Properties

Label 845.2.bn.a.392.19
Level $845$
Weight $2$
Character 845.392
Analytic conductor $6.747$
Analytic rank $0$
Dimension $4272$
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] = [845,2,Mod(2,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(156))
 
chi = DirichletCharacter(H, H._module([39, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.bn (of order \(156\), degree \(48\), 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: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(4272\)
Relative dimension: \(89\) over \(\Q(\zeta_{156})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{156}]$

Embedding invariants

Embedding label 392.19
Character \(\chi\) \(=\) 845.392
Dual form 845.2.bn.a.748.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.763701 + 1.60947i) q^{2} +(-1.71534 - 1.58244i) q^{3} +(-0.742252 - 0.909094i) q^{4} +(1.90667 - 1.16816i) q^{5} +(3.85690 - 1.55227i) q^{6} +(1.61755 + 0.468530i) q^{7} +(-1.42939 + 0.352312i) q^{8} +(0.196863 + 2.43858i) q^{9} +O(q^{10})\) \(q+(-0.763701 + 1.60947i) q^{2} +(-1.71534 - 1.58244i) q^{3} +(-0.742252 - 0.909094i) q^{4} +(1.90667 - 1.16816i) q^{5} +(3.85690 - 1.55227i) q^{6} +(1.61755 + 0.468530i) q^{7} +(-1.42939 + 0.352312i) q^{8} +(0.196863 + 2.43858i) q^{9} +(0.423992 + 3.96085i) q^{10} +(2.48211 + 2.91806i) q^{11} +(-0.165375 + 2.73398i) q^{12} +(-2.49301 + 2.60479i) q^{13} +(-1.98941 + 2.24558i) q^{14} +(-5.11914 - 1.01340i) q^{15} +(0.994099 - 4.86942i) q^{16} +(-0.609296 - 1.10619i) q^{17} +(-4.07517 - 1.54551i) q^{18} +(1.18800 - 0.318323i) q^{19} +(-2.47720 - 0.866271i) q^{20} +(-2.03323 - 3.36338i) q^{21} +(-6.59211 + 1.76635i) q^{22} +(0.380164 - 1.41879i) q^{23} +(3.00940 + 1.65759i) q^{24} +(2.27079 - 4.45461i) q^{25} +(-2.28840 - 6.00169i) q^{26} +(-0.796618 + 1.01681i) q^{27} +(-0.774694 - 1.81827i) q^{28} +(4.06101 + 1.92697i) q^{29} +(5.54053 - 7.46515i) q^{30} +(0.653009 + 0.511600i) q^{31} +(4.72415 + 3.54997i) q^{32} +(0.359998 - 8.93326i) q^{33} +(2.24570 - 0.135840i) q^{34} +(3.63146 - 0.996233i) q^{35} +(2.07078 - 1.98901i) q^{36} +(6.04609 + 8.04588i) q^{37} +(-0.394945 + 2.15514i) q^{38} +(8.39828 - 0.523049i) q^{39} +(-2.31381 + 2.34150i) q^{40} +(6.18381 + 5.70472i) q^{41} +(6.96602 - 0.703803i) q^{42} +(-0.524541 - 3.69629i) q^{43} +(0.810436 - 4.42240i) q^{44} +(3.22402 + 4.41961i) q^{45} +(1.99316 + 1.69539i) q^{46} +(2.21178 - 0.838818i) q^{47} +(-9.41080 + 6.77960i) q^{48} +(-3.51937 - 2.22552i) q^{49} +(5.43533 + 7.05675i) q^{50} +(-0.705339 + 2.86167i) q^{51} +(4.21843 + 0.332970i) q^{52} +(4.17581 - 6.90763i) q^{53} +(-1.02814 - 2.05867i) q^{54} +(8.14133 + 2.66427i) q^{55} +(-2.47718 - 0.0998268i) q^{56} +(-2.54155 - 1.33391i) q^{57} +(-6.20279 + 5.06442i) q^{58} +(2.56989 + 1.69849i) q^{59} +(2.87841 + 5.40598i) q^{60} +(3.15664 - 3.28641i) q^{61} +(-1.32211 + 0.660287i) q^{62} +(-0.824114 + 4.03678i) q^{63} +(-0.520214 + 0.273029i) q^{64} +(-1.71053 + 7.87871i) q^{65} +(14.1028 + 7.40175i) q^{66} +(-3.83788 + 4.70055i) q^{67} +(-0.553382 + 1.37498i) q^{68} +(-2.89727 + 1.83212i) q^{69} +(-1.16995 + 6.60554i) q^{70} +(-1.75334 + 7.78507i) q^{71} +(-1.14054 - 3.41632i) q^{72} +(0.241133 - 0.349342i) q^{73} +(-17.5670 + 3.58633i) q^{74} +(-10.9443 + 4.04776i) q^{75} +(-1.17118 - 0.843724i) q^{76} +(2.64775 + 5.88306i) q^{77} +(-5.57195 + 13.9162i) q^{78} +(-0.554684 + 0.210364i) q^{79} +(-3.79285 - 10.4456i) q^{80} +(10.2200 - 1.66091i) q^{81} +(-13.9041 + 5.59593i) q^{82} +(4.11957 + 7.84919i) q^{83} +(-1.54845 + 4.34487i) q^{84} +(-2.45394 - 1.39739i) q^{85} +(6.34965 + 1.97863i) q^{86} +(-3.91668 - 9.73172i) q^{87} +(-4.57596 - 3.29655i) q^{88} +(13.4086 + 3.59282i) q^{89} +(-9.57540 + 1.81368i) q^{90} +(-5.25299 + 3.04533i) q^{91} +(-1.57199 + 0.707496i) q^{92} +(-0.310555 - 1.91092i) q^{93} +(-0.339091 + 4.20040i) q^{94} +(1.89327 - 1.99471i) q^{95} +(-2.48590 - 13.5651i) q^{96} +(2.88743 - 0.963965i) q^{97} +(6.26964 - 3.96468i) q^{98} +(-6.62729 + 6.62729i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4272 q - 48 q^{2} - 50 q^{3} + 174 q^{4} - 46 q^{5} - 96 q^{6} - 46 q^{7} - 64 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4272 q - 48 q^{2} - 50 q^{3} + 174 q^{4} - 46 q^{5} - 96 q^{6} - 46 q^{7} - 64 q^{8} + 12 q^{9} - 42 q^{10} - 88 q^{11} - 60 q^{12} - 54 q^{13} + 40 q^{15} + 66 q^{16} - 42 q^{17} - 52 q^{18} - 20 q^{19} - 66 q^{20} - 108 q^{21} - 34 q^{22} - 80 q^{23} + 32 q^{24} - 42 q^{25} - 80 q^{26} - 32 q^{27} - 58 q^{28} + 246 q^{30} - 104 q^{31} - 46 q^{32} - 34 q^{33} + 2 q^{34} - 20 q^{35} - 140 q^{36} - 94 q^{37} - 8 q^{38} + 4 q^{39} - 20 q^{40} - 114 q^{41} - 528 q^{42} - 42 q^{43} - 36 q^{44} + 26 q^{45} - 108 q^{46} - 182 q^{47} - 96 q^{48} + 14 q^{49} - 96 q^{50} - 104 q^{51} - 98 q^{52} - 206 q^{53} - 48 q^{54} - 338 q^{55} - 104 q^{56} - 118 q^{57} + 38 q^{58} + 400 q^{59} - 168 q^{60} - 96 q^{61} - 24 q^{62} - 150 q^{63} - 316 q^{64} - 60 q^{65} - 104 q^{66} - 202 q^{67} - 80 q^{68} - 8 q^{69} + 124 q^{70} - 88 q^{71} + 14 q^{72} - 124 q^{73} + 148 q^{74} + 180 q^{75} - 40 q^{76} - 48 q^{77} - 84 q^{78} - 18 q^{80} - 242 q^{81} - 82 q^{82} - 572 q^{83} - 40 q^{84} - 46 q^{85} - 164 q^{86} + 110 q^{87} + 298 q^{88} - 6 q^{89} - 70 q^{90} - 112 q^{91} + 92 q^{92} - 100 q^{93} + 56 q^{94} - 62 q^{95} - 160 q^{96} + 126 q^{97} - 56 q^{98} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{61}{156}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.763701 + 1.60947i −0.540018 + 1.13806i 0.431721 + 0.902007i \(0.357907\pi\)
−0.971739 + 0.236057i \(0.924145\pi\)
\(3\) −1.71534 1.58244i −0.990352 0.913624i 0.00591228 0.999983i \(-0.498118\pi\)
−0.996264 + 0.0863583i \(0.972477\pi\)
\(4\) −0.742252 0.909094i −0.371126 0.454547i
\(5\) 1.90667 1.16816i 0.852689 0.522418i
\(6\) 3.85690 1.55227i 1.57457 0.633711i
\(7\) 1.61755 + 0.468530i 0.611378 + 0.177088i 0.569441 0.822033i \(-0.307160\pi\)
0.0419372 + 0.999120i \(0.486647\pi\)
\(8\) −1.42939 + 0.352312i −0.505364 + 0.124561i
\(9\) 0.196863 + 2.43858i 0.0656210 + 0.812862i
\(10\) 0.423992 + 3.96085i 0.134078 + 1.25253i
\(11\) 2.48211 + 2.91806i 0.748384 + 0.879827i 0.996030 0.0890236i \(-0.0283746\pi\)
−0.247645 + 0.968851i \(0.579657\pi\)
\(12\) −0.165375 + 2.73398i −0.0477397 + 0.789231i
\(13\) −2.49301 + 2.60479i −0.691436 + 0.722438i
\(14\) −1.98941 + 2.24558i −0.531692 + 0.600157i
\(15\) −5.11914 1.01340i −1.32176 0.261660i
\(16\) 0.994099 4.86942i 0.248525 1.21735i
\(17\) −0.609296 1.10619i −0.147776 0.268291i 0.791697 0.610914i \(-0.209198\pi\)
−0.939473 + 0.342622i \(0.888685\pi\)
\(18\) −4.07517 1.54551i −0.960526 0.364279i
\(19\) 1.18800 0.318323i 0.272545 0.0730283i −0.119958 0.992779i \(-0.538276\pi\)
0.392503 + 0.919751i \(0.371609\pi\)
\(20\) −2.47720 0.866271i −0.553919 0.193704i
\(21\) −2.03323 3.36338i −0.443687 0.733949i
\(22\) −6.59211 + 1.76635i −1.40544 + 0.376587i
\(23\) 0.380164 1.41879i 0.0792696 0.295838i −0.914898 0.403685i \(-0.867729\pi\)
0.994167 + 0.107847i \(0.0343957\pi\)
\(24\) 3.00940 + 1.65759i 0.614290 + 0.338354i
\(25\) 2.27079 4.45461i 0.454158 0.890921i
\(26\) −2.28840 6.00169i −0.448793 1.17703i
\(27\) −0.796618 + 1.01681i −0.153309 + 0.195685i
\(28\) −0.774694 1.81827i −0.146403 0.343622i
\(29\) 4.06101 + 1.92697i 0.754110 + 0.357830i 0.766628 0.642092i \(-0.221933\pi\)
−0.0125177 + 0.999922i \(0.503985\pi\)
\(30\) 5.54053 7.46515i 1.01156 1.36294i
\(31\) 0.653009 + 0.511600i 0.117284 + 0.0918861i 0.673647 0.739053i \(-0.264727\pi\)
−0.556363 + 0.830939i \(0.687804\pi\)
\(32\) 4.72415 + 3.54997i 0.835119 + 0.627551i
\(33\) 0.359998 8.93326i 0.0626676 1.55508i
\(34\) 2.24570 0.135840i 0.385134 0.0232963i
\(35\) 3.63146 0.996233i 0.613829 0.168394i
\(36\) 2.07078 1.98901i 0.345130 0.331502i
\(37\) 6.04609 + 8.04588i 0.993971 + 1.32273i 0.946098 + 0.323881i \(0.104988\pi\)
0.0478731 + 0.998853i \(0.484756\pi\)
\(38\) −0.394945 + 2.15514i −0.0640685 + 0.349611i
\(39\) 8.39828 0.523049i 1.34480 0.0837548i
\(40\) −2.31381 + 2.34150i −0.365846 + 0.370223i
\(41\) 6.18381 + 5.70472i 0.965749 + 0.890927i 0.994078 0.108671i \(-0.0346596\pi\)
−0.0283288 + 0.999599i \(0.509019\pi\)
\(42\) 6.96602 0.703803i 1.07488 0.108599i
\(43\) −0.524541 3.69629i −0.0799918 0.563679i −0.989114 0.147150i \(-0.952990\pi\)
0.909122 0.416529i \(-0.136754\pi\)
\(44\) 0.810436 4.42240i 0.122178 0.666702i
\(45\) 3.22402 + 4.41961i 0.480608 + 0.658837i
\(46\) 1.99316 + 1.69539i 0.293876 + 0.249972i
\(47\) 2.21178 0.838818i 0.322622 0.122354i −0.187977 0.982173i \(-0.560193\pi\)
0.510599 + 0.859819i \(0.329424\pi\)
\(48\) −9.41080 + 6.77960i −1.35833 + 0.978551i
\(49\) −3.51937 2.22552i −0.502767 0.317931i
\(50\) 5.43533 + 7.05675i 0.768672 + 0.997975i
\(51\) −0.705339 + 2.86167i −0.0987672 + 0.400714i
\(52\) 4.21843 + 0.332970i 0.584992 + 0.0461746i
\(53\) 4.17581 6.90763i 0.573591 0.948836i −0.425447 0.904984i \(-0.639883\pi\)
0.999038 0.0438525i \(-0.0139632\pi\)
\(54\) −1.02814 2.05867i −0.139912 0.280149i
\(55\) 8.14133 + 2.66427i 1.09778 + 0.359250i
\(56\) −2.47718 0.0998268i −0.331027 0.0133399i
\(57\) −2.54155 1.33391i −0.336636 0.176680i
\(58\) −6.20279 + 5.06442i −0.814466 + 0.664991i
\(59\) 2.56989 + 1.69849i 0.334571 + 0.221125i 0.707464 0.706750i \(-0.249839\pi\)
−0.372893 + 0.927874i \(0.621634\pi\)
\(60\) 2.87841 + 5.40598i 0.371602 + 0.697909i
\(61\) 3.15664 3.28641i 0.404166 0.420781i −0.487750 0.872984i \(-0.662182\pi\)
0.891915 + 0.452202i \(0.149362\pi\)
\(62\) −1.32211 + 0.660287i −0.167908 + 0.0838565i
\(63\) −0.824114 + 4.03678i −0.103829 + 0.508586i
\(64\) −0.520214 + 0.273029i −0.0650268 + 0.0341287i
\(65\) −1.71053 + 7.87871i −0.212165 + 0.977234i
\(66\) 14.1028 + 7.40175i 1.73594 + 0.911092i
\(67\) −3.83788 + 4.70055i −0.468872 + 0.574264i −0.953858 0.300258i \(-0.902927\pi\)
0.484986 + 0.874522i \(0.338825\pi\)
\(68\) −0.553382 + 1.37498i −0.0671074 + 0.166741i
\(69\) −2.89727 + 1.83212i −0.348790 + 0.220561i
\(70\) −1.16995 + 6.60554i −0.139836 + 0.789513i
\(71\) −1.75334 + 7.78507i −0.208083 + 0.923918i 0.755213 + 0.655479i \(0.227533\pi\)
−0.963297 + 0.268439i \(0.913492\pi\)
\(72\) −1.14054 3.41632i −0.134413 0.402617i
\(73\) 0.241133 0.349342i 0.0282225 0.0408874i −0.808619 0.588333i \(-0.799784\pi\)
0.836841 + 0.547446i \(0.184400\pi\)
\(74\) −17.5670 + 3.58633i −2.04212 + 0.416902i
\(75\) −10.9443 + 4.04776i −1.26374 + 0.467396i
\(76\) −1.17118 0.843724i −0.134343 0.0967818i
\(77\) 2.64775 + 5.88306i 0.301739 + 0.670436i
\(78\) −5.57195 + 13.9162i −0.630899 + 1.57570i
\(79\) −0.554684 + 0.210364i −0.0624068 + 0.0236678i −0.385611 0.922662i \(-0.626009\pi\)
0.323204 + 0.946329i \(0.395240\pi\)
\(80\) −3.79285 10.4456i −0.424054 1.16786i
\(81\) 10.2200 1.66091i 1.13556 0.184546i
\(82\) −13.9041 + 5.59593i −1.53546 + 0.617968i
\(83\) 4.11957 + 7.84919i 0.452182 + 0.861561i 0.999693 + 0.0247625i \(0.00788296\pi\)
−0.547511 + 0.836798i \(0.684425\pi\)
\(84\) −1.54845 + 4.34487i −0.168950 + 0.474064i
\(85\) −2.45394 1.39739i −0.266167 0.151568i
\(86\) 6.34965 + 1.97863i 0.684700 + 0.213361i
\(87\) −3.91668 9.73172i −0.419912 1.04335i
\(88\) −4.57596 3.29655i −0.487799 0.351414i
\(89\) 13.4086 + 3.59282i 1.42131 + 0.380838i 0.885947 0.463787i \(-0.153510\pi\)
0.535359 + 0.844625i \(0.320176\pi\)
\(90\) −9.57540 + 1.81368i −1.00934 + 0.191179i
\(91\) −5.25299 + 3.04533i −0.550663 + 0.319237i
\(92\) −1.57199 + 0.707496i −0.163891 + 0.0737615i
\(93\) −0.310555 1.91092i −0.0322030 0.198153i
\(94\) −0.339091 + 4.20040i −0.0349746 + 0.433238i
\(95\) 1.89327 1.99471i 0.194245 0.204653i
\(96\) −2.48590 13.5651i −0.253716 1.38448i
\(97\) 2.88743 0.963965i 0.293174 0.0978758i −0.166277 0.986079i \(-0.553175\pi\)
0.459451 + 0.888203i \(0.348046\pi\)
\(98\) 6.26964 3.96468i 0.633330 0.400493i
\(99\) −6.62729 + 6.62729i −0.666068 + 0.666068i
\(100\) −5.73515 + 1.24208i −0.573515 + 0.124208i
\(101\) 3.76797 + 8.84376i 0.374928 + 0.879987i 0.995404 + 0.0957624i \(0.0305289\pi\)
−0.620477 + 0.784225i \(0.713061\pi\)
\(102\) −4.06710 3.32068i −0.402703 0.328797i
\(103\) 4.86815 + 15.6225i 0.479673 + 1.53933i 0.804736 + 0.593633i \(0.202307\pi\)
−0.325062 + 0.945693i \(0.605385\pi\)
\(104\) 2.64577 4.60156i 0.259439 0.451220i
\(105\) −7.80567 4.03771i −0.761756 0.394040i
\(106\) 7.92853 + 11.9962i 0.770087 + 1.16517i
\(107\) 0.115794 + 0.231856i 0.0111942 + 0.0224144i 0.900162 0.435556i \(-0.143448\pi\)
−0.888967 + 0.457971i \(0.848576\pi\)
\(108\) 1.51566 0.0305272i 0.145845 0.00293748i
\(109\) 13.6326 10.6804i 1.30576 1.02300i 0.308338 0.951277i \(-0.400227\pi\)
0.997425 0.0717231i \(-0.0228498\pi\)
\(110\) −10.5056 + 11.0685i −1.00167 + 1.05534i
\(111\) 2.36106 23.3690i 0.224102 2.21809i
\(112\) 3.88948 7.41078i 0.367521 0.700253i
\(113\) −5.60691 6.07779i −0.527454 0.571751i 0.413406 0.910547i \(-0.364339\pi\)
−0.940860 + 0.338796i \(0.889980\pi\)
\(114\) 4.08786 3.07183i 0.382863 0.287703i
\(115\) −0.932532 3.14926i −0.0869590 0.293670i
\(116\) −1.26249 5.12213i −0.117219 0.475578i
\(117\) −6.84277 5.56663i −0.632615 0.514635i
\(118\) −4.69629 + 2.83901i −0.432328 + 0.261352i
\(119\) −0.467283 2.07480i −0.0428358 0.190197i
\(120\) 7.67426 0.354990i 0.700561 0.0324060i
\(121\) −0.589660 + 3.62833i −0.0536055 + 0.329848i
\(122\) 2.87863 + 7.59033i 0.260619 + 0.687196i
\(123\) −1.57994 19.5711i −0.142458 1.76466i
\(124\) −0.0196050 0.973383i −0.00176058 0.0874124i
\(125\) −0.874055 11.1461i −0.0781778 0.996939i
\(126\) −5.86768 4.40928i −0.522735 0.392810i
\(127\) −0.989473 9.79349i −0.0878015 0.869031i −0.938938 0.344087i \(-0.888189\pi\)
0.851136 0.524945i \(-0.175914\pi\)
\(128\) 0.433744 + 10.7632i 0.0383379 + 0.951345i
\(129\) −4.94941 + 7.17045i −0.435771 + 0.631323i
\(130\) −11.3742 8.77003i −0.997582 0.769182i
\(131\) 7.45763 + 10.8042i 0.651576 + 0.943971i 0.999978 + 0.00662552i \(0.00210898\pi\)
−0.348402 + 0.937345i \(0.613276\pi\)
\(132\) −8.38838 + 6.30346i −0.730114 + 0.548645i
\(133\) 2.07079 + 0.0417081i 0.179560 + 0.00361655i
\(134\) −4.63438 9.76676i −0.400350 0.843719i
\(135\) −0.331091 + 2.86930i −0.0284958 + 0.246950i
\(136\) 1.26064 + 1.36651i 0.108099 + 0.117178i
\(137\) 0.625600 0.832523i 0.0534486 0.0711272i −0.771927 0.635711i \(-0.780707\pi\)
0.825376 + 0.564584i \(0.190963\pi\)
\(138\) −0.736090 6.06225i −0.0626601 0.516053i
\(139\) −1.70987 5.12169i −0.145029 0.434416i 0.850817 0.525461i \(-0.176107\pi\)
−0.995847 + 0.0910457i \(0.970979\pi\)
\(140\) −3.60113 2.56188i −0.304351 0.216519i
\(141\) −5.12134 2.06116i −0.431295 0.173581i
\(142\) −11.1908 8.76741i −0.939109 0.735745i
\(143\) −13.7888 0.809372i −1.15308 0.0676831i
\(144\) 12.0702 + 1.46559i 1.00585 + 0.122132i
\(145\) 9.99402 1.06982i 0.829958 0.0888434i
\(146\) 0.378100 + 0.654889i 0.0312918 + 0.0541990i
\(147\) 2.51517 + 9.38672i 0.207447 + 0.774204i
\(148\) 2.82674 11.4685i 0.232357 0.942707i
\(149\) −2.29312 3.18309i −0.187859 0.260769i 0.706904 0.707310i \(-0.250091\pi\)
−0.894763 + 0.446541i \(0.852656\pi\)
\(150\) 1.84347 20.7058i 0.150518 1.69062i
\(151\) −6.69837 + 3.01469i −0.545105 + 0.245332i −0.664205 0.747550i \(-0.731230\pi\)
0.119100 + 0.992882i \(0.461999\pi\)
\(152\) −1.58596 + 0.873552i −0.128638 + 0.0708544i
\(153\) 2.57760 1.70359i 0.208386 0.137727i
\(154\) −11.4907 0.231435i −0.925945 0.0186496i
\(155\) 1.84271 + 0.212632i 0.148010 + 0.0170790i
\(156\) −6.70914 7.24659i −0.537161 0.580192i
\(157\) −14.6289 0.884888i −1.16752 0.0706217i −0.534782 0.844990i \(-0.679606\pi\)
−0.632735 + 0.774369i \(0.718068\pi\)
\(158\) 0.0850393 1.05340i 0.00676536 0.0838040i
\(159\) −18.0939 + 5.24095i −1.43494 + 0.415635i
\(160\) 13.1543 + 1.25004i 1.03994 + 0.0988247i
\(161\) 1.27968 2.11685i 0.100853 0.166831i
\(162\) −5.13186 + 17.7172i −0.403197 + 1.39200i
\(163\) −10.8645 4.62893i −0.850973 0.362566i −0.0779603 0.996956i \(-0.524841\pi\)
−0.773012 + 0.634391i \(0.781251\pi\)
\(164\) 0.596178 9.85600i 0.0465537 0.769624i
\(165\) −9.74910 17.4533i −0.758967 1.35874i
\(166\) −15.7791 + 0.635877i −1.22470 + 0.0493537i
\(167\) 16.8301 + 7.98599i 1.30235 + 0.617975i 0.948337 0.317264i \(-0.102764\pi\)
0.354017 + 0.935239i \(0.384816\pi\)
\(168\) 4.09123 + 4.09123i 0.315645 + 0.315645i
\(169\) −0.569823 12.9875i −0.0438325 0.999039i
\(170\) 4.12313 2.88235i 0.316230 0.221066i
\(171\) 1.01013 + 2.83437i 0.0772465 + 0.216749i
\(172\) −2.97093 + 3.22044i −0.226532 + 0.245556i
\(173\) 1.94015 19.2030i 0.147507 1.45998i −0.602272 0.798291i \(-0.705738\pi\)
0.749779 0.661688i \(-0.230160\pi\)
\(174\) 18.6541 + 1.12836i 1.41416 + 0.0855409i
\(175\) 5.76024 6.14163i 0.435433 0.464263i
\(176\) 16.6767 9.18560i 1.25705 0.692390i
\(177\) −1.72046 6.98019i −0.129318 0.524663i
\(178\) −16.0227 + 18.8368i −1.20095 + 1.41188i
\(179\) 0.776548 + 2.68095i 0.0580419 + 0.200384i 0.984299 0.176508i \(-0.0564801\pi\)
−0.926257 + 0.376892i \(0.876993\pi\)
\(180\) 1.62481 6.21140i 0.121106 0.462970i
\(181\) −10.8362 12.2316i −0.805451 0.909167i 0.191936 0.981407i \(-0.438523\pi\)
−0.997387 + 0.0722409i \(0.976985\pi\)
\(182\) −0.889641 10.7802i −0.0659445 0.799085i
\(183\) −10.6153 + 0.642105i −0.784702 + 0.0474657i
\(184\) −0.0435439 + 2.16194i −0.00321010 + 0.159380i
\(185\) 20.9268 + 8.27804i 1.53857 + 0.608613i
\(186\) 3.31273 + 0.959544i 0.242901 + 0.0703572i
\(187\) 1.71559 4.52365i 0.125457 0.330802i
\(188\) −2.40426 1.38810i −0.175349 0.101238i
\(189\) −1.76498 + 1.27150i −0.128383 + 0.0924881i
\(190\) 1.76453 + 4.57051i 0.128012 + 0.331580i
\(191\) −1.40892 + 2.44032i −0.101946 + 0.176575i −0.912486 0.409107i \(-0.865840\pi\)
0.810541 + 0.585683i \(0.199173\pi\)
\(192\) 1.32440 + 0.354871i 0.0955802 + 0.0256106i
\(193\) −4.50437 15.5509i −0.324231 1.11938i −0.942721 0.333583i \(-0.891742\pi\)
0.618489 0.785793i \(-0.287745\pi\)
\(194\) −0.653663 + 5.38340i −0.0469303 + 0.386506i
\(195\) 15.4018 10.8078i 1.10294 0.773966i
\(196\) 0.589058 + 4.85133i 0.0420756 + 0.346524i
\(197\) 10.8582 4.62626i 0.773618 0.329608i 0.0311721 0.999514i \(-0.490076\pi\)
0.742446 + 0.669906i \(0.233666\pi\)
\(198\) −5.60513 15.7277i −0.398340 1.11772i
\(199\) −23.6502 + 7.89559i −1.67652 + 0.559704i −0.986453 0.164044i \(-0.947546\pi\)
−0.690064 + 0.723748i \(0.742418\pi\)
\(200\) −1.67642 + 7.16738i −0.118541 + 0.506810i
\(201\) 14.0216 1.98981i 0.989009 0.140350i
\(202\) −17.1113 0.689564i −1.20395 0.0485175i
\(203\) 5.66605 + 5.01968i 0.397679 + 0.352313i
\(204\) 3.12507 1.48286i 0.218798 0.103821i
\(205\) 18.4545 + 3.65333i 1.28892 + 0.255159i
\(206\) −28.8616 4.09576i −2.01089 0.285365i
\(207\) 3.53468 + 0.647755i 0.245677 + 0.0450221i
\(208\) 10.2055 + 14.7289i 0.707624 + 1.02127i
\(209\) 3.87762 + 2.67653i 0.268221 + 0.185139i
\(210\) 12.4598 9.47937i 0.859805 0.654139i
\(211\) 3.15095 3.85921i 0.216920 0.265679i −0.654669 0.755916i \(-0.727192\pi\)
0.871590 + 0.490236i \(0.163089\pi\)
\(212\) −9.37918 + 1.33100i −0.644165 + 0.0914136i
\(213\) 15.3270 10.5795i 1.05019 0.724893i
\(214\) −0.461597 + 0.00929709i −0.0315541 + 0.000635536i
\(215\) −5.31800 6.43486i −0.362685 0.438854i
\(216\) 0.780441 1.73407i 0.0531023 0.117988i
\(217\) 0.816577 + 1.13350i 0.0554329 + 0.0769467i
\(218\) 6.77859 + 30.0978i 0.459104 + 2.03848i
\(219\) −0.966440 + 0.217660i −0.0653060 + 0.0147081i
\(220\) −3.62085 9.37879i −0.244118 0.632318i
\(221\) 4.40037 + 1.17066i 0.296001 + 0.0787473i
\(222\) 35.8085 + 21.6470i 2.40331 + 1.45285i
\(223\) −6.78614 + 20.3270i −0.454434 + 1.36119i 0.433471 + 0.901167i \(0.357289\pi\)
−0.887905 + 0.460027i \(0.847840\pi\)
\(224\) 5.97830 + 7.95567i 0.399442 + 0.531560i
\(225\) 11.3100 + 4.66057i 0.753998 + 0.310705i
\(226\) 14.0640 4.38252i 0.935524 0.291521i
\(227\) −7.63360 9.34947i −0.506660 0.620546i 0.456419 0.889765i \(-0.349132\pi\)
−0.963079 + 0.269219i \(0.913234\pi\)
\(228\) 0.673822 + 3.30060i 0.0446249 + 0.218587i
\(229\) 13.4266 + 17.1377i 0.887252 + 1.13249i 0.990456 + 0.137833i \(0.0440136\pi\)
−0.103204 + 0.994660i \(0.532909\pi\)
\(230\) 5.78081 + 0.904217i 0.381175 + 0.0596223i
\(231\) 4.76782 14.2814i 0.313699 0.939644i
\(232\) −6.48364 1.32364i −0.425672 0.0869015i
\(233\) 23.4492 + 7.30705i 1.53620 + 0.478701i 0.944793 0.327669i \(-0.106263\pi\)
0.591412 + 0.806369i \(0.298571\pi\)
\(234\) 14.1851 6.76197i 0.927311 0.442044i
\(235\) 3.23727 4.18307i 0.211176 0.272874i
\(236\) −0.363416 3.59697i −0.0236564 0.234143i
\(237\) 1.28436 + 0.516910i 0.0834282 + 0.0335769i
\(238\) 3.69618 + 0.832450i 0.239588 + 0.0539597i
\(239\) −18.9870 18.9870i −1.22817 1.22817i −0.964657 0.263508i \(-0.915120\pi\)
−0.263508 0.964657i \(-0.584880\pi\)
\(240\) −10.0236 + 23.9198i −0.647022 + 1.54402i
\(241\) −24.2306 12.1012i −1.56083 0.779509i −0.561964 0.827162i \(-0.689954\pi\)
−0.998864 + 0.0476531i \(0.984826\pi\)
\(242\) −5.38934 3.72000i −0.346440 0.239130i
\(243\) −16.9263 11.1869i −1.08582 0.717642i
\(244\) −5.33067 0.430336i −0.341261 0.0275494i
\(245\) −9.31005 0.132127i −0.594797 0.00844129i
\(246\) 32.7056 + 12.4036i 2.08523 + 0.790824i
\(247\) −2.13252 + 3.88806i −0.135689 + 0.247391i
\(248\) −1.11365 0.501211i −0.0707165 0.0318269i
\(249\) 5.35444 19.9830i 0.339324 1.26637i
\(250\) 18.6068 + 7.10555i 1.17680 + 0.449394i
\(251\) −5.88505 + 13.8127i −0.371461 + 0.871851i 0.624412 + 0.781095i \(0.285339\pi\)
−0.995873 + 0.0907561i \(0.971072\pi\)
\(252\) 4.28151 2.24711i 0.269710 0.141555i
\(253\) 5.08372 2.41226i 0.319611 0.151657i
\(254\) 16.5179 + 5.88678i 1.03643 + 0.369369i
\(255\) 1.99805 + 6.28022i 0.125123 + 0.393283i
\(256\) −18.7353 7.98237i −1.17096 0.498898i
\(257\) −6.49866 + 9.02082i −0.405375 + 0.562703i −0.963723 0.266903i \(-0.914000\pi\)
0.558348 + 0.829607i \(0.311435\pi\)
\(258\) −7.76074 13.4420i −0.483162 0.836862i
\(259\) 6.01013 + 15.8474i 0.373451 + 0.984711i
\(260\) 8.43213 4.29295i 0.522939 0.266238i
\(261\) −3.89962 + 10.2825i −0.241381 + 0.636468i
\(262\) −23.0845 + 3.75159i −1.42616 + 0.231774i
\(263\) 6.44929 5.48579i 0.397680 0.338268i −0.426610 0.904436i \(-0.640292\pi\)
0.824290 + 0.566167i \(0.191574\pi\)
\(264\) 2.63272 + 12.8959i 0.162033 + 0.793688i
\(265\) −0.107345 18.0486i −0.00659416 1.10872i
\(266\) −1.64859 + 3.30102i −0.101082 + 0.202398i
\(267\) −17.3148 27.3812i −1.05965 1.67570i
\(268\) 7.12191 0.435040
\(269\) 5.48738 + 8.67760i 0.334572 + 0.529083i 0.970009 0.243070i \(-0.0781544\pi\)
−0.635437 + 0.772153i \(0.719180\pi\)
\(270\) −4.36518 2.72417i −0.265657 0.165787i
\(271\) −24.9109 + 2.51684i −1.51323 + 0.152887i −0.821891 0.569645i \(-0.807081\pi\)
−0.691338 + 0.722532i \(0.742978\pi\)
\(272\) −5.99221 + 1.86725i −0.363331 + 0.113219i
\(273\) 13.8297 + 3.08879i 0.837014 + 0.186942i
\(274\) 0.862146 + 1.64268i 0.0520841 + 0.0992380i
\(275\) 18.6351 4.43053i 1.12374 0.267171i
\(276\) 3.81607 + 1.27399i 0.229700 + 0.0766853i
\(277\) 0.00621375 + 0.308510i 0.000373348 + 0.0185366i 0.999941 0.0108679i \(-0.00345943\pi\)
−0.999568 + 0.0294045i \(0.990639\pi\)
\(278\) 9.54901 + 1.15946i 0.572712 + 0.0695398i
\(279\) −1.11903 + 1.69313i −0.0669944 + 0.101365i
\(280\) −4.83978 + 2.70341i −0.289232 + 0.161560i
\(281\) 0.358937 + 1.15187i 0.0214124 + 0.0687148i 0.964809 0.262953i \(-0.0846964\pi\)
−0.943396 + 0.331668i \(0.892389\pi\)
\(282\) 7.22855 6.66851i 0.430454 0.397104i
\(283\) −9.15256 1.29884i −0.544063 0.0772081i −0.136937 0.990580i \(-0.543726\pi\)
−0.407127 + 0.913372i \(0.633469\pi\)
\(284\) 8.37878 4.18453i 0.497189 0.248306i
\(285\) −6.40411 + 0.425619i −0.379347 + 0.0252115i
\(286\) 11.8332 21.5745i 0.699712 1.27573i
\(287\) 7.32981 + 12.1250i 0.432665 + 0.715715i
\(288\) −7.72689 + 12.2191i −0.455311 + 0.720017i
\(289\) 8.23350 13.0202i 0.484323 0.765896i
\(290\) −5.91061 + 16.9021i −0.347083 + 0.992523i
\(291\) −6.47834 2.91566i −0.379767 0.170919i
\(292\) −0.496566 + 0.0400870i −0.0290594 + 0.00234591i
\(293\) −1.31319 + 1.36718i −0.0767174 + 0.0798712i −0.758455 0.651726i \(-0.774045\pi\)
0.681737 + 0.731597i \(0.261225\pi\)
\(294\) −17.0285 3.12058i −0.993120 0.181996i
\(295\) 6.88404 + 0.236418i 0.400804 + 0.0137648i
\(296\) −11.4769 9.37056i −0.667079 0.544653i
\(297\) −4.94440 + 0.199252i −0.286903 + 0.0115618i
\(298\) 6.87433 1.25977i 0.398219 0.0729763i
\(299\) 2.74790 + 4.52730i 0.158915 + 0.261821i
\(300\) 11.8033 + 6.94497i 0.681461 + 0.400968i
\(301\) 0.883350 6.22471i 0.0509155 0.358786i
\(302\) 0.263509 13.0831i 0.0151632 0.752849i
\(303\) 7.53140 21.1327i 0.432668 1.21404i
\(304\) −0.369060 6.10130i −0.0211671 0.349933i
\(305\) 2.17961 9.95356i 0.124804 0.569939i
\(306\) 0.773352 + 5.44959i 0.0442096 + 0.311532i
\(307\) −13.3665 + 1.62299i −0.762869 + 0.0926291i −0.492718 0.870189i \(-0.663997\pi\)
−0.270151 + 0.962818i \(0.587074\pi\)
\(308\) 3.38295 6.77376i 0.192762 0.385971i
\(309\) 16.3711 34.5014i 0.931320 1.96272i
\(310\) −1.74950 + 2.80339i −0.0993650 + 0.159222i
\(311\) −23.3470 + 2.83484i −1.32389 + 0.160749i −0.751771 0.659425i \(-0.770800\pi\)
−0.572115 + 0.820173i \(0.693877\pi\)
\(312\) −11.8201 + 3.70645i −0.669182 + 0.209837i
\(313\) −2.88380 3.68090i −0.163002 0.208056i 0.698778 0.715338i \(-0.253727\pi\)
−0.861780 + 0.507282i \(0.830650\pi\)
\(314\) 12.5963 22.8690i 0.710853 1.29057i
\(315\) 3.14430 + 8.65951i 0.177161 + 0.487908i
\(316\) 0.602955 + 0.348117i 0.0339189 + 0.0195831i
\(317\) 10.0393 + 2.47447i 0.563864 + 0.138980i 0.510936 0.859618i \(-0.329299\pi\)
0.0529271 + 0.998598i \(0.483145\pi\)
\(318\) 5.38317 33.1240i 0.301873 1.85750i
\(319\) 4.45685 + 16.6332i 0.249536 + 0.931281i
\(320\) −0.672934 + 1.12827i −0.0376182 + 0.0630723i
\(321\) 0.168274 0.580950i 0.00939215 0.0324255i
\(322\) 2.42971 + 3.67625i 0.135402 + 0.204869i
\(323\) −1.07597 1.12020i −0.0598684 0.0623296i
\(324\) −9.09576 8.05814i −0.505320 0.447674i
\(325\) 5.94220 + 17.0203i 0.329614 + 0.944116i
\(326\) 15.7473 13.9509i 0.872164 0.772670i
\(327\) −40.2857 3.25219i −2.22780 0.179847i
\(328\) −10.8489 5.97561i −0.599030 0.329948i
\(329\) 3.97069 0.320547i 0.218911 0.0176723i
\(330\) 35.5359 2.36173i 1.95619 0.130009i
\(331\) −14.1274 25.6487i −0.776514 1.40978i −0.908220 0.418493i \(-0.862558\pi\)
0.131706 0.991289i \(-0.457955\pi\)
\(332\) 4.07789 9.57116i 0.223803 0.525285i
\(333\) −18.4303 + 16.3278i −1.00998 + 0.894760i
\(334\) −25.7064 + 20.9886i −1.40659 + 1.14845i
\(335\) −1.82657 + 13.4457i −0.0997960 + 0.734616i
\(336\) −18.3989 + 6.55713i −1.00374 + 0.357721i
\(337\) −8.42602 + 8.42602i −0.458995 + 0.458995i −0.898325 0.439331i \(-0.855216\pi\)
0.439331 + 0.898325i \(0.355216\pi\)
\(338\) 21.3381 + 9.00146i 1.16064 + 0.489615i
\(339\) 19.2981i 1.04813i
\(340\) 0.551084 + 3.26808i 0.0298867 + 0.177236i
\(341\) 0.127963 + 3.17537i 0.00692958 + 0.171956i
\(342\) −5.33325 0.538839i −0.288389 0.0291371i
\(343\) −12.4671 14.0725i −0.673162 0.759843i
\(344\) 2.05202 + 5.09863i 0.110638 + 0.274899i
\(345\) −3.38392 + 6.87773i −0.182184 + 0.370285i
\(346\) 29.4249 + 17.7880i 1.58189 + 0.956288i
\(347\) 0.744700 + 0.633445i 0.0399776 + 0.0340051i 0.667681 0.744447i \(-0.267287\pi\)
−0.627703 + 0.778453i \(0.716005\pi\)
\(348\) −5.93988 + 10.7840i −0.318411 + 0.578084i
\(349\) −11.3664 + 9.66828i −0.608428 + 0.517531i −0.898213 0.439561i \(-0.855134\pi\)
0.289785 + 0.957092i \(0.406416\pi\)
\(350\) 5.48564 + 13.9613i 0.293220 + 0.746262i
\(351\) −0.662592 4.60993i −0.0353665 0.246060i
\(352\) 1.36685 + 22.5967i 0.0728534 + 1.20441i
\(353\) −19.9131 + 19.1268i −1.05987 + 1.01801i −0.0600621 + 0.998195i \(0.519130\pi\)
−0.999804 + 0.0198201i \(0.993691\pi\)
\(354\) 12.5483 + 2.56175i 0.666935 + 0.136156i
\(355\) 5.75118 + 16.8918i 0.305241 + 0.896521i
\(356\) −6.68633 14.8564i −0.354375 0.787389i
\(357\) −2.48170 + 4.29844i −0.131346 + 0.227497i
\(358\) −4.90796 0.797621i −0.259394 0.0421556i
\(359\) −8.79695 + 5.31794i −0.464285 + 0.280670i −0.730083 0.683359i \(-0.760519\pi\)
0.265798 + 0.964029i \(0.414365\pi\)
\(360\) −6.16545 5.18147i −0.324948 0.273087i
\(361\) −15.1445 + 8.74367i −0.797078 + 0.460193i
\(362\) 27.9620 8.09929i 1.46965 0.425689i
\(363\) 6.75309 5.29071i 0.354445 0.277690i
\(364\) 6.66754 + 2.51506i 0.349474 + 0.131825i
\(365\) 0.0516737 0.947764i 0.00270472 0.0496082i
\(366\) 7.07344 17.5753i 0.369735 0.918674i
\(367\) 25.0016 8.91025i 1.30508 0.465111i 0.410432 0.911891i \(-0.365378\pi\)
0.894644 + 0.446780i \(0.147429\pi\)
\(368\) −6.53077 3.26160i −0.340440 0.170022i
\(369\) −12.6941 + 16.2028i −0.660827 + 0.843484i
\(370\) −29.3050 + 27.3590i −1.52350 + 1.42233i
\(371\) 9.99103 9.21697i 0.518708 0.478521i
\(372\) −1.50669 + 1.70071i −0.0781184 + 0.0881775i
\(373\) 23.6262 + 8.42007i 1.22332 + 0.435975i 0.866962 0.498375i \(-0.166070\pi\)
0.356358 + 0.934349i \(0.384018\pi\)
\(374\) 5.97046 + 6.21591i 0.308725 + 0.321417i
\(375\) −16.1388 + 20.5025i −0.833404 + 1.05875i
\(376\) −2.86596 + 1.97823i −0.147801 + 0.102020i
\(377\) −15.1435 + 5.77410i −0.779928 + 0.297381i
\(378\) −0.698523 3.81172i −0.0359282 0.196054i
\(379\) −9.62151 + 10.4295i −0.494224 + 0.535730i −0.931569 0.363564i \(-0.881560\pi\)
0.437345 + 0.899294i \(0.355919\pi\)
\(380\) −3.21866 0.240578i −0.165114 0.0123414i
\(381\) −13.8004 + 18.3649i −0.707014 + 0.940864i
\(382\) −2.85162 4.13128i −0.145901 0.211375i
\(383\) 10.1512 + 9.75036i 0.518702 + 0.498220i 0.905734 0.423846i \(-0.139320\pi\)
−0.387032 + 0.922066i \(0.626500\pi\)
\(384\) 16.2882 19.1490i 0.831204 0.977192i
\(385\) 11.9208 + 8.12405i 0.607538 + 0.414040i
\(386\) 28.4686 + 4.62660i 1.44901 + 0.235488i
\(387\) 8.91046 2.00680i 0.452944 0.102011i
\(388\) −3.01953 1.90944i −0.153294 0.0969370i
\(389\) −9.09332 2.24130i −0.461050 0.113639i 0.00194795 0.999998i \(-0.499380\pi\)
−0.462997 + 0.886360i \(0.653226\pi\)
\(390\) 5.63252 + 33.0426i 0.285214 + 1.67318i
\(391\) −1.80109 + 0.443928i −0.0910850 + 0.0224504i
\(392\) 5.81462 + 1.94120i 0.293683 + 0.0980456i
\(393\) 4.30473 30.3342i 0.217145 1.53016i
\(394\) −0.846636 + 21.0091i −0.0426529 + 1.05842i
\(395\) −0.811860 + 1.04906i −0.0408491 + 0.0527837i
\(396\) 10.9440 + 1.10571i 0.549954 + 0.0555639i
\(397\) −23.3111 + 4.75899i −1.16995 + 0.238847i −0.745438 0.666575i \(-0.767760\pi\)
−0.424512 + 0.905422i \(0.639554\pi\)
\(398\) 5.35399 44.0941i 0.268371 2.21024i
\(399\) −3.48611 3.34846i −0.174524 0.167632i
\(400\) −19.4339 15.4857i −0.971697 0.774287i
\(401\) −19.8709 + 13.1331i −0.992303 + 0.655834i −0.939420 0.342767i \(-0.888636\pi\)
−0.0528827 + 0.998601i \(0.516841\pi\)
\(402\) −7.50580 + 24.0870i −0.374355 + 1.20135i
\(403\) −2.96057 + 0.425527i −0.147476 + 0.0211970i
\(404\) 5.24302 9.98974i 0.260850 0.497008i
\(405\) 17.5460 15.1055i 0.871868 0.750597i
\(406\) −12.4062 + 5.28578i −0.615708 + 0.262329i
\(407\) −8.47128 + 37.6136i −0.419906 + 1.86444i
\(408\) 4.33893i 0.214809i
\(409\) 24.9839 + 5.62684i 1.23537 + 0.278229i 0.787751 0.615994i \(-0.211245\pi\)
0.447622 + 0.894223i \(0.352271\pi\)
\(410\) −19.9737 + 26.9119i −0.986429 + 1.32908i
\(411\) −2.39054 + 0.438082i −0.117917 + 0.0216090i
\(412\) 10.5889 16.0214i 0.521676 0.789318i
\(413\) 3.36113 + 3.95147i 0.165391 + 0.194439i
\(414\) −3.74198 + 5.19426i −0.183908 + 0.255284i
\(415\) 17.0238 + 10.1535i 0.835666 + 0.498415i
\(416\) −21.0242 + 3.45530i −1.03080 + 0.169410i
\(417\) −5.17177 + 11.4912i −0.253263 + 0.562727i
\(418\) −7.26913 + 4.19683i −0.355545 + 0.205274i
\(419\) −2.21572 13.6339i −0.108245 0.666058i −0.983294 0.182024i \(-0.941735\pi\)
0.875049 0.484034i \(-0.160829\pi\)
\(420\) 2.12312 + 10.0931i 0.103598 + 0.492492i
\(421\) 9.33982 29.9725i 0.455195 1.46077i −0.387243 0.921978i \(-0.626572\pi\)
0.842438 0.538794i \(-0.181120\pi\)
\(422\) 3.80489 + 8.01864i 0.185219 + 0.390341i
\(423\) 2.48095 + 5.22849i 0.120628 + 0.254218i
\(424\) −3.53520 + 11.3449i −0.171685 + 0.550955i
\(425\) −6.31123 + 0.202239i −0.306140 + 0.00981005i
\(426\) 5.32205 + 32.7479i 0.257854 + 1.58664i
\(427\) 6.64581 3.83696i 0.321613 0.185683i
\(428\) 0.124831 0.277363i 0.00603394 0.0134069i
\(429\) 22.3718 + 23.2084i 1.08012 + 1.12051i
\(430\) 14.4181 3.64483i 0.695301 0.175769i
\(431\) −3.34595 + 4.64453i −0.161169 + 0.223719i −0.884215 0.467081i \(-0.845306\pi\)
0.723046 + 0.690800i \(0.242742\pi\)
\(432\) 4.15934 + 4.88987i 0.200117 + 0.235264i
\(433\) 16.0548 24.2916i 0.771547 1.16738i −0.210287 0.977640i \(-0.567440\pi\)
0.981834 0.189742i \(-0.0607652\pi\)
\(434\) −2.44794 + 0.448602i −0.117505 + 0.0215336i
\(435\) −18.8361 13.9799i −0.903120 0.670284i
\(436\) −19.8283 4.46571i −0.949604 0.213868i
\(437\) 1.80653i 0.0864182i
\(438\) 0.387755 1.72168i 0.0185276 0.0822651i
\(439\) −37.1593 + 15.8321i −1.77352 + 0.755625i −0.782377 + 0.622805i \(0.785993\pi\)
−0.991140 + 0.132820i \(0.957597\pi\)
\(440\) −12.5758 0.939974i −0.599526 0.0448115i
\(441\) 4.73428 9.02041i 0.225442 0.429543i
\(442\) −5.24471 + 6.18822i −0.249466 + 0.294344i
\(443\) 8.05847 25.8605i 0.382869 1.22867i −0.539376 0.842065i \(-0.681340\pi\)
0.922245 0.386606i \(-0.126353\pi\)
\(444\) −22.9971 + 15.1993i −1.09140 + 0.721326i
\(445\) 29.7627 8.81308i 1.41089 0.417780i
\(446\) −27.5330 26.4458i −1.30373 1.25225i
\(447\) −1.10358 + 9.08880i −0.0521975 + 0.429885i
\(448\) −0.969397 + 0.197904i −0.0457997 + 0.00935007i
\(449\) −29.9199 3.02292i −1.41201 0.142660i −0.635175 0.772368i \(-0.719072\pi\)
−0.776832 + 0.629708i \(0.783175\pi\)
\(450\) −16.1385 + 14.6437i −0.760775 + 0.690312i
\(451\) −1.29780 + 32.2045i −0.0611108 + 1.51645i
\(452\) −1.36354 + 9.60846i −0.0641355 + 0.451944i
\(453\) 16.2606 + 5.42857i 0.763988 + 0.255057i
\(454\) 20.8774 5.14583i 0.979827 0.241506i
\(455\) −6.45829 + 11.9428i −0.302769 + 0.559887i
\(456\) 4.10280 + 1.01125i 0.192131 + 0.0473561i
\(457\) 7.75745 + 4.90551i 0.362878 + 0.229470i 0.703444 0.710750i \(-0.251644\pi\)
−0.340566 + 0.940220i \(0.610619\pi\)
\(458\) −37.8365 + 8.52148i −1.76798 + 0.398183i
\(459\) 1.61016 + 0.261677i 0.0751559 + 0.0122140i
\(460\) −2.17080 + 3.18530i −0.101214 + 0.148516i
\(461\) 22.5797 26.5454i 1.05164 1.23634i 0.0807709 0.996733i \(-0.474262\pi\)
0.970869 0.239612i \(-0.0770203\pi\)
\(462\) 19.3442 + 18.5803i 0.899972 + 0.864435i
\(463\) −4.35658 6.31160i −0.202468 0.293325i 0.708576 0.705634i \(-0.249338\pi\)
−0.911044 + 0.412309i \(0.864722\pi\)
\(464\) 13.4203 17.8591i 0.623020 0.829090i
\(465\) −2.82439 3.28072i −0.130978 0.152140i
\(466\) −29.6686 + 32.1602i −1.37437 + 1.48979i
\(467\) 2.04940 + 11.1832i 0.0948347 + 0.517496i 0.996394 + 0.0848417i \(0.0270385\pi\)
−0.901560 + 0.432655i \(0.857577\pi\)
\(468\) 0.0184780 + 10.3526i 0.000854145 + 0.478547i
\(469\) −8.41033 + 5.80523i −0.388353 + 0.268061i
\(470\) 4.26021 + 8.40489i 0.196509 + 0.387689i
\(471\) 23.6933 + 24.6674i 1.09173 + 1.13661i
\(472\) −4.27176 1.52240i −0.196624 0.0700740i
\(473\) 9.48402 10.7052i 0.436076 0.492228i
\(474\) −1.81282 + 1.67237i −0.0832655 + 0.0768145i
\(475\) 1.27969 6.01490i 0.0587162 0.275983i
\(476\) −1.53934 + 1.96483i −0.0705557 + 0.0900577i
\(477\) 17.6669 + 8.82321i 0.808912 + 0.403987i
\(478\) 45.0593 16.0585i 2.06096 0.734500i
\(479\) 15.3426 38.1215i 0.701021 1.74182i 0.0309498 0.999521i \(-0.490147\pi\)
0.670071 0.742297i \(-0.266263\pi\)
\(480\) −20.5860 22.9602i −0.939619 1.04799i
\(481\) −36.0307 4.30968i −1.64286 0.196505i
\(482\) 37.9814 29.7566i 1.73001 1.35537i
\(483\) −5.54489 + 1.60610i −0.252301 + 0.0730799i
\(484\) 3.73616 2.15708i 0.169826 0.0980489i
\(485\) 4.37931 5.21095i 0.198854 0.236617i
\(486\) 30.9316 18.6988i 1.40309 0.848195i
\(487\) −29.3335 4.76716i −1.32923 0.216020i −0.546015 0.837775i \(-0.683856\pi\)
−0.783212 + 0.621755i \(0.786420\pi\)
\(488\) −3.35421 + 5.80966i −0.151838 + 0.262991i
\(489\) 11.3113 + 25.1326i 0.511514 + 1.13654i
\(490\) 7.32275 14.8833i 0.330808 0.672359i
\(491\) 35.8435 + 7.31750i 1.61759 + 0.330234i 0.921698 0.387909i \(-0.126803\pi\)
0.695896 + 0.718143i \(0.255008\pi\)
\(492\) −16.6192 + 15.9630i −0.749252 + 0.719666i
\(493\) −0.342751 5.66635i −0.0154367 0.255200i
\(494\) −4.62909 6.40154i −0.208273 0.288019i
\(495\) −4.89431 + 20.3778i −0.219983 + 0.915915i
\(496\) 3.14035 2.67119i 0.141006 0.119940i
\(497\) −6.48366 + 11.7713i −0.290832 + 0.528014i
\(498\) 28.0728 + 23.8788i 1.25797 + 1.07004i
\(499\) 15.0928 + 9.12389i 0.675645 + 0.408441i 0.813146 0.582060i \(-0.197753\pi\)
−0.137501 + 0.990502i \(0.543907\pi\)
\(500\) −9.48410 + 9.06783i −0.424142 + 0.405526i
\(501\) −16.2320 40.3314i −0.725192 1.80187i
\(502\) −17.7367 20.0206i −0.791627 0.893562i
\(503\) 10.4971 + 1.06056i 0.468044 + 0.0472882i 0.331724 0.943377i \(-0.392370\pi\)
0.136320 + 0.990665i \(0.456472\pi\)
\(504\) −0.244228 6.06046i −0.0108788 0.269954i
\(505\) 17.5152 + 12.4605i 0.779418 + 0.554487i
\(506\) 10.0243i 0.445635i
\(507\) −19.5746 + 23.1797i −0.869337 + 1.02945i
\(508\) −8.16876 + 8.16876i −0.362430 + 0.362430i
\(509\) 14.7117 5.24306i 0.652085 0.232394i 0.0110891 0.999939i \(-0.496470\pi\)
0.640996 + 0.767544i \(0.278521\pi\)
\(510\) −11.6337 1.58042i −0.515150 0.0699820i
\(511\) 0.553724 0.452101i 0.0244953 0.0199998i
\(512\) 11.0297 9.77143i 0.487447 0.431840i
\(513\) −0.622706 + 1.46155i −0.0274932 + 0.0645288i
\(514\) −9.55568 17.3486i −0.421483 0.765214i
\(515\) 27.5315 + 24.1001i 1.21318 + 1.06198i
\(516\) 10.1923 0.822809i 0.448692 0.0362221i
\(517\) 7.93761 + 4.37207i 0.349096 + 0.192283i
\(518\) −30.0958 2.42959i −1.32234 0.106750i
\(519\) −33.7157 + 29.8695i −1.47996 + 1.31113i
\(520\) −0.330754 11.8644i −0.0145045 0.520287i
\(521\) −21.2025 18.7838i −0.928899 0.822933i 0.0555766 0.998454i \(-0.482300\pi\)
−0.984476 + 0.175522i \(0.943839\pi\)
\(522\) −13.5711 14.1290i −0.593992 0.618411i
\(523\) 24.1957 + 36.6090i 1.05800 + 1.60080i 0.764250 + 0.644920i \(0.223109\pi\)
0.293753 + 0.955881i \(0.405096\pi\)
\(524\) 4.28663 14.7991i 0.187262 0.646504i
\(525\) −19.5996 + 1.41972i −0.855395 + 0.0619618i
\(526\) 3.90386 + 14.5694i 0.170217 + 0.635257i
\(527\) 0.168053 1.03407i 0.00732049 0.0450448i
\(528\) −43.1419 10.6335i −1.87751 0.462765i
\(529\) 18.0501 + 10.4213i 0.784789 + 0.453098i
\(530\) 29.1306 + 13.6110i 1.26535 + 0.591223i
\(531\) −3.63600 + 6.60126i −0.157789 + 0.286470i
\(532\) −1.49913 1.91350i −0.0649956 0.0829608i
\(533\) −30.2759 + 1.88559i −1.31139 + 0.0816742i
\(534\) 57.2925 6.95657i 2.47929 0.301040i
\(535\) 0.491627 + 0.306808i 0.0212549 + 0.0132645i
\(536\) 3.82975 8.07103i 0.165420 0.348615i
\(537\) 2.91042 5.82759i 0.125594 0.251479i
\(538\) −18.1570 + 2.20466i −0.782805 + 0.0950498i
\(539\) −2.24129 15.7937i −0.0965391 0.680283i
\(540\) 2.85421 1.82875i 0.122826 0.0786968i
\(541\) 0.993488 + 16.4243i 0.0427134 + 0.706136i 0.955004 + 0.296593i \(0.0958504\pi\)
−0.912291 + 0.409543i \(0.865688\pi\)
\(542\) 14.9737 42.0153i 0.643176 1.80471i
\(543\) −0.767963 + 38.1291i −0.0329564 + 1.63627i
\(544\) 1.04855 7.38880i 0.0449560 0.316792i
\(545\) 13.5163 36.2891i 0.578976 1.55446i
\(546\) −15.5331 + 19.8996i −0.664755 + 0.851624i
\(547\) 7.67116 1.40579i 0.327995 0.0601073i −0.0137345 0.999906i \(-0.504372\pi\)
0.341729 + 0.939798i \(0.388987\pi\)
\(548\) −1.22119 + 0.0492124i −0.0521668 + 0.00210225i
\(549\) 8.63560 + 7.05075i 0.368559 + 0.300919i
\(550\) −7.10090 + 33.3762i −0.302783 + 1.42317i
\(551\) 5.43786 + 0.996525i 0.231661 + 0.0424534i
\(552\) 3.49583 3.63955i 0.148793 0.154910i
\(553\) −0.995792 + 0.0803887i −0.0423454 + 0.00341847i
\(554\) −0.501282 0.225609i −0.0212974 0.00958520i
\(555\) −22.7971 47.3151i −0.967681 2.00842i
\(556\) −3.38694 + 5.35601i −0.143638 + 0.227146i
\(557\) 11.6414 18.4095i 0.493264 0.780035i −0.503190 0.864176i \(-0.667840\pi\)
0.996454 + 0.0841413i \(0.0268147\pi\)
\(558\) −1.87044 3.09409i −0.0791820 0.130983i
\(559\) 10.9357 + 7.84857i 0.462532 + 0.331959i
\(560\) −1.24104 18.6735i −0.0524437 0.789098i
\(561\) −10.1013 + 5.04477i −0.426475 + 0.212990i
\(562\) −2.12802 0.301987i −0.0897650 0.0127386i
\(563\) 29.0939 26.8398i 1.22616 1.13116i 0.239070 0.971002i \(-0.423157\pi\)
0.987091 0.160162i \(-0.0512017\pi\)
\(564\) 1.92754 + 6.18568i 0.0811639 + 0.260464i
\(565\) −17.7904 5.03856i −0.748448 0.211974i
\(566\) 9.08026 13.7388i 0.381672 0.577485i
\(567\) 17.3096 + 2.10177i 0.726936 + 0.0882660i
\(568\) −0.236570 11.7456i −0.00992624 0.492834i
\(569\) −5.71166 1.90683i −0.239445 0.0799385i 0.194413 0.980920i \(-0.437720\pi\)
−0.433858 + 0.900981i \(0.642848\pi\)
\(570\) 4.20581 10.6323i 0.176162 0.445336i
\(571\) −13.7571 26.2120i −0.575718 1.09694i −0.982995 0.183634i \(-0.941214\pi\)
0.407277 0.913305i \(-0.366478\pi\)
\(572\) 9.49899 + 13.1361i 0.397173 + 0.549248i
\(573\) 6.27844 1.95644i 0.262286 0.0817315i
\(574\) −25.1125 + 2.53722i −1.04818 + 0.105901i
\(575\) −5.45688 4.91526i −0.227568 0.204980i
\(576\) −0.768216 1.21484i −0.0320090 0.0506182i
\(577\) −6.28412 −0.261611 −0.130806 0.991408i \(-0.541756\pi\)
−0.130806 + 0.991408i \(0.541756\pi\)
\(578\) 14.6677 + 23.1951i 0.610096 + 0.964789i
\(579\) −16.8819 + 33.8029i −0.701586 + 1.40480i
\(580\) −8.39064 8.29143i −0.348402 0.344283i
\(581\) 2.98605 + 14.6266i 0.123882 + 0.606815i
\(582\) 9.64018 8.19997i 0.399598 0.339900i
\(583\) 30.5217 4.96026i 1.26408 0.205433i
\(584\) −0.221595 + 0.584299i −0.00916968 + 0.0241785i
\(585\) −19.5496 2.62025i −0.808278 0.108334i
\(586\) −1.19754 3.15765i −0.0494698 0.130441i
\(587\) −9.13944 15.8300i −0.377225 0.653373i 0.613432 0.789747i \(-0.289788\pi\)
−0.990657 + 0.136374i \(0.956455\pi\)
\(588\) 6.66652 9.25383i 0.274923 0.381622i
\(589\) 0.938627 + 0.399912i 0.0386755 + 0.0164781i
\(590\) −5.63786 + 10.8991i −0.232107 + 0.448708i
\(591\) −25.9464 9.24694i −1.06729 0.380368i
\(592\) 45.1892 21.4425i 1.85726 0.881282i
\(593\) −30.7147 + 16.1203i −1.26130 + 0.661982i −0.956860 0.290549i \(-0.906162\pi\)
−0.304441 + 0.952531i \(0.598470\pi\)
\(594\) 3.45535 8.11001i 0.141775 0.332758i
\(595\) −3.31466 3.41010i −0.135888 0.139800i
\(596\) −1.19165 + 4.44731i −0.0488120 + 0.182169i
\(597\) 53.0624 + 23.8815i 2.17170 + 0.977403i
\(598\) −9.38511 + 0.965139i −0.383786 + 0.0394675i
\(599\) −19.0627 7.22953i −0.778881 0.295391i −0.0670578 0.997749i \(-0.521361\pi\)
−0.711824 + 0.702358i \(0.752130\pi\)
\(600\) 14.2176 9.64164i 0.580431 0.393618i
\(601\) −21.0428 1.69875i −0.858354 0.0692935i −0.356552 0.934276i \(-0.616048\pi\)
−0.501803 + 0.864982i \(0.667330\pi\)
\(602\) 9.34385 + 6.17554i 0.380827 + 0.251696i
\(603\) −12.2182 8.43363i −0.497565 0.343444i
\(604\) 7.71251 + 3.85178i 0.313818 + 0.156727i
\(605\) 3.11419 + 7.60684i 0.126610 + 0.309262i
\(606\) 28.2606 + 28.2606i 1.14801 + 1.14801i
\(607\) 41.7286 + 9.39807i 1.69371 + 0.381456i 0.955933 0.293586i \(-0.0948486\pi\)
0.737780 + 0.675041i \(0.235874\pi\)
\(608\) 6.74231 + 2.71355i 0.273437 + 0.110049i
\(609\) −1.77584 17.5767i −0.0719605 0.712242i
\(610\) 14.3554 + 11.1096i 0.581231 + 0.449813i
\(611\) −3.32905 + 7.85240i −0.134679 + 0.317674i
\(612\) −3.46195 1.07879i −0.139941 0.0436073i
\(613\) 29.1743 + 5.95598i 1.17834 + 0.240560i 0.748992 0.662579i \(-0.230538\pi\)
0.429348 + 0.903139i \(0.358743\pi\)
\(614\) 7.59590 22.7525i 0.306546 0.918216i
\(615\) −25.8746 35.4700i −1.04337 1.43029i
\(616\) −5.85733 7.47632i −0.235998 0.301230i
\(617\) 1.98339 + 9.71529i 0.0798483 + 0.391123i 1.00000 0.000439376i \(-0.000139858\pi\)
−0.920152 + 0.391562i \(0.871935\pi\)
\(618\) 43.0262 + 52.6975i 1.73077 + 2.11981i
\(619\) −7.47307 + 2.32870i −0.300368 + 0.0935984i −0.443983 0.896035i \(-0.646435\pi\)
0.143615 + 0.989634i \(0.454127\pi\)
\(620\) −1.17445 1.83302i −0.0471671 0.0736158i
\(621\) 1.13979 + 1.51679i 0.0457383 + 0.0608666i
\(622\) 13.2675 39.7411i 0.531980 1.59347i
\(623\) 20.0057 + 12.0939i 0.801513 + 0.484532i
\(624\) 5.80178 41.4147i 0.232257 1.65792i
\(625\) −14.6870 20.2310i −0.587481 0.809238i
\(626\) 8.12664 1.83027i 0.324806 0.0731523i
\(627\) −2.41598 10.7273i −0.0964851 0.428406i
\(628\) 10.0539 + 13.9559i 0.401195 + 0.556900i
\(629\) 5.21644 11.5905i 0.207993 0.462142i
\(630\) −16.3385 1.55263i −0.650941 0.0618583i
\(631\) 35.9173 0.723416i 1.42985 0.0287987i 0.700846 0.713312i \(-0.252806\pi\)
0.729000 + 0.684514i \(0.239985\pi\)
\(632\) 0.718744 0.496113i 0.0285901 0.0197343i
\(633\) −11.5119 + 1.63366i −0.457559 + 0.0649322i
\(634\) −11.6496 + 14.2682i −0.462665 + 0.566662i
\(635\) −13.3270 17.5171i −0.528865 0.695145i
\(636\) 18.1947 + 12.5589i 0.721468 + 0.497993i
\(637\) 14.5708 3.61898i 0.577317 0.143389i
\(638\) −30.1743 5.52964i −1.19461 0.218921i
\(639\) −19.3297 2.74308i −0.764672 0.108515i
\(640\) 13.4002 + 20.0153i 0.529690 + 0.791173i
\(641\) −31.9028 + 15.1381i −1.26009 + 0.597918i −0.937290 0.348551i \(-0.886674\pi\)
−0.322796 + 0.946469i \(0.604623\pi\)
\(642\) 0.806508 + 0.714504i 0.0318303 + 0.0281992i
\(643\) 22.9920 + 0.926544i 0.906714 + 0.0365393i 0.489240 0.872149i \(-0.337274\pi\)
0.417475 + 0.908689i \(0.362915\pi\)
\(644\) −2.87426 + 0.407887i −0.113262 + 0.0160730i
\(645\) −1.06063 + 19.4534i −0.0417624 + 0.765977i
\(646\) 2.62464 0.876235i 0.103265 0.0344750i
\(647\) 10.0783 + 28.2793i 0.396221 + 1.11177i 0.958566 + 0.284870i \(0.0919504\pi\)
−0.562346 + 0.826902i \(0.690101\pi\)
\(648\) −14.0232 + 5.97472i −0.550883 + 0.234709i
\(649\) 1.42245 + 11.7149i 0.0558360 + 0.459851i
\(650\) −31.9317 3.43465i −1.25246 0.134718i
\(651\) 0.392984 3.23652i 0.0154023 0.126849i
\(652\) 3.85606 + 13.3127i 0.151015 + 0.521364i
\(653\) 7.63202 + 2.04499i 0.298664 + 0.0800268i 0.405039 0.914299i \(-0.367258\pi\)
−0.106375 + 0.994326i \(0.533924\pi\)
\(654\) 36.0005 62.3547i 1.40773 2.43826i
\(655\) 26.8404 + 11.8884i 1.04874 + 0.464518i
\(656\) 33.9260 24.4405i 1.32459 0.954241i
\(657\) 0.899371 + 0.519252i 0.0350878 + 0.0202579i
\(658\) −2.51651 + 6.63549i −0.0981038 + 0.258678i
\(659\) −4.63274 1.34189i −0.180466 0.0522726i 0.186754 0.982407i \(-0.440203\pi\)
−0.367220 + 0.930134i \(0.619690\pi\)
\(660\) −8.63041 + 21.8176i −0.335938 + 0.849249i
\(661\) 0.457552 22.7173i 0.0177967 0.883599i −0.887989 0.459864i \(-0.847898\pi\)
0.905786 0.423735i \(-0.139281\pi\)
\(662\) 52.0699 3.14965i 2.02376 0.122415i
\(663\) −5.69563 8.97143i −0.221200 0.348421i
\(664\) −8.65382 9.76815i −0.335834 0.379078i
\(665\) 3.99704 2.33950i 0.154999 0.0907219i
\(666\) −12.2038 42.1326i −0.472889 1.63260i
\(667\) 4.27782 5.02915i 0.165638 0.194730i
\(668\) −5.23218 21.2278i −0.202439 0.821327i
\(669\) 43.8068 24.1290i 1.69367 0.932880i
\(670\) −20.2454 13.2083i −0.782148 0.510280i
\(671\) 17.4250 + 1.05402i 0.672686 + 0.0406900i
\(672\) 2.33459 23.1070i 0.0900586 0.891371i
\(673\) −2.60579 + 2.82463i −0.100446 + 0.108882i −0.783210 0.621758i \(-0.786419\pi\)
0.682764 + 0.730639i \(0.260778\pi\)
\(674\) −7.12643 19.9964i −0.274500 0.770231i
\(675\) 2.72052 + 5.85757i 0.104713 + 0.225458i
\(676\) −11.3839 + 10.1580i −0.437843 + 0.390693i
\(677\) 5.86431 + 5.86431i 0.225384 + 0.225384i 0.810761 0.585377i \(-0.199054\pi\)
−0.585377 + 0.810761i \(0.699054\pi\)
\(678\) −31.0597 14.7380i −1.19284 0.566009i
\(679\) 5.12222 0.206418i 0.196573 0.00792160i
\(680\) 3.99994 + 1.13286i 0.153391 + 0.0434431i
\(681\) −1.70078 + 28.1173i −0.0651741 + 1.07746i
\(682\) −5.20837 2.21908i −0.199439 0.0849730i
\(683\) −2.79205 + 9.63929i −0.106835 + 0.368837i −0.996065 0.0886227i \(-0.971753\pi\)
0.889230 + 0.457460i \(0.151241\pi\)
\(684\) 1.82693 3.02212i 0.0698545 0.115553i
\(685\) 0.220292 2.31815i 0.00841692 0.0885720i
\(686\) 32.1704 9.31826i 1.22827 0.355773i
\(687\) 4.08839 50.6438i 0.155982 1.93218i
\(688\) −18.5202 1.12027i −0.706077 0.0427098i
\(689\) 7.58258 + 28.0979i 0.288873 + 1.07044i
\(690\) −8.48517 10.6988i −0.323025 0.407298i
\(691\) −28.9262 0.582606i −1.10040 0.0221634i −0.533388 0.845871i \(-0.679081\pi\)
−0.567015 + 0.823707i \(0.691902\pi\)
\(692\) −18.8974 + 12.4897i −0.718373 + 0.474787i
\(693\) −13.8251 + 7.61492i −0.525172 + 0.289267i
\(694\) −1.58824 + 0.714807i −0.0602886 + 0.0271337i
\(695\) −9.24312 7.76796i −0.350612 0.294656i
\(696\) 9.02705 + 12.5305i 0.342170 + 0.474967i
\(697\) 2.54275 10.3163i 0.0963136 0.390759i
\(698\) −6.88026 25.6775i −0.260422 0.971907i
\(699\) −28.6603 49.6410i −1.08403 1.87760i
\(700\) −9.85886 0.677962i −0.372630 0.0256246i
\(701\) −8.28783 1.00632i −0.313027 0.0380084i −0.0374844 0.999297i \(-0.511934\pi\)
−0.275543 + 0.961289i \(0.588858\pi\)
\(702\) 7.92555 + 2.45419i 0.299130 + 0.0926274i
\(703\) 9.74392 + 7.63387i 0.367499 + 0.287917i
\(704\) −2.08794 0.840325i −0.0786924 0.0316709i
\(705\) −12.1725 + 2.05260i −0.458442 + 0.0773055i
\(706\) −15.5762 46.6565i −0.586220 1.75594i
\(707\) 1.95133 + 16.0707i 0.0733874 + 0.604400i
\(708\) −5.06863 + 6.74512i −0.190491 + 0.253497i
\(709\) 5.56465 + 6.03198i 0.208985 + 0.226536i 0.830718 0.556693i \(-0.187930\pi\)
−0.621733 + 0.783229i \(0.713571\pi\)
\(710\) −31.5789 3.64392i −1.18514 0.136754i
\(711\) −0.622187 1.31123i −0.0233338 0.0491750i
\(712\) −20.4318 0.411520i −0.765715 0.0154224i
\(713\) 0.974104 0.731992i 0.0364805 0.0274133i
\(714\) −5.02291 7.27694i −0.187978 0.272333i
\(715\) −27.2363 + 14.5644i −1.01858 + 0.544678i
\(716\) 1.86084 2.69590i 0.0695430 0.100750i
\(717\) 2.52330 + 62.6149i 0.0942342 + 2.33840i
\(718\) −1.84081 18.2197i −0.0686983 0.679954i
\(719\) −14.3320 10.7698i −0.534493 0.401646i 0.298935 0.954274i \(-0.403369\pi\)
−0.833428 + 0.552628i \(0.813625\pi\)
\(720\) 24.7259 11.3056i 0.921481 0.421333i
\(721\) 0.554909 + 27.5510i 0.0206659 + 1.02605i
\(722\) −2.50678 31.0521i −0.0932928 1.15564i
\(723\) 22.4141 + 59.1012i 0.833591 + 2.19800i
\(724\) −3.07644 + 18.9301i −0.114335 + 0.703531i
\(725\) 17.8056 13.7144i 0.661283 0.509341i
\(726\) 3.35787 + 14.9094i 0.124622 + 0.553339i
\(727\) 6.74243 4.07594i 0.250063 0.151168i −0.386755 0.922183i \(-0.626404\pi\)
0.636818 + 0.771014i \(0.280250\pi\)
\(728\) 6.43565 6.20365i 0.238521 0.229922i
\(729\) 3.89794 + 15.8146i 0.144368 + 0.585725i
\(730\) 1.48593 + 0.806976i 0.0549968 + 0.0298675i
\(731\) −3.76921 + 2.83238i −0.139409 + 0.104759i
\(732\) 8.46293 + 9.17365i 0.312799 + 0.339068i
\(733\) −10.1198 + 19.2816i −0.373782 + 0.712182i −0.997589 0.0693962i \(-0.977893\pi\)
0.623807 + 0.781578i \(0.285585\pi\)
\(734\) −4.75304 + 47.0441i −0.175438 + 1.73643i
\(735\) 15.7608 + 14.9593i 0.581346 + 0.551781i
\(736\) 6.83261 5.35301i 0.251853 0.197315i
\(737\) −23.2425 + 0.468131i −0.856149 + 0.0172438i
\(738\) −16.3834 32.8048i −0.603080 1.20756i
\(739\) −20.3013 30.7167i −0.746796 1.12993i −0.987235 0.159269i \(-0.949086\pi\)
0.240439 0.970664i \(-0.422709\pi\)
\(740\) −8.00745 25.1688i −0.294360 0.925224i
\(741\) 9.81063 3.29475i 0.360403 0.121035i
\(742\) 7.20424 + 23.1192i 0.264476 + 0.848734i
\(743\) 19.8724 + 16.2253i 0.729047 + 0.595248i 0.922562 0.385849i \(-0.126091\pi\)
−0.193515 + 0.981097i \(0.561989\pi\)
\(744\) 1.11714 + 2.62203i 0.0409564 + 0.0961282i
\(745\) −8.09058 3.39036i −0.296416 0.124213i
\(746\) −31.5952 + 31.5952i −1.15678 + 1.15678i
\(747\) −18.3299 + 11.5911i −0.670657 + 0.424098i
\(748\) −5.38583 + 1.79805i −0.196925 + 0.0657433i
\(749\) 0.0786709 + 0.429293i 0.00287457 + 0.0156860i
\(750\) −20.6729 41.6327i −0.754868 1.52021i
\(751\) −0.663564 + 8.21972i −0.0242138 + 0.299942i 0.973304 + 0.229521i \(0.0737161\pi\)
−0.997517 + 0.0704203i \(0.977566\pi\)
\(752\) −1.88583 11.6040i −0.0687690 0.423153i
\(753\) 31.9527 14.3807i 1.16442 0.524064i
\(754\) 2.27187 28.7826i 0.0827366 1.04820i
\(755\) −9.24994 + 13.5728i −0.336640 + 0.493965i
\(756\) 2.46597 + 0.660755i 0.0896865 + 0.0240314i
\(757\) 8.75215 + 6.30511i 0.318102 + 0.229163i 0.732233 0.681055i \(-0.238478\pi\)
−0.414130 + 0.910218i \(0.635914\pi\)
\(758\) −9.43804 23.4506i −0.342805 0.851763i
\(759\) −12.5376 3.90686i −0.455085 0.141810i
\(760\) −2.00345 + 3.51823i −0.0726727 + 0.127620i
\(761\) −3.40951 + 9.56689i −0.123595 + 0.346800i −0.987667 0.156568i \(-0.949957\pi\)
0.864072 + 0.503367i \(0.167906\pi\)
\(762\) −19.0184 36.2365i −0.688964 1.31271i
\(763\) 27.0555 10.8889i 0.979475 0.394205i
\(764\) 3.26425 0.530492i 0.118096 0.0191925i
\(765\) 2.92456 6.25923i 0.105738 0.226303i
\(766\) −23.4454 + 8.89165i −0.847115 + 0.321268i
\(767\) −10.8310 + 2.45965i −0.391083 + 0.0888129i
\(768\) 19.5058 + 43.3401i 0.703854 + 1.56390i
\(769\) −17.1319 12.3419i −0.617792 0.445061i 0.231610 0.972809i \(-0.425601\pi\)
−0.849401 + 0.527748i \(0.823037\pi\)
\(770\) −22.1793 + 12.9817i −0.799286 + 0.467828i
\(771\) 25.4224 5.19001i 0.915564 0.186914i
\(772\) −10.7938 + 15.6376i −0.388478 + 0.562808i
\(773\) −0.390846 1.17073i −0.0140578 0.0421081i 0.941274 0.337644i \(-0.109630\pi\)
−0.955332 + 0.295536i \(0.904502\pi\)
\(774\) −3.57505 + 15.8737i −0.128502 + 0.570568i
\(775\) 3.76182 1.74716i 0.135129 0.0627599i
\(776\) −3.78763 + 2.39515i −0.135968 + 0.0859810i
\(777\) 14.7682 36.6944i 0.529807 1.31640i
\(778\) 10.5519 12.9237i 0.378303 0.463337i
\(779\) 9.16229 + 4.80874i 0.328273 + 0.172291i
\(780\) −21.2573 5.97949i −0.761134 0.214100i
\(781\) −27.0693 + 14.2070i −0.968614 + 0.508368i
\(782\) 0.661006 3.23782i 0.0236375 0.115784i
\(783\) −5.19443 + 2.59420i −0.185634 + 0.0927092i
\(784\) −14.3356 + 14.9249i −0.511985 + 0.533033i
\(785\) −28.9263 + 15.4018i −1.03242 + 0.549714i
\(786\) 45.5344 + 30.0946i 1.62416 + 1.07344i
\(787\) 33.8953 27.6746i 1.20824 0.986495i 0.208272 0.978071i \(-0.433216\pi\)
0.999965 0.00842377i \(-0.00268140\pi\)
\(788\) −12.2653 6.43730i −0.436932 0.229319i
\(789\) −19.7437 0.795643i −0.702894 0.0283256i
\(790\) −1.06840 2.10783i −0.0380120 0.0749931i
\(791\) −6.22186 12.4582i −0.221224 0.442961i
\(792\) 7.13809 11.8078i 0.253641 0.419573i
\(793\) 0.690867 + 16.4154i 0.0245334 + 0.582928i
\(794\) 10.1433 41.1529i 0.359971 1.46046i
\(795\) −28.3768 + 31.1294i −1.00642 + 1.10404i
\(796\) 24.7322 + 15.6397i 0.876610 + 0.554335i
\(797\) −33.4524 + 24.0994i −1.18495 + 0.853643i −0.991834 0.127534i \(-0.959294\pi\)
−0.193112 + 0.981177i \(0.561858\pi\)
\(798\) 8.05157 3.05356i 0.285023 0.108095i
\(799\) −2.27552 1.93557i −0.0805022 0.0684755i
\(800\) 26.5413 12.9830i 0.938375 0.459018i
\(801\) −6.12174 + 33.4052i −0.216301 + 1.18032i
\(802\) −5.96182 42.0112i −0.210519 1.48347i
\(803\) 1.61792 0.163465i 0.0570952 0.00576854i
\(804\) −12.2165 11.2700i −0.430843 0.397463i
\(805\) −0.0328960 5.53102i −0.00115943 0.194943i
\(806\) 1.57612 5.08991i 0.0555164 0.179284i
\(807\) 4.31909 23.5685i 0.152039 0.829651i
\(808\) −8.50165 11.3136i −0.299087 0.398013i
\(809\) 11.0389 10.6030i 0.388106 0.372780i −0.473125 0.880995i \(-0.656874\pi\)
0.861230 + 0.508215i \(0.169694\pi\)
\(810\) 10.9118 + 39.7758i 0.383403 + 1.39758i
\(811\) 2.52899 0.152976i 0.0888049 0.00537171i −0.0159163 0.999873i \(-0.505067\pi\)
0.104721 + 0.994502i \(0.466605\pi\)
\(812\) 0.357724 8.87684i 0.0125537 0.311516i
\(813\) 46.7134 + 35.1028i 1.63831 + 1.23111i
\(814\) −54.0683 42.3598i −1.89509 1.48471i
\(815\) −26.1224 + 3.86566i −0.915026 + 0.135408i
\(816\) 13.2335 + 6.27937i 0.463265 + 0.219822i
\(817\) −1.79977 4.22421i −0.0629659 0.147786i
\(818\) −28.1364 + 35.9135i −0.983767 + 1.25569i
\(819\) −8.46042 12.2104i −0.295631 0.426664i
\(820\) −10.3767 19.4886i −0.362370 0.680571i
\(821\) 14.0123 + 7.71801i 0.489031 + 0.269361i 0.707796 0.706417i \(-0.249690\pi\)
−0.218764 + 0.975778i \(0.570203\pi\)
\(822\) 1.12058 4.18205i 0.0390847 0.145866i
\(823\) 43.1356 11.5581i 1.50361 0.402892i 0.589304 0.807912i \(-0.299402\pi\)
0.914308 + 0.405020i \(0.132735\pi\)
\(824\) −12.4624 20.6154i −0.434150 0.718172i
\(825\) −38.9767 21.8892i −1.35699 0.762084i
\(826\) −8.92666 + 2.39189i −0.310598 + 0.0832245i
\(827\) −30.2255 11.4630i −1.05105 0.398609i −0.232227 0.972662i \(-0.574601\pi\)
−0.818818 + 0.574053i \(0.805370\pi\)
\(828\) −2.03476 3.69415i −0.0707126 0.128381i
\(829\) −2.04625 + 10.0232i −0.0710694 + 0.348121i −0.999740 0.0227836i \(-0.992747\pi\)
0.928671 + 0.370904i \(0.120952\pi\)
\(830\) −29.3428 + 19.6450i −1.01850 + 0.681888i
\(831\) 0.477541 0.539033i 0.0165657 0.0186988i
\(832\) 0.585715 2.03571i 0.0203060 0.0705756i
\(833\) −0.317512 + 5.24910i −0.0110011 + 0.181871i
\(834\) −14.5450 17.0996i −0.503653 0.592112i
\(835\) 41.4185 4.43367i 1.43334 0.153433i
\(836\) −0.444957 5.51178i −0.0153892 0.190629i
\(837\) −1.04040 + 0.256435i −0.0359614 + 0.00886369i
\(838\) 23.6354 + 6.84608i 0.816471 + 0.236494i
\(839\) 0.425522 0.171258i 0.0146906 0.00591247i −0.366004 0.930613i \(-0.619275\pi\)
0.380695 + 0.924701i \(0.375685\pi\)
\(840\) 12.5799 + 3.02141i 0.434046 + 0.104248i
\(841\) −5.56237 6.81266i −0.191806 0.234919i
\(842\) 41.1070 + 37.9222i 1.41664 + 1.30688i
\(843\) 1.20707 2.54385i 0.0415737 0.0876147i
\(844\) −5.84719 −0.201268
\(845\) −16.2580 24.0973i −0.559292 0.828971i
\(846\) −10.3098 −0.354457
\(847\) −2.65379 + 5.59274i −0.0911852 + 0.192169i
\(848\) −29.4850 27.2006i −1.01252 0.934073i
\(849\) 13.6444 + 16.7114i 0.468275 + 0.573532i
\(850\) 4.49440 10.3122i 0.154157 0.353705i
\(851\) 13.7139 5.51938i 0.470107 0.189202i
\(852\) −20.9942 6.08105i −0.719251 0.208333i
\(853\) 41.5907 10.2512i 1.42404 0.350994i 0.549316 0.835615i \(-0.314888\pi\)
0.874724 + 0.484621i \(0.161042\pi\)
\(854\) 1.10004 + 13.6265i 0.0376427 + 0.466289i
\(855\) 5.23699 + 4.22421i 0.179101 + 0.144465i
\(856\) −0.247200 0.290617i −0.00844912 0.00993308i
\(857\) 1.92724 31.8610i 0.0658332 1.08835i −0.803879 0.594793i \(-0.797234\pi\)
0.869712 0.493560i \(-0.164304\pi\)
\(858\) −54.4385 + 18.2823i −1.85850 + 0.624147i
\(859\) −7.32952 + 8.27332i −0.250080 + 0.282282i −0.860123 0.510086i \(-0.829614\pi\)
0.610043 + 0.792368i \(0.291152\pi\)
\(860\) −1.90260 + 9.61085i −0.0648780 + 0.327727i
\(861\) 6.61399 32.3975i 0.225404 1.10410i
\(862\) −4.91991 8.93224i −0.167573 0.304233i
\(863\) −31.9989 12.1356i −1.08925 0.413100i −0.256388 0.966574i \(-0.582533\pi\)
−0.832866 + 0.553474i \(0.813302\pi\)
\(864\) −7.37297 + 1.97558i −0.250834 + 0.0672107i
\(865\) −18.7330 38.8803i −0.636942 1.32197i
\(866\) 26.8355 + 44.3913i 0.911906 + 1.50848i
\(867\) −34.7270 + 9.30508i −1.17939 + 0.316017i
\(868\) 0.424347 1.58368i 0.0144033 0.0537537i
\(869\) −1.99064 1.09645i −0.0675278 0.0371946i
\(870\) 36.8853 19.6396i 1.25053 0.665844i
\(871\) −2.67606 21.7154i −0.0906749 0.735797i
\(872\) −15.7234 + 20.0694i −0.532460 + 0.679635i
\(873\) 2.91914 + 6.85147i 0.0987979 + 0.231887i
\(874\) 2.90756 + 1.37965i 0.0983495 + 0.0466674i
\(875\) 3.80846 18.4390i 0.128750 0.623351i
\(876\) 0.915216 + 0.717026i 0.0309223 + 0.0242260i
\(877\) −38.1511 28.6687i −1.28827 0.968072i −0.999944 0.0105401i \(-0.996645\pi\)
−0.288326 0.957532i \(-0.593099\pi\)
\(878\) 2.89738 71.8977i 0.0977817 2.42643i
\(879\) 4.41604 0.267121i 0.148949 0.00900978i
\(880\) 21.0667 36.9950i 0.710159 1.24710i
\(881\) −20.7284 + 19.9099i −0.698357 + 0.670781i −0.955298 0.295646i \(-0.904465\pi\)
0.256940 + 0.966427i \(0.417286\pi\)
\(882\) 10.9025 + 14.5086i 0.367105 + 0.488529i
\(883\) 1.68260 9.18163i 0.0566239 0.308986i −0.943099 0.332511i \(-0.892104\pi\)
0.999723 + 0.0235245i \(0.00748878\pi\)
\(884\) −2.20194 4.86928i −0.0740594 0.163772i
\(885\) −11.4344 11.2991i −0.384362 0.379817i
\(886\) 35.4674 + 32.7195i 1.19155 + 1.09923i
\(887\) −7.66439 + 0.774362i −0.257345 + 0.0260005i −0.228350 0.973579i \(-0.573333\pi\)
−0.0289946 + 0.999580i \(0.509231\pi\)
\(888\) 4.85832 + 34.2352i 0.163035 + 1.14886i
\(889\) 2.98802 16.3051i 0.100215 0.546855i
\(890\) −8.54549 + 54.6327i −0.286445 + 1.83129i
\(891\) 30.2139 + 25.7000i 1.01220 + 0.860983i
\(892\) 23.5161 8.91850i 0.787379 0.298613i
\(893\) 2.36058 1.70057i 0.0789936 0.0569075i
\(894\) −13.7853 8.71730i −0.461050 0.291550i
\(895\) 4.61241 + 4.20456i 0.154176 + 0.140543i
\(896\) −4.34130 + 17.6133i −0.145033 + 0.588420i
\(897\) 2.45063 12.1143i 0.0818241 0.404483i
\(898\) 27.7151 45.8465i 0.924867 1.52992i
\(899\) 1.66604 + 3.33594i 0.0555654 + 0.111260i
\(900\) −4.15795 13.7411i −0.138598 0.458038i
\(901\) −10.1855 0.410461i −0.339327 0.0136744i
\(902\) −50.8409 26.6833i −1.69282 0.888458i
\(903\) −11.3655 + 9.27965i −0.378220 + 0.308807i
\(904\) 10.1557 + 6.71213i 0.337774 + 0.223242i
\(905\) −34.9496 10.6631i −1.16177 0.354454i
\(906\) −21.1553 + 22.0250i −0.702838 + 0.731732i
\(907\) −45.2149 + 22.5812i −1.50134 + 0.749798i −0.993732 0.111791i \(-0.964341\pi\)
−0.507606 + 0.861589i \(0.669469\pi\)
\(908\) −2.83348 + 13.8793i −0.0940325 + 0.460601i
\(909\) −20.8245 + 10.9295i −0.690705 + 0.362510i
\(910\) −14.2893 19.5151i −0.473687 0.646920i
\(911\) −12.4362 6.52700i −0.412029 0.216249i 0.245955 0.969281i \(-0.420898\pi\)
−0.657984 + 0.753032i \(0.728591\pi\)
\(912\) −9.02189 + 11.0498i −0.298745 + 0.365896i
\(913\) −12.6792 + 31.5037i −0.419619 + 1.04262i
\(914\) −13.8196 + 8.73900i −0.457113 + 0.289061i
\(915\) −19.4897 + 13.6246i −0.644310 + 0.450416i
\(916\) 5.61391 24.9265i 0.185489 0.823595i
\(917\) 7.00100 + 20.9706i 0.231193 + 0.692509i
\(918\) −1.65084 + 2.39166i −0.0544859 + 0.0789364i
\(919\) 43.0502 8.78875i 1.42009 0.289914i 0.572215 0.820104i \(-0.306084\pi\)
0.847879 + 0.530190i \(0.177879\pi\)
\(920\) 2.44247 + 4.17297i 0.0805258 + 0.137579i
\(921\) 25.4965 + 18.3678i 0.840137 + 0.605240i
\(922\) 25.4799 + 56.6140i 0.839136 + 1.86448i
\(923\) −15.9073 23.9753i −0.523597 0.789157i
\(924\) −16.5220 + 6.26597i −0.543534 + 0.206135i
\(925\) 49.5706 8.66243i 1.62987 0.284819i
\(926\) 13.4854 2.19160i 0.443159 0.0720203i
\(927\) −37.1383 + 14.9469i −1.21978 + 0.490920i
\(928\) 12.3441 + 23.5197i 0.405215 + 0.772073i
\(929\) −14.9562 + 41.9662i −0.490697 + 1.37687i 0.397584 + 0.917566i \(0.369849\pi\)
−0.888281 + 0.459300i \(0.848100\pi\)
\(930\) 7.43719 2.04027i 0.243875 0.0669032i
\(931\) −4.88944 1.52361i −0.160245 0.0499343i
\(932\) −10.7624 26.7411i −0.352534 0.875935i
\(933\) 44.5340 + 32.0826i 1.45798 + 1.05034i
\(934\) −19.5641 5.24218i −0.640157 0.171530i
\(935\) −2.01329 10.6292i −0.0658415 0.347612i
\(936\) 11.7422 + 5.54607i 0.383804 + 0.181279i
\(937\) −3.26914 + 1.47132i −0.106798 + 0.0480659i −0.463108 0.886302i \(-0.653266\pi\)
0.356309 + 0.934368i \(0.384035\pi\)
\(938\) −2.92034 17.9696i −0.0953526 0.586728i
\(939\) −0.878117 + 10.8774i −0.0286563 + 0.354972i
\(940\) −6.20567 + 0.161917i −0.202407 + 0.00528116i
\(941\) 7.49353 + 40.8909i 0.244282 + 1.33300i 0.845524 + 0.533937i \(0.179288\pi\)
−0.601242 + 0.799067i \(0.705327\pi\)
\(942\) −57.7959 + 19.2951i −1.88309 + 0.628669i
\(943\) 10.4447 6.60481i 0.340125 0.215082i
\(944\) 10.8254 10.8254i 0.352336 0.352336i
\(945\) −1.87991 + 4.48611i −0.0611535 + 0.145933i
\(946\) 9.98678 + 23.4398i 0.324698 + 0.762094i
\(947\) 30.7645 + 25.1185i 0.999713 + 0.816241i 0.982997 0.183620i \(-0.0587815\pi\)
0.0167158 + 0.999860i \(0.494679\pi\)
\(948\) −0.483399 1.55128i −0.0157001 0.0503833i
\(949\) 0.308814 + 1.49901i 0.0100245 + 0.0486600i
\(950\) 8.70348 + 6.65321i 0.282378 + 0.215858i
\(951\) −13.3051 20.1312i −0.431448 0.652798i
\(952\) 1.39891 + 2.80106i 0.0453388 + 0.0907828i
\(953\) −52.5531 + 1.05848i −1.70236 + 0.0342875i −0.861745 0.507342i \(-0.830628\pi\)
−0.840617 + 0.541629i \(0.817808\pi\)
\(954\) −27.6929 + 21.6960i −0.896591 + 0.702434i
\(955\) 0.164345 + 6.29873i 0.00531809 + 0.203822i
\(956\) −3.16782 + 31.3541i −0.102455 + 1.01406i
\(957\) 18.6761 35.5843i 0.603712 1.15028i
\(958\) 49.6382 + 53.8069i 1.60374 + 1.73842i
\(959\) 1.40200 1.05354i 0.0452731 0.0340205i
\(960\) 2.93974 0.870489i 0.0948796 0.0280949i
\(961\) −7.25410 29.4310i −0.234003 0.949388i
\(962\) 34.4530 54.6990i 1.11081 1.76357i
\(963\) −0.542606 + 0.328017i −0.0174852 + 0.0105702i
\(964\) 6.98403 + 31.0100i 0.224941 + 0.998765i
\(965\) −26.7543 24.3886i −0.861251 0.785096i
\(966\) 1.64968 10.1509i 0.0530776 0.326599i
\(967\) −17.7552 46.8167i −0.570970 1.50552i −0.840106 0.542422i \(-0.817507\pi\)
0.269136 0.963102i \(-0.413262\pi\)
\(968\) −0.435450 5.39402i −0.0139959 0.173370i
\(969\) 0.0729952 + 3.62418i 0.00234494 + 0.116426i
\(970\) 5.04237 + 11.0280i 0.161901 + 0.354086i
\(971\) 35.3482 + 26.5625i 1.13438 + 0.852430i 0.990547 0.137173i \(-0.0438015\pi\)
0.143831 + 0.989602i \(0.454058\pi\)
\(972\) 2.39360 + 23.6911i 0.0767747 + 0.759892i
\(973\) −0.366142 9.08572i −0.0117380 0.291275i
\(974\) 30.0746 43.5706i 0.963652 1.39609i
\(975\) 16.7408 38.5988i 0.536134 1.23615i
\(976\) −12.8649 18.6380i −0.411795 0.596587i
\(977\) 30.4966 22.9167i 0.975674 0.733171i 0.0119100 0.999929i \(-0.496209\pi\)
0.963764 + 0.266758i \(0.0859524\pi\)
\(978\) −49.0886 0.988700i −1.56968 0.0316151i
\(979\) 22.7975 + 48.0447i 0.728612 + 1.53552i
\(980\) 6.79029 + 8.56178i 0.216908 + 0.273496i
\(981\) 28.7289 + 31.1416i 0.917243 + 0.994274i
\(982\) −39.1510 + 52.1005i −1.24936 + 1.66259i
\(983\) −5.33778 43.9605i −0.170249 1.40212i −0.787964 0.615722i \(-0.788865\pi\)
0.617715 0.786402i \(-0.288059\pi\)
\(984\) 9.15346 + 27.4180i 0.291802 + 0.874053i
\(985\) 15.2989 21.5050i 0.487462 0.685205i
\(986\) 9.38156 + 3.77575i 0.298770 + 0.120244i
\(987\) −7.31833 5.73354i −0.232945 0.182501i
\(988\) 5.11748 0.947257i 0.162809 0.0301362i
\(989\) −5.44368 0.660982i −0.173099 0.0210180i
\(990\) −29.0596 23.4398i −0.923576 0.744966i
\(991\) −2.29922 3.98237i −0.0730371 0.126504i 0.827194 0.561917i \(-0.189936\pi\)
−0.900231 + 0.435413i \(0.856602\pi\)
\(992\) 1.26875 + 4.73504i 0.0402828 + 0.150338i
\(993\) −16.3543 + 66.3522i −0.518989 + 2.10562i
\(994\) −13.9939 19.4250i −0.443859 0.616123i
\(995\) −35.8698 + 42.6816i −1.13715 + 1.35310i
\(996\) −22.1408 + 9.96475i −0.701557 + 0.315745i
\(997\) 10.7912 5.94386i 0.341762 0.188244i −0.302308 0.953210i \(-0.597757\pi\)
0.644070 + 0.764966i \(0.277244\pi\)
\(998\) −26.2110 + 17.3234i −0.829693 + 0.548362i
\(999\) −12.9975 0.261785i −0.411224 0.00828251i
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 845.2.bn.a.392.19 yes 4272
5.3 odd 4 845.2.bi.a.223.71 yes 4272
169.72 odd 156 845.2.bi.a.72.71 4272
845.748 even 156 inner 845.2.bn.a.748.19 yes 4272
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
845.2.bi.a.72.71 4272 169.72 odd 156
845.2.bi.a.223.71 yes 4272 5.3 odd 4
845.2.bn.a.392.19 yes 4272 1.1 even 1 trivial
845.2.bn.a.748.19 yes 4272 845.748 even 156 inner