Properties

Label 720.2.z.d.163.1
Level $720$
Weight $2$
Character 720.163
Analytic conductor $5.749$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [720,2,Mod(163,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.163");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.z (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: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 163.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 720.163
Dual form 720.2.z.d.667.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(2.00000 + 1.00000i) q^{5} +(-3.00000 + 3.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(2.00000 + 1.00000i) q^{5} +(-3.00000 + 3.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(1.00000 + 3.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} -2.00000i q^{13} -6.00000 q^{14} -4.00000 q^{16} +(-1.00000 + 1.00000i) q^{17} +(-3.00000 - 3.00000i) q^{19} +(-2.00000 + 4.00000i) q^{20} +2.00000i q^{22} +(1.00000 + 1.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(2.00000 - 2.00000i) q^{26} +(-6.00000 - 6.00000i) q^{28} +(7.00000 - 7.00000i) q^{29} +2.00000i q^{31} +(-4.00000 - 4.00000i) q^{32} -2.00000 q^{34} +(-9.00000 + 3.00000i) q^{35} +6.00000i q^{37} -6.00000i q^{38} +(-6.00000 + 2.00000i) q^{40} +4.00000i q^{41} +4.00000i q^{43} +(-2.00000 + 2.00000i) q^{44} +2.00000i q^{46} +(7.00000 + 7.00000i) q^{47} -11.0000i q^{49} +(-1.00000 + 7.00000i) q^{50} +4.00000 q^{52} +8.00000 q^{53} +(1.00000 + 3.00000i) q^{55} -12.0000i q^{56} +14.0000 q^{58} +(-3.00000 + 3.00000i) q^{59} +(-1.00000 - 1.00000i) q^{61} +(-2.00000 + 2.00000i) q^{62} -8.00000i q^{64} +(2.00000 - 4.00000i) q^{65} -4.00000i q^{67} +(-2.00000 - 2.00000i) q^{68} +(-12.0000 - 6.00000i) q^{70} +(3.00000 - 3.00000i) q^{73} +(-6.00000 + 6.00000i) q^{74} +(6.00000 - 6.00000i) q^{76} -6.00000 q^{77} +8.00000 q^{79} +(-8.00000 - 4.00000i) q^{80} +(-4.00000 + 4.00000i) q^{82} +2.00000 q^{83} +(-3.00000 + 1.00000i) q^{85} +(-4.00000 + 4.00000i) q^{86} -4.00000 q^{88} +6.00000 q^{89} +(6.00000 + 6.00000i) q^{91} +(-2.00000 + 2.00000i) q^{92} +14.0000i q^{94} +(-3.00000 - 9.00000i) q^{95} +(-11.0000 + 11.0000i) q^{97} +(11.0000 - 11.0000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 4 q^{5} - 6 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 4 q^{5} - 6 q^{7} - 4 q^{8} + 2 q^{10} + 2 q^{11} - 12 q^{14} - 8 q^{16} - 2 q^{17} - 6 q^{19} - 4 q^{20} + 2 q^{23} + 6 q^{25} + 4 q^{26} - 12 q^{28} + 14 q^{29} - 8 q^{32} - 4 q^{34} - 18 q^{35} - 12 q^{40} - 4 q^{44} + 14 q^{47} - 2 q^{50} + 8 q^{52} + 16 q^{53} + 2 q^{55} + 28 q^{58} - 6 q^{59} - 2 q^{61} - 4 q^{62} + 4 q^{65} - 4 q^{68} - 24 q^{70} + 6 q^{73} - 12 q^{74} + 12 q^{76} - 12 q^{77} + 16 q^{79} - 16 q^{80} - 8 q^{82} + 4 q^{83} - 6 q^{85} - 8 q^{86} - 8 q^{88} + 12 q^{89} + 12 q^{91} - 4 q^{92} - 6 q^{95} - 22 q^{97} + 22 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.707107 + 0.707107i
\(3\) 0 0
\(4\) 2.00000i 1.00000i
\(5\) 2.00000 + 1.00000i 0.894427 + 0.447214i
\(6\) 0 0
\(7\) −3.00000 + 3.00000i −1.13389 + 1.13389i −0.144370 + 0.989524i \(0.546115\pi\)
−0.989524 + 0.144370i \(0.953885\pi\)
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) 0 0
\(10\) 1.00000 + 3.00000i 0.316228 + 0.948683i
\(11\) 1.00000 + 1.00000i 0.301511 + 0.301511i 0.841605 0.540094i \(-0.181611\pi\)
−0.540094 + 0.841605i \(0.681611\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) −6.00000 −1.60357
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) −1.00000 + 1.00000i −0.242536 + 0.242536i −0.817898 0.575363i \(-0.804861\pi\)
0.575363 + 0.817898i \(0.304861\pi\)
\(18\) 0 0
\(19\) −3.00000 3.00000i −0.688247 0.688247i 0.273597 0.961844i \(-0.411786\pi\)
−0.961844 + 0.273597i \(0.911786\pi\)
\(20\) −2.00000 + 4.00000i −0.447214 + 0.894427i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) 1.00000 + 1.00000i 0.208514 + 0.208514i 0.803636 0.595121i \(-0.202896\pi\)
−0.595121 + 0.803636i \(0.702896\pi\)
\(24\) 0 0
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) 2.00000 2.00000i 0.392232 0.392232i
\(27\) 0 0
\(28\) −6.00000 6.00000i −1.13389 1.13389i
\(29\) 7.00000 7.00000i 1.29987 1.29987i 0.371391 0.928477i \(-0.378881\pi\)
0.928477 0.371391i \(-0.121119\pi\)
\(30\) 0 0
\(31\) 2.00000i 0.359211i 0.983739 + 0.179605i \(0.0574821\pi\)
−0.983739 + 0.179605i \(0.942518\pi\)
\(32\) −4.00000 4.00000i −0.707107 0.707107i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) −9.00000 + 3.00000i −1.52128 + 0.507093i
\(36\) 0 0
\(37\) 6.00000i 0.986394i 0.869918 + 0.493197i \(0.164172\pi\)
−0.869918 + 0.493197i \(0.835828\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 0 0
\(40\) −6.00000 + 2.00000i −0.948683 + 0.316228i
\(41\) 4.00000i 0.624695i 0.949968 + 0.312348i \(0.101115\pi\)
−0.949968 + 0.312348i \(0.898885\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) −2.00000 + 2.00000i −0.301511 + 0.301511i
\(45\) 0 0
\(46\) 2.00000i 0.294884i
\(47\) 7.00000 + 7.00000i 1.02105 + 1.02105i 0.999774 + 0.0212814i \(0.00677460\pi\)
0.0212814 + 0.999774i \(0.493225\pi\)
\(48\) 0 0
\(49\) 11.0000i 1.57143i
\(50\) −1.00000 + 7.00000i −0.141421 + 0.989949i
\(51\) 0 0
\(52\) 4.00000 0.554700
\(53\) 8.00000 1.09888 0.549442 0.835532i \(-0.314840\pi\)
0.549442 + 0.835532i \(0.314840\pi\)
\(54\) 0 0
\(55\) 1.00000 + 3.00000i 0.134840 + 0.404520i
\(56\) 12.0000i 1.60357i
\(57\) 0 0
\(58\) 14.0000 1.83829
\(59\) −3.00000 + 3.00000i −0.390567 + 0.390567i −0.874889 0.484323i \(-0.839066\pi\)
0.484323 + 0.874889i \(0.339066\pi\)
\(60\) 0 0
\(61\) −1.00000 1.00000i −0.128037 0.128037i 0.640184 0.768221i \(-0.278858\pi\)
−0.768221 + 0.640184i \(0.778858\pi\)
\(62\) −2.00000 + 2.00000i −0.254000 + 0.254000i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 2.00000 4.00000i 0.248069 0.496139i
\(66\) 0 0
\(67\) 4.00000i 0.488678i −0.969690 0.244339i \(-0.921429\pi\)
0.969690 0.244339i \(-0.0785709\pi\)
\(68\) −2.00000 2.00000i −0.242536 0.242536i
\(69\) 0 0
\(70\) −12.0000 6.00000i −1.43427 0.717137i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 3.00000 3.00000i 0.351123 0.351123i −0.509404 0.860527i \(-0.670134\pi\)
0.860527 + 0.509404i \(0.170134\pi\)
\(74\) −6.00000 + 6.00000i −0.697486 + 0.697486i
\(75\) 0 0
\(76\) 6.00000 6.00000i 0.688247 0.688247i
\(77\) −6.00000 −0.683763
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −8.00000 4.00000i −0.894427 0.447214i
\(81\) 0 0
\(82\) −4.00000 + 4.00000i −0.441726 + 0.441726i
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 0 0
\(85\) −3.00000 + 1.00000i −0.325396 + 0.108465i
\(86\) −4.00000 + 4.00000i −0.431331 + 0.431331i
\(87\) 0 0
\(88\) −4.00000 −0.426401
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 6.00000 + 6.00000i 0.628971 + 0.628971i
\(92\) −2.00000 + 2.00000i −0.208514 + 0.208514i
\(93\) 0 0
\(94\) 14.0000i 1.44399i
\(95\) −3.00000 9.00000i −0.307794 0.923381i
\(96\) 0 0
\(97\) −11.0000 + 11.0000i −1.11688 + 1.11688i −0.124684 + 0.992196i \(0.539792\pi\)
−0.992196 + 0.124684i \(0.960208\pi\)
\(98\) 11.0000 11.0000i 1.11117 1.11117i
\(99\) 0 0
\(100\) −8.00000 + 6.00000i −0.800000 + 0.600000i
\(101\) 5.00000 5.00000i 0.497519 0.497519i −0.413146 0.910665i \(-0.635570\pi\)
0.910665 + 0.413146i \(0.135570\pi\)
\(102\) 0 0
\(103\) −5.00000 5.00000i −0.492665 0.492665i 0.416480 0.909145i \(-0.363264\pi\)
−0.909145 + 0.416480i \(0.863264\pi\)
\(104\) 4.00000 + 4.00000i 0.392232 + 0.392232i
\(105\) 0 0
\(106\) 8.00000 + 8.00000i 0.777029 + 0.777029i
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) 0 0
\(109\) 5.00000 5.00000i 0.478913 0.478913i −0.425871 0.904784i \(-0.640032\pi\)
0.904784 + 0.425871i \(0.140032\pi\)
\(110\) −2.00000 + 4.00000i −0.190693 + 0.381385i
\(111\) 0 0
\(112\) 12.0000 12.0000i 1.13389 1.13389i
\(113\) −13.0000 13.0000i −1.22294 1.22294i −0.966583 0.256354i \(-0.917479\pi\)
−0.256354 0.966583i \(-0.582521\pi\)
\(114\) 0 0
\(115\) 1.00000 + 3.00000i 0.0932505 + 0.279751i
\(116\) 14.0000 + 14.0000i 1.29987 + 1.29987i
\(117\) 0 0
\(118\) −6.00000 −0.552345
\(119\) 6.00000i 0.550019i
\(120\) 0 0
\(121\) 9.00000i 0.818182i
\(122\) 2.00000i 0.181071i
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 0 0
\(127\) −7.00000 7.00000i −0.621150 0.621150i 0.324676 0.945825i \(-0.394745\pi\)
−0.945825 + 0.324676i \(0.894745\pi\)
\(128\) 8.00000 8.00000i 0.707107 0.707107i
\(129\) 0 0
\(130\) 6.00000 2.00000i 0.526235 0.175412i
\(131\) 7.00000 7.00000i 0.611593 0.611593i −0.331768 0.943361i \(-0.607645\pi\)
0.943361 + 0.331768i \(0.107645\pi\)
\(132\) 0 0
\(133\) 18.0000 1.56080
\(134\) 4.00000 4.00000i 0.345547 0.345547i
\(135\) 0 0
\(136\) 4.00000i 0.342997i
\(137\) 9.00000 + 9.00000i 0.768922 + 0.768922i 0.977917 0.208995i \(-0.0670192\pi\)
−0.208995 + 0.977917i \(0.567019\pi\)
\(138\) 0 0
\(139\) −9.00000 + 9.00000i −0.763370 + 0.763370i −0.976930 0.213560i \(-0.931494\pi\)
0.213560 + 0.976930i \(0.431494\pi\)
\(140\) −6.00000 18.0000i −0.507093 1.52128i
\(141\) 0 0
\(142\) 0 0
\(143\) 2.00000 2.00000i 0.167248 0.167248i
\(144\) 0 0
\(145\) 21.0000 7.00000i 1.74396 0.581318i
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) −12.0000 −0.986394
\(149\) −1.00000 1.00000i −0.0819232 0.0819232i 0.664958 0.746881i \(-0.268450\pi\)
−0.746881 + 0.664958i \(0.768450\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 12.0000 0.973329
\(153\) 0 0
\(154\) −6.00000 6.00000i −0.483494 0.483494i
\(155\) −2.00000 + 4.00000i −0.160644 + 0.321288i
\(156\) 0 0
\(157\) 20.0000 1.59617 0.798087 0.602542i \(-0.205846\pi\)
0.798087 + 0.602542i \(0.205846\pi\)
\(158\) 8.00000 + 8.00000i 0.636446 + 0.636446i
\(159\) 0 0
\(160\) −4.00000 12.0000i −0.316228 0.948683i
\(161\) −6.00000 −0.472866
\(162\) 0 0
\(163\) 14.0000 1.09656 0.548282 0.836293i \(-0.315282\pi\)
0.548282 + 0.836293i \(0.315282\pi\)
\(164\) −8.00000 −0.624695
\(165\) 0 0
\(166\) 2.00000 + 2.00000i 0.155230 + 0.155230i
\(167\) 3.00000 3.00000i 0.232147 0.232147i −0.581441 0.813588i \(-0.697511\pi\)
0.813588 + 0.581441i \(0.197511\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) −4.00000 2.00000i −0.306786 0.153393i
\(171\) 0 0
\(172\) −8.00000 −0.609994
\(173\) 6.00000i 0.456172i 0.973641 + 0.228086i \(0.0732467\pi\)
−0.973641 + 0.228086i \(0.926753\pi\)
\(174\) 0 0
\(175\) −21.0000 3.00000i −1.58745 0.226779i
\(176\) −4.00000 4.00000i −0.301511 0.301511i
\(177\) 0 0
\(178\) 6.00000 + 6.00000i 0.449719 + 0.449719i
\(179\) −5.00000 5.00000i −0.373718 0.373718i 0.495112 0.868829i \(-0.335127\pi\)
−0.868829 + 0.495112i \(0.835127\pi\)
\(180\) 0 0
\(181\) 3.00000 3.00000i 0.222988 0.222988i −0.586767 0.809756i \(-0.699600\pi\)
0.809756 + 0.586767i \(0.199600\pi\)
\(182\) 12.0000i 0.889499i
\(183\) 0 0
\(184\) −4.00000 −0.294884
\(185\) −6.00000 + 12.0000i −0.441129 + 0.882258i
\(186\) 0 0
\(187\) −2.00000 −0.146254
\(188\) −14.0000 + 14.0000i −1.02105 + 1.02105i
\(189\) 0 0
\(190\) 6.00000 12.0000i 0.435286 0.870572i
\(191\) 18.0000i 1.30243i −0.758891 0.651217i \(-0.774259\pi\)
0.758891 0.651217i \(-0.225741\pi\)
\(192\) 0 0
\(193\) −15.0000 15.0000i −1.07972 1.07972i −0.996534 0.0831899i \(-0.973489\pi\)
−0.0831899 0.996534i \(-0.526511\pi\)
\(194\) −22.0000 −1.57951
\(195\) 0 0
\(196\) 22.0000 1.57143
\(197\) 6.00000i 0.427482i 0.976890 + 0.213741i \(0.0685649\pi\)
−0.976890 + 0.213741i \(0.931435\pi\)
\(198\) 0 0
\(199\) 10.0000i 0.708881i −0.935079 0.354441i \(-0.884671\pi\)
0.935079 0.354441i \(-0.115329\pi\)
\(200\) −14.0000 2.00000i −0.989949 0.141421i
\(201\) 0 0
\(202\) 10.0000 0.703598
\(203\) 42.0000i 2.94782i
\(204\) 0 0
\(205\) −4.00000 + 8.00000i −0.279372 + 0.558744i
\(206\) 10.0000i 0.696733i
\(207\) 0 0
\(208\) 8.00000i 0.554700i
\(209\) 6.00000i 0.415029i
\(210\) 0 0
\(211\) −19.0000 + 19.0000i −1.30801 + 1.30801i −0.385167 + 0.922847i \(0.625856\pi\)
−0.922847 + 0.385167i \(0.874144\pi\)
\(212\) 16.0000i 1.09888i
\(213\) 0 0
\(214\) 6.00000 + 6.00000i 0.410152 + 0.410152i
\(215\) −4.00000 + 8.00000i −0.272798 + 0.545595i
\(216\) 0 0
\(217\) −6.00000 6.00000i −0.407307 0.407307i
\(218\) 10.0000 0.677285
\(219\) 0 0
\(220\) −6.00000 + 2.00000i −0.404520 + 0.134840i
\(221\) 2.00000 + 2.00000i 0.134535 + 0.134535i
\(222\) 0 0
\(223\) −9.00000 + 9.00000i −0.602685 + 0.602685i −0.941024 0.338340i \(-0.890135\pi\)
0.338340 + 0.941024i \(0.390135\pi\)
\(224\) 24.0000 1.60357
\(225\) 0 0
\(226\) 26.0000i 1.72949i
\(227\) 12.0000i 0.796468i 0.917284 + 0.398234i \(0.130377\pi\)
−0.917284 + 0.398234i \(0.869623\pi\)
\(228\) 0 0
\(229\) 1.00000 + 1.00000i 0.0660819 + 0.0660819i 0.739375 0.673293i \(-0.235121\pi\)
−0.673293 + 0.739375i \(0.735121\pi\)
\(230\) −2.00000 + 4.00000i −0.131876 + 0.263752i
\(231\) 0 0
\(232\) 28.0000i 1.83829i
\(233\) 9.00000 9.00000i 0.589610 0.589610i −0.347916 0.937526i \(-0.613111\pi\)
0.937526 + 0.347916i \(0.113111\pi\)
\(234\) 0 0
\(235\) 7.00000 + 21.0000i 0.456630 + 1.36989i
\(236\) −6.00000 6.00000i −0.390567 0.390567i
\(237\) 0 0
\(238\) 6.00000 6.00000i 0.388922 0.388922i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −14.0000 −0.901819 −0.450910 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 9.00000 9.00000i 0.578542 0.578542i
\(243\) 0 0
\(244\) 2.00000 2.00000i 0.128037 0.128037i
\(245\) 11.0000 22.0000i 0.702764 1.40553i
\(246\) 0 0
\(247\) −6.00000 + 6.00000i −0.381771 + 0.381771i
\(248\) −4.00000 4.00000i −0.254000 0.254000i
\(249\) 0 0
\(250\) −9.00000 + 13.0000i −0.569210 + 0.822192i
\(251\) −11.0000 11.0000i −0.694314 0.694314i 0.268864 0.963178i \(-0.413352\pi\)
−0.963178 + 0.268864i \(0.913352\pi\)
\(252\) 0 0
\(253\) 2.00000i 0.125739i
\(254\) 14.0000i 0.878438i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −13.0000 + 13.0000i −0.810918 + 0.810918i −0.984771 0.173854i \(-0.944378\pi\)
0.173854 + 0.984771i \(0.444378\pi\)
\(258\) 0 0
\(259\) −18.0000 18.0000i −1.11847 1.11847i
\(260\) 8.00000 + 4.00000i 0.496139 + 0.248069i
\(261\) 0 0
\(262\) 14.0000 0.864923
\(263\) −7.00000 7.00000i −0.431638 0.431638i 0.457547 0.889185i \(-0.348728\pi\)
−0.889185 + 0.457547i \(0.848728\pi\)
\(264\) 0 0
\(265\) 16.0000 + 8.00000i 0.982872 + 0.491436i
\(266\) 18.0000 + 18.0000i 1.10365 + 1.10365i
\(267\) 0 0
\(268\) 8.00000 0.488678
\(269\) −1.00000 + 1.00000i −0.0609711 + 0.0609711i −0.736935 0.675964i \(-0.763728\pi\)
0.675964 + 0.736935i \(0.263728\pi\)
\(270\) 0 0
\(271\) 30.0000i 1.82237i −0.411997 0.911185i \(-0.635169\pi\)
0.411997 0.911185i \(-0.364831\pi\)
\(272\) 4.00000 4.00000i 0.242536 0.242536i
\(273\) 0 0
\(274\) 18.0000i 1.08742i
\(275\) −1.00000 + 7.00000i −0.0603023 + 0.422116i
\(276\) 0 0
\(277\) 18.0000i 1.08152i −0.841178 0.540758i \(-0.818138\pi\)
0.841178 0.540758i \(-0.181862\pi\)
\(278\) −18.0000 −1.07957
\(279\) 0 0
\(280\) 12.0000 24.0000i 0.717137 1.43427i
\(281\) 16.0000i 0.954480i −0.878773 0.477240i \(-0.841637\pi\)
0.878773 0.477240i \(-0.158363\pi\)
\(282\) 0 0
\(283\) 12.0000i 0.713326i 0.934233 + 0.356663i \(0.116086\pi\)
−0.934233 + 0.356663i \(0.883914\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) −12.0000 12.0000i −0.708338 0.708338i
\(288\) 0 0
\(289\) 15.0000i 0.882353i
\(290\) 28.0000 + 14.0000i 1.64422 + 0.822108i
\(291\) 0 0
\(292\) 6.00000 + 6.00000i 0.351123 + 0.351123i
\(293\) 12.0000 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 0 0
\(295\) −9.00000 + 3.00000i −0.524000 + 0.174667i
\(296\) −12.0000 12.0000i −0.697486 0.697486i
\(297\) 0 0
\(298\) 2.00000i 0.115857i
\(299\) 2.00000 2.00000i 0.115663 0.115663i
\(300\) 0 0
\(301\) −12.0000 12.0000i −0.691669 0.691669i
\(302\) 8.00000 + 8.00000i 0.460348 + 0.460348i
\(303\) 0 0
\(304\) 12.0000 + 12.0000i 0.688247 + 0.688247i
\(305\) −1.00000 3.00000i −0.0572598 0.171780i
\(306\) 0 0
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) 12.0000i 0.683763i
\(309\) 0 0
\(310\) −6.00000 + 2.00000i −0.340777 + 0.113592i
\(311\) −16.0000 −0.907277 −0.453638 0.891186i \(-0.649874\pi\)
−0.453638 + 0.891186i \(0.649874\pi\)
\(312\) 0 0
\(313\) −13.0000 + 13.0000i −0.734803 + 0.734803i −0.971567 0.236764i \(-0.923913\pi\)
0.236764 + 0.971567i \(0.423913\pi\)
\(314\) 20.0000 + 20.0000i 1.12867 + 1.12867i
\(315\) 0 0
\(316\) 16.0000i 0.900070i
\(317\) −8.00000 −0.449325 −0.224662 0.974437i \(-0.572128\pi\)
−0.224662 + 0.974437i \(0.572128\pi\)
\(318\) 0 0
\(319\) 14.0000 0.783850
\(320\) 8.00000 16.0000i 0.447214 0.894427i
\(321\) 0 0
\(322\) −6.00000 6.00000i −0.334367 0.334367i
\(323\) 6.00000 0.333849
\(324\) 0 0
\(325\) 8.00000 6.00000i 0.443760 0.332820i
\(326\) 14.0000 + 14.0000i 0.775388 + 0.775388i
\(327\) 0 0
\(328\) −8.00000 8.00000i −0.441726 0.441726i
\(329\) −42.0000 −2.31553
\(330\) 0 0
\(331\) −21.0000 21.0000i −1.15426 1.15426i −0.985689 0.168576i \(-0.946083\pi\)
−0.168576 0.985689i \(-0.553917\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 0 0
\(334\) 6.00000 0.328305
\(335\) 4.00000 8.00000i 0.218543 0.437087i
\(336\) 0 0
\(337\) −11.0000 + 11.0000i −0.599208 + 0.599208i −0.940102 0.340894i \(-0.889270\pi\)
0.340894 + 0.940102i \(0.389270\pi\)
\(338\) 9.00000 + 9.00000i 0.489535 + 0.489535i
\(339\) 0 0
\(340\) −2.00000 6.00000i −0.108465 0.325396i
\(341\) −2.00000 + 2.00000i −0.108306 + 0.108306i
\(342\) 0 0
\(343\) 12.0000 + 12.0000i 0.647939 + 0.647939i
\(344\) −8.00000 8.00000i −0.431331 0.431331i
\(345\) 0 0
\(346\) −6.00000 + 6.00000i −0.322562 + 0.322562i
\(347\) −2.00000 −0.107366 −0.0536828 0.998558i \(-0.517096\pi\)
−0.0536828 + 0.998558i \(0.517096\pi\)
\(348\) 0 0
\(349\) −3.00000 + 3.00000i −0.160586 + 0.160586i −0.782826 0.622240i \(-0.786223\pi\)
0.622240 + 0.782826i \(0.286223\pi\)
\(350\) −18.0000 24.0000i −0.962140 1.28285i
\(351\) 0 0
\(352\) 8.00000i 0.426401i
\(353\) −13.0000 13.0000i −0.691920 0.691920i 0.270734 0.962654i \(-0.412734\pi\)
−0.962654 + 0.270734i \(0.912734\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 12.0000i 0.635999i
\(357\) 0 0
\(358\) 10.0000i 0.528516i
\(359\) 14.0000i 0.738892i −0.929252 0.369446i \(-0.879548\pi\)
0.929252 0.369446i \(-0.120452\pi\)
\(360\) 0 0
\(361\) 1.00000i 0.0526316i
\(362\) 6.00000 0.315353
\(363\) 0 0
\(364\) −12.0000 + 12.0000i −0.628971 + 0.628971i
\(365\) 9.00000 3.00000i 0.471082 0.157027i
\(366\) 0 0
\(367\) 21.0000 + 21.0000i 1.09619 + 1.09619i 0.994852 + 0.101339i \(0.0323127\pi\)
0.101339 + 0.994852i \(0.467687\pi\)
\(368\) −4.00000 4.00000i −0.208514 0.208514i
\(369\) 0 0
\(370\) −18.0000 + 6.00000i −0.935775 + 0.311925i
\(371\) −24.0000 + 24.0000i −1.24602 + 1.24602i
\(372\) 0 0
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) −2.00000 2.00000i −0.103418 0.103418i
\(375\) 0 0
\(376\) −28.0000 −1.44399
\(377\) −14.0000 14.0000i −0.721037 0.721037i
\(378\) 0 0
\(379\) 15.0000 15.0000i 0.770498 0.770498i −0.207695 0.978194i \(-0.566596\pi\)
0.978194 + 0.207695i \(0.0665963\pi\)
\(380\) 18.0000 6.00000i 0.923381 0.307794i
\(381\) 0 0
\(382\) 18.0000 18.0000i 0.920960 0.920960i
\(383\) 5.00000 5.00000i 0.255488 0.255488i −0.567728 0.823216i \(-0.692177\pi\)
0.823216 + 0.567728i \(0.192177\pi\)
\(384\) 0 0
\(385\) −12.0000 6.00000i −0.611577 0.305788i
\(386\) 30.0000i 1.52696i
\(387\) 0 0
\(388\) −22.0000 22.0000i −1.11688 1.11688i
\(389\) 23.0000 + 23.0000i 1.16615 + 1.16615i 0.983105 + 0.183041i \(0.0585941\pi\)
0.183041 + 0.983105i \(0.441406\pi\)
\(390\) 0 0
\(391\) −2.00000 −0.101144
\(392\) 22.0000 + 22.0000i 1.11117 + 1.11117i
\(393\) 0 0
\(394\) −6.00000 + 6.00000i −0.302276 + 0.302276i
\(395\) 16.0000 + 8.00000i 0.805047 + 0.402524i
\(396\) 0 0
\(397\) −32.0000 −1.60603 −0.803017 0.595956i \(-0.796773\pi\)
−0.803017 + 0.595956i \(0.796773\pi\)
\(398\) 10.0000 10.0000i 0.501255 0.501255i
\(399\) 0 0
\(400\) −12.0000 16.0000i −0.600000 0.800000i
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 0 0
\(403\) 4.00000 0.199254
\(404\) 10.0000 + 10.0000i 0.497519 + 0.497519i
\(405\) 0 0
\(406\) −42.0000 + 42.0000i −2.08443 + 2.08443i
\(407\) −6.00000 + 6.00000i −0.297409 + 0.297409i
\(408\) 0 0
\(409\) −38.0000 −1.87898 −0.939490 0.342578i \(-0.888700\pi\)
−0.939490 + 0.342578i \(0.888700\pi\)
\(410\) −12.0000 + 4.00000i −0.592638 + 0.197546i
\(411\) 0 0
\(412\) 10.0000 10.0000i 0.492665 0.492665i
\(413\) 18.0000i 0.885722i
\(414\) 0 0
\(415\) 4.00000 + 2.00000i 0.196352 + 0.0981761i
\(416\) −8.00000 + 8.00000i −0.392232 + 0.392232i
\(417\) 0 0
\(418\) 6.00000 6.00000i 0.293470 0.293470i
\(419\) −17.0000 17.0000i −0.830504 0.830504i 0.157081 0.987586i \(-0.449792\pi\)
−0.987586 + 0.157081i \(0.949792\pi\)
\(420\) 0 0
\(421\) −5.00000 + 5.00000i −0.243685 + 0.243685i −0.818373 0.574688i \(-0.805124\pi\)
0.574688 + 0.818373i \(0.305124\pi\)
\(422\) −38.0000 −1.84981
\(423\) 0 0
\(424\) −16.0000 + 16.0000i −0.777029 + 0.777029i
\(425\) −7.00000 1.00000i −0.339550 0.0485071i
\(426\) 0 0
\(427\) 6.00000 0.290360
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) −12.0000 + 4.00000i −0.578691 + 0.192897i
\(431\) 2.00000i 0.0963366i −0.998839 0.0481683i \(-0.984662\pi\)
0.998839 0.0481683i \(-0.0153384\pi\)
\(432\) 0 0
\(433\) 5.00000 + 5.00000i 0.240285 + 0.240285i 0.816968 0.576683i \(-0.195653\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) 12.0000i 0.576018i
\(435\) 0 0
\(436\) 10.0000 + 10.0000i 0.478913 + 0.478913i
\(437\) 6.00000i 0.287019i
\(438\) 0 0
\(439\) 26.0000i 1.24091i −0.784241 0.620456i \(-0.786947\pi\)
0.784241 0.620456i \(-0.213053\pi\)
\(440\) −8.00000 4.00000i −0.381385 0.190693i
\(441\) 0 0
\(442\) 4.00000i 0.190261i
\(443\) 4.00000i 0.190046i 0.995475 + 0.0950229i \(0.0302924\pi\)
−0.995475 + 0.0950229i \(0.969708\pi\)
\(444\) 0 0
\(445\) 12.0000 + 6.00000i 0.568855 + 0.284427i
\(446\) −18.0000 −0.852325
\(447\) 0 0
\(448\) 24.0000 + 24.0000i 1.13389 + 1.13389i
\(449\) 24.0000i 1.13263i 0.824189 + 0.566315i \(0.191631\pi\)
−0.824189 + 0.566315i \(0.808369\pi\)
\(450\) 0 0
\(451\) −4.00000 + 4.00000i −0.188353 + 0.188353i
\(452\) 26.0000 26.0000i 1.22294 1.22294i
\(453\) 0 0
\(454\) −12.0000 + 12.0000i −0.563188 + 0.563188i
\(455\) 6.00000 + 18.0000i 0.281284 + 0.843853i
\(456\) 0 0
\(457\) 7.00000 + 7.00000i 0.327446 + 0.327446i 0.851615 0.524168i \(-0.175624\pi\)
−0.524168 + 0.851615i \(0.675624\pi\)
\(458\) 2.00000i 0.0934539i
\(459\) 0 0
\(460\) −6.00000 + 2.00000i −0.279751 + 0.0932505i
\(461\) 21.0000 + 21.0000i 0.978068 + 0.978068i 0.999765 0.0216971i \(-0.00690694\pi\)
−0.0216971 + 0.999765i \(0.506907\pi\)
\(462\) 0 0
\(463\) 19.0000 19.0000i 0.883005 0.883005i −0.110834 0.993839i \(-0.535352\pi\)
0.993839 + 0.110834i \(0.0353522\pi\)
\(464\) −28.0000 + 28.0000i −1.29987 + 1.29987i
\(465\) 0 0
\(466\) 18.0000 0.833834
\(467\) 28.0000i 1.29569i −0.761774 0.647843i \(-0.775671\pi\)
0.761774 0.647843i \(-0.224329\pi\)
\(468\) 0 0
\(469\) 12.0000 + 12.0000i 0.554109 + 0.554109i
\(470\) −14.0000 + 28.0000i −0.645772 + 1.29154i
\(471\) 0 0
\(472\) 12.0000i 0.552345i
\(473\) −4.00000 + 4.00000i −0.183920 + 0.183920i
\(474\) 0 0
\(475\) 3.00000 21.0000i 0.137649 0.963546i
\(476\) 12.0000 0.550019
\(477\) 0 0
\(478\) 0 0
\(479\) 32.0000 1.46212 0.731059 0.682315i \(-0.239027\pi\)
0.731059 + 0.682315i \(0.239027\pi\)
\(480\) 0 0
\(481\) 12.0000 0.547153
\(482\) −14.0000 14.0000i −0.637683 0.637683i
\(483\) 0 0
\(484\) 18.0000 0.818182
\(485\) −33.0000 + 11.0000i −1.49845 + 0.499484i
\(486\) 0 0
\(487\) −15.0000 + 15.0000i −0.679715 + 0.679715i −0.959936 0.280221i \(-0.909592\pi\)
0.280221 + 0.959936i \(0.409592\pi\)
\(488\) 4.00000 0.181071
\(489\) 0 0
\(490\) 33.0000 11.0000i 1.49079 0.496929i
\(491\) 9.00000 + 9.00000i 0.406164 + 0.406164i 0.880399 0.474234i \(-0.157275\pi\)
−0.474234 + 0.880399i \(0.657275\pi\)
\(492\) 0 0
\(493\) 14.0000i 0.630528i
\(494\) −12.0000 −0.539906
\(495\) 0 0
\(496\) 8.00000i 0.359211i
\(497\) 0 0
\(498\) 0 0
\(499\) 29.0000 + 29.0000i 1.29822 + 1.29822i 0.929568 + 0.368650i \(0.120180\pi\)
0.368650 + 0.929568i \(0.379820\pi\)
\(500\) −22.0000 + 4.00000i −0.983870 + 0.178885i
\(501\) 0 0
\(502\) 22.0000i 0.981908i
\(503\) 29.0000 + 29.0000i 1.29305 + 1.29305i 0.932893 + 0.360153i \(0.117275\pi\)
0.360153 + 0.932893i \(0.382725\pi\)
\(504\) 0 0
\(505\) 15.0000 5.00000i 0.667491 0.222497i
\(506\) −2.00000 + 2.00000i −0.0889108 + 0.0889108i
\(507\) 0 0
\(508\) 14.0000 14.0000i 0.621150 0.621150i
\(509\) −17.0000 + 17.0000i −0.753512 + 0.753512i −0.975133 0.221621i \(-0.928865\pi\)
0.221621 + 0.975133i \(0.428865\pi\)
\(510\) 0 0
\(511\) 18.0000i 0.796273i
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) 0 0
\(514\) −26.0000 −1.14681
\(515\) −5.00000 15.0000i −0.220326 0.660979i
\(516\) 0 0
\(517\) 14.0000i 0.615719i
\(518\) 36.0000i 1.58175i
\(519\) 0 0
\(520\) 4.00000 + 12.0000i 0.175412 + 0.526235i
\(521\) 16.0000i 0.700973i 0.936568 + 0.350486i \(0.113984\pi\)
−0.936568 + 0.350486i \(0.886016\pi\)
\(522\) 0 0
\(523\) 20.0000i 0.874539i 0.899331 + 0.437269i \(0.144054\pi\)
−0.899331 + 0.437269i \(0.855946\pi\)
\(524\) 14.0000 + 14.0000i 0.611593 + 0.611593i
\(525\) 0 0
\(526\) 14.0000i 0.610429i
\(527\) −2.00000 2.00000i −0.0871214 0.0871214i
\(528\) 0 0
\(529\) 21.0000i 0.913043i
\(530\) 8.00000 + 24.0000i 0.347498 + 1.04249i
\(531\) 0 0
\(532\) 36.0000i 1.56080i
\(533\) 8.00000 0.346518
\(534\) 0 0
\(535\) 12.0000 + 6.00000i 0.518805 + 0.259403i
\(536\) 8.00000 + 8.00000i 0.345547 + 0.345547i
\(537\) 0 0
\(538\) −2.00000 −0.0862261
\(539\) 11.0000 11.0000i 0.473804 0.473804i
\(540\) 0 0
\(541\) 15.0000 + 15.0000i 0.644900 + 0.644900i 0.951756 0.306856i \(-0.0992769\pi\)
−0.306856 + 0.951756i \(0.599277\pi\)
\(542\) 30.0000 30.0000i 1.28861 1.28861i
\(543\) 0 0
\(544\) 8.00000 0.342997
\(545\) 15.0000 5.00000i 0.642529 0.214176i
\(546\) 0 0
\(547\) 28.0000i 1.19719i −0.801050 0.598597i \(-0.795725\pi\)
0.801050 0.598597i \(-0.204275\pi\)
\(548\) −18.0000 + 18.0000i −0.768922 + 0.768922i
\(549\) 0 0
\(550\) −8.00000 + 6.00000i −0.341121 + 0.255841i
\(551\) −42.0000 −1.78926
\(552\) 0 0
\(553\) −24.0000 + 24.0000i −1.02058 + 1.02058i
\(554\) 18.0000 18.0000i 0.764747 0.764747i
\(555\) 0 0
\(556\) −18.0000 18.0000i −0.763370 0.763370i
\(557\) −28.0000 −1.18640 −0.593199 0.805056i \(-0.702135\pi\)
−0.593199 + 0.805056i \(0.702135\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 36.0000 12.0000i 1.52128 0.507093i
\(561\) 0 0
\(562\) 16.0000 16.0000i 0.674919 0.674919i
\(563\) 18.0000 0.758610 0.379305 0.925272i \(-0.376163\pi\)
0.379305 + 0.925272i \(0.376163\pi\)
\(564\) 0 0
\(565\) −13.0000 39.0000i −0.546914 1.64074i
\(566\) −12.0000 + 12.0000i −0.504398 + 0.504398i
\(567\) 0 0
\(568\) 0 0
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) −25.0000 25.0000i −1.04622 1.04622i −0.998879 0.0473385i \(-0.984926\pi\)
−0.0473385 0.998879i \(-0.515074\pi\)
\(572\) 4.00000 + 4.00000i 0.167248 + 0.167248i
\(573\) 0 0
\(574\) 24.0000i 1.00174i
\(575\) −1.00000 + 7.00000i −0.0417029 + 0.291920i
\(576\) 0 0
\(577\) 9.00000 9.00000i 0.374675 0.374675i −0.494502 0.869177i \(-0.664649\pi\)
0.869177 + 0.494502i \(0.164649\pi\)
\(578\) −15.0000 + 15.0000i −0.623918 + 0.623918i
\(579\) 0 0
\(580\) 14.0000 + 42.0000i 0.581318 + 1.74396i
\(581\) −6.00000 + 6.00000i −0.248922 + 0.248922i
\(582\) 0 0
\(583\) 8.00000 + 8.00000i 0.331326 + 0.331326i
\(584\) 12.0000i 0.496564i
\(585\) 0 0
\(586\) 12.0000 + 12.0000i 0.495715 + 0.495715i
\(587\) −2.00000 −0.0825488 −0.0412744 0.999148i \(-0.513142\pi\)
−0.0412744 + 0.999148i \(0.513142\pi\)
\(588\) 0 0
\(589\) 6.00000 6.00000i 0.247226 0.247226i
\(590\) −12.0000 6.00000i −0.494032 0.247016i
\(591\) 0 0
\(592\) 24.0000i 0.986394i
\(593\) −17.0000 17.0000i −0.698106 0.698106i 0.265896 0.964002i \(-0.414332\pi\)
−0.964002 + 0.265896i \(0.914332\pi\)
\(594\) 0 0
\(595\) 6.00000 12.0000i 0.245976 0.491952i
\(596\) 2.00000 2.00000i 0.0819232 0.0819232i
\(597\) 0 0
\(598\) 4.00000 0.163572
\(599\) 30.0000i 1.22577i −0.790173 0.612883i \(-0.790010\pi\)
0.790173 0.612883i \(-0.209990\pi\)
\(600\) 0 0
\(601\) 16.0000i 0.652654i 0.945257 + 0.326327i \(0.105811\pi\)
−0.945257 + 0.326327i \(0.894189\pi\)
\(602\) 24.0000i 0.978167i
\(603\) 0 0
\(604\) 16.0000i 0.651031i
\(605\) 9.00000 18.0000i 0.365902 0.731804i
\(606\) 0 0
\(607\) −23.0000 23.0000i −0.933541 0.933541i 0.0643840 0.997925i \(-0.479492\pi\)
−0.997925 + 0.0643840i \(0.979492\pi\)
\(608\) 24.0000i 0.973329i
\(609\) 0 0
\(610\) 2.00000 4.00000i 0.0809776 0.161955i
\(611\) 14.0000 14.0000i 0.566379 0.566379i
\(612\) 0 0
\(613\) 8.00000 0.323117 0.161558 0.986863i \(-0.448348\pi\)
0.161558 + 0.986863i \(0.448348\pi\)
\(614\) −4.00000 + 4.00000i −0.161427 + 0.161427i
\(615\) 0 0
\(616\) 12.0000 12.0000i 0.483494 0.483494i
\(617\) 25.0000 + 25.0000i 1.00646 + 1.00646i 0.999979 + 0.00648312i \(0.00206366\pi\)
0.00648312 + 0.999979i \(0.497936\pi\)
\(618\) 0 0
\(619\) 7.00000 7.00000i 0.281354 0.281354i −0.552295 0.833649i \(-0.686248\pi\)
0.833649 + 0.552295i \(0.186248\pi\)
\(620\) −8.00000 4.00000i −0.321288 0.160644i
\(621\) 0 0
\(622\) −16.0000 16.0000i −0.641542 0.641542i
\(623\) −18.0000 + 18.0000i −0.721155 + 0.721155i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −26.0000 −1.03917
\(627\) 0 0
\(628\) 40.0000i 1.59617i
\(629\) −6.00000 6.00000i −0.239236 0.239236i
\(630\) 0 0
\(631\) 24.0000 0.955425 0.477712 0.878516i \(-0.341466\pi\)
0.477712 + 0.878516i \(0.341466\pi\)
\(632\) −16.0000 + 16.0000i −0.636446 + 0.636446i
\(633\) 0 0
\(634\) −8.00000 8.00000i −0.317721 0.317721i
\(635\) −7.00000 21.0000i −0.277787 0.833360i
\(636\) 0 0
\(637\) −22.0000 −0.871672
\(638\) 14.0000 + 14.0000i 0.554265 + 0.554265i
\(639\) 0 0
\(640\) 24.0000 8.00000i 0.948683 0.316228i
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) −26.0000 −1.02534 −0.512670 0.858586i \(-0.671344\pi\)
−0.512670 + 0.858586i \(0.671344\pi\)
\(644\) 12.0000i 0.472866i
\(645\) 0 0
\(646\) 6.00000 + 6.00000i 0.236067 + 0.236067i
\(647\) 15.0000 15.0000i 0.589711 0.589711i −0.347842 0.937553i \(-0.613086\pi\)
0.937553 + 0.347842i \(0.113086\pi\)
\(648\) 0 0
\(649\) −6.00000 −0.235521
\(650\) 14.0000 + 2.00000i 0.549125 + 0.0784465i
\(651\) 0 0
\(652\) 28.0000i 1.09656i
\(653\) 2.00000i 0.0782660i 0.999234 + 0.0391330i \(0.0124596\pi\)
−0.999234 + 0.0391330i \(0.987540\pi\)
\(654\) 0 0
\(655\) 21.0000 7.00000i 0.820538 0.273513i
\(656\) 16.0000i 0.624695i
\(657\) 0 0
\(658\) −42.0000 42.0000i −1.63733 1.63733i
\(659\) 11.0000 + 11.0000i 0.428499 + 0.428499i 0.888117 0.459618i \(-0.152014\pi\)
−0.459618 + 0.888117i \(0.652014\pi\)
\(660\) 0 0
\(661\) −25.0000 + 25.0000i −0.972387 + 0.972387i −0.999629 0.0272416i \(-0.991328\pi\)
0.0272416 + 0.999629i \(0.491328\pi\)
\(662\) 42.0000i 1.63238i
\(663\) 0 0
\(664\) −4.00000 + 4.00000i −0.155230 + 0.155230i
\(665\) 36.0000 + 18.0000i 1.39602 + 0.698010i
\(666\) 0 0
\(667\) 14.0000 0.542082
\(668\) 6.00000 + 6.00000i 0.232147 + 0.232147i
\(669\) 0 0
\(670\) 12.0000 4.00000i 0.463600 0.154533i
\(671\) 2.00000i 0.0772091i
\(672\) 0 0
\(673\) 1.00000 + 1.00000i 0.0385472 + 0.0385472i 0.726118 0.687570i \(-0.241323\pi\)
−0.687570 + 0.726118i \(0.741323\pi\)
\(674\) −22.0000 −0.847408
\(675\) 0 0
\(676\) 18.0000i 0.692308i
\(677\) 42.0000i 1.61419i −0.590421 0.807096i \(-0.701038\pi\)
0.590421 0.807096i \(-0.298962\pi\)
\(678\) 0 0
\(679\) 66.0000i 2.53285i
\(680\) 4.00000 8.00000i 0.153393 0.306786i
\(681\) 0 0
\(682\) −4.00000 −0.153168
\(683\) 4.00000i 0.153056i 0.997067 + 0.0765279i \(0.0243834\pi\)
−0.997067 + 0.0765279i \(0.975617\pi\)
\(684\) 0 0
\(685\) 9.00000 + 27.0000i 0.343872 + 1.03162i
\(686\) 24.0000i 0.916324i
\(687\) 0 0
\(688\) 16.0000i 0.609994i
\(689\) 16.0000i 0.609551i
\(690\) 0 0
\(691\) 21.0000 21.0000i 0.798878 0.798878i −0.184041 0.982919i \(-0.558918\pi\)
0.982919 + 0.184041i \(0.0589179\pi\)
\(692\) −12.0000 −0.456172
\(693\) 0 0
\(694\) −2.00000 2.00000i −0.0759190 0.0759190i
\(695\) −27.0000 + 9.00000i −1.02417 + 0.341389i
\(696\) 0 0
\(697\) −4.00000 4.00000i −0.151511 0.151511i
\(698\) −6.00000 −0.227103
\(699\) 0 0
\(700\) 6.00000 42.0000i 0.226779 1.58745i
\(701\) 13.0000 + 13.0000i 0.491003 + 0.491003i 0.908622 0.417619i \(-0.137135\pi\)
−0.417619 + 0.908622i \(0.637135\pi\)
\(702\) 0 0
\(703\) 18.0000 18.0000i 0.678883 0.678883i
\(704\) 8.00000 8.00000i 0.301511 0.301511i
\(705\) 0 0
\(706\) 26.0000i 0.978523i
\(707\) 30.0000i 1.12827i
\(708\) 0 0
\(709\) 1.00000 + 1.00000i 0.0375558 + 0.0375558i 0.725635 0.688080i \(-0.241546\pi\)
−0.688080 + 0.725635i \(0.741546\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −12.0000 + 12.0000i −0.449719 + 0.449719i
\(713\) −2.00000 + 2.00000i −0.0749006 + 0.0749006i
\(714\) 0 0
\(715\) 6.00000 2.00000i 0.224387 0.0747958i
\(716\) 10.0000 10.0000i 0.373718 0.373718i
\(717\) 0 0
\(718\) 14.0000 14.0000i 0.522475 0.522475i
\(719\) 32.0000 1.19340 0.596699 0.802465i \(-0.296479\pi\)
0.596699 + 0.802465i \(0.296479\pi\)
\(720\) 0 0
\(721\) 30.0000 1.11726
\(722\) 1.00000 1.00000i 0.0372161 0.0372161i
\(723\) 0 0
\(724\) 6.00000 + 6.00000i 0.222988 + 0.222988i
\(725\) 49.0000 + 7.00000i 1.81981 + 0.259973i
\(726\) 0 0
\(727\) −7.00000 + 7.00000i −0.259616 + 0.259616i −0.824898 0.565282i \(-0.808767\pi\)
0.565282 + 0.824898i \(0.308767\pi\)
\(728\) −24.0000 −0.889499
\(729\) 0 0
\(730\) 12.0000 + 6.00000i 0.444140 + 0.222070i
\(731\) −4.00000 4.00000i −0.147945 0.147945i
\(732\) 0 0
\(733\) 30.0000i 1.10808i −0.832492 0.554038i \(-0.813086\pi\)
0.832492 0.554038i \(-0.186914\pi\)
\(734\) 42.0000i 1.55025i
\(735\) 0 0
\(736\) 8.00000i 0.294884i
\(737\) 4.00000 4.00000i 0.147342 0.147342i
\(738\) 0 0
\(739\) 21.0000 + 21.0000i 0.772497 + 0.772497i 0.978543 0.206045i \(-0.0660593\pi\)
−0.206045 + 0.978543i \(0.566059\pi\)
\(740\) −24.0000 12.0000i −0.882258 0.441129i
\(741\) 0 0
\(742\) −48.0000 −1.76214
\(743\) −31.0000 31.0000i −1.13728 1.13728i −0.988936 0.148344i \(-0.952606\pi\)
−0.148344 0.988936i \(-0.547394\pi\)
\(744\) 0 0
\(745\) −1.00000 3.00000i −0.0366372 0.109911i
\(746\) −4.00000 4.00000i −0.146450 0.146450i
\(747\) 0 0
\(748\) 4.00000i 0.146254i
\(749\) −18.0000 + 18.0000i −0.657706 + 0.657706i
\(750\) 0 0
\(751\) 50.0000i 1.82453i 0.409605 + 0.912263i \(0.365667\pi\)
−0.409605 + 0.912263i \(0.634333\pi\)
\(752\) −28.0000 28.0000i −1.02105 1.02105i
\(753\) 0 0
\(754\) 28.0000i 1.01970i
\(755\) 16.0000 + 8.00000i 0.582300 + 0.291150i
\(756\) 0 0
\(757\) 2.00000i 0.0726912i −0.999339 0.0363456i \(-0.988428\pi\)
0.999339 0.0363456i \(-0.0115717\pi\)
\(758\) 30.0000 1.08965
\(759\) 0 0
\(760\) 24.0000 + 12.0000i 0.870572 + 0.435286i
\(761\) 40.0000i 1.45000i −0.688749 0.724999i \(-0.741840\pi\)
0.688749 0.724999i \(-0.258160\pi\)
\(762\) 0 0
\(763\) 30.0000i 1.08607i
\(764\) 36.0000 1.30243
\(765\) 0 0
\(766\) 10.0000 0.361315
\(767\) 6.00000 + 6.00000i 0.216647 + 0.216647i
\(768\) 0 0
\(769\) 4.00000i 0.144244i −0.997396 0.0721218i \(-0.977023\pi\)
0.997396 0.0721218i \(-0.0229770\pi\)
\(770\) −6.00000 18.0000i −0.216225 0.648675i
\(771\) 0 0
\(772\) 30.0000 30.0000i 1.07972 1.07972i
\(773\) −48.0000 −1.72644 −0.863220 0.504828i \(-0.831556\pi\)
−0.863220 + 0.504828i \(0.831556\pi\)
\(774\) 0 0
\(775\) −8.00000 + 6.00000i −0.287368 + 0.215526i
\(776\) 44.0000i 1.57951i
\(777\) 0 0
\(778\) 46.0000i 1.64918i
\(779\) 12.0000 12.0000i 0.429945 0.429945i
\(780\) 0 0
\(781\) 0 0
\(782\) −2.00000 2.00000i −0.0715199 0.0715199i
\(783\) 0 0
\(784\) 44.0000i 1.57143i
\(785\) 40.0000 + 20.0000i 1.42766 + 0.713831i
\(786\) 0 0
\(787\) 4.00000i 0.142585i 0.997455 + 0.0712923i \(0.0227123\pi\)
−0.997455 + 0.0712923i \(0.977288\pi\)
\(788\) −12.0000 −0.427482
\(789\) 0 0
\(790\) 8.00000 + 24.0000i 0.284627 + 0.853882i
\(791\) 78.0000 2.77336
\(792\) 0 0
\(793\) −2.00000 + 2.00000i −0.0710221 + 0.0710221i
\(794\) −32.0000 32.0000i −1.13564 1.13564i
\(795\) 0 0
\(796\) 20.0000 0.708881
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) −14.0000 −0.495284
\(800\) 4.00000 28.0000i 0.141421 0.989949i
\(801\) 0 0
\(802\) 2.00000 + 2.00000i 0.0706225 + 0.0706225i
\(803\) 6.00000 0.211735
\(804\) 0 0
\(805\) −12.0000 6.00000i −0.422944 0.211472i
\(806\) 4.00000 + 4.00000i 0.140894 + 0.140894i
\(807\) 0 0
\(808\) 20.0000i 0.703598i
\(809\) 26.0000 0.914111 0.457056 0.889438i \(-0.348904\pi\)
0.457056 + 0.889438i \(0.348904\pi\)
\(810\) 0 0
\(811\) −9.00000 9.00000i −0.316033 0.316033i 0.531208 0.847241i \(-0.321738\pi\)
−0.847241 + 0.531208i \(0.821738\pi\)
\(812\) −84.0000 −2.94782
\(813\) 0 0
\(814\) −12.0000 −0.420600
\(815\) 28.0000 + 14.0000i 0.980797 + 0.490399i
\(816\) 0 0
\(817\) 12.0000 12.0000i 0.419827 0.419827i
\(818\) −38.0000 38.0000i −1.32864 1.32864i
\(819\) 0 0
\(820\) −16.0000 8.00000i −0.558744 0.279372i
\(821\) −15.0000 + 15.0000i −0.523504 + 0.523504i −0.918628 0.395124i \(-0.870702\pi\)
0.395124 + 0.918628i \(0.370702\pi\)
\(822\) 0 0
\(823\) −21.0000 21.0000i −0.732014 0.732014i 0.239004 0.971018i \(-0.423179\pi\)
−0.971018 + 0.239004i \(0.923179\pi\)
\(824\) 20.0000 0.696733
\(825\) 0 0
\(826\) 18.0000 18.0000i 0.626300 0.626300i
\(827\) 54.0000 1.87776 0.938882 0.344239i \(-0.111863\pi\)
0.938882 + 0.344239i \(0.111863\pi\)
\(828\) 0 0
\(829\) −27.0000 + 27.0000i −0.937749 + 0.937749i −0.998173 0.0604240i \(-0.980755\pi\)
0.0604240 + 0.998173i \(0.480755\pi\)
\(830\) 2.00000 + 6.00000i 0.0694210 + 0.208263i
\(831\) 0 0
\(832\) −16.0000 −0.554700
\(833\) 11.0000 + 11.0000i 0.381127 + 0.381127i
\(834\) 0 0
\(835\) 9.00000 3.00000i 0.311458 0.103819i
\(836\) 12.0000 0.415029
\(837\) 0 0
\(838\) 34.0000i 1.17451i
\(839\) 18.0000i 0.621429i 0.950503 + 0.310715i \(0.100568\pi\)
−0.950503 + 0.310715i \(0.899432\pi\)
\(840\) 0 0
\(841\) 69.0000i 2.37931i
\(842\) −10.0000 −0.344623
\(843\) 0 0
\(844\) −38.0000 38.0000i −1.30801 1.30801i
\(845\) 18.0000 + 9.00000i 0.619219 + 0.309609i
\(846\) 0 0
\(847\) 27.0000 + 27.0000i 0.927731 + 0.927731i
\(848\) −32.0000 −1.09888
\(849\) 0 0
\(850\) −6.00000 8.00000i −0.205798 0.274398i
\(851\) −6.00000 + 6.00000i −0.205677 + 0.205677i
\(852\) 0 0
\(853\) 16.0000 0.547830 0.273915 0.961754i \(-0.411681\pi\)
0.273915 + 0.961754i \(0.411681\pi\)
\(854\) 6.00000 + 6.00000i 0.205316 + 0.205316i
\(855\) 0 0
\(856\) −12.0000 + 12.0000i −0.410152 + 0.410152i
\(857\) −27.0000 27.0000i −0.922302 0.922302i 0.0748894 0.997192i \(-0.476140\pi\)
−0.997192 + 0.0748894i \(0.976140\pi\)
\(858\) 0 0
\(859\) 19.0000 19.0000i 0.648272 0.648272i −0.304303 0.952575i \(-0.598424\pi\)
0.952575 + 0.304303i \(0.0984237\pi\)
\(860\) −16.0000 8.00000i −0.545595 0.272798i
\(861\) 0 0
\(862\) 2.00000 2.00000i 0.0681203 0.0681203i
\(863\) 5.00000 5.00000i 0.170202 0.170202i −0.616866 0.787068i \(-0.711598\pi\)
0.787068 + 0.616866i \(0.211598\pi\)
\(864\) 0 0
\(865\) −6.00000 + 12.0000i −0.204006 + 0.408012i
\(866\) 10.0000i 0.339814i
\(867\) 0 0
\(868\) 12.0000 12.0000i 0.407307 0.407307i
\(869\) 8.00000 + 8.00000i 0.271381 + 0.271381i
\(870\) 0 0
\(871\) −8.00000 −0.271070
\(872\) 20.0000i 0.677285i
\(873\) 0 0
\(874\) 6.00000 6.00000i 0.202953 0.202953i
\(875\) −39.0000 27.0000i −1.31844 0.912767i
\(876\) 0 0
\(877\) 4.00000 0.135070 0.0675352 0.997717i \(-0.478487\pi\)
0.0675352 + 0.997717i \(0.478487\pi\)
\(878\) 26.0000 26.0000i 0.877457 0.877457i
\(879\) 0 0
\(880\) −4.00000 12.0000i −0.134840 0.404520i
\(881\) −46.0000 −1.54978 −0.774890 0.632096i \(-0.782195\pi\)
−0.774890 + 0.632096i \(0.782195\pi\)
\(882\) 0 0
\(883\) 6.00000 0.201916 0.100958 0.994891i \(-0.467809\pi\)
0.100958 + 0.994891i \(0.467809\pi\)
\(884\) −4.00000 + 4.00000i −0.134535 + 0.134535i
\(885\) 0 0
\(886\) −4.00000 + 4.00000i −0.134383 + 0.134383i
\(887\) 23.0000 23.0000i 0.772264 0.772264i −0.206238 0.978502i \(-0.566122\pi\)
0.978502 + 0.206238i \(0.0661220\pi\)
\(888\) 0 0
\(889\) 42.0000 1.40863
\(890\) 6.00000 + 18.0000i 0.201120 + 0.603361i
\(891\) 0 0
\(892\) −18.0000 18.0000i −0.602685 0.602685i
\(893\) 42.0000i 1.40548i
\(894\) 0 0
\(895\) −5.00000 15.0000i −0.167132 0.501395i
\(896\) 48.0000i 1.60357i
\(897\) 0 0
\(898\) −24.0000 + 24.0000i −0.800890 + 0.800890i
\(899\) 14.0000 + 14.0000i 0.466926 + 0.466926i
\(900\) 0 0
\(901\) −8.00000 + 8.00000i −0.266519 + 0.266519i
\(902\) −8.00000 −0.266371
\(903\) 0 0
\(904\) 52.0000 1.72949
\(905\) 9.00000 3.00000i 0.299170 0.0997234i
\(906\) 0 0
\(907\) 50.0000 1.66022 0.830111 0.557598i \(-0.188277\pi\)
0.830111 + 0.557598i \(0.188277\pi\)
\(908\) −24.0000 −0.796468
\(909\) 0 0
\(910\) −12.0000 + 24.0000i −0.397796 + 0.795592i
\(911\) 38.0000i 1.25900i 0.777002 + 0.629498i \(0.216739\pi\)
−0.777002 + 0.629498i \(0.783261\pi\)
\(912\) 0 0
\(913\) 2.00000 + 2.00000i 0.0661903 + 0.0661903i
\(914\) 14.0000i 0.463079i
\(915\) 0 0
\(916\) −2.00000 + 2.00000i −0.0660819 + 0.0660819i
\(917\) 42.0000i 1.38696i
\(918\) 0 0
\(919\) 46.0000i 1.51740i 0.651440 + 0.758700i \(0.274165\pi\)
−0.651440 + 0.758700i \(0.725835\pi\)
\(920\) −8.00000 4.00000i −0.263752 0.131876i
\(921\) 0 0
\(922\) 42.0000i 1.38320i
\(923\) 0 0
\(924\) 0 0
\(925\) −24.0000 + 18.0000i −0.789115 + 0.591836i
\(926\) 38.0000 1.24876
\(927\) 0 0
\(928\) −56.0000 −1.83829
\(929\) 16.0000i 0.524943i −0.964940 0.262471i \(-0.915462\pi\)
0.964940 0.262471i \(-0.0845376\pi\)
\(930\) 0 0
\(931\) −33.0000 + 33.0000i −1.08153 + 1.08153i
\(932\) 18.0000 + 18.0000i 0.589610 + 0.589610i
\(933\) 0 0
\(934\) 28.0000 28.0000i 0.916188 0.916188i
\(935\) −4.00000 2.00000i −0.130814 0.0654070i
\(936\) 0 0
\(937\) 3.00000 + 3.00000i 0.0980057 + 0.0980057i 0.754410 0.656404i \(-0.227923\pi\)
−0.656404 + 0.754410i \(0.727923\pi\)
\(938\) 24.0000i 0.783628i
\(939\) 0 0
\(940\) −42.0000 + 14.0000i −1.36989 + 0.456630i
\(941\) 1.00000 + 1.00000i 0.0325991 + 0.0325991i 0.723218 0.690619i \(-0.242662\pi\)
−0.690619 + 0.723218i \(0.742662\pi\)
\(942\) 0 0
\(943\) −4.00000 + 4.00000i −0.130258 + 0.130258i
\(944\) 12.0000 12.0000i 0.390567 0.390567i
\(945\) 0 0
\(946\) −8.00000 −0.260102
\(947\) 28.0000i 0.909878i 0.890523 + 0.454939i \(0.150339\pi\)
−0.890523 + 0.454939i \(0.849661\pi\)
\(948\) 0 0
\(949\) −6.00000 6.00000i −0.194768 0.194768i
\(950\) 24.0000 18.0000i 0.778663 0.583997i
\(951\) 0 0
\(952\) 12.0000 + 12.0000i 0.388922 + 0.388922i
\(953\) −31.0000 + 31.0000i −1.00419 + 1.00419i −0.00419731 + 0.999991i \(0.501336\pi\)
−0.999991 + 0.00419731i \(0.998664\pi\)
\(954\) 0 0
\(955\) 18.0000 36.0000i 0.582466 1.16493i
\(956\) 0 0
\(957\) 0 0
\(958\) 32.0000 + 32.0000i 1.03387 + 1.03387i
\(959\) −54.0000 −1.74375
\(960\) 0 0
\(961\) 27.0000 0.870968
\(962\) 12.0000 + 12.0000i 0.386896 + 0.386896i
\(963\) 0 0
\(964\) 28.0000i 0.901819i
\(965\) −15.0000 45.0000i −0.482867 1.44860i
\(966\) 0 0
\(967\) 33.0000 33.0000i 1.06121 1.06121i 0.0632081 0.998000i \(-0.479867\pi\)
0.998000 0.0632081i \(-0.0201332\pi\)
\(968\) 18.0000 + 18.0000i 0.578542 + 0.578542i
\(969\) 0 0
\(970\) −44.0000 22.0000i −1.41275 0.706377i
\(971\) −31.0000 31.0000i −0.994837 0.994837i 0.00514940 0.999987i \(-0.498361\pi\)
−0.999987 + 0.00514940i \(0.998361\pi\)
\(972\) 0 0
\(973\) 54.0000i 1.73116i
\(974\) −30.0000 −0.961262
\(975\) 0 0
\(976\) 4.00000 + 4.00000i 0.128037 + 0.128037i
\(977\) −17.0000 + 17.0000i −0.543878 + 0.543878i −0.924663 0.380785i \(-0.875654\pi\)
0.380785 + 0.924663i \(0.375654\pi\)
\(978\) 0 0
\(979\) 6.00000 + 6.00000i 0.191761 + 0.191761i
\(980\) 44.0000 + 22.0000i 1.40553 + 0.702764i
\(981\) 0 0
\(982\) 18.0000i 0.574403i
\(983\) 5.00000 + 5.00000i 0.159475 + 0.159475i 0.782334 0.622859i \(-0.214029\pi\)
−0.622859 + 0.782334i \(0.714029\pi\)
\(984\) 0 0
\(985\) −6.00000 + 12.0000i −0.191176 + 0.382352i
\(986\) −14.0000 + 14.0000i −0.445851 + 0.445851i
\(987\) 0 0
\(988\) −12.0000 12.0000i −0.381771 0.381771i
\(989\) −4.00000 + 4.00000i −0.127193 + 0.127193i
\(990\) 0 0
\(991\) 10.0000i 0.317660i 0.987306 + 0.158830i \(0.0507723\pi\)
−0.987306 + 0.158830i \(0.949228\pi\)
\(992\) 8.00000 8.00000i 0.254000 0.254000i
\(993\) 0 0
\(994\) 0 0
\(995\) 10.0000 20.0000i 0.317021 0.634043i
\(996\) 0 0
\(997\) 22.0000i 0.696747i −0.937356 0.348373i \(-0.886734\pi\)
0.937356 0.348373i \(-0.113266\pi\)
\(998\) 58.0000i 1.83596i
\(999\) 0 0
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 720.2.z.d.163.1 2
3.2 odd 2 80.2.s.a.3.1 yes 2
5.2 odd 4 720.2.bd.a.307.1 2
12.11 even 2 320.2.s.a.303.1 2
15.2 even 4 80.2.j.a.67.1 yes 2
15.8 even 4 400.2.j.a.307.1 2
15.14 odd 2 400.2.s.a.243.1 2
16.11 odd 4 720.2.bd.a.523.1 2
24.5 odd 2 640.2.s.b.223.1 2
24.11 even 2 640.2.s.a.223.1 2
48.5 odd 4 320.2.j.a.143.1 2
48.11 even 4 80.2.j.a.43.1 2
48.29 odd 4 640.2.j.b.543.1 2
48.35 even 4 640.2.j.a.543.1 2
60.23 odd 4 1600.2.j.a.1007.1 2
60.47 odd 4 320.2.j.a.47.1 2
60.59 even 2 1600.2.s.a.943.1 2
80.27 even 4 inner 720.2.z.d.667.1 2
120.77 even 4 640.2.j.a.607.1 2
120.107 odd 4 640.2.j.b.607.1 2
240.53 even 4 1600.2.s.a.207.1 2
240.59 even 4 400.2.j.a.43.1 2
240.77 even 4 640.2.s.a.287.1 2
240.107 odd 4 80.2.s.a.27.1 yes 2
240.149 odd 4 1600.2.j.a.143.1 2
240.197 even 4 320.2.s.a.207.1 2
240.203 odd 4 400.2.s.a.107.1 2
240.227 odd 4 640.2.s.b.287.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
80.2.j.a.43.1 2 48.11 even 4
80.2.j.a.67.1 yes 2 15.2 even 4
80.2.s.a.3.1 yes 2 3.2 odd 2
80.2.s.a.27.1 yes 2 240.107 odd 4
320.2.j.a.47.1 2 60.47 odd 4
320.2.j.a.143.1 2 48.5 odd 4
320.2.s.a.207.1 2 240.197 even 4
320.2.s.a.303.1 2 12.11 even 2
400.2.j.a.43.1 2 240.59 even 4
400.2.j.a.307.1 2 15.8 even 4
400.2.s.a.107.1 2 240.203 odd 4
400.2.s.a.243.1 2 15.14 odd 2
640.2.j.a.543.1 2 48.35 even 4
640.2.j.a.607.1 2 120.77 even 4
640.2.j.b.543.1 2 48.29 odd 4
640.2.j.b.607.1 2 120.107 odd 4
640.2.s.a.223.1 2 24.11 even 2
640.2.s.a.287.1 2 240.77 even 4
640.2.s.b.223.1 2 24.5 odd 2
640.2.s.b.287.1 2 240.227 odd 4
720.2.z.d.163.1 2 1.1 even 1 trivial
720.2.z.d.667.1 2 80.27 even 4 inner
720.2.bd.a.307.1 2 5.2 odd 4
720.2.bd.a.523.1 2 16.11 odd 4
1600.2.j.a.143.1 2 240.149 odd 4
1600.2.j.a.1007.1 2 60.23 odd 4
1600.2.s.a.207.1 2 240.53 even 4
1600.2.s.a.943.1 2 60.59 even 2