Properties

Label 637.2.k.i.569.6
Level $637$
Weight $2$
Character 637.569
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
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] = [637,2,Mod(459,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.459");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.k (of order \(6\), degree \(2\), 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 569.6
Root \(1.32725 + 0.488273i\) of defining polynomial
Character \(\chi\) \(=\) 637.569
Dual form 637.2.k.i.459.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.58860i q^{2} +(0.259233 - 0.449005i) q^{3} -4.70085 q^{4} +(1.39608 + 0.806027i) q^{5} +(1.16229 + 0.671051i) q^{6} -6.99143i q^{8} +(1.36560 + 2.36528i) q^{9} +O(q^{10})\) \(q+2.58860i q^{2} +(0.259233 - 0.449005i) q^{3} -4.70085 q^{4} +(1.39608 + 0.806027i) q^{5} +(1.16229 + 0.671051i) q^{6} -6.99143i q^{8} +(1.36560 + 2.36528i) q^{9} +(-2.08648 + 3.61389i) q^{10} +(2.34256 + 1.35248i) q^{11} +(-1.21862 + 2.11070i) q^{12} +(-2.36840 + 2.71858i) q^{13} +(0.723819 - 0.417897i) q^{15} +8.69632 q^{16} +3.12661 q^{17} +(-6.12277 + 3.53498i) q^{18} +(-3.18828 + 1.84075i) q^{19} +(-6.56276 - 3.78901i) q^{20} +(-3.50103 + 6.06396i) q^{22} -1.98604 q^{23} +(-3.13918 - 1.81241i) q^{24} +(-1.20064 - 2.07957i) q^{25} +(-7.03732 - 6.13084i) q^{26} +2.97143 q^{27} +(2.68636 + 4.65290i) q^{29} +(1.08177 + 1.87368i) q^{30} +(-9.07425 + 5.23902i) q^{31} +8.52843i q^{32} +(1.21454 - 0.701214i) q^{33} +8.09354i q^{34} +(-6.41947 - 11.1188i) q^{36} -5.95346i q^{37} +(-4.76497 - 8.25317i) q^{38} +(0.606687 + 1.76817i) q^{39} +(5.63528 - 9.76059i) q^{40} +(6.66970 - 3.85075i) q^{41} +(-1.67800 + 2.90638i) q^{43} +(-11.0120 - 6.35780i) q^{44} +4.40283i q^{45} -5.14106i q^{46} +(-0.913730 - 0.527542i) q^{47} +(2.25437 - 3.90469i) q^{48} +(5.38318 - 3.10798i) q^{50} +(0.810520 - 1.40386i) q^{51} +(11.1335 - 12.7796i) q^{52} +(-3.63284 - 6.29226i) q^{53} +7.69184i q^{54} +(2.18027 + 3.77633i) q^{55} +1.90873i q^{57} +(-12.0445 + 6.95390i) q^{58} +11.4241i q^{59} +(-3.40257 + 1.96447i) q^{60} +(-1.46254 - 2.53319i) q^{61} +(-13.5617 - 23.4896i) q^{62} -4.68406 q^{64} +(-5.49772 + 1.88636i) q^{65} +(1.81516 + 3.14395i) q^{66} +(11.7622 + 6.79091i) q^{67} -14.6977 q^{68} +(-0.514846 + 0.891740i) q^{69} +(1.17009 + 0.675554i) q^{71} +(16.5367 - 9.54747i) q^{72} +(7.88374 - 4.55168i) q^{73} +15.4111 q^{74} -1.24498 q^{75} +(14.9876 - 8.65311i) q^{76} +(-4.57708 + 1.57047i) q^{78} +(3.10289 - 5.37436i) q^{79} +(12.1407 + 7.00946i) q^{80} +(-3.32650 + 5.76166i) q^{81} +(9.96806 + 17.2652i) q^{82} +2.69672i q^{83} +(4.36499 + 2.52013i) q^{85} +(-7.52346 - 4.34367i) q^{86} +2.78557 q^{87} +(9.45576 - 16.3779i) q^{88} +1.75988i q^{89} -11.3972 q^{90} +9.33607 q^{92} +5.43251i q^{93} +(1.36560 - 2.36528i) q^{94} -5.93478 q^{95} +(3.82930 + 2.21085i) q^{96} +(13.4078 + 7.74102i) q^{97} +7.38776i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{3} - 8 q^{4} + 3 q^{5} + 9 q^{6} - q^{9} - 12 q^{10} + 12 q^{11} + q^{12} + 2 q^{13} - 12 q^{15} + 16 q^{16} + 34 q^{17} + 3 q^{18} - 9 q^{19} + 3 q^{20} - 15 q^{22} - 6 q^{23} - 15 q^{24} - 5 q^{25} + 6 q^{26} - 12 q^{27} - q^{29} + 11 q^{30} - 18 q^{31} + 6 q^{33} - 13 q^{36} - 19 q^{38} - 4 q^{39} + q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} + 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} + 7 q^{52} - 8 q^{53} + 15 q^{55} - 24 q^{58} - 30 q^{60} - 5 q^{61} - 41 q^{62} + 2 q^{64} + 21 q^{65} + 34 q^{66} + 15 q^{67} - 22 q^{68} - 7 q^{69} + 30 q^{71} + 57 q^{72} - 42 q^{73} + 66 q^{74} + 2 q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} + 63 q^{80} + 14 q^{81} - 5 q^{82} - 21 q^{85} - 57 q^{86} + 20 q^{87} - 14 q^{88} - 66 q^{92} - q^{94} - 4 q^{95} - 21 q^{96} + 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58860i 1.83042i 0.402981 + 0.915209i \(0.367974\pi\)
−0.402981 + 0.915209i \(0.632026\pi\)
\(3\) 0.259233 0.449005i 0.149668 0.259233i −0.781437 0.623985i \(-0.785513\pi\)
0.931105 + 0.364752i \(0.118846\pi\)
\(4\) −4.70085 −2.35043
\(5\) 1.39608 + 0.806027i 0.624346 + 0.360466i 0.778559 0.627571i \(-0.215951\pi\)
−0.154213 + 0.988038i \(0.549284\pi\)
\(6\) 1.16229 + 0.671051i 0.474504 + 0.273955i
\(7\) 0 0
\(8\) 6.99143i 2.47184i
\(9\) 1.36560 + 2.36528i 0.455199 + 0.788428i
\(10\) −2.08648 + 3.61389i −0.659803 + 1.14281i
\(11\) 2.34256 + 1.35248i 0.706309 + 0.407788i 0.809693 0.586854i \(-0.199634\pi\)
−0.103384 + 0.994642i \(0.532967\pi\)
\(12\) −1.21862 + 2.11070i −0.351784 + 0.609308i
\(13\) −2.36840 + 2.71858i −0.656876 + 0.753998i
\(14\) 0 0
\(15\) 0.723819 0.417897i 0.186889 0.107901i
\(16\) 8.69632 2.17408
\(17\) 3.12661 0.758314 0.379157 0.925332i \(-0.376214\pi\)
0.379157 + 0.925332i \(0.376214\pi\)
\(18\) −6.12277 + 3.53498i −1.44315 + 0.833204i
\(19\) −3.18828 + 1.84075i −0.731441 + 0.422297i −0.818949 0.573866i \(-0.805443\pi\)
0.0875083 + 0.996164i \(0.472110\pi\)
\(20\) −6.56276 3.78901i −1.46748 0.847249i
\(21\) 0 0
\(22\) −3.50103 + 6.06396i −0.746421 + 1.29284i
\(23\) −1.98604 −0.414117 −0.207059 0.978329i \(-0.566389\pi\)
−0.207059 + 0.978329i \(0.566389\pi\)
\(24\) −3.13918 1.81241i −0.640783 0.369956i
\(25\) −1.20064 2.07957i −0.240128 0.415914i
\(26\) −7.03732 6.13084i −1.38013 1.20236i
\(27\) 2.97143 0.571852
\(28\) 0 0
\(29\) 2.68636 + 4.65290i 0.498844 + 0.864023i 0.999999 0.00133469i \(-0.000424845\pi\)
−0.501155 + 0.865357i \(0.667092\pi\)
\(30\) 1.08177 + 1.87368i 0.197503 + 0.342086i
\(31\) −9.07425 + 5.23902i −1.62978 + 0.940956i −0.645627 + 0.763653i \(0.723404\pi\)
−0.984156 + 0.177303i \(0.943263\pi\)
\(32\) 8.52843i 1.50763i
\(33\) 1.21454 0.701214i 0.211424 0.122066i
\(34\) 8.09354i 1.38803i
\(35\) 0 0
\(36\) −6.41947 11.1188i −1.06991 1.85314i
\(37\) 5.95346i 0.978743i −0.872075 0.489371i \(-0.837226\pi\)
0.872075 0.489371i \(-0.162774\pi\)
\(38\) −4.76497 8.25317i −0.772981 1.33884i
\(39\) 0.606687 + 1.76817i 0.0971477 + 0.283134i
\(40\) 5.63528 9.76059i 0.891016 1.54329i
\(41\) 6.66970 3.85075i 1.04163 0.601386i 0.121337 0.992611i \(-0.461282\pi\)
0.920295 + 0.391225i \(0.127949\pi\)
\(42\) 0 0
\(43\) −1.67800 + 2.90638i −0.255892 + 0.443219i −0.965138 0.261743i \(-0.915703\pi\)
0.709245 + 0.704962i \(0.249036\pi\)
\(44\) −11.0120 6.35780i −1.66013 0.958475i
\(45\) 4.40283i 0.656335i
\(46\) 5.14106i 0.758008i
\(47\) −0.913730 0.527542i −0.133281 0.0769500i 0.431877 0.901933i \(-0.357852\pi\)
−0.565158 + 0.824983i \(0.691185\pi\)
\(48\) 2.25437 3.90469i 0.325390 0.563593i
\(49\) 0 0
\(50\) 5.38318 3.10798i 0.761297 0.439535i
\(51\) 0.810520 1.40386i 0.113495 0.196580i
\(52\) 11.1335 12.7796i 1.54394 1.77222i
\(53\) −3.63284 6.29226i −0.499009 0.864308i 0.500991 0.865453i \(-0.332969\pi\)
−0.999999 + 0.00114437i \(0.999636\pi\)
\(54\) 7.69184i 1.04673i
\(55\) 2.18027 + 3.77633i 0.293987 + 0.509201i
\(56\) 0 0
\(57\) 1.90873i 0.252818i
\(58\) −12.0445 + 6.95390i −1.58152 + 0.913092i
\(59\) 11.4241i 1.48729i 0.668577 + 0.743643i \(0.266904\pi\)
−0.668577 + 0.743643i \(0.733096\pi\)
\(60\) −3.40257 + 1.96447i −0.439270 + 0.253613i
\(61\) −1.46254 2.53319i −0.187259 0.324341i 0.757077 0.653326i \(-0.226627\pi\)
−0.944335 + 0.328985i \(0.893294\pi\)
\(62\) −13.5617 23.4896i −1.72234 2.98318i
\(63\) 0 0
\(64\) −4.68406 −0.585507
\(65\) −5.49772 + 1.88636i −0.681909 + 0.233974i
\(66\) 1.81516 + 3.14395i 0.223431 + 0.386994i
\(67\) 11.7622 + 6.79091i 1.43698 + 0.829642i 0.997639 0.0686778i \(-0.0218780\pi\)
0.439343 + 0.898320i \(0.355211\pi\)
\(68\) −14.6977 −1.78236
\(69\) −0.514846 + 0.891740i −0.0619802 + 0.107353i
\(70\) 0 0
\(71\) 1.17009 + 0.675554i 0.138865 + 0.0801736i 0.567823 0.823151i \(-0.307786\pi\)
−0.428958 + 0.903324i \(0.641119\pi\)
\(72\) 16.5367 9.54747i 1.94887 1.12518i
\(73\) 7.88374 4.55168i 0.922721 0.532733i 0.0382192 0.999269i \(-0.487831\pi\)
0.884502 + 0.466536i \(0.154498\pi\)
\(74\) 15.4111 1.79151
\(75\) −1.24498 −0.143758
\(76\) 14.9876 8.65311i 1.71920 0.992579i
\(77\) 0 0
\(78\) −4.57708 + 1.57047i −0.518252 + 0.177821i
\(79\) 3.10289 5.37436i 0.349102 0.604663i −0.636988 0.770874i \(-0.719820\pi\)
0.986090 + 0.166211i \(0.0531532\pi\)
\(80\) 12.1407 + 7.00946i 1.35738 + 0.783682i
\(81\) −3.32650 + 5.76166i −0.369611 + 0.640185i
\(82\) 9.96806 + 17.2652i 1.10079 + 1.90662i
\(83\) 2.69672i 0.296003i 0.988987 + 0.148002i \(0.0472841\pi\)
−0.988987 + 0.148002i \(0.952716\pi\)
\(84\) 0 0
\(85\) 4.36499 + 2.52013i 0.473450 + 0.273346i
\(86\) −7.52346 4.34367i −0.811275 0.468390i
\(87\) 2.78557 0.298644
\(88\) 9.45576 16.3779i 1.00799 1.74589i
\(89\) 1.75988i 0.186546i 0.995641 + 0.0932732i \(0.0297330\pi\)
−0.995641 + 0.0932732i \(0.970267\pi\)
\(90\) −11.3972 −1.20137
\(91\) 0 0
\(92\) 9.33607 0.973353
\(93\) 5.43251i 0.563325i
\(94\) 1.36560 2.36528i 0.140851 0.243960i
\(95\) −5.93478 −0.608896
\(96\) 3.82930 + 2.21085i 0.390827 + 0.225644i
\(97\) 13.4078 + 7.74102i 1.36136 + 0.785981i 0.989805 0.142430i \(-0.0454915\pi\)
0.371555 + 0.928411i \(0.378825\pi\)
\(98\) 0 0
\(99\) 7.38776i 0.742498i
\(100\) 5.64404 + 9.77576i 0.564404 + 0.977576i
\(101\) 0.639651 1.10791i 0.0636477 0.110241i −0.832446 0.554107i \(-0.813060\pi\)
0.896093 + 0.443866i \(0.146393\pi\)
\(102\) 3.63404 + 2.09811i 0.359823 + 0.207744i
\(103\) 5.73367 9.93101i 0.564956 0.978532i −0.432098 0.901827i \(-0.642227\pi\)
0.997054 0.0767054i \(-0.0244401\pi\)
\(104\) 19.0068 + 16.5585i 1.86377 + 1.62370i
\(105\) 0 0
\(106\) 16.2881 9.40397i 1.58204 0.913394i
\(107\) −5.13525 −0.496444 −0.248222 0.968703i \(-0.579846\pi\)
−0.248222 + 0.968703i \(0.579846\pi\)
\(108\) −13.9682 −1.34410
\(109\) 1.49635 0.863916i 0.143324 0.0827481i −0.426623 0.904429i \(-0.640297\pi\)
0.569947 + 0.821681i \(0.306964\pi\)
\(110\) −9.77542 + 5.64384i −0.932050 + 0.538119i
\(111\) −2.67313 1.54333i −0.253722 0.146487i
\(112\) 0 0
\(113\) 4.29556 7.44014i 0.404093 0.699909i −0.590123 0.807314i \(-0.700921\pi\)
0.994215 + 0.107404i \(0.0342540\pi\)
\(114\) −4.94095 −0.462762
\(115\) −2.77267 1.60080i −0.258552 0.149275i
\(116\) −12.6282 21.8726i −1.17250 2.03082i
\(117\) −9.66449 1.88945i −0.893482 0.174680i
\(118\) −29.5723 −2.72235
\(119\) 0 0
\(120\) −2.92170 5.06053i −0.266714 0.461961i
\(121\) −1.84160 3.18975i −0.167419 0.289977i
\(122\) 6.55741 3.78592i 0.593680 0.342761i
\(123\) 3.99297i 0.360034i
\(124\) 42.6567 24.6279i 3.83069 2.21165i
\(125\) 11.9313i 1.06716i
\(126\) 0 0
\(127\) −1.56206 2.70556i −0.138610 0.240080i 0.788361 0.615214i \(-0.210930\pi\)
−0.926971 + 0.375133i \(0.877597\pi\)
\(128\) 4.93170i 0.435904i
\(129\) 0.869985 + 1.50686i 0.0765979 + 0.132671i
\(130\) −4.88303 14.2314i −0.428270 1.24818i
\(131\) 5.10460 8.84142i 0.445991 0.772479i −0.552130 0.833758i \(-0.686185\pi\)
0.998121 + 0.0612793i \(0.0195180\pi\)
\(132\) −5.70937 + 3.29630i −0.496936 + 0.286906i
\(133\) 0 0
\(134\) −17.5790 + 30.4476i −1.51859 + 2.63028i
\(135\) 4.14835 + 2.39505i 0.357033 + 0.206133i
\(136\) 21.8595i 1.87443i
\(137\) 9.99261i 0.853726i 0.904316 + 0.426863i \(0.140381\pi\)
−0.904316 + 0.426863i \(0.859619\pi\)
\(138\) −2.30836 1.33273i −0.196501 0.113450i
\(139\) −0.832100 + 1.44124i −0.0705778 + 0.122244i −0.899155 0.437631i \(-0.855818\pi\)
0.828577 + 0.559875i \(0.189151\pi\)
\(140\) 0 0
\(141\) −0.473738 + 0.273513i −0.0398959 + 0.0230339i
\(142\) −1.74874 + 3.02891i −0.146751 + 0.254180i
\(143\) −9.22495 + 3.16523i −0.771429 + 0.264690i
\(144\) 11.8757 + 20.5692i 0.989638 + 1.71410i
\(145\) 8.66110i 0.719265i
\(146\) 11.7825 + 20.4078i 0.975124 + 1.68897i
\(147\) 0 0
\(148\) 27.9863i 2.30046i
\(149\) 17.1456 9.89902i 1.40462 0.810959i 0.409760 0.912193i \(-0.365613\pi\)
0.994863 + 0.101234i \(0.0322792\pi\)
\(150\) 3.22276i 0.263138i
\(151\) −6.52544 + 3.76746i −0.531033 + 0.306592i −0.741437 0.671023i \(-0.765855\pi\)
0.210404 + 0.977614i \(0.432522\pi\)
\(152\) 12.8695 + 22.2906i 1.04385 + 1.80801i
\(153\) 4.26968 + 7.39531i 0.345183 + 0.597875i
\(154\) 0 0
\(155\) −16.8912 −1.35673
\(156\) −2.85195 8.31190i −0.228339 0.665485i
\(157\) 7.00223 + 12.1282i 0.558839 + 0.967938i 0.997594 + 0.0693309i \(0.0220864\pi\)
−0.438755 + 0.898607i \(0.644580\pi\)
\(158\) 13.9121 + 8.03214i 1.10679 + 0.639003i
\(159\) −3.76700 −0.298743
\(160\) −6.87414 + 11.9064i −0.543448 + 0.941280i
\(161\) 0 0
\(162\) −14.9146 8.61097i −1.17181 0.676542i
\(163\) 6.20936 3.58498i 0.486355 0.280797i −0.236706 0.971581i \(-0.576068\pi\)
0.723061 + 0.690784i \(0.242735\pi\)
\(164\) −31.3533 + 18.1018i −2.44828 + 1.41351i
\(165\) 2.26079 0.176002
\(166\) −6.98072 −0.541809
\(167\) −15.5716 + 8.99027i −1.20497 + 0.695688i −0.961656 0.274260i \(-0.911567\pi\)
−0.243312 + 0.969948i \(0.578234\pi\)
\(168\) 0 0
\(169\) −1.78135 12.8774i −0.137027 0.990567i
\(170\) −6.52361 + 11.2992i −0.500338 + 0.866611i
\(171\) −8.70780 5.02745i −0.665902 0.384459i
\(172\) 7.88803 13.6625i 0.601456 1.04175i
\(173\) 6.40579 + 11.0952i 0.487023 + 0.843549i 0.999889 0.0149198i \(-0.00474930\pi\)
−0.512865 + 0.858469i \(0.671416\pi\)
\(174\) 7.21072i 0.546643i
\(175\) 0 0
\(176\) 20.3717 + 11.7616i 1.53557 + 0.886562i
\(177\) 5.12945 + 2.96149i 0.385553 + 0.222599i
\(178\) −4.55561 −0.341458
\(179\) 0.920110 1.59368i 0.0687723 0.119117i −0.829589 0.558375i \(-0.811425\pi\)
0.898361 + 0.439258i \(0.144758\pi\)
\(180\) 20.6971i 1.54267i
\(181\) 3.29928 0.245234 0.122617 0.992454i \(-0.460871\pi\)
0.122617 + 0.992454i \(0.460871\pi\)
\(182\) 0 0
\(183\) −1.51655 −0.112107
\(184\) 13.8852i 1.02363i
\(185\) 4.79865 8.31150i 0.352804 0.611074i
\(186\) −14.0626 −1.03112
\(187\) 7.32427 + 4.22867i 0.535604 + 0.309231i
\(188\) 4.29531 + 2.47990i 0.313268 + 0.180865i
\(189\) 0 0
\(190\) 15.3628i 1.11453i
\(191\) −2.44807 4.24018i −0.177136 0.306809i 0.763762 0.645498i \(-0.223350\pi\)
−0.940898 + 0.338689i \(0.890017\pi\)
\(192\) −1.21426 + 2.10316i −0.0876318 + 0.151783i
\(193\) 2.61462 + 1.50955i 0.188204 + 0.108660i 0.591142 0.806568i \(-0.298677\pi\)
−0.402937 + 0.915228i \(0.632011\pi\)
\(194\) −20.0384 + 34.7075i −1.43867 + 2.49186i
\(195\) −0.578207 + 2.95751i −0.0414063 + 0.211792i
\(196\) 0 0
\(197\) 4.02694 2.32496i 0.286908 0.165646i −0.349639 0.936885i \(-0.613696\pi\)
0.636546 + 0.771238i \(0.280362\pi\)
\(198\) −19.1240 −1.35908
\(199\) 0.410721 0.0291152 0.0145576 0.999894i \(-0.495366\pi\)
0.0145576 + 0.999894i \(0.495366\pi\)
\(200\) −14.5392 + 8.39420i −1.02808 + 0.593560i
\(201\) 6.09830 3.52085i 0.430141 0.248342i
\(202\) 2.86793 + 1.65580i 0.201787 + 0.116502i
\(203\) 0 0
\(204\) −3.81013 + 6.59934i −0.266763 + 0.462047i
\(205\) 12.4152 0.867118
\(206\) 25.7074 + 14.8422i 1.79112 + 1.03410i
\(207\) −2.71213 4.69754i −0.188506 0.326502i
\(208\) −20.5964 + 23.6416i −1.42810 + 1.63925i
\(209\) −9.95831 −0.688831
\(210\) 0 0
\(211\) 3.75800 + 6.50905i 0.258711 + 0.448101i 0.965897 0.258927i \(-0.0833688\pi\)
−0.707186 + 0.707028i \(0.750035\pi\)
\(212\) 17.0774 + 29.5790i 1.17288 + 2.03149i
\(213\) 0.606654 0.350252i 0.0415672 0.0239989i
\(214\) 13.2931i 0.908699i
\(215\) −4.68524 + 2.70502i −0.319531 + 0.184481i
\(216\) 20.7745i 1.41353i
\(217\) 0 0
\(218\) 2.23633 + 3.87344i 0.151464 + 0.262343i
\(219\) 4.71978i 0.318933i
\(220\) −10.2491 17.7520i −0.690996 1.19684i
\(221\) −7.40506 + 8.49993i −0.498118 + 0.571767i
\(222\) 3.99507 6.91967i 0.268132 0.464418i
\(223\) 19.5544 11.2897i 1.30946 0.756016i 0.327452 0.944868i \(-0.393810\pi\)
0.982006 + 0.188852i \(0.0604766\pi\)
\(224\) 0 0
\(225\) 3.27918 5.67971i 0.218612 0.378648i
\(226\) 19.2595 + 11.1195i 1.28113 + 0.739658i
\(227\) 13.6717i 0.907424i −0.891148 0.453712i \(-0.850099\pi\)
0.891148 0.453712i \(-0.149901\pi\)
\(228\) 8.97268i 0.594230i
\(229\) −6.86832 3.96543i −0.453872 0.262043i 0.255592 0.966785i \(-0.417730\pi\)
−0.709464 + 0.704742i \(0.751063\pi\)
\(230\) 4.14383 7.17733i 0.273236 0.473259i
\(231\) 0 0
\(232\) 32.5305 18.7815i 2.13573 1.23306i
\(233\) −3.28585 + 5.69127i −0.215263 + 0.372847i −0.953354 0.301854i \(-0.902394\pi\)
0.738091 + 0.674702i \(0.235728\pi\)
\(234\) 4.89104 25.0175i 0.319738 1.63545i
\(235\) −0.850427 1.47298i −0.0554757 0.0960868i
\(236\) 53.7028i 3.49576i
\(237\) −1.60874 2.78642i −0.104499 0.180998i
\(238\) 0 0
\(239\) 9.39284i 0.607572i −0.952740 0.303786i \(-0.901749\pi\)
0.952740 0.303786i \(-0.0982508\pi\)
\(240\) 6.29456 3.63417i 0.406312 0.234584i
\(241\) 10.0858i 0.649686i −0.945768 0.324843i \(-0.894689\pi\)
0.945768 0.324843i \(-0.105311\pi\)
\(242\) 8.25699 4.76718i 0.530780 0.306446i
\(243\) 6.18182 + 10.7072i 0.396564 + 0.686869i
\(244\) 6.87517 + 11.9081i 0.440137 + 0.762340i
\(245\) 0 0
\(246\) 10.3362 0.659012
\(247\) 2.54689 13.0272i 0.162054 0.828902i
\(248\) 36.6282 + 63.4420i 2.32590 + 4.02857i
\(249\) 1.21084 + 0.699078i 0.0767337 + 0.0443022i
\(250\) 30.8853 1.95336
\(251\) 5.17427 8.96209i 0.326597 0.565682i −0.655237 0.755423i \(-0.727431\pi\)
0.981834 + 0.189741i \(0.0607648\pi\)
\(252\) 0 0
\(253\) −4.65242 2.68607i −0.292495 0.168872i
\(254\) 7.00363 4.04355i 0.439447 0.253715i
\(255\) 2.26310 1.30660i 0.141721 0.0818225i
\(256\) −22.1343 −1.38339
\(257\) 7.98658 0.498189 0.249095 0.968479i \(-0.419867\pi\)
0.249095 + 0.968479i \(0.419867\pi\)
\(258\) −3.90065 + 2.25204i −0.242844 + 0.140206i
\(259\) 0 0
\(260\) 25.8440 8.86749i 1.60278 0.549939i
\(261\) −7.33696 + 12.7080i −0.454146 + 0.786604i
\(262\) 22.8869 + 13.2138i 1.41396 + 0.816349i
\(263\) −2.52967 + 4.38152i −0.155986 + 0.270176i −0.933418 0.358792i \(-0.883189\pi\)
0.777431 + 0.628968i \(0.216522\pi\)
\(264\) −4.90249 8.49136i −0.301727 0.522607i
\(265\) 11.7127i 0.719503i
\(266\) 0 0
\(267\) 0.790192 + 0.456218i 0.0483590 + 0.0279201i
\(268\) −55.2924 31.9231i −3.37752 1.95001i
\(269\) −13.8902 −0.846902 −0.423451 0.905919i \(-0.639181\pi\)
−0.423451 + 0.905919i \(0.639181\pi\)
\(270\) −6.19983 + 10.7384i −0.377310 + 0.653519i
\(271\) 8.32721i 0.505842i −0.967487 0.252921i \(-0.918609\pi\)
0.967487 0.252921i \(-0.0813913\pi\)
\(272\) 27.1900 1.64863
\(273\) 0 0
\(274\) −25.8669 −1.56267
\(275\) 6.49537i 0.391685i
\(276\) 2.42022 4.19194i 0.145680 0.252325i
\(277\) 23.2116 1.39465 0.697325 0.716755i \(-0.254374\pi\)
0.697325 + 0.716755i \(0.254374\pi\)
\(278\) −3.73080 2.15398i −0.223758 0.129187i
\(279\) −24.7835 14.3088i −1.48375 0.856644i
\(280\) 0 0
\(281\) 27.1595i 1.62020i −0.586292 0.810100i \(-0.699413\pi\)
0.586292 0.810100i \(-0.300587\pi\)
\(282\) −0.708015 1.22632i −0.0421617 0.0730262i
\(283\) 8.07563 13.9874i 0.480046 0.831464i −0.519692 0.854354i \(-0.673953\pi\)
0.999738 + 0.0228894i \(0.00728654\pi\)
\(284\) −5.50044 3.17568i −0.326391 0.188442i
\(285\) −1.53849 + 2.66474i −0.0911323 + 0.157846i
\(286\) −8.19351 23.8797i −0.484493 1.41204i
\(287\) 0 0
\(288\) −20.1721 + 11.6464i −1.18865 + 0.686270i
\(289\) −7.22433 −0.424960
\(290\) −22.4201 −1.31656
\(291\) 6.95151 4.01345i 0.407504 0.235273i
\(292\) −37.0603 + 21.3968i −2.16879 + 1.25215i
\(293\) 12.6831 + 7.32260i 0.740956 + 0.427791i 0.822417 0.568885i \(-0.192625\pi\)
−0.0814609 + 0.996677i \(0.525959\pi\)
\(294\) 0 0
\(295\) −9.20810 + 15.9489i −0.536116 + 0.928580i
\(296\) −41.6232 −2.41930
\(297\) 6.96075 + 4.01879i 0.403904 + 0.233194i
\(298\) 25.6246 + 44.3831i 1.48439 + 2.57104i
\(299\) 4.70373 5.39920i 0.272024 0.312244i
\(300\) 5.85248 0.337893
\(301\) 0 0
\(302\) −9.75246 16.8918i −0.561191 0.972011i
\(303\) −0.331637 0.574412i −0.0190521 0.0329991i
\(304\) −27.7263 + 16.0078i −1.59021 + 0.918108i
\(305\) 4.71537i 0.270001i
\(306\) −19.1435 + 11.0525i −1.09436 + 0.631830i
\(307\) 8.97844i 0.512427i −0.966620 0.256213i \(-0.917525\pi\)
0.966620 0.256213i \(-0.0824750\pi\)
\(308\) 0 0
\(309\) −2.97271 5.14889i −0.169112 0.292910i
\(310\) 43.7245i 2.48338i
\(311\) −6.09080 10.5496i −0.345378 0.598212i 0.640045 0.768338i \(-0.278916\pi\)
−0.985422 + 0.170126i \(0.945583\pi\)
\(312\) 12.3620 4.24161i 0.699862 0.240134i
\(313\) 6.56198 11.3657i 0.370905 0.642427i −0.618800 0.785549i \(-0.712381\pi\)
0.989705 + 0.143122i \(0.0457141\pi\)
\(314\) −31.3951 + 18.1260i −1.77173 + 1.02291i
\(315\) 0 0
\(316\) −14.5862 + 25.2641i −0.820540 + 1.42122i
\(317\) 14.4761 + 8.35775i 0.813056 + 0.469418i 0.848016 0.529971i \(-0.177797\pi\)
−0.0349599 + 0.999389i \(0.511130\pi\)
\(318\) 9.75127i 0.546824i
\(319\) 14.5330i 0.813689i
\(320\) −6.53932 3.77548i −0.365559 0.211056i
\(321\) −1.33123 + 2.30575i −0.0743018 + 0.128695i
\(322\) 0 0
\(323\) −9.96849 + 5.75531i −0.554661 + 0.320234i
\(324\) 15.6374 27.0847i 0.868743 1.50471i
\(325\) 8.49708 + 1.66122i 0.471333 + 0.0921480i
\(326\) 9.28007 + 16.0736i 0.513976 + 0.890232i
\(327\) 0.895821i 0.0495390i
\(328\) −26.9223 46.6307i −1.48653 2.57475i
\(329\) 0 0
\(330\) 5.85228i 0.322157i
\(331\) −3.43522 + 1.98332i −0.188817 + 0.109013i −0.591428 0.806357i \(-0.701436\pi\)
0.402612 + 0.915371i \(0.368102\pi\)
\(332\) 12.6769i 0.695733i
\(333\) 14.0816 8.13002i 0.771668 0.445523i
\(334\) −23.2722 40.3087i −1.27340 2.20559i
\(335\) 10.9473 + 18.9613i 0.598116 + 1.03597i
\(336\) 0 0
\(337\) −13.7032 −0.746461 −0.373230 0.927739i \(-0.621750\pi\)
−0.373230 + 0.927739i \(0.621750\pi\)
\(338\) 33.3344 4.61121i 1.81315 0.250817i
\(339\) −2.22710 3.85746i −0.120960 0.209508i
\(340\) −20.5192 11.8468i −1.11281 0.642481i
\(341\) −28.3426 −1.53484
\(342\) 13.0141 22.5410i 0.703720 1.21888i
\(343\) 0 0
\(344\) 20.3197 + 11.7316i 1.09557 + 0.632526i
\(345\) −1.43753 + 0.829960i −0.0773942 + 0.0446835i
\(346\) −28.7209 + 16.5820i −1.54405 + 0.891456i
\(347\) −26.3979 −1.41711 −0.708556 0.705655i \(-0.750653\pi\)
−0.708556 + 0.705655i \(0.750653\pi\)
\(348\) −13.0945 −0.701941
\(349\) 4.23507 2.44512i 0.226698 0.130884i −0.382350 0.924018i \(-0.624885\pi\)
0.609048 + 0.793133i \(0.291552\pi\)
\(350\) 0 0
\(351\) −7.03753 + 8.07806i −0.375636 + 0.431175i
\(352\) −11.5345 + 19.9784i −0.614792 + 1.06485i
\(353\) 11.7413 + 6.77886i 0.624928 + 0.360802i 0.778785 0.627291i \(-0.215836\pi\)
−0.153857 + 0.988093i \(0.549170\pi\)
\(354\) −7.66612 + 13.2781i −0.407450 + 0.705724i
\(355\) 1.08903 + 1.88626i 0.0577997 + 0.100112i
\(356\) 8.27291i 0.438464i
\(357\) 0 0
\(358\) 4.12540 + 2.38180i 0.218034 + 0.125882i
\(359\) 7.43541 + 4.29284i 0.392426 + 0.226567i 0.683211 0.730221i \(-0.260583\pi\)
−0.290785 + 0.956789i \(0.593916\pi\)
\(360\) 30.7821 1.62236
\(361\) −2.72326 + 4.71683i −0.143330 + 0.248254i
\(362\) 8.54053i 0.448880i
\(363\) −1.90962 −0.100229
\(364\) 0 0
\(365\) 14.6751 0.768130
\(366\) 3.92574i 0.205202i
\(367\) −0.831612 + 1.44039i −0.0434098 + 0.0751880i −0.886914 0.461935i \(-0.847155\pi\)
0.843504 + 0.537123i \(0.180489\pi\)
\(368\) −17.2712 −0.900324
\(369\) 18.2162 + 10.5171i 0.948299 + 0.547501i
\(370\) 21.5152 + 12.4218i 1.11852 + 0.645778i
\(371\) 0 0
\(372\) 25.5374i 1.32405i
\(373\) −6.98174 12.0927i −0.361501 0.626138i 0.626707 0.779255i \(-0.284402\pi\)
−0.988208 + 0.153117i \(0.951069\pi\)
\(374\) −10.9463 + 18.9596i −0.566022 + 0.980378i
\(375\) −5.35719 3.09298i −0.276644 0.159721i
\(376\) −3.68828 + 6.38828i −0.190208 + 0.329450i
\(377\) −19.0117 3.71687i −0.979150 0.191429i
\(378\) 0 0
\(379\) −27.3454 + 15.7879i −1.40464 + 0.810969i −0.994864 0.101218i \(-0.967726\pi\)
−0.409775 + 0.912187i \(0.634393\pi\)
\(380\) 27.8985 1.43116
\(381\) −1.61975 −0.0829822
\(382\) 10.9761 6.33707i 0.561588 0.324233i
\(383\) 27.6333 15.9541i 1.41200 0.815217i 0.416420 0.909172i \(-0.363284\pi\)
0.995576 + 0.0939554i \(0.0299511\pi\)
\(384\) 2.21435 + 1.27846i 0.113001 + 0.0652410i
\(385\) 0 0
\(386\) −3.90762 + 6.76820i −0.198893 + 0.344492i
\(387\) −9.16588 −0.465928
\(388\) −63.0283 36.3894i −3.19978 1.84739i
\(389\) −12.7075 22.0100i −0.644296 1.11595i −0.984464 0.175589i \(-0.943817\pi\)
0.340168 0.940365i \(-0.389516\pi\)
\(390\) −7.65581 1.49675i −0.387667 0.0757908i
\(391\) −6.20956 −0.314031
\(392\) 0 0
\(393\) −2.64656 4.58398i −0.133501 0.231231i
\(394\) 6.01838 + 10.4241i 0.303202 + 0.525161i
\(395\) 8.66376 5.00203i 0.435921 0.251679i
\(396\) 34.7288i 1.74519i
\(397\) 3.60178 2.07949i 0.180768 0.104366i −0.406885 0.913479i \(-0.633385\pi\)
0.587653 + 0.809113i \(0.300052\pi\)
\(398\) 1.06319i 0.0532930i
\(399\) 0 0
\(400\) −10.4412 18.0846i −0.522058 0.904231i
\(401\) 19.6013i 0.978844i 0.872047 + 0.489422i \(0.162792\pi\)
−0.872047 + 0.489422i \(0.837208\pi\)
\(402\) 9.11409 + 15.7861i 0.454569 + 0.787337i
\(403\) 7.24877 37.0772i 0.361087 1.84695i
\(404\) −3.00691 + 5.20811i −0.149599 + 0.259113i
\(405\) −9.28811 + 5.36249i −0.461530 + 0.266464i
\(406\) 0 0
\(407\) 8.05193 13.9463i 0.399119 0.691295i
\(408\) −9.81500 5.66669i −0.485915 0.280543i
\(409\) 17.6337i 0.871930i 0.899964 + 0.435965i \(0.143593\pi\)
−0.899964 + 0.435965i \(0.856407\pi\)
\(410\) 32.1381i 1.58719i
\(411\) 4.48673 + 2.59041i 0.221314 + 0.127776i
\(412\) −26.9532 + 46.6842i −1.32789 + 2.29997i
\(413\) 0 0
\(414\) 12.1601 7.02061i 0.597634 0.345044i
\(415\) −2.17363 + 3.76483i −0.106699 + 0.184808i
\(416\) −23.1852 20.1987i −1.13675 0.990324i
\(417\) 0.431416 + 0.747234i 0.0211265 + 0.0365922i
\(418\) 25.7781i 1.26085i
\(419\) 14.9455 + 25.8864i 0.730137 + 1.26463i 0.956824 + 0.290666i \(0.0938770\pi\)
−0.226688 + 0.973968i \(0.572790\pi\)
\(420\) 0 0
\(421\) 12.8528i 0.626407i −0.949686 0.313203i \(-0.898598\pi\)
0.949686 0.313203i \(-0.101402\pi\)
\(422\) −16.8493 + 9.72796i −0.820212 + 0.473550i
\(423\) 2.88164i 0.140110i
\(424\) −43.9919 + 25.3987i −2.13644 + 1.23347i
\(425\) −3.75393 6.50200i −0.182093 0.315394i
\(426\) 0.906662 + 1.57038i 0.0439279 + 0.0760854i
\(427\) 0 0
\(428\) 24.1401 1.16685
\(429\) −0.970207 + 4.96257i −0.0468421 + 0.239595i
\(430\) −7.00223 12.1282i −0.337677 0.584874i
\(431\) 7.76876 + 4.48530i 0.374208 + 0.216049i 0.675295 0.737547i \(-0.264016\pi\)
−0.301087 + 0.953597i \(0.597350\pi\)
\(432\) 25.8405 1.24325
\(433\) 1.72531 2.98833i 0.0829132 0.143610i −0.821587 0.570083i \(-0.806911\pi\)
0.904500 + 0.426473i \(0.140244\pi\)
\(434\) 0 0
\(435\) 3.88887 + 2.24524i 0.186457 + 0.107651i
\(436\) −7.03410 + 4.06114i −0.336872 + 0.194493i
\(437\) 6.33204 3.65580i 0.302902 0.174881i
\(438\) 12.2176 0.583780
\(439\) −38.5144 −1.83819 −0.919096 0.394034i \(-0.871079\pi\)
−0.919096 + 0.394034i \(0.871079\pi\)
\(440\) 26.4020 15.2432i 1.25867 0.726691i
\(441\) 0 0
\(442\) −22.0029 19.1687i −1.04657 0.911764i
\(443\) 7.51997 13.0250i 0.357284 0.618835i −0.630222 0.776415i \(-0.717036\pi\)
0.987506 + 0.157580i \(0.0503693\pi\)
\(444\) 12.5660 + 7.25498i 0.596356 + 0.344306i
\(445\) −1.41851 + 2.45693i −0.0672437 + 0.116469i
\(446\) 29.2246 + 50.6185i 1.38382 + 2.39685i
\(447\) 10.2646i 0.485499i
\(448\) 0 0
\(449\) 33.7087 + 19.4617i 1.59081 + 0.918456i 0.993168 + 0.116696i \(0.0372304\pi\)
0.597646 + 0.801760i \(0.296103\pi\)
\(450\) 14.7025 + 8.48850i 0.693083 + 0.400152i
\(451\) 20.8322 0.980952
\(452\) −20.1928 + 34.9750i −0.949790 + 1.64509i
\(453\) 3.90660i 0.183548i
\(454\) 35.3906 1.66097
\(455\) 0 0
\(456\) 13.3448 0.624927
\(457\) 13.9396i 0.652069i 0.945358 + 0.326034i \(0.105713\pi\)
−0.945358 + 0.326034i \(0.894287\pi\)
\(458\) 10.2649 17.7793i 0.479648 0.830774i
\(459\) 9.29049 0.433643
\(460\) 13.0339 + 7.52512i 0.607709 + 0.350861i
\(461\) −32.4443 18.7317i −1.51108 0.872424i −0.999916 0.0129430i \(-0.995880\pi\)
−0.511167 0.859481i \(-0.670787\pi\)
\(462\) 0 0
\(463\) 6.75275i 0.313827i 0.987612 + 0.156913i \(0.0501544\pi\)
−0.987612 + 0.156913i \(0.949846\pi\)
\(464\) 23.3614 + 40.4631i 1.08453 + 1.87845i
\(465\) −4.37875 + 7.58421i −0.203059 + 0.351709i
\(466\) −14.7324 8.50576i −0.682466 0.394022i
\(467\) −2.52516 + 4.37371i −0.116851 + 0.202391i −0.918518 0.395379i \(-0.870613\pi\)
0.801667 + 0.597770i \(0.203947\pi\)
\(468\) 45.4314 + 8.88205i 2.10006 + 0.410573i
\(469\) 0 0
\(470\) 3.81296 2.20141i 0.175879 0.101544i
\(471\) 7.26084 0.334562
\(472\) 79.8705 3.67634
\(473\) −7.86163 + 4.53892i −0.361478 + 0.208700i
\(474\) 7.21294 4.16439i 0.331301 0.191277i
\(475\) 7.65595 + 4.42017i 0.351279 + 0.202811i
\(476\) 0 0
\(477\) 9.92198 17.1854i 0.454296 0.786864i
\(478\) 24.3143 1.11211
\(479\) −8.18670 4.72659i −0.374060 0.215964i 0.301171 0.953570i \(-0.402623\pi\)
−0.675231 + 0.737607i \(0.735956\pi\)
\(480\) 3.56401 + 6.17304i 0.162674 + 0.281759i
\(481\) 16.1850 + 14.1002i 0.737971 + 0.642913i
\(482\) 26.1082 1.18920
\(483\) 0 0
\(484\) 8.65711 + 14.9946i 0.393505 + 0.681571i
\(485\) 12.4789 + 21.6142i 0.566639 + 0.981448i
\(486\) −27.7167 + 16.0023i −1.25726 + 0.725877i
\(487\) 39.9996i 1.81255i 0.422684 + 0.906277i \(0.361088\pi\)
−0.422684 + 0.906277i \(0.638912\pi\)
\(488\) −17.7106 + 10.2252i −0.801721 + 0.462874i
\(489\) 3.71737i 0.168105i
\(490\) 0 0
\(491\) −3.38049 5.85517i −0.152559 0.264240i 0.779608 0.626267i \(-0.215418\pi\)
−0.932168 + 0.362027i \(0.882085\pi\)
\(492\) 18.7704i 0.846233i
\(493\) 8.39918 + 14.5478i 0.378280 + 0.655200i
\(494\) 33.7223 + 6.59287i 1.51724 + 0.296627i
\(495\) −5.95473 + 10.3139i −0.267645 + 0.463575i
\(496\) −78.9125 + 45.5602i −3.54328 + 2.04571i
\(497\) 0 0
\(498\) −1.80963 + 3.13438i −0.0810916 + 0.140455i
\(499\) −9.83591 5.67877i −0.440316 0.254217i 0.263416 0.964682i \(-0.415151\pi\)
−0.703732 + 0.710466i \(0.748484\pi\)
\(500\) 56.0871i 2.50829i
\(501\) 9.32230i 0.416490i
\(502\) 23.1993 + 13.3941i 1.03543 + 0.597808i
\(503\) −6.96423 + 12.0624i −0.310520 + 0.537836i −0.978475 0.206365i \(-0.933836\pi\)
0.667955 + 0.744202i \(0.267170\pi\)
\(504\) 0 0
\(505\) 1.78601 1.03115i 0.0794763 0.0458857i
\(506\) 6.95317 12.0432i 0.309106 0.535388i
\(507\) −6.24379 2.53840i −0.277296 0.112734i
\(508\) 7.34301 + 12.7185i 0.325793 + 0.564290i
\(509\) 19.8149i 0.878281i 0.898418 + 0.439141i \(0.144717\pi\)
−0.898418 + 0.439141i \(0.855283\pi\)
\(510\) 3.38227 + 5.85826i 0.149769 + 0.259408i
\(511\) 0 0
\(512\) 47.4335i 2.09628i
\(513\) −9.47373 + 5.46966i −0.418276 + 0.241491i
\(514\) 20.6741i 0.911894i
\(515\) 16.0093 9.24299i 0.705455 0.407295i
\(516\) −4.08967 7.08352i −0.180038 0.311835i
\(517\) −1.42698 2.47160i −0.0627585 0.108701i
\(518\) 0 0
\(519\) 6.64237 0.291568
\(520\) 13.1883 + 38.4370i 0.578347 + 1.68557i
\(521\) −15.5476 26.9292i −0.681151 1.17979i −0.974630 0.223823i \(-0.928146\pi\)
0.293479 0.955966i \(-0.405187\pi\)
\(522\) −32.8959 18.9924i −1.43981 0.831277i
\(523\) −22.7202 −0.993485 −0.496742 0.867898i \(-0.665471\pi\)
−0.496742 + 0.867898i \(0.665471\pi\)
\(524\) −23.9960 + 41.5622i −1.04827 + 1.81565i
\(525\) 0 0
\(526\) −11.3420 6.54831i −0.494535 0.285520i
\(527\) −28.3716 + 16.3804i −1.23589 + 0.713540i
\(528\) 10.5620 6.09798i 0.459652 0.265380i
\(529\) −19.0557 −0.828507
\(530\) 30.3194 1.31699
\(531\) −27.0211 + 15.6007i −1.17262 + 0.677011i
\(532\) 0 0
\(533\) −5.32794 + 27.2522i −0.230779 + 1.18043i
\(534\) −1.18097 + 2.04549i −0.0511054 + 0.0885171i
\(535\) −7.16922 4.13915i −0.309952 0.178951i
\(536\) 47.4782 82.2346i 2.05074 3.55199i
\(537\) −0.477046 0.826267i −0.0205860 0.0356561i
\(538\) 35.9563i 1.55018i
\(539\) 0 0
\(540\) −19.5008 11.2588i −0.839180 0.484501i
\(541\) 1.81754 + 1.04936i 0.0781423 + 0.0451155i 0.538562 0.842586i \(-0.318968\pi\)
−0.460420 + 0.887701i \(0.652301\pi\)
\(542\) 21.5558 0.925902
\(543\) 0.855283 1.48139i 0.0367037 0.0635727i
\(544\) 26.6650i 1.14325i
\(545\) 2.78536 0.119312
\(546\) 0 0
\(547\) 25.3770 1.08504 0.542521 0.840042i \(-0.317470\pi\)
0.542521 + 0.840042i \(0.317470\pi\)
\(548\) 46.9738i 2.00662i
\(549\) 3.99447 6.91862i 0.170480 0.295280i
\(550\) 16.8139 0.716948
\(551\) −17.1297 9.88983i −0.729749 0.421321i
\(552\) 6.23454 + 3.59951i 0.265360 + 0.153205i
\(553\) 0 0
\(554\) 60.0855i 2.55279i
\(555\) −2.48794 4.30923i −0.105607 0.182917i
\(556\) 3.91158 6.77506i 0.165888 0.287327i
\(557\) −38.3219 22.1252i −1.62375 0.937473i −0.985904 0.167309i \(-0.946492\pi\)
−0.637846 0.770164i \(-0.720174\pi\)
\(558\) 37.0397 64.1547i 1.56802 2.71588i
\(559\) −3.92705 11.4452i −0.166097 0.484082i
\(560\) 0 0
\(561\) 3.79738 2.19242i 0.160326 0.0925641i
\(562\) 70.3051 2.96564
\(563\) −38.8907 −1.63905 −0.819523 0.573046i \(-0.805762\pi\)
−0.819523 + 0.573046i \(0.805762\pi\)
\(564\) 2.22697 1.28574i 0.0937725 0.0541396i
\(565\) 11.9939 6.92468i 0.504587 0.291324i
\(566\) 36.2078 + 20.9046i 1.52193 + 0.878685i
\(567\) 0 0
\(568\) 4.72309 8.18063i 0.198177 0.343252i
\(569\) −46.1579 −1.93504 −0.967520 0.252796i \(-0.918650\pi\)
−0.967520 + 0.252796i \(0.918650\pi\)
\(570\) −6.89796 3.98254i −0.288924 0.166810i
\(571\) 10.5684 + 18.3050i 0.442274 + 0.766041i 0.997858 0.0654194i \(-0.0208385\pi\)
−0.555584 + 0.831461i \(0.687505\pi\)
\(572\) 43.3651 14.8793i 1.81319 0.622134i
\(573\) −2.53848 −0.106047
\(574\) 0 0
\(575\) 2.38452 + 4.13011i 0.0994413 + 0.172237i
\(576\) −6.39653 11.0791i −0.266522 0.461630i
\(577\) −21.9368 + 12.6652i −0.913239 + 0.527259i −0.881472 0.472237i \(-0.843447\pi\)
−0.0317671 + 0.999495i \(0.510113\pi\)
\(578\) 18.7009i 0.777855i
\(579\) 1.35559 0.782650i 0.0563364 0.0325258i
\(580\) 40.7146i 1.69058i
\(581\) 0 0
\(582\) 10.3892 + 17.9947i 0.430647 + 0.745903i
\(583\) 19.6533i 0.813958i
\(584\) −31.8227 55.1186i −1.31683 2.28082i
\(585\) −11.9694 10.4277i −0.494876 0.431131i
\(586\) −18.9553 + 32.8315i −0.783036 + 1.35626i
\(587\) −3.08554 + 1.78144i −0.127354 + 0.0735278i −0.562324 0.826917i \(-0.690092\pi\)
0.434970 + 0.900445i \(0.356759\pi\)
\(588\) 0 0
\(589\) 19.2875 33.4069i 0.794727 1.37651i
\(590\) −41.2853 23.8361i −1.69969 0.981316i
\(591\) 2.41082i 0.0991679i
\(592\) 51.7732i 2.12786i
\(593\) −21.9568 12.6768i −0.901659 0.520573i −0.0239212 0.999714i \(-0.507615\pi\)
−0.877738 + 0.479141i \(0.840948\pi\)
\(594\) −10.4030 + 18.0186i −0.426842 + 0.739312i
\(595\) 0 0
\(596\) −80.5990 + 46.5338i −3.30146 + 1.90610i
\(597\) 0.106472 0.184415i 0.00435762 0.00754762i
\(598\) 13.9764 + 12.1761i 0.571537 + 0.497917i
\(599\) −5.46078 9.45835i −0.223122 0.386458i 0.732633 0.680624i \(-0.238291\pi\)
−0.955754 + 0.294166i \(0.904958\pi\)
\(600\) 8.70421i 0.355348i
\(601\) 12.1282 + 21.0067i 0.494720 + 0.856880i 0.999981 0.00608649i \(-0.00193740\pi\)
−0.505262 + 0.862966i \(0.668604\pi\)
\(602\) 0 0
\(603\) 37.0946i 1.51061i
\(604\) 30.6751 17.7103i 1.24815 0.720621i
\(605\) 5.93753i 0.241395i
\(606\) 1.48692 0.858476i 0.0604022 0.0348732i
\(607\) −4.92724 8.53422i −0.199990 0.346393i 0.748535 0.663096i \(-0.230758\pi\)
−0.948525 + 0.316702i \(0.897424\pi\)
\(608\) −15.6987 27.1910i −0.636667 1.10274i
\(609\) 0 0
\(610\) 12.2062 0.494215
\(611\) 3.59825 1.23462i 0.145569 0.0499472i
\(612\) −20.0712 34.7643i −0.811328 1.40526i
\(613\) −3.18428 1.83844i −0.128612 0.0742540i 0.434314 0.900762i \(-0.356991\pi\)
−0.562926 + 0.826508i \(0.690324\pi\)
\(614\) 23.2416 0.937955
\(615\) 3.21844 5.57450i 0.129780 0.224785i
\(616\) 0 0
\(617\) 16.2352 + 9.37341i 0.653605 + 0.377359i 0.789836 0.613318i \(-0.210166\pi\)
−0.136231 + 0.990677i \(0.543499\pi\)
\(618\) 13.3284 7.69517i 0.536148 0.309545i
\(619\) −13.7650 + 7.94725i −0.553264 + 0.319427i −0.750437 0.660942i \(-0.770157\pi\)
0.197174 + 0.980369i \(0.436824\pi\)
\(620\) 79.4029 3.18890
\(621\) −5.90137 −0.236814
\(622\) 27.3086 15.7667i 1.09498 0.632185i
\(623\) 0 0
\(624\) 5.27594 + 15.3765i 0.211207 + 0.615555i
\(625\) 3.61371 6.25913i 0.144549 0.250365i
\(626\) 29.4212 + 16.9864i 1.17591 + 0.678911i
\(627\) −2.58152 + 4.47133i −0.103096 + 0.178568i
\(628\) −32.9165 57.0130i −1.31351 2.27507i
\(629\) 18.6141i 0.742194i
\(630\) 0 0
\(631\) −17.0998 9.87255i −0.680731 0.393020i 0.119400 0.992846i \(-0.461903\pi\)
−0.800130 + 0.599826i \(0.795236\pi\)
\(632\) −37.5745 21.6936i −1.49463 0.862927i
\(633\) 3.89679 0.154883
\(634\) −21.6349 + 37.4727i −0.859231 + 1.48823i
\(635\) 5.03624i 0.199857i
\(636\) 17.7081 0.702173
\(637\) 0 0
\(638\) −37.6200 −1.48939
\(639\) 3.69014i 0.145980i
\(640\) −3.97508 + 6.88504i −0.157129 + 0.272155i
\(641\) 29.7786 1.17618 0.588092 0.808794i \(-0.299879\pi\)
0.588092 + 0.808794i \(0.299879\pi\)
\(642\) −5.96867 3.44601i −0.235565 0.136003i
\(643\) −10.0220 5.78623i −0.395231 0.228187i 0.289193 0.957271i \(-0.406613\pi\)
−0.684424 + 0.729084i \(0.739946\pi\)
\(644\) 0 0
\(645\) 2.80493i 0.110444i
\(646\) −14.8982 25.8044i −0.586162 1.01526i
\(647\) −12.7533 + 22.0893i −0.501382 + 0.868420i 0.498616 + 0.866823i \(0.333842\pi\)
−0.999999 + 0.00159698i \(0.999492\pi\)
\(648\) 40.2823 + 23.2570i 1.58244 + 0.913620i
\(649\) −15.4508 + 26.7616i −0.606497 + 1.05048i
\(650\) −4.30024 + 21.9956i −0.168669 + 0.862737i
\(651\) 0 0
\(652\) −29.1893 + 16.8524i −1.14314 + 0.659993i
\(653\) −44.8293 −1.75430 −0.877152 0.480212i \(-0.840560\pi\)
−0.877152 + 0.480212i \(0.840560\pi\)
\(654\) 2.31892 0.0906771
\(655\) 14.2529 8.22889i 0.556905 0.321529i
\(656\) 58.0018 33.4874i 2.26459 1.30746i
\(657\) 21.5320 + 12.4315i 0.840043 + 0.484999i
\(658\) 0 0
\(659\) −20.5867 + 35.6572i −0.801944 + 1.38901i 0.116390 + 0.993204i \(0.462868\pi\)
−0.918335 + 0.395805i \(0.870466\pi\)
\(660\) −10.6276 −0.413680
\(661\) 18.9606 + 10.9469i 0.737481 + 0.425785i 0.821153 0.570709i \(-0.193331\pi\)
−0.0836719 + 0.996493i \(0.526665\pi\)
\(662\) −5.13404 8.89241i −0.199540 0.345613i
\(663\) 1.89687 + 5.52837i 0.0736684 + 0.214704i
\(664\) 18.8539 0.731673
\(665\) 0 0
\(666\) 21.0454 + 36.4517i 0.815492 + 1.41247i
\(667\) −5.33520 9.24084i −0.206580 0.357807i
\(668\) 73.1999 42.2620i 2.83219 1.63516i
\(669\) 11.7067i 0.452606i
\(670\) −49.0832 + 28.3382i −1.89625 + 1.09480i
\(671\) 7.91219i 0.305447i
\(672\) 0 0
\(673\) 17.8344 + 30.8901i 0.687466 + 1.19073i 0.972655 + 0.232254i \(0.0746102\pi\)
−0.285189 + 0.958471i \(0.592056\pi\)
\(674\) 35.4721i 1.36633i
\(675\) −3.56762 6.17930i −0.137318 0.237841i
\(676\) 8.37388 + 60.5347i 0.322072 + 2.32826i
\(677\) 1.27766 2.21297i 0.0491044 0.0850514i −0.840428 0.541923i \(-0.817697\pi\)
0.889533 + 0.456871i \(0.151030\pi\)
\(678\) 9.98541 5.76508i 0.383488 0.221407i
\(679\) 0 0
\(680\) 17.6193 30.5175i 0.675670 1.17029i
\(681\) −6.13867 3.54416i −0.235234 0.135813i
\(682\) 73.3678i 2.80940i
\(683\) 35.7399i 1.36755i −0.729693 0.683775i \(-0.760337\pi\)
0.729693 0.683775i \(-0.239663\pi\)
\(684\) 40.9341 + 23.6333i 1.56515 + 0.903642i
\(685\) −8.05431 + 13.9505i −0.307739 + 0.533020i
\(686\) 0 0
\(687\) −3.56099 + 2.05594i −0.135860 + 0.0784390i
\(688\) −14.5924 + 25.2748i −0.556330 + 0.963592i
\(689\) 25.7100 + 5.02643i 0.979474 + 0.191492i
\(690\) −2.14843 3.72120i −0.0817895 0.141664i
\(691\) 26.0292i 0.990197i 0.868837 + 0.495099i \(0.164868\pi\)
−0.868837 + 0.495099i \(0.835132\pi\)
\(692\) −30.1127 52.1567i −1.14471 1.98270i
\(693\) 0 0
\(694\) 68.3335i 2.59391i
\(695\) −2.32336 + 1.34139i −0.0881299 + 0.0508818i
\(696\) 19.4751i 0.738202i
\(697\) 20.8535 12.0398i 0.789884 0.456040i
\(698\) 6.32944 + 10.9629i 0.239573 + 0.414952i
\(699\) 1.70360 + 2.95073i 0.0644362 + 0.111607i
\(700\) 0 0
\(701\) −1.12731 −0.0425779 −0.0212890 0.999773i \(-0.506777\pi\)
−0.0212890 + 0.999773i \(0.506777\pi\)
\(702\) −20.9109 18.2174i −0.789230 0.687570i
\(703\) 10.9588 + 18.9813i 0.413321 + 0.715892i
\(704\) −10.9727 6.33509i −0.413549 0.238763i
\(705\) −0.881834 −0.0332118
\(706\) −17.5478 + 30.3936i −0.660419 + 1.14388i
\(707\) 0 0
\(708\) −24.1128 13.9215i −0.906215 0.523203i
\(709\) −5.23972 + 3.02515i −0.196782 + 0.113612i −0.595153 0.803612i \(-0.702909\pi\)
0.398372 + 0.917224i \(0.369575\pi\)
\(710\) −4.88276 + 2.81906i −0.183247 + 0.105798i
\(711\) 16.9492 0.635644
\(712\) 12.3040 0.461114
\(713\) 18.0218 10.4049i 0.674922 0.389666i
\(714\) 0 0
\(715\) −15.4300 3.01664i −0.577050 0.112816i
\(716\) −4.32530 + 7.49164i −0.161644 + 0.279976i
\(717\) −4.21743 2.43493i −0.157503 0.0909342i
\(718\) −11.1124 + 19.2473i −0.414713 + 0.718304i
\(719\) −23.5589 40.8052i −0.878597 1.52178i −0.852880 0.522106i \(-0.825146\pi\)
−0.0257170 0.999669i \(-0.508187\pi\)
\(720\) 38.2884i 1.42692i
\(721\) 0 0
\(722\) −12.2100 7.04944i −0.454409 0.262353i
\(723\) −4.52859 2.61458i −0.168420 0.0972374i
\(724\) −15.5095 −0.576404
\(725\) 6.45070 11.1729i 0.239573 0.414953i
\(726\) 4.94324i 0.183461i
\(727\) −17.9215 −0.664671 −0.332335 0.943161i \(-0.607837\pi\)
−0.332335 + 0.943161i \(0.607837\pi\)
\(728\) 0 0
\(729\) −13.5489 −0.501810
\(730\) 37.9880i 1.40600i
\(731\) −5.24644 + 9.08711i −0.194047 + 0.336099i
\(732\) 7.12908 0.263498
\(733\) 39.2037 + 22.6343i 1.44802 + 0.836016i 0.998364 0.0571848i \(-0.0182124\pi\)
0.449658 + 0.893201i \(0.351546\pi\)
\(734\) −3.72861 2.15271i −0.137625 0.0794581i
\(735\) 0 0
\(736\) 16.9378i 0.624335i
\(737\) 18.3691 + 31.8163i 0.676635 + 1.17197i
\(738\) −27.2247 + 47.1546i −1.00215 + 1.73578i
\(739\) 16.6808 + 9.63066i 0.613613 + 0.354270i 0.774378 0.632723i \(-0.218063\pi\)
−0.160765 + 0.986993i \(0.551396\pi\)
\(740\) −22.5577 + 39.0712i −0.829239 + 1.43628i
\(741\) −5.18905 4.52065i −0.190624 0.166070i
\(742\) 0 0
\(743\) 30.2115 17.4426i 1.10835 0.639908i 0.169951 0.985453i \(-0.445639\pi\)
0.938402 + 0.345545i \(0.112306\pi\)
\(744\) 37.9810 1.39245
\(745\) 31.9155 1.16929
\(746\) 31.3032 18.0729i 1.14609 0.661697i
\(747\) −6.37850 + 3.68263i −0.233377 + 0.134740i
\(748\) −34.4303 19.8784i −1.25890 0.726825i
\(749\) 0 0
\(750\) 8.00648 13.8676i 0.292355 0.506374i
\(751\) 24.9668 0.911051 0.455526 0.890223i \(-0.349451\pi\)
0.455526 + 0.890223i \(0.349451\pi\)
\(752\) −7.94609 4.58767i −0.289764 0.167295i
\(753\) −2.68268 4.64654i −0.0977623 0.169329i
\(754\) 9.62150 49.2136i 0.350394 1.79225i
\(755\) −12.1467 −0.442064
\(756\) 0 0
\(757\) 5.30243 + 9.18408i 0.192720 + 0.333801i 0.946151 0.323726i \(-0.104936\pi\)
−0.753431 + 0.657527i \(0.771602\pi\)
\(758\) −40.8685 70.7863i −1.48441 2.57108i
\(759\) −2.41212 + 1.39264i −0.0875543 + 0.0505495i
\(760\) 41.4926i 1.50510i
\(761\) −28.2660 + 16.3194i −1.02464 + 0.591578i −0.915446 0.402442i \(-0.868162\pi\)
−0.109198 + 0.994020i \(0.534828\pi\)
\(762\) 4.19288i 0.151892i
\(763\) 0 0
\(764\) 11.5080 + 19.9325i 0.416345 + 0.721131i
\(765\) 13.7659i 0.497708i
\(766\) 41.2988 + 71.5316i 1.49219 + 2.58454i
\(767\) −31.0572 27.0568i −1.12141 0.976963i
\(768\) −5.73794 + 9.93841i −0.207050 + 0.358621i
\(769\) 45.1851 26.0876i 1.62942 0.940744i 0.645148 0.764057i \(-0.276796\pi\)
0.984267 0.176686i \(-0.0565378\pi\)
\(770\) 0 0
\(771\) 2.07039 3.58601i 0.0745631 0.129147i
\(772\) −12.2909 7.09618i −0.442360 0.255397i
\(773\) 35.7057i 1.28425i 0.766602 + 0.642123i \(0.221946\pi\)
−0.766602 + 0.642123i \(0.778054\pi\)
\(774\) 23.7268i 0.852842i
\(775\) 21.7898 + 12.5804i 0.782714 + 0.451900i
\(776\) 54.1208 93.7400i 1.94282 3.36507i
\(777\) 0 0
\(778\) 56.9752 32.8947i 2.04266 1.17933i
\(779\) −14.1766 + 24.5545i −0.507928 + 0.879757i
\(780\) 2.71807 13.9028i 0.0973225 0.497801i
\(781\) 1.82735 + 3.16506i 0.0653876 + 0.113255i
\(782\) 16.0741i 0.574808i
\(783\) 7.98231 + 13.8258i 0.285265 + 0.494093i
\(784\) 0 0
\(785\) 22.5760i 0.805770i
\(786\) 11.8661 6.85089i 0.423249 0.244363i
\(787\) 6.10621i 0.217663i −0.994060 0.108831i \(-0.965289\pi\)
0.994060 0.108831i \(-0.0347109\pi\)
\(788\) −18.9301 + 10.9293i −0.674356 + 0.389339i
\(789\) 1.31155 + 2.27167i 0.0466923 + 0.0808735i
\(790\) 12.9482 + 22.4270i 0.460678 + 0.797918i
\(791\) 0 0
\(792\) 51.6510 1.83534
\(793\) 10.3505 + 2.02358i 0.367559 + 0.0718595i
\(794\) 5.38296 + 9.32356i 0.191034 + 0.330881i
\(795\) −5.25904 3.03631i −0.186519 0.107687i
\(796\) −1.93074 −0.0684332
\(797\) 23.1149 40.0363i 0.818773 1.41816i −0.0878129 0.996137i \(-0.527988\pi\)
0.906586 0.422020i \(-0.138679\pi\)
\(798\) 0 0
\(799\) −2.85688 1.64942i −0.101069 0.0583522i
\(800\) 17.7355 10.2396i 0.627044 0.362024i
\(801\) −4.16260 + 2.40328i −0.147078 + 0.0849157i
\(802\) −50.7400 −1.79169
\(803\) 24.6242 0.868968
\(804\) −28.6672 + 16.5510i −1.01101 + 0.583710i
\(805\) 0 0
\(806\) 95.9780 + 18.7642i 3.38068 + 0.660939i
\(807\) −3.60080 + 6.23678i −0.126754 + 0.219545i
\(808\) −7.74586 4.47208i −0.272498 0.157327i
\(809\) −19.6439 + 34.0243i −0.690644 + 1.19623i 0.280983 + 0.959713i \(0.409339\pi\)
−0.971627 + 0.236518i \(0.923994\pi\)
\(810\) −13.8814 24.0432i −0.487741 0.844792i
\(811\) 6.90664i 0.242525i 0.992620 + 0.121262i \(0.0386943\pi\)
−0.992620 + 0.121262i \(0.961306\pi\)
\(812\) 0 0
\(813\) −3.73896 2.15869i −0.131131 0.0757085i
\(814\) 36.1015 + 20.8432i 1.26536 + 0.730555i
\(815\) 11.5583 0.404871
\(816\) 7.04853 12.2084i 0.246748 0.427380i
\(817\) 12.3551i 0.432251i
\(818\) −45.6466 −1.59600
\(819\) 0 0
\(820\) −58.3622 −2.03810
\(821\) 1.91049i 0.0666765i 0.999444 + 0.0333382i \(0.0106139\pi\)
−0.999444 + 0.0333382i \(0.989386\pi\)
\(822\) −6.70554 + 11.6143i −0.233883 + 0.405097i
\(823\) −1.57969 −0.0550645 −0.0275322 0.999621i \(-0.508765\pi\)
−0.0275322 + 0.999621i \(0.508765\pi\)
\(824\) −69.4320 40.0866i −2.41878 1.39648i
\(825\) −2.91645 1.68381i −0.101538 0.0586228i
\(826\) 0 0
\(827\) 32.5050i 1.13031i −0.824985 0.565155i \(-0.808816\pi\)
0.824985 0.565155i \(-0.191184\pi\)
\(828\) 12.7493 + 22.0824i 0.443069 + 0.767418i
\(829\) 17.5269 30.3575i 0.608735 1.05436i −0.382714 0.923867i \(-0.625011\pi\)
0.991449 0.130493i \(-0.0416561\pi\)
\(830\) −9.74564 5.62665i −0.338276 0.195304i
\(831\) 6.01721 10.4221i 0.208735 0.361539i
\(832\) 11.0937 12.7340i 0.384606 0.441472i
\(833\) 0 0
\(834\) −1.93429 + 1.11676i −0.0669790 + 0.0386703i
\(835\) −28.9856 −1.00309
\(836\) 46.8126 1.61905
\(837\) −26.9635 + 15.5674i −0.931994 + 0.538087i
\(838\) −67.0096 + 38.6880i −2.31481 + 1.33645i
\(839\) −4.63746 2.67744i −0.160103 0.0924354i 0.417808 0.908535i \(-0.362798\pi\)
−0.577911 + 0.816100i \(0.696132\pi\)
\(840\) 0 0
\(841\) 0.0669890 0.116028i 0.00230997 0.00400098i
\(842\) 33.2708 1.14659
\(843\) −12.1947 7.04064i −0.420009 0.242492i
\(844\) −17.6658 30.5981i −0.608082 1.05323i
\(845\) 7.89260 19.4137i 0.271514 0.667850i
\(846\) 7.45942 0.256460
\(847\) 0 0
\(848\) −31.5923 54.7195i −1.08488 1.87907i
\(849\) −4.18694 7.25199i −0.143695 0.248888i
\(850\) 16.8311 9.71744i 0.577302 0.333305i
\(851\) 11.8238i 0.405314i
\(852\) −2.85179 + 1.64648i −0.0977008 + 0.0564076i
\(853\) 49.6270i 1.69920i 0.527431 + 0.849598i \(0.323155\pi\)
−0.527431 + 0.849598i \(0.676845\pi\)
\(854\) 0 0
\(855\) −8.10452 14.0374i −0.277169 0.480070i
\(856\) 35.9028i 1.22713i
\(857\) −2.94196 5.09563i −0.100496 0.174063i 0.811393 0.584500i \(-0.198709\pi\)
−0.911889 + 0.410437i \(0.865376\pi\)
\(858\) −12.8461 2.51148i −0.438559 0.0857405i
\(859\) 21.6931 37.5735i 0.740159 1.28199i −0.212264 0.977212i \(-0.568084\pi\)
0.952423 0.304780i \(-0.0985830\pi\)
\(860\) 22.0246 12.7159i 0.751033 0.433609i
\(861\) 0 0
\(862\) −11.6106 + 20.1102i −0.395460 + 0.684957i
\(863\) 26.9570 + 15.5636i 0.917626 + 0.529792i 0.882877 0.469604i \(-0.155603\pi\)
0.0347490 + 0.999396i \(0.488937\pi\)
\(864\) 25.3416i 0.862139i
\(865\) 20.6530i 0.702222i
\(866\) 7.73558 + 4.46614i 0.262866 + 0.151766i
\(867\) −1.87278 + 3.24376i −0.0636031 + 0.110164i
\(868\) 0 0
\(869\) 14.5374 8.39318i 0.493148 0.284719i
\(870\) −5.81203 + 10.0667i −0.197046 + 0.341294i
\(871\) −46.3192 + 15.8929i −1.56947 + 0.538510i
\(872\) −6.04001 10.4616i −0.204540 0.354274i
\(873\) 42.2844i 1.43111i
\(874\) 9.46341 + 16.3911i 0.320105 + 0.554438i
\(875\) 0 0
\(876\) 22.1870i 0.749629i
\(877\) 25.9033 14.9553i 0.874693 0.505004i 0.00578807 0.999983i \(-0.498158\pi\)
0.868905 + 0.494979i \(0.164824\pi\)
\(878\) 99.6984i 3.36466i
\(879\) 6.57576 3.79652i 0.221795 0.128053i
\(880\) 18.9603 + 32.8402i 0.639152 + 1.10704i
\(881\) −7.28477 12.6176i −0.245430 0.425097i 0.716822 0.697256i \(-0.245596\pi\)
−0.962252 + 0.272159i \(0.912262\pi\)
\(882\) 0 0
\(883\) 48.9296 1.64661 0.823307 0.567597i \(-0.192127\pi\)
0.823307 + 0.567597i \(0.192127\pi\)
\(884\) 34.8101 39.9569i 1.17079 1.34390i
\(885\) 4.77408 + 8.26896i 0.160479 + 0.277958i
\(886\) 33.7164 + 19.4662i 1.13273 + 0.653980i
\(887\) −54.5902 −1.83296 −0.916480 0.400080i \(-0.868982\pi\)
−0.916480 + 0.400080i \(0.868982\pi\)
\(888\) −10.7901 + 18.6890i −0.362092 + 0.627162i
\(889\) 0 0
\(890\) −6.36000 3.67195i −0.213188 0.123084i
\(891\) −15.5851 + 8.99803i −0.522119 + 0.301445i
\(892\) −91.9222 + 53.0713i −3.07778 + 1.77696i
\(893\) 3.88430 0.129983
\(894\) 26.5710 0.888666
\(895\) 2.56909 1.48327i 0.0858753 0.0495801i
\(896\) 0 0
\(897\) −1.20490 3.51165i −0.0402306 0.117251i
\(898\) −50.3787 + 87.2584i −1.68116 + 2.91185i
\(899\) −48.7533 28.1477i −1.62601 0.938780i
\(900\) −15.4150 + 26.6995i −0.513832 + 0.889983i
\(901\) −11.3585 19.6734i −0.378405 0.655417i
\(902\) 53.9263i 1.79555i
\(903\) 0 0
\(904\) −52.0172 30.0321i −1.73007 0.998854i
\(905\) 4.60606 + 2.65931i 0.153111 + 0.0883985i
\(906\) −10.1126 −0.335970
\(907\) 11.3628 19.6809i 0.377295 0.653494i −0.613373 0.789793i \(-0.710188\pi\)
0.990668 + 0.136300i \(0.0435211\pi\)
\(908\) 64.2688i 2.13283i
\(909\) 3.49402 0.115889
\(910\) 0 0
\(911\) −42.2359 −1.39934 −0.699669 0.714467i \(-0.746669\pi\)
−0.699669 + 0.714467i \(0.746669\pi\)
\(912\) 16.5990i 0.549646i
\(913\) −3.64725 + 6.31722i −0.120706 + 0.209070i
\(914\) −36.0842 −1.19356
\(915\) −2.11722 1.22238i −0.0699933 0.0404106i
\(916\) 32.2870 + 18.6409i 1.06679 + 0.615912i
\(917\) 0 0
\(918\) 24.0494i 0.793747i
\(919\) −15.3470 26.5818i −0.506251 0.876853i −0.999974 0.00723365i \(-0.997697\pi\)
0.493722 0.869620i \(-0.335636\pi\)
\(920\) −11.1919 + 19.3849i −0.368985 + 0.639101i
\(921\) −4.03136 2.32751i −0.132838 0.0766940i
\(922\) 48.4890 83.9854i 1.59690 2.76591i
\(923\) −4.60780 + 1.58101i −0.151668 + 0.0520396i
\(924\) 0 0
\(925\) −12.3806 + 7.14797i −0.407073 + 0.235024i
\(926\) −17.4802 −0.574434
\(927\) 31.3195 1.02867
\(928\) −39.6819 + 22.9104i −1.30262 + 0.752070i
\(929\) 32.4110 18.7125i 1.06337 0.613936i 0.137007 0.990570i \(-0.456252\pi\)
0.926362 + 0.376634i \(0.122918\pi\)
\(930\) −19.6325 11.3348i −0.643775 0.371684i
\(931\) 0 0
\(932\) 15.4463 26.7538i 0.505961 0.876350i
\(933\) −6.31574 −0.206768
\(934\) −11.3218 6.53663i −0.370460 0.213885i
\(935\) 6.81684 + 11.8071i 0.222935 + 0.386134i
\(936\) −13.2100 + 67.5686i −0.431782 + 2.20855i
\(937\) −44.3386 −1.44848 −0.724239 0.689549i \(-0.757809\pi\)
−0.724239 + 0.689549i \(0.757809\pi\)
\(938\) 0 0
\(939\) −3.40216 5.89272i −0.111025 0.192302i
\(940\) 3.99773 + 6.92427i 0.130392 + 0.225845i
\(941\) 23.8202 13.7526i 0.776518 0.448323i −0.0586770 0.998277i \(-0.518688\pi\)
0.835195 + 0.549954i \(0.185355\pi\)
\(942\) 18.7954i 0.612388i
\(943\) −13.2463 + 7.64774i −0.431358 + 0.249045i
\(944\) 99.3472i 3.23348i
\(945\) 0 0
\(946\) −11.7494 20.3506i −0.382007 0.661656i
\(947\) 5.08330i 0.165185i −0.996583 0.0825925i \(-0.973680\pi\)
0.996583 0.0825925i \(-0.0263200\pi\)
\(948\) 7.56246 + 13.0986i 0.245617 + 0.425422i
\(949\) −6.29775 + 32.2128i −0.204434 + 1.04567i
\(950\) −11.4420 + 19.8182i −0.371229 + 0.642987i
\(951\) 7.50534 4.33321i 0.243377 0.140514i
\(952\) 0 0
\(953\) 4.90718 8.49949i 0.158959 0.275326i −0.775534 0.631305i \(-0.782519\pi\)
0.934494 + 0.355980i \(0.115853\pi\)
\(954\) 44.4861 + 25.6840i 1.44029 + 0.831552i
\(955\) 7.89284i 0.255406i
\(956\) 44.1543i 1.42805i
\(957\) 6.52536 + 3.76742i 0.210935 + 0.121783i
\(958\) 12.2353 21.1921i 0.395303 0.684685i
\(959\) 0 0
\(960\) −3.39041 + 1.95746i −0.109425 + 0.0631766i
\(961\) 39.3947 68.2336i 1.27080 2.20108i
\(962\) −36.4997 + 41.8964i −1.17680 + 1.35079i
\(963\) −7.01268 12.1463i −0.225981 0.391410i
\(964\) 47.4121i 1.52704i
\(965\) 2.43348 + 4.21490i 0.0783364 + 0.135683i
\(966\) 0 0
\(967\) 2.69619i 0.0867036i −0.999060 0.0433518i \(-0.986196\pi\)
0.999060 0.0433518i \(-0.0138036\pi\)
\(968\) −22.3009 + 12.8754i −0.716779 + 0.413832i
\(969\) 5.96786i 0.191715i
\(970\) −55.9504 + 32.3030i −1.79646 + 1.03719i
\(971\) 12.4620 + 21.5848i 0.399925 + 0.692691i 0.993716 0.111929i \(-0.0357028\pi\)
−0.593791 + 0.804619i \(0.702369\pi\)
\(972\) −29.0598 50.3331i −0.932094 1.61443i
\(973\) 0 0
\(974\) −103.543 −3.31773
\(975\) 2.94862 3.38459i 0.0944314 0.108394i
\(976\) −12.7187 22.0294i −0.407115 0.705144i
\(977\) 24.5197 + 14.1565i 0.784456 + 0.452906i 0.838007 0.545659i \(-0.183721\pi\)
−0.0535514 + 0.998565i \(0.517054\pi\)
\(978\) 9.62280 0.307703
\(979\) −2.38019 + 4.12262i −0.0760713 + 0.131759i
\(980\) 0 0
\(981\) 4.08681 + 2.35952i 0.130482 + 0.0753337i
\(982\) 15.1567 8.75073i 0.483670 0.279247i
\(983\) 32.7805 18.9258i 1.04554 0.603641i 0.124140 0.992265i \(-0.460383\pi\)
0.921396 + 0.388624i \(0.127049\pi\)
\(984\) −27.9166 −0.889947
\(985\) 7.49591 0.238839
\(986\) −37.6585 + 21.7421i −1.19929 + 0.692410i
\(987\) 0 0
\(988\) −11.9725 + 61.2391i −0.380897 + 1.94827i
\(989\) 3.33257 5.77218i 0.105970 0.183545i
\(990\) −26.6986 15.4144i −0.848536 0.489903i
\(991\) −29.2079 + 50.5896i −0.927820 + 1.60703i −0.140858 + 0.990030i \(0.544986\pi\)
−0.786962 + 0.617001i \(0.788347\pi\)
\(992\) −44.6806 77.3891i −1.41861 2.45711i
\(993\) 2.05657i 0.0652633i
\(994\) 0 0
\(995\) 0.573399 + 0.331052i 0.0181780 + 0.0104950i
\(996\) −5.69197 3.28626i −0.180357 0.104129i
\(997\) −28.0588 −0.888632 −0.444316 0.895870i \(-0.646553\pi\)
−0.444316 + 0.895870i \(0.646553\pi\)
\(998\) 14.7001 25.4613i 0.465322 0.805962i
\(999\) 17.6903i 0.559696i
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 637.2.k.i.569.6 12
7.2 even 3 637.2.q.i.491.6 12
7.3 odd 6 91.2.u.b.88.1 yes 12
7.4 even 3 637.2.u.g.361.1 12
7.5 odd 6 637.2.q.g.491.6 12
7.6 odd 2 91.2.k.b.23.6 yes 12
13.4 even 6 637.2.u.g.30.1 12
21.17 even 6 819.2.do.e.361.6 12
21.20 even 2 819.2.bm.f.478.1 12
91.2 odd 12 8281.2.a.co.1.12 12
91.4 even 6 inner 637.2.k.i.459.1 12
91.17 odd 6 91.2.k.b.4.1 12
91.24 even 12 1183.2.e.j.508.12 24
91.30 even 6 637.2.q.i.589.6 12
91.37 odd 12 8281.2.a.co.1.1 12
91.41 even 12 1183.2.e.j.170.1 24
91.54 even 12 8281.2.a.cp.1.12 12
91.69 odd 6 91.2.u.b.30.1 yes 12
91.76 even 12 1183.2.e.j.170.12 24
91.80 even 12 1183.2.e.j.508.1 24
91.82 odd 6 637.2.q.g.589.6 12
91.89 even 12 8281.2.a.cp.1.1 12
273.17 even 6 819.2.bm.f.550.6 12
273.251 even 6 819.2.do.e.667.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.k.b.4.1 12 91.17 odd 6
91.2.k.b.23.6 yes 12 7.6 odd 2
91.2.u.b.30.1 yes 12 91.69 odd 6
91.2.u.b.88.1 yes 12 7.3 odd 6
637.2.k.i.459.1 12 91.4 even 6 inner
637.2.k.i.569.6 12 1.1 even 1 trivial
637.2.q.g.491.6 12 7.5 odd 6
637.2.q.g.589.6 12 91.82 odd 6
637.2.q.i.491.6 12 7.2 even 3
637.2.q.i.589.6 12 91.30 even 6
637.2.u.g.30.1 12 13.4 even 6
637.2.u.g.361.1 12 7.4 even 3
819.2.bm.f.478.1 12 21.20 even 2
819.2.bm.f.550.6 12 273.17 even 6
819.2.do.e.361.6 12 21.17 even 6
819.2.do.e.667.6 12 273.251 even 6
1183.2.e.j.170.1 24 91.41 even 12
1183.2.e.j.170.12 24 91.76 even 12
1183.2.e.j.508.1 24 91.80 even 12
1183.2.e.j.508.12 24 91.24 even 12
8281.2.a.co.1.1 12 91.37 odd 12
8281.2.a.co.1.12 12 91.2 odd 12
8281.2.a.cp.1.1 12 91.89 even 12
8281.2.a.cp.1.12 12 91.54 even 12