Properties

Label 525.2.g.f.524.1
Level $525$
Weight $2$
Character 525.524
Analytic conductor $4.192$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(524,525)]
 
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, 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("525.524");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 32x^{14} + 386x^{12} + 2208x^{10} + 6263x^{8} + 8496x^{6} + 4790x^{4} + 704x^{2} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 524.1
Root \(-3.32519i\) of defining polynomial
Character \(\chi\) \(=\) 525.524
Dual form 525.2.g.f.524.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.40651 q^{2} +(-1.54779 - 0.777403i) q^{3} +3.79129 q^{4} +(3.72476 + 1.87083i) q^{6} +(2.44949 - 1.00000i) q^{7} -4.31075 q^{8} +(1.79129 + 2.40651i) q^{9} +O(q^{10})\) \(q-2.40651 q^{2} +(-1.54779 - 0.777403i) q^{3} +3.79129 q^{4} +(3.72476 + 1.87083i) q^{6} +(2.44949 - 1.00000i) q^{7} -4.31075 q^{8} +(1.79129 + 2.40651i) q^{9} -4.31075i q^{11} +(-5.86811 - 2.94736i) q^{12} +2.44949 q^{13} +(-5.89472 + 2.40651i) q^{14} +2.79129 q^{16} +5.89472i q^{17} +(-4.31075 - 5.79129i) q^{18} +6.83723i q^{19} +(-4.56869 - 0.356455i) q^{21} +10.3739i q^{22} +0.502268 q^{23} +(6.67212 + 3.35119i) q^{24} -5.89472 q^{26} +(-0.901703 - 5.11732i) q^{27} +(9.28672 - 3.79129i) q^{28} +0.502268i q^{29} -4.38774i q^{31} +1.90424 q^{32} +(-3.35119 + 6.67212i) q^{33} -14.1857i q^{34} +(6.79129 + 9.12377i) q^{36} -0.582576i q^{37} -16.4539i q^{38} +(-3.79129 - 1.90424i) q^{39} +4.66442 q^{41} +(10.9946 + 0.857812i) q^{42} -2.58258i q^{43} -16.3433i q^{44} -1.20871 q^{46} +5.89472i q^{47} +(-4.32032 - 2.16996i) q^{48} +(5.00000 - 4.89898i) q^{49} +(4.58258 - 9.12377i) q^{51} +9.28672 q^{52} +13.4345 q^{53} +(2.16996 + 12.3149i) q^{54} +(-10.5591 + 4.31075i) q^{56} +(5.31529 - 10.5826i) q^{57} -1.20871i q^{58} +10.5591 q^{59} +4.38774i q^{61} +10.5591i q^{62} +(6.79425 + 4.10343i) q^{63} -10.1652 q^{64} +(8.06468 - 16.0565i) q^{66} -14.1652i q^{67} +22.3486i q^{68} +(-0.777403 - 0.390465i) q^{69} -4.31075i q^{71} +(-7.72180 - 10.3739i) q^{72} -6.32599 q^{73} +1.40197i q^{74} +25.9219i q^{76} +(-4.31075 - 10.5591i) q^{77} +(9.12377 + 4.58258i) q^{78} +8.58258 q^{79} +(-2.58258 + 8.62150i) q^{81} -11.2250 q^{82} -7.12502i q^{83} +(-17.3212 - 1.35142i) q^{84} +6.21499i q^{86} +(0.390465 - 0.777403i) q^{87} +18.5826i q^{88} -10.5591 q^{89} +(6.00000 - 2.44949i) q^{91} +1.90424 q^{92} +(-3.41105 + 6.79129i) q^{93} -14.1857i q^{94} +(-2.94736 - 1.48036i) q^{96} +0.511238 q^{97} +(-12.0325 + 11.7894i) q^{98} +(10.3739 - 7.72180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 24 q^{4} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 24 q^{4} - 8 q^{9} + 8 q^{16} - 24 q^{21} + 72 q^{36} - 24 q^{39} - 56 q^{46} + 80 q^{49} - 16 q^{64} + 64 q^{79} + 32 q^{81} - 120 q^{84} + 96 q^{91} + 56 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.40651 −1.70166 −0.850830 0.525442i \(-0.823900\pi\)
−0.850830 + 0.525442i \(0.823900\pi\)
\(3\) −1.54779 0.777403i −0.893615 0.448834i
\(4\) 3.79129 1.89564
\(5\) 0 0
\(6\) 3.72476 + 1.87083i 1.52063 + 0.763763i
\(7\) 2.44949 1.00000i 0.925820 0.377964i
\(8\) −4.31075 −1.52408
\(9\) 1.79129 + 2.40651i 0.597096 + 0.802170i
\(10\) 0 0
\(11\) 4.31075i 1.29974i −0.760045 0.649870i \(-0.774823\pi\)
0.760045 0.649870i \(-0.225177\pi\)
\(12\) −5.86811 2.94736i −1.69398 0.850830i
\(13\) 2.44949 0.679366 0.339683 0.940540i \(-0.389680\pi\)
0.339683 + 0.940540i \(0.389680\pi\)
\(14\) −5.89472 + 2.40651i −1.57543 + 0.643167i
\(15\) 0 0
\(16\) 2.79129 0.697822
\(17\) 5.89472i 1.42968i 0.699288 + 0.714840i \(0.253500\pi\)
−0.699288 + 0.714840i \(0.746500\pi\)
\(18\) −4.31075 5.79129i −1.01605 1.36502i
\(19\) 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
\(22\) 10.3739i 2.21172i
\(23\) 0.502268 0.104730 0.0523650 0.998628i \(-0.483324\pi\)
0.0523650 + 0.998628i \(0.483324\pi\)
\(24\) 6.67212 + 3.35119i 1.36194 + 0.684059i
\(25\) 0 0
\(26\) −5.89472 −1.15605
\(27\) −0.901703 5.11732i −0.173533 0.984828i
\(28\) 9.28672 3.79129i 1.75503 0.716486i
\(29\) 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 \(-0.871080\pi\)
0.919097 0.394031i \(-0.128920\pi\)
\(32\) 1.90424 0.336626
\(33\) −3.35119 + 6.67212i −0.583368 + 1.16147i
\(34\) 14.1857i 2.43283i
\(35\) 0 0
\(36\) 6.79129 + 9.12377i 1.13188 + 1.52063i
\(37\) 0.582576i 0.0957749i −0.998853 0.0478874i \(-0.984751\pi\)
0.998853 0.0478874i \(-0.0152489\pi\)
\(38\) 16.4539i 2.66917i
\(39\) −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 \(0.381332\pi\)
\(42\) 10.9946 + 0.857812i 1.69650 + 0.132363i
\(43\) 2.58258i 0.393839i −0.980420 0.196920i \(-0.936906\pi\)
0.980420 0.196920i \(-0.0630938\pi\)
\(44\) 16.3433i 2.46384i
\(45\) 0 0
\(46\) −1.20871 −0.178215
\(47\) 5.89472i 0.859833i 0.902869 + 0.429917i \(0.141457\pi\)
−0.902869 + 0.429917i \(0.858543\pi\)
\(48\) −4.32032 2.16996i −0.623584 0.313206i
\(49\) 5.00000 4.89898i 0.714286 0.699854i
\(50\) 0 0
\(51\) 4.58258 9.12377i 0.641689 1.27758i
\(52\) 9.28672 1.28784
\(53\) 13.4345 1.84537 0.922687 0.385551i \(-0.125988\pi\)
0.922687 + 0.385551i \(0.125988\pi\)
\(54\) 2.16996 + 12.3149i 0.295294 + 1.67584i
\(55\) 0 0
\(56\) −10.5591 + 4.31075i −1.41102 + 0.576048i
\(57\) 5.31529 10.5826i 0.704027 1.40170i
\(58\) 1.20871i 0.158712i
\(59\) 10.5591 1.37468 0.687342 0.726334i \(-0.258778\pi\)
0.687342 + 0.726334i \(0.258778\pi\)
\(60\) 0 0
\(61\) 4.38774i 0.561793i 0.959738 + 0.280896i \(0.0906317\pi\)
−0.959738 + 0.280896i \(0.909368\pi\)
\(62\) 10.5591i 1.34101i
\(63\) 6.79425 + 4.10343i 0.855995 + 0.516984i
\(64\) −10.1652 −1.27064
\(65\) 0 0
\(66\) 8.06468 16.0565i 0.992693 1.97642i
\(67\) 14.1652i 1.73055i −0.501299 0.865274i \(-0.667144\pi\)
0.501299 0.865274i \(-0.332856\pi\)
\(68\) 22.3486i 2.71016i
\(69\) −0.777403 0.390465i −0.0935884 0.0470064i
\(70\) 0 0
\(71\) 4.31075i 0.511592i −0.966731 0.255796i \(-0.917662\pi\)
0.966731 0.255796i \(-0.0823375\pi\)
\(72\) −7.72180 10.3739i −0.910022 1.22257i
\(73\) −6.32599 −0.740401 −0.370201 0.928952i \(-0.620711\pi\)
−0.370201 + 0.928952i \(0.620711\pi\)
\(74\) 1.40197i 0.162976i
\(75\) 0 0
\(76\) 25.9219i 2.97345i
\(77\) −4.31075 10.5591i −0.491256 1.20333i
\(78\) 9.12377 + 4.58258i 1.03306 + 0.518875i
\(79\) 8.58258 0.965615 0.482808 0.875726i \(-0.339617\pi\)
0.482808 + 0.875726i \(0.339617\pi\)
\(80\) 0 0
\(81\) −2.58258 + 8.62150i −0.286953 + 0.957945i
\(82\) −11.2250 −1.23959
\(83\) 7.12502i 0.782073i −0.920375 0.391036i \(-0.872117\pi\)
0.920375 0.391036i \(-0.127883\pi\)
\(84\) −17.3212 1.35142i −1.88990 0.147452i
\(85\) 0 0
\(86\) 6.21499i 0.670180i
\(87\) 0.390465 0.777403i 0.0418622 0.0833464i
\(88\) 18.5826i 1.98091i
\(89\) −10.5591 −1.11927 −0.559633 0.828740i \(-0.689058\pi\)
−0.559633 + 0.828740i \(0.689058\pi\)
\(90\) 0 0
\(91\) 6.00000 2.44949i 0.628971 0.256776i
\(92\) 1.90424 0.198531
\(93\) −3.41105 + 6.79129i −0.353709 + 0.704224i
\(94\) 14.1857i 1.46314i
\(95\) 0 0
\(96\) −2.94736 1.48036i −0.300814 0.151089i
\(97\) 0.511238 0.0519084 0.0259542 0.999663i \(-0.491738\pi\)
0.0259542 + 0.999663i \(0.491738\pi\)
\(98\) −12.0325 + 11.7894i −1.21547 + 1.19091i
\(99\) 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 \(0.275708\pi\)
\(102\) −11.0280 + 21.9564i −1.09194 + 2.17401i
\(103\) 6.83723 0.673692 0.336846 0.941560i \(-0.390640\pi\)
0.336846 + 0.941560i \(0.390640\pi\)
\(104\) −10.5591 −1.03541
\(105\) 0 0
\(106\) −32.3303 −3.14020
\(107\) 1.00454 0.0971121 0.0485561 0.998820i \(-0.484538\pi\)
0.0485561 + 0.998820i \(0.484538\pi\)
\(108\) −3.41862 19.4012i −0.328956 1.86688i
\(109\) −5.00000 −0.478913 −0.239457 0.970907i \(-0.576969\pi\)
−0.239457 + 0.970907i \(0.576969\pi\)
\(110\) 0 0
\(111\) −0.452896 + 0.901703i −0.0429870 + 0.0855859i
\(112\) 6.83723 2.79129i 0.646058 0.263752i
\(113\) −6.31982 −0.594519 −0.297259 0.954797i \(-0.596073\pi\)
−0.297259 + 0.954797i \(0.596073\pi\)
\(114\) −12.7913 + 25.4671i −1.19801 + 2.38521i
\(115\) 0 0
\(116\) 1.90424i 0.176804i
\(117\) 4.38774 + 5.89472i 0.405647 + 0.544967i
\(118\) −25.4107 −2.33924
\(119\) 5.89472 + 14.4391i 0.540368 + 1.32363i
\(120\) 0 0
\(121\) −7.58258 −0.689325
\(122\) 10.5591i 0.955980i
\(123\) −7.21953 3.62614i −0.650963 0.326958i
\(124\) 16.6352i 1.49388i
\(125\) 0 0
\(126\) −16.3504 9.87495i −1.45661 0.879730i
\(127\) 10.1652i 0.902011i 0.892521 + 0.451006i \(0.148935\pi\)
−0.892521 + 0.451006i \(0.851065\pi\)
\(128\) 20.6540 1.82558
\(129\) −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 \(0.582903\pi\)
\(132\) −12.7053 + 25.2959i −1.10586 + 2.20173i
\(133\) 6.83723 + 16.7477i 0.592863 + 1.45221i
\(134\) 34.0886i 2.94480i
\(135\) 0 0
\(136\) 25.4107i 2.17895i
\(137\) 1.00454 0.0858233 0.0429116 0.999079i \(-0.486337\pi\)
0.0429116 + 0.999079i \(0.486337\pi\)
\(138\) 1.87083 + 0.939657i 0.159256 + 0.0799889i
\(139\) 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
\(142\) 10.3739i 0.870555i
\(143\) 10.5591i 0.883000i
\(144\) 5.00000 + 6.71726i 0.416667 + 0.559772i
\(145\) 0 0
\(146\) 15.2236 1.25991
\(147\) −11.5474 + 3.69556i −0.952415 + 0.304805i
\(148\) 2.20871i 0.181555i
\(149\) 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 \(0.304468\pi\)
\(152\) 29.4736i 2.39062i
\(153\) −14.1857 + 10.5591i −1.14685 + 0.853656i
\(154\) 10.3739 + 25.4107i 0.835950 + 2.04765i
\(155\) 0 0
\(156\) −14.3739 7.21953i −1.15083 0.578025i
\(157\) 9.28672 0.741161 0.370580 0.928800i \(-0.379159\pi\)
0.370580 + 0.928800i \(0.379159\pi\)
\(158\) −20.6540 −1.64315
\(159\) −20.7938 10.4440i −1.64905 0.828266i
\(160\) 0 0
\(161\) 1.23030 0.502268i 0.0969612 0.0395842i
\(162\) 6.21499 20.7477i 0.488296 1.63010i
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) 17.6842 1.38090
\(165\) 0 0
\(166\) 17.1464i 1.33082i
\(167\) 13.0197i 1.00750i −0.863850 0.503749i \(-0.831954\pi\)
0.863850 0.503749i \(-0.168046\pi\)
\(168\) 19.6945 + 1.53659i 1.51946 + 0.118550i
\(169\) −7.00000 −0.538462
\(170\) 0 0
\(171\) −16.4539 + 12.2474i −1.25826 + 0.936586i
\(172\) 9.79129i 0.746579i
\(173\) 17.6842i 1.34450i −0.740323 0.672251i \(-0.765328\pi\)
0.740323 0.672251i \(-0.234672\pi\)
\(174\) −0.939657 + 1.87083i −0.0712352 + 0.141827i
\(175\) 0 0
\(176\) 12.0325i 0.906987i
\(177\) −16.3433 8.20871i −1.22844 0.617005i
\(178\) 25.4107 1.90461
\(179\) 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 \(-0.849577\pi\)
0.890403 0.455173i \(-0.150423\pi\)
\(182\) −14.4391 + 5.89472i −1.07029 + 0.436946i
\(183\) 3.41105 6.79129i 0.252152 0.502026i
\(184\) −2.16515 −0.159617
\(185\) 0 0
\(186\) 8.20871 16.3433i 0.601892 1.19835i
\(187\) 25.4107 1.85821
\(188\) 22.3486i 1.62994i
\(189\) −7.32603 11.6331i −0.532890 0.846184i
\(190\) 0 0
\(191\) 15.4436i 1.11746i 0.829350 + 0.558730i \(0.188711\pi\)
−0.829350 + 0.558730i \(0.811289\pi\)
\(192\) 15.7335 + 7.90242i 1.13547 + 0.570308i
\(193\) 11.0000i 0.791797i 0.918294 + 0.395899i \(0.129567\pi\)
−0.918294 + 0.395899i \(0.870433\pi\)
\(194\) −1.23030 −0.0883304
\(195\) 0 0
\(196\) 18.9564 18.5734i 1.35403 1.32667i
\(197\) −18.7498 −1.33587 −0.667934 0.744220i \(-0.732821\pi\)
−0.667934 + 0.744220i \(0.732821\pi\)
\(198\) −24.9648 + 18.5826i −1.77417 + 1.32061i
\(199\) 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
\(202\) −31.3321 −2.20452
\(203\) 0.502268 + 1.23030i 0.0352523 + 0.0863501i
\(204\) 17.3739 34.5908i 1.21641 2.42184i
\(205\) 0 0
\(206\) −16.4539 −1.14639
\(207\) 0.899706 + 1.20871i 0.0625339 + 0.0840113i
\(208\) 6.83723 0.474077
\(209\) 29.4736 2.03873
\(210\) 0 0
\(211\) 12.7477 0.877590 0.438795 0.898587i \(-0.355405\pi\)
0.438795 + 0.898587i \(0.355405\pi\)
\(212\) 50.9341 3.49817
\(213\) −3.35119 + 6.67212i −0.229620 + 0.457166i
\(214\) −2.41742 −0.165252
\(215\) 0 0
\(216\) 3.88702 + 22.0595i 0.264478 + 1.50096i
\(217\) −4.38774 10.7477i −0.297859 0.729603i
\(218\) 12.0325 0.814947
\(219\) 9.79129 + 4.91785i 0.661634 + 0.332317i
\(220\) 0 0
\(221\) 14.4391i 0.971276i
\(222\) 1.08990 2.16996i 0.0731493 0.145638i
\(223\) 2.44949 0.164030 0.0820150 0.996631i \(-0.473864\pi\)
0.0820150 + 0.996631i \(0.473864\pi\)
\(224\) 4.66442 1.90424i 0.311655 0.127233i
\(225\) 0 0
\(226\) 15.2087 1.01167
\(227\) 5.89472i 0.391246i 0.980679 + 0.195623i \(0.0626729\pi\)
−0.980679 + 0.195623i \(0.937327\pi\)
\(228\) 20.1518 40.1216i 1.33458 2.65712i
\(229\) 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
\(232\) 2.16515i 0.142149i
\(233\) 0.502268 0.0329047 0.0164523 0.999865i \(-0.494763\pi\)
0.0164523 + 0.999865i \(0.494763\pi\)
\(234\) −10.5591 14.1857i −0.690273 0.927348i
\(235\) 0 0
\(236\) 40.0327 2.60591
\(237\) −13.2840 6.67212i −0.862888 0.433401i
\(238\) −14.1857 34.7477i −0.919522 2.25236i
\(239\) 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 \(-0.918535\pi\)
0.967429 0.253144i \(-0.0814647\pi\)
\(242\) 18.2475 1.17300
\(243\) 10.6997 11.3365i 0.686384 0.727240i
\(244\) 16.6352i 1.06496i
\(245\) 0 0
\(246\) 17.3739 + 8.72633i 1.10772 + 0.556371i
\(247\) 16.7477i 1.06563i
\(248\) 18.9145i 1.20107i
\(249\) −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 \(0.340473\pi\)
\(252\) 25.7590 + 15.5573i 1.62266 + 0.980017i
\(253\) 2.16515i 0.136122i
\(254\) 24.4625i 1.53492i
\(255\) 0 0
\(256\) −29.3739 −1.83587
\(257\) 16.4539i 1.02636i 0.858280 + 0.513182i \(0.171533\pi\)
−0.858280 + 0.513182i \(0.828467\pi\)
\(258\) 4.83156 9.61948i 0.300800 0.598883i
\(259\) −0.582576 1.42701i −0.0361995 0.0886703i
\(260\) 0 0
\(261\) −1.20871 + 0.899706i −0.0748174 + 0.0556904i
\(262\) 14.1857 0.876395
\(263\) 7.32436 0.451639 0.225820 0.974169i \(-0.427494\pi\)
0.225820 + 0.974169i \(0.427494\pi\)
\(264\) 14.4462 28.7619i 0.889100 1.77017i
\(265\) 0 0
\(266\) −16.4539 40.3036i −1.00885 2.47117i
\(267\) 16.3433 + 8.20871i 1.00019 + 0.502365i
\(268\) 53.7042i 3.28050i
\(269\) −18.9145 −1.15324 −0.576618 0.817014i \(-0.695628\pi\)
−0.576618 + 0.817014i \(0.695628\pi\)
\(270\) 0 0
\(271\) 3.47197i 0.210907i −0.994424 0.105453i \(-0.966371\pi\)
0.994424 0.105453i \(-0.0336294\pi\)
\(272\) 16.4539i 0.997662i
\(273\) −11.1910 0.873133i −0.677308 0.0528444i
\(274\) −2.41742 −0.146042
\(275\) 0 0
\(276\) −2.94736 1.48036i −0.177410 0.0891074i
\(277\) 8.74773i 0.525600i 0.964850 + 0.262800i \(0.0846459\pi\)
−0.964850 + 0.262800i \(0.915354\pi\)
\(278\) 5.89472i 0.353542i
\(279\) 10.5591 7.85971i 0.632159 0.470548i
\(280\) 0 0
\(281\) 21.5538i 1.28579i 0.765955 + 0.642895i \(0.222267\pi\)
−0.765955 + 0.642895i \(0.777733\pi\)
\(282\) −11.0280 + 21.9564i −0.656709 + 1.30749i
\(283\) −1.02248 −0.0607799 −0.0303900 0.999538i \(-0.509675\pi\)
−0.0303900 + 0.999538i \(0.509675\pi\)
\(284\) 16.3433i 0.969796i
\(285\) 0 0
\(286\) 25.4107i 1.50256i
\(287\) 11.4255 4.66442i 0.674423 0.275332i
\(288\) 3.41105 + 4.58258i 0.200998 + 0.270031i
\(289\) −17.7477 −1.04398
\(290\) 0 0
\(291\) −0.791288 0.397438i −0.0463861 0.0232983i
\(292\) −23.9837 −1.40354
\(293\) 22.3486i 1.30562i 0.757523 + 0.652809i \(0.226410\pi\)
−0.757523 + 0.652809i \(0.773590\pi\)
\(294\) 27.7890 8.89340i 1.62069 0.518673i
\(295\) 0 0
\(296\) 2.51134i 0.145969i
\(297\) −22.0595 + 3.88702i −1.28002 + 0.225548i
\(298\) 15.2087i 0.881017i
\(299\) 1.23030 0.0711501
\(300\) 0 0
\(301\) −2.58258 6.32599i −0.148857 0.364624i
\(302\) −34.0886 −1.96158
\(303\) −20.1518 10.1216i −1.15769 0.581470i
\(304\) 19.0847i 1.09458i
\(305\) 0 0
\(306\) 34.1380 25.4107i 1.95154 1.45263i
\(307\) −20.5117 −1.17066 −0.585332 0.810794i \(-0.699036\pi\)
−0.585332 + 0.810794i \(0.699036\pi\)
\(308\) −16.3433 40.0327i −0.931246 2.28108i
\(309\) −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 \(0.777698\pi\)
\(312\) 16.3433 + 8.20871i 0.925257 + 0.464727i
\(313\) −10.7137 −0.605576 −0.302788 0.953058i \(-0.597917\pi\)
−0.302788 + 0.953058i \(0.597917\pi\)
\(314\) −22.3486 −1.26120
\(315\) 0 0
\(316\) 32.5390 1.83046
\(317\) 13.9368 0.782768 0.391384 0.920227i \(-0.371996\pi\)
0.391384 + 0.920227i \(0.371996\pi\)
\(318\) 50.0404 + 25.1337i 2.80613 + 1.40943i
\(319\) 2.16515 0.121225
\(320\) 0 0
\(321\) −1.55481 0.780929i −0.0867809 0.0435872i
\(322\) −2.96073 + 1.20871i −0.164995 + 0.0673589i
\(323\) −40.3036 −2.24255
\(324\) −9.79129 + 32.6866i −0.543960 + 1.81592i
\(325\) 0 0
\(326\) 9.62604i 0.533137i
\(327\) 7.73893 + 3.88702i 0.427964 + 0.214953i
\(328\) −20.1072 −1.11023
\(329\) 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 \(0.345262\pi\)
\(332\) 27.0130i 1.48253i
\(333\) 1.40197 1.04356i 0.0768277 0.0571868i
\(334\) 31.3321i 1.71442i
\(335\) 0 0
\(336\) −12.7525 0.994968i −0.695708 0.0542800i
\(337\) 2.00000i 0.108947i −0.998515 0.0544735i \(-0.982652\pi\)
0.998515 0.0544735i \(-0.0173480\pi\)
\(338\) 16.8456 0.916278
\(339\) 9.78174 + 4.91305i 0.531271 + 0.266840i
\(340\) 0 0
\(341\) −18.9145 −1.02428
\(342\) 39.5964 29.4736i 2.14113 1.59375i
\(343\) 7.34847 17.0000i 0.396780 0.917914i
\(344\) 11.1328i 0.600243i
\(345\) 0 0
\(346\) 42.5571i 2.28788i
\(347\) −18.7498 −1.00654 −0.503271 0.864129i \(-0.667870\pi\)
−0.503271 + 0.864129i \(0.667870\pi\)
\(348\) 1.48036 2.94736i 0.0793558 0.157995i
\(349\) 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
\(352\) 8.20871i 0.437526i
\(353\) 13.9933i 0.744786i 0.928075 + 0.372393i \(0.121463\pi\)
−0.928075 + 0.372393i \(0.878537\pi\)
\(354\) 39.3303 + 19.7543i 2.09038 + 1.04993i
\(355\) 0 0
\(356\) −40.0327 −2.12173
\(357\) 2.10120 26.9312i 0.111207 1.42535i
\(358\) 29.9129i 1.58094i
\(359\) 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
\(362\) 29.4736i 1.54910i
\(363\) 11.7362 + 5.89472i 0.615991 + 0.309393i
\(364\) 22.7477 9.28672i 1.19230 0.486756i
\(365\) 0 0
\(366\) −8.20871 + 16.3433i −0.429076 + 0.854278i
\(367\) −32.7591 −1.71001 −0.855007 0.518617i \(-0.826447\pi\)
−0.855007 + 0.518617i \(0.826447\pi\)
\(368\) 1.40197 0.0730829
\(369\) 8.35532 + 11.2250i 0.434961 + 0.584349i
\(370\) 0 0
\(371\) 32.9077 13.4345i 1.70848 0.697486i
\(372\) −12.9323 + 25.7477i −0.670506 + 1.33496i
\(373\) 18.9129i 0.979272i 0.871927 + 0.489636i \(0.162870\pi\)
−0.871927 + 0.489636i \(0.837130\pi\)
\(374\) −61.1510 −3.16204
\(375\) 0 0
\(376\) 25.4107i 1.31046i
\(377\) 1.23030i 0.0633637i
\(378\) 17.6302 + 27.9952i 0.906797 + 1.43992i
\(379\) 19.3303 0.992931 0.496465 0.868056i \(-0.334631\pi\)
0.496465 + 0.868056i \(0.334631\pi\)
\(380\) 0 0
\(381\) 7.90242 15.7335i 0.404853 0.806051i
\(382\) 37.1652i 1.90153i
\(383\) 19.8880i 1.01623i −0.861290 0.508114i \(-0.830343\pi\)
0.861290 0.508114i \(-0.169657\pi\)
\(384\) −31.9681 16.0565i −1.63136 0.819381i
\(385\) 0 0
\(386\) 26.4716i 1.34737i
\(387\) 6.21499 4.62614i 0.315926 0.235160i
\(388\) 1.93825 0.0983998
\(389\) 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
\(392\) −21.5538 + 21.1183i −1.08863 + 1.06663i
\(393\) 9.12377 + 4.58258i 0.460233 + 0.231160i
\(394\) 45.1216 2.27319
\(395\) 0 0
\(396\) 39.3303 29.2756i 1.97642 1.47115i
\(397\) 13.6745 0.686302 0.343151 0.939280i \(-0.388506\pi\)
0.343151 + 0.939280i \(0.388506\pi\)
\(398\) 45.9275i 2.30214i
\(399\) 2.43716 31.2372i 0.122011 1.56382i
\(400\) 0 0
\(401\) 11.1328i 0.555948i −0.960589 0.277974i \(-0.910337\pi\)
0.960589 0.277974i \(-0.0896628\pi\)
\(402\) 26.5006 52.7618i 1.32173 2.63152i
\(403\) 10.7477i 0.535382i
\(404\) 49.3616 2.45583
\(405\) 0 0
\(406\) −1.20871 2.96073i −0.0599874 0.146938i
\(407\) −2.51134 −0.124482
\(408\) −19.7543 + 39.3303i −0.977986 + 1.94714i
\(409\) 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
\(412\) 25.9219 1.27708
\(413\) 25.8645 10.5591i 1.27271 0.519581i
\(414\) −2.16515 2.90878i −0.106411 0.142959i
\(415\) 0 0
\(416\) 4.66442 0.228692
\(417\) 1.90424 3.79129i 0.0932511 0.185660i
\(418\) −70.9285 −3.46923
\(419\) −18.9145 −0.924032 −0.462016 0.886872i \(-0.652874\pi\)
−0.462016 + 0.886872i \(0.652874\pi\)
\(420\) 0 0
\(421\) −10.1652 −0.495419 −0.247710 0.968834i \(-0.579678\pi\)
−0.247710 + 0.968834i \(0.579678\pi\)
\(422\) −30.6775 −1.49336
\(423\) −14.1857 + 10.5591i −0.689732 + 0.513403i
\(424\) −57.9129 −2.81250
\(425\) 0 0
\(426\) 8.06468 16.0565i 0.390735 0.777941i
\(427\) 4.38774 + 10.7477i 0.212338 + 0.520119i
\(428\) 3.80848 0.184090
\(429\) −8.20871 + 16.3433i −0.396320 + 0.789062i
\(430\) 0 0
\(431\) 30.8872i 1.48778i −0.668300 0.743892i \(-0.732978\pi\)
0.668300 0.743892i \(-0.267022\pi\)
\(432\) −2.51691 14.2839i −0.121095 0.687235i
\(433\) 23.4724 1.12801 0.564006 0.825770i \(-0.309259\pi\)
0.564006 + 0.825770i \(0.309259\pi\)
\(434\) 10.5591 + 25.8645i 0.506855 + 1.24154i
\(435\) 0 0
\(436\) −18.9564 −0.907849
\(437\) 3.43412i 0.164276i
\(438\) −23.5628 11.8348i −1.12588 0.565491i
\(439\) 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
\(442\) 34.7477i 1.65278i
\(443\) 13.4345 0.638293 0.319147 0.947705i \(-0.396604\pi\)
0.319147 + 0.947705i \(0.396604\pi\)
\(444\) −1.71706 + 3.41862i −0.0814881 + 0.162240i
\(445\) 0 0
\(446\) −5.89472 −0.279123
\(447\) −4.91305 + 9.78174i −0.232379 + 0.462660i
\(448\) −24.8994 + 10.1652i −1.17639 + 0.480258i
\(449\) 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
\(452\) −23.9603 −1.12700
\(453\) −21.9246 11.0120i −1.03011 0.517391i
\(454\) 14.1857i 0.665768i
\(455\) 0 0
\(456\) −22.9129 + 45.6189i −1.07299 + 2.13630i
\(457\) 15.8348i 0.740723i 0.928888 + 0.370361i \(0.120766\pi\)
−0.928888 + 0.370361i \(0.879234\pi\)
\(458\) 44.6972i 2.08856i
\(459\) 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 \(0.560393\pi\)
\(462\) 3.69781 47.3950i 0.172038 2.20501i
\(463\) 14.7477i 0.685385i −0.939448 0.342693i \(-0.888661\pi\)
0.939448 0.342693i \(-0.111339\pi\)
\(464\) 1.40197i 0.0650850i
\(465\) 0 0
\(466\) −1.20871 −0.0559925
\(467\) 35.3683i 1.63665i 0.574755 + 0.818325i \(0.305097\pi\)
−0.574755 + 0.818325i \(0.694903\pi\)
\(468\) 16.6352 + 22.3486i 0.768962 + 1.03306i
\(469\) −14.1652 34.6974i −0.654086 1.60218i
\(470\) 0 0
\(471\) −14.3739 7.21953i −0.662313 0.332658i
\(472\) −45.5178 −2.09513
\(473\) −11.1328 −0.511889
\(474\) 31.9681 + 16.0565i 1.46834 + 0.737501i
\(475\) 0 0
\(476\) 22.3486 + 54.7426i 1.02435 + 2.50912i
\(477\) 24.0651 + 32.3303i 1.10186 + 1.48030i
\(478\) 29.9129i 1.36818i
\(479\) 10.5591 0.482459 0.241230 0.970468i \(-0.422449\pi\)
0.241230 + 0.970468i \(0.422449\pi\)
\(480\) 0 0
\(481\) 1.42701i 0.0650662i
\(482\) 18.9145i 0.861530i
\(483\) −2.29471 0.179036i −0.104413 0.00814641i
\(484\) −28.7477 −1.30671
\(485\) 0 0
\(486\) −25.7488 + 27.2815i −1.16799 + 1.23751i
\(487\) 40.1652i 1.82006i 0.414546 + 0.910028i \(0.363940\pi\)
−0.414546 + 0.910028i \(0.636060\pi\)
\(488\) 18.9145i 0.856217i
\(489\) −3.10961 + 6.19115i −0.140622 + 0.279973i
\(490\) 0 0
\(491\) 2.51134i 0.113335i 0.998393 + 0.0566676i \(0.0180475\pi\)
−0.998393 + 0.0566676i \(0.981952\pi\)
\(492\) −27.3713 13.7477i −1.23399 0.619795i
\(493\) −2.96073 −0.133344
\(494\) 40.3036i 1.81334i
\(495\) 0 0
\(496\) 12.2474i 0.549927i
\(497\) −4.31075 10.5591i −0.193364 0.473642i
\(498\) 13.3297 26.5390i 0.597318 1.18924i
\(499\) −30.7477 −1.37646 −0.688229 0.725494i \(-0.741611\pi\)
−0.688229 + 0.725494i \(0.741611\pi\)
\(500\) 0 0
\(501\) −10.1216 + 20.1518i −0.452199 + 0.900315i
\(502\) −36.6356 −1.63513
\(503\) 11.7894i 0.525665i 0.964841 + 0.262833i \(0.0846567\pi\)
−0.964841 + 0.262833i \(0.915343\pi\)
\(504\) −29.2883 17.6889i −1.30461 0.787925i
\(505\) 0 0
\(506\) 5.21046i 0.231633i
\(507\) 10.8345 + 5.44182i 0.481177 + 0.241680i
\(508\) 38.5390i 1.70989i
\(509\) −31.6774 −1.40408 −0.702039 0.712139i \(-0.747727\pi\)
−0.702039 + 0.712139i \(0.747727\pi\)
\(510\) 0 0
\(511\) −15.4955 + 6.32599i −0.685479 + 0.279845i
\(512\) 29.3804 1.29844
\(513\) 34.9883 6.16515i 1.54477 0.272198i
\(514\) 39.5964i 1.74652i
\(515\) 0 0
\(516\) −7.61178 + 15.1548i −0.335090 + 0.667154i
\(517\) 25.4107 1.11756
\(518\) 1.40197 + 3.43412i 0.0615992 + 0.150887i
\(519\) −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 \(0.782128\pi\)
\(522\) 2.90878 2.16515i 0.127314 0.0947661i
\(523\) 14.6969 0.642652 0.321326 0.946969i \(-0.395871\pi\)
0.321326 + 0.946969i \(0.395871\pi\)
\(524\) −22.3486 −0.976302
\(525\) 0 0
\(526\) −17.6261 −0.768536
\(527\) 25.8645 1.12668
\(528\) −9.35414 + 18.6238i −0.407087 + 0.810498i
\(529\) −22.7477 −0.989032
\(530\) 0 0
\(531\) 18.9145 + 25.4107i 0.820818 + 1.10273i
\(532\) 25.9219 + 63.4955i 1.12386 + 2.75288i
\(533\) 11.4255 0.494891
\(534\) −39.3303 19.7543i −1.70199 0.854854i
\(535\) 0 0
\(536\) 61.0624i 2.63750i
\(537\) −9.66311 + 19.2390i −0.416994 + 0.830223i
\(538\) 45.5178 1.96241
\(539\) −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 \(0.496014\pi\)
\(542\) 8.35532i 0.358892i
\(543\) −9.52121 + 18.9564i −0.408594 + 0.813499i
\(544\) 11.2250i 0.481267i
\(545\) 0 0
\(546\) 26.9312 + 2.10120i 1.15255 + 0.0899231i
\(547\) 41.3303i 1.76716i −0.468284 0.883578i \(-0.655128\pi\)
0.468284 0.883578i \(-0.344872\pi\)
\(548\) 3.80848 0.162690
\(549\) −10.5591 + 7.85971i −0.450653 + 0.335444i
\(550\) 0 0
\(551\) −3.43412 −0.146298
\(552\) 3.35119 + 1.68320i 0.142636 + 0.0716416i
\(553\) 21.0229 8.58258i 0.893986 0.364968i
\(554\) 21.0515i 0.894392i
\(555\) 0 0
\(556\) 9.28672i 0.393845i
\(557\) 46.6234 1.97550 0.987748 0.156056i \(-0.0498782\pi\)
0.987748 + 0.156056i \(0.0498782\pi\)
\(558\) −25.4107 + 18.9145i −1.07572 + 0.800713i
\(559\) 6.32599i 0.267561i
\(560\) 0 0
\(561\) −39.3303 19.7543i −1.66053 0.834029i
\(562\) 51.8693i 2.18798i
\(563\) 32.9077i 1.38690i 0.720507 + 0.693448i \(0.243909\pi\)
−0.720507 + 0.693448i \(0.756091\pi\)
\(564\) 17.3739 34.5908i 0.731572 1.45654i
\(565\) 0 0
\(566\) 2.46060 0.103427
\(567\) 2.29551 + 23.7009i 0.0964023 + 0.995342i
\(568\) 18.5826i 0.779708i
\(569\) 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 \(0.515007\pi\)
\(572\) 40.0327i 1.67385i
\(573\) 12.0059 23.9034i 0.501554 0.998578i
\(574\) −27.4955 + 11.2250i −1.14764 + 0.468521i
\(575\) 0 0
\(576\) −18.2087 24.4625i −0.758696 1.01927i
\(577\) 12.7587 0.531151 0.265576 0.964090i \(-0.414438\pi\)
0.265576 + 0.964090i \(0.414438\pi\)
\(578\) 42.7101 1.77650
\(579\) 8.55144 17.0257i 0.355386 0.707562i
\(580\) 0 0
\(581\) −7.12502 17.4527i −0.295596 0.724058i
\(582\) 1.90424 + 0.956439i 0.0789334 + 0.0396457i
\(583\) 57.9129i 2.39851i
\(584\) 27.2698 1.12843
\(585\) 0 0
\(586\) 53.7821i 2.22172i
\(587\) 34.1380i 1.40903i −0.709691 0.704513i \(-0.751165\pi\)
0.709691 0.704513i \(-0.248835\pi\)
\(588\) −43.7796 + 14.0109i −1.80544 + 0.577801i
\(589\) 30.0000 1.23613
\(590\) 0 0
\(591\) 29.0207 + 14.5762i 1.19375 + 0.599583i
\(592\) 1.62614i 0.0668338i
\(593\) 11.7894i 0.484134i 0.970259 + 0.242067i \(0.0778254\pi\)
−0.970259 + 0.242067i \(0.922175\pi\)
\(594\) 53.0863 9.35414i 2.17816 0.383805i
\(595\) 0 0
\(596\) 23.9603i 0.981451i
\(597\) 14.8365 29.5390i 0.607217 1.20895i
\(598\) −2.96073 −0.121073
\(599\) 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 \(-0.671990\pi\)
0.514412 0.857543i \(-0.328010\pi\)
\(602\) 6.21499 + 15.2236i 0.253304 + 0.620466i
\(603\) 34.0886 25.3739i 1.38819 1.03330i
\(604\) 53.7042 2.18519
\(605\) 0 0
\(606\) 48.4955 + 24.3577i 1.96999 + 0.989464i
\(607\) 1.42701 0.0579207 0.0289603 0.999581i \(-0.490780\pi\)
0.0289603 + 0.999581i \(0.490780\pi\)
\(608\) 13.0197i 0.528020i
\(609\) 0.179036 2.29471i 0.00725490 0.0929862i
\(610\) 0 0
\(611\) 14.4391i 0.584142i
\(612\) −53.7821 + 40.0327i −2.17401 + 1.61823i
\(613\) 27.4174i 1.10738i 0.832723 + 0.553690i \(0.186781\pi\)
−0.832723 + 0.553690i \(0.813219\pi\)
\(614\) 49.3616 1.99207
\(615\) 0 0
\(616\) 18.5826 + 45.5178i 0.748713 + 1.83397i
\(617\) 13.9368 0.561074 0.280537 0.959843i \(-0.409487\pi\)
0.280537 + 0.959843i \(0.409487\pi\)
\(618\) 25.4671 + 12.7913i 1.02444 + 0.514541i
\(619\) 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
\(622\) 65.0070 2.60655
\(623\) −25.8645 + 10.5591i −1.03624 + 0.423043i
\(624\) −10.5826 5.31529i −0.423642 0.212782i
\(625\) 0 0
\(626\) 25.7827 1.03048
\(627\) −45.6189 22.9129i −1.82184 0.915052i
\(628\) 35.2086 1.40498
\(629\) 3.43412 0.136927
\(630\) 0 0
\(631\) 6.25227 0.248899 0.124450 0.992226i \(-0.460284\pi\)
0.124450 + 0.992226i \(0.460284\pi\)
\(632\) −36.9973 −1.47168
\(633\) −19.7308 9.91013i −0.784227 0.393892i
\(634\) −33.5390 −1.33200
\(635\) 0 0
\(636\) −78.8352 39.5964i −3.12602 1.57010i
\(637\) 12.2474 12.0000i 0.485262 0.475457i
\(638\) −5.21046 −0.206284
\(639\) 10.3739 7.72180i 0.410384 0.305470i
\(640\) 0 0
\(641\) 36.9973i 1.46131i −0.682748 0.730654i \(-0.739215\pi\)
0.682748 0.730654i \(-0.260785\pi\)
\(642\) 3.74166 + 1.87931i 0.147671 + 0.0741706i
\(643\) −43.0683 −1.69845 −0.849225 0.528032i \(-0.822930\pi\)
−0.849225 + 0.528032i \(0.822930\pi\)
\(644\) 4.66442 1.90424i 0.183804 0.0750376i
\(645\) 0 0
\(646\) 96.9909 3.81606
\(647\) 18.6577i 0.733509i 0.930318 + 0.366755i \(0.119531\pi\)
−0.930318 + 0.366755i \(0.880469\pi\)
\(648\) 11.1328 37.1652i 0.437339 1.45999i
\(649\) 45.5178i 1.78673i
\(650\) 0 0
\(651\) −1.56403 + 20.0462i −0.0612992 + 0.785674i
\(652\) 15.1652i 0.593913i
\(653\) −12.4300 −0.486423 −0.243211 0.969973i \(-0.578201\pi\)
−0.243211 + 0.969973i \(0.578201\pi\)
\(654\) −18.6238 9.35414i −0.728249 0.365776i
\(655\) 0 0
\(656\) 13.0197 0.508335
\(657\) −11.3317 15.2236i −0.442091 0.593928i
\(658\) −14.1857 34.7477i −0.553016 1.35461i
\(659\) 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 \(0.216627\pi\)
−0.777224 + 0.629224i \(0.783373\pi\)
\(662\) −40.9107 −1.59004
\(663\) 11.2250 22.3486i 0.435942 0.867947i
\(664\) 30.7142i 1.19194i
\(665\) 0 0
\(666\) −3.37386 + 2.51134i −0.130735 + 0.0973124i
\(667\) 0.252273i 0.00976805i
\(668\) 49.3616i 1.90986i
\(669\) −3.79129 1.90424i −0.146580 0.0736222i
\(670\) 0 0
\(671\) 18.9145 0.730185
\(672\) −8.69989 0.678776i −0.335606 0.0261844i
\(673\) 47.4955i 1.83082i 0.402528 + 0.915408i \(0.368132\pi\)
−0.402528 + 0.915408i \(0.631868\pi\)
\(674\) 4.81302i 0.185391i
\(675\) 0 0
\(676\) −26.5390 −1.02073
\(677\) 23.5789i 0.906210i −0.891457 0.453105i \(-0.850316\pi\)
0.891457 0.453105i \(-0.149684\pi\)
\(678\) −23.5398 11.8233i −0.904042 0.454071i
\(679\) 1.25227 0.511238i 0.0480578 0.0196195i
\(680\) 0 0
\(681\) 4.58258 9.12377i 0.175605 0.349624i
\(682\) 45.5178 1.74297
\(683\) 33.1889 1.26994 0.634968 0.772538i \(-0.281013\pi\)
0.634968 + 0.772538i \(0.281013\pi\)
\(684\) −62.3813 + 46.4336i −2.38521 + 1.77543i
\(685\) 0 0
\(686\) −17.6842 + 40.9107i −0.675184 + 1.56198i
\(687\) −14.4391 + 28.7477i −0.550884 + 1.09679i
\(688\) 7.20871i 0.274830i
\(689\) 32.9077 1.25368
\(690\) 0 0
\(691\) 4.38774i 0.166918i 0.996511 + 0.0834588i \(0.0265967\pi\)
−0.996511 + 0.0834588i \(0.973403\pi\)
\(692\) 67.0457i 2.54870i
\(693\) 17.6889 29.2883i 0.671945 1.11257i
\(694\) 45.1216 1.71279
\(695\) 0 0
\(696\) −1.68320 + 3.35119i −0.0638014 + 0.127027i
\(697\) 27.4955i 1.04146i
\(698\) 4.66442i 0.176551i
\(699\) −0.777403 0.390465i −0.0294041 0.0147687i
\(700\) 0 0
\(701\) 15.4436i 0.583296i 0.956526 + 0.291648i \(0.0942037\pi\)
−0.956526 + 0.291648i \(0.905796\pi\)
\(702\) 5.31529 + 30.1652i 0.200613 + 1.13851i
\(703\) 3.98320 0.150229
\(704\) 43.8194i 1.65151i
\(705\) 0 0
\(706\) 33.6749i 1.26737i
\(707\) 31.8917 13.0197i 1.19941 0.489658i
\(708\) −61.9621 31.1216i −2.32868 1.16962i
\(709\) 31.4955 1.18284 0.591418 0.806365i \(-0.298568\pi\)
0.591418 + 0.806365i \(0.298568\pi\)
\(710\) 0 0
\(711\) 15.3739 + 20.6540i 0.576565 + 0.774587i
\(712\) 45.5178 1.70585
\(713\) 2.20382i 0.0825337i
\(714\) −5.05656 + 64.8101i −0.189237 + 2.42546i
\(715\) 0 0
\(716\) 47.1257i 1.76117i
\(717\) −9.66311 + 19.2390i −0.360876 + 0.718492i
\(718\) 15.2087i 0.567584i
\(719\) −40.0327 −1.49297 −0.746485 0.665403i \(-0.768260\pi\)
−0.746485 + 0.665403i \(0.768260\pi\)
\(720\) 0 0
\(721\) 16.7477 6.83723i 0.623718 0.254632i
\(722\) 66.7752 2.48511
\(723\) −6.11016 + 12.1652i −0.227239 + 0.452427i
\(724\) 46.4336i 1.72569i
\(725\) 0 0
\(726\) −28.2433 14.1857i −1.04821 0.526481i
\(727\) −45.0066 −1.66920 −0.834601 0.550855i \(-0.814302\pi\)
−0.834601 + 0.550855i \(0.814302\pi\)
\(728\) −25.8645 + 10.5591i −0.958602 + 0.391348i
\(729\) −25.3739 + 9.22860i −0.939773 + 0.341800i
\(730\) 0 0
\(731\) 15.2236 0.563064
\(732\) 12.9323 25.7477i 0.477990 0.951663i
\(733\) 32.2479 1.19110 0.595552 0.803317i \(-0.296933\pi\)
0.595552 + 0.803317i \(0.296933\pi\)
\(734\) 78.8352 2.90986
\(735\) 0 0
\(736\) 0.956439 0.0352548
\(737\) −61.0624 −2.24926
\(738\) −20.1072 27.0130i −0.740155 0.994362i
\(739\) 40.8258 1.50180 0.750900 0.660416i \(-0.229620\pi\)
0.750900 + 0.660416i \(0.229620\pi\)
\(740\) 0 0
\(741\) 13.0197 25.9219i 0.478292 0.952265i
\(742\) −79.1927 + 32.3303i −2.90726 + 1.18688i
\(743\) −12.4300 −0.456012 −0.228006 0.973660i \(-0.573221\pi\)
−0.228006 + 0.973660i \(0.573221\pi\)
\(744\) 14.7042 29.2756i 0.539081 1.07329i
\(745\) 0 0
\(746\) 45.5140i 1.66639i
\(747\) 17.1464 12.7630i 0.627355 0.466972i
\(748\) 96.3392 3.52251
\(749\) 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 \(0.749935\pi\)
\(752\) 16.4539i 0.600011i
\(753\) −23.5628 11.8348i −0.858677 0.431286i
\(754\) 2.96073i 0.107823i
\(755\) 0 0
\(756\) −27.7751 44.1045i −1.01017 1.60406i
\(757\) 6.25227i 0.227243i −0.993524 0.113621i \(-0.963755\pi\)
0.993524 0.113621i \(-0.0362451\pi\)
\(758\) −46.5186 −1.68963
\(759\) −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 \(0.199394\pi\)
\(762\) −19.0173 + 37.8628i −0.688923 + 1.37162i
\(763\) −12.2474 + 5.00000i −0.443387 + 0.181012i
\(764\) 58.5511i 2.11830i
\(765\) 0 0
\(766\) 47.8606i 1.72927i
\(767\) 25.8645 0.933913
\(768\) 45.4645 + 22.8353i 1.64056 + 0.823999i
\(769\) 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
\(772\) 41.7042i 1.50097i
\(773\) 7.12502i 0.256269i −0.991757 0.128135i \(-0.959101\pi\)
0.991757 0.128135i \(-0.0408989\pi\)
\(774\) −14.9564 + 11.1328i −0.537598 + 0.400162i
\(775\) 0 0
\(776\) −2.20382 −0.0791126
\(777\) −0.207662 + 2.66161i −0.00744983 + 0.0954847i
\(778\) 63.4519i 2.27486i
\(779\) 31.8917i 1.14264i
\(780\) 0 0
\(781\) −18.5826 −0.664937
\(782\) 7.12502i 0.254790i
\(783\) 2.57026 0.452896i 0.0918537 0.0161852i
\(784\) 13.9564 13.6745i 0.498444 0.488374i
\(785\) 0 0
\(786\) −21.9564 11.0280i −0.783160 0.393356i
\(787\) −16.1240 −0.574757 −0.287378 0.957817i \(-0.592784\pi\)
−0.287378 + 0.957817i \(0.592784\pi\)
\(788\) −71.0859 −2.53233
\(789\) −11.3365 5.69398i −0.403592 0.202711i
\(790\) 0 0
\(791\) −15.4803 + 6.31982i −0.550418 + 0.224707i
\(792\) −44.7191 + 33.2867i −1.58903 + 1.18279i
\(793\) 10.7477i 0.381663i
\(794\) −32.9077 −1.16785
\(795\) 0 0
\(796\) 72.3555i 2.56457i
\(797\) 15.2236i 0.539246i −0.962966 0.269623i \(-0.913101\pi\)
0.962966 0.269623i \(-0.0868991\pi\)
\(798\) −5.86506 + 75.1726i −0.207621 + 2.66108i
\(799\) −34.7477 −1.22929
\(800\) 0 0
\(801\) −18.9145 25.4107i −0.668310 0.897842i
\(802\) 26.7913i 0.946033i
\(803\) 27.2698i 0.962330i
\(804\) −41.7498 + 83.1226i −1.47240 + 2.93151i
\(805\) 0 0
\(806\) 25.8645i 0.911038i
\(807\) 29.2756 + 14.7042i 1.03055 + 0.517611i
\(808\) −56.1249 −1.97447
\(809\) 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 \(0.0492396\pi\)
−0.988059 + 0.154074i \(0.950760\pi\)
\(812\) 1.90424 + 4.66442i 0.0668258 + 0.163689i
\(813\) −2.69912 + 5.37386i −0.0946622 + 0.188470i
\(814\) 6.04356 0.211827
\(815\) 0 0
\(816\) 12.7913 25.4671i 0.447785 0.891526i
\(817\) 17.6577 0.617764
\(818\) 58.6904i 2.05206i
\(819\) 16.6424 + 10.0513i 0.581534 + 0.351221i
\(820\) 0 0
\(821\) 15.4436i 0.538985i 0.963002 + 0.269493i \(0.0868560\pi\)
−0.963002 + 0.269493i \(0.913144\pi\)
\(822\) 3.74166 + 1.87931i 0.130505 + 0.0655486i
\(823\) 29.7477i 1.03694i −0.855096 0.518470i \(-0.826502\pi\)
0.855096 0.518470i \(-0.173498\pi\)
\(824\) −29.4736 −1.02676
\(825\) 0 0
\(826\) −62.2432 + 25.4107i −2.16572 + 0.884150i
\(827\) −44.6143 −1.55139 −0.775696 0.631107i \(-0.782601\pi\)
−0.775696 + 0.631107i \(0.782601\pi\)
\(828\) 3.41105 + 4.58258i 0.118542 + 0.159256i
\(829\) 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
\(832\) −24.8994 −0.863233
\(833\) 28.8781 + 29.4736i 1.00057 + 1.02120i
\(834\) −4.58258 + 9.12377i −0.158682 + 0.315930i
\(835\) 0 0
\(836\) 111.743 3.86471
\(837\) −22.4535 + 3.95644i −0.776105 + 0.136755i
\(838\) 45.5178 1.57239
\(839\) 10.5591 0.364542 0.182271 0.983248i \(-0.441655\pi\)
0.182271 + 0.983248i \(0.441655\pi\)
\(840\) 0 0
\(841\) 28.7477 0.991301
\(842\) 24.4625 0.843035
\(843\) 16.7560 33.3606i 0.577106 1.14900i
\(844\) 48.3303 1.66360
\(845\) 0 0
\(846\) 34.1380 25.4107i 1.17369 0.873637i
\(847\) −18.5734 + 7.58258i −0.638191 + 0.260540i
\(848\) 37.4996 1.28774
\(849\) 1.58258 + 0.794877i 0.0543139 + 0.0272801i
\(850\) 0 0
\(851\) 0.292609i 0.0100305i
\(852\) −12.7053 + 25.2959i −0.435278 + 0.866625i
\(853\) −27.3489 −0.936409 −0.468205 0.883620i \(-0.655099\pi\)
−0.468205 + 0.883620i \(0.655099\pi\)
\(854\) −10.5591 25.8645i −0.361326 0.885065i
\(855\) 0 0
\(856\) −4.33030 −0.148007
\(857\) 21.3751i 0.730158i −0.930977 0.365079i \(-0.881042\pi\)
0.930977 0.365079i \(-0.118958\pi\)
\(858\) 19.7543 39.3303i 0.674402 1.34271i
\(859\) 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
\(862\) 74.3303i 2.53170i
\(863\) −39.0064 −1.32779 −0.663897 0.747824i \(-0.731099\pi\)
−0.663897 + 0.747824i \(0.731099\pi\)
\(864\) −1.71706 9.74461i −0.0584156 0.331518i
\(865\) 0 0
\(866\) −56.4866 −1.91949
\(867\) 27.4697 + 13.7971i 0.932920 + 0.468576i
\(868\) −16.6352 40.7477i −0.564635 1.38307i
\(869\) 36.9973i 1.25505i
\(870\) 0 0
\(871\) 34.6974i 1.17568i
\(872\) 21.5538 0.729902
\(873\) 0.915775 + 1.23030i 0.0309943 + 0.0416393i
\(874\) 8.26424i 0.279542i
\(875\) 0 0
\(876\) 37.1216 + 18.6450i 1.25422 + 0.629955i
\(877\) 23.4955i 0.793385i −0.917952 0.396693i \(-0.870158\pi\)
0.917952 0.396693i \(-0.129842\pi\)
\(878\) 64.8419i 2.18831i
\(879\) 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 \(0.952029\pi\)
\(882\) −49.9252 7.83816i −1.68107 0.263924i
\(883\) 24.5826i 0.827270i 0.910443 + 0.413635i \(0.135741\pi\)
−0.910443 + 0.413635i \(0.864259\pi\)
\(884\) 54.7426i 1.84119i
\(885\) 0 0
\(886\) −32.3303 −1.08616
\(887\) 46.9010i 1.57478i −0.616455 0.787390i \(-0.711432\pi\)
0.616455 0.787390i \(-0.288568\pi\)
\(888\) 1.95232 3.88702i 0.0655157 0.130440i
\(889\) 10.1652 + 24.8994i 0.340928 + 0.835100i
\(890\) 0 0
\(891\) 37.1652 + 11.1328i 1.24508 + 0.372964i
\(892\) 9.28672 0.310942
\(893\) −40.3036 −1.34871
\(894\) 11.8233 23.5398i 0.395430 0.787290i
\(895\) 0 0
\(896\) 50.5919 20.6540i 1.69016 0.690003i
\(897\) −1.90424 0.956439i −0.0635808 0.0319346i
\(898\) 47.0345i 1.56956i
\(899\) 2.20382 0.0735015
\(900\) 0 0
\(901\) 79.1927i 2.63829i
\(902\) 48.3881i 1.61115i
\(903\) −0.920572 + 11.7990i −0.0306347 + 0.392646i
\(904\) 27.2432 0.906095
\(905\) 0 0
\(906\) 52.7618 + 26.5006i 1.75289 + 0.880423i
\(907\) 53.4955i 1.77629i −0.459566 0.888144i \(-0.651995\pi\)
0.459566 0.888144i \(-0.348005\pi\)
\(908\) 22.3486i 0.741664i
\(909\) 23.3221 + 31.3321i 0.773545 + 1.03922i
\(910\) 0 0
\(911\) 54.2404i 1.79706i 0.438909 + 0.898532i \(0.355365\pi\)
−0.438909 + 0.898532i \(0.644635\pi\)
\(912\) 14.8365 29.5390i 0.491285 0.978135i
\(913\) −30.7142 −1.01649
\(914\) 38.1067i 1.26046i
\(915\) 0 0
\(916\) 70.4173i 2.32665i
\(917\) −14.4391 + 5.89472i −0.476820 + 0.194661i
\(918\) −72.5927 + 12.7913i −2.39592 + 0.422175i
\(919\) −40.0780 −1.32205 −0.661026 0.750363i \(-0.729879\pi\)
−0.661026 + 0.750363i \(0.729879\pi\)
\(920\) 0 0
\(921\) 31.7477 + 15.9459i 1.04612 + 0.525434i
\(922\) 19.4892 0.641843
\(923\) 10.5591i 0.347558i
\(924\) −5.82565 + 74.6675i −0.191650 + 2.45638i
\(925\) 0 0
\(926\) 35.4905i 1.16629i
\(927\) 12.2474 + 16.4539i 0.402259 + 0.540416i
\(928\) 0.956439i 0.0313967i
\(929\) −10.5591 −0.346434 −0.173217 0.984884i \(-0.555416\pi\)
−0.173217 + 0.984884i \(0.555416\pi\)
\(930\) 0 0
\(931\) 33.4955 + 34.1862i 1.09777 + 1.12041i
\(932\) 1.90424 0.0623755
\(933\) 41.8104 + 21.0000i 1.36881 + 0.687509i
\(934\) 85.1142i 2.78502i
\(935\) 0 0
\(936\) −18.9145 25.4107i −0.618238 0.830574i
\(937\) 25.0061 0.816915 0.408457 0.912777i \(-0.366067\pi\)
0.408457 + 0.912777i \(0.366067\pi\)
\(938\) 34.0886 + 83.4996i 1.11303 + 2.72636i
\(939\) 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 \(0.361944\pi\)
\(942\) 34.5908 + 17.3739i 1.12703 + 0.566071i
\(943\) 2.34279 0.0762917
\(944\) 29.4736 0.959284
\(945\) 0 0
\(946\) 26.7913 0.871060
\(947\) −24.8600 −0.807841 −0.403920 0.914794i \(-0.632353\pi\)
−0.403920 + 0.914794i \(0.632353\pi\)
\(948\) −50.3635 25.2959i −1.63573 0.821574i
\(949\) −15.4955 −0.503004
\(950\) 0 0
\(951\) −21.5712 10.8345i −0.699493 0.351333i
\(952\) −25.4107 62.2432i −0.823565 2.01731i
\(953\) 0.502268 0.0162700 0.00813502 0.999967i \(-0.497411\pi\)
0.00813502 + 0.999967i \(0.497411\pi\)
\(954\) −57.9129 77.8032i −1.87500 2.51897i
\(955\) 0 0
\(956\) 47.1257i 1.52415i
\(957\) −3.35119 1.68320i −0.108329 0.0544100i
\(958\) −25.4107 −0.820982
\(959\) 2.46060 1.00454i 0.0794569 0.0324381i
\(960\) 0 0
\(961\) 11.7477 0.378959
\(962\) 3.43412i 0.110720i
\(963\) 1.79941 + 2.41742i 0.0579853 + 0.0779004i
\(964\) 29.7984i 0.959742i
\(965\) 0 0
\(966\) 5.52223 + 0.430851i 0.177675 + 0.0138624i
\(967\) 12.7477i 0.409939i −0.978768 0.204970i \(-0.934290\pi\)
0.978768 0.204970i \(-0.0657096\pi\)
\(968\) 32.6866 1.05059
\(969\) 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 \(0.780895\pi\)
\(972\) 40.5655 42.9801i 1.30114 1.37859i
\(973\) 2.44949 + 6.00000i 0.0785270 + 0.192351i
\(974\) 96.6578i 3.09712i
\(975\) 0 0
\(976\) 12.2474i 0.392031i
\(977\) 13.9368 0.445877 0.222939 0.974832i \(-0.428435\pi\)
0.222939 + 0.974832i \(0.428435\pi\)
\(978\) 7.48331 14.8991i 0.239290 0.476419i
\(979\) 45.5178i 1.45476i
\(980\) 0 0
\(981\) −8.95644 12.0325i −0.285957 0.384170i
\(982\) 6.04356i 0.192858i
\(983\) 7.12502i 0.227253i −0.993524 0.113626i \(-0.963753\pi\)
0.993524 0.113626i \(-0.0362467\pi\)
\(984\) 31.1216 + 15.6314i 0.992120 + 0.498310i
\(985\) 0 0
\(986\) 7.12502 0.226907
\(987\) 2.10120 26.9312i 0.0668820 0.857228i
\(988\) 63.4955i 2.02006i
\(989\) 1.29714i 0.0412468i
\(990\) 0 0
\(991\) 22.0780 0.701332 0.350666 0.936501i \(-0.385955\pi\)
0.350666 + 0.936501i \(0.385955\pi\)
\(992\) 8.35532i 0.265282i
\(993\) −26.3124 13.2159i −0.834998 0.419393i
\(994\) 10.3739 + 25.4107i 0.329039 + 0.805978i
\(995\) 0 0
\(996\) −21.0000 + 41.8104i −0.665410 + 1.32481i
\(997\) −36.2311 −1.14745 −0.573725 0.819048i \(-0.694502\pi\)
−0.573725 + 0.819048i \(0.694502\pi\)
\(998\) 73.9947 2.34226
\(999\) −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.g.f.524.1 16
3.2 odd 2 inner 525.2.g.f.524.14 16
5.2 odd 4 525.2.b.i.251.1 yes 8
5.3 odd 4 525.2.b.h.251.8 yes 8
5.4 even 2 inner 525.2.g.f.524.16 16
7.6 odd 2 inner 525.2.g.f.524.4 16
15.2 even 4 525.2.b.i.251.8 yes 8
15.8 even 4 525.2.b.h.251.1 8
15.14 odd 2 inner 525.2.g.f.524.3 16
21.20 even 2 inner 525.2.g.f.524.15 16
35.13 even 4 525.2.b.h.251.7 yes 8
35.27 even 4 525.2.b.i.251.2 yes 8
35.34 odd 2 inner 525.2.g.f.524.13 16
105.62 odd 4 525.2.b.i.251.7 yes 8
105.83 odd 4 525.2.b.h.251.2 yes 8
105.104 even 2 inner 525.2.g.f.524.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.b.h.251.1 8 15.8 even 4
525.2.b.h.251.2 yes 8 105.83 odd 4
525.2.b.h.251.7 yes 8 35.13 even 4
525.2.b.h.251.8 yes 8 5.3 odd 4
525.2.b.i.251.1 yes 8 5.2 odd 4
525.2.b.i.251.2 yes 8 35.27 even 4
525.2.b.i.251.7 yes 8 105.62 odd 4
525.2.b.i.251.8 yes 8 15.2 even 4
525.2.g.f.524.1 16 1.1 even 1 trivial
525.2.g.f.524.2 16 105.104 even 2 inner
525.2.g.f.524.3 16 15.14 odd 2 inner
525.2.g.f.524.4 16 7.6 odd 2 inner
525.2.g.f.524.13 16 35.34 odd 2 inner
525.2.g.f.524.14 16 3.2 odd 2 inner
525.2.g.f.524.15 16 21.20 even 2 inner
525.2.g.f.524.16 16 5.4 even 2 inner