Properties

Label 69.2.g.a.5.4
Level $69$
Weight $2$
Character 69.5
Analytic conductor $0.551$
Analytic rank $0$
Dimension $60$
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] = [69,2,Mod(5,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 69.g (of order \(22\), degree \(10\), 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: \(0.550967773947\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.4
Character \(\chi\) \(=\) 69.5
Dual form 69.2.g.a.14.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.298617 - 1.01700i) q^{2} +(-0.239057 + 1.71547i) q^{3} +(0.737395 + 0.473895i) q^{4} +(0.228939 - 1.59231i) q^{5} +(1.67325 + 0.755391i) q^{6} +(-1.28446 + 0.586593i) q^{7} +(2.30424 - 1.99663i) q^{8} +(-2.88570 - 0.820191i) q^{9} +O(q^{10})\) \(q+(0.298617 - 1.01700i) q^{2} +(-0.239057 + 1.71547i) q^{3} +(0.737395 + 0.473895i) q^{4} +(0.228939 - 1.59231i) q^{5} +(1.67325 + 0.755391i) q^{6} +(-1.28446 + 0.586593i) q^{7} +(2.30424 - 1.99663i) q^{8} +(-2.88570 - 0.820191i) q^{9} +(-1.55101 - 0.708322i) q^{10} +(-4.31116 + 1.26587i) q^{11} +(-0.989235 + 1.15170i) q^{12} +(1.54864 - 3.39104i) q^{13} +(0.213002 + 1.48146i) q^{14} +(2.67684 + 0.773392i) q^{15} +(-0.614226 - 1.34497i) q^{16} +(-3.34349 + 2.14873i) q^{17} +(-1.69585 + 2.68983i) q^{18} +(-1.74911 + 2.72167i) q^{19} +(0.923407 - 1.06567i) q^{20} +(-0.699227 - 2.34369i) q^{21} +4.76245i q^{22} +(4.78334 + 0.345872i) q^{23} +(2.87433 + 4.43017i) q^{24} +(2.31443 + 0.679578i) q^{25} +(-2.98623 - 2.58758i) q^{26} +(2.09686 - 4.75428i) q^{27} +(-1.22514 - 0.176148i) q^{28} +(-0.915281 - 1.42420i) q^{29} +(1.58589 - 2.49139i) q^{30} +(-5.36145 - 6.18744i) q^{31} +(4.48457 - 0.644784i) q^{32} +(-1.14096 - 7.69830i) q^{33} +(1.18683 + 4.04197i) q^{34} +(0.639974 + 2.17955i) q^{35} +(-1.73922 - 1.97233i) q^{36} +(3.88889 - 0.559137i) q^{37} +(2.24562 + 2.59158i) q^{38} +(5.44703 + 3.46729i) q^{39} +(-2.65172 - 4.12616i) q^{40} +(1.40816 + 0.202463i) q^{41} +(-2.59233 + 0.0112461i) q^{42} +(7.30732 + 6.33183i) q^{43} +(-3.77892 - 1.10959i) q^{44} +(-1.96665 + 4.40716i) q^{45} +(1.78014 - 4.76136i) q^{46} +9.42076i q^{47} +(2.45409 - 0.732165i) q^{48} +(-3.27828 + 3.78334i) q^{49} +(1.38226 - 2.15084i) q^{50} +(-2.88680 - 6.24933i) q^{51} +(2.74895 - 1.76665i) q^{52} +(0.748661 + 1.63934i) q^{53} +(-4.20893 - 3.55222i) q^{54} +(1.02866 + 7.15451i) q^{55} +(-1.78849 + 3.91624i) q^{56} +(-4.25082 - 3.65119i) q^{57} +(-1.72173 + 0.505546i) q^{58} +(5.57035 + 2.54389i) q^{59} +(1.60738 + 1.83884i) q^{60} +(-1.67433 + 1.45081i) q^{61} +(-7.89364 + 3.60490i) q^{62} +(4.18769 - 0.639231i) q^{63} +(1.10428 - 7.68041i) q^{64} +(-5.04504 - 3.24225i) q^{65} +(-8.16986 - 1.13850i) q^{66} +(3.35387 - 11.4222i) q^{67} -3.48374 q^{68} +(-1.73683 + 8.12302i) q^{69} +2.40771 q^{70} +(-1.99326 + 6.78844i) q^{71} +(-8.28696 + 3.87177i) q^{72} +(-8.24368 - 5.29789i) q^{73} +(0.592648 - 4.12196i) q^{74} +(-1.71908 + 3.80789i) q^{75} +(-2.57957 + 1.17805i) q^{76} +(4.79496 - 4.15486i) q^{77} +(5.15281 - 4.50422i) q^{78} +(-3.41100 - 1.55775i) q^{79} +(-2.28222 + 0.670121i) q^{80} +(7.65457 + 4.73366i) q^{81} +(0.626405 - 1.37163i) q^{82} +(-2.14609 - 14.9264i) q^{83} +(0.595056 - 2.05958i) q^{84} +(2.65598 + 5.81579i) q^{85} +(8.62155 - 5.54073i) q^{86} +(2.66199 - 1.22967i) q^{87} +(-7.40645 + 11.5247i) q^{88} +(0.298008 - 0.343919i) q^{89} +(3.89479 + 3.31613i) q^{90} +5.26407i q^{91} +(3.36331 + 2.52185i) q^{92} +(11.8961 - 7.71828i) q^{93} +(9.58089 + 2.81320i) q^{94} +(3.93330 + 3.40822i) q^{95} +(0.0340433 + 7.84730i) q^{96} +(-8.23456 - 1.18395i) q^{97} +(2.86869 + 4.46377i) q^{98} +(13.4790 - 0.116952i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9} - 22 q^{10} + 4 q^{12} - 22 q^{13} - 46 q^{16} + 12 q^{18} - 22 q^{19} + 22 q^{21} + 50 q^{24} + 8 q^{25} + 10 q^{27} - 22 q^{28} + 33 q^{30} - 22 q^{31} + 22 q^{36} + 22 q^{37} + 13 q^{39} + 132 q^{40} - 11 q^{42} + 22 q^{43} + 66 q^{46} - 58 q^{48} + 68 q^{49} - 11 q^{51} + 94 q^{52} - 33 q^{54} - 44 q^{57} - 8 q^{58} - 121 q^{60} - 66 q^{61} - 66 q^{63} - 20 q^{64} - 66 q^{66} - 44 q^{67} - 66 q^{69} - 132 q^{70} - 101 q^{72} - 44 q^{73} - 44 q^{75} - 110 q^{76} + 84 q^{78} - 66 q^{79} + 77 q^{81} - 132 q^{82} + 77 q^{84} - 44 q^{85} + 73 q^{87} + 66 q^{88} + 176 q^{90} + 116 q^{93} + 100 q^{94} + 85 q^{96} + 44 q^{97} + 121 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{1}{22}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.298617 1.01700i 0.211154 0.719126i −0.783996 0.620765i \(-0.786822\pi\)
0.995151 0.0983605i \(-0.0313598\pi\)
\(3\) −0.239057 + 1.71547i −0.138019 + 0.990430i
\(4\) 0.737395 + 0.473895i 0.368698 + 0.236948i
\(5\) 0.228939 1.59231i 0.102385 0.712102i −0.872374 0.488840i \(-0.837420\pi\)
0.974758 0.223262i \(-0.0716707\pi\)
\(6\) 1.67325 + 0.755391i 0.683100 + 0.308387i
\(7\) −1.28446 + 0.586593i −0.485480 + 0.221711i −0.643091 0.765790i \(-0.722348\pi\)
0.157611 + 0.987501i \(0.449621\pi\)
\(8\) 2.30424 1.99663i 0.814670 0.705916i
\(9\) −2.88570 0.820191i −0.961901 0.273397i
\(10\) −1.55101 0.708322i −0.490472 0.223991i
\(11\) −4.31116 + 1.26587i −1.29986 + 0.381674i −0.857186 0.515007i \(-0.827789\pi\)
−0.442677 + 0.896681i \(0.645971\pi\)
\(12\) −0.989235 + 1.15170i −0.285567 + 0.332466i
\(13\) 1.54864 3.39104i 0.429514 0.940505i −0.563891 0.825849i \(-0.690696\pi\)
0.993405 0.114656i \(-0.0365765\pi\)
\(14\) 0.213002 + 1.48146i 0.0569271 + 0.395937i
\(15\) 2.67684 + 0.773392i 0.691156 + 0.199689i
\(16\) −0.614226 1.34497i −0.153556 0.336242i
\(17\) −3.34349 + 2.14873i −0.810915 + 0.521143i −0.879161 0.476525i \(-0.841896\pi\)
0.0682462 + 0.997669i \(0.478260\pi\)
\(18\) −1.69585 + 2.68983i −0.399717 + 0.633999i
\(19\) −1.74911 + 2.72167i −0.401273 + 0.624394i −0.981816 0.189836i \(-0.939204\pi\)
0.580542 + 0.814230i \(0.302841\pi\)
\(20\) 0.923407 1.06567i 0.206480 0.238291i
\(21\) −0.699227 2.34369i −0.152584 0.511434i
\(22\) 4.76245i 1.01536i
\(23\) 4.78334 + 0.345872i 0.997396 + 0.0721194i
\(24\) 2.87433 + 4.43017i 0.586720 + 0.904304i
\(25\) 2.31443 + 0.679578i 0.462886 + 0.135916i
\(26\) −2.98623 2.58758i −0.585648 0.507466i
\(27\) 2.09686 4.75428i 0.403542 0.914961i
\(28\) −1.22514 0.176148i −0.231529 0.0332889i
\(29\) −0.915281 1.42420i −0.169963 0.264468i 0.745814 0.666154i \(-0.232061\pi\)
−0.915777 + 0.401686i \(0.868424\pi\)
\(30\) 1.58589 2.49139i 0.289542 0.454863i
\(31\) −5.36145 6.18744i −0.962945 1.11130i −0.993734 0.111772i \(-0.964347\pi\)
0.0307889 0.999526i \(-0.490198\pi\)
\(32\) 4.48457 0.644784i 0.792767 0.113983i
\(33\) −1.14096 7.69830i −0.198615 1.34010i
\(34\) 1.18683 + 4.04197i 0.203539 + 0.693191i
\(35\) 0.639974 + 2.17955i 0.108175 + 0.368411i
\(36\) −1.73922 1.97233i −0.289870 0.328721i
\(37\) 3.88889 0.559137i 0.639329 0.0919216i 0.184975 0.982743i \(-0.440779\pi\)
0.454353 + 0.890822i \(0.349870\pi\)
\(38\) 2.24562 + 2.59158i 0.364287 + 0.420410i
\(39\) 5.44703 + 3.46729i 0.872222 + 0.555211i
\(40\) −2.65172 4.12616i −0.419274 0.652404i
\(41\) 1.40816 + 0.202463i 0.219917 + 0.0316193i 0.251393 0.967885i \(-0.419111\pi\)
−0.0314753 + 0.999505i \(0.510021\pi\)
\(42\) −2.59233 + 0.0112461i −0.400004 + 0.00173530i
\(43\) 7.30732 + 6.33183i 1.11436 + 0.965595i 0.999613 0.0278003i \(-0.00885026\pi\)
0.114742 + 0.993395i \(0.463396\pi\)
\(44\) −3.77892 1.10959i −0.569694 0.167277i
\(45\) −1.96665 + 4.40716i −0.293171 + 0.656980i
\(46\) 1.78014 4.76136i 0.262467 0.702025i
\(47\) 9.42076i 1.37416i 0.726582 + 0.687080i \(0.241108\pi\)
−0.726582 + 0.687080i \(0.758892\pi\)
\(48\) 2.45409 0.732165i 0.354218 0.105679i
\(49\) −3.27828 + 3.78334i −0.468326 + 0.540477i
\(50\) 1.38226 2.15084i 0.195481 0.304174i
\(51\) −2.88680 6.24933i −0.404234 0.875082i
\(52\) 2.74895 1.76665i 0.381211 0.244990i
\(53\) 0.748661 + 1.63934i 0.102837 + 0.225181i 0.954055 0.299630i \(-0.0968633\pi\)
−0.851219 + 0.524811i \(0.824136\pi\)
\(54\) −4.20893 3.55222i −0.572763 0.483395i
\(55\) 1.02866 + 7.15451i 0.138705 + 0.964713i
\(56\) −1.78849 + 3.91624i −0.238997 + 0.523330i
\(57\) −4.25082 3.65119i −0.563034 0.483612i
\(58\) −1.72173 + 0.505546i −0.226074 + 0.0663814i
\(59\) 5.57035 + 2.54389i 0.725198 + 0.331187i 0.743582 0.668644i \(-0.233125\pi\)
−0.0183847 + 0.999831i \(0.505852\pi\)
\(60\) 1.60738 + 1.83884i 0.207512 + 0.237393i
\(61\) −1.67433 + 1.45081i −0.214376 + 0.185758i −0.755429 0.655231i \(-0.772571\pi\)
0.541053 + 0.840989i \(0.318026\pi\)
\(62\) −7.89364 + 3.60490i −1.00249 + 0.457823i
\(63\) 4.18769 0.639231i 0.527599 0.0805356i
\(64\) 1.10428 7.68041i 0.138034 0.960051i
\(65\) −5.04504 3.24225i −0.625760 0.402151i
\(66\) −8.16986 1.13850i −1.00564 0.140139i
\(67\) 3.35387 11.4222i 0.409741 1.39545i −0.453770 0.891119i \(-0.649921\pi\)
0.863511 0.504331i \(-0.168261\pi\)
\(68\) −3.48374 −0.422466
\(69\) −1.73683 + 8.12302i −0.209089 + 0.977897i
\(70\) 2.40771 0.287776
\(71\) −1.99326 + 6.78844i −0.236557 + 0.805639i 0.752562 + 0.658521i \(0.228818\pi\)
−0.989119 + 0.147118i \(0.953000\pi\)
\(72\) −8.28696 + 3.87177i −0.976628 + 0.456293i
\(73\) −8.24368 5.29789i −0.964850 0.620072i −0.0395139 0.999219i \(-0.512581\pi\)
−0.925336 + 0.379147i \(0.876217\pi\)
\(74\) 0.592648 4.12196i 0.0688939 0.479168i
\(75\) −1.71908 + 3.80789i −0.198502 + 0.439697i
\(76\) −2.57957 + 1.17805i −0.295897 + 0.135132i
\(77\) 4.79496 4.15486i 0.546436 0.473490i
\(78\) 5.15281 4.50422i 0.583441 0.510002i
\(79\) −3.41100 1.55775i −0.383767 0.175261i 0.214184 0.976793i \(-0.431291\pi\)
−0.597951 + 0.801533i \(0.704018\pi\)
\(80\) −2.28222 + 0.670121i −0.255160 + 0.0749218i
\(81\) 7.65457 + 4.73366i 0.850508 + 0.525962i
\(82\) 0.626405 1.37163i 0.0691748 0.151472i
\(83\) −2.14609 14.9264i −0.235564 1.63838i −0.673364 0.739311i \(-0.735151\pi\)
0.437800 0.899073i \(-0.355758\pi\)
\(84\) 0.595056 2.05958i 0.0649259 0.224719i
\(85\) 2.65598 + 5.81579i 0.288082 + 0.630811i
\(86\) 8.62155 5.54073i 0.929685 0.597473i
\(87\) 2.66199 1.22967i 0.285395 0.131835i
\(88\) −7.40645 + 11.5247i −0.789530 + 1.22853i
\(89\) 0.298008 0.343919i 0.0315887 0.0364554i −0.739735 0.672898i \(-0.765049\pi\)
0.771324 + 0.636443i \(0.219595\pi\)
\(90\) 3.89479 + 3.31613i 0.410547 + 0.349551i
\(91\) 5.26407i 0.551825i
\(92\) 3.36331 + 2.52185i 0.350649 + 0.262921i
\(93\) 11.8961 7.71828i 1.23357 0.800348i
\(94\) 9.58089 + 2.81320i 0.988194 + 0.290160i
\(95\) 3.93330 + 3.40822i 0.403548 + 0.349676i
\(96\) 0.0340433 + 7.84730i 0.00347453 + 0.800912i
\(97\) −8.23456 1.18395i −0.836093 0.120212i −0.289047 0.957315i \(-0.593338\pi\)
−0.547045 + 0.837103i \(0.684248\pi\)
\(98\) 2.86869 + 4.46377i 0.289782 + 0.450909i
\(99\) 13.4790 0.116952i 1.35469 0.0117541i
\(100\) 1.38460 + 1.59792i 0.138460 + 0.159792i
\(101\) −6.96023 + 1.00073i −0.692569 + 0.0995763i −0.479606 0.877484i \(-0.659220\pi\)
−0.212963 + 0.977060i \(0.568311\pi\)
\(102\) −7.21761 + 1.06971i −0.714649 + 0.105917i
\(103\) 3.32222 + 11.3144i 0.327348 + 1.11484i 0.944640 + 0.328109i \(0.106411\pi\)
−0.617292 + 0.786734i \(0.711770\pi\)
\(104\) −3.20223 10.9058i −0.314005 1.06940i
\(105\) −3.89195 + 0.576822i −0.379816 + 0.0562921i
\(106\) 1.89077 0.271851i 0.183648 0.0264045i
\(107\) −11.8206 13.6417i −1.14274 1.31879i −0.940633 0.339424i \(-0.889768\pi\)
−0.202103 0.979364i \(-0.564778\pi\)
\(108\) 3.79925 2.51209i 0.365583 0.241726i
\(109\) −4.16074 6.47424i −0.398527 0.620120i 0.582766 0.812640i \(-0.301970\pi\)
−0.981293 + 0.192520i \(0.938334\pi\)
\(110\) 7.58329 + 1.09031i 0.723038 + 0.103957i
\(111\) 0.0295213 + 6.80495i 0.00280204 + 0.645897i
\(112\) 1.57790 + 1.36726i 0.149097 + 0.129194i
\(113\) 13.5081 + 3.96634i 1.27074 + 0.373121i 0.846480 0.532421i \(-0.178718\pi\)
0.424255 + 0.905543i \(0.360536\pi\)
\(114\) −4.98262 + 3.23276i −0.466665 + 0.302776i
\(115\) 1.64583 7.53738i 0.153475 0.702864i
\(116\) 1.48395i 0.137781i
\(117\) −7.25020 + 8.51535i −0.670282 + 0.787245i
\(118\) 4.25054 4.90538i 0.391294 0.451577i
\(119\) 3.03415 4.72122i 0.278140 0.432794i
\(120\) 7.71224 3.56258i 0.704028 0.325217i
\(121\) 7.72988 4.96769i 0.702716 0.451608i
\(122\) 0.975490 + 2.13603i 0.0883167 + 0.193387i
\(123\) −0.683949 + 2.36726i −0.0616696 + 0.213449i
\(124\) −1.02131 7.10336i −0.0917163 0.637901i
\(125\) 4.95332 10.8463i 0.443038 0.970118i
\(126\) 0.600421 4.44976i 0.0534897 0.396416i
\(127\) −1.24954 + 0.366898i −0.110879 + 0.0325570i −0.336701 0.941612i \(-0.609311\pi\)
0.225822 + 0.974168i \(0.427493\pi\)
\(128\) 0.761312 + 0.347680i 0.0672912 + 0.0307308i
\(129\) −12.6090 + 11.0219i −1.11016 + 0.970420i
\(130\) −4.80389 + 4.16260i −0.421329 + 0.365084i
\(131\) −7.54331 + 3.44491i −0.659062 + 0.300984i −0.716729 0.697352i \(-0.754361\pi\)
0.0576663 + 0.998336i \(0.481634\pi\)
\(132\) 2.80685 6.21738i 0.244305 0.541154i
\(133\) 0.650150 4.52189i 0.0563751 0.392098i
\(134\) −10.6149 6.82176i −0.916985 0.589311i
\(135\) −7.09022 4.42730i −0.610229 0.381041i
\(136\) −3.41396 + 11.6269i −0.292745 + 0.996998i
\(137\) −5.82629 −0.497773 −0.248887 0.968533i \(-0.580065\pi\)
−0.248887 + 0.968533i \(0.580065\pi\)
\(138\) 7.74244 + 4.19202i 0.659081 + 0.356849i
\(139\) −9.61035 −0.815139 −0.407569 0.913174i \(-0.633624\pi\)
−0.407569 + 0.913174i \(0.633624\pi\)
\(140\) −0.560965 + 1.91047i −0.0474102 + 0.161464i
\(141\) −16.1611 2.25210i −1.36101 0.189661i
\(142\) 6.30860 + 4.05429i 0.529406 + 0.340229i
\(143\) −2.38380 + 16.5797i −0.199343 + 1.38646i
\(144\) 0.669343 + 4.38496i 0.0557786 + 0.365413i
\(145\) −2.47732 + 1.13135i −0.205730 + 0.0939538i
\(146\) −7.84965 + 6.80176i −0.649642 + 0.562918i
\(147\) −5.70652 6.52824i −0.470666 0.538440i
\(148\) 3.13262 + 1.43062i 0.257500 + 0.117596i
\(149\) 19.1223 5.61482i 1.56656 0.459984i 0.620564 0.784155i \(-0.286904\pi\)
0.945998 + 0.324171i \(0.105085\pi\)
\(150\) 3.35927 + 2.88540i 0.274283 + 0.235592i
\(151\) 0.585077 1.28114i 0.0476129 0.104258i −0.884331 0.466861i \(-0.845385\pi\)
0.931944 + 0.362603i \(0.118112\pi\)
\(152\) 1.40381 + 9.76370i 0.113864 + 0.791940i
\(153\) 11.4107 3.45829i 0.922499 0.279587i
\(154\) −2.79362 6.11718i −0.225116 0.492936i
\(155\) −11.0798 + 7.12054i −0.889949 + 0.571935i
\(156\) 2.37348 + 5.13809i 0.190030 + 0.411376i
\(157\) 6.23984 9.70938i 0.497994 0.774893i −0.497724 0.867335i \(-0.665831\pi\)
0.995718 + 0.0924420i \(0.0294673\pi\)
\(158\) −2.60281 + 3.00381i −0.207069 + 0.238970i
\(159\) −2.99122 + 0.892414i −0.237219 + 0.0707730i
\(160\) 7.28843i 0.576201i
\(161\) −6.34690 + 2.36162i −0.500206 + 0.186122i
\(162\) 7.09991 6.37113i 0.557821 0.500563i
\(163\) 3.75567 + 1.10276i 0.294167 + 0.0863751i 0.425486 0.904965i \(-0.360103\pi\)
−0.131319 + 0.991340i \(0.541921\pi\)
\(164\) 0.942423 + 0.816615i 0.0735909 + 0.0637669i
\(165\) −12.5193 + 0.0543113i −0.974624 + 0.00422813i
\(166\) −15.8210 2.27471i −1.22794 0.176552i
\(167\) −5.44450 8.47181i −0.421308 0.655568i 0.564114 0.825697i \(-0.309218\pi\)
−0.985422 + 0.170129i \(0.945582\pi\)
\(168\) −6.29066 4.00431i −0.485335 0.308939i
\(169\) −0.587680 0.678219i −0.0452062 0.0521707i
\(170\) 6.70777 0.964432i 0.514462 0.0739685i
\(171\) 7.27970 6.41932i 0.556693 0.490898i
\(172\) 2.38776 + 8.13197i 0.182065 + 0.620057i
\(173\) 0.652717 + 2.22295i 0.0496252 + 0.169008i 0.980577 0.196134i \(-0.0628387\pi\)
−0.930952 + 0.365142i \(0.881021\pi\)
\(174\) −0.455660 3.07444i −0.0345435 0.233073i
\(175\) −3.37143 + 0.484738i −0.254856 + 0.0366428i
\(176\) 4.35058 + 5.02084i 0.327937 + 0.378460i
\(177\) −5.69561 + 8.94766i −0.428109 + 0.672547i
\(178\) −0.260775 0.405773i −0.0195459 0.0304140i
\(179\) −4.76707 0.685402i −0.356308 0.0512293i −0.0381632 0.999272i \(-0.512151\pi\)
−0.318145 + 0.948042i \(0.603060\pi\)
\(180\) −3.53873 + 2.31783i −0.263761 + 0.172761i
\(181\) 13.1782 + 11.4190i 0.979527 + 0.848765i 0.988504 0.151195i \(-0.0483121\pi\)
−0.00897721 + 0.999960i \(0.502858\pi\)
\(182\) 5.35355 + 1.57194i 0.396831 + 0.116520i
\(183\) −2.08857 3.21909i −0.154392 0.237962i
\(184\) 11.7125 8.75360i 0.863459 0.645324i
\(185\) 6.32032i 0.464679i
\(186\) −4.29709 14.4031i −0.315078 1.05609i
\(187\) 11.6943 13.4959i 0.855171 0.986920i
\(188\) −4.46446 + 6.94683i −0.325604 + 0.506649i
\(189\) 0.0954891 + 7.33669i 0.00694581 + 0.533665i
\(190\) 4.64070 2.98240i 0.336672 0.216366i
\(191\) 1.17349 + 2.56958i 0.0849105 + 0.185928i 0.947324 0.320276i \(-0.103776\pi\)
−0.862414 + 0.506204i \(0.831048\pi\)
\(192\) 12.9116 + 3.73041i 0.931811 + 0.269219i
\(193\) 2.77756 + 19.3183i 0.199933 + 1.39056i 0.804473 + 0.593990i \(0.202448\pi\)
−0.604540 + 0.796575i \(0.706643\pi\)
\(194\) −3.66306 + 8.02098i −0.262992 + 0.575873i
\(195\) 6.76804 7.87955i 0.484670 0.564266i
\(196\) −4.21029 + 1.23625i −0.300735 + 0.0883038i
\(197\) 12.3272 + 5.62965i 0.878278 + 0.401096i 0.802939 0.596062i \(-0.203269\pi\)
0.0753397 + 0.997158i \(0.475996\pi\)
\(198\) 3.90612 13.7430i 0.277596 0.976674i
\(199\) −11.0680 + 9.59051i −0.784592 + 0.679853i −0.952022 0.306031i \(-0.900999\pi\)
0.167429 + 0.985884i \(0.446453\pi\)
\(200\) 6.68986 3.05516i 0.473045 0.216032i
\(201\) 18.7928 + 8.48405i 1.32554 + 0.598419i
\(202\) −1.06071 + 7.37737i −0.0746310 + 0.519070i
\(203\) 2.01107 + 1.29244i 0.141149 + 0.0907113i
\(204\) 0.832813 5.97627i 0.0583085 0.418423i
\(205\) 0.644766 2.19587i 0.0450324 0.153366i
\(206\) 12.4988 0.870834
\(207\) −13.5196 4.92134i −0.939679 0.342057i
\(208\) −5.51205 −0.382192
\(209\) 4.09541 13.9477i 0.283286 0.964782i
\(210\) −0.575578 + 4.13036i −0.0397187 + 0.285022i
\(211\) −9.49791 6.10393i −0.653863 0.420212i 0.171213 0.985234i \(-0.445231\pi\)
−0.825076 + 0.565022i \(0.808868\pi\)
\(212\) −0.224816 + 1.56363i −0.0154404 + 0.107390i
\(213\) −11.1689 5.04222i −0.765279 0.345487i
\(214\) −17.4034 + 7.94785i −1.18967 + 0.543304i
\(215\) 11.7552 10.1859i 0.801695 0.694673i
\(216\) −4.66087 15.1416i −0.317132 1.03026i
\(217\) 10.5161 + 4.80253i 0.713878 + 0.326017i
\(218\) −7.82676 + 2.29814i −0.530095 + 0.155650i
\(219\) 11.0591 12.8753i 0.747305 0.870034i
\(220\) −2.63196 + 5.76318i −0.177446 + 0.388553i
\(221\) 2.10858 + 14.6655i 0.141838 + 0.986507i
\(222\) 6.92943 + 2.00205i 0.465073 + 0.134369i
\(223\) −4.76293 10.4294i −0.318949 0.698402i 0.680459 0.732786i \(-0.261780\pi\)
−0.999409 + 0.0343841i \(0.989053\pi\)
\(224\) −5.38202 + 3.45882i −0.359602 + 0.231102i
\(225\) −6.12138 3.85934i −0.408092 0.257289i
\(226\) 8.06751 12.5533i 0.536643 0.835032i
\(227\) 0.308514 0.356044i 0.0204768 0.0236315i −0.745419 0.666596i \(-0.767750\pi\)
0.765896 + 0.642965i \(0.222296\pi\)
\(228\) −1.40425 4.70681i −0.0929989 0.311716i
\(229\) 1.12917i 0.0746174i 0.999304 + 0.0373087i \(0.0118785\pi\)
−0.999304 + 0.0373087i \(0.988122\pi\)
\(230\) −7.17402 3.92460i −0.473041 0.258780i
\(231\) 5.98128 + 9.21888i 0.393539 + 0.606558i
\(232\) −4.95264 1.45422i −0.325156 0.0954745i
\(233\) 2.56406 + 2.22177i 0.167977 + 0.145553i 0.734793 0.678292i \(-0.237279\pi\)
−0.566816 + 0.823845i \(0.691825\pi\)
\(234\) 6.49506 + 9.91627i 0.424595 + 0.648247i
\(235\) 15.0008 + 2.15678i 0.978542 + 0.140693i
\(236\) 2.90201 + 4.51562i 0.188905 + 0.293942i
\(237\) 3.48770 5.47909i 0.226551 0.355905i
\(238\) −3.89542 4.49556i −0.252503 0.291404i
\(239\) −2.87786 + 0.413774i −0.186153 + 0.0267648i −0.234761 0.972053i \(-0.575431\pi\)
0.0486076 + 0.998818i \(0.484522\pi\)
\(240\) −0.603995 4.07529i −0.0389877 0.263059i
\(241\) 0.629154 + 2.14270i 0.0405274 + 0.138023i 0.977272 0.211991i \(-0.0679948\pi\)
−0.936744 + 0.350015i \(0.886177\pi\)
\(242\) −2.74385 9.34471i −0.176382 0.600700i
\(243\) −9.95035 + 11.9996i −0.638315 + 0.769775i
\(244\) −1.92218 + 0.276367i −0.123055 + 0.0176926i
\(245\) 5.27371 + 6.08619i 0.336925 + 0.388832i
\(246\) 2.20326 + 1.40248i 0.140475 + 0.0894188i
\(247\) 6.52055 + 10.1462i 0.414893 + 0.645585i
\(248\) −24.7081 3.55249i −1.56897 0.225583i
\(249\) 26.1189 0.113309i 1.65522 0.00718068i
\(250\) −9.55147 8.27639i −0.604088 0.523445i
\(251\) −11.1678 3.27916i −0.704904 0.206978i −0.0904154 0.995904i \(-0.528819\pi\)
−0.614489 + 0.788926i \(0.710638\pi\)
\(252\) 3.39091 + 1.51316i 0.213607 + 0.0953201i
\(253\) −21.0596 + 4.56398i −1.32400 + 0.286935i
\(254\) 1.38034i 0.0866104i
\(255\) −10.6118 + 3.16597i −0.664535 + 0.198261i
\(256\) 10.7436 12.3987i 0.671473 0.774921i
\(257\) −1.38747 + 2.15894i −0.0865477 + 0.134671i −0.881828 0.471571i \(-0.843687\pi\)
0.795281 + 0.606242i \(0.207324\pi\)
\(258\) 7.44394 + 16.1146i 0.463440 + 1.00325i
\(259\) −4.66713 + 2.99938i −0.290001 + 0.186373i
\(260\) −2.18370 4.78164i −0.135427 0.296545i
\(261\) 1.47311 + 4.86054i 0.0911831 + 0.300860i
\(262\) 1.25091 + 8.70024i 0.0772812 + 0.537503i
\(263\) −8.69346 + 19.0360i −0.536062 + 1.17381i 0.426931 + 0.904284i \(0.359595\pi\)
−0.962993 + 0.269528i \(0.913132\pi\)
\(264\) −17.9997 15.4606i −1.10781 0.951536i
\(265\) 2.78173 0.816791i 0.170881 0.0501750i
\(266\) −4.40461 2.01152i −0.270064 0.123334i
\(267\) 0.518744 + 0.593441i 0.0317466 + 0.0363180i
\(268\) 7.88608 6.83333i 0.481719 0.417412i
\(269\) 25.9223 11.8383i 1.58051 0.721795i 0.584531 0.811372i \(-0.301279\pi\)
0.995980 + 0.0895767i \(0.0285514\pi\)
\(270\) −6.61982 + 5.88867i −0.402869 + 0.358373i
\(271\) 0.00475284 0.0330567i 0.000288715 0.00200805i −0.989677 0.143319i \(-0.954223\pi\)
0.989965 + 0.141311i \(0.0451317\pi\)
\(272\) 4.94362 + 3.17707i 0.299751 + 0.192638i
\(273\) −9.03038 1.25841i −0.546543 0.0761626i
\(274\) −1.73983 + 5.92532i −0.105107 + 0.357962i
\(275\) −10.8381 −0.653564
\(276\) −5.13019 + 5.16680i −0.308801 + 0.311005i
\(277\) −30.3604 −1.82418 −0.912091 0.409987i \(-0.865533\pi\)
−0.912091 + 0.409987i \(0.865533\pi\)
\(278\) −2.86982 + 9.77370i −0.172120 + 0.586187i
\(279\) 10.3967 + 22.2525i 0.622432 + 1.33223i
\(280\) 5.82641 + 3.74441i 0.348195 + 0.223771i
\(281\) 3.30204 22.9662i 0.196983 1.37005i −0.615992 0.787752i \(-0.711245\pi\)
0.812976 0.582298i \(-0.197846\pi\)
\(282\) −7.11636 + 15.7633i −0.423773 + 0.938688i
\(283\) 15.1659 6.92603i 0.901519 0.411710i 0.0899361 0.995948i \(-0.471334\pi\)
0.811583 + 0.584238i \(0.198606\pi\)
\(284\) −4.68683 + 4.06116i −0.278112 + 0.240986i
\(285\) −6.78700 + 5.93271i −0.402027 + 0.351423i
\(286\) 16.1496 + 7.37530i 0.954949 + 0.436110i
\(287\) −1.92749 + 0.565961i −0.113776 + 0.0334076i
\(288\) −13.4700 1.81755i −0.793726 0.107100i
\(289\) −0.500187 + 1.09526i −0.0294228 + 0.0644269i
\(290\) 0.410813 + 2.85727i 0.0241238 + 0.167785i
\(291\) 3.99956 13.8431i 0.234459 0.811499i
\(292\) −3.56821 7.81329i −0.208814 0.457238i
\(293\) −6.12390 + 3.93559i −0.357762 + 0.229920i −0.707158 0.707055i \(-0.750023\pi\)
0.349396 + 0.936975i \(0.386387\pi\)
\(294\) −8.34327 + 3.85407i −0.486589 + 0.224774i
\(295\) 5.32594 8.28732i 0.310088 0.482506i
\(296\) 7.84452 9.05306i 0.455953 0.526198i
\(297\) −3.02162 + 23.1508i −0.175332 + 1.34335i
\(298\) 21.1241i 1.22368i
\(299\) 8.58052 15.6849i 0.496224 0.907079i
\(300\) −3.07218 + 1.99326i −0.177372 + 0.115081i
\(301\) −13.1002 3.84656i −0.755081 0.221712i
\(302\) −1.12820 0.977593i −0.0649208 0.0562542i
\(303\) −0.0528365 12.1793i −0.00303538 0.699684i
\(304\) 4.73490 + 0.680776i 0.271565 + 0.0390452i
\(305\) 1.92682 + 2.99820i 0.110330 + 0.171676i
\(306\) −0.109649 12.6373i −0.00626821 0.722429i
\(307\) 0.473561 + 0.546519i 0.0270276 + 0.0311915i 0.769102 0.639126i \(-0.220704\pi\)
−0.742075 + 0.670317i \(0.766158\pi\)
\(308\) 5.50475 0.791464i 0.313662 0.0450978i
\(309\) −20.2038 + 2.99438i −1.14935 + 0.170345i
\(310\) 3.93296 + 13.3944i 0.223377 + 0.760752i
\(311\) 0.566562 + 1.92953i 0.0321268 + 0.109414i 0.973996 0.226567i \(-0.0727503\pi\)
−0.941869 + 0.335981i \(0.890932\pi\)
\(312\) 19.4741 2.88624i 1.10251 0.163401i
\(313\) 13.5345 1.94597i 0.765015 0.109993i 0.251249 0.967923i \(-0.419159\pi\)
0.513767 + 0.857930i \(0.328250\pi\)
\(314\) −8.01109 9.24530i −0.452092 0.521742i
\(315\) −0.0591261 6.81444i −0.00333138 0.383950i
\(316\) −1.77704 2.76513i −0.0999665 0.155551i
\(317\) 8.43499 + 1.21277i 0.473756 + 0.0681159i 0.375058 0.927002i \(-0.377623\pi\)
0.0986986 + 0.995117i \(0.468532\pi\)
\(318\) 0.0143532 + 3.30855i 0.000804887 + 0.185534i
\(319\) 5.74878 + 4.98135i 0.321870 + 0.278902i
\(320\) −11.9768 3.51670i −0.669522 0.196589i
\(321\) 26.2277 17.0167i 1.46389 0.949782i
\(322\) 0.506464 + 7.16000i 0.0282242 + 0.399011i
\(323\) 12.8582i 0.715451i
\(324\) 3.40119 + 7.11804i 0.188955 + 0.395447i
\(325\) 5.88868 6.79590i 0.326645 0.376969i
\(326\) 2.24302 3.49020i 0.124229 0.193304i
\(327\) 12.1010 5.58993i 0.669189 0.309124i
\(328\) 3.64897 2.34505i 0.201481 0.129484i
\(329\) −5.52616 12.1006i −0.304667 0.667127i
\(330\) −3.68324 + 12.7483i −0.202756 + 0.701770i
\(331\) 0.444763 + 3.09339i 0.0244464 + 0.170028i 0.998387 0.0567748i \(-0.0180817\pi\)
−0.973941 + 0.226803i \(0.927173\pi\)
\(332\) 5.49103 12.0237i 0.301359 0.659885i
\(333\) −11.6808 1.57613i −0.640102 0.0863712i
\(334\) −10.2416 + 3.00722i −0.560397 + 0.164547i
\(335\) −17.4199 7.95541i −0.951751 0.434650i
\(336\) −2.72270 + 2.37999i −0.148535 + 0.129839i
\(337\) −9.14689 + 7.92582i −0.498263 + 0.431747i −0.867388 0.497633i \(-0.834203\pi\)
0.369125 + 0.929380i \(0.379657\pi\)
\(338\) −0.865239 + 0.395141i −0.0470628 + 0.0214929i
\(339\) −10.0333 + 22.2246i −0.544937 + 1.20708i
\(340\) −0.797566 + 5.54720i −0.0432541 + 0.300839i
\(341\) 30.9466 + 19.8882i 1.67585 + 1.07700i
\(342\) −4.35459 9.32036i −0.235469 0.503987i
\(343\) 4.77631 16.2666i 0.257897 0.878315i
\(344\) 29.4801 1.58946
\(345\) 12.5367 + 4.62524i 0.674955 + 0.249015i
\(346\) 2.45565 0.132016
\(347\) 4.63661 15.7908i 0.248906 0.847696i −0.736349 0.676602i \(-0.763452\pi\)
0.985255 0.171094i \(-0.0547302\pi\)
\(348\) 2.54568 + 0.354748i 0.136463 + 0.0190165i
\(349\) 26.2501 + 16.8699i 1.40514 + 0.903026i 0.999937 0.0112031i \(-0.00356614\pi\)
0.405198 + 0.914229i \(0.367203\pi\)
\(350\) −0.513790 + 3.57349i −0.0274632 + 0.191011i
\(351\) −12.8747 14.4732i −0.687199 0.772522i
\(352\) −18.5175 + 8.45665i −0.986985 + 0.450741i
\(353\) −15.9800 + 13.8468i −0.850531 + 0.736989i −0.966610 0.256251i \(-0.917513\pi\)
0.116080 + 0.993240i \(0.462967\pi\)
\(354\) 7.39894 + 8.46435i 0.393249 + 0.449875i
\(355\) 10.3530 + 4.72803i 0.549478 + 0.250938i
\(356\) 0.382731 0.112380i 0.0202847 0.00595613i
\(357\) 7.37380 + 6.33364i 0.390263 + 0.335212i
\(358\) −2.12058 + 4.64343i −0.112076 + 0.245413i
\(359\) −0.608756 4.23399i −0.0321289 0.223462i 0.967431 0.253136i \(-0.0814620\pi\)
−0.999560 + 0.0296745i \(0.990553\pi\)
\(360\) 4.26785 + 14.0818i 0.224935 + 0.742176i
\(361\) 3.54479 + 7.76201i 0.186568 + 0.408527i
\(362\) 15.5483 9.99228i 0.817200 0.525183i
\(363\) 6.67407 + 14.4480i 0.350298 + 0.758322i
\(364\) −2.49462 + 3.88170i −0.130754 + 0.203457i
\(365\) −10.3232 + 11.9136i −0.540340 + 0.623586i
\(366\) −3.89749 + 1.16280i −0.203725 + 0.0607804i
\(367\) 11.2014i 0.584709i −0.956310 0.292354i \(-0.905561\pi\)
0.956310 0.292354i \(-0.0944387\pi\)
\(368\) −2.47287 6.64588i −0.128907 0.346441i
\(369\) −3.89747 1.73921i −0.202894 0.0905395i
\(370\) −6.42775 1.88736i −0.334163 0.0981190i
\(371\) −1.92325 1.66651i −0.0998502 0.0865207i
\(372\) 12.4298 0.0539230i 0.644454 0.00279578i
\(373\) −3.22490 0.463670i −0.166979 0.0240079i 0.0583183 0.998298i \(-0.481426\pi\)
−0.225297 + 0.974290i \(0.572335\pi\)
\(374\) −10.2332 15.9232i −0.529147 0.823368i
\(375\) 17.4223 + 11.0902i 0.899686 + 0.572693i
\(376\) 18.8098 + 21.7077i 0.970041 + 1.11949i
\(377\) −6.24697 + 0.898178i −0.321735 + 0.0462585i
\(378\) 7.48991 + 2.09375i 0.385239 + 0.107691i
\(379\) −6.15345 20.9567i −0.316081 1.07647i −0.952350 0.305007i \(-0.901341\pi\)
0.636269 0.771467i \(-0.280477\pi\)
\(380\) 1.28526 + 4.37718i 0.0659322 + 0.224544i
\(381\) −0.330694 2.23127i −0.0169419 0.114311i
\(382\) 2.96368 0.426113i 0.151635 0.0218018i
\(383\) 9.92748 + 11.4569i 0.507270 + 0.585421i 0.950398 0.311038i \(-0.100676\pi\)
−0.443127 + 0.896459i \(0.646131\pi\)
\(384\) −0.778433 + 1.22290i −0.0397242 + 0.0624057i
\(385\) −5.51806 8.58627i −0.281226 0.437597i
\(386\) 20.4761 + 2.94402i 1.04221 + 0.149847i
\(387\) −15.8935 24.2652i −0.807909 1.23347i
\(388\) −5.51106 4.77536i −0.279782 0.242432i
\(389\) −24.9651 7.33041i −1.26578 0.371667i −0.421137 0.906997i \(-0.638369\pi\)
−0.844643 + 0.535330i \(0.820187\pi\)
\(390\) −5.99243 9.23605i −0.303438 0.467686i
\(391\) −16.7362 + 9.12169i −0.846387 + 0.461303i
\(392\) 15.2632i 0.770909i
\(393\) −4.10638 13.7639i −0.207140 0.694296i
\(394\) 9.40647 10.8556i 0.473891 0.546899i
\(395\) −3.26133 + 5.07473i −0.164095 + 0.255338i
\(396\) 9.99477 + 6.30139i 0.502256 + 0.316657i
\(397\) −0.819795 + 0.526850i −0.0411443 + 0.0264418i −0.561051 0.827781i \(-0.689603\pi\)
0.519907 + 0.854223i \(0.325967\pi\)
\(398\) 6.44841 + 14.1201i 0.323230 + 0.707774i
\(399\) 7.60176 + 2.19630i 0.380564 + 0.109953i
\(400\) −0.507573 3.53025i −0.0253786 0.176512i
\(401\) −5.62068 + 12.3076i −0.280684 + 0.614611i −0.996492 0.0836852i \(-0.973331\pi\)
0.715809 + 0.698296i \(0.246058\pi\)
\(402\) 14.2401 16.5787i 0.710232 0.826873i
\(403\) −29.2848 + 8.59879i −1.45878 + 0.428336i
\(404\) −5.60668 2.56049i −0.278943 0.127389i
\(405\) 9.28988 11.1047i 0.461618 0.551798i
\(406\) 1.91495 1.65931i 0.0950371 0.0823501i
\(407\) −16.0578 + 7.33336i −0.795956 + 0.363501i
\(408\) −19.1295 8.63605i −0.947051 0.427548i
\(409\) 2.19405 15.2599i 0.108489 0.754555i −0.860856 0.508849i \(-0.830071\pi\)
0.969344 0.245706i \(-0.0790199\pi\)
\(410\) −2.04066 1.31145i −0.100781 0.0647679i
\(411\) 1.39281 9.99484i 0.0687024 0.493009i
\(412\) −2.91207 + 9.91759i −0.143467 + 0.488605i
\(413\) −8.64712 −0.425497
\(414\) −9.04219 + 12.2798i −0.444399 + 0.603521i
\(415\) −24.2587 −1.19081
\(416\) 4.75848 16.2059i 0.233303 0.794559i
\(417\) 2.29742 16.4863i 0.112505 0.807338i
\(418\) −12.9618 8.33005i −0.633983 0.407436i
\(419\) −3.62086 + 25.1837i −0.176891 + 1.23030i 0.687013 + 0.726645i \(0.258922\pi\)
−0.863904 + 0.503657i \(0.831988\pi\)
\(420\) −3.14326 1.41903i −0.153376 0.0692417i
\(421\) −24.4417 + 11.1622i −1.19122 + 0.544010i −0.909587 0.415513i \(-0.863602\pi\)
−0.281629 + 0.959523i \(0.590875\pi\)
\(422\) −9.04393 + 7.83661i −0.440251 + 0.381480i
\(423\) 7.72683 27.1855i 0.375691 1.32181i
\(424\) 4.99825 + 2.28262i 0.242736 + 0.110854i
\(425\) −9.19850 + 2.70092i −0.446193 + 0.131014i
\(426\) −8.46315 + 9.85304i −0.410041 + 0.477381i
\(427\) 1.29957 2.84566i 0.0628906 0.137711i
\(428\) −2.25171 15.6610i −0.108841 0.757003i
\(429\) −27.8721 8.05283i −1.34568 0.388794i
\(430\) −6.84875 14.9967i −0.330276 0.723203i
\(431\) 1.84035 1.18272i 0.0886465 0.0569697i −0.495567 0.868570i \(-0.665040\pi\)
0.584213 + 0.811600i \(0.301403\pi\)
\(432\) −7.68230 + 0.0999873i −0.369615 + 0.00481064i
\(433\) 12.7704 19.8711i 0.613704 0.954942i −0.385772 0.922594i \(-0.626065\pi\)
0.999477 0.0323485i \(-0.0102986\pi\)
\(434\) 8.02445 9.26071i 0.385186 0.444528i
\(435\) −1.34859 4.52023i −0.0646598 0.216729i
\(436\) 6.74583i 0.323067i
\(437\) −9.30794 + 12.4137i −0.445259 + 0.593828i
\(438\) −9.79174 15.0919i −0.467867 0.721118i
\(439\) 30.6380 + 8.99614i 1.46227 + 0.429362i 0.913579 0.406661i \(-0.133307\pi\)
0.548694 + 0.836023i \(0.315125\pi\)
\(440\) 16.6552 + 14.4318i 0.794005 + 0.688009i
\(441\) 12.5632 8.22877i 0.598248 0.391846i
\(442\) 15.5444 + 2.23495i 0.739373 + 0.106306i
\(443\) 14.2088 + 22.1093i 0.675078 + 1.05044i 0.994692 + 0.102895i \(0.0328104\pi\)
−0.319614 + 0.947548i \(0.603553\pi\)
\(444\) −3.20306 + 5.03193i −0.152011 + 0.238805i
\(445\) −0.479400 0.553257i −0.0227257 0.0262269i
\(446\) −12.0289 + 1.72950i −0.569586 + 0.0818941i
\(447\) 5.06076 + 34.1461i 0.239366 + 1.61506i
\(448\) 3.08688 + 10.5129i 0.145841 + 0.496689i
\(449\) 10.7313 + 36.5474i 0.506440 + 1.72478i 0.673830 + 0.738886i \(0.264648\pi\)
−0.167390 + 0.985891i \(0.553534\pi\)
\(450\) −5.75289 + 5.07296i −0.271194 + 0.239142i
\(451\) −6.32709 + 0.909698i −0.297931 + 0.0428360i
\(452\) 8.08118 + 9.32618i 0.380107 + 0.438667i
\(453\) 2.05790 + 1.30995i 0.0966884 + 0.0615468i
\(454\) −0.269968 0.420079i −0.0126702 0.0197153i
\(455\) 8.38203 + 1.20515i 0.392956 + 0.0564985i
\(456\) −17.0850 + 0.0741182i −0.800077 + 0.00347090i
\(457\) 3.07782 + 2.66694i 0.143974 + 0.124754i 0.723870 0.689936i \(-0.242361\pi\)
−0.579896 + 0.814690i \(0.696907\pi\)
\(458\) 1.14836 + 0.337189i 0.0536593 + 0.0157558i
\(459\) 3.20481 + 20.4015i 0.149588 + 0.952258i
\(460\) 4.78556 4.77808i 0.223128 0.222779i
\(461\) 21.2506i 0.989741i −0.868967 0.494871i \(-0.835215\pi\)
0.868967 0.494871i \(-0.164785\pi\)
\(462\) 11.1617 3.33003i 0.519289 0.154927i
\(463\) −8.61186 + 9.93861i −0.400227 + 0.461887i −0.919712 0.392593i \(-0.871578\pi\)
0.519485 + 0.854479i \(0.326124\pi\)
\(464\) −1.35332 + 2.10581i −0.0628263 + 0.0977596i
\(465\) −9.56640 20.7093i −0.443631 0.960370i
\(466\) 3.02521 1.94418i 0.140140 0.0900625i
\(467\) 5.23053 + 11.4533i 0.242040 + 0.529994i 0.991196 0.132399i \(-0.0422681\pi\)
−0.749156 + 0.662393i \(0.769541\pi\)
\(468\) −9.38165 + 2.84335i −0.433667 + 0.131434i
\(469\) 2.39230 + 16.6388i 0.110466 + 0.768307i
\(470\) 6.67293 14.6117i 0.307799 0.673987i
\(471\) 15.1645 + 13.0254i 0.698744 + 0.600178i
\(472\) 17.9146 5.26021i 0.824587 0.242121i
\(473\) −39.5183 18.0474i −1.81705 0.829820i
\(474\) −4.53073 5.18314i −0.208103 0.238069i
\(475\) −5.89778 + 5.11046i −0.270609 + 0.234484i
\(476\) 4.47473 2.04354i 0.205099 0.0936655i
\(477\) −0.815842 5.34469i −0.0373549 0.244717i
\(478\) −0.438572 + 3.05034i −0.0200598 + 0.139519i
\(479\) 9.44493 + 6.06989i 0.431550 + 0.277340i 0.738329 0.674440i \(-0.235615\pi\)
−0.306779 + 0.951781i \(0.599251\pi\)
\(480\) 12.5031 + 1.74235i 0.570687 + 0.0795270i
\(481\) 4.12641 14.0533i 0.188148 0.640774i
\(482\) 2.36700 0.107814
\(483\) −2.53402 11.4525i −0.115302 0.521107i
\(484\) 8.05414 0.366097
\(485\) −3.77043 + 12.8409i −0.171206 + 0.583076i
\(486\) 9.23222 + 13.7028i 0.418782 + 0.621570i
\(487\) 6.86912 + 4.41452i 0.311270 + 0.200041i 0.686943 0.726711i \(-0.258952\pi\)
−0.375673 + 0.926752i \(0.622589\pi\)
\(488\) −0.961306 + 6.68603i −0.0435163 + 0.302662i
\(489\) −2.78958 + 6.17913i −0.126149 + 0.279430i
\(490\) 7.76446 3.54591i 0.350763 0.160188i
\(491\) −2.83742 + 2.45864i −0.128051 + 0.110957i −0.716532 0.697554i \(-0.754272\pi\)
0.588481 + 0.808511i \(0.299726\pi\)
\(492\) −1.62617 + 1.42149i −0.0733136 + 0.0640855i
\(493\) 6.12046 + 2.79512i 0.275652 + 0.125886i
\(494\) 12.2658 3.60156i 0.551864 0.162042i
\(495\) 2.89965 21.4895i 0.130330 0.965880i
\(496\) −5.02877 + 11.0115i −0.225798 + 0.494429i
\(497\) −1.42178 9.88871i −0.0637756 0.443569i
\(498\) 7.68431 26.5967i 0.344342 1.19182i
\(499\) −5.68350 12.4451i −0.254428 0.557120i 0.738716 0.674017i \(-0.235433\pi\)
−0.993144 + 0.116897i \(0.962705\pi\)
\(500\) 8.79254 5.65062i 0.393214 0.252704i
\(501\) 15.8347 7.31466i 0.707443 0.326795i
\(502\) −6.66979 + 10.3784i −0.297687 + 0.463210i
\(503\) 12.7240 14.6842i 0.567334 0.654738i −0.397499 0.917603i \(-0.630122\pi\)
0.964833 + 0.262864i \(0.0846672\pi\)
\(504\) 8.37312 9.83421i 0.372968 0.438051i
\(505\) 11.3119i 0.503375i
\(506\) −1.64720 + 22.7804i −0.0732270 + 1.01271i
\(507\) 1.30396 0.846018i 0.0579107 0.0375730i
\(508\) −1.09528 0.321603i −0.0485951 0.0142688i
\(509\) −10.1882 8.82816i −0.451586 0.391301i 0.399158 0.916882i \(-0.369303\pi\)
−0.850744 + 0.525581i \(0.823848\pi\)
\(510\) 0.0509200 + 11.7376i 0.00225478 + 0.519748i
\(511\) 13.6964 + 1.96924i 0.605893 + 0.0871142i
\(512\) −8.49629 13.2205i −0.375487 0.584269i
\(513\) 9.27192 + 14.0227i 0.409365 + 0.619119i
\(514\) 1.78131 + 2.05575i 0.0785704 + 0.0906751i
\(515\) 18.7766 2.69967i 0.827398 0.118962i
\(516\) −14.5210 + 2.15214i −0.639251 + 0.0947427i
\(517\) −11.9255 40.6144i −0.524481 1.78622i
\(518\) 1.65668 + 5.64213i 0.0727903 + 0.247901i
\(519\) −3.96945 + 0.588308i −0.174240 + 0.0258239i
\(520\) −18.0985 + 2.60218i −0.793673 + 0.114113i
\(521\) −4.39954 5.07734i −0.192747 0.222442i 0.651147 0.758952i \(-0.274288\pi\)
−0.843894 + 0.536509i \(0.819743\pi\)
\(522\) 5.38305 0.0467065i 0.235610 0.00204429i
\(523\) 6.99787 + 10.8889i 0.305996 + 0.476138i 0.959862 0.280471i \(-0.0904907\pi\)
−0.653867 + 0.756610i \(0.726854\pi\)
\(524\) −7.19493 1.03448i −0.314312 0.0451913i
\(525\) −0.0255932 5.89948i −0.00111698 0.257474i
\(526\) 16.7636 + 14.5257i 0.730927 + 0.633352i
\(527\) 31.2211 + 9.16733i 1.36001 + 0.399335i
\(528\) −9.65315 + 6.26304i −0.420100 + 0.272564i
\(529\) 22.7607 + 3.30885i 0.989598 + 0.143863i
\(530\) 3.07292i 0.133479i
\(531\) −13.9879 11.9097i −0.607023 0.516836i
\(532\) 2.62232 3.02632i 0.113692 0.131208i
\(533\) 2.86728 4.46158i 0.124196 0.193252i
\(534\) 0.758433 0.350349i 0.0328206 0.0151611i
\(535\) −24.4279 + 15.6989i −1.05611 + 0.678721i
\(536\) −15.0779 33.0160i −0.651266 1.42607i
\(537\) 2.31539 8.01394i 0.0999165 0.345827i
\(538\) −4.29869 29.8980i −0.185330 1.28900i
\(539\) 9.34397 20.4604i 0.402473 0.881294i
\(540\) −3.13022 6.62469i −0.134703 0.285081i
\(541\) 16.4836 4.84001i 0.708684 0.208088i 0.0925251 0.995710i \(-0.470506\pi\)
0.616159 + 0.787622i \(0.288688\pi\)
\(542\) −0.0321993 0.0147049i −0.00138308 0.000631632i
\(543\) −22.7393 + 19.8771i −0.975835 + 0.853006i
\(544\) −13.6086 + 11.7919i −0.583465 + 0.505575i
\(545\) −11.2615 + 5.14298i −0.482392 + 0.220301i
\(546\) −3.97643 + 8.80809i −0.170176 + 0.376951i
\(547\) −2.06388 + 14.3546i −0.0882449 + 0.613757i 0.896926 + 0.442181i \(0.145795\pi\)
−0.985171 + 0.171576i \(0.945114\pi\)
\(548\) −4.29628 2.76105i −0.183528 0.117946i
\(549\) 6.02156 2.81335i 0.256994 0.120071i
\(550\) −3.23646 + 11.0224i −0.138003 + 0.469995i
\(551\) 5.47714 0.233334
\(552\) 12.2166 + 22.1852i 0.519974 + 0.944263i
\(553\) 5.29506 0.225169
\(554\) −9.06616 + 30.8765i −0.385184 + 1.31182i
\(555\) 10.8423 + 1.51091i 0.460232 + 0.0641347i
\(556\) −7.08663 4.55430i −0.300540 0.193145i
\(557\) 4.48426 31.1887i 0.190004 1.32151i −0.641985 0.766717i \(-0.721889\pi\)
0.831989 0.554792i \(-0.187202\pi\)
\(558\) 25.7354 3.92839i 1.08947 0.166302i
\(559\) 32.7879 14.9737i 1.38678 0.633320i
\(560\) 2.53834 2.19948i 0.107264 0.0929450i
\(561\) 20.3563 + 23.2875i 0.859445 + 0.983201i
\(562\) −22.3705 10.2163i −0.943644 0.430948i
\(563\) −5.54381 + 1.62781i −0.233644 + 0.0686041i −0.396459 0.918053i \(-0.629761\pi\)
0.162815 + 0.986657i \(0.447943\pi\)
\(564\) −10.8498 9.31934i −0.456861 0.392415i
\(565\) 9.40817 20.6010i 0.395805 0.866691i
\(566\) −2.51496 17.4919i −0.105712 0.735240i
\(567\) −12.6087 1.59008i −0.529517 0.0667769i
\(568\) 8.96106 + 19.6220i 0.375998 + 0.823320i
\(569\) 5.87229 3.77389i 0.246179 0.158210i −0.411733 0.911305i \(-0.635076\pi\)
0.657912 + 0.753095i \(0.271440\pi\)
\(570\) 4.00684 + 8.67397i 0.167828 + 0.363313i
\(571\) −1.26613 + 1.97013i −0.0529857 + 0.0824474i −0.866736 0.498768i \(-0.833786\pi\)
0.813750 + 0.581215i \(0.197422\pi\)
\(572\) −9.61483 + 11.0961i −0.402016 + 0.463952i
\(573\) −4.68858 + 1.39881i −0.195868 + 0.0584362i
\(574\) 2.12925i 0.0888734i
\(575\) 10.8357 + 4.05115i 0.451879 + 0.168945i
\(576\) −9.48602 + 21.2577i −0.395251 + 0.885736i
\(577\) −23.0132 6.75728i −0.958051 0.281309i −0.234916 0.972016i \(-0.575482\pi\)
−0.723135 + 0.690706i \(0.757300\pi\)
\(578\) 0.964509 + 0.835752i 0.0401183 + 0.0347627i
\(579\) −33.8041 + 0.146649i −1.40485 + 0.00609454i
\(580\) −2.36291 0.339735i −0.0981143 0.0141067i
\(581\) 11.5123 + 17.9135i 0.477610 + 0.743176i
\(582\) −12.8841 8.20135i −0.534063 0.339957i
\(583\) −5.30279 6.11975i −0.219619 0.253454i
\(584\) −29.5733 + 4.25200i −1.22375 + 0.175949i
\(585\) 11.8992 + 13.4941i 0.491972 + 0.557911i
\(586\) 2.17379 + 7.40323i 0.0897982 + 0.305825i
\(587\) −1.66435 5.66827i −0.0686953 0.233955i 0.917988 0.396608i \(-0.129813\pi\)
−0.986683 + 0.162654i \(0.947995\pi\)
\(588\) −1.11426 7.51818i −0.0459514 0.310045i
\(589\) 26.2179 3.76957i 1.08029 0.155322i
\(590\) −6.83777 7.89120i −0.281506 0.324876i
\(591\) −12.6044 + 19.8012i −0.518477 + 0.814514i
\(592\) −3.14068 4.88699i −0.129081 0.200854i
\(593\) −11.6702 1.67792i −0.479238 0.0689040i −0.101537 0.994832i \(-0.532376\pi\)
−0.377701 + 0.925928i \(0.623285\pi\)
\(594\) 22.6420 + 9.98621i 0.929013 + 0.409739i
\(595\) −6.82301 5.91217i −0.279716 0.242375i
\(596\) 16.7616 + 4.92164i 0.686580 + 0.201598i
\(597\) −13.8064 21.2796i −0.565057 0.870916i
\(598\) −13.3892 13.4101i −0.547524 0.548382i
\(599\) 27.3519i 1.11757i −0.829313 0.558784i \(-0.811268\pi\)
0.829313 0.558784i \(-0.188732\pi\)
\(600\) 3.64179 + 12.2066i 0.148675 + 0.498334i
\(601\) −14.9084 + 17.2052i −0.608125 + 0.701813i −0.973407 0.229084i \(-0.926427\pi\)
0.365282 + 0.930897i \(0.380973\pi\)
\(602\) −7.82388 + 12.1742i −0.318877 + 0.496183i
\(603\) −19.0467 + 30.2104i −0.775642 + 1.23026i
\(604\) 1.03856 0.667442i 0.0422584 0.0271578i
\(605\) −6.14042 13.4457i −0.249644 0.546644i
\(606\) −12.4021 3.58322i −0.503802 0.145559i
\(607\) 0.491879 + 3.42109i 0.0199647 + 0.138858i 0.997366 0.0725354i \(-0.0231090\pi\)
−0.977401 + 0.211393i \(0.932200\pi\)
\(608\) −6.08912 + 13.3333i −0.246946 + 0.540737i
\(609\) −2.69790 + 3.14097i −0.109324 + 0.127279i
\(610\) 3.62454 1.06426i 0.146753 0.0430907i
\(611\) 31.9462 + 14.5893i 1.29240 + 0.590221i
\(612\) 10.0531 + 2.85734i 0.406371 + 0.115501i
\(613\) 5.90988 5.12094i 0.238698 0.206833i −0.527295 0.849683i \(-0.676794\pi\)
0.765992 + 0.642850i \(0.222248\pi\)
\(614\) 0.697222 0.318411i 0.0281376 0.0128500i
\(615\) 3.61283 + 1.63102i 0.145683 + 0.0657690i
\(616\) 2.75300 19.1475i 0.110922 0.771477i
\(617\) −11.0304 7.08879i −0.444066 0.285384i 0.299437 0.954116i \(-0.403201\pi\)
−0.743504 + 0.668732i \(0.766837\pi\)
\(618\) −2.98793 + 21.4414i −0.120192 + 0.862499i
\(619\) −8.27724 + 28.1897i −0.332690 + 1.13304i 0.608046 + 0.793902i \(0.291954\pi\)
−0.940737 + 0.339138i \(0.889865\pi\)
\(620\) −11.5446 −0.463641
\(621\) 11.6744 22.0161i 0.468477 0.883476i
\(622\) 2.13152 0.0854660
\(623\) −0.181038 + 0.616560i −0.00725314 + 0.0247019i
\(624\) 1.31769 9.45577i 0.0527499 0.378534i
\(625\) −5.99047 3.84984i −0.239619 0.153994i
\(626\) 2.06259 14.3457i 0.0824378 0.573368i
\(627\) 22.9479 + 10.3599i 0.916450 + 0.413733i
\(628\) 9.20246 4.20262i 0.367218 0.167703i
\(629\) −11.8010 + 10.2256i −0.470537 + 0.407722i
\(630\) −6.94793 1.97478i −0.276812 0.0786771i
\(631\) −24.9917 11.4133i −0.994902 0.454357i −0.149659 0.988738i \(-0.547817\pi\)
−0.845244 + 0.534381i \(0.820545\pi\)
\(632\) −10.9700 + 3.22108i −0.436363 + 0.128128i
\(633\) 12.7417 14.8342i 0.506436 0.589608i
\(634\) 3.75222 8.21621i 0.149020 0.326307i
\(635\) 0.298146 + 2.07365i 0.0118316 + 0.0822904i
\(636\) −2.62862 0.759462i −0.104232 0.0301146i
\(637\) 7.75258 + 16.9758i 0.307168 + 0.672605i
\(638\) 6.78270 4.35898i 0.268530 0.172574i
\(639\) 11.3198 17.9546i 0.447804 0.710271i
\(640\) 0.727908 1.13265i 0.0287731 0.0447718i
\(641\) −29.5322 + 34.0820i −1.16645 + 1.34616i −0.239536 + 0.970887i \(0.576995\pi\)
−0.926916 + 0.375270i \(0.877550\pi\)
\(642\) −9.47393 31.7550i −0.373906 1.25327i
\(643\) 40.9797i 1.61608i 0.589126 + 0.808041i \(0.299472\pi\)
−0.589126 + 0.808041i \(0.700528\pi\)
\(644\) −5.79933 1.26632i −0.228526 0.0499000i
\(645\) 14.6635 + 22.6007i 0.577375 + 0.889901i
\(646\) −13.0768 3.83969i −0.514499 0.151071i
\(647\) −22.7458 19.7094i −0.894231 0.774855i 0.0808452 0.996727i \(-0.474238\pi\)
−0.975076 + 0.221871i \(0.928784\pi\)
\(648\) 27.0893 4.37590i 1.06417 0.171901i
\(649\) −27.2349 3.91579i −1.06906 0.153708i
\(650\) −5.15295 8.01815i −0.202115 0.314498i
\(651\) −10.7526 + 16.8920i −0.421426 + 0.662049i
\(652\) 2.24682 + 2.59297i 0.0879922 + 0.101548i
\(653\) 16.3778 2.35477i 0.640913 0.0921494i 0.185807 0.982586i \(-0.440510\pi\)
0.455107 + 0.890437i \(0.349601\pi\)
\(654\) −2.07137 13.9760i −0.0809968 0.546504i
\(655\) 3.75841 + 12.8000i 0.146853 + 0.500136i
\(656\) −0.592622 2.01828i −0.0231380 0.0788008i
\(657\) 19.4435 + 22.0496i 0.758565 + 0.860235i
\(658\) −13.9565 + 2.00664i −0.544080 + 0.0782269i
\(659\) 11.7423 + 13.5514i 0.457416 + 0.527886i 0.936869 0.349682i \(-0.113710\pi\)
−0.479453 + 0.877568i \(0.659165\pi\)
\(660\) −9.25740 5.89278i −0.360344 0.229376i
\(661\) 3.11846 + 4.85242i 0.121294 + 0.188737i 0.896591 0.442860i \(-0.146036\pi\)
−0.775297 + 0.631597i \(0.782400\pi\)
\(662\) 3.27879 + 0.471418i 0.127434 + 0.0183222i
\(663\) −25.6623 + 0.111329i −0.996643 + 0.00432365i
\(664\) −34.7476 30.1090i −1.34847 1.16845i
\(665\) −7.05140 2.07048i −0.273442 0.0802897i
\(666\) −5.09100 + 11.4087i −0.197272 + 0.442076i
\(667\) −3.88551 7.12903i −0.150448 0.276037i
\(668\) 8.82720i 0.341535i
\(669\) 19.0299 5.67747i 0.735739 0.219504i
\(670\) −13.2925 + 15.3404i −0.513535 + 0.592651i
\(671\) 5.38175 8.37417i 0.207760 0.323281i
\(672\) −4.64690 10.0596i −0.179258 0.388057i
\(673\) 18.4088 11.8306i 0.709606 0.456036i −0.135402 0.990791i \(-0.543232\pi\)
0.845007 + 0.534755i \(0.179596\pi\)
\(674\) 5.32912 + 11.6692i 0.205270 + 0.449479i
\(675\) 8.08395 9.57846i 0.311151 0.368675i
\(676\) −0.111948 0.778615i −0.00430569 0.0299467i
\(677\) 16.0670 35.1818i 0.617505 1.35215i −0.299815 0.953997i \(-0.596925\pi\)
0.917320 0.398151i \(-0.130348\pi\)
\(678\) 19.6062 + 16.8405i 0.752973 + 0.646757i
\(679\) 11.2715 3.30960i 0.432559 0.127011i
\(680\) 17.7320 + 8.09794i 0.679991 + 0.310542i
\(681\) 0.537032 + 0.614362i 0.0205791 + 0.0235424i
\(682\) 29.4674 25.5336i 1.12836 0.977734i
\(683\) 40.2698 18.3906i 1.54088 0.703697i 0.549596 0.835431i \(-0.314782\pi\)
0.991285 + 0.131734i \(0.0420545\pi\)
\(684\) 8.41011 1.28376i 0.321569 0.0490859i
\(685\) −1.33387 + 9.27725i −0.0509644 + 0.354465i
\(686\) −15.1168 9.71500i −0.577163 0.370920i
\(687\) −1.93706 0.269935i −0.0739033 0.0102987i
\(688\) 4.02776 13.7173i 0.153557 0.522966i
\(689\) 6.71847 0.255953
\(690\) 8.44755 11.3686i 0.321593 0.432797i
\(691\) 32.7374 1.24539 0.622694 0.782465i \(-0.286038\pi\)
0.622694 + 0.782465i \(0.286038\pi\)
\(692\) −0.572135 + 1.94851i −0.0217493 + 0.0740714i
\(693\) −17.2446 + 8.05690i −0.655069 + 0.306056i
\(694\) −14.6747 9.43083i −0.557043 0.357990i
\(695\) −2.20019 + 15.3026i −0.0834579 + 0.580462i
\(696\) 3.67865 8.14848i 0.139439 0.308867i
\(697\) −5.14320 + 2.34882i −0.194812 + 0.0889678i
\(698\) 24.9954 21.6586i 0.946090 0.819791i
\(699\) −4.42434 + 3.86745i −0.167344 + 0.146280i
\(700\) −2.71579 1.24026i −0.102647 0.0468774i
\(701\) 10.5436 3.09589i 0.398228 0.116930i −0.0764857 0.997071i \(-0.524370\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(702\) −18.5638 + 8.77155i −0.700645 + 0.331061i
\(703\) −5.28030 + 11.5623i −0.199150 + 0.436079i
\(704\) 4.96169 + 34.5093i 0.187001 + 1.30062i
\(705\) −7.28594 + 25.2178i −0.274404 + 0.949758i
\(706\) 9.31021 + 20.3865i 0.350395 + 0.767257i
\(707\) 8.35311 5.36822i 0.314151 0.201893i
\(708\) −8.44017 + 3.89884i −0.317201 + 0.146527i
\(709\) −22.5622 + 35.1075i −0.847342 + 1.31849i 0.0989220 + 0.995095i \(0.468461\pi\)
−0.946264 + 0.323395i \(0.895176\pi\)
\(710\) 7.89997 9.11705i 0.296481 0.342157i
\(711\) 8.56548 + 7.29288i 0.321230 + 0.273504i
\(712\) 1.38748i 0.0519981i
\(713\) −23.5056 31.4510i −0.880291 1.17785i
\(714\) 8.64324 5.60780i 0.323465 0.209867i
\(715\) 25.8542 + 7.59149i 0.966893 + 0.283905i
\(716\) −3.19041 2.76451i −0.119231 0.103314i
\(717\) −0.0218464 5.03581i −0.000815870 0.188066i
\(718\) −4.48775 0.645240i −0.167481 0.0240802i
\(719\) −19.7432 30.7211i −0.736299 1.14570i −0.984224 0.176924i \(-0.943385\pi\)
0.247926 0.968779i \(-0.420251\pi\)
\(720\) 7.13545 0.0619113i 0.265922 0.00230730i
\(721\) −10.9042 12.5841i −0.406094 0.468658i
\(722\) 8.95248 1.28717i 0.333177 0.0479036i
\(723\) −3.82615 + 0.567070i −0.142296 + 0.0210896i
\(724\) 4.30614 + 14.6654i 0.160036 + 0.545034i
\(725\) −1.15050 3.91823i −0.0427283 0.145519i
\(726\) 16.6865 2.47309i 0.619296 0.0917851i
\(727\) 3.85722 0.554585i 0.143057 0.0205684i −0.0704145 0.997518i \(-0.522432\pi\)
0.213471 + 0.976949i \(0.431523\pi\)
\(728\) 10.5104 + 12.1297i 0.389542 + 0.449555i
\(729\) −18.2063 19.9382i −0.674308 0.738450i
\(730\) 9.03341 + 14.0563i 0.334342 + 0.520246i
\(731\) −38.0373 5.46894i −1.40686 0.202276i
\(732\) −0.0145916 3.36351i −0.000539322 0.124319i
\(733\) 22.5664 + 19.5539i 0.833509 + 0.722240i 0.963047 0.269335i \(-0.0868038\pi\)
−0.129538 + 0.991575i \(0.541349\pi\)
\(734\) −11.3918 3.34494i −0.420479 0.123464i
\(735\) −11.7014 + 7.59197i −0.431613 + 0.280034i
\(736\) 21.6742 1.53313i 0.798923 0.0565120i
\(737\) 53.4887i 1.97028i
\(738\) −2.93262 + 3.44436i −0.107951 + 0.126789i
\(739\) 3.35207 3.86850i 0.123308 0.142305i −0.690739 0.723104i \(-0.742715\pi\)
0.814047 + 0.580799i \(0.197260\pi\)
\(740\) 2.99517 4.66057i 0.110105 0.171326i
\(741\) −18.9643 + 8.76032i −0.696670 + 0.321819i
\(742\) −2.26915 + 1.45829i −0.0833031 + 0.0535356i
\(743\) 12.0053 + 26.2880i 0.440433 + 0.964413i 0.991519 + 0.129965i \(0.0414864\pi\)
−0.551086 + 0.834449i \(0.685786\pi\)
\(744\) 12.0008 41.5369i 0.439972 1.52282i
\(745\) −4.56268 31.7341i −0.167164 1.16265i
\(746\) −1.43456 + 3.14125i −0.0525230 + 0.115009i
\(747\) −6.04951 + 44.8333i −0.221340 + 1.64037i
\(748\) 15.0190 4.40997i 0.549148 0.161244i
\(749\) 23.1851 + 10.5883i 0.847167 + 0.386888i
\(750\) 16.4813 14.4068i 0.601811 0.526061i
\(751\) 25.7822 22.3404i 0.940807 0.815214i −0.0421386 0.999112i \(-0.513417\pi\)
0.982945 + 0.183898i \(0.0588717\pi\)
\(752\) 12.6706 5.78648i 0.462050 0.211011i
\(753\) 8.29504 18.3741i 0.302288 0.669591i
\(754\) −0.952008 + 6.62136i −0.0346701 + 0.241136i
\(755\) −1.90602 1.22493i −0.0693673 0.0445797i
\(756\) −3.40641 + 5.45529i −0.123890 + 0.198407i
\(757\) 2.92187 9.95098i 0.106197 0.361674i −0.889199 0.457521i \(-0.848738\pi\)
0.995396 + 0.0958464i \(0.0305557\pi\)
\(758\) −23.1505 −0.840862
\(759\) −2.79496 37.2182i −0.101451 1.35094i
\(760\) 15.8682 0.575600
\(761\) 7.97071 27.1457i 0.288938 0.984033i −0.679271 0.733888i \(-0.737704\pi\)
0.968209 0.250145i \(-0.0804781\pi\)
\(762\) −2.36794 0.329980i −0.0857815 0.0119539i
\(763\) 9.14205 + 5.87524i 0.330965 + 0.212698i
\(764\) −0.352387 + 2.45091i −0.0127489 + 0.0886706i
\(765\) −2.89432 18.9611i −0.104644 0.685539i
\(766\) 14.6162 6.67498i 0.528104 0.241177i
\(767\) 17.2529 14.9497i 0.622965 0.539803i
\(768\) 18.7014 + 21.3943i 0.674828 + 0.772001i
\(769\) −40.0709 18.2998i −1.44500 0.659907i −0.470109 0.882609i \(-0.655785\pi\)
−0.974887 + 0.222701i \(0.928513\pi\)
\(770\) −10.3800 + 3.04784i −0.374069 + 0.109837i
\(771\) −3.37192 2.89627i −0.121437 0.104307i
\(772\) −7.10671 + 15.5615i −0.255776 + 0.560072i
\(773\) 3.68503 + 25.6300i 0.132541 + 0.921846i 0.942225 + 0.334980i \(0.108729\pi\)
−0.809684 + 0.586866i \(0.800361\pi\)
\(774\) −29.4237 + 8.91759i −1.05761 + 0.320536i
\(775\) −8.20385 17.9639i −0.294691 0.645284i
\(776\) −21.3383 + 13.7133i −0.766000 + 0.492278i
\(777\) −4.02966 8.72337i −0.144563 0.312949i
\(778\) −14.9100 + 23.2004i −0.534550 + 0.831776i
\(779\) −3.01406 + 3.47841i −0.107990 + 0.124627i
\(780\) 8.72481 2.60300i 0.312398 0.0932024i
\(781\) 31.7892i 1.13751i
\(782\) 4.27900 + 19.7446i 0.153017 + 0.706065i
\(783\) −8.69028 + 1.36514i −0.310565 + 0.0487860i
\(784\) 7.10207 + 2.08535i 0.253645 + 0.0744770i
\(785\) −14.0318 12.1586i −0.500816 0.433960i
\(786\) −15.2241 + 0.0660453i −0.543025 + 0.00235576i
\(787\) 24.6361 + 3.54214i 0.878182 + 0.126264i 0.566637 0.823968i \(-0.308244\pi\)
0.311546 + 0.950231i \(0.399153\pi\)
\(788\) 6.42217 + 9.99310i 0.228780 + 0.355989i
\(789\) −30.5776 19.4641i −1.08859 0.692941i
\(790\) 4.18710 + 4.83217i 0.148970 + 0.171921i
\(791\) −19.6772 + 2.82916i −0.699642 + 0.100593i
\(792\) 30.8253 27.1821i 1.09533 0.965872i
\(793\) 2.32684 + 7.92449i 0.0826285 + 0.281407i
\(794\) 0.291000 + 0.991056i 0.0103272 + 0.0351712i
\(795\) 0.736191 + 4.96725i 0.0261100 + 0.176170i
\(796\) −12.7064 + 1.82691i −0.450367 + 0.0647530i
\(797\) 12.1916 + 14.0699i 0.431849 + 0.498380i 0.929410 0.369049i \(-0.120316\pi\)
−0.497561 + 0.867429i \(0.665771\pi\)
\(798\) 4.50365 7.07512i 0.159428 0.250457i
\(799\) −20.2427 31.4982i −0.716134 1.11433i
\(800\) 10.8174 + 1.55531i 0.382453 + 0.0549884i
\(801\) −1.14204 + 0.748025i −0.0403520 + 0.0264302i
\(802\) 10.8383 + 9.39148i 0.382715 + 0.331625i
\(803\) 42.2463 + 12.4046i 1.49084 + 0.437750i
\(804\) 9.83718 + 15.1619i 0.346930 + 0.534720i
\(805\) 2.30737 + 10.6469i 0.0813241 + 0.375254i
\(806\) 32.3503i 1.13949i
\(807\) 14.1114 + 47.2991i 0.496746 + 1.66501i
\(808\) −14.0399 + 16.2029i −0.493923 + 0.570017i
\(809\) −20.6545 + 32.1390i −0.726174 + 1.12995i 0.260220 + 0.965549i \(0.416205\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(810\) −8.51935 12.7638i −0.299340 0.448476i
\(811\) −6.36974 + 4.09358i −0.223672 + 0.143745i −0.647678 0.761914i \(-0.724260\pi\)
0.424006 + 0.905659i \(0.360623\pi\)
\(812\) 0.870475 + 1.90607i 0.0305477 + 0.0668901i
\(813\) 0.0555718 + 0.0160558i 0.00194899 + 0.000563102i
\(814\) 2.66286 + 18.5206i 0.0933333 + 0.649147i
\(815\) 2.61576 5.72772i 0.0916261 0.200633i
\(816\) −6.63200 + 7.72116i −0.232166 + 0.270295i
\(817\) −30.0145 + 8.81304i −1.05007 + 0.308329i
\(818\) −14.8641 6.78823i −0.519712 0.237345i
\(819\) 4.31755 15.1906i 0.150867 0.530801i
\(820\) 1.51606 1.31367i 0.0529431 0.0458755i
\(821\) −48.0854 + 21.9599i −1.67819 + 0.766405i −0.678704 + 0.734412i \(0.737458\pi\)
−0.999488 + 0.0319923i \(0.989815\pi\)
\(822\) −9.74881 4.40112i −0.340029 0.153507i
\(823\) 1.34935 9.38492i 0.0470353 0.327138i −0.952695 0.303927i \(-0.901702\pi\)
0.999731 0.0232106i \(-0.00738884\pi\)
\(824\) 30.2459 + 19.4379i 1.05367 + 0.677150i
\(825\) 2.59093 18.5925i 0.0902046 0.647309i
\(826\) −2.58218 + 8.79410i −0.0898456 + 0.305986i
\(827\) −49.1675 −1.70972 −0.854860 0.518859i \(-0.826357\pi\)
−0.854860 + 0.518859i \(0.826357\pi\)
\(828\) −7.63711 10.0359i −0.265408 0.348770i
\(829\) 57.2339 1.98782 0.993908 0.110215i \(-0.0351539\pi\)
0.993908 + 0.110215i \(0.0351539\pi\)
\(830\) −7.24408 + 24.6711i −0.251446 + 0.856346i
\(831\) 7.25787 52.0826i 0.251773 1.80672i
\(832\) −24.3344 15.6388i −0.843645 0.542177i
\(833\) 2.83152 19.6937i 0.0981064 0.682345i
\(834\) −16.0805 7.25957i −0.556821 0.251378i
\(835\) −14.7362 + 6.72980i −0.509967 + 0.232894i
\(836\) 9.62969 8.34417i 0.333050 0.288589i
\(837\) −40.6591 + 12.5156i −1.40538 + 0.432602i
\(838\) 24.5305 + 11.2027i 0.847391 + 0.386990i
\(839\) 6.50174 1.90908i 0.224465 0.0659089i −0.167566 0.985861i \(-0.553591\pi\)
0.392031 + 0.919952i \(0.371773\pi\)
\(840\) −7.81628 + 9.09994i −0.269687 + 0.313978i
\(841\) 10.8564 23.7722i 0.374359 0.819732i
\(842\) 4.05317 + 28.1904i 0.139681 + 0.971505i
\(843\) 38.6086 + 11.1548i 1.32975 + 0.384192i
\(844\) −4.11109 9.00203i −0.141509 0.309863i
\(845\) −1.21448 + 0.780497i −0.0417793 + 0.0268499i
\(846\) −25.3403 15.9762i −0.871216 0.549274i
\(847\) −7.01471 + 10.9151i −0.241028 + 0.375047i
\(848\) 1.74501 2.01385i 0.0599239 0.0691559i
\(849\) 8.25592 + 27.6724i 0.283342 + 0.949715i
\(850\) 10.1614i 0.348533i
\(851\) 18.7953 1.32949i 0.644293 0.0455743i
\(852\) −5.84640 9.01099i −0.200294 0.308711i
\(853\) −25.2839 7.42402i −0.865704 0.254194i −0.181417 0.983406i \(-0.558068\pi\)
−0.684287 + 0.729213i \(0.739886\pi\)
\(854\) −2.50596 2.17142i −0.0857520 0.0743046i
\(855\) −8.55494 13.0612i −0.292573 0.446683i
\(856\) −54.4747 7.83228i −1.86191 0.267702i
\(857\) 23.4245 + 36.4493i 0.800166 + 1.24508i 0.965901 + 0.258913i \(0.0833642\pi\)
−0.165735 + 0.986170i \(0.552999\pi\)
\(858\) −16.5128 + 25.9412i −0.563738 + 0.885618i
\(859\) −33.6570 38.8423i −1.14836 1.32528i −0.937588 0.347747i \(-0.886947\pi\)
−0.210775 0.977535i \(-0.567599\pi\)
\(860\) 13.4953 1.94033i 0.460184 0.0661645i
\(861\) −0.510113 3.44185i −0.0173846 0.117298i
\(862\) −0.653264 2.22481i −0.0222503 0.0757774i
\(863\) −13.6113 46.3557i −0.463333 1.57797i −0.777681 0.628659i \(-0.783604\pi\)
0.314349 0.949308i \(-0.398214\pi\)
\(864\) 6.33805 22.6729i 0.215625 0.771348i
\(865\) 3.68906 0.530406i 0.125432 0.0180344i
\(866\) −16.3954 18.9213i −0.557137 0.642971i
\(867\) −1.75931 1.11989i −0.0597493 0.0380333i
\(868\) 5.47861 + 8.52489i 0.185956 + 0.289354i
\(869\) 16.6773 + 2.39783i 0.565738 + 0.0813408i
\(870\) −4.99978 + 0.0216901i −0.169508 + 0.000735363i
\(871\) −33.5393 29.0620i −1.13644 0.984729i
\(872\) −22.5140 6.61071i −0.762421 0.223867i
\(873\) 22.7914 + 10.1704i 0.771373 + 0.344217i
\(874\) 9.84519 + 13.1731i 0.333019 + 0.445587i
\(875\) 16.8372i 0.569200i
\(876\) 14.2565 4.25335i 0.481682 0.143707i
\(877\) −28.6924 + 33.1128i −0.968873 + 1.11814i 0.0240894 + 0.999710i \(0.492331\pi\)
−0.992962 + 0.118429i \(0.962214\pi\)
\(878\) 18.2981 28.4724i 0.617531 0.960897i
\(879\) −5.28745 11.4462i −0.178341 0.386072i
\(880\) 8.99074 5.77800i 0.303078 0.194776i
\(881\) −4.94883 10.8364i −0.166730 0.365089i 0.807762 0.589508i \(-0.200679\pi\)
−0.974493 + 0.224420i \(0.927951\pi\)
\(882\) −4.61705 15.2340i −0.155464 0.512955i
\(883\) −4.97510 34.6026i −0.167425 1.16447i −0.884181 0.467145i \(-0.845283\pi\)
0.716755 0.697325i \(-0.245626\pi\)
\(884\) −5.39505 + 11.8135i −0.181455 + 0.397331i
\(885\) 12.9435 + 11.1176i 0.435090 + 0.373716i
\(886\) 26.7280 7.84806i 0.897946 0.263661i
\(887\) −12.5334 5.72381i −0.420830 0.192187i 0.193733 0.981054i \(-0.437940\pi\)
−0.614563 + 0.788868i \(0.710668\pi\)
\(888\) 13.6550 + 15.6213i 0.458232 + 0.524215i
\(889\) 1.38977 1.20424i 0.0466112 0.0403889i
\(890\) −0.705818 + 0.322336i −0.0236591 + 0.0108047i
\(891\) −38.9923 10.7179i −1.30629 0.359062i
\(892\) 1.43026 9.94769i 0.0478887 0.333073i
\(893\) −25.6402 16.4780i −0.858016 0.551414i
\(894\) 36.2378 + 5.04985i 1.21197 + 0.168892i
\(895\) −2.18274 + 7.43374i −0.0729611 + 0.248483i
\(896\) −1.18182 −0.0394819
\(897\) 24.8558 + 18.4692i 0.829910 + 0.616670i
\(898\) 40.3731 1.34727
\(899\) −3.90495 + 13.2991i −0.130238 + 0.443548i
\(900\) −2.68495 5.74675i −0.0894985 0.191558i
\(901\) −6.02563 3.87244i −0.200743 0.129010i
\(902\) −0.964218 + 6.70628i −0.0321049 + 0.223295i
\(903\) 9.73035 21.5535i 0.323806 0.717254i
\(904\) 39.0452 17.8313i 1.29862 0.593061i
\(905\) 21.1995 18.3695i 0.704696 0.610623i
\(906\) 1.94674 1.70170i 0.0646761 0.0565353i
\(907\) −10.2997 4.70372i −0.341997 0.156185i 0.237011 0.971507i \(-0.423832\pi\)
−0.579007 + 0.815322i \(0.696560\pi\)
\(908\) 0.396224 0.116342i 0.0131492 0.00386094i
\(909\) 20.9060 + 2.82091i 0.693407 + 0.0935637i
\(910\) 3.72866 8.16462i 0.123604 0.270655i
\(911\) 1.37642 + 9.57320i 0.0456028 + 0.317174i 0.999836 + 0.0181108i \(0.00576517\pi\)
−0.954233 + 0.299064i \(0.903326\pi\)
\(912\) −2.29977 + 7.95986i −0.0761528 + 0.263577i
\(913\) 28.1470 + 61.6334i 0.931530 + 2.03977i
\(914\) 3.63136 2.33374i 0.120115 0.0771931i
\(915\) −5.60395 + 2.58868i −0.185261 + 0.0855790i
\(916\) −0.535107 + 0.832642i −0.0176804 + 0.0275113i
\(917\) 7.66832 8.84971i 0.253230 0.292243i
\(918\) 21.7052 + 2.83294i 0.716380 + 0.0935010i
\(919\) 48.2925i 1.59302i 0.604623 + 0.796512i \(0.293324\pi\)
−0.604623 + 0.796512i \(0.706676\pi\)
\(920\) −11.2570 20.6540i −0.371132 0.680943i
\(921\) −1.05075 + 0.681733i −0.0346233 + 0.0224639i
\(922\) −21.6119 6.34581i −0.711749 0.208988i
\(923\) 19.9330 + 17.2721i 0.656103 + 0.568516i
\(924\) 0.0417877 + 9.63246i 0.00137471 + 0.316885i
\(925\) 9.38053 + 1.34872i 0.308430 + 0.0443455i
\(926\) 7.53589 + 11.7261i 0.247645 + 0.385343i
\(927\) −0.306934 35.3749i −0.0100810 1.16187i
\(928\) −5.02294 5.79678i −0.164886 0.190289i
\(929\) −12.3923 + 1.78174i −0.406577 + 0.0584569i −0.342570 0.939492i \(-0.611297\pi\)
−0.0640075 + 0.997949i \(0.520388\pi\)
\(930\) −23.9180 + 3.54486i −0.784301 + 0.116240i
\(931\) −4.56292 15.5399i −0.149544 0.509298i
\(932\) 0.837839 + 2.85342i 0.0274443 + 0.0934668i
\(933\) −3.44551 + 0.510655i −0.112801 + 0.0167181i
\(934\) 13.2099 1.89929i 0.432240 0.0621468i
\(935\) −18.8124 21.7107i −0.615231 0.710015i
\(936\) 0.295849 + 34.0974i 0.00967012 + 1.11451i
\(937\) 9.87548 + 15.3665i 0.322618 + 0.502003i 0.964245 0.265014i \(-0.0853765\pi\)
−0.641627 + 0.767017i \(0.721740\pi\)
\(938\) 17.6360 + 2.53567i 0.575835 + 0.0827926i
\(939\) 0.102743 + 23.6833i 0.00335290 + 0.772875i
\(940\) 10.0394 + 8.69919i 0.327449 + 0.283736i
\(941\) −10.7847 3.16668i −0.351572 0.103231i 0.101178 0.994868i \(-0.467739\pi\)
−0.452750 + 0.891638i \(0.649557\pi\)
\(942\) 17.7752 11.5327i 0.579146 0.375755i
\(943\) 6.66568 + 1.45549i 0.217064 + 0.0473973i
\(944\) 9.05446i 0.294698i
\(945\) 11.7041 + 1.52761i 0.380735 + 0.0496931i
\(946\) −30.1550 + 34.8007i −0.980424 + 1.13147i
\(947\) 13.4195 20.8811i 0.436075 0.678546i −0.551768 0.833997i \(-0.686047\pi\)
0.987844 + 0.155451i \(0.0496831\pi\)
\(948\) 5.16833 2.38745i 0.167860 0.0775407i
\(949\) −30.7318 + 19.7501i −0.997597 + 0.641117i
\(950\) 3.43614 + 7.52410i 0.111483 + 0.244114i
\(951\) −4.09691 + 14.1801i −0.132852 + 0.459821i
\(952\) −2.43516 16.9369i −0.0789239 0.548927i
\(953\) −1.10582 + 2.42141i −0.0358210 + 0.0784370i −0.926697 0.375810i \(-0.877364\pi\)
0.890876 + 0.454247i \(0.150092\pi\)
\(954\) −5.67917 0.766309i −0.183870 0.0248102i
\(955\) 4.36022 1.28028i 0.141093 0.0414288i
\(956\) −2.31821 1.05869i −0.0749762 0.0342405i
\(957\) −9.91966 + 8.67106i −0.320657 + 0.280296i
\(958\) 8.99348 7.79289i 0.290566 0.251777i
\(959\) 7.48363 3.41766i 0.241659 0.110362i
\(960\) 8.89593 19.7051i 0.287115 0.635981i
\(961\) −5.12755 + 35.6629i −0.165405 + 1.15042i
\(962\) −13.0599 8.39310i −0.421069 0.270604i
\(963\) 22.9219 + 49.0609i 0.738647 + 1.58097i
\(964\) −0.551481 + 1.87817i −0.0177620 + 0.0604918i
\(965\) 31.3967 1.01069
\(966\) −12.4039 0.842820i −0.399088 0.0271173i
\(967\) 1.99729 0.0642286 0.0321143 0.999484i \(-0.489776\pi\)
0.0321143 + 0.999484i \(0.489776\pi\)
\(968\) 7.89281 26.8805i 0.253685 0.863971i
\(969\) 22.0580 + 3.07385i 0.708604 + 0.0987461i
\(970\) 11.9333 + 7.66904i 0.383154 + 0.246238i
\(971\) 3.09698 21.5400i 0.0993869 0.691251i −0.877824 0.478983i \(-0.841006\pi\)
0.977211 0.212269i \(-0.0680852\pi\)
\(972\) −13.0239 + 4.13303i −0.417742 + 0.132567i
\(973\) 12.3441 5.63736i 0.395734 0.180726i
\(974\) 6.54079 5.66763i 0.209580 0.181603i
\(975\) 10.2505 + 11.7265i 0.328278 + 0.375548i
\(976\) 2.97971 + 1.36079i 0.0953782 + 0.0435578i
\(977\) −1.03752 + 0.304644i −0.0331933 + 0.00974644i −0.298287 0.954476i \(-0.596415\pi\)
0.265094 + 0.964223i \(0.414597\pi\)
\(978\) 5.45114 + 4.68219i 0.174308 + 0.149720i
\(979\) −0.849401 + 1.85993i −0.0271470 + 0.0594436i
\(980\) 1.00460 + 6.98712i 0.0320906 + 0.223195i
\(981\) 6.69655 + 22.0953i 0.213804 + 0.705450i
\(982\) 1.65313 + 3.61984i 0.0527533 + 0.115514i
\(983\) 33.3880 21.4572i 1.06491 0.684378i 0.113889 0.993494i \(-0.463669\pi\)
0.951025 + 0.309115i \(0.100033\pi\)
\(984\) 3.15057 + 6.82032i 0.100436 + 0.217424i
\(985\) 11.7863 18.3399i 0.375544 0.584358i
\(986\) 4.67030 5.38982i 0.148733 0.171647i
\(987\) 22.0793 6.58725i 0.702792 0.209674i
\(988\) 10.5718i 0.336334i
\(989\) 32.7634 + 32.8147i 1.04182 + 1.04345i
\(990\) −20.9889 9.36607i −0.667070 0.297673i
\(991\) 45.2455 + 13.2853i 1.43727 + 0.422020i 0.905311 0.424750i \(-0.139638\pi\)
0.531959 + 0.846770i \(0.321456\pi\)
\(992\) −28.0334 24.2910i −0.890060 0.771241i
\(993\) −5.41296 + 0.0234826i −0.171775 + 0.000745197i
\(994\) −10.4814 1.50699i −0.332449 0.0477989i
\(995\) 12.7371 + 19.8194i 0.403794 + 0.628316i
\(996\) 19.3136 + 12.2941i 0.611976 + 0.389552i
\(997\) 26.3103 + 30.3637i 0.833256 + 0.961628i 0.999702 0.0244223i \(-0.00777463\pi\)
−0.166446 + 0.986051i \(0.553229\pi\)
\(998\) −14.3539 + 2.06377i −0.454363 + 0.0653276i
\(999\) 5.49617 19.6613i 0.173891 0.622055i
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 69.2.g.a.5.4 yes 60
3.2 odd 2 inner 69.2.g.a.5.3 60
23.14 odd 22 inner 69.2.g.a.14.3 yes 60
69.14 even 22 inner 69.2.g.a.14.4 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.2.g.a.5.3 60 3.2 odd 2 inner
69.2.g.a.5.4 yes 60 1.1 even 1 trivial
69.2.g.a.14.3 yes 60 23.14 odd 22 inner
69.2.g.a.14.4 yes 60 69.14 even 22 inner