Properties

Label 136.2.s.c.107.8
Level $136$
Weight $2$
Character 136.107
Analytic conductor $1.086$
Analytic rank $0$
Dimension $112$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [136,2,Mod(3,136)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(136, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([8, 8, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("136.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 136.s (of order \(16\), 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: \(1.08596546749\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(14\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 107.8
Character \(\chi\) \(=\) 136.107
Dual form 136.2.s.c.75.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0241236 + 1.41401i) q^{2} +(-1.25761 - 1.88214i) q^{3} +(-1.99884 - 0.0682220i) q^{4} +(-1.55757 - 0.309820i) q^{5} +(2.69170 - 1.73286i) q^{6} +(-3.91750 + 0.779239i) q^{7} +(0.144686 - 2.82472i) q^{8} +(-0.812832 + 1.96235i) q^{9} +O(q^{10})\) \(q+(-0.0241236 + 1.41401i) q^{2} +(-1.25761 - 1.88214i) q^{3} +(-1.99884 - 0.0682220i) q^{4} +(-1.55757 - 0.309820i) q^{5} +(2.69170 - 1.73286i) q^{6} +(-3.91750 + 0.779239i) q^{7} +(0.144686 - 2.82472i) q^{8} +(-0.812832 + 1.96235i) q^{9} +(0.475662 - 2.19494i) q^{10} +(-2.04236 - 1.36466i) q^{11} +(2.38535 + 3.84789i) q^{12} +(1.67634 - 1.67634i) q^{13} +(-1.00735 - 5.55817i) q^{14} +(1.37568 + 3.32120i) q^{15} +(3.99069 + 0.272729i) q^{16} +(-0.0531197 + 4.12276i) q^{17} +(-2.75517 - 1.19669i) q^{18} +(-1.36178 - 3.28763i) q^{19} +(3.09219 + 0.725539i) q^{20} +(6.39331 + 6.39331i) q^{21} +(1.97891 - 2.85499i) q^{22} +(5.72685 + 3.82656i) q^{23} +(-5.49849 + 3.28007i) q^{24} +(-2.28937 - 0.948286i) q^{25} +(2.32992 + 2.41080i) q^{26} +(-1.94477 + 0.386838i) q^{27} +(7.88360 - 1.29031i) q^{28} +(0.362301 - 1.82141i) q^{29} +(-4.72938 + 1.86511i) q^{30} +(-5.41149 - 8.09887i) q^{31} +(-0.481911 + 5.63629i) q^{32} +5.56021i q^{33} +(-5.82834 - 0.174568i) q^{34} +6.34320 q^{35} +(1.75859 - 3.86696i) q^{36} +(-5.16270 + 3.44961i) q^{37} +(4.68158 - 1.84626i) q^{38} +(-5.26329 - 1.04693i) q^{39} +(-1.10051 + 4.35488i) q^{40} +(-0.977918 - 4.91633i) q^{41} +(-9.19442 + 8.88596i) q^{42} +(-1.08459 + 2.61842i) q^{43} +(3.98923 + 2.86706i) q^{44} +(1.87402 - 2.80466i) q^{45} +(-5.54894 + 8.00550i) q^{46} +(2.87182 - 2.87182i) q^{47} +(-4.50541 - 7.85403i) q^{48} +(8.27242 - 3.42655i) q^{49} +(1.39611 - 3.21431i) q^{50} +(7.82643 - 5.08484i) q^{51} +(-3.46510 + 3.23637i) q^{52} +(-3.16997 + 1.31304i) q^{53} +(-0.500078 - 2.75925i) q^{54} +(2.75831 + 2.75831i) q^{55} +(1.63433 + 11.1786i) q^{56} +(-4.47520 + 6.69761i) q^{57} +(2.56674 + 0.556235i) q^{58} +(6.57678 + 2.72419i) q^{59} +(-2.52319 - 6.73238i) q^{60} +(-1.72880 - 8.69128i) q^{61} +(11.5824 - 7.45652i) q^{62} +(1.65513 - 8.32089i) q^{63} +(-7.95813 - 0.817393i) q^{64} +(-3.13038 + 2.09165i) q^{65} +(-7.86217 - 0.134132i) q^{66} -6.11894i q^{67} +(0.387441 - 8.23710i) q^{68} -15.5911i q^{69} +(-0.153021 + 8.96933i) q^{70} +(5.58989 - 3.73504i) q^{71} +(5.42549 + 2.57995i) q^{72} +(2.78015 - 13.9768i) q^{73} +(-4.75323 - 7.38332i) q^{74} +(1.09431 + 5.50148i) q^{75} +(2.49769 + 6.66433i) q^{76} +(9.06432 + 3.75456i) q^{77} +(1.60734 - 7.41708i) q^{78} +(-7.05875 + 10.5642i) q^{79} +(-6.13128 - 1.66119i) q^{80} +(7.67959 + 7.67959i) q^{81} +(6.97532 - 1.26418i) q^{82} +(-16.0062 + 6.62999i) q^{83} +(-12.3430 - 13.2153i) q^{84} +(1.36005 - 6.40503i) q^{85} +(-3.67631 - 1.59678i) q^{86} +(-3.88378 + 1.60871i) q^{87} +(-4.15028 + 5.57164i) q^{88} +(0.443072 - 0.443072i) q^{89} +(3.92061 + 2.71753i) q^{90} +(-5.26080 + 7.87334i) q^{91} +(-11.1860 - 8.03937i) q^{92} +(-8.43769 + 20.3704i) q^{93} +(3.99149 + 4.13005i) q^{94} +(1.10249 + 5.54261i) q^{95} +(11.2144 - 6.18121i) q^{96} +(9.17174 + 1.82437i) q^{97} +(4.64561 + 11.7799i) q^{98} +(4.33803 - 2.89858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 8 q^{20} - 8 q^{22} - 56 q^{24} - 16 q^{25} - 40 q^{26} + 32 q^{27} + 40 q^{28} - 72 q^{30} + 32 q^{32} - 72 q^{34} - 32 q^{35} + 56 q^{36} + 48 q^{38} + 56 q^{40} - 16 q^{41} - 56 q^{42} - 96 q^{43} + 24 q^{44} - 24 q^{46} + 16 q^{48} - 16 q^{49} - 16 q^{51} - 16 q^{52} - 24 q^{54} + 32 q^{56} + 32 q^{57} + 48 q^{58} - 16 q^{59} + 96 q^{60} + 48 q^{62} + 40 q^{64} + 64 q^{65} - 16 q^{66} + 80 q^{68} + 64 q^{70} + 96 q^{72} - 96 q^{73} + 40 q^{74} - 16 q^{75} + 48 q^{76} + 96 q^{78} + 8 q^{80} - 96 q^{81} + 32 q^{82} + 128 q^{83} + 64 q^{86} - 72 q^{88} - 16 q^{89} + 152 q^{90} - 16 q^{91} - 120 q^{92} + 88 q^{94} - 160 q^{96} - 16 q^{97} + 128 q^{98} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).

\(n\) \(69\) \(103\) \(105\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{16}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0241236 + 1.41401i −0.0170580 + 0.999855i
\(3\) −1.25761 1.88214i −0.726080 1.08666i −0.992434 0.122780i \(-0.960819\pi\)
0.266354 0.963875i \(-0.414181\pi\)
\(4\) −1.99884 0.0682220i −0.999418 0.0341110i
\(5\) −1.55757 0.309820i −0.696566 0.138556i −0.165907 0.986141i \(-0.553055\pi\)
−0.530658 + 0.847586i \(0.678055\pi\)
\(6\) 2.69170 1.73286i 1.09888 0.707438i
\(7\) −3.91750 + 0.779239i −1.48068 + 0.294525i −0.868299 0.496042i \(-0.834786\pi\)
−0.612376 + 0.790566i \(0.709786\pi\)
\(8\) 0.144686 2.82472i 0.0511541 0.998691i
\(9\) −0.812832 + 1.96235i −0.270944 + 0.654117i
\(10\) 0.475662 2.19494i 0.150417 0.694101i
\(11\) −2.04236 1.36466i −0.615793 0.411460i 0.208178 0.978091i \(-0.433247\pi\)
−0.823972 + 0.566631i \(0.808247\pi\)
\(12\) 2.38535 + 3.84789i 0.688590 + 1.11079i
\(13\) 1.67634 1.67634i 0.464934 0.464934i −0.435335 0.900269i \(-0.643370\pi\)
0.900269 + 0.435335i \(0.143370\pi\)
\(14\) −1.00735 5.55817i −0.269224 1.48548i
\(15\) 1.37568 + 3.32120i 0.355200 + 0.857529i
\(16\) 3.99069 + 0.272729i 0.997673 + 0.0681823i
\(17\) −0.0531197 + 4.12276i −0.0128834 + 0.999917i
\(18\) −2.75517 1.19669i −0.649400 0.282062i
\(19\) −1.36178 3.28763i −0.312414 0.754233i −0.999614 0.0277659i \(-0.991161\pi\)
0.687201 0.726468i \(-0.258839\pi\)
\(20\) 3.09219 + 0.725539i 0.691434 + 0.162235i
\(21\) 6.39331 + 6.39331i 1.39513 + 1.39513i
\(22\) 1.97891 2.85499i 0.421904 0.608685i
\(23\) 5.72685 + 3.82656i 1.19413 + 0.797893i 0.983718 0.179719i \(-0.0575190\pi\)
0.210413 + 0.977612i \(0.432519\pi\)
\(24\) −5.49849 + 3.28007i −1.12237 + 0.669542i
\(25\) −2.28937 0.948286i −0.457873 0.189657i
\(26\) 2.32992 + 2.41080i 0.456935 + 0.472797i
\(27\) −1.94477 + 0.386838i −0.374271 + 0.0744471i
\(28\) 7.88360 1.29031i 1.48986 0.243846i
\(29\) 0.362301 1.82141i 0.0672775 0.338227i −0.932457 0.361282i \(-0.882339\pi\)
0.999734 + 0.0230549i \(0.00733924\pi\)
\(30\) −4.72938 + 1.86511i −0.863463 + 0.340521i
\(31\) −5.41149 8.09887i −0.971933 1.45460i −0.888926 0.458051i \(-0.848548\pi\)
−0.0830072 0.996549i \(-0.526452\pi\)
\(32\) −0.481911 + 5.63629i −0.0851906 + 0.996365i
\(33\) 5.56021i 0.967907i
\(34\) −5.82834 0.174568i −0.999552 0.0299381i
\(35\) 6.34320 1.07220
\(36\) 1.75859 3.86696i 0.293099 0.644494i
\(37\) −5.16270 + 3.44961i −0.848743 + 0.567112i −0.902131 0.431462i \(-0.857998\pi\)
0.0533879 + 0.998574i \(0.482998\pi\)
\(38\) 4.68158 1.84626i 0.759453 0.299503i
\(39\) −5.26329 1.04693i −0.842801 0.167644i
\(40\) −1.10051 + 4.35488i −0.174006 + 0.688566i
\(41\) −0.977918 4.91633i −0.152725 0.767801i −0.978892 0.204376i \(-0.934483\pi\)
0.826167 0.563425i \(-0.190517\pi\)
\(42\) −9.19442 + 8.88596i −1.41873 + 1.37113i
\(43\) −1.08459 + 2.61842i −0.165398 + 0.399306i −0.984748 0.173988i \(-0.944335\pi\)
0.819350 + 0.573294i \(0.194335\pi\)
\(44\) 3.98923 + 2.86706i 0.601400 + 0.432226i
\(45\) 1.87402 2.80466i 0.279362 0.418095i
\(46\) −5.54894 + 8.00550i −0.818146 + 1.18035i
\(47\) 2.87182 2.87182i 0.418898 0.418898i −0.465926 0.884824i \(-0.654279\pi\)
0.884824 + 0.465926i \(0.154279\pi\)
\(48\) −4.50541 7.85403i −0.650299 1.13363i
\(49\) 8.27242 3.42655i 1.18177 0.489507i
\(50\) 1.39611 3.21431i 0.197440 0.454571i
\(51\) 7.82643 5.08484i 1.09592 0.712020i
\(52\) −3.46510 + 3.23637i −0.480523 + 0.448804i
\(53\) −3.16997 + 1.31304i −0.435428 + 0.180360i −0.589620 0.807681i \(-0.700723\pi\)
0.154192 + 0.988041i \(0.450723\pi\)
\(54\) −0.500078 2.75925i −0.0680520 0.375486i
\(55\) 2.75831 + 2.75831i 0.371930 + 0.371930i
\(56\) 1.63433 + 11.1786i 0.218396 + 1.49380i
\(57\) −4.47520 + 6.69761i −0.592754 + 0.887120i
\(58\) 2.56674 + 0.556235i 0.337030 + 0.0730372i
\(59\) 6.57678 + 2.72419i 0.856224 + 0.354660i 0.767230 0.641372i \(-0.221635\pi\)
0.0889946 + 0.996032i \(0.471635\pi\)
\(60\) −2.52319 6.73238i −0.325742 0.869146i
\(61\) −1.72880 8.69128i −0.221351 1.11280i −0.918361 0.395744i \(-0.870487\pi\)
0.697010 0.717061i \(-0.254513\pi\)
\(62\) 11.5824 7.45652i 1.47097 0.946979i
\(63\) 1.65513 8.32089i 0.208527 1.04833i
\(64\) −7.95813 0.817393i −0.994767 0.102174i
\(65\) −3.13038 + 2.09165i −0.388276 + 0.259438i
\(66\) −7.86217 0.134132i −0.967767 0.0165105i
\(67\) 6.11894i 0.747548i −0.927520 0.373774i \(-0.878064\pi\)
0.927520 0.373774i \(-0.121936\pi\)
\(68\) 0.387441 8.23710i 0.0469841 0.998896i
\(69\) 15.5911i 1.87694i
\(70\) −0.153021 + 8.96933i −0.0182895 + 1.07204i
\(71\) 5.58989 3.73504i 0.663398 0.443268i −0.177749 0.984076i \(-0.556881\pi\)
0.841146 + 0.540808i \(0.181881\pi\)
\(72\) 5.42549 + 2.57995i 0.639400 + 0.304050i
\(73\) 2.78015 13.9768i 0.325392 1.63586i −0.378538 0.925586i \(-0.623573\pi\)
0.703930 0.710270i \(-0.251427\pi\)
\(74\) −4.75323 7.38332i −0.552552 0.858294i
\(75\) 1.09431 + 5.50148i 0.126360 + 0.635256i
\(76\) 2.49769 + 6.66433i 0.286504 + 0.764451i
\(77\) 9.06432 + 3.75456i 1.03297 + 0.427872i
\(78\) 1.60734 7.41708i 0.181996 0.839819i
\(79\) −7.05875 + 10.5642i −0.794171 + 1.18856i 0.184440 + 0.982844i \(0.440953\pi\)
−0.978611 + 0.205717i \(0.934047\pi\)
\(80\) −6.13128 1.66119i −0.685498 0.185727i
\(81\) 7.67959 + 7.67959i 0.853288 + 0.853288i
\(82\) 6.97532 1.26418i 0.770295 0.139606i
\(83\) −16.0062 + 6.62999i −1.75691 + 0.727736i −0.759936 + 0.649998i \(0.774770\pi\)
−0.996974 + 0.0777381i \(0.975230\pi\)
\(84\) −12.3430 13.2153i −1.34673 1.44191i
\(85\) 1.36005 6.40503i 0.147518 0.694723i
\(86\) −3.67631 1.59678i −0.396426 0.172185i
\(87\) −3.88378 + 1.60871i −0.416385 + 0.172472i
\(88\) −4.15028 + 5.57164i −0.442422 + 0.593939i
\(89\) 0.443072 0.443072i 0.0469655 0.0469655i −0.683234 0.730200i \(-0.739427\pi\)
0.730200 + 0.683234i \(0.239427\pi\)
\(90\) 3.92061 + 2.71753i 0.413268 + 0.286453i
\(91\) −5.26080 + 7.87334i −0.551481 + 0.825350i
\(92\) −11.1860 8.03937i −1.16622 0.838162i
\(93\) −8.43769 + 20.3704i −0.874948 + 2.11231i
\(94\) 3.99149 + 4.13005i 0.411691 + 0.425982i
\(95\) 1.10249 + 5.54261i 0.113113 + 0.568660i
\(96\) 11.2144 6.18121i 1.14456 0.630867i
\(97\) 9.17174 + 1.82437i 0.931249 + 0.185237i 0.637328 0.770593i \(-0.280040\pi\)
0.293921 + 0.955830i \(0.405040\pi\)
\(98\) 4.64561 + 11.7799i 0.469277 + 1.18995i
\(99\) 4.33803 2.89858i 0.435988 0.291318i
\(100\) 4.51137 + 2.05165i 0.451137 + 0.205165i
\(101\) −5.10512 −0.507978 −0.253989 0.967207i \(-0.581743\pi\)
−0.253989 + 0.967207i \(0.581743\pi\)
\(102\) 7.00120 + 11.1893i 0.693222 + 1.10791i
\(103\) 0.265102i 0.0261212i −0.999915 0.0130606i \(-0.995843\pi\)
0.999915 0.0130606i \(-0.00415744\pi\)
\(104\) −4.49266 4.97775i −0.440542 0.488108i
\(105\) −7.97725 11.9388i −0.778500 1.16511i
\(106\) −1.78018 4.51403i −0.172907 0.438442i
\(107\) −1.02449 + 5.15045i −0.0990410 + 0.497913i 0.899142 + 0.437657i \(0.144192\pi\)
−0.998183 + 0.0602556i \(0.980808\pi\)
\(108\) 3.91366 0.640551i 0.376592 0.0616370i
\(109\) −9.58462 + 1.90650i −0.918040 + 0.182609i −0.631425 0.775437i \(-0.717530\pi\)
−0.286614 + 0.958046i \(0.592530\pi\)
\(110\) −3.96681 + 3.83373i −0.378221 + 0.365532i
\(111\) 12.9853 + 5.37869i 1.23251 + 0.510523i
\(112\) −15.8460 + 2.04129i −1.49731 + 0.192883i
\(113\) −6.70304 4.47883i −0.630569 0.421333i 0.198795 0.980041i \(-0.436297\pi\)
−0.829364 + 0.558708i \(0.811297\pi\)
\(114\) −9.36251 6.48953i −0.876879 0.607801i
\(115\) −7.73442 7.73442i −0.721239 0.721239i
\(116\) −0.848439 + 3.61598i −0.0787756 + 0.335735i
\(117\) 1.92699 + 4.65216i 0.178150 + 0.430092i
\(118\) −4.01069 + 9.23391i −0.369214 + 0.850050i
\(119\) −3.00452 16.1923i −0.275424 1.48435i
\(120\) 9.58050 3.40540i 0.874576 0.310869i
\(121\) −1.90059 4.58844i −0.172781 0.417131i
\(122\) 12.3312 2.23488i 1.11642 0.202336i
\(123\) −8.02339 + 8.02339i −0.723445 + 0.723445i
\(124\) 10.2642 + 16.5575i 0.921749 + 1.48691i
\(125\) 9.87426 + 6.59777i 0.883181 + 0.590123i
\(126\) 11.7259 + 2.54109i 1.04462 + 0.226379i
\(127\) 0.215916 0.521267i 0.0191594 0.0462550i −0.914010 0.405691i \(-0.867031\pi\)
0.933170 + 0.359436i \(0.117031\pi\)
\(128\) 1.34778 11.2331i 0.119128 0.992879i
\(129\) 6.29223 1.25160i 0.554000 0.110197i
\(130\) −2.88210 4.47684i −0.252777 0.392645i
\(131\) 19.6039 + 3.89946i 1.71280 + 0.340697i 0.951487 0.307688i \(-0.0995553\pi\)
0.761313 + 0.648385i \(0.224555\pi\)
\(132\) 0.379328 11.1139i 0.0330163 0.967344i
\(133\) 7.89662 + 11.8181i 0.684723 + 1.02476i
\(134\) 8.65224 + 0.147611i 0.747439 + 0.0127517i
\(135\) 3.14896 0.271019
\(136\) 11.6380 + 0.746553i 0.997949 + 0.0640164i
\(137\) −3.05874 −0.261326 −0.130663 0.991427i \(-0.541711\pi\)
−0.130663 + 0.991427i \(0.541711\pi\)
\(138\) 22.0459 + 0.376113i 1.87667 + 0.0320168i
\(139\) 4.93873 + 7.39132i 0.418897 + 0.626924i 0.979568 0.201115i \(-0.0644565\pi\)
−0.560670 + 0.828039i \(0.689457\pi\)
\(140\) −12.6790 0.432745i −1.07157 0.0365736i
\(141\) −9.01678 1.79355i −0.759350 0.151044i
\(142\) 5.14653 + 7.99425i 0.431887 + 0.670862i
\(143\) −5.71132 + 1.13605i −0.477605 + 0.0950015i
\(144\) −3.77895 + 7.60945i −0.314913 + 0.634121i
\(145\) −1.12862 + 2.72472i −0.0937264 + 0.226276i
\(146\) 19.6962 + 4.26832i 1.63007 + 0.353249i
\(147\) −16.8527 11.2606i −1.38999 0.928760i
\(148\) 10.5547 6.54299i 0.867594 0.537831i
\(149\) 8.62399 8.62399i 0.706505 0.706505i −0.259294 0.965798i \(-0.583490\pi\)
0.965798 + 0.259294i \(0.0834898\pi\)
\(150\) −7.80554 + 1.41465i −0.637319 + 0.115506i
\(151\) 3.92551 + 9.47701i 0.319453 + 0.771228i 0.999283 + 0.0378583i \(0.0120535\pi\)
−0.679830 + 0.733370i \(0.737946\pi\)
\(152\) −9.48367 + 3.37098i −0.769227 + 0.273423i
\(153\) −8.04713 3.45535i −0.650572 0.279349i
\(154\) −5.52765 + 12.7264i −0.445430 + 1.02553i
\(155\) 5.91958 + 14.2911i 0.475472 + 1.14789i
\(156\) 10.4490 + 2.45172i 0.836593 + 0.196295i
\(157\) −13.4869 13.4869i −1.07637 1.07637i −0.996832 0.0795382i \(-0.974655\pi\)
−0.0795382 0.996832i \(-0.525345\pi\)
\(158\) −14.7675 10.2360i −1.17484 0.814330i
\(159\) 6.45790 + 4.31503i 0.512145 + 0.342204i
\(160\) 2.49684 8.62960i 0.197393 0.682230i
\(161\) −25.4167 10.5280i −2.00312 0.829719i
\(162\) −11.0443 + 10.6737i −0.867719 + 0.838609i
\(163\) 3.46089 0.688413i 0.271078 0.0539207i −0.0576797 0.998335i \(-0.518370\pi\)
0.328757 + 0.944414i \(0.393370\pi\)
\(164\) 1.61930 + 9.89365i 0.126446 + 0.772564i
\(165\) 1.72266 8.66040i 0.134109 0.674211i
\(166\) −8.98873 22.7928i −0.697661 1.76907i
\(167\) 7.07994 + 10.5959i 0.547863 + 0.819934i 0.997304 0.0733754i \(-0.0233771\pi\)
−0.449442 + 0.893310i \(0.648377\pi\)
\(168\) 18.9844 17.1343i 1.46467 1.32194i
\(169\) 7.37975i 0.567673i
\(170\) 9.02395 + 2.07763i 0.692106 + 0.159347i
\(171\) 7.55837 0.578003
\(172\) 2.34655 5.15981i 0.178922 0.393432i
\(173\) −9.27081 + 6.19456i −0.704847 + 0.470964i −0.855620 0.517605i \(-0.826824\pi\)
0.150773 + 0.988568i \(0.451824\pi\)
\(174\) −2.18104 5.53050i −0.165344 0.419266i
\(175\) 9.70753 + 1.93095i 0.733820 + 0.145966i
\(176\) −7.77823 6.00294i −0.586306 0.452489i
\(177\) −3.14369 15.8044i −0.236294 1.18793i
\(178\) 0.615819 + 0.637196i 0.0461576 + 0.0477598i
\(179\) 1.32051 3.18798i 0.0986992 0.238281i −0.866816 0.498629i \(-0.833837\pi\)
0.965515 + 0.260348i \(0.0838372\pi\)
\(180\) −3.93719 + 5.47821i −0.293461 + 0.408322i
\(181\) −7.57255 + 11.3331i −0.562863 + 0.842385i −0.998327 0.0578218i \(-0.981584\pi\)
0.435464 + 0.900206i \(0.356584\pi\)
\(182\) −11.0061 7.62874i −0.815823 0.565480i
\(183\) −14.1841 + 14.1841i −1.04852 + 1.04852i
\(184\) 11.6376 15.6231i 0.857933 1.15175i
\(185\) 9.11002 3.77350i 0.669782 0.277433i
\(186\) −28.6003 12.4224i −2.09708 0.910853i
\(187\) 5.73465 8.34766i 0.419359 0.610441i
\(188\) −5.93621 + 5.54437i −0.432943 + 0.404365i
\(189\) 7.31719 3.03088i 0.532247 0.220464i
\(190\) −7.86389 + 1.42523i −0.570507 + 0.103397i
\(191\) −15.5081 15.5081i −1.12212 1.12212i −0.991422 0.130703i \(-0.958276\pi\)
−0.130703 0.991422i \(-0.541724\pi\)
\(192\) 8.46975 + 16.0063i 0.611252 + 1.15515i
\(193\) 0.764638 1.14436i 0.0550398 0.0823730i −0.802929 0.596075i \(-0.796726\pi\)
0.857969 + 0.513702i \(0.171726\pi\)
\(194\) −2.80093 + 12.9249i −0.201095 + 0.927954i
\(195\) 7.87358 + 3.26134i 0.563839 + 0.233550i
\(196\) −16.7690 + 6.28475i −1.19778 + 0.448911i
\(197\) 2.05749 + 10.3437i 0.146590 + 0.736957i 0.982230 + 0.187680i \(0.0600967\pi\)
−0.835641 + 0.549277i \(0.814903\pi\)
\(198\) 3.99396 + 6.20393i 0.283839 + 0.440894i
\(199\) 3.58491 18.0226i 0.254128 1.27759i −0.617169 0.786831i \(-0.711721\pi\)
0.871297 0.490756i \(-0.163279\pi\)
\(200\) −3.00989 + 6.32962i −0.212831 + 0.447572i
\(201\) −11.5167 + 7.69523i −0.812327 + 0.542779i
\(202\) 0.123154 7.21867i 0.00866507 0.507904i
\(203\) 7.41768i 0.520619i
\(204\) −15.9906 + 9.62982i −1.11957 + 0.674222i
\(205\) 7.96050i 0.555985i
\(206\) 0.374856 + 0.00639521i 0.0261174 + 0.000445575i
\(207\) −12.1640 + 8.12774i −0.845458 + 0.564917i
\(208\) 7.14695 6.23258i 0.495552 0.432152i
\(209\) −1.70525 + 8.57287i −0.117955 + 0.592998i
\(210\) 17.0740 10.9919i 1.17822 0.758512i
\(211\) −0.365262 1.83630i −0.0251457 0.126416i 0.966174 0.257893i \(-0.0830281\pi\)
−0.991319 + 0.131477i \(0.958028\pi\)
\(212\) 6.42582 2.40830i 0.441327 0.165402i
\(213\) −14.0598 5.82374i −0.963359 0.399036i
\(214\) −7.25806 1.57288i −0.496151 0.107520i
\(215\) 2.50056 3.74235i 0.170537 0.255226i
\(216\) 0.811332 + 5.54940i 0.0552042 + 0.377589i
\(217\) 27.5105 + 27.5105i 1.86753 + 1.86753i
\(218\) −2.46459 13.5987i −0.166923 0.921021i
\(219\) −29.8026 + 12.3446i −2.01387 + 0.834173i
\(220\) −5.32523 5.70159i −0.359027 0.384401i
\(221\) 6.82212 + 7.00021i 0.458905 + 0.470885i
\(222\) −7.91876 + 18.2316i −0.531472 + 1.22362i
\(223\) 12.4584 5.16043i 0.834275 0.345568i 0.0756812 0.997132i \(-0.475887\pi\)
0.758594 + 0.651564i \(0.225887\pi\)
\(224\) −2.50413 22.4557i −0.167314 1.50038i
\(225\) 3.72174 3.72174i 0.248116 0.248116i
\(226\) 6.49480 9.37011i 0.432028 0.623291i
\(227\) 11.5521 17.2889i 0.766738 1.14750i −0.218420 0.975855i \(-0.570090\pi\)
0.985158 0.171650i \(-0.0549098\pi\)
\(228\) 9.40211 13.0821i 0.622670 0.866384i
\(229\) 9.64260 23.2793i 0.637201 1.53834i −0.193193 0.981161i \(-0.561884\pi\)
0.830393 0.557178i \(-0.188116\pi\)
\(230\) 11.1231 10.7500i 0.733437 0.708831i
\(231\) −4.33273 21.7821i −0.285073 1.43316i
\(232\) −5.09255 1.28693i −0.334343 0.0844911i
\(233\) −2.27157 0.451844i −0.148816 0.0296013i 0.120120 0.992759i \(-0.461672\pi\)
−0.268936 + 0.963158i \(0.586672\pi\)
\(234\) −6.62467 + 2.61255i −0.433068 + 0.170787i
\(235\) −5.36280 + 3.58331i −0.349830 + 0.233749i
\(236\) −12.9601 5.89390i −0.843628 0.383660i
\(237\) 28.7604 1.86819
\(238\) 22.9685 3.85780i 1.48883 0.250064i
\(239\) 11.2231i 0.725965i −0.931796 0.362982i \(-0.881759\pi\)
0.931796 0.362982i \(-0.118241\pi\)
\(240\) 4.58415 + 13.6291i 0.295905 + 0.879752i
\(241\) −3.12364 4.67486i −0.201211 0.301134i 0.717118 0.696952i \(-0.245461\pi\)
−0.918329 + 0.395818i \(0.870461\pi\)
\(242\) 6.53394 2.57677i 0.420018 0.165641i
\(243\) 3.63566 18.2777i 0.233228 1.17251i
\(244\) 2.86266 + 17.4904i 0.183263 + 1.11971i
\(245\) −13.9465 + 2.77413i −0.891008 + 0.177232i
\(246\) −11.1516 11.5387i −0.710999 0.735680i
\(247\) −7.79400 3.22838i −0.495920 0.205417i
\(248\) −23.6600 + 14.1142i −1.50241 + 0.896252i
\(249\) 32.6081 + 21.7880i 2.06645 + 1.38076i
\(250\) −9.56750 + 13.8031i −0.605102 + 0.872986i
\(251\) −11.1300 11.1300i −0.702519 0.702519i 0.262432 0.964951i \(-0.415476\pi\)
−0.964951 + 0.262432i \(0.915476\pi\)
\(252\) −3.87600 + 16.5192i −0.244165 + 1.04061i
\(253\) −6.47432 15.6304i −0.407037 0.982674i
\(254\) 0.731867 + 0.317882i 0.0459214 + 0.0199457i
\(255\) −13.7656 + 5.49520i −0.862034 + 0.344123i
\(256\) 15.8512 + 2.17675i 0.990702 + 0.136047i
\(257\) 1.55502 + 3.75414i 0.0969992 + 0.234177i 0.964929 0.262509i \(-0.0845500\pi\)
−0.867930 + 0.496686i \(0.834550\pi\)
\(258\) 1.61798 + 8.92745i 0.100731 + 0.555799i
\(259\) 17.5368 17.5368i 1.08968 1.08968i
\(260\) 6.39982 3.96731i 0.396900 0.246042i
\(261\) 3.27975 + 2.19146i 0.203011 + 0.135648i
\(262\) −5.98678 + 27.6260i −0.369864 + 1.70674i
\(263\) −5.20634 + 12.5692i −0.321037 + 0.775051i 0.678158 + 0.734916i \(0.262779\pi\)
−0.999194 + 0.0401344i \(0.987221\pi\)
\(264\) 15.7060 + 0.804481i 0.966640 + 0.0495124i
\(265\) 5.34425 1.06304i 0.328294 0.0653018i
\(266\) −16.9014 + 10.8808i −1.03629 + 0.667144i
\(267\) −1.39113 0.276714i −0.0851360 0.0169346i
\(268\) −0.417446 + 12.2308i −0.0254996 + 0.747113i
\(269\) −0.757121 1.13311i −0.0461625 0.0690871i 0.807670 0.589634i \(-0.200728\pi\)
−0.853833 + 0.520547i \(0.825728\pi\)
\(270\) −0.0759643 + 4.45265i −0.00462304 + 0.270980i
\(271\) −1.17410 −0.0713212 −0.0356606 0.999364i \(-0.511354\pi\)
−0.0356606 + 0.999364i \(0.511354\pi\)
\(272\) −1.33638 + 16.4382i −0.0810300 + 0.996712i
\(273\) 21.4348 1.29729
\(274\) 0.0737879 4.32508i 0.00445769 0.261288i
\(275\) 3.38161 + 5.06094i 0.203919 + 0.305186i
\(276\) −1.06365 + 31.1640i −0.0640244 + 1.87585i
\(277\) 25.2299 + 5.01854i 1.51592 + 0.301535i 0.881771 0.471677i \(-0.156351\pi\)
0.634147 + 0.773212i \(0.281351\pi\)
\(278\) −10.5705 + 6.80509i −0.633978 + 0.408142i
\(279\) 20.2915 4.03622i 1.21482 0.241642i
\(280\) 0.917769 17.9178i 0.0548472 1.07079i
\(281\) −1.11240 + 2.68556i −0.0663600 + 0.160207i −0.953580 0.301139i \(-0.902633\pi\)
0.887220 + 0.461346i \(0.152633\pi\)
\(282\) 2.75361 12.7065i 0.163975 0.756663i
\(283\) −5.74499 3.83868i −0.341504 0.228186i 0.372977 0.927841i \(-0.378337\pi\)
−0.714481 + 0.699655i \(0.753337\pi\)
\(284\) −11.4281 + 7.08439i −0.678132 + 0.420381i
\(285\) 9.04548 9.04548i 0.535808 0.535808i
\(286\) −1.46861 8.10326i −0.0868407 0.479156i
\(287\) 7.66199 + 18.4977i 0.452273 + 1.09188i
\(288\) −10.6687 5.52703i −0.628657 0.325684i
\(289\) −16.9944 0.438000i −0.999668 0.0257647i
\(290\) −3.82555 1.66160i −0.224644 0.0975726i
\(291\) −8.10072 19.5569i −0.474872 1.14644i
\(292\) −6.51058 + 27.7476i −0.381003 + 1.62380i
\(293\) −10.3468 10.3468i −0.604467 0.604467i 0.337028 0.941495i \(-0.390578\pi\)
−0.941495 + 0.337028i \(0.890578\pi\)
\(294\) 16.3291 23.5582i 0.952335 1.37394i
\(295\) −9.39978 6.28073i −0.547277 0.365678i
\(296\) 8.99722 + 15.0823i 0.522953 + 0.876642i
\(297\) 4.49981 + 1.86388i 0.261105 + 0.108153i
\(298\) 11.9863 + 12.4024i 0.694350 + 0.718453i
\(299\) 16.0148 3.18554i 0.926159 0.184225i
\(300\) −1.81203 11.0712i −0.104618 0.639197i
\(301\) 2.20849 11.1028i 0.127295 0.639956i
\(302\) −13.4953 + 5.32208i −0.776565 + 0.306251i
\(303\) 6.42023 + 9.60855i 0.368833 + 0.551997i
\(304\) −4.53781 13.4913i −0.260261 0.773779i
\(305\) 14.0729i 0.805811i
\(306\) 5.08002 11.2953i 0.290406 0.645712i
\(307\) −26.5174 −1.51343 −0.756715 0.653745i \(-0.773197\pi\)
−0.756715 + 0.653745i \(0.773197\pi\)
\(308\) −17.8619 8.12314i −1.01778 0.462859i
\(309\) −0.498959 + 0.333394i −0.0283848 + 0.0189661i
\(310\) −20.3506 + 8.02558i −1.15584 + 0.455822i
\(311\) −6.62139 1.31708i −0.375465 0.0746846i 0.00375083 0.999993i \(-0.498806\pi\)
−0.379215 + 0.925308i \(0.623806\pi\)
\(312\) −3.71882 + 14.7159i −0.210537 + 0.833122i
\(313\) −0.830614 4.17578i −0.0469491 0.236029i 0.950185 0.311687i \(-0.100894\pi\)
−0.997134 + 0.0756583i \(0.975894\pi\)
\(314\) 19.3959 18.7452i 1.09457 1.05785i
\(315\) −5.15595 + 12.4476i −0.290505 + 0.701341i
\(316\) 14.8300 20.6345i 0.834252 1.16078i
\(317\) 6.65233 9.95591i 0.373632 0.559180i −0.596237 0.802809i \(-0.703338\pi\)
0.969868 + 0.243629i \(0.0783379\pi\)
\(318\) −6.25728 + 9.02743i −0.350891 + 0.506233i
\(319\) −3.22555 + 3.22555i −0.180596 + 0.180596i
\(320\) 12.1421 + 3.73873i 0.678764 + 0.209001i
\(321\) 10.9823 4.54901i 0.612971 0.253901i
\(322\) 15.4998 35.6855i 0.863768 1.98867i
\(323\) 13.6264 5.43966i 0.758196 0.302671i
\(324\) −14.8263 15.8742i −0.823685 0.881898i
\(325\) −5.42741 + 2.24811i −0.301059 + 0.124703i
\(326\) 0.889933 + 4.91033i 0.0492888 + 0.271958i
\(327\) 15.6420 + 15.6420i 0.865004 + 0.865004i
\(328\) −14.0288 + 2.05103i −0.774609 + 0.113249i
\(329\) −9.01250 + 13.4882i −0.496875 + 0.743627i
\(330\) 12.2043 + 2.64478i 0.671826 + 0.145590i
\(331\) 7.49253 + 3.10351i 0.411827 + 0.170584i 0.578971 0.815348i \(-0.303455\pi\)
−0.167144 + 0.985932i \(0.553455\pi\)
\(332\) 32.4461 12.1603i 1.78071 0.667382i
\(333\) −2.57293 12.9350i −0.140996 0.708833i
\(334\) −15.1535 + 9.75548i −0.829160 + 0.533796i
\(335\) −1.89577 + 9.53068i −0.103577 + 0.520717i
\(336\) 23.7701 + 27.2574i 1.29676 + 1.48701i
\(337\) −22.3238 + 14.9163i −1.21605 + 0.812541i −0.986976 0.160868i \(-0.948571\pi\)
−0.229077 + 0.973408i \(0.573571\pi\)
\(338\) −10.4350 0.178026i −0.567591 0.00968335i
\(339\) 18.2487i 0.991133i
\(340\) −3.15548 + 12.7098i −0.171130 + 0.689287i
\(341\) 23.9256i 1.29564i
\(342\) −0.182335 + 10.6876i −0.00985956 + 0.577919i
\(343\) −6.48943 + 4.33610i −0.350396 + 0.234127i
\(344\) 7.23940 + 3.44251i 0.390322 + 0.185608i
\(345\) −4.83042 + 24.2841i −0.260061 + 1.30741i
\(346\) −8.53551 13.2584i −0.458872 0.712778i
\(347\) −0.808226 4.06323i −0.0433878 0.218125i 0.953009 0.302943i \(-0.0979692\pi\)
−0.996396 + 0.0848177i \(0.972969\pi\)
\(348\) 7.87279 2.95060i 0.422026 0.158169i
\(349\) 10.7699 + 4.46102i 0.576497 + 0.238793i 0.651829 0.758366i \(-0.274002\pi\)
−0.0753324 + 0.997158i \(0.524002\pi\)
\(350\) −2.96456 + 13.6799i −0.158462 + 0.731223i
\(351\) −2.61162 + 3.90857i −0.139398 + 0.208624i
\(352\) 8.67584 10.8537i 0.462424 0.578502i
\(353\) −14.2069 14.2069i −0.756155 0.756155i 0.219466 0.975620i \(-0.429569\pi\)
−0.975620 + 0.219466i \(0.929569\pi\)
\(354\) 22.4234 4.06394i 1.19179 0.215996i
\(355\) −9.86382 + 4.08573i −0.523517 + 0.216848i
\(356\) −0.915855 + 0.855401i −0.0485402 + 0.0453362i
\(357\) −26.6977 + 26.0185i −1.41299 + 1.37704i
\(358\) 4.47597 + 1.94411i 0.236563 + 0.102749i
\(359\) −7.57532 + 3.13780i −0.399810 + 0.165607i −0.573523 0.819190i \(-0.694424\pi\)
0.173713 + 0.984796i \(0.444424\pi\)
\(360\) −7.65126 5.69937i −0.403257 0.300383i
\(361\) 4.48098 4.48098i 0.235841 0.235841i
\(362\) −15.8424 10.9810i −0.832661 0.577151i
\(363\) −6.24590 + 9.34765i −0.327825 + 0.490624i
\(364\) 11.0526 15.3786i 0.579314 0.806058i
\(365\) −8.66055 + 20.9084i −0.453314 + 1.09440i
\(366\) −19.7142 20.3986i −1.03048 1.06625i
\(367\) −2.36264 11.8778i −0.123329 0.620017i −0.992167 0.124920i \(-0.960133\pi\)
0.868838 0.495097i \(-0.164867\pi\)
\(368\) 21.8105 + 16.8325i 1.13695 + 0.877455i
\(369\) 10.4424 + 2.07713i 0.543612 + 0.108131i
\(370\) 5.11599 + 12.9727i 0.265967 + 0.674417i
\(371\) 11.3952 7.61400i 0.591607 0.395299i
\(372\) 18.2553 40.1414i 0.946492 2.08124i
\(373\) 26.2968 1.36160 0.680798 0.732471i \(-0.261633\pi\)
0.680798 + 0.732471i \(0.261633\pi\)
\(374\) 11.6653 + 8.31022i 0.603199 + 0.429711i
\(375\) 26.8822i 1.38819i
\(376\) −7.69658 8.52760i −0.396921 0.439777i
\(377\) −2.44596 3.66064i −0.125974 0.188533i
\(378\) 4.10917 + 10.4197i 0.211353 + 0.535930i
\(379\) 1.94490 9.77769i 0.0999030 0.502246i −0.898140 0.439710i \(-0.855081\pi\)
0.998043 0.0625360i \(-0.0199188\pi\)
\(380\) −1.82558 11.1540i −0.0936501 0.572187i
\(381\) −1.25264 + 0.249165i −0.0641745 + 0.0127651i
\(382\) 22.3027 21.5544i 1.14110 1.10282i
\(383\) −10.5148 4.35536i −0.537280 0.222549i 0.0975084 0.995235i \(-0.468913\pi\)
−0.634788 + 0.772686i \(0.718913\pi\)
\(384\) −22.8373 + 11.5902i −1.16541 + 0.591458i
\(385\) −12.9551 8.65629i −0.660251 0.441166i
\(386\) 1.59969 + 1.10881i 0.0814221 + 0.0564370i
\(387\) −4.25668 4.25668i −0.216379 0.216379i
\(388\) −18.2083 4.27234i −0.924389 0.216895i
\(389\) 7.68665 + 18.5572i 0.389729 + 0.940889i 0.989997 + 0.141090i \(0.0450606\pi\)
−0.600268 + 0.799799i \(0.704939\pi\)
\(390\) −4.80150 + 11.0546i −0.243134 + 0.559773i
\(391\) −16.0802 + 23.4072i −0.813211 + 1.18375i
\(392\) −8.48216 23.8631i −0.428414 1.20527i
\(393\) −17.3147 41.8013i −0.873409 2.10860i
\(394\) −14.6757 + 2.65977i −0.739350 + 0.133997i
\(395\) 14.2675 14.2675i 0.717874 0.717874i
\(396\) −8.86875 + 5.49783i −0.445672 + 0.276277i
\(397\) −2.64896 1.76998i −0.132948 0.0888328i 0.487318 0.873225i \(-0.337975\pi\)
−0.620266 + 0.784392i \(0.712975\pi\)
\(398\) 25.3976 + 5.50387i 1.27307 + 0.275884i
\(399\) 12.3125 29.7251i 0.616398 1.48812i
\(400\) −8.87753 4.40869i −0.443876 0.220435i
\(401\) −25.1811 + 5.00882i −1.25748 + 0.250129i −0.778471 0.627680i \(-0.784005\pi\)
−0.479011 + 0.877809i \(0.659005\pi\)
\(402\) −10.6033 16.4704i −0.528844 0.821467i
\(403\) −22.6480 4.50497i −1.12818 0.224408i
\(404\) 10.2043 + 0.348281i 0.507682 + 0.0173276i
\(405\) −9.58220 14.3408i −0.476144 0.712599i
\(406\) −10.4887 0.178941i −0.520543 0.00888070i
\(407\) 15.2516 0.755994
\(408\) −13.2309 22.8432i −0.655027 1.13091i
\(409\) 6.70044 0.331316 0.165658 0.986183i \(-0.447025\pi\)
0.165658 + 0.986183i \(0.447025\pi\)
\(410\) −11.2562 0.192036i −0.555904 0.00948398i
\(411\) 3.84669 + 5.75699i 0.189743 + 0.283971i
\(412\) −0.0180858 + 0.529895i −0.000891021 + 0.0261060i
\(413\) −27.8873 5.54714i −1.37225 0.272957i
\(414\) −11.1992 17.3961i −0.550413 0.854971i
\(415\) 26.9849 5.36763i 1.32464 0.263486i
\(416\) 8.64050 + 10.2562i 0.423636 + 0.502852i
\(417\) 7.70055 18.5908i 0.377097 0.910393i
\(418\) −12.0810 2.61804i −0.590899 0.128053i
\(419\) 5.44403 + 3.63759i 0.265958 + 0.177708i 0.681398 0.731913i \(-0.261372\pi\)
−0.415440 + 0.909621i \(0.636372\pi\)
\(420\) 15.1307 + 24.4079i 0.738304 + 1.19098i
\(421\) −21.5388 + 21.5388i −1.04973 + 1.04973i −0.0510380 + 0.998697i \(0.516253\pi\)
−0.998697 + 0.0510380i \(0.983747\pi\)
\(422\) 2.60535 0.472185i 0.126826 0.0229856i
\(423\) 3.30121 + 7.96981i 0.160510 + 0.387506i
\(424\) 3.25034 + 9.14426i 0.157850 + 0.444084i
\(425\) 4.03117 9.38814i 0.195541 0.455392i
\(426\) 8.57399 19.7401i 0.415411 0.956412i
\(427\) 13.5452 + 32.7009i 0.655497 + 1.58251i
\(428\) 2.39916 10.2250i 0.115968 0.494244i
\(429\) 9.32081 + 9.32081i 0.450013 + 0.450013i
\(430\) 5.23139 + 3.62609i 0.252280 + 0.174865i
\(431\) −17.7741 11.8762i −0.856146 0.572059i 0.0482099 0.998837i \(-0.484648\pi\)
−0.904356 + 0.426779i \(0.859648\pi\)
\(432\) −7.86647 + 1.01336i −0.378476 + 0.0487552i
\(433\) 6.61056 + 2.73819i 0.317683 + 0.131589i 0.535827 0.844328i \(-0.320000\pi\)
−0.218143 + 0.975917i \(0.570000\pi\)
\(434\) −39.5637 + 38.2364i −1.89912 + 1.83540i
\(435\) 6.54766 1.30241i 0.313936 0.0624458i
\(436\) 19.2881 3.15690i 0.923735 0.151188i
\(437\) 4.78159 24.0387i 0.228735 1.14993i
\(438\) −16.7365 42.4389i −0.799699 2.02781i
\(439\) 3.66708 + 5.48817i 0.175020 + 0.261936i 0.908600 0.417667i \(-0.137152\pi\)
−0.733580 + 0.679603i \(0.762152\pi\)
\(440\) 8.19055 7.39238i 0.390469 0.352418i
\(441\) 19.0186i 0.905647i
\(442\) −10.0629 + 9.47766i −0.478645 + 0.450806i
\(443\) −0.0876330 −0.00416357 −0.00208179 0.999998i \(-0.500663\pi\)
−0.00208179 + 0.999998i \(0.500663\pi\)
\(444\) −25.5886 11.6370i −1.21438 0.552268i
\(445\) −0.827387 + 0.552843i −0.0392219 + 0.0262072i
\(446\) 6.99635 + 17.7407i 0.331287 + 0.840048i
\(447\) −27.0772 5.38598i −1.28071 0.254748i
\(448\) 31.8129 2.99915i 1.50302 0.141696i
\(449\) −7.14374 35.9140i −0.337134 1.69489i −0.662308 0.749232i \(-0.730423\pi\)
0.325174 0.945654i \(-0.394577\pi\)
\(450\) 5.17279 + 5.35235i 0.243848 + 0.252312i
\(451\) −4.71185 + 11.3754i −0.221872 + 0.535647i
\(452\) 13.0927 + 9.40974i 0.615830 + 0.442597i
\(453\) 12.9003 19.3067i 0.606110 0.907108i
\(454\) 24.1680 + 16.7518i 1.13426 + 0.786201i
\(455\) 10.6334 10.6334i 0.498500 0.498500i
\(456\) 18.2714 + 13.6102i 0.855636 + 0.637358i
\(457\) −6.50023 + 2.69248i −0.304068 + 0.125949i −0.529500 0.848310i \(-0.677621\pi\)
0.225432 + 0.974259i \(0.427621\pi\)
\(458\) 32.6845 + 14.1963i 1.52725 + 0.663349i
\(459\) −1.49154 8.03837i −0.0696190 0.375199i
\(460\) 14.9322 + 15.9875i 0.696217 + 0.745421i
\(461\) −12.8491 + 5.32227i −0.598442 + 0.247883i −0.661278 0.750141i \(-0.729986\pi\)
0.0628356 + 0.998024i \(0.479986\pi\)
\(462\) 30.9046 5.60105i 1.43781 0.260584i
\(463\) −7.89732 7.89732i −0.367019 0.367019i 0.499370 0.866389i \(-0.333565\pi\)
−0.866389 + 0.499370i \(0.833565\pi\)
\(464\) 1.94258 7.16987i 0.0901820 0.332853i
\(465\) 19.4534 29.1141i 0.902131 1.35014i
\(466\) 0.693709 3.20112i 0.0321354 0.148289i
\(467\) −20.6714 8.56237i −0.956557 0.396219i −0.150866 0.988554i \(-0.548206\pi\)
−0.805692 + 0.592335i \(0.798206\pi\)
\(468\) −3.53435 9.43036i −0.163375 0.435919i
\(469\) 4.76812 + 23.9710i 0.220171 + 1.10688i
\(470\) −4.93745 7.66948i −0.227748 0.353767i
\(471\) −8.42303 + 42.3454i −0.388113 + 1.95117i
\(472\) 8.64666 18.1834i 0.397995 0.836961i
\(473\) 5.78837 3.86766i 0.266149 0.177835i
\(474\) −0.693804 + 40.6674i −0.0318675 + 1.86792i
\(475\) 8.81794i 0.404595i
\(476\) 4.90087 + 32.5707i 0.224631 + 1.49288i
\(477\) 7.28787i 0.333689i
\(478\) 15.8696 + 0.270743i 0.725859 + 0.0123835i
\(479\) 13.6534 9.12292i 0.623841 0.416837i −0.203075 0.979163i \(-0.565093\pi\)
0.826916 + 0.562326i \(0.190093\pi\)
\(480\) −19.3822 + 6.15324i −0.884672 + 0.280856i
\(481\) −2.87173 + 14.4372i −0.130940 + 0.658279i
\(482\) 6.68564 4.30407i 0.304522 0.196045i
\(483\) 12.1492 + 61.0779i 0.552806 + 2.77914i
\(484\) 3.48595 + 9.30121i 0.158452 + 0.422782i
\(485\) −13.7204 5.68317i −0.623011 0.258060i
\(486\) 25.7571 + 5.58177i 1.16836 + 0.253194i
\(487\) −1.02911 + 1.54017i −0.0466334 + 0.0697918i −0.854054 0.520185i \(-0.825863\pi\)
0.807420 + 0.589977i \(0.200863\pi\)
\(488\) −24.8006 + 3.62589i −1.12267 + 0.164136i
\(489\) −5.64813 5.64813i −0.255417 0.255417i
\(490\) −3.58620 19.7873i −0.162008 0.893901i
\(491\) −8.00880 + 3.31735i −0.361432 + 0.149710i −0.556007 0.831178i \(-0.687667\pi\)
0.194575 + 0.980888i \(0.437667\pi\)
\(492\) 16.5848 15.4901i 0.747701 0.698346i
\(493\) 7.48999 + 1.59043i 0.337332 + 0.0716295i
\(494\) 4.75297 10.9429i 0.213846 0.492344i
\(495\) −7.65481 + 3.17073i −0.344058 + 0.142514i
\(496\) −19.3868 33.7960i −0.870493 1.51748i
\(497\) −18.9879 + 18.9879i −0.851723 + 0.851723i
\(498\) −31.5951 + 45.5825i −1.41581 + 2.04260i
\(499\) 15.5586 23.2852i 0.696501 1.04239i −0.299592 0.954068i \(-0.596850\pi\)
0.996092 0.0883192i \(-0.0281496\pi\)
\(500\) −19.2869 13.8615i −0.862537 0.619905i
\(501\) 11.0392 26.6509i 0.493194 1.19068i
\(502\) 16.0064 15.4694i 0.714400 0.690433i
\(503\) 1.42171 + 7.14743i 0.0633910 + 0.318688i 0.999450 0.0331543i \(-0.0105553\pi\)
−0.936059 + 0.351842i \(0.885555\pi\)
\(504\) −23.2648 5.87919i −1.03629 0.261880i
\(505\) 7.95157 + 1.58167i 0.353840 + 0.0703832i
\(506\) 22.2577 8.77768i 0.989475 0.390215i
\(507\) 13.8897 9.28083i 0.616865 0.412176i
\(508\) −0.467143 + 1.02720i −0.0207261 + 0.0455745i
\(509\) −21.5629 −0.955760 −0.477880 0.878425i \(-0.658595\pi\)
−0.477880 + 0.878425i \(0.658595\pi\)
\(510\) −7.43818 19.5972i −0.329368 0.867779i
\(511\) 56.9203i 2.51801i
\(512\) −3.46034 + 22.3613i −0.152927 + 0.988238i
\(513\) 3.92013 + 5.86688i 0.173078 + 0.259029i
\(514\) −5.34590 + 2.10824i −0.235797 + 0.0929906i
\(515\) −0.0821337 + 0.412914i −0.00361924 + 0.0181952i
\(516\) −12.6625 + 2.07248i −0.557436 + 0.0912358i
\(517\) −9.78432 + 1.94622i −0.430314 + 0.0855947i
\(518\) 24.3741 + 25.2202i 1.07094 + 1.10811i
\(519\) 23.3181 + 9.65866i 1.02355 + 0.423968i
\(520\) 5.45543 + 9.14510i 0.239236 + 0.401039i
\(521\) 4.85313 + 3.24276i 0.212619 + 0.142068i 0.657320 0.753611i \(-0.271690\pi\)
−0.444701 + 0.895679i \(0.646690\pi\)
\(522\) −3.17786 + 4.58473i −0.139091 + 0.200668i
\(523\) −0.928399 0.928399i −0.0405961 0.0405961i 0.686517 0.727113i \(-0.259139\pi\)
−0.727113 + 0.686517i \(0.759139\pi\)
\(524\) −38.9189 9.13179i −1.70018 0.398924i
\(525\) −8.57394 20.6993i −0.374197 0.903392i
\(526\) −17.6474 7.66502i −0.769462 0.334211i
\(527\) 33.6772 21.8801i 1.46700 0.953112i
\(528\) −1.51643 + 22.1891i −0.0659941 + 0.965655i
\(529\) 9.35256 + 22.5791i 0.406633 + 0.981699i
\(530\) 1.37422 + 7.58245i 0.0596923 + 0.329361i
\(531\) −10.6916 + 10.6916i −0.463978 + 0.463978i
\(532\) −14.9778 24.1612i −0.649369 1.04752i
\(533\) −9.88077 6.60212i −0.427984 0.285970i
\(534\) 0.424835 1.96040i 0.0183844 0.0848348i
\(535\) 3.19142 7.70477i 0.137977 0.333106i
\(536\) −17.2843 0.885323i −0.746569 0.0382401i
\(537\) −7.66091 + 1.52385i −0.330593 + 0.0657590i
\(538\) 1.62049 1.04324i 0.0698645 0.0449773i
\(539\) −21.5713 4.29080i −0.929141 0.184818i
\(540\) −6.29426 0.214828i −0.270862 0.00924473i
\(541\) 20.1913 + 30.2184i 0.868092 + 1.29919i 0.953052 + 0.302807i \(0.0979237\pi\)
−0.0849601 + 0.996384i \(0.527076\pi\)
\(542\) 0.0283234 1.66018i 0.00121660 0.0713109i
\(543\) 30.8538 1.32406
\(544\) −23.2115 2.28620i −0.995184 0.0980201i
\(545\) 15.5194 0.664777
\(546\) −0.517084 + 30.3089i −0.0221291 + 1.29710i
\(547\) −4.20366 6.29123i −0.179736 0.268993i 0.730652 0.682750i \(-0.239216\pi\)
−0.910387 + 0.413757i \(0.864216\pi\)
\(548\) 6.11392 + 0.208673i 0.261174 + 0.00891408i
\(549\) 18.4606 + 3.67204i 0.787878 + 0.156719i
\(550\) −7.23778 + 4.65954i −0.308620 + 0.198683i
\(551\) −6.48148 + 1.28925i −0.276120 + 0.0549238i
\(552\) −44.0404 2.25580i −1.87449 0.0960132i
\(553\) 19.4206 46.8855i 0.825849 1.99378i
\(554\) −7.70489 + 35.5542i −0.327350 + 1.51055i
\(555\) −18.5591 12.4008i −0.787789 0.526384i
\(556\) −9.36745 15.1110i −0.397268 0.640848i
\(557\) 26.1434 26.1434i 1.10773 1.10773i 0.114283 0.993448i \(-0.463543\pi\)
0.993448 0.114283i \(-0.0364570\pi\)
\(558\) 5.21775 + 28.7896i 0.220885 + 1.21876i
\(559\) 2.57124 + 6.20751i 0.108752 + 0.262550i
\(560\) 25.3137 + 1.72997i 1.06970 + 0.0731047i
\(561\) −22.9234 0.295356i −0.967827 0.0124700i
\(562\) −3.77057 1.63772i −0.159052 0.0690831i
\(563\) 9.43760 + 22.7844i 0.397748 + 0.960248i 0.988199 + 0.153175i \(0.0489497\pi\)
−0.590452 + 0.807073i \(0.701050\pi\)
\(564\) 17.9007 + 4.20015i 0.753756 + 0.176858i
\(565\) 9.05282 + 9.05282i 0.380855 + 0.380855i
\(566\) 5.56652 8.03086i 0.233978 0.337562i
\(567\) −36.0690 24.1006i −1.51476 1.01213i
\(568\) −9.74169 16.3303i −0.408752 0.685204i
\(569\) 21.6080 + 8.95034i 0.905856 + 0.375218i 0.786469 0.617630i \(-0.211907\pi\)
0.119387 + 0.992848i \(0.461907\pi\)
\(570\) 12.5722 + 13.0086i 0.526590 + 0.544870i
\(571\) 7.43083 1.47808i 0.310971 0.0618559i −0.0371378 0.999310i \(-0.511824\pi\)
0.348109 + 0.937454i \(0.386824\pi\)
\(572\) 11.4935 1.88114i 0.480567 0.0786546i
\(573\) −9.68533 + 48.6915i −0.404611 + 2.03411i
\(574\) −26.3407 + 10.3879i −1.09944 + 0.433582i
\(575\) −9.48219 14.1911i −0.395434 0.591810i
\(576\) 8.07264 14.9522i 0.336360 0.623010i
\(577\) 15.4426i 0.642884i −0.946929 0.321442i \(-0.895832\pi\)
0.946929 0.321442i \(-0.104168\pi\)
\(578\) 1.02930 24.0196i 0.0428133 0.999083i
\(579\) −3.11546 −0.129474
\(580\) 2.44180 5.36927i 0.101390 0.222947i
\(581\) 57.5380 38.4456i 2.38708 1.59499i
\(582\) 27.8490 10.9827i 1.15438 0.455247i
\(583\) 8.26605 + 1.64422i 0.342345 + 0.0680966i
\(584\) −39.0782 9.87539i −1.61707 0.408647i
\(585\) −1.56008 7.84307i −0.0645015 0.324271i
\(586\) 14.8801 14.3809i 0.614690 0.594068i
\(587\) −4.61264 + 11.1359i −0.190384 + 0.459628i −0.990032 0.140841i \(-0.955019\pi\)
0.799648 + 0.600469i \(0.205019\pi\)
\(588\) 32.9176 + 23.6579i 1.35750 + 0.975633i
\(589\) −19.2568 + 28.8199i −0.793463 + 1.18750i
\(590\) 9.10776 13.1399i 0.374961 0.540959i
\(591\) 16.8808 16.8808i 0.694382 0.694382i
\(592\) −21.5436 + 12.3583i −0.885435 + 0.507923i
\(593\) 27.8859 11.5507i 1.14514 0.474332i 0.272237 0.962230i \(-0.412236\pi\)
0.872900 + 0.487898i \(0.162236\pi\)
\(594\) −2.74410 + 6.31780i −0.112592 + 0.259223i
\(595\) −0.336949 + 26.1515i −0.0138136 + 1.07211i
\(596\) −17.8263 + 16.6496i −0.730193 + 0.681994i
\(597\) −38.4295 + 15.9180i −1.57281 + 0.651481i
\(598\) 4.11804 + 22.7219i 0.168399 + 0.929167i
\(599\) −11.1432 11.1432i −0.455299 0.455299i 0.441810 0.897109i \(-0.354337\pi\)
−0.897109 + 0.441810i \(0.854337\pi\)
\(600\) 15.6985 2.29515i 0.640889 0.0936990i
\(601\) −24.8557 + 37.1992i −1.01389 + 1.51739i −0.166759 + 0.985998i \(0.553330\pi\)
−0.847127 + 0.531390i \(0.821670\pi\)
\(602\) 15.6462 + 3.39066i 0.637692 + 0.138193i
\(603\) 12.0075 + 4.97367i 0.488984 + 0.202544i
\(604\) −7.19990 19.2108i −0.292960 0.781676i
\(605\) 1.53872 + 7.73566i 0.0625578 + 0.314499i
\(606\) −13.7414 + 8.84646i −0.558208 + 0.359363i
\(607\) 2.44705 12.3021i 0.0993225 0.499328i −0.898815 0.438328i \(-0.855571\pi\)
0.998138 0.0610004i \(-0.0194291\pi\)
\(608\) 19.1863 6.09104i 0.778106 0.247024i
\(609\) 13.9611 9.32853i 0.565733 0.378011i
\(610\) −19.8992 0.339489i −0.805694 0.0137455i
\(611\) 9.62830i 0.389519i
\(612\) 15.8492 + 7.45568i 0.640664 + 0.301378i
\(613\) 37.9509i 1.53282i −0.642351 0.766411i \(-0.722041\pi\)
0.642351 0.766411i \(-0.277959\pi\)
\(614\) 0.639696 37.4959i 0.0258160 1.51321i
\(615\) 14.9828 10.0112i 0.604164 0.403690i
\(616\) 11.9171 25.0610i 0.480153 1.00973i
\(617\) −1.83441 + 9.22219i −0.0738505 + 0.371272i −0.999982 0.00592821i \(-0.998113\pi\)
0.926132 + 0.377200i \(0.123113\pi\)
\(618\) −0.459385 0.713575i −0.0184792 0.0287042i
\(619\) 7.07536 + 35.5702i 0.284383 + 1.42969i 0.813710 + 0.581271i \(0.197444\pi\)
−0.529328 + 0.848418i \(0.677556\pi\)
\(620\) −10.8573 28.9695i −0.436040 1.16344i
\(621\) −12.6177 5.22641i −0.506329 0.209729i
\(622\) 2.02209 9.33092i 0.0810784 0.374136i
\(623\) −1.39047 + 2.08099i −0.0557082 + 0.0833732i
\(624\) −20.7187 5.61344i −0.829410 0.224718i
\(625\) −4.57470 4.57470i −0.182988 0.182988i
\(626\) 5.92462 1.07376i 0.236796 0.0429161i
\(627\) 18.2799 7.57178i 0.730028 0.302388i
\(628\) 26.0380 + 27.8782i 1.03903 + 1.11246i
\(629\) −13.9477 21.4679i −0.556130 0.855979i
\(630\) −17.4766 7.59084i −0.696284 0.302426i
\(631\) 31.6304 13.1018i 1.25919 0.521573i 0.349528 0.936926i \(-0.386342\pi\)
0.909660 + 0.415353i \(0.136342\pi\)
\(632\) 28.8195 + 21.4675i 1.14638 + 0.853931i
\(633\) −2.99681 + 2.99681i −0.119113 + 0.119113i
\(634\) 13.9173 + 9.64662i 0.552725 + 0.383116i
\(635\) −0.497803 + 0.745015i −0.0197547 + 0.0295650i
\(636\) −12.6139 9.06562i −0.500174 0.359475i
\(637\) 8.12334 19.6115i 0.321858 0.777035i
\(638\) −4.48313 4.63876i −0.177489 0.183650i
\(639\) 2.78582 + 14.0053i 0.110205 + 0.554040i
\(640\) −5.57951 + 17.0788i −0.220549 + 0.675100i
\(641\) 41.0725 + 8.16982i 1.62226 + 0.322688i 0.920806 0.390022i \(-0.127532\pi\)
0.701459 + 0.712710i \(0.252532\pi\)
\(642\) 6.16740 + 15.6388i 0.243408 + 0.617213i
\(643\) −12.8831 + 8.60823i −0.508061 + 0.339475i −0.783037 0.621976i \(-0.786330\pi\)
0.274976 + 0.961451i \(0.411330\pi\)
\(644\) 50.0857 + 22.7776i 1.97365 + 0.897565i
\(645\) −10.1883 −0.401166
\(646\) 7.36300 + 19.3991i 0.289693 + 0.763248i
\(647\) 4.31868i 0.169785i 0.996390 + 0.0848923i \(0.0270546\pi\)
−0.996390 + 0.0848923i \(0.972945\pi\)
\(648\) 22.8039 20.5816i 0.895820 0.808522i
\(649\) −9.71454 14.5388i −0.381329 0.570699i
\(650\) −3.04791 7.72864i −0.119549 0.303142i
\(651\) 17.1812 86.3760i 0.673386 3.38534i
\(652\) −6.96471 + 1.13992i −0.272759 + 0.0446426i
\(653\) 16.4937 3.28079i 0.645447 0.128387i 0.138497 0.990363i \(-0.455773\pi\)
0.506950 + 0.861975i \(0.330773\pi\)
\(654\) −22.4952 + 21.7405i −0.879633 + 0.850123i
\(655\) −29.3263 12.1473i −1.14587 0.474636i
\(656\) −2.56175 19.8863i −0.100019 0.776428i
\(657\) 25.1675 + 16.8164i 0.981877 + 0.656070i
\(658\) −18.8550 13.0691i −0.735043 0.509488i
\(659\) 24.3424 + 24.3424i 0.948246 + 0.948246i 0.998725 0.0504793i \(-0.0160749\pi\)
−0.0504793 + 0.998725i \(0.516075\pi\)
\(660\) −4.03415 + 17.1932i −0.157029 + 0.669244i
\(661\) −13.8353 33.4013i −0.538130 1.29916i −0.926027 0.377457i \(-0.876798\pi\)
0.387897 0.921703i \(-0.373202\pi\)
\(662\) −4.56913 + 10.5196i −0.177584 + 0.408857i
\(663\) 4.59585 21.6437i 0.178488 0.840572i
\(664\) 16.4120 + 46.1724i 0.636910 + 1.79184i
\(665\) −8.63804 20.8541i −0.334969 0.808686i
\(666\) 18.3522 3.32610i 0.711135 0.128884i
\(667\) 9.04457 9.04457i 0.350207 0.350207i
\(668\) −13.4288 21.6624i −0.519575 0.838145i
\(669\) −25.3804 16.9586i −0.981263 0.655659i
\(670\) −13.4307 2.91055i −0.518874 0.112444i
\(671\) −8.32980 + 20.1099i −0.321568 + 0.776335i
\(672\) −39.1156 + 32.9535i −1.50892 + 1.27121i
\(673\) −37.1218 + 7.38398i −1.43094 + 0.284631i −0.848910 0.528537i \(-0.822741\pi\)
−0.582028 + 0.813168i \(0.697741\pi\)
\(674\) −20.5532 31.9258i −0.791679 1.22974i
\(675\) 4.81912 + 0.958583i 0.185488 + 0.0368959i
\(676\) 0.503461 14.7509i 0.0193639 0.567343i
\(677\) 5.75120 + 8.60728i 0.221037 + 0.330805i 0.925370 0.379064i \(-0.123754\pi\)
−0.704334 + 0.709869i \(0.748754\pi\)
\(678\) −25.8038 0.440224i −0.990989 0.0169067i
\(679\) −37.3519 −1.43343
\(680\) −17.8957 4.76848i −0.686267 0.182863i
\(681\) −47.0681 −1.80366
\(682\) −33.8310 0.577172i −1.29546 0.0221011i
\(683\) −2.82528 4.22832i −0.108106 0.161792i 0.773472 0.633831i \(-0.218518\pi\)
−0.881578 + 0.472038i \(0.843518\pi\)
\(684\) −15.1080 0.515647i −0.577667 0.0197163i
\(685\) 4.76420 + 0.947658i 0.182031 + 0.0362082i
\(686\) −5.97473 9.28071i −0.228116 0.354339i
\(687\) −55.9415 + 11.1275i −2.13430 + 0.424539i
\(688\) −5.04237 + 10.1535i −0.192239 + 0.387100i
\(689\) −3.11284 + 7.51506i −0.118590 + 0.286301i
\(690\) −34.2214 7.41607i −1.30279 0.282325i
\(691\) −1.80294 1.20468i −0.0685870 0.0458283i 0.520804 0.853676i \(-0.325632\pi\)
−0.589391 + 0.807848i \(0.700632\pi\)
\(692\) 18.9534 11.7494i 0.720502 0.446646i
\(693\) −14.7355 + 14.7355i −0.559757 + 0.559757i
\(694\) 5.76493 1.04482i 0.218834 0.0396607i
\(695\) −5.40243 13.0426i −0.204926 0.494734i
\(696\) 3.98225 + 11.2034i 0.150947 + 0.424662i
\(697\) 20.3208 3.77057i 0.769705 0.142821i
\(698\) −6.56772 + 15.1210i −0.248592 + 0.572340i
\(699\) 2.00631 + 4.84366i 0.0758856 + 0.183204i
\(700\) −19.2720 4.52191i −0.728414 0.170912i
\(701\) 29.0858 + 29.0858i 1.09856 + 1.09856i 0.994580 + 0.103977i \(0.0331568\pi\)
0.103977 + 0.994580i \(0.466843\pi\)
\(702\) −5.46375 3.78715i −0.206216 0.142937i
\(703\) 18.3715 + 12.2754i 0.692894 + 0.462977i
\(704\) 15.1379 + 12.5295i 0.570530 + 0.472225i
\(705\) 13.4886 + 5.58715i 0.508009 + 0.210424i
\(706\) 20.4313 19.7459i 0.768943 0.743146i
\(707\) 19.9993 3.97810i 0.752150 0.149612i
\(708\) 5.20552 + 31.8049i 0.195635 + 1.19530i
\(709\) −2.89581 + 14.5582i −0.108754 + 0.546745i 0.887540 + 0.460731i \(0.152413\pi\)
−0.996294 + 0.0860136i \(0.972587\pi\)
\(710\) −5.53930 14.0461i −0.207886 0.527140i
\(711\) −14.9930 22.4386i −0.562282 0.841514i
\(712\) −1.18745 1.31566i −0.0445016 0.0493065i
\(713\) 67.0885i 2.51248i
\(714\) −36.1463 38.3784i −1.35274 1.43628i
\(715\) 9.24775 0.345846
\(716\) −2.85696 + 6.28216i −0.106770 + 0.234776i
\(717\) −21.1235 + 14.1143i −0.788873 + 0.527108i
\(718\) −4.25413 10.7873i −0.158763 0.402577i
\(719\) −17.5647 3.49383i −0.655052 0.130298i −0.143635 0.989631i \(-0.545879\pi\)
−0.511417 + 0.859333i \(0.670879\pi\)
\(720\) 8.24353 10.6814i 0.307218 0.398074i
\(721\) 0.206578 + 1.03854i 0.00769335 + 0.0386771i
\(722\) 6.22804 + 6.44424i 0.231784 + 0.239830i
\(723\) −4.87043 + 11.7583i −0.181133 + 0.437294i
\(724\) 15.9095 22.1364i 0.591270 0.822694i
\(725\) −2.55665 + 3.82630i −0.0949518 + 0.142105i
\(726\) −13.0670 9.05725i −0.484961 0.336146i
\(727\) 9.14200 9.14200i 0.339058 0.339058i −0.516955 0.856013i \(-0.672934\pi\)
0.856013 + 0.516955i \(0.172934\pi\)
\(728\) 21.4788 + 15.9995i 0.796059 + 0.592979i
\(729\) −8.87181 + 3.67482i −0.328585 + 0.136105i
\(730\) −29.3557 12.7505i −1.08650 0.471916i
\(731\) −10.7375 4.61058i −0.397142 0.170529i
\(732\) 29.3193 27.3840i 1.08367 1.01214i
\(733\) 12.0200 4.97884i 0.443968 0.183898i −0.149489 0.988763i \(-0.547763\pi\)
0.593457 + 0.804866i \(0.297763\pi\)
\(734\) 16.8523 3.05426i 0.622030 0.112735i
\(735\) 22.7605 + 22.7605i 0.839533 + 0.839533i
\(736\) −24.3274 + 30.4341i −0.896721 + 1.12182i
\(737\) −8.35027 + 12.4971i −0.307586 + 0.460335i
\(738\) −3.18899 + 14.7156i −0.117388 + 0.541688i
\(739\) −27.1906 11.2627i −1.00022 0.414305i −0.178343 0.983968i \(-0.557074\pi\)
−0.821878 + 0.569663i \(0.807074\pi\)
\(740\) −18.4669 + 6.92110i −0.678856 + 0.254425i
\(741\) 3.72552 + 18.7294i 0.136860 + 0.688043i
\(742\) 10.4914 + 16.2965i 0.385150 + 0.598264i
\(743\) −1.16420 + 5.85282i −0.0427103 + 0.214719i −0.996247 0.0865584i \(-0.972413\pi\)
0.953536 + 0.301278i \(0.0974131\pi\)
\(744\) 56.3199 + 26.7815i 2.06479 + 0.981856i
\(745\) −16.1043 + 10.7606i −0.590017 + 0.394237i
\(746\) −0.634374 + 37.1839i −0.0232261 + 1.36140i
\(747\) 36.7989i 1.34640i
\(748\) −12.0321 + 16.2944i −0.439938 + 0.595781i
\(749\) 20.9752i 0.766417i
\(750\) 38.0116 + 0.648495i 1.38799 + 0.0236797i
\(751\) 4.76539 3.18413i 0.173891 0.116191i −0.465579 0.885007i \(-0.654154\pi\)
0.639470 + 0.768816i \(0.279154\pi\)
\(752\) 12.2438 10.6773i 0.446484 0.389361i
\(753\) −6.95107 + 34.9454i −0.253311 + 1.27348i
\(754\) 5.23518 3.37030i 0.190654 0.122739i
\(755\) −3.17808 15.9773i −0.115662 0.581473i
\(756\) −14.8326 + 5.55904i −0.539457 + 0.202180i
\(757\) −5.74019 2.37766i −0.208631 0.0864177i 0.275921 0.961180i \(-0.411017\pi\)
−0.484552 + 0.874763i \(0.661017\pi\)
\(758\) 13.7788 + 2.98598i 0.500469 + 0.108456i
\(759\) −21.2765 + 31.8425i −0.772287 + 1.15581i
\(760\) 15.8159 2.31231i 0.573702 0.0838761i
\(761\) 34.6524 + 34.6524i 1.25615 + 1.25615i 0.952917 + 0.303231i \(0.0980654\pi\)
0.303231 + 0.952917i \(0.401935\pi\)
\(762\) −0.322103 1.77725i −0.0116686 0.0643829i
\(763\) 36.0621 14.9374i 1.30554 0.540771i
\(764\) 29.9401 + 32.0561i 1.08320 + 1.15975i
\(765\) 11.4634 + 7.87511i 0.414461 + 0.284725i
\(766\) 6.41217 14.7629i 0.231681 0.533406i
\(767\) 15.5916 6.45826i 0.562981 0.233194i
\(768\) −15.8377 32.5718i −0.571493 1.17533i
\(769\) −20.7436 + 20.7436i −0.748035 + 0.748035i −0.974110 0.226075i \(-0.927410\pi\)
0.226075 + 0.974110i \(0.427410\pi\)
\(770\) 12.5526 18.1097i 0.452364 0.652629i
\(771\) 5.11023 7.64799i 0.184040 0.275436i
\(772\) −1.60646 + 2.23523i −0.0578176 + 0.0804476i
\(773\) −15.5416 + 37.5208i −0.558994 + 1.34953i 0.351570 + 0.936162i \(0.385648\pi\)
−0.910564 + 0.413369i \(0.864352\pi\)
\(774\) 6.12166 5.91629i 0.220039 0.212657i
\(775\) 4.70884 + 23.6729i 0.169146 + 0.850357i
\(776\) 6.48037 25.6437i 0.232632 0.920554i
\(777\) −55.0612 10.9524i −1.97531 0.392913i
\(778\) −26.4255 + 10.4213i −0.947400 + 0.373622i
\(779\) −14.8313 + 9.90999i −0.531388 + 0.355062i
\(780\) −15.5155 7.05604i −0.555544 0.252647i
\(781\) −16.5136 −0.590903
\(782\) −32.7100 23.3022i −1.16971 0.833285i
\(783\) 3.68237i 0.131597i
\(784\) 33.9472 11.4182i 1.21240 0.407792i
\(785\) 16.8282 + 25.1852i 0.600626 + 0.898900i
\(786\) 59.5250 23.4747i 2.12319 0.837314i
\(787\) −6.57472 + 33.0533i −0.234363 + 1.17822i 0.666965 + 0.745089i \(0.267593\pi\)
−0.901329 + 0.433136i \(0.857407\pi\)
\(788\) −3.40691 20.8157i −0.121366 0.741528i
\(789\) 30.2046 6.00806i 1.07531 0.213893i
\(790\) 19.8301 + 20.5185i 0.705524 + 0.730015i
\(791\) 29.7492 + 12.3225i 1.05776 + 0.438139i
\(792\) −7.56003 12.6731i −0.268634 0.450320i
\(793\) −17.4676 11.6715i −0.620294 0.414467i
\(794\) 2.56667 3.70296i 0.0910876 0.131413i
\(795\) −8.72175 8.72175i −0.309329 0.309329i
\(796\) −8.39519 + 35.7796i −0.297560 + 1.26817i
\(797\) −3.63700 8.78050i −0.128829 0.311021i 0.846283 0.532734i \(-0.178835\pi\)
−0.975112 + 0.221713i \(0.928835\pi\)
\(798\) 41.7345 + 18.1271i 1.47739 + 0.641693i
\(799\) 11.6873 + 11.9924i 0.413466 + 0.424260i
\(800\) 6.44809 12.4465i 0.227974 0.440052i
\(801\) 0.509319 + 1.22961i 0.0179959 + 0.0434460i
\(802\) −6.47506 35.7271i −0.228642 1.26157i
\(803\) −24.7515 + 24.7515i −0.873463 + 0.873463i
\(804\) 23.5450 14.5958i 0.830369 0.514754i
\(805\) 36.3265 + 24.2726i 1.28034 + 0.855498i
\(806\) 6.91641 31.9158i 0.243620 1.12419i
\(807\) −1.18052 + 2.85002i −0.0415562 + 0.100325i
\(808\) −0.738636 + 14.4205i −0.0259851 + 0.507313i
\(809\) −19.9757 + 3.97341i −0.702308 + 0.139698i −0.533311 0.845919i \(-0.679053\pi\)
−0.168996 + 0.985617i \(0.554053\pi\)
\(810\) 20.5091 13.2034i 0.720617 0.463919i
\(811\) −43.7391 8.70024i −1.53589 0.305507i −0.646590 0.762838i \(-0.723805\pi\)
−0.889296 + 0.457331i \(0.848805\pi\)
\(812\) 0.506049 14.8267i 0.0177588 0.520316i
\(813\) 1.47655 + 2.20981i 0.0517849 + 0.0775016i
\(814\) −0.367924 + 21.5659i −0.0128957 + 0.755884i
\(815\) −5.60385 −0.196294
\(816\) 32.6196 18.1575i 1.14192 0.635640i
\(817\) 10.0854 0.352842
\(818\) −0.161639 + 9.47448i −0.00565157 + 0.331267i
\(819\) −11.1741 16.7232i −0.390455 0.584357i
\(820\) 0.543081 15.9117i 0.0189652 0.555662i
\(821\) 46.0889 + 9.16766i 1.60851 + 0.319953i 0.915916 0.401370i \(-0.131466\pi\)
0.692599 + 0.721323i \(0.256466\pi\)
\(822\) −8.23322 + 5.30038i −0.287166 + 0.184872i
\(823\) 49.8672 9.91920i 1.73826 0.345762i 0.778729 0.627360i \(-0.215865\pi\)
0.959532 + 0.281599i \(0.0908647\pi\)
\(824\) −0.748839 0.0383564i −0.0260870 0.00133621i
\(825\) 5.27267 12.7293i 0.183571 0.443179i
\(826\) 8.51644 39.2991i 0.296325 1.36739i
\(827\) −4.87246 3.25567i −0.169432 0.113211i 0.467963 0.883748i \(-0.344988\pi\)
−0.637395 + 0.770537i \(0.719988\pi\)
\(828\) 24.8684 15.4162i 0.864236 0.535749i
\(829\) 1.74130 1.74130i 0.0604779 0.0604779i −0.676221 0.736699i \(-0.736384\pi\)
0.736699 + 0.676221i \(0.236384\pi\)
\(830\) 6.93889 + 38.2863i 0.240852 + 1.32894i
\(831\) −22.2837 53.7976i −0.773013 1.86622i
\(832\) −14.7108 + 11.9703i −0.510005 + 0.414996i
\(833\) 13.6874 + 34.2872i 0.474241 + 1.18798i
\(834\) 26.1017 + 11.3371i 0.903829 + 0.392572i
\(835\) −7.74469 18.6973i −0.268016 0.647048i
\(836\) 3.99337 17.0194i 0.138114 0.588629i
\(837\) 13.6571 + 13.6571i 0.472057 + 0.472057i
\(838\) −5.27491 + 7.61016i −0.182219 + 0.262888i
\(839\) 25.9855 + 17.3630i 0.897120 + 0.599436i 0.916350 0.400379i \(-0.131122\pi\)
−0.0192301 + 0.999815i \(0.506122\pi\)
\(840\) −34.8780 + 20.8061i −1.20340 + 0.717880i
\(841\) 23.6062 + 9.77803i 0.814008 + 0.337173i
\(842\) −29.9364 30.9756i −1.03168 1.06749i
\(843\) 6.45356 1.28369i 0.222272 0.0442127i
\(844\) 0.604823 + 3.69538i 0.0208189 + 0.127200i
\(845\) 2.28639 11.4945i 0.0786543 0.395422i
\(846\) −11.3490 + 4.47567i −0.390187 + 0.153877i
\(847\) 11.0211 + 16.4942i 0.378688 + 0.566747i
\(848\) −13.0085 + 4.37541i −0.446712 + 0.150252i
\(849\) 15.6404i 0.536779i
\(850\) 13.1777 + 5.92658i 0.451990 + 0.203280i
\(851\) −42.7662 −1.46601
\(852\) 27.7059 + 12.5999i 0.949187 + 0.431665i
\(853\) −29.0938 + 19.4398i −0.996152 + 0.665608i −0.942936 0.332975i \(-0.891947\pi\)
−0.0532168 + 0.998583i \(0.516947\pi\)
\(854\) −46.5661 + 18.3641i −1.59346 + 0.628407i
\(855\) −11.7727 2.34173i −0.402617 0.0800856i
\(856\) 14.4004 + 3.63909i 0.492194 + 0.124382i
\(857\) 4.73913 + 23.8252i 0.161886 + 0.813854i 0.973327 + 0.229421i \(0.0736831\pi\)
−0.811442 + 0.584433i \(0.801317\pi\)
\(858\) −13.4045 + 12.9548i −0.457624 + 0.442271i
\(859\) 8.98480 21.6912i 0.306557 0.740095i −0.693254 0.720693i \(-0.743824\pi\)
0.999812 0.0194021i \(-0.00617627\pi\)
\(860\) −5.25352 + 7.30975i −0.179143 + 0.249260i
\(861\) 25.1795 37.6837i 0.858114 1.28426i
\(862\) 17.2219 24.8462i 0.586579 0.846263i
\(863\) −39.7230 + 39.7230i −1.35219 + 1.35219i −0.468979 + 0.883210i \(0.655378\pi\)
−0.883210 + 0.468979i \(0.844622\pi\)
\(864\) −1.24313 11.1477i −0.0422921 0.379252i
\(865\) 16.3591 6.77617i 0.556227 0.230397i
\(866\) −4.03129 + 9.28133i −0.136989 + 0.315393i
\(867\) 20.5478 + 32.5366i 0.697841 + 1.10500i
\(868\) −53.1121 56.8657i −1.80274 1.93015i
\(869\) 28.8329 11.9430i 0.978090 0.405138i
\(870\) 1.68367 + 9.28987i 0.0570816 + 0.314956i
\(871\) −10.2574 10.2574i −0.347560 0.347560i
\(872\) 3.99858 + 27.3497i 0.135409 + 0.926179i
\(873\) −11.0351 + 16.5153i −0.373483 + 0.558957i
\(874\) 33.8755 + 7.34111i 1.14586 + 0.248317i
\(875\) −43.8236 18.1523i −1.48151 0.613661i
\(876\) 60.4126 22.6417i 2.04115 0.764992i
\(877\) −0.834949 4.19757i −0.0281942 0.141742i 0.964124 0.265451i \(-0.0855210\pi\)
−0.992318 + 0.123709i \(0.960521\pi\)
\(878\) −7.84877 + 5.05288i −0.264883 + 0.170526i
\(879\) −6.46194 + 32.4864i −0.217956 + 1.09574i
\(880\) 10.2553 + 11.7598i 0.345706 + 0.396424i
\(881\) 30.0537 20.0813i 1.01254 0.676555i 0.0655561 0.997849i \(-0.479118\pi\)
0.946979 + 0.321294i \(0.104118\pi\)
\(882\) −26.8924 0.458797i −0.905516 0.0154485i
\(883\) 11.1632i 0.375672i 0.982200 + 0.187836i \(0.0601474\pi\)
−0.982200 + 0.187836i \(0.939853\pi\)
\(884\) −13.1587 14.4577i −0.442576 0.486265i
\(885\) 25.5904i 0.860212i
\(886\) 0.00211403 0.123914i 7.10221e−5 0.00416297i
\(887\) −24.1279 + 16.1217i −0.810135 + 0.541315i −0.890251 0.455471i \(-0.849471\pi\)
0.0801157 + 0.996786i \(0.474471\pi\)
\(888\) 17.0721 35.9017i 0.572902 1.20478i
\(889\) −0.439659 + 2.21031i −0.0147457 + 0.0741316i
\(890\) −0.761764 1.18327i −0.0255344 0.0396633i
\(891\) −5.20444 26.1645i −0.174355 0.876543i
\(892\) −25.2543 + 9.46492i −0.845577 + 0.316909i
\(893\) −13.3522 5.53068i −0.446816 0.185077i
\(894\) 8.26902 38.1574i 0.276557 1.27617i
\(895\) −3.04448 + 4.55638i −0.101766 + 0.152303i
\(896\) 3.47338 + 45.0561i 0.116037 + 1.50522i
\(897\) −26.1360 26.1360i −0.872654 0.872654i
\(898\) 50.9550 9.23492i 1.70039 0.308173i
\(899\) −16.7119 + 6.92231i −0.557374 + 0.230872i
\(900\) −7.69305 + 7.18524i −0.256435 + 0.239508i
\(901\) −5.24498 13.1388i −0.174736 0.437716i
\(902\) −15.9713 6.93701i −0.531785 0.230977i
\(903\) −23.6745 + 9.80630i −0.787838 + 0.326333i
\(904\) −13.6213 + 18.2862i −0.453038 + 0.608191i
\(905\) 15.3060 15.3060i 0.508788 0.508788i
\(906\) 26.9886 + 18.7069i 0.896637 + 0.621496i
\(907\) 28.9723 43.3602i 0.962011 1.43975i 0.0649269 0.997890i \(-0.479319\pi\)
0.897084 0.441861i \(-0.145681\pi\)
\(908\) −24.2702 + 33.7696i −0.805435 + 1.12068i
\(909\) 4.14960 10.0180i 0.137634 0.332277i
\(910\) 14.7791 + 15.2922i 0.489924 + 0.506931i
\(911\) 0.592380 + 2.97809i 0.0196264 + 0.0986687i 0.989357 0.145509i \(-0.0464820\pi\)
−0.969731 + 0.244178i \(0.921482\pi\)
\(912\) −19.6858 + 25.5076i −0.651861 + 0.844640i
\(913\) 41.7380 + 8.30221i 1.38133 + 0.274763i
\(914\) −3.65038 9.25632i −0.120744 0.306172i
\(915\) 26.4872 17.6982i 0.875639 0.585083i
\(916\) −20.8621 + 45.8736i −0.689304 + 1.51571i
\(917\) −79.8368 −2.63644
\(918\) 11.4023 1.91513i 0.376332 0.0632088i
\(919\) 6.84897i 0.225927i 0.993599 + 0.112963i \(0.0360343\pi\)
−0.993599 + 0.112963i \(0.963966\pi\)
\(920\) −22.9667 + 20.7286i −0.757189 + 0.683400i
\(921\) 33.3485 + 49.9096i 1.09887 + 1.64458i
\(922\) −7.21577 18.2971i −0.237639 0.602584i
\(923\) 3.10935 15.6318i 0.102346 0.514526i
\(924\) 7.17440 + 43.8344i 0.236020 + 1.44205i
\(925\) 15.0905 3.00169i 0.496174 0.0986951i
\(926\) 11.3574 10.9764i 0.373227 0.360705i
\(927\) 0.520222 + 0.215483i 0.0170863 + 0.00707740i
\(928\) 10.0914 + 2.91979i 0.331266 + 0.0958467i
\(929\) −13.6512 9.12141i −0.447880 0.299264i 0.311101 0.950377i \(-0.399302\pi\)
−0.758981 + 0.651113i \(0.774302\pi\)
\(930\) 40.6983 + 28.2096i 1.33455 + 0.925031i
\(931\) −22.5304 22.5304i −0.738405 0.738405i
\(932\) 4.50967 + 1.05813i 0.147719 + 0.0346603i
\(933\) 5.84818 + 14.1188i 0.191461 + 0.462227i
\(934\) 12.6059 29.0229i 0.412478 0.949660i
\(935\) −11.5184 + 11.2253i −0.376691 + 0.367108i
\(936\) 13.4199 4.77010i 0.438642 0.155916i
\(937\) −12.9063 31.1586i −0.421631 1.01791i −0.981866 0.189575i \(-0.939289\pi\)
0.560235 0.828334i \(-0.310711\pi\)
\(938\) −34.0101 + 6.16389i −1.11047 + 0.201258i
\(939\) −6.81482 + 6.81482i −0.222393 + 0.222393i
\(940\) 10.9638 6.79658i 0.357600 0.221680i
\(941\) −1.56839 1.04797i −0.0511281 0.0341627i 0.529744 0.848158i \(-0.322288\pi\)
−0.580872 + 0.813995i \(0.697288\pi\)
\(942\) −59.6735 12.9317i −1.94427 0.421339i
\(943\) 13.2122 31.8971i 0.430249 1.03871i
\(944\) 25.5029 + 12.6651i 0.830050 + 0.412214i
\(945\) −12.3360 + 2.45379i −0.401292 + 0.0798219i
\(946\) 5.32927 + 8.27810i 0.173269 + 0.269144i
\(947\) 22.7008 + 4.51548i 0.737678 + 0.146733i 0.549609 0.835422i \(-0.314777\pi\)
0.188070 + 0.982156i \(0.439777\pi\)
\(948\) −57.4873 1.96209i −1.86710 0.0637257i
\(949\) −18.7693 28.0903i −0.609279 0.911850i
\(950\) −12.4686 0.212721i −0.404536 0.00690157i
\(951\) −27.1045 −0.878922
\(952\) −46.1735 + 6.14415i −1.49649 + 0.199133i
\(953\) 22.0527 0.714358 0.357179 0.934036i \(-0.383739\pi\)
0.357179 + 0.934036i \(0.383739\pi\)
\(954\) 10.3051 + 0.175810i 0.333640 + 0.00569205i
\(955\) 19.3502 + 28.9596i 0.626157 + 0.937111i
\(956\) −0.765664 + 22.4332i −0.0247634 + 0.725542i
\(957\) 10.1274 + 2.01447i 0.327372 + 0.0651184i
\(958\) 12.5705 + 19.5261i 0.406135 + 0.630860i
\(959\) 11.9826 2.38349i 0.386939 0.0769669i
\(960\) −8.23316 27.5550i −0.265724 0.889334i
\(961\) −24.4443 + 59.0137i −0.788525 + 1.90367i
\(962\) −20.3450 4.40893i −0.655950 0.142150i
\(963\) −9.27425 6.19685i −0.298858 0.199691i
\(964\) 5.92471 + 9.55737i 0.190822 + 0.307822i
\(965\) −1.54552 + 1.54552i −0.0497521 + 0.0497521i
\(966\) −86.6578 + 15.7056i −2.78817 + 0.505319i
\(967\) −21.2143 51.2160i −0.682207 1.64699i −0.759919 0.650018i \(-0.774761\pi\)
0.0777115 0.996976i \(-0.475239\pi\)
\(968\) −13.2361 + 4.70478i −0.425423 + 0.151217i
\(969\) −27.3749 18.8060i −0.879409 0.604134i
\(970\) 8.36703 19.2636i 0.268649 0.618518i
\(971\) −0.393875 0.950898i −0.0126401 0.0305158i 0.917434 0.397889i \(-0.130257\pi\)
−0.930074 + 0.367373i \(0.880257\pi\)
\(972\) −8.51402 + 36.2861i −0.273087 + 1.16388i
\(973\) −25.1071 25.1071i −0.804895 0.804895i
\(974\) −2.15299 1.49232i −0.0689862 0.0478171i
\(975\) 11.0568 + 7.38792i 0.354101 + 0.236603i
\(976\) −4.52876 35.1557i −0.144962 1.12531i
\(977\) 11.0562 + 4.57961i 0.353718 + 0.146515i 0.552465 0.833536i \(-0.313687\pi\)
−0.198747 + 0.980051i \(0.563687\pi\)
\(978\) 8.12275 7.85024i 0.259737 0.251023i
\(979\) −1.50955 + 0.300269i −0.0482455 + 0.00959662i
\(980\) 28.0660 4.59357i 0.896535 0.146736i
\(981\) 4.04947 20.3580i 0.129289 0.649982i
\(982\) −4.49756 11.4045i −0.143523 0.363933i
\(983\) −11.5932 17.3504i −0.369765 0.553393i 0.599197 0.800602i \(-0.295487\pi\)
−0.968962 + 0.247209i \(0.920487\pi\)
\(984\) 21.5030 + 23.8247i 0.685490 + 0.759505i
\(985\) 16.7484i 0.533650i
\(986\) −2.42957 + 10.5525i −0.0773732 + 0.336061i
\(987\) 36.7208 1.16884
\(988\) 15.3587 + 6.98472i 0.488625 + 0.222214i
\(989\) −16.2308 + 10.8451i −0.516110 + 0.344854i
\(990\) −4.29877 10.9005i −0.136624 0.346439i
\(991\) −32.6899 6.50243i −1.03843 0.206557i −0.353704 0.935357i \(-0.615078\pi\)
−0.684726 + 0.728801i \(0.740078\pi\)
\(992\) 48.2554 26.5978i 1.53211 0.844481i
\(993\) −3.58142 18.0050i −0.113653 0.571371i
\(994\) −26.3910 27.3071i −0.837070 0.866128i
\(995\) −11.1675 + 26.9607i −0.354034 + 0.854713i
\(996\) −63.6918 45.7753i −2.01815 1.45045i
\(997\) 3.46448 5.18496i 0.109721 0.164209i −0.772545 0.634960i \(-0.781017\pi\)
0.882267 + 0.470750i \(0.156017\pi\)
\(998\) 32.5501 + 22.5618i 1.03035 + 0.714180i
\(999\) 8.70582 8.70582i 0.275440 0.275440i
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 136.2.s.c.107.8 yes 112
4.3 odd 2 544.2.cc.c.175.11 112
8.3 odd 2 inner 136.2.s.c.107.10 yes 112
8.5 even 2 544.2.cc.c.175.12 112
17.7 odd 16 inner 136.2.s.c.75.10 yes 112
68.7 even 16 544.2.cc.c.143.12 112
136.75 even 16 inner 136.2.s.c.75.8 112
136.109 odd 16 544.2.cc.c.143.11 112
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
136.2.s.c.75.8 112 136.75 even 16 inner
136.2.s.c.75.10 yes 112 17.7 odd 16 inner
136.2.s.c.107.8 yes 112 1.1 even 1 trivial
136.2.s.c.107.10 yes 112 8.3 odd 2 inner
544.2.cc.c.143.11 112 136.109 odd 16
544.2.cc.c.143.12 112 68.7 even 16
544.2.cc.c.175.11 112 4.3 odd 2
544.2.cc.c.175.12 112 8.5 even 2