Properties

Label 775.2.f.a.743.2
Level $775$
Weight $2$
Character 775.743
Analytic conductor $6.188$
Analytic rank $0$
Dimension $4$
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] = [775,2,Mod(557,775)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(775, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("775.557");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 775.f (of order \(4\), degree \(2\), 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: \(6.18840615665\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 743.2
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 775.743
Dual form 775.2.f.a.557.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 - 1.22474i) q^{2} +(-1.00000 + 1.00000i) q^{3} -1.00000i q^{4} +2.44949i q^{6} +(2.44949 - 2.44949i) q^{7} +(1.22474 + 1.22474i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(1.22474 - 1.22474i) q^{2} +(-1.00000 + 1.00000i) q^{3} -1.00000i q^{4} +2.44949i q^{6} +(2.44949 - 2.44949i) q^{7} +(1.22474 + 1.22474i) q^{8} +1.00000i q^{9} -4.89898i q^{11} +(1.00000 + 1.00000i) q^{12} +(-3.00000 + 3.00000i) q^{13} -6.00000i q^{14} +5.00000 q^{16} +(5.00000 + 5.00000i) q^{17} +(1.22474 + 1.22474i) q^{18} -2.00000i q^{19} +4.89898i q^{21} +(-6.00000 - 6.00000i) q^{22} +(1.00000 - 1.00000i) q^{23} -2.44949 q^{24} +7.34847i q^{26} +(-4.00000 - 4.00000i) q^{27} +(-2.44949 - 2.44949i) q^{28} +9.79796 q^{29} +(5.00000 - 2.44949i) q^{31} +(3.67423 - 3.67423i) q^{32} +(4.89898 + 4.89898i) q^{33} +12.2474 q^{34} +1.00000 q^{36} +(3.00000 + 3.00000i) q^{37} +(-2.44949 - 2.44949i) q^{38} -6.00000i q^{39} -6.00000 q^{41} +(6.00000 + 6.00000i) q^{42} +(3.00000 - 3.00000i) q^{43} -4.89898 q^{44} -2.44949i q^{46} +(-7.34847 + 7.34847i) q^{47} +(-5.00000 + 5.00000i) q^{48} -5.00000i q^{49} -10.0000 q^{51} +(3.00000 + 3.00000i) q^{52} +(1.00000 - 1.00000i) q^{53} -9.79796 q^{54} +6.00000 q^{56} +(2.00000 + 2.00000i) q^{57} +(12.0000 - 12.0000i) q^{58} -12.0000i q^{59} -4.89898i q^{61} +(3.12372 - 9.12372i) q^{62} +(2.44949 + 2.44949i) q^{63} +1.00000i q^{64} +12.0000 q^{66} +(-2.44949 + 2.44949i) q^{67} +(5.00000 - 5.00000i) q^{68} +2.00000i q^{69} +6.00000 q^{71} +(-1.22474 + 1.22474i) q^{72} +(-3.00000 + 3.00000i) q^{73} +7.34847 q^{74} -2.00000 q^{76} +(-12.0000 - 12.0000i) q^{77} +(-7.34847 - 7.34847i) q^{78} -9.79796 q^{79} +5.00000 q^{81} +(-7.34847 + 7.34847i) q^{82} +(-7.00000 + 7.00000i) q^{83} +4.89898 q^{84} -7.34847i q^{86} +(-9.79796 + 9.79796i) q^{87} +(6.00000 - 6.00000i) q^{88} -9.79796 q^{89} +14.6969i q^{91} +(-1.00000 - 1.00000i) q^{92} +(-2.55051 + 7.44949i) q^{93} +18.0000i q^{94} +7.34847i q^{96} +(-6.12372 - 6.12372i) q^{98} +4.89898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} + 4 q^{12} - 12 q^{13} + 20 q^{16} + 20 q^{17} - 24 q^{22} + 4 q^{23} - 16 q^{27} + 20 q^{31} + 4 q^{36} + 12 q^{37} - 24 q^{41} + 24 q^{42} + 12 q^{43} - 20 q^{48} - 40 q^{51} + 12 q^{52} + 4 q^{53} + 24 q^{56} + 8 q^{57} + 48 q^{58} - 12 q^{62} + 48 q^{66} + 20 q^{68} + 24 q^{71} - 12 q^{73} - 8 q^{76} - 48 q^{77} + 20 q^{81} - 28 q^{83} + 24 q^{88} - 4 q^{92} - 20 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/775\mathbb{Z}\right)^\times\).

\(n\) \(251\) \(652\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 1.22474i 0.866025 0.866025i −0.126004 0.992030i \(-0.540215\pi\)
0.992030 + 0.126004i \(0.0402153\pi\)
\(3\) −1.00000 + 1.00000i −0.577350 + 0.577350i −0.934172 0.356822i \(-0.883860\pi\)
0.356822 + 0.934172i \(0.383860\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 2.44949i 1.00000i
\(7\) 2.44949 2.44949i 0.925820 0.925820i −0.0716124 0.997433i \(-0.522814\pi\)
0.997433 + 0.0716124i \(0.0228145\pi\)
\(8\) 1.22474 + 1.22474i 0.433013 + 0.433013i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 4.89898i 1.47710i −0.674200 0.738549i \(-0.735511\pi\)
0.674200 0.738549i \(-0.264489\pi\)
\(12\) 1.00000 + 1.00000i 0.288675 + 0.288675i
\(13\) −3.00000 + 3.00000i −0.832050 + 0.832050i −0.987797 0.155747i \(-0.950222\pi\)
0.155747 + 0.987797i \(0.450222\pi\)
\(14\) 6.00000i 1.60357i
\(15\) 0 0
\(16\) 5.00000 1.25000
\(17\) 5.00000 + 5.00000i 1.21268 + 1.21268i 0.970143 + 0.242536i \(0.0779791\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 1.22474 + 1.22474i 0.288675 + 0.288675i
\(19\) 2.00000i 0.458831i −0.973329 0.229416i \(-0.926318\pi\)
0.973329 0.229416i \(-0.0736815\pi\)
\(20\) 0 0
\(21\) 4.89898i 1.06904i
\(22\) −6.00000 6.00000i −1.27920 1.27920i
\(23\) 1.00000 1.00000i 0.208514 0.208514i −0.595121 0.803636i \(-0.702896\pi\)
0.803636 + 0.595121i \(0.202896\pi\)
\(24\) −2.44949 −0.500000
\(25\) 0 0
\(26\) 7.34847i 1.44115i
\(27\) −4.00000 4.00000i −0.769800 0.769800i
\(28\) −2.44949 2.44949i −0.462910 0.462910i
\(29\) 9.79796 1.81944 0.909718 0.415227i \(-0.136298\pi\)
0.909718 + 0.415227i \(0.136298\pi\)
\(30\) 0 0
\(31\) 5.00000 2.44949i 0.898027 0.439941i
\(32\) 3.67423 3.67423i 0.649519 0.649519i
\(33\) 4.89898 + 4.89898i 0.852803 + 0.852803i
\(34\) 12.2474 2.10042
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 3.00000 + 3.00000i 0.493197 + 0.493197i 0.909312 0.416115i \(-0.136609\pi\)
−0.416115 + 0.909312i \(0.636609\pi\)
\(38\) −2.44949 2.44949i −0.397360 0.397360i
\(39\) 6.00000i 0.960769i
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 6.00000 + 6.00000i 0.925820 + 0.925820i
\(43\) 3.00000 3.00000i 0.457496 0.457496i −0.440337 0.897833i \(-0.645141\pi\)
0.897833 + 0.440337i \(0.145141\pi\)
\(44\) −4.89898 −0.738549
\(45\) 0 0
\(46\) 2.44949i 0.361158i
\(47\) −7.34847 + 7.34847i −1.07188 + 1.07188i −0.0746766 + 0.997208i \(0.523792\pi\)
−0.997208 + 0.0746766i \(0.976208\pi\)
\(48\) −5.00000 + 5.00000i −0.721688 + 0.721688i
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) −10.0000 −1.40028
\(52\) 3.00000 + 3.00000i 0.416025 + 0.416025i
\(53\) 1.00000 1.00000i 0.137361 0.137361i −0.635083 0.772444i \(-0.719034\pi\)
0.772444 + 0.635083i \(0.219034\pi\)
\(54\) −9.79796 −1.33333
\(55\) 0 0
\(56\) 6.00000 0.801784
\(57\) 2.00000 + 2.00000i 0.264906 + 0.264906i
\(58\) 12.0000 12.0000i 1.57568 1.57568i
\(59\) 12.0000i 1.56227i −0.624364 0.781133i \(-0.714642\pi\)
0.624364 0.781133i \(-0.285358\pi\)
\(60\) 0 0
\(61\) 4.89898i 0.627250i −0.949547 0.313625i \(-0.898457\pi\)
0.949547 0.313625i \(-0.101543\pi\)
\(62\) 3.12372 9.12372i 0.396713 1.15871i
\(63\) 2.44949 + 2.44949i 0.308607 + 0.308607i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 12.0000 1.47710
\(67\) −2.44949 + 2.44949i −0.299253 + 0.299253i −0.840721 0.541468i \(-0.817869\pi\)
0.541468 + 0.840721i \(0.317869\pi\)
\(68\) 5.00000 5.00000i 0.606339 0.606339i
\(69\) 2.00000i 0.240772i
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) −1.22474 + 1.22474i −0.144338 + 0.144338i
\(73\) −3.00000 + 3.00000i −0.351123 + 0.351123i −0.860527 0.509404i \(-0.829866\pi\)
0.509404 + 0.860527i \(0.329866\pi\)
\(74\) 7.34847 0.854242
\(75\) 0 0
\(76\) −2.00000 −0.229416
\(77\) −12.0000 12.0000i −1.36753 1.36753i
\(78\) −7.34847 7.34847i −0.832050 0.832050i
\(79\) −9.79796 −1.10236 −0.551178 0.834388i \(-0.685822\pi\)
−0.551178 + 0.834388i \(0.685822\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) −7.34847 + 7.34847i −0.811503 + 0.811503i
\(83\) −7.00000 + 7.00000i −0.768350 + 0.768350i −0.977816 0.209466i \(-0.932827\pi\)
0.209466 + 0.977816i \(0.432827\pi\)
\(84\) 4.89898 0.534522
\(85\) 0 0
\(86\) 7.34847i 0.792406i
\(87\) −9.79796 + 9.79796i −1.05045 + 1.05045i
\(88\) 6.00000 6.00000i 0.639602 0.639602i
\(89\) −9.79796 −1.03858 −0.519291 0.854598i \(-0.673804\pi\)
−0.519291 + 0.854598i \(0.673804\pi\)
\(90\) 0 0
\(91\) 14.6969i 1.54066i
\(92\) −1.00000 1.00000i −0.104257 0.104257i
\(93\) −2.55051 + 7.44949i −0.264476 + 0.772476i
\(94\) 18.0000i 1.85656i
\(95\) 0 0
\(96\) 7.34847i 0.750000i
\(97\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(98\) −6.12372 6.12372i −0.618590 0.618590i
\(99\) 4.89898 0.492366
\(100\) 0 0
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) −12.2474 + 12.2474i −1.21268 + 1.21268i
\(103\) −2.44949 2.44949i −0.241355 0.241355i 0.576055 0.817411i \(-0.304591\pi\)
−0.817411 + 0.576055i \(0.804591\pi\)
\(104\) −7.34847 −0.720577
\(105\) 0 0
\(106\) 2.44949i 0.237915i
\(107\) −7.34847 + 7.34847i −0.710403 + 0.710403i −0.966620 0.256216i \(-0.917524\pi\)
0.256216 + 0.966620i \(0.417524\pi\)
\(108\) −4.00000 + 4.00000i −0.384900 + 0.384900i
\(109\) 16.0000i 1.53252i 0.642529 + 0.766261i \(0.277885\pi\)
−0.642529 + 0.766261i \(0.722115\pi\)
\(110\) 0 0
\(111\) −6.00000 −0.569495
\(112\) 12.2474 12.2474i 1.15728 1.15728i
\(113\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(114\) 4.89898 0.458831
\(115\) 0 0
\(116\) 9.79796i 0.909718i
\(117\) −3.00000 3.00000i −0.277350 0.277350i
\(118\) −14.6969 14.6969i −1.35296 1.35296i
\(119\) 24.4949 2.24544
\(120\) 0 0
\(121\) −13.0000 −1.18182
\(122\) −6.00000 6.00000i −0.543214 0.543214i
\(123\) 6.00000 6.00000i 0.541002 0.541002i
\(124\) −2.44949 5.00000i −0.219971 0.449013i
\(125\) 0 0
\(126\) 6.00000 0.534522
\(127\) 3.00000 + 3.00000i 0.266207 + 0.266207i 0.827570 0.561363i \(-0.189723\pi\)
−0.561363 + 0.827570i \(0.689723\pi\)
\(128\) 8.57321 + 8.57321i 0.757772 + 0.757772i
\(129\) 6.00000i 0.528271i
\(130\) 0 0
\(131\) −6.00000 −0.524222 −0.262111 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(132\) 4.89898 4.89898i 0.426401 0.426401i
\(133\) −4.89898 4.89898i −0.424795 0.424795i
\(134\) 6.00000i 0.518321i
\(135\) 0 0
\(136\) 12.2474i 1.05021i
\(137\) −5.00000 5.00000i −0.427179 0.427179i 0.460487 0.887666i \(-0.347675\pi\)
−0.887666 + 0.460487i \(0.847675\pi\)
\(138\) 2.44949 + 2.44949i 0.208514 + 0.208514i
\(139\) −14.6969 −1.24658 −0.623289 0.781992i \(-0.714204\pi\)
−0.623289 + 0.781992i \(0.714204\pi\)
\(140\) 0 0
\(141\) 14.6969i 1.23771i
\(142\) 7.34847 7.34847i 0.616670 0.616670i
\(143\) 14.6969 + 14.6969i 1.22902 + 1.22902i
\(144\) 5.00000i 0.416667i
\(145\) 0 0
\(146\) 7.34847i 0.608164i
\(147\) 5.00000 + 5.00000i 0.412393 + 0.412393i
\(148\) 3.00000 3.00000i 0.246598 0.246598i
\(149\) 6.00000i 0.491539i −0.969328 0.245770i \(-0.920959\pi\)
0.969328 0.245770i \(-0.0790407\pi\)
\(150\) 0 0
\(151\) 14.6969i 1.19602i −0.801489 0.598010i \(-0.795958\pi\)
0.801489 0.598010i \(-0.204042\pi\)
\(152\) 2.44949 2.44949i 0.198680 0.198680i
\(153\) −5.00000 + 5.00000i −0.404226 + 0.404226i
\(154\) −29.3939 −2.36863
\(155\) 0 0
\(156\) −6.00000 −0.480384
\(157\) 9.79796 9.79796i 0.781962 0.781962i −0.198199 0.980162i \(-0.563509\pi\)
0.980162 + 0.198199i \(0.0635094\pi\)
\(158\) −12.0000 + 12.0000i −0.954669 + 0.954669i
\(159\) 2.00000i 0.158610i
\(160\) 0 0
\(161\) 4.89898i 0.386094i
\(162\) 6.12372 6.12372i 0.481125 0.481125i
\(163\) −12.2474 12.2474i −0.959294 0.959294i 0.0399091 0.999203i \(-0.487293\pi\)
−0.999203 + 0.0399091i \(0.987293\pi\)
\(164\) 6.00000i 0.468521i
\(165\) 0 0
\(166\) 17.1464i 1.33082i
\(167\) 7.00000 + 7.00000i 0.541676 + 0.541676i 0.924020 0.382344i \(-0.124883\pi\)
−0.382344 + 0.924020i \(0.624883\pi\)
\(168\) −6.00000 + 6.00000i −0.462910 + 0.462910i
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) 2.00000 0.152944
\(172\) −3.00000 3.00000i −0.228748 0.228748i
\(173\) 4.89898 + 4.89898i 0.372463 + 0.372463i 0.868373 0.495911i \(-0.165166\pi\)
−0.495911 + 0.868373i \(0.665166\pi\)
\(174\) 24.0000i 1.81944i
\(175\) 0 0
\(176\) 24.4949i 1.84637i
\(177\) 12.0000 + 12.0000i 0.901975 + 0.901975i
\(178\) −12.0000 + 12.0000i −0.899438 + 0.899438i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 9.79796i 0.728277i −0.931345 0.364138i \(-0.881364\pi\)
0.931345 0.364138i \(-0.118636\pi\)
\(182\) 18.0000 + 18.0000i 1.33425 + 1.33425i
\(183\) 4.89898 + 4.89898i 0.362143 + 0.362143i
\(184\) 2.44949 0.180579
\(185\) 0 0
\(186\) 6.00000 + 12.2474i 0.439941 + 0.898027i
\(187\) 24.4949 24.4949i 1.79124 1.79124i
\(188\) 7.34847 + 7.34847i 0.535942 + 0.535942i
\(189\) −19.5959 −1.42539
\(190\) 0 0
\(191\) −24.0000 −1.73658 −0.868290 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) −1.00000 1.00000i −0.0721688 0.0721688i
\(193\) 9.79796 + 9.79796i 0.705273 + 0.705273i 0.965537 0.260265i \(-0.0838099\pi\)
−0.260265 + 0.965537i \(0.583810\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −5.00000 −0.357143
\(197\) −17.0000 17.0000i −1.21120 1.21120i −0.970632 0.240567i \(-0.922666\pi\)
−0.240567 0.970632i \(-0.577334\pi\)
\(198\) 6.00000 6.00000i 0.426401 0.426401i
\(199\) 14.6969 1.04184 0.520919 0.853606i \(-0.325589\pi\)
0.520919 + 0.853606i \(0.325589\pi\)
\(200\) 0 0
\(201\) 4.89898i 0.345547i
\(202\) −14.6969 + 14.6969i −1.03407 + 1.03407i
\(203\) 24.0000 24.0000i 1.68447 1.68447i
\(204\) 10.0000i 0.700140i
\(205\) 0 0
\(206\) −6.00000 −0.418040
\(207\) 1.00000 + 1.00000i 0.0695048 + 0.0695048i
\(208\) −15.0000 + 15.0000i −1.04006 + 1.04006i
\(209\) −9.79796 −0.677739
\(210\) 0 0
\(211\) 10.0000 0.688428 0.344214 0.938891i \(-0.388145\pi\)
0.344214 + 0.938891i \(0.388145\pi\)
\(212\) −1.00000 1.00000i −0.0686803 0.0686803i
\(213\) −6.00000 + 6.00000i −0.411113 + 0.411113i
\(214\) 18.0000i 1.23045i
\(215\) 0 0
\(216\) 9.79796i 0.666667i
\(217\) 6.24745 18.2474i 0.424104 1.23872i
\(218\) 19.5959 + 19.5959i 1.32720 + 1.32720i
\(219\) 6.00000i 0.405442i
\(220\) 0 0
\(221\) −30.0000 −2.01802
\(222\) −7.34847 + 7.34847i −0.493197 + 0.493197i
\(223\) 3.00000 3.00000i 0.200895 0.200895i −0.599489 0.800383i \(-0.704629\pi\)
0.800383 + 0.599489i \(0.204629\pi\)
\(224\) 18.0000i 1.20268i
\(225\) 0 0
\(226\) 0 0
\(227\) −2.44949 + 2.44949i −0.162578 + 0.162578i −0.783708 0.621130i \(-0.786674\pi\)
0.621130 + 0.783708i \(0.286674\pi\)
\(228\) 2.00000 2.00000i 0.132453 0.132453i
\(229\) 19.5959 1.29493 0.647467 0.762093i \(-0.275828\pi\)
0.647467 + 0.762093i \(0.275828\pi\)
\(230\) 0 0
\(231\) 24.0000 1.57908
\(232\) 12.0000 + 12.0000i 0.787839 + 0.787839i
\(233\) −14.6969 14.6969i −0.962828 0.962828i 0.0365050 0.999333i \(-0.488378\pi\)
−0.999333 + 0.0365050i \(0.988378\pi\)
\(234\) −7.34847 −0.480384
\(235\) 0 0
\(236\) −12.0000 −0.781133
\(237\) 9.79796 9.79796i 0.636446 0.636446i
\(238\) 30.0000 30.0000i 1.94461 1.94461i
\(239\) 4.89898 0.316889 0.158444 0.987368i \(-0.449352\pi\)
0.158444 + 0.987368i \(0.449352\pi\)
\(240\) 0 0
\(241\) 24.4949i 1.57786i 0.614486 + 0.788928i \(0.289363\pi\)
−0.614486 + 0.788928i \(0.710637\pi\)
\(242\) −15.9217 + 15.9217i −1.02348 + 1.02348i
\(243\) 7.00000 7.00000i 0.449050 0.449050i
\(244\) −4.89898 −0.313625
\(245\) 0 0
\(246\) 14.6969i 0.937043i
\(247\) 6.00000 + 6.00000i 0.381771 + 0.381771i
\(248\) 9.12372 + 3.12372i 0.579357 + 0.198357i
\(249\) 14.0000i 0.887214i
\(250\) 0 0
\(251\) 9.79796i 0.618442i 0.950990 + 0.309221i \(0.100068\pi\)
−0.950990 + 0.309221i \(0.899932\pi\)
\(252\) 2.44949 2.44949i 0.154303 0.154303i
\(253\) −4.89898 4.89898i −0.307996 0.307996i
\(254\) 7.34847 0.461084
\(255\) 0 0
\(256\) 19.0000 1.18750
\(257\) −4.89898 + 4.89898i −0.305590 + 0.305590i −0.843196 0.537606i \(-0.819329\pi\)
0.537606 + 0.843196i \(0.319329\pi\)
\(258\) 7.34847 + 7.34847i 0.457496 + 0.457496i
\(259\) 14.6969 0.913223
\(260\) 0 0
\(261\) 9.79796i 0.606478i
\(262\) −7.34847 + 7.34847i −0.453990 + 0.453990i
\(263\) −17.0000 + 17.0000i −1.04826 + 1.04826i −0.0494903 + 0.998775i \(0.515760\pi\)
−0.998775 + 0.0494903i \(0.984240\pi\)
\(264\) 12.0000i 0.738549i
\(265\) 0 0
\(266\) −12.0000 −0.735767
\(267\) 9.79796 9.79796i 0.599625 0.599625i
\(268\) 2.44949 + 2.44949i 0.149626 + 0.149626i
\(269\) −24.4949 −1.49348 −0.746740 0.665116i \(-0.768382\pi\)
−0.746740 + 0.665116i \(0.768382\pi\)
\(270\) 0 0
\(271\) 9.79796i 0.595184i −0.954693 0.297592i \(-0.903817\pi\)
0.954693 0.297592i \(-0.0961834\pi\)
\(272\) 25.0000 + 25.0000i 1.51585 + 1.51585i
\(273\) −14.6969 14.6969i −0.889499 0.889499i
\(274\) −12.2474 −0.739895
\(275\) 0 0
\(276\) 2.00000 0.120386
\(277\) 3.00000 + 3.00000i 0.180253 + 0.180253i 0.791466 0.611213i \(-0.209318\pi\)
−0.611213 + 0.791466i \(0.709318\pi\)
\(278\) −18.0000 + 18.0000i −1.07957 + 1.07957i
\(279\) 2.44949 + 5.00000i 0.146647 + 0.299342i
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) −18.0000 18.0000i −1.07188 1.07188i
\(283\) −2.44949 2.44949i −0.145607 0.145607i 0.630545 0.776152i \(-0.282831\pi\)
−0.776152 + 0.630545i \(0.782831\pi\)
\(284\) 6.00000i 0.356034i
\(285\) 0 0
\(286\) 36.0000 2.12872
\(287\) −14.6969 + 14.6969i −0.867533 + 0.867533i
\(288\) 3.67423 + 3.67423i 0.216506 + 0.216506i
\(289\) 33.0000i 1.94118i
\(290\) 0 0
\(291\) 0 0
\(292\) 3.00000 + 3.00000i 0.175562 + 0.175562i
\(293\) −4.89898 4.89898i −0.286201 0.286201i 0.549375 0.835576i \(-0.314866\pi\)
−0.835576 + 0.549375i \(0.814866\pi\)
\(294\) 12.2474 0.714286
\(295\) 0 0
\(296\) 7.34847i 0.427121i
\(297\) −19.5959 + 19.5959i −1.13707 + 1.13707i
\(298\) −7.34847 7.34847i −0.425685 0.425685i
\(299\) 6.00000i 0.346989i
\(300\) 0 0
\(301\) 14.6969i 0.847117i
\(302\) −18.0000 18.0000i −1.03578 1.03578i
\(303\) 12.0000 12.0000i 0.689382 0.689382i
\(304\) 10.0000i 0.573539i
\(305\) 0 0
\(306\) 12.2474i 0.700140i
\(307\) 12.2474 12.2474i 0.698999 0.698999i −0.265196 0.964195i \(-0.585437\pi\)
0.964195 + 0.265196i \(0.0854366\pi\)
\(308\) −12.0000 + 12.0000i −0.683763 + 0.683763i
\(309\) 4.89898 0.278693
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 7.34847 7.34847i 0.416025 0.416025i
\(313\) 15.0000 15.0000i 0.847850 0.847850i −0.142014 0.989865i \(-0.545358\pi\)
0.989865 + 0.142014i \(0.0453579\pi\)
\(314\) 24.0000i 1.35440i
\(315\) 0 0
\(316\) 9.79796i 0.551178i
\(317\) 24.4949 24.4949i 1.37577 1.37577i 0.524136 0.851635i \(-0.324388\pi\)
0.851635 0.524136i \(-0.175612\pi\)
\(318\) 2.44949 + 2.44949i 0.137361 + 0.137361i
\(319\) 48.0000i 2.68748i
\(320\) 0 0
\(321\) 14.6969i 0.820303i
\(322\) −6.00000 6.00000i −0.334367 0.334367i
\(323\) 10.0000 10.0000i 0.556415 0.556415i
\(324\) 5.00000i 0.277778i
\(325\) 0 0
\(326\) −30.0000 −1.66155
\(327\) −16.0000 16.0000i −0.884802 0.884802i
\(328\) −7.34847 7.34847i −0.405751 0.405751i
\(329\) 36.0000i 1.98474i
\(330\) 0 0
\(331\) 29.3939i 1.61563i 0.589434 + 0.807817i \(0.299351\pi\)
−0.589434 + 0.807817i \(0.700649\pi\)
\(332\) 7.00000 + 7.00000i 0.384175 + 0.384175i
\(333\) −3.00000 + 3.00000i −0.164399 + 0.164399i
\(334\) 17.1464 0.938211
\(335\) 0 0
\(336\) 24.4949i 1.33631i
\(337\) 9.00000 + 9.00000i 0.490261 + 0.490261i 0.908388 0.418127i \(-0.137313\pi\)
−0.418127 + 0.908388i \(0.637313\pi\)
\(338\) −6.12372 6.12372i −0.333087 0.333087i
\(339\) 0 0
\(340\) 0 0
\(341\) −12.0000 24.4949i −0.649836 1.32647i
\(342\) 2.44949 2.44949i 0.132453 0.132453i
\(343\) 4.89898 + 4.89898i 0.264520 + 0.264520i
\(344\) 7.34847 0.396203
\(345\) 0 0
\(346\) 12.0000 0.645124
\(347\) −5.00000 5.00000i −0.268414 0.268414i 0.560047 0.828461i \(-0.310783\pi\)
−0.828461 + 0.560047i \(0.810783\pi\)
\(348\) 9.79796 + 9.79796i 0.525226 + 0.525226i
\(349\) 10.0000i 0.535288i −0.963518 0.267644i \(-0.913755\pi\)
0.963518 0.267644i \(-0.0862451\pi\)
\(350\) 0 0
\(351\) 24.0000 1.28103
\(352\) −18.0000 18.0000i −0.959403 0.959403i
\(353\) −11.0000 + 11.0000i −0.585471 + 0.585471i −0.936401 0.350931i \(-0.885865\pi\)
0.350931 + 0.936401i \(0.385865\pi\)
\(354\) 29.3939 1.56227
\(355\) 0 0
\(356\) 9.79796i 0.519291i
\(357\) −24.4949 + 24.4949i −1.29641 + 1.29641i
\(358\) 0 0
\(359\) 6.00000i 0.316668i −0.987386 0.158334i \(-0.949388\pi\)
0.987386 0.158334i \(-0.0506123\pi\)
\(360\) 0 0
\(361\) 15.0000 0.789474
\(362\) −12.0000 12.0000i −0.630706 0.630706i
\(363\) 13.0000 13.0000i 0.682323 0.682323i
\(364\) 14.6969 0.770329
\(365\) 0 0
\(366\) 12.0000 0.627250
\(367\) 15.0000 + 15.0000i 0.782994 + 0.782994i 0.980335 0.197341i \(-0.0632307\pi\)
−0.197341 + 0.980335i \(0.563231\pi\)
\(368\) 5.00000 5.00000i 0.260643 0.260643i
\(369\) 6.00000i 0.312348i
\(370\) 0 0
\(371\) 4.89898i 0.254342i
\(372\) 7.44949 + 2.55051i 0.386238 + 0.132238i
\(373\) −14.6969 14.6969i −0.760979 0.760979i 0.215521 0.976499i \(-0.430855\pi\)
−0.976499 + 0.215521i \(0.930855\pi\)
\(374\) 60.0000i 3.10253i
\(375\) 0 0
\(376\) −18.0000 −0.928279
\(377\) −29.3939 + 29.3939i −1.51386 + 1.51386i
\(378\) −24.0000 + 24.0000i −1.23443 + 1.23443i
\(379\) 20.0000i 1.02733i −0.857991 0.513665i \(-0.828287\pi\)
0.857991 0.513665i \(-0.171713\pi\)
\(380\) 0 0
\(381\) −6.00000 −0.307389
\(382\) −29.3939 + 29.3939i −1.50392 + 1.50392i
\(383\) −19.0000 + 19.0000i −0.970855 + 0.970855i −0.999587 0.0287325i \(-0.990853\pi\)
0.0287325 + 0.999587i \(0.490853\pi\)
\(384\) −17.1464 −0.875000
\(385\) 0 0
\(386\) 24.0000 1.22157
\(387\) 3.00000 + 3.00000i 0.152499 + 0.152499i
\(388\) 0 0
\(389\) 4.89898 0.248388 0.124194 0.992258i \(-0.460365\pi\)
0.124194 + 0.992258i \(0.460365\pi\)
\(390\) 0 0
\(391\) 10.0000 0.505722
\(392\) 6.12372 6.12372i 0.309295 0.309295i
\(393\) 6.00000 6.00000i 0.302660 0.302660i
\(394\) −41.6413 −2.09786
\(395\) 0 0
\(396\) 4.89898i 0.246183i
\(397\) −19.5959 + 19.5959i −0.983491 + 0.983491i −0.999866 0.0163750i \(-0.994787\pi\)
0.0163750 + 0.999866i \(0.494787\pi\)
\(398\) 18.0000 18.0000i 0.902258 0.902258i
\(399\) 9.79796 0.490511
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) −6.00000 6.00000i −0.299253 0.299253i
\(403\) −7.65153 + 22.3485i −0.381150 + 1.11326i
\(404\) 12.0000i 0.597022i
\(405\) 0 0
\(406\) 58.7878i 2.91759i
\(407\) 14.6969 14.6969i 0.728500 0.728500i
\(408\) −12.2474 12.2474i −0.606339 0.606339i
\(409\) −4.89898 −0.242239 −0.121119 0.992638i \(-0.538648\pi\)
−0.121119 + 0.992638i \(0.538648\pi\)
\(410\) 0 0
\(411\) 10.0000 0.493264
\(412\) −2.44949 + 2.44949i −0.120678 + 0.120678i
\(413\) −29.3939 29.3939i −1.44638 1.44638i
\(414\) 2.44949 0.120386
\(415\) 0 0
\(416\) 22.0454i 1.08087i
\(417\) 14.6969 14.6969i 0.719712 0.719712i
\(418\) −12.0000 + 12.0000i −0.586939 + 0.586939i
\(419\) 12.0000i 0.586238i 0.956076 + 0.293119i \(0.0946933\pi\)
−0.956076 + 0.293119i \(0.905307\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 12.2474 12.2474i 0.596196 0.596196i
\(423\) −7.34847 7.34847i −0.357295 0.357295i
\(424\) 2.44949 0.118958
\(425\) 0 0
\(426\) 14.6969i 0.712069i
\(427\) −12.0000 12.0000i −0.580721 0.580721i
\(428\) 7.34847 + 7.34847i 0.355202 + 0.355202i
\(429\) −29.3939 −1.41915
\(430\) 0 0
\(431\) 6.00000 0.289010 0.144505 0.989504i \(-0.453841\pi\)
0.144505 + 0.989504i \(0.453841\pi\)
\(432\) −20.0000 20.0000i −0.962250 0.962250i
\(433\) 15.0000 15.0000i 0.720854 0.720854i −0.247925 0.968779i \(-0.579749\pi\)
0.968779 + 0.247925i \(0.0797487\pi\)
\(434\) −14.6969 30.0000i −0.705476 1.44005i
\(435\) 0 0
\(436\) 16.0000 0.766261
\(437\) −2.00000 2.00000i −0.0956730 0.0956730i
\(438\) −7.34847 7.34847i −0.351123 0.351123i
\(439\) 8.00000i 0.381819i −0.981608 0.190910i \(-0.938856\pi\)
0.981608 0.190910i \(-0.0611437\pi\)
\(440\) 0 0
\(441\) 5.00000 0.238095
\(442\) −36.7423 + 36.7423i −1.74766 + 1.74766i
\(443\) −12.2474 12.2474i −0.581894 0.581894i 0.353530 0.935423i \(-0.384981\pi\)
−0.935423 + 0.353530i \(0.884981\pi\)
\(444\) 6.00000i 0.284747i
\(445\) 0 0
\(446\) 7.34847i 0.347960i
\(447\) 6.00000 + 6.00000i 0.283790 + 0.283790i
\(448\) 2.44949 + 2.44949i 0.115728 + 0.115728i
\(449\) 34.2929 1.61838 0.809190 0.587547i \(-0.199906\pi\)
0.809190 + 0.587547i \(0.199906\pi\)
\(450\) 0 0
\(451\) 29.3939i 1.38410i
\(452\) 0 0
\(453\) 14.6969 + 14.6969i 0.690522 + 0.690522i
\(454\) 6.00000i 0.281594i
\(455\) 0 0
\(456\) 4.89898i 0.229416i
\(457\) −21.0000 21.0000i −0.982339 0.982339i 0.0175082 0.999847i \(-0.494427\pi\)
−0.999847 + 0.0175082i \(0.994427\pi\)
\(458\) 24.0000 24.0000i 1.12145 1.12145i
\(459\) 40.0000i 1.86704i
\(460\) 0 0
\(461\) 19.5959i 0.912673i 0.889807 + 0.456336i \(0.150839\pi\)
−0.889807 + 0.456336i \(0.849161\pi\)
\(462\) 29.3939 29.3939i 1.36753 1.36753i
\(463\) −21.0000 + 21.0000i −0.975953 + 0.975953i −0.999718 0.0237648i \(-0.992435\pi\)
0.0237648 + 0.999718i \(0.492435\pi\)
\(464\) 48.9898 2.27429
\(465\) 0 0
\(466\) −36.0000 −1.66767
\(467\) −12.2474 + 12.2474i −0.566744 + 0.566744i −0.931215 0.364471i \(-0.881250\pi\)
0.364471 + 0.931215i \(0.381250\pi\)
\(468\) −3.00000 + 3.00000i −0.138675 + 0.138675i
\(469\) 12.0000i 0.554109i
\(470\) 0 0
\(471\) 19.5959i 0.902932i
\(472\) 14.6969 14.6969i 0.676481 0.676481i
\(473\) −14.6969 14.6969i −0.675766 0.675766i
\(474\) 24.0000i 1.10236i
\(475\) 0 0
\(476\) 24.4949i 1.12272i
\(477\) 1.00000 + 1.00000i 0.0457869 + 0.0457869i
\(478\) 6.00000 6.00000i 0.274434 0.274434i
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) −18.0000 −0.820729
\(482\) 30.0000 + 30.0000i 1.36646 + 1.36646i
\(483\) 4.89898 + 4.89898i 0.222911 + 0.222911i
\(484\) 13.0000i 0.590909i
\(485\) 0 0
\(486\) 17.1464i 0.777778i
\(487\) −15.0000 15.0000i −0.679715 0.679715i 0.280221 0.959936i \(-0.409592\pi\)
−0.959936 + 0.280221i \(0.909592\pi\)
\(488\) 6.00000 6.00000i 0.271607 0.271607i
\(489\) 24.4949 1.10770
\(490\) 0 0
\(491\) 19.5959i 0.884351i −0.896928 0.442176i \(-0.854207\pi\)
0.896928 0.442176i \(-0.145793\pi\)
\(492\) −6.00000 6.00000i −0.270501 0.270501i
\(493\) 48.9898 + 48.9898i 2.20639 + 2.20639i
\(494\) 14.6969 0.661247
\(495\) 0 0
\(496\) 25.0000 12.2474i 1.12253 0.549927i
\(497\) 14.6969 14.6969i 0.659248 0.659248i
\(498\) −17.1464 17.1464i −0.768350 0.768350i
\(499\) 19.5959 0.877234 0.438617 0.898674i \(-0.355469\pi\)
0.438617 + 0.898674i \(0.355469\pi\)
\(500\) 0 0
\(501\) −14.0000 −0.625474
\(502\) 12.0000 + 12.0000i 0.535586 + 0.535586i
\(503\) 2.44949 + 2.44949i 0.109217 + 0.109217i 0.759604 0.650386i \(-0.225393\pi\)
−0.650386 + 0.759604i \(0.725393\pi\)
\(504\) 6.00000i 0.267261i
\(505\) 0 0
\(506\) −12.0000 −0.533465
\(507\) 5.00000 + 5.00000i 0.222058 + 0.222058i
\(508\) 3.00000 3.00000i 0.133103 0.133103i
\(509\) −19.5959 −0.868574 −0.434287 0.900775i \(-0.643000\pi\)
−0.434287 + 0.900775i \(0.643000\pi\)
\(510\) 0 0
\(511\) 14.6969i 0.650154i
\(512\) 6.12372 6.12372i 0.270633 0.270633i
\(513\) −8.00000 + 8.00000i −0.353209 + 0.353209i
\(514\) 12.0000i 0.529297i
\(515\) 0 0
\(516\) 6.00000 0.264135
\(517\) 36.0000 + 36.0000i 1.58328 + 1.58328i
\(518\) 18.0000 18.0000i 0.790875 0.790875i
\(519\) −9.79796 −0.430083
\(520\) 0 0
\(521\) 24.0000 1.05146 0.525730 0.850652i \(-0.323792\pi\)
0.525730 + 0.850652i \(0.323792\pi\)
\(522\) 12.0000 + 12.0000i 0.525226 + 0.525226i
\(523\) 9.00000 9.00000i 0.393543 0.393543i −0.482405 0.875948i \(-0.660237\pi\)
0.875948 + 0.482405i \(0.160237\pi\)
\(524\) 6.00000i 0.262111i
\(525\) 0 0
\(526\) 41.6413i 1.81565i
\(527\) 37.2474 + 12.7526i 1.62252 + 0.555510i
\(528\) 24.4949 + 24.4949i 1.06600 + 1.06600i
\(529\) 21.0000i 0.913043i
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) −4.89898 + 4.89898i −0.212398 + 0.212398i
\(533\) 18.0000 18.0000i 0.779667 0.779667i
\(534\) 24.0000i 1.03858i
\(535\) 0 0
\(536\) −6.00000 −0.259161
\(537\) 0 0
\(538\) −30.0000 + 30.0000i −1.29339 + 1.29339i
\(539\) −24.4949 −1.05507
\(540\) 0 0
\(541\) 44.0000 1.89171 0.945854 0.324593i \(-0.105227\pi\)
0.945854 + 0.324593i \(0.105227\pi\)
\(542\) −12.0000 12.0000i −0.515444 0.515444i
\(543\) 9.79796 + 9.79796i 0.420471 + 0.420471i
\(544\) 36.7423 1.57532
\(545\) 0 0
\(546\) −36.0000 −1.54066
\(547\) 22.0454 22.0454i 0.942594 0.942594i −0.0558458 0.998439i \(-0.517786\pi\)
0.998439 + 0.0558458i \(0.0177855\pi\)
\(548\) −5.00000 + 5.00000i −0.213589 + 0.213589i
\(549\) 4.89898 0.209083
\(550\) 0 0
\(551\) 19.5959i 0.834814i
\(552\) −2.44949 + 2.44949i −0.104257 + 0.104257i
\(553\) −24.0000 + 24.0000i −1.02058 + 1.02058i
\(554\) 7.34847 0.312207
\(555\) 0 0
\(556\) 14.6969i 0.623289i
\(557\) 11.0000 + 11.0000i 0.466085 + 0.466085i 0.900644 0.434559i \(-0.143096\pi\)
−0.434559 + 0.900644i \(0.643096\pi\)
\(558\) 9.12372 + 3.12372i 0.386238 + 0.132238i
\(559\) 18.0000i 0.761319i
\(560\) 0 0
\(561\) 48.9898i 2.06835i
\(562\) 14.6969 14.6969i 0.619953 0.619953i
\(563\) −7.34847 7.34847i −0.309701 0.309701i 0.535092 0.844794i \(-0.320277\pi\)
−0.844794 + 0.535092i \(0.820277\pi\)
\(564\) −14.6969 −0.618853
\(565\) 0 0
\(566\) −6.00000 −0.252199
\(567\) 12.2474 12.2474i 0.514344 0.514344i
\(568\) 7.34847 + 7.34847i 0.308335 + 0.308335i
\(569\) −24.4949 −1.02688 −0.513440 0.858126i \(-0.671629\pi\)
−0.513440 + 0.858126i \(0.671629\pi\)
\(570\) 0 0
\(571\) 9.79796i 0.410032i −0.978759 0.205016i \(-0.934275\pi\)
0.978759 0.205016i \(-0.0657246\pi\)
\(572\) 14.6969 14.6969i 0.614510 0.614510i
\(573\) 24.0000 24.0000i 1.00261 1.00261i
\(574\) 36.0000i 1.50261i
\(575\) 0 0
\(576\) −1.00000 −0.0416667
\(577\) 4.89898 4.89898i 0.203947 0.203947i −0.597742 0.801689i \(-0.703935\pi\)
0.801689 + 0.597742i \(0.203935\pi\)
\(578\) 40.4166 + 40.4166i 1.68111 + 1.68111i
\(579\) −19.5959 −0.814379
\(580\) 0 0
\(581\) 34.2929i 1.42271i
\(582\) 0 0
\(583\) −4.89898 4.89898i −0.202895 0.202895i
\(584\) −7.34847 −0.304082
\(585\) 0 0
\(586\) −12.0000 −0.495715
\(587\) 11.0000 + 11.0000i 0.454019 + 0.454019i 0.896686 0.442667i \(-0.145968\pi\)
−0.442667 + 0.896686i \(0.645968\pi\)
\(588\) 5.00000 5.00000i 0.206197 0.206197i
\(589\) −4.89898 10.0000i −0.201859 0.412043i
\(590\) 0 0
\(591\) 34.0000 1.39857
\(592\) 15.0000 + 15.0000i 0.616496 + 0.616496i
\(593\) 24.4949 + 24.4949i 1.00588 + 1.00588i 0.999983 + 0.00590230i \(0.00187877\pi\)
0.00590230 + 0.999983i \(0.498121\pi\)
\(594\) 48.0000i 1.96946i
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −14.6969 + 14.6969i −0.601506 + 0.601506i
\(598\) 7.34847 + 7.34847i 0.300501 + 0.300501i
\(599\) 18.0000i 0.735460i 0.929933 + 0.367730i \(0.119865\pi\)
−0.929933 + 0.367730i \(0.880135\pi\)
\(600\) 0 0
\(601\) 34.2929i 1.39883i −0.714713 0.699417i \(-0.753443\pi\)
0.714713 0.699417i \(-0.246557\pi\)
\(602\) −18.0000 18.0000i −0.733625 0.733625i
\(603\) −2.44949 2.44949i −0.0997509 0.0997509i
\(604\) −14.6969 −0.598010
\(605\) 0 0
\(606\) 29.3939i 1.19404i
\(607\) −22.0454 + 22.0454i −0.894795 + 0.894795i −0.994970 0.100174i \(-0.968060\pi\)
0.100174 + 0.994970i \(0.468060\pi\)
\(608\) −7.34847 7.34847i −0.298020 0.298020i
\(609\) 48.0000i 1.94506i
\(610\) 0 0
\(611\) 44.0908i 1.78372i
\(612\) 5.00000 + 5.00000i 0.202113 + 0.202113i
\(613\) 3.00000 3.00000i 0.121169 0.121169i −0.643922 0.765091i \(-0.722694\pi\)
0.765091 + 0.643922i \(0.222694\pi\)
\(614\) 30.0000i 1.21070i
\(615\) 0 0
\(616\) 29.3939i 1.18431i
\(617\) 24.4949 24.4949i 0.986127 0.986127i −0.0137776 0.999905i \(-0.504386\pi\)
0.999905 + 0.0137776i \(0.00438570\pi\)
\(618\) 6.00000 6.00000i 0.241355 0.241355i
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) −8.00000 −0.321029
\(622\) 0 0
\(623\) −24.0000 + 24.0000i −0.961540 + 0.961540i
\(624\) 30.0000i 1.20096i
\(625\) 0 0
\(626\) 36.7423i 1.46852i
\(627\) 9.79796 9.79796i 0.391293 0.391293i
\(628\) −9.79796 9.79796i −0.390981 0.390981i
\(629\) 30.0000i 1.19618i
\(630\) 0 0
\(631\) 39.1918i 1.56020i 0.625653 + 0.780101i \(0.284832\pi\)
−0.625653 + 0.780101i \(0.715168\pi\)
\(632\) −12.0000 12.0000i −0.477334 0.477334i
\(633\) −10.0000 + 10.0000i −0.397464 + 0.397464i
\(634\) 60.0000i 2.38290i
\(635\) 0 0
\(636\) 2.00000 0.0793052
\(637\) 15.0000 + 15.0000i 0.594322 + 0.594322i
\(638\) −58.7878 58.7878i −2.32743 2.32743i
\(639\) 6.00000i 0.237356i
\(640\) 0 0
\(641\) 14.6969i 0.580494i −0.956952 0.290247i \(-0.906263\pi\)
0.956952 0.290247i \(-0.0937375\pi\)
\(642\) −18.0000 18.0000i −0.710403 0.710403i
\(643\) −27.0000 + 27.0000i −1.06478 + 1.06478i −0.0670247 + 0.997751i \(0.521351\pi\)
−0.997751 + 0.0670247i \(0.978649\pi\)
\(644\) −4.89898 −0.193047
\(645\) 0 0
\(646\) 24.4949i 0.963739i
\(647\) −23.0000 23.0000i −0.904223 0.904223i 0.0915749 0.995798i \(-0.470810\pi\)
−0.995798 + 0.0915749i \(0.970810\pi\)
\(648\) 6.12372 + 6.12372i 0.240563 + 0.240563i
\(649\) −58.7878 −2.30762
\(650\) 0 0
\(651\) 12.0000 + 24.4949i 0.470317 + 0.960031i
\(652\) −12.2474 + 12.2474i −0.479647 + 0.479647i
\(653\) −9.79796 9.79796i −0.383424 0.383424i 0.488910 0.872334i \(-0.337395\pi\)
−0.872334 + 0.488910i \(0.837395\pi\)
\(654\) −39.1918 −1.53252
\(655\) 0 0
\(656\) −30.0000 −1.17130
\(657\) −3.00000 3.00000i −0.117041 0.117041i
\(658\) 44.0908 + 44.0908i 1.71884 + 1.71884i
\(659\) 30.0000i 1.16863i −0.811525 0.584317i \(-0.801362\pi\)
0.811525 0.584317i \(-0.198638\pi\)
\(660\) 0 0
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) 36.0000 + 36.0000i 1.39918 + 1.39918i
\(663\) 30.0000 30.0000i 1.16510 1.16510i
\(664\) −17.1464 −0.665410
\(665\) 0 0
\(666\) 7.34847i 0.284747i
\(667\) 9.79796 9.79796i 0.379378 0.379378i
\(668\) 7.00000 7.00000i 0.270838 0.270838i
\(669\) 6.00000i 0.231973i
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 18.0000 + 18.0000i 0.694365 + 0.694365i
\(673\) −15.0000 + 15.0000i −0.578208 + 0.578208i −0.934409 0.356202i \(-0.884072\pi\)
0.356202 + 0.934409i \(0.384072\pi\)
\(674\) 22.0454 0.849157
\(675\) 0 0
\(676\) −5.00000 −0.192308
\(677\) −1.00000 1.00000i −0.0384331 0.0384331i 0.687629 0.726062i \(-0.258652\pi\)
−0.726062 + 0.687629i \(0.758652\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 4.89898i 0.187729i
\(682\) −44.6969 15.3031i −1.71153 0.585985i
\(683\) 2.44949 + 2.44949i 0.0937271 + 0.0937271i 0.752416 0.658689i \(-0.228889\pi\)
−0.658689 + 0.752416i \(0.728889\pi\)
\(684\) 2.00000i 0.0764719i
\(685\) 0 0
\(686\) 12.0000 0.458162
\(687\) −19.5959 + 19.5959i −0.747631 + 0.747631i
\(688\) 15.0000 15.0000i 0.571870 0.571870i
\(689\) 6.00000i 0.228582i
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 4.89898 4.89898i 0.186231 0.186231i
\(693\) 12.0000 12.0000i 0.455842 0.455842i
\(694\) −12.2474 −0.464907
\(695\) 0 0
\(696\) −24.0000 −0.909718
\(697\) −30.0000 30.0000i −1.13633 1.13633i
\(698\) −12.2474 12.2474i −0.463573 0.463573i
\(699\) 29.3939 1.11178
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 29.3939 29.3939i 1.10940 1.10940i
\(703\) 6.00000 6.00000i 0.226294 0.226294i
\(704\) 4.89898 0.184637
\(705\) 0 0
\(706\) 26.9444i 1.01407i
\(707\) −29.3939 + 29.3939i −1.10547 + 1.10547i
\(708\) 12.0000 12.0000i 0.450988 0.450988i
\(709\) 29.3939 1.10391 0.551955 0.833874i \(-0.313882\pi\)
0.551955 + 0.833874i \(0.313882\pi\)
\(710\) 0 0
\(711\) 9.79796i 0.367452i
\(712\) −12.0000 12.0000i −0.449719 0.449719i
\(713\) 2.55051 7.44949i 0.0955174 0.278986i
\(714\) 60.0000i 2.24544i
\(715\) 0 0
\(716\) 0 0
\(717\) −4.89898 + 4.89898i −0.182956 + 0.182956i
\(718\) −7.34847 7.34847i −0.274242 0.274242i
\(719\) −4.89898 −0.182701 −0.0913506 0.995819i \(-0.529118\pi\)
−0.0913506 + 0.995819i \(0.529118\pi\)
\(720\) 0 0
\(721\) −12.0000 −0.446903
\(722\) 18.3712 18.3712i 0.683704 0.683704i
\(723\) −24.4949 24.4949i −0.910975 0.910975i
\(724\) −9.79796 −0.364138
\(725\) 0 0
\(726\) 31.8434i 1.18182i
\(727\) −17.1464 + 17.1464i −0.635926 + 0.635926i −0.949548 0.313622i \(-0.898458\pi\)
0.313622 + 0.949548i \(0.398458\pi\)
\(728\) −18.0000 + 18.0000i −0.667124 + 0.667124i
\(729\) 29.0000i 1.07407i
\(730\) 0 0
\(731\) 30.0000 1.10959
\(732\) 4.89898 4.89898i 0.181071 0.181071i
\(733\) 9.79796 + 9.79796i 0.361896 + 0.361896i 0.864511 0.502615i \(-0.167629\pi\)
−0.502615 + 0.864511i \(0.667629\pi\)
\(734\) 36.7423 1.35618
\(735\) 0 0
\(736\) 7.34847i 0.270868i
\(737\) 12.0000 + 12.0000i 0.442026 + 0.442026i
\(738\) −7.34847 7.34847i −0.270501 0.270501i
\(739\) 24.4949 0.901059 0.450530 0.892761i \(-0.351235\pi\)
0.450530 + 0.892761i \(0.351235\pi\)
\(740\) 0 0
\(741\) −12.0000 −0.440831
\(742\) −6.00000 6.00000i −0.220267 0.220267i
\(743\) −23.0000 + 23.0000i −0.843788 + 0.843788i −0.989349 0.145561i \(-0.953501\pi\)
0.145561 + 0.989349i \(0.453501\pi\)
\(744\) −12.2474 + 6.00000i −0.449013 + 0.219971i
\(745\) 0 0
\(746\) −36.0000 −1.31805
\(747\) −7.00000 7.00000i −0.256117 0.256117i
\(748\) −24.4949 24.4949i −0.895622 0.895622i
\(749\) 36.0000i 1.31541i
\(750\) 0 0
\(751\) −14.0000 −0.510867 −0.255434 0.966827i \(-0.582218\pi\)
−0.255434 + 0.966827i \(0.582218\pi\)
\(752\) −36.7423 + 36.7423i −1.33986 + 1.33986i
\(753\) −9.79796 9.79796i −0.357057 0.357057i
\(754\) 72.0000i 2.62209i
\(755\) 0 0
\(756\) 19.5959i 0.712697i
\(757\) 9.00000 + 9.00000i 0.327111 + 0.327111i 0.851487 0.524376i \(-0.175701\pi\)
−0.524376 + 0.851487i \(0.675701\pi\)
\(758\) −24.4949 24.4949i −0.889695 0.889695i
\(759\) 9.79796 0.355643
\(760\) 0 0
\(761\) 29.3939i 1.06553i 0.846264 + 0.532764i \(0.178847\pi\)
−0.846264 + 0.532764i \(0.821153\pi\)
\(762\) −7.34847 + 7.34847i −0.266207 + 0.266207i
\(763\) 39.1918 + 39.1918i 1.41884 + 1.41884i
\(764\) 24.0000i 0.868290i
\(765\) 0 0
\(766\) 46.5403i 1.68157i
\(767\) 36.0000 + 36.0000i 1.29988 + 1.29988i
\(768\) −19.0000 + 19.0000i −0.685603 + 0.685603i
\(769\) 10.0000i 0.360609i 0.983611 + 0.180305i \(0.0577084\pi\)
−0.983611 + 0.180305i \(0.942292\pi\)
\(770\) 0 0
\(771\) 9.79796i 0.352865i
\(772\) 9.79796 9.79796i 0.352636 0.352636i
\(773\) 1.00000 1.00000i 0.0359675 0.0359675i −0.688894 0.724862i \(-0.741904\pi\)
0.724862 + 0.688894i \(0.241904\pi\)
\(774\) 7.34847 0.264135
\(775\) 0 0
\(776\) 0 0
\(777\) −14.6969 + 14.6969i −0.527250 + 0.527250i
\(778\) 6.00000 6.00000i 0.215110 0.215110i
\(779\) 12.0000i 0.429945i
\(780\) 0 0
\(781\) 29.3939i 1.05180i
\(782\) 12.2474 12.2474i 0.437968 0.437968i
\(783\) −39.1918 39.1918i −1.40060 1.40060i
\(784\) 25.0000i 0.892857i
\(785\) 0 0
\(786\) 14.6969i 0.524222i
\(787\) 3.00000 + 3.00000i 0.106938 + 0.106938i 0.758552 0.651613i \(-0.225907\pi\)
−0.651613 + 0.758552i \(0.725907\pi\)
\(788\) −17.0000 + 17.0000i −0.605600 + 0.605600i
\(789\) 34.0000i 1.21043i
\(790\) 0 0
\(791\) 0 0
\(792\) 6.00000 + 6.00000i 0.213201 + 0.213201i
\(793\) 14.6969 + 14.6969i 0.521904 + 0.521904i
\(794\) 48.0000i 1.70346i
\(795\) 0 0
\(796\) 14.6969i 0.520919i
\(797\) −19.0000 19.0000i −0.673015 0.673015i 0.285395 0.958410i \(-0.407875\pi\)
−0.958410 + 0.285395i \(0.907875\pi\)
\(798\) 12.0000 12.0000i 0.424795 0.424795i
\(799\) −73.4847 −2.59970
\(800\) 0 0
\(801\) 9.79796i 0.346194i
\(802\) 0 0
\(803\) 14.6969 + 14.6969i 0.518644 + 0.518644i
\(804\) −4.89898 −0.172774
\(805\) 0 0
\(806\) 18.0000 + 36.7423i 0.634023 + 1.29419i
\(807\) 24.4949 24.4949i 0.862261 0.862261i
\(808\) −14.6969 14.6969i −0.517036 0.517036i
\(809\) −29.3939 −1.03343 −0.516717 0.856156i \(-0.672846\pi\)
−0.516717 + 0.856156i \(0.672846\pi\)
\(810\) 0 0
\(811\) 44.0000 1.54505 0.772524 0.634985i \(-0.218994\pi\)
0.772524 + 0.634985i \(0.218994\pi\)
\(812\) −24.0000 24.0000i −0.842235 0.842235i
\(813\) 9.79796 + 9.79796i 0.343629 + 0.343629i
\(814\) 36.0000i 1.26180i
\(815\) 0 0
\(816\) −50.0000 −1.75035
\(817\) −6.00000 6.00000i −0.209913 0.209913i
\(818\) −6.00000 + 6.00000i −0.209785 + 0.209785i
\(819\) −14.6969 −0.513553
\(820\) 0 0
\(821\) 14.6969i 0.512927i −0.966554 0.256463i \(-0.917443\pi\)
0.966554 0.256463i \(-0.0825573\pi\)
\(822\) 12.2474 12.2474i 0.427179 0.427179i
\(823\) −27.0000 + 27.0000i −0.941161 + 0.941161i −0.998363 0.0572018i \(-0.981782\pi\)
0.0572018 + 0.998363i \(0.481782\pi\)
\(824\) 6.00000i 0.209020i
\(825\) 0 0
\(826\) −72.0000 −2.50520
\(827\) −35.0000 35.0000i −1.21707 1.21707i −0.968654 0.248416i \(-0.920090\pi\)
−0.248416 0.968654i \(-0.579910\pi\)
\(828\) 1.00000 1.00000i 0.0347524 0.0347524i
\(829\) 44.0908 1.53134 0.765669 0.643235i \(-0.222408\pi\)
0.765669 + 0.643235i \(0.222408\pi\)
\(830\) 0 0
\(831\) −6.00000 −0.208138
\(832\) −3.00000 3.00000i −0.104006 0.104006i
\(833\) 25.0000 25.0000i 0.866199 0.866199i
\(834\) 36.0000i 1.24658i
\(835\) 0 0
\(836\) 9.79796i 0.338869i
\(837\) −29.7980 10.2020i −1.02997 0.352634i
\(838\) 14.6969 + 14.6969i 0.507697 + 0.507697i
\(839\) 42.0000i 1.45000i −0.688748 0.725001i \(-0.741839\pi\)
0.688748 0.725001i \(-0.258161\pi\)
\(840\) 0 0
\(841\) 67.0000 2.31034
\(842\) −12.2474 + 12.2474i −0.422075 + 0.422075i
\(843\) −12.0000 + 12.0000i −0.413302 + 0.413302i
\(844\) 10.0000i 0.344214i
\(845\) 0 0
\(846\) −18.0000 −0.618853
\(847\) −31.8434 + 31.8434i −1.09415 + 1.09415i
\(848\) 5.00000 5.00000i 0.171701 0.171701i
\(849\) 4.89898 0.168133
\(850\) 0 0
\(851\) 6.00000 0.205677
\(852\) 6.00000 + 6.00000i 0.205557 + 0.205557i
\(853\) −9.79796 9.79796i −0.335476 0.335476i 0.519186 0.854661i \(-0.326235\pi\)
−0.854661 + 0.519186i \(0.826235\pi\)
\(854\) −29.3939 −1.00584
\(855\) 0 0
\(856\) −18.0000 −0.615227
\(857\) 24.4949 24.4949i 0.836730 0.836730i −0.151697 0.988427i \(-0.548474\pi\)
0.988427 + 0.151697i \(0.0484739\pi\)
\(858\) −36.0000 + 36.0000i −1.22902 + 1.22902i
\(859\) 39.1918 1.33721 0.668604 0.743619i \(-0.266892\pi\)
0.668604 + 0.743619i \(0.266892\pi\)
\(860\) 0 0
\(861\) 29.3939i 1.00174i
\(862\) 7.34847 7.34847i 0.250290 0.250290i
\(863\) 31.0000 31.0000i 1.05525 1.05525i 0.0568707 0.998382i \(-0.481888\pi\)
0.998382 0.0568707i \(-0.0181123\pi\)
\(864\) −29.3939 −1.00000
\(865\) 0 0
\(866\) 36.7423i 1.24856i
\(867\) −33.0000 33.0000i −1.12074 1.12074i
\(868\) −18.2474 6.24745i −0.619359 0.212052i
\(869\) 48.0000i 1.62829i
\(870\) 0 0
\(871\) 14.6969i 0.497987i
\(872\) −19.5959 + 19.5959i −0.663602 + 0.663602i
\(873\) 0 0
\(874\) −4.89898 −0.165710
\(875\) 0 0
\(876\) −6.00000 −0.202721
\(877\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(878\) −9.79796 9.79796i −0.330665 0.330665i
\(879\) 9.79796 0.330477
\(880\) 0 0
\(881\) 4.89898i 0.165051i −0.996589 0.0825254i \(-0.973701\pi\)
0.996589 0.0825254i \(-0.0262986\pi\)
\(882\) 6.12372 6.12372i 0.206197 0.206197i
\(883\) 9.00000 9.00000i 0.302874 0.302874i −0.539263 0.842137i \(-0.681297\pi\)
0.842137 + 0.539263i \(0.181297\pi\)
\(884\) 30.0000i 1.00901i
\(885\) 0 0
\(886\) −30.0000 −1.00787
\(887\) −26.9444 + 26.9444i −0.904704 + 0.904704i −0.995839 0.0911346i \(-0.970951\pi\)
0.0911346 + 0.995839i \(0.470951\pi\)
\(888\) −7.34847 7.34847i −0.246598 0.246598i
\(889\) 14.6969 0.492919
\(890\) 0 0
\(891\) 24.4949i 0.820610i
\(892\) −3.00000 3.00000i −0.100447 0.100447i
\(893\) 14.6969 + 14.6969i 0.491814 + 0.491814i
\(894\) 14.6969 0.491539
\(895\) 0 0
\(896\) 42.0000 1.40312
\(897\) −6.00000 6.00000i −0.200334 0.200334i
\(898\) 42.0000 42.0000i 1.40156 1.40156i
\(899\) 48.9898 24.0000i 1.63390 0.800445i
\(900\) 0 0
\(901\) 10.0000 0.333148
\(902\) 36.0000 + 36.0000i 1.19867 + 1.19867i
\(903\) 14.6969 + 14.6969i 0.489083 + 0.489083i
\(904\) 0 0
\(905\) 0 0
\(906\) 36.0000 1.19602
\(907\) −31.8434 + 31.8434i −1.05734 + 1.05734i −0.0590889 + 0.998253i \(0.518820\pi\)
−0.998253 + 0.0590889i \(0.981180\pi\)
\(908\) 2.44949 + 2.44949i 0.0812892 + 0.0812892i
\(909\) 12.0000i 0.398015i
\(910\) 0 0
\(911\) 24.4949i 0.811552i 0.913973 + 0.405776i \(0.132999\pi\)
−0.913973 + 0.405776i \(0.867001\pi\)
\(912\) 10.0000 + 10.0000i 0.331133 + 0.331133i
\(913\) 34.2929 + 34.2929i 1.13493 + 1.13493i
\(914\) −51.4393 −1.70146
\(915\) 0 0
\(916\) 19.5959i 0.647467i
\(917\) −14.6969 + 14.6969i −0.485336 + 0.485336i
\(918\) −48.9898 48.9898i −1.61690 1.61690i
\(919\) 10.0000i 0.329870i 0.986304 + 0.164935i \(0.0527414\pi\)
−0.986304 + 0.164935i \(0.947259\pi\)
\(920\) 0 0
\(921\) 24.4949i 0.807134i
\(922\) 24.0000 + 24.0000i 0.790398 + 0.790398i
\(923\) −18.0000 + 18.0000i −0.592477 + 0.592477i
\(924\) 24.0000i 0.789542i
\(925\) 0 0
\(926\) 51.4393i 1.69040i
\(927\) 2.44949 2.44949i 0.0804518 0.0804518i
\(928\) 36.0000 36.0000i 1.18176 1.18176i
\(929\) −24.4949 −0.803652 −0.401826 0.915716i \(-0.631624\pi\)
−0.401826 + 0.915716i \(0.631624\pi\)
\(930\) 0 0
\(931\) −10.0000 −0.327737
\(932\) −14.6969 + 14.6969i −0.481414 + 0.481414i
\(933\) 0 0
\(934\) 30.0000i 0.981630i
\(935\) 0 0
\(936\) 7.34847i 0.240192i
\(937\) 19.5959 19.5959i 0.640171 0.640171i −0.310427 0.950597i \(-0.600472\pi\)
0.950597 + 0.310427i \(0.100472\pi\)
\(938\) 14.6969 + 14.6969i 0.479872 + 0.479872i
\(939\) 30.0000i 0.979013i
\(940\) 0 0
\(941\) 29.3939i 0.958213i 0.877757 + 0.479107i \(0.159039\pi\)
−0.877757 + 0.479107i \(0.840961\pi\)
\(942\) 24.0000 + 24.0000i 0.781962 + 0.781962i
\(943\) −6.00000 + 6.00000i −0.195387 + 0.195387i
\(944\) 60.0000i 1.95283i
\(945\) 0 0
\(946\) −36.0000 −1.17046
\(947\) −31.0000 31.0000i −1.00736 1.00736i −0.999973 0.00739197i \(-0.997647\pi\)
−0.00739197 0.999973i \(-0.502353\pi\)
\(948\) −9.79796 9.79796i −0.318223 0.318223i
\(949\) 18.0000i 0.584305i
\(950\) 0 0
\(951\) 48.9898i 1.58860i
\(952\) 30.0000 + 30.0000i 0.972306 + 0.972306i
\(953\) 5.00000 5.00000i 0.161966 0.161966i −0.621471 0.783437i \(-0.713465\pi\)
0.783437 + 0.621471i \(0.213465\pi\)
\(954\) 2.44949 0.0793052
\(955\) 0 0
\(956\) 4.89898i 0.158444i
\(957\) 48.0000 + 48.0000i 1.55162 + 1.55162i
\(958\) 0 0
\(959\) −24.4949 −0.790981
\(960\) 0 0
\(961\) 19.0000 24.4949i 0.612903 0.790158i
\(962\) −22.0454 + 22.0454i −0.710772 + 0.710772i
\(963\) −7.34847 7.34847i −0.236801 0.236801i
\(964\) 24.4949 0.788928
\(965\) 0 0
\(966\) 12.0000 0.386094
\(967\) −3.00000 3.00000i −0.0964735 0.0964735i 0.657223 0.753696i \(-0.271731\pi\)
−0.753696 + 0.657223i \(0.771731\pi\)
\(968\) −15.9217 15.9217i −0.511742 0.511742i
\(969\) 20.0000i 0.642493i
\(970\) 0 0
\(971\) −36.0000 −1.15529 −0.577647 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) −7.00000 7.00000i −0.224525 0.224525i
\(973\) −36.0000 + 36.0000i −1.15411 + 1.15411i
\(974\) −36.7423 −1.17730
\(975\) 0 0
\(976\) 24.4949i 0.784063i
\(977\) −14.6969 + 14.6969i −0.470197 + 0.470197i −0.901978 0.431782i \(-0.857885\pi\)
0.431782 + 0.901978i \(0.357885\pi\)
\(978\) 30.0000 30.0000i 0.959294 0.959294i
\(979\) 48.0000i 1.53409i
\(980\) 0 0
\(981\) −16.0000 −0.510841
\(982\) −24.0000 24.0000i −0.765871 0.765871i
\(983\) −7.00000 + 7.00000i −0.223265 + 0.223265i −0.809872 0.586607i \(-0.800463\pi\)
0.586607 + 0.809872i \(0.300463\pi\)
\(984\) 14.6969 0.468521
\(985\) 0 0
\(986\) 120.000 3.82158
\(987\) −36.0000 36.0000i −1.14589 1.14589i
\(988\) 6.00000 6.00000i 0.190885 0.190885i
\(989\) 6.00000i 0.190789i
\(990\) 0 0
\(991\) 9.79796i 0.311242i 0.987817 + 0.155621i \(0.0497379\pi\)
−0.987817 + 0.155621i \(0.950262\pi\)
\(992\) 9.37117 27.3712i 0.297535 0.869036i
\(993\) −29.3939 29.3939i −0.932786 0.932786i
\(994\) 36.0000i 1.14185i
\(995\) 0 0
\(996\) −14.0000 −0.443607
\(997\) −9.79796 + 9.79796i −0.310304 + 0.310304i −0.845027 0.534723i \(-0.820416\pi\)
0.534723 + 0.845027i \(0.320416\pi\)
\(998\) 24.0000 24.0000i 0.759707 0.759707i
\(999\) 24.0000i 0.759326i
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 775.2.f.a.743.2 yes 4
5.2 odd 4 775.2.f.b.557.2 yes 4
5.3 odd 4 inner 775.2.f.a.557.1 4
5.4 even 2 775.2.f.b.743.1 yes 4
31.30 odd 2 775.2.f.b.743.2 yes 4
155.92 even 4 inner 775.2.f.a.557.2 yes 4
155.123 even 4 775.2.f.b.557.1 yes 4
155.154 odd 2 inner 775.2.f.a.743.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
775.2.f.a.557.1 4 5.3 odd 4 inner
775.2.f.a.557.2 yes 4 155.92 even 4 inner
775.2.f.a.743.1 yes 4 155.154 odd 2 inner
775.2.f.a.743.2 yes 4 1.1 even 1 trivial
775.2.f.b.557.1 yes 4 155.123 even 4
775.2.f.b.557.2 yes 4 5.2 odd 4
775.2.f.b.743.1 yes 4 5.4 even 2
775.2.f.b.743.2 yes 4 31.30 odd 2