Properties

Label 99.2.m.b.49.9
Level $99$
Weight $2$
Character 99.49
Analytic conductor $0.791$
Analytic rank $0$
Dimension $72$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,2,Mod(4,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 99.m (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.790518980011\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(9\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 49.9
Character \(\chi\) \(=\) 99.49
Dual form 99.2.m.b.97.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.55841 - 1.73079i) q^{2} +(0.0128080 + 1.73200i) q^{3} +(-0.357932 - 3.40549i) q^{4} +(-0.212128 - 0.235592i) q^{5} +(3.01769 + 2.67700i) q^{6} +(-1.29586 - 0.576953i) q^{7} +(-2.68358 - 1.94973i) q^{8} +(-2.99967 + 0.0443670i) q^{9} -0.738340 q^{10} +(2.21923 + 2.46476i) q^{11} +(5.89374 - 0.663556i) q^{12} +(-4.10532 - 0.872613i) q^{13} +(-3.01805 + 1.34372i) q^{14} +(0.405329 - 0.370423i) q^{15} +(-0.857827 + 0.182337i) q^{16} +(-1.92957 + 5.93860i) q^{17} +(-4.59792 + 5.26093i) q^{18} +(-2.50622 - 1.82087i) q^{19} +(-0.726379 + 0.806725i) q^{20} +(0.982687 - 2.25182i) q^{21} +(7.72443 + 7.98214e-5i) q^{22} +(2.26025 - 3.91487i) q^{23} +(3.34257 - 4.67294i) q^{24} +(0.512137 - 4.87266i) q^{25} +(-7.90807 + 5.74555i) q^{26} +(-0.115264 - 5.19487i) q^{27} +(-1.50098 + 4.61954i) q^{28} +(2.67527 + 1.19111i) q^{29} +(-0.00945666 - 1.27881i) q^{30} +(9.33325 + 1.98384i) q^{31} +(2.29583 - 3.97649i) q^{32} +(-4.24054 + 3.87528i) q^{33} +(7.27140 + 12.5944i) q^{34} +(0.138962 + 0.427681i) q^{35} +(1.22477 + 10.1995i) q^{36} +(-0.685637 + 0.498145i) q^{37} +(-7.05725 + 1.50006i) q^{38} +(1.45879 - 7.12161i) q^{39} +(0.109920 + 1.04582i) q^{40} +(-3.53506 + 1.57391i) q^{41} +(-2.36599 - 5.21007i) q^{42} +(-1.77651 - 3.07700i) q^{43} +(7.59937 - 8.43978i) q^{44} +(0.646766 + 0.697286i) q^{45} +(-3.25341 - 10.0130i) q^{46} +(0.778841 - 7.41018i) q^{47} +(-0.326795 - 1.48342i) q^{48} +(-3.33754 - 3.70672i) q^{49} +(-7.63541 - 8.47998i) q^{50} +(-10.3104 - 3.26596i) q^{51} +(-1.50225 + 14.2930i) q^{52} +(2.06517 + 6.35595i) q^{53} +(-9.17084 - 7.89623i) q^{54} +(0.109916 - 1.04568i) q^{55} +(2.35263 + 4.07487i) q^{56} +(3.12166 - 4.36410i) q^{57} +(6.23070 - 2.77409i) q^{58} +(1.26216 + 12.0086i) q^{59} +(-1.40655 - 1.24776i) q^{60} +(-4.51935 + 0.960618i) q^{61} +(17.9786 - 13.0622i) q^{62} +(3.91274 + 1.67318i) q^{63} +(-3.84663 - 11.8387i) q^{64} +(0.665272 + 1.15229i) q^{65} +(0.0987962 + 13.3787i) q^{66} +(-4.98385 + 8.63229i) q^{67} +(20.9145 + 4.44552i) q^{68} +(6.80951 + 3.86462i) q^{69} +(0.956783 + 0.425987i) q^{70} +(0.905630 - 2.78724i) q^{71} +(8.13635 + 5.72949i) q^{72} +(-3.43158 + 2.49319i) q^{73} +(-0.206320 + 1.96300i) q^{74} +(8.44602 + 0.824614i) q^{75} +(-5.30392 + 9.18665i) q^{76} +(-1.45376 - 4.47436i) q^{77} +(-10.0526 - 13.6232i) q^{78} +(-2.26299 + 2.51331i) q^{79} +(0.224926 + 0.163418i) q^{80} +(8.99606 - 0.266173i) q^{81} +(-2.78496 + 8.57123i) q^{82} +(13.1927 - 2.80420i) q^{83} +(-8.02029 - 2.54054i) q^{84} +(1.80840 - 0.805152i) q^{85} +(-8.09416 - 1.72047i) q^{86} +(-2.02873 + 4.64883i) q^{87} +(-1.14986 - 10.9413i) q^{88} +2.69745 q^{89} +(2.21478 - 0.0327579i) q^{90} +(4.81645 + 3.49936i) q^{91} +(-14.1411 - 6.29601i) q^{92} +(-3.31648 + 16.1906i) q^{93} +(-11.6117 - 12.8961i) q^{94} +(0.102656 + 0.976702i) q^{95} +(6.91669 + 3.92545i) q^{96} +(-3.51792 + 3.90704i) q^{97} -11.6168 q^{98} +(-6.76631 - 7.29500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - q^{2} - 12 q^{3} + 11 q^{4} - 8 q^{5} - 7 q^{6} - 2 q^{7} + 6 q^{8} - 22 q^{9} - 8 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 10 q^{14} - 20 q^{15} - 9 q^{16} - 20 q^{17} - 21 q^{18} + 8 q^{19}+ \cdots - 182 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.55841 1.73079i 1.10196 1.22385i 0.129303 0.991605i \(-0.458726\pi\)
0.972657 0.232245i \(-0.0746072\pi\)
\(3\) 0.0128080 + 1.73200i 0.00739470 + 0.999973i
\(4\) −0.357932 3.40549i −0.178966 1.70275i
\(5\) −0.212128 0.235592i −0.0948664 0.105360i 0.693842 0.720127i \(-0.255917\pi\)
−0.788708 + 0.614767i \(0.789250\pi\)
\(6\) 3.01769 + 2.67700i 1.23197 + 1.09288i
\(7\) −1.29586 0.576953i −0.489788 0.218068i 0.146956 0.989143i \(-0.453052\pi\)
−0.636744 + 0.771075i \(0.719719\pi\)
\(8\) −2.68358 1.94973i −0.948787 0.689334i
\(9\) −2.99967 + 0.0443670i −0.999891 + 0.0147890i
\(10\) −0.738340 −0.233484
\(11\) 2.21923 + 2.46476i 0.669123 + 0.743152i
\(12\) 5.89374 0.663556i 1.70138 0.191552i
\(13\) −4.10532 0.872613i −1.13861 0.242019i −0.400238 0.916411i \(-0.631072\pi\)
−0.738373 + 0.674392i \(0.764406\pi\)
\(14\) −3.01805 + 1.34372i −0.806609 + 0.359125i
\(15\) 0.405329 0.370423i 0.104655 0.0956429i
\(16\) −0.857827 + 0.182337i −0.214457 + 0.0455842i
\(17\) −1.92957 + 5.93860i −0.467989 + 1.44032i 0.387195 + 0.921998i \(0.373444\pi\)
−0.855184 + 0.518325i \(0.826556\pi\)
\(18\) −4.59792 + 5.26093i −1.08374 + 1.24001i
\(19\) −2.50622 1.82087i −0.574966 0.417737i 0.261940 0.965084i \(-0.415638\pi\)
−0.836906 + 0.547347i \(0.815638\pi\)
\(20\) −0.726379 + 0.806725i −0.162423 + 0.180389i
\(21\) 0.982687 2.25182i 0.214440 0.491387i
\(22\) 7.72443 7.98214e-5i 1.64685 1.70180e-5i
\(23\) 2.26025 3.91487i 0.471295 0.816306i −0.528166 0.849141i \(-0.677120\pi\)
0.999461 + 0.0328349i \(0.0104536\pi\)
\(24\) 3.34257 4.67294i 0.682300 0.953859i
\(25\) 0.512137 4.87266i 0.102427 0.974532i
\(26\) −7.90807 + 5.74555i −1.55090 + 1.12679i
\(27\) −0.115264 5.19487i −0.0221825 0.999754i
\(28\) −1.50098 + 4.61954i −0.283659 + 0.873011i
\(29\) 2.67527 + 1.19111i 0.496785 + 0.221183i 0.639805 0.768537i \(-0.279015\pi\)
−0.143021 + 0.989720i \(0.545682\pi\)
\(30\) −0.00945666 1.27881i −0.00172654 0.233477i
\(31\) 9.33325 + 1.98384i 1.67630 + 0.356309i 0.945334 0.326103i \(-0.105736\pi\)
0.730967 + 0.682412i \(0.239069\pi\)
\(32\) 2.29583 3.97649i 0.405848 0.702950i
\(33\) −4.24054 + 3.87528i −0.738183 + 0.674600i
\(34\) 7.27140 + 12.5944i 1.24703 + 2.15993i
\(35\) 0.138962 + 0.427681i 0.0234889 + 0.0722913i
\(36\) 1.22477 + 10.1995i 0.204128 + 1.69991i
\(37\) −0.685637 + 0.498145i −0.112718 + 0.0818945i −0.642716 0.766104i \(-0.722193\pi\)
0.529998 + 0.847999i \(0.322193\pi\)
\(38\) −7.05725 + 1.50006i −1.14484 + 0.243343i
\(39\) 1.45879 7.12161i 0.233593 1.14037i
\(40\) 0.109920 + 1.04582i 0.0173799 + 0.165359i
\(41\) −3.53506 + 1.57391i −0.552084 + 0.245804i −0.663766 0.747940i \(-0.731043\pi\)
0.111682 + 0.993744i \(0.464376\pi\)
\(42\) −2.36599 5.21007i −0.365080 0.803931i
\(43\) −1.77651 3.07700i −0.270915 0.469239i 0.698181 0.715921i \(-0.253993\pi\)
−0.969096 + 0.246682i \(0.920660\pi\)
\(44\) 7.59937 8.43978i 1.14565 1.27235i
\(45\) 0.646766 + 0.697286i 0.0964142 + 0.103945i
\(46\) −3.25341 10.0130i −0.479689 1.47633i
\(47\) 0.778841 7.41018i 0.113606 1.08089i −0.778059 0.628191i \(-0.783796\pi\)
0.891665 0.452695i \(-0.149538\pi\)
\(48\) −0.326795 1.48342i −0.0471688 0.214114i
\(49\) −3.33754 3.70672i −0.476792 0.529531i
\(50\) −7.63541 8.47998i −1.07981 1.19925i
\(51\) −10.3104 3.26596i −1.44374 0.457326i
\(52\) −1.50225 + 14.2930i −0.208325 + 1.98208i
\(53\) 2.06517 + 6.35595i 0.283673 + 0.873057i 0.986793 + 0.161986i \(0.0517898\pi\)
−0.703120 + 0.711071i \(0.748210\pi\)
\(54\) −9.17084 7.89623i −1.24799 1.07454i
\(55\) 0.109916 1.04568i 0.0148210 0.140999i
\(56\) 2.35263 + 4.07487i 0.314383 + 0.544528i
\(57\) 3.12166 4.36410i 0.413474 0.578039i
\(58\) 6.23070 2.77409i 0.818132 0.364256i
\(59\) 1.26216 + 12.0086i 0.164319 + 1.56339i 0.696998 + 0.717073i \(0.254518\pi\)
−0.532680 + 0.846317i \(0.678815\pi\)
\(60\) −1.40655 1.24776i −0.181585 0.161085i
\(61\) −4.51935 + 0.960618i −0.578644 + 0.122995i −0.487931 0.872882i \(-0.662248\pi\)
−0.0907135 + 0.995877i \(0.528915\pi\)
\(62\) 17.9786 13.0622i 2.28329 1.65890i
\(63\) 3.91274 + 1.67318i 0.492960 + 0.210800i
\(64\) −3.84663 11.8387i −0.480828 1.47984i
\(65\) 0.665272 + 1.15229i 0.0825169 + 0.142923i
\(66\) 0.0987962 + 13.3787i 0.0121610 + 1.64681i
\(67\) −4.98385 + 8.63229i −0.608875 + 1.05460i 0.382552 + 0.923934i \(0.375045\pi\)
−0.991426 + 0.130668i \(0.958288\pi\)
\(68\) 20.9145 + 4.44552i 2.53626 + 0.539098i
\(69\) 6.80951 + 3.86462i 0.819769 + 0.465245i
\(70\) 0.956783 + 0.425987i 0.114357 + 0.0509152i
\(71\) 0.905630 2.78724i 0.107479 0.330785i −0.882826 0.469701i \(-0.844362\pi\)
0.990304 + 0.138916i \(0.0443618\pi\)
\(72\) 8.13635 + 5.72949i 0.958878 + 0.675227i
\(73\) −3.43158 + 2.49319i −0.401636 + 0.291806i −0.770207 0.637794i \(-0.779847\pi\)
0.368571 + 0.929600i \(0.379847\pi\)
\(74\) −0.206320 + 1.96300i −0.0239842 + 0.228195i
\(75\) 8.44602 + 0.824614i 0.975262 + 0.0952182i
\(76\) −5.30392 + 9.18665i −0.608401 + 1.05378i
\(77\) −1.45376 4.47436i −0.165671 0.509901i
\(78\) −10.0526 13.6232i −1.13823 1.54252i
\(79\) −2.26299 + 2.51331i −0.254606 + 0.282769i −0.856875 0.515525i \(-0.827597\pi\)
0.602268 + 0.798294i \(0.294264\pi\)
\(80\) 0.224926 + 0.163418i 0.0251475 + 0.0182707i
\(81\) 8.99606 0.266173i 0.999563 0.0295748i
\(82\) −2.78496 + 8.57123i −0.307548 + 0.946534i
\(83\) 13.1927 2.80420i 1.44809 0.307801i 0.584253 0.811571i \(-0.301387\pi\)
0.863838 + 0.503770i \(0.168054\pi\)
\(84\) −8.02029 2.54054i −0.875085 0.277195i
\(85\) 1.80840 0.805152i 0.196149 0.0873310i
\(86\) −8.09416 1.72047i −0.872815 0.185523i
\(87\) −2.02873 + 4.64883i −0.217503 + 0.498407i
\(88\) −1.14986 10.9413i −0.122575 1.16634i
\(89\) 2.69745 0.285929 0.142965 0.989728i \(-0.454336\pi\)
0.142965 + 0.989728i \(0.454336\pi\)
\(90\) 2.21478 0.0327579i 0.233458 0.00345299i
\(91\) 4.81645 + 3.49936i 0.504902 + 0.366833i
\(92\) −14.1411 6.29601i −1.47431 0.656404i
\(93\) −3.31648 + 16.1906i −0.343903 + 1.67889i
\(94\) −11.6117 12.8961i −1.19765 1.33013i
\(95\) 0.102656 + 0.976702i 0.0105322 + 0.100208i
\(96\) 6.91669 + 3.92545i 0.705932 + 0.400639i
\(97\) −3.51792 + 3.90704i −0.357190 + 0.396700i −0.894781 0.446506i \(-0.852668\pi\)
0.537590 + 0.843206i \(0.319335\pi\)
\(98\) −11.6168 −1.17347
\(99\) −6.76631 7.29500i −0.680040 0.733175i
\(100\) −16.7771 −1.67771
\(101\) −6.37664 + 7.08198i −0.634500 + 0.704683i −0.971558 0.236800i \(-0.923901\pi\)
0.337059 + 0.941484i \(0.390568\pi\)
\(102\) −21.7205 + 12.7554i −2.15065 + 1.26297i
\(103\) −0.996745 9.48339i −0.0982122 0.934426i −0.927050 0.374938i \(-0.877664\pi\)
0.828838 0.559489i \(-0.189003\pi\)
\(104\) 9.31558 + 10.3460i 0.913468 + 1.01451i
\(105\) −0.738965 + 0.246160i −0.0721156 + 0.0240228i
\(106\) 14.2192 + 6.33078i 1.38109 + 0.614900i
\(107\) −4.18472 3.04038i −0.404552 0.293924i 0.366840 0.930284i \(-0.380440\pi\)
−0.771393 + 0.636359i \(0.780440\pi\)
\(108\) −17.6498 + 2.25194i −1.69836 + 0.216693i
\(109\) 14.4767 1.38661 0.693307 0.720643i \(-0.256153\pi\)
0.693307 + 0.720643i \(0.256153\pi\)
\(110\) −1.63855 1.81983i −0.156229 0.173514i
\(111\) −0.871570 1.18115i −0.0827258 0.112109i
\(112\) 1.21682 + 0.258643i 0.114979 + 0.0244395i
\(113\) −6.78911 + 3.02271i −0.638666 + 0.284352i −0.700411 0.713740i \(-0.747000\pi\)
0.0617453 + 0.998092i \(0.480333\pi\)
\(114\) −2.68851 12.2040i −0.251802 1.14301i
\(115\) −1.40177 + 0.297956i −0.130716 + 0.0277845i
\(116\) 3.09874 9.53694i 0.287711 0.885482i
\(117\) 12.3533 + 2.43541i 1.14207 + 0.225154i
\(118\) 22.7513 + 16.5298i 2.09443 + 1.52169i
\(119\) 5.92674 6.58231i 0.543303 0.603400i
\(120\) −1.80996 + 0.203777i −0.165226 + 0.0186022i
\(121\) −1.15004 + 10.9397i −0.104549 + 0.994520i
\(122\) −5.38037 + 9.31907i −0.487116 + 0.843709i
\(123\) −2.77130 6.10258i −0.249880 0.550251i
\(124\) 3.41530 32.4944i 0.306703 2.91808i
\(125\) −2.53897 + 1.84467i −0.227092 + 0.164992i
\(126\) 8.99356 4.16463i 0.801210 0.371015i
\(127\) −4.08040 + 12.5582i −0.362077 + 1.11436i 0.589715 + 0.807612i \(0.299240\pi\)
−0.951791 + 0.306746i \(0.900760\pi\)
\(128\) −18.0955 8.05664i −1.59943 0.712113i
\(129\) 5.30663 3.11633i 0.467222 0.274377i
\(130\) 3.03112 + 0.644285i 0.265847 + 0.0565075i
\(131\) 3.65021 6.32236i 0.318921 0.552387i −0.661342 0.750084i \(-0.730013\pi\)
0.980263 + 0.197697i \(0.0633463\pi\)
\(132\) 14.7151 + 13.0540i 1.28078 + 1.13621i
\(133\) 2.19714 + 3.80556i 0.190516 + 0.329984i
\(134\) 7.17377 + 22.0786i 0.619719 + 1.90730i
\(135\) −1.19942 + 1.12913i −0.103230 + 0.0971802i
\(136\) 16.7568 12.1746i 1.43689 1.04396i
\(137\) −9.59302 + 2.03906i −0.819587 + 0.174209i −0.598579 0.801064i \(-0.704268\pi\)
−0.221008 + 0.975272i \(0.570935\pi\)
\(138\) 17.3008 5.76316i 1.47274 0.490593i
\(139\) 0.990605 + 9.42498i 0.0840220 + 0.799416i 0.952674 + 0.303994i \(0.0983202\pi\)
−0.868652 + 0.495423i \(0.835013\pi\)
\(140\) 1.40673 0.626314i 0.118890 0.0529332i
\(141\) 12.8444 + 1.25405i 1.08170 + 0.105610i
\(142\) −3.41278 5.91111i −0.286394 0.496049i
\(143\) −6.95987 12.0551i −0.582014 1.00810i
\(144\) 2.56511 0.585009i 0.213759 0.0487508i
\(145\) −0.286884 0.882938i −0.0238244 0.0733240i
\(146\) −1.03262 + 9.82474i −0.0854604 + 0.813101i
\(147\) 6.37730 5.82811i 0.525991 0.480694i
\(148\) 1.94184 + 2.15663i 0.159618 + 0.177274i
\(149\) −2.76180 3.06729i −0.226256 0.251282i 0.619319 0.785139i \(-0.287409\pi\)
−0.845575 + 0.533857i \(0.820742\pi\)
\(150\) 14.5896 13.3332i 1.19123 1.08865i
\(151\) 1.85802 17.6779i 0.151204 1.43861i −0.611186 0.791487i \(-0.709307\pi\)
0.762389 0.647119i \(-0.224026\pi\)
\(152\) 3.17541 + 9.77291i 0.257560 + 0.792688i
\(153\) 5.52460 17.8995i 0.446637 1.44709i
\(154\) −10.0097 4.45673i −0.806605 0.359134i
\(155\) −1.51246 2.61967i −0.121484 0.210417i
\(156\) −24.7747 2.41884i −1.98357 0.193662i
\(157\) −1.84286 + 0.820493i −0.147076 + 0.0654825i −0.478955 0.877840i \(-0.658984\pi\)
0.331879 + 0.943322i \(0.392318\pi\)
\(158\) 0.823335 + 7.83351i 0.0655010 + 0.623200i
\(159\) −10.9821 + 3.65830i −0.870935 + 0.290122i
\(160\) −1.42384 + 0.302646i −0.112564 + 0.0239262i
\(161\) −5.18765 + 3.76905i −0.408844 + 0.297043i
\(162\) 13.5588 15.9851i 1.06528 1.25591i
\(163\) −0.488377 1.50307i −0.0382526 0.117729i 0.930107 0.367289i \(-0.119714\pi\)
−0.968359 + 0.249560i \(0.919714\pi\)
\(164\) 6.62526 + 11.4753i 0.517346 + 0.896069i
\(165\) 1.81252 + 0.176982i 0.141105 + 0.0137780i
\(166\) 15.7062 27.2039i 1.21904 2.11143i
\(167\) −14.9868 3.18555i −1.15971 0.246505i −0.412417 0.910995i \(-0.635315\pi\)
−0.747297 + 0.664490i \(0.768649\pi\)
\(168\) −7.02756 + 4.12695i −0.542188 + 0.318401i
\(169\) 4.21612 + 1.87714i 0.324317 + 0.144395i
\(170\) 1.42468 4.38471i 0.109268 0.336292i
\(171\) 7.59862 + 5.35083i 0.581081 + 0.409188i
\(172\) −9.84284 + 7.15124i −0.750510 + 0.545277i
\(173\) 0.103069 0.980638i 0.00783620 0.0745565i −0.989905 0.141733i \(-0.954732\pi\)
0.997741 + 0.0671768i \(0.0213991\pi\)
\(174\) 4.88453 + 10.7561i 0.370295 + 0.815416i
\(175\) −3.47495 + 6.01879i −0.262682 + 0.454978i
\(176\) −2.35313 1.70969i −0.177374 0.128872i
\(177\) −20.7828 + 2.33987i −1.56213 + 0.175875i
\(178\) 4.20373 4.66871i 0.315083 0.349935i
\(179\) 9.08186 + 6.59836i 0.678810 + 0.493185i 0.872963 0.487787i \(-0.162196\pi\)
−0.194153 + 0.980971i \(0.562196\pi\)
\(180\) 2.14311 2.45214i 0.159738 0.182772i
\(181\) 5.53932 17.0483i 0.411735 1.26719i −0.503405 0.864051i \(-0.667919\pi\)
0.915139 0.403138i \(-0.132081\pi\)
\(182\) 13.5626 2.88283i 1.00533 0.213689i
\(183\) −1.72168 7.81523i −0.127270 0.577719i
\(184\) −13.6985 + 6.09896i −1.00987 + 0.449621i
\(185\) 0.262801 + 0.0558602i 0.0193216 + 0.00410692i
\(186\) 22.8541 + 30.9717i 1.67574 + 2.27096i
\(187\) −18.9194 + 8.42321i −1.38352 + 0.615966i
\(188\) −25.5141 −1.86081
\(189\) −2.84783 + 6.79832i −0.207149 + 0.494505i
\(190\) 1.85044 + 1.34442i 0.134245 + 0.0975348i
\(191\) 11.7737 + 5.24200i 0.851917 + 0.379298i 0.785775 0.618513i \(-0.212264\pi\)
0.0661416 + 0.997810i \(0.478931\pi\)
\(192\) 20.4554 6.81400i 1.47624 0.491758i
\(193\) −15.4911 17.2046i −1.11507 1.23841i −0.968447 0.249219i \(-0.919826\pi\)
−0.146624 0.989192i \(-0.546841\pi\)
\(194\) 1.27991 + 12.1775i 0.0918921 + 0.874295i
\(195\) −1.98724 + 1.16701i −0.142309 + 0.0835715i
\(196\) −11.4286 + 12.6927i −0.816327 + 0.906623i
\(197\) 1.07766 0.0767801 0.0383900 0.999263i \(-0.487777\pi\)
0.0383900 + 0.999263i \(0.487777\pi\)
\(198\) −23.1707 + 0.342470i −1.64667 + 0.0243383i
\(199\) 16.4307 1.16474 0.582371 0.812923i \(-0.302125\pi\)
0.582371 + 0.812923i \(0.302125\pi\)
\(200\) −10.8747 + 12.0776i −0.768960 + 0.854017i
\(201\) −15.0150 8.52149i −1.05908 0.601060i
\(202\) 2.31999 + 22.0732i 0.163234 + 1.55307i
\(203\) −2.77955 3.08701i −0.195086 0.216665i
\(204\) −7.43178 + 36.2810i −0.520329 + 2.54018i
\(205\) 1.12069 + 0.498961i 0.0782721 + 0.0348490i
\(206\) −17.9671 13.0538i −1.25182 0.909503i
\(207\) −6.60631 + 11.8436i −0.459171 + 0.823187i
\(208\) 3.68076 0.255215
\(209\) −1.07386 10.2182i −0.0742807 0.706804i
\(210\) −0.725557 + 1.66261i −0.0500682 + 0.114731i
\(211\) 14.6231 + 3.10824i 1.00670 + 0.213980i 0.681618 0.731708i \(-0.261276\pi\)
0.325077 + 0.945688i \(0.394610\pi\)
\(212\) 20.9060 9.30793i 1.43583 0.639271i
\(213\) 4.83911 + 1.53286i 0.331571 + 0.105030i
\(214\) −11.7837 + 2.50471i −0.805520 + 0.171219i
\(215\) −0.348070 + 1.07125i −0.0237382 + 0.0730585i
\(216\) −9.81929 + 14.1656i −0.668118 + 0.963845i
\(217\) −10.9500 7.95563i −0.743333 0.540063i
\(218\) 22.5605 25.0560i 1.52799 1.69701i
\(219\) −4.36217 5.91158i −0.294768 0.399468i
\(220\) −3.60038 3.72050e-5i −0.242738 2.50836e-6i
\(221\) 13.1036 22.6961i 0.881444 1.52671i
\(222\) −3.40257 0.332205i −0.228366 0.0222961i
\(223\) −0.201351 + 1.91573i −0.0134835 + 0.128286i −0.999193 0.0401676i \(-0.987211\pi\)
0.985710 + 0.168454i \(0.0538775\pi\)
\(224\) −5.26931 + 3.82838i −0.352070 + 0.255794i
\(225\) −1.32006 + 14.6391i −0.0880039 + 0.975940i
\(226\) −5.34854 + 16.4611i −0.355779 + 1.09498i
\(227\) −14.6269 6.51230i −0.970819 0.432236i −0.140841 0.990032i \(-0.544980\pi\)
−0.829978 + 0.557796i \(0.811647\pi\)
\(228\) −15.9792 9.06874i −1.05825 0.600592i
\(229\) 0.511498 + 0.108722i 0.0338007 + 0.00718457i 0.224781 0.974409i \(-0.427833\pi\)
−0.190980 + 0.981594i \(0.561167\pi\)
\(230\) −1.66883 + 2.89050i −0.110040 + 0.190594i
\(231\) 7.73099 2.57522i 0.508662 0.169437i
\(232\) −4.85695 8.41248i −0.318874 0.552306i
\(233\) −3.16820 9.75073i −0.207556 0.638792i −0.999599 0.0283260i \(-0.990982\pi\)
0.792043 0.610466i \(-0.209018\pi\)
\(234\) 23.4667 17.5856i 1.53407 1.14961i
\(235\) −1.91099 + 1.38842i −0.124659 + 0.0905703i
\(236\) 40.4435 8.59653i 2.63265 0.559587i
\(237\) −4.38204 3.88732i −0.284644 0.252508i
\(238\) −2.15630 20.5158i −0.139772 1.32984i
\(239\) −8.80753 + 3.92137i −0.569712 + 0.253652i −0.671314 0.741173i \(-0.734270\pi\)
0.101602 + 0.994825i \(0.467603\pi\)
\(240\) −0.280160 + 0.391665i −0.0180843 + 0.0252819i
\(241\) 0.139366 + 0.241388i 0.00897733 + 0.0155492i 0.870479 0.492205i \(-0.163809\pi\)
−0.861502 + 0.507754i \(0.830476\pi\)
\(242\) 17.1421 + 19.0390i 1.10193 + 1.22387i
\(243\) 0.576234 + 15.5778i 0.0369654 + 0.999317i
\(244\) 4.88900 + 15.0468i 0.312986 + 0.963272i
\(245\) −0.165286 + 1.57259i −0.0105598 + 0.100469i
\(246\) −14.8811 4.71378i −0.948783 0.300540i
\(247\) 8.69991 + 9.66223i 0.553562 + 0.614793i
\(248\) −21.1785 23.5211i −1.34484 1.49359i
\(249\) 5.02586 + 22.8140i 0.318501 + 1.44578i
\(250\) −0.764019 + 7.26916i −0.0483208 + 0.459742i
\(251\) 1.36753 + 4.20881i 0.0863175 + 0.265658i 0.984894 0.173159i \(-0.0553975\pi\)
−0.898576 + 0.438817i \(0.855398\pi\)
\(252\) 4.29749 13.9237i 0.270717 0.877111i
\(253\) 14.6652 3.11703i 0.921993 0.195966i
\(254\) 15.3766 + 26.6330i 0.964813 + 1.67111i
\(255\) 1.41769 + 3.12184i 0.0887791 + 0.195497i
\(256\) −19.4009 + 8.63785i −1.21256 + 0.539866i
\(257\) −0.382002 3.63450i −0.0238286 0.226714i −0.999955 0.00950980i \(-0.996973\pi\)
0.976126 0.217204i \(-0.0696938\pi\)
\(258\) 2.87618 14.0411i 0.179063 0.874163i
\(259\) 1.17589 0.249944i 0.0730665 0.0155308i
\(260\) 3.68598 2.67802i 0.228595 0.166084i
\(261\) −8.07777 3.45423i −0.500001 0.213812i
\(262\) −5.25413 16.1705i −0.324601 0.999019i
\(263\) 7.22621 + 12.5162i 0.445587 + 0.771780i 0.998093 0.0617294i \(-0.0196616\pi\)
−0.552506 + 0.833509i \(0.686328\pi\)
\(264\) 18.9356 2.13170i 1.16540 0.131197i
\(265\) 1.05933 1.83481i 0.0650741 0.112712i
\(266\) 10.0107 + 2.12783i 0.613793 + 0.130466i
\(267\) 0.0345490 + 4.67200i 0.00211436 + 0.285922i
\(268\) 31.1811 + 13.8827i 1.90469 + 0.848021i
\(269\) 0.283600 0.872830i 0.0172914 0.0532174i −0.942039 0.335505i \(-0.891093\pi\)
0.959330 + 0.282287i \(0.0910931\pi\)
\(270\) 0.0851038 + 3.83558i 0.00517925 + 0.233426i
\(271\) 2.13921 1.55422i 0.129948 0.0944124i −0.520913 0.853610i \(-0.674408\pi\)
0.650860 + 0.759197i \(0.274408\pi\)
\(272\) 0.572411 5.44612i 0.0347075 0.330220i
\(273\) −5.99921 + 8.38694i −0.363089 + 0.507600i
\(274\) −11.4206 + 19.7811i −0.689947 + 1.19502i
\(275\) 13.1465 9.55126i 0.792761 0.575962i
\(276\) 10.7236 24.5730i 0.645484 1.47912i
\(277\) 19.3409 21.4802i 1.16208 1.29062i 0.212478 0.977166i \(-0.431847\pi\)
0.949603 0.313456i \(-0.101487\pi\)
\(278\) 17.8564 + 12.9734i 1.07095 + 0.778094i
\(279\) −28.0847 5.53679i −1.68139 0.331479i
\(280\) 0.460948 1.41865i 0.0275469 0.0847807i
\(281\) −8.55152 + 1.81768i −0.510141 + 0.108434i −0.455789 0.890088i \(-0.650643\pi\)
−0.0543523 + 0.998522i \(0.517309\pi\)
\(282\) 22.1873 20.2767i 1.32124 1.20746i
\(283\) −21.2100 + 9.44331i −1.26081 + 0.561347i −0.924778 0.380506i \(-0.875750\pi\)
−0.336027 + 0.941852i \(0.609083\pi\)
\(284\) −9.81609 2.08647i −0.582478 0.123809i
\(285\) −1.69034 + 0.190309i −0.100127 + 0.0112730i
\(286\) −31.7112 6.74076i −1.87512 0.398590i
\(287\) 5.48901 0.324006
\(288\) −6.71030 + 12.0300i −0.395408 + 0.708875i
\(289\) −17.7905 12.9255i −1.04650 0.760326i
\(290\) −1.97526 0.879441i −0.115991 0.0516426i
\(291\) −6.81207 6.04300i −0.399330 0.354247i
\(292\) 9.71881 + 10.7938i 0.568751 + 0.631662i
\(293\) 2.19253 + 20.8605i 0.128089 + 1.21868i 0.850032 + 0.526731i \(0.176582\pi\)
−0.721944 + 0.691952i \(0.756751\pi\)
\(294\) −0.148788 20.1203i −0.00867748 1.17344i
\(295\) 2.56139 2.84472i 0.149130 0.165626i
\(296\) 2.81121 0.163398
\(297\) 12.5483 11.8127i 0.728126 0.685443i
\(298\) −9.61284 −0.556857
\(299\) −12.6952 + 14.0995i −0.734183 + 0.815393i
\(300\) −0.214881 29.0580i −0.0124062 1.67767i
\(301\) 0.526816 + 5.01232i 0.0303652 + 0.288905i
\(302\) −27.7011 30.7652i −1.59402 1.77034i
\(303\) −12.3477 10.9537i −0.709356 0.629272i
\(304\) 2.48191 + 1.10502i 0.142347 + 0.0633772i
\(305\) 1.18499 + 0.860949i 0.0678526 + 0.0492978i
\(306\) −22.3706 37.4565i −1.27884 2.14125i
\(307\) 23.1324 1.32024 0.660118 0.751162i \(-0.270506\pi\)
0.660118 + 0.751162i \(0.270506\pi\)
\(308\) −14.7171 + 6.55228i −0.838582 + 0.373351i
\(309\) 16.4125 1.84783i 0.933675 0.105119i
\(310\) −6.89111 1.46475i −0.391389 0.0831923i
\(311\) 18.6499 8.30346i 1.05754 0.470846i 0.197090 0.980385i \(-0.436851\pi\)
0.860447 + 0.509540i \(0.170184\pi\)
\(312\) −17.8000 + 16.2671i −1.00773 + 0.920945i
\(313\) 33.2955 7.07718i 1.88197 0.400026i 0.884222 0.467066i \(-0.154689\pi\)
0.997750 + 0.0670406i \(0.0213557\pi\)
\(314\) −1.45182 + 4.46825i −0.0819311 + 0.252158i
\(315\) −0.435815 1.27674i −0.0245554 0.0719360i
\(316\) 9.36904 + 6.80701i 0.527050 + 0.382924i
\(317\) −18.3478 + 20.3773i −1.03052 + 1.14451i −0.0411371 + 0.999154i \(0.513098\pi\)
−0.989380 + 0.145352i \(0.953569\pi\)
\(318\) −10.7828 + 24.7087i −0.604670 + 1.38560i
\(319\) 3.00125 + 9.23722i 0.168038 + 0.517185i
\(320\) −1.97312 + 3.41755i −0.110301 + 0.191047i
\(321\) 5.21235 7.28689i 0.290925 0.406715i
\(322\) −1.56105 + 14.8524i −0.0869941 + 0.827694i
\(323\) 15.6494 11.3699i 0.870754 0.632640i
\(324\) −4.12643 30.5408i −0.229246 1.69671i
\(325\) −6.35443 + 19.5569i −0.352480 + 1.08482i
\(326\) −3.36258 1.49712i −0.186236 0.0829176i
\(327\) 0.185417 + 25.0736i 0.0102536 + 1.38658i
\(328\) 12.5553 + 2.66872i 0.693252 + 0.147355i
\(329\) −5.28459 + 9.15318i −0.291349 + 0.504631i
\(330\) 3.13096 2.86128i 0.172354 0.157508i
\(331\) 8.98622 + 15.5646i 0.493927 + 0.855507i 0.999976 0.00699827i \(-0.00222764\pi\)
−0.506048 + 0.862505i \(0.668894\pi\)
\(332\) −14.2718 43.9241i −0.783266 2.41065i
\(333\) 2.03459 1.52469i 0.111495 0.0835525i
\(334\) −28.8690 + 20.9746i −1.57964 + 1.14768i
\(335\) 3.09091 0.656993i 0.168874 0.0358954i
\(336\) −0.432386 + 2.11085i −0.0235886 + 0.115156i
\(337\) −1.14690 10.9120i −0.0624757 0.594417i −0.980312 0.197457i \(-0.936732\pi\)
0.917836 0.396960i \(-0.129935\pi\)
\(338\) 9.81935 4.37186i 0.534102 0.237798i
\(339\) −5.32229 11.7201i −0.289067 0.636546i
\(340\) −3.38922 5.87031i −0.183806 0.318362i
\(341\) 15.8229 + 27.4068i 0.856860 + 1.48416i
\(342\) 21.1029 4.81281i 1.14111 0.260247i
\(343\) 5.25475 + 16.1724i 0.283730 + 0.873230i
\(344\) −1.23194 + 11.7211i −0.0664215 + 0.631959i
\(345\) −0.534014 2.42406i −0.0287504 0.130507i
\(346\) −1.53665 1.70662i −0.0826108 0.0917486i
\(347\) 14.7870 + 16.4226i 0.793807 + 0.881612i 0.995196 0.0978989i \(-0.0312122\pi\)
−0.201389 + 0.979511i \(0.564546\pi\)
\(348\) 16.5577 + 5.24488i 0.887586 + 0.281155i
\(349\) 1.92371 18.3029i 0.102974 0.979732i −0.814022 0.580835i \(-0.802726\pi\)
0.916996 0.398897i \(-0.130607\pi\)
\(350\) 5.00185 + 15.3941i 0.267360 + 0.822850i
\(351\) −4.05992 + 21.4272i −0.216703 + 1.14370i
\(352\) 14.8960 3.16609i 0.793961 0.168753i
\(353\) −16.5354 28.6401i −0.880089 1.52436i −0.851241 0.524776i \(-0.824149\pi\)
−0.0288486 0.999584i \(-0.509184\pi\)
\(354\) −28.3383 + 39.6171i −1.50616 + 2.10562i
\(355\) −0.848761 + 0.377893i −0.0450475 + 0.0200565i
\(356\) −0.965504 9.18616i −0.0511716 0.486865i
\(357\) 11.4765 + 10.1808i 0.607401 + 0.538827i
\(358\) 25.5736 5.43583i 1.35161 0.287293i
\(359\) −2.42595 + 1.76256i −0.128037 + 0.0930242i −0.649960 0.759968i \(-0.725215\pi\)
0.521924 + 0.852992i \(0.325215\pi\)
\(360\) −0.376124 3.13224i −0.0198235 0.165084i
\(361\) −2.90578 8.94306i −0.152936 0.470687i
\(362\) −20.8744 36.1555i −1.09713 1.90029i
\(363\) −18.9624 1.85176i −0.995266 0.0971920i
\(364\) 10.1931 17.6549i 0.534262 0.925370i
\(365\) 1.31531 + 0.279578i 0.0688464 + 0.0146338i
\(366\) −16.2096 9.19945i −0.847288 0.480863i
\(367\) 1.51873 + 0.676183i 0.0792772 + 0.0352965i 0.445992 0.895037i \(-0.352851\pi\)
−0.366715 + 0.930333i \(0.619518\pi\)
\(368\) −1.22508 + 3.77040i −0.0638616 + 0.196546i
\(369\) 10.5342 4.87806i 0.548389 0.253942i
\(370\) 0.506234 0.367800i 0.0263178 0.0191210i
\(371\) 0.990914 9.42791i 0.0514457 0.489473i
\(372\) 56.3242 + 5.49912i 2.92027 + 0.285116i
\(373\) 10.7543 18.6271i 0.556839 0.964473i −0.440919 0.897547i \(-0.645348\pi\)
0.997758 0.0669259i \(-0.0213191\pi\)
\(374\) −14.9053 + 45.8721i −0.770734 + 2.37199i
\(375\) −3.22749 4.37388i −0.166667 0.225866i
\(376\) −16.5380 + 18.3673i −0.852880 + 0.947219i
\(377\) −9.94346 7.22435i −0.512114 0.372073i
\(378\) 7.32835 + 15.5235i 0.376930 + 0.798444i
\(379\) 3.83779 11.8115i 0.197134 0.606715i −0.802811 0.596233i \(-0.796663\pi\)
0.999945 0.0104822i \(-0.00333665\pi\)
\(380\) 3.28941 0.699185i 0.168743 0.0358674i
\(381\) −21.8031 6.90642i −1.11700 0.353827i
\(382\) 27.4210 12.2086i 1.40298 0.624648i
\(383\) −0.782202 0.166262i −0.0399686 0.00849560i 0.187884 0.982191i \(-0.439837\pi\)
−0.227853 + 0.973696i \(0.573170\pi\)
\(384\) 13.7224 31.4447i 0.700266 1.60465i
\(385\) −0.745741 + 1.29163i −0.0380065 + 0.0658275i
\(386\) −53.9188 −2.74439
\(387\) 5.46546 + 9.15118i 0.277825 + 0.465181i
\(388\) 14.5646 + 10.5818i 0.739404 + 0.537209i
\(389\) −1.58654 0.706374i −0.0804408 0.0358146i 0.366122 0.930567i \(-0.380685\pi\)
−0.446563 + 0.894752i \(0.647352\pi\)
\(390\) −1.07708 + 5.25817i −0.0545401 + 0.266258i
\(391\) 18.8875 + 20.9767i 0.955184 + 1.06084i
\(392\) 1.72945 + 16.4546i 0.0873502 + 0.831081i
\(393\) 10.9971 + 6.24121i 0.554730 + 0.314827i
\(394\) 1.67943 1.86520i 0.0846086 0.0939673i
\(395\) 1.07216 0.0539461
\(396\) −22.4212 + 25.6537i −1.12671 + 1.28915i
\(397\) −24.7599 −1.24267 −0.621333 0.783547i \(-0.713409\pi\)
−0.621333 + 0.783547i \(0.713409\pi\)
\(398\) 25.6057 28.4380i 1.28350 1.42547i
\(399\) −6.56311 + 3.85420i −0.328566 + 0.192951i
\(400\) 0.449140 + 4.27328i 0.0224570 + 0.213664i
\(401\) 14.6221 + 16.2395i 0.730191 + 0.810960i 0.987872 0.155271i \(-0.0496249\pi\)
−0.257681 + 0.966230i \(0.582958\pi\)
\(402\) −38.1483 + 12.7078i −1.90267 + 0.633806i
\(403\) −36.5849 16.2886i −1.82242 0.811395i
\(404\) 26.4000 + 19.1807i 1.31345 + 0.954278i
\(405\) −1.97102 2.06294i −0.0979409 0.102508i
\(406\) −9.67462 −0.480143
\(407\) −2.74939 0.584431i −0.136282 0.0289692i
\(408\) 21.3010 + 28.8670i 1.05456 + 1.42913i
\(409\) −7.85919 1.67052i −0.388612 0.0826020i 0.00946221 0.999955i \(-0.496988\pi\)
−0.398074 + 0.917353i \(0.630321\pi\)
\(410\) 2.61008 1.16208i 0.128903 0.0573911i
\(411\) −3.65452 16.5890i −0.180264 0.818276i
\(412\) −31.9389 + 6.78881i −1.57351 + 0.334461i
\(413\) 5.29283 16.2897i 0.260443 0.801562i
\(414\) 10.2034 + 29.8913i 0.501470 + 1.46907i
\(415\) −3.45919 2.51325i −0.169805 0.123371i
\(416\) −12.8950 + 14.3214i −0.632231 + 0.702164i
\(417\) −16.3114 + 1.83645i −0.798773 + 0.0899312i
\(418\) −19.3590 14.0654i −0.946877 0.687962i
\(419\) 2.79840 4.84698i 0.136711 0.236790i −0.789539 0.613701i \(-0.789680\pi\)
0.926250 + 0.376910i \(0.123014\pi\)
\(420\) 1.10280 + 2.42843i 0.0538109 + 0.118495i
\(421\) −3.95686 + 37.6470i −0.192846 + 1.83480i 0.287567 + 0.957760i \(0.407154\pi\)
−0.480413 + 0.877043i \(0.659513\pi\)
\(422\) 28.1684 20.4656i 1.37122 0.996248i
\(423\) −2.00750 + 22.2627i −0.0976081 + 1.08245i
\(424\) 6.85035 21.0832i 0.332682 1.02389i
\(425\) 27.9486 + 12.4435i 1.35571 + 0.603599i
\(426\) 10.1944 5.98666i 0.493918 0.290055i
\(427\) 6.41067 + 1.36263i 0.310234 + 0.0659423i
\(428\) −8.85614 + 15.3393i −0.428078 + 0.741452i
\(429\) 20.7904 12.2089i 1.00377 0.589453i
\(430\) 1.31167 + 2.27187i 0.0632542 + 0.109560i
\(431\) −9.20389 28.3267i −0.443336 1.36445i −0.884299 0.466922i \(-0.845363\pi\)
0.440963 0.897525i \(-0.354637\pi\)
\(432\) 1.04609 + 4.43528i 0.0503301 + 0.213393i
\(433\) 0.225935 0.164152i 0.0108578 0.00788862i −0.582343 0.812943i \(-0.697864\pi\)
0.593201 + 0.805054i \(0.297864\pi\)
\(434\) −30.8340 + 6.55397i −1.48008 + 0.314601i
\(435\) 1.52558 0.508192i 0.0731458 0.0243660i
\(436\) −5.18166 49.3002i −0.248156 2.36105i
\(437\) −12.7932 + 5.69588i −0.611980 + 0.272471i
\(438\) −17.0297 1.66267i −0.813711 0.0794454i
\(439\) −7.49827 12.9874i −0.357873 0.619854i 0.629732 0.776812i \(-0.283165\pi\)
−0.987605 + 0.156958i \(0.949831\pi\)
\(440\) −2.33375 + 2.59184i −0.111257 + 0.123561i
\(441\) 10.1760 + 10.9709i 0.484571 + 0.522422i
\(442\) −18.8614 58.0493i −0.897143 2.76112i
\(443\) −1.51564 + 14.4204i −0.0720104 + 0.685133i 0.897655 + 0.440698i \(0.145269\pi\)
−0.969666 + 0.244435i \(0.921398\pi\)
\(444\) −3.71042 + 3.39089i −0.176089 + 0.160925i
\(445\) −0.572205 0.635498i −0.0271251 0.0301255i
\(446\) 3.00192 + 3.33397i 0.142145 + 0.157868i
\(447\) 5.27719 4.82274i 0.249602 0.228108i
\(448\) −1.84569 + 17.5606i −0.0872008 + 0.829660i
\(449\) −6.55787 20.1830i −0.309485 0.952497i −0.977965 0.208767i \(-0.933055\pi\)
0.668481 0.743730i \(-0.266945\pi\)
\(450\) 23.2800 + 25.0984i 1.09743 + 1.18315i
\(451\) −11.7244 5.22020i −0.552082 0.245809i
\(452\) 12.7238 + 22.0383i 0.598479 + 1.03660i
\(453\) 30.6420 + 2.99168i 1.43968 + 0.140561i
\(454\) −34.0660 + 15.1672i −1.59880 + 0.711830i
\(455\) −0.197284 1.87703i −0.00924880 0.0879964i
\(456\) −16.8860 + 5.62499i −0.790761 + 0.263414i
\(457\) 3.13937 0.667293i 0.146853 0.0312146i −0.133898 0.990995i \(-0.542750\pi\)
0.280752 + 0.959780i \(0.409416\pi\)
\(458\) 0.985297 0.715860i 0.0460399 0.0334499i
\(459\) 31.0727 + 9.33936i 1.45035 + 0.435924i
\(460\) 1.51642 + 4.66707i 0.0707037 + 0.217603i
\(461\) −13.1628 22.7986i −0.613052 1.06184i −0.990723 0.135897i \(-0.956608\pi\)
0.377671 0.925940i \(-0.376725\pi\)
\(462\) 7.59087 17.3939i 0.353159 0.809239i
\(463\) −1.81412 + 3.14215i −0.0843093 + 0.146028i −0.905097 0.425206i \(-0.860202\pi\)
0.820787 + 0.571234i \(0.193535\pi\)
\(464\) −2.51210 0.533963i −0.116621 0.0247886i
\(465\) 4.51790 2.65315i 0.209512 0.123037i
\(466\) −21.8138 9.71212i −1.01050 0.449905i
\(467\) −5.71532 + 17.5899i −0.264473 + 0.813965i 0.727341 + 0.686276i \(0.240756\pi\)
−0.991814 + 0.127689i \(0.959244\pi\)
\(468\) 3.87213 42.9409i 0.178989 1.98494i
\(469\) 11.4388 8.31077i 0.528194 0.383756i
\(470\) −0.575050 + 5.47123i −0.0265251 + 0.252369i
\(471\) −1.44470 3.18133i −0.0665682 0.146588i
\(472\) 20.0265 34.6869i 0.921795 1.59660i
\(473\) 3.64158 11.2072i 0.167440 0.515309i
\(474\) −13.5571 + 1.52635i −0.622699 + 0.0701076i
\(475\) −10.1560 + 11.2794i −0.465990 + 0.517535i
\(476\) −24.5374 17.8275i −1.12467 0.817120i
\(477\) −6.47684 18.9741i −0.296554 0.868766i
\(478\) −6.93867 + 21.3550i −0.317367 + 0.976756i
\(479\) 0.153567 0.0326418i 0.00701668 0.00149144i −0.204402 0.978887i \(-0.565525\pi\)
0.211419 + 0.977396i \(0.432192\pi\)
\(480\) −0.542420 2.46221i −0.0247580 0.112384i
\(481\) 3.24945 1.44675i 0.148162 0.0659660i
\(482\) 0.634980 + 0.134969i 0.0289225 + 0.00614767i
\(483\) −6.59445 8.93676i −0.300058 0.406637i
\(484\) 37.6668 0.000778469i 1.71213 3.53850e-5i
\(485\) 1.66671 0.0756816
\(486\) 27.8598 + 23.2792i 1.26375 + 1.05597i
\(487\) −14.5028 10.5369i −0.657187 0.477474i 0.208525 0.978017i \(-0.433134\pi\)
−0.865712 + 0.500543i \(0.833134\pi\)
\(488\) 14.0010 + 6.23364i 0.633795 + 0.282184i
\(489\) 2.59706 0.865121i 0.117443 0.0391221i
\(490\) 2.46424 + 2.73682i 0.111323 + 0.123637i
\(491\) 0.694902 + 6.61155i 0.0313605 + 0.298375i 0.998949 + 0.0458419i \(0.0145971\pi\)
−0.967588 + 0.252533i \(0.918736\pi\)
\(492\) −19.7904 + 11.6219i −0.892219 + 0.523958i
\(493\) −12.2356 + 13.5890i −0.551065 + 0.612019i
\(494\) 30.2813 1.36242
\(495\) −0.283318 + 3.14156i −0.0127342 + 0.141203i
\(496\) −8.36804 −0.375736
\(497\) −2.78168 + 3.08936i −0.124775 + 0.138577i
\(498\) 47.3184 + 26.8547i 2.12039 + 1.20339i
\(499\) −3.54846 33.7614i −0.158851 1.51137i −0.725968 0.687729i \(-0.758608\pi\)
0.567117 0.823638i \(-0.308059\pi\)
\(500\) 7.19078 + 7.98617i 0.321582 + 0.357153i
\(501\) 5.32543 25.9980i 0.237922 1.16151i
\(502\) 9.41572 + 4.19215i 0.420244 + 0.187105i
\(503\) −2.53812 1.84405i −0.113169 0.0822222i 0.529761 0.848147i \(-0.322282\pi\)
−0.642930 + 0.765925i \(0.722282\pi\)
\(504\) −7.23790 12.1189i −0.322402 0.539819i
\(505\) 3.02112 0.134438
\(506\) 17.4594 30.2399i 0.776167 1.34433i
\(507\) −3.19721 + 7.32638i −0.141993 + 0.325376i
\(508\) 44.2273 + 9.40080i 1.96227 + 0.417093i
\(509\) 20.8320 9.27502i 0.923364 0.411108i 0.110709 0.993853i \(-0.464688\pi\)
0.812655 + 0.582745i \(0.198021\pi\)
\(510\) 7.61258 + 2.41139i 0.337091 + 0.106778i
\(511\) 5.88530 1.25096i 0.260350 0.0553391i
\(512\) −3.04225 + 9.36310i −0.134450 + 0.413794i
\(513\) −9.17033 + 13.2294i −0.404880 + 0.584091i
\(514\) −6.88586 5.00287i −0.303722 0.220667i
\(515\) −2.02277 + 2.24652i −0.0891340 + 0.0989933i
\(516\) −12.5120 16.9562i −0.550812 0.746457i
\(517\) 19.9927 14.5252i 0.879279 0.638819i
\(518\) 1.39992 2.42474i 0.0615090 0.106537i
\(519\) 1.69979 + 0.165956i 0.0746124 + 0.00728467i
\(520\) 0.461339 4.38935i 0.0202311 0.192486i
\(521\) −4.26200 + 3.09653i −0.186722 + 0.135661i −0.677219 0.735781i \(-0.736815\pi\)
0.490497 + 0.871443i \(0.336815\pi\)
\(522\) −18.5670 + 8.59779i −0.812655 + 0.376315i
\(523\) 3.67595 11.3134i 0.160738 0.494701i −0.837959 0.545733i \(-0.816251\pi\)
0.998697 + 0.0510325i \(0.0162512\pi\)
\(524\) −22.8373 10.1678i −0.997651 0.444183i
\(525\) −10.4691 5.94154i −0.456908 0.259310i
\(526\) 32.9242 + 6.99825i 1.43556 + 0.305138i
\(527\) −29.7904 + 51.5985i −1.29769 + 2.24767i
\(528\) 2.93104 4.09753i 0.127557 0.178322i
\(529\) 1.28255 + 2.22144i 0.0557629 + 0.0965843i
\(530\) −1.52480 4.69285i −0.0662331 0.203845i
\(531\) −4.31884 35.9659i −0.187422 1.56079i
\(532\) 12.1734 8.84448i 0.527783 0.383457i
\(533\) 15.8860 3.37667i 0.688099 0.146260i
\(534\) 8.14007 + 7.22108i 0.352255 + 0.312487i
\(535\) 0.171408 + 1.63083i 0.00741060 + 0.0705071i
\(536\) 30.2052 13.4482i 1.30467 0.580875i
\(537\) −11.3121 + 15.8143i −0.488151 + 0.682439i
\(538\) −1.06872 1.85108i −0.0460757 0.0798055i
\(539\) 1.72938 16.4523i 0.0744895 0.708650i
\(540\) 4.27456 + 3.68046i 0.183948 + 0.158382i
\(541\) 12.5401 + 38.5945i 0.539142 + 1.65931i 0.734525 + 0.678581i \(0.237405\pi\)
−0.195383 + 0.980727i \(0.562595\pi\)
\(542\) 0.643724 6.12462i 0.0276503 0.263075i
\(543\) 29.5986 + 9.37577i 1.27020 + 0.402353i
\(544\) 19.1848 + 21.3069i 0.822542 + 0.913526i
\(545\) −3.07090 3.41058i −0.131543 0.146093i
\(546\) 5.16678 + 23.4536i 0.221118 + 1.00372i
\(547\) −2.46000 + 23.4054i −0.105182 + 1.00074i 0.806887 + 0.590706i \(0.201151\pi\)
−0.912069 + 0.410036i \(0.865516\pi\)
\(548\) 10.3776 + 31.9391i 0.443311 + 1.36437i
\(549\) 13.5140 3.08205i 0.576762 0.131539i
\(550\) 3.95635 37.6384i 0.168699 1.60491i
\(551\) −4.53595 7.85650i −0.193238 0.334698i
\(552\) −10.7389 23.6477i −0.457077 1.00651i
\(553\) 4.38257 1.95125i 0.186366 0.0829755i
\(554\) −7.03671 66.9498i −0.298961 2.84443i
\(555\) −0.0933841 + 0.455889i −0.00396393 + 0.0193514i
\(556\) 31.7421 6.74700i 1.34617 0.286136i
\(557\) 5.08590 3.69513i 0.215497 0.156568i −0.474800 0.880093i \(-0.657480\pi\)
0.690297 + 0.723526i \(0.257480\pi\)
\(558\) −53.3504 + 39.9800i −2.25850 + 1.69249i
\(559\) 4.60811 + 14.1823i 0.194902 + 0.599847i
\(560\) −0.197187 0.341538i −0.00833268 0.0144326i
\(561\) −14.8313 32.6605i −0.626180 1.37893i
\(562\) −10.1807 + 17.6335i −0.429448 + 0.743826i
\(563\) 16.5956 + 3.52751i 0.699423 + 0.148667i 0.543881 0.839162i \(-0.316954\pi\)
0.155542 + 0.987829i \(0.450288\pi\)
\(564\) −0.326785 44.1905i −0.0137601 1.86076i
\(565\) 2.15228 + 0.958259i 0.0905473 + 0.0403142i
\(566\) −16.7095 + 51.4265i −0.702352 + 2.16162i
\(567\) −11.8112 4.84538i −0.496023 0.203487i
\(568\) −7.86471 + 5.71404i −0.329996 + 0.239756i
\(569\) −2.32581 + 22.1286i −0.0975031 + 0.927680i 0.830979 + 0.556303i \(0.187781\pi\)
−0.928482 + 0.371376i \(0.878886\pi\)
\(570\) −2.30485 + 3.22219i −0.0965394 + 0.134963i
\(571\) −17.6576 + 30.5838i −0.738947 + 1.27989i 0.214023 + 0.976829i \(0.431343\pi\)
−0.952970 + 0.303065i \(0.901990\pi\)
\(572\) −38.5625 + 28.0167i −1.61238 + 1.17144i
\(573\) −8.92836 + 20.4593i −0.372988 + 0.854698i
\(574\) 8.55411 9.50030i 0.357042 0.396535i
\(575\) −17.9182 13.0184i −0.747243 0.542904i
\(576\) 12.0639 + 35.3416i 0.502661 + 1.47256i
\(577\) −11.8156 + 36.3646i −0.491889 + 1.51388i 0.329859 + 0.944030i \(0.392999\pi\)
−0.821749 + 0.569850i \(0.807001\pi\)
\(578\) −50.0962 + 10.6483i −2.08373 + 0.442910i
\(579\) 29.6000 27.0509i 1.23013 1.12420i
\(580\) −2.90415 + 1.29301i −0.120588 + 0.0536894i
\(581\) −18.7138 3.97774i −0.776379 0.165025i
\(582\) −21.0751 + 2.37278i −0.873592 + 0.0983547i
\(583\) −11.0828 + 19.1955i −0.459001 + 0.794995i
\(584\) 14.0700 0.582219
\(585\) −2.04672 3.42696i −0.0846215 0.141687i
\(586\) 39.5219 + 28.7143i 1.63263 + 1.18618i
\(587\) −11.3185 5.03932i −0.467165 0.207995i 0.159634 0.987176i \(-0.448969\pi\)
−0.626799 + 0.779181i \(0.715635\pi\)
\(588\) −22.1302 19.6318i −0.912635 0.809601i
\(589\) −19.7788 21.9666i −0.814973 0.905119i
\(590\) −0.931901 8.86645i −0.0383658 0.365026i
\(591\) 0.0138027 + 1.86651i 0.000567766 + 0.0767780i
\(592\) 0.497328 0.552339i 0.0204401 0.0227010i
\(593\) 4.18039 0.171668 0.0858340 0.996309i \(-0.472645\pi\)
0.0858340 + 0.996309i \(0.472645\pi\)
\(594\) −0.889931 40.1274i −0.0365143 1.64645i
\(595\) −2.80796 −0.115115
\(596\) −9.45710 + 10.5032i −0.387378 + 0.430227i
\(597\) 0.210445 + 28.4580i 0.00861292 + 1.16471i
\(598\) 4.61885 + 43.9454i 0.188879 + 1.79706i
\(599\) −29.4944 32.7569i −1.20511 1.33841i −0.925709 0.378236i \(-0.876531\pi\)
−0.279401 0.960174i \(-0.590136\pi\)
\(600\) −21.0578 18.6804i −0.859680 0.762624i
\(601\) −1.59991 0.712324i −0.0652616 0.0290563i 0.373846 0.927491i \(-0.378039\pi\)
−0.439108 + 0.898434i \(0.644705\pi\)
\(602\) 9.49624 + 6.89943i 0.387038 + 0.281200i
\(603\) 14.5669 26.1152i 0.593212 1.06349i
\(604\) −60.8670 −2.47664
\(605\) 2.82126 2.04968i 0.114701 0.0833312i
\(606\) −38.2012 + 4.30094i −1.55182 + 0.174714i
\(607\) 10.6316 + 2.25982i 0.431525 + 0.0917234i 0.418553 0.908192i \(-0.362538\pi\)
0.0129718 + 0.999916i \(0.495871\pi\)
\(608\) −12.9945 + 5.78553i −0.526997 + 0.234634i
\(609\) 5.31111 4.85373i 0.215217 0.196683i
\(610\) 3.33682 0.709263i 0.135104 0.0287172i
\(611\) −9.66362 + 29.7416i −0.390948 + 1.20321i
\(612\) −62.9339 12.4072i −2.54395 0.501531i
\(613\) −14.3951 10.4586i −0.581412 0.422421i 0.257821 0.966193i \(-0.416996\pi\)
−0.839233 + 0.543772i \(0.816996\pi\)
\(614\) 36.0497 40.0372i 1.45485 1.61577i
\(615\) −0.849849 + 1.94742i −0.0342692 + 0.0785276i
\(616\) −4.82254 + 14.8417i −0.194306 + 0.597990i
\(617\) −1.99805 + 3.46073i −0.0804386 + 0.139324i −0.903438 0.428718i \(-0.858965\pi\)
0.823000 + 0.568042i \(0.192299\pi\)
\(618\) 22.3792 31.2862i 0.900222 1.25852i
\(619\) 1.14724 10.9153i 0.0461115 0.438721i −0.946972 0.321315i \(-0.895875\pi\)
0.993084 0.117407i \(-0.0374581\pi\)
\(620\) −8.37989 + 6.08835i −0.336544 + 0.244514i
\(621\) −20.5978 11.2905i −0.826560 0.453071i
\(622\) 14.6926 45.2191i 0.589118 1.81312i
\(623\) −3.49552 1.55630i −0.140045 0.0623520i
\(624\) 0.0471432 + 6.37510i 0.00188724 + 0.255208i
\(625\) −22.9890 4.88646i −0.919560 0.195458i
\(626\) 39.6388 68.6565i 1.58429 2.74407i
\(627\) 17.6841 1.99081i 0.706236 0.0795053i
\(628\) 3.45380 + 5.98216i 0.137822 + 0.238714i
\(629\) −1.63530 5.03293i −0.0652037 0.200676i
\(630\) −2.88894 1.23537i −0.115098 0.0492184i
\(631\) −6.99735 + 5.08388i −0.278560 + 0.202386i −0.718289 0.695745i \(-0.755075\pi\)
0.439729 + 0.898131i \(0.355075\pi\)
\(632\) 10.9732 2.33242i 0.436490 0.0927788i
\(633\) −5.19618 + 25.3671i −0.206530 + 1.00825i
\(634\) 6.67542 + 63.5123i 0.265115 + 2.52240i
\(635\) 3.82417 1.70263i 0.151757 0.0675668i
\(636\) 16.3891 + 36.0900i 0.649871 + 1.43106i
\(637\) 10.4672 + 18.1296i 0.414724 + 0.718323i
\(638\) 20.6648 + 9.20082i 0.818128 + 0.364264i
\(639\) −2.59293 + 8.40100i −0.102575 + 0.332338i
\(640\) 1.94048 + 5.97219i 0.0767042 + 0.236071i
\(641\) −3.87671 + 36.8844i −0.153121 + 1.45685i 0.600546 + 0.799591i \(0.294950\pi\)
−0.753666 + 0.657257i \(0.771717\pi\)
\(642\) −4.48910 20.3774i −0.177170 0.804232i
\(643\) −27.2554 30.2702i −1.07485 1.19374i −0.980155 0.198234i \(-0.936479\pi\)
−0.0946941 0.995506i \(-0.530187\pi\)
\(644\) 14.6923 + 16.3175i 0.578958 + 0.642998i
\(645\) −1.85986 0.589137i −0.0732321 0.0231973i
\(646\) 4.70916 44.8047i 0.185280 1.76282i
\(647\) −0.175813 0.541098i −0.00691193 0.0212727i 0.947541 0.319634i \(-0.103560\pi\)
−0.954453 + 0.298361i \(0.903560\pi\)
\(648\) −24.6606 16.8256i −0.968759 0.660973i
\(649\) −26.7973 + 29.7608i −1.05189 + 1.16821i
\(650\) 23.9461 + 41.4758i 0.939242 + 1.62682i
\(651\) 13.6389 19.0673i 0.534552 0.747306i
\(652\) −4.94388 + 2.20116i −0.193617 + 0.0862040i
\(653\) 3.81817 + 36.3275i 0.149417 + 1.42160i 0.770290 + 0.637694i \(0.220111\pi\)
−0.620873 + 0.783911i \(0.713222\pi\)
\(654\) 43.6861 + 38.7540i 1.70826 + 1.51540i
\(655\) −2.26381 + 0.481187i −0.0884542 + 0.0188015i
\(656\) 2.74549 1.99472i 0.107193 0.0778806i
\(657\) 10.1830 7.63100i 0.397277 0.297714i
\(658\) 7.60666 + 23.4109i 0.296538 + 0.912651i
\(659\) 12.0035 + 20.7907i 0.467590 + 0.809889i 0.999314 0.0370284i \(-0.0117892\pi\)
−0.531725 + 0.846917i \(0.678456\pi\)
\(660\) −0.0460493 6.23587i −0.00179246 0.242731i
\(661\) −6.49165 + 11.2439i −0.252496 + 0.437336i −0.964212 0.265131i \(-0.914585\pi\)
0.711717 + 0.702467i \(0.247918\pi\)
\(662\) 40.9431 + 8.70273i 1.59130 + 0.338241i
\(663\) 39.4776 + 22.4048i 1.53318 + 0.870130i
\(664\) −40.8712 18.1970i −1.58611 0.706181i
\(665\) 0.430484 1.32489i 0.0166935 0.0513772i
\(666\) 0.531800 5.89752i 0.0206068 0.228524i
\(667\) 10.7098 7.78112i 0.414685 0.301286i
\(668\) −5.48410 + 52.1777i −0.212186 + 2.01882i
\(669\) −3.32062 0.324204i −0.128383 0.0125344i
\(670\) 3.67978 6.37356i 0.142162 0.246232i
\(671\) −12.3972 9.00727i −0.478588 0.347722i
\(672\) −6.69825 9.07743i −0.258391 0.350169i
\(673\) 11.3924 12.6525i 0.439144 0.487719i −0.482423 0.875939i \(-0.660243\pi\)
0.921567 + 0.388219i \(0.126910\pi\)
\(674\) −20.6737 15.0204i −0.796323 0.578562i
\(675\) −25.3719 2.09885i −0.976564 0.0807847i
\(676\) 4.88349 15.0298i 0.187827 0.578071i
\(677\) 34.6574 7.36665i 1.33199 0.283123i 0.513721 0.857957i \(-0.328267\pi\)
0.818270 + 0.574834i \(0.194933\pi\)
\(678\) −28.5792 9.05285i −1.09758 0.347673i
\(679\) 6.81290 3.03330i 0.261455 0.116407i
\(680\) −6.42281 1.36521i −0.246304 0.0523535i
\(681\) 11.0920 25.4172i 0.425046 0.973988i
\(682\) 72.0939 + 15.3248i 2.76062 + 0.586817i
\(683\) 23.8967 0.914381 0.457191 0.889369i \(-0.348856\pi\)
0.457191 + 0.889369i \(0.348856\pi\)
\(684\) 15.5024 27.7923i 0.592750 1.06266i
\(685\) 2.51533 + 1.82749i 0.0961058 + 0.0698250i
\(686\) 36.1801 + 16.1084i 1.38136 + 0.615022i
\(687\) −0.181756 + 0.887309i −0.00693443 + 0.0338530i
\(688\) 2.08499 + 2.31561i 0.0794894 + 0.0882819i
\(689\) −2.93192 27.8953i −0.111697 1.06273i
\(690\) −5.02773 2.85340i −0.191403 0.108627i
\(691\) −0.396537 + 0.440399i −0.0150850 + 0.0167536i −0.750640 0.660711i \(-0.770255\pi\)
0.735555 + 0.677465i \(0.236921\pi\)
\(692\) −3.37645 −0.128353
\(693\) 4.55931 + 13.3571i 0.173194 + 0.507395i
\(694\) 51.4682 1.95371
\(695\) 2.01031 2.23268i 0.0762555 0.0846903i
\(696\) 14.5082 8.52000i 0.549933 0.322950i
\(697\) −2.52569 24.0303i −0.0956672 0.910213i
\(698\) −28.6805 31.8529i −1.08557 1.20565i
\(699\) 16.8477 5.61223i 0.637239 0.212274i
\(700\) 21.7407 + 9.67960i 0.821723 + 0.365855i
\(701\) 20.5701 + 14.9451i 0.776922 + 0.564467i 0.904054 0.427419i \(-0.140577\pi\)
−0.127131 + 0.991886i \(0.540577\pi\)
\(702\) 30.7589 + 40.4192i 1.16092 + 1.52552i
\(703\) 2.62542 0.0990194
\(704\) 20.6430 35.7538i 0.778011 1.34752i
\(705\) −2.42922 3.29206i −0.0914896 0.123986i
\(706\) −75.3387 16.0137i −2.83541 0.602685i
\(707\) 12.3492 5.49821i 0.464439 0.206782i
\(708\) 15.4072 + 69.9382i 0.579039 + 2.62844i
\(709\) −14.7746 + 3.14044i −0.554871 + 0.117942i −0.476809 0.879007i \(-0.658207\pi\)
−0.0780624 + 0.996948i \(0.524873\pi\)
\(710\) −0.668663 + 2.05793i −0.0250945 + 0.0772329i
\(711\) 6.67672 7.63950i 0.250397 0.286504i
\(712\) −7.23882 5.25931i −0.271286 0.197101i
\(713\) 28.8620 32.0545i 1.08089 1.20045i
\(714\) 35.5059 3.99749i 1.32877 0.149602i
\(715\) −1.36371 + 4.19692i −0.0509998 + 0.156956i
\(716\) 19.2200 33.2900i 0.718284 1.24410i
\(717\) −6.90463 15.2045i −0.257858 0.567821i
\(718\) −0.730010 + 6.94558i −0.0272437 + 0.259207i
\(719\) −9.74281 + 7.07857i −0.363345 + 0.263986i −0.754446 0.656362i \(-0.772094\pi\)
0.391101 + 0.920348i \(0.372094\pi\)
\(720\) −0.681954 0.480222i −0.0254149 0.0178968i
\(721\) −4.17983 + 12.8642i −0.155665 + 0.479088i
\(722\) −20.0069 8.90765i −0.744580 0.331508i
\(723\) −0.416300 + 0.244473i −0.0154824 + 0.00909206i
\(724\) −60.0405 12.7620i −2.23139 0.474296i
\(725\) 7.17396 12.4257i 0.266434 0.461477i
\(726\) −32.7561 + 29.9340i −1.21569 + 1.11095i
\(727\) −24.7966 42.9489i −0.919654 1.59289i −0.799940 0.600079i \(-0.795136\pi\)
−0.119714 0.992808i \(-0.538198\pi\)
\(728\) −6.10251 18.7816i −0.226174 0.696092i
\(729\) −26.9734 + 1.19756i −0.999016 + 0.0443541i
\(730\) 2.53368 1.84082i 0.0937755 0.0681319i
\(731\) 21.7010 4.61269i 0.802640 0.170606i
\(732\) −25.9985 + 8.66048i −0.960931 + 0.320101i
\(733\) 3.37265 + 32.0886i 0.124572 + 1.18522i 0.860964 + 0.508666i \(0.169861\pi\)
−0.736392 + 0.676555i \(0.763472\pi\)
\(734\) 3.53713 1.57483i 0.130558 0.0581281i
\(735\) −2.72586 0.266135i −0.100545 0.00981653i
\(736\) −10.3783 17.9757i −0.382548 0.662593i
\(737\) −32.3368 + 6.87305i −1.19114 + 0.253172i
\(738\) 7.97369 25.8344i 0.293516 0.950979i
\(739\) −0.968005 2.97921i −0.0356086 0.109592i 0.931672 0.363300i \(-0.118350\pi\)
−0.967281 + 0.253708i \(0.918350\pi\)
\(740\) 0.0961664 0.914963i 0.00353515 0.0336347i
\(741\) −16.6236 + 15.1920i −0.610683 + 0.558093i
\(742\) −14.7735 16.4076i −0.542351 0.602341i
\(743\) 5.21170 + 5.78818i 0.191199 + 0.212348i 0.831121 0.556092i \(-0.187700\pi\)
−0.639922 + 0.768440i \(0.721033\pi\)
\(744\) 40.4674 36.9825i 1.48361 1.35585i
\(745\) −0.136774 + 1.30132i −0.00501100 + 0.0476765i
\(746\) −15.4798 47.6420i −0.566756 1.74430i
\(747\) −39.4495 + 8.99701i −1.44338 + 0.329183i
\(748\) 35.4570 + 61.4148i 1.29644 + 2.24555i
\(749\) 3.66865 + 6.35428i 0.134049 + 0.232180i
\(750\) −12.6000 1.23018i −0.460087 0.0449198i
\(751\) 45.3932 20.2103i 1.65642 0.737486i 0.656562 0.754272i \(-0.272010\pi\)
0.999859 + 0.0167864i \(0.00534354\pi\)
\(752\) 0.683037 + 6.49866i 0.0249078 + 0.236982i
\(753\) −7.27216 + 2.42247i −0.265012 + 0.0882796i
\(754\) −27.9997 + 5.95153i −1.01969 + 0.216742i
\(755\) −4.55890 + 3.31224i −0.165915 + 0.120545i
\(756\) 24.1709 + 7.26494i 0.879089 + 0.264223i
\(757\) −8.35296 25.7078i −0.303594 0.934365i −0.980198 0.198018i \(-0.936549\pi\)
0.676605 0.736346i \(-0.263451\pi\)
\(758\) −14.4623 25.0495i −0.525295 0.909838i
\(759\) 5.58653 + 25.3603i 0.202778 + 0.920519i
\(760\) 1.62882 2.82121i 0.0590836 0.102336i
\(761\) −43.5379 9.25426i −1.57825 0.335467i −0.666271 0.745710i \(-0.732111\pi\)
−0.911976 + 0.410243i \(0.865444\pi\)
\(762\) −45.9316 + 26.9734i −1.66393 + 0.977144i
\(763\) −18.7597 8.35235i −0.679147 0.302376i
\(764\) 13.6374 41.9716i 0.493384 1.51848i
\(765\) −5.38889 + 2.49543i −0.194836 + 0.0902223i
\(766\) −1.50675 + 1.09472i −0.0544412 + 0.0395538i
\(767\) 5.29732 50.4006i 0.191275 1.81986i
\(768\) −15.2093 33.4918i −0.548817 1.20853i
\(769\) 1.65952 2.87438i 0.0598440 0.103653i −0.834551 0.550930i \(-0.814273\pi\)
0.894395 + 0.447277i \(0.147606\pi\)
\(770\) 1.07337 + 3.30360i 0.0386815 + 0.119054i
\(771\) 6.29008 0.708179i 0.226532 0.0255044i
\(772\) −53.0453 + 58.9127i −1.90914 + 2.12032i
\(773\) −23.0471 16.7447i −0.828946 0.602264i 0.0903152 0.995913i \(-0.471213\pi\)
−0.919261 + 0.393649i \(0.871213\pi\)
\(774\) 24.3561 + 4.80172i 0.875464 + 0.172594i
\(775\) 14.4465 44.4617i 0.518934 1.59711i
\(776\) 17.0583 3.62585i 0.612357 0.130160i
\(777\) 0.447965 + 2.03345i 0.0160707 + 0.0729497i
\(778\) −3.69506 + 1.64515i −0.132474 + 0.0589813i
\(779\) 11.7255 + 2.49234i 0.420111 + 0.0892973i
\(780\) 4.68555 + 6.34982i 0.167769 + 0.227360i
\(781\) 8.87968 3.95338i 0.317740 0.141463i
\(782\) 65.7407 2.35088
\(783\) 5.87928 14.0350i 0.210108 0.501569i
\(784\) 3.53890 + 2.57116i 0.126389 + 0.0918273i
\(785\) 0.584222 + 0.260113i 0.0208518 + 0.00928382i
\(786\) 27.9401 9.30728i 0.996592 0.331980i
\(787\) 8.73129 + 9.69708i 0.311237 + 0.345663i 0.878386 0.477951i \(-0.158621\pi\)
−0.567150 + 0.823615i \(0.691954\pi\)
\(788\) −0.385729 3.66996i −0.0137410 0.130737i
\(789\) −21.5855 + 12.6761i −0.768464 + 0.451282i
\(790\) 1.67086 1.85568i 0.0594464 0.0660220i
\(791\) 10.5417 0.374819
\(792\) 3.93463 + 32.7692i 0.139811 + 1.16440i
\(793\) 19.3917 0.688618
\(794\) −38.5861 + 42.8542i −1.36937 + 1.52084i
\(795\) 3.19147 + 1.81126i 0.113190 + 0.0642388i
\(796\) −5.88107 55.9547i −0.208449 1.98326i
\(797\) 33.5725 + 37.2861i 1.18920 + 1.32074i 0.935445 + 0.353471i \(0.114999\pi\)
0.253754 + 0.967269i \(0.418334\pi\)
\(798\) −3.55719 + 17.3657i −0.125923 + 0.614741i
\(799\) 42.5033 + 18.9237i 1.50366 + 0.669472i
\(800\) −18.2003 13.2233i −0.643477 0.467514i
\(801\) −8.09148 + 0.119678i −0.285898 + 0.00422861i
\(802\) 50.8941 1.79713
\(803\) −13.7606 2.92505i −0.485600 0.103223i
\(804\) −23.6455 + 54.1835i −0.833914 + 1.91091i
\(805\) 1.98840 + 0.422648i 0.0700820 + 0.0148964i
\(806\) −85.2062 + 37.9363i −3.00126 + 1.33625i
\(807\) 1.51538 + 0.480017i 0.0533438 + 0.0168974i
\(808\) 30.9202 6.57229i 1.08777 0.231212i
\(809\) −10.8621 + 33.4301i −0.381892 + 1.17534i 0.556819 + 0.830634i \(0.312022\pi\)
−0.938710 + 0.344707i \(0.887978\pi\)
\(810\) −6.64215 + 0.196526i −0.233381 + 0.00690523i
\(811\) −17.8837 12.9933i −0.627981 0.456255i 0.227719 0.973727i \(-0.426873\pi\)
−0.855700 + 0.517472i \(0.826873\pi\)
\(812\) −9.51789 + 10.5707i −0.334012 + 0.370958i
\(813\) 2.71932 + 3.68521i 0.0953708 + 0.129246i
\(814\) −5.29620 + 3.84783i −0.185632 + 0.134866i
\(815\) −0.250512 + 0.433900i −0.00877506 + 0.0151989i
\(816\) 9.44004 + 0.921663i 0.330467 + 0.0322647i
\(817\) −1.15052 + 10.9464i −0.0402515 + 0.382967i
\(818\) −15.1391 + 10.9992i −0.529327 + 0.384579i
\(819\) −14.6030 10.2832i −0.510272 0.359325i
\(820\) 1.29808 3.99508i 0.0453309 0.139514i
\(821\) 2.31785 + 1.03197i 0.0808934 + 0.0360160i 0.446784 0.894642i \(-0.352569\pi\)
−0.365891 + 0.930658i \(0.619236\pi\)
\(822\) −34.4073 19.5272i −1.20009 0.681091i
\(823\) 10.1460 + 2.15660i 0.353668 + 0.0751745i 0.381320 0.924443i \(-0.375470\pi\)
−0.0276517 + 0.999618i \(0.508803\pi\)
\(824\) −15.8152 + 27.3928i −0.550950 + 0.954273i
\(825\) 16.7112 + 22.6474i 0.581809 + 0.788481i
\(826\) −19.9455 34.5467i −0.693994 1.20203i
\(827\) 16.2925 + 50.1431i 0.566546 + 1.74365i 0.663314 + 0.748341i \(0.269149\pi\)
−0.0967683 + 0.995307i \(0.530851\pi\)
\(828\) 42.6979 + 18.2586i 1.48385 + 0.634529i
\(829\) −30.6163 + 22.2440i −1.06335 + 0.772566i −0.974705 0.223497i \(-0.928253\pi\)
−0.0886419 + 0.996064i \(0.528253\pi\)
\(830\) −9.74073 + 2.07046i −0.338106 + 0.0718666i
\(831\) 37.4515 + 33.2234i 1.29918 + 1.15251i
\(832\) 5.46104 + 51.9583i 0.189327 + 1.80133i
\(833\) 28.4527 12.6680i 0.985829 0.438919i
\(834\) −22.2413 + 31.0935i −0.770154 + 1.07668i
\(835\) 2.42863 + 4.20651i 0.0840462 + 0.145572i
\(836\) −34.4135 + 7.31444i −1.19021 + 0.252975i
\(837\) 9.23003 48.7137i 0.319037 1.68379i
\(838\) −4.02803 12.3970i −0.139146 0.428247i
\(839\) 2.10265 20.0054i 0.0725915 0.690662i −0.896346 0.443355i \(-0.853788\pi\)
0.968937 0.247306i \(-0.0795454\pi\)
\(840\) 2.46302 + 0.780194i 0.0849821 + 0.0269193i
\(841\) −13.6665 15.1781i −0.471257 0.523384i
\(842\) 58.9925 + 65.5178i 2.03302 + 2.25789i
\(843\) −3.25776 14.7880i −0.112203 0.509325i
\(844\) 5.35100 50.9114i 0.184189 1.75244i
\(845\) −0.452118 1.39148i −0.0155533 0.0478682i
\(846\) 35.4034 + 38.1688i 1.21719 + 1.31227i
\(847\) 7.80199 13.5128i 0.268079 0.464305i
\(848\) −2.93048 5.07575i −0.100633 0.174302i
\(849\) −16.6275 36.6149i −0.570655 1.25662i
\(850\) 65.0923 28.9810i 2.23265 0.994039i
\(851\) 0.400459 + 3.81011i 0.0137275 + 0.130609i
\(852\) 3.48806 17.0282i 0.119499 0.583377i
\(853\) −8.92089 + 1.89619i −0.305446 + 0.0649245i −0.358085 0.933689i \(-0.616570\pi\)
0.0526390 + 0.998614i \(0.483237\pi\)
\(854\) 12.3489 8.97197i 0.422569 0.307014i
\(855\) −0.351266 2.92523i −0.0120131 0.100041i
\(856\) 5.30210 + 16.3182i 0.181222 + 0.557744i
\(857\) 0.922678 + 1.59813i 0.0315181 + 0.0545909i 0.881354 0.472456i \(-0.156632\pi\)
−0.849836 + 0.527047i \(0.823299\pi\)
\(858\) 11.2689 55.0102i 0.384713 1.87802i
\(859\) −14.2555 + 24.6913i −0.486392 + 0.842456i −0.999878 0.0156422i \(-0.995021\pi\)
0.513485 + 0.858098i \(0.328354\pi\)
\(860\) 3.77271 + 0.801915i 0.128648 + 0.0273451i
\(861\) 0.0703033 + 9.50699i 0.00239593 + 0.323997i
\(862\) −63.3708 28.2145i −2.15842 0.960989i
\(863\) −3.30628 + 10.1757i −0.112547 + 0.346385i −0.991428 0.130658i \(-0.958291\pi\)
0.878880 + 0.477042i \(0.158291\pi\)
\(864\) −20.9220 11.4682i −0.711780 0.390155i
\(865\) −0.252894 + 0.183738i −0.00859865 + 0.00624729i
\(866\) 0.0679878 0.646861i 0.00231032 0.0219812i
\(867\) 22.1592 30.9787i 0.752567 1.05209i
\(868\) −23.1735 + 40.1376i −0.786559 + 1.36236i
\(869\) −11.2168 0.000115910i −0.380503 3.93198e-6i
\(870\) 1.49790 3.43242i 0.0507834 0.116370i
\(871\) 27.9930 31.0893i 0.948506 1.05342i
\(872\) −38.8492 28.2256i −1.31560 0.955840i
\(873\) 10.3793 11.8759i 0.351284 0.401939i
\(874\) −10.0786 + 31.0187i −0.340913 + 1.04922i
\(875\) 4.35443 0.925562i 0.147207 0.0312897i
\(876\) −18.5705 + 16.9713i −0.627439 + 0.573406i
\(877\) 37.3021 16.6080i 1.25960 0.560811i 0.335171 0.942157i \(-0.391206\pi\)
0.924432 + 0.381346i \(0.124539\pi\)
\(878\) −34.1637 7.26173i −1.15297 0.245071i
\(879\) −36.1024 + 4.06464i −1.21770 + 0.137097i
\(880\) 0.0963762 + 0.917050i 0.00324884 + 0.0309137i
\(881\) 21.0458 0.709050 0.354525 0.935047i \(-0.384643\pi\)
0.354525 + 0.935047i \(0.384643\pi\)
\(882\) 34.8465 0.515402i 1.17334 0.0173545i
\(883\) −10.2973 7.48145i −0.346533 0.251771i 0.400880 0.916130i \(-0.368704\pi\)
−0.747413 + 0.664360i \(0.768704\pi\)
\(884\) −81.9816 36.5006i −2.75734 1.22765i
\(885\) 4.95986 + 4.39991i 0.166724 + 0.147901i
\(886\) 22.5966 + 25.0961i 0.759148 + 0.843119i
\(887\) −1.12107 10.6662i −0.0376417 0.358137i −0.997089 0.0762484i \(-0.975706\pi\)
0.959447 0.281889i \(-0.0909609\pi\)
\(888\) 0.0360060 + 4.86902i 0.00120828 + 0.163394i
\(889\) 12.5331 13.9194i 0.420346 0.466842i
\(890\) −1.99164 −0.0667599
\(891\) 20.6204 + 21.5824i 0.690809 + 0.723038i
\(892\) 6.59606 0.220852
\(893\) −15.4450 + 17.1534i −0.516846 + 0.574015i
\(894\) −0.123121 16.6495i −0.00411779 0.556841i
\(895\) −0.371996 3.53931i −0.0124345 0.118306i
\(896\) 18.8009 + 20.8805i 0.628094 + 0.697569i
\(897\) −24.5829 21.8076i −0.820800 0.728133i
\(898\) −45.1523 20.1031i −1.50675 0.670850i
\(899\) 22.6060 + 16.4242i 0.753952 + 0.547778i
\(900\) 50.3258 0.744350i 1.67753 0.0248117i
\(901\) −41.7304 −1.39024
\(902\) −27.3065 + 12.1573i −0.909206 + 0.404793i
\(903\) −8.67461 + 0.976645i −0.288673 + 0.0325007i
\(904\) 24.1126 + 5.12529i 0.801972 + 0.170464i
\(905\) −5.19148 + 2.31139i −0.172571 + 0.0768334i
\(906\) 52.9306 48.3724i 1.75850 1.60707i
\(907\) 12.9561 2.75391i 0.430201 0.0914421i 0.0122784 0.999925i \(-0.496092\pi\)
0.417923 + 0.908483i \(0.362758\pi\)
\(908\) −16.9422 + 52.1426i −0.562245 + 1.73041i
\(909\) 18.8136 21.5265i 0.624009 0.713990i
\(910\) −3.55618 2.58372i −0.117886 0.0856494i
\(911\) −38.2237 + 42.4518i −1.26641 + 1.40649i −0.392973 + 0.919550i \(0.628553\pi\)
−0.873436 + 0.486939i \(0.838113\pi\)
\(912\) −1.88211 + 4.31283i −0.0623228 + 0.142812i
\(913\) 36.1894 + 26.2937i 1.19769 + 0.870195i
\(914\) 3.73747 6.47348i 0.123624 0.214124i
\(915\) −1.47599 + 2.06344i −0.0487947 + 0.0682153i
\(916\) 0.187172 1.78082i 0.00618432 0.0588399i
\(917\) −8.37786 + 6.08687i −0.276661 + 0.201006i
\(918\) 64.5883 39.2257i 2.13173 1.29464i
\(919\) 5.12287 15.7666i 0.168988 0.520091i −0.830320 0.557287i \(-0.811842\pi\)
0.999308 + 0.0371955i \(0.0118424\pi\)
\(920\) 4.34269 + 1.93349i 0.143174 + 0.0637454i
\(921\) 0.296280 + 40.0654i 0.00976275 + 1.32020i
\(922\) −59.9725 12.7475i −1.97509 0.419818i
\(923\) −6.15009 + 10.6523i −0.202433 + 0.350624i
\(924\) −11.5371 25.4061i −0.379541 0.835799i
\(925\) 2.07615 + 3.59600i 0.0682634 + 0.118236i
\(926\) 2.61125 + 8.03660i 0.0858109 + 0.264099i
\(927\) 3.41066 + 28.4028i 0.112021 + 0.932872i
\(928\) 10.8784 7.90359i 0.357100 0.259448i
\(929\) 7.20288 1.53102i 0.236319 0.0502311i −0.0882298 0.996100i \(-0.528121\pi\)
0.324549 + 0.945869i \(0.394788\pi\)
\(930\) 2.44869 11.9542i 0.0802958 0.391993i
\(931\) 1.61515 + 15.3671i 0.0529343 + 0.503636i
\(932\) −32.0720 + 14.2794i −1.05055 + 0.467737i
\(933\) 14.6205 + 32.1953i 0.478653 + 1.05403i
\(934\) 21.5376 + 37.3043i 0.704733 + 1.22063i
\(935\) 5.99776 + 2.67045i 0.196148 + 0.0873330i
\(936\) −28.4027 30.6213i −0.928372 1.00089i
\(937\) 14.6033 + 44.9444i 0.477069 + 1.46827i 0.843147 + 0.537684i \(0.180701\pi\)
−0.366077 + 0.930584i \(0.619299\pi\)
\(938\) 3.44213 32.7496i 0.112389 1.06931i
\(939\) 12.6841 + 57.5773i 0.413931 + 1.87896i
\(940\) 5.41225 + 6.01091i 0.176528 + 0.196054i
\(941\) −37.5574 41.7118i −1.22434 1.35976i −0.912209 0.409725i \(-0.865625\pi\)
−0.312128 0.950040i \(-0.601042\pi\)
\(942\) −7.75762 2.45733i −0.252757 0.0800642i
\(943\) −1.82847 + 17.3967i −0.0595432 + 0.566516i
\(944\) −3.27233 10.0712i −0.106505 0.327789i
\(945\) 2.20573 0.771186i 0.0717525 0.0250867i
\(946\) −13.7223 23.7682i −0.446149 0.772772i
\(947\) 6.39323 + 11.0734i 0.207752 + 0.359837i 0.951006 0.309172i \(-0.100052\pi\)
−0.743254 + 0.669009i \(0.766719\pi\)
\(948\) −11.6698 + 16.3144i −0.379016 + 0.529867i
\(949\) 16.2633 7.24091i 0.527930 0.235050i
\(950\) 3.69502 + 35.1558i 0.119882 + 1.14060i
\(951\) −35.5286 31.5175i −1.15209 1.02203i
\(952\) −28.7386 + 6.10858i −0.931424 + 0.197980i
\(953\) 18.8480 13.6939i 0.610547 0.443588i −0.239060 0.971005i \(-0.576839\pi\)
0.849607 + 0.527417i \(0.176839\pi\)
\(954\) −42.9337 18.3594i −1.39003 0.594408i
\(955\) −1.26256 3.88576i −0.0408555 0.125740i
\(956\) 16.5067 + 28.5904i 0.533864 + 0.924680i
\(957\) −15.9605 + 5.31648i −0.515928 + 0.171857i
\(958\) 0.182825 0.316662i 0.00590680 0.0102309i
\(959\) 13.6076 + 2.89239i 0.439413 + 0.0934001i
\(960\) −5.94448 3.37369i −0.191857 0.108885i
\(961\) 54.8540 + 24.4226i 1.76949 + 0.787826i
\(962\) 2.55995 7.87872i 0.0825362 0.254020i
\(963\) 12.6877 + 8.93447i 0.408855 + 0.287909i
\(964\) 0.772163 0.561009i 0.0248697 0.0180689i
\(965\) −0.767170 + 7.29913i −0.0246961 + 0.234967i
\(966\) −25.7445 2.51352i −0.828314 0.0808712i
\(967\) 27.7586 48.0794i 0.892657 1.54613i 0.0559798 0.998432i \(-0.482172\pi\)
0.836677 0.547696i \(-0.184495\pi\)
\(968\) 24.4157 27.1153i 0.784752 0.871519i
\(969\) 19.8932 + 26.9591i 0.639062 + 0.866052i
\(970\) 2.59742 2.88473i 0.0833981 0.0926230i
\(971\) 3.65698 + 2.65695i 0.117358 + 0.0852656i 0.644916 0.764253i \(-0.276892\pi\)
−0.527558 + 0.849519i \(0.676892\pi\)
\(972\) 52.8438 7.53815i 1.69497 0.241786i
\(973\) 4.15409 12.7850i 0.133174 0.409867i
\(974\) −40.8385 + 8.68049i −1.30855 + 0.278141i
\(975\) −33.9541 10.7554i −1.08740 0.344449i
\(976\) 3.70167 1.64809i 0.118487 0.0527540i
\(977\) 26.4484 + 5.62178i 0.846159 + 0.179857i 0.610537 0.791988i \(-0.290954\pi\)
0.235623 + 0.971845i \(0.424287\pi\)
\(978\) 2.54994 5.84317i 0.0815382 0.186844i
\(979\) 5.98627 + 6.64856i 0.191322 + 0.212489i
\(980\) 5.41462 0.172964
\(981\) −43.4253 + 0.642286i −1.38646 + 0.0205066i
\(982\) 12.5261 + 9.10076i 0.399725 + 0.290417i
\(983\) 9.71793 + 4.32670i 0.309954 + 0.138000i 0.555818 0.831304i \(-0.312405\pi\)
−0.245864 + 0.969304i \(0.579072\pi\)
\(984\) −4.46142 + 21.7800i −0.142225 + 0.694322i
\(985\) −0.228602 0.253888i −0.00728385 0.00808953i
\(986\) 4.45163 + 42.3545i 0.141769 + 1.34884i
\(987\) −15.9210 9.03570i −0.506772 0.287609i
\(988\) 29.7907 33.0859i 0.947768 1.05260i
\(989\) −16.0614 −0.510723
\(990\) 4.99584 + 5.38619i 0.158778 + 0.171184i
\(991\) −18.7938 −0.597005 −0.298502 0.954409i \(-0.596487\pi\)
−0.298502 + 0.954409i \(0.596487\pi\)
\(992\) 29.3162 32.5590i 0.930792 1.03375i
\(993\) −26.8428 + 15.7635i −0.851831 + 0.500240i
\(994\) 1.01205 + 9.62897i 0.0321001 + 0.305412i
\(995\) −3.48541 3.87094i −0.110495 0.122717i
\(996\) 75.8938 25.2814i 2.40479 0.801071i
\(997\) −23.8686 10.6270i −0.755926 0.336560i −0.00767052 0.999971i \(-0.502442\pi\)
−0.748256 + 0.663411i \(0.769108\pi\)
\(998\) −63.9637 46.4723i −2.02473 1.47106i
\(999\) 2.66683 + 3.50438i 0.0843747 + 0.110874i
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 99.2.m.b.49.9 yes 72
3.2 odd 2 297.2.n.b.280.1 72
9.2 odd 6 297.2.n.b.181.9 72
9.4 even 3 891.2.f.f.82.9 36
9.5 odd 6 891.2.f.e.82.1 36
9.7 even 3 inner 99.2.m.b.16.1 72
11.3 even 5 1089.2.e.p.364.1 36
11.8 odd 10 1089.2.e.o.364.18 36
11.9 even 5 inner 99.2.m.b.31.1 yes 72
33.20 odd 10 297.2.n.b.64.9 72
99.14 odd 30 9801.2.a.cp.1.1 18
99.20 odd 30 297.2.n.b.262.1 72
99.25 even 15 1089.2.e.p.727.1 36
99.31 even 15 891.2.f.f.163.9 36
99.41 even 30 9801.2.a.cn.1.18 18
99.52 odd 30 1089.2.e.o.727.18 36
99.58 even 15 9801.2.a.cm.1.18 18
99.85 odd 30 9801.2.a.co.1.1 18
99.86 odd 30 891.2.f.e.163.1 36
99.97 even 15 inner 99.2.m.b.97.9 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.16.1 72 9.7 even 3 inner
99.2.m.b.31.1 yes 72 11.9 even 5 inner
99.2.m.b.49.9 yes 72 1.1 even 1 trivial
99.2.m.b.97.9 yes 72 99.97 even 15 inner
297.2.n.b.64.9 72 33.20 odd 10
297.2.n.b.181.9 72 9.2 odd 6
297.2.n.b.262.1 72 99.20 odd 30
297.2.n.b.280.1 72 3.2 odd 2
891.2.f.e.82.1 36 9.5 odd 6
891.2.f.e.163.1 36 99.86 odd 30
891.2.f.f.82.9 36 9.4 even 3
891.2.f.f.163.9 36 99.31 even 15
1089.2.e.o.364.18 36 11.8 odd 10
1089.2.e.o.727.18 36 99.52 odd 30
1089.2.e.p.364.1 36 11.3 even 5
1089.2.e.p.727.1 36 99.25 even 15
9801.2.a.cm.1.18 18 99.58 even 15
9801.2.a.cn.1.18 18 99.41 even 30
9801.2.a.co.1.1 18 99.85 odd 30
9801.2.a.cp.1.1 18 99.14 odd 30