Properties

Label 525.2.b.h.251.2
Level $525$
Weight $2$
Character 525.251
Analytic conductor $4.192$
Analytic rank $0$
Dimension $8$
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] = [525,2,Mod(251,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.b (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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.624529833984.7
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{6} - 2x^{4} - 18x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.2
Root \(0.777403 - 1.54779i\) of defining polynomial
Character \(\chi\) \(=\) 525.251
Dual form 525.2.b.h.251.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.40651i q^{2} +(0.777403 + 1.54779i) q^{3} -3.79129 q^{4} +(3.72476 - 1.87083i) q^{6} +(-1.00000 + 2.44949i) q^{7} +4.31075i q^{8} +(-1.79129 + 2.40651i) q^{9} +O(q^{10})\) \(q-2.40651i q^{2} +(0.777403 + 1.54779i) q^{3} -3.79129 q^{4} +(3.72476 - 1.87083i) q^{6} +(-1.00000 + 2.44949i) q^{7} +4.31075i q^{8} +(-1.79129 + 2.40651i) q^{9} +4.31075i q^{11} +(-2.94736 - 5.86811i) q^{12} -2.44949i q^{13} +(5.89472 + 2.40651i) q^{14} +2.79129 q^{16} +5.89472 q^{17} +(5.79129 + 4.31075i) q^{18} +6.83723i q^{19} +(-4.56869 + 0.356455i) q^{21} +10.3739 q^{22} -0.502268i q^{23} +(-6.67212 + 3.35119i) q^{24} -5.89472 q^{26} +(-5.11732 - 0.901703i) q^{27} +(3.79129 - 9.28672i) q^{28} +0.502268i q^{29} +4.38774i q^{31} +1.90424i q^{32} +(-6.67212 + 3.35119i) q^{33} -14.1857i q^{34} +(6.79129 - 9.12377i) q^{36} -0.582576 q^{37} +16.4539 q^{38} +(3.79129 - 1.90424i) q^{39} +4.66442 q^{41} +(0.857812 + 10.9946i) q^{42} +2.58258 q^{43} -16.3433i q^{44} -1.20871 q^{46} +5.89472 q^{47} +(2.16996 + 4.32032i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(4.58258 + 9.12377i) q^{51} +9.28672i q^{52} -13.4345i q^{53} +(-2.16996 + 12.3149i) q^{54} +(-10.5591 - 4.31075i) q^{56} +(-10.5826 + 5.31529i) q^{57} +1.20871 q^{58} -10.5591 q^{59} -4.38774i q^{61} +10.5591 q^{62} +(-4.10343 - 6.79425i) q^{63} +10.1652 q^{64} +(8.06468 + 16.0565i) q^{66} -14.1652 q^{67} -22.3486 q^{68} +(0.777403 - 0.390465i) q^{69} +4.31075i q^{71} +(-10.3739 - 7.72180i) q^{72} +6.32599i q^{73} +1.40197i q^{74} -25.9219i q^{76} +(-10.5591 - 4.31075i) q^{77} +(-4.58258 - 9.12377i) q^{78} -8.58258 q^{79} +(-2.58258 - 8.62150i) q^{81} -11.2250i q^{82} +7.12502 q^{83} +(17.3212 - 1.35142i) q^{84} -6.21499i q^{86} +(-0.777403 + 0.390465i) q^{87} -18.5826 q^{88} +10.5591 q^{89} +(6.00000 + 2.44949i) q^{91} +1.90424i q^{92} +(-6.79129 + 3.41105i) q^{93} -14.1857i q^{94} +(-2.94736 + 1.48036i) q^{96} +0.511238i q^{97} +(-11.7894 + 12.0325i) q^{98} +(-10.3739 - 7.72180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 12 q^{4} - 8 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{4} - 8 q^{7} + 4 q^{9} + 4 q^{16} + 28 q^{18} - 12 q^{21} + 28 q^{22} + 12 q^{28} + 36 q^{36} + 32 q^{37} + 12 q^{39} - 16 q^{43} - 28 q^{46} - 40 q^{49} - 48 q^{57} + 28 q^{58} - 4 q^{63} + 8 q^{64} - 40 q^{67} - 28 q^{72} - 32 q^{79} + 16 q^{81} + 60 q^{84} - 112 q^{88} + 48 q^{91} - 36 q^{93} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.40651i 1.70166i −0.525442 0.850830i \(-0.676100\pi\)
0.525442 0.850830i \(-0.323900\pi\)
\(3\) 0.777403 + 1.54779i 0.448834 + 0.893615i
\(4\) −3.79129 −1.89564
\(5\) 0 0
\(6\) 3.72476 1.87083i 1.52063 0.763763i
\(7\) −1.00000 + 2.44949i −0.377964 + 0.925820i
\(8\) 4.31075i 1.52408i
\(9\) −1.79129 + 2.40651i −0.597096 + 0.802170i
\(10\) 0 0
\(11\) 4.31075i 1.29974i 0.760045 + 0.649870i \(0.225177\pi\)
−0.760045 + 0.649870i \(0.774823\pi\)
\(12\) −2.94736 5.86811i −0.850830 1.69398i
\(13\) 2.44949i 0.679366i −0.940540 0.339683i \(-0.889680\pi\)
0.940540 0.339683i \(-0.110320\pi\)
\(14\) 5.89472 + 2.40651i 1.57543 + 0.643167i
\(15\) 0 0
\(16\) 2.79129 0.697822
\(17\) 5.89472 1.42968 0.714840 0.699288i \(-0.246500\pi\)
0.714840 + 0.699288i \(0.246500\pi\)
\(18\) 5.79129 + 4.31075i 1.36502 + 1.01605i
\(19\) 6.83723i 1.56857i 0.620402 + 0.784284i \(0.286970\pi\)
−0.620402 + 0.784284i \(0.713030\pi\)
\(20\) 0 0
\(21\) −4.56869 + 0.356455i −0.996970 + 0.0777848i
\(22\) 10.3739 2.21172
\(23\) 0.502268i 0.104730i −0.998628 0.0523650i \(-0.983324\pi\)
0.998628 0.0523650i \(-0.0166759\pi\)
\(24\) −6.67212 + 3.35119i −1.36194 + 0.684059i
\(25\) 0 0
\(26\) −5.89472 −1.15605
\(27\) −5.11732 0.901703i −0.984828 0.173533i
\(28\) 3.79129 9.28672i 0.716486 1.75503i
\(29\) 0.502268i 0.0932688i 0.998912 + 0.0466344i \(0.0148496\pi\)
−0.998912 + 0.0466344i \(0.985150\pi\)
\(30\) 0 0
\(31\) 4.38774i 0.788062i 0.919097 + 0.394031i \(0.128920\pi\)
−0.919097 + 0.394031i \(0.871080\pi\)
\(32\) 1.90424i 0.336626i
\(33\) −6.67212 + 3.35119i −1.16147 + 0.583368i
\(34\) 14.1857i 2.43283i
\(35\) 0 0
\(36\) 6.79129 9.12377i 1.13188 1.52063i
\(37\) −0.582576 −0.0957749 −0.0478874 0.998853i \(-0.515249\pi\)
−0.0478874 + 0.998853i \(0.515249\pi\)
\(38\) 16.4539 2.66917
\(39\) 3.79129 1.90424i 0.607092 0.304923i
\(40\) 0 0
\(41\) 4.66442 0.728460 0.364230 0.931309i \(-0.381332\pi\)
0.364230 + 0.931309i \(0.381332\pi\)
\(42\) 0.857812 + 10.9946i 0.132363 + 1.69650i
\(43\) 2.58258 0.393839 0.196920 0.980420i \(-0.436906\pi\)
0.196920 + 0.980420i \(0.436906\pi\)
\(44\) 16.3433i 2.46384i
\(45\) 0 0
\(46\) −1.20871 −0.178215
\(47\) 5.89472 0.859833 0.429917 0.902869i \(-0.358543\pi\)
0.429917 + 0.902869i \(0.358543\pi\)
\(48\) 2.16996 + 4.32032i 0.313206 + 0.623584i
\(49\) −5.00000 4.89898i −0.714286 0.699854i
\(50\) 0 0
\(51\) 4.58258 + 9.12377i 0.641689 + 1.27758i
\(52\) 9.28672i 1.28784i
\(53\) 13.4345i 1.84537i −0.385551 0.922687i \(-0.625988\pi\)
0.385551 0.922687i \(-0.374012\pi\)
\(54\) −2.16996 + 12.3149i −0.295294 + 1.67584i
\(55\) 0 0
\(56\) −10.5591 4.31075i −1.41102 0.576048i
\(57\) −10.5826 + 5.31529i −1.40170 + 0.704027i
\(58\) 1.20871 0.158712
\(59\) −10.5591 −1.37468 −0.687342 0.726334i \(-0.741222\pi\)
−0.687342 + 0.726334i \(0.741222\pi\)
\(60\) 0 0
\(61\) 4.38774i 0.561793i −0.959738 0.280896i \(-0.909368\pi\)
0.959738 0.280896i \(-0.0906317\pi\)
\(62\) 10.5591 1.34101
\(63\) −4.10343 6.79425i −0.516984 0.855995i
\(64\) 10.1652 1.27064
\(65\) 0 0
\(66\) 8.06468 + 16.0565i 0.992693 + 1.97642i
\(67\) −14.1652 −1.73055 −0.865274 0.501299i \(-0.832856\pi\)
−0.865274 + 0.501299i \(0.832856\pi\)
\(68\) −22.3486 −2.71016
\(69\) 0.777403 0.390465i 0.0935884 0.0470064i
\(70\) 0 0
\(71\) 4.31075i 0.511592i 0.966731 + 0.255796i \(0.0823375\pi\)
−0.966731 + 0.255796i \(0.917662\pi\)
\(72\) −10.3739 7.72180i −1.22257 0.910022i
\(73\) 6.32599i 0.740401i 0.928952 + 0.370201i \(0.120711\pi\)
−0.928952 + 0.370201i \(0.879289\pi\)
\(74\) 1.40197i 0.162976i
\(75\) 0 0
\(76\) 25.9219i 2.97345i
\(77\) −10.5591 4.31075i −1.20333 0.491256i
\(78\) −4.58258 9.12377i −0.518875 1.03306i
\(79\) −8.58258 −0.965615 −0.482808 0.875726i \(-0.660383\pi\)
−0.482808 + 0.875726i \(0.660383\pi\)
\(80\) 0 0
\(81\) −2.58258 8.62150i −0.286953 0.957945i
\(82\) 11.2250i 1.23959i
\(83\) 7.12502 0.782073 0.391036 0.920375i \(-0.372117\pi\)
0.391036 + 0.920375i \(0.372117\pi\)
\(84\) 17.3212 1.35142i 1.88990 0.147452i
\(85\) 0 0
\(86\) 6.21499i 0.670180i
\(87\) −0.777403 + 0.390465i −0.0833464 + 0.0418622i
\(88\) −18.5826 −1.98091
\(89\) 10.5591 1.11927 0.559633 0.828740i \(-0.310942\pi\)
0.559633 + 0.828740i \(0.310942\pi\)
\(90\) 0 0
\(91\) 6.00000 + 2.44949i 0.628971 + 0.256776i
\(92\) 1.90424i 0.198531i
\(93\) −6.79129 + 3.41105i −0.704224 + 0.353709i
\(94\) 14.1857i 1.46314i
\(95\) 0 0
\(96\) −2.94736 + 1.48036i −0.300814 + 0.151089i
\(97\) 0.511238i 0.0519084i 0.999663 + 0.0259542i \(0.00826240\pi\)
−0.999663 + 0.0259542i \(0.991738\pi\)
\(98\) −11.7894 + 12.0325i −1.19091 + 1.21547i
\(99\) −10.3739 7.72180i −1.04261 0.776070i
\(100\) 0 0
\(101\) 13.0197 1.29551 0.647756 0.761848i \(-0.275708\pi\)
0.647756 + 0.761848i \(0.275708\pi\)
\(102\) 21.9564 11.0280i 2.17401 1.09194i
\(103\) 6.83723i 0.673692i −0.941560 0.336846i \(-0.890640\pi\)
0.941560 0.336846i \(-0.109360\pi\)
\(104\) 10.5591 1.03541
\(105\) 0 0
\(106\) −32.3303 −3.14020
\(107\) 1.00454i 0.0971121i 0.998820 + 0.0485561i \(0.0154620\pi\)
−0.998820 + 0.0485561i \(0.984538\pi\)
\(108\) 19.4012 + 3.41862i 1.86688 + 0.328956i
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 0 0
\(111\) −0.452896 0.901703i −0.0429870 0.0855859i
\(112\) −2.79129 + 6.83723i −0.263752 + 0.646058i
\(113\) 6.31982i 0.594519i 0.954797 + 0.297259i \(0.0960726\pi\)
−0.954797 + 0.297259i \(0.903927\pi\)
\(114\) 12.7913 + 25.4671i 1.19801 + 2.38521i
\(115\) 0 0
\(116\) 1.90424i 0.176804i
\(117\) 5.89472 + 4.38774i 0.544967 + 0.405647i
\(118\) 25.4107i 2.33924i
\(119\) −5.89472 + 14.4391i −0.540368 + 1.32363i
\(120\) 0 0
\(121\) −7.58258 −0.689325
\(122\) −10.5591 −0.955980
\(123\) 3.62614 + 7.21953i 0.326958 + 0.650963i
\(124\) 16.6352i 1.49388i
\(125\) 0 0
\(126\) −16.3504 + 9.87495i −1.45661 + 0.879730i
\(127\) 10.1652 0.902011 0.451006 0.892521i \(-0.351065\pi\)
0.451006 + 0.892521i \(0.351065\pi\)
\(128\) 20.6540i 1.82558i
\(129\) 2.00770 + 3.99728i 0.176768 + 0.351941i
\(130\) 0 0
\(131\) −5.89472 −0.515024 −0.257512 0.966275i \(-0.582903\pi\)
−0.257512 + 0.966275i \(0.582903\pi\)
\(132\) 25.2959 12.7053i 2.20173 1.10586i
\(133\) −16.7477 6.83723i −1.45221 0.592863i
\(134\) 34.0886i 2.94480i
\(135\) 0 0
\(136\) 25.4107i 2.17895i
\(137\) 1.00454i 0.0858233i 0.999079 + 0.0429116i \(0.0136634\pi\)
−0.999079 + 0.0429116i \(0.986337\pi\)
\(138\) −0.939657 1.87083i −0.0799889 0.159256i
\(139\) 2.44949i 0.207763i 0.994590 + 0.103882i \(0.0331263\pi\)
−0.994590 + 0.103882i \(0.966874\pi\)
\(140\) 0 0
\(141\) 4.58258 + 9.12377i 0.385922 + 0.768360i
\(142\) 10.3739 0.870555
\(143\) 10.5591 0.883000
\(144\) −5.00000 + 6.71726i −0.416667 + 0.559772i
\(145\) 0 0
\(146\) 15.2236 1.25991
\(147\) 3.69556 11.5474i 0.304805 0.952415i
\(148\) 2.20871 0.181555
\(149\) 6.31982i 0.517740i −0.965912 0.258870i \(-0.916650\pi\)
0.965912 0.258870i \(-0.0833501\pi\)
\(150\) 0 0
\(151\) 14.1652 1.15274 0.576372 0.817188i \(-0.304468\pi\)
0.576372 + 0.817188i \(0.304468\pi\)
\(152\) −29.4736 −2.39062
\(153\) −10.5591 + 14.1857i −0.853656 + 1.14685i
\(154\) −10.3739 + 25.4107i −0.835950 + 2.04765i
\(155\) 0 0
\(156\) −14.3739 + 7.21953i −1.15083 + 0.578025i
\(157\) 9.28672i 0.741161i 0.928800 + 0.370580i \(0.120841\pi\)
−0.928800 + 0.370580i \(0.879159\pi\)
\(158\) 20.6540i 1.64315i
\(159\) 20.7938 10.4440i 1.64905 0.828266i
\(160\) 0 0
\(161\) 1.23030 + 0.502268i 0.0969612 + 0.0395842i
\(162\) −20.7477 + 6.21499i −1.63010 + 0.488296i
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −17.6842 −1.38090
\(165\) 0 0
\(166\) 17.1464i 1.33082i
\(167\) −13.0197 −1.00750 −0.503749 0.863850i \(-0.668046\pi\)
−0.503749 + 0.863850i \(0.668046\pi\)
\(168\) −1.53659 19.6945i −0.118550 1.51946i
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) −16.4539 12.2474i −1.25826 0.936586i
\(172\) −9.79129 −0.746579
\(173\) 17.6842 1.34450 0.672251 0.740323i \(-0.265328\pi\)
0.672251 + 0.740323i \(0.265328\pi\)
\(174\) 0.939657 + 1.87083i 0.0712352 + 0.141827i
\(175\) 0 0
\(176\) 12.0325i 0.906987i
\(177\) −8.20871 16.3433i −0.617005 1.22844i
\(178\) 25.4107i 1.90461i
\(179\) 12.4300i 0.929061i −0.885557 0.464530i \(-0.846223\pi\)
0.885557 0.464530i \(-0.153777\pi\)
\(180\) 0 0
\(181\) 12.2474i 0.910346i 0.890403 + 0.455173i \(0.150423\pi\)
−0.890403 + 0.455173i \(0.849577\pi\)
\(182\) 5.89472 14.4391i 0.436946 1.07029i
\(183\) 6.79129 3.41105i 0.502026 0.252152i
\(184\) 2.16515 0.159617
\(185\) 0 0
\(186\) 8.20871 + 16.3433i 0.601892 + 1.19835i
\(187\) 25.4107i 1.85821i
\(188\) −22.3486 −1.62994
\(189\) 7.32603 11.6331i 0.532890 0.846184i
\(190\) 0 0
\(191\) 15.4436i 1.11746i −0.829350 0.558730i \(-0.811289\pi\)
0.829350 0.558730i \(-0.188711\pi\)
\(192\) 7.90242 + 15.7335i 0.570308 + 1.13547i
\(193\) −11.0000 −0.791797 −0.395899 0.918294i \(-0.629567\pi\)
−0.395899 + 0.918294i \(0.629567\pi\)
\(194\) 1.23030 0.0883304
\(195\) 0 0
\(196\) 18.9564 + 18.5734i 1.35403 + 1.32667i
\(197\) 18.7498i 1.33587i −0.744220 0.667934i \(-0.767179\pi\)
0.744220 0.667934i \(-0.232821\pi\)
\(198\) −18.5826 + 24.9648i −1.32061 + 1.77417i
\(199\) 19.0847i 1.35288i 0.736499 + 0.676439i \(0.236478\pi\)
−0.736499 + 0.676439i \(0.763522\pi\)
\(200\) 0 0
\(201\) −11.0120 21.9246i −0.776729 1.54644i
\(202\) 31.3321i 2.20452i
\(203\) −1.23030 0.502268i −0.0863501 0.0352523i
\(204\) −17.3739 34.5908i −1.21641 2.42184i
\(205\) 0 0
\(206\) −16.4539 −1.14639
\(207\) 1.20871 + 0.899706i 0.0840113 + 0.0625339i
\(208\) 6.83723i 0.474077i
\(209\) −29.4736 −2.03873
\(210\) 0 0
\(211\) 12.7477 0.877590 0.438795 0.898587i \(-0.355405\pi\)
0.438795 + 0.898587i \(0.355405\pi\)
\(212\) 50.9341i 3.49817i
\(213\) −6.67212 + 3.35119i −0.457166 + 0.229620i
\(214\) 2.41742 0.165252
\(215\) 0 0
\(216\) 3.88702 22.0595i 0.264478 1.50096i
\(217\) −10.7477 4.38774i −0.729603 0.297859i
\(218\) 12.0325i 0.814947i
\(219\) −9.79129 + 4.91785i −0.661634 + 0.332317i
\(220\) 0 0
\(221\) 14.4391i 0.971276i
\(222\) −2.16996 + 1.08990i −0.145638 + 0.0731493i
\(223\) 2.44949i 0.164030i −0.996631 0.0820150i \(-0.973864\pi\)
0.996631 0.0820150i \(-0.0261355\pi\)
\(224\) −4.66442 1.90424i −0.311655 0.127233i
\(225\) 0 0
\(226\) 15.2087 1.01167
\(227\) 5.89472 0.391246 0.195623 0.980679i \(-0.437327\pi\)
0.195623 + 0.980679i \(0.437327\pi\)
\(228\) 40.1216 20.1518i 2.65712 1.33458i
\(229\) 18.5734i 1.22737i −0.789552 0.613684i \(-0.789687\pi\)
0.789552 0.613684i \(-0.210313\pi\)
\(230\) 0 0
\(231\) −1.53659 19.6945i −0.101100 1.29580i
\(232\) −2.16515 −0.142149
\(233\) 0.502268i 0.0329047i −0.999865 0.0164523i \(-0.994763\pi\)
0.999865 0.0164523i \(-0.00523717\pi\)
\(234\) 10.5591 14.1857i 0.690273 0.927348i
\(235\) 0 0
\(236\) 40.0327 2.60591
\(237\) −6.67212 13.2840i −0.433401 0.862888i
\(238\) 34.7477 + 14.1857i 2.25236 + 0.919522i
\(239\) 12.4300i 0.804029i −0.915633 0.402014i \(-0.868310\pi\)
0.915633 0.402014i \(-0.131690\pi\)
\(240\) 0 0
\(241\) 7.85971i 0.506288i 0.967429 + 0.253144i \(0.0814647\pi\)
−0.967429 + 0.253144i \(0.918535\pi\)
\(242\) 18.2475i 1.17300i
\(243\) 11.3365 10.6997i 0.727240 0.686384i
\(244\) 16.6352i 1.06496i
\(245\) 0 0
\(246\) 17.3739 8.72633i 1.10772 0.556371i
\(247\) 16.7477 1.06563
\(248\) −18.9145 −1.20107
\(249\) 5.53901 + 11.0280i 0.351021 + 0.698872i
\(250\) 0 0
\(251\) 15.2236 0.960903 0.480451 0.877021i \(-0.340473\pi\)
0.480451 + 0.877021i \(0.340473\pi\)
\(252\) 15.5573 + 25.7590i 0.980017 + 1.62266i
\(253\) 2.16515 0.136122
\(254\) 24.4625i 1.53492i
\(255\) 0 0
\(256\) −29.3739 −1.83587
\(257\) 16.4539 1.02636 0.513182 0.858280i \(-0.328467\pi\)
0.513182 + 0.858280i \(0.328467\pi\)
\(258\) 9.61948 4.83156i 0.598883 0.300800i
\(259\) 0.582576 1.42701i 0.0361995 0.0886703i
\(260\) 0 0
\(261\) −1.20871 0.899706i −0.0748174 0.0556904i
\(262\) 14.1857i 0.876395i
\(263\) 7.32436i 0.451639i −0.974169 0.225820i \(-0.927494\pi\)
0.974169 0.225820i \(-0.0725060\pi\)
\(264\) −14.4462 28.7619i −0.889100 1.77017i
\(265\) 0 0
\(266\) −16.4539 + 40.3036i −1.00885 + 2.47117i
\(267\) 8.20871 + 16.3433i 0.502365 + 1.00019i
\(268\) 53.7042 3.28050
\(269\) 18.9145 1.15324 0.576618 0.817014i \(-0.304372\pi\)
0.576618 + 0.817014i \(0.304372\pi\)
\(270\) 0 0
\(271\) 3.47197i 0.210907i 0.994424 + 0.105453i \(0.0336294\pi\)
−0.994424 + 0.105453i \(0.966371\pi\)
\(272\) 16.4539 0.997662
\(273\) 0.873133 + 11.1910i 0.0528444 + 0.677308i
\(274\) 2.41742 0.146042
\(275\) 0 0
\(276\) −2.94736 + 1.48036i −0.177410 + 0.0891074i
\(277\) 8.74773 0.525600 0.262800 0.964850i \(-0.415354\pi\)
0.262800 + 0.964850i \(0.415354\pi\)
\(278\) 5.89472 0.353542
\(279\) −10.5591 7.85971i −0.632159 0.470548i
\(280\) 0 0
\(281\) 21.5538i 1.28579i −0.765955 0.642895i \(-0.777733\pi\)
0.765955 0.642895i \(-0.222267\pi\)
\(282\) 21.9564 11.0280i 1.30749 0.656709i
\(283\) 1.02248i 0.0607799i 0.999538 + 0.0303900i \(0.00967491\pi\)
−0.999538 + 0.0303900i \(0.990325\pi\)
\(284\) 16.3433i 0.969796i
\(285\) 0 0
\(286\) 25.4107i 1.50256i
\(287\) −4.66442 + 11.4255i −0.275332 + 0.674423i
\(288\) −4.58258 3.41105i −0.270031 0.200998i
\(289\) 17.7477 1.04398
\(290\) 0 0
\(291\) −0.791288 + 0.397438i −0.0463861 + 0.0232983i
\(292\) 23.9837i 1.40354i
\(293\) −22.3486 −1.30562 −0.652809 0.757523i \(-0.726410\pi\)
−0.652809 + 0.757523i \(0.726410\pi\)
\(294\) −27.7890 8.89340i −1.62069 0.518673i
\(295\) 0 0
\(296\) 2.51134i 0.145969i
\(297\) 3.88702 22.0595i 0.225548 1.28002i
\(298\) −15.2087 −0.881017
\(299\) −1.23030 −0.0711501
\(300\) 0 0
\(301\) −2.58258 + 6.32599i −0.148857 + 0.364624i
\(302\) 34.0886i 1.96158i
\(303\) 10.1216 + 20.1518i 0.581470 + 1.15769i
\(304\) 19.0847i 1.09458i
\(305\) 0 0
\(306\) 34.1380 + 25.4107i 1.95154 + 1.45263i
\(307\) 20.5117i 1.17066i −0.810794 0.585332i \(-0.800964\pi\)
0.810794 0.585332i \(-0.199036\pi\)
\(308\) 40.0327 + 16.3433i 2.28108 + 0.931246i
\(309\) 10.5826 5.31529i 0.602022 0.302376i
\(310\) 0 0
\(311\) −27.0130 −1.53177 −0.765883 0.642979i \(-0.777698\pi\)
−0.765883 + 0.642979i \(0.777698\pi\)
\(312\) 8.20871 + 16.3433i 0.464727 + 0.925257i
\(313\) 10.7137i 0.605576i 0.953058 + 0.302788i \(0.0979174\pi\)
−0.953058 + 0.302788i \(0.902083\pi\)
\(314\) 22.3486 1.26120
\(315\) 0 0
\(316\) 32.5390 1.83046
\(317\) 13.9368i 0.782768i 0.920227 + 0.391384i \(0.128004\pi\)
−0.920227 + 0.391384i \(0.871996\pi\)
\(318\) −25.1337 50.0404i −1.40943 2.80613i
\(319\) −2.16515 −0.121225
\(320\) 0 0
\(321\) −1.55481 + 0.780929i −0.0867809 + 0.0435872i
\(322\) 1.20871 2.96073i 0.0673589 0.164995i
\(323\) 40.3036i 2.24255i
\(324\) 9.79129 + 32.6866i 0.543960 + 1.81592i
\(325\) 0 0
\(326\) 9.62604i 0.533137i
\(327\) 3.88702 + 7.73893i 0.214953 + 0.427964i
\(328\) 20.1072i 1.11023i
\(329\) −5.89472 + 14.4391i −0.324986 + 0.796051i
\(330\) 0 0
\(331\) 17.0000 0.934405 0.467202 0.884150i \(-0.345262\pi\)
0.467202 + 0.884150i \(0.345262\pi\)
\(332\) −27.0130 −1.48253
\(333\) 1.04356 1.40197i 0.0571868 0.0768277i
\(334\) 31.3321i 1.71442i
\(335\) 0 0
\(336\) −12.7525 + 0.994968i −0.695708 + 0.0542800i
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 16.8456i 0.916278i
\(339\) −9.78174 + 4.91305i −0.531271 + 0.266840i
\(340\) 0 0
\(341\) −18.9145 −1.02428
\(342\) −29.4736 + 39.5964i −1.59375 + 2.14113i
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) 11.1328i 0.600243i
\(345\) 0 0
\(346\) 42.5571i 2.28788i
\(347\) 18.7498i 1.00654i −0.864129 0.503271i \(-0.832130\pi\)
0.864129 0.503271i \(-0.167870\pi\)
\(348\) 2.94736 1.48036i 0.157995 0.0793558i
\(349\) 1.93825i 0.103752i −0.998654 0.0518761i \(-0.983480\pi\)
0.998654 0.0518761i \(-0.0165201\pi\)
\(350\) 0 0
\(351\) −2.20871 + 12.5348i −0.117892 + 0.669059i
\(352\) −8.20871 −0.437526
\(353\) −13.9933 −0.744786 −0.372393 0.928075i \(-0.621463\pi\)
−0.372393 + 0.928075i \(0.621463\pi\)
\(354\) −39.3303 + 19.7543i −2.09038 + 1.04993i
\(355\) 0 0
\(356\) −40.0327 −2.12173
\(357\) −26.9312 + 2.10120i −1.42535 + 0.111207i
\(358\) −29.9129 −1.58094
\(359\) 6.31982i 0.333547i −0.985995 0.166774i \(-0.946665\pi\)
0.985995 0.166774i \(-0.0533349\pi\)
\(360\) 0 0
\(361\) −27.7477 −1.46041
\(362\) 29.4736 1.54910
\(363\) −5.89472 11.7362i −0.309393 0.615991i
\(364\) −22.7477 9.28672i −1.19230 0.486756i
\(365\) 0 0
\(366\) −8.20871 16.3433i −0.429076 0.854278i
\(367\) 32.7591i 1.71001i −0.518617 0.855007i \(-0.673553\pi\)
0.518617 0.855007i \(-0.326447\pi\)
\(368\) 1.40197i 0.0730829i
\(369\) −8.35532 + 11.2250i −0.434961 + 0.584349i
\(370\) 0 0
\(371\) 32.9077 + 13.4345i 1.70848 + 0.697486i
\(372\) 25.7477 12.9323i 1.33496 0.670506i
\(373\) −18.9129 −0.979272 −0.489636 0.871927i \(-0.662870\pi\)
−0.489636 + 0.871927i \(0.662870\pi\)
\(374\) 61.1510 3.16204
\(375\) 0 0
\(376\) 25.4107i 1.31046i
\(377\) 1.23030 0.0633637
\(378\) −27.9952 17.6302i −1.43992 0.906797i
\(379\) −19.3303 −0.992931 −0.496465 0.868056i \(-0.665369\pi\)
−0.496465 + 0.868056i \(0.665369\pi\)
\(380\) 0 0
\(381\) 7.90242 + 15.7335i 0.404853 + 0.806051i
\(382\) −37.1652 −1.90153
\(383\) 19.8880 1.01623 0.508114 0.861290i \(-0.330343\pi\)
0.508114 + 0.861290i \(0.330343\pi\)
\(384\) 31.9681 16.0565i 1.63136 0.819381i
\(385\) 0 0
\(386\) 26.4716i 1.34737i
\(387\) −4.62614 + 6.21499i −0.235160 + 0.315926i
\(388\) 1.93825i 0.0983998i
\(389\) 26.3668i 1.33685i 0.743780 + 0.668424i \(0.233031\pi\)
−0.743780 + 0.668424i \(0.766969\pi\)
\(390\) 0 0
\(391\) 2.96073i 0.149730i
\(392\) 21.1183 21.5538i 1.06663 1.08863i
\(393\) −4.58258 9.12377i −0.231160 0.460233i
\(394\) −45.1216 −2.27319
\(395\) 0 0
\(396\) 39.3303 + 29.2756i 1.97642 + 1.47115i
\(397\) 13.6745i 0.686302i 0.939280 + 0.343151i \(0.111494\pi\)
−0.939280 + 0.343151i \(0.888506\pi\)
\(398\) 45.9275 2.30214
\(399\) −2.43716 31.2372i −0.122011 1.56382i
\(400\) 0 0
\(401\) 11.1328i 0.555948i 0.960589 + 0.277974i \(0.0896628\pi\)
−0.960589 + 0.277974i \(0.910337\pi\)
\(402\) −52.7618 + 26.5006i −2.63152 + 1.32173i
\(403\) 10.7477 0.535382
\(404\) −49.3616 −2.45583
\(405\) 0 0
\(406\) −1.20871 + 2.96073i −0.0599874 + 0.146938i
\(407\) 2.51134i 0.124482i
\(408\) −39.3303 + 19.7543i −1.94714 + 0.977986i
\(409\) 24.3882i 1.20592i 0.797772 + 0.602959i \(0.206012\pi\)
−0.797772 + 0.602959i \(0.793988\pi\)
\(410\) 0 0
\(411\) −1.55481 + 0.780929i −0.0766930 + 0.0385204i
\(412\) 25.9219i 1.27708i
\(413\) 10.5591 25.8645i 0.519581 1.27271i
\(414\) 2.16515 2.90878i 0.106411 0.142959i
\(415\) 0 0
\(416\) 4.66442 0.228692
\(417\) −3.79129 + 1.90424i −0.185660 + 0.0932511i
\(418\) 70.9285i 3.46923i
\(419\) 18.9145 0.924032 0.462016 0.886872i \(-0.347126\pi\)
0.462016 + 0.886872i \(0.347126\pi\)
\(420\) 0 0
\(421\) −10.1652 −0.495419 −0.247710 0.968834i \(-0.579678\pi\)
−0.247710 + 0.968834i \(0.579678\pi\)
\(422\) 30.6775i 1.49336i
\(423\) −10.5591 + 14.1857i −0.513403 + 0.689732i
\(424\) 57.9129 2.81250
\(425\) 0 0
\(426\) 8.06468 + 16.0565i 0.390735 + 0.777941i
\(427\) 10.7477 + 4.38774i 0.520119 + 0.212338i
\(428\) 3.80848i 0.184090i
\(429\) 8.20871 + 16.3433i 0.396320 + 0.789062i
\(430\) 0 0
\(431\) 30.8872i 1.48778i 0.668300 + 0.743892i \(0.267022\pi\)
−0.668300 + 0.743892i \(0.732978\pi\)
\(432\) −14.2839 2.51691i −0.687235 0.121095i
\(433\) 23.4724i 1.12801i −0.825770 0.564006i \(-0.809259\pi\)
0.825770 0.564006i \(-0.190741\pi\)
\(434\) −10.5591 + 25.8645i −0.506855 + 1.24154i
\(435\) 0 0
\(436\) −18.9564 −0.907849
\(437\) 3.43412 0.164276
\(438\) 11.8348 + 23.5628i 0.565491 + 1.12588i
\(439\) 26.9444i 1.28599i 0.765872 + 0.642993i \(0.222307\pi\)
−0.765872 + 0.642993i \(0.777693\pi\)
\(440\) 0 0
\(441\) 20.7459 3.25706i 0.987899 0.155098i
\(442\) −34.7477 −1.65278
\(443\) 13.4345i 0.638293i −0.947705 0.319147i \(-0.896604\pi\)
0.947705 0.319147i \(-0.103396\pi\)
\(444\) 1.71706 + 3.41862i 0.0814881 + 0.162240i
\(445\) 0 0
\(446\) −5.89472 −0.279123
\(447\) 9.78174 4.91305i 0.462660 0.232379i
\(448\) −10.1652 + 24.8994i −0.480258 + 1.17639i
\(449\) 19.5447i 0.922371i 0.887304 + 0.461185i \(0.152576\pi\)
−0.887304 + 0.461185i \(0.847424\pi\)
\(450\) 0 0
\(451\) 20.1072i 0.946809i
\(452\) 23.9603i 1.12700i
\(453\) 11.0120 + 21.9246i 0.517391 + 1.03011i
\(454\) 14.1857i 0.665768i
\(455\) 0 0
\(456\) −22.9129 45.6189i −1.07299 2.13630i
\(457\) 15.8348 0.740723 0.370361 0.928888i \(-0.379234\pi\)
0.370361 + 0.928888i \(0.379234\pi\)
\(458\) −44.6972 −2.08856
\(459\) −30.1652 5.31529i −1.40799 0.248096i
\(460\) 0 0
\(461\) −8.09854 −0.377187 −0.188593 0.982055i \(-0.560393\pi\)
−0.188593 + 0.982055i \(0.560393\pi\)
\(462\) −47.3950 + 3.69781i −2.20501 + 0.172038i
\(463\) 14.7477 0.685385 0.342693 0.939448i \(-0.388661\pi\)
0.342693 + 0.939448i \(0.388661\pi\)
\(464\) 1.40197i 0.0650850i
\(465\) 0 0
\(466\) −1.20871 −0.0559925
\(467\) 35.3683 1.63665 0.818325 0.574755i \(-0.194903\pi\)
0.818325 + 0.574755i \(0.194903\pi\)
\(468\) −22.3486 16.6352i −1.03306 0.768962i
\(469\) 14.1652 34.6974i 0.654086 1.60218i
\(470\) 0 0
\(471\) −14.3739 + 7.21953i −0.662313 + 0.332658i
\(472\) 45.5178i 2.09513i
\(473\) 11.1328i 0.511889i
\(474\) −31.9681 + 16.0565i −1.46834 + 0.737501i
\(475\) 0 0
\(476\) 22.3486 54.7426i 1.02435 2.50912i
\(477\) 32.3303 + 24.0651i 1.48030 + 1.10186i
\(478\) −29.9129 −1.36818
\(479\) −10.5591 −0.482459 −0.241230 0.970468i \(-0.577551\pi\)
−0.241230 + 0.970468i \(0.577551\pi\)
\(480\) 0 0
\(481\) 1.42701i 0.0650662i
\(482\) 18.9145 0.861530
\(483\) 0.179036 + 2.29471i 0.00814641 + 0.104413i
\(484\) 28.7477 1.30671
\(485\) 0 0
\(486\) −25.7488 27.2815i −1.16799 1.23751i
\(487\) 40.1652 1.82006 0.910028 0.414546i \(-0.136060\pi\)
0.910028 + 0.414546i \(0.136060\pi\)
\(488\) 18.9145 0.856217
\(489\) 3.10961 + 6.19115i 0.140622 + 0.279973i
\(490\) 0 0
\(491\) 2.51134i 0.113335i −0.998393 0.0566676i \(-0.981952\pi\)
0.998393 0.0566676i \(-0.0180475\pi\)
\(492\) −13.7477 27.3713i −0.619795 1.23399i
\(493\) 2.96073i 0.133344i
\(494\) 40.3036i 1.81334i
\(495\) 0 0
\(496\) 12.2474i 0.549927i
\(497\) −10.5591 4.31075i −0.473642 0.193364i
\(498\) 26.5390 13.3297i 1.18924 0.597318i
\(499\) 30.7477 1.37646 0.688229 0.725494i \(-0.258389\pi\)
0.688229 + 0.725494i \(0.258389\pi\)
\(500\) 0 0
\(501\) −10.1216 20.1518i −0.452199 0.900315i
\(502\) 36.6356i 1.63513i
\(503\) −11.7894 −0.525665 −0.262833 0.964841i \(-0.584657\pi\)
−0.262833 + 0.964841i \(0.584657\pi\)
\(504\) 29.2883 17.6889i 1.30461 0.787925i
\(505\) 0 0
\(506\) 5.21046i 0.231633i
\(507\) 5.44182 + 10.8345i 0.241680 + 0.481177i
\(508\) −38.5390 −1.70989
\(509\) 31.6774 1.40408 0.702039 0.712139i \(-0.252273\pi\)
0.702039 + 0.712139i \(0.252273\pi\)
\(510\) 0 0
\(511\) −15.4955 6.32599i −0.685479 0.279845i
\(512\) 29.3804i 1.29844i
\(513\) 6.16515 34.9883i 0.272198 1.54477i
\(514\) 39.5964i 1.74652i
\(515\) 0 0
\(516\) −7.61178 15.1548i −0.335090 0.667154i
\(517\) 25.4107i 1.11756i
\(518\) −3.43412 1.40197i −0.150887 0.0615992i
\(519\) 13.7477 + 27.3713i 0.603458 + 1.20147i
\(520\) 0 0
\(521\) −35.3683 −1.54951 −0.774757 0.632259i \(-0.782128\pi\)
−0.774757 + 0.632259i \(0.782128\pi\)
\(522\) −2.16515 + 2.90878i −0.0947661 + 0.127314i
\(523\) 14.6969i 0.642652i −0.946969 0.321326i \(-0.895871\pi\)
0.946969 0.321326i \(-0.104129\pi\)
\(524\) 22.3486 0.976302
\(525\) 0 0
\(526\) −17.6261 −0.768536
\(527\) 25.8645i 1.12668i
\(528\) −18.6238 + 9.35414i −0.810498 + 0.407087i
\(529\) 22.7477 0.989032
\(530\) 0 0
\(531\) 18.9145 25.4107i 0.820818 1.10273i
\(532\) 63.4955 + 25.9219i 2.75288 + 1.12386i
\(533\) 11.4255i 0.494891i
\(534\) 39.3303 19.7543i 1.70199 0.854854i
\(535\) 0 0
\(536\) 61.0624i 2.63750i
\(537\) 19.2390 9.66311i 0.830223 0.416994i
\(538\) 45.5178i 1.96241i
\(539\) 21.1183 21.5538i 0.909629 0.928386i
\(540\) 0 0
\(541\) 0.582576 0.0250469 0.0125234 0.999922i \(-0.496014\pi\)
0.0125234 + 0.999922i \(0.496014\pi\)
\(542\) 8.35532 0.358892
\(543\) −18.9564 + 9.52121i −0.813499 + 0.408594i
\(544\) 11.2250i 0.481267i
\(545\) 0 0
\(546\) 26.9312 2.10120i 1.15255 0.0899231i
\(547\) −41.3303 −1.76716 −0.883578 0.468284i \(-0.844872\pi\)
−0.883578 + 0.468284i \(0.844872\pi\)
\(548\) 3.80848i 0.162690i
\(549\) 10.5591 + 7.85971i 0.450653 + 0.335444i
\(550\) 0 0
\(551\) −3.43412 −0.146298
\(552\) 1.68320 + 3.35119i 0.0716416 + 0.142636i
\(553\) 8.58258 21.0229i 0.364968 0.893986i
\(554\) 21.0515i 0.894392i
\(555\) 0 0
\(556\) 9.28672i 0.393845i
\(557\) 46.6234i 1.97550i 0.156056 + 0.987748i \(0.450122\pi\)
−0.156056 + 0.987748i \(0.549878\pi\)
\(558\) −18.9145 + 25.4107i −0.800713 + 1.07572i
\(559\) 6.32599i 0.267561i
\(560\) 0 0
\(561\) −39.3303 + 19.7543i −1.66053 + 0.834029i
\(562\) −51.8693 −2.18798
\(563\) −32.9077 −1.38690 −0.693448 0.720507i \(-0.743909\pi\)
−0.693448 + 0.720507i \(0.743909\pi\)
\(564\) −17.3739 34.5908i −0.731572 1.45654i
\(565\) 0 0
\(566\) 2.46060 0.103427
\(567\) 23.7009 + 2.29551i 0.995342 + 0.0964023i
\(568\) −18.5826 −0.779708
\(569\) 32.1843i 1.34924i −0.738166 0.674619i \(-0.764308\pi\)
0.738166 0.674619i \(-0.235692\pi\)
\(570\) 0 0
\(571\) −2.25227 −0.0942547 −0.0471273 0.998889i \(-0.515007\pi\)
−0.0471273 + 0.998889i \(0.515007\pi\)
\(572\) −40.0327 −1.67385
\(573\) 23.9034 12.0059i 0.998578 0.501554i
\(574\) 27.4955 + 11.2250i 1.14764 + 0.468521i
\(575\) 0 0
\(576\) −18.2087 + 24.4625i −0.758696 + 1.01927i
\(577\) 12.7587i 0.531151i 0.964090 + 0.265576i \(0.0855620\pi\)
−0.964090 + 0.265576i \(0.914438\pi\)
\(578\) 42.7101i 1.77650i
\(579\) −8.55144 17.0257i −0.355386 0.707562i
\(580\) 0 0
\(581\) −7.12502 + 17.4527i −0.295596 + 0.724058i
\(582\) 0.956439 + 1.90424i 0.0396457 + 0.0789334i
\(583\) 57.9129 2.39851
\(584\) −27.2698 −1.12843
\(585\) 0 0
\(586\) 53.7821i 2.22172i
\(587\) −34.1380 −1.40903 −0.704513 0.709691i \(-0.748835\pi\)
−0.704513 + 0.709691i \(0.748835\pi\)
\(588\) −14.0109 + 43.7796i −0.577801 + 1.80544i
\(589\) −30.0000 −1.23613
\(590\) 0 0
\(591\) 29.0207 14.5762i 1.19375 0.599583i
\(592\) −1.62614 −0.0668338
\(593\) −11.7894 −0.484134 −0.242067 0.970259i \(-0.577825\pi\)
−0.242067 + 0.970259i \(0.577825\pi\)
\(594\) −53.0863 9.35414i −2.17816 0.383805i
\(595\) 0 0
\(596\) 23.9603i 0.981451i
\(597\) −29.5390 + 14.8365i −1.20895 + 0.607217i
\(598\) 2.96073i 0.121073i
\(599\) 19.5447i 0.798574i 0.916826 + 0.399287i \(0.130742\pi\)
−0.916826 + 0.399287i \(0.869258\pi\)
\(600\) 0 0
\(601\) 42.0459i 1.71509i 0.514412 + 0.857543i \(0.328010\pi\)
−0.514412 + 0.857543i \(0.671990\pi\)
\(602\) 15.2236 + 6.21499i 0.620466 + 0.253304i
\(603\) 25.3739 34.0886i 1.03330 1.38819i
\(604\) −53.7042 −2.18519
\(605\) 0 0
\(606\) 48.4955 24.3577i 1.96999 0.989464i
\(607\) 1.42701i 0.0579207i 0.999581 + 0.0289603i \(0.00921965\pi\)
−0.999581 + 0.0289603i \(0.990780\pi\)
\(608\) −13.0197 −0.528020
\(609\) −0.179036 2.29471i −0.00725490 0.0929862i
\(610\) 0 0
\(611\) 14.4391i 0.584142i
\(612\) 40.0327 53.7821i 1.61823 2.17401i
\(613\) −27.4174 −1.10738 −0.553690 0.832723i \(-0.686781\pi\)
−0.553690 + 0.832723i \(0.686781\pi\)
\(614\) −49.3616 −1.99207
\(615\) 0 0
\(616\) 18.5826 45.5178i 0.748713 1.83397i
\(617\) 13.9368i 0.561074i 0.959843 + 0.280537i \(0.0905125\pi\)
−0.959843 + 0.280537i \(0.909487\pi\)
\(618\) −12.7913 25.4671i −0.514541 1.02444i
\(619\) 35.7199i 1.43570i 0.696196 + 0.717851i \(0.254874\pi\)
−0.696196 + 0.717851i \(0.745126\pi\)
\(620\) 0 0
\(621\) −0.452896 + 2.57026i −0.0181741 + 0.103141i
\(622\) 65.0070i 2.60655i
\(623\) −10.5591 + 25.8645i −0.423043 + 1.03624i
\(624\) 10.5826 5.31529i 0.423642 0.212782i
\(625\) 0 0
\(626\) 25.7827 1.03048
\(627\) −22.9129 45.6189i −0.915052 1.82184i
\(628\) 35.2086i 1.40498i
\(629\) −3.43412 −0.136927
\(630\) 0 0
\(631\) 6.25227 0.248899 0.124450 0.992226i \(-0.460284\pi\)
0.124450 + 0.992226i \(0.460284\pi\)
\(632\) 36.9973i 1.47168i
\(633\) 9.91013 + 19.7308i 0.393892 + 0.784227i
\(634\) 33.5390 1.33200
\(635\) 0 0
\(636\) −78.8352 + 39.5964i −3.12602 + 1.57010i
\(637\) −12.0000 + 12.2474i −0.475457 + 0.485262i
\(638\) 5.21046i 0.206284i
\(639\) −10.3739 7.72180i −0.410384 0.305470i
\(640\) 0 0
\(641\) 36.9973i 1.46131i 0.682748 + 0.730654i \(0.260785\pi\)
−0.682748 + 0.730654i \(0.739215\pi\)
\(642\) 1.87931 + 3.74166i 0.0741706 + 0.147671i
\(643\) 43.0683i 1.69845i 0.528032 + 0.849225i \(0.322930\pi\)
−0.528032 + 0.849225i \(0.677070\pi\)
\(644\) −4.66442 1.90424i −0.183804 0.0750376i
\(645\) 0 0
\(646\) 96.9909 3.81606
\(647\) 18.6577 0.733509 0.366755 0.930318i \(-0.380469\pi\)
0.366755 + 0.930318i \(0.380469\pi\)
\(648\) 37.1652 11.1328i 1.45999 0.437339i
\(649\) 45.5178i 1.78673i
\(650\) 0 0
\(651\) −1.56403 20.0462i −0.0612992 0.785674i
\(652\) −15.1652 −0.593913
\(653\) 12.4300i 0.486423i 0.969973 + 0.243211i \(0.0782009\pi\)
−0.969973 + 0.243211i \(0.921799\pi\)
\(654\) 18.6238 9.35414i 0.728249 0.365776i
\(655\) 0 0
\(656\) 13.0197 0.508335
\(657\) −15.2236 11.3317i −0.593928 0.442091i
\(658\) 34.7477 + 14.1857i 1.35461 + 0.553016i
\(659\) 12.4300i 0.484203i −0.970251 0.242102i \(-0.922163\pi\)
0.970251 0.242102i \(-0.0778368\pi\)
\(660\) 0 0
\(661\) 32.3546i 1.25845i −0.777224 0.629224i \(-0.783373\pi\)
0.777224 0.629224i \(-0.216627\pi\)
\(662\) 40.9107i 1.59004i
\(663\) 22.3486 11.2250i 0.867947 0.435942i
\(664\) 30.7142i 1.19194i
\(665\) 0 0
\(666\) −3.37386 2.51134i −0.130735 0.0973124i
\(667\) 0.252273 0.00976805
\(668\) 49.3616 1.90986
\(669\) 3.79129 1.90424i 0.146580 0.0736222i
\(670\) 0 0
\(671\) 18.9145 0.730185
\(672\) −0.678776 8.69989i −0.0261844 0.335606i
\(673\) −47.4955 −1.83082 −0.915408 0.402528i \(-0.868132\pi\)
−0.915408 + 0.402528i \(0.868132\pi\)
\(674\) 4.81302i 0.185391i
\(675\) 0 0
\(676\) −26.5390 −1.02073
\(677\) −23.5789 −0.906210 −0.453105 0.891457i \(-0.649684\pi\)
−0.453105 + 0.891457i \(0.649684\pi\)
\(678\) 11.8233 + 23.5398i 0.454071 + 0.904042i
\(679\) −1.25227 0.511238i −0.0480578 0.0196195i
\(680\) 0 0
\(681\) 4.58258 + 9.12377i 0.175605 + 0.349624i
\(682\) 45.5178i 1.74297i
\(683\) 33.1889i 1.26994i −0.772538 0.634968i \(-0.781013\pi\)
0.772538 0.634968i \(-0.218987\pi\)
\(684\) 62.3813 + 46.4336i 2.38521 + 1.77543i
\(685\) 0 0
\(686\) −17.6842 40.9107i −0.675184 1.56198i
\(687\) 28.7477 14.4391i 1.09679 0.550884i
\(688\) 7.20871 0.274830
\(689\) −32.9077 −1.25368
\(690\) 0 0
\(691\) 4.38774i 0.166918i −0.996511 0.0834588i \(-0.973403\pi\)
0.996511 0.0834588i \(-0.0265967\pi\)
\(692\) −67.0457 −2.54870
\(693\) 29.2883 17.6889i 1.11257 0.671945i
\(694\) −45.1216 −1.71279
\(695\) 0 0
\(696\) −1.68320 3.35119i −0.0638014 0.127027i
\(697\) 27.4955 1.04146
\(698\) −4.66442 −0.176551
\(699\) 0.777403 0.390465i 0.0294041 0.0147687i
\(700\) 0 0
\(701\) 15.4436i 0.583296i −0.956526 0.291648i \(-0.905796\pi\)
0.956526 0.291648i \(-0.0942037\pi\)
\(702\) 30.1652 + 5.31529i 1.13851 + 0.200613i
\(703\) 3.98320i 0.150229i
\(704\) 43.8194i 1.65151i
\(705\) 0 0
\(706\) 33.6749i 1.26737i
\(707\) −13.0197 + 31.8917i −0.489658 + 1.19941i
\(708\) 31.1216 + 61.9621i 1.16962 + 2.32868i
\(709\) −31.4955 −1.18284 −0.591418 0.806365i \(-0.701432\pi\)
−0.591418 + 0.806365i \(0.701432\pi\)
\(710\) 0 0
\(711\) 15.3739 20.6540i 0.576565 0.774587i
\(712\) 45.5178i 1.70585i
\(713\) 2.20382 0.0825337
\(714\) 5.05656 + 64.8101i 0.189237 + 2.42546i
\(715\) 0 0
\(716\) 47.1257i 1.76117i
\(717\) 19.2390 9.66311i 0.718492 0.360876i
\(718\) −15.2087 −0.567584
\(719\) 40.0327 1.49297 0.746485 0.665403i \(-0.231740\pi\)
0.746485 + 0.665403i \(0.231740\pi\)
\(720\) 0 0
\(721\) 16.7477 + 6.83723i 0.623718 + 0.254632i
\(722\) 66.7752i 2.48511i
\(723\) −12.1652 + 6.11016i −0.452427 + 0.227239i
\(724\) 46.4336i 1.72569i
\(725\) 0 0
\(726\) −28.2433 + 14.1857i −1.04821 + 0.526481i
\(727\) 45.0066i 1.66920i −0.550855 0.834601i \(-0.685698\pi\)
0.550855 0.834601i \(-0.314302\pi\)
\(728\) −10.5591 + 25.8645i −0.391348 + 0.958602i
\(729\) 25.3739 + 9.22860i 0.939773 + 0.341800i
\(730\) 0 0
\(731\) 15.2236 0.563064
\(732\) −25.7477 + 12.9323i −0.951663 + 0.477990i
\(733\) 32.2479i 1.19110i −0.803317 0.595552i \(-0.796933\pi\)
0.803317 0.595552i \(-0.203067\pi\)
\(734\) −78.8352 −2.90986
\(735\) 0 0
\(736\) 0.956439 0.0352548
\(737\) 61.0624i 2.24926i
\(738\) 27.0130 + 20.1072i 0.994362 + 0.740155i
\(739\) −40.8258 −1.50180 −0.750900 0.660416i \(-0.770380\pi\)
−0.750900 + 0.660416i \(0.770380\pi\)
\(740\) 0 0
\(741\) 13.0197 + 25.9219i 0.478292 + 0.952265i
\(742\) 32.3303 79.1927i 1.18688 2.90726i
\(743\) 12.4300i 0.456012i 0.973660 + 0.228006i \(0.0732206\pi\)
−0.973660 + 0.228006i \(0.926779\pi\)
\(744\) −14.7042 29.2756i −0.539081 1.07329i
\(745\) 0 0
\(746\) 45.5140i 1.66639i
\(747\) −12.7630 + 17.1464i −0.466972 + 0.627355i
\(748\) 96.3392i 3.52251i
\(749\) −2.46060 1.00454i −0.0899083 0.0367049i
\(750\) 0 0
\(751\) −38.7477 −1.41392 −0.706962 0.707251i \(-0.749935\pi\)
−0.706962 + 0.707251i \(0.749935\pi\)
\(752\) 16.4539 0.600011
\(753\) 11.8348 + 23.5628i 0.431286 + 0.858677i
\(754\) 2.96073i 0.107823i
\(755\) 0 0
\(756\) −27.7751 + 44.1045i −1.01017 + 1.60406i
\(757\) −6.25227 −0.227243 −0.113621 0.993524i \(-0.536245\pi\)
−0.113621 + 0.993524i \(0.536245\pi\)
\(758\) 46.5186i 1.68963i
\(759\) 1.68320 + 3.35119i 0.0610961 + 0.121641i
\(760\) 0 0
\(761\) 44.6972 1.62027 0.810135 0.586243i \(-0.199394\pi\)
0.810135 + 0.586243i \(0.199394\pi\)
\(762\) 37.8628 19.0173i 1.37162 0.688923i
\(763\) −5.00000 + 12.2474i −0.181012 + 0.443387i
\(764\) 58.5511i 2.11830i
\(765\) 0 0
\(766\) 47.8606i 1.72927i
\(767\) 25.8645i 0.933913i
\(768\) −22.8353 45.4645i −0.823999 1.64056i
\(769\) 3.36526i 0.121355i 0.998157 + 0.0606773i \(0.0193260\pi\)
−0.998157 + 0.0606773i \(0.980674\pi\)
\(770\) 0 0
\(771\) 12.7913 + 25.4671i 0.460667 + 0.917174i
\(772\) 41.7042 1.50097
\(773\) 7.12502 0.256269 0.128135 0.991757i \(-0.459101\pi\)
0.128135 + 0.991757i \(0.459101\pi\)
\(774\) 14.9564 + 11.1328i 0.537598 + 0.400162i
\(775\) 0 0
\(776\) −2.20382 −0.0791126
\(777\) 2.66161 0.207662i 0.0954847 0.00744983i
\(778\) 63.4519 2.27486
\(779\) 31.8917i 1.14264i
\(780\) 0 0
\(781\) −18.5826 −0.664937
\(782\) −7.12502 −0.254790
\(783\) 0.452896 2.57026i 0.0161852 0.0918537i
\(784\) −13.9564 13.6745i −0.498444 0.488374i
\(785\) 0 0
\(786\) −21.9564 + 11.0280i −0.783160 + 0.393356i
\(787\) 16.1240i 0.574757i −0.957817 0.287378i \(-0.907216\pi\)
0.957817 0.287378i \(-0.0927837\pi\)
\(788\) 71.0859i 2.53233i
\(789\) 11.3365 5.69398i 0.403592 0.202711i
\(790\) 0 0
\(791\) −15.4803 6.31982i −0.550418 0.224707i
\(792\) 33.2867 44.7191i 1.18279 1.58903i
\(793\) −10.7477 −0.381663
\(794\) 32.9077 1.16785
\(795\) 0 0
\(796\) 72.3555i 2.56457i
\(797\) −15.2236 −0.539246 −0.269623 0.962966i \(-0.586899\pi\)
−0.269623 + 0.962966i \(0.586899\pi\)
\(798\) −75.1726 + 5.86506i −2.66108 + 0.207621i
\(799\) 34.7477 1.22929
\(800\) 0 0
\(801\) −18.9145 + 25.4107i −0.668310 + 0.897842i
\(802\) 26.7913 0.946033
\(803\) −27.2698 −0.962330
\(804\) 41.7498 + 83.1226i 1.47240 + 2.93151i
\(805\) 0 0
\(806\) 25.8645i 0.911038i
\(807\) 14.7042 + 29.2756i 0.517611 + 1.03055i
\(808\) 56.1249i 1.97447i
\(809\) 7.32436i 0.257511i 0.991676 + 0.128755i \(0.0410982\pi\)
−0.991676 + 0.128755i \(0.958902\pi\)
\(810\) 0 0
\(811\) 8.77548i 0.308149i −0.988059 0.154074i \(-0.950760\pi\)
0.988059 0.154074i \(-0.0492396\pi\)
\(812\) 4.66442 + 1.90424i 0.163689 + 0.0668258i
\(813\) −5.37386 + 2.69912i −0.188470 + 0.0946622i
\(814\) −6.04356 −0.211827
\(815\) 0 0
\(816\) 12.7913 + 25.4671i 0.447785 + 0.891526i
\(817\) 17.6577i 0.617764i
\(818\) 58.6904 2.05206
\(819\) −16.6424 + 10.0513i −0.581534 + 0.351221i
\(820\) 0 0
\(821\) 15.4436i 0.538985i −0.963002 0.269493i \(-0.913144\pi\)
0.963002 0.269493i \(-0.0868560\pi\)
\(822\) 1.87931 + 3.74166i 0.0655486 + 0.130505i
\(823\) 29.7477 1.03694 0.518470 0.855096i \(-0.326502\pi\)
0.518470 + 0.855096i \(0.326502\pi\)
\(824\) 29.4736 1.02676
\(825\) 0 0
\(826\) −62.2432 25.4107i −2.16572 0.884150i
\(827\) 44.6143i 1.55139i −0.631107 0.775696i \(-0.717399\pi\)
0.631107 0.775696i \(-0.282601\pi\)
\(828\) −4.58258 3.41105i −0.159256 0.118542i
\(829\) 26.4331i 0.918061i −0.888420 0.459031i \(-0.848197\pi\)
0.888420 0.459031i \(-0.151803\pi\)
\(830\) 0 0
\(831\) 6.80051 + 13.5396i 0.235907 + 0.469684i
\(832\) 24.8994i 0.863233i
\(833\) −29.4736 28.8781i −1.02120 1.00057i
\(834\) 4.58258 + 9.12377i 0.158682 + 0.315930i
\(835\) 0 0
\(836\) 111.743 3.86471
\(837\) 3.95644 22.4535i 0.136755 0.776105i
\(838\) 45.5178i 1.57239i
\(839\) −10.5591 −0.364542 −0.182271 0.983248i \(-0.558345\pi\)
−0.182271 + 0.983248i \(0.558345\pi\)
\(840\) 0 0
\(841\) 28.7477 0.991301
\(842\) 24.4625i 0.843035i
\(843\) 33.3606 16.7560i 1.14900 0.577106i
\(844\) −48.3303 −1.66360
\(845\) 0 0
\(846\) 34.1380 + 25.4107i 1.17369 + 0.873637i
\(847\) 7.58258 18.5734i 0.260540 0.638191i
\(848\) 37.4996i 1.28774i
\(849\) −1.58258 + 0.794877i −0.0543139 + 0.0272801i
\(850\) 0 0
\(851\) 0.292609i 0.0100305i
\(852\) 25.2959 12.7053i 0.866625 0.435278i
\(853\) 27.3489i 0.936409i 0.883620 + 0.468205i \(0.155099\pi\)
−0.883620 + 0.468205i \(0.844901\pi\)
\(854\) 10.5591 25.8645i 0.361326 0.885065i
\(855\) 0 0
\(856\) −4.33030 −0.148007
\(857\) −21.3751 −0.730158 −0.365079 0.930977i \(-0.618958\pi\)
−0.365079 + 0.930977i \(0.618958\pi\)
\(858\) 39.3303 19.7543i 1.34271 0.674402i
\(859\) 25.5174i 0.870642i −0.900275 0.435321i \(-0.856635\pi\)
0.900275 0.435321i \(-0.143365\pi\)
\(860\) 0 0
\(861\) −21.3103 + 1.66266i −0.726253 + 0.0566632i
\(862\) 74.3303 2.53170
\(863\) 39.0064i 1.32779i 0.747824 + 0.663897i \(0.231099\pi\)
−0.747824 + 0.663897i \(0.768901\pi\)
\(864\) 1.71706 9.74461i 0.0584156 0.331518i
\(865\) 0 0
\(866\) −56.4866 −1.91949
\(867\) 13.7971 + 27.4697i 0.468576 + 0.932920i
\(868\) 40.7477 + 16.6352i 1.38307 + 0.564635i
\(869\) 36.9973i 1.25505i
\(870\) 0 0
\(871\) 34.6974i 1.17568i
\(872\) 21.5538i 0.729902i
\(873\) −1.23030 0.915775i −0.0416393 0.0309943i
\(874\) 8.26424i 0.279542i
\(875\) 0 0
\(876\) 37.1216 18.6450i 1.25422 0.629955i
\(877\) −23.4955 −0.793385 −0.396693 0.917952i \(-0.629842\pi\)
−0.396693 + 0.917952i \(0.629842\pi\)
\(878\) 64.8419 2.18831
\(879\) −17.3739 34.5908i −0.586006 1.16672i
\(880\) 0 0
\(881\) −58.6904 −1.97733 −0.988665 0.150136i \(-0.952029\pi\)
−0.988665 + 0.150136i \(0.952029\pi\)
\(882\) −7.83816 49.9252i −0.263924 1.68107i
\(883\) −24.5826 −0.827270 −0.413635 0.910443i \(-0.635741\pi\)
−0.413635 + 0.910443i \(0.635741\pi\)
\(884\) 54.7426i 1.84119i
\(885\) 0 0
\(886\) −32.3303 −1.08616
\(887\) −46.9010 −1.57478 −0.787390 0.616455i \(-0.788568\pi\)
−0.787390 + 0.616455i \(0.788568\pi\)
\(888\) 3.88702 1.95232i 0.130440 0.0655157i
\(889\) −10.1652 + 24.8994i −0.340928 + 0.835100i
\(890\) 0 0
\(891\) 37.1652 11.1328i 1.24508 0.372964i
\(892\) 9.28672i 0.310942i
\(893\) 40.3036i 1.34871i
\(894\) −11.8233 23.5398i −0.395430 0.787290i
\(895\) 0 0
\(896\) 50.5919 + 20.6540i 1.69016 + 0.690003i
\(897\) −0.956439 1.90424i −0.0319346 0.0635808i
\(898\) 47.0345 1.56956
\(899\) −2.20382 −0.0735015
\(900\) 0 0
\(901\) 79.1927i 2.63829i
\(902\) 48.3881 1.61115
\(903\) −11.7990 + 0.920572i −0.392646 + 0.0306347i
\(904\) −27.2432 −0.906095
\(905\) 0 0
\(906\) 52.7618 26.5006i 1.75289 0.880423i
\(907\) −53.4955 −1.77629 −0.888144 0.459566i \(-0.848005\pi\)
−0.888144 + 0.459566i \(0.848005\pi\)
\(908\) −22.3486 −0.741664
\(909\) −23.3221 + 31.3321i −0.773545 + 1.03922i
\(910\) 0 0
\(911\) 54.2404i 1.79706i −0.438909 0.898532i \(-0.644635\pi\)
0.438909 0.898532i \(-0.355365\pi\)
\(912\) −29.5390 + 14.8365i −0.978135 + 0.491285i
\(913\) 30.7142i 1.01649i
\(914\) 38.1067i 1.26046i
\(915\) 0 0
\(916\) 70.4173i 2.32665i
\(917\) 5.89472 14.4391i 0.194661 0.476820i
\(918\) −12.7913 + 72.5927i −0.422175 + 2.39592i
\(919\) 40.0780 1.32205 0.661026 0.750363i \(-0.270121\pi\)
0.661026 + 0.750363i \(0.270121\pi\)
\(920\) 0 0
\(921\) 31.7477 15.9459i 1.04612 0.525434i
\(922\) 19.4892i 0.641843i
\(923\) 10.5591 0.347558
\(924\) 5.82565 + 74.6675i 0.191650 + 2.45638i
\(925\) 0 0
\(926\) 35.4905i 1.16629i
\(927\) 16.4539 + 12.2474i 0.540416 + 0.402259i
\(928\) −0.956439 −0.0313967
\(929\) 10.5591 0.346434 0.173217 0.984884i \(-0.444584\pi\)
0.173217 + 0.984884i \(0.444584\pi\)
\(930\) 0 0
\(931\) 33.4955 34.1862i 1.09777 1.12041i
\(932\) 1.90424i 0.0623755i
\(933\) −21.0000 41.8104i −0.687509 1.36881i
\(934\) 85.1142i 2.78502i
\(935\) 0 0
\(936\) −18.9145 + 25.4107i −0.618238 + 0.830574i
\(937\) 25.0061i 0.816915i 0.912777 + 0.408457i \(0.133933\pi\)
−0.912777 + 0.408457i \(0.866067\pi\)
\(938\) −83.4996 34.0886i −2.72636 1.11303i
\(939\) −16.5826 + 8.32889i −0.541152 + 0.271803i
\(940\) 0 0
\(941\) 25.7827 0.840492 0.420246 0.907410i \(-0.361944\pi\)
0.420246 + 0.907410i \(0.361944\pi\)
\(942\) 17.3739 + 34.5908i 0.566071 + 1.12703i
\(943\) 2.34279i 0.0762917i
\(944\) −29.4736 −0.959284
\(945\) 0 0
\(946\) 26.7913 0.871060
\(947\) 24.8600i 0.807841i −0.914794 0.403920i \(-0.867647\pi\)
0.914794 0.403920i \(-0.132353\pi\)
\(948\) 25.2959 + 50.3635i 0.821574 + 1.63573i
\(949\) 15.4955 0.503004
\(950\) 0 0
\(951\) −21.5712 + 10.8345i −0.699493 + 0.351333i
\(952\) −62.2432 25.4107i −2.01731 0.823565i
\(953\) 0.502268i 0.0162700i −0.999967 0.00813502i \(-0.997411\pi\)
0.999967 0.00813502i \(-0.00258949\pi\)
\(954\) 57.9129 77.8032i 1.87500 2.51897i
\(955\) 0 0
\(956\) 47.1257i 1.52415i
\(957\) −1.68320 3.35119i −0.0544100 0.108329i
\(958\) 25.4107i 0.820982i
\(959\) −2.46060 1.00454i −0.0794569 0.0324381i
\(960\) 0 0
\(961\) 11.7477 0.378959
\(962\) 3.43412 0.110720
\(963\) −2.41742 1.79941i −0.0779004 0.0579853i
\(964\) 29.7984i 0.959742i
\(965\) 0 0
\(966\) 5.52223 0.430851i 0.177675 0.0138624i
\(967\) −12.7477 −0.409939 −0.204970 0.978768i \(-0.565710\pi\)
−0.204970 + 0.978768i \(0.565710\pi\)
\(968\) 32.6866i 1.05059i
\(969\) −62.3813 + 31.3321i −2.00398 + 1.00653i
\(970\) 0 0
\(971\) −48.1313 −1.54461 −0.772303 0.635254i \(-0.780895\pi\)
−0.772303 + 0.635254i \(0.780895\pi\)
\(972\) −42.9801 + 40.5655i −1.37859 + 1.30114i
\(973\) −6.00000 2.44949i −0.192351 0.0785270i
\(974\) 96.6578i 3.09712i
\(975\) 0 0
\(976\) 12.2474i 0.392031i
\(977\) 13.9368i 0.445877i 0.974832 + 0.222939i \(0.0715650\pi\)
−0.974832 + 0.222939i \(0.928435\pi\)
\(978\) 14.8991 7.48331i 0.476419 0.239290i
\(979\) 45.5178i 1.45476i
\(980\) 0 0
\(981\) −8.95644 + 12.0325i −0.285957 + 0.384170i
\(982\) −6.04356 −0.192858
\(983\) 7.12502 0.227253 0.113626 0.993524i \(-0.463753\pi\)
0.113626 + 0.993524i \(0.463753\pi\)
\(984\) −31.1216 + 15.6314i −0.992120 + 0.498310i
\(985\) 0 0
\(986\) 7.12502 0.226907
\(987\) −26.9312 + 2.10120i −0.857228 + 0.0668820i
\(988\) −63.4955 −2.02006
\(989\) 1.29714i 0.0412468i
\(990\) 0 0
\(991\) 22.0780 0.701332 0.350666 0.936501i \(-0.385955\pi\)
0.350666 + 0.936501i \(0.385955\pi\)
\(992\) −8.35532 −0.265282
\(993\) 13.2159 + 26.3124i 0.419393 + 0.834998i
\(994\) −10.3739 + 25.4107i −0.329039 + 0.805978i
\(995\) 0 0
\(996\) −21.0000 41.8104i −0.665410 1.32481i
\(997\) 36.2311i 1.14745i −0.819048 0.573725i \(-0.805498\pi\)
0.819048 0.573725i \(-0.194502\pi\)
\(998\) 73.9947i 2.34226i
\(999\) 2.98122 + 0.525310i 0.0943218 + 0.0166201i
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 525.2.b.h.251.2 yes 8
3.2 odd 2 inner 525.2.b.h.251.7 yes 8
5.2 odd 4 525.2.g.f.524.15 16
5.3 odd 4 525.2.g.f.524.2 16
5.4 even 2 525.2.b.i.251.7 yes 8
7.6 odd 2 inner 525.2.b.h.251.1 8
15.2 even 4 525.2.g.f.524.4 16
15.8 even 4 525.2.g.f.524.13 16
15.14 odd 2 525.2.b.i.251.2 yes 8
21.20 even 2 inner 525.2.b.h.251.8 yes 8
35.13 even 4 525.2.g.f.524.3 16
35.27 even 4 525.2.g.f.524.14 16
35.34 odd 2 525.2.b.i.251.8 yes 8
105.62 odd 4 525.2.g.f.524.1 16
105.83 odd 4 525.2.g.f.524.16 16
105.104 even 2 525.2.b.i.251.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.b.h.251.1 8 7.6 odd 2 inner
525.2.b.h.251.2 yes 8 1.1 even 1 trivial
525.2.b.h.251.7 yes 8 3.2 odd 2 inner
525.2.b.h.251.8 yes 8 21.20 even 2 inner
525.2.b.i.251.1 yes 8 105.104 even 2
525.2.b.i.251.2 yes 8 15.14 odd 2
525.2.b.i.251.7 yes 8 5.4 even 2
525.2.b.i.251.8 yes 8 35.34 odd 2
525.2.g.f.524.1 16 105.62 odd 4
525.2.g.f.524.2 16 5.3 odd 4
525.2.g.f.524.3 16 35.13 even 4
525.2.g.f.524.4 16 15.2 even 4
525.2.g.f.524.13 16 15.8 even 4
525.2.g.f.524.14 16 35.27 even 4
525.2.g.f.524.15 16 5.2 odd 4
525.2.g.f.524.16 16 105.83 odd 4