Properties

Label 675.2.r.a.181.1
Level $675$
Weight $2$
Character 675.181
Analytic conductor $5.390$
Analytic rank $0$
Dimension $224$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [675,2,Mod(46,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 18]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.46");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.r (of order \(15\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 225)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 181.1
Character \(\chi\) \(=\) 675.181
Dual form 675.2.r.a.496.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.68409 - 0.570520i) q^{2} +(5.05174 + 2.24918i) q^{4} +(-0.420615 + 2.19615i) q^{5} +(-0.931182 + 1.61286i) q^{7} +(-7.83615 - 5.69329i) q^{8} +(2.38192 - 5.65469i) q^{10} +(2.70264 + 0.574464i) q^{11} +(-1.65646 + 0.352091i) q^{13} +(3.41954 - 3.79779i) q^{14} +(10.3844 + 11.5331i) q^{16} +(5.11464 + 3.71600i) q^{17} +(1.23445 + 0.896882i) q^{19} +(-7.06438 + 10.1484i) q^{20} +(-6.92639 - 3.08383i) q^{22} +(-0.327461 + 0.363683i) q^{23} +(-4.64617 - 1.84747i) q^{25} +4.64695 q^{26} +(-8.33169 + 6.05333i) q^{28} +(0.189122 + 1.79938i) q^{29} +(0.285758 - 2.71880i) q^{31} +(-11.6068 - 20.1036i) q^{32} +(-11.6081 - 12.8921i) q^{34} +(-3.15040 - 2.72341i) q^{35} +(1.30318 - 4.01076i) q^{37} +(-2.80169 - 3.11159i) q^{38} +(15.7993 - 14.8147i) q^{40} +(-3.71670 + 0.790010i) q^{41} +(-5.30871 + 9.19495i) q^{43} +(12.3610 + 8.98078i) q^{44} +(1.08642 - 0.789333i) q^{46} +(-0.670718 - 6.38145i) q^{47} +(1.76580 + 3.05845i) q^{49} +(11.4167 + 7.60951i) q^{50} +(-9.15992 - 1.94700i) q^{52} +(-4.80881 + 3.49380i) q^{53} +(-2.39838 + 5.69379i) q^{55} +(16.4793 - 7.33707i) q^{56} +(0.518961 - 4.93758i) q^{58} +(-9.93588 + 2.11194i) q^{59} +(-7.13090 - 1.51572i) q^{61} +(-2.31813 + 7.13448i) q^{62} +(10.0928 + 31.0624i) q^{64} +(-0.0765136 - 3.78593i) q^{65} +(0.914005 - 8.69618i) q^{67} +(17.4799 + 30.2760i) q^{68} +(6.90220 + 9.10724i) q^{70} +(-2.74292 + 1.99285i) q^{71} +(4.80018 + 14.7734i) q^{73} +(-5.78606 + 10.0218i) q^{74} +(4.21888 + 7.30732i) q^{76} +(-3.44318 + 3.82404i) q^{77} +(1.34121 + 12.7607i) q^{79} +(-29.6962 + 17.9548i) q^{80} +10.4267 q^{82} +(0.803423 - 0.357707i) q^{83} +(-10.3122 + 9.66951i) q^{85} +(19.4950 - 21.6513i) q^{86} +(-17.9077 - 19.8885i) q^{88} +(-1.51233 - 4.65447i) q^{89} +(0.974593 - 2.99949i) q^{91} +(-2.47224 + 1.10071i) q^{92} +(-1.84048 + 17.5110i) q^{94} +(-2.48892 + 2.33380i) q^{95} +(0.396958 + 3.77680i) q^{97} +(-2.99465 - 9.21658i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68409 0.570520i −1.89794 0.403419i −0.898564 0.438842i \(-0.855389\pi\)
−0.999372 + 0.0354233i \(0.988722\pi\)
\(3\) 0 0
\(4\) 5.05174 + 2.24918i 2.52587 + 1.12459i
\(5\) −0.420615 + 2.19615i −0.188105 + 0.982149i
\(6\) 0 0
\(7\) −0.931182 + 1.61286i −0.351954 + 0.609602i −0.986592 0.163208i \(-0.947816\pi\)
0.634638 + 0.772810i \(0.281149\pi\)
\(8\) −7.83615 5.69329i −2.77050 2.01288i
\(9\) 0 0
\(10\) 2.38192 5.65469i 0.753229 1.78817i
\(11\) 2.70264 + 0.574464i 0.814878 + 0.173208i 0.596455 0.802647i \(-0.296576\pi\)
0.218423 + 0.975854i \(0.429909\pi\)
\(12\) 0 0
\(13\) −1.65646 + 0.352091i −0.459419 + 0.0976525i −0.431807 0.901966i \(-0.642124\pi\)
−0.0276122 + 0.999619i \(0.508790\pi\)
\(14\) 3.41954 3.79779i 0.913911 1.01500i
\(15\) 0 0
\(16\) 10.3844 + 11.5331i 2.59610 + 2.88327i
\(17\) 5.11464 + 3.71600i 1.24048 + 0.901263i 0.997630 0.0688008i \(-0.0219173\pi\)
0.242851 + 0.970064i \(0.421917\pi\)
\(18\) 0 0
\(19\) 1.23445 + 0.896882i 0.283203 + 0.205759i 0.720313 0.693649i \(-0.243998\pi\)
−0.437110 + 0.899408i \(0.643998\pi\)
\(20\) −7.06438 + 10.1484i −1.57964 + 2.26924i
\(21\) 0 0
\(22\) −6.92639 3.08383i −1.47671 0.657474i
\(23\) −0.327461 + 0.363683i −0.0682804 + 0.0758331i −0.776317 0.630343i \(-0.782914\pi\)
0.708037 + 0.706176i \(0.249581\pi\)
\(24\) 0 0
\(25\) −4.64617 1.84747i −0.929233 0.369494i
\(26\) 4.64695 0.911343
\(27\) 0 0
\(28\) −8.33169 + 6.05333i −1.57454 + 1.14397i
\(29\) 0.189122 + 1.79938i 0.0351191 + 0.334136i 0.997948 + 0.0640249i \(0.0203937\pi\)
−0.962829 + 0.270111i \(0.912940\pi\)
\(30\) 0 0
\(31\) 0.285758 2.71880i 0.0513236 0.488312i −0.938424 0.345485i \(-0.887714\pi\)
0.989748 0.142826i \(-0.0456190\pi\)
\(32\) −11.6068 20.1036i −2.05182 3.55385i
\(33\) 0 0
\(34\) −11.6081 12.8921i −1.99077 2.21097i
\(35\) −3.15040 2.72341i −0.532516 0.460340i
\(36\) 0 0
\(37\) 1.30318 4.01076i 0.214241 0.659366i −0.784966 0.619539i \(-0.787319\pi\)
0.999207 0.0398264i \(-0.0126805\pi\)
\(38\) −2.80169 3.11159i −0.454494 0.504766i
\(39\) 0 0
\(40\) 15.7993 14.8147i 2.49809 2.34241i
\(41\) −3.71670 + 0.790010i −0.580452 + 0.123379i −0.488775 0.872410i \(-0.662556\pi\)
−0.0916768 + 0.995789i \(0.529223\pi\)
\(42\) 0 0
\(43\) −5.30871 + 9.19495i −0.809571 + 1.40222i 0.103591 + 0.994620i \(0.466967\pi\)
−0.913162 + 0.407597i \(0.866367\pi\)
\(44\) 12.3610 + 8.98078i 1.86349 + 1.35390i
\(45\) 0 0
\(46\) 1.08642 0.789333i 0.160184 0.116381i
\(47\) −0.670718 6.38145i −0.0978342 0.930831i −0.927816 0.373039i \(-0.878316\pi\)
0.829981 0.557791i \(-0.188351\pi\)
\(48\) 0 0
\(49\) 1.76580 + 3.05845i 0.252257 + 0.436922i
\(50\) 11.4167 + 7.60951i 1.61456 + 1.07615i
\(51\) 0 0
\(52\) −9.15992 1.94700i −1.27025 0.270000i
\(53\) −4.80881 + 3.49380i −0.660540 + 0.479911i −0.866845 0.498577i \(-0.833856\pi\)
0.206305 + 0.978488i \(0.433856\pi\)
\(54\) 0 0
\(55\) −2.39838 + 5.69379i −0.323398 + 0.767750i
\(56\) 16.4793 7.33707i 2.20214 0.980458i
\(57\) 0 0
\(58\) 0.518961 4.93758i 0.0681429 0.648336i
\(59\) −9.93588 + 2.11194i −1.29354 + 0.274951i −0.802744 0.596323i \(-0.796628\pi\)
−0.490797 + 0.871274i \(0.663294\pi\)
\(60\) 0 0
\(61\) −7.13090 1.51572i −0.913019 0.194068i −0.272630 0.962119i \(-0.587893\pi\)
−0.640389 + 0.768051i \(0.721227\pi\)
\(62\) −2.31813 + 7.13448i −0.294403 + 0.906079i
\(63\) 0 0
\(64\) 10.0928 + 31.0624i 1.26160 + 3.88280i
\(65\) −0.0765136 3.78593i −0.00949034 0.469587i
\(66\) 0 0
\(67\) 0.914005 8.69618i 0.111664 1.06241i −0.784939 0.619572i \(-0.787306\pi\)
0.896603 0.442835i \(-0.146027\pi\)
\(68\) 17.4799 + 30.2760i 2.11975 + 3.67151i
\(69\) 0 0
\(70\) 6.90220 + 9.10724i 0.824971 + 1.08852i
\(71\) −2.74292 + 1.99285i −0.325524 + 0.236507i −0.738529 0.674222i \(-0.764479\pi\)
0.413005 + 0.910729i \(0.364479\pi\)
\(72\) 0 0
\(73\) 4.80018 + 14.7734i 0.561818 + 1.72910i 0.677221 + 0.735780i \(0.263184\pi\)
−0.115403 + 0.993319i \(0.536816\pi\)
\(74\) −5.78606 + 10.0218i −0.672616 + 1.16501i
\(75\) 0 0
\(76\) 4.21888 + 7.30732i 0.483939 + 0.838207i
\(77\) −3.44318 + 3.82404i −0.392387 + 0.435790i
\(78\) 0 0
\(79\) 1.34121 + 12.7607i 0.150898 + 1.43570i 0.763757 + 0.645503i \(0.223352\pi\)
−0.612860 + 0.790192i \(0.709981\pi\)
\(80\) −29.6962 + 17.9548i −3.32014 + 2.00740i
\(81\) 0 0
\(82\) 10.4267 1.15143
\(83\) 0.803423 0.357707i 0.0881871 0.0392634i −0.362169 0.932112i \(-0.617964\pi\)
0.450356 + 0.892849i \(0.351297\pi\)
\(84\) 0 0
\(85\) −10.3122 + 9.66951i −1.11851 + 1.04881i
\(86\) 19.4950 21.6513i 2.10219 2.33472i
\(87\) 0 0
\(88\) −17.9077 19.8885i −1.90897 2.12012i
\(89\) −1.51233 4.65447i −0.160306 0.493372i 0.838353 0.545127i \(-0.183519\pi\)
−0.998660 + 0.0517547i \(0.983519\pi\)
\(90\) 0 0
\(91\) 0.974593 2.99949i 0.102165 0.314432i
\(92\) −2.47224 + 1.10071i −0.257749 + 0.114757i
\(93\) 0 0
\(94\) −1.84048 + 17.5110i −0.189831 + 1.80613i
\(95\) −2.48892 + 2.33380i −0.255358 + 0.239443i
\(96\) 0 0
\(97\) 0.396958 + 3.77680i 0.0403049 + 0.383476i 0.996016 + 0.0891705i \(0.0284216\pi\)
−0.955711 + 0.294305i \(0.904912\pi\)
\(98\) −2.99465 9.21658i −0.302505 0.931015i
\(99\) 0 0
\(100\) −19.3159 19.7830i −1.93159 1.97830i
\(101\) −3.33145 + 5.77025i −0.331492 + 0.574161i −0.982805 0.184648i \(-0.940885\pi\)
0.651313 + 0.758810i \(0.274219\pi\)
\(102\) 0 0
\(103\) −1.40438 0.625269i −0.138377 0.0616096i 0.336380 0.941726i \(-0.390797\pi\)
−0.474757 + 0.880117i \(0.657464\pi\)
\(104\) 14.9848 + 6.67167i 1.46938 + 0.654211i
\(105\) 0 0
\(106\) 14.9005 6.63415i 1.44727 0.644366i
\(107\) 14.6327 1.41460 0.707299 0.706914i \(-0.249913\pi\)
0.707299 + 0.706914i \(0.249913\pi\)
\(108\) 0 0
\(109\) 0.620591 1.90998i 0.0594418 0.182943i −0.916927 0.399056i \(-0.869338\pi\)
0.976368 + 0.216113i \(0.0693379\pi\)
\(110\) 9.68590 13.9143i 0.923514 1.32668i
\(111\) 0 0
\(112\) −28.2709 + 6.00918i −2.67135 + 0.567814i
\(113\) −13.0613 + 2.77626i −1.22870 + 0.261169i −0.776138 0.630563i \(-0.782824\pi\)
−0.452565 + 0.891732i \(0.649491\pi\)
\(114\) 0 0
\(115\) −0.660967 0.872125i −0.0616355 0.0813261i
\(116\) −3.09173 + 9.51536i −0.287060 + 0.883479i
\(117\) 0 0
\(118\) 27.8737 2.56598
\(119\) −10.7560 + 4.78889i −0.986004 + 0.438997i
\(120\) 0 0
\(121\) −3.07473 1.36896i −0.279521 0.124451i
\(122\) 18.2752 + 8.13665i 1.65456 + 0.736658i
\(123\) 0 0
\(124\) 7.55865 13.0920i 0.678787 1.17569i
\(125\) 6.01157 9.42661i 0.537692 0.843142i
\(126\) 0 0
\(127\) 1.59486 + 4.90847i 0.141521 + 0.435556i 0.996547 0.0830282i \(-0.0264591\pi\)
−0.855026 + 0.518585i \(0.826459\pi\)
\(128\) −4.51521 42.9594i −0.399092 3.79711i
\(129\) 0 0
\(130\) −1.95458 + 10.2054i −0.171428 + 0.895074i
\(131\) −1.24905 + 11.8839i −0.109130 + 1.03830i 0.793701 + 0.608307i \(0.208151\pi\)
−0.902831 + 0.429995i \(0.858515\pi\)
\(132\) 0 0
\(133\) −2.59604 + 1.15583i −0.225105 + 0.100223i
\(134\) −7.41462 + 22.8199i −0.640526 + 1.97134i
\(135\) 0 0
\(136\) −18.9228 58.2383i −1.62261 4.99389i
\(137\) 2.90001 + 3.22078i 0.247764 + 0.275170i 0.854180 0.519978i \(-0.174060\pi\)
−0.606415 + 0.795148i \(0.707393\pi\)
\(138\) 0 0
\(139\) 8.91270 9.89856i 0.755966 0.839585i −0.235237 0.971938i \(-0.575587\pi\)
0.991203 + 0.132353i \(0.0422533\pi\)
\(140\) −9.78959 20.8438i −0.827372 1.76162i
\(141\) 0 0
\(142\) 8.49919 3.78408i 0.713236 0.317553i
\(143\) −4.67908 −0.391284
\(144\) 0 0
\(145\) −4.03125 0.341505i −0.334777 0.0283604i
\(146\) −4.45555 42.3918i −0.368744 3.50837i
\(147\) 0 0
\(148\) 15.6042 17.3303i 1.28266 1.42454i
\(149\) 1.42735 + 2.47225i 0.116933 + 0.202535i 0.918551 0.395303i \(-0.129360\pi\)
−0.801618 + 0.597837i \(0.796027\pi\)
\(150\) 0 0
\(151\) 5.61232 9.72082i 0.456724 0.791069i −0.542062 0.840339i \(-0.682356\pi\)
0.998786 + 0.0492697i \(0.0156894\pi\)
\(152\) −4.56713 14.0562i −0.370443 1.14011i
\(153\) 0 0
\(154\) 11.4235 8.29965i 0.920531 0.668805i
\(155\) 5.85071 + 1.77114i 0.469940 + 0.142261i
\(156\) 0 0
\(157\) −7.23692 12.5347i −0.577569 1.00038i −0.995757 0.0920188i \(-0.970668\pi\)
0.418188 0.908360i \(-0.362665\pi\)
\(158\) 3.68034 35.0161i 0.292792 2.78573i
\(159\) 0 0
\(160\) 49.0326 17.0345i 3.87637 1.34669i
\(161\) −0.281641 0.866803i −0.0221964 0.0683136i
\(162\) 0 0
\(163\) 2.58162 7.94542i 0.202208 0.622333i −0.797608 0.603176i \(-0.793902\pi\)
0.999816 0.0191571i \(-0.00609828\pi\)
\(164\) −20.5527 4.36861i −1.60490 0.341131i
\(165\) 0 0
\(166\) −2.36054 + 0.501747i −0.183213 + 0.0389432i
\(167\) 1.18258 11.2515i 0.0915109 0.870668i −0.848425 0.529316i \(-0.822449\pi\)
0.939936 0.341352i \(-0.110885\pi\)
\(168\) 0 0
\(169\) −9.25621 + 4.12113i −0.712016 + 0.317010i
\(170\) 33.1955 20.0705i 2.54598 1.53934i
\(171\) 0 0
\(172\) −47.4993 + 34.5103i −3.62179 + 2.63139i
\(173\) 6.21968 + 1.32203i 0.472874 + 0.100512i 0.438183 0.898886i \(-0.355622\pi\)
0.0346904 + 0.999398i \(0.488955\pi\)
\(174\) 0 0
\(175\) 7.30613 5.77326i 0.552291 0.436417i
\(176\) 21.4400 + 37.1352i 1.61610 + 2.79917i
\(177\) 0 0
\(178\) 1.40375 + 13.3558i 0.105216 + 1.00106i
\(179\) −5.40088 + 3.92397i −0.403681 + 0.293291i −0.771039 0.636788i \(-0.780262\pi\)
0.367358 + 0.930080i \(0.380262\pi\)
\(180\) 0 0
\(181\) 5.85623 + 4.25480i 0.435290 + 0.316257i 0.783761 0.621063i \(-0.213299\pi\)
−0.348470 + 0.937320i \(0.613299\pi\)
\(182\) −4.32716 + 7.49486i −0.320751 + 0.555556i
\(183\) 0 0
\(184\) 4.63659 0.985537i 0.341814 0.0726547i
\(185\) 8.26011 + 4.54896i 0.607295 + 0.334446i
\(186\) 0 0
\(187\) 11.6883 + 12.9812i 0.854735 + 0.949280i
\(188\) 10.9647 33.7460i 0.799686 2.46118i
\(189\) 0 0
\(190\) 8.01195 4.84415i 0.581248 0.351431i
\(191\) −0.759730 0.843766i −0.0549721 0.0610527i 0.715032 0.699092i \(-0.246412\pi\)
−0.770004 + 0.638039i \(0.779746\pi\)
\(192\) 0 0
\(193\) 1.53746 + 2.66296i 0.110669 + 0.191684i 0.916040 0.401087i \(-0.131367\pi\)
−0.805371 + 0.592771i \(0.798034\pi\)
\(194\) 1.08927 10.3637i 0.0782052 0.744073i
\(195\) 0 0
\(196\) 2.04135 + 19.4221i 0.145811 + 1.38729i
\(197\) −18.8592 + 13.7020i −1.34366 + 0.976227i −0.344360 + 0.938838i \(0.611904\pi\)
−0.999301 + 0.0373893i \(0.988096\pi\)
\(198\) 0 0
\(199\) −18.6167 −1.31970 −0.659851 0.751396i \(-0.729381\pi\)
−0.659851 + 0.751396i \(0.729381\pi\)
\(200\) 25.8898 + 40.9290i 1.83069 + 2.89412i
\(201\) 0 0
\(202\) 12.2340 13.5872i 0.860778 0.955991i
\(203\) −3.07824 1.37052i −0.216050 0.0961917i
\(204\) 0 0
\(205\) −0.171679 8.49473i −0.0119905 0.593298i
\(206\) 3.41274 + 2.47950i 0.237777 + 0.172755i
\(207\) 0 0
\(208\) −21.2620 15.4478i −1.47426 1.07111i
\(209\) 2.82106 + 3.13310i 0.195136 + 0.216721i
\(210\) 0 0
\(211\) −7.70340 + 8.55549i −0.530324 + 0.588984i −0.947466 0.319857i \(-0.896365\pi\)
0.417142 + 0.908841i \(0.363032\pi\)
\(212\) −32.1510 + 6.83391i −2.20814 + 0.469355i
\(213\) 0 0
\(214\) −39.2755 8.34827i −2.68482 0.570676i
\(215\) −17.9606 15.5263i −1.22490 1.05888i
\(216\) 0 0
\(217\) 4.11894 + 2.99259i 0.279612 + 0.203150i
\(218\) −2.75541 + 4.77250i −0.186620 + 0.323235i
\(219\) 0 0
\(220\) −24.9224 + 23.3691i −1.68027 + 1.57555i
\(221\) −9.78055 4.35458i −0.657911 0.292921i
\(222\) 0 0
\(223\) 2.00257 + 0.425659i 0.134102 + 0.0285043i 0.274474 0.961595i \(-0.411496\pi\)
−0.140372 + 0.990099i \(0.544830\pi\)
\(224\) 43.2323 2.88858
\(225\) 0 0
\(226\) 36.6416 2.43736
\(227\) 14.8654 + 3.15974i 0.986653 + 0.209720i 0.672858 0.739771i \(-0.265066\pi\)
0.313795 + 0.949491i \(0.398400\pi\)
\(228\) 0 0
\(229\) −0.192216 0.0855802i −0.0127020 0.00565530i 0.400376 0.916351i \(-0.368880\pi\)
−0.413078 + 0.910696i \(0.635546\pi\)
\(230\) 1.27653 + 2.71796i 0.0841718 + 0.179217i
\(231\) 0 0
\(232\) 8.76239 15.1769i 0.575279 0.996413i
\(233\) 13.5683 + 9.85792i 0.888887 + 0.645814i 0.935587 0.353095i \(-0.114871\pi\)
−0.0467009 + 0.998909i \(0.514871\pi\)
\(234\) 0 0
\(235\) 14.2968 + 1.21114i 0.932617 + 0.0790060i
\(236\) −54.9436 11.6786i −3.57653 0.760214i
\(237\) 0 0
\(238\) 31.6023 6.71727i 2.04847 0.435416i
\(239\) 16.5230 18.3506i 1.06878 1.18700i 0.0871544 0.996195i \(-0.472223\pi\)
0.981627 0.190808i \(-0.0611107\pi\)
\(240\) 0 0
\(241\) −2.03608 2.26129i −0.131155 0.145663i 0.673990 0.738741i \(-0.264579\pi\)
−0.805145 + 0.593078i \(0.797913\pi\)
\(242\) 7.47183 + 5.42860i 0.480307 + 0.348964i
\(243\) 0 0
\(244\) −32.6144 23.6957i −2.08792 1.51696i
\(245\) −7.45955 + 2.59153i −0.476573 + 0.165567i
\(246\) 0 0
\(247\) −2.36060 1.05101i −0.150201 0.0668740i
\(248\) −17.7182 + 19.6780i −1.12511 + 1.24956i
\(249\) 0 0
\(250\) −21.5137 + 21.8721i −1.36064 + 1.38331i
\(251\) 24.9480 1.57470 0.787352 0.616504i \(-0.211452\pi\)
0.787352 + 0.616504i \(0.211452\pi\)
\(252\) 0 0
\(253\) −1.09393 + 0.794789i −0.0687750 + 0.0499680i
\(254\) −1.48036 14.0847i −0.0928859 0.883751i
\(255\) 0 0
\(256\) −5.56198 + 52.9187i −0.347624 + 3.30742i
\(257\) 2.15283 + 3.72881i 0.134290 + 0.232597i 0.925326 0.379172i \(-0.123791\pi\)
−0.791036 + 0.611770i \(0.790458\pi\)
\(258\) 0 0
\(259\) 5.25529 + 5.83659i 0.326548 + 0.362668i
\(260\) 8.12871 19.2976i 0.504121 1.19679i
\(261\) 0 0
\(262\) 10.1326 31.1849i 0.625992 1.92661i
\(263\) 8.56916 + 9.51702i 0.528397 + 0.586844i 0.946963 0.321342i \(-0.104134\pi\)
−0.418566 + 0.908186i \(0.637467\pi\)
\(264\) 0 0
\(265\) −5.65026 12.0304i −0.347093 0.739023i
\(266\) 7.62742 1.62126i 0.467667 0.0994058i
\(267\) 0 0
\(268\) 24.1766 41.8751i 1.47682 2.55793i
\(269\) −16.3393 11.8712i −0.996227 0.723801i −0.0349513 0.999389i \(-0.511128\pi\)
−0.961276 + 0.275588i \(0.911128\pi\)
\(270\) 0 0
\(271\) 6.40204 4.65136i 0.388897 0.282550i −0.376107 0.926576i \(-0.622737\pi\)
0.765003 + 0.644027i \(0.222737\pi\)
\(272\) 10.2556 + 97.5760i 0.621840 + 5.91641i
\(273\) 0 0
\(274\) −5.94635 10.2994i −0.359232 0.622208i
\(275\) −11.4956 7.66211i −0.693212 0.462043i
\(276\) 0 0
\(277\) −0.176092 0.0374296i −0.0105804 0.00224892i 0.202618 0.979258i \(-0.435055\pi\)
−0.213199 + 0.977009i \(0.568388\pi\)
\(278\) −29.5698 + 21.4837i −1.77348 + 1.28851i
\(279\) 0 0
\(280\) 9.18186 + 39.2772i 0.548721 + 2.34726i
\(281\) 1.48639 0.661783i 0.0886705 0.0394786i −0.361922 0.932208i \(-0.617879\pi\)
0.450593 + 0.892730i \(0.351213\pi\)
\(282\) 0 0
\(283\) 0.382272 3.63707i 0.0227237 0.216201i −0.977268 0.212010i \(-0.931999\pi\)
0.999991 0.00419159i \(-0.00133423\pi\)
\(284\) −18.3388 + 3.89803i −1.08821 + 0.231305i
\(285\) 0 0
\(286\) 12.5591 + 2.66951i 0.742633 + 0.157851i
\(287\) 2.18676 6.73015i 0.129080 0.397268i
\(288\) 0 0
\(289\) 7.09756 + 21.8440i 0.417503 + 1.28494i
\(290\) 10.6254 + 3.21654i 0.623945 + 0.188882i
\(291\) 0 0
\(292\) −8.97884 + 85.4280i −0.525447 + 4.99929i
\(293\) −12.2406 21.2013i −0.715101 1.23859i −0.962921 0.269785i \(-0.913047\pi\)
0.247820 0.968806i \(-0.420286\pi\)
\(294\) 0 0
\(295\) −0.458949 22.7090i −0.0267210 1.32217i
\(296\) −33.0463 + 24.0096i −1.92078 + 1.39553i
\(297\) 0 0
\(298\) −2.42067 7.45007i −0.140226 0.431571i
\(299\) 0.414377 0.717721i 0.0239640 0.0415069i
\(300\) 0 0
\(301\) −9.88675 17.1244i −0.569863 0.987032i
\(302\) −20.6099 + 22.8896i −1.18597 + 1.31715i
\(303\) 0 0
\(304\) 2.47527 + 23.5506i 0.141966 + 1.35072i
\(305\) 6.32812 15.0230i 0.362347 0.860215i
\(306\) 0 0
\(307\) 3.80945 0.217417 0.108708 0.994074i \(-0.465329\pi\)
0.108708 + 0.994074i \(0.465329\pi\)
\(308\) −25.9950 + 11.5737i −1.48120 + 0.659474i
\(309\) 0 0
\(310\) −14.6934 8.09184i −0.834526 0.459586i
\(311\) 16.8714 18.7375i 0.956687 1.06251i −0.0413039 0.999147i \(-0.513151\pi\)
0.997991 0.0633616i \(-0.0201822\pi\)
\(312\) 0 0
\(313\) 17.3585 + 19.2786i 0.981161 + 1.08969i 0.995960 + 0.0897989i \(0.0286224\pi\)
−0.0147991 + 0.999890i \(0.504711\pi\)
\(314\) 12.2732 + 37.7731i 0.692618 + 2.13166i
\(315\) 0 0
\(316\) −21.9258 + 67.4806i −1.23342 + 3.79608i
\(317\) 20.9744 9.33841i 1.17804 0.524497i 0.278118 0.960547i \(-0.410289\pi\)
0.899923 + 0.436050i \(0.143623\pi\)
\(318\) 0 0
\(319\) −0.522549 + 4.97172i −0.0292571 + 0.278363i
\(320\) −72.4630 + 9.09997i −4.05080 + 0.508704i
\(321\) 0 0
\(322\) 0.261421 + 2.48726i 0.0145684 + 0.138609i
\(323\) 2.98096 + 9.17445i 0.165865 + 0.510480i
\(324\) 0 0
\(325\) 8.34666 + 1.42438i 0.462989 + 0.0790106i
\(326\) −11.4623 + 19.8533i −0.634839 + 1.09957i
\(327\) 0 0
\(328\) 33.6224 + 14.9697i 1.85649 + 0.826561i
\(329\) 10.9169 + 4.86053i 0.601869 + 0.267969i
\(330\) 0 0
\(331\) 5.62038 2.50235i 0.308924 0.137542i −0.246419 0.969163i \(-0.579254\pi\)
0.555343 + 0.831622i \(0.312587\pi\)
\(332\) 4.86323 0.266904
\(333\) 0 0
\(334\) −9.59337 + 29.5254i −0.524926 + 1.61556i
\(335\) 18.7137 + 5.66504i 1.02244 + 0.309514i
\(336\) 0 0
\(337\) 14.7319 3.13136i 0.802498 0.170576i 0.211636 0.977349i \(-0.432121\pi\)
0.590862 + 0.806772i \(0.298788\pi\)
\(338\) 27.1957 5.78061i 1.47925 0.314424i
\(339\) 0 0
\(340\) −73.8430 + 25.6539i −4.00470 + 1.39128i
\(341\) 2.33416 7.18380i 0.126402 0.389024i
\(342\) 0 0
\(343\) −19.6137 −1.05904
\(344\) 93.9494 41.8290i 5.06541 2.25527i
\(345\) 0 0
\(346\) −15.9399 7.09691i −0.856935 0.381532i
\(347\) 15.3731 + 6.84453i 0.825269 + 0.367434i 0.775516 0.631328i \(-0.217490\pi\)
0.0497533 + 0.998762i \(0.484156\pi\)
\(348\) 0 0
\(349\) −7.75462 + 13.4314i −0.415096 + 0.718967i −0.995438 0.0954057i \(-0.969585\pi\)
0.580343 + 0.814372i \(0.302919\pi\)
\(350\) −22.9041 + 11.3276i −1.22427 + 0.605488i
\(351\) 0 0
\(352\) −19.8203 61.0006i −1.05643 3.25134i
\(353\) 0.982184 + 9.34486i 0.0522764 + 0.497377i 0.989065 + 0.147481i \(0.0471164\pi\)
−0.936789 + 0.349896i \(0.886217\pi\)
\(354\) 0 0
\(355\) −3.22288 6.86209i −0.171053 0.364202i
\(356\) 2.82885 26.9147i 0.149928 1.42647i
\(357\) 0 0
\(358\) 16.7351 7.45097i 0.884480 0.393796i
\(359\) 2.47394 7.61399i 0.130569 0.401851i −0.864305 0.502968i \(-0.832241\pi\)
0.994875 + 0.101116i \(0.0322415\pi\)
\(360\) 0 0
\(361\) −5.15185 15.8558i −0.271150 0.834514i
\(362\) −13.2912 14.7614i −0.698569 0.775840i
\(363\) 0 0
\(364\) 11.6698 12.9606i 0.611663 0.679320i
\(365\) −34.4637 + 4.32799i −1.80391 + 0.226537i
\(366\) 0 0
\(367\) 24.1256 10.7414i 1.25935 0.560698i 0.334990 0.942222i \(-0.391267\pi\)
0.924359 + 0.381524i \(0.124601\pi\)
\(368\) −7.59487 −0.395910
\(369\) 0 0
\(370\) −19.5756 16.9224i −1.01769 0.879752i
\(371\) −1.15712 11.0093i −0.0600747 0.571573i
\(372\) 0 0
\(373\) −13.8997 + 15.4372i −0.719700 + 0.799308i −0.986381 0.164477i \(-0.947406\pi\)
0.266681 + 0.963785i \(0.414073\pi\)
\(374\) −23.9665 41.5111i −1.23928 2.14649i
\(375\) 0 0
\(376\) −31.0756 + 53.8246i −1.60260 + 2.77579i
\(377\) −0.946817 2.91400i −0.0487636 0.150079i
\(378\) 0 0
\(379\) 15.5059 11.2657i 0.796485 0.578680i −0.113396 0.993550i \(-0.536173\pi\)
0.909881 + 0.414870i \(0.136173\pi\)
\(380\) −17.8225 + 6.19174i −0.914276 + 0.317629i
\(381\) 0 0
\(382\) 1.55780 + 2.69818i 0.0797038 + 0.138051i
\(383\) −2.52616 + 24.0348i −0.129081 + 1.22812i 0.717765 + 0.696285i \(0.245165\pi\)
−0.846846 + 0.531838i \(0.821502\pi\)
\(384\) 0 0
\(385\) −6.94992 9.17020i −0.354201 0.467357i
\(386\) −2.60740 8.02476i −0.132713 0.408449i
\(387\) 0 0
\(388\) −6.48938 + 19.9722i −0.329448 + 1.01394i
\(389\) −36.8855 7.84025i −1.87017 0.397517i −0.874073 0.485795i \(-0.838530\pi\)
−0.996096 + 0.0882786i \(0.971863\pi\)
\(390\) 0 0
\(391\) −3.02629 + 0.643258i −0.153046 + 0.0325310i
\(392\) 3.57561 34.0197i 0.180596 1.71825i
\(393\) 0 0
\(394\) 58.4370 26.0178i 2.94401 1.31076i
\(395\) −28.5887 2.42187i −1.43845 0.121857i
\(396\) 0 0
\(397\) 22.7545 16.5321i 1.14202 0.829724i 0.154618 0.987974i \(-0.450585\pi\)
0.987399 + 0.158251i \(0.0505855\pi\)
\(398\) 49.9688 + 10.6212i 2.50471 + 0.532393i
\(399\) 0 0
\(400\) −26.9407 72.7694i −1.34704 3.63847i
\(401\) 11.7822 + 20.4073i 0.588373 + 1.01909i 0.994446 + 0.105251i \(0.0335647\pi\)
−0.406073 + 0.913841i \(0.633102\pi\)
\(402\) 0 0
\(403\) 0.483921 + 4.60420i 0.0241058 + 0.229351i
\(404\) −29.8080 + 21.6568i −1.48300 + 1.07746i
\(405\) 0 0
\(406\) 7.48036 + 5.43480i 0.371244 + 0.269725i
\(407\) 5.82606 10.0910i 0.288787 0.500194i
\(408\) 0 0
\(409\) −10.2783 + 2.18473i −0.508231 + 0.108028i −0.454888 0.890548i \(-0.650321\pi\)
−0.0533426 + 0.998576i \(0.516988\pi\)
\(410\) −4.38562 + 22.8986i −0.216590 + 1.13088i
\(411\) 0 0
\(412\) −5.68821 6.31740i −0.280238 0.311236i
\(413\) 5.84587 17.9917i 0.287656 0.885315i
\(414\) 0 0
\(415\) 0.447647 + 1.91490i 0.0219741 + 0.0939985i
\(416\) 26.3045 + 29.2141i 1.28969 + 1.43234i
\(417\) 0 0
\(418\) −5.78446 10.0190i −0.282927 0.490045i
\(419\) 0.989526 9.41471i 0.0483415 0.459939i −0.943397 0.331665i \(-0.892390\pi\)
0.991739 0.128274i \(-0.0409437\pi\)
\(420\) 0 0
\(421\) 0.707686 + 6.73319i 0.0344905 + 0.328155i 0.998139 + 0.0609816i \(0.0194231\pi\)
−0.963648 + 0.267174i \(0.913910\pi\)
\(422\) 25.5577 18.5687i 1.24413 0.903912i
\(423\) 0 0
\(424\) 57.5737 2.79603
\(425\) −16.8982 26.7143i −0.819685 1.29583i
\(426\) 0 0
\(427\) 9.08481 10.0897i 0.439645 0.488275i
\(428\) 73.9207 + 32.9116i 3.57309 + 1.59084i
\(429\) 0 0
\(430\) 39.3497 + 51.9208i 1.89761 + 2.50384i
\(431\) 20.0354 + 14.5565i 0.965069 + 0.701164i 0.954322 0.298779i \(-0.0965792\pi\)
0.0107465 + 0.999942i \(0.496579\pi\)
\(432\) 0 0
\(433\) 5.18591 + 3.76779i 0.249219 + 0.181068i 0.705381 0.708829i \(-0.250776\pi\)
−0.456162 + 0.889897i \(0.650776\pi\)
\(434\) −9.34827 10.3823i −0.448731 0.498367i
\(435\) 0 0
\(436\) 7.43096 8.25292i 0.355879 0.395243i
\(437\) −0.730416 + 0.155255i −0.0349405 + 0.00742684i
\(438\) 0 0
\(439\) 0.251052 + 0.0533628i 0.0119821 + 0.00254687i 0.213899 0.976856i \(-0.431384\pi\)
−0.201917 + 0.979403i \(0.564717\pi\)
\(440\) 51.2105 30.9626i 2.44136 1.47609i
\(441\) 0 0
\(442\) 23.7675 + 17.2681i 1.13050 + 0.821359i
\(443\) −7.32776 + 12.6920i −0.348152 + 0.603017i −0.985921 0.167210i \(-0.946524\pi\)
0.637769 + 0.770228i \(0.279857\pi\)
\(444\) 0 0
\(445\) 10.8580 1.36356i 0.514720 0.0646390i
\(446\) −5.13223 2.28501i −0.243018 0.108199i
\(447\) 0 0
\(448\) −59.4974 12.6466i −2.81099 0.597494i
\(449\) −15.5412 −0.733436 −0.366718 0.930332i \(-0.619519\pi\)
−0.366718 + 0.930332i \(0.619519\pi\)
\(450\) 0 0
\(451\) −10.4988 −0.494367
\(452\) −72.2266 15.3522i −3.39725 0.722108i
\(453\) 0 0
\(454\) −38.0974 16.9621i −1.78800 0.796069i
\(455\) 6.17740 + 3.40198i 0.289601 + 0.159487i
\(456\) 0 0
\(457\) 7.26861 12.5896i 0.340011 0.588916i −0.644423 0.764669i \(-0.722903\pi\)
0.984434 + 0.175752i \(0.0562358\pi\)
\(458\) 0.467100 + 0.339368i 0.0218262 + 0.0158576i
\(459\) 0 0
\(460\) −1.37747 5.89239i −0.0642248 0.274734i
\(461\) 3.21841 + 0.684094i 0.149896 + 0.0318614i 0.282249 0.959341i \(-0.408920\pi\)
−0.132352 + 0.991203i \(0.542253\pi\)
\(462\) 0 0
\(463\) 37.4109 7.95194i 1.73863 0.369558i 0.774007 0.633177i \(-0.218249\pi\)
0.964627 + 0.263619i \(0.0849161\pi\)
\(464\) −18.7884 + 20.8666i −0.872230 + 0.968709i
\(465\) 0 0
\(466\) −30.7943 34.2005i −1.42652 1.58431i
\(467\) −4.63677 3.36881i −0.214564 0.155890i 0.475312 0.879817i \(-0.342335\pi\)
−0.689876 + 0.723927i \(0.742335\pi\)
\(468\) 0 0
\(469\) 13.1746 + 9.57189i 0.608345 + 0.441989i
\(470\) −37.6828 11.4074i −1.73818 0.526184i
\(471\) 0 0
\(472\) 89.8829 + 40.0184i 4.13720 + 1.84200i
\(473\) −19.6297 + 21.8010i −0.902576 + 1.00241i
\(474\) 0 0
\(475\) −4.07850 6.44767i −0.187135 0.295840i
\(476\) −65.1078 −2.98421
\(477\) 0 0
\(478\) −54.8185 + 39.8280i −2.50734 + 1.82169i
\(479\) −1.40830 13.3991i −0.0643469 0.612220i −0.978414 0.206656i \(-0.933742\pi\)
0.914067 0.405564i \(-0.132925\pi\)
\(480\) 0 0
\(481\) −0.746503 + 7.10250i −0.0340376 + 0.323846i
\(482\) 4.17490 + 7.23113i 0.190161 + 0.329369i
\(483\) 0 0
\(484\) −12.4537 13.8312i −0.566078 0.628693i
\(485\) −8.46139 0.716801i −0.384212 0.0325483i
\(486\) 0 0
\(487\) −8.88128 + 27.3338i −0.402449 + 1.23861i 0.520557 + 0.853827i \(0.325724\pi\)
−0.923006 + 0.384785i \(0.874276\pi\)
\(488\) 47.2494 + 52.4757i 2.13888 + 2.37547i
\(489\) 0 0
\(490\) 21.5006 2.70007i 0.971299 0.121977i
\(491\) 15.6203 3.32021i 0.704936 0.149839i 0.158524 0.987355i \(-0.449327\pi\)
0.546412 + 0.837516i \(0.315993\pi\)
\(492\) 0 0
\(493\) −5.71920 + 9.90594i −0.257580 + 0.446141i
\(494\) 5.73644 + 4.16777i 0.258095 + 0.187517i
\(495\) 0 0
\(496\) 34.3236 24.9375i 1.54117 1.11973i
\(497\) −0.660016 6.27963i −0.0296058 0.281680i
\(498\) 0 0
\(499\) 10.4973 + 18.1818i 0.469922 + 0.813929i 0.999409 0.0343894i \(-0.0109486\pi\)
−0.529486 + 0.848318i \(0.677615\pi\)
\(500\) 51.5711 34.0997i 2.30633 1.52498i
\(501\) 0 0
\(502\) −66.9626 14.2333i −2.98869 0.635265i
\(503\) −3.48380 + 2.53113i −0.155335 + 0.112857i −0.662738 0.748852i \(-0.730606\pi\)
0.507403 + 0.861709i \(0.330606\pi\)
\(504\) 0 0
\(505\) −11.2711 9.74344i −0.501557 0.433577i
\(506\) 3.38966 1.50917i 0.150689 0.0670909i
\(507\) 0 0
\(508\) −2.98322 + 28.3835i −0.132359 + 1.25931i
\(509\) 41.2503 8.76803i 1.82839 0.388636i 0.840251 0.542198i \(-0.182408\pi\)
0.988139 + 0.153562i \(0.0490745\pi\)
\(510\) 0 0
\(511\) −28.2972 6.01476i −1.25180 0.266077i
\(512\) 18.4234 56.7015i 0.814209 2.50588i
\(513\) 0 0
\(514\) −3.65103 11.2367i −0.161040 0.495630i
\(515\) 1.96389 2.82123i 0.0865393 0.124318i
\(516\) 0 0
\(517\) 1.85321 17.6321i 0.0815040 0.775459i
\(518\) −10.7758 18.6642i −0.473460 0.820056i
\(519\) 0 0
\(520\) −20.9548 + 30.1027i −0.918930 + 1.32009i
\(521\) 25.2789 18.3662i 1.10749 0.804637i 0.125222 0.992129i \(-0.460036\pi\)
0.982266 + 0.187491i \(0.0600356\pi\)
\(522\) 0 0
\(523\) −11.4494 35.2378i −0.500649 1.54084i −0.807964 0.589232i \(-0.799430\pi\)
0.307314 0.951608i \(-0.400570\pi\)
\(524\) −33.0389 + 57.2251i −1.44331 + 2.49989i
\(525\) 0 0
\(526\) −17.5707 30.4334i −0.766120 1.32696i
\(527\) 11.5646 12.8438i 0.503763 0.559486i
\(528\) 0 0
\(529\) 2.37912 + 22.6358i 0.103440 + 0.984166i
\(530\) 8.30220 + 35.5143i 0.360625 + 1.54264i
\(531\) 0 0
\(532\) −15.7142 −0.681297
\(533\) 5.87841 2.61724i 0.254622 0.113365i
\(534\) 0 0
\(535\) −6.15475 + 32.1357i −0.266093 + 1.38935i
\(536\) −56.6722 + 62.9408i −2.44787 + 2.71863i
\(537\) 0 0
\(538\) 37.0834 + 41.1853i 1.59878 + 1.77563i
\(539\) 3.01535 + 9.28030i 0.129880 + 0.399731i
\(540\) 0 0
\(541\) −10.3961 + 31.9960i −0.446965 + 1.37562i 0.433350 + 0.901226i \(0.357332\pi\)
−0.880314 + 0.474391i \(0.842668\pi\)
\(542\) −19.8373 + 8.83215i −0.852087 + 0.379374i
\(543\) 0 0
\(544\) 15.3404 145.954i 0.657712 6.25771i
\(545\) 3.93358 + 2.16628i 0.168496 + 0.0927933i
\(546\) 0 0
\(547\) −0.581655 5.53408i −0.0248698 0.236620i −0.999895 0.0145239i \(-0.995377\pi\)
0.975025 0.222096i \(-0.0712899\pi\)
\(548\) 7.40596 + 22.7932i 0.316367 + 0.973678i
\(549\) 0 0
\(550\) 26.4839 + 27.1243i 1.12928 + 1.15658i
\(551\) −1.38037 + 2.39086i −0.0588056 + 0.101854i
\(552\) 0 0
\(553\) −21.8301 9.71940i −0.928312 0.413311i
\(554\) 0.451293 + 0.200928i 0.0191736 + 0.00853663i
\(555\) 0 0
\(556\) 67.2883 29.9587i 2.85366 1.27053i
\(557\) −37.0966 −1.57183 −0.785917 0.618332i \(-0.787809\pi\)
−0.785917 + 0.618332i \(0.787809\pi\)
\(558\) 0 0
\(559\) 5.55619 17.1002i 0.235002 0.723262i
\(560\) −1.30587 64.6148i −0.0551829 2.73048i
\(561\) 0 0
\(562\) −4.36716 + 0.928268i −0.184217 + 0.0391566i
\(563\) −20.9186 + 4.44638i −0.881612 + 0.187392i −0.626408 0.779495i \(-0.715476\pi\)
−0.255203 + 0.966887i \(0.582142\pi\)
\(564\) 0 0
\(565\) −0.603315 29.8523i −0.0253817 1.25590i
\(566\) −3.10107 + 9.54412i −0.130348 + 0.401169i
\(567\) 0 0
\(568\) 32.8398 1.37793
\(569\) 13.8567 6.16939i 0.580902 0.258634i −0.0951807 0.995460i \(-0.530343\pi\)
0.676083 + 0.736826i \(0.263676\pi\)
\(570\) 0 0
\(571\) 34.7764 + 15.4834i 1.45535 + 0.647962i 0.973582 0.228339i \(-0.0733296\pi\)
0.481764 + 0.876301i \(0.339996\pi\)
\(572\) −23.6375 10.5241i −0.988333 0.440034i
\(573\) 0 0
\(574\) −9.70913 + 16.8167i −0.405251 + 0.701916i
\(575\) 2.19333 1.08475i 0.0914683 0.0452374i
\(576\) 0 0
\(577\) 2.27456 + 7.00039i 0.0946913 + 0.291430i 0.987173 0.159653i \(-0.0510377\pi\)
−0.892482 + 0.451083i \(0.851038\pi\)
\(578\) −6.58800 62.6806i −0.274025 2.60717i
\(579\) 0 0
\(580\) −19.5967 10.7922i −0.813710 0.448122i
\(581\) −0.171204 + 1.62889i −0.00710273 + 0.0675779i
\(582\) 0 0
\(583\) −15.0036 + 6.68001i −0.621384 + 0.276658i
\(584\) 46.4946 143.096i 1.92396 5.92133i
\(585\) 0 0
\(586\) 20.7590 + 63.8895i 0.857545 + 2.63925i
\(587\) 16.6264 + 18.4655i 0.686247 + 0.762154i 0.981124 0.193381i \(-0.0619454\pi\)
−0.294877 + 0.955535i \(0.595279\pi\)
\(588\) 0 0
\(589\) 2.79120 3.09994i 0.115009 0.127731i
\(590\) −11.7241 + 61.2148i −0.482673 + 2.52017i
\(591\) 0 0
\(592\) 59.7891 26.6198i 2.45732 1.09407i
\(593\) −43.3690 −1.78095 −0.890476 0.455030i \(-0.849629\pi\)
−0.890476 + 0.455030i \(0.849629\pi\)
\(594\) 0 0
\(595\) −5.99299 25.6362i −0.245688 1.05098i
\(596\) 1.65009 + 15.6995i 0.0675903 + 0.643079i
\(597\) 0 0
\(598\) −1.52170 + 1.69002i −0.0622268 + 0.0691099i
\(599\) 5.35663 + 9.27796i 0.218866 + 0.379087i 0.954462 0.298334i \(-0.0964309\pi\)
−0.735596 + 0.677421i \(0.763098\pi\)
\(600\) 0 0
\(601\) 8.90717 15.4277i 0.363331 0.629308i −0.625176 0.780484i \(-0.714973\pi\)
0.988507 + 0.151176i \(0.0483060\pi\)
\(602\) 16.7671 + 51.6039i 0.683377 + 2.10322i
\(603\) 0 0
\(604\) 50.2159 36.4840i 2.04325 1.48451i
\(605\) 4.29972 6.17677i 0.174808 0.251121i
\(606\) 0 0
\(607\) 21.1667 + 36.6618i 0.859129 + 1.48805i 0.872761 + 0.488148i \(0.162327\pi\)
−0.0136324 + 0.999907i \(0.504339\pi\)
\(608\) 3.70250 35.2269i 0.150156 1.42864i
\(609\) 0 0
\(610\) −25.5562 + 36.7128i −1.03474 + 1.48646i
\(611\) 3.35787 + 10.3345i 0.135845 + 0.418087i
\(612\) 0 0
\(613\) 13.3402 41.0570i 0.538806 1.65828i −0.196471 0.980510i \(-0.562948\pi\)
0.735278 0.677766i \(-0.237052\pi\)
\(614\) −10.2249 2.17337i −0.412643 0.0877100i
\(615\) 0 0
\(616\) 48.7527 10.3627i 1.96430 0.417525i
\(617\) −3.95649 + 37.6435i −0.159282 + 1.51547i 0.564496 + 0.825436i \(0.309071\pi\)
−0.723778 + 0.690033i \(0.757596\pi\)
\(618\) 0 0
\(619\) −14.5465 + 6.47652i −0.584674 + 0.260313i −0.677686 0.735351i \(-0.737017\pi\)
0.0930123 + 0.995665i \(0.470350\pi\)
\(620\) 25.5727 + 22.1066i 1.02702 + 0.887824i
\(621\) 0 0
\(622\) −55.9743 + 40.6677i −2.24437 + 1.63063i
\(623\) 8.91523 + 1.89499i 0.357181 + 0.0759212i
\(624\) 0 0
\(625\) 18.1737 + 17.1673i 0.726948 + 0.686692i
\(626\) −35.5929 61.6488i −1.42258 2.46398i
\(627\) 0 0
\(628\) −8.36622 79.5993i −0.333849 3.17636i
\(629\) 21.5693 15.6710i 0.860024 0.624844i
\(630\) 0 0
\(631\) −11.5984 8.42673i −0.461725 0.335463i 0.332483 0.943109i \(-0.392114\pi\)
−0.794208 + 0.607647i \(0.792114\pi\)
\(632\) 62.1407 107.631i 2.47183 4.28133i
\(633\) 0 0
\(634\) −61.6249 + 13.0988i −2.44744 + 0.520219i
\(635\) −11.4506 + 1.43797i −0.454402 + 0.0570643i
\(636\) 0 0
\(637\) −4.00183 4.44448i −0.158558 0.176097i
\(638\) 4.23903 13.0464i 0.167825 0.516512i
\(639\) 0 0
\(640\) 96.2445 + 8.15328i 3.80440 + 0.322287i
\(641\) 15.0892 + 16.7583i 0.595989 + 0.661913i 0.963376 0.268156i \(-0.0864141\pi\)
−0.367387 + 0.930068i \(0.619747\pi\)
\(642\) 0 0
\(643\) −21.0243 36.4152i −0.829119 1.43608i −0.898730 0.438502i \(-0.855509\pi\)
0.0696109 0.997574i \(-0.477824\pi\)
\(644\) 0.526817 5.01232i 0.0207595 0.197513i
\(645\) 0 0
\(646\) −2.76695 26.3257i −0.108864 1.03577i
\(647\) −9.23613 + 6.71044i −0.363110 + 0.263815i −0.754348 0.656475i \(-0.772047\pi\)
0.391238 + 0.920289i \(0.372047\pi\)
\(648\) 0 0
\(649\) −28.0664 −1.10170
\(650\) −21.5905 8.58511i −0.846850 0.336736i
\(651\) 0 0
\(652\) 30.9124 34.3317i 1.21062 1.34453i
\(653\) −7.83342 3.48766i −0.306545 0.136483i 0.247698 0.968837i \(-0.420326\pi\)
−0.554244 + 0.832354i \(0.686992\pi\)
\(654\) 0 0
\(655\) −25.5735 7.74166i −0.999239 0.302492i
\(656\) −47.7070 34.6612i −1.86265 1.35329i
\(657\) 0 0
\(658\) −26.5289 19.2744i −1.03421 0.751395i
\(659\) 20.3348 + 22.5840i 0.792130 + 0.879749i 0.995043 0.0994474i \(-0.0317075\pi\)
−0.202913 + 0.979197i \(0.565041\pi\)
\(660\) 0 0
\(661\) −14.3063 + 15.8887i −0.556449 + 0.618000i −0.954082 0.299545i \(-0.903165\pi\)
0.397633 + 0.917545i \(0.369832\pi\)
\(662\) −16.5132 + 3.51000i −0.641805 + 0.136420i
\(663\) 0 0
\(664\) −8.33227 1.77108i −0.323355 0.0687312i
\(665\) −1.44645 6.18746i −0.0560908 0.239939i
\(666\) 0 0
\(667\) −0.716332 0.520446i −0.0277365 0.0201517i
\(668\) 31.2808 54.1799i 1.21029 2.09628i
\(669\) 0 0
\(670\) −46.9972 25.8820i −1.81566 0.999909i
\(671\) −18.4016 8.19290i −0.710384 0.316284i
\(672\) 0 0
\(673\) −21.8048 4.63475i −0.840513 0.178657i −0.232513 0.972593i \(-0.574695\pi\)
−0.608000 + 0.793937i \(0.708028\pi\)
\(674\) −41.3282 −1.59190
\(675\) 0 0
\(676\) −56.0291 −2.15497
\(677\) −30.7046 6.52646i −1.18007 0.250832i −0.424211 0.905563i \(-0.639449\pi\)
−0.755862 + 0.654731i \(0.772782\pi\)
\(678\) 0 0
\(679\) −6.46107 2.87665i −0.247953 0.110396i
\(680\) 135.859 17.0613i 5.20996 0.654273i
\(681\) 0 0
\(682\) −10.3636 + 17.9503i −0.396842 + 0.687351i
\(683\) 41.1891 + 29.9257i 1.57606 + 1.14507i 0.921045 + 0.389457i \(0.127337\pi\)
0.655014 + 0.755617i \(0.272663\pi\)
\(684\) 0 0
\(685\) −8.29312 + 5.01414i −0.316864 + 0.191581i
\(686\) 52.6448 + 11.1900i 2.00999 + 0.427236i
\(687\) 0 0
\(688\) −161.174 + 34.2586i −6.14470 + 1.30610i
\(689\) 6.73545 7.48047i 0.256600 0.284983i
\(690\) 0 0
\(691\) −4.76023 5.28677i −0.181088 0.201118i 0.645766 0.763535i \(-0.276538\pi\)
−0.826854 + 0.562417i \(0.809872\pi\)
\(692\) 28.4467 + 20.6678i 1.08138 + 0.785670i
\(693\) 0 0
\(694\) −37.3577 27.1420i −1.41808 1.03029i
\(695\) 17.9899 + 23.7371i 0.682397 + 0.900401i
\(696\) 0 0
\(697\) −21.9453 9.77066i −0.831236 0.370090i
\(698\) 28.4770 31.6269i 1.07787 1.19710i
\(699\) 0 0
\(700\) 49.8938 12.7322i 1.88581 0.481232i
\(701\) 42.2657 1.59635 0.798177 0.602423i \(-0.205798\pi\)
0.798177 + 0.602423i \(0.205798\pi\)
\(702\) 0 0
\(703\) 5.20589 3.78230i 0.196344 0.142652i
\(704\) 9.43295 + 89.7486i 0.355518 + 3.38253i
\(705\) 0 0
\(706\) 2.69516 25.6428i 0.101434 0.965079i
\(707\) −6.20438 10.7463i −0.233340 0.404156i
\(708\) 0 0
\(709\) 6.41778 + 7.12767i 0.241025 + 0.267685i 0.851505 0.524346i \(-0.175690\pi\)
−0.610480 + 0.792031i \(0.709024\pi\)
\(710\) 4.73553 + 20.2572i 0.177721 + 0.760238i
\(711\) 0 0
\(712\) −14.6484 + 45.0832i −0.548973 + 1.68956i
\(713\) 0.895207 + 0.994228i 0.0335258 + 0.0372341i
\(714\) 0 0
\(715\) 1.96809 10.2760i 0.0736025 0.384299i
\(716\) −36.1096 + 7.67533i −1.34948 + 0.286840i
\(717\) 0 0
\(718\) −10.9842 + 19.0252i −0.409927 + 0.710014i
\(719\) 35.1893 + 25.5666i 1.31234 + 0.953472i 0.999994 + 0.00350360i \(0.00111523\pi\)
0.312347 + 0.949968i \(0.398885\pi\)
\(720\) 0 0
\(721\) 2.31620 1.68282i 0.0862598 0.0626714i
\(722\) 4.78198 + 45.4975i 0.177967 + 1.69324i
\(723\) 0 0
\(724\) 20.0144 + 34.6659i 0.743828 + 1.28835i
\(725\) 2.44560 8.70960i 0.0908274 0.323466i
\(726\) 0 0
\(727\) 25.6825 + 5.45899i 0.952511 + 0.202463i 0.657858 0.753142i \(-0.271463\pi\)
0.294653 + 0.955604i \(0.404796\pi\)
\(728\) −24.7140 + 17.9558i −0.915962 + 0.665486i
\(729\) 0 0
\(730\) 94.9728 + 8.04556i 3.51510 + 0.297779i
\(731\) −61.3206 + 27.3017i −2.26802 + 1.00979i
\(732\) 0 0
\(733\) −5.43558 + 51.7161i −0.200768 + 1.91018i 0.176885 + 0.984231i \(0.443398\pi\)
−0.377653 + 0.925947i \(0.623269\pi\)
\(734\) −70.8836 + 15.0668i −2.61636 + 0.556124i
\(735\) 0 0
\(736\) 11.1121 + 2.36196i 0.409598 + 0.0870628i
\(737\) 7.46588 22.9776i 0.275009 0.846391i
\(738\) 0 0
\(739\) −7.71260 23.7369i −0.283712 0.873177i −0.986782 0.162056i \(-0.948188\pi\)
0.703069 0.711121i \(-0.251812\pi\)
\(740\) 31.4965 + 41.5587i 1.15783 + 1.52773i
\(741\) 0 0
\(742\) −3.17520 + 30.2100i −0.116565 + 1.10904i
\(743\) 0.897873 + 1.55516i 0.0329398 + 0.0570534i 0.882025 0.471202i \(-0.156180\pi\)
−0.849086 + 0.528255i \(0.822846\pi\)
\(744\) 0 0
\(745\) −6.02980 + 2.09482i −0.220915 + 0.0767483i
\(746\) 46.1153 33.5047i 1.68840 1.22669i
\(747\) 0 0
\(748\) 29.8493 + 91.8668i 1.09140 + 3.35898i
\(749\) −13.6257 + 23.6005i −0.497873 + 0.862342i
\(750\) 0 0
\(751\) 9.00025 + 15.5889i 0.328424 + 0.568846i 0.982199 0.187842i \(-0.0601493\pi\)
−0.653776 + 0.756688i \(0.726816\pi\)
\(752\) 66.6327 74.0031i 2.42984 2.69862i
\(753\) 0 0
\(754\) 0.878842 + 8.36162i 0.0320055 + 0.304512i
\(755\) 18.9878 + 16.4142i 0.691036 + 0.597375i
\(756\) 0 0
\(757\) −9.03751 −0.328474 −0.164237 0.986421i \(-0.552516\pi\)
−0.164237 + 0.986421i \(0.552516\pi\)
\(758\) −48.0465 + 21.3917i −1.74513 + 0.776981i
\(759\) 0 0
\(760\) 32.7905 4.11787i 1.18944 0.149371i
\(761\) −26.4976 + 29.4286i −0.960539 + 1.06679i 0.0371821 + 0.999309i \(0.488162\pi\)
−0.997721 + 0.0674778i \(0.978505\pi\)
\(762\) 0 0
\(763\) 2.50264 + 2.77947i 0.0906017 + 0.100623i
\(764\) −1.94018 5.97126i −0.0701932 0.216032i
\(765\) 0 0
\(766\) 20.4928 63.0704i 0.740435 2.27883i
\(767\) 15.7148 6.99667i 0.567428 0.252635i
\(768\) 0 0
\(769\) −3.52699 + 33.5571i −0.127187 + 1.21010i 0.725703 + 0.688008i \(0.241515\pi\)
−0.852890 + 0.522091i \(0.825152\pi\)
\(770\) 13.4224 + 28.5787i 0.483710 + 1.02990i
\(771\) 0 0
\(772\) 1.77737 + 16.9106i 0.0639691 + 0.608625i
\(773\) −8.69380 26.7568i −0.312694 0.962374i −0.976693 0.214640i \(-0.931142\pi\)
0.663999 0.747734i \(-0.268858\pi\)
\(774\) 0 0
\(775\) −6.35059 + 12.1041i −0.228120 + 0.434791i
\(776\) 18.3918 31.8556i 0.660228 1.14355i
\(777\) 0 0
\(778\) 94.5309 + 42.0879i 3.38910 + 1.50892i
\(779\) −5.29664 2.35821i −0.189772 0.0844918i
\(780\) 0 0
\(781\) −8.55795 + 3.81024i −0.306227 + 0.136341i
\(782\) 8.48982 0.303595
\(783\) 0 0
\(784\) −16.9365 + 52.1253i −0.604877 + 1.86162i
\(785\) 30.5721 10.6211i 1.09117 0.379083i
\(786\) 0 0
\(787\) −30.1553 + 6.40972i −1.07492 + 0.228482i −0.711174 0.703016i \(-0.751836\pi\)
−0.363748 + 0.931498i \(0.618503\pi\)
\(788\) −126.090 + 26.8013i −4.49177 + 0.954755i
\(789\) 0 0
\(790\) 75.3527 + 22.8109i 2.68093 + 0.811576i
\(791\) 7.68473 23.6512i 0.273238 0.840939i
\(792\) 0 0
\(793\) 12.3457 0.438409
\(794\) −70.5070 + 31.3918i −2.50220 + 1.11405i
\(795\) 0 0
\(796\) −94.0467 41.8723i −3.33340 1.48412i
\(797\) −10.6082 4.72307i −0.375761 0.167300i 0.210161 0.977667i \(-0.432601\pi\)
−0.585923 + 0.810367i \(0.699268\pi\)
\(798\) 0 0
\(799\) 20.2830 35.1312i 0.717561 1.24285i
\(800\) 16.7864 + 114.848i 0.593489 + 4.06049i
\(801\) 0 0
\(802\) −19.9816 61.4969i −0.705574 2.17153i
\(803\) 4.48636 + 42.6848i 0.158320 + 1.50631i
\(804\) 0 0
\(805\) 2.02209 0.253936i 0.0712694 0.00895008i
\(806\) 1.32790 12.6342i 0.0467734 0.445019i
\(807\) 0 0
\(808\) 58.9575 26.2496i 2.07412 0.923456i
\(809\) −11.6688 + 35.9129i −0.410254 + 1.26263i 0.506174 + 0.862432i \(0.331059\pi\)
−0.916428 + 0.400200i \(0.868941\pi\)
\(810\) 0 0
\(811\) −1.37548 4.23331i −0.0482998 0.148652i 0.923998 0.382398i \(-0.124902\pi\)
−0.972298 + 0.233746i \(0.924902\pi\)
\(812\) −12.4679 13.8470i −0.437539 0.485936i
\(813\) 0 0
\(814\) −21.3948 + 23.7613i −0.749887 + 0.832834i
\(815\) 16.3635 + 9.01160i 0.573187 + 0.315663i
\(816\) 0 0
\(817\) −14.8001 + 6.58944i −0.517791 + 0.230535i
\(818\) 28.8344 1.00817
\(819\) 0 0
\(820\) 18.2389 43.2993i 0.636931 1.51208i
\(821\) 0.872620 + 8.30242i 0.0304546 + 0.289757i 0.999140 + 0.0414649i \(0.0132025\pi\)
−0.968685 + 0.248292i \(0.920131\pi\)
\(822\) 0 0
\(823\) −3.06147 + 3.40010i −0.106716 + 0.118520i −0.794136 0.607740i \(-0.792076\pi\)
0.687420 + 0.726260i \(0.258743\pi\)
\(824\) 7.44507 + 12.8952i 0.259361 + 0.449227i
\(825\) 0 0
\(826\) −25.9555 + 44.9562i −0.903106 + 1.56423i
\(827\) 2.49659 + 7.68370i 0.0868148 + 0.267189i 0.985034 0.172359i \(-0.0551389\pi\)
−0.898219 + 0.439547i \(0.855139\pi\)
\(828\) 0 0
\(829\) −14.9236 + 10.8426i −0.518316 + 0.376579i −0.815969 0.578095i \(-0.803796\pi\)
0.297653 + 0.954674i \(0.403796\pi\)
\(830\) −0.109036 5.39514i −0.00378468 0.187268i
\(831\) 0 0
\(832\) −27.6551 47.9000i −0.958767 1.66063i
\(833\) −2.33380 + 22.2046i −0.0808613 + 0.769344i
\(834\) 0 0
\(835\) 24.2126 + 7.32969i 0.837912 + 0.253654i
\(836\) 7.20434 + 22.1727i 0.249167 + 0.766858i
\(837\) 0 0
\(838\) −8.02726 + 24.7054i −0.277297 + 0.853433i
\(839\) −13.0629 2.77660i −0.450981 0.0958589i −0.0231787 0.999731i \(-0.507379\pi\)
−0.427802 + 0.903872i \(0.640712\pi\)
\(840\) 0 0
\(841\) 25.1643 5.34884i 0.867734 0.184443i
\(842\) 1.94193 18.4762i 0.0669233 0.636732i
\(843\) 0 0
\(844\) −58.1584 + 25.8938i −2.00189 + 0.891301i
\(845\) −5.15732 22.0614i −0.177417 0.758937i
\(846\) 0 0
\(847\) 5.07107 3.68435i 0.174244 0.126596i
\(848\) −90.2309 19.1792i −3.09854 0.658615i
\(849\) 0 0
\(850\) 30.1153 + 81.3443i 1.03295 + 2.79009i
\(851\) 1.03191 + 1.78731i 0.0353733 + 0.0612683i
\(852\) 0 0
\(853\) −5.56890 52.9846i −0.190676 1.81416i −0.503116 0.864219i \(-0.667813\pi\)
0.312440 0.949937i \(-0.398854\pi\)
\(854\) −30.1408 + 21.8986i −1.03140 + 0.749354i
\(855\) 0 0
\(856\) −114.664 83.3084i −3.91914 2.84742i
\(857\) 3.75868 6.51022i 0.128394 0.222385i −0.794661 0.607054i \(-0.792351\pi\)
0.923054 + 0.384669i \(0.125684\pi\)
\(858\) 0 0
\(859\) 23.4780 4.99040i 0.801058 0.170270i 0.210847 0.977519i \(-0.432378\pi\)
0.590211 + 0.807249i \(0.299044\pi\)
\(860\) −55.8109 118.831i −1.90314 4.05211i
\(861\) 0 0
\(862\) −45.4718 50.5016i −1.54878 1.72009i
\(863\) 13.5353 41.6575i 0.460748 1.41804i −0.403504 0.914978i \(-0.632208\pi\)
0.864252 0.503059i \(-0.167792\pi\)
\(864\) 0 0
\(865\) −5.51948 + 13.1033i −0.187668 + 0.445525i
\(866\) −11.7698 13.0717i −0.399956 0.444196i
\(867\) 0 0
\(868\) 14.0770 + 24.3820i 0.477804 + 0.827580i
\(869\) −3.70579 + 35.2582i −0.125710 + 1.19605i
\(870\) 0 0
\(871\) 1.54784 + 14.7267i 0.0524464 + 0.498994i
\(872\) −15.7371 + 11.4337i −0.532927 + 0.387194i
\(873\) 0 0
\(874\) 2.04908 0.0693110
\(875\) 9.60588 + 18.4737i 0.324738 + 0.624525i
\(876\) 0 0
\(877\) −17.2909 + 19.2035i −0.583871 + 0.648454i −0.960621 0.277860i \(-0.910375\pi\)
0.376750 + 0.926315i \(0.377041\pi\)
\(878\) −0.643402 0.286461i −0.0217138 0.00966759i
\(879\) 0 0
\(880\) −90.5726 + 31.4659i −3.05320 + 1.06072i
\(881\) 8.85610 + 6.43433i 0.298369 + 0.216778i 0.726890 0.686754i \(-0.240965\pi\)
−0.428520 + 0.903532i \(0.640965\pi\)
\(882\) 0 0
\(883\) 34.4894 + 25.0580i 1.16066 + 0.843270i 0.989862 0.142036i \(-0.0453648\pi\)
0.170800 + 0.985306i \(0.445365\pi\)
\(884\) −39.6146 43.9965i −1.33238 1.47976i
\(885\) 0 0
\(886\) 26.9094 29.8859i 0.904039 1.00404i
\(887\) 54.9183 11.6733i 1.84398 0.391949i 0.852554 0.522639i \(-0.175052\pi\)
0.991423 + 0.130690i \(0.0417191\pi\)
\(888\) 0 0
\(889\) −9.40176 1.99841i −0.315325 0.0670244i
\(890\) −29.9218 2.53481i −1.00298 0.0849669i
\(891\) 0 0
\(892\) 9.15908 + 6.65446i 0.306669 + 0.222808i
\(893\) 4.89544 8.47915i 0.163820 0.283744i
\(894\) 0 0
\(895\) −6.34594 13.5116i −0.212121 0.451644i
\(896\) 73.4917 + 32.7206i 2.45519 + 1.09312i
\(897\) 0 0
\(898\) 41.7140 + 8.86659i 1.39201 + 0.295882i
\(899\) 4.94620 0.164965
\(900\) 0 0
\(901\) −37.5783 −1.25191
\(902\) 28.1796 + 5.98975i 0.938277 + 0.199437i
\(903\) 0 0
\(904\) 118.156 + 52.6066i 3.92982 + 1.74967i
\(905\) −11.8074 + 11.0715i −0.392492 + 0.368030i
\(906\) 0 0
\(907\) 19.3181 33.4600i 0.641448 1.11102i −0.343662 0.939093i \(-0.611667\pi\)
0.985110 0.171927i \(-0.0549992\pi\)
\(908\) 67.9895 + 49.3972i 2.25631 + 1.63931i
\(909\) 0 0
\(910\) −14.6398 12.6556i −0.485304 0.419528i
\(911\) −21.0207 4.46810i −0.696448 0.148035i −0.153934 0.988081i \(-0.549194\pi\)
−0.542514 + 0.840047i \(0.682528\pi\)
\(912\) 0 0
\(913\) 2.37685 0.505216i 0.0786624 0.0167202i
\(914\) −26.6922 + 29.6447i −0.882900 + 0.980559i
\(915\) 0 0
\(916\) −0.778542 0.864658i −0.0257237 0.0285691i
\(917\) −18.0039 13.0806i −0.594542 0.431960i
\(918\) 0 0
\(919\) 10.5406 + 7.65821i 0.347703 + 0.252621i 0.747905 0.663806i \(-0.231060\pi\)
−0.400202 + 0.916427i \(0.631060\pi\)
\(920\) 0.214169 + 10.5972i 0.00706094 + 0.349379i
\(921\) 0 0
\(922\) −8.24821 3.67234i −0.271640 0.120942i
\(923\) 3.84187 4.26682i 0.126457 0.140444i
\(924\) 0 0
\(925\) −13.4645 + 16.2271i −0.442711 + 0.533544i
\(926\) −104.951 −3.44890
\(927\) 0 0
\(928\) 33.9789 24.6871i 1.11541 0.810394i
\(929\) −2.50268 23.8114i −0.0821101 0.781226i −0.955656 0.294484i \(-0.904852\pi\)
0.873546 0.486741i \(-0.161815\pi\)
\(930\) 0 0
\(931\) −0.563277 + 5.35923i −0.0184607 + 0.175642i
\(932\) 46.3711 + 80.3172i 1.51894 + 2.63088i
\(933\) 0 0
\(934\) 10.5235 + 11.6876i 0.344340 + 0.382429i
\(935\) −33.4250 + 20.2092i −1.09311 + 0.660913i
\(936\) 0 0
\(937\) 5.43437 16.7253i 0.177533 0.546390i −0.822207 0.569188i \(-0.807257\pi\)
0.999740 + 0.0227980i \(0.00725746\pi\)
\(938\) −29.9008 33.2082i −0.976294 1.08428i
\(939\) 0 0
\(940\) 69.4994 + 38.2743i 2.26682 + 1.24837i
\(941\) 13.7789 2.92879i 0.449179 0.0954759i 0.0222325 0.999753i \(-0.492923\pi\)
0.426947 + 0.904277i \(0.359589\pi\)
\(942\) 0 0
\(943\) 0.929764 1.61040i 0.0302773 0.0524418i
\(944\) −127.535 92.6599i −4.15093 3.01582i
\(945\) 0 0
\(946\) 65.1258 47.3167i 2.11742 1.53840i
\(947\) −2.31050 21.9829i −0.0750810 0.714348i −0.965711 0.259619i \(-0.916403\pi\)
0.890630 0.454729i \(-0.150264\pi\)
\(948\) 0 0
\(949\) −13.1529 22.7815i −0.426961 0.739517i
\(950\) 7.26853 + 19.6330i 0.235822 + 0.636978i
\(951\) 0 0
\(952\) 111.550 + 23.7108i 3.61537 + 0.768471i
\(953\) 25.0086 18.1698i 0.810108 0.588578i −0.103754 0.994603i \(-0.533085\pi\)
0.913862 + 0.406025i \(0.133085\pi\)
\(954\) 0 0
\(955\) 2.17259 1.31358i 0.0703034 0.0425065i
\(956\) 124.744 55.5394i 4.03450 1.79627i
\(957\) 0 0
\(958\) −3.86445 + 36.7678i −0.124855 + 1.18791i
\(959\) −7.89509 + 1.67815i −0.254946 + 0.0541904i
\(960\) 0 0
\(961\) 23.0123 + 4.89142i 0.742334 + 0.157788i
\(962\) 6.05580 18.6378i 0.195247 0.600908i
\(963\) 0 0
\(964\) −5.19968 16.0030i −0.167470 0.515421i
\(965\) −6.49493 + 2.25641i −0.209079 + 0.0726364i
\(966\) 0 0
\(967\) 2.69303 25.6224i 0.0866019 0.823962i −0.861876 0.507119i \(-0.830711\pi\)
0.948478 0.316843i \(-0.102623\pi\)
\(968\) 16.3002 + 28.2327i 0.523907 + 0.907433i
\(969\) 0 0
\(970\) 22.3022 + 6.75135i 0.716079 + 0.216773i
\(971\) −27.8824 + 20.2577i −0.894787 + 0.650101i −0.937122 0.349002i \(-0.886521\pi\)
0.0423344 + 0.999103i \(0.486521\pi\)
\(972\) 0 0
\(973\) 7.66559 + 23.5923i 0.245748 + 0.756333i
\(974\) 39.4326 68.2993i 1.26350 2.18845i
\(975\) 0 0
\(976\) −56.5694 97.9811i −1.81074 3.13630i
\(977\) −4.17072 + 4.63205i −0.133433 + 0.148192i −0.806158 0.591700i \(-0.798457\pi\)
0.672725 + 0.739892i \(0.265124\pi\)
\(978\) 0 0
\(979\) −1.41346 13.4481i −0.0451743 0.429804i
\(980\) −43.5125 3.68613i −1.38996 0.117749i
\(981\) 0 0
\(982\) −43.8206 −1.39837
\(983\) 1.85033 0.823819i 0.0590163 0.0262757i −0.377016 0.926207i \(-0.623050\pi\)
0.436033 + 0.899931i \(0.356383\pi\)
\(984\) 0 0
\(985\) −22.1592 47.1809i −0.706051 1.50331i
\(986\) 21.0024 23.3255i 0.668852 0.742835i
\(987\) 0 0
\(988\) −9.56125 10.6188i −0.304184 0.337830i
\(989\) −1.60565 4.94168i −0.0510566 0.157136i
\(990\) 0 0
\(991\) −0.263346 + 0.810497i −0.00836547 + 0.0257463i −0.955152 0.296116i \(-0.904309\pi\)
0.946787 + 0.321862i \(0.104309\pi\)
\(992\) −57.9745 + 25.8119i −1.84069 + 0.819530i
\(993\) 0 0
\(994\) −1.81112 + 17.2316i −0.0574452 + 0.546554i
\(995\) 7.83047 40.8851i 0.248243 1.29614i
\(996\) 0 0
\(997\) 6.02165 + 57.2921i 0.190707 + 1.81446i 0.502793 + 0.864407i \(0.332306\pi\)
−0.312086 + 0.950054i \(0.601028\pi\)
\(998\) −17.8025 54.7904i −0.563528 1.73436i
\(999\) 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 675.2.r.a.181.1 224
3.2 odd 2 225.2.q.a.106.28 yes 224
9.4 even 3 inner 675.2.r.a.631.28 224
9.5 odd 6 225.2.q.a.31.1 224
25.21 even 5 inner 675.2.r.a.46.28 224
75.71 odd 10 225.2.q.a.196.1 yes 224
225.121 even 15 inner 675.2.r.a.496.1 224
225.221 odd 30 225.2.q.a.121.28 yes 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.q.a.31.1 224 9.5 odd 6
225.2.q.a.106.28 yes 224 3.2 odd 2
225.2.q.a.121.28 yes 224 225.221 odd 30
225.2.q.a.196.1 yes 224 75.71 odd 10
675.2.r.a.46.28 224 25.21 even 5 inner
675.2.r.a.181.1 224 1.1 even 1 trivial
675.2.r.a.496.1 224 225.121 even 15 inner
675.2.r.a.631.28 224 9.4 even 3 inner