Properties

Label 637.2.q.j.491.9
Level $637$
Weight $2$
Character 637.491
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(491,637)]
 
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([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.491");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.q (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 491.9
Character \(\chi\) \(=\) 637.491
Dual form 637.2.q.j.589.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.489742 - 0.282753i) q^{2} +(-1.54556 - 2.67698i) q^{3} +(-0.840102 + 1.45510i) q^{4} +1.80514i q^{5} +(-1.51385 - 0.874021i) q^{6} +2.08118i q^{8} +(-3.27749 + 5.67679i) q^{9} +O(q^{10})\) \(q+(0.489742 - 0.282753i) q^{2} +(-1.54556 - 2.67698i) q^{3} +(-0.840102 + 1.45510i) q^{4} +1.80514i q^{5} +(-1.51385 - 0.874021i) q^{6} +2.08118i q^{8} +(-3.27749 + 5.67679i) q^{9} +(0.510408 + 0.884053i) q^{10} +(3.10412 - 1.79216i) q^{11} +5.19370 q^{12} +(0.328042 - 3.59060i) q^{13} +(4.83233 - 2.78995i) q^{15} +(-1.09175 - 1.89096i) q^{16} +(3.07459 - 5.32535i) q^{17} +3.70688i q^{18} +(2.17438 + 1.25538i) q^{19} +(-2.62666 - 1.51650i) q^{20} +(1.01348 - 1.75540i) q^{22} +(2.06593 + 3.57829i) q^{23} +(5.57127 - 3.21657i) q^{24} +1.74147 q^{25} +(-0.854595 - 1.85122i) q^{26} +10.9889 q^{27} +(-2.55567 - 4.42655i) q^{29} +(1.57773 - 2.73271i) q^{30} +4.55318i q^{31} +(-4.67405 - 2.69856i) q^{32} +(-9.59518 - 5.53978i) q^{33} -3.47740i q^{34} +(-5.50686 - 9.53816i) q^{36} +(10.1511 - 5.86074i) q^{37} +1.41984 q^{38} +(-10.1190 + 4.67131i) q^{39} -3.75681 q^{40} +(-1.61635 + 0.933202i) q^{41} +(-0.711568 + 1.23247i) q^{43} +6.02240i q^{44} +(-10.2474 - 5.91634i) q^{45} +(2.02354 + 1.16829i) q^{46} -8.86595i q^{47} +(-3.37471 + 5.84517i) q^{48} +(0.852870 - 0.492405i) q^{50} -19.0078 q^{51} +(4.94909 + 3.49380i) q^{52} +2.02920 q^{53} +(5.38171 - 3.10713i) q^{54} +(3.23511 + 5.60337i) q^{55} -7.76102i q^{57} +(-2.50324 - 1.44524i) q^{58} +(7.88734 + 4.55376i) q^{59} +9.37536i q^{60} +(-2.73920 + 4.74444i) q^{61} +(1.28742 + 2.22988i) q^{62} +1.31488 q^{64} +(6.48153 + 0.592162i) q^{65} -6.26555 q^{66} +(6.07998 - 3.51028i) q^{67} +(5.16594 + 8.94768i) q^{68} +(6.38601 - 11.0609i) q^{69} +(3.89200 + 2.24705i) q^{71} +(-11.8144 - 6.82104i) q^{72} -9.35564i q^{73} +(3.31428 - 5.74050i) q^{74} +(-2.69154 - 4.66188i) q^{75} +(-3.65339 + 2.10929i) q^{76} +(-3.63486 + 5.14890i) q^{78} +5.20970 q^{79} +(3.41345 - 1.97075i) q^{80} +(-7.15145 - 12.3867i) q^{81} +(-0.527731 + 0.914056i) q^{82} +9.42491i q^{83} +(9.61301 + 5.55007i) q^{85} +0.804791i q^{86} +(-7.89986 + 13.6830i) q^{87} +(3.72981 + 6.46021i) q^{88} +(-0.308000 + 0.177824i) q^{89} -6.69144 q^{90} -6.94235 q^{92} +(12.1888 - 7.03720i) q^{93} +(-2.50687 - 4.34203i) q^{94} +(-2.26613 + 3.92505i) q^{95} +16.6831i q^{96} +(-9.18293 - 5.30176i) q^{97} +23.4952i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 20 q^{4} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 20 q^{4} - 28 q^{9} - 12 q^{15} - 28 q^{16} + 8 q^{22} + 24 q^{23} - 40 q^{25} - 24 q^{29} + 24 q^{30} - 60 q^{32} + 92 q^{36} - 32 q^{39} + 12 q^{43} - 24 q^{46} + 12 q^{50} + 72 q^{53} - 132 q^{58} + 32 q^{64} + 48 q^{67} - 48 q^{71} + 72 q^{72} + 24 q^{74} - 156 q^{78} + 96 q^{79} - 64 q^{81} + 12 q^{85} + 56 q^{88} + 168 q^{92} - 48 q^{93} + 84 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.489742 0.282753i 0.346300 0.199936i −0.316754 0.948508i \(-0.602593\pi\)
0.663054 + 0.748571i \(0.269260\pi\)
\(3\) −1.54556 2.67698i −0.892328 1.54556i −0.837077 0.547085i \(-0.815738\pi\)
−0.0552505 0.998473i \(-0.517596\pi\)
\(4\) −0.840102 + 1.45510i −0.420051 + 0.727550i
\(5\) 1.80514i 0.807283i 0.914917 + 0.403642i \(0.132256\pi\)
−0.914917 + 0.403642i \(0.867744\pi\)
\(6\) −1.51385 0.874021i −0.618026 0.356818i
\(7\) 0 0
\(8\) 2.08118i 0.735806i
\(9\) −3.27749 + 5.67679i −1.09250 + 1.89226i
\(10\) 0.510408 + 0.884053i 0.161405 + 0.279562i
\(11\) 3.10412 1.79216i 0.935927 0.540358i 0.0472456 0.998883i \(-0.484956\pi\)
0.888681 + 0.458526i \(0.151622\pi\)
\(12\) 5.19370 1.49929
\(13\) 0.328042 3.59060i 0.0909825 0.995852i
\(14\) 0 0
\(15\) 4.83233 2.78995i 1.24770 0.720361i
\(16\) −1.09175 1.89096i −0.272936 0.472740i
\(17\) 3.07459 5.32535i 0.745699 1.29159i −0.204169 0.978936i \(-0.565449\pi\)
0.949868 0.312652i \(-0.101217\pi\)
\(18\) 3.70688i 0.873720i
\(19\) 2.17438 + 1.25538i 0.498836 + 0.288003i 0.728233 0.685330i \(-0.240342\pi\)
−0.229397 + 0.973333i \(0.573675\pi\)
\(20\) −2.62666 1.51650i −0.587339 0.339100i
\(21\) 0 0
\(22\) 1.01348 1.75540i 0.216074 0.374252i
\(23\) 2.06593 + 3.57829i 0.430775 + 0.746125i 0.996940 0.0781674i \(-0.0249069\pi\)
−0.566165 + 0.824292i \(0.691574\pi\)
\(24\) 5.57127 3.21657i 1.13723 0.656581i
\(25\) 1.74147 0.348294
\(26\) −0.854595 1.85122i −0.167600 0.363054i
\(27\) 10.9889 2.11481
\(28\) 0 0
\(29\) −2.55567 4.42655i −0.474576 0.821989i 0.525001 0.851102i \(-0.324065\pi\)
−0.999576 + 0.0291130i \(0.990732\pi\)
\(30\) 1.57773 2.73271i 0.288053 0.498922i
\(31\) 4.55318i 0.817775i 0.912585 + 0.408888i \(0.134083\pi\)
−0.912585 + 0.408888i \(0.865917\pi\)
\(32\) −4.67405 2.69856i −0.826263 0.477043i
\(33\) −9.59518 5.53978i −1.67031 0.964352i
\(34\) 3.47740i 0.596369i
\(35\) 0 0
\(36\) −5.50686 9.53816i −0.917809 1.58969i
\(37\) 10.1511 5.86074i 1.66883 0.963500i 0.700561 0.713592i \(-0.252933\pi\)
0.968270 0.249908i \(-0.0804004\pi\)
\(38\) 1.41984 0.230329
\(39\) −10.1190 + 4.67131i −1.62033 + 0.748008i
\(40\) −3.75681 −0.594004
\(41\) −1.61635 + 0.933202i −0.252432 + 0.145742i −0.620877 0.783908i \(-0.713223\pi\)
0.368445 + 0.929649i \(0.379890\pi\)
\(42\) 0 0
\(43\) −0.711568 + 1.23247i −0.108513 + 0.187950i −0.915168 0.403072i \(-0.867942\pi\)
0.806655 + 0.591023i \(0.201276\pi\)
\(44\) 6.02240i 0.907911i
\(45\) −10.2474 5.91634i −1.52759 0.881955i
\(46\) 2.02354 + 1.16829i 0.298355 + 0.172255i
\(47\) 8.86595i 1.29323i −0.762816 0.646616i \(-0.776184\pi\)
0.762816 0.646616i \(-0.223816\pi\)
\(48\) −3.37471 + 5.84517i −0.487098 + 0.843678i
\(49\) 0 0
\(50\) 0.852870 0.492405i 0.120614 0.0696366i
\(51\) −19.0078 −2.66163
\(52\) 4.94909 + 3.49380i 0.686315 + 0.484503i
\(53\) 2.02920 0.278732 0.139366 0.990241i \(-0.455494\pi\)
0.139366 + 0.990241i \(0.455494\pi\)
\(54\) 5.38171 3.10713i 0.732358 0.422827i
\(55\) 3.23511 + 5.60337i 0.436222 + 0.755558i
\(56\) 0 0
\(57\) 7.76102i 1.02797i
\(58\) −2.50324 1.44524i −0.328691 0.189770i
\(59\) 7.88734 + 4.55376i 1.02684 + 0.592849i 0.916079 0.400997i \(-0.131336\pi\)
0.110766 + 0.993847i \(0.464670\pi\)
\(60\) 9.37536i 1.21035i
\(61\) −2.73920 + 4.74444i −0.350719 + 0.607463i −0.986376 0.164509i \(-0.947396\pi\)
0.635656 + 0.771972i \(0.280729\pi\)
\(62\) 1.28742 + 2.22988i 0.163503 + 0.283195i
\(63\) 0 0
\(64\) 1.31488 0.164360
\(65\) 6.48153 + 0.592162i 0.803935 + 0.0734486i
\(66\) −6.26555 −0.771236
\(67\) 6.07998 3.51028i 0.742788 0.428849i −0.0802944 0.996771i \(-0.525586\pi\)
0.823082 + 0.567923i \(0.192253\pi\)
\(68\) 5.16594 + 8.94768i 0.626463 + 1.08507i
\(69\) 6.38601 11.0609i 0.768785 1.33158i
\(70\) 0 0
\(71\) 3.89200 + 2.24705i 0.461896 + 0.266676i 0.712841 0.701326i \(-0.247408\pi\)
−0.250945 + 0.968001i \(0.580741\pi\)
\(72\) −11.8144 6.82104i −1.39234 0.803867i
\(73\) 9.35564i 1.09499i −0.836807 0.547497i \(-0.815581\pi\)
0.836807 0.547497i \(-0.184419\pi\)
\(74\) 3.31428 5.74050i 0.385277 0.667320i
\(75\) −2.69154 4.66188i −0.310792 0.538308i
\(76\) −3.65339 + 2.10929i −0.419073 + 0.241952i
\(77\) 0 0
\(78\) −3.63486 + 5.14890i −0.411567 + 0.582999i
\(79\) 5.20970 0.586137 0.293069 0.956091i \(-0.405324\pi\)
0.293069 + 0.956091i \(0.405324\pi\)
\(80\) 3.41345 1.97075i 0.381635 0.220337i
\(81\) −7.15145 12.3867i −0.794605 1.37630i
\(82\) −0.527731 + 0.914056i −0.0582781 + 0.100941i
\(83\) 9.42491i 1.03452i 0.855829 + 0.517259i \(0.173048\pi\)
−0.855829 + 0.517259i \(0.826952\pi\)
\(84\) 0 0
\(85\) 9.61301 + 5.55007i 1.04268 + 0.601990i
\(86\) 0.804791i 0.0867829i
\(87\) −7.89986 + 13.6830i −0.846954 + 1.46697i
\(88\) 3.72981 + 6.46021i 0.397599 + 0.688661i
\(89\) −0.308000 + 0.177824i −0.0326479 + 0.0188493i −0.516235 0.856447i \(-0.672667\pi\)
0.483587 + 0.875296i \(0.339334\pi\)
\(90\) −6.69144 −0.705340
\(91\) 0 0
\(92\) −6.94235 −0.723790
\(93\) 12.1888 7.03720i 1.26392 0.729723i
\(94\) −2.50687 4.34203i −0.258564 0.447846i
\(95\) −2.26613 + 3.92505i −0.232500 + 0.402702i
\(96\) 16.6831i 1.70272i
\(97\) −9.18293 5.30176i −0.932385 0.538313i −0.0448198 0.998995i \(-0.514271\pi\)
−0.887565 + 0.460682i \(0.847605\pi\)
\(98\) 0 0
\(99\) 23.4952i 2.36136i
\(100\) −1.46301 + 2.53401i −0.146301 + 0.253401i
\(101\) −1.71254 2.96620i −0.170404 0.295148i 0.768157 0.640261i \(-0.221174\pi\)
−0.938561 + 0.345113i \(0.887841\pi\)
\(102\) −9.30894 + 5.37452i −0.921722 + 0.532157i
\(103\) −12.9558 −1.27658 −0.638288 0.769798i \(-0.720357\pi\)
−0.638288 + 0.769798i \(0.720357\pi\)
\(104\) 7.47266 + 0.682713i 0.732755 + 0.0669455i
\(105\) 0 0
\(106\) 0.993783 0.573761i 0.0965248 0.0557286i
\(107\) 9.08482 + 15.7354i 0.878263 + 1.52120i 0.853246 + 0.521508i \(0.174630\pi\)
0.0250164 + 0.999687i \(0.492036\pi\)
\(108\) −9.23177 + 15.9899i −0.888328 + 1.53863i
\(109\) 13.9294i 1.33420i −0.744970 0.667098i \(-0.767536\pi\)
0.744970 0.667098i \(-0.232464\pi\)
\(110\) 3.16873 + 1.82947i 0.302127 + 0.174433i
\(111\) −31.3782 18.1162i −2.97829 1.71952i
\(112\) 0 0
\(113\) 5.06404 8.77118i 0.476385 0.825123i −0.523249 0.852180i \(-0.675280\pi\)
0.999634 + 0.0270569i \(0.00861353\pi\)
\(114\) −2.19445 3.80090i −0.205529 0.355987i
\(115\) −6.45931 + 3.72928i −0.602334 + 0.347758i
\(116\) 8.58808 0.797383
\(117\) 19.3079 + 13.6304i 1.78502 + 1.26013i
\(118\) 5.15035 0.474128
\(119\) 0 0
\(120\) 5.80637 + 10.0569i 0.530047 + 0.918068i
\(121\) 0.923697 1.59989i 0.0839725 0.145445i
\(122\) 3.09807i 0.280486i
\(123\) 4.99633 + 2.88463i 0.450504 + 0.260099i
\(124\) −6.62533 3.82513i −0.594972 0.343507i
\(125\) 12.1693i 1.08845i
\(126\) 0 0
\(127\) 3.05109 + 5.28465i 0.270741 + 0.468937i 0.969052 0.246858i \(-0.0793980\pi\)
−0.698311 + 0.715795i \(0.746065\pi\)
\(128\) 9.99205 5.76891i 0.883181 0.509905i
\(129\) 4.39908 0.387317
\(130\) 3.34171 1.54266i 0.293088 0.135301i
\(131\) 5.97266 0.521833 0.260917 0.965361i \(-0.415975\pi\)
0.260917 + 0.965361i \(0.415975\pi\)
\(132\) 16.1219 9.30796i 1.40323 0.810154i
\(133\) 0 0
\(134\) 1.98508 3.43826i 0.171485 0.297020i
\(135\) 19.8365i 1.70725i
\(136\) 11.0830 + 6.39877i 0.950359 + 0.548690i
\(137\) −3.12407 1.80368i −0.266907 0.154099i 0.360574 0.932731i \(-0.382581\pi\)
−0.627481 + 0.778632i \(0.715914\pi\)
\(138\) 7.22265i 0.614833i
\(139\) −6.45833 + 11.1862i −0.547789 + 0.948798i 0.450637 + 0.892707i \(0.351197\pi\)
−0.998426 + 0.0560906i \(0.982136\pi\)
\(140\) 0 0
\(141\) −23.7340 + 13.7028i −1.99876 + 1.15399i
\(142\) 2.54144 0.213273
\(143\) −5.41665 11.7335i −0.452963 0.981208i
\(144\) 14.3128 1.19273
\(145\) 7.99054 4.61334i 0.663578 0.383117i
\(146\) −2.64533 4.58185i −0.218929 0.379197i
\(147\) 0 0
\(148\) 19.6945i 1.61888i
\(149\) 1.90020 + 1.09708i 0.155670 + 0.0898763i 0.575812 0.817582i \(-0.304686\pi\)
−0.420141 + 0.907459i \(0.638019\pi\)
\(150\) −2.63632 1.52208i −0.215255 0.124277i
\(151\) 1.94893i 0.158602i 0.996851 + 0.0793009i \(0.0252688\pi\)
−0.996851 + 0.0793009i \(0.974731\pi\)
\(152\) −2.61266 + 4.52526i −0.211915 + 0.367047i
\(153\) 20.1539 + 34.9076i 1.62935 + 2.82211i
\(154\) 0 0
\(155\) −8.21913 −0.660176
\(156\) 1.70375 18.6485i 0.136409 1.49307i
\(157\) 18.3508 1.46455 0.732275 0.681009i \(-0.238459\pi\)
0.732275 + 0.681009i \(0.238459\pi\)
\(158\) 2.55141 1.47306i 0.202979 0.117190i
\(159\) −3.13624 5.43213i −0.248720 0.430796i
\(160\) 4.87128 8.43731i 0.385109 0.667028i
\(161\) 0 0
\(162\) −7.00473 4.04418i −0.550344 0.317741i
\(163\) −19.1044 11.0299i −1.49637 0.863931i −0.496380 0.868105i \(-0.665338\pi\)
−0.999991 + 0.00417469i \(0.998671\pi\)
\(164\) 3.13594i 0.244876i
\(165\) 10.0001 17.3206i 0.778505 1.34841i
\(166\) 2.66492 + 4.61578i 0.206838 + 0.358254i
\(167\) 2.45846 1.41939i 0.190241 0.109836i −0.401854 0.915704i \(-0.631634\pi\)
0.592096 + 0.805868i \(0.298301\pi\)
\(168\) 0 0
\(169\) −12.7848 2.35573i −0.983444 0.181210i
\(170\) 6.27719 0.481439
\(171\) −14.2530 + 8.22898i −1.08995 + 0.629286i
\(172\) −1.19558 2.07080i −0.0911621 0.157897i
\(173\) −1.76411 + 3.05553i −0.134123 + 0.232308i −0.925262 0.379329i \(-0.876155\pi\)
0.791139 + 0.611636i \(0.209488\pi\)
\(174\) 8.93483i 0.677347i
\(175\) 0 0
\(176\) −6.77781 3.91317i −0.510897 0.294967i
\(177\) 28.1524i 2.11606i
\(178\) −0.100560 + 0.174176i −0.00753732 + 0.0130550i
\(179\) −3.34735 5.79778i −0.250193 0.433346i 0.713386 0.700771i \(-0.247161\pi\)
−0.963579 + 0.267425i \(0.913827\pi\)
\(180\) 17.2177 9.94065i 1.28333 0.740932i
\(181\) −12.5317 −0.931476 −0.465738 0.884923i \(-0.654211\pi\)
−0.465738 + 0.884923i \(0.654211\pi\)
\(182\) 0 0
\(183\) 16.9344 1.25183
\(184\) −7.44704 + 4.29955i −0.549003 + 0.316967i
\(185\) 10.5795 + 18.3242i 0.777817 + 1.34722i
\(186\) 3.97957 6.89282i 0.291797 0.505406i
\(187\) 22.0407i 1.61178i
\(188\) 12.9008 + 7.44830i 0.940890 + 0.543223i
\(189\) 0 0
\(190\) 2.56302i 0.185941i
\(191\) −1.51821 + 2.62961i −0.109854 + 0.190272i −0.915711 0.401838i \(-0.868372\pi\)
0.805857 + 0.592110i \(0.201705\pi\)
\(192\) −2.03222 3.51991i −0.146663 0.254028i
\(193\) −23.3350 + 13.4725i −1.67969 + 0.969769i −0.717833 + 0.696215i \(0.754866\pi\)
−0.961857 + 0.273554i \(0.911801\pi\)
\(194\) −5.99635 −0.430513
\(195\) −8.43237 18.2662i −0.603855 1.30807i
\(196\) 0 0
\(197\) −8.05315 + 4.64949i −0.573763 + 0.331262i −0.758651 0.651497i \(-0.774141\pi\)
0.184888 + 0.982760i \(0.440808\pi\)
\(198\) 6.64333 + 11.5066i 0.472121 + 0.817738i
\(199\) −8.69242 + 15.0557i −0.616190 + 1.06727i 0.373985 + 0.927435i \(0.377991\pi\)
−0.990175 + 0.139837i \(0.955342\pi\)
\(200\) 3.62430i 0.256277i
\(201\) −18.7939 10.8507i −1.32562 0.765347i
\(202\) −1.67740 0.968450i −0.118022 0.0681399i
\(203\) 0 0
\(204\) 15.9685 27.6583i 1.11802 1.93647i
\(205\) −1.68456 2.91774i −0.117655 0.203784i
\(206\) −6.34501 + 3.66329i −0.442078 + 0.255234i
\(207\) −27.0842 −1.88248
\(208\) −7.14781 + 3.29971i −0.495612 + 0.228793i
\(209\) 8.99936 0.622499
\(210\) 0 0
\(211\) −10.9118 18.8998i −0.751199 1.30112i −0.947242 0.320520i \(-0.896142\pi\)
0.196042 0.980595i \(-0.437191\pi\)
\(212\) −1.70473 + 2.95268i −0.117082 + 0.202791i
\(213\) 13.8918i 0.951849i
\(214\) 8.89844 + 5.13751i 0.608285 + 0.351193i
\(215\) −2.22479 1.28448i −0.151729 0.0876009i
\(216\) 22.8698i 1.55609i
\(217\) 0 0
\(218\) −3.93858 6.82182i −0.266754 0.462032i
\(219\) −25.0449 + 14.4597i −1.69238 + 0.977094i
\(220\) −10.8713 −0.732941
\(221\) −18.1126 12.7866i −1.21839 0.860118i
\(222\) −20.4896 −1.37517
\(223\) −1.65573 + 0.955937i −0.110876 + 0.0640143i −0.554413 0.832242i \(-0.687057\pi\)
0.443536 + 0.896256i \(0.353724\pi\)
\(224\) 0 0
\(225\) −5.70765 + 9.88594i −0.380510 + 0.659063i
\(226\) 5.72749i 0.380987i
\(227\) 8.95012 + 5.16735i 0.594040 + 0.342969i 0.766693 0.642013i \(-0.221901\pi\)
−0.172653 + 0.984983i \(0.555234\pi\)
\(228\) 11.2931 + 6.52005i 0.747901 + 0.431801i
\(229\) 6.10394i 0.403360i −0.979451 0.201680i \(-0.935360\pi\)
0.979451 0.201680i \(-0.0646401\pi\)
\(230\) −2.10893 + 3.65278i −0.139059 + 0.240857i
\(231\) 0 0
\(232\) 9.21242 5.31879i 0.604825 0.349196i
\(233\) −7.12776 −0.466955 −0.233478 0.972362i \(-0.575011\pi\)
−0.233478 + 0.972362i \(0.575011\pi\)
\(234\) 13.3099 + 1.21601i 0.870096 + 0.0794932i
\(235\) 16.0043 1.04400
\(236\) −13.2523 + 7.65124i −0.862654 + 0.498054i
\(237\) −8.05189 13.9463i −0.523027 0.905909i
\(238\) 0 0
\(239\) 7.32349i 0.473717i −0.971544 0.236859i \(-0.923882\pi\)
0.971544 0.236859i \(-0.0761178\pi\)
\(240\) −10.5514 6.09183i −0.681087 0.393226i
\(241\) −0.227850 0.131549i −0.0146771 0.00847383i 0.492643 0.870231i \(-0.336031\pi\)
−0.507321 + 0.861757i \(0.669364\pi\)
\(242\) 1.04471i 0.0671566i
\(243\) −5.62264 + 9.73869i −0.360692 + 0.624737i
\(244\) −4.60242 7.97163i −0.294640 0.510331i
\(245\) 0 0
\(246\) 3.26255 0.208013
\(247\) 5.22084 7.39549i 0.332194 0.470564i
\(248\) −9.47596 −0.601724
\(249\) 25.2303 14.5667i 1.59891 0.923130i
\(250\) 3.44090 + 5.95982i 0.217622 + 0.376932i
\(251\) 6.64096 11.5025i 0.419173 0.726030i −0.576683 0.816968i \(-0.695653\pi\)
0.995857 + 0.0909383i \(0.0289866\pi\)
\(252\) 0 0
\(253\) 12.8257 + 7.40495i 0.806348 + 0.465545i
\(254\) 2.98850 + 1.72541i 0.187515 + 0.108262i
\(255\) 34.3118i 2.14869i
\(256\) 1.94747 3.37312i 0.121717 0.210820i
\(257\) 8.70718 + 15.0813i 0.543139 + 0.940745i 0.998721 + 0.0505509i \(0.0160977\pi\)
−0.455582 + 0.890194i \(0.650569\pi\)
\(258\) 2.15441 1.24385i 0.134128 0.0774388i
\(259\) 0 0
\(260\) −6.30680 + 8.93379i −0.391131 + 0.554050i
\(261\) 33.5047 2.07389
\(262\) 2.92506 1.68878i 0.180711 0.104333i
\(263\) 6.36382 + 11.0225i 0.392410 + 0.679674i 0.992767 0.120058i \(-0.0383081\pi\)
−0.600357 + 0.799732i \(0.704975\pi\)
\(264\) 11.5293 19.9693i 0.709577 1.22902i
\(265\) 3.66299i 0.225015i
\(266\) 0 0
\(267\) 0.952063 + 0.549674i 0.0582653 + 0.0336395i
\(268\) 11.7960i 0.720553i
\(269\) −1.08082 + 1.87203i −0.0658985 + 0.114140i −0.897092 0.441843i \(-0.854325\pi\)
0.831194 + 0.555983i \(0.187658\pi\)
\(270\) 5.60881 + 9.71475i 0.341341 + 0.591221i
\(271\) 5.04864 2.91483i 0.306683 0.177063i −0.338758 0.940873i \(-0.610007\pi\)
0.645441 + 0.763810i \(0.276674\pi\)
\(272\) −13.4267 −0.814113
\(273\) 0 0
\(274\) −2.03999 −0.123240
\(275\) 5.40572 3.12100i 0.325977 0.188203i
\(276\) 10.7298 + 18.5846i 0.645858 + 1.11866i
\(277\) −5.82366 + 10.0869i −0.349910 + 0.606062i −0.986233 0.165361i \(-0.947121\pi\)
0.636323 + 0.771423i \(0.280455\pi\)
\(278\) 7.30445i 0.438092i
\(279\) −25.8474 14.9230i −1.54744 0.893418i
\(280\) 0 0
\(281\) 24.7940i 1.47908i −0.673110 0.739542i \(-0.735042\pi\)
0.673110 0.739542i \(-0.264958\pi\)
\(282\) −7.74903 + 13.4217i −0.461448 + 0.799251i
\(283\) −7.57162 13.1144i −0.450086 0.779572i 0.548305 0.836279i \(-0.315273\pi\)
−0.998391 + 0.0567067i \(0.981940\pi\)
\(284\) −6.53936 + 3.77550i −0.388040 + 0.224035i
\(285\) 14.0097 0.829865
\(286\) −5.97045 4.21483i −0.353040 0.249228i
\(287\) 0 0
\(288\) 30.6383 17.6890i 1.80538 1.04234i
\(289\) −10.4063 18.0242i −0.612133 1.06025i
\(290\) 2.60887 4.51869i 0.153198 0.265347i
\(291\) 32.7767i 1.92141i
\(292\) 13.6134 + 7.85969i 0.796663 + 0.459954i
\(293\) 21.5816 + 12.4601i 1.26081 + 0.727929i 0.973231 0.229827i \(-0.0738162\pi\)
0.287579 + 0.957757i \(0.407149\pi\)
\(294\) 0 0
\(295\) −8.22018 + 14.2378i −0.478597 + 0.828955i
\(296\) 12.1972 + 21.1262i 0.708950 + 1.22794i
\(297\) 34.1107 19.6939i 1.97931 1.14275i
\(298\) 1.24081 0.0718782
\(299\) 13.5259 6.24408i 0.782223 0.361104i
\(300\) 9.04467 0.522194
\(301\) 0 0
\(302\) 0.551066 + 0.954474i 0.0317103 + 0.0549238i
\(303\) −5.29365 + 9.16888i −0.304112 + 0.526738i
\(304\) 5.48221i 0.314426i
\(305\) −8.56438 4.94465i −0.490395 0.283130i
\(306\) 19.7404 + 11.3972i 1.12849 + 0.651532i
\(307\) 3.90158i 0.222675i −0.993783 0.111337i \(-0.964487\pi\)
0.993783 0.111337i \(-0.0355134\pi\)
\(308\) 0 0
\(309\) 20.0240 + 34.6825i 1.13912 + 1.97302i
\(310\) −4.02525 + 2.32398i −0.228619 + 0.131993i
\(311\) 19.7180 1.11810 0.559052 0.829132i \(-0.311165\pi\)
0.559052 + 0.829132i \(0.311165\pi\)
\(312\) −9.72181 21.0594i −0.550389 1.19225i
\(313\) −2.89235 −0.163485 −0.0817427 0.996653i \(-0.526049\pi\)
−0.0817427 + 0.996653i \(0.526049\pi\)
\(314\) 8.98714 5.18873i 0.507173 0.292817i
\(315\) 0 0
\(316\) −4.37668 + 7.58063i −0.246207 + 0.426444i
\(317\) 15.9537i 0.896046i 0.894022 + 0.448023i \(0.147872\pi\)
−0.894022 + 0.448023i \(0.852128\pi\)
\(318\) −3.07190 1.77356i −0.172263 0.0994564i
\(319\) −15.8662 9.16035i −0.888336 0.512881i
\(320\) 2.37354i 0.132685i
\(321\) 28.0822 48.6398i 1.56740 2.71481i
\(322\) 0 0
\(323\) 13.3706 7.71955i 0.743963 0.429527i
\(324\) 24.0318 1.33510
\(325\) 0.571275 6.25291i 0.0316886 0.346849i
\(326\) −12.4750 −0.690924
\(327\) −37.2888 + 21.5287i −2.06208 + 1.19054i
\(328\) −1.94216 3.36391i −0.107238 0.185741i
\(329\) 0 0
\(330\) 11.3102i 0.622606i
\(331\) 3.31409 + 1.91339i 0.182159 + 0.105169i 0.588307 0.808638i \(-0.299795\pi\)
−0.406148 + 0.913807i \(0.633128\pi\)
\(332\) −13.7142 7.91789i −0.752664 0.434551i
\(333\) 76.8342i 4.21049i
\(334\) 0.802674 1.39027i 0.0439204 0.0760723i
\(335\) 6.33654 + 10.9752i 0.346202 + 0.599640i
\(336\) 0 0
\(337\) 9.78172 0.532844 0.266422 0.963856i \(-0.414158\pi\)
0.266422 + 0.963856i \(0.414158\pi\)
\(338\) −6.92733 + 2.46123i −0.376797 + 0.133873i
\(339\) −31.3071 −1.70037
\(340\) −16.1518 + 9.32525i −0.875955 + 0.505733i
\(341\) 8.16004 + 14.1336i 0.441891 + 0.765378i
\(342\) −4.65353 + 8.06015i −0.251634 + 0.435843i
\(343\) 0 0
\(344\) −2.56499 1.48090i −0.138295 0.0798447i
\(345\) 19.9665 + 11.5276i 1.07496 + 0.620628i
\(346\) 1.99523i 0.107264i
\(347\) −2.66702 + 4.61941i −0.143173 + 0.247983i −0.928690 0.370857i \(-0.879064\pi\)
0.785517 + 0.618840i \(0.212397\pi\)
\(348\) −13.2734 22.9902i −0.711527 1.23240i
\(349\) −12.7332 + 7.35149i −0.681590 + 0.393516i −0.800454 0.599394i \(-0.795408\pi\)
0.118864 + 0.992911i \(0.462075\pi\)
\(350\) 0 0
\(351\) 3.60481 39.4566i 0.192411 2.10604i
\(352\) −19.3451 −1.03110
\(353\) −30.7588 + 17.7586i −1.63713 + 0.945196i −0.655313 + 0.755357i \(0.727463\pi\)
−0.981815 + 0.189839i \(0.939203\pi\)
\(354\) −7.96016 13.7874i −0.423078 0.732792i
\(355\) −4.05624 + 7.02561i −0.215283 + 0.372881i
\(356\) 0.597560i 0.0316706i
\(357\) 0 0
\(358\) −3.27867 1.89294i −0.173283 0.100045i
\(359\) 15.9147i 0.839945i 0.907537 + 0.419972i \(0.137960\pi\)
−0.907537 + 0.419972i \(0.862040\pi\)
\(360\) 12.3129 21.3266i 0.648948 1.12401i
\(361\) −6.34806 10.9952i −0.334108 0.578693i
\(362\) −6.13731 + 3.54338i −0.322570 + 0.186236i
\(363\) −5.71051 −0.299724
\(364\) 0 0
\(365\) 16.8882 0.883971
\(366\) 8.29348 4.78824i 0.433507 0.250286i
\(367\) −9.12231 15.8003i −0.476181 0.824769i 0.523447 0.852058i \(-0.324646\pi\)
−0.999628 + 0.0272893i \(0.991312\pi\)
\(368\) 4.51093 7.81316i 0.235149 0.407289i
\(369\) 12.2343i 0.636890i
\(370\) 10.3624 + 5.98274i 0.538716 + 0.311028i
\(371\) 0 0
\(372\) 23.6479i 1.22608i
\(373\) 6.78720 11.7558i 0.351428 0.608691i −0.635072 0.772453i \(-0.719030\pi\)
0.986500 + 0.163762i \(0.0523629\pi\)
\(374\) −6.23207 10.7943i −0.322252 0.558158i
\(375\) 32.5770 18.8083i 1.68227 0.971259i
\(376\) 18.4516 0.951568
\(377\) −16.7323 + 7.72428i −0.861758 + 0.397821i
\(378\) 0 0
\(379\) −6.26632 + 3.61786i −0.321879 + 0.185837i −0.652230 0.758021i \(-0.726166\pi\)
0.330351 + 0.943858i \(0.392833\pi\)
\(380\) −3.80756 6.59489i −0.195324 0.338311i
\(381\) 9.43128 16.3355i 0.483179 0.836891i
\(382\) 1.71711i 0.0878549i
\(383\) 17.6205 + 10.1732i 0.900367 + 0.519827i 0.877319 0.479907i \(-0.159330\pi\)
0.0230476 + 0.999734i \(0.492663\pi\)
\(384\) −30.8866 17.8324i −1.57617 0.910004i
\(385\) 0 0
\(386\) −7.61875 + 13.1961i −0.387784 + 0.671662i
\(387\) −4.66432 8.07884i −0.237101 0.410671i
\(388\) 15.4292 8.90804i 0.783298 0.452237i
\(389\) −2.48306 −0.125896 −0.0629481 0.998017i \(-0.520050\pi\)
−0.0629481 + 0.998017i \(0.520050\pi\)
\(390\) −9.29450 6.56144i −0.470645 0.332251i
\(391\) 25.4075 1.28491
\(392\) 0 0
\(393\) −9.23108 15.9887i −0.465646 0.806523i
\(394\) −2.62931 + 4.55410i −0.132463 + 0.229432i
\(395\) 9.40424i 0.473179i
\(396\) −34.1879 19.7384i −1.71800 0.991890i
\(397\) 9.30034 + 5.36955i 0.466771 + 0.269490i 0.714887 0.699240i \(-0.246478\pi\)
−0.248116 + 0.968730i \(0.579812\pi\)
\(398\) 9.83122i 0.492795i
\(399\) 0 0
\(400\) −1.90124 3.29305i −0.0950621 0.164652i
\(401\) 12.7773 7.37698i 0.638068 0.368389i −0.145802 0.989314i \(-0.546576\pi\)
0.783870 + 0.620925i \(0.213243\pi\)
\(402\) −12.2722 −0.612083
\(403\) 16.3486 + 1.49363i 0.814383 + 0.0744032i
\(404\) 5.75483 0.286313
\(405\) 22.3597 12.9094i 1.11106 0.641472i
\(406\) 0 0
\(407\) 21.0068 36.3849i 1.04127 1.80353i
\(408\) 39.5586i 1.95844i
\(409\) −5.49448 3.17224i −0.271685 0.156857i 0.357968 0.933734i \(-0.383470\pi\)
−0.629653 + 0.776877i \(0.716803\pi\)
\(410\) −1.65000 0.952628i −0.0814877 0.0470469i
\(411\) 11.1508i 0.550028i
\(412\) 10.8842 18.8520i 0.536227 0.928772i
\(413\) 0 0
\(414\) −13.2643 + 7.65814i −0.651904 + 0.376377i
\(415\) −17.0133 −0.835150
\(416\) −11.2227 + 15.8974i −0.550240 + 0.779433i
\(417\) 39.9269 1.95523
\(418\) 4.40736 2.54459i 0.215571 0.124460i
\(419\) 9.04253 + 15.6621i 0.441756 + 0.765144i 0.997820 0.0659953i \(-0.0210222\pi\)
−0.556064 + 0.831140i \(0.687689\pi\)
\(420\) 0 0
\(421\) 19.7043i 0.960327i −0.877179 0.480164i \(-0.840577\pi\)
0.877179 0.480164i \(-0.159423\pi\)
\(422\) −10.6879 6.17068i −0.520281 0.300384i
\(423\) 50.3301 + 29.0581i 2.44713 + 1.41285i
\(424\) 4.22312i 0.205093i
\(425\) 5.35431 9.27394i 0.259722 0.449852i
\(426\) −3.92794 6.80338i −0.190309 0.329625i
\(427\) 0 0
\(428\) −30.5287 −1.47566
\(429\) −23.0387 + 32.6352i −1.11232 + 1.57564i
\(430\) −1.45276 −0.0700584
\(431\) −9.09662 + 5.25193i −0.438169 + 0.252977i −0.702820 0.711367i \(-0.748076\pi\)
0.264652 + 0.964344i \(0.414743\pi\)
\(432\) −11.9971 20.7795i −0.577209 0.999755i
\(433\) 4.55903 7.89646i 0.219093 0.379480i −0.735438 0.677592i \(-0.763024\pi\)
0.954531 + 0.298112i \(0.0963569\pi\)
\(434\) 0 0
\(435\) −24.6997 14.2604i −1.18426 0.683732i
\(436\) 20.2687 + 11.7021i 0.970694 + 0.560430i
\(437\) 10.3741i 0.496258i
\(438\) −8.17703 + 14.1630i −0.390713 + 0.676735i
\(439\) −14.6400 25.3573i −0.698731 1.21024i −0.968907 0.247427i \(-0.920415\pi\)
0.270175 0.962811i \(-0.412918\pi\)
\(440\) −11.6616 + 6.73282i −0.555944 + 0.320975i
\(441\) 0 0
\(442\) −12.4859 1.14073i −0.593896 0.0542591i
\(443\) −26.7353 −1.27023 −0.635117 0.772416i \(-0.719048\pi\)
−0.635117 + 0.772416i \(0.719048\pi\)
\(444\) 52.7218 30.4389i 2.50207 1.44457i
\(445\) −0.320997 0.555983i −0.0152167 0.0263561i
\(446\) −0.540588 + 0.936325i −0.0255976 + 0.0443363i
\(447\) 6.78240i 0.320797i
\(448\) 0 0
\(449\) −18.3732 10.6077i −0.867083 0.500611i −0.000705260 1.00000i \(-0.500224\pi\)
−0.866378 + 0.499389i \(0.833558\pi\)
\(450\) 6.45542i 0.304311i
\(451\) −3.34490 + 5.79354i −0.157505 + 0.272807i
\(452\) 8.50862 + 14.7374i 0.400212 + 0.693187i
\(453\) 5.21726 3.01219i 0.245128 0.141525i
\(454\) 5.84433 0.274288
\(455\) 0 0
\(456\) 16.1521 0.756389
\(457\) −12.6826 + 7.32231i −0.593267 + 0.342523i −0.766388 0.642377i \(-0.777948\pi\)
0.173121 + 0.984901i \(0.444615\pi\)
\(458\) −1.72591 2.98936i −0.0806463 0.139684i
\(459\) 33.7863 58.5196i 1.57701 2.73146i
\(460\) 12.5319i 0.584304i
\(461\) 21.5594 + 12.4473i 1.00412 + 0.579729i 0.909464 0.415782i \(-0.136492\pi\)
0.0946548 + 0.995510i \(0.469825\pi\)
\(462\) 0 0
\(463\) 10.1069i 0.469706i 0.972031 + 0.234853i \(0.0754608\pi\)
−0.972031 + 0.234853i \(0.924539\pi\)
\(464\) −5.58028 + 9.66533i −0.259058 + 0.448701i
\(465\) 12.7031 + 22.0025i 0.589094 + 1.02034i
\(466\) −3.49076 + 2.01539i −0.161706 + 0.0933613i
\(467\) 11.4825 0.531346 0.265673 0.964063i \(-0.414406\pi\)
0.265673 + 0.964063i \(0.414406\pi\)
\(468\) −36.0542 + 16.6440i −1.66660 + 0.769369i
\(469\) 0 0
\(470\) 7.83797 4.52525i 0.361539 0.208734i
\(471\) −28.3621 49.1247i −1.30686 2.26354i
\(472\) −9.47717 + 16.4149i −0.436222 + 0.755559i
\(473\) 5.10099i 0.234544i
\(474\) −7.88670 4.55339i −0.362248 0.209144i
\(475\) 3.78661 + 2.18620i 0.173741 + 0.100310i
\(476\) 0 0
\(477\) −6.65068 + 11.5193i −0.304514 + 0.527433i
\(478\) −2.07074 3.58662i −0.0947133 0.164048i
\(479\) −0.936316 + 0.540582i −0.0427814 + 0.0246998i −0.521238 0.853411i \(-0.674530\pi\)
0.478457 + 0.878111i \(0.341196\pi\)
\(480\) −30.1154 −1.37457
\(481\) −17.7136 38.3711i −0.807670 1.74957i
\(482\) −0.148784 −0.00677691
\(483\) 0 0
\(484\) 1.55200 + 2.68814i 0.0705454 + 0.122188i
\(485\) 9.57043 16.5765i 0.434571 0.752699i
\(486\) 6.35926i 0.288462i
\(487\) 21.8824 + 12.6338i 0.991588 + 0.572493i 0.905748 0.423816i \(-0.139310\pi\)
0.0858391 + 0.996309i \(0.472643\pi\)
\(488\) −9.87401 5.70076i −0.446976 0.258061i
\(489\) 68.1895i 3.08364i
\(490\) 0 0
\(491\) 20.8590 + 36.1289i 0.941355 + 1.63047i 0.762891 + 0.646527i \(0.223779\pi\)
0.178464 + 0.983946i \(0.442887\pi\)
\(492\) −8.39485 + 4.84677i −0.378469 + 0.218509i
\(493\) −31.4306 −1.41556
\(494\) 0.465769 5.09809i 0.0209559 0.229374i
\(495\) −42.4122 −1.90628
\(496\) 8.60988 4.97091i 0.386595 0.223201i
\(497\) 0 0
\(498\) 8.23757 14.2679i 0.369134 0.639360i
\(499\) 10.4684i 0.468628i −0.972161 0.234314i \(-0.924716\pi\)
0.972161 0.234314i \(-0.0752844\pi\)
\(500\) −17.7075 10.2234i −0.791905 0.457206i
\(501\) −7.59938 4.38750i −0.339515 0.196019i
\(502\) 7.51099i 0.335232i
\(503\) 1.28735 2.22976i 0.0574001 0.0994199i −0.835897 0.548886i \(-0.815052\pi\)
0.893298 + 0.449466i \(0.148386\pi\)
\(504\) 0 0
\(505\) 5.35441 3.09137i 0.238268 0.137564i
\(506\) 8.37508 0.372318
\(507\) 13.4533 + 37.8656i 0.597484 + 1.68167i
\(508\) −10.2529 −0.454900
\(509\) −6.51841 + 3.76340i −0.288923 + 0.166810i −0.637456 0.770487i \(-0.720013\pi\)
0.348533 + 0.937297i \(0.386680\pi\)
\(510\) −9.70176 16.8039i −0.429601 0.744091i
\(511\) 0 0
\(512\) 20.8730i 0.922467i
\(513\) 23.8939 + 13.7952i 1.05494 + 0.609072i
\(514\) 8.52855 + 4.92396i 0.376178 + 0.217187i
\(515\) 23.3871i 1.03056i
\(516\) −3.69567 + 6.40109i −0.162693 + 0.281792i
\(517\) −15.8892 27.5210i −0.698807 1.21037i
\(518\) 0 0
\(519\) 10.9061 0.478726
\(520\) −1.23239 + 13.4892i −0.0540440 + 0.591541i
\(521\) −0.0156677 −0.000686413 −0.000343207 1.00000i \(-0.500109\pi\)
−0.000343207 1.00000i \(0.500109\pi\)
\(522\) 16.4087 9.47355i 0.718188 0.414646i
\(523\) 12.0357 + 20.8465i 0.526286 + 0.911554i 0.999531 + 0.0306229i \(0.00974911\pi\)
−0.473245 + 0.880931i \(0.656918\pi\)
\(524\) −5.01764 + 8.69081i −0.219197 + 0.379660i
\(525\) 0 0
\(526\) 6.23326 + 3.59878i 0.271783 + 0.156914i
\(527\) 24.2473 + 13.9992i 1.05623 + 0.609814i
\(528\) 24.1921i 1.05283i
\(529\) 2.96391 5.13363i 0.128865 0.223202i
\(530\) 1.03572 + 1.79392i 0.0449888 + 0.0779228i
\(531\) −51.7014 + 29.8498i −2.24365 + 1.29537i
\(532\) 0 0
\(533\) 2.82052 + 6.10980i 0.122170 + 0.264645i
\(534\) 0.621687 0.0269030
\(535\) −28.4045 + 16.3994i −1.22804 + 0.709007i
\(536\) 7.30550 + 12.6535i 0.315550 + 0.546548i
\(537\) −10.3470 + 17.9216i −0.446508 + 0.773374i
\(538\) 1.22241i 0.0527020i
\(539\) 0 0
\(540\) −28.8640 16.6646i −1.24211 0.717132i
\(541\) 37.7763i 1.62413i 0.583567 + 0.812065i \(0.301656\pi\)
−0.583567 + 0.812065i \(0.698344\pi\)
\(542\) 1.64835 2.85503i 0.0708028 0.122634i
\(543\) 19.3685 + 33.5472i 0.831182 + 1.43965i
\(544\) −28.7416 + 16.5940i −1.23229 + 0.711461i
\(545\) 25.1445 1.07707
\(546\) 0 0
\(547\) 28.4925 1.21825 0.609126 0.793074i \(-0.291521\pi\)
0.609126 + 0.793074i \(0.291521\pi\)
\(548\) 5.24908 3.03056i 0.224229 0.129459i
\(549\) −17.9554 31.0998i −0.766320 1.32731i
\(550\) 1.76494 3.05697i 0.0752573 0.130349i
\(551\) 12.8333i 0.546717i
\(552\) 23.0197 + 13.2904i 0.979782 + 0.565677i
\(553\) 0 0
\(554\) 6.58663i 0.279839i
\(555\) 32.7023 56.6421i 1.38814 2.40432i
\(556\) −10.8513 18.7950i −0.460198 0.797087i
\(557\) −17.2033 + 9.93232i −0.728927 + 0.420846i −0.818029 0.575177i \(-0.804933\pi\)
0.0891028 + 0.996022i \(0.471600\pi\)
\(558\) −16.8781 −0.714507
\(559\) 4.19189 + 2.95926i 0.177298 + 0.125163i
\(560\) 0 0
\(561\) −59.0026 + 34.0652i −2.49109 + 1.43823i
\(562\) −7.01056 12.1427i −0.295723 0.512207i
\(563\) 7.76983 13.4577i 0.327459 0.567176i −0.654548 0.756021i \(-0.727141\pi\)
0.982007 + 0.188844i \(0.0604742\pi\)
\(564\) 46.0471i 1.93893i
\(565\) 15.8332 + 9.14131i 0.666108 + 0.384578i
\(566\) −7.41628 4.28179i −0.311729 0.179977i
\(567\) 0 0
\(568\) −4.67650 + 8.09994i −0.196222 + 0.339866i
\(569\) −15.5544 26.9410i −0.652075 1.12943i −0.982618 0.185637i \(-0.940565\pi\)
0.330543 0.943791i \(-0.392768\pi\)
\(570\) 6.86116 3.96129i 0.287382 0.165920i
\(571\) 0.602653 0.0252202 0.0126101 0.999920i \(-0.495986\pi\)
0.0126101 + 0.999920i \(0.495986\pi\)
\(572\) 21.6240 + 1.97560i 0.904145 + 0.0826040i
\(573\) 9.38590 0.392102
\(574\) 0 0
\(575\) 3.59774 + 6.23148i 0.150036 + 0.259871i
\(576\) −4.30951 + 7.46429i −0.179563 + 0.311012i
\(577\) 5.21634i 0.217159i 0.994088 + 0.108580i \(0.0346302\pi\)
−0.994088 + 0.108580i \(0.965370\pi\)
\(578\) −10.1928 5.88479i −0.423963 0.244775i
\(579\) 72.1311 + 41.6449i 2.99767 + 1.73070i
\(580\) 15.5027i 0.643714i
\(581\) 0 0
\(582\) 9.26771 + 16.0521i 0.384159 + 0.665383i
\(583\) 6.29887 3.63665i 0.260872 0.150615i
\(584\) 19.4707 0.805704
\(585\) −24.6048 + 34.8535i −1.01728 + 1.44101i
\(586\) 14.0926 0.582158
\(587\) −14.8865 + 8.59475i −0.614433 + 0.354743i −0.774699 0.632331i \(-0.782098\pi\)
0.160265 + 0.987074i \(0.448765\pi\)
\(588\) 0 0
\(589\) −5.71595 + 9.90032i −0.235522 + 0.407936i
\(590\) 9.29711i 0.382756i
\(591\) 24.8932 + 14.3721i 1.02397 + 0.591189i
\(592\) −22.1648 12.7969i −0.910970 0.525949i
\(593\) 10.6452i 0.437147i −0.975820 0.218574i \(-0.929860\pi\)
0.975820 0.218574i \(-0.0701404\pi\)
\(594\) 11.1370 19.2898i 0.456956 0.791471i
\(595\) 0 0
\(596\) −3.19272 + 1.84332i −0.130779 + 0.0755053i
\(597\) 53.7385 2.19937
\(598\) 4.85867 6.88247i 0.198686 0.281445i
\(599\) 25.1472 1.02749 0.513744 0.857944i \(-0.328258\pi\)
0.513744 + 0.857944i \(0.328258\pi\)
\(600\) 9.70219 5.60156i 0.396090 0.228683i
\(601\) −1.62334 2.81170i −0.0662172 0.114692i 0.831016 0.556248i \(-0.187760\pi\)
−0.897233 + 0.441557i \(0.854426\pi\)
\(602\) 0 0
\(603\) 46.0196i 1.87406i
\(604\) −2.83589 1.63730i −0.115391 0.0666208i
\(605\) 2.88803 + 1.66740i 0.117415 + 0.0677896i
\(606\) 5.98718i 0.243213i
\(607\) 8.55622 14.8198i 0.347286 0.601517i −0.638480 0.769638i \(-0.720437\pi\)
0.985766 + 0.168121i \(0.0537699\pi\)
\(608\) −6.77543 11.7354i −0.274780 0.475933i
\(609\) 0 0
\(610\) −5.59245 −0.226432
\(611\) −31.8341 2.90840i −1.28787 0.117661i
\(612\) −67.7254 −2.73764
\(613\) 24.2857 14.0214i 0.980891 0.566318i 0.0783519 0.996926i \(-0.475034\pi\)
0.902539 + 0.430608i \(0.141701\pi\)
\(614\) −1.10318 1.91077i −0.0445208 0.0771122i
\(615\) −5.20717 + 9.01908i −0.209973 + 0.363684i
\(616\) 0 0
\(617\) −36.4533 21.0463i −1.46755 0.847293i −0.468214 0.883615i \(-0.655102\pi\)
−0.999340 + 0.0363226i \(0.988436\pi\)
\(618\) 19.6132 + 11.3237i 0.788957 + 0.455504i
\(619\) 27.1308i 1.09048i −0.838280 0.545239i \(-0.816439\pi\)
0.838280 0.545239i \(-0.183561\pi\)
\(620\) 6.90490 11.9596i 0.277308 0.480311i
\(621\) 22.7022 + 39.3213i 0.911007 + 1.57791i
\(622\) 9.65673 5.57531i 0.387200 0.223550i
\(623\) 0 0
\(624\) 19.8806 + 14.0347i 0.795861 + 0.561837i
\(625\) −13.2599 −0.530398
\(626\) −1.41651 + 0.817820i −0.0566150 + 0.0326867i
\(627\) −13.9090 24.0911i −0.555473 0.962107i
\(628\) −15.4165 + 26.7022i −0.615185 + 1.06553i
\(629\) 72.0776i 2.87392i
\(630\) 0 0
\(631\) 13.8647 + 8.00476i 0.551943 + 0.318665i 0.749905 0.661545i \(-0.230099\pi\)
−0.197962 + 0.980210i \(0.563432\pi\)
\(632\) 10.8423i 0.431284i
\(633\) −33.7296 + 58.4214i −1.34063 + 2.32204i
\(634\) 4.51094 + 7.81317i 0.179152 + 0.310301i
\(635\) −9.53954 + 5.50765i −0.378565 + 0.218565i
\(636\) 10.5390 0.417900
\(637\) 0 0
\(638\) −10.3604 −0.410174
\(639\) −25.5120 + 14.7294i −1.00924 + 0.582685i
\(640\) 10.4137 + 18.0370i 0.411637 + 0.712977i
\(641\) −7.34069 + 12.7145i −0.289940 + 0.502191i −0.973795 0.227427i \(-0.926969\pi\)
0.683855 + 0.729618i \(0.260302\pi\)
\(642\) 31.7613i 1.25352i
\(643\) −32.1673 18.5718i −1.26855 0.732399i −0.293839 0.955855i \(-0.594933\pi\)
−0.974714 + 0.223456i \(0.928266\pi\)
\(644\) 0 0
\(645\) 7.94095i 0.312675i
\(646\) 4.36545 7.56117i 0.171756 0.297490i
\(647\) −7.11422 12.3222i −0.279689 0.484435i 0.691619 0.722263i \(-0.256898\pi\)
−0.971307 + 0.237828i \(0.923565\pi\)
\(648\) 25.7788 14.8834i 1.01269 0.584676i
\(649\) 32.6443 1.28140
\(650\) −1.48825 3.22384i −0.0583740 0.126450i
\(651\) 0 0
\(652\) 32.0993 18.5325i 1.25710 0.725790i
\(653\) 10.9227 + 18.9188i 0.427440 + 0.740348i 0.996645 0.0818478i \(-0.0260821\pi\)
−0.569205 + 0.822196i \(0.692749\pi\)
\(654\) −12.1746 + 21.0870i −0.476064 + 0.824568i
\(655\) 10.7815i 0.421267i
\(656\) 3.52929 + 2.03764i 0.137796 + 0.0795564i
\(657\) 53.1100 + 30.6631i 2.07202 + 1.19628i
\(658\) 0 0
\(659\) −16.5525 + 28.6698i −0.644796 + 1.11682i 0.339553 + 0.940587i \(0.389724\pi\)
−0.984349 + 0.176232i \(0.943609\pi\)
\(660\) 16.8022 + 29.1022i 0.654024 + 1.13280i
\(661\) −20.2155 + 11.6714i −0.786290 + 0.453965i −0.838655 0.544663i \(-0.816658\pi\)
0.0523646 + 0.998628i \(0.483324\pi\)
\(662\) 2.16406 0.0841087
\(663\) −6.23537 + 68.2495i −0.242162 + 2.65059i
\(664\) −19.6149 −0.761206
\(665\) 0 0
\(666\) 21.7251 + 37.6289i 0.841829 + 1.45809i
\(667\) 10.5596 18.2898i 0.408871 0.708185i
\(668\) 4.76974i 0.184547i
\(669\) 5.11806 + 2.95491i 0.197876 + 0.114243i
\(670\) 6.20654 + 3.58335i 0.239780 + 0.138437i
\(671\) 19.6364i 0.758055i
\(672\) 0 0
\(673\) −24.2424 41.9890i −0.934474 1.61856i −0.775569 0.631263i \(-0.782537\pi\)
−0.158906 0.987294i \(-0.550797\pi\)
\(674\) 4.79052 2.76581i 0.184524 0.106535i
\(675\) 19.1368 0.736575
\(676\) 14.1683 16.6241i 0.544936 0.639387i
\(677\) 43.8976 1.68712 0.843560 0.537034i \(-0.180455\pi\)
0.843560 + 0.537034i \(0.180455\pi\)
\(678\) −15.3324 + 8.85216i −0.588837 + 0.339965i
\(679\) 0 0
\(680\) −11.5507 + 20.0064i −0.442948 + 0.767209i
\(681\) 31.9458i 1.22416i
\(682\) 7.99263 + 4.61455i 0.306054 + 0.176700i
\(683\) −38.9086 22.4639i −1.48880 0.859558i −0.488879 0.872351i \(-0.662594\pi\)
−0.999918 + 0.0127938i \(0.995927\pi\)
\(684\) 27.6527i 1.05733i
\(685\) 3.25590 5.63939i 0.124402 0.215470i
\(686\) 0 0
\(687\) −16.3402 + 9.43400i −0.623416 + 0.359929i
\(688\) 3.10741 0.118469
\(689\) 0.665662 7.28603i 0.0253597 0.277576i
\(690\) 13.0379 0.496344
\(691\) −39.3602 + 22.7246i −1.49733 + 0.864486i −0.999995 0.00306990i \(-0.999023\pi\)
−0.497339 + 0.867556i \(0.665689\pi\)
\(692\) −2.96406 5.13391i −0.112677 0.195162i
\(693\) 0 0
\(694\) 3.01643i 0.114502i
\(695\) −20.1926 11.6582i −0.765949 0.442221i
\(696\) −28.4766 16.4410i −1.07940 0.623194i
\(697\) 11.4769i 0.434717i
\(698\) −4.15731 + 7.20067i −0.157356 + 0.272549i
\(699\) 11.0164 + 19.0809i 0.416677 + 0.721706i
\(700\) 0 0
\(701\) 28.7914 1.08744 0.543718 0.839268i \(-0.317016\pi\)
0.543718 + 0.839268i \(0.317016\pi\)
\(702\) −9.39104 20.3428i −0.354442 0.767791i
\(703\) 29.4298 1.10996
\(704\) 4.08154 2.35648i 0.153829 0.0888131i
\(705\) −24.7355 42.8432i −0.931594 1.61357i
\(706\) −10.0426 + 17.3943i −0.377958 + 0.654643i
\(707\) 0 0
\(708\) 40.9645 + 23.6509i 1.53954 + 0.888854i
\(709\) 15.0365 + 8.68132i 0.564707 + 0.326034i 0.755033 0.655687i \(-0.227621\pi\)
−0.190325 + 0.981721i \(0.560954\pi\)
\(710\) 4.58765i 0.172171i
\(711\) −17.0748 + 29.5744i −0.640354 + 1.10913i
\(712\) −0.370082 0.641002i −0.0138694 0.0240226i
\(713\) −16.2926 + 9.40653i −0.610162 + 0.352277i
\(714\) 0 0
\(715\) 21.1807 9.77782i 0.792113 0.365670i
\(716\) 11.2485 0.420374
\(717\) −19.6049 + 11.3189i −0.732157 + 0.422711i
\(718\) 4.49992 + 7.79409i 0.167935 + 0.290873i
\(719\) −4.99354 + 8.64906i −0.186228 + 0.322556i −0.943989 0.329976i \(-0.892960\pi\)
0.757762 + 0.652531i \(0.226293\pi\)
\(720\) 25.8365i 0.962871i
\(721\) 0 0
\(722\) −6.21782 3.58986i −0.231403 0.133601i
\(723\) 0.813267i 0.0302457i
\(724\) 10.5279 18.2349i 0.391267 0.677695i
\(725\) −4.45061 7.70869i −0.165292 0.286294i
\(726\) −2.79668 + 1.61466i −0.103794 + 0.0599257i
\(727\) −8.00409 −0.296855 −0.148428 0.988923i \(-0.547421\pi\)
−0.148428 + 0.988923i \(0.547421\pi\)
\(728\) 0 0
\(729\) −8.14827 −0.301788
\(730\) 8.27088 4.77520i 0.306119 0.176738i
\(731\) 4.37557 + 7.57871i 0.161836 + 0.280309i
\(732\) −14.2266 + 24.6412i −0.525831 + 0.910765i
\(733\) 44.8461i 1.65643i 0.560412 + 0.828214i \(0.310643\pi\)
−0.560412 + 0.828214i \(0.689357\pi\)
\(734\) −8.93516 5.15871i −0.329803 0.190412i
\(735\) 0 0
\(736\) 22.3001i 0.821993i
\(737\) 12.5820 21.7926i 0.463463 0.802742i
\(738\) −3.45927 5.99163i −0.127337 0.220555i
\(739\) −21.7161 + 12.5378i −0.798840 + 0.461210i −0.843065 0.537811i \(-0.819251\pi\)
0.0442255 + 0.999022i \(0.485918\pi\)
\(740\) −35.5513 −1.30689
\(741\) −27.8667 2.54594i −1.02371 0.0935275i
\(742\) 0 0
\(743\) 15.9514 9.20957i 0.585202 0.337866i −0.177996 0.984031i \(-0.556961\pi\)
0.763198 + 0.646165i \(0.223628\pi\)
\(744\) 14.6456 + 25.3670i 0.536935 + 0.929999i
\(745\) −1.98038 + 3.43013i −0.0725556 + 0.125670i
\(746\) 7.67639i 0.281053i
\(747\) −53.5032 30.8901i −1.95758 1.13021i
\(748\) 32.0714 + 18.5164i 1.17265 + 0.677028i
\(749\) 0 0
\(750\) 10.6362 18.4225i 0.388380 0.672694i
\(751\) 5.84588 + 10.1254i 0.213319 + 0.369480i 0.952751 0.303752i \(-0.0982393\pi\)
−0.739432 + 0.673231i \(0.764906\pi\)
\(752\) −16.7651 + 9.67936i −0.611362 + 0.352970i
\(753\) −41.0559 −1.49616
\(754\) −6.01045 + 8.51401i −0.218888 + 0.310062i
\(755\) −3.51810 −0.128037
\(756\) 0 0
\(757\) −7.77449 13.4658i −0.282569 0.489423i 0.689448 0.724335i \(-0.257853\pi\)
−0.972017 + 0.234912i \(0.924520\pi\)
\(758\) −2.04592 + 3.54364i −0.0743112 + 0.128711i
\(759\) 45.7791i 1.66168i
\(760\) −8.16872 4.71621i −0.296311 0.171075i
\(761\) −27.6700 15.9753i −1.00304 0.579103i −0.0938908 0.995582i \(-0.529930\pi\)
−0.909145 + 0.416479i \(0.863264\pi\)
\(762\) 10.6669i 0.386420i
\(763\) 0 0
\(764\) −2.55090 4.41828i −0.0922882 0.159848i
\(765\) −63.0132 + 36.3807i −2.27825 + 1.31535i
\(766\) 11.5060 0.415729
\(767\) 18.9381 26.8265i 0.683815 0.968647i
\(768\) −12.0397 −0.434446
\(769\) 12.5835 7.26510i 0.453773 0.261986i −0.255649 0.966770i \(-0.582289\pi\)
0.709422 + 0.704783i \(0.248956\pi\)
\(770\) 0 0
\(771\) 26.9149 46.6180i 0.969316 1.67891i
\(772\) 45.2730i 1.62941i
\(773\) 36.4686 + 21.0551i 1.31168 + 0.757301i 0.982375 0.186922i \(-0.0598511\pi\)
0.329308 + 0.944222i \(0.393184\pi\)
\(774\) −4.56863 2.63770i −0.164216 0.0948101i
\(775\) 7.92922i 0.284826i
\(776\) 11.0339 19.1113i 0.396094 0.686055i
\(777\) 0 0
\(778\) −1.21606 + 0.702092i −0.0435978 + 0.0251712i
\(779\) −4.68608 −0.167896
\(780\) 33.6631 + 3.07551i 1.20533 + 0.110121i
\(781\) 16.1083 0.576401
\(782\) 12.4431 7.18405i 0.444966 0.256901i
\(783\) −28.0839 48.6427i −1.00364 1.73835i
\(784\) 0 0
\(785\) 33.1257i 1.18231i
\(786\) −9.04170 5.22023i −0.322507 0.186199i
\(787\) −5.27820 3.04737i −0.188148 0.108627i 0.402968 0.915214i \(-0.367979\pi\)
−0.591115 + 0.806587i \(0.701312\pi\)
\(788\) 15.6242i 0.556588i
\(789\) 19.6713 34.0717i 0.700317 1.21298i
\(790\) 2.65907 + 4.60565i 0.0946056 + 0.163862i
\(791\) 0 0
\(792\) −48.8976 −1.73750
\(793\) 16.1368 + 11.3918i 0.573035 + 0.404533i
\(794\) 6.07302 0.215523
\(795\) 9.80575 5.66135i 0.347774 0.200788i
\(796\) −14.6050 25.2967i −0.517662 0.896617i
\(797\) −18.4019 + 31.8731i −0.651830 + 1.12900i 0.330849 + 0.943684i \(0.392665\pi\)
−0.982679 + 0.185318i \(0.940668\pi\)
\(798\) 0 0
\(799\) −47.2143 27.2592i −1.67032 0.964361i
\(800\) −8.13971 4.69946i −0.287782 0.166151i
\(801\) 2.33127i 0.0823712i
\(802\) 4.17172 7.22564i 0.147309 0.255146i
\(803\) −16.7668 29.0410i −0.591689 1.02483i
\(804\) 31.5776 18.2313i 1.11366 0.642969i
\(805\) 0 0
\(806\) 8.42894 3.89112i 0.296897 0.137059i
\(807\) 6.68185 0.235212
\(808\) 6.17319 3.56409i 0.217172 0.125384i
\(809\) 4.36667 + 7.56329i 0.153524 + 0.265911i 0.932521 0.361117i \(-0.117604\pi\)
−0.778997 + 0.627028i \(0.784271\pi\)
\(810\) 7.30032 12.6445i 0.256507 0.444283i
\(811\) 37.1024i 1.30284i 0.758716 + 0.651421i \(0.225827\pi\)
−0.758716 + 0.651421i \(0.774173\pi\)
\(812\) 0 0
\(813\) −15.6059 9.01008i −0.547323 0.315997i
\(814\) 23.7589i 0.832750i
\(815\) 19.9106 34.4861i 0.697437 1.20800i
\(816\) 20.7517 + 35.9431i 0.726456 + 1.25826i
\(817\) −3.09443 + 1.78657i −0.108261 + 0.0625043i
\(818\) −3.58784 −0.125446
\(819\) 0 0
\(820\) 5.66081 0.197684
\(821\) −36.5097 + 21.0789i −1.27420 + 0.735658i −0.975775 0.218776i \(-0.929794\pi\)
−0.298422 + 0.954434i \(0.596460\pi\)
\(822\) 3.15291 + 5.46101i 0.109971 + 0.190475i
\(823\) −9.27261 + 16.0606i −0.323223 + 0.559838i −0.981151 0.193242i \(-0.938100\pi\)
0.657928 + 0.753081i \(0.271433\pi\)
\(824\) 26.9633i 0.939312i
\(825\) −16.7097 9.64736i −0.581757 0.335878i
\(826\) 0 0
\(827\) 12.5050i 0.434841i 0.976078 + 0.217420i \(0.0697642\pi\)
−0.976078 + 0.217420i \(0.930236\pi\)
\(828\) 22.7535 39.4102i 0.790739 1.36960i
\(829\) 22.8833 + 39.6351i 0.794770 + 1.37658i 0.922985 + 0.384836i \(0.125742\pi\)
−0.128215 + 0.991746i \(0.540925\pi\)
\(830\) −8.33212 + 4.81055i −0.289212 + 0.166977i
\(831\) 36.0032 1.24894
\(832\) 0.431336 4.72120i 0.0149539 0.163678i
\(833\) 0 0
\(834\) 19.5539 11.2894i 0.677095 0.390921i
\(835\) 2.56220 + 4.43786i 0.0886687 + 0.153579i
\(836\) −7.56038 + 13.0950i −0.261481 + 0.452899i
\(837\) 50.0343i 1.72944i
\(838\) 8.85701 + 5.11360i 0.305960 + 0.176646i
\(839\) 11.1021 + 6.40978i 0.383286 + 0.221290i 0.679247 0.733910i \(-0.262307\pi\)
−0.295961 + 0.955200i \(0.595640\pi\)
\(840\) 0 0
\(841\) 1.43713 2.48918i 0.0495562 0.0858338i
\(842\) −5.57144 9.65001i −0.192004 0.332561i
\(843\) −66.3731 + 38.3205i −2.28601 + 1.31983i
\(844\) 36.6681 1.26217
\(845\) 4.25243 23.0783i 0.146288 0.793918i
\(846\) 32.8650 1.12992
\(847\) 0 0
\(848\) −2.21537 3.83713i −0.0760761 0.131768i
\(849\) −23.4047 + 40.5382i −0.803249 + 1.39127i
\(850\) 6.05578i 0.207712i
\(851\) 41.9428 + 24.2157i 1.43778 + 0.830104i
\(852\) 20.2139 + 11.6705i 0.692517 + 0.399825i
\(853\) 4.51954i 0.154746i 0.997002 + 0.0773730i \(0.0246532\pi\)
−0.997002 + 0.0773730i \(0.975347\pi\)
\(854\) 0 0
\(855\) −14.8545 25.7287i −0.508012 0.879902i
\(856\) −32.7481 + 18.9071i −1.11931 + 0.646231i
\(857\) 47.2746 1.61487 0.807435 0.589957i \(-0.200855\pi\)
0.807435 + 0.589957i \(0.200855\pi\)
\(858\) −2.05536 + 22.4971i −0.0701690 + 0.768037i
\(859\) −48.0543 −1.63959 −0.819795 0.572657i \(-0.805913\pi\)
−0.819795 + 0.572657i \(0.805913\pi\)
\(860\) 3.73809 2.15819i 0.127468 0.0735936i
\(861\) 0 0
\(862\) −2.97000 + 5.14419i −0.101158 + 0.175212i
\(863\) 27.5799i 0.938831i 0.882977 + 0.469415i \(0.155535\pi\)
−0.882977 + 0.469415i \(0.844465\pi\)
\(864\) −51.3625 29.6542i −1.74739 1.00886i
\(865\) −5.51566 3.18447i −0.187538 0.108275i
\(866\) 5.15631i 0.175218i
\(867\) −32.1669 + 55.7148i −1.09245 + 1.89217i
\(868\) 0 0
\(869\) 16.1715 9.33664i 0.548581 0.316724i
\(870\) −16.1286 −0.546811
\(871\) −10.6095 22.9823i −0.359489 0.778725i
\(872\) 28.9895 0.981710
\(873\) 60.1940 34.7530i 2.03726 1.17621i
\(874\) 2.93329 + 5.08061i 0.0992201 + 0.171854i
\(875\) 0 0
\(876\) 48.5904i 1.64172i
\(877\) 42.8238 + 24.7243i 1.44606 + 0.834882i 0.998243 0.0592452i \(-0.0188694\pi\)
0.447814 + 0.894127i \(0.352203\pi\)
\(878\) −14.3397 8.27903i −0.483941 0.279404i
\(879\) 77.0315i 2.59821i
\(880\) 7.06383 12.2349i 0.238122 0.412439i
\(881\) 0.618953 + 1.07206i 0.0208530 + 0.0361185i 0.876264 0.481832i \(-0.160028\pi\)
−0.855411 + 0.517951i \(0.826695\pi\)
\(882\) 0 0
\(883\) −41.4537 −1.39503 −0.697514 0.716571i \(-0.745711\pi\)
−0.697514 + 0.716571i \(0.745711\pi\)
\(884\) 33.8222 15.6136i 1.13756 0.525143i
\(885\) 50.8190 1.70826
\(886\) −13.0934 + 7.55948i −0.439882 + 0.253966i
\(887\) −0.585862 1.01474i −0.0196713 0.0340717i 0.856022 0.516939i \(-0.172929\pi\)
−0.875693 + 0.482867i \(0.839595\pi\)
\(888\) 37.7030 65.3036i 1.26523 2.19144i
\(889\) 0 0
\(890\) −0.314411 0.181525i −0.0105391 0.00608475i
\(891\) −44.3979 25.6331i −1.48738 0.858742i
\(892\) 3.21234i 0.107557i
\(893\) 11.1301 19.2779i 0.372455 0.645111i
\(894\) −1.91774 3.32163i −0.0641389 0.111092i
\(895\) 10.4658 6.04243i 0.349833 0.201976i
\(896\) 0 0
\(897\) −37.6203 26.5580i −1.25611 0.886747i
\(898\) −11.9975 −0.400361
\(899\) 20.1549 11.6364i 0.672202 0.388096i
\(900\) −9.59002 16.6104i −0.319667 0.553680i
\(901\) 6.23896 10.8062i 0.207850 0.360007i
\(902\) 3.78312i 0.125964i
\(903\) 0 0
\(904\) 18.2544 + 10.5392i 0.607131 + 0.350527i
\(905\) 22.6215i 0.751965i
\(906\) 1.70341 2.95039i 0.0565919 0.0980201i
\(907\) −21.4768 37.1990i −0.713127 1.23517i −0.963677 0.267069i \(-0.913945\pi\)
0.250550 0.968104i \(-0.419388\pi\)
\(908\) −15.0380 + 8.68221i −0.499054 + 0.288129i
\(909\) 22.4513 0.744664
\(910\) 0 0
\(911\) 24.5412 0.813085 0.406543 0.913632i \(-0.366734\pi\)
0.406543 + 0.913632i \(0.366734\pi\)
\(912\) −14.6758 + 8.47307i −0.485964 + 0.280571i
\(913\) 16.8910 + 29.2560i 0.559010 + 0.968234i
\(914\) −4.14080 + 7.17208i −0.136966 + 0.237231i
\(915\) 30.5689i 1.01058i
\(916\) 8.88184 + 5.12794i 0.293464 + 0.169432i
\(917\) 0 0
\(918\) 38.2127i 1.26121i
\(919\) −18.3307 + 31.7498i −0.604675 + 1.04733i 0.387428 + 0.921900i \(0.373364\pi\)
−0.992103 + 0.125428i \(0.959970\pi\)
\(920\) −7.76129 13.4430i −0.255882 0.443201i
\(921\) −10.4445 + 6.03011i −0.344156 + 0.198699i
\(922\) 14.0780 0.463635
\(923\) 9.34499 13.2375i 0.307594 0.435717i
\(924\) 0 0
\(925\) 17.6778 10.2063i 0.581243 0.335581i
\(926\) 2.85774 + 4.94976i 0.0939113 + 0.162659i
\(927\) 42.4626 73.5474i 1.39466 2.41561i
\(928\) 27.5865i 0.905572i
\(929\) −22.4866 12.9826i −0.737762 0.425947i 0.0834933 0.996508i \(-0.473392\pi\)
−0.821255 + 0.570562i \(0.806726\pi\)
\(930\) 12.4425 + 7.18369i 0.408006 + 0.235562i
\(931\) 0 0
\(932\) 5.98804 10.3716i 0.196145 0.339733i
\(933\) −30.4753 52.7847i −0.997716 1.72809i
\(934\) 5.62345 3.24670i 0.184005 0.106235i
\(935\) 39.7865 1.30116
\(936\) −28.3672 + 40.1831i −0.927211 + 1.31343i
\(937\) −11.8632 −0.387554 −0.193777 0.981046i \(-0.562074\pi\)
−0.193777 + 0.981046i \(0.562074\pi\)
\(938\) 0 0
\(939\) 4.47029 + 7.74278i 0.145883 + 0.252676i
\(940\) −13.4452 + 23.2878i −0.438535 + 0.759565i
\(941\) 9.51954i 0.310328i −0.987889 0.155164i \(-0.950409\pi\)
0.987889 0.155164i \(-0.0495906\pi\)
\(942\) −27.7803 16.0389i −0.905130 0.522577i
\(943\) −6.67853 3.85585i −0.217483 0.125564i
\(944\) 19.8862i 0.647241i
\(945\) 0 0
\(946\) 1.44232 + 2.49817i 0.0468938 + 0.0812224i
\(947\) 36.8812 21.2934i 1.19848 0.691942i 0.238263 0.971201i \(-0.423422\pi\)
0.960216 + 0.279258i \(0.0900885\pi\)
\(948\) 27.0576 0.878791
\(949\) −33.5923 3.06904i −1.09045 0.0996254i
\(950\) 2.47261 0.0802222
\(951\) 42.7077 24.6573i 1.38489 0.799567i
\(952\) 0 0
\(953\) 15.7195 27.2270i 0.509204 0.881968i −0.490739 0.871307i \(-0.663273\pi\)
0.999943 0.0106611i \(-0.00339359\pi\)
\(954\) 7.52199i 0.243534i
\(955\) −4.74682 2.74058i −0.153603 0.0886830i
\(956\) 10.6564 + 6.15248i 0.344653 + 0.198985i
\(957\) 56.6313i 1.83063i
\(958\) −0.305702 + 0.529492i −0.00987679 + 0.0171071i
\(959\) 0 0
\(960\) 6.35393 3.66844i 0.205072 0.118398i
\(961\) 10.2686 0.331244
\(962\) −19.5246 13.7834i −0.629499 0.444394i
\(963\) −119.102 −3.83800
\(964\) 0.382834 0.221029i 0.0123303 0.00711888i
\(965\) −24.3197 42.1229i −0.782879 1.35599i
\(966\) 0 0
\(967\) 6.05894i 0.194842i 0.995243 + 0.0974212i \(0.0310594\pi\)
−0.995243 + 0.0974212i \(0.968941\pi\)
\(968\) 3.32965 + 1.92238i 0.107019 + 0.0617875i
\(969\) −41.3302 23.8620i −1.32772 0.766558i
\(970\) 10.8243i 0.347546i
\(971\) −21.7346 + 37.6454i −0.697497 + 1.20810i 0.271835 + 0.962344i \(0.412369\pi\)
−0.969332 + 0.245756i \(0.920964\pi\)
\(972\) −9.44717 16.3630i −0.303018 0.524843i
\(973\) 0 0
\(974\) 14.2890 0.457849
\(975\) −17.6219 + 8.13494i −0.564352 + 0.260527i
\(976\) 11.9621 0.382896
\(977\) −24.9570 + 14.4089i −0.798445 + 0.460982i −0.842927 0.538028i \(-0.819169\pi\)
0.0444824 + 0.999010i \(0.485836\pi\)
\(978\) 19.2808 + 33.3953i 0.616531 + 1.06786i
\(979\) −0.637379 + 1.10397i −0.0203707 + 0.0352831i
\(980\) 0 0
\(981\) 79.0743 + 45.6536i 2.52465 + 1.45761i
\(982\) 20.4311 + 11.7959i 0.651982 + 0.376422i
\(983\) 31.1850i 0.994647i −0.867565 0.497323i \(-0.834316\pi\)
0.867565 0.497323i \(-0.165684\pi\)
\(984\) −6.00343 + 10.3982i −0.191382 + 0.331484i
\(985\) −8.39298 14.5371i −0.267423 0.463189i
\(986\) −15.3929 + 8.88708i −0.490209 + 0.283022i
\(987\) 0 0
\(988\) 6.37514 + 13.8098i 0.202820 + 0.439348i
\(989\) −5.88019 −0.186979
\(990\) −20.7710 + 11.9922i −0.660146 + 0.381136i
\(991\) 31.0698 + 53.8144i 0.986963 + 1.70947i 0.632865 + 0.774262i \(0.281879\pi\)
0.354099 + 0.935208i \(0.384788\pi\)
\(992\) 12.2870 21.2818i 0.390114 0.675697i
\(993\) 11.8290i 0.375382i
\(994\) 0 0
\(995\) −27.1777 15.6910i −0.861590 0.497440i
\(996\) 48.9502i 1.55105i
\(997\) 8.65718 14.9947i 0.274176 0.474886i −0.695751 0.718283i \(-0.744928\pi\)
0.969927 + 0.243397i \(0.0782617\pi\)
\(998\) −2.95996 5.12679i −0.0936958 0.162286i
\(999\) 111.549 64.4029i 3.52926 2.03762i
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.q.j.491.9 32
7.2 even 3 637.2.u.j.361.8 32
7.3 odd 6 637.2.k.j.569.10 32
7.4 even 3 637.2.k.j.569.9 32
7.5 odd 6 637.2.u.j.361.7 32
7.6 odd 2 inner 637.2.q.j.491.10 yes 32
13.2 odd 12 8281.2.a.cx.1.20 32
13.4 even 6 inner 637.2.q.j.589.9 yes 32
13.11 odd 12 8281.2.a.cx.1.14 32
91.4 even 6 637.2.u.j.30.8 32
91.17 odd 6 637.2.u.j.30.7 32
91.30 even 6 637.2.k.j.459.7 32
91.41 even 12 8281.2.a.cx.1.19 32
91.69 odd 6 inner 637.2.q.j.589.10 yes 32
91.76 even 12 8281.2.a.cx.1.13 32
91.82 odd 6 637.2.k.j.459.8 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.k.j.459.7 32 91.30 even 6
637.2.k.j.459.8 32 91.82 odd 6
637.2.k.j.569.9 32 7.4 even 3
637.2.k.j.569.10 32 7.3 odd 6
637.2.q.j.491.9 32 1.1 even 1 trivial
637.2.q.j.491.10 yes 32 7.6 odd 2 inner
637.2.q.j.589.9 yes 32 13.4 even 6 inner
637.2.q.j.589.10 yes 32 91.69 odd 6 inner
637.2.u.j.30.7 32 91.17 odd 6
637.2.u.j.30.8 32 91.4 even 6
637.2.u.j.361.7 32 7.5 odd 6
637.2.u.j.361.8 32 7.2 even 3
8281.2.a.cx.1.13 32 91.76 even 12
8281.2.a.cx.1.14 32 13.11 odd 12
8281.2.a.cx.1.19 32 91.41 even 12
8281.2.a.cx.1.20 32 13.2 odd 12