Properties

Label 630.2.bv.c.397.3
Level $630$
Weight $2$
Character 630.397
Analytic conductor $5.031$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [630,2,Mod(73,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.73");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.bv (of order \(12\), degree \(4\), 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: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 397.3
Root \(1.01089 + 0.750919i\) of defining polynomial
Character \(\chi\) \(=\) 630.397
Dual form 630.2.bv.c.73.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.20382 + 0.378409i) q^{5} +(0.126334 + 2.64273i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.20382 + 0.378409i) q^{5} +(0.126334 + 2.64273i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.03078 + 0.935904i) q^{10} +(2.81288 + 4.87205i) q^{11} +(-1.42962 - 1.42962i) q^{13} +(0.806019 + 2.51999i) q^{14} +(0.500000 - 0.866025i) q^{16} +(5.12784 + 1.37400i) q^{17} +(-1.94590 + 3.37040i) q^{19} +(-1.71936 + 1.42962i) q^{20} +(3.97801 + 3.97801i) q^{22} +(0.290892 + 1.08562i) q^{23} +(4.71361 - 1.66789i) q^{25} +(-1.75092 - 1.01089i) q^{26} +(1.43078 + 2.22551i) q^{28} +3.15502i q^{29} +(-3.33287 + 1.92423i) q^{31} +(0.258819 - 0.965926i) q^{32} +5.30873 q^{34} +(-1.27845 - 5.77629i) q^{35} +(4.86824 - 1.30444i) q^{37} +(-1.00727 + 3.75919i) q^{38} +(-1.29076 + 1.82591i) q^{40} -7.21050i q^{41} +(1.85669 - 1.85669i) q^{43} +(4.87205 + 2.81288i) q^{44} +(0.561961 + 0.973344i) q^{46} +(1.52590 + 5.69475i) q^{47} +(-6.96808 + 0.667734i) q^{49} +(4.12132 - 2.83103i) q^{50} +(-1.95290 - 0.523277i) q^{52} +(-1.33599 - 0.357978i) q^{53} +(-8.04270 - 9.67269i) q^{55} +(1.95803 + 1.77936i) q^{56} +(0.816578 + 3.04751i) q^{58} +(-2.73923 - 4.74448i) q^{59} +(-3.99172 - 2.30462i) q^{61} +(-2.72127 + 2.72127i) q^{62} -1.00000i q^{64} +(3.69160 + 2.60964i) q^{65} +(0.218698 - 0.816193i) q^{67} +(5.12784 - 1.37400i) q^{68} +(-2.72990 - 5.24858i) q^{70} -4.77710 q^{71} +(1.45256 - 5.42104i) q^{73} +(4.36475 - 2.51999i) q^{74} +3.89180i q^{76} +(-12.5202 + 8.04920i) q^{77} +(5.41079 + 3.12392i) q^{79} +(-0.774197 + 2.09777i) q^{80} +(-1.86622 - 6.96481i) q^{82} +(-5.67281 - 5.67281i) q^{83} +(-11.8207 - 1.08763i) q^{85} +(1.31288 - 2.27397i) q^{86} +(5.43407 + 1.45605i) q^{88} +(5.96090 - 10.3246i) q^{89} +(3.59749 - 3.95871i) q^{91} +(0.794732 + 0.794732i) q^{92} +(2.94782 + 5.10577i) q^{94} +(3.01302 - 8.16409i) q^{95} +(-6.63103 + 6.63103i) q^{97} +(-6.55783 + 2.44845i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 12 q^{5} + 8 q^{7} - 12 q^{10} + 12 q^{11} + 8 q^{16} + 36 q^{17} - 8 q^{22} + 4 q^{23} + 12 q^{25} - 12 q^{26} + 4 q^{28} + 24 q^{31} - 8 q^{35} + 4 q^{37} - 24 q^{38} - 8 q^{43} - 8 q^{46} - 12 q^{47} + 32 q^{50} + 28 q^{53} + 4 q^{56} - 32 q^{58} - 12 q^{61} + 8 q^{65} + 32 q^{67} + 36 q^{68} - 12 q^{70} - 16 q^{71} - 12 q^{73} - 16 q^{77} + 12 q^{80} - 48 q^{82} + 24 q^{85} - 12 q^{86} - 4 q^{88} - 16 q^{91} - 8 q^{92} - 20 q^{95} - 40 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) 0 0
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) −2.20382 + 0.378409i −0.985577 + 0.169230i
\(6\) 0 0
\(7\) 0.126334 + 2.64273i 0.0477497 + 0.998859i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 0 0
\(10\) −2.03078 + 0.935904i −0.642190 + 0.295959i
\(11\) 2.81288 + 4.87205i 0.848115 + 1.46898i 0.882888 + 0.469583i \(0.155596\pi\)
−0.0347729 + 0.999395i \(0.511071\pi\)
\(12\) 0 0
\(13\) −1.42962 1.42962i −0.396505 0.396505i 0.480493 0.876998i \(-0.340458\pi\)
−0.876998 + 0.480493i \(0.840458\pi\)
\(14\) 0.806019 + 2.51999i 0.215418 + 0.673495i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 5.12784 + 1.37400i 1.24368 + 0.333244i 0.819893 0.572516i \(-0.194033\pi\)
0.423790 + 0.905760i \(0.360699\pi\)
\(18\) 0 0
\(19\) −1.94590 + 3.37040i −0.446420 + 0.773223i −0.998150 0.0608002i \(-0.980635\pi\)
0.551729 + 0.834023i \(0.313968\pi\)
\(20\) −1.71936 + 1.42962i −0.384460 + 0.319673i
\(21\) 0 0
\(22\) 3.97801 + 3.97801i 0.848115 + 0.848115i
\(23\) 0.290892 + 1.08562i 0.0606552 + 0.226368i 0.989599 0.143852i \(-0.0459489\pi\)
−0.928944 + 0.370220i \(0.879282\pi\)
\(24\) 0 0
\(25\) 4.71361 1.66789i 0.942723 0.333577i
\(26\) −1.75092 1.01089i −0.343384 0.198253i
\(27\) 0 0
\(28\) 1.43078 + 2.22551i 0.270391 + 0.420581i
\(29\) 3.15502i 0.585872i 0.956132 + 0.292936i \(0.0946322\pi\)
−0.956132 + 0.292936i \(0.905368\pi\)
\(30\) 0 0
\(31\) −3.33287 + 1.92423i −0.598601 + 0.345602i −0.768491 0.639861i \(-0.778992\pi\)
0.169890 + 0.985463i \(0.445659\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) 0 0
\(34\) 5.30873 0.910440
\(35\) −1.27845 5.77629i −0.216098 0.976372i
\(36\) 0 0
\(37\) 4.86824 1.30444i 0.800334 0.214449i 0.164603 0.986360i \(-0.447366\pi\)
0.635731 + 0.771911i \(0.280699\pi\)
\(38\) −1.00727 + 3.75919i −0.163401 + 0.609822i
\(39\) 0 0
\(40\) −1.29076 + 1.82591i −0.204087 + 0.288702i
\(41\) 7.21050i 1.12609i −0.826426 0.563046i \(-0.809629\pi\)
0.826426 0.563046i \(-0.190371\pi\)
\(42\) 0 0
\(43\) 1.85669 1.85669i 0.283143 0.283143i −0.551218 0.834361i \(-0.685837\pi\)
0.834361 + 0.551218i \(0.185837\pi\)
\(44\) 4.87205 + 2.81288i 0.734489 + 0.424058i
\(45\) 0 0
\(46\) 0.561961 + 0.973344i 0.0828566 + 0.143512i
\(47\) 1.52590 + 5.69475i 0.222576 + 0.830665i 0.983361 + 0.181661i \(0.0581474\pi\)
−0.760785 + 0.649004i \(0.775186\pi\)
\(48\) 0 0
\(49\) −6.96808 + 0.667734i −0.995440 + 0.0953905i
\(50\) 4.12132 2.83103i 0.582843 0.400368i
\(51\) 0 0
\(52\) −1.95290 0.523277i −0.270818 0.0725655i
\(53\) −1.33599 0.357978i −0.183512 0.0491720i 0.165892 0.986144i \(-0.446950\pi\)
−0.349405 + 0.936972i \(0.613616\pi\)
\(54\) 0 0
\(55\) −8.04270 9.67269i −1.08448 1.30426i
\(56\) 1.95803 + 1.77936i 0.261652 + 0.237777i
\(57\) 0 0
\(58\) 0.816578 + 3.04751i 0.107222 + 0.400158i
\(59\) −2.73923 4.74448i −0.356617 0.617679i 0.630776 0.775965i \(-0.282737\pi\)
−0.987393 + 0.158286i \(0.949403\pi\)
\(60\) 0 0
\(61\) −3.99172 2.30462i −0.511088 0.295077i 0.222193 0.975003i \(-0.428678\pi\)
−0.733281 + 0.679926i \(0.762012\pi\)
\(62\) −2.72127 + 2.72127i −0.345602 + 0.345602i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 3.69160 + 2.60964i 0.457887 + 0.323686i
\(66\) 0 0
\(67\) 0.218698 0.816193i 0.0267182 0.0997138i −0.951279 0.308331i \(-0.900230\pi\)
0.977997 + 0.208617i \(0.0668963\pi\)
\(68\) 5.12784 1.37400i 0.621842 0.166622i
\(69\) 0 0
\(70\) −2.72990 5.24858i −0.326286 0.627326i
\(71\) −4.77710 −0.566937 −0.283469 0.958982i \(-0.591485\pi\)
−0.283469 + 0.958982i \(0.591485\pi\)
\(72\) 0 0
\(73\) 1.45256 5.42104i 0.170010 0.634485i −0.827338 0.561704i \(-0.810146\pi\)
0.997348 0.0727807i \(-0.0231873\pi\)
\(74\) 4.36475 2.51999i 0.507391 0.292943i
\(75\) 0 0
\(76\) 3.89180i 0.446420i
\(77\) −12.5202 + 8.04920i −1.42681 + 0.917291i
\(78\) 0 0
\(79\) 5.41079 + 3.12392i 0.608761 + 0.351469i 0.772481 0.635038i \(-0.219016\pi\)
−0.163719 + 0.986507i \(0.552349\pi\)
\(80\) −0.774197 + 2.09777i −0.0865578 + 0.234537i
\(81\) 0 0
\(82\) −1.86622 6.96481i −0.206089 0.769135i
\(83\) −5.67281 5.67281i −0.622672 0.622672i 0.323542 0.946214i \(-0.395126\pi\)
−0.946214 + 0.323542i \(0.895126\pi\)
\(84\) 0 0
\(85\) −11.8207 1.08763i −1.28214 0.117970i
\(86\) 1.31288 2.27397i 0.141571 0.245209i
\(87\) 0 0
\(88\) 5.43407 + 1.45605i 0.579273 + 0.155216i
\(89\) 5.96090 10.3246i 0.631855 1.09440i −0.355318 0.934746i \(-0.615627\pi\)
0.987172 0.159659i \(-0.0510393\pi\)
\(90\) 0 0
\(91\) 3.59749 3.95871i 0.377120 0.414986i
\(92\) 0.794732 + 0.794732i 0.0828566 + 0.0828566i
\(93\) 0 0
\(94\) 2.94782 + 5.10577i 0.304044 + 0.526620i
\(95\) 3.01302 8.16409i 0.309129 0.837618i
\(96\) 0 0
\(97\) −6.63103 + 6.63103i −0.673279 + 0.673279i −0.958471 0.285191i \(-0.907943\pi\)
0.285191 + 0.958471i \(0.407943\pi\)
\(98\) −6.55783 + 2.44845i −0.662440 + 0.247331i
\(99\) 0 0
\(100\) 3.24817 3.80124i 0.324817 0.380124i
\(101\) −13.9423 + 8.04960i −1.38731 + 0.800965i −0.993012 0.118016i \(-0.962347\pi\)
−0.394301 + 0.918981i \(0.629013\pi\)
\(102\) 0 0
\(103\) 18.9993 5.09084i 1.87206 0.501616i 0.872132 0.489271i \(-0.162737\pi\)
0.999924 0.0123445i \(-0.00392947\pi\)
\(104\) −2.02179 −0.198253
\(105\) 0 0
\(106\) −1.38312 −0.134340
\(107\) 2.70557 0.724955i 0.261557 0.0700840i −0.125657 0.992074i \(-0.540104\pi\)
0.387214 + 0.921990i \(0.373437\pi\)
\(108\) 0 0
\(109\) −5.11895 + 2.95543i −0.490306 + 0.283078i −0.724701 0.689063i \(-0.758022\pi\)
0.234395 + 0.972141i \(0.424689\pi\)
\(110\) −10.2721 7.26150i −0.979409 0.692356i
\(111\) 0 0
\(112\) 2.35184 + 1.21196i 0.222228 + 0.114519i
\(113\) 13.5818 13.5818i 1.27767 1.27767i 0.335697 0.941970i \(-0.391028\pi\)
0.941970 0.335697i \(-0.108972\pi\)
\(114\) 0 0
\(115\) −1.05188 2.28244i −0.0980886 0.212839i
\(116\) 1.57751 + 2.73232i 0.146468 + 0.253690i
\(117\) 0 0
\(118\) −3.87385 3.87385i −0.356617 0.356617i
\(119\) −2.98330 + 13.7251i −0.273478 + 1.25818i
\(120\) 0 0
\(121\) −10.3246 + 17.8827i −0.938599 + 1.62570i
\(122\) −4.45219 1.19296i −0.403082 0.108006i
\(123\) 0 0
\(124\) −1.92423 + 3.33287i −0.172801 + 0.299300i
\(125\) −9.75680 + 5.45939i −0.872674 + 0.488303i
\(126\) 0 0
\(127\) 4.63487 + 4.63487i 0.411278 + 0.411278i 0.882184 0.470906i \(-0.156073\pi\)
−0.470906 + 0.882184i \(0.656073\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) 0 0
\(130\) 4.24124 + 1.56526i 0.371981 + 0.137282i
\(131\) 6.66437 + 3.84768i 0.582269 + 0.336173i 0.762035 0.647536i \(-0.224201\pi\)
−0.179766 + 0.983709i \(0.557534\pi\)
\(132\) 0 0
\(133\) −9.15290 4.71670i −0.793657 0.408990i
\(134\) 0.844985i 0.0729956i
\(135\) 0 0
\(136\) 4.59749 2.65436i 0.394232 0.227610i
\(137\) 2.28687 8.53471i 0.195380 0.729170i −0.796788 0.604259i \(-0.793469\pi\)
0.992168 0.124910i \(-0.0398643\pi\)
\(138\) 0 0
\(139\) 11.0631 0.938361 0.469180 0.883102i \(-0.344549\pi\)
0.469180 + 0.883102i \(0.344549\pi\)
\(140\) −3.99532 4.36319i −0.337666 0.368757i
\(141\) 0 0
\(142\) −4.61432 + 1.23640i −0.387225 + 0.103757i
\(143\) 2.94383 10.9865i 0.246176 0.918740i
\(144\) 0 0
\(145\) −1.19389 6.95307i −0.0991468 0.577421i
\(146\) 5.61227i 0.464475i
\(147\) 0 0
\(148\) 3.56380 3.56380i 0.292943 0.292943i
\(149\) 4.37243 + 2.52443i 0.358204 + 0.206809i 0.668293 0.743899i \(-0.267025\pi\)
−0.310089 + 0.950708i \(0.600359\pi\)
\(150\) 0 0
\(151\) −6.72142 11.6418i −0.546981 0.947399i −0.998479 0.0551270i \(-0.982444\pi\)
0.451498 0.892272i \(-0.350890\pi\)
\(152\) 1.00727 + 3.75919i 0.0817006 + 0.304911i
\(153\) 0 0
\(154\) −10.0103 + 11.0154i −0.806651 + 0.887645i
\(155\) 6.61688 5.50184i 0.531481 0.441918i
\(156\) 0 0
\(157\) −1.06529 0.285443i −0.0850191 0.0227808i 0.216059 0.976380i \(-0.430680\pi\)
−0.301078 + 0.953600i \(0.597346\pi\)
\(158\) 6.03495 + 1.61706i 0.480115 + 0.128646i
\(159\) 0 0
\(160\) −0.204875 + 2.22666i −0.0161968 + 0.176033i
\(161\) −2.83227 + 0.905902i −0.223214 + 0.0713951i
\(162\) 0 0
\(163\) −3.42705 12.7899i −0.268428 1.00179i −0.960119 0.279592i \(-0.909801\pi\)
0.691691 0.722193i \(-0.256866\pi\)
\(164\) −3.60525 6.24448i −0.281523 0.487612i
\(165\) 0 0
\(166\) −6.94775 4.01128i −0.539250 0.311336i
\(167\) 4.70680 4.70680i 0.364223 0.364223i −0.501142 0.865365i \(-0.667087\pi\)
0.865365 + 0.501142i \(0.167087\pi\)
\(168\) 0 0
\(169\) 8.91237i 0.685567i
\(170\) −11.6995 + 2.00887i −0.897308 + 0.154073i
\(171\) 0 0
\(172\) 0.679597 2.53629i 0.0518188 0.193390i
\(173\) 6.81421 1.82586i 0.518075 0.138818i 0.00969875 0.999953i \(-0.496913\pi\)
0.508376 + 0.861135i \(0.330246\pi\)
\(174\) 0 0
\(175\) 5.00327 + 12.2461i 0.378212 + 0.925719i
\(176\) 5.62576 0.424058
\(177\) 0 0
\(178\) 3.08559 11.5156i 0.231275 0.863129i
\(179\) −1.91075 + 1.10317i −0.142816 + 0.0824550i −0.569706 0.821849i \(-0.692943\pi\)
0.426889 + 0.904304i \(0.359609\pi\)
\(180\) 0 0
\(181\) 4.11867i 0.306139i −0.988215 0.153069i \(-0.951084\pi\)
0.988215 0.153069i \(-0.0489158\pi\)
\(182\) 2.45032 4.75492i 0.181630 0.352458i
\(183\) 0 0
\(184\) 0.973344 + 0.561961i 0.0717559 + 0.0414283i
\(185\) −10.2351 + 4.71693i −0.752499 + 0.346796i
\(186\) 0 0
\(187\) 7.72980 + 28.8480i 0.565259 + 2.10957i
\(188\) 4.16885 + 4.16885i 0.304044 + 0.304044i
\(189\) 0 0
\(190\) 0.797333 8.66573i 0.0578446 0.628678i
\(191\) −8.60117 + 14.8977i −0.622359 + 1.07796i 0.366686 + 0.930345i \(0.380492\pi\)
−0.989045 + 0.147613i \(0.952841\pi\)
\(192\) 0 0
\(193\) 11.6562 + 3.12327i 0.839032 + 0.224818i 0.652650 0.757659i \(-0.273657\pi\)
0.186382 + 0.982477i \(0.440324\pi\)
\(194\) −4.68885 + 8.12132i −0.336640 + 0.583077i
\(195\) 0 0
\(196\) −5.70067 + 4.06231i −0.407190 + 0.290165i
\(197\) −14.3135 14.3135i −1.01979 1.01979i −0.999800 0.0199932i \(-0.993636\pi\)
−0.0199932 0.999800i \(-0.506364\pi\)
\(198\) 0 0
\(199\) −3.76653 6.52383i −0.267002 0.462462i 0.701084 0.713079i \(-0.252700\pi\)
−0.968086 + 0.250617i \(0.919367\pi\)
\(200\) 2.15365 4.51240i 0.152286 0.319075i
\(201\) 0 0
\(202\) −11.3839 + 11.3839i −0.800965 + 0.800965i
\(203\) −8.33786 + 0.398585i −0.585203 + 0.0279752i
\(204\) 0 0
\(205\) 2.72852 + 15.8906i 0.190568 + 1.10985i
\(206\) 17.0343 9.83476i 1.18684 0.685220i
\(207\) 0 0
\(208\) −1.95290 + 0.523277i −0.135409 + 0.0362827i
\(209\) −21.8944 −1.51446
\(210\) 0 0
\(211\) 19.5766 1.34771 0.673854 0.738865i \(-0.264638\pi\)
0.673854 + 0.738865i \(0.264638\pi\)
\(212\) −1.33599 + 0.357978i −0.0917562 + 0.0245860i
\(213\) 0 0
\(214\) 2.42575 1.40051i 0.165821 0.0957366i
\(215\) −3.38922 + 4.79440i −0.231143 + 0.326975i
\(216\) 0 0
\(217\) −5.50629 8.56478i −0.373791 0.581415i
\(218\) −4.17960 + 4.17960i −0.283078 + 0.283078i
\(219\) 0 0
\(220\) −11.8015 4.35544i −0.795659 0.293644i
\(221\) −5.36656 9.29516i −0.360994 0.625260i
\(222\) 0 0
\(223\) 1.46027 + 1.46027i 0.0977867 + 0.0977867i 0.754308 0.656521i \(-0.227973\pi\)
−0.656521 + 0.754308i \(0.727973\pi\)
\(224\) 2.58538 + 0.561961i 0.172743 + 0.0375476i
\(225\) 0 0
\(226\) 9.60377 16.6342i 0.638833 1.10649i
\(227\) 18.0081 + 4.82525i 1.19524 + 0.320263i 0.800954 0.598726i \(-0.204326\pi\)
0.394283 + 0.918989i \(0.370993\pi\)
\(228\) 0 0
\(229\) −2.00384 + 3.47074i −0.132417 + 0.229353i −0.924608 0.380920i \(-0.875607\pi\)
0.792191 + 0.610274i \(0.208941\pi\)
\(230\) −1.60678 1.93242i −0.105948 0.127420i
\(231\) 0 0
\(232\) 2.23093 + 2.23093i 0.146468 + 0.146468i
\(233\) 3.55400 + 13.2637i 0.232830 + 0.868934i 0.979115 + 0.203307i \(0.0651691\pi\)
−0.746285 + 0.665627i \(0.768164\pi\)
\(234\) 0 0
\(235\) −5.51775 11.9728i −0.359939 0.781017i
\(236\) −4.74448 2.73923i −0.308839 0.178308i
\(237\) 0 0
\(238\) 0.670673 + 14.0296i 0.0434732 + 0.909401i
\(239\) 19.6621i 1.27183i −0.771758 0.635916i \(-0.780622\pi\)
0.771758 0.635916i \(-0.219378\pi\)
\(240\) 0 0
\(241\) −5.09667 + 2.94256i −0.328305 + 0.189547i −0.655088 0.755552i \(-0.727369\pi\)
0.326783 + 0.945099i \(0.394035\pi\)
\(242\) −5.34440 + 19.9456i −0.343551 + 1.28215i
\(243\) 0 0
\(244\) −4.60924 −0.295077
\(245\) 15.1037 4.10834i 0.964939 0.262473i
\(246\) 0 0
\(247\) 7.60029 2.03649i 0.483595 0.129579i
\(248\) −0.996056 + 3.71733i −0.0632496 + 0.236051i
\(249\) 0 0
\(250\) −8.01135 + 7.79861i −0.506682 + 0.493227i
\(251\) 7.09950i 0.448116i 0.974576 + 0.224058i \(0.0719306\pi\)
−0.974576 + 0.224058i \(0.928069\pi\)
\(252\) 0 0
\(253\) −4.47097 + 4.47097i −0.281088 + 0.281088i
\(254\) 5.67653 + 3.27735i 0.356177 + 0.205639i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 2.55891 + 9.54998i 0.159620 + 0.595711i 0.998665 + 0.0516491i \(0.0164478\pi\)
−0.839045 + 0.544062i \(0.816886\pi\)
\(258\) 0 0
\(259\) 4.06231 + 12.7007i 0.252420 + 0.789181i
\(260\) 4.50184 + 0.414214i 0.279192 + 0.0256884i
\(261\) 0 0
\(262\) 7.43314 + 1.99170i 0.459221 + 0.123048i
\(263\) 13.2797 + 3.55829i 0.818861 + 0.219413i 0.643849 0.765153i \(-0.277337\pi\)
0.175013 + 0.984566i \(0.444003\pi\)
\(264\) 0 0
\(265\) 3.07974 + 0.283366i 0.189187 + 0.0174071i
\(266\) −10.0618 2.18704i −0.616929 0.134096i
\(267\) 0 0
\(268\) −0.218698 0.816193i −0.0133591 0.0498569i
\(269\) 13.2510 + 22.9514i 0.807928 + 1.39937i 0.914296 + 0.405046i \(0.132745\pi\)
−0.106368 + 0.994327i \(0.533922\pi\)
\(270\) 0 0
\(271\) −11.0824 6.39844i −0.673209 0.388678i 0.124082 0.992272i \(-0.460401\pi\)
−0.797292 + 0.603594i \(0.793735\pi\)
\(272\) 3.75384 3.75384i 0.227610 0.227610i
\(273\) 0 0
\(274\) 8.83578i 0.533789i
\(275\) 21.3849 + 18.2734i 1.28956 + 1.10193i
\(276\) 0 0
\(277\) 5.20313 19.4184i 0.312626 1.16674i −0.613554 0.789653i \(-0.710261\pi\)
0.926180 0.377083i \(-0.123073\pi\)
\(278\) 10.6861 2.86334i 0.640912 0.171732i
\(279\) 0 0
\(280\) −4.98846 3.18046i −0.298117 0.190069i
\(281\) 14.1498 0.844107 0.422054 0.906571i \(-0.361309\pi\)
0.422054 + 0.906571i \(0.361309\pi\)
\(282\) 0 0
\(283\) −7.00563 + 26.1454i −0.416442 + 1.55418i 0.365489 + 0.930816i \(0.380902\pi\)
−0.781930 + 0.623366i \(0.785765\pi\)
\(284\) −4.13709 + 2.38855i −0.245491 + 0.141734i
\(285\) 0 0
\(286\) 11.3741i 0.672564i
\(287\) 19.0554 0.910931i 1.12481 0.0537706i
\(288\) 0 0
\(289\) 9.68442 + 5.59130i 0.569672 + 0.328900i
\(290\) −2.95279 6.40715i −0.173394 0.376241i
\(291\) 0 0
\(292\) −1.45256 5.42104i −0.0850048 0.317242i
\(293\) −17.1191 17.1191i −1.00011 1.00011i −1.00000 0.000106876i \(-0.999966\pi\)
−0.000106876 1.00000i \(-0.500034\pi\)
\(294\) 0 0
\(295\) 7.83211 + 9.41941i 0.456003 + 0.548420i
\(296\) 2.51999 4.36475i 0.146471 0.253696i
\(297\) 0 0
\(298\) 4.87682 + 1.30674i 0.282506 + 0.0756974i
\(299\) 1.13616 1.96790i 0.0657061 0.113806i
\(300\) 0 0
\(301\) 5.14131 + 4.67218i 0.296340 + 0.269300i
\(302\) −9.50552 9.50552i −0.546981 0.546981i
\(303\) 0 0
\(304\) 1.94590 + 3.37040i 0.111605 + 0.193306i
\(305\) 9.66911 + 3.56846i 0.553652 + 0.204329i
\(306\) 0 0
\(307\) 17.2974 17.2974i 0.987217 0.987217i −0.0127019 0.999919i \(-0.504043\pi\)
0.999919 + 0.0127019i \(0.00404326\pi\)
\(308\) −6.81819 + 13.2309i −0.388502 + 0.753900i
\(309\) 0 0
\(310\) 4.96744 7.02694i 0.282131 0.399104i
\(311\) 9.51095 5.49115i 0.539316 0.311374i −0.205486 0.978660i \(-0.565877\pi\)
0.744802 + 0.667286i \(0.232544\pi\)
\(312\) 0 0
\(313\) 28.4088 7.61212i 1.60576 0.430262i 0.658985 0.752156i \(-0.270986\pi\)
0.946776 + 0.321893i \(0.104319\pi\)
\(314\) −1.10287 −0.0622383
\(315\) 0 0
\(316\) 6.24784 0.351469
\(317\) 4.14766 1.11136i 0.232956 0.0624203i −0.140453 0.990087i \(-0.544856\pi\)
0.373408 + 0.927667i \(0.378189\pi\)
\(318\) 0 0
\(319\) −15.3714 + 8.87468i −0.860633 + 0.496887i
\(320\) 0.378409 + 2.20382i 0.0211537 + 0.123197i
\(321\) 0 0
\(322\) −2.50129 + 1.60808i −0.139392 + 0.0896147i
\(323\) −14.6092 + 14.6092i −0.812878 + 0.812878i
\(324\) 0 0
\(325\) −9.12312 4.35423i −0.506060 0.241529i
\(326\) −6.62056 11.4671i −0.366679 0.635106i
\(327\) 0 0
\(328\) −5.09860 5.09860i −0.281523 0.281523i
\(329\) −14.8569 + 4.75200i −0.819089 + 0.261986i
\(330\) 0 0
\(331\) −17.7249 + 30.7005i −0.974250 + 1.68745i −0.291863 + 0.956460i \(0.594275\pi\)
−0.682387 + 0.730991i \(0.739058\pi\)
\(332\) −7.74921 2.07639i −0.425293 0.113957i
\(333\) 0 0
\(334\) 3.32821 5.76463i 0.182112 0.315426i
\(335\) −0.173116 + 1.88150i −0.00945835 + 0.102797i
\(336\) 0 0
\(337\) −12.1473 12.1473i −0.661708 0.661708i 0.294075 0.955782i \(-0.404989\pi\)
−0.955782 + 0.294075i \(0.904989\pi\)
\(338\) −2.30669 8.60869i −0.125468 0.468251i
\(339\) 0 0
\(340\) −10.7809 + 4.96846i −0.584675 + 0.269453i
\(341\) −18.7499 10.8253i −1.01536 0.586221i
\(342\) 0 0
\(343\) −2.64495 18.3304i −0.142814 0.989750i
\(344\) 2.62576i 0.141571i
\(345\) 0 0
\(346\) 6.10945 3.52729i 0.328446 0.189628i
\(347\) −2.32323 + 8.67040i −0.124717 + 0.465452i −0.999829 0.0184687i \(-0.994121\pi\)
0.875112 + 0.483920i \(0.160788\pi\)
\(348\) 0 0
\(349\) −26.0251 −1.39309 −0.696546 0.717512i \(-0.745281\pi\)
−0.696546 + 0.717512i \(0.745281\pi\)
\(350\) 8.00231 + 10.5339i 0.427742 + 0.563060i
\(351\) 0 0
\(352\) 5.43407 1.45605i 0.289637 0.0776079i
\(353\) −2.57944 + 9.62659i −0.137290 + 0.512372i 0.862688 + 0.505736i \(0.168779\pi\)
−0.999978 + 0.00663577i \(0.997888\pi\)
\(354\) 0 0
\(355\) 10.5278 1.80770i 0.558760 0.0959425i
\(356\) 11.9218i 0.631855i
\(357\) 0 0
\(358\) −1.56012 + 1.56012i −0.0824550 + 0.0824550i
\(359\) −10.0235 5.78705i −0.529019 0.305429i 0.211598 0.977357i \(-0.432133\pi\)
−0.740617 + 0.671928i \(0.765467\pi\)
\(360\) 0 0
\(361\) 1.92693 + 3.33754i 0.101417 + 0.175660i
\(362\) −1.06599 3.97833i −0.0560273 0.209097i
\(363\) 0 0
\(364\) 1.13616 5.22709i 0.0595512 0.273974i
\(365\) −1.14981 + 12.4966i −0.0601840 + 0.654104i
\(366\) 0 0
\(367\) 16.1256 + 4.32083i 0.841747 + 0.225545i 0.653832 0.756640i \(-0.273160\pi\)
0.187915 + 0.982185i \(0.439827\pi\)
\(368\) 1.08562 + 0.290892i 0.0565921 + 0.0151638i
\(369\) 0 0
\(370\) −8.66551 + 7.20525i −0.450499 + 0.374583i
\(371\) 0.777258 3.57589i 0.0403532 0.185651i
\(372\) 0 0
\(373\) 0.822767 + 3.07061i 0.0426013 + 0.158990i 0.983950 0.178446i \(-0.0571070\pi\)
−0.941348 + 0.337436i \(0.890440\pi\)
\(374\) 14.9328 + 25.8644i 0.772158 + 1.33742i
\(375\) 0 0
\(376\) 5.10577 + 2.94782i 0.263310 + 0.152022i
\(377\) 4.51047 4.51047i 0.232301 0.232301i
\(378\) 0 0
\(379\) 7.15349i 0.367450i 0.982978 + 0.183725i \(0.0588156\pi\)
−0.982978 + 0.183725i \(0.941184\pi\)
\(380\) −1.47269 8.57682i −0.0755475 0.439982i
\(381\) 0 0
\(382\) −4.45229 + 16.6162i −0.227799 + 0.850158i
\(383\) 14.0961 3.77704i 0.720278 0.192998i 0.119982 0.992776i \(-0.461716\pi\)
0.600296 + 0.799778i \(0.295050\pi\)
\(384\) 0 0
\(385\) 24.5463 22.4767i 1.25099 1.14552i
\(386\) 12.0674 0.614214
\(387\) 0 0
\(388\) −2.42713 + 9.05816i −0.123219 + 0.459858i
\(389\) −5.36634 + 3.09826i −0.272084 + 0.157088i −0.629834 0.776729i \(-0.716877\pi\)
0.357750 + 0.933817i \(0.383544\pi\)
\(390\) 0 0
\(391\) 5.96659i 0.301744i
\(392\) −4.45502 + 5.39934i −0.225012 + 0.272708i
\(393\) 0 0
\(394\) −17.5304 10.1212i −0.883167 0.509897i
\(395\) −13.1065 4.83706i −0.659460 0.243379i
\(396\) 0 0
\(397\) 0.754685 + 2.81652i 0.0378766 + 0.141357i 0.982275 0.187447i \(-0.0600212\pi\)
−0.944398 + 0.328804i \(0.893354\pi\)
\(398\) −5.32668 5.32668i −0.267002 0.267002i
\(399\) 0 0
\(400\) 0.912375 4.91605i 0.0456187 0.245803i
\(401\) −9.98528 + 17.2950i −0.498641 + 0.863672i −0.999999 0.00156835i \(-0.999501\pi\)
0.501358 + 0.865240i \(0.332834\pi\)
\(402\) 0 0
\(403\) 7.51565 + 2.01381i 0.374381 + 0.100315i
\(404\) −8.04960 + 13.9423i −0.400483 + 0.693656i
\(405\) 0 0
\(406\) −7.95060 + 2.54300i −0.394581 + 0.126207i
\(407\) 20.0491 + 20.0491i 0.993796 + 0.993796i
\(408\) 0 0
\(409\) 17.1791 + 29.7550i 0.849451 + 1.47129i 0.881699 + 0.471812i \(0.156400\pi\)
−0.0322484 + 0.999480i \(0.510267\pi\)
\(410\) 6.74834 + 14.6430i 0.333277 + 0.723165i
\(411\) 0 0
\(412\) 13.9084 13.9084i 0.685220 0.685220i
\(413\) 12.1923 7.83843i 0.599946 0.385704i
\(414\) 0 0
\(415\) 14.6485 + 10.3552i 0.719065 + 0.508317i
\(416\) −1.75092 + 1.01089i −0.0858459 + 0.0495631i
\(417\) 0 0
\(418\) −21.1483 + 5.66668i −1.03440 + 0.277166i
\(419\) 31.1360 1.52109 0.760547 0.649283i \(-0.224931\pi\)
0.760547 + 0.649283i \(0.224931\pi\)
\(420\) 0 0
\(421\) −33.6728 −1.64111 −0.820555 0.571567i \(-0.806336\pi\)
−0.820555 + 0.571567i \(0.806336\pi\)
\(422\) 18.9095 5.06679i 0.920501 0.246648i
\(423\) 0 0
\(424\) −1.19782 + 0.691560i −0.0581711 + 0.0335851i
\(425\) 26.4623 2.07615i 1.28361 0.100708i
\(426\) 0 0
\(427\) 5.58621 10.8402i 0.270336 0.524594i
\(428\) 1.98061 1.98061i 0.0957366 0.0957366i
\(429\) 0 0
\(430\) −2.03285 + 5.50823i −0.0980330 + 0.265630i
\(431\) −7.37284 12.7701i −0.355137 0.615116i 0.632004 0.774965i \(-0.282233\pi\)
−0.987141 + 0.159849i \(0.948899\pi\)
\(432\) 0 0
\(433\) −9.98256 9.98256i −0.479731 0.479731i 0.425315 0.905046i \(-0.360163\pi\)
−0.905046 + 0.425315i \(0.860163\pi\)
\(434\) −7.53539 6.84781i −0.361710 0.328706i
\(435\) 0 0
\(436\) −2.95543 + 5.11895i −0.141539 + 0.245153i
\(437\) −4.22504 1.13210i −0.202111 0.0541555i
\(438\) 0 0
\(439\) 19.2142 33.2800i 0.917046 1.58837i 0.113167 0.993576i \(-0.463900\pi\)
0.803878 0.594794i \(-0.202766\pi\)
\(440\) −12.5267 1.15258i −0.597186 0.0549470i
\(441\) 0 0
\(442\) −7.58946 7.58946i −0.360994 0.360994i
\(443\) −1.48448 5.54016i −0.0705299 0.263221i 0.921653 0.388016i \(-0.126839\pi\)
−0.992183 + 0.124795i \(0.960173\pi\)
\(444\) 0 0
\(445\) −9.22982 + 25.0092i −0.437536 + 1.18555i
\(446\) 1.78845 + 1.03256i 0.0846857 + 0.0488933i
\(447\) 0 0
\(448\) 2.64273 0.126334i 0.124857 0.00596872i
\(449\) 7.30267i 0.344635i −0.985042 0.172317i \(-0.944875\pi\)
0.985042 0.172317i \(-0.0551254\pi\)
\(450\) 0 0
\(451\) 35.1299 20.2823i 1.65420 0.955055i
\(452\) 4.97128 18.5531i 0.233829 0.872663i
\(453\) 0 0
\(454\) 18.6433 0.874974
\(455\) −6.43021 + 10.0856i −0.301453 + 0.472820i
\(456\) 0 0
\(457\) −4.97047 + 1.33183i −0.232509 + 0.0623006i −0.373192 0.927754i \(-0.621737\pi\)
0.140683 + 0.990055i \(0.455070\pi\)
\(458\) −1.03726 + 3.87111i −0.0484680 + 0.180885i
\(459\) 0 0
\(460\) −2.05218 1.45071i −0.0956833 0.0676397i
\(461\) 29.4110i 1.36981i 0.728634 + 0.684903i \(0.240155\pi\)
−0.728634 + 0.684903i \(0.759845\pi\)
\(462\) 0 0
\(463\) −4.04625 + 4.04625i −0.188045 + 0.188045i −0.794851 0.606805i \(-0.792451\pi\)
0.606805 + 0.794851i \(0.292451\pi\)
\(464\) 2.73232 + 1.57751i 0.126845 + 0.0732340i
\(465\) 0 0
\(466\) 6.86580 + 11.8919i 0.318052 + 0.550882i
\(467\) −4.30747 16.0757i −0.199326 0.743894i −0.991105 0.133086i \(-0.957511\pi\)
0.791779 0.610808i \(-0.209155\pi\)
\(468\) 0 0
\(469\) 2.18461 + 0.474848i 0.100876 + 0.0219264i
\(470\) −8.42852 10.1367i −0.388779 0.467571i
\(471\) 0 0
\(472\) −5.29178 1.41793i −0.243574 0.0652654i
\(473\) 14.2686 + 3.82325i 0.656069 + 0.175793i
\(474\) 0 0
\(475\) −3.55078 + 19.1323i −0.162921 + 0.877851i
\(476\) 4.27894 + 13.3779i 0.196125 + 0.613176i
\(477\) 0 0
\(478\) −5.08891 18.9921i −0.232762 0.868678i
\(479\) −7.69460 13.3274i −0.351575 0.608946i 0.634950 0.772553i \(-0.281021\pi\)
−0.986526 + 0.163607i \(0.947687\pi\)
\(480\) 0 0
\(481\) −8.82459 5.09488i −0.402367 0.232306i
\(482\) −4.16141 + 4.16141i −0.189547 + 0.189547i
\(483\) 0 0
\(484\) 20.6492i 0.938599i
\(485\) 12.1043 17.1228i 0.549629 0.777507i
\(486\) 0 0
\(487\) −9.31541 + 34.7656i −0.422122 + 1.57538i 0.348007 + 0.937492i \(0.386858\pi\)
−0.770129 + 0.637888i \(0.779808\pi\)
\(488\) −4.45219 + 1.19296i −0.201541 + 0.0540028i
\(489\) 0 0
\(490\) 13.5257 7.87748i 0.611030 0.355868i
\(491\) 15.2823 0.689680 0.344840 0.938661i \(-0.387933\pi\)
0.344840 + 0.938661i \(0.387933\pi\)
\(492\) 0 0
\(493\) −4.33499 + 16.1784i −0.195238 + 0.728639i
\(494\) 6.81423 3.93420i 0.306587 0.177008i
\(495\) 0 0
\(496\) 3.84846i 0.172801i
\(497\) −0.603509 12.6246i −0.0270711 0.566290i
\(498\) 0 0
\(499\) −27.3534 15.7925i −1.22451 0.706969i −0.258630 0.965976i \(-0.583271\pi\)
−0.965875 + 0.259008i \(0.916604\pi\)
\(500\) −5.71994 + 9.60637i −0.255803 + 0.429610i
\(501\) 0 0
\(502\) 1.83749 + 6.85759i 0.0820110 + 0.306069i
\(503\) −16.9777 16.9777i −0.756997 0.756997i 0.218778 0.975775i \(-0.429793\pi\)
−0.975775 + 0.218778i \(0.929793\pi\)
\(504\) 0 0
\(505\) 27.6803 23.0157i 1.23176 1.02419i
\(506\) −3.16146 + 5.47580i −0.140544 + 0.243429i
\(507\) 0 0
\(508\) 6.33135 + 1.69648i 0.280908 + 0.0752691i
\(509\) −10.7571 + 18.6318i −0.476799 + 0.825840i −0.999647 0.0265865i \(-0.991536\pi\)
0.522848 + 0.852426i \(0.324870\pi\)
\(510\) 0 0
\(511\) 14.5099 + 3.15388i 0.641879 + 0.139519i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0 0
\(514\) 4.94343 + 8.56228i 0.218045 + 0.377666i
\(515\) −39.9445 + 18.4088i −1.76017 + 0.811188i
\(516\) 0 0
\(517\) −23.4529 + 23.4529i −1.03146 + 1.03146i
\(518\) 7.21107 + 11.2165i 0.316836 + 0.492825i
\(519\) 0 0
\(520\) 4.45565 0.765062i 0.195393 0.0335502i
\(521\) −11.4657 + 6.61973i −0.502322 + 0.290016i −0.729672 0.683798i \(-0.760327\pi\)
0.227350 + 0.973813i \(0.426994\pi\)
\(522\) 0 0
\(523\) −26.0126 + 6.97006i −1.13745 + 0.304779i −0.777926 0.628356i \(-0.783728\pi\)
−0.359526 + 0.933135i \(0.617062\pi\)
\(524\) 7.69535 0.336173
\(525\) 0 0
\(526\) 13.7482 0.599448
\(527\) −19.7343 + 5.28779i −0.859640 + 0.230340i
\(528\) 0 0
\(529\) 18.8246 10.8684i 0.818462 0.472539i
\(530\) 3.04814 0.523384i 0.132403 0.0227344i
\(531\) 0 0
\(532\) −10.2850 + 0.491667i −0.445911 + 0.0213165i
\(533\) −10.3083 + 10.3083i −0.446501 + 0.446501i
\(534\) 0 0
\(535\) −5.68825 + 2.62148i −0.245924 + 0.113336i
\(536\) −0.422492 0.731778i −0.0182489 0.0316080i
\(537\) 0 0
\(538\) 18.7398 + 18.7398i 0.807928 + 0.807928i
\(539\) −22.8536 32.0706i −0.984374 1.38138i
\(540\) 0 0
\(541\) 5.66491 9.81190i 0.243553 0.421847i −0.718171 0.695867i \(-0.755020\pi\)
0.961724 + 0.274020i \(0.0883536\pi\)
\(542\) −12.3608 3.31208i −0.530943 0.142266i
\(543\) 0 0
\(544\) 2.65436 4.59749i 0.113805 0.197116i
\(545\) 10.1629 8.45027i 0.435329 0.361970i
\(546\) 0 0
\(547\) −30.9149 30.9149i −1.32182 1.32182i −0.912298 0.409527i \(-0.865694\pi\)
−0.409527 0.912298i \(-0.634306\pi\)
\(548\) −2.28687 8.53471i −0.0976902 0.364585i
\(549\) 0 0
\(550\) 25.3857 + 12.1159i 1.08245 + 0.516625i
\(551\) −10.6337 6.13935i −0.453009 0.261545i
\(552\) 0 0
\(553\) −7.57212 + 14.6939i −0.321999 + 0.624850i
\(554\) 20.1034i 0.854110i
\(555\) 0 0
\(556\) 9.58094 5.53156i 0.406322 0.234590i
\(557\) 6.83277 25.5003i 0.289514 1.08048i −0.655963 0.754793i \(-0.727737\pi\)
0.945477 0.325688i \(-0.105596\pi\)
\(558\) 0 0
\(559\) −5.30873 −0.224535
\(560\) −5.64164 1.78098i −0.238403 0.0752600i
\(561\) 0 0
\(562\) 13.6677 3.66224i 0.576536 0.154482i
\(563\) −5.22648 + 19.5055i −0.220270 + 0.822058i 0.763975 + 0.645246i \(0.223245\pi\)
−0.984245 + 0.176812i \(0.943422\pi\)
\(564\) 0 0
\(565\) −24.7923 + 35.0712i −1.04302 + 1.47546i
\(566\) 27.0677i 1.13774i
\(567\) 0 0
\(568\) −3.37792 + 3.37792i −0.141734 + 0.141734i
\(569\) −21.4890 12.4067i −0.900867 0.520116i −0.0233856 0.999727i \(-0.507445\pi\)
−0.877481 + 0.479611i \(0.840778\pi\)
\(570\) 0 0
\(571\) −2.29029 3.96690i −0.0958458 0.166010i 0.814116 0.580703i \(-0.197222\pi\)
−0.909961 + 0.414693i \(0.863889\pi\)
\(572\) −2.94383 10.9865i −0.123088 0.459370i
\(573\) 0 0
\(574\) 18.1704 5.81180i 0.758417 0.242580i
\(575\) 3.18185 + 4.63204i 0.132692 + 0.193169i
\(576\) 0 0
\(577\) −19.1065 5.11957i −0.795414 0.213131i −0.161845 0.986816i \(-0.551744\pi\)
−0.633570 + 0.773686i \(0.718411\pi\)
\(578\) 10.8016 + 2.89427i 0.449286 + 0.120386i
\(579\) 0 0
\(580\) −4.51047 5.42460i −0.187287 0.225244i
\(581\) 14.2751 15.7084i 0.592229 0.651694i
\(582\) 0 0
\(583\) −2.01390 7.51596i −0.0834071 0.311279i
\(584\) −2.80614 4.86037i −0.116119 0.201124i
\(585\) 0 0
\(586\) −20.9665 12.1050i −0.866118 0.500053i
\(587\) −19.3782 + 19.3782i −0.799824 + 0.799824i −0.983068 0.183244i \(-0.941340\pi\)
0.183244 + 0.983068i \(0.441340\pi\)
\(588\) 0 0
\(589\) 14.9775i 0.617136i
\(590\) 10.0032 + 7.07136i 0.411823 + 0.291123i
\(591\) 0 0
\(592\) 1.30444 4.86824i 0.0536122 0.200083i
\(593\) −3.12741 + 0.837988i −0.128428 + 0.0344121i −0.322460 0.946583i \(-0.604510\pi\)
0.194033 + 0.980995i \(0.437843\pi\)
\(594\) 0 0
\(595\) 1.38094 31.3765i 0.0566131 1.28631i
\(596\) 5.04885 0.206809
\(597\) 0 0
\(598\) 0.588122 2.19490i 0.0240501 0.0897562i
\(599\) −6.75802 + 3.90174i −0.276125 + 0.159421i −0.631668 0.775239i \(-0.717629\pi\)
0.355543 + 0.934660i \(0.384296\pi\)
\(600\) 0 0
\(601\) 31.7170i 1.29377i −0.762590 0.646883i \(-0.776072\pi\)
0.762590 0.646883i \(-0.223928\pi\)
\(602\) 6.17537 + 3.18231i 0.251689 + 0.129701i
\(603\) 0 0
\(604\) −11.6418 6.72142i −0.473699 0.273491i
\(605\) 15.9865 43.3171i 0.649945 1.76109i
\(606\) 0 0
\(607\) 0.199219 + 0.743495i 0.00808604 + 0.0301775i 0.969851 0.243699i \(-0.0783608\pi\)
−0.961765 + 0.273876i \(0.911694\pi\)
\(608\) 2.75192 + 2.75192i 0.111605 + 0.111605i
\(609\) 0 0
\(610\) 10.2632 + 0.944318i 0.415546 + 0.0382343i
\(611\) 5.95987 10.3228i 0.241110 0.417615i
\(612\) 0 0
\(613\) −33.8086 9.05898i −1.36552 0.365889i −0.499676 0.866212i \(-0.666548\pi\)
−0.865839 + 0.500323i \(0.833214\pi\)
\(614\) 12.2311 21.1850i 0.493609 0.854955i
\(615\) 0 0
\(616\) −3.16146 + 14.5447i −0.127379 + 0.586024i
\(617\) −21.5403 21.5403i −0.867179 0.867179i 0.124980 0.992159i \(-0.460113\pi\)
−0.992159 + 0.124980i \(0.960113\pi\)
\(618\) 0 0
\(619\) −21.6707 37.5348i −0.871021 1.50865i −0.860942 0.508703i \(-0.830125\pi\)
−0.0100783 0.999949i \(-0.503208\pi\)
\(620\) 2.97947 8.07317i 0.119658 0.324226i
\(621\) 0 0
\(622\) 7.76566 7.76566i 0.311374 0.311374i
\(623\) 28.0382 + 14.4487i 1.12333 + 0.578876i
\(624\) 0 0
\(625\) 19.4363 15.7235i 0.777452 0.628942i
\(626\) 25.4707 14.7055i 1.01801 0.587749i
\(627\) 0 0
\(628\) −1.06529 + 0.285443i −0.0425096 + 0.0113904i
\(629\) 26.7559 1.06683
\(630\) 0 0
\(631\) 7.53463 0.299949 0.149974 0.988690i \(-0.452081\pi\)
0.149974 + 0.988690i \(0.452081\pi\)
\(632\) 6.03495 1.61706i 0.240058 0.0643232i
\(633\) 0 0
\(634\) 3.71869 2.14699i 0.147688 0.0852677i
\(635\) −11.9683 8.46052i −0.474946 0.335746i
\(636\) 0 0
\(637\) 10.9163 + 9.00710i 0.432520 + 0.356874i
\(638\) −12.5507 + 12.5507i −0.496887 + 0.496887i
\(639\) 0 0
\(640\) 0.935904 + 2.03078i 0.0369949 + 0.0802738i
\(641\) 12.1657 + 21.0717i 0.480518 + 0.832281i 0.999750 0.0223521i \(-0.00711549\pi\)
−0.519233 + 0.854633i \(0.673782\pi\)
\(642\) 0 0
\(643\) −6.21713 6.21713i −0.245180 0.245180i 0.573809 0.818989i \(-0.305465\pi\)
−0.818989 + 0.573809i \(0.805465\pi\)
\(644\) −1.99986 + 2.20067i −0.0788057 + 0.0867184i
\(645\) 0 0
\(646\) −10.3303 + 17.8925i −0.406439 + 0.703973i
\(647\) −19.9243 5.33869i −0.783304 0.209886i −0.155063 0.987905i \(-0.549558\pi\)
−0.628241 + 0.778019i \(0.716225\pi\)
\(648\) 0 0
\(649\) 15.4102 26.6913i 0.604905 1.04773i
\(650\) −9.93921 1.84463i −0.389848 0.0723523i
\(651\) 0 0
\(652\) −9.36288 9.36288i −0.366679 0.366679i
\(653\) −6.76544 25.2490i −0.264752 0.988069i −0.962402 0.271630i \(-0.912437\pi\)
0.697650 0.716439i \(-0.254229\pi\)
\(654\) 0 0
\(655\) −16.1430 5.95772i −0.630761 0.232787i
\(656\) −6.24448 3.60525i −0.243806 0.140761i
\(657\) 0 0
\(658\) −13.1208 + 8.43533i −0.511502 + 0.328844i
\(659\) 24.2448i 0.944443i −0.881480 0.472222i \(-0.843452\pi\)
0.881480 0.472222i \(-0.156548\pi\)
\(660\) 0 0
\(661\) 15.5301 8.96630i 0.604050 0.348749i −0.166583 0.986027i \(-0.553273\pi\)
0.770633 + 0.637279i \(0.219940\pi\)
\(662\) −9.17510 + 34.2419i −0.356600 + 1.33085i
\(663\) 0 0
\(664\) −8.02257 −0.311336
\(665\) 21.9562 + 6.93121i 0.851423 + 0.268781i
\(666\) 0 0
\(667\) −3.42516 + 0.917769i −0.132623 + 0.0355362i
\(668\) 1.72281 6.42961i 0.0666574 0.248769i
\(669\) 0 0
\(670\) 0.319750 + 1.86219i 0.0123530 + 0.0719427i
\(671\) 25.9305i 1.00104i
\(672\) 0 0
\(673\) −4.85386 + 4.85386i −0.187103 + 0.187103i −0.794442 0.607340i \(-0.792237\pi\)
0.607340 + 0.794442i \(0.292237\pi\)
\(674\) −14.8774 8.58946i −0.573056 0.330854i
\(675\) 0 0
\(676\) −4.45619 7.71834i −0.171392 0.296859i
\(677\) 4.78306 + 17.8506i 0.183828 + 0.686055i 0.994878 + 0.101079i \(0.0322294\pi\)
−0.811051 + 0.584976i \(0.801104\pi\)
\(678\) 0 0
\(679\) −18.3618 16.6863i −0.704660 0.640362i
\(680\) −9.12760 + 7.58946i −0.350027 + 0.291043i
\(681\) 0 0
\(682\) −20.9128 5.60357i −0.800793 0.214572i
\(683\) −25.8878 6.93661i −0.990569 0.265422i −0.273079 0.961992i \(-0.588042\pi\)
−0.717489 + 0.696569i \(0.754709\pi\)
\(684\) 0 0
\(685\) −1.81023 + 19.6743i −0.0691653 + 0.751717i
\(686\) −7.29908 17.0213i −0.278680 0.649875i
\(687\) 0 0
\(688\) −0.679597 2.53629i −0.0259094 0.0966951i
\(689\) 1.39819 + 2.42173i 0.0532667 + 0.0922606i
\(690\) 0 0
\(691\) 25.1773 + 14.5361i 0.957790 + 0.552980i 0.895492 0.445077i \(-0.146824\pi\)
0.0622976 + 0.998058i \(0.480157\pi\)
\(692\) 4.98835 4.98835i 0.189628 0.189628i
\(693\) 0 0
\(694\) 8.97626i 0.340734i
\(695\) −24.3811 + 4.18638i −0.924827 + 0.158798i
\(696\) 0 0
\(697\) 9.90723 36.9743i 0.375263 1.40050i
\(698\) −25.1383 + 6.73580i −0.951500 + 0.254954i
\(699\) 0 0
\(700\) 10.4560 + 8.10381i 0.395200 + 0.306295i
\(701\) −25.4462 −0.961089 −0.480545 0.876970i \(-0.659561\pi\)
−0.480545 + 0.876970i \(0.659561\pi\)
\(702\) 0 0
\(703\) −5.07663 + 18.9462i −0.191469 + 0.714571i
\(704\) 4.87205 2.81288i 0.183622 0.106014i
\(705\) 0 0
\(706\) 9.96618i 0.375082i
\(707\) −23.0343 35.8289i −0.866295 1.34748i
\(708\) 0 0
\(709\) −27.1994 15.7036i −1.02150 0.589760i −0.106958 0.994263i \(-0.534111\pi\)
−0.914537 + 0.404503i \(0.867445\pi\)
\(710\) 9.70125 4.47091i 0.364081 0.167790i
\(711\) 0 0
\(712\) −3.08559 11.5156i −0.115637 0.431565i
\(713\) −3.05850 3.05850i −0.114542 0.114542i
\(714\) 0 0
\(715\) −2.33027 + 25.3263i −0.0871470 + 0.947149i
\(716\) −1.10317 + 1.91075i −0.0412275 + 0.0714081i
\(717\) 0 0
\(718\) −11.1797 2.99560i −0.417224 0.111795i
\(719\) 5.40214 9.35678i 0.201466 0.348949i −0.747535 0.664222i \(-0.768763\pi\)
0.949001 + 0.315273i \(0.102096\pi\)
\(720\) 0 0
\(721\) 15.8540 + 49.5669i 0.590434 + 1.84597i
\(722\) 2.72509 + 2.72509i 0.101417 + 0.101417i
\(723\) 0 0
\(724\) −2.05934 3.56688i −0.0765347 0.132562i
\(725\) 5.26221 + 14.8715i 0.195433 + 0.552315i
\(726\) 0 0
\(727\) 33.6108 33.6108i 1.24656 1.24656i 0.289326 0.957231i \(-0.406569\pi\)
0.957231 0.289326i \(-0.0934311\pi\)
\(728\) −0.255420 5.34305i −0.00946651 0.198026i
\(729\) 0 0
\(730\) 2.12373 + 12.3684i 0.0786029 + 0.457776i
\(731\) 12.0719 6.96972i 0.446496 0.257785i
\(732\) 0 0
\(733\) 24.8800 6.66658i 0.918964 0.246236i 0.231822 0.972758i \(-0.425531\pi\)
0.687143 + 0.726523i \(0.258865\pi\)
\(734\) 16.6944 0.616202
\(735\) 0 0
\(736\) 1.12392 0.0414283
\(737\) 4.59170 1.23034i 0.169138 0.0453203i
\(738\) 0 0
\(739\) 10.4948 6.05920i 0.386059 0.222891i −0.294392 0.955685i \(-0.595117\pi\)
0.680451 + 0.732793i \(0.261784\pi\)
\(740\) −6.50539 + 9.20253i −0.239143 + 0.338292i
\(741\) 0 0
\(742\) −0.174735 3.65522i −0.00641472 0.134187i
\(743\) −23.2618 + 23.2618i −0.853393 + 0.853393i −0.990549 0.137157i \(-0.956204\pi\)
0.137157 + 0.990549i \(0.456204\pi\)
\(744\) 0 0
\(745\) −10.5913 3.90881i −0.388036 0.143208i
\(746\) 1.58946 + 2.75303i 0.0581944 + 0.100796i
\(747\) 0 0
\(748\) 21.1182 + 21.1182i 0.772158 + 0.772158i
\(749\) 2.25767 + 7.05851i 0.0824934 + 0.257912i
\(750\) 0 0
\(751\) −6.98887 + 12.1051i −0.255028 + 0.441721i −0.964903 0.262607i \(-0.915418\pi\)
0.709875 + 0.704327i \(0.248751\pi\)
\(752\) 5.69475 + 1.52590i 0.207666 + 0.0556440i
\(753\) 0 0
\(754\) 3.18939 5.52418i 0.116151 0.201179i
\(755\) 19.2181 + 23.1130i 0.699420 + 0.841169i
\(756\) 0 0
\(757\) 17.5547 + 17.5547i 0.638036 + 0.638036i 0.950071 0.312035i \(-0.101010\pi\)
−0.312035 + 0.950071i \(0.601010\pi\)
\(758\) 1.85146 + 6.90974i 0.0672481 + 0.250973i
\(759\) 0 0
\(760\) −3.64236 7.90341i −0.132122 0.286687i
\(761\) −18.9372 10.9334i −0.686471 0.396334i 0.115817 0.993271i \(-0.463051\pi\)
−0.802289 + 0.596936i \(0.796385\pi\)
\(762\) 0 0
\(763\) −8.45710 13.1546i −0.306168 0.476230i
\(764\) 17.2023i 0.622359i
\(765\) 0 0
\(766\) 12.6382 7.29669i 0.456638 0.263640i
\(767\) −2.86675 + 10.6989i −0.103512 + 0.386313i
\(768\) 0 0
\(769\) 31.0506 1.11971 0.559857 0.828589i \(-0.310856\pi\)
0.559857 + 0.828589i \(0.310856\pi\)
\(770\) 17.8925 28.0639i 0.644800 1.01135i
\(771\) 0 0
\(772\) 11.6562 3.12327i 0.419516 0.112409i
\(773\) 1.57065 5.86173i 0.0564922 0.210832i −0.931910 0.362689i \(-0.881859\pi\)
0.988402 + 0.151857i \(0.0485254\pi\)
\(774\) 0 0
\(775\) −12.5004 + 14.6289i −0.449029 + 0.525487i
\(776\) 9.37769i 0.336640i
\(777\) 0 0
\(778\) −4.38160 + 4.38160i −0.157088 + 0.157088i
\(779\) 24.3023 + 14.0309i 0.870720 + 0.502710i
\(780\) 0 0
\(781\) −13.4374 23.2743i −0.480828 0.832819i
\(782\) 1.54427 + 5.76329i 0.0552229 + 0.206095i
\(783\) 0 0
\(784\) −2.90577 + 6.36840i −0.103777 + 0.227443i
\(785\) 2.45571 + 0.225950i 0.0876481 + 0.00806449i
\(786\) 0 0
\(787\) −21.5993 5.78752i −0.769932 0.206303i −0.147591 0.989049i \(-0.547152\pi\)
−0.622342 + 0.782746i \(0.713818\pi\)
\(788\) −19.5526 5.23910i −0.696532 0.186635i
\(789\) 0 0
\(790\) −13.9118 1.28003i −0.494961 0.0455413i
\(791\) 37.6089 + 34.1772i 1.33722 + 1.21520i
\(792\) 0 0
\(793\) 2.41191 + 9.00138i 0.0856495 + 0.319648i
\(794\) 1.45794 + 2.52523i 0.0517403 + 0.0896169i
\(795\) 0 0
\(796\) −6.52383 3.76653i −0.231231 0.133501i
\(797\) −16.5528 + 16.5528i −0.586330 + 0.586330i −0.936636 0.350305i \(-0.886078\pi\)
0.350305 + 0.936636i \(0.386078\pi\)
\(798\) 0 0
\(799\) 31.2984i 1.10726i
\(800\) −0.391082 4.98468i −0.0138268 0.176235i
\(801\) 0 0
\(802\) −5.16876 + 19.2901i −0.182515 + 0.681156i
\(803\) 30.4975 8.17177i 1.07623 0.288376i
\(804\) 0 0
\(805\) 5.89899 3.06820i 0.207912 0.108140i
\(806\) 7.78078 0.274066
\(807\) 0 0
\(808\) −4.16678 + 15.5506i −0.146587 + 0.547069i
\(809\) −2.84139 + 1.64048i −0.0998980 + 0.0576762i −0.549117 0.835746i \(-0.685036\pi\)
0.449219 + 0.893422i \(0.351702\pi\)
\(810\) 0 0
\(811\) 17.8693i 0.627476i 0.949510 + 0.313738i \(0.101581\pi\)
−0.949510 + 0.313738i \(0.898419\pi\)
\(812\) −7.02151 + 4.51412i −0.246407 + 0.158414i
\(813\) 0 0
\(814\) 24.5550 + 14.1768i 0.860653 + 0.496898i
\(815\) 12.3924 + 26.8898i 0.434088 + 0.941910i
\(816\) 0 0
\(817\) 2.64486 + 9.87074i 0.0925318 + 0.345333i
\(818\) 24.2949 + 24.2949i 0.849451 + 0.849451i
\(819\) 0 0
\(820\) 10.3083 + 12.3974i 0.359981 + 0.432937i
\(821\) −5.90837 + 10.2336i −0.206204 + 0.357155i −0.950516 0.310677i \(-0.899444\pi\)
0.744312 + 0.667832i \(0.232778\pi\)
\(822\) 0 0
\(823\) −34.0995 9.13692i −1.18863 0.318493i −0.390287 0.920693i \(-0.627624\pi\)
−0.798345 + 0.602200i \(0.794291\pi\)
\(824\) 9.83476 17.0343i 0.342610 0.593418i
\(825\) 0 0
\(826\) 9.74816 10.7270i 0.339182 0.373239i
\(827\) 17.2835 + 17.2835i 0.601005 + 0.601005i 0.940579 0.339574i \(-0.110283\pi\)
−0.339574 + 0.940579i \(0.610283\pi\)
\(828\) 0 0
\(829\) 17.2877 + 29.9431i 0.600426 + 1.03997i 0.992756 + 0.120144i \(0.0383357\pi\)
−0.392330 + 0.919824i \(0.628331\pi\)
\(830\) 16.8295 + 6.21104i 0.584159 + 0.215589i
\(831\) 0 0
\(832\) −1.42962 + 1.42962i −0.0495631 + 0.0495631i
\(833\) −36.6487 6.15011i −1.26980 0.213089i
\(834\) 0 0
\(835\) −8.59183 + 12.1540i −0.297332 + 0.420607i
\(836\) −18.9611 + 10.9472i −0.655782 + 0.378616i
\(837\) 0 0
\(838\) 30.0751 8.05859i 1.03893 0.278379i
\(839\) 50.1328 1.73078 0.865388 0.501102i \(-0.167072\pi\)
0.865388 + 0.501102i \(0.167072\pi\)
\(840\) 0 0
\(841\) 19.0459 0.656754
\(842\) −32.5254 + 8.71515i −1.12090 + 0.300344i
\(843\) 0 0
\(844\) 16.9538 9.78829i 0.583575 0.336927i
\(845\) 3.37252 + 19.6412i 0.116018 + 0.675679i
\(846\) 0 0
\(847\) −48.5636 25.0259i −1.66866 0.859901i
\(848\) −0.978013 + 0.978013i −0.0335851 + 0.0335851i
\(849\) 0 0
\(850\) 25.0233 8.85436i 0.858292 0.303702i
\(851\) 2.83227 + 4.90563i 0.0970888 + 0.168163i
\(852\) 0 0
\(853\) −2.37500 2.37500i −0.0813183 0.0813183i 0.665278 0.746596i \(-0.268313\pi\)
−0.746596 + 0.665278i \(0.768313\pi\)
\(854\) 2.59021 11.9167i 0.0886352 0.407779i
\(855\) 0 0
\(856\) 1.40051 2.42575i 0.0478683 0.0829103i
\(857\) 40.5097 + 10.8545i 1.38378 + 0.370784i 0.872494 0.488624i \(-0.162501\pi\)
0.511290 + 0.859408i \(0.329168\pi\)
\(858\) 0 0
\(859\) −1.17847 + 2.04117i −0.0402090 + 0.0696440i −0.885430 0.464774i \(-0.846136\pi\)
0.845221 + 0.534418i \(0.179469\pi\)
\(860\) −0.537952 + 5.84668i −0.0183440 + 0.199370i
\(861\) 0 0
\(862\) −10.4268 10.4268i −0.355137 0.355137i
\(863\) −12.5138 46.7022i −0.425975 1.58976i −0.761784 0.647831i \(-0.775676\pi\)
0.335808 0.941930i \(-0.390991\pi\)
\(864\) 0 0
\(865\) −14.3263 + 6.60242i −0.487110 + 0.224489i
\(866\) −12.2261 7.05873i −0.415459 0.239865i
\(867\) 0 0
\(868\) −9.05097 4.66418i −0.307210 0.158312i
\(869\) 35.1489i 1.19234i
\(870\) 0 0
\(871\) −1.47950 + 0.854190i −0.0501310 + 0.0289431i
\(872\) −1.52984 + 5.70944i −0.0518069 + 0.193346i
\(873\) 0 0
\(874\) −4.37408 −0.147955
\(875\) −15.6603 25.0949i −0.529416 0.848363i
\(876\) 0 0
\(877\) 13.3115 3.56681i 0.449498 0.120443i −0.0269665 0.999636i \(-0.508585\pi\)
0.476465 + 0.879194i \(0.341918\pi\)
\(878\) 9.94602 37.1191i 0.335662 1.25271i
\(879\) 0 0
\(880\) −12.3981 + 2.12884i −0.417941 + 0.0717631i
\(881\) 3.32542i 0.112036i −0.998430 0.0560181i \(-0.982160\pi\)
0.998430 0.0560181i \(-0.0178405\pi\)
\(882\) 0 0
\(883\) −36.8930 + 36.8930i −1.24155 + 1.24155i −0.282191 + 0.959358i \(0.591061\pi\)
−0.959358 + 0.282191i \(0.908939\pi\)
\(884\) −9.29516 5.36656i −0.312630 0.180497i
\(885\) 0 0
\(886\) −2.86780 4.96718i −0.0963456 0.166876i
\(887\) 9.27107 + 34.6001i 0.311292 + 1.16176i 0.927392 + 0.374090i \(0.122045\pi\)
−0.616101 + 0.787668i \(0.711289\pi\)
\(888\) 0 0
\(889\) −11.6632 + 12.8343i −0.391170 + 0.430447i
\(890\) −2.44248 + 26.5458i −0.0818721 + 0.889819i
\(891\) 0 0
\(892\) 1.99476 + 0.534495i 0.0667895 + 0.0178962i
\(893\) −22.1628 5.93852i −0.741651 0.198725i
\(894\) 0 0
\(895\) 3.79349 3.15423i 0.126803 0.105434i
\(896\) 2.51999 0.806019i 0.0841869 0.0269272i
\(897\) 0 0
\(898\) −1.89007 7.05384i −0.0630725 0.235390i
\(899\) −6.07098 10.5152i −0.202479 0.350703i
\(900\) 0 0
\(901\) −6.35888 3.67130i −0.211845 0.122309i
\(902\) 28.6835 28.6835i 0.955055 0.955055i
\(903\) 0 0
\(904\) 19.2075i 0.638833i
\(905\) 1.55854 + 9.07680i 0.0518077 + 0.301723i
\(906\) 0 0
\(907\) −4.46661 + 16.6696i −0.148312 + 0.553506i 0.851274 + 0.524721i \(0.175830\pi\)
−0.999586 + 0.0287849i \(0.990836\pi\)
\(908\) 18.0081 4.82525i 0.597618 0.160131i
\(909\) 0 0
\(910\) −3.60076 + 11.4062i −0.119364 + 0.378112i
\(911\) −5.56820 −0.184483 −0.0922414 0.995737i \(-0.529403\pi\)
−0.0922414 + 0.995737i \(0.529403\pi\)
\(912\) 0 0
\(913\) 11.6813 43.5952i 0.386594 1.44279i
\(914\) −4.45641 + 2.57291i −0.147405 + 0.0851042i
\(915\) 0 0
\(916\) 4.00767i 0.132417i
\(917\) −9.32645 + 18.0982i −0.307986 + 0.597657i
\(918\) 0 0
\(919\) 5.37964 + 3.10593i 0.177458 + 0.102455i 0.586098 0.810240i \(-0.300663\pi\)
−0.408640 + 0.912696i \(0.633997\pi\)
\(920\) −2.35772 0.870136i −0.0777318 0.0286875i
\(921\) 0 0
\(922\) 7.61212 + 28.4088i 0.250692 + 0.935595i
\(923\) 6.82943 + 6.82943i 0.224794 + 0.224794i
\(924\) 0 0
\(925\) 20.7713 14.2683i 0.682958 0.469139i
\(926\) −2.86113 + 4.95563i −0.0940226 + 0.162852i
\(927\) 0 0
\(928\) 3.04751 + 0.816578i 0.100039 + 0.0268055i
\(929\) −0.0947297 + 0.164077i −0.00310798 + 0.00538318i −0.867575 0.497306i \(-0.834323\pi\)
0.864467 + 0.502689i \(0.167656\pi\)
\(930\) 0 0
\(931\) 11.3087 24.7846i 0.370627 0.812281i
\(932\) 9.70971 + 9.70971i 0.318052 + 0.318052i
\(933\) 0 0
\(934\) −8.32139 14.4131i −0.272284 0.471610i
\(935\) −27.9514 60.6507i −0.914108 1.98349i
\(936\) 0 0
\(937\) −34.2022 + 34.2022i −1.11734 + 1.11734i −0.125208 + 0.992131i \(0.539960\pi\)
−0.992131 + 0.125208i \(0.960040\pi\)
\(938\) 2.23307 0.106750i 0.0729123 0.00348552i
\(939\) 0 0
\(940\) −10.7649 7.60984i −0.351112 0.248206i
\(941\) 16.3826 9.45851i 0.534058 0.308339i −0.208609 0.977999i \(-0.566894\pi\)
0.742667 + 0.669660i \(0.233560\pi\)
\(942\) 0 0
\(943\) 7.82790 2.09748i 0.254911 0.0683033i
\(944\) −5.47845 −0.178308
\(945\) 0 0
\(946\) 14.7719 0.480276
\(947\) 45.5435 12.2033i 1.47996 0.396555i 0.573629 0.819115i \(-0.305535\pi\)
0.906335 + 0.422560i \(0.138869\pi\)
\(948\) 0 0
\(949\) −9.82664 + 5.67341i −0.318986 + 0.184167i
\(950\) 1.52201 + 19.3994i 0.0493806 + 0.629400i
\(951\) 0 0
\(952\) 7.59560 + 11.8146i 0.246175 + 0.382914i
\(953\) −18.8431 + 18.8431i −0.610389 + 0.610389i −0.943047 0.332658i \(-0.892054\pi\)
0.332658 + 0.943047i \(0.392054\pi\)
\(954\) 0 0
\(955\) 13.3180 36.0865i 0.430960 1.16773i
\(956\) −9.83103 17.0278i −0.317958 0.550720i
\(957\) 0 0
\(958\) −10.8818 10.8818i −0.351575 0.351575i
\(959\) 22.8439 + 4.96536i 0.737667 + 0.160340i
\(960\) 0 0
\(961\) −8.09467 + 14.0204i −0.261118 + 0.452270i
\(962\) −9.84255 2.63730i −0.317337 0.0850301i
\(963\) 0 0
\(964\) −2.94256 + 5.09667i −0.0947735 + 0.164153i
\(965\) −26.8700 2.47231i −0.864976 0.0795863i
\(966\) 0 0
\(967\) 27.3703 + 27.3703i 0.880169 + 0.880169i 0.993551 0.113383i \(-0.0361687\pi\)
−0.113383 + 0.993551i \(0.536169\pi\)
\(968\) 5.34440 + 19.9456i 0.171776 + 0.641075i
\(969\) 0 0
\(970\) 7.26018 19.6722i 0.233110 0.631636i
\(971\) 27.8750 + 16.0936i 0.894550 + 0.516469i 0.875428 0.483348i \(-0.160580\pi\)
0.0191221 + 0.999817i \(0.493913\pi\)
\(972\) 0 0
\(973\) 1.39765 + 29.2369i 0.0448065 + 0.937291i
\(974\) 35.9920i 1.15326i
\(975\) 0 0
\(976\) −3.99172 + 2.30462i −0.127772 + 0.0737691i
\(977\) 6.02479 22.4848i 0.192750 0.719353i −0.800088 0.599883i \(-0.795214\pi\)
0.992838 0.119470i \(-0.0381195\pi\)
\(978\) 0 0
\(979\) 67.0692 2.14354
\(980\) 11.0260 11.1098i 0.352213 0.354889i
\(981\) 0 0
\(982\) 14.7616 3.95535i 0.471060 0.126220i
\(983\) −14.7630 + 55.0964i −0.470868 + 1.75730i 0.165793 + 0.986160i \(0.446981\pi\)
−0.636662 + 0.771143i \(0.719685\pi\)
\(984\) 0 0
\(985\) 36.9606 + 26.1279i 1.17766 + 0.832505i
\(986\) 16.7491i 0.533401i
\(987\) 0 0
\(988\) 5.56380 5.56380i 0.177008 0.177008i
\(989\) 2.55577 + 1.47557i 0.0812687 + 0.0469205i
\(990\) 0 0
\(991\) 28.7703 + 49.8316i 0.913918 + 1.58295i 0.808478 + 0.588526i \(0.200292\pi\)
0.105440 + 0.994426i \(0.466375\pi\)
\(992\) 0.996056 + 3.71733i 0.0316248 + 0.118025i
\(993\) 0 0
\(994\) −3.85043 12.0382i −0.122128 0.381829i
\(995\) 10.7694 + 12.9520i 0.341414 + 0.410607i
\(996\) 0 0
\(997\) 23.4284 + 6.27762i 0.741985 + 0.198814i 0.609960 0.792432i \(-0.291185\pi\)
0.132025 + 0.991246i \(0.457852\pi\)
\(998\) −30.5087 8.17479i −0.965737 0.258768i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 630.2.bv.c.397.3 16
3.2 odd 2 70.2.k.a.47.1 yes 16
5.3 odd 4 inner 630.2.bv.c.523.1 16
7.3 odd 6 inner 630.2.bv.c.577.1 16
12.11 even 2 560.2.ci.c.257.3 16
15.2 even 4 350.2.o.c.243.2 16
15.8 even 4 70.2.k.a.33.3 yes 16
15.14 odd 2 350.2.o.c.257.4 16
21.2 odd 6 490.2.g.c.97.6 16
21.5 even 6 490.2.g.c.97.7 16
21.11 odd 6 490.2.l.c.227.4 16
21.17 even 6 70.2.k.a.17.3 yes 16
21.20 even 2 490.2.l.c.117.2 16
35.3 even 12 inner 630.2.bv.c.73.3 16
60.23 odd 4 560.2.ci.c.33.3 16
84.59 odd 6 560.2.ci.c.17.3 16
105.17 odd 12 350.2.o.c.143.4 16
105.23 even 12 490.2.g.c.293.7 16
105.38 odd 12 70.2.k.a.3.1 16
105.53 even 12 490.2.l.c.423.2 16
105.59 even 6 350.2.o.c.157.2 16
105.68 odd 12 490.2.g.c.293.6 16
105.83 odd 4 490.2.l.c.313.4 16
420.143 even 12 560.2.ci.c.353.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.k.a.3.1 16 105.38 odd 12
70.2.k.a.17.3 yes 16 21.17 even 6
70.2.k.a.33.3 yes 16 15.8 even 4
70.2.k.a.47.1 yes 16 3.2 odd 2
350.2.o.c.143.4 16 105.17 odd 12
350.2.o.c.157.2 16 105.59 even 6
350.2.o.c.243.2 16 15.2 even 4
350.2.o.c.257.4 16 15.14 odd 2
490.2.g.c.97.6 16 21.2 odd 6
490.2.g.c.97.7 16 21.5 even 6
490.2.g.c.293.6 16 105.68 odd 12
490.2.g.c.293.7 16 105.23 even 12
490.2.l.c.117.2 16 21.20 even 2
490.2.l.c.227.4 16 21.11 odd 6
490.2.l.c.313.4 16 105.83 odd 4
490.2.l.c.423.2 16 105.53 even 12
560.2.ci.c.17.3 16 84.59 odd 6
560.2.ci.c.33.3 16 60.23 odd 4
560.2.ci.c.257.3 16 12.11 even 2
560.2.ci.c.353.3 16 420.143 even 12
630.2.bv.c.73.3 16 35.3 even 12 inner
630.2.bv.c.397.3 16 1.1 even 1 trivial
630.2.bv.c.523.1 16 5.3 odd 4 inner
630.2.bv.c.577.1 16 7.3 odd 6 inner