5.64927 9.64810i 0.505286 0.862952i
\(126\) 4.56101 13.1203i 0.406327 1.16885i
\(127\) 14.8935 1.32159 0.660794 0.750567i \(-0.270220\pi\)
0.660794 + 0.750567i \(0.270220\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 9.21267 + 1.55564i 0.811131 + 0.136967i
\(130\) 7.87326 2.84747i 0.690530 0.249740i
\(131\) 2.10228i 0.183677i −0.995774 0.0918386i \(-0.970726\pi\)
0.995774 0.0918386i \(-0.0292744\pi\)
\(132\) 3.19490 + 0.539487i 0.278080 + 0.0469563i
\(133\) 26.3468i 2.28455i
\(134\) 8.18959i 0.707472i
\(135\) −11.4800 1.79162i −0.988040 0.154198i
\(136\) 7.48978i 0.642243i
\(137\) 9.53533i 0.814658i 0.913281 + 0.407329i \(0.133540\pi\)
−0.913281 + 0.407329i \(0.866460\pi\)
\(138\) 2.04556 12.1140i 0.174130 1.03122i
\(139\) 12.9885i 1.10167i 0.834613 + 0.550837i \(0.185691\pi\)
−0.834613 + 0.550837i \(0.814309\pi\)
\(140\) 3.52121 + 9.73615i 0.297597 + 0.822855i
\(141\) 10.8266 + 1.82817i 0.911762 + 0.153959i
\(142\) 14.8896i 1.24950i
\(143\) 7.00428 0.585727
\(144\) 2.83366 + 0.985067i 0.236139 + 0.0820889i
\(145\) 13.0188 4.70844i 1.08115 0.391014i
\(146\) 11.5855 0.958823
\(147\) 24.6588 + 4.16386i 2.03382 + 0.343429i
\(148\) −1.89952 −0.156139
\(149\) 0.757439i 0.0620518i 0.999519 + 0.0310259i \(0.00987744\pi\)
−0.999519 + 0.0310259i \(0.990123\pi\)
\(150\) 7.48621 4.35392i 0.611247 0.355496i
\(151\) 8.33372i 0.678188i 0.940752 + 0.339094i \(0.110121\pi\)
−0.940752 + 0.339094i \(0.889879\pi\)
\(152\) 5.69026 0.461541
\(153\) −7.37794 + 21.2235i −0.596471 + 1.71582i
\(154\) 8.66156i 0.697969i
\(155\) −12.3411 1.64237i −0.991261 0.131919i
\(156\) 6.39467 + 1.07980i 0.511983 + 0.0864530i
\(157\) 14.7100i 1.17399i 0.809592 + 0.586993i \(0.199688\pi\)
−0.809592 + 0.586993i \(0.800312\pi\)
\(158\) 10.6362i 0.846173i
\(159\) −0.647751 + 3.83604i −0.0513700 + 0.304218i
\(160\) −2.10277 + 0.760496i −0.166239 + 0.0601225i
\(161\) 32.8419 2.58830
\(162\) −7.05929 5.58269i −0.554630 0.438618i
\(163\) 23.1406i 1.81251i 0.422733 + 0.906254i \(0.361071\pi\)
−0.422733 + 0.906254i \(0.638929\pi\)
\(164\) 3.77682i 0.294920i
\(165\) 7.12841 1.29529i 0.554946 0.100838i
\(166\) 1.01351i 0.0786633i
\(167\) 1.74440i 0.134985i 0.997720 + 0.0674927i \(0.0214999\pi\)
−0.997720 + 0.0674927i \(0.978500\pi\)
\(168\) −1.33529 + 7.90771i −0.103020 + 0.610093i
\(169\) 1.01926 0.0784045
\(170\) −5.69595 15.7493i −0.436859 1.20792i
\(171\) −16.1243 5.60528i −1.23305 0.428647i
\(172\) −5.39424 −0.411307
\(173\) 4.69003 0.356576 0.178288 0.983978i \(-0.442944\pi\)
0.178288 + 0.983978i \(0.442944\pi\)
\(174\) 10.5739 + 1.78550i 0.801606 + 0.135358i
\(175\) 14.8086 + 17.7950i 1.11942 + 1.34518i
\(176\) −1.87069 −0.141008
\(177\) −1.32083 + 7.82207i −0.0992795 + 0.587943i
\(178\) 11.8892 0.891133
\(179\) 13.9875 1.04548 0.522738 0.852493i \(-0.324911\pi\)
0.522738 + 0.852493i \(0.324911\pi\)
\(180\) 6.70768 0.0836188i 0.499961 0.00623257i
\(181\) 10.1423i 0.753870i −0.926240 0.376935i \(-0.876978\pi\)
0.926240 0.376935i \(-0.123022\pi\)
\(182\) 17.3364i 1.28506i
\(183\) 2.15510 12.7627i 0.159309 0.943446i
\(184\) 7.09305i 0.522907i
\(185\) −3.99425 + 1.44457i −0.293663 + 0.106207i
\(186\) −7.69688 5.81017i −0.564362 0.426022i
\(187\) 14.0110i 1.02459i
\(188\) −6.33921 −0.462335
\(189\) 11.5734 21.0924i 0.841840 1.53425i
\(190\) 11.9653 4.32742i 0.868055 0.313944i
\(191\) 19.0402i 1.37770i −0.724904 0.688850i \(-0.758116\pi\)
0.724904 0.688850i \(-0.241884\pi\)
\(192\) −1.70787 0.288390i −0.123255 0.0208127i
\(193\) 8.94203i 0.643661i 0.946797 + 0.321831i \(0.104298\pi\)
−0.946797 + 0.321831i \(0.895702\pi\)
\(194\) 1.87390i 0.134538i
\(195\) 14.2677 2.59255i 1.02173 0.185657i
\(196\) −14.4383 −1.03131
\(197\) 23.0376i 1.64136i −0.571389 0.820680i \(-0.693595\pi\)
0.571389 0.820680i \(-0.306405\pi\)
\(198\) 5.30089 + 1.84275i 0.376718 + 0.130959i
\(199\) 26.0461i 1.84636i 0.384372 + 0.923178i \(0.374418\pi\)
−0.384372 + 0.923178i \(0.625582\pi\)
\(200\) −3.84329 + 3.19830i −0.271762 + 0.226154i
\(201\) −2.36179 + 13.9868i −0.166588 + 0.986551i
\(202\) 0.0683091i 0.00480621i
\(203\) 28.6665i 2.01200i
\(204\) 2.15998 12.7916i 0.151229 0.895591i
\(205\) −2.87225 7.94178i −0.200607 0.554678i
\(206\) 4.29810i 0.299463i
\(207\) 6.98713 20.0993i 0.485639 1.39700i
\(208\) −3.74423 −0.259616
\(209\) 10.6447 0.736309
\(210\) 3.20598 + 17.6436i 0.221233 + 1.21752i
\(211\) 12.5032 0.860756 0.430378 0.902649i \(-0.358380\pi\)
0.430378 + 0.902649i \(0.358380\pi\)
\(212\) 2.24609i 0.154262i
\(213\) 4.29400 25.4295i 0.294220 1.74240i
\(214\) 3.57584 0.244440
\(215\) −11.3428 + 4.10230i −0.773576 + 0.279774i
\(216\) 4.55545 + 2.49957i 0.309959 + 0.170074i
\(217\) 11.8892 22.8743i 0.807091 1.55281i
\(218\) −0.722467 −0.0489316
\(219\) 19.7866 + 3.34114i 1.33705 + 0.225774i
\(220\) −3.93363 + 1.42265i −0.265205 + 0.0959150i
\(221\) 28.0435i 1.88641i
\(222\) −3.24413 0.547801i −0.217732 0.0367660i
\(223\) 10.7677 0.721056 0.360528 0.932748i \(-0.382596\pi\)
0.360528 + 0.932748i \(0.382596\pi\)
\(224\) 4.63015i 0.309365i
\(225\) 14.0411 5.27700i 0.936075 0.351800i
\(226\) −5.66365 −0.376741
\(227\) −18.5144 −1.22885 −0.614424 0.788976i \(-0.710611\pi\)
−0.614424 + 0.788976i \(0.710611\pi\)
\(228\) 9.71824 + 1.64101i 0.643606 + 0.108679i
\(229\) 13.3537i 0.882435i −0.897400 0.441218i \(-0.854547\pi\)
0.897400 0.441218i \(-0.145453\pi\)
\(230\) 5.39424 + 14.9151i 0.355685 + 0.983470i
\(231\) −2.49791 + 14.7929i −0.164350 + 0.973298i
\(232\) −6.19127 −0.406477
\(233\) −15.4812 −1.01420 −0.507102 0.861886i \(-0.669283\pi\)
−0.507102 + 0.861886i \(0.669283\pi\)
\(234\) 10.6099 + 3.68832i 0.693590 + 0.241113i
\(235\) −13.3299 + 4.82095i −0.869548 + 0.314484i
\(236\) 4.58001i 0.298133i
\(237\) 3.06738 18.1653i 0.199248 1.17997i
\(238\) 34.6788 2.24789
\(239\) 0.761904 0.0492834 0.0246417 0.999696i \(-0.492156\pi\)
0.0246417 + 0.999696i \(0.492156\pi\)
\(240\) −3.81059 + 0.692413i −0.245972 + 0.0446950i
\(241\) 18.2543i 1.17586i 0.808910 + 0.587932i \(0.200058\pi\)
−0.808910 + 0.587932i \(0.799942\pi\)
\(242\) 7.50053 0.482152
\(243\) −10.4464 11.5704i −0.670135 0.742239i
\(244\) 7.47286i 0.478401i
\(245\) −30.3604 + 10.9803i −1.93966 + 0.701503i
\(246\) 1.08920 6.45033i 0.0694446 0.411258i
\(247\) 21.3056 1.35564
\(248\) 4.94030 + 2.56778i 0.313709 + 0.163054i
\(249\) −0.292285 + 1.73094i −0.0185228 + 0.109694i
\(250\) −5.64927 + 9.64810i −0.357291 + 0.610199i
\(251\) 11.4833 0.724821 0.362411 0.932019i \(-0.381954\pi\)
0.362411 + 0.932019i \(0.381954\pi\)
\(252\) −4.56101 + 13.1203i −0.287317 + 0.826500i
\(253\) 13.2689i 0.834207i
\(254\) −14.8935 −0.934504
\(255\) −5.18602 28.5405i −0.324761 1.78727i
\(256\) 1.00000 0.0625000
\(257\) 16.8528 1.05125 0.525625 0.850716i \(-0.323831\pi\)
0.525625 + 0.850716i \(0.323831\pi\)
\(258\) −9.21267 1.55564i −0.573556 0.0968501i
\(259\) 8.79505i 0.546498i
\(260\) −7.87326 + 2.84747i −0.488279 + 0.176593i
\(261\) 17.5440 + 6.09882i 1.08594 + 0.377507i
\(262\) 2.10228i 0.129879i
\(263\) 8.89826i 0.548690i 0.961631 + 0.274345i \(0.0884610\pi\)
−0.961631 + 0.274345i \(0.911539\pi\)
\(264\) −3.19490 0.539487i −0.196632 0.0332031i
\(265\) −1.70815 4.72302i −0.104931 0.290133i
\(266\) 26.3468i 1.61542i
\(267\) 20.3052 + 3.42872i 1.24266 + 0.209834i
\(268\) 8.18959i 0.500259i
\(269\) −9.75034 −0.594489 −0.297244 0.954801i \(-0.596068\pi\)
−0.297244 + 0.954801i \(0.596068\pi\)
\(270\) 11.4800 + 1.79162i 0.698650 + 0.109034i
\(271\) 11.9409i 0.725360i 0.931914 + 0.362680i \(0.118138\pi\)
−0.931914 + 0.362680i \(0.881862\pi\)
\(272\) 7.48978i 0.454135i
\(273\) −4.99963 + 29.6083i −0.302591 + 1.79198i
\(274\) 9.53533i 0.576050i
\(275\) −7.18960 + 5.98301i −0.433549 + 0.360789i
\(276\) −2.04556 + 12.1140i −0.123129 + 0.729179i
\(277\) −0.764760 −0.0459500 −0.0229750 0.999736i \(-0.507314\pi\)
−0.0229750 + 0.999736i \(0.507314\pi\)
\(278\) 12.9885i 0.779001i
\(279\) −11.4697 12.1427i −0.686673 0.726967i
\(280\) −3.52121 9.73615i −0.210433 0.581846i
\(281\) 20.0130i 1.19388i −0.802287 0.596938i \(-0.796384\pi\)
0.802287 0.596938i \(-0.203616\pi\)
\(282\) −10.8266 1.82817i −0.644713 0.108866i
\(283\) 16.2273i 0.964611i −0.876003 0.482306i \(-0.839799\pi\)
0.876003 0.482306i \(-0.160201\pi\)
\(284\) 14.8896i 0.883532i
\(285\) 21.6832 3.94001i 1.28440 0.233386i
\(286\) −7.00428 −0.414172
\(287\) 17.4872 1.03224
\(288\) −2.83366 0.985067i −0.166975 0.0580456i
\(289\) −39.0968 −2.29981
\(290\) −13.0188 + 4.70844i −0.764492 + 0.276489i
\(291\) 0.540415 3.20039i 0.0316797 0.187610i
\(292\) −11.5855 −0.677991
\(293\) −11.1515 −0.651479 −0.325739 0.945460i \(-0.605613\pi\)
−0.325739 + 0.945460i \(0.605613\pi\)
\(294\) −24.6588 4.16386i −1.43813 0.242841i
\(295\) −3.48308 9.63070i −0.202792 0.560721i
\(296\) 1.89952 0.110407
\(297\) 8.52183 + 4.67591i 0.494486 + 0.271324i
\(298\) 0.757439i 0.0438773i
\(299\) 26.5580i 1.53589i
\(300\) −7.48621 + 4.35392i −0.432217 + 0.251374i
\(301\) 24.9761i 1.43960i
\(302\) 8.33372i 0.479552i
\(303\) −0.0196997 + 0.116663i −0.00113172 + 0.00670213i
\(304\) −5.69026 −0.326359
\(305\) 5.68308 + 15.7137i 0.325412 + 0.899765i
\(306\) 7.37794 21.2235i 0.421769 1.21327i
\(307\) 8.36560i 0.477450i −0.971087 0.238725i \(-0.923271\pi\)
0.971087 0.238725i \(-0.0767294\pi\)
\(308\) 8.66156i 0.493538i
\(309\) −1.23953 + 7.34061i −0.0705143 + 0.417593i
\(310\) 12.3411 + 1.64237i 0.700927 + 0.0932805i
\(311\) 0.660154i 0.0374339i 0.999825 + 0.0187170i \(0.00595814\pi\)
−0.999825 + 0.0187170i \(0.994042\pi\)
\(312\) −6.39467 1.07980i −0.362027 0.0611315i
\(313\) −18.7240 −1.05834 −0.529171 0.848515i \(-0.677497\pi\)
−0.529171 + 0.848515i \(0.677497\pi\)
\(314\) 14.7100i 0.830133i
\(315\) 0.387167 + 31.0576i 0.0218144 + 1.74990i
\(316\) 10.6362i 0.598335i
\(317\) −13.9521 −0.783631 −0.391815 0.920044i \(-0.628153\pi\)
−0.391815 + 0.920044i \(0.628153\pi\)
\(318\) 0.647751 3.83604i 0.0363241 0.215115i
\(319\) −11.5819 −0.648464
\(320\) 2.10277 0.760496i 0.117548 0.0425130i
\(321\) 6.10709 + 1.03124i 0.340864 + 0.0575581i
\(322\) −32.8419 −1.83021
\(323\) 42.6188i 2.37137i
\(324\) 7.05929 + 5.58269i 0.392183 + 0.310150i
\(325\) −14.3902 + 11.9752i −0.798223 + 0.664262i
\(326\) 23.1406i 1.28164i
\(327\) −1.23388 0.208352i −0.0682338 0.0115219i
\(328\) 3.77682i 0.208540i
\(329\) 29.3515i 1.61820i
\(330\) −7.12841 + 1.29529i −0.392406 + 0.0713032i
\(331\) 6.38971i 0.351210i 0.984461 + 0.175605i \(0.0561882\pi\)
−0.984461 + 0.175605i \(0.943812\pi\)
\(332\) 1.01351i 0.0556234i
\(333\) −5.38259 1.87115i −0.294964 0.102538i
\(334\) 1.74440i 0.0954491i
\(335\) −6.22815 17.2208i −0.340280 0.940874i
\(336\) 1.33529 7.90771i 0.0728460 0.431401i
\(337\) 18.0566 0.983606 0.491803 0.870706i \(-0.336338\pi\)
0.491803 + 0.870706i \(0.336338\pi\)
\(338\) −1.01926 −0.0554404
\(339\) −9.67280 1.63334i −0.525354 0.0887108i
\(340\) 5.69595 + 15.7493i 0.308906 + 0.854126i
\(341\) 9.24175 + 4.80351i 0.500469 + 0.260124i
\(342\) 16.1243 + 5.60528i 0.871901 + 0.303099i
\(343\) 34.4404i 1.85961i
\(344\) 5.39424 0.290838
\(345\) 4.91132 + 27.0287i 0.264417 + 1.45518i
\(346\) −4.69003 −0.252137
\(347\) 9.00187i 0.483246i 0.970370 + 0.241623i \(0.0776797\pi\)
−0.970370 + 0.241623i \(0.922320\pi\)
\(348\) −10.5739 1.78550i −0.566821 0.0957129i
\(349\) 7.59014 0.406291 0.203145 0.979149i \(-0.434884\pi\)
0.203145 + 0.979149i \(0.434884\pi\)
\(350\) −14.8086 17.7950i −0.791553 0.951184i
\(351\) 17.0567 + 9.35896i 0.910417 + 0.499544i
\(352\) 1.87069 0.0997079
\(353\) 15.9984i 0.851510i 0.904838 + 0.425755i \(0.139991\pi\)
−0.904838 + 0.425755i \(0.860009\pi\)
\(354\) 1.32083 7.82207i 0.0702012 0.415738i
\(355\) 11.3234 + 31.3093i 0.600986 + 1.66173i
\(356\) −11.8892 −0.630126
\(357\) 59.2270 + 10.0010i 3.13463 + 0.529310i
\(358\) −13.9875 −0.739263
\(359\) 20.9131i 1.10375i 0.833927 + 0.551875i \(0.186088\pi\)
−0.833927 + 0.551875i \(0.813912\pi\)
\(360\) −6.70768 + 0.0836188i −0.353526 + 0.00440710i
\(361\) 13.3790 0.704159
\(362\) 10.1423i 0.533066i
\(363\) 12.8100 + 2.16308i 0.672348 + 0.113532i
\(364\) 17.3364i 0.908672i
\(365\) −24.3617 + 8.81073i −1.27515 + 0.461175i
\(366\) −2.15510 + 12.7627i −0.112649 + 0.667117i
\(367\) −21.3709 −1.11555 −0.557777 0.829991i \(-0.688346\pi\)
−0.557777 + 0.829991i \(0.688346\pi\)
\(368\) 7.09305i 0.369751i
\(369\) 3.72042 10.7022i 0.193677 0.557136i
\(370\) 3.99425 1.44457i 0.207651 0.0750999i
\(371\) 10.3998 0.539928
\(372\) 7.69688 + 5.81017i 0.399065 + 0.301243i
\(373\) 4.72525i 0.244664i −0.992489 0.122332i \(-0.960963\pi\)
0.992489 0.122332i \(-0.0390373\pi\)
\(374\) 14.0110i 0.724493i
\(375\) −12.4307 + 14.8485i −0.641916 + 0.766775i
\(376\) 6.33921 0.326920
\(377\) −23.1815 −1.19391
\(378\) −11.5734 + 21.0924i −0.595271 + 1.08488i
\(379\) −5.68757 −0.292151 −0.146075 0.989273i \(-0.546664\pi\)
−0.146075 + 0.989273i \(0.546664\pi\)
\(380\) −11.9653 + 4.32742i −0.613807 + 0.221992i
\(381\) −25.4363 4.29515i −1.30314 0.220047i
\(382\) 19.0402i 0.974180i
\(383\) 13.3422i 0.681753i −0.940108 0.340876i \(-0.889276\pi\)
0.940108 0.340876i \(-0.110724\pi\)
\(384\) 1.70787 + 0.288390i 0.0871545 + 0.0147168i
\(385\) −6.58708 18.2133i −0.335709 0.928235i
\(386\) 8.94203i 0.455137i
\(387\) −15.2854 5.31368i −0.777003 0.270110i
\(388\) 1.87390i 0.0951331i
\(389\) 26.3747 1.33725 0.668626 0.743598i \(-0.266883\pi\)
0.668626 + 0.743598i \(0.266883\pi\)
\(390\) −14.2677 + 2.59255i −0.722474 + 0.131279i
\(391\) 53.1254 2.68667
\(392\) 14.4383 0.729244
\(393\) −0.606277 + 3.59043i −0.0305826 + 0.181113i
\(394\) 23.0376i 1.16062i
\(395\) 8.08881 + 22.3656i 0.406992 + 1.12533i
\(396\) −5.30089 1.84275i −0.266380 0.0926017i
\(397\) 0.462918i 0.0232332i −0.999933 0.0116166i \(-0.996302\pi\)
0.999933 0.0116166i \(-0.00369776\pi\)
\(398\) 26.0461i 1.30557i
\(399\) −7.59814 + 44.9969i −0.380383 + 2.25266i
\(400\) 3.84329 3.19830i 0.192165 0.159915i
\(401\) 21.9242 1.09484 0.547421 0.836858i \(-0.315610\pi\)
0.547421 + 0.836858i \(0.315610\pi\)
\(402\) 2.36179 13.9868i 0.117796 0.697597i
\(403\) 18.4976 + 9.61435i 0.921431 + 0.478925i
\(404\) 0.0683091i 0.00339851i
\(405\) 19.0897 + 6.37057i 0.948574 + 0.316556i
\(406\) 28.6665i 1.42270i
\(407\) 3.55340 0.176136
\(408\) −2.15998 + 12.7916i −0.106935 + 0.633278i
\(409\) 29.5580i 1.46155i −0.682618 0.730775i \(-0.739159\pi\)
0.682618 0.730775i \(-0.260841\pi\)
\(410\) 2.87225 + 7.94178i 0.141851 + 0.392217i
\(411\) 2.74989 16.2851i 0.135642 0.803287i
\(412\) 4.29810i 0.211752i
\(413\) 21.2061 1.04348
\(414\) −6.98713 + 20.0993i −0.343399 + 0.987827i
\(415\) −0.770767 2.13117i −0.0378355 0.104615i
\(416\) 3.74423 0.183576
\(417\) 3.74576 22.1828i 0.183431 1.08630i
\(418\) −10.6447 −0.520649
\(419\) 14.8158i 0.723797i 0.932218 + 0.361898i \(0.117871\pi\)
−0.932218 + 0.361898i \(0.882129\pi\)
\(420\) −3.20598 17.6436i −0.156436 0.860919i
\(421\) 6.36850 0.310382 0.155191 0.987885i \(-0.450401\pi\)
0.155191 + 0.987885i \(0.450401\pi\)
\(422\) −12.5032 −0.608646
\(423\) −17.9632 6.24455i −0.873400 0.303620i
\(424\) 2.24609i 0.109080i
\(425\) 23.9546 + 28.7854i 1.16197 + 1.39630i
\(426\) −4.29400 + 25.4295i −0.208045 + 1.23206i
\(427\) −34.6005 −1.67444
\(428\) −3.57584 −0.172845
\(429\) −11.9624 2.01996i −0.577551 0.0975248i
\(430\) 11.3428 4.10230i 0.547001 0.197830i
\(431\) 3.42192i 0.164828i 0.996598 + 0.0824141i \(0.0262630\pi\)
−0.996598 + 0.0824141i \(0.973737\pi\)
\(432\) −4.55545 2.49957i −0.219174 0.120261i
\(433\) 9.25300 0.444671 0.222335 0.974970i \(-0.428632\pi\)
0.222335 + 0.974970i \(0.428632\pi\)
\(434\) −11.8892 + 22.8743i −0.570700 + 1.09800i
\(435\) −23.5924 + 4.28692i −1.13117 + 0.205542i
\(436\) 0.722467 0.0345999
\(437\) 40.3613i 1.93074i
\(438\) −19.7866 3.34114i −0.945439 0.159646i
\(439\) −1.50233 −0.0717025 −0.0358512 0.999357i \(-0.511414\pi\)
−0.0358512 + 0.999357i \(0.511414\pi\)
\(440\) 3.93363 1.42265i 0.187528 0.0678222i
\(441\) −40.9133 14.2227i −1.94825 0.677271i
\(442\) 28.0435i 1.33389i
\(443\) 16.4755 0.782773 0.391387 0.920226i \(-0.371996\pi\)
0.391387 + 0.920226i \(0.371996\pi\)
\(444\) 3.24413 + 0.547801i 0.153960 + 0.0259975i
\(445\) −25.0003 + 9.04168i −1.18513 + 0.428617i
\(446\) −10.7677 −0.509864
\(447\) 0.218438 1.29361i 0.0103317 0.0611856i
\(448\) 4.63015i 0.218754i
\(449\) −36.9554 −1.74403 −0.872016 0.489477i \(-0.837188\pi\)
−0.872016 + 0.489477i \(0.837188\pi\)
\(450\) −14.0411 + 5.27700i −0.661905 + 0.248760i
\(451\) 7.06524i 0.332689i
\(452\) 5.66365 0.266396
\(453\) 2.40336 14.2329i 0.112920 0.668722i
\(454\) 18.5144 0.868926
\(455\) −13.1842 36.4544i −0.618086 1.70901i
\(456\) −9.71824 1.64101i −0.455098 0.0768475i
\(457\) 10.2884 0.481272 0.240636 0.970615i \(-0.422644\pi\)
0.240636 + 0.970615i \(0.422644\pi\)
\(458\) 13.3537i 0.623976i
\(459\) 18.7212 34.1194i 0.873832 1.59255i
\(460\) −5.39424 14.9151i −0.251508 0.695418i
\(461\) −2.30344 −0.107282 −0.0536409 0.998560i \(-0.517083\pi\)
−0.0536409 + 0.998560i \(0.517083\pi\)
\(462\) 2.49791 14.7929i 0.116213 0.688226i
\(463\) −25.3450 −1.17788 −0.588941 0.808176i \(-0.700455\pi\)
−0.588941 + 0.808176i \(0.700455\pi\)
\(464\) 6.19127 0.287423
\(465\) 20.6034 + 6.36401i 0.955459 + 0.295124i
\(466\) 15.4812 0.717150
\(467\) 17.8054 0.823936 0.411968 0.911198i \(-0.364842\pi\)
0.411968 + 0.911198i \(0.364842\pi\)
\(468\) −10.6099 3.68832i −0.490442 0.170493i
\(469\) 37.9190 1.75094
\(470\) 13.3299 4.82095i 0.614863 0.222374i
\(471\) 4.24221 25.1228i 0.195471 1.15760i
\(472\) 4.58001i 0.210812i
\(473\) 10.0909 0.463981
\(474\) −3.06738 + 18.1653i −0.140890 + 0.834362i
\(475\) −21.8693 + 18.1991i −1.00343 + 0.835034i
\(476\) −34.6788 −1.58950
\(477\) 2.21255 6.36467i 0.101306 0.291418i
\(478\) −0.761904 −0.0348487
\(479\) 2.01777i 0.0921943i 0.998937 + 0.0460972i \(0.0146784\pi\)
−0.998937 + 0.0460972i \(0.985322\pi\)
\(480\) 3.81059 0.692413i 0.173929 0.0316042i
\(481\) 7.11223 0.324290
\(482\) 18.2543i 0.831462i
\(483\) −56.0898 9.47127i −2.55217 0.430958i
\(484\) −7.50053 −0.340933
\(485\) 1.42510 + 3.94039i 0.0647103 + 0.178924i
\(486\) 10.4464 + 11.5704i 0.473857 + 0.524842i
\(487\) −3.07265 −0.139235 −0.0696175 0.997574i \(-0.522178\pi\)
−0.0696175 + 0.997574i \(0.522178\pi\)
\(488\) 7.47286i 0.338281i
\(489\) 6.67350 39.5212i 0.301786 1.78721i
\(490\) 30.3604 10.9803i 1.37154 0.496038i
\(491\) −29.3658 −1.32526 −0.662631 0.748946i \(-0.730560\pi\)
−0.662631 + 0.748946i \(0.730560\pi\)
\(492\) −1.08920 + 6.45033i −0.0491048 + 0.290803i
\(493\) 46.3713i 2.08846i
\(494\) −21.3056 −0.958586
\(495\) −12.5480 + 0.156424i −0.563989 + 0.00703076i
\(496\) −4.94030 2.56778i −0.221826 0.115297i
\(497\) −68.9409 −3.09242
\(498\) 0.292285 1.73094i 0.0130976 0.0775653i
\(499\) 5.25604i 0.235293i 0.993056 + 0.117646i \(0.0375349\pi\)
−0.993056 + 0.117646i \(0.962465\pi\)
\(500\) 5.64927 9.64810i 0.252643 0.431476i
\(501\) 0.503066 2.97921i 0.0224753 0.133101i
\(502\) −11.4833 −0.512526
\(503\) 36.0788 1.60868 0.804338 0.594172i \(-0.202520\pi\)
0.804338 + 0.594172i \(0.202520\pi\)
\(504\) 4.56101 13.1203i 0.203163 0.584424i
\(505\) −0.0519488 0.143638i −0.00231169 0.00639183i
\(506\) 13.2689i 0.589874i
\(507\) −1.74077 0.293944i −0.0773101 0.0130545i
\(508\) 14.8935 0.660794
\(509\) 19.4979 0.864229 0.432115 0.901819i \(-0.357768\pi\)
0.432115 + 0.901819i \(0.357768\pi\)
\(510\) 5.18602 + 28.5405i 0.229641 + 1.26379i
\(511\) 53.6427i 2.37301i
\(512\) −1.00000 −0.0441942
\(513\) 25.9217 + 14.2232i 1.14447 + 0.627969i
\(514\) −16.8528 −0.743346
\(515\) −3.26869 9.03792i −0.144036 0.398258i
\(516\) 9.21267 + 1.55564i 0.405565 + 0.0684834i
\(517\) 11.8587 0.521544
\(518\) 8.79505i 0.386432i
\(519\) −8.00997 1.35256i −0.351599 0.0593706i
\(520\) 7.87326 2.84747i 0.345265 0.124870i
\(521\) 29.8201i 1.30644i 0.757168 + 0.653220i \(0.226583\pi\)
−0.757168 + 0.653220i \(0.773417\pi\)
\(522\) −17.5440 6.09882i −0.767879 0.266938i
\(523\) 39.1450 1.71169 0.855847 0.517230i \(-0.173037\pi\)
0.855847 + 0.517230i \(0.173037\pi\)
\(524\) 2.10228i 0.0918386i
\(525\) −20.1593 34.6623i −0.879824 1.51279i
\(526\) 8.89826i 0.387982i
\(527\) 19.2321 37.0017i 0.837763 1.61182i
\(528\) 3.19490 + 0.539487i 0.139040 + 0.0234782i
\(529\) −27.3114 −1.18745
\(530\) 1.70815 + 4.72302i 0.0741971 + 0.205155i
\(531\) 4.51161 12.9782i 0.195787 0.563205i
\(532\) 26.3468i 1.14228i
\(533\) 14.1413i 0.612527i
\(534\) −20.3052 3.42872i −0.878694 0.148375i
\(535\) −7.51918 + 2.71942i −0.325083 + 0.117571i
\(536\) 8.18959i 0.353736i
\(537\) −23.8889 4.03386i −1.03088 0.174074i
\(538\) 9.75034 0.420367
\(539\) 27.0095 1.16338
\(540\) −11.4800 1.79162i −0.494020 0.0770990i
\(541\) −34.5072 −1.48358 −0.741790 0.670632i \(-0.766023\pi\)
−0.741790 + 0.670632i \(0.766023\pi\)
\(542\) 11.9409i 0.512907i
\(543\) −2.92493 + 17.3217i −0.125521 + 0.743346i
\(544\) 7.48978i 0.321122i
\(545\) 1.51918 0.549433i 0.0650746 0.0235351i
\(546\) 4.99963 29.6083i 0.213964 1.26712i
\(547\) 35.9520i 1.53720i 0.639733 + 0.768598i \(0.279045\pi\)
−0.639733 + 0.768598i \(0.720955\pi\)
\(548\) 9.53533i 0.407329i
\(549\) −7.36127 + 21.1756i −0.314171 + 0.903752i
\(550\) 7.18960 5.98301i 0.306565 0.255117i
\(551\) −35.2299 −1.50085
\(552\) 2.04556 12.1140i 0.0870650 0.515608i
\(553\) −49.2474 −2.09421
\(554\) 0.764760 0.0324916
\(555\) 7.23827 1.31525i 0.307248 0.0558292i
\(556\) 12.9885i 0.550837i
\(557\) 1.42329i 0.0603066i 0.999545 + 0.0301533i \(0.00959955\pi\)
−0.999545 + 0.0301533i \(0.990400\pi\)
\(558\) 11.4697 + 12.1427i 0.485551 + 0.514043i
\(559\) 20.1973 0.854253
\(560\) 3.52121 + 9.73615i 0.148798 + 0.411427i
\(561\) −4.04064 + 23.9291i −0.170596 + 1.01029i
\(562\) 20.0130i 0.844198i
\(563\) −25.8966 −1.09141 −0.545706 0.837976i \(-0.683739\pi\)
−0.545706 + 0.837976i \(0.683739\pi\)
\(564\) 10.8266 + 1.82817i 0.455881 + 0.0769796i
\(565\) 11.9094 4.30718i 0.501031 0.181205i
\(566\) 16.2273i 0.682083i
\(567\) −25.8487 + 32.6856i −1.08554 + 1.37266i
\(568\) 14.8896i 0.624752i
\(569\) 28.1930 1.18191 0.590956 0.806704i \(-0.298751\pi\)
0.590956 + 0.806704i \(0.298751\pi\)
\(570\) −21.6832 + 3.94001i −0.908210 + 0.165029i
\(571\) 40.1560i 1.68047i −0.542219 0.840237i \(-0.682416\pi\)
0.542219 0.840237i \(-0.317584\pi\)
\(572\) 7.00428 0.292864
\(573\) −5.49100 + 32.5182i −0.229390 + 1.35847i
\(574\) −17.4872 −0.729903
\(575\) −22.6857 27.2607i −0.946059 1.13685i
\(576\) 2.83366 + 0.985067i 0.118069 + 0.0410445i
\(577\) 34.9593i 1.45537i 0.685909 + 0.727687i \(0.259405\pi\)
−0.685909 + 0.727687i \(0.740595\pi\)
\(578\) 39.0968 1.62621
\(579\) 2.57879 15.2719i 0.107171 0.634676i
\(580\) 13.0188 4.70844i 0.540577 0.195507i
\(581\) 4.69269 0.194685
\(582\) −0.540415 + 3.20039i −0.0224009 + 0.132660i
\(583\) 4.20174i 0.174018i
\(584\) 11.5855 0.479412
\(585\) −25.1151 + 0.313088i −1.03838 + 0.0129446i
\(586\) 11.1515 0.460665
\(587\) 20.1909i 0.833370i 0.909051 + 0.416685i \(0.136808\pi\)
−0.909051 + 0.416685i \(0.863192\pi\)
\(588\) 24.6588 + 4.16386i 1.01691 + 0.171715i
\(589\) 28.1116 + 14.6113i 1.15832 + 0.602049i
\(590\) 3.48308 + 9.63070i 0.143396 + 0.396490i
\(591\) −6.64380 + 39.3453i −0.273290 + 1.61845i
\(592\) −1.89952 −0.0780697
\(593\) 17.1815 0.705561 0.352781 0.935706i \(-0.385236\pi\)
0.352781 + 0.935706i \(0.385236\pi\)
\(594\) −8.52183 4.67591i −0.349655 0.191855i
\(595\) −72.9216 + 26.3731i −2.98949 + 1.08119i
\(596\) 0.757439i 0.0310259i
\(597\) 7.51142 44.4834i 0.307422 1.82058i
\(598\) 26.5580i 1.08604i
\(599\) 3.82810i 0.156412i −0.996937 0.0782059i \(-0.975081\pi\)
0.996937 0.0782059i \(-0.0249192\pi\)
\(600\) 7.48621 4.35392i 0.305623 0.177748i
\(601\) 29.1438i 1.18880i 0.804169 + 0.594401i \(0.202611\pi\)
−0.804169 + 0.594401i \(0.797389\pi\)
\(602\) 24.9761i 1.01795i
\(603\) 8.06729 23.2065i 0.328525 0.945043i
\(604\) 8.33372i 0.339094i
\(605\) −15.7719 + 5.70412i −0.641219 + 0.231906i
\(606\) 0.0196997 0.116663i 0.000800244 0.00473912i
\(607\) 12.0048i 0.487260i −0.969868 0.243630i \(-0.921662\pi\)
0.969868 0.243630i \(-0.0783382\pi\)
\(608\) 5.69026 0.230770
\(609\) 8.26713 48.9588i 0.335001 1.98391i
\(610\) −5.68308 15.7137i −0.230101 0.636230i
\(611\) 23.7355 0.960235
\(612\) −7.37794 + 21.2235i −0.298235 + 0.857910i
\(613\) −11.0775 −0.447414 −0.223707 0.974656i \(-0.571816\pi\)
−0.223707 + 0.974656i \(0.571816\pi\)
\(614\) 8.36560i 0.337608i
\(615\) 2.61512 + 14.3919i 0.105452 + 0.580337i
\(616\) 8.66156i 0.348984i
\(617\) 17.7290 0.713744 0.356872 0.934153i \(-0.383843\pi\)
0.356872 + 0.934153i \(0.383843\pi\)
\(618\) 1.23953 7.34061i 0.0498612 0.295283i
\(619\) 18.8323i 0.756932i −0.925615 0.378466i \(-0.876452\pi\)
0.925615 0.378466i \(-0.123548\pi\)
\(620\) −12.3411 1.64237i −0.495630 0.0659593i
\(621\) −17.7296 + 32.3121i −0.711463 + 1.29664i
\(622\) 0.660154i 0.0264698i
\(623\) 55.0488i 2.20548i
\(624\) 6.39467 + 1.07980i 0.255992 + 0.0432265i
\(625\) 4.54179 24.5840i 0.181671 0.983359i
\(626\) 18.7240 0.748361
\(627\) −18.1798 3.06982i −0.726030 0.122597i
\(628\) 14.7100i 0.586993i
\(629\) 14.2270i 0.567266i
\(630\) −0.387167 31.0576i −0.0154251 1.23736i
\(631\) 3.44163i 0.137009i −0.997651 0.0685046i \(-0.978177\pi\)
0.997651 0.0685046i \(-0.0218228\pi\)
\(632\) 10.6362i 0.423087i
\(633\) −21.3539 3.60580i −0.848740 0.143318i
\(634\) 13.9521 0.554111
\(635\) 31.3177 11.3265i 1.24281 0.449478i
\(636\) −0.647751 + 3.83604i −0.0256850 + 0.152109i
\(637\) 54.0603 2.14195
\(638\) 11.5819 0.458533
\(639\) −14.6672 + 42.1920i −0.580226 + 1.66909i
\(640\) −2.10277 + 0.760496i −0.0831193 + 0.0300612i
\(641\) −17.8008 −0.703089 −0.351544 0.936171i \(-0.614343\pi\)
−0.351544 + 0.936171i \(0.614343\pi\)
\(642\) −6.10709 1.03124i −0.241028 0.0406997i
\(643\) 39.9209 1.57433 0.787163 0.616745i \(-0.211549\pi\)
0.787163 + 0.616745i \(0.211549\pi\)
\(644\) 32.8419 1.29415
\(645\) 20.5552 3.73504i 0.809360 0.147067i
\(646\) 42.6188i 1.67681i
\(647\) 4.44082i 0.174587i −0.996183 0.0872933i \(-0.972178\pi\)
0.996183 0.0872933i \(-0.0278217\pi\)
\(648\) −7.05929 5.58269i −0.277315 0.219309i
\(649\) 8.56776i 0.336314i
\(650\) 14.3902 11.9752i 0.564429 0.469704i
\(651\) −26.9020 + 35.6377i −1.05437 + 1.39675i
\(652\) 23.1406i 0.906254i
\(653\) 1.38460 0.0541836 0.0270918 0.999633i \(-0.491375\pi\)
0.0270918 + 0.999633i \(0.491375\pi\)
\(654\) 1.23388 + 0.208352i 0.0482486 + 0.00814721i
\(655\) −1.59878 4.42062i −0.0624694 0.172728i
\(656\) 3.77682i 0.147460i
\(657\) −32.8294 11.4125i −1.28080 0.445244i
\(658\) 29.3515i 1.14424i
\(659\) 13.6889i 0.533244i −0.963801 0.266622i \(-0.914093\pi\)
0.963801 0.266622i \(-0.0859075\pi\)
\(660\) 7.12841 1.29529i 0.277473 0.0504190i
\(661\) −12.5113 −0.486635 −0.243317 0.969947i \(-0.578236\pi\)
−0.243317 + 0.969947i \(0.578236\pi\)
\(662\) 6.38971i 0.248343i
\(663\) −8.08745 + 47.8947i −0.314091 + 1.86008i
\(664\) 1.01351i 0.0393317i
\(665\) −20.0366 55.4012i −0.776986 2.14837i
\(666\) 5.38259 + 1.87115i 0.208571 + 0.0725056i
\(667\) 43.9150i 1.70040i
\(668\) 1.74440i 0.0674927i
\(669\) −18.3898 3.10529i −0.710991 0.120057i
\(670\) 6.22815 + 17.2208i 0.240614 + 0.665298i
\(671\) 13.9794i 0.539668i
\(672\) −1.33529 + 7.90771i −0.0515099 + 0.305047i
\(673\) 5.78515 0.223001 0.111501 0.993764i \(-0.464434\pi\)
0.111501 + 0.993764i \(0.464434\pi\)
\(674\) −18.0566 −0.695515
\(675\) −25.5023 + 4.96312i −0.981584 + 0.191031i
\(676\) 1.01926 0.0392023
\(677\) 2.68779i 0.103300i −0.998665 0.0516500i \(-0.983552\pi\)
0.998665 0.0516500i \(-0.0164480\pi\)
\(678\) 9.67280 + 1.63334i 0.371482 + 0.0627280i
\(679\) −8.67646 −0.332972
\(680\) −5.69595 15.7493i −0.218430 0.603958i
\(681\) 31.6203 + 5.33938i 1.21169 + 0.204605i
\(682\) −9.24175 4.80351i −0.353885 0.183936i
\(683\) 48.7180 1.86414 0.932071 0.362275i \(-0.118000\pi\)
0.932071 + 0.362275i \(0.118000\pi\)
\(684\) −16.1243 5.60528i −0.616527 0.214323i
\(685\) 7.25158 + 20.0506i 0.277069 + 0.766095i
\(686\) 34.4404i 1.31494i
\(687\) −3.85106 + 22.8064i −0.146927 + 0.870117i
\(688\) −5.39424 −0.205653
\(689\) 8.40989i 0.320391i
\(690\) −4.91132 27.0287i −0.186971 1.02896i
\(691\) −14.1466 −0.538162 −0.269081 0.963118i \(-0.586720\pi\)
−0.269081 + 0.963118i \(0.586720\pi\)
\(692\) 4.69003 0.178288
\(693\) 8.53222 24.5439i 0.324112 0.932347i
\(694\) 9.00187i 0.341706i
\(695\) 9.87773 + 27.3119i 0.374684 + 1.03600i
\(696\) 10.5739 + 1.78550i 0.400803 + 0.0676792i
\(697\) 28.2875 1.07147
\(698\) −7.59014 −0.287291
\(699\) 26.4398 + 4.46461i 1.00005 + 0.168867i
\(700\) 14.8086 + 17.7950i 0.559712 + 0.672589i
\(701\) 33.4256i 1.26247i 0.775593 + 0.631234i \(0.217451\pi\)
−0.775593 + 0.631234i \(0.782549\pi\)
\(702\) −17.0567 9.35896i −0.643762 0.353231i
\(703\) 10.8087 0.407659
\(704\) −1.87069 −0.0705042
\(705\) 24.1561 4.38935i 0.909772 0.165313i
\(706\) 15.9984i 0.602109i
\(707\) 0.316282 0.0118950
\(708\) −1.32083 + 7.82207i −0.0496397 + 0.293971i
\(709\) 0.905420i 0.0340037i 0.999855 + 0.0170019i \(0.00541213\pi\)
−0.999855 + 0.0170019i \(0.994588\pi\)
\(710\) −11.3234 31.3093i −0.424961 1.17502i
\(711\) −10.4774 + 30.1395i −0.392933 + 1.13032i
\(712\) 11.8892 0.445566
\(713\) −18.2134 + 35.0418i −0.682096 + 1.31232i
\(714\) −59.2270 10.0010i −2.21652 0.374279i
\(715\) 14.7284 5.32673i 0.550811 0.199208i
\(716\) 13.9875 0.522738
\(717\) −1.30123 0.219725i −0.0485955 0.00820579i
\(718\) 20.9131i 0.780470i
\(719\) −3.58919 −0.133854 −0.0669272 0.997758i \(-0.521320\pi\)
−0.0669272 + 0.997758i \(0.521320\pi\)
\(720\) 6.70768 0.0836188i 0.249981 0.00311629i
\(721\) 19.9009 0.741147
\(722\) −13.3790 −0.497916
\(723\) 5.26436 31.1761i 0.195784 1.15945i
\(724\) 10.1423i 0.376935i
\(725\) 23.7949 19.8015i 0.883719 0.735410i
\(726\) −12.8100 2.16308i −0.475422 0.0802793i
\(727\) 12.1901i 0.452107i 0.974115 + 0.226053i \(0.0725824\pi\)
−0.974115 + 0.226053i \(0.927418\pi\)
\(728\) 17.3364i 0.642528i
\(729\) 14.5043 + 22.7733i 0.537197 + 0.843457i
\(730\) 24.3617 8.81073i 0.901666 0.326100i
\(731\) 40.4017i 1.49431i
\(732\) 2.15510 12.7627i 0.0796547 0.471723i
\(733\) 24.0067i 0.886708i 0.896347 + 0.443354i \(0.146211\pi\)
−0.896347 + 0.443354i \(0.853789\pi\)
\(734\) 21.3709 0.788816
\(735\) 55.0184 9.99726i 2.02938 0.368755i
\(736\) 7.09305i 0.261453i
\(737\) 15.3201i 0.564325i
\(738\) −3.72042 + 10.7022i −0.136950 + 0.393954i
\(739\) 3.10103i 0.114073i −0.998372 0.0570366i \(-0.981835\pi\)
0.998372 0.0570366i \(-0.0181652\pi\)
\(740\) −3.99425 + 1.44457i −0.146832 + 0.0531036i
\(741\) −36.3873 6.14433i −1.33672 0.225718i
\(742\) −10.3998 −0.381787
\(743\) 42.2873i 1.55137i 0.631119 + 0.775686i \(0.282596\pi\)
−0.631119 + 0.775686i \(0.717404\pi\)
\(744\) −7.69688 5.81017i −0.282181 0.213011i
\(745\) 0.576029 + 1.59272i 0.0211041 + 0.0583528i
\(746\) 4.72525i 0.173004i
\(747\) 0.998371 2.87193i 0.0365285 0.105079i
\(748\) 14.0110i 0.512294i
\(749\) 16.5567i 0.604969i
\(750\) 12.4307 14.8485i 0.453903 0.542192i
\(751\) 10.7908 0.393764 0.196882 0.980427i \(-0.436918\pi\)
0.196882 + 0.980427i \(0.436918\pi\)
\(752\) −6.33921 −0.231167
\(753\) −19.6121 3.31167i −0.714703 0.120684i
\(754\) 23.1815 0.844222
\(755\) 6.33776 + 17.5239i 0.230655 + 0.637760i
\(756\) 11.5734 21.0924i 0.420920 0.767124i
\(757\) −20.2869 −0.737340 −0.368670 0.929560i \(-0.620187\pi\)
−0.368670 + 0.929560i \(0.620187\pi\)
\(758\) 5.68757 0.206582
\(759\) 3.82661 22.6616i 0.138897 0.822563i
\(760\) 11.9653 4.32742i 0.434027 0.156972i
\(761\) −30.3962 −1.10186 −0.550931 0.834550i \(-0.685727\pi\)
−0.550931 + 0.834550i \(0.685727\pi\)
\(762\) 25.4363 + 4.29515i 0.921459 + 0.155597i
\(763\) 3.34513i 0.121102i
\(764\) 19.0402i 0.688850i
\(765\) 0.626286 + 50.2391i 0.0226434 + 1.81640i
\(766\) 13.3422i 0.482072i
\(767\) 17.1486i 0.619200i
\(768\) −1.70787 0.288390i −0.0616276 0.0104064i
\(769\) 45.1078 1.62663 0.813314 0.581825i \(-0.197661\pi\)
0.813314 + 0.581825i \(0.197661\pi\)
\(770\) 6.58708 + 18.2133i 0.237382 + 0.656361i
\(771\) −28.7825 4.86018i −1.03658 0.175035i
\(772\) 8.94203i 0.321831i
\(773\) 26.1504i 0.940564i 0.882516 + 0.470282i \(0.155848\pi\)
−0.882516 + 0.470282i \(0.844152\pi\)
\(774\) 15.2854 + 5.31368i 0.549424 + 0.190996i
\(775\) −27.1995 + 5.93182i −0.977035 + 0.213077i
\(776\) 1.87390i 0.0672692i
\(777\) −2.53640 + 15.0208i −0.0909930 + 0.538869i
\(778\) −26.3747 −0.945581
\(779\) 21.4911i 0.769997i
\(780\) 14.2677 2.59255i 0.510866 0.0928283i
\(781\) 27.8537i 0.996683i
\(782\) −53.1254 −1.89976
\(783\) −28.2040 15.4755i −1.00793 0.553050i
\(784\) −14.4383 −0.515653
\(785\) 11.1869 + 30.9318i 0.399277 + 1.10400i
\(786\) 0.606277 3.59043i 0.0216252 0.128066i
\(787\) −22.0946 −0.787588 −0.393794 0.919199i \(-0.628838\pi\)
−0.393794 + 0.919199i \(0.628838\pi\)
\(788\) 23.0376i 0.820680i
\(789\) 2.56617 15.1971i 0.0913580 0.541031i
\(790\) −8.08881 22.3656i −0.287787 0.795731i
\(791\) 26.2236i 0.932403i
\(792\) 5.30089 + 1.84275i 0.188359 + 0.0654793i
\(793\) 27.9801i 0.993603i
\(794\) 0.462918i 0.0164283i
\(795\) 1.55522 + 8.55894i 0.0551581 + 0.303554i
\(796\) 26.0461i 0.923178i
\(797\) 15.1280i 0.535860i 0.963438 + 0.267930i \(0.0863396\pi\)
−0.963438 + 0.267930i \(0.913660\pi\)
\(798\) 7.59814 44.9969i 0.268971 1.59287i
\(799\) 47.4793i 1.67970i
\(800\) −3.84329 + 3.19830i −0.135881 + 0.113077i
\(801\) −33.6900 11.7117i −1.19038 0.413811i
\(802\) −21.9242 −0.774170
\(803\) 21.6729 0.764818
\(804\) −2.36179 + 13.9868i −0.0832940 + 0.493276i
\(805\) 69.0590 24.9761i 2.43401 0.880293i
\(806\) −18.4976 9.61435i −0.651550 0.338651i
\(807\) 16.6523 + 2.81190i 0.586190 + 0.0989836i
\(808\) 0.0683091i 0.00240311i
\(809\) −1.94130 −0.0682523 −0.0341262 0.999418i \(-0.510865\pi\)
−0.0341262 + 0.999418i \(0.510865\pi\)
\(810\) −19.0897 6.37057i −0.670743 0.223839i
\(811\) −11.1717 −0.392291 −0.196146 0.980575i \(-0.562843\pi\)
−0.196146 + 0.980575i \(0.562843\pi\)
\(812\) 28.6665i 1.00600i
\(813\) 3.44364 20.3936i 0.120774 0.715235i
\(814\) −3.55340 −0.124547
\(815\) 17.5983 + 48.6593i 0.616442 + 1.70446i
\(816\) 2.15998 12.7916i 0.0756143 0.447796i
\(817\) 30.6946 1.07387
\(818\) 29.5580i 1.03347i
\(819\) 17.0775 49.1254i 0.596735 1.71658i
\(820\) −2.87225 7.94178i −0.100303 0.277339i
\(821\) −17.4325 −0.608400 −0.304200 0.952608i \(-0.598389\pi\)
−0.304200 + 0.952608i \(0.598389\pi\)
\(822\) −2.74989 + 16.2851i −0.0959135 + 0.568009i
\(823\) 32.8244 1.14419 0.572093 0.820189i \(-0.306132\pi\)
0.572093 + 0.820189i \(0.306132\pi\)
\(824\) 4.29810i 0.149731i
\(825\) 14.0044 8.14482i 0.487569 0.283566i
\(826\) −21.2061 −0.737855
\(827\) 14.8857i 0.517626i −0.965927 0.258813i \(-0.916669\pi\)
0.965927 0.258813i \(-0.0833314\pi\)
\(828\) 6.98713 20.0993i 0.242820 0.698500i
\(829\) 22.5880i 0.784512i −0.919856 0.392256i \(-0.871695\pi\)
0.919856 0.392256i \(-0.128305\pi\)
\(830\) 0.770767 + 2.13117i 0.0267537 + 0.0739740i
\(831\) 1.30611 + 0.220549i 0.0453086 + 0.00765077i
\(832\) −3.74423 −0.129808
\(833\) 108.140i 3.74682i
\(834\) −3.74576 + 22.1828i −0.129705 + 0.768127i
\(835\) 1.32661 + 3.66807i 0.0459091 + 0.126939i
\(836\) 10.6447 0.368154
\(837\) 16.0870 + 24.0460i 0.556046 + 0.831151i
\(838\) 14.8158i 0.511802i
\(839\) 47.8538i 1.65210i −0.563600 0.826048i \(-0.690584\pi\)
0.563600 0.826048i \(-0.309416\pi\)
\(840\) 3.20598 + 17.6436i 0.110617 + 0.608762i
\(841\) 9.33184 0.321788
\(842\) −6.36850 −0.219473
\(843\) −5.77155 + 34.1797i −0.198783 + 1.17721i
\(844\) 12.5032 0.430378
\(845\) 2.14327 0.775142i 0.0737307 0.0266657i
\(846\) 17.9632 + 6.24455i 0.617587 + 0.214692i
\(847\) 34.7286i 1.19329i
\(848\) 2.24609i 0.0771312i
\(849\) −4.67978 + 27.7141i −0.160610 + 0.951146i
\(850\) −23.9546 28.7854i −0.821634 0.987332i
\(851\) 13.4734i 0.461861i
\(852\) 4.29400 25.4295i 0.147110 0.871199i
\(853\) 24.3315i 0.833095i −0.909114 0.416548i \(-0.863240\pi\)
0.909114 0.416548i \(-0.136760\pi\)
\(854\) 34.6005 1.18400
\(855\) −38.1684 + 0.475812i −1.30533 + 0.0162724i
\(856\) 3.57584 0.122220
\(857\) −37.7357 −1.28903 −0.644514 0.764592i \(-0.722940\pi\)
−0.644514 + 0.764592i \(0.722940\pi\)
\(858\) 11.9624 + 2.01996i 0.408390 + 0.0689604i
\(859\) 51.9973i 1.77413i 0.461649 + 0.887063i \(0.347258\pi\)
−0.461649 + 0.887063i \(0.652742\pi\)
\(860\) −11.3428 + 4.10230i −0.386788 + 0.139887i
\(861\) −29.8660 5.04314i −1.01783 0.171870i
\(862\) 3.42192i 0.116551i
\(863\) 6.11060i 0.208007i −0.994577 0.104004i \(-0.966835\pi\)
0.994577 0.104004i \(-0.0331654\pi\)
\(864\) 4.55545 + 2.49957i 0.154980 + 0.0850371i
\(865\) 9.86205 3.56675i 0.335320 0.121273i
\(866\) −9.25300 −0.314430
\(867\) 66.7724 + 11.2751i 2.26771 + 0.382924i
\(868\) 11.8892 22.8743i 0.403546 0.776405i
\(869\) 19.8971i 0.674962i
\(870\) 23.5924 4.28692i 0.799856 0.145340i
\(871\) 30.6637i 1.03900i
\(872\) −0.722467 −0.0244658
\(873\) −1.84592 + 5.31001i −0.0624750 + 0.179717i
\(874\) 40.3613i 1.36524i
\(875\) 44.6721 + 26.1570i 1.51019 + 0.884267i
\(876\) 19.7866 + 3.34114i 0.668527 + 0.112887i
\(877\) 45.1985i 1.52624i −0.646254 0.763122i \(-0.723665\pi\)
0.646254 0.763122i \(-0.276335\pi\)
\(878\) 1.50233 0.0507013
\(879\) 19.0454 + 3.21599i 0.642385 + 0.108473i
\(880\) −3.93363 + 1.42265i −0.132602 + 0.0479575i
\(881\) −21.6660 −0.729945 −0.364973 0.931018i \(-0.618922\pi\)
−0.364973 + 0.931018i \(0.618922\pi\)
\(882\) 40.9133 + 14.2227i 1.37762 + 0.478903i
\(883\) 5.80117 0.195225 0.0976125 0.995224i \(-0.468879\pi\)
0.0976125 + 0.995224i \(0.468879\pi\)
\(884\) 28.0435i 0.943204i
\(885\) 3.17125 + 17.4525i 0.106601 + 0.586659i
\(886\) −16.4755 −0.553504
\(887\) 9.42333 0.316404 0.158202 0.987407i \(-0.449430\pi\)
0.158202 + 0.987407i \(0.449430\pi\)
\(888\) −3.24413 0.547801i −0.108866 0.0183830i
\(889\) 68.9594i 2.31282i
\(890\) 25.0003 9.04168i 0.838010 0.303078i
\(891\) −13.2057 10.4435i −0.442408 0.349869i
\(892\) 10.7677 0.360528
\(893\) 36.0718 1.20710
\(894\) −0.218438 + 1.29361i −0.00730565 + 0.0432648i
\(895\) 29.4125 10.6375i 0.983153 0.355571i
\(896\) 4.63015i 0.154682i
\(897\) 7.65906 45.3577i 0.255729 1.51445i
\(898\) 36.9554 1.23322
\(899\) −30.5867 15.8978i −1.02012 0.530221i
\(900\) 14.0411 5.27700i 0.468038 0.175900i
\(901\) 16.8228 0.560447
\(902\) 7.06524i 0.235247i
\(903\) −7.20286 + 42.6561i −0.239696 + 1.41951i
\(904\) −5.66365 −0.188370
\(905\) −7.71316 21.3269i −0.256394 0.708930i
\(906\) −2.40336 + 14.2329i −0.0798463 + 0.472858i
\(907\) 9.16441i 0.304299i 0.988357 + 0.152150i \(0.0486195\pi\)
−0.988357 + 0.152150i \(0.951380\pi\)
\(908\) −18.5144 −0.614424
\(909\) 0.0672890 0.193565i 0.00223184 0.00642015i
\(910\) 13.1842 + 36.4544i 0.437053 + 1.20845i
\(911\) −29.4678 −0.976311 −0.488155 0.872757i \(-0.662330\pi\)
−0.488155 + 0.872757i \(0.662330\pi\)
\(912\) 9.71824 + 1.64101i 0.321803 + 0.0543394i
\(913\) 1.89595i 0.0627469i
\(914\) −10.2884 −0.340311
\(915\) −5.17431 28.4760i −0.171057 0.941387i
\(916\) 13.3537i 0.441218i
\(917\) 9.73388 0.321441
\(918\) −18.7212 + 34.1194i −0.617893 + 1.12611i
\(919\) −20.2080 −0.666601 −0.333301 0.942821i \(-0.608162\pi\)
−0.333301 + 0.942821i \(0.608162\pi\)
\(920\) 5.39424 + 14.9151i 0.177843 + 0.491735i
\(921\) −2.41255 + 14.2874i −0.0794963 + 0.470785i
\(922\) 2.30344 0.0758597
\(923\) 55.7499i 1.83503i
\(924\) −2.49791 + 14.7929i −0.0821751 + 0.486649i
\(925\) −7.30040 + 6.07522i −0.240036 + 0.199752i
\(926\) 25.3450 0.832888
\(927\) 4.23392 12.1794i 0.139060 0.400023i
\(928\) −6.19127 −0.203238
\(929\) 37.6365 1.23481 0.617407 0.786644i \(-0.288183\pi\)
0.617407 + 0.786644i \(0.288183\pi\)
\(930\) −20.6034 6.36401i −0.675612 0.208684i
\(931\) 82.1576 2.69261
\(932\) −15.4812 −0.507102
\(933\) 0.190382 1.12746i 0.00623282 0.0369114i
\(934\) −17.8054 −0.582611
\(935\) −10.6553 29.4620i −0.348467 0.963510i
\(936\) 10.6099 + 3.68832i 0.346795 + 0.120556i
\(937\) 5.14759i 0.168164i 0.996459 + 0.0840822i \(0.0267958\pi\)
−0.996459 + 0.0840822i \(0.973204\pi\)
\(938\) −37.9190 −1.23810
\(939\) 31.9782 + 5.39981i 1.04357 + 0.176216i
\(940\) −13.3299 + 4.82095i −0.434774 + 0.157242i
\(941\) −34.0980 −1.11156 −0.555782 0.831328i \(-0.687581\pi\)
−0.555782 + 0.831328i \(0.687581\pi\)
\(942\) −4.24221 + 25.1228i −0.138219 + 0.818545i
\(943\) −26.7892 −0.872375
\(944\) 4.58001i 0.149066i
\(945\) 8.29546 53.1541i 0.269851 1.72910i
\(946\) −10.0909 −0.328084
\(947\) 51.3009i 1.66705i −0.552479 0.833527i \(-0.686318\pi\)
0.552479 0.833527i \(-0.313682\pi\)
\(948\) 3.06738 18.1653i 0.0996240 0.589983i
\(949\) 43.3788 1.40814
\(950\) 21.8693 18.1991i 0.709534 0.590458i
\(951\) 23.8285 + 4.02366i 0.772692 + 0.130476i
\(952\) 34.6788 1.12395
\(953\) 43.1734i 1.39852i −0.714866 0.699261i \(-0.753513\pi\)
0.714866 0.699261i \(-0.246487\pi\)
\(954\) −2.21255 + 6.36467i −0.0716341 + 0.206064i
\(955\) −14.4800 40.0371i −0.468561 1.29557i
\(956\) 0.761904 0.0246417
\(957\) 19.7805 + 3.34011i 0.639412 + 0.107970i
\(958\) 2.01777i 0.0651912i
\(959\) −44.1500 −1.42568
\(960\) −3.81059 + 0.692413i −0.122986 + 0.0223475i
\(961\) 17.8130 + 25.3712i 0.574614 + 0.818424i
\(962\) −7.11223 −0.229307
\(963\) −10.1327 3.52245i −0.326523 0.113509i
\(964\) 18.2543i 0.587932i
\(965\) 6.80038 + 18.8030i 0.218912 + 0.605291i
\(966\) 56.0898 + 9.47127i 1.80466 + 0.304733i
\(967\) 0.964929 0.0310300 0.0155150 0.999880i \(-0.495061\pi\)
0.0155150 + 0.999880i \(0.495061\pi\)
\(968\) 7.50053 0.241076
\(969\) −12.2908 + 72.7875i −0.394838 + 2.33827i
\(970\) −1.42510 3.94039i −0.0457571 0.126518i
\(971\) 15.5198i 0.498054i 0.968496 + 0.249027i \(0.0801109\pi\)
−0.968496 + 0.249027i \(0.919889\pi\)
\(972\) −10.4464 11.5704i −0.335068 0.371120i
\(973\) −60.1389 −1.92796
\(974\) 3.07265 0.0984540
\(975\) 28.0301 16.3021i 0.897682 0.522084i
\(976\) 7.47286i 0.239201i
\(977\) −22.2030 −0.710336 −0.355168 0.934803i \(-0.615576\pi\)
−0.355168 + 0.934803i \(0.615576\pi\)
\(978\) −6.67350 + 39.5212i −0.213395 + 1.26375i
\(979\) 22.2410 0.710824
\(980\) −30.3604 + 10.9803i −0.969828 + 0.350752i
\(981\) 2.04723 + 0.711678i 0.0653629 + 0.0227221i
\(982\) 29.3658 0.937101
\(983\) 58.4300i 1.86363i −0.362935 0.931814i \(-0.618225\pi\)
0.362935 0.931814i \(-0.381775\pi\)
\(984\) 1.08920 6.45033i 0.0347223 0.205629i
\(985\) −17.5200 48.4427i −0.558233 1.54351i
\(986\) 46.3713i 1.47676i
\(987\) −8.46468 + 50.1287i −0.269434 + 1.59561i
\(988\) 21.3056 0.677822
\(989\) 38.2616i 1.21665i
\(990\) 12.5480 0.156424i 0.398801 0.00497150i
\(991\) 16.9793i 0.539366i 0.962949 + 0.269683i \(0.0869189\pi\)
−0.962949 + 0.269683i \(0.913081\pi\)
\(992\) 4.94030 + 2.56778i 0.156855 + 0.0815270i
\(993\) 1.84273 10.9128i 0.0584772 0.346308i
\(994\) 68.9409 2.18667
\(995\) 19.8079 + 54.7689i 0.627953 + 1.73629i
\(996\) −0.292285 + 1.73094i −0.00926140 + 0.0548469i
\(997\) 29.9879i 0.949727i 0.880059 + 0.474864i \(0.157503\pi\)
−0.880059 + 0.474864i \(0.842497\pi\)
\(998\) 5.25604i 0.166377i
\(999\) 8.65316 + 4.74797i 0.273774 + 0.150219i
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 930.2.e.a.929.1 32
3.2 odd 2 930.2.e.b.929.2 yes 32
5.4 even 2 930.2.e.b.929.32 yes 32
15.14 odd 2 inner 930.2.e.a.929.31 yes 32
31.30 odd 2 inner 930.2.e.a.929.32 yes 32
93.92 even 2 930.2.e.b.929.31 yes 32
155.154 odd 2 930.2.e.b.929.1 yes 32
465.464 even 2 inner 930.2.e.a.929.2 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.e.a.929.1 32 1.1 even 1 trivial
930.2.e.a.929.2 yes 32 465.464 even 2 inner
930.2.e.a.929.31 yes 32 15.14 odd 2 inner
930.2.e.a.929.32 yes 32 31.30 odd 2 inner
930.2.e.b.929.1 yes 32 155.154 odd 2
930.2.e.b.929.2 yes 32 3.2 odd 2
930.2.e.b.929.31 yes 32 93.92 even 2
930.2.e.b.929.32 yes 32 5.4 even 2