Properties

Label 630.2.cd.a.23.5
Level $630$
Weight $2$
Character 630.23
Analytic conductor $5.031$
Analytic rank $0$
Dimension $192$
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] = [630,2,Mod(23,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.cd (of order \(12\), degree \(4\), 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: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(48\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 23.5
Character \(\chi\) \(=\) 630.23
Dual form 630.2.cd.a.137.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.48287 - 0.895033i) q^{3} +1.00000i q^{4} +(1.60407 - 1.55787i) q^{5} +(0.415666 + 1.68143i) q^{6} +(-0.441381 + 2.60867i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.39783 + 2.65444i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-1.48287 - 0.895033i) q^{3} +1.00000i q^{4} +(1.60407 - 1.55787i) q^{5} +(0.415666 + 1.68143i) q^{6} +(-0.441381 + 2.60867i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.39783 + 2.65444i) q^{9} +(-2.23583 - 0.0326704i) q^{10} +(-5.45229 - 3.14788i) q^{11} +(0.895033 - 1.48287i) q^{12} +(5.72800 - 1.53481i) q^{13} +(2.15671 - 1.53251i) q^{14} +(-3.77298 + 0.874425i) q^{15} -1.00000 q^{16} +(1.12337 - 4.19247i) q^{17} +(0.888559 - 2.86539i) q^{18} +(-1.36418 - 0.787607i) q^{19} +(1.55787 + 1.60407i) q^{20} +(2.98936 - 3.47329i) q^{21} +(1.62946 + 6.08124i) q^{22} +(1.13445 + 0.303976i) q^{23} +(-1.68143 + 0.415666i) q^{24} +(0.146091 - 4.99787i) q^{25} +(-5.13559 - 2.96503i) q^{26} +(0.303009 - 5.18731i) q^{27} +(-2.60867 - 0.441381i) q^{28} +(-0.461965 - 0.800147i) q^{29} +(3.28621 + 2.04959i) q^{30} -3.20319 q^{31} +(0.707107 + 0.707107i) q^{32} +(5.26760 + 9.54789i) q^{33} +(-3.75886 + 2.17018i) q^{34} +(3.35597 + 4.87211i) q^{35} +(-2.65444 + 1.39783i) q^{36} +(-0.625472 - 2.33429i) q^{37} +(0.407696 + 1.52154i) q^{38} +(-9.86762 - 2.85082i) q^{39} +(0.0326704 - 2.23583i) q^{40} +(-5.94493 - 3.43231i) q^{41} +(-4.56978 + 0.342185i) q^{42} +(-0.485278 + 1.81108i) q^{43} +(3.14788 - 5.45229i) q^{44} +(6.37749 + 2.08028i) q^{45} +(-0.587236 - 1.01712i) q^{46} +(-4.13599 - 4.13599i) q^{47} +(1.48287 + 0.895033i) q^{48} +(-6.61037 - 2.30284i) q^{49} +(-3.63733 + 3.43072i) q^{50} +(-5.41821 + 5.21145i) q^{51} +(1.53481 + 5.72800i) q^{52} +(-5.91945 - 1.58611i) q^{53} +(-3.88224 + 3.45372i) q^{54} +(-13.6499 + 3.44453i) q^{55} +(1.53251 + 2.15671i) q^{56} +(1.31797 + 2.38891i) q^{57} +(-0.239131 + 0.892448i) q^{58} +8.32434 q^{59} +(-0.874425 - 3.77298i) q^{60} -12.3608 q^{61} +(2.26500 + 2.26500i) q^{62} +(-7.54155 + 2.47487i) q^{63} -1.00000i q^{64} +(6.79709 - 11.3854i) q^{65} +(3.02662 - 10.4761i) q^{66} +(4.51921 - 4.51921i) q^{67} +(4.19247 + 1.12337i) q^{68} +(-1.41018 - 1.46613i) q^{69} +(1.07208 - 5.81813i) q^{70} -9.47913i q^{71} +(2.86539 + 0.888559i) q^{72} +(-1.54938 + 5.78236i) q^{73} +(-1.20832 + 2.09287i) q^{74} +(-4.68989 + 7.28045i) q^{75} +(0.787607 - 1.36418i) q^{76} +(10.6183 - 12.8338i) q^{77} +(4.96163 + 8.99329i) q^{78} -13.3166i q^{79} +(-1.60407 + 1.55787i) q^{80} +(-5.09214 + 7.42092i) q^{81} +(1.77669 + 6.63071i) q^{82} +(17.4269 + 4.66953i) q^{83} +(3.47329 + 2.98936i) q^{84} +(-4.72935 - 8.47507i) q^{85} +(1.62377 - 0.937485i) q^{86} +(-0.0311222 + 1.59999i) q^{87} +(-6.08124 + 1.62946i) q^{88} +(-6.67816 + 11.5669i) q^{89} +(-3.03859 - 5.98055i) q^{90} +(1.47560 + 15.6199i) q^{91} +(-0.303976 + 1.13445i) q^{92} +(4.74993 + 2.86697i) q^{93} +5.84918i q^{94} +(-3.41522 + 0.861828i) q^{95} +(-0.415666 - 1.68143i) q^{96} +(-0.0834947 - 0.0223723i) q^{97} +(3.04588 + 6.30259i) q^{98} +(0.734495 - 18.8730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) −1.48287 0.895033i −0.856138 0.516748i
\(4\) 1.00000i 0.500000i
\(5\) 1.60407 1.55787i 0.717363 0.696700i
\(6\) 0.415666 + 1.68143i 0.169695 + 0.686443i
\(7\) −0.441381 + 2.60867i −0.166826 + 0.985986i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 1.39783 + 2.65444i 0.465944 + 0.884814i
\(10\) −2.23583 0.0326704i −0.707031 0.0103313i
\(11\) −5.45229 3.14788i −1.64393 0.949122i −0.979418 0.201842i \(-0.935307\pi\)
−0.664510 0.747280i \(-0.731360\pi\)
\(12\) 0.895033 1.48287i 0.258374 0.428069i
\(13\) 5.72800 1.53481i 1.58866 0.425681i 0.647069 0.762432i \(-0.275995\pi\)
0.941594 + 0.336751i \(0.109328\pi\)
\(14\) 2.15671 1.53251i 0.576406 0.409580i
\(15\) −3.77298 + 0.874425i −0.974179 + 0.225776i
\(16\) −1.00000 −0.250000
\(17\) 1.12337 4.19247i 0.272457 1.01682i −0.685070 0.728477i \(-0.740228\pi\)
0.957527 0.288345i \(-0.0931050\pi\)
\(18\) 0.888559 2.86539i 0.209435 0.675379i
\(19\) −1.36418 0.787607i −0.312963 0.180690i 0.335288 0.942116i \(-0.391166\pi\)
−0.648252 + 0.761426i \(0.724500\pi\)
\(20\) 1.55787 + 1.60407i 0.348350 + 0.358681i
\(21\) 2.98936 3.47329i 0.652332 0.757933i
\(22\) 1.62946 + 6.08124i 0.347403 + 1.29652i
\(23\) 1.13445 + 0.303976i 0.236550 + 0.0633833i 0.375146 0.926966i \(-0.377592\pi\)
−0.138597 + 0.990349i \(0.544259\pi\)
\(24\) −1.68143 + 0.415666i −0.343221 + 0.0848475i
\(25\) 0.146091 4.99787i 0.0292182 0.999573i
\(26\) −5.13559 2.96503i −1.00717 0.581491i
\(27\) 0.303009 5.18731i 0.0583141 0.998298i
\(28\) −2.60867 0.441381i −0.492993 0.0834131i
\(29\) −0.461965 0.800147i −0.0857848 0.148584i 0.819941 0.572449i \(-0.194006\pi\)
−0.905725 + 0.423865i \(0.860673\pi\)
\(30\) 3.28621 + 2.04959i 0.599977 + 0.374202i
\(31\) −3.20319 −0.575311 −0.287655 0.957734i \(-0.592876\pi\)
−0.287655 + 0.957734i \(0.592876\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 5.26760 + 9.54789i 0.916972 + 1.66208i
\(34\) −3.75886 + 2.17018i −0.644639 + 0.372183i
\(35\) 3.35597 + 4.87211i 0.567262 + 0.823537i
\(36\) −2.65444 + 1.39783i −0.442407 + 0.232972i
\(37\) −0.625472 2.33429i −0.102827 0.383755i 0.895263 0.445539i \(-0.146988\pi\)
−0.998090 + 0.0617835i \(0.980321\pi\)
\(38\) 0.407696 + 1.52154i 0.0661370 + 0.246826i
\(39\) −9.86762 2.85082i −1.58008 0.456496i
\(40\) 0.0326704 2.23583i 0.00516564 0.353516i
\(41\) −5.94493 3.43231i −0.928443 0.536037i −0.0421240 0.999112i \(-0.513412\pi\)
−0.886319 + 0.463076i \(0.846746\pi\)
\(42\) −4.56978 + 0.342185i −0.705133 + 0.0528003i
\(43\) −0.485278 + 1.81108i −0.0740042 + 0.276187i −0.993006 0.118067i \(-0.962330\pi\)
0.919001 + 0.394254i \(0.128997\pi\)
\(44\) 3.14788 5.45229i 0.474561 0.821964i
\(45\) 6.37749 + 2.08028i 0.950701 + 0.310110i
\(46\) −0.587236 1.01712i −0.0865832 0.149966i
\(47\) −4.13599 4.13599i −0.603296 0.603296i 0.337889 0.941186i \(-0.390287\pi\)
−0.941186 + 0.337889i \(0.890287\pi\)
\(48\) 1.48287 + 0.895033i 0.214034 + 0.129187i
\(49\) −6.61037 2.30284i −0.944338 0.328977i
\(50\) −3.63733 + 3.43072i −0.514396 + 0.485177i
\(51\) −5.41821 + 5.21145i −0.758701 + 0.729748i
\(52\) 1.53481 + 5.72800i 0.212840 + 0.794331i
\(53\) −5.91945 1.58611i −0.813099 0.217869i −0.171772 0.985137i \(-0.554949\pi\)
−0.641327 + 0.767267i \(0.721616\pi\)
\(54\) −3.88224 + 3.45372i −0.528306 + 0.469992i
\(55\) −13.6499 + 3.44453i −1.84055 + 0.464460i
\(56\) 1.53251 + 2.15671i 0.204790 + 0.288203i
\(57\) 1.31797 + 2.38891i 0.174569 + 0.316418i
\(58\) −0.239131 + 0.892448i −0.0313994 + 0.117184i
\(59\) 8.32434 1.08374 0.541868 0.840463i \(-0.317717\pi\)
0.541868 + 0.840463i \(0.317717\pi\)
\(60\) −0.874425 3.77298i −0.112888 0.487090i
\(61\) −12.3608 −1.58264 −0.791322 0.611400i \(-0.790607\pi\)
−0.791322 + 0.611400i \(0.790607\pi\)
\(62\) 2.26500 + 2.26500i 0.287655 + 0.287655i
\(63\) −7.54155 + 2.47487i −0.950147 + 0.311804i
\(64\) 1.00000i 0.125000i
\(65\) 6.79709 11.3854i 0.843075 1.41219i
\(66\) 3.02662 10.4761i 0.372552 1.28952i
\(67\) 4.51921 4.51921i 0.552109 0.552109i −0.374940 0.927049i \(-0.622337\pi\)
0.927049 + 0.374940i \(0.122337\pi\)
\(68\) 4.19247 + 1.12337i 0.508411 + 0.136228i
\(69\) −1.41018 1.46613i −0.169766 0.176501i
\(70\) 1.07208 5.81813i 0.128138 0.695400i
\(71\) 9.47913i 1.12497i −0.826809 0.562483i \(-0.809846\pi\)
0.826809 0.562483i \(-0.190154\pi\)
\(72\) 2.86539 + 0.888559i 0.337689 + 0.104718i
\(73\) −1.54938 + 5.78236i −0.181341 + 0.676774i 0.814043 + 0.580804i \(0.197262\pi\)
−0.995384 + 0.0959699i \(0.969405\pi\)
\(74\) −1.20832 + 2.09287i −0.140464 + 0.243291i
\(75\) −4.68989 + 7.28045i −0.541542 + 0.840674i
\(76\) 0.787607 1.36418i 0.0903448 0.156482i
\(77\) 10.6183 12.8338i 1.21007 1.46255i
\(78\) 4.96163 + 8.99329i 0.561794 + 1.01829i
\(79\) 13.3166i 1.49823i −0.662440 0.749115i \(-0.730479\pi\)
0.662440 0.749115i \(-0.269521\pi\)
\(80\) −1.60407 + 1.55787i −0.179341 + 0.174175i
\(81\) −5.09214 + 7.42092i −0.565793 + 0.824547i
\(82\) 1.77669 + 6.63071i 0.196203 + 0.732240i
\(83\) 17.4269 + 4.66953i 1.91285 + 0.512547i 0.992636 + 0.121137i \(0.0386539\pi\)
0.920216 + 0.391411i \(0.128013\pi\)
\(84\) 3.47329 + 2.98936i 0.378967 + 0.326166i
\(85\) −4.72935 8.47507i −0.512970 0.919251i
\(86\) 1.62377 0.937485i 0.175096 0.101092i
\(87\) −0.0311222 + 1.59999i −0.00333666 + 0.171537i
\(88\) −6.08124 + 1.62946i −0.648262 + 0.173701i
\(89\) −6.67816 + 11.5669i −0.707884 + 1.22609i 0.257757 + 0.966210i \(0.417017\pi\)
−0.965641 + 0.259881i \(0.916317\pi\)
\(90\) −3.03859 5.98055i −0.320295 0.630405i
\(91\) 1.47560 + 15.6199i 0.154685 + 1.63741i
\(92\) −0.303976 + 1.13445i −0.0316916 + 0.118275i
\(93\) 4.74993 + 2.86697i 0.492545 + 0.297290i
\(94\) 5.84918i 0.603296i
\(95\) −3.41522 + 0.861828i −0.350395 + 0.0884217i
\(96\) −0.415666 1.68143i −0.0424237 0.171611i
\(97\) −0.0834947 0.0223723i −0.00847760 0.00227157i 0.254578 0.967052i \(-0.418064\pi\)
−0.263055 + 0.964781i \(0.584730\pi\)
\(98\) 3.04588 + 6.30259i 0.307681 + 0.636657i
\(99\) 0.734495 18.8730i 0.0738195 1.89681i
\(100\) 4.99787 + 0.146091i 0.499787 + 0.0146091i
\(101\) 9.81937 + 5.66922i 0.977064 + 0.564108i 0.901383 0.433024i \(-0.142553\pi\)
0.0756817 + 0.997132i \(0.475887\pi\)
\(102\) 7.51630 + 0.146203i 0.744225 + 0.0144763i
\(103\) −1.17223 + 4.37483i −0.115503 + 0.431064i −0.999324 0.0367614i \(-0.988296\pi\)
0.883821 + 0.467826i \(0.154963\pi\)
\(104\) 2.96503 5.13559i 0.290745 0.503586i
\(105\) −0.615771 10.2284i −0.0600931 0.998193i
\(106\) 3.06413 + 5.30724i 0.297615 + 0.515484i
\(107\) 1.02305 0.274125i 0.0989020 0.0265007i −0.209029 0.977910i \(-0.567030\pi\)
0.307931 + 0.951409i \(0.400364\pi\)
\(108\) 5.18731 + 0.303009i 0.499149 + 0.0291570i
\(109\) 0.201442 0.116303i 0.0192947 0.0111398i −0.490322 0.871542i \(-0.663121\pi\)
0.509616 + 0.860402i \(0.329787\pi\)
\(110\) 12.0876 + 7.21626i 1.15250 + 0.688043i
\(111\) −1.16177 + 4.02128i −0.110271 + 0.381683i
\(112\) 0.441381 2.60867i 0.0417065 0.246497i
\(113\) −3.94167 14.7105i −0.370801 1.38385i −0.859384 0.511331i \(-0.829153\pi\)
0.488583 0.872518i \(-0.337514\pi\)
\(114\) 0.757268 2.62115i 0.0709247 0.245494i
\(115\) 2.29330 1.27973i 0.213851 0.119335i
\(116\) 0.800147 0.461965i 0.0742918 0.0428924i
\(117\) 12.0809 + 13.0593i 1.11688 + 1.20733i
\(118\) −5.88620 5.88620i −0.541868 0.541868i
\(119\) 10.4409 + 4.78097i 0.957120 + 0.438271i
\(120\) −2.04959 + 3.28621i −0.187101 + 0.299989i
\(121\) 14.3183 + 24.8001i 1.30167 + 2.25455i
\(122\) 8.74043 + 8.74043i 0.791322 + 0.791322i
\(123\) 5.74356 + 10.4106i 0.517879 + 0.938692i
\(124\) 3.20319i 0.287655i
\(125\) −7.55168 8.24452i −0.675443 0.737413i
\(126\) 7.08268 + 3.58269i 0.630975 + 0.319171i
\(127\) 8.24335 8.24335i 0.731479 0.731479i −0.239433 0.970913i \(-0.576962\pi\)
0.970913 + 0.239433i \(0.0769617\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 2.34058 2.25127i 0.206077 0.198213i
\(130\) −12.8570 + 3.24445i −1.12763 + 0.284557i
\(131\) 4.97306 2.87120i 0.434498 0.250858i −0.266763 0.963762i \(-0.585954\pi\)
0.701261 + 0.712904i \(0.252621\pi\)
\(132\) −9.54789 + 5.26760i −0.831038 + 0.458486i
\(133\) 2.65673 3.21106i 0.230368 0.278434i
\(134\) −6.39112 −0.552109
\(135\) −7.59510 8.79286i −0.653682 0.756769i
\(136\) −2.17018 3.75886i −0.186091 0.322320i
\(137\) −3.93655 + 1.05479i −0.336322 + 0.0901172i −0.423028 0.906117i \(-0.639033\pi\)
0.0867057 + 0.996234i \(0.472366\pi\)
\(138\) −0.0395616 + 2.03386i −0.00336771 + 0.173134i
\(139\) 1.39830 + 0.807308i 0.118602 + 0.0684750i 0.558127 0.829755i \(-0.311520\pi\)
−0.439525 + 0.898230i \(0.644853\pi\)
\(140\) −4.87211 + 3.35597i −0.411769 + 0.283631i
\(141\) 2.43130 + 9.83501i 0.204753 + 0.828257i
\(142\) −6.70276 + 6.70276i −0.562483 + 0.562483i
\(143\) −36.0622 9.66283i −3.01567 0.808046i
\(144\) −1.39783 2.65444i −0.116486 0.221204i
\(145\) −1.98755 0.563812i −0.165057 0.0468221i
\(146\) 5.18432 2.99317i 0.429058 0.247717i
\(147\) 7.74122 + 9.33131i 0.638485 + 0.769634i
\(148\) 2.33429 0.625472i 0.191878 0.0514135i
\(149\) 3.99291 + 6.91592i 0.327112 + 0.566574i 0.981937 0.189206i \(-0.0605913\pi\)
−0.654826 + 0.755780i \(0.727258\pi\)
\(150\) 8.46431 1.83180i 0.691108 0.149566i
\(151\) 2.67237 4.62868i 0.217474 0.376677i −0.736561 0.676371i \(-0.763552\pi\)
0.954035 + 0.299695i \(0.0968848\pi\)
\(152\) −1.52154 + 0.407696i −0.123413 + 0.0330685i
\(153\) 12.6989 2.87844i 1.02665 0.232708i
\(154\) −16.5832 + 1.56660i −1.33631 + 0.126240i
\(155\) −5.13815 + 4.99016i −0.412706 + 0.400819i
\(156\) 2.85082 9.86762i 0.228248 0.790042i
\(157\) 16.0894 16.0894i 1.28407 1.28407i 0.345744 0.938329i \(-0.387627\pi\)
0.938329 0.345744i \(-0.112373\pi\)
\(158\) −9.41623 + 9.41623i −0.749115 + 0.749115i
\(159\) 7.35818 + 7.65011i 0.583541 + 0.606693i
\(160\) 2.23583 + 0.0326704i 0.176758 + 0.00258282i
\(161\) −1.29370 + 2.82525i −0.101958 + 0.222661i
\(162\) 8.84807 1.64670i 0.695170 0.129377i
\(163\) 15.5338 4.16228i 1.21670 0.326015i 0.407314 0.913288i \(-0.366465\pi\)
0.809389 + 0.587274i \(0.199799\pi\)
\(164\) 3.43231 5.94493i 0.268018 0.464221i
\(165\) 23.3240 + 7.10927i 1.81577 + 0.553456i
\(166\) −9.02083 15.6245i −0.700152 1.21270i
\(167\) −3.19541 + 0.856206i −0.247268 + 0.0662552i −0.380324 0.924853i \(-0.624188\pi\)
0.133056 + 0.991108i \(0.457521\pi\)
\(168\) −0.342185 4.56978i −0.0264002 0.352566i
\(169\) 19.1961 11.0828i 1.47662 0.852527i
\(170\) −2.64863 + 9.33694i −0.203140 + 0.716110i
\(171\) 0.183772 4.72207i 0.0140534 0.361106i
\(172\) −1.81108 0.485278i −0.138094 0.0370021i
\(173\) 4.11813 4.11813i 0.313096 0.313096i −0.533012 0.846108i \(-0.678940\pi\)
0.846108 + 0.533012i \(0.178940\pi\)
\(174\) 1.15337 1.10936i 0.0874369 0.0841002i
\(175\) 12.9733 + 2.58706i 0.980691 + 0.195564i
\(176\) 5.45229 + 3.14788i 0.410982 + 0.237281i
\(177\) −12.3439 7.45056i −0.927828 0.560018i
\(178\) 12.9012 3.45687i 0.966987 0.259103i
\(179\) −2.90382 5.02957i −0.217042 0.375927i 0.736860 0.676045i \(-0.236307\pi\)
−0.953902 + 0.300117i \(0.902974\pi\)
\(180\) −2.08028 + 6.37749i −0.155055 + 0.475350i
\(181\) 5.33095 0.396247 0.198123 0.980177i \(-0.436515\pi\)
0.198123 + 0.980177i \(0.436515\pi\)
\(182\) 10.0016 12.0884i 0.741365 0.896050i
\(183\) 18.3296 + 11.0634i 1.35496 + 0.817827i
\(184\) 1.01712 0.587236i 0.0749832 0.0432916i
\(185\) −4.63982 2.76997i −0.341126 0.203652i
\(186\) −1.33146 5.38596i −0.0976273 0.394918i
\(187\) −19.3223 + 19.3223i −1.41299 + 1.41299i
\(188\) 4.13599 4.13599i 0.301648 0.301648i
\(189\) 13.3983 + 3.08003i 0.974580 + 0.224039i
\(190\) 3.02433 + 1.80552i 0.219408 + 0.130986i
\(191\) 1.31228i 0.0949531i 0.998872 + 0.0474766i \(0.0151179\pi\)
−0.998872 + 0.0474766i \(0.984882\pi\)
\(192\) −0.895033 + 1.48287i −0.0645935 + 0.107017i
\(193\) −0.459893 0.459893i −0.0331038 0.0331038i 0.690361 0.723465i \(-0.257452\pi\)
−0.723465 + 0.690361i \(0.757452\pi\)
\(194\) 0.0432200 + 0.0748593i 0.00310302 + 0.00537458i
\(195\) −20.2696 + 10.7995i −1.45153 + 0.773371i
\(196\) 2.30284 6.61037i 0.164488 0.472169i
\(197\) −4.43627 4.43627i −0.316071 0.316071i 0.531185 0.847256i \(-0.321747\pi\)
−0.847256 + 0.531185i \(0.821747\pi\)
\(198\) −13.8646 + 12.8259i −0.985314 + 0.911494i
\(199\) −7.75962 + 4.48002i −0.550065 + 0.317580i −0.749148 0.662403i \(-0.769537\pi\)
0.199083 + 0.979983i \(0.436204\pi\)
\(200\) −3.43072 3.63733i −0.242589 0.257198i
\(201\) −10.7463 + 2.65657i −0.757982 + 0.187380i
\(202\) −2.93460 10.9521i −0.206478 0.770586i
\(203\) 2.29123 0.851948i 0.160813 0.0597950i
\(204\) −5.21145 5.41821i −0.364874 0.379350i
\(205\) −14.8832 + 3.75576i −1.03949 + 0.262313i
\(206\) 3.92236 2.26458i 0.273284 0.157781i
\(207\) 0.778886 + 3.43625i 0.0541363 + 0.238836i
\(208\) −5.72800 + 1.53481i −0.397166 + 0.106420i
\(209\) 4.95859 + 8.58853i 0.342993 + 0.594081i
\(210\) −6.79718 + 7.66801i −0.469050 + 0.529143i
\(211\) −1.30948 + 2.26808i −0.0901481 + 0.156141i −0.907573 0.419894i \(-0.862067\pi\)
0.817425 + 0.576035i \(0.195401\pi\)
\(212\) 1.58611 5.91945i 0.108935 0.406550i
\(213\) −8.48414 + 14.0564i −0.581323 + 0.963125i
\(214\) −0.917241 0.529570i −0.0627013 0.0362006i
\(215\) 2.04301 + 3.66110i 0.139332 + 0.249685i
\(216\) −3.45372 3.88224i −0.234996 0.264153i
\(217\) 1.41383 8.35609i 0.0959769 0.567248i
\(218\) −0.224680 0.0602028i −0.0152172 0.00407745i
\(219\) 7.47294 7.18777i 0.504975 0.485704i
\(220\) −3.44453 13.6499i −0.232230 0.920273i
\(221\) 25.7386i 1.73137i
\(222\) 3.66497 2.02198i 0.245977 0.135706i
\(223\) −6.49461 + 24.2382i −0.434911 + 1.62311i 0.306367 + 0.951913i \(0.400886\pi\)
−0.741279 + 0.671197i \(0.765780\pi\)
\(224\) −2.15671 + 1.53251i −0.144102 + 0.102395i
\(225\) 13.4708 6.59838i 0.898051 0.439892i
\(226\) −7.61472 + 13.1891i −0.506524 + 0.877325i
\(227\) −24.1560 + 6.47257i −1.60329 + 0.429600i −0.946033 0.324069i \(-0.894949\pi\)
−0.657255 + 0.753669i \(0.728282\pi\)
\(228\) −2.38891 + 1.31797i −0.158209 + 0.0872844i
\(229\) 7.93914 4.58366i 0.524633 0.302897i −0.214195 0.976791i \(-0.568713\pi\)
0.738828 + 0.673894i \(0.235379\pi\)
\(230\) −2.52651 0.716701i −0.166593 0.0472578i
\(231\) −27.2324 + 9.52720i −1.79176 + 0.626844i
\(232\) −0.892448 0.239131i −0.0585921 0.0156997i
\(233\) 5.49236 + 20.4978i 0.359817 + 1.34285i 0.874314 + 0.485362i \(0.161312\pi\)
−0.514497 + 0.857492i \(0.672021\pi\)
\(234\) 0.691830 17.7767i 0.0452264 1.16210i
\(235\) −13.0778 0.191095i −0.853099 0.0124657i
\(236\) 8.32434i 0.541868i
\(237\) −11.9188 + 19.7468i −0.774207 + 1.28269i
\(238\) −4.00220 10.7635i −0.259424 0.697695i
\(239\) 2.96499 5.13552i 0.191789 0.332189i −0.754054 0.656813i \(-0.771904\pi\)
0.945843 + 0.324624i \(0.105238\pi\)
\(240\) 3.77298 0.874425i 0.243545 0.0564439i
\(241\) 11.3514 19.6612i 0.731209 1.26649i −0.225158 0.974322i \(-0.572290\pi\)
0.956367 0.292168i \(-0.0943767\pi\)
\(242\) 7.41171 27.6609i 0.476443 1.77811i
\(243\) 14.1930 6.44666i 0.910480 0.413554i
\(244\) 12.3608i 0.791322i
\(245\) −14.1910 + 6.60417i −0.906631 + 0.421925i
\(246\) 3.30010 11.4227i 0.210406 0.728286i
\(247\) −9.02284 2.41766i −0.574109 0.153832i
\(248\) −2.26500 + 2.26500i −0.143828 + 0.143828i
\(249\) −21.6625 22.5220i −1.37281 1.42727i
\(250\) −0.489916 + 11.1696i −0.0309850 + 0.706428i
\(251\) 7.87318i 0.496951i 0.968638 + 0.248475i \(0.0799295\pi\)
−0.968638 + 0.248475i \(0.920070\pi\)
\(252\) −2.47487 7.54155i −0.155902 0.475073i
\(253\) −5.22849 5.22849i −0.328712 0.328712i
\(254\) −11.6579 −0.731479
\(255\) −0.572446 + 16.8004i −0.0358480 + 1.05208i
\(256\) 1.00000 0.0625000
\(257\) 3.60224 13.4437i 0.224701 0.838597i −0.757823 0.652461i \(-0.773737\pi\)
0.982524 0.186136i \(-0.0595965\pi\)
\(258\) −3.24693 0.0631577i −0.202145 0.00393202i
\(259\) 6.36548 0.601341i 0.395532 0.0373655i
\(260\) 11.3854 + 6.79709i 0.706094 + 0.421538i
\(261\) 1.47820 2.34473i 0.0914981 0.145135i
\(262\) −5.54673 1.48624i −0.342678 0.0918203i
\(263\) 1.40058 + 5.22702i 0.0863633 + 0.322312i 0.995569 0.0940353i \(-0.0299767\pi\)
−0.909206 + 0.416347i \(0.863310\pi\)
\(264\) 10.4761 + 3.02662i 0.644762 + 0.186276i
\(265\) −11.9662 + 6.67749i −0.735077 + 0.410195i
\(266\) −4.14915 + 0.391967i −0.254401 + 0.0240330i
\(267\) 20.2557 11.1751i 1.23963 0.683905i
\(268\) 4.51921 + 4.51921i 0.276055 + 0.276055i
\(269\) 14.0186 + 24.2810i 0.854732 + 1.48044i 0.876894 + 0.480684i \(0.159612\pi\)
−0.0221622 + 0.999754i \(0.507055\pi\)
\(270\) −0.846947 + 11.5880i −0.0515436 + 0.705226i
\(271\) −4.39946 + 7.62008i −0.267248 + 0.462887i −0.968150 0.250370i \(-0.919448\pi\)
0.700902 + 0.713257i \(0.252781\pi\)
\(272\) −1.12337 + 4.19247i −0.0681142 + 0.254206i
\(273\) 11.7922 24.4831i 0.713698 1.48179i
\(274\) 3.52941 + 2.03771i 0.213220 + 0.123102i
\(275\) −16.5292 + 26.7899i −0.996749 + 1.61549i
\(276\) 1.46613 1.41018i 0.0882507 0.0848830i
\(277\) 3.49664 + 13.0496i 0.210092 + 0.784076i 0.987837 + 0.155495i \(0.0496972\pi\)
−0.777744 + 0.628581i \(0.783636\pi\)
\(278\) −0.417893 1.55960i −0.0250636 0.0935386i
\(279\) −4.47752 8.50270i −0.268062 0.509043i
\(280\) 5.81813 + 1.07208i 0.347700 + 0.0640689i
\(281\) −14.4482 + 8.34169i −0.861909 + 0.497623i −0.864651 0.502373i \(-0.832460\pi\)
0.00274228 + 0.999996i \(0.499127\pi\)
\(282\) 5.23521 8.67359i 0.311752 0.516505i
\(283\) 9.71304 + 9.71304i 0.577380 + 0.577380i 0.934181 0.356800i \(-0.116132\pi\)
−0.356800 + 0.934181i \(0.616132\pi\)
\(284\) 9.47913 0.562483
\(285\) 5.83571 + 1.77876i 0.345678 + 0.105364i
\(286\) 18.6671 + 32.3325i 1.10381 + 1.91186i
\(287\) 11.5778 13.9934i 0.683413 0.826007i
\(288\) −0.888559 + 2.86539i −0.0523589 + 0.168845i
\(289\) −1.59238 0.919360i −0.0936693 0.0540800i
\(290\) 1.00673 + 1.80409i 0.0591175 + 0.105940i
\(291\) 0.103788 + 0.107906i 0.00608417 + 0.00632555i
\(292\) −5.78236 1.54938i −0.338387 0.0906706i
\(293\) −1.45533 5.43138i −0.0850215 0.317305i 0.910297 0.413956i \(-0.135853\pi\)
−0.995318 + 0.0966517i \(0.969187\pi\)
\(294\) 1.12436 12.0721i 0.0655742 0.704060i
\(295\) 13.3528 12.9682i 0.777432 0.755039i
\(296\) −2.09287 1.20832i −0.121646 0.0702321i
\(297\) −17.9811 + 27.3289i −1.04337 + 1.58578i
\(298\) 2.06688 7.71371i 0.119731 0.446843i
\(299\) 6.96469 0.402779
\(300\) −7.28045 4.68989i −0.420337 0.270771i
\(301\) −4.51033 2.06531i −0.259971 0.119042i
\(302\) −5.16262 + 1.38332i −0.297075 + 0.0796011i
\(303\) −9.48676 17.1954i −0.545000 0.987850i
\(304\) 1.36418 + 0.787607i 0.0782409 + 0.0451724i
\(305\) −19.8277 + 19.2566i −1.13533 + 1.10263i
\(306\) −11.0149 6.94414i −0.629678 0.396970i
\(307\) 4.71179 4.71179i 0.268916 0.268916i −0.559747 0.828663i \(-0.689102\pi\)
0.828663 + 0.559747i \(0.189102\pi\)
\(308\) 12.8338 + 10.6183i 0.731276 + 0.605036i
\(309\) 5.65389 5.43813i 0.321638 0.309364i
\(310\) 7.16180 + 0.104650i 0.406763 + 0.00594370i
\(311\) 21.0289i 1.19244i 0.802821 + 0.596220i \(0.203331\pi\)
−0.802821 + 0.596220i \(0.796669\pi\)
\(312\) −8.99329 + 4.96163i −0.509145 + 0.280897i
\(313\) 0.287266 + 0.287266i 0.0162372 + 0.0162372i 0.715179 0.698942i \(-0.246345\pi\)
−0.698942 + 0.715179i \(0.746345\pi\)
\(314\) −22.7538 −1.28407
\(315\) −8.24168 + 15.7186i −0.464366 + 0.885643i
\(316\) 13.3166 0.749115
\(317\) 6.57722 + 6.57722i 0.369413 + 0.369413i 0.867263 0.497850i \(-0.165877\pi\)
−0.497850 + 0.867263i \(0.665877\pi\)
\(318\) 0.206428 10.6125i 0.0115759 0.595117i
\(319\) 5.81685i 0.325681i
\(320\) −1.55787 1.60407i −0.0870875 0.0896703i
\(321\) −1.76241 0.509170i −0.0983679 0.0284191i
\(322\) 2.91254 1.08297i 0.162309 0.0603515i
\(323\) −4.83449 + 4.83449i −0.268998 + 0.268998i
\(324\) −7.42092 5.09214i −0.412274 0.282897i
\(325\) −6.83399 28.8520i −0.379081 1.60042i
\(326\) −13.9272 8.04090i −0.771359 0.445344i
\(327\) −0.402809 0.00783523i −0.0222754 0.000433289i
\(328\) −6.63071 + 1.77669i −0.366120 + 0.0981015i
\(329\) 12.6150 8.96391i 0.695488 0.494196i
\(330\) −11.4655 21.5196i −0.631156 1.18461i
\(331\) 26.0974 1.43444 0.717222 0.696845i \(-0.245414\pi\)
0.717222 + 0.696845i \(0.245414\pi\)
\(332\) −4.66953 + 17.4269i −0.256274 + 0.956426i
\(333\) 5.32194 4.92322i 0.291641 0.269791i
\(334\) 2.86492 + 1.65406i 0.156762 + 0.0905063i
\(335\) 0.208800 14.2895i 0.0114080 0.780717i
\(336\) −2.98936 + 3.47329i −0.163083 + 0.189483i
\(337\) 6.58481 + 24.5748i 0.358697 + 1.33868i 0.875767 + 0.482733i \(0.160356\pi\)
−0.517070 + 0.855943i \(0.672977\pi\)
\(338\) −21.4104 5.73690i −1.16457 0.312046i
\(339\) −7.32140 + 25.3418i −0.397644 + 1.37638i
\(340\) 8.47507 4.72935i 0.459625 0.256485i
\(341\) 17.4647 + 10.0833i 0.945769 + 0.546040i
\(342\) −3.46895 + 3.20906i −0.187580 + 0.173526i
\(343\) 8.92504 16.2279i 0.481907 0.876222i
\(344\) 0.937485 + 1.62377i 0.0505458 + 0.0875479i
\(345\) −4.54607 0.154900i −0.244752 0.00833954i
\(346\) −5.82392 −0.313096
\(347\) −23.7875 23.7875i −1.27698 1.27698i −0.942350 0.334630i \(-0.891389\pi\)
−0.334630 0.942350i \(-0.608611\pi\)
\(348\) −1.59999 0.0311222i −0.0857686 0.00166833i
\(349\) −16.9808 + 9.80384i −0.908959 + 0.524788i −0.880096 0.474796i \(-0.842522\pi\)
−0.0288628 + 0.999583i \(0.509189\pi\)
\(350\) −7.34419 11.0029i −0.392564 0.588127i
\(351\) −6.22592 30.1780i −0.332315 1.61078i
\(352\) −1.62946 6.08124i −0.0868507 0.324131i
\(353\) 4.95115 + 18.4779i 0.263523 + 0.983481i 0.963148 + 0.268971i \(0.0866836\pi\)
−0.699625 + 0.714510i \(0.746650\pi\)
\(354\) 3.46015 + 13.9968i 0.183905 + 0.743923i
\(355\) −14.7672 15.2052i −0.783763 0.807008i
\(356\) −11.5669 6.67816i −0.613045 0.353942i
\(357\) −11.2035 16.4346i −0.592951 0.869810i
\(358\) −1.50313 + 5.60975i −0.0794428 + 0.296485i
\(359\) 6.21763 10.7692i 0.328154 0.568379i −0.653992 0.756502i \(-0.726907\pi\)
0.982146 + 0.188123i \(0.0602403\pi\)
\(360\) 5.98055 3.03859i 0.315203 0.160148i
\(361\) −8.25935 14.3056i −0.434703 0.752927i
\(362\) −3.76955 3.76955i −0.198123 0.198123i
\(363\) 0.964614 49.5907i 0.0506291 2.60284i
\(364\) −15.6199 + 1.47560i −0.818707 + 0.0773425i
\(365\) 6.52285 + 11.6891i 0.341421 + 0.611833i
\(366\) −5.13798 20.7839i −0.268567 1.08639i
\(367\) −0.454718 1.69703i −0.0237361 0.0885843i 0.953042 0.302839i \(-0.0979344\pi\)
−0.976778 + 0.214255i \(0.931268\pi\)
\(368\) −1.13445 0.303976i −0.0591374 0.0158458i
\(369\) 0.800860 20.5783i 0.0416911 1.07126i
\(370\) 1.32219 + 5.23951i 0.0687372 + 0.272389i
\(371\) 6.75038 14.7418i 0.350462 0.765358i
\(372\) −2.86697 + 4.74993i −0.148645 + 0.246273i
\(373\) 3.27088 12.2071i 0.169360 0.632060i −0.828084 0.560604i \(-0.810569\pi\)
0.997444 0.0714555i \(-0.0227644\pi\)
\(374\) 27.3259 1.41299
\(375\) 3.81906 + 18.9846i 0.197216 + 0.980360i
\(376\) −5.84918 −0.301648
\(377\) −3.87422 3.87422i −0.199532 0.199532i
\(378\) −7.29609 11.6519i −0.375271 0.599310i
\(379\) 23.9709i 1.23130i 0.788019 + 0.615651i \(0.211107\pi\)
−0.788019 + 0.615651i \(0.788893\pi\)
\(380\) −0.861828 3.41522i −0.0442109 0.175197i
\(381\) −19.6019 + 4.84578i −1.00424 + 0.248257i
\(382\) 0.927921 0.927921i 0.0474766 0.0474766i
\(383\) −14.6830 3.93430i −0.750266 0.201033i −0.136630 0.990622i \(-0.543627\pi\)
−0.613636 + 0.789589i \(0.710294\pi\)
\(384\) 1.68143 0.415666i 0.0858053 0.0212119i
\(385\) −2.96087 37.1284i −0.150900 1.89224i
\(386\) 0.650387i 0.0331038i
\(387\) −5.48575 + 1.24344i −0.278856 + 0.0632078i
\(388\) 0.0223723 0.0834947i 0.00113578 0.00423880i
\(389\) −4.46656 + 7.73631i −0.226464 + 0.392247i −0.956758 0.290887i \(-0.906050\pi\)
0.730294 + 0.683133i \(0.239383\pi\)
\(390\) 21.9692 + 6.69632i 1.11245 + 0.339082i
\(391\) 2.54881 4.41468i 0.128899 0.223260i
\(392\) −6.30259 + 3.04588i −0.318329 + 0.153840i
\(393\) −9.94424 0.193430i −0.501621 0.00975728i
\(394\) 6.27383i 0.316071i
\(395\) −20.7455 21.3607i −1.04382 1.07477i
\(396\) 18.8730 + 0.734495i 0.948404 + 0.0369097i
\(397\) −1.85320 6.91625i −0.0930096 0.347116i 0.903701 0.428165i \(-0.140840\pi\)
−0.996710 + 0.0810486i \(0.974173\pi\)
\(398\) 8.65473 + 2.31903i 0.433822 + 0.116242i
\(399\) −6.81360 + 2.38373i −0.341107 + 0.119336i
\(400\) −0.146091 + 4.99787i −0.00730454 + 0.249893i
\(401\) −5.47738 + 3.16237i −0.273527 + 0.157921i −0.630489 0.776198i \(-0.717146\pi\)
0.356962 + 0.934119i \(0.383812\pi\)
\(402\) 9.47723 + 5.72027i 0.472681 + 0.285301i
\(403\) −18.3479 + 4.91631i −0.913975 + 0.244899i
\(404\) −5.66922 + 9.81937i −0.282054 + 0.488532i
\(405\) 3.39267 + 19.8366i 0.168583 + 0.985687i
\(406\) −2.22256 1.01772i −0.110304 0.0505088i
\(407\) −3.93782 + 14.6962i −0.195191 + 0.728461i
\(408\) −0.146203 + 7.51630i −0.00723814 + 0.372112i
\(409\) 6.13817i 0.303513i 0.988418 + 0.151757i \(0.0484930\pi\)
−0.988418 + 0.151757i \(0.951507\pi\)
\(410\) 13.1797 + 7.86828i 0.650900 + 0.388587i
\(411\) 6.78148 + 1.95921i 0.334506 + 0.0966409i
\(412\) −4.37483 1.17223i −0.215532 0.0577517i
\(413\) −3.67420 + 21.7155i −0.180796 + 1.06855i
\(414\) 1.87904 2.98055i 0.0923496 0.146486i
\(415\) 35.2285 19.6586i 1.72930 0.965002i
\(416\) 5.13559 + 2.96503i 0.251793 + 0.145373i
\(417\) −1.35093 2.44866i −0.0661555 0.119911i
\(418\) 2.56675 9.57926i 0.125544 0.468537i
\(419\) 15.9180 27.5708i 0.777645 1.34692i −0.155651 0.987812i \(-0.549748\pi\)
0.933296 0.359108i \(-0.116919\pi\)
\(420\) 10.2284 0.615771i 0.499096 0.0300465i
\(421\) 4.03625 + 6.99099i 0.196715 + 0.340720i 0.947461 0.319870i \(-0.103639\pi\)
−0.750747 + 0.660590i \(0.770306\pi\)
\(422\) 2.52971 0.677835i 0.123145 0.0329965i
\(423\) 5.19734 16.7602i 0.252703 0.814908i
\(424\) −5.30724 + 3.06413i −0.257742 + 0.148807i
\(425\) −20.7893 6.22692i −1.00843 0.302050i
\(426\) 15.9385 3.94015i 0.772224 0.190901i
\(427\) 5.45583 32.2454i 0.264026 1.56046i
\(428\) 0.274125 + 1.02305i 0.0132503 + 0.0494510i
\(429\) 44.8271 + 46.6056i 2.16427 + 2.25014i
\(430\) 1.14417 4.03342i 0.0551767 0.194509i
\(431\) 21.0923 12.1776i 1.01598 0.586576i 0.103042 0.994677i \(-0.467142\pi\)
0.912937 + 0.408101i \(0.133809\pi\)
\(432\) −0.303009 + 5.18731i −0.0145785 + 0.249575i
\(433\) 18.6284 + 18.6284i 0.895224 + 0.895224i 0.995009 0.0997846i \(-0.0318154\pi\)
−0.0997846 + 0.995009i \(0.531815\pi\)
\(434\) −6.90838 + 4.90892i −0.331613 + 0.235636i
\(435\) 2.44265 + 2.61499i 0.117116 + 0.125379i
\(436\) 0.116303 + 0.201442i 0.00556989 + 0.00964734i
\(437\) −1.30818 1.30818i −0.0625787 0.0625787i
\(438\) −10.3667 0.201648i −0.495339 0.00963510i
\(439\) 13.1054i 0.625485i 0.949838 + 0.312743i \(0.101248\pi\)
−0.949838 + 0.312743i \(0.898752\pi\)
\(440\) −7.21626 + 12.0876i −0.344021 + 0.576251i
\(441\) −3.12742 20.7658i −0.148925 0.988849i
\(442\) −18.2000 + 18.2000i −0.865683 + 0.865683i
\(443\) −1.88960 + 1.88960i −0.0897778 + 0.0897778i −0.750569 0.660792i \(-0.770221\pi\)
0.660792 + 0.750569i \(0.270221\pi\)
\(444\) −4.02128 1.16177i −0.190841 0.0551353i
\(445\) 7.30749 + 28.9579i 0.346408 + 1.37273i
\(446\) 21.7314 12.5466i 1.02901 0.594100i
\(447\) 0.268999 13.8292i 0.0127232 0.654100i
\(448\) 2.60867 + 0.441381i 0.123248 + 0.0208533i
\(449\) −15.7386 −0.742749 −0.371374 0.928483i \(-0.621113\pi\)
−0.371374 + 0.928483i \(0.621113\pi\)
\(450\) −14.1910 4.85951i −0.668971 0.229079i
\(451\) 21.6090 + 37.4279i 1.01753 + 1.76241i
\(452\) 14.7105 3.94167i 0.691924 0.185401i
\(453\) −8.10561 + 4.47189i −0.380835 + 0.210108i
\(454\) 21.6577 + 12.5041i 1.01644 + 0.586844i
\(455\) 26.7008 + 22.7567i 1.25175 + 1.06685i
\(456\) 2.62115 + 0.757268i 0.122747 + 0.0354623i
\(457\) 6.59771 6.59771i 0.308628 0.308628i −0.535749 0.844377i \(-0.679971\pi\)
0.844377 + 0.535749i \(0.179971\pi\)
\(458\) −8.85496 2.37268i −0.413765 0.110868i
\(459\) −21.4072 7.09761i −0.999204 0.331288i
\(460\) 1.27973 + 2.29330i 0.0596677 + 0.106926i
\(461\) −23.1959 + 13.3922i −1.08034 + 0.623735i −0.930988 0.365049i \(-0.881052\pi\)
−0.149352 + 0.988784i \(0.547719\pi\)
\(462\) 25.9929 + 12.5194i 1.20930 + 0.582457i
\(463\) −40.0588 + 10.7337i −1.86169 + 0.498838i −0.999964 0.00853803i \(-0.997282\pi\)
−0.861725 + 0.507376i \(0.830616\pi\)
\(464\) 0.461965 + 0.800147i 0.0214462 + 0.0371459i
\(465\) 12.0856 2.80095i 0.560456 0.129891i
\(466\) 10.6104 18.3778i 0.491519 0.851335i
\(467\) 23.6435 6.33527i 1.09409 0.293161i 0.333736 0.942667i \(-0.391691\pi\)
0.760357 + 0.649505i \(0.225024\pi\)
\(468\) −13.0593 + 12.0809i −0.603664 + 0.558438i
\(469\) 9.79445 + 13.7838i 0.452266 + 0.636478i
\(470\) 9.11225 + 9.38250i 0.420317 + 0.432782i
\(471\) −38.2591 + 9.45799i −1.76288 + 0.435801i
\(472\) 5.88620 5.88620i 0.270934 0.270934i
\(473\) 8.34695 8.34695i 0.383793 0.383793i
\(474\) 22.3909 5.53524i 1.02845 0.254242i
\(475\) −4.13565 + 6.70291i −0.189757 + 0.307550i
\(476\) −4.78097 + 10.4409i −0.219136 + 0.478560i
\(477\) −4.06415 17.9300i −0.186084 0.820957i
\(478\) −5.72792 + 1.53479i −0.261989 + 0.0701998i
\(479\) 1.67282 2.89742i 0.0764333 0.132386i −0.825275 0.564731i \(-0.808980\pi\)
0.901709 + 0.432344i \(0.142313\pi\)
\(480\) −3.28621 2.04959i −0.149994 0.0935505i
\(481\) −7.16541 12.4109i −0.326715 0.565886i
\(482\) −21.9292 + 5.87592i −0.998850 + 0.267641i
\(483\) 4.44708 3.03158i 0.202349 0.137942i
\(484\) −24.8001 + 14.3183i −1.12728 + 0.650833i
\(485\) −0.168785 + 0.0941869i −0.00766411 + 0.00427681i
\(486\) −14.5944 5.47747i −0.662017 0.248463i
\(487\) 13.4334 + 3.59947i 0.608726 + 0.163108i 0.549998 0.835166i \(-0.314629\pi\)
0.0587288 + 0.998274i \(0.481295\pi\)
\(488\) −8.74043 + 8.74043i −0.395661 + 0.395661i
\(489\) −26.7601 7.73116i −1.21013 0.349615i
\(490\) 14.7044 + 5.36471i 0.664278 + 0.242353i
\(491\) −31.2490 18.0416i −1.41025 0.814207i −0.414836 0.909896i \(-0.636161\pi\)
−0.995411 + 0.0956893i \(0.969494\pi\)
\(492\) −10.4106 + 5.74356i −0.469346 + 0.258940i
\(493\) −3.87355 + 1.03791i −0.174456 + 0.0467453i
\(494\) 4.67056 + 8.08965i 0.210139 + 0.363971i
\(495\) −28.2235 31.4179i −1.26855 1.41213i
\(496\) 3.20319 0.143828
\(497\) 24.7280 + 4.18390i 1.10920 + 0.187674i
\(498\) −0.607727 + 31.2432i −0.0272329 + 1.40004i
\(499\) −30.9349 + 17.8603i −1.38484 + 0.799535i −0.992727 0.120383i \(-0.961588\pi\)
−0.392109 + 0.919919i \(0.628254\pi\)
\(500\) 8.24452 7.55168i 0.368706 0.337721i
\(501\) 5.50472 + 1.59035i 0.245933 + 0.0710515i
\(502\) 5.56718 5.56718i 0.248475 0.248475i
\(503\) 18.8085 18.8085i 0.838628 0.838628i −0.150050 0.988678i \(-0.547944\pi\)
0.988678 + 0.150050i \(0.0479436\pi\)
\(504\) −3.58269 + 7.08268i −0.159586 + 0.315488i
\(505\) 24.5829 6.20346i 1.09392 0.276050i
\(506\) 7.39420i 0.328712i
\(507\) −38.3848 0.746643i −1.70473 0.0331596i
\(508\) 8.24335 + 8.24335i 0.365740 + 0.365740i
\(509\) 13.8762 + 24.0343i 0.615052 + 1.06530i 0.990375 + 0.138408i \(0.0441984\pi\)
−0.375323 + 0.926894i \(0.622468\pi\)
\(510\) 12.2845 11.4749i 0.543965 0.508117i
\(511\) −14.4004 6.59405i −0.637038 0.291704i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −4.49892 + 6.83775i −0.198632 + 0.301894i
\(514\) −12.0533 + 6.95899i −0.531649 + 0.306948i
\(515\) 4.93506 + 8.84371i 0.217465 + 0.389701i
\(516\) 2.25127 + 2.34058i 0.0991065 + 0.103039i
\(517\) 9.53102 + 35.5702i 0.419174 + 1.56438i
\(518\) −4.92629 4.07586i −0.216449 0.179083i
\(519\) −9.79254 + 2.42081i −0.429845 + 0.106262i
\(520\) −3.24445 12.8570i −0.142278 0.563816i
\(521\) 31.4799 18.1749i 1.37916 0.796257i 0.387100 0.922038i \(-0.373477\pi\)
0.992058 + 0.125780i \(0.0401434\pi\)
\(522\) −2.70322 + 0.612732i −0.118317 + 0.0268186i
\(523\) 28.4540 7.62423i 1.24421 0.333384i 0.424111 0.905610i \(-0.360587\pi\)
0.820096 + 0.572226i \(0.193920\pi\)
\(524\) 2.87120 + 4.97306i 0.125429 + 0.217249i
\(525\) −16.9223 15.4478i −0.738549 0.674199i
\(526\) 2.70571 4.68642i 0.117974 0.204338i
\(527\) −3.59836 + 13.4293i −0.156747 + 0.584989i
\(528\) −5.26760 9.54789i −0.229243 0.415519i
\(529\) −18.7240 10.8103i −0.814087 0.470013i
\(530\) 13.1831 + 3.73967i 0.572636 + 0.162441i
\(531\) 11.6360 + 22.0965i 0.504960 + 0.958906i
\(532\) 3.21106 + 2.65673i 0.139217 + 0.115184i
\(533\) −39.3206 10.5359i −1.70316 0.456361i
\(534\) −22.2249 6.42092i −0.961765 0.277860i
\(535\) 1.21399 2.03349i 0.0524855 0.0879156i
\(536\) 6.39112i 0.276055i
\(537\) −0.195628 + 10.0572i −0.00844198 + 0.434002i
\(538\) 7.25658 27.0819i 0.312853 1.16759i
\(539\) 28.7926 + 33.3644i 1.24018 + 1.43711i
\(540\) 8.79286 7.59510i 0.378385 0.326841i
\(541\) 2.92530 5.06677i 0.125769 0.217838i −0.796265 0.604949i \(-0.793194\pi\)
0.922033 + 0.387111i \(0.126527\pi\)
\(542\) 8.49910 2.27733i 0.365068 0.0978196i
\(543\) −7.90513 4.77138i −0.339242 0.204760i
\(544\) 3.75886 2.17018i 0.161160 0.0930457i
\(545\) 0.141943 0.500379i 0.00608019 0.0214339i
\(546\) −25.6505 + 8.97380i −1.09774 + 0.384043i
\(547\) 33.3167 + 8.92718i 1.42452 + 0.381699i 0.887085 0.461607i \(-0.152727\pi\)
0.537434 + 0.843306i \(0.319394\pi\)
\(548\) −1.05479 3.93655i −0.0450586 0.168161i
\(549\) −17.2784 32.8112i −0.737422 1.40035i
\(550\) 30.6313 7.25543i 1.30612 0.309372i
\(551\) 1.45539i 0.0620017i
\(552\) −2.03386 0.0395616i −0.0865668 0.00168385i
\(553\) 34.7386 + 5.87767i 1.47723 + 0.249944i
\(554\) 6.75498 11.7000i 0.286992 0.497084i
\(555\) 4.40106 + 8.26031i 0.186814 + 0.350631i
\(556\) −0.807308 + 1.39830i −0.0342375 + 0.0593011i
\(557\) −9.37795 + 34.9990i −0.397356 + 1.48295i 0.420373 + 0.907351i \(0.361899\pi\)
−0.817729 + 0.575603i \(0.804767\pi\)
\(558\) −2.84623 + 9.17840i −0.120490 + 0.388553i
\(559\) 11.1187i 0.470271i
\(560\) −3.35597 4.87211i −0.141815 0.205884i
\(561\) 45.9467 11.3584i 1.93987 0.479554i
\(562\) 16.1149 + 4.31797i 0.679766 + 0.182143i
\(563\) 10.7610 10.7610i 0.453523 0.453523i −0.442999 0.896522i \(-0.646086\pi\)
0.896522 + 0.442999i \(0.146086\pi\)
\(564\) −9.83501 + 2.43130i −0.414128 + 0.102376i
\(565\) −29.2398 17.4561i −1.23013 0.734384i
\(566\) 13.7363i 0.577380i
\(567\) −17.1112 16.5592i −0.718603 0.695420i
\(568\) −6.70276 6.70276i −0.281241 0.281241i
\(569\) 13.4096 0.562160 0.281080 0.959684i \(-0.409307\pi\)
0.281080 + 0.959684i \(0.409307\pi\)
\(570\) −2.86870 5.38424i −0.120157 0.225521i
\(571\) 12.1254 0.507434 0.253717 0.967278i \(-0.418347\pi\)
0.253717 + 0.967278i \(0.418347\pi\)
\(572\) 9.66283 36.0622i 0.404023 1.50783i
\(573\) 1.17453 1.94594i 0.0490668 0.0812929i
\(574\) −18.0816 + 1.70815i −0.754710 + 0.0712968i
\(575\) 1.68496 5.62543i 0.0702678 0.234597i
\(576\) 2.65444 1.39783i 0.110602 0.0582429i
\(577\) 45.2410 + 12.1223i 1.88341 + 0.504657i 0.999301 + 0.0373702i \(0.0118981\pi\)
0.884106 + 0.467287i \(0.154769\pi\)
\(578\) 0.475896 + 1.77607i 0.0197946 + 0.0738746i
\(579\) 0.270344 + 1.09358i 0.0112351 + 0.0454478i
\(580\) 0.563812 1.98755i 0.0234110 0.0825285i
\(581\) −19.8732 + 43.4001i −0.824478 + 1.80054i
\(582\) 0.00291170 0.149690i 0.000120694 0.00620486i
\(583\) 27.2817 + 27.2817i 1.12989 + 1.12989i
\(584\) 2.99317 + 5.18432i 0.123858 + 0.214529i
\(585\) 39.7232 + 2.12759i 1.64235 + 0.0879649i
\(586\) −2.81149 + 4.86964i −0.116142 + 0.201163i
\(587\) 1.68871 6.30235i 0.0697005 0.260126i −0.922279 0.386525i \(-0.873675\pi\)
0.991979 + 0.126399i \(0.0403420\pi\)
\(588\) −9.33131 + 7.74122i −0.384817 + 0.319243i
\(589\) 4.36972 + 2.52286i 0.180051 + 0.103953i
\(590\) −18.6118 0.271959i −0.766236 0.0111964i
\(591\) 2.60782 + 10.5490i 0.107271 + 0.433929i
\(592\) 0.625472 + 2.33429i 0.0257067 + 0.0959388i
\(593\) 2.13956 + 7.98493i 0.0878610 + 0.327902i 0.995841 0.0911127i \(-0.0290423\pi\)
−0.907980 + 0.419014i \(0.862376\pi\)
\(594\) 32.0390 6.60986i 1.31458 0.271206i
\(595\) 24.1962 8.59660i 0.991945 0.352426i
\(596\) −6.91592 + 3.99291i −0.283287 + 0.163556i
\(597\) 15.5163 + 0.301815i 0.635040 + 0.0123525i
\(598\) −4.92478 4.92478i −0.201389 0.201389i
\(599\) 5.64607 0.230692 0.115346 0.993325i \(-0.463202\pi\)
0.115346 + 0.993325i \(0.463202\pi\)
\(600\) 1.83180 + 8.46431i 0.0747830 + 0.345554i
\(601\) 6.35844 + 11.0131i 0.259366 + 0.449236i 0.966072 0.258272i \(-0.0831530\pi\)
−0.706706 + 0.707507i \(0.749820\pi\)
\(602\) 1.72889 + 4.64968i 0.0704644 + 0.189507i
\(603\) 18.3131 + 5.67889i 0.745766 + 0.231262i
\(604\) 4.62868 + 2.67237i 0.188338 + 0.108737i
\(605\) 61.6028 + 17.4750i 2.50451 + 0.710460i
\(606\) −5.45084 + 18.8671i −0.221425 + 0.766425i
\(607\) 16.0087 + 4.28953i 0.649774 + 0.174106i 0.568627 0.822596i \(-0.307475\pi\)
0.0811474 + 0.996702i \(0.474142\pi\)
\(608\) −0.407696 1.52154i −0.0165342 0.0617066i
\(609\) −4.16012 0.787393i −0.168577 0.0319068i
\(610\) 27.6367 + 0.403833i 1.11898 + 0.0163507i
\(611\) −30.0390 17.3430i −1.21525 0.701623i
\(612\) 2.87844 + 12.6989i 0.116354 + 0.513324i
\(613\) 7.55823 28.2077i 0.305274 1.13930i −0.627435 0.778669i \(-0.715895\pi\)
0.932709 0.360629i \(-0.117438\pi\)
\(614\) −6.66347 −0.268916
\(615\) 25.4314 + 7.75163i 1.02549 + 0.312576i
\(616\) −1.56660 16.5832i −0.0631201 0.668156i
\(617\) 18.1977 4.87605i 0.732610 0.196302i 0.126819 0.991926i \(-0.459523\pi\)
0.605791 + 0.795624i \(0.292857\pi\)
\(618\) −7.84324 0.152563i −0.315501 0.00613697i
\(619\) −3.20771 1.85197i −0.128929 0.0744370i 0.434148 0.900841i \(-0.357049\pi\)
−0.563077 + 0.826404i \(0.690383\pi\)
\(620\) −4.99016 5.13815i −0.200409 0.206353i
\(621\) 1.92056 5.79265i 0.0770696 0.232451i
\(622\) 14.8697 14.8697i 0.596220 0.596220i
\(623\) −27.2267 22.5266i −1.09082 0.902508i
\(624\) 9.86762 + 2.85082i 0.395021 + 0.114124i
\(625\) −24.9573 1.46028i −0.998293 0.0584114i
\(626\) 0.406255i 0.0162372i
\(627\) 0.334056 17.1738i 0.0133409 0.685856i
\(628\) 16.0894 + 16.0894i 0.642036 + 0.642036i
\(629\) −10.4891 −0.418227
\(630\) 16.9425 5.28699i 0.675005 0.210639i
\(631\) −21.5905 −0.859502 −0.429751 0.902947i \(-0.641399\pi\)
−0.429751 + 0.902947i \(0.641399\pi\)
\(632\) −9.41623 9.41623i −0.374558 0.374558i
\(633\) 3.97180 2.19125i 0.157865 0.0870944i
\(634\) 9.30159i 0.369413i
\(635\) 0.380867 26.0650i 0.0151142 1.03436i
\(636\) −7.65011 + 7.35818i −0.303347 + 0.291771i
\(637\) −41.3986 3.04497i −1.64027 0.120646i
\(638\) 4.11313 4.11313i 0.162840 0.162840i
\(639\) 25.1618 13.2502i 0.995386 0.524170i
\(640\) −0.0326704 + 2.23583i −0.00129141 + 0.0883789i
\(641\) 1.34965 + 0.779223i 0.0533081 + 0.0307774i 0.526417 0.850226i \(-0.323535\pi\)
−0.473109 + 0.881004i \(0.656868\pi\)
\(642\) 0.886171 + 1.60625i 0.0349744 + 0.0633935i
\(643\) 8.46183 2.26734i 0.333702 0.0894152i −0.0880774 0.996114i \(-0.528072\pi\)
0.421780 + 0.906698i \(0.361406\pi\)
\(644\) −2.82525 1.29370i −0.111330 0.0509789i
\(645\) 0.247288 7.25752i 0.00973696 0.285764i
\(646\) 6.83700 0.268998
\(647\) 3.76645 14.0566i 0.148074 0.552621i −0.851525 0.524314i \(-0.824322\pi\)
0.999599 0.0283070i \(-0.00901159\pi\)
\(648\) 1.64670 + 8.84807i 0.0646885 + 0.347585i
\(649\) −45.3867 26.2040i −1.78158 1.02860i
\(650\) −15.5691 + 25.2338i −0.610670 + 0.989752i
\(651\) −9.57551 + 11.1256i −0.375294 + 0.436047i
\(652\) 4.16228 + 15.5338i 0.163007 + 0.608351i
\(653\) −27.7389 7.43262i −1.08551 0.290861i −0.328657 0.944449i \(-0.606596\pi\)
−0.756850 + 0.653588i \(0.773263\pi\)
\(654\) 0.279288 + 0.290369i 0.0109210 + 0.0113543i
\(655\) 3.50420 12.3530i 0.136920 0.482671i
\(656\) 5.94493 + 3.43231i 0.232111 + 0.134009i
\(657\) −17.5147 + 3.97002i −0.683314 + 0.154885i
\(658\) −15.2586 2.58171i −0.594842 0.100646i
\(659\) 9.41467 + 16.3067i 0.366743 + 0.635218i 0.989054 0.147552i \(-0.0471393\pi\)
−0.622311 + 0.782770i \(0.713806\pi\)
\(660\) −7.10927 + 23.3240i −0.276728 + 0.907885i
\(661\) 7.26978 0.282762 0.141381 0.989955i \(-0.454846\pi\)
0.141381 + 0.989955i \(0.454846\pi\)
\(662\) −18.4537 18.4537i −0.717222 0.717222i
\(663\) −23.0369 + 38.1671i −0.894680 + 1.48229i
\(664\) 15.6245 9.02083i 0.606350 0.350076i
\(665\) −0.740816 9.28960i −0.0287276 0.360235i
\(666\) −7.24443 0.281937i −0.280716 0.0109248i
\(667\) −0.280852 1.04816i −0.0108746 0.0405847i
\(668\) −0.856206 3.19541i −0.0331276 0.123634i
\(669\) 31.3247 30.1293i 1.21108 1.16487i
\(670\) −10.2518 + 9.95653i −0.396062 + 0.384654i
\(671\) 67.3949 + 38.9105i 2.60175 + 1.50212i
\(672\) 4.56978 0.342185i 0.176283 0.0132001i
\(673\) 6.42725 23.9868i 0.247752 0.924624i −0.724228 0.689561i \(-0.757804\pi\)
0.971980 0.235063i \(-0.0755297\pi\)
\(674\) 12.7209 22.0332i 0.489990 0.848687i
\(675\) −25.8812 2.27222i −0.996168 0.0874576i
\(676\) 11.0828 + 19.1961i 0.426263 + 0.738310i
\(677\) −12.5245 12.5245i −0.481355 0.481355i 0.424209 0.905564i \(-0.360552\pi\)
−0.905564 + 0.424209i \(0.860552\pi\)
\(678\) 23.0963 12.7423i 0.887010 0.489366i
\(679\) 0.0952151 0.207936i 0.00365402 0.00797984i
\(680\) −9.33694 2.64863i −0.358055 0.101570i
\(681\) 41.6134 + 12.0224i 1.59463 + 0.460699i
\(682\) −5.21949 19.4794i −0.199865 0.745905i
\(683\) −19.4964 5.22405i −0.746010 0.199893i −0.134262 0.990946i \(-0.542866\pi\)
−0.611748 + 0.791053i \(0.709533\pi\)
\(684\) 4.72207 + 0.183772i 0.180553 + 0.00702671i
\(685\) −4.67127 + 7.82459i −0.178480 + 0.298962i
\(686\) −17.7858 + 5.16388i −0.679065 + 0.197158i
\(687\) −15.8753 0.308798i −0.605680 0.0117814i
\(688\) 0.485278 1.81108i 0.0185010 0.0690469i
\(689\) −36.3410 −1.38448
\(690\) 3.10503 + 3.32409i 0.118206 + 0.126546i
\(691\) −34.9314 −1.32885 −0.664427 0.747353i \(-0.731324\pi\)
−0.664427 + 0.747353i \(0.731324\pi\)
\(692\) 4.11813 + 4.11813i 0.156548 + 0.156548i
\(693\) 48.9093 + 10.2462i 1.85791 + 0.389222i
\(694\) 33.6406i 1.27698i
\(695\) 3.50065 0.883386i 0.132787 0.0335087i
\(696\) 1.10936 + 1.15337i 0.0420501 + 0.0437185i
\(697\) −21.0682 + 21.0682i −0.798014 + 0.798014i
\(698\) 18.9396 + 5.07484i 0.716873 + 0.192086i
\(699\) 10.2017 35.3115i 0.385864 1.33560i
\(700\) −2.58706 + 12.9733i −0.0977818 + 0.490346i
\(701\) 26.6507i 1.00658i −0.864117 0.503292i \(-0.832122\pi\)
0.864117 0.503292i \(-0.167878\pi\)
\(702\) −16.9367 + 25.7415i −0.639234 + 0.971549i
\(703\) −0.985252 + 3.67701i −0.0371595 + 0.138681i
\(704\) −3.14788 + 5.45229i −0.118640 + 0.205491i
\(705\) 19.2216 + 11.9884i 0.723929 + 0.451509i
\(706\) 9.56488 16.5669i 0.359979 0.623502i
\(707\) −19.1232 + 23.1133i −0.719203 + 0.869264i
\(708\) 7.45056 12.3439i 0.280009 0.463914i
\(709\) 51.6335i 1.93914i −0.244817 0.969569i \(-0.578728\pi\)
0.244817 0.969569i \(-0.421272\pi\)
\(710\) −0.309687 + 21.1937i −0.0116223 + 0.795386i
\(711\) 35.3481 18.6143i 1.32566 0.698091i
\(712\) 3.45687 + 12.9012i 0.129552 + 0.483494i
\(713\) −3.63387 0.973693i −0.136090 0.0364651i
\(714\) −3.69895 + 19.5431i −0.138430 + 0.731380i
\(715\) −72.8997 + 40.6802i −2.72629 + 1.52135i
\(716\) 5.02957 2.90382i 0.187964 0.108521i
\(717\) −8.99317 + 4.96156i −0.335856 + 0.185293i
\(718\) −12.0115 + 3.21848i −0.448266 + 0.120113i
\(719\) −6.06041 + 10.4969i −0.226015 + 0.391469i −0.956623 0.291327i \(-0.905903\pi\)
0.730608 + 0.682797i \(0.239237\pi\)
\(720\) −6.37749 2.08028i −0.237675 0.0775275i
\(721\) −10.8951 4.98893i −0.405755 0.185798i
\(722\) −4.27535 + 15.9558i −0.159112 + 0.593815i
\(723\) −34.4302 + 18.9952i −1.28047 + 0.706440i
\(724\) 5.33095i 0.198123i
\(725\) −4.06652 + 2.19195i −0.151027 + 0.0814068i
\(726\) −35.7480 + 34.3839i −1.32673 + 1.27610i
\(727\) −28.9765 7.76423i −1.07468 0.287959i −0.322265 0.946649i \(-0.604444\pi\)
−0.752414 + 0.658690i \(0.771111\pi\)
\(728\) 12.0884 + 10.0016i 0.448025 + 0.370682i
\(729\) −26.8164 3.14360i −0.993199 0.116430i
\(730\) 3.65306 12.8778i 0.135206 0.476627i
\(731\) 7.04775 + 4.06902i 0.260671 + 0.150498i
\(732\) −11.0634 + 18.3296i −0.408914 + 0.677480i
\(733\) 1.12373 4.19382i 0.0415059 0.154902i −0.942063 0.335437i \(-0.891116\pi\)
0.983569 + 0.180535i \(0.0577828\pi\)
\(734\) −0.878448 + 1.52152i −0.0324241 + 0.0561602i
\(735\) 26.9544 + 2.90829i 0.994230 + 0.107274i
\(736\) 0.587236 + 1.01712i 0.0216458 + 0.0374916i
\(737\) −38.8660 + 10.4141i −1.43165 + 0.383608i
\(738\) −15.1173 + 13.9847i −0.556477 + 0.514786i
\(739\) 18.6590 10.7728i 0.686382 0.396283i −0.115873 0.993264i \(-0.536967\pi\)
0.802255 + 0.596981i \(0.203633\pi\)
\(740\) 2.76997 4.63982i 0.101826 0.170563i
\(741\) 11.2158 + 11.6608i 0.412024 + 0.428371i
\(742\) −15.1973 + 5.65082i −0.557910 + 0.207448i
\(743\) 4.26833 + 15.9296i 0.156590 + 0.584401i 0.998964 + 0.0455079i \(0.0144906\pi\)
−0.842374 + 0.538893i \(0.818843\pi\)
\(744\) 5.38596 1.33146i 0.197459 0.0488137i
\(745\) 17.1790 + 4.87320i 0.629390 + 0.178540i
\(746\) −10.9446 + 6.31886i −0.400710 + 0.231350i
\(747\) 11.9649 + 52.7860i 0.437772 + 1.93134i
\(748\) −19.3223 19.3223i −0.706494 0.706494i
\(749\) 0.263550 + 2.78980i 0.00962989 + 0.101937i
\(750\) 10.7236 16.1246i 0.391572 0.588788i
\(751\) −8.13144 14.0841i −0.296721 0.513935i 0.678663 0.734450i \(-0.262560\pi\)
−0.975384 + 0.220515i \(0.929226\pi\)
\(752\) 4.13599 + 4.13599i 0.150824 + 0.150824i
\(753\) 7.04676 11.6749i 0.256798 0.425458i
\(754\) 5.47897i 0.199532i
\(755\) −2.92420 11.5879i −0.106423 0.421728i
\(756\) −3.08003 + 13.3983i −0.112020 + 0.487290i
\(757\) 17.7496 17.7496i 0.645121 0.645121i −0.306689 0.951810i \(-0.599221\pi\)
0.951810 + 0.306689i \(0.0992212\pi\)
\(758\) 16.9500 16.9500i 0.615651 0.615651i
\(759\) 3.07352 + 12.4329i 0.111562 + 0.451284i
\(760\) −1.80552 + 3.02433i −0.0654932 + 0.109704i
\(761\) 31.2162 18.0227i 1.13159 0.653321i 0.187252 0.982312i \(-0.440042\pi\)
0.944333 + 0.328991i \(0.106709\pi\)
\(762\) 17.2871 + 10.4342i 0.626247 + 0.377990i
\(763\) 0.214483 + 0.576831i 0.00776482 + 0.0208827i
\(764\) −1.31228 −0.0474766
\(765\) 15.8858 24.4005i 0.574351 0.882202i
\(766\) 7.60048 + 13.1644i 0.274616 + 0.475650i
\(767\) 47.6818 12.7763i 1.72169 0.461326i
\(768\) −1.48287 0.895033i −0.0535086 0.0322967i
\(769\) 8.44111 + 4.87348i 0.304394 + 0.175742i 0.644415 0.764676i \(-0.277101\pi\)
−0.340021 + 0.940418i \(0.610434\pi\)
\(770\) −24.1601 + 28.3474i −0.870669 + 1.02157i
\(771\) −17.3742 + 16.7112i −0.625718 + 0.601840i
\(772\) 0.459893 0.459893i 0.0165519 0.0165519i
\(773\) −18.7358 5.02024i −0.673880 0.180566i −0.0943779 0.995536i \(-0.530086\pi\)
−0.579502 + 0.814971i \(0.696753\pi\)
\(774\) 4.75826 + 2.99976i 0.171032 + 0.107824i
\(775\) −0.467957 + 16.0091i −0.0168095 + 0.575065i
\(776\) −0.0748593 + 0.0432200i −0.00268729 + 0.00155151i
\(777\) −9.97742 4.80560i −0.357938 0.172400i
\(778\) 8.62873 2.31206i 0.309355 0.0828915i
\(779\) 5.40662 + 9.36455i 0.193712 + 0.335520i
\(780\) −10.7995 20.2696i −0.386685 0.725767i
\(781\) −29.8392 + 51.6830i −1.06773 + 1.84936i
\(782\) −4.92393 + 1.31936i −0.176079 + 0.0471803i
\(783\) −4.29059 + 2.15391i −0.153333 + 0.0769743i
\(784\) 6.61037 + 2.30284i 0.236085 + 0.0822442i
\(785\) 0.743376 50.8737i 0.0265322 1.81576i
\(786\) 6.89487 + 7.16842i 0.245932 + 0.255689i
\(787\) 4.70519 4.70519i 0.167722 0.167722i −0.618255 0.785977i \(-0.712160\pi\)
0.785977 + 0.618255i \(0.212160\pi\)
\(788\) 4.43627 4.43627i 0.158036 0.158036i
\(789\) 2.60148 9.00458i 0.0926152 0.320572i
\(790\) −0.435057 + 29.7736i −0.0154786 + 1.05930i
\(791\) 40.1147 3.78960i 1.42632 0.134743i
\(792\) −12.8259 13.8646i −0.455747 0.492657i
\(793\) −70.8029 + 18.9716i −2.51429 + 0.673701i
\(794\) −3.58011 + 6.20094i −0.127053 + 0.220063i
\(795\) 23.7209 + 0.808252i 0.841294 + 0.0286657i
\(796\) −4.48002 7.75962i −0.158790 0.275032i
\(797\) −25.4066 + 6.80768i −0.899948 + 0.241140i −0.678994 0.734144i \(-0.737584\pi\)
−0.220954 + 0.975284i \(0.570917\pi\)
\(798\) 6.50349 + 3.13239i 0.230221 + 0.110886i
\(799\) −21.9862 + 12.6938i −0.777817 + 0.449073i
\(800\) 3.63733 3.43072i 0.128599 0.121294i
\(801\) −40.0387 1.55821i −1.41470 0.0550568i
\(802\) 6.10922 + 1.63696i 0.215724 + 0.0578031i
\(803\) 26.6499 26.6499i 0.940453 0.940453i
\(804\) −2.65657 10.7463i −0.0936901 0.378991i
\(805\) 2.32618 + 6.54731i 0.0819871 + 0.230762i
\(806\) 16.4503 + 9.49758i 0.579437 + 0.334538i
\(807\) 0.944425 48.5528i 0.0332453 1.70914i
\(808\) 10.9521 2.93460i 0.385293 0.103239i
\(809\) −21.7494 37.6710i −0.764667 1.32444i −0.940422 0.340009i \(-0.889570\pi\)
0.175755 0.984434i \(-0.443763\pi\)
\(810\) 11.6276 16.4256i 0.408552 0.577135i
\(811\) −0.175349 −0.00615732 −0.00307866 0.999995i \(-0.500980\pi\)
−0.00307866 + 0.999995i \(0.500980\pi\)
\(812\) 0.851948 + 2.29123i 0.0298975 + 0.0804063i
\(813\) 13.3441 7.36196i 0.467997 0.258195i
\(814\) 13.1762 7.60729i 0.461826 0.266635i
\(815\) 18.4331 30.8762i 0.645683 1.08155i
\(816\) 5.41821 5.21145i 0.189675 0.182437i
\(817\) 2.08843 2.08843i 0.0730648 0.0730648i
\(818\) 4.34034 4.34034i 0.151757 0.151757i
\(819\) −39.3996 + 25.7509i −1.37673 + 0.899810i
\(820\) −3.75576 14.8832i −0.131157 0.519743i
\(821\) 9.65918i 0.337108i −0.985692 0.168554i \(-0.946090\pi\)
0.985692 0.168554i \(-0.0539097\pi\)
\(822\) −3.40986 6.18061i −0.118932 0.215573i
\(823\) −0.382332 0.382332i −0.0133273 0.0133273i 0.700412 0.713739i \(-0.253000\pi\)
−0.713739 + 0.700412i \(0.753000\pi\)
\(824\) 2.26458 + 3.92236i 0.0788903 + 0.136642i
\(825\) 48.4886 24.9319i 1.68816 0.868018i
\(826\) 17.9532 12.7571i 0.624672 0.443877i
\(827\) −10.0375 10.0375i −0.349039 0.349039i 0.510713 0.859751i \(-0.329382\pi\)
−0.859751 + 0.510713i \(0.829382\pi\)
\(828\) −3.43625 + 0.778886i −0.119418 + 0.0270682i
\(829\) −10.9598 + 6.32766i −0.380651 + 0.219769i −0.678101 0.734968i \(-0.737197\pi\)
0.297451 + 0.954737i \(0.403864\pi\)
\(830\) −38.8110 11.0096i −1.34715 0.382149i
\(831\) 6.49478 22.4805i 0.225301 0.779842i
\(832\) −1.53481 5.72800i −0.0532101 0.198583i
\(833\) −17.0804 + 25.1268i −0.591802 + 0.870592i
\(834\) −0.776210 + 2.68672i −0.0268780 + 0.0930334i
\(835\) −3.79180 + 6.35144i −0.131221 + 0.219801i
\(836\) −8.58853 + 4.95859i −0.297041 + 0.171496i
\(837\) −0.970596 + 16.6160i −0.0335487 + 0.574332i
\(838\) −30.7512 + 8.23976i −1.06228 + 0.284638i
\(839\) 27.0536 + 46.8582i 0.933994 + 1.61772i 0.776419 + 0.630217i \(0.217034\pi\)
0.157575 + 0.987507i \(0.449632\pi\)
\(840\) −7.66801 6.79718i −0.264571 0.234525i
\(841\) 14.0732 24.3755i 0.485282 0.840533i
\(842\) 2.08932 7.79743i 0.0720026 0.268717i
\(843\) 28.8910 + 0.561973i 0.995058 + 0.0193554i
\(844\) −2.26808 1.30948i −0.0780705 0.0450740i
\(845\) 13.5262 47.6826i 0.465316 1.64033i
\(846\) −15.5263 + 8.17616i −0.533805 + 0.281102i
\(847\) −71.0151 + 26.4056i −2.44011 + 0.907306i
\(848\) 5.91945 + 1.58611i 0.203275 + 0.0544673i
\(849\) −5.70972 23.0967i −0.195957 0.792677i
\(850\) 10.2971 + 19.1033i 0.353189 + 0.655239i
\(851\) 2.83827i 0.0972947i
\(852\) −14.0564 8.48414i −0.481563 0.290662i
\(853\) 9.62299 35.9135i 0.329485 1.22965i −0.580241 0.814445i \(-0.697042\pi\)
0.909726 0.415210i \(-0.136292\pi\)
\(854\) −26.6588 + 18.9431i −0.912246 + 0.648219i
\(855\) −7.06158 7.86083i −0.241501 0.268835i
\(856\) 0.529570 0.917241i 0.0181003 0.0313507i
\(857\) −29.6840 + 7.95381i −1.01399 + 0.271697i −0.727294 0.686326i \(-0.759222\pi\)
−0.286693 + 0.958023i \(0.592556\pi\)
\(858\) 1.25759 64.6527i 0.0429335 2.20721i
\(859\) −32.1032 + 18.5348i −1.09535 + 0.632398i −0.934995 0.354662i \(-0.884596\pi\)
−0.160351 + 0.987060i \(0.551263\pi\)
\(860\) −3.66110 + 2.04301i −0.124843 + 0.0696660i
\(861\) −29.6930 + 10.3880i −1.01193 + 0.354023i
\(862\) −23.5254 6.30361i −0.801278 0.214702i
\(863\) −0.0278709 0.104015i −0.000948735 0.00354073i 0.965450 0.260589i \(-0.0839167\pi\)
−0.966399 + 0.257048i \(0.917250\pi\)
\(864\) 3.88224 3.45372i 0.132077 0.117498i
\(865\) 0.190270 13.0213i 0.00646937 0.442737i
\(866\) 26.3446i 0.895224i
\(867\) 1.53844 + 2.78853i 0.0522481 + 0.0947033i
\(868\) 8.35609 + 1.41383i 0.283624 + 0.0479884i
\(869\) −41.9190 + 72.6058i −1.42200 + 2.46298i
\(870\) 0.121856 3.57629i 0.00413132 0.121248i
\(871\) 18.9499 32.8222i 0.642093 1.11214i
\(872\) 0.0602028 0.224680i 0.00203872 0.00760862i
\(873\) −0.0573253 0.252905i −0.00194017 0.00855953i
\(874\) 1.85004i 0.0625787i
\(875\) 24.8404 16.0609i 0.839760 0.542957i
\(876\) 7.18777 + 7.47294i 0.242852 + 0.252487i
\(877\) 37.6779 + 10.0958i 1.27229 + 0.340910i 0.830909 0.556408i \(-0.187821\pi\)
0.441384 + 0.897318i \(0.354488\pi\)
\(878\) 9.26690 9.26690i 0.312743 0.312743i
\(879\) −2.70319 + 9.35662i −0.0911763 + 0.315591i
\(880\) 13.6499 3.44453i 0.460136 0.116115i
\(881\) 36.5900i 1.23275i 0.787454 + 0.616374i \(0.211399\pi\)
−0.787454 + 0.616374i \(0.788601\pi\)
\(882\) −12.4722 + 16.8951i −0.419962 + 0.568887i
\(883\) 11.2799 + 11.2799i 0.379597 + 0.379597i 0.870957 0.491360i \(-0.163500\pi\)
−0.491360 + 0.870957i \(0.663500\pi\)
\(884\) 25.7386 0.865683
\(885\) −31.4076 + 7.27901i −1.05575 + 0.244681i
\(886\) 2.67230 0.0897778
\(887\) 1.04693 3.90720i 0.0351525 0.131191i −0.946120 0.323817i \(-0.895034\pi\)
0.981272 + 0.192626i \(0.0617004\pi\)
\(888\) 2.02198 + 3.66497i 0.0678531 + 0.122988i
\(889\) 17.8658 + 25.1427i 0.599199 + 0.843259i
\(890\) 15.3091 25.6435i 0.513163 0.859571i
\(891\) 51.1240 24.4316i 1.71272 0.818489i
\(892\) −24.2382 6.49461i −0.811555 0.217456i
\(893\) 2.38468 + 8.89976i 0.0798004 + 0.297819i
\(894\) −9.96895 + 9.58853i −0.333412 + 0.320688i
\(895\) −12.4933 3.54401i −0.417606 0.118463i
\(896\) −1.53251 2.15671i −0.0511975 0.0720508i
\(897\) −10.3278 6.23363i −0.344834 0.208135i
\(898\) 11.1288 + 11.1288i 0.371374 + 0.371374i
\(899\) 1.47976 + 2.56303i 0.0493529 + 0.0854817i
\(900\) 6.59838 + 13.4708i 0.219946 + 0.449025i
\(901\) −13.2994 + 23.0353i −0.443069 + 0.767417i
\(902\) 11.1856 41.7454i 0.372441 1.38997i
\(903\) 4.83973 + 7.09949i 0.161056 + 0.236256i
\(904\) −13.1891 7.61472i −0.438662 0.253262i
\(905\) 8.55123 8.30492i 0.284252 0.276065i
\(906\) 8.89363 + 2.56943i 0.295471 + 0.0853635i
\(907\) 14.0850 + 52.5659i 0.467685 + 1.74542i 0.647832 + 0.761783i \(0.275676\pi\)
−0.180147 + 0.983640i \(0.557657\pi\)
\(908\) −6.47257 24.1560i −0.214800 0.801644i
\(909\) −1.32280 + 33.9896i −0.0438744 + 1.12736i
\(910\) −2.78888 34.9717i −0.0924505 1.15930i
\(911\) −22.5707 + 13.0312i −0.747800 + 0.431743i −0.824899 0.565281i \(-0.808768\pi\)
0.0770981 + 0.997024i \(0.475435\pi\)
\(912\) −1.31797 2.38891i −0.0436422 0.0791046i
\(913\) −80.3175 80.3175i −2.65812 2.65812i
\(914\) −9.33057 −0.308628
\(915\) 46.6372 10.8086i 1.54178 0.357322i
\(916\) 4.58366 + 7.93914i 0.151449 + 0.262317i
\(917\) 5.29501 + 14.2404i 0.174857 + 0.470259i
\(918\) 10.1184 + 20.1560i 0.333958 + 0.665246i
\(919\) −25.4695 14.7048i −0.840160 0.485067i 0.0171585 0.999853i \(-0.494538\pi\)
−0.857319 + 0.514786i \(0.827871\pi\)
\(920\) 0.716701 2.52651i 0.0236289 0.0832966i
\(921\) −11.2042 + 2.76978i −0.369191 + 0.0912674i
\(922\) 25.8717 + 6.93229i 0.852038 + 0.228303i
\(923\) −14.5487 54.2965i −0.478876 1.78719i
\(924\) −9.52720 27.2324i −0.313422 0.895879i
\(925\) −11.7579 + 2.78500i −0.386596 + 0.0915704i
\(926\) 35.9157 + 20.7359i 1.18026 + 0.681425i
\(927\) −13.2513 + 3.00364i −0.435230 + 0.0986526i
\(928\) 0.239131 0.892448i 0.00784985 0.0292961i
\(929\) −57.0607 −1.87210 −0.936051 0.351865i \(-0.885548\pi\)
−0.936051 + 0.351865i \(0.885548\pi\)
\(930\) −10.5264 6.56523i −0.345173 0.215282i
\(931\) 7.20397 + 8.34785i 0.236101 + 0.273590i
\(932\) −20.4978 + 5.49236i −0.671427 + 0.179908i
\(933\) 18.8216 31.1832i 0.616191 1.02089i
\(934\) −21.1982 12.2388i −0.693627 0.400466i
\(935\) −0.892747 + 61.0960i −0.0291959 + 1.99805i
\(936\) 17.7767 + 0.691830i 0.581051 + 0.0226132i
\(937\) 31.6113 31.6113i 1.03270 1.03270i 0.0332500 0.999447i \(-0.489414\pi\)
0.999447 0.0332500i \(-0.0105857\pi\)
\(938\) 2.82092 16.6724i 0.0921062 0.544372i
\(939\) −0.168866 0.683091i −0.00551074 0.0222918i
\(940\) 0.191095 13.0778i 0.00623283 0.426549i
\(941\) 0.882115i 0.0287561i 0.999897 + 0.0143781i \(0.00457684\pi\)
−0.999897 + 0.0143781i \(0.995423\pi\)
\(942\) 33.7411 + 20.3654i 1.09934 + 0.663542i
\(943\) −5.70091 5.70091i −0.185647 0.185647i
\(944\) −8.32434 −0.270934
\(945\) 26.2901 15.9321i 0.855215 0.518273i
\(946\) −11.8044 −0.383793
\(947\) −3.71719 3.71719i −0.120793 0.120793i 0.644126 0.764919i \(-0.277221\pi\)
−0.764919 + 0.644126i \(0.777221\pi\)
\(948\) −19.7468 11.9188i −0.641346 0.387104i
\(949\) 35.4994i 1.15236i
\(950\) 7.66402 1.81532i 0.248653 0.0588969i
\(951\) −3.86636 15.6400i −0.125375 0.507162i
\(952\) 10.7635 4.00220i 0.348848 0.129712i
\(953\) −3.95814 + 3.95814i −0.128217 + 0.128217i −0.768303 0.640086i \(-0.778899\pi\)
0.640086 + 0.768303i \(0.278899\pi\)
\(954\) −9.80462 + 15.5522i −0.317436 + 0.503521i
\(955\) 2.04436 + 2.10499i 0.0661538 + 0.0681158i
\(956\) 5.13552 + 2.96499i 0.166094 + 0.0958947i
\(957\) 5.20627 8.62565i 0.168295 0.278828i
\(958\) −3.23165 + 0.865918i −0.104410 + 0.0279765i
\(959\) −1.01410 10.7347i −0.0327470 0.346643i
\(960\) 0.874425 + 3.77298i 0.0282220 + 0.121772i
\(961\) −20.7395 −0.669018
\(962\) −3.70909 + 13.8425i −0.119586 + 0.446300i
\(963\) 2.15770 + 2.33245i 0.0695309 + 0.0751621i
\(964\) 19.6612 + 11.3514i 0.633245 + 0.365604i
\(965\) −1.45415 0.0212484i −0.0468109 0.000684010i
\(966\) −5.28822 1.00091i −0.170146 0.0322037i
\(967\) −2.59154 9.67174i −0.0833382 0.311022i 0.911656 0.410954i \(-0.134804\pi\)
−0.994994 + 0.0999316i \(0.968138\pi\)
\(968\) 27.6609 + 7.41171i 0.889054 + 0.238221i
\(969\) 11.4960 2.84191i 0.369304 0.0912952i
\(970\) 0.185949 + 0.0527485i 0.00597046 + 0.00169365i
\(971\) −35.9311 20.7448i −1.15308 0.665733i −0.203447 0.979086i \(-0.565214\pi\)
−0.949637 + 0.313353i \(0.898548\pi\)
\(972\) 6.44666 + 14.1930i 0.206777 + 0.455240i
\(973\) −2.72319 + 3.29138i −0.0873013 + 0.105517i
\(974\) −6.95365 12.0441i −0.222809 0.385917i
\(975\) −15.6896 + 48.9006i −0.502469 + 1.56607i
\(976\) 12.3608 0.395661
\(977\) 22.6090 + 22.6090i 0.723327 + 0.723327i 0.969281 0.245955i \(-0.0791014\pi\)
−0.245955 + 0.969281i \(0.579101\pi\)
\(978\) 13.4555 + 24.3890i 0.430259 + 0.779874i
\(979\) 72.8226 42.0441i 2.32742 1.34374i
\(980\) −6.60417 14.1910i −0.210962 0.453315i
\(981\) 0.590302 + 0.372146i 0.0188469 + 0.0118817i
\(982\) 9.33903 + 34.8537i 0.298020 + 1.11223i
\(983\) 4.32878 + 16.1552i 0.138067 + 0.515271i 0.999966 + 0.00819281i \(0.00260788\pi\)
−0.861900 + 0.507078i \(0.830725\pi\)
\(984\) 11.4227 + 3.30010i 0.364143 + 0.105203i
\(985\) −14.0272 0.204969i −0.446944 0.00653084i
\(986\) 3.47293 + 2.00510i 0.110601 + 0.0638552i
\(987\) −26.7295 + 2.00150i −0.850808 + 0.0637085i
\(988\) 2.41766 9.02284i 0.0769161 0.287055i
\(989\) −1.10105 + 1.90707i −0.0350113 + 0.0606414i
\(990\) −2.25879 + 42.1728i −0.0717891 + 1.34034i
\(991\) −20.4353 35.3951i −0.649150 1.12436i −0.983326 0.181850i \(-0.941791\pi\)
0.334176 0.942511i \(-0.391542\pi\)
\(992\) −2.26500 2.26500i −0.0719138 0.0719138i
\(993\) −38.6992 23.3580i −1.22808 0.741245i
\(994\) −14.5268 20.4438i −0.460763 0.648437i
\(995\) −5.46770 + 19.2747i −0.173338 + 0.611050i
\(996\) 22.5220 21.6625i 0.713636 0.686404i
\(997\) −0.752943 2.81002i −0.0238459 0.0889943i 0.952977 0.303041i \(-0.0980021\pi\)
−0.976823 + 0.214047i \(0.931335\pi\)
\(998\) 34.5034 + 9.24516i 1.09219 + 0.292650i
\(999\) −12.2982 + 2.53720i −0.389098 + 0.0802736i
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 630.2.cd.a.23.5 yes 192
5.2 odd 4 inner 630.2.cd.a.527.32 yes 192
7.4 even 3 630.2.bt.a.473.36 yes 192
9.2 odd 6 630.2.bt.a.443.48 yes 192
35.32 odd 12 630.2.bt.a.347.48 yes 192
45.2 even 12 630.2.bt.a.317.36 192
63.11 odd 6 inner 630.2.cd.a.263.32 yes 192
315.137 even 12 inner 630.2.cd.a.137.5 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.bt.a.317.36 192 45.2 even 12
630.2.bt.a.347.48 yes 192 35.32 odd 12
630.2.bt.a.443.48 yes 192 9.2 odd 6
630.2.bt.a.473.36 yes 192 7.4 even 3
630.2.cd.a.23.5 yes 192 1.1 even 1 trivial
630.2.cd.a.137.5 yes 192 315.137 even 12 inner
630.2.cd.a.263.32 yes 192 63.11 odd 6 inner
630.2.cd.a.527.32 yes 192 5.2 odd 4 inner