Properties

Label 637.2.f.k.393.4
Level $637$
Weight $2$
Character 637.393
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(295,637)]
 
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, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.295");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.f (of order \(3\), 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: \(12\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 393.4
Root \(0.756174 - 1.30973i\) of defining polynomial
Character \(\chi\) \(=\) 637.393
Dual form 637.2.f.k.295.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.425563 + 0.737096i) q^{2} +(-0.330612 - 0.572636i) q^{3} +(0.637793 - 1.10469i) q^{4} +3.44148 q^{5} +(0.281392 - 0.487385i) q^{6} +2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +O(q^{10})\) \(q+(0.425563 + 0.737096i) q^{2} +(-0.330612 - 0.572636i) q^{3} +(0.637793 - 1.10469i) q^{4} +3.44148 q^{5} +(0.281392 - 0.487385i) q^{6} +2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +(1.46456 + 2.53670i) q^{10} +(0.448993 + 0.777679i) q^{11} -0.843447 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} +2.18125 q^{18} +(-0.519020 + 0.898968i) q^{19} +(2.19495 - 3.80177i) q^{20} +(-0.382150 + 0.661902i) q^{22} +(-2.82506 - 4.89315i) q^{23} +(-0.921723 - 1.59647i) q^{24} +6.84378 q^{25} +(-2.69617 - 1.46563i) q^{26} -3.67824 q^{27} +(0.917969 + 1.58997i) q^{29} +(0.968404 - 1.67733i) q^{30} -9.13385 q^{31} +(2.86381 - 4.96026i) q^{32} +(0.296885 - 0.514219i) q^{33} -1.64847 q^{34} +(-1.63452 - 2.83108i) q^{36} +(5.30001 + 9.17989i) q^{37} -0.883501 q^{38} +(2.09460 + 1.13862i) q^{39} +9.59462 q^{40} +(2.66571 + 4.61715i) q^{41} +(1.95732 - 3.39018i) q^{43} +1.14546 q^{44} +(4.40988 - 7.63814i) q^{45} +(2.40448 - 4.16469i) q^{46} +7.19129 q^{47} +(-0.0589445 + 0.102095i) q^{48} +(2.91246 + 5.04452i) q^{50} +1.28066 q^{51} +(0.118109 + 4.59767i) q^{52} -9.38648 q^{53} +(-1.56532 - 2.71122i) q^{54} +(1.54520 + 2.67637i) q^{55} +0.686375 q^{57} +(-0.781307 + 1.35326i) q^{58} +(0.255259 - 0.442121i) q^{59} -2.90270 q^{60} +(-0.718095 + 1.24378i) q^{61} +(-3.88702 - 6.73252i) q^{62} +4.51834 q^{64} +(-10.5831 + 6.47813i) q^{65} +0.505372 q^{66} +(4.22466 + 7.31732i) q^{67} +(1.23528 + 2.13957i) q^{68} +(-1.86800 + 3.23547i) q^{69} +(1.72419 - 2.98638i) q^{71} +(3.57244 - 6.18764i) q^{72} +10.9005 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} -12.0918 q^{79} +(-0.306789 - 0.531375i) q^{80} +(-2.62811 - 4.55201i) q^{81} +(-2.26886 + 3.92977i) q^{82} +1.51669 q^{83} +(-3.33274 + 5.77248i) q^{85} +3.33185 q^{86} +(0.606982 - 1.05132i) q^{87} +(1.25176 + 2.16812i) q^{88} +(-6.80391 - 11.7847i) q^{89} +7.50673 q^{90} -7.20722 q^{92} +(3.01976 + 5.23037i) q^{93} +(3.06035 + 5.30067i) q^{94} +(-1.78619 + 3.09378i) q^{95} -3.78723 q^{96} +(-0.253120 + 0.438417i) q^{97} +2.30134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} + q^{3} - 4 q^{4} - 2 q^{5} - 9 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} + q^{3} - 4 q^{4} - 2 q^{5} - 9 q^{6} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} - 10 q^{12} - 2 q^{13} - 2 q^{15} + 8 q^{16} + 5 q^{17} - 6 q^{18} - q^{19} - q^{20} - 5 q^{22} - q^{23} - 11 q^{24} - 14 q^{25} + 11 q^{26} - 8 q^{27} + 3 q^{29} - 5 q^{30} - 32 q^{31} + 8 q^{32} + 16 q^{33} + 32 q^{34} - 21 q^{36} - 13 q^{37} + 34 q^{38} + 43 q^{39} + 10 q^{40} - 8 q^{41} - 11 q^{43} - 42 q^{44} - 7 q^{45} + 16 q^{46} + 2 q^{47} + 21 q^{48} + 6 q^{50} + 40 q^{51} - 16 q^{52} + 4 q^{53} - 18 q^{54} + 9 q^{55} + 42 q^{57} - 8 q^{58} + 13 q^{59} - 40 q^{60} - 5 q^{61} + 5 q^{62} - 30 q^{64} - 14 q^{65} - 36 q^{66} - 11 q^{67} + 29 q^{68} + 23 q^{69} + 6 q^{71} + 25 q^{72} + 60 q^{73} - 3 q^{74} - 3 q^{75} - 9 q^{76} + 16 q^{78} - 14 q^{79} - 7 q^{80} - 6 q^{81} + q^{82} - 54 q^{83} - q^{85} + 14 q^{86} + 16 q^{87} + 4 q^{89} - 16 q^{90} + 54 q^{92} - 7 q^{93} + 45 q^{94} - 6 q^{95} - 38 q^{96} - 35 q^{97} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.425563 + 0.737096i 0.300918 + 0.521206i 0.976344 0.216222i \(-0.0693735\pi\)
−0.675426 + 0.737428i \(0.736040\pi\)
\(3\) −0.330612 0.572636i −0.190879 0.330612i 0.754663 0.656113i \(-0.227800\pi\)
−0.945542 + 0.325501i \(0.894467\pi\)
\(4\) 0.637793 1.10469i 0.318896 0.552345i
\(5\) 3.44148 1.53908 0.769538 0.638601i \(-0.220487\pi\)
0.769538 + 0.638601i \(0.220487\pi\)
\(6\) 0.281392 0.487385i 0.114878 0.198974i
\(7\) 0 0
\(8\) 2.78793 0.985684
\(9\) 1.28139 2.21944i 0.427131 0.739812i
\(10\) 1.46456 + 2.53670i 0.463136 + 0.802175i
\(11\) 0.448993 + 0.777679i 0.135377 + 0.234479i 0.925741 0.378158i \(-0.123442\pi\)
−0.790365 + 0.612637i \(0.790109\pi\)
\(12\) −0.843447 −0.243482
\(13\) −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 \(-0.908801\pi\)
0.724363 + 0.689419i \(0.242134\pi\)
\(18\) 2.18125 0.514126
\(19\) −0.519020 + 0.898968i −0.119071 + 0.206237i −0.919400 0.393324i \(-0.871325\pi\)
0.800329 + 0.599562i \(0.204658\pi\)
\(20\) 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 −0.994355 0.106104i \(-0.966162\pi\)
0.405288 0.914189i \(-0.367171\pi\)
\(24\) −0.921723 1.59647i −0.188146 0.325878i
\(25\) 6.84378 1.36876
\(26\) −2.69617 1.46563i −0.528762 0.287434i
\(27\) −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 \(0.778807\pi\)
\(30\) 0.968404 1.67733i 0.176806 0.306236i
\(31\) −9.13385 −1.64049 −0.820244 0.572014i \(-0.806162\pi\)
−0.820244 + 0.572014i \(0.806162\pi\)
\(32\) 2.86381 4.96026i 0.506254 0.876858i
\(33\) 0.296885 0.514219i 0.0516810 0.0895141i
\(34\) −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 0.860636 + 0.509221i \(0.170067\pi\)
0.0106808 + 0.999943i \(0.496600\pi\)
\(38\) −0.883501 −0.143323
\(39\) 2.09460 + 1.13862i 0.335404 + 0.182325i
\(40\) 9.59462 1.51704
\(41\) 2.66571 + 4.61715i 0.416314 + 0.721078i 0.995565 0.0940715i \(-0.0299882\pi\)
−0.579251 + 0.815149i \(0.696655\pi\)
\(42\) 0 0
\(43\) 1.95732 3.39018i 0.298489 0.516998i −0.677302 0.735706i \(-0.736851\pi\)
0.975790 + 0.218708i \(0.0701841\pi\)
\(44\) 1.14546 0.172684
\(45\) 4.40988 7.63814i 0.657387 1.13863i
\(46\) 2.40448 4.16469i 0.354522 0.614050i
\(47\) 7.19129 1.04896 0.524479 0.851423i \(-0.324260\pi\)
0.524479 + 0.851423i \(0.324260\pi\)
\(48\) −0.0589445 + 0.102095i −0.00850791 + 0.0147361i
\(49\) 0 0
\(50\) 2.91246 + 5.04452i 0.411883 + 0.713403i
\(51\) 1.28066 0.179329
\(52\) 0.118109 + 4.59767i 0.0163788 + 0.637582i
\(53\) −9.38648 −1.28933 −0.644666 0.764464i \(-0.723004\pi\)
−0.644666 + 0.764464i \(0.723004\pi\)
\(54\) −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
\(58\) −0.781307 + 1.35326i −0.102591 + 0.177692i
\(59\) 0.255259 0.442121i 0.0332318 0.0575592i −0.848931 0.528503i \(-0.822753\pi\)
0.882163 + 0.470944i \(0.156087\pi\)
\(60\) −2.90270 −0.374737
\(61\) −0.718095 + 1.24378i −0.0919426 + 0.159249i −0.908328 0.418258i \(-0.862641\pi\)
0.816386 + 0.577507i \(0.195974\pi\)
\(62\) −3.88702 6.73252i −0.493653 0.855031i
\(63\) 0 0
\(64\) 4.51834 0.564792
\(65\) −10.5831 + 6.47813i −1.31268 + 0.803513i
\(66\) 0.505372 0.0622070
\(67\) 4.22466 + 7.31732i 0.516124 + 0.893953i 0.999825 + 0.0187197i \(0.00595900\pi\)
−0.483701 + 0.875233i \(0.660708\pi\)
\(68\) 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 \(0.101070\pi\)
\(72\) 3.57244 6.18764i 0.421016 0.729221i
\(73\) 10.9005 1.27581 0.637905 0.770115i \(-0.279801\pi\)
0.637905 + 0.770115i \(0.279801\pi\)
\(74\) −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
\(79\) −12.0918 −1.36043 −0.680216 0.733012i \(-0.738114\pi\)
−0.680216 + 0.733012i \(0.738114\pi\)
\(80\) −0.306789 0.531375i −0.0343001 0.0594095i
\(81\) −2.62811 4.55201i −0.292012 0.505779i
\(82\) −2.26886 + 3.92977i −0.250553 + 0.433971i
\(83\) 1.51669 0.166479 0.0832393 0.996530i \(-0.473473\pi\)
0.0832393 + 0.996530i \(0.473473\pi\)
\(84\) 0 0
\(85\) −3.33274 + 5.77248i −0.361487 + 0.626113i
\(86\) 3.33185 0.359283
\(87\) 0.606982 1.05132i 0.0650754 0.112714i
\(88\) 1.25176 + 2.16812i 0.133438 + 0.231122i
\(89\) −6.80391 11.7847i −0.721213 1.24918i −0.960514 0.278232i \(-0.910252\pi\)
0.239301 0.970945i \(-0.423082\pi\)
\(90\) 7.50673 0.791279
\(91\) 0 0
\(92\) −7.20722 −0.751405
\(93\) 3.01976 + 5.23037i 0.313134 + 0.542364i
\(94\) 3.06035 + 5.30067i 0.315651 + 0.546723i
\(95\) −1.78619 + 3.09378i −0.183260 + 0.317415i
\(96\) −3.78723 −0.386533
\(97\) −0.253120 + 0.438417i −0.0257005 + 0.0445145i −0.878590 0.477578i \(-0.841515\pi\)
0.852889 + 0.522092i \(0.174848\pi\)
\(98\) 0 0
\(99\) 2.30134 0.231294
\(100\) 4.36491 7.56025i 0.436491 0.756025i
\(101\) 2.99327 + 5.18450i 0.297842 + 0.515877i 0.975642 0.219369i \(-0.0703999\pi\)
−0.677800 + 0.735246i \(0.737067\pi\)
\(102\) 0.545002 + 0.943972i 0.0539633 + 0.0934671i
\(103\) −4.13302 −0.407239 −0.203619 0.979050i \(-0.565270\pi\)
−0.203619 + 0.979050i \(0.565270\pi\)
\(104\) −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 0.974160 + 0.225858i \(0.0725186\pi\)
−0.291481 + 0.956577i \(0.594148\pi\)
\(108\) −2.34596 + 4.06331i −0.225740 + 0.390993i
\(109\) −4.20237 −0.402514 −0.201257 0.979538i \(-0.564503\pi\)
−0.201257 + 0.979538i \(0.564503\pi\)
\(110\) −1.31516 + 2.27792i −0.125396 + 0.217191i
\(111\) 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
\(115\) −9.72240 16.8397i −0.906618 1.57031i
\(116\) 2.34190 0.217440
\(117\) 0.237294 + 9.23720i 0.0219379 + 0.853980i
\(118\) 0.434514 0.0400003
\(119\) 0 0
\(120\) −3.17209 5.49422i −0.289571 0.501552i
\(121\) 5.09681 8.82793i 0.463346 0.802539i
\(122\) −1.22238 −0.110669
\(123\) 1.76263 3.05297i 0.158931 0.275277i
\(124\) −5.82550 + 10.0901i −0.523145 + 0.906114i
\(125\) 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
\(129\) −2.58845 −0.227901
\(130\) −9.27880 5.04394i −0.813804 0.442383i
\(131\) −12.0354 −1.05154 −0.525769 0.850627i \(-0.676222\pi\)
−0.525769 + 0.850627i \(0.676222\pi\)
\(132\) −0.378702 0.655931i −0.0329618 0.0570914i
\(133\) 0 0
\(134\) −3.59571 + 6.22796i −0.310622 + 0.538014i
\(135\) −12.6586 −1.08948
\(136\) −2.69985 + 4.67627i −0.231510 + 0.400987i
\(137\) −4.35857 + 7.54927i −0.372378 + 0.644978i −0.989931 0.141552i \(-0.954791\pi\)
0.617553 + 0.786529i \(0.288124\pi\)
\(138\) −3.17980 −0.270683
\(139\) −2.10625 + 3.64813i −0.178650 + 0.309430i −0.941418 0.337241i \(-0.890506\pi\)
0.762769 + 0.646672i \(0.223840\pi\)
\(140\) 0 0
\(141\) −2.37752 4.11799i −0.200224 0.346798i
\(142\) 2.93500 0.246300
\(143\) −2.84461 1.54633i −0.237878 0.129310i
\(144\) −0.456917 −0.0380764
\(145\) 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
\(149\) −2.93242 + 5.07910i −0.240233 + 0.416096i −0.960781 0.277310i \(-0.910557\pi\)
0.720548 + 0.693406i \(0.243891\pi\)
\(150\) 1.92578 3.33555i 0.157240 0.272347i
\(151\) −16.8568 −1.37179 −0.685893 0.727702i \(-0.740588\pi\)
−0.685893 + 0.727702i \(0.740588\pi\)
\(152\) −1.44699 + 2.50626i −0.117367 + 0.203285i
\(153\) 2.48181 + 4.29862i 0.200643 + 0.347523i
\(154\) 0 0
\(155\) −31.4339 −2.52483
\(156\) 2.59374 1.58768i 0.207666 0.127116i
\(157\) −1.93900 −0.154749 −0.0773746 0.997002i \(-0.524654\pi\)
−0.0773746 + 0.997002i \(0.524654\pi\)
\(158\) −5.14581 8.91280i −0.409379 0.709065i
\(159\) 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
\(163\) 5.94797 10.3022i 0.465881 0.806929i −0.533360 0.845888i \(-0.679071\pi\)
0.999241 + 0.0389590i \(0.0124042\pi\)
\(164\) 6.80069 0.531045
\(165\) 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 \(-0.945043\pi\)
0.343787 0.939048i \(-0.388290\pi\)
\(168\) 0 0
\(169\) 5.91338 11.5772i 0.454875 0.890555i
\(170\) −5.67316 −0.435112
\(171\) 1.33013 + 2.30386i 0.101718 + 0.176181i
\(172\) −2.49673 4.32447i −0.190374 0.329738i
\(173\) 4.99328 8.64862i 0.379632 0.657542i −0.611377 0.791340i \(-0.709384\pi\)
0.991009 + 0.133798i \(0.0427172\pi\)
\(174\) 1.03324 0.0783295
\(175\) 0 0
\(176\) 0.0800507 0.138652i 0.00603405 0.0104513i
\(177\) −0.337566 −0.0253730
\(178\) 5.79098 10.0303i 0.434052 0.751801i
\(179\) −4.58829 7.94715i −0.342945 0.593998i 0.642033 0.766677i \(-0.278091\pi\)
−0.984978 + 0.172679i \(0.944758\pi\)
\(180\) −5.62518 9.74310i −0.419276 0.726208i
\(181\) 6.00489 0.446340 0.223170 0.974780i \(-0.428360\pi\)
0.223170 + 0.974780i \(0.428360\pi\)
\(182\) 0 0
\(183\) 0.949642 0.0701995
\(184\) −7.87609 13.6418i −0.580633 1.00569i
\(185\) 18.2399 + 31.5924i 1.34102 + 2.32272i
\(186\) −2.57019 + 4.45170i −0.188456 + 0.326415i
\(187\) −1.73923 −0.127185
\(188\) 4.58655 7.94415i 0.334509 0.579386i
\(189\) 0 0
\(190\) −3.04055 −0.220585
\(191\) −0.658061 + 1.13980i −0.0476156 + 0.0824727i −0.888851 0.458197i \(-0.848496\pi\)
0.841235 + 0.540669i \(0.181829\pi\)
\(192\) −1.49382 2.58736i −0.107807 0.186727i
\(193\) 8.21270 + 14.2248i 0.591163 + 1.02392i 0.994076 + 0.108686i \(0.0346643\pi\)
−0.402913 + 0.915238i \(0.632002\pi\)
\(194\) −0.430874 −0.0309350
\(195\) 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 0.0714284 0.997446i \(-0.477244\pi\)
0.828099 0.560582i \(-0.189422\pi\)
\(200\) 19.0800 1.34916
\(201\) 2.79344 4.83838i 0.197034 0.341273i
\(202\) −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
\(206\) −1.75886 3.04643i −0.122546 0.212255i
\(207\) −14.4801 −1.00643
\(208\) 0.564779 + 0.307013i 0.0391604 + 0.0212875i
\(209\) −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 \(0.770512\pi\)
\(212\) −5.98663 + 10.3691i −0.411164 + 0.712156i
\(213\) −2.28014 −0.156233
\(214\) −6.01038 + 10.4103i −0.410861 + 0.711633i
\(215\) 6.73608 11.6672i 0.459397 0.795699i
\(216\) −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
\(220\) 3.94207 0.265774
\(221\) −0.179334 6.98096i −0.0120633 0.469590i
\(222\) 5.96552 0.400380
\(223\) −1.17906 2.04219i −0.0789558 0.136755i 0.823844 0.566817i \(-0.191825\pi\)
−0.902800 + 0.430061i \(0.858492\pi\)
\(224\) 0 0
\(225\) 8.76956 15.1893i 0.584637 1.01262i
\(226\) −11.7195 −0.779571
\(227\) −13.1463 + 22.7701i −0.872551 + 1.51130i −0.0132022 + 0.999913i \(0.504203\pi\)
−0.859349 + 0.511390i \(0.829131\pi\)
\(228\) 0.437765 0.758232i 0.0289917 0.0502151i
\(229\) 0.0685555 0.00453027 0.00226514 0.999997i \(-0.499279\pi\)
0.00226514 + 0.999997i \(0.499279\pi\)
\(230\) 8.27498 14.3327i 0.545636 0.945069i
\(231\) 0 0
\(232\) 2.55924 + 4.43273i 0.168022 + 0.291023i
\(233\) 14.6703 0.961082 0.480541 0.876972i \(-0.340440\pi\)
0.480541 + 0.876972i \(0.340440\pi\)
\(234\) −6.70772 + 4.10592i −0.438498 + 0.268412i
\(235\) 24.7487 1.61443
\(236\) −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 \(0.465399\pi\)
\(240\) −0.202856 + 0.351357i −0.0130943 + 0.0226800i
\(241\) 4.28989 7.43031i 0.276336 0.478628i −0.694135 0.719845i \(-0.744213\pi\)
0.970471 + 0.241216i \(0.0775464\pi\)
\(242\) 8.67605 0.557718
\(243\) −7.25513 + 12.5662i −0.465417 + 0.806125i
\(244\) 0.915991 + 1.58654i 0.0586403 + 0.101568i
\(245\) 0 0
\(246\) 3.00044 0.191301
\(247\) −0.0961145 3.74147i −0.00611562 0.238064i
\(248\) −25.4646 −1.61700
\(249\) −0.501436 0.868513i −0.0317772 0.0550398i
\(250\) 2.70033 + 4.67711i 0.170784 + 0.295806i
\(251\) −10.7575 + 18.6326i −0.679010 + 1.17608i 0.296270 + 0.955104i \(0.404257\pi\)
−0.975280 + 0.220975i \(0.929076\pi\)
\(252\) 0 0
\(253\) 2.53687 4.39399i 0.159492 0.276248i
\(254\) 0.827704 1.43363i 0.0519348 0.0899537i
\(255\) 4.40737 0.276000
\(256\) 7.75668 13.4350i 0.484793 0.839686i
\(257\) −2.46896 4.27636i −0.154010 0.266752i 0.778688 0.627411i \(-0.215885\pi\)
−0.932698 + 0.360659i \(0.882552\pi\)
\(258\) −1.10155 1.90794i −0.0685795 0.118783i
\(259\) 0 0
\(260\) 0.406471 + 15.8228i 0.0252083 + 0.981288i
\(261\) 4.70511 0.291239
\(262\) −5.12182 8.87125i −0.316427 0.548068i
\(263\) 4.47719 + 7.75473i 0.276076 + 0.478177i 0.970406 0.241480i \(-0.0776327\pi\)
−0.694330 + 0.719656i \(0.744299\pi\)
\(264\) 0.827695 1.43361i 0.0509411 0.0882326i
\(265\) −32.3034 −1.98438
\(266\) 0 0
\(267\) −4.49890 + 7.79233i −0.275328 + 0.476883i
\(268\) 10.7778 0.658360
\(269\) 2.41172 4.17723i 0.147045 0.254690i −0.783089 0.621910i \(-0.786357\pi\)
0.930134 + 0.367220i \(0.119690\pi\)
\(270\) −5.38702 9.33060i −0.327844 0.567842i
\(271\) 3.71072 + 6.42715i 0.225410 + 0.390422i 0.956442 0.291921i \(-0.0942945\pi\)
−0.731032 + 0.682343i \(0.760961\pi\)
\(272\) 0.345312 0.0209376
\(273\) 0 0
\(274\) −7.41938 −0.448221
\(275\) 3.07281 + 5.32226i 0.185297 + 0.320944i
\(276\) 2.38279 + 4.12712i 0.143427 + 0.248423i
\(277\) −1.90816 + 3.30503i −0.114650 + 0.198580i −0.917640 0.397413i \(-0.869908\pi\)
0.802990 + 0.595993i \(0.203241\pi\)
\(278\) −3.58536 −0.215036
\(279\) −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 \(0.417918\pi\)
\(282\) 2.02357 3.50493i 0.120502 0.208715i
\(283\) −7.63217 13.2193i −0.453686 0.785807i 0.544926 0.838484i \(-0.316558\pi\)
−0.998612 + 0.0526775i \(0.983224\pi\)
\(284\) −2.19935 3.80938i −0.130507 0.226045i
\(285\) 2.36215 0.139921
\(286\) −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
\(291\) 0.334738 0.0196227
\(292\) 6.95227 12.0417i 0.406851 0.704687i
\(293\) 2.96982 5.14388i 0.173499 0.300509i −0.766142 0.642671i \(-0.777826\pi\)
0.939641 + 0.342163i \(0.111159\pi\)
\(294\) 0 0
\(295\) 0.878467 1.52155i 0.0511463 0.0885881i
\(296\) 14.7761 + 25.5929i 0.858842 + 1.48756i
\(297\) −1.65151 2.86049i −0.0958301 0.165983i
\(298\) −4.99171 −0.289162
\(299\) 17.8983 + 9.72949i 1.03508 + 0.562671i
\(300\) −5.77236 −0.333267
\(301\) 0 0
\(302\) −7.17362 12.4251i −0.412796 0.714983i
\(303\) 1.97922 3.42811i 0.113703 0.196940i
\(304\) 0.185071 0.0106146
\(305\) −2.47131 + 4.28043i −0.141507 + 0.245097i
\(306\) −2.11233 + 3.65867i −0.120754 + 0.209152i
\(307\) 22.2133 1.26778 0.633891 0.773422i \(-0.281457\pi\)
0.633891 + 0.773422i \(0.281457\pi\)
\(308\) 0 0
\(309\) 1.36642 + 2.36672i 0.0777332 + 0.134638i
\(310\) −13.3771 23.1698i −0.759769 1.31596i
\(311\) 9.84259 0.558122 0.279061 0.960273i \(-0.409977\pi\)
0.279061 + 0.960273i \(0.409977\pi\)
\(312\) 5.83961 + 3.17440i 0.330603 + 0.179715i
\(313\) −20.9125 −1.18205 −0.591023 0.806655i \(-0.701276\pi\)
−0.591023 + 0.806655i \(0.701276\pi\)
\(314\) −0.825166 1.42923i −0.0465668 0.0806561i
\(315\) 0 0
\(316\) −7.71205 + 13.3577i −0.433837 + 0.751427i
\(317\) −25.3603 −1.42438 −0.712188 0.701989i \(-0.752295\pi\)
−0.712188 + 0.701989i \(0.752295\pi\)
\(318\) −2.64128 + 4.57483i −0.148116 + 0.256544i
\(319\) −0.824324 + 1.42777i −0.0461533 + 0.0799398i
\(320\) 15.5498 0.869259
\(321\) 4.66935 8.08755i 0.260618 0.451403i
\(322\) 0 0
\(323\) −1.00524 1.74113i −0.0559331 0.0968790i
\(324\) −6.70475 −0.372486
\(325\) −21.0458 + 12.8825i −1.16741 + 0.714593i
\(326\) 10.1249 0.560768
\(327\) 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
\(331\) −0.891417 + 1.54398i −0.0489967 + 0.0848648i −0.889484 0.456967i \(-0.848936\pi\)
0.840487 + 0.541832i \(0.182269\pi\)
\(332\) 0.967335 1.67547i 0.0530894 0.0919536i
\(333\) 27.1656 1.48866
\(334\) 7.05414 12.2181i 0.385985 0.668546i
\(335\) 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 \(0.416138\pi\)
\(338\) 11.0500 0.568103i 0.601043 0.0309007i
\(339\) 9.10468 0.494498
\(340\) 4.25120 + 7.36329i 0.230554 + 0.399331i
\(341\) −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
\(345\) −6.42867 + 11.1348i −0.346108 + 0.599477i
\(346\) 8.49982 0.456953
\(347\) −0.316694 + 0.548531i −0.0170010 + 0.0294467i −0.874401 0.485204i \(-0.838745\pi\)
0.857400 + 0.514651i \(0.172079\pi\)
\(348\) −0.774258 1.34105i −0.0415046 0.0718881i
\(349\) −15.2994 26.4994i −0.818960 1.41848i −0.906449 0.422315i \(-0.861217\pi\)
0.0874885 0.996166i \(-0.472116\pi\)
\(350\) 0 0
\(351\) 11.3112 6.92381i 0.603749 0.369565i
\(352\) 5.14332 0.274140
\(353\) 0.550173 + 0.952928i 0.0292828 + 0.0507192i 0.880295 0.474426i \(-0.157344\pi\)
−0.851013 + 0.525145i \(0.824011\pi\)
\(354\) −0.143655 0.248819i −0.00763520 0.0132246i
\(355\) 5.93375 10.2776i 0.314931 0.545476i
\(356\) −17.3579 −0.919969
\(357\) 0 0
\(358\) 3.90521 6.76402i 0.206397 0.357489i
\(359\) −9.77386 −0.515845 −0.257922 0.966166i \(-0.583038\pi\)
−0.257922 + 0.966166i \(0.583038\pi\)
\(360\) 12.2945 21.2946i 0.647975 1.12233i
\(361\) 8.96124 + 15.5213i 0.471644 + 0.816912i
\(362\) 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
\(367\) 5.57363 + 9.65381i 0.290941 + 0.503925i 0.974033 0.226408i \(-0.0726983\pi\)
−0.683092 + 0.730333i \(0.739365\pi\)
\(368\) −0.503679 + 0.872397i −0.0262561 + 0.0454769i
\(369\) 13.6633 0.711283
\(370\) −15.5244 + 26.8891i −0.807076 + 1.39790i
\(371\) 0 0
\(372\) 7.70391 0.399429
\(373\) 15.3651 26.6131i 0.795573 1.37797i −0.126902 0.991915i \(-0.540504\pi\)
0.922475 0.386057i \(-0.126163\pi\)
\(374\) −0.740150 1.28198i −0.0382723 0.0662895i
\(375\) −2.09783 3.63355i −0.108332 0.187636i
\(376\) 20.0489 1.03394
\(377\) −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
\(382\) −1.12019 −0.0573137
\(383\) 0.294631 0.510317i 0.0150550 0.0260760i −0.858400 0.512981i \(-0.828541\pi\)
0.873455 + 0.486905i \(0.161874\pi\)
\(384\) −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
\(388\) 0.322877 + 0.559239i 0.0163916 + 0.0283910i
\(389\) 5.69945 0.288974 0.144487 0.989507i \(-0.453847\pi\)
0.144487 + 0.989507i \(0.453847\pi\)
\(390\) 0.179334 + 6.98096i 0.00908091 + 0.353495i
\(391\) 10.9432 0.553422
\(392\) 0 0
\(393\) 3.97904 + 6.89191i 0.200716 + 0.347651i
\(394\) −10.8891 + 18.8605i −0.548584 + 0.950176i
\(395\) −41.6136 −2.09381
\(396\) 1.46778 2.54227i 0.0737588 0.127754i
\(397\) 12.7641 22.1082i 0.640614 1.10958i −0.344682 0.938720i \(-0.612013\pi\)
0.985296 0.170857i \(-0.0546535\pi\)
\(398\) 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 −0.986145 0.165884i \(-0.946952\pi\)
0.349413 0.936969i \(-0.386381\pi\)
\(402\) 4.75514 0.237165
\(403\) 28.0882 17.1933i 1.39917 0.856457i
\(404\) 7.63635 0.379922
\(405\) −9.04457 15.6657i −0.449428 0.778433i
\(406\) 0 0
\(407\) −4.75934 + 8.24341i −0.235912 + 0.408611i
\(408\) 3.57040 0.176761
\(409\) −0.0734938 + 0.127295i −0.00363403 + 0.00629433i −0.867837 0.496850i \(-0.834490\pi\)
0.864203 + 0.503144i \(0.167823\pi\)
\(410\) −7.80822 + 13.5242i −0.385621 + 0.667914i
\(411\) 5.76398 0.284316
\(412\) −2.63601 + 4.56570i −0.129867 + 0.224936i
\(413\) 0 0
\(414\) −6.16217 10.6732i −0.302854 0.524559i
\(415\) 5.21966 0.256223
\(416\) 0.530333 + 20.6444i 0.0260017 + 1.01217i
\(417\) 2.78540 0.136402
\(418\) −0.396686 0.687080i −0.0194026 0.0336062i
\(419\) −6.84795 11.8610i −0.334544 0.579447i 0.648853 0.760914i \(-0.275249\pi\)
−0.983397 + 0.181466i \(0.941916\pi\)
\(420\) 0 0
\(421\) 3.44169 0.167738 0.0838688 0.996477i \(-0.473272\pi\)
0.0838688 + 0.996477i \(0.473272\pi\)
\(422\) −2.42421 + 4.19885i −0.118009 + 0.204397i
\(423\) 9.21486 15.9606i 0.448042 0.776032i
\(424\) −26.1689 −1.27087
\(425\) −6.62754 + 11.4792i −0.321483 + 0.556825i
\(426\) −0.970345 1.68069i −0.0470134 0.0814295i
\(427\) 0 0
\(428\) 18.0156 0.870816
\(429\) 0.0549785 + 2.14016i 0.00265439 + 0.103328i
\(430\) 11.4665 0.552964
\(431\) −11.1455 19.3046i −0.536861 0.929870i −0.999071 0.0430997i \(-0.986277\pi\)
0.462210 0.886771i \(-0.347057\pi\)
\(432\) 0.327896 + 0.567932i 0.0157759 + 0.0273246i
\(433\) 12.9481 22.4268i 0.622247 1.07776i −0.366819 0.930292i \(-0.619553\pi\)
0.989066 0.147472i \(-0.0471136\pi\)
\(434\) 0 0
\(435\) 2.08892 3.61811i 0.100156 0.173475i
\(436\) −2.68024 + 4.64232i −0.128360 + 0.222327i
\(437\) 5.86505 0.280564
\(438\) 3.06732 5.31275i 0.146562 0.253853i
\(439\) 13.9919 + 24.2347i 0.667798 + 1.15666i 0.978519 + 0.206159i \(0.0660963\pi\)
−0.310721 + 0.950501i \(0.600570\pi\)
\(440\) 4.30792 + 7.46153i 0.205372 + 0.355715i
\(441\) 0 0
\(442\) 5.06932 3.10302i 0.241123 0.147596i
\(443\) 33.2089 1.57780 0.788900 0.614521i \(-0.210651\pi\)
0.788900 + 0.614521i \(0.210651\pi\)
\(444\) −4.47028 7.74275i −0.212150 0.367454i
\(445\) −23.4155 40.5568i −1.11000 1.92258i
\(446\) 1.00353 1.73816i 0.0475185 0.0823044i
\(447\) 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 \(0.320443\pi\)
\(450\) 14.9280 0.703712
\(451\) −2.39377 + 4.14614i −0.112718 + 0.195234i
\(452\) 8.78205 + 15.2110i 0.413073 + 0.715464i
\(453\) 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 0.874628 0.484794i \(-0.161105\pi\)
−0.857158 + 0.515053i \(0.827772\pi\)
\(458\) 0.0291746 + 0.0505320i 0.00136324 + 0.00236120i
\(459\) 3.56203 6.16961i 0.166261 0.287973i
\(460\) −24.8035 −1.15647
\(461\) 16.5855 28.7269i 0.772464 1.33795i −0.163744 0.986503i \(-0.552357\pi\)
0.936209 0.351445i \(-0.114309\pi\)
\(462\) 0 0
\(463\) −30.7521 −1.42917 −0.714586 0.699548i \(-0.753385\pi\)
−0.714586 + 0.699548i \(0.753385\pi\)
\(464\) 0.163664 0.283475i 0.00759792 0.0131600i
\(465\) 10.3924 + 18.0002i 0.481937 + 0.834740i
\(466\) 6.24313 + 10.8134i 0.289207 + 0.500922i
\(467\) −29.6065 −1.37003 −0.685013 0.728531i \(-0.740203\pi\)
−0.685013 + 0.728531i \(0.740203\pi\)
\(468\) 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
\(473\) 3.51530 0.161634
\(474\) −3.40253 + 5.89335i −0.156283 + 0.270691i
\(475\) −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
\(479\) −7.04527 12.2028i −0.321907 0.557559i 0.658975 0.752165i \(-0.270990\pi\)
−0.980881 + 0.194606i \(0.937657\pi\)
\(480\) −13.0337 −0.594903
\(481\) −33.5784 18.2532i −1.53104 0.832273i
\(482\) 7.30247 0.332618
\(483\) 0 0
\(484\) −6.50142 11.2608i −0.295519 0.511854i
\(485\) −0.871108 + 1.50880i −0.0395550 + 0.0685112i
\(486\) −12.3500 −0.560210
\(487\) 8.39773 14.5453i 0.380537 0.659110i −0.610602 0.791938i \(-0.709072\pi\)
0.991139 + 0.132828i \(0.0424057\pi\)
\(488\) −2.00200 + 3.46757i −0.0906263 + 0.156969i
\(489\) −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
\(493\) −3.55586 −0.160148
\(494\) 2.71692 1.66308i 0.122240 0.0748253i
\(495\) 7.92003 0.355979
\(496\) 0.814234 + 1.41029i 0.0365602 + 0.0633241i
\(497\) 0 0
\(498\) 0.426785 0.739213i 0.0191247 0.0331249i
\(499\) −23.3048 −1.04327 −0.521633 0.853170i \(-0.674677\pi\)
−0.521633 + 0.853170i \(0.674677\pi\)
\(500\) 4.04699 7.00960i 0.180987 0.313479i
\(501\) −5.48023 + 9.49203i −0.244838 + 0.424073i
\(502\) −18.3120 −0.817306
\(503\) 21.9415 38.0037i 0.978322 1.69450i 0.309816 0.950796i \(-0.399732\pi\)
0.668506 0.743707i \(-0.266934\pi\)
\(504\) 0 0
\(505\) 10.3013 + 17.8423i 0.458401 + 0.793974i
\(506\) 4.31839 0.191976
\(507\) −8.58456 + 0.441349i −0.381254 + 0.0196010i
\(508\) −2.48097 −0.110075
\(509\) −9.96210 17.2549i −0.441563 0.764809i 0.556243 0.831020i \(-0.312242\pi\)
−0.997806 + 0.0662109i \(0.978909\pi\)
\(510\) 1.87561 + 3.24866i 0.0830536 + 0.143853i
\(511\) 0 0
\(512\) −2.01529 −0.0890641
\(513\) 1.90908 3.30662i 0.0842879 0.145991i
\(514\) 2.10139 3.63972i 0.0926886 0.160541i
\(515\) −14.2237 −0.626771
\(516\) −1.65090 + 2.85944i −0.0726767 + 0.125880i
\(517\) 3.22884 + 5.59252i 0.142004 + 0.245959i
\(518\) 0 0
\(519\) −6.60335 −0.289855
\(520\) −29.5051 + 18.0606i −1.29388 + 0.792010i
\(521\) −16.5241 −0.723933 −0.361967 0.932191i \(-0.617895\pi\)
−0.361967 + 0.932191i \(0.617895\pi\)
\(522\) 2.00232 + 3.46812i 0.0876392 + 0.151796i
\(523\) 5.99809 + 10.3890i 0.262278 + 0.454279i 0.966847 0.255357i \(-0.0821929\pi\)
−0.704569 + 0.709636i \(0.748860\pi\)
\(524\) −7.67609 + 13.2954i −0.335332 + 0.580812i
\(525\) 0 0
\(526\) −3.81065 + 6.60024i −0.166152 + 0.287784i
\(527\) 8.84526 15.3204i 0.385305 0.667369i
\(528\) −0.105863 −0.00460709
\(529\) −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
\(534\) −7.65826 −0.331405
\(535\) 24.3026 + 42.0934i 1.05070 + 1.81986i
\(536\) 11.7781 + 20.4002i 0.508735 + 0.881155i
\(537\) −3.03388 + 5.25484i −0.130922 + 0.226763i
\(538\) 4.10536 0.176995
\(539\) 0 0
\(540\) −8.07356 + 13.9838i −0.347431 + 0.601767i
\(541\) 36.2317 1.55772 0.778860 0.627197i \(-0.215798\pi\)
0.778860 + 0.627197i \(0.215798\pi\)
\(542\) −3.15829 + 5.47031i −0.135660 + 0.234970i
\(543\) −1.98529 3.43862i −0.0851968 0.147565i
\(544\) 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
\(549\) 1.84032 + 3.18753i 0.0785430 + 0.136040i
\(550\) −2.61535 + 4.52991i −0.111519 + 0.193156i
\(551\) −1.90578 −0.0811888
\(552\) −5.20786 + 9.02027i −0.221661 + 0.383928i
\(553\) 0 0
\(554\) −3.24816 −0.138001
\(555\) 12.0606 20.8896i 0.511945 0.886715i
\(556\) 2.68670 + 4.65350i 0.113941 + 0.197352i
\(557\) −5.41399 9.37731i −0.229398 0.397329i 0.728232 0.685331i \(-0.240342\pi\)
−0.957630 + 0.288002i \(0.907009\pi\)
\(558\) −19.9232 −0.843417
\(559\) 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 \(-0.738991\pi\)
0.974298 + 0.225265i \(0.0723248\pi\)
\(564\) −6.06547 −0.255402
\(565\) −23.6936 + 41.0386i −0.996798 + 1.72651i
\(566\) 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 −0.996086 0.0883842i \(-0.971830\pi\)
0.421500 0.906828i \(-0.361504\pi\)
\(570\) 1.00524 + 1.74113i 0.0421049 + 0.0729279i
\(571\) −0.207758 −0.00869439 −0.00434719 0.999991i \(-0.501384\pi\)
−0.00434719 + 0.999991i \(0.501384\pi\)
\(572\) −3.52248 + 2.15617i −0.147282 + 0.0901542i
\(573\) 0.870251 0.0363552
\(574\) 0 0
\(575\) −19.3341 33.4876i −0.806288 1.39653i
\(576\) 5.78976 10.0282i 0.241240 0.417840i
\(577\) −3.32656 −0.138487 −0.0692434 0.997600i \(-0.522058\pi\)
−0.0692434 + 0.997600i \(0.522058\pi\)
\(578\) −5.63818 + 9.76562i −0.234518 + 0.406196i
\(579\) 5.43043 9.40577i 0.225681 0.390891i
\(580\) 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
\(584\) 30.3899 1.25754
\(585\) 0.816643 + 31.7896i 0.0337640 + 1.31434i
\(586\) 5.05538 0.208836
\(587\) 7.54051 + 13.0606i 0.311230 + 0.539067i 0.978629 0.205634i \(-0.0659256\pi\)
−0.667399 + 0.744701i \(0.732592\pi\)
\(588\) 0 0
\(589\) 4.74064 8.21104i 0.195335 0.338330i
\(590\) 1.49537 0.0615635
\(591\) 8.45953 14.6523i 0.347978 0.602716i
\(592\) 0.944935 1.63668i 0.0388366 0.0672670i
\(593\) 25.8491 1.06149 0.530747 0.847530i \(-0.321911\pi\)
0.530747 + 0.847530i \(0.321911\pi\)
\(594\) 1.40564 2.43464i 0.0576740 0.0998944i
\(595\) 0 0
\(596\) 3.74055 + 6.47882i 0.153219 + 0.265383i
\(597\) −16.7810 −0.686803
\(598\) 0.445274 + 17.3333i 0.0182086 + 0.708810i
\(599\) −35.5469 −1.45241 −0.726203 0.687480i \(-0.758717\pi\)
−0.726203 + 0.687480i \(0.758717\pi\)
\(600\) −6.30807 10.9259i −0.257526 0.446048i
\(601\) 13.6474 + 23.6379i 0.556688 + 0.964212i 0.997770 + 0.0667449i \(0.0212614\pi\)
−0.441082 + 0.897467i \(0.645405\pi\)
\(602\) 0 0
\(603\) 21.6538 0.881810
\(604\) −10.7511 + 18.6215i −0.437458 + 0.757699i
\(605\) 17.5406 30.3811i 0.713125 1.23517i
\(606\) 3.36913 0.136862
\(607\) 19.4629 33.7108i 0.789976 1.36828i −0.136006 0.990708i \(-0.543426\pi\)
0.925981 0.377570i \(-0.123240\pi\)
\(608\) 2.97274 + 5.14894i 0.120561 + 0.208817i
\(609\) 0 0
\(610\) −4.20679 −0.170328
\(611\) −22.1145 + 13.5367i −0.894656 + 0.547635i
\(612\) 6.33152 0.255937
\(613\) −0.443322 0.767857i −0.0179056 0.0310135i 0.856934 0.515427i \(-0.172367\pi\)
−0.874839 + 0.484413i \(0.839033\pi\)
\(614\) 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 \(0.919729\pi\)
\(618\) −1.16300 + 2.01437i −0.0467827 + 0.0810300i
\(619\) 2.05562 0.0826221 0.0413111 0.999146i \(-0.486847\pi\)
0.0413111 + 0.999146i \(0.486847\pi\)
\(620\) −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
\(625\) −12.3816 −0.495265
\(626\) −8.89959 15.4145i −0.355699 0.616089i
\(627\) 0.308178 + 0.533780i 0.0123074 + 0.0213171i
\(628\) −1.23668 + 2.14199i −0.0493489 + 0.0854749i
\(629\) −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 \(-0.190033\pi\)
\(632\) −33.7111 −1.34095
\(633\) 1.88332 3.26201i 0.0748554 0.129653i
\(634\) −10.7924 18.6930i −0.428621 0.742393i
\(635\) −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
\(640\) −13.0941 22.6796i −0.517588 0.896489i
\(641\) 9.53097 16.5081i 0.376451 0.652032i −0.614092 0.789234i \(-0.710478\pi\)
0.990543 + 0.137202i \(0.0438111\pi\)
\(642\) 7.94841 0.313699
\(643\) 5.26755 9.12367i 0.207732 0.359802i −0.743268 0.668994i \(-0.766725\pi\)
0.951000 + 0.309192i \(0.100058\pi\)
\(644\) 0 0
\(645\) −8.90811 −0.350756
\(646\) 0.855587 1.48192i 0.0336626 0.0583053i
\(647\) 12.0804 + 20.9239i 0.474930 + 0.822603i 0.999588 0.0287105i \(-0.00914011\pi\)
−0.524658 + 0.851313i \(0.675807\pi\)
\(648\) −7.32699 12.6907i −0.287831 0.498538i
\(649\) 0.458438 0.0179952
\(650\) −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 0.980829 + 0.194869i \(0.0624282\pi\)
−0.321653 + 0.946858i \(0.604238\pi\)
\(654\) −1.18251 + 2.04817i −0.0462400 + 0.0800900i
\(655\) −41.4196 −1.61840
\(656\) 0.475268 0.823189i 0.0185561 0.0321401i
\(657\) 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
\(661\) −8.83631 15.3049i −0.343693 0.595293i 0.641423 0.767188i \(-0.278345\pi\)
−0.985115 + 0.171894i \(0.945011\pi\)
\(662\) −1.51742 −0.0589760
\(663\) −3.93826 + 2.41068i −0.152949 + 0.0936230i
\(664\) 4.22844 0.164095
\(665\) 0 0
\(666\) 11.5607 + 20.0236i 0.447966 + 0.775900i
\(667\) 5.18664 8.98353i 0.200828 0.347844i
\(668\) −21.1441 −0.818091
\(669\) −0.779623 + 1.35035i −0.0301420 + 0.0522074i
\(670\) −12.3746 + 21.4334i −0.478071 + 0.828044i
\(671\) −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
\(675\) −25.1731 −0.968911
\(676\) −9.01772 13.9163i −0.346835 0.535243i
\(677\) −21.3074 −0.818909 −0.409455 0.912330i \(-0.634281\pi\)
−0.409455 + 0.912330i \(0.634281\pi\)
\(678\) 3.87461 + 6.71102i 0.148804 + 0.257735i
\(679\) 0 0
\(680\) −9.29147 + 16.0933i −0.356312 + 0.617150i
\(681\) 17.3853 0.666206
\(682\) 3.49049 6.04571i 0.133658 0.231502i
\(683\) 3.34878 5.80026i 0.128138 0.221941i −0.794817 0.606849i \(-0.792433\pi\)
0.922955 + 0.384908i \(0.125767\pi\)
\(684\) 3.39340 0.129750
\(685\) −14.9999 + 25.9806i −0.573118 + 0.992670i
\(686\) 0 0
\(687\) −0.0226652 0.0392573i −0.000864732 0.00149776i
\(688\) −0.697939 −0.0266087
\(689\) 28.8651 17.6688i 1.09967 0.673128i
\(690\) −10.9432 −0.416601
\(691\) 12.4632 + 21.5868i 0.474121 + 0.821202i 0.999561 0.0296291i \(-0.00943262\pi\)
−0.525440 + 0.850831i \(0.676099\pi\)
\(692\) −6.36936 11.0321i −0.242127 0.419376i
\(693\) 0 0
\(694\) −0.539093 −0.0204637
\(695\) −7.24861 + 12.5550i −0.274955 + 0.476237i
\(696\) 1.69223 2.93102i 0.0641437 0.111100i
\(697\) −10.3260 −0.391123
\(698\) 13.0217 22.5543i 0.492880 0.853694i
\(699\) −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 \(0.529774\pi\)
\(702\) 9.91715 + 5.39095i 0.374299 + 0.203468i
\(703\) −11.0032 −0.414995
\(704\) 2.02870 + 3.51382i 0.0764597 + 0.132432i
\(705\) −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
\(709\) 2.32249 4.02267i 0.0872228 0.151074i −0.819113 0.573632i \(-0.805534\pi\)
0.906336 + 0.422557i \(0.138867\pi\)
\(710\) 10.1007 0.379074
\(711\) −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
\(716\) −11.7055 −0.437455
\(717\) −1.10898 1.92082i −0.0414157 0.0717342i
\(718\) −4.15939 7.20427i −0.155227 0.268861i
\(719\) −15.8706 + 27.4887i −0.591875 + 1.02516i 0.402105 + 0.915594i \(0.368279\pi\)
−0.993980 + 0.109564i \(0.965055\pi\)
\(720\) −1.57247 −0.0586025
\(721\) 0 0
\(722\) −7.62714 + 13.2106i −0.283853 + 0.491647i
\(723\) −5.67315 −0.210987
\(724\) 3.82987 6.63354i 0.142336 0.246533i
\(725\) 6.28237 + 10.8814i 0.233322 + 0.404125i
\(726\) −2.86840 4.96822i −0.106456 0.184388i
\(727\) 47.8755 1.77560 0.887801 0.460227i \(-0.152232\pi\)
0.887801 + 0.460227i \(0.152232\pi\)
\(728\) 0 0
\(729\) −6.17412 −0.228671
\(730\) 15.9645 + 27.6514i 0.590873 + 1.02342i
\(731\) 3.79096 + 6.56613i 0.140214 + 0.242857i
\(732\) 0.605675 1.04906i 0.0223864 0.0387743i
\(733\) −7.60208 −0.280789 −0.140395 0.990096i \(-0.544837\pi\)
−0.140395 + 0.990096i \(0.544837\pi\)
\(734\) −4.74386 + 8.21660i −0.175099 + 0.303280i
\(735\) 0 0
\(736\) −32.3618 −1.19287
\(737\) −3.79368 + 6.57086i −0.139742 + 0.242041i
\(738\) 5.81459 + 10.0712i 0.214038 + 0.370725i
\(739\) 16.7118 + 28.9457i 0.614754 + 1.06479i 0.990428 + 0.138033i \(0.0440781\pi\)
−0.375673 + 0.926752i \(0.622589\pi\)
\(740\) 46.5330 1.71059
\(741\) −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
\(746\) 26.1552 0.957609
\(747\) 1.94348 3.36620i 0.0711081 0.123163i
\(748\) −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 0.854901 0.518791i \(-0.173618\pi\)
−0.876737 + 0.480971i \(0.840284\pi\)
\(752\) −0.641065 1.11036i −0.0233773 0.0404906i
\(753\) 14.2263 0.518434
\(754\) −0.144686 5.63223i −0.00526916 0.205114i
\(755\) −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 \(0.900625\pi\)
\(758\) 9.64207 16.7006i 0.350216 0.606592i
\(759\) −3.35487 −0.121774
\(760\) −4.97979 + 8.62525i −0.180636 + 0.312871i
\(761\) −17.3249 + 30.0075i −0.628026 + 1.08777i 0.359921 + 0.932983i \(0.382803\pi\)
−0.987947 + 0.154790i \(0.950530\pi\)
\(762\) −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
\(766\) 0.501537 0.0181213
\(767\) 0.0472700 + 1.84009i 0.00170682 + 0.0664418i
\(768\) −10.2578 −0.370146
\(769\) 3.27437 + 5.67138i 0.118077 + 0.204515i 0.919006 0.394245i \(-0.128994\pi\)
−0.800929 + 0.598760i \(0.795660\pi\)
\(770\) 0 0
\(771\) −1.63253 + 2.82763i −0.0587943 + 0.101835i
\(772\) 20.9520 0.754079
\(773\) −16.9637 + 29.3821i −0.610143 + 1.05680i 0.381073 + 0.924545i \(0.375555\pi\)
−0.991216 + 0.132254i \(0.957779\pi\)
\(774\) 4.26941 7.39484i 0.153461 0.265802i
\(775\) −62.5100 −2.24542
\(776\) −0.705683 + 1.22228i −0.0253325 + 0.0438772i
\(777\) 0 0
\(778\) 2.42547 + 4.20104i 0.0869575 + 0.150615i
\(779\) −5.53423 −0.198284
\(780\) 8.92632 5.46396i 0.319613 0.195641i
\(781\) 3.09659 0.110805
\(782\) 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
\(786\) −3.38667 + 5.86588i −0.120798 + 0.209229i
\(787\) −6.48717 + 11.2361i −0.231243 + 0.400524i −0.958174 0.286186i \(-0.907612\pi\)
0.726932 + 0.686710i \(0.240946\pi\)
\(788\) 32.6390 1.16272
\(789\) 2.96042 5.12760i 0.105394 0.182548i
\(790\) −17.7092 30.6732i −0.630065 1.09130i
\(791\) 0 0
\(792\) 6.41600 0.227983
\(793\) −0.132980 5.17655i −0.00472226 0.183825i
\(794\) 21.7278 0.771090
\(795\) 10.6799 + 18.4981i 0.378776 + 0.656059i
\(796\) −16.1864 28.0357i −0.573712 0.993699i
\(797\) −2.20956 + 3.82707i −0.0782667 + 0.135562i −0.902502 0.430685i \(-0.858272\pi\)
0.824235 + 0.566247i \(0.191605\pi\)
\(798\) 0 0
\(799\) −6.96408 + 12.0621i −0.246371 + 0.426728i
\(800\) 19.5993 33.9469i 0.692938 1.20020i
\(801\) −34.8739 −1.23221
\(802\) 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
\(807\) −3.18937 −0.112271
\(808\) 8.34504 + 14.4540i 0.293578 + 0.508491i
\(809\) −5.73580 9.93470i −0.201660 0.349285i 0.747403 0.664371i \(-0.231300\pi\)
−0.949063 + 0.315085i \(0.897967\pi\)
\(810\) 7.69807 13.3334i 0.270482 0.468489i
\(811\) 23.8664 0.838063 0.419032 0.907972i \(-0.362370\pi\)
0.419032 + 0.907972i \(0.362370\pi\)
\(812\) 0 0
\(813\) 2.45361 4.24978i 0.0860520 0.149046i
\(814\) −8.10159 −0.283960
\(815\) 20.4698 35.4548i 0.717026 1.24193i
\(816\) −0.114164 0.197738i −0.00399655 0.00692223i
\(817\) 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 −0.998880 0.0473197i \(-0.984932\pi\)
0.458460 0.888715i \(-0.348401\pi\)
\(822\) 2.45293 + 4.24861i 0.0855559 + 0.148187i
\(823\) 4.30678 7.45957i 0.150125 0.260024i −0.781148 0.624346i \(-0.785366\pi\)
0.931273 + 0.364321i \(0.118699\pi\)
\(824\) −11.5226 −0.401408
\(825\) 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 \(0.369573\pi\)
\(828\) −9.23528 + 15.9960i −0.320948 + 0.555898i
\(829\) 21.2806 + 36.8590i 0.739104 + 1.28017i 0.952899 + 0.303287i \(0.0980842\pi\)
−0.213795 + 0.976879i \(0.568582\pi\)
\(830\) 2.22129 + 3.84739i 0.0771022 + 0.133545i
\(831\) 2.52344 0.0875370
\(832\) −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
\(837\) 33.5965 1.16126
\(838\) 5.82846 10.0952i 0.201341 0.348733i
\(839\) −0.920524 + 1.59439i −0.0317800 + 0.0550446i −0.881478 0.472225i \(-0.843451\pi\)
0.849698 + 0.527270i \(0.176784\pi\)
\(840\) 0 0
\(841\) 12.8147 22.1957i 0.441885 0.765367i
\(842\) 1.46465 + 2.53686i 0.0504753 + 0.0874258i
\(843\) −2.82666 4.89591i −0.0973553 0.168624i
\(844\) 7.26635 0.250118
\(845\) 20.3508 39.8427i 0.700088 1.37063i
\(846\) 15.6860 0.539296
\(847\) 0 0
\(848\) 0.836755 + 1.44930i 0.0287343 + 0.0497692i
\(849\) −5.04657 + 8.74092i −0.173198 + 0.299988i
\(850\) −11.2817 −0.386960
\(851\) 29.9457 51.8675i 1.02653 1.77800i
\(852\) −1.45426 + 2.51885i −0.0498221 + 0.0862944i
\(853\) −27.0293 −0.925466 −0.462733 0.886498i \(-0.653131\pi\)
−0.462733 + 0.886498i \(0.653131\pi\)
\(854\) 0 0
\(855\) 4.57763 + 7.92869i 0.156552 + 0.271155i
\(856\) 19.6875 + 34.0998i 0.672906 + 1.16551i
\(857\) 16.7854 0.573377 0.286688 0.958024i \(-0.407446\pi\)
0.286688 + 0.958024i \(0.407446\pi\)
\(858\) −1.55411 + 0.951297i −0.0530563 + 0.0324767i
\(859\) 51.6116 1.76096 0.880482 0.474079i \(-0.157219\pi\)
0.880482 + 0.474079i \(0.157219\pi\)
\(860\) −8.59245 14.8826i −0.293000 0.507491i
\(861\) 0 0
\(862\) 9.48624 16.4306i 0.323102 0.559630i
\(863\) 21.9614 0.747573 0.373787 0.927515i \(-0.378059\pi\)
0.373787 + 0.927515i \(0.378059\pi\)
\(864\) −10.5338 + 18.2450i −0.358366 + 0.620709i
\(865\) 17.1843 29.7640i 0.584283 1.01201i
\(866\) 22.0410 0.748983
\(867\) 4.38020 7.58673i 0.148759 0.257659i
\(868\) 0 0
\(869\) −5.42913 9.40352i −0.184170 0.318993i
\(870\) 3.55586 0.120555
\(871\) −26.7654 14.5497i −0.906913 0.492997i
\(872\) −11.7159 −0.396752
\(873\) 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
\(877\) 4.80873 8.32896i 0.162379 0.281249i −0.773342 0.633989i \(-0.781417\pi\)
0.935721 + 0.352740i \(0.114750\pi\)
\(878\) −11.9089 + 20.6268i −0.401905 + 0.696120i
\(879\) −3.92743 −0.132469
\(880\) 0.275493 0.477167i 0.00928686 0.0160853i
\(881\) −14.4863 25.0910i −0.488055 0.845336i 0.511851 0.859075i \(-0.328960\pi\)
−0.999906 + 0.0137383i \(0.995627\pi\)
\(882\) 0 0
\(883\) 6.60727 0.222352 0.111176 0.993801i \(-0.464538\pi\)
0.111176 + 0.993801i \(0.464538\pi\)
\(884\) −7.82617 4.25430i −0.263223 0.143088i
\(885\) −1.16173 −0.0390510
\(886\) 14.1325 + 24.4781i 0.474789 + 0.822359i
\(887\) 15.7072 + 27.2057i 0.527397 + 0.913478i 0.999490 + 0.0319293i \(0.0101651\pi\)
−0.472094 + 0.881548i \(0.656502\pi\)
\(888\) 9.77029 16.9226i 0.327869 0.567886i
\(889\) 0 0
\(890\) 19.9295 34.5190i 0.668039 1.15708i
\(891\) 2.36000 4.08765i 0.0790631 0.136941i
\(892\) −3.00799 −0.100715
\(893\) −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
\(898\) −16.7556 −0.559142
\(899\) −8.38459 14.5225i −0.279642 0.484354i
\(900\) −11.1863 19.3753i −0.372877 0.645843i
\(901\) 9.08991 15.7442i 0.302829 0.524515i
\(902\) −4.07480 −0.135676
\(903\) 0 0
\(904\) −19.1942 + 33.2453i −0.638388 + 1.10572i
\(905\) 20.6657 0.686951
\(906\) −4.74337 + 8.21575i −0.157588 + 0.272950i
\(907\) −4.86821 8.43198i −0.161646 0.279979i 0.773813 0.633414i \(-0.218347\pi\)
−0.935459 + 0.353435i \(0.885014\pi\)
\(908\) 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
\(913\) 0.680984 + 1.17950i 0.0225373 + 0.0390357i
\(914\) −0.317871 + 0.550568i −0.0105142 + 0.0182112i
\(915\) 3.26817 0.108042
\(916\) 0.0437242 0.0757325i 0.00144469 0.00250227i
\(917\) 0 0
\(918\) 6.06346 0.200124
\(919\) −27.1402 + 47.0082i −0.895273 + 1.55066i −0.0618056 + 0.998088i \(0.519686\pi\)
−0.833467 + 0.552569i \(0.813647\pi\)
\(920\) −27.1054 46.9479i −0.893639 1.54783i
\(921\) −7.34398 12.7202i −0.241993 0.419143i
\(922\) 28.2327 0.929795
\(923\) 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
\(928\) 10.5155 0.345190
\(929\) 19.0960 33.0752i 0.626519 1.08516i −0.361726 0.932284i \(-0.617812\pi\)
0.988245 0.152878i \(-0.0488542\pi\)
\(930\) −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
\(934\) −12.5994 21.8228i −0.412266 0.714065i
\(935\) −5.98552 −0.195747
\(936\) 0.661561 + 25.7527i 0.0216238 + 0.841754i
\(937\) −19.0376 −0.621931 −0.310966 0.950421i \(-0.600652\pi\)
−0.310966 + 0.950421i \(0.600652\pi\)
\(938\) 0 0
\(939\) 6.91392 + 11.9753i 0.225627 + 0.390798i
\(940\) 15.7845 27.3396i 0.514835 0.891720i
\(941\) 46.1622 1.50484 0.752422 0.658682i \(-0.228886\pi\)
0.752422 + 0.658682i \(0.228886\pi\)
\(942\) −0.545619 + 0.945040i −0.0177772 + 0.0307911i
\(943\) 15.0616 26.0875i 0.490474 0.849526i
\(944\) −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 0.930998 0.365025i \(-0.118940\pi\)
−0.781620 + 0.623755i \(0.785606\pi\)
\(948\) 10.1988 0.331241
\(949\) −33.5210 + 20.5188i −1.08814 + 0.666068i
\(950\) −6.04648 −0.196174
\(951\) 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 \(-0.0906250\pi\)
\(954\) −20.4743 −0.662879
\(955\) −2.26470 + 3.92258i −0.0732841 + 0.126932i
\(956\) 2.13937 3.70550i 0.0691923 0.119844i
\(957\) 1.09012 0.0352387
\(958\) 5.99641 10.3861i 0.193735 0.335559i
\(959\) 0 0
\(960\) −5.14093 8.90436i −0.165923 0.287387i
\(961\) 52.4271 1.69120
\(962\) −0.835363 32.5184i −0.0269332 1.04843i
\(963\) 36.1952 1.16637
\(964\) −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 \(0.428637\pi\)
\(968\) 14.2096 24.6117i 0.456713 0.791050i
\(969\) −0.664689 + 1.15128i −0.0213529 + 0.0369843i
\(970\) −1.48284 −0.0476113
\(971\) −3.63437 + 6.29491i −0.116632 + 0.202013i −0.918431 0.395581i \(-0.870543\pi\)
0.801799 + 0.597594i \(0.203877\pi\)
\(972\) 9.25454 + 16.0293i 0.296839 + 0.514141i
\(973\) 0 0
\(974\) 14.2950 0.458043
\(975\) 14.3350 + 7.79247i 0.459086 + 0.249559i
\(976\) 0.256057 0.00819619
\(977\) −21.4050 37.0746i −0.684808 1.18612i −0.973497 0.228699i \(-0.926553\pi\)
0.288689 0.957423i \(-0.406781\pi\)
\(978\) −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
\(982\) 9.22152 15.9721i 0.294270 0.509691i
\(983\) −46.3088 −1.47702 −0.738511 0.674242i \(-0.764471\pi\)
−0.738511 + 0.674242i \(0.764471\pi\)
\(984\) 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
\(989\) −22.1182 −0.703319
\(990\) 3.37047 + 5.83782i 0.107121 + 0.185538i
\(991\) 29.1162 + 50.4307i 0.924907 + 1.60199i 0.791711 + 0.610896i \(0.209190\pi\)
0.133195 + 0.991090i \(0.457476\pi\)
\(992\) −26.1576 + 45.3062i −0.830504 + 1.43847i
\(993\) 1.17885 0.0374097
\(994\) 0 0
\(995\) 43.6703 75.6392i 1.38444 2.39792i
\(996\) −1.27925 −0.0405346
\(997\) 2.24739 3.89260i 0.0711757 0.123280i −0.828241 0.560372i \(-0.810658\pi\)
0.899417 + 0.437092i \(0.143992\pi\)
\(998\) −9.91765 17.1779i −0.313938 0.543756i
\(999\) −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.f.k.393.4 12
7.2 even 3 91.2.g.b.81.4 yes 12
7.3 odd 6 637.2.h.l.471.3 12
7.4 even 3 91.2.h.b.16.3 yes 12
7.5 odd 6 637.2.g.l.263.4 12
7.6 odd 2 637.2.f.j.393.4 12
13.3 even 3 8281.2.a.bz.1.3 6
13.9 even 3 inner 637.2.f.k.295.4 12
13.10 even 6 8281.2.a.ce.1.4 6
21.2 odd 6 819.2.n.d.172.3 12
21.11 odd 6 819.2.s.d.289.4 12
91.9 even 3 91.2.h.b.74.3 yes 12
91.16 even 3 1183.2.e.h.508.4 12
91.23 even 6 1183.2.e.g.508.3 12
91.48 odd 6 637.2.f.j.295.4 12
91.55 odd 6 8281.2.a.ca.1.3 6
91.61 odd 6 637.2.h.l.165.3 12
91.62 odd 6 8281.2.a.cf.1.4 6
91.74 even 3 91.2.g.b.9.4 12
91.81 even 3 1183.2.e.h.170.4 12
91.87 odd 6 637.2.g.l.373.4 12
91.88 even 6 1183.2.e.g.170.3 12
273.74 odd 6 819.2.n.d.100.3 12
273.191 odd 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 91.74 even 3
91.2.g.b.81.4 yes 12 7.2 even 3
91.2.h.b.16.3 yes 12 7.4 even 3
91.2.h.b.74.3 yes 12 91.9 even 3
637.2.f.j.295.4 12 91.48 odd 6
637.2.f.j.393.4 12 7.6 odd 2
637.2.f.k.295.4 12 13.9 even 3 inner
637.2.f.k.393.4 12 1.1 even 1 trivial
637.2.g.l.263.4 12 7.5 odd 6
637.2.g.l.373.4 12 91.87 odd 6
637.2.h.l.165.3 12 91.61 odd 6
637.2.h.l.471.3 12 7.3 odd 6
819.2.n.d.100.3 12 273.74 odd 6
819.2.n.d.172.3 12 21.2 odd 6
819.2.s.d.289.4 12 21.11 odd 6
819.2.s.d.802.4 12 273.191 odd 6
1183.2.e.g.170.3 12 91.88 even 6
1183.2.e.g.508.3 12 91.23 even 6
1183.2.e.h.170.4 12 91.81 even 3
1183.2.e.h.508.4 12 91.16 even 3
8281.2.a.bz.1.3 6 13.3 even 3
8281.2.a.ca.1.3 6 91.55 odd 6
8281.2.a.ce.1.4 6 13.10 even 6
8281.2.a.cf.1.4 6 91.62 odd 6