Properties

Label 690.2.m.e.601.2
Level $690$
Weight $2$
Character 690.601
Analytic conductor $5.510$
Analytic rank $0$
Dimension $20$
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] = [690,2,Mod(31,690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(690, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("690.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.m (of order \(11\), degree \(10\), 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: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 6 x^{19} + 21 x^{18} - 47 x^{17} + 44 x^{16} + 232 x^{15} - 1084 x^{14} + 1484 x^{13} + 2670 x^{12} - 12826 x^{11} + 18393 x^{10} - 2728 x^{9} - 12654 x^{8} - 6818 x^{7} + \cdots + 1849 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 601.2
Root \(-0.205162 + 0.236769i\) of defining polynomial
Character \(\chi\) \(=\) 690.601
Dual form 690.2.m.e.31.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.142315 + 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(4.30262 - 2.76513i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\) \(q+(0.142315 + 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(4.30262 - 2.76513i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-0.841254 - 0.540641i) q^{10} +(0.877534 - 6.10338i) q^{11} +(0.142315 - 0.989821i) q^{12} +(-1.50568 - 0.967644i) q^{13} +(3.34931 + 3.86531i) q^{14} +(-0.415415 - 0.909632i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-1.59556 - 0.468498i) q^{17} +(0.654861 - 0.755750i) q^{18} +(6.35426 - 1.86578i) q^{19} +(0.415415 - 0.909632i) q^{20} +(0.727875 + 5.06248i) q^{21} +6.16614 q^{22} +(-1.76703 - 4.45843i) q^{23} +1.00000 q^{24} +(-0.142315 - 0.989821i) q^{25} +(0.743514 - 1.62807i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-3.34931 + 3.86531i) q^{28} +(-4.10832 - 1.20631i) q^{29} +(0.841254 - 0.540641i) q^{30} +(-0.672836 - 1.47331i) q^{31} +(0.654861 + 0.755750i) q^{32} +(5.18729 + 3.33367i) q^{33} +(0.236658 - 1.64599i) q^{34} +(-0.727875 + 5.06248i) q^{35} +(0.841254 + 0.540641i) q^{36} +(4.51174 + 5.20683i) q^{37} +(2.75109 + 6.02405i) q^{38} +(1.50568 - 0.967644i) q^{39} +(0.959493 + 0.281733i) q^{40} +(-5.47035 + 6.31312i) q^{41} +(-4.90736 + 1.44093i) q^{42} +(-5.39942 + 11.8231i) q^{43} +(0.877534 + 6.10338i) q^{44} +1.00000 q^{45} +(4.16158 - 2.38355i) q^{46} +9.71133 q^{47} +(0.142315 + 0.989821i) q^{48} +(7.95873 - 17.4272i) q^{49} +(0.959493 - 0.281733i) q^{50} +(1.08898 - 1.25675i) q^{51} +(1.71731 + 0.504247i) q^{52} +(3.12713 - 2.00968i) q^{53} +(0.415415 + 0.909632i) q^{54} +(4.03797 + 4.66006i) q^{55} +(-4.30262 - 2.76513i) q^{56} +(-0.942482 + 6.55511i) q^{57} +(0.609358 - 4.23818i) q^{58} +(-5.44994 - 3.50246i) q^{59} +(0.654861 + 0.755750i) q^{60} +(2.76439 + 6.05316i) q^{61} +(1.36256 - 0.875661i) q^{62} +(-4.90736 - 1.44093i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(1.71731 - 0.504247i) q^{65} +(-2.56151 + 5.60892i) q^{66} +(-0.166394 - 1.15729i) q^{67} +1.66292 q^{68} +(4.78958 + 0.244751i) q^{69} -5.11454 q^{70} +(0.910284 + 6.33116i) q^{71} +(-0.415415 + 0.909632i) q^{72} +(3.56349 - 1.04634i) q^{73} +(-4.51174 + 5.20683i) q^{74} +(0.959493 + 0.281733i) q^{75} +(-5.57121 + 3.58040i) q^{76} +(-13.1009 - 28.6870i) q^{77} +(1.17208 + 1.35265i) q^{78} +(-4.73008 - 3.03984i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-7.02738 - 4.51622i) q^{82} +(4.22002 + 4.87017i) q^{83} +(-2.12466 - 4.65235i) q^{84} +(1.39894 - 0.899042i) q^{85} +(-12.4712 - 3.66186i) q^{86} +(2.80396 - 3.23594i) q^{87} +(-5.91637 + 1.73720i) q^{88} +(1.04410 - 2.28626i) q^{89} +(0.142315 + 0.989821i) q^{90} -9.15405 q^{91} +(2.95154 + 3.78000i) q^{92} +1.61967 q^{93} +(1.38207 + 9.61248i) q^{94} +(-2.75109 + 6.02405i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(3.42386 - 3.95135i) q^{97} +(18.3824 + 5.39757i) q^{98} +(-5.18729 + 3.33367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{8}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.142315 + 0.989821i 0.100632 + 0.699909i
\(3\) −0.415415 + 0.909632i −0.239840 + 0.525176i
\(4\) −0.959493 + 0.281733i −0.479746 + 0.140866i
\(5\) −0.654861 + 0.755750i −0.292863 + 0.337981i
\(6\) −0.959493 0.281733i −0.391711 0.115017i
\(7\) 4.30262 2.76513i 1.62624 1.04512i 0.674470 0.738302i \(-0.264372\pi\)
0.951768 0.306818i \(-0.0992643\pi\)
\(8\) −0.415415 0.909632i −0.146871 0.321603i
\(9\) −0.654861 0.755750i −0.218287 0.251917i
\(10\) −0.841254 0.540641i −0.266028 0.170966i
\(11\) 0.877534 6.10338i 0.264586 1.84024i −0.232572 0.972579i \(-0.574714\pi\)
0.497158 0.867660i \(-0.334377\pi\)
\(12\) 0.142315 0.989821i 0.0410828 0.285737i
\(13\) −1.50568 0.967644i −0.417601 0.268376i 0.314923 0.949117i \(-0.398021\pi\)
−0.732524 + 0.680741i \(0.761658\pi\)
\(14\) 3.34931 + 3.86531i 0.895141 + 1.03305i
\(15\) −0.415415 0.909632i −0.107260 0.234866i
\(16\) 0.841254 0.540641i 0.210313 0.135160i
\(17\) −1.59556 0.468498i −0.386980 0.113628i 0.0824546 0.996595i \(-0.473724\pi\)
−0.469435 + 0.882967i \(0.655542\pi\)
\(18\) 0.654861 0.755750i 0.154352 0.178132i
\(19\) 6.35426 1.86578i 1.45777 0.428039i 0.545665 0.838004i \(-0.316277\pi\)
0.912101 + 0.409965i \(0.134459\pi\)
\(20\) 0.415415 0.909632i 0.0928896 0.203400i
\(21\) 0.727875 + 5.06248i 0.158835 + 1.10472i
\(22\) 6.16614 1.31463
\(23\) −1.76703 4.45843i −0.368451 0.929647i
\(24\) 1.00000 0.204124
\(25\) −0.142315 0.989821i −0.0284630 0.197964i
\(26\) 0.743514 1.62807i 0.145815 0.319290i
\(27\) 0.959493 0.281733i 0.184655 0.0542195i
\(28\) −3.34931 + 3.86531i −0.632960 + 0.730475i
\(29\) −4.10832 1.20631i −0.762895 0.224006i −0.122935 0.992415i \(-0.539231\pi\)
−0.639960 + 0.768408i \(0.721049\pi\)
\(30\) 0.841254 0.540641i 0.153591 0.0987071i
\(31\) −0.672836 1.47331i −0.120845 0.264614i 0.839536 0.543304i \(-0.182827\pi\)
−0.960381 + 0.278690i \(0.910100\pi\)
\(32\) 0.654861 + 0.755750i 0.115764 + 0.133599i
\(33\) 5.18729 + 3.33367i 0.902991 + 0.580317i
\(34\) 0.236658 1.64599i 0.0405865 0.282285i
\(35\) −0.727875 + 5.06248i −0.123033 + 0.855715i
\(36\) 0.841254 + 0.540641i 0.140209 + 0.0901068i
\(37\) 4.51174 + 5.20683i 0.741726 + 0.855998i 0.993739 0.111726i \(-0.0356380\pi\)
−0.252013 + 0.967724i \(0.581093\pi\)
\(38\) 2.75109 + 6.02405i 0.446286 + 0.977230i
\(39\) 1.50568 0.967644i 0.241102 0.154947i
\(40\) 0.959493 + 0.281733i 0.151709 + 0.0445458i
\(41\) −5.47035 + 6.31312i −0.854326 + 0.985944i −0.999994 0.00338920i \(-0.998921\pi\)
0.145669 + 0.989333i \(0.453467\pi\)
\(42\) −4.90736 + 1.44093i −0.757223 + 0.222341i
\(43\) −5.39942 + 11.8231i −0.823404 + 1.80300i −0.290354 + 0.956919i \(0.593773\pi\)
−0.533050 + 0.846084i \(0.678954\pi\)
\(44\) 0.877534 + 6.10338i 0.132293 + 0.920120i
\(45\) 1.00000 0.149071
\(46\) 4.16158 2.38355i 0.613591 0.351435i
\(47\) 9.71133 1.41654 0.708272 0.705940i \(-0.249475\pi\)
0.708272 + 0.705940i \(0.249475\pi\)
\(48\) 0.142315 + 0.989821i 0.0205414 + 0.142868i
\(49\) 7.95873 17.4272i 1.13696 2.48960i
\(50\) 0.959493 0.281733i 0.135693 0.0398430i
\(51\) 1.08898 1.25675i 0.152488 0.175980i
\(52\) 1.71731 + 0.504247i 0.238148 + 0.0699265i
\(53\) 3.12713 2.00968i 0.429544 0.276051i −0.307953 0.951402i \(-0.599644\pi\)
0.737497 + 0.675350i \(0.236008\pi\)
\(54\) 0.415415 + 0.909632i 0.0565308 + 0.123785i
\(55\) 4.03797 + 4.66006i 0.544479 + 0.628363i
\(56\) −4.30262 2.76513i −0.574962 0.369506i
\(57\) −0.942482 + 6.55511i −0.124835 + 0.868245i
\(58\) 0.609358 4.23818i 0.0800126 0.556500i
\(59\) −5.44994 3.50246i −0.709522 0.455982i 0.135456 0.990783i \(-0.456750\pi\)
−0.844978 + 0.534801i \(0.820386\pi\)
\(60\) 0.654861 + 0.755750i 0.0845422 + 0.0975669i
\(61\) 2.76439 + 6.05316i 0.353943 + 0.775028i 0.999932 + 0.0116808i \(0.00371818\pi\)
−0.645988 + 0.763347i \(0.723555\pi\)
\(62\) 1.36256 0.875661i 0.173045 0.111209i
\(63\) −4.90736 1.44093i −0.618270 0.181540i
\(64\) −0.654861 + 0.755750i −0.0818576 + 0.0944687i
\(65\) 1.71731 0.504247i 0.213006 0.0625442i
\(66\) −2.56151 + 5.60892i −0.315300 + 0.690411i
\(67\) −0.166394 1.15729i −0.0203282 0.141386i 0.977130 0.212644i \(-0.0682076\pi\)
−0.997458 + 0.0712585i \(0.977298\pi\)
\(68\) 1.66292 0.201659
\(69\) 4.78958 + 0.244751i 0.576598 + 0.0294646i
\(70\) −5.11454 −0.611304
\(71\) 0.910284 + 6.33116i 0.108031 + 0.751371i 0.969770 + 0.244020i \(0.0784661\pi\)
−0.861739 + 0.507351i \(0.830625\pi\)
\(72\) −0.415415 + 0.909632i −0.0489571 + 0.107201i
\(73\) 3.56349 1.04634i 0.417075 0.122464i −0.0664602 0.997789i \(-0.521171\pi\)
0.483536 + 0.875325i \(0.339352\pi\)
\(74\) −4.51174 + 5.20683i −0.524480 + 0.605282i
\(75\) 0.959493 + 0.281733i 0.110793 + 0.0325317i
\(76\) −5.57121 + 3.58040i −0.639062 + 0.410700i
\(77\) −13.1009 28.6870i −1.49299 3.26919i
\(78\) 1.17208 + 1.35265i 0.132711 + 0.153157i
\(79\) −4.73008 3.03984i −0.532176 0.342008i 0.246796 0.969067i \(-0.420622\pi\)
−0.778972 + 0.627059i \(0.784259\pi\)
\(80\) −0.142315 + 0.989821i −0.0159113 + 0.110665i
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) −7.02738 4.51622i −0.776044 0.498733i
\(83\) 4.22002 + 4.87017i 0.463208 + 0.534570i 0.938510 0.345252i \(-0.112207\pi\)
−0.475302 + 0.879823i \(0.657661\pi\)
\(84\) −2.12466 4.65235i −0.231819 0.507613i
\(85\) 1.39894 0.899042i 0.151736 0.0975148i
\(86\) −12.4712 3.66186i −1.34480 0.394869i
\(87\) 2.80396 3.23594i 0.300616 0.346929i
\(88\) −5.91637 + 1.73720i −0.630687 + 0.185187i
\(89\) 1.04410 2.28626i 0.110674 0.242343i −0.846188 0.532884i \(-0.821108\pi\)
0.956862 + 0.290541i \(0.0938354\pi\)
\(90\) 0.142315 + 0.989821i 0.0150013 + 0.104336i
\(91\) −9.15405 −0.959605
\(92\) 2.95154 + 3.78000i 0.307719 + 0.394093i
\(93\) 1.61967 0.167952
\(94\) 1.38207 + 9.61248i 0.142549 + 0.991452i
\(95\) −2.75109 + 6.02405i −0.282256 + 0.618055i
\(96\) −0.959493 + 0.281733i −0.0979278 + 0.0287542i
\(97\) 3.42386 3.95135i 0.347641 0.401199i −0.554820 0.831970i \(-0.687213\pi\)
0.902461 + 0.430771i \(0.141758\pi\)
\(98\) 18.3824 + 5.39757i 1.85691 + 0.545237i
\(99\) −5.18729 + 3.33367i −0.521342 + 0.335046i
\(100\) 0.415415 + 0.909632i 0.0415415 + 0.0909632i
\(101\) −2.88438 3.32875i −0.287007 0.331223i 0.593877 0.804556i \(-0.297596\pi\)
−0.880884 + 0.473332i \(0.843051\pi\)
\(102\) 1.39894 + 0.899042i 0.138515 + 0.0890184i
\(103\) 1.29711 9.02163i 0.127808 0.888927i −0.820516 0.571624i \(-0.806314\pi\)
0.948324 0.317303i \(-0.102777\pi\)
\(104\) −0.254716 + 1.77159i −0.0249770 + 0.173719i
\(105\) −4.30262 2.76513i −0.419893 0.269849i
\(106\) 2.43427 + 2.80929i 0.236437 + 0.272863i
\(107\) 1.14039 + 2.49710i 0.110245 + 0.241404i 0.956711 0.291040i \(-0.0940012\pi\)
−0.846466 + 0.532443i \(0.821274\pi\)
\(108\) −0.841254 + 0.540641i −0.0809497 + 0.0520232i
\(109\) −6.51247 1.91223i −0.623782 0.183159i −0.0454581 0.998966i \(-0.514475\pi\)
−0.578324 + 0.815807i \(0.696293\pi\)
\(110\) −4.03797 + 4.66006i −0.385005 + 0.444319i
\(111\) −6.61055 + 1.94103i −0.627445 + 0.184235i
\(112\) 2.12466 4.65235i 0.200761 0.439605i
\(113\) −0.0204510 0.142240i −0.00192386 0.0133808i 0.988837 0.149002i \(-0.0476061\pi\)
−0.990761 + 0.135621i \(0.956697\pi\)
\(114\) −6.62251 −0.620255
\(115\) 4.52662 + 1.58422i 0.422109 + 0.147729i
\(116\) 4.28176 0.397551
\(117\) 0.254716 + 1.77159i 0.0235485 + 0.163784i
\(118\) 2.69121 5.89292i 0.247746 0.542487i
\(119\) −8.16055 + 2.39615i −0.748076 + 0.219655i
\(120\) −0.654861 + 0.755750i −0.0597803 + 0.0689902i
\(121\) −25.9268 7.61279i −2.35698 0.692072i
\(122\) −5.59814 + 3.59770i −0.506831 + 0.325721i
\(123\) −3.47015 7.59857i −0.312893 0.685140i
\(124\) 1.06066 + 1.22407i 0.0952501 + 0.109924i
\(125\) 0.841254 + 0.540641i 0.0752440 + 0.0483564i
\(126\) 0.727875 5.06248i 0.0648442 0.451001i
\(127\) 0.161686 1.12455i 0.0143473 0.0997877i −0.981389 0.192028i \(-0.938494\pi\)
0.995737 + 0.0922401i \(0.0294027\pi\)
\(128\) −0.841254 0.540641i −0.0743570 0.0477863i
\(129\) −8.51165 9.82297i −0.749409 0.864864i
\(130\) 0.743514 + 1.62807i 0.0652104 + 0.142791i
\(131\) −7.84965 + 5.04466i −0.685827 + 0.440754i −0.836600 0.547814i \(-0.815460\pi\)
0.150773 + 0.988568i \(0.451824\pi\)
\(132\) −5.91637 1.73720i −0.514954 0.151204i
\(133\) 22.1808 25.5981i 1.92332 2.21963i
\(134\) 1.12183 0.329400i 0.0969117 0.0284558i
\(135\) −0.415415 + 0.909632i −0.0357532 + 0.0782887i
\(136\) 0.236658 + 1.64599i 0.0202933 + 0.141143i
\(137\) 17.9958 1.53749 0.768743 0.639557i \(-0.220882\pi\)
0.768743 + 0.639557i \(0.220882\pi\)
\(138\) 0.439369 + 4.77566i 0.0374015 + 0.406531i
\(139\) 21.7368 1.84369 0.921845 0.387558i \(-0.126681\pi\)
0.921845 + 0.387558i \(0.126681\pi\)
\(140\) −0.727875 5.06248i −0.0615166 0.427858i
\(141\) −4.03423 + 8.83374i −0.339744 + 0.743935i
\(142\) −6.13717 + 1.80204i −0.515020 + 0.151224i
\(143\) −7.22719 + 8.34062i −0.604368 + 0.697478i
\(144\) −0.959493 0.281733i −0.0799577 0.0234777i
\(145\) 3.60204 2.31489i 0.299133 0.192241i
\(146\) 1.54282 + 3.37831i 0.127685 + 0.279591i
\(147\) 12.5461 + 14.4790i 1.03479 + 1.19421i
\(148\) −5.79592 3.72481i −0.476422 0.306178i
\(149\) −2.72811 + 18.9744i −0.223495 + 1.55444i 0.501174 + 0.865347i \(0.332902\pi\)
−0.724669 + 0.689097i \(0.758007\pi\)
\(150\) −0.142315 + 0.989821i −0.0116200 + 0.0808186i
\(151\) −2.27569 1.46250i −0.185193 0.119017i 0.444759 0.895650i \(-0.353289\pi\)
−0.629952 + 0.776634i \(0.716926\pi\)
\(152\) −4.33682 5.00496i −0.351763 0.405956i
\(153\) 0.690802 + 1.51264i 0.0558480 + 0.122290i
\(154\) 26.5306 17.0502i 2.13790 1.37394i
\(155\) 1.55406 + 0.456315i 0.124825 + 0.0366521i
\(156\) −1.17208 + 1.35265i −0.0938412 + 0.108298i
\(157\) 9.30164 2.73121i 0.742352 0.217974i 0.111378 0.993778i \(-0.464474\pi\)
0.630974 + 0.775804i \(0.282655\pi\)
\(158\) 2.33574 5.11455i 0.185821 0.406892i
\(159\) 0.529016 + 3.67939i 0.0419537 + 0.291795i
\(160\) −1.00000 −0.0790569
\(161\) −19.9310 14.2969i −1.57078 1.12675i
\(162\) −1.00000 −0.0785674
\(163\) 0.893813 + 6.21661i 0.0700088 + 0.486922i 0.994417 + 0.105518i \(0.0336502\pi\)
−0.924409 + 0.381404i \(0.875441\pi\)
\(164\) 3.47015 7.59857i 0.270973 0.593349i
\(165\) −5.91637 + 1.73720i −0.460589 + 0.135241i
\(166\) −4.22002 + 4.87017i −0.327537 + 0.377998i
\(167\) −6.45420 1.89512i −0.499441 0.146649i 0.0223031 0.999751i \(-0.492900\pi\)
−0.521744 + 0.853102i \(0.674718\pi\)
\(168\) 4.30262 2.76513i 0.331955 0.213334i
\(169\) −4.06965 8.91129i −0.313050 0.685484i
\(170\) 1.08898 + 1.25675i 0.0835210 + 0.0963884i
\(171\) −5.57121 3.58040i −0.426041 0.273800i
\(172\) 1.84976 12.8654i 0.141043 0.980974i
\(173\) −3.60369 + 25.0642i −0.273984 + 1.90560i 0.131188 + 0.991357i \(0.458121\pi\)
−0.405172 + 0.914241i \(0.632788\pi\)
\(174\) 3.60204 + 2.31489i 0.273070 + 0.175492i
\(175\) −3.34931 3.86531i −0.253184 0.292190i
\(176\) −2.56151 5.60892i −0.193081 0.422788i
\(177\) 5.44994 3.50246i 0.409643 0.263261i
\(178\) 2.41158 + 0.708104i 0.180756 + 0.0530746i
\(179\) −9.19122 + 10.6072i −0.686984 + 0.792821i −0.986933 0.161134i \(-0.948485\pi\)
0.299949 + 0.953955i \(0.403030\pi\)
\(180\) −0.959493 + 0.281733i −0.0715164 + 0.0209991i
\(181\) 5.26373 11.5260i 0.391250 0.856718i −0.606833 0.794829i \(-0.707560\pi\)
0.998083 0.0618886i \(-0.0197123\pi\)
\(182\) −1.30276 9.06087i −0.0965667 0.671636i
\(183\) −6.65452 −0.491916
\(184\) −3.32148 + 3.45945i −0.244863 + 0.255034i
\(185\) −6.88962 −0.506535
\(186\) 0.230503 + 1.60319i 0.0169013 + 0.117551i
\(187\) −4.25958 + 9.32718i −0.311492 + 0.682071i
\(188\) −9.31795 + 2.73600i −0.679582 + 0.199543i
\(189\) 3.34931 3.86531i 0.243626 0.281160i
\(190\) −6.35426 1.86578i −0.460986 0.135358i
\(191\) −0.359597 + 0.231099i −0.0260195 + 0.0167217i −0.553586 0.832792i \(-0.686741\pi\)
0.527566 + 0.849514i \(0.323105\pi\)
\(192\) −0.415415 0.909632i −0.0299800 0.0656470i
\(193\) 8.01079 + 9.24495i 0.576629 + 0.665466i 0.966877 0.255244i \(-0.0821559\pi\)
−0.390247 + 0.920710i \(0.627610\pi\)
\(194\) 4.39840 + 2.82668i 0.315787 + 0.202944i
\(195\) −0.254716 + 1.77159i −0.0182406 + 0.126866i
\(196\) −2.72654 + 18.9635i −0.194753 + 1.35453i
\(197\) 14.3933 + 9.25002i 1.02548 + 0.659037i 0.941355 0.337418i \(-0.109554\pi\)
0.0841263 + 0.996455i \(0.473190\pi\)
\(198\) −4.03797 4.66006i −0.286966 0.331176i
\(199\) 6.58923 + 14.4284i 0.467098 + 1.02280i 0.985812 + 0.167854i \(0.0536837\pi\)
−0.518714 + 0.854948i \(0.673589\pi\)
\(200\) −0.841254 + 0.540641i −0.0594856 + 0.0382291i
\(201\) 1.12183 + 0.329400i 0.0791280 + 0.0232341i
\(202\) 2.88438 3.32875i 0.202944 0.234210i
\(203\) −21.0121 + 6.16972i −1.47476 + 0.433030i
\(204\) −0.690802 + 1.51264i −0.0483658 + 0.105906i
\(205\) −1.18882 8.26843i −0.0830309 0.577492i
\(206\) 9.11440 0.635030
\(207\) −2.21230 + 4.25508i −0.153765 + 0.295749i
\(208\) −1.78981 −0.124101
\(209\) −5.81148 40.4197i −0.401988 2.79589i
\(210\) 2.12466 4.65235i 0.146615 0.321042i
\(211\) −10.2887 + 3.02102i −0.708300 + 0.207976i −0.615989 0.787754i \(-0.711244\pi\)
−0.0923110 + 0.995730i \(0.529425\pi\)
\(212\) −2.43427 + 2.80929i −0.167186 + 0.192943i
\(213\) −6.13717 1.80204i −0.420512 0.123474i
\(214\) −2.30939 + 1.48415i −0.157867 + 0.101455i
\(215\) −5.39942 11.8231i −0.368237 0.806328i
\(216\) −0.654861 0.755750i −0.0445576 0.0514222i
\(217\) −6.96884 4.47860i −0.473076 0.304027i
\(218\) 0.965949 6.71832i 0.0654223 0.455022i
\(219\) −0.528548 + 3.67613i −0.0357160 + 0.248410i
\(220\) −5.18729 3.33367i −0.349727 0.224756i
\(221\) 1.94907 + 2.24934i 0.131108 + 0.151307i
\(222\) −2.86205 6.26702i −0.192088 0.420615i
\(223\) −4.25609 + 2.73522i −0.285009 + 0.183164i −0.675332 0.737514i \(-0.736000\pi\)
0.390323 + 0.920678i \(0.372363\pi\)
\(224\) 4.90736 + 1.44093i 0.327887 + 0.0962763i
\(225\) −0.654861 + 0.755750i −0.0436574 + 0.0503833i
\(226\) 0.137881 0.0404856i 0.00917173 0.00269306i
\(227\) 9.32891 20.4275i 0.619182 1.35582i −0.296931 0.954899i \(-0.595963\pi\)
0.916113 0.400920i \(-0.131309\pi\)
\(228\) −0.942482 6.55511i −0.0624174 0.434122i
\(229\) −24.7812 −1.63759 −0.818795 0.574086i \(-0.805357\pi\)
−0.818795 + 0.574086i \(0.805357\pi\)
\(230\) −0.923889 + 4.70600i −0.0609194 + 0.310304i
\(231\) 31.5370 2.07498
\(232\) 0.609358 + 4.23818i 0.0400063 + 0.278250i
\(233\) 5.55582 12.1655i 0.363974 0.796991i −0.635712 0.771926i \(-0.719293\pi\)
0.999686 0.0250649i \(-0.00797923\pi\)
\(234\) −1.71731 + 0.504247i −0.112264 + 0.0329637i
\(235\) −6.35957 + 7.33933i −0.414853 + 0.478765i
\(236\) 6.21594 + 1.82516i 0.404623 + 0.118808i
\(237\) 4.73008 3.03984i 0.307252 0.197459i
\(238\) −3.53313 7.73648i −0.229019 0.501481i
\(239\) 0.206167 + 0.237930i 0.0133359 + 0.0153904i 0.762378 0.647132i \(-0.224032\pi\)
−0.749042 + 0.662522i \(0.769486\pi\)
\(240\) −0.841254 0.540641i −0.0543027 0.0348982i
\(241\) −1.32767 + 9.23413i −0.0855226 + 0.594823i 0.901322 + 0.433150i \(0.142598\pi\)
−0.986844 + 0.161673i \(0.948311\pi\)
\(242\) 3.84554 26.7463i 0.247201 1.71932i
\(243\) −0.841254 0.540641i −0.0539664 0.0346821i
\(244\) −4.35778 5.02915i −0.278978 0.321958i
\(245\) 7.95873 + 17.4272i 0.508464 + 1.11338i
\(246\) 7.02738 4.51622i 0.448049 0.287944i
\(247\) −11.3729 3.33939i −0.723641 0.212480i
\(248\) −1.06066 + 1.22407i −0.0673520 + 0.0777283i
\(249\) −6.18312 + 1.81553i −0.391839 + 0.115054i
\(250\) −0.415415 + 0.909632i −0.0262732 + 0.0575302i
\(251\) 2.30752 + 16.0492i 0.145650 + 1.01301i 0.923235 + 0.384237i \(0.125535\pi\)
−0.777585 + 0.628778i \(0.783556\pi\)
\(252\) 5.11454 0.322186
\(253\) −28.7621 + 6.87244i −1.80826 + 0.432067i
\(254\) 1.13611 0.0712862
\(255\) 0.236658 + 1.64599i 0.0148201 + 0.103076i
\(256\) 0.415415 0.909632i 0.0259634 0.0568520i
\(257\) 4.69240 1.37781i 0.292704 0.0859457i −0.132084 0.991239i \(-0.542167\pi\)
0.424788 + 0.905293i \(0.360349\pi\)
\(258\) 8.51165 9.82297i 0.529912 0.611552i
\(259\) 33.8099 + 9.92748i 2.10084 + 0.616863i
\(260\) −1.50568 + 0.967644i −0.0933785 + 0.0600107i
\(261\) 1.77871 + 3.89482i 0.110099 + 0.241084i
\(262\) −6.11044 7.05182i −0.377504 0.435663i
\(263\) 16.8321 + 10.8174i 1.03791 + 0.667027i 0.944470 0.328598i \(-0.106576\pi\)
0.0934441 + 0.995625i \(0.470212\pi\)
\(264\) 0.877534 6.10338i 0.0540085 0.375637i
\(265\) −0.529016 + 3.67939i −0.0324972 + 0.226023i
\(266\) 28.4942 + 18.3121i 1.74709 + 1.12279i
\(267\) 1.64592 + 1.89949i 0.100729 + 0.116247i
\(268\) 0.485701 + 1.06354i 0.0296689 + 0.0649658i
\(269\) 15.5465 9.99111i 0.947885 0.609169i 0.0272651 0.999628i \(-0.491320\pi\)
0.920620 + 0.390459i \(0.127684\pi\)
\(270\) −0.959493 0.281733i −0.0583929 0.0171457i
\(271\) 10.4649 12.0771i 0.635696 0.733633i −0.342911 0.939368i \(-0.611413\pi\)
0.978608 + 0.205735i \(0.0659585\pi\)
\(272\) −1.59556 + 0.468498i −0.0967450 + 0.0284069i
\(273\) 3.80273 8.32681i 0.230152 0.503962i
\(274\) 2.56107 + 17.8126i 0.154720 + 1.07610i
\(275\) −6.16614 −0.371833
\(276\) −4.66452 + 1.11454i −0.280771 + 0.0670877i
\(277\) −12.6852 −0.762177 −0.381088 0.924539i \(-0.624451\pi\)
−0.381088 + 0.924539i \(0.624451\pi\)
\(278\) 3.09347 + 21.5155i 0.185534 + 1.29042i
\(279\) −0.672836 + 1.47331i −0.0402817 + 0.0882045i
\(280\) 4.90736 1.44093i 0.293271 0.0861121i
\(281\) 11.3225 13.0668i 0.675442 0.779501i −0.309776 0.950810i \(-0.600254\pi\)
0.985217 + 0.171308i \(0.0547994\pi\)
\(282\) −9.31795 2.73600i −0.554876 0.162926i
\(283\) 7.68878 4.94128i 0.457051 0.293729i −0.291785 0.956484i \(-0.594249\pi\)
0.748836 + 0.662755i \(0.230613\pi\)
\(284\) −2.65711 5.81825i −0.157670 0.345250i
\(285\) −4.33682 5.00496i −0.256891 0.296468i
\(286\) −9.28426 5.96663i −0.548990 0.352814i
\(287\) −6.08027 + 42.2892i −0.358907 + 2.49625i
\(288\) 0.142315 0.989821i 0.00838598 0.0583258i
\(289\) −11.9750 7.69586i −0.704411 0.452698i
\(290\) 2.80396 + 3.23594i 0.164654 + 0.190021i
\(291\) 2.17195 + 4.75591i 0.127322 + 0.278796i
\(292\) −3.12436 + 2.00790i −0.182839 + 0.117504i
\(293\) 8.30101 + 2.43740i 0.484950 + 0.142394i 0.515063 0.857152i \(-0.327769\pi\)
−0.0301130 + 0.999547i \(0.509587\pi\)
\(294\) −12.5461 + 14.4790i −0.731706 + 0.844434i
\(295\) 6.21594 1.82516i 0.361906 0.106265i
\(296\) 2.86205 6.26702i 0.166353 0.364263i
\(297\) −0.877534 6.10338i −0.0509197 0.354154i
\(298\) −19.1695 −1.11046
\(299\) −1.65358 + 8.42284i −0.0956292 + 0.487105i
\(300\) −1.00000 −0.0577350
\(301\) 9.46066 + 65.8004i 0.545304 + 3.79267i
\(302\) 1.12375 2.46067i 0.0646644 0.141595i
\(303\) 4.22616 1.24091i 0.242786 0.0712885i
\(304\) 4.33682 5.00496i 0.248734 0.287054i
\(305\) −6.38496 1.87479i −0.365602 0.107350i
\(306\) −1.39894 + 0.899042i −0.0799719 + 0.0513948i
\(307\) 13.1279 + 28.7462i 0.749251 + 1.64063i 0.767707 + 0.640801i \(0.221398\pi\)
−0.0184563 + 0.999830i \(0.505875\pi\)
\(308\) 20.6523 + 23.8341i 1.17678 + 1.35807i
\(309\) 7.66752 + 4.92762i 0.436190 + 0.280322i
\(310\) −0.230503 + 1.60319i −0.0130917 + 0.0910549i
\(311\) 2.86213 19.9065i 0.162296 1.12880i −0.731995 0.681310i \(-0.761410\pi\)
0.894291 0.447486i \(-0.147680\pi\)
\(312\) −1.50568 0.967644i −0.0852425 0.0547820i
\(313\) −4.56559 5.26897i −0.258063 0.297820i 0.611903 0.790933i \(-0.290404\pi\)
−0.869965 + 0.493113i \(0.835859\pi\)
\(314\) 4.02717 + 8.81827i 0.227266 + 0.497644i
\(315\) 4.30262 2.76513i 0.242425 0.155797i
\(316\) 5.39490 + 1.58409i 0.303487 + 0.0891118i
\(317\) −11.5193 + 13.2940i −0.646988 + 0.746664i −0.980594 0.196048i \(-0.937189\pi\)
0.333606 + 0.942713i \(0.391735\pi\)
\(318\) −3.56665 + 1.04726i −0.200008 + 0.0587276i
\(319\) −10.9678 + 24.0160i −0.614077 + 1.34464i
\(320\) −0.142315 0.989821i −0.00795564 0.0553327i
\(321\) −2.74518 −0.153221
\(322\) 11.3149 21.7628i 0.630554 1.21279i
\(323\) −11.0127 −0.612763
\(324\) −0.142315 0.989821i −0.00790638 0.0549901i
\(325\) −0.743514 + 1.62807i −0.0412427 + 0.0903089i
\(326\) −6.02613 + 1.76943i −0.333756 + 0.0979997i
\(327\) 4.44481 5.12958i 0.245798 0.283667i
\(328\) 8.01509 + 2.35344i 0.442559 + 0.129947i
\(329\) 41.7842 26.8531i 2.30364 1.48046i
\(330\) −2.56151 5.60892i −0.141006 0.308761i
\(331\) 10.7668 + 12.4256i 0.591799 + 0.682973i 0.970099 0.242710i \(-0.0780365\pi\)
−0.378299 + 0.925683i \(0.623491\pi\)
\(332\) −5.42117 3.48397i −0.297525 0.191208i
\(333\) 0.980496 6.81950i 0.0537308 0.373706i
\(334\) 0.957306 6.65821i 0.0523814 0.364321i
\(335\) 0.983589 + 0.632114i 0.0537392 + 0.0345361i
\(336\) 3.34931 + 3.86531i 0.182720 + 0.210870i
\(337\) 13.5417 + 29.6521i 0.737662 + 1.61526i 0.787362 + 0.616491i \(0.211446\pi\)
−0.0496997 + 0.998764i \(0.515826\pi\)
\(338\) 8.24141 5.29643i 0.448274 0.288088i
\(339\) 0.137881 + 0.0404856i 0.00748869 + 0.00219888i
\(340\) −1.08898 + 1.25675i −0.0590583 + 0.0681569i
\(341\) −9.58259 + 2.81370i −0.518926 + 0.152370i
\(342\) 2.75109 6.02405i 0.148762 0.325743i
\(343\) −8.84986 61.5521i −0.477847 3.32350i
\(344\) 12.9977 0.700787
\(345\) −3.32148 + 3.45945i −0.178822 + 0.186250i
\(346\) −25.3220 −1.36132
\(347\) 0.0380499 + 0.264643i 0.00204263 + 0.0142068i 0.990817 0.135208i \(-0.0431702\pi\)
−0.988775 + 0.149415i \(0.952261\pi\)
\(348\) −1.77871 + 3.89482i −0.0953487 + 0.208784i
\(349\) −15.6363 + 4.59122i −0.836990 + 0.245763i −0.672017 0.740536i \(-0.734572\pi\)
−0.164973 + 0.986298i \(0.552754\pi\)
\(350\) 3.34931 3.86531i 0.179028 0.206609i
\(351\) −1.71731 0.504247i −0.0916632 0.0269147i
\(352\) 5.18729 3.33367i 0.276484 0.177685i
\(353\) 0.966587 + 2.11653i 0.0514462 + 0.112652i 0.933610 0.358292i \(-0.116641\pi\)
−0.882163 + 0.470944i \(0.843914\pi\)
\(354\) 4.24242 + 4.89602i 0.225482 + 0.260220i
\(355\) −5.38088 3.45808i −0.285588 0.183536i
\(356\) −0.357693 + 2.48781i −0.0189577 + 0.131854i
\(357\) 1.21040 8.41849i 0.0640610 0.445554i
\(358\) −11.8073 7.58810i −0.624036 0.401043i
\(359\) −12.3529 14.2560i −0.651960 0.752402i 0.329482 0.944162i \(-0.393126\pi\)
−0.981442 + 0.191760i \(0.938581\pi\)
\(360\) −0.415415 0.909632i −0.0218943 0.0479418i
\(361\) 20.9116 13.4391i 1.10061 0.707320i
\(362\) 12.1577 + 3.56984i 0.638997 + 0.187626i
\(363\) 17.6952 20.4214i 0.928758 1.07184i
\(364\) 8.78324 2.57899i 0.460367 0.135176i
\(365\) −1.54282 + 3.37831i −0.0807551 + 0.176829i
\(366\) −0.947037 6.58678i −0.0495024 0.344297i
\(367\) −9.02677 −0.471194 −0.235597 0.971851i \(-0.575705\pi\)
−0.235597 + 0.971851i \(0.575705\pi\)
\(368\) −3.89693 2.79534i −0.203142 0.145717i
\(369\) 8.35346 0.434864
\(370\) −0.980496 6.81950i −0.0509735 0.354529i
\(371\) 7.89783 17.2938i 0.410035 0.897851i
\(372\) −1.55406 + 0.456315i −0.0805745 + 0.0236588i
\(373\) −9.64245 + 11.1280i −0.499267 + 0.576185i −0.948318 0.317321i \(-0.897217\pi\)
0.449051 + 0.893506i \(0.351762\pi\)
\(374\) −9.83845 2.88883i −0.508734 0.149378i
\(375\) −0.841254 + 0.540641i −0.0434421 + 0.0279186i
\(376\) −4.03423 8.83374i −0.208050 0.455565i
\(377\) 5.01854 + 5.79171i 0.258468 + 0.298288i
\(378\) 4.30262 + 2.76513i 0.221303 + 0.142223i
\(379\) −1.60338 + 11.1518i −0.0823602 + 0.572828i 0.906297 + 0.422641i \(0.138897\pi\)
−0.988658 + 0.150187i \(0.952012\pi\)
\(380\) 0.942482 6.55511i 0.0483483 0.336270i
\(381\) 0.955760 + 0.614230i 0.0489651 + 0.0314679i
\(382\) −0.279923 0.323048i −0.0143221 0.0165286i
\(383\) 3.03726 + 6.65067i 0.155197 + 0.339834i 0.971219 0.238186i \(-0.0765529\pi\)
−0.816023 + 0.578020i \(0.803826\pi\)
\(384\) 0.841254 0.540641i 0.0429300 0.0275895i
\(385\) 30.2595 + 8.88499i 1.54217 + 0.452821i
\(386\) −8.01079 + 9.24495i −0.407739 + 0.470555i
\(387\) 12.4712 3.66186i 0.633945 0.186143i
\(388\) −2.17195 + 4.75591i −0.110264 + 0.241445i
\(389\) −0.290327 2.01927i −0.0147201 0.102381i 0.981137 0.193315i \(-0.0619239\pi\)
−0.995857 + 0.0909340i \(0.971015\pi\)
\(390\) −1.78981 −0.0906305
\(391\) 0.730634 + 7.94154i 0.0369498 + 0.401621i
\(392\) −19.1585 −0.967650
\(393\) −1.32793 9.23592i −0.0669850 0.465891i
\(394\) −7.10749 + 15.5632i −0.358070 + 0.784064i
\(395\) 5.39490 1.58409i 0.271447 0.0797040i
\(396\) 4.03797 4.66006i 0.202915 0.234177i
\(397\) −0.0886769 0.0260379i −0.00445057 0.00130680i 0.279507 0.960144i \(-0.409829\pi\)
−0.283957 + 0.958837i \(0.591647\pi\)
\(398\) −13.3438 + 8.57553i −0.668864 + 0.429853i
\(399\) 14.0706 + 30.8102i 0.704409 + 1.54244i
\(400\) −0.654861 0.755750i −0.0327430 0.0377875i
\(401\) −16.0700 10.3276i −0.802497 0.515733i 0.0739330 0.997263i \(-0.476445\pi\)
−0.876430 + 0.481530i \(0.840081\pi\)
\(402\) −0.166394 + 1.15729i −0.00829896 + 0.0577206i
\(403\) −0.412557 + 2.86940i −0.0205509 + 0.142935i
\(404\) 3.70536 + 2.38129i 0.184349 + 0.118474i
\(405\) −0.654861 0.755750i −0.0325403 0.0375535i
\(406\) −9.09726 19.9202i −0.451490 0.988624i
\(407\) 35.7385 22.9677i 1.77149 1.13847i
\(408\) −1.59556 0.468498i −0.0789919 0.0231941i
\(409\) −12.8467 + 14.8259i −0.635230 + 0.733094i −0.978524 0.206134i \(-0.933912\pi\)
0.343294 + 0.939228i \(0.388457\pi\)
\(410\) 8.01509 2.35344i 0.395837 0.116228i
\(411\) −7.47573 + 16.3696i −0.368751 + 0.807452i
\(412\) 1.29711 + 9.02163i 0.0639042 + 0.444464i
\(413\) −33.1338 −1.63041
\(414\) −4.52662 1.58422i −0.222471 0.0778601i
\(415\) −6.44415 −0.316331
\(416\) −0.254716 1.77159i −0.0124885 0.0868594i
\(417\) −9.02979 + 19.7725i −0.442191 + 0.968263i
\(418\) 39.1813 11.5047i 1.91642 0.562711i
\(419\) 9.29774 10.7302i 0.454224 0.524203i −0.481732 0.876319i \(-0.659992\pi\)
0.935957 + 0.352116i \(0.114538\pi\)
\(420\) 4.90736 + 1.44093i 0.239455 + 0.0703103i
\(421\) 6.06829 3.89986i 0.295751 0.190067i −0.384347 0.923189i \(-0.625574\pi\)
0.680098 + 0.733121i \(0.261937\pi\)
\(422\) −4.45450 9.75400i −0.216842 0.474817i
\(423\) −6.35957 7.33933i −0.309213 0.356851i
\(424\) −3.12713 2.00968i −0.151867 0.0975989i
\(425\) −0.236658 + 1.64599i −0.0114796 + 0.0798424i
\(426\) 0.910284 6.33116i 0.0441034 0.306746i
\(427\) 28.6319 + 18.4006i 1.38559 + 0.890467i
\(428\) −1.79771 2.07467i −0.0868955 0.100283i
\(429\) −4.58461 10.0389i −0.221347 0.484683i
\(430\) 10.9343 7.02706i 0.527300 0.338875i
\(431\) −25.1735 7.39160i −1.21256 0.356041i −0.387920 0.921693i \(-0.626806\pi\)
−0.824644 + 0.565652i \(0.808625\pi\)
\(432\) 0.654861 0.755750i 0.0315070 0.0363610i
\(433\) −5.80119 + 1.70338i −0.278787 + 0.0818594i −0.418137 0.908384i \(-0.637317\pi\)
0.139350 + 0.990243i \(0.455499\pi\)
\(434\) 3.44125 7.53528i 0.165185 0.361705i
\(435\) 0.609358 + 4.23818i 0.0292165 + 0.203205i
\(436\) 6.78741 0.325058
\(437\) −19.5466 25.0331i −0.935041 1.19750i
\(438\) −3.71393 −0.177459
\(439\) −3.02749 21.0567i −0.144494 1.00498i −0.925037 0.379877i \(-0.875966\pi\)
0.780543 0.625102i \(-0.214943\pi\)
\(440\) 2.56151 5.60892i 0.122115 0.267395i
\(441\) −18.3824 + 5.39757i −0.875354 + 0.257027i
\(442\) −1.94907 + 2.24934i −0.0927077 + 0.106990i
\(443\) 6.71539 + 1.97182i 0.319058 + 0.0936839i 0.437340 0.899296i \(-0.355921\pi\)
−0.118282 + 0.992980i \(0.537739\pi\)
\(444\) 5.79592 3.72481i 0.275062 0.176772i
\(445\) 1.04410 + 2.28626i 0.0494951 + 0.108379i
\(446\) −3.31308 3.82350i −0.156879 0.181048i
\(447\) −16.1264 10.3638i −0.762754 0.490192i
\(448\) −0.727875 + 5.06248i −0.0343888 + 0.239180i
\(449\) −3.63804 + 25.3031i −0.171690 + 1.19413i 0.703624 + 0.710573i \(0.251564\pi\)
−0.875314 + 0.483556i \(0.839345\pi\)
\(450\) −0.841254 0.540641i −0.0396571 0.0254861i
\(451\) 33.7310 + 38.9276i 1.58833 + 1.83303i
\(452\) 0.0596961 + 0.130716i 0.00280787 + 0.00614837i
\(453\) 2.27569 1.46250i 0.106921 0.0687142i
\(454\) 21.5472 + 6.32683i 1.01126 + 0.296933i
\(455\) 5.99462 6.91817i 0.281032 0.324329i
\(456\) 6.35426 1.86578i 0.297565 0.0873730i
\(457\) −5.36804 + 11.7544i −0.251106 + 0.549847i −0.992645 0.121064i \(-0.961369\pi\)
0.741538 + 0.670911i \(0.234097\pi\)
\(458\) −3.52674 24.5290i −0.164794 1.14616i
\(459\) −1.66292 −0.0776184
\(460\) −4.78958 0.244751i −0.223315 0.0114116i
\(461\) −8.30672 −0.386882 −0.193441 0.981112i \(-0.561965\pi\)
−0.193441 + 0.981112i \(0.561965\pi\)
\(462\) 4.48818 + 31.2160i 0.208809 + 1.45230i
\(463\) −13.3226 + 29.1725i −0.619156 + 1.35576i 0.296976 + 0.954885i \(0.404022\pi\)
−0.916132 + 0.400877i \(0.868705\pi\)
\(464\) −4.10832 + 1.20631i −0.190724 + 0.0560016i
\(465\) −1.06066 + 1.22407i −0.0491869 + 0.0567647i
\(466\) 12.8324 + 3.76793i 0.594449 + 0.174546i
\(467\) −15.5129 + 9.96954i −0.717852 + 0.461335i −0.847889 0.530174i \(-0.822127\pi\)
0.130037 + 0.991509i \(0.458490\pi\)
\(468\) −0.743514 1.62807i −0.0343689 0.0752574i
\(469\) −3.91599 4.51930i −0.180824 0.208682i
\(470\) −8.16969 5.25034i −0.376840 0.242180i
\(471\) −1.37965 + 9.59566i −0.0635708 + 0.442145i
\(472\) −0.921966 + 6.41242i −0.0424369 + 0.295155i
\(473\) 67.4226 + 43.3299i 3.10010 + 1.99231i
\(474\) 3.68206 + 4.24932i 0.169122 + 0.195178i
\(475\) −2.75109 6.02405i −0.126229 0.276402i
\(476\) 7.15491 4.59818i 0.327945 0.210757i
\(477\) −3.56665 1.04726i −0.163306 0.0479509i
\(478\) −0.206167 + 0.237930i −0.00942987 + 0.0108827i
\(479\) 17.0231 4.99844i 0.777806 0.228385i 0.131351 0.991336i \(-0.458069\pi\)
0.646456 + 0.762951i \(0.276250\pi\)
\(480\) 0.415415 0.909632i 0.0189610 0.0415188i
\(481\) −1.75490 12.2056i −0.0800166 0.556527i
\(482\) −9.32909 −0.424928
\(483\) 21.2845 12.1907i 0.968480 0.554698i
\(484\) 27.0213 1.22824
\(485\) 0.744077 + 5.17517i 0.0337868 + 0.234992i
\(486\) 0.415415 0.909632i 0.0188436 0.0412617i
\(487\) −1.55651 + 0.457033i −0.0705323 + 0.0207101i −0.316808 0.948490i \(-0.602611\pi\)
0.246276 + 0.969200i \(0.420793\pi\)
\(488\) 4.35778 5.02915i 0.197268 0.227659i
\(489\) −6.02613 1.76943i −0.272511 0.0800164i
\(490\) −16.1172 + 10.3579i −0.728099 + 0.467921i
\(491\) 3.30608 + 7.23931i 0.149201 + 0.326706i 0.969445 0.245309i \(-0.0788894\pi\)
−0.820243 + 0.572015i \(0.806162\pi\)
\(492\) 5.47035 + 6.31312i 0.246623 + 0.284618i
\(493\) 5.98991 + 3.84948i 0.269772 + 0.173372i
\(494\) 1.68686 11.7324i 0.0758955 0.527865i
\(495\) 0.877534 6.10338i 0.0394422 0.274327i
\(496\) −1.36256 0.875661i −0.0611805 0.0393183i
\(497\) 21.4231 + 24.7236i 0.960956 + 1.10900i
\(498\) −2.67700 5.86181i −0.119959 0.262674i
\(499\) 27.5072 17.6778i 1.23139 0.791368i 0.247285 0.968943i \(-0.420462\pi\)
0.984107 + 0.177575i \(0.0568253\pi\)
\(500\) −0.959493 0.281733i −0.0429098 0.0125995i
\(501\) 4.40503 5.08368i 0.196802 0.227122i
\(502\) −15.5574 + 4.56807i −0.694361 + 0.203883i
\(503\) 6.52186 14.2809i 0.290795 0.636753i −0.706698 0.707516i \(-0.749816\pi\)
0.997493 + 0.0707623i \(0.0225432\pi\)
\(504\) 0.727875 + 5.06248i 0.0324221 + 0.225501i
\(505\) 4.40457 0.196001
\(506\) −10.8958 27.4913i −0.484376 1.22214i
\(507\) 9.79658 0.435082
\(508\) 0.161686 + 1.12455i 0.00717365 + 0.0498939i
\(509\) −16.5646 + 36.2714i −0.734213 + 1.60770i 0.0586336 + 0.998280i \(0.481326\pi\)
−0.792846 + 0.609422i \(0.791402\pi\)
\(510\) −1.59556 + 0.468498i −0.0706525 + 0.0207455i
\(511\) 12.4391 14.3555i 0.550274 0.635050i
\(512\) 0.959493 + 0.281733i 0.0424040 + 0.0124509i
\(513\) 5.57121 3.58040i 0.245975 0.158079i
\(514\) 2.03159 + 4.44856i 0.0896095 + 0.196217i
\(515\) 5.96866 + 6.88820i 0.263011 + 0.303530i
\(516\) 10.9343 + 7.02706i 0.481357 + 0.309349i
\(517\) 8.52202 59.2720i 0.374798 2.60678i
\(518\) −5.01478 + 34.8786i −0.220337 + 1.53248i
\(519\) −21.3022 13.6901i −0.935063 0.600928i
\(520\) −1.17208 1.35265i −0.0513989 0.0593175i
\(521\) −5.16504 11.3099i −0.226285 0.495494i 0.762102 0.647458i \(-0.224168\pi\)
−0.988386 + 0.151963i \(0.951440\pi\)
\(522\) −3.60204 + 2.31489i −0.157657 + 0.101320i
\(523\) −40.1995 11.8036i −1.75780 0.516137i −0.765880 0.642984i \(-0.777696\pi\)
−0.991922 + 0.126846i \(0.959514\pi\)
\(524\) 6.11044 7.05182i 0.266936 0.308060i
\(525\) 4.90736 1.44093i 0.214175 0.0628874i
\(526\) −8.31179 + 18.2003i −0.362411 + 0.793570i
\(527\) 0.383309 + 2.66597i 0.0166972 + 0.116131i
\(528\) 6.16614 0.268347
\(529\) −16.7552 + 15.7564i −0.728487 + 0.685059i
\(530\) −3.71723 −0.161466
\(531\) 0.921966 + 6.41242i 0.0400099 + 0.278275i
\(532\) −14.0706 + 30.8102i −0.610036 + 1.33579i
\(533\) 14.3455 4.21221i 0.621371 0.182451i
\(534\) −1.64592 + 1.89949i −0.0712259 + 0.0821991i
\(535\) −2.63398 0.773406i −0.113877 0.0334372i
\(536\) −0.983589 + 0.632114i −0.0424846 + 0.0273032i
\(537\) −5.83051 12.7670i −0.251605 0.550938i
\(538\) 12.1019 + 13.9664i 0.521750 + 0.602132i
\(539\) −99.3807 63.8681i −4.28063 2.75099i
\(540\) 0.142315 0.989821i 0.00612426 0.0425951i
\(541\) 4.69834 32.6777i 0.201997 1.40492i −0.596350 0.802725i \(-0.703383\pi\)
0.798347 0.602198i \(-0.205708\pi\)
\(542\) 13.4435 + 8.63961i 0.577448 + 0.371103i
\(543\) 8.29775 + 9.57611i 0.356090 + 0.410950i
\(544\) −0.690802 1.51264i −0.0296179 0.0648541i
\(545\) 5.70993 3.66955i 0.244587 0.157186i
\(546\) 8.78324 + 2.57899i 0.375888 + 0.110371i
\(547\) −25.4170 + 29.3328i −1.08675 + 1.25418i −0.121577 + 0.992582i \(0.538795\pi\)
−0.965177 + 0.261599i \(0.915750\pi\)
\(548\) −17.2669 + 5.07001i −0.737604 + 0.216580i
\(549\) 2.76439 6.05316i 0.117981 0.258343i
\(550\) −0.877534 6.10338i −0.0374182 0.260249i
\(551\) −28.3560 −1.20801
\(552\) −1.76703 4.45843i −0.0752098 0.189763i
\(553\) −28.7573 −1.22288
\(554\) −1.80529 12.5560i −0.0766992 0.533455i
\(555\) 2.86205 6.26702i 0.121487 0.266020i
\(556\) −20.8563 + 6.12396i −0.884504 + 0.259714i
\(557\) 20.1450 23.2486i 0.853571 0.985074i −0.146420 0.989222i \(-0.546775\pi\)
0.999991 + 0.00414893i \(0.00132065\pi\)
\(558\) −1.55406 0.456315i −0.0657888 0.0193173i
\(559\) 19.5703 12.5771i 0.827738 0.531955i
\(560\) 2.12466 + 4.65235i 0.0897831 + 0.196598i
\(561\) −6.71481 7.74930i −0.283500 0.327176i
\(562\) 14.5452 + 9.34762i 0.613551 + 0.394305i
\(563\) 1.81244 12.6058i 0.0763852 0.531271i −0.915319 0.402730i \(-0.868061\pi\)
0.991704 0.128541i \(-0.0410294\pi\)
\(564\) 1.38207 9.61248i 0.0581955 0.404759i
\(565\) 0.120890 + 0.0776913i 0.00508588 + 0.00326850i
\(566\) 5.98521 + 6.90731i 0.251577 + 0.290336i
\(567\) 2.12466 + 4.65235i 0.0892272 + 0.195380i
\(568\) 5.38088 3.45808i 0.225777 0.145098i
\(569\) 30.0584 + 8.82595i 1.26011 + 0.370003i 0.842537 0.538638i \(-0.181061\pi\)
0.417577 + 0.908641i \(0.362879\pi\)
\(570\) 4.33682 5.00496i 0.181650 0.209635i
\(571\) 6.01757 1.76692i 0.251827 0.0739432i −0.153382 0.988167i \(-0.549017\pi\)
0.405210 + 0.914224i \(0.367198\pi\)
\(572\) 4.58461 10.0389i 0.191692 0.419747i
\(573\) −0.0608330 0.423103i −0.00254134 0.0176754i
\(574\) −42.7241 −1.78327
\(575\) −4.16158 + 2.38355i −0.173550 + 0.0994007i
\(576\) 1.00000 0.0416667
\(577\) −3.04523 21.1800i −0.126774 0.881736i −0.949605 0.313449i \(-0.898516\pi\)
0.822831 0.568287i \(-0.192394\pi\)
\(578\) 5.91331 12.9483i 0.245961 0.538580i
\(579\) −11.7373 + 3.44638i −0.487786 + 0.143227i
\(580\) −2.80396 + 3.23594i −0.116428 + 0.134365i
\(581\) 31.6238 + 9.28558i 1.31198 + 0.385231i
\(582\) −4.39840 + 2.82668i −0.182319 + 0.117170i
\(583\) −9.52171 20.8496i −0.394349 0.863504i
\(584\) −2.43211 2.80680i −0.100641 0.116146i
\(585\) −1.50568 0.967644i −0.0622523 0.0400071i
\(586\) −1.23123 + 8.56339i −0.0508616 + 0.353750i
\(587\) −1.81659 + 12.6346i −0.0749785 + 0.521487i 0.917372 + 0.398032i \(0.130307\pi\)
−0.992350 + 0.123455i \(0.960602\pi\)
\(588\) −16.1172 10.3579i −0.664660 0.427151i
\(589\) −7.02424 8.10640i −0.289429 0.334018i
\(590\) 2.69121 + 5.89292i 0.110795 + 0.242608i
\(591\) −14.3933 + 9.25002i −0.592062 + 0.380495i
\(592\) 6.61055 + 1.94103i 0.271692 + 0.0797759i
\(593\) 2.90737 3.35529i 0.119392 0.137785i −0.692907 0.721027i \(-0.743670\pi\)
0.812299 + 0.583242i \(0.198216\pi\)
\(594\) 5.91637 1.73720i 0.242752 0.0712783i
\(595\) 3.53313 7.73648i 0.144844 0.317165i
\(596\) −2.72811 18.9744i −0.111748 0.777222i
\(597\) −15.8618 −0.649180
\(598\) −8.57244 0.438058i −0.350553 0.0179135i
\(599\) 8.39611 0.343056 0.171528 0.985179i \(-0.445130\pi\)
0.171528 + 0.985179i \(0.445130\pi\)
\(600\) −0.142315 0.989821i −0.00580998 0.0404093i
\(601\) −2.93777 + 6.43283i −0.119834 + 0.262401i −0.960038 0.279871i \(-0.909708\pi\)
0.840203 + 0.542272i \(0.182436\pi\)
\(602\) −63.7842 + 18.7287i −2.59965 + 0.763326i
\(603\) −0.765659 + 0.883618i −0.0311801 + 0.0359837i
\(604\) 2.59555 + 0.762121i 0.105611 + 0.0310103i
\(605\) 22.7318 14.6088i 0.924179 0.593934i
\(606\) 1.82973 + 4.00654i 0.0743275 + 0.162755i
\(607\) −3.63697 4.19728i −0.147620 0.170362i 0.677124 0.735869i \(-0.263226\pi\)
−0.824744 + 0.565507i \(0.808681\pi\)
\(608\) 5.57121 + 3.58040i 0.225943 + 0.145204i
\(609\) 3.11658 21.6763i 0.126290 0.878368i
\(610\) 0.947037 6.58678i 0.0383444 0.266691i
\(611\) −14.6222 9.39711i −0.591550 0.380166i
\(612\) −1.08898 1.25675i −0.0440194 0.0508011i
\(613\) −3.80448 8.33066i −0.153662 0.336472i 0.817108 0.576484i \(-0.195576\pi\)
−0.970770 + 0.240012i \(0.922849\pi\)
\(614\) −26.5853 + 17.0853i −1.07289 + 0.689507i
\(615\) 8.01509 + 2.35344i 0.323199 + 0.0948999i
\(616\) −20.6523 + 23.8341i −0.832106 + 0.960302i
\(617\) −27.0711 + 7.94881i −1.08984 + 0.320007i −0.776810 0.629735i \(-0.783163\pi\)
−0.313034 + 0.949742i \(0.601345\pi\)
\(618\) −3.78626 + 8.29075i −0.152306 + 0.333503i
\(619\) 3.52770 + 24.5357i 0.141790 + 0.986172i 0.929156 + 0.369687i \(0.120535\pi\)
−0.787366 + 0.616486i \(0.788556\pi\)
\(620\) −1.61967 −0.0650476
\(621\) −2.95154 3.78000i −0.118441 0.151686i
\(622\) 20.1112 0.806387
\(623\) −1.82943 12.7240i −0.0732947 0.509776i
\(624\) 0.743514 1.62807i 0.0297644 0.0651749i
\(625\) −0.959493 + 0.281733i −0.0383797 + 0.0112693i
\(626\) 4.56559 5.26897i 0.182478 0.210591i
\(627\) 39.1813 + 11.5047i 1.56475 + 0.459452i
\(628\) −8.15539 + 5.24115i −0.325435 + 0.209145i
\(629\) −4.75936 10.4216i −0.189768 0.415534i
\(630\) 3.34931 + 3.86531i 0.133440 + 0.153998i
\(631\) −6.43132 4.13316i −0.256027 0.164539i 0.406331 0.913726i \(-0.366808\pi\)
−0.662358 + 0.749187i \(0.730444\pi\)
\(632\) −0.800187 + 5.56543i −0.0318297 + 0.221381i
\(633\) 1.52604 10.6139i 0.0606548 0.421863i
\(634\) −14.7980 9.51012i −0.587705 0.377695i
\(635\) 0.743997 + 0.858618i 0.0295246 + 0.0340732i
\(636\) −1.54419 3.38131i −0.0612312 0.134078i
\(637\) −28.8466 + 18.5386i −1.14294 + 0.734526i
\(638\) −25.3325 7.43829i −1.00292 0.294485i
\(639\) 4.18866 4.83398i 0.165701 0.191229i
\(640\) 0.959493 0.281733i 0.0379273 0.0111365i
\(641\) 7.43603 16.2826i 0.293706 0.643126i −0.704045 0.710155i \(-0.748625\pi\)
0.997751 + 0.0670294i \(0.0213521\pi\)
\(642\) −0.390679 2.71723i −0.0154189 0.107241i
\(643\) −47.5033 −1.87335 −0.936673 0.350204i \(-0.886112\pi\)
−0.936673 + 0.350204i \(0.886112\pi\)
\(644\) 23.1515 + 8.10254i 0.912299 + 0.319285i
\(645\) 12.9977 0.511782
\(646\) −1.56727 10.9006i −0.0616635 0.428879i
\(647\) 4.22982 9.26202i 0.166291 0.364127i −0.808080 0.589073i \(-0.799493\pi\)
0.974371 + 0.224945i \(0.0722204\pi\)
\(648\) 0.959493 0.281733i 0.0376924 0.0110675i
\(649\) −26.1594 + 30.1895i −1.02685 + 1.18504i
\(650\) −1.71731 0.504247i −0.0673584 0.0197782i
\(651\) 6.96884 4.47860i 0.273130 0.175530i
\(652\) −2.60903 5.71297i −0.102177 0.223737i
\(653\) −15.6285 18.0363i −0.611591 0.705813i 0.362497 0.931985i \(-0.381924\pi\)
−0.974087 + 0.226172i \(0.927379\pi\)
\(654\) 5.70993 + 3.66955i 0.223276 + 0.143491i
\(655\) 1.32793 9.23592i 0.0518863 0.360877i
\(656\) −1.18882 + 8.26843i −0.0464157 + 0.322828i
\(657\) −3.12436 2.00790i −0.121893 0.0783358i
\(658\) 32.5263 + 37.5373i 1.26801 + 1.46336i
\(659\) 12.8619 + 28.1636i 0.501027 + 1.09710i 0.976134 + 0.217169i \(0.0696822\pi\)
−0.475107 + 0.879928i \(0.657591\pi\)
\(660\) 5.18729 3.33367i 0.201915 0.129763i
\(661\) −23.2981 6.84095i −0.906193 0.266082i −0.204755 0.978813i \(-0.565640\pi\)
−0.701438 + 0.712731i \(0.747458\pi\)
\(662\) −10.7668 + 12.4256i −0.418465 + 0.482935i
\(663\) −2.85575 + 0.838523i −0.110908 + 0.0325655i
\(664\) 2.67700 5.86181i 0.103888 0.227482i
\(665\) 4.82036 + 33.5263i 0.186926 + 1.30010i
\(666\) 6.88962 0.266968
\(667\) 1.88127 + 20.4482i 0.0728431 + 0.791759i
\(668\) 6.72667 0.260263
\(669\) −0.720002 5.00772i −0.0278369 0.193610i
\(670\) −0.485701 + 1.06354i −0.0187643 + 0.0410880i
\(671\) 39.3706 11.5603i 1.51989 0.446279i
\(672\) −3.34931 + 3.86531i −0.129202 + 0.149108i
\(673\) 1.88294 + 0.552880i 0.0725818 + 0.0213119i 0.317822 0.948150i \(-0.397049\pi\)
−0.245240 + 0.969462i \(0.578867\pi\)
\(674\) −27.4231 + 17.6238i −1.05630 + 0.678843i
\(675\) −0.415415 0.909632i −0.0159893 0.0350118i
\(676\) 6.41540 + 7.40376i 0.246746 + 0.284760i
\(677\) −20.9703 13.4768i −0.805954 0.517955i 0.0715999 0.997433i \(-0.477190\pi\)
−0.877554 + 0.479478i \(0.840826\pi\)
\(678\) −0.0204510 + 0.142240i −0.000785415 + 0.00546268i
\(679\) 3.80561 26.4686i 0.146046 1.01577i
\(680\) −1.39894 0.899042i −0.0536468 0.0344767i
\(681\) 14.7061 + 16.9718i 0.563539 + 0.650359i
\(682\) −4.14881 9.08462i −0.158866 0.347868i
\(683\) −4.41687 + 2.83855i −0.169007 + 0.108614i −0.622410 0.782692i \(-0.713846\pi\)
0.453403 + 0.891306i \(0.350210\pi\)
\(684\) 6.35426 + 1.86578i 0.242961 + 0.0713398i
\(685\) −11.7848 + 13.6003i −0.450272 + 0.519642i
\(686\) 59.6661 17.5196i 2.27806 0.668900i
\(687\) 10.2945 22.5418i 0.392759 0.860023i
\(688\) 1.84976 + 12.8654i 0.0705214 + 0.490487i
\(689\) −6.65312 −0.253464
\(690\) −3.89693 2.79534i −0.148354 0.106417i
\(691\) 41.3134 1.57163 0.785817 0.618459i \(-0.212243\pi\)
0.785817 + 0.618459i \(0.212243\pi\)
\(692\) −3.60369 25.0642i −0.136992 0.952799i
\(693\) −13.1009 + 28.6870i −0.497663 + 1.08973i
\(694\) −0.256534 + 0.0753252i −0.00973790 + 0.00285931i
\(695\) −14.2346 + 16.4276i −0.539948 + 0.623133i
\(696\) −4.10832 1.20631i −0.155725 0.0457251i
\(697\) 11.6860 7.51011i 0.442637 0.284466i
\(698\) −6.76976 14.8237i −0.256239 0.561086i
\(699\) 8.75819 + 10.1075i 0.331265 + 0.382301i
\(700\) 4.30262 + 2.76513i 0.162624 + 0.104512i
\(701\) 4.51308 31.3891i 0.170457 1.18555i −0.707465 0.706748i \(-0.750161\pi\)
0.877922 0.478804i \(-0.158929\pi\)
\(702\) 0.254716 1.77159i 0.00961365 0.0668644i
\(703\) 38.3836 + 24.6676i 1.44766 + 0.930357i
\(704\) 4.03797 + 4.66006i 0.152187 + 0.175633i
\(705\) −4.03423 8.83374i −0.151938 0.332698i
\(706\) −1.95743 + 1.25796i −0.0736687 + 0.0473440i
\(707\) −21.6148 6.34669i −0.812910 0.238692i
\(708\) −4.24242 + 4.89602i −0.159440 + 0.184004i
\(709\) −25.5591 + 7.50482i −0.959891 + 0.281849i −0.723899 0.689906i \(-0.757652\pi\)
−0.235991 + 0.971755i \(0.575834\pi\)
\(710\) 2.65711 5.81825i 0.0997194 0.218355i
\(711\) 0.800187 + 5.56543i 0.0300094 + 0.208720i
\(712\) −2.51339 −0.0941933
\(713\) −5.37971 + 5.60317i −0.201472 + 0.209840i
\(714\) 8.50506 0.318294
\(715\) −1.57062 10.9239i −0.0587378 0.408530i
\(716\) 5.83051 12.7670i 0.217896 0.477126i
\(717\) −0.302073 + 0.0886968i −0.0112811 + 0.00331244i
\(718\) 12.3529 14.2560i 0.461006 0.532029i
\(719\) −33.6534 9.88154i −1.25506 0.368519i −0.414407 0.910091i \(-0.636011\pi\)
−0.840654 + 0.541572i \(0.817829\pi\)
\(720\) 0.841254 0.540641i 0.0313517 0.0201485i
\(721\) −19.3650 42.4033i −0.721189 1.57918i
\(722\) 16.2783 + 18.7862i 0.605816 + 0.699149i
\(723\) −7.84813 5.04369i −0.291875 0.187577i
\(724\) −1.80327 + 12.5420i −0.0670181 + 0.466121i
\(725\) −0.609358 + 4.23818i −0.0226310 + 0.157402i
\(726\) 22.7318 + 14.6088i 0.843656 + 0.542185i
\(727\) −25.7037 29.6636i −0.953297 1.10016i −0.994884 0.101029i \(-0.967787\pi\)
0.0415864 0.999135i \(-0.486759\pi\)
\(728\) 3.80273 + 8.32681i 0.140938 + 0.308612i
\(729\) 0.841254 0.540641i 0.0311575 0.0200237i
\(730\) −3.56349 1.04634i −0.131891 0.0387266i
\(731\) 14.1542 16.3348i 0.523512 0.604165i
\(732\) 6.38496 1.87479i 0.235995 0.0692944i
\(733\) −1.94592 + 4.26098i −0.0718743 + 0.157383i −0.942159 0.335166i \(-0.891208\pi\)
0.870285 + 0.492549i \(0.163935\pi\)
\(734\) −1.28464 8.93490i −0.0474171 0.329793i
\(735\) −19.1585 −0.706672
\(736\) 2.21230 4.25508i 0.0815464 0.156844i
\(737\) −7.20942 −0.265562
\(738\) 1.18882 + 8.26843i 0.0437611 + 0.304365i
\(739\) −6.67984 + 14.6268i −0.245722 + 0.538056i −0.991800 0.127803i \(-0.959207\pi\)
0.746078 + 0.665859i \(0.231935\pi\)
\(740\) 6.61055 1.94103i 0.243008 0.0713537i
\(741\) 7.76209 8.95793i 0.285147 0.329078i
\(742\) 18.2418 + 5.35627i 0.669677 + 0.196635i
\(743\) −30.9872 + 19.9143i −1.13681 + 0.730583i −0.966971 0.254888i \(-0.917961\pi\)
−0.169840 + 0.985472i \(0.554325\pi\)
\(744\) −0.672836 1.47331i −0.0246674 0.0540140i
\(745\) −12.5534 14.4874i −0.459920 0.530776i
\(746\) −12.3870 7.96062i −0.453519 0.291459i
\(747\) 0.917099 6.37856i 0.0335549 0.233379i
\(748\) 1.45927 10.1494i 0.0533561 0.371100i
\(749\) 11.8115 + 7.59076i 0.431581 + 0.277360i
\(750\) −0.654861 0.755750i −0.0239121 0.0275961i
\(751\) 21.8918 + 47.9363i 0.798841 + 1.74922i 0.649398 + 0.760448i \(0.275021\pi\)
0.149443 + 0.988770i \(0.452252\pi\)
\(752\) 8.16969 5.25034i 0.297918 0.191460i
\(753\) −15.5574 4.56807i −0.566944 0.166470i
\(754\) −5.01854 + 5.79171i −0.182765 + 0.210922i
\(755\) 2.59555 0.762121i 0.0944616 0.0277364i
\(756\) −2.12466 + 4.65235i −0.0772730 + 0.169204i
\(757\) −0.390678 2.71723i −0.0141994 0.0987593i 0.981489 0.191517i \(-0.0613408\pi\)
−0.995689 + 0.0927580i \(0.970432\pi\)
\(758\) −11.2664 −0.409216
\(759\) 5.69683 29.0179i 0.206782 1.05328i
\(760\) 6.62251 0.240224
\(761\) −2.00413 13.9390i −0.0726496 0.505289i −0.993360 0.115044i \(-0.963299\pi\)
0.920711 0.390246i \(-0.127610\pi\)
\(762\) −0.471959 + 1.03345i −0.0170973 + 0.0374378i
\(763\) −33.3083 + 9.78020i −1.20584 + 0.354067i
\(764\) 0.279923 0.323048i 0.0101272 0.0116875i
\(765\) −1.59556 0.468498i −0.0576876 0.0169386i
\(766\) −6.15073 + 3.95284i −0.222235 + 0.142822i
\(767\) 4.81675 + 10.5472i 0.173923 + 0.380837i
\(768\) 0.654861 + 0.755750i 0.0236303 + 0.0272708i
\(769\) 12.4613 + 8.00839i 0.449366 + 0.288790i 0.745685 0.666299i \(-0.232123\pi\)
−0.296318 + 0.955089i \(0.595759\pi\)
\(770\) −4.48818 + 31.2160i −0.161743 + 1.12495i
\(771\) −0.695991 + 4.84072i −0.0250655 + 0.174334i
\(772\) −10.2909 6.61356i −0.370378 0.238027i
\(773\) 6.55636 + 7.56644i 0.235816 + 0.272146i 0.861307 0.508086i \(-0.169647\pi\)
−0.625491 + 0.780232i \(0.715101\pi\)
\(774\) 5.39942 + 11.8231i 0.194078 + 0.424972i
\(775\) −1.36256 + 0.875661i −0.0489444 + 0.0314547i
\(776\) −5.01660 1.47301i −0.180085 0.0528779i
\(777\) −23.0755 + 26.6305i −0.827828 + 0.955365i
\(778\) 1.95740 0.574743i 0.0701760 0.0206055i
\(779\) −22.9811 + 50.3217i −0.823384 + 1.80296i
\(780\) −0.254716 1.77159i −0.00912031 0.0634331i
\(781\) 39.4403 1.41129
\(782\) −7.75673 + 1.85340i −0.277380 + 0.0662773i
\(783\) −4.28176 −0.153018
\(784\) −2.72654 18.9635i −0.0973764 0.677267i
\(785\) −4.02717 + 8.81827i −0.143736 + 0.314738i
\(786\) 8.95293 2.62882i 0.319340 0.0937668i
\(787\) 7.02889 8.11177i 0.250553 0.289153i −0.616515 0.787343i \(-0.711456\pi\)
0.867068 + 0.498190i \(0.166002\pi\)
\(788\) −16.4163 4.82026i −0.584807 0.171715i
\(789\) −16.8321 + 10.8174i −0.599240 + 0.385108i
\(790\) 2.33574 + 5.11455i 0.0831018 + 0.181967i
\(791\) −0.481303 0.555454i −0.0171132 0.0197497i
\(792\) 5.18729 + 3.33367i 0.184322 + 0.118457i
\(793\) 1.69501 11.7891i 0.0601917 0.418643i
\(794\) 0.0131528 0.0914799i 0.000466776 0.00324650i
\(795\) −3.12713 2.00968i −0.110908 0.0712762i
\(796\) −10.3873 11.9875i −0.368167 0.424887i
\(797\) −16.5757 36.2958i −0.587143 1.28566i −0.937153 0.348918i \(-0.886549\pi\)
0.350010 0.936746i \(-0.386178\pi\)
\(798\) −28.4942 + 18.3121i −1.00868 + 0.648241i
\(799\) −15.4950 4.54974i −0.548174 0.160958i
\(800\) 0.654861 0.755750i 0.0231528 0.0267198i
\(801\) −2.41158 + 0.708104i −0.0852090 + 0.0250196i
\(802\) 7.93543 17.3762i 0.280210 0.613574i
\(803\) −3.25910 22.6676i −0.115011 0.799921i
\(804\) −1.16919 −0.0412343
\(805\) 23.8569 5.70038i 0.840845 0.200912i
\(806\) −2.89890 −0.102110
\(807\) 2.63000 + 18.2920i 0.0925803 + 0.643910i
\(808\) −1.82973 + 4.00654i −0.0643695 + 0.140950i
\(809\) 24.3123 7.13875i 0.854776 0.250985i 0.175148 0.984542i \(-0.443959\pi\)
0.679628 + 0.733557i \(0.262141\pi\)
\(810\) 0.654861 0.755750i 0.0230095 0.0265543i
\(811\) 37.9822 + 11.1526i 1.33374 + 0.391620i 0.869431 0.494055i \(-0.164486\pi\)
0.464306 + 0.885675i \(0.346304\pi\)
\(812\) 18.4228 11.8396i 0.646513 0.415489i
\(813\) 6.63846 + 14.5362i 0.232821 + 0.509807i
\(814\) 27.8201 + 32.1061i 0.975093 + 1.12532i
\(815\) −5.28352 3.39551i −0.185074 0.118940i
\(816\) 0.236658 1.64599i 0.00828469 0.0576213i
\(817\) −12.2501 + 85.2010i −0.428575 + 2.98081i
\(818\) −16.5033 10.6060i −0.577024 0.370831i
\(819\) 5.99462 + 6.91817i 0.209469 + 0.241740i
\(820\) 3.47015 + 7.59857i 0.121183 + 0.265354i
\(821\) 1.26608 0.813661i 0.0441865 0.0283970i −0.518361 0.855162i \(-0.673458\pi\)
0.562548 + 0.826765i \(0.309821\pi\)
\(822\) −17.2669 5.07001i −0.602251 0.176837i
\(823\) 31.9657 36.8904i 1.11425 1.28592i 0.159935 0.987128i \(-0.448872\pi\)
0.954319 0.298790i \(-0.0965829\pi\)
\(824\) −8.74520 + 2.56782i −0.304654 + 0.0894543i
\(825\) 2.56151 5.60892i 0.0891803 0.195278i
\(826\) −4.71543 32.7965i −0.164071 1.14114i
\(827\) 27.4912 0.955961 0.477981 0.878370i \(-0.341369\pi\)
0.477981 + 0.878370i \(0.341369\pi\)
\(828\) 0.923889 4.70600i 0.0321074 0.163545i
\(829\) 7.58981 0.263605 0.131803 0.991276i \(-0.457924\pi\)
0.131803 + 0.991276i \(0.457924\pi\)
\(830\) −0.917099 6.37856i −0.0318330 0.221403i
\(831\) 5.26960 11.5388i 0.182800 0.400277i
\(832\) 1.71731 0.504247i 0.0595370 0.0174816i
\(833\) −20.8632 + 24.0774i −0.722868 + 0.834234i
\(834\) −20.8563 6.12396i −0.722195 0.212055i
\(835\) 5.65884 3.63671i 0.195832 0.125854i
\(836\) 16.9636 + 37.1452i 0.586699 + 1.28469i
\(837\) −1.06066 1.22407i −0.0366618 0.0423099i
\(838\) 11.9442 + 7.67604i 0.412604 + 0.265165i
\(839\) −3.79933 + 26.4249i −0.131167 + 0.912289i 0.812869 + 0.582447i \(0.197905\pi\)
−0.944036 + 0.329842i \(0.893005\pi\)
\(840\) −0.727875 + 5.06248i −0.0251141 + 0.174672i
\(841\) −8.97327 5.76677i −0.309423 0.198854i
\(842\) 4.72377 + 5.45152i 0.162792 + 0.187872i
\(843\) 7.18248 + 15.7274i 0.247378 + 0.541682i
\(844\) 9.02077 5.79730i 0.310508 0.199551i
\(845\) 9.39975 + 2.76002i 0.323361 + 0.0949475i
\(846\) 6.35957 7.33933i 0.218647 0.252332i
\(847\) −132.604 + 38.9359i −4.55631 + 1.33785i
\(848\) 1.54419 3.38131i 0.0530278 0.116115i
\(849\) 1.30071 + 9.04665i 0.0446403 + 0.310480i
\(850\) −1.66292 −0.0570377
\(851\) 15.2419 29.3159i 0.522486 1.00494i
\(852\) 6.39627 0.219132
\(853\) −1.71043 11.8963i −0.0585639 0.407321i −0.997925 0.0643906i \(-0.979490\pi\)
0.939361 0.342930i \(-0.111419\pi\)
\(854\) −14.1386 + 30.9591i −0.483812 + 1.05940i
\(855\) 6.35426 1.86578i 0.217311 0.0638083i
\(856\) 1.79771 2.07467i 0.0614444 0.0709106i
\(857\) 45.9527 + 13.4929i 1.56971 + 0.460909i 0.946918 0.321475i \(-0.104179\pi\)
0.622795 + 0.782385i \(0.285997\pi\)
\(858\) 9.28426 5.96663i 0.316959 0.203697i
\(859\) −19.6794 43.0918i −0.671451 1.47027i −0.871454 0.490478i \(-0.836822\pi\)
0.200002 0.979795i \(-0.435905\pi\)
\(860\) 8.51165 + 9.82297i 0.290245 + 0.334961i
\(861\) −35.9418 23.0984i −1.22489 0.787191i
\(862\) 3.73381 25.9692i 0.127174 0.884514i
\(863\) −4.41057 + 30.6762i −0.150137 + 1.04423i 0.765849 + 0.643020i \(0.222319\pi\)
−0.915987 + 0.401208i \(0.868590\pi\)
\(864\) 0.841254 + 0.540641i 0.0286200 + 0.0183930i
\(865\) −16.5824 19.1371i −0.563817 0.650680i
\(866\) −2.51164 5.49973i −0.0853490 0.186888i
\(867\) 11.9750 7.69586i 0.406692 0.261365i
\(868\) 7.94832 + 2.33384i 0.269784 + 0.0792156i
\(869\) −22.7041 + 26.2019i −0.770184 + 0.888839i
\(870\) −4.10832 + 1.20631i −0.139285 + 0.0408978i
\(871\) −0.869312 + 1.90353i −0.0294555 + 0.0644986i
\(872\) 0.965949 + 6.71832i 0.0327112 + 0.227511i
\(873\) −5.22839 −0.176954
\(874\) 21.9965 22.9102i 0.744044 0.774950i
\(875\) 5.11454 0.172903
\(876\) −0.528548 3.67613i −0.0178580 0.124205i
\(877\) 19.1370 41.9043i 0.646212 1.41501i −0.248619 0.968601i \(-0.579977\pi\)
0.894831 0.446406i \(-0.147296\pi\)
\(878\) 20.4115 5.99335i 0.688854 0.202266i
\(879\) −5.66550 + 6.53833i −0.191092 + 0.220532i
\(880\) 5.91637 + 1.73720i 0.199441 + 0.0585611i
\(881\) 14.6714 9.42875i 0.494293 0.317663i −0.269637 0.962962i \(-0.586904\pi\)
0.763930 + 0.645299i \(0.223267\pi\)
\(882\) −7.95873 17.4272i −0.267984 0.586804i
\(883\) 36.5044 + 42.1283i 1.22847 + 1.41773i 0.876280 + 0.481801i \(0.160017\pi\)
0.352190 + 0.935929i \(0.385437\pi\)
\(884\) −2.50383 1.60911i −0.0842129 0.0541203i
\(885\) −0.921966 + 6.41242i −0.0309916 + 0.215551i
\(886\) −0.996047 + 6.92766i −0.0334629 + 0.232739i
\(887\) 23.1789 + 14.8962i 0.778271 + 0.500165i 0.868460 0.495760i \(-0.165110\pi\)
−0.0901881 + 0.995925i \(0.528747\pi\)
\(888\) 4.51174 + 5.20683i 0.151404 + 0.174730i
\(889\) −2.41385 5.28560i −0.0809580 0.177273i
\(890\) −2.11440 + 1.35884i −0.0708748 + 0.0455485i
\(891\) 5.91637 + 1.73720i 0.198206 + 0.0581985i
\(892\) 3.31308 3.82350i 0.110930 0.128020i
\(893\) 61.7083 18.1192i 2.06499 0.606335i
\(894\) 7.96331 17.4372i 0.266333 0.583188i
\(895\) −1.99744 13.8925i −0.0667671 0.464376i
\(896\) −5.11454 −0.170865
\(897\) −6.97476 5.00313i −0.232880 0.167050i
\(898\) −25.5633 −0.853059
\(899\) 0.986960 + 6.86446i 0.0329170 + 0.228942i
\(900\) 0.415415 0.909632i 0.0138472 0.0303211i
\(901\) −5.93105 + 1.74151i −0.197592 + 0.0580183i
\(902\) −33.7310 + 38.9276i −1.12312 + 1.29615i
\(903\) −63.7842 18.7287i −2.12261 0.623253i
\(904\) −0.120890 + 0.0776913i −0.00402074 + 0.00258397i
\(905\) 5.26373 + 11.5260i 0.174972 + 0.383136i
\(906\) 1.77148 + 2.04439i 0.0588534 + 0.0679205i
\(907\) 17.3024 + 11.1196i 0.574518 + 0.369220i 0.795404 0.606079i \(-0.207259\pi\)
−0.220886 + 0.975300i \(0.570895\pi\)
\(908\) −3.19594 + 22.2283i −0.106061 + 0.737671i
\(909\) −0.626836 + 4.35974i −0.0207908 + 0.144603i
\(910\) 7.70087 + 4.94905i 0.255281 + 0.164059i
\(911\) −21.2963 24.5773i −0.705580 0.814282i 0.283915 0.958849i \(-0.408366\pi\)
−0.989495 + 0.144567i \(0.953821\pi\)
\(912\) 2.75109 + 6.02405i 0.0910977 + 0.199476i
\(913\) 33.4277 21.4827i 1.10630 0.710973i
\(914\) −12.3987 3.64058i −0.410112 0.120420i
\(915\) 4.35778 5.02915i 0.144064 0.166259i
\(916\) 23.7774 6.98168i 0.785628 0.230681i
\(917\) −19.8249 + 43.4106i −0.654677 + 1.43354i
\(918\) −0.236658 1.64599i −0.00781088 0.0543259i
\(919\) −37.3525 −1.23214 −0.616072 0.787690i \(-0.711277\pi\)
−0.616072 + 0.787690i \(0.711277\pi\)
\(920\) −0.439369 4.77566i −0.0144856 0.157449i
\(921\) −31.6020 −1.04132
\(922\) −1.18217 8.22217i −0.0389327 0.270783i
\(923\) 4.75571 10.4136i 0.156536 0.342766i
\(924\) −30.2595 + 8.88499i −0.995465 + 0.292295i
\(925\) 4.51174 5.20683i 0.148345 0.171200i
\(926\) −30.7716 9.03536i −1.01122 0.296920i
\(927\) −7.66752 + 4.92762i −0.251834 + 0.161844i
\(928\) −1.77871 3.89482i −0.0583889 0.127854i
\(929\) 3.26519 + 3.76823i 0.107127 + 0.123632i 0.806781 0.590851i \(-0.201208\pi\)
−0.699654 + 0.714482i \(0.746662\pi\)
\(930\) −1.36256 0.875661i −0.0446799 0.0287141i
\(931\) 18.0565 125.586i 0.591779 4.11591i
\(932\) −1.90334 + 13.2380i −0.0623459 + 0.433625i
\(933\) 16.9186 + 10.8730i 0.553892 + 0.355965i
\(934\) −12.0758 13.9362i −0.395132 0.456006i
\(935\) −4.25958 9.32718i −0.139303 0.305032i
\(936\) 1.50568 0.967644i 0.0492148 0.0316284i
\(937\) 40.3571 + 11.8499i 1.31841 + 0.387120i 0.863918 0.503632i \(-0.168003\pi\)
0.454491 + 0.890752i \(0.349821\pi\)
\(938\) 3.91599 4.51930i 0.127862 0.147560i
\(939\) 6.68944 1.96420i 0.218302 0.0640992i
\(940\) 4.03423 8.83374i 0.131582 0.288125i
\(941\) 5.13220 + 35.6952i 0.167305 + 1.16363i 0.884425 + 0.466681i \(0.154551\pi\)
−0.717121 + 0.696949i \(0.754540\pi\)
\(942\) −9.69433 −0.315858
\(943\) 37.8129 + 13.2337i 1.23136 + 0.430949i
\(944\) −6.47836 −0.210853
\(945\) 0.727875 + 5.06248i 0.0236778 + 0.164682i
\(946\) −33.2936 + 72.9028i −1.08247 + 2.37028i
\(947\) −27.3449 + 8.02918i −0.888589 + 0.260913i −0.694003 0.719972i \(-0.744155\pi\)
−0.194586 + 0.980885i \(0.562336\pi\)
\(948\) −3.68206 + 4.24932i −0.119588 + 0.138012i
\(949\) −6.37797 1.87274i −0.207038 0.0607918i
\(950\) 5.57121 3.58040i 0.180754 0.116164i
\(951\) −7.30734 16.0008i −0.236957 0.518863i
\(952\) 5.56963 + 6.42770i 0.180513 + 0.208323i
\(953\) 42.7687 + 27.4858i 1.38541 + 0.890351i 0.999482 0.0321763i \(-0.0102438\pi\)
0.385931 + 0.922528i \(0.373880\pi\)
\(954\) 0.529016 3.67939i 0.0171275 0.119125i
\(955\) 0.0608330 0.423103i 0.00196851 0.0136913i
\(956\) −0.264849 0.170208i −0.00856582 0.00550492i
\(957\) −17.2896 19.9533i −0.558893 0.644997i
\(958\) 7.37021 + 16.1385i 0.238121 + 0.521411i
\(959\) 77.4292 49.7607i 2.50032 1.60686i
\(960\) 0.959493 + 0.281733i 0.0309675 + 0.00909288i
\(961\) 18.5828 21.4456i 0.599444 0.691795i
\(962\) 11.8316 3.47408i 0.381467 0.112009i
\(963\) 1.14039 2.49710i 0.0367485 0.0804679i
\(964\) −1.32767 9.23413i −0.0427613 0.297411i
\(965\) −12.2328 −0.393788
\(966\) 15.0958 + 19.3330i 0.485698 + 0.622028i
\(967\) 24.7582 0.796172 0.398086 0.917348i \(-0.369675\pi\)
0.398086 + 0.917348i \(0.369675\pi\)
\(968\) 3.84554 + 26.7463i 0.123600 + 0.859659i
\(969\) 4.57484 10.0175i 0.146965 0.321809i
\(970\) −5.01660 + 1.47301i −0.161073 + 0.0472954i
\(971\) 15.4558 17.8369i 0.495999 0.572414i −0.451459 0.892292i \(-0.649096\pi\)
0.947459 + 0.319878i \(0.103642\pi\)
\(972\) 0.959493 + 0.281733i 0.0307758 + 0.00903658i
\(973\) 93.5252 60.1050i 2.99828 1.92688i
\(974\) −0.673896 1.47563i −0.0215930 0.0472821i
\(975\) −1.17208 1.35265i −0.0375365 0.0433194i
\(976\) 5.59814 + 3.59770i 0.179192 + 0.115160i
\(977\) 0.123395 0.858229i 0.00394775 0.0274572i −0.987752 0.156030i \(-0.950130\pi\)
0.991700 + 0.128573i \(0.0410395\pi\)
\(978\) 0.893813 6.21661i 0.0285810 0.198785i
\(979\) −13.0377 8.37881i −0.416686 0.267788i
\(980\) −12.5461 14.4790i −0.400772 0.462515i
\(981\) 2.81959 + 6.17405i 0.0900227 + 0.197122i
\(982\) −6.69512 + 4.30269i −0.213650 + 0.137305i
\(983\) −38.2878 11.2423i −1.22119 0.358574i −0.393272 0.919422i \(-0.628657\pi\)
−0.827919 + 0.560848i \(0.810475\pi\)
\(984\) −5.47035 + 6.31312i −0.174388 + 0.201255i
\(985\) −16.4163 + 4.82026i −0.523067 + 0.153586i
\(986\) −2.95784 + 6.47678i −0.0941970 + 0.206263i
\(987\) 7.06863 + 49.1634i 0.224997 + 1.56489i
\(988\) 11.8530 0.377095
\(989\) 62.2533 + 3.18119i 1.97954 + 0.101156i
\(990\) 6.16614 0.195973
\(991\) −0.277943 1.93314i −0.00882916 0.0614081i 0.984931 0.172950i \(-0.0553300\pi\)
−0.993760 + 0.111542i \(0.964421\pi\)
\(992\) 0.672836 1.47331i 0.0213626 0.0467775i
\(993\) −15.7754 + 4.63209i −0.500618 + 0.146995i
\(994\) −21.4231 + 24.7236i −0.679499 + 0.784183i
\(995\) −15.2193 4.46878i −0.482484 0.141670i
\(996\) 5.42117 3.48397i 0.171776 0.110394i
\(997\) −1.32756 2.90695i −0.0420443 0.0920641i 0.887444 0.460915i \(-0.152479\pi\)
−0.929489 + 0.368851i \(0.879751\pi\)
\(998\) 21.4126 + 24.7114i 0.677803 + 0.782226i
\(999\) 5.79592 + 3.72481i 0.183375 + 0.117848i
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 690.2.m.e.601.2 yes 20
23.8 even 11 inner 690.2.m.e.31.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.m.e.31.2 20 23.8 even 11 inner
690.2.m.e.601.2 yes 20 1.1 even 1 trivial