Properties

Label 637.2.g.l.263.4
Level $637$
Weight $2$
Character 637.263
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(263,637)]
 
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, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.263");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (of order \(3\), 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 \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 263.4
Root \(0.756174 + 1.30973i\) of defining polynomial
Character \(\chi\) \(=\) 637.263
Dual form 637.2.g.l.373.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.425563 - 0.737096i) q^{2} -0.661223 q^{3} +(0.637793 + 1.10469i) q^{4} +(1.72074 + 2.98041i) q^{5} +(-0.281392 + 0.487385i) q^{6} +2.78793 q^{8} -2.56278 q^{9} +O(q^{10})\) \(q+(0.425563 - 0.737096i) q^{2} -0.661223 q^{3} +(0.637793 + 1.10469i) q^{4} +(1.72074 + 2.98041i) q^{5} +(-0.281392 + 0.487385i) q^{6} +2.78793 q^{8} -2.56278 q^{9} +2.92913 q^{10} -0.897986 q^{11} +(-0.421723 - 0.730446i) q^{12} +(3.07517 - 1.88237i) q^{13} +(-1.13779 - 1.97071i) q^{15} +(-0.0891447 + 0.154403i) q^{16} +(0.968404 + 1.67733i) q^{17} +(-1.09063 + 1.88902i) q^{18} -1.03804 q^{19} +(-2.19495 + 3.80177i) q^{20} +(-0.382150 + 0.661902i) q^{22} +(-2.82506 + 4.89315i) q^{23} -1.84345 q^{24} +(-3.42189 + 5.92688i) q^{25} +(-0.0788077 - 3.06776i) q^{26} +3.67824 q^{27} +(0.917969 + 1.58997i) q^{29} -1.93681 q^{30} +(-4.56692 + 7.91014i) q^{31} +(2.86381 + 4.96026i) q^{32} +0.593769 q^{33} +1.64847 q^{34} +(-1.63452 - 2.83108i) q^{36} +(5.30001 - 9.17989i) q^{37} +(-0.441751 + 0.765135i) q^{38} +(-2.03338 + 1.24467i) q^{39} +(4.79731 + 8.30918i) q^{40} +(-2.66571 - 4.61715i) q^{41} +(1.95732 - 3.39018i) q^{43} +(-0.572729 - 0.991996i) q^{44} +(-4.40988 - 7.63814i) q^{45} +(2.40448 + 4.16469i) q^{46} +(3.59565 + 6.22784i) q^{47} +(0.0589445 - 0.102095i) q^{48} +(2.91246 + 5.04452i) q^{50} +(-0.640331 - 1.10909i) q^{51} +(4.04076 + 2.19655i) q^{52} +(4.69324 - 8.12893i) q^{53} +(1.56532 - 2.71122i) q^{54} +(-1.54520 - 2.67637i) q^{55} +0.686375 q^{57} +1.56261 q^{58} +(-0.255259 - 0.442121i) q^{59} +(1.45135 - 2.51382i) q^{60} -1.43619 q^{61} +(3.88702 + 6.73252i) q^{62} +4.51834 q^{64} +(10.9018 + 5.92620i) q^{65} +(0.252686 - 0.437665i) q^{66} -8.44932 q^{67} +(-1.23528 + 2.13957i) q^{68} +(1.86800 - 3.23547i) q^{69} +(1.72419 - 2.98638i) q^{71} -7.14487 q^{72} +(5.45026 - 9.44013i) q^{73} +(-4.51097 - 7.81324i) q^{74} +(2.26263 - 3.91899i) q^{75} +(-0.662054 - 1.14671i) q^{76} +(0.0521095 + 2.02848i) q^{78} +(6.04589 + 10.4718i) q^{79} -0.613579 q^{80} +5.25621 q^{81} -4.53771 q^{82} -1.51669 q^{83} +(-3.33274 + 5.77248i) q^{85} +(-1.66593 - 2.88547i) q^{86} +(-0.606982 - 1.05132i) q^{87} -2.50353 q^{88} +(6.80391 - 11.7847i) q^{89} -7.50673 q^{90} -7.20722 q^{92} +(3.01976 - 5.23037i) q^{93} +6.12069 q^{94} +(-1.78619 - 3.09378i) q^{95} +(-1.89362 - 3.27984i) q^{96} +(0.253120 - 0.438417i) q^{97} +2.30134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23} - 22 q^{24} + 7 q^{25} - 5 q^{26} + 8 q^{27} + 3 q^{29} + 10 q^{30} - 16 q^{31} + 8 q^{32} + 32 q^{33} - 32 q^{34} - 21 q^{36} - 13 q^{37} + 17 q^{38} - 23 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} + 7 q^{45} + 16 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} + 25 q^{52} - 2 q^{53} + 18 q^{54} - 9 q^{55} + 42 q^{57} + 16 q^{58} - 13 q^{59} + 20 q^{60} - 10 q^{61} - 5 q^{62} - 30 q^{64} + 19 q^{65} - 18 q^{66} + 22 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} - 50 q^{72} + 30 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} - 14 q^{80} + 12 q^{81} + 2 q^{82} + 54 q^{83} - q^{85} - 7 q^{86} - 16 q^{87} - 4 q^{89} + 16 q^{90} + 54 q^{92} - 7 q^{93} + 90 q^{94} - 6 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.425563 0.737096i 0.300918 0.521206i −0.675426 0.737428i \(-0.736040\pi\)
0.976344 + 0.216222i \(0.0693735\pi\)
\(3\) −0.661223 −0.381757 −0.190879 0.981614i \(-0.561134\pi\)
−0.190879 + 0.981614i \(0.561134\pi\)
\(4\) 0.637793 + 1.10469i 0.318896 + 0.552345i
\(5\) 1.72074 + 2.98041i 0.769538 + 1.33288i 0.937814 + 0.347139i \(0.112847\pi\)
−0.168276 + 0.985740i \(0.553820\pi\)
\(6\) −0.281392 + 0.487385i −0.114878 + 0.198974i
\(7\) 0 0
\(8\) 2.78793 0.985684
\(9\) −2.56278 −0.854261
\(10\) 2.92913 0.926272
\(11\) −0.897986 −0.270753 −0.135377 0.990794i \(-0.543224\pi\)
−0.135377 + 0.990794i \(0.543224\pi\)
\(12\) −0.421723 0.730446i −0.121741 0.210862i
\(13\) 3.07517 1.88237i 0.852900 0.522075i
\(14\) 0 0
\(15\) −1.13779 1.97071i −0.293777 0.508836i
\(16\) −0.0891447 + 0.154403i −0.0222862 + 0.0386008i
\(17\) 0.968404 + 1.67733i 0.234873 + 0.406811i 0.959236 0.282607i \(-0.0911994\pi\)
−0.724363 + 0.689419i \(0.757866\pi\)
\(18\) −1.09063 + 1.88902i −0.257063 + 0.445246i
\(19\) −1.03804 −0.238142 −0.119071 0.992886i \(-0.537992\pi\)
−0.119071 + 0.992886i \(0.537992\pi\)
\(20\) −2.19495 + 3.80177i −0.490806 + 0.850101i
\(21\) 0 0
\(22\) −0.382150 + 0.661902i −0.0814745 + 0.141118i
\(23\) −2.82506 + 4.89315i −0.589067 + 1.02029i 0.405288 + 0.914189i \(0.367171\pi\)
−0.994355 + 0.106104i \(0.966162\pi\)
\(24\) −1.84345 −0.376292
\(25\) −3.42189 + 5.92688i −0.684378 + 1.18538i
\(26\) −0.0788077 3.06776i −0.0154555 0.601638i
\(27\) 3.67824 0.707878
\(28\) 0 0
\(29\) 0.917969 + 1.58997i 0.170463 + 0.295250i 0.938582 0.345057i \(-0.112140\pi\)
−0.768119 + 0.640307i \(0.778807\pi\)
\(30\) −1.93681 −0.353611
\(31\) −4.56692 + 7.91014i −0.820244 + 1.42070i 0.0852573 + 0.996359i \(0.472829\pi\)
−0.905501 + 0.424345i \(0.860505\pi\)
\(32\) 2.86381 + 4.96026i 0.506254 + 0.876858i
\(33\) 0.593769 0.103362
\(34\) 1.64847 0.282710
\(35\) 0 0
\(36\) −1.63452 2.83108i −0.272421 0.471847i
\(37\) 5.30001 9.17989i 0.871316 1.50916i 0.0106808 0.999943i \(-0.496600\pi\)
0.860636 0.509221i \(-0.170067\pi\)
\(38\) −0.441751 + 0.765135i −0.0716614 + 0.124121i
\(39\) −2.03338 + 1.24467i −0.325601 + 0.199306i
\(40\) 4.79731 + 8.30918i 0.758521 + 1.31380i
\(41\) −2.66571 4.61715i −0.416314 0.721078i 0.579251 0.815149i \(-0.303345\pi\)
−0.995565 + 0.0940715i \(0.970012\pi\)
\(42\) 0 0
\(43\) 1.95732 3.39018i 0.298489 0.516998i −0.677302 0.735706i \(-0.736851\pi\)
0.975790 + 0.218708i \(0.0701841\pi\)
\(44\) −0.572729 0.991996i −0.0863422 0.149549i
\(45\) −4.40988 7.63814i −0.657387 1.13863i
\(46\) 2.40448 + 4.16469i 0.354522 + 0.614050i
\(47\) 3.59565 + 6.22784i 0.524479 + 0.908424i 0.999594 + 0.0285004i \(0.00907317\pi\)
−0.475115 + 0.879924i \(0.657593\pi\)
\(48\) 0.0589445 0.102095i 0.00850791 0.0147361i
\(49\) 0 0
\(50\) 2.91246 + 5.04452i 0.411883 + 0.713403i
\(51\) −0.640331 1.10909i −0.0896643 0.155303i
\(52\) 4.04076 + 2.19655i 0.560352 + 0.304607i
\(53\) 4.69324 8.12893i 0.644666 1.11659i −0.339712 0.940529i \(-0.610330\pi\)
0.984378 0.176065i \(-0.0563370\pi\)
\(54\) 1.56532 2.71122i 0.213013 0.368950i
\(55\) −1.54520 2.67637i −0.208355 0.360881i
\(56\) 0 0
\(57\) 0.686375 0.0909127
\(58\) 1.56261 0.205181
\(59\) −0.255259 0.442121i −0.0332318 0.0575592i 0.848931 0.528503i \(-0.177247\pi\)
−0.882163 + 0.470944i \(0.843913\pi\)
\(60\) 1.45135 2.51382i 0.187369 0.324532i
\(61\) −1.43619 −0.183885 −0.0919426 0.995764i \(-0.529308\pi\)
−0.0919426 + 0.995764i \(0.529308\pi\)
\(62\) 3.88702 + 6.73252i 0.493653 + 0.855031i
\(63\) 0 0
\(64\) 4.51834 0.564792
\(65\) 10.9018 + 5.92620i 1.35220 + 0.735055i
\(66\) 0.252686 0.437665i 0.0311035 0.0538729i
\(67\) −8.44932 −1.03225 −0.516124 0.856514i \(-0.672626\pi\)
−0.516124 + 0.856514i \(0.672626\pi\)
\(68\) −1.23528 + 2.13957i −0.149800 + 0.259461i
\(69\) 1.86800 3.23547i 0.224881 0.389504i
\(70\) 0 0
\(71\) 1.72419 2.98638i 0.204623 0.354418i −0.745389 0.666629i \(-0.767736\pi\)
0.950013 + 0.312211i \(0.101070\pi\)
\(72\) −7.14487 −0.842031
\(73\) 5.45026 9.44013i 0.637905 1.10488i −0.347987 0.937499i \(-0.613135\pi\)
0.985892 0.167384i \(-0.0535320\pi\)
\(74\) −4.51097 7.81324i −0.524390 0.908270i
\(75\) 2.26263 3.91899i 0.261266 0.452526i
\(76\) −0.662054 1.14671i −0.0759428 0.131537i
\(77\) 0 0
\(78\) 0.0521095 + 2.02848i 0.00590024 + 0.229680i
\(79\) 6.04589 + 10.4718i 0.680216 + 1.17817i 0.974915 + 0.222578i \(0.0714472\pi\)
−0.294699 + 0.955590i \(0.595219\pi\)
\(80\) −0.613579 −0.0686002
\(81\) 5.25621 0.584024
\(82\) −4.53771 −0.501107
\(83\) −1.51669 −0.166479 −0.0832393 0.996530i \(-0.526527\pi\)
−0.0832393 + 0.996530i \(0.526527\pi\)
\(84\) 0 0
\(85\) −3.33274 + 5.77248i −0.361487 + 0.626113i
\(86\) −1.66593 2.88547i −0.179642 0.311148i
\(87\) −0.606982 1.05132i −0.0650754 0.112714i
\(88\) −2.50353 −0.266877
\(89\) 6.80391 11.7847i 0.721213 1.24918i −0.239301 0.970945i \(-0.576918\pi\)
0.960514 0.278232i \(-0.0897484\pi\)
\(90\) −7.50673 −0.791279
\(91\) 0 0
\(92\) −7.20722 −0.751405
\(93\) 3.01976 5.23037i 0.313134 0.542364i
\(94\) 6.12069 0.631301
\(95\) −1.78619 3.09378i −0.183260 0.317415i
\(96\) −1.89362 3.27984i −0.193266 0.334747i
\(97\) 0.253120 0.438417i 0.0257005 0.0445145i −0.852889 0.522092i \(-0.825152\pi\)
0.878590 + 0.477578i \(0.158485\pi\)
\(98\) 0 0
\(99\) 2.30134 0.231294
\(100\) −8.72982 −0.872982
\(101\) 5.98654 0.595683 0.297842 0.954615i \(-0.403733\pi\)
0.297842 + 0.954615i \(0.403733\pi\)
\(102\) −1.09000 −0.107927
\(103\) −2.06651 3.57930i −0.203619 0.352679i 0.746073 0.665865i \(-0.231937\pi\)
−0.949692 + 0.313186i \(0.898604\pi\)
\(104\) 8.57338 5.24792i 0.840689 0.514601i
\(105\) 0 0
\(106\) −3.99454 6.91874i −0.387984 0.672008i
\(107\) 7.06169 12.2312i 0.682679 1.18243i −0.291481 0.956577i \(-0.594148\pi\)
0.974160 0.225858i \(-0.0725186\pi\)
\(108\) 2.34596 + 4.06331i 0.225740 + 0.390993i
\(109\) 2.10119 3.63936i 0.201257 0.348588i −0.747677 0.664063i \(-0.768831\pi\)
0.948934 + 0.315475i \(0.102164\pi\)
\(110\) −2.63032 −0.250791
\(111\) −3.50449 + 6.06995i −0.332631 + 0.576135i
\(112\) 0 0
\(113\) −6.88472 + 11.9247i −0.647660 + 1.12178i 0.336020 + 0.941855i \(0.390919\pi\)
−0.983680 + 0.179926i \(0.942414\pi\)
\(114\) 0.292096 0.505925i 0.0273573 0.0473842i
\(115\) −19.4448 −1.81324
\(116\) −1.17095 + 2.02814i −0.108720 + 0.188308i
\(117\) −7.88100 + 4.82410i −0.728599 + 0.445989i
\(118\) −0.434514 −0.0400003
\(119\) 0 0
\(120\) −3.17209 5.49422i −0.289571 0.501552i
\(121\) −10.1936 −0.926693
\(122\) −0.611189 + 1.05861i −0.0553344 + 0.0958420i
\(123\) 1.76263 + 3.05297i 0.158931 + 0.275277i
\(124\) −11.6510 −1.04629
\(125\) −6.34531 −0.567542
\(126\) 0 0
\(127\) −0.972482 1.68439i −0.0862938 0.149465i 0.819648 0.572868i \(-0.194169\pi\)
−0.905942 + 0.423402i \(0.860836\pi\)
\(128\) −3.80478 + 6.59007i −0.336298 + 0.582485i
\(129\) −1.29423 + 2.24167i −0.113950 + 0.197368i
\(130\) 9.00758 5.51370i 0.790017 0.483584i
\(131\) −6.01770 10.4230i −0.525769 0.910659i −0.999549 0.0300158i \(-0.990444\pi\)
0.473780 0.880643i \(-0.342889\pi\)
\(132\) 0.378702 + 0.655931i 0.0329618 + 0.0570914i
\(133\) 0 0
\(134\) −3.59571 + 6.22796i −0.310622 + 0.538014i
\(135\) 6.32930 + 10.9627i 0.544739 + 0.943516i
\(136\) 2.69985 + 4.67627i 0.231510 + 0.400987i
\(137\) −4.35857 7.54927i −0.372378 0.644978i 0.617553 0.786529i \(-0.288124\pi\)
−0.989931 + 0.141552i \(0.954791\pi\)
\(138\) −1.58990 2.75379i −0.135341 0.234418i
\(139\) 2.10625 3.64813i 0.178650 0.309430i −0.762769 0.646672i \(-0.776160\pi\)
0.941418 + 0.337241i \(0.109494\pi\)
\(140\) 0 0
\(141\) −2.37752 4.11799i −0.200224 0.346798i
\(142\) −1.46750 2.54178i −0.123150 0.213302i
\(143\) −2.76146 + 1.69034i −0.230925 + 0.141353i
\(144\) 0.228459 0.395702i 0.0190382 0.0329751i
\(145\) −3.15917 + 5.47184i −0.262355 + 0.454412i
\(146\) −4.63885 8.03473i −0.383914 0.664959i
\(147\) 0 0
\(148\) 13.5212 1.11144
\(149\) 5.86484 0.480466 0.240233 0.970715i \(-0.422776\pi\)
0.240233 + 0.970715i \(0.422776\pi\)
\(150\) −1.92578 3.33555i −0.157240 0.272347i
\(151\) 8.42840 14.5984i 0.685893 1.18800i −0.287262 0.957852i \(-0.592745\pi\)
0.973155 0.230150i \(-0.0739216\pi\)
\(152\) −2.89398 −0.234733
\(153\) −2.48181 4.29862i −0.200643 0.347523i
\(154\) 0 0
\(155\) −31.4339 −2.52483
\(156\) −2.67184 1.45241i −0.213919 0.116286i
\(157\) −0.969500 + 1.67922i −0.0773746 + 0.134017i −0.902116 0.431493i \(-0.857987\pi\)
0.824742 + 0.565509i \(0.191320\pi\)
\(158\) 10.2916 0.818757
\(159\) −3.10328 + 5.37504i −0.246106 + 0.426268i
\(160\) −9.85573 + 17.0706i −0.779164 + 1.34955i
\(161\) 0 0
\(162\) 2.23685 3.87433i 0.175743 0.304396i
\(163\) −11.8959 −0.931762 −0.465881 0.884847i \(-0.654262\pi\)
−0.465881 + 0.884847i \(0.654262\pi\)
\(164\) 3.40035 5.88957i 0.265522 0.459898i
\(165\) 1.02172 + 1.76968i 0.0795410 + 0.137769i
\(166\) −0.645448 + 1.11795i −0.0500965 + 0.0867696i
\(167\) 8.28801 + 14.3553i 0.641346 + 1.11084i 0.985133 + 0.171796i \(0.0549569\pi\)
−0.343787 + 0.939048i \(0.611710\pi\)
\(168\) 0 0
\(169\) 5.91338 11.5772i 0.454875 0.890555i
\(170\) 2.83658 + 4.91310i 0.217556 + 0.376818i
\(171\) 2.66027 0.203436
\(172\) 4.99346 0.380748
\(173\) 9.98656 0.759264 0.379632 0.925138i \(-0.376051\pi\)
0.379632 + 0.925138i \(0.376051\pi\)
\(174\) −1.03324 −0.0783295
\(175\) 0 0
\(176\) 0.0800507 0.138652i 0.00603405 0.0104513i
\(177\) 0.168783 + 0.292341i 0.0126865 + 0.0219737i
\(178\) −5.79098 10.0303i −0.434052 0.751801i
\(179\) 9.17657 0.685889 0.342945 0.939356i \(-0.388576\pi\)
0.342945 + 0.939356i \(0.388576\pi\)
\(180\) 5.62518 9.74310i 0.419276 0.726208i
\(181\) −6.00489 −0.446340 −0.223170 0.974780i \(-0.571640\pi\)
−0.223170 + 0.974780i \(0.571640\pi\)
\(182\) 0 0
\(183\) 0.949642 0.0701995
\(184\) −7.87609 + 13.6418i −0.580633 + 1.00569i
\(185\) 36.4797 2.68204
\(186\) −2.57019 4.45170i −0.188456 0.326415i
\(187\) −0.869614 1.50622i −0.0635925 0.110145i
\(188\) −4.58655 + 7.94415i −0.334509 + 0.579386i
\(189\) 0 0
\(190\) −3.04055 −0.220585
\(191\) 1.31612 0.0952313 0.0476156 0.998866i \(-0.484838\pi\)
0.0476156 + 0.998866i \(0.484838\pi\)
\(192\) −2.98763 −0.215614
\(193\) −16.4254 −1.18233 −0.591163 0.806552i \(-0.701331\pi\)
−0.591163 + 0.806552i \(0.701331\pi\)
\(194\) −0.215437 0.373148i −0.0154675 0.0267905i
\(195\) −7.20852 3.91854i −0.516213 0.280613i
\(196\) 0 0
\(197\) 12.7938 + 22.1594i 0.911517 + 1.57879i 0.811922 + 0.583766i \(0.198421\pi\)
0.0995951 + 0.995028i \(0.468245\pi\)
\(198\) 0.979367 1.69631i 0.0696006 0.120552i
\(199\) −12.6894 21.9787i −0.899528 1.55803i −0.828099 0.560582i \(-0.810578\pi\)
−0.0714284 0.997446i \(-0.522756\pi\)
\(200\) −9.54000 + 16.5238i −0.674580 + 1.16841i
\(201\) 5.58688 0.394068
\(202\) 2.54765 4.41266i 0.179252 0.310473i
\(203\) 0 0
\(204\) 0.816797 1.41473i 0.0571873 0.0990512i
\(205\) 9.17399 15.8898i 0.640740 1.10979i
\(206\) −3.51772 −0.245091
\(207\) 7.24003 12.5401i 0.503217 0.871597i
\(208\) 0.0165082 + 0.642619i 0.00114464 + 0.0445576i
\(209\) 0.932145 0.0644778
\(210\) 0 0
\(211\) 2.84824 + 4.93330i 0.196081 + 0.339622i 0.947254 0.320483i \(-0.103845\pi\)
−0.751173 + 0.660105i \(0.770512\pi\)
\(212\) 11.9733 0.822327
\(213\) −1.14007 + 1.97466i −0.0781165 + 0.135302i
\(214\) −6.01038 10.4103i −0.410861 0.711633i
\(215\) 13.4722 0.918794
\(216\) 10.2547 0.697744
\(217\) 0 0
\(218\) −1.78837 3.09755i −0.121124 0.209793i
\(219\) −3.60384 + 6.24203i −0.243525 + 0.421797i
\(220\) 1.97104 3.41393i 0.132887 0.230167i
\(221\) 6.13536 + 3.33517i 0.412709 + 0.224348i
\(222\) 2.98276 + 5.16629i 0.200190 + 0.346739i
\(223\) 1.17906 + 2.04219i 0.0789558 + 0.136755i 0.902800 0.430061i \(-0.141508\pi\)
−0.823844 + 0.566817i \(0.808175\pi\)
\(224\) 0 0
\(225\) 8.76956 15.1893i 0.584637 1.01262i
\(226\) 5.85976 + 10.1494i 0.389786 + 0.675129i
\(227\) 13.1463 + 22.7701i 0.872551 + 1.51130i 0.859349 + 0.511390i \(0.170869\pi\)
0.0132022 + 0.999913i \(0.495797\pi\)
\(228\) 0.437765 + 0.758232i 0.0289917 + 0.0502151i
\(229\) 0.0342777 + 0.0593708i 0.00226514 + 0.00392333i 0.867156 0.498037i \(-0.165946\pi\)
−0.864891 + 0.501960i \(0.832612\pi\)
\(230\) −8.27498 + 14.3327i −0.545636 + 0.945069i
\(231\) 0 0
\(232\) 2.55924 + 4.43273i 0.168022 + 0.291023i
\(233\) −7.33514 12.7048i −0.480541 0.832322i 0.519210 0.854647i \(-0.326226\pi\)
−0.999751 + 0.0223253i \(0.992893\pi\)
\(234\) 0.201967 + 7.86202i 0.0132030 + 0.513956i
\(235\) −12.3743 + 21.4330i −0.807213 + 1.39813i
\(236\) 0.325604 0.563963i 0.0211950 0.0367109i
\(237\) −3.99768 6.92419i −0.259677 0.449774i
\(238\) 0 0
\(239\) 3.35434 0.216974 0.108487 0.994098i \(-0.465399\pi\)
0.108487 + 0.994098i \(0.465399\pi\)
\(240\) 0.405713 0.0261886
\(241\) −4.28989 7.43031i −0.276336 0.478628i 0.694135 0.719845i \(-0.255787\pi\)
−0.970471 + 0.241216i \(0.922454\pi\)
\(242\) −4.33802 + 7.51368i −0.278859 + 0.482998i
\(243\) −14.5103 −0.930833
\(244\) −0.915991 1.58654i −0.0586403 0.101568i
\(245\) 0 0
\(246\) 3.00044 0.191301
\(247\) −3.19215 + 1.95397i −0.203112 + 0.124328i
\(248\) −12.7323 + 22.0530i −0.808501 + 1.40036i
\(249\) 1.00287 0.0635544
\(250\) −2.70033 + 4.67711i −0.170784 + 0.295806i
\(251\) 10.7575 18.6326i 0.679010 1.17608i −0.296270 0.955104i \(-0.595743\pi\)
0.975280 0.220975i \(-0.0709238\pi\)
\(252\) 0 0
\(253\) 2.53687 4.39399i 0.159492 0.276248i
\(254\) −1.65541 −0.103870
\(255\) 2.20369 3.81690i 0.138000 0.239023i
\(256\) 7.75668 + 13.4350i 0.484793 + 0.839686i
\(257\) 2.46896 4.27636i 0.154010 0.266752i −0.778688 0.627411i \(-0.784115\pi\)
0.932698 + 0.360659i \(0.117448\pi\)
\(258\) 1.10155 + 1.90794i 0.0685795 + 0.118783i
\(259\) 0 0
\(260\) 0.406471 + 15.8228i 0.0252083 + 0.981288i
\(261\) −2.35256 4.07475i −0.145620 0.252221i
\(262\) −10.2436 −0.632854
\(263\) −8.95439 −0.552151 −0.276076 0.961136i \(-0.589034\pi\)
−0.276076 + 0.961136i \(0.589034\pi\)
\(264\) 1.65539 0.101882
\(265\) 32.3034 1.98438
\(266\) 0 0
\(267\) −4.49890 + 7.79233i −0.275328 + 0.476883i
\(268\) −5.38891 9.33387i −0.329180 0.570157i
\(269\) −2.41172 4.17723i −0.147045 0.254690i 0.783089 0.621910i \(-0.213643\pi\)
−0.930134 + 0.367220i \(0.880310\pi\)
\(270\) 10.7740 0.655688
\(271\) −3.71072 + 6.42715i −0.225410 + 0.390422i −0.956442 0.291921i \(-0.905706\pi\)
0.731032 + 0.682343i \(0.239039\pi\)
\(272\) −0.345312 −0.0209376
\(273\) 0 0
\(274\) −7.41938 −0.448221
\(275\) 3.07281 5.32226i 0.185297 0.320944i
\(276\) 4.76558 0.286854
\(277\) −1.90816 3.30503i −0.114650 0.198580i 0.802990 0.595993i \(-0.203241\pi\)
−0.917640 + 0.397413i \(0.869908\pi\)
\(278\) −1.79268 3.10502i −0.107518 0.186226i
\(279\) 11.7040 20.2720i 0.700702 1.21365i
\(280\) 0 0
\(281\) 8.54978 0.510037 0.255019 0.966936i \(-0.417918\pi\)
0.255019 + 0.966936i \(0.417918\pi\)
\(282\) −4.04714 −0.241004
\(283\) −15.2643 −0.907371 −0.453686 0.891162i \(-0.649891\pi\)
−0.453686 + 0.891162i \(0.649891\pi\)
\(284\) 4.39870 0.261015
\(285\) 1.18107 + 2.04568i 0.0699607 + 0.121176i
\(286\) 0.0707683 + 2.75481i 0.00418461 + 0.162895i
\(287\) 0 0
\(288\) −7.33932 12.7121i −0.432474 0.749066i
\(289\) 6.62439 11.4738i 0.389670 0.674928i
\(290\) 2.68885 + 4.65723i 0.157895 + 0.273482i
\(291\) −0.167369 + 0.289892i −0.00981135 + 0.0169938i
\(292\) 13.9045 0.813702
\(293\) −2.96982 + 5.14388i −0.173499 + 0.300509i −0.939641 0.342163i \(-0.888841\pi\)
0.766142 + 0.642671i \(0.222174\pi\)
\(294\) 0 0
\(295\) 0.878467 1.52155i 0.0511463 0.0885881i
\(296\) 14.7761 25.5929i 0.858842 1.48756i
\(297\) −3.30301 −0.191660
\(298\) 2.49586 4.32295i 0.144581 0.250422i
\(299\) 0.523159 + 20.3651i 0.0302551 + 1.17774i
\(300\) 5.77236 0.333267
\(301\) 0 0
\(302\) −7.17362 12.4251i −0.412796 0.714983i
\(303\) −3.95844 −0.227406
\(304\) 0.0925356 0.160276i 0.00530728 0.00919248i
\(305\) −2.47131 4.28043i −0.141507 0.245097i
\(306\) −4.22467 −0.241508
\(307\) −22.2133 −1.26778 −0.633891 0.773422i \(-0.718543\pi\)
−0.633891 + 0.773422i \(0.718543\pi\)
\(308\) 0 0
\(309\) 1.36642 + 2.36672i 0.0777332 + 0.134638i
\(310\) −13.3771 + 23.1698i −0.759769 + 1.31596i
\(311\) 4.92130 8.52394i 0.279061 0.483348i −0.692091 0.721811i \(-0.743310\pi\)
0.971152 + 0.238463i \(0.0766435\pi\)
\(312\) −5.66892 + 3.47005i −0.320939 + 0.196453i
\(313\) −10.4563 18.1108i −0.591023 1.02368i −0.994095 0.108513i \(-0.965391\pi\)
0.403072 0.915168i \(-0.367942\pi\)
\(314\) 0.825166 + 1.42923i 0.0465668 + 0.0806561i
\(315\) 0 0
\(316\) −7.71205 + 13.3577i −0.433837 + 0.751427i
\(317\) 12.6801 + 21.9626i 0.712188 + 1.23355i 0.964034 + 0.265778i \(0.0856288\pi\)
−0.251847 + 0.967767i \(0.581038\pi\)
\(318\) 2.64128 + 4.57483i 0.148116 + 0.256544i
\(319\) −0.824324 1.42777i −0.0461533 0.0799398i
\(320\) 7.77489 + 13.4665i 0.434629 + 0.752800i
\(321\) −4.66935 + 8.08755i −0.260618 + 0.451403i
\(322\) 0 0
\(323\) −1.00524 1.74113i −0.0559331 0.0968790i
\(324\) 3.35237 + 5.80648i 0.186243 + 0.322582i
\(325\) 0.633681 + 24.6674i 0.0351503 + 1.36830i
\(326\) −5.06247 + 8.76845i −0.280384 + 0.485640i
\(327\) −1.38935 + 2.40643i −0.0768314 + 0.133076i
\(328\) −7.43183 12.8723i −0.410354 0.710755i
\(329\) 0 0
\(330\) 1.73923 0.0957413
\(331\) 1.78283 0.0979935 0.0489967 0.998799i \(-0.484398\pi\)
0.0489967 + 0.998799i \(0.484398\pi\)
\(332\) −0.967335 1.67547i −0.0530894 0.0919536i
\(333\) −13.5828 + 23.5261i −0.744332 + 1.28922i
\(334\) 14.1083 0.771971
\(335\) −14.5391 25.1824i −0.794354 1.37586i
\(336\) 0 0
\(337\) 9.56149 0.520848 0.260424 0.965494i \(-0.416138\pi\)
0.260424 + 0.965494i \(0.416138\pi\)
\(338\) −6.01701 9.28556i −0.327282 0.505068i
\(339\) 4.55234 7.88488i 0.247249 0.428248i
\(340\) −8.50240 −0.461107
\(341\) 4.10103 7.10320i 0.222083 0.384660i
\(342\) 1.13211 1.96087i 0.0612176 0.106032i
\(343\) 0 0
\(344\) 5.45689 9.45160i 0.294216 0.509596i
\(345\) 12.8573 0.692216
\(346\) 4.24991 7.36106i 0.228477 0.395733i
\(347\) −0.316694 0.548531i −0.0170010 0.0294467i 0.857400 0.514651i \(-0.172079\pi\)
−0.874401 + 0.485204i \(0.838745\pi\)
\(348\) 0.774258 1.34105i 0.0415046 0.0718881i
\(349\) 15.2994 + 26.4994i 0.818960 + 1.41848i 0.906449 + 0.422315i \(0.138783\pi\)
−0.0874885 + 0.996166i \(0.527884\pi\)
\(350\) 0 0
\(351\) 11.3112 6.92381i 0.603749 0.369565i
\(352\) −2.57166 4.45425i −0.137070 0.237412i
\(353\) 1.10035 0.0585655 0.0292828 0.999571i \(-0.490678\pi\)
0.0292828 + 0.999571i \(0.490678\pi\)
\(354\) 0.287311 0.0152704
\(355\) 11.8675 0.629862
\(356\) 17.3579 0.919969
\(357\) 0 0
\(358\) 3.90521 6.76402i 0.206397 0.357489i
\(359\) 4.88693 + 8.46441i 0.257922 + 0.446734i 0.965685 0.259716i \(-0.0836288\pi\)
−0.707763 + 0.706450i \(0.750295\pi\)
\(360\) −12.2945 21.2946i −0.647975 1.12233i
\(361\) −17.9225 −0.943288
\(362\) −2.55546 + 4.42618i −0.134312 + 0.232635i
\(363\) 6.74026 0.353772
\(364\) 0 0
\(365\) 37.5139 1.96357
\(366\) 0.404132 0.699977i 0.0211243 0.0365884i
\(367\) 11.1473 0.581882 0.290941 0.956741i \(-0.406032\pi\)
0.290941 + 0.956741i \(0.406032\pi\)
\(368\) −0.503679 0.872397i −0.0262561 0.0454769i
\(369\) 6.83165 + 11.8328i 0.355641 + 0.615989i
\(370\) 15.5244 26.8891i 0.807076 1.39790i
\(371\) 0 0
\(372\) 7.70391 0.399429
\(373\) −30.7301 −1.59115 −0.795573 0.605858i \(-0.792830\pi\)
−0.795573 + 0.605858i \(0.792830\pi\)
\(374\) −1.48030 −0.0765445
\(375\) 4.19567 0.216663
\(376\) 10.0244 + 17.3628i 0.516970 + 0.895419i
\(377\) 5.81582 + 3.16147i 0.299530 + 0.162824i
\(378\) 0 0
\(379\) −11.3286 19.6217i −0.581912 1.00790i −0.995253 0.0973246i \(-0.968972\pi\)
0.413341 0.910576i \(-0.364362\pi\)
\(380\) 2.27844 3.94638i 0.116882 0.202445i
\(381\) 0.643028 + 1.11376i 0.0329433 + 0.0570595i
\(382\) 0.560093 0.970109i 0.0286568 0.0496351i
\(383\) 0.589263 0.0301099 0.0150550 0.999887i \(-0.495208\pi\)
0.0150550 + 0.999887i \(0.495208\pi\)
\(384\) 2.51581 4.35751i 0.128384 0.222368i
\(385\) 0 0
\(386\) −6.99004 + 12.1071i −0.355783 + 0.616235i
\(387\) −5.01619 + 8.68830i −0.254988 + 0.441651i
\(388\) 0.645753 0.0327832
\(389\) −2.84973 + 4.93587i −0.144487 + 0.250259i −0.929181 0.369624i \(-0.879486\pi\)
0.784695 + 0.619883i \(0.212820\pi\)
\(390\) −5.95602 + 3.64579i −0.301595 + 0.184612i
\(391\) −10.9432 −0.553422
\(392\) 0 0
\(393\) 3.97904 + 6.89191i 0.200716 + 0.347651i
\(394\) 21.7782 1.09717
\(395\) −20.8068 + 36.0384i −1.04690 + 1.81329i
\(396\) 1.46778 + 2.54227i 0.0737588 + 0.127754i
\(397\) 25.5283 1.28123 0.640614 0.767863i \(-0.278680\pi\)
0.640614 + 0.767863i \(0.278680\pi\)
\(398\) −21.6005 −1.08274
\(399\) 0 0
\(400\) −0.610086 1.05670i −0.0305043 0.0528350i
\(401\) −12.7506 + 22.0846i −0.636733 + 1.10285i 0.349413 + 0.936969i \(0.386381\pi\)
−0.986145 + 0.165884i \(0.946952\pi\)
\(402\) 2.37757 4.11807i 0.118582 0.205391i
\(403\) 0.845724 + 32.9217i 0.0421285 + 1.63995i
\(404\) 3.81817 + 6.61327i 0.189961 + 0.329022i
\(405\) 9.04457 + 15.6657i 0.449428 + 0.778433i
\(406\) 0 0
\(407\) −4.75934 + 8.24341i −0.235912 + 0.408611i
\(408\) −1.78520 3.09206i −0.0883807 0.153080i
\(409\) 0.0734938 + 0.127295i 0.00363403 + 0.00629433i 0.867837 0.496850i \(-0.165510\pi\)
−0.864203 + 0.503144i \(0.832177\pi\)
\(410\) −7.80822 13.5242i −0.385621 0.667914i
\(411\) 2.88199 + 4.99175i 0.142158 + 0.246225i
\(412\) 2.63601 4.56570i 0.129867 0.224936i
\(413\) 0 0
\(414\) −6.16217 10.6732i −0.302854 0.524559i
\(415\) −2.60983 4.52036i −0.128112 0.221896i
\(416\) 18.1437 + 9.86292i 0.889570 + 0.483569i
\(417\) −1.39270 + 2.41223i −0.0682008 + 0.118127i
\(418\) 0.396686 0.687080i 0.0194026 0.0336062i
\(419\) 6.84795 + 11.8610i 0.334544 + 0.579447i 0.983397 0.181466i \(-0.0580844\pi\)
−0.648853 + 0.760914i \(0.724751\pi\)
\(420\) 0 0
\(421\) 3.44169 0.167738 0.0838688 0.996477i \(-0.473272\pi\)
0.0838688 + 0.996477i \(0.473272\pi\)
\(422\) 4.84842 0.236017
\(423\) −9.21486 15.9606i −0.448042 0.776032i
\(424\) 13.0844 22.6629i 0.635437 1.10061i
\(425\) −13.2551 −0.642966
\(426\) 0.970345 + 1.68069i 0.0470134 + 0.0814295i
\(427\) 0 0
\(428\) 18.0156 0.870816
\(429\) 1.82594 1.11769i 0.0881574 0.0539627i
\(430\) 5.73325 9.93028i 0.276482 0.478881i
\(431\) 22.2910 1.07372 0.536861 0.843671i \(-0.319610\pi\)
0.536861 + 0.843671i \(0.319610\pi\)
\(432\) −0.327896 + 0.567932i −0.0157759 + 0.0273246i
\(433\) −12.9481 + 22.4268i −0.622247 + 1.07776i 0.366819 + 0.930292i \(0.380447\pi\)
−0.989066 + 0.147472i \(0.952886\pi\)
\(434\) 0 0
\(435\) 2.08892 3.61811i 0.100156 0.173475i
\(436\) 5.36049 0.256721
\(437\) 2.93253 5.07929i 0.140282 0.242975i
\(438\) 3.06732 + 5.31275i 0.146562 + 0.253853i
\(439\) −13.9919 + 24.2347i −0.667798 + 1.15666i 0.310721 + 0.950501i \(0.399430\pi\)
−0.978519 + 0.206159i \(0.933904\pi\)
\(440\) −4.30792 7.46153i −0.205372 0.355715i
\(441\) 0 0
\(442\) 5.06932 3.10302i 0.241123 0.147596i
\(443\) −16.6044 28.7597i −0.788900 1.36642i −0.926641 0.375947i \(-0.877317\pi\)
0.137741 0.990468i \(-0.456016\pi\)
\(444\) −8.94055 −0.424300
\(445\) 46.8310 2.22000
\(446\) 2.00706 0.0950370
\(447\) −3.87796 −0.183421
\(448\) 0 0
\(449\) −9.84320 + 17.0489i −0.464529 + 0.804589i −0.999180 0.0404845i \(-0.987110\pi\)
0.534651 + 0.845073i \(0.320443\pi\)
\(450\) −7.46399 12.9280i −0.351856 0.609433i
\(451\) 2.39377 + 4.14614i 0.112718 + 0.195234i
\(452\) −17.5641 −0.826146
\(453\) −5.57305 + 9.65281i −0.261845 + 0.453528i
\(454\) 22.3783 1.05027
\(455\) 0 0
\(456\) 1.91357 0.0896111
\(457\) 0.373471 0.646871i 0.0174702 0.0302593i −0.857158 0.515053i \(-0.827772\pi\)
0.874628 + 0.484794i \(0.161105\pi\)
\(458\) 0.0583493 0.00272648
\(459\) 3.56203 + 6.16961i 0.166261 + 0.287973i
\(460\) −12.4017 21.4805i −0.578235 1.00153i
\(461\) −16.5855 + 28.7269i −0.772464 + 1.33795i 0.163744 + 0.986503i \(0.447643\pi\)
−0.936209 + 0.351445i \(0.885691\pi\)
\(462\) 0 0
\(463\) −30.7521 −1.42917 −0.714586 0.699548i \(-0.753385\pi\)
−0.714586 + 0.699548i \(0.753385\pi\)
\(464\) −0.327328 −0.0151958
\(465\) 20.7848 0.963874
\(466\) −12.4863 −0.578414
\(467\) −14.8033 25.6400i −0.685013 1.18648i −0.973433 0.228973i \(-0.926463\pi\)
0.288420 0.957504i \(-0.406870\pi\)
\(468\) −10.3556 5.62928i −0.478687 0.260214i
\(469\) 0 0
\(470\) 10.5321 + 18.2422i 0.485810 + 0.841448i
\(471\) 0.641056 1.11034i 0.0295383 0.0511618i
\(472\) −0.711644 1.23260i −0.0327561 0.0567352i
\(473\) −1.75765 + 3.04434i −0.0808168 + 0.139979i
\(474\) −6.80506 −0.312567
\(475\) 3.55205 6.15234i 0.162979 0.282289i
\(476\) 0 0
\(477\) −12.0278 + 20.8327i −0.550714 + 0.953864i
\(478\) 1.42748 2.47247i 0.0652915 0.113088i
\(479\) −14.0905 −0.643813 −0.321907 0.946771i \(-0.604324\pi\)
−0.321907 + 0.946771i \(0.604324\pi\)
\(480\) 6.51684 11.2875i 0.297452 0.515201i
\(481\) −0.981481 38.2063i −0.0447517 1.74206i
\(482\) −7.30247 −0.332618
\(483\) 0 0
\(484\) −6.50142 11.2608i −0.295519 0.511854i
\(485\) 1.74222 0.0791100
\(486\) −6.17502 + 10.6955i −0.280105 + 0.485156i
\(487\) 8.39773 + 14.5453i 0.380537 + 0.659110i 0.991139 0.132828i \(-0.0424057\pi\)
−0.610602 + 0.791938i \(0.709072\pi\)
\(488\) −4.00400 −0.181253
\(489\) 7.86587 0.355707
\(490\) 0 0
\(491\) −10.8345 18.7659i −0.488954 0.846893i 0.510965 0.859601i \(-0.329288\pi\)
−0.999919 + 0.0127081i \(0.995955\pi\)
\(492\) −2.24839 + 3.89432i −0.101365 + 0.175570i
\(493\) −1.77793 + 3.07947i −0.0800740 + 0.138692i
\(494\) 0.0818055 + 3.18446i 0.00368060 + 0.143276i
\(495\) 3.96001 + 6.85895i 0.177989 + 0.308287i
\(496\) −0.814234 1.41029i −0.0365602 0.0633241i
\(497\) 0 0
\(498\) 0.426785 0.739213i 0.0191247 0.0331249i
\(499\) 11.6524 + 20.1825i 0.521633 + 0.903495i 0.999683 + 0.0251622i \(0.00801023\pi\)
−0.478051 + 0.878332i \(0.658656\pi\)
\(500\) −4.04699 7.00960i −0.180987 0.313479i
\(501\) −5.48023 9.49203i −0.244838 0.424073i
\(502\) −9.15601 15.8587i −0.408653 0.707807i
\(503\) −21.9415 + 38.0037i −0.978322 + 1.69450i −0.309816 + 0.950796i \(0.600268\pi\)
−0.668506 + 0.743707i \(0.733066\pi\)
\(504\) 0 0
\(505\) 10.3013 + 17.8423i 0.458401 + 0.793974i
\(506\) −2.15919 3.73983i −0.0959879 0.166256i
\(507\) −3.91006 + 7.65512i −0.173652 + 0.339976i
\(508\) 1.24048 2.14858i 0.0550376 0.0953279i
\(509\) 9.96210 17.2549i 0.441563 0.764809i −0.556243 0.831020i \(-0.687758\pi\)
0.997806 + 0.0662109i \(0.0210910\pi\)
\(510\) −1.87561 3.24866i −0.0830536 0.143853i
\(511\) 0 0
\(512\) −2.01529 −0.0890641
\(513\) −3.81816 −0.168576
\(514\) −2.10139 3.63972i −0.0926886 0.160541i
\(515\) 7.11185 12.3181i 0.313386 0.542800i
\(516\) −3.30179 −0.145353
\(517\) −3.22884 5.59252i −0.142004 0.245959i
\(518\) 0 0
\(519\) −6.60335 −0.289855
\(520\) 30.3935 + 16.5219i 1.33284 + 0.724532i
\(521\) −8.26204 + 14.3103i −0.361967 + 0.626944i −0.988284 0.152623i \(-0.951228\pi\)
0.626318 + 0.779568i \(0.284561\pi\)
\(522\) −4.00464 −0.175278
\(523\) −5.99809 + 10.3890i −0.262278 + 0.454279i −0.966847 0.255357i \(-0.917807\pi\)
0.704569 + 0.709636i \(0.251140\pi\)
\(524\) 7.67609 13.2954i 0.335332 0.580812i
\(525\) 0 0
\(526\) −3.81065 + 6.60024i −0.166152 + 0.287784i
\(527\) −17.6905 −0.770611
\(528\) −0.0529314 + 0.0916798i −0.00230354 + 0.00398985i
\(529\) −4.46197 7.72837i −0.193999 0.336016i
\(530\) 13.7471 23.8107i 0.597137 1.03427i
\(531\) 0.654173 + 1.13306i 0.0283887 + 0.0491706i
\(532\) 0 0
\(533\) −16.8887 9.18068i −0.731531 0.397660i
\(534\) 3.82913 + 6.63225i 0.165703 + 0.287005i
\(535\) 48.6053 2.10139
\(536\) −23.5561 −1.01747
\(537\) −6.06776 −0.261843
\(538\) −4.10536 −0.176995
\(539\) 0 0
\(540\) −8.07356 + 13.9838i −0.347431 + 0.601767i
\(541\) −18.1158 31.3775i −0.778860 1.34903i −0.932599 0.360914i \(-0.882465\pi\)
0.153739 0.988112i \(-0.450869\pi\)
\(542\) 3.15829 + 5.47031i 0.135660 + 0.234970i
\(543\) 3.97057 0.170394
\(544\) −5.54665 + 9.60707i −0.237811 + 0.411900i
\(545\) 14.4624 0.619500
\(546\) 0 0
\(547\) −7.34857 −0.314202 −0.157101 0.987583i \(-0.550215\pi\)
−0.157101 + 0.987583i \(0.550215\pi\)
\(548\) 5.55973 9.62974i 0.237500 0.411362i
\(549\) 3.68064 0.157086
\(550\) −2.61535 4.52991i −0.111519 0.193156i
\(551\) −0.952888 1.65045i −0.0405944 0.0703115i
\(552\) 5.20786 9.02027i 0.221661 0.383928i
\(553\) 0 0
\(554\) −3.24816 −0.138001
\(555\) −24.1213 −1.02389
\(556\) 5.37340 0.227883
\(557\) 10.8280 0.458796 0.229398 0.973333i \(-0.426324\pi\)
0.229398 + 0.973333i \(0.426324\pi\)
\(558\) −9.96160 17.2540i −0.421708 0.730420i
\(559\) −0.362466 14.1098i −0.0153307 0.596781i
\(560\) 0 0
\(561\) 0.575009 + 0.995945i 0.0242769 + 0.0420488i
\(562\) 3.63847 6.30201i 0.153480 0.265834i
\(563\) −6.92997 12.0031i −0.292064 0.505869i 0.682234 0.731134i \(-0.261009\pi\)
−0.974298 + 0.225265i \(0.927675\pi\)
\(564\) 3.03274 5.25285i 0.127701 0.221185i
\(565\) −47.3873 −1.99360
\(566\) −6.49594 + 11.2513i −0.273045 + 0.472927i
\(567\) 0 0
\(568\) 4.80692 8.32583i 0.201694 0.349344i
\(569\) −13.7060 + 23.7395i −0.574586 + 0.995212i 0.421500 + 0.906828i \(0.361504\pi\)
−0.996086 + 0.0883842i \(0.971830\pi\)
\(570\) 2.01048 0.0842099
\(571\) 0.103879 0.179923i 0.00434719 0.00752956i −0.863844 0.503760i \(-0.831950\pi\)
0.868191 + 0.496230i \(0.165283\pi\)
\(572\) −3.62854 1.97247i −0.151717 0.0824732i
\(573\) −0.870251 −0.0363552
\(574\) 0 0
\(575\) −19.3341 33.4876i −0.806288 1.39653i
\(576\) −11.5795 −0.482480
\(577\) −1.66328 + 2.88089i −0.0692434 + 0.119933i −0.898568 0.438833i \(-0.855392\pi\)
0.829325 + 0.558766i \(0.188725\pi\)
\(578\) −5.63818 9.76562i −0.234518 0.406196i
\(579\) 10.8609 0.451362
\(580\) −8.05959 −0.334656
\(581\) 0 0
\(582\) 0.142452 + 0.246734i 0.00590483 + 0.0102275i
\(583\) −4.21447 + 7.29967i −0.174545 + 0.302321i
\(584\) 15.1950 26.3185i 0.628772 1.08907i
\(585\) −27.9389 15.1876i −1.15513 0.627929i
\(586\) 2.52769 + 4.37809i 0.104418 + 0.180857i
\(587\) −7.54051 13.0606i −0.311230 0.539067i 0.667399 0.744701i \(-0.267408\pi\)
−0.978629 + 0.205634i \(0.934074\pi\)
\(588\) 0 0
\(589\) 4.74064 8.21104i 0.195335 0.338330i
\(590\) −0.747686 1.29503i −0.0307817 0.0533155i
\(591\) −8.45953 14.6523i −0.347978 0.602716i
\(592\) 0.944935 + 1.63668i 0.0388366 + 0.0672670i
\(593\) 12.9245 + 22.3859i 0.530747 + 0.919281i 0.999356 + 0.0358751i \(0.0114218\pi\)
−0.468609 + 0.883405i \(0.655245\pi\)
\(594\) −1.40564 + 2.43464i −0.0576740 + 0.0998944i
\(595\) 0 0
\(596\) 3.74055 + 6.47882i 0.153219 + 0.265383i
\(597\) 8.39052 + 14.5328i 0.343401 + 0.594788i
\(598\) 15.2337 + 8.28101i 0.622952 + 0.338636i
\(599\) 17.7734 30.7845i 0.726203 1.25782i −0.232274 0.972650i \(-0.574617\pi\)
0.958477 0.285170i \(-0.0920501\pi\)
\(600\) 6.30807 10.9259i 0.257526 0.446048i
\(601\) −13.6474 23.6379i −0.556688 0.964212i −0.997770 0.0667449i \(-0.978739\pi\)
0.441082 0.897467i \(-0.354595\pi\)
\(602\) 0 0
\(603\) 21.6538 0.881810
\(604\) 21.5023 0.874915
\(605\) −17.5406 30.3811i −0.713125 1.23517i
\(606\) −1.68456 + 2.91775i −0.0684308 + 0.118526i
\(607\) 38.9258 1.57995 0.789976 0.613138i \(-0.210093\pi\)
0.789976 + 0.613138i \(0.210093\pi\)
\(608\) −2.97274 5.14894i −0.120561 0.208817i
\(609\) 0 0
\(610\) −4.20679 −0.170328
\(611\) 22.7803 + 12.3834i 0.921593 + 0.500977i
\(612\) 3.16576 5.48326i 0.127968 0.221648i
\(613\) 0.886645 0.0358113 0.0179056 0.999840i \(-0.494300\pi\)
0.0179056 + 0.999840i \(0.494300\pi\)
\(614\) −9.45317 + 16.3734i −0.381499 + 0.660775i
\(615\) −6.06606 + 10.5067i −0.244607 + 0.423672i
\(616\) 0 0
\(617\) −17.3944 + 30.1280i −0.700272 + 1.21291i 0.268099 + 0.963391i \(0.413605\pi\)
−0.968371 + 0.249515i \(0.919729\pi\)
\(618\) 2.32600 0.0935653
\(619\) 1.02781 1.78021i 0.0413111 0.0715529i −0.844631 0.535350i \(-0.820180\pi\)
0.885942 + 0.463797i \(0.153513\pi\)
\(620\) −20.0483 34.7247i −0.805161 1.39458i
\(621\) −10.3913 + 17.9982i −0.416987 + 0.722243i
\(622\) −4.18864 7.25494i −0.167949 0.290897i
\(623\) 0 0
\(624\) −0.0109156 0.424915i −0.000436975 0.0170102i
\(625\) 6.19081 + 10.7228i 0.247632 + 0.428912i
\(626\) −17.7992 −0.711398
\(627\) −0.616356 −0.0246149
\(628\) −2.47336 −0.0986979
\(629\) 20.5302 0.818593
\(630\) 0 0
\(631\) 22.6169 39.1736i 0.900363 1.55947i 0.0733401 0.997307i \(-0.476634\pi\)
0.827023 0.562168i \(-0.190033\pi\)
\(632\) 16.8555 + 29.1946i 0.670477 + 1.16130i
\(633\) −1.88332 3.26201i −0.0748554 0.129653i
\(634\) 21.5848 0.857241
\(635\) 3.34678 5.79679i 0.132813 0.230038i
\(636\) −7.91700 −0.313929
\(637\) 0 0
\(638\) −1.40321 −0.0555534
\(639\) −4.41872 + 7.65345i −0.174802 + 0.302766i
\(640\) −26.1881 −1.03518
\(641\) 9.53097 + 16.5081i 0.376451 + 0.652032i 0.990543 0.137202i \(-0.0438111\pi\)
−0.614092 + 0.789234i \(0.710478\pi\)
\(642\) 3.97420 + 6.88352i 0.156849 + 0.271671i
\(643\) −5.26755 + 9.12367i −0.207732 + 0.359802i −0.951000 0.309192i \(-0.899942\pi\)
0.743268 + 0.668994i \(0.233275\pi\)
\(644\) 0 0
\(645\) −8.90811 −0.350756
\(646\) −1.71117 −0.0673252
\(647\) 24.1608 0.949860 0.474930 0.880024i \(-0.342473\pi\)
0.474930 + 0.880024i \(0.342473\pi\)
\(648\) 14.6540 0.575663
\(649\) 0.229219 + 0.397019i 0.00899762 + 0.0155843i
\(650\) 18.4520 + 10.0305i 0.723745 + 0.393427i
\(651\) 0 0
\(652\) −7.58714 13.1413i −0.297135 0.514654i
\(653\) 16.8445 29.1755i 0.659176 1.14173i −0.321653 0.946858i \(-0.604238\pi\)
0.980829 0.194869i \(-0.0624282\pi\)
\(654\) 1.18251 + 2.04817i 0.0462400 + 0.0800900i
\(655\) 20.7098 35.8704i 0.809199 1.40157i
\(656\) 0.950537 0.0371122
\(657\) −13.9678 + 24.1930i −0.544937 + 0.943859i
\(658\) 0 0
\(659\) 2.10030 3.63782i 0.0818159 0.141709i −0.822214 0.569178i \(-0.807261\pi\)
0.904030 + 0.427469i \(0.140595\pi\)
\(660\) −1.30329 + 2.25737i −0.0507307 + 0.0878681i
\(661\) −17.6726 −0.687385 −0.343693 0.939082i \(-0.611678\pi\)
−0.343693 + 0.939082i \(0.611678\pi\)
\(662\) 0.758708 1.31412i 0.0294880 0.0510748i
\(663\) −4.05684 2.20529i −0.157555 0.0856465i
\(664\) −4.22844 −0.164095
\(665\) 0 0
\(666\) 11.5607 + 20.0236i 0.447966 + 0.775900i
\(667\) −10.3733 −0.401655
\(668\) −10.5721 + 18.3114i −0.409046 + 0.708488i
\(669\) −0.779623 1.35035i −0.0301420 0.0522074i
\(670\) −24.7491 −0.956143
\(671\) 1.28968 0.0497875
\(672\) 0 0
\(673\) 10.3052 + 17.8491i 0.397235 + 0.688031i 0.993384 0.114843i \(-0.0366366\pi\)
−0.596149 + 0.802874i \(0.703303\pi\)
\(674\) 4.06901 7.04774i 0.156733 0.271469i
\(675\) −12.5865 + 21.8005i −0.484456 + 0.839102i
\(676\) 16.5607 0.851419i 0.636952 0.0327469i
\(677\) −10.6537 18.4527i −0.409455 0.709196i 0.585374 0.810763i \(-0.300948\pi\)
−0.994829 + 0.101567i \(0.967614\pi\)
\(678\) −3.87461 6.71102i −0.148804 0.257735i
\(679\) 0 0
\(680\) −9.29147 + 16.0933i −0.356312 + 0.617150i
\(681\) −8.69264 15.0561i −0.333103 0.576951i
\(682\) −3.49049 6.04571i −0.133658 0.231502i
\(683\) 3.34878 + 5.80026i 0.128138 + 0.221941i 0.922955 0.384908i \(-0.125767\pi\)
−0.794817 + 0.606849i \(0.792433\pi\)
\(684\) 1.69670 + 2.93877i 0.0648750 + 0.112367i
\(685\) 14.9999 25.9806i 0.573118 0.992670i
\(686\) 0 0
\(687\) −0.0226652 0.0392573i −0.000864732 0.00149776i
\(688\) 0.348970 + 0.604433i 0.0133043 + 0.0230438i
\(689\) −0.869117 33.8323i −0.0331107 1.28891i
\(690\) 5.47161 9.47710i 0.208301 0.360787i
\(691\) −12.4632 + 21.5868i −0.474121 + 0.821202i −0.999561 0.0296291i \(-0.990567\pi\)
0.525440 + 0.850831i \(0.323901\pi\)
\(692\) 6.36936 + 11.0321i 0.242127 + 0.419376i
\(693\) 0 0
\(694\) −0.539093 −0.0204637
\(695\) 14.4972 0.549911
\(696\) −1.69223 2.93102i −0.0641437 0.111100i
\(697\) 5.16298 8.94254i 0.195562 0.338723i
\(698\) 26.0435 0.985761
\(699\) 4.85017 + 8.40073i 0.183450 + 0.317745i
\(700\) 0 0
\(701\) −4.94583 −0.186801 −0.0934007 0.995629i \(-0.529774\pi\)
−0.0934007 + 0.995629i \(0.529774\pi\)
\(702\) −0.289874 11.2840i −0.0109406 0.425886i
\(703\) −5.50162 + 9.52908i −0.207497 + 0.359396i
\(704\) −4.05741 −0.152919
\(705\) 8.18220 14.1720i 0.308160 0.533748i
\(706\) 0.468266 0.811061i 0.0176234 0.0305247i
\(707\) 0 0
\(708\) −0.215297 + 0.372905i −0.00809136 + 0.0140146i
\(709\) −4.64497 −0.174446 −0.0872228 0.996189i \(-0.527799\pi\)
−0.0872228 + 0.996189i \(0.527799\pi\)
\(710\) 5.05037 8.74749i 0.189537 0.328288i
\(711\) −15.4943 26.8369i −0.581082 1.00646i
\(712\) 18.9688 32.8550i 0.710888 1.23129i
\(713\) −25.8037 44.6933i −0.966356 1.67378i
\(714\) 0 0
\(715\) −9.78966 5.32165i −0.366113 0.199018i
\(716\) 5.85275 + 10.1373i 0.218728 + 0.378847i
\(717\) −2.21797 −0.0828315
\(718\) 8.31878 0.310454
\(719\) −31.7413 −1.18375 −0.591875 0.806030i \(-0.701612\pi\)
−0.591875 + 0.806030i \(0.701612\pi\)
\(720\) 1.57247 0.0586025
\(721\) 0 0
\(722\) −7.62714 + 13.2106i −0.283853 + 0.491647i
\(723\) 2.83658 + 4.91309i 0.105493 + 0.182720i
\(724\) −3.82987 6.63354i −0.142336 0.246533i
\(725\) −12.5647 −0.466643
\(726\) 2.86840 4.96822i 0.106456 0.184388i
\(727\) −47.8755 −1.77560 −0.887801 0.460227i \(-0.847768\pi\)
−0.887801 + 0.460227i \(0.847768\pi\)
\(728\) 0 0
\(729\) −6.17412 −0.228671
\(730\) 15.9645 27.6514i 0.590873 1.02342i
\(731\) 7.58192 0.280427
\(732\) 0.605675 + 1.04906i 0.0223864 + 0.0387743i
\(733\) −3.80104 6.58359i −0.140395 0.243171i 0.787251 0.616633i \(-0.211504\pi\)
−0.927645 + 0.373463i \(0.878170\pi\)
\(734\) 4.74386 8.21660i 0.175099 0.303280i
\(735\) 0 0
\(736\) −32.3618 −1.19287
\(737\) 7.58737 0.279484
\(738\) 11.6292 0.428076
\(739\) −33.4236 −1.22951 −0.614754 0.788719i \(-0.710745\pi\)
−0.614754 + 0.788719i \(0.710745\pi\)
\(740\) 23.2665 + 40.2988i 0.855294 + 1.48141i
\(741\) 2.11072 1.29201i 0.0775394 0.0474632i
\(742\) 0 0
\(743\) 1.46912 + 2.54458i 0.0538966 + 0.0933517i 0.891715 0.452597i \(-0.149503\pi\)
−0.837818 + 0.545949i \(0.816169\pi\)
\(744\) 8.41888 14.5819i 0.308651 0.534599i
\(745\) 10.0919 + 17.4796i 0.369737 + 0.640403i
\(746\) −13.0776 + 22.6511i −0.478805 + 0.829314i
\(747\) 3.88695 0.142216
\(748\) 1.10927 1.92131i 0.0405588 0.0702499i
\(749\) 0 0
\(750\) 1.78552 3.09261i 0.0651980 0.112926i
\(751\) −0.598389 + 1.03644i −0.0218355 + 0.0378202i −0.876737 0.480971i \(-0.840284\pi\)
0.854901 + 0.518791i \(0.173618\pi\)
\(752\) −1.28213 −0.0467545
\(753\) −7.11313 + 12.3203i −0.259217 + 0.448977i
\(754\) 4.80531 2.94141i 0.174999 0.107120i
\(755\) 58.0123 2.11128
\(756\) 0 0
\(757\) −5.77321 9.99950i −0.209831 0.363438i 0.741830 0.670588i \(-0.233958\pi\)
−0.951661 + 0.307150i \(0.900625\pi\)
\(758\) −19.2841 −0.700432
\(759\) −1.67744 + 2.90541i −0.0608871 + 0.105460i
\(760\) −4.97979 8.62525i −0.180636 0.312871i
\(761\) −34.6497 −1.25605 −0.628026 0.778192i \(-0.716137\pi\)
−0.628026 + 0.778192i \(0.716137\pi\)
\(762\) 1.09459 0.0396530
\(763\) 0 0
\(764\) 0.839413 + 1.45391i 0.0303689 + 0.0526005i
\(765\) 8.54110 14.7936i 0.308804 0.534864i
\(766\) 0.250768 0.434344i 0.00906063 0.0156935i
\(767\) −1.61720 0.879108i −0.0583937 0.0317427i
\(768\) −5.12890 8.88351i −0.185073 0.320556i
\(769\) −3.27437 5.67138i −0.118077 0.204515i 0.800929 0.598760i \(-0.204340\pi\)
−0.919006 + 0.394245i \(0.871006\pi\)
\(770\) 0 0
\(771\) −1.63253 + 2.82763i −0.0587943 + 0.101835i
\(772\) −10.4760 18.1450i −0.377039 0.653051i
\(773\) 16.9637 + 29.3821i 0.610143 + 1.05680i 0.991216 + 0.132254i \(0.0422214\pi\)
−0.381073 + 0.924545i \(0.624445\pi\)
\(774\) 4.26941 + 7.39484i 0.153461 + 0.265802i
\(775\) −31.2550 54.1352i −1.12271 1.94459i
\(776\) 0.705683 1.22228i 0.0253325 0.0438772i
\(777\) 0 0
\(778\) 2.42547 + 4.20104i 0.0869575 + 0.150615i
\(779\) 2.76711 + 4.79278i 0.0991422 + 0.171719i
\(780\) −0.268768 10.4624i −0.00962345 0.374614i
\(781\) −1.54830 + 2.68173i −0.0554024 + 0.0959598i
\(782\) −4.65703 + 8.06620i −0.166535 + 0.288447i
\(783\) 3.37651 + 5.84829i 0.120667 + 0.209001i
\(784\) 0 0
\(785\) −6.67303 −0.238171
\(786\) 6.77333 0.241597
\(787\) 6.48717 + 11.2361i 0.231243 + 0.400524i 0.958174 0.286186i \(-0.0923876\pi\)
−0.726932 + 0.686710i \(0.759054\pi\)
\(788\) −16.3195 + 28.2662i −0.581359 + 1.00694i
\(789\) 5.92085 0.210788
\(790\) 17.7092 + 30.6732i 0.630065 + 1.09130i
\(791\) 0 0
\(792\) 6.41600 0.227983
\(793\) −4.41653 + 2.70344i −0.156836 + 0.0960019i
\(794\) 10.8639 18.8168i 0.385545 0.667784i
\(795\) −21.3597 −0.757552
\(796\) 16.1864 28.0357i 0.573712 0.993699i
\(797\) 2.20956 3.82707i 0.0782667 0.135562i −0.824235 0.566247i \(-0.808395\pi\)
0.902502 + 0.430685i \(0.141728\pi\)
\(798\) 0 0
\(799\) −6.96408 + 12.0621i −0.246371 + 0.426728i
\(800\) −39.1985 −1.38588
\(801\) −17.4369 + 30.2017i −0.616104 + 1.06712i
\(802\) 10.8523 + 18.7968i 0.383209 + 0.663737i
\(803\) −4.89426 + 8.47711i −0.172715 + 0.299151i
\(804\) 3.56327 + 6.17177i 0.125667 + 0.217662i
\(805\) 0 0
\(806\) 24.6264 + 13.3869i 0.867427 + 0.471532i
\(807\) 1.59469 + 2.76208i 0.0561356 + 0.0972298i
\(808\) 16.6901 0.587155
\(809\) 11.4716 0.403320 0.201660 0.979456i \(-0.435366\pi\)
0.201660 + 0.979456i \(0.435366\pi\)
\(810\) 15.3961 0.540965
\(811\) −23.8664 −0.838063 −0.419032 0.907972i \(-0.637630\pi\)
−0.419032 + 0.907972i \(0.637630\pi\)
\(812\) 0 0
\(813\) 2.45361 4.24978i 0.0860520 0.149046i
\(814\) 4.05079 + 7.01618i 0.141980 + 0.245917i
\(815\) −20.4698 35.4548i −0.717026 1.24193i
\(816\) 0.228329 0.00799310
\(817\) −2.03178 + 3.51914i −0.0710829 + 0.123119i
\(818\) 0.125105 0.00437419
\(819\) 0 0
\(820\) 23.4044 0.817318
\(821\) −15.4847 + 26.8203i −0.540420 + 0.936035i 0.458460 + 0.888715i \(0.348401\pi\)
−0.998880 + 0.0473197i \(0.984932\pi\)
\(822\) 4.90587 0.171112
\(823\) 4.30678 + 7.45957i 0.150125 + 0.260024i 0.931273 0.364321i \(-0.118699\pi\)
−0.781148 + 0.624346i \(0.785366\pi\)
\(824\) −5.76129 9.97885i −0.200704 0.347630i
\(825\) −2.03181 + 3.51920i −0.0707386 + 0.122523i
\(826\) 0 0
\(827\) 22.9128 0.796756 0.398378 0.917221i \(-0.369573\pi\)
0.398378 + 0.917221i \(0.369573\pi\)
\(828\) 18.4706 0.641896
\(829\) 42.5611 1.47821 0.739104 0.673591i \(-0.235249\pi\)
0.739104 + 0.673591i \(0.235249\pi\)
\(830\) −4.44259 −0.154204
\(831\) 1.26172 + 2.18536i 0.0437685 + 0.0758093i
\(832\) 13.8947 8.50518i 0.481711 0.294864i
\(833\) 0 0
\(834\) 1.18536 + 2.05311i 0.0410458 + 0.0710933i
\(835\) −28.5230 + 49.4033i −0.987080 + 1.70967i
\(836\) 0.594515 + 1.02973i 0.0205617 + 0.0356140i
\(837\) −16.7982 + 29.0954i −0.580632 + 1.00568i
\(838\) 11.6569 0.402682
\(839\) 0.920524 1.59439i 0.0317800 0.0550446i −0.849698 0.527270i \(-0.823216\pi\)
0.881478 + 0.472225i \(0.156549\pi\)
\(840\) 0 0
\(841\) 12.8147 22.1957i 0.441885 0.765367i
\(842\) 1.46465 2.53686i 0.0504753 0.0874258i
\(843\) −5.65332 −0.194711
\(844\) −3.63317 + 6.29284i −0.125059 + 0.216609i
\(845\) 44.6802 2.29709i 1.53705 0.0790224i
\(846\) −15.6860 −0.539296
\(847\) 0 0
\(848\) 0.836755 + 1.44930i 0.0287343 + 0.0497692i
\(849\) 10.0931 0.346396
\(850\) −5.64087 + 9.77027i −0.193480 + 0.335118i
\(851\) 29.9457 + 51.8675i 1.02653 + 1.77800i
\(852\) −2.90852 −0.0996442
\(853\) 27.0293 0.925466 0.462733 0.886498i \(-0.346869\pi\)
0.462733 + 0.886498i \(0.346869\pi\)
\(854\) 0 0
\(855\) 4.57763 + 7.92869i 0.156552 + 0.271155i
\(856\) 19.6875 34.0998i 0.672906 1.16551i
\(857\) 8.39268 14.5365i 0.286688 0.496559i −0.686329 0.727291i \(-0.740779\pi\)
0.973017 + 0.230732i \(0.0741122\pi\)
\(858\) −0.0467936 1.82154i −0.00159751 0.0621865i
\(859\) 25.8058 + 44.6969i 0.880482 + 1.52504i 0.850806 + 0.525481i \(0.176114\pi\)
0.0296769 + 0.999560i \(0.490552\pi\)
\(860\) 8.59245 + 14.8826i 0.293000 + 0.507491i
\(861\) 0 0
\(862\) 9.48624 16.4306i 0.323102 0.559630i
\(863\) −10.9807 19.0191i −0.373787 0.647417i 0.616358 0.787466i \(-0.288607\pi\)
−0.990145 + 0.140049i \(0.955274\pi\)
\(864\) 10.5338 + 18.2450i 0.358366 + 0.620709i
\(865\) 17.1843 + 29.7640i 0.584283 + 1.01201i
\(866\) 11.0205 + 19.0880i 0.374491 + 0.648638i
\(867\) −4.38020 + 7.58673i −0.148759 + 0.257659i
\(868\) 0 0
\(869\) −5.42913 9.40352i −0.184170 0.318993i
\(870\) −1.77793 3.07947i −0.0602775 0.104404i
\(871\) −25.9831 + 15.9047i −0.880404 + 0.538911i
\(872\) 5.85797 10.1463i 0.198376 0.343597i
\(873\) −0.648693 + 1.12357i −0.0219549 + 0.0380270i
\(874\) −2.49595 4.32311i −0.0844267 0.146231i
\(875\) 0 0
\(876\) −9.19401 −0.310637
\(877\) −9.61745 −0.324758 −0.162379 0.986728i \(-0.551917\pi\)
−0.162379 + 0.986728i \(0.551917\pi\)
\(878\) 11.9089 + 20.6268i 0.401905 + 0.696120i
\(879\) 1.96371 3.40125i 0.0662344 0.114721i
\(880\) 0.550986 0.0185737
\(881\) 14.4863 + 25.0910i 0.488055 + 0.845336i 0.999906 0.0137383i \(-0.00437318\pi\)
−0.511851 + 0.859075i \(0.671040\pi\)
\(882\) 0 0
\(883\) 6.60727 0.222352 0.111176 0.993801i \(-0.464538\pi\)
0.111176 + 0.993801i \(0.464538\pi\)
\(884\) 0.228755 + 8.90481i 0.00769388 + 0.299501i
\(885\) −0.580863 + 1.00608i −0.0195255 + 0.0338191i
\(886\) −28.2649 −0.949578
\(887\) −15.7072 + 27.2057i −0.527397 + 0.913478i 0.472094 + 0.881548i \(0.343498\pi\)
−0.999490 + 0.0319293i \(0.989835\pi\)
\(888\) −9.77029 + 16.9226i −0.327869 + 0.567886i
\(889\) 0 0
\(890\) 19.9295 34.5190i 0.668039 1.15708i
\(891\) −4.72001 −0.158126
\(892\) −1.50399 + 2.60499i −0.0503574 + 0.0872216i
\(893\) −3.73242 6.46474i −0.124901 0.216334i
\(894\) −1.65032 + 2.85843i −0.0551949 + 0.0956003i
\(895\) 15.7905 + 27.3499i 0.527818 + 0.914208i
\(896\) 0 0
\(897\) −0.345925 13.4659i −0.0115501 0.449613i
\(898\) 8.37780 + 14.5108i 0.279571 + 0.484231i
\(899\) −16.7692 −0.559283
\(900\) 22.3726 0.745755
\(901\) 18.1798 0.605658
\(902\) 4.07480 0.135676
\(903\) 0 0
\(904\) −19.1942 + 33.2453i −0.638388 + 1.10572i
\(905\) −10.3328 17.8970i −0.343475 0.594917i
\(906\) 4.74337 + 8.21575i 0.157588 + 0.272950i
\(907\) 9.73642 0.323292 0.161646 0.986849i \(-0.448320\pi\)
0.161646 + 0.986849i \(0.448320\pi\)
\(908\) −16.7692 + 29.0452i −0.556507 + 0.963898i
\(909\) −15.3422 −0.508869
\(910\) 0 0
\(911\) −38.4372 −1.27348 −0.636740 0.771078i \(-0.719718\pi\)
−0.636740 + 0.771078i \(0.719718\pi\)
\(912\) −0.0611867 + 0.105979i −0.00202609 + 0.00350930i
\(913\) 1.36197 0.0450746
\(914\) −0.317871 0.550568i −0.0105142 0.0182112i
\(915\) 1.63409 + 2.83032i 0.0540212 + 0.0935675i
\(916\) −0.0437242 + 0.0757325i −0.00144469 + 0.00250227i
\(917\) 0 0
\(918\) 6.06346 0.200124
\(919\) 54.2804 1.79055 0.895273 0.445519i \(-0.146981\pi\)
0.895273 + 0.445519i \(0.146981\pi\)
\(920\) −54.2108 −1.78728
\(921\) 14.6880 0.483985
\(922\) 14.1164 + 24.4502i 0.464897 + 0.805226i
\(923\) −0.319293 12.4292i −0.0105097 0.409112i
\(924\) 0 0
\(925\) 36.2721 + 62.8251i 1.19262 + 2.06568i
\(926\) −13.0869 + 22.6673i −0.430064 + 0.744892i
\(927\) 5.29602 + 9.17297i 0.173944 + 0.301280i
\(928\) −5.25777 + 9.10673i −0.172595 + 0.298943i
\(929\) 38.1920 1.25304 0.626519 0.779406i \(-0.284479\pi\)
0.626519 + 0.779406i \(0.284479\pi\)
\(930\) 8.84526 15.3204i 0.290047 0.502377i
\(931\) 0 0
\(932\) 9.35660 16.2061i 0.306486 0.530849i
\(933\) −3.25408 + 5.63622i −0.106534 + 0.184522i
\(934\) −25.1988 −0.824531
\(935\) 2.99276 5.18361i 0.0978736 0.169522i
\(936\) −21.9717 + 13.4493i −0.718168 + 0.439604i
\(937\) 19.0376 0.621931 0.310966 0.950421i \(-0.399348\pi\)
0.310966 + 0.950421i \(0.399348\pi\)
\(938\) 0 0
\(939\) 6.91392 + 11.9753i 0.225627 + 0.390798i
\(940\) −31.5691 −1.02967
\(941\) 23.0811 39.9776i 0.752422 1.30323i −0.194224 0.980957i \(-0.562219\pi\)
0.946646 0.322275i \(-0.104448\pi\)
\(942\) −0.545619 0.945040i −0.0177772 0.0307911i
\(943\) 30.1232 0.980948
\(944\) 0.0910198 0.00296244
\(945\) 0 0
\(946\) 1.49598 + 2.59111i 0.0486385 + 0.0842443i
\(947\) 4.59687 7.96201i 0.149378 0.258730i −0.781620 0.623755i \(-0.785606\pi\)
0.930998 + 0.365025i \(0.118940\pi\)
\(948\) 5.09938 8.83239i 0.165620 0.286863i
\(949\) −1.00930 39.2894i −0.0327634 1.27539i
\(950\) −3.02324 5.23641i −0.0980869 0.169892i
\(951\) −8.38440 14.5222i −0.271883 0.470915i
\(952\) 0 0
\(953\) 22.3232 38.6648i 0.723118 1.25248i −0.236626 0.971601i \(-0.576042\pi\)
0.959744 0.280876i \(-0.0906250\pi\)
\(954\) 10.2371 + 17.7312i 0.331440 + 0.574070i
\(955\) 2.26470 + 3.92258i 0.0732841 + 0.126932i
\(956\) 2.13937 + 3.70550i 0.0691923 + 0.119844i
\(957\) 0.545062 + 0.944075i 0.0176194 + 0.0305176i
\(958\) −5.99641 + 10.3861i −0.193735 + 0.335559i
\(959\) 0 0
\(960\) −5.14093 8.90436i −0.165923 0.287387i
\(961\) −26.2136 45.4032i −0.845599 1.46462i
\(962\) −28.5794 15.5357i −0.921437 0.500892i
\(963\) −18.0976 + 31.3459i −0.583186 + 1.01011i
\(964\) 5.47212 9.47799i 0.176245 0.305266i
\(965\) −28.2638 48.9544i −0.909845 1.57590i
\(966\) 0 0
\(967\) 13.8268 0.444639 0.222320 0.974974i \(-0.428637\pi\)
0.222320 + 0.974974i \(0.428637\pi\)
\(968\) −28.4191 −0.913426
\(969\) 0.664689 + 1.15128i 0.0213529 + 0.0369843i
\(970\) 0.741422 1.28418i 0.0238056 0.0412326i
\(971\) −7.26873 −0.233265 −0.116632 0.993175i \(-0.537210\pi\)
−0.116632 + 0.993175i \(0.537210\pi\)
\(972\) −9.25454 16.0293i −0.296839 0.514141i
\(973\) 0 0
\(974\) 14.2950 0.458043
\(975\) −0.419005 16.3107i −0.0134189 0.522360i
\(976\) 0.128029 0.221752i 0.00409810 0.00709811i
\(977\) 42.8101 1.36962 0.684808 0.728723i \(-0.259886\pi\)
0.684808 + 0.728723i \(0.259886\pi\)
\(978\) 3.34742 5.79790i 0.107039 0.185397i
\(979\) −6.10982 + 10.5825i −0.195271 + 0.338219i
\(980\) 0 0
\(981\) −5.38489 + 9.32690i −0.171926 + 0.297785i
\(982\) −18.4430 −0.588541
\(983\) −23.1544 + 40.1046i −0.738511 + 1.27914i 0.214655 + 0.976690i \(0.431137\pi\)
−0.953166 + 0.302448i \(0.902196\pi\)
\(984\) 4.91410 + 8.51147i 0.156656 + 0.271336i
\(985\) −44.0294 + 76.2612i −1.40289 + 2.42988i
\(986\) 1.51324 + 2.62101i 0.0481914 + 0.0834700i
\(987\) 0 0
\(988\) −4.19446 2.28010i −0.133444 0.0725398i
\(989\) 11.0591 + 19.1550i 0.351660 + 0.609092i
\(990\) 6.74094 0.214241
\(991\) −58.2324 −1.84981 −0.924907 0.380194i \(-0.875857\pi\)
−0.924907 + 0.380194i \(0.875857\pi\)
\(992\) −52.3151 −1.66101
\(993\) −1.17885 −0.0374097
\(994\) 0 0
\(995\) 43.6703 75.6392i 1.38444 2.39792i
\(996\) 0.639625 + 1.10786i 0.0202673 + 0.0351040i
\(997\) −2.24739 3.89260i −0.0711757 0.123280i 0.828241 0.560372i \(-0.189342\pi\)
−0.899417 + 0.437092i \(0.856008\pi\)
\(998\) 19.8353 0.627875
\(999\) 19.4947 33.7658i 0.616786 1.06830i
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.g.l.263.4 12
7.2 even 3 637.2.h.l.471.3 12
7.3 odd 6 637.2.f.k.393.4 12
7.4 even 3 637.2.f.j.393.4 12
7.5 odd 6 91.2.h.b.16.3 yes 12
7.6 odd 2 91.2.g.b.81.4 yes 12
13.9 even 3 637.2.h.l.165.3 12
21.5 even 6 819.2.s.d.289.4 12
21.20 even 2 819.2.n.d.172.3 12
91.3 odd 6 8281.2.a.bz.1.3 6
91.9 even 3 inner 637.2.g.l.373.4 12
91.10 odd 6 8281.2.a.ce.1.4 6
91.48 odd 6 91.2.h.b.74.3 yes 12
91.55 odd 6 1183.2.e.h.508.4 12
91.61 odd 6 91.2.g.b.9.4 12
91.62 odd 6 1183.2.e.g.508.3 12
91.68 odd 6 1183.2.e.h.170.4 12
91.74 even 3 637.2.f.j.295.4 12
91.75 odd 6 1183.2.e.g.170.3 12
91.81 even 3 8281.2.a.ca.1.3 6
91.87 odd 6 637.2.f.k.295.4 12
91.88 even 6 8281.2.a.cf.1.4 6
273.152 even 6 819.2.n.d.100.3 12
273.230 even 6 819.2.s.d.802.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.g.b.9.4 12 91.61 odd 6
91.2.g.b.81.4 yes 12 7.6 odd 2
91.2.h.b.16.3 yes 12 7.5 odd 6
91.2.h.b.74.3 yes 12 91.48 odd 6
637.2.f.j.295.4 12 91.74 even 3
637.2.f.j.393.4 12 7.4 even 3
637.2.f.k.295.4 12 91.87 odd 6
637.2.f.k.393.4 12 7.3 odd 6
637.2.g.l.263.4 12 1.1 even 1 trivial
637.2.g.l.373.4 12 91.9 even 3 inner
637.2.h.l.165.3 12 13.9 even 3
637.2.h.l.471.3 12 7.2 even 3
819.2.n.d.100.3 12 273.152 even 6
819.2.n.d.172.3 12 21.20 even 2
819.2.s.d.289.4 12 21.5 even 6
819.2.s.d.802.4 12 273.230 even 6
1183.2.e.g.170.3 12 91.75 odd 6
1183.2.e.g.508.3 12 91.62 odd 6
1183.2.e.h.170.4 12 91.68 odd 6
1183.2.e.h.508.4 12 91.55 odd 6
8281.2.a.bz.1.3 6 91.3 odd 6
8281.2.a.ca.1.3 6 91.81 even 3
8281.2.a.ce.1.4 6 91.10 odd 6
8281.2.a.cf.1.4 6 91.88 even 6