Properties

Label 350.2.q.c.81.10
Level $350$
Weight $2$
Character 350.81
Analytic conductor $2.795$
Analytic rank $0$
Dimension $80$
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] = [350,2,Mod(11,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([24, 20]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.q (of order \(15\), degree \(8\), 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: \(2.79476407074\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 81.10
Character \(\chi\) \(=\) 350.81
Dual form 350.2.q.c.121.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.669131 - 0.743145i) q^{2} +(0.306337 + 2.91460i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(0.374350 - 2.20451i) q^{5} +(2.37095 + 1.72260i) q^{6} +(2.62131 - 0.358777i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-5.46662 + 1.16197i) q^{9} +O(q^{10})\) \(q+(0.669131 - 0.743145i) q^{2} +(0.306337 + 2.91460i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(0.374350 - 2.20451i) q^{5} +(2.37095 + 1.72260i) q^{6} +(2.62131 - 0.358777i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-5.46662 + 1.16197i) q^{9} +(-1.38778 - 1.75330i) q^{10} +(5.82141 + 1.23738i) q^{11} +(2.86661 - 0.609318i) q^{12} +(0.457017 - 1.40655i) q^{13} +(1.48738 - 2.18808i) q^{14} +(6.53995 + 0.415758i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-5.90587 + 2.62946i) q^{17} +(-2.79437 + 4.84000i) q^{18} +(-0.362756 + 3.45139i) q^{19} +(-2.23156 - 0.141865i) q^{20} +(1.84870 + 7.53018i) q^{21} +(4.81484 - 3.49818i) q^{22} +(-0.804009 + 0.892943i) q^{23} +(1.46533 - 2.53802i) q^{24} +(-4.71972 - 1.65052i) q^{25} +(-0.739468 - 1.28080i) q^{26} +(-2.34443 - 7.21541i) q^{27} +(-0.630814 - 2.56945i) q^{28} +(5.66526 - 4.11605i) q^{29} +(4.68505 - 4.58193i) q^{30} +(-2.43917 + 1.08599i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.82315 + 17.3462i) q^{33} +(-1.99773 + 6.14837i) q^{34} +(0.190360 - 5.91302i) q^{35} +(1.72702 + 5.31522i) q^{36} +(1.37237 - 0.291705i) q^{37} +(2.32215 + 2.57901i) q^{38} +(4.23954 + 0.901142i) q^{39} +(-1.59863 + 1.56345i) q^{40} +(1.36788 - 4.20992i) q^{41} +(6.83303 + 3.66482i) q^{42} -7.31280 q^{43} +(0.622098 - 5.91886i) q^{44} +(0.515136 + 12.4862i) q^{45} +(0.125599 + 1.19499i) q^{46} +(-5.66313 - 2.52139i) q^{47} +(-0.905623 - 2.78722i) q^{48} +(6.74256 - 1.88093i) q^{49} +(-4.38468 + 2.40303i) q^{50} +(-9.47303 - 16.4078i) q^{51} +(-1.44662 - 0.307488i) q^{52} +(-1.00080 - 9.52195i) q^{53} +(-6.93082 - 3.08580i) q^{54} +(4.90706 - 12.3701i) q^{55} +(-2.33157 - 1.25051i) q^{56} -10.1705 q^{57} +(0.731975 - 6.96428i) q^{58} +(-4.07903 - 4.53022i) q^{59} +(-0.270130 - 6.54758i) q^{60} +(-5.87475 + 6.52457i) q^{61} +(-0.825077 + 2.53933i) q^{62} +(-13.9128 + 5.00718i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-2.92967 - 1.53404i) q^{65} +(11.6708 + 12.9617i) q^{66} +(-7.56908 + 3.36997i) q^{67} +(3.23239 + 5.59867i) q^{68} +(-2.84887 - 2.06983i) q^{69} +(-4.26685 - 4.09805i) q^{70} +(8.21420 - 5.96797i) q^{71} +(5.10558 + 2.27315i) q^{72} +(0.344740 + 0.0732768i) q^{73} +(0.701513 - 1.21506i) q^{74} +(3.36477 - 14.2617i) q^{75} +3.47040 q^{76} +(15.7037 + 1.15497i) q^{77} +(3.50649 - 2.54761i) q^{78} +(-9.52004 - 4.23860i) q^{79} +(0.0921738 + 2.23417i) q^{80} +(4.99514 - 2.22398i) q^{81} +(-2.21328 - 3.83352i) q^{82} +(4.84131 + 3.51741i) q^{83} +(7.29568 - 2.62569i) q^{84} +(3.58581 + 14.0039i) q^{85} +(-4.89322 + 5.43447i) q^{86} +(13.7321 + 15.2511i) q^{87} +(-3.98231 - 4.42280i) q^{88} +(-0.714003 + 0.792981i) q^{89} +(9.62375 + 7.97208i) q^{90} +(0.693344 - 3.85098i) q^{91} +(0.972093 + 0.706267i) q^{92} +(-3.91244 - 6.77654i) q^{93} +(-5.66313 + 2.52139i) q^{94} +(7.47282 + 2.09173i) q^{95} +(-2.67729 - 1.19201i) q^{96} +(-8.61836 + 6.26160i) q^{97} +(3.11385 - 6.26929i) q^{98} -33.2612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 20 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 20 q^{8} + 4 q^{9} + 3 q^{10} + 10 q^{11} + 2 q^{12} - 12 q^{13} - 7 q^{14} + 22 q^{15} + 10 q^{16} - 8 q^{17} - 36 q^{18} + 8 q^{19} + 4 q^{20} + 17 q^{21} + 20 q^{22} + 5 q^{23} - 8 q^{24} + 32 q^{25} - 24 q^{26} + 32 q^{27} - 7 q^{28} + 12 q^{29} - 11 q^{30} - 9 q^{31} - 40 q^{32} + 33 q^{33} - 4 q^{34} - 22 q^{35} - 8 q^{36} - 14 q^{37} - 2 q^{38} - 2 q^{40} - 18 q^{41} - 19 q^{42} - 8 q^{43} - 10 q^{44} + 33 q^{45} - 10 q^{46} + 10 q^{47} - 4 q^{48} + 12 q^{49} + 36 q^{50} + 46 q^{51} + 6 q^{52} - 30 q^{53} + 14 q^{54} + 2 q^{55} - q^{56} - 52 q^{57} - 6 q^{58} + 40 q^{59} + 4 q^{60} + 16 q^{61} - 32 q^{62} - 100 q^{63} - 20 q^{64} - 25 q^{65} - 7 q^{66} + q^{67} + 12 q^{68} - 142 q^{69} + 25 q^{70} - 84 q^{71} + 14 q^{72} + 22 q^{73} + 6 q^{74} - 29 q^{75} + 24 q^{76} + 38 q^{77} - 30 q^{78} + 10 q^{79} + 3 q^{80} + 52 q^{81} - 6 q^{82} - 98 q^{83} + 2 q^{84} - 36 q^{85} - 26 q^{86} + 34 q^{87} + 10 q^{88} + 45 q^{89} + 24 q^{90} - 63 q^{91} + 20 q^{92} - 20 q^{93} + 10 q^{94} - 33 q^{95} + 2 q^{96} - 106 q^{97} - 55 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.669131 0.743145i 0.473147 0.525483i
\(3\) 0.306337 + 2.91460i 0.176864 + 1.68275i 0.618682 + 0.785642i \(0.287667\pi\)
−0.441818 + 0.897105i \(0.645666\pi\)
\(4\) −0.104528 0.994522i −0.0522642 0.497261i
\(5\) 0.374350 2.20451i 0.167414 0.985887i
\(6\) 2.37095 + 1.72260i 0.967937 + 0.703247i
\(7\) 2.62131 0.358777i 0.990763 0.135605i
\(8\) −0.809017 0.587785i −0.286031 0.207813i
\(9\) −5.46662 + 1.16197i −1.82221 + 0.387322i
\(10\) −1.38778 1.75330i −0.438855 0.554442i
\(11\) 5.82141 + 1.23738i 1.75522 + 0.373084i 0.969423 0.245397i \(-0.0789185\pi\)
0.785799 + 0.618481i \(0.212252\pi\)
\(12\) 2.86661 0.609318i 0.827520 0.175895i
\(13\) 0.457017 1.40655i 0.126754 0.390107i −0.867463 0.497502i \(-0.834251\pi\)
0.994216 + 0.107394i \(0.0342508\pi\)
\(14\) 1.48738 2.18808i 0.397518 0.584790i
\(15\) 6.53995 + 0.415758i 1.68861 + 0.107348i
\(16\) −0.978148 + 0.207912i −0.244537 + 0.0519779i
\(17\) −5.90587 + 2.62946i −1.43238 + 0.637739i −0.968694 0.248258i \(-0.920142\pi\)
−0.463691 + 0.885997i \(0.653475\pi\)
\(18\) −2.79437 + 4.84000i −0.658640 + 1.14080i
\(19\) −0.362756 + 3.45139i −0.0832218 + 0.791803i 0.870714 + 0.491791i \(0.163657\pi\)
−0.953935 + 0.300012i \(0.903009\pi\)
\(20\) −2.23156 0.141865i −0.498993 0.0317220i
\(21\) 1.84870 + 7.53018i 0.403419 + 1.64322i
\(22\) 4.81484 3.49818i 1.02653 0.745815i
\(23\) −0.804009 + 0.892943i −0.167648 + 0.186191i −0.821114 0.570764i \(-0.806647\pi\)
0.653467 + 0.756955i \(0.273314\pi\)
\(24\) 1.46533 2.53802i 0.299109 0.518072i
\(25\) −4.71972 1.65052i −0.943945 0.330103i
\(26\) −0.739468 1.28080i −0.145022 0.251185i
\(27\) −2.34443 7.21541i −0.451186 1.38861i
\(28\) −0.630814 2.56945i −0.119213 0.485580i
\(29\) 5.66526 4.11605i 1.05201 0.764331i 0.0794175 0.996841i \(-0.474694\pi\)
0.972594 + 0.232510i \(0.0746940\pi\)
\(30\) 4.68505 4.58193i 0.855369 0.836542i
\(31\) −2.43917 + 1.08599i −0.438088 + 0.195049i −0.613916 0.789372i \(-0.710407\pi\)
0.175828 + 0.984421i \(0.443740\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −1.82315 + 17.3462i −0.317370 + 3.01958i
\(34\) −1.99773 + 6.14837i −0.342607 + 1.05444i
\(35\) 0.190360 5.91302i 0.0321768 0.999482i
\(36\) 1.72702 + 5.31522i 0.287836 + 0.885869i
\(37\) 1.37237 0.291705i 0.225616 0.0479561i −0.0937166 0.995599i \(-0.529875\pi\)
0.319332 + 0.947643i \(0.396541\pi\)
\(38\) 2.32215 + 2.57901i 0.376703 + 0.418371i
\(39\) 4.23954 + 0.901142i 0.678870 + 0.144298i
\(40\) −1.59863 + 1.56345i −0.252766 + 0.247203i
\(41\) 1.36788 4.20992i 0.213628 0.657478i −0.785621 0.618709i \(-0.787656\pi\)
0.999248 0.0387697i \(-0.0123439\pi\)
\(42\) 6.83303 + 3.66482i 1.05436 + 0.565494i
\(43\) −7.31280 −1.11519 −0.557596 0.830113i \(-0.688276\pi\)
−0.557596 + 0.830113i \(0.688276\pi\)
\(44\) 0.622098 5.91886i 0.0937848 0.892302i
\(45\) 0.515136 + 12.4862i 0.0767919 + 1.86133i
\(46\) 0.125599 + 1.19499i 0.0185185 + 0.176192i
\(47\) −5.66313 2.52139i −0.826053 0.367782i −0.0502334 0.998738i \(-0.515997\pi\)
−0.775819 + 0.630955i \(0.782663\pi\)
\(48\) −0.905623 2.78722i −0.130715 0.402301i
\(49\) 6.74256 1.88093i 0.963223 0.268705i
\(50\) −4.38468 + 2.40303i −0.620088 + 0.339839i
\(51\) −9.47303 16.4078i −1.32649 2.29755i
\(52\) −1.44662 0.307488i −0.200610 0.0426409i
\(53\) −1.00080 9.52195i −0.137470 1.30794i −0.817999 0.575220i \(-0.804917\pi\)
0.680529 0.732721i \(-0.261750\pi\)
\(54\) −6.93082 3.08580i −0.943166 0.419924i
\(55\) 4.90706 12.3701i 0.661668 1.66799i
\(56\) −2.33157 1.25051i −0.311569 0.167107i
\(57\) −10.1705 −1.34712
\(58\) 0.731975 6.96428i 0.0961131 0.914455i
\(59\) −4.07903 4.53022i −0.531044 0.589784i 0.416609 0.909086i \(-0.363218\pi\)
−0.947653 + 0.319302i \(0.896552\pi\)
\(60\) −0.270130 6.54758i −0.0348736 0.845289i
\(61\) −5.87475 + 6.52457i −0.752185 + 0.835386i −0.990744 0.135742i \(-0.956658\pi\)
0.238559 + 0.971128i \(0.423325\pi\)
\(62\) −0.825077 + 2.53933i −0.104785 + 0.322495i
\(63\) −13.9128 + 5.00718i −1.75285 + 0.630845i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) −2.92967 1.53404i −0.363381 0.190274i
\(66\) 11.6708 + 12.9617i 1.43657 + 1.59548i
\(67\) −7.56908 + 3.36997i −0.924710 + 0.411707i −0.813153 0.582051i \(-0.802251\pi\)
−0.111557 + 0.993758i \(0.535584\pi\)
\(68\) 3.23239 + 5.59867i 0.391985 + 0.678938i
\(69\) −2.84887 2.06983i −0.342964 0.249178i
\(70\) −4.26685 4.09805i −0.509986 0.489810i
\(71\) 8.21420 5.96797i 0.974847 0.708268i 0.0182957 0.999833i \(-0.494176\pi\)
0.956551 + 0.291565i \(0.0941760\pi\)
\(72\) 5.10558 + 2.27315i 0.601698 + 0.267893i
\(73\) 0.344740 + 0.0732768i 0.0403488 + 0.00857640i 0.228042 0.973651i \(-0.426768\pi\)
−0.187693 + 0.982228i \(0.560101\pi\)
\(74\) 0.701513 1.21506i 0.0815492 0.141247i
\(75\) 3.36477 14.2617i 0.388530 1.64680i
\(76\) 3.47040 0.398082
\(77\) 15.7037 + 1.15497i 1.78960 + 0.131621i
\(78\) 3.50649 2.54761i 0.397031 0.288460i
\(79\) −9.52004 4.23860i −1.07109 0.476879i −0.206028 0.978546i \(-0.566054\pi\)
−0.865061 + 0.501667i \(0.832720\pi\)
\(80\) 0.0921738 + 2.23417i 0.0103053 + 0.249788i
\(81\) 4.99514 2.22398i 0.555015 0.247109i
\(82\) −2.21328 3.83352i −0.244416 0.423341i
\(83\) 4.84131 + 3.51741i 0.531402 + 0.386086i 0.820882 0.571098i \(-0.193482\pi\)
−0.289480 + 0.957184i \(0.593482\pi\)
\(84\) 7.29568 2.62569i 0.796024 0.286486i
\(85\) 3.58581 + 14.0039i 0.388936 + 1.51894i
\(86\) −4.89322 + 5.43447i −0.527649 + 0.586014i
\(87\) 13.7321 + 15.2511i 1.47224 + 1.63509i
\(88\) −3.98231 4.42280i −0.424516 0.471472i
\(89\) −0.714003 + 0.792981i −0.0756842 + 0.0840558i −0.779798 0.626032i \(-0.784678\pi\)
0.704113 + 0.710088i \(0.251345\pi\)
\(90\) 9.62375 + 7.97208i 1.01443 + 0.840331i
\(91\) 0.693344 3.85098i 0.0726822 0.403692i
\(92\) 0.972093 + 0.706267i 0.101348 + 0.0736334i
\(93\) −3.91244 6.77654i −0.405701 0.702694i
\(94\) −5.66313 + 2.52139i −0.584107 + 0.260061i
\(95\) 7.47282 + 2.09173i 0.766695 + 0.214606i
\(96\) −2.67729 1.19201i −0.273250 0.121659i
\(97\) −8.61836 + 6.26160i −0.875062 + 0.635770i −0.931940 0.362611i \(-0.881885\pi\)
0.0568786 + 0.998381i \(0.481885\pi\)
\(98\) 3.11385 6.26929i 0.314546 0.633294i
\(99\) −33.2612 −3.34288
\(100\) −1.14813 + 4.86639i −0.114813 + 0.486639i
\(101\) −4.91028 + 8.50486i −0.488591 + 0.846265i −0.999914 0.0131240i \(-0.995822\pi\)
0.511323 + 0.859389i \(0.329156\pi\)
\(102\) −18.5320 3.93911i −1.83495 0.390030i
\(103\) 11.7200 + 5.21810i 1.15481 + 0.514154i 0.892597 0.450856i \(-0.148881\pi\)
0.262213 + 0.965010i \(0.415548\pi\)
\(104\) −1.19648 + 0.869297i −0.117325 + 0.0852416i
\(105\) 17.2924 1.25655i 1.68757 0.122627i
\(106\) −7.74586 5.62769i −0.752344 0.546610i
\(107\) 5.69552 + 9.86493i 0.550607 + 0.953679i 0.998231 + 0.0594570i \(0.0189369\pi\)
−0.447624 + 0.894222i \(0.647730\pi\)
\(108\) −6.93082 + 3.08580i −0.666919 + 0.296931i
\(109\) −5.50806 6.11732i −0.527576 0.585933i 0.419172 0.907907i \(-0.362320\pi\)
−0.946749 + 0.321974i \(0.895654\pi\)
\(110\) −5.90935 11.9239i −0.563434 1.13690i
\(111\) 1.27061 + 3.91054i 0.120601 + 0.371172i
\(112\) −2.48944 + 0.895939i −0.235230 + 0.0846582i
\(113\) −0.287837 + 0.885873i −0.0270775 + 0.0833359i −0.963682 0.267052i \(-0.913950\pi\)
0.936605 + 0.350388i \(0.113950\pi\)
\(114\) −6.80543 + 7.55819i −0.637386 + 0.707889i
\(115\) 1.66752 + 2.10672i 0.155497 + 0.196453i
\(116\) −4.68568 5.20398i −0.435055 0.483177i
\(117\) −0.863970 + 8.22012i −0.0798741 + 0.759951i
\(118\) −6.09601 −0.561183
\(119\) −14.5377 + 9.01154i −1.33267 + 0.826086i
\(120\) −5.04655 4.18044i −0.460685 0.381620i
\(121\) 22.3087 + 9.93249i 2.02807 + 0.902954i
\(122\) 0.917727 + 8.73158i 0.0830871 + 0.790521i
\(123\) 12.6893 + 2.69719i 1.14415 + 0.243197i
\(124\) 1.33500 + 2.31229i 0.119887 + 0.207650i
\(125\) −5.40541 + 9.78681i −0.483474 + 0.875359i
\(126\) −5.58845 + 13.6897i −0.497858 + 1.21958i
\(127\) 3.94990 + 12.1565i 0.350497 + 1.07872i 0.958575 + 0.284841i \(0.0919408\pi\)
−0.608078 + 0.793877i \(0.708059\pi\)
\(128\) 0.913545 + 0.406737i 0.0807468 + 0.0359508i
\(129\) −2.24018 21.3139i −0.197237 1.87658i
\(130\) −3.10035 + 1.15070i −0.271919 + 0.100923i
\(131\) 2.03941 19.4037i 0.178184 1.69531i −0.431058 0.902324i \(-0.641859\pi\)
0.609242 0.792984i \(-0.291474\pi\)
\(132\) 17.4417 1.51811
\(133\) 0.287384 + 9.17732i 0.0249194 + 0.795774i
\(134\) −2.56033 + 7.87987i −0.221178 + 0.680717i
\(135\) −16.7841 + 2.46723i −1.44454 + 0.212345i
\(136\) 6.32351 + 1.34410i 0.542237 + 0.115256i
\(137\) −8.69107 9.65241i −0.742528 0.824661i 0.246998 0.969016i \(-0.420556\pi\)
−0.989526 + 0.144355i \(0.953889\pi\)
\(138\) −3.44445 + 0.732140i −0.293211 + 0.0623239i
\(139\) −0.0879688 0.270740i −0.00746142 0.0229639i 0.947256 0.320476i \(-0.103843\pi\)
−0.954718 + 0.297513i \(0.903843\pi\)
\(140\) −5.90052 + 0.428761i −0.498685 + 0.0362369i
\(141\) 5.61402 17.2782i 0.472786 1.45508i
\(142\) 1.06131 10.0977i 0.0890632 0.847380i
\(143\) 4.40092 7.62262i 0.368023 0.637435i
\(144\) 5.10558 2.27315i 0.425465 0.189429i
\(145\) −6.95308 14.0300i −0.577422 1.16512i
\(146\) 0.285132 0.207160i 0.0235977 0.0171447i
\(147\) 7.54767 + 19.0757i 0.622521 + 1.57334i
\(148\) −0.433559 1.33436i −0.0356383 0.109683i
\(149\) 7.21713 + 12.5004i 0.591250 + 1.02408i 0.994064 + 0.108793i \(0.0346987\pi\)
−0.402814 + 0.915282i \(0.631968\pi\)
\(150\) −8.34706 12.0435i −0.681535 0.983346i
\(151\) 3.21548 5.56938i 0.261672 0.453230i −0.705014 0.709193i \(-0.749059\pi\)
0.966686 + 0.255964i \(0.0823927\pi\)
\(152\) 2.32215 2.57901i 0.188351 0.209185i
\(153\) 29.2298 21.2367i 2.36309 1.71689i
\(154\) 11.3661 10.8973i 0.915908 0.878129i
\(155\) 1.48097 + 5.78372i 0.118954 + 0.464559i
\(156\) 0.453053 4.31051i 0.0362733 0.345117i
\(157\) −2.38380 + 4.12885i −0.190248 + 0.329518i −0.945332 0.326109i \(-0.894262\pi\)
0.755085 + 0.655627i \(0.227596\pi\)
\(158\) −9.52004 + 4.23860i −0.757374 + 0.337205i
\(159\) 27.4461 5.83385i 2.17662 0.462655i
\(160\) 1.72199 + 1.42645i 0.136135 + 0.112771i
\(161\) −1.78719 + 2.62914i −0.140850 + 0.207205i
\(162\) 1.68966 5.20024i 0.132752 0.408570i
\(163\) −10.6637 + 2.26665i −0.835249 + 0.177538i −0.605633 0.795744i \(-0.707080\pi\)
−0.229615 + 0.973281i \(0.573747\pi\)
\(164\) −4.32984 0.920335i −0.338103 0.0718661i
\(165\) 37.5573 + 10.5127i 2.92383 + 0.818412i
\(166\) 5.85341 1.24418i 0.454313 0.0965672i
\(167\) −0.814472 0.591749i −0.0630257 0.0457909i 0.555826 0.831298i \(-0.312402\pi\)
−0.618852 + 0.785508i \(0.712402\pi\)
\(168\) 2.93050 7.17868i 0.226093 0.553847i
\(169\) 8.74770 + 6.35557i 0.672900 + 0.488890i
\(170\) 12.8063 + 6.70565i 0.982198 + 0.514300i
\(171\) −2.02735 19.2889i −0.155035 1.47506i
\(172\) 0.764396 + 7.27274i 0.0582846 + 0.554541i
\(173\) 0.818415 0.908942i 0.0622230 0.0691056i −0.711230 0.702960i \(-0.751861\pi\)
0.773453 + 0.633854i \(0.218528\pi\)
\(174\) 20.5223 1.55579
\(175\) −12.9640 2.63319i −0.979989 0.199050i
\(176\) −5.95147 −0.448609
\(177\) 11.9542 13.2765i 0.898534 0.997924i
\(178\) 0.111538 + 1.06122i 0.00836015 + 0.0795415i
\(179\) 0.373872 + 3.55716i 0.0279445 + 0.265874i 0.999569 + 0.0293467i \(0.00934270\pi\)
−0.971625 + 0.236528i \(0.923991\pi\)
\(180\) 12.3640 1.81748i 0.921555 0.135467i
\(181\) −12.0151 8.72952i −0.893079 0.648860i 0.0436001 0.999049i \(-0.486117\pi\)
−0.936679 + 0.350189i \(0.886117\pi\)
\(182\) −2.39790 3.09206i −0.177744 0.229199i
\(183\) −20.8162 15.1238i −1.53878 1.11799i
\(184\) 1.17532 0.249821i 0.0866454 0.0184171i
\(185\) −0.129322 3.13459i −0.00950795 0.230460i
\(186\) −7.65388 1.62688i −0.561210 0.119289i
\(187\) −37.6342 + 7.99939i −2.75208 + 0.584973i
\(188\) −1.91562 + 5.89567i −0.139711 + 0.429986i
\(189\) −8.73421 18.0727i −0.635320 1.31460i
\(190\) 6.55475 4.15375i 0.475531 0.301345i
\(191\) 19.6458 4.17585i 1.42152 0.302154i 0.567922 0.823083i \(-0.307748\pi\)
0.853600 + 0.520929i \(0.174414\pi\)
\(192\) −2.67729 + 1.19201i −0.193217 + 0.0860256i
\(193\) 1.86568 3.23145i 0.134294 0.232605i −0.791033 0.611773i \(-0.790457\pi\)
0.925328 + 0.379168i \(0.123790\pi\)
\(194\) −1.11353 + 10.5945i −0.0799467 + 0.760642i
\(195\) 3.57365 9.00877i 0.255914 0.645131i
\(196\) −2.57542 6.50901i −0.183959 0.464929i
\(197\) 0.0353552 0.0256871i 0.00251896 0.00183013i −0.586525 0.809931i \(-0.699504\pi\)
0.589044 + 0.808101i \(0.299504\pi\)
\(198\) −22.2561 + 24.7179i −1.58167 + 1.75663i
\(199\) −0.225640 + 0.390820i −0.0159952 + 0.0277045i −0.873912 0.486084i \(-0.838425\pi\)
0.857917 + 0.513788i \(0.171758\pi\)
\(200\) 2.84819 + 4.10948i 0.201397 + 0.290584i
\(201\) −12.1408 21.0285i −0.856347 1.48324i
\(202\) 3.03472 + 9.33991i 0.213522 + 0.657154i
\(203\) 13.3737 12.8220i 0.938647 0.899929i
\(204\) −15.3277 + 11.1362i −1.07315 + 0.779691i
\(205\) −8.76873 4.59150i −0.612435 0.320684i
\(206\) 11.7200 5.21810i 0.816573 0.363562i
\(207\) 3.35764 5.81561i 0.233372 0.404213i
\(208\) −0.154591 + 1.47083i −0.0107190 + 0.101984i
\(209\) −6.38243 + 19.6431i −0.441482 + 1.35874i
\(210\) 10.6371 13.6916i 0.734028 0.944807i
\(211\) −0.845355 2.60173i −0.0581966 0.179111i 0.917732 0.397199i \(-0.130018\pi\)
−0.975929 + 0.218089i \(0.930018\pi\)
\(212\) −9.36518 + 1.99063i −0.643203 + 0.136717i
\(213\) 19.9106 + 22.1129i 1.36425 + 1.51515i
\(214\) 11.1421 + 2.36833i 0.761660 + 0.161896i
\(215\) −2.73755 + 16.1211i −0.186699 + 1.09945i
\(216\) −2.34443 + 7.21541i −0.159518 + 0.490946i
\(217\) −6.00420 + 3.72184i −0.407592 + 0.252655i
\(218\) −8.23166 −0.557519
\(219\) −0.107966 + 1.02723i −0.00729567 + 0.0694137i
\(220\) −12.8153 3.58715i −0.864008 0.241845i
\(221\) 0.999397 + 9.50863i 0.0672267 + 0.639619i
\(222\) 3.75630 + 1.67241i 0.252107 + 0.112245i
\(223\) −0.708459 2.18041i −0.0474419 0.146011i 0.924529 0.381111i \(-0.124458\pi\)
−0.971971 + 0.235100i \(0.924458\pi\)
\(224\) −0.999946 + 2.44951i −0.0668117 + 0.163665i
\(225\) 27.7188 + 3.53859i 1.84792 + 0.235906i
\(226\) 0.465731 + 0.806669i 0.0309800 + 0.0536588i
\(227\) 17.8693 + 3.79824i 1.18603 + 0.252098i 0.758359 0.651837i \(-0.226002\pi\)
0.427669 + 0.903935i \(0.359335\pi\)
\(228\) 1.06311 + 10.1148i 0.0704063 + 0.669871i
\(229\) 0.502371 + 0.223670i 0.0331976 + 0.0147805i 0.423268 0.906004i \(-0.360883\pi\)
−0.390071 + 0.920785i \(0.627549\pi\)
\(230\) 2.68139 + 0.170461i 0.176805 + 0.0112399i
\(231\) 1.44435 + 46.1238i 0.0950312 + 3.03472i
\(232\) −7.00264 −0.459746
\(233\) 2.47371 23.5358i 0.162058 1.54188i −0.547243 0.836974i \(-0.684323\pi\)
0.709301 0.704906i \(-0.249011\pi\)
\(234\) 5.53063 + 6.14239i 0.361549 + 0.401541i
\(235\) −7.67842 + 11.5405i −0.500885 + 0.752822i
\(236\) −4.07903 + 4.53022i −0.265522 + 0.294892i
\(237\) 9.43748 29.0456i 0.613030 1.88671i
\(238\) −3.03077 + 16.8335i −0.196456 + 1.09116i
\(239\) −3.03903 9.35318i −0.196579 0.605007i −0.999955 0.00953457i \(-0.996965\pi\)
0.803376 0.595472i \(-0.203035\pi\)
\(240\) −6.48347 + 0.953058i −0.418506 + 0.0615196i
\(241\) 8.94220 + 9.93132i 0.576018 + 0.639733i 0.958792 0.284109i \(-0.0916979\pi\)
−0.382774 + 0.923842i \(0.625031\pi\)
\(242\) 22.3087 9.93249i 1.43406 0.638485i
\(243\) −3.36789 5.83335i −0.216050 0.374210i
\(244\) 7.10291 + 5.16057i 0.454717 + 0.330371i
\(245\) −1.62246 15.5682i −0.103655 0.994613i
\(246\) 10.4952 7.62519i 0.669148 0.486164i
\(247\) 4.68877 + 2.08758i 0.298339 + 0.132829i
\(248\) 2.61166 + 0.555126i 0.165841 + 0.0352505i
\(249\) −8.76879 + 15.1880i −0.555700 + 0.962500i
\(250\) 3.65609 + 10.5657i 0.231231 + 0.668230i
\(251\) 16.6006 1.04782 0.523911 0.851773i \(-0.324472\pi\)
0.523911 + 0.851773i \(0.324472\pi\)
\(252\) 6.43403 + 13.3132i 0.405306 + 0.838654i
\(253\) −5.78538 + 4.20332i −0.363724 + 0.264261i
\(254\) 11.6771 + 5.19896i 0.732684 + 0.326212i
\(255\) −39.7173 + 14.7411i −2.48719 + 0.923126i
\(256\) 0.913545 0.406737i 0.0570966 0.0254210i
\(257\) 13.9627 + 24.1841i 0.870970 + 1.50857i 0.860994 + 0.508615i \(0.169842\pi\)
0.00997635 + 0.999950i \(0.496824\pi\)
\(258\) −17.3383 12.5970i −1.07943 0.784255i
\(259\) 3.49274 1.25702i 0.217029 0.0781077i
\(260\) −1.21940 + 3.07398i −0.0756241 + 0.190640i
\(261\) −26.1871 + 29.0837i −1.62094 + 1.80024i
\(262\) −13.0551 14.4992i −0.806548 0.895763i
\(263\) 5.31163 + 5.89916i 0.327529 + 0.363758i 0.884309 0.466902i \(-0.154630\pi\)
−0.556780 + 0.830660i \(0.687963\pi\)
\(264\) 11.6708 12.9617i 0.718287 0.797738i
\(265\) −21.3659 1.35828i −1.31250 0.0834382i
\(266\) 7.01237 + 5.92725i 0.429956 + 0.363423i
\(267\) −2.52995 1.83812i −0.154830 0.112491i
\(268\) 4.14269 + 7.17536i 0.253055 + 0.438305i
\(269\) 18.7861 8.36412i 1.14541 0.509970i 0.255818 0.966725i \(-0.417655\pi\)
0.889592 + 0.456755i \(0.150989\pi\)
\(270\) −9.39723 + 14.1239i −0.571897 + 0.859553i
\(271\) −4.83484 2.15261i −0.293696 0.130762i 0.254600 0.967047i \(-0.418056\pi\)
−0.548295 + 0.836285i \(0.684723\pi\)
\(272\) 5.23012 3.79990i 0.317123 0.230403i
\(273\) 11.4365 + 0.841125i 0.692167 + 0.0509072i
\(274\) −12.9886 −0.784670
\(275\) −25.4331 15.4484i −1.53368 0.931575i
\(276\) −1.76070 + 3.04962i −0.105982 + 0.183566i
\(277\) −22.5295 4.78879i −1.35367 0.287731i −0.526733 0.850031i \(-0.676583\pi\)
−0.826933 + 0.562300i \(0.809916\pi\)
\(278\) −0.260062 0.115787i −0.0155975 0.00694444i
\(279\) 12.0721 8.77093i 0.722741 0.525102i
\(280\) −3.62959 + 4.67184i −0.216909 + 0.279196i
\(281\) 23.1389 + 16.8114i 1.38035 + 1.00288i 0.996847 + 0.0793422i \(0.0252820\pi\)
0.383502 + 0.923540i \(0.374718\pi\)
\(282\) −9.08367 15.7334i −0.540925 0.936909i
\(283\) −15.1425 + 6.74187i −0.900128 + 0.400763i −0.804016 0.594608i \(-0.797307\pi\)
−0.0961118 + 0.995371i \(0.530641\pi\)
\(284\) −6.79389 7.54538i −0.403143 0.447736i
\(285\) −3.80734 + 22.4211i −0.225528 + 1.32811i
\(286\) −2.71992 8.37105i −0.160832 0.494990i
\(287\) 2.07523 11.5263i 0.122497 0.680374i
\(288\) 1.72702 5.31522i 0.101766 0.313202i
\(289\) 16.5900 18.4251i 0.975884 1.08383i
\(290\) −15.0788 4.22072i −0.885458 0.247849i
\(291\) −20.8902 23.2009i −1.22461 1.36006i
\(292\) 0.0368402 0.350511i 0.00215591 0.0205121i
\(293\) −24.7917 −1.44835 −0.724173 0.689618i \(-0.757778\pi\)
−0.724173 + 0.689618i \(0.757778\pi\)
\(294\) 19.2264 + 7.15510i 1.12130 + 0.417294i
\(295\) −11.5139 + 7.29636i −0.670365 + 0.424811i
\(296\) −1.28173 0.570662i −0.0744989 0.0331691i
\(297\) −4.71969 44.9048i −0.273864 2.60564i
\(298\) 14.1188 + 3.00105i 0.817882 + 0.173846i
\(299\) 0.888525 + 1.53897i 0.0513847 + 0.0890010i
\(300\) −14.5353 1.85558i −0.839197 0.107132i
\(301\) −19.1691 + 2.62367i −1.10489 + 0.151226i
\(302\) −1.98728 6.11621i −0.114355 0.351948i
\(303\) −26.2925 11.7062i −1.51046 0.672501i
\(304\) −0.362756 3.45139i −0.0208055 0.197951i
\(305\) 12.1843 + 15.3934i 0.697669 + 0.881425i
\(306\) 3.77662 35.9321i 0.215895 2.05410i
\(307\) 4.29982 0.245404 0.122702 0.992444i \(-0.460844\pi\)
0.122702 + 0.992444i \(0.460844\pi\)
\(308\) −0.492841 15.7384i −0.0280822 0.896778i
\(309\) −11.6184 + 35.7577i −0.660947 + 2.03419i
\(310\) 5.28910 + 2.76949i 0.300401 + 0.157296i
\(311\) 22.3838 + 4.75783i 1.26927 + 0.269792i 0.792845 0.609424i \(-0.208599\pi\)
0.476425 + 0.879215i \(0.341932\pi\)
\(312\) −2.90018 3.22098i −0.164191 0.182352i
\(313\) 24.0724 5.11674i 1.36065 0.289215i 0.530941 0.847409i \(-0.321839\pi\)
0.829711 + 0.558193i \(0.188505\pi\)
\(314\) 1.47327 + 4.53425i 0.0831412 + 0.255882i
\(315\) 5.83010 + 32.5454i 0.328489 + 1.83373i
\(316\) −3.22026 + 9.91095i −0.181154 + 0.557534i
\(317\) −1.41080 + 13.4229i −0.0792386 + 0.753905i 0.880696 + 0.473682i \(0.157075\pi\)
−0.959935 + 0.280224i \(0.909591\pi\)
\(318\) 14.0296 24.3001i 0.786743 1.36268i
\(319\) 38.0729 16.9511i 2.13167 0.949082i
\(320\) 2.21229 0.325203i 0.123671 0.0181794i
\(321\) −27.0076 + 19.6222i −1.50742 + 1.09520i
\(322\) 0.757969 + 3.08738i 0.0422399 + 0.172053i
\(323\) −6.93291 21.3373i −0.385758 1.18724i
\(324\) −2.73393 4.73531i −0.151885 0.263073i
\(325\) −4.47853 + 5.88423i −0.248424 + 0.326398i
\(326\) −5.45099 + 9.44139i −0.301902 + 0.522910i
\(327\) 16.1422 17.9278i 0.892667 0.991407i
\(328\) −3.58117 + 2.60187i −0.197737 + 0.143664i
\(329\) −15.7495 4.57755i −0.868296 0.252368i
\(330\) 32.9432 20.8761i 1.81346 1.14919i
\(331\) −1.32519 + 12.6083i −0.0728389 + 0.693016i 0.895785 + 0.444487i \(0.146614\pi\)
−0.968624 + 0.248529i \(0.920053\pi\)
\(332\) 2.99209 5.18245i 0.164212 0.284424i
\(333\) −7.16325 + 3.18929i −0.392544 + 0.174772i
\(334\) −0.984743 + 0.209314i −0.0538827 + 0.0114531i
\(335\) 4.59565 + 17.9477i 0.251087 + 0.980585i
\(336\) −3.37391 6.98126i −0.184062 0.380859i
\(337\) −8.64421 + 26.6041i −0.470880 + 1.44922i 0.380555 + 0.924758i \(0.375733\pi\)
−0.851434 + 0.524461i \(0.824267\pi\)
\(338\) 10.5765 2.24810i 0.575284 0.122280i
\(339\) −2.67014 0.567556i −0.145022 0.0308254i
\(340\) 13.5524 5.02998i 0.734980 0.272789i
\(341\) −15.5432 + 3.30381i −0.841712 + 0.178911i
\(342\) −15.6910 11.4002i −0.848474 0.616453i
\(343\) 16.9995 7.34959i 0.917887 0.396841i
\(344\) 5.91618 + 4.29836i 0.318979 + 0.231752i
\(345\) −5.62942 + 5.50552i −0.303078 + 0.296407i
\(346\) −0.127849 1.21640i −0.00687321 0.0653942i
\(347\) −2.63437 25.0644i −0.141420 1.34553i −0.803147 0.595780i \(-0.796843\pi\)
0.661727 0.749745i \(-0.269824\pi\)
\(348\) 13.7321 15.2511i 0.736119 0.817543i
\(349\) 13.7969 0.738532 0.369266 0.929324i \(-0.379609\pi\)
0.369266 + 0.929324i \(0.379609\pi\)
\(350\) −10.6315 + 7.87221i −0.568276 + 0.420787i
\(351\) −11.2203 −0.598895
\(352\) −3.98231 + 4.42280i −0.212258 + 0.235736i
\(353\) −0.916362 8.71860i −0.0487730 0.464044i −0.991464 0.130378i \(-0.958381\pi\)
0.942691 0.333666i \(-0.108286\pi\)
\(354\) −1.86743 17.7674i −0.0992529 0.944329i
\(355\) −10.0815 20.3424i −0.535068 1.07966i
\(356\) 0.863271 + 0.627203i 0.0457533 + 0.0332417i
\(357\) −30.7185 39.6112i −1.62580 2.09645i
\(358\) 2.89365 + 2.10236i 0.152934 + 0.111113i
\(359\) 20.8034 4.42190i 1.09796 0.233379i 0.376902 0.926253i \(-0.376989\pi\)
0.721058 + 0.692874i \(0.243656\pi\)
\(360\) 6.92245 10.4043i 0.364845 0.548357i
\(361\) 6.80432 + 1.44630i 0.358122 + 0.0761212i
\(362\) −14.5270 + 3.08781i −0.763522 + 0.162292i
\(363\) −22.1153 + 68.0638i −1.16075 + 3.57242i
\(364\) −3.90236 0.287009i −0.204539 0.0150434i
\(365\) 0.290593 0.732552i 0.0152103 0.0383435i
\(366\) −25.1680 + 5.34962i −1.31555 + 0.279629i
\(367\) 8.62151 3.83854i 0.450039 0.200370i −0.169185 0.985584i \(-0.554114\pi\)
0.619225 + 0.785214i \(0.287447\pi\)
\(368\) 0.600786 1.04059i 0.0313182 0.0542446i
\(369\) −2.58593 + 24.6034i −0.134618 + 1.28080i
\(370\) −2.41599 2.00135i −0.125601 0.104045i
\(371\) −6.03966 24.6010i −0.313564 1.27722i
\(372\) −6.33045 + 4.59934i −0.328219 + 0.238465i
\(373\) 14.3700 15.9595i 0.744052 0.826353i −0.245671 0.969353i \(-0.579008\pi\)
0.989723 + 0.143000i \(0.0456750\pi\)
\(374\) −19.2375 + 33.3203i −0.994746 + 1.72295i
\(375\) −30.1805 12.7566i −1.55852 0.658745i
\(376\) 3.09954 + 5.36855i 0.159846 + 0.276862i
\(377\) −3.20032 9.84958i −0.164825 0.507279i
\(378\) −19.2750 5.60223i −0.991397 0.288148i
\(379\) 3.04868 2.21500i 0.156600 0.113777i −0.506726 0.862107i \(-0.669144\pi\)
0.663326 + 0.748331i \(0.269144\pi\)
\(380\) 1.29914 7.65053i 0.0666447 0.392464i
\(381\) −34.2215 + 15.2364i −1.75322 + 0.780583i
\(382\) 10.0424 17.3939i 0.513812 0.889948i
\(383\) −2.26167 + 21.5183i −0.115566 + 1.09953i 0.770969 + 0.636873i \(0.219772\pi\)
−0.886535 + 0.462662i \(0.846894\pi\)
\(384\) −0.905623 + 2.78722i −0.0462149 + 0.142235i
\(385\) 8.42481 34.1866i 0.429368 1.74231i
\(386\) −1.15305 3.54873i −0.0586888 0.180625i
\(387\) 39.9763 8.49722i 2.03211 0.431938i
\(388\) 7.12817 + 7.91663i 0.361878 + 0.401906i
\(389\) −18.3825 3.90732i −0.932029 0.198109i −0.283216 0.959056i \(-0.591401\pi\)
−0.648814 + 0.760947i \(0.724735\pi\)
\(390\) −4.30358 8.68378i −0.217920 0.439720i
\(391\) 2.40042 7.38772i 0.121394 0.373613i
\(392\) −6.56043 2.44147i −0.331352 0.123313i
\(393\) 57.1788 2.88429
\(394\) 0.00456805 0.0434621i 0.000230135 0.00218959i
\(395\) −12.9079 + 19.4003i −0.649465 + 0.976136i
\(396\) 3.47675 + 33.0790i 0.174713 + 1.66228i
\(397\) −7.05780 3.14234i −0.354221 0.157709i 0.221909 0.975067i \(-0.428771\pi\)
−0.576130 + 0.817358i \(0.695438\pi\)
\(398\) 0.139453 + 0.429193i 0.00699017 + 0.0215135i
\(399\) −26.6602 + 3.64896i −1.33468 + 0.182677i
\(400\) 4.95975 + 0.633163i 0.247987 + 0.0316581i
\(401\) 3.57000 + 6.18342i 0.178277 + 0.308785i 0.941291 0.337598i \(-0.109614\pi\)
−0.763013 + 0.646383i \(0.776281\pi\)
\(402\) −23.7510 5.04843i −1.18459 0.251793i
\(403\) 0.412759 + 3.92714i 0.0205610 + 0.195625i
\(404\) 8.97153 + 3.99438i 0.446350 + 0.198728i
\(405\) −3.03285 11.8444i −0.150704 0.588552i
\(406\) −0.579889 18.5182i −0.0287794 0.919041i
\(407\) 8.35006 0.413897
\(408\) −1.98040 + 18.8423i −0.0980445 + 0.932831i
\(409\) −15.0284 16.6907i −0.743105 0.825302i 0.246495 0.969144i \(-0.420721\pi\)
−0.989601 + 0.143842i \(0.954054\pi\)
\(410\) −9.27957 + 3.44413i −0.458285 + 0.170093i
\(411\) 25.4705 28.2879i 1.25637 1.39534i
\(412\) 3.96443 12.2013i 0.195314 0.601113i
\(413\) −12.3177 10.4117i −0.606116 0.512324i
\(414\) −2.07514 6.38662i −0.101987 0.313885i
\(415\) 9.56652 9.35596i 0.469602 0.459266i
\(416\) 0.989602 + 1.09906i 0.0485192 + 0.0538860i
\(417\) 0.762152 0.339332i 0.0373227 0.0166172i
\(418\) 10.3270 + 17.8869i 0.505109 + 0.874875i
\(419\) −18.9052 13.7355i −0.923581 0.671021i 0.0208320 0.999783i \(-0.493369\pi\)
−0.944413 + 0.328762i \(0.893369\pi\)
\(420\) −3.05722 17.0663i −0.149177 0.832752i
\(421\) 0.109993 0.0799144i 0.00536072 0.00389479i −0.585102 0.810960i \(-0.698945\pi\)
0.590462 + 0.807065i \(0.298945\pi\)
\(422\) −2.49912 1.11268i −0.121655 0.0541644i
\(423\) 33.8880 + 7.20311i 1.64769 + 0.350227i
\(424\) −4.78720 + 8.29168i −0.232487 + 0.402679i
\(425\) 32.2141 2.66261i 1.56261 0.129155i
\(426\) 29.7559 1.44168
\(427\) −13.0587 + 19.2107i −0.631955 + 0.929670i
\(428\) 9.21555 6.69549i 0.445450 0.323639i
\(429\) 23.5651 + 10.4918i 1.13773 + 0.506551i
\(430\) 10.1486 + 12.8215i 0.489407 + 0.618309i
\(431\) −22.7977 + 10.1502i −1.09813 + 0.488918i −0.874140 0.485674i \(-0.838574\pi\)
−0.223988 + 0.974592i \(0.571908\pi\)
\(432\) 3.79337 + 6.57030i 0.182508 + 0.316114i
\(433\) −5.03607 3.65892i −0.242018 0.175836i 0.460164 0.887834i \(-0.347791\pi\)
−0.702182 + 0.711998i \(0.747791\pi\)
\(434\) −1.25173 + 6.95239i −0.0600851 + 0.333725i
\(435\) 38.7617 24.5634i 1.85848 1.17772i
\(436\) −5.50806 + 6.11732i −0.263788 + 0.292966i
\(437\) −2.79023 3.09887i −0.133475 0.148239i
\(438\) 0.691136 + 0.767584i 0.0330238 + 0.0366766i
\(439\) −16.1732 + 17.9621i −0.771903 + 0.857285i −0.993018 0.117963i \(-0.962364\pi\)
0.221115 + 0.975248i \(0.429030\pi\)
\(440\) −11.2409 + 7.12336i −0.535888 + 0.339593i
\(441\) −34.6734 + 18.1170i −1.65112 + 0.862713i
\(442\) 7.73501 + 5.61982i 0.367917 + 0.267307i
\(443\) 7.64049 + 13.2337i 0.363010 + 0.628753i 0.988455 0.151516i \(-0.0484156\pi\)
−0.625444 + 0.780269i \(0.715082\pi\)
\(444\) 3.75630 1.67241i 0.178266 0.0793693i
\(445\) 1.48085 + 1.87088i 0.0701989 + 0.0886882i
\(446\) −2.09441 0.932493i −0.0991734 0.0441548i
\(447\) −34.2229 + 24.8644i −1.61869 + 1.17605i
\(448\) 1.15125 + 2.38215i 0.0543913 + 0.112546i
\(449\) −20.3492 −0.960339 −0.480169 0.877176i \(-0.659425\pi\)
−0.480169 + 0.877176i \(0.659425\pi\)
\(450\) 21.1772 18.2313i 0.998301 0.859431i
\(451\) 13.1723 22.8151i 0.620259 1.07432i
\(452\) 0.911107 + 0.193662i 0.0428549 + 0.00910908i
\(453\) 17.2175 + 7.66574i 0.808951 + 0.360168i
\(454\) 14.7795 10.7380i 0.693638 0.503958i
\(455\) −8.22997 2.97010i −0.385827 0.139240i
\(456\) 8.22815 + 5.97810i 0.385318 + 0.279950i
\(457\) −10.8338 18.7646i −0.506782 0.877773i −0.999969 0.00784937i \(-0.997501\pi\)
0.493187 0.869923i \(-0.335832\pi\)
\(458\) 0.502371 0.223670i 0.0234743 0.0104514i
\(459\) 32.8186 + 36.4487i 1.53184 + 1.70128i
\(460\) 1.92087 1.87860i 0.0895613 0.0875900i
\(461\) 0.376041 + 1.15734i 0.0175140 + 0.0539025i 0.959432 0.281942i \(-0.0909784\pi\)
−0.941918 + 0.335844i \(0.890978\pi\)
\(462\) 35.2431 + 29.7895i 1.63966 + 1.38593i
\(463\) 0.317916 0.978445i 0.0147748 0.0454722i −0.943397 0.331665i \(-0.892390\pi\)
0.958172 + 0.286193i \(0.0923897\pi\)
\(464\) −4.68568 + 5.20398i −0.217527 + 0.241589i
\(465\) −16.4036 + 6.08821i −0.760697 + 0.282334i
\(466\) −15.8352 17.5868i −0.733554 0.814694i
\(467\) −1.34425 + 12.7897i −0.0622043 + 0.591835i 0.918375 + 0.395711i \(0.129502\pi\)
−0.980579 + 0.196123i \(0.937165\pi\)
\(468\) 8.26540 0.382068
\(469\) −18.6319 + 11.5494i −0.860339 + 0.533300i
\(470\) 3.43843 + 13.4283i 0.158603 + 0.619402i
\(471\) −12.7642 5.68299i −0.588144 0.261859i
\(472\) 0.637206 + 6.06261i 0.0293298 + 0.279054i
\(473\) −42.5708 9.04871i −1.95741 0.416060i
\(474\) −15.2702 26.4487i −0.701382 1.21483i
\(475\) 7.40868 15.6909i 0.339933 0.719946i
\(476\) 10.4818 + 13.5161i 0.480432 + 0.619511i
\(477\) 16.5352 + 50.8900i 0.757093 + 2.33009i
\(478\) −8.98427 4.00006i −0.410931 0.182958i
\(479\) −2.15758 20.5280i −0.0985821 0.937946i −0.926296 0.376796i \(-0.877026\pi\)
0.827714 0.561150i \(-0.189641\pi\)
\(480\) −3.63003 + 5.45588i −0.165687 + 0.249026i
\(481\) 0.216895 2.06362i 0.00988956 0.0940929i
\(482\) 13.3639 0.608710
\(483\) −8.21039 4.40355i −0.373585 0.200368i
\(484\) 7.54618 23.2248i 0.343008 1.05567i
\(485\) 10.5775 + 21.3433i 0.480299 + 0.969149i
\(486\) −6.58858 1.40045i −0.298864 0.0635255i
\(487\) 24.1603 + 26.8327i 1.09481 + 1.21591i 0.974788 + 0.223134i \(0.0716288\pi\)
0.120019 + 0.992772i \(0.461705\pi\)
\(488\) 8.58782 1.82540i 0.388753 0.0826319i
\(489\) −9.87307 30.3862i −0.446476 1.37411i
\(490\) −12.6550 9.21141i −0.571696 0.416129i
\(491\) −2.79870 + 8.61350i −0.126303 + 0.388722i −0.994136 0.108134i \(-0.965512\pi\)
0.867833 + 0.496856i \(0.165512\pi\)
\(492\) 1.35602 12.9017i 0.0611342 0.581653i
\(493\) −22.6353 + 39.2054i −1.01944 + 1.76572i
\(494\) 4.68877 2.08758i 0.210958 0.0939245i
\(495\) −12.4513 + 73.3247i −0.559646 + 3.29570i
\(496\) 2.16008 1.56939i 0.0969905 0.0704677i
\(497\) 19.3908 18.5910i 0.869797 0.833919i
\(498\) 5.41941 + 16.6792i 0.242850 + 0.747414i
\(499\) 10.3954 + 18.0054i 0.465362 + 0.806030i 0.999218 0.0395451i \(-0.0125909\pi\)
−0.533856 + 0.845575i \(0.679258\pi\)
\(500\) 10.2982 + 4.35280i 0.460550 + 0.194663i
\(501\) 1.47521 2.55514i 0.0659075 0.114155i
\(502\) 11.1080 12.3367i 0.495774 0.550613i
\(503\) 20.8956 15.1816i 0.931691 0.676913i −0.0147155 0.999892i \(-0.504684\pi\)
0.946406 + 0.322979i \(0.104684\pi\)
\(504\) 14.1989 + 4.12687i 0.632468 + 0.183825i
\(505\) 16.9109 + 14.0086i 0.752524 + 0.623372i
\(506\) −0.747496 + 7.11195i −0.0332302 + 0.316165i
\(507\) −15.8442 + 27.4430i −0.703667 + 1.21879i
\(508\) 11.6771 5.19896i 0.518086 0.230667i
\(509\) −28.1240 + 5.97795i −1.24658 + 0.264968i −0.783523 0.621363i \(-0.786579\pi\)
−0.463053 + 0.886331i \(0.653246\pi\)
\(510\) −15.6213 + 39.3795i −0.691721 + 1.74375i
\(511\) 0.929962 + 0.0683964i 0.0411391 + 0.00302568i
\(512\) 0.309017 0.951057i 0.0136568 0.0420312i
\(513\) 25.7536 5.47410i 1.13705 0.241688i
\(514\) 27.3152 + 5.80603i 1.20482 + 0.256093i
\(515\) 15.8907 23.8835i 0.700229 1.05243i
\(516\) −20.9630 + 4.45582i −0.922844 + 0.196156i
\(517\) −29.8475 21.6855i −1.31269 0.953727i
\(518\) 1.40295 3.43673i 0.0616421 0.151001i
\(519\) 2.89992 + 2.10691i 0.127292 + 0.0924832i
\(520\) 1.46847 + 2.96308i 0.0643967 + 0.129940i
\(521\) −2.62995 25.0223i −0.115220 1.09625i −0.887451 0.460903i \(-0.847526\pi\)
0.772231 0.635342i \(-0.219141\pi\)
\(522\) 4.09083 + 38.9216i 0.179051 + 1.70355i
\(523\) −5.18068 + 5.75373i −0.226536 + 0.251593i −0.845688 0.533678i \(-0.820810\pi\)
0.619153 + 0.785271i \(0.287476\pi\)
\(524\) −19.5106 −0.852324
\(525\) 3.70333 38.5917i 0.161627 1.68428i
\(526\) 7.93810 0.346118
\(527\) 11.5499 12.8274i 0.503120 0.558772i
\(528\) −1.82315 17.3462i −0.0793426 0.754895i
\(529\) 2.25324 + 21.4381i 0.0979669 + 0.932093i
\(530\) −15.3060 + 14.9691i −0.664849 + 0.650215i
\(531\) 27.5624 + 20.0253i 1.19611 + 0.869023i
\(532\) 9.09700 1.24510i 0.394405 0.0539819i
\(533\) −5.29632 3.84800i −0.229409 0.166675i
\(534\) −3.05885 + 0.650179i −0.132370 + 0.0281360i
\(535\) 23.8795 8.86289i 1.03240 0.383176i
\(536\) 8.10433 + 1.72263i 0.350054 + 0.0744062i
\(537\) −10.2532 + 2.17938i −0.442457 + 0.0940471i
\(538\) 6.35462 19.5575i 0.273967 0.843184i
\(539\) 41.5786 2.60659i 1.79092 0.112274i
\(540\) 4.20813 + 16.4342i 0.181089 + 0.707217i
\(541\) 35.8084 7.61132i 1.53952 0.327236i 0.641480 0.767140i \(-0.278321\pi\)
0.898045 + 0.439904i \(0.144987\pi\)
\(542\) −4.83484 + 2.15261i −0.207674 + 0.0924625i
\(543\) 21.7624 37.6935i 0.933913 1.61758i
\(544\) 0.675754 6.42937i 0.0289727 0.275657i
\(545\) −15.5476 + 9.85255i −0.665987 + 0.422037i
\(546\) 8.27757 7.93613i 0.354247 0.339635i
\(547\) 22.5921 16.4142i 0.965970 0.701819i 0.0114408 0.999935i \(-0.496358\pi\)
0.954530 + 0.298116i \(0.0963582\pi\)
\(548\) −8.69107 + 9.65241i −0.371264 + 0.412331i
\(549\) 24.5337 42.4936i 1.04707 1.81358i
\(550\) −28.4985 + 8.56350i −1.21518 + 0.365149i
\(551\) 12.1510 + 21.0461i 0.517649 + 0.896595i
\(552\) 1.08817 + 3.34905i 0.0463157 + 0.142545i
\(553\) −26.4757 7.69511i −1.12586 0.327229i
\(554\) −18.6339 + 13.5383i −0.791680 + 0.575189i
\(555\) 9.09648 1.33716i 0.386124 0.0567595i
\(556\) −0.260062 + 0.115787i −0.0110291 + 0.00491046i
\(557\) 16.2818 28.2009i 0.689881 1.19491i −0.281995 0.959416i \(-0.590996\pi\)
0.971876 0.235493i \(-0.0756705\pi\)
\(558\) 1.55977 14.8402i 0.0660305 0.628238i
\(559\) −3.34207 + 10.2858i −0.141355 + 0.435044i
\(560\) 1.04318 + 5.82338i 0.0440826 + 0.246083i
\(561\) −34.8438 107.238i −1.47111 4.52760i
\(562\) 27.9762 5.94653i 1.18011 0.250839i
\(563\) −10.0472 11.1586i −0.423440 0.470278i 0.493244 0.869891i \(-0.335811\pi\)
−0.916684 + 0.399613i \(0.869144\pi\)
\(564\) −17.7703 3.77720i −0.748267 0.159049i
\(565\) 1.84516 + 0.966167i 0.0776266 + 0.0406469i
\(566\) −5.12212 + 15.7643i −0.215299 + 0.662621i
\(567\) 12.2959 7.62189i 0.516380 0.320089i
\(568\) −10.1533 −0.426024
\(569\) −2.28413 + 21.7321i −0.0957558 + 0.911055i 0.836186 + 0.548446i \(0.184781\pi\)
−0.931941 + 0.362609i \(0.881886\pi\)
\(570\) 14.1145 + 17.8320i 0.591191 + 0.746902i
\(571\) 2.28111 + 21.7033i 0.0954614 + 0.908255i 0.932514 + 0.361133i \(0.117610\pi\)
−0.837053 + 0.547122i \(0.815723\pi\)
\(572\) −8.04088 3.58003i −0.336206 0.149689i
\(573\) 18.1892 + 55.9805i 0.759864 + 2.33862i
\(574\) −7.17709 9.25478i −0.299566 0.386287i
\(575\) 5.26852 2.88741i 0.219712 0.120413i
\(576\) −2.79437 4.84000i −0.116432 0.201667i
\(577\) 2.23764 + 0.475625i 0.0931542 + 0.0198005i 0.254253 0.967138i \(-0.418170\pi\)
−0.161099 + 0.986938i \(0.551504\pi\)
\(578\) −2.59162 24.6576i −0.107797 1.02562i
\(579\) 9.98991 + 4.44779i 0.415166 + 0.184844i
\(580\) −13.2263 + 8.38152i −0.549192 + 0.348024i
\(581\) 13.9525 + 7.48329i 0.578849 + 0.310459i
\(582\) −31.2199 −1.29411
\(583\) 5.95621 56.6696i 0.246681 2.34701i
\(584\) −0.235830 0.261915i −0.00975870 0.0108381i
\(585\) 17.7979 + 4.98183i 0.735853 + 0.205973i
\(586\) −16.5889 + 18.4238i −0.685280 + 0.761081i
\(587\) −2.14586 + 6.60428i −0.0885691 + 0.272588i −0.985524 0.169533i \(-0.945774\pi\)
0.896955 + 0.442121i \(0.145774\pi\)
\(588\) 18.1822 9.50027i 0.749822 0.391785i
\(589\) −2.86335 8.81248i −0.117982 0.363112i
\(590\) −2.28204 + 13.4387i −0.0939501 + 0.553263i
\(591\) 0.0856982 + 0.0951775i 0.00352515 + 0.00391508i
\(592\) −1.28173 + 0.570662i −0.0526787 + 0.0234541i
\(593\) −15.2501 26.4139i −0.626245 1.08469i −0.988299 0.152531i \(-0.951258\pi\)
0.362054 0.932157i \(-0.382076\pi\)
\(594\) −36.5289 26.5398i −1.49880 1.08894i
\(595\) 14.4238 + 35.4221i 0.591319 + 1.45216i
\(596\) 11.6776 8.48424i 0.478331 0.347528i
\(597\) −1.20821 0.537929i −0.0494487 0.0220160i
\(598\) 1.73822 + 0.369469i 0.0710810 + 0.0151087i
\(599\) −16.5890 + 28.7330i −0.677808 + 1.17400i 0.297832 + 0.954618i \(0.403737\pi\)
−0.975640 + 0.219379i \(0.929597\pi\)
\(600\) −11.1050 + 9.56022i −0.453359 + 0.390294i
\(601\) 17.7128 0.722522 0.361261 0.932465i \(-0.382346\pi\)
0.361261 + 0.932465i \(0.382346\pi\)
\(602\) −10.8769 + 16.0010i −0.443309 + 0.652153i
\(603\) 37.4615 27.2174i 1.52555 1.10838i
\(604\) −5.87498 2.61571i −0.239049 0.106432i
\(605\) 30.2475 45.4616i 1.22974 1.84828i
\(606\) −26.2925 + 11.7062i −1.06806 + 0.475530i
\(607\) −10.2315 17.7215i −0.415285 0.719294i 0.580174 0.814493i \(-0.302985\pi\)
−0.995458 + 0.0951985i \(0.969651\pi\)
\(608\) −2.80761 2.03985i −0.113864 0.0827268i
\(609\) 41.4679 + 35.0510i 1.68036 + 1.42034i
\(610\) 19.5924 + 1.24553i 0.793274 + 0.0504301i
\(611\) −6.13461 + 6.81318i −0.248180 + 0.275632i
\(612\) −24.1757 26.8499i −0.977245 1.08534i
\(613\) 12.8155 + 14.2330i 0.517612 + 0.574866i 0.944113 0.329621i \(-0.106921\pi\)
−0.426502 + 0.904487i \(0.640254\pi\)
\(614\) 2.87714 3.19539i 0.116112 0.128955i
\(615\) 10.6962 26.9639i 0.431312 1.08729i
\(616\) −12.0257 10.1648i −0.484528 0.409551i
\(617\) 15.9324 + 11.5755i 0.641413 + 0.466014i 0.860335 0.509728i \(-0.170254\pi\)
−0.218922 + 0.975742i \(0.570254\pi\)
\(618\) 18.7990 + 32.5607i 0.756205 + 1.30979i
\(619\) 6.84318 3.04678i 0.275051 0.122460i −0.264576 0.964365i \(-0.585232\pi\)
0.539627 + 0.841904i \(0.318565\pi\)
\(620\) 5.59723 2.07742i 0.224790 0.0834312i
\(621\) 8.32789 + 3.70782i 0.334187 + 0.148790i
\(622\) 18.5134 13.4508i 0.742322 0.539328i
\(623\) −1.58712 + 2.33482i −0.0635867 + 0.0935426i
\(624\) −4.33426 −0.173509
\(625\) 19.5516 + 15.5800i 0.782064 + 0.623198i
\(626\) 12.3051 21.3130i 0.491810 0.851840i
\(627\) −59.2070 12.5848i −2.36450 0.502590i
\(628\) 4.35541 + 1.93915i 0.173800 + 0.0773807i
\(629\) −7.33799 + 5.33136i −0.292585 + 0.212575i
\(630\) 28.0870 + 17.4445i 1.11901 + 0.695006i
\(631\) −35.4257 25.7383i −1.41028 1.02463i −0.993282 0.115717i \(-0.963083\pi\)
−0.416994 0.908909i \(-0.636917\pi\)
\(632\) 5.21049 + 9.02484i 0.207262 + 0.358989i
\(633\) 7.32406 3.26088i 0.291105 0.129608i
\(634\) 9.03115 + 10.0301i 0.358673 + 0.398346i
\(635\) 28.2778 4.15679i 1.12217 0.164957i
\(636\) −8.67080 26.6860i −0.343819 1.05817i
\(637\) 0.435828 10.3434i 0.0172681 0.409820i
\(638\) 12.8786 39.6362i 0.509868 1.56921i
\(639\) −37.9694 + 42.1692i −1.50204 + 1.66819i
\(640\) 1.23864 1.86166i 0.0489616 0.0735885i
\(641\) −0.458000 0.508660i −0.0180899 0.0200909i 0.734032 0.679115i \(-0.237636\pi\)
−0.752122 + 0.659024i \(0.770970\pi\)
\(642\) −3.48950 + 33.2004i −0.137719 + 1.31031i
\(643\) 34.3814 1.35587 0.677935 0.735122i \(-0.262875\pi\)
0.677935 + 0.735122i \(0.262875\pi\)
\(644\) 2.80155 + 1.50258i 0.110397 + 0.0592100i
\(645\) −47.8253 3.04036i −1.88312 0.119714i
\(646\) −20.4957 9.12529i −0.806394 0.359030i
\(647\) −0.867778 8.25635i −0.0341159 0.324591i −0.998248 0.0591682i \(-0.981155\pi\)
0.964132 0.265423i \(-0.0855115\pi\)
\(648\) −5.34837 1.13683i −0.210104 0.0446590i
\(649\) −18.1401 31.4196i −0.712061 1.23333i
\(650\) 1.37611 + 7.26551i 0.0539755 + 0.284977i
\(651\) −12.6870 16.3597i −0.497242 0.641188i
\(652\) 3.36890 + 10.3684i 0.131936 + 0.406058i
\(653\) −9.01117 4.01203i −0.352634 0.157003i 0.222772 0.974871i \(-0.428489\pi\)
−0.575406 + 0.817868i \(0.695156\pi\)
\(654\) −2.52166 23.9920i −0.0986048 0.938162i
\(655\) −42.0122 11.7597i −1.64155 0.459488i
\(656\) −0.462702 + 4.40232i −0.0180655 + 0.171882i
\(657\) −1.96971 −0.0768457
\(658\) −13.9402 + 8.64115i −0.543446 + 0.336867i
\(659\) 4.93110 15.1764i 0.192088 0.591187i −0.807910 0.589306i \(-0.799401\pi\)
0.999998 0.00188097i \(-0.000598731\pi\)
\(660\) 6.52930 38.4504i 0.254153 1.49668i
\(661\) 11.1410 + 2.36810i 0.433335 + 0.0921083i 0.419415 0.907795i \(-0.362235\pi\)
0.0139208 + 0.999903i \(0.495569\pi\)
\(662\) 8.48309 + 9.42142i 0.329704 + 0.366174i
\(663\) −27.4077 + 5.82569i −1.06443 + 0.226251i
\(664\) −1.84921 5.69130i −0.0717634 0.220865i
\(665\) 20.3391 + 2.80199i 0.788715 + 0.108656i
\(666\) −2.42305 + 7.45738i −0.0938913 + 0.288968i
\(667\) −0.879522 + 8.36809i −0.0340552 + 0.324014i
\(668\) −0.503371 + 0.871865i −0.0194760 + 0.0337335i
\(669\) 6.13801 2.73282i 0.237309 0.105657i
\(670\) 16.4128 + 8.59409i 0.634082 + 0.332019i
\(671\) −42.2727 + 30.7129i −1.63192 + 1.18566i
\(672\) −7.44567 2.16407i −0.287223 0.0834808i
\(673\) 9.65789 + 29.7239i 0.372284 + 1.14577i 0.945293 + 0.326224i \(0.105776\pi\)
−0.573008 + 0.819550i \(0.694224\pi\)
\(674\) 13.9866 + 24.2255i 0.538744 + 0.933133i
\(675\) −0.844093 + 37.9243i −0.0324892 + 1.45971i
\(676\) 5.40637 9.36411i 0.207937 0.360158i
\(677\) 22.6620 25.1687i 0.870972 0.967313i −0.128731 0.991680i \(-0.541090\pi\)
0.999703 + 0.0243669i \(0.00775700\pi\)
\(678\) −2.20845 + 1.60453i −0.0848150 + 0.0616217i
\(679\) −20.3449 + 19.5057i −0.780765 + 0.748560i
\(680\) 5.33030 13.4371i 0.204408 0.515288i
\(681\) −5.59633 + 53.2455i −0.214452 + 2.04037i
\(682\) −7.94523 + 13.7615i −0.304238 + 0.526957i
\(683\) −28.4623 + 12.6722i −1.08908 + 0.484889i −0.871121 0.491069i \(-0.836606\pi\)
−0.217958 + 0.975958i \(0.569940\pi\)
\(684\) −18.9714 + 4.03249i −0.725388 + 0.154186i
\(685\) −24.5323 + 15.5462i −0.937333 + 0.593989i
\(686\) 5.91308 17.5509i 0.225763 0.670098i
\(687\) −0.498015 + 1.53273i −0.0190004 + 0.0584773i
\(688\) 7.15300 1.52042i 0.272705 0.0579653i
\(689\) −13.8505 2.94402i −0.527662 0.112158i
\(690\) 0.324580 + 7.86739i 0.0123566 + 0.299506i
\(691\) 12.3330 2.62147i 0.469170 0.0997253i 0.0327412 0.999464i \(-0.489576\pi\)
0.436429 + 0.899739i \(0.356243\pi\)
\(692\) −0.989511 0.718922i −0.0376156 0.0273293i
\(693\) −87.1881 + 11.9334i −3.31200 + 0.453312i
\(694\) −20.3892 14.8136i −0.773963 0.562317i
\(695\) −0.629780 + 0.0925765i −0.0238889 + 0.00351163i
\(696\) −2.14517 20.4099i −0.0813124 0.773636i
\(697\) 2.99127 + 28.4600i 0.113302 + 1.07800i
\(698\) 9.23193 10.2531i 0.349434 0.388086i
\(699\) 69.3552 2.62325
\(700\) −1.26365 + 13.1683i −0.0477616 + 0.497714i
\(701\) −31.1561 −1.17675 −0.588374 0.808589i \(-0.700232\pi\)
−0.588374 + 0.808589i \(0.700232\pi\)
\(702\) −7.50784 + 8.33830i −0.283365 + 0.314709i
\(703\) 0.508955 + 4.84239i 0.0191956 + 0.182634i
\(704\) 0.622098 + 5.91886i 0.0234462 + 0.223076i
\(705\) −35.9883 18.8442i −1.35540 0.709715i
\(706\) −7.09235 5.15289i −0.266924 0.193932i
\(707\) −9.82003 + 24.0556i −0.369320 + 0.904703i
\(708\) −14.4533 10.5010i −0.543190 0.394650i
\(709\) −13.9040 + 2.95539i −0.522177 + 0.110992i −0.461457 0.887163i \(-0.652673\pi\)
−0.0607203 + 0.998155i \(0.519340\pi\)
\(710\) −21.8632 6.11974i −0.820510 0.229670i
\(711\) 56.9676 + 12.1088i 2.13645 + 0.454117i
\(712\) 1.04374 0.221855i 0.0391159 0.00831435i
\(713\) 0.991391 3.05119i 0.0371279 0.114268i
\(714\) −49.9915 3.67676i −1.87089 0.137599i
\(715\) −15.1567 12.5554i −0.566827 0.469545i
\(716\) 3.49859 0.743648i 0.130748 0.0277914i
\(717\) 26.3298 11.7228i 0.983305 0.437796i
\(718\) 10.6341 18.4188i 0.396860 0.687382i
\(719\) 5.39700 51.3491i 0.201274 1.91500i −0.168194 0.985754i \(-0.553794\pi\)
0.369469 0.929243i \(-0.379540\pi\)
\(720\) −3.09991 12.1062i −0.115527 0.451173i
\(721\) 32.5940 + 9.47338i 1.21386 + 0.352807i
\(722\) 5.62779 4.08883i 0.209445 0.152170i
\(723\) −26.2065 + 29.1053i −0.974631 + 1.08244i
\(724\) −7.42577 + 12.8618i −0.275977 + 0.478005i
\(725\) −33.5320 + 10.0760i −1.24535 + 0.374214i
\(726\) 35.7833 + 61.9784i 1.32804 + 2.30023i
\(727\) −10.9925 33.8315i −0.407691 1.25474i −0.918628 0.395124i \(-0.870701\pi\)
0.510937 0.859618i \(-0.329299\pi\)
\(728\) −2.82448 + 2.70797i −0.104682 + 0.100364i
\(729\) 29.2410 21.2448i 1.08300 0.786845i
\(730\) −0.349948 0.706126i −0.0129521 0.0261349i
\(731\) 43.1885 19.2287i 1.59738 0.711201i
\(732\) −12.8651 + 22.2830i −0.475508 + 0.823605i
\(733\) 0.843645 8.02674i 0.0311607 0.296475i −0.967832 0.251598i \(-0.919044\pi\)
0.998993 0.0448765i \(-0.0142894\pi\)
\(734\) 2.91632 8.97552i 0.107643 0.331292i
\(735\) 44.8780 9.49793i 1.65535 0.350337i
\(736\) −0.371306 1.14276i −0.0136865 0.0421228i
\(737\) −48.2327 + 10.2522i −1.77667 + 0.377644i
\(738\) 16.5536 + 18.3846i 0.609346 + 0.676748i
\(739\) 29.6651 + 6.30550i 1.09125 + 0.231952i 0.718183 0.695854i \(-0.244974\pi\)
0.373064 + 0.927806i \(0.378307\pi\)
\(740\) −3.10390 + 0.456268i −0.114102 + 0.0167727i
\(741\) −4.64811 + 14.3054i −0.170753 + 0.525522i
\(742\) −22.3234 11.9729i −0.819518 0.439539i
\(743\) −9.84460 −0.361163 −0.180582 0.983560i \(-0.557798\pi\)
−0.180582 + 0.983560i \(0.557798\pi\)
\(744\) −0.817922 + 7.78201i −0.0299865 + 0.285302i
\(745\) 30.2590 11.2307i 1.10861 0.411461i
\(746\) −2.24482 21.3580i −0.0821886 0.781973i
\(747\) −30.5527 13.6029i −1.11786 0.497705i
\(748\) 11.8894 + 36.5918i 0.434720 + 1.33793i
\(749\) 18.4691 + 23.8156i 0.674844 + 0.870205i
\(750\) −29.6747 + 13.8927i −1.08357 + 0.507290i
\(751\) 13.8917 + 24.0612i 0.506917 + 0.878006i 0.999968 + 0.00800529i \(0.00254819\pi\)
−0.493051 + 0.870000i \(0.664118\pi\)
\(752\) 6.06361 + 1.28886i 0.221117 + 0.0469999i
\(753\) 5.08539 + 48.3843i 0.185322 + 1.76322i
\(754\) −9.46110 4.21235i −0.344553 0.153405i
\(755\) −11.0740 9.17346i −0.403025 0.333856i
\(756\) −17.0607 + 10.5755i −0.620493 + 0.384626i
\(757\) −18.4713 −0.671351 −0.335676 0.941978i \(-0.608965\pi\)
−0.335676 + 0.941978i \(0.608965\pi\)
\(758\) 0.393902 3.74773i 0.0143072 0.136124i
\(759\) −14.0233 15.5744i −0.509013 0.565316i
\(760\) −4.81615 6.08465i −0.174700 0.220714i
\(761\) −4.73593 + 5.25978i −0.171677 + 0.190667i −0.822843 0.568269i \(-0.807613\pi\)
0.651166 + 0.758935i \(0.274280\pi\)
\(762\) −11.5758 + 35.6266i −0.419347 + 1.29062i
\(763\) −16.6331 14.0592i −0.602158 0.508978i
\(764\) −6.20652 19.1017i −0.224544 0.691075i
\(765\) −35.8743 72.3874i −1.29704 2.61717i
\(766\) 14.4779 + 16.0793i 0.523107 + 0.580969i
\(767\) −8.23617 + 3.66698i −0.297391 + 0.132407i
\(768\) 1.46533 + 2.53802i 0.0528755 + 0.0915830i
\(769\) 40.4106 + 29.3600i 1.45724 + 1.05875i 0.984071 + 0.177779i \(0.0568911\pi\)
0.473172 + 0.880970i \(0.343109\pi\)
\(770\) −19.7683 29.1361i −0.712399 1.04999i
\(771\) −66.2098 + 48.1043i −2.38449 + 1.73243i
\(772\) −3.40876 1.51768i −0.122684 0.0546224i
\(773\) −25.1719 5.35046i −0.905371 0.192443i −0.268379 0.963313i \(-0.586488\pi\)
−0.636992 + 0.770871i \(0.719821\pi\)
\(774\) 20.4347 35.3939i 0.734510 1.27221i
\(775\) 13.3047 1.09968i 0.477918 0.0395016i
\(776\) 10.6529 0.382416
\(777\) 4.73368 + 9.79488i 0.169820 + 0.351389i
\(778\) −15.2040 + 11.0463i −0.545089 + 0.396031i
\(779\) 14.0338 + 6.24827i 0.502815 + 0.223868i
\(780\) −9.33296 2.61240i −0.334174 0.0935389i
\(781\) 55.2029 24.5779i 1.97532 0.879467i
\(782\) −3.88395 6.72721i −0.138890 0.240564i
\(783\) −42.9808 31.2274i −1.53601 1.11597i
\(784\) −6.20415 + 3.24169i −0.221577 + 0.115775i
\(785\) 8.20973 + 6.80074i 0.293018 + 0.242729i
\(786\) 38.2601 42.4921i 1.36469 1.51564i
\(787\) −13.1177 14.5686i −0.467594 0.519316i 0.462509 0.886615i \(-0.346949\pi\)
−0.930103 + 0.367299i \(0.880283\pi\)
\(788\) −0.0292420 0.0324765i −0.00104170 0.00115693i
\(789\) −15.5666 + 17.2884i −0.554184 + 0.615484i
\(790\) 5.78020 + 22.5737i 0.205650 + 0.803138i
\(791\) −0.436681 + 2.42542i −0.0155266 + 0.0862379i
\(792\) 26.9089 + 19.5505i 0.956167 + 0.694696i
\(793\) 6.49230 + 11.2450i 0.230548 + 0.399321i
\(794\) −7.05780 + 3.14234i −0.250472 + 0.111517i
\(795\) −2.58633 62.6891i −0.0917277 2.22336i
\(796\) 0.412265 + 0.183552i 0.0146124 + 0.00650584i
\(797\) 3.90005 2.83356i 0.138147 0.100370i −0.516565 0.856248i \(-0.672790\pi\)
0.654712 + 0.755878i \(0.272790\pi\)
\(798\) −15.1274 + 22.2540i −0.535506 + 0.787783i
\(799\) 40.0756 1.41777
\(800\) 3.78925 3.26214i 0.133970 0.115334i
\(801\) 2.98177 5.16457i 0.105356 0.182481i
\(802\) 6.98397 + 1.48449i 0.246613 + 0.0524191i
\(803\) 1.91620 + 0.853149i 0.0676214 + 0.0301070i
\(804\) −19.6442 + 14.2724i −0.692799 + 0.503348i
\(805\) 5.12693 + 4.92410i 0.180701 + 0.173552i
\(806\) 3.19462 + 2.32103i 0.112526 + 0.0817548i
\(807\) 30.1330 + 52.1918i 1.06073 + 1.83724i
\(808\) 8.97153 3.99438i 0.315617 0.140522i
\(809\) −17.4898 19.4244i −0.614909 0.682926i 0.352596 0.935776i \(-0.385299\pi\)
−0.967506 + 0.252849i \(0.918632\pi\)
\(810\) −10.8315 5.67159i −0.380579 0.199279i
\(811\) −7.27414 22.3875i −0.255430 0.786131i −0.993745 0.111675i \(-0.964378\pi\)
0.738315 0.674456i \(-0.235622\pi\)
\(812\) −14.1497 11.9601i −0.496557 0.419718i
\(813\) 4.79291 14.7511i 0.168095 0.517342i
\(814\) 5.58728 6.20530i 0.195834 0.217496i
\(815\) 1.00488 + 24.3568i 0.0351993 + 0.853183i
\(816\) 12.6774 + 14.0797i 0.443797 + 0.492887i
\(817\) 2.65276 25.2393i 0.0928083 0.883012i
\(818\) −22.4596 −0.785280
\(819\) 0.684459 + 21.8575i 0.0239169 + 0.763762i
\(820\) −3.64976 + 9.20064i −0.127455 + 0.321300i
\(821\) −35.4027 15.7623i −1.23556 0.550107i −0.318147 0.948041i \(-0.603061\pi\)
−0.917414 + 0.397934i \(0.869727\pi\)
\(822\) −3.97889 37.8566i −0.138780 1.32040i
\(823\) 6.60695 + 1.40435i 0.230304 + 0.0489526i 0.321618 0.946870i \(-0.395773\pi\)
−0.0913140 + 0.995822i \(0.529107\pi\)
\(824\) −6.41459 11.1104i −0.223463 0.387049i
\(825\) 37.2349 78.8599i 1.29635 2.74555i
\(826\) −15.9795 + 2.18711i −0.555999 + 0.0760993i
\(827\) 13.0956 + 40.3041i 0.455378 + 1.40151i 0.870691 + 0.491831i \(0.163672\pi\)
−0.415313 + 0.909679i \(0.636328\pi\)
\(828\) −6.13472 2.73135i −0.213196 0.0949211i
\(829\) 0.119547 + 1.13741i 0.00415204 + 0.0395040i 0.996402 0.0847558i \(-0.0270110\pi\)
−0.992250 + 0.124260i \(0.960344\pi\)
\(830\) −0.551585 13.3697i −0.0191458 0.464068i
\(831\) 7.05580 67.1315i 0.244763 2.32877i
\(832\) 1.47894 0.0512729
\(833\) −34.8748 + 28.8379i −1.20834 + 0.999173i
\(834\) 0.257806 0.793446i 0.00892710 0.0274748i
\(835\) −1.60941 + 1.57399i −0.0556960 + 0.0544702i
\(836\) 20.2026 + 4.29420i 0.698722 + 0.148518i
\(837\) 13.5543 + 15.0536i 0.468506 + 0.520329i
\(838\) −22.8575 + 4.85851i −0.789599 + 0.167834i
\(839\) 6.03586 + 18.5765i 0.208381 + 0.641330i 0.999558 + 0.0297428i \(0.00946882\pi\)
−0.791177 + 0.611588i \(0.790531\pi\)
\(840\) −14.7284 9.14765i −0.508179 0.315624i
\(841\) 6.19176 19.0563i 0.213509 0.657114i
\(842\) 0.0142115 0.135214i 0.000489762 0.00465977i
\(843\) −41.9102 + 72.5905i −1.44346 + 2.50015i
\(844\) −2.49912 + 1.11268i −0.0860232 + 0.0383000i
\(845\) 17.2856 16.9052i 0.594643 0.581556i
\(846\) 28.0284 20.3638i 0.963637 0.700123i
\(847\) 62.0417 + 18.0323i 2.13178 + 0.619597i
\(848\) 2.95865 + 9.10580i 0.101601 + 0.312694i
\(849\) −24.2886 42.0691i −0.833582 1.44381i
\(850\) 19.5767 25.7213i 0.671476 0.882235i
\(851\) −0.842919 + 1.45998i −0.0288949 + 0.0500474i
\(852\) 19.9106 22.1129i 0.682125 0.757576i
\(853\) −15.1661 + 11.0188i −0.519278 + 0.377278i −0.816332 0.577583i \(-0.803996\pi\)
0.297054 + 0.954861i \(0.403996\pi\)
\(854\) 5.53834 + 22.5590i 0.189518 + 0.771951i
\(855\) −43.2816 2.75150i −1.48020 0.0940994i
\(856\) 1.19069 11.3286i 0.0406969 0.387205i
\(857\) 21.9700 38.0532i 0.750482 1.29987i −0.197108 0.980382i \(-0.563155\pi\)
0.947589 0.319491i \(-0.103512\pi\)
\(858\) 23.5651 10.4918i 0.804498 0.358186i
\(859\) −26.8760 + 5.71266i −0.916996 + 0.194913i −0.642154 0.766576i \(-0.721959\pi\)
−0.274842 + 0.961489i \(0.588626\pi\)
\(860\) 16.3190 + 1.03743i 0.556472 + 0.0353761i
\(861\) 34.2302 + 2.51755i 1.16656 + 0.0857978i
\(862\) −7.71159 + 23.7338i −0.262658 + 0.808378i
\(863\) −31.7390 + 6.74633i −1.08041 + 0.229648i −0.713532 0.700622i \(-0.752906\pi\)
−0.366875 + 0.930270i \(0.619572\pi\)
\(864\) 7.42094 + 1.57737i 0.252466 + 0.0536632i
\(865\) −1.69740 2.14447i −0.0577133 0.0729141i
\(866\) −6.08889 + 1.29423i −0.206909 + 0.0439799i
\(867\) 58.7840 + 42.7091i 1.99641 + 1.45048i
\(868\) 4.32906 + 5.58227i 0.146938 + 0.189475i
\(869\) −50.1754 36.4545i −1.70208 1.23664i
\(870\) 7.68254 45.2417i 0.260462 1.53384i
\(871\) 1.28085 + 12.1864i 0.0433998 + 0.412922i
\(872\) 0.860443 + 8.18657i 0.0291383 + 0.277232i
\(873\) 39.8375 44.2441i 1.34830 1.49743i
\(874\) −4.16994 −0.141050
\(875\) −10.6580 + 27.5936i −0.360305 + 0.932834i
\(876\) 1.03289 0.0348980
\(877\) 10.4383 11.5929i 0.352476 0.391465i −0.540667 0.841237i \(-0.681828\pi\)
0.893143 + 0.449772i \(0.148495\pi\)
\(878\) 2.52650 + 24.0380i 0.0852651 + 0.811243i
\(879\) −7.59461 72.2579i −0.256160 2.43720i
\(880\) −2.22793 + 13.1201i −0.0751036 + 0.442277i
\(881\) −19.7864 14.3756i −0.666620 0.484328i 0.202272 0.979329i \(-0.435167\pi\)
−0.868892 + 0.495002i \(0.835167\pi\)
\(882\) −9.73751 + 37.8900i −0.327879 + 1.27582i
\(883\) −3.96239 2.87884i −0.133345 0.0968807i 0.519113 0.854705i \(-0.326262\pi\)
−0.652458 + 0.757825i \(0.726262\pi\)
\(884\) 9.35207 1.98784i 0.314544 0.0668584i
\(885\) −24.7931 31.3233i −0.833412 1.05292i
\(886\) 14.9470 + 3.17709i 0.502156 + 0.106737i
\(887\) 44.3771 9.43264i 1.49004 0.316717i 0.610296 0.792173i \(-0.291050\pi\)
0.879739 + 0.475456i \(0.157717\pi\)
\(888\) 1.27061 3.91054i 0.0426389 0.131229i
\(889\) 14.7154 + 30.4489i 0.493539 + 1.02122i
\(890\) 2.38121 + 0.151379i 0.0798185 + 0.00507423i
\(891\) 31.8307 6.76582i 1.06637 0.226663i
\(892\) −2.09441 + 0.932493i −0.0701262 + 0.0312222i
\(893\) 10.7566 18.6310i 0.359957 0.623463i
\(894\) −4.42175 + 42.0701i −0.147885 + 1.40703i
\(895\) 7.98174 + 0.507417i 0.266800 + 0.0169611i
\(896\) 2.54062 + 0.738424i 0.0848760 + 0.0246690i
\(897\) −4.21330 + 3.06114i −0.140678 + 0.102209i
\(898\) −13.6163 + 15.1224i −0.454381 + 0.504642i
\(899\) −9.34855 + 16.1922i −0.311792 + 0.540039i
\(900\) 0.621799 27.9368i 0.0207266 0.931227i
\(901\) 30.9482 + 53.6039i 1.03103 + 1.78580i
\(902\) −8.14092 25.0552i −0.271063 0.834246i
\(903\) −13.5192 55.0667i −0.449889 1.83250i
\(904\) 0.753568 0.547499i 0.0250633 0.0182096i
\(905\) −23.7422 + 23.2196i −0.789216 + 0.771846i
\(906\) 17.2175 7.66574i 0.572015 0.254677i
\(907\) 5.70695 9.88473i 0.189496 0.328217i −0.755586 0.655049i \(-0.772648\pi\)
0.945082 + 0.326832i \(0.105981\pi\)
\(908\) 1.90958 18.1684i 0.0633717 0.602941i
\(909\) 16.9603 52.1984i 0.562537 1.73131i
\(910\) −7.71414 + 4.12868i −0.255721 + 0.136864i
\(911\) 14.2222 + 43.7714i 0.471202 + 1.45021i 0.851012 + 0.525146i \(0.175989\pi\)
−0.379810 + 0.925064i \(0.624011\pi\)
\(912\) 9.94830 2.11458i 0.329421 0.0700206i
\(913\) 23.8309 + 26.4669i 0.788686 + 0.875925i
\(914\) −21.1941 4.50493i −0.701037 0.149010i
\(915\) −41.1332 + 40.2279i −1.35982 + 1.32989i
\(916\) 0.169933 0.522999i 0.00561474 0.0172804i
\(917\) −1.61567 51.5948i −0.0533542 1.70381i
\(918\) 49.0466 1.61878
\(919\) 4.94153 47.0155i 0.163006 1.55090i −0.541195 0.840897i \(-0.682028\pi\)
0.704201 0.710001i \(-0.251305\pi\)
\(920\) −0.110754 2.68452i −0.00365143 0.0885058i
\(921\) 1.31719 + 12.5323i 0.0434030 + 0.412952i
\(922\) 1.11169 + 0.494956i 0.0366115 + 0.0163005i
\(923\) −4.64023 14.2812i −0.152735 0.470070i
\(924\) 45.7202 6.25769i 1.50408 0.205863i
\(925\) −6.95865 0.888343i −0.228799 0.0292085i
\(926\) −0.514399 0.890965i −0.0169042 0.0292789i
\(927\) −70.1322 14.9071i −2.30344 0.489612i
\(928\) 0.731975 + 6.96428i 0.0240283 + 0.228614i
\(929\) −33.3822 14.8627i −1.09524 0.487630i −0.222058 0.975033i \(-0.571278\pi\)
−0.873177 + 0.487403i \(0.837944\pi\)
\(930\) −6.45171 + 16.2640i −0.211560 + 0.533318i
\(931\) 4.04594 + 23.9535i 0.132600 + 0.785044i
\(932\) −23.6654 −0.775186
\(933\) −7.01018 + 66.6974i −0.229503 + 2.18358i
\(934\) 8.60509 + 9.55692i 0.281567 + 0.312712i
\(935\) 3.54638 + 85.9595i 0.115979 + 2.81117i
\(936\) 5.53063 6.14239i 0.180774 0.200770i
\(937\) −2.82486 + 8.69402i −0.0922841 + 0.284021i −0.986536 0.163542i \(-0.947708\pi\)
0.894252 + 0.447563i \(0.147708\pi\)
\(938\) −3.88429 + 21.5742i −0.126827 + 0.704422i
\(939\) 22.2875 + 68.5940i 0.727326 + 2.23848i
\(940\) 12.2799 + 6.43004i 0.400527 + 0.209725i
\(941\) 30.2914 + 33.6420i 0.987471 + 1.09670i 0.995311 + 0.0967282i \(0.0308378\pi\)
−0.00783995 + 0.999969i \(0.502496\pi\)
\(942\) −12.7642 + 5.68299i −0.415881 + 0.185162i
\(943\) 2.65942 + 4.60625i 0.0866027 + 0.150000i
\(944\) 4.93177 + 3.58314i 0.160516 + 0.116621i
\(945\) −43.1111 + 12.4891i −1.40241 + 0.406271i
\(946\) −35.2099 + 25.5815i −1.14477 + 0.831727i
\(947\) 17.7179 + 7.88853i 0.575755 + 0.256343i 0.673892 0.738830i \(-0.264621\pi\)
−0.0981363 + 0.995173i \(0.531288\pi\)
\(948\) −29.8730 6.34969i −0.970228 0.206228i
\(949\) 0.260620 0.451407i 0.00846007 0.0146533i
\(950\) −6.70321 16.0050i −0.217481 0.519269i
\(951\) −39.5546 −1.28265
\(952\) 17.0581 + 1.25458i 0.552857 + 0.0406613i
\(953\) −18.6738 + 13.5673i −0.604904 + 0.439488i −0.847616 0.530610i \(-0.821963\pi\)
0.242712 + 0.970098i \(0.421963\pi\)
\(954\) 48.8828 + 21.7640i 1.58264 + 0.704637i
\(955\) −1.85128 44.8726i −0.0599062 1.45204i
\(956\) −8.98427 + 4.00006i −0.290572 + 0.129371i
\(957\) 61.0690 + 105.775i 1.97408 + 3.41921i
\(958\) −16.6989 12.1325i −0.539518 0.391983i
\(959\) −26.2451 22.1838i −0.847498 0.716353i
\(960\) 1.62554 + 6.34833i 0.0524642 + 0.204892i
\(961\) −15.9729 + 17.7397i −0.515254 + 0.572247i
\(962\) −1.38844 1.54202i −0.0447650 0.0497166i
\(963\) −42.5980 47.3098i −1.37270 1.52454i
\(964\) 8.94220 9.93132i 0.288009 0.319866i
\(965\) −6.42534 5.32259i −0.206839 0.171340i
\(966\) −8.76630 + 3.15496i −0.282051 + 0.101509i
\(967\) −0.898637 0.652898i −0.0288982 0.0209958i 0.573242 0.819386i \(-0.305685\pi\)
−0.602141 + 0.798390i \(0.705685\pi\)
\(968\) −12.2100 21.1483i −0.392444 0.679732i
\(969\) 60.0660 26.7431i 1.92960 0.859112i
\(970\) 22.9389 + 6.42084i 0.736523 + 0.206161i
\(971\) 13.0331 + 5.80272i 0.418253 + 0.186218i 0.605063 0.796178i \(-0.293148\pi\)
−0.186810 + 0.982396i \(0.559815\pi\)
\(972\) −5.44936 + 3.95919i −0.174788 + 0.126991i
\(973\) −0.327729 0.678133i −0.0105065 0.0217400i
\(974\) 36.1070 1.15694
\(975\) −18.5221 11.2506i −0.593182 0.360307i
\(976\) 4.38984 7.60343i 0.140515 0.243380i
\(977\) −22.5318 4.78928i −0.720856 0.153223i −0.167146 0.985932i \(-0.553455\pi\)
−0.553710 + 0.832709i \(0.686788\pi\)
\(978\) −29.1877 12.9952i −0.933320 0.415541i
\(979\) −5.13773 + 3.73278i −0.164202 + 0.119300i
\(980\) −15.3133 + 3.24089i −0.489165 + 0.103526i
\(981\) 37.2186 + 27.0409i 1.18830 + 0.863349i
\(982\) 4.52839 + 7.84339i 0.144507 + 0.250293i
\(983\) 16.8262 7.49149i 0.536671 0.238941i −0.120459 0.992718i \(-0.538437\pi\)
0.657130 + 0.753777i \(0.271770\pi\)
\(984\) −8.68046 9.64063i −0.276723 0.307332i
\(985\) −0.0433922 0.0875569i −0.00138259 0.00278979i
\(986\) 13.9894 + 43.0548i 0.445512 + 1.37115i
\(987\) 8.51708 47.3057i 0.271102 1.50576i
\(988\) 1.58603 4.88130i 0.0504583 0.155295i
\(989\) 5.87956 6.52991i 0.186959 0.207639i
\(990\) 46.1593 + 58.3170i 1.46704 + 1.85344i
\(991\) 12.6772 + 14.0794i 0.402704 + 0.447248i 0.910052 0.414493i \(-0.136041\pi\)
−0.507349 + 0.861741i \(0.669374\pi\)
\(992\) 0.279092 2.65538i 0.00886117 0.0843084i
\(993\) −37.1542 −1.17905
\(994\) −0.840797 26.8500i −0.0266685 0.851630i
\(995\) 0.777099 + 0.643730i 0.0246357 + 0.0204076i
\(996\) 16.0214 + 7.13318i 0.507657 + 0.226023i
\(997\) 3.80841 + 36.2346i 0.120613 + 1.14756i 0.872618 + 0.488403i \(0.162420\pi\)
−0.752005 + 0.659157i \(0.770913\pi\)
\(998\) 20.3365 + 4.32265i 0.643740 + 0.136831i
\(999\) −5.32219 9.21830i −0.168387 0.291654i
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 350.2.q.c.81.10 80
7.2 even 3 inner 350.2.q.c.331.1 yes 80
25.21 even 5 inner 350.2.q.c.221.1 yes 80
175.121 even 15 inner 350.2.q.c.121.10 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.2.q.c.81.10 80 1.1 even 1 trivial
350.2.q.c.121.10 yes 80 175.121 even 15 inner
350.2.q.c.221.1 yes 80 25.21 even 5 inner
350.2.q.c.331.1 yes 80 7.2 even 3 inner