Properties

Label 105.3.v.a.88.8
Level $105$
Weight $3$
Character 105.88
Analytic conductor $2.861$
Analytic rank $0$
Dimension $64$
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] = [105,3,Mod(37,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.37");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.v (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: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 88.8
Character \(\chi\) \(=\) 105.88
Dual form 105.3.v.a.37.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.435396 - 0.116664i) q^{2} +(1.67303 - 0.448288i) q^{3} +(-3.28814 - 1.89841i) q^{4} +(3.62365 + 3.44517i) q^{5} -0.780730 q^{6} +(6.87993 - 1.29096i) q^{7} +(2.48509 + 2.48509i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(-0.435396 - 0.116664i) q^{2} +(1.67303 - 0.448288i) q^{3} +(-3.28814 - 1.89841i) q^{4} +(3.62365 + 3.44517i) q^{5} -0.780730 q^{6} +(6.87993 - 1.29096i) q^{7} +(2.48509 + 2.48509i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-1.17579 - 1.92276i) q^{10} +(10.0112 - 17.3398i) q^{11} +(-6.35220 - 1.70207i) q^{12} +(-2.67217 - 2.67217i) q^{13} +(-3.14610 - 0.240560i) q^{14} +(7.60691 + 4.13944i) q^{15} +(6.80156 + 11.7807i) q^{16} +(3.22785 + 12.0465i) q^{17} +(-1.30619 + 0.349992i) q^{18} +(-18.7697 + 10.8367i) q^{19} +(-5.37472 - 18.2074i) q^{20} +(10.9316 - 5.24401i) q^{21} +(-6.38175 + 6.38175i) q^{22} +(7.07907 - 26.4195i) q^{23} +(5.27168 + 3.04361i) q^{24} +(1.26162 + 24.9681i) q^{25} +(0.851706 + 1.47520i) q^{26} +(3.67423 - 3.67423i) q^{27} +(-25.0730 - 8.81606i) q^{28} +29.0697i q^{29} +(-2.82909 - 2.68975i) q^{30} +(-22.1260 + 38.3234i) q^{31} +(-5.22542 - 19.5015i) q^{32} +(8.97576 - 33.4980i) q^{33} -5.62157i q^{34} +(29.3780 + 19.0245i) q^{35} -11.3905 q^{36} +(-59.0392 - 15.8195i) q^{37} +(9.43648 - 2.52850i) q^{38} +(-5.66854 - 3.27273i) q^{39} +(0.443533 + 17.5667i) q^{40} -19.8782 q^{41} +(-5.37137 + 1.00789i) q^{42} +(-14.0418 - 14.0418i) q^{43} +(-65.8363 + 38.0106i) q^{44} +(14.5823 + 3.51534i) q^{45} +(-6.16439 + 10.6770i) q^{46} +(-10.8275 - 2.90122i) q^{47} +(16.6604 + 16.6604i) q^{48} +(45.6668 - 17.7635i) q^{49} +(2.36358 - 11.0182i) q^{50} +(10.8006 + 18.7072i) q^{51} +(3.71361 + 13.8594i) q^{52} +(-31.2612 + 8.37642i) q^{53} +(-2.02840 + 1.17109i) q^{54} +(96.0156 - 28.3433i) q^{55} +(20.3054 + 13.8891i) q^{56} +(-26.5443 + 26.5443i) q^{57} +(3.39139 - 12.6568i) q^{58} +(49.6246 + 28.6507i) q^{59} +(-17.1542 - 28.0521i) q^{60} +(-9.82028 - 17.0092i) q^{61} +(14.1045 - 14.1045i) q^{62} +(15.9381 - 13.6739i) q^{63} -45.3120i q^{64} +(-0.476922 - 18.8891i) q^{65} +(-7.81601 + 13.5377i) q^{66} +(-3.54467 - 13.2289i) q^{67} +(12.2556 - 45.7384i) q^{68} -47.3741i q^{69} +(-10.5716 - 11.7105i) q^{70} +71.1638 q^{71} +(10.1841 + 2.72882i) q^{72} +(90.0261 - 24.1224i) q^{73} +(23.8598 + 13.7755i) q^{74} +(13.3037 + 41.2070i) q^{75} +82.2898 q^{76} +(46.4910 - 132.221i) q^{77} +(2.08625 + 2.08625i) q^{78} +(-112.260 + 64.8134i) q^{79} +(-15.9399 + 66.1214i) q^{80} +(4.50000 - 7.79423i) q^{81} +(8.65488 + 2.31907i) q^{82} +(-20.5661 - 20.5661i) q^{83} +(-45.9000 - 3.50965i) q^{84} +(-29.8056 + 54.7727i) q^{85} +(4.47558 + 7.75193i) q^{86} +(13.0316 + 48.6346i) q^{87} +(67.9698 - 18.2125i) q^{88} +(-29.0452 + 16.7692i) q^{89} +(-5.93894 - 3.23179i) q^{90} +(-21.8340 - 14.9347i) q^{91} +(-73.4319 + 73.4319i) q^{92} +(-19.8376 + 74.0351i) q^{93} +(4.37578 + 2.52635i) q^{94} +(-105.349 - 25.3964i) q^{95} +(-17.4846 - 30.2842i) q^{96} +(-36.1403 + 36.1403i) q^{97} +(-21.9555 + 2.40646i) q^{98} -60.0670i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 4 q^{5} - 4 q^{7} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 4 q^{5} - 4 q^{7} + 24 q^{8} - 16 q^{10} + 16 q^{11} - 48 q^{15} + 80 q^{16} + 56 q^{17} + 24 q^{21} - 96 q^{22} + 72 q^{23} - 4 q^{25} - 288 q^{26} - 380 q^{28} - 48 q^{30} - 136 q^{31} - 48 q^{32} - 72 q^{33} + 76 q^{35} + 384 q^{36} - 28 q^{37} - 68 q^{38} + 164 q^{40} + 128 q^{41} - 12 q^{42} + 344 q^{43} + 240 q^{46} + 412 q^{47} - 288 q^{48} - 72 q^{50} - 24 q^{51} + 388 q^{52} - 40 q^{53} - 8 q^{55} - 864 q^{56} - 192 q^{57} + 56 q^{58} - 180 q^{60} - 216 q^{61} - 912 q^{62} - 84 q^{63} + 20 q^{65} - 72 q^{66} - 368 q^{67} - 492 q^{68} + 416 q^{70} + 784 q^{71} + 36 q^{72} - 316 q^{73} + 96 q^{75} - 32 q^{76} + 844 q^{77} + 624 q^{78} + 908 q^{80} + 288 q^{81} + 556 q^{82} + 1408 q^{83} - 536 q^{85} + 1024 q^{86} + 108 q^{87} + 372 q^{88} + 216 q^{90} - 1064 q^{91} - 1704 q^{92} + 144 q^{93} + 260 q^{95} + 352 q^{97} + 272 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.435396 0.116664i −0.217698 0.0583319i 0.148322 0.988939i \(-0.452613\pi\)
−0.366019 + 0.930607i \(0.619280\pi\)
\(3\) 1.67303 0.448288i 0.557678 0.149429i
\(4\) −3.28814 1.89841i −0.822036 0.474603i
\(5\) 3.62365 + 3.44517i 0.724729 + 0.689034i
\(6\) −0.780730 −0.130122
\(7\) 6.87993 1.29096i 0.982847 0.184423i
\(8\) 2.48509 + 2.48509i 0.310637 + 0.310637i
\(9\) 2.59808 1.50000i 0.288675 0.166667i
\(10\) −1.17579 1.92276i −0.117579 0.192276i
\(11\) 10.0112 17.3398i 0.910106 1.57635i 0.0961926 0.995363i \(-0.469334\pi\)
0.813913 0.580987i \(-0.197333\pi\)
\(12\) −6.35220 1.70207i −0.529350 0.141839i
\(13\) −2.67217 2.67217i −0.205552 0.205552i 0.596822 0.802374i \(-0.296430\pi\)
−0.802374 + 0.596822i \(0.796430\pi\)
\(14\) −3.14610 0.240560i −0.224721 0.0171828i
\(15\) 7.60691 + 4.13944i 0.507127 + 0.275963i
\(16\) 6.80156 + 11.7807i 0.425098 + 0.736291i
\(17\) 3.22785 + 12.0465i 0.189874 + 0.708618i 0.993535 + 0.113530i \(0.0362159\pi\)
−0.803661 + 0.595087i \(0.797117\pi\)
\(18\) −1.30619 + 0.349992i −0.0725659 + 0.0194440i
\(19\) −18.7697 + 10.8367i −0.987878 + 0.570352i −0.904639 0.426178i \(-0.859860\pi\)
−0.0832385 + 0.996530i \(0.526526\pi\)
\(20\) −5.37472 18.2074i −0.268736 0.910369i
\(21\) 10.9316 5.24401i 0.520553 0.249715i
\(22\) −6.38175 + 6.38175i −0.290080 + 0.290080i
\(23\) 7.07907 26.4195i 0.307786 1.14867i −0.622735 0.782433i \(-0.713979\pi\)
0.930521 0.366239i \(-0.119355\pi\)
\(24\) 5.27168 + 3.04361i 0.219653 + 0.126817i
\(25\) 1.26162 + 24.9681i 0.0504649 + 0.998726i
\(26\) 0.851706 + 1.47520i 0.0327579 + 0.0567384i
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) −25.0730 8.81606i −0.895463 0.314859i
\(29\) 29.0697i 1.00240i 0.865330 + 0.501202i \(0.167109\pi\)
−0.865330 + 0.501202i \(0.832891\pi\)
\(30\) −2.82909 2.68975i −0.0943030 0.0896582i
\(31\) −22.1260 + 38.3234i −0.713742 + 1.23624i 0.249701 + 0.968323i \(0.419668\pi\)
−0.963443 + 0.267915i \(0.913666\pi\)
\(32\) −5.22542 19.5015i −0.163294 0.609423i
\(33\) 8.97576 33.4980i 0.271993 1.01509i
\(34\) 5.62157i 0.165340i
\(35\) 29.3780 + 19.0245i 0.839372 + 0.543558i
\(36\) −11.3905 −0.316402
\(37\) −59.0392 15.8195i −1.59565 0.427554i −0.651928 0.758281i \(-0.726040\pi\)
−0.943727 + 0.330727i \(0.892706\pi\)
\(38\) 9.43648 2.52850i 0.248329 0.0665394i
\(39\) −5.66854 3.27273i −0.145347 0.0839162i
\(40\) 0.443533 + 17.5667i 0.0110883 + 0.439167i
\(41\) −19.8782 −0.484834 −0.242417 0.970172i \(-0.577940\pi\)
−0.242417 + 0.970172i \(0.577940\pi\)
\(42\) −5.37137 + 1.00789i −0.127890 + 0.0239975i
\(43\) −14.0418 14.0418i −0.326555 0.326555i 0.524720 0.851275i \(-0.324170\pi\)
−0.851275 + 0.524720i \(0.824170\pi\)
\(44\) −65.8363 + 38.0106i −1.49628 + 0.863877i
\(45\) 14.5823 + 3.51534i 0.324050 + 0.0781187i
\(46\) −6.16439 + 10.6770i −0.134009 + 0.232110i
\(47\) −10.8275 2.90122i −0.230372 0.0617280i 0.141786 0.989897i \(-0.454715\pi\)
−0.372158 + 0.928169i \(0.621382\pi\)
\(48\) 16.6604 + 16.6604i 0.347091 + 0.347091i
\(49\) 45.6668 17.7635i 0.931976 0.362520i
\(50\) 2.36358 11.0182i 0.0472715 0.220364i
\(51\) 10.8006 + 18.7072i 0.211776 + 0.366808i
\(52\) 3.71361 + 13.8594i 0.0714155 + 0.266526i
\(53\) −31.2612 + 8.37642i −0.589834 + 0.158046i −0.541377 0.840780i \(-0.682097\pi\)
−0.0484568 + 0.998825i \(0.515430\pi\)
\(54\) −2.02840 + 1.17109i −0.0375629 + 0.0216869i
\(55\) 96.0156 28.3433i 1.74574 0.515333i
\(56\) 20.3054 + 13.8891i 0.362597 + 0.248020i
\(57\) −26.5443 + 26.5443i −0.465690 + 0.465690i
\(58\) 3.39139 12.6568i 0.0584722 0.218221i
\(59\) 49.6246 + 28.6507i 0.841094 + 0.485606i 0.857636 0.514257i \(-0.171932\pi\)
−0.0165419 + 0.999863i \(0.505266\pi\)
\(60\) −17.1542 28.0521i −0.285904 0.467535i
\(61\) −9.82028 17.0092i −0.160988 0.278840i 0.774235 0.632898i \(-0.218135\pi\)
−0.935223 + 0.354058i \(0.884801\pi\)
\(62\) 14.1045 14.1045i 0.227492 0.227492i
\(63\) 15.9381 13.6739i 0.252986 0.217046i
\(64\) 45.3120i 0.708000i
\(65\) −0.476922 18.8891i −0.00733727 0.290602i
\(66\) −7.81601 + 13.5377i −0.118424 + 0.205117i
\(67\) −3.54467 13.2289i −0.0529055 0.197446i 0.934415 0.356187i \(-0.115923\pi\)
−0.987320 + 0.158741i \(0.949257\pi\)
\(68\) 12.2556 45.7384i 0.180229 0.672624i
\(69\) 47.3741i 0.686581i
\(70\) −10.5716 11.7105i −0.151023 0.167294i
\(71\) 71.1638 1.00231 0.501153 0.865358i \(-0.332909\pi\)
0.501153 + 0.865358i \(0.332909\pi\)
\(72\) 10.1841 + 2.72882i 0.141446 + 0.0379003i
\(73\) 90.0261 24.1224i 1.23323 0.330444i 0.417396 0.908725i \(-0.362943\pi\)
0.815838 + 0.578281i \(0.196276\pi\)
\(74\) 23.8598 + 13.7755i 0.322430 + 0.186155i
\(75\) 13.3037 + 41.2070i 0.177382 + 0.549426i
\(76\) 82.2898 1.08276
\(77\) 46.4910 132.221i 0.603779 1.71715i
\(78\) 2.08625 + 2.08625i 0.0267467 + 0.0267467i
\(79\) −112.260 + 64.8134i −1.42101 + 0.820423i −0.996386 0.0849448i \(-0.972929\pi\)
−0.424629 + 0.905368i \(0.639595\pi\)
\(80\) −15.9399 + 66.1214i −0.199248 + 0.826518i
\(81\) 4.50000 7.79423i 0.0555556 0.0962250i
\(82\) 8.65488 + 2.31907i 0.105547 + 0.0282813i
\(83\) −20.5661 20.5661i −0.247785 0.247785i 0.572276 0.820061i \(-0.306061\pi\)
−0.820061 + 0.572276i \(0.806061\pi\)
\(84\) −45.9000 3.50965i −0.546429 0.0417815i
\(85\) −29.8056 + 54.7727i −0.350655 + 0.644385i
\(86\) 4.47558 + 7.75193i 0.0520416 + 0.0901388i
\(87\) 13.0316 + 48.6346i 0.149788 + 0.559018i
\(88\) 67.9698 18.2125i 0.772384 0.206960i
\(89\) −29.0452 + 16.7692i −0.326350 + 0.188418i −0.654219 0.756305i \(-0.727003\pi\)
0.327869 + 0.944723i \(0.393669\pi\)
\(90\) −5.93894 3.23179i −0.0659882 0.0359088i
\(91\) −21.8340 14.9347i −0.239935 0.164117i
\(92\) −73.4319 + 73.4319i −0.798173 + 0.798173i
\(93\) −19.8376 + 74.0351i −0.213308 + 0.796076i
\(94\) 4.37578 + 2.52635i 0.0465508 + 0.0268761i
\(95\) −105.349 25.3964i −1.10894 0.267331i
\(96\) −17.4846 30.2842i −0.182131 0.315461i
\(97\) −36.1403 + 36.1403i −0.372580 + 0.372580i −0.868416 0.495836i \(-0.834862\pi\)
0.495836 + 0.868416i \(0.334862\pi\)
\(98\) −21.9555 + 2.40646i −0.224036 + 0.0245557i
\(99\) 60.0670i 0.606737i
\(100\) 43.2514 84.4939i 0.432514 0.844939i
\(101\) −40.1000 + 69.4552i −0.397030 + 0.687676i −0.993358 0.115065i \(-0.963292\pi\)
0.596328 + 0.802741i \(0.296626\pi\)
\(102\) −2.52008 9.40506i −0.0247067 0.0922065i
\(103\) −8.04297 + 30.0168i −0.0780871 + 0.291425i −0.993916 0.110145i \(-0.964869\pi\)
0.915828 + 0.401570i \(0.131535\pi\)
\(104\) 13.2812i 0.127704i
\(105\) 57.6788 + 18.6588i 0.549322 + 0.177703i
\(106\) 14.5882 0.137625
\(107\) 101.272 + 27.1358i 0.946469 + 0.253606i 0.698863 0.715255i \(-0.253689\pi\)
0.247606 + 0.968861i \(0.420356\pi\)
\(108\) −19.0566 + 5.10620i −0.176450 + 0.0472797i
\(109\) 11.9781 + 6.91555i 0.109891 + 0.0634454i 0.553938 0.832558i \(-0.313124\pi\)
−0.444047 + 0.896003i \(0.646458\pi\)
\(110\) −45.1114 + 1.13900i −0.410104 + 0.0103545i
\(111\) −105.866 −0.953750
\(112\) 62.0026 + 72.2695i 0.553595 + 0.645263i
\(113\) −67.9147 67.9147i −0.601015 0.601015i 0.339567 0.940582i \(-0.389720\pi\)
−0.940582 + 0.339567i \(0.889720\pi\)
\(114\) 14.6540 8.46052i 0.128544 0.0742151i
\(115\) 116.672 71.3461i 1.01453 0.620401i
\(116\) 55.1862 95.5854i 0.475743 0.824012i
\(117\) −10.9508 2.93425i −0.0935963 0.0250791i
\(118\) −18.2638 18.2638i −0.154778 0.154778i
\(119\) 37.7590 + 78.7120i 0.317302 + 0.661446i
\(120\) 8.61697 + 29.1908i 0.0718080 + 0.243256i
\(121\) −139.947 242.395i −1.15658 2.00326i
\(122\) 2.29134 + 8.55141i 0.0187815 + 0.0700936i
\(123\) −33.2569 + 8.91115i −0.270381 + 0.0724484i
\(124\) 145.507 84.0085i 1.17344 0.677488i
\(125\) −81.4478 + 94.8222i −0.651582 + 0.758578i
\(126\) −8.53464 + 4.09416i −0.0677353 + 0.0324933i
\(127\) −1.81108 + 1.81108i −0.0142604 + 0.0142604i −0.714201 0.699941i \(-0.753210\pi\)
0.699941 + 0.714201i \(0.253210\pi\)
\(128\) −26.1880 + 97.7348i −0.204593 + 0.763553i
\(129\) −29.7872 17.1977i −0.230909 0.133315i
\(130\) −1.99603 + 8.27987i −0.0153540 + 0.0636913i
\(131\) 66.0246 + 114.358i 0.504005 + 0.872961i 0.999989 + 0.00463021i \(0.00147385\pi\)
−0.495985 + 0.868331i \(0.665193\pi\)
\(132\) −93.1065 + 93.1065i −0.705353 + 0.705353i
\(133\) −115.144 + 98.7865i −0.865747 + 0.742756i
\(134\) 6.17334i 0.0460697i
\(135\) 25.9725 0.655768i 0.192389 0.00485754i
\(136\) −21.9152 + 37.9582i −0.161141 + 0.279104i
\(137\) 11.7173 + 43.7294i 0.0855275 + 0.319193i 0.995414 0.0956653i \(-0.0304979\pi\)
−0.909886 + 0.414858i \(0.863831\pi\)
\(138\) −5.52684 + 20.6265i −0.0400496 + 0.149467i
\(139\) 104.614i 0.752620i −0.926494 0.376310i \(-0.877193\pi\)
0.926494 0.376310i \(-0.122807\pi\)
\(140\) −60.4827 118.327i −0.432020 0.845192i
\(141\) −19.4153 −0.137697
\(142\) −30.9844 8.30224i −0.218200 0.0584665i
\(143\) −73.0866 + 19.5835i −0.511095 + 0.136948i
\(144\) 35.3420 + 20.4047i 0.245430 + 0.141699i
\(145\) −100.150 + 105.338i −0.690690 + 0.726471i
\(146\) −42.0112 −0.287748
\(147\) 68.4390 50.1907i 0.465571 0.341434i
\(148\) 164.097 + 164.097i 1.10877 + 1.10877i
\(149\) 39.0472 22.5439i 0.262061 0.151301i −0.363213 0.931706i \(-0.618320\pi\)
0.625275 + 0.780405i \(0.284987\pi\)
\(150\) −0.984987 19.4934i −0.00656658 0.129956i
\(151\) −84.2120 + 145.859i −0.557695 + 0.965956i 0.439993 + 0.898001i \(0.354981\pi\)
−0.997688 + 0.0679552i \(0.978353\pi\)
\(152\) −73.5746 19.7142i −0.484043 0.129699i
\(153\) 26.4560 + 26.4560i 0.172915 + 0.172915i
\(154\) −35.6674 + 52.1446i −0.231606 + 0.338601i
\(155\) −212.207 + 62.6425i −1.36908 + 0.404145i
\(156\) 12.4260 + 21.5224i 0.0796537 + 0.137964i
\(157\) −61.9280 231.119i −0.394446 1.47209i −0.822722 0.568444i \(-0.807545\pi\)
0.428276 0.903648i \(-0.359121\pi\)
\(158\) 56.4389 15.1228i 0.357208 0.0957137i
\(159\) −48.5460 + 28.0280i −0.305321 + 0.176277i
\(160\) 48.2510 88.6692i 0.301569 0.554182i
\(161\) 14.5970 190.903i 0.0906645 1.18573i
\(162\) −2.86858 + 2.86858i −0.0177073 + 0.0177073i
\(163\) −7.78599 + 29.0577i −0.0477668 + 0.178268i −0.985688 0.168581i \(-0.946082\pi\)
0.937921 + 0.346849i \(0.112748\pi\)
\(164\) 65.3624 + 37.7370i 0.398551 + 0.230103i
\(165\) 147.931 90.4619i 0.896553 0.548254i
\(166\) 6.55508 + 11.3537i 0.0394884 + 0.0683959i
\(167\) 205.571 205.571i 1.23096 1.23096i 0.267371 0.963594i \(-0.413845\pi\)
0.963594 0.267371i \(-0.0861549\pi\)
\(168\) 40.1980 + 14.1342i 0.239274 + 0.0841324i
\(169\) 154.719i 0.915497i
\(170\) 19.3672 20.3706i 0.113925 0.119827i
\(171\) −32.5100 + 56.3090i −0.190117 + 0.329293i
\(172\) 19.5144 + 72.8288i 0.113456 + 0.423423i
\(173\) 12.9989 48.5124i 0.0751379 0.280418i −0.918127 0.396287i \(-0.870299\pi\)
0.993265 + 0.115869i \(0.0369652\pi\)
\(174\) 22.6956i 0.130434i
\(175\) 40.9128 + 170.150i 0.233788 + 0.972288i
\(176\) 272.366 1.54754
\(177\) 95.8673 + 25.6876i 0.541623 + 0.145127i
\(178\) 14.6025 3.91273i 0.0820365 0.0219816i
\(179\) 100.688 + 58.1320i 0.562500 + 0.324760i 0.754148 0.656704i \(-0.228050\pi\)
−0.191648 + 0.981464i \(0.561383\pi\)
\(180\) −41.2750 39.2421i −0.229306 0.218011i
\(181\) 43.1119 0.238187 0.119094 0.992883i \(-0.462001\pi\)
0.119094 + 0.992883i \(0.462001\pi\)
\(182\) 7.76411 + 9.04974i 0.0426599 + 0.0497239i
\(183\) −24.0547 24.0547i −0.131446 0.131446i
\(184\) 83.2470 48.0627i 0.452429 0.261210i
\(185\) −159.436 260.724i −0.861818 1.40932i
\(186\) 17.2744 29.9202i 0.0928733 0.160861i
\(187\) 241.199 + 64.6291i 1.28983 + 0.345610i
\(188\) 30.0946 + 30.0946i 0.160078 + 0.160078i
\(189\) 20.5352 30.0218i 0.108652 0.158845i
\(190\) 42.9056 + 23.3479i 0.225819 + 0.122884i
\(191\) 65.1517 + 112.846i 0.341109 + 0.590817i 0.984639 0.174603i \(-0.0558643\pi\)
−0.643530 + 0.765421i \(0.722531\pi\)
\(192\) −20.3128 75.8084i −0.105796 0.394836i
\(193\) −327.789 + 87.8309i −1.69839 + 0.455082i −0.972533 0.232763i \(-0.925223\pi\)
−0.725857 + 0.687846i \(0.758557\pi\)
\(194\) 19.9516 11.5191i 0.102843 0.0593766i
\(195\) −9.26566 31.3883i −0.0475162 0.160966i
\(196\) −183.881 28.2856i −0.938170 0.144314i
\(197\) 90.1542 90.1542i 0.457636 0.457636i −0.440243 0.897879i \(-0.645108\pi\)
0.897879 + 0.440243i \(0.145108\pi\)
\(198\) −7.00765 + 26.1529i −0.0353922 + 0.132085i
\(199\) 25.6088 + 14.7853i 0.128688 + 0.0742979i 0.562962 0.826483i \(-0.309662\pi\)
−0.434274 + 0.900781i \(0.642995\pi\)
\(200\) −58.9129 + 65.1834i −0.294565 + 0.325917i
\(201\) −11.8607 20.5433i −0.0590085 0.102206i
\(202\) 25.5623 25.5623i 0.126546 0.126546i
\(203\) 37.5279 + 199.998i 0.184867 + 0.985210i
\(204\) 82.0159i 0.402038i
\(205\) −72.0316 68.4837i −0.351373 0.334067i
\(206\) 7.00375 12.1308i 0.0339988 0.0588876i
\(207\) −21.2372 79.2584i −0.102595 0.382891i
\(208\) 13.3050 49.6549i 0.0639663 0.238726i
\(209\) 433.951i 2.07632i
\(210\) −22.9363 14.8530i −0.109220 0.0707286i
\(211\) 116.220 0.550808 0.275404 0.961329i \(-0.411188\pi\)
0.275404 + 0.961329i \(0.411188\pi\)
\(212\) 118.693 + 31.8038i 0.559874 + 0.150018i
\(213\) 119.059 31.9018i 0.558964 0.149774i
\(214\) −40.9277 23.6296i −0.191251 0.110419i
\(215\) −2.50615 99.2592i −0.0116565 0.461671i
\(216\) 18.2616 0.0845446
\(217\) −102.751 + 292.226i −0.473508 + 1.34666i
\(218\) −4.40841 4.40841i −0.0202221 0.0202221i
\(219\) 139.803 80.7152i 0.638369 0.368562i
\(220\) −369.520 89.0801i −1.67964 0.404910i
\(221\) 23.5650 40.8157i 0.106629 0.184687i
\(222\) 46.0937 + 12.3508i 0.207629 + 0.0556341i
\(223\) 268.713 + 268.713i 1.20499 + 1.20499i 0.972629 + 0.232363i \(0.0746456\pi\)
0.232363 + 0.972629i \(0.425354\pi\)
\(224\) −61.1263 127.423i −0.272885 0.568854i
\(225\) 40.7300 + 62.9767i 0.181022 + 0.279896i
\(226\) 21.6466 + 37.4930i 0.0957813 + 0.165898i
\(227\) −48.3424 180.416i −0.212962 0.794785i −0.986874 0.161492i \(-0.948369\pi\)
0.773912 0.633293i \(-0.218297\pi\)
\(228\) 137.674 36.8895i 0.603832 0.161796i
\(229\) 8.99125 5.19110i 0.0392631 0.0226686i −0.480240 0.877137i \(-0.659450\pi\)
0.519503 + 0.854469i \(0.326117\pi\)
\(230\) −59.1218 + 17.4524i −0.257051 + 0.0758802i
\(231\) 18.5079 242.051i 0.0801210 1.04784i
\(232\) −72.2410 + 72.2410i −0.311383 + 0.311383i
\(233\) 28.9305 107.970i 0.124165 0.463391i −0.875643 0.482959i \(-0.839562\pi\)
0.999809 + 0.0195672i \(0.00622883\pi\)
\(234\) 4.42560 + 2.55512i 0.0189128 + 0.0109193i
\(235\) −29.2398 47.8155i −0.124425 0.203470i
\(236\) −108.782 188.416i −0.460940 0.798371i
\(237\) −158.760 + 158.760i −0.669873 + 0.669873i
\(238\) −7.25723 38.6760i −0.0304926 0.162504i
\(239\) 196.209i 0.820956i −0.911870 0.410478i \(-0.865362\pi\)
0.911870 0.410478i \(-0.134638\pi\)
\(240\) 2.97350 + 117.769i 0.0123896 + 0.490704i
\(241\) −20.5135 + 35.5305i −0.0851183 + 0.147429i −0.905442 0.424471i \(-0.860460\pi\)
0.820323 + 0.571900i \(0.193794\pi\)
\(242\) 32.6535 + 121.864i 0.134932 + 0.503572i
\(243\) 4.03459 15.0573i 0.0166032 0.0619642i
\(244\) 74.5717i 0.305622i
\(245\) 226.679 + 92.9615i 0.925219 + 0.379435i
\(246\) 15.5195 0.0630874
\(247\) 79.1133 + 21.1984i 0.320297 + 0.0858233i
\(248\) −150.222 + 40.2520i −0.605735 + 0.162306i
\(249\) −43.6273 25.1883i −0.175210 0.101158i
\(250\) 46.5243 31.7832i 0.186097 0.127133i
\(251\) −495.319 −1.97338 −0.986692 0.162600i \(-0.948012\pi\)
−0.986692 + 0.162600i \(0.948012\pi\)
\(252\) −78.3656 + 14.7047i −0.310974 + 0.0583518i
\(253\) −387.239 387.239i −1.53059 1.53059i
\(254\) 0.999822 0.577247i 0.00393631 0.00227263i
\(255\) −25.3119 + 104.998i −0.0992622 + 0.411757i
\(256\) −67.8197 + 117.467i −0.264921 + 0.458856i
\(257\) −55.3682 14.8359i −0.215440 0.0577271i 0.149484 0.988764i \(-0.452239\pi\)
−0.364925 + 0.931037i \(0.618905\pi\)
\(258\) 10.9629 + 10.9629i 0.0424918 + 0.0424918i
\(259\) −426.608 32.6197i −1.64713 0.125945i
\(260\) −34.2911 + 63.0155i −0.131889 + 0.242367i
\(261\) 43.6046 + 75.5253i 0.167067 + 0.289369i
\(262\) −15.4054 57.4936i −0.0587991 0.219441i
\(263\) 299.121 80.1492i 1.13734 0.304750i 0.359460 0.933160i \(-0.382961\pi\)
0.777882 + 0.628410i \(0.216294\pi\)
\(264\) 105.551 60.9401i 0.399815 0.230834i
\(265\) −142.138 77.3470i −0.536369 0.291875i
\(266\) 61.6581 29.5780i 0.231797 0.111196i
\(267\) −41.0760 + 41.0760i −0.153843 + 0.153843i
\(268\) −13.4585 + 50.2277i −0.0502182 + 0.187417i
\(269\) 231.086 + 133.418i 0.859056 + 0.495976i 0.863696 0.504013i \(-0.168144\pi\)
−0.00464016 + 0.999989i \(0.501477\pi\)
\(270\) −11.3848 2.74453i −0.0421660 0.0101649i
\(271\) 135.488 + 234.673i 0.499957 + 0.865951i 1.00000 4.97359e-5i \(-1.58314e-5\pi\)
−0.500043 + 0.866001i \(0.666682\pi\)
\(272\) −119.961 + 119.961i −0.441034 + 0.441034i
\(273\) −43.2241 15.1983i −0.158330 0.0556714i
\(274\) 20.4066i 0.0744766i
\(275\) 445.574 + 228.084i 1.62027 + 0.829396i
\(276\) −89.9354 + 155.773i −0.325853 + 0.564394i
\(277\) 68.0999 + 254.152i 0.245848 + 0.917517i 0.972955 + 0.230994i \(0.0741976\pi\)
−0.727107 + 0.686524i \(0.759136\pi\)
\(278\) −12.2047 + 45.5486i −0.0439018 + 0.163844i
\(279\) 132.756i 0.475828i
\(280\) 25.7294 + 120.285i 0.0918906 + 0.429589i
\(281\) −4.50255 −0.0160233 −0.00801165 0.999968i \(-0.502550\pi\)
−0.00801165 + 0.999968i \(0.502550\pi\)
\(282\) 8.45335 + 2.26507i 0.0299764 + 0.00803216i
\(283\) 352.367 94.4165i 1.24511 0.333627i 0.424667 0.905350i \(-0.360391\pi\)
0.820447 + 0.571722i \(0.193725\pi\)
\(284\) −233.997 135.098i −0.823932 0.475697i
\(285\) −187.637 + 4.73756i −0.658375 + 0.0166230i
\(286\) 34.1063 0.119253
\(287\) −136.761 + 25.6620i −0.476518 + 0.0894147i
\(288\) −42.8284 42.8284i −0.148710 0.148710i
\(289\) 115.582 66.7314i 0.399938 0.230905i
\(290\) 55.8941 34.1800i 0.192738 0.117862i
\(291\) −44.2627 + 76.6652i −0.152105 + 0.263454i
\(292\) −341.813 91.5885i −1.17059 0.313659i
\(293\) −159.329 159.329i −0.543786 0.543786i 0.380851 0.924637i \(-0.375631\pi\)
−0.924637 + 0.380851i \(0.875631\pi\)
\(294\) −35.6535 + 13.8685i −0.121270 + 0.0471716i
\(295\) 81.1152 + 274.785i 0.274967 + 0.931475i
\(296\) −107.405 186.031i −0.362855 0.628483i
\(297\) −26.9273 100.494i −0.0906643 0.338364i
\(298\) −19.6310 + 5.26011i −0.0658759 + 0.0176514i
\(299\) −89.5139 + 51.6809i −0.299378 + 0.172846i
\(300\) 34.4834 160.750i 0.114945 0.535834i
\(301\) −114.734 78.4794i −0.381177 0.260729i
\(302\) 53.6820 53.6820i 0.177755 0.177755i
\(303\) −35.9527 + 134.177i −0.118656 + 0.442829i
\(304\) −255.326 147.413i −0.839889 0.484910i
\(305\) 23.0144 95.4680i 0.0754572 0.313010i
\(306\) −8.43235 14.6053i −0.0275567 0.0477296i
\(307\) 170.687 170.687i 0.555983 0.555983i −0.372179 0.928161i \(-0.621389\pi\)
0.928161 + 0.372179i \(0.121389\pi\)
\(308\) −403.879 + 346.502i −1.31129 + 1.12501i
\(309\) 53.8246i 0.174190i
\(310\) 99.7022 2.51734i 0.321620 0.00812044i
\(311\) 21.6690 37.5319i 0.0696754 0.120681i −0.829083 0.559126i \(-0.811137\pi\)
0.898758 + 0.438444i \(0.144470\pi\)
\(312\) −5.95380 22.2199i −0.0190827 0.0712176i
\(313\) 49.7049 185.501i 0.158802 0.592656i −0.839948 0.542667i \(-0.817415\pi\)
0.998750 0.0499891i \(-0.0159186\pi\)
\(314\) 107.853i 0.343480i
\(315\) 104.863 + 5.36015i 0.332899 + 0.0170163i
\(316\) 492.170 1.55750
\(317\) 15.9228 + 4.26650i 0.0502296 + 0.0134590i 0.283846 0.958870i \(-0.408389\pi\)
−0.233617 + 0.972329i \(0.575056\pi\)
\(318\) 24.4066 6.53972i 0.0767502 0.0205652i
\(319\) 504.064 + 291.022i 1.58014 + 0.912294i
\(320\) 156.107 164.195i 0.487836 0.513108i
\(321\) 181.596 0.565721
\(322\) −28.6269 + 81.4153i −0.0889035 + 0.252842i
\(323\) −191.130 191.130i −0.591733 0.591733i
\(324\) −29.5933 + 17.0857i −0.0913373 + 0.0527336i
\(325\) 63.3480 70.0905i 0.194917 0.215663i
\(326\) 6.77997 11.7432i 0.0207974 0.0360222i
\(327\) 23.1399 + 6.20031i 0.0707641 + 0.0189612i
\(328\) −49.3992 49.3992i −0.150607 0.150607i
\(329\) −78.2377 5.98229i −0.237805 0.0181832i
\(330\) −74.9623 + 22.1285i −0.227158 + 0.0670560i
\(331\) −270.891 469.197i −0.818402 1.41751i −0.906859 0.421434i \(-0.861527\pi\)
0.0884570 0.996080i \(-0.471806\pi\)
\(332\) 28.5814 + 106.667i 0.0860886 + 0.321287i
\(333\) −177.118 + 47.4585i −0.531885 + 0.142518i
\(334\) −113.487 + 65.5220i −0.339783 + 0.196174i
\(335\) 32.7311 60.1488i 0.0977049 0.179549i
\(336\) 136.130 + 93.1142i 0.405149 + 0.277126i
\(337\) 182.640 182.640i 0.541959 0.541959i −0.382144 0.924103i \(-0.624814\pi\)
0.924103 + 0.382144i \(0.124814\pi\)
\(338\) −18.0501 + 67.3640i −0.0534027 + 0.199302i
\(339\) −144.069 83.1782i −0.424982 0.245363i
\(340\) 201.986 123.517i 0.594077 0.363286i
\(341\) 443.014 + 767.323i 1.29916 + 2.25021i
\(342\) 20.7240 20.7240i 0.0605964 0.0605964i
\(343\) 291.253 181.165i 0.849133 0.528179i
\(344\) 69.7906i 0.202880i
\(345\) 163.212 171.667i 0.473077 0.497585i
\(346\) −11.3193 + 19.6056i −0.0327147 + 0.0566635i
\(347\) −110.100 410.897i −0.317290 1.18414i −0.921839 0.387573i \(-0.873313\pi\)
0.604549 0.796568i \(-0.293353\pi\)
\(348\) 49.4786 184.657i 0.142180 0.530623i
\(349\) 205.632i 0.589202i 0.955620 + 0.294601i \(0.0951868\pi\)
−0.955620 + 0.294601i \(0.904813\pi\)
\(350\) 2.03714 78.8558i 0.00582041 0.225302i
\(351\) −19.6364 −0.0559441
\(352\) −390.466 104.625i −1.10928 0.297230i
\(353\) 302.605 81.0827i 0.857237 0.229696i 0.196676 0.980468i \(-0.436985\pi\)
0.660561 + 0.750772i \(0.270319\pi\)
\(354\) −38.7434 22.3685i −0.109445 0.0631878i
\(355\) 257.872 + 245.171i 0.726401 + 0.690623i
\(356\) 127.339 0.357695
\(357\) 98.4576 + 114.761i 0.275792 + 0.321459i
\(358\) −37.0570 37.0570i −0.103511 0.103511i
\(359\) −327.820 + 189.267i −0.913149 + 0.527207i −0.881443 0.472291i \(-0.843427\pi\)
−0.0317058 + 0.999497i \(0.510094\pi\)
\(360\) 27.5023 + 44.9742i 0.0763954 + 0.124928i
\(361\) 54.3672 94.1668i 0.150602 0.260850i
\(362\) −18.7707 5.02960i −0.0518528 0.0138939i
\(363\) −342.798 342.798i −0.944348 0.944348i
\(364\) 43.4413 + 90.5574i 0.119344 + 0.248784i
\(365\) 409.328 + 222.744i 1.12145 + 0.610257i
\(366\) 7.66699 + 13.2796i 0.0209481 + 0.0362831i
\(367\) −57.1272 213.202i −0.155660 0.580931i −0.999048 0.0436259i \(-0.986109\pi\)
0.843388 0.537305i \(-0.180558\pi\)
\(368\) 359.387 96.2975i 0.976595 0.261678i
\(369\) −51.6451 + 29.8173i −0.139960 + 0.0808057i
\(370\) 39.0008 + 132.119i 0.105407 + 0.357078i
\(371\) −204.261 + 97.9862i −0.550570 + 0.264114i
\(372\) 205.778 205.778i 0.553166 0.553166i
\(373\) −63.4330 + 236.735i −0.170062 + 0.634679i 0.827279 + 0.561792i \(0.189888\pi\)
−0.997340 + 0.0728868i \(0.976779\pi\)
\(374\) −97.4771 56.2784i −0.260634 0.150477i
\(375\) −93.7572 + 195.153i −0.250019 + 0.520407i
\(376\) −19.6975 34.1171i −0.0523871 0.0907371i
\(377\) 77.6793 77.6793i 0.206046 0.206046i
\(378\) −12.4434 + 10.6756i −0.0329190 + 0.0282424i
\(379\) 238.727i 0.629888i −0.949110 0.314944i \(-0.898014\pi\)
0.949110 0.314944i \(-0.101986\pi\)
\(380\) 298.189 + 283.502i 0.784709 + 0.746059i
\(381\) −2.21811 + 3.84187i −0.00582180 + 0.0100837i
\(382\) −15.2017 56.7335i −0.0397950 0.148517i
\(383\) 54.5095 203.432i 0.142322 0.531154i −0.857538 0.514421i \(-0.828007\pi\)
0.999860 0.0167331i \(-0.00532656\pi\)
\(384\) 175.253i 0.456389i
\(385\) 623.990 318.952i 1.62075 0.828448i
\(386\) 152.965 0.396282
\(387\) −57.5445 15.4190i −0.148694 0.0398424i
\(388\) 187.444 50.2254i 0.483102 0.129447i
\(389\) −322.620 186.264i −0.829356 0.478829i 0.0242760 0.999705i \(-0.492272\pi\)
−0.853632 + 0.520876i \(0.825605\pi\)
\(390\) 0.372348 + 14.7473i 0.000954738 + 0.0378136i
\(391\) 341.112 0.872409
\(392\) 157.630 + 69.3425i 0.402118 + 0.176894i
\(393\) 161.727 + 161.727i 0.411518 + 0.411518i
\(394\) −49.7705 + 28.7350i −0.126321 + 0.0729315i
\(395\) −630.084 151.894i −1.59515 0.384542i
\(396\) −114.032 + 197.509i −0.287959 + 0.498760i
\(397\) −209.470 56.1274i −0.527633 0.141379i −0.0148382 0.999890i \(-0.504723\pi\)
−0.512795 + 0.858511i \(0.671390\pi\)
\(398\) −9.42507 9.42507i −0.0236811 0.0236811i
\(399\) −148.355 + 216.891i −0.371818 + 0.543586i
\(400\) −285.560 + 184.685i −0.713900 + 0.461713i
\(401\) −207.883 360.064i −0.518412 0.897915i −0.999771 0.0213919i \(-0.993190\pi\)
0.481360 0.876523i \(-0.340143\pi\)
\(402\) 2.76743 + 10.3282i 0.00688416 + 0.0256920i
\(403\) 161.531 43.2822i 0.400822 0.107400i
\(404\) 263.709 152.252i 0.652745 0.376863i
\(405\) 43.1588 12.7403i 0.106565 0.0314574i
\(406\) 6.99301 91.4562i 0.0172242 0.225262i
\(407\) −865.359 + 865.359i −2.12619 + 2.12619i
\(408\) −19.6486 + 73.3296i −0.0481583 + 0.179729i
\(409\) 360.314 + 208.027i 0.880963 + 0.508624i 0.870976 0.491326i \(-0.163488\pi\)
0.00998686 + 0.999950i \(0.496821\pi\)
\(410\) 23.3726 + 38.2210i 0.0570064 + 0.0932220i
\(411\) 39.2067 + 67.9080i 0.0953935 + 0.165226i
\(412\) 83.4306 83.4306i 0.202501 0.202501i
\(413\) 378.400 + 133.052i 0.916224 + 0.322159i
\(414\) 36.9863i 0.0893390i
\(415\) −3.67059 145.378i −0.00884479 0.350309i
\(416\) −38.1483 + 66.0748i −0.0917026 + 0.158834i
\(417\) −46.8973 175.023i −0.112463 0.419719i
\(418\) 50.6264 188.940i 0.121116 0.452010i
\(419\) 655.999i 1.56563i −0.622254 0.782815i \(-0.713783\pi\)
0.622254 0.782815i \(-0.286217\pi\)
\(420\) −154.234 170.851i −0.367224 0.406788i
\(421\) 65.9825 0.156728 0.0783641 0.996925i \(-0.475030\pi\)
0.0783641 + 0.996925i \(0.475030\pi\)
\(422\) −50.6019 13.5587i −0.119910 0.0321297i
\(423\) −32.4825 + 8.70365i −0.0767907 + 0.0205760i
\(424\) −98.5032 56.8709i −0.232319 0.134129i
\(425\) −296.706 + 95.7916i −0.698133 + 0.225392i
\(426\) −55.5597 −0.130422
\(427\) −89.5211 104.345i −0.209651 0.244367i
\(428\) −281.483 281.483i −0.657670 0.657670i
\(429\) −113.497 + 65.5277i −0.264562 + 0.152745i
\(430\) −10.4888 + 43.5094i −0.0243926 + 0.101185i
\(431\) −355.868 + 616.382i −0.825681 + 1.43012i 0.0757171 + 0.997129i \(0.475875\pi\)
−0.901398 + 0.432992i \(0.857458\pi\)
\(432\) 68.2754 + 18.2943i 0.158045 + 0.0423480i
\(433\) −8.06832 8.06832i −0.0186335 0.0186335i 0.697729 0.716362i \(-0.254194\pi\)
−0.716362 + 0.697729i \(0.754194\pi\)
\(434\) 78.8297 115.246i 0.181635 0.265545i
\(435\) −120.332 + 221.131i −0.276626 + 0.508346i
\(436\) −26.2571 45.4786i −0.0602227 0.104309i
\(437\) 153.427 + 572.598i 0.351092 + 1.31029i
\(438\) −70.2860 + 18.8331i −0.160470 + 0.0429979i
\(439\) −103.783 + 59.9191i −0.236408 + 0.136490i −0.613525 0.789676i \(-0.710249\pi\)
0.377117 + 0.926166i \(0.376915\pi\)
\(440\) 309.044 + 168.172i 0.702372 + 0.382209i
\(441\) 92.0007 114.651i 0.208618 0.259980i
\(442\) −15.0218 + 15.0218i −0.0339860 + 0.0339860i
\(443\) 86.6536 323.396i 0.195606 0.730012i −0.796503 0.604635i \(-0.793319\pi\)
0.992109 0.125378i \(-0.0400143\pi\)
\(444\) 348.103 + 200.978i 0.784016 + 0.452652i
\(445\) −163.022 39.2997i −0.366342 0.0883140i
\(446\) −85.6474 148.346i −0.192035 0.332614i
\(447\) 55.2210 55.2210i 0.123537 0.123537i
\(448\) −58.4961 311.743i −0.130572 0.695856i
\(449\) 63.6098i 0.141670i −0.997488 0.0708349i \(-0.977434\pi\)
0.997488 0.0708349i \(-0.0225664\pi\)
\(450\) −10.3866 32.1715i −0.0230812 0.0714922i
\(451\) −199.004 + 344.685i −0.441250 + 0.764268i
\(452\) 94.3833 + 352.243i 0.208813 + 0.779299i
\(453\) −75.5024 + 281.779i −0.166672 + 0.622028i
\(454\) 84.1922i 0.185445i
\(455\) −27.6663 129.340i −0.0608051 0.284264i
\(456\) −131.930 −0.289321
\(457\) 644.842 + 172.785i 1.41103 + 0.378085i 0.882294 0.470699i \(-0.155998\pi\)
0.528739 + 0.848784i \(0.322665\pi\)
\(458\) −4.52036 + 1.21123i −0.00986979 + 0.00264460i
\(459\) 56.1215 + 32.4018i 0.122269 + 0.0705921i
\(460\) −519.077 + 13.1059i −1.12843 + 0.0284912i
\(461\) −3.62806 −0.00786997 −0.00393499 0.999992i \(-0.501253\pi\)
−0.00393499 + 0.999992i \(0.501253\pi\)
\(462\) −36.2969 + 103.229i −0.0785647 + 0.223439i
\(463\) −283.246 283.246i −0.611763 0.611763i 0.331642 0.943405i \(-0.392397\pi\)
−0.943405 + 0.331642i \(0.892397\pi\)
\(464\) −342.460 + 197.719i −0.738061 + 0.426120i
\(465\) −326.948 + 199.933i −0.703114 + 0.429963i
\(466\) −25.1924 + 43.6346i −0.0540610 + 0.0936365i
\(467\) −791.002 211.948i −1.69379 0.453851i −0.722430 0.691444i \(-0.756975\pi\)
−0.971365 + 0.237593i \(0.923642\pi\)
\(468\) 30.4373 + 30.4373i 0.0650369 + 0.0650369i
\(469\) −41.4651 86.4378i −0.0884117 0.184302i
\(470\) 7.15254 + 24.2299i 0.0152182 + 0.0515530i
\(471\) −207.215 358.907i −0.439947 0.762011i
\(472\) 52.1219 + 194.521i 0.110428 + 0.412122i
\(473\) −384.059 + 102.908i −0.811963 + 0.217565i
\(474\) 87.6448 50.6018i 0.184905 0.106755i
\(475\) −294.252 454.972i −0.619478 0.957836i
\(476\) 25.2709 330.498i 0.0530901 0.694324i
\(477\) −68.6544 + 68.6544i −0.143930 + 0.143930i
\(478\) −22.8905 + 85.4283i −0.0478880 + 0.178720i
\(479\) 464.561 + 268.214i 0.969856 + 0.559947i 0.899192 0.437554i \(-0.144155\pi\)
0.0706637 + 0.997500i \(0.477488\pi\)
\(480\) 40.9762 169.977i 0.0853672 0.354118i
\(481\) 115.491 + 200.036i 0.240105 + 0.415874i
\(482\) 13.0766 13.0766i 0.0271299 0.0271299i
\(483\) −61.1581 325.930i −0.126621 0.674804i
\(484\) 1062.71i 2.19567i
\(485\) −255.469 + 6.45023i −0.526741 + 0.0132994i
\(486\) −3.51328 + 6.08519i −0.00722898 + 0.0125210i
\(487\) −97.5549 364.080i −0.200318 0.747597i −0.990826 0.135145i \(-0.956850\pi\)
0.790508 0.612452i \(-0.209817\pi\)
\(488\) 17.8652 66.6738i 0.0366090 0.136627i
\(489\) 52.1048i 0.106554i
\(490\) −87.8496 66.9202i −0.179285 0.136572i
\(491\) 142.980 0.291202 0.145601 0.989343i \(-0.453488\pi\)
0.145601 + 0.989343i \(0.453488\pi\)
\(492\) 126.270 + 33.8340i 0.256647 + 0.0687684i
\(493\) −350.188 + 93.8327i −0.710321 + 0.190330i
\(494\) −31.9725 18.4593i −0.0647217 0.0373671i
\(495\) 206.941 217.661i 0.418062 0.439720i
\(496\) −601.966 −1.21364
\(497\) 489.602 91.8698i 0.985114 0.184849i
\(498\) 16.0566 + 16.0566i 0.0322422 + 0.0322422i
\(499\) −536.150 + 309.546i −1.07445 + 0.620334i −0.929394 0.369090i \(-0.879669\pi\)
−0.145056 + 0.989424i \(0.546336\pi\)
\(500\) 447.823 157.168i 0.895647 0.314335i
\(501\) 251.772 436.082i 0.502539 0.870423i
\(502\) 215.660 + 57.7859i 0.429601 + 0.115111i
\(503\) 661.069 + 661.069i 1.31425 + 1.31425i 0.918249 + 0.396004i \(0.129603\pi\)
0.396004 + 0.918249i \(0.370397\pi\)
\(504\) 73.5887 + 5.62681i 0.146009 + 0.0111643i
\(505\) −384.593 + 113.530i −0.761571 + 0.224812i
\(506\) 123.425 + 213.779i 0.243924 + 0.422488i
\(507\) −69.3586 258.850i −0.136802 0.510552i
\(508\) 9.39324 2.51691i 0.0184906 0.00495455i
\(509\) 416.656 240.557i 0.818578 0.472606i −0.0313476 0.999509i \(-0.509980\pi\)
0.849926 + 0.526902i \(0.176647\pi\)
\(510\) 23.2702 42.7627i 0.0456278 0.0838485i
\(511\) 588.232 282.181i 1.15114 0.552213i
\(512\) 329.420 329.420i 0.643398 0.643398i
\(513\) −29.1477 + 108.781i −0.0568181 + 0.212048i
\(514\) 22.3762 + 12.9189i 0.0435336 + 0.0251341i
\(515\) −132.558 + 81.0608i −0.257394 + 0.157400i
\(516\) 65.2965 + 113.097i 0.126544 + 0.219180i
\(517\) −158.702 + 158.702i −0.306968 + 0.306968i
\(518\) 181.938 + 63.9722i 0.351231 + 0.123498i
\(519\) 86.9900i 0.167611i
\(520\) 45.7560 48.1264i 0.0879923 0.0925507i
\(521\) −164.031 + 284.110i −0.314839 + 0.545318i −0.979403 0.201914i \(-0.935284\pi\)
0.664564 + 0.747231i \(0.268617\pi\)
\(522\) −10.1742 37.9705i −0.0194907 0.0727404i
\(523\) −88.9020 + 331.787i −0.169985 + 0.634391i 0.827367 + 0.561662i \(0.189838\pi\)
−0.997352 + 0.0727298i \(0.976829\pi\)
\(524\) 501.367i 0.956807i
\(525\) 144.725 + 266.326i 0.275666 + 0.507288i
\(526\) −139.586 −0.265374
\(527\) −533.082 142.839i −1.01154 0.271041i
\(528\) 455.678 122.098i 0.863026 0.231247i
\(529\) −189.747 109.550i −0.358689 0.207089i
\(530\) 52.8625 + 50.2589i 0.0997407 + 0.0948281i
\(531\) 171.904 0.323737
\(532\) 566.148 106.233i 1.06419 0.199686i
\(533\) 53.1180 + 53.1180i 0.0996585 + 0.0996585i
\(534\) 22.6764 13.0922i 0.0424652 0.0245173i
\(535\) 273.487 + 447.231i 0.511191 + 0.835945i
\(536\) 24.0662 41.6839i 0.0448996 0.0777684i
\(537\) 194.513 + 52.1197i 0.362222 + 0.0970572i
\(538\) −85.0488 85.0488i −0.158083 0.158083i
\(539\) 149.163 969.689i 0.276739 1.79905i
\(540\) −86.6462 47.1502i −0.160456 0.0873151i
\(541\) 253.542 + 439.148i 0.468655 + 0.811735i 0.999358 0.0358232i \(-0.0114053\pi\)
−0.530703 + 0.847558i \(0.678072\pi\)
\(542\) −31.6132 117.982i −0.0583269 0.217679i
\(543\) 72.1276 19.3265i 0.132832 0.0355921i
\(544\) 218.058 125.896i 0.400843 0.231427i
\(545\) 19.5791 + 66.3260i 0.0359249 + 0.121699i
\(546\) 17.0465 + 11.6600i 0.0312207 + 0.0213552i
\(547\) −24.1757 + 24.1757i −0.0441969 + 0.0441969i −0.728860 0.684663i \(-0.759949\pi\)
0.684663 + 0.728860i \(0.259949\pi\)
\(548\) 44.4883 166.033i 0.0811831 0.302979i
\(549\) −51.0277 29.4608i −0.0929466 0.0536627i
\(550\) −167.392 151.289i −0.304349 0.275071i
\(551\) −315.019 545.629i −0.571723 0.990253i
\(552\) 117.729 117.729i 0.213277 0.213277i
\(553\) −688.670 + 590.835i −1.24533 + 1.06842i
\(554\) 118.602i 0.214082i
\(555\) −383.622 364.727i −0.691210 0.657166i
\(556\) −198.601 + 343.986i −0.357195 + 0.618681i
\(557\) −31.2217 116.521i −0.0560533 0.209194i 0.932219 0.361894i \(-0.117870\pi\)
−0.988273 + 0.152700i \(0.951203\pi\)
\(558\) 15.4878 57.8014i 0.0277560 0.103587i
\(559\) 75.0445i 0.134248i
\(560\) −24.3049 + 475.489i −0.0434016 + 0.849087i
\(561\) 432.506 0.770956
\(562\) 1.96039 + 0.525284i 0.00348824 + 0.000934670i
\(563\) 89.6915 24.0328i 0.159310 0.0426870i −0.178283 0.983979i \(-0.557054\pi\)
0.337592 + 0.941292i \(0.390387\pi\)
\(564\) 63.8404 + 36.8583i 0.113192 + 0.0653515i
\(565\) −12.1212 480.077i −0.0214535 0.849693i
\(566\) −164.434 −0.290520
\(567\) 20.8976 59.4331i 0.0368565 0.104820i
\(568\) 176.849 + 176.849i 0.311353 + 0.311353i
\(569\) −123.242 + 71.1541i −0.216595 + 0.125051i −0.604373 0.796702i \(-0.706576\pi\)
0.387778 + 0.921753i \(0.373243\pi\)
\(570\) 82.2490 + 19.8277i 0.144297 + 0.0347855i
\(571\) 288.489 499.678i 0.505235 0.875092i −0.494747 0.869037i \(-0.664739\pi\)
0.999982 0.00605499i \(-0.00192738\pi\)
\(572\) 277.497 + 74.3551i 0.485134 + 0.129991i
\(573\) 159.588 + 159.588i 0.278514 + 0.278514i
\(574\) 62.5388 + 4.78190i 0.108953 + 0.00833083i
\(575\) 668.576 + 143.420i 1.16274 + 0.249426i
\(576\) −67.9680 117.724i −0.118000 0.204382i
\(577\) 164.767 + 614.920i 0.285559 + 1.06572i 0.948430 + 0.316986i \(0.102671\pi\)
−0.662871 + 0.748733i \(0.730662\pi\)
\(578\) −58.1091 + 15.5703i −0.100535 + 0.0269382i
\(579\) −509.029 + 293.888i −0.879152 + 0.507578i
\(580\) 529.283 156.242i 0.912557 0.269382i
\(581\) −168.044 114.943i −0.289232 0.197837i
\(582\) 28.2158 28.2158i 0.0484808 0.0484808i
\(583\) −167.715 + 625.922i −0.287676 + 1.07362i
\(584\) 283.670 + 163.777i 0.485736 + 0.280440i
\(585\) −29.5727 48.3599i −0.0505517 0.0826666i
\(586\) 50.7833 + 87.9592i 0.0866609 + 0.150101i
\(587\) 584.066 584.066i 0.995002 0.995002i −0.00498534 0.999988i \(-0.501587\pi\)
0.999988 + 0.00498534i \(0.00158689\pi\)
\(588\) −320.320 + 35.1091i −0.544761 + 0.0597093i
\(589\) 959.090i 1.62834i
\(590\) −3.25967 129.103i −0.00552487 0.218819i
\(591\) 110.416 191.246i 0.186829 0.323597i
\(592\) −215.195 803.118i −0.363505 1.35662i
\(593\) −197.236 + 736.094i −0.332607 + 1.24131i 0.573833 + 0.818972i \(0.305456\pi\)
−0.906440 + 0.422334i \(0.861211\pi\)
\(594\) 46.8961i 0.0789496i
\(595\) −134.351 + 415.311i −0.225800 + 0.698001i
\(596\) −171.190 −0.287232
\(597\) 49.4725 + 13.2561i 0.0828685 + 0.0222045i
\(598\) 45.0032 12.0586i 0.0752562 0.0201648i
\(599\) 385.326 + 222.468i 0.643282 + 0.371399i 0.785878 0.618382i \(-0.212212\pi\)
−0.142596 + 0.989781i \(0.545545\pi\)
\(600\) −69.3423 + 135.464i −0.115571 + 0.225773i
\(601\) −618.650 −1.02937 −0.514684 0.857380i \(-0.672091\pi\)
−0.514684 + 0.857380i \(0.672091\pi\)
\(602\) 40.7991 + 47.5549i 0.0677726 + 0.0789949i
\(603\) −29.0527 29.0527i −0.0481802 0.0481802i
\(604\) 553.802 319.738i 0.916891 0.529367i
\(605\) 327.974 1360.49i 0.542105 2.24875i
\(606\) 31.3073 54.2258i 0.0516622 0.0894815i
\(607\) −203.819 54.6130i −0.335780 0.0899721i 0.0869894 0.996209i \(-0.472275\pi\)
−0.422770 + 0.906237i \(0.638942\pi\)
\(608\) 309.411 + 309.411i 0.508900 + 0.508900i
\(609\) 152.442 + 317.779i 0.250315 + 0.521805i
\(610\) −21.1580 + 38.8814i −0.0346853 + 0.0637399i
\(611\) 21.1804 + 36.6855i 0.0346651 + 0.0600417i
\(612\) −36.7667 137.215i −0.0600763 0.224208i
\(613\) −238.755 + 63.9742i −0.389486 + 0.104362i −0.448247 0.893910i \(-0.647952\pi\)
0.0587613 + 0.998272i \(0.481285\pi\)
\(614\) −94.2292 + 54.4032i −0.153468 + 0.0886046i
\(615\) −151.212 82.2847i −0.245872 0.133796i
\(616\) 444.116 213.047i 0.720967 0.345855i
\(617\) −396.280 + 396.280i −0.642268 + 0.642268i −0.951113 0.308844i \(-0.900058\pi\)
0.308844 + 0.951113i \(0.400058\pi\)
\(618\) 6.27939 23.4350i 0.0101608 0.0379207i
\(619\) −93.8294 54.1724i −0.151582 0.0875160i 0.422290 0.906461i \(-0.361226\pi\)
−0.573873 + 0.818945i \(0.694560\pi\)
\(620\) 816.689 + 196.879i 1.31724 + 0.317547i
\(621\) −71.0611 123.081i −0.114430 0.198199i
\(622\) −13.8132 + 13.8132i −0.0222078 + 0.0222078i
\(623\) −178.180 + 152.867i −0.286003 + 0.245373i
\(624\) 89.0387i 0.142690i
\(625\) −621.817 + 63.0008i −0.994907 + 0.100801i
\(626\) −43.2826 + 74.9676i −0.0691415 + 0.119757i
\(627\) 194.535 + 726.014i 0.310263 + 1.15792i
\(628\) −235.130 + 877.515i −0.374410 + 1.39732i
\(629\) 762.279i 1.21189i
\(630\) −45.0316 14.5675i −0.0714787 0.0231230i
\(631\) 185.595 0.294129 0.147064 0.989127i \(-0.453018\pi\)
0.147064 + 0.989127i \(0.453018\pi\)
\(632\) −440.044 117.910i −0.696273 0.186566i
\(633\) 194.441 52.1002i 0.307173 0.0823068i
\(634\) −6.43497 3.71523i −0.0101498 0.00585999i
\(635\) −12.8022 + 0.323236i −0.0201609 + 0.000509033i
\(636\) 212.835 0.334646
\(637\) −169.497 74.5627i −0.266086 0.117053i
\(638\) −185.516 185.516i −0.290777 0.290777i
\(639\) 184.889 106.746i 0.289341 0.167051i
\(640\) −431.609 + 263.934i −0.674389 + 0.412398i
\(641\) 253.276 438.688i 0.395127 0.684380i −0.597990 0.801503i \(-0.704034\pi\)
0.993117 + 0.117123i \(0.0373672\pi\)
\(642\) −79.0663 21.1857i −0.123156 0.0329996i
\(643\) −521.287 521.287i −0.810711 0.810711i 0.174030 0.984740i \(-0.444321\pi\)
−0.984740 + 0.174030i \(0.944321\pi\)
\(644\) −410.409 + 600.004i −0.637281 + 0.931684i
\(645\) −48.6896 164.940i −0.0754877 0.255722i
\(646\) 60.9191 + 105.515i 0.0943020 + 0.163336i
\(647\) 235.372 + 878.419i 0.363789 + 1.35768i 0.869054 + 0.494717i \(0.164728\pi\)
−0.505265 + 0.862964i \(0.668605\pi\)
\(648\) 30.5523 8.18647i 0.0471486 0.0126334i
\(649\) 993.599 573.655i 1.53097 0.883905i
\(650\) −35.7584 + 23.1267i −0.0550130 + 0.0355795i
\(651\) −40.9050 + 534.966i −0.0628341 + 0.821760i
\(652\) 80.7648 80.7648i 0.123872 0.123872i
\(653\) 42.2998 157.865i 0.0647777 0.241754i −0.925944 0.377661i \(-0.876728\pi\)
0.990722 + 0.135908i \(0.0433951\pi\)
\(654\) −9.35164 5.39917i −0.0142991 0.00825562i
\(655\) −154.733 + 641.859i −0.236233 + 0.979937i
\(656\) −135.203 234.178i −0.206102 0.356979i
\(657\) 197.711 197.711i 0.300930 0.300930i
\(658\) 33.3664 + 11.7322i 0.0507089 + 0.0178301i
\(659\) 242.026i 0.367262i −0.982995 0.183631i \(-0.941215\pi\)
0.982995 0.183631i \(-0.0587852\pi\)
\(660\) −658.153 + 16.6174i −0.997201 + 0.0251779i
\(661\) 9.69682 16.7954i 0.0146699 0.0254090i −0.858597 0.512651i \(-0.828664\pi\)
0.873267 + 0.487242i \(0.161997\pi\)
\(662\) 63.2064 + 235.890i 0.0954780 + 0.356329i
\(663\) 21.1278 78.8499i 0.0318669 0.118929i
\(664\) 102.218i 0.153942i
\(665\) −757.578 38.7241i −1.13922 0.0582318i
\(666\) 82.6529 0.124103
\(667\) 768.006 + 205.787i 1.15143 + 0.308526i
\(668\) −1066.21 + 285.689i −1.59612 + 0.427678i
\(669\) 570.027 + 329.105i 0.852058 + 0.491936i
\(670\) −21.2682 + 22.3700i −0.0317436 + 0.0333880i
\(671\) −393.250 −0.586065
\(672\) −159.389 185.781i −0.237185 0.276460i
\(673\) 520.888 + 520.888i 0.773980 + 0.773980i 0.978800 0.204820i \(-0.0656608\pi\)
−0.204820 + 0.978800i \(0.565661\pi\)
\(674\) −100.828 + 58.2132i −0.149597 + 0.0863697i
\(675\) 96.3743 + 87.1033i 0.142777 + 0.129042i
\(676\) −293.720 + 508.738i −0.434497 + 0.752571i
\(677\) 1141.49 + 305.862i 1.68610 + 0.451790i 0.969379 0.245568i \(-0.0789746\pi\)
0.716723 + 0.697358i \(0.245641\pi\)
\(678\) 53.0230 + 53.0230i 0.0782051 + 0.0782051i
\(679\) −201.987 + 295.299i −0.297477 + 0.434902i
\(680\) −210.185 + 62.0456i −0.309096 + 0.0912435i
\(681\) −161.757 280.171i −0.237528 0.411411i
\(682\) −103.367 385.773i −0.151565 0.565649i
\(683\) 546.188 146.351i 0.799689 0.214276i 0.164242 0.986420i \(-0.447482\pi\)
0.635448 + 0.772144i \(0.280816\pi\)
\(684\) 213.795 123.435i 0.312566 0.180460i
\(685\) −108.196 + 198.828i −0.157950 + 0.290260i
\(686\) −147.946 + 44.9000i −0.215664 + 0.0654519i
\(687\) 12.7155 12.7155i 0.0185088 0.0185088i
\(688\) 69.9156 260.929i 0.101622 0.379257i
\(689\) 105.919 + 61.1522i 0.153728 + 0.0887550i
\(690\) −91.0889 + 55.7021i −0.132013 + 0.0807276i
\(691\) −664.985 1151.79i −0.962352 1.66684i −0.716567 0.697518i \(-0.754288\pi\)
−0.245785 0.969324i \(-0.579046\pi\)
\(692\) −134.838 + 134.838i −0.194853 + 0.194853i
\(693\) −77.5442 413.257i −0.111896 0.596330i
\(694\) 191.747i 0.276293i
\(695\) 360.414 379.085i 0.518581 0.545446i
\(696\) −88.4767 + 153.246i −0.127122 + 0.220181i
\(697\) −64.1638 239.463i −0.0920572 0.343562i
\(698\) 23.9898 89.5311i 0.0343693 0.128268i
\(699\) 193.607i 0.276977i
\(700\) 188.488 637.148i 0.269269 0.910211i
\(701\) −316.598 −0.451638 −0.225819 0.974169i \(-0.572506\pi\)
−0.225819 + 0.974169i \(0.572506\pi\)
\(702\) 8.54960 + 2.29086i 0.0121789 + 0.00326333i
\(703\) 1279.58 342.862i 1.82017 0.487712i
\(704\) −785.703 453.626i −1.11606 0.644355i
\(705\) −70.3543 66.8891i −0.0997933 0.0948781i
\(706\) −141.212 −0.200017
\(707\) −186.221 + 529.615i −0.263396 + 0.749101i
\(708\) −266.460 266.460i −0.376356 0.376356i
\(709\) −233.680 + 134.915i −0.329591 + 0.190290i −0.655660 0.755057i \(-0.727609\pi\)
0.326068 + 0.945346i \(0.394276\pi\)
\(710\) −83.6738 136.831i −0.117850 0.192720i
\(711\) −194.440 + 336.780i −0.273474 + 0.473671i
\(712\) −113.853 30.5068i −0.159906 0.0428467i
\(713\) 855.851 + 855.851i 1.20035 + 1.20035i
\(714\) −29.4795 61.4528i −0.0412879 0.0860684i
\(715\) −332.309 180.832i −0.464767 0.252912i
\(716\) −220.717 382.293i −0.308264 0.533928i
\(717\) −87.9579 328.263i −0.122675 0.457829i
\(718\) 164.812 44.1613i 0.229543 0.0615060i
\(719\) −977.193 + 564.183i −1.35910 + 0.784677i −0.989503 0.144515i \(-0.953838\pi\)
−0.369598 + 0.929192i \(0.620505\pi\)
\(720\) 57.7691 + 195.698i 0.0802349 + 0.271803i
\(721\) −16.5845 + 216.896i −0.0230021 + 0.300827i
\(722\) −34.6571 + 34.6571i −0.0480015 + 0.0480015i
\(723\) −18.3919 + 68.6396i −0.0254383 + 0.0949372i
\(724\) −141.758 81.8440i −0.195798 0.113044i
\(725\) −725.817 + 36.6750i −1.00113 + 0.0505862i
\(726\) 109.261 + 189.245i 0.150497 + 0.260668i
\(727\) −704.249 + 704.249i −0.968705 + 0.968705i −0.999525 0.0308196i \(-0.990188\pi\)
0.0308196 + 0.999525i \(0.490188\pi\)
\(728\) −17.1455 91.3737i −0.0235516 0.125513i
\(729\) 27.0000i 0.0370370i
\(730\) −152.234 144.736i −0.208539 0.198268i
\(731\) 123.830 214.480i 0.169398 0.293406i
\(732\) 33.4296 + 124.761i 0.0456688 + 0.170438i
\(733\) 248.412 927.085i 0.338897 1.26478i −0.560684 0.828030i \(-0.689462\pi\)
0.899582 0.436753i \(-0.143872\pi\)
\(734\) 99.4917i 0.135547i
\(735\) 420.914 + 53.9103i 0.572672 + 0.0733474i
\(736\) −552.211 −0.750287
\(737\) −264.873 70.9726i −0.359394 0.0962993i
\(738\) 25.9646 6.95720i 0.0351824 0.00942711i
\(739\) 201.038 + 116.069i 0.272040 + 0.157063i 0.629815 0.776746i \(-0.283131\pi\)
−0.357774 + 0.933808i \(0.616464\pi\)
\(740\) 29.2877 + 1159.97i 0.0395779 + 1.56753i
\(741\) 141.862 0.191447
\(742\) 100.366 18.8328i 0.135264 0.0253812i
\(743\) 678.958 + 678.958i 0.913806 + 0.913806i 0.996569 0.0827629i \(-0.0263744\pi\)
−0.0827629 + 0.996569i \(0.526374\pi\)
\(744\) −233.282 + 134.686i −0.313552 + 0.181029i
\(745\) 219.161 + 52.8330i 0.294175 + 0.0709168i
\(746\) 55.2369 95.6731i 0.0740441 0.128248i
\(747\) −84.2816 22.5832i −0.112827 0.0302318i
\(748\) −670.404 670.404i −0.896262 0.896262i
\(749\) 731.777 + 55.9538i 0.977005 + 0.0747047i
\(750\) 63.5887 74.0306i 0.0847850 0.0987074i
\(751\) 617.773 + 1070.01i 0.822601 + 1.42479i 0.903739 + 0.428083i \(0.140811\pi\)
−0.0811386 + 0.996703i \(0.525856\pi\)
\(752\) −39.4656 147.288i −0.0524809 0.195861i
\(753\) −828.686 + 222.046i −1.10051 + 0.294881i
\(754\) −42.8836 + 24.7589i −0.0568748 + 0.0328367i
\(755\) −807.665 + 238.418i −1.06975 + 0.315786i
\(756\) −124.516 + 59.7317i −0.164704 + 0.0790102i
\(757\) −256.783 + 256.783i −0.339212 + 0.339212i −0.856071 0.516859i \(-0.827101\pi\)
0.516859 + 0.856071i \(0.327101\pi\)
\(758\) −27.8509 + 103.941i −0.0367426 + 0.137125i
\(759\) −821.459 474.269i −1.08229 0.624861i
\(760\) −198.689 324.914i −0.261433 0.427519i
\(761\) 486.625 + 842.859i 0.639455 + 1.10757i 0.985553 + 0.169369i \(0.0541731\pi\)
−0.346098 + 0.938198i \(0.612494\pi\)
\(762\) 1.41396 1.41396i 0.00185559 0.00185559i
\(763\) 91.3360 + 32.1152i 0.119706 + 0.0420907i
\(764\) 494.739i 0.647564i
\(765\) 4.72179 + 187.012i 0.00617227 + 0.244460i
\(766\) −47.4664 + 82.2142i −0.0619665 + 0.107329i
\(767\) −56.0457 209.165i −0.0730713 0.272706i
\(768\) −60.8055 + 226.929i −0.0791739 + 0.295481i
\(769\) 1319.36i 1.71568i 0.513917 + 0.857840i \(0.328194\pi\)
−0.513917 + 0.857840i \(0.671806\pi\)
\(770\) −308.893 + 66.0734i −0.401160 + 0.0858095i
\(771\) −99.2835 −0.128772
\(772\) 1244.56 + 333.478i 1.61212 + 0.431966i
\(773\) −1379.80 + 369.715i −1.78499 + 0.478286i −0.991479 0.130270i \(-0.958416\pi\)
−0.793511 + 0.608557i \(0.791749\pi\)
\(774\) 23.2558 + 13.4267i 0.0300463 + 0.0173472i
\(775\) −984.778 504.096i −1.27068 0.650446i
\(776\) −179.624 −0.231474
\(777\) −728.352 + 136.669i −0.937390 + 0.175894i
\(778\) 118.737 + 118.737i 0.152618 + 0.152618i
\(779\) 373.107 215.414i 0.478957 0.276526i
\(780\) −29.1210 + 120.799i −0.0373347 + 0.154871i
\(781\) 712.432 1233.97i 0.912205 1.57999i
\(782\) −148.519 39.7955i −0.189922 0.0508893i
\(783\) 106.809 + 106.809i 0.136410 + 0.136410i
\(784\) 519.871 + 417.166i 0.663101 + 0.532099i
\(785\) 571.837 1050.84i 0.728455 1.33866i
\(786\) −51.5474 89.2827i −0.0655819 0.113591i
\(787\) −12.1345 45.2867i −0.0154187 0.0575434i 0.957788 0.287476i \(-0.0928161\pi\)
−0.973207 + 0.229932i \(0.926149\pi\)
\(788\) −467.590 + 125.290i −0.593388 + 0.158998i
\(789\) 464.509 268.185i 0.588732 0.339904i
\(790\) 256.615 + 139.642i 0.324829 + 0.176762i
\(791\) −554.924 379.573i −0.701547 0.479865i
\(792\) 149.272 149.272i 0.188475 0.188475i
\(793\) −19.2101 + 71.6931i −0.0242246 + 0.0904075i
\(794\) 84.6545 + 48.8753i 0.106618 + 0.0615558i
\(795\) −272.475 65.6854i −0.342736 0.0826232i
\(796\) −56.1370 97.2322i −0.0705239 0.122151i
\(797\) −764.370 + 764.370i −0.959059 + 0.959059i −0.999194 0.0401348i \(-0.987221\pi\)
0.0401348 + 0.999194i \(0.487221\pi\)
\(798\) 89.8966 77.1256i 0.112652 0.0966486i
\(799\) 139.798i 0.174966i
\(800\) 480.325 155.073i 0.600406 0.193841i
\(801\) −50.3077 + 87.1355i −0.0628061 + 0.108783i
\(802\) 48.5049 + 181.023i 0.0604799 + 0.225714i
\(803\) 482.987 1802.53i 0.601478 2.24475i
\(804\) 90.0659i 0.112022i
\(805\) 710.586 641.475i 0.882716 0.796863i
\(806\) −75.3794 −0.0935229
\(807\) 446.424 + 119.619i 0.553189 + 0.148227i
\(808\) −272.255 + 72.9505i −0.336949 + 0.0902853i
\(809\) 915.835 + 528.758i 1.13206 + 0.653594i 0.944452 0.328650i \(-0.106594\pi\)
0.187607 + 0.982244i \(0.439927\pi\)
\(810\) −20.2775 + 0.511977i −0.0250339 + 0.000632071i
\(811\) 1365.86 1.68417 0.842083 0.539349i \(-0.181330\pi\)
0.842083 + 0.539349i \(0.181330\pi\)
\(812\) 256.280 728.864i 0.315616 0.897616i
\(813\) 331.877 + 331.877i 0.408213 + 0.408213i
\(814\) 477.730 275.817i 0.586891 0.338842i
\(815\) −128.322 + 78.4708i −0.157451 + 0.0962831i
\(816\) −146.922 + 254.476i −0.180051 + 0.311858i
\(817\) 415.728 + 111.394i 0.508847 + 0.136345i
\(818\) −132.610 132.610i −0.162115 0.162115i
\(819\) −79.1285 6.05040i −0.0966160 0.00738754i
\(820\) 106.840 + 361.930i 0.130292 + 0.441378i
\(821\) 460.776 + 798.087i 0.561237 + 0.972091i 0.997389 + 0.0722182i \(0.0230078\pi\)
−0.436152 + 0.899873i \(0.643659\pi\)
\(822\) −9.14802 34.1409i −0.0111290 0.0415339i
\(823\) 969.882 259.879i 1.17847 0.315770i 0.384151 0.923270i \(-0.374494\pi\)
0.794320 + 0.607500i \(0.207827\pi\)
\(824\) −94.5820 + 54.6070i −0.114784 + 0.0662706i
\(825\) 847.707 + 181.846i 1.02752 + 0.220420i
\(826\) −149.232 102.076i −0.180668 0.123578i
\(827\) 993.021 993.021i 1.20075 1.20075i 0.226813 0.973938i \(-0.427169\pi\)
0.973938 0.226813i \(-0.0728305\pi\)
\(828\) −80.6339 + 300.930i −0.0973839 + 0.363442i
\(829\) −901.880 520.701i −1.08791 0.628107i −0.154893 0.987931i \(-0.549503\pi\)
−0.933020 + 0.359824i \(0.882837\pi\)
\(830\) −15.3622 + 63.7252i −0.0185087 + 0.0767774i
\(831\) 227.867 + 394.677i 0.274208 + 0.474942i
\(832\) −121.082 + 121.082i −0.145531 + 0.145531i
\(833\) 361.393 + 492.788i 0.433845 + 0.591582i
\(834\) 81.6755i 0.0979322i
\(835\) 1453.14 36.6898i 1.74029 0.0439399i
\(836\) 823.817 1426.89i 0.985427 1.70681i
\(837\) 59.5129 + 222.105i 0.0711026 + 0.265359i
\(838\) −76.5314 + 285.619i −0.0913262 + 0.340834i
\(839\) 1063.92i 1.26808i −0.773300 0.634041i \(-0.781395\pi\)
0.773300 0.634041i \(-0.218605\pi\)
\(840\) 96.9683 + 189.706i 0.115438 + 0.225841i
\(841\) −4.04821 −0.00481357
\(842\) −28.7285 7.69778i −0.0341194 0.00914226i
\(843\) −7.53291 + 2.01844i −0.00893583 + 0.00239435i
\(844\) −382.149 220.634i −0.452784 0.261415i
\(845\) 533.033 560.647i 0.630808 0.663487i
\(846\) 15.1581 0.0179174
\(847\) −1275.75 1486.99i −1.50619 1.75560i
\(848\) −311.305 311.305i −0.367105 0.367105i
\(849\) 547.196 315.924i 0.644518 0.372113i
\(850\) 140.360 7.09230i 0.165130 0.00834388i
\(851\) −835.886 + 1447.80i −0.982239 + 1.70129i
\(852\) −452.047 121.126i −0.530571 0.142166i
\(853\) −94.3742 94.3742i −0.110638 0.110638i 0.649621 0.760259i \(-0.274928\pi\)
−0.760259 + 0.649621i \(0.774928\pi\)
\(854\) 26.8038 + 55.8751i 0.0313862 + 0.0654275i
\(855\) −311.799 + 92.0415i −0.364677 + 0.107651i
\(856\) 184.236 + 319.106i 0.215229 + 0.372787i
\(857\) −263.085 981.846i −0.306984 1.14568i −0.931224 0.364446i \(-0.881258\pi\)
0.624241 0.781232i \(-0.285408\pi\)
\(858\) 57.0609 15.2894i 0.0665046 0.0178198i
\(859\) −537.700 + 310.441i −0.625961 + 0.361399i −0.779186 0.626793i \(-0.784367\pi\)
0.153225 + 0.988191i \(0.451034\pi\)
\(860\) −180.194 + 331.136i −0.209528 + 0.385042i
\(861\) −217.301 + 104.241i −0.252382 + 0.121070i
\(862\) 226.853 226.853i 0.263171 0.263171i
\(863\) 266.243 993.632i 0.308509 1.15137i −0.621374 0.783514i \(-0.713425\pi\)
0.929883 0.367856i \(-0.119908\pi\)
\(864\) −90.8527 52.4538i −0.105154 0.0607104i
\(865\) 214.237 131.008i 0.247672 0.151455i
\(866\) 2.57163 + 4.45419i 0.00296955 + 0.00514341i
\(867\) 163.458 163.458i 0.188533 0.188533i
\(868\) 892.626 765.816i 1.02837 0.882277i
\(869\) 2595.43i 2.98669i
\(870\) 78.1902 82.2408i 0.0898737 0.0945297i
\(871\) −25.8779 + 44.8219i −0.0297106 + 0.0514602i
\(872\) 12.5809 + 46.9524i 0.0144276 + 0.0538445i
\(873\) −39.6848 + 148.106i −0.0454580 + 0.169651i
\(874\) 267.206i 0.305728i
\(875\) −437.943 + 757.516i −0.500506 + 0.865733i
\(876\) −612.922 −0.699683
\(877\) −330.191 88.4744i −0.376501 0.100883i 0.0656059 0.997846i \(-0.479102\pi\)
−0.442106 + 0.896963i \(0.645769\pi\)
\(878\) 52.1770 13.9808i 0.0594271 0.0159235i
\(879\) −337.988 195.138i −0.384515 0.222000i
\(880\) 986.959 + 938.348i 1.12154 + 1.06630i
\(881\) 1000.15 1.13524 0.567621 0.823290i \(-0.307864\pi\)
0.567621 + 0.823290i \(0.307864\pi\)
\(882\) −53.4323 + 39.1854i −0.0605809 + 0.0444279i
\(883\) −141.373 141.373i −0.160106 0.160106i 0.622508 0.782614i \(-0.286114\pi\)
−0.782614 + 0.622508i \(0.786114\pi\)
\(884\) −154.970 + 89.4719i −0.175305 + 0.101213i
\(885\) 258.891 + 423.362i 0.292532 + 0.478375i
\(886\) −75.4572 + 130.696i −0.0851661 + 0.147512i
\(887\) −291.915 78.2183i −0.329104 0.0881830i 0.0904840 0.995898i \(-0.471159\pi\)
−0.419588 + 0.907715i \(0.637825\pi\)
\(888\) −263.087 263.087i −0.296270 0.296270i
\(889\) −10.1220 + 14.7981i −0.0113859 + 0.0166458i
\(890\) 66.3943 + 36.1297i 0.0746003 + 0.0405952i
\(891\) −90.1005 156.059i −0.101123 0.175150i
\(892\) −373.439 1393.70i −0.418654 1.56244i
\(893\) 234.668 62.8791i 0.262786 0.0704134i
\(894\) −30.4853 + 17.6007i −0.0340999 + 0.0196876i
\(895\) 164.582 + 557.535i 0.183890 + 0.622945i
\(896\) −53.9993 + 706.216i −0.0602671 + 0.788188i
\(897\) −126.592 + 126.592i −0.141128 + 0.141128i
\(898\) −7.42096 + 27.6954i −0.00826388 + 0.0308412i
\(899\) −1114.05 643.197i −1.23921 0.715458i
\(900\) −14.3705 284.399i −0.0159672 0.315999i
\(901\) −201.813 349.550i −0.223988 0.387958i
\(902\) 126.858 126.858i 0.140640 0.140640i
\(903\) −227.136 79.8646i −0.251535 0.0884436i
\(904\) 337.549i 0.373395i
\(905\) 156.222 + 148.528i 0.172621 + 0.164119i
\(906\) 65.7468 113.877i 0.0725682 0.125692i
\(907\) 163.597 + 610.552i 0.180371 + 0.673155i 0.995574 + 0.0939796i \(0.0299589\pi\)
−0.815203 + 0.579176i \(0.803374\pi\)
\(908\) −183.547 + 685.008i −0.202145 + 0.754414i
\(909\) 240.600i 0.264686i
\(910\) −3.04352 + 59.5417i −0.00334452 + 0.0654305i
\(911\) 1345.46 1.47691 0.738453 0.674305i \(-0.235557\pi\)
0.738453 + 0.674305i \(0.235557\pi\)
\(912\) −493.252 132.167i −0.540847 0.144920i
\(913\) −562.504 + 150.723i −0.616105 + 0.165085i
\(914\) −260.604 150.460i −0.285124 0.164617i
\(915\) −4.29322 170.038i −0.00469204 0.185834i
\(916\) −39.4194 −0.0430342
\(917\) 601.876 + 701.539i 0.656354 + 0.765037i
\(918\) −20.6550 20.6550i −0.0224999 0.0224999i
\(919\) 236.556 136.575i 0.257405 0.148613i −0.365745 0.930715i \(-0.619186\pi\)
0.623150 + 0.782102i \(0.285852\pi\)
\(920\) 467.241 + 112.638i 0.507871 + 0.122432i
\(921\) 209.048 362.081i 0.226979 0.393139i
\(922\) 1.57964 + 0.423263i 0.00171328 + 0.000459071i
\(923\) −190.162 190.162i −0.206026 0.206026i
\(924\) −520.369 + 760.763i −0.563170 + 0.823337i
\(925\) 320.499 1494.06i 0.346485 1.61520i
\(926\) 90.2795 + 156.369i 0.0974941 + 0.168865i
\(927\) 24.1289 + 90.0503i 0.0260290 + 0.0971417i
\(928\) 566.904 151.902i 0.610888 0.163687i
\(929\) −463.310 + 267.492i −0.498719 + 0.287936i −0.728184 0.685381i \(-0.759636\pi\)
0.229465 + 0.973317i \(0.426302\pi\)
\(930\) 165.677 48.9069i 0.178147 0.0525880i
\(931\) −664.655 + 828.291i −0.713915 + 0.889679i
\(932\) −300.099 + 300.099i −0.321995 + 0.321995i
\(933\) 19.4279 72.5060i 0.0208231 0.0777128i
\(934\) 319.672 + 184.563i 0.342261 + 0.197605i
\(935\) 651.362 + 1065.16i 0.696643 + 1.13921i
\(936\) −19.9218 34.5056i −0.0212840 0.0368649i
\(937\) −993.941 + 993.941i −1.06077 + 1.06077i −0.0627391 + 0.998030i \(0.519984\pi\)
−0.998030 + 0.0627391i \(0.980016\pi\)
\(938\) 7.96954 + 42.4721i 0.00849632 + 0.0452794i
\(939\) 332.632i 0.354240i
\(940\) 5.37121 + 212.733i 0.00571405 + 0.226312i
\(941\) 411.864 713.369i 0.437687 0.758097i −0.559823 0.828612i \(-0.689131\pi\)
0.997511 + 0.0705152i \(0.0224643\pi\)
\(942\) 48.3491 + 180.441i 0.0513260 + 0.191551i
\(943\) −140.719 + 525.171i −0.149225 + 0.556915i
\(944\) 779.479i 0.825720i
\(945\) 177.842 38.0411i 0.188193 0.0402552i
\(946\) 179.223 0.189454
\(947\) −789.991 211.678i −0.834204 0.223524i −0.183657 0.982990i \(-0.558794\pi\)
−0.650547 + 0.759466i \(0.725460\pi\)
\(948\) 823.416 220.634i 0.868582 0.232736i
\(949\) −305.025 176.106i −0.321417 0.185570i
\(950\) 75.0372 + 232.421i 0.0789865 + 0.244654i
\(951\) 28.5520 0.0300231
\(952\) −101.772 + 289.441i −0.106904 + 0.304035i
\(953\) −1249.74 1249.74i −1.31138 1.31138i −0.920401 0.390975i \(-0.872138\pi\)
−0.390975 0.920401i \(-0.627862\pi\)
\(954\) 37.9013 21.8823i 0.0397288 0.0229375i
\(955\) −152.687 + 633.373i −0.159882 + 0.663218i
\(956\) −372.484 + 645.162i −0.389628 + 0.674855i
\(957\) 973.777 + 260.923i 1.01753 + 0.272647i
\(958\) −170.977 170.977i −0.178473 0.178473i
\(959\) 137.067 + 285.729i 0.142927 + 0.297944i
\(960\) 187.566 344.684i 0.195382 0.359046i
\(961\) −498.620 863.636i −0.518856 0.898684i
\(962\) −26.9472 100.568i −0.0280116 0.104541i
\(963\) 303.817 81.4074i 0.315490 0.0845352i
\(964\) 134.903 77.8862i 0.139941 0.0807948i
\(965\) −1490.38 811.022i −1.54444 0.840437i
\(966\) −11.3963 + 149.043i −0.0117974 + 0.154289i
\(967\) −367.218 + 367.218i −0.379750 + 0.379750i −0.871012 0.491262i \(-0.836536\pi\)
0.491262 + 0.871012i \(0.336536\pi\)
\(968\) 254.593 950.155i 0.263010 0.981565i
\(969\) −405.447 234.085i −0.418418 0.241574i
\(970\) 111.983 + 26.9956i 0.115446 + 0.0278305i
\(971\) 87.0711 + 150.812i 0.0896716 + 0.155316i 0.907372 0.420328i \(-0.138085\pi\)
−0.817701 + 0.575644i \(0.804752\pi\)
\(972\) −41.8512 + 41.8512i −0.0430568 + 0.0430568i
\(973\) −135.053 719.738i −0.138801 0.739711i
\(974\) 169.900i 0.174435i
\(975\) 74.5625 145.662i 0.0764743 0.149397i
\(976\) 133.587 231.379i 0.136871 0.237068i
\(977\) −410.121 1530.59i −0.419776 1.56662i −0.775074 0.631871i \(-0.782287\pi\)
0.355298 0.934753i \(-0.384379\pi\)
\(978\) 6.07875 22.6862i 0.00621549 0.0231965i
\(979\) 671.518i 0.685922i
\(980\) −568.872 735.999i −0.580482 0.751020i
\(981\) 41.4933 0.0422969
\(982\) −62.2529 16.6806i −0.0633940 0.0169864i
\(983\) −1496.43 + 400.967i −1.52231 + 0.407901i −0.920501 0.390741i \(-0.872219\pi\)
−0.601807 + 0.798642i \(0.705552\pi\)
\(984\) −104.791 60.5014i −0.106495 0.0614852i
\(985\) 637.284 16.0905i 0.646988 0.0163355i
\(986\) 163.417 0.165738
\(987\) −133.576 + 25.0645i −0.135335 + 0.0253946i
\(988\) −219.893 219.893i −0.222564 0.222564i
\(989\) −470.381 + 271.575i −0.475613 + 0.274595i
\(990\) −115.494 + 70.6263i −0.116661 + 0.0713397i
\(991\) 311.136 538.904i 0.313962 0.543798i −0.665255 0.746617i \(-0.731677\pi\)
0.979216 + 0.202819i \(0.0650103\pi\)
\(992\) 862.983 + 231.235i 0.869942 + 0.233100i
\(993\) −663.545 663.545i −0.668223 0.668223i
\(994\) −223.888 17.1191i −0.225240 0.0172225i
\(995\) 41.8596 + 141.803i 0.0420700 + 0.142516i
\(996\) 95.6353 + 165.645i 0.0960194 + 0.166310i
\(997\) 135.088 + 504.154i 0.135494 + 0.505671i 0.999995 + 0.00304053i \(0.000967833\pi\)
−0.864501 + 0.502631i \(0.832366\pi\)
\(998\) 269.550 72.2258i 0.270090 0.0723705i
\(999\) −275.049 + 158.799i −0.275324 + 0.158958i
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 105.3.v.a.88.8 yes 64
3.2 odd 2 315.3.ca.b.298.9 64
5.2 odd 4 inner 105.3.v.a.67.9 yes 64
7.2 even 3 inner 105.3.v.a.58.9 yes 64
15.2 even 4 315.3.ca.b.172.8 64
21.2 odd 6 315.3.ca.b.163.8 64
35.2 odd 12 inner 105.3.v.a.37.8 64
105.2 even 12 315.3.ca.b.37.9 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.v.a.37.8 64 35.2 odd 12 inner
105.3.v.a.58.9 yes 64 7.2 even 3 inner
105.3.v.a.67.9 yes 64 5.2 odd 4 inner
105.3.v.a.88.8 yes 64 1.1 even 1 trivial
315.3.ca.b.37.9 64 105.2 even 12
315.3.ca.b.163.8 64 21.2 odd 6
315.3.ca.b.172.8 64 15.2 even 4
315.3.ca.b.298.9 64 3.2 odd 2