Properties

Label 644.2.y.a.261.12
Level $644$
Weight $2$
Character 644.261
Analytic conductor $5.142$
Analytic rank $0$
Dimension $320$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [644,2,Mod(9,644)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(644, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([0, 22, 30]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("644.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 644.y (of order \(33\), degree \(20\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.14236589017\)
Analytic rank: \(0\)
Dimension: \(320\)
Relative dimension: \(16\) over \(\Q(\zeta_{33})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 261.12
Character \(\chi\) \(=\) 644.261
Dual form 644.2.y.a.417.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.682046 - 0.957799i) q^{3} +(4.10551 - 0.791273i) q^{5} +(1.83915 - 1.90198i) q^{7} +(0.529011 + 1.52848i) q^{9} +O(q^{10})\) \(q+(0.682046 - 0.957799i) q^{3} +(4.10551 - 0.791273i) q^{5} +(1.83915 - 1.90198i) q^{7} +(0.529011 + 1.52848i) q^{9} +(-0.376669 + 0.296216i) q^{11} +(1.11002 - 0.713363i) q^{13} +(2.04227 - 4.47194i) q^{15} +(0.181133 + 0.172710i) q^{17} +(-6.05065 + 5.76929i) q^{19} +(-0.567327 - 3.05877i) q^{21} +(-4.03108 + 2.59814i) q^{23} +(11.5873 - 4.63885i) q^{25} +(5.20937 + 1.52961i) q^{27} +(-8.65285 + 2.54071i) q^{29} +(-9.23174 + 0.881524i) q^{31} +(0.0268097 + 0.562806i) q^{33} +(6.04568 - 9.26387i) q^{35} +(-1.12906 - 3.26221i) q^{37} +(0.0738222 - 1.54972i) q^{39} +(2.55635 + 2.95018i) q^{41} +(-1.31058 - 2.86978i) q^{43} +(3.38130 + 5.85659i) q^{45} +(1.20447 - 2.08620i) q^{47} +(-0.235037 - 6.99605i) q^{49} +(0.288962 - 0.0556929i) q^{51} +(0.336451 - 7.06297i) q^{53} +(-1.31203 + 1.51416i) q^{55} +(1.39900 + 9.73023i) q^{57} +(-6.85114 - 3.53201i) q^{59} +(6.99274 + 9.81993i) q^{61} +(3.88006 + 1.80493i) q^{63} +(3.99272 - 3.80705i) q^{65} +(10.8266 - 4.33430i) q^{67} +(-0.260883 + 5.63302i) q^{69} +(1.26767 - 8.81683i) q^{71} +(0.444351 + 1.83164i) q^{73} +(3.45997 - 14.2622i) q^{75} +(-0.129356 + 1.26120i) q^{77} +(-0.0445425 - 0.935061i) q^{79} +(1.20392 - 0.946776i) q^{81} +(-1.40519 + 1.62167i) q^{83} +(0.880303 + 0.565737i) q^{85} +(-3.46815 + 10.0206i) q^{87} +(4.31572 + 0.412101i) q^{89} +(0.684686 - 3.42321i) q^{91} +(-5.45215 + 9.44339i) q^{93} +(-20.2760 + 28.4736i) q^{95} +(-11.2294 - 12.9594i) q^{97} +(-0.652020 - 0.419028i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9} - 2 q^{11} - 16 q^{15} + 4 q^{17} - 50 q^{21} + 25 q^{23} + 44 q^{25} + 54 q^{27} + 12 q^{29} + 2 q^{31} - 12 q^{33} - 22 q^{35} - 44 q^{37} - 4 q^{39} + 12 q^{41} + 76 q^{43} - 114 q^{45} - 10 q^{47} - 74 q^{49} - 30 q^{51} - 20 q^{53} + 32 q^{55} + 52 q^{57} - 32 q^{59} + 74 q^{61} + 87 q^{63} - 75 q^{65} - 8 q^{67} + 10 q^{69} + 8 q^{73} + 118 q^{75} + 5 q^{77} - 40 q^{79} - 44 q^{81} - 52 q^{83} - 100 q^{85} + 84 q^{87} + 36 q^{89} + 30 q^{91} - 12 q^{93} - 25 q^{95} + 72 q^{97} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/644\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\) \(323\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{11}\right)\) \(1\)

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
\(3\) 0.682046 0.957799i 0.393779 0.552986i −0.569325 0.822112i \(-0.692796\pi\)
0.963105 + 0.269126i \(0.0867350\pi\)
\(4\) 0 0
\(5\) 4.10551 0.791273i 1.83604 0.353868i 0.850861 0.525390i \(-0.176081\pi\)
0.985180 + 0.171522i \(0.0548686\pi\)
\(6\) 0 0
\(7\) 1.83915 1.90198i 0.695134 0.718880i
\(8\) 0 0
\(9\) 0.529011 + 1.52848i 0.176337 + 0.509492i
\(10\) 0 0
\(11\) −0.376669 + 0.296216i −0.113570 + 0.0893123i −0.673329 0.739343i \(-0.735136\pi\)
0.559759 + 0.828655i \(0.310894\pi\)
\(12\) 0 0
\(13\) 1.11002 0.713363i 0.307863 0.197851i −0.377582 0.925976i \(-0.623244\pi\)
0.685445 + 0.728125i \(0.259608\pi\)
\(14\) 0 0
\(15\) 2.04227 4.47194i 0.527311 1.15465i
\(16\) 0 0
\(17\) 0.181133 + 0.172710i 0.0439311 + 0.0418883i 0.711727 0.702457i \(-0.247913\pi\)
−0.667796 + 0.744345i \(0.732762\pi\)
\(18\) 0 0
\(19\) −6.05065 + 5.76929i −1.38812 + 1.32357i −0.498475 + 0.866904i \(0.666106\pi\)
−0.889641 + 0.456661i \(0.849045\pi\)
\(20\) 0 0
\(21\) −0.567327 3.05877i −0.123801 0.667479i
\(22\) 0 0
\(23\) −4.03108 + 2.59814i −0.840539 + 0.541751i
\(24\) 0 0
\(25\) 11.5873 4.63885i 2.31746 0.927770i
\(26\) 0 0
\(27\) 5.20937 + 1.52961i 1.00254 + 0.294374i
\(28\) 0 0
\(29\) −8.65285 + 2.54071i −1.60679 + 0.471797i −0.957426 0.288678i \(-0.906784\pi\)
−0.649367 + 0.760475i \(0.724966\pi\)
\(30\) 0 0
\(31\) −9.23174 + 0.881524i −1.65807 + 0.158326i −0.881654 0.471896i \(-0.843570\pi\)
−0.776415 + 0.630222i \(0.782964\pi\)
\(32\) 0 0
\(33\) 0.0268097 + 0.562806i 0.00466698 + 0.0979719i
\(34\) 0 0
\(35\) 6.04568 9.26387i 1.02191 1.56588i
\(36\) 0 0
\(37\) −1.12906 3.26221i −0.185617 0.536305i 0.813349 0.581776i \(-0.197642\pi\)
−0.998966 + 0.0454717i \(0.985521\pi\)
\(38\) 0 0
\(39\) 0.0738222 1.54972i 0.0118210 0.248154i
\(40\) 0 0
\(41\) 2.55635 + 2.95018i 0.399235 + 0.460741i 0.919400 0.393324i \(-0.128675\pi\)
−0.520165 + 0.854066i \(0.674130\pi\)
\(42\) 0 0
\(43\) −1.31058 2.86978i −0.199862 0.437637i 0.782989 0.622035i \(-0.213694\pi\)
−0.982852 + 0.184398i \(0.940967\pi\)
\(44\) 0 0
\(45\) 3.38130 + 5.85659i 0.504055 + 0.873049i
\(46\) 0 0
\(47\) 1.20447 2.08620i 0.175690 0.304304i −0.764710 0.644375i \(-0.777118\pi\)
0.940400 + 0.340071i \(0.110451\pi\)
\(48\) 0 0
\(49\) −0.235037 6.99605i −0.0335767 0.999436i
\(50\) 0 0
\(51\) 0.288962 0.0556929i 0.0404628 0.00779856i
\(52\) 0 0
\(53\) 0.336451 7.06297i 0.0462151 0.970173i −0.850063 0.526681i \(-0.823436\pi\)
0.896278 0.443492i \(-0.146261\pi\)
\(54\) 0 0
\(55\) −1.31203 + 1.51416i −0.176914 + 0.204170i
\(56\) 0 0
\(57\) 1.39900 + 9.73023i 0.185302 + 1.28880i
\(58\) 0 0
\(59\) −6.85114 3.53201i −0.891942 0.459828i −0.0495985 0.998769i \(-0.515794\pi\)
−0.842343 + 0.538941i \(0.818824\pi\)
\(60\) 0 0
\(61\) 6.99274 + 9.81993i 0.895328 + 1.25731i 0.965665 + 0.259789i \(0.0836531\pi\)
−0.0703370 + 0.997523i \(0.522407\pi\)
\(62\) 0 0
\(63\) 3.88006 + 1.80493i 0.488841 + 0.227400i
\(64\) 0 0
\(65\) 3.99272 3.80705i 0.495236 0.472206i
\(66\) 0 0
\(67\) 10.8266 4.33430i 1.32267 0.529519i 0.400501 0.916296i \(-0.368836\pi\)
0.922173 + 0.386777i \(0.126412\pi\)
\(68\) 0 0
\(69\) −0.260883 + 5.63302i −0.0314067 + 0.678136i
\(70\) 0 0
\(71\) 1.26767 8.81683i 0.150445 1.04637i −0.765031 0.643993i \(-0.777277\pi\)
0.915476 0.402372i \(-0.131814\pi\)
\(72\) 0 0
\(73\) 0.444351 + 1.83164i 0.0520073 + 0.214377i 0.991886 0.127132i \(-0.0405771\pi\)
−0.939878 + 0.341509i \(0.889062\pi\)
\(74\) 0 0
\(75\) 3.45997 14.2622i 0.399523 1.64686i
\(76\) 0 0
\(77\) −0.129356 + 1.26120i −0.0147415 + 0.143727i
\(78\) 0 0
\(79\) −0.0445425 0.935061i −0.00501142 0.105203i −0.999987 0.00508542i \(-0.998381\pi\)
0.994976 0.100117i \(-0.0319218\pi\)
\(80\) 0 0
\(81\) 1.20392 0.946776i 0.133769 0.105197i
\(82\) 0 0
\(83\) −1.40519 + 1.62167i −0.154239 + 0.178002i −0.827610 0.561303i \(-0.810300\pi\)
0.673371 + 0.739305i \(0.264846\pi\)
\(84\) 0 0
\(85\) 0.880303 + 0.565737i 0.0954823 + 0.0613627i
\(86\) 0 0
\(87\) −3.46815 + 10.0206i −0.371825 + 1.07432i
\(88\) 0 0
\(89\) 4.31572 + 0.412101i 0.457465 + 0.0436826i 0.321245 0.946996i \(-0.395899\pi\)
0.136220 + 0.990679i \(0.456505\pi\)
\(90\) 0 0
\(91\) 0.684686 3.42321i 0.0717746 0.358850i
\(92\) 0 0
\(93\) −5.45215 + 9.44339i −0.565361 + 0.979234i
\(94\) 0 0
\(95\) −20.2760 + 28.4736i −2.08027 + 2.92133i
\(96\) 0 0
\(97\) −11.2294 12.9594i −1.14017 1.31583i −0.941981 0.335666i \(-0.891039\pi\)
−0.198192 0.980163i \(-0.563507\pi\)
\(98\) 0 0
\(99\) −0.652020 0.419028i −0.0655305 0.0421139i
\(100\) 0 0
\(101\) −9.40244 1.81217i −0.935578 0.180318i −0.301394 0.953500i \(-0.597452\pi\)
−0.634184 + 0.773182i \(0.718664\pi\)
\(102\) 0 0
\(103\) −9.89860 3.96280i −0.975338 0.390467i −0.171415 0.985199i \(-0.554834\pi\)
−0.803924 + 0.594732i \(0.797258\pi\)
\(104\) 0 0
\(105\) −4.74949 12.1089i −0.463503 1.18171i
\(106\) 0 0
\(107\) 6.50850 + 9.13991i 0.629201 + 0.883589i 0.998963 0.0455377i \(-0.0145001\pi\)
−0.369762 + 0.929127i \(0.620561\pi\)
\(108\) 0 0
\(109\) −4.08827 3.89816i −0.391586 0.373376i 0.468554 0.883435i \(-0.344775\pi\)
−0.860140 + 0.510059i \(0.829624\pi\)
\(110\) 0 0
\(111\) −3.89462 1.14356i −0.369661 0.108542i
\(112\) 0 0
\(113\) −0.839549 + 5.83919i −0.0789781 + 0.549305i 0.911464 + 0.411379i \(0.134953\pi\)
−0.990443 + 0.137926i \(0.955956\pi\)
\(114\) 0 0
\(115\) −14.4938 + 13.8564i −1.35156 + 1.29212i
\(116\) 0 0
\(117\) 1.67757 + 1.31925i 0.155091 + 0.121965i
\(118\) 0 0
\(119\) 0.661621 0.0268709i 0.0606507 0.00246325i
\(120\) 0 0
\(121\) −2.53921 + 10.4668i −0.230838 + 0.951525i
\(122\) 0 0
\(123\) 4.56923 0.436309i 0.411994 0.0393406i
\(124\) 0 0
\(125\) 26.3145 16.9113i 2.35364 1.51259i
\(126\) 0 0
\(127\) 0.545744 + 3.79573i 0.0484269 + 0.336817i 0.999603 + 0.0281684i \(0.00896748\pi\)
−0.951176 + 0.308648i \(0.900123\pi\)
\(128\) 0 0
\(129\) −3.64255 0.702044i −0.320709 0.0618116i
\(130\) 0 0
\(131\) 7.06772 3.64366i 0.617510 0.318348i −0.120937 0.992660i \(-0.538590\pi\)
0.738447 + 0.674312i \(0.235560\pi\)
\(132\) 0 0
\(133\) −0.155021 + 22.1188i −0.0134420 + 1.91794i
\(134\) 0 0
\(135\) 22.5975 + 2.15780i 1.94488 + 0.185714i
\(136\) 0 0
\(137\) 6.88720 + 11.9290i 0.588413 + 1.01916i 0.994440 + 0.105300i \(0.0335804\pi\)
−0.406027 + 0.913861i \(0.633086\pi\)
\(138\) 0 0
\(139\) 10.2810 0.872019 0.436010 0.899942i \(-0.356391\pi\)
0.436010 + 0.899942i \(0.356391\pi\)
\(140\) 0 0
\(141\) −1.17666 2.57652i −0.0990926 0.216982i
\(142\) 0 0
\(143\) −0.206799 + 0.597505i −0.0172934 + 0.0499659i
\(144\) 0 0
\(145\) −33.5140 + 17.2777i −2.78319 + 1.43483i
\(146\) 0 0
\(147\) −6.86112 4.54651i −0.565896 0.374990i
\(148\) 0 0
\(149\) 10.3311 + 4.13596i 0.846359 + 0.338831i 0.753984 0.656893i \(-0.228130\pi\)
0.0923755 + 0.995724i \(0.470554\pi\)
\(150\) 0 0
\(151\) −15.7550 8.12228i −1.28213 0.660981i −0.323655 0.946175i \(-0.604912\pi\)
−0.958470 + 0.285194i \(0.907942\pi\)
\(152\) 0 0
\(153\) −0.168162 + 0.368222i −0.0135951 + 0.0297690i
\(154\) 0 0
\(155\) −37.2035 + 10.9239i −2.98826 + 0.877432i
\(156\) 0 0
\(157\) −4.55001 18.7554i −0.363130 1.49684i −0.801471 0.598033i \(-0.795949\pi\)
0.438341 0.898809i \(-0.355566\pi\)
\(158\) 0 0
\(159\) −6.53543 5.13952i −0.518294 0.407591i
\(160\) 0 0
\(161\) −2.47217 + 12.4454i −0.194834 + 0.980836i
\(162\) 0 0
\(163\) 4.52989 + 3.56235i 0.354809 + 0.279025i 0.779614 0.626260i \(-0.215415\pi\)
−0.424806 + 0.905285i \(0.639658\pi\)
\(164\) 0 0
\(165\) 0.555401 + 2.28939i 0.0432379 + 0.178229i
\(166\) 0 0
\(167\) 2.35897 0.692655i 0.182542 0.0535993i −0.189184 0.981942i \(-0.560584\pi\)
0.371726 + 0.928342i \(0.378766\pi\)
\(168\) 0 0
\(169\) −4.67715 + 10.2415i −0.359781 + 0.787810i
\(170\) 0 0
\(171\) −12.0191 6.19627i −0.919122 0.473840i
\(172\) 0 0
\(173\) 15.6543 + 6.26703i 1.19017 + 0.476473i 0.880352 0.474322i \(-0.157307\pi\)
0.309821 + 0.950795i \(0.399731\pi\)
\(174\) 0 0
\(175\) 12.4878 30.5703i 0.943989 2.31090i
\(176\) 0 0
\(177\) −8.05574 + 4.15302i −0.605507 + 0.312160i
\(178\) 0 0
\(179\) −1.29220 + 3.73356i −0.0965834 + 0.279060i −0.982935 0.183953i \(-0.941110\pi\)
0.886352 + 0.463013i \(0.153232\pi\)
\(180\) 0 0
\(181\) −0.247994 0.543031i −0.0184332 0.0403632i 0.900191 0.435494i \(-0.143426\pi\)
−0.918625 + 0.395131i \(0.870699\pi\)
\(182\) 0 0
\(183\) 14.1749 1.04784
\(184\) 0 0
\(185\) −7.21669 12.4997i −0.530581 0.918994i
\(186\) 0 0
\(187\) −0.119386 0.0114000i −0.00873039 0.000833651i
\(188\) 0 0
\(189\) 12.4901 7.09492i 0.908522 0.516080i
\(190\) 0 0
\(191\) 4.53211 2.33646i 0.327932 0.169061i −0.286396 0.958111i \(-0.592457\pi\)
0.614328 + 0.789051i \(0.289427\pi\)
\(192\) 0 0
\(193\) 2.01751 + 0.388844i 0.145224 + 0.0279896i 0.261345 0.965245i \(-0.415834\pi\)
−0.116121 + 0.993235i \(0.537046\pi\)
\(194\) 0 0
\(195\) −0.923172 6.42080i −0.0661097 0.459803i
\(196\) 0 0
\(197\) 9.78832 6.29057i 0.697389 0.448185i −0.143317 0.989677i \(-0.545777\pi\)
0.840706 + 0.541492i \(0.182140\pi\)
\(198\) 0 0
\(199\) 8.70747 0.831462i 0.617256 0.0589408i 0.218256 0.975892i \(-0.429963\pi\)
0.399000 + 0.916951i \(0.369357\pi\)
\(200\) 0 0
\(201\) 3.23282 13.3259i 0.228025 0.939934i
\(202\) 0 0
\(203\) −11.0815 + 21.1303i −0.777772 + 1.48305i
\(204\) 0 0
\(205\) 12.8295 + 10.0893i 0.896053 + 0.704664i
\(206\) 0 0
\(207\) −6.10369 4.78697i −0.424236 0.332717i
\(208\) 0 0
\(209\) 0.570140 3.96541i 0.0394374 0.274293i
\(210\) 0 0
\(211\) −4.03576 1.18501i −0.277833 0.0815791i 0.139848 0.990173i \(-0.455339\pi\)
−0.417681 + 0.908594i \(0.637157\pi\)
\(212\) 0 0
\(213\) −7.58015 7.22766i −0.519383 0.495231i
\(214\) 0 0
\(215\) −7.65140 10.7449i −0.521821 0.732795i
\(216\) 0 0
\(217\) −15.3019 + 19.1798i −1.03876 + 1.30201i
\(218\) 0 0
\(219\) 2.05741 + 0.823663i 0.139027 + 0.0556580i
\(220\) 0 0
\(221\) 0.324265 + 0.0624969i 0.0218124 + 0.00420400i
\(222\) 0 0
\(223\) −20.9312 13.4517i −1.40166 0.900792i −0.401771 0.915740i \(-0.631605\pi\)
−0.999888 + 0.0149486i \(0.995242\pi\)
\(224\) 0 0
\(225\) 13.2202 + 15.2569i 0.881345 + 1.01713i
\(226\) 0 0
\(227\) −2.87711 + 4.04033i −0.190960 + 0.268166i −0.898945 0.438062i \(-0.855665\pi\)
0.707985 + 0.706228i \(0.249605\pi\)
\(228\) 0 0
\(229\) −9.49777 + 16.4506i −0.627630 + 1.08709i 0.360396 + 0.932800i \(0.382642\pi\)
−0.988026 + 0.154288i \(0.950692\pi\)
\(230\) 0 0
\(231\) 1.11975 + 0.984094i 0.0736742 + 0.0647486i
\(232\) 0 0
\(233\) 9.66231 + 0.922638i 0.632999 + 0.0604440i 0.406623 0.913596i \(-0.366706\pi\)
0.226376 + 0.974040i \(0.427312\pi\)
\(234\) 0 0
\(235\) 3.29421 9.51799i 0.214890 0.620885i
\(236\) 0 0
\(237\) −0.925981 0.595092i −0.0601489 0.0386554i
\(238\) 0 0
\(239\) 11.7079 13.5117i 0.757324 0.873998i −0.237933 0.971282i \(-0.576470\pi\)
0.995257 + 0.0972836i \(0.0310154\pi\)
\(240\) 0 0
\(241\) 1.43026 1.12477i 0.0921310 0.0724526i −0.571031 0.820928i \(-0.693456\pi\)
0.663162 + 0.748476i \(0.269214\pi\)
\(242\) 0 0
\(243\) 0.689319 + 14.4706i 0.0442198 + 0.928288i
\(244\) 0 0
\(245\) −6.50073 28.5364i −0.415317 1.82312i
\(246\) 0 0
\(247\) −2.60072 + 10.7203i −0.165480 + 0.682117i
\(248\) 0 0
\(249\) 0.594834 + 2.45194i 0.0376961 + 0.155385i
\(250\) 0 0
\(251\) −1.67120 + 11.6234i −0.105485 + 0.733664i 0.866595 + 0.499013i \(0.166304\pi\)
−0.972080 + 0.234651i \(0.924605\pi\)
\(252\) 0 0
\(253\) 0.748773 2.17271i 0.0470749 0.136597i
\(254\) 0 0
\(255\) 1.14227 0.457296i 0.0715317 0.0286370i
\(256\) 0 0
\(257\) 13.4913 12.8639i 0.841566 0.802431i −0.140675 0.990056i \(-0.544927\pi\)
0.982241 + 0.187625i \(0.0600789\pi\)
\(258\) 0 0
\(259\) −8.28118 3.85226i −0.514567 0.239368i
\(260\) 0 0
\(261\) −8.46086 11.8816i −0.523714 0.735453i
\(262\) 0 0
\(263\) 23.9971 + 12.3714i 1.47973 + 0.762851i 0.993804 0.111151i \(-0.0354537\pi\)
0.485922 + 0.874002i \(0.338484\pi\)
\(264\) 0 0
\(265\) −4.20743 29.2633i −0.258461 1.79763i
\(266\) 0 0
\(267\) 3.33823 3.85252i 0.204296 0.235770i
\(268\) 0 0
\(269\) −1.06400 + 22.3361i −0.0648732 + 1.36186i 0.698366 + 0.715741i \(0.253911\pi\)
−0.763239 + 0.646116i \(0.776392\pi\)
\(270\) 0 0
\(271\) 19.7787 3.81204i 1.20147 0.231565i 0.451035 0.892506i \(-0.351055\pi\)
0.750437 + 0.660941i \(0.229843\pi\)
\(272\) 0 0
\(273\) −2.81176 2.99058i −0.170175 0.180998i
\(274\) 0 0
\(275\) −2.99047 + 5.17964i −0.180332 + 0.312344i
\(276\) 0 0
\(277\) −0.781827 1.35416i −0.0469755 0.0813639i 0.841582 0.540130i \(-0.181625\pi\)
−0.888557 + 0.458766i \(0.848292\pi\)
\(278\) 0 0
\(279\) −6.23108 13.6442i −0.373045 0.816854i
\(280\) 0 0
\(281\) 20.7365 + 23.9312i 1.23704 + 1.42762i 0.866784 + 0.498684i \(0.166183\pi\)
0.370252 + 0.928931i \(0.379271\pi\)
\(282\) 0 0
\(283\) 0.521671 10.9512i 0.0310101 0.650982i −0.928842 0.370476i \(-0.879195\pi\)
0.959852 0.280506i \(-0.0905023\pi\)
\(284\) 0 0
\(285\) 13.4429 + 38.8406i 0.796287 + 2.30072i
\(286\) 0 0
\(287\) 10.3127 + 0.563720i 0.608740 + 0.0332753i
\(288\) 0 0
\(289\) −0.805912 16.9182i −0.0474066 0.995187i
\(290\) 0 0
\(291\) −20.0715 + 1.91659i −1.17661 + 0.112353i
\(292\) 0 0
\(293\) −20.1593 + 5.91930i −1.17772 + 0.345809i −0.811294 0.584638i \(-0.801236\pi\)
−0.366425 + 0.930448i \(0.619418\pi\)
\(294\) 0 0
\(295\) −30.9222 9.07958i −1.80036 0.528634i
\(296\) 0 0
\(297\) −2.41530 + 0.966941i −0.140150 + 0.0561076i
\(298\) 0 0
\(299\) −2.62114 + 5.75961i −0.151585 + 0.333087i
\(300\) 0 0
\(301\) −7.86862 2.78526i −0.453540 0.160540i
\(302\) 0 0
\(303\) −8.14859 + 7.76967i −0.468124 + 0.446356i
\(304\) 0 0
\(305\) 36.4790 + 34.7827i 2.08878 + 1.99165i
\(306\) 0 0
\(307\) 4.66854 10.2227i 0.266447 0.583439i −0.728362 0.685192i \(-0.759718\pi\)
0.994810 + 0.101754i \(0.0324454\pi\)
\(308\) 0 0
\(309\) −10.5469 + 6.77806i −0.599991 + 0.385591i
\(310\) 0 0
\(311\) 13.7288 10.7964i 0.778489 0.612210i −0.147803 0.989017i \(-0.547220\pi\)
0.926292 + 0.376807i \(0.122978\pi\)
\(312\) 0 0
\(313\) −5.51137 15.9241i −0.311521 0.900081i −0.986718 0.162444i \(-0.948062\pi\)
0.675197 0.737638i \(-0.264059\pi\)
\(314\) 0 0
\(315\) 17.3578 + 4.34000i 0.978003 + 0.244531i
\(316\) 0 0
\(317\) 23.5785 4.54439i 1.32430 0.255238i 0.522404 0.852698i \(-0.325035\pi\)
0.801899 + 0.597460i \(0.203823\pi\)
\(318\) 0 0
\(319\) 2.50666 3.52011i 0.140346 0.197088i
\(320\) 0 0
\(321\) 13.1933 0.736378
\(322\) 0 0
\(323\) −2.09238 −0.116423
\(324\) 0 0
\(325\) 9.55288 13.4151i 0.529898 0.744138i
\(326\) 0 0
\(327\) −6.52205 + 1.25702i −0.360670 + 0.0695134i
\(328\) 0 0
\(329\) −1.75271 6.12771i −0.0966298 0.337832i
\(330\) 0 0
\(331\) 6.36796 + 18.3990i 0.350015 + 1.01130i 0.973346 + 0.229343i \(0.0736577\pi\)
−0.623331 + 0.781958i \(0.714221\pi\)
\(332\) 0 0
\(333\) 4.38893 3.45149i 0.240512 0.189141i
\(334\) 0 0
\(335\) 41.0190 26.3613i 2.24111 1.44027i
\(336\) 0 0
\(337\) 6.26208 13.7120i 0.341117 0.746942i −0.658869 0.752258i \(-0.728965\pi\)
0.999986 + 0.00531552i \(0.00169199\pi\)
\(338\) 0 0
\(339\) 5.02016 + 4.78671i 0.272658 + 0.259979i
\(340\) 0 0
\(341\) 3.21619 3.06663i 0.174166 0.166067i
\(342\) 0 0
\(343\) −13.7386 12.4198i −0.741815 0.670605i
\(344\) 0 0
\(345\) 3.38620 + 23.3329i 0.182307 + 1.25620i
\(346\) 0 0
\(347\) 13.9569 5.58748i 0.749243 0.299952i 0.0345626 0.999403i \(-0.488996\pi\)
0.714681 + 0.699451i \(0.246572\pi\)
\(348\) 0 0
\(349\) 10.9902 + 3.22703i 0.588294 + 0.172739i 0.562314 0.826924i \(-0.309911\pi\)
0.0259800 + 0.999662i \(0.491729\pi\)
\(350\) 0 0
\(351\) 6.87365 2.01829i 0.366888 0.107728i
\(352\) 0 0
\(353\) −25.2657 + 2.41258i −1.34476 + 0.128409i −0.742474 0.669874i \(-0.766348\pi\)
−0.602282 + 0.798283i \(0.705742\pi\)
\(354\) 0 0
\(355\) −1.77209 37.2007i −0.0940526 1.97441i
\(356\) 0 0
\(357\) 0.425519 0.652027i 0.0225208 0.0345089i
\(358\) 0 0
\(359\) 1.34111 + 3.87488i 0.0707810 + 0.204508i 0.974843 0.222894i \(-0.0715502\pi\)
−0.904062 + 0.427402i \(0.859429\pi\)
\(360\) 0 0
\(361\) 2.42169 50.8375i 0.127457 2.67566i
\(362\) 0 0
\(363\) 8.29321 + 9.57088i 0.435281 + 0.502341i
\(364\) 0 0
\(365\) 3.27362 + 7.16822i 0.171349 + 0.375202i
\(366\) 0 0
\(367\) −3.66823 6.35356i −0.191480 0.331653i 0.754261 0.656575i \(-0.227995\pi\)
−0.945741 + 0.324922i \(0.894662\pi\)
\(368\) 0 0
\(369\) −3.15695 + 5.46800i −0.164344 + 0.284653i
\(370\) 0 0
\(371\) −12.8148 13.6298i −0.665313 0.707624i
\(372\) 0 0
\(373\) −18.1223 + 3.49278i −0.938335 + 0.180849i −0.635419 0.772168i \(-0.719172\pi\)
−0.302917 + 0.953017i \(0.597960\pi\)
\(374\) 0 0
\(375\) 1.75006 36.7383i 0.0903727 1.89716i
\(376\) 0 0
\(377\) −7.79235 + 8.99285i −0.401326 + 0.463155i
\(378\) 0 0
\(379\) 3.13327 + 21.7923i 0.160945 + 1.11940i 0.896857 + 0.442320i \(0.145845\pi\)
−0.735912 + 0.677077i \(0.763246\pi\)
\(380\) 0 0
\(381\) 4.00777 + 2.06615i 0.205324 + 0.105852i
\(382\) 0 0
\(383\) 16.7562 + 23.5307i 0.856200 + 1.20236i 0.977749 + 0.209779i \(0.0672744\pi\)
−0.121549 + 0.992585i \(0.538786\pi\)
\(384\) 0 0
\(385\) 0.466882 + 5.28023i 0.0237945 + 0.269106i
\(386\) 0 0
\(387\) 3.69308 3.52134i 0.187730 0.179000i
\(388\) 0 0
\(389\) −7.66489 + 3.06856i −0.388625 + 0.155582i −0.557743 0.830014i \(-0.688332\pi\)
0.169118 + 0.985596i \(0.445908\pi\)
\(390\) 0 0
\(391\) −1.17889 0.225598i −0.0596188 0.0114090i
\(392\) 0 0
\(393\) 1.33061 9.25461i 0.0671205 0.466833i
\(394\) 0 0
\(395\) −0.922758 3.80366i −0.0464290 0.191383i
\(396\) 0 0
\(397\) 4.65760 19.1989i 0.233758 0.963564i −0.727102 0.686530i \(-0.759133\pi\)
0.960860 0.277035i \(-0.0893517\pi\)
\(398\) 0 0
\(399\) 21.0796 + 15.2345i 1.05530 + 0.762680i
\(400\) 0 0
\(401\) −0.802775 16.8523i −0.0400887 0.841564i −0.925957 0.377628i \(-0.876740\pi\)
0.885869 0.463936i \(-0.153563\pi\)
\(402\) 0 0
\(403\) −9.61852 + 7.56409i −0.479133 + 0.376794i
\(404\) 0 0
\(405\) 4.19357 4.83964i 0.208380 0.240483i
\(406\) 0 0
\(407\) 1.39160 + 0.894328i 0.0689791 + 0.0443302i
\(408\) 0 0
\(409\) 3.21864 9.29966i 0.159152 0.459838i −0.837029 0.547159i \(-0.815709\pi\)
0.996180 + 0.0873206i \(0.0278305\pi\)
\(410\) 0 0
\(411\) 16.1230 + 1.53956i 0.795287 + 0.0759407i
\(412\) 0 0
\(413\) −19.3181 + 6.53481i −0.950580 + 0.321557i
\(414\) 0 0
\(415\) −4.48583 + 7.76968i −0.220201 + 0.381399i
\(416\) 0 0
\(417\) 7.01208 9.84709i 0.343383 0.482214i
\(418\) 0 0
\(419\) 5.99929 + 6.92355i 0.293085 + 0.338238i 0.883126 0.469135i \(-0.155434\pi\)
−0.590042 + 0.807373i \(0.700889\pi\)
\(420\) 0 0
\(421\) −1.08324 0.696159i −0.0527941 0.0339287i 0.513978 0.857804i \(-0.328171\pi\)
−0.566772 + 0.823875i \(0.691808\pi\)
\(422\) 0 0
\(423\) 3.82589 + 0.737379i 0.186021 + 0.0358526i
\(424\) 0 0
\(425\) 2.90001 + 1.16099i 0.140671 + 0.0563163i
\(426\) 0 0
\(427\) 31.5380 + 4.76031i 1.52623 + 0.230368i
\(428\) 0 0
\(429\) 0.431244 + 0.605598i 0.0208207 + 0.0292385i
\(430\) 0 0
\(431\) 4.43664 + 4.23033i 0.213705 + 0.203768i 0.789369 0.613919i \(-0.210408\pi\)
−0.575664 + 0.817686i \(0.695256\pi\)
\(432\) 0 0
\(433\) 5.52525 + 1.62236i 0.265527 + 0.0779657i 0.411786 0.911281i \(-0.364905\pi\)
−0.146259 + 0.989246i \(0.546723\pi\)
\(434\) 0 0
\(435\) −6.30954 + 43.8838i −0.302519 + 2.10407i
\(436\) 0 0
\(437\) 9.40126 38.9770i 0.449723 1.86452i
\(438\) 0 0
\(439\) 5.68118 + 4.46773i 0.271148 + 0.213233i 0.744469 0.667657i \(-0.232703\pi\)
−0.473321 + 0.880890i \(0.656945\pi\)
\(440\) 0 0
\(441\) 10.5690 4.06024i 0.503284 0.193345i
\(442\) 0 0
\(443\) −2.68977 + 11.0874i −0.127795 + 0.526777i 0.871541 + 0.490324i \(0.163121\pi\)
−0.999335 + 0.0364539i \(0.988394\pi\)
\(444\) 0 0
\(445\) 18.0443 1.72302i 0.855383 0.0816791i
\(446\) 0 0
\(447\) 11.0077 7.07424i 0.520648 0.334600i
\(448\) 0 0
\(449\) −1.94753 13.5453i −0.0919094 0.639244i −0.982752 0.184931i \(-0.940794\pi\)
0.890842 0.454313i \(-0.150115\pi\)
\(450\) 0 0
\(451\) −1.83679 0.354012i −0.0864909 0.0166698i
\(452\) 0 0
\(453\) −18.5252 + 9.55038i −0.870388 + 0.448716i
\(454\) 0 0
\(455\) 0.102295 14.5958i 0.00479568 0.684262i
\(456\) 0 0
\(457\) −28.3468 2.70679i −1.32601 0.126618i −0.592098 0.805866i \(-0.701700\pi\)
−0.733909 + 0.679247i \(0.762306\pi\)
\(458\) 0 0
\(459\) 0.679409 + 1.17677i 0.0317121 + 0.0549270i
\(460\) 0 0
\(461\) −21.6390 −1.00783 −0.503914 0.863754i \(-0.668107\pi\)
−0.503914 + 0.863754i \(0.668107\pi\)
\(462\) 0 0
\(463\) −5.02073 10.9939i −0.233333 0.510929i 0.756356 0.654160i \(-0.226978\pi\)
−0.989689 + 0.143232i \(0.954251\pi\)
\(464\) 0 0
\(465\) −14.9116 + 43.0841i −0.691507 + 1.99798i
\(466\) 0 0
\(467\) −11.7826 + 6.07437i −0.545236 + 0.281088i −0.708759 0.705451i \(-0.750744\pi\)
0.163523 + 0.986540i \(0.447714\pi\)
\(468\) 0 0
\(469\) 11.6679 28.5633i 0.538776 1.31893i
\(470\) 0 0
\(471\) −21.0672 8.43404i −0.970725 0.388620i
\(472\) 0 0
\(473\) 1.34373 + 0.692741i 0.0617847 + 0.0318522i
\(474\) 0 0
\(475\) −43.3478 + 94.9185i −1.98893 + 4.35516i
\(476\) 0 0
\(477\) 10.9736 3.22213i 0.502445 0.147531i
\(478\) 0 0
\(479\) −2.37275 9.78062i −0.108414 0.446888i 0.891568 0.452887i \(-0.149606\pi\)
−0.999982 + 0.00599853i \(0.998091\pi\)
\(480\) 0 0
\(481\) −3.58042 2.81567i −0.163253 0.128384i
\(482\) 0 0
\(483\) 10.2341 + 10.8562i 0.465667 + 0.493973i
\(484\) 0 0
\(485\) −56.3569 44.3196i −2.55903 2.01245i
\(486\) 0 0
\(487\) 7.32837 + 30.2079i 0.332080 + 1.36885i 0.855952 + 0.517056i \(0.172972\pi\)
−0.523872 + 0.851797i \(0.675513\pi\)
\(488\) 0 0
\(489\) 6.50161 1.90904i 0.294013 0.0863300i
\(490\) 0 0
\(491\) 1.54913 3.39213i 0.0699114 0.153085i −0.871450 0.490484i \(-0.836820\pi\)
0.941362 + 0.337399i \(0.109547\pi\)
\(492\) 0 0
\(493\) −2.00612 1.03423i −0.0903510 0.0465792i
\(494\) 0 0
\(495\) −3.00844 1.20440i −0.135219 0.0541337i
\(496\) 0 0
\(497\) −14.4380 18.6266i −0.647632 0.835516i
\(498\) 0 0
\(499\) −4.73178 + 2.43940i −0.211823 + 0.109203i −0.560874 0.827901i \(-0.689535\pi\)
0.349050 + 0.937104i \(0.386504\pi\)
\(500\) 0 0
\(501\) 0.945499 2.73184i 0.0422418 0.122050i
\(502\) 0 0
\(503\) 8.82443 + 19.3228i 0.393462 + 0.861562i 0.997892 + 0.0649032i \(0.0206739\pi\)
−0.604429 + 0.796659i \(0.706599\pi\)
\(504\) 0 0
\(505\) −40.0358 −1.78157
\(506\) 0 0
\(507\) 6.61930 + 11.4650i 0.293973 + 0.509177i
\(508\) 0 0
\(509\) 16.0026 + 1.52806i 0.709303 + 0.0677303i 0.443471 0.896289i \(-0.353747\pi\)
0.265833 + 0.964019i \(0.414353\pi\)
\(510\) 0 0
\(511\) 4.30097 + 2.52352i 0.190264 + 0.111634i
\(512\) 0 0
\(513\) −40.3449 + 20.7992i −1.78127 + 0.918308i
\(514\) 0 0
\(515\) −43.7745 8.43685i −1.92894 0.371772i
\(516\) 0 0
\(517\) 0.164279 + 1.14259i 0.00722500 + 0.0502510i
\(518\) 0 0
\(519\) 16.6795 10.7193i 0.732148 0.470523i
\(520\) 0 0
\(521\) −23.1284 + 2.20849i −1.01327 + 0.0967558i −0.588461 0.808526i \(-0.700266\pi\)
−0.424812 + 0.905282i \(0.639660\pi\)
\(522\) 0 0
\(523\) −7.33356 + 30.2294i −0.320674 + 1.32184i 0.552126 + 0.833760i \(0.313817\pi\)
−0.872801 + 0.488077i \(0.837699\pi\)
\(524\) 0 0
\(525\) −20.7630 32.8112i −0.906171 1.43200i
\(526\) 0 0
\(527\) −1.82442 1.43474i −0.0794729 0.0624982i
\(528\) 0 0
\(529\) 9.49929 20.9467i 0.413013 0.910725i
\(530\) 0 0
\(531\) 1.77426 12.3403i 0.0769964 0.535522i
\(532\) 0 0
\(533\) 4.94214 + 1.45114i 0.214068 + 0.0628560i
\(534\) 0 0
\(535\) 33.9529 + 32.3740i 1.46791 + 1.39965i
\(536\) 0 0
\(537\) 2.69466 + 3.78413i 0.116283 + 0.163297i
\(538\) 0 0
\(539\) 2.16087 + 2.56557i 0.0930753 + 0.110507i
\(540\) 0 0
\(541\) 14.5740 + 5.83453i 0.626583 + 0.250846i 0.663152 0.748485i \(-0.269218\pi\)
−0.0365683 + 0.999331i \(0.511643\pi\)
\(542\) 0 0
\(543\) −0.689258 0.132844i −0.0295789 0.00570086i
\(544\) 0 0
\(545\) −19.8690 12.7690i −0.851093 0.546964i
\(546\) 0 0
\(547\) 4.06678 + 4.69332i 0.173883 + 0.200672i 0.836001 0.548728i \(-0.184888\pi\)
−0.662118 + 0.749400i \(0.730342\pi\)
\(548\) 0 0
\(549\) −11.3103 + 15.8831i −0.482711 + 0.677873i
\(550\) 0 0
\(551\) 37.6973 65.2937i 1.60596 2.78161i
\(552\) 0 0
\(553\) −1.86039 1.63500i −0.0791117 0.0695273i
\(554\) 0 0
\(555\) −16.8943 1.61321i −0.717123 0.0684769i
\(556\) 0 0
\(557\) −7.69400 + 22.2303i −0.326005 + 0.941930i 0.656277 + 0.754520i \(0.272130\pi\)
−0.982282 + 0.187410i \(0.939991\pi\)
\(558\) 0 0
\(559\) −3.50196 2.25058i −0.148117 0.0951892i
\(560\) 0 0
\(561\) −0.0923459 + 0.106573i −0.00389885 + 0.00449951i
\(562\) 0 0
\(563\) −12.4030 + 9.75386i −0.522726 + 0.411076i −0.844351 0.535791i \(-0.820014\pi\)
0.321625 + 0.946867i \(0.395771\pi\)
\(564\) 0 0
\(565\) 1.17361 + 24.6372i 0.0493743 + 1.03649i
\(566\) 0 0
\(567\) 0.413453 4.03110i 0.0173634 0.169290i
\(568\) 0 0
\(569\) 4.05805 16.7275i 0.170122 0.701253i −0.821293 0.570506i \(-0.806747\pi\)
0.991416 0.130747i \(-0.0417377\pi\)
\(570\) 0 0
\(571\) 8.26697 + 34.0769i 0.345962 + 1.42607i 0.833281 + 0.552850i \(0.186460\pi\)
−0.487319 + 0.873224i \(0.662025\pi\)
\(572\) 0 0
\(573\) 0.853242 5.93443i 0.0356447 0.247914i
\(574\) 0 0
\(575\) −34.6569 + 48.8051i −1.44529 + 2.03531i
\(576\) 0 0
\(577\) −21.5401 + 8.62336i −0.896726 + 0.358995i −0.773807 0.633422i \(-0.781650\pi\)
−0.122919 + 0.992417i \(0.539226\pi\)
\(578\) 0 0
\(579\) 1.74847 1.66716i 0.0726640 0.0692850i
\(580\) 0 0
\(581\) 0.500031 + 5.65513i 0.0207448 + 0.234615i
\(582\) 0 0
\(583\) 1.96543 + 2.76006i 0.0813998 + 0.114310i
\(584\) 0 0
\(585\) 7.93117 + 4.08880i 0.327914 + 0.169051i
\(586\) 0 0
\(587\) 3.76917 + 26.2152i 0.155570 + 1.08202i 0.906674 + 0.421832i \(0.138613\pi\)
−0.751104 + 0.660184i \(0.770478\pi\)
\(588\) 0 0
\(589\) 50.7723 58.5944i 2.09204 2.41434i
\(590\) 0 0
\(591\) 0.650978 13.6657i 0.0267777 0.562132i
\(592\) 0 0
\(593\) −10.8174 + 2.08489i −0.444218 + 0.0856161i −0.406455 0.913671i \(-0.633235\pi\)
−0.0377630 + 0.999287i \(0.512023\pi\)
\(594\) 0 0
\(595\) 2.69503 0.633841i 0.110485 0.0259850i
\(596\) 0 0
\(597\) 5.14252 8.90710i 0.210469 0.364543i
\(598\) 0 0
\(599\) −7.35854 12.7454i −0.300662 0.520762i 0.675624 0.737246i \(-0.263874\pi\)
−0.976286 + 0.216484i \(0.930541\pi\)
\(600\) 0 0
\(601\) 9.36587 + 20.5084i 0.382042 + 0.836555i 0.998780 + 0.0493866i \(0.0157266\pi\)
−0.616738 + 0.787169i \(0.711546\pi\)
\(602\) 0 0
\(603\) 12.3522 + 14.2552i 0.503022 + 0.580518i
\(604\) 0 0
\(605\) −2.14270 + 44.9807i −0.0871129 + 1.82873i
\(606\) 0 0
\(607\) −8.17682 23.6254i −0.331887 0.958925i −0.980279 0.197618i \(-0.936679\pi\)
0.648392 0.761307i \(-0.275442\pi\)
\(608\) 0 0
\(609\) 12.6804 + 25.0257i 0.513837 + 1.01409i
\(610\) 0 0
\(611\) −0.151241 3.17494i −0.00611855 0.128444i
\(612\) 0 0
\(613\) −40.7720 + 3.89325i −1.64676 + 0.157247i −0.876805 0.480846i \(-0.840330\pi\)
−0.769959 + 0.638093i \(0.779724\pi\)
\(614\) 0 0
\(615\) 18.4138 5.40678i 0.742516 0.218023i
\(616\) 0 0
\(617\) −11.8520 3.48005i −0.477143 0.140102i 0.0343134 0.999411i \(-0.489076\pi\)
−0.511456 + 0.859309i \(0.670894\pi\)
\(618\) 0 0
\(619\) −31.9252 + 12.7809i −1.28318 + 0.513708i −0.910215 0.414136i \(-0.864084\pi\)
−0.372967 + 0.927845i \(0.621659\pi\)
\(620\) 0 0
\(621\) −24.9736 + 7.36872i −1.00215 + 0.295696i
\(622\) 0 0
\(623\) 8.72107 7.45048i 0.349402 0.298497i
\(624\) 0 0
\(625\) 49.4871 47.1858i 1.97948 1.88743i
\(626\) 0 0
\(627\) −3.40920 3.25067i −0.136150 0.129819i
\(628\) 0 0
\(629\) 0.358906 0.785894i 0.0143105 0.0313356i
\(630\) 0 0
\(631\) −10.1279 + 6.50882i −0.403186 + 0.259112i −0.726481 0.687186i \(-0.758846\pi\)
0.323295 + 0.946298i \(0.395209\pi\)
\(632\) 0 0
\(633\) −3.88757 + 3.05722i −0.154517 + 0.121513i
\(634\) 0 0
\(635\) 5.24402 + 15.1516i 0.208102 + 0.601273i
\(636\) 0 0
\(637\) −5.25162 7.59806i −0.208077 0.301046i
\(638\) 0 0
\(639\) 14.1469 2.72660i 0.559644 0.107863i
\(640\) 0 0
\(641\) 19.6829 27.6407i 0.777427 1.09174i −0.215901 0.976415i \(-0.569269\pi\)
0.993327 0.115328i \(-0.0367918\pi\)
\(642\) 0 0
\(643\) −23.3294 −0.920021 −0.460011 0.887913i \(-0.652154\pi\)
−0.460011 + 0.887913i \(0.652154\pi\)
\(644\) 0 0
\(645\) −15.5101 −0.610708
\(646\) 0 0
\(647\) 16.0670 22.5629i 0.631659 0.887041i −0.367416 0.930057i \(-0.619757\pi\)
0.999074 + 0.0430163i \(0.0136967\pi\)
\(648\) 0 0
\(649\) 3.62684 0.699017i 0.142366 0.0274388i
\(650\) 0 0
\(651\) 7.93380 + 27.7377i 0.310950 + 1.08713i
\(652\) 0 0
\(653\) 10.7688 + 31.1145i 0.421418 + 1.21761i 0.933471 + 0.358653i \(0.116764\pi\)
−0.512053 + 0.858954i \(0.671115\pi\)
\(654\) 0 0
\(655\) 26.1335 20.5516i 1.02112 0.803018i
\(656\) 0 0
\(657\) −2.56455 + 1.64814i −0.100053 + 0.0643000i
\(658\) 0 0
\(659\) 3.49641 7.65608i 0.136201 0.298238i −0.829225 0.558914i \(-0.811218\pi\)
0.965426 + 0.260676i \(0.0839454\pi\)
\(660\) 0 0
\(661\) −20.6241 19.6650i −0.802184 0.764881i 0.173319 0.984866i \(-0.444551\pi\)
−0.975503 + 0.219985i \(0.929399\pi\)
\(662\) 0 0
\(663\) 0.281023 0.267955i 0.0109140 0.0104065i
\(664\) 0 0
\(665\) 16.8656 + 90.9317i 0.654019 + 3.52618i
\(666\) 0 0
\(667\) 28.2792 32.7232i 1.09498 1.26705i
\(668\) 0 0
\(669\) −27.1601 + 10.8733i −1.05007 + 0.420384i
\(670\) 0 0
\(671\) −5.54276 1.62750i −0.213976 0.0628290i
\(672\) 0 0
\(673\) 24.2961 7.13399i 0.936548 0.274995i 0.222372 0.974962i \(-0.428620\pi\)
0.714175 + 0.699967i \(0.246802\pi\)
\(674\) 0 0
\(675\) 67.4581 6.44147i 2.59647 0.247932i
\(676\) 0 0
\(677\) −0.516723 10.8474i −0.0198593 0.416898i −0.986805 0.161915i \(-0.948233\pi\)
0.966945 0.254983i \(-0.0820699\pi\)
\(678\) 0 0
\(679\) −45.3011 2.47628i −1.73850 0.0950309i
\(680\) 0 0
\(681\) 1.90751 + 5.51138i 0.0730959 + 0.211197i
\(682\) 0 0
\(683\) 0.857266 17.9962i 0.0328024 0.688607i −0.921251 0.388969i \(-0.872831\pi\)
0.954053 0.299638i \(-0.0968658\pi\)
\(684\) 0 0
\(685\) 37.7146 + 43.5249i 1.44100 + 1.66300i
\(686\) 0 0
\(687\) 9.27848 + 20.3170i 0.353996 + 0.775143i
\(688\) 0 0
\(689\) −4.66500 8.08001i −0.177722 0.307824i
\(690\) 0 0
\(691\) −0.678474 + 1.17515i −0.0258104 + 0.0447049i −0.878642 0.477481i \(-0.841550\pi\)
0.852832 + 0.522186i \(0.174883\pi\)
\(692\) 0 0
\(693\) −1.99615 + 0.469471i −0.0758273 + 0.0178337i
\(694\) 0 0
\(695\) 42.2086 8.13504i 1.60106 0.308580i
\(696\) 0 0
\(697\) −0.0464870 + 0.975881i −0.00176082 + 0.0369641i
\(698\) 0 0
\(699\) 7.47384 8.62527i 0.282687 0.326238i
\(700\) 0 0
\(701\) −2.72100 18.9250i −0.102771 0.714787i −0.974433 0.224679i \(-0.927867\pi\)
0.871662 0.490108i \(-0.163043\pi\)
\(702\) 0 0
\(703\) 25.6522 + 13.2246i 0.967492 + 0.498777i
\(704\) 0 0
\(705\) −6.86952 9.64690i −0.258721 0.363323i
\(706\) 0 0
\(707\) −20.7392 + 14.5504i −0.779979 + 0.547223i
\(708\) 0 0
\(709\) −12.9466 + 12.3445i −0.486219 + 0.463609i −0.893091 0.449876i \(-0.851468\pi\)
0.406872 + 0.913485i \(0.366620\pi\)
\(710\) 0 0
\(711\) 1.40566 0.562740i 0.0527162 0.0211044i
\(712\) 0 0
\(713\) 34.9236 27.5389i 1.30790 1.03134i
\(714\) 0 0
\(715\) −0.376225 + 2.61670i −0.0140700 + 0.0978591i
\(716\) 0 0
\(717\) −4.95613 20.4294i −0.185090 0.762951i
\(718\) 0 0
\(719\) 5.83686 24.0599i 0.217678 0.897282i −0.753216 0.657773i \(-0.771499\pi\)
0.970894 0.239508i \(-0.0769863\pi\)
\(720\) 0 0
\(721\) −25.7422 + 11.5387i −0.958690 + 0.429724i
\(722\) 0 0
\(723\) −0.101800 2.13704i −0.00378598 0.0794775i
\(724\) 0 0
\(725\) −88.4771 + 69.5792i −3.28596 + 2.58411i
\(726\) 0 0
\(727\) 17.0729 19.7032i 0.633200 0.730752i −0.344957 0.938619i \(-0.612106\pi\)
0.978157 + 0.207866i \(0.0666519\pi\)
\(728\) 0 0
\(729\) 18.1955 + 11.6935i 0.673906 + 0.433093i
\(730\) 0 0
\(731\) 0.258249 0.746162i 0.00955168 0.0275978i
\(732\) 0 0
\(733\) −36.2171 3.45832i −1.33771 0.127736i −0.598452 0.801159i \(-0.704217\pi\)
−0.739258 + 0.673423i \(0.764823\pi\)
\(734\) 0 0
\(735\) −31.7660 13.2367i −1.17170 0.488245i
\(736\) 0 0
\(737\) −2.79414 + 4.83959i −0.102923 + 0.178269i
\(738\) 0 0
\(739\) 3.84585 5.40074i 0.141472 0.198670i −0.737761 0.675063i \(-0.764117\pi\)
0.879232 + 0.476393i \(0.158056\pi\)
\(740\) 0 0
\(741\) 8.49410 + 9.80271i 0.312039 + 0.360112i
\(742\) 0 0
\(743\) 6.27045 + 4.02977i 0.230041 + 0.147838i 0.650584 0.759434i \(-0.274524\pi\)
−0.420543 + 0.907272i \(0.638161\pi\)
\(744\) 0 0
\(745\) 45.6873 + 8.80550i 1.67385 + 0.322609i
\(746\) 0 0
\(747\) −3.22205 1.28991i −0.117888 0.0471954i
\(748\) 0 0
\(749\) 29.3540 + 4.43067i 1.07257 + 0.161893i
\(750\) 0 0
\(751\) −10.6010 14.8870i −0.386835 0.543233i 0.574540 0.818477i \(-0.305181\pi\)
−0.961375 + 0.275243i \(0.911242\pi\)
\(752\) 0 0
\(753\) 9.99307 + 9.52838i 0.364168 + 0.347233i
\(754\) 0 0
\(755\) −71.1094 20.8796i −2.58794 0.759886i
\(756\) 0 0
\(757\) 0.806408 5.60869i 0.0293094 0.203851i −0.969905 0.243484i \(-0.921710\pi\)
0.999214 + 0.0396327i \(0.0126188\pi\)
\(758\) 0 0
\(759\) −1.57032 2.19906i −0.0569991 0.0798209i
\(760\) 0 0
\(761\) −26.3254 20.7025i −0.954294 0.750465i 0.0140972 0.999901i \(-0.495513\pi\)
−0.968391 + 0.249435i \(0.919755\pi\)
\(762\) 0 0
\(763\) −14.9332 + 0.606492i −0.540617 + 0.0219565i
\(764\) 0 0
\(765\) −0.399025 + 1.64480i −0.0144268 + 0.0594680i
\(766\) 0 0
\(767\) −10.1245 + 0.966769i −0.365573 + 0.0349080i
\(768\) 0 0
\(769\) −35.2920 + 22.6808i −1.27266 + 0.817889i −0.989964 0.141320i \(-0.954865\pi\)
−0.282697 + 0.959209i \(0.591229\pi\)
\(770\) 0 0
\(771\) −3.11938 21.6958i −0.112342 0.781355i
\(772\) 0 0
\(773\) 33.0908 + 6.37773i 1.19019 + 0.229391i 0.745632 0.666358i \(-0.232148\pi\)
0.444561 + 0.895749i \(0.353360\pi\)
\(774\) 0 0
\(775\) −102.882 + 53.0391i −3.69562 + 1.90522i
\(776\) 0 0
\(777\) −9.33783 + 5.30429i −0.334993 + 0.190290i
\(778\) 0 0
\(779\) −32.4881 3.10223i −1.16401 0.111149i
\(780\) 0 0
\(781\) 2.13419 + 3.69653i 0.0763674 + 0.132272i
\(782\) 0 0
\(783\) −48.9622 −1.74977
\(784\) 0 0
\(785\) −33.5207 73.4002i −1.19641 2.61976i
\(786\) 0 0
\(787\) −1.31627 + 3.80312i −0.0469201 + 0.135567i −0.966027 0.258442i \(-0.916791\pi\)
0.919107 + 0.394009i \(0.128912\pi\)
\(788\) 0 0
\(789\) 28.2164 14.5466i 1.00453 0.517872i
\(790\) 0 0
\(791\) 9.56195 + 12.3360i 0.339984 + 0.438616i
\(792\) 0 0
\(793\) 14.7672 + 5.91190i 0.524399 + 0.209938i
\(794\) 0 0
\(795\) −30.8981 15.9291i −1.09584 0.564946i
\(796\) 0 0
\(797\) 3.43410 7.51962i 0.121642 0.266359i −0.839009 0.544118i \(-0.816864\pi\)
0.960651 + 0.277759i \(0.0895917\pi\)
\(798\) 0 0
\(799\) 0.578476 0.169856i 0.0204650 0.00600907i
\(800\) 0 0
\(801\) 1.65317 + 6.81448i 0.0584120 + 0.240778i
\(802\) 0 0
\(803\) −0.709933 0.558298i −0.0250530 0.0197019i
\(804\) 0 0
\(805\) −0.301792 + 53.0510i −0.0106368 + 1.86980i
\(806\) 0 0
\(807\) 20.6678 + 16.2534i 0.727542 + 0.572145i
\(808\) 0 0
\(809\) 8.35965 + 34.4589i 0.293910 + 1.21151i 0.906874 + 0.421401i \(0.138462\pi\)
−0.612965 + 0.790110i \(0.710023\pi\)
\(810\) 0 0
\(811\) 36.5455 10.7307i 1.28329 0.376807i 0.432174 0.901790i \(-0.357747\pi\)
0.851112 + 0.524984i \(0.175929\pi\)
\(812\) 0 0
\(813\) 9.83883 21.5440i 0.345063 0.755583i
\(814\) 0 0
\(815\) 21.4163 + 11.0409i 0.750181 + 0.386745i
\(816\) 0 0
\(817\) 24.4865 + 9.80291i 0.856673 + 0.342960i
\(818\) 0 0
\(819\) 5.59450 0.764388i 0.195488 0.0267099i
\(820\) 0 0
\(821\) 27.0841 13.9628i 0.945240 0.487305i 0.0845414 0.996420i \(-0.473057\pi\)
0.860699 + 0.509115i \(0.170027\pi\)
\(822\) 0 0
\(823\) 3.22090 9.30618i 0.112273 0.324393i −0.874841 0.484411i \(-0.839034\pi\)
0.987114 + 0.160018i \(0.0511552\pi\)
\(824\) 0 0
\(825\) 2.92142 + 6.39702i 0.101711 + 0.222716i
\(826\) 0 0
\(827\) −20.3258 −0.706798 −0.353399 0.935473i \(-0.614974\pi\)
−0.353399 + 0.935473i \(0.614974\pi\)
\(828\) 0 0
\(829\) −6.17562 10.6965i −0.214488 0.371504i 0.738626 0.674115i \(-0.235475\pi\)
−0.953114 + 0.302611i \(0.902142\pi\)
\(830\) 0 0
\(831\) −1.83026 0.174769i −0.0634910 0.00606266i
\(832\) 0 0
\(833\) 1.16571 1.30781i 0.0403896 0.0453128i
\(834\) 0 0
\(835\) 9.13669 4.71029i 0.316188 0.163006i
\(836\) 0 0
\(837\) −49.4400 9.52877i −1.70890 0.329363i
\(838\) 0 0
\(839\) −4.75231 33.0531i −0.164068 1.14112i −0.890866 0.454267i \(-0.849901\pi\)
0.726797 0.686852i \(-0.241008\pi\)
\(840\) 0 0
\(841\) 44.0203 28.2901i 1.51794 0.975521i
\(842\) 0 0
\(843\) 37.0645 3.53923i 1.27657 0.121898i
\(844\) 0 0
\(845\) −11.0983 + 45.7476i −0.381792 + 1.57377i
\(846\) 0 0
\(847\) 15.2376 + 24.0795i 0.523569 + 0.827382i
\(848\) 0 0
\(849\) −10.1333 7.96889i −0.347773 0.273491i
\(850\) 0 0
\(851\) 13.0271 + 10.2168i 0.446562 + 0.350227i
\(852\) 0 0
\(853\) −4.45465 + 30.9827i −0.152524 + 1.06083i 0.759445 + 0.650571i \(0.225470\pi\)
−0.911970 + 0.410258i \(0.865439\pi\)
\(854\) 0 0
\(855\) −54.2474 15.9285i −1.85522 0.544743i
\(856\) 0 0
\(857\) −29.5018 28.1299i −1.00776 0.960898i −0.00852400 0.999964i \(-0.502713\pi\)
−0.999237 + 0.0390658i \(0.987562\pi\)
\(858\) 0 0
\(859\) 5.63624 + 7.91499i 0.192306 + 0.270056i 0.899460 0.437004i \(-0.143960\pi\)
−0.707154 + 0.707060i \(0.750021\pi\)
\(860\) 0 0
\(861\) 7.57367 9.49302i 0.258110 0.323521i
\(862\) 0 0
\(863\) −24.4329 9.78144i −0.831704 0.332964i −0.0835618 0.996503i \(-0.526630\pi\)
−0.748142 + 0.663539i \(0.769054\pi\)
\(864\) 0 0
\(865\) 69.2278 + 13.3426i 2.35381 + 0.453661i
\(866\) 0 0
\(867\) −16.7539 10.7671i −0.568992 0.365669i
\(868\) 0 0
\(869\) 0.293757 + 0.339014i 0.00996504 + 0.0115003i
\(870\) 0 0
\(871\) 8.92571 12.5344i 0.302436 0.424712i
\(872\) 0 0
\(873\) 13.8677 24.0195i 0.469350 0.812938i
\(874\) 0 0
\(875\) 16.2314 81.1520i 0.548723 2.74344i
\(876\) 0 0
\(877\) 20.8778 + 1.99359i 0.704994 + 0.0673188i 0.441394 0.897313i \(-0.354484\pi\)
0.263600 + 0.964632i \(0.415090\pi\)
\(878\) 0 0
\(879\) −8.08006 + 23.3458i −0.272534 + 0.787434i
\(880\) 0 0
\(881\) −31.1124 19.9947i −1.04820 0.673638i −0.101200 0.994866i \(-0.532268\pi\)
−0.947002 + 0.321228i \(0.895905\pi\)
\(882\) 0 0
\(883\) −12.2654 + 14.1550i −0.412762 + 0.476353i −0.923618 0.383313i \(-0.874783\pi\)
0.510856 + 0.859666i \(0.329328\pi\)
\(884\) 0 0
\(885\) −29.7868 + 23.4246i −1.00127 + 0.787409i
\(886\) 0 0
\(887\) −1.35291 28.4012i −0.0454264 0.953618i −0.900431 0.434998i \(-0.856749\pi\)
0.855005 0.518620i \(-0.173554\pi\)
\(888\) 0 0
\(889\) 8.22310 + 5.94293i 0.275794 + 0.199320i
\(890\) 0 0
\(891\) −0.173031 + 0.713242i −0.00579674 + 0.0238945i
\(892\) 0 0
\(893\) 4.74807 + 19.5718i 0.158888 + 0.654946i
\(894\) 0 0
\(895\) −2.35087 + 16.3507i −0.0785810 + 0.546543i
\(896\) 0 0
\(897\) 3.72881 + 6.43885i 0.124501 + 0.214987i
\(898\) 0 0
\(899\) 77.6411 31.0828i 2.58948 1.03667i
\(900\) 0 0
\(901\) 1.28079 1.22123i 0.0426691 0.0406849i
\(902\) 0 0
\(903\) −8.03448 + 5.63688i −0.267371 + 0.187584i
\(904\) 0 0
\(905\) −1.44783 2.03319i −0.0481274 0.0675855i
\(906\) 0 0
\(907\) 20.2090 + 10.4184i 0.671027 + 0.345939i 0.759840 0.650110i \(-0.225277\pi\)
−0.0888129 + 0.996048i \(0.528307\pi\)
\(908\) 0 0
\(909\) −2.20413 15.3301i −0.0731064 0.508466i
\(910\) 0 0
\(911\) −11.1348 + 12.8503i −0.368914 + 0.425749i −0.909606 0.415471i \(-0.863617\pi\)
0.540693 + 0.841220i \(0.318162\pi\)
\(912\) 0 0
\(913\) 0.0489254 1.02707i 0.00161920 0.0339911i
\(914\) 0 0
\(915\) 58.1952 11.2162i 1.92387 0.370796i
\(916\) 0 0
\(917\) 6.06845 20.1439i 0.200398 0.665210i
\(918\) 0 0
\(919\) −10.2718 + 17.7913i −0.338836 + 0.586880i −0.984214 0.176983i \(-0.943366\pi\)
0.645378 + 0.763863i \(0.276700\pi\)
\(920\) 0 0
\(921\) −6.60711 11.4439i −0.217712 0.377088i
\(922\) 0 0
\(923\) −4.88247 10.6911i −0.160709 0.351903i
\(924\) 0 0
\(925\) −28.2157 32.5627i −0.927727 1.07065i
\(926\) 0 0
\(927\) 0.820582 17.2261i 0.0269515 0.565781i
\(928\) 0 0
\(929\) 12.1647 + 35.1477i 0.399112 + 1.15316i 0.948277 + 0.317445i \(0.102825\pi\)
−0.549165 + 0.835714i \(0.685054\pi\)
\(930\) 0 0
\(931\) 41.7844 + 40.9747i 1.36943 + 1.34289i
\(932\) 0 0
\(933\) −0.977160 20.5131i −0.0319908 0.671569i
\(934\) 0 0
\(935\) −0.499163 + 0.0476643i −0.0163244 + 0.00155879i
\(936\) 0 0
\(937\) −26.2554 + 7.70928i −0.857726 + 0.251851i −0.680887 0.732389i \(-0.738405\pi\)
−0.176839 + 0.984240i \(0.556587\pi\)
\(938\) 0 0
\(939\) −19.0111 5.58215i −0.620403 0.182167i
\(940\) 0 0
\(941\) −8.40286 + 3.36400i −0.273925 + 0.109663i −0.504558 0.863378i \(-0.668345\pi\)
0.230633 + 0.973041i \(0.425920\pi\)
\(942\) 0 0
\(943\) −17.9699 5.25068i −0.585179 0.170986i
\(944\) 0 0
\(945\) 45.6643 39.0114i 1.48546 1.26904i
\(946\) 0 0
\(947\) −0.932462 + 0.889101i −0.0303010 + 0.0288919i −0.705078 0.709129i \(-0.749088\pi\)
0.674777 + 0.738021i \(0.264240\pi\)
\(948\) 0 0
\(949\) 1.79986 + 1.71616i 0.0584260 + 0.0557090i
\(950\) 0 0
\(951\) 11.7290 25.6830i 0.380340 0.832828i
\(952\) 0 0
\(953\) 6.66673 4.28444i 0.215956 0.138787i −0.428191 0.903688i \(-0.640849\pi\)
0.644147 + 0.764902i \(0.277212\pi\)
\(954\) 0 0
\(955\) 16.7579 13.1785i 0.542271 0.426447i
\(956\) 0 0
\(957\) −1.66190 4.80176i −0.0537217 0.155219i
\(958\) 0 0
\(959\) 35.3553 + 8.83991i 1.14168 + 0.285456i
\(960\) 0 0
\(961\) 54.0081 10.4092i 1.74220 0.335781i
\(962\) 0 0
\(963\) −10.5271 + 14.7832i −0.339230 + 0.476382i
\(964\) 0 0
\(965\) 8.59062 0.276542
\(966\) 0 0
\(967\) 58.3749 1.87721 0.938605 0.344994i \(-0.112119\pi\)
0.938605 + 0.344994i \(0.112119\pi\)
\(968\) 0 0
\(969\) −1.42710 + 2.00408i −0.0458451 + 0.0643804i
\(970\) 0 0
\(971\) 32.8238 6.32627i 1.05337 0.203020i 0.366959 0.930237i \(-0.380399\pi\)
0.686407 + 0.727218i \(0.259187\pi\)
\(972\) 0 0
\(973\) 18.9082 19.5541i 0.606170 0.626877i
\(974\) 0 0
\(975\) −6.33351 18.2995i −0.202835 0.586053i
\(976\) 0 0
\(977\) 4.01705 3.15904i 0.128517 0.101067i −0.551832 0.833956i \(-0.686071\pi\)
0.680348 + 0.732889i \(0.261828\pi\)
\(978\) 0 0
\(979\) −1.74767 + 1.12316i −0.0558556 + 0.0358962i
\(980\) 0 0
\(981\) 3.79551 8.31100i 0.121181 0.265350i
\(982\) 0 0
\(983\) 16.5013 + 15.7340i 0.526310 + 0.501835i 0.906000 0.423279i \(-0.139121\pi\)
−0.379690 + 0.925114i \(0.623969\pi\)
\(984\) 0 0
\(985\) 35.2085 33.5713i 1.12184 1.06967i
\(986\) 0 0
\(987\) −7.06455 2.50064i −0.224867 0.0795963i
\(988\) 0 0
\(989\) 12.7392 + 8.16324i 0.405082 + 0.259576i
\(990\) 0 0
\(991\) 12.8105 5.12855i 0.406939 0.162914i −0.159157 0.987253i \(-0.550878\pi\)
0.566095 + 0.824340i \(0.308453\pi\)
\(992\) 0 0
\(993\) 21.9658 + 6.44974i 0.697064 + 0.204676i
\(994\) 0 0
\(995\) 35.0907 10.3036i 1.11245 0.326645i
\(996\) 0 0
\(997\) 15.6317 1.49264i 0.495060 0.0472725i 0.155459 0.987842i \(-0.450314\pi\)
0.339600 + 0.940570i \(0.389708\pi\)
\(998\) 0 0
\(999\) −0.891797 18.7211i −0.0282152 0.592310i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 644.2.y.a.261.12 yes 320
7.4 even 3 inner 644.2.y.a.445.5 yes 320
23.3 even 11 inner 644.2.y.a.233.5 320
161.95 even 33 inner 644.2.y.a.417.12 yes 320
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
644.2.y.a.233.5 320 23.3 even 11 inner
644.2.y.a.261.12 yes 320 1.1 even 1 trivial
644.2.y.a.417.12 yes 320 161.95 even 33 inner
644.2.y.a.445.5 yes 320 7.4 even 3 inner