Properties

Label 380.2.bj.a.347.41
Level $380$
Weight $2$
Character 380.347
Analytic conductor $3.034$
Analytic rank $0$
Dimension $672$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(23,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 27, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.bj (of order \(36\), 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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(672\)
Relative dimension: \(56\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 347.41
Character \(\chi\) \(=\) 380.347
Dual form 380.2.bj.a.23.41

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.896489 - 1.09376i) q^{2} +(1.49450 - 1.04646i) q^{3} +(-0.392614 - 1.96108i) q^{4} +(2.23475 - 0.0767528i) q^{5} +(0.195229 - 2.57276i) q^{6} +(-3.56968 - 0.956492i) q^{7} +(-2.49693 - 1.32867i) q^{8} +(0.112392 - 0.308794i) q^{9} +O(q^{10})\) \(q+(0.896489 - 1.09376i) q^{2} +(1.49450 - 1.04646i) q^{3} +(-0.392614 - 1.96108i) q^{4} +(2.23475 - 0.0767528i) q^{5} +(0.195229 - 2.57276i) q^{6} +(-3.56968 - 0.956492i) q^{7} +(-2.49693 - 1.32867i) q^{8} +(0.112392 - 0.308794i) q^{9} +(1.91948 - 2.51308i) q^{10} +(-1.25503 - 0.724594i) q^{11} +(-2.63896 - 2.51999i) q^{12} +(1.43625 + 1.00567i) q^{13} +(-4.24635 + 3.04688i) q^{14} +(3.25952 - 2.45329i) q^{15} +(-3.69171 + 1.53990i) q^{16} +(2.70456 + 1.26116i) q^{17} +(-0.236988 - 0.399761i) q^{18} +(4.14223 + 1.35717i) q^{19} +(-1.02791 - 4.35240i) q^{20} +(-6.33582 + 2.30605i) q^{21} +(-1.91765 + 0.723113i) q^{22} +(2.89729 + 0.253480i) q^{23} +(-5.12206 + 0.627243i) q^{24} +(4.98822 - 0.343047i) q^{25} +(2.38755 - 0.669336i) q^{26} +(1.26143 + 4.70774i) q^{27} +(-0.474256 + 7.37598i) q^{28} +(-0.843569 + 2.31769i) q^{29} +(0.238821 - 5.76447i) q^{30} +(3.46816 - 2.00234i) q^{31} +(-1.62530 + 5.41834i) q^{32} +(-2.63391 + 0.230437i) q^{33} +(3.80402 - 1.82752i) q^{34} +(-8.05075 - 1.86354i) q^{35} +(-0.649699 - 0.0991731i) q^{36} +(-2.69446 - 2.69446i) q^{37} +(5.19788 - 3.31391i) q^{38} +3.19888 q^{39} +(-5.68199 - 2.77759i) q^{40} +(-1.47047 + 8.33946i) q^{41} +(-3.15773 + 8.99720i) q^{42} +(-0.813252 - 9.29551i) q^{43} +(-0.928246 + 2.74571i) q^{44} +(0.227467 - 0.698705i) q^{45} +(2.87464 - 2.94169i) q^{46} +(-7.48285 + 3.48931i) q^{47} +(-3.90582 + 6.16461i) q^{48} +(5.76555 + 3.32874i) q^{49} +(4.09667 - 5.76344i) q^{50} +(5.36173 - 0.945417i) q^{51} +(1.40832 - 3.21145i) q^{52} +(1.17104 - 13.3850i) q^{53} +(6.27999 + 2.84073i) q^{54} +(-2.86030 - 1.52296i) q^{55} +(7.64237 + 7.13120i) q^{56} +(7.61079 - 2.30639i) q^{57} +(1.77874 + 3.00044i) q^{58} +(-8.54159 + 3.10888i) q^{59} +(-6.09083 - 5.42900i) q^{60} +(-7.83784 + 6.57673i) q^{61} +(0.919087 - 5.58840i) q^{62} +(-0.696563 + 0.994795i) q^{63} +(4.46929 + 6.63517i) q^{64} +(3.28685 + 2.13719i) q^{65} +(-2.10923 + 3.08744i) q^{66} +(-2.66437 + 1.24242i) q^{67} +(1.41139 - 5.79903i) q^{68} +(4.59526 - 2.65307i) q^{69} +(-9.25567 + 7.13494i) q^{70} +(1.72712 - 2.05830i) q^{71} +(-0.690919 + 0.621706i) q^{72} +(4.43946 + 6.34020i) q^{73} +(-5.36265 + 0.531535i) q^{74} +(7.09591 - 5.73266i) q^{75} +(1.03523 - 8.65611i) q^{76} +(3.78700 + 3.78700i) q^{77} +(2.86776 - 3.49880i) q^{78} +(-1.28046 + 7.26184i) q^{79} +(-8.13185 + 3.72464i) q^{80} +(7.56687 + 6.34936i) q^{81} +(7.80309 + 9.08457i) q^{82} +(-1.51489 + 5.65367i) q^{83} +(7.00989 + 11.5197i) q^{84} +(6.14082 + 2.61079i) q^{85} +(-10.8961 - 7.44382i) q^{86} +(1.16465 + 4.34655i) q^{87} +(2.17098 + 3.47678i) q^{88} +(2.65698 - 0.468497i) q^{89} +(-0.560292 - 0.875175i) q^{90} +(-4.16504 - 4.96370i) q^{91} +(-0.640421 - 5.78135i) q^{92} +(3.08779 - 6.62179i) q^{93} +(-2.89183 + 11.3126i) q^{94} +(9.36102 + 2.71501i) q^{95} +(3.24107 + 9.79852i) q^{96} +(-7.86923 - 3.66948i) q^{97} +(8.80959 - 3.32194i) q^{98} +(-0.364806 + 0.306109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.896489 1.09376i 0.633914 0.773404i
\(3\) 1.49450 1.04646i 0.862850 0.604174i −0.0561538 0.998422i \(-0.517884\pi\)
0.919004 + 0.394248i \(0.128995\pi\)
\(4\) −0.392614 1.96108i −0.196307 0.980542i
\(5\) 2.23475 0.0767528i 0.999411 0.0343249i
\(6\) 0.195229 2.57276i 0.0797018 1.05033i
\(7\) −3.56968 0.956492i −1.34921 0.361520i −0.489368 0.872077i \(-0.662772\pi\)
−0.859844 + 0.510557i \(0.829439\pi\)
\(8\) −2.49693 1.32867i −0.882797 0.469754i
\(9\) 0.112392 0.308794i 0.0374640 0.102931i
\(10\) 1.91948 2.51308i 0.606993 0.794707i
\(11\) −1.25503 0.724594i −0.378407 0.218473i 0.298718 0.954341i \(-0.403441\pi\)
−0.677125 + 0.735868i \(0.736774\pi\)
\(12\) −2.63896 2.51999i −0.761802 0.727458i
\(13\) 1.43625 + 1.00567i 0.398344 + 0.278924i 0.755536 0.655107i \(-0.227377\pi\)
−0.357191 + 0.934031i \(0.616266\pi\)
\(14\) −4.24635 + 3.04688i −1.13488 + 0.814313i
\(15\) 3.25952 2.45329i 0.841604 0.633436i
\(16\) −3.69171 + 1.53990i −0.922927 + 0.384975i
\(17\) 2.70456 + 1.26116i 0.655953 + 0.305876i 0.721951 0.691944i \(-0.243245\pi\)
−0.0659982 + 0.997820i \(0.521023\pi\)
\(18\) −0.236988 0.399761i −0.0558587 0.0942245i
\(19\) 4.14223 + 1.35717i 0.950293 + 0.311356i
\(20\) −1.02791 4.35240i −0.229848 0.973226i
\(21\) −6.33582 + 2.30605i −1.38259 + 0.503221i
\(22\) −1.91765 + 0.723113i −0.408845 + 0.154168i
\(23\) 2.89729 + 0.253480i 0.604127 + 0.0528542i 0.385116 0.922868i \(-0.374161\pi\)
0.219011 + 0.975722i \(0.429717\pi\)
\(24\) −5.12206 + 0.627243i −1.04554 + 0.128036i
\(25\) 4.98822 0.343047i 0.997644 0.0686093i
\(26\) 2.38755 0.669336i 0.468237 0.131268i
\(27\) 1.26143 + 4.70774i 0.242763 + 0.906005i
\(28\) −0.474256 + 7.37598i −0.0896260 + 1.39393i
\(29\) −0.843569 + 2.31769i −0.156647 + 0.430384i −0.993045 0.117739i \(-0.962435\pi\)
0.836398 + 0.548123i \(0.184657\pi\)
\(30\) 0.238821 5.76447i 0.0436025 1.05244i
\(31\) 3.46816 2.00234i 0.622899 0.359631i −0.155098 0.987899i \(-0.549569\pi\)
0.777997 + 0.628268i \(0.216236\pi\)
\(32\) −1.62530 + 5.41834i −0.287315 + 0.957836i
\(33\) −2.63391 + 0.230437i −0.458505 + 0.0401139i
\(34\) 3.80402 1.82752i 0.652383 0.313418i
\(35\) −8.05075 1.86354i −1.36083 0.314996i
\(36\) −0.649699 0.0991731i −0.108283 0.0165289i
\(37\) −2.69446 2.69446i −0.442967 0.442967i 0.450041 0.893008i \(-0.351409\pi\)
−0.893008 + 0.450041i \(0.851409\pi\)
\(38\) 5.19788 3.31391i 0.843208 0.537588i
\(39\) 3.19888 0.512230
\(40\) −5.68199 2.77759i −0.898401 0.439176i
\(41\) −1.47047 + 8.33946i −0.229649 + 1.30240i 0.623946 + 0.781467i \(0.285529\pi\)
−0.853595 + 0.520937i \(0.825583\pi\)
\(42\) −3.15773 + 8.99720i −0.487249 + 1.38830i
\(43\) −0.813252 9.29551i −0.124020 1.41755i −0.762039 0.647531i \(-0.775801\pi\)
0.638019 0.770021i \(-0.279754\pi\)
\(44\) −0.928246 + 2.74571i −0.139938 + 0.413932i
\(45\) 0.227467 0.698705i 0.0339088 0.104157i
\(46\) 2.87464 2.94169i 0.423842 0.433729i
\(47\) −7.48285 + 3.48931i −1.09149 + 0.508968i −0.883151 0.469089i \(-0.844582\pi\)
−0.208335 + 0.978058i \(0.566804\pi\)
\(48\) −3.90582 + 6.16461i −0.563756 + 0.889785i
\(49\) 5.76555 + 3.32874i 0.823650 + 0.475534i
\(50\) 4.09667 5.76344i 0.579357 0.815074i
\(51\) 5.36173 0.945417i 0.750792 0.132385i
\(52\) 1.40832 3.21145i 0.195299 0.445348i
\(53\) 1.17104 13.3850i 0.160854 1.83857i −0.303388 0.952867i \(-0.598118\pi\)
0.464243 0.885708i \(-0.346326\pi\)
\(54\) 6.27999 + 2.84073i 0.854598 + 0.386575i
\(55\) −2.86030 1.52296i −0.385683 0.205356i
\(56\) 7.64237 + 7.13120i 1.02125 + 0.952947i
\(57\) 7.61079 2.30639i 1.00807 0.305489i
\(58\) 1.77874 + 3.00044i 0.233560 + 0.393977i
\(59\) −8.54159 + 3.10888i −1.11202 + 0.404742i −0.831734 0.555174i \(-0.812652\pi\)
−0.280286 + 0.959917i \(0.590429\pi\)
\(60\) −6.09083 5.42900i −0.786323 0.700880i
\(61\) −7.83784 + 6.57673i −1.00353 + 0.842064i −0.987470 0.157807i \(-0.949557\pi\)
−0.0160624 + 0.999871i \(0.505113\pi\)
\(62\) 0.919087 5.58840i 0.116724 0.709728i
\(63\) −0.696563 + 0.994795i −0.0877587 + 0.125332i
\(64\) 4.46929 + 6.63517i 0.558661 + 0.829396i
\(65\) 3.28685 + 2.13719i 0.407684 + 0.265086i
\(66\) −2.10923 + 3.08744i −0.259628 + 0.380038i
\(67\) −2.66437 + 1.24242i −0.325504 + 0.151785i −0.578500 0.815682i \(-0.696362\pi\)
0.252996 + 0.967467i \(0.418584\pi\)
\(68\) 1.41139 5.79903i 0.171156 0.703236i
\(69\) 4.59526 2.65307i 0.553204 0.319393i
\(70\) −9.25567 + 7.13494i −1.10626 + 0.852788i
\(71\) 1.72712 2.05830i 0.204971 0.244275i −0.653760 0.756702i \(-0.726809\pi\)
0.858731 + 0.512427i \(0.171254\pi\)
\(72\) −0.690919 + 0.621706i −0.0814256 + 0.0732687i
\(73\) 4.43946 + 6.34020i 0.519599 + 0.742064i 0.990104 0.140333i \(-0.0448173\pi\)
−0.470505 + 0.882397i \(0.655928\pi\)
\(74\) −5.36265 + 0.531535i −0.623396 + 0.0617896i
\(75\) 7.09591 5.73266i 0.819365 0.661950i
\(76\) 1.03523 8.65611i 0.118749 0.992924i
\(77\) 3.78700 + 3.78700i 0.431568 + 0.431568i
\(78\) 2.86776 3.49880i 0.324710 0.396161i
\(79\) −1.28046 + 7.26184i −0.144063 + 0.817021i 0.824052 + 0.566514i \(0.191708\pi\)
−0.968115 + 0.250507i \(0.919403\pi\)
\(80\) −8.13185 + 3.72464i −0.909169 + 0.416427i
\(81\) 7.56687 + 6.34936i 0.840764 + 0.705484i
\(82\) 7.80309 + 9.08457i 0.861707 + 1.00322i
\(83\) −1.51489 + 5.65367i −0.166281 + 0.620570i 0.831592 + 0.555387i \(0.187430\pi\)
−0.997873 + 0.0651833i \(0.979237\pi\)
\(84\) 7.00989 + 11.5197i 0.764842 + 1.25690i
\(85\) 6.14082 + 2.61079i 0.666066 + 0.283180i
\(86\) −10.8961 7.44382i −1.17496 0.802688i
\(87\) 1.16465 + 4.34655i 0.124864 + 0.465999i
\(88\) 2.17098 + 3.47678i 0.231428 + 0.370626i
\(89\) 2.65698 0.468497i 0.281639 0.0496606i −0.0310442 0.999518i \(-0.509883\pi\)
0.312683 + 0.949857i \(0.398772\pi\)
\(90\) −0.560292 0.875175i −0.0590600 0.0922516i
\(91\) −4.16504 4.96370i −0.436614 0.520337i
\(92\) −0.640421 5.78135i −0.0667686 0.602748i
\(93\) 3.08779 6.62179i 0.320189 0.686647i
\(94\) −2.89183 + 11.3126i −0.298270 + 1.16680i
\(95\) 9.36102 + 2.71501i 0.960421 + 0.278554i
\(96\) 3.24107 + 9.79852i 0.330790 + 1.00006i
\(97\) −7.86923 3.66948i −0.798999 0.372579i −0.0201549 0.999797i \(-0.506416\pi\)
−0.778844 + 0.627217i \(0.784194\pi\)
\(98\) 8.80959 3.32194i 0.889903 0.335566i
\(99\) −0.364806 + 0.306109i −0.0366644 + 0.0307651i
\(100\) −2.63119 9.64763i −0.263119 0.964763i
\(101\) −2.97125 16.8508i −0.295650 1.67671i −0.664549 0.747245i \(-0.731376\pi\)
0.368899 0.929470i \(-0.379735\pi\)
\(102\) 3.77267 6.71199i 0.373550 0.664586i
\(103\) 2.12583 0.569613i 0.209464 0.0561257i −0.152561 0.988294i \(-0.548752\pi\)
0.362025 + 0.932168i \(0.382085\pi\)
\(104\) −2.25001 4.41939i −0.220632 0.433357i
\(105\) −13.9820 + 5.63974i −1.36450 + 0.550382i
\(106\) −13.5902 13.2804i −1.31999 1.28990i
\(107\) 6.65817 + 1.78405i 0.643669 + 0.172471i 0.565865 0.824498i \(-0.308542\pi\)
0.0778043 + 0.996969i \(0.475209\pi\)
\(108\) 8.73702 4.32211i 0.840720 0.415895i
\(109\) −8.14891 + 9.71150i −0.780524 + 0.930193i −0.998957 0.0456593i \(-0.985461\pi\)
0.218433 + 0.975852i \(0.429906\pi\)
\(110\) −4.22998 + 1.76316i −0.403313 + 0.168111i
\(111\) −6.84653 1.20723i −0.649844 0.114585i
\(112\) 14.6511 1.96586i 1.38440 0.185756i
\(113\) 4.01747 4.01747i 0.377932 0.377932i −0.492424 0.870356i \(-0.663889\pi\)
0.870356 + 0.492424i \(0.163889\pi\)
\(114\) 4.30036 10.3920i 0.402766 0.973302i
\(115\) 6.49417 + 0.344090i 0.605585 + 0.0320865i
\(116\) 4.87638 + 0.744354i 0.452760 + 0.0691115i
\(117\) 0.471970 0.330477i 0.0436336 0.0305526i
\(118\) −4.25707 + 12.1295i −0.391895 + 1.11661i
\(119\) −8.44814 7.08883i −0.774439 0.649832i
\(120\) −11.3984 + 1.79486i −1.04052 + 0.163848i
\(121\) −4.44993 7.70750i −0.404539 0.700682i
\(122\) 0.166812 + 14.4687i 0.0151025 + 1.30993i
\(123\) 6.52929 + 14.0021i 0.588727 + 1.26253i
\(124\) −5.28841 6.01520i −0.474913 0.540181i
\(125\) 11.1211 1.14948i 0.994701 0.102813i
\(126\) 0.463604 + 1.65369i 0.0413011 + 0.147323i
\(127\) −16.4025 11.4851i −1.45548 1.01914i −0.991044 0.133534i \(-0.957367\pi\)
−0.464438 0.885605i \(-0.653744\pi\)
\(128\) 11.2639 + 1.06003i 0.995601 + 0.0936944i
\(129\) −10.9428 13.0411i −0.963459 1.14821i
\(130\) 5.28420 1.67905i 0.463455 0.147262i
\(131\) 5.21063 + 14.3161i 0.455255 + 1.25080i 0.928980 + 0.370130i \(0.120687\pi\)
−0.473725 + 0.880673i \(0.657091\pi\)
\(132\) 1.48602 + 5.07484i 0.129341 + 0.441708i
\(133\) −13.4883 8.80667i −1.16959 0.763636i
\(134\) −1.02968 + 4.02799i −0.0889504 + 0.347965i
\(135\) 3.18032 + 10.4238i 0.273719 + 0.897138i
\(136\) −5.07744 6.74249i −0.435387 0.578163i
\(137\) 19.0460 + 1.66631i 1.62721 + 0.142362i 0.863896 0.503670i \(-0.168017\pi\)
0.763310 + 0.646032i \(0.223573\pi\)
\(138\) 1.21778 7.40455i 0.103664 0.630318i
\(139\) 2.64152 + 14.9808i 0.224051 + 1.27066i 0.864491 + 0.502649i \(0.167641\pi\)
−0.640440 + 0.768008i \(0.721248\pi\)
\(140\) −0.493718 + 16.5199i −0.0417268 + 1.39618i
\(141\) −7.53170 + 13.0453i −0.634283 + 1.09861i
\(142\) −0.702938 3.73429i −0.0589893 0.313375i
\(143\) −1.07384 2.30285i −0.0897989 0.192574i
\(144\) 0.0605941 + 1.31305i 0.00504951 + 0.109421i
\(145\) −1.70728 + 5.24420i −0.141782 + 0.435507i
\(146\) 10.9146 + 0.828229i 0.903296 + 0.0685447i
\(147\) 12.1000 1.05861i 0.997992 0.0873130i
\(148\) −4.22619 + 6.34196i −0.347391 + 0.521306i
\(149\) −21.0607 3.71356i −1.72536 0.304227i −0.778921 0.627122i \(-0.784233\pi\)
−0.946435 + 0.322895i \(0.895344\pi\)
\(150\) 0.0912659 12.9005i 0.00745183 1.05332i
\(151\) 13.1509i 1.07020i 0.844787 + 0.535102i \(0.179727\pi\)
−0.844787 + 0.535102i \(0.820273\pi\)
\(152\) −8.53963 8.89240i −0.692655 0.721269i
\(153\) 0.693410 0.693410i 0.0560589 0.0560589i
\(154\) 7.53706 0.747058i 0.607354 0.0601996i
\(155\) 7.59678 4.74092i 0.610188 0.380800i
\(156\) −1.25592 6.27327i −0.100554 0.502264i
\(157\) 1.13449 + 12.9673i 0.0905422 + 1.03490i 0.896534 + 0.442975i \(0.146077\pi\)
−0.805992 + 0.591927i \(0.798367\pi\)
\(158\) 6.79478 + 7.91068i 0.540564 + 0.629340i
\(159\) −12.2568 21.2294i −0.972026 1.68360i
\(160\) −3.21626 + 12.2334i −0.254268 + 0.967134i
\(161\) −10.0999 3.67608i −0.795987 0.289716i
\(162\) 13.7283 2.58420i 1.07860 0.203034i
\(163\) −2.20191 + 0.590000i −0.172467 + 0.0462124i −0.344019 0.938963i \(-0.611788\pi\)
0.171552 + 0.985175i \(0.445122\pi\)
\(164\) 16.9317 0.390471i 1.32214 0.0304906i
\(165\) −5.86844 + 0.717129i −0.456857 + 0.0558284i
\(166\) 4.82566 + 6.72538i 0.374544 + 0.521991i
\(167\) −0.432407 + 4.94244i −0.0334607 + 0.382457i 0.960938 + 0.276764i \(0.0892619\pi\)
−0.994399 + 0.105694i \(0.966294\pi\)
\(168\) 18.8840 + 2.66015i 1.45694 + 0.205235i
\(169\) −3.39482 9.32720i −0.261140 0.717477i
\(170\) 8.36076 4.37603i 0.641241 0.335626i
\(171\) 0.884640 1.12656i 0.0676501 0.0861504i
\(172\) −17.9100 + 5.24441i −1.36562 + 0.399882i
\(173\) 9.04772 19.4029i 0.687886 1.47518i −0.182705 0.983168i \(-0.558485\pi\)
0.870591 0.492008i \(-0.163737\pi\)
\(174\) 5.79817 + 2.62278i 0.439558 + 0.198833i
\(175\) −18.1345 3.54663i −1.37084 0.268100i
\(176\) 5.74902 + 0.742364i 0.433349 + 0.0559578i
\(177\) −9.51209 + 13.5847i −0.714972 + 1.02109i
\(178\) 1.86953 3.32609i 0.140127 0.249301i
\(179\) 2.33527 4.04480i 0.174546 0.302322i −0.765458 0.643486i \(-0.777488\pi\)
0.940004 + 0.341163i \(0.110821\pi\)
\(180\) −1.45953 0.171761i −0.108787 0.0128023i
\(181\) −3.10753 1.13105i −0.230981 0.0840702i 0.223937 0.974604i \(-0.428109\pi\)
−0.454918 + 0.890533i \(0.650331\pi\)
\(182\) −9.16299 + 0.105642i −0.679206 + 0.00783072i
\(183\) −4.83137 + 18.0309i −0.357145 + 1.33288i
\(184\) −6.89753 4.48245i −0.508493 0.330451i
\(185\) −6.22826 5.81465i −0.457911 0.427501i
\(186\) −4.47446 9.31366i −0.328084 0.682910i
\(187\) −2.48049 3.54251i −0.181391 0.259054i
\(188\) 9.78071 + 13.3046i 0.713331 + 0.970334i
\(189\) 18.0117i 1.31016i
\(190\) 11.3616 7.80472i 0.824258 0.566214i
\(191\) 9.23832i 0.668461i −0.942491 0.334231i \(-0.891524\pi\)
0.942491 0.334231i \(-0.108476\pi\)
\(192\) 13.6228 + 5.23932i 0.983141 + 0.378116i
\(193\) −0.281879 0.402565i −0.0202901 0.0289773i 0.808879 0.587975i \(-0.200075\pi\)
−0.829169 + 0.558998i \(0.811186\pi\)
\(194\) −11.0682 + 5.31738i −0.794651 + 0.381766i
\(195\) 7.14869 0.245523i 0.511928 0.0175822i
\(196\) 4.26431 12.6136i 0.304593 0.900974i
\(197\) 4.93990 18.4360i 0.351953 1.31351i −0.532322 0.846542i \(-0.678681\pi\)
0.884275 0.466966i \(-0.154653\pi\)
\(198\) 0.00776416 + 0.673433i 0.000551775 + 0.0478588i
\(199\) −11.2947 4.11094i −0.800660 0.291417i −0.0909003 0.995860i \(-0.528974\pi\)
−0.709760 + 0.704443i \(0.751197\pi\)
\(200\) −12.9110 5.77112i −0.912946 0.408079i
\(201\) −2.68176 + 4.64495i −0.189157 + 0.327629i
\(202\) −21.0944 11.8567i −1.48419 0.834235i
\(203\) 5.22812 7.46653i 0.366942 0.524048i
\(204\) −3.95913 10.1436i −0.277195 0.710195i
\(205\) −2.64606 + 18.7495i −0.184809 + 1.30952i
\(206\) 1.28276 2.83579i 0.0893742 0.197579i
\(207\) 0.403905 0.866178i 0.0280734 0.0602035i
\(208\) −6.85086 1.50097i −0.475022 0.104074i
\(209\) −4.21524 4.70473i −0.291575 0.325433i
\(210\) −6.36618 + 20.3489i −0.439308 + 1.40421i
\(211\) −7.65682 21.0370i −0.527118 1.44824i −0.862449 0.506143i \(-0.831071\pi\)
0.335332 0.942100i \(-0.391152\pi\)
\(212\) −26.7089 + 2.95865i −1.83438 + 0.203201i
\(213\) 0.427250 4.88349i 0.0292747 0.334611i
\(214\) 7.92029 5.68304i 0.541420 0.388485i
\(215\) −2.53087 20.7107i −0.172604 1.41246i
\(216\) 3.10530 13.4309i 0.211289 0.913857i
\(217\) −14.2954 + 3.83045i −0.970437 + 0.260028i
\(218\) 3.31662 + 17.6192i 0.224630 + 1.19332i
\(219\) 13.2695 + 4.82972i 0.896672 + 0.326362i
\(220\) −1.86366 + 6.20723i −0.125648 + 0.418491i
\(221\) 2.61612 + 4.53125i 0.175979 + 0.304805i
\(222\) −7.45826 + 6.40618i −0.500565 + 0.429955i
\(223\) −1.09821 12.5526i −0.0735418 0.840587i −0.939964 0.341274i \(-0.889141\pi\)
0.866422 0.499313i \(-0.166414\pi\)
\(224\) 10.9844 17.7871i 0.733926 1.18845i
\(225\) 0.454705 1.57889i 0.0303137 0.105259i
\(226\) −0.792523 7.99576i −0.0527178 0.531870i
\(227\) 15.6148 15.6148i 1.03639 1.03639i 0.0370778 0.999312i \(-0.488195\pi\)
0.999312 0.0370778i \(-0.0118049\pi\)
\(228\) −7.51114 14.0199i −0.497437 0.928490i
\(229\) 5.68132i 0.375432i 0.982223 + 0.187716i \(0.0601085\pi\)
−0.982223 + 0.187716i \(0.939891\pi\)
\(230\) 6.19831 6.79458i 0.408704 0.448022i
\(231\) 9.62262 + 1.69673i 0.633122 + 0.111636i
\(232\) 5.18576 4.66627i 0.340462 0.306356i
\(233\) −16.7861 + 1.46860i −1.09970 + 0.0962109i −0.622525 0.782600i \(-0.713893\pi\)
−0.477171 + 0.878811i \(0.658338\pi\)
\(234\) 0.0616541 0.812490i 0.00403045 0.0531141i
\(235\) −16.4545 + 8.37207i −1.07337 + 0.546133i
\(236\) 9.45033 + 15.5302i 0.615164 + 1.01093i
\(237\) 5.68559 + 12.1928i 0.369318 + 0.792006i
\(238\) −15.3271 + 2.88516i −0.993510 + 0.187017i
\(239\) −5.47203 + 9.47783i −0.353956 + 0.613070i −0.986939 0.161096i \(-0.948497\pi\)
0.632983 + 0.774166i \(0.281830\pi\)
\(240\) −8.25537 + 14.0761i −0.532882 + 0.908611i
\(241\) 2.43737 + 13.8230i 0.157005 + 0.890419i 0.956930 + 0.290319i \(0.0937613\pi\)
−0.799925 + 0.600100i \(0.795128\pi\)
\(242\) −12.4195 2.04255i −0.798353 0.131300i
\(243\) 3.38726 + 0.296347i 0.217293 + 0.0190107i
\(244\) 15.9748 + 12.7885i 1.02268 + 0.818703i
\(245\) 13.1401 + 6.99638i 0.839487 + 0.446983i
\(246\) 21.1684 + 5.41128i 1.34965 + 0.345010i
\(247\) 4.58442 + 6.11497i 0.291699 + 0.389086i
\(248\) −11.3202 + 0.391677i −0.718832 + 0.0248715i
\(249\) 3.65233 + 10.0347i 0.231457 + 0.635922i
\(250\) 8.71268 13.1943i 0.551038 0.834480i
\(251\) 0.850481 + 1.01356i 0.0536819 + 0.0639756i 0.792217 0.610239i \(-0.208927\pi\)
−0.738535 + 0.674215i \(0.764482\pi\)
\(252\) 2.22436 + 0.975448i 0.140121 + 0.0614475i
\(253\) −3.45253 2.41749i −0.217058 0.151986i
\(254\) −27.2666 + 7.64403i −1.71086 + 0.479629i
\(255\) 11.9096 2.52430i 0.745805 0.158078i
\(256\) 11.2574 11.3697i 0.703589 0.710608i
\(257\) 0.740058 + 1.58706i 0.0461635 + 0.0989980i 0.928037 0.372488i \(-0.121495\pi\)
−0.881873 + 0.471486i \(0.843718\pi\)
\(258\) −24.0739 + 0.277553i −1.49878 + 0.0172797i
\(259\) 7.04114 + 12.1956i 0.437515 + 0.757798i
\(260\) 2.90075 7.28489i 0.179897 0.451790i
\(261\) 0.620878 + 0.520979i 0.0384314 + 0.0322478i
\(262\) 20.3296 + 7.13505i 1.25597 + 0.440805i
\(263\) −4.64747 + 3.25419i −0.286575 + 0.200662i −0.708021 0.706191i \(-0.750412\pi\)
0.421446 + 0.906854i \(0.361523\pi\)
\(264\) 6.88285 + 2.92420i 0.423610 + 0.179972i
\(265\) 1.58964 30.0021i 0.0976508 1.84301i
\(266\) −21.7245 + 6.85787i −1.33201 + 0.420483i
\(267\) 3.48059 3.48059i 0.213009 0.213009i
\(268\) 3.48255 + 4.73726i 0.212731 + 0.289374i
\(269\) 0.699204 + 0.123288i 0.0426312 + 0.00751703i 0.194923 0.980819i \(-0.437554\pi\)
−0.152292 + 0.988336i \(0.548665\pi\)
\(270\) 14.2522 + 5.86632i 0.867364 + 0.357013i
\(271\) −0.239492 + 0.285416i −0.0145481 + 0.0173378i −0.773269 0.634078i \(-0.781380\pi\)
0.758721 + 0.651415i \(0.225824\pi\)
\(272\) −11.9265 0.491073i −0.723152 0.0297757i
\(273\) −11.4190 3.05970i −0.691107 0.185182i
\(274\) 18.8970 19.3379i 1.14161 1.16824i
\(275\) −6.50895 3.18390i −0.392505 0.191996i
\(276\) −7.00707 7.97006i −0.421776 0.479741i
\(277\) 20.4764 5.48663i 1.23031 0.329660i 0.415608 0.909544i \(-0.363569\pi\)
0.814699 + 0.579884i \(0.196902\pi\)
\(278\) 18.7535 + 10.5410i 1.12476 + 0.632205i
\(279\) −0.228519 1.29599i −0.0136811 0.0775891i
\(280\) 17.6261 + 15.3499i 1.05336 + 0.917331i
\(281\) 14.3109 12.0083i 0.853720 0.716356i −0.106886 0.994271i \(-0.534088\pi\)
0.960606 + 0.277916i \(0.0896435\pi\)
\(282\) 7.51630 + 19.9328i 0.447589 + 1.18698i
\(283\) 2.37506 + 1.10751i 0.141182 + 0.0658345i 0.491926 0.870637i \(-0.336293\pi\)
−0.350743 + 0.936472i \(0.614071\pi\)
\(284\) −4.71459 2.57890i −0.279759 0.153030i
\(285\) 16.8312 5.73836i 0.996994 0.339911i
\(286\) −3.48145 0.889964i −0.205862 0.0526247i
\(287\) 13.2257 28.3627i 0.780691 1.67420i
\(288\) 1.49048 + 1.11086i 0.0878275 + 0.0654581i
\(289\) −5.20324 6.20098i −0.306073 0.364764i
\(290\) 4.20533 + 6.56872i 0.246945 + 0.385728i
\(291\) −15.6005 + 2.75080i −0.914520 + 0.161254i
\(292\) 10.6907 11.1954i 0.625625 0.655161i
\(293\) 7.04774 + 26.3025i 0.411733 + 1.53661i 0.791290 + 0.611441i \(0.209410\pi\)
−0.379557 + 0.925168i \(0.623924\pi\)
\(294\) 9.68966 14.1835i 0.565113 0.827200i
\(295\) −18.8497 + 7.60317i −1.09747 + 0.442674i
\(296\) 3.14784 + 10.3079i 0.182964 + 0.599136i
\(297\) 1.82806 6.82240i 0.106075 0.395876i
\(298\) −22.9424 + 19.7061i −1.32902 + 1.14154i
\(299\) 3.90632 + 3.27779i 0.225908 + 0.189560i
\(300\) −14.0282 11.6650i −0.809918 0.673477i
\(301\) −5.98804 + 33.9598i −0.345145 + 1.95741i
\(302\) 14.3839 + 11.7896i 0.827700 + 0.678417i
\(303\) −22.0742 22.0742i −1.26813 1.26813i
\(304\) −17.3818 + 1.36835i −0.996916 + 0.0784801i
\(305\) −17.0108 + 15.2989i −0.974037 + 0.876014i
\(306\) −0.136788 1.38006i −0.00781967 0.0788927i
\(307\) 11.6735 + 16.6715i 0.666241 + 0.951491i 0.999961 + 0.00881875i \(0.00280713\pi\)
−0.333720 + 0.942672i \(0.608304\pi\)
\(308\) 5.93980 8.91345i 0.338451 0.507891i
\(309\) 2.58097 3.07588i 0.146826 0.174981i
\(310\) 1.62501 12.5592i 0.0922941 0.713316i
\(311\) −14.6115 + 8.43597i −0.828543 + 0.478360i −0.853354 0.521332i \(-0.825435\pi\)
0.0248102 + 0.999692i \(0.492102\pi\)
\(312\) −7.98736 4.25024i −0.452195 0.240622i
\(313\) −11.6912 + 5.45170i −0.660826 + 0.308148i −0.723945 0.689858i \(-0.757673\pi\)
0.0631191 + 0.998006i \(0.479895\pi\)
\(314\) 15.2001 + 10.3842i 0.857793 + 0.586013i
\(315\) −1.48029 + 2.27658i −0.0834049 + 0.128271i
\(316\) 14.7438 0.340015i 0.829404 0.0191273i
\(317\) 19.8855 28.3995i 1.11688 1.59507i 0.371506 0.928431i \(-0.378842\pi\)
0.745377 0.666643i \(-0.232270\pi\)
\(318\) −34.2079 5.62595i −1.91828 0.315487i
\(319\) 2.73809 2.29753i 0.153304 0.128637i
\(320\) 10.4970 + 14.4849i 0.586801 + 0.809731i
\(321\) 11.8176 4.30124i 0.659593 0.240072i
\(322\) −13.0752 + 7.75133i −0.728654 + 0.431965i
\(323\) 9.49133 + 8.89457i 0.528112 + 0.494907i
\(324\) 9.48077 17.3321i 0.526710 0.962896i
\(325\) 7.50933 + 4.52382i 0.416543 + 0.250936i
\(326\) −1.32867 + 2.93729i −0.0735883 + 0.162681i
\(327\) −2.01586 + 23.0414i −0.111477 + 1.27419i
\(328\) 14.7520 18.8693i 0.814544 1.04188i
\(329\) 30.0489 5.29843i 1.65665 0.292112i
\(330\) −4.47663 + 7.06155i −0.246430 + 0.388726i
\(331\) 19.7925 + 11.4272i 1.08790 + 0.628097i 0.933016 0.359836i \(-0.117167\pi\)
0.154881 + 0.987933i \(0.450501\pi\)
\(332\) 11.6821 + 0.751128i 0.641138 + 0.0412235i
\(333\) −1.13487 + 0.529199i −0.0621906 + 0.0290000i
\(334\) 5.01818 + 4.90379i 0.274583 + 0.268323i
\(335\) −5.85884 + 2.98099i −0.320103 + 0.162869i
\(336\) 19.8389 18.2698i 1.08230 0.996699i
\(337\) −0.249363 2.85024i −0.0135837 0.155262i 0.986373 0.164522i \(-0.0526081\pi\)
−0.999957 + 0.00925956i \(0.997053\pi\)
\(338\) −13.2451 4.64862i −0.720440 0.252852i
\(339\) 1.79999 10.2082i 0.0977619 0.554435i
\(340\) 2.70901 13.0677i 0.146917 0.708696i
\(341\) −5.80354 −0.314279
\(342\) −0.439117 1.97753i −0.0237448 0.106933i
\(343\) 0.895062 + 0.895062i 0.0483288 + 0.0483288i
\(344\) −10.3200 + 24.2908i −0.556417 + 1.30967i
\(345\) 10.0656 6.28166i 0.541915 0.338193i
\(346\) −13.1109 27.2905i −0.704846 1.46715i
\(347\) 5.82423 0.509554i 0.312661 0.0273543i 0.0702545 0.997529i \(-0.477619\pi\)
0.242406 + 0.970175i \(0.422063\pi\)
\(348\) 8.06669 3.99050i 0.432420 0.213913i
\(349\) −5.42727 + 3.13344i −0.290515 + 0.167729i −0.638174 0.769892i \(-0.720310\pi\)
0.347659 + 0.937621i \(0.386977\pi\)
\(350\) −20.1365 + 16.6552i −1.07634 + 0.890258i
\(351\) −2.92271 + 8.03009i −0.156003 + 0.428614i
\(352\) 5.96590 5.62252i 0.317984 0.299681i
\(353\) −2.17797 8.12830i −0.115922 0.432626i 0.883432 0.468558i \(-0.155226\pi\)
−0.999354 + 0.0359327i \(0.988560\pi\)
\(354\) 6.33086 + 22.5824i 0.336481 + 1.20024i
\(355\) 3.70169 4.73234i 0.196465 0.251167i
\(356\) −1.96193 5.02662i −0.103982 0.266410i
\(357\) −20.0439 1.75362i −1.06084 0.0928112i
\(358\) −2.33049 6.18033i −0.123170 0.326641i
\(359\) −16.7290 + 6.08887i −0.882925 + 0.321358i −0.743390 0.668859i \(-0.766783\pi\)
−0.139535 + 0.990217i \(0.544561\pi\)
\(360\) −1.49631 + 1.44239i −0.0788627 + 0.0760205i
\(361\) 15.3162 + 11.2434i 0.806115 + 0.591759i
\(362\) −4.02296 + 2.38492i −0.211442 + 0.125348i
\(363\) −14.7160 6.86219i −0.772390 0.360172i
\(364\) −8.09898 + 10.1168i −0.424502 + 0.530265i
\(365\) 10.4077 + 13.8280i 0.544764 + 0.723792i
\(366\) 15.3902 + 21.4489i 0.804458 + 1.12115i
\(367\) −5.42878 3.80127i −0.283380 0.198425i 0.423241 0.906017i \(-0.360892\pi\)
−0.706621 + 0.707592i \(0.749781\pi\)
\(368\) −11.0863 + 3.52576i −0.577912 + 0.183793i
\(369\) 2.40991 + 1.39136i 0.125455 + 0.0724314i
\(370\) −11.9434 + 1.59945i −0.620907 + 0.0831512i
\(371\) −16.9829 + 46.6602i −0.881709 + 2.42247i
\(372\) −14.1982 3.45561i −0.736142 0.179165i
\(373\) 4.55305 + 1.21999i 0.235748 + 0.0631686i 0.374759 0.927122i \(-0.377726\pi\)
−0.139011 + 0.990291i \(0.544392\pi\)
\(374\) −6.09838 0.462763i −0.315340 0.0239289i
\(375\) 15.4176 13.3557i 0.796161 0.689685i
\(376\) 23.3203 + 1.22966i 1.20265 + 0.0634147i
\(377\) −3.54242 + 2.48043i −0.182444 + 0.127748i
\(378\) −19.7004 16.1473i −1.01328 0.830526i
\(379\) 10.0688 0.517201 0.258601 0.965984i \(-0.416739\pi\)
0.258601 + 0.965984i \(0.416739\pi\)
\(380\) 1.64909 19.4237i 0.0845966 0.996415i
\(381\) −36.5322 −1.87160
\(382\) −10.1045 8.28205i −0.516991 0.423747i
\(383\) 6.81602 4.77263i 0.348283 0.243870i −0.386324 0.922363i \(-0.626255\pi\)
0.734607 + 0.678493i \(0.237367\pi\)
\(384\) 17.9432 10.2031i 0.915662 0.520672i
\(385\) 8.75366 + 8.17233i 0.446128 + 0.416501i
\(386\) −0.693010 0.0525876i −0.0352733 0.00267664i
\(387\) −2.96180 0.793613i −0.150557 0.0403416i
\(388\) −4.10659 + 16.8729i −0.208481 + 0.856593i
\(389\) 0.855706 2.35103i 0.0433860 0.119202i −0.916108 0.400933i \(-0.868686\pi\)
0.959494 + 0.281730i \(0.0909084\pi\)
\(390\) 6.14018 8.03905i 0.310920 0.407073i
\(391\) 7.51623 + 4.33950i 0.380112 + 0.219458i
\(392\) −9.97337 15.9721i −0.503731 0.806714i
\(393\) 22.7685 + 15.9427i 1.14852 + 0.804202i
\(394\) −15.7359 21.9307i −0.792764 1.10485i
\(395\) −2.30414 + 16.3267i −0.115934 + 0.821485i
\(396\) 0.743534 + 0.595233i 0.0373640 + 0.0299116i
\(397\) −33.7554 15.7404i −1.69413 0.789987i −0.997354 0.0727025i \(-0.976838\pi\)
−0.696780 0.717285i \(-0.745385\pi\)
\(398\) −14.6220 + 8.66827i −0.732932 + 0.434501i
\(399\) −29.3741 + 0.953410i −1.47055 + 0.0477302i
\(400\) −17.8868 + 8.94778i −0.894339 + 0.447389i
\(401\) 15.3592 5.59029i 0.767001 0.279166i 0.0712597 0.997458i \(-0.477298\pi\)
0.695742 + 0.718292i \(0.255076\pi\)
\(402\) 2.67628 + 7.09734i 0.133481 + 0.353983i
\(403\) 6.99485 + 0.611970i 0.348438 + 0.0304844i
\(404\) −31.8792 + 12.4427i −1.58605 + 0.619048i
\(405\) 17.3974 + 13.6085i 0.864484 + 0.676210i
\(406\) −3.47963 12.4120i −0.172691 0.615995i
\(407\) 1.42925 + 5.33404i 0.0708453 + 0.264398i
\(408\) −14.6440 4.76331i −0.724985 0.235819i
\(409\) −6.19941 + 17.0327i −0.306541 + 0.842215i 0.686783 + 0.726862i \(0.259022\pi\)
−0.993325 + 0.115353i \(0.963200\pi\)
\(410\) 18.1352 + 19.7028i 0.895635 + 0.973054i
\(411\) 30.2079 17.4406i 1.49005 0.860279i
\(412\) −1.95169 3.94529i −0.0961529 0.194370i
\(413\) 33.4643 2.92775i 1.64667 0.144065i
\(414\) −0.585292 1.21829i −0.0287656 0.0598759i
\(415\) −2.95148 + 12.7508i −0.144882 + 0.625912i
\(416\) −7.78342 + 6.14758i −0.381614 + 0.301410i
\(417\) 19.6246 + 19.6246i 0.961021 + 0.961021i
\(418\) −8.92476 + 0.392717i −0.436524 + 0.0192084i
\(419\) 26.1306 1.27656 0.638281 0.769803i \(-0.279646\pi\)
0.638281 + 0.769803i \(0.279646\pi\)
\(420\) 16.5495 + 25.2056i 0.807534 + 1.22991i
\(421\) 0.937711 5.31803i 0.0457013 0.259185i −0.953393 0.301731i \(-0.902436\pi\)
0.999095 + 0.0425458i \(0.0135468\pi\)
\(422\) −29.8736 10.4847i −1.45422 0.510387i
\(423\) 0.236467 + 2.70283i 0.0114974 + 0.131416i
\(424\) −20.7082 + 31.8655i −1.00568 + 1.54753i
\(425\) 13.9236 + 5.36314i 0.675393 + 0.260151i
\(426\) −4.95833 4.84530i −0.240232 0.234756i
\(427\) 34.2692 15.9800i 1.65840 0.773325i
\(428\) 0.884583 13.7577i 0.0427579 0.665002i
\(429\) −4.01470 2.31789i −0.193831 0.111909i
\(430\) −24.9214 15.7988i −1.20182 0.761885i
\(431\) 17.9158 3.15904i 0.862975 0.152166i 0.275394 0.961331i \(-0.411192\pi\)
0.587581 + 0.809166i \(0.300080\pi\)
\(432\) −11.9063 15.4371i −0.572842 0.742718i
\(433\) 0.334373 3.82190i 0.0160689 0.183669i −0.983918 0.178619i \(-0.942837\pi\)
0.999987 0.00504975i \(-0.00160739\pi\)
\(434\) −8.62611 + 19.0697i −0.414067 + 0.915375i
\(435\) 2.93632 + 9.62406i 0.140786 + 0.461438i
\(436\) 22.2444 + 12.1678i 1.06532 + 0.582734i
\(437\) 11.6572 + 4.98209i 0.557641 + 0.238326i
\(438\) 17.1785 10.1839i 0.820822 0.486605i
\(439\) 30.6188 11.1443i 1.46135 0.531890i 0.515616 0.856820i \(-0.327563\pi\)
0.945738 + 0.324930i \(0.105341\pi\)
\(440\) 5.11846 + 7.60311i 0.244013 + 0.362464i
\(441\) 1.67590 1.40625i 0.0798047 0.0669641i
\(442\) 7.30142 + 1.20082i 0.347293 + 0.0571170i
\(443\) −12.0663 + 17.2324i −0.573285 + 0.818736i −0.996169 0.0874479i \(-0.972129\pi\)
0.422884 + 0.906184i \(0.361018\pi\)
\(444\) 0.320569 + 13.9006i 0.0152135 + 0.659693i
\(445\) 5.90172 1.25090i 0.279768 0.0592985i
\(446\) −14.7141 10.0521i −0.696733 0.475982i
\(447\) −35.3613 + 16.4892i −1.67253 + 0.779914i
\(448\) −9.60745 27.9603i −0.453909 1.32100i
\(449\) −3.23960 + 1.87038i −0.152886 + 0.0882689i −0.574491 0.818511i \(-0.694800\pi\)
0.421605 + 0.906779i \(0.361467\pi\)
\(450\) −1.31929 1.91279i −0.0621917 0.0901700i
\(451\) 7.88821 9.40081i 0.371441 0.442667i
\(452\) −9.45592 6.30128i −0.444769 0.296387i
\(453\) 13.7619 + 19.6540i 0.646590 + 0.923426i
\(454\) −3.08032 31.0773i −0.144566 1.45853i
\(455\) −9.68879 10.7729i −0.454218 0.505043i
\(456\) −22.0680 4.35331i −1.03343 0.203863i
\(457\) −19.7227 19.7227i −0.922590 0.922590i 0.0746215 0.997212i \(-0.476225\pi\)
−0.997212 + 0.0746215i \(0.976225\pi\)
\(458\) 6.21399 + 5.09324i 0.290361 + 0.237992i
\(459\) −2.52558 + 14.3233i −0.117884 + 0.668552i
\(460\) −1.87492 12.8707i −0.0874185 0.600101i
\(461\) 8.89150 + 7.46086i 0.414119 + 0.347487i 0.825920 0.563787i \(-0.190656\pi\)
−0.411802 + 0.911273i \(0.635100\pi\)
\(462\) 10.4824 9.00372i 0.487684 0.418891i
\(463\) −8.02731 + 29.9583i −0.373061 + 1.39228i 0.483097 + 0.875567i \(0.339512\pi\)
−0.856158 + 0.516715i \(0.827155\pi\)
\(464\) −0.454795 9.85524i −0.0211133 0.457518i
\(465\) 6.39220 15.0350i 0.296431 0.697233i
\(466\) −13.4423 + 19.6766i −0.622702 + 0.911499i
\(467\) −7.03778 26.2653i −0.325669 1.21541i −0.913637 0.406531i \(-0.866738\pi\)
0.587968 0.808884i \(-0.299928\pi\)
\(468\) −0.833395 0.795823i −0.0385237 0.0367869i
\(469\) 10.6993 1.88657i 0.494048 0.0871139i
\(470\) −5.59425 + 25.5027i −0.258044 + 1.17635i
\(471\) 15.2653 + 18.1924i 0.703386 + 0.838263i
\(472\) 25.4584 + 3.58626i 1.17182 + 0.165071i
\(473\) −5.71481 + 12.2555i −0.262767 + 0.563506i
\(474\) 18.4330 + 4.71204i 0.846657 + 0.216431i
\(475\) 21.1279 + 5.34888i 0.969416 + 0.245423i
\(476\) −10.5849 + 19.3507i −0.485160 + 0.886937i
\(477\) −4.00161 1.86598i −0.183221 0.0854373i
\(478\) 5.46084 + 14.4818i 0.249773 + 0.662384i
\(479\) 26.3116 22.0781i 1.20221 1.00877i 0.202644 0.979252i \(-0.435047\pi\)
0.999564 0.0295199i \(-0.00939785\pi\)
\(480\) 7.99505 + 21.6485i 0.364922 + 0.988114i
\(481\) −1.16018 6.57968i −0.0528995 0.300008i
\(482\) 17.3041 + 9.72629i 0.788181 + 0.443020i
\(483\) −18.9412 + 5.07529i −0.861856 + 0.230934i
\(484\) −13.3680 + 11.7528i −0.607634 + 0.534216i
\(485\) −17.8674 7.59639i −0.811317 0.344934i
\(486\) 3.36078 3.43917i 0.152448 0.156004i
\(487\) −26.0902 6.99084i −1.18226 0.316785i −0.386436 0.922316i \(-0.626294\pi\)
−0.795822 + 0.605531i \(0.792961\pi\)
\(488\) 28.3088 6.00774i 1.28148 0.271957i
\(489\) −2.67334 + 3.18597i −0.120893 + 0.144074i
\(490\) 19.4323 8.09986i 0.877860 0.365914i
\(491\) −24.6257 4.34217i −1.11134 0.195959i −0.412305 0.911046i \(-0.635276\pi\)
−0.699036 + 0.715086i \(0.746387\pi\)
\(492\) 24.8958 18.3019i 1.12239 0.825115i
\(493\) −5.20446 + 5.20446i −0.234397 + 0.234397i
\(494\) 10.7982 + 0.467764i 0.485833 + 0.0210457i
\(495\) −0.791756 + 0.712077i −0.0355868 + 0.0320055i
\(496\) −9.72001 + 12.7327i −0.436442 + 0.571714i
\(497\) −8.13400 + 5.69548i −0.364860 + 0.255477i
\(498\) 14.2498 + 5.00122i 0.638548 + 0.224110i
\(499\) 4.27496 + 3.58711i 0.191373 + 0.160581i 0.733440 0.679754i \(-0.237914\pi\)
−0.542067 + 0.840335i \(0.682358\pi\)
\(500\) −6.62053 21.3581i −0.296079 0.955163i
\(501\) 4.52583 + 7.83897i 0.202199 + 0.350219i
\(502\) 1.87104 0.0215716i 0.0835087 0.000962790i
\(503\) −0.732366 1.57056i −0.0326546 0.0700280i 0.889304 0.457317i \(-0.151189\pi\)
−0.921958 + 0.387289i \(0.873412\pi\)
\(504\) 3.06102 1.55843i 0.136349 0.0694180i
\(505\) −7.93334 37.4292i −0.353029 1.66558i
\(506\) −5.73930 + 1.60898i −0.255143 + 0.0715279i
\(507\) −14.8341 10.3870i −0.658806 0.461301i
\(508\) −16.0835 + 36.6758i −0.713588 + 1.62723i
\(509\) 17.0633 + 20.3352i 0.756317 + 0.901343i 0.997609 0.0691092i \(-0.0220157\pi\)
−0.241292 + 0.970452i \(0.577571\pi\)
\(510\) 7.91582 15.2892i 0.350518 0.677016i
\(511\) −9.78308 26.8788i −0.432778 1.18905i
\(512\) −2.34357 22.5057i −0.103572 0.994622i
\(513\) −1.16405 + 21.2125i −0.0513939 + 0.936556i
\(514\) 2.39931 + 0.613337i 0.105829 + 0.0270531i
\(515\) 4.70697 1.43611i 0.207414 0.0632824i
\(516\) −21.2784 + 26.5799i −0.936731 + 1.17011i
\(517\) 11.9196 + 1.04283i 0.524222 + 0.0458635i
\(518\) 19.6514 + 3.23193i 0.863431 + 0.142003i
\(519\) −6.78255 38.4657i −0.297721 1.68846i
\(520\) −5.36741 9.70355i −0.235377 0.425529i
\(521\) 17.9741 31.1320i 0.787458 1.36392i −0.140061 0.990143i \(-0.544730\pi\)
0.927519 0.373775i \(-0.121937\pi\)
\(522\) 1.12644 0.212039i 0.0493028 0.00928070i
\(523\) −14.8332 31.8098i −0.648609 1.39095i −0.905434 0.424488i \(-0.860454\pi\)
0.256825 0.966458i \(-0.417324\pi\)
\(524\) 26.0293 15.8392i 1.13710 0.691938i
\(525\) −30.8134 + 13.6766i −1.34481 + 0.596894i
\(526\) −0.607106 + 8.00056i −0.0264711 + 0.348841i
\(527\) 11.9051 1.04156i 0.518595 0.0453712i
\(528\) 9.36877 4.90666i 0.407723 0.213535i
\(529\) −14.3205 2.52510i −0.622632 0.109787i
\(530\) −31.3899 28.6352i −1.36349 1.24383i
\(531\) 2.98701i 0.129625i
\(532\) −11.9749 + 29.9094i −0.519179 + 1.29674i
\(533\) −10.4987 + 10.4987i −0.454751 + 0.454751i
\(534\) −0.686613 6.92724i −0.0297126 0.299771i
\(535\) 15.0163 + 3.47587i 0.649210 + 0.150275i
\(536\) 8.30349 + 0.437836i 0.358656 + 0.0189116i
\(537\) −0.742667 8.48872i −0.0320484 0.366315i
\(538\) 0.761676 0.654233i 0.0328382 0.0282060i
\(539\) −4.82397 8.35536i −0.207783 0.359891i
\(540\) 19.1933 10.3294i 0.825949 0.444507i
\(541\) −27.7414 10.0970i −1.19270 0.434106i −0.332026 0.943270i \(-0.607732\pi\)
−0.860669 + 0.509164i \(0.829955\pi\)
\(542\) 0.0974736 + 0.517819i 0.00418685 + 0.0222422i
\(543\) −5.82781 + 1.56156i −0.250095 + 0.0670128i
\(544\) −11.2291 + 12.6045i −0.481444 + 0.540413i
\(545\) −17.4654 + 22.3282i −0.748136 + 0.956436i
\(546\) −13.5836 + 9.74660i −0.581322 + 0.417116i
\(547\) −2.51303 + 28.7241i −0.107449 + 1.22815i 0.730695 + 0.682704i \(0.239196\pi\)
−0.838144 + 0.545448i \(0.816359\pi\)
\(548\) −4.20995 38.0050i −0.179840 1.62349i
\(549\) 1.14995 + 3.15945i 0.0490785 + 0.134842i
\(550\) −9.31762 + 4.26489i −0.397305 + 0.181855i
\(551\) −6.63976 + 8.45553i −0.282863 + 0.360218i
\(552\) −14.9991 + 0.518967i −0.638403 + 0.0220887i
\(553\) 11.5167 24.6977i 0.489741 1.05025i
\(554\) 12.3558 27.3149i 0.524948 1.16050i
\(555\) −15.3929 2.17236i −0.653394 0.0922117i
\(556\) 28.3416 11.0619i 1.20195 0.469131i
\(557\) −21.8595 + 31.2186i −0.926216 + 1.32277i 0.0201906 + 0.999796i \(0.493573\pi\)
−0.946407 + 0.322977i \(0.895316\pi\)
\(558\) −1.62237 0.911900i −0.0686803 0.0386038i
\(559\) 8.18022 14.1686i 0.345986 0.599266i
\(560\) 32.5907 5.51771i 1.37721 0.233166i
\(561\) −7.41419 2.69854i −0.313027 0.113933i
\(562\) −0.304579 26.4180i −0.0128479 1.11438i
\(563\) 10.9515 40.8715i 0.461551 1.72253i −0.206529 0.978440i \(-0.566217\pi\)
0.668080 0.744090i \(-0.267116\pi\)
\(564\) 28.5400 + 9.64853i 1.20175 + 0.406277i
\(565\) 8.66969 9.28639i 0.364737 0.390682i
\(566\) 3.34056 1.60487i 0.140414 0.0674577i
\(567\) −20.9382 29.9028i −0.879321 1.25580i
\(568\) −7.04727 + 2.84466i −0.295697 + 0.119359i
\(569\) 28.7547i 1.20546i 0.797945 + 0.602730i \(0.205921\pi\)
−0.797945 + 0.602730i \(0.794079\pi\)
\(570\) 8.81261 23.5536i 0.369120 0.986554i
\(571\) 43.1979i 1.80777i −0.427770 0.903887i \(-0.640701\pi\)
0.427770 0.903887i \(-0.359299\pi\)
\(572\) −4.09449 + 3.01002i −0.171199 + 0.125855i
\(573\) −9.66754 13.8067i −0.403867 0.576782i
\(574\) −19.1652 39.8926i −0.799940 1.66509i
\(575\) 14.5393 + 0.270508i 0.606329 + 0.0112810i
\(576\) 2.55121 0.634353i 0.106301 0.0264314i
\(577\) −1.70954 + 6.38007i −0.0711689 + 0.265606i −0.992337 0.123558i \(-0.960569\pi\)
0.921168 + 0.389164i \(0.127236\pi\)
\(578\) −11.4470 + 0.131975i −0.476134 + 0.00548945i
\(579\) −0.842537 0.306658i −0.0350146 0.0127443i
\(580\) 10.9546 + 1.28917i 0.454866 + 0.0535298i
\(581\) 10.8154 18.7328i 0.448697 0.777167i
\(582\) −10.9770 + 19.5293i −0.455012 + 0.809514i
\(583\) −11.1684 + 15.9501i −0.462548 + 0.660587i
\(584\) −2.66099 21.7296i −0.110112 0.899176i
\(585\) 1.02937 0.774758i 0.0425592 0.0320323i
\(586\) 35.0868 + 15.8714i 1.44942 + 0.655641i
\(587\) −4.69696 + 10.0727i −0.193864 + 0.415744i −0.979079 0.203480i \(-0.934775\pi\)
0.785215 + 0.619224i \(0.212553\pi\)
\(588\) −6.82667 23.3135i −0.281527 0.961434i
\(589\) 17.0834 3.58728i 0.703910 0.147811i
\(590\) −8.58252 + 27.4332i −0.353337 + 1.12941i
\(591\) −11.9098 32.7220i −0.489904 1.34600i
\(592\) 14.0964 + 5.79797i 0.579358 + 0.238295i
\(593\) −0.706451 + 8.07477i −0.0290105 + 0.331591i 0.967796 + 0.251736i \(0.0810014\pi\)
−0.996806 + 0.0798553i \(0.974554\pi\)
\(594\) −5.82322 8.11566i −0.238930 0.332989i
\(595\) −19.4236 15.1933i −0.796288 0.622866i
\(596\) 0.986104 + 42.7597i 0.0403924 + 1.75151i
\(597\) −21.1819 + 5.67567i −0.866917 + 0.232290i
\(598\) 7.08708 1.33406i 0.289812 0.0545540i
\(599\) 1.29816 + 0.472492i 0.0530414 + 0.0193055i 0.368405 0.929666i \(-0.379904\pi\)
−0.315363 + 0.948971i \(0.602126\pi\)
\(600\) −25.3348 + 4.88593i −1.03429 + 0.199467i
\(601\) 0.00476483 + 0.00825292i 0.000194361 + 0.000336644i 0.866123 0.499832i \(-0.166605\pi\)
−0.865928 + 0.500168i \(0.833271\pi\)
\(602\) 31.7757 + 36.9941i 1.29508 + 1.50777i
\(603\) 0.0841973 + 0.962379i 0.00342878 + 0.0391911i
\(604\) 25.7900 5.16323i 1.04938 0.210089i
\(605\) −10.5360 16.8828i −0.428351 0.686383i
\(606\) −43.9331 + 4.35456i −1.78466 + 0.176892i
\(607\) −4.47283 + 4.47283i −0.181547 + 0.181547i −0.792030 0.610483i \(-0.790975\pi\)
0.610483 + 0.792030i \(0.290975\pi\)
\(608\) −14.0860 + 20.2382i −0.571262 + 0.820768i
\(609\) 16.6298i 0.673872i
\(610\) 1.48329 + 32.3210i 0.0600568 + 1.30864i
\(611\) −14.2564 2.51378i −0.576751 0.101697i
\(612\) −1.63208 1.08759i −0.0659729 0.0439634i
\(613\) −5.69989 + 0.498676i −0.230217 + 0.0201413i −0.201680 0.979451i \(-0.564640\pi\)
−0.0285363 + 0.999593i \(0.509085\pi\)
\(614\) 28.6997 + 2.17782i 1.15823 + 0.0878896i
\(615\) 15.6660 + 30.7901i 0.631716 + 1.24158i
\(616\) −4.42420 14.4875i −0.178256 0.583719i
\(617\) −14.6041 31.3186i −0.587940 1.26084i −0.945095 0.326796i \(-0.894031\pi\)
0.357155 0.934045i \(-0.383747\pi\)
\(618\) −1.05046 5.58045i −0.0422556 0.224479i
\(619\) 9.48809 16.4339i 0.381358 0.660532i −0.609898 0.792480i \(-0.708790\pi\)
0.991257 + 0.131947i \(0.0421230\pi\)
\(620\) −12.2800 13.0366i −0.493175 0.523561i
\(621\) 2.46142 + 13.9594i 0.0987736 + 0.560173i
\(622\) −3.87216 + 23.5442i −0.155260 + 0.944038i
\(623\) −9.93267 0.868996i −0.397944 0.0348156i
\(624\) −11.8093 + 4.92595i −0.472751 + 0.197196i
\(625\) 24.7646 3.42238i 0.990586 0.136895i
\(626\) −4.51820 + 17.6747i −0.180583 + 0.706424i
\(627\) −11.2230 2.62014i −0.448203 0.104638i
\(628\) 24.9845 7.31597i 0.996992 0.291939i
\(629\) −3.88920 10.6855i −0.155073 0.426059i
\(630\) 1.16296 + 3.66001i 0.0463336 + 0.145818i
\(631\) 26.6447 + 31.7539i 1.06071 + 1.26410i 0.963177 + 0.268870i \(0.0866501\pi\)
0.0975310 + 0.995232i \(0.468905\pi\)
\(632\) 12.8458 16.4310i 0.510978 0.653590i
\(633\) −33.4575 23.4272i −1.32982 0.931147i
\(634\) −13.2350 47.2098i −0.525629 1.87494i
\(635\) −37.5369 24.4074i −1.48961 0.968580i
\(636\) −36.8204 + 32.3716i −1.46002 + 1.28362i
\(637\) 4.93315 + 10.5792i 0.195458 + 0.419162i
\(638\) −0.0582747 5.05452i −0.00230712 0.200110i
\(639\) −0.441477 0.764660i −0.0174645 0.0302495i
\(640\) 25.2535 + 1.50437i 0.998230 + 0.0594652i
\(641\) −14.1764 11.8954i −0.559935 0.469841i 0.318354 0.947972i \(-0.396870\pi\)
−0.878289 + 0.478131i \(0.841314\pi\)
\(642\) 5.88980 16.7816i 0.232452 0.662316i
\(643\) 31.6019 22.1279i 1.24626 0.872640i 0.250819 0.968034i \(-0.419300\pi\)
0.995440 + 0.0953942i \(0.0304112\pi\)
\(644\) −3.24372 + 21.2501i −0.127820 + 0.837372i
\(645\) −25.4553 28.3037i −1.00230 1.11446i
\(646\) 18.2374 2.40733i 0.717540 0.0947153i
\(647\) 34.4411 34.4411i 1.35402 1.35402i 0.472911 0.881110i \(-0.343203\pi\)
0.881110 0.472911i \(-0.156797\pi\)
\(648\) −10.4577 25.9077i −0.410819 1.01775i
\(649\) 12.9727 + 2.28743i 0.509221 + 0.0897895i
\(650\) 11.6800 4.15783i 0.458127 0.163084i
\(651\) −17.3561 + 20.6842i −0.680240 + 0.810678i
\(652\) 2.02154 + 4.08649i 0.0791697 + 0.160039i
\(653\) −6.16014 1.65061i −0.241065 0.0645932i 0.136264 0.990673i \(-0.456491\pi\)
−0.377329 + 0.926079i \(0.623157\pi\)
\(654\) 23.3945 + 22.8612i 0.914796 + 0.893943i
\(655\) 12.7433 + 31.5930i 0.497920 + 1.23444i
\(656\) −7.41338 33.0512i −0.289444 1.29043i
\(657\) 2.45678 0.658292i 0.0958480 0.0256824i
\(658\) 21.1433 37.6162i 0.824251 1.46643i
\(659\) 6.58560 + 37.3488i 0.256538 + 1.45490i 0.792092 + 0.610401i \(0.208992\pi\)
−0.535554 + 0.844501i \(0.679897\pi\)
\(660\) 3.71038 + 11.2270i 0.144427 + 0.437009i
\(661\) 15.6747 13.1526i 0.609674 0.511577i −0.284865 0.958568i \(-0.591949\pi\)
0.894539 + 0.446991i \(0.147504\pi\)
\(662\) 30.2424 11.4039i 1.17540 0.443224i
\(663\) 8.65157 + 4.03429i 0.335999 + 0.156679i
\(664\) 11.2944 12.1040i 0.438308 0.469726i
\(665\) −30.8190 18.6455i −1.19511 0.723040i
\(666\) −0.438584 + 1.71570i −0.0169948 + 0.0664819i
\(667\) −3.03155 + 6.50118i −0.117382 + 0.251727i
\(668\) 9.86231 1.09248i 0.381584 0.0422695i
\(669\) −14.7771 17.6107i −0.571317 0.680869i
\(670\) −1.99191 + 9.08057i −0.0769541 + 0.350813i
\(671\) 14.6022 2.57476i 0.563712 0.0993976i
\(672\) −2.19736 38.0776i −0.0847651 1.46888i
\(673\) 7.37274 + 27.5155i 0.284198 + 1.06064i 0.949423 + 0.314000i \(0.101669\pi\)
−0.665225 + 0.746643i \(0.731664\pi\)
\(674\) −3.34102 2.28246i −0.128691 0.0879172i
\(675\) 7.90728 + 23.0505i 0.304352 + 0.887214i
\(676\) −16.9586 + 10.3195i −0.652253 + 0.396905i
\(677\) −1.49118 + 5.56517i −0.0573108 + 0.213887i −0.988643 0.150284i \(-0.951981\pi\)
0.931332 + 0.364171i \(0.118648\pi\)
\(678\) −9.55167 11.1203i −0.366830 0.427073i
\(679\) 24.5808 + 20.6257i 0.943324 + 0.791543i
\(680\) −11.8643 14.6781i −0.454976 0.562878i
\(681\) 6.99605 39.6766i 0.268089 1.52041i
\(682\) −5.20281 + 6.34767i −0.199226 + 0.243065i
\(683\) −3.79394 3.79394i −0.145171 0.145171i 0.630786 0.775957i \(-0.282733\pi\)
−0.775957 + 0.630786i \(0.782733\pi\)
\(684\) −2.55661 1.29255i −0.0977544 0.0494219i
\(685\) 42.6909 + 2.26195i 1.63113 + 0.0864245i
\(686\) 1.78140 0.176568i 0.0680140 0.00674140i
\(687\) 5.94528 + 8.49074i 0.226827 + 0.323942i
\(688\) 17.3164 + 33.0640i 0.660183 + 1.26055i
\(689\) 15.1429 18.0466i 0.576898 0.687520i
\(690\) 2.15311 16.6408i 0.0819675 0.633504i
\(691\) −0.184618 + 0.106589i −0.00702318 + 0.00405484i −0.503507 0.863991i \(-0.667957\pi\)
0.496484 + 0.868046i \(0.334624\pi\)
\(692\) −41.6030 10.1255i −1.58151 0.384914i
\(693\) 1.59503 0.743776i 0.0605903 0.0282537i
\(694\) 4.66403 6.82710i 0.177044 0.259153i
\(695\) 7.05297 + 33.2757i 0.267534 + 1.26222i
\(696\) 2.86706 12.4004i 0.108675 0.470038i
\(697\) −14.4944 + 20.7001i −0.549013 + 0.784072i
\(698\) −1.43827 + 8.74522i −0.0544393 + 0.331011i
\(699\) −23.5501 + 19.7608i −0.890745 + 0.747424i
\(700\) 0.164609 + 36.9557i 0.00622165 + 1.39679i
\(701\) 14.6848 5.34482i 0.554636 0.201871i −0.0494691 0.998776i \(-0.515753\pi\)
0.604105 + 0.796905i \(0.293531\pi\)
\(702\) 6.16279 + 10.3956i 0.232600 + 0.392358i
\(703\) −7.50425 14.8179i −0.283028 0.558869i
\(704\) −0.801309 11.5658i −0.0302005 0.435902i
\(705\) −15.8302 + 29.7310i −0.596200 + 1.11974i
\(706\) −10.8429 4.90476i −0.408079 0.184593i
\(707\) −5.51125 + 62.9938i −0.207272 + 2.36913i
\(708\) 30.3753 + 13.3205i 1.14157 + 0.500614i
\(709\) 17.6590 3.11375i 0.663196 0.116939i 0.168090 0.985772i \(-0.446240\pi\)
0.495106 + 0.868832i \(0.335129\pi\)
\(710\) −1.85751 8.29125i −0.0697111 0.311165i
\(711\) 2.09850 + 1.21157i 0.0787000 + 0.0454375i
\(712\) −7.25676 2.36043i −0.271958 0.0884610i
\(713\) 10.5558 4.92225i 0.395318 0.184340i
\(714\) −19.8872 + 20.3511i −0.744259 + 0.761621i
\(715\) −2.57651 5.06388i −0.0963561 0.189379i
\(716\) −8.84905 2.99161i −0.330705 0.111802i
\(717\) 1.74023 + 19.8909i 0.0649900 + 0.742839i
\(718\) −8.33765 + 23.7561i −0.311158 + 0.886571i
\(719\) −0.476092 + 2.70005i −0.0177552 + 0.100695i −0.992398 0.123074i \(-0.960725\pi\)
0.974642 + 0.223769i \(0.0718360\pi\)
\(720\) 0.236193 + 2.92969i 0.00880239 + 0.109183i
\(721\) −8.13335 −0.302902
\(722\) 26.0284 6.67259i 0.968676 0.248328i
\(723\) 18.1079 + 18.1079i 0.673440 + 0.673440i
\(724\) −0.998022 + 6.53820i −0.0370912 + 0.242990i
\(725\) −3.41283 + 11.8505i −0.126749 + 0.440117i
\(726\) −20.6983 + 9.94388i −0.768187 + 0.369052i
\(727\) −24.8385 + 2.17309i −0.921208 + 0.0805953i −0.537884 0.843019i \(-0.680776\pi\)
−0.383324 + 0.923614i \(0.625221\pi\)
\(728\) 3.80470 + 17.9279i 0.141011 + 0.664453i
\(729\) −20.2910 + 11.7150i −0.751520 + 0.433890i
\(730\) 24.4549 + 1.01316i 0.905117 + 0.0374988i
\(731\) 9.52362 26.1659i 0.352244 0.967782i
\(732\) 37.2570 + 2.39553i 1.37706 + 0.0885414i
\(733\) −0.975433 3.64037i −0.0360285 0.134460i 0.945569 0.325421i \(-0.105506\pi\)
−0.981598 + 0.190961i \(0.938839\pi\)
\(734\) −9.02451 + 2.52997i −0.333101 + 0.0933830i
\(735\) 26.9593 3.29445i 0.994407 0.121518i
\(736\) −6.08240 + 15.2865i −0.224200 + 0.563469i
\(737\) 4.24412 + 0.371312i 0.156334 + 0.0136775i
\(738\) 3.68227 1.38852i 0.135546 0.0511120i
\(739\) −10.3871 + 3.78061i −0.382097 + 0.139072i −0.525925 0.850531i \(-0.676281\pi\)
0.143828 + 0.989603i \(0.454059\pi\)
\(740\) −8.95771 + 14.4971i −0.329292 + 0.532923i
\(741\) 13.2505 + 4.34142i 0.486769 + 0.159486i
\(742\) 35.8099 + 60.4055i 1.31462 + 2.21756i
\(743\) 13.5908 + 6.33748i 0.498597 + 0.232500i 0.655614 0.755096i \(-0.272410\pi\)
−0.157017 + 0.987596i \(0.550188\pi\)
\(744\) −16.5081 + 12.4315i −0.605218 + 0.455760i
\(745\) −47.3503 6.68242i −1.73478 0.244825i
\(746\) 5.41614 3.88624i 0.198299 0.142285i
\(747\) 1.57556 + 1.10322i 0.0576467 + 0.0403646i
\(748\) −5.97328 + 6.25529i −0.218405 + 0.228716i
\(749\) −22.0611 12.7370i −0.806094 0.465399i
\(750\) −0.786191 28.8363i −0.0287076 1.05295i
\(751\) −8.28994 + 22.7764i −0.302504 + 0.831124i 0.691559 + 0.722320i \(0.256924\pi\)
−0.994063 + 0.108804i \(0.965298\pi\)
\(752\) 22.2513 24.4044i 0.811422 0.889935i
\(753\) 2.33170 + 0.624777i 0.0849719 + 0.0227681i
\(754\) −0.462751 + 6.09822i −0.0168524 + 0.222084i
\(755\) 1.00937 + 29.3890i 0.0367346 + 1.06957i
\(756\) −35.3224 + 7.07164i −1.28466 + 0.257193i
\(757\) 4.47980 3.13679i 0.162821 0.114009i −0.489326 0.872101i \(-0.662757\pi\)
0.652147 + 0.758092i \(0.273868\pi\)
\(758\) 9.02660 11.0129i 0.327861 0.400005i
\(759\) −7.68961 −0.279115
\(760\) −19.7665 19.2169i −0.717005 0.697069i
\(761\) −18.2163 −0.660340 −0.330170 0.943922i \(-0.607106\pi\)
−0.330170 + 0.943922i \(0.607106\pi\)
\(762\) −32.7507 + 39.9574i −1.18643 + 1.44750i
\(763\) 38.3780 26.8725i 1.38938 0.972851i
\(764\) −18.1171 + 3.62710i −0.655455 + 0.131224i
\(765\) 1.49638 1.60282i 0.0541016 0.0579501i
\(766\) 0.890387 11.7337i 0.0321710 0.423956i
\(767\) −15.3944 4.12492i −0.555859 0.148942i
\(768\) 4.92625 28.7725i 0.177761 1.03824i
\(769\) −16.8252 + 46.2269i −0.606733 + 1.66699i 0.130583 + 0.991437i \(0.458315\pi\)
−0.737316 + 0.675548i \(0.763907\pi\)
\(770\) 16.7861 2.24798i 0.604930 0.0810115i
\(771\) 2.76681 + 1.59742i 0.0996443 + 0.0575297i
\(772\) −0.678794 + 0.710841i −0.0244303 + 0.0255837i
\(773\) −14.0033 9.80524i −0.503665 0.352670i 0.293966 0.955816i \(-0.405025\pi\)
−0.797631 + 0.603146i \(0.793914\pi\)
\(774\) −3.52325 + 2.52803i −0.126640 + 0.0908683i
\(775\) 16.6130 11.1778i 0.596757 0.401520i
\(776\) 14.7734 + 19.6180i 0.530333 + 0.704245i
\(777\) 23.2852 + 10.8581i 0.835352 + 0.389531i
\(778\) −1.80433 3.04361i −0.0646884 0.109119i
\(779\) −17.4091 + 32.5483i −0.623746 + 1.16616i
\(780\) −3.28817 13.9228i −0.117735 0.498516i
\(781\) −3.65902 + 1.33177i −0.130930 + 0.0476546i
\(782\) 11.4846 4.33063i 0.410688 0.154863i
\(783\) −11.9752 1.04769i −0.427958 0.0374415i
\(784\) −26.4107 3.41037i −0.943238 0.121799i
\(785\) 3.53058 + 28.8916i 0.126012 + 1.03118i
\(786\) 37.8492 10.6108i 1.35004 0.378475i
\(787\) 11.5885 + 43.2488i 0.413084 + 1.54165i 0.788642 + 0.614853i \(0.210785\pi\)
−0.375558 + 0.926799i \(0.622549\pi\)
\(788\) −38.0939 2.44934i −1.35704 0.0872542i
\(789\) −3.54026 + 9.72679i −0.126037 + 0.346283i
\(790\) 15.7918 + 17.1569i 0.561847 + 0.610414i
\(791\) −18.1838 + 10.4984i −0.646540 + 0.373280i
\(792\) 1.31761 0.279626i 0.0468193 0.00993606i
\(793\) −17.8712 + 1.56352i −0.634623 + 0.0555223i
\(794\) −47.4775 + 22.8091i −1.68491 + 0.809466i
\(795\) −29.0203 46.5016i −1.02924 1.64924i
\(796\) −3.62743 + 23.7639i −0.128571 + 0.842289i
\(797\) 34.7672 + 34.7672i 1.23152 + 1.23152i 0.963381 + 0.268137i \(0.0864079\pi\)
0.268137 + 0.963381i \(0.413592\pi\)
\(798\) −25.2908 + 32.9829i −0.895284 + 1.16758i
\(799\) −24.6384 −0.871645
\(800\) −6.24860 + 27.5854i −0.220921 + 0.975292i
\(801\) 0.153954 0.873115i 0.00543969 0.0308500i
\(802\) 7.65492 21.8109i 0.270305 0.770169i
\(803\) −0.977596 11.1740i −0.0344986 0.394321i
\(804\) 10.1620 + 3.43549i 0.358387 + 0.121160i
\(805\) −22.8530 7.43992i −0.805462 0.262223i
\(806\) 6.94015 7.10205i 0.244456 0.250159i
\(807\) 1.17398 0.547434i 0.0413259 0.0192706i
\(808\) −14.9701 + 46.0230i −0.526645 + 1.61908i
\(809\) −21.9850 12.6931i −0.772953 0.446265i 0.0609740 0.998139i \(-0.480579\pi\)
−0.833927 + 0.551875i \(0.813913\pi\)
\(810\) 30.4809 6.82872i 1.07099 0.239937i
\(811\) −39.6787 + 6.99643i −1.39331 + 0.245678i −0.819391 0.573235i \(-0.805688\pi\)
−0.573918 + 0.818913i \(0.694577\pi\)
\(812\) −16.6951 7.32132i −0.585884 0.256928i
\(813\) −0.0592450 + 0.677173i −0.00207781 + 0.0237495i
\(814\) 7.11546 + 3.21865i 0.249397 + 0.112814i
\(815\) −4.87543 + 1.48751i −0.170779 + 0.0521050i
\(816\) −18.3381 + 11.7467i −0.641961 + 0.411218i
\(817\) 9.24691 39.6079i 0.323508 1.38570i
\(818\) 13.0720 + 22.0503i 0.457052 + 0.770972i
\(819\) −2.00088 + 0.728260i −0.0699164 + 0.0254475i
\(820\) 37.8082 2.17216i 1.32032 0.0758551i
\(821\) 22.8216 19.1496i 0.796479 0.668325i −0.150861 0.988555i \(-0.548204\pi\)
0.947340 + 0.320230i \(0.103760\pi\)
\(822\) 8.00533 48.6754i 0.279218 1.69775i
\(823\) −15.2466 + 21.7744i −0.531463 + 0.759008i −0.991670 0.128804i \(-0.958886\pi\)
0.460207 + 0.887812i \(0.347775\pi\)
\(824\) −6.06486 1.40223i −0.211279 0.0488490i
\(825\) −13.0595 + 2.05302i −0.454672 + 0.0714771i
\(826\) 26.7982 39.2266i 0.932428 1.36487i
\(827\) 6.73479 3.14049i 0.234192 0.109205i −0.301980 0.953314i \(-0.597648\pi\)
0.536172 + 0.844109i \(0.319870\pi\)
\(828\) −1.85723 0.452019i −0.0645431 0.0157087i
\(829\) 20.7120 11.9581i 0.719358 0.415321i −0.0951585 0.995462i \(-0.530336\pi\)
0.814516 + 0.580141i \(0.197002\pi\)
\(830\) 11.3003 + 14.6592i 0.392240 + 0.508827i
\(831\) 24.8604 29.6275i 0.862398 1.02777i
\(832\) −0.253789 + 14.0244i −0.00879854 + 0.486209i
\(833\) 11.3952 + 16.2741i 0.394821 + 0.563863i
\(834\) 39.0578 3.87133i 1.35246 0.134053i
\(835\) −0.586976 + 11.0783i −0.0203132 + 0.383380i
\(836\) −7.57141 + 10.1136i −0.261863 + 0.349786i
\(837\) 13.8013 + 13.8013i 0.477044 + 0.477044i
\(838\) 23.4258 28.5805i 0.809230 0.987298i
\(839\) −1.03851 + 5.88969i −0.0358534 + 0.203335i −0.997473 0.0710531i \(-0.977364\pi\)
0.961619 + 0.274388i \(0.0884751\pi\)
\(840\) 42.4053 + 4.49537i 1.46312 + 0.155105i
\(841\) 17.5552 + 14.7306i 0.605353 + 0.507951i
\(842\) −4.97599 5.79318i −0.171484 0.199646i
\(843\) 8.82150 32.9223i 0.303828 1.13390i
\(844\) −38.2491 + 23.2751i −1.31659 + 0.801162i
\(845\) −8.30247 20.5834i −0.285614 0.708091i
\(846\) 3.16824 + 2.16442i 0.108926 + 0.0744144i
\(847\) 8.51264 + 31.7696i 0.292498 + 1.09162i
\(848\) 16.2885 + 51.2169i 0.559348 + 1.75880i
\(849\) 4.70849 0.830233i 0.161595 0.0284935i
\(850\) 18.3483 10.4210i 0.629343 0.357439i
\(851\) −7.12365 8.48964i −0.244196 0.291021i
\(852\) −9.74467 + 1.07945i −0.333847 + 0.0369815i
\(853\) −14.0027 + 30.0288i −0.479442 + 1.02817i 0.506678 + 0.862135i \(0.330873\pi\)
−0.986120 + 0.166032i \(0.946904\pi\)
\(854\) 13.2437 51.8080i 0.453190 1.77283i
\(855\) 1.89048 2.58549i 0.0646532 0.0884218i
\(856\) −14.2545 13.3011i −0.487210 0.454623i
\(857\) −48.6348 22.6788i −1.66133 0.774693i −0.999691 0.0248748i \(-0.992081\pi\)
−0.661644 0.749818i \(-0.730141\pi\)
\(858\) −6.13434 + 2.31315i −0.209423 + 0.0789696i
\(859\) 11.8249 9.92228i 0.403461 0.338544i −0.418369 0.908277i \(-0.637398\pi\)
0.821829 + 0.569734i \(0.192954\pi\)
\(860\) −39.6218 + 13.0946i −1.35109 + 0.446521i
\(861\) −9.91456 56.2283i −0.337887 1.91625i
\(862\) 12.6061 22.4276i 0.429366 0.763888i
\(863\) 5.78423 1.54988i 0.196898 0.0527586i −0.159022 0.987275i \(-0.550834\pi\)
0.355920 + 0.934516i \(0.384168\pi\)
\(864\) −27.5583 0.816597i −0.937554 0.0277812i
\(865\) 18.7302 44.0551i 0.636845 1.49792i
\(866\) −3.88047 3.79201i −0.131864 0.128858i
\(867\) −14.2653 3.82239i −0.484476 0.129815i
\(868\) 13.1244 + 26.5307i 0.445472 + 0.900509i
\(869\) 6.86891 8.18604i 0.233012 0.277693i
\(870\) 13.1588 + 5.41624i 0.446124 + 0.183628i
\(871\) −5.07617 0.895065i −0.171999 0.0303281i
\(872\) 33.2506 13.4217i 1.12601 0.454517i
\(873\) −2.01755 + 2.01755i −0.0682838 + 0.0682838i
\(874\) 15.8998 8.28381i 0.537818 0.280204i
\(875\) −40.7982 6.53396i −1.37923 0.220888i
\(876\) 4.26168 27.9189i 0.143989 0.943293i
\(877\) 21.5291 15.0749i 0.726987 0.509042i −0.150519 0.988607i \(-0.548095\pi\)
0.877506 + 0.479565i \(0.159206\pi\)
\(878\) 15.2602 43.4803i 0.515007 1.46739i
\(879\) 38.0574 + 31.9339i 1.28364 + 1.07711i
\(880\) 12.9046 + 1.21774i 0.435014 + 0.0410501i
\(881\) 12.2079 + 21.1447i 0.411294 + 0.712382i 0.995032 0.0995603i \(-0.0317436\pi\)
−0.583737 + 0.811942i \(0.698410\pi\)
\(882\) −0.0356681 3.09371i −0.00120101 0.104171i
\(883\) 4.72937 + 10.1422i 0.159156 + 0.341311i 0.969674 0.244403i \(-0.0785920\pi\)
−0.810518 + 0.585714i \(0.800814\pi\)
\(884\) 7.85904 6.90947i 0.264328 0.232391i
\(885\) −20.2145 + 31.0884i −0.679502 + 1.04503i
\(886\) 8.03081 + 28.6462i 0.269800 + 0.962389i
\(887\) 0.599872 + 0.420035i 0.0201417 + 0.0141034i 0.583604 0.812038i \(-0.301642\pi\)
−0.563462 + 0.826142i \(0.690531\pi\)
\(888\) 15.4913 + 12.1111i 0.519854 + 0.406422i
\(889\) 47.5661 + 56.6870i 1.59531 + 1.90122i
\(890\) 3.92264 7.57648i 0.131487 0.253964i
\(891\) −4.89597 13.4516i −0.164021 0.450645i
\(892\) −24.1856 + 7.08204i −0.809795 + 0.237124i
\(893\) −35.7313 + 4.29803i −1.19570 + 0.143828i
\(894\) −13.6658 + 53.4591i −0.457051 + 1.78794i
\(895\) 4.90829 9.21835i 0.164066 0.308136i
\(896\) −39.1947 14.5578i −1.30940 0.486343i
\(897\) 9.26807 + 0.810851i 0.309452 + 0.0270735i
\(898\) −0.858519 + 5.22012i −0.0286491 + 0.174198i
\(899\) 1.71517 + 9.72721i 0.0572041 + 0.324421i
\(900\) −3.27486 0.271820i −0.109162 0.00906067i
\(901\) 20.0478 34.7238i 0.667889 1.15682i
\(902\) −3.21051 17.0555i −0.106898 0.567887i
\(903\) 26.5885 + 57.0193i 0.884811 + 1.89748i
\(904\) −15.3692 + 4.69345i −0.511172 + 0.156102i
\(905\) −7.03137 2.28910i −0.233731 0.0760923i
\(906\) 33.8341 + 2.56743i 1.12406 + 0.0852972i
\(907\) 35.7252 3.12555i 1.18624 0.103782i 0.523093 0.852275i \(-0.324778\pi\)
0.663143 + 0.748493i \(0.269222\pi\)
\(908\) −36.7525 24.4913i −1.21968 0.812774i
\(909\) −5.53737 0.976388i −0.183663 0.0323847i
\(910\) −20.4689 + 0.939369i −0.678537 + 0.0311398i
\(911\) 36.9833i 1.22531i −0.790350 0.612656i \(-0.790101\pi\)
0.790350 0.612656i \(-0.209899\pi\)
\(912\) −24.5452 + 20.2344i −0.812773 + 0.670027i
\(913\) 5.99786 5.99786i 0.198500 0.198500i
\(914\) −39.2531 + 3.89068i −1.29838 + 0.128692i
\(915\) −9.41298 + 40.6654i −0.311183 + 1.34436i
\(916\) 11.1416 2.23057i 0.368127 0.0737000i
\(917\) −4.90705 56.0878i −0.162045 1.85218i
\(918\) 13.4020 + 15.6030i 0.442333 + 0.514976i
\(919\) −2.68819 4.65609i −0.0886753 0.153590i 0.818276 0.574825i \(-0.194930\pi\)
−0.906951 + 0.421235i \(0.861597\pi\)
\(920\) −15.7583 9.48776i −0.519536 0.312802i
\(921\) 34.8921 + 12.6997i 1.14973 + 0.418469i
\(922\) 16.1315 3.03658i 0.531263 0.100004i
\(923\) 4.55055 1.21932i 0.149783 0.0401343i
\(924\) −0.450551 19.5369i −0.0148220 0.642718i
\(925\) −14.3649 12.5163i −0.472315 0.411532i
\(926\) 25.5708 + 35.6373i 0.840308 + 1.17111i
\(927\) 0.0630324 0.720463i 0.00207025 0.0236631i
\(928\) −11.1870 8.33768i −0.367230 0.273698i
\(929\) −5.34036 14.6725i −0.175212 0.481390i 0.820738 0.571305i \(-0.193563\pi\)
−0.995949 + 0.0899151i \(0.971340\pi\)
\(930\) −10.7142 20.4703i −0.351331 0.671247i
\(931\) 19.3646 + 21.6132i 0.634648 + 0.708346i
\(932\) 9.47052 + 32.3424i 0.310217 + 1.05941i
\(933\) −13.0090 + 27.8979i −0.425896 + 0.913338i
\(934\) −35.0372 15.8490i −1.14645 0.518594i
\(935\) −5.81518 7.72624i −0.190177 0.252675i
\(936\) −1.61757 + 0.198086i −0.0528718 + 0.00647465i
\(937\) −31.7236 + 45.3060i −1.03636 + 1.48008i −0.166970 + 0.985962i \(0.553398\pi\)
−0.869394 + 0.494119i \(0.835491\pi\)
\(938\) 7.52835 13.3937i 0.245809 0.437321i
\(939\) −11.7675 + 20.3819i −0.384019 + 0.665140i
\(940\) 22.8786 + 28.9817i 0.746218 + 0.945277i
\(941\) 46.7746 + 17.0246i 1.52481 + 0.554985i 0.962344 0.271835i \(-0.0876306\pi\)
0.562466 + 0.826821i \(0.309853\pi\)
\(942\) 33.5832 0.387189i 1.09420 0.0126153i
\(943\) −6.37427 + 23.7891i −0.207575 + 0.774679i
\(944\) 26.7457 24.6303i 0.870498 0.801647i
\(945\) −1.38245 40.2516i −0.0449710 1.30938i
\(946\) 8.28124 + 17.2375i 0.269246 + 0.560440i
\(947\) −20.6761 29.5285i −0.671883 0.959548i −0.999889 0.0148728i \(-0.995266\pi\)
0.328006 0.944675i \(-0.393623\pi\)
\(948\) 21.6788 15.9370i 0.704096 0.517609i
\(949\) 13.5708i 0.440526i
\(950\) 24.7913 18.3136i 0.804337 0.594173i
\(951\) 63.2525i 2.05110i
\(952\) 11.6757 + 28.9250i 0.378411 + 0.937466i
\(953\) 6.74982 + 9.63975i 0.218648 + 0.312262i 0.913459 0.406930i \(-0.133401\pi\)
−0.694811 + 0.719192i \(0.744512\pi\)
\(954\) −5.62833 + 2.70396i −0.182224 + 0.0875439i
\(955\) −0.709067 20.6453i −0.0229449 0.668068i
\(956\) 20.7352 + 7.00998i 0.670625 + 0.226719i
\(957\) 1.68780 6.29896i 0.0545589 0.203617i
\(958\) −0.559989 48.5713i −0.0180924 1.56927i
\(959\) −66.3942 24.1655i −2.14398 0.780345i
\(960\) 30.8457 + 10.6630i 0.995540 + 0.344147i
\(961\) −7.48127 + 12.9579i −0.241331 + 0.417998i
\(962\) −8.23667 4.62966i −0.265561 0.149266i
\(963\) 1.29923 1.85549i 0.0418671 0.0597924i
\(964\) 26.1512 10.2070i 0.842272 0.328745i
\(965\) −0.660827 0.877997i −0.0212728 0.0282637i
\(966\) −11.4295 + 25.2671i −0.367737 + 0.812955i
\(967\) −5.15104 + 11.0464i −0.165646 + 0.355229i −0.971556 0.236808i \(-0.923899\pi\)
0.805910 + 0.592038i \(0.201676\pi\)
\(968\) 0.870449 + 25.1575i 0.0279773 + 0.808594i
\(969\) 23.4926 + 3.36064i 0.754691 + 0.107959i
\(970\) −24.3265 + 12.7325i −0.781078 + 0.408817i
\(971\) −2.96300 8.14078i −0.0950872 0.261250i 0.883026 0.469325i \(-0.155503\pi\)
−0.978113 + 0.208075i \(0.933280\pi\)
\(972\) −0.748726 6.75906i −0.0240154 0.216797i
\(973\) 4.89966 56.0033i 0.157076 1.79538i
\(974\) −31.0358 + 22.2691i −0.994452 + 0.713548i
\(975\) 15.9567 1.09736i 0.511023 0.0351438i
\(976\) 18.8075 36.3488i 0.602014 1.16350i
\(977\) −1.33905 + 0.358797i −0.0428399 + 0.0114789i −0.280175 0.959949i \(-0.590393\pi\)
0.237335 + 0.971428i \(0.423726\pi\)
\(978\) 1.08805 + 5.78018i 0.0347921 + 0.184830i
\(979\) −3.67407 1.33725i −0.117424 0.0427387i
\(980\) 8.56153 28.5156i 0.273488 0.910899i
\(981\) 2.08298 + 3.60783i 0.0665045 + 0.115189i
\(982\) −26.8259 + 23.0418i −0.856050 + 0.735294i
\(983\) −0.667009 7.62395i −0.0212743 0.243166i −0.999385 0.0350789i \(-0.988832\pi\)
0.978110 0.208087i \(-0.0667238\pi\)
\(984\) 2.30097 43.6375i 0.0733522 1.39111i
\(985\) 9.62443 41.5789i 0.306660 1.32481i
\(986\) 1.02668 + 10.3582i 0.0326961 + 0.329871i
\(987\) 39.3635 39.3635i 1.25295 1.25295i
\(988\) 10.1921 11.3913i 0.324253 0.362404i
\(989\) 27.1379i 0.862936i
\(990\) 0.0690388 + 1.50436i 0.00219420 + 0.0478117i
\(991\) 2.84862 + 0.502288i 0.0904893 + 0.0159557i 0.218709 0.975790i \(-0.429815\pi\)
−0.128220 + 0.991746i \(0.540926\pi\)
\(992\) 5.21257 + 22.0460i 0.165499 + 0.699963i
\(993\) 41.5381 3.63411i 1.31817 0.115325i
\(994\) −1.06256 + 14.0026i −0.0337022 + 0.444134i
\(995\) −25.5564 8.32002i −0.810191 0.263762i
\(996\) 18.2449 11.1023i 0.578112 0.351789i
\(997\) 12.6561 + 27.1411i 0.400823 + 0.859568i 0.998334 + 0.0577069i \(0.0183789\pi\)
−0.597510 + 0.801861i \(0.703843\pi\)
\(998\) 7.75589 1.45996i 0.245508 0.0462142i
\(999\) 9.28594 16.0837i 0.293794 0.508867i
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 380.2.bj.a.347.41 yes 672
4.3 odd 2 inner 380.2.bj.a.347.27 yes 672
5.3 odd 4 inner 380.2.bj.a.43.13 yes 672
19.4 even 9 inner 380.2.bj.a.327.54 yes 672
20.3 even 4 inner 380.2.bj.a.43.54 yes 672
76.23 odd 18 inner 380.2.bj.a.327.13 yes 672
95.23 odd 36 inner 380.2.bj.a.23.27 672
380.23 even 36 inner 380.2.bj.a.23.41 yes 672
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.bj.a.23.27 672 95.23 odd 36 inner
380.2.bj.a.23.41 yes 672 380.23 even 36 inner
380.2.bj.a.43.13 yes 672 5.3 odd 4 inner
380.2.bj.a.43.54 yes 672 20.3 even 4 inner
380.2.bj.a.327.13 yes 672 76.23 odd 18 inner
380.2.bj.a.327.54 yes 672 19.4 even 9 inner
380.2.bj.a.347.27 yes 672 4.3 odd 2 inner
380.2.bj.a.347.41 yes 672 1.1 even 1 trivial