Properties

Label 975.2.bb.k.724.4
Level $975$
Weight $2$
Character 975.724
Analytic conductor $7.785$
Analytic rank $0$
Dimension $12$
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] = [975,2,Mod(724,975)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(975, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("975.724");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 975.bb (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.78541419707\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 195)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 724.4
Root \(1.75780 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 975.724
Dual form 975.2.bb.k.874.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.294342 + 0.169938i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.942242 - 1.63201i) q^{4} +(-0.169938 - 0.294342i) q^{6} +(0.571683 - 0.330062i) q^{7} -1.32025i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.294342 + 0.169938i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.942242 - 1.63201i) q^{4} +(-0.169938 - 0.294342i) q^{6} +(0.571683 - 0.330062i) q^{7} -1.32025i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.339877 + 0.588684i) q^{11} +1.88448i q^{12} +(3.04397 - 1.93243i) q^{13} +0.224361 q^{14} +(-1.66012 + 2.87542i) q^{16} +(6.43378 - 3.71455i) q^{17} +0.339877i q^{18} +(0.0577581 + 0.100040i) q^{19} -0.660123 q^{21} +(-0.200080 + 0.115516i) q^{22} +(-6.72812 - 3.88448i) q^{23} +(-0.660123 + 1.14337i) q^{24} +(1.22436 - 0.0515075i) q^{26} -1.00000i q^{27} +(-1.07733 - 0.621996i) q^{28} +(2.77230 - 4.80177i) q^{29} -9.97370 q^{31} +(-3.26402 + 1.88448i) q^{32} +(0.588684 - 0.339877i) q^{33} +2.52498 q^{34} +(0.942242 - 1.63201i) q^{36} +(-8.46017 - 4.88448i) q^{37} +0.0392613i q^{38} +(-3.60236 + 0.151548i) q^{39} +(-2.11218 + 3.65840i) q^{41} +(-0.194302 - 0.112180i) q^{42} +(0.471643 - 0.272303i) q^{43} +1.28098 q^{44} +(-1.32025 - 2.28673i) q^{46} -5.01963i q^{47} +(2.87542 - 1.66012i) q^{48} +(-3.28212 + 5.68480i) q^{49} -7.42909 q^{51} +(-6.02189 - 3.14697i) q^{52} -0.679754i q^{53} +(0.169938 - 0.294342i) q^{54} +(-0.435763 - 0.754763i) q^{56} -0.115516i q^{57} +(1.63201 - 0.942242i) q^{58} +(1.11218 + 1.92635i) q^{59} +(2.10236 + 3.64140i) q^{61} +(-2.93568 - 1.69491i) q^{62} +(0.571683 + 0.330062i) q^{63} +5.35951 q^{64} +0.231033 q^{66} +(6.61108 + 3.81691i) q^{67} +(-12.1244 - 7.00000i) q^{68} +(3.88448 + 6.72812i) q^{69} +(-3.65679 - 6.33374i) q^{71} +(1.14337 - 0.660123i) q^{72} -8.01963i q^{73} +(-1.66012 - 2.87542i) q^{74} +(0.108844 - 0.188524i) q^{76} +0.448721i q^{77} +(-1.08608 - 0.567573i) q^{78} -9.97370 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.24341 + 0.717881i) q^{82} -1.76897i q^{83} +(0.621996 + 1.07733i) q^{84} +0.185099 q^{86} +(-4.80177 + 2.77230i) q^{87} +(0.777208 + 0.448721i) q^{88} +(6.77230 - 11.7300i) q^{89} +(1.10236 - 2.10943i) q^{91} +14.6405i q^{92} +(8.63748 + 4.98685i) q^{93} +(0.853028 - 1.47749i) q^{94} +3.76897 q^{96} +(8.57721 - 4.95206i) q^{97} +(-1.93213 + 1.11552i) q^{98} -0.679754 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 12 q^{4} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 12 q^{4} + 6 q^{9} - 48 q^{14} - 24 q^{16} + 24 q^{19} - 12 q^{21} - 12 q^{24} - 36 q^{26} + 12 q^{29} + 12 q^{31} - 12 q^{36} - 24 q^{39} + 48 q^{44} - 24 q^{46} - 12 q^{49} - 60 q^{56} - 12 q^{59} + 6 q^{61} + 48 q^{64} + 96 q^{66} + 24 q^{71} - 24 q^{74} - 96 q^{76} + 12 q^{79} - 6 q^{81} - 24 q^{84} - 24 q^{86} + 60 q^{89} - 6 q^{91} + 72 q^{94} - 48 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.294342 + 0.169938i 0.208131 + 0.120165i 0.600443 0.799668i \(-0.294991\pi\)
−0.392311 + 0.919832i \(0.628324\pi\)
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) −0.942242 1.63201i −0.471121 0.816005i
\(5\) 0 0
\(6\) −0.169938 0.294342i −0.0693771 0.120165i
\(7\) 0.571683 0.330062i 0.216076 0.124752i −0.388056 0.921636i \(-0.626853\pi\)
0.604132 + 0.796884i \(0.293520\pi\)
\(8\) 1.32025i 0.466778i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.339877 + 0.588684i −0.102477 + 0.177495i −0.912704 0.408620i \(-0.866010\pi\)
0.810228 + 0.586115i \(0.199343\pi\)
\(12\) 1.88448i 0.544004i
\(13\) 3.04397 1.93243i 0.844244 0.535959i
\(14\) 0.224361 0.0599629
\(15\) 0 0
\(16\) −1.66012 + 2.87542i −0.415031 + 0.718854i
\(17\) 6.43378 3.71455i 1.56042 0.900910i 0.563207 0.826316i \(-0.309567\pi\)
0.997214 0.0745938i \(-0.0237660\pi\)
\(18\) 0.339877i 0.0801098i
\(19\) 0.0577581 + 0.100040i 0.0132506 + 0.0229508i 0.872575 0.488481i \(-0.162449\pi\)
−0.859324 + 0.511431i \(0.829115\pi\)
\(20\) 0 0
\(21\) −0.660123 −0.144051
\(22\) −0.200080 + 0.115516i −0.0426572 + 0.0246282i
\(23\) −6.72812 3.88448i −1.40291 0.809971i −0.408220 0.912883i \(-0.633850\pi\)
−0.994690 + 0.102913i \(0.967184\pi\)
\(24\) −0.660123 + 1.14337i −0.134747 + 0.233389i
\(25\) 0 0
\(26\) 1.22436 0.0515075i 0.240117 0.0101015i
\(27\) 1.00000i 0.192450i
\(28\) −1.07733 0.621996i −0.203596 0.117546i
\(29\) 2.77230 4.80177i 0.514804 0.891666i −0.485049 0.874487i \(-0.661198\pi\)
0.999852 0.0171792i \(-0.00546857\pi\)
\(30\) 0 0
\(31\) −9.97370 −1.79133 −0.895664 0.444730i \(-0.853299\pi\)
−0.895664 + 0.444730i \(0.853299\pi\)
\(32\) −3.26402 + 1.88448i −0.577003 + 0.333133i
\(33\) 0.588684 0.339877i 0.102477 0.0591650i
\(34\) 2.52498 0.433030
\(35\) 0 0
\(36\) 0.942242 1.63201i 0.157040 0.272002i
\(37\) −8.46017 4.88448i −1.39084 0.803004i −0.397435 0.917630i \(-0.630100\pi\)
−0.993409 + 0.114626i \(0.963433\pi\)
\(38\) 0.0392613i 0.00636903i
\(39\) −3.60236 + 0.151548i −0.576840 + 0.0242670i
\(40\) 0 0
\(41\) −2.11218 + 3.65840i −0.329867 + 0.571347i −0.982485 0.186340i \(-0.940337\pi\)
0.652618 + 0.757687i \(0.273671\pi\)
\(42\) −0.194302 0.112180i −0.0299814 0.0173098i
\(43\) 0.471643 0.272303i 0.0719249 0.0415259i −0.463606 0.886041i \(-0.653445\pi\)
0.535531 + 0.844515i \(0.320111\pi\)
\(44\) 1.28098 0.193116
\(45\) 0 0
\(46\) −1.32025 2.28673i −0.194660 0.337160i
\(47\) 5.01963i 0.732188i −0.930578 0.366094i \(-0.880695\pi\)
0.930578 0.366094i \(-0.119305\pi\)
\(48\) 2.87542 1.66012i 0.415031 0.239618i
\(49\) −3.28212 + 5.68480i −0.468874 + 0.812114i
\(50\) 0 0
\(51\) −7.42909 −1.04028
\(52\) −6.02189 3.14697i −0.835086 0.436406i
\(53\) 0.679754i 0.0933714i −0.998910 0.0466857i \(-0.985134\pi\)
0.998910 0.0466857i \(-0.0148659\pi\)
\(54\) 0.169938 0.294342i 0.0231257 0.0400549i
\(55\) 0 0
\(56\) −0.435763 0.754763i −0.0582312 0.100859i
\(57\) 0.115516i 0.0153005i
\(58\) 1.63201 0.942242i 0.214294 0.123722i
\(59\) 1.11218 + 1.92635i 0.144794 + 0.250790i 0.929296 0.369336i \(-0.120415\pi\)
−0.784502 + 0.620126i \(0.787082\pi\)
\(60\) 0 0
\(61\) 2.10236 + 3.64140i 0.269180 + 0.466234i 0.968650 0.248428i \(-0.0799139\pi\)
−0.699470 + 0.714662i \(0.746581\pi\)
\(62\) −2.93568 1.69491i −0.372832 0.215254i
\(63\) 0.571683 + 0.330062i 0.0720253 + 0.0415838i
\(64\) 5.35951 0.669938
\(65\) 0 0
\(66\) 0.231033 0.0284381
\(67\) 6.61108 + 3.81691i 0.807672 + 0.466310i 0.846147 0.532950i \(-0.178917\pi\)
−0.0384746 + 0.999260i \(0.512250\pi\)
\(68\) −12.1244 7.00000i −1.47029 0.848875i
\(69\) 3.88448 + 6.72812i 0.467637 + 0.809971i
\(70\) 0 0
\(71\) −3.65679 6.33374i −0.433981 0.751677i 0.563231 0.826299i \(-0.309558\pi\)
−0.997212 + 0.0746227i \(0.976225\pi\)
\(72\) 1.14337 0.660123i 0.134747 0.0777963i
\(73\) 8.01963i 0.938627i −0.883032 0.469313i \(-0.844501\pi\)
0.883032 0.469313i \(-0.155499\pi\)
\(74\) −1.66012 2.87542i −0.192985 0.334261i
\(75\) 0 0
\(76\) 0.108844 0.188524i 0.0124853 0.0216252i
\(77\) 0.448721i 0.0511365i
\(78\) −1.08608 0.567573i −0.122974 0.0642650i
\(79\) −9.97370 −1.12213 −0.561064 0.827772i \(-0.689608\pi\)
−0.561064 + 0.827772i \(0.689608\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.24341 + 0.717881i −0.137311 + 0.0792767i
\(83\) 1.76897i 0.194169i −0.995276 0.0970847i \(-0.969048\pi\)
0.995276 0.0970847i \(-0.0309518\pi\)
\(84\) 0.621996 + 1.07733i 0.0678653 + 0.117546i
\(85\) 0 0
\(86\) 0.185099 0.0199598
\(87\) −4.80177 + 2.77230i −0.514804 + 0.297222i
\(88\) 0.777208 + 0.448721i 0.0828506 + 0.0478338i
\(89\) 6.77230 11.7300i 0.717863 1.24337i −0.243982 0.969780i \(-0.578454\pi\)
0.961845 0.273595i \(-0.0882128\pi\)
\(90\) 0 0
\(91\) 1.10236 2.10943i 0.115559 0.221129i
\(92\) 14.6405i 1.52638i
\(93\) 8.63748 + 4.98685i 0.895664 + 0.517112i
\(94\) 0.853028 1.47749i 0.0879831 0.152391i
\(95\) 0 0
\(96\) 3.76897 0.384669
\(97\) 8.57721 4.95206i 0.870884 0.502805i 0.00324223 0.999995i \(-0.498968\pi\)
0.867642 + 0.497190i \(0.165635\pi\)
\(98\) −1.93213 + 1.11552i −0.195175 + 0.112684i
\(99\) −0.679754 −0.0683178
\(100\) 0 0
\(101\) 4.67975 8.10557i 0.465653 0.806534i −0.533578 0.845751i \(-0.679153\pi\)
0.999231 + 0.0392165i \(0.0124862\pi\)
\(102\) −2.18669 1.26249i −0.216515 0.125005i
\(103\) 4.50535i 0.443925i −0.975055 0.221962i \(-0.928754\pi\)
0.975055 0.221962i \(-0.0712462\pi\)
\(104\) −2.55128 4.01878i −0.250173 0.394074i
\(105\) 0 0
\(106\) 0.115516 0.200080i 0.0112199 0.0194335i
\(107\) −0.494422 0.285455i −0.0477976 0.0275960i 0.475911 0.879494i \(-0.342119\pi\)
−0.523708 + 0.851898i \(0.675452\pi\)
\(108\) −1.63201 + 0.942242i −0.157040 + 0.0906673i
\(109\) −15.4095 −1.47596 −0.737979 0.674823i \(-0.764220\pi\)
−0.737979 + 0.674823i \(0.764220\pi\)
\(110\) 0 0
\(111\) 4.88448 + 8.46017i 0.463615 + 0.803004i
\(112\) 2.19177i 0.207103i
\(113\) 4.60747 2.66012i 0.433434 0.250243i −0.267374 0.963593i \(-0.586156\pi\)
0.700809 + 0.713349i \(0.252823\pi\)
\(114\) 0.0196307 0.0340013i 0.00183858 0.00318451i
\(115\) 0 0
\(116\) −10.4487 −0.970139
\(117\) 3.19551 + 1.66994i 0.295425 + 0.154386i
\(118\) 0.756009i 0.0695962i
\(119\) 2.45206 4.24709i 0.224780 0.389330i
\(120\) 0 0
\(121\) 5.26897 + 9.12612i 0.478997 + 0.829647i
\(122\) 1.42909i 0.129384i
\(123\) 3.65840 2.11218i 0.329867 0.190449i
\(124\) 9.39764 + 16.2772i 0.843933 + 1.46173i
\(125\) 0 0
\(126\) 0.112180 + 0.194302i 0.00999381 + 0.0173098i
\(127\) 10.4093 + 6.00982i 0.923676 + 0.533285i 0.884806 0.465959i \(-0.154291\pi\)
0.0388704 + 0.999244i \(0.487624\pi\)
\(128\) 8.10557 + 4.67975i 0.716438 + 0.413636i
\(129\) −0.544607 −0.0479500
\(130\) 0 0
\(131\) 10.9041 0.952697 0.476348 0.879257i \(-0.341960\pi\)
0.476348 + 0.879257i \(0.341960\pi\)
\(132\) −1.10937 0.640492i −0.0965579 0.0557477i
\(133\) 0.0660387 + 0.0381275i 0.00572629 + 0.00330607i
\(134\) 1.29728 + 2.24695i 0.112068 + 0.194107i
\(135\) 0 0
\(136\) −4.90411 8.49418i −0.420524 0.728370i
\(137\) 2.93568 1.69491i 0.250812 0.144806i −0.369324 0.929301i \(-0.620411\pi\)
0.620136 + 0.784494i \(0.287077\pi\)
\(138\) 2.64049i 0.224774i
\(139\) 7.40411 + 12.8243i 0.628009 + 1.08774i 0.987951 + 0.154768i \(0.0494631\pi\)
−0.359942 + 0.932975i \(0.617204\pi\)
\(140\) 0 0
\(141\) −2.50982 + 4.34713i −0.211365 + 0.366094i
\(142\) 2.48571i 0.208597i
\(143\) 0.103015 + 2.44872i 0.00861455 + 0.204772i
\(144\) −3.32025 −0.276687
\(145\) 0 0
\(146\) 1.36284 2.36051i 0.112790 0.195358i
\(147\) 5.68480 3.28212i 0.468874 0.270705i
\(148\) 18.4095i 1.51325i
\(149\) −8.54461 14.7997i −0.700001 1.21244i −0.968465 0.249148i \(-0.919849\pi\)
0.268464 0.963290i \(-0.413484\pi\)
\(150\) 0 0
\(151\) 13.0130 1.05898 0.529490 0.848316i \(-0.322383\pi\)
0.529490 + 0.848316i \(0.322383\pi\)
\(152\) 0.132077 0.0762550i 0.0107129 0.00618510i
\(153\) 6.43378 + 3.71455i 0.520140 + 0.300303i
\(154\) −0.0762550 + 0.132077i −0.00614480 + 0.0106431i
\(155\) 0 0
\(156\) 3.64163 + 5.73630i 0.291563 + 0.459272i
\(157\) 0.775639i 0.0619028i −0.999521 0.0309514i \(-0.990146\pi\)
0.999521 0.0309514i \(-0.00985370\pi\)
\(158\) −2.93568 1.69491i −0.233550 0.134840i
\(159\) −0.339877 + 0.588684i −0.0269540 + 0.0466857i
\(160\) 0 0
\(161\) −5.12847 −0.404180
\(162\) −0.294342 + 0.169938i −0.0231257 + 0.0133516i
\(163\) −10.5638 + 6.09903i −0.827423 + 0.477713i −0.852969 0.521961i \(-0.825201\pi\)
0.0255466 + 0.999674i \(0.491867\pi\)
\(164\) 7.96074 0.621629
\(165\) 0 0
\(166\) 0.300616 0.520681i 0.0233323 0.0404127i
\(167\) 1.37745 + 0.795270i 0.106590 + 0.0615398i 0.552347 0.833614i \(-0.313732\pi\)
−0.445757 + 0.895154i \(0.647066\pi\)
\(168\) 0.871525i 0.0672396i
\(169\) 5.53146 11.7645i 0.425497 0.904960i
\(170\) 0 0
\(171\) −0.0577581 + 0.100040i −0.00441688 + 0.00765025i
\(172\) −0.888804 0.513151i −0.0677707 0.0391274i
\(173\) −11.0412 + 6.37467i −0.839451 + 0.484657i −0.857077 0.515188i \(-0.827722\pi\)
0.0176268 + 0.999845i \(0.494389\pi\)
\(174\) −1.88448 −0.142862
\(175\) 0 0
\(176\) −1.12847 1.95458i −0.0850620 0.147332i
\(177\) 2.22436i 0.167193i
\(178\) 3.98675 2.30175i 0.298819 0.172523i
\(179\) 8.88115 15.3826i 0.663808 1.14975i −0.315799 0.948826i \(-0.602272\pi\)
0.979607 0.200923i \(-0.0643942\pi\)
\(180\) 0 0
\(181\) 7.02630 0.522261 0.261130 0.965304i \(-0.415905\pi\)
0.261130 + 0.965304i \(0.415905\pi\)
\(182\) 0.682946 0.433560i 0.0506233 0.0321376i
\(183\) 4.20473i 0.310823i
\(184\) −5.12847 + 8.88278i −0.378076 + 0.654847i
\(185\) 0 0
\(186\) 1.69491 + 2.93568i 0.124277 + 0.215254i
\(187\) 5.04995i 0.369289i
\(188\) −8.19209 + 4.72971i −0.597470 + 0.344949i
\(189\) −0.330062 0.571683i −0.0240084 0.0415838i
\(190\) 0 0
\(191\) 6.97703 + 12.0846i 0.504840 + 0.874409i 0.999984 + 0.00559828i \(0.00178200\pi\)
−0.495144 + 0.868811i \(0.664885\pi\)
\(192\) −4.64147 2.67975i −0.334969 0.193395i
\(193\) 20.5675 + 11.8747i 1.48048 + 0.854757i 0.999755 0.0221126i \(-0.00703924\pi\)
0.480728 + 0.876870i \(0.340373\pi\)
\(194\) 3.36618 0.241678
\(195\) 0 0
\(196\) 12.3702 0.883586
\(197\) −13.6903 7.90411i −0.975395 0.563145i −0.0745186 0.997220i \(-0.523742\pi\)
−0.900877 + 0.434075i \(0.857075\pi\)
\(198\) −0.200080 0.115516i −0.0142191 0.00820939i
\(199\) 4.38448 + 7.59415i 0.310808 + 0.538335i 0.978537 0.206069i \(-0.0660671\pi\)
−0.667730 + 0.744404i \(0.732734\pi\)
\(200\) 0 0
\(201\) −3.81691 6.61108i −0.269224 0.466310i
\(202\) 2.75490 1.59054i 0.193834 0.111910i
\(203\) 3.66012i 0.256890i
\(204\) 7.00000 + 12.1244i 0.490098 + 0.848875i
\(205\) 0 0
\(206\) 0.765631 1.32611i 0.0533441 0.0923946i
\(207\) 7.76897i 0.539981i
\(208\) 0.503175 + 11.9607i 0.0348889 + 0.829328i
\(209\) −0.0785226 −0.00543152
\(210\) 0 0
\(211\) −4.40411 + 7.62815i −0.303192 + 0.525143i −0.976857 0.213893i \(-0.931386\pi\)
0.673665 + 0.739037i \(0.264719\pi\)
\(212\) −1.10937 + 0.640492i −0.0761915 + 0.0439892i
\(213\) 7.31357i 0.501118i
\(214\) −0.0970195 0.168043i −0.00663211 0.0114872i
\(215\) 0 0
\(216\) −1.32025 −0.0898314
\(217\) −5.70180 + 3.29193i −0.387063 + 0.223471i
\(218\) −4.53565 2.61866i −0.307193 0.177358i
\(219\) −4.00982 + 6.94520i −0.270958 + 0.469313i
\(220\) 0 0
\(221\) 12.4061 23.7398i 0.834526 1.59691i
\(222\) 3.32025i 0.222840i
\(223\) 8.69426 + 5.01963i 0.582210 + 0.336139i 0.762011 0.647564i \(-0.224212\pi\)
−0.179801 + 0.983703i \(0.557545\pi\)
\(224\) −1.24399 + 2.15466i −0.0831177 + 0.143964i
\(225\) 0 0
\(226\) 1.80823 0.120282
\(227\) 1.04910 0.605701i 0.0696315 0.0402018i −0.464780 0.885426i \(-0.653867\pi\)
0.534412 + 0.845224i \(0.320533\pi\)
\(228\) −0.188524 + 0.108844i −0.0124853 + 0.00720839i
\(229\) −19.2440 −1.27168 −0.635839 0.771821i \(-0.719346\pi\)
−0.635839 + 0.771821i \(0.719346\pi\)
\(230\) 0 0
\(231\) 0.224361 0.388604i 0.0147618 0.0255683i
\(232\) −6.33952 3.66012i −0.416210 0.240299i
\(233\) 23.9081i 1.56627i 0.621849 + 0.783137i \(0.286382\pi\)
−0.621849 + 0.783137i \(0.713618\pi\)
\(234\) 0.656787 + 1.03457i 0.0429355 + 0.0676322i
\(235\) 0 0
\(236\) 2.09589 3.63018i 0.136431 0.236305i
\(237\) 8.63748 + 4.98685i 0.561064 + 0.323931i
\(238\) 1.44349 0.833398i 0.0935674 0.0540211i
\(239\) −18.6798 −1.20829 −0.604146 0.796873i \(-0.706486\pi\)
−0.604146 + 0.796873i \(0.706486\pi\)
\(240\) 0 0
\(241\) −3.05776 5.29619i −0.196968 0.341158i 0.750576 0.660784i \(-0.229776\pi\)
−0.947544 + 0.319626i \(0.896443\pi\)
\(242\) 3.58160i 0.230234i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) 3.96187 6.86216i 0.253633 0.439305i
\(245\) 0 0
\(246\) 1.43576 0.0915409
\(247\) 0.369134 + 0.192905i 0.0234874 + 0.0122743i
\(248\) 13.1677i 0.836152i
\(249\) −0.884484 + 1.53197i −0.0560519 + 0.0970847i
\(250\) 0 0
\(251\) −1.67975 2.90942i −0.106025 0.183641i 0.808131 0.589002i \(-0.200479\pi\)
−0.914157 + 0.405361i \(0.867146\pi\)
\(252\) 1.24399i 0.0783641i
\(253\) 4.57347 2.64049i 0.287531 0.166006i
\(254\) 2.04260 + 3.53788i 0.128164 + 0.221986i
\(255\) 0 0
\(256\) −3.76897 6.52804i −0.235560 0.408003i
\(257\) 8.75452 + 5.05442i 0.546092 + 0.315286i 0.747544 0.664212i \(-0.231233\pi\)
−0.201452 + 0.979498i \(0.564566\pi\)
\(258\) −0.160301 0.0925496i −0.00997988 0.00576189i
\(259\) −6.44872 −0.400704
\(260\) 0 0
\(261\) 5.54461 0.343203
\(262\) 3.20954 + 1.85303i 0.198286 + 0.114480i
\(263\) −19.5014 11.2592i −1.20251 0.694269i −0.241397 0.970426i \(-0.577606\pi\)
−0.961112 + 0.276157i \(0.910939\pi\)
\(264\) −0.448721 0.777208i −0.0276169 0.0478338i
\(265\) 0 0
\(266\) 0.0129587 + 0.0224450i 0.000794546 + 0.00137619i
\(267\) −11.7300 + 6.77230i −0.717863 + 0.414458i
\(268\) 14.3858i 0.878753i
\(269\) 4.24733 + 7.35659i 0.258964 + 0.448539i 0.965965 0.258674i \(-0.0832855\pi\)
−0.707001 + 0.707213i \(0.749952\pi\)
\(270\) 0 0
\(271\) −4.68510 + 8.11483i −0.284600 + 0.492941i −0.972512 0.232853i \(-0.925194\pi\)
0.687912 + 0.725794i \(0.258527\pi\)
\(272\) 24.6664i 1.49562i
\(273\) −2.00939 + 1.27564i −0.121614 + 0.0772052i
\(274\) 1.15212 0.0696024
\(275\) 0 0
\(276\) 7.32025 12.6790i 0.440627 0.763188i
\(277\) 0.622685 0.359508i 0.0374135 0.0216007i −0.481177 0.876624i \(-0.659790\pi\)
0.518590 + 0.855023i \(0.326457\pi\)
\(278\) 5.03297i 0.301858i
\(279\) −4.98685 8.63748i −0.298555 0.517112i
\(280\) 0 0
\(281\) 1.54461 0.0921435 0.0460718 0.998938i \(-0.485330\pi\)
0.0460718 + 0.998938i \(0.485330\pi\)
\(282\) −1.47749 + 0.853028i −0.0879831 + 0.0507971i
\(283\) −15.6920 9.05977i −0.932791 0.538547i −0.0450980 0.998983i \(-0.514360\pi\)
−0.887693 + 0.460435i \(0.847693\pi\)
\(284\) −6.89116 + 11.9358i −0.408915 + 0.708261i
\(285\) 0 0
\(286\) −0.385810 + 0.738268i −0.0228134 + 0.0436547i
\(287\) 2.78860i 0.164606i
\(288\) −3.26402 1.88448i −0.192334 0.111044i
\(289\) 19.0957 33.0747i 1.12328 1.94557i
\(290\) 0 0
\(291\) −9.90411 −0.580589
\(292\) −13.0881 + 7.55643i −0.765924 + 0.442207i
\(293\) 26.4181 15.2525i 1.54336 0.891059i 0.544737 0.838607i \(-0.316630\pi\)
0.998623 0.0524523i \(-0.0167037\pi\)
\(294\) 2.23103 0.130116
\(295\) 0 0
\(296\) −6.44872 + 11.1695i −0.374824 + 0.649215i
\(297\) 0.588684 + 0.339877i 0.0341589 + 0.0197217i
\(298\) 5.80823i 0.336462i
\(299\) −27.9867 + 1.17737i −1.61851 + 0.0680890i
\(300\) 0 0
\(301\) 0.179754 0.311343i 0.0103608 0.0179455i
\(302\) 3.83026 + 2.21140i 0.220407 + 0.127252i
\(303\) −8.10557 + 4.67975i −0.465653 + 0.268845i
\(304\) −0.383543 −0.0219977
\(305\) 0 0
\(306\) 1.26249 + 2.18669i 0.0721716 + 0.125005i
\(307\) 4.77564i 0.272560i −0.990670 0.136280i \(-0.956485\pi\)
0.990670 0.136280i \(-0.0435147\pi\)
\(308\) 0.732318 0.422804i 0.0417277 0.0240915i
\(309\) −2.25267 + 3.90174i −0.128150 + 0.221962i
\(310\) 0 0
\(311\) 30.5812 1.73410 0.867051 0.498220i \(-0.166013\pi\)
0.867051 + 0.498220i \(0.166013\pi\)
\(312\) 0.200080 + 4.75601i 0.0113273 + 0.269256i
\(313\) 26.7230i 1.51048i 0.655451 + 0.755238i \(0.272479\pi\)
−0.655451 + 0.755238i \(0.727521\pi\)
\(314\) 0.131811 0.228303i 0.00743852 0.0128839i
\(315\) 0 0
\(316\) 9.39764 + 16.2772i 0.528658 + 0.915663i
\(317\) 20.6271i 1.15854i −0.815137 0.579268i \(-0.803338\pi\)
0.815137 0.579268i \(-0.196662\pi\)
\(318\) −0.200080 + 0.115516i −0.0112199 + 0.00647783i
\(319\) 1.88448 + 3.26402i 0.105511 + 0.182750i
\(320\) 0 0
\(321\) 0.285455 + 0.494422i 0.0159325 + 0.0275960i
\(322\) −1.50953 0.871525i −0.0841226 0.0485682i
\(323\) 0.743207 + 0.429091i 0.0413531 + 0.0238752i
\(324\) 1.88448 0.104694
\(325\) 0 0
\(326\) −4.14584 −0.229617
\(327\) 13.3450 + 7.70473i 0.737979 + 0.426073i
\(328\) 4.82999 + 2.78860i 0.266692 + 0.153975i
\(329\) −1.65679 2.86964i −0.0913416 0.158208i
\(330\) 0 0
\(331\) −2.68510 4.65073i −0.147586 0.255627i 0.782749 0.622338i \(-0.213817\pi\)
−0.930335 + 0.366711i \(0.880484\pi\)
\(332\) −2.88697 + 1.66680i −0.158443 + 0.0914773i
\(333\) 9.76897i 0.535336i
\(334\) 0.270294 + 0.468163i 0.0147898 + 0.0256167i
\(335\) 0 0
\(336\) 1.09589 1.89813i 0.0597855 0.103551i
\(337\) 28.7623i 1.56678i 0.621529 + 0.783391i \(0.286512\pi\)
−0.621529 + 0.783391i \(0.713488\pi\)
\(338\) 3.62738 2.52277i 0.197303 0.137221i
\(339\) −5.32025 −0.288956
\(340\) 0 0
\(341\) 3.38983 5.87136i 0.183570 0.317952i
\(342\) −0.0340013 + 0.0196307i −0.00183858 + 0.00106150i
\(343\) 8.95407i 0.483474i
\(344\) −0.359508 0.622685i −0.0193833 0.0335729i
\(345\) 0 0
\(346\) −4.33320 −0.232955
\(347\) 19.3956 11.1981i 1.04121 0.601143i 0.121035 0.992648i \(-0.461379\pi\)
0.920176 + 0.391505i \(0.128045\pi\)
\(348\) 9.04886 + 5.22436i 0.485070 + 0.280055i
\(349\) −5.98685 + 10.3695i −0.320469 + 0.555068i −0.980585 0.196096i \(-0.937174\pi\)
0.660116 + 0.751164i \(0.270507\pi\)
\(350\) 0 0
\(351\) −1.93243 3.04397i −0.103145 0.162475i
\(352\) 2.56197i 0.136553i
\(353\) −14.7541 8.51830i −0.785283 0.453384i 0.0530161 0.998594i \(-0.483117\pi\)
−0.838299 + 0.545210i \(0.816450\pi\)
\(354\) 0.378004 0.654723i 0.0200907 0.0347981i
\(355\) 0 0
\(356\) −25.5246 −1.35280
\(357\) −4.24709 + 2.45206i −0.224780 + 0.129777i
\(358\) 5.22819 3.01850i 0.276318 0.159533i
\(359\) 35.0825 1.85159 0.925793 0.378031i \(-0.123399\pi\)
0.925793 + 0.378031i \(0.123399\pi\)
\(360\) 0 0
\(361\) 9.49333 16.4429i 0.499649 0.865417i
\(362\) 2.06814 + 1.19404i 0.108699 + 0.0627573i
\(363\) 10.5379i 0.553098i
\(364\) −4.48131 + 0.188524i −0.234884 + 0.00988133i
\(365\) 0 0
\(366\) 0.714545 1.23763i 0.0373499 0.0646919i
\(367\) −17.3920 10.0413i −0.907855 0.524150i −0.0281143 0.999605i \(-0.508950\pi\)
−0.879740 + 0.475455i \(0.842284\pi\)
\(368\) 22.3390 12.8974i 1.16450 0.672326i
\(369\) −4.22436 −0.219911
\(370\) 0 0
\(371\) −0.224361 0.388604i −0.0116482 0.0201753i
\(372\) 18.7953i 0.974489i
\(373\) 20.3334 11.7395i 1.05283 0.607849i 0.129387 0.991594i \(-0.458699\pi\)
0.923439 + 0.383745i \(0.125366\pi\)
\(374\) −0.858181 + 1.48641i −0.0443755 + 0.0768606i
\(375\) 0 0
\(376\) −6.62715 −0.341769
\(377\) −0.840272 19.9737i −0.0432762 1.02870i
\(378\) 0.224361i 0.0115399i
\(379\) 10.5707 18.3090i 0.542981 0.940471i −0.455750 0.890108i \(-0.650629\pi\)
0.998731 0.0503631i \(-0.0160379\pi\)
\(380\) 0 0
\(381\) −6.00982 10.4093i −0.307892 0.533285i
\(382\) 4.74266i 0.242656i
\(383\) −1.50571 + 0.869323i −0.0769383 + 0.0444203i −0.537976 0.842960i \(-0.680811\pi\)
0.461037 + 0.887381i \(0.347477\pi\)
\(384\) −4.67975 8.10557i −0.238813 0.413636i
\(385\) 0 0
\(386\) 4.03593 + 6.99043i 0.205423 + 0.355803i
\(387\) 0.471643 + 0.272303i 0.0239750 + 0.0138420i
\(388\) −16.1636 9.33207i −0.820584 0.473764i
\(389\) 26.6664 1.35204 0.676020 0.736883i \(-0.263703\pi\)
0.676020 + 0.736883i \(0.263703\pi\)
\(390\) 0 0
\(391\) −57.7164 −2.91884
\(392\) 7.50533 + 4.33320i 0.379076 + 0.218860i
\(393\) −9.44324 5.45206i −0.476348 0.275020i
\(394\) −2.68643 4.65303i −0.135340 0.234416i
\(395\) 0 0
\(396\) 0.640492 + 1.10937i 0.0321860 + 0.0557477i
\(397\) 12.5960 7.27230i 0.632175 0.364986i −0.149419 0.988774i \(-0.547740\pi\)
0.781594 + 0.623788i \(0.214407\pi\)
\(398\) 2.98037i 0.149392i
\(399\) −0.0381275 0.0660387i −0.00190876 0.00330607i
\(400\) 0 0
\(401\) 4.18510 7.24880i 0.208994 0.361988i −0.742404 0.669952i \(-0.766314\pi\)
0.951398 + 0.307964i \(0.0996478\pi\)
\(402\) 2.59456i 0.129405i
\(403\) −30.3596 + 19.2734i −1.51232 + 0.960078i
\(404\) −17.6378 −0.877515
\(405\) 0 0
\(406\) 0.621996 1.07733i 0.0308691 0.0534669i
\(407\) 5.75084 3.32025i 0.285058 0.164578i
\(408\) 9.80823i 0.485580i
\(409\) 8.62734 + 14.9430i 0.426595 + 0.738883i 0.996568 0.0827798i \(-0.0263798\pi\)
−0.569973 + 0.821663i \(0.693046\pi\)
\(410\) 0 0
\(411\) −3.38983 −0.167208
\(412\) −7.35277 + 4.24513i −0.362245 + 0.209142i
\(413\) 1.27163 + 0.734176i 0.0625728 + 0.0361264i
\(414\) 1.32025 2.28673i 0.0648866 0.112387i
\(415\) 0 0
\(416\) −6.29394 + 12.0438i −0.308586 + 0.590495i
\(417\) 14.8082i 0.725162i
\(418\) −0.0231125 0.0133440i −0.00113047 0.000652677i
\(419\) 6.43243 11.1413i 0.314245 0.544288i −0.665032 0.746815i \(-0.731582\pi\)
0.979277 + 0.202527i \(0.0649155\pi\)
\(420\) 0 0
\(421\) 24.5616 1.19706 0.598529 0.801101i \(-0.295752\pi\)
0.598529 + 0.801101i \(0.295752\pi\)
\(422\) −2.59263 + 1.49686i −0.126207 + 0.0728658i
\(423\) 4.34713 2.50982i 0.211365 0.122031i
\(424\) −0.897442 −0.0435837
\(425\) 0 0
\(426\) −1.24286 + 2.15269i −0.0602166 + 0.104298i
\(427\) 2.40377 + 1.38782i 0.116327 + 0.0671613i
\(428\) 1.07587i 0.0520041i
\(429\) 1.13515 2.17216i 0.0548054 0.104873i
\(430\) 0 0
\(431\) −12.3898 + 21.4598i −0.596797 + 1.03368i 0.396493 + 0.918038i \(0.370227\pi\)
−0.993291 + 0.115645i \(0.963106\pi\)
\(432\) 2.87542 + 1.66012i 0.138344 + 0.0798727i
\(433\) 12.1754 7.02945i 0.585110 0.337814i −0.178051 0.984021i \(-0.556979\pi\)
0.763162 + 0.646208i \(0.223646\pi\)
\(434\) −2.23770 −0.107413
\(435\) 0 0
\(436\) 14.5194 + 25.1484i 0.695355 + 1.20439i
\(437\) 0.897442i 0.0429305i
\(438\) −2.36051 + 1.36284i −0.112790 + 0.0651192i
\(439\) 10.4226 18.0525i 0.497444 0.861598i −0.502552 0.864547i \(-0.667605\pi\)
0.999996 + 0.00294880i \(0.000938633\pi\)
\(440\) 0 0
\(441\) −6.56424 −0.312583
\(442\) 7.68594 4.87933i 0.365583 0.232086i
\(443\) 11.4291i 0.543012i 0.962437 + 0.271506i \(0.0875218\pi\)
−0.962437 + 0.271506i \(0.912478\pi\)
\(444\) 9.20473 15.9431i 0.436837 0.756624i
\(445\) 0 0
\(446\) 1.70606 + 2.95498i 0.0807841 + 0.139922i
\(447\) 17.0892i 0.808292i
\(448\) 3.06394 1.76897i 0.144758 0.0835759i
\(449\) 12.9541 + 22.4371i 0.611340 + 1.05887i 0.991015 + 0.133752i \(0.0427026\pi\)
−0.379675 + 0.925120i \(0.623964\pi\)
\(450\) 0 0
\(451\) −1.43576 2.48681i −0.0676074 0.117099i
\(452\) −8.68270 5.01296i −0.408400 0.235790i
\(453\) −11.2696 6.50648i −0.529490 0.305701i
\(454\) 0.411728 0.0193233
\(455\) 0 0
\(456\) −0.152510 −0.00714193
\(457\) −5.11311 2.95206i −0.239181 0.138091i 0.375619 0.926774i \(-0.377430\pi\)
−0.614800 + 0.788683i \(0.710763\pi\)
\(458\) −5.66432 3.27029i −0.264676 0.152811i
\(459\) −3.71455 6.43378i −0.173380 0.300303i
\(460\) 0 0
\(461\) 7.74600 + 13.4165i 0.360767 + 0.624867i 0.988087 0.153894i \(-0.0491815\pi\)
−0.627320 + 0.778762i \(0.715848\pi\)
\(462\) 0.132077 0.0762550i 0.00614480 0.00354770i
\(463\) 17.4420i 0.810601i −0.914184 0.405300i \(-0.867167\pi\)
0.914184 0.405300i \(-0.132833\pi\)
\(464\) 9.20473 + 15.9431i 0.427319 + 0.740138i
\(465\) 0 0
\(466\) −4.06291 + 7.03717i −0.188211 + 0.325991i
\(467\) 20.4790i 0.947657i −0.880617 0.473829i \(-0.842872\pi\)
0.880617 0.473829i \(-0.157128\pi\)
\(468\) −0.285589 6.78860i −0.0132014 0.313803i
\(469\) 5.03926 0.232691
\(470\) 0 0
\(471\) −0.387820 + 0.671723i −0.0178698 + 0.0309514i
\(472\) 2.54326 1.46835i 0.117063 0.0675864i
\(473\) 0.370199i 0.0170217i
\(474\) 1.69491 + 2.93568i 0.0778500 + 0.134840i
\(475\) 0 0
\(476\) −9.24172 −0.423594
\(477\) 0.588684 0.339877i 0.0269540 0.0155619i
\(478\) −5.49824 3.17441i −0.251483 0.145194i
\(479\) −20.4953 + 35.4990i −0.936456 + 1.62199i −0.164439 + 0.986387i \(0.552581\pi\)
−0.772017 + 0.635602i \(0.780752\pi\)
\(480\) 0 0
\(481\) −35.1914 + 1.48046i −1.60459 + 0.0675033i
\(482\) 2.07852i 0.0946741i
\(483\) 4.44139 + 2.56424i 0.202090 + 0.116677i
\(484\) 9.92928 17.1980i 0.451331 0.781728i
\(485\) 0 0
\(486\) 0.339877 0.0154171
\(487\) 20.8391 12.0315i 0.944309 0.545197i 0.0530008 0.998594i \(-0.483121\pi\)
0.891309 + 0.453397i \(0.149788\pi\)
\(488\) 4.80755 2.77564i 0.217627 0.125647i
\(489\) 12.1981 0.551615
\(490\) 0 0
\(491\) −18.3865 + 31.8463i −0.829771 + 1.43721i 0.0684471 + 0.997655i \(0.478196\pi\)
−0.898218 + 0.439550i \(0.855138\pi\)
\(492\) −6.89420 3.98037i −0.310815 0.179449i
\(493\) 41.1914i 1.85517i
\(494\) 0.0758696 + 0.119510i 0.00341354 + 0.00537701i
\(495\) 0 0
\(496\) 16.5576 28.6785i 0.743457 1.28770i
\(497\) −4.18105 2.41393i −0.187546 0.108280i
\(498\) −0.520681 + 0.300616i −0.0233323 + 0.0134709i
\(499\) −34.8212 −1.55881 −0.779405 0.626520i \(-0.784479\pi\)
−0.779405 + 0.626520i \(0.784479\pi\)
\(500\) 0 0
\(501\) −0.795270 1.37745i −0.0355300 0.0615398i
\(502\) 1.14182i 0.0509619i
\(503\) 27.7353 16.0130i 1.23665 0.713983i 0.268245 0.963351i \(-0.413556\pi\)
0.968409 + 0.249368i \(0.0802229\pi\)
\(504\) 0.435763 0.754763i 0.0194104 0.0336198i
\(505\) 0 0
\(506\) 1.79488 0.0797924
\(507\) −10.6726 + 7.42261i −0.473988 + 0.329650i
\(508\) 22.6508i 1.00497i
\(509\) −20.6731 + 35.8068i −0.916318 + 1.58711i −0.111359 + 0.993780i \(0.535520\pi\)
−0.804960 + 0.593329i \(0.797813\pi\)
\(510\) 0 0
\(511\) −2.64697 4.58469i −0.117095 0.202815i
\(512\) 21.2810i 0.940496i
\(513\) 0.100040 0.0577581i 0.00441688 0.00255008i
\(514\) 1.71788 + 2.97546i 0.0757725 + 0.131242i
\(515\) 0 0
\(516\) 0.513151 + 0.888804i 0.0225902 + 0.0391274i
\(517\) 2.95498 + 1.70606i 0.129960 + 0.0750323i
\(518\) −1.89813 1.09589i −0.0833990 0.0481505i
\(519\) 12.7493 0.559634
\(520\) 0 0
\(521\) 4.40279 0.192890 0.0964448 0.995338i \(-0.469253\pi\)
0.0964448 + 0.995338i \(0.469253\pi\)
\(522\) 1.63201 + 0.942242i 0.0714312 + 0.0412408i
\(523\) −28.1014 16.2244i −1.22879 0.709442i −0.262013 0.965064i \(-0.584386\pi\)
−0.966777 + 0.255623i \(0.917720\pi\)
\(524\) −10.2743 17.7956i −0.448835 0.777406i
\(525\) 0 0
\(526\) −3.82673 6.62808i −0.166853 0.288998i
\(527\) −64.1686 + 37.0478i −2.79523 + 1.61383i
\(528\) 2.25695i 0.0982211i
\(529\) 18.6784 + 32.3520i 0.812106 + 1.40661i
\(530\) 0 0
\(531\) −1.11218 + 1.92635i −0.0482645 + 0.0835966i
\(532\) 0.143701i 0.00623024i
\(533\) 0.640192 + 15.2177i 0.0277298 + 0.659151i
\(534\) −4.60350 −0.199213
\(535\) 0 0
\(536\) 5.03926 8.72826i 0.217663 0.377003i
\(537\) −15.3826 + 8.88115i −0.663808 + 0.383250i
\(538\) 2.88714i 0.124473i
\(539\) −2.23103 3.86426i −0.0960974 0.166446i
\(540\) 0 0
\(541\) −8.57720 −0.368762 −0.184381 0.982855i \(-0.559028\pi\)
−0.184381 + 0.982855i \(0.559028\pi\)
\(542\) −2.75804 + 1.59236i −0.118468 + 0.0683976i
\(543\) −6.08496 3.51315i −0.261130 0.150764i
\(544\) −14.0000 + 24.2487i −0.600245 + 1.03965i
\(545\) 0 0
\(546\) −0.808229 + 0.0340013i −0.0345890 + 0.00145512i
\(547\) 32.4920i 1.38926i −0.719368 0.694629i \(-0.755569\pi\)
0.719368 0.694629i \(-0.244431\pi\)
\(548\) −5.53224 3.19404i −0.236325 0.136443i
\(549\) −2.10236 + 3.64140i −0.0897268 + 0.155411i
\(550\) 0 0
\(551\) 0.640492 0.0272859
\(552\) 8.88278 5.12847i 0.378076 0.218282i
\(553\) −5.70180 + 3.29193i −0.242465 + 0.139987i
\(554\) 0.244377 0.0103826
\(555\) 0 0
\(556\) 13.9529 24.1672i 0.591736 1.02492i
\(557\) 35.6933 + 20.6075i 1.51237 + 0.873169i 0.999895 + 0.0144676i \(0.00460533\pi\)
0.512477 + 0.858701i \(0.328728\pi\)
\(558\) 3.38983i 0.143503i
\(559\) 0.909460 1.74030i 0.0384661 0.0736068i
\(560\) 0 0
\(561\) 2.52498 4.37339i 0.106605 0.184645i
\(562\) 0.454643 + 0.262488i 0.0191779 + 0.0110724i
\(563\) 10.5468 6.08921i 0.444496 0.256630i −0.261007 0.965337i \(-0.584055\pi\)
0.705503 + 0.708707i \(0.250721\pi\)
\(564\) 9.45941 0.398313
\(565\) 0 0
\(566\) −3.07921 5.33334i −0.129429 0.224177i
\(567\) 0.660123i 0.0277226i
\(568\) −8.36210 + 4.82786i −0.350866 + 0.202572i
\(569\) 3.47169 6.01314i 0.145541 0.252084i −0.784034 0.620718i \(-0.786841\pi\)
0.929575 + 0.368634i \(0.120174\pi\)
\(570\) 0 0
\(571\) 3.51429 0.147068 0.0735341 0.997293i \(-0.476572\pi\)
0.0735341 + 0.997293i \(0.476572\pi\)
\(572\) 3.89927 2.47541i 0.163037 0.103502i
\(573\) 13.9541i 0.582939i
\(574\) −0.473890 + 0.820802i −0.0197798 + 0.0342596i
\(575\) 0 0
\(576\) 2.67975 + 4.64147i 0.111656 + 0.193395i
\(577\) 3.14182i 0.130796i 0.997859 + 0.0653978i \(0.0208316\pi\)
−0.997859 + 0.0653978i \(0.979168\pi\)
\(578\) 11.2413 6.49018i 0.467578 0.269956i
\(579\) −11.8747 20.5675i −0.493494 0.854757i
\(580\) 0 0
\(581\) −0.583868 1.01129i −0.0242229 0.0419553i
\(582\) −2.91520 1.68309i −0.120839 0.0697663i
\(583\) 0.400160 + 0.231033i 0.0165729 + 0.00956839i
\(584\) −10.5879 −0.438130
\(585\) 0 0
\(586\) 10.3679 0.428295
\(587\) −32.8897 18.9889i −1.35750 0.783754i −0.368215 0.929741i \(-0.620031\pi\)
−0.989287 + 0.145987i \(0.953364\pi\)
\(588\) −10.7129 6.18510i −0.441793 0.255069i
\(589\) −0.576062 0.997769i −0.0237362 0.0411124i
\(590\) 0 0
\(591\) 7.90411 + 13.6903i 0.325132 + 0.563145i
\(592\) 28.0899 16.2177i 1.15449 0.666543i
\(593\) 10.4487i 0.429078i −0.976715 0.214539i \(-0.931175\pi\)
0.976715 0.214539i \(-0.0688248\pi\)
\(594\) 0.115516 + 0.200080i 0.00473969 + 0.00820939i
\(595\) 0 0
\(596\) −16.1022 + 27.8898i −0.659571 + 1.14241i
\(597\) 8.76897i 0.358890i
\(598\) −8.43773 4.40946i −0.345044 0.180316i
\(599\) 45.5705 1.86196 0.930981 0.365069i \(-0.118955\pi\)
0.930981 + 0.365069i \(0.118955\pi\)
\(600\) 0 0
\(601\) 7.39096 12.8015i 0.301484 0.522185i −0.674989 0.737828i \(-0.735851\pi\)
0.976472 + 0.215643i \(0.0691848\pi\)
\(602\) 0.105818 0.0610942i 0.00431283 0.00249001i
\(603\) 7.63382i 0.310873i
\(604\) −12.2614 21.2373i −0.498907 0.864133i
\(605\) 0 0
\(606\) −3.18108 −0.129223
\(607\) −16.3977 + 9.46722i −0.665562 + 0.384263i −0.794393 0.607404i \(-0.792211\pi\)
0.128831 + 0.991667i \(0.458878\pi\)
\(608\) −0.377048 0.217689i −0.0152913 0.00882844i
\(609\) −1.83006 + 3.16976i −0.0741578 + 0.128445i
\(610\) 0 0
\(611\) −9.70007 15.2796i −0.392423 0.618146i
\(612\) 14.0000i 0.565916i
\(613\) −2.23770 1.29193i −0.0903797 0.0521807i 0.454129 0.890936i \(-0.349951\pi\)
−0.544509 + 0.838755i \(0.683284\pi\)
\(614\) 0.811565 1.40567i 0.0327521 0.0567283i
\(615\) 0 0
\(616\) 0.592422 0.0238694
\(617\) 12.1584 7.01963i 0.489477 0.282600i −0.234880 0.972024i \(-0.575470\pi\)
0.724357 + 0.689425i \(0.242137\pi\)
\(618\) −1.32611 + 0.765631i −0.0533441 + 0.0307982i
\(619\) 17.8582 0.717781 0.358890 0.933380i \(-0.383155\pi\)
0.358890 + 0.933380i \(0.383155\pi\)
\(620\) 0 0
\(621\) −3.88448 + 6.72812i −0.155879 + 0.269990i
\(622\) 9.00134 + 5.19692i 0.360921 + 0.208378i
\(623\) 8.94111i 0.358218i
\(624\) 5.54461 10.6099i 0.221962 0.424736i
\(625\) 0 0
\(626\) −4.54127 + 7.86571i −0.181506 + 0.314377i
\(627\) 0.0680026 + 0.0392613i 0.00271576 + 0.00156795i
\(628\) −1.26585 + 0.730840i −0.0505130 + 0.0291637i
\(629\) −72.5745 −2.89374
\(630\) 0 0
\(631\) 12.4815 + 21.6186i 0.496881 + 0.860623i 0.999994 0.00359801i \(-0.00114528\pi\)
−0.503113 + 0.864221i \(0.667812\pi\)
\(632\) 13.1677i 0.523784i
\(633\) 7.62815 4.40411i 0.303192 0.175048i
\(634\) 3.50535 6.07144i 0.139215 0.241128i
\(635\) 0 0
\(636\) 1.28098 0.0507944
\(637\) 0.994794 + 23.6468i 0.0394152 + 0.936920i
\(638\) 1.28098i 0.0507147i
\(639\) 3.65679 6.33374i 0.144660 0.250559i
\(640\) 0 0
\(641\) −11.6535 20.1844i −0.460284 0.797235i 0.538691 0.842503i \(-0.318919\pi\)
−0.998975 + 0.0452686i \(0.985586\pi\)
\(642\) 0.194039i 0.00765811i
\(643\) −39.3860 + 22.7395i −1.55323 + 0.896759i −0.555357 + 0.831612i \(0.687418\pi\)
−0.997876 + 0.0651470i \(0.979248\pi\)
\(644\) 4.83226 + 8.36973i 0.190418 + 0.329813i
\(645\) 0 0
\(646\) 0.145838 + 0.252599i 0.00573792 + 0.00993836i
\(647\) −5.55076 3.20473i −0.218223 0.125991i 0.386904 0.922120i \(-0.373544\pi\)
−0.605127 + 0.796129i \(0.706878\pi\)
\(648\) 1.14337 + 0.660123i 0.0449157 + 0.0259321i
\(649\) −1.51202 −0.0593519
\(650\) 0 0
\(651\) 6.58387 0.258042
\(652\) 19.9074 + 11.4935i 0.779632 + 0.450121i
\(653\) 1.28319 + 0.740848i 0.0502150 + 0.0289916i 0.524897 0.851166i \(-0.324104\pi\)
−0.474682 + 0.880157i \(0.657437\pi\)
\(654\) 2.61866 + 4.53565i 0.102398 + 0.177358i
\(655\) 0 0
\(656\) −7.01296 12.1468i −0.273810 0.474253i
\(657\) 6.94520 4.00982i 0.270958 0.156438i
\(658\) 1.12621i 0.0439041i
\(659\) −3.54461 6.13944i −0.138078 0.239159i 0.788691 0.614790i \(-0.210759\pi\)
−0.926769 + 0.375631i \(0.877426\pi\)
\(660\) 0 0
\(661\) −0.589214 + 1.02055i −0.0229178 + 0.0396947i −0.877257 0.480021i \(-0.840629\pi\)
0.854339 + 0.519716i \(0.173962\pi\)
\(662\) 1.82521i 0.0709387i
\(663\) −22.6139 + 14.3562i −0.878251 + 0.557548i
\(664\) −2.33547 −0.0906339
\(665\) 0 0
\(666\) 1.66012 2.87542i 0.0643285 0.111420i
\(667\) −37.3048 + 21.5379i −1.44445 + 0.833952i
\(668\) 2.99735i 0.115971i
\(669\) −5.01963 8.69426i −0.194070 0.336139i
\(670\) 0 0
\(671\) −2.85818 −0.110339
\(672\) 2.15466 1.24399i 0.0831177 0.0479880i
\(673\) 11.7412 + 6.77878i 0.452590 + 0.261303i 0.708923 0.705286i \(-0.249181\pi\)
−0.256334 + 0.966588i \(0.582515\pi\)
\(674\) −4.88782 + 8.46595i −0.188272 + 0.326096i
\(675\) 0 0
\(676\) −24.4117 + 2.05759i −0.938913 + 0.0791381i
\(677\) 9.53793i 0.366573i 0.983060 + 0.183286i \(0.0586735\pi\)
−0.983060 + 0.183286i \(0.941326\pi\)
\(678\) −1.56597 0.904114i −0.0601408 0.0347223i
\(679\) 3.26897 5.66202i 0.125451 0.217288i
\(680\) 0 0
\(681\) −1.21140 −0.0464210
\(682\) 1.99554 1.15212i 0.0764131 0.0441171i
\(683\) 38.5540 22.2592i 1.47523 0.851723i 0.475617 0.879652i \(-0.342225\pi\)
0.999610 + 0.0279296i \(0.00889141\pi\)
\(684\) 0.217689 0.00832353
\(685\) 0 0
\(686\) −1.52164 + 2.63556i −0.0580965 + 0.100626i
\(687\) 16.6658 + 9.62200i 0.635839 + 0.367102i
\(688\) 1.80823i 0.0689381i
\(689\) −1.31357 2.06915i −0.0500432 0.0788282i
\(690\) 0 0
\(691\) 2.64030 4.57313i 0.100442 0.173970i −0.811425 0.584457i \(-0.801308\pi\)
0.911867 + 0.410486i \(0.134641\pi\)
\(692\) 20.8071 + 12.0130i 0.790966 + 0.456664i
\(693\) −0.388604 + 0.224361i −0.0147618 + 0.00852275i
\(694\) 7.61192 0.288945
\(695\) 0 0
\(696\) 3.66012 + 6.33952i 0.138737 + 0.240299i
\(697\) 31.3832i 1.18872i
\(698\) −3.52436 + 2.03479i −0.133399 + 0.0770180i
\(699\) 11.9541 20.7051i 0.452144 0.783137i
\(700\) 0 0
\(701\) 20.1392 0.760646 0.380323 0.924854i \(-0.375813\pi\)
0.380323 + 0.924854i \(0.375813\pi\)
\(702\) −0.0515075 1.22436i −0.00194403 0.0462105i
\(703\) 1.12847i 0.0425612i
\(704\) −1.82157 + 3.15506i −0.0686531 + 0.118911i
\(705\) 0 0
\(706\) −2.89517 5.01459i −0.108961 0.188727i
\(707\) 6.17843i 0.232364i
\(708\) −3.63018 + 2.09589i −0.136431 + 0.0787682i
\(709\) 0.770294 + 1.33419i 0.0289290 + 0.0501065i 0.880127 0.474737i \(-0.157457\pi\)
−0.851198 + 0.524844i \(0.824124\pi\)
\(710\) 0 0
\(711\) −4.98685 8.63748i −0.187021 0.323931i
\(712\) −15.4865 8.94111i −0.580379 0.335082i
\(713\) 67.1043 + 38.7427i 2.51307 + 1.45092i
\(714\) −1.66680 −0.0623782
\(715\) 0 0
\(716\) −33.4728 −1.25094
\(717\) 16.1771 + 9.33988i 0.604146 + 0.348804i
\(718\) 10.3263 + 5.96187i 0.385373 + 0.222495i
\(719\) 18.5020 + 32.0464i 0.690009 + 1.19513i 0.971835 + 0.235664i \(0.0757266\pi\)
−0.281826 + 0.959466i \(0.590940\pi\)
\(720\) 0 0
\(721\) −1.48704 2.57563i −0.0553803 0.0959215i
\(722\) 5.58857 3.22656i 0.207985 0.120080i
\(723\) 6.11552i 0.227438i
\(724\) −6.62048 11.4670i −0.246048 0.426168i
\(725\) 0 0
\(726\) 1.79080 3.10176i 0.0664628 0.115117i
\(727\) 44.9015i 1.66530i −0.553797 0.832652i \(-0.686822\pi\)
0.553797 0.832652i \(-0.313178\pi\)
\(728\) −2.78497 1.45539i −0.103218 0.0539405i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 2.02297 3.50388i 0.0748221 0.129596i
\(732\) −6.86216 + 3.96187i −0.253633 + 0.146435i
\(733\) 4.94072i 0.182490i 0.995828 + 0.0912449i \(0.0290846\pi\)
−0.995828 + 0.0912449i \(0.970915\pi\)
\(734\) −3.41280 5.91114i −0.125969 0.218184i
\(735\) 0 0
\(736\) 29.2810 1.07931
\(737\) −4.49391 + 2.59456i −0.165535 + 0.0955718i
\(738\) −1.24341 0.717881i −0.0457704 0.0264256i
\(739\) 3.01963 5.23015i 0.111079 0.192394i −0.805127 0.593103i \(-0.797903\pi\)
0.916206 + 0.400709i \(0.131236\pi\)
\(740\) 0 0
\(741\) −0.223227 0.351628i −0.00820044 0.0129174i
\(742\) 0.152510i 0.00559882i
\(743\) −11.3093 6.52945i −0.414899 0.239542i 0.277993 0.960583i \(-0.410331\pi\)
−0.692893 + 0.721041i \(0.743664\pi\)
\(744\) 6.58387 11.4036i 0.241376 0.418076i
\(745\) 0 0
\(746\) 7.97998 0.292168
\(747\) 1.53197 0.884484i 0.0560519 0.0323616i
\(748\) 8.24158 4.75828i 0.301342 0.173980i
\(749\) −0.376871 −0.0137706
\(750\) 0 0
\(751\) −24.0118 + 41.5897i −0.876204 + 1.51763i −0.0207292 + 0.999785i \(0.506599\pi\)
−0.855475 + 0.517845i \(0.826735\pi\)
\(752\) 14.4335 + 8.33320i 0.526337 + 0.303881i
\(753\) 3.35951i 0.122427i
\(754\) 3.14697 6.02189i 0.114606 0.219304i
\(755\) 0 0
\(756\) −0.621996 + 1.07733i −0.0226218 + 0.0391820i
\(757\) 3.95275 + 2.28212i 0.143665 + 0.0829450i 0.570110 0.821569i \(-0.306901\pi\)
−0.426445 + 0.904514i \(0.640234\pi\)
\(758\) 6.22281 3.59274i 0.226023 0.130494i
\(759\) −5.28098 −0.191688
\(760\) 0 0
\(761\) −10.5446 18.2638i −0.382242 0.662062i 0.609141 0.793062i \(-0.291514\pi\)
−0.991382 + 0.131000i \(0.958181\pi\)
\(762\) 4.08519i 0.147991i
\(763\) −8.80933 + 5.08607i −0.318919 + 0.184128i
\(764\) 13.1481 22.7732i 0.475682 0.823905i
\(765\) 0 0
\(766\) −0.590926 −0.0213510
\(767\) 7.10797 + 3.71455i 0.256654 + 0.134124i
\(768\) 7.53793i 0.272002i
\(769\) 21.1666 36.6616i 0.763287 1.32205i −0.177860 0.984056i \(-0.556917\pi\)
0.941147 0.337996i \(-0.109749\pi\)
\(770\) 0 0
\(771\) −5.05442 8.75452i −0.182031 0.315286i
\(772\) 44.7552i 1.61078i
\(773\) −43.5122 + 25.1218i −1.56503 + 0.903568i −0.568291 + 0.822827i \(0.692395\pi\)
−0.996735 + 0.0807410i \(0.974271\pi\)
\(774\) 0.0925496 + 0.160301i 0.00332663 + 0.00576189i
\(775\) 0 0
\(776\) −6.53793 11.3240i −0.234698 0.406509i
\(777\) 5.58476 + 3.22436i 0.200352 + 0.115673i
\(778\) 7.84904 + 4.53165i 0.281402 + 0.162467i
\(779\) −0.487982 −0.0174838
\(780\) 0 0
\(781\) 4.97143 0.177892
\(782\) −16.9884 9.80823i −0.607502 0.350742i
\(783\) −4.80177 2.77230i −0.171601 0.0990740i
\(784\) −10.8974 18.8749i −0.389194 0.674104i
\(785\) 0 0
\(786\) −1.85303 3.20954i −0.0660953 0.114480i
\(787\) −9.16393 + 5.29080i −0.326659 + 0.188597i −0.654357 0.756186i \(-0.727061\pi\)
0.327698 + 0.944783i \(0.393727\pi\)
\(788\) 29.7903i 1.06124i
\(789\) 11.2592 + 19.5014i 0.400836 + 0.694269i
\(790\) 0 0
\(791\) 1.75601 3.04150i 0.0624365 0.108143i
\(792\) 0.897442i 0.0318892i
\(793\) 13.4363 + 7.02164i 0.477136 + 0.249346i
\(794\) 4.94338 0.175434
\(795\) 0 0
\(796\) 8.26249 14.3110i 0.292856 0.507242i
\(797\) −17.4488 + 10.0741i −0.618067 + 0.356841i −0.776116 0.630590i \(-0.782813\pi\)
0.158049 + 0.987431i \(0.449480\pi\)
\(798\) 0.0259173i 0.000917463i
\(799\) −18.6456 32.2952i −0.659636 1.14252i
\(800\) 0 0
\(801\) 13.5446 0.478575
\(802\) 2.46370 1.42242i 0.0869963 0.0502273i
\(803\) 4.72103 + 2.72569i 0.166601 + 0.0961874i
\(804\) −7.19291 + 12.4585i −0.253674 + 0.439377i
\(805\) 0 0
\(806\) −12.2114 + 0.513720i −0.430128 + 0.0180950i
\(807\) 8.49465i 0.299026i
\(808\) −10.7013 6.17843i −0.376472 0.217356i
\(809\) 6.45539 11.1811i 0.226960 0.393105i −0.729946 0.683505i \(-0.760455\pi\)
0.956906 + 0.290399i \(0.0937882\pi\)
\(810\) 0 0
\(811\) −15.8974 −0.558235 −0.279117 0.960257i \(-0.590042\pi\)
−0.279117 + 0.960257i \(0.590042\pi\)
\(812\) −5.97336 + 3.44872i −0.209624 + 0.121026i
\(813\) 8.11483 4.68510i 0.284600 0.164314i
\(814\) 2.25695 0.0791061
\(815\) 0 0
\(816\) 12.3332 21.3617i 0.431749 0.747810i
\(817\) 0.0544825 + 0.0314555i 0.00190610 + 0.00110049i
\(818\) 5.86447i 0.205046i
\(819\) 2.37800 0.100040i 0.0830942 0.00349568i
\(820\) 0 0
\(821\) 18.6142 32.2407i 0.649640 1.12521i −0.333569 0.942726i \(-0.608253\pi\)
0.983209 0.182483i \(-0.0584136\pi\)
\(822\) −0.997769 0.576062i −0.0348012 0.0200925i
\(823\) 4.24131 2.44872i 0.147843 0.0853571i −0.424254 0.905543i \(-0.639464\pi\)
0.572097 + 0.820186i \(0.306130\pi\)
\(824\) −5.94817 −0.207214
\(825\) 0 0
\(826\) 0.249529 + 0.432198i 0.00868224 + 0.0150381i
\(827\) 37.6334i 1.30864i 0.756217 + 0.654321i \(0.227046\pi\)
−0.756217 + 0.654321i \(0.772954\pi\)
\(828\) −12.6790 + 7.32025i −0.440627 + 0.254396i
\(829\) −24.4552 + 42.3576i −0.849364 + 1.47114i 0.0324123 + 0.999475i \(0.489681\pi\)
−0.881777 + 0.471667i \(0.843652\pi\)
\(830\) 0 0
\(831\) −0.719015 −0.0249424
\(832\) 16.3142 10.3569i 0.565592 0.359059i
\(833\) 48.7663i 1.68965i
\(834\) 2.51649 4.35868i 0.0871388 0.150929i
\(835\) 0 0
\(836\) 0.0739873 + 0.128150i 0.00255890 + 0.00443215i
\(837\) 9.97370i 0.344741i
\(838\) 3.78667 2.18623i 0.130808 0.0755222i
\(839\) 24.1392 + 41.8103i 0.833377 + 1.44345i 0.895345 + 0.445372i \(0.146929\pi\)
−0.0619688 + 0.998078i \(0.519738\pi\)
\(840\) 0 0
\(841\) −0.871332 1.50919i −0.0300459 0.0520411i
\(842\) 7.22951 + 4.17396i 0.249145 + 0.143844i
\(843\) −1.33767 0.772303i −0.0460718 0.0265995i
\(844\) 16.5990 0.571360
\(845\) 0 0
\(846\) 1.70606 0.0586554
\(847\) 6.02436 + 3.47817i 0.207000 + 0.119511i
\(848\) 1.95458 + 1.12847i 0.0671204 + 0.0387520i
\(849\) 9.05977 + 15.6920i 0.310930 + 0.538547i
\(850\) 0 0
\(851\) 37.9474 + 65.7268i 1.30082 + 2.25309i
\(852\) 11.9358 6.89116i 0.408915 0.236087i
\(853\) 14.4291i 0.494043i 0.969010 + 0.247021i \(0.0794518\pi\)
−0.969010 + 0.247021i \(0.920548\pi\)
\(854\) 0.471688 + 0.816987i 0.0161408 + 0.0279567i
\(855\) 0 0
\(856\) −0.376871 + 0.652759i −0.0128812 + 0.0223108i
\(857\) 3.64678i 0.124572i 0.998058 + 0.0622858i \(0.0198390\pi\)
−0.998058 + 0.0622858i \(0.980161\pi\)
\(858\) 0.703255 0.446454i 0.0240087 0.0152417i
\(859\) −21.7427 −0.741850 −0.370925 0.928663i \(-0.620959\pi\)
−0.370925 + 0.928663i \(0.620959\pi\)
\(860\) 0 0
\(861\) 1.39430 2.41500i 0.0475176 0.0823029i
\(862\) −7.29369 + 4.21102i −0.248424 + 0.143428i
\(863\) 17.0892i 0.581724i 0.956765 + 0.290862i \(0.0939420\pi\)
−0.956765 + 0.290862i \(0.906058\pi\)
\(864\) 1.88448 + 3.26402i 0.0641114 + 0.111044i
\(865\) 0 0
\(866\) 4.77829 0.162373
\(867\) −33.0747 + 19.0957i −1.12328 + 0.648524i
\(868\) 10.7449 + 6.20360i 0.364707 + 0.210564i
\(869\) 3.38983 5.87136i 0.114992 0.199172i
\(870\) 0 0
\(871\) 27.4998 1.15689i 0.931795 0.0391996i
\(872\) 20.3443i 0.688944i
\(873\) 8.57721 + 4.95206i 0.290295 + 0.167602i
\(874\) 0.152510 0.264155i 0.00515873 0.00893518i
\(875\) 0 0
\(876\) 15.1129 0.510616
\(877\) −4.20731 + 2.42909i −0.142071 + 0.0820246i −0.569351 0.822095i \(-0.692805\pi\)
0.427280 + 0.904119i \(0.359472\pi\)
\(878\) 6.13562 3.54240i 0.207067 0.119550i
\(879\) −30.5050 −1.02891
\(880\) 0 0
\(881\) 11.6601 20.1959i 0.392840 0.680418i −0.599983 0.800013i \(-0.704826\pi\)
0.992823 + 0.119595i \(0.0381595\pi\)
\(882\) −1.93213 1.11552i −0.0650582 0.0375614i
\(883\) 12.8934i 0.433898i 0.976183 + 0.216949i \(0.0696106\pi\)
−0.976183 + 0.216949i \(0.930389\pi\)
\(884\) −50.4331 + 2.12167i −1.69625 + 0.0713593i
\(885\) 0 0
\(886\) −1.94224 + 3.36406i −0.0652509 + 0.113018i
\(887\) −26.7842 15.4639i −0.899326 0.519226i −0.0223448 0.999750i \(-0.507113\pi\)
−0.876982 + 0.480524i \(0.840447\pi\)
\(888\) 11.1695 6.44872i 0.374824 0.216405i
\(889\) 7.93444 0.266112
\(890\) 0 0
\(891\) −0.339877 0.588684i −0.0113863 0.0197217i
\(892\) 18.9188i 0.633449i
\(893\) 0.502164 0.289925i 0.0168043 0.00970196i
\(894\) −2.90411 + 5.03007i −0.0971281 + 0.168231i
\(895\) 0 0
\(896\) 6.17843 0.206407
\(897\) 24.8258 + 12.9737i 0.828911 + 0.433179i
\(898\) 8.80558i 0.293846i
\(899\) −27.6501 + 47.8914i −0.922183 + 1.59727i
\(900\) 0 0
\(901\) −2.52498 4.37339i −0.0841192 0.145699i
\(902\) 0.975965i 0.0324961i
\(903\) −0.311343 + 0.179754i −0.0103608 + 0.00598183i
\(904\) −3.51202 6.08299i −0.116808 0.202317i
\(905\) 0 0
\(906\) −2.21140 3.83026i −0.0734689 0.127252i
\(907\) 14.6881 + 8.48018i 0.487710 + 0.281580i 0.723624 0.690194i \(-0.242475\pi\)
−0.235914 + 0.971774i \(0.575808\pi\)
\(908\) −1.97702 1.14143i −0.0656097 0.0378798i
\(909\) 9.35951 0.310435
\(910\) 0 0
\(911\) 37.7297 1.25004 0.625020 0.780608i \(-0.285091\pi\)
0.625020 + 0.780608i \(0.285091\pi\)
\(912\) 0.332158 + 0.191771i 0.0109988 + 0.00635018i
\(913\) 1.04136 + 0.601231i 0.0344641 + 0.0198978i
\(914\) −1.00334 1.73783i −0.0331874 0.0574823i
\(915\) 0 0
\(916\) 18.1325 + 31.4064i 0.599114 + 1.03770i
\(917\) 6.23370 3.59903i 0.205855 0.118850i
\(918\) 2.52498i 0.0833366i
\(919\) 20.0814 + 34.7820i 0.662425 + 1.14735i 0.979977 + 0.199112i \(0.0638058\pi\)
−0.317552 + 0.948241i \(0.602861\pi\)
\(920\) 0 0
\(921\) −2.38782 + 4.13583i −0.0786813 + 0.136280i
\(922\) 5.26537i 0.173406i
\(923\) −23.3706 12.2132i −0.769253 0.402003i
\(924\) −0.845608 −0.0278185
\(925\) 0 0
\(926\) 2.96407 5.13393i 0.0974055 0.168711i
\(927\) 3.90174 2.25267i 0.128150 0.0739875i
\(928\) 20.8974i 0.685992i
\(929\) 11.8845 + 20.5845i 0.389917 + 0.675357i 0.992438 0.122747i \(-0.0391703\pi\)
−0.602521 + 0.798103i \(0.705837\pi\)
\(930\) 0 0
\(931\) −0.758276 −0.0248515
\(932\) 39.0183 22.5272i 1.27809 0.737904i
\(933\) −26.4841 15.2906i −0.867051 0.500592i
\(934\) 3.48018 6.02784i 0.113875 0.197237i
\(935\) 0 0
\(936\) 2.20473 4.21886i 0.0720639 0.137898i
\(937\) 7.43803i 0.242990i −0.992592 0.121495i \(-0.961231\pi\)
0.992592 0.121495i \(-0.0387688\pi\)
\(938\) 1.48327 + 0.856364i 0.0484304 + 0.0279613i
\(939\) 13.3615 23.1428i 0.436037 0.755238i
\(940\) 0 0
\(941\) −19.3528 −0.630884 −0.315442 0.948945i \(-0.602153\pi\)
−0.315442 + 0.948945i \(0.602153\pi\)
\(942\) −0.228303 + 0.131811i −0.00743852 + 0.00429463i
\(943\) 28.4220 16.4095i 0.925548 0.534366i
\(944\) −7.38542 −0.240375
\(945\) 0 0
\(946\) −0.0629110 + 0.108965i −0.00204541 + 0.00354276i
\(947\) −12.0525 6.95854i −0.391655 0.226122i 0.291222 0.956655i \(-0.405938\pi\)
−0.682877 + 0.730533i \(0.739271\pi\)
\(948\) 18.7953i 0.610442i
\(949\) −15.4973 24.4115i −0.503065 0.792430i
\(950\) 0 0
\(951\) −10.3136 + 17.8636i −0.334441 + 0.579268i
\(952\) −5.60720 3.23732i −0.181730 0.104922i
\(953\) 9.20338 5.31357i 0.298127 0.172124i −0.343474 0.939162i \(-0.611604\pi\)
0.641601 + 0.767039i \(0.278271\pi\)
\(954\) 0.231033 0.00747996
\(955\) 0 0
\(956\) 17.6008 + 30.4856i 0.569252 + 0.985973i
\(957\) 3.76897i 0.121833i
\(958\) −12.0653 + 6.96589i −0.389811 + 0.225058i
\(959\) 1.11885 1.93791i 0.0361296 0.0625783i
\(960\) 0 0
\(961\) 68.4746 2.20886
\(962\) −10.6099 5.54461i −0.342077 0.178765i
\(963\) 0.570909i 0.0183973i
\(964\) −5.76230 + 9.98059i −0.185591 + 0.321453i
\(965\) 0 0
\(966\) 0.871525 + 1.50953i 0.0280409 + 0.0485682i
\(967\) 51.6771i 1.66182i 0.556404 + 0.830912i \(0.312181\pi\)
−0.556404 + 0.830912i \(0.687819\pi\)
\(968\) 12.0487 6.95633i 0.387261 0.223585i
\(969\) −0.429091 0.743207i −0.0137844 0.0238752i
\(970\) 0 0
\(971\) 21.4487 + 37.1503i 0.688322 + 1.19221i 0.972380 + 0.233402i \(0.0749858\pi\)
−0.284058 + 0.958807i \(0.591681\pi\)
\(972\) −1.63201 0.942242i −0.0523468 0.0302224i
\(973\) 8.46562 + 4.88763i 0.271395 + 0.156690i
\(974\) 8.17843 0.262054
\(975\) 0 0
\(976\) −13.9607 −0.446872
\(977\) −15.7314 9.08254i −0.503293 0.290576i 0.226780 0.973946i \(-0.427180\pi\)
−0.730072 + 0.683370i \(0.760514\pi\)
\(978\) 3.59040 + 2.07292i 0.114808 + 0.0662846i
\(979\) 4.60350 + 7.97349i 0.147128 + 0.254834i
\(980\) 0 0
\(981\) −7.70473 13.3450i −0.245993 0.426073i
\(982\) −10.8238 + 6.24914i −0.345402 + 0.199418i
\(983\) 10.8582i 0.346322i 0.984894 + 0.173161i \(0.0553981\pi\)
−0.984894 + 0.173161i \(0.944602\pi\)
\(984\) −2.78860 4.82999i −0.0888973 0.153975i
\(985\) 0 0
\(986\) 7.00000 12.1244i 0.222925 0.386118i
\(987\) 3.31357i 0.105472i
\(988\) −0.0329902 0.784194i −0.00104956 0.0249485i
\(989\) −4.23103 −0.134539
\(990\) 0 0
\(991\) 11.1862 19.3751i 0.355342 0.615471i −0.631834 0.775104i \(-0.717698\pi\)
0.987177 + 0.159633i \(0.0510309\pi\)
\(992\) 32.5544 18.7953i 1.03360 0.596750i
\(993\) 5.37020i 0.170418i
\(994\) −0.820439 1.42104i −0.0260227 0.0450727i
\(995\) 0 0
\(996\) 3.33359 0.105629
\(997\) −20.9901 + 12.1187i −0.664764 + 0.383802i −0.794090 0.607800i \(-0.792052\pi\)
0.129326 + 0.991602i \(0.458719\pi\)
\(998\) −10.2493 5.91746i −0.324437 0.187314i
\(999\) −4.88448 + 8.46017i −0.154538 + 0.267668i
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 975.2.bb.k.724.4 12
5.2 odd 4 975.2.i.l.451.2 6
5.3 odd 4 195.2.i.d.61.2 yes 6
5.4 even 2 inner 975.2.bb.k.724.3 12
13.3 even 3 inner 975.2.bb.k.874.3 12
15.8 even 4 585.2.j.f.451.2 6
65.3 odd 12 195.2.i.d.16.2 6
65.29 even 6 inner 975.2.bb.k.874.4 12
65.42 odd 12 975.2.i.l.601.2 6
65.43 odd 12 2535.2.a.ba.1.2 3
65.48 odd 12 2535.2.a.bb.1.2 3
195.68 even 12 585.2.j.f.406.2 6
195.113 even 12 7605.2.a.bv.1.2 3
195.173 even 12 7605.2.a.bw.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.i.d.16.2 6 65.3 odd 12
195.2.i.d.61.2 yes 6 5.3 odd 4
585.2.j.f.406.2 6 195.68 even 12
585.2.j.f.451.2 6 15.8 even 4
975.2.i.l.451.2 6 5.2 odd 4
975.2.i.l.601.2 6 65.42 odd 12
975.2.bb.k.724.3 12 5.4 even 2 inner
975.2.bb.k.724.4 12 1.1 even 1 trivial
975.2.bb.k.874.3 12 13.3 even 3 inner
975.2.bb.k.874.4 12 65.29 even 6 inner
2535.2.a.ba.1.2 3 65.43 odd 12
2535.2.a.bb.1.2 3 65.48 odd 12
7605.2.a.bv.1.2 3 195.113 even 12
7605.2.a.bw.1.2 3 195.173 even 12