Properties

Label 1350.2.e.l.901.1
Level $1350$
Weight $2$
Character 1350.901
Analytic conductor $10.780$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1350,2,Mod(451,1350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1350, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1350.451");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1350.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.7798042729\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 901.1
Root \(-1.18614 - 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 1350.901
Dual form 1350.2.e.l.451.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.18614 - 2.05446i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.18614 - 2.05446i) q^{7} -1.00000 q^{8} +(0.686141 + 1.18843i) q^{11} +(2.37228 - 4.10891i) q^{13} +(1.18614 - 2.05446i) q^{14} +(-0.500000 - 0.866025i) q^{16} -7.37228 q^{17} +3.37228 q^{19} +(-0.686141 + 1.18843i) q^{22} +(2.18614 - 3.78651i) q^{23} +4.74456 q^{26} +2.37228 q^{28} +(-2.18614 - 3.78651i) q^{29} +(3.37228 - 5.84096i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.68614 - 6.38458i) q^{34} +4.00000 q^{37} +(1.68614 + 2.92048i) q^{38} +(-1.50000 + 2.59808i) q^{41} +(-5.68614 - 9.84868i) q^{43} -1.37228 q^{44} +4.37228 q^{46} +(0.813859 + 1.40965i) q^{47} +(0.686141 - 1.18843i) q^{49} +(2.37228 + 4.10891i) q^{52} +11.4891 q^{53} +(1.18614 + 2.05446i) q^{56} +(2.18614 - 3.78651i) q^{58} +(-0.686141 + 1.18843i) q^{59} +(-4.55842 - 7.89542i) q^{61} +6.74456 q^{62} +1.00000 q^{64} +(-3.50000 + 6.06218i) q^{67} +(3.68614 - 6.38458i) q^{68} +6.00000 q^{71} +14.1168 q^{73} +(2.00000 + 3.46410i) q^{74} +(-1.68614 + 2.92048i) q^{76} +(1.62772 - 2.81929i) q^{77} +(-1.00000 - 1.73205i) q^{79} -3.00000 q^{82} +(-0.813859 - 1.40965i) q^{83} +(5.68614 - 9.84868i) q^{86} +(-0.686141 - 1.18843i) q^{88} +1.11684 q^{89} -11.2554 q^{91} +(2.18614 + 3.78651i) q^{92} +(-0.813859 + 1.40965i) q^{94} +(-1.31386 - 2.27567i) q^{97} +1.37228 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} + q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} + q^{7} - 4 q^{8} - 3 q^{11} - 2 q^{13} - q^{14} - 2 q^{16} - 18 q^{17} + 2 q^{19} + 3 q^{22} + 3 q^{23} - 4 q^{26} - 2 q^{28} - 3 q^{29} + 2 q^{31} + 2 q^{32} - 9 q^{34} + 16 q^{37} + q^{38} - 6 q^{41} - 17 q^{43} + 6 q^{44} + 6 q^{46} + 9 q^{47} - 3 q^{49} - 2 q^{52} - q^{56} + 3 q^{58} + 3 q^{59} - q^{61} + 4 q^{62} + 4 q^{64} - 14 q^{67} + 9 q^{68} + 24 q^{71} + 22 q^{73} + 8 q^{74} - q^{76} + 18 q^{77} - 4 q^{79} - 12 q^{82} - 9 q^{83} + 17 q^{86} + 3 q^{88} - 30 q^{89} - 68 q^{91} + 3 q^{92} - 9 q^{94} - 11 q^{97} - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).

\(n\) \(1001\) \(1027\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −1.18614 2.05446i −0.448319 0.776511i 0.549958 0.835192i \(-0.314644\pi\)
−0.998277 + 0.0586811i \(0.981310\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 0.686141 + 1.18843i 0.206879 + 0.358325i 0.950730 0.310021i \(-0.100336\pi\)
−0.743851 + 0.668346i \(0.767003\pi\)
\(12\) 0 0
\(13\) 2.37228 4.10891i 0.657952 1.13961i −0.323192 0.946333i \(-0.604756\pi\)
0.981145 0.193274i \(-0.0619106\pi\)
\(14\) 1.18614 2.05446i 0.317009 0.549076i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −7.37228 −1.78804 −0.894020 0.448026i \(-0.852127\pi\)
−0.894020 + 0.448026i \(0.852127\pi\)
\(18\) 0 0
\(19\) 3.37228 0.773654 0.386827 0.922152i \(-0.373571\pi\)
0.386827 + 0.922152i \(0.373571\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.686141 + 1.18843i −0.146286 + 0.253374i
\(23\) 2.18614 3.78651i 0.455842 0.789541i −0.542894 0.839801i \(-0.682672\pi\)
0.998736 + 0.0502598i \(0.0160049\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 4.74456 0.930485
\(27\) 0 0
\(28\) 2.37228 0.448319
\(29\) −2.18614 3.78651i −0.405956 0.703137i 0.588476 0.808515i \(-0.299728\pi\)
−0.994432 + 0.105378i \(0.966395\pi\)
\(30\) 0 0
\(31\) 3.37228 5.84096i 0.605680 1.04907i −0.386264 0.922388i \(-0.626235\pi\)
0.991944 0.126680i \(-0.0404320\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −3.68614 6.38458i −0.632168 1.09495i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 1.68614 + 2.92048i 0.273528 + 0.473765i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.50000 + 2.59808i −0.234261 + 0.405751i −0.959058 0.283211i \(-0.908600\pi\)
0.724797 + 0.688963i \(0.241934\pi\)
\(42\) 0 0
\(43\) −5.68614 9.84868i −0.867128 1.50191i −0.864918 0.501913i \(-0.832630\pi\)
−0.00221007 0.999998i \(-0.500703\pi\)
\(44\) −1.37228 −0.206879
\(45\) 0 0
\(46\) 4.37228 0.644658
\(47\) 0.813859 + 1.40965i 0.118714 + 0.205618i 0.919258 0.393655i \(-0.128790\pi\)
−0.800545 + 0.599273i \(0.795456\pi\)
\(48\) 0 0
\(49\) 0.686141 1.18843i 0.0980201 0.169776i
\(50\) 0 0
\(51\) 0 0
\(52\) 2.37228 + 4.10891i 0.328976 + 0.569804i
\(53\) 11.4891 1.57815 0.789076 0.614295i \(-0.210560\pi\)
0.789076 + 0.614295i \(0.210560\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.18614 + 2.05446i 0.158505 + 0.274538i
\(57\) 0 0
\(58\) 2.18614 3.78651i 0.287054 0.497193i
\(59\) −0.686141 + 1.18843i −0.0893279 + 0.154720i −0.907227 0.420641i \(-0.861805\pi\)
0.817899 + 0.575361i \(0.195139\pi\)
\(60\) 0 0
\(61\) −4.55842 7.89542i −0.583646 1.01090i −0.995043 0.0994483i \(-0.968292\pi\)
0.411397 0.911456i \(-0.365041\pi\)
\(62\) 6.74456 0.856560
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −3.50000 + 6.06218i −0.427593 + 0.740613i −0.996659 0.0816792i \(-0.973972\pi\)
0.569066 + 0.822292i \(0.307305\pi\)
\(68\) 3.68614 6.38458i 0.447010 0.774244i
\(69\) 0 0
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 14.1168 1.65225 0.826126 0.563486i \(-0.190540\pi\)
0.826126 + 0.563486i \(0.190540\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) 0 0
\(76\) −1.68614 + 2.92048i −0.193414 + 0.335002i
\(77\) 1.62772 2.81929i 0.185496 0.321288i
\(78\) 0 0
\(79\) −1.00000 1.73205i −0.112509 0.194871i 0.804272 0.594261i \(-0.202555\pi\)
−0.916781 + 0.399390i \(0.869222\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −3.00000 −0.331295
\(83\) −0.813859 1.40965i −0.0893327 0.154729i 0.817897 0.575365i \(-0.195140\pi\)
−0.907229 + 0.420637i \(0.861807\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 5.68614 9.84868i 0.613152 1.06201i
\(87\) 0 0
\(88\) −0.686141 1.18843i −0.0731428 0.126687i
\(89\) 1.11684 0.118385 0.0591926 0.998247i \(-0.481147\pi\)
0.0591926 + 0.998247i \(0.481147\pi\)
\(90\) 0 0
\(91\) −11.2554 −1.17989
\(92\) 2.18614 + 3.78651i 0.227921 + 0.394771i
\(93\) 0 0
\(94\) −0.813859 + 1.40965i −0.0839432 + 0.145394i
\(95\) 0 0
\(96\) 0 0
\(97\) −1.31386 2.27567i −0.133402 0.231059i 0.791584 0.611061i \(-0.209257\pi\)
−0.924986 + 0.380001i \(0.875924\pi\)
\(98\) 1.37228 0.138621
\(99\) 0 0
\(100\) 0 0
\(101\) −4.37228 7.57301i −0.435058 0.753543i 0.562242 0.826973i \(-0.309939\pi\)
−0.997300 + 0.0734297i \(0.976606\pi\)
\(102\) 0 0
\(103\) −8.00000 + 13.8564i −0.788263 + 1.36531i 0.138767 + 0.990325i \(0.455686\pi\)
−0.927030 + 0.374987i \(0.877647\pi\)
\(104\) −2.37228 + 4.10891i −0.232621 + 0.402912i
\(105\) 0 0
\(106\) 5.74456 + 9.94987i 0.557961 + 0.966417i
\(107\) −14.4891 −1.40072 −0.700358 0.713791i \(-0.746976\pi\)
−0.700358 + 0.713791i \(0.746976\pi\)
\(108\) 0 0
\(109\) 9.62772 0.922168 0.461084 0.887356i \(-0.347461\pi\)
0.461084 + 0.887356i \(0.347461\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.18614 + 2.05446i −0.112080 + 0.194128i
\(113\) −7.37228 + 12.7692i −0.693526 + 1.20122i 0.277149 + 0.960827i \(0.410610\pi\)
−0.970675 + 0.240395i \(0.922723\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 4.37228 0.405956
\(117\) 0 0
\(118\) −1.37228 −0.126329
\(119\) 8.74456 + 15.1460i 0.801613 + 1.38843i
\(120\) 0 0
\(121\) 4.55842 7.89542i 0.414402 0.717765i
\(122\) 4.55842 7.89542i 0.412700 0.714818i
\(123\) 0 0
\(124\) 3.37228 + 5.84096i 0.302840 + 0.524534i
\(125\) 0 0
\(126\) 0 0
\(127\) −9.11684 −0.808989 −0.404495 0.914540i \(-0.632553\pi\)
−0.404495 + 0.914540i \(0.632553\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 4.37228 7.57301i 0.382008 0.661657i −0.609341 0.792908i \(-0.708566\pi\)
0.991349 + 0.131251i \(0.0418993\pi\)
\(132\) 0 0
\(133\) −4.00000 6.92820i −0.346844 0.600751i
\(134\) −7.00000 −0.604708
\(135\) 0 0
\(136\) 7.37228 0.632168
\(137\) 0.941578 + 1.63086i 0.0804444 + 0.139334i 0.903441 0.428713i \(-0.141033\pi\)
−0.822996 + 0.568046i \(0.807699\pi\)
\(138\) 0 0
\(139\) −9.05842 + 15.6896i −0.768325 + 1.33078i 0.170145 + 0.985419i \(0.445576\pi\)
−0.938470 + 0.345359i \(0.887757\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 3.00000 + 5.19615i 0.251754 + 0.436051i
\(143\) 6.51087 0.544467
\(144\) 0 0
\(145\) 0 0
\(146\) 7.05842 + 12.2255i 0.584159 + 1.01179i
\(147\) 0 0
\(148\) −2.00000 + 3.46410i −0.164399 + 0.284747i
\(149\) 9.55842 16.5557i 0.783056 1.35629i −0.147097 0.989122i \(-0.546993\pi\)
0.930153 0.367171i \(-0.119674\pi\)
\(150\) 0 0
\(151\) 5.00000 + 8.66025i 0.406894 + 0.704761i 0.994540 0.104357i \(-0.0332784\pi\)
−0.587646 + 0.809118i \(0.699945\pi\)
\(152\) −3.37228 −0.273528
\(153\) 0 0
\(154\) 3.25544 0.262331
\(155\) 0 0
\(156\) 0 0
\(157\) 2.37228 4.10891i 0.189329 0.327927i −0.755698 0.654920i \(-0.772702\pi\)
0.945027 + 0.326993i \(0.106036\pi\)
\(158\) 1.00000 1.73205i 0.0795557 0.137795i
\(159\) 0 0
\(160\) 0 0
\(161\) −10.3723 −0.817450
\(162\) 0 0
\(163\) −1.48913 −0.116637 −0.0583186 0.998298i \(-0.518574\pi\)
−0.0583186 + 0.998298i \(0.518574\pi\)
\(164\) −1.50000 2.59808i −0.117130 0.202876i
\(165\) 0 0
\(166\) 0.813859 1.40965i 0.0631677 0.109410i
\(167\) −3.81386 + 6.60580i −0.295125 + 0.511172i −0.975014 0.222143i \(-0.928695\pi\)
0.679889 + 0.733315i \(0.262028\pi\)
\(168\) 0 0
\(169\) −4.75544 8.23666i −0.365803 0.633589i
\(170\) 0 0
\(171\) 0 0
\(172\) 11.3723 0.867128
\(173\) −4.62772 8.01544i −0.351839 0.609403i 0.634733 0.772732i \(-0.281110\pi\)
−0.986572 + 0.163329i \(0.947777\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.686141 1.18843i 0.0517198 0.0895813i
\(177\) 0 0
\(178\) 0.558422 + 0.967215i 0.0418555 + 0.0724958i
\(179\) 3.25544 0.243323 0.121661 0.992572i \(-0.461178\pi\)
0.121661 + 0.992572i \(0.461178\pi\)
\(180\) 0 0
\(181\) −7.86141 −0.584334 −0.292167 0.956367i \(-0.594376\pi\)
−0.292167 + 0.956367i \(0.594376\pi\)
\(182\) −5.62772 9.74749i −0.417154 0.722532i
\(183\) 0 0
\(184\) −2.18614 + 3.78651i −0.161164 + 0.279145i
\(185\) 0 0
\(186\) 0 0
\(187\) −5.05842 8.76144i −0.369908 0.640700i
\(188\) −1.62772 −0.118714
\(189\) 0 0
\(190\) 0 0
\(191\) −2.74456 4.75372i −0.198590 0.343967i 0.749482 0.662025i \(-0.230303\pi\)
−0.948071 + 0.318058i \(0.896969\pi\)
\(192\) 0 0
\(193\) 1.94158 3.36291i 0.139758 0.242068i −0.787647 0.616127i \(-0.788701\pi\)
0.927405 + 0.374059i \(0.122034\pi\)
\(194\) 1.31386 2.27567i 0.0943296 0.163384i
\(195\) 0 0
\(196\) 0.686141 + 1.18843i 0.0490100 + 0.0848879i
\(197\) 17.4891 1.24605 0.623024 0.782202i \(-0.285904\pi\)
0.623024 + 0.782202i \(0.285904\pi\)
\(198\) 0 0
\(199\) −9.48913 −0.672666 −0.336333 0.941743i \(-0.609187\pi\)
−0.336333 + 0.941743i \(0.609187\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 4.37228 7.57301i 0.307633 0.532835i
\(203\) −5.18614 + 8.98266i −0.363996 + 0.630459i
\(204\) 0 0
\(205\) 0 0
\(206\) −16.0000 −1.11477
\(207\) 0 0
\(208\) −4.74456 −0.328976
\(209\) 2.31386 + 4.00772i 0.160053 + 0.277220i
\(210\) 0 0
\(211\) 3.62772 6.28339i 0.249742 0.432567i −0.713712 0.700439i \(-0.752987\pi\)
0.963454 + 0.267873i \(0.0863207\pi\)
\(212\) −5.74456 + 9.94987i −0.394538 + 0.683360i
\(213\) 0 0
\(214\) −7.24456 12.5480i −0.495228 0.857760i
\(215\) 0 0
\(216\) 0 0
\(217\) −16.0000 −1.08615
\(218\) 4.81386 + 8.33785i 0.326036 + 0.564710i
\(219\) 0 0
\(220\) 0 0
\(221\) −17.4891 + 30.2921i −1.17645 + 2.03766i
\(222\) 0 0
\(223\) 6.18614 + 10.7147i 0.414255 + 0.717510i 0.995350 0.0963255i \(-0.0307090\pi\)
−0.581095 + 0.813836i \(0.697376\pi\)
\(224\) −2.37228 −0.158505
\(225\) 0 0
\(226\) −14.7446 −0.980794
\(227\) −0.941578 1.63086i −0.0624947 0.108244i 0.833085 0.553145i \(-0.186572\pi\)
−0.895580 + 0.444901i \(0.853239\pi\)
\(228\) 0 0
\(229\) −9.18614 + 15.9109i −0.607037 + 1.05142i 0.384689 + 0.923046i \(0.374309\pi\)
−0.991726 + 0.128373i \(0.959025\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2.18614 + 3.78651i 0.143527 + 0.248596i
\(233\) −10.1168 −0.662776 −0.331388 0.943494i \(-0.607517\pi\)
−0.331388 + 0.943494i \(0.607517\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.686141 1.18843i −0.0446640 0.0773602i
\(237\) 0 0
\(238\) −8.74456 + 15.1460i −0.566826 + 0.981771i
\(239\) −7.37228 + 12.7692i −0.476873 + 0.825969i −0.999649 0.0265017i \(-0.991563\pi\)
0.522776 + 0.852470i \(0.324897\pi\)
\(240\) 0 0
\(241\) −5.24456 9.08385i −0.337832 0.585142i 0.646193 0.763174i \(-0.276360\pi\)
−0.984025 + 0.178032i \(0.943027\pi\)
\(242\) 9.11684 0.586053
\(243\) 0 0
\(244\) 9.11684 0.583646
\(245\) 0 0
\(246\) 0 0
\(247\) 8.00000 13.8564i 0.509028 0.881662i
\(248\) −3.37228 + 5.84096i −0.214140 + 0.370901i
\(249\) 0 0
\(250\) 0 0
\(251\) −15.6060 −0.985040 −0.492520 0.870301i \(-0.663924\pi\)
−0.492520 + 0.870301i \(0.663924\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) −4.55842 7.89542i −0.286021 0.495403i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0.686141 1.18843i 0.0428003 0.0741323i −0.843832 0.536608i \(-0.819705\pi\)
0.886632 + 0.462476i \(0.153039\pi\)
\(258\) 0 0
\(259\) −4.74456 8.21782i −0.294813 0.510631i
\(260\) 0 0
\(261\) 0 0
\(262\) 8.74456 0.540241
\(263\) −2.74456 4.75372i −0.169237 0.293127i 0.768915 0.639351i \(-0.220797\pi\)
−0.938152 + 0.346224i \(0.887464\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.00000 6.92820i 0.245256 0.424795i
\(267\) 0 0
\(268\) −3.50000 6.06218i −0.213797 0.370306i
\(269\) −4.37228 −0.266583 −0.133291 0.991077i \(-0.542555\pi\)
−0.133291 + 0.991077i \(0.542555\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 3.68614 + 6.38458i 0.223505 + 0.387122i
\(273\) 0 0
\(274\) −0.941578 + 1.63086i −0.0568828 + 0.0985239i
\(275\) 0 0
\(276\) 0 0
\(277\) 2.62772 + 4.55134i 0.157884 + 0.273464i 0.934106 0.356997i \(-0.116199\pi\)
−0.776221 + 0.630461i \(0.782866\pi\)
\(278\) −18.1168 −1.08658
\(279\) 0 0
\(280\) 0 0
\(281\) 2.18614 + 3.78651i 0.130414 + 0.225884i 0.923836 0.382788i \(-0.125036\pi\)
−0.793422 + 0.608672i \(0.791703\pi\)
\(282\) 0 0
\(283\) −15.9307 + 27.5928i −0.946982 + 1.64022i −0.195249 + 0.980754i \(0.562551\pi\)
−0.751733 + 0.659467i \(0.770782\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) 0 0
\(286\) 3.25544 + 5.63858i 0.192498 + 0.333416i
\(287\) 7.11684 0.420094
\(288\) 0 0
\(289\) 37.3505 2.19709
\(290\) 0 0
\(291\) 0 0
\(292\) −7.05842 + 12.2255i −0.413063 + 0.715446i
\(293\) 4.11684 7.13058i 0.240509 0.416573i −0.720351 0.693610i \(-0.756019\pi\)
0.960859 + 0.277037i \(0.0893524\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) 0 0
\(298\) 19.1168 1.10741
\(299\) −10.3723 17.9653i −0.599845 1.03896i
\(300\) 0 0
\(301\) −13.4891 + 23.3639i −0.777500 + 1.34667i
\(302\) −5.00000 + 8.66025i −0.287718 + 0.498342i
\(303\) 0 0
\(304\) −1.68614 2.92048i −0.0967068 0.167501i
\(305\) 0 0
\(306\) 0 0
\(307\) 33.2337 1.89675 0.948373 0.317156i \(-0.102728\pi\)
0.948373 + 0.317156i \(0.102728\pi\)
\(308\) 1.62772 + 2.81929i 0.0927479 + 0.160644i
\(309\) 0 0
\(310\) 0 0
\(311\) −4.62772 + 8.01544i −0.262414 + 0.454514i −0.966883 0.255221i \(-0.917852\pi\)
0.704469 + 0.709735i \(0.251185\pi\)
\(312\) 0 0
\(313\) 4.68614 + 8.11663i 0.264876 + 0.458779i 0.967531 0.252752i \(-0.0813355\pi\)
−0.702655 + 0.711531i \(0.748002\pi\)
\(314\) 4.74456 0.267751
\(315\) 0 0
\(316\) 2.00000 0.112509
\(317\) 4.37228 + 7.57301i 0.245572 + 0.425343i 0.962292 0.272018i \(-0.0876910\pi\)
−0.716720 + 0.697361i \(0.754358\pi\)
\(318\) 0 0
\(319\) 3.00000 5.19615i 0.167968 0.290929i
\(320\) 0 0
\(321\) 0 0
\(322\) −5.18614 8.98266i −0.289012 0.500584i
\(323\) −24.8614 −1.38333
\(324\) 0 0
\(325\) 0 0
\(326\) −0.744563 1.28962i −0.0412375 0.0714255i
\(327\) 0 0
\(328\) 1.50000 2.59808i 0.0828236 0.143455i
\(329\) 1.93070 3.34408i 0.106443 0.184365i
\(330\) 0 0
\(331\) 9.11684 + 15.7908i 0.501107 + 0.867943i 0.999999 + 0.00127880i \(0.000407055\pi\)
−0.498892 + 0.866664i \(0.666260\pi\)
\(332\) 1.62772 0.0893327
\(333\) 0 0
\(334\) −7.62772 −0.417370
\(335\) 0 0
\(336\) 0 0
\(337\) 1.68614 2.92048i 0.0918499 0.159089i −0.816440 0.577431i \(-0.804055\pi\)
0.908290 + 0.418342i \(0.137389\pi\)
\(338\) 4.75544 8.23666i 0.258662 0.448015i
\(339\) 0 0
\(340\) 0 0
\(341\) 9.25544 0.501210
\(342\) 0 0
\(343\) −19.8614 −1.07242
\(344\) 5.68614 + 9.84868i 0.306576 + 0.531005i
\(345\) 0 0
\(346\) 4.62772 8.01544i 0.248788 0.430913i
\(347\) 11.0584 19.1537i 0.593647 1.02823i −0.400089 0.916476i \(-0.631021\pi\)
0.993736 0.111751i \(-0.0356459\pi\)
\(348\) 0 0
\(349\) −0.441578 0.764836i −0.0236371 0.0409407i 0.853965 0.520331i \(-0.174191\pi\)
−0.877602 + 0.479390i \(0.840858\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.37228 0.0731428
\(353\) −15.1753 26.2843i −0.807698 1.39897i −0.914455 0.404689i \(-0.867380\pi\)
0.106757 0.994285i \(-0.465953\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.558422 + 0.967215i −0.0295963 + 0.0512623i
\(357\) 0 0
\(358\) 1.62772 + 2.81929i 0.0860276 + 0.149004i
\(359\) −5.48913 −0.289705 −0.144852 0.989453i \(-0.546271\pi\)
−0.144852 + 0.989453i \(0.546271\pi\)
\(360\) 0 0
\(361\) −7.62772 −0.401459
\(362\) −3.93070 6.80818i −0.206593 0.357830i
\(363\) 0 0
\(364\) 5.62772 9.74749i 0.294973 0.510908i
\(365\) 0 0
\(366\) 0 0
\(367\) −8.00000 13.8564i −0.417597 0.723299i 0.578101 0.815966i \(-0.303794\pi\)
−0.995697 + 0.0926670i \(0.970461\pi\)
\(368\) −4.37228 −0.227921
\(369\) 0 0
\(370\) 0 0
\(371\) −13.6277 23.6039i −0.707516 1.22545i
\(372\) 0 0
\(373\) 3.74456 6.48577i 0.193886 0.335821i −0.752649 0.658422i \(-0.771224\pi\)
0.946535 + 0.322602i \(0.104557\pi\)
\(374\) 5.05842 8.76144i 0.261565 0.453043i
\(375\) 0 0
\(376\) −0.813859 1.40965i −0.0419716 0.0726969i
\(377\) −20.7446 −1.06840
\(378\) 0 0
\(379\) −10.8614 −0.557913 −0.278956 0.960304i \(-0.589989\pi\)
−0.278956 + 0.960304i \(0.589989\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 2.74456 4.75372i 0.140424 0.243222i
\(383\) −11.4891 + 19.8997i −0.587067 + 1.01683i 0.407547 + 0.913184i \(0.366384\pi\)
−0.994614 + 0.103646i \(0.966949\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 3.88316 0.197647
\(387\) 0 0
\(388\) 2.62772 0.133402
\(389\) −5.18614 8.98266i −0.262948 0.455439i 0.704076 0.710124i \(-0.251361\pi\)
−0.967024 + 0.254686i \(0.918028\pi\)
\(390\) 0 0
\(391\) −16.1168 + 27.9152i −0.815064 + 1.41173i
\(392\) −0.686141 + 1.18843i −0.0346553 + 0.0600248i
\(393\) 0 0
\(394\) 8.74456 + 15.1460i 0.440545 + 0.763046i
\(395\) 0 0
\(396\) 0 0
\(397\) −11.2554 −0.564894 −0.282447 0.959283i \(-0.591146\pi\)
−0.282447 + 0.959283i \(0.591146\pi\)
\(398\) −4.74456 8.21782i −0.237823 0.411922i
\(399\) 0 0
\(400\) 0 0
\(401\) 8.05842 13.9576i 0.402418 0.697009i −0.591599 0.806232i \(-0.701503\pi\)
0.994017 + 0.109223i \(0.0348364\pi\)
\(402\) 0 0
\(403\) −16.0000 27.7128i −0.797017 1.38047i
\(404\) 8.74456 0.435058
\(405\) 0 0
\(406\) −10.3723 −0.514768
\(407\) 2.74456 + 4.75372i 0.136043 + 0.235633i
\(408\) 0 0
\(409\) 5.43070 9.40625i 0.268531 0.465109i −0.699952 0.714190i \(-0.746795\pi\)
0.968483 + 0.249081i \(0.0801285\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −8.00000 13.8564i −0.394132 0.682656i
\(413\) 3.25544 0.160190
\(414\) 0 0
\(415\) 0 0
\(416\) −2.37228 4.10891i −0.116311 0.201456i
\(417\) 0 0
\(418\) −2.31386 + 4.00772i −0.113175 + 0.196024i
\(419\) −15.8614 + 27.4728i −0.774880 + 1.34213i 0.159981 + 0.987120i \(0.448857\pi\)
−0.934862 + 0.355012i \(0.884477\pi\)
\(420\) 0 0
\(421\) 19.2337 + 33.3137i 0.937393 + 1.62361i 0.770311 + 0.637669i \(0.220101\pi\)
0.167082 + 0.985943i \(0.446566\pi\)
\(422\) 7.25544 0.353189
\(423\) 0 0
\(424\) −11.4891 −0.557961
\(425\) 0 0
\(426\) 0 0
\(427\) −10.8139 + 18.7302i −0.523319 + 0.906416i
\(428\) 7.24456 12.5480i 0.350179 0.606528i
\(429\) 0 0
\(430\) 0 0
\(431\) 26.2337 1.26363 0.631816 0.775118i \(-0.282310\pi\)
0.631816 + 0.775118i \(0.282310\pi\)
\(432\) 0 0
\(433\) −0.627719 −0.0301662 −0.0150831 0.999886i \(-0.504801\pi\)
−0.0150831 + 0.999886i \(0.504801\pi\)
\(434\) −8.00000 13.8564i −0.384012 0.665129i
\(435\) 0 0
\(436\) −4.81386 + 8.33785i −0.230542 + 0.399311i
\(437\) 7.37228 12.7692i 0.352664 0.610832i
\(438\) 0 0
\(439\) −8.11684 14.0588i −0.387396 0.670989i 0.604703 0.796451i \(-0.293292\pi\)
−0.992098 + 0.125462i \(0.959959\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −34.9783 −1.66375
\(443\) 13.2446 + 22.9403i 0.629268 + 1.08992i 0.987699 + 0.156368i \(0.0499786\pi\)
−0.358431 + 0.933556i \(0.616688\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −6.18614 + 10.7147i −0.292922 + 0.507356i
\(447\) 0 0
\(448\) −1.18614 2.05446i −0.0560399 0.0970639i
\(449\) 18.8614 0.890125 0.445062 0.895500i \(-0.353181\pi\)
0.445062 + 0.895500i \(0.353181\pi\)
\(450\) 0 0
\(451\) −4.11684 −0.193855
\(452\) −7.37228 12.7692i −0.346763 0.600611i
\(453\) 0 0
\(454\) 0.941578 1.63086i 0.0441904 0.0765401i
\(455\) 0 0
\(456\) 0 0
\(457\) 15.0584 + 26.0820i 0.704403 + 1.22006i 0.966906 + 0.255131i \(0.0821186\pi\)
−0.262503 + 0.964931i \(0.584548\pi\)
\(458\) −18.3723 −0.858480
\(459\) 0 0
\(460\) 0 0
\(461\) 9.55842 + 16.5557i 0.445180 + 0.771075i 0.998065 0.0621833i \(-0.0198063\pi\)
−0.552885 + 0.833258i \(0.686473\pi\)
\(462\) 0 0
\(463\) 10.0000 17.3205i 0.464739 0.804952i −0.534450 0.845200i \(-0.679481\pi\)
0.999190 + 0.0402476i \(0.0128147\pi\)
\(464\) −2.18614 + 3.78651i −0.101489 + 0.175784i
\(465\) 0 0
\(466\) −5.05842 8.76144i −0.234327 0.405866i
\(467\) 25.8832 1.19773 0.598865 0.800850i \(-0.295619\pi\)
0.598865 + 0.800850i \(0.295619\pi\)
\(468\) 0 0
\(469\) 16.6060 0.766792
\(470\) 0 0
\(471\) 0 0
\(472\) 0.686141 1.18843i 0.0315822 0.0547019i
\(473\) 7.80298 13.5152i 0.358782 0.621428i
\(474\) 0 0
\(475\) 0 0
\(476\) −17.4891 −0.801613
\(477\) 0 0
\(478\) −14.7446 −0.674401
\(479\) −11.7446 20.3422i −0.536623 0.929458i −0.999083 0.0428178i \(-0.986366\pi\)
0.462460 0.886640i \(-0.346967\pi\)
\(480\) 0 0
\(481\) 9.48913 16.4356i 0.432667 0.749401i
\(482\) 5.24456 9.08385i 0.238883 0.413758i
\(483\) 0 0
\(484\) 4.55842 + 7.89542i 0.207201 + 0.358883i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.25544 0.0568893 0.0284446 0.999595i \(-0.490945\pi\)
0.0284446 + 0.999595i \(0.490945\pi\)
\(488\) 4.55842 + 7.89542i 0.206350 + 0.357409i
\(489\) 0 0
\(490\) 0 0
\(491\) 1.80298 3.12286i 0.0813676 0.140933i −0.822470 0.568808i \(-0.807405\pi\)
0.903838 + 0.427876i \(0.140738\pi\)
\(492\) 0 0
\(493\) 16.1168 + 27.9152i 0.725866 + 1.25724i
\(494\) 16.0000 0.719874
\(495\) 0 0
\(496\) −6.74456 −0.302840
\(497\) −7.11684 12.3267i −0.319234 0.552930i
\(498\) 0 0
\(499\) 1.05842 1.83324i 0.0473815 0.0820671i −0.841362 0.540472i \(-0.818246\pi\)
0.888743 + 0.458405i \(0.151579\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −7.80298 13.5152i −0.348264 0.603211i
\(503\) 21.8614 0.974752 0.487376 0.873192i \(-0.337954\pi\)
0.487376 + 0.873192i \(0.337954\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 3.00000 + 5.19615i 0.133366 + 0.230997i
\(507\) 0 0
\(508\) 4.55842 7.89542i 0.202247 0.350303i
\(509\) 4.67527 8.09780i 0.207228 0.358929i −0.743613 0.668611i \(-0.766889\pi\)
0.950840 + 0.309682i \(0.100223\pi\)
\(510\) 0 0
\(511\) −16.7446 29.0024i −0.740736 1.28299i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 1.37228 0.0605287
\(515\) 0 0
\(516\) 0 0
\(517\) −1.11684 + 1.93443i −0.0491187 + 0.0850762i
\(518\) 4.74456 8.21782i 0.208464 0.361070i
\(519\) 0 0
\(520\) 0 0
\(521\) 41.2337 1.80648 0.903240 0.429135i \(-0.141182\pi\)
0.903240 + 0.429135i \(0.141182\pi\)
\(522\) 0 0
\(523\) 11.1168 0.486106 0.243053 0.970013i \(-0.421851\pi\)
0.243053 + 0.970013i \(0.421851\pi\)
\(524\) 4.37228 + 7.57301i 0.191004 + 0.330829i
\(525\) 0 0
\(526\) 2.74456 4.75372i 0.119669 0.207272i
\(527\) −24.8614 + 43.0612i −1.08298 + 1.87578i
\(528\) 0 0
\(529\) 1.94158 + 3.36291i 0.0844164 + 0.146214i
\(530\) 0 0
\(531\) 0 0
\(532\) 8.00000 0.346844
\(533\) 7.11684 + 12.3267i 0.308265 + 0.533930i
\(534\) 0 0
\(535\) 0 0
\(536\) 3.50000 6.06218i 0.151177 0.261846i
\(537\) 0 0
\(538\) −2.18614 3.78651i −0.0942512 0.163248i
\(539\) 1.88316 0.0811133
\(540\) 0 0
\(541\) 21.6277 0.929848 0.464924 0.885351i \(-0.346082\pi\)
0.464924 + 0.885351i \(0.346082\pi\)
\(542\) 4.00000 + 6.92820i 0.171815 + 0.297592i
\(543\) 0 0
\(544\) −3.68614 + 6.38458i −0.158042 + 0.273737i
\(545\) 0 0
\(546\) 0 0
\(547\) 19.7337 + 34.1798i 0.843752 + 1.46142i 0.886701 + 0.462343i \(0.152991\pi\)
−0.0429494 + 0.999077i \(0.513675\pi\)
\(548\) −1.88316 −0.0804444
\(549\) 0 0
\(550\) 0 0
\(551\) −7.37228 12.7692i −0.314070 0.543985i
\(552\) 0 0
\(553\) −2.37228 + 4.10891i −0.100880 + 0.174729i
\(554\) −2.62772 + 4.55134i −0.111641 + 0.193368i
\(555\) 0 0
\(556\) −9.05842 15.6896i −0.384163 0.665389i
\(557\) −9.76631 −0.413812 −0.206906 0.978361i \(-0.566339\pi\)
−0.206906 + 0.978361i \(0.566339\pi\)
\(558\) 0 0
\(559\) −53.9565 −2.28212
\(560\) 0 0
\(561\) 0 0
\(562\) −2.18614 + 3.78651i −0.0922168 + 0.159724i
\(563\) −8.36141 + 14.4824i −0.352391 + 0.610360i −0.986668 0.162747i \(-0.947965\pi\)
0.634277 + 0.773106i \(0.281298\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −31.8614 −1.33923
\(567\) 0 0
\(568\) −6.00000 −0.251754
\(569\) 4.80298 + 8.31901i 0.201352 + 0.348751i 0.948964 0.315384i \(-0.102133\pi\)
−0.747613 + 0.664135i \(0.768800\pi\)
\(570\) 0 0
\(571\) 15.8030 27.3716i 0.661334 1.14546i −0.318931 0.947778i \(-0.603324\pi\)
0.980265 0.197687i \(-0.0633429\pi\)
\(572\) −3.25544 + 5.63858i −0.136117 + 0.235761i
\(573\) 0 0
\(574\) 3.55842 + 6.16337i 0.148526 + 0.257254i
\(575\) 0 0
\(576\) 0 0
\(577\) 23.8832 0.994269 0.497134 0.867674i \(-0.334386\pi\)
0.497134 + 0.867674i \(0.334386\pi\)
\(578\) 18.6753 + 32.3465i 0.776789 + 1.34544i
\(579\) 0 0
\(580\) 0 0
\(581\) −1.93070 + 3.34408i −0.0800991 + 0.138736i
\(582\) 0 0
\(583\) 7.88316 + 13.6540i 0.326487 + 0.565492i
\(584\) −14.1168 −0.584159
\(585\) 0 0
\(586\) 8.23369 0.340131
\(587\) −13.5000 23.3827i −0.557205 0.965107i −0.997728 0.0673658i \(-0.978541\pi\)
0.440524 0.897741i \(-0.354793\pi\)
\(588\) 0 0
\(589\) 11.3723 19.6974i 0.468587 0.811616i
\(590\) 0 0
\(591\) 0 0
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) 37.7228 1.54909 0.774545 0.632519i \(-0.217979\pi\)
0.774545 + 0.632519i \(0.217979\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.55842 + 16.5557i 0.391528 + 0.678147i
\(597\) 0 0
\(598\) 10.3723 17.9653i 0.424154 0.734656i
\(599\) −19.1168 + 33.1113i −0.781093 + 1.35289i 0.150212 + 0.988654i \(0.452004\pi\)
−0.931305 + 0.364239i \(0.881329\pi\)
\(600\) 0 0
\(601\) −13.4307 23.2627i −0.547850 0.948904i −0.998422 0.0561635i \(-0.982113\pi\)
0.450572 0.892740i \(-0.351220\pi\)
\(602\) −26.9783 −1.09955
\(603\) 0 0
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) 0 0
\(607\) 0.441578 0.764836i 0.0179231 0.0310437i −0.856925 0.515442i \(-0.827628\pi\)
0.874848 + 0.484398i \(0.160961\pi\)
\(608\) 1.68614 2.92048i 0.0683820 0.118441i
\(609\) 0 0
\(610\) 0 0
\(611\) 7.72281 0.312432
\(612\) 0 0
\(613\) 0.233688 0.00943857 0.00471928 0.999989i \(-0.498498\pi\)
0.00471928 + 0.999989i \(0.498498\pi\)
\(614\) 16.6168 + 28.7812i 0.670601 + 1.16152i
\(615\) 0 0
\(616\) −1.62772 + 2.81929i −0.0655827 + 0.113592i
\(617\) 11.0584 19.1537i 0.445195 0.771101i −0.552870 0.833267i \(-0.686468\pi\)
0.998066 + 0.0621663i \(0.0198009\pi\)
\(618\) 0 0
\(619\) 19.0584 + 33.0102i 0.766023 + 1.32679i 0.939704 + 0.341988i \(0.111100\pi\)
−0.173682 + 0.984802i \(0.555566\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −9.25544 −0.371109
\(623\) −1.32473 2.29451i −0.0530743 0.0919275i
\(624\) 0 0
\(625\) 0 0
\(626\) −4.68614 + 8.11663i −0.187296 + 0.324406i
\(627\) 0 0
\(628\) 2.37228 + 4.10891i 0.0946643 + 0.163963i
\(629\) −29.4891 −1.17581
\(630\) 0 0
\(631\) 33.7228 1.34248 0.671242 0.741238i \(-0.265761\pi\)
0.671242 + 0.741238i \(0.265761\pi\)
\(632\) 1.00000 + 1.73205i 0.0397779 + 0.0688973i
\(633\) 0 0
\(634\) −4.37228 + 7.57301i −0.173645 + 0.300763i
\(635\) 0 0
\(636\) 0 0
\(637\) −3.25544 5.63858i −0.128985 0.223409i
\(638\) 6.00000 0.237542
\(639\) 0 0
\(640\) 0 0
\(641\) −19.5000 33.7750i −0.770204 1.33403i −0.937451 0.348117i \(-0.886821\pi\)
0.167247 0.985915i \(-0.446512\pi\)
\(642\) 0 0
\(643\) 5.50000 9.52628i 0.216899 0.375680i −0.736959 0.675937i \(-0.763739\pi\)
0.953858 + 0.300257i \(0.0970725\pi\)
\(644\) 5.18614 8.98266i 0.204363 0.353966i
\(645\) 0 0
\(646\) −12.4307 21.5306i −0.489079 0.847111i
\(647\) 24.0951 0.947276 0.473638 0.880720i \(-0.342941\pi\)
0.473638 + 0.880720i \(0.342941\pi\)
\(648\) 0 0
\(649\) −1.88316 −0.0739203
\(650\) 0 0
\(651\) 0 0
\(652\) 0.744563 1.28962i 0.0291593 0.0505054i
\(653\) 18.8614 32.6689i 0.738104 1.27843i −0.215244 0.976560i \(-0.569055\pi\)
0.953348 0.301873i \(-0.0976119\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.00000 0.117130
\(657\) 0 0
\(658\) 3.86141 0.150533
\(659\) −2.74456 4.75372i −0.106913 0.185179i 0.807605 0.589724i \(-0.200763\pi\)
−0.914518 + 0.404545i \(0.867430\pi\)
\(660\) 0 0
\(661\) −11.1168 + 19.2549i −0.432395 + 0.748930i −0.997079 0.0763770i \(-0.975665\pi\)
0.564684 + 0.825307i \(0.308998\pi\)
\(662\) −9.11684 + 15.7908i −0.354336 + 0.613728i
\(663\) 0 0
\(664\) 0.813859 + 1.40965i 0.0315839 + 0.0547049i
\(665\) 0 0
\(666\) 0 0
\(667\) −19.1168 −0.740207
\(668\) −3.81386 6.60580i −0.147563 0.255586i
\(669\) 0 0
\(670\) 0 0
\(671\) 6.25544 10.8347i 0.241488 0.418270i
\(672\) 0 0
\(673\) −5.00000 8.66025i −0.192736 0.333828i 0.753420 0.657539i \(-0.228403\pi\)
−0.946156 + 0.323711i \(0.895069\pi\)
\(674\) 3.37228 0.129895
\(675\) 0 0
\(676\) 9.51087 0.365803
\(677\) 21.8614 + 37.8651i 0.840202 + 1.45527i 0.889724 + 0.456500i \(0.150897\pi\)
−0.0495215 + 0.998773i \(0.515770\pi\)
\(678\) 0 0
\(679\) −3.11684 + 5.39853i −0.119613 + 0.207177i
\(680\) 0 0
\(681\) 0 0
\(682\) 4.62772 + 8.01544i 0.177205 + 0.306927i
\(683\) 33.0951 1.26635 0.633174 0.774009i \(-0.281752\pi\)
0.633174 + 0.774009i \(0.281752\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −9.93070 17.2005i −0.379156 0.656717i
\(687\) 0 0
\(688\) −5.68614 + 9.84868i −0.216782 + 0.375478i
\(689\) 27.2554 47.2078i 1.03835 1.79847i
\(690\) 0 0
\(691\) 0.883156 + 1.52967i 0.0335968 + 0.0581914i 0.882335 0.470622i \(-0.155970\pi\)
−0.848738 + 0.528813i \(0.822637\pi\)
\(692\) 9.25544 0.351839
\(693\) 0 0
\(694\) 22.1168 0.839544
\(695\) 0 0
\(696\) 0 0
\(697\) 11.0584 19.1537i 0.418868 0.725500i
\(698\) 0.441578 0.764836i 0.0167140 0.0289495i
\(699\) 0 0
\(700\) 0 0
\(701\) −14.1386 −0.534007 −0.267004 0.963696i \(-0.586034\pi\)
−0.267004 + 0.963696i \(0.586034\pi\)
\(702\) 0 0
\(703\) 13.4891 0.508752
\(704\) 0.686141 + 1.18843i 0.0258599 + 0.0447907i
\(705\) 0 0
\(706\) 15.1753 26.2843i 0.571129 0.989224i
\(707\) −10.3723 + 17.9653i −0.390090 + 0.675655i
\(708\) 0 0
\(709\) 12.9307 + 22.3966i 0.485623 + 0.841123i 0.999863 0.0165226i \(-0.00525955\pi\)
−0.514241 + 0.857646i \(0.671926\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.11684 −0.0418555
\(713\) −14.7446 25.5383i −0.552188 0.956418i
\(714\) 0 0
\(715\) 0 0
\(716\) −1.62772 + 2.81929i −0.0608307 + 0.105362i
\(717\) 0 0
\(718\) −2.74456 4.75372i −0.102426 0.177407i
\(719\) 38.2337 1.42588 0.712938 0.701227i \(-0.247364\pi\)
0.712938 + 0.701227i \(0.247364\pi\)
\(720\) 0 0
\(721\) 37.9565 1.41357
\(722\) −3.81386 6.60580i −0.141937 0.245842i
\(723\) 0 0
\(724\) 3.93070 6.80818i 0.146083 0.253024i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.441578 + 0.764836i 0.0163772 + 0.0283662i 0.874098 0.485750i \(-0.161453\pi\)
−0.857721 + 0.514116i \(0.828120\pi\)
\(728\) 11.2554 0.417154
\(729\) 0 0
\(730\) 0 0
\(731\) 41.9198 + 72.6073i 1.55046 + 2.68548i
\(732\) 0 0
\(733\) 17.1168 29.6472i 0.632225 1.09505i −0.354871 0.934915i \(-0.615475\pi\)
0.987096 0.160131i \(-0.0511915\pi\)
\(734\) 8.00000 13.8564i 0.295285 0.511449i
\(735\) 0 0
\(736\) −2.18614 3.78651i −0.0805822 0.139572i
\(737\) −9.60597 −0.353840
\(738\) 0 0
\(739\) −23.8832 −0.878556 −0.439278 0.898351i \(-0.644766\pi\)
−0.439278 + 0.898351i \(0.644766\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 13.6277 23.6039i 0.500289 0.866526i
\(743\) −12.5584 + 21.7518i −0.460724 + 0.797997i −0.998997 0.0447732i \(-0.985743\pi\)
0.538273 + 0.842770i \(0.319077\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 7.48913 0.274196
\(747\) 0 0
\(748\) 10.1168 0.369908
\(749\) 17.1861 + 29.7673i 0.627968 + 1.08767i
\(750\) 0 0
\(751\) 9.11684 15.7908i 0.332678 0.576216i −0.650358 0.759628i \(-0.725381\pi\)
0.983036 + 0.183412i \(0.0587143\pi\)
\(752\) 0.813859 1.40965i 0.0296784 0.0514045i
\(753\) 0 0
\(754\) −10.3723 17.9653i −0.377736 0.654258i
\(755\) 0 0
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) −5.43070 9.40625i −0.197252 0.341651i
\(759\) 0 0
\(760\) 0 0
\(761\) 6.04755 10.4747i 0.219223 0.379706i −0.735347 0.677690i \(-0.762981\pi\)
0.954571 + 0.297984i \(0.0963143\pi\)
\(762\) 0 0
\(763\) −11.4198 19.7797i −0.413426 0.716074i
\(764\) 5.48913 0.198590
\(765\) 0 0
\(766\) −22.9783 −0.830238
\(767\) 3.25544 + 5.63858i 0.117547 + 0.203597i
\(768\) 0 0
\(769\) 9.06930 15.7085i 0.327047 0.566462i −0.654877 0.755735i \(-0.727280\pi\)
0.981925 + 0.189273i \(0.0606131\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.94158 + 3.36291i 0.0698789 + 0.121034i
\(773\) 14.7446 0.530325 0.265163 0.964204i \(-0.414574\pi\)
0.265163 + 0.964204i \(0.414574\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.31386 + 2.27567i 0.0471648 + 0.0816918i
\(777\) 0 0
\(778\) 5.18614 8.98266i 0.185932 0.322044i
\(779\) −5.05842 + 8.76144i −0.181237 + 0.313911i
\(780\) 0 0
\(781\) 4.11684 + 7.13058i 0.147312 + 0.255152i
\(782\) −32.2337 −1.15267
\(783\) 0 0
\(784\) −1.37228 −0.0490100
\(785\) 0 0
\(786\) 0 0
\(787\) −14.0000 + 24.2487i −0.499046 + 0.864373i −0.999999 0.00110111i \(-0.999650\pi\)
0.500953 + 0.865474i \(0.332983\pi\)
\(788\) −8.74456 + 15.1460i −0.311512 + 0.539555i
\(789\) 0