Properties

Label 140.2.w.b.123.6
Level $140$
Weight $2$
Character 140.123
Analytic conductor $1.118$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [140,2,Mod(23,140)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(140, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("140.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.w (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: \(1.11790562830\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 123.6
Character \(\chi\) \(=\) 140.123
Dual form 140.2.w.b.107.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.675113 + 1.24267i) q^{2} +(-0.107770 - 0.402205i) q^{3} +(-1.08845 - 1.67788i) q^{4} +(1.27747 - 1.83523i) q^{5} +(0.572564 + 0.137611i) q^{6} +(1.30345 + 2.30240i) q^{7} +(2.81987 - 0.219816i) q^{8} +(2.44792 - 1.41331i) q^{9} +O(q^{10})\) \(q+(-0.675113 + 1.24267i) q^{2} +(-0.107770 - 0.402205i) q^{3} +(-1.08845 - 1.67788i) q^{4} +(1.27747 - 1.83523i) q^{5} +(0.572564 + 0.137611i) q^{6} +(1.30345 + 2.30240i) q^{7} +(2.81987 - 0.219816i) q^{8} +(2.44792 - 1.41331i) q^{9} +(1.41814 + 2.82646i) q^{10} +(0.725638 + 0.418947i) q^{11} +(-0.557549 + 0.618604i) q^{12} +(-1.16367 - 1.16367i) q^{13} +(-3.74109 + 0.0653744i) q^{14} +(-0.875811 - 0.316023i) q^{15} +(-1.63057 + 3.65256i) q^{16} +(1.32592 + 4.94841i) q^{17} +(0.103649 + 3.99610i) q^{18} +(-2.91741 - 5.05309i) q^{19} +(-4.46976 - 0.145905i) q^{20} +(0.785561 - 0.772382i) q^{21} +(-1.01050 + 0.618890i) q^{22} +(3.34713 + 0.896861i) q^{23} +(-0.392310 - 1.11048i) q^{24} +(-1.73612 - 4.68891i) q^{25} +(2.23166 - 0.660445i) q^{26} +(-1.71555 - 1.71555i) q^{27} +(2.44442 - 4.69306i) q^{28} +5.00172i q^{29} +(0.983982 - 0.874991i) q^{30} +(-7.03267 - 4.06031i) q^{31} +(-3.43810 - 4.49215i) q^{32} +(0.0903002 - 0.337005i) q^{33} +(-7.04437 - 1.69305i) q^{34} +(5.89054 + 0.549128i) q^{35} +(-5.03579 - 2.56901i) q^{36} +(0.711408 + 0.190621i) q^{37} +(8.24889 - 0.213956i) q^{38} +(-0.342623 + 0.593441i) q^{39} +(3.19890 - 5.45592i) q^{40} +0.0958388 q^{41} +(0.429472 + 1.49764i) q^{42} +(-4.87975 + 4.87975i) q^{43} +(-0.0868733 - 1.67354i) q^{44} +(0.533414 - 6.29796i) q^{45} +(-3.37419 + 3.55389i) q^{46} +(-1.41603 + 5.28468i) q^{47} +(1.64481 + 0.262186i) q^{48} +(-3.60205 + 6.00210i) q^{49} +(6.99883 + 1.00812i) q^{50} +(1.84738 - 1.06658i) q^{51} +(-0.685908 + 3.21908i) q^{52} +(-12.8172 + 3.43436i) q^{53} +(3.29006 - 0.973671i) q^{54} +(1.69585 - 0.796517i) q^{55} +(4.18166 + 6.20594i) q^{56} +(-1.71797 + 1.71797i) q^{57} +(-6.21547 - 3.37672i) q^{58} +(4.46933 - 7.74111i) q^{59} +(0.423023 + 1.81348i) q^{60} +(0.919379 + 1.59241i) q^{61} +(9.79346 - 5.99810i) q^{62} +(6.44473 + 3.79391i) q^{63} +(7.90336 - 1.23971i) q^{64} +(-3.62215 + 0.649040i) q^{65} +(0.357822 + 0.339730i) q^{66} +(0.515535 - 0.138137i) q^{67} +(6.85965 - 7.61081i) q^{68} -1.44289i q^{69} +(-4.65916 + 6.94926i) q^{70} +13.6494i q^{71} +(6.59216 - 4.52344i) q^{72} +(-5.78744 + 1.55074i) q^{73} +(-0.717160 + 0.755353i) q^{74} +(-1.69880 + 1.20360i) q^{75} +(-5.30306 + 10.3951i) q^{76} +(-0.0187518 + 2.21678i) q^{77} +(-0.506141 - 0.826407i) q^{78} +(5.30723 + 9.19239i) q^{79} +(4.62027 + 7.65853i) q^{80} +(3.73481 - 6.46888i) q^{81} +(-0.0647020 + 0.119096i) q^{82} +(4.36830 - 4.36830i) q^{83} +(-2.15101 - 0.477382i) q^{84} +(10.7753 + 3.88809i) q^{85} +(-2.76953 - 9.35829i) q^{86} +(2.01171 - 0.539037i) q^{87} +(2.13830 + 1.02187i) q^{88} +(2.50474 - 1.44611i) q^{89} +(7.46616 + 4.91469i) q^{90} +(1.16244 - 4.19600i) q^{91} +(-2.13834 - 6.59227i) q^{92} +(-0.875163 + 3.26615i) q^{93} +(-5.61112 - 5.32740i) q^{94} +(-13.0005 - 1.10109i) q^{95} +(-1.43624 + 1.86694i) q^{96} +(4.24461 - 4.24461i) q^{97} +(-5.02683 - 8.52825i) q^{98} +2.36841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33} + 16 q^{36} - 4 q^{37} + 12 q^{38} + 2 q^{40} - 40 q^{41} + 78 q^{42} - 12 q^{45} - 28 q^{46} + 12 q^{48} - 28 q^{50} + 48 q^{52} - 24 q^{53} + 36 q^{56} - 16 q^{57} + 30 q^{58} - 10 q^{60} - 20 q^{61} + 56 q^{62} + 4 q^{65} + 44 q^{66} - 12 q^{68} + 84 q^{70} + 44 q^{72} - 12 q^{73} + 112 q^{76} + 16 q^{77} + 64 q^{78} + 52 q^{80} - 52 q^{81} - 34 q^{82} + 16 q^{85} + 64 q^{86} + 16 q^{88} - 32 q^{90} + 44 q^{92} + 12 q^{93} - 48 q^{96} - 24 q^{97} - 90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(101\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.675113 + 1.24267i −0.477377 + 0.878699i
\(3\) −0.107770 0.402205i −0.0622213 0.232213i 0.927812 0.373049i \(-0.121688\pi\)
−0.990033 + 0.140836i \(0.955021\pi\)
\(4\) −1.08845 1.67788i −0.544223 0.838941i
\(5\) 1.27747 1.83523i 0.571304 0.820739i
\(6\) 0.572564 + 0.137611i 0.233748 + 0.0561793i
\(7\) 1.30345 + 2.30240i 0.492657 + 0.870224i
\(8\) 2.81987 0.219816i 0.996975 0.0777167i
\(9\) 2.44792 1.41331i 0.815974 0.471103i
\(10\) 1.41814 + 2.82646i 0.448455 + 0.893805i
\(11\) 0.725638 + 0.418947i 0.218788 + 0.126317i 0.605389 0.795930i \(-0.293018\pi\)
−0.386601 + 0.922247i \(0.626351\pi\)
\(12\) −0.557549 + 0.618604i −0.160951 + 0.178575i
\(13\) −1.16367 1.16367i −0.322743 0.322743i 0.527075 0.849819i \(-0.323289\pi\)
−0.849819 + 0.527075i \(0.823289\pi\)
\(14\) −3.74109 + 0.0653744i −0.999847 + 0.0174720i
\(15\) −0.875811 0.316023i −0.226133 0.0815967i
\(16\) −1.63057 + 3.65256i −0.407643 + 0.913141i
\(17\) 1.32592 + 4.94841i 0.321583 + 1.20016i 0.917702 + 0.397269i \(0.130042\pi\)
−0.596119 + 0.802896i \(0.703291\pi\)
\(18\) 0.103649 + 3.99610i 0.0244303 + 0.941889i
\(19\) −2.91741 5.05309i −0.669299 1.15926i −0.978101 0.208133i \(-0.933261\pi\)
0.308802 0.951126i \(-0.400072\pi\)
\(20\) −4.46976 0.145905i −0.999468 0.0326254i
\(21\) 0.785561 0.772382i 0.171423 0.168548i
\(22\) −1.01050 + 0.618890i −0.215439 + 0.131948i
\(23\) 3.34713 + 0.896861i 0.697925 + 0.187008i 0.590301 0.807183i \(-0.299009\pi\)
0.107624 + 0.994192i \(0.465676\pi\)
\(24\) −0.392310 1.11048i −0.0800799 0.226675i
\(25\) −1.73612 4.68891i −0.347224 0.937782i
\(26\) 2.23166 0.660445i 0.437664 0.129524i
\(27\) −1.71555 1.71555i −0.330159 0.330159i
\(28\) 2.44442 4.69306i 0.461951 0.886905i
\(29\) 5.00172i 0.928795i 0.885627 + 0.464398i \(0.153729\pi\)
−0.885627 + 0.464398i \(0.846271\pi\)
\(30\) 0.983982 0.874991i 0.179650 0.159751i
\(31\) −7.03267 4.06031i −1.26310 0.729254i −0.289430 0.957199i \(-0.593466\pi\)
−0.973674 + 0.227945i \(0.926799\pi\)
\(32\) −3.43810 4.49215i −0.607776 0.794108i
\(33\) 0.0903002 0.337005i 0.0157192 0.0586650i
\(34\) −7.04437 1.69305i −1.20810 0.290356i
\(35\) 5.89054 + 0.549128i 0.995683 + 0.0928196i
\(36\) −5.03579 2.56901i −0.839299 0.428169i
\(37\) 0.711408 + 0.190621i 0.116955 + 0.0313379i 0.316822 0.948485i \(-0.397384\pi\)
−0.199867 + 0.979823i \(0.564051\pi\)
\(38\) 8.24889 0.213956i 1.33815 0.0347083i
\(39\) −0.342623 + 0.593441i −0.0548637 + 0.0950266i
\(40\) 3.19890 5.45592i 0.505791 0.862656i
\(41\) 0.0958388 0.0149675 0.00748375 0.999972i \(-0.497618\pi\)
0.00748375 + 0.999972i \(0.497618\pi\)
\(42\) 0.429472 + 1.49764i 0.0662690 + 0.231090i
\(43\) −4.87975 + 4.87975i −0.744155 + 0.744155i −0.973375 0.229220i \(-0.926383\pi\)
0.229220 + 0.973375i \(0.426383\pi\)
\(44\) −0.0868733 1.67354i −0.0130966 0.252295i
\(45\) 0.533414 6.29796i 0.0795166 0.938844i
\(46\) −3.37419 + 3.55389i −0.497497 + 0.523992i
\(47\) −1.41603 + 5.28468i −0.206549 + 0.770850i 0.782423 + 0.622747i \(0.213983\pi\)
−0.988972 + 0.148103i \(0.952683\pi\)
\(48\) 1.64481 + 0.262186i 0.237407 + 0.0378433i
\(49\) −3.60205 + 6.00210i −0.514579 + 0.857443i
\(50\) 6.99883 + 1.00812i 0.989785 + 0.142570i
\(51\) 1.84738 1.06658i 0.258684 0.149352i
\(52\) −0.685908 + 3.21908i −0.0951183 + 0.446407i
\(53\) −12.8172 + 3.43436i −1.76058 + 0.471745i −0.986832 0.161752i \(-0.948286\pi\)
−0.773745 + 0.633497i \(0.781619\pi\)
\(54\) 3.29006 0.973671i 0.447720 0.132500i
\(55\) 1.69585 0.796517i 0.228668 0.107402i
\(56\) 4.18166 + 6.20594i 0.558798 + 0.829304i
\(57\) −1.71797 + 1.71797i −0.227550 + 0.227550i
\(58\) −6.21547 3.37672i −0.816131 0.443385i
\(59\) 4.46933 7.74111i 0.581858 1.00781i −0.413402 0.910549i \(-0.635659\pi\)
0.995259 0.0972582i \(-0.0310073\pi\)
\(60\) 0.423023 + 1.81348i 0.0546121 + 0.234119i
\(61\) 0.919379 + 1.59241i 0.117714 + 0.203887i 0.918862 0.394580i \(-0.129110\pi\)
−0.801147 + 0.598467i \(0.795777\pi\)
\(62\) 9.79346 5.99810i 1.24377 0.761759i
\(63\) 6.44473 + 3.79391i 0.811960 + 0.477988i
\(64\) 7.90336 1.23971i 0.987920 0.154963i
\(65\) −3.62215 + 0.649040i −0.449272 + 0.0805035i
\(66\) 0.357822 + 0.339730i 0.0440449 + 0.0418178i
\(67\) 0.515535 0.138137i 0.0629826 0.0168761i −0.227190 0.973850i \(-0.572954\pi\)
0.290173 + 0.956974i \(0.406287\pi\)
\(68\) 6.85965 7.61081i 0.831855 0.922946i
\(69\) 1.44289i 0.173703i
\(70\) −4.65916 + 6.94926i −0.556877 + 0.830595i
\(71\) 13.6494i 1.61989i 0.586505 + 0.809946i \(0.300503\pi\)
−0.586505 + 0.809946i \(0.699497\pi\)
\(72\) 6.59216 4.52344i 0.776894 0.533093i
\(73\) −5.78744 + 1.55074i −0.677368 + 0.181500i −0.581072 0.813852i \(-0.697366\pi\)
−0.0962967 + 0.995353i \(0.530700\pi\)
\(74\) −0.717160 + 0.755353i −0.0833681 + 0.0878080i
\(75\) −1.69880 + 1.20360i −0.196160 + 0.138980i
\(76\) −5.30306 + 10.3951i −0.608303 + 1.19240i
\(77\) −0.0187518 + 2.21678i −0.00213696 + 0.252626i
\(78\) −0.506141 0.826407i −0.0573091 0.0935721i
\(79\) 5.30723 + 9.19239i 0.597110 + 1.03422i 0.993245 + 0.116033i \(0.0370177\pi\)
−0.396136 + 0.918192i \(0.629649\pi\)
\(80\) 4.62027 + 7.65853i 0.516562 + 0.856250i
\(81\) 3.73481 6.46888i 0.414979 0.718764i
\(82\) −0.0647020 + 0.119096i −0.00714514 + 0.0131519i
\(83\) 4.36830 4.36830i 0.479483 0.479483i −0.425483 0.904966i \(-0.639896\pi\)
0.904966 + 0.425483i \(0.139896\pi\)
\(84\) −2.15101 0.477382i −0.234694 0.0520867i
\(85\) 10.7753 + 3.88809i 1.16874 + 0.421723i
\(86\) −2.76953 9.35829i −0.298646 1.00913i
\(87\) 2.01171 0.539037i 0.215678 0.0577908i
\(88\) 2.13830 + 1.02187i 0.227943 + 0.108932i
\(89\) 2.50474 1.44611i 0.265502 0.153288i −0.361340 0.932434i \(-0.617681\pi\)
0.626842 + 0.779147i \(0.284347\pi\)
\(90\) 7.46616 + 4.91469i 0.787002 + 0.518054i
\(91\) 1.16244 4.19600i 0.121857 0.439860i
\(92\) −2.13834 6.59227i −0.222937 0.687292i
\(93\) −0.875163 + 3.26615i −0.0907502 + 0.338684i
\(94\) −5.61112 5.32740i −0.578743 0.549480i
\(95\) −13.0005 1.10109i −1.33382 0.112970i
\(96\) −1.43624 + 1.86694i −0.146586 + 0.190544i
\(97\) 4.24461 4.24461i 0.430975 0.430975i −0.457985 0.888960i \(-0.651429\pi\)
0.888960 + 0.457985i \(0.151429\pi\)
\(98\) −5.02683 8.52825i −0.507786 0.861483i
\(99\) 2.36841 0.238034
\(100\) −5.97776 + 8.01663i −0.597776 + 0.801663i
\(101\) −0.859895 + 1.48938i −0.0855628 + 0.148199i −0.905631 0.424067i \(-0.860602\pi\)
0.820068 + 0.572266i \(0.193935\pi\)
\(102\) 0.0782209 + 3.01574i 0.00774502 + 0.298603i
\(103\) −15.1726 4.06549i −1.49500 0.400584i −0.583579 0.812057i \(-0.698348\pi\)
−0.911422 + 0.411472i \(0.865015\pi\)
\(104\) −3.53719 3.02560i −0.346850 0.296685i
\(105\) −0.413964 2.42838i −0.0403987 0.236986i
\(106\) 4.38529 18.2461i 0.425937 1.77222i
\(107\) 3.60029 13.4365i 0.348053 1.29895i −0.540951 0.841054i \(-0.681936\pi\)
0.889004 0.457899i \(-0.151398\pi\)
\(108\) −1.01121 + 4.74579i −0.0973038 + 0.456663i
\(109\) 9.23440 + 5.33148i 0.884495 + 0.510664i 0.872138 0.489260i \(-0.162733\pi\)
0.0123573 + 0.999924i \(0.496066\pi\)
\(110\) −0.155083 + 2.64511i −0.0147866 + 0.252202i
\(111\) 0.306675i 0.0291083i
\(112\) −10.5350 + 1.00670i −0.995465 + 0.0951241i
\(113\) −5.62032 5.62032i −0.528715 0.528715i 0.391474 0.920189i \(-0.371965\pi\)
−0.920189 + 0.391474i \(0.871965\pi\)
\(114\) −0.975040 3.29468i −0.0913209 0.308575i
\(115\) 5.92181 4.99703i 0.552212 0.465975i
\(116\) 8.39229 5.44409i 0.779204 0.505472i
\(117\) −4.49319 1.20395i −0.415395 0.111305i
\(118\) 6.60233 + 10.7800i 0.607793 + 0.992381i
\(119\) −9.66492 + 9.50278i −0.885982 + 0.871119i
\(120\) −2.53914 0.698626i −0.231791 0.0637755i
\(121\) −5.14897 8.91827i −0.468088 0.810752i
\(122\) −2.59952 + 0.0674252i −0.235350 + 0.00610439i
\(123\) −0.0103286 0.0385468i −0.000931297 0.00347565i
\(124\) 0.841950 + 16.2194i 0.0756093 + 1.45655i
\(125\) −10.8231 2.80378i −0.968045 0.250778i
\(126\) −9.06549 + 5.44734i −0.807618 + 0.485288i
\(127\) −4.54633 4.54633i −0.403421 0.403421i 0.476016 0.879437i \(-0.342081\pi\)
−0.879437 + 0.476016i \(0.842081\pi\)
\(128\) −3.79512 + 10.6582i −0.335444 + 0.942060i
\(129\) 2.48855 + 1.43677i 0.219105 + 0.126500i
\(130\) 1.63882 4.93930i 0.143734 0.433206i
\(131\) 11.9545 6.90194i 1.04447 0.603025i 0.123374 0.992360i \(-0.460629\pi\)
0.921096 + 0.389335i \(0.127295\pi\)
\(132\) −0.663741 + 0.215298i −0.0577713 + 0.0187393i
\(133\) 7.83154 13.3035i 0.679081 1.15356i
\(134\) −0.176386 + 0.733896i −0.0152374 + 0.0633990i
\(135\) −5.34001 + 0.956857i −0.459595 + 0.0823532i
\(136\) 4.82667 + 13.6624i 0.413884 + 1.17154i
\(137\) 3.72240 + 13.8922i 0.318026 + 1.18689i 0.921139 + 0.389235i \(0.127260\pi\)
−0.603112 + 0.797656i \(0.706073\pi\)
\(138\) 1.79303 + 0.974111i 0.152633 + 0.0829218i
\(139\) −1.45615 −0.123509 −0.0617544 0.998091i \(-0.519670\pi\)
−0.0617544 + 0.998091i \(0.519670\pi\)
\(140\) −5.49016 10.4813i −0.464003 0.885834i
\(141\) 2.27813 0.191853
\(142\) −16.9617 9.21492i −1.42340 0.773299i
\(143\) −0.356886 1.33192i −0.0298443 0.111380i
\(144\) 1.17068 + 11.2457i 0.0975569 + 0.937142i
\(145\) 9.17929 + 6.38956i 0.762298 + 0.530624i
\(146\) 1.98012 8.23879i 0.163876 0.681847i
\(147\) 2.80227 + 0.801913i 0.231127 + 0.0661407i
\(148\) −0.454489 1.40114i −0.0373588 0.115173i
\(149\) 10.0147 5.78197i 0.820433 0.473677i −0.0301327 0.999546i \(-0.509593\pi\)
0.850566 + 0.525869i \(0.176260\pi\)
\(150\) −0.348796 2.92361i −0.0284790 0.238712i
\(151\) 4.17078 + 2.40800i 0.339414 + 0.195961i 0.660013 0.751254i \(-0.270551\pi\)
−0.320599 + 0.947215i \(0.603884\pi\)
\(152\) −9.33746 13.6078i −0.757368 1.10374i
\(153\) 10.2394 + 10.2394i 0.827805 + 0.827805i
\(154\) −2.74206 1.51988i −0.220962 0.122475i
\(155\) −16.4356 + 7.71960i −1.32014 + 0.620053i
\(156\) 1.36865 0.0710467i 0.109580 0.00568829i
\(157\) −1.10435 4.12149i −0.0881368 0.328931i 0.907753 0.419505i \(-0.137796\pi\)
−0.995890 + 0.0905743i \(0.971130\pi\)
\(158\) −15.0061 + 0.389220i −1.19382 + 0.0309647i
\(159\) 2.76263 + 4.78501i 0.219091 + 0.379476i
\(160\) −12.6362 + 0.571090i −0.998980 + 0.0451487i
\(161\) 2.29788 + 8.87543i 0.181098 + 0.699482i
\(162\) 5.51725 + 9.00835i 0.433476 + 0.707763i
\(163\) 7.85417 + 2.10452i 0.615186 + 0.164839i 0.552938 0.833222i \(-0.313506\pi\)
0.0622476 + 0.998061i \(0.480173\pi\)
\(164\) −0.104315 0.160806i −0.00814566 0.0125569i
\(165\) −0.503125 0.596236i −0.0391682 0.0464169i
\(166\) 2.47925 + 8.37743i 0.192427 + 0.650215i
\(167\) 5.50649 + 5.50649i 0.426105 + 0.426105i 0.887299 0.461194i \(-0.152579\pi\)
−0.461194 + 0.887299i \(0.652579\pi\)
\(168\) 2.04540 2.35070i 0.157806 0.181360i
\(169\) 10.2918i 0.791674i
\(170\) −12.1061 + 10.7652i −0.928498 + 0.825653i
\(171\) −14.2832 8.24639i −1.09226 0.630617i
\(172\) 13.4990 + 2.87630i 1.02929 + 0.219316i
\(173\) −0.810358 + 3.02430i −0.0616104 + 0.229933i −0.989865 0.142013i \(-0.954643\pi\)
0.928254 + 0.371946i \(0.121309\pi\)
\(174\) −0.688290 + 2.86380i −0.0521791 + 0.217104i
\(175\) 8.53279 10.1090i 0.645018 0.764167i
\(176\) −2.71344 + 1.96732i −0.204533 + 0.148292i
\(177\) −3.59517 0.963323i −0.270230 0.0724078i
\(178\) 0.106055 + 4.08885i 0.00794914 + 0.306472i
\(179\) 8.05255 13.9474i 0.601876 1.04248i −0.390661 0.920535i \(-0.627754\pi\)
0.992537 0.121945i \(-0.0389131\pi\)
\(180\) −11.1478 + 5.95998i −0.830910 + 0.444231i
\(181\) −3.83256 −0.284872 −0.142436 0.989804i \(-0.545493\pi\)
−0.142436 + 0.989804i \(0.545493\pi\)
\(182\) 4.42945 + 4.27731i 0.328333 + 0.317055i
\(183\) 0.541393 0.541393i 0.0400209 0.0400209i
\(184\) 9.63562 + 1.79328i 0.710348 + 0.132202i
\(185\) 1.25864 1.06208i 0.0925369 0.0780858i
\(186\) −3.46791 3.29256i −0.254279 0.241422i
\(187\) −1.11098 + 4.14624i −0.0812431 + 0.303203i
\(188\) 10.4083 3.37616i 0.759106 0.246232i
\(189\) 1.71375 6.18602i 0.124657 0.449967i
\(190\) 10.1451 15.4119i 0.736002 1.11810i
\(191\) 2.42531 1.40025i 0.175489 0.101319i −0.409682 0.912228i \(-0.634360\pi\)
0.585172 + 0.810909i \(0.301027\pi\)
\(192\) −1.35036 3.04516i −0.0974541 0.219766i
\(193\) 8.35378 2.23839i 0.601318 0.161123i 0.0546973 0.998503i \(-0.482581\pi\)
0.546621 + 0.837380i \(0.315914\pi\)
\(194\) 2.40905 + 8.14024i 0.172960 + 0.584435i
\(195\) 0.651407 + 1.38690i 0.0466482 + 0.0993178i
\(196\) 13.9915 0.489142i 0.999389 0.0349387i
\(197\) −4.90073 + 4.90073i −0.349162 + 0.349162i −0.859798 0.510635i \(-0.829410\pi\)
0.510635 + 0.859798i \(0.329410\pi\)
\(198\) −1.59894 + 2.94314i −0.113632 + 0.209160i
\(199\) −6.19859 + 10.7363i −0.439406 + 0.761074i −0.997644 0.0686071i \(-0.978145\pi\)
0.558237 + 0.829681i \(0.311478\pi\)
\(200\) −5.92634 12.8405i −0.419055 0.907961i
\(201\) −0.111119 0.192463i −0.00783771 0.0135753i
\(202\) −1.27028 2.07406i −0.0893766 0.145931i
\(203\) −11.5159 + 6.51947i −0.808260 + 0.457577i
\(204\) −3.80037 1.93876i −0.266079 0.135740i
\(205\) 0.122432 0.175886i 0.00855099 0.0122844i
\(206\) 15.2953 16.1098i 1.06567 1.12243i
\(207\) 9.46105 2.53508i 0.657589 0.176200i
\(208\) 6.14782 2.35293i 0.426274 0.163146i
\(209\) 4.88896i 0.338176i
\(210\) 3.29714 + 1.12501i 0.227524 + 0.0776332i
\(211\) 0.877438i 0.0604053i −0.999544 0.0302027i \(-0.990385\pi\)
0.999544 0.0302027i \(-0.00961527\pi\)
\(212\) 19.7133 + 17.7676i 1.35391 + 1.22029i
\(213\) 5.48987 1.47101i 0.376160 0.100792i
\(214\) 14.2665 + 13.5451i 0.975235 + 0.925924i
\(215\) 2.72170 + 15.1892i 0.185618 + 1.03590i
\(216\) −5.21475 4.46054i −0.354819 0.303501i
\(217\) 0.181737 21.4844i 0.0123371 1.45846i
\(218\) −12.8595 + 7.87594i −0.870957 + 0.533426i
\(219\) 1.24743 + 2.16061i 0.0842934 + 0.146000i
\(220\) −3.18230 1.97847i −0.214550 0.133388i
\(221\) 4.21537 7.30123i 0.283556 0.491134i
\(222\) 0.381095 + 0.207040i 0.0255774 + 0.0138956i
\(223\) 12.6059 12.6059i 0.844153 0.844153i −0.145243 0.989396i \(-0.546396\pi\)
0.989396 + 0.145243i \(0.0463963\pi\)
\(224\) 5.86133 13.7712i 0.391627 0.920124i
\(225\) −10.8768 9.02441i −0.725118 0.601628i
\(226\) 10.7785 3.18984i 0.716978 0.212185i
\(227\) −10.1432 + 2.71787i −0.673230 + 0.180392i −0.579210 0.815179i \(-0.696639\pi\)
−0.0940208 + 0.995570i \(0.529972\pi\)
\(228\) 4.75246 + 1.01263i 0.314739 + 0.0670632i
\(229\) −23.5981 + 13.6244i −1.55941 + 0.900324i −0.562094 + 0.827073i \(0.690004\pi\)
−0.997314 + 0.0732513i \(0.976662\pi\)
\(230\) 2.21175 + 10.7324i 0.145839 + 0.707674i
\(231\) 0.893620 0.231361i 0.0587959 0.0152225i
\(232\) 1.09946 + 14.1042i 0.0721830 + 0.925986i
\(233\) −3.39933 + 12.6865i −0.222697 + 0.831118i 0.760617 + 0.649201i \(0.224897\pi\)
−0.983314 + 0.181917i \(0.941770\pi\)
\(234\) 4.52951 4.77074i 0.296104 0.311873i
\(235\) 7.88965 + 9.34977i 0.514664 + 0.609912i
\(236\) −17.8533 + 0.926765i −1.16215 + 0.0603272i
\(237\) 3.12526 3.12526i 0.203007 0.203007i
\(238\) −5.28389 18.4257i −0.342503 1.19436i
\(239\) 10.7078 0.692631 0.346315 0.938118i \(-0.387433\pi\)
0.346315 + 0.938118i \(0.387433\pi\)
\(240\) 2.58237 2.68366i 0.166691 0.173229i
\(241\) −6.28701 + 10.8894i −0.404982 + 0.701449i −0.994319 0.106438i \(-0.966056\pi\)
0.589337 + 0.807887i \(0.299389\pi\)
\(242\) 14.5586 0.377614i 0.935861 0.0242739i
\(243\) −10.0348 2.68881i −0.643732 0.172487i
\(244\) 1.67118 3.27586i 0.106987 0.209716i
\(245\) 6.41370 + 14.2781i 0.409756 + 0.912195i
\(246\) 0.0548738 + 0.0131884i 0.00349863 + 0.000840864i
\(247\) −2.48523 + 9.27501i −0.158132 + 0.590155i
\(248\) −20.7237 9.90367i −1.31596 0.628884i
\(249\) −2.22772 1.28618i −0.141176 0.0815080i
\(250\) 10.7910 11.5566i 0.682480 0.730904i
\(251\) 14.8357i 0.936420i 0.883617 + 0.468210i \(0.155101\pi\)
−0.883617 + 0.468210i \(0.844899\pi\)
\(252\) −0.649002 14.9430i −0.0408833 0.941318i
\(253\) 2.05307 + 2.05307i 0.129075 + 0.129075i
\(254\) 8.71886 2.58029i 0.547070 0.161902i
\(255\) 0.402552 4.75289i 0.0252088 0.297637i
\(256\) −10.6825 11.9116i −0.667654 0.744472i
\(257\) −14.6681 3.93031i −0.914972 0.245166i −0.229537 0.973300i \(-0.573721\pi\)
−0.685435 + 0.728134i \(0.740388\pi\)
\(258\) −3.46547 + 2.12246i −0.215751 + 0.132139i
\(259\) 0.488397 + 1.88641i 0.0303475 + 0.117216i
\(260\) 5.03152 + 5.37109i 0.312042 + 0.333101i
\(261\) 7.06897 + 12.2438i 0.437558 + 0.757873i
\(262\) 0.506173 + 19.5151i 0.0312715 + 1.20564i
\(263\) −3.03340 11.3208i −0.187048 0.698072i −0.994183 0.107705i \(-0.965650\pi\)
0.807135 0.590367i \(-0.201017\pi\)
\(264\) 0.180556 0.970160i 0.0111124 0.0597092i
\(265\) −10.0708 + 27.9098i −0.618645 + 1.71448i
\(266\) 11.2446 + 18.7133i 0.689451 + 1.14739i
\(267\) −0.851570 0.851570i −0.0521153 0.0521153i
\(268\) −0.792909 0.714651i −0.0484346 0.0436543i
\(269\) −17.9195 10.3458i −1.09257 0.630797i −0.158313 0.987389i \(-0.550605\pi\)
−0.934260 + 0.356592i \(0.883939\pi\)
\(270\) 2.41605 7.28184i 0.147036 0.443159i
\(271\) 18.2735 10.5502i 1.11003 0.640878i 0.171195 0.985237i \(-0.445237\pi\)
0.938838 + 0.344359i \(0.111904\pi\)
\(272\) −20.2364 3.22573i −1.22701 0.195588i
\(273\) −1.81293 0.0153356i −0.109723 0.000928151i
\(274\) −19.7764 4.75309i −1.19474 0.287145i
\(275\) 0.704611 4.12979i 0.0424896 0.249036i
\(276\) −2.42099 + 1.57050i −0.145727 + 0.0945331i
\(277\) −0.846505 3.15920i −0.0508616 0.189818i 0.935821 0.352476i \(-0.114660\pi\)
−0.986683 + 0.162658i \(0.947993\pi\)
\(278\) 0.983064 1.80951i 0.0589603 0.108527i
\(279\) −22.9539 −1.37421
\(280\) 16.7313 + 0.253636i 0.999885 + 0.0151577i
\(281\) 2.60091 0.155157 0.0775787 0.996986i \(-0.475281\pi\)
0.0775787 + 0.996986i \(0.475281\pi\)
\(282\) −1.53799 + 2.83095i −0.0915861 + 0.168581i
\(283\) 7.17330 + 26.7711i 0.426409 + 1.59138i 0.760828 + 0.648954i \(0.224793\pi\)
−0.334419 + 0.942424i \(0.608540\pi\)
\(284\) 22.9022 14.8567i 1.35899 0.881582i
\(285\) 0.958203 + 5.34752i 0.0567590 + 0.316760i
\(286\) 1.89607 + 0.455703i 0.112117 + 0.0269463i
\(287\) 0.124921 + 0.220659i 0.00737384 + 0.0130251i
\(288\) −14.7650 6.13735i −0.870036 0.361647i
\(289\) −8.00623 + 4.62240i −0.470955 + 0.271906i
\(290\) −14.1372 + 7.09313i −0.830162 + 0.416523i
\(291\) −2.16465 1.24976i −0.126894 0.0732622i
\(292\) 8.90127 + 8.02274i 0.520907 + 0.469495i
\(293\) 11.9223 + 11.9223i 0.696506 + 0.696506i 0.963655 0.267149i \(-0.0860815\pi\)
−0.267149 + 0.963655i \(0.586082\pi\)
\(294\) −2.88836 + 2.94090i −0.168452 + 0.171517i
\(295\) −8.49725 18.0913i −0.494729 1.05332i
\(296\) 2.04798 + 0.381149i 0.119037 + 0.0221538i
\(297\) −0.526145 1.96360i −0.0305300 0.113940i
\(298\) 0.424037 + 16.3484i 0.0245638 + 0.947036i
\(299\) −2.85130 4.93859i −0.164895 0.285606i
\(300\) 3.86855 + 1.54033i 0.223351 + 0.0889309i
\(301\) −17.5956 4.87462i −1.01419 0.280968i
\(302\) −5.80810 + 3.55722i −0.334218 + 0.204695i
\(303\) 0.691707 + 0.185342i 0.0397376 + 0.0106476i
\(304\) 23.2138 2.41657i 1.33140 0.138600i
\(305\) 4.09692 + 0.346994i 0.234589 + 0.0198688i
\(306\) −19.6369 + 5.81141i −1.12257 + 0.332216i
\(307\) −13.0364 13.0364i −0.744028 0.744028i 0.229323 0.973350i \(-0.426349\pi\)
−0.973350 + 0.229323i \(0.926349\pi\)
\(308\) 3.73991 2.38138i 0.213101 0.135692i
\(309\) 6.54063i 0.372083i
\(310\) 1.50302 25.6356i 0.0853656 1.45601i
\(311\) 10.1447 + 5.85707i 0.575255 + 0.332124i 0.759246 0.650804i \(-0.225568\pi\)
−0.183990 + 0.982928i \(0.558901\pi\)
\(312\) −0.835706 + 1.74874i −0.0473126 + 0.0990031i
\(313\) 4.94295 18.4473i 0.279392 1.04270i −0.673449 0.739234i \(-0.735188\pi\)
0.952841 0.303471i \(-0.0981455\pi\)
\(314\) 5.86721 + 1.41013i 0.331106 + 0.0795783i
\(315\) 15.1957 6.98093i 0.856179 0.393331i
\(316\) 9.64711 18.9103i 0.542693 1.06379i
\(317\) 2.78952 + 0.747448i 0.156675 + 0.0419809i 0.336304 0.941754i \(-0.390823\pi\)
−0.179629 + 0.983734i \(0.557490\pi\)
\(318\) −7.81126 + 0.202605i −0.438034 + 0.0113615i
\(319\) −2.09546 + 3.62944i −0.117323 + 0.203209i
\(320\) 7.82119 16.0882i 0.437218 0.899356i
\(321\) −5.79221 −0.323290
\(322\) −12.5805 3.13642i −0.701086 0.174786i
\(323\) 21.1365 21.1365i 1.17607 1.17607i
\(324\) −14.9191 + 0.774453i −0.828841 + 0.0430252i
\(325\) −3.43607 + 7.47660i −0.190599 + 0.414727i
\(326\) −7.91767 + 8.33933i −0.438519 + 0.461873i
\(327\) 1.14915 4.28869i 0.0635482 0.237165i
\(328\) 0.270253 0.0210669i 0.0149222 0.00116323i
\(329\) −14.0131 + 3.62805i −0.772569 + 0.200021i
\(330\) 1.08059 0.222690i 0.0594845 0.0122587i
\(331\) −30.1984 + 17.4351i −1.65986 + 0.958318i −0.687075 + 0.726586i \(0.741106\pi\)
−0.972780 + 0.231732i \(0.925561\pi\)
\(332\) −12.0841 2.57483i −0.663203 0.141312i
\(333\) 2.01088 0.538813i 0.110195 0.0295268i
\(334\) −10.5602 + 3.12523i −0.577831 + 0.171005i
\(335\) 0.405069 1.12259i 0.0221313 0.0613336i
\(336\) 1.54026 + 4.12874i 0.0840281 + 0.225241i
\(337\) 15.8847 15.8847i 0.865292 0.865292i −0.126655 0.991947i \(-0.540424\pi\)
0.991947 + 0.126655i \(0.0404240\pi\)
\(338\) 12.7892 + 6.94810i 0.695642 + 0.377927i
\(339\) −1.65481 + 2.86622i −0.0898771 + 0.155672i
\(340\) −5.20455 22.3116i −0.282256 1.21002i
\(341\) −3.40211 5.89263i −0.184235 0.319104i
\(342\) 19.8903 12.1820i 1.07554 0.658726i
\(343\) −18.5143 0.469928i −0.999678 0.0253737i
\(344\) −12.6876 + 14.8329i −0.684071 + 0.799738i
\(345\) −2.64802 1.84325i −0.142565 0.0992372i
\(346\) −3.21111 3.04875i −0.172630 0.163902i
\(347\) −23.1956 + 6.21524i −1.24520 + 0.333651i −0.820482 0.571673i \(-0.806295\pi\)
−0.424722 + 0.905324i \(0.639628\pi\)
\(348\) −3.09408 2.78870i −0.165860 0.149490i
\(349\) 20.0084i 1.07102i −0.844528 0.535512i \(-0.820119\pi\)
0.844528 0.535512i \(-0.179881\pi\)
\(350\) 6.80151 + 17.4281i 0.363556 + 0.931572i
\(351\) 3.99267i 0.213113i
\(352\) −0.612842 4.70006i −0.0326646 0.250514i
\(353\) 22.6305 6.06381i 1.20450 0.322744i 0.399897 0.916560i \(-0.369046\pi\)
0.804601 + 0.593816i \(0.202379\pi\)
\(354\) 3.62424 3.81725i 0.192626 0.202885i
\(355\) 25.0498 + 17.4368i 1.32951 + 0.925450i
\(356\) −5.15268 2.62865i −0.273092 0.139318i
\(357\) 4.86365 + 2.86316i 0.257412 + 0.151534i
\(358\) 11.8956 + 19.4227i 0.628704 + 1.02652i
\(359\) −13.4523 23.3000i −0.709984 1.22973i −0.964862 0.262756i \(-0.915369\pi\)
0.254878 0.966973i \(-0.417965\pi\)
\(360\) 0.119766 17.8767i 0.00631221 0.942185i
\(361\) −7.52251 + 13.0294i −0.395922 + 0.685756i
\(362\) 2.58741 4.76260i 0.135991 0.250317i
\(363\) −3.03206 + 3.03206i −0.159142 + 0.159142i
\(364\) −8.30565 + 2.61667i −0.435334 + 0.137151i
\(365\) −4.54734 + 12.6023i −0.238019 + 0.659634i
\(366\) 0.307270 + 1.03827i 0.0160613 + 0.0542714i
\(367\) 26.4682 7.09214i 1.38163 0.370207i 0.509917 0.860223i \(-0.329676\pi\)
0.871713 + 0.490017i \(0.163009\pi\)
\(368\) −8.73358 + 10.7632i −0.455270 + 0.561071i
\(369\) 0.234606 0.135450i 0.0122131 0.00705123i
\(370\) 0.470092 + 2.28109i 0.0244389 + 0.118588i
\(371\) −24.6138 25.0337i −1.27788 1.29969i
\(372\) 6.43278 2.08661i 0.333524 0.108186i
\(373\) 5.67531 21.1806i 0.293857 1.09669i −0.648265 0.761415i \(-0.724505\pi\)
0.942121 0.335272i \(-0.108828\pi\)
\(374\) −4.40236 4.17976i −0.227641 0.216130i
\(375\) 0.0387116 + 4.65525i 0.00199906 + 0.240396i
\(376\) −2.83135 + 15.2134i −0.146016 + 0.784570i
\(377\) 5.82033 5.82033i 0.299762 0.299762i
\(378\) 6.53019 + 6.30589i 0.335877 + 0.324340i
\(379\) 20.4602 1.05097 0.525484 0.850803i \(-0.323884\pi\)
0.525484 + 0.850803i \(0.323884\pi\)
\(380\) 12.3028 + 23.0118i 0.631121 + 1.18048i
\(381\) −1.33859 + 2.31851i −0.0685783 + 0.118781i
\(382\) 0.102691 + 3.95918i 0.00525415 + 0.202569i
\(383\) −7.01910 1.88076i −0.358659 0.0961024i 0.0749899 0.997184i \(-0.476108\pi\)
−0.433649 + 0.901082i \(0.642774\pi\)
\(384\) 4.69577 + 0.377776i 0.239630 + 0.0192783i
\(385\) 4.04434 + 2.86629i 0.206119 + 0.146080i
\(386\) −2.85817 + 11.8921i −0.145477 + 0.605294i
\(387\) −5.04866 + 18.8418i −0.256638 + 0.957785i
\(388\) −11.7420 2.50193i −0.596109 0.127016i
\(389\) −4.81003 2.77707i −0.243878 0.140803i 0.373080 0.927799i \(-0.378302\pi\)
−0.616958 + 0.786996i \(0.711635\pi\)
\(390\) −2.16323 0.126830i −0.109539 0.00642228i
\(391\) 17.7521i 0.897764i
\(392\) −8.83797 + 17.7169i −0.446385 + 0.894841i
\(393\) −4.06433 4.06433i −0.205018 0.205018i
\(394\) −2.78143 9.39852i −0.140126 0.473491i
\(395\) 23.6500 + 2.00306i 1.18996 + 0.100785i
\(396\) −2.57788 3.97391i −0.129543 0.199696i
\(397\) 29.0677 + 7.78865i 1.45886 + 0.390901i 0.899097 0.437749i \(-0.144224\pi\)
0.559766 + 0.828650i \(0.310891\pi\)
\(398\) −9.15687 14.9510i −0.458992 0.749425i
\(399\) −6.19472 1.71616i −0.310124 0.0859155i
\(400\) 19.9574 + 1.30432i 0.997871 + 0.0652160i
\(401\) 2.31962 + 4.01770i 0.115836 + 0.200634i 0.918114 0.396317i \(-0.129712\pi\)
−0.802277 + 0.596951i \(0.796379\pi\)
\(402\) 0.314185 0.00814920i 0.0156701 0.000406445i
\(403\) 3.45883 + 12.9085i 0.172297 + 0.643020i
\(404\) 3.43496 0.178309i 0.170895 0.00887118i
\(405\) −7.10074 15.1180i −0.352839 0.751222i
\(406\) −0.326984 18.7119i −0.0162279 0.928654i
\(407\) 0.436364 + 0.436364i 0.0216298 + 0.0216298i
\(408\) 4.97491 3.41371i 0.246295 0.169004i
\(409\) 30.0868 + 17.3706i 1.48770 + 0.858922i 0.999901 0.0140366i \(-0.00446813\pi\)
0.487795 + 0.872958i \(0.337801\pi\)
\(410\) 0.135913 + 0.270885i 0.00671225 + 0.0133780i
\(411\) 5.18634 2.99434i 0.255823 0.147700i
\(412\) 9.69314 + 29.8829i 0.477547 + 1.47222i
\(413\) 23.6486 + 0.200044i 1.16367 + 0.00984353i
\(414\) −3.23702 + 13.4684i −0.159091 + 0.661936i
\(415\) −2.43643 13.5972i −0.119600 0.667460i
\(416\) −1.22657 + 9.22818i −0.0601374 + 0.452449i
\(417\) 0.156930 + 0.585669i 0.00768487 + 0.0286803i
\(418\) 6.07535 + 3.30060i 0.297155 + 0.161437i
\(419\) 28.1311 1.37429 0.687147 0.726518i \(-0.258863\pi\)
0.687147 + 0.726518i \(0.258863\pi\)
\(420\) −3.62396 + 3.33774i −0.176831 + 0.162865i
\(421\) 3.94616 0.192324 0.0961621 0.995366i \(-0.469343\pi\)
0.0961621 + 0.995366i \(0.469343\pi\)
\(422\) 1.09036 + 0.592370i 0.0530781 + 0.0288361i
\(423\) 4.00256 + 14.9378i 0.194611 + 0.726299i
\(424\) −35.3879 + 12.5019i −1.71859 + 0.607145i
\(425\) 20.9007 14.8082i 1.01383 0.718301i
\(426\) −1.87831 + 7.81518i −0.0910044 + 0.378647i
\(427\) −2.46800 + 4.19240i −0.119435 + 0.202884i
\(428\) −26.4635 + 8.58400i −1.27916 + 0.414923i
\(429\) −0.497241 + 0.287082i −0.0240070 + 0.0138605i
\(430\) −20.7126 6.87226i −0.998850 0.331410i
\(431\) 12.1350 + 7.00616i 0.584523 + 0.337475i 0.762929 0.646482i \(-0.223761\pi\)
−0.178406 + 0.983957i \(0.557094\pi\)
\(432\) 9.06351 3.46884i 0.436069 0.166894i
\(433\) −2.21951 2.21951i −0.106663 0.106663i 0.651761 0.758424i \(-0.274030\pi\)
−0.758424 + 0.651761i \(0.774030\pi\)
\(434\) 26.5753 + 14.7302i 1.27565 + 0.707073i
\(435\) 1.58066 4.38056i 0.0757866 0.210032i
\(436\) −1.10554 21.2973i −0.0529458 1.01995i
\(437\) −5.23301 19.5299i −0.250329 0.934240i
\(438\) −3.52707 + 0.0914837i −0.168530 + 0.00437126i
\(439\) −12.5163 21.6788i −0.597369 1.03467i −0.993208 0.116354i \(-0.962879\pi\)
0.395839 0.918320i \(-0.370454\pi\)
\(440\) 4.60699 2.61885i 0.219629 0.124849i
\(441\) −0.334721 + 19.7835i −0.0159391 + 0.942071i
\(442\) 6.22715 + 10.1675i 0.296196 + 0.483617i
\(443\) −4.25262 1.13949i −0.202048 0.0541386i 0.156376 0.987698i \(-0.450019\pi\)
−0.358424 + 0.933559i \(0.616686\pi\)
\(444\) −0.514564 + 0.333799i −0.0244201 + 0.0158414i
\(445\) 0.545795 6.44414i 0.0258732 0.305482i
\(446\) 7.15454 + 24.1753i 0.338777 + 1.14474i
\(447\) −3.40482 3.40482i −0.161042 0.161042i
\(448\) 13.1559 + 16.5808i 0.621558 + 0.783368i
\(449\) 24.2255i 1.14327i −0.820507 0.571636i \(-0.806309\pi\)
0.820507 0.571636i \(-0.193691\pi\)
\(450\) 18.5574 7.42371i 0.874804 0.349957i
\(451\) 0.0695443 + 0.0401514i 0.00327471 + 0.00189066i
\(452\) −3.31282 + 15.5476i −0.155822 + 0.731299i
\(453\) 0.519023 1.93702i 0.0243858 0.0910091i
\(454\) 3.47042 14.4395i 0.162875 0.677681i
\(455\) −6.21563 7.49363i −0.291393 0.351307i
\(456\) −4.46681 + 5.22209i −0.209178 + 0.244547i
\(457\) 9.04568 + 2.42378i 0.423139 + 0.113380i 0.464104 0.885781i \(-0.346376\pi\)
−0.0409647 + 0.999161i \(0.513043\pi\)
\(458\) −0.999182 38.5226i −0.0466887 1.80004i
\(459\) 6.21457 10.7640i 0.290071 0.502418i
\(460\) −14.8300 4.49711i −0.691452 0.209679i
\(461\) 12.3582 0.575580 0.287790 0.957693i \(-0.407079\pi\)
0.287790 + 0.957693i \(0.407079\pi\)
\(462\) −0.315789 + 1.26667i −0.0146919 + 0.0589307i
\(463\) 29.6788 29.6788i 1.37929 1.37929i 0.533471 0.845818i \(-0.320887\pi\)
0.845818 0.533471i \(-0.179113\pi\)
\(464\) −18.2691 8.15567i −0.848121 0.378617i
\(465\) 4.87613 + 5.77855i 0.226125 + 0.267974i
\(466\) −13.4701 12.7890i −0.623992 0.592440i
\(467\) −9.36749 + 34.9600i −0.433476 + 1.61775i 0.311212 + 0.950341i \(0.399265\pi\)
−0.744687 + 0.667413i \(0.767401\pi\)
\(468\) 2.87051 + 8.84947i 0.132689 + 0.409067i
\(469\) 0.990018 + 1.00691i 0.0457148 + 0.0464948i
\(470\) −16.9451 + 3.49207i −0.781617 + 0.161077i
\(471\) −1.53867 + 0.888349i −0.0708980 + 0.0409330i
\(472\) 10.9013 22.8114i 0.501774 1.04998i
\(473\) −5.58529 + 1.49657i −0.256812 + 0.0688125i
\(474\) 1.77375 + 5.99356i 0.0814713 + 0.275293i
\(475\) −18.6285 + 22.4522i −0.854736 + 1.03018i
\(476\) 26.4643 + 5.87334i 1.21299 + 0.269204i
\(477\) −26.5217 + 26.5217i −1.21434 + 1.21434i
\(478\) −7.22898 + 13.3062i −0.330646 + 0.608614i
\(479\) −15.9325 + 27.5959i −0.727974 + 1.26089i 0.229764 + 0.973246i \(0.426205\pi\)
−0.957738 + 0.287642i \(0.907129\pi\)
\(480\) 1.59150 + 5.02079i 0.0726419 + 0.229167i
\(481\) −0.606023 1.04966i −0.0276323 0.0478605i
\(482\) −9.28749 15.1643i −0.423034 0.690713i
\(483\) 3.32209 1.88072i 0.151160 0.0855759i
\(484\) −9.35944 + 18.3464i −0.425429 + 0.833928i
\(485\) −2.36745 13.2122i −0.107500 0.599936i
\(486\) 10.1159 10.6547i 0.458867 0.483305i
\(487\) 9.64618 2.58469i 0.437110 0.117123i −0.0335518 0.999437i \(-0.510682\pi\)
0.470662 + 0.882314i \(0.344015\pi\)
\(488\) 2.94257 + 4.28830i 0.133204 + 0.194122i
\(489\) 3.38579i 0.153111i
\(490\) −22.0729 1.66925i −0.997153 0.0754089i
\(491\) 16.3501i 0.737871i 0.929455 + 0.368936i \(0.120278\pi\)
−0.929455 + 0.368936i \(0.879722\pi\)
\(492\) −0.0534349 + 0.0592862i −0.00240903 + 0.00267283i
\(493\) −24.7505 + 6.63188i −1.11471 + 0.298685i
\(494\) −9.84794 9.35000i −0.443080 0.420676i
\(495\) 3.02558 4.34657i 0.135990 0.195364i
\(496\) 26.2978 19.0666i 1.18081 0.856117i
\(497\) −31.4264 + 17.7913i −1.40967 + 0.798050i
\(498\) 3.10225 1.90000i 0.139015 0.0851412i
\(499\) −4.74809 8.22393i −0.212554 0.368154i 0.739959 0.672652i \(-0.234845\pi\)
−0.952513 + 0.304498i \(0.901511\pi\)
\(500\) 7.07590 + 21.2116i 0.316444 + 0.948611i
\(501\) 1.62130 2.80817i 0.0724343 0.125460i
\(502\) −18.4358 10.0158i −0.822831 0.447025i
\(503\) −9.76866 + 9.76866i −0.435563 + 0.435563i −0.890516 0.454953i \(-0.849656\pi\)
0.454953 + 0.890516i \(0.349656\pi\)
\(504\) 19.0073 + 9.28169i 0.846652 + 0.413440i
\(505\) 1.63486 + 3.48075i 0.0727504 + 0.154891i
\(506\) −3.93733 + 1.16523i −0.175036 + 0.0518007i
\(507\) −4.13939 + 1.10915i −0.183837 + 0.0492589i
\(508\) −2.67977 + 12.5766i −0.118896 + 0.557998i
\(509\) 17.0075 9.81931i 0.753846 0.435233i −0.0732360 0.997315i \(-0.523333\pi\)
0.827082 + 0.562082i \(0.189999\pi\)
\(510\) 5.63449 + 3.70897i 0.249500 + 0.164236i
\(511\) −11.1140 11.3037i −0.491656 0.500045i
\(512\) 22.0140 5.23310i 0.972889 0.231273i
\(513\) −3.66389 + 13.6738i −0.161765 + 0.603714i
\(514\) 14.7867 15.5742i 0.652214 0.686948i
\(515\) −26.8437 + 22.6516i −1.18287 + 0.998150i
\(516\) −0.297929 5.73933i −0.0131156 0.252660i
\(517\) −3.24152 + 3.24152i −0.142562 + 0.142562i
\(518\) −2.67390 0.666623i −0.117484 0.0292897i
\(519\) 1.30372 0.0572269
\(520\) −10.0713 + 2.62642i −0.441657 + 0.115176i
\(521\) 21.2862 36.8688i 0.932565 1.61525i 0.153645 0.988126i \(-0.450899\pi\)
0.778920 0.627124i \(-0.215768\pi\)
\(522\) −19.9873 + 0.518422i −0.874822 + 0.0226907i
\(523\) −1.97787 0.529969i −0.0864862 0.0231739i 0.215316 0.976544i \(-0.430922\pi\)
−0.301803 + 0.953370i \(0.597588\pi\)
\(524\) −24.5925 12.5459i −1.07433 0.548069i
\(525\) −4.98546 2.34248i −0.217583 0.102234i
\(526\) 16.1159 + 3.87332i 0.702687 + 0.168885i
\(527\) 10.7673 40.1842i 0.469032 1.75045i
\(528\) 1.08369 + 0.879339i 0.0471616 + 0.0382683i
\(529\) −9.51967 5.49618i −0.413899 0.238964i
\(530\) −27.8836 31.3569i −1.21119 1.36206i
\(531\) 25.2662i 1.09646i
\(532\) −30.8458 + 1.33969i −1.33734 + 0.0580831i
\(533\) −0.111524 0.111524i −0.00483066 0.00483066i
\(534\) 1.63312 0.483313i 0.0706722 0.0209150i
\(535\) −20.0597 23.7721i −0.867257 1.02776i
\(536\) 1.42338 0.502852i 0.0614805 0.0217199i
\(537\) −6.47754 1.73565i −0.279527 0.0748989i
\(538\) 24.9542 15.2834i 1.07585 0.658915i
\(539\) −5.12835 + 2.84628i −0.220894 + 0.122598i
\(540\) 7.41780 + 7.91842i 0.319211 + 0.340754i
\(541\) −2.22119 3.84722i −0.0954965 0.165405i 0.814319 0.580417i \(-0.197111\pi\)
−0.909816 + 0.415012i \(0.863777\pi\)
\(542\) 0.773727 + 29.8304i 0.0332344 + 1.28133i
\(543\) 0.413036 + 1.54147i 0.0177251 + 0.0661509i
\(544\) 17.6704 22.9694i 0.757610 0.984804i
\(545\) 21.5812 10.1364i 0.924437 0.434196i
\(546\) 1.24299 2.24251i 0.0531950 0.0959707i
\(547\) −13.7530 13.7530i −0.588037 0.588037i 0.349062 0.937099i \(-0.386500\pi\)
−0.937099 + 0.349062i \(0.886500\pi\)
\(548\) 19.2578 21.3667i 0.822654 0.912738i
\(549\) 4.50114 + 2.59873i 0.192104 + 0.110911i
\(550\) 4.65627 + 3.66367i 0.198544 + 0.156220i
\(551\) 25.2741 14.5920i 1.07671 0.621642i
\(552\) −0.317170 4.06875i −0.0134996 0.173178i
\(553\) −14.2468 + 24.2011i −0.605837 + 1.02914i
\(554\) 4.49732 + 1.08089i 0.191073 + 0.0459227i
\(555\) −0.562818 0.391769i −0.0238903 0.0166297i
\(556\) 1.58494 + 2.44324i 0.0672163 + 0.103617i
\(557\) −3.23476 12.0723i −0.137061 0.511519i −0.999981 0.00617797i \(-0.998033\pi\)
0.862920 0.505341i \(-0.168633\pi\)
\(558\) 15.4965 28.5241i 0.656018 1.20752i
\(559\) 11.3568 0.480342
\(560\) −11.6107 + 20.6202i −0.490641 + 0.871362i
\(561\) 1.78737 0.0754628
\(562\) −1.75591 + 3.23207i −0.0740685 + 0.136337i
\(563\) −1.99709 7.45322i −0.0841671 0.314116i 0.910988 0.412433i \(-0.135321\pi\)
−0.995155 + 0.0983168i \(0.968654\pi\)
\(564\) −2.47962 3.82243i −0.104411 0.160953i
\(565\) −17.4944 + 3.13475i −0.735994 + 0.131880i
\(566\) −38.1104 9.15950i −1.60190 0.385003i
\(567\) 19.7620 + 0.167167i 0.829928 + 0.00702037i
\(568\) 3.00037 + 38.4897i 0.125893 + 1.61499i
\(569\) −22.8689 + 13.2033i −0.958712 + 0.553513i −0.895776 0.444505i \(-0.853380\pi\)
−0.0629358 + 0.998018i \(0.520046\pi\)
\(570\) −7.29208 2.41945i −0.305432 0.101340i
\(571\) 4.41042 + 2.54636i 0.184570 + 0.106562i 0.589438 0.807813i \(-0.299349\pi\)
−0.404868 + 0.914375i \(0.632682\pi\)
\(572\) −1.84635 + 2.04853i −0.0771997 + 0.0856534i
\(573\) −0.824564 0.824564i −0.0344467 0.0344467i
\(574\) −0.358541 + 0.00626540i −0.0149652 + 0.000261513i
\(575\) −1.60572 17.2515i −0.0669633 0.719435i
\(576\) 17.5947 14.2046i 0.733114 0.591858i
\(577\) 5.11195 + 19.0781i 0.212813 + 0.794230i 0.986925 + 0.161181i \(0.0515303\pi\)
−0.774111 + 0.633049i \(0.781803\pi\)
\(578\) −0.338997 13.0697i −0.0141004 0.543629i
\(579\) −1.80058 3.11870i −0.0748295 0.129609i
\(580\) 0.729776 22.3564i 0.0303023 0.928301i
\(581\) 15.7514 + 4.36370i 0.653478 + 0.181037i
\(582\) 3.01442 1.84621i 0.124952 0.0765278i
\(583\) −10.7395 2.87763i −0.444783 0.119179i
\(584\) −15.9790 + 5.64506i −0.661214 + 0.233594i
\(585\) −7.94945 + 6.70801i −0.328669 + 0.277342i
\(586\) −22.8643 + 6.76654i −0.944515 + 0.279523i
\(587\) 8.18830 + 8.18830i 0.337967 + 0.337967i 0.855602 0.517635i \(-0.173187\pi\)
−0.517635 + 0.855602i \(0.673187\pi\)
\(588\) −1.70460 5.57471i −0.0702965 0.229897i
\(589\) 47.3823i 1.95235i
\(590\) 28.2181 + 1.65443i 1.16172 + 0.0681116i
\(591\) 2.49925 + 1.44294i 0.102805 + 0.0593547i
\(592\) −1.85626 + 2.28764i −0.0762918 + 0.0940215i
\(593\) −1.63207 + 6.09096i −0.0670210 + 0.250126i −0.991306 0.131578i \(-0.957996\pi\)
0.924285 + 0.381703i \(0.124662\pi\)
\(594\) 2.79531 + 0.671828i 0.114693 + 0.0275654i
\(595\) 5.09308 + 29.8769i 0.208796 + 1.22483i
\(596\) −20.6019 10.5101i −0.843886 0.430509i
\(597\) 4.98620 + 1.33605i 0.204072 + 0.0546808i
\(598\) 8.06198 0.209108i 0.329679 0.00855106i
\(599\) −12.5631 + 21.7600i −0.513315 + 0.889088i 0.486566 + 0.873644i \(0.338249\pi\)
−0.999881 + 0.0154439i \(0.995084\pi\)
\(600\) −4.52582 + 3.76743i −0.184766 + 0.153805i
\(601\) −23.9702 −0.977766 −0.488883 0.872349i \(-0.662595\pi\)
−0.488883 + 0.872349i \(0.662595\pi\)
\(602\) 17.9366 18.5746i 0.731039 0.757043i
\(603\) 1.06676 1.06676i 0.0434417 0.0434417i
\(604\) −0.499326 9.61906i −0.0203173 0.391394i
\(605\) −22.9447 1.94333i −0.932836 0.0790077i
\(606\) −0.697300 + 0.734435i −0.0283259 + 0.0298344i
\(607\) 0.531386 1.98316i 0.0215683 0.0804940i −0.954303 0.298841i \(-0.903400\pi\)
0.975871 + 0.218347i \(0.0700666\pi\)
\(608\) −12.6689 + 30.4785i −0.513793 + 1.23607i
\(609\) 3.86324 + 3.92915i 0.156546 + 0.159217i
\(610\) −3.19708 + 4.85685i −0.129446 + 0.196648i
\(611\) 7.79739 4.50183i 0.315449 0.182124i
\(612\) 6.03546 28.3255i 0.243969 1.14499i
\(613\) −35.4100 + 9.48807i −1.43020 + 0.383220i −0.889089 0.457735i \(-0.848661\pi\)
−0.541106 + 0.840954i \(0.681994\pi\)
\(614\) 25.0010 7.39888i 1.00896 0.298595i
\(615\) −0.0839366 0.0302872i −0.00338465 0.00122130i
\(616\) 0.434407 + 6.25516i 0.0175027 + 0.252028i
\(617\) 7.99905 7.99905i 0.322029 0.322029i −0.527516 0.849545i \(-0.676876\pi\)
0.849545 + 0.527516i \(0.176876\pi\)
\(618\) −8.12783 4.41566i −0.326949 0.177624i
\(619\) −13.8212 + 23.9391i −0.555523 + 0.962194i 0.442340 + 0.896847i \(0.354148\pi\)
−0.997863 + 0.0653461i \(0.979185\pi\)
\(620\) 30.8419 + 19.1747i 1.23864 + 0.770075i
\(621\) −4.20357 7.28080i −0.168683 0.292168i
\(622\) −14.1272 + 8.65236i −0.566450 + 0.346928i
\(623\) 6.59432 + 3.88197i 0.264196 + 0.155528i
\(624\) −1.60891 2.21910i −0.0644079 0.0888352i
\(625\) −18.9718 + 16.2810i −0.758871 + 0.651241i
\(626\) 19.5868 + 18.5965i 0.782848 + 0.743264i
\(627\) −1.96636 + 0.526885i −0.0785289 + 0.0210417i
\(628\) −5.71335 + 6.33899i −0.227988 + 0.252953i
\(629\) 3.77309i 0.150443i
\(630\) −1.58382 + 23.5961i −0.0631010 + 0.940090i
\(631\) 11.5488i 0.459750i 0.973220 + 0.229875i \(0.0738318\pi\)
−0.973220 + 0.229875i \(0.926168\pi\)
\(632\) 16.9863 + 24.7547i 0.675680 + 0.984691i
\(633\) −0.352910 + 0.0945618i −0.0140269 + 0.00375850i
\(634\) −2.81207 + 2.96183i −0.111681 + 0.117629i
\(635\) −14.1514 + 2.53573i −0.561580 + 0.100627i
\(636\) 5.02171 9.84358i 0.199124 0.390324i
\(637\) 11.1760 2.79286i 0.442811 0.110657i
\(638\) −3.09551 5.05423i −0.122553 0.200099i
\(639\) 19.2909 + 33.4128i 0.763135 + 1.32179i
\(640\) 14.7120 + 20.5805i 0.581545 + 0.813514i
\(641\) 8.55730 14.8217i 0.337993 0.585421i −0.646062 0.763285i \(-0.723585\pi\)
0.984055 + 0.177864i \(0.0569186\pi\)
\(642\) 3.91040 7.19780i 0.154331 0.284074i
\(643\) −18.4696 + 18.4696i −0.728370 + 0.728370i −0.970295 0.241925i \(-0.922221\pi\)
0.241925 + 0.970295i \(0.422221\pi\)
\(644\) 12.3908 13.5160i 0.488266 0.532604i
\(645\) 5.81585 2.73163i 0.228999 0.107558i
\(646\) 11.9961 + 40.5352i 0.471981 + 1.59484i
\(647\) 32.3254 8.66156i 1.27084 0.340521i 0.440489 0.897758i \(-0.354805\pi\)
0.830353 + 0.557237i \(0.188139\pi\)
\(648\) 9.10972 19.0624i 0.357864 0.748841i
\(649\) 6.48624 3.74483i 0.254607 0.146997i
\(650\) −6.97120 9.31744i −0.273433 0.365460i
\(651\) −8.66070 + 2.24228i −0.339440 + 0.0878821i
\(652\) −5.01770 15.4690i −0.196508 0.605813i
\(653\) 2.75226 10.2716i 0.107704 0.401958i −0.890934 0.454133i \(-0.849949\pi\)
0.998638 + 0.0521757i \(0.0166156\pi\)
\(654\) 4.55361 + 4.32337i 0.178060 + 0.169057i
\(655\) 2.60494 30.7563i 0.101784 1.20175i
\(656\) −0.156272 + 0.350057i −0.00610141 + 0.0136674i
\(657\) −11.9755 + 11.9755i −0.467210 + 0.467210i
\(658\) 4.95199 19.8630i 0.193049 0.774341i
\(659\) 21.6586 0.843698 0.421849 0.906666i \(-0.361381\pi\)
0.421849 + 0.906666i \(0.361381\pi\)
\(660\) −0.452791 + 1.49315i −0.0176248 + 0.0581210i
\(661\) −11.2670 + 19.5150i −0.438236 + 0.759046i −0.997554 0.0699068i \(-0.977730\pi\)
0.559318 + 0.828953i \(0.311063\pi\)
\(662\) −1.27865 49.2972i −0.0496961 1.91599i
\(663\) −3.39088 0.908584i −0.131691 0.0352865i
\(664\) 11.3578 13.2783i 0.440769 0.515296i
\(665\) −14.4103 31.3675i −0.558807 1.21638i
\(666\) −0.688004 + 2.86261i −0.0266596 + 0.110924i
\(667\) −4.48584 + 16.7414i −0.173693 + 0.648229i
\(668\) 3.24573 15.2328i 0.125581 0.589373i
\(669\) −6.42869 3.71161i −0.248548 0.143499i
\(670\) 1.12154 + 1.26124i 0.0433288 + 0.0487260i
\(671\) 1.54069i 0.0594775i
\(672\) −6.17050 0.873332i −0.238032 0.0336895i
\(673\) −12.3425 12.3425i −0.475769 0.475769i 0.428007 0.903776i \(-0.359216\pi\)
−0.903776 + 0.428007i \(0.859216\pi\)
\(674\) 9.01541 + 30.4633i 0.347261 + 1.17340i
\(675\) −5.06567 + 11.0225i −0.194978 + 0.424256i
\(676\) −17.2683 + 11.2020i −0.664167 + 0.430847i
\(677\) −13.2169 3.54145i −0.507966 0.136109i −0.00427157 0.999991i \(-0.501360\pi\)
−0.503695 + 0.863882i \(0.668026\pi\)
\(678\) −2.44457 3.99141i −0.0938833 0.153289i
\(679\) 15.3054 + 4.24015i 0.587368 + 0.162722i
\(680\) 31.2396 + 8.59534i 1.19798 + 0.329616i
\(681\) 2.18628 + 3.78675i 0.0837785 + 0.145109i
\(682\) 9.61940 0.249503i 0.368346 0.00955398i
\(683\) −0.572913 2.13814i −0.0219219 0.0818137i 0.954098 0.299494i \(-0.0968177\pi\)
−0.976020 + 0.217680i \(0.930151\pi\)
\(684\) 1.70998 + 32.9412i 0.0653826 + 1.25954i
\(685\) 30.2506 + 10.9155i 1.15582 + 0.417059i
\(686\) 13.0832 22.6899i 0.499519 0.866303i
\(687\) 8.02297 + 8.02297i 0.306095 + 0.306095i
\(688\) −9.86681 25.7804i −0.376169 0.982868i
\(689\) 18.9114 + 10.9185i 0.720467 + 0.415962i
\(690\) 4.07826 2.04621i 0.155257 0.0778980i
\(691\) 19.0959 11.0250i 0.726442 0.419411i −0.0906771 0.995880i \(-0.528903\pi\)
0.817119 + 0.576469i \(0.195570\pi\)
\(692\) 5.95644 1.93210i 0.226430 0.0734473i
\(693\) 3.08709 + 5.45301i 0.117269 + 0.207143i
\(694\) 7.93616 33.0204i 0.301252 1.25344i
\(695\) −1.86019 + 2.67236i −0.0705611 + 0.101368i
\(696\) 5.55428 1.96222i 0.210535 0.0743778i
\(697\) 0.127075 + 0.474249i 0.00481330 + 0.0179635i
\(698\) 24.8638 + 13.5079i 0.941107 + 0.511282i
\(699\) 5.46890 0.206853
\(700\) −26.2491 3.31393i −0.992125 0.125255i
\(701\) 3.86536 0.145993 0.0729964 0.997332i \(-0.476744\pi\)
0.0729964 + 0.997332i \(0.476744\pi\)
\(702\) −4.96156 2.69550i −0.187262 0.101735i
\(703\) −1.11224 4.15093i −0.0419489 0.156555i
\(704\) 6.25435 + 2.41151i 0.235720 + 0.0908873i
\(705\) 2.91025 4.18088i 0.109606 0.157461i
\(706\) −7.74281 + 32.2159i −0.291404 + 1.21246i
\(707\) −4.54997 0.0384883i −0.171119 0.00144750i
\(708\) 2.29681 + 7.08080i 0.0863192 + 0.266113i
\(709\) 27.5158 15.8862i 1.03338 0.596620i 0.115427 0.993316i \(-0.463177\pi\)
0.917950 + 0.396696i \(0.129843\pi\)
\(710\) −38.5796 + 19.3568i −1.44787 + 0.726448i
\(711\) 25.9834 + 15.0015i 0.974452 + 0.562600i
\(712\) 6.74517 4.62844i 0.252786 0.173458i
\(713\) −19.8977 19.8977i −0.745175 0.745175i
\(714\) −6.84147 + 4.11095i −0.256035 + 0.153848i
\(715\) −2.90028 1.04652i −0.108464 0.0391377i
\(716\) −32.1669 + 1.66978i −1.20213 + 0.0624027i
\(717\) −1.15398 4.30673i −0.0430963 0.160838i
\(718\) 38.0360 0.986561i 1.41949 0.0368181i
\(719\) −5.63438 9.75903i −0.210127 0.363950i 0.741627 0.670812i \(-0.234054\pi\)
−0.951754 + 0.306862i \(0.900721\pi\)
\(720\) 22.1339 + 12.2176i 0.824883 + 0.455324i
\(721\) −10.4163 40.2325i −0.387924 1.49834i
\(722\) −11.1126 18.1443i −0.413569 0.675260i
\(723\) 5.05733 + 1.35511i 0.188084 + 0.0503970i
\(724\) 4.17153 + 6.43058i 0.155034 + 0.238991i
\(725\) 23.4526 8.68359i 0.871008 0.322500i
\(726\) −1.72086 5.81483i −0.0638672 0.215809i
\(727\) −21.9895 21.9895i −0.815544 0.815544i 0.169915 0.985459i \(-0.445651\pi\)
−0.985459 + 0.169915i \(0.945651\pi\)
\(728\) 2.35560 12.0877i 0.0873042 0.448000i
\(729\) 18.0830i 0.669742i
\(730\) −12.5905 14.1588i −0.465995 0.524041i
\(731\) −30.6172 17.6768i −1.13242 0.653801i
\(732\) −1.49767 0.319117i −0.0553555 0.0117949i
\(733\) −10.4591 + 39.0339i −0.386316 + 1.44175i 0.449766 + 0.893146i \(0.351507\pi\)
−0.836082 + 0.548604i \(0.815159\pi\)
\(734\) −9.05587 + 37.6792i −0.334258 + 1.39077i
\(735\) 5.05152 4.11837i 0.186328 0.151909i
\(736\) −7.47894 18.1193i −0.275677 0.667887i
\(737\) 0.431964 + 0.115744i 0.0159116 + 0.00426350i
\(738\) 0.00993359 + 0.382981i 0.000365660 + 0.0140977i
\(739\) 15.6220 27.0581i 0.574665 0.995349i −0.421413 0.906869i \(-0.638466\pi\)
0.996078 0.0884798i \(-0.0282009\pi\)
\(740\) −3.15201 0.955828i −0.115870 0.0351369i
\(741\) 3.99829 0.146881
\(742\) 47.7257 13.6861i 1.75207 0.502434i
\(743\) −13.4261 + 13.4261i −0.492557 + 0.492557i −0.909111 0.416554i \(-0.863238\pi\)
0.416554 + 0.909111i \(0.363238\pi\)
\(744\) −1.74989 + 9.40251i −0.0641542 + 0.344713i
\(745\) 2.18224 25.7655i 0.0799512 0.943975i
\(746\) 22.4889 + 21.3518i 0.823378 + 0.781745i
\(747\) 4.51950 16.8670i 0.165360 0.617131i
\(748\) 8.16615 2.64886i 0.298584 0.0968520i
\(749\) 35.6289 9.22443i 1.30185 0.337053i
\(750\) −5.81106 3.09471i −0.212190 0.113003i
\(751\) −29.3693 + 16.9564i −1.07170 + 0.618748i −0.928646 0.370967i \(-0.879026\pi\)
−0.143056 + 0.989715i \(0.545693\pi\)
\(752\) −16.9937 13.7892i −0.619696 0.502840i
\(753\) 5.96698 1.59885i 0.217449 0.0582652i
\(754\) 3.30336 + 11.1621i 0.120301 + 0.406501i
\(755\) 9.74730 4.57818i 0.354741 0.166617i
\(756\) −12.2447 + 3.85767i −0.445337 + 0.140302i
\(757\) 10.7202 10.7202i 0.389633 0.389633i −0.484924 0.874556i \(-0.661153\pi\)
0.874556 + 0.484924i \(0.161153\pi\)
\(758\) −13.8129 + 25.4252i −0.501708 + 0.923484i
\(759\) 0.604493 1.04701i 0.0219417 0.0380041i
\(760\) −36.9018 0.247225i −1.33857 0.00896779i
\(761\) 12.2719 + 21.2555i 0.444854 + 0.770510i 0.998042 0.0625464i \(-0.0199221\pi\)
−0.553188 + 0.833057i \(0.686589\pi\)
\(762\) −1.97744 3.22869i −0.0716351 0.116963i
\(763\) −0.238633 + 28.2106i −0.00863911 + 1.02129i
\(764\) −4.98927 2.54528i −0.180506 0.0920851i
\(765\) 31.8721 5.71105i 1.15234 0.206484i
\(766\) 7.07584 7.45268i 0.255661 0.269276i
\(767\) −14.2089 + 3.80726i −0.513054 + 0.137472i
\(768\) −3.63963 + 5.58025i −0.131334 + 0.201360i
\(769\) 38.3029i 1.38124i 0.723219 + 0.690619i \(0.242662\pi\)
−0.723219 + 0.690619i \(0.757338\pi\)
\(770\) −6.29224 + 3.09070i −0.226757 + 0.111381i
\(771\) 6.32315i 0.227723i
\(772\) −12.8484 11.5803i −0.462423 0.416784i
\(773\) −1.38674 + 0.371576i −0.0498776 + 0.0133647i −0.283672 0.958922i \(-0.591553\pi\)
0.233794 + 0.972286i \(0.424886\pi\)
\(774\) −20.0057 18.9942i −0.719091 0.682731i
\(775\) −6.82888 + 40.0247i −0.245301 + 1.43773i
\(776\) 11.0362 12.9023i 0.396178 0.463166i
\(777\) 0.706087 0.399734i 0.0253307 0.0143404i
\(778\) 6.69829 4.10243i 0.240145 0.147079i
\(779\) −0.279601 0.484282i −0.0100177 0.0173512i
\(780\) 1.61803 2.60255i 0.0579347 0.0931861i
\(781\) −5.71840 + 9.90456i −0.204620 + 0.354413i
\(782\) −22.0600 11.9847i −0.788864 0.428572i
\(783\) 8.58072 8.58072i 0.306650 0.306650i
\(784\) −16.0497 22.9436i −0.573202 0.819414i
\(785\) −8.97465 3.23836i −0.320319 0.115582i
\(786\) 7.79449 2.30673i 0.278020 0.0822783i
\(787\) 13.8248 3.70435i 0.492801 0.132046i −0.00385583 0.999993i \(-0.501227\pi\)
0.496657 + 0.867947i \(0.334561\pi\)
\(788\) 13.5570 + 2.88867i 0.482949 + 0.102905i
\(789\) −4.22637 + 2.44010i −0.150463 + 0.0868698i
\(790\) −18.4555 + 28.0368i −0.656619 + 0.997503i
\(791\) 5.61441 20.2660i 0.199625 0.720575i
\(792\) 6.67861 0.520614i 0.237314 0.0184992i
\(793\) 0.783185 2.92289i 0.0278117 0.103795i
\(794\) −29.3027 + 30.8632i −1.03991 + 1.09529i
\(795\) 12.3108 + 1.04268i 0.436618 + 0.0369799i
\(796\) 24.7610 1.28534i 0.877631 0.0455578i
\(797\) −9.85742 + 9.85742i −0.349168 + 0.349168i −0.859800 0.510632i \(-0.829412\pi\)
0.510632 + 0.859800i \(0.329412\pi\)
\(798\) 6.31475 6.53938i 0.223540 0.231491i
\(799\) −28.0283 −0.991569
\(800\) −15.0943 + 23.9199i −0.533666 + 0.845695i
\(801\) 4.08761 7.07995i 0.144429 0.250158i
\(802\) −6.55867 + 0.170116i −0.231595 + 0.00600699i
\(803\) −4.84926 1.29936i −0.171127 0.0458533i
\(804\) −0.201984 + 0.395930i −0.00712342 + 0.0139634i
\(805\) 19.2239 + 7.12100i 0.677554 + 0.250982i
\(806\) −18.3761 4.41654i −0.647271 0.155566i
\(807\) −2.22995 + 8.32229i −0.0784980 + 0.292959i
\(808\) −2.09740 + 4.38889i −0.0737864 + 0.154400i
\(809\) 30.8498 + 17.8112i 1.08462 + 0.626207i 0.932140 0.362099i \(-0.117940\pi\)
0.152483 + 0.988306i \(0.451273\pi\)
\(810\) 23.5805 + 1.38252i 0.828534 + 0.0485769i
\(811\) 11.1150i 0.390299i −0.980774 0.195149i \(-0.937481\pi\)
0.980774 0.195149i \(-0.0625192\pi\)
\(812\) 23.4734 + 12.2263i 0.823754 + 0.429058i
\(813\) −6.21267 6.21267i −0.217888 0.217888i
\(814\) −0.836851 + 0.247661i −0.0293316 + 0.00868050i
\(815\) 13.8958 11.7257i 0.486747 0.410734i
\(816\) 0.883481 + 8.48680i 0.0309280 + 0.297098i
\(817\) 38.8940 + 10.4216i 1.36073 + 0.364607i
\(818\) −41.8979 + 25.6608i −1.46493 + 0.897207i
\(819\) −3.08467 11.9144i −0.107787 0.416322i
\(820\) −0.428376 0.0139834i −0.0149595 0.000488321i
\(821\) −6.79984 11.7777i −0.237316 0.411043i 0.722627 0.691238i \(-0.242934\pi\)
−0.959943 + 0.280195i \(0.909601\pi\)
\(822\) 0.219598 + 8.46641i 0.00765936 + 0.295300i
\(823\) −6.57048 24.5214i −0.229033 0.854761i −0.980749 0.195274i \(-0.937440\pi\)
0.751716 0.659487i \(-0.229226\pi\)
\(824\) −43.6785 8.12897i −1.52161 0.283186i
\(825\) −1.73696 + 0.161672i −0.0604731 + 0.00562869i
\(826\) −16.2141 + 29.2524i −0.564160 + 1.01782i
\(827\) −17.3478 17.3478i −0.603242 0.603242i 0.337929 0.941172i \(-0.390274\pi\)
−0.941172 + 0.337929i \(0.890274\pi\)
\(828\) −14.5514 13.1152i −0.505696 0.455786i
\(829\) −16.3045 9.41343i −0.566280 0.326942i 0.189382 0.981903i \(-0.439351\pi\)
−0.755662 + 0.654962i \(0.772685\pi\)
\(830\) 18.5417 + 6.15197i 0.643591 + 0.213538i
\(831\) −1.17942 + 0.680936i −0.0409135 + 0.0236214i
\(832\) −10.6395 7.75428i −0.368858 0.268831i
\(833\) −34.4769 9.86610i −1.19455 0.341840i
\(834\) −0.833737 0.200381i −0.0288700 0.00693864i
\(835\) 17.1401 3.07127i 0.593156 0.106286i
\(836\) −8.20309 + 5.32136i −0.283710 + 0.184043i
\(837\) 5.09924 + 19.0306i 0.176255 + 0.657794i
\(838\) −18.9917 + 34.9576i −0.656056 + 1.20759i
\(839\) 3.21211 0.110894 0.0554472 0.998462i \(-0.482342\pi\)
0.0554472 + 0.998462i \(0.482342\pi\)
\(840\) −1.70112 6.75673i −0.0586943 0.233129i
\(841\) 3.98283 0.137339
\(842\) −2.66410 + 4.90377i −0.0918111 + 0.168995i
\(843\) −0.280301 1.04610i −0.00965408 0.0360295i
\(844\) −1.47224 + 0.955043i −0.0506765 + 0.0328739i
\(845\) −18.8877 13.1474i −0.649757 0.452286i
\(846\) −21.2649 5.11082i −0.731101 0.175714i
\(847\) 13.8220 23.4795i 0.474929 0.806764i
\(848\) 8.35517 52.4156i 0.286918 1.79996i
\(849\) 9.99440 5.77027i 0.343007 0.198035i
\(850\) 4.29131 + 35.9698i 0.147191 + 1.23375i
\(851\) 2.21021 + 1.27607i 0.0757652 + 0.0437430i
\(852\) −8.44360 7.61024i −0.289273 0.260723i
\(853\) −31.7184 31.7184i −1.08602 1.08602i −0.995934 0.0900831i \(-0.971287\pi\)
−0.0900831 0.995934i \(-0.528713\pi\)
\(854\) −3.54358 5.89724i −0.121259 0.201799i
\(855\) −33.3804 + 15.6783i −1.14158 + 0.536187i
\(856\) 7.19881 38.6805i 0.246050 1.32207i
\(857\) 9.50091 + 35.4579i 0.324545 + 1.21122i 0.914769 + 0.403978i \(0.132373\pi\)
−0.590224 + 0.807240i \(0.700960\pi\)
\(858\) −0.0210540 0.811718i −0.000718771 0.0277116i
\(859\) −5.30651 9.19114i −0.181056 0.313598i 0.761185 0.648535i \(-0.224618\pi\)
−0.942240 + 0.334938i \(0.891285\pi\)
\(860\) 22.5233 21.0993i 0.768037 0.719480i
\(861\) 0.0752872 0.0740242i 0.00256578 0.00252274i
\(862\) −16.8988 + 10.3498i −0.575576 + 0.352517i
\(863\) 21.1660 + 5.67140i 0.720498 + 0.193057i 0.600394 0.799705i \(-0.295011\pi\)
0.120104 + 0.992761i \(0.461677\pi\)
\(864\) −1.80828 + 13.6048i −0.0615191 + 0.462844i
\(865\) 4.51506 + 5.35065i 0.153517 + 0.181928i
\(866\) 4.25653 1.25969i 0.144643 0.0428061i
\(867\) 2.72198 + 2.72198i 0.0924434 + 0.0924434i
\(868\) −36.2461 + 23.0796i −1.23027 + 0.783374i
\(869\) 8.89379i 0.301701i
\(870\) 4.37645 + 4.92160i 0.148376 + 0.166858i
\(871\) −0.760656 0.439165i −0.0257739 0.0148805i
\(872\) 27.2118 + 13.0042i 0.921507 + 0.440379i
\(873\) 4.39154 16.3894i 0.148631 0.554698i
\(874\) 27.8020 + 6.68197i 0.940417 + 0.226021i
\(875\) −7.65188 28.5736i −0.258681 0.965963i
\(876\) 2.26749 4.44474i 0.0766114 0.150174i
\(877\) −11.0320 2.95602i −0.372524 0.0998175i 0.0676994 0.997706i \(-0.478434\pi\)
−0.440224 + 0.897888i \(0.645101\pi\)
\(878\) 35.3895 0.917916i 1.19434 0.0309782i
\(879\) 3.51032 6.08006i 0.118400 0.205075i
\(880\) 0.144125 + 7.49297i 0.00485844 + 0.252588i
\(881\) 27.2610 0.918447 0.459224 0.888321i \(-0.348128\pi\)
0.459224 + 0.888321i \(0.348128\pi\)
\(882\) −24.3583 13.7720i −0.820187 0.463729i
\(883\) −29.9932 + 29.9932i −1.00935 + 1.00935i −0.00939636 + 0.999956i \(0.502991\pi\)
−0.999956 + 0.00939636i \(0.997009\pi\)
\(884\) −16.8388 + 0.874102i −0.566350 + 0.0293992i
\(885\) −6.36066 + 5.36734i −0.213811 + 0.180421i
\(886\) 4.28700 4.51531i 0.144024 0.151695i
\(887\) −5.85632 + 21.8561i −0.196636 + 0.733855i 0.795201 + 0.606345i \(0.207365\pi\)
−0.991837 + 0.127510i \(0.959302\pi\)
\(888\) −0.0674121 0.864784i −0.00226220 0.0290202i
\(889\) 4.54155 16.3933i 0.152319 0.549815i
\(890\) 7.63946 + 5.02877i 0.256075 + 0.168565i
\(891\) 5.42024 3.12937i 0.181585 0.104838i
\(892\) −34.8720 7.43038i −1.16760 0.248787i
\(893\) 30.8351 8.26224i 1.03186 0.276485i
\(894\) 6.52969 1.93242i 0.218386 0.0646298i
\(895\) −15.3098 32.5957i −0.511749 1.08956i
\(896\) −29.4861 + 5.15453i −0.985062 + 0.172201i
\(897\) −1.67904 + 1.67904i −0.0560615 + 0.0560615i
\(898\) 30.1042 + 16.3549i 1.00459 + 0.545772i
\(899\) 20.3085 35.1754i 0.677327 1.17317i
\(900\) −3.30313 + 28.0725i −0.110104 + 0.935750i
\(901\) −33.9892 58.8710i −1.13234 1.96128i
\(902\) −0.0968451 + 0.0593137i −0.00322459 + 0.00197493i
\(903\) −0.0643086 + 7.60237i −0.00214005 + 0.252991i
\(904\) −17.0840 14.6131i −0.568206 0.486026i
\(905\) −4.89599 + 7.03362i −0.162748 + 0.233805i
\(906\) 2.05667 + 1.95268i 0.0683284 + 0.0648734i
\(907\) −4.01423 + 1.07561i −0.133290 + 0.0357151i −0.324847 0.945766i \(-0.605313\pi\)
0.191557 + 0.981481i \(0.438646\pi\)
\(908\) 15.6006 + 14.0609i 0.517725 + 0.466627i
\(909\) 4.86119i 0.161235i
\(910\) 13.5083 2.66491i 0.447797 0.0883409i
\(911\) 29.4464i 0.975603i 0.872955 + 0.487801i \(0.162201\pi\)
−0.872955 + 0.487801i \(0.837799\pi\)
\(912\) −3.47371 9.07626i −0.115026 0.300545i
\(913\) 4.99989 1.33972i 0.165472 0.0443381i
\(914\) −9.11881 + 9.60445i −0.301624 + 0.317687i
\(915\) −0.301964 1.68519i −0.00998262 0.0557108i
\(916\) 48.5454 + 24.7655i 1.60398 + 0.818274i
\(917\) 31.4731 + 18.5277i 1.03933 + 0.611838i
\(918\) 9.18048 + 14.9895i 0.303001 + 0.494728i
\(919\) 4.57597 + 7.92582i 0.150947 + 0.261449i 0.931576 0.363547i \(-0.118434\pi\)
−0.780629 + 0.624995i \(0.785101\pi\)
\(920\) 15.6003 15.3927i 0.514328 0.507482i
\(921\) −3.83837 + 6.64825i −0.126479 + 0.219067i
\(922\) −8.34320 + 15.3572i −0.274769 + 0.505762i
\(923\) 15.8834 15.8834i 0.522809 0.522809i
\(924\) −1.36085 1.24756i −0.0447688 0.0410419i
\(925\) −0.341285 3.66667i −0.0112214 0.120559i
\(926\) 16.8443 + 56.9174i 0.553539 + 1.87042i
\(927\) −42.8871 + 11.4916i −1.40860 + 0.377433i
\(928\) 22.4685 17.1964i 0.737564 0.564500i
\(929\) −26.0531 + 15.0417i −0.854773 + 0.493504i −0.862259 0.506468i \(-0.830951\pi\)
0.00748525 + 0.999972i \(0.497617\pi\)
\(930\) −10.4728 + 2.15824i −0.343415 + 0.0707716i
\(931\) 40.8378 + 0.690945i 1.33841 + 0.0226448i
\(932\) 24.9864 8.10485i 0.818456 0.265483i
\(933\) 1.26244 4.71148i 0.0413303 0.154247i
\(934\) −37.1195 35.2426i −1.21459 1.15317i
\(935\) 6.19005 + 7.33562i 0.202436 + 0.239901i
\(936\) −12.9349 2.40730i −0.422789 0.0786850i
\(937\) −6.79581 + 6.79581i −0.222009 + 0.222009i −0.809344 0.587335i \(-0.800177\pi\)
0.587335 + 0.809344i \(0.300177\pi\)
\(938\) −1.91963 + 0.550485i −0.0626781 + 0.0179740i
\(939\) −7.95230 −0.259514
\(940\) 7.10035 23.4146i 0.231588 0.763701i
\(941\) −9.08044 + 15.7278i −0.296014 + 0.512711i −0.975220 0.221236i \(-0.928991\pi\)
0.679206 + 0.733947i \(0.262324\pi\)
\(942\) −0.0651496 2.51179i −0.00212269 0.0818384i
\(943\) 0.320785 + 0.0859540i 0.0104462 + 0.00279905i
\(944\) 20.9873 + 28.9470i 0.683080 + 0.942144i
\(945\) −9.16348 11.0476i −0.298088 0.359379i
\(946\) 1.91096 7.95101i 0.0621306 0.258510i
\(947\) 4.55237 16.9897i 0.147932 0.552091i −0.851675 0.524070i \(-0.824413\pi\)
0.999607 0.0280205i \(-0.00892037\pi\)
\(948\) −8.64549 1.84214i −0.280792 0.0598300i
\(949\) 8.53920 + 4.93011i 0.277194 + 0.160038i
\(950\) −15.3243 38.3069i −0.497186 1.24284i
\(951\) 1.20251i 0.0389940i
\(952\) −25.1650 + 28.9211i −0.815602 + 0.937340i
\(953\) 12.8804 + 12.8804i 0.417238 + 0.417238i 0.884251 0.467013i \(-0.154670\pi\)
−0.467013 + 0.884251i \(0.654670\pi\)
\(954\) −15.0525 50.8628i −0.487343 1.64674i
\(955\) 0.528486 6.23978i 0.0171014 0.201915i
\(956\) −11.6549 17.9664i −0.376945 0.581076i
\(957\) 1.68560 + 0.451656i 0.0544878 + 0.0146000i
\(958\) −23.5363 38.4291i −0.760423 1.24159i
\(959\) −27.1334 + 26.6782i −0.876183 + 0.861484i
\(960\) −7.31362 1.41189i −0.236046 0.0455686i
\(961\) 17.4723 + 30.2629i 0.563622 + 0.976222i
\(962\) 1.71351 0.0444444i 0.0552459 0.00143294i
\(963\) −10.1766 37.9798i −0.327938 1.22388i
\(964\) 25.1142 1.30368i 0.808875 0.0419887i
\(965\) 6.56378 18.1906i 0.211296 0.585575i
\(966\) 0.0943277 + 5.39796i 0.00303494 + 0.173676i
\(967\) 21.8531 + 21.8531i 0.702748 + 0.702748i 0.965000 0.262251i \(-0.0844649\pi\)
−0.262251 + 0.965000i \(0.584465\pi\)
\(968\) −16.4798 24.0166i −0.529681 0.771922i
\(969\) −10.7791 6.22331i −0.346274 0.199922i
\(970\) 18.0167 + 5.97778i 0.578481 + 0.191935i
\(971\) −49.5916 + 28.6317i −1.59147 + 0.918836i −0.598416 + 0.801186i \(0.704203\pi\)
−0.993055 + 0.117650i \(0.962464\pi\)
\(972\) 6.41081 + 19.7638i 0.205627 + 0.633925i
\(973\) −1.89801 3.35263i −0.0608475 0.107480i
\(974\) −3.30035 + 13.7319i −0.105750 + 0.440000i
\(975\) 3.37743 + 0.576245i 0.108164 + 0.0184546i
\(976\) −7.31550 + 0.761547i −0.234163 + 0.0243765i
\(977\) −6.27313 23.4116i −0.200695 0.749004i −0.990719 0.135928i \(-0.956598\pi\)
0.790024 0.613076i \(-0.210068\pi\)
\(978\) 4.20741 + 2.28579i 0.134538 + 0.0730914i
\(979\) 2.42338 0.0774516
\(980\) 16.9760 26.3024i 0.542279 0.840198i
\(981\) 30.1401 0.962300
\(982\) −20.3178 11.0382i −0.648366 0.352243i
\(983\) −3.67869 13.7291i −0.117332 0.437889i 0.882119 0.471027i \(-0.156117\pi\)
−0.999451 + 0.0331380i \(0.989450\pi\)
\(984\) −0.0375985 0.106427i −0.00119860 0.00339276i
\(985\) 2.73340 + 15.2545i 0.0870934 + 0.486049i
\(986\) 8.46817 35.2339i 0.269682 1.12208i
\(987\) 2.96942 + 5.24515i 0.0945176 + 0.166955i
\(988\) 18.2674 5.92542i 0.581164 0.188513i
\(989\) −20.7096 + 11.9567i −0.658527 + 0.380201i
\(990\) 3.35873 + 6.69421i 0.106747 + 0.212756i
\(991\) −40.1223 23.1646i −1.27453 0.735848i −0.298689 0.954350i \(-0.596549\pi\)
−0.975836 + 0.218503i \(0.929883\pi\)
\(992\) 5.93948 + 45.5516i 0.188579 + 1.44626i
\(993\) 10.2670 + 10.2670i 0.325812 + 0.325812i
\(994\) −0.892324 51.0638i −0.0283028 1.61964i
\(995\) 11.7850 + 25.0911i 0.373609 + 0.795442i
\(996\) 0.266702 + 5.13778i 0.00845079 + 0.162797i
\(997\) −11.9107 44.4512i −0.377214 1.40778i −0.850083 0.526649i \(-0.823448\pi\)
0.472869 0.881133i \(-0.343219\pi\)
\(998\) 13.4251 0.348214i 0.424965 0.0110225i
\(999\) −0.893438 1.54748i −0.0282671 0.0489601i
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 140.2.w.b.123.6 yes 72
4.3 odd 2 inner 140.2.w.b.123.8 yes 72
5.2 odd 4 inner 140.2.w.b.67.4 yes 72
5.3 odd 4 700.2.be.e.207.15 72
5.4 even 2 700.2.be.e.543.13 72
7.2 even 3 inner 140.2.w.b.23.18 yes 72
7.3 odd 6 980.2.k.j.883.7 36
7.4 even 3 980.2.k.k.883.7 36
7.5 odd 6 980.2.x.m.863.18 72
7.6 odd 2 980.2.x.m.263.6 72
20.3 even 4 700.2.be.e.207.1 72
20.7 even 4 inner 140.2.w.b.67.18 yes 72
20.19 odd 2 700.2.be.e.543.11 72
28.3 even 6 980.2.k.j.883.15 36
28.11 odd 6 980.2.k.k.883.15 36
28.19 even 6 980.2.x.m.863.4 72
28.23 odd 6 inner 140.2.w.b.23.4 72
28.27 even 2 980.2.x.m.263.8 72
35.2 odd 12 inner 140.2.w.b.107.8 yes 72
35.9 even 6 700.2.be.e.443.1 72
35.12 even 12 980.2.x.m.667.8 72
35.17 even 12 980.2.k.j.687.15 36
35.23 odd 12 700.2.be.e.107.11 72
35.27 even 4 980.2.x.m.67.4 72
35.32 odd 12 980.2.k.k.687.15 36
140.23 even 12 700.2.be.e.107.13 72
140.27 odd 4 980.2.x.m.67.18 72
140.47 odd 12 980.2.x.m.667.6 72
140.67 even 12 980.2.k.k.687.7 36
140.79 odd 6 700.2.be.e.443.15 72
140.87 odd 12 980.2.k.j.687.7 36
140.107 even 12 inner 140.2.w.b.107.6 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.w.b.23.4 72 28.23 odd 6 inner
140.2.w.b.23.18 yes 72 7.2 even 3 inner
140.2.w.b.67.4 yes 72 5.2 odd 4 inner
140.2.w.b.67.18 yes 72 20.7 even 4 inner
140.2.w.b.107.6 yes 72 140.107 even 12 inner
140.2.w.b.107.8 yes 72 35.2 odd 12 inner
140.2.w.b.123.6 yes 72 1.1 even 1 trivial
140.2.w.b.123.8 yes 72 4.3 odd 2 inner
700.2.be.e.107.11 72 35.23 odd 12
700.2.be.e.107.13 72 140.23 even 12
700.2.be.e.207.1 72 20.3 even 4
700.2.be.e.207.15 72 5.3 odd 4
700.2.be.e.443.1 72 35.9 even 6
700.2.be.e.443.15 72 140.79 odd 6
700.2.be.e.543.11 72 20.19 odd 2
700.2.be.e.543.13 72 5.4 even 2
980.2.k.j.687.7 36 140.87 odd 12
980.2.k.j.687.15 36 35.17 even 12
980.2.k.j.883.7 36 7.3 odd 6
980.2.k.j.883.15 36 28.3 even 6
980.2.k.k.687.7 36 140.67 even 12
980.2.k.k.687.15 36 35.32 odd 12
980.2.k.k.883.7 36 7.4 even 3
980.2.k.k.883.15 36 28.11 odd 6
980.2.x.m.67.4 72 35.27 even 4
980.2.x.m.67.18 72 140.27 odd 4
980.2.x.m.263.6 72 7.6 odd 2
980.2.x.m.263.8 72 28.27 even 2
980.2.x.m.667.6 72 140.47 odd 12
980.2.x.m.667.8 72 35.12 even 12
980.2.x.m.863.4 72 28.19 even 6
980.2.x.m.863.18 72 7.5 odd 6