Properties

Label 273.2.c.b.64.1
Level $273$
Weight $2$
Character 273.64
Analytic conductor $2.180$
Analytic rank $0$
Dimension $6$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(64,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.c (of order \(2\), degree \(1\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.1
Root \(-0.854638 - 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 273.64
Dual form 273.2.c.b.64.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.17009i q^{2} +1.00000 q^{3} -2.70928 q^{4} +0.630898i q^{5} -2.17009i q^{6} -1.00000i q^{7} +1.53919i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.17009i q^{2} +1.00000 q^{3} -2.70928 q^{4} +0.630898i q^{5} -2.17009i q^{6} -1.00000i q^{7} +1.53919i q^{8} +1.00000 q^{9} +1.36910 q^{10} -5.70928i q^{11} -2.70928 q^{12} +(-2.17009 - 2.87936i) q^{13} -2.17009 q^{14} +0.630898i q^{15} -2.07838 q^{16} +1.07838 q^{17} -2.17009i q^{18} +7.41855i q^{19} -1.70928i q^{20} -1.00000i q^{21} -12.3896 q^{22} +5.41855 q^{23} +1.53919i q^{24} +4.60197 q^{25} +(-6.24846 + 4.70928i) q^{26} +1.00000 q^{27} +2.70928i q^{28} +6.68035 q^{29} +1.36910 q^{30} +6.15676i q^{31} +7.58864i q^{32} -5.70928i q^{33} -2.34017i q^{34} +0.630898 q^{35} -2.70928 q^{36} +3.41855i q^{37} +16.0989 q^{38} +(-2.17009 - 2.87936i) q^{39} -0.971071 q^{40} +1.21235i q^{41} -2.17009 q^{42} -12.6803 q^{43} +15.4680i q^{44} +0.630898i q^{45} -11.7587i q^{46} +6.04945i q^{47} -2.07838 q^{48} -1.00000 q^{49} -9.98667i q^{50} +1.07838 q^{51} +(5.87936 + 7.80098i) q^{52} -6.00000 q^{53} -2.17009i q^{54} +3.60197 q^{55} +1.53919 q^{56} +7.41855i q^{57} -14.4969i q^{58} -1.36910i q^{59} -1.70928i q^{60} +12.6537 q^{61} +13.3607 q^{62} -1.00000i q^{63} +12.3112 q^{64} +(1.81658 - 1.36910i) q^{65} -12.3896 q^{66} +0.581449i q^{67} -2.92162 q^{68} +5.41855 q^{69} -1.36910i q^{70} -4.81432i q^{71} +1.53919i q^{72} -3.81658i q^{73} +7.41855 q^{74} +4.60197 q^{75} -20.0989i q^{76} -5.70928 q^{77} +(-6.24846 + 4.70928i) q^{78} -1.65983 q^{79} -1.31124i q^{80} +1.00000 q^{81} +2.63090 q^{82} -12.8865i q^{83} +2.70928i q^{84} +0.680346i q^{85} +27.5174i q^{86} +6.68035 q^{87} +8.78765 q^{88} +6.20620i q^{89} +1.36910 q^{90} +(-2.87936 + 2.17009i) q^{91} -14.6803 q^{92} +6.15676i q^{93} +13.1278 q^{94} -4.68035 q^{95} +7.58864i q^{96} -1.07838i q^{97} +2.17009i q^{98} -5.70928i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{3} - 2 q^{4} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{3} - 2 q^{4} + 6 q^{9} + 16 q^{10} - 2 q^{12} - 2 q^{13} - 2 q^{14} - 6 q^{16} - 16 q^{22} + 4 q^{23} - 10 q^{25} - 20 q^{26} + 6 q^{27} - 4 q^{29} + 16 q^{30} - 4 q^{35} - 2 q^{36} + 24 q^{38} - 2 q^{39} + 24 q^{40} - 2 q^{42} - 32 q^{43} - 6 q^{48} - 6 q^{49} + 10 q^{52} - 36 q^{53} - 16 q^{55} + 6 q^{56} + 28 q^{61} - 8 q^{62} + 22 q^{64} + 20 q^{65} - 16 q^{66} - 24 q^{68} + 4 q^{69} + 16 q^{74} - 10 q^{75} - 20 q^{77} - 20 q^{78} - 32 q^{79} + 6 q^{81} + 8 q^{82} - 4 q^{87} + 32 q^{88} + 16 q^{90} + 8 q^{91} - 44 q^{92} + 36 q^{94} + 16 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.17009i 1.53448i −0.641358 0.767241i \(-0.721629\pi\)
0.641358 0.767241i \(-0.278371\pi\)
\(3\) 1.00000 0.577350
\(4\) −2.70928 −1.35464
\(5\) 0.630898i 0.282146i 0.989999 + 0.141073i \(0.0450552\pi\)
−0.989999 + 0.141073i \(0.954945\pi\)
\(6\) 2.17009i 0.885934i
\(7\) 1.00000i 0.377964i
\(8\) 1.53919i 0.544185i
\(9\) 1.00000 0.333333
\(10\) 1.36910 0.432948
\(11\) 5.70928i 1.72141i −0.509103 0.860706i \(-0.670023\pi\)
0.509103 0.860706i \(-0.329977\pi\)
\(12\) −2.70928 −0.782100
\(13\) −2.17009 2.87936i −0.601874 0.798591i
\(14\) −2.17009 −0.579980
\(15\) 0.630898i 0.162897i
\(16\) −2.07838 −0.519594
\(17\) 1.07838 0.261545 0.130773 0.991412i \(-0.458254\pi\)
0.130773 + 0.991412i \(0.458254\pi\)
\(18\) 2.17009i 0.511494i
\(19\) 7.41855i 1.70193i 0.525221 + 0.850966i \(0.323983\pi\)
−0.525221 + 0.850966i \(0.676017\pi\)
\(20\) 1.70928i 0.382206i
\(21\) 1.00000i 0.218218i
\(22\) −12.3896 −2.64148
\(23\) 5.41855 1.12985 0.564923 0.825144i \(-0.308906\pi\)
0.564923 + 0.825144i \(0.308906\pi\)
\(24\) 1.53919i 0.314186i
\(25\) 4.60197 0.920394
\(26\) −6.24846 + 4.70928i −1.22542 + 0.923565i
\(27\) 1.00000 0.192450
\(28\) 2.70928i 0.512005i
\(29\) 6.68035 1.24051 0.620255 0.784401i \(-0.287029\pi\)
0.620255 + 0.784401i \(0.287029\pi\)
\(30\) 1.36910 0.249963
\(31\) 6.15676i 1.10579i 0.833252 + 0.552893i \(0.186476\pi\)
−0.833252 + 0.552893i \(0.813524\pi\)
\(32\) 7.58864i 1.34149i
\(33\) 5.70928i 0.993857i
\(34\) 2.34017i 0.401336i
\(35\) 0.630898 0.106641
\(36\) −2.70928 −0.451546
\(37\) 3.41855i 0.562006i 0.959707 + 0.281003i \(0.0906671\pi\)
−0.959707 + 0.281003i \(0.909333\pi\)
\(38\) 16.0989 2.61159
\(39\) −2.17009 2.87936i −0.347492 0.461067i
\(40\) −0.971071 −0.153540
\(41\) 1.21235i 0.189337i 0.995509 + 0.0946684i \(0.0301791\pi\)
−0.995509 + 0.0946684i \(0.969821\pi\)
\(42\) −2.17009 −0.334852
\(43\) −12.6803 −1.93373 −0.966867 0.255279i \(-0.917833\pi\)
−0.966867 + 0.255279i \(0.917833\pi\)
\(44\) 15.4680i 2.33189i
\(45\) 0.630898i 0.0940487i
\(46\) 11.7587i 1.73373i
\(47\) 6.04945i 0.882403i 0.897408 + 0.441201i \(0.145448\pi\)
−0.897408 + 0.441201i \(0.854552\pi\)
\(48\) −2.07838 −0.299988
\(49\) −1.00000 −0.142857
\(50\) 9.98667i 1.41233i
\(51\) 1.07838 0.151003
\(52\) 5.87936 + 7.80098i 0.815321 + 1.08180i
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 2.17009i 0.295311i
\(55\) 3.60197 0.485689
\(56\) 1.53919 0.205683
\(57\) 7.41855i 0.982611i
\(58\) 14.4969i 1.90354i
\(59\) 1.36910i 0.178242i −0.996021 0.0891210i \(-0.971594\pi\)
0.996021 0.0891210i \(-0.0284058\pi\)
\(60\) 1.70928i 0.220667i
\(61\) 12.6537 1.62014 0.810069 0.586334i \(-0.199430\pi\)
0.810069 + 0.586334i \(0.199430\pi\)
\(62\) 13.3607 1.69681
\(63\) 1.00000i 0.125988i
\(64\) 12.3112 1.53891
\(65\) 1.81658 1.36910i 0.225319 0.169816i
\(66\) −12.3896 −1.52506
\(67\) 0.581449i 0.0710353i 0.999369 + 0.0355177i \(0.0113080\pi\)
−0.999369 + 0.0355177i \(0.988692\pi\)
\(68\) −2.92162 −0.354299
\(69\) 5.41855 0.652317
\(70\) 1.36910i 0.163639i
\(71\) 4.81432i 0.571354i −0.958326 0.285677i \(-0.907782\pi\)
0.958326 0.285677i \(-0.0922185\pi\)
\(72\) 1.53919i 0.181395i
\(73\) 3.81658i 0.446697i −0.974739 0.223349i \(-0.928301\pi\)
0.974739 0.223349i \(-0.0716988\pi\)
\(74\) 7.41855 0.862389
\(75\) 4.60197 0.531390
\(76\) 20.0989i 2.30550i
\(77\) −5.70928 −0.650632
\(78\) −6.24846 + 4.70928i −0.707499 + 0.533220i
\(79\) −1.65983 −0.186745 −0.0933726 0.995631i \(-0.529765\pi\)
−0.0933726 + 0.995631i \(0.529765\pi\)
\(80\) 1.31124i 0.146601i
\(81\) 1.00000 0.111111
\(82\) 2.63090 0.290534
\(83\) 12.8865i 1.41448i −0.706972 0.707241i \(-0.749939\pi\)
0.706972 0.707241i \(-0.250061\pi\)
\(84\) 2.70928i 0.295606i
\(85\) 0.680346i 0.0737939i
\(86\) 27.5174i 2.96728i
\(87\) 6.68035 0.716208
\(88\) 8.78765 0.936767
\(89\) 6.20620i 0.657856i 0.944355 + 0.328928i \(0.106687\pi\)
−0.944355 + 0.328928i \(0.893313\pi\)
\(90\) 1.36910 0.144316
\(91\) −2.87936 + 2.17009i −0.301839 + 0.227487i
\(92\) −14.6803 −1.53053
\(93\) 6.15676i 0.638426i
\(94\) 13.1278 1.35403
\(95\) −4.68035 −0.480193
\(96\) 7.58864i 0.774512i
\(97\) 1.07838i 0.109493i −0.998500 0.0547463i \(-0.982565\pi\)
0.998500 0.0547463i \(-0.0174350\pi\)
\(98\) 2.17009i 0.219212i
\(99\) 5.70928i 0.573804i
\(100\) −12.4680 −1.24680
\(101\) −7.23513 −0.719923 −0.359961 0.932967i \(-0.617210\pi\)
−0.359961 + 0.932967i \(0.617210\pi\)
\(102\) 2.34017i 0.231712i
\(103\) 13.7587 1.35569 0.677844 0.735206i \(-0.262915\pi\)
0.677844 + 0.735206i \(0.262915\pi\)
\(104\) 4.43188 3.34017i 0.434582 0.327531i
\(105\) 0.630898 0.0615693
\(106\) 13.0205i 1.26466i
\(107\) −10.0989 −0.976297 −0.488149 0.872761i \(-0.662328\pi\)
−0.488149 + 0.872761i \(0.662328\pi\)
\(108\) −2.70928 −0.260700
\(109\) 17.9421i 1.71855i 0.511518 + 0.859273i \(0.329083\pi\)
−0.511518 + 0.859273i \(0.670917\pi\)
\(110\) 7.81658i 0.745282i
\(111\) 3.41855i 0.324474i
\(112\) 2.07838i 0.196388i
\(113\) 10.6803 1.00472 0.502361 0.864658i \(-0.332465\pi\)
0.502361 + 0.864658i \(0.332465\pi\)
\(114\) 16.0989 1.50780
\(115\) 3.41855i 0.318781i
\(116\) −18.0989 −1.68044
\(117\) −2.17009 2.87936i −0.200625 0.266197i
\(118\) −2.97107 −0.273509
\(119\) 1.07838i 0.0988547i
\(120\) −0.971071 −0.0886462
\(121\) −21.5958 −1.96326
\(122\) 27.4596i 2.48607i
\(123\) 1.21235i 0.109314i
\(124\) 16.6803i 1.49794i
\(125\) 6.05786i 0.541831i
\(126\) −2.17009 −0.193327
\(127\) 6.34017 0.562599 0.281300 0.959620i \(-0.409235\pi\)
0.281300 + 0.959620i \(0.409235\pi\)
\(128\) 11.5392i 1.01993i
\(129\) −12.6803 −1.11644
\(130\) −2.97107 3.94214i −0.260580 0.345749i
\(131\) −7.51745 −0.656802 −0.328401 0.944538i \(-0.606510\pi\)
−0.328401 + 0.944538i \(0.606510\pi\)
\(132\) 15.4680i 1.34632i
\(133\) 7.41855 0.643270
\(134\) 1.26180 0.109003
\(135\) 0.630898i 0.0542990i
\(136\) 1.65983i 0.142329i
\(137\) 4.47414i 0.382252i −0.981566 0.191126i \(-0.938786\pi\)
0.981566 0.191126i \(-0.0612139\pi\)
\(138\) 11.7587i 1.00097i
\(139\) −9.75872 −0.827724 −0.413862 0.910340i \(-0.635820\pi\)
−0.413862 + 0.910340i \(0.635820\pi\)
\(140\) −1.70928 −0.144460
\(141\) 6.04945i 0.509455i
\(142\) −10.4475 −0.876733
\(143\) −16.4391 + 12.3896i −1.37470 + 1.03607i
\(144\) −2.07838 −0.173198
\(145\) 4.21461i 0.350005i
\(146\) −8.28231 −0.685449
\(147\) −1.00000 −0.0824786
\(148\) 9.26180i 0.761315i
\(149\) 1.46800i 0.120263i 0.998190 + 0.0601316i \(0.0191520\pi\)
−0.998190 + 0.0601316i \(0.980848\pi\)
\(150\) 9.98667i 0.815408i
\(151\) 13.3607i 1.08728i −0.839319 0.543639i \(-0.817046\pi\)
0.839319 0.543639i \(-0.182954\pi\)
\(152\) −11.4186 −0.926167
\(153\) 1.07838 0.0871817
\(154\) 12.3896i 0.998384i
\(155\) −3.88428 −0.311993
\(156\) 5.87936 + 7.80098i 0.470726 + 0.624579i
\(157\) −8.15676 −0.650980 −0.325490 0.945545i \(-0.605529\pi\)
−0.325490 + 0.945545i \(0.605529\pi\)
\(158\) 3.60197i 0.286557i
\(159\) −6.00000 −0.475831
\(160\) −4.78765 −0.378497
\(161\) 5.41855i 0.427042i
\(162\) 2.17009i 0.170498i
\(163\) 4.58145i 0.358847i −0.983772 0.179423i \(-0.942577\pi\)
0.983772 0.179423i \(-0.0574232\pi\)
\(164\) 3.28458i 0.256483i
\(165\) 3.60197 0.280413
\(166\) −27.9649 −2.17050
\(167\) 7.31124i 0.565761i −0.959155 0.282881i \(-0.908710\pi\)
0.959155 0.282881i \(-0.0912900\pi\)
\(168\) 1.53919 0.118751
\(169\) −3.58145 + 12.4969i −0.275496 + 0.961302i
\(170\) 1.47641 0.113235
\(171\) 7.41855i 0.567311i
\(172\) 34.3545 2.61951
\(173\) 7.60197 0.577967 0.288983 0.957334i \(-0.406683\pi\)
0.288983 + 0.957334i \(0.406683\pi\)
\(174\) 14.4969i 1.09901i
\(175\) 4.60197i 0.347876i
\(176\) 11.8660i 0.894436i
\(177\) 1.36910i 0.102908i
\(178\) 13.4680 1.00947
\(179\) 9.10504 0.680543 0.340271 0.940327i \(-0.389481\pi\)
0.340271 + 0.940327i \(0.389481\pi\)
\(180\) 1.70928i 0.127402i
\(181\) 15.3607 1.14175 0.570876 0.821037i \(-0.306604\pi\)
0.570876 + 0.821037i \(0.306604\pi\)
\(182\) 4.70928 + 6.24846i 0.349075 + 0.463167i
\(183\) 12.6537 0.935387
\(184\) 8.34017i 0.614846i
\(185\) −2.15676 −0.158568
\(186\) 13.3607 0.979653
\(187\) 6.15676i 0.450227i
\(188\) 16.3896i 1.19534i
\(189\) 1.00000i 0.0727393i
\(190\) 10.1568i 0.736848i
\(191\) −24.5692 −1.77776 −0.888881 0.458138i \(-0.848517\pi\)
−0.888881 + 0.458138i \(0.848517\pi\)
\(192\) 12.3112 0.888487
\(193\) 13.5753i 0.977172i −0.872516 0.488586i \(-0.837513\pi\)
0.872516 0.488586i \(-0.162487\pi\)
\(194\) −2.34017 −0.168015
\(195\) 1.81658 1.36910i 0.130088 0.0980435i
\(196\) 2.70928 0.193520
\(197\) 2.94441i 0.209780i −0.994484 0.104890i \(-0.966551\pi\)
0.994484 0.104890i \(-0.0334491\pi\)
\(198\) −12.3896 −0.880492
\(199\) −10.5236 −0.745998 −0.372999 0.927832i \(-0.621670\pi\)
−0.372999 + 0.927832i \(0.621670\pi\)
\(200\) 7.08330i 0.500865i
\(201\) 0.581449i 0.0410123i
\(202\) 15.7009i 1.10471i
\(203\) 6.68035i 0.468868i
\(204\) −2.92162 −0.204554
\(205\) −0.764867 −0.0534206
\(206\) 29.8576i 2.08028i
\(207\) 5.41855 0.376615
\(208\) 4.51026 + 5.98440i 0.312730 + 0.414944i
\(209\) 42.3545 2.92973
\(210\) 1.36910i 0.0944770i
\(211\) −3.02052 −0.207941 −0.103971 0.994580i \(-0.533155\pi\)
−0.103971 + 0.994580i \(0.533155\pi\)
\(212\) 16.2557 1.11644
\(213\) 4.81432i 0.329871i
\(214\) 21.9155i 1.49811i
\(215\) 8.00000i 0.545595i
\(216\) 1.53919i 0.104729i
\(217\) 6.15676 0.417948
\(218\) 38.9360 2.63708
\(219\) 3.81658i 0.257901i
\(220\) −9.75872 −0.657933
\(221\) −2.34017 3.10504i −0.157417 0.208868i
\(222\) 7.41855 0.497901
\(223\) 22.6225i 1.51491i 0.652885 + 0.757457i \(0.273558\pi\)
−0.652885 + 0.757457i \(0.726442\pi\)
\(224\) 7.58864 0.507037
\(225\) 4.60197 0.306798
\(226\) 23.1773i 1.54173i
\(227\) 22.9444i 1.52287i −0.648239 0.761437i \(-0.724494\pi\)
0.648239 0.761437i \(-0.275506\pi\)
\(228\) 20.0989i 1.33108i
\(229\) 21.5441i 1.42367i 0.702344 + 0.711837i \(0.252137\pi\)
−0.702344 + 0.711837i \(0.747863\pi\)
\(230\) 7.41855 0.489165
\(231\) −5.70928 −0.375643
\(232\) 10.2823i 0.675067i
\(233\) 7.36069 0.482215 0.241107 0.970498i \(-0.422489\pi\)
0.241107 + 0.970498i \(0.422489\pi\)
\(234\) −6.24846 + 4.70928i −0.408475 + 0.307855i
\(235\) −3.81658 −0.248966
\(236\) 3.70928i 0.241453i
\(237\) −1.65983 −0.107817
\(238\) −2.34017 −0.151691
\(239\) 15.5525i 1.00601i 0.864284 + 0.503004i \(0.167772\pi\)
−0.864284 + 0.503004i \(0.832228\pi\)
\(240\) 1.31124i 0.0846404i
\(241\) 7.33403i 0.472426i 0.971701 + 0.236213i \(0.0759064\pi\)
−0.971701 + 0.236213i \(0.924094\pi\)
\(242\) 46.8648i 3.01258i
\(243\) 1.00000 0.0641500
\(244\) −34.2823 −2.19470
\(245\) 0.630898i 0.0403066i
\(246\) 2.63090 0.167740
\(247\) 21.3607 16.0989i 1.35915 1.02435i
\(248\) −9.47641 −0.601753
\(249\) 12.8865i 0.816652i
\(250\) 13.1461 0.831431
\(251\) −13.6742 −0.863108 −0.431554 0.902087i \(-0.642035\pi\)
−0.431554 + 0.902087i \(0.642035\pi\)
\(252\) 2.70928i 0.170668i
\(253\) 30.9360i 1.94493i
\(254\) 13.7587i 0.863299i
\(255\) 0.680346i 0.0426049i
\(256\) −0.418551 −0.0261594
\(257\) −26.1256 −1.62967 −0.814834 0.579695i \(-0.803172\pi\)
−0.814834 + 0.579695i \(0.803172\pi\)
\(258\) 27.5174i 1.71316i
\(259\) 3.41855 0.212418
\(260\) −4.92162 + 3.70928i −0.305226 + 0.230039i
\(261\) 6.68035 0.413503
\(262\) 16.3135i 1.00785i
\(263\) −30.7792 −1.89793 −0.948965 0.315382i \(-0.897867\pi\)
−0.948965 + 0.315382i \(0.897867\pi\)
\(264\) 8.78765 0.540843
\(265\) 3.78539i 0.232534i
\(266\) 16.0989i 0.987087i
\(267\) 6.20620i 0.379814i
\(268\) 1.57531i 0.0962271i
\(269\) 5.39189 0.328749 0.164375 0.986398i \(-0.447439\pi\)
0.164375 + 0.986398i \(0.447439\pi\)
\(270\) 1.36910 0.0833209
\(271\) 11.4186i 0.693628i 0.937934 + 0.346814i \(0.112736\pi\)
−0.937934 + 0.346814i \(0.887264\pi\)
\(272\) −2.24128 −0.135897
\(273\) −2.87936 + 2.17009i −0.174267 + 0.131340i
\(274\) −9.70928 −0.586559
\(275\) 26.2739i 1.58438i
\(276\) −14.6803 −0.883653
\(277\) 13.1506 0.790144 0.395072 0.918650i \(-0.370720\pi\)
0.395072 + 0.918650i \(0.370720\pi\)
\(278\) 21.1773i 1.27013i
\(279\) 6.15676i 0.368595i
\(280\) 0.971071i 0.0580326i
\(281\) 2.14834i 0.128160i −0.997945 0.0640798i \(-0.979589\pi\)
0.997945 0.0640798i \(-0.0204112\pi\)
\(282\) 13.1278 0.781751
\(283\) −12.1978 −0.725084 −0.362542 0.931968i \(-0.618091\pi\)
−0.362542 + 0.931968i \(0.618091\pi\)
\(284\) 13.0433i 0.773978i
\(285\) −4.68035 −0.277240
\(286\) 26.8865 + 35.6742i 1.58984 + 2.10946i
\(287\) 1.21235 0.0715626
\(288\) 7.58864i 0.447165i
\(289\) −15.8371 −0.931594
\(290\) 9.14608 0.537076
\(291\) 1.07838i 0.0632156i
\(292\) 10.3402i 0.605113i
\(293\) 7.15449i 0.417970i 0.977919 + 0.208985i \(0.0670159\pi\)
−0.977919 + 0.208985i \(0.932984\pi\)
\(294\) 2.17009i 0.126562i
\(295\) 0.863763 0.0502903
\(296\) −5.26180 −0.305836
\(297\) 5.70928i 0.331286i
\(298\) 3.18568 0.184542
\(299\) −11.7587 15.6020i −0.680025 0.902285i
\(300\) −12.4680 −0.719840
\(301\) 12.6803i 0.730883i
\(302\) −28.9939 −1.66841
\(303\) −7.23513 −0.415648
\(304\) 15.4186i 0.884315i
\(305\) 7.98318i 0.457116i
\(306\) 2.34017i 0.133779i
\(307\) 21.8432i 1.24666i −0.781959 0.623330i \(-0.785779\pi\)
0.781959 0.623330i \(-0.214221\pi\)
\(308\) 15.4680 0.881371
\(309\) 13.7587 0.782706
\(310\) 8.42923i 0.478748i
\(311\) −7.51745 −0.426275 −0.213138 0.977022i \(-0.568368\pi\)
−0.213138 + 0.977022i \(0.568368\pi\)
\(312\) 4.43188 3.34017i 0.250906 0.189100i
\(313\) 25.7009 1.45270 0.726349 0.687326i \(-0.241215\pi\)
0.726349 + 0.687326i \(0.241215\pi\)
\(314\) 17.7009i 0.998918i
\(315\) 0.630898 0.0355471
\(316\) 4.49693 0.252972
\(317\) 9.36910i 0.526221i 0.964766 + 0.263111i \(0.0847484\pi\)
−0.964766 + 0.263111i \(0.915252\pi\)
\(318\) 13.0205i 0.730154i
\(319\) 38.1399i 2.13543i
\(320\) 7.76713i 0.434196i
\(321\) −10.0989 −0.563665
\(322\) −11.7587 −0.655288
\(323\) 8.00000i 0.445132i
\(324\) −2.70928 −0.150515
\(325\) −9.98667 13.2507i −0.553961 0.735018i
\(326\) −9.94214 −0.550644
\(327\) 17.9421i 0.992203i
\(328\) −1.86603 −0.103034
\(329\) 6.04945 0.333517
\(330\) 7.81658i 0.430289i
\(331\) 21.0472i 1.15686i 0.815733 + 0.578429i \(0.196334\pi\)
−0.815733 + 0.578429i \(0.803666\pi\)
\(332\) 34.9132i 1.91611i
\(333\) 3.41855i 0.187335i
\(334\) −15.8660 −0.868151
\(335\) −0.366835 −0.0200423
\(336\) 2.07838i 0.113385i
\(337\) 15.4452 0.841354 0.420677 0.907210i \(-0.361793\pi\)
0.420677 + 0.907210i \(0.361793\pi\)
\(338\) 27.1194 + 7.77205i 1.47510 + 0.422744i
\(339\) 10.6803 0.580077
\(340\) 1.84324i 0.0999640i
\(341\) 35.1506 1.90351
\(342\) 16.0989 0.870529
\(343\) 1.00000i 0.0539949i
\(344\) 19.5174i 1.05231i
\(345\) 3.41855i 0.184049i
\(346\) 16.4969i 0.886880i
\(347\) 21.7321 1.16664 0.583319 0.812243i \(-0.301754\pi\)
0.583319 + 0.812243i \(0.301754\pi\)
\(348\) −18.0989 −0.970203
\(349\) 5.65983i 0.302964i −0.988460 0.151482i \(-0.951596\pi\)
0.988460 0.151482i \(-0.0484045\pi\)
\(350\) −9.98667 −0.533810
\(351\) −2.17009 2.87936i −0.115831 0.153689i
\(352\) 43.3256 2.30926
\(353\) 33.7237i 1.79493i 0.441087 + 0.897464i \(0.354593\pi\)
−0.441087 + 0.897464i \(0.645407\pi\)
\(354\) −2.97107 −0.157911
\(355\) 3.03734 0.161205
\(356\) 16.8143i 0.891157i
\(357\) 1.07838i 0.0570738i
\(358\) 19.7587i 1.04428i
\(359\) 18.7031i 0.987114i −0.869714 0.493557i \(-0.835697\pi\)
0.869714 0.493557i \(-0.164303\pi\)
\(360\) −0.971071 −0.0511799
\(361\) −36.0349 −1.89657
\(362\) 33.3340i 1.75200i
\(363\) −21.5958 −1.13349
\(364\) 7.80098 5.87936i 0.408883 0.308162i
\(365\) 2.40787 0.126034
\(366\) 27.4596i 1.43534i
\(367\) 10.0722 0.525766 0.262883 0.964828i \(-0.415327\pi\)
0.262883 + 0.964828i \(0.415327\pi\)
\(368\) −11.2618 −0.587062
\(369\) 1.21235i 0.0631123i
\(370\) 4.68035i 0.243320i
\(371\) 6.00000i 0.311504i
\(372\) 16.6803i 0.864836i
\(373\) 4.24128 0.219605 0.109802 0.993953i \(-0.464978\pi\)
0.109802 + 0.993953i \(0.464978\pi\)
\(374\) −13.3607 −0.690865
\(375\) 6.05786i 0.312826i
\(376\) −9.31124 −0.480191
\(377\) −14.4969 19.2351i −0.746630 0.990660i
\(378\) −2.17009 −0.111617
\(379\) 20.1978i 1.03749i −0.854929 0.518745i \(-0.826399\pi\)
0.854929 0.518745i \(-0.173601\pi\)
\(380\) 12.6803 0.650488
\(381\) 6.34017 0.324817
\(382\) 53.3172i 2.72795i
\(383\) 7.04331i 0.359896i 0.983676 + 0.179948i \(0.0575930\pi\)
−0.983676 + 0.179948i \(0.942407\pi\)
\(384\) 11.5392i 0.588857i
\(385\) 3.60197i 0.183573i
\(386\) −29.4596 −1.49945
\(387\) −12.6803 −0.644578
\(388\) 2.92162i 0.148323i
\(389\) −3.84324 −0.194860 −0.0974301 0.995242i \(-0.531062\pi\)
−0.0974301 + 0.995242i \(0.531062\pi\)
\(390\) −2.97107 3.94214i −0.150446 0.199618i
\(391\) 5.84324 0.295506
\(392\) 1.53919i 0.0777408i
\(393\) −7.51745 −0.379205
\(394\) −6.38962 −0.321904
\(395\) 1.04718i 0.0526894i
\(396\) 15.4680i 0.777296i
\(397\) 14.4391i 0.724676i −0.932047 0.362338i \(-0.881979\pi\)
0.932047 0.362338i \(-0.118021\pi\)
\(398\) 22.8371i 1.14472i
\(399\) 7.41855 0.371392
\(400\) −9.56463 −0.478231
\(401\) 9.83483i 0.491128i 0.969380 + 0.245564i \(0.0789732\pi\)
−0.969380 + 0.245564i \(0.921027\pi\)
\(402\) 1.26180 0.0629326
\(403\) 17.7275 13.3607i 0.883071 0.665543i
\(404\) 19.6020 0.975234
\(405\) 0.630898i 0.0313496i
\(406\) −14.4969 −0.719470
\(407\) 19.5174 0.967444
\(408\) 1.65983i 0.0821737i
\(409\) 7.54864i 0.373256i 0.982431 + 0.186628i \(0.0597560\pi\)
−0.982431 + 0.186628i \(0.940244\pi\)
\(410\) 1.65983i 0.0819730i
\(411\) 4.47414i 0.220693i
\(412\) −37.2762 −1.83647
\(413\) −1.36910 −0.0673691
\(414\) 11.7587i 0.577910i
\(415\) 8.13009 0.399091
\(416\) 21.8504 16.4680i 1.07131 0.807410i
\(417\) −9.75872 −0.477887
\(418\) 91.9130i 4.49561i
\(419\) −35.1506 −1.71722 −0.858610 0.512630i \(-0.828671\pi\)
−0.858610 + 0.512630i \(0.828671\pi\)
\(420\) −1.70928 −0.0834041
\(421\) 25.6742i 1.25128i −0.780110 0.625642i \(-0.784837\pi\)
0.780110 0.625642i \(-0.215163\pi\)
\(422\) 6.55479i 0.319082i
\(423\) 6.04945i 0.294134i
\(424\) 9.23513i 0.448498i
\(425\) 4.96266 0.240724
\(426\) −10.4475 −0.506182
\(427\) 12.6537i 0.612355i
\(428\) 27.3607 1.32253
\(429\) −16.4391 + 12.3896i −0.793686 + 0.598177i
\(430\) −17.3607 −0.837207
\(431\) 16.2329i 0.781910i −0.920410 0.390955i \(-0.872145\pi\)
0.920410 0.390955i \(-0.127855\pi\)
\(432\) −2.07838 −0.0999960
\(433\) −5.38735 −0.258900 −0.129450 0.991586i \(-0.541321\pi\)
−0.129450 + 0.991586i \(0.541321\pi\)
\(434\) 13.3607i 0.641334i
\(435\) 4.21461i 0.202075i
\(436\) 48.6102i 2.32801i
\(437\) 40.1978i 1.92292i
\(438\) −8.28231 −0.395744
\(439\) −10.2413 −0.488789 −0.244395 0.969676i \(-0.578589\pi\)
−0.244395 + 0.969676i \(0.578589\pi\)
\(440\) 5.54411i 0.264305i
\(441\) −1.00000 −0.0476190
\(442\) −6.73820 + 5.07838i −0.320504 + 0.241554i
\(443\) 15.9421 0.757434 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(444\) 9.26180i 0.439545i
\(445\) −3.91548 −0.185612
\(446\) 49.0928 2.32461
\(447\) 1.46800i 0.0694340i
\(448\) 12.3112i 0.581652i
\(449\) 13.2001i 0.622949i −0.950254 0.311475i \(-0.899177\pi\)
0.950254 0.311475i \(-0.100823\pi\)
\(450\) 9.98667i 0.470776i
\(451\) 6.92162 0.325926
\(452\) −28.9360 −1.36103
\(453\) 13.3607i 0.627740i
\(454\) −49.7914 −2.33682
\(455\) −1.36910 1.81658i −0.0641845 0.0851627i
\(456\) −11.4186 −0.534723
\(457\) 18.3090i 0.856458i 0.903670 + 0.428229i \(0.140862\pi\)
−0.903670 + 0.428229i \(0.859138\pi\)
\(458\) 46.7526 2.18460
\(459\) 1.07838 0.0503344
\(460\) 9.26180i 0.431833i
\(461\) 18.9399i 0.882118i −0.897478 0.441059i \(-0.854603\pi\)
0.897478 0.441059i \(-0.145397\pi\)
\(462\) 12.3896i 0.576417i
\(463\) 1.74435i 0.0810667i −0.999178 0.0405334i \(-0.987094\pi\)
0.999178 0.0405334i \(-0.0129057\pi\)
\(464\) −13.8843 −0.644562
\(465\) −3.88428 −0.180129
\(466\) 15.9733i 0.739951i
\(467\) −18.1568 −0.840194 −0.420097 0.907479i \(-0.638004\pi\)
−0.420097 + 0.907479i \(0.638004\pi\)
\(468\) 5.87936 + 7.80098i 0.271774 + 0.360601i
\(469\) 0.581449 0.0268488
\(470\) 8.28231i 0.382035i
\(471\) −8.15676 −0.375843
\(472\) 2.10731 0.0969967
\(473\) 72.3956i 3.32875i
\(474\) 3.60197i 0.165444i
\(475\) 34.1399i 1.56645i
\(476\) 2.92162i 0.133912i
\(477\) −6.00000 −0.274721
\(478\) 33.7503 1.54370
\(479\) 30.4619i 1.39184i 0.718120 + 0.695919i \(0.245003\pi\)
−0.718120 + 0.695919i \(0.754997\pi\)
\(480\) −4.78765 −0.218525
\(481\) 9.84324 7.41855i 0.448813 0.338257i
\(482\) 15.9155 0.724930
\(483\) 5.41855i 0.246553i
\(484\) 58.5090 2.65950
\(485\) 0.680346 0.0308929
\(486\) 2.17009i 0.0984371i
\(487\) 0.313511i 0.0142065i −0.999975 0.00710327i \(-0.997739\pi\)
0.999975 0.00710327i \(-0.00226106\pi\)
\(488\) 19.4764i 0.881656i
\(489\) 4.58145i 0.207180i
\(490\) −1.36910 −0.0618497
\(491\) −8.93600 −0.403276 −0.201638 0.979460i \(-0.564626\pi\)
−0.201638 + 0.979460i \(0.564626\pi\)
\(492\) 3.28458i 0.148080i
\(493\) 7.20394 0.324449
\(494\) −34.9360 46.3545i −1.57184 2.08559i
\(495\) 3.60197 0.161896
\(496\) 12.7961i 0.574560i
\(497\) −4.81432 −0.215952
\(498\) −27.9649 −1.25314
\(499\) 33.9877i 1.52150i 0.649046 + 0.760750i \(0.275168\pi\)
−0.649046 + 0.760750i \(0.724832\pi\)
\(500\) 16.4124i 0.733985i
\(501\) 7.31124i 0.326642i
\(502\) 29.6742i 1.32442i
\(503\) 33.5585 1.49630 0.748149 0.663530i \(-0.230943\pi\)
0.748149 + 0.663530i \(0.230943\pi\)
\(504\) 1.53919 0.0685609
\(505\) 4.56463i 0.203123i
\(506\) −67.1338 −2.98446
\(507\) −3.58145 + 12.4969i −0.159058 + 0.555008i
\(508\) −17.1773 −0.762118
\(509\) 24.8287i 1.10051i 0.834996 + 0.550256i \(0.185470\pi\)
−0.834996 + 0.550256i \(0.814530\pi\)
\(510\) 1.47641 0.0653765
\(511\) −3.81658 −0.168836
\(512\) 22.1701i 0.979789i
\(513\) 7.41855i 0.327537i
\(514\) 56.6947i 2.50070i
\(515\) 8.68035i 0.382502i
\(516\) 34.3545 1.51237
\(517\) 34.5380 1.51898
\(518\) 7.41855i 0.325952i
\(519\) 7.60197 0.333689
\(520\) 2.10731 + 2.79606i 0.0924115 + 0.122616i
\(521\) 20.2290 0.886248 0.443124 0.896460i \(-0.353870\pi\)
0.443124 + 0.896460i \(0.353870\pi\)
\(522\) 14.4969i 0.634513i
\(523\) −40.1666 −1.75636 −0.878181 0.478328i \(-0.841243\pi\)
−0.878181 + 0.478328i \(0.841243\pi\)
\(524\) 20.3668 0.889729
\(525\) 4.60197i 0.200846i
\(526\) 66.7936i 2.91234i
\(527\) 6.63931i 0.289213i
\(528\) 11.8660i 0.516403i
\(529\) 6.36069 0.276552
\(530\) −8.21461 −0.356820
\(531\) 1.36910i 0.0594140i
\(532\) −20.0989 −0.871398
\(533\) 3.49079 2.63090i 0.151203 0.113957i
\(534\) 13.4680 0.582817
\(535\) 6.37137i 0.275458i
\(536\) −0.894960 −0.0386564
\(537\) 9.10504 0.392911
\(538\) 11.7009i 0.504460i
\(539\) 5.70928i 0.245916i
\(540\) 1.70928i 0.0735555i
\(541\) 18.2101i 0.782912i −0.920197 0.391456i \(-0.871971\pi\)
0.920197 0.391456i \(-0.128029\pi\)
\(542\) 24.7792 1.06436
\(543\) 15.3607 0.659190
\(544\) 8.18342i 0.350861i
\(545\) −11.3197 −0.484881
\(546\) 4.70928 + 6.24846i 0.201538 + 0.267410i
\(547\) −6.32580 −0.270472 −0.135236 0.990813i \(-0.543179\pi\)
−0.135236 + 0.990813i \(0.543179\pi\)
\(548\) 12.1217i 0.517813i
\(549\) 12.6537 0.540046
\(550\) −57.0166 −2.43120
\(551\) 49.5585i 2.11126i
\(552\) 8.34017i 0.354981i
\(553\) 1.65983i 0.0705830i
\(554\) 28.5380i 1.21246i
\(555\) −2.15676 −0.0915492
\(556\) 26.4391 1.12127
\(557\) 10.6309i 0.450446i −0.974307 0.225223i \(-0.927689\pi\)
0.974307 0.225223i \(-0.0723110\pi\)
\(558\) 13.3607 0.565603
\(559\) 27.5174 + 36.5113i 1.16386 + 1.54426i
\(560\) −1.31124 −0.0554102
\(561\) 6.15676i 0.259938i
\(562\) −4.66209 −0.196659
\(563\) −37.0472 −1.56135 −0.780676 0.624936i \(-0.785125\pi\)
−0.780676 + 0.624936i \(0.785125\pi\)
\(564\) 16.3896i 0.690128i
\(565\) 6.73820i 0.283478i
\(566\) 26.4703i 1.11263i
\(567\) 1.00000i 0.0419961i
\(568\) 7.41014 0.310923
\(569\) 25.7152 1.07804 0.539019 0.842293i \(-0.318795\pi\)
0.539019 + 0.842293i \(0.318795\pi\)
\(570\) 10.1568i 0.425420i
\(571\) −12.4969 −0.522980 −0.261490 0.965206i \(-0.584214\pi\)
−0.261490 + 0.965206i \(0.584214\pi\)
\(572\) 44.5380 33.5669i 1.86223 1.40350i
\(573\) −24.5692 −1.02639
\(574\) 2.63090i 0.109812i
\(575\) 24.9360 1.03990
\(576\) 12.3112 0.512968
\(577\) 3.91548i 0.163004i −0.996673 0.0815018i \(-0.974028\pi\)
0.996673 0.0815018i \(-0.0259716\pi\)
\(578\) 34.3679i 1.42952i
\(579\) 13.5753i 0.564170i
\(580\) 11.4186i 0.474130i
\(581\) −12.8865 −0.534624
\(582\) −2.34017 −0.0970033
\(583\) 34.2557i 1.41872i
\(584\) 5.87444 0.243086
\(585\) 1.81658 1.36910i 0.0751064 0.0566054i
\(586\) 15.5259 0.641367
\(587\) 6.94441i 0.286626i 0.989677 + 0.143313i \(0.0457756\pi\)
−0.989677 + 0.143313i \(0.954224\pi\)
\(588\) 2.70928 0.111729
\(589\) −45.6742 −1.88197
\(590\) 1.87444i 0.0771695i
\(591\) 2.94441i 0.121117i
\(592\) 7.10504i 0.292015i
\(593\) 29.9383i 1.22942i −0.788754 0.614709i \(-0.789274\pi\)
0.788754 0.614709i \(-0.210726\pi\)
\(594\) −12.3896 −0.508352
\(595\) 0.680346 0.0278915
\(596\) 3.97721i 0.162913i
\(597\) −10.5236 −0.430702
\(598\) −33.8576 + 25.5174i −1.38454 + 1.04349i
\(599\) 43.2905 1.76880 0.884402 0.466726i \(-0.154567\pi\)
0.884402 + 0.466726i \(0.154567\pi\)
\(600\) 7.08330i 0.289174i
\(601\) −31.2306 −1.27392 −0.636961 0.770896i \(-0.719809\pi\)
−0.636961 + 0.770896i \(0.719809\pi\)
\(602\) 27.5174 1.12153
\(603\) 0.581449i 0.0236784i
\(604\) 36.1978i 1.47287i
\(605\) 13.6248i 0.553925i
\(606\) 15.7009i 0.637804i
\(607\) 4.96266 0.201428 0.100714 0.994915i \(-0.467887\pi\)
0.100714 + 0.994915i \(0.467887\pi\)
\(608\) −56.2967 −2.28313
\(609\) 6.68035i 0.270701i
\(610\) 17.3242 0.701436
\(611\) 17.4186 13.1278i 0.704679 0.531095i
\(612\) −2.92162 −0.118100
\(613\) 0.366835i 0.0148163i −0.999973 0.00740816i \(-0.997642\pi\)
0.999973 0.00740816i \(-0.00235811\pi\)
\(614\) −47.4017 −1.91298
\(615\) −0.764867 −0.0308424
\(616\) 8.78765i 0.354065i
\(617\) 47.7237i 1.92128i −0.277793 0.960641i \(-0.589603\pi\)
0.277793 0.960641i \(-0.410397\pi\)
\(618\) 29.8576i 1.20105i
\(619\) 19.7854i 0.795242i −0.917550 0.397621i \(-0.869836\pi\)
0.917550 0.397621i \(-0.130164\pi\)
\(620\) 10.5236 0.422638
\(621\) 5.41855 0.217439
\(622\) 16.3135i 0.654112i
\(623\) 6.20620 0.248646
\(624\) 4.51026 + 5.98440i 0.180555 + 0.239568i
\(625\) 19.1880 0.767518
\(626\) 55.7731i 2.22914i
\(627\) 42.3545 1.69148
\(628\) 22.0989 0.881842
\(629\) 3.68649i 0.146990i
\(630\) 1.36910i 0.0545463i
\(631\) 20.1522i 0.802247i 0.916024 + 0.401124i \(0.131380\pi\)
−0.916024 + 0.401124i \(0.868620\pi\)
\(632\) 2.55479i 0.101624i
\(633\) −3.02052 −0.120055
\(634\) 20.3318 0.807477
\(635\) 4.00000i 0.158735i
\(636\) 16.2557 0.644579
\(637\) 2.17009 + 2.87936i 0.0859820 + 0.114084i
\(638\) −82.7670 −3.27678
\(639\) 4.81432i 0.190451i
\(640\) 7.28005 0.287769
\(641\) −12.1034 −0.478057 −0.239028 0.971013i \(-0.576829\pi\)
−0.239028 + 0.971013i \(0.576829\pi\)
\(642\) 21.9155i 0.864935i
\(643\) 20.6803i 0.815553i 0.913082 + 0.407777i \(0.133696\pi\)
−0.913082 + 0.407777i \(0.866304\pi\)
\(644\) 14.6803i 0.578487i
\(645\) 8.00000i 0.315000i
\(646\) 17.3607 0.683047
\(647\) 40.8781 1.60709 0.803543 0.595247i \(-0.202946\pi\)
0.803543 + 0.595247i \(0.202946\pi\)
\(648\) 1.53919i 0.0604650i
\(649\) −7.81658 −0.306828
\(650\) −28.7552 + 21.6719i −1.12787 + 0.850043i
\(651\) 6.15676 0.241302
\(652\) 12.4124i 0.486107i
\(653\) 6.31351 0.247067 0.123533 0.992340i \(-0.460577\pi\)
0.123533 + 0.992340i \(0.460577\pi\)
\(654\) 38.9360 1.52252
\(655\) 4.74274i 0.185314i
\(656\) 2.51971i 0.0983783i
\(657\) 3.81658i 0.148899i
\(658\) 13.1278i 0.511776i
\(659\) −20.9360 −0.815551 −0.407775 0.913082i \(-0.633695\pi\)
−0.407775 + 0.913082i \(0.633695\pi\)
\(660\) −9.75872 −0.379858
\(661\) 22.2245i 0.864431i 0.901770 + 0.432216i \(0.142268\pi\)
−0.901770 + 0.432216i \(0.857732\pi\)
\(662\) 45.6742 1.77518
\(663\) −2.34017 3.10504i −0.0908848 0.120590i
\(664\) 19.8348 0.769741
\(665\) 4.68035i 0.181496i
\(666\) 7.41855 0.287463
\(667\) 36.1978 1.40158
\(668\) 19.8082i 0.766401i
\(669\) 22.6225i 0.874636i
\(670\) 0.796064i 0.0307546i
\(671\) 72.2434i 2.78892i
\(672\) 7.58864 0.292738
\(673\) −1.15061 −0.0443528 −0.0221764 0.999754i \(-0.507060\pi\)
−0.0221764 + 0.999754i \(0.507060\pi\)
\(674\) 33.5174i 1.29104i
\(675\) 4.60197 0.177130
\(676\) 9.70313 33.8576i 0.373197 1.30222i
\(677\) −33.5897 −1.29096 −0.645478 0.763779i \(-0.723342\pi\)
−0.645478 + 0.763779i \(0.723342\pi\)
\(678\) 23.1773i 0.890118i
\(679\) −1.07838 −0.0413843
\(680\) −1.04718 −0.0401576
\(681\) 22.9444i 0.879232i
\(682\) 76.2799i 2.92091i
\(683\) 25.1110i 0.960846i −0.877037 0.480423i \(-0.840483\pi\)
0.877037 0.480423i \(-0.159517\pi\)
\(684\) 20.0989i 0.768501i
\(685\) 2.82273 0.107851
\(686\) 2.17009 0.0828543
\(687\) 21.5441i 0.821959i
\(688\) 26.3545 1.00476
\(689\) 13.0205 + 17.2762i 0.496042 + 0.658170i
\(690\) 7.41855 0.282419
\(691\) 6.30898i 0.240005i −0.992774 0.120002i \(-0.961710\pi\)
0.992774 0.120002i \(-0.0382902\pi\)
\(692\) −20.5958 −0.782936
\(693\) −5.70928 −0.216877
\(694\) 47.1605i 1.79019i
\(695\) 6.15676i 0.233539i
\(696\) 10.2823i 0.389750i
\(697\) 1.30737i 0.0495201i
\(698\) −12.2823 −0.464892
\(699\) 7.36069 0.278407
\(700\) 12.4680i 0.471246i
\(701\) 45.8843 1.73303 0.866513 0.499155i \(-0.166356\pi\)
0.866513 + 0.499155i \(0.166356\pi\)
\(702\) −6.24846 + 4.70928i −0.235833 + 0.177740i
\(703\) −25.3607 −0.956497
\(704\) 70.2883i 2.64909i
\(705\) −3.81658 −0.143741
\(706\) 73.1832 2.75429
\(707\) 7.23513i 0.272105i
\(708\) 3.70928i 0.139403i
\(709\) 46.4534i 1.74460i 0.488975 + 0.872298i \(0.337371\pi\)
−0.488975 + 0.872298i \(0.662629\pi\)
\(710\) 6.59129i 0.247367i
\(711\) −1.65983 −0.0622484
\(712\) −9.55252 −0.357996
\(713\) 33.3607i 1.24937i
\(714\) −2.34017 −0.0875788
\(715\) −7.81658 10.3714i −0.292324 0.387867i
\(716\) −24.6681 −0.921889
\(717\) 15.5525i 0.580819i
\(718\) −40.5874 −1.51471
\(719\) −7.20394 −0.268661 −0.134331 0.990937i \(-0.542888\pi\)
−0.134331 + 0.990937i \(0.542888\pi\)
\(720\) 1.31124i 0.0488672i
\(721\) 13.7587i 0.512402i
\(722\) 78.1988i 2.91026i
\(723\) 7.33403i 0.272756i
\(724\) −41.6163 −1.54666
\(725\) 30.7427 1.14176
\(726\) 46.8648i 1.73932i
\(727\) 13.6742 0.507148 0.253574 0.967316i \(-0.418394\pi\)
0.253574 + 0.967316i \(0.418394\pi\)
\(728\) −3.34017 4.43188i −0.123795 0.164256i
\(729\) 1.00000 0.0370370
\(730\) 5.22529i 0.193397i
\(731\) −13.6742 −0.505759
\(732\) −34.2823 −1.26711
\(733\) 7.70086i 0.284438i −0.989835 0.142219i \(-0.954576\pi\)
0.989835 0.142219i \(-0.0454237\pi\)
\(734\) 21.8576i 0.806779i
\(735\) 0.630898i 0.0232710i
\(736\) 41.1194i 1.51568i
\(737\) 3.31965 0.122281
\(738\) 2.63090 0.0968447
\(739\) 24.5814i 0.904243i 0.891956 + 0.452122i \(0.149333\pi\)
−0.891956 + 0.452122i \(0.850667\pi\)
\(740\) 5.84324 0.214802
\(741\) 21.3607 16.0989i 0.784705 0.591408i
\(742\) 13.0205 0.477998
\(743\) 24.3773i 0.894318i 0.894455 + 0.447159i \(0.147564\pi\)
−0.894455 + 0.447159i \(0.852436\pi\)
\(744\) −9.47641 −0.347422
\(745\) −0.926157 −0.0339318
\(746\) 9.20394i 0.336980i
\(747\) 12.8865i 0.471494i
\(748\) 16.6803i 0.609894i
\(749\) 10.0989i 0.369006i
\(750\) 13.1461 0.480027
\(751\) −24.6803 −0.900599 −0.450299 0.892878i \(-0.648683\pi\)
−0.450299 + 0.892878i \(0.648683\pi\)
\(752\) 12.5730i 0.458492i
\(753\) −13.6742 −0.498316
\(754\) −41.7419 + 31.4596i −1.52015 + 1.14569i
\(755\) 8.42923 0.306771
\(756\) 2.70928i 0.0985354i
\(757\) −41.3172 −1.50170 −0.750850 0.660473i \(-0.770356\pi\)
−0.750850 + 0.660473i \(0.770356\pi\)
\(758\) −43.8310 −1.59201
\(759\) 30.9360i 1.12291i
\(760\) 7.20394i 0.261314i
\(761\) 15.9506i 0.578207i 0.957298 + 0.289104i \(0.0933572\pi\)
−0.957298 + 0.289104i \(0.906643\pi\)
\(762\) 13.7587i 0.498426i
\(763\) 17.9421 0.649549
\(764\) 66.5646 2.40822
\(765\) 0.680346i 0.0245980i
\(766\) 15.2846 0.552254
\(767\) −3.94214 + 2.97107i −0.142342 + 0.107279i
\(768\) −0.418551 −0.0151031
\(769\) 6.22446i 0.224460i −0.993682 0.112230i \(-0.964201\pi\)
0.993682 0.112230i \(-0.0357993\pi\)
\(770\) −7.81658 −0.281690
\(771\) −26.1256 −0.940889
\(772\) 36.7792i 1.32371i
\(773\) 39.1545i 1.40829i −0.710057 0.704145i \(-0.751331\pi\)
0.710057 0.704145i \(-0.248669\pi\)
\(774\) 27.5174i 0.989094i
\(775\) 28.3332i 1.01776i
\(776\) 1.65983 0.0595843
\(777\) 3.41855 0.122640
\(778\) 8.34017i 0.299010i
\(779\) −8.99386 −0.322238
\(780\) −4.92162 + 3.70928i −0.176222 + 0.132813i
\(781\) −27.4863 −0.983535
\(782\) 12.6803i 0.453448i
\(783\) 6.68035 0.238736
\(784\) 2.07838 0.0742278
\(785\)