Properties

Label 570.2.d.b.229.2
Level $570$
Weight $2$
Character 570.229
Analytic conductor $4.551$
Analytic rank $0$
Dimension $2$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [570,2,Mod(229,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("570.229");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.55147291521\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 229.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 570.229
Dual form 570.2.d.b.229.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 + 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} -4.00000 q^{11} -1.00000i q^{12} +4.00000i q^{13} +(-1.00000 + 2.00000i) q^{15} +1.00000 q^{16} +6.00000i q^{17} -1.00000i q^{18} +1.00000 q^{19} +(-2.00000 - 1.00000i) q^{20} -4.00000i q^{22} +1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} -4.00000 q^{26} -1.00000i q^{27} +2.00000 q^{29} +(-2.00000 - 1.00000i) q^{30} +1.00000i q^{32} -4.00000i q^{33} -6.00000 q^{34} +1.00000 q^{36} -4.00000i q^{37} +1.00000i q^{38} -4.00000 q^{39} +(1.00000 - 2.00000i) q^{40} -12.0000 q^{41} -6.00000i q^{43} +4.00000 q^{44} +(-2.00000 - 1.00000i) q^{45} +1.00000i q^{48} +7.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} -6.00000 q^{51} -4.00000i q^{52} +14.0000i q^{53} +1.00000 q^{54} +(-8.00000 - 4.00000i) q^{55} +1.00000i q^{57} +2.00000i q^{58} +10.0000 q^{59} +(1.00000 - 2.00000i) q^{60} -6.00000 q^{61} -1.00000 q^{64} +(-4.00000 + 8.00000i) q^{65} +4.00000 q^{66} -4.00000i q^{67} -6.00000i q^{68} +12.0000 q^{71} +1.00000i q^{72} -8.00000i q^{73} +4.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} -1.00000 q^{76} -4.00000i q^{78} +8.00000 q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} -12.0000i q^{82} -12.0000i q^{83} +(-6.00000 + 12.0000i) q^{85} +6.00000 q^{86} +2.00000i q^{87} +4.00000i q^{88} +8.00000 q^{89} +(1.00000 - 2.00000i) q^{90} +(2.00000 + 1.00000i) q^{95} -1.00000 q^{96} -10.0000i q^{97} +7.00000i q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{9} - 2 q^{10} - 8 q^{11} - 2 q^{15} + 2 q^{16} + 2 q^{19} - 4 q^{20} + 2 q^{24} + 6 q^{25} - 8 q^{26} + 4 q^{29} - 4 q^{30} - 12 q^{34} + 2 q^{36} - 8 q^{39} + 2 q^{40} - 24 q^{41} + 8 q^{44} - 4 q^{45} + 14 q^{49} - 8 q^{50} - 12 q^{51} + 2 q^{54} - 16 q^{55} + 20 q^{59} + 2 q^{60} - 12 q^{61} - 2 q^{64} - 8 q^{65} + 8 q^{66} + 24 q^{71} + 8 q^{74} - 8 q^{75} - 2 q^{76} + 16 q^{79} + 4 q^{80} + 2 q^{81} - 12 q^{85} + 12 q^{86} + 16 q^{89} + 2 q^{90} + 4 q^{95} - 2 q^{96} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 2.00000 + 1.00000i 0.894427 + 0.447214i
\(6\) −1.00000 −0.408248
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −1.00000 + 2.00000i −0.316228 + 0.632456i
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) −1.00000 + 2.00000i −0.258199 + 0.516398i
\(16\) 1.00000 0.250000
\(17\) 6.00000i 1.45521i 0.685994 + 0.727607i \(0.259367\pi\)
−0.685994 + 0.727607i \(0.740633\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.00000 0.229416
\(20\) −2.00000 1.00000i −0.447214 0.223607i
\(21\) 0 0
\(22\) 4.00000i 0.852803i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 1.00000 0.204124
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) −4.00000 −0.784465
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −2.00000 1.00000i −0.365148 0.182574i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 4.00000i 0.696311i
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 4.00000i 0.657596i −0.944400 0.328798i \(-0.893356\pi\)
0.944400 0.328798i \(-0.106644\pi\)
\(38\) 1.00000i 0.162221i
\(39\) −4.00000 −0.640513
\(40\) 1.00000 2.00000i 0.158114 0.316228i
\(41\) −12.0000 −1.87409 −0.937043 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) 0 0
\(43\) 6.00000i 0.914991i −0.889212 0.457496i \(-0.848747\pi\)
0.889212 0.457496i \(-0.151253\pi\)
\(44\) 4.00000 0.603023
\(45\) −2.00000 1.00000i −0.298142 0.149071i
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 7.00000 1.00000
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) −6.00000 −0.840168
\(52\) 4.00000i 0.554700i
\(53\) 14.0000i 1.92305i 0.274721 + 0.961524i \(0.411414\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 1.00000 0.136083
\(55\) −8.00000 4.00000i −1.07872 0.539360i
\(56\) 0 0
\(57\) 1.00000i 0.132453i
\(58\) 2.00000i 0.262613i
\(59\) 10.0000 1.30189 0.650945 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(60\) 1.00000 2.00000i 0.129099 0.258199i
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −4.00000 + 8.00000i −0.496139 + 0.992278i
\(66\) 4.00000 0.492366
\(67\) 4.00000i 0.488678i −0.969690 0.244339i \(-0.921429\pi\)
0.969690 0.244339i \(-0.0785709\pi\)
\(68\) 6.00000i 0.727607i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 8.00000i 0.936329i −0.883641 0.468165i \(-0.844915\pi\)
0.883641 0.468165i \(-0.155085\pi\)
\(74\) 4.00000 0.464991
\(75\) −4.00000 + 3.00000i −0.461880 + 0.346410i
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) 4.00000i 0.452911i
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 2.00000 + 1.00000i 0.223607 + 0.111803i
\(81\) 1.00000 0.111111
\(82\) 12.0000i 1.32518i
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 0 0
\(85\) −6.00000 + 12.0000i −0.650791 + 1.30158i
\(86\) 6.00000 0.646997
\(87\) 2.00000i 0.214423i
\(88\) 4.00000i 0.426401i
\(89\) 8.00000 0.847998 0.423999 0.905663i \(-0.360626\pi\)
0.423999 + 0.905663i \(0.360626\pi\)
\(90\) 1.00000 2.00000i 0.105409 0.210819i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.00000 + 1.00000i 0.205196 + 0.102598i
\(96\) −1.00000 −0.102062
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 7.00000i 0.707107i
\(99\) 4.00000 0.402015
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 6.00000i 0.594089i
\(103\) 2.00000i 0.197066i −0.995134 0.0985329i \(-0.968585\pi\)
0.995134 0.0985329i \(-0.0314150\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) −14.0000 −1.35980
\(107\) 20.0000i 1.93347i 0.255774 + 0.966736i \(0.417670\pi\)
−0.255774 + 0.966736i \(0.582330\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 4.00000 8.00000i 0.381385 0.762770i
\(111\) 4.00000 0.379663
\(112\) 0 0
\(113\) 10.0000i 0.940721i 0.882474 + 0.470360i \(0.155876\pi\)
−0.882474 + 0.470360i \(0.844124\pi\)
\(114\) −1.00000 −0.0936586
\(115\) 0 0
\(116\) −2.00000 −0.185695
\(117\) 4.00000i 0.369800i
\(118\) 10.0000i 0.920575i
\(119\) 0 0
\(120\) 2.00000 + 1.00000i 0.182574 + 0.0912871i
\(121\) 5.00000 0.454545
\(122\) 6.00000i 0.543214i
\(123\) 12.0000i 1.08200i
\(124\) 0 0
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 0 0
\(127\) 10.0000i 0.887357i −0.896186 0.443678i \(-0.853673\pi\)
0.896186 0.443678i \(-0.146327\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 6.00000 0.528271
\(130\) −8.00000 4.00000i −0.701646 0.350823i
\(131\) −20.0000 −1.74741 −0.873704 0.486458i \(-0.838289\pi\)
−0.873704 + 0.486458i \(0.838289\pi\)
\(132\) 4.00000i 0.348155i
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 1.00000 2.00000i 0.0860663 0.172133i
\(136\) 6.00000 0.514496
\(137\) 6.00000i 0.512615i −0.966595 0.256307i \(-0.917494\pi\)
0.966595 0.256307i \(-0.0825059\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 12.0000i 1.00702i
\(143\) 16.0000i 1.33799i
\(144\) −1.00000 −0.0833333
\(145\) 4.00000 + 2.00000i 0.332182 + 0.166091i
\(146\) 8.00000 0.662085
\(147\) 7.00000i 0.577350i
\(148\) 4.00000i 0.328798i
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) −3.00000 4.00000i −0.244949 0.326599i
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 0 0
\(156\) 4.00000 0.320256
\(157\) 6.00000i 0.478852i 0.970915 + 0.239426i \(0.0769593\pi\)
−0.970915 + 0.239426i \(0.923041\pi\)
\(158\) 8.00000i 0.636446i
\(159\) −14.0000 −1.11027
\(160\) −1.00000 + 2.00000i −0.0790569 + 0.158114i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 10.0000i 0.783260i 0.920123 + 0.391630i \(0.128089\pi\)
−0.920123 + 0.391630i \(0.871911\pi\)
\(164\) 12.0000 0.937043
\(165\) 4.00000 8.00000i 0.311400 0.622799i
\(166\) 12.0000 0.931381
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) −12.0000 6.00000i −0.920358 0.460179i
\(171\) −1.00000 −0.0764719
\(172\) 6.00000i 0.457496i
\(173\) 2.00000i 0.152057i 0.997106 + 0.0760286i \(0.0242240\pi\)
−0.997106 + 0.0760286i \(0.975776\pi\)
\(174\) −2.00000 −0.151620
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 10.0000i 0.751646i
\(178\) 8.00000i 0.599625i
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 2.00000 + 1.00000i 0.149071 + 0.0745356i
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 6.00000i 0.443533i
\(184\) 0 0
\(185\) 4.00000 8.00000i 0.294086 0.588172i
\(186\) 0 0
\(187\) 24.0000i 1.75505i
\(188\) 0 0
\(189\) 0 0
\(190\) −1.00000 + 2.00000i −0.0725476 + 0.145095i
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 10.0000i 0.719816i 0.932988 + 0.359908i \(0.117192\pi\)
−0.932988 + 0.359908i \(0.882808\pi\)
\(194\) 10.0000 0.717958
\(195\) −8.00000 4.00000i −0.572892 0.286446i
\(196\) −7.00000 −0.500000
\(197\) 10.0000i 0.712470i −0.934396 0.356235i \(-0.884060\pi\)
0.934396 0.356235i \(-0.115940\pi\)
\(198\) 4.00000i 0.284268i
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 4.00000 3.00000i 0.282843 0.212132i
\(201\) 4.00000 0.282138
\(202\) 12.0000i 0.844317i
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) −24.0000 12.0000i −1.67623 0.838116i
\(206\) 2.00000 0.139347
\(207\) 0 0
\(208\) 4.00000i 0.277350i
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 14.0000i 0.961524i
\(213\) 12.0000i 0.822226i
\(214\) −20.0000 −1.36717
\(215\) 6.00000 12.0000i 0.409197 0.818393i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 14.0000i 0.948200i
\(219\) 8.00000 0.540590
\(220\) 8.00000 + 4.00000i 0.539360 + 0.269680i
\(221\) −24.0000 −1.61441
\(222\) 4.00000i 0.268462i
\(223\) 10.0000i 0.669650i −0.942280 0.334825i \(-0.891323\pi\)
0.942280 0.334825i \(-0.108677\pi\)
\(224\) 0 0
\(225\) −3.00000 4.00000i −0.200000 0.266667i
\(226\) −10.0000 −0.665190
\(227\) 12.0000i 0.796468i −0.917284 0.398234i \(-0.869623\pi\)
0.917284 0.398234i \(-0.130377\pi\)
\(228\) 1.00000i 0.0662266i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2.00000i 0.131306i
\(233\) 14.0000i 0.917170i −0.888650 0.458585i \(-0.848356\pi\)
0.888650 0.458585i \(-0.151644\pi\)
\(234\) 4.00000 0.261488
\(235\) 0 0
\(236\) −10.0000 −0.650945
\(237\) 8.00000i 0.519656i
\(238\) 0 0
\(239\) −10.0000 −0.646846 −0.323423 0.946254i \(-0.604834\pi\)
−0.323423 + 0.946254i \(0.604834\pi\)
\(240\) −1.00000 + 2.00000i −0.0645497 + 0.129099i
\(241\) 26.0000 1.67481 0.837404 0.546585i \(-0.184072\pi\)
0.837404 + 0.546585i \(0.184072\pi\)
\(242\) 5.00000i 0.321412i
\(243\) 1.00000i 0.0641500i
\(244\) 6.00000 0.384111
\(245\) 14.0000 + 7.00000i 0.894427 + 0.447214i
\(246\) 12.0000 0.765092
\(247\) 4.00000i 0.254514i
\(248\) 0 0
\(249\) 12.0000 0.760469
\(250\) −11.0000 + 2.00000i −0.695701 + 0.126491i
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 10.0000 0.627456
\(255\) −12.0000 6.00000i −0.751469 0.375735i
\(256\) 1.00000 0.0625000
\(257\) 2.00000i 0.124757i −0.998053 0.0623783i \(-0.980131\pi\)
0.998053 0.0623783i \(-0.0198685\pi\)
\(258\) 6.00000i 0.373544i
\(259\) 0 0
\(260\) 4.00000 8.00000i 0.248069 0.496139i
\(261\) −2.00000 −0.123797
\(262\) 20.0000i 1.23560i
\(263\) 16.0000i 0.986602i −0.869859 0.493301i \(-0.835790\pi\)
0.869859 0.493301i \(-0.164210\pi\)
\(264\) −4.00000 −0.246183
\(265\) −14.0000 + 28.0000i −0.860013 + 1.72003i
\(266\) 0 0
\(267\) 8.00000i 0.489592i
\(268\) 4.00000i 0.244339i
\(269\) 2.00000 0.121942 0.0609711 0.998140i \(-0.480580\pi\)
0.0609711 + 0.998140i \(0.480580\pi\)
\(270\) 2.00000 + 1.00000i 0.121716 + 0.0608581i
\(271\) −28.0000 −1.70088 −0.850439 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 6.00000i 0.363803i
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) −12.0000 16.0000i −0.723627 0.964836i
\(276\) 0 0
\(277\) 14.0000i 0.841178i −0.907251 0.420589i \(-0.861823\pi\)
0.907251 0.420589i \(-0.138177\pi\)
\(278\) 12.0000i 0.719712i
\(279\) 0 0
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 0 0
\(283\) 2.00000i 0.118888i 0.998232 + 0.0594438i \(0.0189327\pi\)
−0.998232 + 0.0594438i \(0.981067\pi\)
\(284\) −12.0000 −0.712069
\(285\) −1.00000 + 2.00000i −0.0592349 + 0.118470i
\(286\) 16.0000 0.946100
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −19.0000 −1.11765
\(290\) −2.00000 + 4.00000i −0.117444 + 0.234888i
\(291\) 10.0000 0.586210
\(292\) 8.00000i 0.468165i
\(293\) 14.0000i 0.817889i −0.912559 0.408944i \(-0.865897\pi\)
0.912559 0.408944i \(-0.134103\pi\)
\(294\) −7.00000 −0.408248
\(295\) 20.0000 + 10.0000i 1.16445 + 0.582223i
\(296\) −4.00000 −0.232495
\(297\) 4.00000i 0.232104i
\(298\) 0 0
\(299\) 0 0
\(300\) 4.00000 3.00000i 0.230940 0.173205i
\(301\) 0 0
\(302\) 16.0000i 0.920697i
\(303\) 12.0000i 0.689382i
\(304\) 1.00000 0.0573539
\(305\) −12.0000 6.00000i −0.687118 0.343559i
\(306\) 6.00000 0.342997
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 2.00000 0.113776
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 4.00000i 0.226455i
\(313\) 4.00000i 0.226093i −0.993590 0.113047i \(-0.963939\pi\)
0.993590 0.113047i \(-0.0360610\pi\)
\(314\) −6.00000 −0.338600
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) 14.0000i 0.785081i
\(319\) −8.00000 −0.447914
\(320\) −2.00000 1.00000i −0.111803 0.0559017i
\(321\) −20.0000 −1.11629
\(322\) 0 0
\(323\) 6.00000i 0.333849i
\(324\) −1.00000 −0.0555556
\(325\) −16.0000 + 12.0000i −0.887520 + 0.665640i
\(326\) −10.0000 −0.553849
\(327\) 14.0000i 0.774202i
\(328\) 12.0000i 0.662589i
\(329\) 0 0
\(330\) 8.00000 + 4.00000i 0.440386 + 0.220193i
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 12.0000i 0.658586i
\(333\) 4.00000i 0.219199i
\(334\) −12.0000 −0.656611
\(335\) 4.00000 8.00000i 0.218543 0.437087i
\(336\) 0 0
\(337\) 18.0000i 0.980522i 0.871576 + 0.490261i \(0.163099\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) 3.00000i 0.163178i
\(339\) −10.0000 −0.543125
\(340\) 6.00000 12.0000i 0.325396 0.650791i
\(341\) 0 0
\(342\) 1.00000i 0.0540738i
\(343\) 0 0
\(344\) −6.00000 −0.323498
\(345\) 0 0
\(346\) −2.00000 −0.107521
\(347\) 32.0000i 1.71785i 0.512101 + 0.858925i \(0.328867\pi\)
−0.512101 + 0.858925i \(0.671133\pi\)
\(348\) 2.00000i 0.107211i
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) 0 0
\(351\) 4.00000 0.213504
\(352\) 4.00000i 0.213201i
\(353\) 22.0000i 1.17094i −0.810693 0.585471i \(-0.800910\pi\)
0.810693 0.585471i \(-0.199090\pi\)
\(354\) −10.0000 −0.531494
\(355\) 24.0000 + 12.0000i 1.27379 + 0.636894i
\(356\) −8.00000 −0.423999
\(357\) 0 0
\(358\) 6.00000i 0.317110i
\(359\) −34.0000 −1.79445 −0.897226 0.441572i \(-0.854421\pi\)
−0.897226 + 0.441572i \(0.854421\pi\)
\(360\) −1.00000 + 2.00000i −0.0527046 + 0.105409i
\(361\) 1.00000 0.0526316
\(362\) 10.0000i 0.525588i
\(363\) 5.00000i 0.262432i
\(364\) 0 0
\(365\) 8.00000 16.0000i 0.418739 0.837478i
\(366\) 6.00000 0.313625
\(367\) 12.0000i 0.626395i −0.949688 0.313197i \(-0.898600\pi\)
0.949688 0.313197i \(-0.101400\pi\)
\(368\) 0 0
\(369\) 12.0000 0.624695
\(370\) 8.00000 + 4.00000i 0.415900 + 0.207950i
\(371\) 0 0
\(372\) 0 0
\(373\) 12.0000i 0.621336i −0.950518 0.310668i \(-0.899447\pi\)
0.950518 0.310668i \(-0.100553\pi\)
\(374\) 24.0000 1.24101
\(375\) −11.0000 + 2.00000i −0.568038 + 0.103280i
\(376\) 0 0
\(377\) 8.00000i 0.412021i
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) −2.00000 1.00000i −0.102598 0.0512989i
\(381\) 10.0000 0.512316
\(382\) 6.00000i 0.306987i
\(383\) 36.0000i 1.83951i −0.392488 0.919757i \(-0.628386\pi\)
0.392488 0.919757i \(-0.371614\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 6.00000i 0.304997i
\(388\) 10.0000i 0.507673i
\(389\) 4.00000 0.202808 0.101404 0.994845i \(-0.467667\pi\)
0.101404 + 0.994845i \(0.467667\pi\)
\(390\) 4.00000 8.00000i 0.202548 0.405096i
\(391\) 0 0
\(392\) 7.00000i 0.353553i
\(393\) 20.0000i 1.00887i
\(394\) 10.0000 0.503793
\(395\) 16.0000 + 8.00000i 0.805047 + 0.402524i
\(396\) −4.00000 −0.201008
\(397\) 18.0000i 0.903394i 0.892171 + 0.451697i \(0.149181\pi\)
−0.892171 + 0.451697i \(0.850819\pi\)
\(398\) 4.00000i 0.200502i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) 28.0000 1.39825 0.699127 0.714998i \(-0.253572\pi\)
0.699127 + 0.714998i \(0.253572\pi\)
\(402\) 4.00000i 0.199502i
\(403\) 0 0
\(404\) −12.0000 −0.597022
\(405\) 2.00000 + 1.00000i 0.0993808 + 0.0496904i
\(406\) 0 0
\(407\) 16.0000i 0.793091i
\(408\) 6.00000i 0.297044i
\(409\) 34.0000 1.68119 0.840596 0.541663i \(-0.182205\pi\)
0.840596 + 0.541663i \(0.182205\pi\)
\(410\) 12.0000 24.0000i 0.592638 1.18528i
\(411\) 6.00000 0.295958
\(412\) 2.00000i 0.0985329i
\(413\) 0 0
\(414\) 0 0
\(415\) 12.0000 24.0000i 0.589057 1.17811i
\(416\) −4.00000 −0.196116
\(417\) 12.0000i 0.587643i
\(418\) 4.00000i 0.195646i
\(419\) −8.00000 −0.390826 −0.195413 0.980721i \(-0.562605\pi\)
−0.195413 + 0.980721i \(0.562605\pi\)
\(420\) 0 0
\(421\) −14.0000 −0.682318 −0.341159 0.940006i \(-0.610819\pi\)
−0.341159 + 0.940006i \(0.610819\pi\)
\(422\) 8.00000i 0.389434i
\(423\) 0 0
\(424\) 14.0000 0.679900
\(425\) −24.0000 + 18.0000i −1.16417 + 0.873128i
\(426\) −12.0000 −0.581402
\(427\) 0 0
\(428\) 20.0000i 0.966736i
\(429\) 16.0000 0.772487
\(430\) 12.0000 + 6.00000i 0.578691 + 0.289346i
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 18.0000i 0.865025i 0.901628 + 0.432512i \(0.142373\pi\)
−0.901628 + 0.432512i \(0.857627\pi\)
\(434\) 0 0
\(435\) −2.00000 + 4.00000i −0.0958927 + 0.191785i
\(436\) −14.0000 −0.670478
\(437\) 0 0
\(438\) 8.00000i 0.382255i
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) −4.00000 + 8.00000i −0.190693 + 0.381385i
\(441\) −7.00000 −0.333333
\(442\) 24.0000i 1.14156i
\(443\) 12.0000i 0.570137i 0.958507 + 0.285069i \(0.0920164\pi\)
−0.958507 + 0.285069i \(0.907984\pi\)
\(444\) −4.00000 −0.189832
\(445\) 16.0000 + 8.00000i 0.758473 + 0.379236i
\(446\) 10.0000 0.473514
\(447\) 0 0
\(448\) 0 0
\(449\) 32.0000 1.51017 0.755087 0.655625i \(-0.227595\pi\)
0.755087 + 0.655625i \(0.227595\pi\)
\(450\) 4.00000 3.00000i 0.188562 0.141421i
\(451\) 48.0000 2.26023
\(452\) 10.0000i 0.470360i
\(453\) 16.0000i 0.751746i
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 1.00000 0.0468293
\(457\) 32.0000i 1.49690i −0.663193 0.748448i \(-0.730799\pi\)
0.663193 0.748448i \(-0.269201\pi\)
\(458\) 10.0000i 0.467269i
\(459\) 6.00000 0.280056
\(460\) 0 0
\(461\) 24.0000 1.11779 0.558896 0.829238i \(-0.311225\pi\)
0.558896 + 0.829238i \(0.311225\pi\)
\(462\) 0 0
\(463\) 16.0000i 0.743583i −0.928316 0.371792i \(-0.878744\pi\)
0.928316 0.371792i \(-0.121256\pi\)
\(464\) 2.00000 0.0928477
\(465\) 0 0
\(466\) 14.0000 0.648537
\(467\) 24.0000i 1.11059i −0.831654 0.555294i \(-0.812606\pi\)
0.831654 0.555294i \(-0.187394\pi\)
\(468\) 4.00000i 0.184900i
\(469\) 0 0
\(470\) 0 0
\(471\) −6.00000 −0.276465
\(472\) 10.0000i 0.460287i
\(473\) 24.0000i 1.10352i
\(474\) −8.00000 −0.367452
\(475\) 3.00000 + 4.00000i 0.137649 + 0.183533i
\(476\) 0 0
\(477\) 14.0000i 0.641016i
\(478\) 10.0000i 0.457389i
\(479\) −38.0000 −1.73626 −0.868132 0.496333i \(-0.834679\pi\)
−0.868132 + 0.496333i \(0.834679\pi\)
\(480\) −2.00000 1.00000i −0.0912871 0.0456435i
\(481\) 16.0000 0.729537
\(482\) 26.0000i 1.18427i
\(483\) 0 0
\(484\) −5.00000 −0.227273
\(485\) 10.0000 20.0000i 0.454077 0.908153i
\(486\) −1.00000 −0.0453609
\(487\) 18.0000i 0.815658i −0.913058 0.407829i \(-0.866286\pi\)
0.913058 0.407829i \(-0.133714\pi\)
\(488\) 6.00000i 0.271607i
\(489\) −10.0000 −0.452216
\(490\) −7.00000 + 14.0000i −0.316228 + 0.632456i
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 12.0000i 0.541002i
\(493\) 12.0000i 0.540453i
\(494\) −4.00000 −0.179969
\(495\) 8.00000 + 4.00000i 0.359573 + 0.179787i
\(496\) 0 0
\(497\) 0 0
\(498\) 12.0000i 0.537733i
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) −2.00000 11.0000i −0.0894427 0.491935i
\(501\) −12.0000 −0.536120
\(502\) 24.0000i 1.07117i
\(503\) 16.0000i 0.713405i −0.934218 0.356702i \(-0.883901\pi\)
0.934218 0.356702i \(-0.116099\pi\)
\(504\) 0 0
\(505\) 24.0000 + 12.0000i 1.06799 + 0.533993i
\(506\) 0 0
\(507\) 3.00000i 0.133235i
\(508\) 10.0000i 0.443678i
\(509\) −18.0000 −0.797836 −0.398918 0.916987i \(-0.630614\pi\)
−0.398918 + 0.916987i \(0.630614\pi\)
\(510\) 6.00000 12.0000i 0.265684 0.531369i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 1.00000i 0.0441511i
\(514\) 2.00000 0.0882162
\(515\) 2.00000 4.00000i 0.0881305 0.176261i
\(516\) −6.00000 −0.264135
\(517\) 0 0
\(518\) 0 0
\(519\) −2.00000 −0.0877903
\(520\) 8.00000 + 4.00000i 0.350823 + 0.175412i
\(521\) −12.0000 −0.525730 −0.262865 0.964833i \(-0.584667\pi\)
−0.262865 + 0.964833i \(0.584667\pi\)
\(522\) 2.00000i 0.0875376i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 20.0000 0.873704
\(525\) 0 0
\(526\) 16.0000 0.697633
\(527\) 0 0
\(528\) 4.00000i 0.174078i
\(529\) 23.0000 1.00000
\(530\) −28.0000 14.0000i −1.21624 0.608121i
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) 48.0000i 2.07911i
\(534\) −8.00000 −0.346194
\(535\) −20.0000 + 40.0000i −0.864675 + 1.72935i
\(536\) −4.00000 −0.172774
\(537\) 6.00000i 0.258919i
\(538\) 2.00000i 0.0862261i
\(539\) −28.0000 −1.20605
\(540\) −1.00000 + 2.00000i −0.0430331 + 0.0860663i
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 28.0000i 1.20270i
\(543\) 10.0000i 0.429141i
\(544\) −6.00000 −0.257248
\(545\) 28.0000 + 14.0000i 1.19939 + 0.599694i
\(546\) 0 0
\(547\) 24.0000i 1.02617i 0.858339 + 0.513083i \(0.171497\pi\)
−0.858339 + 0.513083i \(0.828503\pi\)
\(548\) 6.00000i 0.256307i
\(549\) 6.00000 0.256074
\(550\) 16.0000 12.0000i 0.682242 0.511682i
\(551\) 2.00000 0.0852029
\(552\) 0 0
\(553\) 0 0
\(554\) 14.0000 0.594803
\(555\) 8.00000 + 4.00000i 0.339581 + 0.169791i
\(556\) −12.0000 −0.508913
\(557\) 30.0000i 1.27114i −0.772043 0.635570i \(-0.780765\pi\)
0.772043 0.635570i \(-0.219235\pi\)
\(558\) 0 0
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) 12.0000i 0.506189i
\(563\) 36.0000i 1.51722i 0.651546 + 0.758610i \(0.274121\pi\)
−0.651546 + 0.758610i \(0.725879\pi\)
\(564\) 0 0
\(565\) −10.0000 + 20.0000i −0.420703 + 0.841406i
\(566\) −2.00000 −0.0840663
\(567\) 0 0
\(568\) 12.0000i 0.503509i
\(569\) −32.0000 −1.34151 −0.670755 0.741679i \(-0.734030\pi\)
−0.670755 + 0.741679i \(0.734030\pi\)
\(570\) −2.00000 1.00000i −0.0837708 0.0418854i
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 16.0000i 0.668994i
\(573\) 6.00000i 0.250654i
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 8.00000i 0.333044i −0.986038 0.166522i \(-0.946746\pi\)
0.986038 0.166522i \(-0.0532537\pi\)
\(578\) 19.0000i 0.790296i
\(579\) −10.0000 −0.415586
\(580\) −4.00000 2.00000i −0.166091 0.0830455i
\(581\) 0 0
\(582\) 10.0000i 0.414513i
\(583\) 56.0000i 2.31928i
\(584\) −8.00000 −0.331042
\(585\) 4.00000 8.00000i 0.165380 0.330759i
\(586\) 14.0000 0.578335
\(587\) 32.0000i 1.32078i 0.750922 + 0.660391i \(0.229609\pi\)
−0.750922 + 0.660391i \(0.770391\pi\)
\(588\) 7.00000i 0.288675i
\(589\) 0 0
\(590\) −10.0000 + 20.0000i −0.411693 + 0.823387i
\(591\) 10.0000 0.411345
\(592\) 4.00000i 0.164399i
\(593\) 22.0000i 0.903432i 0.892162 + 0.451716i \(0.149188\pi\)
−0.892162 + 0.451716i \(0.850812\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) 0 0
\(597\) 4.00000i 0.163709i
\(598\) 0 0
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 3.00000 + 4.00000i 0.122474 + 0.163299i
\(601\) −42.0000 −1.71322 −0.856608 0.515968i \(-0.827432\pi\)
−0.856608 + 0.515968i \(0.827432\pi\)
\(602\) 0 0
\(603\) 4.00000i 0.162893i
\(604\) −16.0000 −0.651031
\(605\) 10.0000 + 5.00000i 0.406558 + 0.203279i
\(606\) −12.0000 −0.487467
\(607\) 30.0000i 1.21766i 0.793300 + 0.608831i \(0.208361\pi\)
−0.793300 + 0.608831i \(0.791639\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) 0 0
\(610\) 6.00000 12.0000i 0.242933 0.485866i
\(611\) 0 0
\(612\) 6.00000i 0.242536i
\(613\) 46.0000i 1.85792i 0.370177 + 0.928961i \(0.379297\pi\)
−0.370177 + 0.928961i \(0.620703\pi\)
\(614\) 0 0
\(615\) 12.0000 24.0000i 0.483887 0.967773i
\(616\) 0 0
\(617\) 6.00000i 0.241551i 0.992680 + 0.120775i \(0.0385381\pi\)
−0.992680 + 0.120775i \(0.961462\pi\)
\(618\) 2.00000i 0.0804518i
\(619\) 28.0000 1.12542 0.562708 0.826656i \(-0.309760\pi\)
0.562708 + 0.826656i \(0.309760\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 18.0000i 0.721734i
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 4.00000 0.159872
\(627\) 4.00000i 0.159745i
\(628\) 6.00000i 0.239426i
\(629\) 24.0000 0.956943
\(630\) 0 0
\(631\) 28.0000 1.11466 0.557331 0.830290i \(-0.311825\pi\)
0.557331 + 0.830290i \(0.311825\pi\)
\(632\) 8.00000i 0.318223i
\(633\) 8.00000i 0.317971i
\(634\) −18.0000 −0.714871
\(635\) 10.0000 20.0000i 0.396838 0.793676i
\(636\) 14.0000 0.555136
\(637\) 28.0000i 1.10940i
\(638\) 8.00000i 0.316723i
\(639\) −12.0000 −0.474713
\(640\) 1.00000 2.00000i 0.0395285 0.0790569i
\(641\) 36.0000 1.42191 0.710957 0.703235i \(-0.248262\pi\)
0.710957 + 0.703235i \(0.248262\pi\)
\(642\) 20.0000i 0.789337i
\(643\) 26.0000i 1.02534i 0.858586 + 0.512670i \(0.171344\pi\)
−0.858586 + 0.512670i \(0.828656\pi\)
\(644\) 0 0
\(645\) 12.0000 + 6.00000i 0.472500 + 0.236250i
\(646\) −6.00000 −0.236067
\(647\) 24.0000i 0.943537i −0.881722 0.471769i \(-0.843616\pi\)
0.881722 0.471769i \(-0.156384\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −40.0000 −1.57014
\(650\) −12.0000 16.0000i −0.470679 0.627572i
\(651\) 0 0
\(652\) 10.0000i 0.391630i
\(653\) 18.0000i 0.704394i −0.935926 0.352197i \(-0.885435\pi\)
0.935926 0.352197i \(-0.114565\pi\)
\(654\) −14.0000 −0.547443
\(655\) −40.0000 20.0000i −1.56293 0.781465i
\(656\) −12.0000 −0.468521
\(657\) 8.00000i 0.312110i
\(658\) 0 0
\(659\) 26.0000 1.01282 0.506408 0.862294i \(-0.330973\pi\)
0.506408 + 0.862294i \(0.330973\pi\)
\(660\) −4.00000 + 8.00000i −0.155700 + 0.311400i
\(661\) −2.00000 −0.0777910 −0.0388955 0.999243i \(-0.512384\pi\)
−0.0388955 + 0.999243i \(0.512384\pi\)
\(662\) 8.00000i 0.310929i
\(663\) 24.0000i 0.932083i
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) 0 0
\(668\) 12.0000i 0.464294i
\(669\) 10.0000 0.386622
\(670\) 8.00000 + 4.00000i 0.309067 + 0.154533i
\(671\) 24.0000 0.926510
\(672\) 0 0
\(673\) 26.0000i 1.00223i −0.865382 0.501113i \(-0.832924\pi\)
0.865382 0.501113i \(-0.167076\pi\)
\(674\) −18.0000 −0.693334
\(675\) 4.00000 3.00000i 0.153960 0.115470i
\(676\) 3.00000 0.115385
\(677\) 30.0000i 1.15299i −0.817099 0.576497i \(-0.804419\pi\)
0.817099 0.576497i \(-0.195581\pi\)
\(678\) 10.0000i 0.384048i
\(679\) 0 0
\(680\) 12.0000 + 6.00000i 0.460179 + 0.230089i
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) 12.0000i 0.459167i 0.973289 + 0.229584i \(0.0737364\pi\)
−0.973289 + 0.229584i \(0.926264\pi\)
\(684\) 1.00000 0.0382360
\(685\) 6.00000 12.0000i 0.229248 0.458496i
\(686\) 0 0
\(687\) 10.0000i 0.381524i
\(688\) 6.00000i 0.228748i
\(689\) −56.0000 −2.13343
\(690\) 0 0
\(691\) −4.00000 −0.152167 −0.0760836 0.997101i \(-0.524242\pi\)
−0.0760836 + 0.997101i \(0.524242\pi\)
\(692\) 2.00000i 0.0760286i
\(693\) 0 0
\(694\) −32.0000 −1.21470
\(695\) 24.0000 + 12.0000i 0.910372 + 0.455186i
\(696\) 2.00000 0.0758098
\(697\) 72.0000i 2.72719i
\(698\) 34.0000i 1.28692i
\(699\) 14.0000 0.529529
\(700\) 0 0
\(701\) 20.0000 0.755390 0.377695 0.925930i \(-0.376717\pi\)
0.377695 + 0.925930i \(0.376717\pi\)
\(702\) 4.00000i 0.150970i
\(703\) 4.00000i 0.150863i
\(704\) 4.00000 0.150756
\(705\) 0 0
\(706\) 22.0000 0.827981
\(707\) 0 0
\(708\) 10.0000i 0.375823i
\(709\) −22.0000 −0.826227 −0.413114 0.910679i \(-0.635559\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) −12.0000 + 24.0000i −0.450352 + 0.900704i
\(711\) −8.00000 −0.300023
\(712\) 8.00000i 0.299813i
\(713\) 0 0
\(714\) 0 0
\(715\) 16.0000 32.0000i 0.598366 1.19673i
\(716\) 6.00000 0.224231
\(717\) 10.0000i 0.373457i
\(718\) 34.0000i 1.26887i
\(719\) −6.00000 −0.223762 −0.111881 0.993722i \(-0.535688\pi\)
−0.111881 + 0.993722i \(0.535688\pi\)
\(720\) −2.00000 1.00000i −0.0745356 0.0372678i
\(721\) 0 0
\(722\) 1.00000i 0.0372161i
\(723\) 26.0000i 0.966950i
\(724\) 10.0000 0.371647
\(725\) 6.00000 + 8.00000i 0.222834 + 0.297113i
\(726\) −5.00000 −0.185567
\(727\) 40.0000i 1.48352i −0.670667 0.741759i \(-0.733992\pi\)
0.670667 0.741759i \(-0.266008\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 16.0000 + 8.00000i 0.592187 + 0.296093i
\(731\) 36.0000 1.33151
\(732\) 6.00000i 0.221766i
\(733\) 26.0000i 0.960332i 0.877178 + 0.480166i \(0.159424\pi\)
−0.877178 + 0.480166i \(0.840576\pi\)
\(734\) 12.0000 0.442928
\(735\) −7.00000 + 14.0000i −0.258199 + 0.516398i
\(736\) 0 0
\(737\) 16.0000i 0.589368i
\(738\) 12.0000i 0.441726i
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) −4.00000 + 8.00000i −0.147043 + 0.294086i
\(741\) −4.00000 −0.146944
\(742\) 0 0
\(743\) 44.0000i 1.61420i 0.590412 + 0.807102i \(0.298965\pi\)
−0.590412 + 0.807102i \(0.701035\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 12.0000 0.439351
\(747\) 12.0000i 0.439057i
\(748\) 24.0000i 0.877527i
\(749\) 0 0
\(750\) −2.00000 11.0000i −0.0730297 0.401663i
\(751\) −8.00000 −0.291924 −0.145962 0.989290i \(-0.546628\pi\)
−0.145962 + 0.989290i \(0.546628\pi\)
\(752\) 0 0
\(753\) 24.0000i 0.874609i
\(754\) −8.00000 −0.291343
\(755\) 32.0000 + 16.0000i 1.16460 + 0.582300i
\(756\) 0 0
\(757\) 2.00000i 0.0726912i −0.999339 0.0363456i \(-0.988428\pi\)
0.999339 0.0363456i \(-0.0115717\pi\)
\(758\) 12.0000i 0.435860i
\(759\) 0 0
\(760\) 1.00000 2.00000i 0.0362738 0.0725476i
\(761\) −30.0000 −1.08750 −0.543750 0.839248i \(-0.682996\pi\)
−0.543750 + 0.839248i \(0.682996\pi\)
\(762\) 10.0000i 0.362262i
\(763\) 0 0
\(764\) −6.00000 −0.217072
\(765\) 6.00000 12.0000i 0.216930 0.433861i
\(766\) 36.0000 1.30073
\(767\) 40.0000i 1.44432i
\(768\) 1.00000i 0.0360844i
\(769\) −50.0000 −1.80305 −0.901523 0.432731i \(-0.857550\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 0 0
\(771\) 2.00000 0.0720282
\(772\) 10.0000i 0.359908i
\(773\) 38.0000i 1.36677i 0.730061 + 0.683383i \(0.239492\pi\)
−0.730061 + 0.683383i \(0.760508\pi\)
\(774\) −6.00000 −0.215666
\(775\) 0 0
\(776\) −10.0000 −0.358979
\(777\) 0 0
\(778\) 4.00000i 0.143407i
\(779\) −12.0000 −0.429945
\(780\) 8.00000 + 4.00000i 0.286446 + 0.143223i
\(781\) −48.0000 −1.71758
\(782\) 0 0
\(783\) 2.00000i 0.0714742i
\(784\) 7.00000 0.250000
\(785\) −6.00000 + 12.0000i −0.214149 + 0.428298i
\(786\) 20.0000 0.713376
\(787\) 48.0000i 1.71102i</