Properties

Label 418.2.u.b.251.8
Level $418$
Weight $2$
Character 418.251
Analytic conductor $3.338$
Analytic rank $0$
Dimension $264$
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] = [418,2,Mod(5,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(90))
 
chi = DirichletCharacter(H, H._module([36, 80]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.u (of order \(45\), degree \(24\), 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: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(264\)
Relative dimension: \(11\) over \(\Q(\zeta_{45})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label 251.8
Character \(\chi\) \(=\) 418.251
Dual form 418.2.u.b.5.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.615661 + 0.788011i) q^{2} +(1.20057 + 1.15938i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-2.39453 - 1.49627i) q^{5} +(-1.65275 + 0.232278i) q^{6} +(2.61504 - 1.16429i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-0.00748509 - 0.214345i) q^{9} +O(q^{10})\) \(q+(-0.615661 + 0.788011i) q^{2} +(1.20057 + 1.15938i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-2.39453 - 1.49627i) q^{5} +(-1.65275 + 0.232278i) q^{6} +(2.61504 - 1.16429i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-0.00748509 - 0.214345i) q^{9} +(2.65330 - 0.965720i) q^{10} +(-0.230878 + 3.30858i) q^{11} +(0.834495 - 1.44539i) q^{12} +(5.51978 + 2.93492i) q^{13} +(-0.692507 + 2.77749i) q^{14} +(-1.14006 - 4.57254i) q^{15} +(-0.882948 + 0.469472i) q^{16} +(0.0973339 - 2.78728i) q^{17} +(0.173514 + 0.126066i) q^{18} +(3.77584 + 2.17785i) q^{19} +(-0.872534 + 2.68538i) q^{20} +(4.48940 + 1.63401i) q^{21} +(-2.46505 - 2.21890i) q^{22} +(6.61248 + 5.54853i) q^{23} +(0.625214 + 1.54746i) q^{24} +(1.30310 + 2.67175i) q^{25} +(-5.71106 + 2.54273i) q^{26} +(3.58984 - 3.98692i) q^{27} +(-1.76234 - 2.25570i) q^{28} +(-4.42511 - 1.26888i) q^{29} +(4.30510 + 1.91675i) q^{30} +(-0.618020 - 0.686381i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-4.11308 + 3.70451i) q^{33} +(2.13648 + 1.79272i) q^{34} +(-8.00390 - 1.12487i) q^{35} +(-0.206167 + 0.0591175i) q^{36} +(-2.96494 - 2.15416i) q^{37} +(-4.04081 + 1.63458i) q^{38} +(3.22420 + 9.92308i) q^{39} +(-1.57892 - 2.34085i) q^{40} +(-8.19481 - 7.91363i) q^{41} +(-4.05157 + 2.53170i) q^{42} +(3.86050 - 3.23934i) q^{43} +(3.26615 - 0.576398i) q^{44} +(-0.302794 + 0.524455i) q^{45} +(-8.44335 + 1.79469i) q^{46} +(-3.79034 + 5.61941i) q^{47} +(-1.60434 - 0.460036i) q^{48} +(0.798964 - 0.887340i) q^{49} +(-2.90763 - 0.618037i) q^{50} +(3.34836 - 3.23348i) q^{51} +(1.51238 - 6.06584i) q^{52} +(8.09265 - 5.05685i) q^{53} +(0.931609 + 5.28342i) q^{54} +(5.50337 - 7.57704i) q^{55} +2.86252 q^{56} +(2.00821 + 6.99228i) q^{57} +(3.72426 - 2.70584i) q^{58} +(5.54524 + 8.22116i) q^{59} +(-4.16091 + 2.21239i) q^{60} +(-2.68635 + 6.64896i) q^{61} +(0.921366 - 0.0644282i) q^{62} +(-0.269134 - 0.551807i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-8.82585 - 15.2868i) q^{65} +(-0.386929 - 5.52187i) q^{66} +(-0.957233 + 0.348404i) q^{67} +(-2.72803 + 0.579861i) q^{68} +(1.50591 + 14.3278i) q^{69} +(5.81410 - 5.61461i) q^{70} +(-1.96324 - 1.22677i) q^{71} +(0.0803440 - 0.198858i) q^{72} +(0.623780 - 1.27894i) q^{73} +(3.52290 - 1.01018i) q^{74} +(-1.53310 + 4.71840i) q^{75} +(1.19970 - 4.19055i) q^{76} +(3.24840 + 8.92089i) q^{77} +(-9.80451 - 3.56855i) q^{78} +(-12.1730 - 1.71081i) q^{79} +(2.81670 + 0.196963i) q^{80} +(8.29033 - 0.579716i) q^{81} +(11.2813 - 1.58548i) q^{82} +(-4.27619 - 0.908932i) q^{83} +(0.499387 - 4.75135i) q^{84} +(-4.40359 + 6.52859i) q^{85} +(0.175877 + 5.03645i) q^{86} +(-3.84155 - 6.65376i) q^{87} +(-1.55664 + 2.92863i) q^{88} +(2.08231 - 11.8094i) q^{89} +(-0.226858 - 0.561492i) q^{90} +(17.8516 + 1.24830i) q^{91} +(3.78401 - 7.75838i) q^{92} +(0.0537978 - 1.54057i) q^{93} +(-2.09459 - 6.44648i) q^{94} +(-5.78271 - 10.8646i) q^{95} +(1.35024 - 0.981007i) q^{96} +(-0.0681272 + 0.0871988i) q^{97} +(0.207342 + 1.17589i) q^{98} +(0.710906 + 0.0247225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.615661 + 0.788011i −0.435338 + 0.557208i
\(3\) 1.20057 + 1.15938i 0.693150 + 0.669367i 0.955293 0.295662i \(-0.0955403\pi\)
−0.262143 + 0.965029i \(0.584429\pi\)
\(4\) −0.241922 0.970296i −0.120961 0.485148i
\(5\) −2.39453 1.49627i −1.07087 0.669152i −0.124491 0.992221i \(-0.539730\pi\)
−0.946375 + 0.323069i \(0.895285\pi\)
\(6\) −1.65275 + 0.232278i −0.674731 + 0.0948273i
\(7\) 2.61504 1.16429i 0.988394 0.440061i 0.152113 0.988363i \(-0.451392\pi\)
0.836281 + 0.548302i \(0.184725\pi\)
\(8\) 0.913545 + 0.406737i 0.322987 + 0.143803i
\(9\) −0.00748509 0.214345i −0.00249503 0.0714483i
\(10\) 2.65330 0.965720i 0.839046 0.305388i
\(11\) −0.230878 + 3.30858i −0.0696122 + 0.997574i
\(12\) 0.834495 1.44539i 0.240898 0.417247i
\(13\) 5.51978 + 2.93492i 1.53091 + 0.814000i 0.999453 0.0330848i \(-0.0105331\pi\)
0.531458 + 0.847084i \(0.321644\pi\)
\(14\) −0.692507 + 2.77749i −0.185080 + 0.742316i
\(15\) −1.14006 4.57254i −0.294363 1.18062i
\(16\) −0.882948 + 0.469472i −0.220737 + 0.117368i
\(17\) 0.0973339 2.78728i 0.0236069 0.676015i −0.928693 0.370850i \(-0.879066\pi\)
0.952300 0.305164i \(-0.0987114\pi\)
\(18\) 0.173514 + 0.126066i 0.0408977 + 0.0297140i
\(19\) 3.77584 + 2.17785i 0.866237 + 0.499633i
\(20\) −0.872534 + 2.68538i −0.195104 + 0.600470i
\(21\) 4.48940 + 1.63401i 0.979667 + 0.356570i
\(22\) −2.46505 2.21890i −0.525551 0.473071i
\(23\) 6.61248 + 5.54853i 1.37880 + 1.15695i 0.969655 + 0.244479i \(0.0786168\pi\)
0.409143 + 0.912470i \(0.365828\pi\)
\(24\) 0.625214 + 1.54746i 0.127621 + 0.315874i
\(25\) 1.30310 + 2.67175i 0.260620 + 0.534350i
\(26\) −5.71106 + 2.54273i −1.12003 + 0.498670i
\(27\) 3.58984 3.98692i 0.690864 0.767282i
\(28\) −1.76234 2.25570i −0.333052 0.426287i
\(29\) −4.42511 1.26888i −0.821723 0.235625i −0.161671 0.986845i \(-0.551688\pi\)
−0.660053 + 0.751219i \(0.729466\pi\)
\(30\) 4.30510 + 1.91675i 0.786000 + 0.349950i
\(31\) −0.618020 0.686381i −0.111000 0.123278i 0.685084 0.728464i \(-0.259765\pi\)
−0.796084 + 0.605186i \(0.793099\pi\)
\(32\) 0.173648 0.984808i 0.0306970 0.174091i
\(33\) −4.11308 + 3.70451i −0.715995 + 0.644872i
\(34\) 2.13648 + 1.79272i 0.366404 + 0.307449i
\(35\) −8.00390 1.12487i −1.35291 0.190138i
\(36\) −0.206167 + 0.0591175i −0.0343612 + 0.00985292i
\(37\) −2.96494 2.15416i −0.487434 0.354141i 0.316763 0.948505i \(-0.397404\pi\)
−0.804197 + 0.594364i \(0.797404\pi\)
\(38\) −4.04081 + 1.63458i −0.655506 + 0.265165i
\(39\) 3.22420 + 9.92308i 0.516286 + 1.58896i
\(40\) −1.57892 2.34085i −0.249650 0.370121i
\(41\) −8.19481 7.91363i −1.27981 1.23590i −0.957219 0.289364i \(-0.906556\pi\)
−0.322595 0.946537i \(-0.604555\pi\)
\(42\) −4.05157 + 2.53170i −0.625170 + 0.390650i
\(43\) 3.86050 3.23934i 0.588721 0.493995i −0.299077 0.954229i \(-0.596679\pi\)
0.887798 + 0.460234i \(0.152234\pi\)
\(44\) 3.26615 0.576398i 0.492391 0.0868953i
\(45\) −0.302794 + 0.524455i −0.0451379 + 0.0781812i
\(46\) −8.44335 + 1.79469i −1.24490 + 0.264613i
\(47\) −3.79034 + 5.61941i −0.552878 + 0.819675i −0.997089 0.0762468i \(-0.975706\pi\)
0.444211 + 0.895922i \(0.353484\pi\)
\(48\) −1.60434 0.460036i −0.231566 0.0664004i
\(49\) 0.798964 0.887340i 0.114138 0.126763i
\(50\) −2.90763 0.618037i −0.411201 0.0874036i
\(51\) 3.34836 3.23348i 0.468865 0.452777i
\(52\) 1.51238 6.06584i 0.209730 0.841180i
\(53\) 8.09265 5.05685i 1.11161 0.694611i 0.155564 0.987826i \(-0.450281\pi\)
0.956047 + 0.293214i \(0.0947250\pi\)
\(54\) 0.931609 + 5.28342i 0.126776 + 0.718982i
\(55\) 5.50337 7.57704i 0.742074 1.02169i
\(56\) 2.86252 0.382521
\(57\) 2.00821 + 6.99228i 0.265994 + 0.926151i
\(58\) 3.72426 2.70584i 0.489020 0.355294i
\(59\) 5.54524 + 8.22116i 0.721929 + 1.07030i 0.994144 + 0.108067i \(0.0344662\pi\)
−0.272215 + 0.962237i \(0.587756\pi\)
\(60\) −4.16091 + 2.21239i −0.537171 + 0.285619i
\(61\) −2.68635 + 6.64896i −0.343952 + 0.851312i 0.651727 + 0.758454i \(0.274045\pi\)
−0.995679 + 0.0928585i \(0.970400\pi\)
\(62\) 0.921366 0.0644282i 0.117014 0.00818239i
\(63\) −0.269134 0.551807i −0.0339077 0.0695211i
\(64\) 0.669131 + 0.743145i 0.0836413 + 0.0928931i
\(65\) −8.82585 15.2868i −1.09471 1.89610i
\(66\) −0.386929 5.52187i −0.0476277 0.679695i
\(67\) −0.957233 + 0.348404i −0.116945 + 0.0425644i −0.399830 0.916589i \(-0.630931\pi\)
0.282885 + 0.959154i \(0.408709\pi\)
\(68\) −2.72803 + 0.579861i −0.330823 + 0.0703185i
\(69\) 1.50591 + 14.3278i 0.181290 + 1.72486i
\(70\) 5.81410 5.61461i 0.694918 0.671075i
\(71\) −1.96324 1.22677i −0.232994 0.145591i 0.408399 0.912804i \(-0.366087\pi\)
−0.641392 + 0.767213i \(0.721643\pi\)
\(72\) 0.0803440 0.198858i 0.00946863 0.0234357i
\(73\) 0.623780 1.27894i 0.0730079 0.149688i −0.859168 0.511693i \(-0.829019\pi\)
0.932176 + 0.362004i \(0.117907\pi\)
\(74\) 3.52290 1.01018i 0.409529 0.117430i
\(75\) −1.53310 + 4.71840i −0.177027 + 0.544834i
\(76\) 1.19970 4.19055i 0.137615 0.480689i
\(77\) 3.24840 + 8.92089i 0.370189 + 1.01663i
\(78\) −9.80451 3.56855i −1.11014 0.404059i
\(79\) −12.1730 1.71081i −1.36957 0.192481i −0.584253 0.811572i \(-0.698612\pi\)
−0.785319 + 0.619091i \(0.787501\pi\)
\(80\) 2.81670 + 0.196963i 0.314917 + 0.0220211i
\(81\) 8.29033 0.579716i 0.921148 0.0644129i
\(82\) 11.2813 1.58548i 1.24581 0.175087i
\(83\) −4.27619 0.908932i −0.469373 0.0997682i −0.0328477 0.999460i \(-0.510458\pi\)
−0.436525 + 0.899692i \(0.643791\pi\)
\(84\) 0.499387 4.75135i 0.0544875 0.518414i
\(85\) −4.40359 + 6.52859i −0.477636 + 0.708125i
\(86\) 0.175877 + 5.03645i 0.0189653 + 0.543095i
\(87\) −3.84155 6.65376i −0.411857 0.713358i
\(88\) −1.55664 + 2.92863i −0.165938 + 0.312193i
\(89\) 2.08231 11.8094i 0.220725 1.25179i −0.649967 0.759962i \(-0.725217\pi\)
0.870692 0.491829i \(-0.163672\pi\)
\(90\) −0.226858 0.561492i −0.0239129 0.0591865i
\(91\) 17.8516 + 1.24830i 1.87135 + 0.130858i
\(92\) 3.78401 7.75838i 0.394511 0.808867i
\(93\) 0.0537978 1.54057i 0.00557857 0.159749i
\(94\) −2.09459 6.44648i −0.216040 0.664904i
\(95\) −5.78271 10.8646i −0.593294 1.11468i
\(96\) 1.35024 0.981007i 0.137808 0.100124i
\(97\) −0.0681272 + 0.0871988i −0.00691727 + 0.00885370i −0.791457 0.611225i \(-0.790677\pi\)
0.784540 + 0.620079i \(0.212899\pi\)
\(98\) 0.207342 + 1.17589i 0.0209447 + 0.118783i
\(99\) 0.710906 + 0.0247225i 0.0714487 + 0.00248470i
\(100\) 2.27714 1.91074i 0.227714 0.191074i
\(101\) 11.8622 + 6.30722i 1.18033 + 0.627592i 0.939357 0.342940i \(-0.111423\pi\)
0.240972 + 0.970532i \(0.422534\pi\)
\(102\) 0.486556 + 4.62927i 0.0481763 + 0.458367i
\(103\) −0.0980939 + 0.933301i −0.00966548 + 0.0919609i −0.998291 0.0584362i \(-0.981389\pi\)
0.988626 + 0.150397i \(0.0480552\pi\)
\(104\) 3.84883 + 4.92628i 0.377409 + 0.483061i
\(105\) −8.30509 10.6300i −0.810493 1.03738i
\(106\) −0.997481 + 9.49040i −0.0968839 + 0.921789i
\(107\) −2.02145 19.2328i −0.195421 1.85930i −0.451011 0.892518i \(-0.648937\pi\)
0.255591 0.966785i \(-0.417730\pi\)
\(108\) −4.73695 2.51868i −0.455813 0.242360i
\(109\) −5.05028 + 4.23769i −0.483729 + 0.405897i −0.851772 0.523912i \(-0.824472\pi\)
0.368044 + 0.929808i \(0.380028\pi\)
\(110\) 2.58258 + 9.00160i 0.246239 + 0.858269i
\(111\) −1.06214 6.02370i −0.100814 0.571745i
\(112\) −1.76234 + 2.25570i −0.166526 + 0.213143i
\(113\) −11.9332 + 8.66999i −1.12258 + 0.815604i −0.984599 0.174831i \(-0.944062\pi\)
−0.137984 + 0.990434i \(0.544062\pi\)
\(114\) −6.74637 2.72239i −0.631856 0.254975i
\(115\) −7.53169 23.1802i −0.702334 2.16156i
\(116\) −0.160658 + 4.60064i −0.0149167 + 0.427159i
\(117\) 0.587769 1.20510i 0.0543393 0.111412i
\(118\) −9.89235 0.691741i −0.910665 0.0636799i
\(119\) −2.99068 7.40218i −0.274155 0.678557i
\(120\) 0.818321 4.64093i 0.0747021 0.423657i
\(121\) −10.8934 1.52775i −0.990308 0.138887i
\(122\) −3.58557 6.21039i −0.324622 0.562262i
\(123\) −0.663555 19.0017i −0.0598308 1.71333i
\(124\) −0.516480 + 0.765712i −0.0463812 + 0.0687630i
\(125\) −0.598378 + 5.69319i −0.0535206 + 0.509214i
\(126\) 0.600525 + 0.127646i 0.0534990 + 0.0113716i
\(127\) −14.4027 + 2.02417i −1.27803 + 0.179616i −0.745335 0.666691i \(-0.767710\pi\)
−0.532697 + 0.846306i \(0.678821\pi\)
\(128\) −0.997564 + 0.0697565i −0.0881730 + 0.00616566i
\(129\) 8.39042 + 0.586715i 0.738735 + 0.0516574i
\(130\) 17.4799 + 2.45664i 1.53309 + 0.215462i
\(131\) −16.2600 5.91817i −1.42065 0.517073i −0.486411 0.873730i \(-0.661694\pi\)
−0.934235 + 0.356657i \(0.883916\pi\)
\(132\) 4.58951 + 3.09470i 0.399466 + 0.269359i
\(133\) 12.4096 + 1.29899i 1.07605 + 0.112637i
\(134\) 0.314785 0.968809i 0.0271933 0.0836924i
\(135\) −14.5615 + 4.17543i −1.25325 + 0.359364i
\(136\) 1.22261 2.50672i 0.104838 0.214949i
\(137\) −4.43149 + 10.9683i −0.378608 + 0.937087i 0.610782 + 0.791799i \(0.290855\pi\)
−0.989389 + 0.145288i \(0.953589\pi\)
\(138\) −12.2176 7.63438i −1.04003 0.649882i
\(139\) 5.98937 5.78386i 0.508011 0.490581i −0.395904 0.918292i \(-0.629569\pi\)
0.903916 + 0.427711i \(0.140680\pi\)
\(140\) 0.844857 + 8.03828i 0.0714034 + 0.679358i
\(141\) −11.0656 + 2.35206i −0.931891 + 0.198079i
\(142\) 2.17540 0.791780i 0.182555 0.0664447i
\(143\) −10.9848 + 17.5850i −0.918595 + 1.47053i
\(144\) 0.107238 + 0.185741i 0.00893649 + 0.0154784i
\(145\) 8.69748 + 9.65953i 0.722287 + 0.802181i
\(146\) 0.623780 + 1.27894i 0.0516244 + 0.105846i
\(147\) 1.98797 0.139013i 0.163965 0.0114656i
\(148\) −1.37288 + 3.39801i −0.112850 + 0.279315i
\(149\) −5.33553 + 2.83695i −0.437103 + 0.232412i −0.673414 0.739266i \(-0.735173\pi\)
0.236311 + 0.971678i \(0.424062\pi\)
\(150\) −2.77428 4.11304i −0.226519 0.335828i
\(151\) 11.8549 8.61309i 0.964738 0.700923i 0.0104917 0.999945i \(-0.496660\pi\)
0.954246 + 0.299022i \(0.0966603\pi\)
\(152\) 2.56359 + 3.52534i 0.207935 + 0.285943i
\(153\) −0.598168 −0.0483590
\(154\) −9.02967 2.93247i −0.727632 0.236306i
\(155\) 0.452857 + 2.56828i 0.0363744 + 0.206289i
\(156\) 8.84832 5.52904i 0.708432 0.442678i
\(157\) 1.19629 4.79804i 0.0954740 0.382925i −0.903481 0.428628i \(-0.858997\pi\)
0.998955 + 0.0457026i \(0.0145527\pi\)
\(158\) 8.84260 8.53920i 0.703479 0.679342i
\(159\) 15.5786 + 3.31133i 1.23546 + 0.262606i
\(160\) −1.88934 + 2.09833i −0.149366 + 0.165887i
\(161\) 23.7521 + 6.81079i 1.87192 + 0.536766i
\(162\) −4.64721 + 6.88978i −0.365120 + 0.541312i
\(163\) −12.3516 + 2.62542i −0.967455 + 0.205639i −0.664436 0.747345i \(-0.731328\pi\)
−0.303019 + 0.952984i \(0.597995\pi\)
\(164\) −5.69606 + 9.86587i −0.444788 + 0.770395i
\(165\) 15.3918 2.71629i 1.19825 0.211463i
\(166\) 3.34893 2.81009i 0.259928 0.218105i
\(167\) −8.43168 + 5.26870i −0.652463 + 0.407704i −0.815372 0.578937i \(-0.803468\pi\)
0.162910 + 0.986641i \(0.447912\pi\)
\(168\) 3.43666 + 3.31874i 0.265144 + 0.256047i
\(169\) 14.5847 + 21.6227i 1.12190 + 1.66328i
\(170\) −2.43348 7.48947i −0.186639 0.574416i
\(171\) 0.438549 0.825634i 0.0335367 0.0631378i
\(172\) −4.07706 2.96216i −0.310873 0.225862i
\(173\) −0.210275 + 0.0602955i −0.0159869 + 0.00458418i −0.283621 0.958936i \(-0.591536\pi\)
0.267634 + 0.963521i \(0.413758\pi\)
\(174\) 7.60833 + 1.06928i 0.576786 + 0.0810620i
\(175\) 6.51836 + 5.46955i 0.492741 + 0.413459i
\(176\) −1.34943 3.02969i −0.101717 0.228372i
\(177\) −2.87397 + 16.2991i −0.216021 + 1.22512i
\(178\) 8.02392 + 8.91146i 0.601418 + 0.667942i
\(179\) 5.79586 + 2.58048i 0.433203 + 0.192874i 0.611740 0.791059i \(-0.290470\pi\)
−0.178537 + 0.983933i \(0.557137\pi\)
\(180\) 0.582129 + 0.166923i 0.0433893 + 0.0124417i
\(181\) −9.95346 12.7398i −0.739835 0.946945i 0.259991 0.965611i \(-0.416280\pi\)
−0.999826 + 0.0186659i \(0.994058\pi\)
\(182\) −11.9742 + 13.2987i −0.887587 + 0.985765i
\(183\) −10.9338 + 4.86805i −0.808251 + 0.359856i
\(184\) 3.78401 + 7.75838i 0.278961 + 0.571955i
\(185\) 3.87645 + 9.59454i 0.285002 + 0.705405i
\(186\) 1.18086 + 0.990860i 0.0865850 + 0.0726534i
\(187\) 9.19946 + 0.965558i 0.672731 + 0.0706086i
\(188\) 6.36946 + 2.31829i 0.464540 + 0.169079i
\(189\) 4.74564 14.6056i 0.345195 1.06240i
\(190\) 12.1216 + 2.13207i 0.879394 + 0.154677i
\(191\) 11.3365 + 8.23642i 0.820277 + 0.595966i 0.916792 0.399365i \(-0.130769\pi\)
−0.0965147 + 0.995332i \(0.530769\pi\)
\(192\) −0.0582469 + 1.66797i −0.00420361 + 0.120376i
\(193\) 20.4903 10.8949i 1.47492 0.784231i 0.479298 0.877652i \(-0.340891\pi\)
0.995627 + 0.0934206i \(0.0297801\pi\)
\(194\) −0.0267703 0.107370i −0.00192200 0.00770871i
\(195\) 7.12714 28.5854i 0.510385 2.04704i
\(196\) −1.05427 0.560565i −0.0753049 0.0400403i
\(197\) −5.25904 + 9.10893i −0.374691 + 0.648984i −0.990281 0.139083i \(-0.955585\pi\)
0.615590 + 0.788067i \(0.288918\pi\)
\(198\) −0.457159 + 0.544981i −0.0324889 + 0.0387301i
\(199\) −7.86659 + 2.86320i −0.557648 + 0.202967i −0.605441 0.795890i \(-0.707003\pi\)
0.0477934 + 0.998857i \(0.484781\pi\)
\(200\) 0.103742 + 2.97078i 0.00733566 + 0.210066i
\(201\) −1.55316 0.691510i −0.109551 0.0487754i
\(202\) −12.2732 + 5.46440i −0.863542 + 0.384474i
\(203\) −13.0492 + 1.83395i −0.915876 + 0.128718i
\(204\) −3.94747 2.46665i −0.276378 0.172700i
\(205\) 7.78179 + 31.2111i 0.543504 + 2.17987i
\(206\) −0.675059 0.651897i −0.0470336 0.0454198i
\(207\) 1.13981 1.45888i 0.0792219 0.101399i
\(208\) −6.25153 −0.433466
\(209\) −8.07735 + 11.9898i −0.558722 + 0.829355i
\(210\) 13.4897 0.930877
\(211\) 4.21967 5.40093i 0.290494 0.371816i −0.620520 0.784191i \(-0.713078\pi\)
0.911014 + 0.412375i \(0.135301\pi\)
\(212\) −6.86443 6.62890i −0.471451 0.455275i
\(213\) −0.934720 3.74896i −0.0640460 0.256874i
\(214\) 16.4002 + 10.2480i 1.12109 + 0.700536i
\(215\) −14.0910 + 1.98036i −0.960999 + 0.135060i
\(216\) 4.90110 2.18211i 0.333478 0.148474i
\(217\) −2.41530 1.07536i −0.163961 0.0730002i
\(218\) −0.230081 6.58865i −0.0155830 0.446240i
\(219\) 2.23166 0.812259i 0.150802 0.0548874i
\(220\) −8.68335 3.50684i −0.585431 0.236431i
\(221\) 8.71770 15.0995i 0.586416 1.01570i
\(222\) 5.40066 + 2.87158i 0.362469 + 0.192728i
\(223\) −3.63607 + 14.5835i −0.243489 + 0.976582i 0.716733 + 0.697347i \(0.245636\pi\)
−0.960223 + 0.279235i \(0.909919\pi\)
\(224\) −0.692507 2.77749i −0.0462701 0.185579i
\(225\) 0.562922 0.299311i 0.0375281 0.0199541i
\(226\) 0.514777 14.7413i 0.0342424 0.980575i
\(227\) 16.8623 + 12.2512i 1.11919 + 0.813141i 0.984086 0.177691i \(-0.0568626\pi\)
0.135106 + 0.990831i \(0.456863\pi\)
\(228\) 6.29875 3.64015i 0.417145 0.241075i
\(229\) −2.43847 + 7.50483i −0.161139 + 0.495933i −0.998731 0.0503621i \(-0.983962\pi\)
0.837592 + 0.546296i \(0.183962\pi\)
\(230\) 22.9032 + 8.33608i 1.51019 + 0.549665i
\(231\) −6.44274 + 14.4763i −0.423901 + 0.952469i
\(232\) −3.52644 2.95904i −0.231522 0.194270i
\(233\) −6.77653 16.7725i −0.443945 1.09880i −0.968851 0.247643i \(-0.920344\pi\)
0.524906 0.851160i \(-0.324100\pi\)
\(234\) 0.587769 + 1.20510i 0.0384237 + 0.0787802i
\(235\) 17.4842 7.78448i 1.14055 0.507804i
\(236\) 6.63544 7.36940i 0.431930 0.479707i
\(237\) −12.6311 16.1671i −0.820478 1.05016i
\(238\) 7.67424 + 2.20055i 0.497447 + 0.142641i
\(239\) −11.5792 5.15539i −0.748996 0.333474i −0.00350808 0.999994i \(-0.501117\pi\)
−0.745488 + 0.666519i \(0.767783\pi\)
\(240\) 3.15329 + 3.50209i 0.203544 + 0.226059i
\(241\) −0.993270 + 5.63312i −0.0639822 + 0.362861i 0.935960 + 0.352106i \(0.114534\pi\)
−0.999942 + 0.0107545i \(0.996577\pi\)
\(242\) 7.91053 7.64353i 0.508508 0.491345i
\(243\) −1.70408 1.42989i −0.109317 0.0917277i
\(244\) 7.10135 + 0.998029i 0.454617 + 0.0638923i
\(245\) −3.24084 + 0.929297i −0.207050 + 0.0593706i
\(246\) 15.3821 + 11.1758i 0.980727 + 0.712540i
\(247\) 14.4500 + 23.1030i 0.919431 + 1.47001i
\(248\) −0.285413 0.878411i −0.0181237 0.0557792i
\(249\) −4.08007 6.04895i −0.258564 0.383337i
\(250\) −4.11789 3.97660i −0.260438 0.251502i
\(251\) 15.3260 9.57673i 0.967367 0.604478i 0.0484064 0.998828i \(-0.484586\pi\)
0.918960 + 0.394350i \(0.129030\pi\)
\(252\) −0.470306 + 0.394634i −0.0296265 + 0.0248596i
\(253\) −19.8844 + 20.5969i −1.25012 + 1.29492i
\(254\) 7.27211 12.5957i 0.456293 0.790323i
\(255\) −12.8559 + 2.73261i −0.805068 + 0.171123i
\(256\) 0.559193 0.829038i 0.0349496 0.0518148i
\(257\) −14.2781 4.09418i −0.890644 0.255388i −0.201047 0.979582i \(-0.564434\pi\)
−0.689597 + 0.724194i \(0.742212\pi\)
\(258\) −5.62800 + 6.25052i −0.350384 + 0.389141i
\(259\) −10.2615 2.18115i −0.637620 0.135530i
\(260\) −12.6976 + 12.2619i −0.787470 + 0.760451i
\(261\) −0.238856 + 0.957999i −0.0147848 + 0.0592986i
\(262\) 14.6743 9.16949i 0.906579 0.566493i
\(263\) 3.17460 + 18.0041i 0.195754 + 1.11018i 0.911340 + 0.411654i \(0.135049\pi\)
−0.715586 + 0.698525i \(0.753840\pi\)
\(264\) −5.26424 + 1.71130i −0.323992 + 0.105323i
\(265\) −26.9445 −1.65519
\(266\) −8.66376 + 8.97919i −0.531209 + 0.550550i
\(267\) 16.1915 11.7638i 0.990903 0.719933i
\(268\) 0.569631 + 0.844513i 0.0347957 + 0.0515868i
\(269\) −21.5562 + 11.4616i −1.31430 + 0.698827i −0.970701 0.240289i \(-0.922758\pi\)
−0.343601 + 0.939116i \(0.611647\pi\)
\(270\) 5.67465 14.0452i 0.345348 0.854766i
\(271\) −14.8394 + 1.03767i −0.901432 + 0.0630342i −0.512946 0.858421i \(-0.671446\pi\)
−0.388485 + 0.921455i \(0.627002\pi\)
\(272\) 1.22261 + 2.50672i 0.0741315 + 0.151992i
\(273\) 19.9848 + 22.1954i 1.20954 + 1.34333i
\(274\) −5.91486 10.2448i −0.357330 0.618913i
\(275\) −9.14054 + 3.69456i −0.551196 + 0.222790i
\(276\) 13.5379 4.92738i 0.814883 0.296593i
\(277\) 8.91990 1.89598i 0.535945 0.113919i 0.0680151 0.997684i \(-0.478333\pi\)
0.467930 + 0.883766i \(0.345000\pi\)
\(278\) 0.870325 + 8.28059i 0.0521986 + 0.496637i
\(279\) −0.142496 + 0.137607i −0.00853103 + 0.00823832i
\(280\) −6.85439 4.28310i −0.409628 0.255964i
\(281\) 6.27332 15.5270i 0.374235 0.926263i −0.616113 0.787658i \(-0.711294\pi\)
0.990348 0.138605i \(-0.0442620\pi\)
\(282\) 4.95921 10.1679i 0.295316 0.605488i
\(283\) −19.6738 + 5.64137i −1.16949 + 0.335345i −0.803517 0.595282i \(-0.797040\pi\)
−0.365970 + 0.930627i \(0.619263\pi\)
\(284\) −0.715378 + 2.20171i −0.0424498 + 0.130647i
\(285\) 5.65361 19.7481i 0.334891 1.16977i
\(286\) −7.09426 19.4826i −0.419492 1.15203i
\(287\) −30.6436 11.1533i −1.80883 0.658361i
\(288\) −0.212388 0.0298492i −0.0125151 0.00175888i
\(289\) 9.19914 + 0.643266i 0.541126 + 0.0378392i
\(290\) −12.9665 + 0.906707i −0.761420 + 0.0532437i
\(291\) −0.182888 + 0.0257032i −0.0107211 + 0.00150675i
\(292\) −1.39185 0.295848i −0.0814521 0.0173132i
\(293\) −0.422798 + 4.02265i −0.0247001 + 0.235006i 0.975206 + 0.221299i \(0.0710298\pi\)
−0.999906 + 0.0137067i \(0.995637\pi\)
\(294\) −1.11438 + 1.65213i −0.0649917 + 0.0963542i
\(295\) −0.977187 27.9830i −0.0568940 1.62923i
\(296\) −1.83244 3.17387i −0.106508 0.184478i
\(297\) 12.3622 + 12.7977i 0.717328 + 0.742600i
\(298\) 1.04933 5.95105i 0.0607861 0.344735i
\(299\) 20.2149 + 50.0338i 1.16906 + 2.89353i
\(300\) 4.94914 + 0.346077i 0.285739 + 0.0199808i
\(301\) 6.32383 12.9658i 0.364500 0.747335i
\(302\) −0.511398 + 14.6445i −0.0294277 + 0.842698i
\(303\) 6.92891 + 21.3250i 0.398055 + 1.22509i
\(304\) −4.35631 0.150278i −0.249851 0.00861902i
\(305\) 16.3812 11.9016i 0.937984 0.681485i
\(306\) 0.368269 0.471363i 0.0210525 0.0269460i
\(307\) −2.67931 15.1951i −0.152916 0.867231i −0.960666 0.277706i \(-0.910426\pi\)
0.807750 0.589525i \(-0.200685\pi\)
\(308\) 7.87004 5.31007i 0.448437 0.302569i
\(309\) −1.19982 + 1.00677i −0.0682552 + 0.0572729i
\(310\) −2.30264 1.22434i −0.130781 0.0695376i
\(311\) −1.65237 15.7212i −0.0936971 0.891468i −0.935890 0.352292i \(-0.885402\pi\)
0.842193 0.539176i \(-0.181264\pi\)
\(312\) −1.09062 + 10.3766i −0.0617444 + 0.587458i
\(313\) −3.35126 4.28941i −0.189424 0.242452i 0.683918 0.729559i \(-0.260275\pi\)
−0.873342 + 0.487107i \(0.838052\pi\)
\(314\) 3.04440 + 3.89665i 0.171805 + 0.219901i
\(315\) −0.181201 + 1.72401i −0.0102095 + 0.0971372i
\(316\) 1.28493 + 12.2253i 0.0722831 + 0.687728i
\(317\) 13.2196 + 7.02901i 0.742489 + 0.394788i 0.797201 0.603714i \(-0.206313\pi\)
−0.0547121 + 0.998502i \(0.517424\pi\)
\(318\) −12.2005 + 10.2374i −0.684170 + 0.574087i
\(319\) 5.21985 14.3479i 0.292256 0.803327i
\(320\) −0.490309 2.78068i −0.0274091 0.155445i
\(321\) 19.8712 25.4339i 1.10910 1.41958i
\(322\) −19.9902 + 14.5237i −1.11401 + 0.809376i
\(323\) 6.43779 10.3123i 0.358208 0.573794i
\(324\) −2.56811 7.90382i −0.142673 0.439101i
\(325\) −0.648546 + 18.5719i −0.0359749 + 1.03019i
\(326\) 5.53557 11.3496i 0.306587 0.628596i
\(327\) −10.9763 0.767537i −0.606990 0.0424449i
\(328\) −4.26756 10.5626i −0.235637 0.583221i
\(329\) −3.36927 + 19.1081i −0.185754 + 1.05346i
\(330\) −7.33569 + 13.8012i −0.403816 + 0.759733i
\(331\) −8.98838 15.5683i −0.494046 0.855712i 0.505931 0.862574i \(-0.331149\pi\)
−0.999976 + 0.00686173i \(0.997816\pi\)
\(332\) 0.152571 + 4.36906i 0.00837341 + 0.239783i
\(333\) −0.439540 + 0.651645i −0.0240866 + 0.0357099i
\(334\) 1.03927 9.88798i 0.0568663 0.541046i
\(335\) 2.81343 + 0.598013i 0.153714 + 0.0326729i
\(336\) −4.73102 + 0.664902i −0.258099 + 0.0362734i
\(337\) −9.33368 + 0.652675i −0.508438 + 0.0355535i −0.321672 0.946851i \(-0.604245\pi\)
−0.186766 + 0.982404i \(0.559801\pi\)
\(338\) −26.0182 1.81937i −1.41520 0.0989605i
\(339\) −24.3784 3.42617i −1.32406 0.186084i
\(340\) 7.39998 + 2.69337i 0.401320 + 0.146069i
\(341\) 2.41363 1.88630i 0.130705 0.102149i
\(342\) 0.380611 + 0.853892i 0.0205811 + 0.0461732i
\(343\) −5.13577 + 15.8063i −0.277306 + 0.853459i
\(344\) 4.84430 1.38908i 0.261187 0.0748942i
\(345\) 17.8322 36.5615i 0.960055 1.96841i
\(346\) 0.0819450 0.202821i 0.00440539 0.0109037i
\(347\) −1.23475 0.771557i −0.0662848 0.0414194i 0.496372 0.868110i \(-0.334665\pi\)
−0.562657 + 0.826691i \(0.690221\pi\)
\(348\) −5.52676 + 5.33713i −0.296265 + 0.286100i
\(349\) −0.265528 2.52633i −0.0142134 0.135231i 0.985114 0.171902i \(-0.0549913\pi\)
−0.999327 + 0.0366709i \(0.988325\pi\)
\(350\) −8.32316 + 1.76914i −0.444892 + 0.0945647i
\(351\) 31.5164 11.4710i 1.68222 0.612278i
\(352\) 3.21822 + 0.801899i 0.171532 + 0.0427414i
\(353\) 5.98650 + 10.3689i 0.318629 + 0.551882i 0.980202 0.197999i \(-0.0634441\pi\)
−0.661573 + 0.749881i \(0.730111\pi\)
\(354\) −11.0745 12.2995i −0.588602 0.653709i
\(355\) 2.86546 + 5.87507i 0.152083 + 0.311816i
\(356\) −11.9623 + 0.836489i −0.634003 + 0.0443338i
\(357\) 4.99141 12.3542i 0.264173 0.653852i
\(358\) −5.60173 + 2.97849i −0.296061 + 0.157418i
\(359\) −11.7638 17.4406i −0.620872 0.920480i 0.379116 0.925349i \(-0.376228\pi\)
−0.999988 + 0.00486859i \(0.998450\pi\)
\(360\) −0.489932 + 0.355956i −0.0258217 + 0.0187605i
\(361\) 9.51394 + 16.4464i 0.500734 + 0.865601i
\(362\) 16.1671 0.849724
\(363\) −11.3070 14.4637i −0.593466 0.759149i
\(364\) −3.10746 17.6233i −0.162875 0.923711i
\(365\) −3.40729 + 2.12911i −0.178346 + 0.111443i
\(366\) 2.89545 11.6130i 0.151348 0.607023i
\(367\) 6.72164 6.49101i 0.350866 0.338828i −0.498250 0.867033i \(-0.666024\pi\)
0.849117 + 0.528206i \(0.177135\pi\)
\(368\) −8.44335 1.79469i −0.440140 0.0935547i
\(369\) −1.63491 + 1.81575i −0.0851099 + 0.0945242i
\(370\) −9.94718 2.85231i −0.517129 0.148284i
\(371\) 15.2750 22.6461i 0.793037 1.17573i
\(372\) −1.50782 + 0.320497i −0.0781768 + 0.0166170i
\(373\) 5.55655 9.62423i 0.287707 0.498324i −0.685555 0.728021i \(-0.740440\pi\)
0.973262 + 0.229697i \(0.0737736\pi\)
\(374\) −6.42462 + 6.65482i −0.332209 + 0.344112i
\(375\) −7.31894 + 6.14132i −0.377949 + 0.317137i
\(376\) −5.74827 + 3.59192i −0.296444 + 0.185239i
\(377\) −20.7016 19.9913i −1.06619 1.02960i
\(378\) 8.58765 + 12.7317i 0.441701 + 0.654848i
\(379\) 3.49326 + 10.7512i 0.179437 + 0.552250i 0.999808 0.0195811i \(-0.00623325\pi\)
−0.820371 + 0.571831i \(0.806233\pi\)
\(380\) −9.14291 + 8.23933i −0.469021 + 0.422669i
\(381\) −19.6382 14.2680i −1.00610 0.730971i
\(382\) −13.4698 + 3.86240i −0.689175 + 0.197618i
\(383\) −7.86487 1.10534i −0.401876 0.0564800i −0.0646603 0.997907i \(-0.520596\pi\)
−0.337216 + 0.941427i \(0.609485\pi\)
\(384\) −1.27852 1.07281i −0.0652442 0.0547464i
\(385\) 5.56966 26.2218i 0.283856 1.33639i
\(386\) −4.02980 + 22.8542i −0.205112 + 1.16325i
\(387\) −0.723233 0.803232i −0.0367640 0.0408306i
\(388\) 0.101090 + 0.0450082i 0.00513207 + 0.00228495i
\(389\) 16.6707 + 4.78025i 0.845238 + 0.242368i 0.670188 0.742191i \(-0.266213\pi\)
0.175050 + 0.984560i \(0.443991\pi\)
\(390\) 18.1377 + 23.2152i 0.918437 + 1.17555i
\(391\) 16.1089 17.8908i 0.814663 0.904775i
\(392\) 1.09080 0.485657i 0.0550939 0.0245294i
\(393\) −12.6599 25.9567i −0.638609 1.30934i
\(394\) −3.94014 9.75220i −0.198502 0.491309i
\(395\) 26.5888 + 22.3107i 1.33783 + 1.12257i
\(396\) −0.147996 0.695769i −0.00743705 0.0349637i
\(397\) −28.5137 10.3781i −1.43106 0.520863i −0.493824 0.869562i \(-0.664401\pi\)
−0.937235 + 0.348699i \(0.886624\pi\)
\(398\) 2.58692 7.96172i 0.129671 0.399085i
\(399\) 13.3926 + 15.9470i 0.670470 + 0.798348i
\(400\) −2.40488 1.74725i −0.120244 0.0873623i
\(401\) −0.698077 + 19.9903i −0.0348603 + 0.998269i 0.848391 + 0.529369i \(0.177571\pi\)
−0.883252 + 0.468899i \(0.844651\pi\)
\(402\) 1.50114 0.798169i 0.0748699 0.0398090i
\(403\) −1.39686 5.60250i −0.0695826 0.279081i
\(404\) 3.25015 13.0357i 0.161701 0.648548i
\(405\) −20.7189 11.0164i −1.02953 0.547410i
\(406\) 6.58873 11.4120i 0.326993 0.566369i
\(407\) 7.81174 9.31240i 0.387213 0.461599i
\(408\) 4.37406 1.59203i 0.216548 0.0788171i
\(409\) −0.697807 19.9826i −0.0345043 0.988074i −0.885992 0.463700i \(-0.846522\pi\)
0.851488 0.524374i \(-0.175701\pi\)
\(410\) −29.3856 13.0833i −1.45125 0.646139i
\(411\) −18.0367 + 8.03047i −0.889687 + 0.396114i
\(412\) 0.929309 0.130606i 0.0457838 0.00643449i
\(413\) 24.0729 + 15.0424i 1.18455 + 0.740189i
\(414\) 0.447882 + 1.79636i 0.0220122 + 0.0882861i
\(415\) 8.87945 + 8.57479i 0.435875 + 0.420920i
\(416\) 3.84883 4.92628i 0.188704 0.241531i
\(417\) 13.8963 0.680506
\(418\) −4.47522 13.7467i −0.218890 0.672374i
\(419\) 22.4564 1.09707 0.548533 0.836129i \(-0.315186\pi\)
0.548533 + 0.836129i \(0.315186\pi\)
\(420\) −8.30509 + 10.6300i −0.405247 + 0.518692i
\(421\) 8.26017 + 7.97676i 0.402576 + 0.388763i 0.868196 0.496222i \(-0.165280\pi\)
−0.465620 + 0.884985i \(0.654169\pi\)
\(422\) 1.65810 + 6.65029i 0.0807153 + 0.323731i
\(423\) 1.23286 + 0.770379i 0.0599439 + 0.0374571i
\(424\) 9.44981 1.32808i 0.458923 0.0644974i
\(425\) 7.57374 3.37205i 0.367380 0.163568i
\(426\) 3.52969 + 1.57152i 0.171014 + 0.0761404i
\(427\) 0.716401 + 20.5150i 0.0346691 + 0.992792i
\(428\) −18.1725 + 6.61423i −0.878399 + 0.319711i
\(429\) −33.5757 + 8.37652i −1.62105 + 0.404422i
\(430\) 7.11474 12.3231i 0.343103 0.594272i
\(431\) 22.3895 + 11.9047i 1.07846 + 0.573429i 0.910982 0.412446i \(-0.135325\pi\)
0.167482 + 0.985875i \(0.446437\pi\)
\(432\) −1.29789 + 5.20556i −0.0624449 + 0.250453i
\(433\) 4.51426 + 18.1057i 0.216941 + 0.870105i 0.975767 + 0.218811i \(0.0702178\pi\)
−0.758826 + 0.651294i \(0.774227\pi\)
\(434\) 2.33440 1.24122i 0.112055 0.0595806i
\(435\) −0.757104 + 21.6806i −0.0363003 + 1.03951i
\(436\) 5.33358 + 3.87507i 0.255432 + 0.185582i
\(437\) 12.8838 + 35.3514i 0.616316 + 1.69109i
\(438\) −0.733880 + 2.25865i −0.0350662 + 0.107923i
\(439\) −8.98858 3.27158i −0.429002 0.156144i 0.118490 0.992955i \(-0.462195\pi\)
−0.547491 + 0.836811i \(0.684417\pi\)
\(440\) 8.10943 4.68355i 0.386602 0.223279i
\(441\) −0.196177 0.164612i −0.00934177 0.00783868i
\(442\) 6.53141 + 16.1658i 0.310668 + 0.768929i
\(443\) −3.46251 7.09920i −0.164509 0.337293i 0.800576 0.599232i \(-0.204527\pi\)
−0.965085 + 0.261938i \(0.915638\pi\)
\(444\) −5.58782 + 2.48786i −0.265186 + 0.118068i
\(445\) −22.6562 + 25.1622i −1.07400 + 1.19280i
\(446\) −9.25335 11.8438i −0.438159 0.560818i
\(447\) −9.69477 2.77993i −0.458547 0.131486i
\(448\) 2.61504 + 1.16429i 0.123549 + 0.0550077i
\(449\) −1.75183 1.94561i −0.0826741 0.0918189i 0.700388 0.713762i \(-0.253010\pi\)
−0.783062 + 0.621943i \(0.786344\pi\)
\(450\) −0.110709 + 0.627863i −0.00521888 + 0.0295977i
\(451\) 28.0749 25.2861i 1.32199 1.19068i
\(452\) 11.2994 + 9.48129i 0.531477 + 0.445962i
\(453\) 24.2185 + 3.40368i 1.13788 + 0.159919i
\(454\) −20.0356 + 5.74510i −0.940315 + 0.269631i
\(455\) −40.8783 29.6998i −1.91640 1.39235i
\(456\) −1.00943 + 7.20458i −0.0472707 + 0.337386i
\(457\) 0.761660 + 2.34415i 0.0356289 + 0.109655i 0.967289 0.253676i \(-0.0816396\pi\)
−0.931660 + 0.363330i \(0.881640\pi\)
\(458\) −4.41262 6.54198i −0.206188 0.305687i
\(459\) −10.7632 10.3939i −0.502385 0.485147i
\(460\) −20.6695 + 12.9158i −0.963722 + 0.602201i
\(461\) −7.14302 + 5.99371i −0.332684 + 0.279155i −0.793792 0.608189i \(-0.791896\pi\)
0.461109 + 0.887344i \(0.347452\pi\)
\(462\) −7.44091 13.9894i −0.346182 0.650847i
\(463\) 6.71560 11.6318i 0.312100 0.540574i −0.666716 0.745311i \(-0.732301\pi\)
0.978817 + 0.204738i \(0.0656341\pi\)
\(464\) 4.50285 0.957110i 0.209039 0.0444327i
\(465\) −2.43392 + 3.60844i −0.112870 + 0.167337i
\(466\) 17.3890 + 4.98620i 0.805528 + 0.230981i
\(467\) 21.5399 23.9225i 0.996748 1.10700i 0.00248961 0.999997i \(-0.499208\pi\)
0.994259 0.107004i \(-0.0341258\pi\)
\(468\) −1.31150 0.278768i −0.0606242 0.0128861i
\(469\) −2.09756 + 2.02559i −0.0968564 + 0.0935332i
\(470\) −4.63011 + 18.5704i −0.213571 + 0.856587i
\(471\) 6.99896 4.37344i 0.322495 0.201517i
\(472\) 1.72198 + 9.76586i 0.0792607 + 0.449510i
\(473\) 9.82632 + 13.5207i 0.451815 + 0.621680i
\(474\) 20.5163 0.942345
\(475\) −0.898374 + 12.9260i −0.0412202 + 0.593088i
\(476\) −6.45880 + 4.69259i −0.296038 + 0.215085i
\(477\) −1.14448 1.69677i −0.0524023 0.0776896i
\(478\) 11.1914 5.95055i 0.511881 0.272172i
\(479\) 7.64328 18.9178i 0.349230 0.864376i −0.645680 0.763608i \(-0.723426\pi\)
0.994910 0.100767i \(-0.0321297\pi\)
\(480\) −4.70104 + 0.328729i −0.214572 + 0.0150043i
\(481\) −10.0436 20.5923i −0.457946 0.938929i
\(482\) −3.82744 4.25080i −0.174335 0.193619i
\(483\) 20.6197 + 35.7144i 0.938230 + 1.62506i
\(484\) 1.15298 + 10.9394i 0.0524080 + 0.497246i
\(485\) 0.293605 0.106864i 0.0133319 0.00485243i
\(486\) 2.17591 0.462503i 0.0987012 0.0209796i
\(487\) 2.52294 + 24.0042i 0.114325 + 1.08773i 0.889799 + 0.456353i \(0.150845\pi\)
−0.775473 + 0.631380i \(0.782489\pi\)
\(488\) −5.15848 + 4.98149i −0.233514 + 0.225501i
\(489\) −17.8729 11.1682i −0.808239 0.505044i
\(490\) 1.26297 3.12595i 0.0570550 0.141216i
\(491\) −3.90290 + 8.00213i −0.176135 + 0.361131i −0.968537 0.248868i \(-0.919941\pi\)
0.792402 + 0.609999i \(0.208830\pi\)
\(492\) −18.2768 + 5.24078i −0.823981 + 0.236273i
\(493\) −3.96744 + 12.2105i −0.178685 + 0.549934i
\(494\) −27.1017 2.83690i −1.21936 0.127638i
\(495\) −1.66529 1.12290i −0.0748494 0.0504708i
\(496\) 0.867915 + 0.315895i 0.0389705 + 0.0141841i
\(497\) −6.56228 0.922268i −0.294358 0.0413694i
\(498\) 7.27858 + 0.508968i 0.326161 + 0.0228074i
\(499\) −2.19898 + 0.153768i −0.0984398 + 0.00688358i −0.118891 0.992907i \(-0.537934\pi\)
0.0204516 + 0.999791i \(0.493490\pi\)
\(500\) 5.66883 0.796703i 0.253518 0.0356296i
\(501\) −16.2312 3.45005i −0.725158 0.154137i
\(502\) −1.88904 + 17.9731i −0.0843122 + 0.802177i
\(503\) 12.7405 18.8885i 0.568070 0.842199i −0.430093 0.902785i \(-0.641519\pi\)
0.998163 + 0.0605859i \(0.0192969\pi\)
\(504\) −0.0214262 0.613567i −0.000954401 0.0273305i
\(505\) −18.9670 32.8518i −0.844020 1.46189i
\(506\) −3.98849 28.3499i −0.177310 1.26030i
\(507\) −7.55891 + 42.8687i −0.335703 + 1.90387i
\(508\) 5.44836 + 13.4852i 0.241732 + 0.598308i
\(509\) −17.4279 1.21868i −0.772480 0.0540170i −0.321924 0.946765i \(-0.604330\pi\)
−0.450556 + 0.892748i \(0.648774\pi\)
\(510\) 5.76156 11.8130i 0.255126 0.523086i
\(511\) 0.142153 4.07074i 0.00628850 0.180079i
\(512\) 0.309017 + 0.951057i 0.0136568 + 0.0420312i
\(513\) 22.2375 7.23583i 0.981812 0.319470i
\(514\) 12.0167 8.73067i 0.530035 0.385093i
\(515\) 1.63136 2.08804i 0.0718862 0.0920101i
\(516\) −1.46054 8.28313i −0.0642966 0.364644i
\(517\) −17.7172 13.8380i −0.779200 0.608596i
\(518\) 8.03640 6.74334i 0.353099 0.296285i
\(519\) −0.322356 0.171400i −0.0141498 0.00752360i
\(520\) −1.84510 17.5550i −0.0809132 0.769838i
\(521\) 0.500413 4.76111i 0.0219235 0.208588i −0.978076 0.208246i \(-0.933224\pi\)
1.00000 0.000341953i \(-0.000108847\pi\)
\(522\) −0.607859 0.778024i −0.0266053 0.0340532i
\(523\) 2.41630 + 3.09272i 0.105657 + 0.135235i 0.837933 0.545773i \(-0.183764\pi\)
−0.732276 + 0.681008i \(0.761542\pi\)
\(524\) −1.80872 + 17.2088i −0.0790141 + 0.751769i
\(525\) 1.48447 + 14.1238i 0.0647877 + 0.616414i
\(526\) −16.1419 8.58279i −0.703820 0.374228i
\(527\) −1.97329 + 1.65579i −0.0859578 + 0.0721272i
\(528\) 1.89247 5.20186i 0.0823592 0.226382i
\(529\) 8.94482 + 50.7286i 0.388905 + 2.20559i
\(530\) 16.5887 21.2325i 0.720566 0.922283i
\(531\) 1.72066 1.25013i 0.0746702 0.0542511i
\(532\) −1.74176 12.3553i −0.0755148 0.535669i
\(533\) −22.0076 67.7326i −0.953257 2.93382i
\(534\) −0.698471 + 20.0016i −0.0302258 + 0.865553i
\(535\) −23.9370 + 49.0781i −1.03489 + 2.12183i
\(536\) −1.01618 0.0710586i −0.0438925 0.00306926i
\(537\) 3.96658 + 9.81764i 0.171171 + 0.423662i
\(538\) 4.23942 24.0430i 0.182774 1.03657i
\(539\) 2.75137 + 2.84830i 0.118510 + 0.122685i
\(540\) 7.57414 + 13.1188i 0.325939 + 0.564543i
\(541\) −0.308507 8.83448i −0.0132637 0.379824i −0.987813 0.155648i \(-0.950253\pi\)
0.974549 0.224176i \(-0.0719689\pi\)
\(542\) 8.31837 12.3325i 0.357305 0.529726i
\(543\) 2.82046 26.8349i 0.121038 1.15160i
\(544\) −2.72803 0.579861i −0.116963 0.0248613i
\(545\) 18.4338 2.59069i 0.789615 0.110973i
\(546\) −29.7941 + 2.08340i −1.27507 + 0.0891615i
\(547\) 2.36867 + 0.165633i 0.101277 + 0.00708198i 0.120305 0.992737i \(-0.461613\pi\)
−0.0190281 + 0.999819i \(0.506057\pi\)
\(548\) 11.7146 + 1.64638i 0.500422 + 0.0703298i
\(549\) 1.44528 + 0.526039i 0.0616830 + 0.0224508i
\(550\) 2.71613 9.47744i 0.115816 0.404120i
\(551\) −13.9451 14.4283i −0.594081 0.614667i
\(552\) −4.45191 + 13.7016i −0.189486 + 0.583178i
\(553\) −33.8249 + 9.69913i −1.43838 + 0.412449i
\(554\) −3.99758 + 8.19626i −0.169841 + 0.348226i
\(555\) −6.46975 + 16.0132i −0.274625 + 0.679722i
\(556\) −7.06102 4.41221i −0.299454 0.187119i
\(557\) 22.6188 21.8427i 0.958390 0.925506i −0.0388878 0.999244i \(-0.512381\pi\)
0.997278 + 0.0737372i \(0.0234926\pi\)
\(558\) −0.0207064 0.197008i −0.000876571 0.00834001i
\(559\) 30.8163 6.55021i 1.30339 0.277044i
\(560\) 7.59512 2.76440i 0.320952 0.116817i
\(561\) 9.92515 + 11.8249i 0.419040 + 0.499246i
\(562\) 8.37320 + 14.5028i 0.353202 + 0.611764i
\(563\) −10.8520 12.0524i −0.457357 0.507946i 0.469721 0.882815i \(-0.344354\pi\)
−0.927078 + 0.374869i \(0.877688\pi\)
\(564\) 4.95921 + 10.1679i 0.208820 + 0.428145i
\(565\) 41.5471 2.90525i 1.74790 0.122225i
\(566\) 7.66694 18.9764i 0.322266 0.797636i
\(567\) 21.0046 11.1684i 0.882111 0.469027i
\(568\) −1.29454 1.91923i −0.0543176 0.0805291i
\(569\) −6.62574 + 4.81388i −0.277766 + 0.201808i −0.717942 0.696103i \(-0.754916\pi\)
0.440177 + 0.897911i \(0.354916\pi\)
\(570\) 12.0810 + 16.6132i 0.506016 + 0.695851i
\(571\) 16.7807 0.702250 0.351125 0.936329i \(-0.385799\pi\)
0.351125 + 0.936329i \(0.385799\pi\)
\(572\) 19.7201 + 6.40431i 0.824540 + 0.267777i
\(573\) 4.06110 + 23.0316i 0.169655 + 0.962160i
\(574\) 27.6550 17.2808i 1.15430 0.721285i
\(575\) −6.20756 + 24.8972i −0.258873 + 1.03828i
\(576\) 0.154281 0.148987i 0.00642837 0.00620780i
\(577\) −40.6911 8.64917i −1.69399 0.360070i −0.743003 0.669288i \(-0.766599\pi\)
−0.950991 + 0.309219i \(0.899933\pi\)
\(578\) −6.17045 + 6.85298i −0.256657 + 0.285047i
\(579\) 37.2313 + 10.6759i 1.54728 + 0.443676i
\(580\) 7.26849 10.7760i 0.301808 0.447448i
\(581\) −12.2407 + 2.60184i −0.507829 + 0.107942i
\(582\) 0.0923426 0.159942i 0.00382772 0.00662981i
\(583\) 14.8626 + 27.9427i 0.615545 + 1.15727i
\(584\) 1.09004 0.914654i 0.0451063 0.0378487i
\(585\) −3.21059 + 2.00620i −0.132742 + 0.0829461i
\(586\) −2.90959 2.80976i −0.120194 0.116070i
\(587\) 20.7887 + 30.8206i 0.858043 + 1.27210i 0.960757 + 0.277390i \(0.0894696\pi\)
−0.102714 + 0.994711i \(0.532753\pi\)
\(588\) −0.615818 1.89529i −0.0253959 0.0781606i
\(589\) −0.838710 3.93762i −0.0345584 0.162247i
\(590\) 22.6525 + 16.4580i 0.932589 + 0.677566i
\(591\) −16.8745 + 4.83869i −0.694126 + 0.199037i
\(592\) 3.62920 + 0.510051i 0.149159 + 0.0209630i
\(593\) −12.1029 10.1556i −0.497008 0.417039i 0.359522 0.933137i \(-0.382940\pi\)
−0.856530 + 0.516098i \(0.827384\pi\)
\(594\) −17.6957 + 1.86248i −0.726063 + 0.0764185i
\(595\) −3.91439 + 22.1996i −0.160474 + 0.910095i
\(596\) 4.04346 + 4.49072i 0.165627 + 0.183947i
\(597\) −12.7639 5.68287i −0.522393 0.232584i
\(598\) −51.8727 14.8743i −2.12123 0.608254i
\(599\) 7.31801 + 9.36662i 0.299006 + 0.382710i 0.913927 0.405879i \(-0.133034\pi\)
−0.614921 + 0.788589i \(0.710812\pi\)
\(600\) −3.31971 + 3.68691i −0.135526 + 0.150517i
\(601\) −13.0204 + 5.79707i −0.531114 + 0.236467i −0.654730 0.755863i \(-0.727218\pi\)
0.123616 + 0.992330i \(0.460551\pi\)
\(602\) 6.32383 + 12.9658i 0.257740 + 0.528446i
\(603\) 0.0818437 + 0.202570i 0.00333293 + 0.00824930i
\(604\) −11.2252 9.41906i −0.456747 0.383256i
\(605\) 23.7986 + 19.9577i 0.967551 + 0.811395i
\(606\) −21.0702 7.66892i −0.855917 0.311528i
\(607\) 10.5058 32.3337i 0.426419 1.31238i −0.475210 0.879873i \(-0.657628\pi\)
0.901629 0.432511i \(-0.142372\pi\)
\(608\) 2.80043 3.34030i 0.113572 0.135467i
\(609\) −17.7927 12.9272i −0.720998 0.523836i
\(610\) −0.706654 + 20.2359i −0.0286116 + 0.819329i
\(611\) −37.4143 + 19.8936i −1.51362 + 0.804807i
\(612\) 0.144710 + 0.580400i 0.00584955 + 0.0234613i
\(613\) −0.706162 + 2.83226i −0.0285216 + 0.114394i −0.982869 0.184304i \(-0.940997\pi\)
0.954348 + 0.298698i \(0.0965524\pi\)
\(614\) 13.6235 + 7.24372i 0.549798 + 0.292333i
\(615\) −26.8428 + 46.4931i −1.08241 + 1.87478i
\(616\) −0.660892 + 9.47088i −0.0266281 + 0.381593i
\(617\) 18.1205 6.59531i 0.729502 0.265517i 0.0495482 0.998772i \(-0.484222\pi\)
0.679954 + 0.733255i \(0.262000\pi\)
\(618\) −0.0546613 1.56530i −0.00219880 0.0629654i
\(619\) −13.8288 6.15696i −0.555825 0.247469i 0.109546 0.993982i \(-0.465060\pi\)
−0.665372 + 0.746512i \(0.731727\pi\)
\(620\) 2.38244 1.06073i 0.0956810 0.0425999i
\(621\) 45.8593 6.44510i 1.84027 0.258633i
\(622\) 13.4058 + 8.37687i 0.537523 + 0.335882i
\(623\) −8.30424 33.3065i −0.332702 1.33440i
\(624\) −7.50541 7.24789i −0.300457 0.290148i
\(625\) 19.1019 24.4493i 0.764077 0.977974i
\(626\) 5.44334 0.217560
\(627\) −23.5982 + 5.02996i −0.942420 + 0.200877i
\(628\) −4.94493 −0.197324
\(629\) −6.29283 + 8.05445i −0.250911 + 0.321152i
\(630\) −1.24698 1.20420i −0.0496810 0.0479764i
\(631\) 6.33038 + 25.3898i 0.252008 + 1.01075i 0.954297 + 0.298858i \(0.0966058\pi\)
−0.702289 + 0.711892i \(0.747839\pi\)
\(632\) −10.4248 6.51412i −0.414675 0.259118i
\(633\) 11.3277 1.59201i 0.450237 0.0632767i
\(634\) −13.6778 + 6.08973i −0.543213 + 0.241854i
\(635\) 37.5163 + 16.7034i 1.48879 + 0.662852i
\(636\) −0.555831 15.9169i −0.0220401 0.631147i
\(637\) 7.01438 2.55302i 0.277920 0.101154i
\(638\) 8.09262 + 12.9467i 0.320390 + 0.512566i
\(639\) −0.248257 + 0.429993i −0.00982088 + 0.0170103i
\(640\) 2.49307 + 1.32559i 0.0985473 + 0.0523985i
\(641\) 11.5922 46.4936i 0.457862 1.83639i −0.0847490 0.996402i \(-0.527009\pi\)
0.542611 0.839984i \(-0.317436\pi\)
\(642\) 7.80830 + 31.3174i 0.308169 + 1.23600i
\(643\) −13.5415 + 7.20015i −0.534025 + 0.283946i −0.714503 0.699633i \(-0.753347\pi\)
0.180477 + 0.983579i \(0.442236\pi\)
\(644\) 0.862340 24.6942i 0.0339810 0.973087i
\(645\) −19.2132 13.9592i −0.756520 0.549644i
\(646\) 4.16274 + 11.4220i 0.163781 + 0.449391i
\(647\) −1.56106 + 4.80445i −0.0613717 + 0.188883i −0.977042 0.213048i \(-0.931661\pi\)
0.915670 + 0.401931i \(0.131661\pi\)
\(648\) 7.80938 + 2.84238i 0.306782 + 0.111659i
\(649\) −28.4806 + 16.4488i −1.11796 + 0.645671i
\(650\) −14.2356 11.9451i −0.558366 0.468525i
\(651\) −1.65299 4.09128i −0.0647856 0.160350i
\(652\) 5.53557 + 11.3496i 0.216790 + 0.444484i
\(653\) 43.4782 19.3577i 1.70143 0.757526i 0.702482 0.711701i \(-0.252075\pi\)
0.998949 0.0458247i \(-0.0145916\pi\)
\(654\) 7.36250 8.17689i 0.287897 0.319742i
\(655\) 30.0800 + 38.5006i 1.17532 + 1.50434i
\(656\) 10.9508 + 3.14009i 0.427557 + 0.122600i
\(657\) −0.278803 0.124131i −0.0108771 0.00484282i
\(658\) −12.9830 14.4191i −0.506132 0.562116i
\(659\) 4.81988 27.3349i 0.187756 1.06482i −0.734608 0.678492i \(-0.762634\pi\)
0.922363 0.386323i \(-0.126255\pi\)
\(660\) −6.35922 14.2775i −0.247532 0.555750i
\(661\) 5.42959 + 4.55597i 0.211187 + 0.177207i 0.742245 0.670129i \(-0.233761\pi\)
−0.531058 + 0.847335i \(0.678206\pi\)
\(662\) 17.8018 + 2.50188i 0.691887 + 0.0972383i
\(663\) 27.9722 8.02090i 1.08635 0.311506i
\(664\) −3.53680 2.56963i −0.137254 0.0997211i
\(665\) −27.7716 21.6786i −1.07694 0.840661i
\(666\) −0.242895 0.747555i −0.00941200 0.0289672i
\(667\) −22.2206 32.9433i −0.860384 1.27557i
\(668\) 7.15200 + 6.90661i 0.276719 + 0.267225i
\(669\) −21.2731 + 13.2929i −0.822466 + 0.513934i
\(670\) −2.20336 + 1.84884i −0.0851233 + 0.0714269i
\(671\) −21.3784 10.4231i −0.825304 0.402380i
\(672\) 2.38876 4.13745i 0.0921484 0.159606i
\(673\) −10.4100 + 2.21271i −0.401275 + 0.0852936i −0.404128 0.914702i \(-0.632425\pi\)
0.00285338 + 0.999996i \(0.499092\pi\)
\(674\) 5.23207 7.75687i 0.201532 0.298783i
\(675\) 15.3299 + 4.39579i 0.590050 + 0.169194i
\(676\) 17.4521 19.3825i 0.671233 0.745480i
\(677\) 5.76398 + 1.22517i 0.221528 + 0.0470871i 0.317338 0.948312i \(-0.397211\pi\)
−0.0958106 + 0.995400i \(0.530544\pi\)
\(678\) 17.7087 17.1011i 0.680100 0.656765i
\(679\) −0.0766307 + 0.307349i −0.00294081 + 0.0117950i
\(680\) −6.67829 + 4.17306i −0.256101 + 0.160030i
\(681\) 6.04065 + 34.2582i 0.231478 + 1.31278i
\(682\) 0.000442924 3.06329i 1.69605e−5 0.117299i
\(683\) −12.9719 −0.496357 −0.248178 0.968714i \(-0.579832\pi\)
−0.248178 + 0.968714i \(0.579832\pi\)
\(684\) −0.907204 0.225783i −0.0346878 0.00863303i
\(685\) 27.0229 19.6333i 1.03249 0.750149i
\(686\) −9.29362 13.7784i −0.354832 0.526060i
\(687\) −11.6285 + 6.18298i −0.443654 + 0.235895i
\(688\) −1.88784 + 4.67256i −0.0719732 + 0.178140i
\(689\) 59.5110 4.16142i 2.26719 0.158537i
\(690\) 17.8322 + 36.5615i 0.678862 + 1.39187i
\(691\) 8.48023 + 9.41825i 0.322603 + 0.358287i 0.882531 0.470254i \(-0.155838\pi\)
−0.559928 + 0.828541i \(0.689171\pi\)
\(692\) 0.109375 + 0.189443i 0.00415780 + 0.00720152i
\(693\) 1.88783 0.763052i 0.0717129 0.0289859i
\(694\) 1.36818 0.497978i 0.0519355 0.0189030i
\(695\) −22.9959 + 4.88793i −0.872285 + 0.185410i
\(696\) −0.803102 7.64101i −0.0304415 0.289632i
\(697\) −22.8551 + 22.0709i −0.865700 + 0.835997i
\(698\) 2.15425 + 1.34613i 0.0815396 + 0.0509516i
\(699\) 11.3100 27.9931i 0.427782 1.05880i
\(700\) 3.73015 7.64794i 0.140986 0.289065i
\(701\) 26.4010 7.57035i 0.997150 0.285928i 0.262912 0.964820i \(-0.415317\pi\)
0.734238 + 0.678892i \(0.237539\pi\)
\(702\) −10.3641 + 31.8975i −0.391169 + 1.20389i
\(703\) −6.50372 14.5910i −0.245292 0.550308i
\(704\) −2.61324 + 2.04230i −0.0984902 + 0.0769719i
\(705\) 30.0162 + 10.9250i 1.13048 + 0.411459i
\(706\) −11.8565 1.66632i −0.446225 0.0627128i
\(707\) 38.3635 + 2.68264i 1.44281 + 0.100891i
\(708\) 16.5102 1.15451i 0.620492 0.0433891i
\(709\) 19.7239 2.77201i 0.740747 0.104105i 0.241301 0.970450i \(-0.422426\pi\)
0.499446 + 0.866345i \(0.333537\pi\)
\(710\) −6.39377 1.35904i −0.239954 0.0510038i
\(711\) −0.275587 + 2.62203i −0.0103353 + 0.0983339i
\(712\) 6.70559 9.94145i 0.251303 0.372572i
\(713\) −0.278241 7.96778i −0.0104202 0.298396i
\(714\) 6.66220 + 11.5393i 0.249326 + 0.431846i
\(715\) 52.6153 25.6716i 1.96770 0.960064i
\(716\) 1.10169 6.24797i 0.0411719 0.233498i
\(717\) −7.92459 19.6141i −0.295949 0.732500i
\(718\) 20.9859 + 1.46748i 0.783188 + 0.0547659i
\(719\) −7.04806 + 14.4507i −0.262848 + 0.538919i −0.988875 0.148747i \(-0.952476\pi\)
0.726027 + 0.687666i \(0.241365\pi\)
\(720\) 0.0211347 0.605220i 0.000787645 0.0225552i
\(721\) 0.830116 + 2.55483i 0.0309151 + 0.0951470i
\(722\) −18.8173 2.62835i −0.700308 0.0978169i
\(723\) −7.72340 + 5.61138i −0.287236 + 0.208689i
\(724\) −9.95346 + 12.7398i −0.369917 + 0.473473i
\(725\) −2.37623 13.4763i −0.0882509 0.500496i
\(726\) 18.3589 0.00530906i 0.681362 0.000197038i
\(727\) −8.42514 + 7.06953i −0.312471 + 0.262194i −0.785512 0.618846i \(-0.787601\pi\)
0.473041 + 0.881040i \(0.343156\pi\)
\(728\) 15.8005 + 8.40127i 0.585605 + 0.311372i
\(729\) −2.99416 28.4875i −0.110895 1.05509i
\(730\) 0.419975 3.99580i 0.0155440 0.147891i
\(731\) −8.65320 11.0756i −0.320050 0.409645i
\(732\) 7.36857 + 9.43134i 0.272350 + 0.348593i
\(733\) −5.52843 + 52.5995i −0.204197 + 1.94281i 0.111090 + 0.993810i \(0.464566\pi\)
−0.315287 + 0.948996i \(0.602101\pi\)
\(734\) 0.976732 + 9.29298i 0.0360518 + 0.343010i
\(735\) −4.96826 2.64167i −0.183257 0.0974396i
\(736\) 6.61248 5.54853i 0.243739 0.204522i
\(737\) −0.931720 3.24752i −0.0343203 0.119624i
\(738\) −0.424280 2.40621i −0.0156180 0.0885739i
\(739\) −22.7335 + 29.0975i −0.836264 + 1.07037i 0.160261 + 0.987075i \(0.448766\pi\)
−0.996525 + 0.0832939i \(0.973456\pi\)
\(740\) 8.37175 6.08243i 0.307752 0.223595i
\(741\) −9.43690 + 44.4898i −0.346673 + 1.63437i
\(742\) 8.44115 + 25.9792i 0.309884 + 0.953725i
\(743\) −0.0233715 + 0.669271i −0.000857416 + 0.0245532i −0.999744 0.0226203i \(-0.992799\pi\)
0.998887 + 0.0471735i \(0.0150214\pi\)
\(744\) 0.675751 1.38550i 0.0247742 0.0507947i
\(745\) 17.0209 + 1.19022i 0.623598 + 0.0436062i
\(746\) 4.16304 + 10.3039i 0.152420 + 0.377252i
\(747\) −0.162817 + 0.923383i −0.00595717 + 0.0337848i
\(748\) −1.28867 9.15979i −0.0471186 0.334915i
\(749\) −27.6788 47.9410i −1.01136 1.75173i
\(750\) −0.333437 9.54838i −0.0121754 0.348658i
\(751\) 2.28744 3.39127i 0.0834699 0.123749i −0.784990 0.619508i \(-0.787332\pi\)
0.868460 + 0.495759i \(0.165110\pi\)
\(752\) 0.708519 6.74110i 0.0258370 0.245823i
\(753\) 29.5030 + 6.27105i 1.07515 + 0.228530i
\(754\) 28.4985 4.00521i 1.03785 0.145861i
\(755\) −41.2744 + 2.88619i −1.50213 + 0.105039i
\(756\) −15.3198 1.07127i −0.557176 0.0389615i
\(757\) −21.8844 3.07565i −0.795402 0.111786i −0.270245 0.962792i \(-0.587105\pi\)
−0.525157 + 0.851005i \(0.675994\pi\)
\(758\) −10.6227 3.86635i −0.385834 0.140432i
\(759\) −47.7522 + 1.67446i −1.73330 + 0.0607790i
\(760\) −0.863742 12.2773i −0.0313312 0.445346i
\(761\) −11.4780 + 35.3257i −0.416077 + 1.28055i 0.495207 + 0.868775i \(0.335092\pi\)
−0.911284 + 0.411779i \(0.864908\pi\)
\(762\) 23.3338 6.69086i 0.845295 0.242384i
\(763\) −8.27279 + 16.9617i −0.299495 + 0.614056i
\(764\) 5.24922 12.9923i 0.189910 0.470044i
\(765\) 1.43233 + 0.895020i 0.0517860 + 0.0323595i
\(766\) 5.71312 5.51709i 0.206423 0.199341i
\(767\) 6.48008 + 61.6538i 0.233982 + 2.22619i
\(768\) 1.63252 0.347002i 0.0589084 0.0125214i
\(769\) −20.4965 + 7.46013i −0.739124 + 0.269019i −0.684022 0.729462i \(-0.739771\pi\)
−0.0551021 + 0.998481i \(0.517548\pi\)
\(770\) 17.2340 + 20.5327i 0.621072 + 0.739947i
\(771\) −12.3952 21.4691i −0.446401 0.773189i
\(772\) −15.5283 17.2459i −0.558877 0.620695i
\(773\) −4.09032 8.38639i −0.147118 0.301638i 0.812491 0.582974i \(-0.198111\pi\)
−0.959609 + 0.281337i \(0.909222\pi\)
\(774\) 1.07822 0.0753966i 0.0387559 0.00271008i
\(775\) 1.02849 2.54561i 0.0369446 0.0914412i
\(776\) −0.0977042 + 0.0519503i −0.00350738 + 0.00186491i
\(777\) −9.79090 14.5156i −0.351247 0.520745i
\(778\) −14.0304 + 10.1937i −0.503014 + 0.365461i
\(779\) −13.7076 47.7277i −0.491125 1.71002i
\(780\) −29.4605 −1.05485
\(781\) 4.51213 6.21230i 0.161457 0.222294i
\(782\) 4.18048 + 23.7087i 0.149494 + 0.847820i
\(783\) −20.9444 + 13.0875i −0.748490 + 0.467709i
\(784\) −0.288863 + 1.15857i −0.0103165 + 0.0413773i
\(785\) −10.0437 + 9.69909i −0.358475 + 0.346175i
\(786\) 28.2484 + 6.00438i 1.00759 + 0.214169i
\(787\) −7.55082 + 8.38603i −0.269158 + 0.298930i −0.862538 0.505992i \(-0.831126\pi\)
0.593380 + 0.804922i \(0.297793\pi\)
\(788\) 10.1106 + 2.89918i 0.360176 + 0.103279i
\(789\) −17.0622 + 25.2957i −0.607430 + 0.900552i
\(790\) −33.9508 + 7.21646i −1.20792 + 0.256750i
\(791\) −21.1115 + 36.5662i −0.750638 + 1.30014i
\(792\) 0.639389 + 0.311736i 0.0227197 + 0.0110771i
\(793\) −34.3422 + 28.8166i −1.21953 + 1.02331i
\(794\) 25.7328 16.0797i 0.913224 0.570646i
\(795\) −32.3487 31.2388i −1.14729 1.10793i
\(796\) 4.68126 + 6.94025i 0.165923 + 0.245991i
\(797\) 6.75861 + 20.8009i 0.239402 + 0.736804i 0.996507 + 0.0835106i \(0.0266132\pi\)
−0.757105 + 0.653294i \(0.773387\pi\)
\(798\) −20.8117 + 0.735589i −0.736727 + 0.0260396i
\(799\) 15.2939 + 11.1117i 0.541061 + 0.393104i
\(800\) 2.85744 0.819357i 0.101026 0.0289687i
\(801\) −2.54687 0.357939i −0.0899891 0.0126471i
\(802\) −15.3228 12.8574i −0.541067 0.454009i
\(803\) 4.08745 + 2.35910i 0.144243 + 0.0832510i
\(804\) −0.295227 + 1.67431i −0.0104118 + 0.0590485i
\(805\) −46.6842 51.8481i −1.64540 1.82740i
\(806\) 5.27483 + 2.34850i 0.185798 + 0.0827225i
\(807\) −39.1680 11.2312i −1.37878 0.395359i
\(808\) 8.27124 + 10.5867i 0.290981 + 0.372439i
\(809\) 26.2462 29.1493i 0.922766 1.02484i −0.0768476 0.997043i \(-0.524485\pi\)
0.999614 0.0277928i \(-0.00884786\pi\)
\(810\) 21.4368 9.54430i 0.753214 0.335352i
\(811\) 8.98730 + 18.4267i 0.315587 + 0.647049i 0.996341 0.0854628i \(-0.0272369\pi\)
−0.680755 + 0.732512i \(0.738348\pi\)
\(812\) 4.93636 + 12.2179i 0.173232 + 0.428765i
\(813\) −19.0188 15.9587i −0.667020 0.559696i
\(814\) 2.52889 + 11.8890i 0.0886374 + 0.416710i
\(815\) 33.5047 + 12.1947i 1.17362 + 0.427162i
\(816\) −1.43840 + 4.42695i −0.0503542 + 0.154974i
\(817\) 21.6314 3.82365i 0.756788 0.133773i
\(818\) 16.1761 + 11.7526i 0.565584 + 0.410921i
\(819\) 0.133947 3.83574i 0.00468048 0.134032i
\(820\) 28.4014 15.1013i 0.991819 0.527359i
\(821\) 5.03534 + 20.1956i 0.175734 + 0.704832i 0.991901 + 0.127015i \(0.0405398\pi\)
−0.816166 + 0.577817i \(0.803905\pi\)
\(822\) 4.77642 19.1572i 0.166597 0.668184i
\(823\) 41.0260 + 21.8139i 1.43008 + 0.760385i 0.990460 0.137800i \(-0.0440032\pi\)
0.439617 + 0.898186i \(0.355114\pi\)
\(824\) −0.469221 + 0.812715i −0.0163461 + 0.0283123i
\(825\) −15.2573 6.16176i −0.531189 0.214525i
\(826\) −26.6743 + 9.70866i −0.928119 + 0.337808i
\(827\) −0.546241 15.6423i −0.0189947 0.543936i −0.971171 0.238386i \(-0.923382\pi\)
0.952176 0.305550i \(-0.0988404\pi\)
\(828\) −1.69129 0.753012i −0.0587765 0.0261690i
\(829\) 24.0089 10.6894i 0.833862 0.371259i 0.0550247 0.998485i \(-0.482476\pi\)
0.778838 + 0.627226i \(0.215810\pi\)
\(830\) −12.2238 + 1.71794i −0.424293 + 0.0596305i
\(831\) 12.9071 + 8.06527i 0.447743 + 0.279781i
\(832\) 1.51238 + 6.06584i 0.0524324 + 0.210295i
\(833\) −2.39550 2.31331i −0.0829991 0.0801513i
\(834\) −8.55544 + 10.9505i −0.296251 + 0.379183i
\(835\) 28.0733 0.971516
\(836\) 13.5878 + 4.93681i 0.469943 + 0.170743i
\(837\) −4.95513 −0.171274
\(838\) −13.8255 + 17.6959i −0.477595 + 0.611294i
\(839\) −20.1866 19.4939i −0.696918 0.673006i 0.259255 0.965809i \(-0.416523\pi\)
−0.956173 + 0.292803i \(0.905412\pi\)
\(840\) −3.26345 13.0890i −0.112600 0.451613i
\(841\) −6.62181 4.13777i −0.228338 0.142682i
\(842\) −11.3712 + 1.59812i −0.391879 + 0.0550750i
\(843\) 25.5332 11.3681i 0.879410 0.391539i
\(844\) −6.26134 2.78773i −0.215524 0.0959575i
\(845\) −2.57013 73.5988i −0.0884150 2.53188i
\(846\) −1.36609 + 0.497217i −0.0469673 + 0.0170947i
\(847\) −30.2655 + 8.68795i −1.03993 + 0.298522i
\(848\) −4.77134 + 8.26420i −0.163848 + 0.283794i
\(849\) −30.1603 16.0365i −1.03510 0.550371i
\(850\) −2.00565 + 8.04423i −0.0687933 + 0.275915i
\(851\) −7.65322 30.6954i −0.262349 1.05223i
\(852\) −3.41147 + 1.81391i −0.116875 + 0.0621435i
\(853\) −0.453211 + 12.9783i −0.0155176 + 0.444367i 0.966621 + 0.256210i \(0.0824737\pi\)
−0.982139 + 0.188157i \(0.939748\pi\)
\(854\) −16.6071 12.0658i −0.568284 0.412883i
\(855\) −2.28549 + 1.32082i −0.0781620 + 0.0451710i
\(856\) 5.97599 18.3922i 0.204255 0.628633i
\(857\) −20.4588 7.44638i −0.698858 0.254363i −0.0319346 0.999490i \(-0.510167\pi\)
−0.666923 + 0.745127i \(0.732389\pi\)
\(858\) 14.0705 31.6151i 0.480358 1.07932i
\(859\) 9.49431 + 7.96667i 0.323942 + 0.271819i 0.790226 0.612816i \(-0.209963\pi\)
−0.466284 + 0.884635i \(0.654408\pi\)
\(860\) 5.33046 + 13.1933i 0.181767 + 0.449889i
\(861\) −23.8588 48.9178i −0.813106 1.66711i
\(862\) −23.1654 + 10.3139i −0.789016 + 0.351293i
\(863\) −8.04912 + 8.93945i −0.273995 + 0.304303i −0.864400 0.502805i \(-0.832301\pi\)
0.590405 + 0.807107i \(0.298968\pi\)
\(864\) −3.30298 4.22762i −0.112370 0.143826i
\(865\) 0.593729 + 0.170249i 0.0201874 + 0.00578864i
\(866\) −17.0467 7.58970i −0.579272 0.257908i
\(867\) 10.2984 + 11.4376i 0.349753 + 0.388440i
\(868\) −0.459103 + 2.60371i −0.0155830 + 0.0883755i
\(869\) 8.47082 39.8804i 0.287353 1.35285i
\(870\) −16.6184 13.9445i −0.563418 0.472764i
\(871\) −6.30625 0.886286i −0.213679 0.0300307i
\(872\) −6.33728 + 1.81719i −0.214607 + 0.0615377i
\(873\) 0.0192006 + 0.0139500i 0.000649841 + 0.000472137i
\(874\) −35.7893 11.6119i −1.21059 0.392778i
\(875\) 5.06375 + 15.5846i 0.171186 + 0.526856i
\(876\) −1.32802 1.96887i −0.0448696 0.0665220i
\(877\) 24.9150 + 24.0601i 0.841318 + 0.812452i 0.984158 0.177294i \(-0.0567344\pi\)
−0.142840 + 0.989746i \(0.545623\pi\)
\(878\) 8.11196 5.06892i 0.273765 0.171068i
\(879\) −5.17137 + 4.33930i −0.174426 + 0.146361i
\(880\) −1.30198 + 9.27380i −0.0438897 + 0.312620i
\(881\) −22.9162 + 39.6921i −0.772068 + 1.33726i 0.164360 + 0.986400i \(0.447444\pi\)
−0.936428 + 0.350861i \(0.885889\pi\)
\(882\) 0.250495 0.0532443i 0.00843460 0.00179283i
\(883\) −24.6664 + 36.5695i −0.830091 + 1.23066i 0.140537 + 0.990075i \(0.455117\pi\)
−0.970628 + 0.240585i \(0.922661\pi\)
\(884\) −16.7600 4.80585i −0.563699 0.161638i
\(885\) 31.2696 34.7285i 1.05112 1.16738i
\(886\) 7.72599 + 1.64221i 0.259560 + 0.0551711i
\(887\) 17.9074 17.2930i 0.601271 0.580641i −0.330446 0.943825i \(-0.607199\pi\)
0.931717 + 0.363184i \(0.118310\pi\)
\(888\) 1.47975 5.93494i 0.0496570 0.199164i
\(889\) −35.3069 + 22.0622i −1.18416 + 0.739943i
\(890\) −5.87957 33.3447i −0.197084 1.11772i
\(891\) 0.00398538 + 27.5631i 0.000133515 + 0.923397i
\(892\) 15.0299 0.503239
\(893\) −26.5500 + 12.9632i −0.888460 + 0.433797i
\(894\) 8.15931 5.92809i 0.272888 0.198265i
\(895\) −10.0173 14.8512i −0.334840 0.496421i
\(896\) −2.52746 + 1.34387i −0.0844364 + 0.0448956i
\(897\) −33.7385 + 83.5058i −1.12650 + 2.78818i
\(898\) 2.61170 0.182628i 0.0871534 0.00609436i
\(899\) 1.86387 + 3.82151i 0.0621636 + 0.127454i
\(900\) −0.426603 0.473791i −0.0142201 0.0157930i
\(901\) −13.3072 23.0487i −0.443326 0.767863i
\(902\) 2.64109 + 37.6910i 0.0879385 + 1.25497i
\(903\) 22.6244 8.23462i 0.752894 0.274031i
\(904\) −14.4279 + 3.06675i −0.479866 + 0.101999i
\(905\) 4.77162 + 45.3990i 0.158614 + 1.50911i
\(906\) −17.5925 + 16.9889i −0.584472 + 0.564418i
\(907\) 19.3590 + 12.0969i 0.642806 + 0.401670i 0.811790 0.583949i \(-0.198493\pi\)
−0.168984 + 0.985619i \(0.554049\pi\)
\(908\) 7.80792 19.3253i 0.259115 0.641332i
\(909\) 1.26313 2.58980i 0.0418954 0.0858984i
\(910\) 48.5710 13.9275i 1.61011 0.461692i
\(911\) 13.9150 42.8259i 0.461024 1.41889i −0.402890 0.915248i \(-0.631994\pi\)
0.863915 0.503638i \(-0.168006\pi\)
\(912\) −5.05582 5.23102i −0.167415 0.173216i
\(913\) 3.99455 13.9383i 0.132200 0.461289i
\(914\) −2.31614 0.843005i −0.0766110 0.0278841i
\(915\) 33.4652 + 4.70323i 1.10633 + 0.155484i
\(916\) 7.87183 + 0.550452i 0.260093 + 0.0181874i
\(917\) −49.4112 + 3.45517i −1.63170 + 0.114100i
\(918\) 14.8170 2.08240i 0.489035 0.0687294i
\(919\) 1.97575 + 0.419958i 0.0651738 + 0.0138531i 0.240383 0.970678i \(-0.422727\pi\)
−0.175209 + 0.984531i \(0.556060\pi\)
\(920\) 2.54768 24.2396i 0.0839945 0.799155i
\(921\) 14.4002 21.3491i 0.474502 0.703478i
\(922\) −0.325422 9.31887i −0.0107172 0.306901i
\(923\) −7.23618 12.5334i −0.238182 0.412543i
\(924\) 15.6049 + 2.74924i 0.513364 + 0.0904434i
\(925\) 1.89175 10.7287i 0.0622004 0.352756i
\(926\) 5.03142 + 12.4532i 0.165343 + 0.409237i
\(927\) 0.200783 + 0.0140401i 0.00659457 + 0.000461137i
\(928\) −2.01802 + 4.13755i −0.0662447 + 0.135822i
\(929\) −1.08013 + 30.9309i −0.0354379 + 1.01481i 0.843282 + 0.537471i \(0.180620\pi\)
−0.878720 + 0.477337i \(0.841602\pi\)
\(930\) −1.34501 4.13953i −0.0441048 0.135741i
\(931\) 4.94926 1.61043i 0.162205 0.0527797i
\(932\) −14.6349 + 10.6329i −0.479382 + 0.348291i
\(933\) 16.2430 20.7901i 0.531773 0.680639i
\(934\) 5.58989 + 31.7018i 0.182907 + 1.03732i
\(935\) −20.5837 16.0769i −0.673157 0.525771i
\(936\) 1.02711 0.861851i 0.0335723 0.0281705i
\(937\) −12.3222 6.55183i −0.402549 0.214039i 0.255837 0.966720i \(-0.417649\pi\)
−0.658385 + 0.752681i \(0.728760\pi\)
\(938\) −0.304800 2.89998i −0.00995208 0.0946877i
\(939\) 0.949629 9.03511i 0.0309900 0.294850i
\(940\) −11.7831 15.0816i −0.384321 0.491909i
\(941\) −25.2224 32.2833i −0.822228 1.05240i −0.997691 0.0679179i \(-0.978364\pi\)
0.175463 0.984486i \(-0.443858\pi\)
\(942\) −0.862676 + 8.20782i −0.0281075 + 0.267425i
\(943\) −10.2790 97.7979i −0.334729 3.18474i
\(944\) −8.75576 4.65552i −0.284976 0.151524i
\(945\) −33.2174 + 27.8727i −1.08056 + 0.906700i
\(946\) −16.7041 0.580902i −0.543097 0.0188868i
\(947\) 5.83666 + 33.1013i 0.189666 + 1.07565i 0.919813 + 0.392358i \(0.128341\pi\)
−0.730147 + 0.683290i \(0.760548\pi\)
\(948\) −12.6311 + 16.1671i −0.410239 + 0.525082i
\(949\) 7.19671 5.22871i 0.233615 0.169731i
\(950\) −9.63277 8.66600i −0.312528 0.281162i
\(951\) 7.72184 + 23.7654i 0.250398 + 0.770645i
\(952\) 0.278621 7.97865i 0.00903014 0.258590i
\(953\) 12.6667 25.9705i 0.410314 0.841268i −0.589134 0.808035i \(-0.700531\pi\)
0.999448 0.0332322i \(-0.0105801\pi\)
\(954\) 2.04169 + 0.142769i 0.0661020 + 0.00462230i
\(955\) −14.8216 36.6847i −0.479615 1.18709i
\(956\) −2.20099 + 12.4824i −0.0711851 + 0.403711i
\(957\) 22.9014 11.1739i 0.740298 0.361200i
\(958\) 10.2017 + 17.6699i 0.329603 + 0.570890i
\(959\) 1.18180 + 33.8422i 0.0381622 + 1.09282i
\(960\) 2.63521 3.90686i 0.0850510 0.126093i
\(961\) 3.15121 29.9818i 0.101652 0.967154i
\(962\) 22.4104 + 4.76348i 0.722540 + 0.153581i
\(963\) −4.10732 + 0.577246i −0.132357 + 0.0186015i
\(964\) 5.70608 0.399008i 0.183781 0.0128512i
\(965\) −65.3663 4.57086i −2.10422 0.147141i
\(966\) −40.8381 5.73942i −1.31394 0.184663i
\(967\) −31.7186 11.5446i −1.02000 0.371250i −0.222736 0.974879i \(-0.571499\pi\)
−0.797265 + 0.603629i \(0.793721\pi\)
\(968\) −9.33021 5.82641i −0.299884 0.187268i
\(969\) 19.6849 4.91686i 0.632371 0.157952i
\(970\) −0.0965519 + 0.297156i −0.00310009 + 0.00954111i
\(971\) 46.3767 13.2983i 1.48830 0.426763i 0.569667 0.821876i \(-0.307072\pi\)
0.918633 + 0.395113i \(0.129294\pi\)
\(972\) −0.975165 + 1.99938i −0.0312784 + 0.0641303i
\(973\) 8.92835 22.0984i 0.286230 0.708443i
\(974\) −20.4688 12.7903i −0.655864 0.409829i
\(975\) −22.3105 + 21.5450i −0.714508 + 0.689992i
\(976\) −0.749588 7.13185i −0.0239937 0.228285i
\(977\) 14.9548 3.17874i 0.478446 0.101697i 0.0376253 0.999292i \(-0.488021\pi\)
0.440821 + 0.897595i \(0.354687\pi\)
\(978\) 19.8043 7.20818i 0.633272 0.230492i
\(979\) 38.5915 + 9.61602i 1.23339 + 0.307329i
\(980\) 1.68572 + 2.91976i 0.0538485 + 0.0932683i
\(981\) 0.946128 + 1.05078i 0.0302076 + 0.0335489i
\(982\) −3.90290 8.00213i −0.124547 0.255358i
\(983\) 2.25322 0.157560i 0.0718665 0.00502539i −0.0337780 0.999429i \(-0.510754\pi\)
0.105644 + 0.994404i \(0.466309\pi\)
\(984\) 7.12252 17.6288i 0.227058 0.561987i
\(985\) 26.2223 13.9427i 0.835513 0.444250i
\(986\) −7.17943 10.6439i −0.228639 0.338972i
\(987\) −26.1985 + 19.0343i −0.833908 + 0.605870i
\(988\) 18.9210 19.6099i 0.601957 0.623874i
\(989\) 43.5011 1.38325
\(990\) 1.91012 0.620940i 0.0607075 0.0197348i
\(991\) −7.19519 40.8060i −0.228563 1.29624i −0.855756 0.517380i \(-0.826907\pi\)
0.627193 0.778864i \(-0.284204\pi\)
\(992\) −0.783271 + 0.489442i −0.0248689 + 0.0155398i
\(993\) 7.25838 29.1118i 0.230338 0.923834i
\(994\) 4.76690 4.60334i 0.151197 0.146009i
\(995\) 23.1209 + 4.91450i 0.732982 + 0.155800i
\(996\) −4.88221 + 5.42225i −0.154699 + 0.171810i
\(997\) −9.53560 2.73429i −0.301995 0.0865958i 0.121218 0.992626i \(-0.461320\pi\)
−0.423213 + 0.906030i \(0.639098\pi\)
\(998\) 1.23266 1.82749i 0.0390190 0.0578481i
\(999\) −19.2321 + 4.08791i −0.608477 + 0.129336i
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 418.2.u.b.251.8 yes 264
11.5 even 5 inner 418.2.u.b.137.4 yes 264
19.5 even 9 inner 418.2.u.b.119.4 yes 264
209.5 even 45 inner 418.2.u.b.5.8 264
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.u.b.5.8 264 209.5 even 45 inner
418.2.u.b.119.4 yes 264 19.5 even 9 inner
418.2.u.b.137.4 yes 264 11.5 even 5 inner
418.2.u.b.251.8 yes 264 1.1 even 1 trivial