Properties

Label 880.2.bo.i.81.1
Level $880$
Weight $2$
Character 880.81
Analytic conductor $7.027$
Analytic rank $0$
Dimension $12$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [880,2,Mod(81,880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(880, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("880.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.bo (of order \(5\), degree \(4\), 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: \(7.02683537787\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 5 x^{10} + 4 x^{9} + 28 x^{8} - 81 x^{7} + 335 x^{6} - 235 x^{5} + 782 x^{4} + \cdots + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 440)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 81.1
Root \(-2.19470 + 1.59454i\) of defining polynomial
Character \(\chi\) \(=\) 880.81
Dual form 880.2.bo.i.641.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.529284 + 1.62897i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-1.14492 - 3.52372i) q^{7} +(0.0536500 + 0.0389790i) q^{9} +O(q^{10})\) \(q+(-0.529284 + 1.62897i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-1.14492 - 3.52372i) q^{7} +(0.0536500 + 0.0389790i) q^{9} +(-2.68927 + 1.94109i) q^{11} +(0.952617 + 0.692117i) q^{13} +(0.529284 + 1.62897i) q^{15} +(4.36891 - 3.17420i) q^{17} +(1.18895 - 3.65921i) q^{19} +6.34602 q^{21} +8.68237 q^{23} +(0.309017 - 0.951057i) q^{25} +(-4.24895 + 3.08704i) q^{27} +(-2.12479 - 6.53944i) q^{29} +(7.08327 + 5.14630i) q^{31} +(-1.73859 - 5.40813i) q^{33} +(-2.99745 - 2.17778i) q^{35} +(0.696735 + 2.14433i) q^{37} +(-1.63164 + 1.18546i) q^{39} +(0.493602 - 1.51915i) q^{41} -4.11979 q^{43} +0.0663151 q^{45} +(3.91833 - 12.0594i) q^{47} +(-5.44260 + 3.95428i) q^{49} +(2.85828 + 8.79688i) q^{51} +(10.0152 + 7.27650i) q^{53} +(-1.03472 + 3.15109i) q^{55} +(5.33145 + 3.87353i) q^{57} +(0.121753 + 0.374716i) q^{59} +(-1.45692 + 1.05851i) q^{61} +(0.0759258 - 0.233676i) q^{63} +1.17750 q^{65} +14.3809 q^{67} +(-4.59544 + 14.1433i) q^{69} +(-5.54603 + 4.02943i) q^{71} +(3.10719 + 9.56296i) q^{73} +(1.38568 + 1.00676i) q^{75} +(9.91887 + 7.25381i) q^{77} +(-0.901110 - 0.654695i) q^{79} +(-2.71832 - 8.36612i) q^{81} +(0.0140132 - 0.0101812i) q^{83} +(1.66878 - 5.13596i) q^{85} +11.7772 q^{87} -8.49434 q^{89} +(1.34815 - 4.14917i) q^{91} +(-12.1322 + 8.81458i) q^{93} +(-1.18895 - 3.65921i) q^{95} +(-8.50719 - 6.18083i) q^{97} +(-0.219941 - 0.000685401i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + q^{3} + 3 q^{5} + q^{7} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + q^{3} + 3 q^{5} + q^{7} - 10 q^{9} - 4 q^{11} + 18 q^{13} - q^{15} + 3 q^{17} - 4 q^{19} - 28 q^{21} + 18 q^{23} - 3 q^{25} - 23 q^{27} + 15 q^{29} + 8 q^{31} + 4 q^{33} - 6 q^{35} + 6 q^{37} + 33 q^{39} + 2 q^{41} + 36 q^{43} - 10 q^{45} + 16 q^{47} - 16 q^{49} + 10 q^{51} + 19 q^{53} - 6 q^{55} + 62 q^{57} - 46 q^{59} + 18 q^{61} + 7 q^{63} + 2 q^{65} + 44 q^{67} - q^{69} + 6 q^{71} + 25 q^{73} - 4 q^{75} + 10 q^{77} - 19 q^{79} + 30 q^{81} - 3 q^{85} - 6 q^{87} - 50 q^{89} + 46 q^{91} - 37 q^{93} + 4 q^{95} - 31 q^{97} - 79 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).

\(n\) \(111\) \(177\) \(321\) \(661\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(1\)

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 0
\(3\) −0.529284 + 1.62897i −0.305582 + 0.940486i 0.673877 + 0.738844i \(0.264628\pi\)
−0.979459 + 0.201642i \(0.935372\pi\)
\(4\) 0 0
\(5\) 0.809017 0.587785i 0.361803 0.262866i
\(6\) 0 0
\(7\) −1.14492 3.52372i −0.432741 1.33184i −0.895384 0.445295i \(-0.853099\pi\)
0.462643 0.886545i \(-0.346901\pi\)
\(8\) 0 0
\(9\) 0.0536500 + 0.0389790i 0.0178833 + 0.0129930i
\(10\) 0 0
\(11\) −2.68927 + 1.94109i −0.810845 + 0.585261i
\(12\) 0 0
\(13\) 0.952617 + 0.692117i 0.264208 + 0.191959i 0.712000 0.702179i \(-0.247789\pi\)
−0.447792 + 0.894138i \(0.647789\pi\)
\(14\) 0 0
\(15\) 0.529284 + 1.62897i 0.136661 + 0.420598i
\(16\) 0 0
\(17\) 4.36891 3.17420i 1.05962 0.769856i 0.0855991 0.996330i \(-0.472720\pi\)
0.974017 + 0.226473i \(0.0727196\pi\)
\(18\) 0 0
\(19\) 1.18895 3.65921i 0.272764 0.839480i −0.717039 0.697033i \(-0.754503\pi\)
0.989802 0.142447i \(-0.0454971\pi\)
\(20\) 0 0
\(21\) 6.34602 1.38481
\(22\) 0 0
\(23\) 8.68237 1.81040 0.905200 0.424986i \(-0.139721\pi\)
0.905200 + 0.424986i \(0.139721\pi\)
\(24\) 0 0
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) 0 0
\(27\) −4.24895 + 3.08704i −0.817710 + 0.594101i
\(28\) 0 0
\(29\) −2.12479 6.53944i −0.394564 1.21434i −0.929301 0.369324i \(-0.879589\pi\)
0.534736 0.845019i \(-0.320411\pi\)
\(30\) 0 0
\(31\) 7.08327 + 5.14630i 1.27219 + 0.924302i 0.999288 0.0377385i \(-0.0120154\pi\)
0.272905 + 0.962041i \(0.412015\pi\)
\(32\) 0 0
\(33\) −1.73859 5.40813i −0.302650 0.941434i
\(34\) 0 0
\(35\) −2.99745 2.17778i −0.506662 0.368111i
\(36\) 0 0
\(37\) 0.696735 + 2.14433i 0.114543 + 0.352526i 0.991851 0.127401i \(-0.0406634\pi\)
−0.877309 + 0.479926i \(0.840663\pi\)
\(38\) 0 0
\(39\) −1.63164 + 1.18546i −0.261272 + 0.189825i
\(40\) 0 0
\(41\) 0.493602 1.51915i 0.0770877 0.237251i −0.905086 0.425229i \(-0.860193\pi\)
0.982173 + 0.187978i \(0.0601934\pi\)
\(42\) 0 0
\(43\) −4.11979 −0.628262 −0.314131 0.949380i \(-0.601713\pi\)
−0.314131 + 0.949380i \(0.601713\pi\)
\(44\) 0 0
\(45\) 0.0663151 0.00988567
\(46\) 0 0
\(47\) 3.91833 12.0594i 0.571547 1.75904i −0.0761009 0.997100i \(-0.524247\pi\)
0.647648 0.761940i \(-0.275753\pi\)
\(48\) 0 0
\(49\) −5.44260 + 3.95428i −0.777514 + 0.564897i
\(50\) 0 0
\(51\) 2.85828 + 8.79688i 0.400239 + 1.23181i
\(52\) 0 0
\(53\) 10.0152 + 7.27650i 1.37570 + 0.999504i 0.997268 + 0.0738747i \(0.0235365\pi\)
0.378432 + 0.925629i \(0.376464\pi\)
\(54\) 0 0
\(55\) −1.03472 + 3.15109i −0.139521 + 0.424893i
\(56\) 0 0
\(57\) 5.33145 + 3.87353i 0.706168 + 0.513061i
\(58\) 0 0
\(59\) 0.121753 + 0.374716i 0.0158508 + 0.0487838i 0.958669 0.284523i \(-0.0918354\pi\)
−0.942818 + 0.333307i \(0.891835\pi\)
\(60\) 0 0
\(61\) −1.45692 + 1.05851i −0.186539 + 0.135529i −0.677136 0.735858i \(-0.736779\pi\)
0.490596 + 0.871387i \(0.336779\pi\)
\(62\) 0 0
\(63\) 0.0759258 0.233676i 0.00956575 0.0294404i
\(64\) 0 0
\(65\) 1.17750 0.146051
\(66\) 0 0
\(67\) 14.3809 1.75691 0.878455 0.477826i \(-0.158575\pi\)
0.878455 + 0.477826i \(0.158575\pi\)
\(68\) 0 0
\(69\) −4.59544 + 14.1433i −0.553227 + 1.70266i
\(70\) 0 0
\(71\) −5.54603 + 4.02943i −0.658192 + 0.478205i −0.866052 0.499954i \(-0.833350\pi\)
0.207860 + 0.978159i \(0.433350\pi\)
\(72\) 0 0
\(73\) 3.10719 + 9.56296i 0.363670 + 1.11926i 0.950810 + 0.309775i \(0.100254\pi\)
−0.587140 + 0.809485i \(0.699746\pi\)
\(74\) 0 0
\(75\) 1.38568 + 1.00676i 0.160005 + 0.116250i
\(76\) 0 0
\(77\) 9.91887 + 7.25381i 1.13036 + 0.826649i
\(78\) 0 0
\(79\) −0.901110 0.654695i −0.101383 0.0736589i 0.535939 0.844257i \(-0.319958\pi\)
−0.637322 + 0.770598i \(0.719958\pi\)
\(80\) 0 0
\(81\) −2.71832 8.36612i −0.302035 0.929569i
\(82\) 0 0
\(83\) 0.0140132 0.0101812i 0.00153814 0.00111753i −0.587016 0.809575i \(-0.699697\pi\)
0.588554 + 0.808458i \(0.299697\pi\)
\(84\) 0 0
\(85\) 1.66878 5.13596i 0.181004 0.557073i
\(86\) 0 0
\(87\) 11.7772 1.26265
\(88\) 0 0
\(89\) −8.49434 −0.900399 −0.450199 0.892928i \(-0.648647\pi\)
−0.450199 + 0.892928i \(0.648647\pi\)
\(90\) 0 0
\(91\) 1.34815 4.14917i 0.141324 0.434951i
\(92\) 0 0
\(93\) −12.1322 + 8.81458i −1.25805 + 0.914029i
\(94\) 0 0
\(95\) −1.18895 3.65921i −0.121984 0.375427i
\(96\) 0 0
\(97\) −8.50719 6.18083i −0.863774 0.627569i 0.0651351 0.997876i \(-0.479252\pi\)
−0.928909 + 0.370308i \(0.879252\pi\)
\(98\) 0 0
\(99\) −0.219941 0.000685401i −0.0221049 6.88853e-5i
\(100\) 0 0
\(101\) −5.80762 4.21949i −0.577880 0.419855i 0.260079 0.965587i \(-0.416251\pi\)
−0.837959 + 0.545733i \(0.816251\pi\)
\(102\) 0 0
\(103\) 1.15886 + 3.56662i 0.114186 + 0.351429i 0.991776 0.127982i \(-0.0408501\pi\)
−0.877590 + 0.479412i \(0.840850\pi\)
\(104\) 0 0
\(105\) 5.13404 3.73010i 0.501031 0.364020i
\(106\) 0 0
\(107\) 1.96265 6.04042i 0.189737 0.583950i −0.810261 0.586069i \(-0.800675\pi\)
0.999998 + 0.00211949i \(0.000674656\pi\)
\(108\) 0 0
\(109\) 1.32407 0.126823 0.0634115 0.997987i \(-0.479802\pi\)
0.0634115 + 0.997987i \(0.479802\pi\)
\(110\) 0 0
\(111\) −3.86182 −0.366548
\(112\) 0 0
\(113\) 1.64758 5.07074i 0.154992 0.477015i −0.843168 0.537649i \(-0.819312\pi\)
0.998160 + 0.0606344i \(0.0193124\pi\)
\(114\) 0 0
\(115\) 7.02419 5.10337i 0.655009 0.475892i
\(116\) 0 0
\(117\) 0.0241299 + 0.0742642i 0.00223081 + 0.00686572i
\(118\) 0 0
\(119\) −16.1870 11.7606i −1.48386 1.07809i
\(120\) 0 0
\(121\) 3.46432 10.4402i 0.314938 0.949112i
\(122\) 0 0
\(123\) 2.21339 + 1.60813i 0.199575 + 0.145000i
\(124\) 0 0
\(125\) −0.309017 0.951057i −0.0276393 0.0850651i
\(126\) 0 0
\(127\) 11.8445 8.60553i 1.05103 0.763617i 0.0786209 0.996905i \(-0.474948\pi\)
0.972408 + 0.233288i \(0.0749484\pi\)
\(128\) 0 0
\(129\) 2.18054 6.71101i 0.191986 0.590871i
\(130\) 0 0
\(131\) −5.93922 −0.518912 −0.259456 0.965755i \(-0.583543\pi\)
−0.259456 + 0.965755i \(0.583543\pi\)
\(132\) 0 0
\(133\) −14.2553 −1.23609
\(134\) 0 0
\(135\) −1.62295 + 4.99493i −0.139682 + 0.429896i
\(136\) 0 0
\(137\) −11.9490 + 8.68146i −1.02087 + 0.741707i −0.966461 0.256812i \(-0.917328\pi\)
−0.0544107 + 0.998519i \(0.517328\pi\)
\(138\) 0 0
\(139\) −0.399410 1.22926i −0.0338775 0.104264i 0.932688 0.360684i \(-0.117457\pi\)
−0.966565 + 0.256420i \(0.917457\pi\)
\(140\) 0 0
\(141\) 17.5704 + 12.7657i 1.47970 + 1.07506i
\(142\) 0 0
\(143\) −3.90530 0.0121701i −0.326578 0.00101771i
\(144\) 0 0
\(145\) −5.56278 4.04160i −0.461964 0.335636i
\(146\) 0 0
\(147\) −3.56072 10.9588i −0.293683 0.903864i
\(148\) 0 0
\(149\) −19.3404 + 14.0516i −1.58443 + 1.15115i −0.673036 + 0.739610i \(0.735010\pi\)
−0.911390 + 0.411543i \(0.864990\pi\)
\(150\) 0 0
\(151\) −2.55881 + 7.87521i −0.208233 + 0.640875i 0.791332 + 0.611387i \(0.209388\pi\)
−0.999565 + 0.0294888i \(0.990612\pi\)
\(152\) 0 0
\(153\) 0.358119 0.0289522
\(154\) 0 0
\(155\) 8.75541 0.703251
\(156\) 0 0
\(157\) −2.46115 + 7.57463i −0.196421 + 0.604521i 0.803536 + 0.595256i \(0.202949\pi\)
−0.999957 + 0.00926547i \(0.997051\pi\)
\(158\) 0 0
\(159\) −17.1541 + 12.4632i −1.36041 + 0.988395i
\(160\) 0 0
\(161\) −9.94066 30.5942i −0.783434 2.41116i
\(162\) 0 0
\(163\) −3.30709 2.40274i −0.259031 0.188197i 0.450689 0.892681i \(-0.351178\pi\)
−0.709720 + 0.704484i \(0.751178\pi\)
\(164\) 0 0
\(165\) −4.58537 3.35335i −0.356970 0.261058i
\(166\) 0 0
\(167\) −3.22174 2.34073i −0.249306 0.181131i 0.456113 0.889922i \(-0.349241\pi\)
−0.705419 + 0.708790i \(0.749241\pi\)
\(168\) 0 0
\(169\) −3.58877 11.0451i −0.276059 0.849622i
\(170\) 0 0
\(171\) 0.206420 0.149973i 0.0157853 0.0114687i
\(172\) 0 0
\(173\) 5.45640 16.7931i 0.414843 1.27675i −0.497549 0.867436i \(-0.665766\pi\)
0.912392 0.409319i \(-0.134234\pi\)
\(174\) 0 0
\(175\) −3.70505 −0.280076
\(176\) 0 0
\(177\) −0.674842 −0.0507243
\(178\) 0 0
\(179\) −3.69018 + 11.3572i −0.275817 + 0.848877i 0.713185 + 0.700976i \(0.247252\pi\)
−0.989002 + 0.147902i \(0.952748\pi\)
\(180\) 0 0
\(181\) 0.834670 0.606423i 0.0620405 0.0450751i −0.556333 0.830960i \(-0.687792\pi\)
0.618373 + 0.785885i \(0.287792\pi\)
\(182\) 0 0
\(183\) −0.953162 2.93353i −0.0704598 0.216853i
\(184\) 0 0
\(185\) 1.82408 + 1.32527i 0.134109 + 0.0974357i
\(186\) 0 0
\(187\) −5.58776 + 17.0167i −0.408617 + 1.24439i
\(188\) 0 0
\(189\) 15.7426 + 11.4376i 1.14510 + 0.831967i
\(190\) 0 0
\(191\) −5.87606 18.0846i −0.425176 1.30856i −0.902825 0.430008i \(-0.858511\pi\)
0.477649 0.878551i \(-0.341489\pi\)
\(192\) 0 0
\(193\) −4.37576 + 3.17918i −0.314974 + 0.228842i −0.734028 0.679119i \(-0.762362\pi\)
0.419054 + 0.907961i \(0.362362\pi\)
\(194\) 0 0
\(195\) −0.623232 + 1.91811i −0.0446306 + 0.137359i
\(196\) 0 0
\(197\) 4.07618 0.290416 0.145208 0.989401i \(-0.453615\pi\)
0.145208 + 0.989401i \(0.453615\pi\)
\(198\) 0 0
\(199\) 12.0711 0.855700 0.427850 0.903850i \(-0.359271\pi\)
0.427850 + 0.903850i \(0.359271\pi\)
\(200\) 0 0
\(201\) −7.61160 + 23.4261i −0.536881 + 1.65235i
\(202\) 0 0
\(203\) −20.6104 + 14.9743i −1.44657 + 1.05099i
\(204\) 0 0
\(205\) −0.493602 1.51915i −0.0344746 0.106102i
\(206\) 0 0
\(207\) 0.465810 + 0.338431i 0.0323760 + 0.0235225i
\(208\) 0 0
\(209\) 3.90546 + 12.1485i 0.270146 + 0.840326i
\(210\) 0 0
\(211\) −7.53429 5.47398i −0.518682 0.376844i 0.297425 0.954745i \(-0.403872\pi\)
−0.816107 + 0.577901i \(0.803872\pi\)
\(212\) 0 0
\(213\) −3.62839 11.1670i −0.248613 0.765152i
\(214\) 0 0
\(215\) −3.33298 + 2.42155i −0.227307 + 0.165148i
\(216\) 0 0
\(217\) 10.0243 30.8516i 0.680492 2.09434i
\(218\) 0 0
\(219\) −17.2224 −1.16378
\(220\) 0 0
\(221\) 6.35881 0.427740
\(222\) 0 0
\(223\) 1.46586 4.51147i 0.0981616 0.302110i −0.889903 0.456150i \(-0.849228\pi\)
0.988065 + 0.154039i \(0.0492282\pi\)
\(224\) 0 0
\(225\) 0.0536500 0.0389790i 0.00357667 0.00259860i
\(226\) 0 0
\(227\) −1.08627 3.34318i −0.0720980 0.221895i 0.908514 0.417855i \(-0.137218\pi\)
−0.980612 + 0.195960i \(0.937218\pi\)
\(228\) 0 0
\(229\) 7.38320 + 5.36421i 0.487895 + 0.354477i 0.804374 0.594123i \(-0.202501\pi\)
−0.316479 + 0.948600i \(0.602501\pi\)
\(230\) 0 0
\(231\) −17.0661 + 12.3182i −1.12287 + 0.810478i
\(232\) 0 0
\(233\) 17.4142 + 12.6522i 1.14084 + 0.828870i 0.987236 0.159262i \(-0.0509114\pi\)
0.153606 + 0.988132i \(0.450911\pi\)
\(234\) 0 0
\(235\) −3.91833 12.0594i −0.255603 0.786667i
\(236\) 0 0
\(237\) 1.54342 1.12136i 0.100256 0.0728403i
\(238\) 0 0
\(239\) −3.49419 + 10.7540i −0.226020 + 0.695619i 0.772166 + 0.635421i \(0.219173\pi\)
−0.998186 + 0.0601983i \(0.980827\pi\)
\(240\) 0 0
\(241\) −26.1144 −1.68218 −0.841089 0.540897i \(-0.818085\pi\)
−0.841089 + 0.540897i \(0.818085\pi\)
\(242\) 0 0
\(243\) −0.689039 −0.0442019
\(244\) 0 0
\(245\) −2.07889 + 6.39816i −0.132815 + 0.408764i
\(246\) 0 0
\(247\) 3.66521 2.66293i 0.233212 0.169438i
\(248\) 0 0
\(249\) 0.00916785 + 0.0282158i 0.000580989 + 0.00178810i
\(250\) 0 0
\(251\) −3.00802 2.18545i −0.189865 0.137945i 0.488792 0.872400i \(-0.337438\pi\)
−0.678657 + 0.734456i \(0.737438\pi\)
\(252\) 0 0
\(253\) −23.3492 + 16.8533i −1.46795 + 1.05956i
\(254\) 0 0
\(255\) 7.48307 + 5.43677i 0.468608 + 0.340464i
\(256\) 0 0
\(257\) −2.19179 6.74564i −0.136720 0.420781i 0.859133 0.511752i \(-0.171003\pi\)
−0.995854 + 0.0909703i \(0.971003\pi\)
\(258\) 0 0
\(259\) 6.75830 4.91019i 0.419940 0.305104i
\(260\) 0 0
\(261\) 0.140906 0.433664i 0.00872185 0.0268431i
\(262\) 0 0
\(263\) −23.3578 −1.44030 −0.720151 0.693817i \(-0.755927\pi\)
−0.720151 + 0.693817i \(0.755927\pi\)
\(264\) 0 0
\(265\) 12.3795 0.760468
\(266\) 0 0
\(267\) 4.49592 13.8370i 0.275146 0.846813i
\(268\) 0 0
\(269\) 13.8194 10.0404i 0.842585 0.612174i −0.0805064 0.996754i \(-0.525654\pi\)
0.923092 + 0.384580i \(0.125654\pi\)
\(270\) 0 0
\(271\) 8.47767 + 26.0916i 0.514982 + 1.58495i 0.783315 + 0.621624i \(0.213527\pi\)
−0.268334 + 0.963326i \(0.586473\pi\)
\(272\) 0 0
\(273\) 6.04532 + 4.39218i 0.365880 + 0.265827i
\(274\) 0 0
\(275\) 1.01506 + 3.15748i 0.0612103 + 0.190403i
\(276\) 0 0
\(277\) 19.5985 + 14.2391i 1.17756 + 0.855546i 0.991894 0.127067i \(-0.0405565\pi\)
0.185664 + 0.982613i \(0.440556\pi\)
\(278\) 0 0
\(279\) 0.179420 + 0.552198i 0.0107416 + 0.0330592i
\(280\) 0 0
\(281\) 13.8855 10.0884i 0.828338 0.601823i −0.0907503 0.995874i \(-0.528927\pi\)
0.919089 + 0.394051i \(0.128927\pi\)
\(282\) 0 0
\(283\) −1.43047 + 4.40252i −0.0850324 + 0.261703i −0.984528 0.175227i \(-0.943934\pi\)
0.899496 + 0.436930i \(0.143934\pi\)
\(284\) 0 0
\(285\) 6.59004 0.390360
\(286\) 0 0
\(287\) −5.91819 −0.349340
\(288\) 0 0
\(289\) 3.75855 11.5676i 0.221091 0.680449i
\(290\) 0 0
\(291\) 14.5711 10.5865i 0.854174 0.620594i
\(292\) 0 0
\(293\) −5.71701 17.5951i −0.333991 1.02792i −0.967217 0.253952i \(-0.918270\pi\)
0.633226 0.773967i \(-0.281730\pi\)
\(294\) 0 0
\(295\) 0.318752 + 0.231587i 0.0185585 + 0.0134835i
\(296\) 0 0
\(297\) 5.43432 16.5495i 0.315331 0.960298i
\(298\) 0 0
\(299\) 8.27098 + 6.00922i 0.478323 + 0.347522i
\(300\) 0 0
\(301\) 4.71685 + 14.5170i 0.271874 + 0.836744i
\(302\) 0 0
\(303\) 9.94730 7.22714i 0.571458 0.415188i
\(304\) 0 0
\(305\) −0.556493 + 1.71271i −0.0318647 + 0.0980695i
\(306\) 0 0
\(307\) 27.2021 1.55250 0.776252 0.630422i \(-0.217118\pi\)
0.776252 + 0.630422i \(0.217118\pi\)
\(308\) 0 0
\(309\) −6.42328 −0.365408
\(310\) 0 0
\(311\) −9.96884 + 30.6809i −0.565281 + 1.73976i 0.101834 + 0.994801i \(0.467529\pi\)
−0.667115 + 0.744955i \(0.732471\pi\)
\(312\) 0 0
\(313\) 0.235220 0.170898i 0.0132954 0.00965970i −0.581118 0.813820i \(-0.697384\pi\)
0.594413 + 0.804160i \(0.297384\pi\)
\(314\) 0 0
\(315\) −0.0759258 0.233676i −0.00427793 0.0131661i
\(316\) 0 0
\(317\) −18.4735 13.4218i −1.03758 0.753844i −0.0677665 0.997701i \(-0.521587\pi\)
−0.969811 + 0.243857i \(0.921587\pi\)
\(318\) 0 0
\(319\) 18.4078 + 13.4619i 1.03064 + 0.753721i
\(320\) 0 0
\(321\) 8.80087 + 6.39420i 0.491216 + 0.356890i
\(322\) 0 0
\(323\) −6.42065 19.7607i −0.357254 1.09952i
\(324\) 0 0
\(325\) 0.952617 0.692117i 0.0528417 0.0383917i
\(326\) 0 0
\(327\) −0.700810 + 2.15687i −0.0387549 + 0.119275i
\(328\) 0 0
\(329\) −46.9800 −2.59009
\(330\) 0 0
\(331\) 14.5262 0.798433 0.399217 0.916857i \(-0.369282\pi\)
0.399217 + 0.916857i \(0.369282\pi\)
\(332\) 0 0
\(333\) −0.0462040 + 0.142201i −0.00253197 + 0.00779259i
\(334\) 0 0
\(335\) 11.6344 8.45289i 0.635656 0.461831i
\(336\) 0 0
\(337\) 4.33684 + 13.3474i 0.236243 + 0.727081i 0.996954 + 0.0779903i \(0.0248503\pi\)
−0.760711 + 0.649090i \(0.775150\pi\)
\(338\) 0 0
\(339\) 7.38804 + 5.36773i 0.401263 + 0.291535i
\(340\) 0 0
\(341\) −29.0383 0.0904916i −1.57251 0.00490040i
\(342\) 0 0
\(343\) −0.817029 0.593607i −0.0441154 0.0320517i
\(344\) 0 0
\(345\) 4.59544 + 14.1433i 0.247410 + 0.761451i
\(346\) 0 0
\(347\) −22.0640 + 16.0304i −1.18446 + 0.860558i −0.992667 0.120878i \(-0.961429\pi\)
−0.191789 + 0.981436i \(0.561429\pi\)
\(348\) 0 0
\(349\) −7.69815 + 23.6925i −0.412073 + 1.26823i 0.502771 + 0.864420i \(0.332314\pi\)
−0.914843 + 0.403809i \(0.867686\pi\)
\(350\) 0 0
\(351\) −6.18421 −0.330089
\(352\) 0 0
\(353\) −22.2916 −1.18646 −0.593232 0.805031i \(-0.702148\pi\)
−0.593232 + 0.805031i \(0.702148\pi\)
\(354\) 0 0
\(355\) −2.11839 + 6.51975i −0.112433 + 0.346032i
\(356\) 0 0
\(357\) 27.7252 20.1435i 1.46737 1.06611i
\(358\) 0 0
\(359\) −0.577219 1.77650i −0.0304645 0.0937599i 0.934668 0.355521i \(-0.115697\pi\)
−0.965133 + 0.261761i \(0.915697\pi\)
\(360\) 0 0
\(361\) 3.39510 + 2.46669i 0.178690 + 0.129826i
\(362\) 0 0
\(363\) 15.1732 + 11.1691i 0.796387 + 0.586227i
\(364\) 0 0
\(365\) 8.13474 + 5.91023i 0.425792 + 0.309356i
\(366\) 0 0
\(367\) −0.796316 2.45081i −0.0415674 0.127931i 0.928119 0.372283i \(-0.121425\pi\)
−0.969687 + 0.244352i \(0.921425\pi\)
\(368\) 0 0
\(369\) 0.0856968 0.0622623i 0.00446120 0.00324125i
\(370\) 0 0
\(371\) 14.1736 43.6219i 0.735858 2.26474i
\(372\) 0 0
\(373\) 7.12031 0.368675 0.184338 0.982863i \(-0.440986\pi\)
0.184338 + 0.982863i \(0.440986\pi\)
\(374\) 0 0
\(375\) 1.71280 0.0884486
\(376\) 0 0
\(377\) 2.50194 7.70018i 0.128857 0.396580i
\(378\) 0 0
\(379\) −23.0912 + 16.7768i −1.18612 + 0.861765i −0.992849 0.119381i \(-0.961909\pi\)
−0.193269 + 0.981146i \(0.561909\pi\)
\(380\) 0 0
\(381\) 7.74904 + 23.8491i 0.396995 + 1.22183i
\(382\) 0 0
\(383\) −7.54866 5.48442i −0.385718 0.280241i 0.377980 0.925814i \(-0.376619\pi\)
−0.763699 + 0.645573i \(0.776619\pi\)
\(384\) 0 0
\(385\) 12.2882 + 0.0382936i 0.626265 + 0.00195162i
\(386\) 0 0
\(387\) −0.221027 0.160585i −0.0112354 0.00816301i
\(388\) 0 0
\(389\) 0.137494 + 0.423163i 0.00697123 + 0.0214552i 0.954482 0.298270i \(-0.0964095\pi\)
−0.947510 + 0.319725i \(0.896409\pi\)
\(390\) 0 0
\(391\) 37.9325 27.5596i 1.91833 1.39375i
\(392\) 0 0
\(393\) 3.14354 9.67481i 0.158570 0.488030i
\(394\) 0 0
\(395\) −1.11383 −0.0560431
\(396\) 0 0
\(397\) 1.66941 0.0837850 0.0418925 0.999122i \(-0.486661\pi\)
0.0418925 + 0.999122i \(0.486661\pi\)
\(398\) 0 0
\(399\) 7.54510 23.2214i 0.377727 1.16252i
\(400\) 0 0
\(401\) −27.3906 + 19.9004i −1.36782 + 0.993780i −0.369917 + 0.929065i \(0.620614\pi\)
−0.997904 + 0.0647154i \(0.979386\pi\)
\(402\) 0 0
\(403\) 3.18581 + 9.80490i 0.158696 + 0.488417i
\(404\) 0 0
\(405\) −7.11665 5.17055i −0.353629 0.256926i
\(406\) 0 0
\(407\) −6.03605 4.41425i −0.299196 0.218806i
\(408\) 0 0
\(409\) 17.5651 + 12.7618i 0.868539 + 0.631031i 0.930195 0.367067i \(-0.119638\pi\)
−0.0616554 + 0.998097i \(0.519638\pi\)
\(410\) 0 0
\(411\) −7.81741 24.0595i −0.385605 1.18677i
\(412\) 0 0
\(413\) 1.18099 0.858043i 0.0581129 0.0422215i
\(414\) 0 0
\(415\) 0.00535255 0.0164735i 0.000262746 0.000808651i
\(416\) 0 0
\(417\) 2.21382 0.108411
\(418\) 0 0
\(419\) 26.5502 1.29706 0.648532 0.761187i \(-0.275383\pi\)
0.648532 + 0.761187i \(0.275383\pi\)
\(420\) 0 0
\(421\) −3.23989 + 9.97137i −0.157903 + 0.485975i −0.998443 0.0557736i \(-0.982237\pi\)
0.840541 + 0.541749i \(0.182237\pi\)
\(422\) 0 0
\(423\) 0.680281 0.494253i 0.0330764 0.0240314i
\(424\) 0 0
\(425\) −1.66878 5.13596i −0.0809475 0.249131i
\(426\) 0 0
\(427\) 5.39796 + 3.92185i 0.261226 + 0.189792i
\(428\) 0 0
\(429\) 2.08684 6.35518i 0.100754 0.306831i
\(430\) 0 0
\(431\) 4.37855 + 3.18120i 0.210907 + 0.153233i 0.688224 0.725498i \(-0.258391\pi\)
−0.477317 + 0.878731i \(0.658391\pi\)
\(432\) 0 0
\(433\) 2.80625 + 8.63676i 0.134860 + 0.415056i 0.995568 0.0940422i \(-0.0299789\pi\)
−0.860708 + 0.509099i \(0.829979\pi\)
\(434\) 0 0
\(435\) 9.52793 6.92245i 0.456829 0.331906i
\(436\) 0 0
\(437\) 10.3229 31.7706i 0.493811 1.51980i
\(438\) 0 0
\(439\) −17.3683 −0.828945 −0.414473 0.910062i \(-0.636034\pi\)
−0.414473 + 0.910062i \(0.636034\pi\)
\(440\) 0 0
\(441\) −0.446130 −0.0212443
\(442\) 0 0
\(443\) 4.22224 12.9947i 0.200604 0.617397i −0.799261 0.600984i \(-0.794775\pi\)
0.999865 0.0164128i \(-0.00522459\pi\)
\(444\) 0 0
\(445\) −6.87207 + 4.99285i −0.325767 + 0.236684i
\(446\) 0 0
\(447\) −12.6531 38.9422i −0.598471 1.84190i
\(448\) 0 0
\(449\) 12.1532 + 8.82983i 0.573546 + 0.416706i 0.836392 0.548132i \(-0.184661\pi\)
−0.262846 + 0.964838i \(0.584661\pi\)
\(450\) 0 0
\(451\) 1.62138 + 5.04353i 0.0763479 + 0.237490i
\(452\) 0 0
\(453\) −11.4741 8.33645i −0.539102 0.391681i
\(454\) 0 0
\(455\) −1.34815 4.14917i −0.0632021 0.194516i
\(456\) 0 0
\(457\) 2.12304 1.54248i 0.0993115 0.0721540i −0.537021 0.843569i \(-0.680451\pi\)
0.636333 + 0.771415i \(0.280451\pi\)
\(458\) 0 0
\(459\) −8.76438 + 26.9740i −0.409086 + 1.25904i
\(460\) 0 0
\(461\) 39.2715 1.82906 0.914529 0.404521i \(-0.132562\pi\)
0.914529 + 0.404521i \(0.132562\pi\)
\(462\) 0 0
\(463\) 3.26421 0.151701 0.0758505 0.997119i \(-0.475833\pi\)
0.0758505 + 0.997119i \(0.475833\pi\)
\(464\) 0 0
\(465\) −4.63410 + 14.2623i −0.214901 + 0.661398i
\(466\) 0 0
\(467\) −20.3484 + 14.7840i −0.941613 + 0.684122i −0.948809 0.315852i \(-0.897710\pi\)
0.00719505 + 0.999974i \(0.497710\pi\)
\(468\) 0 0
\(469\) −16.4651 50.6743i −0.760286 2.33992i
\(470\) 0 0
\(471\) −11.0362 8.01827i −0.508521 0.369462i
\(472\) 0 0
\(473\) 11.0792 7.99689i 0.509423 0.367697i
\(474\) 0 0
\(475\) −3.11271 2.26152i −0.142821 0.103765i
\(476\) 0 0
\(477\) 0.253687 + 0.780769i 0.0116155 + 0.0357490i
\(478\) 0 0
\(479\) 24.1885 17.5740i 1.10520 0.802977i 0.123301 0.992369i \(-0.460652\pi\)
0.981901 + 0.189393i \(0.0606519\pi\)
\(480\) 0 0
\(481\) −0.820405 + 2.52495i −0.0374072 + 0.115128i
\(482\) 0 0
\(483\) 55.0985 2.50707
\(484\) 0 0
\(485\) −10.5155 −0.477483
\(486\) 0 0
\(487\) −9.66165 + 29.7355i −0.437811 + 1.34744i 0.452367 + 0.891832i \(0.350580\pi\)
−0.890178 + 0.455612i \(0.849420\pi\)
\(488\) 0 0
\(489\) 5.66438 4.11541i 0.256152 0.186105i
\(490\) 0 0
\(491\) −2.52081 7.75827i −0.113763 0.350126i 0.877924 0.478800i \(-0.158928\pi\)
−0.991687 + 0.128674i \(0.958928\pi\)
\(492\) 0 0
\(493\) −30.0405 21.8257i −1.35296 0.982980i
\(494\) 0 0
\(495\) −0.178339 + 0.128724i −0.00801574 + 0.00578570i
\(496\) 0 0
\(497\) 20.5483 + 14.9292i 0.921719 + 0.669668i
\(498\) 0 0
\(499\) −2.63513 8.11010i −0.117965 0.363058i 0.874589 0.484865i \(-0.161131\pi\)
−0.992554 + 0.121807i \(0.961131\pi\)
\(500\) 0 0
\(501\) 5.51820 4.00921i 0.246535 0.179118i
\(502\) 0 0
\(503\) −3.04027 + 9.35700i −0.135559 + 0.417208i −0.995677 0.0928880i \(-0.970390\pi\)
0.860117 + 0.510096i \(0.170390\pi\)
\(504\) 0 0
\(505\) −7.17862 −0.319444
\(506\) 0 0
\(507\) 19.8916 0.883417
\(508\) 0 0
\(509\) −0.151062 + 0.464920i −0.00669569 + 0.0206072i −0.954349 0.298695i \(-0.903449\pi\)
0.947653 + 0.319302i \(0.103449\pi\)
\(510\) 0 0
\(511\) 30.1397 21.8977i 1.33330 0.968699i
\(512\) 0 0
\(513\) 6.24435 + 19.2181i 0.275695 + 0.848501i
\(514\) 0 0
\(515\) 3.03395 + 2.20429i 0.133692 + 0.0971327i
\(516\) 0 0
\(517\) 12.8709 + 40.0367i 0.566062 + 1.76081i
\(518\) 0 0
\(519\) 24.4674 + 17.7766i 1.07400 + 0.780308i
\(520\) 0 0
\(521\) 3.44666 + 10.6077i 0.151001 + 0.464734i 0.997734 0.0672849i \(-0.0214337\pi\)
−0.846733 + 0.532019i \(0.821434\pi\)
\(522\) 0 0
\(523\) 2.72056 1.97660i 0.118962 0.0864307i −0.526714 0.850043i \(-0.676576\pi\)
0.645675 + 0.763612i \(0.276576\pi\)
\(524\) 0 0
\(525\) 1.96103 6.03542i 0.0855862 0.263407i
\(526\) 0 0
\(527\) 47.2816 2.05962
\(528\) 0 0
\(529\) 52.3836 2.27755
\(530\) 0 0
\(531\) −0.00807403 + 0.0248493i −0.000350383 + 0.00107837i
\(532\) 0 0
\(533\) 1.52164 1.10554i 0.0659097 0.0478862i
\(534\) 0 0
\(535\) −1.96265 6.04042i −0.0848529 0.261150i
\(536\) 0 0
\(537\) −16.5474 12.0224i −0.714072 0.518804i
\(538\) 0 0
\(539\) 6.96099 21.1987i 0.299831 0.913093i
\(540\) 0 0
\(541\) −2.13323 1.54988i −0.0917145 0.0666345i 0.540983 0.841034i \(-0.318052\pi\)
−0.632697 + 0.774399i \(0.718052\pi\)
\(542\) 0 0
\(543\) 0.546067 + 1.68062i 0.0234340 + 0.0721224i
\(544\) 0 0
\(545\) 1.07120 0.778270i 0.0458850 0.0333374i
\(546\) 0 0
\(547\) −11.8276 + 36.4018i −0.505714 + 1.55643i 0.293854 + 0.955850i \(0.405062\pi\)
−0.799567 + 0.600577i \(0.794938\pi\)
\(548\) 0 0
\(549\) −0.119424 −0.00509687
\(550\) 0 0
\(551\) −26.4555 −1.12704
\(552\) 0 0
\(553\) −1.27526 + 3.92483i −0.0542294 + 0.166901i
\(554\) 0 0
\(555\) −3.12428 + 2.26992i −0.132618 + 0.0963528i
\(556\) 0 0
\(557\) −5.59589 17.2224i −0.237105 0.729736i −0.996835 0.0794966i \(-0.974669\pi\)
0.759730 0.650239i \(-0.225331\pi\)
\(558\) 0 0
\(559\) −3.92458 2.85137i −0.165992 0.120600i
\(560\) 0 0
\(561\) −24.7622 18.1090i −1.04546 0.764562i
\(562\) 0 0
\(563\) 2.88702 + 2.09754i 0.121673 + 0.0884008i 0.646958 0.762526i \(-0.276041\pi\)
−0.525284 + 0.850927i \(0.676041\pi\)
\(564\) 0 0
\(565\) −1.64758 5.07074i −0.0693143 0.213328i
\(566\) 0 0
\(567\) −26.3676 + 19.1571i −1.10733 + 0.804525i
\(568\) 0 0
\(569\) −12.4766 + 38.3990i −0.523046 + 1.60977i 0.245100 + 0.969498i \(0.421179\pi\)
−0.768147 + 0.640274i \(0.778821\pi\)
\(570\) 0 0
\(571\) −36.3873 −1.52276 −0.761381 0.648305i \(-0.775478\pi\)
−0.761381 + 0.648305i \(0.775478\pi\)
\(572\) 0 0
\(573\) 32.5694 1.36061
\(574\) 0 0
\(575\) 2.68300 8.25743i 0.111889 0.344359i
\(576\) 0 0
\(577\) 1.20076 0.872400i 0.0499881 0.0363185i −0.562511 0.826790i \(-0.690164\pi\)
0.612499 + 0.790472i \(0.290164\pi\)
\(578\) 0 0
\(579\) −2.86276 8.81067i −0.118972 0.366159i
\(580\) 0 0
\(581\) −0.0519195 0.0377217i −0.00215399 0.00156496i
\(582\) 0 0
\(583\) −41.0580 0.127949i −1.70045 0.00529909i
\(584\) 0 0
\(585\) 0.0631729 + 0.0458978i 0.00261188 + 0.00189764i
\(586\) 0 0
\(587\) 12.1618 + 37.4300i 0.501969 + 1.54490i 0.805806 + 0.592179i \(0.201732\pi\)
−0.303837 + 0.952724i \(0.598268\pi\)
\(588\) 0 0
\(589\) 27.2530 19.8005i 1.12294 0.815865i
\(590\) 0 0
\(591\) −2.15746 + 6.63998i −0.0887460 + 0.273132i
\(592\) 0 0
\(593\) 27.2990 1.12104 0.560518 0.828142i \(-0.310602\pi\)
0.560518 + 0.828142i \(0.310602\pi\)
\(594\) 0 0
\(595\) −20.0083 −0.820260
\(596\) 0 0
\(597\) −6.38907 + 19.6635i −0.261487 + 0.804774i
\(598\) 0 0
\(599\) 17.0954 12.4205i 0.698499 0.507490i −0.180944 0.983493i \(-0.557915\pi\)
0.879443 + 0.476004i \(0.157915\pi\)
\(600\) 0 0
\(601\) −0.884593 2.72250i −0.0360833 0.111053i 0.931393 0.364016i \(-0.118595\pi\)
−0.967476 + 0.252963i \(0.918595\pi\)
\(602\) 0 0
\(603\) 0.771537 + 0.560554i 0.0314194 + 0.0228275i
\(604\) 0 0
\(605\) −3.33392 10.4826i −0.135543 0.426178i
\(606\) 0 0
\(607\) 25.8840 + 18.8058i 1.05060 + 0.763305i 0.972326 0.233627i \(-0.0750593\pi\)
0.0782733 + 0.996932i \(0.475059\pi\)
\(608\) 0 0
\(609\) −13.4840 41.4994i −0.546398 1.68164i
\(610\) 0 0
\(611\) 12.0792 8.77602i 0.488670 0.355040i
\(612\) 0 0
\(613\) −11.0013 + 33.8584i −0.444337 + 1.36753i 0.438873 + 0.898549i \(0.355378\pi\)
−0.883209 + 0.468979i \(0.844622\pi\)
\(614\) 0 0
\(615\) 2.73591 0.110322
\(616\) 0 0
\(617\) −36.9894 −1.48914 −0.744568 0.667546i \(-0.767345\pi\)
−0.744568 + 0.667546i \(0.767345\pi\)
\(618\) 0 0
\(619\) −10.5038 + 32.3274i −0.422184 + 1.29935i 0.483480 + 0.875355i \(0.339372\pi\)
−0.905665 + 0.423995i \(0.860628\pi\)
\(620\) 0 0
\(621\) −36.8909 + 26.8028i −1.48038 + 1.07556i
\(622\) 0 0
\(623\) 9.72538 + 29.9317i 0.389639 + 1.19919i
\(624\) 0 0
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) 0 0
\(627\) −21.8566 0.0681114i −0.872867 0.00272011i
\(628\) 0 0
\(629\) 9.85050 + 7.15681i 0.392765 + 0.285361i
\(630\) 0 0
\(631\) −0.891987 2.74525i −0.0355094 0.109287i 0.931731 0.363150i \(-0.118299\pi\)
−0.967240 + 0.253863i \(0.918299\pi\)
\(632\) 0 0
\(633\) 12.9047 9.37584i 0.512917 0.372656i
\(634\) 0 0
\(635\) 4.52419 13.9240i 0.179537 0.552558i
\(636\) 0 0
\(637\) −7.92154 −0.313863
\(638\) 0 0
\(639\) −0.454608 −0.0179840
\(640\) 0 0
\(641\) 3.59179 11.0544i 0.141867 0.436623i −0.854728 0.519077i \(-0.826276\pi\)
0.996595 + 0.0824541i \(0.0262758\pi\)
\(642\) 0 0
\(643\) −21.9133 + 15.9210i −0.864178 + 0.627862i −0.929018 0.370033i \(-0.879346\pi\)
0.0648403 + 0.997896i \(0.479346\pi\)
\(644\) 0 0
\(645\) −2.18054 6.71101i −0.0858586 0.264246i
\(646\) 0 0
\(647\) 1.34353 + 0.976135i 0.0528198 + 0.0383758i 0.613882 0.789398i \(-0.289607\pi\)
−0.561062 + 0.827774i \(0.689607\pi\)
\(648\) 0 0
\(649\) −1.05478 0.771378i −0.0414039 0.0302792i
\(650\) 0 0
\(651\) 44.9506 + 32.6585i 1.76175 + 1.27999i
\(652\) 0 0
\(653\) −12.4505 38.3186i −0.487224 1.49952i −0.828734 0.559643i \(-0.810938\pi\)
0.341510 0.939878i \(-0.389062\pi\)
\(654\) 0 0
\(655\) −4.80493 + 3.49099i −0.187744 + 0.136404i
\(656\) 0 0
\(657\) −0.206054 + 0.634169i −0.00803893 + 0.0247413i
\(658\) 0 0
\(659\) −33.7115 −1.31321 −0.656607 0.754233i \(-0.728009\pi\)
−0.656607 + 0.754233i \(0.728009\pi\)
\(660\) 0 0
\(661\) 42.4279 1.65026 0.825128 0.564946i \(-0.191103\pi\)
0.825128 + 0.564946i \(0.191103\pi\)
\(662\) 0 0
\(663\) −3.36562 + 10.3583i −0.130710 + 0.402284i
\(664\) 0 0
\(665\) −11.5328 + 8.37904i −0.447221 + 0.324925i
\(666\) 0 0
\(667\) −18.4482 56.7779i −0.714319 2.19845i
\(668\) 0 0
\(669\) 6.57319 + 4.77570i 0.254134 + 0.184639i
\(670\) 0 0
\(671\) 1.86337 5.67464i 0.0719347 0.219067i
\(672\) 0 0
\(673\) 30.8456 + 22.4107i 1.18901 + 0.863868i 0.993160 0.116765i \(-0.0372525\pi\)
0.195853 + 0.980633i \(0.437253\pi\)
\(674\) 0 0
\(675\) 1.62295 + 4.99493i 0.0624675 + 0.192255i
\(676\) 0 0
\(677\) 9.71587 7.05899i 0.373411 0.271299i −0.385213 0.922828i \(-0.625872\pi\)
0.758624 + 0.651529i \(0.225872\pi\)
\(678\) 0 0
\(679\) −12.0394 + 37.0535i −0.462030 + 1.42198i
\(680\) 0 0
\(681\) 6.02089 0.230721
\(682\) 0 0
\(683\) −37.6564 −1.44088 −0.720441 0.693516i \(-0.756061\pi\)
−0.720441 + 0.693516i \(0.756061\pi\)
\(684\) 0 0
\(685\) −4.56411 + 14.0469i −0.174386 + 0.536704i
\(686\) 0 0
\(687\) −12.6459 + 9.18782i −0.482473 + 0.350537i
\(688\) 0 0
\(689\) 4.50450 + 13.8634i 0.171608 + 0.528155i
\(690\) 0 0
\(691\) −8.03817 5.84007i −0.305786 0.222167i 0.424300 0.905522i \(-0.360520\pi\)
−0.730086 + 0.683355i \(0.760520\pi\)
\(692\) 0 0
\(693\) 0.249401 + 0.775795i 0.00947396 + 0.0294700i
\(694\) 0 0
\(695\) −1.04567 0.759722i −0.0396644 0.0288179i
\(696\) 0 0
\(697\) −2.66558 8.20382i −0.100966 0.310742i
\(698\) 0 0
\(699\) −29.8270 + 21.6706i −1.12816 + 0.819658i
\(700\) 0 0
\(701\) 3.11652 9.59166i 0.117709 0.362272i −0.874793 0.484497i \(-0.839003\pi\)
0.992502 + 0.122225i \(0.0390028\pi\)
\(702\) 0 0
\(703\) 8.67494 0.327181
\(704\) 0 0
\(705\) 21.7183 0.817957
\(706\) 0 0
\(707\) −8.21898 + 25.2954i −0.309106 + 0.951332i
\(708\) 0 0
\(709\) −4.22013 + 3.06611i −0.158490 + 0.115150i −0.664204 0.747552i \(-0.731229\pi\)
0.505713 + 0.862702i \(0.331229\pi\)
\(710\) 0 0
\(711\) −0.0228252 0.0702488i −0.000856013 0.00263454i
\(712\) 0 0
\(713\) 61.4996 + 44.6821i 2.30318 + 1.67336i
\(714\) 0 0
\(715\) −3.16661 + 2.28563i −0.118425 + 0.0854779i
\(716\) 0 0
\(717\) −15.6685 11.3839i −0.585152 0.425138i
\(718\) 0 0
\(719\) 2.44416 + 7.52235i 0.0911518 + 0.280536i 0.986232 0.165369i \(-0.0528816\pi\)
−0.895080 + 0.445906i \(0.852882\pi\)
\(720\) 0 0
\(721\) 11.2409 8.16702i 0.418634 0.304156i
\(722\) 0 0
\(723\) 13.8220 42.5396i 0.514044 1.58206i
\(724\) 0 0
\(725\) −6.87597 −0.255367
\(726\) 0 0
\(727\) −10.2281 −0.379338 −0.189669 0.981848i \(-0.560742\pi\)
−0.189669 + 0.981848i \(0.560742\pi\)
\(728\) 0 0
\(729\) 8.51965 26.2208i 0.315542 0.971140i
\(730\) 0 0
\(731\) −17.9990 + 13.0770i −0.665716 + 0.483671i
\(732\) 0 0
\(733\) −4.74873 14.6151i −0.175398 0.539821i 0.824253 0.566222i \(-0.191595\pi\)
−0.999651 + 0.0264009i \(0.991595\pi\)
\(734\) 0 0
\(735\) −9.32209 6.77289i −0.343850 0.249822i
\(736\) 0 0
\(737\) −38.6742 + 27.9147i −1.42458 + 1.02825i
\(738\) 0 0
\(739\) −22.8200 16.5797i −0.839449 0.609895i 0.0827676 0.996569i \(-0.473624\pi\)
−0.922217 + 0.386673i \(0.873624\pi\)
\(740\) 0 0
\(741\) 2.39790 + 7.37997i 0.0880890 + 0.271110i
\(742\) 0 0
\(743\) 35.6824 25.9248i 1.30906 0.951089i 0.309061 0.951042i \(-0.399985\pi\)
1.00000 4.66582e-5i \(-1.48518e-5\pi\)
\(744\) 0 0
\(745\) −7.38737 + 22.7360i −0.270652 + 0.832982i
\(746\) 0 0
\(747\) 0.00114866 4.20272e−5
\(748\) 0 0
\(749\) −23.5318 −0.859834
\(750\) 0 0
\(751\) 13.3439 41.0682i 0.486924 1.49860i −0.342250 0.939609i \(-0.611189\pi\)
0.829174 0.558990i \(-0.188811\pi\)
\(752\) 0 0
\(753\) 5.15214 3.74325i 0.187754 0.136411i
\(754\) 0 0
\(755\) 2.55881 + 7.87521i 0.0931246 + 0.286608i
\(756\) 0 0
\(757\) −15.5978 11.3325i −0.566913 0.411886i 0.267070 0.963677i \(-0.413945\pi\)
−0.833982 + 0.551791i \(0.813945\pi\)
\(758\) 0 0
\(759\) −15.0951 46.9554i −0.547918 1.70437i
\(760\) 0 0
\(761\) −28.2423 20.5193i −1.02378 0.743823i −0.0567289 0.998390i \(-0.518067\pi\)
−0.967055 + 0.254567i \(0.918067\pi\)
\(762\) 0 0
\(763\) −1.51596 4.66565i −0.0548815 0.168908i
\(764\) 0 0
\(765\) 0.289725 0.210497i 0.0104750 0.00761055i
\(766\) 0 0
\(767\) −0.143364 + 0.441228i −0.00517656 + 0.0159318i
\(768\) 0 0
\(769\) 10.7367 0.387177 0.193588 0.981083i \(-0.437987\pi\)
0.193588 + 0.981083i \(0.437987\pi\)
\(770\) 0 0
\(771\) 12.1485 0.437518
\(772\) 0 0
\(773\) 9.77736 30.0916i 0.351667 1.08232i −0.606249 0.795275i \(-0.707327\pi\)
0.957917 0.287046i \(-0.0926733\pi\)
\(774\) 0 0
\(775\) 7.08327 5.14630i 0.254439 0.184860i
\(776\) 0 0
\(777\) 4.42149 + 13.6080i 0.158620 + 0.488183i
\(778\) 0 0
\(779\) −4.97202 3.61239i −0.178141 0.129427i
\(780\) 0 0
\(781\) 7.09327 21.6016i 0.253817 0.772964i
\(782\) 0 0
\(783\) 29.2156 + 21.2264i 1.04408 + 0.758570i
\(784\) 0 0
\(785\) 2.46115 + 7.57463i 0.0878421 + 0.270350i
\(786\) 0 0
\(787\) 12.6566 9.19553i 0.451158 0.327785i −0.338895 0.940824i \(-0.610053\pi\)
0.790053 + 0.613039