Properties

Label 165.2.c.a.34.2
Level $165$
Weight $2$
Character 165.34
Analytic conductor $1.318$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [165,2,Mod(34,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.34");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.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: \(1.31753163335\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 34.2
Root \(-0.854638 + 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 165.34
Dual form 165.2.c.a.34.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.53919i q^{2} -1.00000i q^{3} -0.369102 q^{4} +(2.17009 + 0.539189i) q^{5} -1.53919 q^{6} -0.290725i q^{7} -2.51026i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.53919i q^{2} -1.00000i q^{3} -0.369102 q^{4} +(2.17009 + 0.539189i) q^{5} -1.53919 q^{6} -0.290725i q^{7} -2.51026i q^{8} -1.00000 q^{9} +(0.829914 - 3.34017i) q^{10} -1.00000 q^{11} +0.369102i q^{12} +6.97107i q^{13} -0.447480 q^{14} +(0.539189 - 2.17009i) q^{15} -4.60197 q^{16} -4.78765i q^{17} +1.53919i q^{18} -7.75872 q^{19} +(-0.800984 - 0.199016i) q^{20} -0.290725 q^{21} +1.53919i q^{22} +4.00000i q^{23} -2.51026 q^{24} +(4.41855 + 2.34017i) q^{25} +10.7298 q^{26} +1.00000i q^{27} +0.107307i q^{28} +7.41855 q^{29} +(-3.34017 - 0.829914i) q^{30} +6.34017 q^{31} +2.06278i q^{32} +1.00000i q^{33} -7.36910 q^{34} +(0.156755 - 0.630898i) q^{35} +0.369102 q^{36} +3.41855i q^{37} +11.9421i q^{38} +6.97107 q^{39} +(1.35350 - 5.44748i) q^{40} -7.41855 q^{41} +0.447480i q^{42} +0.290725i q^{43} +0.369102 q^{44} +(-2.17009 - 0.539189i) q^{45} +6.15676 q^{46} -5.26180i q^{47} +4.60197i q^{48} +6.91548 q^{49} +(3.60197 - 6.80098i) q^{50} -4.78765 q^{51} -2.57304i q^{52} +5.75872i q^{53} +1.53919 q^{54} +(-2.17009 - 0.539189i) q^{55} -0.729794 q^{56} +7.75872i q^{57} -11.4186i q^{58} -3.60197 q^{59} +(-0.199016 + 0.800984i) q^{60} -6.68035 q^{61} -9.75872i q^{62} +0.290725i q^{63} -6.02893 q^{64} +(-3.75872 + 15.1278i) q^{65} +1.53919 q^{66} -6.15676i q^{67} +1.76713i q^{68} +4.00000 q^{69} +(-0.971071 - 0.241276i) q^{70} -5.07838 q^{71} +2.51026i q^{72} -1.12783i q^{73} +5.26180 q^{74} +(2.34017 - 4.41855i) q^{75} +2.86376 q^{76} +0.290725i q^{77} -10.7298i q^{78} +0.921622 q^{79} +(-9.98667 - 2.48133i) q^{80} +1.00000 q^{81} +11.4186i q^{82} +1.70928i q^{83} +0.107307 q^{84} +(2.58145 - 10.3896i) q^{85} +0.447480 q^{86} -7.41855i q^{87} +2.51026i q^{88} -4.34017 q^{89} +(-0.829914 + 3.34017i) q^{90} +2.02666 q^{91} -1.47641i q^{92} -6.34017i q^{93} -8.09890 q^{94} +(-16.8371 - 4.18342i) q^{95} +2.06278 q^{96} -4.68035i q^{97} -10.6442i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 10 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 10 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 16 q^{10} - 6 q^{11} - 4 q^{14} + 10 q^{16} + 4 q^{19} + 14 q^{20} - 16 q^{21} + 18 q^{24} - 2 q^{25} - 16 q^{26} + 16 q^{29} + 2 q^{30} + 16 q^{31} - 52 q^{34} - 12 q^{35} + 10 q^{36} + 12 q^{39} - 12 q^{40} - 16 q^{41} + 10 q^{44} - 2 q^{45} + 24 q^{46} - 22 q^{49} - 16 q^{50} - 8 q^{51} + 6 q^{54} - 2 q^{55} + 76 q^{56} + 16 q^{59} - 20 q^{60} + 4 q^{61} - 66 q^{64} + 28 q^{65} + 6 q^{66} + 24 q^{69} + 24 q^{70} - 24 q^{71} + 16 q^{74} - 8 q^{75} - 36 q^{76} + 12 q^{79} - 58 q^{80} + 6 q^{81} + 24 q^{84} + 44 q^{85} + 4 q^{86} - 4 q^{89} - 16 q^{90} + 16 q^{91} + 24 q^{94} - 44 q^{95} - 22 q^{96} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.53919i 1.08837i −0.838965 0.544185i \(-0.816839\pi\)
0.838965 0.544185i \(-0.183161\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −0.369102 −0.184551
\(5\) 2.17009 + 0.539189i 0.970492 + 0.241133i
\(6\) −1.53919 −0.628371
\(7\) 0.290725i 0.109884i −0.998490 0.0549418i \(-0.982503\pi\)
0.998490 0.0549418i \(-0.0174973\pi\)
\(8\) 2.51026i 0.887511i
\(9\) −1.00000 −0.333333
\(10\) 0.829914 3.34017i 0.262442 1.05626i
\(11\) −1.00000 −0.301511
\(12\) 0.369102i 0.106551i
\(13\) 6.97107i 1.93343i 0.255861 + 0.966714i \(0.417641\pi\)
−0.255861 + 0.966714i \(0.582359\pi\)
\(14\) −0.447480 −0.119594
\(15\) 0.539189 2.17009i 0.139218 0.560314i
\(16\) −4.60197 −1.15049
\(17\) 4.78765i 1.16118i −0.814197 0.580588i \(-0.802823\pi\)
0.814197 0.580588i \(-0.197177\pi\)
\(18\) 1.53919i 0.362790i
\(19\) −7.75872 −1.77997 −0.889987 0.455987i \(-0.849286\pi\)
−0.889987 + 0.455987i \(0.849286\pi\)
\(20\) −0.800984 0.199016i −0.179105 0.0445013i
\(21\) −0.290725 −0.0634413
\(22\) 1.53919i 0.328156i
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) −2.51026 −0.512405
\(25\) 4.41855 + 2.34017i 0.883710 + 0.468035i
\(26\) 10.7298 2.10429
\(27\) 1.00000i 0.192450i
\(28\) 0.107307i 0.0202791i
\(29\) 7.41855 1.37759 0.688795 0.724956i \(-0.258140\pi\)
0.688795 + 0.724956i \(0.258140\pi\)
\(30\) −3.34017 0.829914i −0.609829 0.151521i
\(31\) 6.34017 1.13873 0.569364 0.822085i \(-0.307189\pi\)
0.569364 + 0.822085i \(0.307189\pi\)
\(32\) 2.06278i 0.364651i
\(33\) 1.00000i 0.174078i
\(34\) −7.36910 −1.26379
\(35\) 0.156755 0.630898i 0.0264965 0.106641i
\(36\) 0.369102 0.0615171
\(37\) 3.41855i 0.562006i 0.959707 + 0.281003i \(0.0906671\pi\)
−0.959707 + 0.281003i \(0.909333\pi\)
\(38\) 11.9421i 1.93727i
\(39\) 6.97107 1.11626
\(40\) 1.35350 5.44748i 0.214008 0.861322i
\(41\) −7.41855 −1.15858 −0.579291 0.815120i \(-0.696671\pi\)
−0.579291 + 0.815120i \(0.696671\pi\)
\(42\) 0.447480i 0.0690477i
\(43\) 0.290725i 0.0443351i 0.999754 + 0.0221675i \(0.00705673\pi\)
−0.999754 + 0.0221675i \(0.992943\pi\)
\(44\) 0.369102 0.0556443
\(45\) −2.17009 0.539189i −0.323497 0.0803775i
\(46\) 6.15676 0.907764
\(47\) 5.26180i 0.767512i −0.923435 0.383756i \(-0.874630\pi\)
0.923435 0.383756i \(-0.125370\pi\)
\(48\) 4.60197i 0.664237i
\(49\) 6.91548 0.987926
\(50\) 3.60197 6.80098i 0.509395 0.961804i
\(51\) −4.78765 −0.670406
\(52\) 2.57304i 0.356816i
\(53\) 5.75872i 0.791022i 0.918461 + 0.395511i \(0.129432\pi\)
−0.918461 + 0.395511i \(0.870568\pi\)
\(54\) 1.53919 0.209457
\(55\) −2.17009 0.539189i −0.292614 0.0727042i
\(56\) −0.729794 −0.0975229
\(57\) 7.75872i 1.02767i
\(58\) 11.4186i 1.49933i
\(59\) −3.60197 −0.468936 −0.234468 0.972124i \(-0.575335\pi\)
−0.234468 + 0.972124i \(0.575335\pi\)
\(60\) −0.199016 + 0.800984i −0.0256928 + 0.103407i
\(61\) −6.68035 −0.855331 −0.427665 0.903937i \(-0.640664\pi\)
−0.427665 + 0.903937i \(0.640664\pi\)
\(62\) 9.75872i 1.23936i
\(63\) 0.290725i 0.0366279i
\(64\) −6.02893 −0.753616
\(65\) −3.75872 + 15.1278i −0.466212 + 1.87638i
\(66\) 1.53919 0.189461
\(67\) 6.15676i 0.752167i −0.926586 0.376084i \(-0.877271\pi\)
0.926586 0.376084i \(-0.122729\pi\)
\(68\) 1.76713i 0.214296i
\(69\) 4.00000 0.481543
\(70\) −0.971071 0.241276i −0.116065 0.0288380i
\(71\) −5.07838 −0.602693 −0.301346 0.953515i \(-0.597436\pi\)
−0.301346 + 0.953515i \(0.597436\pi\)
\(72\) 2.51026i 0.295837i
\(73\) 1.12783i 0.132002i −0.997820 0.0660010i \(-0.978976\pi\)
0.997820 0.0660010i \(-0.0210241\pi\)
\(74\) 5.26180 0.611671
\(75\) 2.34017 4.41855i 0.270220 0.510210i
\(76\) 2.86376 0.328496
\(77\) 0.290725i 0.0331311i
\(78\) 10.7298i 1.21491i
\(79\) 0.921622 0.103691 0.0518453 0.998655i \(-0.483490\pi\)
0.0518453 + 0.998655i \(0.483490\pi\)
\(80\) −9.98667 2.48133i −1.11654 0.277421i
\(81\) 1.00000 0.111111
\(82\) 11.4186i 1.26097i
\(83\) 1.70928i 0.187617i 0.995590 + 0.0938087i \(0.0299042\pi\)
−0.995590 + 0.0938087i \(0.970096\pi\)
\(84\) 0.107307 0.0117082
\(85\) 2.58145 10.3896i 0.279997 1.12691i
\(86\) 0.447480 0.0482530
\(87\) 7.41855i 0.795352i
\(88\) 2.51026i 0.267595i
\(89\) −4.34017 −0.460057 −0.230029 0.973184i \(-0.573882\pi\)
−0.230029 + 0.973184i \(0.573882\pi\)
\(90\) −0.829914 + 3.34017i −0.0874806 + 0.352085i
\(91\) 2.02666 0.212452
\(92\) 1.47641i 0.153926i
\(93\) 6.34017i 0.657445i
\(94\) −8.09890 −0.835337
\(95\) −16.8371 4.18342i −1.72745 0.429210i
\(96\) 2.06278 0.210532
\(97\) 4.68035i 0.475217i −0.971361 0.237609i \(-0.923636\pi\)
0.971361 0.237609i \(-0.0763635\pi\)
\(98\) 10.6442i 1.07523i
\(99\) 1.00000 0.100504
\(100\) −1.63090 0.863763i −0.163090 0.0863763i
\(101\) −8.58145 −0.853886 −0.426943 0.904279i \(-0.640410\pi\)
−0.426943 + 0.904279i \(0.640410\pi\)
\(102\) 7.36910i 0.729650i
\(103\) 6.73820i 0.663935i 0.943291 + 0.331968i \(0.107712\pi\)
−0.943291 + 0.331968i \(0.892288\pi\)
\(104\) 17.4992 1.71594
\(105\) −0.630898 0.156755i −0.0615693 0.0152978i
\(106\) 8.86376 0.860925
\(107\) 12.2329i 1.18260i −0.806453 0.591298i \(-0.798616\pi\)
0.806453 0.591298i \(-0.201384\pi\)
\(108\) 0.369102i 0.0355169i
\(109\) 6.31351 0.604725 0.302362 0.953193i \(-0.402225\pi\)
0.302362 + 0.953193i \(0.402225\pi\)
\(110\) −0.829914 + 3.34017i −0.0791291 + 0.318473i
\(111\) 3.41855 0.324474
\(112\) 1.33791i 0.126420i
\(113\) 16.4969i 1.55190i −0.630794 0.775950i \(-0.717271\pi\)
0.630794 0.775950i \(-0.282729\pi\)
\(114\) 11.9421 1.11848
\(115\) −2.15676 + 8.68035i −0.201118 + 0.809446i
\(116\) −2.73820 −0.254236
\(117\) 6.97107i 0.644476i
\(118\) 5.54411i 0.510377i
\(119\) −1.39189 −0.127594
\(120\) −5.44748 1.35350i −0.497285 0.123557i
\(121\) 1.00000 0.0909091
\(122\) 10.2823i 0.930917i
\(123\) 7.41855i 0.668908i
\(124\) −2.34017 −0.210154
\(125\) 8.32684 + 7.46081i 0.744775 + 0.667315i
\(126\) 0.447480 0.0398647
\(127\) 4.87217i 0.432336i −0.976356 0.216168i \(-0.930644\pi\)
0.976356 0.216168i \(-0.0693558\pi\)
\(128\) 13.4052i 1.18487i
\(129\) 0.290725 0.0255969
\(130\) 23.2846 + 5.78539i 2.04219 + 0.507412i
\(131\) −8.68035 −0.758405 −0.379203 0.925314i \(-0.623802\pi\)
−0.379203 + 0.925314i \(0.623802\pi\)
\(132\) 0.369102i 0.0321262i
\(133\) 2.25565i 0.195590i
\(134\) −9.47641 −0.818637
\(135\) −0.539189 + 2.17009i −0.0464060 + 0.186771i
\(136\) −12.0183 −1.03056
\(137\) 12.5958i 1.07613i 0.842902 + 0.538067i \(0.180845\pi\)
−0.842902 + 0.538067i \(0.819155\pi\)
\(138\) 6.15676i 0.524098i
\(139\) 9.91548 0.841020 0.420510 0.907288i \(-0.361851\pi\)
0.420510 + 0.907288i \(0.361851\pi\)
\(140\) −0.0578588 + 0.232866i −0.00488996 + 0.0196808i
\(141\) −5.26180 −0.443123
\(142\) 7.81658i 0.655953i
\(143\) 6.97107i 0.582950i
\(144\) 4.60197 0.383497
\(145\) 16.0989 + 4.00000i 1.33694 + 0.332182i
\(146\) −1.73594 −0.143667
\(147\) 6.91548i 0.570379i
\(148\) 1.26180i 0.103719i
\(149\) 1.26180 0.103370 0.0516851 0.998663i \(-0.483541\pi\)
0.0516851 + 0.998663i \(0.483541\pi\)
\(150\) −6.80098 3.60197i −0.555298 0.294099i
\(151\) 1.60197 0.130366 0.0651832 0.997873i \(-0.479237\pi\)
0.0651832 + 0.997873i \(0.479237\pi\)
\(152\) 19.4764i 1.57975i
\(153\) 4.78765i 0.387059i
\(154\) 0.447480 0.0360590
\(155\) 13.7587 + 3.41855i 1.10513 + 0.274585i
\(156\) −2.57304 −0.206008
\(157\) 7.10504i 0.567044i 0.958966 + 0.283522i \(0.0915029\pi\)
−0.958966 + 0.283522i \(0.908497\pi\)
\(158\) 1.41855i 0.112854i
\(159\) 5.75872 0.456696
\(160\) −1.11223 + 4.47641i −0.0879293 + 0.353891i
\(161\) 1.16290 0.0916492
\(162\) 1.53919i 0.120930i
\(163\) 22.9360i 1.79649i −0.439499 0.898243i \(-0.644844\pi\)
0.439499 0.898243i \(-0.355156\pi\)
\(164\) 2.73820 0.213818
\(165\) −0.539189 + 2.17009i −0.0419758 + 0.168941i
\(166\) 2.63090 0.204197
\(167\) 4.81432i 0.372543i −0.982498 0.186271i \(-0.940360\pi\)
0.982498 0.186271i \(-0.0596404\pi\)
\(168\) 0.729794i 0.0563049i
\(169\) −35.5958 −2.73814
\(170\) −15.9916 3.97334i −1.22650 0.304741i
\(171\) 7.75872 0.593324
\(172\) 0.107307i 0.00818209i
\(173\) 12.8865i 0.979746i −0.871794 0.489873i \(-0.837043\pi\)
0.871794 0.489873i \(-0.162957\pi\)
\(174\) −11.4186 −0.865638
\(175\) 0.680346 1.28458i 0.0514293 0.0971052i
\(176\) 4.60197 0.346886
\(177\) 3.60197i 0.270741i
\(178\) 6.68035i 0.500713i
\(179\) −1.84324 −0.137771 −0.0688853 0.997625i \(-0.521944\pi\)
−0.0688853 + 0.997625i \(0.521944\pi\)
\(180\) 0.800984 + 0.199016i 0.0597018 + 0.0148338i
\(181\) 10.2823 0.764278 0.382139 0.924105i \(-0.375187\pi\)
0.382139 + 0.924105i \(0.375187\pi\)
\(182\) 3.11942i 0.231226i
\(183\) 6.68035i 0.493825i
\(184\) 10.0410 0.740235
\(185\) −1.84324 + 7.41855i −0.135518 + 0.545423i
\(186\) −9.75872 −0.715544
\(187\) 4.78765i 0.350108i
\(188\) 1.94214i 0.141645i
\(189\) 0.290725 0.0211471
\(190\) −6.43907 + 25.9155i −0.467139 + 1.88011i
\(191\) −11.5174 −0.833373 −0.416687 0.909050i \(-0.636809\pi\)
−0.416687 + 0.909050i \(0.636809\pi\)
\(192\) 6.02893i 0.435101i
\(193\) 3.86603i 0.278283i 0.990273 + 0.139141i \(0.0444343\pi\)
−0.990273 + 0.139141i \(0.955566\pi\)
\(194\) −7.20394 −0.517212
\(195\) 15.1278 + 3.75872i 1.08333 + 0.269168i
\(196\) −2.55252 −0.182323
\(197\) 8.57304i 0.610804i 0.952224 + 0.305402i \(0.0987908\pi\)
−0.952224 + 0.305402i \(0.901209\pi\)
\(198\) 1.53919i 0.109385i
\(199\) −8.31351 −0.589329 −0.294665 0.955601i \(-0.595208\pi\)
−0.294665 + 0.955601i \(0.595208\pi\)
\(200\) 5.87444 11.0917i 0.415386 0.784302i
\(201\) −6.15676 −0.434264
\(202\) 13.2085i 0.929345i
\(203\) 2.15676i 0.151375i
\(204\) 1.76713 0.123724
\(205\) −16.0989 4.00000i −1.12440 0.279372i
\(206\) 10.3714 0.722608
\(207\) 4.00000i 0.278019i
\(208\) 32.0806i 2.22439i
\(209\) 7.75872 0.536682
\(210\) −0.241276 + 0.971071i −0.0166496 + 0.0670102i
\(211\) 25.9155 1.78410 0.892048 0.451941i \(-0.149268\pi\)
0.892048 + 0.451941i \(0.149268\pi\)
\(212\) 2.12556i 0.145984i
\(213\) 5.07838i 0.347965i
\(214\) −18.8287 −1.28710
\(215\) −0.156755 + 0.630898i −0.0106906 + 0.0430269i
\(216\) 2.51026 0.170802
\(217\) 1.84324i 0.125128i
\(218\) 9.71769i 0.658165i
\(219\) −1.12783 −0.0762114
\(220\) 0.800984 + 0.199016i 0.0540023 + 0.0134176i
\(221\) 33.3751 2.24505
\(222\) 5.26180i 0.353149i
\(223\) 9.62863i 0.644781i −0.946607 0.322390i \(-0.895514\pi\)
0.946607 0.322390i \(-0.104486\pi\)
\(224\) 0.599701 0.0400692
\(225\) −4.41855 2.34017i −0.294570 0.156012i
\(226\) −25.3919 −1.68904
\(227\) 18.3896i 1.22056i 0.792185 + 0.610281i \(0.208943\pi\)
−0.792185 + 0.610281i \(0.791057\pi\)
\(228\) 2.86376i 0.189657i
\(229\) −17.1506 −1.13334 −0.566672 0.823943i \(-0.691769\pi\)
−0.566672 + 0.823943i \(0.691769\pi\)
\(230\) 13.3607 + 3.31965i 0.880978 + 0.218892i
\(231\) 0.290725 0.0191283
\(232\) 18.6225i 1.22263i
\(233\) 4.10731i 0.269079i −0.990908 0.134539i \(-0.957045\pi\)
0.990908 0.134539i \(-0.0429555\pi\)
\(234\) −10.7298 −0.701429
\(235\) 2.83710 11.4186i 0.185072 0.744864i
\(236\) 1.32950 0.0865428
\(237\) 0.921622i 0.0598658i
\(238\) 2.14238i 0.138870i
\(239\) 4.36683 0.282467 0.141234 0.989976i \(-0.454893\pi\)
0.141234 + 0.989976i \(0.454893\pi\)
\(240\) −2.48133 + 9.98667i −0.160169 + 0.644637i
\(241\) −5.20394 −0.335215 −0.167608 0.985854i \(-0.553604\pi\)
−0.167608 + 0.985854i \(0.553604\pi\)
\(242\) 1.53919i 0.0989428i
\(243\) 1.00000i 0.0641500i
\(244\) 2.46573 0.157852
\(245\) 15.0072 + 3.72875i 0.958774 + 0.238221i
\(246\) 11.4186 0.728020
\(247\) 54.0866i 3.44145i
\(248\) 15.9155i 1.01063i
\(249\) 1.70928 0.108321
\(250\) 11.4836 12.8166i 0.726286 0.810592i
\(251\) −8.28231 −0.522775 −0.261388 0.965234i \(-0.584180\pi\)
−0.261388 + 0.965234i \(0.584180\pi\)
\(252\) 0.107307i 0.00675972i
\(253\) 4.00000i 0.251478i
\(254\) −7.49920 −0.470541
\(255\) −10.3896 2.58145i −0.650623 0.161657i
\(256\) 8.57531 0.535957
\(257\) 11.0205i 0.687441i −0.939072 0.343721i \(-0.888313\pi\)
0.939072 0.343721i \(-0.111687\pi\)
\(258\) 0.447480i 0.0278589i
\(259\) 0.993857 0.0617553
\(260\) 1.38735 5.58372i 0.0860400 0.346287i
\(261\) −7.41855 −0.459197
\(262\) 13.3607i 0.825426i
\(263\) 2.97107i 0.183204i −0.995796 0.0916020i \(-0.970801\pi\)
0.995796 0.0916020i \(-0.0291988\pi\)
\(264\) 2.51026 0.154496
\(265\) −3.10504 + 12.4969i −0.190741 + 0.767680i
\(266\) 3.47187 0.212874
\(267\) 4.34017i 0.265614i
\(268\) 2.27247i 0.138813i
\(269\) 15.8432 0.965980 0.482990 0.875626i \(-0.339551\pi\)
0.482990 + 0.875626i \(0.339551\pi\)
\(270\) 3.34017 + 0.829914i 0.203276 + 0.0505069i
\(271\) −6.28231 −0.381623 −0.190812 0.981627i \(-0.561112\pi\)
−0.190812 + 0.981627i \(0.561112\pi\)
\(272\) 22.0326i 1.33592i
\(273\) 2.02666i 0.122659i
\(274\) 19.3874 1.17123
\(275\) −4.41855 2.34017i −0.266449 0.141118i
\(276\) −1.47641 −0.0888694
\(277\) 5.12783i 0.308101i −0.988063 0.154051i \(-0.950768\pi\)
0.988063 0.154051i \(-0.0492319\pi\)
\(278\) 15.2618i 0.915342i
\(279\) −6.34017 −0.379576
\(280\) −1.58372 0.393497i −0.0946452 0.0235159i
\(281\) 21.8888 1.30578 0.652889 0.757454i \(-0.273557\pi\)
0.652889 + 0.757454i \(0.273557\pi\)
\(282\) 8.09890i 0.482282i
\(283\) 25.9649i 1.54345i 0.635954 + 0.771727i \(0.280607\pi\)
−0.635954 + 0.771727i \(0.719393\pi\)
\(284\) 1.87444 0.111228
\(285\) −4.18342 + 16.8371i −0.247804 + 0.997344i
\(286\) −10.7298 −0.634466
\(287\) 2.15676i 0.127309i
\(288\) 2.06278i 0.121550i
\(289\) −5.92162 −0.348331
\(290\) 6.15676 24.7792i 0.361537 1.45509i
\(291\) −4.68035 −0.274367
\(292\) 0.416283i 0.0243611i
\(293\) 10.4163i 0.608526i 0.952588 + 0.304263i \(0.0984101\pi\)
−0.952588 + 0.304263i \(0.901590\pi\)
\(294\) −10.6442 −0.620784
\(295\) −7.81658 1.94214i −0.455099 0.113076i
\(296\) 8.58145 0.498787
\(297\) 1.00000i 0.0580259i
\(298\) 1.94214i 0.112505i
\(299\) −27.8843 −1.61259
\(300\) −0.863763 + 1.63090i −0.0498694 + 0.0941599i
\(301\) 0.0845208 0.00487170
\(302\) 2.46573i 0.141887i
\(303\) 8.58145i 0.492991i
\(304\) 35.7054 2.04785
\(305\) −14.4969 3.60197i −0.830092 0.206248i
\(306\) 7.36910 0.421264
\(307\) 29.0700i 1.65911i 0.558425 + 0.829555i \(0.311406\pi\)
−0.558425 + 0.829555i \(0.688594\pi\)
\(308\) 0.107307i 0.00611439i
\(309\) 6.73820 0.383323
\(310\) 5.26180 21.1773i 0.298850 1.20279i
\(311\) 5.44521 0.308770 0.154385 0.988011i \(-0.450660\pi\)
0.154385 + 0.988011i \(0.450660\pi\)
\(312\) 17.4992i 0.990697i
\(313\) 25.0928i 1.41833i 0.705044 + 0.709163i \(0.250927\pi\)
−0.705044 + 0.709163i \(0.749073\pi\)
\(314\) 10.9360 0.617154
\(315\) −0.156755 + 0.630898i −0.00883217 + 0.0355471i
\(316\) −0.340173 −0.0191362
\(317\) 21.1773i 1.18943i −0.803935 0.594717i \(-0.797264\pi\)
0.803935 0.594717i \(-0.202736\pi\)
\(318\) 8.86376i 0.497055i
\(319\) −7.41855 −0.415359
\(320\) −13.0833 3.25073i −0.731379 0.181721i
\(321\) −12.2329 −0.682772
\(322\) 1.78992i 0.0997484i
\(323\) 37.1461i 2.06686i
\(324\) −0.369102 −0.0205057
\(325\) −16.3135 + 30.8020i −0.904911 + 1.70859i
\(326\) −35.3028 −1.95524
\(327\) 6.31351i 0.349138i
\(328\) 18.6225i 1.02825i
\(329\) −1.52973 −0.0843369
\(330\) 3.34017 + 0.829914i 0.183870 + 0.0456852i
\(331\) −6.70701 −0.368650 −0.184325 0.982865i \(-0.559010\pi\)
−0.184325 + 0.982865i \(0.559010\pi\)
\(332\) 0.630898i 0.0346250i
\(333\) 3.41855i 0.187335i
\(334\) −7.41014 −0.405465
\(335\) 3.31965 13.3607i 0.181372 0.729973i
\(336\) 1.33791 0.0729887
\(337\) 23.7503i 1.29376i −0.762591 0.646881i \(-0.776073\pi\)
0.762591 0.646881i \(-0.223927\pi\)
\(338\) 54.7887i 2.98011i
\(339\) −16.4969 −0.895990
\(340\) −0.952819 + 3.83483i −0.0516739 + 0.207973i
\(341\) −6.34017 −0.343340
\(342\) 11.9421i 0.645757i
\(343\) 4.04557i 0.218440i
\(344\) 0.729794 0.0393479
\(345\) 8.68035 + 2.15676i 0.467334 + 0.116116i
\(346\) −19.8348 −1.06633
\(347\) 31.1689i 1.67323i 0.547790 + 0.836616i \(0.315469\pi\)
−0.547790 + 0.836616i \(0.684531\pi\)
\(348\) 2.73820i 0.146783i
\(349\) −11.0472 −0.591342 −0.295671 0.955290i \(-0.595543\pi\)
−0.295671 + 0.955290i \(0.595543\pi\)
\(350\) −1.97721 1.04718i −0.105687 0.0559742i
\(351\) −6.97107 −0.372088
\(352\) 2.06278i 0.109947i
\(353\) 27.4329i 1.46011i −0.683390 0.730054i \(-0.739495\pi\)
0.683390 0.730054i \(-0.260505\pi\)
\(354\) 5.54411 0.294666
\(355\) −11.0205 2.73820i −0.584908 0.145329i
\(356\) 1.60197 0.0849041
\(357\) 1.39189i 0.0736666i
\(358\) 2.83710i 0.149945i
\(359\) 19.1506 1.01073 0.505365 0.862905i \(-0.331358\pi\)
0.505365 + 0.862905i \(0.331358\pi\)
\(360\) −1.35350 + 5.44748i −0.0713359 + 0.287107i
\(361\) 41.1978 2.16830
\(362\) 15.8264i 0.831818i
\(363\) 1.00000i 0.0524864i
\(364\) −0.748046 −0.0392083
\(365\) 0.608111 2.44748i 0.0318300 0.128107i
\(366\) 10.2823 0.537465
\(367\) 14.5692i 0.760504i 0.924883 + 0.380252i \(0.124163\pi\)
−0.924883 + 0.380252i \(0.875837\pi\)
\(368\) 18.4079i 0.959577i
\(369\) 7.41855 0.386194
\(370\) 11.4186 + 2.83710i 0.593622 + 0.147494i
\(371\) 1.67420 0.0869203
\(372\) 2.34017i 0.121332i
\(373\) 8.81432i 0.456388i −0.973616 0.228194i \(-0.926718\pi\)
0.973616 0.228194i \(-0.0732820\pi\)
\(374\) 7.36910 0.381047
\(375\) 7.46081 8.32684i 0.385275 0.429996i
\(376\) −13.2085 −0.681175
\(377\) 51.7152i 2.66347i
\(378\) 0.447480i 0.0230159i
\(379\) 23.5174 1.20801 0.604005 0.796980i \(-0.293571\pi\)
0.604005 + 0.796980i \(0.293571\pi\)
\(380\) 6.21461 + 1.54411i 0.318803 + 0.0792111i
\(381\) −4.87217 −0.249609
\(382\) 17.7275i 0.907019i
\(383\) 19.3028i 0.986329i −0.869936 0.493164i \(-0.835840\pi\)
0.869936 0.493164i \(-0.164160\pi\)
\(384\) 13.4052 0.684082
\(385\) −0.156755 + 0.630898i −0.00798900 + 0.0321535i
\(386\) 5.95055 0.302875
\(387\) 0.290725i 0.0147784i
\(388\) 1.72753i 0.0877019i
\(389\) 20.0410 1.01612 0.508060 0.861321i \(-0.330363\pi\)
0.508060 + 0.861321i \(0.330363\pi\)
\(390\) 5.78539 23.2846i 0.292954 1.17906i
\(391\) 19.1506 0.968488
\(392\) 17.3596i 0.876795i
\(393\) 8.68035i 0.437866i
\(394\) 13.1955 0.664781
\(395\) 2.00000 + 0.496928i 0.100631 + 0.0250032i
\(396\) −0.369102 −0.0185481
\(397\) 33.3607i 1.67433i 0.546954 + 0.837163i \(0.315787\pi\)
−0.546954 + 0.837163i \(0.684213\pi\)
\(398\) 12.7961i 0.641409i
\(399\) 2.25565 0.112924
\(400\) −20.3340 10.7694i −1.01670 0.538470i
\(401\) −37.6475 −1.88003 −0.940014 0.341135i \(-0.889189\pi\)
−0.940014 + 0.341135i \(0.889189\pi\)
\(402\) 9.47641i 0.472640i
\(403\) 44.1978i 2.20165i
\(404\) 3.16743 0.157586
\(405\) 2.17009 + 0.539189i 0.107832 + 0.0267925i
\(406\) −3.31965 −0.164752
\(407\) 3.41855i 0.169451i
\(408\) 12.0183i 0.594992i
\(409\) 25.2039 1.24625 0.623127 0.782120i \(-0.285862\pi\)
0.623127 + 0.782120i \(0.285862\pi\)
\(410\) −6.15676 + 24.7792i −0.304060 + 1.22376i
\(411\) 12.5958 0.621306
\(412\) 2.48709i 0.122530i
\(413\) 1.04718i 0.0515284i
\(414\) −6.15676 −0.302588
\(415\) −0.921622 + 3.70928i −0.0452407 + 0.182081i
\(416\) −14.3798 −0.705027
\(417\) 9.91548i 0.485563i
\(418\) 11.9421i 0.584109i
\(419\) −17.8432 −0.871700 −0.435850 0.900019i \(-0.643552\pi\)
−0.435850 + 0.900019i \(0.643552\pi\)
\(420\) 0.232866 + 0.0578588i 0.0113627 + 0.00282322i
\(421\) −11.8120 −0.575684 −0.287842 0.957678i \(-0.592938\pi\)
−0.287842 + 0.957678i \(0.592938\pi\)
\(422\) 39.8888i 1.94176i
\(423\) 5.26180i 0.255837i
\(424\) 14.4559 0.702040
\(425\) 11.2039 21.1545i 0.543471 1.02614i
\(426\) 7.81658 0.378715
\(427\) 1.94214i 0.0939868i
\(428\) 4.51518i 0.218249i
\(429\) −6.97107 −0.336566
\(430\) 0.971071 + 0.241276i 0.0468292 + 0.0116354i
\(431\) 16.6803 0.803464 0.401732 0.915757i \(-0.368408\pi\)
0.401732 + 0.915757i \(0.368408\pi\)
\(432\) 4.60197i 0.221412i
\(433\) 28.3135i 1.36066i −0.732906 0.680330i \(-0.761836\pi\)
0.732906 0.680330i \(-0.238164\pi\)
\(434\) −2.83710 −0.136185
\(435\) 4.00000 16.0989i 0.191785 0.771883i
\(436\) −2.33033 −0.111603
\(437\) 31.0349i 1.48460i
\(438\) 1.73594i 0.0829463i
\(439\) 27.4452 1.30989 0.654944 0.755677i \(-0.272692\pi\)
0.654944 + 0.755677i \(0.272692\pi\)
\(440\) −1.35350 + 5.44748i −0.0645258 + 0.259698i
\(441\) −6.91548 −0.329309
\(442\) 51.3705i 2.44345i
\(443\) 0.412408i 0.0195941i 0.999952 + 0.00979704i \(0.00311854\pi\)
−0.999952 + 0.00979704i \(0.996881\pi\)
\(444\) −1.26180 −0.0598822
\(445\) −9.41855 2.34017i −0.446482 0.110935i
\(446\) −14.8203 −0.701761
\(447\) 1.26180i 0.0596809i
\(448\) 1.75276i 0.0828100i
\(449\) −1.33403 −0.0629568 −0.0314784 0.999504i \(-0.510022\pi\)
−0.0314784 + 0.999504i \(0.510022\pi\)
\(450\) −3.60197 + 6.80098i −0.169798 + 0.320601i
\(451\) 7.41855 0.349326
\(452\) 6.08906i 0.286405i
\(453\) 1.60197i 0.0752670i
\(454\) 28.3051 1.32842
\(455\) 4.39803 + 1.09275i 0.206183 + 0.0512291i
\(456\) 19.4764 0.912066
\(457\) 11.6514i 0.545030i −0.962151 0.272515i \(-0.912145\pi\)
0.962151 0.272515i \(-0.0878555\pi\)
\(458\) 26.3980i 1.23350i
\(459\) 4.78765 0.223469
\(460\) 0.796064 3.20394i 0.0371167 0.149384i
\(461\) −2.05786 −0.0958440 −0.0479220 0.998851i \(-0.515260\pi\)
−0.0479220 + 0.998851i \(0.515260\pi\)
\(462\) 0.447480i 0.0208187i
\(463\) 28.7792i 1.33748i 0.743494 + 0.668742i \(0.233167\pi\)
−0.743494 + 0.668742i \(0.766833\pi\)
\(464\) −34.1399 −1.58491
\(465\) 3.41855 13.7587i 0.158531 0.638046i
\(466\) −6.32192 −0.292857
\(467\) 1.84324i 0.0852952i −0.999090 0.0426476i \(-0.986421\pi\)
0.999090 0.0426476i \(-0.0135793\pi\)
\(468\) 2.57304i 0.118939i
\(469\) −1.78992 −0.0826509
\(470\) −17.5753 4.36683i −0.810688 0.201427i
\(471\) 7.10504 0.327383
\(472\) 9.04187i 0.416186i
\(473\) 0.290725i 0.0133675i
\(474\) −1.41855 −0.0651562
\(475\) −34.2823 18.1568i −1.57298 0.833089i
\(476\) 0.513749 0.0235477
\(477\) 5.75872i 0.263674i
\(478\) 6.72138i 0.307429i
\(479\) −26.8371 −1.22622 −0.613109 0.789998i \(-0.710081\pi\)
−0.613109 + 0.789998i \(0.710081\pi\)
\(480\) 4.47641 + 1.11223i 0.204319 + 0.0507660i
\(481\) −23.8310 −1.08660
\(482\) 8.00984i 0.364838i
\(483\) 1.16290i 0.0529137i
\(484\) −0.369102 −0.0167774
\(485\) 2.52359 10.1568i 0.114590 0.461195i
\(486\) −1.53919 −0.0698190
\(487\) 28.5646i 1.29439i −0.762326 0.647193i \(-0.775943\pi\)
0.762326 0.647193i \(-0.224057\pi\)
\(488\) 16.7694i 0.759115i
\(489\) −22.9360 −1.03720
\(490\) 5.73925 23.0989i 0.259273 1.04350i
\(491\) 25.9877 1.17281 0.586405 0.810018i \(-0.300543\pi\)
0.586405 + 0.810018i \(0.300543\pi\)
\(492\) 2.73820i 0.123448i
\(493\) 35.5174i 1.59963i
\(494\) −83.2495 −3.74557
\(495\) 2.17009 + 0.539189i 0.0975381 + 0.0242347i
\(496\) −29.1773 −1.31010
\(497\) 1.47641i 0.0662260i
\(498\) 2.63090i 0.117893i
\(499\) 27.5174 1.23185 0.615925 0.787805i \(-0.288782\pi\)
0.615925 + 0.787805i \(0.288782\pi\)
\(500\) −3.07346 2.75380i −0.137449 0.123154i
\(501\) −4.81432 −0.215088
\(502\) 12.7480i 0.568973i
\(503\) 22.6576i 1.01025i 0.863046 + 0.505125i \(0.168554\pi\)
−0.863046 + 0.505125i \(0.831446\pi\)
\(504\) 0.729794 0.0325076
\(505\) −18.6225 4.62702i −0.828690 0.205900i
\(506\) −6.15676 −0.273701
\(507\) 35.5958i 1.58087i
\(508\) 1.79833i 0.0797880i
\(509\) 27.8432 1.23413 0.617065 0.786912i \(-0.288322\pi\)
0.617065 + 0.786912i \(0.288322\pi\)
\(510\) −3.97334 + 15.9916i −0.175942 + 0.708119i
\(511\) −0.327887 −0.0145049
\(512\) 13.6114i 0.601546i
\(513\) 7.75872i 0.342556i
\(514\) −16.9627 −0.748191
\(515\) −3.63317 + 14.6225i −0.160096 + 0.644344i
\(516\) −0.107307 −0.00472393
\(517\) 5.26180i 0.231413i
\(518\) 1.52973i 0.0672126i
\(519\) −12.8865 −0.565657
\(520\) 37.9748 + 9.43537i 1.66530 + 0.413768i
\(521\) 29.7009 1.30122 0.650609 0.759413i \(-0.274514\pi\)
0.650609 + 0.759413i \(0.274514\pi\)
\(522\) 11.4186i 0.499776i
\(523\) 24.7565i 1.08252i 0.840854 + 0.541262i \(0.182053\pi\)
−0.840854 + 0.541262i \(0.817947\pi\)
\(524\) 3.20394 0.139965
\(525\) −1.28458 0.680346i −0.0560637 0.0296927i
\(526\) −4.57304 −0.199394
\(527\) 30.3545i 1.32226i
\(528\) 4.60197i 0.200275i
\(529\) 7.00000 0.304348
\(530\) 19.2351 + 4.77924i 0.835521 + 0.207597i
\(531\) 3.60197 0.156312
\(532\) 0.832567i 0.0360963i
\(533\) 51.7152i 2.24004i
\(534\) 6.68035 0.289087
\(535\) 6.59583 26.5464i 0.285162 1.14770i
\(536\) −15.4551 −0.667557
\(537\) 1.84324i 0.0795419i
\(538\) 24.3857i 1.05134i
\(539\) −6.91548 −0.297871
\(540\) 0.199016 0.800984i 0.00856428 0.0344689i
\(541\) −12.5236 −0.538431 −0.269216 0.963080i \(-0.586764\pi\)
−0.269216 + 0.963080i \(0.586764\pi\)
\(542\) 9.66967i 0.415348i
\(543\) 10.2823i 0.441256i
\(544\) 9.87587 0.423425
\(545\) 13.7009 + 3.40417i 0.586881 + 0.145819i
\(546\) −3.11942 −0.133499
\(547\) 14.2784i 0.610502i 0.952272 + 0.305251i \(0.0987404\pi\)
−0.952272 + 0.305251i \(0.901260\pi\)
\(548\) 4.64915i 0.198602i
\(549\) 6.68035 0.285110
\(550\) −3.60197 + 6.80098i −0.153588 + 0.289995i
\(551\) −57.5585 −2.45207
\(552\) 10.0410i 0.427375i
\(553\) 0.267938i 0.0113939i
\(554\) −7.89269 −0.335328
\(555\) 7.41855 + 1.84324i 0.314900 + 0.0782414i
\(556\) −3.65983 −0.155211
\(557\) 3.57918i 0.151655i 0.997121 + 0.0758274i \(0.0241598\pi\)
−0.997121 + 0.0758274i \(0.975840\pi\)
\(558\) 9.75872i 0.413120i
\(559\) −2.02666 −0.0857187
\(560\) −0.721384 + 2.90337i −0.0304840 + 0.122690i
\(561\) 4.78765 0.202135
\(562\) 33.6910i 1.42117i
\(563\) 28.9588i 1.22047i 0.792222 + 0.610234i \(0.208924\pi\)
−0.792222 + 0.610234i \(0.791076\pi\)
\(564\) 1.94214 0.0817789
\(565\) 8.89496 35.7998i 0.374214 1.50611i
\(566\) 39.9649 1.67985
\(567\) 0.290725i 0.0122093i
\(568\) 12.7480i 0.534896i
\(569\) 25.8264 1.08270 0.541350 0.840797i \(-0.317913\pi\)
0.541350 + 0.840797i \(0.317913\pi\)
\(570\) 25.9155 + 6.43907i 1.08548 + 0.269703i
\(571\) 17.1194 0.716425 0.358213 0.933640i \(-0.383386\pi\)
0.358213 + 0.933640i \(0.383386\pi\)
\(572\) 2.57304i 0.107584i
\(573\) 11.5174i 0.481148i
\(574\) 3.31965 0.138560
\(575\) −9.36069 + 17.6742i −0.390368 + 0.737065i
\(576\) 6.02893 0.251205
\(577\) 22.5692i 0.939567i −0.882782 0.469783i \(-0.844332\pi\)
0.882782 0.469783i \(-0.155668\pi\)
\(578\) 9.11450i 0.379113i
\(579\) 3.86603 0.160667
\(580\) −5.94214 1.47641i −0.246734 0.0613046i
\(581\) 0.496928 0.0206161
\(582\) 7.20394i 0.298613i
\(583\) 5.75872i 0.238502i
\(584\) −2.83114 −0.117153
\(585\) 3.75872 15.1278i 0.155404 0.625459i
\(586\) 16.0326 0.662302
\(587\) 3.63317i 0.149957i −0.997185 0.0749784i \(-0.976111\pi\)
0.997185 0.0749784i \(-0.0238888\pi\)
\(588\) 2.55252i 0.105264i
\(589\) −49.1917 −2.02691
\(590\) −2.98932 + 12.0312i −0.123068 + 0.495317i
\(591\) 8.57304 0.352648
\(592\) 15.7321i 0.646584i
\(593\) 12.3051i 0.505310i 0.967556 + 0.252655i \(0.0813037\pi\)
−0.967556 + 0.252655i \(0.918696\pi\)
\(594\) −1.53919 −0.0631537
\(595\) −3.02052 0.750491i −0.123829 0.0307671i
\(596\) −0.465732 −0.0190771
\(597\) 8.31351i 0.340249i
\(598\) 42.9192i 1.75510i
\(599\) −19.6865 −0.804368 −0.402184 0.915559i \(-0.631749\pi\)
−0.402184 + 0.915559i \(0.631749\pi\)
\(600\) −11.0917 5.87444i −0.452817 0.239823i
\(601\) 25.8843 1.05584 0.527921 0.849294i \(-0.322972\pi\)
0.527921 + 0.849294i \(0.322972\pi\)
\(602\) 0.130094i 0.00530222i
\(603\) 6.15676i 0.250722i
\(604\) −0.591290 −0.0240593
\(605\) 2.17009 + 0.539189i 0.0882266 + 0.0219211i
\(606\) 13.2085 0.536557
\(607\) 41.5357i 1.68588i 0.538006 + 0.842941i \(0.319178\pi\)
−0.538006 + 0.842941i \(0.680822\pi\)
\(608\) 16.0045i 0.649070i
\(609\) −2.15676 −0.0873961
\(610\) −5.54411 + 22.3135i −0.224474 + 0.903448i
\(611\) 36.6803 1.48393
\(612\) 1.76713i 0.0714322i
\(613\) 20.6453i 0.833855i −0.908940 0.416927i \(-0.863107\pi\)
0.908940 0.416927i \(-0.136893\pi\)
\(614\) 44.7442 1.80573
\(615\) −4.00000 + 16.0989i −0.161296 + 0.649170i
\(616\) 0.729794 0.0294042
\(617\) 8.69472i 0.350036i −0.984565 0.175018i \(-0.944002\pi\)
0.984565 0.175018i \(-0.0559984\pi\)
\(618\) 10.3714i 0.417198i
\(619\) −2.65368 −0.106661 −0.0533303 0.998577i \(-0.516984\pi\)
−0.0533303 + 0.998577i \(0.516984\pi\)
\(620\) −5.07838 1.26180i −0.203953 0.0506749i
\(621\) −4.00000 −0.160514
\(622\) 8.38121i 0.336056i
\(623\) 1.26180i 0.0505528i
\(624\) −32.0806 −1.28425
\(625\) 14.0472 + 20.6803i 0.561887 + 0.827214i
\(626\) 38.6225 1.54367
\(627\) 7.75872i 0.309854i
\(628\) 2.62249i 0.104649i
\(629\) 16.3668 0.652588
\(630\) 0.971071 + 0.241276i 0.0386884 + 0.00961268i
\(631\) −10.6393 −0.423544 −0.211772 0.977319i \(-0.567923\pi\)
−0.211772 + 0.977319i \(0.567923\pi\)
\(632\) 2.31351i 0.0920265i
\(633\) 25.9155i 1.03005i
\(634\) −32.5958 −1.29455
\(635\) 2.62702 10.5730i 0.104250 0.419578i
\(636\) −2.12556 −0.0842839
\(637\) 48.2083i 1.91008i
\(638\) 11.4186i 0.452065i
\(639\) 5.07838 0.200898
\(640\) −7.22795 + 29.0905i −0.285710 + 1.14990i
\(641\) −35.8576 −1.41629 −0.708145 0.706067i \(-0.750468\pi\)
−0.708145 + 0.706067i \(0.750468\pi\)
\(642\) 18.8287i 0.743109i
\(643\) 12.2146i 0.481697i 0.970563 + 0.240849i \(0.0774258\pi\)
−0.970563 + 0.240849i \(0.922574\pi\)
\(644\) −0.429229 −0.0169140
\(645\) 0.630898 + 0.156755i 0.0248416 + 0.00617224i
\(646\) 57.1748 2.24951
\(647\) 25.9421i 1.01989i −0.860207 0.509945i \(-0.829666\pi\)
0.860207 0.509945i \(-0.170334\pi\)
\(648\) 2.51026i 0.0986123i
\(649\) 3.60197 0.141390
\(650\) 47.4101 + 25.1096i 1.85958 + 0.984879i
\(651\) −1.84324 −0.0722424
\(652\) 8.46573i 0.331544i
\(653\) 14.3402i 0.561174i −0.959829 0.280587i \(-0.909471\pi\)
0.959829 0.280587i \(-0.0905292\pi\)
\(654\) −9.71769 −0.379992
\(655\) −18.8371 4.68035i −0.736026 0.182876i
\(656\) 34.1399 1.33294
\(657\) 1.12783i 0.0440007i
\(658\) 2.35455i 0.0917899i
\(659\) −6.52359 −0.254123 −0.127062 0.991895i \(-0.540555\pi\)
−0.127062 + 0.991895i \(0.540555\pi\)
\(660\) 0.199016 0.800984i 0.00774668 0.0311783i
\(661\) 3.16290 0.123022 0.0615112 0.998106i \(-0.480408\pi\)
0.0615112 + 0.998106i \(0.480408\pi\)
\(662\) 10.3234i 0.401228i
\(663\) 33.3751i 1.29618i
\(664\) 4.29072 0.166512
\(665\) −1.21622 + 4.89496i −0.0471631 + 0.189818i
\(666\) −5.26180 −0.203890
\(667\) 29.6742i 1.14899i
\(668\) 1.77698i 0.0687532i
\(669\) −9.62863 −0.372264
\(670\) −20.5646 5.10957i −0.794481 0.197400i
\(671\) 6.68035 0.257892
\(672\) 0.599701i 0.0231340i
\(673\) 18.4885i 0.712680i −0.934356 0.356340i \(-0.884024\pi\)
0.934356 0.356340i \(-0.115976\pi\)
\(674\) −36.5562 −1.40809
\(675\) −2.34017 + 4.41855i −0.0900733 + 0.170070i
\(676\) 13.1385 0.505327
\(677\) 15.0966i 0.580211i −0.956995 0.290105i \(-0.906310\pi\)
0.956995 0.290105i \(-0.0936903\pi\)
\(678\) 25.3919i 0.975170i
\(679\) −1.36069 −0.0522186
\(680\) −26.0806 6.48011i −1.00015 0.248501i
\(681\) 18.3896 0.704692
\(682\) 9.75872i 0.373681i
\(683\) 12.4657i 0.476988i −0.971144 0.238494i \(-0.923346\pi\)
0.971144 0.238494i \(-0.0766537\pi\)
\(684\) −2.86376 −0.109499
\(685\) −6.79153 + 27.3340i −0.259491 + 1.04438i
\(686\) −6.22690 −0.237744
\(687\) 17.1506i 0.654337i
\(688\) 1.33791i 0.0510072i
\(689\) −40.1445 −1.52938
\(690\) 3.31965 13.3607i 0.126377 0.508633i
\(691\) −30.7214 −1.16870 −0.584348 0.811503i \(-0.698650\pi\)
−0.584348 + 0.811503i \(0.698650\pi\)
\(692\) 4.75646i 0.180813i
\(693\) 0.290725i 0.0110437i
\(694\) 47.9748 1.82110
\(695\) 21.5174 + 5.34632i 0.816203 + 0.202797i
\(696\) −18.6225 −0.705884
\(697\) 35.5174i 1.34532i
\(698\) 17.0037i 0.643599i
\(699\) −4.10731 −0.155353
\(700\) −0.251117 + 0.474142i −0.00949134 + 0.0179209i
\(701\) 17.9955 0.679679 0.339840 0.940483i \(-0.389627\pi\)
0.339840 + 0.940483i \(0.389627\pi\)
\(702\) 10.7298i 0.404970i
\(703\) 26.5236i 1.00036i
\(704\) 6.02893 0.227224
\(705\) −11.4186 2.83710i −0.430047 0.106851i
\(706\) −42.2245 −1.58914
\(707\) 2.49484i 0.0938281i
\(708\) 1.32950i 0.0499655i
\(709\) −23.5897 −0.885929 −0.442965 0.896539i \(-0.646073\pi\)
−0.442965 + 0.896539i \(0.646073\pi\)
\(710\) −4.21461 + 16.9627i −0.158172 + 0.636597i
\(711\) −0.921622 −0.0345635
\(712\) 10.8950i 0.408306i
\(713\) 25.3607i 0.949765i
\(714\) 2.14238 0.0801765
\(715\) 3.75872 15.1278i 0.140568 0.565749i
\(716\) 0.680346 0.0254257
\(717\) 4.36683i 0.163082i
\(718\) 29.4764i 1.10005i
\(719\) −24.5646 −0.916106 −0.458053 0.888925i \(-0.651453\pi\)
−0.458053 + 0.888925i \(0.651453\pi\)
\(720\) 9.98667 + 2.48133i 0.372181 + 0.0924737i
\(721\) 1.95896 0.0729556
\(722\) 63.4112i 2.35992i
\(723\) 5.20394i 0.193536i
\(724\) −3.79523 −0.141048
\(725\) 32.7792 + 17.3607i 1.21739 + 0.644760i
\(726\) −1.53919 −0.0571247
\(727\) 8.51130i 0.315667i −0.987466 0.157833i \(-0.949549\pi\)
0.987466 0.157833i \(-0.0504509\pi\)
\(728\) 5.08745i 0.188553i
\(729\) −1.00000 −0.0370370
\(730\) −3.76713 0.935998i −0.139428 0.0346428i
\(731\) 1.39189 0.0514809
\(732\) 2.46573i 0.0911361i
\(733\) 29.8615i 1.10296i −0.834188 0.551480i \(-0.814063\pi\)
0.834188 0.551480i \(-0.185937\pi\)
\(734\) 22.4247 0.827711
\(735\) 3.72875 15.0072i 0.137537 0.553548i
\(736\) −8.25112 −0.304140
\(737\) 6.15676i 0.226787i
\(738\) 11.4186i 0.420323i
\(739\) 36.7526 1.35197 0.675983 0.736917i \(-0.263719\pi\)
0.675983 + 0.736917i \(0.263719\pi\)
\(740\) 0.680346 2.73820i 0.0250100 0.100658i
\(741\) −54.0866 −1.98692
\(742\) 2.57691i 0.0946015i
\(743\) 2.17501i 0.0797933i −0.999204 0.0398966i \(-0.987297\pi\)
0.999204 0.0398966i \(-0.0127029\pi\)
\(744\) −15.9155 −0.583490
\(745\) 2.73820 + 0.680346i 0.100320 + 0.0249259i
\(746\) −13.5669 −0.496719
\(747\) 1.70928i 0.0625391i
\(748\) 1.76713i 0.0646128i
\(749\) −3.55640 −0.129948
\(750\) −12.8166 11.4836i −0.467995 0.419322i
\(751\) −44.4580 −1.62229 −0.811147 0.584842i \(-0.801157\pi\)
−0.811147 + 0.584842i \(0.801157\pi\)
\(752\) 24.2146i 0.883016i
\(753\) 8.28231i 0.301824i
\(754\) 79.5995 2.89884
\(755\) 3.47641 + 0.863763i 0.126519 + 0.0314356i
\(756\) −0.107307 −0.00390272
\(757\) 26.4247i 0.960422i 0.877153 + 0.480211i \(0.159440\pi\)
−0.877153 + 0.480211i \(0.840560\pi\)
\(758\) 36.1978i 1.31476i
\(759\) −4.00000 −0.145191
\(760\) −10.5015 + 42.2655i −0.380928 + 1.53313i
\(761\) −27.6163 −1.00109 −0.500546 0.865710i \(-0.666867\pi\)
−0.500546 + 0.865710i \(0.666867\pi\)
\(762\) 7.49920i 0.271667i
\(763\) 1.83549i 0.0664493i
\(764\) 4.25112 0.153800
\(765\) −2.58145 + 10.3896i −0.0933325 + 0.375638i
\(766\) −29.7107 −1.07349
\(767\) 25.1096i 0.906654i
\(768\) 8.57531i 0.309435i
\(769\) −27.8432 −1.00405 −0.502027 0.864852i \(-0.667412\pi\)
−0.502027 + 0.864852i \(0.667412\pi\)
\(770\) 0.971071 + 0.241276i 0.0349950 + 0.00869499i
\(771\) −11.0205 −0.396894
\(772\) 1.42696i 0.0513575i
\(773\) 18.0267i 0.648374i −0.945993 0.324187i \(-0.894909\pi\)
0.945993 0.324187i \(-0.105091\pi\)
\(774\) −0.447480 −0.0160843
\(775\) 28.0144 + 14.8371i 1.00631 + 0.532964i
\(776\) −11.7489 −0.421760
\(777\) 0.993857i 0.0356544i
\(778\) 30.8469i 1.10592i
\(779\) 57.5585 2.06225
\(780\) −5.58372 1.38735i −0.199929 &minus