Properties

Label 441.2.z.a.142.34
Level $441$
Weight $2$
Character 441.142
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(4,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([14, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.z (of order \(21\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 142.34
Character \(\chi\) \(=\) 441.142
Dual form 441.2.z.a.382.34

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.276882 - 0.705483i) q^{2} +(1.34213 - 1.09484i) q^{3} +(1.04506 + 0.969674i) q^{4} +(1.69583 - 0.816667i) q^{5} +(-0.400783 - 1.24999i) q^{6} +(0.217648 + 2.63678i) q^{7} +(2.33909 - 1.12644i) q^{8} +(0.602632 - 2.93885i) q^{9} +O(q^{10})\) \(q+(0.276882 - 0.705483i) q^{2} +(1.34213 - 1.09484i) q^{3} +(1.04506 + 0.969674i) q^{4} +(1.69583 - 0.816667i) q^{5} +(-0.400783 - 1.24999i) q^{6} +(0.217648 + 2.63678i) q^{7} +(2.33909 - 1.12644i) q^{8} +(0.602632 - 2.93885i) q^{9} +(-0.106601 - 1.42250i) q^{10} +(-2.98107 - 3.73814i) q^{11} +(2.46425 + 0.157252i) q^{12} +(-2.16063 + 5.50519i) q^{13} +(1.92047 + 0.576530i) q^{14} +(1.38190 - 2.95274i) q^{15} +(0.0660374 + 0.881208i) q^{16} +(-1.74050 + 1.61495i) q^{17} +(-1.90645 - 1.23886i) q^{18} +(1.93830 - 3.35723i) q^{19} +(2.56414 + 0.790933i) q^{20} +(3.17898 + 3.30062i) q^{21} +(-3.46260 + 1.06807i) q^{22} +(-1.01287 + 4.43768i) q^{23} +(1.90608 - 4.07277i) q^{24} +(-0.908565 + 1.13930i) q^{25} +(3.28558 + 3.04857i) q^{26} +(-2.40877 - 4.60411i) q^{27} +(-2.32937 + 2.96665i) q^{28} +(-1.66432 - 0.513375i) q^{29} +(-1.70049 - 1.79247i) q^{30} +(4.63394 - 8.02622i) q^{31} +(5.60166 + 1.72788i) q^{32} +(-8.09366 - 1.75327i) q^{33} +(0.657406 + 1.67504i) q^{34} +(2.52247 + 4.29378i) q^{35} +(3.47951 - 2.48692i) q^{36} +(-8.97230 - 2.76759i) q^{37} +(-1.83179 - 2.29699i) q^{38} +(3.12748 + 9.75424i) q^{39} +(3.04675 - 3.82051i) q^{40} +(-7.34181 - 5.00556i) q^{41} +(3.20873 - 1.32884i) q^{42} +(-3.53466 + 2.40989i) q^{43} +(0.509383 - 6.79725i) q^{44} +(-1.37810 - 5.47593i) q^{45} +(2.85026 + 1.94328i) q^{46} +(-0.214642 + 0.546898i) q^{47} +(1.05342 + 1.11040i) q^{48} +(-6.90526 + 1.14778i) q^{49} +(0.552195 + 0.956431i) q^{50} +(-0.567863 + 4.07305i) q^{51} +(-7.59623 + 3.65815i) q^{52} +(11.2661 - 3.47513i) q^{53} +(-3.91507 + 0.424553i) q^{54} +(-8.10819 - 3.90470i) q^{55} +(3.47929 + 5.92250i) q^{56} +(-1.07419 - 6.62798i) q^{57} +(-0.822998 + 1.03201i) q^{58} +(-0.827861 + 0.564426i) q^{59} +(4.30737 - 1.74580i) q^{60} +(3.82808 - 3.55194i) q^{61} +(-4.37931 - 5.49148i) q^{62} +(7.88027 + 0.949375i) q^{63} +(1.66806 - 2.09168i) q^{64} +(0.831857 + 11.1004i) q^{65} +(-3.47789 + 5.22450i) q^{66} +(-3.65476 + 6.33022i) q^{67} -3.38490 q^{68} +(3.49916 + 7.06488i) q^{69} +(3.72762 - 0.590690i) q^{70} +(-0.543665 + 2.38195i) q^{71} +(-1.90084 - 7.55305i) q^{72} +(7.22035 + 1.08829i) q^{73} +(-4.43676 + 5.56352i) q^{74} +(0.0279475 + 2.52383i) q^{75} +(5.28106 - 1.62899i) q^{76} +(9.20784 - 8.67403i) q^{77} +(7.74740 + 0.494387i) q^{78} +(6.31424 + 10.9366i) q^{79} +(0.831642 + 1.44045i) q^{80} +(-8.27367 - 3.54209i) q^{81} +(-5.56416 + 3.79358i) q^{82} +(-0.517250 - 1.31793i) q^{83} +(0.121701 + 6.53192i) q^{84} +(-1.63271 + 4.16008i) q^{85} +(0.721454 + 3.16090i) q^{86} +(-2.79580 + 1.13316i) q^{87} +(-11.1838 - 5.38583i) q^{88} +(-0.792868 - 2.02020i) q^{89} +(-4.24475 - 0.543958i) q^{90} +(-14.9863 - 4.49891i) q^{91} +(-5.36161 + 3.65548i) q^{92} +(-2.56811 - 15.8457i) q^{93} +(0.326397 + 0.302852i) q^{94} +(0.545278 - 7.27622i) q^{95} +(9.40992 - 3.81390i) q^{96} +(1.86733 - 3.23432i) q^{97} +(-1.10220 + 5.18935i) q^{98} +(-12.7823 + 6.50818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9} - 22 q^{10} - 5 q^{11} + 2 q^{12} - 4 q^{13} + 52 q^{14} - 4 q^{15} + 38 q^{16} - 37 q^{17} - 16 q^{18} - 14 q^{19} - 11 q^{20} - 6 q^{21} - q^{22} - 20 q^{23} - 26 q^{24} - 97 q^{25} - 44 q^{26} + 14 q^{27} - 22 q^{28} - 53 q^{29} - 9 q^{30} + 10 q^{31} - 10 q^{32} + 2 q^{33} - 7 q^{34} - 32 q^{35} - 22 q^{36} - 39 q^{37} + 59 q^{38} - 26 q^{39} - 19 q^{40} - 17 q^{41} - 83 q^{42} - q^{43} - 31 q^{44} + 81 q^{45} + 56 q^{46} + 50 q^{47} - 23 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} - 9 q^{52} + 50 q^{53} + 48 q^{54} + 20 q^{55} - 239 q^{56} + 33 q^{57} + 17 q^{58} - 37 q^{59} - 152 q^{60} - 105 q^{61} - 30 q^{62} + 6 q^{63} - 88 q^{64} - 5 q^{65} - 99 q^{66} + 13 q^{67} - 290 q^{68} + 64 q^{69} + 17 q^{70} - 19 q^{71} + 11 q^{72} - 40 q^{73} - 57 q^{74} + 69 q^{75} - 41 q^{76} + 19 q^{77} + 81 q^{78} + 13 q^{79} + 163 q^{80} - 179 q^{81} - 28 q^{82} + 73 q^{83} - 341 q^{84} - 10 q^{85} + 15 q^{86} + 13 q^{87} - 13 q^{88} - 104 q^{89} + 171 q^{90} - 49 q^{91} - 91 q^{92} - 275 q^{93} - 4 q^{94} - 29 q^{95} + 231 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.276882 0.705483i 0.195785 0.498852i −0.798942 0.601408i \(-0.794607\pi\)
0.994727 + 0.102556i \(0.0327020\pi\)
\(3\) 1.34213 1.09484i 0.774880 0.632109i
\(4\) 1.04506 + 0.969674i 0.522530 + 0.484837i
\(5\) 1.69583 0.816667i 0.758397 0.365225i −0.0143849 0.999897i \(-0.504579\pi\)
0.772782 + 0.634672i \(0.218865\pi\)
\(6\) −0.400783 1.24999i −0.163619 0.510308i
\(7\) 0.217648 + 2.63678i 0.0822634 + 0.996611i
\(8\) 2.33909 1.12644i 0.826992 0.398258i
\(9\) 0.602632 2.93885i 0.200877 0.979616i
\(10\) −0.106601 1.42250i −0.0337104 0.449833i
\(11\) −2.98107 3.73814i −0.898826 1.12709i −0.991332 0.131380i \(-0.958059\pi\)
0.0925065 0.995712i \(-0.470512\pi\)
\(12\) 2.46425 + 0.157252i 0.711368 + 0.0453947i
\(13\) −2.16063 + 5.50519i −0.599250 + 1.52687i 0.233007 + 0.972475i \(0.425144\pi\)
−0.832257 + 0.554390i \(0.812952\pi\)
\(14\) 1.92047 + 0.576530i 0.513267 + 0.154084i
\(15\) 1.38190 2.95274i 0.356805 0.762394i
\(16\) 0.0660374 + 0.881208i 0.0165094 + 0.220302i
\(17\) −1.74050 + 1.61495i −0.422133 + 0.391682i −0.862435 0.506167i \(-0.831062\pi\)
0.440302 + 0.897850i \(0.354871\pi\)
\(18\) −1.90645 1.23886i −0.449355 0.292002i
\(19\) 1.93830 3.35723i 0.444676 0.770201i −0.553354 0.832946i \(-0.686652\pi\)
0.998030 + 0.0627452i \(0.0199855\pi\)
\(20\) 2.56414 + 0.790933i 0.573360 + 0.176858i
\(21\) 3.17898 + 3.30062i 0.693710 + 0.720254i
\(22\) −3.46260 + 1.06807i −0.738229 + 0.227713i
\(23\) −1.01287 + 4.43768i −0.211198 + 0.925319i 0.752556 + 0.658528i \(0.228821\pi\)
−0.963754 + 0.266791i \(0.914037\pi\)
\(24\) 1.90608 4.07277i 0.389077 0.831351i
\(25\) −0.908565 + 1.13930i −0.181713 + 0.227861i
\(26\) 3.28558 + 3.04857i 0.644356 + 0.597875i
\(27\) −2.40877 4.60411i −0.463568 0.886061i
\(28\) −2.32937 + 2.96665i −0.440209 + 0.560644i
\(29\) −1.66432 0.513375i −0.309057 0.0953314i 0.136347 0.990661i \(-0.456464\pi\)
−0.445404 + 0.895330i \(0.646940\pi\)
\(30\) −1.70049 1.79247i −0.310465 0.327258i
\(31\) 4.63394 8.02622i 0.832281 1.44155i −0.0639450 0.997953i \(-0.520368\pi\)
0.896226 0.443599i \(-0.146298\pi\)
\(32\) 5.60166 + 1.72788i 0.990243 + 0.305449i
\(33\) −8.09366 1.75327i −1.40893 0.305205i
\(34\) 0.657406 + 1.67504i 0.112744 + 0.287267i
\(35\) 2.52247 + 4.29378i 0.426375 + 0.725782i
\(36\) 3.47951 2.48692i 0.579919 0.414486i
\(37\) −8.97230 2.76759i −1.47504 0.454989i −0.550097 0.835101i \(-0.685409\pi\)
−0.924941 + 0.380112i \(0.875886\pi\)
\(38\) −1.83179 2.29699i −0.297156 0.372621i
\(39\) 3.12748 + 9.75424i 0.500798 + 1.56193i
\(40\) 3.04675 3.82051i 0.481734 0.604076i
\(41\) −7.34181 5.00556i −1.14660 0.781738i −0.167651 0.985846i \(-0.553618\pi\)
−0.978948 + 0.204109i \(0.934570\pi\)
\(42\) 3.20873 1.32884i 0.495118 0.205044i
\(43\) −3.53466 + 2.40989i −0.539030 + 0.367504i −0.802023 0.597293i \(-0.796243\pi\)
0.262993 + 0.964798i \(0.415290\pi\)
\(44\) 0.509383 6.79725i 0.0767924 1.02472i
\(45\) −1.37810 5.47593i −0.205435 0.816303i
\(46\) 2.85026 + 1.94328i 0.420248 + 0.286520i
\(47\) −0.214642 + 0.546898i −0.0313087 + 0.0797733i −0.945673 0.325119i \(-0.894596\pi\)
0.914364 + 0.404892i \(0.132691\pi\)
\(48\) 1.05342 + 1.11040i 0.152048 + 0.160272i
\(49\) −6.90526 + 1.14778i −0.986465 + 0.163969i
\(50\) 0.552195 + 0.956431i 0.0780922 + 0.135260i
\(51\) −0.567863 + 4.07305i −0.0795167 + 0.570340i
\(52\) −7.59623 + 3.65815i −1.05341 + 0.507294i
\(53\) 11.2661 3.47513i 1.54752 0.477346i 0.600797 0.799402i \(-0.294850\pi\)
0.946721 + 0.322056i \(0.104374\pi\)
\(54\) −3.91507 + 0.424553i −0.532773 + 0.0577744i
\(55\) −8.10819 3.90470i −1.09331 0.526510i
\(56\) 3.47929 + 5.92250i 0.464940 + 0.791427i
\(57\) −1.07419 6.62798i −0.142280 0.877897i
\(58\) −0.822998 + 1.03201i −0.108065 + 0.135509i
\(59\) −0.827861 + 0.564426i −0.107778 + 0.0734820i −0.616010 0.787739i \(-0.711252\pi\)
0.508231 + 0.861221i \(0.330299\pi\)
\(60\) 4.30737 1.74580i 0.556078 0.225382i
\(61\) 3.82808 3.55194i 0.490136 0.454779i −0.395970 0.918264i \(-0.629591\pi\)
0.886105 + 0.463484i \(0.153401\pi\)
\(62\) −4.37931 5.49148i −0.556173 0.697419i
\(63\) 7.88027 + 0.949375i 0.992821 + 0.119610i
\(64\) 1.66806 2.09168i 0.208508 0.261460i
\(65\) 0.831857 + 11.1004i 0.103179 + 1.37683i
\(66\) −3.47789 + 5.22450i −0.428099 + 0.643091i
\(67\) −3.65476 + 6.33022i −0.446500 + 0.773360i −0.998155 0.0607119i \(-0.980663\pi\)
0.551656 + 0.834072i \(0.313996\pi\)
\(68\) −3.38490 −0.410479
\(69\) 3.49916 + 7.06488i 0.421249 + 0.850511i
\(70\) 3.72762 0.590690i 0.445536 0.0706009i
\(71\) −0.543665 + 2.38195i −0.0645211 + 0.282686i −0.996888 0.0788272i \(-0.974882\pi\)
0.932367 + 0.361513i \(0.117740\pi\)
\(72\) −1.90084 7.55305i −0.224016 0.890136i
\(73\) 7.22035 + 1.08829i 0.845078 + 0.127375i 0.557289 0.830319i \(-0.311842\pi\)
0.287789 + 0.957694i \(0.407080\pi\)
\(74\) −4.43676 + 5.56352i −0.515762 + 0.646746i
\(75\) 0.0279475 + 2.52383i 0.00322709 + 0.291427i
\(76\) 5.28106 1.62899i 0.605779 0.186858i
\(77\) 9.20784 8.67403i 1.04933 0.988498i
\(78\) 7.74740 + 0.494387i 0.877220 + 0.0559783i
\(79\) 6.31424 + 10.9366i 0.710407 + 1.23046i 0.964704 + 0.263335i \(0.0848224\pi\)
−0.254297 + 0.967126i \(0.581844\pi\)
\(80\) 0.831642 + 1.44045i 0.0929804 + 0.161047i
\(81\) −8.27367 3.54209i −0.919296 0.393566i
\(82\) −5.56416 + 3.79358i −0.614458 + 0.418931i
\(83\) −0.517250 1.31793i −0.0567755 0.144662i 0.899672 0.436567i \(-0.143806\pi\)
−0.956447 + 0.291906i \(0.905711\pi\)
\(84\) 0.121701 + 6.53192i 0.0132787 + 0.712691i
\(85\) −1.63271 + 4.16008i −0.177092 + 0.451224i
\(86\) 0.721454 + 3.16090i 0.0777964 + 0.340848i
\(87\) −2.79580 + 1.13316i −0.299742 + 0.121487i
\(88\) −11.1838 5.38583i −1.19220 0.574131i
\(89\) −0.792868 2.02020i −0.0840439 0.214140i 0.882674 0.469986i \(-0.155741\pi\)
−0.966718 + 0.255846i \(0.917646\pi\)
\(90\) −4.24475 0.543958i −0.447436 0.0573382i
\(91\) −14.9863 4.49891i −1.57099 0.471614i
\(92\) −5.36161 + 3.65548i −0.558987 + 0.381111i
\(93\) −2.56811 15.8457i −0.266300 1.64312i
\(94\) 0.326397 + 0.302852i 0.0336653 + 0.0312368i
\(95\) 0.545278 7.27622i 0.0559443 0.746525i
\(96\) 9.40992 3.81390i 0.960396 0.389254i
\(97\) 1.86733 3.23432i 0.189599 0.328395i −0.755518 0.655128i \(-0.772615\pi\)
0.945117 + 0.326733i \(0.105948\pi\)
\(98\) −1.10220 + 5.18935i −0.111339 + 0.524203i
\(99\) −12.7823 + 6.50818i −1.28467 + 0.654097i
\(100\) −2.05426 + 0.309630i −0.205426 + 0.0309630i
\(101\) 5.14515 2.47777i 0.511961 0.246548i −0.160023 0.987113i \(-0.551157\pi\)
0.671984 + 0.740566i \(0.265442\pi\)
\(102\) 2.71624 + 1.52837i 0.268947 + 0.151331i
\(103\) 9.35408 4.50469i 0.921685 0.443860i 0.0880126 0.996119i \(-0.471948\pi\)
0.833672 + 0.552259i \(0.186234\pi\)
\(104\) 1.14740 + 15.3109i 0.112511 + 1.50136i
\(105\) 8.08651 + 3.00111i 0.789162 + 0.292878i
\(106\) 0.667731 8.91025i 0.0648557 0.865440i
\(107\) 5.60050 + 14.2699i 0.541421 + 1.37952i 0.895817 + 0.444423i \(0.146591\pi\)
−0.354396 + 0.935096i \(0.615313\pi\)
\(108\) 1.94718 7.14730i 0.187367 0.687749i
\(109\) −3.96716 + 10.1082i −0.379985 + 0.968187i 0.605105 + 0.796146i \(0.293131\pi\)
−0.985090 + 0.172041i \(0.944964\pi\)
\(110\) −4.99971 + 4.63905i −0.476704 + 0.442316i
\(111\) −15.0721 + 6.10881i −1.43058 + 0.579822i
\(112\) −2.30918 + 0.365920i −0.218197 + 0.0345762i
\(113\) −9.39870 1.41663i −0.884155 0.133265i −0.308759 0.951140i \(-0.599914\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(114\) −4.97335 1.07734i −0.465797 0.100902i
\(115\) 1.90645 + 8.35271i 0.177777 + 0.778894i
\(116\) −1.24151 2.15036i −0.115271 0.199656i
\(117\) 14.8769 + 9.66737i 1.37537 + 0.893748i
\(118\) 0.168974 + 0.740321i 0.0155553 + 0.0681521i
\(119\) −4.63708 4.23783i −0.425081 0.388481i
\(120\) −0.0937181 8.46335i −0.00855526 0.772594i
\(121\) −2.63920 + 11.5631i −0.239927 + 1.05119i
\(122\) −1.44591 3.68412i −0.130906 0.333544i
\(123\) −15.3340 + 1.32002i −1.38262 + 0.119022i
\(124\) 12.6256 3.89447i 1.13381 0.349734i
\(125\) −2.70451 + 11.8492i −0.241899 + 1.05983i
\(126\) 2.85167 5.29654i 0.254047 0.471853i
\(127\) 1.86811 + 8.18474i 0.165768 + 0.726278i 0.987657 + 0.156630i \(0.0500631\pi\)
−0.821889 + 0.569647i \(0.807080\pi\)
\(128\) 4.84830 + 8.39751i 0.428534 + 0.742242i
\(129\) −2.10552 + 7.10428i −0.185381 + 0.625497i
\(130\) 8.06145 + 2.48663i 0.707036 + 0.218092i
\(131\) 15.2209 + 7.33002i 1.32986 + 0.640427i 0.957707 0.287745i \(-0.0929056\pi\)
0.372152 + 0.928172i \(0.378620\pi\)
\(132\) −6.75827 9.68049i −0.588232 0.842579i
\(133\) 9.27416 + 4.38018i 0.804171 + 0.379809i
\(134\) 3.45393 + 4.33109i 0.298374 + 0.374150i
\(135\) −7.84488 5.84061i −0.675180 0.502680i
\(136\) −2.25203 + 5.73808i −0.193110 + 0.492036i
\(137\) −9.04250 4.35464i −0.772553 0.372042i 0.00570747 0.999984i \(-0.498183\pi\)
−0.778260 + 0.627942i \(0.783898\pi\)
\(138\) 5.95301 0.512462i 0.506754 0.0436236i
\(139\) −5.31211 3.62174i −0.450568 0.307192i 0.316692 0.948528i \(-0.397428\pi\)
−0.767260 + 0.641337i \(0.778380\pi\)
\(140\) −1.52744 + 6.93324i −0.129092 + 0.585965i
\(141\) 0.310691 + 0.969008i 0.0261649 + 0.0816052i
\(142\) 1.52990 + 1.04307i 0.128386 + 0.0875321i
\(143\) 27.0202 8.33461i 2.25954 0.696975i
\(144\) 2.62953 + 0.336971i 0.219128 + 0.0280809i
\(145\) −3.24166 + 0.488601i −0.269205 + 0.0405761i
\(146\) 2.76696 4.79251i 0.228995 0.396631i
\(147\) −8.01112 + 9.10066i −0.660746 + 0.750610i
\(148\) −6.69294 11.5925i −0.550156 0.952899i
\(149\) −11.9605 14.9980i −0.979843 1.22868i −0.973496 0.228704i \(-0.926551\pi\)
−0.00634704 0.999980i \(-0.502020\pi\)
\(150\) 1.78826 + 0.679087i 0.146011 + 0.0554472i
\(151\) −1.73282 + 7.59198i −0.141015 + 0.617827i 0.854185 + 0.519969i \(0.174056\pi\)
−0.995200 + 0.0978583i \(0.968801\pi\)
\(152\) 0.752112 10.0362i 0.0610043 0.814046i
\(153\) 3.69720 + 6.08828i 0.298901 + 0.492209i
\(154\) −3.56990 8.89766i −0.287671 0.716994i
\(155\) 1.30361 17.3955i 0.104709 1.39724i
\(156\) −6.19003 + 13.2264i −0.495599 + 1.05896i
\(157\) −6.27817 + 4.28038i −0.501052 + 0.341612i −0.787327 0.616536i \(-0.788536\pi\)
0.286274 + 0.958148i \(0.407583\pi\)
\(158\) 9.46387 1.42645i 0.752905 0.113482i
\(159\) 11.3159 16.9987i 0.897406 1.34808i
\(160\) 10.9105 1.64450i 0.862555 0.130009i
\(161\) −11.9216 1.70487i −0.939557 0.134362i
\(162\) −4.78972 + 4.85619i −0.376316 + 0.381539i
\(163\) 18.9561 12.9240i 1.48476 1.01229i 0.495099 0.868837i \(-0.335132\pi\)
0.989657 0.143453i \(-0.0458205\pi\)
\(164\) −2.81887 12.3503i −0.220117 0.964395i
\(165\) −15.1573 + 3.63659i −1.17999 + 0.283108i
\(166\) −1.07299 −0.0832806
\(167\) 0.364970 0.338643i 0.0282422 0.0262049i −0.665925 0.746018i \(-0.731963\pi\)
0.694168 + 0.719813i \(0.255773\pi\)
\(168\) 11.1539 + 4.13949i 0.860540 + 0.319368i
\(169\) −16.1091 14.9471i −1.23916 1.14978i
\(170\) 2.48280 + 2.30370i 0.190422 + 0.176686i
\(171\) −8.69831 7.71954i −0.665176 0.590328i
\(172\) −6.03074 0.908987i −0.459839 0.0693096i
\(173\) −6.35758 + 1.96105i −0.483358 + 0.149096i −0.526851 0.849958i \(-0.676627\pi\)
0.0434933 + 0.999054i \(0.486151\pi\)
\(174\) 0.0253154 + 2.28614i 0.00191916 + 0.173312i
\(175\) −3.20185 2.14772i −0.242037 0.162353i
\(176\) 3.09722 2.87380i 0.233462 0.216621i
\(177\) −0.493139 + 1.66391i −0.0370666 + 0.125067i
\(178\) −1.64474 −0.123279
\(179\) −1.11193 + 1.03172i −0.0831093 + 0.0771141i −0.720634 0.693316i \(-0.756149\pi\)
0.637524 + 0.770430i \(0.279959\pi\)
\(180\) 3.86967 7.05899i 0.288428 0.526146i
\(181\) 11.3222 14.1976i 0.841574 1.05530i −0.156141 0.987735i \(-0.549906\pi\)
0.997715 0.0675652i \(-0.0215231\pi\)
\(182\) −7.32333 + 9.32689i −0.542841 + 0.691355i
\(183\) 1.24897 8.95832i 0.0923262 0.662218i
\(184\) 2.62960 + 11.5210i 0.193857 + 0.849343i
\(185\) −17.4757 + 2.63403i −1.28484 + 0.193658i
\(186\) −11.8899 2.57563i −0.871812 0.188854i
\(187\) 11.2254 + 1.69196i 0.820886 + 0.123729i
\(188\) −0.754627 + 0.363409i −0.0550368 + 0.0265043i
\(189\) 11.6158 7.35348i 0.844923 0.534887i
\(190\) −4.98228 2.39934i −0.361452 0.174066i
\(191\) 7.29704 + 4.97504i 0.527996 + 0.359981i 0.797789 0.602937i \(-0.206003\pi\)
−0.269793 + 0.962918i \(0.586955\pi\)
\(192\) −0.0513095 4.63358i −0.00370294 0.334400i
\(193\) 0.374280 4.99442i 0.0269413 0.359506i −0.967399 0.253259i \(-0.918498\pi\)
0.994340 0.106247i \(-0.0338834\pi\)
\(194\) −1.76473 2.21290i −0.126700 0.158877i
\(195\) 13.2696 + 13.9874i 0.950258 + 1.00166i
\(196\) −8.32939 5.49635i −0.594956 0.392596i
\(197\) 5.34731 0.380980 0.190490 0.981689i \(-0.438992\pi\)
0.190490 + 0.981689i \(0.438992\pi\)
\(198\) 1.05222 + 10.8197i 0.0747783 + 0.768923i
\(199\) −3.44134 2.34626i −0.243950 0.166322i 0.435173 0.900347i \(-0.356687\pi\)
−0.679123 + 0.734025i \(0.737640\pi\)
\(200\) −0.841849 + 3.68838i −0.0595277 + 0.260808i
\(201\) 2.02545 + 12.4974i 0.142864 + 0.881497i
\(202\) −0.323429 4.31587i −0.0227564 0.303663i
\(203\) 0.991423 4.50019i 0.0695842 0.315852i
\(204\) −4.54298 + 3.70594i −0.318072 + 0.259468i
\(205\) −16.5383 2.49275i −1.15509 0.174101i
\(206\) −0.588008 7.84642i −0.0409684 0.546686i
\(207\) 12.4313 + 5.65096i 0.864033 + 0.392769i
\(208\) −4.99390 1.54041i −0.346265 0.106809i
\(209\) −18.3280 + 2.76250i −1.26777 + 0.191086i
\(210\) 4.35624 4.87394i 0.300609 0.336334i
\(211\) 4.04542 + 0.609749i 0.278498 + 0.0419768i 0.286806 0.957989i \(-0.407406\pi\)
−0.00830796 + 0.999965i \(0.502645\pi\)
\(212\) 15.1435 + 7.29272i 1.04006 + 0.500866i
\(213\) 1.87820 + 3.79212i 0.128692 + 0.259832i
\(214\) 11.6178 0.794178
\(215\) −4.02609 + 6.97339i −0.274577 + 0.475581i
\(216\) −10.8206 8.05606i −0.736248 0.548146i
\(217\) 22.1720 + 10.4718i 1.50513 + 0.710873i
\(218\) 6.03271 + 5.59753i 0.408586 + 0.379113i
\(219\) 10.8822 6.44453i 0.735349 0.435481i
\(220\) −4.68726 11.9430i −0.316015 0.805194i
\(221\) −5.13002 13.0711i −0.345082 0.879256i
\(222\) 0.136475 + 12.3245i 0.00915957 + 0.827168i
\(223\) −8.66735 8.04213i −0.580409 0.538541i 0.334398 0.942432i \(-0.391467\pi\)
−0.914807 + 0.403891i \(0.867657\pi\)
\(224\) −3.33686 + 15.1464i −0.222953 + 1.01201i
\(225\) 2.80071 + 3.35672i 0.186714 + 0.223781i
\(226\) −3.60173 + 6.23839i −0.239584 + 0.414971i
\(227\) 22.7859 1.51235 0.756175 0.654369i \(-0.227066\pi\)
0.756175 + 0.654369i \(0.227066\pi\)
\(228\) 5.30438 7.96825i 0.351291 0.527710i
\(229\) −0.883438 0.425441i −0.0583792 0.0281140i 0.404466 0.914553i \(-0.367457\pi\)
−0.462846 + 0.886439i \(0.653172\pi\)
\(230\) 6.42056 + 0.967744i 0.423359 + 0.0638111i
\(231\) 2.86142 21.7228i 0.188268 1.42926i
\(232\) −4.47128 + 0.673937i −0.293554 + 0.0442461i
\(233\) 16.3699 + 5.04944i 1.07243 + 0.330800i 0.780188 0.625545i \(-0.215123\pi\)
0.292240 + 0.956345i \(0.405600\pi\)
\(234\) 10.9393 7.81866i 0.715124 0.511122i
\(235\) 0.0826386 + 1.10274i 0.00539075 + 0.0719345i
\(236\) −1.41247 0.212896i −0.0919442 0.0138584i
\(237\) 20.4484 + 7.76522i 1.32827 + 0.504405i
\(238\) −4.27364 + 2.09801i −0.277019 + 0.135994i
\(239\) −1.76853 23.5994i −0.114397 1.52652i −0.698956 0.715165i \(-0.746352\pi\)
0.584560 0.811351i \(-0.301267\pi\)
\(240\) 2.69324 + 1.02275i 0.173848 + 0.0660182i
\(241\) 1.61538 7.07743i 0.104056 0.455897i −0.895877 0.444302i \(-0.853452\pi\)
0.999933 0.0115955i \(-0.00369105\pi\)
\(242\) 7.42682 + 5.06352i 0.477414 + 0.325495i
\(243\) −14.9824 + 4.30443i −0.961121 + 0.276129i
\(244\) 7.44480 0.476605
\(245\) −10.7728 + 7.58574i −0.688247 + 0.484635i
\(246\) −3.31445 + 11.1834i −0.211322 + 0.713025i
\(247\) 14.2942 + 17.9244i 0.909521 + 1.14050i
\(248\) 1.79809 23.9939i 0.114179 1.52361i
\(249\) −2.13715 1.20253i −0.135436 0.0762071i
\(250\) 7.61061 + 5.18882i 0.481337 + 0.328170i
\(251\) −16.7812 8.08142i −1.05922 0.510095i −0.178604 0.983921i \(-0.557158\pi\)
−0.880618 + 0.473826i \(0.842872\pi\)
\(252\) 7.31478 + 8.63345i 0.460788 + 0.543856i
\(253\) 19.6081 9.44276i 1.23275 0.593661i
\(254\) 6.29144 + 0.948282i 0.394760 + 0.0595005i
\(255\) 2.36333 + 7.37094i 0.147997 + 0.461586i
\(256\) 12.5577 1.89276i 0.784854 0.118298i
\(257\) −4.90403 21.4859i −0.305905 1.34026i −0.861057 0.508508i \(-0.830197\pi\)
0.555153 0.831748i \(-0.312660\pi\)
\(258\) 4.42897 + 3.45246i 0.275736 + 0.214941i
\(259\) 5.34473 24.2604i 0.332105 1.50747i
\(260\) −9.89440 + 12.4072i −0.613625 + 0.769461i
\(261\) −2.51171 + 4.58181i −0.155471 + 0.283607i
\(262\) 9.38561 8.70857i 0.579845 0.538017i
\(263\) −31.7515 −1.95788 −0.978939 0.204151i \(-0.934557\pi\)
−0.978939 + 0.204151i \(0.934557\pi\)
\(264\) −20.9067 + 5.01601i −1.28672 + 0.308714i
\(265\) 16.2673 15.0939i 0.999294 0.927209i
\(266\) 5.65799 5.32997i 0.346913 0.326802i
\(267\) −3.27593 1.84330i −0.200484 0.112808i
\(268\) −9.95770 + 3.07154i −0.608263 + 0.187624i
\(269\) 20.3207 + 3.06286i 1.23898 + 0.186746i 0.735657 0.677354i \(-0.236873\pi\)
0.503321 + 0.864100i \(0.332111\pi\)
\(270\) −6.29256 + 3.91728i −0.382953 + 0.238398i
\(271\) 19.1052 + 17.7270i 1.16056 + 1.07684i 0.995897 + 0.0904890i \(0.0288430\pi\)
0.164660 + 0.986350i \(0.447347\pi\)
\(272\) −1.53804 1.42709i −0.0932575 0.0865303i
\(273\) −25.0391 + 10.3695i −1.51544 + 0.627590i
\(274\) −5.57583 + 5.17361i −0.336848 + 0.312549i
\(275\) 6.96738 0.420149
\(276\) −3.19380 + 10.7763i −0.192244 + 0.648655i
\(277\) 0.531425 + 2.32832i 0.0319302 + 0.139895i 0.988381 0.152000i \(-0.0485713\pi\)
−0.956450 + 0.291895i \(0.905714\pi\)
\(278\) −4.02590 + 2.74482i −0.241458 + 0.164623i
\(279\) −20.7953 18.4553i −1.24498 1.10489i
\(280\) 10.7370 + 7.20211i 0.641657 + 0.430408i
\(281\) −9.79073 + 1.47572i −0.584066 + 0.0880338i −0.434427 0.900707i \(-0.643049\pi\)
−0.149639 + 0.988741i \(0.547811\pi\)
\(282\) 0.769644 + 0.0491135i 0.0458316 + 0.00292467i
\(283\) 23.5509 3.54973i 1.39996 0.211010i 0.594706 0.803943i \(-0.297268\pi\)
0.805251 + 0.592934i \(0.202030\pi\)
\(284\) −2.87788 + 1.96210i −0.170771 + 0.116430i
\(285\) −7.23450 10.3626i −0.428535 0.613830i
\(286\) 1.60146 21.3700i 0.0946962 1.26363i
\(287\) 11.6007 20.4482i 0.684765 1.20702i
\(288\) 8.45373 15.4212i 0.498141 0.908700i
\(289\) −0.849129 + 11.3308i −0.0499488 + 0.666520i
\(290\) −0.552856 + 2.42222i −0.0324648 + 0.142238i
\(291\) −1.03487 6.38532i −0.0606650 0.374314i
\(292\) 6.49041 + 8.13872i 0.379823 + 0.476283i
\(293\) −5.42286 9.39267i −0.316807 0.548726i 0.663013 0.748608i \(-0.269277\pi\)
−0.979820 + 0.199882i \(0.935944\pi\)
\(294\) 4.20223 + 8.17152i 0.245079 + 0.476573i
\(295\) −0.942960 + 1.63326i −0.0549013 + 0.0950918i
\(296\) −24.1045 + 3.63317i −1.40105 + 0.211174i
\(297\) −10.0301 + 22.7295i −0.582006 + 1.31890i
\(298\) −13.8925 + 4.28527i −0.804770 + 0.248239i
\(299\) −22.2418 15.1642i −1.28628 0.876969i
\(300\) −2.41809 + 2.66466i −0.139609 + 0.153844i
\(301\) −7.12367 8.79562i −0.410601 0.506971i
\(302\) 4.87623 + 3.32456i 0.280596 + 0.191307i
\(303\) 4.19269 8.95863i 0.240864 0.514660i
\(304\) 3.08642 + 1.48634i 0.177018 + 0.0852475i
\(305\) 3.59101 9.14975i 0.205621 0.523913i
\(306\) 5.31887 0.922581i 0.304060 0.0527405i
\(307\) 8.91959 + 11.1848i 0.509068 + 0.638351i 0.968248 0.249992i \(-0.0804281\pi\)
−0.459180 + 0.888343i \(0.651857\pi\)
\(308\) 18.0337 0.136277i 1.02757 0.00776508i
\(309\) 7.62247 16.2871i 0.433627 0.926543i
\(310\) −11.9113 5.73617i −0.676515 0.325792i
\(311\) −5.54296 1.70978i −0.314312 0.0969525i 0.133585 0.991037i \(-0.457351\pi\)
−0.447898 + 0.894085i \(0.647827\pi\)
\(312\) 18.3031 + 19.2931i 1.03621 + 1.09226i
\(313\) −1.08985 1.88768i −0.0616021 0.106698i 0.833580 0.552399i \(-0.186288\pi\)
−0.895182 + 0.445701i \(0.852954\pi\)
\(314\) 1.28143 + 5.61430i 0.0723152 + 0.316834i
\(315\) 14.1389 4.82558i 0.796637 0.271891i
\(316\) −4.00616 + 17.5521i −0.225364 + 0.987385i
\(317\) 11.5510 3.56300i 0.648767 0.200118i 0.0471311 0.998889i \(-0.484992\pi\)
0.601636 + 0.798771i \(0.294516\pi\)
\(318\) −8.85915 12.6898i −0.496796 0.711608i
\(319\) 3.04239 + 7.75188i 0.170341 + 0.434022i
\(320\) 1.12053 4.90938i 0.0626398 0.274443i
\(321\) 23.1399 + 13.0203i 1.29154 + 0.726724i
\(322\) −4.50364 + 7.93847i −0.250978 + 0.442394i
\(323\) 2.04814 + 8.97350i 0.113962 + 0.499299i
\(324\) −5.21181 11.7245i −0.289545 0.651359i
\(325\) −4.30902 7.46344i −0.239021 0.413997i
\(326\) −3.86910 16.9516i −0.214290 0.938865i
\(327\) 5.74241 + 17.9099i 0.317556 + 0.990420i
\(328\) −22.8116 3.43830i −1.25956 0.189848i
\(329\) −1.48877 0.446932i −0.0820785 0.0246402i
\(330\) −1.63123 + 11.7001i −0.0897961 + 0.644071i
\(331\) 13.4294 12.4607i 0.738147 0.684901i −0.218602 0.975814i \(-0.570150\pi\)
0.956749 + 0.290913i \(0.0939592\pi\)
\(332\) 0.737406 1.87888i 0.0404704 0.103117i
\(333\) −13.5405 + 24.7004i −0.742016 + 1.35357i
\(334\) −0.137853 0.351244i −0.00754299 0.0192192i
\(335\) −1.02815 + 13.7197i −0.0561737 + 0.749587i
\(336\) −2.69860 + 3.01931i −0.147221 + 0.164717i
\(337\) 0.663178 + 8.84949i 0.0361256 + 0.482063i 0.985699 + 0.168517i \(0.0538978\pi\)
−0.949573 + 0.313546i \(0.898483\pi\)
\(338\) −15.0053 + 7.22615i −0.816178 + 0.393051i
\(339\) −14.1653 + 8.38881i −0.769352 + 0.455618i
\(340\) −5.74020 + 2.76434i −0.311306 + 0.149917i
\(341\) −43.8172 + 6.60439i −2.37284 + 0.357648i
\(342\) −7.85441 + 3.99911i −0.424718 + 0.216247i
\(343\) −4.52938 17.9579i −0.244563 0.969633i
\(344\) −5.55326 + 9.61853i −0.299412 + 0.518596i
\(345\) 11.7036 + 9.12316i 0.630102 + 0.491175i
\(346\) −0.376808 + 5.02815i −0.0202573 + 0.270315i
\(347\) −24.8772 23.0827i −1.33548 1.23914i −0.948392 0.317100i \(-0.897291\pi\)
−0.387086 0.922043i \(-0.626519\pi\)
\(348\) −4.02058 1.52680i −0.215526 0.0818453i
\(349\) −11.6180 + 7.92103i −0.621898 + 0.424003i −0.832854 0.553492i \(-0.813295\pi\)
0.210956 + 0.977496i \(0.432342\pi\)
\(350\) −2.40172 + 1.66419i −0.128377 + 0.0889545i
\(351\) 30.5510 3.31297i 1.63069 0.176833i
\(352\) −10.2399 26.0907i −0.545786 1.39064i
\(353\) −8.02772 3.86595i −0.427273 0.205764i 0.207873 0.978156i \(-0.433346\pi\)
−0.635146 + 0.772392i \(0.719060\pi\)
\(354\) 1.03732 + 0.808609i 0.0551330 + 0.0429771i
\(355\) 1.02330 + 4.48337i 0.0543111 + 0.237953i
\(356\) 1.13034 2.88005i 0.0599077 0.152642i
\(357\) −10.8633 0.610839i −0.574949 0.0323290i
\(358\) 0.419987 + 1.07011i 0.0221970 + 0.0565570i
\(359\) −2.59762 + 1.77103i −0.137097 + 0.0934713i −0.629927 0.776655i \(-0.716915\pi\)
0.492829 + 0.870126i \(0.335963\pi\)
\(360\) −9.39183 11.2563i −0.494993 0.593260i
\(361\) 1.98601 + 3.43987i 0.104527 + 0.181046i
\(362\) −6.88126 11.9187i −0.361671 0.626433i
\(363\) 9.11763 + 18.4087i 0.478551 + 0.966206i
\(364\) −11.2991 19.2334i −0.592232 1.00811i
\(365\) 13.1332 4.05107i 0.687425 0.212043i
\(366\) −5.97413 3.36152i −0.312273 0.175710i
\(367\) −21.8897 + 27.4488i −1.14263 + 1.43281i −0.258233 + 0.966083i \(0.583140\pi\)
−0.884399 + 0.466732i \(0.845431\pi\)
\(368\) −3.97740 0.599497i −0.207336 0.0312509i
\(369\) −19.1350 + 18.5600i −0.996129 + 0.966193i
\(370\) −2.98043 + 13.0581i −0.154945 + 0.678859i
\(371\) 11.6152 + 28.9499i 0.603032 + 1.50300i
\(372\) 12.6813 19.0499i 0.657496 0.987693i
\(373\) −0.300864 −0.0155781 −0.00778907 0.999970i \(-0.502479\pi\)
−0.00778907 + 0.999970i \(0.502479\pi\)
\(374\) 4.30177 7.45089i 0.222439 0.385276i
\(375\) 9.34326 + 18.8642i 0.482484 + 0.974145i
\(376\) 0.113985 + 1.52102i 0.00587833 + 0.0784408i
\(377\) 6.42221 8.05320i 0.330761 0.414761i
\(378\) −1.97156 10.2308i −0.101406 0.526215i
\(379\) 12.1334 + 15.2148i 0.623249 + 0.781529i 0.988798 0.149263i \(-0.0476901\pi\)
−0.365549 + 0.930792i \(0.619119\pi\)
\(380\) 7.62542 7.07535i 0.391176 0.362958i
\(381\) 11.4683 + 8.93970i 0.587537 + 0.457995i
\(382\) 5.53023 3.77044i 0.282951 0.192913i
\(383\) 2.01122 2.52200i 0.102769 0.128868i −0.727787 0.685803i \(-0.759451\pi\)
0.830556 + 0.556935i \(0.188023\pi\)
\(384\) 15.7010 + 5.96242i 0.801240 + 0.304269i
\(385\) 8.53111 22.2294i 0.434786 1.13292i
\(386\) −3.41985 1.64691i −0.174066 0.0838256i
\(387\) 4.95220 + 11.8401i 0.251734 + 0.601866i
\(388\) 5.08771 1.56935i 0.258289 0.0796718i
\(389\) 3.08779 1.48700i 0.156557 0.0753940i −0.353964 0.935259i \(-0.615167\pi\)
0.510522 + 0.859865i \(0.329452\pi\)
\(390\) 13.5420 5.48865i 0.685725 0.277929i
\(391\) −5.40371 9.35950i −0.273277 0.473330i
\(392\) −14.8591 + 10.4632i −0.750497 + 0.528469i
\(393\) 28.4537 6.82671i 1.43530 0.344362i
\(394\) 1.48057 3.77244i 0.0745902 0.190053i
\(395\) 19.6394 + 13.3899i 0.988165 + 0.673720i
\(396\) −19.6691 5.59324i −0.988410 0.281071i
\(397\) 1.61785 21.5887i 0.0811975 1.08351i −0.796611 0.604493i \(-0.793376\pi\)
0.877808 0.479012i \(-0.159005\pi\)
\(398\) −2.60809 + 1.77817i −0.130732 + 0.0891315i
\(399\) 17.2427 4.27499i 0.863217 0.214017i
\(400\) −1.06396 0.725398i −0.0531982 0.0362699i
\(401\) −1.40479 + 1.76155i −0.0701517 + 0.0879675i −0.815669 0.578519i \(-0.803631\pi\)
0.745517 + 0.666486i \(0.232202\pi\)
\(402\) 9.37750 + 2.03138i 0.467707 + 0.101316i
\(403\) 34.1737 + 42.8524i 1.70231 + 2.13463i
\(404\) 7.77962 + 2.39970i 0.387051 + 0.119389i
\(405\) −16.9234 + 0.750060i −0.840931 + 0.0372708i
\(406\) −2.90030 1.94545i −0.143940 0.0965513i
\(407\) 16.4014 + 41.7901i 0.812988 + 2.07146i
\(408\) 3.25978 + 10.1669i 0.161383 + 0.503335i
\(409\) −10.8316 3.34109i −0.535586 0.165206i 0.0151511 0.999885i \(-0.495177\pi\)
−0.550737 + 0.834679i \(0.685653\pi\)
\(410\) −6.33776 + 10.9773i −0.313000 + 0.542131i
\(411\) −16.9039 + 4.05563i −0.833806 + 0.200050i
\(412\) 14.1437 + 4.36274i 0.696808 + 0.214937i
\(413\) −1.66845 2.06004i −0.0820991 0.101368i
\(414\) 7.42865 7.20541i 0.365098 0.354126i
\(415\) −1.95348 1.81256i −0.0958924 0.0889751i
\(416\) −21.6154 + 27.1049i −1.05978 + 1.32893i
\(417\) −11.0948 + 0.955090i −0.543314 + 0.0467709i
\(418\) −3.12579 + 13.6950i −0.152887 + 0.669843i
\(419\) 9.90285 3.05462i 0.483786 0.149228i −0.0432621 0.999064i \(-0.513775\pi\)
0.527048 + 0.849836i \(0.323299\pi\)
\(420\) 5.54079 + 10.9776i 0.270363 + 0.535653i
\(421\) −20.7157 6.38993i −1.00962 0.311426i −0.254542 0.967062i \(-0.581925\pi\)
−0.755077 + 0.655636i \(0.772401\pi\)
\(422\) 1.55027 2.68515i 0.0754660 0.130711i
\(423\) 1.47790 + 0.960378i 0.0718580 + 0.0466952i
\(424\) 22.4378 20.8193i 1.08968 1.01107i
\(425\) −0.258560 3.45024i −0.0125420 0.167361i
\(426\) 3.19532 0.275067i 0.154814 0.0133270i
\(427\) 10.1989 + 9.32075i 0.493558 + 0.451063i
\(428\) −7.98425 + 20.3435i −0.385933 + 0.983341i
\(429\) 27.1395 40.7690i 1.31031 1.96835i
\(430\) 3.80486 + 4.77114i 0.183487 + 0.230085i
\(431\) −0.960930 12.8227i −0.0462864 0.617649i −0.971322 0.237768i \(-0.923584\pi\)
0.925036 0.379881i \(-0.124035\pi\)
\(432\) 3.89811 2.42667i 0.187548 0.116753i
\(433\) −11.6241 + 5.59789i −0.558620 + 0.269017i −0.691818 0.722072i \(-0.743190\pi\)
0.133198 + 0.991090i \(0.457476\pi\)
\(434\) 13.5267 12.7425i 0.649303 0.611660i
\(435\) −3.81579 + 4.20488i −0.182953 + 0.201609i
\(436\) −13.9476 + 6.71679i −0.667967 + 0.321676i
\(437\) 12.9351 + 12.0020i 0.618767 + 0.574132i
\(438\) −1.53343 9.46156i −0.0732702 0.452091i
\(439\) −0.0281167 + 0.0716402i −0.00134194 + 0.00341920i −0.931543 0.363631i \(-0.881537\pi\)
0.930201 + 0.367050i \(0.119632\pi\)
\(440\) −23.3642 −1.11384
\(441\) −0.788169 + 20.9852i −0.0375319 + 0.999295i
\(442\) −10.6418 −0.506181
\(443\) 13.1485 33.5018i 0.624703 1.59172i −0.170488 0.985360i \(-0.554534\pi\)
0.795191 0.606358i \(-0.207370\pi\)
\(444\) −21.6748 8.23095i −1.02864 0.390623i
\(445\) −2.99439 2.77839i −0.141948 0.131708i
\(446\) −8.07342 + 3.88795i −0.382287 + 0.184100i
\(447\) −32.4730 7.03439i −1.53592 0.332715i
\(448\) 5.87836 + 3.94306i 0.277727 + 0.186292i
\(449\) −30.3297 + 14.6060i −1.43135 + 0.689301i −0.979248 0.202665i \(-0.935040\pi\)
−0.452101 + 0.891967i \(0.649325\pi\)
\(450\) 3.14358 1.04644i 0.148190 0.0493298i
\(451\) 3.17494 + 42.3667i 0.149502 + 1.99497i
\(452\) −8.44854 10.5941i −0.397386 0.498306i
\(453\) 5.98637 + 12.0866i 0.281264 + 0.567878i
\(454\) 6.30899 16.0750i 0.296095 0.754439i
\(455\) −29.0882 + 4.60940i −1.36368 + 0.216092i
\(456\) −9.97868 14.2934i −0.467294 0.669349i
\(457\) 0.111907 + 1.49329i 0.00523477 + 0.0698532i 0.999209 0.0397577i \(-0.0126586\pi\)
−0.993975 + 0.109611i \(0.965040\pi\)
\(458\) −0.544750 + 0.505454i −0.0254545 + 0.0236183i
\(459\) 11.6279 + 4.12341i 0.542742 + 0.192464i
\(460\) −6.10705 + 10.5777i −0.284743 + 0.493189i
\(461\) 1.79960 + 0.555104i 0.0838158 + 0.0258538i 0.336379 0.941727i \(-0.390798\pi\)
−0.252564 + 0.967580i \(0.581274\pi\)
\(462\) −14.5328 8.03335i −0.676128 0.373745i
\(463\) −11.3234 + 3.49281i −0.526244 + 0.162325i −0.546483 0.837470i \(-0.684034\pi\)
0.0202388 + 0.999795i \(0.493557\pi\)
\(464\) 0.342483 1.50052i 0.0158994 0.0696597i
\(465\) −17.2957 24.7743i −0.802070 1.14888i
\(466\) 8.09483 10.1506i 0.374986 0.470217i
\(467\) −13.5592 12.5811i −0.627445 0.582184i 0.301013 0.953620i \(-0.402675\pi\)
−0.928459 + 0.371436i \(0.878866\pi\)
\(468\) 6.17302 + 24.5287i 0.285348 + 1.13384i
\(469\) −17.4869 8.25904i −0.807469 0.381367i
\(470\) 0.800843 + 0.247027i 0.0369401 + 0.0113945i
\(471\) −3.73977 + 12.6185i −0.172320 + 0.581428i
\(472\) −1.30064 + 2.25278i −0.0598670 + 0.103693i
\(473\) 19.5455 + 6.02900i 0.898705 + 0.277214i
\(474\) 11.1400 12.2759i 0.511678 0.563853i
\(475\) 2.06384 + 5.25857i 0.0946954 + 0.241280i
\(476\) −0.736718 8.92525i −0.0337674 0.409088i
\(477\) −3.42357 35.2036i −0.156755 1.61186i
\(478\) −17.1386 5.28657i −0.783902 0.241802i
\(479\) 10.3209 + 12.9420i 0.471576 + 0.591337i 0.959556 0.281517i \(-0.0908377\pi\)
−0.487981 + 0.872855i \(0.662266\pi\)
\(480\) 12.8429 14.1525i 0.586196 0.645970i
\(481\) 34.6219 43.4145i 1.57862 1.97953i
\(482\) −4.54574 3.09923i −0.207053 0.141166i
\(483\) −17.8670 + 10.7642i −0.812975 + 0.489787i
\(484\) −13.9706 + 9.52496i −0.635025 + 0.432953i
\(485\) 0.525314 7.00983i 0.0238533 0.318300i
\(486\) −1.11165 + 11.7616i −0.0504254 + 0.533519i
\(487\) 3.47655 + 2.37027i 0.157537 + 0.107407i 0.639523 0.768772i \(-0.279132\pi\)
−0.481986 + 0.876179i \(0.660084\pi\)
\(488\) 4.95315 12.6204i 0.224219 0.571299i
\(489\) 11.2917 38.0997i 0.510631 1.72293i
\(490\) 2.36883 + 9.70036i 0.107013 + 0.438218i
\(491\) 13.3357 + 23.0980i 0.601830 + 1.04240i 0.992544 + 0.121887i \(0.0388947\pi\)
−0.390714 + 0.920512i \(0.627772\pi\)
\(492\) −17.3049 13.4895i −0.780167 0.608153i
\(493\) 3.72582 1.79426i 0.167803 0.0808095i
\(494\) 16.6032 5.12141i 0.747013 0.230423i
\(495\) −16.3616 + 21.4757i −0.735398 + 0.965259i
\(496\) 7.37879 + 3.55344i 0.331317 + 0.159554i
\(497\) −6.39902 0.915099i −0.287035 0.0410478i
\(498\) −1.44010 + 1.17476i −0.0645324 + 0.0526424i
\(499\) −1.33315 + 1.67172i −0.0596801 + 0.0748365i −0.810776 0.585357i \(-0.800954\pi\)
0.751096 + 0.660194i \(0.229526\pi\)
\(500\) −14.3163 + 9.76067i −0.640243 + 0.436510i
\(501\) 0.119077 0.854088i 0.00531995 0.0381578i
\(502\) −10.3477 + 9.60129i −0.461842 + 0.428526i
\(503\) −10.5084 13.1771i −0.468545 0.587537i 0.490269 0.871571i \(-0.336898\pi\)
−0.958814 + 0.284034i \(0.908327\pi\)
\(504\) 19.5021 6.65602i 0.868690 0.296483i
\(505\) 6.70176 8.40375i 0.298225 0.373962i
\(506\) −1.23259 16.4477i −0.0547951 0.731190i
\(507\) −37.9853 2.42397i −1.68699 0.107652i
\(508\) −5.98424 + 10.3650i −0.265508 + 0.459873i
\(509\) 20.6314 0.914471 0.457236 0.889346i \(-0.348840\pi\)
0.457236 + 0.889346i \(0.348840\pi\)
\(510\) 5.85443 + 0.373591i 0.259239 + 0.0165429i
\(511\) −1.29809 + 19.2754i −0.0574243 + 0.852692i
\(512\) −2.17372 + 9.52369i −0.0960658 + 0.420892i
\(513\) −20.1260 0.837339i −0.888583 0.0369694i
\(514\) −16.5158 2.48936i −0.728481 0.109801i
\(515\) 12.1841 15.2783i 0.536894 0.673244i
\(516\) −9.08924 + 5.38274i −0.400131 + 0.236962i
\(517\) 2.68424 0.827979i 0.118053 0.0364145i
\(518\) −15.6354 10.4879i −0.686982 0.460811i
\(519\) −6.38566 + 9.59255i −0.280299 + 0.421066i
\(520\) 14.4497 + 25.0277i 0.633663 + 1.09754i
\(521\) −1.38912 2.40602i −0.0608583 0.105410i 0.833991 0.551778i \(-0.186050\pi\)
−0.894849 + 0.446368i \(0.852717\pi\)
\(522\) 2.53695 + 3.04059i 0.111039 + 0.133083i
\(523\) 17.6852 12.0576i 0.773321 0.527242i −0.111168 0.993802i \(-0.535459\pi\)
0.884490 + 0.466560i \(0.154507\pi\)
\(524\) 8.79907 + 22.4197i 0.384389 + 0.979407i
\(525\) −6.64872 + 0.623000i −0.290174 + 0.0271899i
\(526\) −8.79140 + 22.4001i −0.383323 + 0.976692i
\(527\) 4.89655 + 21.4532i 0.213297 + 0.934516i
\(528\) 1.01051 7.24799i 0.0439769 0.315428i
\(529\) 2.05522 + 0.989744i 0.0893576 + 0.0430323i
\(530\) −6.14435 15.6555i −0.266894 0.680034i
\(531\) 1.15987 + 2.77310i 0.0503339 + 0.120342i
\(532\) 5.44471 + 13.5705i 0.236058 + 0.588354i
\(533\) 43.4195 29.6029i 1.88071 1.28225i
\(534\) −2.20746 + 1.80074i −0.0955263 + 0.0779256i
\(535\) 21.1512 + 19.6255i 0.914447 + 0.848482i
\(536\) −1.41814 + 18.9238i −0.0612545 + 0.817385i
\(537\) −0.362782 + 2.60209i −0.0156552 + 0.112288i
\(538\) 7.78724 13.4879i 0.335732 0.581505i
\(539\) 24.8756 + 22.3912i 1.07147 + 0.964457i
\(540\) −2.53489 13.7108i −0.109084 0.590018i
\(541\) 10.3778 1.56420i 0.446176 0.0672502i 0.0778882 0.996962i \(-0.475182\pi\)
0.368288 + 0.929712i \(0.379944\pi\)
\(542\) 17.7960 8.57010i 0.764403 0.368117i
\(543\) −0.348271 31.4511i −0.0149457 1.34970i
\(544\) −12.5401 + 6.03900i −0.537653 + 0.258920i
\(545\) 1.52739 + 20.3815i 0.0654260 + 0.873050i
\(546\) 0.382618 + 20.5358i 0.0163745 + 0.878852i
\(547\) −1.00022 + 13.3470i −0.0427663 + 0.570677i 0.934126 + 0.356944i \(0.116181\pi\)
−0.976892 + 0.213733i \(0.931438\pi\)
\(548\) −5.22738 13.3191i −0.223302 0.568965i
\(549\) −8.13169 13.3907i −0.347052 0.571500i
\(550\) 1.92914 4.91537i 0.0822588 0.209592i
\(551\) −4.94947 + 4.59244i −0.210854 + 0.195644i
\(552\) 16.1430 + 12.5838i 0.687093 + 0.535600i
\(553\) −27.4631 + 19.0296i −1.16785 + 0.809221i
\(554\) 1.78974 + 0.269759i 0.0760386 + 0.0114610i
\(555\) −20.5708 + 22.6684i −0.873182 + 0.962218i
\(556\) −2.03957 8.93596i −0.0864972 0.378969i
\(557\) 18.1941 + 31.5131i 0.770909 + 1.33525i 0.937066 + 0.349154i \(0.113531\pi\)
−0.166157 + 0.986099i \(0.553136\pi\)
\(558\) −18.7778 + 9.56079i −0.794926 + 0.404741i
\(559\) −5.62981 24.6658i −0.238116 1.04325i
\(560\) −3.61714 + 2.50637i −0.152852 + 0.105913i
\(561\) 16.9185 10.0193i 0.714298 0.423014i
\(562\) −1.66978 + 7.31580i −0.0704356 + 0.308598i
\(563\) −5.28089 13.4555i −0.222563 0.567081i 0.775359 0.631521i \(-0.217569\pi\)
−0.997922 + 0.0644401i \(0.979474\pi\)
\(564\) −0.614932 + 1.31394i −0.0258933 + 0.0553269i
\(565\) −17.0955 + 5.27326i −0.719212 + 0.221848i
\(566\) 4.01655 17.5976i 0.168828 0.739684i
\(567\) 7.53898 22.5868i 0.316607 0.948557i
\(568\) 1.41146 + 6.18400i 0.0592234 + 0.259475i
\(569\) −14.5970 25.2828i −0.611939 1.05991i −0.990913 0.134502i \(-0.957056\pi\)
0.378974 0.925407i \(-0.376277\pi\)
\(570\) −9.31377 + 2.23459i −0.390111 + 0.0935967i
\(571\) −4.06249 1.25311i −0.170010 0.0524412i 0.208582 0.978005i \(-0.433115\pi\)
−0.378592 + 0.925564i \(0.623592\pi\)
\(572\) 36.3196 + 17.4906i 1.51860 + 0.731318i
\(573\) 15.2405 1.31197i 0.636680 0.0548083i
\(574\) −11.2139 13.8458i −0.468058 0.577913i
\(575\) −4.13561 5.18589i −0.172467 0.216266i
\(576\) −5.14191 6.16269i −0.214246 0.256779i
\(577\) 7.40996 18.8803i 0.308481 0.785996i −0.689607 0.724184i \(-0.742217\pi\)
0.998088 0.0618122i \(-0.0196880\pi\)
\(578\) 7.75861 + 3.73635i 0.322716 + 0.155412i
\(579\) −4.96578 7.11294i −0.206371 0.295604i
\(580\) −3.86151 2.63274i −0.160341 0.109318i
\(581\) 3.36252 1.65072i 0.139501 0.0684834i
\(582\) −4.79127 1.03790i −0.198605 0.0430222i
\(583\) −46.5755 31.7547i −1.92896 1.31514i
\(584\) 18.1149 5.58771i 0.749601 0.231221i
\(585\) 33.1236 + 4.24474i 1.36949 + 0.175498i
\(586\) −8.12787 + 1.22508i −0.335759 + 0.0506075i
\(587\) −6.39302 + 11.0730i −0.263868 + 0.457033i −0.967266 0.253763i \(-0.918332\pi\)
0.703398 + 0.710796i \(0.251665\pi\)
\(588\) −17.1968 + 1.74256i −0.709183 + 0.0718620i
\(589\) −17.9639 31.1144i −0.740190 1.28205i
\(590\) 0.891146 + 1.11746i 0.0366879 + 0.0460052i
\(591\) 7.17679 5.85447i 0.295214 0.240821i
\(592\) 1.84631 8.08923i 0.0758831 0.332465i
\(593\) −0.577069 + 7.70045i −0.0236974 + 0.316220i 0.972741 + 0.231895i \(0.0744924\pi\)
−0.996438 + 0.0843250i \(0.973127\pi\)
\(594\) 13.2581 + 13.3695i 0.543987 + 0.548555i
\(595\) −11.3246 3.39967i −0.464263 0.139373i
\(596\) 2.04373 27.2716i 0.0837142 1.11709i
\(597\) −7.18752 + 0.618734i −0.294165 + 0.0253231i
\(598\) −16.8565 + 11.4925i −0.689312 + 0.469965i
\(599\) 27.0724 4.08050i 1.10615 0.166725i 0.429525 0.903055i \(-0.358681\pi\)
0.676622 + 0.736330i \(0.263443\pi\)
\(600\) 2.90833 + 5.87198i 0.118732 + 0.239723i
\(601\) −15.7852 + 2.37924i −0.643892 + 0.0970512i −0.462868 0.886427i \(-0.653180\pi\)
−0.181025 + 0.983479i \(0.557941\pi\)
\(602\) −8.17758 + 2.59028i −0.333293 + 0.105572i
\(603\) 16.4011 + 14.5556i 0.667904 + 0.592749i
\(604\) −9.17265 + 6.25381i −0.373230 + 0.254464i
\(605\) 4.96757 + 21.7643i 0.201960 + 0.884847i
\(606\) −5.15929 5.43835i −0.209582 0.220918i
\(607\) −8.99912 −0.365263 −0.182631 0.983181i \(-0.558462\pi\)
−0.182631 + 0.983181i \(0.558462\pi\)
\(608\) 16.6586 15.4569i 0.675595 0.626860i
\(609\) −3.59639 7.12530i −0.145733 0.288732i
\(610\) −5.46071 5.06680i −0.221098 0.205149i
\(611\) −2.54702 2.36329i −0.103041 0.0956083i
\(612\) −2.03985 + 9.94771i −0.0824560 + 0.402112i
\(613\) −27.6979 4.17479i −1.11871 0.168618i −0.436449 0.899729i \(-0.643764\pi\)
−0.682259 + 0.731111i \(0.739002\pi\)
\(614\) 10.3604 3.19575i 0.418111 0.128970i
\(615\) −24.9258 + 14.7613i −1.00510 + 0.595233i
\(616\) 11.7671 30.6614i 0.474111 1.23538i
\(617\) −14.7162 + 13.6547i −0.592453 + 0.549716i −0.918390 0.395675i \(-0.870511\pi\)
0.325938 + 0.945391i \(0.394320\pi\)
\(618\) −9.37979 9.88714i −0.377310 0.397719i
\(619\) 9.53272 0.383152 0.191576 0.981478i \(-0.438640\pi\)
0.191576 + 0.981478i \(0.438640\pi\)
\(620\) 18.2303 16.9152i 0.732146 0.679333i
\(621\) 22.8713 6.02597i 0.917794 0.241814i
\(622\) −2.74096 + 3.43706i −0.109903 + 0.137814i
\(623\) 5.15425 2.53031i 0.206501 0.101375i
\(624\) −8.38898 + 3.40011i −0.335828 + 0.136113i
\(625\) 3.46918 + 15.1995i 0.138767 + 0.607979i
\(626\) −1.63349 + 0.246209i −0.0652873 + 0.00984047i
\(627\) −21.5741 + 23.7739i −0.861585 + 0.949439i
\(628\) −10.7116 1.61452i −0.427441 0.0644264i
\(629\) 20.0858 9.67281i 0.800873 0.385680i
\(630\) 0.510436 11.3109i 0.0203363 0.450636i
\(631\) 9.83846 + 4.73795i 0.391663 + 0.188615i 0.619342 0.785121i \(-0.287399\pi\)
−0.227679 + 0.973736i \(0.573114\pi\)
\(632\) 27.0890 + 18.4690i 1.07754 + 0.734656i
\(633\) 6.09706 3.61074i 0.242337 0.143514i
\(634\) 0.684614 9.13554i 0.0271895 0.362819i
\(635\) 9.85220 + 12.3543i 0.390973 + 0.490264i
\(636\) 28.3090 6.79198i 1.12252 0.269319i
\(637\) 8.60093 40.4947i 0.340781 1.60446i
\(638\) 6.31120 0.249863
\(639\) 6.67256 + 3.03319i 0.263963 + 0.119991i
\(640\) 15.0799 + 10.2813i 0.596084 + 0.406403i
\(641\) −5.84289 + 25.5994i −0.230780 + 1.01111i 0.718214 + 0.695822i \(0.244960\pi\)
−0.948995 + 0.315292i \(0.897897\pi\)
\(642\) 15.5926 12.7197i 0.615393 0.502007i
\(643\) −3.70563 49.4482i −0.146136 1.95004i −0.282225 0.959348i \(-0.591073\pi\)
0.136089 0.990697i \(-0.456547\pi\)
\(644\) −10.8057 13.3418i −0.425803 0.525741i
\(645\) 2.23124 + 13.7671i 0.0878549 + 0.542081i
\(646\) 6.89775 + 1.03967i 0.271388 + 0.0409052i
\(647\) −1.36978 18.2785i −0.0538518 0.718602i −0.957151 0.289590i \(-0.906481\pi\)
0.903299 0.429012i \(-0.141138\pi\)
\(648\) −23.3428 + 1.03457i −0.916991 + 0.0406418i
\(649\) 4.57781 + 1.41207i 0.179695 + 0.0554285i
\(650\) −6.45842 + 0.973450i −0.253320 + 0.0381819i
\(651\) 41.2227 10.2203i 1.61565 0.400566i
\(652\) 32.3424 + 4.87483i 1.26663 + 0.190913i
\(653\) 1.56056 + 0.751526i 0.0610695 + 0.0294095i 0.464169 0.885747i \(-0.346353\pi\)
−0.403100 + 0.915156i \(0.632067\pi\)
\(654\) 14.2251 + 0.907751i 0.556246 + 0.0354959i
\(655\) 31.7983 1.24246
\(656\) 3.92611 6.80022i 0.153289 0.265504i
\(657\) 7.54954 20.5637i 0.294536 0.802266i
\(658\) −0.727516 + 0.926554i −0.0283615 + 0.0361208i
\(659\) −5.34688 4.96118i −0.208285 0.193260i 0.569131 0.822247i \(-0.307280\pi\)
−0.777416 + 0.628987i \(0.783470\pi\)
\(660\) −19.3666 10.8972i −0.753844 0.424172i
\(661\) 10.6210 + 27.0618i 0.413109 + 1.05258i 0.974371 + 0.224946i \(0.0722206\pi\)
−0.561262 + 0.827638i \(0.689684\pi\)
\(662\) −5.07244 12.9244i −0.197146 0.502320i
\(663\) −21.1960 11.9265i −0.823183 0.463188i
\(664\) −2.69447 2.50010i −0.104566 0.0970227i
\(665\) 19.3045 0.145879i 0.748597 0.00565696i
\(666\) 13.6766 + 16.3917i 0.529958 + 0.635166i
\(667\) 3.96394 6.86574i 0.153484 0.265842i
\(668\) 0.709789 0.0274625
\(669\) −20.4376 1.30419i −0.790163 0.0504229i
\(670\) 9.39434 + 4.52407i 0.362935 + 0.174780i
\(671\) −24.6894 3.72133i −0.953125 0.143660i
\(672\) 12.1045 + 23.9818i 0.466940 + 0.925120i
\(673\) 13.0392 1.96534i 0.502623 0.0757583i 0.107163 0.994241i \(-0.465823\pi\)
0.395460 + 0.918483i \(0.370585\pi\)
\(674\) 6.42679 + 1.98240i 0.247551 + 0.0763593i
\(675\) 7.43401 + 1.43881i 0.286135 + 0.0553799i
\(676\) −2.34121 31.2412i −0.0900464 1.20159i
\(677\) 1.99242 + 0.300309i 0.0765750 + 0.0115418i 0.187218 0.982318i \(-0.440053\pi\)
−0.110643 + 0.993860i \(0.535291\pi\)
\(678\) 1.99606 + 12.3161i 0.0766583 + 0.472996i
\(679\) 8.93462 + 4.21981i 0.342879 + 0.161942i
\(680\) 0.867047 + 11.5699i 0.0332497 + 0.443687i
\(681\) 30.5816 24.9470i 1.17189 0.955969i
\(682\) −7.47291 + 32.7410i −0.286153 + 1.25372i
\(683\) 16.3664 + 11.1584i 0.626244 + 0.426966i 0.834423 0.551125i \(-0.185801\pi\)
−0.208179 + 0.978091i \(0.566754\pi\)
\(684\) −1.60482 16.5019i −0.0613619 0.630966i
\(685\) −18.8908 −0.721780
\(686\) −13.9231 1.77681i −0.531585 0.0678388i
\(687\) −1.65148 + 0.396229i −0.0630080 + 0.0151171i
\(688\) −2.35703 2.95563i −0.0898610 0.112682i
\(689\) −5.21059 + 69.5305i −0.198508 + 2.64890i
\(690\) 9.67676 5.73067i 0.368388 0.218163i
\(691\) 6.83602 + 4.66072i 0.260054 + 0.177302i 0.686328 0.727292i \(-0.259221\pi\)
−0.426273 + 0.904594i \(0.640174\pi\)
\(692\) −8.54564 4.11536i −0.324856 0.156443i
\(693\) −19.9427 32.2877i −0.757561 1.22651i
\(694\) −23.1725 + 11.1593i −0.879616 + 0.423601i
\(695\) −11.9662 1.80361i −0.453903 0.0684149i
\(696\) −5.26319 + 5.79987i −0.199501 + 0.219843i
\(697\) 20.8621 3.14446i 0.790210 0.119105i
\(698\) 2.37134 + 10.3895i 0.0897565 + 0.393249i
\(699\) 27.4989 11.1455i 1.04010 0.421560i
\(700\) −1.26353 5.34925i −0.0477571 0.202183i
\(701\) 0.816964 1.02444i 0.0308563 0.0386926i −0.766164 0.642645i \(-0.777837\pi\)
0.797020 + 0.603953i \(0.206408\pi\)
\(702\) 6.12176 22.4705i 0.231051 0.848094i
\(703\) −26.6824 + 24.7577i −1.00635 + 0.933753i
\(704\) −12.7916 −0.482102
\(705\) 1.31824 + 1.38954i 0.0496476 + 0.0523331i
\(706\) −4.95009 + 4.59301i −0.186299 + 0.172860i
\(707\) 7.65318 + 13.0274i 0.287828 + 0.489944i
\(708\) −2.12881 + 1.26070i −0.0800057 + 0.0473802i
\(709\) 6.51457 2.00948i 0.244660 0.0754676i −0.170000 0.985444i \(-0.554377\pi\)
0.414660 + 0.909976i \(0.363901\pi\)
\(710\) 3.44628 + 0.519443i 0.129336 + 0.0194943i
\(711\) 35.9461 11.9659i 1.34808 0.448754i
\(712\) −4.13022 3.83229i −0.154787 0.143621i
\(713\) 30.9242 + 28.6935i 1.15812 + 1.07458i
\(714\) −3.43880 + 7.49477i −0.128694 + 0.280485i
\(715\) 39.0149 36.2005i 1.45907 1.35382i
\(716\) −2.16246 −0.0808149
\(717\) −28.2112 29.7372i −1.05357 1.11055i
\(718\) 0.530197 + 2.32294i 0.0197868 + 0.0866915i
\(719\) 29.1882 19.9002i 1.08854 0.742152i 0.120439 0.992721i \(-0.461570\pi\)
0.968099 + 0.250569i \(0.0806175\pi\)
\(720\) 4.73443 1.57601i 0.176442 0.0587344i
\(721\) 13.9138 + 23.6843i 0.518177 + 0.882048i
\(722\) 2.97666 0.448659i 0.110780 0.0166974i
\(723\) −5.58063 11.2674i −0.207546 0.419040i
\(724\) 25.5995 3.85850i 0.951396 0.143400i
\(725\) 2.09704 1.42974i 0.0778820 0.0530990i
\(726\) 15.5115 1.33530i 0.575687 0.0495577i
\(727\) −3.34961 + 44.6974i −0.124230 + 1.65774i 0.492315 + 0.870417i \(0.336151\pi\)
−0.616545 + 0.787319i \(0.711468\pi\)
\(728\) −40.1219 + 6.35784i −1.48702 + 0.235637i
\(729\) −15.3957 + 22.1805i −0.570209 + 0.821499i
\(730\) 0.778394 10.3869i 0.0288097 0.384438i
\(731\) 2.26022 9.90269i 0.0835974 0.366264i
\(732\) 9.99190 8.15090i 0.369311 0.301266i
\(733\) −32.2887 40.4887i −1.19261 1.49548i −0.824651 0.565641i \(-0.808629\pi\)
−0.367957 0.929843i \(-0.619943\pi\)
\(734\) 13.3038 + 23.0429i 0.491052 + 0.850528i
\(735\) −6.15326 + 21.9756i −0.226966 + 0.810581i
\(736\) −13.3415 + 23.1082i −0.491776 + 0.851780i
\(737\) 34.5583 5.20883i 1.27297 0.191870i
\(738\) 7.79561 + 18.6384i 0.286960 + 0.686087i
\(739\) 30.2114 9.31900i 1.11135 0.342805i 0.315878 0.948800i \(-0.397701\pi\)
0.795468 + 0.605995i \(0.207225\pi\)
\(740\) −20.8173 14.1930i −0.765259 0.521745i
\(741\) 38.8092 + 8.40695i 1.42569 + 0.308837i
\(742\) 23.6397 0.178640i 0.867842 0.00655807i
\(743\) 20.2418 + 13.8006i 0.742599 + 0.506295i 0.874535 0.484963i \(-0.161167\pi\)
−0.131936 + 0.991258i \(0.542119\pi\)
\(744\) −23.8563 34.1716i −0.874615 1.25279i
\(745\) −32.5313 15.6663i −1.19186 0.573967i
\(746\) −0.0833037 + 0.212254i −0.00304997 + 0.00777118i
\(747\) −4.18491 + 0.725891i −0.153118 + 0.0265590i
\(748\) 10.0906 + 12.6532i 0.368949 + 0.462648i
\(749\) −36.4076 + 17.8731i −1.33030 + 0.653070i
\(750\) 15.8954 1.36835i 0.580417 0.0499649i
\(751\) −8.36355 4.02767i −0.305190 0.146972i 0.275020 0.961438i \(-0.411315\pi\)
−0.580210 + 0.814467i \(0.697030\pi\)
\(752\) −0.496105 0.153028i −0.0180911 0.00558037i
\(753\) −31.3705 + 7.52652i −1.14321 + 0.274282i
\(754\) −3.90320 6.76055i −0.142146 0.246205i
\(755\) 3.26156 + 14.2898i 0.118700 + 0.520060i
\(756\) 19.2697 + 3.57869i 0.700831 + 0.130156i
\(757\) −2.34801 + 10.2873i −0.0853400 + 0.373899i −0.999506 0.0314420i \(-0.989990\pi\)
0.914166 + 0.405341i \(0.132847\pi\)
\(758\) 14.0933 4.34720i 0.511890 0.157897i
\(759\) 15.9783 34.1412i 0.579975 1.23925i
\(760\) −6.92081 17.6339i −0.251044 0.639650i
\(761\) −8.88739 + 38.9382i −0.322168 + 1.41151i 0.511519 + 0.859272i \(0.329083\pi\)
−0.833687 + 0.552237i \(0.813774\pi\)
\(762\) 9.48216 5.61543i 0.343502 0.203426i
\(763\) −27.5165 8.26052i −0.996164 0.299051i
\(764\) 2.80168 + 12.2750i 0.101361 + 0.444093i
\(765\) 11.2419 + 7.30529i 0.406452 + 0.264123i
\(766\) −1.22235 2.11718i −0.0441655 0.0764968i
\(767\) −1.31857 5.77705i −0.0476109 0.208597i
\(768\) 14.7818 16.2890i 0.533391 0.587780i
\(769\) 1.69145 + 0.254945i 0.0609952 + 0.00919355i 0.179469 0.983764i \(-0.442562\pi\)
−0.118474 + 0.992957i \(0.537800\pi\)
\(770\) −13.3204 12.1735i −0.480033 0.438702i
\(771\) −30.1056 23.4678i −1.08423 0.845172i
\(772\) 5.23410 4.85654i 0.188380 0.174791i
\(773\) 9.98422 25.4394i 0.359107 0.914991i −0.631140 0.775669i \(-0.717413\pi\)
0.990247 0.139322i \(-0.0444922\pi\)
\(774\) 9.72417 0.215386i 0.349528 0.00774188i
\(775\) 4.93408 + 12.5718i 0.177237 + 0.451593i
\(776\) 0.724576 9.66880i 0.0260108 0.347090i
\(777\) −19.3880 38.4123i −0.695541 1.37803i
\(778\) −0.194102 2.59011i −0.00695889 0.0928600i
\(779\) −31.0354 + 14.9459i −1.11196 + 0.535492i
\(780\) 0.304352 + 27.4849i 0.0108975 + 0.984117i
\(781\) 10.5248 5.06846i 0.376606 0.181364i
\(782\) −8.09916 + 1.22075i −0.289625 + 0.0436540i
\(783\) 1.64533 + 8.89932i 0.0587994 + 0.318036i
\(784\) −1.46744 6.00917i −0.0524086 0.214613i
\(785\) −7.15104 + 12.3860i −0.255232 + 0.442074i
\(786\) 3.06219 21.9638i 0.109225 0.783423i
\(787\) −2.02871 + 27.0712i −0.0723157 + 0.964986i 0.836548 + 0.547893i \(0.184570\pi\)
−0.908864 + 0.417092i \(0.863049\pi\)
\(788\) 5.58826 + 5.18515i 0.199074 + 0.184713i
\(789\) −42.6146 + 34.7629i −1.51712 + 1.23759i
\(790\) 14.8842 10.1478i 0.529554 0.361044i
\(791\) 1.68972 25.0907i 0.0600797 0.892121i
\(792\) −22.5678 + 29.6218i −0.801913 + 1.05256i
\(793\) 11.2831 + 28.7487i 0.400673 + 1.02090i
\(794\) −14.7825 7.11888i −0.524612 0.252640i
\(795\) 5.30745 38.0681i 0.188236 1.35014i
\(796\) −1.32129 5.78896i −0.0468320 0.205184i
\(797\) −18.9697 + 48.3340i −0.671941 + 1.71208i 0.0297125 + 0.999558i \(0.490541\pi\)
−0.701653 + 0.712519i \(0.747554\pi\)
\(798\) 1.75827 13.3481i 0.0622421 0.472519i
\(799\) −0.509628 1.29851i −0.0180293 0.0459380i
\(800\) −7.05806 + 4.81210i −0.249540 + 0.170134i
\(801\) −6.41486 + 1.11268i −0.226658 + 0.0393148i
\(802\) 0.853782 + 1.47879i 0.0301481 + 0.0522180i
\(803\) −17.4562 30.2350i −0.616015 1.06697i
\(804\) −10.0017 + 15.0245i −0.352732 + 0.529875i
\(805\) −21.6094 + 6.84485i −0.761630 + 0.241249i
\(806\) 39.6937 12.2439i 1.39815 0.431273i
\(807\) 30.6265 18.1373i 1.07810 0.638463i
\(808\) 9.24387 11.5914i 0.325198 0.407786i
\(809\) −43.9364 6.62234i −1.54472 0.232829i −0.679294 0.733866i \(-0.737714\pi\)
−0.865426 + 0.501037i \(0.832952\pi\)
\(810\) −4.15663 + 12.1469i −0.146049 + 0.426797i
\(811\) −0.959828 + 4.20528i −0.0337041 + 0.147667i −0.988980 0.148048i \(-0.952701\pi\)
0.955276 + 0.295716i \(0.0955581\pi\)
\(812\) 5.39982 3.74162i 0.189496 0.131305i
\(813\) 45.0500 + 2.87479i 1.57997 + 0.100823i
\(814\) 34.0235 1.19252
\(815\) 21.5916 37.3978i 0.756321 1.30999i
\(816\) −3.62670 0.231432i −0.126960 0.00810173i
\(817\) 1.23933 + 16.5377i 0.0433587 + 0.578582i
\(818\) −5.35614 + 6.71639i −0.187273 + 0.234833i
\(819\) −22.2528 + 41.3312i −0.777577 + 1.44423i
\(820\) −14.8664 18.6419i −0.519157 0.651002i
\(821\) 7.37612 6.84404i 0.257428 0.238859i −0.540891 0.841092i \(-0.681913\pi\)
0.798320 + 0.602234i \(0.205722\pi\)
\(822\) −1.81919 + 13.0483i −0.0634517 + 0.455113i
\(823\) −0.991741 + 0.676158i −0.0345699 + 0.0235694i −0.580482 0.814273i \(-0.697136\pi\)
0.545912 + 0.837843i \(0.316183\pi\)
\(824\) 16.8057 21.0737i 0.585455 0.734137i
\(825\) 9.35113 7.62819i 0.325565 0.265580i
\(826\) −1.91529 + 0.606676i −0.0666415 + 0.0211090i
\(827\) 6.22448 + 2.99755i 0.216446 + 0.104235i 0.538965 0.842328i \(-0.318815\pi\)
−0.322519 + 0.946563i \(0.604530\pi\)
\(828\) 7.51184 + 17.9599i 0.261054 + 0.624149i
\(829\) −52.2938 + 16.1305i −1.81624 + 0.560235i −0.999851 0.0172704i \(-0.994502\pi\)
−0.816387 + 0.577506i \(0.804026\pi\)
\(830\) −1.81961 + 0.876280i −0.0631597 + 0.0304161i
\(831\) 3.26239 + 2.54309i 0.113171 + 0.0882188i
\(832\) 7.91105 + 13.7023i 0.274266 + 0.475043i
\(833\) 10.1650 13.1493i 0.352196 0.455598i
\(834\) −2.39815 + 8.09164i −0.0830410 + 0.280191i
\(835\) 0.342367 0.872338i 0.0118481 0.0301885i
\(836\) −21.8326 14.8852i −0.755096 0.514815i
\(837\) −48.1157 2.00185i −1.66312 0.0691941i
\(838\) 0.586932 7.83206i 0.0202752 0.270554i
\(839\) 37.2381 25.3885i 1.28560 0.876509i 0.288877 0.957366i \(-0.406718\pi\)
0.996726 + 0.0808569i \(0.0257657\pi\)
\(840\) 22.2956 2.08915i 0.769272 0.0720825i
\(841\) −21.4545 14.6274i −0.739811 0.504394i
\(842\) −10.2438 + 12.8453i −0.353024 + 0.442678i
\(843\) −11.5248 + 12.6999i −0.396934 + 0.437409i
\(844\) 3.63645 + 4.55996i 0.125172 + 0.156960i
\(845\) −39.5251 12.1919i −1.35970 0.419413i
\(846\) 1.08673 0.776723i 0.0373627 0.0267043i
\(847\) −31.0638 4.44231i −1.06736 0.152640i
\(848\) 3.80630 + 9.69829i 0.130709 + 0.333041i
\(849\) 27.7220 30.5488i 0.951418 1.04843i
\(850\) −2.50568 0.772900i −0.0859441 0.0265102i
\(851\) 21.3694 37.0130i 0.732535 1.26879i
\(852\) −1.71429 + 5.78423i −0.0587307 + 0.198165i
\(853\) 50.6278 + 15.6166i 1.73346 + 0.534702i 0.990844 0.135013i \(-0.0431076\pi\)
0.742618 + 0.669715i \(0.233584\pi\)
\(854\) 9.39952 4.61439i 0.321645 0.157901i
\(855\) −21.0551 5.98738i −0.720070 0.204764i
\(856\) 29.1743 + 27.0698i 0.997156 + 0.925225i
\(857\) 8.16100 10.2336i 0.278775 0.349572i −0.622656 0.782496i \(-0.713946\pi\)
0.901431 + 0.432923i \(0.142518\pi\)
\(858\) −21.2474 30.4347i −0.725375 1.03902i
\(859\) −11.6179 + 50.9014i −0.396398 + 1.73673i 0.245000 + 0.969523i \(0.421212\pi\)
−0.641397 + 0.767209i \(0.721645\pi\)
\(860\) −10.9694 + 3.38362i −0.374054 + 0.115380i
\(861\) −6.81802 40.1451i −0.232358 1.36814i
\(862\) −9.31228 2.87246i −0.317178 0.0978363i
\(863\) −12.5278 + 21.6987i −0.426450 + 0.738634i −0.996555 0.0829388i \(-0.973569\pi\)
0.570104 + 0.821572i \(0.306903\pi\)
\(864\) −5.53775 29.9527i −0.188398 1.01901i
\(865\) −9.17983 + 8.51764i −0.312124 + 0.289608i
\(866\) 0.730705 + 9.75059i 0.0248304 + 0.331338i
\(867\) 11.2659 + 16.1371i 0.382609 + 0.548046i
\(868\) 13.0168 + 32.4433i 0.441820 + 1.10120i
\(869\) 22.0593 56.2062i 0.748310 1.90666i
\(870\) 1.90995 + 3.85623i 0.0647534 + 0.130738i
\(871\) −26.9525 33.7974i −0.913251 1.14518i
\(872\) 2.10675 + 28.1127i 0.0713436 + 0.952015i
\(873\) −8.37986 7.43692i −0.283615 0.251702i
\(874\) 12.0487 5.80234i 0.407552 0.196267i
\(875\) −31.8325 4.55224i −1.07613 0.153894i
\(876\) 17.6216 + 3.81724i 0.595379 + 0.128973i
\(877\) −4.54980 + 2.19107i −0.153636 + 0.0739871i −0.509122 0.860695i \(-0.670030\pi\)
0.355486 + 0.934682i \(0.384315\pi\)
\(878\) 0.0427560 + 0.0396717i 0.00144294 + 0.00133886i
\(879\) −17.5617 6.66901i −0.592342 0.224940i
\(880\) 2.90541 7.40286i 0.0979413 0.249550i
\(881\) −34.0081 −1.14576 −0.572880 0.819639i \(-0.694174\pi\)
−0.572880 + 0.819639i \(0.694174\pi\)
\(882\) 14.5865 + 6.36646i 0.491152 + 0.214370i
\(883\) −27.5643 −0.927614 −0.463807 0.885936i \(-0.653517\pi\)
−0.463807 + 0.885936i \(0.653517\pi\)
\(884\) 7.31351 18.6345i 0.245980 0.626747i
\(885\) 0.522584 + 3.22444i 0.0175665 + 0.108388i
\(886\) −19.9944 18.5521i −0.671724 0.623269i
\(887\) −53.0922 + 25.5678i −1.78266 + 0.858484i −0.828035 + 0.560676i \(0.810541\pi\)
−0.954626 + 0.297808i \(0.903744\pi\)
\(888\) −28.3737 + 31.2669i −0.952158 + 1.04925i
\(889\) −21.1748 + 6.70720i −0.710180 + 0.224952i
\(890\) −2.78920 + 1.34321i −0.0934943 + 0.0450245i
\(891\) 11.4235 + 41.4873i 0.382703 + 1.38988i
\(892\) −1.25966 16.8090i −0.0421766 0.562808i
\(893\) 1.42002 + 1.78065i 0.0475193 + 0.0595873i
\(894\) −13.9538 + 20.9615i −0.466686 + 0.701057i
\(895\) −1.04307 + 2.65769i −0.0348658 + 0.0888367i
\(896\) −21.0872 + 14.6116i −0.704474 + 0.488140i
\(897\) −46.4539 + 3.99896i −1.55105 + 0.133521i
\(898\) 1.90656 + 25.4413i 0.0636227 + 0.848986i
\(899\) −11.8328 + 10.9793i −0.394647 + 0.366179i
\(900\) −0.328008 + 6.22375i −0.0109336 + 0.207458i
\(901\) −13.9965 + 24.2426i −0.466290 + 0.807639i
\(902\) 30.7681 + 9.49069i 1.02446 + 0.316005i
\(903\) −19.1907 4.00557i −0.638627 0.133297i
\(904\) −23.5801 + 7.27350i −0.784263 + 0.241913i
\(905\) 7.60580 33.3232i 0.252825 1.10770i
\(906\) 10.1844 0.876720i 0.338355 0.0291271i
\(907\) −15.0494 + 18.8714i −0.499707 + 0.626613i −0.966163 0.257931i \(-0.916959\pi\)
0.466456 + 0.884544i \(0.345531\pi\)
\(908\) 23.8126 + 22.0949i 0.790249 + 0.733244i
\(909\) −4.18117 16.6140i −0.138681 0.551052i
\(910\) −4.80214 + 21.7975i −0.159189 + 0.722580i
\(911\) −20.0636 6.18882i −0.664738 0.205045i −0.0560183 0.998430i \(-0.517841\pi\)
−0.608720 + 0.793385i \(0.708317\pi\)
\(912\) 5.76969 1.38428i 0.191053 0.0458382i
\(913\) −3.38465 + 5.86239i −0.112016 + 0.194017i
\(914\) 1.08448 + 0.334517i 0.0358713 + 0.0110648i
\(915\) −5.19794 16.2118i −0.171839 0.535944i
\(916\) −0.510707 1.30126i −0.0168742 0.0429948i
\(917\) −16.0149 + 41.7297i −0.528857 + 1.37804i
\(918\) 6.12854 7.06156i 0.202272 0.233066i
\(919\) −49.7011 15.3308i −1.63949 0.505716i −0.668273 0.743916i \(-0.732966\pi\)
−0.971216 + 0.238200i \(0.923443\pi\)
\(920\) 13.8682 + 17.3902i 0.457222 + 0.573338i
\(921\) 24.2169 + 5.24592i 0.797974 + 0.172859i
\(922\) 0.889894 1.11589i 0.0293071 0.0367499i
\(923\) −11.9384 8.13949i −0.392958 0.267914i
\(924\) 24.0544 19.9270i 0.791333 0.655551i
\(925\) 11.3051 7.70765i 0.371708 0.253426i
\(926\) −0.671128 + 8.95558i −0.0220546 + 0.294299i
\(927\) −7.60153 30.2049i −0.249667 0.992059i
\(928\) −8.43591 5.75151i −0.276922 0.188802i
\(929\) −2.20661 + 5.62234i −0.0723964 + 0.184463i −0.962492 0.271312i \(-0.912543\pi\)
0.890095 + 0.455775i \(0.150638\pi\)
\(930\) −22.2667 + 5.34230i −0.730154 + 0.175181i
\(931\) −9.53107 + 25.4073i −0.312368 + 0.832690i
\(932\) 12.2112 + 21.1504i 0.399992 + 0.692806i
\(933\) −9.31132 + 3.77393i −0.304839 + 0.123553i
\(934\) −12.6301 + 6.08232i −0.413268 + 0.199020i
\(935\) 20.4182 6.29817i 0.667746 0.205972i
\(936\) 45.6880 + 5.85484i 1.49336 + 0.191372i
\(937\) 25.2791 + 12.1738i 0.825832 + 0.397700i 0.798550 0.601928i \(-0.205601\pi\)
0.0272818 + 0.999628i \(0.491315\pi\)
\(938\) −10.6684 + 10.0499i −0.348336 + 0.328142i
\(939\) −3.52944 1.34030i −0.115179 0.0437389i
\(940\) −0.982932 + 1.23256i −0.0320597 + 0.0402016i
\(941\) −16.1185 + 10.9894i −0.525450 + 0.358245i −0.796808 0.604233i \(-0.793480\pi\)
0.271358 + 0.962478i \(0.412527\pi\)
\(942\) 7.86663 + 6.13217i 0.256309 + 0.199797i
\(943\) 29.6494 27.5106i 0.965517 0.895869i
\(944\) −0.552047 0.692244i −0.0179676 0.0225306i
\(945\) 13.6930 21.9565i 0.445433 0.714244i
\(946\) 9.66517 12.1197i 0.314242 0.394047i
\(947\) 1.68767 + 22.5204i 0.0548419 + 0.731814i 0.955067 + 0.296390i \(0.0957827\pi\)
−0.900225 + 0.435425i \(0.856598\pi\)
\(948\) 13.8401 + 27.9434i 0.449504 + 0.907559i
\(949\) −21.5917 + 37.3980i −0.700898 + 1.21399i
\(950\) 4.28128 0.138903
\(951\) 11.6020 17.4285i 0.376220 0.565158i
\(952\) −15.6202 4.68923i −0.506254 0.151979i
\(953\) −11.3695 + 49.8132i −0.368296 + 1.61361i 0.363165 + 0.931725i \(0.381696\pi\)
−0.731461 + 0.681884i \(0.761161\pi\)
\(954\) −25.7835 7.33196i −0.834771 0.237381i
\(955\) 16.4375 + 2.47755i 0.531904 + 0.0801717i
\(956\) 21.0355 26.3776i 0.680336 0.853114i
\(957\) 12.5704 + 7.07309i 0.406343 + 0.228641i
\(958\) 11.9881 3.69783i 0.387317 0.119472i
\(959\) 9.51415 24.7909i 0.307228 0.800540i
\(960\) −3.87110 7.81584i −0.124939 0.252255i
\(961\) −27.4468 47.5393i −0.885382 1.53353i
\(962\) −21.0420 36.4459i −0.678423 1.17506i
\(963\) 45.3120 7.85956i 1.46016 0.253271i
\(964\) 8.55097 5.82995i 0.275408 0.187770i
\(965\) −3.44406 8.77533i −0.110868 0.282488i
\(966\) 2.64691 + 15.5853i 0.0851630 + 0.501447i
\(967\) −11.3135 + 28.8262i −0.363816 + 0.926989i 0.625370 + 0.780328i \(0.284948\pi\)
−0.989187 + 0.146661i \(0.953147\pi\)
\(968\) 6.85186 + 30.0200i 0.220227 + 0.964879i
\(969\) 12.5735 + 9.80122i 0.403918 + 0.314860i
\(970\) −4.79987 2.31150i −0.154115 0.0742177i
\(971\) 7.37721 + 18.7968i 0.236746 + 0.603219i 0.999031 0.0440230i \(-0.0140175\pi\)
−0.762284 + 0.647242i \(0.775922\pi\)
\(972\) −19.8314 10.0297i −0.636092 0.321701i
\(973\) 8.39357 14.7952i 0.269085 0.474311i
\(974\) 2.63478 1.79636i 0.0844237 0.0575591i
\(975\) −13.9546 5.29921i −0.446904 0.169711i
\(976\) 3.38280 + 3.13878i 0.108281 + 0.100470i
\(977\) 2.03629 27.1724i 0.0651468 0.869323i −0.864915 0.501919i \(-0.832628\pi\)
0.930061 0.367404i \(-0.119753\pi\)
\(978\) −23.7523 18.5153i −0.759513 0.592053i
\(979\) −5.18818 + 8.98619i −0.165815 + 0.287200i
\(980\) −18.6139 2.51852i −0.594599 0.0804511i
\(981\) 27.3156 + 17.7504i 0.872121 + 0.566727i
\(982\) 19.9877 3.01266i 0.637832 0.0961377i
\(983\) −20.4192 + 9.83335i −0.651270 + 0.313635i −0.730188 0.683246i \(-0.760568\pi\)
0.0789184 + 0.996881i \(0.474853\pi\)
\(984\) −34.3806 + 20.3605i −1.09601 + 0.649070i
\(985\) 9.06811 4.36697i 0.288934 0.139143i
\(986\) −0.234209 3.12531i −0.00745874 0.0995300i
\(987\) −2.48744 + 1.03013i −0.0791762 + 0.0327893i
\(988\) −2.44250 + 32.5929i −0.0777062 + 1.03692i
\(989\) −7.11415 18.1266i −0.226217 0.576391i
\(990\) 10.6205 + 17.4890i 0.337541 + 0.555838i
\(991\) 10.9332 27.8573i 0.347304 0.884916i −0.645346 0.763891i \(-0.723287\pi\)
0.992649 0.121025i \(-0.0386182\pi\)
\(992\) 39.8261 36.9533i 1.26448 1.17327i
\(993\) 4.38154 31.4270i 0.139044 0.997305i
\(994\) −2.41736 + 4.26103i −0.0766740 + 0.135152i
\(995\) −7.75203 1.16843i −0.245756 0.0370417i
\(996\) −1.06739 3.32905i −0.0338214 0.105485i
\(997\) 8.56194 + 37.5123i 0.271160 + 1.18803i 0.908646 + 0.417566i \(0.137117\pi\)
−0.637487 + 0.770461i \(0.720026\pi\)
\(998\) 0.810245 + 1.40339i 0.0256479 + 0.0444234i
\(999\) 8.86993 + 47.9760i 0.280632 + 1.51789i
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 441.2.z.a.142.34 yes 648
9.4 even 3 441.2.y.a.436.34 yes 648
49.39 even 21 441.2.y.a.88.34 648
441.382 even 21 inner 441.2.z.a.382.34 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.y.a.88.34 648 49.39 even 21
441.2.y.a.436.34 yes 648 9.4 even 3
441.2.z.a.142.34 yes 648 1.1 even 1 trivial
441.2.z.a.382.34 yes 648 441.382 even 21 inner