Properties

Label 360.2.d.f.109.6
Level $360$
Weight $2$
Character 360.109
Analytic conductor $2.875$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(109,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.839056.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 6x^{4} + 8x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 109.6
Root \(1.32132i\) of defining polynomial
Character \(\chi\) \(=\) 360.109
Dual form 360.2.d.f.109.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.34067 + 0.450129i) q^{2} +(1.59477 + 1.20695i) q^{4} +(0.254102 - 2.22158i) q^{5} +2.64265i q^{7} +(1.59477 + 2.33596i) q^{8} +O(q^{10})\) \(q+(1.34067 + 0.450129i) q^{2} +(1.59477 + 1.20695i) q^{4} +(0.254102 - 2.22158i) q^{5} +2.64265i q^{7} +(1.59477 + 2.33596i) q^{8} +(1.34067 - 2.86402i) q^{10} +1.51363i q^{11} +3.87086 q^{13} +(-1.18953 + 3.54291i) q^{14} +(1.08656 + 3.84959i) q^{16} -3.31415i q^{17} -7.08582i q^{19} +(3.08656 - 3.23622i) q^{20} +(-0.681331 + 2.02927i) q^{22} +4.82778i q^{23} +(-4.87086 - 1.12902i) q^{25} +(5.18953 + 1.74239i) q^{26} +(-3.18953 + 4.21441i) q^{28} -2.18513i q^{29} -7.36266 q^{31} +(-0.276098 + 5.65011i) q^{32} +(1.49180 - 4.44317i) q^{34} +(5.87086 + 0.671502i) q^{35} -7.87086 q^{37} +(3.18953 - 9.49971i) q^{38} +(5.59477 - 2.94934i) q^{40} -8.72532 q^{41} +1.01641 q^{43} +(-1.82687 + 2.41389i) q^{44} +(-2.17313 + 6.47244i) q^{46} +7.08582i q^{47} +0.0164068 q^{49} +(-6.02200 - 3.70615i) q^{50} +(6.17313 + 4.67192i) q^{52} -4.50820 q^{53} +(3.36266 + 0.384617i) q^{55} +(-6.17313 + 4.21441i) q^{56} +(0.983593 - 2.92953i) q^{58} -6.79893i q^{59} -3.60104i q^{61} +(-9.87086 - 3.31415i) q^{62} +(-2.91344 + 7.45063i) q^{64} +(0.983593 - 8.59945i) q^{65} -1.01641 q^{67} +(4.00000 - 5.28530i) q^{68} +(7.56860 + 3.54291i) q^{70} +6.72532 q^{71} -15.5146i q^{73} +(-10.5522 - 3.54291i) q^{74} +(8.55220 - 11.3002i) q^{76} -4.00000 q^{77} +7.36266 q^{79} +(8.82829 - 1.43570i) q^{80} +(-11.6977 - 3.92752i) q^{82} -7.74173 q^{83} +(-7.36266 - 0.842131i) q^{85} +(1.36266 + 0.457515i) q^{86} +(-3.53579 + 2.41389i) q^{88} +14.7581 q^{89} +10.2293i q^{91} +(-5.82687 + 7.69919i) q^{92} +(-3.18953 + 9.49971i) q^{94} +(-15.7417 - 1.80052i) q^{95} +11.1444i q^{97} +(0.0219960 + 0.00738516i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} + q^{4} + q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} + q^{4} + q^{8} + q^{10} - 8 q^{13} + 10 q^{14} + q^{16} + 13 q^{20} + 10 q^{22} + 2 q^{25} + 14 q^{26} - 2 q^{28} - 16 q^{31} + 21 q^{32} + 12 q^{34} + 4 q^{35} - 16 q^{37} + 2 q^{38} + 25 q^{40} + 4 q^{41} - 22 q^{44} - 2 q^{46} - 6 q^{49} - 15 q^{50} + 26 q^{52} - 24 q^{53} - 8 q^{55} - 26 q^{56} + 12 q^{58} - 28 q^{62} - 23 q^{64} + 12 q^{65} + 24 q^{68} - 6 q^{70} - 16 q^{71} - 18 q^{74} + 6 q^{76} - 24 q^{77} + 16 q^{79} - 15 q^{80} - 50 q^{82} + 16 q^{83} - 16 q^{85} - 20 q^{86} + 18 q^{88} + 20 q^{89} - 46 q^{92} - 2 q^{94} - 32 q^{95} - 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.34067 + 0.450129i 0.947994 + 0.318290i
\(3\) 0 0
\(4\) 1.59477 + 1.20695i 0.797384 + 0.603473i
\(5\) 0.254102 2.22158i 0.113638 0.993522i
\(6\) 0 0
\(7\) 2.64265i 0.998827i 0.866364 + 0.499414i \(0.166451\pi\)
−0.866364 + 0.499414i \(0.833549\pi\)
\(8\) 1.59477 + 2.33596i 0.563835 + 0.825887i
\(9\) 0 0
\(10\) 1.34067 2.86402i 0.423956 0.905683i
\(11\) 1.51363i 0.456377i 0.973617 + 0.228189i \(0.0732803\pi\)
−0.973617 + 0.228189i \(0.926720\pi\)
\(12\) 0 0
\(13\) 3.87086 1.07358 0.536792 0.843714i \(-0.319636\pi\)
0.536792 + 0.843714i \(0.319636\pi\)
\(14\) −1.18953 + 3.54291i −0.317916 + 0.946882i
\(15\) 0 0
\(16\) 1.08656 + 3.84959i 0.271641 + 0.962399i
\(17\) 3.31415i 0.803800i −0.915684 0.401900i \(-0.868350\pi\)
0.915684 0.401900i \(-0.131650\pi\)
\(18\) 0 0
\(19\) 7.08582i 1.62560i −0.582545 0.812799i \(-0.697943\pi\)
0.582545 0.812799i \(-0.302057\pi\)
\(20\) 3.08656 3.23622i 0.690177 0.723641i
\(21\) 0 0
\(22\) −0.681331 + 2.02927i −0.145260 + 0.432643i
\(23\) 4.82778i 1.00666i 0.864094 + 0.503331i \(0.167892\pi\)
−0.864094 + 0.503331i \(0.832108\pi\)
\(24\) 0 0
\(25\) −4.87086 1.12902i −0.974173 0.225803i
\(26\) 5.18953 + 1.74239i 1.01775 + 0.341711i
\(27\) 0 0
\(28\) −3.18953 + 4.21441i −0.602765 + 0.796448i
\(29\) 2.18513i 0.405769i −0.979203 0.202885i \(-0.934968\pi\)
0.979203 0.202885i \(-0.0650316\pi\)
\(30\) 0 0
\(31\) −7.36266 −1.32237 −0.661187 0.750222i \(-0.729947\pi\)
−0.661187 + 0.750222i \(0.729947\pi\)
\(32\) −0.276098 + 5.65011i −0.0488076 + 0.998808i
\(33\) 0 0
\(34\) 1.49180 4.44317i 0.255841 0.761997i
\(35\) 5.87086 + 0.671502i 0.992357 + 0.113504i
\(36\) 0 0
\(37\) −7.87086 −1.29396 −0.646981 0.762506i \(-0.723969\pi\)
−0.646981 + 0.762506i \(0.723969\pi\)
\(38\) 3.18953 9.49971i 0.517411 1.54106i
\(39\) 0 0
\(40\) 5.59477 2.94934i 0.884610 0.466331i
\(41\) −8.72532 −1.36267 −0.681333 0.731973i \(-0.738600\pi\)
−0.681333 + 0.731973i \(0.738600\pi\)
\(42\) 0 0
\(43\) 1.01641 0.155001 0.0775003 0.996992i \(-0.475306\pi\)
0.0775003 + 0.996992i \(0.475306\pi\)
\(44\) −1.82687 + 2.41389i −0.275411 + 0.363908i
\(45\) 0 0
\(46\) −2.17313 + 6.47244i −0.320410 + 0.954309i
\(47\) 7.08582i 1.03357i 0.856114 + 0.516786i \(0.172872\pi\)
−0.856114 + 0.516786i \(0.827128\pi\)
\(48\) 0 0
\(49\) 0.0164068 0.00234382
\(50\) −6.02200 3.70615i −0.851639 0.524129i
\(51\) 0 0
\(52\) 6.17313 + 4.67192i 0.856059 + 0.647879i
\(53\) −4.50820 −0.619249 −0.309625 0.950859i \(-0.600203\pi\)
−0.309625 + 0.950859i \(0.600203\pi\)
\(54\) 0 0
\(55\) 3.36266 + 0.384617i 0.453421 + 0.0518617i
\(56\) −6.17313 + 4.21441i −0.824919 + 0.563174i
\(57\) 0 0
\(58\) 0.983593 2.92953i 0.129152 0.384667i
\(59\) 6.79893i 0.885145i −0.896733 0.442573i \(-0.854066\pi\)
0.896733 0.442573i \(-0.145934\pi\)
\(60\) 0 0
\(61\) 3.60104i 0.461065i −0.973065 0.230533i \(-0.925953\pi\)
0.973065 0.230533i \(-0.0740469\pi\)
\(62\) −9.87086 3.31415i −1.25360 0.420898i
\(63\) 0 0
\(64\) −2.91344 + 7.45063i −0.364180 + 0.931329i
\(65\) 0.983593 8.59945i 0.122000 1.06663i
\(66\) 0 0
\(67\) −1.01641 −0.124174 −0.0620869 0.998071i \(-0.519776\pi\)
−0.0620869 + 0.998071i \(0.519776\pi\)
\(68\) 4.00000 5.28530i 0.485071 0.640937i
\(69\) 0 0
\(70\) 7.56860 + 3.54291i 0.904621 + 0.423458i
\(71\) 6.72532 0.798149 0.399074 0.916919i \(-0.369331\pi\)
0.399074 + 0.916919i \(0.369331\pi\)
\(72\) 0 0
\(73\) 15.5146i 1.81585i −0.419132 0.907925i \(-0.637666\pi\)
0.419132 0.907925i \(-0.362334\pi\)
\(74\) −10.5522 3.54291i −1.22667 0.411855i
\(75\) 0 0
\(76\) 8.55220 11.3002i 0.981004 1.29622i
\(77\) −4.00000 −0.455842
\(78\) 0 0
\(79\) 7.36266 0.828364 0.414182 0.910194i \(-0.364068\pi\)
0.414182 + 0.910194i \(0.364068\pi\)
\(80\) 8.82829 1.43570i 0.987033 0.160516i
\(81\) 0 0
\(82\) −11.6977 3.92752i −1.29180 0.433723i
\(83\) −7.74173 −0.849765 −0.424883 0.905248i \(-0.639685\pi\)
−0.424883 + 0.905248i \(0.639685\pi\)
\(84\) 0 0
\(85\) −7.36266 0.842131i −0.798593 0.0913420i
\(86\) 1.36266 + 0.457515i 0.146940 + 0.0493351i
\(87\) 0 0
\(88\) −3.53579 + 2.41389i −0.376916 + 0.257322i
\(89\) 14.7581 1.56436 0.782180 0.623053i \(-0.214108\pi\)
0.782180 + 0.623053i \(0.214108\pi\)
\(90\) 0 0
\(91\) 10.2293i 1.07233i
\(92\) −5.82687 + 7.69919i −0.607493 + 0.802696i
\(93\) 0 0
\(94\) −3.18953 + 9.49971i −0.328975 + 0.979820i
\(95\) −15.7417 1.80052i −1.61507 0.184729i
\(96\) 0 0
\(97\) 11.1444i 1.13154i 0.824563 + 0.565769i \(0.191421\pi\)
−0.824563 + 0.565769i \(0.808579\pi\)
\(98\) 0.0219960 + 0.00738516i 0.00222193 + 0.000746014i
\(99\) 0 0
\(100\) −6.40523 7.67939i −0.640523 0.767939i
\(101\) 13.3295i 1.32633i 0.748471 + 0.663167i \(0.230788\pi\)
−0.748471 + 0.663167i \(0.769212\pi\)
\(102\) 0 0
\(103\) 0.958386i 0.0944326i 0.998885 + 0.0472163i \(0.0150350\pi\)
−0.998885 + 0.0472163i \(0.984965\pi\)
\(104\) 6.17313 + 9.04219i 0.605325 + 0.886660i
\(105\) 0 0
\(106\) −6.04399 2.02927i −0.587044 0.197101i
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) 0.769233i 0.0736792i −0.999321 0.0368396i \(-0.988271\pi\)
0.999321 0.0368396i \(-0.0117291\pi\)
\(110\) 4.33508 + 2.02927i 0.413333 + 0.193484i
\(111\) 0 0
\(112\) −10.1731 + 2.87141i −0.961270 + 0.271322i
\(113\) 14.4585i 1.36014i −0.733146 0.680071i \(-0.761949\pi\)
0.733146 0.680071i \(-0.238051\pi\)
\(114\) 0 0
\(115\) 10.7253 + 1.22675i 1.00014 + 0.114395i
\(116\) 2.63734 3.48478i 0.244871 0.323554i
\(117\) 0 0
\(118\) 3.06040 9.11509i 0.281733 0.839112i
\(119\) 8.75814 0.802857
\(120\) 0 0
\(121\) 8.70892 0.791720
\(122\) 1.62093 4.82778i 0.146752 0.437087i
\(123\) 0 0
\(124\) −11.7417 8.88633i −1.05444 0.798016i
\(125\) −3.74590 + 10.5341i −0.335043 + 0.942203i
\(126\) 0 0
\(127\) 11.5290i 1.02303i 0.859274 + 0.511516i \(0.170916\pi\)
−0.859274 + 0.511516i \(0.829084\pi\)
\(128\) −7.25969 + 8.67738i −0.641672 + 0.766979i
\(129\) 0 0
\(130\) 5.18953 11.0862i 0.455152 0.972327i
\(131\) 7.37270i 0.644156i −0.946713 0.322078i \(-0.895619\pi\)
0.946713 0.322078i \(-0.104381\pi\)
\(132\) 0 0
\(133\) 18.7253 1.62369
\(134\) −1.36266 0.457515i −0.117716 0.0395232i
\(135\) 0 0
\(136\) 7.74173 5.28530i 0.663848 0.453211i
\(137\) 3.88792i 0.332167i 0.986112 + 0.166084i \(0.0531122\pi\)
−0.986112 + 0.166084i \(0.946888\pi\)
\(138\) 0 0
\(139\) 14.6291i 1.24083i 0.784275 + 0.620414i \(0.213035\pi\)
−0.784275 + 0.620414i \(0.786965\pi\)
\(140\) 8.55220 + 8.15670i 0.722792 + 0.689367i
\(141\) 0 0
\(142\) 9.01641 + 3.02727i 0.756640 + 0.254042i
\(143\) 5.85907i 0.489960i
\(144\) 0 0
\(145\) −4.85446 0.555246i −0.403141 0.0461107i
\(146\) 6.98359 20.7999i 0.577966 1.72141i
\(147\) 0 0
\(148\) −12.5522 9.49971i −1.03178 0.780871i
\(149\) 11.0715i 0.907010i −0.891254 0.453505i \(-0.850173\pi\)
0.891254 0.453505i \(-0.149827\pi\)
\(150\) 0 0
\(151\) 0.637339 0.0518659 0.0259329 0.999664i \(-0.491744\pi\)
0.0259329 + 0.999664i \(0.491744\pi\)
\(152\) 16.5522 11.3002i 1.34256 0.916569i
\(153\) 0 0
\(154\) −5.36266 1.80052i −0.432136 0.145090i
\(155\) −1.87086 + 16.3568i −0.150271 + 1.31381i
\(156\) 0 0
\(157\) 0.129135 0.0103061 0.00515306 0.999987i \(-0.498360\pi\)
0.00515306 + 0.999987i \(0.498360\pi\)
\(158\) 9.87086 + 3.31415i 0.785284 + 0.263660i
\(159\) 0 0
\(160\) 12.4820 + 2.04908i 0.986792 + 0.161994i
\(161\) −12.7581 −1.00548
\(162\) 0 0
\(163\) −19.4835 −1.52606 −0.763031 0.646362i \(-0.776290\pi\)
−0.763031 + 0.646362i \(0.776290\pi\)
\(164\) −13.9149 10.5310i −1.08657 0.822332i
\(165\) 0 0
\(166\) −10.3791 3.48478i −0.805572 0.270471i
\(167\) 1.80052i 0.139328i −0.997571 0.0696641i \(-0.977807\pi\)
0.997571 0.0696641i \(-0.0221928\pi\)
\(168\) 0 0
\(169\) 1.98359 0.152584
\(170\) −9.49180 4.44317i −0.727988 0.340775i
\(171\) 0 0
\(172\) 1.62093 + 1.22675i 0.123595 + 0.0935386i
\(173\) 23.2335 1.76641 0.883206 0.468985i \(-0.155380\pi\)
0.883206 + 0.468985i \(0.155380\pi\)
\(174\) 0 0
\(175\) 2.98359 12.8720i 0.225538 0.973031i
\(176\) −5.82687 + 1.64466i −0.439217 + 0.123971i
\(177\) 0 0
\(178\) 19.7857 + 6.64307i 1.48300 + 0.497919i
\(179\) 2.85664i 0.213515i −0.994285 0.106757i \(-0.965953\pi\)
0.994285 0.106757i \(-0.0340468\pi\)
\(180\) 0 0
\(181\) 5.28530i 0.392853i 0.980519 + 0.196427i \(0.0629337\pi\)
−0.980519 + 0.196427i \(0.937066\pi\)
\(182\) −4.60453 + 13.7141i −0.341310 + 1.01656i
\(183\) 0 0
\(184\) −11.2775 + 7.69919i −0.831390 + 0.567592i
\(185\) −2.00000 + 17.4858i −0.147043 + 1.28558i
\(186\) 0 0
\(187\) 5.01641 0.366836
\(188\) −8.55220 + 11.3002i −0.623733 + 0.824154i
\(189\) 0 0
\(190\) −20.2939 9.49971i −1.47228 0.689181i
\(191\) 5.96719 0.431770 0.215885 0.976419i \(-0.430736\pi\)
0.215885 + 0.976419i \(0.430736\pi\)
\(192\) 0 0
\(193\) 14.9409i 1.07547i 0.843115 + 0.537733i \(0.180719\pi\)
−0.843115 + 0.537733i \(0.819281\pi\)
\(194\) −5.01641 + 14.9409i −0.360157 + 1.07269i
\(195\) 0 0
\(196\) 0.0261649 + 0.0198021i 0.00186892 + 0.00141443i
\(197\) −3.23353 −0.230379 −0.115190 0.993344i \(-0.536748\pi\)
−0.115190 + 0.993344i \(0.536748\pi\)
\(198\) 0 0
\(199\) 8.12080 0.575668 0.287834 0.957680i \(-0.407065\pi\)
0.287834 + 0.957680i \(0.407065\pi\)
\(200\) −5.13056 13.1787i −0.362785 0.931873i
\(201\) 0 0
\(202\) −6.00000 + 17.8704i −0.422159 + 1.25736i
\(203\) 5.77454 0.405293
\(204\) 0 0
\(205\) −2.21712 + 19.3840i −0.154850 + 1.35384i
\(206\) −0.431398 + 1.28488i −0.0300569 + 0.0895215i
\(207\) 0 0
\(208\) 4.20594 + 14.9013i 0.291630 + 1.03322i
\(209\) 10.7253 0.741886
\(210\) 0 0
\(211\) 13.7141i 0.944119i −0.881567 0.472059i \(-0.843511\pi\)
0.881567 0.472059i \(-0.156489\pi\)
\(212\) −7.18953 5.44116i −0.493779 0.373700i
\(213\) 0 0
\(214\) 5.36266 + 1.80052i 0.366584 + 0.123081i
\(215\) 0.258271 2.25803i 0.0176139 0.153997i
\(216\) 0 0
\(217\) 19.4569i 1.32082i
\(218\) 0.346255 1.03128i 0.0234513 0.0698474i
\(219\) 0 0
\(220\) 4.89845 + 4.67192i 0.330253 + 0.314981i
\(221\) 12.8286i 0.862947i
\(222\) 0 0
\(223\) 9.84472i 0.659251i 0.944112 + 0.329626i \(0.106923\pi\)
−0.944112 + 0.329626i \(0.893077\pi\)
\(224\) −14.9313 0.729629i −0.997637 0.0487504i
\(225\) 0 0
\(226\) 6.50820 19.3840i 0.432919 1.28941i
\(227\) 5.70892 0.378914 0.189457 0.981889i \(-0.439327\pi\)
0.189457 + 0.981889i \(0.439327\pi\)
\(228\) 0 0
\(229\) 0.769233i 0.0508324i 0.999677 + 0.0254162i \(0.00809109\pi\)
−0.999677 + 0.0254162i \(0.991909\pi\)
\(230\) 13.8269 + 6.47244i 0.911717 + 0.426780i
\(231\) 0 0
\(232\) 5.10439 3.48478i 0.335120 0.228787i
\(233\) 18.4008i 1.20548i 0.797939 + 0.602739i \(0.205924\pi\)
−0.797939 + 0.602739i \(0.794076\pi\)
\(234\) 0 0
\(235\) 15.7417 + 1.80052i 1.02688 + 0.117453i
\(236\) 8.20594 10.8427i 0.534161 0.705800i
\(237\) 0 0
\(238\) 11.7417 + 3.94229i 0.761103 + 0.255541i
\(239\) 10.0328 0.648969 0.324484 0.945891i \(-0.394809\pi\)
0.324484 + 0.945891i \(0.394809\pi\)
\(240\) 0 0
\(241\) 10.7581 0.692992 0.346496 0.938051i \(-0.387371\pi\)
0.346496 + 0.938051i \(0.387371\pi\)
\(242\) 11.6757 + 3.92014i 0.750545 + 0.251996i
\(243\) 0 0
\(244\) 4.34625 5.74281i 0.278240 0.367646i
\(245\) 0.00416898 0.0364490i 0.000266347 0.00232864i
\(246\) 0 0
\(247\) 27.4282i 1.74522i
\(248\) −11.7417 17.1989i −0.745601 1.09213i
\(249\) 0 0
\(250\) −9.76373 + 12.4366i −0.617512 + 0.786561i
\(251\) 12.6580i 0.798966i 0.916741 + 0.399483i \(0.130810\pi\)
−0.916741 + 0.399483i \(0.869190\pi\)
\(252\) 0 0
\(253\) −7.30749 −0.459418
\(254\) −5.18953 + 15.4565i −0.325620 + 0.969827i
\(255\) 0 0
\(256\) −13.6388 + 8.36566i −0.852422 + 0.522854i
\(257\) 13.3110i 0.830316i 0.909749 + 0.415158i \(0.136274\pi\)
−0.909749 + 0.415158i \(0.863726\pi\)
\(258\) 0 0
\(259\) 20.7999i 1.29244i
\(260\) 11.9477 12.5270i 0.740963 0.776890i
\(261\) 0 0
\(262\) 3.31867 9.88432i 0.205028 0.610656i
\(263\) 18.4256i 1.13617i −0.822969 0.568087i \(-0.807684\pi\)
0.822969 0.568087i \(-0.192316\pi\)
\(264\) 0 0
\(265\) −1.14554 + 10.0153i −0.0703701 + 0.615238i
\(266\) 25.1044 + 8.42882i 1.53925 + 0.516804i
\(267\) 0 0
\(268\) −1.62093 1.22675i −0.0990142 0.0749356i
\(269\) 3.86940i 0.235921i −0.993018 0.117961i \(-0.962364\pi\)
0.993018 0.117961i \(-0.0376357\pi\)
\(270\) 0 0
\(271\) −17.3955 −1.05670 −0.528350 0.849027i \(-0.677189\pi\)
−0.528350 + 0.849027i \(0.677189\pi\)
\(272\) 12.7581 3.60104i 0.773576 0.218345i
\(273\) 0 0
\(274\) −1.75007 + 5.21240i −0.105725 + 0.314893i
\(275\) 1.70892 7.37270i 0.103052 0.444591i
\(276\) 0 0
\(277\) 0.887271 0.0533110 0.0266555 0.999645i \(-0.491514\pi\)
0.0266555 + 0.999645i \(0.491514\pi\)
\(278\) −6.58501 + 19.6128i −0.394943 + 1.17630i
\(279\) 0 0
\(280\) 7.79406 + 14.7850i 0.465784 + 0.883573i
\(281\) 13.4835 0.804356 0.402178 0.915562i \(-0.368253\pi\)
0.402178 + 0.915562i \(0.368253\pi\)
\(282\) 0 0
\(283\) −28.4342 −1.69024 −0.845120 0.534577i \(-0.820471\pi\)
−0.845120 + 0.534577i \(0.820471\pi\)
\(284\) 10.7253 + 8.11710i 0.636431 + 0.481661i
\(285\) 0 0
\(286\) −2.63734 + 7.85505i −0.155949 + 0.464479i
\(287\) 23.0580i 1.36107i
\(288\) 0 0
\(289\) 6.01641 0.353906
\(290\) −6.25827 2.92953i −0.367498 0.172028i
\(291\) 0 0
\(292\) 18.7253 24.7422i 1.09582 1.44793i
\(293\) 7.99166 0.466878 0.233439 0.972371i \(-0.425002\pi\)
0.233439 + 0.972371i \(0.425002\pi\)
\(294\) 0 0
\(295\) −15.1044 1.72762i −0.879412 0.100586i
\(296\) −12.5522 18.3860i −0.729582 1.06867i
\(297\) 0 0
\(298\) 4.98359 14.8431i 0.288692 0.859840i
\(299\) 18.6877i 1.08074i
\(300\) 0 0
\(301\) 2.68601i 0.154819i
\(302\) 0.854458 + 0.286885i 0.0491685 + 0.0165084i
\(303\) 0 0
\(304\) 27.2775 7.69919i 1.56447 0.441579i
\(305\) −8.00000 0.915029i −0.458079 0.0523944i
\(306\) 0 0
\(307\) 17.4506 0.995961 0.497980 0.867188i \(-0.334075\pi\)
0.497980 + 0.867188i \(0.334075\pi\)
\(308\) −6.37907 4.82778i −0.363481 0.275088i
\(309\) 0 0
\(310\) −9.87086 + 21.0868i −0.560627 + 1.19765i
\(311\) −21.4506 −1.21635 −0.608177 0.793801i \(-0.708099\pi\)
−0.608177 + 0.793801i \(0.708099\pi\)
\(312\) 0 0
\(313\) 7.73879i 0.437422i 0.975790 + 0.218711i \(0.0701853\pi\)
−0.975790 + 0.218711i \(0.929815\pi\)
\(314\) 0.173127 + 0.0581276i 0.00977014 + 0.00328033i
\(315\) 0 0
\(316\) 11.7417 + 8.88633i 0.660524 + 0.499895i
\(317\) −11.2335 −0.630938 −0.315469 0.948936i \(-0.602162\pi\)
−0.315469 + 0.948936i \(0.602162\pi\)
\(318\) 0 0
\(319\) 3.30749 0.185184
\(320\) 15.8119 + 8.36566i 0.883911 + 0.467655i
\(321\) 0 0
\(322\) −17.1044 5.74281i −0.953190 0.320034i
\(323\) −23.4835 −1.30665
\(324\) 0 0
\(325\) −18.8545 4.37027i −1.04586 0.242419i
\(326\) −26.1208 8.77008i −1.44670 0.485730i
\(327\) 0 0
\(328\) −13.9149 20.3820i −0.768319 1.12541i
\(329\) −18.7253 −1.03236
\(330\) 0 0
\(331\) 8.00084i 0.439766i 0.975526 + 0.219883i \(0.0705676\pi\)
−0.975526 + 0.219883i \(0.929432\pi\)
\(332\) −12.3463 9.34385i −0.677589 0.512810i
\(333\) 0 0
\(334\) 0.810466 2.41389i 0.0443467 0.132082i
\(335\) −0.258271 + 2.25803i −0.0141108 + 0.123369i
\(336\) 0 0
\(337\) 21.5692i 1.17495i 0.809243 + 0.587474i \(0.199877\pi\)
−0.809243 + 0.587474i \(0.800123\pi\)
\(338\) 2.65933 + 0.892874i 0.144649 + 0.0485659i
\(339\) 0 0
\(340\) −10.7253 10.2293i −0.581662 0.554764i
\(341\) 11.1444i 0.603501i
\(342\) 0 0
\(343\) 18.5419i 1.00117i
\(344\) 1.62093 + 2.37429i 0.0873948 + 0.128013i
\(345\) 0 0
\(346\) 31.1484 + 10.4581i 1.67455 + 0.562231i
\(347\) −21.7089 −1.16540 −0.582698 0.812689i \(-0.698003\pi\)
−0.582698 + 0.812689i \(0.698003\pi\)
\(348\) 0 0
\(349\) 24.7422i 1.32442i −0.749318 0.662211i \(-0.769618\pi\)
0.749318 0.662211i \(-0.230382\pi\)
\(350\) 9.79406 15.9140i 0.523514 0.850640i
\(351\) 0 0
\(352\) −8.55220 0.417910i −0.455834 0.0222747i
\(353\) 3.31415i 0.176394i −0.996103 0.0881972i \(-0.971889\pi\)
0.996103 0.0881972i \(-0.0281106\pi\)
\(354\) 0 0
\(355\) 1.70892 14.9409i 0.0906998 0.792979i
\(356\) 23.5358 + 17.8123i 1.24739 + 0.944048i
\(357\) 0 0
\(358\) 1.28586 3.82979i 0.0679596 0.202411i
\(359\) −16.7581 −0.884461 −0.442230 0.896902i \(-0.645813\pi\)
−0.442230 + 0.896902i \(0.645813\pi\)
\(360\) 0 0
\(361\) −31.2088 −1.64257
\(362\) −2.37907 + 7.08582i −0.125041 + 0.372422i
\(363\) 0 0
\(364\) −12.3463 + 16.3134i −0.647120 + 0.855055i
\(365\) −34.4671 3.94229i −1.80409 0.206349i
\(366\) 0 0
\(367\) 28.5324i 1.48938i −0.667411 0.744690i \(-0.732597\pi\)
0.667411 0.744690i \(-0.267403\pi\)
\(368\) −18.5850 + 5.24569i −0.968811 + 0.273451i
\(369\) 0 0
\(370\) −10.5522 + 22.5423i −0.548583 + 1.17192i
\(371\) 11.9136i 0.618523i
\(372\) 0 0
\(373\) 37.5798 1.94581 0.972904 0.231211i \(-0.0742688\pi\)
0.972904 + 0.231211i \(0.0742688\pi\)
\(374\) 6.72532 + 2.25803i 0.347758 + 0.116760i
\(375\) 0 0
\(376\) −16.5522 + 11.3002i −0.853614 + 0.582765i
\(377\) 8.45836i 0.435628i
\(378\) 0 0
\(379\) 6.74456i 0.346445i 0.984883 + 0.173222i \(0.0554179\pi\)
−0.984883 + 0.173222i \(0.944582\pi\)
\(380\) −22.9313 21.8708i −1.17635 1.12195i
\(381\) 0 0
\(382\) 8.00000 + 2.68601i 0.409316 + 0.137428i
\(383\) 21.8312i 1.11552i −0.830001 0.557762i \(-0.811660\pi\)
0.830001 0.557762i \(-0.188340\pi\)
\(384\) 0 0
\(385\) −1.01641 + 8.88633i −0.0518009 + 0.452889i
\(386\) −6.72532 + 20.0307i −0.342310 + 1.01954i
\(387\) 0 0
\(388\) −13.4506 + 17.7727i −0.682853 + 0.902270i
\(389\) 8.81344i 0.446859i 0.974720 + 0.223429i \(0.0717252\pi\)
−0.974720 + 0.223429i \(0.928275\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0.0261649 + 0.0383256i 0.00132153 + 0.00193573i
\(393\) 0 0
\(394\) −4.33508 1.45551i −0.218398 0.0733273i
\(395\) 1.87086 16.3568i 0.0941334 0.822998i
\(396\) 0 0
\(397\) −0.821644 −0.0412372 −0.0206186 0.999787i \(-0.506564\pi\)
−0.0206186 + 0.999787i \(0.506564\pi\)
\(398\) 10.8873 + 3.65541i 0.545730 + 0.183229i
\(399\) 0 0
\(400\) −0.946250 19.9776i −0.0473125 0.998880i
\(401\) 12.7253 0.635472 0.317736 0.948179i \(-0.397077\pi\)
0.317736 + 0.948179i \(0.397077\pi\)
\(402\) 0 0
\(403\) −28.4999 −1.41968
\(404\) −16.0880 + 21.2574i −0.800407 + 1.05760i
\(405\) 0 0
\(406\) 7.74173 + 2.59929i 0.384216 + 0.129001i
\(407\) 11.9136i 0.590535i
\(408\) 0 0
\(409\) −2.25827 −0.111664 −0.0558321 0.998440i \(-0.517781\pi\)
−0.0558321 + 0.998440i \(0.517781\pi\)
\(410\) −11.6977 + 24.9895i −0.577710 + 1.23414i
\(411\) 0 0
\(412\) −1.15672 + 1.52840i −0.0569875 + 0.0752990i
\(413\) 17.9672 0.884107
\(414\) 0 0
\(415\) −1.96719 + 17.1989i −0.0965654 + 0.844261i
\(416\) −1.06874 + 21.8708i −0.0523991 + 1.07231i
\(417\) 0 0
\(418\) 14.3791 + 4.82778i 0.703303 + 0.236135i
\(419\) 33.4579i 1.63453i −0.576264 0.817263i \(-0.695490\pi\)
0.576264 0.817263i \(-0.304510\pi\)
\(420\) 0 0
\(421\) 11.3398i 0.552669i −0.961061 0.276335i \(-0.910880\pi\)
0.961061 0.276335i \(-0.0891198\pi\)
\(422\) 6.17313 18.3860i 0.300503 0.895018i
\(423\) 0 0
\(424\) −7.18953 10.5310i −0.349155 0.511430i
\(425\) −3.74173 + 16.1428i −0.181501 + 0.783040i
\(426\) 0 0
\(427\) 9.51627 0.460525
\(428\) 6.37907 + 4.82778i 0.308344 + 0.233360i
\(429\) 0 0
\(430\) 1.36266 2.91101i 0.0657134 0.140381i
\(431\) −10.6597 −0.513459 −0.256730 0.966483i \(-0.582645\pi\)
−0.256730 + 0.966483i \(0.582645\pi\)
\(432\) 0 0
\(433\) 26.5132i 1.27414i −0.770805 0.637072i \(-0.780146\pi\)
0.770805 0.637072i \(-0.219854\pi\)
\(434\) 8.75814 26.0852i 0.420404 1.25213i
\(435\) 0 0
\(436\) 0.928423 1.22675i 0.0444634 0.0587506i
\(437\) 34.2088 1.63643
\(438\) 0 0
\(439\) −32.8789 −1.56923 −0.784613 0.619986i \(-0.787138\pi\)
−0.784613 + 0.619986i \(0.787138\pi\)
\(440\) 4.46421 + 8.46842i 0.212823 + 0.403716i
\(441\) 0 0
\(442\) 5.77454 17.1989i 0.274667 0.818068i
\(443\) −5.70892 −0.271239 −0.135619 0.990761i \(-0.543302\pi\)
−0.135619 + 0.990761i \(0.543302\pi\)
\(444\) 0 0
\(445\) 3.75007 32.7864i 0.177770 1.55423i
\(446\) −4.43140 + 13.1985i −0.209833 + 0.624966i
\(447\) 0 0
\(448\) −19.6894 7.69919i −0.930237 0.363753i
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) 13.2069i 0.621890i
\(452\) 17.4506 23.0580i 0.820809 1.08456i
\(453\) 0 0
\(454\) 7.65375 + 2.56975i 0.359208 + 0.120604i
\(455\) 22.7253 + 2.59929i 1.06538 + 0.121857i
\(456\) 0 0
\(457\) 3.94229i 0.184413i −0.995740 0.0922064i \(-0.970608\pi\)
0.995740 0.0922064i \(-0.0293920\pi\)
\(458\) −0.346255 + 1.03128i −0.0161794 + 0.0481888i
\(459\) 0 0
\(460\) 15.6238 + 14.9013i 0.728462 + 0.694775i
\(461\) 33.8969i 1.57874i 0.613920 + 0.789369i \(0.289592\pi\)
−0.613920 + 0.789369i \(0.710408\pi\)
\(462\) 0 0
\(463\) 22.8688i 1.06280i −0.847120 0.531402i \(-0.821665\pi\)
0.847120 0.531402i \(-0.178335\pi\)
\(464\) 8.41188 2.37429i 0.390512 0.110224i
\(465\) 0 0
\(466\) −8.28275 + 24.6693i −0.383691 + 1.14278i
\(467\) 15.7417 0.728440 0.364220 0.931313i \(-0.381336\pi\)
0.364220 + 0.931313i \(0.381336\pi\)
\(468\) 0 0
\(469\) 2.68601i 0.124028i
\(470\) 20.2939 + 9.49971i 0.936089 + 0.438189i
\(471\) 0 0
\(472\) 15.8820 10.8427i 0.731030 0.499076i
\(473\) 1.53847i 0.0707388i
\(474\) 0 0
\(475\) −8.00000 + 34.5140i −0.367065 + 1.58361i
\(476\) 13.9672 + 10.5706i 0.640185 + 0.484502i
\(477\) 0 0
\(478\) 13.4506 + 4.51606i 0.615218 + 0.206560i
\(479\) 20.6925 0.945465 0.472732 0.881206i \(-0.343268\pi\)
0.472732 + 0.881206i \(0.343268\pi\)
\(480\) 0 0
\(481\) −30.4671 −1.38918
\(482\) 14.4231 + 4.84255i 0.656952 + 0.220572i
\(483\) 0 0
\(484\) 13.8887 + 10.5112i 0.631304 + 0.477781i
\(485\) 24.7581 + 2.83180i 1.12421 + 0.128586i
\(486\) 0 0
\(487\) 30.8401i 1.39750i 0.715366 + 0.698750i \(0.246260\pi\)
−0.715366 + 0.698750i \(0.753740\pi\)
\(488\) 8.41188 5.74281i 0.380788 0.259965i
\(489\) 0 0
\(490\) 0.0219960 0.0469893i 0.000993676 0.00212276i
\(491\) 10.9737i 0.495238i 0.968858 + 0.247619i \(0.0796481\pi\)
−0.968858 + 0.247619i \(0.920352\pi\)
\(492\) 0 0
\(493\) −7.24186 −0.326157
\(494\) 12.3463 36.7721i 0.555484 1.65445i
\(495\) 0 0
\(496\) −8.00000 28.3433i −0.359211 1.27265i
\(497\) 17.7727i 0.797213i
\(498\) 0 0
\(499\) 3.71729i 0.166409i −0.996533 0.0832044i \(-0.973485\pi\)
0.996533 0.0832044i \(-0.0265154\pi\)
\(500\) −18.6880 + 12.2784i −0.835752 + 0.549107i
\(501\) 0 0
\(502\) −5.69774 + 16.9701i −0.254302 + 0.757414i
\(503\) 39.9451i 1.78107i 0.454919 + 0.890533i \(0.349668\pi\)
−0.454919 + 0.890533i \(0.650332\pi\)
\(504\) 0 0
\(505\) 29.6126 + 3.38705i 1.31774 + 0.150722i
\(506\) −9.79690 3.28932i −0.435525 0.146228i
\(507\) 0 0
\(508\) −13.9149 + 18.3860i −0.617372 + 0.815749i
\(509\) 0.0728979i 0.00323114i −0.999999 0.00161557i \(-0.999486\pi\)
0.999999 0.00161557i \(-0.000514253\pi\)
\(510\) 0 0
\(511\) 40.9997 1.81372
\(512\) −22.0506 + 5.07634i −0.974510 + 0.224345i
\(513\) 0 0
\(514\) −5.99166 + 17.8456i −0.264281 + 0.787134i
\(515\) 2.12914 + 0.243528i 0.0938209 + 0.0107311i
\(516\) 0 0
\(517\) −10.7253 −0.471699
\(518\) 9.36266 27.8857i 0.411372 1.22523i
\(519\) 0 0
\(520\) 21.6566 11.4165i 0.949704 0.500646i
\(521\) 11.9672 0.524292 0.262146 0.965028i \(-0.415570\pi\)
0.262146 + 0.965028i \(0.415570\pi\)
\(522\) 0 0
\(523\) 16.0656 0.702501 0.351250 0.936282i \(-0.385757\pi\)
0.351250 + 0.936282i \(0.385757\pi\)
\(524\) 8.89845 11.7577i 0.388731 0.513639i
\(525\) 0 0
\(526\) 8.29392 24.7026i 0.361632 1.07709i
\(527\) 24.4010i 1.06292i
\(528\) 0 0
\(529\) −0.307491 −0.0133692
\(530\) −6.04399 + 12.9116i −0.262534 + 0.560844i
\(531\) 0 0
\(532\) 29.8625 + 22.6004i 1.29470 + 0.979854i
\(533\) −33.7745 −1.46294
\(534\) 0 0
\(535\) 1.01641 8.88633i 0.0439431 0.384190i
\(536\) −1.62093 2.37429i −0.0700136 0.102554i
\(537\) 0 0
\(538\) 1.74173 5.18757i 0.0750913 0.223652i
\(539\) 0.0248338i 0.00106967i
\(540\) 0 0
\(541\) 15.8559i 0.681698i 0.940118 + 0.340849i \(0.110715\pi\)
−0.940118 + 0.340849i \(0.889285\pi\)
\(542\) −23.3215 7.83021i −1.00174 0.336337i
\(543\) 0 0
\(544\) 18.7253 + 0.915029i 0.802842 + 0.0392316i
\(545\) −1.70892 0.195463i −0.0732019 0.00837274i
\(546\) 0 0
\(547\) 4.95078 0.211680 0.105840 0.994383i \(-0.466247\pi\)
0.105840 + 0.994383i \(0.466247\pi\)
\(548\) −4.69251 + 6.20033i −0.200454 + 0.264865i
\(549\) 0 0
\(550\) 5.60975 9.11509i 0.239201 0.388669i
\(551\) −15.4835 −0.659618
\(552\) 0 0
\(553\) 19.4569i 0.827393i
\(554\) 1.18953 + 0.399387i 0.0505385 + 0.0169683i
\(555\) 0 0
\(556\) −17.6566 + 23.3301i −0.748806 + 0.989416i
\(557\) 1.26634 0.0536565 0.0268283 0.999640i \(-0.491459\pi\)
0.0268283 + 0.999640i \(0.491459\pi\)
\(558\) 0 0
\(559\) 3.93437 0.166406
\(560\) 3.79406 + 23.3301i 0.160328 + 0.985876i
\(561\) 0 0
\(562\) 18.0768 + 6.06930i 0.762524 + 0.256018i
\(563\) 5.70892 0.240602 0.120301 0.992737i \(-0.461614\pi\)
0.120301 + 0.992737i \(0.461614\pi\)
\(564\) 0 0
\(565\) −32.1208 3.67393i −1.35133 0.154564i
\(566\) −38.1208 12.7991i −1.60234 0.537986i
\(567\) 0 0
\(568\) 10.7253 + 15.7101i 0.450025 + 0.659181i
\(569\) −2.75814 −0.115627 −0.0578135 0.998327i \(-0.518413\pi\)
−0.0578135 + 0.998327i \(0.518413\pi\)
\(570\) 0 0
\(571\) 25.7735i 1.07859i 0.842118 + 0.539294i \(0.181309\pi\)
−0.842118 + 0.539294i \(0.818691\pi\)
\(572\) −7.07158 + 9.34385i −0.295677 + 0.390686i
\(573\) 0 0
\(574\) 10.3791 30.9130i 0.433214 1.29028i
\(575\) 5.45065 23.5155i 0.227308 0.980663i
\(576\) 0 0
\(577\) 32.7135i 1.36188i −0.732338 0.680941i \(-0.761571\pi\)
0.732338 0.680941i \(-0.238429\pi\)
\(578\) 8.06599 + 2.70816i 0.335501 + 0.112645i
\(579\) 0 0
\(580\) −7.07158 6.74456i −0.293631 0.280052i
\(581\) 20.4587i 0.848769i
\(582\) 0 0
\(583\) 6.82376i 0.282611i
\(584\) 36.2416 24.7422i 1.49969 1.02384i
\(585\) 0 0
\(586\) 10.7141 + 3.59728i 0.442597 + 0.148602i
\(587\) 43.4835 1.79475 0.897377 0.441264i \(-0.145470\pi\)
0.897377 + 0.441264i \(0.145470\pi\)
\(588\) 0 0
\(589\) 52.1705i 2.14965i
\(590\) −19.4723 9.11509i −0.801661 0.375262i
\(591\) 0 0
\(592\) −8.55220 30.2996i −0.351493 1.24531i
\(593\) 7.83021i 0.321548i 0.986991 + 0.160774i \(0.0513991\pi\)
−0.986991 + 0.160774i \(0.948601\pi\)
\(594\) 0 0
\(595\) 2.22546 19.4569i 0.0912348 0.797656i
\(596\) 13.3627 17.6564i 0.547356 0.723235i
\(597\) 0 0
\(598\) −8.41188 + 25.0539i −0.343987 + 1.02453i
\(599\) −32.7581 −1.33846 −0.669231 0.743055i \(-0.733376\pi\)
−0.669231 + 0.743055i \(0.733376\pi\)
\(600\) 0 0
\(601\) 17.8074 0.726377 0.363189 0.931716i \(-0.381688\pi\)
0.363189 + 0.931716i \(0.381688\pi\)
\(602\) −1.20905 + 3.60104i −0.0492772 + 0.146767i
\(603\) 0 0
\(604\) 1.01641 + 0.769233i 0.0413570 + 0.0312997i
\(605\) 2.21295 19.3476i 0.0899692 0.786591i
\(606\) 0 0
\(607\) 3.41188i 0.138484i −0.997600 0.0692420i \(-0.977942\pi\)
0.997600 0.0692420i \(-0.0220581\pi\)
\(608\) 40.0357 + 1.95638i 1.62366 + 0.0793416i
\(609\) 0 0
\(610\) −10.3134 4.82778i −0.417579 0.195471i
\(611\) 27.4282i 1.10963i
\(612\) 0 0
\(613\) 36.6290 1.47943 0.739716 0.672920i \(-0.234960\pi\)
0.739716 + 0.672920i \(0.234960\pi\)
\(614\) 23.3955 + 7.85505i 0.944165 + 0.317004i
\(615\) 0 0
\(616\) −6.37907 9.34385i −0.257020 0.376474i
\(617\) 40.3979i 1.62636i −0.582012 0.813180i \(-0.697734\pi\)
0.582012 0.813180i \(-0.302266\pi\)
\(618\) 0 0
\(619\) 24.5172i 0.985430i 0.870191 + 0.492715i \(0.163996\pi\)
−0.870191 + 0.492715i \(0.836004\pi\)
\(620\) −22.7253 + 23.8272i −0.912671 + 0.956923i
\(621\) 0 0
\(622\) −28.7581 9.65557i −1.15310 0.387153i
\(623\) 39.0006i 1.56252i
\(624\) 0 0
\(625\) 22.4506 + 10.9986i 0.898026 + 0.439943i
\(626\) −3.48346 + 10.3751i −0.139227 + 0.414674i
\(627\) 0 0
\(628\) 0.205941 + 0.155859i 0.00821793 + 0.00621947i
\(629\) 26.0852i 1.04009i
\(630\) 0 0
\(631\) 18.7805 0.747640 0.373820 0.927501i \(-0.378048\pi\)
0.373820 + 0.927501i \(0.378048\pi\)
\(632\) 11.7417 + 17.1989i 0.467061 + 0.684135i
\(633\) 0 0
\(634\) −15.0604 5.05654i −0.598125 0.200821i
\(635\) 25.6126 + 2.92953i 1.01640 + 0.116255i
\(636\) 0 0
\(637\) 0.0635083 0.00251629
\(638\) 4.43424 + 1.48880i 0.175553 + 0.0589421i
\(639\) 0 0
\(640\) 17.4328 + 18.3329i 0.689093 + 0.724673i
\(641\) 15.5163 0.612856 0.306428 0.951894i \(-0.400866\pi\)
0.306428 + 0.951894i \(0.400866\pi\)
\(642\) 0 0
\(643\) 17.4506 0.688186 0.344093 0.938936i \(-0.388186\pi\)
0.344093 + 0.938936i \(0.388186\pi\)
\(644\) −20.3463 15.3984i −0.801755 0.606781i
\(645\) 0 0
\(646\) −31.4835 10.5706i −1.23870 0.415895i
\(647\) 13.1403i 0.516600i 0.966065 + 0.258300i \(0.0831624\pi\)
−0.966065 + 0.258300i \(0.916838\pi\)
\(648\) 0 0
\(649\) 10.2911 0.403960
\(650\) −23.3103 14.3460i −0.914306 0.562697i
\(651\) 0 0
\(652\) −31.0716 23.5155i −1.21686 0.920937i
\(653\) 14.7993 0.579141 0.289570 0.957157i \(-0.406488\pi\)
0.289570 + 0.957157i \(0.406488\pi\)
\(654\) 0 0
\(655\) −16.3791 1.87342i −0.639983 0.0732004i
\(656\) −9.48062 33.5890i −0.370156 1.31143i
\(657\) 0 0
\(658\) −25.1044 8.42882i −0.978671 0.328590i
\(659\) 7.99614i 0.311485i 0.987798 + 0.155743i \(0.0497771\pi\)
−0.987798 + 0.155743i \(0.950223\pi\)
\(660\) 0 0
\(661\) 0.915029i 0.0355905i −0.999842 0.0177953i \(-0.994335\pi\)
0.999842 0.0177953i \(-0.00566470\pi\)
\(662\) −3.60142 + 10.7265i −0.139973 + 0.416896i
\(663\) 0 0
\(664\) −12.3463 18.0844i −0.479128 0.701810i
\(665\) 4.75814 41.5999i 0.184513 1.61317i
\(666\) 0 0
\(667\) 10.5494 0.408473
\(668\) 2.17313 2.87141i 0.0840808 0.111098i
\(669\) 0 0
\(670\) −1.36266 + 2.91101i −0.0526442 + 0.112462i
\(671\) 5.45065 0.210420
\(672\) 0 0
\(673\) 34.3978i 1.32594i −0.748647 0.662969i \(-0.769296\pi\)
0.748647 0.662969i \(-0.230704\pi\)
\(674\) −9.70892 + 28.9170i −0.373973 + 1.11384i
\(675\) 0 0
\(676\) 3.16337 + 2.39409i 0.121668 + 0.0920804i
\(677\) −40.1676 −1.54377 −0.771884 0.635764i \(-0.780685\pi\)
−0.771884 + 0.635764i \(0.780685\pi\)
\(678\) 0 0
\(679\) −29.4506 −1.13021
\(680\) −9.77454 18.5419i −0.374837 0.711049i
\(681\) 0 0
\(682\) 5.01641 14.9409i 0.192088 0.572115i
\(683\) −33.2580 −1.27258 −0.636291 0.771449i \(-0.719532\pi\)
−0.636291 + 0.771449i \(0.719532\pi\)
\(684\) 0 0
\(685\) 8.63734 + 0.987927i 0.330016 + 0.0377468i
\(686\) −8.34625 + 24.8585i −0.318661 + 0.949101i
\(687\) 0 0
\(688\) 1.10439 + 3.91275i 0.0421045 + 0.149172i
\(689\) −17.4506 −0.664817
\(690\) 0 0
\(691\) 50.2241i 1.91062i −0.295611 0.955308i \(-0.595523\pi\)
0.295611 0.955308i \(-0.404477\pi\)
\(692\) 37.0521 + 28.0416i 1.40851 + 1.06598i
\(693\) 0 0
\(694\) −29.1044 9.77182i −1.10479 0.370933i
\(695\) 32.4999 + 3.71729i 1.23279 + 0.141005i
\(696\) 0 0
\(697\) 28.9170i 1.09531i
\(698\) 11.1372 33.1710i 0.421549 1.25554i
\(699\) 0 0
\(700\) 20.2939 16.9268i 0.767038 0.639772i
\(701\) 23.7543i 0.897188i −0.893736 0.448594i \(-0.851925\pi\)
0.893736 0.448594i \(-0.148075\pi\)
\(702\) 0 0
\(703\) 55.7715i 2.10346i
\(704\) −11.2775 4.40987i −0.425037 0.166203i
\(705\) 0 0
\(706\) 1.49180 4.44317i 0.0561445 0.167221i
\(707\) −35.2252 −1.32478
\(708\) 0 0
\(709\) 36.3146i 1.36382i 0.731435 + 0.681911i \(0.238851\pi\)
−0.731435 + 0.681911i \(0.761149\pi\)
\(710\) 9.01641 19.2615i 0.338380 0.722870i
\(711\) 0 0
\(712\) 23.5358 + 34.4744i 0.882041 + 1.29198i
\(713\) 35.5453i 1.33118i
\(714\) 0 0
\(715\) 13.0164 + 1.48880i 0.486786 + 0.0556779i
\(716\) 3.44780 4.55567i 0.128851 0.170253i
\(717\) 0 0
\(718\) −22.4671 7.54333i −0.838463 0.281515i
\(719\) 30.7253 1.14586 0.572931 0.819604i \(-0.305806\pi\)
0.572931 + 0.819604i \(0.305806\pi\)
\(720\) 0 0
\(721\) −2.53268 −0.0943219
\(722\) −41.8405 14.0480i −1.55714 0.522812i
\(723\) 0 0
\(724\) −6.37907 + 8.42882i −0.237076 + 0.313255i
\(725\) −2.46705 + 10.6435i −0.0916240 + 0.395289i
\(726\) 0 0
\(727\) 5.47445i 0.203036i 0.994834 + 0.101518i \(0.0323700\pi\)
−0.994834 + 0.101518i \(0.967630\pi\)
\(728\) −23.8953 + 16.3134i −0.885620 + 0.604615i
\(729\) 0 0
\(730\) −44.4342 20.7999i −1.64458 0.769840i
\(731\) 3.36852i 0.124589i
\(732\) 0 0
\(733\) −17.1455 −0.633285 −0.316643 0.948545i \(-0.602556\pi\)
−0.316643 + 0.948545i \(0.602556\pi\)
\(734\) 12.8433 38.2524i 0.474054 1.41192i
\(735\) 0 0
\(736\) −27.2775 1.33294i −1.00546 0.0491328i
\(737\) 1.53847i 0.0566701i
\(738\) 0 0
\(739\) 11.6019i 0.426782i −0.976967 0.213391i \(-0.931549\pi\)
0.976967 0.213391i \(-0.0684508\pi\)
\(740\) −24.2939 + 25.4719i −0.893062 + 0.936364i
\(741\) 0 0
\(742\) 5.36266 15.9721i 0.196869 0.586356i
\(743\) 23.6613i 0.868048i −0.900901 0.434024i \(-0.857093\pi\)
0.900901 0.434024i \(-0.142907\pi\)
\(744\) 0 0
\(745\) −24.5962 2.81328i −0.901135 0.103071i
\(746\) 50.3819 + 16.9158i 1.84461 + 0.619330i
\(747\) 0 0
\(748\) 8.00000 + 6.05453i 0.292509 + 0.221376i
\(749\) 10.5706i 0.386241i
\(750\) 0 0
\(751\) −11.4283 −0.417024 −0.208512 0.978020i \(-0.566862\pi\)
−0.208512 + 0.978020i \(0.566862\pi\)
\(752\) −27.2775 + 7.69919i −0.994709 + 0.280761i
\(753\) 0 0
\(754\) 3.80736 11.3398i 0.138656 0.412972i
\(755\) 0.161949 1.41590i 0.00589392 0.0515299i
\(756\) 0 0
\(757\) −19.1784 −0.697049 −0.348525 0.937300i \(-0.613317\pi\)
−0.348525 + 0.937300i \(0.613317\pi\)
\(758\) −3.03592 + 9.04219i −0.110270 + 0.328427i
\(759\) 0 0
\(760\) −20.8984 39.6435i −0.758066 1.43802i
\(761\) −4.03281 −0.146189 −0.0730947 0.997325i \(-0.523288\pi\)
−0.0730947 + 0.997325i \(0.523288\pi\)
\(762\) 0 0
\(763\) 2.03281 0.0735928
\(764\) 9.51627 + 7.20207i 0.344287 + 0.260562i
\(765\) 0 0
\(766\) 9.82687 29.2684i 0.355059 1.05751i
\(767\) 26.3177i 0.950279i
\(768\) 0 0
\(769\) 2.95078 0.106408 0.0532039 0.998584i \(-0.483057\pi\)
0.0532039 + 0.998584i \(0.483057\pi\)
\(770\) −5.36266 + 11.4561i −0.193257 + 0.412849i
\(771\) 0 0
\(772\) −18.0328 + 23.8272i −0.649015 + 0.857560i
\(773\) −45.2663 −1.62812 −0.814059 0.580783i \(-0.802747\pi\)
−0.814059 + 0.580783i \(0.802747\pi\)
\(774\) 0 0
\(775\) 35.8625 + 8.31256i 1.28822 + 0.298596i
\(776\) −26.0328 + 17.7727i −0.934524 + 0.638002i
\(777\) 0 0
\(778\) −3.96719 + 11.8159i −0.142231 + 0.423619i
\(779\) 61.8260i 2.21515i
\(780\) 0 0
\(781\) 10.1797i 0.364257i
\(782\) 21.4506 + 7.20207i 0.767074 + 0.257546i
\(783\) 0 0
\(784\) 0.0178270 + 0.0631594i 0.000636678 + 0.00225569i
\(785\) 0.0328135 0.286885i 0.00117116 0.0102394i
\(786\) 0 0
\(787\) −52.9997 −1.88924 −0.944618 0.328171i \(-0.893568\pi\)
−0.944618 + 0.328171i \(0.893568\pi\)
\(788\) −5.15672 3.90269i −0.183701 0.139028i
\(789\) 0 0
\(790\) 9.87086 21.0868i 0.351190 0.750235i
\(791\) 38.2088 1.35855
\(792\) 0 0
\(793\) 13.9391i 0.494993i
\(794\) −1.10155 0.369846i −0.0390926 0.0131254i
\(795\) 0 0
\(796\) 12.9508 + 9.80136i 0.459028 + 0.347400i
\(797\) −16.5738 −0.587075 −0.293538 0.955948i \(-0.594833\pi\)
−0.293538 + 0.955948i \(0.594833\pi\)
\(798\) 0 0
\(799\) 23.4835 0.830785
\(800\) 7.72390 27.2092i 0.273081 0.961991i
\(801\) 0 0
\(802\) 17.0604 + 5.72804i 0.602424 + 0.202264i
\(803\) 23.4835 0.828713
\(804\) 0 0
\(805\) −3.24186 + 28.3433i −0.114261 + 0.998969i
\(806\) −38.2088 12.8286i −1.34585 0.451869i
\(807\) 0 0
\(808\) −31.1372 + 21.2574i −1.09540 + 0.747834i
\(809\) −37.5491 −1.32016 −0.660078 0.751197i \(-0.729477\pi\)
−0.660078 + 0.751197i \(0.729477\pi\)
\(810\) 0 0
\(811\) 32.1102i 1.12754i 0.825931 + 0.563771i \(0.190650\pi\)
−0.825931 + 0.563771i \(0.809350\pi\)
\(812\) 9.20905 + 6.96956i 0.323174 + 0.244584i
\(813\) 0 0
\(814\) 5.36266 15.9721i 0.187961 0.559824i
\(815\) −4.95078 + 43.2841i −0.173418 + 1.51618i
\(816\) 0 0
\(817\) 7.20207i 0.251969i
\(818\) −3.02759 1.01651i −0.105857 0.0355416i
\(819\) 0 0
\(820\) −26.9313 + 28.2371i −0.940481 + 0.986081i
\(821\) 29.3809i 1.02540i −0.858568 0.512699i \(-0.828646\pi\)
0.858568 0.512699i \(-0.171354\pi\)
\(822\) 0 0
\(823\) 28.3866i 0.989495i −0.869037 0.494748i \(-0.835260\pi\)
0.869037 0.494748i \(-0.164740\pi\)
\(824\) −2.23875 + 1.52840i −0.0779907 + 0.0532444i
\(825\) 0 0
\(826\) 24.0880 + 8.08756i 0.838128 + 0.281402i
\(827\) 1.45065 0.0504439 0.0252219 0.999682i \(-0.491971\pi\)
0.0252219 + 0.999682i \(0.491971\pi\)
\(828\) 0 0
\(829\) 37.4621i 1.30111i −0.759458 0.650556i \(-0.774536\pi\)
0.759458 0.650556i \(-0.225464\pi\)
\(830\) −10.3791 + 22.1725i −0.360263 + 0.769618i
\(831\) 0 0
\(832\) −11.2775 + 28.8404i −0.390978 + 0.999860i
\(833\) 0.0543744i 0.00188396i
\(834\) 0 0
\(835\) −4.00000 0.457515i −0.138426 0.0158329i
\(836\) 17.1044 + 12.9449i 0.591568 + 0.447708i
\(837\) 0 0
\(838\) 15.0604 44.8559i 0.520253 1.54952i
\(839\) −48.7581 −1.68332 −0.841659 0.540010i \(-0.818421\pi\)
−0.841659 + 0.540010i \(0.818421\pi\)
\(840\) 0 0
\(841\) 24.2252 0.835351
\(842\) 5.10439 15.2029i 0.175909 0.523927i
\(843\) 0 0
\(844\) 16.5522 21.8708i 0.569750 0.752825i
\(845\) 0.504034 4.40672i 0.0173393 0.151596i
\(846\) 0 0
\(847\) 23.0146i 0.790791i
\(848\) −4.89845 17.3548i −0.168213 0.595965i
\(849\) 0 0
\(850\) −12.2827 + 19.9578i −0.421295 + 0.684547i
\(851\) 37.9988i 1.30258i
\(852\) 0 0
\(853\) −4.37073 −0.149651 −0.0748255 0.997197i \(-0.523840\pi\)
−0.0748255 + 0.997197i \(0.523840\pi\)
\(854\) 12.7581 + 4.28355i 0.436574 + 0.146580i
\(855\) 0 0
\(856\) 6.37907 + 9.34385i 0.218032 + 0.319366i
\(857\) 20.5130i 0.700712i −0.936617 0.350356i \(-0.886061\pi\)
0.936617 0.350356i \(-0.113939\pi\)
\(858\) 0 0
\(859\) 10.1131i 0.345054i 0.985005 + 0.172527i \(0.0551932\pi\)
−0.985005 + 0.172527i \(0.944807\pi\)
\(860\) 3.13720 3.28932i 0.106978 0.112165i
\(861\) 0 0
\(862\) −14.2911 4.79824i −0.486756 0.163429i
\(863\) 13.2861i 0.452266i 0.974096 + 0.226133i \(0.0726083\pi\)
−0.974096 + 0.226133i \(0.927392\pi\)
\(864\) 0 0
\(865\) 5.90368 51.6152i 0.200731 1.75497i
\(866\) 11.9344 35.5453i 0.405547 1.20788i
\(867\) 0 0
\(868\) 23.4835 31.0293i 0.797081 1.05320i
\(869\) 11.1444i 0.378047i
\(870\) 0 0
\(871\) −3.93437 −0.133311
\(872\) 1.79690 1.22675i 0.0608507 0.0415429i
\(873\) 0 0
\(874\) 45.8625 + 15.3984i 1.55132 + 0.520858i
\(875\) −27.8381 9.89909i −0.941098 0.334650i
\(876\) 0 0
\(877\) 33.6454 1.13612 0.568062 0.822986i \(-0.307693\pi\)
0.568062 + 0.822986i \(0.307693\pi\)
\(878\) −44.0796 14.7998i −1.48762 0.499468i
\(879\) 0 0
\(880\) 2.17313 + 13.3628i 0.0732561 + 0.450460i
\(881\) 32.7909 1.10476 0.552378 0.833594i \(-0.313721\pi\)
0.552378 + 0.833594i \(0.313721\pi\)
\(882\) 0 0
\(883\) 33.4506 1.12570 0.562852 0.826558i \(-0.309704\pi\)
0.562852 + 0.826558i \(0.309704\pi\)
\(884\) 15.4835 20.4587i 0.520765 0.688100i
\(885\) 0 0
\(886\) −7.65375 2.56975i −0.257133 0.0863325i
\(887\) 34.8924i 1.17157i 0.810466 + 0.585785i \(0.199214\pi\)
−0.810466 + 0.585785i \(0.800786\pi\)
\(888\) 0 0
\(889\) −30.4671 −1.02183
\(890\) 19.7857 42.2676i 0.663219 1.41681i
\(891\) 0 0
\(892\) −11.8820 + 15.7000i −0.397840 + 0.525676i
\(893\) 50.2088 1.68017
\(894\) 0 0
\(895\) −6.34625 0.725876i −0.212132 0.0242634i
\(896\) −22.9313 19.1848i −0.766080 0.640920i
\(897\) 0 0
\(898\) −2.68133 0.900259i −0.0894772 0.0300420i
\(899\) 16.0884i 0.536578i
\(900\) 0 0
\(901\) 14.9409i 0.497752i
\(902\) 5.94483 17.7061i 0.197941 0.589548i
\(903\) 0 0
\(904\) 33.7745 23.0580i 1.12332 0.766896i
\(905\) 11.7417 + 1.34300i 0.390308 + 0.0446429i
\(906\) 0 0
\(907\) −30.9836 −1.02879 −0.514397 0.857552i \(-0.671984\pi\)
−0.514397 + 0.857552i \(0.671984\pi\)
\(908\) 9.10439 + 6.89035i 0.302140 + 0.228664i
\(909\) 0 0
\(910\) 29.2970 + 13.7141i 0.971187 + 0.454619i
\(911\) −16.0000 −0.530104 −0.265052 0.964234i \(-0.585389\pi\)
−0.265052 + 0.964234i \(0.585389\pi\)
\(912\) 0 0
\(913\) 11.7181i 0.387814i
\(914\) 1.77454 5.28530i 0.0586967 0.174822i
\(915\) 0 0
\(916\) −0.928423 + 1.22675i −0.0306760 + 0.0405329i
\(917\) 19.4835 0.643400
\(918\) 0 0
\(919\) 15.6043 0.514737 0.257368 0.966313i \(-0.417145\pi\)
0.257368 + 0.966313i \(0.417145\pi\)
\(920\) 14.2388 + 27.0103i 0.469438 + 0.890504i
\(921\) 0 0
\(922\) −15.2580 + 45.4444i −0.502496 + 1.49663i
\(923\) 26.0328 0.856880
\(924\) 0 0
\(925\) 38.3379 + 8.88633i 1.26054 + 0.292181i
\(926\) 10.2939 30.6594i 0.338279 1.00753i
\(927\) 0 0
\(928\) 12.3463 + 0.603310i 0.405286 + 0.0198046i
\(929\) −38.9341 −1.27739 −0.638693 0.769461i \(-0.720525\pi\)
−0.638693 + 0.769461i \(0.720525\pi\)
\(930\) 0 0
\(931\) 0.116255i 0.00381011i
\(932\) −22.2088 + 29.3450i −0.727473 + 0.961228i
\(933\) 0 0
\(934\) 21.1044 + 7.08582i 0.690557 + 0.231855i
\(935\) 1.27468 11.1444i 0.0416864 0.364460i
\(936\) 0 0
\(937\) 19.6027i 0.640393i 0.947351 + 0.320197i \(0.103749\pi\)
−0.947351 + 0.320197i \(0.896251\pi\)
\(938\) 1.20905 3.60104i 0.0394769 0.117578i
\(939\) 0 0
\(940\) 22.9313 + 21.8708i 0.747935 + 0.713348i
\(941\) 25.0476i 0.816530i 0.912864 + 0.408265i \(0.133866\pi\)
−0.912864 + 0.408265i \(0.866134\pi\)
\(942\) 0 0
\(943\) 42.1240i 1.37175i
\(944\) 26.1731 7.38747i 0.851863 0.240442i
\(945\) 0 0
\(946\) −0.692509 + 2.06257i −0.0225154 + 0.0670599i
\(947\) 7.93437 0.257832 0.128916 0.991655i \(-0.458850\pi\)
0.128916 + 0.991655i \(0.458850\pi\)
\(948\) 0 0
\(949\) 60.0550i 1.94947i
\(950\) −26.2611 + 42.6708i −0.852023 + 1.38442i
\(951\) 0 0
\(952\) 13.9672 + 20.4587i 0.452679 + 0.663069i
\(953\) 11.4809i 0.371903i −0.982559 0.185952i \(-0.940463\pi\)
0.982559 0.185952i \(-0.0595368\pi\)
\(954\) 0 0
\(955\) 1.51627 13.2566i 0.0490654 0.428974i
\(956\) 16.0000 + 12.1091i 0.517477 + 0.391635i
\(957\) 0 0
\(958\) 27.7417 + 9.31431i 0.896295 + 0.300932i
\(959\) −10.2744 −0.331778
\(960\) 0 0
\(961\) 23.2088 0.748670
\(962\) −40.8461 13.7141i −1.31693 0.442161i
\(963\) 0 0
\(964\) 17.1567 + 12.9845i 0.552581 + 0.418202i
\(965\) 33.1924 + 3.79650i 1.06850 + 0.122214i
\(966\) 0 0
\(967\) 15.8993i 0.511285i 0.966771 + 0.255643i \(0.0822871\pi\)
−0.966771 + 0.255643i \(0.917713\pi\)
\(968\) 13.8887 + 20.3437i 0.446399 + 0.653871i
\(969\) 0 0
\(970\) 31.9177 + 14.9409i 1.02482 + 0.479722i
\(971\) 40.6600i 1.30484i −0.757857 0.652421i \(-0.773754\pi\)
0.757857 0.652421i \(-0.226246\pi\)
\(972\) 0 0
\(973\) −38.6597 −1.23937
\(974\) −13.8820 + 41.3463i −0.444809 + 1.32482i
\(975\) 0 0
\(976\) 13.8625 3.91275i 0.443729 0.125244i
\(977\) 26.5676i 0.849972i 0.905200 + 0.424986i \(0.139721\pi\)
−0.905200 + 0.424986i \(0.860279\pi\)
\(978\) 0 0
\(979\) 22.3384i 0.713938i
\(980\) 0.0506405 0.0530959i 0.00161765 0.00169609i
\(981\) 0 0
\(982\) −4.93960 + 14.7121i −0.157629 + 0.469482i
\(983\) 9.88057i 0.315141i 0.987508 + 0.157571i \(0.0503662\pi\)
−0.987508 + 0.157571i \(0.949634\pi\)
\(984\) 0 0
\(985\) −0.821644 + 7.18355i −0.0261798 + 0.228887i
\(986\) −9.70892 3.25978i −0.309195 0.103812i
\(987\) 0 0
\(988\) 33.1044 43.7416i 1.05319 1.39161i
\(989\) 4.90699i 0.156033i
\(990\) 0 0
\(991\) −53.0549 −1.68534 −0.842672 0.538427i \(-0.819019\pi\)
−0.842672 + 0.538427i \(0.819019\pi\)
\(992\) 2.03281 41.5999i 0.0645419 1.32080i
\(993\) 0 0
\(994\) −8.00000 + 23.8272i −0.253745 + 0.755753i
\(995\) 2.06351 18.0410i 0.0654176 0.571939i
\(996\) 0 0
\(997\) −32.3051 −1.02311 −0.511556 0.859250i \(-0.670931\pi\)
−0.511556 + 0.859250i \(0.670931\pi\)
\(998\) 1.67326 4.98364i 0.0529662 0.157754i
\(999\) 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 360.2.d.f.109.6 6
3.2 odd 2 120.2.d.a.109.1 6
4.3 odd 2 1440.2.d.e.1009.3 6
5.2 odd 4 1800.2.k.u.901.6 12
5.3 odd 4 1800.2.k.u.901.7 12
5.4 even 2 360.2.d.e.109.1 6
8.3 odd 2 1440.2.d.f.1009.4 6
8.5 even 2 360.2.d.e.109.2 6
12.11 even 2 480.2.d.a.49.4 6
15.2 even 4 600.2.k.f.301.7 12
15.8 even 4 600.2.k.f.301.6 12
15.14 odd 2 120.2.d.b.109.6 yes 6
20.3 even 4 7200.2.k.u.3601.3 12
20.7 even 4 7200.2.k.u.3601.9 12
20.19 odd 2 1440.2.d.f.1009.3 6
24.5 odd 2 120.2.d.b.109.5 yes 6
24.11 even 2 480.2.d.b.49.3 6
40.3 even 4 7200.2.k.u.3601.4 12
40.13 odd 4 1800.2.k.u.901.8 12
40.19 odd 2 1440.2.d.e.1009.4 6
40.27 even 4 7200.2.k.u.3601.10 12
40.29 even 2 inner 360.2.d.f.109.5 6
40.37 odd 4 1800.2.k.u.901.5 12
48.5 odd 4 3840.2.f.l.769.1 12
48.11 even 4 3840.2.f.m.769.7 12
48.29 odd 4 3840.2.f.l.769.12 12
48.35 even 4 3840.2.f.m.769.6 12
60.23 odd 4 2400.2.k.f.1201.2 12
60.47 odd 4 2400.2.k.f.1201.11 12
60.59 even 2 480.2.d.b.49.4 6
120.29 odd 2 120.2.d.a.109.2 yes 6
120.53 even 4 600.2.k.f.301.5 12
120.59 even 2 480.2.d.a.49.3 6
120.77 even 4 600.2.k.f.301.8 12
120.83 odd 4 2400.2.k.f.1201.8 12
120.107 odd 4 2400.2.k.f.1201.5 12
240.29 odd 4 3840.2.f.l.769.6 12
240.59 even 4 3840.2.f.m.769.1 12
240.149 odd 4 3840.2.f.l.769.7 12
240.179 even 4 3840.2.f.m.769.12 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.2.d.a.109.1 6 3.2 odd 2
120.2.d.a.109.2 yes 6 120.29 odd 2
120.2.d.b.109.5 yes 6 24.5 odd 2
120.2.d.b.109.6 yes 6 15.14 odd 2
360.2.d.e.109.1 6 5.4 even 2
360.2.d.e.109.2 6 8.5 even 2
360.2.d.f.109.5 6 40.29 even 2 inner
360.2.d.f.109.6 6 1.1 even 1 trivial
480.2.d.a.49.3 6 120.59 even 2
480.2.d.a.49.4 6 12.11 even 2
480.2.d.b.49.3 6 24.11 even 2
480.2.d.b.49.4 6 60.59 even 2
600.2.k.f.301.5 12 120.53 even 4
600.2.k.f.301.6 12 15.8 even 4
600.2.k.f.301.7 12 15.2 even 4
600.2.k.f.301.8 12 120.77 even 4
1440.2.d.e.1009.3 6 4.3 odd 2
1440.2.d.e.1009.4 6 40.19 odd 2
1440.2.d.f.1009.3 6 20.19 odd 2
1440.2.d.f.1009.4 6 8.3 odd 2
1800.2.k.u.901.5 12 40.37 odd 4
1800.2.k.u.901.6 12 5.2 odd 4
1800.2.k.u.901.7 12 5.3 odd 4
1800.2.k.u.901.8 12 40.13 odd 4
2400.2.k.f.1201.2 12 60.23 odd 4
2400.2.k.f.1201.5 12 120.107 odd 4
2400.2.k.f.1201.8 12 120.83 odd 4
2400.2.k.f.1201.11 12 60.47 odd 4
3840.2.f.l.769.1 12 48.5 odd 4
3840.2.f.l.769.6 12 240.29 odd 4
3840.2.f.l.769.7 12 240.149 odd 4
3840.2.f.l.769.12 12 48.29 odd 4
3840.2.f.m.769.1 12 240.59 even 4
3840.2.f.m.769.6 12 48.35 even 4
3840.2.f.m.769.7 12 48.11 even 4
3840.2.f.m.769.12 12 240.179 even 4
7200.2.k.u.3601.3 12 20.3 even 4
7200.2.k.u.3601.4 12 40.3 even 4
7200.2.k.u.3601.9 12 20.7 even 4
7200.2.k.u.3601.10 12 40.27 even 4