Properties

Label 390.2.bn.b.67.2
Level $390$
Weight $2$
Character 390.67
Analytic conductor $3.114$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [390,2,Mod(67,390)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(390, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("390.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.bn (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 67.2
Root \(-1.09227 - 0.838128i\) of defining polynomial
Character \(\chi\) \(=\) 390.67
Dual form 390.2.bn.b.163.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.06394 + 0.860320i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.450069 + 0.259847i) q^{7} -1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.06394 + 0.860320i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.450069 + 0.259847i) q^{7} -1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(0.286912 + 2.21758i) q^{10} +(0.222514 - 0.830435i) q^{11} +(0.707107 - 0.707107i) q^{12} +(1.76341 + 3.14490i) q^{13} +0.519695i q^{14} +(-1.77095 - 1.36519i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.09452 + 4.08479i) q^{17} +1.00000i q^{18} +(0.0538940 - 0.0144409i) q^{19} +(-1.77703 + 1.35727i) q^{20} +(-0.367480 - 0.367480i) q^{21} +(0.830435 - 0.222514i) q^{22} +(0.0474866 - 0.177222i) q^{23} +(0.965926 + 0.258819i) q^{24} +(3.51970 + 3.55130i) q^{25} +(-1.84186 + 3.09961i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.450069 + 0.259847i) q^{28} +(-6.27365 + 3.62210i) q^{29} +(0.296818 - 2.21628i) q^{30} +(3.09986 - 3.09986i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.429865 + 0.744548i) q^{33} +(-2.99027 + 2.99027i) q^{34} +(0.705364 + 0.923513i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-0.195463 + 0.112851i) q^{37} +(0.0394531 + 0.0394531i) q^{38} +(-0.889363 - 3.49414i) q^{39} +(-2.06394 - 0.860320i) q^{40} +(-0.0280536 - 0.00751694i) q^{41} +(0.134507 - 0.501987i) q^{42} +(4.63274 - 1.24134i) q^{43} +(0.607921 + 0.607921i) q^{44} +(1.35727 + 1.77703i) q^{45} +(0.177222 - 0.0474866i) q^{46} +5.53738i q^{47} +(0.258819 + 0.965926i) q^{48} +(-3.36496 - 5.82828i) q^{49} +(-1.31566 + 4.82380i) q^{50} -4.22888i q^{51} +(-3.60527 - 0.0452920i) q^{52} +(2.49867 - 2.49867i) q^{53} +(0.258819 - 0.965926i) q^{54} +(1.17370 - 1.52254i) q^{55} +(-0.450069 - 0.259847i) q^{56} -0.0557952 q^{57} +(-6.27365 - 3.62210i) q^{58} +(-1.31167 - 4.89521i) q^{59} +(2.06776 - 0.851088i) q^{60} +(7.21773 - 12.5015i) q^{61} +(4.23449 + 1.13463i) q^{62} +(0.259847 + 0.450069i) q^{63} +1.00000 q^{64} +(0.933954 + 8.00798i) q^{65} -0.859730 q^{66} +(-6.85698 - 11.8766i) q^{67} +(-4.08479 - 1.09452i) q^{68} +(-0.0917371 + 0.158893i) q^{69} +(-0.447104 + 1.07262i) q^{70} +(-1.78083 - 6.64614i) q^{71} +(-0.866025 - 0.500000i) q^{72} +2.40525 q^{73} +(-0.195463 - 0.112851i) q^{74} +(-2.48063 - 4.34125i) q^{75} +(-0.0144409 + 0.0538940i) q^{76} +(0.315933 - 0.315933i) q^{77} +(2.58133 - 2.51728i) q^{78} -16.0201i q^{79} +(-0.286912 - 2.21758i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.00751694 - 0.0280536i) q^{82} +4.83100i q^{83} +(0.501987 - 0.134507i) q^{84} +(-1.25521 + 9.37239i) q^{85} +(3.39140 + 3.39140i) q^{86} +(6.99735 - 1.87494i) q^{87} +(-0.222514 + 0.830435i) q^{88} +(-14.9100 - 3.99511i) q^{89} +(-0.860320 + 2.06394i) q^{90} +(-0.0235380 + 1.87364i) q^{91} +(0.129736 + 0.129736i) q^{92} +(-3.79654 + 2.19193i) q^{93} +(-4.79551 + 2.76869i) q^{94} +(0.123658 + 0.0165610i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(3.14672 - 5.45027i) q^{97} +(3.36496 - 5.82828i) q^{98} +(0.607921 - 0.607921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{2} - 8 q^{4} + 24 q^{7} - 16 q^{8} + 12 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{16} - 4 q^{17} - 4 q^{19} + 4 q^{23} + 4 q^{25} + 4 q^{26} - 24 q^{28} - 48 q^{29} - 4 q^{30} + 16 q^{31} + 8 q^{32} + 16 q^{33} - 20 q^{34} - 12 q^{35} + 12 q^{37} + 4 q^{38} + 4 q^{39} - 12 q^{41} + 20 q^{43} - 12 q^{44} + 8 q^{45} - 4 q^{46} - 4 q^{49} - 16 q^{50} - 4 q^{52} + 32 q^{53} + 16 q^{55} - 24 q^{56} - 8 q^{57} - 48 q^{58} + 4 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 16 q^{64} - 8 q^{65} + 32 q^{66} - 28 q^{67} - 16 q^{68} + 4 q^{69} - 36 q^{71} + 32 q^{73} + 12 q^{74} - 24 q^{75} + 8 q^{76} + 4 q^{77} + 20 q^{78} + 8 q^{81} - 24 q^{82} + 52 q^{85} + 16 q^{86} + 36 q^{87} - 12 q^{88} - 24 q^{89} + 4 q^{90} - 8 q^{92} + 36 q^{94} - 40 q^{95} - 4 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.965926 0.258819i −0.557678 0.149429i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 2.06394 + 0.860320i 0.923022 + 0.384747i
\(6\) −0.258819 0.965926i −0.105662 0.394338i
\(7\) 0.450069 + 0.259847i 0.170110 + 0.0982131i 0.582638 0.812732i \(-0.302021\pi\)
−0.412528 + 0.910945i \(0.635354\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.866025 + 0.500000i 0.288675 + 0.166667i
\(10\) 0.286912 + 2.21758i 0.0907294 + 0.701262i
\(11\) 0.222514 0.830435i 0.0670906 0.250386i −0.924233 0.381829i \(-0.875294\pi\)
0.991324 + 0.131443i \(0.0419611\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) 1.76341 + 3.14490i 0.489082 + 0.872238i
\(14\) 0.519695i 0.138894i
\(15\) −1.77095 1.36519i −0.457256 0.352491i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.09452 + 4.08479i 0.265459 + 0.990707i 0.961969 + 0.273159i \(0.0880686\pi\)
−0.696510 + 0.717547i \(0.745265\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0.0538940 0.0144409i 0.0123641 0.00331296i −0.252632 0.967563i \(-0.581296\pi\)
0.264996 + 0.964250i \(0.414629\pi\)
\(20\) −1.77703 + 1.35727i −0.397356 + 0.303494i
\(21\) −0.367480 0.367480i −0.0801907 0.0801907i
\(22\) 0.830435 0.222514i 0.177049 0.0474402i
\(23\) 0.0474866 0.177222i 0.00990164 0.0369534i −0.960798 0.277248i \(-0.910578\pi\)
0.970700 + 0.240295i \(0.0772442\pi\)
\(24\) 0.965926 + 0.258819i 0.197169 + 0.0528312i
\(25\) 3.51970 + 3.55130i 0.703940 + 0.710259i
\(26\) −1.84186 + 3.09961i −0.361218 + 0.607883i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) −0.450069 + 0.259847i −0.0850550 + 0.0491066i
\(29\) −6.27365 + 3.62210i −1.16499 + 0.672606i −0.952494 0.304556i \(-0.901492\pi\)
−0.212494 + 0.977162i \(0.568159\pi\)
\(30\) 0.296818 2.21628i 0.0541913 0.404636i
\(31\) 3.09986 3.09986i 0.556752 0.556752i −0.371629 0.928381i \(-0.621201\pi\)
0.928381 + 0.371629i \(0.121201\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −0.429865 + 0.744548i −0.0748299 + 0.129609i
\(34\) −2.99027 + 2.99027i −0.512828 + 0.512828i
\(35\) 0.705364 + 0.923513i 0.119228 + 0.156102i
\(36\) −0.866025 + 0.500000i −0.144338 + 0.0833333i
\(37\) −0.195463 + 0.112851i −0.0321339 + 0.0185525i −0.515981 0.856600i \(-0.672572\pi\)
0.483847 + 0.875153i \(0.339239\pi\)
\(38\) 0.0394531 + 0.0394531i 0.00640014 + 0.00640014i
\(39\) −0.889363 3.49414i −0.142412 0.559511i
\(40\) −2.06394 0.860320i −0.326338 0.136028i
\(41\) −0.0280536 0.00751694i −0.00438124 0.00117395i 0.256628 0.966510i \(-0.417389\pi\)
−0.261009 + 0.965336i \(0.584055\pi\)
\(42\) 0.134507 0.501987i 0.0207549 0.0774582i
\(43\) 4.63274 1.24134i 0.706487 0.189303i 0.112352 0.993668i \(-0.464161\pi\)
0.594134 + 0.804366i \(0.297495\pi\)
\(44\) 0.607921 + 0.607921i 0.0916475 + 0.0916475i
\(45\) 1.35727 + 1.77703i 0.202329 + 0.264904i
\(46\) 0.177222 0.0474866i 0.0261300 0.00700152i
\(47\) 5.53738i 0.807710i 0.914823 + 0.403855i \(0.132330\pi\)
−0.914823 + 0.403855i \(0.867670\pi\)
\(48\) 0.258819 + 0.965926i 0.0373573 + 0.139419i
\(49\) −3.36496 5.82828i −0.480708 0.832611i
\(50\) −1.31566 + 4.82380i −0.186063 + 0.682188i
\(51\) 4.22888i 0.592162i
\(52\) −3.60527 0.0452920i −0.499961 0.00628087i
\(53\) 2.49867 2.49867i 0.343219 0.343219i −0.514357 0.857576i \(-0.671969\pi\)
0.857576 + 0.514357i \(0.171969\pi\)
\(54\) 0.258819 0.965926i 0.0352208 0.131446i
\(55\) 1.17370 1.52254i 0.158261 0.205299i
\(56\) −0.450069 0.259847i −0.0601430 0.0347236i
\(57\) −0.0557952 −0.00739025
\(58\) −6.27365 3.62210i −0.823771 0.475605i
\(59\) −1.31167 4.89521i −0.170765 0.637302i −0.997234 0.0743209i \(-0.976321\pi\)
0.826470 0.562981i \(-0.190346\pi\)
\(60\) 2.06776 0.851088i 0.266947 0.109875i
\(61\) 7.21773 12.5015i 0.924135 1.60065i 0.131189 0.991357i \(-0.458120\pi\)
0.792946 0.609292i \(-0.208546\pi\)
\(62\) 4.23449 + 1.13463i 0.537781 + 0.144098i
\(63\) 0.259847 + 0.450069i 0.0327377 + 0.0567034i
\(64\) 1.00000 0.125000
\(65\) 0.933954 + 8.00798i 0.115843 + 0.993268i
\(66\) −0.859730 −0.105825
\(67\) −6.85698 11.8766i −0.837713 1.45096i −0.891802 0.452426i \(-0.850559\pi\)
0.0540887 0.998536i \(-0.482775\pi\)
\(68\) −4.08479 1.09452i −0.495353 0.132730i
\(69\) −0.0917371 + 0.158893i −0.0110438 + 0.0191285i
\(70\) −0.447104 + 1.07262i −0.0534391 + 0.128203i
\(71\) −1.78083 6.64614i −0.211345 0.788752i −0.987421 0.158112i \(-0.949459\pi\)
0.776076 0.630640i \(-0.217207\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 2.40525 0.281513 0.140756 0.990044i \(-0.455047\pi\)
0.140756 + 0.990044i \(0.455047\pi\)
\(74\) −0.195463 0.112851i −0.0227221 0.0131186i
\(75\) −2.48063 4.34125i −0.286438 0.501285i
\(76\) −0.0144409 + 0.0538940i −0.00165648 + 0.00618206i
\(77\) 0.315933 0.315933i 0.0360039 0.0360039i
\(78\) 2.58133 2.51728i 0.292279 0.285026i
\(79\) 16.0201i 1.80240i −0.433402 0.901201i \(-0.642687\pi\)
0.433402 0.901201i \(-0.357313\pi\)
\(80\) −0.286912 2.21758i −0.0320777 0.247934i
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −0.00751694 0.0280536i −0.000830108 0.00309800i
\(83\) 4.83100i 0.530271i 0.964211 + 0.265136i \(0.0854167\pi\)
−0.964211 + 0.265136i \(0.914583\pi\)
\(84\) 0.501987 0.134507i 0.0547712 0.0146759i
\(85\) −1.25521 + 9.37239i −0.136146 + 1.01658i
\(86\) 3.39140 + 3.39140i 0.365704 + 0.365704i
\(87\) 6.99735 1.87494i 0.750195 0.201014i
\(88\) −0.222514 + 0.830435i −0.0237201 + 0.0885247i
\(89\) −14.9100 3.99511i −1.58045 0.423481i −0.641386 0.767218i \(-0.721640\pi\)
−0.939066 + 0.343737i \(0.888307\pi\)
\(90\) −0.860320 + 2.06394i −0.0906856 + 0.217558i
\(91\) −0.0235380 + 1.87364i −0.00246745 + 0.196411i
\(92\) 0.129736 + 0.129736i 0.0135259 + 0.0135259i
\(93\) −3.79654 + 2.19193i −0.393683 + 0.227293i
\(94\) −4.79551 + 2.76869i −0.494619 + 0.285569i
\(95\) 0.123658 + 0.0165610i 0.0126870 + 0.00169912i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) 3.14672 5.45027i 0.319501 0.553392i −0.660883 0.750489i \(-0.729818\pi\)
0.980384 + 0.197097i \(0.0631515\pi\)
\(98\) 3.36496 5.82828i 0.339912 0.588745i
\(99\) 0.607921 0.607921i 0.0610983 0.0610983i
\(100\) −4.83536 + 1.27250i −0.483536 + 0.127250i
\(101\) 4.39076 2.53501i 0.436897 0.252243i −0.265384 0.964143i \(-0.585499\pi\)
0.702281 + 0.711900i \(0.252165\pi\)
\(102\) 3.66232 2.11444i 0.362624 0.209361i
\(103\) 5.95248 + 5.95248i 0.586515 + 0.586515i 0.936686 0.350171i \(-0.113876\pi\)
−0.350171 + 0.936686i \(0.613876\pi\)
\(104\) −1.76341 3.14490i −0.172917 0.308383i
\(105\) −0.442306 1.07461i −0.0431647 0.104871i
\(106\) 3.41325 + 0.914577i 0.331524 + 0.0888315i
\(107\) −1.81541 + 6.77519i −0.175502 + 0.654982i 0.820964 + 0.570980i \(0.193437\pi\)
−0.996466 + 0.0840016i \(0.973230\pi\)
\(108\) 0.965926 0.258819i 0.0929463 0.0249049i
\(109\) 6.23531 + 6.23531i 0.597235 + 0.597235i 0.939576 0.342341i \(-0.111220\pi\)
−0.342341 + 0.939576i \(0.611220\pi\)
\(110\) 1.90540 + 0.255183i 0.181673 + 0.0243308i
\(111\) 0.218011 0.0584158i 0.0206927 0.00554458i
\(112\) 0.519695i 0.0491066i
\(113\) 1.51348 + 5.64837i 0.142376 + 0.531354i 0.999858 + 0.0168406i \(0.00536077\pi\)
−0.857482 + 0.514513i \(0.827973\pi\)
\(114\) −0.0278976 0.0483200i −0.00261285 0.00452559i
\(115\) 0.250478 0.324923i 0.0233571 0.0302992i
\(116\) 7.24419i 0.672606i
\(117\) −0.0452920 + 3.60527i −0.00418725 + 0.333307i
\(118\) 3.58354 3.58354i 0.329892 0.329892i
\(119\) −0.568814 + 2.12284i −0.0521431 + 0.194601i
\(120\) 1.77095 + 1.36519i 0.161665 + 0.124624i
\(121\) 8.88617 + 5.13043i 0.807834 + 0.466403i
\(122\) 14.4355 1.30692
\(123\) 0.0251522 + 0.0145216i 0.00226790 + 0.00130937i
\(124\) 1.13463 + 4.23449i 0.101893 + 0.380268i
\(125\) 4.20920 + 10.3577i 0.376482 + 0.926424i
\(126\) −0.259847 + 0.450069i −0.0231491 + 0.0400953i
\(127\) −10.0408 2.69043i −0.890979 0.238737i −0.215841 0.976429i \(-0.569249\pi\)
−0.675138 + 0.737691i \(0.735916\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −4.79617 −0.422279
\(130\) −6.46814 + 4.81282i −0.567293 + 0.422112i
\(131\) −17.3948 −1.51979 −0.759894 0.650047i \(-0.774749\pi\)
−0.759894 + 0.650047i \(0.774749\pi\)
\(132\) −0.429865 0.744548i −0.0374149 0.0648046i
\(133\) 0.0280084 + 0.00750484i 0.00242864 + 0.000650752i
\(134\) 6.85698 11.8766i 0.592353 1.02599i
\(135\) −0.851088 2.06776i −0.0732500 0.177965i
\(136\) −1.09452 4.08479i −0.0938540 0.350268i
\(137\) 7.86958 + 4.54350i 0.672343 + 0.388178i 0.796964 0.604027i \(-0.206438\pi\)
−0.124621 + 0.992204i \(0.539771\pi\)
\(138\) −0.183474 −0.0156184
\(139\) 2.33716 + 1.34936i 0.198236 + 0.114451i 0.595832 0.803109i \(-0.296822\pi\)
−0.397597 + 0.917560i \(0.630156\pi\)
\(140\) −1.15247 + 0.149107i −0.0974013 + 0.0126018i
\(141\) 1.43318 5.34870i 0.120695 0.450442i
\(142\) 4.86531 4.86531i 0.408288 0.408288i
\(143\) 3.00402 0.764612i 0.251209 0.0639401i
\(144\) 1.00000i 0.0833333i
\(145\) −16.0646 + 2.07844i −1.33409 + 0.172605i
\(146\) 1.20262 + 2.08300i 0.0995298 + 0.172391i
\(147\) 1.74183 + 6.50060i 0.143664 + 0.536161i
\(148\) 0.225701i 0.0185525i
\(149\) 4.01632 1.07617i 0.329029 0.0881632i −0.0905228 0.995894i \(-0.528854\pi\)
0.419552 + 0.907731i \(0.362187\pi\)
\(150\) 2.51932 4.31891i 0.205702 0.352638i
\(151\) 2.79391 + 2.79391i 0.227365 + 0.227365i 0.811591 0.584226i \(-0.198602\pi\)
−0.584226 + 0.811591i \(0.698602\pi\)
\(152\) −0.0538940 + 0.0144409i −0.00437138 + 0.00117131i
\(153\) −1.09452 + 4.08479i −0.0884864 + 0.330236i
\(154\) 0.431573 + 0.115640i 0.0347771 + 0.00931851i
\(155\) 9.06480 3.73106i 0.728102 0.299686i
\(156\) 3.47070 + 0.976860i 0.277878 + 0.0782114i
\(157\) −9.39011 9.39011i −0.749413 0.749413i 0.224956 0.974369i \(-0.427776\pi\)
−0.974369 + 0.224956i \(0.927776\pi\)
\(158\) 13.8738 8.01005i 1.10374 0.637245i
\(159\) −3.06023 + 1.76683i −0.242692 + 0.140118i
\(160\) 1.77703 1.35727i 0.140486 0.107301i
\(161\) 0.0674231 0.0674231i 0.00531368 0.00531368i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −11.4085 + 19.7602i −0.893585 + 1.54773i −0.0580388 + 0.998314i \(0.518485\pi\)
−0.835546 + 0.549420i \(0.814849\pi\)
\(164\) 0.0205367 0.0205367i 0.00160364 0.00160364i
\(165\) −1.52776 + 1.16688i −0.118936 + 0.0908416i
\(166\) −4.18377 + 2.41550i −0.324723 + 0.187479i
\(167\) 11.5320 6.65800i 0.892372 0.515211i 0.0176545 0.999844i \(-0.494380\pi\)
0.874718 + 0.484633i \(0.161047\pi\)
\(168\) 0.367480 + 0.367480i 0.0283517 + 0.0283517i
\(169\) −6.78077 + 11.0915i −0.521598 + 0.853191i
\(170\) −8.74434 + 3.59915i −0.670660 + 0.276043i
\(171\) 0.0538940 + 0.0144409i 0.00412138 + 0.00110432i
\(172\) −1.24134 + 4.63274i −0.0946513 + 0.353243i
\(173\) −18.6279 + 4.99132i −1.41625 + 0.379483i −0.884152 0.467199i \(-0.845263\pi\)
−0.532099 + 0.846682i \(0.678597\pi\)
\(174\) 5.12242 + 5.12242i 0.388329 + 0.388329i
\(175\) 0.661313 + 2.51291i 0.0499905 + 0.189958i
\(176\) −0.830435 + 0.222514i −0.0625964 + 0.0167727i
\(177\) 5.06789i 0.380926i
\(178\) −3.99511 14.9100i −0.299446 1.11755i
\(179\) −10.1381 17.5596i −0.757754 1.31247i −0.943994 0.329964i \(-0.892963\pi\)
0.186240 0.982504i \(-0.440370\pi\)
\(180\) −2.21758 + 0.286912i −0.165289 + 0.0213851i
\(181\) 14.3123i 1.06382i −0.846799 0.531912i \(-0.821474\pi\)
0.846799 0.531912i \(-0.178526\pi\)
\(182\) −1.63439 + 0.916435i −0.121149 + 0.0679307i
\(183\) −10.2074 + 10.2074i −0.754553 + 0.754553i
\(184\) −0.0474866 + 0.177222i −0.00350076 + 0.0130650i
\(185\) −0.500512 + 0.0647563i −0.0367983 + 0.00476098i
\(186\) −3.79654 2.19193i −0.278376 0.160720i
\(187\) 3.63570 0.265869
\(188\) −4.79551 2.76869i −0.349749 0.201927i
\(189\) −0.134507 0.501987i −0.00978394 0.0365142i
\(190\) 0.0474866 + 0.115371i 0.00344504 + 0.00836991i
\(191\) −6.39485 + 11.0762i −0.462715 + 0.801446i −0.999095 0.0425302i \(-0.986458\pi\)
0.536380 + 0.843977i \(0.319791\pi\)
\(192\) −0.965926 0.258819i −0.0697097 0.0186787i
\(193\) 1.10451 + 1.91307i 0.0795045 + 0.137706i 0.903036 0.429564i \(-0.141333\pi\)
−0.823532 + 0.567270i \(0.808000\pi\)
\(194\) 6.29344 0.451842
\(195\) 1.17049 7.97684i 0.0838203 0.571233i
\(196\) 6.72992 0.480708
\(197\) −6.06986 10.5133i −0.432460 0.749042i 0.564625 0.825348i \(-0.309021\pi\)
−0.997084 + 0.0763056i \(0.975688\pi\)
\(198\) 0.830435 + 0.222514i 0.0590165 + 0.0158134i
\(199\) −2.03805 + 3.53001i −0.144474 + 0.250236i −0.929176 0.369636i \(-0.879482\pi\)
0.784703 + 0.619872i \(0.212816\pi\)
\(200\) −3.51970 3.55130i −0.248880 0.251115i
\(201\) 3.54943 + 13.2467i 0.250358 + 0.934348i
\(202\) 4.39076 + 2.53501i 0.308933 + 0.178362i
\(203\) −3.76477 −0.264235
\(204\) 3.66232 + 2.11444i 0.256414 + 0.148041i
\(205\) −0.0514340 0.0396496i −0.00359231 0.00276925i
\(206\) −2.17876 + 8.13124i −0.151801 + 0.566530i
\(207\) 0.129736 0.129736i 0.00901727 0.00901727i
\(208\) 1.84186 3.09961i 0.127710 0.214919i
\(209\) 0.0479688i 0.00331807i
\(210\) 0.709483 0.920352i 0.0489590 0.0635103i
\(211\) 7.38509 + 12.7914i 0.508411 + 0.880593i 0.999953 + 0.00973918i \(0.00310013\pi\)
−0.491542 + 0.870854i \(0.663567\pi\)
\(212\) 0.914577 + 3.41325i 0.0628134 + 0.234423i
\(213\) 6.88059i 0.471450i
\(214\) −6.77519 + 1.81541i −0.463142 + 0.124099i
\(215\) 10.6297 + 1.42359i 0.724936 + 0.0970879i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) 2.20064 0.589661i 0.149389 0.0400288i
\(218\) −2.28228 + 8.51759i −0.154576 + 0.576884i
\(219\) −2.32329 0.622524i −0.156993 0.0420662i
\(220\) 0.731706 + 1.77772i 0.0493316 + 0.119854i
\(221\) −10.9162 + 10.6453i −0.734301 + 0.716080i
\(222\) 0.159595 + 0.159595i 0.0107113 + 0.0107113i
\(223\) 2.75364 1.58981i 0.184397 0.106462i −0.404960 0.914334i \(-0.632714\pi\)
0.589357 + 0.807873i \(0.299381\pi\)
\(224\) 0.450069 0.259847i 0.0300715 0.0173618i
\(225\) 1.27250 + 4.83536i 0.0848334 + 0.322358i
\(226\) −4.13489 + 4.13489i −0.275049 + 0.275049i
\(227\) 14.4830 25.0852i 0.961267 1.66496i 0.241942 0.970291i \(-0.422216\pi\)
0.719326 0.694673i \(-0.244451\pi\)
\(228\) 0.0278976 0.0483200i 0.00184756 0.00320007i
\(229\) −8.53343 + 8.53343i −0.563905 + 0.563905i −0.930414 0.366509i \(-0.880553\pi\)
0.366509 + 0.930414i \(0.380553\pi\)
\(230\) 0.406630 + 0.0544584i 0.0268124 + 0.00359088i
\(231\) −0.386938 + 0.223399i −0.0254586 + 0.0146985i
\(232\) 6.27365 3.62210i 0.411886 0.237802i
\(233\) 7.11568 + 7.11568i 0.466164 + 0.466164i 0.900669 0.434505i \(-0.143077\pi\)
−0.434505 + 0.900669i \(0.643077\pi\)
\(234\) −3.14490 + 1.76341i −0.205588 + 0.115278i
\(235\) −4.76392 + 11.4288i −0.310764 + 0.745534i
\(236\) 4.89521 + 1.31167i 0.318651 + 0.0853823i
\(237\) −4.14631 + 15.4742i −0.269331 + 1.00516i
\(238\) −2.12284 + 0.568814i −0.137604 + 0.0368708i
\(239\) 15.7046 + 15.7046i 1.01584 + 1.01584i 0.999872 + 0.0159718i \(0.00508419\pi\)
0.0159718 + 0.999872i \(0.494916\pi\)
\(240\) −0.296818 + 2.21628i −0.0191595 + 0.143060i
\(241\) 24.1684 6.47591i 1.55682 0.417150i 0.625168 0.780490i \(-0.285031\pi\)
0.931656 + 0.363341i \(0.118364\pi\)
\(242\) 10.2609i 0.659593i
\(243\) −0.258819 0.965926i −0.0166032 0.0619642i
\(244\) 7.21773 + 12.5015i 0.462068 + 0.800325i
\(245\) −1.93089 14.9242i −0.123360 0.953470i
\(246\) 0.0290432i 0.00185173i
\(247\) 0.140452 + 0.144026i 0.00893676 + 0.00916415i
\(248\) −3.09986 + 3.09986i −0.196841 + 0.196841i
\(249\) 1.25035 4.66639i 0.0792380 0.295720i
\(250\) −6.86546 + 8.82414i −0.434210 + 0.558088i
\(251\) −23.7056 13.6864i −1.49628 0.863878i −0.496290 0.868157i \(-0.665305\pi\)
−0.999991 + 0.00427828i \(0.998638\pi\)
\(252\) −0.519695 −0.0327377
\(253\) −0.136605 0.0788691i −0.00858830 0.00495846i
\(254\) −2.69043 10.0408i −0.168813 0.630017i
\(255\) 3.63819 8.72817i 0.227832 0.546579i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.249933 0.0669693i −0.0155904 0.00417743i 0.251015 0.967983i \(-0.419236\pi\)
−0.266606 + 0.963806i \(0.585902\pi\)
\(258\) −2.39808 4.15360i −0.149298 0.258592i
\(259\) −0.117296 −0.00728840
\(260\) −7.40209 3.19516i −0.459058 0.198156i
\(261\) −7.24419 −0.448404
\(262\) −8.69738 15.0643i −0.537326 0.930676i
\(263\) 6.00425 + 1.60883i 0.370238 + 0.0992050i 0.439140 0.898418i \(-0.355283\pi\)
−0.0689024 + 0.997623i \(0.521950\pi\)
\(264\) 0.429865 0.744548i 0.0264564 0.0458238i
\(265\) 7.30676 3.00745i 0.448851 0.184746i
\(266\) 0.00750484 + 0.0280084i 0.000460151 + 0.00171731i
\(267\) 13.3679 + 7.71796i 0.818102 + 0.472332i
\(268\) 13.7140 0.837713
\(269\) 0.338208 + 0.195264i 0.0206209 + 0.0119055i 0.510275 0.860011i \(-0.329544\pi\)
−0.489654 + 0.871917i \(0.662877\pi\)
\(270\) 1.36519 1.77095i 0.0830829 0.107776i
\(271\) −4.36922 + 16.3061i −0.265411 + 0.990528i 0.696587 + 0.717472i \(0.254701\pi\)
−0.961998 + 0.273056i \(0.911966\pi\)
\(272\) 2.99027 2.99027i 0.181312 0.181312i
\(273\) 0.507669 1.80370i 0.0307255 0.109165i
\(274\) 9.08700i 0.548966i
\(275\) 3.73231 2.13267i 0.225067 0.128605i
\(276\) −0.0917371 0.158893i −0.00552192 0.00956425i
\(277\) −0.273563 1.02095i −0.0164368 0.0613430i 0.957220 0.289360i \(-0.0934425\pi\)
−0.973657 + 0.228017i \(0.926776\pi\)
\(278\) 2.69872i 0.161859i
\(279\) 4.23449 1.13463i 0.253512 0.0679284i
\(280\) −0.705364 0.923513i −0.0421535 0.0551904i
\(281\) 9.59800 + 9.59800i 0.572568 + 0.572568i 0.932845 0.360277i \(-0.117318\pi\)
−0.360277 + 0.932845i \(0.617318\pi\)
\(282\) 5.34870 1.43318i 0.318510 0.0853446i
\(283\) 2.48624 9.27878i 0.147792 0.551566i −0.851823 0.523829i \(-0.824503\pi\)
0.999615 0.0277374i \(-0.00883024\pi\)
\(284\) 6.64614 + 1.78083i 0.394376 + 0.105673i
\(285\) −0.115158 0.0480017i −0.00682136 0.00284337i
\(286\) 2.16418 + 2.21925i 0.127971 + 0.131227i
\(287\) −0.0106728 0.0106728i −0.000629996 0.000629996i
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) −0.765102 + 0.441732i −0.0450060 + 0.0259842i
\(290\) −9.83229 12.8731i −0.577372 0.755937i
\(291\) −4.45013 + 4.45013i −0.260871 + 0.260871i
\(292\) −1.20262 + 2.08300i −0.0703782 + 0.121899i
\(293\) −2.91359 + 5.04648i −0.170214 + 0.294819i −0.938494 0.345294i \(-0.887779\pi\)
0.768281 + 0.640113i \(0.221112\pi\)
\(294\) −4.75877 + 4.75877i −0.277537 + 0.277537i
\(295\) 1.50424 11.2319i 0.0875803 0.653945i
\(296\) 0.195463 0.112851i 0.0113611 0.00655931i
\(297\) −0.744548 + 0.429865i −0.0432031 + 0.0249433i
\(298\) 2.94015 + 2.94015i 0.170318 + 0.170318i
\(299\) 0.641085 0.163175i 0.0370749 0.00943666i
\(300\) 4.99995 + 0.0223420i 0.288672 + 0.00128991i
\(301\) 2.40761 + 0.645118i 0.138772 + 0.0371840i
\(302\) −1.02264 + 3.81656i −0.0588465 + 0.219618i
\(303\) −4.89726 + 1.31222i −0.281340 + 0.0753848i
\(304\) −0.0394531 0.0394531i −0.00226279 0.00226279i
\(305\) 25.6522 19.5927i 1.46884 1.12188i
\(306\) −4.08479 + 1.09452i −0.233512 + 0.0625693i
\(307\) 4.52688i 0.258363i 0.991621 + 0.129181i \(0.0412349\pi\)
−0.991621 + 0.129181i \(0.958765\pi\)
\(308\) 0.115640 + 0.431573i 0.00658918 + 0.0245912i
\(309\) −4.20904 7.29027i −0.239444 0.414729i
\(310\) 7.76359 + 5.98482i 0.440942 + 0.339915i
\(311\) 27.6370i 1.56715i −0.621297 0.783575i \(-0.713394\pi\)
0.621297 0.783575i \(-0.286606\pi\)
\(312\) 0.889363 + 3.49414i 0.0503503 + 0.197817i
\(313\) 22.4963 22.4963i 1.27157 1.27157i 0.326301 0.945266i \(-0.394198\pi\)
0.945266 0.326301i \(-0.105802\pi\)
\(314\) 3.43702 12.8271i 0.193962 0.723877i
\(315\) 0.149107 + 1.15247i 0.00840120 + 0.0649342i
\(316\) 13.8738 + 8.01005i 0.780463 + 0.450600i
\(317\) −1.80472 −0.101363 −0.0506817 0.998715i \(-0.516139\pi\)
−0.0506817 + 0.998715i \(0.516139\pi\)
\(318\) −3.06023 1.76683i −0.171609 0.0990787i
\(319\) 1.61194 + 6.01583i 0.0902512 + 0.336822i
\(320\) 2.06394 + 0.860320i 0.115378 + 0.0480933i
\(321\) 3.50709 6.07447i 0.195747 0.339044i
\(322\) 0.0921016 + 0.0246786i 0.00513262 + 0.00137528i
\(323\) 0.117976 + 0.204340i 0.00656434 + 0.0113698i
\(324\) −1.00000 −0.0555556
\(325\) −4.96180 + 17.3315i −0.275231 + 0.961378i
\(326\) −22.8171 −1.26372
\(327\) −4.40903 7.63667i −0.243820 0.422309i
\(328\) 0.0280536 + 0.00751694i 0.00154900 + 0.000415054i
\(329\) −1.43887 + 2.49220i −0.0793277 + 0.137400i
\(330\) −1.77443 0.739642i −0.0976792 0.0407160i
\(331\) 5.25635 + 19.6170i 0.288915 + 1.07825i 0.945930 + 0.324369i \(0.105152\pi\)
−0.657015 + 0.753877i \(0.728181\pi\)
\(332\) −4.18377 2.41550i −0.229614 0.132568i
\(333\) −0.225701 −0.0123684
\(334\) 11.5320 + 6.65800i 0.631002 + 0.364309i
\(335\) −3.93469 30.4119i −0.214975 1.66158i
\(336\) −0.134507 + 0.501987i −0.00733796 + 0.0273856i
\(337\) −16.0244 + 16.0244i −0.872903 + 0.872903i −0.992788 0.119885i \(-0.961747\pi\)
0.119885 + 0.992788i \(0.461747\pi\)
\(338\) −12.9959 0.326579i −0.706884 0.0177636i
\(339\) 5.84762i 0.317599i
\(340\) −7.48913 5.77324i −0.406155 0.313098i
\(341\) −1.88447 3.26400i −0.102050 0.176755i
\(342\) 0.0144409 + 0.0538940i 0.000780872 + 0.00291425i
\(343\) 7.13537i 0.385274i
\(344\) −4.63274 + 1.24134i −0.249781 + 0.0669285i
\(345\) −0.326039 + 0.249023i −0.0175533 + 0.0134070i
\(346\) −13.6366 13.6366i −0.733106 0.733106i
\(347\) −34.8393 + 9.33516i −1.87027 + 0.501138i −0.870309 + 0.492507i \(0.836081\pi\)
−0.999963 + 0.00863072i \(0.997253\pi\)
\(348\) −1.87494 + 6.99735i −0.100507 + 0.375097i
\(349\) −3.51575 0.942042i −0.188194 0.0504264i 0.163491 0.986545i \(-0.447724\pi\)
−0.351685 + 0.936118i \(0.614391\pi\)
\(350\) −1.84559 + 1.82917i −0.0986510 + 0.0977733i
\(351\) 0.976860 3.47070i 0.0521410 0.185252i
\(352\) −0.607921 0.607921i −0.0324023 0.0324023i
\(353\) 24.5055 14.1482i 1.30429 0.753034i 0.323156 0.946346i \(-0.395256\pi\)
0.981137 + 0.193311i \(0.0619227\pi\)
\(354\) −4.38892 + 2.53395i −0.233269 + 0.134678i
\(355\) 2.04228 15.2493i 0.108393 0.809350i
\(356\) 10.9148 10.9148i 0.578486 0.578486i
\(357\) 1.09886 1.90329i 0.0581581 0.100733i
\(358\) 10.1381 17.5596i 0.535813 0.928055i
\(359\) 4.76749 4.76749i 0.251619 0.251619i −0.570015 0.821634i \(-0.693063\pi\)
0.821634 + 0.570015i \(0.193063\pi\)
\(360\) −1.35727 1.77703i −0.0715342 0.0936576i
\(361\) −16.4518 + 9.49844i −0.865884 + 0.499918i
\(362\) 12.3948 7.15615i 0.651457 0.376119i
\(363\) −7.25553 7.25553i −0.380816 0.380816i
\(364\) −1.61085 0.957204i −0.0844315 0.0501711i
\(365\) 4.96429 + 2.06928i 0.259843 + 0.108311i
\(366\) −13.9436 3.73617i −0.728843 0.195293i
\(367\) −8.05298 + 30.0541i −0.420362 + 1.56881i 0.353485 + 0.935440i \(0.384997\pi\)
−0.773847 + 0.633373i \(0.781670\pi\)
\(368\) −0.177222 + 0.0474866i −0.00923836 + 0.00247541i
\(369\) −0.0205367 0.0205367i −0.00106910 0.00106910i
\(370\) −0.306336 0.401078i −0.0159257 0.0208510i
\(371\) 1.77385 0.475301i 0.0920935 0.0246764i
\(372\) 4.38387i 0.227293i
\(373\) −5.84130 21.8000i −0.302451 1.12876i −0.935117 0.354338i \(-0.884706\pi\)
0.632666 0.774425i \(-0.281961\pi\)
\(374\) 1.81785 + 3.14861i 0.0939987 + 0.162811i
\(375\) −1.38500 11.0942i −0.0715210 0.572903i
\(376\) 5.53738i 0.285569i
\(377\) −22.4541 13.3428i −1.15645 0.687188i
\(378\) 0.367480 0.367480i 0.0189011 0.0189011i
\(379\) −3.85119 + 14.3728i −0.197822 + 0.738283i 0.793696 + 0.608315i \(0.208154\pi\)
−0.991518 + 0.129968i \(0.958512\pi\)
\(380\) −0.0761711 + 0.0988102i −0.00390750 + 0.00506886i
\(381\) 9.00236 + 5.19751i 0.461205 + 0.266277i
\(382\) −12.7897 −0.654378
\(383\) −9.84116 5.68179i −0.502860 0.290326i 0.227034 0.973887i \(-0.427097\pi\)
−0.729894 + 0.683561i \(0.760430\pi\)
\(384\) −0.258819 0.965926i −0.0132078 0.0492922i
\(385\) 0.923871 0.380264i 0.0470848 0.0193800i
\(386\) −1.10451 + 1.91307i −0.0562182 + 0.0973727i
\(387\) 4.63274 + 1.24134i 0.235496 + 0.0631008i
\(388\) 3.14672 + 5.45027i 0.159750 + 0.276696i
\(389\) 0.783134 0.0397065 0.0198532 0.999803i \(-0.493680\pi\)
0.0198532 + 0.999803i \(0.493680\pi\)
\(390\) 7.49339 2.97475i 0.379442 0.150632i
\(391\) 0.775891 0.0392385
\(392\) 3.36496 + 5.82828i 0.169956 + 0.294373i
\(393\) 16.8021 + 4.50210i 0.847552 + 0.227101i
\(394\) 6.06986 10.5133i 0.305795 0.529653i
\(395\) 13.7824 33.0645i 0.693468 1.66366i
\(396\) 0.222514 + 0.830435i 0.0111818 + 0.0417309i
\(397\) −12.3334 7.12070i −0.618996 0.357378i 0.157482 0.987522i \(-0.449662\pi\)
−0.776478 + 0.630144i \(0.782996\pi\)
\(398\) −4.07610 −0.204317
\(399\) −0.0251117 0.0144982i −0.00125716 0.000725819i
\(400\) 1.31566 4.82380i 0.0657831 0.241190i
\(401\) −8.08823 + 30.1857i −0.403907 + 1.50740i 0.402155 + 0.915571i \(0.368261\pi\)
−0.806062 + 0.591830i \(0.798405\pi\)
\(402\) −9.69723 + 9.69723i −0.483654 + 0.483654i
\(403\) 15.2151 + 4.28243i 0.757917 + 0.213323i
\(404\) 5.07001i 0.252243i
\(405\) 0.286912 + 2.21758i 0.0142568 + 0.110193i
\(406\) −1.88239 3.26039i −0.0934212 0.161810i
\(407\) 0.0502218 + 0.187430i 0.00248940 + 0.00929057i
\(408\) 4.22888i 0.209361i
\(409\) 32.5735 8.72803i 1.61065 0.431573i 0.662416 0.749136i \(-0.269531\pi\)
0.948237 + 0.317563i \(0.102864\pi\)
\(410\) 0.00862055 0.0643680i 0.000425739 0.00317891i
\(411\) −6.42548 6.42548i −0.316946 0.316946i
\(412\) −8.13124 + 2.17876i −0.400597 + 0.107340i
\(413\) 0.681667 2.54402i 0.0335426 0.125183i
\(414\) 0.177222 + 0.0474866i 0.00871001 + 0.00233384i
\(415\) −4.15620 + 9.97090i −0.204020 + 0.489452i
\(416\) 3.60527 + 0.0452920i 0.176763 + 0.00222062i
\(417\) −1.90829 1.90829i −0.0934492 0.0934492i
\(418\) 0.0415422 0.0239844i 0.00203189 0.00117311i
\(419\) 9.64226 5.56696i 0.471055 0.271964i −0.245626 0.969365i \(-0.578994\pi\)
0.716681 + 0.697401i \(0.245660\pi\)
\(420\) 1.15179 + 0.154255i 0.0562016 + 0.00752686i
\(421\) 20.6313 20.6313i 1.00551 1.00551i 0.00552546 0.999985i \(-0.498241\pi\)
0.999985 0.00552546i \(-0.00175882\pi\)
\(422\) −7.38509 + 12.7914i −0.359501 + 0.622673i
\(423\) −2.76869 + 4.79551i −0.134618 + 0.233166i
\(424\) −2.49867 + 2.49867i −0.121346 + 0.121346i
\(425\) −10.6539 + 18.2642i −0.516791 + 0.885943i
\(426\) −5.95877 + 3.44030i −0.288703 + 0.166683i
\(427\) 6.49695 3.75102i 0.314409 0.181524i
\(428\) −4.95978 4.95978i −0.239740 0.239740i
\(429\) −3.09956 0.0389389i −0.149648 0.00187999i
\(430\) 4.08196 + 9.91734i 0.196850 + 0.478257i
\(431\) 16.8679 + 4.51975i 0.812500 + 0.217709i 0.641065 0.767487i \(-0.278493\pi\)
0.171435 + 0.985195i \(0.445160\pi\)
\(432\) −0.258819 + 0.965926i −0.0124524 + 0.0464731i
\(433\) −2.14717 + 0.575332i −0.103186 + 0.0276487i −0.310043 0.950723i \(-0.600343\pi\)
0.206856 + 0.978371i \(0.433677\pi\)
\(434\) 1.61098 + 1.61098i 0.0773296 + 0.0773296i
\(435\) 16.0552 + 2.15021i 0.769786 + 0.103094i
\(436\) −8.51759 + 2.28228i −0.407919 + 0.109302i
\(437\) 0.0102370i 0.000489701i
\(438\) −0.622524 2.32329i −0.0297453 0.111011i
\(439\) −18.9701 32.8571i −0.905392 1.56819i −0.820390 0.571805i \(-0.806243\pi\)
−0.0850025 0.996381i \(-0.527090\pi\)
\(440\) −1.17370 + 1.52254i −0.0559538 + 0.0725840i
\(441\) 6.72992i 0.320472i
\(442\) −14.6772 4.13103i −0.698122 0.196493i
\(443\) 15.4941 15.4941i 0.736149 0.736149i −0.235681 0.971830i \(-0.575732\pi\)
0.971830 + 0.235681i \(0.0757322\pi\)
\(444\) −0.0584158 + 0.218011i −0.00277229 + 0.0103463i
\(445\) −27.3362 21.0730i −1.29586 0.998956i
\(446\) 2.75364 + 1.58981i 0.130388 + 0.0752798i
\(447\) −4.15800 −0.196666
\(448\) 0.450069 + 0.259847i 0.0212638 + 0.0122766i
\(449\) 4.09810 + 15.2943i 0.193402 + 0.721784i 0.992675 + 0.120817i \(0.0385513\pi\)
−0.799273 + 0.600968i \(0.794782\pi\)
\(450\) −3.55130 + 3.51970i −0.167410 + 0.165920i
\(451\) −0.0124847 + 0.0216241i −0.000587880 + 0.00101824i
\(452\) −5.64837 1.51348i −0.265677 0.0711879i
\(453\) −1.97560 3.42183i −0.0928216 0.160772i
\(454\) 28.9659 1.35944
\(455\) −1.66051 + 3.84683i −0.0778459 + 0.180342i
\(456\) 0.0557952 0.00261285
\(457\) −19.5983 33.9453i −0.916771 1.58789i −0.804288 0.594240i \(-0.797453\pi\)
−0.112483 0.993654i \(-0.535880\pi\)
\(458\) −11.6569 3.12345i −0.544691 0.145949i
\(459\) 2.11444 3.66232i 0.0986937 0.170943i
\(460\) 0.156153 + 0.379381i 0.00728066 + 0.0176887i
\(461\) −2.72197 10.1585i −0.126775 0.473130i 0.873122 0.487502i \(-0.162092\pi\)
−0.999897 + 0.0143717i \(0.995425\pi\)
\(462\) −0.386938 0.223399i −0.0180020 0.0103934i
\(463\) −31.3265 −1.45586 −0.727932 0.685649i \(-0.759518\pi\)
−0.727932 + 0.685649i \(0.759518\pi\)
\(464\) 6.27365 + 3.62210i 0.291247 + 0.168152i
\(465\) −9.72160 + 1.25778i −0.450828 + 0.0583283i
\(466\) −2.60452 + 9.72020i −0.120652 + 0.450280i
\(467\) −17.1532 + 17.1532i −0.793754 + 0.793754i −0.982102 0.188349i \(-0.939687\pi\)
0.188349 + 0.982102i \(0.439687\pi\)
\(468\) −3.09961 1.84186i −0.143279 0.0851399i
\(469\) 7.12707i 0.329098i
\(470\) −12.2796 + 1.58874i −0.566416 + 0.0732830i
\(471\) 6.63981 + 11.5005i 0.305946 + 0.529915i
\(472\) 1.31167 + 4.89521i 0.0603744 + 0.225320i
\(473\) 4.12341i 0.189595i
\(474\) −15.4742 + 4.14631i −0.710755 + 0.190446i
\(475\) 0.240974 + 0.140566i 0.0110567 + 0.00644961i
\(476\) −1.55403 1.55403i −0.0712288 0.0712288i
\(477\) 3.41325 0.914577i 0.156282 0.0418756i
\(478\) −5.74827 + 21.4528i −0.262920 + 0.981230i
\(479\) 11.2332 + 3.00994i 0.513260 + 0.137528i 0.506147 0.862447i \(-0.331069\pi\)
0.00711279 + 0.999975i \(0.497736\pi\)
\(480\) −2.06776 + 0.851088i −0.0943801 + 0.0388467i
\(481\) −0.699585 0.415709i −0.0318983 0.0189547i
\(482\) 17.6925 + 17.6925i 0.805871 + 0.805871i
\(483\) −0.0825761 + 0.0476753i −0.00375734 + 0.00216930i
\(484\) −8.88617 + 5.13043i −0.403917 + 0.233201i
\(485\) 11.1836 8.54186i 0.507822 0.387866i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) −4.57010 + 7.91564i −0.207091 + 0.358692i −0.950797 0.309815i \(-0.899733\pi\)
0.743706 + 0.668507i \(0.233066\pi\)
\(488\) −7.21773 + 12.5015i −0.326731 + 0.565915i
\(489\) 16.1341 16.1341i 0.729609 0.729609i
\(490\) 11.9593 9.13428i 0.540264 0.412645i
\(491\) −6.88995 + 3.97792i −0.310939 + 0.179521i −0.647347 0.762196i \(-0.724121\pi\)
0.336407 + 0.941717i \(0.390788\pi\)
\(492\) −0.0251522 + 0.0145216i −0.00113395 + 0.000654685i
\(493\) −21.6621 21.6621i −0.975612 0.975612i
\(494\) −0.0545041 + 0.193648i −0.00245225 + 0.00871264i
\(495\) 1.77772 0.731706i 0.0799025 0.0328877i
\(496\) −4.23449 1.13463i −0.190134 0.0509463i
\(497\) 0.925487 3.45397i 0.0415138 0.154932i
\(498\) 4.66639 1.25035i 0.209106 0.0560297i
\(499\) 21.9284 + 21.9284i 0.981650 + 0.981650i 0.999835 0.0181843i \(-0.00578857\pi\)
−0.0181843 + 0.999835i \(0.505789\pi\)
\(500\) −11.0747 1.53359i −0.495274 0.0685842i
\(501\) −12.8623 + 3.44643i −0.574644 + 0.153975i
\(502\) 27.3728i 1.22171i
\(503\) 4.95760 + 18.5020i 0.221049 + 0.824964i 0.983949 + 0.178449i \(0.0571078\pi\)
−0.762901 + 0.646516i \(0.776225\pi\)
\(504\) −0.259847 0.450069i −0.0115745 0.0200477i
\(505\) 11.2432 1.45465i 0.500315 0.0647309i
\(506\) 0.157738i 0.00701232i
\(507\) 9.42041 8.95856i 0.418375 0.397864i
\(508\) 7.35039 7.35039i 0.326121 0.326121i
\(509\) −8.14806 + 30.4090i −0.361156 + 1.34785i 0.511401 + 0.859342i \(0.329127\pi\)
−0.872557 + 0.488512i \(0.837540\pi\)
\(510\) 9.37791 1.21332i 0.415261 0.0537265i
\(511\) 1.08253 + 0.624997i 0.0478882 + 0.0276482i
\(512\) −1.00000 −0.0441942
\(513\) −0.0483200 0.0278976i −0.00213338 0.00123171i
\(514\) −0.0669693 0.249933i −0.00295389 0.0110241i
\(515\) 7.16453 + 17.4066i 0.315707 + 0.767027i
\(516\) 2.39808 4.15360i 0.105570 0.182852i
\(517\) 4.59843 + 1.23215i 0.202239 + 0.0541898i
\(518\) −0.0586479 0.101581i −0.00257684 0.00446322i
\(519\) 19.2850 0.846517
\(520\) −0.933954 8.00798i −0.0409566 0.351173i
\(521\) 38.1901 1.67314 0.836568 0.547862i \(-0.184558\pi\)
0.836568 + 0.547862i \(0.184558\pi\)
\(522\) −3.62210 6.27365i −0.158535 0.274590i
\(523\) 1.41502 + 0.379154i 0.0618747 + 0.0165793i 0.289624 0.957141i \(-0.406470\pi\)
−0.227749 + 0.973720i \(0.573137\pi\)
\(524\) 8.69738 15.0643i 0.379947 0.658087i
\(525\) 0.0116110 2.59845i 0.000506746 0.113406i
\(526\) 1.60883 + 6.00425i 0.0701485 + 0.261798i
\(527\) 16.0551 + 9.26943i 0.699372 + 0.403783i
\(528\) 0.859730 0.0374149
\(529\) 19.8894 + 11.4832i 0.864758 + 0.499268i
\(530\) 6.25791 + 4.82411i 0.271826 + 0.209546i
\(531\) 1.31167 4.89521i 0.0569215 0.212434i
\(532\) −0.0205036 + 0.0205036i −0.000888944 + 0.000888944i
\(533\) −0.0258300 0.101481i −0.00111882 0.00439564i
\(534\) 15.4359i 0.667978i
\(535\) −9.57571 + 12.4218i −0.413994 + 0.537039i
\(536\) 6.85698 + 11.8766i 0.296176 + 0.512993i
\(537\) 5.24784 + 19.5852i 0.226461 + 0.845165i
\(538\) 0.390528i 0.0168369i
\(539\) −5.58876 + 1.49750i −0.240725 + 0.0645021i
\(540\) 2.21628 + 0.296818i 0.0953735 + 0.0127730i
\(541\) −21.3618 21.3618i −0.918417 0.918417i 0.0784970 0.996914i \(-0.474988\pi\)
−0.996914 + 0.0784970i \(0.974988\pi\)
\(542\) −16.3061 + 4.36922i −0.700409 + 0.187674i
\(543\) −3.70429 + 13.8246i −0.158966 + 0.593271i
\(544\) 4.08479 + 1.09452i 0.175134 + 0.0469270i
\(545\) 7.50495 + 18.2337i 0.321477 + 0.781045i
\(546\) 1.81589 0.462197i 0.0777128 0.0197802i
\(547\) 13.4041 + 13.4041i 0.573116 + 0.573116i 0.932998 0.359882i \(-0.117183\pi\)
−0.359882 + 0.932998i \(0.617183\pi\)
\(548\) −7.86958 + 4.54350i −0.336172 + 0.194089i
\(549\) 12.5015 7.21773i 0.533550 0.308045i
\(550\) 3.71310 + 2.16594i 0.158327 + 0.0923559i
\(551\) −0.285806 + 0.285806i −0.0121758 + 0.0121758i
\(552\) 0.0917371 0.158893i 0.00390459 0.00676295i
\(553\) 4.16278 7.21015i 0.177019 0.306607i
\(554\) 0.747388 0.747388i 0.0317535 0.0317535i
\(555\) 0.500217 + 0.0669921i 0.0212330 + 0.00284366i
\(556\) −2.33716 + 1.34936i −0.0991178 + 0.0572257i
\(557\) −28.8536 + 16.6586i −1.22256 + 0.705848i −0.965464 0.260536i \(-0.916101\pi\)
−0.257101 + 0.966385i \(0.582767\pi\)
\(558\) 3.09986 + 3.09986i 0.131228 + 0.131228i
\(559\) 12.0733 + 12.3805i 0.510647 + 0.523640i
\(560\) 0.447104 1.07262i 0.0188936 0.0453264i
\(561\) −3.51181 0.940988i −0.148269 0.0397285i
\(562\) −3.51311 + 13.1111i −0.148192 + 0.553059i
\(563\) −25.7554 + 6.90115i −1.08546 + 0.290849i −0.756832 0.653610i \(-0.773254\pi\)
−0.328631 + 0.944458i \(0.606587\pi\)
\(564\) 3.91552 + 3.91552i 0.164873 + 0.164873i
\(565\) −1.73568 + 12.9600i −0.0730206 + 0.545230i
\(566\) 9.27878 2.48624i 0.390016 0.104505i
\(567\) 0.519695i 0.0218251i
\(568\) 1.78083 + 6.64614i 0.0747219 + 0.278866i
\(569\) 20.0582 + 34.7418i 0.840883 + 1.45645i 0.889149 + 0.457618i \(0.151297\pi\)
−0.0482653 + 0.998835i \(0.515369\pi\)
\(570\) −0.0160083 0.123730i −0.000670513 0.00518250i
\(571\) 5.59408i 0.234105i 0.993126 + 0.117053i \(0.0373446\pi\)
−0.993126 + 0.117053i \(0.962655\pi\)
\(572\) −0.839836 + 2.98386i −0.0351153 + 0.124762i
\(573\) 9.04369 9.04369i 0.377806 0.377806i
\(574\) 0.00390652 0.0145793i 0.000163055 0.000608529i
\(575\) 0.796508 0.455131i 0.0332167 0.0189803i
\(576\) 0.866025 + 0.500000i 0.0360844 + 0.0208333i
\(577\) 12.9781 0.540287 0.270144 0.962820i \(-0.412929\pi\)
0.270144 + 0.962820i \(0.412929\pi\)
\(578\) −0.765102 0.441732i −0.0318240 0.0183736i
\(579\) −0.571737 2.13375i −0.0237606 0.0886757i
\(580\) 6.23232 14.9516i 0.258783 0.620831i
\(581\) −1.25532 + 2.17428i −0.0520796 + 0.0902045i
\(582\) −6.07899 1.62886i −0.251982 0.0675185i
\(583\) −1.51899 2.63097i −0.0629103 0.108964i
\(584\) −2.40525 −0.0995298
\(585\) −3.19516 + 7.40209i −0.132104 + 0.306039i
\(586\) −5.82718 −0.240718
\(587\) 20.9109 + 36.2188i 0.863086 + 1.49491i 0.868935 + 0.494926i \(0.164805\pi\)
−0.00584852 + 0.999983i \(0.501862\pi\)
\(588\) −6.50060 1.74183i −0.268080 0.0718319i
\(589\) 0.122299 0.211829i 0.00503925 0.00872824i
\(590\) 10.4792 4.31323i 0.431422 0.177573i
\(591\) 3.14199 + 11.7261i 0.129244 + 0.482346i
\(592\) 0.195463 + 0.112851i 0.00803348 + 0.00463813i
\(593\) 6.42791 0.263963 0.131981 0.991252i \(-0.457866\pi\)
0.131981 + 0.991252i \(0.457866\pi\)
\(594\) −0.744548 0.429865i −0.0305492 0.0176376i
\(595\) −3.00032 + 3.89206i −0.123001 + 0.159559i
\(596\) −1.07617 + 4.01632i −0.0440816 + 0.164515i
\(597\) 2.88224 2.88224i 0.117962 0.117962i
\(598\) 0.461856 + 0.473608i 0.0188867 + 0.0193673i
\(599\) 17.8641i 0.729906i 0.931026 + 0.364953i \(0.118915\pi\)
−0.931026 + 0.364953i \(0.881085\pi\)
\(600\) 2.48063 + 4.34125i 0.101271 + 0.177231i
\(601\) −16.6635 28.8620i −0.679717 1.17730i −0.975066 0.221914i \(-0.928769\pi\)
0.295349 0.955389i \(-0.404564\pi\)
\(602\) 0.645118 + 2.40761i 0.0262930 + 0.0981270i
\(603\) 13.7140i 0.558476i
\(604\) −3.81656 + 1.02264i −0.155293 + 0.0416108i
\(605\) 13.9267 + 18.2339i 0.566201 + 0.741312i
\(606\) −3.58504 3.58504i −0.145632 0.145632i
\(607\) −16.3187 + 4.37259i −0.662357 + 0.177478i −0.574309 0.818638i \(-0.694729\pi\)
−0.0880472 + 0.996116i \(0.528063\pi\)
\(608\) 0.0144409 0.0538940i 0.000585654 0.00218569i
\(609\) 3.63649 + 0.974394i 0.147358 + 0.0394844i
\(610\) 29.7939 + 12.4191i 1.20632 + 0.502835i
\(611\) −17.4145 + 9.76467i −0.704515 + 0.395036i
\(612\) −2.99027 2.99027i −0.120875 0.120875i
\(613\) −34.3825 + 19.8507i −1.38869 + 0.801763i −0.993168 0.116692i \(-0.962771\pi\)
−0.395526 + 0.918455i \(0.629438\pi\)
\(614\) −3.92039 + 2.26344i −0.158214 + 0.0913450i
\(615\) 0.0394194 + 0.0516107i 0.00158954 + 0.00208114i
\(616\) −0.315933 + 0.315933i −0.0127293 + 0.0127293i
\(617\) 11.6945 20.2554i 0.470802 0.815453i −0.528640 0.848846i \(-0.677298\pi\)
0.999442 + 0.0333930i \(0.0106313\pi\)
\(618\) 4.20904 7.29027i 0.169312 0.293258i
\(619\) −9.00079 + 9.00079i −0.361772 + 0.361772i −0.864465 0.502693i \(-0.832343\pi\)
0.502693 + 0.864465i \(0.332343\pi\)
\(620\) −1.30121 + 9.71588i −0.0522578 + 0.390199i
\(621\) −0.158893 + 0.0917371i −0.00637617 + 0.00368128i
\(622\) 23.9343 13.8185i 0.959680 0.554071i
\(623\) −5.67239 5.67239i −0.227259 0.227259i
\(624\) −2.58133 + 2.51728i −0.103336 + 0.100772i
\(625\) −0.223417 + 24.9990i −0.00893670 + 0.999960i
\(626\) 30.7305 + 8.23422i 1.22824 + 0.329106i
\(627\) −0.0124152 + 0.0463343i −0.000495817 + 0.00185041i
\(628\) 12.8271 3.43702i 0.511858 0.137152i
\(629\) −0.674908 0.674908i −0.0269104 0.0269104i
\(630\) −0.923513 + 0.705364i −0.0367936 + 0.0281024i
\(631\) −5.22065 + 1.39887i −0.207831 + 0.0556881i −0.361232 0.932476i \(-0.617644\pi\)
0.153401 + 0.988164i \(0.450977\pi\)
\(632\) 16.0201i 0.637245i
\(633\) −3.82280 14.2669i −0.151943 0.567058i
\(634\) −0.902361 1.56294i −0.0358373 0.0620721i
\(635\) −18.4090 14.1912i −0.730540 0.563161i
\(636\) 3.53365i 0.140118i
\(637\) 12.3955 20.8601i 0.491129 0.826507i
\(638\) −4.40390 + 4.40390i −0.174352 + 0.174352i
\(639\) 1.78083 6.64614i 0.0704485 0.262917i
\(640\) 0.286912 + 2.21758i 0.0113412 + 0.0876577i
\(641\) −7.68152 4.43492i −0.303402 0.175169i 0.340568 0.940220i \(-0.389381\pi\)
−0.643970 + 0.765051i \(0.722714\pi\)
\(642\) 7.01419 0.276828
\(643\) 15.2956 + 8.83093i 0.603201 + 0.348258i 0.770300 0.637682i \(-0.220107\pi\)
−0.167099 + 0.985940i \(0.553440\pi\)
\(644\) 0.0246786 + 0.0921016i 0.000972471 + 0.00362931i
\(645\) −9.89901 4.12624i −0.389773 0.162470i
\(646\) −0.117976 + 0.204340i −0.00464169 + 0.00803964i
\(647\) 42.4705 + 11.3799i 1.66969 + 0.447391i 0.965026 0.262154i \(-0.0844329\pi\)
0.704660 + 0.709545i \(0.251100\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −4.35702 −0.171028
\(650\) −17.4904 + 4.36870i −0.686030 + 0.171355i
\(651\) −2.27827 −0.0892926
\(652\) −11.4085 19.7602i −0.446792 0.773867i
\(653\) −22.0209 5.90050i −0.861746 0.230904i −0.199231 0.979953i \(-0.563844\pi\)
−0.662515 + 0.749048i \(0.730511\pi\)
\(654\) 4.40903 7.63667i 0.172407 0.298617i
\(655\) −35.9018 14.9651i −1.40280 0.584733i
\(656\) 0.00751694 + 0.0280536i 0.000293487 + 0.00109531i
\(657\) 2.08300 + 1.20262i 0.0812657 + 0.0469188i
\(658\) −2.87775 −0.112186
\(659\) −0.951098 0.549117i −0.0370495 0.0213906i 0.481361 0.876523i \(-0.340143\pi\)
−0.518410 + 0.855132i \(0.673476\pi\)
\(660\) −0.246666 1.90652i −0.00960148 0.0742113i
\(661\) −6.39522 + 23.8673i −0.248745 + 0.928330i 0.722719 + 0.691142i \(0.242892\pi\)
−0.971464 + 0.237187i \(0.923774\pi\)
\(662\) −14.3606 + 14.3606i −0.558142 + 0.558142i
\(663\) 13.2994 7.45725i 0.516506 0.289616i
\(664\) 4.83100i 0.187479i
\(665\) 0.0513512 + 0.0395857i 0.00199131 + 0.00153507i
\(666\) −0.112851 0.195463i −0.00437287 0.00757404i
\(667\) 0.344002 + 1.28383i 0.0133198 + 0.0497102i
\(668\) 13.3160i 0.515211i
\(669\) −3.07128 + 0.822948i −0.118743 + 0.0318170i
\(670\) 24.3701 18.6135i 0.941499 0.719101i
\(671\) −8.77561 8.77561i −0.338779 0.338779i
\(672\) −0.501987 + 0.134507i −0.0193646 + 0.00518872i
\(673\) 1.94265 7.25006i 0.0748836 0.279469i −0.918323 0.395831i \(-0.870457\pi\)
0.993207 + 0.116362i \(0.0371232\pi\)
\(674\) −21.8897 5.86533i −0.843160 0.225924i
\(675\) 0.0223420 4.99995i 0.000859943 0.192448i
\(676\) −6.21512 11.4181i −0.239043 0.439156i
\(677\) −29.5301 29.5301i −1.13493 1.13493i −0.989345 0.145589i \(-0.953492\pi\)
−0.145589 0.989345i \(-0.546508\pi\)
\(678\) 5.06419 2.92381i 0.194489 0.112288i
\(679\) 2.83248 1.63533i 0.108701 0.0627583i
\(680\) 1.25521 9.37239i 0.0481350 0.359415i
\(681\) −20.4820 + 20.4820i −0.784871 + 0.784871i
\(682\) 1.88447 3.26400i 0.0721601 0.124985i
\(683\) −11.3030 + 19.5774i −0.432499 + 0.749110i −0.997088 0.0762622i \(-0.975701\pi\)
0.564589 + 0.825372i \(0.309035\pi\)
\(684\) −0.0394531 + 0.0394531i −0.00150853 + 0.00150853i
\(685\) 12.3335 + 16.1479i 0.471238 + 0.616978i
\(686\) 6.17941 3.56768i 0.235931 0.136215i
\(687\) 10.4513 6.03405i 0.398741 0.230213i
\(688\) −3.39140 3.39140i −0.129296 0.129296i
\(689\) 12.2642 + 3.45189i 0.467230 + 0.131506i
\(690\) −0.378680 0.157846i −0.0144161 0.00600911i
\(691\) 18.9019 + 5.06476i 0.719063 + 0.192672i 0.599754 0.800185i \(-0.295265\pi\)
0.119310 + 0.992857i \(0.461932\pi\)
\(692\) 4.99132 18.6279i 0.189742 0.708126i
\(693\) 0.431573 0.115640i 0.0163941 0.00439279i
\(694\) −25.5041 25.5041i −0.968124 0.968124i
\(695\) 3.66288 + 4.79571i 0.138941 + 0.181912i
\(696\) −6.99735 + 1.87494i −0.265234 + 0.0710692i
\(697\) 0.122821i 0.00465216i
\(698\) −0.942042 3.51575i −0.0356568 0.133073i
\(699\) −5.03155 8.71490i −0.190311 0.329628i
\(700\) −2.50690 0.683743i −0.0947520 0.0258431i
\(701\) 29.4470i 1.11220i −0.831116 0.556098i \(-0.812298\pi\)
0.831116 0.556098i \(-0.187702\pi\)
\(702\) 3.49414 0.889363i 0.131878 0.0335668i
\(703\) −0.00890462 + 0.00890462i −0.000335844 + 0.000335844i
\(704\) 0.222514 0.830435i 0.00838633 0.0312982i
\(705\) 7.55959 9.80640i 0.284710 0.369330i
\(706\) 24.5055 + 14.1482i 0.922275 + 0.532476i
\(707\) 2.63486 0.0990941
\(708\) −4.38892 2.53395i −0.164946 0.0952315i
\(709\) −10.6145 39.6139i −0.398636 1.48773i −0.815497 0.578761i \(-0.803537\pi\)
0.416861 0.908970i \(-0.363130\pi\)
\(710\) 14.2274 5.85599i 0.533946 0.219771i
\(711\) 8.01005 13.8738i 0.300400 0.520308i
\(712\) 14.9100 + 3.99511i 0.558774 + 0.149723i
\(713\) −0.402163 0.696567i −0.0150611 0.0260866i
\(714\) 2.19773 0.0822480
\(715\) 6.85793 + 1.00630i 0.256472 + 0.0376336i
\(716\) 20.2761 0.757754
\(717\) −11.1048 19.2341i −0.414717 0.718310i
\(718\) 6.51252 + 1.74502i 0.243045 + 0.0651237i
\(719\) −15.8538 + 27.4596i −0.591246 + 1.02407i 0.402819 + 0.915280i \(0.368031\pi\)
−0.994065 + 0.108789i \(0.965303\pi\)
\(720\) 0.860320 2.06394i 0.0320622 0.0769185i
\(721\) 1.13229 + 4.22576i 0.0421687 + 0.157376i
\(722\) −16.4518 9.49844i −0.612272 0.353495i
\(723\) −25.0210 −0.930540
\(724\) 12.3948 + 7.15615i 0.460649 + 0.265956i
\(725\) −34.9445 9.53092i −1.29781 0.353969i
\(726\) 2.65571 9.91123i 0.0985625 0.367840i
\(727\) −13.5130 + 13.5130i −0.501169 + 0.501169i −0.911801 0.410632i \(-0.865308\pi\)
0.410632 + 0.911801i \(0.365308\pi\)
\(728\) 0.0235380 1.87364i 0.000872377 0.0694417i
\(729\) 1.00000i 0.0370370i
\(730\) 0.690093 + 5.33384i 0.0255415 + 0.197414i
\(731\) 10.1412 + 17.5651i 0.375087 + 0.649669i
\(732\) −3.73617 13.9436i −0.138093 0.515369i
\(733\) 10.4942i 0.387612i 0.981040 + 0.193806i \(0.0620833\pi\)
−0.981040 + 0.193806i \(0.937917\pi\)
\(734\) −30.0541 + 8.05298i −1.10932 + 0.297241i
\(735\) −1.99756 + 14.9154i −0.0736811 + 0.550162i
\(736\) −0.129736 0.129736i −0.00478213 0.00478213i
\(737\) −11.3886 + 3.05155i −0.419503 + 0.112405i
\(738\) 0.00751694 0.0280536i 0.000276703 0.00103267i
\(739\) −10.6866 2.86346i −0.393112 0.105334i 0.0568477 0.998383i \(-0.481895\pi\)
−0.449960 + 0.893049i \(0.648562\pi\)
\(740\) 0.194175 0.465834i 0.00713802 0.0171244i
\(741\) −0.0983897 0.175470i −0.00361444 0.00644606i
\(742\) 1.29855 + 1.29855i 0.0476711 + 0.0476711i
\(743\) 31.4823 18.1763i 1.15498 0.666825i 0.204881 0.978787i \(-0.434319\pi\)
0.950095 + 0.311962i \(0.100986\pi\)
\(744\) 3.79654 2.19193i 0.139188 0.0803602i
\(745\) 9.21528 + 1.23417i 0.337622 + 0.0452164i
\(746\) 15.9587 15.9587i 0.584291 0.584291i
\(747\) −2.41550 + 4.18377i −0.0883785 + 0.153076i
\(748\) −1.81785 + 3.14861i −0.0664671 + 0.115124i
\(749\) −2.57757 + 2.57757i −0.0941824 + 0.0941824i
\(750\) 8.91538 6.74656i 0.325544 0.246349i
\(751\) −42.3079 + 24.4265i −1.54384 + 0.891335i −0.545246 + 0.838276i \(0.683564\pi\)
−0.998591 + 0.0530591i \(0.983103\pi\)
\(752\) 4.79551 2.76869i 0.174874 0.100964i
\(753\) 19.3555 + 19.3555i 0.705354 + 0.705354i
\(754\) 0.328104 26.1172i 0.0119488 0.951134i
\(755\) 3.36281 + 8.17013i 0.122385 + 0.297341i
\(756\) 0.501987 + 0.134507i 0.0182571 + 0.00489197i
\(757\) 6.98099 26.0534i 0.253728 0.946927i −0.715065 0.699058i \(-0.753603\pi\)
0.968794 0.247869i \(-0.0797303\pi\)
\(758\) −14.3728 + 3.85119i −0.522045 + 0.139881i
\(759\) 0.111538 + 0.111538i 0.00404857 + 0.00404857i
\(760\) −0.123658 0.0165610i −0.00448554 0.000600730i
\(761\) −21.6967 + 5.81362i −0.786505 + 0.210743i −0.629651 0.776878i \(-0.716802\pi\)
−0.156855 + 0.987622i \(0.550135\pi\)
\(762\) 10.3950i 0.376572i
\(763\) 1.18609 + 4.42655i 0.0429394 + 0.160252i
\(764\) −6.39485 11.0762i −0.231358 0.400723i
\(765\) −5.77324 + 7.48913i −0.208732 + 0.270770i
\(766\) 11.3636i 0.410583i
\(767\) 13.0819 12.7573i 0.472361 0.460640i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) −3.23891 + 12.0878i −0.116798 + 0.435897i −0.999415 0.0341962i \(-0.989113\pi\)
0.882617 + 0.470093i \(0.155780\pi\)
\(770\) 0.791254 + 0.609964i 0.0285148 + 0.0219816i
\(771\) 0.224083 + 0.129375i 0.00807017 + 0.00465931i
\(772\) −2.20902 −0.0795045
\(773\) −17.7829 10.2670i −0.639607 0.369278i 0.144856 0.989453i \(-0.453728\pi\)
−0.784463 + 0.620175i \(0.787061\pi\)
\(774\) 1.24134 + 4.63274i 0.0446190 + 0.166520i
\(775\) 21.9191 + 0.0979442i 0.787358 + 0.00351826i
\(776\) −3.14672 + 5.45027i −0.112961 + 0.195653i
\(777\) 0.113299 + 0.0303584i 0.00406458 + 0.00108910i
\(778\) 0.391567 + 0.678214i 0.0140384 + 0.0243151i
\(779\) −0.00162047 −5.80594e−5
\(780\) 6.32290 + 5.00209i 0.226396 + 0.179104i
\(781\) −5.91545 −0.211671
\(782\) 0.387946 + 0.671942i 0.0138729 + 0.0240286i
\(783\) 6.99735 + 1.87494i 0.250065 + 0.0670047i
\(784\) −3.36496 + 5.82828i −0.120177 + 0.208153i
\(785\) −11.3021 27.4591i −0.403391 0.980059i
\(786\) 4.50210 + 16.8021i 0.160584 + 0.599309i
\(787\) 22.0630 + 12.7381i 0.786462 + 0.454064i 0.838716 0.544570i \(-0.183307\pi\)
−0.0522536 + 0.998634i \(0.516640\pi\)
\(788\) 12.1397 0.432460
\(789\) −5.38327 3.10803i −0.191649 0.110649i
\(790\) 35.5259 4.59635i 1.26396 0.163531i
\(791\) −0.786546 + 2.93543i −0.0279664 + 0.104372i
\(792\) −0.607921 + 0.607921i −0.0216015 + 0.0216015i
\(793\) 52.0437 + 0.653810i 1.84812 + 0.0232175i
\(794\) 14.2414i 0.505409i
\(795\) −7.83617 + 1.01385i −0.277920 + 0.0359574i
\(796\) −2.03805 3.53001i −0.0722368 0.125118i
\(797\) −5.98910 22.3516i −0.212145 0.791735i −0.987152 0.159783i \(-0.948921\pi\)
0.775008 0.631952i \(-0.217746\pi\)
\(798\) 0.0289965i 0.00102646i
\(799\) −22.6190 + 6.06075i −0.800203 + 0.214414i
\(800\) 4.83536 1.27250i 0.170956 0.0449897i
\(801\) −10.9148 10.9148i −0.385657 0.385657i
\(802\) −30.1857 + 8.08823i −1.06589 + 0.285605i
\(803\) 0.535202 1.99740i 0.0188869 0.0704868i
\(804\) −13.2467 3.54943i −0.467174 0.125179i
\(805\) 0.197163 0.0811518i 0.00694907 0.00286023i
\(806\) 3.89885 + 15.3179i 0.137331 + 0.539548i
\(807\) −0.276145 0.276145i −0.00972077 0.00972077i
\(808\) −4.39076 + 2.53501i −0.154466 + 0.0891812i
\(809\) 20.3578 11.7536i 0.715742 0.413234i −0.0974414 0.995241i \(-0.531066\pi\)
0.813184 + 0.582007i \(0.197733\pi\)
\(810\) −1.77703 + 1.35727i −0.0624384 + 0.0476894i
\(811\) −18.5083 + 18.5083i −0.649915 + 0.649915i −0.952972 0.303057i \(-0.901993\pi\)
0.303057 + 0.952972i \(0.401993\pi\)
\(812\) 1.88239 3.26039i 0.0660588 0.114417i
\(813\) 8.44068 14.6197i 0.296028 0.512735i
\(814\) −0.137208 + 0.137208i −0.00480915 + 0.00480915i
\(815\) −40.5466 + 30.9688i −1.42028 + 1.08479i
\(816\) −3.66232 + 2.11444i −0.128207 + 0.0740203i
\(817\) 0.231751 0.133801i 0.00810794 0.00468112i
\(818\) 23.8454 + 23.8454i 0.833736 + 0.833736i
\(819\) −0.957204 + 1.61085i −0.0334474 + 0.0562876i
\(820\) 0.0600546 0.0247184i 0.00209720 0.000863203i
\(821\) 49.9927 + 13.3955i 1.74476 + 0.467506i 0.983495 0.180938i \(-0.0579132\pi\)
0.761263 + 0.648444i \(0.224580\pi\)
\(822\) 2.35189 8.77737i 0.0820316 0.306146i
\(823\) −28.2305 + 7.56435i −0.984054 + 0.263677i −0.714751 0.699379i \(-0.753460\pi\)
−0.269303 + 0.963055i \(0.586793\pi\)
\(824\) −5.95248 5.95248i −0.207364 0.207364i
\(825\) −4.15711 + 1.09401i −0.144732 + 0.0380885i
\(826\) 2.54402 0.681667i 0.0885176 0.0237182i
\(827\) 8.43549i 0.293331i −0.989186 0.146665i \(-0.953146\pi\)
0.989186 0.146665i \(-0.0468540\pi\)
\(828\) 0.0474866 + 0.177222i 0.00165027 + 0.00615891i
\(829\) −10.4506 18.1010i −0.362965 0.628674i 0.625482 0.780238i \(-0.284902\pi\)
−0.988447 + 0.151564i \(0.951569\pi\)
\(830\) −10.7132 + 1.38607i −0.371859 + 0.0481112i
\(831\) 1.05697i 0.0366657i
\(832\) 1.76341 + 3.14490i 0.0611352 + 0.109030i
\(833\) 20.1243 20.1243i 0.697265 0.697265i
\(834\) 0.698481 2.60677i 0.0241864 0.0902650i
\(835\) 29.5293 3.82051i 1.02191 0.132214i
\(836\) 0.0415422 + 0.0239844i 0.00143677 + 0.000829517i
\(837\) −4.38387 −0.151529
\(838\) 9.64226 + 5.56696i 0.333086 + 0.192307i
\(839\) −8.60452 32.1125i −0.297061 1.10865i −0.939567 0.342366i \(-0.888772\pi\)
0.642505 0.766281i \(-0.277895\pi\)
\(840\) 0.442306 + 1.07461i 0.0152610 + 0.0370774i
\(841\) 11.7392 20.3328i 0.404799 0.701132i
\(842\) 28.1829 + 7.55160i 0.971248 + 0.260245i
\(843\) −6.78681 11.7551i −0.233750 0.404867i
\(844\) −14.7702 −0.508411
\(845\) −23.5373 + 17.0585i −0.809709 + 0.586831i
\(846\) −5.53738 −0.190379
\(847\) 2.66626 + 4.61810i 0.0916138 + 0.158680i
\(848\) −3.41325 0.914577i −0.117211 0.0314067i
\(849\) −4.80305 + 8.31913i −0.164840 + 0.285512i
\(850\) −21.1442 0.0944816i −0.725240 0.00324069i
\(851\) 0.0107178 + 0.0399993i 0.000367401 + 0.00137116i
\(852\) −5.95877 3.44030i −0.204144 0.117863i
\(853\) −12.3935 −0.424344 −0.212172 0.977232i \(-0.568054\pi\)
−0.212172 + 0.977232i \(0.568054\pi\)
\(854\) 6.49695 + 3.75102i 0.222321 + 0.128357i
\(855\) 0.0988102 + 0.0761711i 0.00337924 + 0.00260500i
\(856\) 1.81541 6.77519i 0.0620493 0.231571i
\(857\) −11.9224 + 11.9224i −0.407262 + 0.407262i −0.880783 0.473520i \(-0.842983\pi\)
0.473520 + 0.880783i \(0.342983\pi\)
\(858\) −1.51606 2.70376i −0.0517573 0.0923050i
\(859\) 37.7546i 1.28817i −0.764954 0.644085i \(-0.777238\pi\)
0.764954 0.644085i \(-0.222762\pi\)
\(860\) −6.54769 + 8.49376i −0.223274 + 0.289635i
\(861\) 0.00754681 + 0.0130715i 0.000257195 + 0.000445474i
\(862\) 4.51975 + 16.8679i 0.153943 + 0.574524i
\(863\) 34.7009i 1.18123i 0.806953 + 0.590615i \(0.201115\pi\)
−0.806953 + 0.590615i \(0.798885\pi\)
\(864\) −0.965926 + 0.258819i −0.0328615 + 0.00880520i
\(865\) −42.7410 5.72413i −1.45324 0.194626i
\(866\) −1.57183 1.57183i −0.0534131 0.0534131i
\(867\) 0.853360 0.228657i 0.0289816 0.00776560i
\(868\) −0.589661 + 2.20064i −0.0200144 + 0.0746947i
\(869\) −13.3037 3.56470i −0.451295 0.120924i
\(870\) 6.16545 + 14.9793i 0.209028 + 0.507845i
\(871\) 25.2592 42.5079i 0.855874 1.44032i
\(872\) −6.23531 6.23531i −0.211154 0.211154i
\(873\) 5.45027 3.14672i 0.184464 0.106500i
\(874\) 0.00886548 0.00511849i 0.000299879 0.000173135i
\(875\) −0.796999 + 5.75544i −0.0269435 + 0.194570i
\(876\) 1.70077 1.70077i 0.0574636 0.0574636i
\(877\) −15.4110 + 26.6926i −0.520391 + 0.901344i 0.479328 + 0.877636i \(0.340880\pi\)
−0.999719 + 0.0237079i \(0.992453\pi\)
\(878\) 18.9701 32.8571i 0.640209 1.10887i
\(879\) 4.12044 4.12044i 0.138979 0.138979i
\(880\) −1.90540 0.255183i −0.0642311 0.00860222i
\(881\) 24.9249 14.3904i 0.839740 0.484824i −0.0174360 0.999848i \(-0.505550\pi\)
0.857176 + 0.515024i \(0.172217\pi\)
\(882\) 5.82828 3.36496i 0.196248 0.113304i
\(883\) −12.4407 12.4407i −0.418662 0.418662i 0.466080 0.884742i \(-0.345666\pi\)
−0.884742 + 0.466080i \(0.845666\pi\)
\(884\) −3.76101 14.7763i −0.126497 0.496982i
\(885\) −4.36001 + 10.4598i −0.146560 + 0.351603i
\(886\) 21.1654 + 5.67125i 0.711065 + 0.190529i
\(887\) 9.95096 37.1375i 0.334121 1.24695i −0.570699 0.821159i \(-0.693328\pi\)
0.904819 0.425796i \(-0.140006\pi\)
\(888\) −0.218011 + 0.0584158i −0.00731596 + 0.00196031i
\(889\) −3.81996 3.81996i −0.128117 0.128117i
\(890\) 4.58166 34.2103i 0.153577 1.14673i
\(891\) 0.830435 0.222514i 0.0278206 0.00745451i
\(892\) 3.17963i 0.106462i
\(893\) 0.0799645 + 0.298431i 0.00267591 + 0.00998663i
\(894\) −2.07900 3.60093i −0.0695321 0.120433i
\(895\) −5.81745 44.9640i −0.194456 1.50298i
\(896\) 0.519695i 0.0173618i
\(897\) −0.661473 0.00830991i −0.0220860 0.000277460i
\(898\) −11.1962 + 11.1962i −0.373623 + 0.373623i
\(899\) −8.21947 + 30.6755i −0.274135 + 1.02308i
\(900\) −4.82380 1.31566i −0.160793 0.0438554i
\(901\) 12.9414 + 7.47171i 0.431140 + 0.248919i
\(902\) −0.0249693 −0.000831388
\(903\) −2.15861 1.24627i −0.0718339 0.0414733i
\(904\) −1.51348 5.64837i −0.0503375 0.187862i
\(905\) 12.3131 29.5397i 0.409303 0.981934i
\(906\) 1.97560 3.42183i 0.0656348 0.113683i
\(907\) 44.4572 + 11.9123i 1.47618 + 0.395540i 0.905044 0.425318i \(-0.139838\pi\)
0.571132 + 0.820858i \(0.306505\pi\)
\(908\) 14.4830 + 25.0852i 0.480634 + 0.832482i
\(909\) 5.07001 0.168162
\(910\) −4.16171 + 0.485371i −0.137959 + 0.0160899i
\(911\) −34.0825 −1.12920 −0.564602 0.825363i \(-0.690970\pi\)
−0.564602 + 0.825363i \(0.690970\pi\)
\(912\) 0.0278976 + 0.0483200i 0.000923781 + 0.00160004i
\(913\) 4.01183 + 1.07497i 0.132772 + 0.0355762i
\(914\) 19.5983 33.9453i 0.648255 1.12281i
\(915\) −29.8491 + 12.2858i −0.986781 + 0.406158i
\(916\) −3.12345 11.6569i −0.103202 0.385154i
\(917\) −7.82884 4.51999i −0.258531 0.149263i
\(918\) 4.22888 0.139574
\(919\) −6.13874 3.54420i −0.202498 0.116913i 0.395322 0.918543i \(-0.370633\pi\)
−0.597820 + 0.801630i \(0.703966\pi\)
\(920\) −0.250478 + 0.324923i −0.00825800 + 0.0107124i
\(921\) 1.17164 4.37263i 0.0386070 0.144083i
\(922\) 7.43657 7.43657i 0.244910 0.244910i
\(923\) 17.7611 17.3204i 0.584614 0.570108i
\(924\) 0.446797i 0.0146985i
\(925\) −1.08874 0.296947i −0.0357975 0.00976355i
\(926\) −15.6632 27.1295i −0.514726 0.891531i
\(927\) 2.17876 + 8.13124i 0.0715598 + 0.267065i
\(928\) 7.24419i 0.237802i
\(929\) −23.6705 + 6.34249i −0.776604 + 0.208090i −0.625287 0.780395i \(-0.715018\pi\)
−0.151317 + 0.988485i \(0.548351\pi\)
\(930\) −5.95007 7.79026i −0.195110 0.255453i
\(931\) −0.265516 0.265516i −0.00870195 0.00870195i
\(932\) −9.72020 + 2.60452i −0.318396 + 0.0853139i
\(933\) −7.15298 + 26.6953i −0.234178 + 0.873964i
\(934\) −23.4317 6.27849i −0.766707 0.205439i
\(935\) 7.50386 + 3.12786i 0.245403 + 0.102292i
\(936\) 0.0452920 3.60527i 0.00148041 0.117842i
\(937\) 23.5857 + 23.5857i 0.770510 + 0.770510i 0.978196 0.207685i \(-0.0665930\pi\)
−0.207685 + 0.978196i \(0.566593\pi\)
\(938\) 6.17223 3.56354i 0.201530 0.116354i
\(939\) −27.5522 + 15.9073i −0.899133 + 0.519115i
\(940\) −7.51569 9.84008i −0.245135 0.320948i
\(941\) −3.01039 + 3.01039i −0.0981360 + 0.0981360i −0.754470 0.656334i \(-0.772106\pi\)
0.656334 + 0.754470i \(0.272106\pi\)
\(942\) −6.63981 + 11.5005i −0.216337 + 0.374706i
\(943\) −0.00266434 + 0.00461478i −8.67629e−5 + 0.000150278i
\(944\) −3.58354 + 3.58354i −0.116634 + 0.116634i
\(945\) 0.154255 1.15179i 0.00501791 0.0374677i
\(946\) 3.57098 2.06170i 0.116102 0.0670318i
\(947\) 39.0911 22.5692i 1.27029 0.733402i 0.295247 0.955421i \(-0.404598\pi\)
0.975042 + 0.222020i \(0.0712649\pi\)
\(948\) −11.3279 11.3279i −0.367914 0.367914i
\(949\) 4.24143 + 7.56426i 0.137683 + 0.245546i
\(950\) −0.00124657 + 0.278973i −4.04442e−5 + 0.00905108i
\(951\) 1.74323 + 0.467097i 0.0565280 + 0.0151466i
\(952\) 0.568814 2.12284i 0.0184354 0.0688018i
\(953\) 12.2640 3.28613i 0.397271 0.106448i −0.0546521 0.998505i \(-0.517405\pi\)
0.451923 + 0.892057i \(0.350738\pi\)
\(954\) 2.49867 + 2.49867i 0.0808974 + 0.0808974i
\(955\) −22.7277 + 17.3590i −0.735450 + 0.561725i
\(956\) −21.4528 + 5.74827i −0.693835 + 0.185912i
\(957\) 6.22805i 0.201324i
\(958\) 3.00994 + 11.2332i 0.0972467 + 0.362930i
\(959\) 2.36124 + 4.08978i 0.0762483 + 0.132066i
\(960\) −1.77095 1.36519i −0.0571570 0.0440614i
\(961\) 11.7817i 0.380055i
\(962\) 0.0102225 0.813713i 0.000329585 0.0262352i
\(963\) −4.95978 + 4.95978i −0.159827 + 0.159827i
\(964\) −6.47591 + 24.1684i −0.208575 + 0.778412i
\(965\) 0.633795 + 4.89870i 0.0204026 + 0.157695i
\(966\) −0.0825761 0.0476753i −0.00265684 0.00153393i
\(967\) 27.7803 0.893353 0.446677 0.894695i \(-0.352607\pi\)
0.446677 + 0.894695i \(0.352607\pi\)
\(968\) −8.88617 5.13043i −0.285612 0.164898i
\(969\) −0.0610687 0.227911i −0.00196181 0.00732157i
\(970\) 12.9893 + 5.41437i 0.417061 + 0.173845i
\(971\) −0.0689099 + 0.119355i −0.00221142 + 0.00383030i −0.867129 0.498084i \(-0.834037\pi\)
0.864918 + 0.501914i \(0.167371\pi\)
\(972\) 0.965926 + 0.258819i 0.0309821 + 0.00830162i
\(973\) 0.701257 + 1.21461i 0.0224813 + 0.0389387i
\(974\) −9.14019 −0.292871
\(975\) 9.27845 15.4567i 0.297148 0.495011i
\(976\) −14.4355 −0.462068
\(977\) −12.6538 21.9169i −0.404829 0.701185i 0.589472 0.807789i \(-0.299336\pi\)
−0.994302 + 0.106604i \(0.966002\pi\)
\(978\) 22.0396 + 5.90549i 0.704748 + 0.188837i
\(979\) −6.63536 + 11.4928i −0.212067 + 0.367311i
\(980\) 13.8901 + 5.78988i 0.443705 + 0.184951i
\(981\) 2.28228 + 8.51759i 0.0728677 + 0.271946i
\(982\) −6.88995 3.97792i −0.219867 0.126940i
\(983\) 19.2981 0.615512 0.307756 0.951465i \(-0.400422\pi\)
0.307756 + 0.951465i \(0.400422\pi\)
\(984\) −0.0251522 0.0145216i −0.000801822 0.000462932i
\(985\) −3.48303 26.9209i −0.110978 0.857770i
\(986\) 7.92888 29.5910i 0.252507 0.942369i
\(987\) 2.03487 2.03487i 0.0647708 0.0647708i
\(988\) −0.194956 + 0.0496222i −0.00620238 + 0.00157869i
\(989\) 0.879973i 0.0279815i
\(990\) 1.52254 + 1.17370i 0.0483894 + 0.0373025i
\(991\) 8.95513 + 15.5107i 0.284469 + 0.492715i 0.972480 0.232985i \(-0.0748493\pi\)
−0.688011 + 0.725700i \(0.741516\pi\)
\(992\) −1.13463 4.23449i −0.0360245 0.134445i
\(993\) 20.3090i 0.644486i
\(994\) 3.45397 0.925487i 0.109553 0.0293547i
\(995\) −7.24336 + 5.53235i −0.229630 + 0.175387i
\(996\) 3.41603 + 3.41603i 0.108241 + 0.108241i
\(997\) 36.2474 9.71246i 1.14797 0.307597i 0.365816 0.930687i \(-0.380790\pi\)
0.782150 + 0.623090i \(0.214123\pi\)
\(998\) −8.02635 + 29.9548i −0.254070 + 0.948201i
\(999\) 0.218011 + 0.0584158i 0.00689755 + 0.00184819i
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 390.2.bn.b.67.2 yes 16
5.3 odd 4 390.2.bd.b.223.3 yes 16
13.7 odd 12 390.2.bd.b.7.3 16
65.33 even 12 inner 390.2.bn.b.163.2 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.bd.b.7.3 16 13.7 odd 12
390.2.bd.b.223.3 yes 16 5.3 odd 4
390.2.bn.b.67.2 yes 16 1.1 even 1 trivial
390.2.bn.b.163.2 yes 16 65.33 even 12 inner