Properties

Label 315.2.bb.b.89.9
Level $315$
Weight $2$
Character 315.89
Analytic conductor $2.515$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [315,2,Mod(89,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.9
Character \(\chi\) \(=\) 315.89
Dual form 315.2.bb.b.269.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.956572 - 1.65683i) q^{2} +(-0.830062 - 1.43771i) q^{4} +(1.54260 + 1.61876i) q^{5} +(1.11878 + 2.39757i) q^{7} +0.650234 q^{8} +O(q^{10})\) \(q+(0.956572 - 1.65683i) q^{2} +(-0.830062 - 1.43771i) q^{4} +(1.54260 + 1.61876i) q^{5} +(1.11878 + 2.39757i) q^{7} +0.650234 q^{8} +(4.15762 - 1.00738i) q^{10} +(2.79501 - 1.61370i) q^{11} -4.86146 q^{13} +(5.04256 + 0.439817i) q^{14} +(2.28212 - 3.95275i) q^{16} +(0.631456 - 0.364571i) q^{17} +(-6.81691 - 3.93574i) q^{19} +(1.04685 - 3.56148i) q^{20} -6.17449i q^{22} +(-2.43410 + 4.21599i) q^{23} +(-0.240749 + 4.99420i) q^{25} +(-4.65034 + 8.05463i) q^{26} +(2.51835 - 3.59861i) q^{28} -7.75958i q^{29} +(-1.23751 + 0.714478i) q^{31} +(-3.71579 - 6.43594i) q^{32} -1.39495i q^{34} +(-2.15525 + 5.50953i) q^{35} +(2.74130 + 1.58269i) q^{37} +(-13.0417 + 7.52965i) q^{38} +(1.00305 + 1.05257i) q^{40} +1.40264 q^{41} -6.42489i q^{43} +(-4.64007 - 2.67894i) q^{44} +(4.65679 + 8.06579i) q^{46} +(4.21797 + 2.43524i) q^{47} +(-4.49666 + 5.36470i) q^{49} +(8.04426 + 5.17620i) q^{50} +(4.03531 + 6.98937i) q^{52} +(0.760733 + 1.31763i) q^{53} +(6.92379 + 2.03515i) q^{55} +(0.727468 + 1.55898i) q^{56} +(-12.8563 - 7.42260i) q^{58} +(-3.15081 - 5.45737i) q^{59} +(-2.05442 - 1.18612i) q^{61} +2.73380i q^{62} -5.08921 q^{64} +(-7.49931 - 7.86953i) q^{65} +(-9.63531 + 5.56295i) q^{67} +(-1.04829 - 0.605233i) q^{68} +(7.06671 + 8.84115i) q^{70} -10.1351i q^{71} +(6.91195 + 11.9718i) q^{73} +(5.24450 - 3.02792i) q^{74} +13.0676i q^{76} +(6.99596 + 4.89586i) q^{77} +(-1.99018 + 3.44710i) q^{79} +(9.91894 - 2.40332i) q^{80} +(1.34173 - 2.32395i) q^{82} -4.19208i q^{83} +(1.56424 + 0.459785i) q^{85} +(-10.6450 - 6.14587i) q^{86} +(1.81741 - 1.04928i) q^{88} +(-5.63672 + 9.76309i) q^{89} +(-5.43891 - 11.6557i) q^{91} +8.08181 q^{92} +(8.06958 - 4.65898i) q^{94} +(-4.14477 - 17.1062i) q^{95} +2.21388 q^{97} +(4.58702 + 12.5819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{4} - 12 q^{10} - 36 q^{19} + 12 q^{25} - 60 q^{31} + 96 q^{40} - 24 q^{46} + 36 q^{49} + 48 q^{61} + 48 q^{64} - 48 q^{70} - 60 q^{79} - 72 q^{85} + 60 q^{91} + 48 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.956572 1.65683i 0.676399 1.17156i −0.299659 0.954046i \(-0.596873\pi\)
0.976058 0.217511i \(-0.0697937\pi\)
\(3\) 0 0
\(4\) −0.830062 1.43771i −0.415031 0.718854i
\(5\) 1.54260 + 1.61876i 0.689873 + 0.723930i
\(6\) 0 0
\(7\) 1.11878 + 2.39757i 0.422859 + 0.906196i
\(8\) 0.650234 0.229892
\(9\) 0 0
\(10\) 4.15762 1.00738i 1.31476 0.318560i
\(11\) 2.79501 1.61370i 0.842728 0.486549i −0.0154625 0.999880i \(-0.504922\pi\)
0.858191 + 0.513331i \(0.171589\pi\)
\(12\) 0 0
\(13\) −4.86146 −1.34833 −0.674164 0.738582i \(-0.735496\pi\)
−0.674164 + 0.738582i \(0.735496\pi\)
\(14\) 5.04256 + 0.439817i 1.34768 + 0.117546i
\(15\) 0 0
\(16\) 2.28212 3.95275i 0.570530 0.988186i
\(17\) 0.631456 0.364571i 0.153150 0.0884215i −0.421466 0.906844i \(-0.638484\pi\)
0.574617 + 0.818423i \(0.305151\pi\)
\(18\) 0 0
\(19\) −6.81691 3.93574i −1.56391 0.902922i −0.996856 0.0792390i \(-0.974751\pi\)
−0.567051 0.823683i \(-0.691916\pi\)
\(20\) 1.04685 3.56148i 0.234082 0.796372i
\(21\) 0 0
\(22\) 6.17449i 1.31641i
\(23\) −2.43410 + 4.21599i −0.507545 + 0.879094i 0.492417 + 0.870360i \(0.336114\pi\)
−0.999962 + 0.00873433i \(0.997220\pi\)
\(24\) 0 0
\(25\) −0.240749 + 4.99420i −0.0481499 + 0.998840i
\(26\) −4.65034 + 8.05463i −0.912007 + 1.57964i
\(27\) 0 0
\(28\) 2.51835 3.59861i 0.475923 0.680073i
\(29\) 7.75958i 1.44092i −0.693498 0.720459i \(-0.743931\pi\)
0.693498 0.720459i \(-0.256069\pi\)
\(30\) 0 0
\(31\) −1.23751 + 0.714478i −0.222264 + 0.128324i −0.606998 0.794703i \(-0.707626\pi\)
0.384734 + 0.923027i \(0.374293\pi\)
\(32\) −3.71579 6.43594i −0.656865 1.13772i
\(33\) 0 0
\(34\) 1.39495i 0.239233i
\(35\) −2.15525 + 5.50953i −0.364303 + 0.931280i
\(36\) 0 0
\(37\) 2.74130 + 1.58269i 0.450667 + 0.260193i 0.708112 0.706100i \(-0.249547\pi\)
−0.257445 + 0.966293i \(0.582881\pi\)
\(38\) −13.0417 + 7.52965i −2.11565 + 1.22147i
\(39\) 0 0
\(40\) 1.00305 + 1.05257i 0.158597 + 0.166426i
\(41\) 1.40264 0.219056 0.109528 0.993984i \(-0.465066\pi\)
0.109528 + 0.993984i \(0.465066\pi\)
\(42\) 0 0
\(43\) 6.42489i 0.979787i −0.871782 0.489893i \(-0.837036\pi\)
0.871782 0.489893i \(-0.162964\pi\)
\(44\) −4.64007 2.67894i −0.699516 0.403866i
\(45\) 0 0
\(46\) 4.65679 + 8.06579i 0.686606 + 1.18924i
\(47\) 4.21797 + 2.43524i 0.615254 + 0.355217i 0.775019 0.631938i \(-0.217740\pi\)
−0.159765 + 0.987155i \(0.551074\pi\)
\(48\) 0 0
\(49\) −4.49666 + 5.36470i −0.642381 + 0.766386i
\(50\) 8.04426 + 5.17620i 1.13763 + 0.732025i
\(51\) 0 0
\(52\) 4.03531 + 6.98937i 0.559597 + 0.969251i
\(53\) 0.760733 + 1.31763i 0.104495 + 0.180990i 0.913532 0.406768i \(-0.133344\pi\)
−0.809037 + 0.587758i \(0.800011\pi\)
\(54\) 0 0
\(55\) 6.92379 + 2.03515i 0.933603 + 0.274419i
\(56\) 0.727468 + 1.55898i 0.0972120 + 0.208327i
\(57\) 0 0
\(58\) −12.8563 7.42260i −1.68812 0.974635i
\(59\) −3.15081 5.45737i −0.410201 0.710489i 0.584711 0.811242i \(-0.301208\pi\)
−0.994911 + 0.100753i \(0.967875\pi\)
\(60\) 0 0
\(61\) −2.05442 1.18612i −0.263042 0.151867i 0.362680 0.931914i \(-0.381862\pi\)
−0.625721 + 0.780047i \(0.715195\pi\)
\(62\) 2.73380i 0.347193i
\(63\) 0 0
\(64\) −5.08921 −0.636152
\(65\) −7.49931 7.86953i −0.930175 0.976095i
\(66\) 0 0
\(67\) −9.63531 + 5.56295i −1.17714 + 0.679622i −0.955351 0.295472i \(-0.904523\pi\)
−0.221789 + 0.975095i \(0.571190\pi\)
\(68\) −1.04829 0.605233i −0.127124 0.0733953i
\(69\) 0 0
\(70\) 7.06671 + 8.84115i 0.844634 + 1.05672i
\(71\) 10.1351i 1.20282i −0.798942 0.601408i \(-0.794607\pi\)
0.798942 0.601408i \(-0.205393\pi\)
\(72\) 0 0
\(73\) 6.91195 + 11.9718i 0.808982 + 1.40120i 0.913570 + 0.406683i \(0.133314\pi\)
−0.104587 + 0.994516i \(0.533352\pi\)
\(74\) 5.24450 3.02792i 0.609661 0.351988i
\(75\) 0 0
\(76\) 13.0676i 1.49896i
\(77\) 6.99596 + 4.89586i 0.797264 + 0.557935i
\(78\) 0 0
\(79\) −1.99018 + 3.44710i −0.223913 + 0.387829i −0.955993 0.293390i \(-0.905217\pi\)
0.732080 + 0.681219i \(0.238550\pi\)
\(80\) 9.91894 2.40332i 1.10897 0.268700i
\(81\) 0 0
\(82\) 1.34173 2.32395i 0.148169 0.256637i
\(83\) 4.19208i 0.460141i −0.973174 0.230070i \(-0.926104\pi\)
0.973174 0.230070i \(-0.0738957\pi\)
\(84\) 0 0
\(85\) 1.56424 + 0.459785i 0.169665 + 0.0498706i
\(86\) −10.6450 6.14587i −1.14788 0.662727i
\(87\) 0 0
\(88\) 1.81741 1.04928i 0.193737 0.111854i
\(89\) −5.63672 + 9.76309i −0.597491 + 1.03489i 0.395699 + 0.918380i \(0.370502\pi\)
−0.993190 + 0.116505i \(0.962831\pi\)
\(90\) 0 0
\(91\) −5.43891 11.6557i −0.570152 1.22185i
\(92\) 8.08181 0.842587
\(93\) 0 0
\(94\) 8.06958 4.65898i 0.832314 0.480537i
\(95\) −4.14477 17.1062i −0.425245 1.75506i
\(96\) 0 0
\(97\) 2.21388 0.224785 0.112393 0.993664i \(-0.464149\pi\)
0.112393 + 0.993664i \(0.464149\pi\)
\(98\) 4.58702 + 12.5819i 0.463359 + 1.27097i
\(99\) 0 0
\(100\) 7.38004 3.79937i 0.738004 0.379937i
\(101\) 5.85104 + 10.1343i 0.582201 + 1.00840i 0.995218 + 0.0976779i \(0.0311415\pi\)
−0.413017 + 0.910723i \(0.635525\pi\)
\(102\) 0 0
\(103\) 0.292630 0.506851i 0.0288337 0.0499415i −0.851248 0.524763i \(-0.824154\pi\)
0.880082 + 0.474821i \(0.157487\pi\)
\(104\) −3.16109 −0.309970
\(105\) 0 0
\(106\) 2.91079 0.282721
\(107\) 0.846073 1.46544i 0.0817929 0.141670i −0.822227 0.569159i \(-0.807269\pi\)
0.904020 + 0.427490i \(0.140602\pi\)
\(108\) 0 0
\(109\) 6.70139 + 11.6072i 0.641877 + 1.11176i 0.985013 + 0.172478i \(0.0551774\pi\)
−0.343136 + 0.939286i \(0.611489\pi\)
\(110\) 9.99500 9.52479i 0.952986 0.908153i
\(111\) 0 0
\(112\) 12.0302 + 1.04928i 1.13674 + 0.0991479i
\(113\) −14.2129 −1.33704 −0.668520 0.743694i \(-0.733072\pi\)
−0.668520 + 0.743694i \(0.733072\pi\)
\(114\) 0 0
\(115\) −10.5795 + 2.56338i −0.986544 + 0.239036i
\(116\) −11.1560 + 6.44093i −1.03581 + 0.598025i
\(117\) 0 0
\(118\) −12.0559 −1.10984
\(119\) 1.58054 + 1.10608i 0.144888 + 0.101394i
\(120\) 0 0
\(121\) −0.291934 + 0.505645i −0.0265395 + 0.0459677i
\(122\) −3.93041 + 2.26922i −0.355842 + 0.205446i
\(123\) 0 0
\(124\) 2.05442 + 1.18612i 0.184493 + 0.106517i
\(125\) −8.45578 + 7.31436i −0.756308 + 0.654216i
\(126\) 0 0
\(127\) 2.08954i 0.185417i 0.995693 + 0.0927084i \(0.0295524\pi\)
−0.995693 + 0.0927084i \(0.970448\pi\)
\(128\) 2.56338 4.43990i 0.226573 0.392436i
\(129\) 0 0
\(130\) −20.2121 + 4.89732i −1.77272 + 0.429524i
\(131\) 5.60241 9.70365i 0.489484 0.847812i −0.510442 0.859912i \(-0.670518\pi\)
0.999927 + 0.0121001i \(0.00385167\pi\)
\(132\) 0 0
\(133\) 1.80960 20.7472i 0.156912 1.79901i
\(134\) 21.2855i 1.83878i
\(135\) 0 0
\(136\) 0.410594 0.237056i 0.0352081 0.0203274i
\(137\) −3.51995 6.09673i −0.300730 0.520879i 0.675572 0.737294i \(-0.263897\pi\)
−0.976301 + 0.216415i \(0.930564\pi\)
\(138\) 0 0
\(139\) 6.45903i 0.547848i −0.961751 0.273924i \(-0.911678\pi\)
0.961751 0.273924i \(-0.0883216\pi\)
\(140\) 9.71009 1.47463i 0.820652 0.124629i
\(141\) 0 0
\(142\) −16.7922 9.69496i −1.40917 0.813583i
\(143\) −13.5879 + 7.84495i −1.13627 + 0.656028i
\(144\) 0 0
\(145\) 12.5609 11.9699i 1.04312 0.994050i
\(146\) 26.4471 2.18878
\(147\) 0 0
\(148\) 5.25492i 0.431952i
\(149\) 20.3962 + 11.7758i 1.67092 + 0.964709i 0.967122 + 0.254312i \(0.0818491\pi\)
0.703802 + 0.710396i \(0.251484\pi\)
\(150\) 0 0
\(151\) −9.05442 15.6827i −0.736838 1.27624i −0.953912 0.300086i \(-0.902985\pi\)
0.217074 0.976155i \(-0.430349\pi\)
\(152\) −4.43258 2.55915i −0.359530 0.207575i
\(153\) 0 0
\(154\) 14.8038 6.90789i 1.19292 0.556654i
\(155\) −3.06556 0.901075i −0.246231 0.0723761i
\(156\) 0 0
\(157\) −1.24227 2.15168i −0.0991441 0.171723i 0.812187 0.583398i \(-0.198277\pi\)
−0.911331 + 0.411675i \(0.864944\pi\)
\(158\) 3.80751 + 6.59480i 0.302909 + 0.524654i
\(159\) 0 0
\(160\) 4.68623 15.9431i 0.370479 1.26041i
\(161\) −12.8313 1.11916i −1.01125 0.0882023i
\(162\) 0 0
\(163\) −3.41015 1.96885i −0.267104 0.154212i 0.360467 0.932772i \(-0.382617\pi\)
−0.627571 + 0.778560i \(0.715951\pi\)
\(164\) −1.16428 2.01659i −0.0909151 0.157470i
\(165\) 0 0
\(166\) −6.94558 4.01003i −0.539081 0.311239i
\(167\) 5.31832i 0.411544i −0.978600 0.205772i \(-0.934029\pi\)
0.978600 0.205772i \(-0.0659705\pi\)
\(168\) 0 0
\(169\) 10.6338 0.817986
\(170\) 2.25809 2.15186i 0.173188 0.165040i
\(171\) 0 0
\(172\) −9.23712 + 5.33306i −0.704324 + 0.406642i
\(173\) −6.45623 3.72751i −0.490858 0.283397i 0.234072 0.972219i \(-0.424795\pi\)
−0.724930 + 0.688822i \(0.758128\pi\)
\(174\) 0 0
\(175\) −12.2433 + 5.01020i −0.925505 + 0.378735i
\(176\) 14.7306i 1.11036i
\(177\) 0 0
\(178\) 10.7839 + 18.6782i 0.808285 + 1.39999i
\(179\) −11.5242 + 6.65349i −0.861358 + 0.497305i −0.864467 0.502690i \(-0.832344\pi\)
0.00310866 + 0.999995i \(0.499010\pi\)
\(180\) 0 0
\(181\) 9.95814i 0.740183i −0.928995 0.370091i \(-0.879326\pi\)
0.928995 0.370091i \(-0.120674\pi\)
\(182\) −24.5142 2.13816i −1.81712 0.158491i
\(183\) 0 0
\(184\) −1.58273 + 2.74138i −0.116681 + 0.202097i
\(185\) 1.66675 + 6.87896i 0.122542 + 0.505751i
\(186\) 0 0
\(187\) 1.17662 2.03796i 0.0860428 0.149031i
\(188\) 8.08561i 0.589704i
\(189\) 0 0
\(190\) −32.3069 9.49614i −2.34379 0.688922i
\(191\) 21.3140 + 12.3056i 1.54223 + 0.890404i 0.998698 + 0.0510125i \(0.0162448\pi\)
0.543527 + 0.839392i \(0.317089\pi\)
\(192\) 0 0
\(193\) 10.8377 6.25714i 0.780113 0.450399i −0.0563571 0.998411i \(-0.517949\pi\)
0.836470 + 0.548012i \(0.184615\pi\)
\(194\) 2.11773 3.66802i 0.152044 0.263349i
\(195\) 0 0
\(196\) 11.4454 + 2.01186i 0.817528 + 0.143704i
\(197\) 15.6968 1.11835 0.559177 0.829049i \(-0.311117\pi\)
0.559177 + 0.829049i \(0.311117\pi\)
\(198\) 0 0
\(199\) 17.1436 9.89788i 1.21528 0.701642i 0.251375 0.967890i \(-0.419117\pi\)
0.963905 + 0.266247i \(0.0857838\pi\)
\(200\) −0.156543 + 3.24740i −0.0110693 + 0.229626i
\(201\) 0 0
\(202\) 22.3878 1.57520
\(203\) 18.6041 8.68126i 1.30575 0.609305i
\(204\) 0 0
\(205\) 2.16372 + 2.27054i 0.151121 + 0.158581i
\(206\) −0.559844 0.969678i −0.0390062 0.0675607i
\(207\) 0 0
\(208\) −11.0944 + 19.2161i −0.769261 + 1.33240i
\(209\) −25.4045 −1.75726
\(210\) 0 0
\(211\) 11.5839 0.797466 0.398733 0.917067i \(-0.369450\pi\)
0.398733 + 0.917067i \(0.369450\pi\)
\(212\) 1.26291 2.18743i 0.0867371 0.150233i
\(213\) 0 0
\(214\) −1.61866 2.80360i −0.110649 0.191650i
\(215\) 10.4003 9.91106i 0.709297 0.675929i
\(216\) 0 0
\(217\) −3.09751 2.16768i −0.210273 0.147151i
\(218\) 25.6415 1.73666
\(219\) 0 0
\(220\) −2.82122 11.6437i −0.190207 0.785017i
\(221\) −3.06980 + 1.77235i −0.206497 + 0.119221i
\(222\) 0 0
\(223\) −24.1321 −1.61600 −0.808002 0.589180i \(-0.799451\pi\)
−0.808002 + 0.589180i \(0.799451\pi\)
\(224\) 11.2734 16.1093i 0.753239 1.07634i
\(225\) 0 0
\(226\) −13.5957 + 23.5484i −0.904372 + 1.56642i
\(227\) 8.82377 5.09441i 0.585654 0.338128i −0.177723 0.984081i \(-0.556873\pi\)
0.763377 + 0.645953i \(0.223540\pi\)
\(228\) 0 0
\(229\) 22.7373 + 13.1274i 1.50252 + 0.867483i 0.999996 + 0.00292226i \(0.000930186\pi\)
0.502529 + 0.864561i \(0.332403\pi\)
\(230\) −5.87298 + 19.9805i −0.387253 + 1.31748i
\(231\) 0 0
\(232\) 5.04554i 0.331256i
\(233\) 9.19667 15.9291i 0.602494 1.04355i −0.389948 0.920837i \(-0.627507\pi\)
0.992442 0.122713i \(-0.0391595\pi\)
\(234\) 0 0
\(235\) 2.56458 + 10.5845i 0.167295 + 0.690455i
\(236\) −5.23074 + 9.05990i −0.340492 + 0.589749i
\(237\) 0 0
\(238\) 3.34450 1.56065i 0.216792 0.101162i
\(239\) 0.961317i 0.0621824i −0.999517 0.0310912i \(-0.990102\pi\)
0.999517 0.0310912i \(-0.00989824\pi\)
\(240\) 0 0
\(241\) −5.63829 + 3.25527i −0.363194 + 0.209690i −0.670481 0.741927i \(-0.733912\pi\)
0.307287 + 0.951617i \(0.400579\pi\)
\(242\) 0.558512 + 0.967371i 0.0359025 + 0.0621850i
\(243\) 0 0
\(244\) 3.93821i 0.252118i
\(245\) −15.6207 + 0.996599i −0.997971 + 0.0636704i
\(246\) 0 0
\(247\) 33.1402 + 19.1335i 2.10866 + 1.21743i
\(248\) −0.804672 + 0.464578i −0.0510967 + 0.0295007i
\(249\) 0 0
\(250\) 4.03010 + 21.0065i 0.254886 + 1.32857i
\(251\) −2.02506 −0.127820 −0.0639102 0.997956i \(-0.520357\pi\)
−0.0639102 + 0.997956i \(0.520357\pi\)
\(252\) 0 0
\(253\) 15.7116i 0.987783i
\(254\) 3.46202 + 1.99880i 0.217226 + 0.125416i
\(255\) 0 0
\(256\) −9.99333 17.3090i −0.624583 1.08181i
\(257\) 15.7532 + 9.09510i 0.982656 + 0.567337i 0.903071 0.429491i \(-0.141307\pi\)
0.0795849 + 0.996828i \(0.474641\pi\)
\(258\) 0 0
\(259\) −0.727697 + 8.34313i −0.0452169 + 0.518417i
\(260\) −5.08920 + 17.3140i −0.315619 + 1.07377i
\(261\) 0 0
\(262\) −10.7182 18.5645i −0.662173 1.14692i
\(263\) 9.78034 + 16.9400i 0.603082 + 1.04457i 0.992351 + 0.123444i \(0.0393940\pi\)
−0.389270 + 0.921124i \(0.627273\pi\)
\(264\) 0 0
\(265\) −0.959411 + 3.26402i −0.0589362 + 0.200507i
\(266\) −32.6437 22.8444i −2.00151 1.40068i
\(267\) 0 0
\(268\) 15.9958 + 9.23518i 0.977099 + 0.564128i
\(269\) 2.30801 + 3.99759i 0.140722 + 0.243738i 0.927769 0.373156i \(-0.121724\pi\)
−0.787047 + 0.616893i \(0.788391\pi\)
\(270\) 0 0
\(271\) −9.33654 5.39045i −0.567154 0.327447i 0.188858 0.982004i \(-0.439522\pi\)
−0.756012 + 0.654558i \(0.772855\pi\)
\(272\) 3.32798i 0.201788i
\(273\) 0 0
\(274\) −13.4684 −0.813653
\(275\) 7.38625 + 14.3474i 0.445408 + 0.865178i
\(276\) 0 0
\(277\) −17.7594 + 10.2534i −1.06706 + 0.616067i −0.927376 0.374130i \(-0.877941\pi\)
−0.139682 + 0.990196i \(0.544608\pi\)
\(278\) −10.7015 6.17853i −0.641835 0.370564i
\(279\) 0 0
\(280\) −1.40141 + 3.58248i −0.0837505 + 0.214094i
\(281\) 0.714666i 0.0426334i 0.999773 + 0.0213167i \(0.00678583\pi\)
−0.999773 + 0.0213167i \(0.993214\pi\)
\(282\) 0 0
\(283\) 14.0110 + 24.2677i 0.832866 + 1.44257i 0.895756 + 0.444545i \(0.146635\pi\)
−0.0628908 + 0.998020i \(0.520032\pi\)
\(284\) −14.5713 + 8.41276i −0.864649 + 0.499206i
\(285\) 0 0
\(286\) 30.0171i 1.77495i
\(287\) 1.56925 + 3.36293i 0.0926299 + 0.198508i
\(288\) 0 0
\(289\) −8.23418 + 14.2620i −0.484363 + 0.838942i
\(290\) −7.81681 32.2614i −0.459019 1.89445i
\(291\) 0 0
\(292\) 11.4747 19.8747i 0.671505 1.16308i
\(293\) 9.79171i 0.572038i −0.958224 0.286019i \(-0.907668\pi\)
0.958224 0.286019i \(-0.0923321\pi\)
\(294\) 0 0
\(295\) 3.97370 13.5190i 0.231358 0.787104i
\(296\) 1.78249 + 1.02912i 0.103605 + 0.0598163i
\(297\) 0 0
\(298\) 39.0209 22.5287i 2.26042 1.30506i
\(299\) 11.8333 20.4959i 0.684337 1.18531i
\(300\) 0 0
\(301\) 15.4041 7.18804i 0.887878 0.414312i
\(302\) −34.6448 −1.99359
\(303\) 0 0
\(304\) −31.1140 + 17.9637i −1.78451 + 1.03029i
\(305\) −1.24912 5.15533i −0.0715242 0.295193i
\(306\) 0 0
\(307\) −25.4778 −1.45410 −0.727048 0.686586i \(-0.759108\pi\)
−0.727048 + 0.686586i \(0.759108\pi\)
\(308\) 1.23174 14.1220i 0.0701847 0.804677i
\(309\) 0 0
\(310\) −4.42536 + 4.21717i −0.251343 + 0.239519i
\(311\) 5.05422 + 8.75417i 0.286599 + 0.496404i 0.972996 0.230824i \(-0.0741420\pi\)
−0.686397 + 0.727227i \(0.740809\pi\)
\(312\) 0 0
\(313\) 11.7375 20.3300i 0.663445 1.14912i −0.316260 0.948673i \(-0.602427\pi\)
0.979705 0.200447i \(-0.0642395\pi\)
\(314\) −4.75329 −0.268244
\(315\) 0 0
\(316\) 6.60790 0.371724
\(317\) −15.7156 + 27.2202i −0.882677 + 1.52884i −0.0343235 + 0.999411i \(0.510928\pi\)
−0.848353 + 0.529430i \(0.822406\pi\)
\(318\) 0 0
\(319\) −12.5216 21.6881i −0.701077 1.21430i
\(320\) −7.85064 8.23820i −0.438864 0.460529i
\(321\) 0 0
\(322\) −14.1284 + 20.1888i −0.787343 + 1.12508i
\(323\) −5.73943 −0.319351
\(324\) 0 0
\(325\) 1.17039 24.2791i 0.0649218 1.34676i
\(326\) −6.52412 + 3.76670i −0.361337 + 0.208618i
\(327\) 0 0
\(328\) 0.912047 0.0503593
\(329\) −1.11969 + 12.8374i −0.0617304 + 0.707747i
\(330\) 0 0
\(331\) 0.589214 1.02055i 0.0323861 0.0560944i −0.849378 0.527785i \(-0.823023\pi\)
0.881764 + 0.471691i \(0.156356\pi\)
\(332\) −6.02700 + 3.47969i −0.330774 + 0.190973i
\(333\) 0 0
\(334\) −8.81156 5.08736i −0.482147 0.278368i
\(335\) −23.8685 7.01580i −1.30408 0.383314i
\(336\) 0 0
\(337\) 3.92868i 0.214009i 0.994259 + 0.107004i \(0.0341259\pi\)
−0.994259 + 0.107004i \(0.965874\pi\)
\(338\) 10.1720 17.6185i 0.553285 0.958318i
\(339\) 0 0
\(340\) −0.637377 2.63057i −0.0345666 0.142663i
\(341\) −2.30591 + 3.99395i −0.124872 + 0.216285i
\(342\) 0 0
\(343\) −17.8930 4.77914i −0.966132 0.258049i
\(344\) 4.17768i 0.225245i
\(345\) 0 0
\(346\) −12.3517 + 7.13126i −0.664032 + 0.383379i
\(347\) 2.41532 + 4.18346i 0.129661 + 0.224580i 0.923545 0.383489i \(-0.125278\pi\)
−0.793884 + 0.608069i \(0.791944\pi\)
\(348\) 0 0
\(349\) 16.0461i 0.858927i −0.903084 0.429463i \(-0.858703\pi\)
0.903084 0.429463i \(-0.141297\pi\)
\(350\) −3.41053 + 25.0777i −0.182300 + 1.34046i
\(351\) 0 0
\(352\) −20.7714 11.9924i −1.10712 0.639195i
\(353\) 5.09305 2.94047i 0.271075 0.156505i −0.358301 0.933606i \(-0.616644\pi\)
0.629376 + 0.777101i \(0.283310\pi\)
\(354\) 0 0
\(355\) 16.4063 15.6344i 0.870755 0.829790i
\(356\) 18.7153 0.991909
\(357\) 0 0
\(358\) 25.4582i 1.34551i
\(359\) −7.00295 4.04315i −0.369601 0.213389i 0.303683 0.952773i \(-0.401784\pi\)
−0.673284 + 0.739384i \(0.735117\pi\)
\(360\) 0 0
\(361\) 21.4802 + 37.2048i 1.13054 + 1.95815i
\(362\) −16.4990 9.52569i −0.867167 0.500659i
\(363\) 0 0
\(364\) −12.2429 + 17.4945i −0.641700 + 0.916961i
\(365\) −8.71711 + 29.6566i −0.456275 + 1.55230i
\(366\) 0 0
\(367\) −9.28484 16.0818i −0.484665 0.839464i 0.515180 0.857082i \(-0.327725\pi\)
−0.999845 + 0.0176181i \(0.994392\pi\)
\(368\) 11.1098 + 19.2428i 0.579139 + 1.00310i
\(369\) 0 0
\(370\) 12.9916 + 3.81870i 0.675404 + 0.198525i
\(371\) −2.30801 + 3.29805i −0.119826 + 0.171226i
\(372\) 0 0
\(373\) 2.28930 + 1.32173i 0.118536 + 0.0684365i 0.558095 0.829777i \(-0.311532\pi\)
−0.439560 + 0.898213i \(0.644866\pi\)
\(374\) −2.25104 3.89892i −0.116399 0.201608i
\(375\) 0 0
\(376\) 2.74266 + 1.58348i 0.141442 + 0.0816617i
\(377\) 37.7229i 1.94283i
\(378\) 0 0
\(379\) −23.8582 −1.22551 −0.612756 0.790272i \(-0.709939\pi\)
−0.612756 + 0.790272i \(0.709939\pi\)
\(380\) −21.1533 + 20.1582i −1.08514 + 1.03409i
\(381\) 0 0
\(382\) 40.7767 23.5425i 2.08632 1.20454i
\(383\) 9.62590 + 5.55752i 0.491861 + 0.283976i 0.725346 0.688384i \(-0.241680\pi\)
−0.233485 + 0.972360i \(0.575013\pi\)
\(384\) 0 0
\(385\) 2.86679 + 18.8771i 0.146105 + 0.962068i
\(386\) 23.9416i 1.21860i
\(387\) 0 0
\(388\) −1.83765 3.18291i −0.0932928 0.161588i
\(389\) 10.8957 6.29064i 0.552434 0.318948i −0.197669 0.980269i \(-0.563337\pi\)
0.750103 + 0.661321i \(0.230004\pi\)
\(390\) 0 0
\(391\) 3.54961i 0.179512i
\(392\) −2.92388 + 3.48831i −0.147678 + 0.176186i
\(393\) 0 0
\(394\) 15.0152 26.0070i 0.756453 1.31021i
\(395\) −8.65008 + 2.09588i −0.435233 + 0.105455i
\(396\) 0 0
\(397\) −14.3154 + 24.7951i −0.718471 + 1.24443i 0.243134 + 0.969993i \(0.421825\pi\)
−0.961605 + 0.274436i \(0.911509\pi\)
\(398\) 37.8722i 1.89836i
\(399\) 0 0
\(400\) 19.1914 + 12.3490i 0.959569 + 0.617449i
\(401\) −10.2994 5.94639i −0.514330 0.296948i 0.220282 0.975436i \(-0.429302\pi\)
−0.734612 + 0.678488i \(0.762636\pi\)
\(402\) 0 0
\(403\) 6.01612 3.47341i 0.299684 0.173023i
\(404\) 9.71345 16.8242i 0.483262 0.837035i
\(405\) 0 0
\(406\) 3.41280 39.1281i 0.169374 1.94190i
\(407\) 10.2160 0.506386
\(408\) 0 0
\(409\) −12.4855 + 7.20852i −0.617369 + 0.356438i −0.775844 0.630925i \(-0.782676\pi\)
0.158475 + 0.987363i \(0.449342\pi\)
\(410\) 5.83166 1.41299i 0.288005 0.0697826i
\(411\) 0 0
\(412\) −0.971605 −0.0478675
\(413\) 9.55934 13.6599i 0.470384 0.672159i
\(414\) 0 0
\(415\) 6.78596 6.46672i 0.333110 0.317439i
\(416\) 18.0642 + 31.2881i 0.885669 + 1.53402i
\(417\) 0 0
\(418\) −24.3012 + 42.0909i −1.18861 + 2.05874i
\(419\) 34.9400 1.70693 0.853466 0.521149i \(-0.174496\pi\)
0.853466 + 0.521149i \(0.174496\pi\)
\(420\) 0 0
\(421\) 23.8515 1.16245 0.581226 0.813742i \(-0.302573\pi\)
0.581226 + 0.813742i \(0.302573\pi\)
\(422\) 11.0808 19.1925i 0.539405 0.934277i
\(423\) 0 0
\(424\) 0.494655 + 0.856767i 0.0240225 + 0.0416083i
\(425\) 1.66872 + 3.24139i 0.0809447 + 0.157230i
\(426\) 0 0
\(427\) 0.545360 6.25262i 0.0263918 0.302586i
\(428\) −2.80917 −0.135786
\(429\) 0 0
\(430\) −6.47228 26.7123i −0.312121 1.28818i
\(431\) 7.06551 4.07928i 0.340334 0.196492i −0.320086 0.947389i \(-0.603712\pi\)
0.660420 + 0.750897i \(0.270378\pi\)
\(432\) 0 0
\(433\) 25.2667 1.21424 0.607121 0.794610i \(-0.292324\pi\)
0.607121 + 0.794610i \(0.292324\pi\)
\(434\) −6.55447 + 3.05852i −0.314625 + 0.146814i
\(435\) 0 0
\(436\) 11.1251 19.2693i 0.532798 0.922832i
\(437\) 33.1861 19.1600i 1.58751 0.916547i
\(438\) 0 0
\(439\) −0.688243 0.397357i −0.0328480 0.0189648i 0.483486 0.875352i \(-0.339370\pi\)
−0.516334 + 0.856387i \(0.672704\pi\)
\(440\) 4.50208 + 1.32332i 0.214628 + 0.0630868i
\(441\) 0 0
\(442\) 6.78152i 0.322564i
\(443\) −11.3244 + 19.6145i −0.538040 + 0.931913i 0.460970 + 0.887416i \(0.347502\pi\)
−0.999010 + 0.0444966i \(0.985832\pi\)
\(444\) 0 0
\(445\) −24.4993 + 5.93609i −1.16138 + 0.281398i
\(446\) −23.0841 + 39.9828i −1.09306 + 1.89324i
\(447\) 0 0
\(448\) −5.69371 12.2017i −0.269002 0.576478i
\(449\) 2.15664i 0.101778i 0.998704 + 0.0508891i \(0.0162055\pi\)
−0.998704 + 0.0508891i \(0.983794\pi\)
\(450\) 0 0
\(451\) 3.92041 2.26345i 0.184605 0.106582i
\(452\) 11.7976 + 20.4340i 0.554913 + 0.961137i
\(453\) 0 0
\(454\) 19.4927i 0.914836i
\(455\) 10.4777 26.7844i 0.491200 1.25567i
\(456\) 0 0
\(457\) 4.74004 + 2.73666i 0.221730 + 0.128016i 0.606751 0.794892i \(-0.292473\pi\)
−0.385021 + 0.922908i \(0.625806\pi\)
\(458\) 43.4998 25.1146i 2.03261 1.17353i
\(459\) 0 0
\(460\) 12.4670 + 13.0825i 0.581278 + 0.609974i
\(461\) 10.1084 0.470797 0.235399 0.971899i \(-0.424360\pi\)
0.235399 + 0.971899i \(0.424360\pi\)
\(462\) 0 0
\(463\) 12.0455i 0.559800i 0.960029 + 0.279900i \(0.0903014\pi\)
−0.960029 + 0.279900i \(0.909699\pi\)
\(464\) −30.6716 17.7083i −1.42389 0.822086i
\(465\) 0 0
\(466\) −17.5946 30.4747i −0.815052 1.41171i
\(467\) −17.2622 9.96636i −0.798801 0.461188i 0.0442505 0.999020i \(-0.485910\pi\)
−0.843052 + 0.537832i \(0.819243\pi\)
\(468\) 0 0
\(469\) −24.1173 16.8776i −1.11363 0.779335i
\(470\) 19.9899 + 5.87574i 0.922066 + 0.271028i
\(471\) 0 0
\(472\) −2.04876 3.54856i −0.0943020 0.163336i
\(473\) −10.3679 17.9577i −0.476715 0.825694i
\(474\) 0 0
\(475\) 21.2971 33.0975i 0.977176 1.51862i
\(476\) 0.278277 3.19048i 0.0127548 0.146235i
\(477\) 0 0
\(478\) −1.59274 0.919569i −0.0728503 0.0420601i
\(479\) −9.69290 16.7886i −0.442880 0.767091i 0.555022 0.831836i \(-0.312710\pi\)
−0.997902 + 0.0647451i \(0.979377\pi\)
\(480\) 0 0
\(481\) −13.3267 7.69419i −0.607646 0.350825i
\(482\) 12.4556i 0.567337i
\(483\) 0 0
\(484\) 0.969293 0.0440588
\(485\) 3.41513 + 3.58373i 0.155073 + 0.162729i
\(486\) 0 0
\(487\) −1.60056 + 0.924082i −0.0725282 + 0.0418742i −0.535826 0.844329i \(-0.680000\pi\)
0.463297 + 0.886203i \(0.346666\pi\)
\(488\) −1.33585 0.771256i −0.0604713 0.0349131i
\(489\) 0 0
\(490\) −13.2912 + 26.8342i −0.600433 + 1.21225i
\(491\) 25.4836i 1.15006i −0.818133 0.575030i \(-0.804991\pi\)
0.818133 0.575030i \(-0.195009\pi\)
\(492\) 0 0
\(493\) −2.82892 4.89983i −0.127408 0.220677i
\(494\) 63.4019 36.6051i 2.85259 1.64694i
\(495\) 0 0
\(496\) 6.52209i 0.292851i
\(497\) 24.2996 11.3390i 1.08999 0.508621i
\(498\) 0 0
\(499\) 13.1142 22.7144i 0.587072 1.01684i −0.407542 0.913187i \(-0.633614\pi\)
0.994614 0.103652i \(-0.0330527\pi\)
\(500\) 17.5347 + 6.08558i 0.784177 + 0.272155i
\(501\) 0 0
\(502\) −1.93711 + 3.35518i −0.0864576 + 0.149749i
\(503\) 4.25713i 0.189816i −0.995486 0.0949081i \(-0.969744\pi\)
0.995486 0.0949081i \(-0.0302557\pi\)
\(504\) 0 0
\(505\) −7.37914 + 25.1046i −0.328367 + 1.11714i
\(506\) 26.0316 + 15.0293i 1.15724 + 0.668135i
\(507\) 0 0
\(508\) 3.00415 1.73445i 0.133288 0.0769537i
\(509\) 9.55960 16.5577i 0.423722 0.733907i −0.572578 0.819850i \(-0.694057\pi\)
0.996300 + 0.0859425i \(0.0273901\pi\)
\(510\) 0 0
\(511\) −20.9704 + 29.9657i −0.927674 + 1.32561i
\(512\) −27.9839 −1.23672
\(513\) 0 0
\(514\) 30.1381 17.4002i 1.32933 0.767492i
\(515\) 1.27188 0.308172i 0.0560457 0.0135797i
\(516\) 0 0
\(517\) 15.7190 0.691322
\(518\) 13.1271 + 9.18648i 0.576771 + 0.403631i
\(519\) 0 0
\(520\) −4.87630 5.11703i −0.213840 0.224397i
\(521\) −11.4068 19.7571i −0.499739 0.865573i 0.500261 0.865875i \(-0.333237\pi\)
−1.00000 0.000301478i \(0.999904\pi\)
\(522\) 0 0
\(523\) 1.56468 2.71011i 0.0684188 0.118505i −0.829787 0.558081i \(-0.811538\pi\)
0.898205 + 0.439576i \(0.144871\pi\)
\(524\) −18.6014 −0.812604
\(525\) 0 0
\(526\) 37.4224 1.63169
\(527\) −0.520956 + 0.902322i −0.0226932 + 0.0393058i
\(528\) 0 0
\(529\) −0.349692 0.605685i −0.0152040 0.0263341i
\(530\) 4.49019 + 4.71186i 0.195041 + 0.204670i
\(531\) 0 0
\(532\) −31.3306 + 14.6198i −1.35835 + 0.633849i
\(533\) −6.81890 −0.295359
\(534\) 0 0
\(535\) 3.67735 0.891008i 0.158986 0.0385216i
\(536\) −6.26520 + 3.61722i −0.270616 + 0.156240i
\(537\) 0 0
\(538\) 8.83112 0.380737
\(539\) −3.91121 + 22.2507i −0.168468 + 0.958405i
\(540\) 0 0
\(541\) 11.2308 19.4524i 0.482852 0.836323i −0.516955 0.856013i \(-0.672934\pi\)
0.999806 + 0.0196894i \(0.00626775\pi\)
\(542\) −17.8622 + 10.3127i −0.767245 + 0.442969i
\(543\) 0 0
\(544\) −4.69271 2.70934i −0.201198 0.116162i
\(545\) −8.45157 + 28.7532i −0.362026 + 1.23165i
\(546\) 0 0
\(547\) 10.4567i 0.447097i 0.974693 + 0.223549i \(0.0717642\pi\)
−0.974693 + 0.223549i \(0.928236\pi\)
\(548\) −5.84355 + 10.1213i −0.249624 + 0.432362i
\(549\) 0 0
\(550\) 30.8366 + 1.48650i 1.31488 + 0.0633848i
\(551\) −30.5397 + 52.8963i −1.30104 + 2.25346i
\(552\) 0 0
\(553\) −10.4912 0.915056i −0.446133 0.0389122i
\(554\) 39.2324i 1.66683i
\(555\) 0 0
\(556\) −9.28620 + 5.36139i −0.393823 + 0.227374i
\(557\) −15.6239 27.0614i −0.662006 1.14663i −0.980088 0.198564i \(-0.936372\pi\)
0.318082 0.948063i \(-0.396961\pi\)
\(558\) 0 0
\(559\) 31.2344i 1.32107i
\(560\) 16.8592 + 21.0925i 0.712433 + 0.891323i
\(561\) 0 0
\(562\) 1.18408 + 0.683630i 0.0499475 + 0.0288372i
\(563\) −25.8689 + 14.9354i −1.09024 + 0.629452i −0.933641 0.358210i \(-0.883387\pi\)
−0.156601 + 0.987662i \(0.550054\pi\)
\(564\) 0 0
\(565\) −21.9249 23.0073i −0.922388 0.967923i
\(566\) 53.6100 2.25340
\(567\) 0 0
\(568\) 6.59019i 0.276518i
\(569\) −25.0218 14.4464i −1.04897 0.605623i −0.126608 0.991953i \(-0.540409\pi\)
−0.922361 + 0.386330i \(0.873743\pi\)
\(570\) 0 0
\(571\) 3.68844 + 6.38856i 0.154356 + 0.267353i 0.932824 0.360331i \(-0.117336\pi\)
−0.778468 + 0.627684i \(0.784003\pi\)
\(572\) 22.5575 + 13.0236i 0.943177 + 0.544543i
\(573\) 0 0
\(574\) 7.07292 + 0.616907i 0.295218 + 0.0257492i
\(575\) −20.4695 13.1714i −0.853636 0.549285i
\(576\) 0 0
\(577\) −9.03785 15.6540i −0.376251 0.651686i 0.614263 0.789102i \(-0.289454\pi\)
−0.990513 + 0.137416i \(0.956120\pi\)
\(578\) 15.7532 + 27.2853i 0.655246 + 1.13492i
\(579\) 0 0
\(580\) −27.6356 8.12308i −1.14751 0.337292i
\(581\) 10.0508 4.69002i 0.416978 0.194575i
\(582\) 0 0
\(583\) 4.25252 + 2.45519i 0.176121 + 0.101684i
\(584\) 4.49438 + 7.78450i 0.185979 + 0.322125i
\(585\) 0 0
\(586\) −16.2232 9.36648i −0.670175 0.386926i
\(587\) 35.0876i 1.44822i −0.689684 0.724111i \(-0.742250\pi\)
0.689684 0.724111i \(-0.257750\pi\)
\(588\) 0 0
\(589\) 11.2480 0.463466
\(590\) −18.5975 19.5156i −0.765647 0.803445i
\(591\) 0 0
\(592\) 12.5119 7.22377i 0.514238 0.296895i
\(593\) 6.11233 + 3.52896i 0.251003 + 0.144917i 0.620224 0.784425i \(-0.287042\pi\)
−0.369220 + 0.929342i \(0.620375\pi\)
\(594\) 0 0
\(595\) 0.647672 + 4.26476i 0.0265520 + 0.174838i
\(596\) 39.0984i 1.60153i
\(597\) 0 0
\(598\) −22.6388 39.2115i −0.925769 1.60348i
\(599\) −4.23198 + 2.44333i −0.172914 + 0.0998318i −0.583959 0.811783i \(-0.698497\pi\)
0.411045 + 0.911615i \(0.365164\pi\)
\(600\) 0 0
\(601\) 36.1905i 1.47624i 0.674669 + 0.738121i \(0.264286\pi\)
−0.674669 + 0.738121i \(0.735714\pi\)
\(602\) 2.82578 32.3979i 0.115170 1.32044i
\(603\) 0 0
\(604\) −15.0315 + 26.0352i −0.611621 + 1.05936i
\(605\) −1.26885 + 0.307439i −0.0515863 + 0.0124992i
\(606\) 0 0
\(607\) 8.46272 14.6579i 0.343491 0.594944i −0.641587 0.767050i \(-0.721724\pi\)
0.985078 + 0.172106i \(0.0550572\pi\)
\(608\) 58.4976i 2.37239i
\(609\) 0 0
\(610\) −9.73638 2.86187i −0.394214 0.115874i
\(611\) −20.5055 11.8389i −0.829563 0.478949i
\(612\) 0 0
\(613\) 16.1128 9.30275i 0.650792 0.375735i −0.137968 0.990437i \(-0.544057\pi\)
0.788759 + 0.614702i \(0.210724\pi\)
\(614\) −24.3714 + 42.2125i −0.983549 + 1.70356i
\(615\) 0 0
\(616\) 4.54901 + 3.18345i 0.183285 + 0.128265i
\(617\) −44.6022 −1.79562 −0.897809 0.440384i \(-0.854842\pi\)
−0.897809 + 0.440384i \(0.854842\pi\)
\(618\) 0 0
\(619\) −9.80175 + 5.65904i −0.393966 + 0.227456i −0.683877 0.729597i \(-0.739707\pi\)
0.289911 + 0.957053i \(0.406374\pi\)
\(620\) 1.24912 + 5.15533i 0.0501657 + 0.207043i
\(621\) 0 0
\(622\) 19.3389 0.775420
\(623\) −29.7139 2.59168i −1.19046 0.103833i
\(624\) 0 0
\(625\) −24.8841 2.40470i −0.995363 0.0961880i
\(626\) −22.4556 38.8942i −0.897506 1.55453i
\(627\) 0 0
\(628\) −2.06233 + 3.57205i −0.0822957 + 0.142540i
\(629\) 2.30801 0.0920265
\(630\) 0 0
\(631\) −6.29394 −0.250558 −0.125279 0.992122i \(-0.539983\pi\)
−0.125279 + 0.992122i \(0.539983\pi\)
\(632\) −1.29409 + 2.24142i −0.0514759 + 0.0891589i
\(633\) 0 0
\(634\) 30.0662 + 52.0763i 1.19408 + 2.06821i
\(635\) −3.38246 + 3.22333i −0.134229 + 0.127914i
\(636\) 0 0
\(637\) 21.8604 26.0803i 0.866139 1.03334i
\(638\) −47.9114 −1.89683
\(639\) 0 0
\(640\) 11.1414 2.69952i 0.440402 0.106708i
\(641\) −0.511044 + 0.295051i −0.0201850 + 0.0116538i −0.510059 0.860140i \(-0.670376\pi\)
0.489874 + 0.871794i \(0.337043\pi\)
\(642\) 0 0
\(643\) −28.7107 −1.13224 −0.566119 0.824323i \(-0.691556\pi\)
−0.566119 + 0.824323i \(0.691556\pi\)
\(644\) 9.04177 + 19.3767i 0.356296 + 0.763549i
\(645\) 0 0
\(646\) −5.49018 + 9.50928i −0.216008 + 0.374138i
\(647\) 10.3303 5.96420i 0.406126 0.234477i −0.282998 0.959121i \(-0.591329\pi\)
0.689124 + 0.724644i \(0.257996\pi\)
\(648\) 0 0
\(649\) −17.6131 10.1689i −0.691375 0.399166i
\(650\) −39.1069 25.1639i −1.53390 0.987009i
\(651\) 0 0
\(652\) 6.53708i 0.256012i
\(653\) 7.99647 13.8503i 0.312926 0.542004i −0.666068 0.745891i \(-0.732024\pi\)
0.978994 + 0.203887i \(0.0653574\pi\)
\(654\) 0 0
\(655\) 24.3501 5.89995i 0.951439 0.230530i
\(656\) 3.20100 5.54430i 0.124978 0.216468i
\(657\) 0 0
\(658\) 20.1983 + 14.1350i 0.787412 + 0.551040i
\(659\) 27.6958i 1.07887i 0.842026 + 0.539437i \(0.181363\pi\)
−0.842026 + 0.539437i \(0.818637\pi\)
\(660\) 0 0
\(661\) −36.1490 + 20.8706i −1.40603 + 0.811773i −0.995003 0.0998487i \(-0.968164\pi\)
−0.411030 + 0.911622i \(0.634831\pi\)
\(662\) −1.12725 1.95246i −0.0438119 0.0758844i
\(663\) 0 0
\(664\) 2.72583i 0.105783i
\(665\) 36.3762 29.0755i 1.41061 1.12750i
\(666\) 0 0
\(667\) 32.7143 + 18.8876i 1.26670 + 0.731330i
\(668\) −7.64620 + 4.41453i −0.295840 + 0.170803i
\(669\) 0 0
\(670\) −34.4560 + 32.8350i −1.33115 + 1.26853i
\(671\) −7.65618 −0.295564
\(672\) 0 0
\(673\) 7.91950i 0.305274i 0.988282 + 0.152637i \(0.0487766\pi\)
−0.988282 + 0.152637i \(0.951223\pi\)
\(674\) 6.50916 + 3.75807i 0.250724 + 0.144755i
\(675\) 0 0
\(676\) −8.82673 15.2883i −0.339489 0.588013i
\(677\) 9.23807 + 5.33360i 0.355048 + 0.204987i 0.666906 0.745142i \(-0.267618\pi\)
−0.311858 + 0.950129i \(0.600951\pi\)
\(678\) 0 0
\(679\) 2.47684 + 5.30792i 0.0950524 + 0.203699i
\(680\) 1.01712 + 0.298967i 0.0390048 + 0.0114649i
\(681\) 0 0
\(682\) 4.41154 + 7.64100i 0.168926 + 0.292589i
\(683\) −1.10463 1.91327i −0.0422674 0.0732093i 0.844118 0.536158i \(-0.180125\pi\)
−0.886385 + 0.462948i \(0.846791\pi\)
\(684\) 0 0
\(685\) 4.43924 15.1028i 0.169615 0.577048i
\(686\) −25.0342 + 25.0741i −0.955810 + 0.957334i
\(687\) 0 0
\(688\) −25.3960 14.6624i −0.968212 0.558997i
\(689\) −3.69828 6.40560i −0.140893 0.244034i
\(690\) 0 0
\(691\) −8.02498 4.63322i −0.305284 0.176256i 0.339530 0.940595i \(-0.389732\pi\)
−0.644814 + 0.764339i \(0.723065\pi\)
\(692\) 12.3762i 0.470474i
\(693\) 0 0
\(694\) 9.24172 0.350811
\(695\) 10.4556 9.96372i 0.396604 0.377945i
\(696\) 0 0
\(697\) 0.885707 0.511363i 0.0335486 0.0193693i
\(698\) −26.5857 15.3492i −1.00628 0.580977i
\(699\) 0 0
\(700\) 17.3659 + 13.4435i 0.656369 + 0.508117i
\(701\) 6.99882i 0.264342i −0.991227 0.132171i \(-0.957805\pi\)
0.991227 0.132171i \(-0.0421948\pi\)
\(702\) 0 0
\(703\) −12.4581 21.5781i −0.469867 0.813834i
\(704\) −14.2244 + 8.21247i −0.536103 + 0.309519i
\(705\) 0 0
\(706\) 11.2511i 0.423441i
\(707\) −17.7517 + 25.3663i −0.667620 + 0.953999i
\(708\) 0 0
\(709\) 15.5805 26.9863i 0.585139 1.01349i −0.409719 0.912212i \(-0.634373\pi\)
0.994858 0.101279i \(-0.0322935\pi\)
\(710\) −10.2099 42.1379i −0.383169 1.58141i
\(711\) 0 0
\(712\) −3.66519 + 6.34829i −0.137359 + 0.237912i
\(713\) 6.95644i 0.260521i
\(714\) 0 0
\(715\) −33.6597 9.89379i −1.25880 0.370007i
\(716\) 19.1316 + 11.0456i 0.714980 + 0.412794i
\(717\) 0 0
\(718\) −13.3976 + 7.73514i −0.499996 + 0.288673i
\(719\) 4.53080 7.84758i 0.168970 0.292665i −0.769088 0.639143i \(-0.779289\pi\)
0.938058 + 0.346478i \(0.112622\pi\)
\(720\) 0 0
\(721\) 1.54260 + 0.134547i 0.0574493 + 0.00501079i
\(722\) 82.1894 3.05877
\(723\) 0 0
\(724\) −14.3169 + 8.26587i −0.532084 + 0.307199i
\(725\) 38.7529 + 1.86811i 1.43925 + 0.0693800i
\(726\) 0 0
\(727\) −17.0567 −0.632599 −0.316300 0.948659i \(-0.602441\pi\)
−0.316300 + 0.948659i \(0.602441\pi\)
\(728\) −3.53656 7.57892i −0.131074 0.280893i
\(729\) 0 0
\(730\) 40.7974 + 42.8114i 1.50998 + 1.58452i
\(731\) −2.34233 4.05703i −0.0866342 0.150055i
\(732\) 0 0
\(733\) 7.98301 13.8270i 0.294859 0.510711i −0.680093 0.733126i \(-0.738061\pi\)
0.974952 + 0.222415i \(0.0713939\pi\)
\(734\) −35.5265 −1.31131
\(735\) 0 0
\(736\) 36.1784 1.33355
\(737\) −17.9539 + 31.0970i −0.661340 + 1.14547i
\(738\) 0 0
\(739\) 6.92575 + 11.9958i 0.254768 + 0.441271i 0.964832 0.262866i \(-0.0846676\pi\)
−0.710064 + 0.704137i \(0.751334\pi\)
\(740\) 8.50644 8.10626i 0.312703 0.297992i
\(741\) 0 0
\(742\) 3.25653 + 6.97881i 0.119551 + 0.256200i
\(743\) 27.6801 1.01548 0.507741 0.861510i \(-0.330481\pi\)
0.507741 + 0.861510i \(0.330481\pi\)
\(744\) 0 0
\(745\) 12.4012 + 51.1819i 0.454344 + 1.87516i
\(746\) 4.37976 2.52866i 0.160355 0.0925807i
\(747\) 0 0
\(748\) −3.90666 −0.142842
\(749\) 4.46006 + 0.389011i 0.162967 + 0.0142142i
\(750\) 0 0
\(751\) −16.6666 + 28.8674i −0.608173 + 1.05339i 0.383368 + 0.923596i \(0.374764\pi\)
−0.991541 + 0.129791i \(0.958569\pi\)
\(752\) 19.2518 11.1150i 0.702041 0.405324i
\(753\) 0 0
\(754\) 62.5005 + 36.0847i 2.27613 + 1.31413i
\(755\) 11.4191 38.8491i 0.415585 1.41386i
\(756\) 0 0
\(757\) 10.1442i 0.368697i 0.982861 + 0.184348i \(0.0590175\pi\)
−0.982861 + 0.184348i \(0.940983\pi\)
\(758\) −22.8221 + 39.5290i −0.828935 + 1.43576i
\(759\) 0 0
\(760\) −2.69507 11.1230i −0.0977605 0.403475i
\(761\) −7.35057 + 12.7316i −0.266458 + 0.461519i −0.967945 0.251164i \(-0.919187\pi\)
0.701487 + 0.712683i \(0.252520\pi\)
\(762\) 0 0
\(763\) −20.3316 + 29.0529i −0.736052 + 1.05179i
\(764\) 40.8577i 1.47818i
\(765\) 0 0
\(766\) 18.4157 10.6323i 0.665388 0.384162i
\(767\) 15.3176 + 26.5308i 0.553085 + 0.957971i
\(768\) 0 0
\(769\) 22.4992i 0.811340i 0.914020 + 0.405670i \(0.132962\pi\)
−0.914020 + 0.405670i \(0.867038\pi\)
\(770\) 34.0185 + 13.3075i 1.22594 + 0.479571i
\(771\) 0 0
\(772\) −17.9919 10.3876i −0.647542 0.373859i
\(773\) −18.4057 + 10.6266i −0.662008 + 0.382211i −0.793042 0.609167i \(-0.791504\pi\)
0.131034 + 0.991378i \(0.458170\pi\)
\(774\) 0 0
\(775\) −3.27032 6.35239i −0.117473 0.228185i
\(776\) 1.43954 0.0516764
\(777\) 0 0
\(778\) 24.0698i 0.862945i
\(779\) −9.56170 5.52045i −0.342583 0.197791i
\(780\) 0 0
\(781\) −16.3550 28.3278i −0.585229 1.01365i
\(782\) 5.88111 + 3.39546i 0.210308 + 0.121421i
\(783\) 0 0
\(784\) 10.9434 + 30.0171i 0.390835 + 1.07204i
\(785\) 1.56671 5.33012i 0.0559183 0.190240i
\(786\) 0 0
\(787\) 7.85952 + 13.6131i 0.280162 + 0.485254i 0.971424 0.237349i \(-0.0762786\pi\)
−0.691263 + 0.722603i \(0.742945\pi\)
\(788\) −13.0293 22.5675i −0.464151 0.803933i
\(789\) 0 0
\(790\) −4.80190 + 16.3366i −0.170844 + 0.581230i
\(791\) −15.9011 34.0765i −0.565379 1.21162i
\(792\) 0 0
\(793\) 9.98750 + 5.76628i 0.354666 + 0.204767i
\(794\) 27.3875 + 47.4366i 0.971946 + 1.68346i
\(795\) 0 0
\(796\) −28.4605 16.4317i −1.00876 0.582406i
\(797\) 39.5812i 1.40204i −0.713143 0.701019i \(-0.752729\pi\)
0.713143 0.701019i \(-0.247271\pi\)
\(798\) 0 0
\(799\) 3.55128 0.125635
\(800\) 33.0369 17.0080i 1.16803 0.601322i
\(801\) 0 0
\(802\) −19.7043 + 11.3763i −0.695784 + 0.401711i
\(803\) 38.6380 + 22.3076i 1.36350 + 0.787220i
\(804\) 0 0
\(805\) −17.9820 22.4972i −0.633783 0.792923i
\(806\) 13.2903i 0.468130i
\(807\) 0 0
\(808\) 3.80455 + 6.58967i 0.133843 + 0.231824i
\(809\) −38.1053 + 22.0001i −1.33971 + 0.773483i −0.986764 0.162160i \(-0.948154\pi\)
−0.352947 + 0.935643i \(0.614820\pi\)
\(810\) 0 0
\(811\) 44.9306i 1.57773i 0.614567 + 0.788864i \(0.289331\pi\)
−0.614567 + 0.788864i \(0.710669\pi\)
\(812\) −27.9237 19.5413i −0.979929 0.685766i
\(813\) 0 0
\(814\) 9.77230 16.9261i 0.342519 0.593260i
\(815\) −2.07342 8.55737i −0.0726287 0.299752i
\(816\) 0 0
\(817\) −25.2867 + 43.7979i −0.884671 + 1.53229i
\(818\) 27.5819i 0.964378i
\(819\) 0 0
\(820\) 1.46835 4.99549i 0.0512771 0.174450i
\(821\) −13.1026 7.56481i −0.457285 0.264014i 0.253617 0.967305i \(-0.418380\pi\)
−0.710902 + 0.703291i \(0.751713\pi\)
\(822\) 0 0
\(823\) −27.3487 + 15.7898i −0.953316 + 0.550397i −0.894109 0.447848i \(-0.852190\pi\)
−0.0592066 + 0.998246i \(0.518857\pi\)
\(824\) 0.190278 0.329571i 0.00662865 0.0114812i
\(825\) 0 0
\(826\) −13.4879 28.9049i −0.469305 1.00573i
\(827\) 48.6368 1.69127 0.845633 0.533765i \(-0.179223\pi\)
0.845633 + 0.533765i \(0.179223\pi\)
\(828\) 0 0
\(829\) 40.4900 23.3769i 1.40628 0.811914i 0.411249 0.911523i \(-0.365093\pi\)
0.995027 + 0.0996095i \(0.0317594\pi\)
\(830\) −4.22301 17.4291i −0.146583 0.604973i
\(831\) 0 0
\(832\) 24.7410 0.857741
\(833\) −0.883629 + 5.02692i −0.0306159 + 0.174173i
\(834\) 0 0
\(835\) 8.60907 8.20406i 0.297929 0.283913i
\(836\) 21.0873 + 36.5242i 0.729319 + 1.26322i
\(837\) 0 0
\(838\) 33.4227 57.8898i 1.15457 1.99977i
\(839\) 29.1067 1.00488 0.502438 0.864613i \(-0.332437\pi\)
0.502438 + 0.864613i \(0.332437\pi\)
\(840\) 0 0
\(841\) −31.2110 −1.07624
\(842\) 22.8157 39.5179i 0.786281 1.36188i
\(843\) 0 0
\(844\) −9.61532 16.6542i −0.330973 0.573262i
\(845\) 16.4038 + 17.2136i 0.564307 + 0.592165i
\(846\) 0 0
\(847\) −1.53893 0.134227i −0.0528782 0.00461209i
\(848\) 6.94434 0.238469
\(849\) 0 0
\(850\) 6.96668 + 0.335834i 0.238955 + 0.0115190i
\(851\) −13.3452 + 7.70485i −0.457467 + 0.264119i
\(852\) 0 0
\(853\) 28.4915 0.975531 0.487766 0.872975i \(-0.337812\pi\)
0.487766 + 0.872975i \(0.337812\pi\)
\(854\) −9.83787 6.88466i −0.336645 0.235588i
\(855\) 0 0
\(856\) 0.550145 0.952879i 0.0188036 0.0325687i
\(857\) −35.1219 + 20.2776i −1.19974 + 0.692670i −0.960497 0.278290i \(-0.910232\pi\)
−0.239243 + 0.970960i \(0.576899\pi\)
\(858\) 0 0
\(859\) 32.6686 + 18.8612i 1.11464 + 0.643537i 0.940027 0.341100i \(-0.110800\pi\)
0.174612 + 0.984637i \(0.444133\pi\)
\(860\) −22.8821 6.72587i −0.780274 0.229350i
\(861\) 0 0
\(862\) 15.6085i 0.531627i
\(863\) −12.8395 + 22.2387i −0.437062 + 0.757014i −0.997461 0.0712087i \(-0.977314\pi\)
0.560399 + 0.828223i \(0.310648\pi\)
\(864\) 0 0
\(865\) −3.92547 16.2011i −0.133470 0.550855i
\(866\) 24.1695 41.8627i 0.821311 1.42255i
\(867\) 0 0
\(868\) −0.545360 + 6.25262i −0.0185107 + 0.212228i
\(869\) 12.8463i 0.435779i
\(870\) 0 0
\(871\) 46.8417 27.0441i 1.58717 0.916353i
\(872\) 4.35747 + 7.54736i 0.147563 + 0.255586i
\(873\) 0 0
\(874\) 73.3117i 2.47981i
\(875\) −26.9968 12.0902i −0.912659 0.408722i
\(876\) 0 0
\(877\) −16.4938 9.52270i −0.556956 0.321559i 0.194967 0.980810i \(-0.437540\pi\)
−0.751923 + 0.659251i \(0.770873\pi\)
\(878\) −1.31671 + 0.760202i −0.0444367 + 0.0256556i
\(879\) 0 0
\(880\) 23.8453 22.7235i 0.803826 0.766010i
\(881\) 30.7115 1.03470 0.517349 0.855774i \(-0.326919\pi\)
0.517349 + 0.855774i \(0.326919\pi\)
\(882\) 0 0
\(883\) 36.8466i 1.23999i −0.784607 0.619993i \(-0.787135\pi\)
0.784607 0.619993i \(-0.212865\pi\)
\(884\) 5.09624 + 2.94232i 0.171405 + 0.0989608i
\(885\) 0 0
\(886\) 21.6653 + 37.5254i 0.727859 + 1.26069i
\(887\) −29.3385 16.9386i −0.985090 0.568742i −0.0812870 0.996691i \(-0.525903\pi\)
−0.903803 + 0.427949i \(0.859236\pi\)
\(888\) 0 0
\(889\) −5.00982 + 2.33774i −0.168024 + 0.0784051i
\(890\) −13.6002 + 46.2695i −0.455881 + 1.55096i
\(891\) 0 0
\(892\) 20.0311 + 34.6949i 0.670691 + 1.16167i
\(893\) −19.1690 33.2017i −0.641466 1.11105i
\(894\) 0 0
\(895\) −28.5476 8.39116i −0.954242 0.280486i
\(896\) 13.5128 + 1.17860i 0.451432 + 0.0393743i
\(897\) 0 0
\(898\) 3.57319 + 2.06298i 0.119239 + 0.0688427i
\(899\) 5.54404 + 9.60257i 0.184904 + 0.320264i
\(900\) 0 0
\(901\) 0.960739 + 0.554683i 0.0320068 + 0.0184792i
\(902\) 8.66061i 0.288367i
\(903\) 0 0
\(904\) −9.24172 −0.307375
\(905\) 16.1198 15.3615i 0.535841 0.510632i
\(906\) 0 0
\(907\) −0.923888 + 0.533407i −0.0306772 + 0.0177115i −0.515260 0.857034i \(-0.672305\pi\)
0.484583 + 0.874745i \(0.338971\pi\)
\(908\) −14.6485 8.45734i −0.486129 0.280667i
\(909\) 0 0
\(910\) −34.3546 42.9809i −1.13884 1.42480i
\(911\) 9.61157i 0.318445i 0.987243 + 0.159223i \(0.0508988\pi\)
−0.987243 + 0.159223i \(0.949101\pi\)
\(912\) 0 0
\(913\) −6.76477 11.7169i −0.223881 0.387774i
\(914\) 9.06839 5.23564i 0.299956 0.173179i
\(915\) 0 0
\(916\) 43.5862i 1.44013i
\(917\) 29.5330 + 2.57590i 0.975266 + 0.0850637i
\(918\) 0 0
\(919\) 3.41594 5.91658i 0.112681 0.195170i −0.804169 0.594401i \(-0.797389\pi\)
0.916851 + 0.399231i \(0.130723\pi\)
\(920\) −6.87915 + 1.66679i −0.226799 + 0.0549526i
\(921\) 0 0
\(922\) 9.66946 16.7480i 0.318447 0.551566i
\(923\) 49.2714i 1.62179i
\(924\) 0 0
\(925\) −8.56424 + 13.3096i −0.281590 + 0.437616i
\(926\) 19.9573 + 11.5224i 0.655838 + 0.378648i
\(927\) 0 0
\(928\) −49.9401 + 28.8330i −1.63937 + 0.946488i
\(929\) 26.9383 46.6585i 0.883818 1.53082i 0.0367547 0.999324i \(-0.488298\pi\)
0.847063 0.531493i \(-0.178369\pi\)
\(930\) 0 0
\(931\) 51.7674 18.8730i 1.69661 0.618536i
\(932\) −30.5352 −1.00021
\(933\) 0 0
\(934\) −33.0252 + 19.0671i −1.08062 + 0.623894i
\(935\) 5.11402 1.23911i 0.167246 0.0405232i
\(936\) 0 0
\(937\) −21.6036 −0.705759 −0.352880 0.935669i \(-0.614797\pi\)
−0.352880 + 0.935669i \(0.614797\pi\)
\(938\) −51.0333 + 23.8137i −1.66630 + 0.777546i
\(939\) 0 0
\(940\) 13.0886 12.4729i 0.426904 0.406821i
\(941\) 29.1006 + 50.4038i 0.948654 + 1.64312i 0.748265 + 0.663400i \(0.230887\pi\)
0.200389 + 0.979716i \(0.435779\pi\)
\(942\) 0 0
\(943\) −3.41418 + 5.91353i −0.111181 + 0.192571i
\(944\) −28.7621 −0.936127
\(945\) 0 0
\(946\) −39.6704 −1.28980
\(947\) −10.2347 + 17.7271i −0.332584 + 0.576053i −0.983018 0.183510i \(-0.941254\pi\)
0.650434 + 0.759563i \(0.274587\pi\)
\(948\) 0 0
\(949\) −33.6022 58.2007i −1.09077 1.88927i
\(950\) −34.4648 66.9458i −1.11819 2.17201i
\(951\) 0 0
\(952\) 1.02772 + 0.719212i 0.0333087 + 0.0233098i
\(953\) −10.4745 −0.339303 −0.169651 0.985504i \(-0.554264\pi\)
−0.169651 + 0.985504i \(0.554264\pi\)
\(954\) 0 0
\(955\) 12.9592 + 53.4849i 0.419349 + 1.73073i
\(956\) −1.38209 + 0.797952i −0.0447001 + 0.0258076i
\(957\) 0 0
\(958\) −37.0879 −1.19825
\(959\) 10.6793 15.2602i 0.344852 0.492778i
\(960\) 0 0
\(961\) −14.4790 + 25.0784i −0.467066 + 0.808982i
\(962\) −25.4960 + 14.7201i −0.822023 + 0.474595i
\(963\) 0 0
\(964\) 9.36026 + 5.40415i 0.301474 + 0.174056i
\(965\) 26.8470 + 7.89129i 0.864236 + 0.254030i
\(966\) 0 0
\(967\) 43.1242i 1.38678i −0.720562 0.693391i \(-0.756116\pi\)
0.720562 0.693391i \(-0.243884\pi\)
\(968\) −0.189825 + 0.328787i −0.00610122 + 0.0105676i
\(969\) 0 0
\(970\) 9.20446 2.23021i 0.295537 0.0716076i
\(971\) 4.17572 7.23256i 0.134005 0.232104i −0.791212 0.611542i \(-0.790549\pi\)
0.925217 + 0.379438i \(0.123883\pi\)
\(972\) 0 0
\(973\) 15.4860 7.22623i 0.496457 0.231662i
\(974\) 3.53581i 0.113295i
\(975\) 0 0
\(976\) −9.37687 + 5.41374i −0.300146 + 0.173290i
\(977\) 13.4044 + 23.2171i 0.428845 + 0.742781i 0.996771 0.0802983i \(-0.0255873\pi\)
−0.567926 + 0.823080i \(0.692254\pi\)
\(978\) 0 0
\(979\) 36.3840i 1.16284i
\(980\) 14.3990 + 21.6308i 0.459958 + 0.690971i
\(981\) 0 0
\(982\) −42.2221 24.3769i −1.34736 0.777899i
\(983\) 25.5109 14.7287i 0.813671 0.469773i −0.0345581 0.999403i \(-0.511002\pi\)
0.848229 + 0.529630i \(0.177669\pi\)
\(984\) 0 0
\(985\) 24.2140 + 25.4094i 0.771522 + 0.809610i
\(986\) −10.8243 −0.344714
\(987\) 0 0
\(988\) 63.5279i 2.02109i
\(989\) 27.0873 + 15.6388i 0.861325 + 0.497286i
\(990\) 0 0
\(991\) 2.50334 + 4.33591i 0.0795211 + 0.137735i 0.903043 0.429549i \(-0.141328\pi\)
−0.823522 + 0.567284i \(0.807994\pi\)
\(992\) 9.19667 + 5.30970i 0.291995 + 0.168583i
\(993\) 0 0
\(994\) 4.45760 51.1069i 0.141386 1.62101i
\(995\) 42.4681 + 12.4829i 1.34633 + 0.395734i
\(996\) 0 0
\(997\) −4.43960 7.68960i −0.140603 0.243532i 0.787121 0.616799i \(-0.211571\pi\)
−0.927724 + 0.373267i \(0.878238\pi\)
\(998\) −25.0893 43.4560i −0.794189 1.37558i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 315.2.bb.b.89.9 yes 24
3.2 odd 2 inner 315.2.bb.b.89.4 yes 24
5.2 odd 4 1575.2.bk.i.26.9 24
5.3 odd 4 1575.2.bk.i.26.3 24
5.4 even 2 inner 315.2.bb.b.89.3 24
7.2 even 3 2205.2.g.b.2204.7 24
7.3 odd 6 inner 315.2.bb.b.269.10 yes 24
7.5 odd 6 2205.2.g.b.2204.8 24
15.2 even 4 1575.2.bk.i.26.4 24
15.8 even 4 1575.2.bk.i.26.10 24
15.14 odd 2 inner 315.2.bb.b.89.10 yes 24
21.2 odd 6 2205.2.g.b.2204.17 24
21.5 even 6 2205.2.g.b.2204.18 24
21.17 even 6 inner 315.2.bb.b.269.3 yes 24
35.3 even 12 1575.2.bk.i.1151.10 24
35.9 even 6 2205.2.g.b.2204.19 24
35.17 even 12 1575.2.bk.i.1151.4 24
35.19 odd 6 2205.2.g.b.2204.20 24
35.24 odd 6 inner 315.2.bb.b.269.4 yes 24
105.17 odd 12 1575.2.bk.i.1151.9 24
105.38 odd 12 1575.2.bk.i.1151.3 24
105.44 odd 6 2205.2.g.b.2204.5 24
105.59 even 6 inner 315.2.bb.b.269.9 yes 24
105.89 even 6 2205.2.g.b.2204.6 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bb.b.89.3 24 5.4 even 2 inner
315.2.bb.b.89.4 yes 24 3.2 odd 2 inner
315.2.bb.b.89.9 yes 24 1.1 even 1 trivial
315.2.bb.b.89.10 yes 24 15.14 odd 2 inner
315.2.bb.b.269.3 yes 24 21.17 even 6 inner
315.2.bb.b.269.4 yes 24 35.24 odd 6 inner
315.2.bb.b.269.9 yes 24 105.59 even 6 inner
315.2.bb.b.269.10 yes 24 7.3 odd 6 inner
1575.2.bk.i.26.3 24 5.3 odd 4
1575.2.bk.i.26.4 24 15.2 even 4
1575.2.bk.i.26.9 24 5.2 odd 4
1575.2.bk.i.26.10 24 15.8 even 4
1575.2.bk.i.1151.3 24 105.38 odd 12
1575.2.bk.i.1151.4 24 35.17 even 12
1575.2.bk.i.1151.9 24 105.17 odd 12
1575.2.bk.i.1151.10 24 35.3 even 12
2205.2.g.b.2204.5 24 105.44 odd 6
2205.2.g.b.2204.6 24 105.89 even 6
2205.2.g.b.2204.7 24 7.2 even 3
2205.2.g.b.2204.8 24 7.5 odd 6
2205.2.g.b.2204.17 24 21.2 odd 6
2205.2.g.b.2204.18 24 21.5 even 6
2205.2.g.b.2204.19 24 35.9 even 6
2205.2.g.b.2204.20 24 35.19 odd 6