Properties

Label 99.2.m.b.97.9
Level $99$
Weight $2$
Character 99.97
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 97.9
Character \(\chi\) \(=\) 99.97
Dual form 99.2.m.b.49.9

$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.55841 + 1.73079i 1.10196 + 1.22385i 0.972657 + 0.232245i \(0.0746072\pi\)
0.129303 + 0.991605i \(0.458726\pi\)
\(3\) 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 −0.788708 0.614767i \(-0.789250\pi\)
0.693842 + 0.720127i \(0.255917\pi\)
\(6\) 3.01769 2.67700i 1.23197 1.09288i
\(7\) −1.29586 + 0.576953i −0.489788 + 0.218068i −0.636744 0.771075i \(-0.719719\pi\)
0.146956 + 0.989143i \(0.453052\pi\)
\(8\) −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 −0.738373 0.674392i \(-0.764406\pi\)
−0.400238 + 0.916411i \(0.631072\pi\)
\(14\) −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 −0.855184 0.518325i \(-0.826556\pi\)
0.387195 0.921998i \(-0.373444\pi\)
\(18\) −4.59792 5.26093i −1.08374 1.24001i
\(19\) −2.50622 + 1.82087i −0.574966 + 0.417737i −0.836906 0.547347i \(-0.815638\pi\)
0.261940 + 0.965084i \(0.415638\pi\)
\(20\) −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 0.999461 0.0328349i \(-0.0104536\pi\)
−0.528166 + 0.849141i \(0.677120\pi\)
\(24\) 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 −0.143021 0.989720i \(-0.545682\pi\)
0.639805 + 0.768537i \(0.279015\pi\)
\(30\) −0.00945666 + 1.27881i −0.00172654 + 0.233477i
\(31\) 9.33325 1.98384i 1.67630 0.356309i 0.730967 0.682412i \(-0.239069\pi\)
0.945334 + 0.326103i \(0.105736\pi\)
\(32\) 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 0.529998 0.847999i \(-0.322193\pi\)
−0.642716 + 0.766104i \(0.722193\pi\)
\(38\) −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 0.111682 0.993744i \(-0.464376\pi\)
−0.663766 + 0.747940i \(0.731043\pi\)
\(42\) −2.36599 + 5.21007i −0.365080 + 0.803931i
\(43\) −1.77651 + 3.07700i −0.270915 + 0.469239i −0.969096 0.246682i \(-0.920660\pi\)
0.698181 + 0.715921i \(0.253993\pi\)
\(44\) 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 0.891665 + 0.452695i \(0.149538\pi\)
−0.778059 + 0.628191i \(0.783796\pi\)
\(48\) −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 −0.703120 0.711071i \(-0.748210\pi\)
0.986793 0.161986i \(-0.0517898\pi\)
\(54\) −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 −0.532680 0.846317i \(-0.678815\pi\)
0.696998 0.717073i \(-0.254518\pi\)
\(60\) −1.40655 + 1.24776i −0.181585 + 0.161085i
\(61\) −4.51935 0.960618i −0.578644 0.122995i −0.0907135 0.995877i \(-0.528915\pi\)
−0.487931 + 0.872882i \(0.662248\pi\)
\(62\) 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 −0.991426 0.130668i \(-0.958288\pi\)
0.382552 0.923934i \(-0.375045\pi\)
\(68\) 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 0.990304 0.138916i \(-0.0443618\pi\)
−0.882826 + 0.469701i \(0.844362\pi\)
\(72\) 8.13635 5.72949i 0.958878 0.675227i
\(73\) −3.43158 2.49319i −0.401636 0.291806i 0.368571 0.929600i \(-0.379847\pi\)
−0.770207 + 0.637794i \(0.779847\pi\)
\(74\) −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 0.602268 0.798294i \(-0.294264\pi\)
−0.856875 + 0.515525i \(0.827597\pi\)
\(80\) 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 0.863838 0.503770i \(-0.168054\pi\)
0.584253 + 0.811571i \(0.301387\pi\)
\(84\) −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 0.537590 0.843206i \(-0.319335\pi\)
−0.894781 + 0.446506i \(0.852668\pi\)
\(98\) −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 0.337059 0.941484i \(-0.390568\pi\)
−0.971558 + 0.236800i \(0.923901\pi\)
\(102\) −21.7205 12.7554i −2.15065 1.26297i
\(103\) −0.996745 + 9.48339i −0.0982122 + 0.934426i 0.828838 + 0.559489i \(0.189003\pi\)
−0.927050 + 0.374938i \(0.877664\pi\)
\(104\) 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 −0.771393 0.636359i \(-0.780440\pi\)
0.366840 + 0.930284i \(0.380440\pi\)
\(108\) −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 0.0617453 0.998092i \(-0.480333\pi\)
−0.700411 + 0.713740i \(0.747000\pi\)
\(114\) −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 −0.951791 0.306746i \(-0.900760\pi\)
0.589715 0.807612i \(-0.299240\pi\)
\(128\) −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 0.980263 0.197697i \(-0.0633463\pi\)
−0.661342 + 0.750084i \(0.730013\pi\)
\(132\) 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 −0.221008 0.975272i \(-0.570935\pi\)
−0.598579 + 0.801064i \(0.704268\pi\)
\(138\) 17.3008 + 5.76316i 1.47274 + 0.490593i
\(139\) 0.990605 9.42498i 0.0840220 0.799416i −0.868652 0.495423i \(-0.835013\pi\)
0.952674 0.303994i \(-0.0983202\pi\)
\(140\) 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 −0.845575 0.533857i \(-0.820742\pi\)
0.619319 + 0.785139i \(0.287409\pi\)
\(150\) 14.5896 + 13.3332i 1.19123 + 1.08865i
\(151\) 1.85802 + 17.6779i 0.151204 + 1.43861i 0.762389 + 0.647119i \(0.224026\pi\)
−0.611186 + 0.791487i \(0.709307\pi\)
\(152\) 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 0.331879 0.943322i \(-0.392318\pi\)
−0.478955 + 0.877840i \(0.658984\pi\)
\(158\) 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 −0.968359 0.249560i \(-0.919714\pi\)
0.930107 + 0.367289i \(0.119714\pi\)
\(164\) 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 −0.747297 0.664490i \(-0.768649\pi\)
−0.412417 + 0.910995i \(0.635315\pi\)
\(168\) −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 0.997741 0.0671768i \(-0.0213991\pi\)
−0.989905 + 0.141733i \(0.954732\pi\)
\(174\) 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 −0.194153 0.980971i \(-0.562196\pi\)
0.872963 + 0.487787i \(0.162196\pi\)
\(180\) 2.14311 + 2.45214i 0.159738 + 0.182772i
\(181\) 5.53932 + 17.0483i 0.411735 + 1.26719i 0.915139 + 0.403138i \(0.132081\pi\)
−0.503405 + 0.864051i \(0.667919\pi\)
\(182\) 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 0.0661416 0.997810i \(-0.478931\pi\)
0.785775 + 0.618513i \(0.212264\pi\)
\(192\) 20.4554 + 6.81400i 1.47624 + 0.491758i
\(193\) −15.4911 + 17.2046i −1.11507 + 1.23841i −0.146624 + 0.989192i \(0.546841\pi\)
−0.968447 + 0.249219i \(0.919826\pi\)
\(194\) 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 0.325077 0.945688i \(-0.394610\pi\)
0.681618 + 0.731708i \(0.261276\pi\)
\(212\) 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 0.985710 0.168454i \(-0.0538775\pi\)
−0.999193 + 0.0401676i \(0.987211\pi\)
\(224\) −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 −0.829978 0.557796i \(-0.811647\pi\)
−0.140841 + 0.990032i \(0.544980\pi\)
\(228\) −15.9792 + 9.06874i −1.05825 + 0.600592i
\(229\) 0.511498 0.108722i 0.0338007 0.00718457i −0.190980 0.981594i \(-0.561167\pi\)
0.224781 + 0.974409i \(0.427833\pi\)
\(230\) −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 0.792043 + 0.610466i \(0.209018\pi\)
−0.999599 + 0.0283260i \(0.990982\pi\)
\(234\) 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 0.101602 0.994825i \(-0.467603\pi\)
−0.671314 + 0.741173i \(0.734270\pi\)
\(240\) −0.280160 0.391665i −0.0180843 0.0252819i
\(241\) 0.139366 0.241388i 0.00897733 0.0155492i −0.861502 0.507754i \(-0.830476\pi\)
0.870479 + 0.492205i \(0.163809\pi\)
\(242\) 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 −0.898576 0.438817i \(-0.855398\pi\)
0.984894 + 0.173159i \(0.0553975\pi\)
\(252\) 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 0.976126 + 0.217204i \(0.0696938\pi\)
−0.999955 + 0.00950980i \(0.996973\pi\)
\(258\) 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 −0.552506 0.833509i \(-0.686328\pi\)
0.998093 + 0.0617294i \(0.0196616\pi\)
\(264\) 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 0.959330 0.282287i \(-0.0910931\pi\)
−0.942039 + 0.335505i \(0.891093\pi\)
\(270\) 0.0851038 3.83558i 0.00517925 0.233426i
\(271\) 2.13921 + 1.55422i 0.129948 + 0.0944124i 0.650860 0.759197i \(-0.274408\pi\)
−0.520913 + 0.853610i \(0.674408\pi\)
\(272\) 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 0.949603 + 0.313456i \(0.101487\pi\)
0.212478 + 0.977166i \(0.431847\pi\)
\(278\) 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 −0.0543523 0.998522i \(-0.517309\pi\)
−0.455789 + 0.890088i \(0.650643\pi\)
\(282\) 22.1873 + 20.2767i 1.32124 + 1.20746i
\(283\) −21.2100 9.44331i −1.26081 0.561347i −0.336027 0.941852i \(-0.609083\pi\)
−0.924778 + 0.380506i \(0.875750\pi\)
\(284\) −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 −0.721944 0.691952i \(-0.756751\pi\)
0.850032 0.526731i \(-0.176582\pi\)
\(294\) −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 0.860447 0.509540i \(-0.170184\pi\)
0.197090 + 0.980385i \(0.436851\pi\)
\(312\) −17.8000 16.2671i −1.00773 0.920945i
\(313\) 33.2955 + 7.07718i 1.88197 + 0.400026i 0.997750 0.0670406i \(-0.0213557\pi\)
0.884222 + 0.467066i \(0.154689\pi\)
\(314\) −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 −0.989380 0.145352i \(-0.953569\pi\)
−0.0411371 0.999154i \(-0.513098\pi\)
\(318\) −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 −0.506048 0.862505i \(-0.668894\pi\)
0.999976 + 0.00699827i \(0.00222764\pi\)
\(332\) −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 0.917836 + 0.396960i \(0.129935\pi\)
−0.980312 + 0.197457i \(0.936732\pi\)
\(338\) 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 −0.201389 0.979511i \(-0.564546\pi\)
0.995196 + 0.0978989i \(0.0312122\pi\)
\(348\) 16.5577 5.24488i 0.887586 0.281155i
\(349\) 1.92371 + 18.3029i 0.102974 + 0.979732i 0.916996 + 0.398897i \(0.130607\pi\)
−0.814022 + 0.580835i \(0.802726\pi\)
\(350\) 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 −0.0288486 + 0.999584i \(0.509184\pi\)
−0.851241 + 0.524776i \(0.824149\pi\)
\(354\) −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 0.521924 0.852992i \(-0.325215\pi\)
−0.649960 + 0.759968i \(0.725215\pi\)
\(360\) −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 −0.366715 0.930333i \(-0.619518\pi\)
0.445992 + 0.895037i \(0.352851\pi\)
\(368\) −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 0.997758 + 0.0669259i \(0.0213191\pi\)
−0.440919 + 0.897547i \(0.645348\pi\)
\(374\) −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 0.999945 + 0.0104822i \(0.00333665\pi\)
−0.802811 + 0.596233i \(0.796663\pi\)
\(380\) 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 −0.227853 0.973696i \(-0.573170\pi\)
0.187884 + 0.982191i \(0.439837\pi\)
\(384\) 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 −0.446563 0.894752i \(-0.647352\pi\)
0.366122 + 0.930567i \(0.380685\pi\)
\(390\) −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 −0.257681 0.966230i \(-0.582958\pi\)
0.987872 + 0.155271i \(0.0496249\pi\)
\(402\) −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 −0.398074 0.917353i \(-0.630321\pi\)
0.00946221 + 0.999955i \(0.496988\pi\)
\(410\) 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 0.926250 0.376910i \(-0.123014\pi\)
−0.789539 + 0.613701i \(0.789680\pi\)
\(420\) 1.10280 2.42843i 0.0538109 0.118495i
\(421\) −3.95686 37.6470i −0.192846 1.83480i −0.480413 0.877043i \(-0.659513\pi\)
0.287567 0.957760i \(-0.407154\pi\)
\(422\) 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 0.440963 + 0.897525i \(0.354637\pi\)
−0.884299 + 0.466922i \(0.845363\pi\)
\(432\) 1.04609 4.43528i 0.0503301 0.213393i
\(433\) 0.225935 + 0.164152i 0.0108578 + 0.00788862i 0.593201 0.805054i \(-0.297864\pi\)
−0.582343 + 0.812943i \(0.697864\pi\)
\(434\) −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 −0.987605 0.156958i \(-0.949831\pi\)
0.629732 + 0.776812i \(0.283165\pi\)
\(440\) −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 −0.969666 0.244435i \(-0.921398\pi\)
0.897655 0.440698i \(-0.145269\pi\)
\(444\) −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 0.668481 + 0.743730i \(0.266945\pi\)
−0.977965 + 0.208767i \(0.933055\pi\)
\(450\) 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 0.280752 0.959780i \(-0.409416\pi\)
−0.133898 + 0.990995i \(0.542750\pi\)
\(458\) 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 0.377671 + 0.925940i \(0.376725\pi\)
−0.990723 + 0.135897i \(0.956608\pi\)
\(462\) 7.59087 + 17.3939i 0.353159 + 0.809239i
\(463\) −1.81412 3.14215i −0.0843093 0.146028i 0.820787 0.571234i \(-0.193535\pi\)
−0.905097 + 0.425206i \(0.860202\pi\)
\(464\) −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 −0.991814 0.127689i \(-0.959244\pi\)
0.727341 0.686276i \(-0.240756\pi\)
\(468\) 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 0.211419 0.977396i \(-0.432192\pi\)
−0.204402 + 0.978887i \(0.565525\pi\)
\(480\) −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 −0.865712 0.500543i \(-0.833134\pi\)
0.208525 + 0.978017i \(0.433134\pi\)
\(488\) 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 −0.967588 0.252533i \(-0.918736\pi\)
0.998949 0.0458419i \(-0.0145971\pi\)
\(492\) −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 0.567117 + 0.823638i \(0.308059\pi\)
−0.725968 + 0.687729i \(0.758608\pi\)
\(500\) 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 −0.642930 0.765925i \(-0.722282\pi\)
0.529761 + 0.848147i \(0.322282\pi\)
\(504\) −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 0.812655 0.582745i \(-0.198021\pi\)
0.110709 + 0.993853i \(0.464688\pi\)
\(510\) 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 0.490497 0.871443i \(-0.336815\pi\)
−0.677219 + 0.735781i \(0.736815\pi\)
\(522\) −18.5670 8.59779i −0.812655 0.376315i
\(523\) 3.67595 + 11.3134i 0.160738 + 0.494701i 0.998697 0.0510325i \(-0.0162512\pi\)
−0.837959 + 0.545733i \(0.816251\pi\)
\(524\) −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 −0.195383 0.980727i \(-0.562595\pi\)
0.734525 0.678581i \(-0.237405\pi\)
\(542\) 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 −0.912069 0.410036i \(-0.865516\pi\)
0.806887 0.590706i \(-0.201151\pi\)
\(548\) 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 0.690297 0.723526i \(-0.257480\pi\)
−0.474800 + 0.880093i \(0.657480\pi\)
\(558\) −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 0.155542 0.987829i \(-0.450288\pi\)
0.543881 + 0.839162i \(0.316954\pi\)
\(564\) −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 −0.928482 0.371376i \(-0.878886\pi\)
0.830979 0.556303i \(-0.187781\pi\)
\(570\) −2.30485 3.22219i −0.0965394 0.134963i
\(571\) −17.6576 30.5838i −0.738947 1.27989i −0.952970 0.303065i \(-0.901990\pi\)
0.214023 0.976829i \(-0.431343\pi\)
\(572\) −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 −0.821749 0.569850i \(-0.807001\pi\)
0.329859 0.944030i \(-0.392999\pi\)
\(578\) −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 −0.626799 0.779181i \(-0.715635\pi\)
0.159634 + 0.987176i \(0.448969\pi\)
\(588\) −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 −0.279401 + 0.960174i \(0.590136\pi\)
−0.925709 + 0.378236i \(0.876531\pi\)
\(600\) −21.0578 + 18.6804i −0.859680 + 0.762624i
\(601\) −1.59991 + 0.712324i −0.0652616 + 0.0290563i −0.439108 0.898434i \(-0.644705\pi\)
0.373846 + 0.927491i \(0.378039\pi\)
\(602\) 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 0.0129718 0.999916i \(-0.495871\pi\)
0.418553 + 0.908192i \(0.362538\pi\)
\(608\) −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 −0.839233 0.543772i \(-0.816996\pi\)
0.257821 + 0.966193i \(0.416996\pi\)
\(614\) 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 0.823000 0.568042i \(-0.192299\pi\)
−0.903438 + 0.428718i \(0.858965\pi\)
\(618\) 22.3792 + 31.2862i 0.900222 + 1.25852i
\(619\) 1.14724 + 10.9153i 0.0461115 + 0.438721i 0.993084 + 0.117407i \(0.0374581\pi\)
−0.946972 + 0.321315i \(0.895875\pi\)
\(620\) −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 0.439729 0.898131i \(-0.355075\pi\)
−0.718289 + 0.695745i \(0.755075\pi\)
\(632\) 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 −0.753666 0.657257i \(-0.771717\pi\)
0.600546 0.799591i \(-0.294950\pi\)
\(642\) −4.48910 + 20.3774i −0.177170 + 0.804232i
\(643\) −27.2554 + 30.2702i −1.07485 + 1.19374i −0.0946941 + 0.995506i \(0.530187\pi\)
−0.980155 + 0.198234i \(0.936479\pi\)
\(644\) 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 −0.954453 0.298361i \(-0.903560\pi\)
0.947541 + 0.319634i \(0.103560\pi\)
\(648\) −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 −0.620873 0.783911i \(-0.713222\pi\)
0.770290 0.637694i \(-0.220111\pi\)
\(654\) 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 −0.531725 0.846917i \(-0.678456\pi\)
0.999314 + 0.0370284i \(0.0117892\pi\)
\(660\) −0.0460493 + 6.23587i −0.00179246 + 0.242731i
\(661\) −6.49165 11.2439i −0.252496 0.437336i 0.711717 0.702467i \(-0.247918\pi\)
−0.964212 + 0.265131i \(0.914585\pi\)
\(662\) 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 0.921567 0.388219i \(-0.126910\pi\)
−0.482423 + 0.875939i \(0.660243\pi\)
\(674\) −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 0.818270 0.574834i \(-0.194933\pi\)
0.513721 + 0.857957i \(0.328267\pi\)
\(678\) −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 0.735555 0.677465i \(-0.236921\pi\)
−0.750640 + 0.660711i \(0.770255\pi\)
\(692\) −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 −0.127131 0.991886i \(-0.540577\pi\)
0.904054 + 0.427419i \(0.140577\pi\)
\(702\) 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 −0.0780624 0.996948i \(-0.524873\pi\)
−0.476809 + 0.879007i \(0.658207\pi\)
\(710\) −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 0.391101 0.920348i \(-0.372094\pi\)
−0.754446 + 0.656362i \(0.772094\pi\)
\(720\) −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 −0.119714 + 0.992808i \(0.538198\pi\)
−0.799940 + 0.600079i \(0.795136\pi\)
\(728\) −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 −0.736392 0.676555i \(-0.763472\pi\)
0.860964 0.508666i \(-0.169861\pi\)
\(734\) 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 −0.967281 0.253708i \(-0.918350\pi\)
0.931672 + 0.363300i \(0.118350\pi\)
\(740\) 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 −0.639922 0.768440i \(-0.721033\pi\)
0.831121 + 0.556092i \(0.187700\pi\)
\(744\) 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 0.999859 0.0167864i \(-0.00534354\pi\)
0.656562 + 0.754272i \(0.272010\pi\)
\(752\) 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 0.676605 + 0.736346i \(0.263451\pi\)
−0.980198 + 0.198018i \(0.936549\pi\)
\(758\) −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 −0.911976 0.410243i \(-0.865444\pi\)
−0.666271 + 0.745710i \(0.732111\pi\)
\(762\) −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 0.894395 0.447277i \(-0.147606\pi\)
−0.834551 + 0.550930i \(0.814273\pi\)
\(770\) 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 −0.919261 0.393649i \(-0.871213\pi\)
0.0903152 + 0.995913i \(0.471213\pi\)
\(774\) 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 −0.567150 0.823615i \(-0.691954\pi\)
0.878386 + 0.477951i \(0.158621\pi\)
\(788\) −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 0.253754 0.967269i \(-0.418334\pi\)
0.935445 0.353471i \(-0.114999\pi\)
\(798\) −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 −0.938710 0.344707i \(-0.887978\pi\)
0.556819 0.830634i \(-0.312022\pi\)
\(810\) −6.64215 0.196526i −0.233381 0.00690523i
\(811\) −17.8837 + 12.9933i −0.627981 + 0.456255i −0.855700 0.517472i \(-0.826873\pi\)
0.227719 + 0.973727i \(0.426873\pi\)
\(812\) −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 −0.365891 0.930658i \(-0.619236\pi\)
0.446784 + 0.894642i \(0.352569\pi\)
\(822\) −34.4073 + 19.5272i −1.20009 + 0.681091i
\(823\) 10.1460 2.15660i 0.353668 0.0751745i −0.0276517 0.999618i \(-0.508803\pi\)
0.381320 + 0.924443i \(0.375470\pi\)
\(824\) −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 −0.0967683 0.995307i \(-0.530851\pi\)
0.663314 0.748341i \(-0.269149\pi\)
\(828\) 42.6979 18.2586i 1.48385 0.634529i
\(829\) −30.6163 22.2440i −1.06335 0.772566i −0.0886419 0.996064i \(-0.528253\pi\)
−0.974705 + 0.223497i \(0.928253\pi\)
\(830\) −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 0.968937 + 0.247306i \(0.0795454\pi\)
−0.896346 + 0.443355i \(0.853788\pi\)
\(840\) 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 0.0526390 0.998614i \(-0.483237\pi\)
−0.358085 + 0.933689i \(0.616570\pi\)
\(854\) 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 −0.849836 0.527047i \(-0.823299\pi\)
0.881354 + 0.472456i \(0.156632\pi\)
\(858\) 11.2689 + 55.0102i 0.384713 + 1.87802i
\(859\) −14.2555 24.6913i −0.486392 0.842456i 0.513485 0.858098i \(-0.328354\pi\)
−0.999878 + 0.0156422i \(0.995021\pi\)
\(860\) 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 0.878880 0.477042i \(-0.158291\pi\)
−0.991428 + 0.130658i \(0.958291\pi\)
\(864\) −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 0.924432 0.381346i \(-0.124539\pi\)
0.335171 + 0.942157i \(0.391206\pi\)
\(878\) −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 −0.747413 0.664360i \(-0.768704\pi\)
0.400880 + 0.916130i \(0.368704\pi\)
\(884\) −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 0.959447 + 0.281889i \(0.0909609\pi\)
−0.997089 + 0.0762484i \(0.975706\pi\)
\(888\) 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 0.417923 0.908483i \(-0.362758\pi\)
0.0122784 + 0.999925i \(0.496092\pi\)
\(908\) −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 −0.873436 0.486939i \(-0.838113\pi\)
−0.392973 0.919550i \(-0.628553\pi\)
\(912\) −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 0.999308 0.0371955i \(-0.0118424\pi\)
−0.830320 + 0.557287i \(0.811842\pi\)
\(920\) 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 0.324549 0.945869i \(-0.394788\pi\)
−0.0882298 + 0.996100i \(0.528121\pi\)
\(930\) 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 −0.366077 0.930584i \(-0.619299\pi\)
0.843147 0.537684i \(-0.180701\pi\)
\(938\) 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 −0.312128 + 0.950040i \(0.601042\pi\)
−0.912209 + 0.409725i \(0.865625\pi\)
\(942\) −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 −0.743254 0.669009i \(-0.766719\pi\)
0.951006 + 0.309172i \(0.100052\pi\)
\(948\) −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 0.849607 0.527417i \(-0.176839\pi\)
−0.239060 + 0.971005i \(0.576839\pi\)
\(954\) −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 0.836677 + 0.547696i \(0.184495\pi\)
0.0559798 + 0.998432i \(0.482172\pi\)
\(968\) 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 −0.527558 0.849519i \(-0.676892\pi\)
0.644916 + 0.764253i \(0.276892\pi\)
\(972\) 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 0.235623 0.971845i \(-0.424287\pi\)
0.610537 + 0.791988i \(0.290954\pi\)
\(978\) 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 −0.245864 0.969304i \(-0.579072\pi\)
0.555818 + 0.831304i \(0.312405\pi\)
\(984\) −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 −0.748256 0.663411i \(-0.769108\pi\)
−0.00767052 + 0.999971i \(0.502442\pi\)
\(998\) −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.97.9 yes 72
3.2 odd 2 297.2.n.b.262.1 72
9.2 odd 6 891.2.f.e.163.1 36
9.4 even 3 inner 99.2.m.b.31.1 yes 72
9.5 odd 6 297.2.n.b.64.9 72
9.7 even 3 891.2.f.f.163.9 36
11.4 even 5 1089.2.e.p.727.1 36
11.5 even 5 inner 99.2.m.b.16.1 72
11.7 odd 10 1089.2.e.o.727.18 36
33.5 odd 10 297.2.n.b.181.9 72
99.4 even 15 1089.2.e.p.364.1 36
99.5 odd 30 297.2.n.b.280.1 72
99.7 odd 30 9801.2.a.co.1.1 18
99.16 even 15 891.2.f.f.82.9 36
99.29 even 30 9801.2.a.cn.1.18 18
99.38 odd 30 891.2.f.e.82.1 36
99.40 odd 30 1089.2.e.o.364.18 36
99.49 even 15 inner 99.2.m.b.49.9 yes 72
99.70 even 15 9801.2.a.cm.1.18 18
99.92 odd 30 9801.2.a.cp.1.1 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.16.1 72 11.5 even 5 inner
99.2.m.b.31.1 yes 72 9.4 even 3 inner
99.2.m.b.49.9 yes 72 99.49 even 15 inner
99.2.m.b.97.9 yes 72 1.1 even 1 trivial
297.2.n.b.64.9 72 9.5 odd 6
297.2.n.b.181.9 72 33.5 odd 10
297.2.n.b.262.1 72 3.2 odd 2
297.2.n.b.280.1 72 99.5 odd 30
891.2.f.e.82.1 36 99.38 odd 30
891.2.f.e.163.1 36 9.2 odd 6
891.2.f.f.82.9 36 99.16 even 15
891.2.f.f.163.9 36 9.7 even 3
1089.2.e.o.364.18 36 99.40 odd 30
1089.2.e.o.727.18 36 11.7 odd 10
1089.2.e.p.364.1 36 99.4 even 15
1089.2.e.p.727.1 36 11.4 even 5
9801.2.a.cm.1.18 18 99.70 even 15
9801.2.a.cn.1.18 18 99.29 even 30
9801.2.a.co.1.1 18 99.7 odd 30
9801.2.a.cp.1.1 18 99.92 odd 30