Properties

Label 456.2.bk.a.253.18
Level $456$
Weight $2$
Character 456.253
Analytic conductor $3.641$
Analytic rank $0$
Dimension $240$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [456,2,Mod(61,456)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(456, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("456.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.bk (of order \(18\), degree \(6\), 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: \(3.64117833217\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(40\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 253.18
Character \(\chi\) \(=\) 456.253
Dual form 456.2.bk.a.301.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.321468 + 1.37719i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-1.79332 - 0.885448i) q^{4} +(1.48904 - 0.262559i) q^{5} +(-1.18419 - 0.773109i) q^{6} +(1.07835 - 1.86775i) q^{7} +(1.79593 - 2.18510i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\) \(q+(-0.321468 + 1.37719i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-1.79332 - 0.885448i) q^{4} +(1.48904 - 0.262559i) q^{5} +(-1.18419 - 0.773109i) q^{6} +(1.07835 - 1.86775i) q^{7} +(1.79593 - 2.18510i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-0.117087 + 2.13510i) q^{10} +(2.84612 - 1.64321i) q^{11} +(1.44540 - 1.38232i) q^{12} +(1.41078 + 3.87609i) q^{13} +(2.22560 + 2.08552i) q^{14} +(-0.262559 + 1.48904i) q^{15} +(2.43196 + 3.17578i) q^{16} +(1.31755 - 1.10555i) q^{17} +(1.13150 - 0.848354i) q^{18} +(4.29243 - 0.758311i) q^{19} +(-2.90281 - 0.847620i) q^{20} +(1.38630 + 1.65213i) q^{21} +(1.34808 + 4.44790i) q^{22} +(0.464555 - 2.63462i) q^{23} +(1.43908 + 2.43497i) q^{24} +(-2.55015 + 0.928178i) q^{25} +(-5.79164 + 0.696876i) q^{26} +(0.866025 - 0.500000i) q^{27} +(-3.58762 + 2.39465i) q^{28} +(-1.48197 + 1.76615i) q^{29} +(-1.96630 - 0.840275i) q^{30} +(-0.588975 + 1.02013i) q^{31} +(-5.15545 + 2.32837i) q^{32} +(0.570681 + 3.23649i) q^{33} +(1.09901 + 2.16992i) q^{34} +(1.11531 - 3.06430i) q^{35} +(0.804605 + 1.83101i) q^{36} +5.85297i q^{37} +(-0.335542 + 6.15528i) q^{38} -4.12485 q^{39} +(2.10050 - 3.72524i) q^{40} +(-3.69110 - 1.34345i) q^{41} +(-2.72095 + 1.37809i) q^{42} +(9.14785 - 1.61301i) q^{43} +(-6.55898 + 0.426702i) q^{44} +(-1.30944 - 0.756008i) q^{45} +(3.47904 + 1.48673i) q^{46} +(-4.24082 - 3.55847i) q^{47} +(-3.81603 + 1.19912i) q^{48} +(1.17433 + 2.03400i) q^{49} +(-0.458487 - 3.81042i) q^{50} +(0.588254 + 1.61621i) q^{51} +(0.902098 - 8.20022i) q^{52} +(1.04533 + 0.184320i) q^{53} +(0.410196 + 1.35342i) q^{54} +(3.80657 - 3.19409i) q^{55} +(-2.14459 - 5.71064i) q^{56} +(-0.755519 + 4.29292i) q^{57} +(-1.95592 - 2.60872i) q^{58} +(7.04593 + 8.39701i) q^{59} +(1.78932 - 2.43785i) q^{60} +(-4.91604 - 0.866831i) q^{61} +(-1.21558 - 1.13907i) q^{62} +(-2.02663 + 0.737634i) q^{63} +(-1.54930 - 7.84855i) q^{64} +(3.11841 + 5.40125i) q^{65} +(-4.64073 - 0.254493i) q^{66} +(-0.902843 + 1.07597i) q^{67} +(-3.34169 + 0.815989i) q^{68} +(2.31685 + 1.33763i) q^{69} +(3.86159 + 2.52108i) q^{70} +(-2.42144 - 13.7327i) q^{71} +(-2.78031 + 0.519482i) q^{72} +(9.10897 + 3.31540i) q^{73} +(-8.06066 - 1.88154i) q^{74} -2.71381i q^{75} +(-8.36913 - 2.44083i) q^{76} -7.08781i q^{77} +(1.32601 - 5.68070i) q^{78} +(-5.05163 - 1.83864i) q^{79} +(4.45513 + 4.09034i) q^{80} +(0.173648 + 0.984808i) q^{81} +(3.03676 - 4.65148i) q^{82} +(-2.61895 - 1.51205i) q^{83} +(-1.02320 - 4.19028i) q^{84} +(1.67162 - 1.99215i) q^{85} +(-0.719317 + 13.1169i) q^{86} +(-1.15277 - 1.99666i) q^{87} +(1.52085 - 9.17014i) q^{88} +(-3.20059 + 1.16492i) q^{89} +(1.46211 - 1.56032i) q^{90} +(8.76089 + 1.54478i) q^{91} +(-3.16591 + 4.31337i) q^{92} +(-0.757172 - 0.902362i) q^{93} +(6.26398 - 4.69648i) q^{94} +(6.19252 - 2.25617i) q^{95} +(-0.424684 - 5.64089i) q^{96} +(9.85764 - 8.27154i) q^{97} +(-3.17872 + 0.963411i) q^{98} +(-3.23649 - 0.570681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 6 q^{4} + 6 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48} - 120 q^{49} + 18 q^{50} + 6 q^{52} - 6 q^{54} + 72 q^{58} - 12 q^{60} + 12 q^{62} + 30 q^{64} - 48 q^{66} - 78 q^{68} - 108 q^{70} - 36 q^{72} - 24 q^{73} - 96 q^{74} - 48 q^{76} - 96 q^{78} - 114 q^{80} - 66 q^{82} - 36 q^{84} - 24 q^{86} - 24 q^{88} + 6 q^{90} - 108 q^{94} + 120 q^{95} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(343\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.321468 + 1.37719i −0.227313 + 0.973822i
\(3\) −0.342020 + 0.939693i −0.197465 + 0.542532i
\(4\) −1.79332 0.885448i −0.896658 0.442724i
\(5\) 1.48904 0.262559i 0.665921 0.117420i 0.169538 0.985524i \(-0.445772\pi\)
0.496383 + 0.868104i \(0.334661\pi\)
\(6\) −1.18419 0.773109i −0.483443 0.315620i
\(7\) 1.07835 1.86775i 0.407577 0.705945i −0.587040 0.809558i \(-0.699707\pi\)
0.994618 + 0.103613i \(0.0330403\pi\)
\(8\) 1.79593 2.18510i 0.634956 0.772548i
\(9\) −0.766044 0.642788i −0.255348 0.214263i
\(10\) −0.117087 + 2.13510i −0.0370262 + 0.675179i
\(11\) 2.84612 1.64321i 0.858139 0.495447i −0.00524994 0.999986i \(-0.501671\pi\)
0.863388 + 0.504540i \(0.168338\pi\)
\(12\) 1.44540 1.38232i 0.417251 0.399043i
\(13\) 1.41078 + 3.87609i 0.391280 + 1.07503i 0.966418 + 0.256976i \(0.0827263\pi\)
−0.575138 + 0.818057i \(0.695051\pi\)
\(14\) 2.22560 + 2.08552i 0.594817 + 0.557378i
\(15\) −0.262559 + 1.48904i −0.0677924 + 0.384470i
\(16\) 2.43196 + 3.17578i 0.607991 + 0.793944i
\(17\) 1.31755 1.10555i 0.319553 0.268136i −0.468874 0.883265i \(-0.655340\pi\)
0.788427 + 0.615128i \(0.210896\pi\)
\(18\) 1.13150 0.848354i 0.266697 0.199959i
\(19\) 4.29243 0.758311i 0.984751 0.173968i
\(20\) −2.90281 0.847620i −0.649088 0.189534i
\(21\) 1.38630 + 1.65213i 0.302515 + 0.360523i
\(22\) 1.34808 + 4.44790i 0.287411 + 0.948295i
\(23\) 0.464555 2.63462i 0.0968664 0.549357i −0.897293 0.441435i \(-0.854469\pi\)
0.994159 0.107921i \(-0.0344195\pi\)
\(24\) 1.43908 + 2.43497i 0.293750 + 0.497035i
\(25\) −2.55015 + 0.928178i −0.510029 + 0.185636i
\(26\) −5.79164 + 0.696876i −1.13583 + 0.136669i
\(27\) 0.866025 0.500000i 0.166667 0.0962250i
\(28\) −3.58762 + 2.39465i −0.677996 + 0.452547i
\(29\) −1.48197 + 1.76615i −0.275196 + 0.327965i −0.885885 0.463905i \(-0.846448\pi\)
0.610689 + 0.791870i \(0.290892\pi\)
\(30\) −1.96630 0.840275i −0.358995 0.153412i
\(31\) −0.588975 + 1.02013i −0.105783 + 0.183222i −0.914058 0.405584i \(-0.867068\pi\)
0.808275 + 0.588805i \(0.200402\pi\)
\(32\) −5.15545 + 2.32837i −0.911364 + 0.411602i
\(33\) 0.570681 + 3.23649i 0.0993428 + 0.563401i
\(34\) 1.09901 + 2.16992i 0.188479 + 0.372138i
\(35\) 1.11531 3.06430i 0.188522 0.517961i
\(36\) 0.804605 + 1.83101i 0.134101 + 0.305169i
\(37\) 5.85297i 0.962222i 0.876660 + 0.481111i \(0.159767\pi\)
−0.876660 + 0.481111i \(0.840233\pi\)
\(38\) −0.335542 + 6.15528i −0.0544321 + 0.998517i
\(39\) −4.12485 −0.660504
\(40\) 2.10050 3.72524i 0.332118 0.589013i
\(41\) −3.69110 1.34345i −0.576454 0.209812i 0.0373074 0.999304i \(-0.488122\pi\)
−0.613761 + 0.789492i \(0.710344\pi\)
\(42\) −2.72095 + 1.37809i −0.419851 + 0.212644i
\(43\) 9.14785 1.61301i 1.39503 0.245982i 0.574933 0.818201i \(-0.305028\pi\)
0.820101 + 0.572219i \(0.193917\pi\)
\(44\) −6.55898 + 0.426702i −0.988803 + 0.0643277i
\(45\) −1.30944 0.756008i −0.195200 0.112699i
\(46\) 3.47904 + 1.48673i 0.512957 + 0.219206i
\(47\) −4.24082 3.55847i −0.618587 0.519056i 0.278772 0.960357i \(-0.410073\pi\)
−0.897359 + 0.441301i \(0.854517\pi\)
\(48\) −3.81603 + 1.19912i −0.550797 + 0.173078i
\(49\) 1.17433 + 2.03400i 0.167761 + 0.290571i
\(50\) −0.458487 3.81042i −0.0648398 0.538875i
\(51\) 0.588254 + 1.61621i 0.0823720 + 0.226315i
\(52\) 0.902098 8.20022i 0.125098 1.13717i
\(53\) 1.04533 + 0.184320i 0.143587 + 0.0253183i 0.244980 0.969528i \(-0.421219\pi\)
−0.101392 + 0.994847i \(0.532330\pi\)
\(54\) 0.410196 + 1.35342i 0.0558206 + 0.184177i
\(55\) 3.80657 3.19409i 0.513277 0.430691i
\(56\) −2.14459 5.71064i −0.286583 0.763117i
\(57\) −0.755519 + 4.29292i −0.100071 + 0.568612i
\(58\) −1.95592 2.60872i −0.256824 0.342542i
\(59\) 7.04593 + 8.39701i 0.917302 + 1.09320i 0.995357 + 0.0962487i \(0.0306844\pi\)
−0.0780556 + 0.996949i \(0.524871\pi\)
\(60\) 1.78932 2.43785i 0.231000 0.314724i
\(61\) −4.91604 0.866831i −0.629434 0.110986i −0.150175 0.988659i \(-0.547984\pi\)
−0.479260 + 0.877673i \(0.659095\pi\)
\(62\) −1.21558 1.13907i −0.154379 0.144662i
\(63\) −2.02663 + 0.737634i −0.255332 + 0.0929331i
\(64\) −1.54930 7.84855i −0.193662 0.981068i
\(65\) 3.11841 + 5.40125i 0.386792 + 0.669943i
\(66\) −4.64073 0.254493i −0.571234 0.0313259i
\(67\) −0.902843 + 1.07597i −0.110300 + 0.131450i −0.818370 0.574692i \(-0.805122\pi\)
0.708070 + 0.706142i \(0.249566\pi\)
\(68\) −3.34169 + 0.815989i −0.405240 + 0.0989532i
\(69\) 2.31685 + 1.33763i 0.278916 + 0.161032i
\(70\) 3.86159 + 2.52108i 0.461548 + 0.301326i
\(71\) −2.42144 13.7327i −0.287372 1.62977i −0.696688 0.717374i \(-0.745344\pi\)
0.409316 0.912393i \(-0.365767\pi\)
\(72\) −2.78031 + 0.519482i −0.327663 + 0.0612216i
\(73\) 9.10897 + 3.31540i 1.06612 + 0.388038i 0.814726 0.579846i \(-0.196887\pi\)
0.251399 + 0.967884i \(0.419109\pi\)
\(74\) −8.06066 1.88154i −0.937033 0.218725i
\(75\) 2.71381i 0.313364i
\(76\) −8.36913 2.44083i −0.960005 0.279983i
\(77\) 7.08781i 0.807731i
\(78\) 1.32601 5.68070i 0.150141 0.643213i
\(79\) −5.05163 1.83864i −0.568353 0.206864i 0.0418290 0.999125i \(-0.486682\pi\)
−0.610182 + 0.792261i \(0.708904\pi\)
\(80\) 4.45513 + 4.09034i 0.498099 + 0.457314i
\(81\) 0.173648 + 0.984808i 0.0192942 + 0.109423i
\(82\) 3.03676 4.65148i 0.335355 0.513670i
\(83\) −2.61895 1.51205i −0.287467 0.165969i 0.349332 0.936999i \(-0.386408\pi\)
−0.636799 + 0.771030i \(0.719742\pi\)
\(84\) −1.02320 4.19028i −0.111640 0.457197i
\(85\) 1.67162 1.99215i 0.181312 0.216079i
\(86\) −0.719317 + 13.1169i −0.0775660 + 1.41443i
\(87\) −1.15277 1.99666i −0.123590 0.214064i
\(88\) 1.52085 9.17014i 0.162124 0.977540i
\(89\) −3.20059 + 1.16492i −0.339262 + 0.123481i −0.506033 0.862514i \(-0.668888\pi\)
0.166770 + 0.985996i \(0.446666\pi\)
\(90\) 1.46211 1.56032i 0.154120 0.164472i
\(91\) 8.76089 + 1.54478i 0.918391 + 0.161937i
\(92\) −3.16591 + 4.31337i −0.330069 + 0.449700i
\(93\) −0.757172 0.902362i −0.0785150 0.0935706i
\(94\) 6.26398 4.69648i 0.646081 0.484405i
\(95\) 6.19252 2.25617i 0.635339 0.231478i
\(96\) −0.424684 5.64089i −0.0433442 0.575721i
\(97\) 9.85764 8.27154i 1.00089 0.839848i 0.0137839 0.999905i \(-0.495612\pi\)
0.987108 + 0.160057i \(0.0511679\pi\)
\(98\) −3.17872 + 0.963411i −0.321099 + 0.0973192i
\(99\) −3.23649 0.570681i −0.325280 0.0573556i
\(100\) 5.39507 + 0.593506i 0.539507 + 0.0593506i
\(101\) −3.04303 8.36066i −0.302793 0.831916i −0.994012 0.109271i \(-0.965148\pi\)
0.691219 0.722645i \(-0.257074\pi\)
\(102\) −2.41494 + 0.290576i −0.239115 + 0.0287714i
\(103\) 7.70260 + 13.3413i 0.758959 + 1.31456i 0.943382 + 0.331709i \(0.107625\pi\)
−0.184422 + 0.982847i \(0.559041\pi\)
\(104\) 11.0033 + 3.87847i 1.07896 + 0.380316i
\(105\) 2.49804 + 2.09610i 0.243784 + 0.204559i
\(106\) −0.589885 + 1.38037i −0.0572947 + 0.134073i
\(107\) −17.5926 10.1571i −1.70074 0.981923i −0.945011 0.327039i \(-0.893949\pi\)
−0.755729 0.654884i \(-0.772717\pi\)
\(108\) −1.99578 + 0.129838i −0.192044 + 0.0124936i
\(109\) −9.62984 + 1.69800i −0.922372 + 0.162639i −0.614616 0.788826i \(-0.710689\pi\)
−0.307756 + 0.951465i \(0.599578\pi\)
\(110\) 3.17518 + 6.26917i 0.302742 + 0.597742i
\(111\) −5.49999 2.00183i −0.522036 0.190006i
\(112\) 8.55407 1.11772i 0.808284 0.105615i
\(113\) 15.1227 1.42262 0.711310 0.702878i \(-0.248102\pi\)
0.711310 + 0.702878i \(0.248102\pi\)
\(114\) −5.66930 2.42053i −0.530979 0.226704i
\(115\) 4.04504i 0.377202i
\(116\) 4.22148 1.85505i 0.391954 0.172237i
\(117\) 1.41078 3.87609i 0.130427 0.358344i
\(118\) −13.8293 + 7.00422i −1.27309 + 0.644791i
\(119\) −0.644128 3.65303i −0.0590471 0.334873i
\(120\) 2.78217 + 3.24793i 0.253976 + 0.296494i
\(121\) −0.0997203 + 0.172721i −0.00906548 + 0.0157019i
\(122\) 2.77414 6.49167i 0.251159 0.587728i
\(123\) 2.52486 3.00902i 0.227659 0.271314i
\(124\) 1.95949 1.30792i 0.175968 0.117454i
\(125\) −10.1008 + 5.83170i −0.903443 + 0.521603i
\(126\) −0.364365 3.02819i −0.0324602 0.269772i
\(127\) −2.73148 + 0.994178i −0.242380 + 0.0882191i −0.460354 0.887736i \(-0.652277\pi\)
0.217974 + 0.975955i \(0.430055\pi\)
\(128\) 11.3070 + 0.389379i 0.999408 + 0.0344166i
\(129\) −1.61301 + 9.14785i −0.142018 + 0.805423i
\(130\) −8.44104 + 2.55832i −0.740328 + 0.224380i
\(131\) 0.316563 + 0.377265i 0.0276582 + 0.0329618i 0.779696 0.626158i \(-0.215373\pi\)
−0.752038 + 0.659120i \(0.770929\pi\)
\(132\) 1.84233 6.30936i 0.160355 0.549159i
\(133\) 3.21240 8.83493i 0.278550 0.766086i
\(134\) −1.19158 1.58928i −0.102937 0.137293i
\(135\) 1.15827 0.971905i 0.0996881 0.0836482i
\(136\) −0.0495240 4.86447i −0.00424664 0.417125i
\(137\) 0.634124 3.59630i 0.0541769 0.307252i −0.945663 0.325148i \(-0.894586\pi\)
0.999840 + 0.0178962i \(0.00569684\pi\)
\(138\) −2.58697 + 2.76074i −0.220218 + 0.235010i
\(139\) −2.32264 6.38139i −0.197004 0.541263i 0.801376 0.598160i \(-0.204101\pi\)
−0.998380 + 0.0568975i \(0.981879\pi\)
\(140\) −4.71339 + 4.50770i −0.398354 + 0.380971i
\(141\) 4.79431 2.76800i 0.403754 0.233107i
\(142\) 19.6909 + 1.07983i 1.65243 + 0.0906175i
\(143\) 10.3845 + 8.71361i 0.868394 + 0.728669i
\(144\) 0.178356 3.99602i 0.0148630 0.333002i
\(145\) −1.74301 + 3.01898i −0.144749 + 0.250712i
\(146\) −7.49418 + 11.4790i −0.620223 + 0.950010i
\(147\) −2.31298 + 0.407840i −0.190771 + 0.0336381i
\(148\) 5.18250 10.4962i 0.425999 0.862784i
\(149\) −0.0190462 + 0.0523290i −0.00156032 + 0.00428696i −0.940470 0.339876i \(-0.889615\pi\)
0.938910 + 0.344163i \(0.111837\pi\)
\(150\) 3.73744 + 0.872404i 0.305160 + 0.0712315i
\(151\) −18.9073 −1.53866 −0.769329 0.638853i \(-0.779409\pi\)
−0.769329 + 0.638853i \(0.779409\pi\)
\(152\) 6.05191 10.7412i 0.490875 0.871230i
\(153\) −1.71994 −0.139049
\(154\) 9.76128 + 2.27851i 0.786586 + 0.183607i
\(155\) −0.609165 + 1.67367i −0.0489293 + 0.134432i
\(156\) 7.39715 + 3.65234i 0.592246 + 0.292421i
\(157\) −19.0822 + 3.36470i −1.52292 + 0.268533i −0.871581 0.490251i \(-0.836905\pi\)
−0.651343 + 0.758784i \(0.725794\pi\)
\(158\) 4.15611 6.36600i 0.330642 0.506452i
\(159\) −0.530729 + 0.919249i −0.0420895 + 0.0729012i
\(160\) −7.06536 + 4.82066i −0.558566 + 0.381106i
\(161\) −4.41988 3.70872i −0.348335 0.292288i
\(162\) −1.41209 0.0774378i −0.110944 0.00608409i
\(163\) −2.09889 + 1.21180i −0.164398 + 0.0949152i −0.579942 0.814658i \(-0.696925\pi\)
0.415544 + 0.909573i \(0.363591\pi\)
\(164\) 5.42976 + 5.67751i 0.423993 + 0.443339i
\(165\) 1.69954 + 4.66944i 0.132309 + 0.363516i
\(166\) 2.92429 3.12072i 0.226969 0.242215i
\(167\) 4.01218 22.7542i 0.310472 1.76077i −0.286088 0.958203i \(-0.592355\pi\)
0.596560 0.802569i \(-0.296534\pi\)
\(168\) 6.09974 0.0621000i 0.470605 0.00479112i
\(169\) −3.07517 + 2.58038i −0.236552 + 0.198490i
\(170\) 2.20621 + 2.94255i 0.169208 + 0.225683i
\(171\) −3.77563 2.17822i −0.288729 0.166573i
\(172\) −17.8332 5.20730i −1.35977 0.397053i
\(173\) 8.88546 + 10.5893i 0.675549 + 0.805088i 0.989528 0.144342i \(-0.0461065\pi\)
−0.313979 + 0.949430i \(0.601662\pi\)
\(174\) 3.12036 0.945724i 0.236554 0.0716952i
\(175\) −1.01634 + 5.76395i −0.0768280 + 0.435713i
\(176\) 12.1401 + 5.04242i 0.915097 + 0.380087i
\(177\) −10.3005 + 3.74906i −0.774230 + 0.281797i
\(178\) −0.575430 4.78232i −0.0431303 0.358450i
\(179\) −13.4410 + 7.76018i −1.00463 + 0.580023i −0.909615 0.415453i \(-0.863623\pi\)
−0.0950149 + 0.995476i \(0.530290\pi\)
\(180\) 1.67884 + 2.51520i 0.125133 + 0.187472i
\(181\) −13.5224 + 16.1153i −1.00511 + 1.19784i −0.0249381 + 0.999689i \(0.507939\pi\)
−0.980171 + 0.198153i \(0.936506\pi\)
\(182\) −4.94381 + 11.5688i −0.366460 + 0.857539i
\(183\) 2.49594 4.32309i 0.184505 0.319572i
\(184\) −4.92260 5.74669i −0.362899 0.423651i
\(185\) 1.53675 + 8.71533i 0.112984 + 0.640764i
\(186\) 1.48613 0.752690i 0.108969 0.0551899i
\(187\) 1.93325 5.31156i 0.141373 0.388419i
\(188\) 4.45429 + 10.1365i 0.324862 + 0.739279i
\(189\) 2.15670i 0.156877i
\(190\) 1.11648 + 9.25358i 0.0809983 + 0.671325i
\(191\) −19.8684 −1.43763 −0.718815 0.695202i \(-0.755315\pi\)
−0.718815 + 0.695202i \(0.755315\pi\)
\(192\) 7.90511 + 1.22850i 0.570502 + 0.0886591i
\(193\) −25.4923 9.27843i −1.83497 0.667876i −0.991400 0.130863i \(-0.958225\pi\)
−0.843574 0.537013i \(-0.819553\pi\)
\(194\) 8.22258 + 16.2349i 0.590347 + 1.16560i
\(195\) −6.14208 + 1.08301i −0.439843 + 0.0775563i
\(196\) −0.304945 4.68741i −0.0217818 0.334815i
\(197\) 3.86498 + 2.23145i 0.275369 + 0.158984i 0.631325 0.775518i \(-0.282511\pi\)
−0.355956 + 0.934503i \(0.615845\pi\)
\(198\) 1.82637 4.27382i 0.129794 0.303727i
\(199\) −3.58954 3.01198i −0.254456 0.213514i 0.506633 0.862162i \(-0.330890\pi\)
−0.761088 + 0.648649i \(0.775335\pi\)
\(200\) −2.55172 + 7.23926i −0.180434 + 0.511893i
\(201\) −0.702287 1.21640i −0.0495355 0.0857981i
\(202\) 12.4925 1.50315i 0.878967 0.105761i
\(203\) 1.70065 + 4.67248i 0.119362 + 0.327944i
\(204\) 0.376148 3.41925i 0.0263356 0.239395i
\(205\) −5.84895 1.03133i −0.408509 0.0720311i
\(206\) −20.8497 + 6.31915i −1.45266 + 0.440276i
\(207\) −2.04937 + 1.71963i −0.142441 + 0.119522i
\(208\) −8.87861 + 13.9068i −0.615621 + 0.964265i
\(209\) 10.9707 9.21161i 0.758861 0.637181i
\(210\) −3.68978 + 2.76645i −0.254619 + 0.190903i
\(211\) 15.6642 + 18.6679i 1.07837 + 1.28515i 0.956224 + 0.292636i \(0.0945325\pi\)
0.122144 + 0.992512i \(0.461023\pi\)
\(212\) −1.71140 1.25613i −0.117540 0.0862714i
\(213\) 13.7327 + 2.42144i 0.940946 + 0.165914i
\(214\) 19.6437 20.9632i 1.34282 1.43301i
\(215\) 13.1980 4.80369i 0.900099 0.327609i
\(216\) 0.462769 2.79031i 0.0314875 0.189857i
\(217\) 1.27024 + 2.20012i 0.0862296 + 0.149354i
\(218\) 0.757217 13.8080i 0.0512852 0.935195i
\(219\) −6.23091 + 7.42570i −0.421046 + 0.501783i
\(220\) −9.65457 + 2.35749i −0.650911 + 0.158942i
\(221\) 6.14400 + 3.54724i 0.413290 + 0.238613i
\(222\) 4.52498 6.93102i 0.303697 0.465179i
\(223\) −0.196499 1.11440i −0.0131585 0.0746257i 0.977521 0.210836i \(-0.0676187\pi\)
−0.990680 + 0.136211i \(0.956508\pi\)
\(224\) −1.21055 + 12.1399i −0.0808832 + 0.811132i
\(225\) 2.55015 + 0.928178i 0.170010 + 0.0618785i
\(226\) −4.86146 + 20.8268i −0.323380 + 1.38538i
\(227\) 13.3600i 0.886738i −0.896339 0.443369i \(-0.853783\pi\)
0.896339 0.443369i \(-0.146217\pi\)
\(228\) 5.15604 7.02960i 0.341467 0.465546i
\(229\) 10.2820i 0.679456i −0.940524 0.339728i \(-0.889665\pi\)
0.940524 0.339728i \(-0.110335\pi\)
\(230\) 5.57080 + 1.30035i 0.367328 + 0.0857428i
\(231\) 6.66037 + 2.42417i 0.438220 + 0.159499i
\(232\) 1.19769 + 6.41013i 0.0786321 + 0.420845i
\(233\) 1.09703 + 6.22159i 0.0718691 + 0.407590i 0.999425 + 0.0339056i \(0.0107945\pi\)
−0.927556 + 0.373684i \(0.878094\pi\)
\(234\) 4.88459 + 3.18896i 0.319316 + 0.208469i
\(235\) −7.24907 4.18525i −0.472877 0.273016i
\(236\) −5.20046 21.2973i −0.338521 1.38634i
\(237\) 3.45552 4.11813i 0.224460 0.267501i
\(238\) 5.23799 + 0.287247i 0.339529 + 0.0186194i
\(239\) 7.57619 + 13.1223i 0.490063 + 0.848814i 0.999935 0.0114365i \(-0.00364043\pi\)
−0.509872 + 0.860251i \(0.670307\pi\)
\(240\) −5.36740 + 2.78748i −0.346464 + 0.179931i
\(241\) −11.5696 + 4.21099i −0.745264 + 0.271254i −0.686611 0.727025i \(-0.740903\pi\)
−0.0586524 + 0.998278i \(0.518680\pi\)
\(242\) −0.205813 0.192858i −0.0132301 0.0123974i
\(243\) −0.984808 0.173648i −0.0631754 0.0111395i
\(244\) 8.04848 + 5.90740i 0.515251 + 0.378182i
\(245\) 2.28267 + 2.72038i 0.145835 + 0.173799i
\(246\) 3.33233 + 4.44453i 0.212461 + 0.283373i
\(247\) 8.99495 + 15.5680i 0.572335 + 0.990570i
\(248\) 1.17134 + 3.11905i 0.0743800 + 0.198060i
\(249\) 2.31659 1.94385i 0.146808 0.123187i
\(250\) −4.78428 15.7854i −0.302585 0.998359i
\(251\) −11.4543 2.01970i −0.722988 0.127482i −0.199967 0.979803i \(-0.564084\pi\)
−0.523020 + 0.852320i \(0.675195\pi\)
\(252\) 4.28753 + 0.471666i 0.270089 + 0.0297122i
\(253\) −3.00706 8.26182i −0.189052 0.519416i
\(254\) −0.491089 4.08137i −0.0308137 0.256088i
\(255\) 1.30029 + 2.25216i 0.0814271 + 0.141036i
\(256\) −4.17110 + 15.4467i −0.260693 + 0.965422i
\(257\) 17.3687 + 14.5741i 1.08343 + 0.909108i 0.996201 0.0870801i \(-0.0277536\pi\)
0.0872313 + 0.996188i \(0.472198\pi\)
\(258\) −12.0798 5.16217i −0.752056 0.321383i
\(259\) 10.9319 + 6.31154i 0.679276 + 0.392180i
\(260\) −0.809776 12.4473i −0.0502202 0.771952i
\(261\) 2.27052 0.400353i 0.140541 0.0247812i
\(262\) −0.621332 + 0.314689i −0.0383860 + 0.0194416i
\(263\) −10.8838 3.96139i −0.671126 0.244270i −0.0160936 0.999870i \(-0.505123\pi\)
−0.655033 + 0.755600i \(0.727345\pi\)
\(264\) 8.09695 + 4.56551i 0.498333 + 0.280988i
\(265\) 1.60494 0.0985907
\(266\) 11.1347 + 7.26424i 0.682713 + 0.445399i
\(267\) 3.40600i 0.208444i
\(268\) 2.57180 1.13013i 0.157097 0.0690335i
\(269\) −1.94994 + 5.35741i −0.118890 + 0.326647i −0.984835 0.173491i \(-0.944495\pi\)
0.865946 + 0.500138i \(0.166717\pi\)
\(270\) 0.966152 + 1.90760i 0.0587981 + 0.116093i
\(271\) 3.60290 + 20.4330i 0.218860 + 1.24122i 0.874080 + 0.485781i \(0.161465\pi\)
−0.655220 + 0.755438i \(0.727424\pi\)
\(272\) 6.71523 + 1.49557i 0.407170 + 0.0906822i
\(273\) −4.44802 + 7.70420i −0.269206 + 0.466279i
\(274\) 4.74894 + 2.02941i 0.286894 + 0.122601i
\(275\) −5.73284 + 6.83214i −0.345703 + 0.411993i
\(276\) −2.97044 4.45025i −0.178799 0.267873i
\(277\) −7.24924 + 4.18535i −0.435564 + 0.251473i −0.701714 0.712458i \(-0.747582\pi\)
0.266150 + 0.963932i \(0.414248\pi\)
\(278\) 9.53506 1.14730i 0.571875 0.0688105i
\(279\) 1.10691 0.402883i 0.0662690 0.0241200i
\(280\) −4.69277 7.94032i −0.280447 0.474525i
\(281\) 2.62353 14.8788i 0.156507 0.887594i −0.800888 0.598814i \(-0.795639\pi\)
0.957395 0.288781i \(-0.0932499\pi\)
\(282\) 2.27084 + 7.49251i 0.135227 + 0.446173i
\(283\) 2.25621 + 2.68885i 0.134118 + 0.159835i 0.828923 0.559362i \(-0.188954\pi\)
−0.694805 + 0.719198i \(0.744510\pi\)
\(284\) −7.81715 + 26.7711i −0.463862 + 1.58857i
\(285\) 0.00214289 + 6.59072i 0.000126934 + 0.390401i
\(286\) −15.3386 + 11.5003i −0.906991 + 0.680025i
\(287\) −6.48953 + 5.44537i −0.383065 + 0.321430i
\(288\) 5.44595 + 1.53023i 0.320906 + 0.0901694i
\(289\) −2.43834 + 13.8285i −0.143431 + 0.813440i
\(290\) −3.59739 3.37096i −0.211246 0.197950i
\(291\) 4.40120 + 12.0922i 0.258003 + 0.708856i
\(292\) −13.3997 14.0111i −0.784156 0.819936i
\(293\) −3.87746 + 2.23865i −0.226524 + 0.130783i −0.608967 0.793195i \(-0.708416\pi\)
0.382444 + 0.923979i \(0.375083\pi\)
\(294\) 0.181875 3.31652i 0.0106072 0.193423i
\(295\) 12.6964 + 10.6536i 0.739213 + 0.620274i
\(296\) 12.7893 + 10.5115i 0.743363 + 0.610968i
\(297\) 1.64321 2.84612i 0.0953487 0.165149i
\(298\) −0.0659443 0.0430524i −0.00382005 0.00249396i
\(299\) 10.8674 1.91622i 0.628479 0.110818i
\(300\) −2.40294 + 4.86672i −0.138734 + 0.280980i
\(301\) 6.85186 18.8253i 0.394934 1.08507i
\(302\) 6.07812 26.0391i 0.349756 1.49838i
\(303\) 8.89722 0.511132
\(304\) 12.8473 + 11.7876i 0.736841 + 0.676066i
\(305\) −7.54780 −0.432186
\(306\) 0.552906 2.36869i 0.0316075 0.135409i
\(307\) 0.156983 0.431308i 0.00895950 0.0246160i −0.935132 0.354299i \(-0.884720\pi\)
0.944092 + 0.329683i \(0.106942\pi\)
\(308\) −6.27589 + 12.7107i −0.357602 + 0.724259i
\(309\) −15.1712 + 2.67508i −0.863057 + 0.152180i
\(310\) −2.10913 1.37697i −0.119791 0.0782065i
\(311\) −7.47472 + 12.9466i −0.423853 + 0.734134i −0.996313 0.0857984i \(-0.972656\pi\)
0.572460 + 0.819933i \(0.305989\pi\)
\(312\) −7.40792 + 9.01319i −0.419391 + 0.510271i
\(313\) −25.2374 21.1767i −1.42650 1.19698i −0.947744 0.319033i \(-0.896642\pi\)
−0.478760 0.877946i \(-0.658914\pi\)
\(314\) 1.50048 27.3615i 0.0846768 1.54410i
\(315\) −2.82407 + 1.63048i −0.159118 + 0.0918671i
\(316\) 7.43115 + 7.77023i 0.418035 + 0.437109i
\(317\) −7.91935 21.7582i −0.444795 1.22206i −0.936304 0.351192i \(-0.885777\pi\)
0.491508 0.870873i \(-0.336446\pi\)
\(318\) −1.09537 1.02643i −0.0614253 0.0575591i
\(319\) −1.31573 + 7.46187i −0.0736667 + 0.417784i
\(320\) −4.36768 11.2801i −0.244161 0.630574i
\(321\) 15.5616 13.0577i 0.868562 0.728810i
\(322\) 6.52846 4.89478i 0.363817 0.272776i
\(323\) 4.81713 5.74463i 0.268033 0.319640i
\(324\) 0.560590 1.91983i 0.0311439 0.106657i
\(325\) −7.19539 8.57514i −0.399129 0.475663i
\(326\) −0.994149 3.28013i −0.0550608 0.181670i
\(327\) 1.69800 9.62984i 0.0938997 0.532531i
\(328\) −9.56452 + 5.65268i −0.528112 + 0.312117i
\(329\) −11.2194 + 4.08354i −0.618547 + 0.225133i
\(330\) −6.97707 + 0.839512i −0.384075 + 0.0462136i
\(331\) 16.0084 9.24246i 0.879901 0.508011i 0.00927551 0.999957i \(-0.497047\pi\)
0.870626 + 0.491946i \(0.163714\pi\)
\(332\) 3.35776 + 5.03052i 0.184281 + 0.276086i
\(333\) 3.76222 4.48363i 0.206168 0.245702i
\(334\) 30.0471 + 12.8403i 1.64410 + 0.702590i
\(335\) −1.06187 + 1.83921i −0.0580161 + 0.100487i
\(336\) −1.87535 + 8.42048i −0.102309 + 0.459375i
\(337\) −4.38301 24.8573i −0.238758 1.35406i −0.834554 0.550926i \(-0.814275\pi\)
0.595797 0.803135i \(-0.296836\pi\)
\(338\) −2.56510 5.06461i −0.139523 0.275479i
\(339\) −5.17226 + 14.2107i −0.280918 + 0.771817i
\(340\) −4.76168 + 2.09243i −0.258239 + 0.113478i
\(341\) 3.87124i 0.209639i
\(342\) 4.21357 4.49953i 0.227844 0.243307i
\(343\) 20.1622 1.08866
\(344\) 12.9043 22.8858i 0.695752 1.23392i
\(345\) 3.80110 + 1.38349i 0.204644 + 0.0744844i
\(346\) −17.4399 + 8.83287i −0.937573 + 0.474858i
\(347\) −15.9900 + 2.81947i −0.858390 + 0.151357i −0.585485 0.810684i \(-0.699096\pi\)
−0.272905 + 0.962041i \(0.587985\pi\)
\(348\) 0.299346 + 4.60136i 0.0160467 + 0.246659i
\(349\) 19.0366 + 10.9908i 1.01901 + 0.588324i 0.913816 0.406128i \(-0.133121\pi\)
0.105190 + 0.994452i \(0.466455\pi\)
\(350\) −7.61134 3.25262i −0.406843 0.173860i
\(351\) 3.15982 + 2.65140i 0.168658 + 0.141521i
\(352\) −10.8471 + 15.0983i −0.578150 + 0.804743i
\(353\) −12.0994 20.9568i −0.643987 1.11542i −0.984534 0.175191i \(-0.943946\pi\)
0.340547 0.940228i \(-0.389388\pi\)
\(354\) −1.85190 15.3909i −0.0984275 0.818018i
\(355\) −7.21126 19.8128i −0.382734 1.05155i
\(356\) 6.77115 + 0.744887i 0.358870 + 0.0394790i
\(357\) 3.65303 + 0.644128i 0.193339 + 0.0340909i
\(358\) −6.36639 21.0055i −0.336474 1.11018i
\(359\) 17.4238 14.6203i 0.919592 0.771629i −0.0543275 0.998523i \(-0.517301\pi\)
0.973919 + 0.226894i \(0.0728570\pi\)
\(360\) −4.00361 + 1.50353i −0.211009 + 0.0792429i
\(361\) 17.8499 6.50999i 0.939470 0.342631i
\(362\) −17.8469 23.8035i −0.938011 1.25108i
\(363\) −0.128198 0.152780i −0.00672865 0.00801889i
\(364\) −14.3432 10.5276i −0.751789 0.551796i
\(365\) 14.4342 + 2.54513i 0.755518 + 0.133218i
\(366\) 5.15136 + 4.82713i 0.269266 + 0.252318i
\(367\) −21.2254 + 7.72542i −1.10796 + 0.403263i −0.830244 0.557401i \(-0.811799\pi\)
−0.277713 + 0.960664i \(0.589577\pi\)
\(368\) 9.49675 4.93199i 0.495052 0.257098i
\(369\) 1.96400 + 3.40174i 0.102242 + 0.177087i
\(370\) −12.4967 0.685307i −0.649672 0.0356274i
\(371\) 1.47150 1.75366i 0.0763963 0.0910456i
\(372\) 0.558854 + 2.28866i 0.0289752 + 0.118661i
\(373\) 30.4999 + 17.6091i 1.57922 + 0.911765i 0.994968 + 0.100196i \(0.0319470\pi\)
0.584256 + 0.811569i \(0.301386\pi\)
\(374\) 6.69355 + 4.36995i 0.346115 + 0.225965i
\(375\) −2.02533 11.4862i −0.104587 0.593145i
\(376\) −15.3918 + 2.87585i −0.793771 + 0.148311i
\(377\) −8.93648 3.25261i −0.460252 0.167518i
\(378\) 2.97019 + 0.693310i 0.152770 + 0.0356600i
\(379\) 9.96349i 0.511790i −0.966705 0.255895i \(-0.917630\pi\)
0.966705 0.255895i \(-0.0823702\pi\)
\(380\) −13.1029 1.43712i −0.672163 0.0737227i
\(381\) 2.90678i 0.148919i
\(382\) 6.38708 27.3627i 0.326791 1.39999i
\(383\) 10.9129 + 3.97197i 0.557623 + 0.202958i 0.605430 0.795898i \(-0.293001\pi\)
−0.0478070 + 0.998857i \(0.515223\pi\)
\(384\) −4.23312 + 10.4919i −0.216021 + 0.535414i
\(385\) −1.86097 10.5541i −0.0948437 0.537885i
\(386\) 20.9731 32.1250i 1.06751 1.63512i
\(387\) −8.04448 4.64448i −0.408924 0.236092i
\(388\) −25.0019 + 6.10506i −1.26928 + 0.309938i
\(389\) 5.93582 7.07403i 0.300958 0.358668i −0.594278 0.804259i \(-0.702562\pi\)
0.895236 + 0.445592i \(0.147007\pi\)
\(390\) 0.482966 8.80698i 0.0244559 0.445959i
\(391\) −2.30065 3.98484i −0.116349 0.201522i
\(392\) 6.55349 + 1.08689i 0.331001 + 0.0548961i
\(393\) −0.462784 + 0.168440i −0.0233444 + 0.00849666i
\(394\) −4.31560 + 4.60548i −0.217417 + 0.232021i
\(395\) −8.00486 1.41147i −0.402768 0.0710189i
\(396\) 5.29875 + 3.88916i 0.266272 + 0.195437i
\(397\) −11.9184 14.2038i −0.598168 0.712868i 0.378986 0.925402i \(-0.376273\pi\)
−0.977154 + 0.212534i \(0.931828\pi\)
\(398\) 5.30200 3.97523i 0.265765 0.199260i
\(399\) 7.20341 + 6.04039i 0.360622 + 0.302398i
\(400\) −9.14955 5.84140i −0.457478 0.292070i
\(401\) −4.08437 + 3.42719i −0.203963 + 0.171146i −0.739048 0.673653i \(-0.764724\pi\)
0.535084 + 0.844799i \(0.320280\pi\)
\(402\) 1.90098 0.576151i 0.0948121 0.0287358i
\(403\) −4.78505 0.843733i −0.238360 0.0420293i
\(404\) −1.94581 + 17.6877i −0.0968076 + 0.879998i
\(405\) 0.517140 + 1.42083i 0.0256969 + 0.0706016i
\(406\) −6.98161 + 0.840059i −0.346492 + 0.0416914i
\(407\) 9.61766 + 16.6583i 0.476730 + 0.825720i
\(408\) 4.58804 + 1.61721i 0.227142 + 0.0800638i
\(409\) 4.41368 + 3.70352i 0.218243 + 0.183127i 0.745354 0.666669i \(-0.232281\pi\)
−0.527111 + 0.849796i \(0.676725\pi\)
\(410\) 3.30059 7.72359i 0.163005 0.381441i
\(411\) 3.16253 + 1.82589i 0.155996 + 0.0900644i
\(412\) −2.00018 30.7454i −0.0985416 1.51472i
\(413\) 23.2815 4.10516i 1.14561 0.202002i
\(414\) −1.70945 3.37519i −0.0840148 0.165881i
\(415\) −4.29673 1.56388i −0.210918 0.0767679i
\(416\) −16.2982 16.6982i −0.799084 0.818695i
\(417\) 6.79094 0.332554
\(418\) 9.15942 + 18.0700i 0.448002 + 0.883835i
\(419\) 1.72624i 0.0843322i 0.999111 + 0.0421661i \(0.0134259\pi\)
−0.999111 + 0.0421661i \(0.986574\pi\)
\(420\) −2.62378 5.97086i −0.128028 0.291348i
\(421\) −5.29114 + 14.5373i −0.257875 + 0.708505i 0.741423 + 0.671038i \(0.234151\pi\)
−0.999298 + 0.0374670i \(0.988071\pi\)
\(422\) −30.7448 + 15.5715i −1.49663 + 0.758008i
\(423\) 0.961315 + 5.45189i 0.0467407 + 0.265080i
\(424\) 2.28010 1.95313i 0.110731 0.0948522i
\(425\) −2.33379 + 4.04225i −0.113206 + 0.196078i
\(426\) −7.74940 + 18.1341i −0.375460 + 0.878600i
\(427\) −6.92023 + 8.24721i −0.334893 + 0.399110i
\(428\) 22.5555 + 33.7922i 1.09026 + 1.63341i
\(429\) −11.7398 + 6.77799i −0.566804 + 0.327244i
\(430\) 2.37286 + 19.7205i 0.114429 + 0.951006i
\(431\) −31.6103 + 11.5052i −1.52261 + 0.554186i −0.961799 0.273757i \(-0.911734\pi\)
−0.560813 + 0.827942i \(0.689511\pi\)
\(432\) 3.69403 + 1.53432i 0.177729 + 0.0738200i
\(433\) 5.61011 31.8165i 0.269605 1.52901i −0.485989 0.873965i \(-0.661541\pi\)
0.755594 0.655040i \(-0.227348\pi\)
\(434\) −3.43833 + 1.04210i −0.165045 + 0.0500222i
\(435\) −2.24077 2.67044i −0.107437 0.128038i
\(436\) 18.7728 + 5.48167i 0.899056 + 0.262524i
\(437\) −0.00379150 11.6612i −0.000181372 0.557831i
\(438\) −8.22358 10.9683i −0.392938 0.524085i
\(439\) 8.18502 6.86805i 0.390650 0.327794i −0.426217 0.904621i \(-0.640154\pi\)
0.816866 + 0.576827i \(0.195709\pi\)
\(440\) −0.143081 14.0541i −0.00682112 0.670001i
\(441\) 0.407840 2.31298i 0.0194210 0.110142i
\(442\) −6.86033 + 7.32114i −0.326313 + 0.348231i
\(443\) 10.3431 + 28.4174i 0.491414 + 1.35015i 0.899386 + 0.437155i \(0.144014\pi\)
−0.407972 + 0.912994i \(0.633764\pi\)
\(444\) 8.09070 + 8.45987i 0.383968 + 0.401488i
\(445\) −4.45997 + 2.57496i −0.211423 + 0.122065i
\(446\) 1.59791 + 0.0876279i 0.0756632 + 0.00414930i
\(447\) −0.0426590 0.0357951i −0.00201770 0.00169305i
\(448\) −16.3298 5.56976i −0.771512 0.263146i
\(449\) −8.36925 + 14.4960i −0.394969 + 0.684107i −0.993097 0.117294i \(-0.962578\pi\)
0.598128 + 0.801401i \(0.295911\pi\)
\(450\) −2.09807 + 3.21366i −0.0989040 + 0.151493i
\(451\) −12.7129 + 2.24163i −0.598628 + 0.105554i
\(452\) −27.1197 13.3903i −1.27560 0.629828i
\(453\) 6.46669 17.7671i 0.303832 0.834771i
\(454\) 18.3994 + 4.29483i 0.863524 + 0.201567i
\(455\) 13.4510 0.630590
\(456\) 8.02360 + 9.36066i 0.375739 + 0.438353i
\(457\) 22.0048 1.02934 0.514671 0.857388i \(-0.327914\pi\)
0.514671 + 0.857388i \(0.327914\pi\)
\(458\) 14.1603 + 3.30535i 0.661669 + 0.154449i
\(459\) 0.588254 1.61621i 0.0274573 0.0754384i
\(460\) −3.58167 + 7.25404i −0.166996 + 0.338221i
\(461\) 38.3848 6.76827i 1.78776 0.315230i 0.821001 0.570927i \(-0.193416\pi\)
0.966757 + 0.255697i \(0.0823051\pi\)
\(462\) −5.47965 + 8.39331i −0.254936 + 0.390492i
\(463\) −13.6096 + 23.5725i −0.632492 + 1.09551i 0.354549 + 0.935037i \(0.384634\pi\)
−0.987041 + 0.160470i \(0.948699\pi\)
\(464\) −9.21299 0.411207i −0.427703 0.0190898i
\(465\) −1.36439 1.14486i −0.0632719 0.0530914i
\(466\) −8.92099 0.489218i −0.413257 0.0226626i
\(467\) 23.0239 13.2929i 1.06542 0.615121i 0.138493 0.990363i \(-0.455774\pi\)
0.926927 + 0.375243i \(0.122441\pi\)
\(468\) −5.96205 + 5.70188i −0.275596 + 0.263569i
\(469\) 1.03606 + 2.84656i 0.0478409 + 0.131442i
\(470\) 8.09425 8.63794i 0.373360 0.398438i
\(471\) 3.36470 19.0822i 0.155037 0.879260i
\(472\) 31.0023 0.315626i 1.42699 0.0145279i
\(473\) 23.3854 19.6227i 1.07526 0.902251i
\(474\) 4.56061 + 6.08276i 0.209476 + 0.279391i
\(475\) −10.2425 + 5.91794i −0.469957 + 0.271534i
\(476\) −2.07944 + 7.12138i −0.0953111 + 0.326408i
\(477\) −0.682292 0.813124i −0.0312400 0.0372304i
\(478\) −20.5075 + 6.21545i −0.937991 + 0.284288i
\(479\) 0.600472 3.40545i 0.0274363 0.155599i −0.968012 0.250905i \(-0.919272\pi\)
0.995448 + 0.0953061i \(0.0303830\pi\)
\(480\) −2.11344 8.28803i −0.0964648 0.378295i
\(481\) −22.6866 + 8.25725i −1.03442 + 0.376498i
\(482\) −2.08008 17.2873i −0.0947451 0.787414i
\(483\) 4.99674 2.88487i 0.227360 0.131266i
\(484\) 0.331765 0.221446i 0.0150802 0.0100657i
\(485\) 12.5067 14.9049i 0.567900 0.676797i
\(486\) 0.555732 1.30045i 0.0252085 0.0589895i
\(487\) 20.6922 35.8399i 0.937653 1.62406i 0.167820 0.985818i \(-0.446327\pi\)
0.769833 0.638245i \(-0.220339\pi\)
\(488\) −10.7230 + 9.18526i −0.485405 + 0.415797i
\(489\) −0.420853 2.38677i −0.0190316 0.107934i
\(490\) −4.48030 + 2.26916i −0.202399 + 0.102510i
\(491\) −6.97834 + 19.1728i −0.314928 + 0.865258i 0.676715 + 0.736245i \(0.263403\pi\)
−0.991643 + 0.129013i \(0.958819\pi\)
\(492\) −7.19220 + 3.16048i −0.324250 + 0.142485i
\(493\) 3.96539i 0.178592i
\(494\) −24.3318 + 7.38315i −1.09474 + 0.332184i
\(495\) −4.96912 −0.223345
\(496\) −4.67208 + 0.610479i −0.209783 + 0.0274113i
\(497\) −28.2604 10.2859i −1.26765 0.461388i
\(498\) 1.93235 + 3.81528i 0.0865905 + 0.170967i
\(499\) −17.8272 + 3.14342i −0.798056 + 0.140719i −0.557783 0.829987i \(-0.688348\pi\)
−0.240273 + 0.970705i \(0.577237\pi\)
\(500\) 23.2776 1.51435i 1.04101 0.0677238i
\(501\) 20.0097 + 11.5526i 0.893967 + 0.516132i
\(502\) 6.46370 15.1255i 0.288489 0.675083i
\(503\) −2.85069 2.39201i −0.127106 0.106655i 0.577019 0.816731i \(-0.304216\pi\)
−0.704125 + 0.710076i \(0.748660\pi\)
\(504\) −2.02788 + 5.75312i −0.0903290 + 0.256265i
\(505\) −6.72637 11.6504i −0.299319 0.518437i
\(506\) 12.3448 1.48538i 0.548793 0.0660332i
\(507\) −1.37299 3.77226i −0.0609766 0.167532i
\(508\) 5.77870 + 0.635709i 0.256389 + 0.0282050i
\(509\) −34.6366 6.10736i −1.53524 0.270704i −0.658837 0.752285i \(-0.728951\pi\)
−0.876401 + 0.481581i \(0.840063\pi\)
\(510\) −3.51966 + 1.06675i −0.155853 + 0.0472363i
\(511\) 16.0150 13.4382i 0.708462 0.594470i
\(512\) −19.9323 10.7100i −0.880890 0.473321i
\(513\) 3.33820 2.80293i 0.147385 0.123752i
\(514\) −25.6549 + 19.2350i −1.13159 + 0.848419i
\(515\) 14.9724 + 17.8434i 0.659762 + 0.786273i
\(516\) 10.9926 14.9767i 0.483921 0.659314i
\(517\) −17.9172 3.15929i −0.787998 0.138945i
\(518\) −12.2065 + 13.0264i −0.536321 + 0.572346i
\(519\) −12.9897 + 4.72786i −0.570184 + 0.207530i
\(520\) 17.4027 + 2.88621i 0.763159 + 0.126569i
\(521\) 3.73877 + 6.47574i 0.163798 + 0.283707i 0.936228 0.351393i \(-0.114292\pi\)
−0.772430 + 0.635100i \(0.780959\pi\)
\(522\) −0.178536 + 3.25564i −0.00781431 + 0.142495i
\(523\) 9.80737 11.6880i 0.428846 0.511079i −0.507743 0.861509i \(-0.669520\pi\)
0.936589 + 0.350429i \(0.113964\pi\)
\(524\) −0.233649 0.956856i −0.0102070 0.0418004i
\(525\) −5.06873 2.92643i −0.221218 0.127720i
\(526\) 8.95441 13.7157i 0.390431 0.598032i
\(527\) 0.351811 + 1.99522i 0.0153251 + 0.0869132i
\(528\) −8.89050 + 9.68339i −0.386909 + 0.421415i
\(529\) 14.8875 + 5.41861i 0.647283 + 0.235592i
\(530\) −0.515938 + 2.21031i −0.0224109 + 0.0960098i
\(531\) 10.9615i 0.475689i
\(532\) −13.5837 + 12.9994i −0.588929 + 0.563596i
\(533\) 16.2024i 0.701802i
\(534\) 4.69072 + 1.09492i 0.202987 + 0.0473819i
\(535\) −28.8630 10.5053i −1.24786 0.454182i
\(536\) 0.729652 + 3.90516i 0.0315162 + 0.168677i
\(537\) −2.69508 15.2846i −0.116301 0.659578i
\(538\) −6.75134 4.40768i −0.291071 0.190028i
\(539\) 6.68457 + 3.85934i 0.287925 + 0.166234i
\(540\) −2.93772 + 0.717344i −0.126419 + 0.0308696i
\(541\) −1.40116 + 1.66983i −0.0602404 + 0.0717917i −0.795323 0.606186i \(-0.792699\pi\)
0.735083 + 0.677977i \(0.237143\pi\)
\(542\) −29.2984 1.60670i −1.25848 0.0690136i
\(543\) −10.5185 18.2186i −0.451393 0.781836i
\(544\) −4.21842 + 8.76738i −0.180863 + 0.375898i
\(545\) −13.8934 + 5.05680i −0.595129 + 0.216609i
\(546\) −9.18026 8.60244i −0.392879 0.368150i
\(547\) 25.6212 + 4.51770i 1.09548 + 0.193163i 0.692052 0.721847i \(-0.256707\pi\)
0.403430 + 0.915010i \(0.367818\pi\)
\(548\) −4.32152 + 5.88781i −0.184606 + 0.251515i
\(549\) 3.20872 + 3.82400i 0.136945 + 0.163204i
\(550\) −7.56623 10.0915i −0.322625 0.430305i
\(551\) −5.02198 + 8.70486i −0.213944 + 0.370840i
\(552\) 7.08375 2.66025i 0.301504 0.113228i
\(553\) −8.88156 + 7.45251i −0.377682 + 0.316913i
\(554\) −3.43363 11.3291i −0.145881 0.481325i
\(555\) −8.71533 1.53675i −0.369945 0.0652313i
\(556\) −1.48517 + 13.5004i −0.0629852 + 0.572546i
\(557\) 12.6080 + 34.6401i 0.534216 + 1.46775i 0.854008 + 0.520260i \(0.174165\pi\)
−0.319792 + 0.947488i \(0.603613\pi\)
\(558\) 0.199010 + 1.65394i 0.00842476 + 0.0700170i
\(559\) 19.1578 + 33.1823i 0.810288 + 1.40346i
\(560\) 12.4439 3.91028i 0.525852 0.165240i
\(561\) 4.33002 + 3.63332i 0.182814 + 0.153399i
\(562\) 19.6476 + 8.39617i 0.828783 + 0.354171i
\(563\) −20.5616 11.8713i −0.866570 0.500314i −0.000363157 1.00000i \(-0.500116\pi\)
−0.866207 + 0.499685i \(0.833449\pi\)
\(564\) −11.0486 + 0.718781i −0.465231 + 0.0302661i
\(565\) 22.5183 3.97059i 0.947353 0.167044i
\(566\) −4.42836 + 2.24286i −0.186138 + 0.0942743i
\(567\) 2.02663 + 0.737634i 0.0851106 + 0.0309777i
\(568\) −34.3559 19.3718i −1.44154 0.812821i
\(569\) −23.8113 −0.998222 −0.499111 0.866538i \(-0.666340\pi\)
−0.499111 + 0.866538i \(0.666340\pi\)
\(570\) −9.07738 2.11576i −0.380210 0.0886194i
\(571\) 33.6456i 1.40802i 0.710189 + 0.704011i \(0.248610\pi\)
−0.710189 + 0.704011i \(0.751390\pi\)
\(572\) −10.9072 24.8212i −0.456053 1.03783i
\(573\) 6.79540 18.6702i 0.283882 0.779960i
\(574\) −5.41313 10.6878i −0.225940 0.446102i
\(575\) 1.26071 + 7.14986i 0.0525754 + 0.298170i
\(576\) −3.85812 + 7.00820i −0.160755 + 0.292009i
\(577\) 12.3399 21.3733i 0.513716 0.889783i −0.486157 0.873871i \(-0.661602\pi\)
0.999873 0.0159113i \(-0.00506494\pi\)
\(578\) −18.2606 7.80348i −0.759542 0.324582i
\(579\) 17.4377 20.7815i 0.724688 0.863650i
\(580\) 5.79891 3.87064i 0.240787 0.160719i
\(581\) −5.64827 + 3.26103i −0.234330 + 0.135290i
\(582\) −18.0681 + 2.17403i −0.748947 + 0.0901166i
\(583\) 3.27802 1.19310i 0.135762 0.0494132i
\(584\) 23.6035 13.9498i 0.976720 0.577246i
\(585\) 1.08301 6.14208i 0.0447771 0.253944i
\(586\) −1.83657 6.05966i −0.0758681 0.250322i
\(587\) −1.83853 2.19108i −0.0758844 0.0904355i 0.726767 0.686885i \(-0.241022\pi\)
−0.802651 + 0.596449i \(0.796578\pi\)
\(588\) 4.50902 + 1.31663i 0.185949 + 0.0542971i
\(589\) −1.75456 + 4.82548i −0.0722952 + 0.198831i
\(590\) −18.7535 + 14.0606i −0.772069 + 0.578866i
\(591\) −3.41878 + 2.86870i −0.140630 + 0.118002i
\(592\) −18.5877 + 14.2342i −0.763950 + 0.585022i
\(593\) −6.42588 + 36.4430i −0.263879 + 1.49653i 0.508329 + 0.861163i \(0.330263\pi\)
−0.772208 + 0.635370i \(0.780848\pi\)
\(594\) 3.39142 + 3.17796i 0.139152 + 0.130393i
\(595\) −1.91827 5.27040i −0.0786414 0.216066i
\(596\) 0.0804904 0.0769780i 0.00329701 0.00315314i
\(597\) 4.05803 2.34290i 0.166084 0.0958887i
\(598\) −0.854530 + 15.5825i −0.0349443 + 0.637216i
\(599\) 24.4535 + 20.5189i 0.999141 + 0.838379i 0.986865 0.161546i \(-0.0516479\pi\)
0.0122758 + 0.999925i \(0.496092\pi\)
\(600\) −5.92994 4.87380i −0.242089 0.198972i
\(601\) −10.8423 + 18.7794i −0.442266 + 0.766026i −0.997857 0.0654289i \(-0.979158\pi\)
0.555592 + 0.831455i \(0.312492\pi\)
\(602\) 23.7234 + 15.4881i 0.966895 + 0.631247i
\(603\) 1.38324 0.243902i 0.0563297 0.00993245i
\(604\) 33.9069 + 16.7415i 1.37965 + 0.681201i
\(605\) −0.103139 + 0.283371i −0.00419318 + 0.0115207i
\(606\) −2.86018 + 12.2532i −0.116187 + 0.497752i
\(607\) 16.9309 0.687203 0.343601 0.939116i \(-0.388353\pi\)
0.343601 + 0.939116i \(0.388353\pi\)
\(608\) −20.3638 + 13.9038i −0.825861 + 0.563874i
\(609\) −4.97235 −0.201490
\(610\) 2.42638 10.3948i 0.0982412 0.420872i
\(611\) 7.81007 21.4580i 0.315962 0.868097i
\(612\) 3.08439 + 1.52292i 0.124679 + 0.0615602i
\(613\) 12.9439 2.28236i 0.522799 0.0921836i 0.0939803 0.995574i \(-0.470041\pi\)
0.428819 + 0.903390i \(0.358930\pi\)
\(614\) 0.543529 + 0.354848i 0.0219350 + 0.0143205i
\(615\) 2.96959 5.14348i 0.119745 0.207405i
\(616\) −15.4876 12.7292i −0.624012 0.512874i
\(617\) 16.0917 + 13.5026i 0.647829 + 0.543593i 0.906411 0.422396i \(-0.138811\pi\)
−0.258583 + 0.965989i \(0.583255\pi\)
\(618\) 1.19294 21.7535i 0.0479872 0.875056i
\(619\) 12.0659 6.96623i 0.484968 0.279997i −0.237516 0.971384i \(-0.576333\pi\)
0.722485 + 0.691387i \(0.243000\pi\)
\(620\) 2.57437 2.46203i 0.103389 0.0988775i
\(621\) −0.914995 2.51393i −0.0367175 0.100880i
\(622\) −15.4271 14.4561i −0.618569 0.579635i
\(623\) −1.27557 + 7.23412i −0.0511046 + 0.289829i
\(624\) −10.0315 13.0996i −0.401581 0.524403i
\(625\) −3.11488 + 2.61370i −0.124595 + 0.104548i
\(626\) 37.2774 27.9491i 1.48991 1.11707i
\(627\) 4.90387 + 13.4597i 0.195842 + 0.537527i
\(628\) 37.1996 + 10.8623i 1.48443 + 0.433453i
\(629\) 6.47078 + 7.71157i 0.258007 + 0.307481i
\(630\) −1.33763 4.41344i −0.0532926 0.175836i
\(631\) 6.96318 39.4901i 0.277200 1.57208i −0.454687 0.890651i \(-0.650249\pi\)
0.731887 0.681426i \(-0.238640\pi\)
\(632\) −13.0900 + 7.73624i −0.520691 + 0.307731i
\(633\) −22.8995 + 8.33475i −0.910174 + 0.331276i
\(634\) 32.5111 3.91188i 1.29118 0.155361i
\(635\) −3.80627 + 2.19755i −0.151047 + 0.0872071i
\(636\) 1.76571 1.17857i 0.0700150 0.0467334i
\(637\) −6.22723 + 7.42133i −0.246732 + 0.294044i
\(638\) −9.85346 4.21077i −0.390102 0.166706i
\(639\) −6.97226 + 12.0763i −0.275818 + 0.477731i
\(640\) 16.9389 2.38895i 0.669568 0.0944315i
\(641\) 3.93020 + 22.2892i 0.155233 + 0.880372i 0.958572 + 0.284850i \(0.0919438\pi\)
−0.803339 + 0.595522i \(0.796945\pi\)
\(642\) 12.9804 + 25.6289i 0.512296 + 1.01149i
\(643\) −3.88057 + 10.6618i −0.153035 + 0.420460i −0.992392 0.123121i \(-0.960710\pi\)
0.839357 + 0.543581i \(0.182932\pi\)
\(644\) 4.64236 + 10.5645i 0.182935 + 0.416298i
\(645\) 14.0451i 0.553024i
\(646\) 6.36290 + 8.48084i 0.250345 + 0.333674i
\(647\) 12.1699 0.478448 0.239224 0.970964i \(-0.423107\pi\)
0.239224 + 0.970964i \(0.423107\pi\)
\(648\) 2.46376 + 1.38920i 0.0967856 + 0.0545731i
\(649\) 33.8516 + 12.3210i 1.32879 + 0.483641i
\(650\) 14.1227 7.15280i 0.553938 0.280556i
\(651\) −2.50189 + 0.441150i −0.0980566 + 0.0172900i
\(652\) 4.83696 0.314674i 0.189430 0.0123236i
\(653\) 23.1361 + 13.3576i 0.905386 + 0.522725i 0.878944 0.476926i \(-0.158249\pi\)
0.0264422 + 0.999650i \(0.491582\pi\)
\(654\) 12.7163 + 5.43416i 0.497246 + 0.212493i
\(655\) 0.570431 + 0.478648i 0.0222886 + 0.0187023i
\(656\) −4.71013 14.9893i −0.183900 0.585236i
\(657\) −4.84678 8.39488i −0.189091 0.327515i
\(658\) −2.01712 16.7640i −0.0786356 0.653530i
\(659\) 4.69365 + 12.8957i 0.182839 + 0.502346i 0.996922 0.0784031i \(-0.0249821\pi\)
−0.814083 + 0.580749i \(0.802760\pi\)
\(660\) 1.08674 9.87864i 0.0423012 0.384526i
\(661\) 5.28545 + 0.931967i 0.205580 + 0.0362493i 0.275490 0.961304i \(-0.411160\pi\)
−0.0699097 + 0.997553i \(0.522271\pi\)
\(662\) 7.58244 + 25.0178i 0.294700 + 0.972345i
\(663\) −5.43469 + 4.56024i −0.211066 + 0.177105i
\(664\) −8.00741 + 3.00712i −0.310748 + 0.116699i
\(665\) 2.46372 13.9990i 0.0955388 0.542860i
\(666\) 4.96539 + 6.62264i 0.192405 + 0.256622i
\(667\) 3.96467 + 4.72491i 0.153513 + 0.182949i
\(668\) −27.3427 + 37.2529i −1.05792 + 1.44136i
\(669\) 1.11440 + 0.196499i 0.0430852 + 0.00759708i
\(670\) −2.19159 2.05365i −0.0846685 0.0793393i
\(671\) −15.4160 + 5.61098i −0.595130 + 0.216610i
\(672\) −10.9938 5.28964i −0.424093 0.204052i
\(673\) 9.91857 + 17.1795i 0.382333 + 0.662220i 0.991395 0.130903i \(-0.0417875\pi\)
−0.609063 + 0.793122i \(0.708454\pi\)
\(674\) 35.6422 + 1.95459i 1.37289 + 0.0752878i
\(675\) −1.74440 + 2.07890i −0.0671421 + 0.0800169i
\(676\) 7.79954 1.90452i 0.299982 0.0732510i
\(677\) −27.5121 15.8841i −1.05737 0.610476i −0.132670 0.991160i \(-0.542355\pi\)
−0.924705 + 0.380685i \(0.875688\pi\)
\(678\) −17.9081 11.6915i −0.687756 0.449008i
\(679\) −4.81924 27.3313i −0.184945 1.04888i
\(680\) −1.35095 7.23041i −0.0518066 0.277273i
\(681\) 12.5543 + 4.56941i 0.481083 + 0.175100i
\(682\) −5.33144 1.24448i −0.204151 0.0476537i
\(683\) 25.2462i 0.966020i 0.875615 + 0.483010i \(0.160457\pi\)
−0.875615 + 0.483010i \(0.839543\pi\)
\(684\) 4.84219 + 7.24936i 0.185146 + 0.277186i
\(685\) 5.52154i 0.210967i
\(686\) −6.48152 + 27.7673i −0.247466 + 1.06016i
\(687\) 9.66195 + 3.51666i 0.368626 + 0.134169i
\(688\) 27.3698 + 25.1287i 1.04346 + 0.958024i
\(689\) 0.760292 + 4.31183i 0.0289648 + 0.164268i
\(690\) −3.12726 + 4.79009i −0.119053 + 0.182356i
\(691\) −11.7380 6.77694i −0.446534 0.257807i 0.259831 0.965654i \(-0.416333\pi\)
−0.706365 + 0.707847i \(0.749666\pi\)
\(692\) −6.55819 26.8575i −0.249305 1.02097i
\(693\) −4.55596 + 5.42958i −0.173067 + 0.206253i
\(694\) 1.25733 22.9277i 0.0477278 0.870324i
\(695\) −5.13400 8.89235i −0.194744 0.337306i
\(696\) −6.43318 1.06693i −0.243849 0.0404420i
\(697\) −6.34847 + 2.31065i −0.240465 + 0.0875223i
\(698\) −21.2561 + 22.6839i −0.804555 + 0.858597i
\(699\) −6.22159 1.09703i −0.235322 0.0414936i
\(700\) 6.92629 9.43666i 0.261789 0.356672i
\(701\) 16.2966 + 19.4216i 0.615516 + 0.733543i 0.980292 0.197552i \(-0.0632991\pi\)
−0.364777 + 0.931095i \(0.618855\pi\)
\(702\) −4.66727 + 3.49933i −0.176155 + 0.132074i
\(703\) 4.43837 + 25.1235i 0.167396 + 0.947549i
\(704\) −17.3063 19.7921i −0.652256 0.745943i
\(705\) 6.41218 5.38046i 0.241497 0.202640i
\(706\) 32.7511 9.92628i 1.23261 0.373580i
\(707\) −18.8971 3.33207i −0.710698 0.125315i
\(708\) 21.7916 + 2.39727i 0.818978 + 0.0900948i
\(709\) 3.32334 + 9.13081i 0.124811 + 0.342915i 0.986323 0.164821i \(-0.0527048\pi\)
−0.861513 + 0.507736i \(0.830483\pi\)
\(710\) 29.6042 3.56211i 1.11103 0.133684i
\(711\) 2.68792 + 4.65561i 0.100805 + 0.174599i
\(712\) −3.20257 + 9.08572i −0.120021 + 0.340502i
\(713\) 2.41406 + 2.02564i 0.0904072 + 0.0758606i
\(714\) −2.06142 + 4.82386i −0.0771468 + 0.180528i
\(715\) 17.7508 + 10.2484i 0.663842 + 0.383269i
\(716\) 30.9752 2.01513i 1.15760 0.0753089i
\(717\) −14.9222 + 2.63118i −0.557279 + 0.0982633i
\(718\) 14.5337 + 28.6959i 0.542395 + 1.07092i
\(719\) −23.0852 8.40234i −0.860934 0.313354i −0.126444 0.991974i \(-0.540356\pi\)
−0.734490 + 0.678619i \(0.762579\pi\)
\(720\) −0.783610 5.99708i −0.0292034 0.223498i
\(721\) 33.2243 1.23734
\(722\) 3.22732 + 26.6755i 0.120108 + 0.992761i
\(723\) 12.3121i 0.457893i
\(724\) 38.5191 16.9265i 1.43155 0.629069i
\(725\) 2.13995 5.87947i 0.0794758 0.218358i
\(726\) 0.251620 0.127439i 0.00933848 0.00472971i
\(727\) −1.56552 8.87852i −0.0580620 0.329286i 0.941916 0.335847i \(-0.109023\pi\)
−0.999978 + 0.00656128i \(0.997911\pi\)
\(728\) 19.1094 16.3691i 0.708242 0.606679i
\(729\) 0.500000 0.866025i 0.0185185 0.0320750i
\(730\) −8.14526 + 19.0604i −0.301470 + 0.705458i
\(731\) 10.2695 12.2387i 0.379830 0.452664i
\(732\) −8.30388 + 5.54265i −0.306920 + 0.204862i
\(733\) 20.7084 11.9560i 0.764884 0.441606i −0.0661627 0.997809i \(-0.521076\pi\)
0.831046 + 0.556203i \(0.187742\pi\)
\(734\) −3.81608 31.7149i −0.140854 1.17062i
\(735\) −3.33704 + 1.21458i −0.123089 + 0.0448006i
\(736\) 3.73939 + 14.6643i 0.137836 + 0.540534i
\(737\) −0.801564 + 4.54590i −0.0295260 + 0.167450i
\(738\) −5.31621 + 1.61125i −0.195692 + 0.0593108i
\(739\) 0.746940 + 0.890169i 0.0274766 + 0.0327454i 0.779608 0.626268i \(-0.215418\pi\)
−0.752131 + 0.659013i \(0.770974\pi\)
\(740\) 4.96109 16.9900i 0.182373 0.624567i
\(741\) −17.7056 + 3.12791i −0.650432 + 0.114907i
\(742\) 1.94209 + 2.59028i 0.0712963 + 0.0950922i
\(743\) −17.6764 + 14.8323i −0.648485 + 0.544144i −0.906611 0.421968i \(-0.861340\pi\)
0.258126 + 0.966111i \(0.416895\pi\)
\(744\) −3.33157 + 0.0339179i −0.122141 + 0.00124349i
\(745\) −0.0146212 + 0.0829209i −0.000535679 + 0.00303799i
\(746\) −34.0559 + 36.3434i −1.24687 + 1.33063i
\(747\) 1.03430 + 2.84172i 0.0378432 + 0.103973i
\(748\) −8.17003 + 7.81351i −0.298726 + 0.285690i
\(749\) −37.9419 + 21.9058i −1.38637 + 0.800419i
\(750\) 16.4698 + 0.903188i 0.601392 + 0.0329797i
\(751\) −21.6508 18.1671i −0.790047 0.662928i 0.155710 0.987803i \(-0.450233\pi\)
−0.945757 + 0.324875i \(0.894678\pi\)
\(752\) 0.987377 22.1220i 0.0360059 0.806705i
\(753\) 5.81549 10.0727i 0.211928 0.367070i
\(754\) 7.35227 11.2616i 0.267754 0.410125i
\(755\) −28.1539 + 4.96429i −1.02462 + 0.180669i
\(756\) −1.90964 + 3.86764i −0.0694530 + 0.140665i
\(757\) 6.67418 18.3372i 0.242577 0.666476i −0.757332 0.653030i \(-0.773498\pi\)
0.999910 0.0134460i \(-0.00428012\pi\)
\(758\) 13.7216 + 3.20295i 0.498393 + 0.116336i
\(759\) 8.79205 0.319131
\(760\) 6.19135 17.5832i 0.224584 0.637809i
\(761\) 33.1022 1.19996 0.599978 0.800017i \(-0.295176\pi\)
0.599978 + 0.800017i \(0.295176\pi\)
\(762\) 4.00320 + 0.934439i 0.145021 + 0.0338512i
\(763\) −7.21288 + 19.8172i −0.261124 + 0.717431i
\(764\) 35.6304 + 17.5925i 1.28906 + 0.636473i
\(765\) −2.56106 + 0.451585i −0.0925955 + 0.0163271i
\(766\) −8.97832 + 13.7523i −0.324400 + 0.496891i
\(767\) −22.6073 + 39.1570i −0.816302 + 1.41388i
\(768\) −13.0886 9.20265i −0.472294 0.332072i
\(769\) −24.5404 20.5918i −0.884950 0.742561i 0.0822409 0.996612i \(-0.473792\pi\)
−0.967191 + 0.254051i \(0.918237\pi\)
\(770\) 15.1332 + 0.829891i 0.545363 + 0.0299072i
\(771\) −19.6356 + 11.3366i −0.707160 + 0.408279i
\(772\) 37.5001 + 39.2112i 1.34966 + 1.41124i
\(773\) −4.91296 13.4982i −0.176707 0.485498i 0.819443 0.573160i \(-0.194283\pi\)
−0.996150 + 0.0876620i \(0.972060\pi\)
\(774\) 8.98240 9.58574i 0.322866 0.344552i
\(775\) 0.555107 3.14817i 0.0199400 0.113085i
\(776\) −0.370528 36.3950i −0.0133012 1.30650i
\(777\) −9.66984 + 8.11396i −0.346904 + 0.291087i
\(778\) 7.83412 + 10.4488i 0.280867 + 0.374609i
\(779\) −16.8626 2.96767i −0.604164 0.106328i
\(780\) 11.9736 + 3.49630i 0.428725 + 0.125188i
\(781\) −29.4574 35.1059i −1.05407 1.25619i
\(782\) 6.22747 1.88743i 0.222694 0.0674944i
\(783\) −0.400353 + 2.27052i −0.0143075 + 0.0811416i
\(784\) −3.60359 + 8.67602i −0.128700 + 0.309858i
\(785\) −27.5308 + 10.0204i −0.982616 + 0.357643i
\(786\) −0.0832032 0.691491i −0.00296776 0.0246647i
\(787\) 38.8604 22.4360i 1.38522 0.799758i 0.392450 0.919773i \(-0.371628\pi\)
0.992772 + 0.120015i \(0.0382943\pi\)
\(788\) −4.95530 7.42393i −0.176525 0.264467i
\(789\) 7.44499 8.87259i 0.265048 0.315872i
\(790\) 4.51718 10.5705i 0.160714 0.376081i
\(791\) 16.3075 28.2454i 0.579828 1.00429i
\(792\) −7.05949 + 6.04715i −0.250848 + 0.214876i
\(793\) −3.57554 20.2779i −0.126971 0.720090i
\(794\) 23.3928 11.8479i 0.830178 0.420465i
\(795\) −0.548922 + 1.50815i −0.0194683 + 0.0534886i
\(796\) 3.77022 + 8.57978i 0.133632 + 0.304102i
\(797\) 51.5044i 1.82438i 0.409768 + 0.912190i \(0.365610\pi\)
−0.409768 + 0.912190i \(0.634390\pi\)
\(798\) −10.6344 + 7.97869i −0.376455 + 0.282442i
\(799\) −9.52157 −0.336849
\(800\) 10.9860 10.7229i 0.388414 0.379110i
\(801\) 3.20059 + 1.16492i 0.113087 + 0.0411605i
\(802\) −3.40690 6.72669i −0.120302 0.237528i
\(803\) 31.3732 5.53193i 1.10713 0.195218i
\(804\) 0.182367 + 2.80322i 0.00643158 + 0.0988621i
\(805\) −7.55515 4.36197i −0.266284 0.153739i
\(806\) 2.70022 6.31869i 0.0951113 0.222566i
\(807\) −4.36740 3.66468i −0.153740 0.129003i
\(808\) −23.7339 8.36580i −0.834956 0.294308i
\(809\) 3.25769 + 5.64248i 0.114534 + 0.198379i 0.917593 0.397520i \(-0.130129\pi\)
−0.803059 + 0.595899i \(0.796796\pi\)
\(810\) −2.12300 + 0.255449i −0.0745946 + 0.00897555i
\(811\) −5.94884 16.3443i −0.208892 0.573926i 0.790358 0.612645i \(-0.209895\pi\)
−0.999250 + 0.0387189i \(0.987672\pi\)
\(812\) 1.08745 9.88507i 0.0381619 0.346898i
\(813\) −20.4330 3.60290i −0.716618 0.126359i
\(814\) −26.0334 + 7.89025i −0.912471 + 0.276553i
\(815\) −2.80718 + 2.35550i −0.0983312 + 0.0825096i
\(816\) −3.70212 + 5.79873i −0.129600 + 0.202996i
\(817\) 38.0433 13.8607i 1.33097 0.484923i
\(818\) −6.51932 + 4.88792i −0.227943 + 0.170902i
\(819\) −5.71827 6.81476i −0.199812 0.238127i
\(820\) 9.57583 + 7.02844i 0.334403 + 0.245444i
\(821\) −37.3691 6.58918i −1.30419 0.229964i −0.521969 0.852964i \(-0.674802\pi\)
−0.782222 + 0.623000i \(0.785914\pi\)
\(822\) −3.53125 + 3.76844i −0.123167 + 0.131440i
\(823\) −3.06516 + 1.11563i −0.106845 + 0.0388883i −0.394889 0.918729i \(-0.629217\pi\)
0.288045 + 0.957617i \(0.406995\pi\)
\(824\) 42.9853 + 7.12905i 1.49746 + 0.248352i
\(825\) −4.45936 7.72384i −0.155255 0.268910i
\(826\) −1.83068 + 33.3828i −0.0636975 + 1.16154i
\(827\) 29.7563 35.4622i 1.03473 1.23314i 0.0627591 0.998029i \(-0.480010\pi\)
0.971968 0.235112i \(-0.0755455\pi\)
\(828\) 5.19781 1.26922i 0.180636 0.0441086i
\(829\) −0.127732 0.0737462i −0.00443632 0.00256131i 0.497780 0.867303i \(-0.334149\pi\)
−0.502217 + 0.864742i \(0.667482\pi\)
\(830\) 3.53503 5.41468i 0.122703 0.187946i
\(831\) −1.45356 8.24353i −0.0504233 0.285965i
\(832\) 28.2359 17.0778i 0.978905 0.592066i
\(833\) 3.79593 + 1.38161i 0.131521 + 0.0478698i
\(834\) −2.18307 + 9.35243i −0.0755936 + 0.323848i
\(835\) 34.9354i 1.20899i
\(836\) −27.8304 + 6.80533i −0.962534 + 0.235367i
\(837\) 1.17795i 0.0407159i
\(838\) −2.37736 0.554931i −0.0821245 0.0191698i
\(839\) −38.3067 13.9425i −1.32249 0.481349i −0.418238 0.908338i \(-0.637352\pi\)
−0.904257 + 0.426989i \(0.859574\pi\)
\(840\) 9.06648 1.69401i 0.312823 0.0584489i
\(841\) 4.11277 + 23.3247i 0.141820 + 0.804299i
\(842\) −18.3197 11.9602i −0.631339 0.412176i
\(843\) 13.0842 + 7.55416i 0.450643 + 0.260179i
\(844\) −11.5614 47.3472i −0.397961 1.62976i
\(845\) −3.90157 + 4.64971i −0.134218 + 0.159955i
\(846\) −7.81733 0.428695i −0.268765 0.0147388i
\(847\) 0.215066 + 0.372506i 0.00738977 + 0.0127995i
\(848\) 1.95685 + 3.76800i 0.0671985 + 0.129394i
\(849\) −3.29836 + 1.20051i −0.113199 + 0.0412012i
\(850\) −4.81671 4.51354i −0.165212 0.154813i
\(851\) 15.4204 + 2.71903i 0.528603 + 0.0932070i
\(852\) −22.4829 16.5020i −0.770253 0.565348i
\(853\) −0.670666 0.799269i −0.0229632 0.0273665i 0.754441 0.656368i \(-0.227908\pi\)
−0.777404 + 0.629002i \(0.783464\pi\)
\(854\) −9.13336 12.1817i −0.312537 0.416849i
\(855\) −6.19399 2.25215i −0.211830 0.0770218i
\(856\) −53.7892 + 20.2001i −1.83848 + 0.690427i
\(857\) −25.8742 + 21.7110i −0.883845 + 0.741634i −0.966966 0.254905i \(-0.917956\pi\)
0.0831208 + 0.996539i \(0.473511\pi\)
\(858\) −5.56061 18.3469i −0.189836 0.626353i
\(859\) −40.8604 7.20479i −1.39414 0.245824i −0.574406 0.818571i \(-0.694767\pi\)
−0.819733 + 0.572747i \(0.805878\pi\)
\(860\) −27.9217 3.07163i −0.952121 0.104742i
\(861\) −2.89742 7.96059i −0.0987438 0.271296i
\(862\) −5.68316 47.2319i −0.193569 1.60873i
\(863\) 3.00327 + 5.20181i 0.102232 + 0.177072i 0.912604 0.408844i \(-0.134068\pi\)
−0.810372 + 0.585916i \(0.800735\pi\)
\(864\) −3.30057 + 4.59415i −0.112288 + 0.156296i
\(865\) 16.0112 + 13.4350i 0.544396 + 0.456802i
\(866\) 42.0140 + 17.9542i 1.42769 + 0.610109i
\(867\) −12.1606 7.02091i −0.412994 0.238442i
\(868\) −0.329850 5.07024i −0.0111959 0.172095i
\(869\) −17.3989 + 3.06789i −0.590216 + 0.104071i
\(870\) 4.39805 2.22750i 0.149108 0.0755194i
\(871\) −5.44425 1.98155i −0.184472 0.0671421i
\(872\) −13.5842 + 24.0916i −0.460019 + 0.815845i
\(873\) −12.8682 −0.435524
\(874\) 16.0609 + 3.74349i 0.543270 + 0.126625i
\(875\) 25.1544i 0.850374i
\(876\) 17.7491 7.79949i 0.599685 0.263520i
\(877\) −11.9150 + 32.7362i −0.402341 + 1.10542i 0.558785 + 0.829312i \(0.311268\pi\)
−0.961126 + 0.276110i \(0.910955\pi\)
\(878\) 6.82739 + 13.4802i 0.230413 + 0.454935i
\(879\) −0.777476 4.40928i −0.0262236 0.148721i
\(880\) 19.4011 + 4.32089i 0.654012 + 0.145657i
\(881\) −1.52775 + 2.64615i −0.0514713 + 0.0891509i −0.890613 0.454762i \(-0.849724\pi\)
0.839142 + 0.543913i \(0.183058\pi\)
\(882\) 3.05431 + 1.30522i 0.102844 + 0.0439492i
\(883\) −18.6461 + 22.2216i −0.627492 + 0.747816i −0.982339 0.187108i \(-0.940089\pi\)
0.354847 + 0.934924i \(0.384533\pi\)
\(884\) −7.87724 11.8015i −0.264940 0.396928i
\(885\) −14.3535 + 8.28699i −0.482487 + 0.278564i
\(886\) −42.4611 + 5.10911i −1.42651 + 0.171644i
\(887\) −9.66781 + 3.51879i −0.324613 + 0.118150i −0.499186 0.866495i \(-0.666368\pi\)
0.174573 + 0.984644i \(0.444145\pi\)
\(888\) −14.2518 + 8.42287i −0.478258 + 0.282653i
\(889\) −1.08861 + 6.17381i −0.0365108 + 0.207063i
\(890\) −2.11248 6.97000i −0.0708105 0.233635i
\(891\) 2.11247 + 2.51754i 0.0707704 + 0.0843409i
\(892\) −0.634358 + 2.17246i −0.0212399 + 0.0727393i
\(893\) −20.9018 12.0586i −0.699453 0.403526i
\(894\) 0.0630103 0.0472426i 0.00210738 0.00158003i
\(895\) −17.9768 + 15.0843i −0.600898 + 0.504213i
\(896\) 12.9202 20.6988i 0.431632 0.691499i
\(897\) −1.91622 + 10.8674i −0.0639806 + 0.362852i
\(898\) −17.2733 16.1861i −0.576417 0.540136i
\(899\) −0.928863 2.55203i −0.0309793 0.0851149i
\(900\) −3.75137 3.92254i −0.125046 0.130751i
\(901\) 1.58105 0.912821i 0.0526725 0.0304105i
\(902\) 0.999646 18.2287i 0.0332846 0.606950i
\(903\) 15.3465 + 12.8773i 0.510701 + 0.428529i
\(904\) 27.1592 33.0445i 0.903301 1.09904i
\(905\) −15.9042 + 27.5468i −0.528673 + 0.915688i
\(906\) 22.3899 + 14.6174i 0.743853 + 0.485632i
\(907\) −40.1764 + 7.08418i −1.33403 + 0.235226i −0.794770 0.606910i \(-0.792409\pi\)
−0.539264 + 0.842136i \(0.681298\pi\)
\(908\) −11.8296 + 23.9588i −0.392580 + 0.795100i
\(909\) −3.04303 + 8.36066i −0.100931 + 0.277305i
\(910\) −4.32406 + 18.5245i −0.143341 + 0.614083i
\(911\) 9.89762 0.327923 0.163961 0.986467i \(-0.447573\pi\)
0.163961 + 0.986467i \(0.447573\pi\)
\(912\) −15.4708 + 8.04088i −0.512288 + 0.266260i
\(913\) −9.93846 −0.328915
\(914\) −7.07386 + 30.3049i −0.233983 + 1.00240i
\(915\) 2.58150 7.09261i 0.0853417 0.234474i
\(916\) −9.10420 + 18.4389i −0.300811 + 0.609240i
\(917\) 1.04600 0.184439i 0.0345421 0.00609070i
\(918\) 2.03673 + 1.32970i 0.0672221 + 0.0438866i
\(919\) 25.5182 44.1989i 0.841769 1.45799i −0.0466293 0.998912i \(-0.514848\pi\)
0.888398 0.459074i \(-0.151819\pi\)
\(920\) −8.83881 7.26460i −0.291407 0.239507i
\(921\) 0.351605 + 0.295032i 0.0115858 + 0.00972163i
\(922\) −3.01829 + 55.0390i −0.0994020 + 1.81261i
\(923\) 49.8129 28.7595i 1.63961 0.946630i
\(924\) −9.79766 10.2447i −0.322319 0.337026i
\(925\) −5.43259 14.9259i −0.178623 0.490762i
\(926\) −28.0888 26.3208i −0.923056 0.864957i
\(927\) 2.67508 15.1712i 0.0878613 0.498286i
\(928\) 3.52800 12.5559i 0.115812 0.412167i
\(929\) 40.1073 33.6540i 1.31588 1.10415i 0.328715 0.944429i \(-0.393384\pi\)
0.987162 0.159723i \(-0.0510601\pi\)
\(930\) 2.01529 1.51099i 0.0660840 0.0495472i
\(931\) 6.58313 + 7.84029i 0.215753 + 0.256955i
\(932\) 3.54156 12.1286i 0.116008 0.397287i
\(933\) −9.60932 11.4519i −0.314595 0.374920i
\(934\) 10.9054 + 35.9816i 0.356834 + 1.17735i
\(935\) 1.48410 8.41673i 0.0485352 0.275257i
\(936\) −5.93597 10.0439i −0.194023 0.328294i
\(937\) 17.4746 6.36024i 0.570871 0.207780i −0.0404245 0.999183i \(-0.512871\pi\)
0.611295 + 0.791403i \(0.290649\pi\)
\(938\) −4.25332 + 0.511778i −0.138876 + 0.0167101i
\(939\) 28.5313 16.4726i 0.931084 0.537562i
\(940\) 9.29405 + 13.9242i 0.303139 + 0.454156i
\(941\) 8.30238 9.89439i 0.270650 0.322548i −0.613551 0.789655i \(-0.710259\pi\)
0.884201 + 0.467107i \(0.154704\pi\)
\(942\) 25.1982 + 10.7682i 0.821001 + 0.350846i
\(943\) −5.25421 + 9.10056i −0.171101 + 0.296355i
\(944\) −9.53157 + 42.7975i −0.310226 + 1.39294i
\(945\) −0.566260 3.21142i −0.0184204 0.104467i
\(946\) 19.5065 + 38.5142i 0.634212 + 1.25221i
\(947\) −5.58326 + 15.3399i −0.181432 + 0.498479i −0.996752 0.0805305i \(-0.974339\pi\)
0.815320 + 0.579010i \(0.196561\pi\)
\(948\) −9.84323 + 4.32542i −0.319693 + 0.140483i
\(949\) 39.9845i 1.29795i
\(950\) −4.85751 16.0083i −0.157598 0.519378i
\(951\) 23.1546 0.750840
\(952\) −9.13904 5.15309i −0.296198 0.167013i
\(953\) −31.9413 11.6257i −1.03468 0.376593i −0.231819 0.972759i \(-0.574468\pi\)
−0.802861 + 0.596166i \(0.796690\pi\)
\(954\) 1.33916 0.678253i 0.0433570 0.0219593i
\(955\) −29.5850 + 5.21663i −0.957347 + 0.168806i
\(956\) −1.96735 30.2408i −0.0636287 0.978058i
\(957\) −6.56186 3.78849i −0.212115 0.122464i
\(958\) 4.49692 + 1.92171i 0.145289 + 0.0620876i
\(959\) −6.03319 5.06245i −0.194822 0.163475i
\(960\) 12.0936 0.246270i 0.390320 0.00794832i
\(961\) 14.8062 + 25.6451i 0.477620 + 0.827262i
\(962\) −4.07879 33.8983i −0.131505 1.09292i
\(963\) 6.94786 + 19.0891i 0.223892 + 0.615137i
\(964\) 24.4766 + 2.69264i 0.788337 + 0.0867241i
\(965\) −40.3953 7.12278i −1.30037 0.229290i
\(966\) 2.36672 + 7.80886i 0.0761481 + 0.251246i
\(967\) 15.3090 12.8458i 0.492305 0.413093i −0.362547 0.931966i \(-0.618093\pi\)
0.854851 + 0.518873i \(0.173648\pi\)
\(968\) 0.198321 + 0.528092i 0.00637428 + 0.0169735i
\(969\) 3.75063 + 6.49141i 0.120488 + 0.208534i
\(970\) 16.5064 + 22.0156i 0.529989 + 0.706878i
\(971\) −18.6759 22.2570i −0.599337 0.714262i 0.378034 0.925792i \(-0.376600\pi\)
−0.977372 + 0.211529i \(0.932156\pi\)
\(972\) 1.61232 + 1.18340i 0.0517150 + 0.0379576i
\(973\) −14.4235 2.54325i −0.462396 0.0815329i
\(974\) 42.7066 + 40.0185i 1.36841 + 1.28228i
\(975\) 10.5190 3.82859i 0.336876 0.122613i
\(976\) −9.20278 17.7203i −0.294574 0.567214i
\(977\) −3.25423 5.63649i −0.104112 0.180327i 0.809263 0.587446i \(-0.199867\pi\)
−0.913375 + 0.407119i \(0.866533\pi\)
\(978\) 3.42234 + 0.187678i 0.109434 + 0.00600127i
\(979\) −7.19508 + 8.57476i −0.229956 + 0.274051i
\(980\) −1.68480 6.89969i −0.0538188 0.220403i
\(981\) 8.46834 + 4.88920i 0.270373 + 0.156100i
\(982\) −24.1614 15.7740i −0.771020 0.503368i
\(983\) −1.67656 9.50824i −0.0534740 0.303266i 0.946327 0.323210i \(-0.104762\pi\)
−0.999801 + 0.0199445i \(0.993651\pi\)
\(984\) −2.04052 10.9210i −0.0650495 0.348150i
\(985\) 6.34102 + 2.30794i 0.202042 + 0.0735371i
\(986\) −5.46110 1.27475i −0.173917 0.0405962i
\(987\) 11.9395i 0.380037i
\(988\) −2.34612 35.8830i −0.0746401 1.14159i
\(989\) 24.8505i 0.790199i
\(990\) 1.59741 6.84343i 0.0507692 0.217498i
\(991\) 1.32510 + 0.482298i 0.0420933 + 0.0153207i 0.362981 0.931797i \(-0.381759\pi\)
−0.320888 + 0.947117i \(0.603981\pi\)
\(992\) 0.661181 6.63061i 0.0209925 0.210522i
\(993\) 3.20987 + 18.2041i 0.101862 + 0.577689i
\(994\) 23.2505 35.6134i 0.737462 1.12959i
\(995\) −6.13580 3.54251i −0.194518 0.112305i
\(996\) −5.87557 + 1.43472i −0.186174 + 0.0454608i
\(997\) −37.5772 + 44.7828i −1.19008 + 1.41828i −0.305314 + 0.952252i \(0.598761\pi\)
−0.884768 + 0.466032i \(0.845683\pi\)
\(998\) 1.40180 25.5620i 0.0443731 0.809152i
\(999\) 2.92648 + 5.06882i 0.0925899 + 0.160370i
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 456.2.bk.a.253.18 yes 240
8.5 even 2 inner 456.2.bk.a.253.1 240
19.16 even 9 inner 456.2.bk.a.301.1 yes 240
152.149 even 18 inner 456.2.bk.a.301.18 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.2.bk.a.253.1 240 8.5 even 2 inner
456.2.bk.a.253.18 yes 240 1.1 even 1 trivial
456.2.bk.a.301.1 yes 240 19.16 even 9 inner
456.2.bk.a.301.18 yes 240 152.149 even 18 inner