Properties

Label 471.2.s.a.2.11
Level $471$
Weight $2$
Character 471.2
Analytic conductor $3.761$
Analytic rank $0$
Dimension $1200$
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] = [471,2,Mod(2,471)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(471, base_ring=CyclotomicField(52))
 
chi = DirichletCharacter(H, H._module([26, 47]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("471.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 471.s (of order \(52\), degree \(24\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.76095393520\)
Analytic rank: \(0\)
Dimension: \(1200\)
Relative dimension: \(50\) over \(\Q(\zeta_{52})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label 2.11
Character \(\chi\) \(=\) 471.2
Dual form 471.2.s.a.236.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.76476 + 0.323404i) q^{2} +(-0.748594 + 1.56192i) q^{3} +(1.13976 - 0.432253i) q^{4} +(-1.29547 - 4.15732i) q^{5} +(0.815956 - 2.99852i) q^{6} +(1.29997 - 0.585071i) q^{7} +(1.19919 - 0.724937i) q^{8} +(-1.87921 - 2.33849i) q^{9} +O(q^{10})\) \(q+(-1.76476 + 0.323404i) q^{2} +(-0.748594 + 1.56192i) q^{3} +(1.13976 - 0.432253i) q^{4} +(-1.29547 - 4.15732i) q^{5} +(0.815956 - 2.99852i) q^{6} +(1.29997 - 0.585071i) q^{7} +(1.19919 - 0.724937i) q^{8} +(-1.87921 - 2.33849i) q^{9} +(3.63069 + 6.91770i) q^{10} +(-4.42757 + 3.05613i) q^{11} +(-0.178069 + 2.10380i) q^{12} -1.06451i q^{13} +(-2.10493 + 1.45293i) q^{14} +(7.46319 + 1.08871i) q^{15} +(-3.70666 + 3.28382i) q^{16} +(0.783207 - 1.49228i) q^{17} +(4.07264 + 3.51914i) q^{18} +(4.02889 + 0.993033i) q^{19} +(-3.27354 - 4.17836i) q^{20} +(-0.0593166 + 2.46844i) q^{21} +(6.82523 - 6.82523i) q^{22} +(-0.453506 + 7.49735i) q^{23} +(0.234588 + 2.41573i) q^{24} +(-11.4901 + 7.93104i) q^{25} +(0.344267 + 1.87860i) q^{26} +(5.05932 - 1.18461i) q^{27} +(1.22876 - 1.22876i) q^{28} +(3.42698 + 1.06789i) q^{29} +(-13.5228 + 0.492312i) q^{30} +(-3.35998 - 0.407976i) q^{31} +(3.75098 - 4.78777i) q^{32} +(-1.45899 - 9.20333i) q^{33} +(-0.899564 + 2.88680i) q^{34} +(-4.11640 - 4.64646i) q^{35} +(-3.15267 - 1.85302i) q^{36} +(-7.81338 + 4.10078i) q^{37} +(-7.43119 - 0.449504i) q^{38} +(1.66268 + 0.796886i) q^{39} +(-4.56731 - 4.04628i) q^{40} +(-0.384206 - 6.35168i) q^{41} +(-0.693625 - 4.37539i) q^{42} +(-5.62635 - 2.53221i) q^{43} +(-3.72533 + 5.39708i) q^{44} +(-7.28739 + 10.8419i) q^{45} +(-1.62435 - 13.3777i) q^{46} +(-2.52427 + 4.80960i) q^{47} +(-2.35429 - 8.24777i) q^{48} +(-3.29423 + 3.71842i) q^{49} +(17.7123 - 17.7123i) q^{50} +(1.74452 + 2.34042i) q^{51} +(-0.460137 - 1.21328i) q^{52} +(-5.19968 + 3.14332i) q^{53} +(-8.54538 + 3.72675i) q^{54} +(18.4411 + 14.4477i) q^{55} +(1.13478 - 1.64401i) q^{56} +(-4.56705 + 5.54945i) q^{57} +(-6.39316 - 0.776270i) q^{58} +(6.76857 + 4.09174i) q^{59} +(8.97683 - 1.98512i) q^{60} +(8.68773 - 5.25192i) q^{61} +(6.06151 - 0.366654i) q^{62} +(-3.81111 - 1.94051i) q^{63} +(-0.468527 + 0.892703i) q^{64} +(-4.42550 + 1.37904i) q^{65} +(5.55117 + 15.7698i) q^{66} +(-1.74040 - 0.428971i) q^{67} +(0.247625 - 2.03938i) q^{68} +(-11.3708 - 6.32081i) q^{69} +(8.76715 + 6.86862i) q^{70} +(-1.69986 + 6.89662i) q^{71} +(-3.94880 - 1.44199i) q^{72} +(1.32575 + 2.94571i) q^{73} +(12.4625 - 9.76377i) q^{74} +(-3.78627 - 23.8838i) q^{75} +(5.02120 - 0.609685i) q^{76} +(-3.96767 + 6.56333i) q^{77} +(-3.19195 - 0.868593i) q^{78} +(-1.34867 + 7.35946i) q^{79} +(18.4537 + 11.1557i) q^{80} +(-1.93711 + 8.78906i) q^{81} +(2.73219 + 11.0849i) q^{82} +(2.78649 + 3.55669i) q^{83} +(0.999384 + 2.83906i) q^{84} +(-7.21848 - 1.32284i) q^{85} +(10.7481 + 2.64917i) q^{86} +(-4.23338 + 4.55327i) q^{87} +(-3.09400 + 6.87459i) q^{88} +(-0.789216 - 0.0958282i) q^{89} +(9.35417 - 21.4902i) q^{90} +(-0.622814 - 1.38383i) q^{91} +(2.72386 + 8.74119i) q^{92} +(3.15249 - 4.94263i) q^{93} +(2.89929 - 9.30415i) q^{94} +(-1.09097 - 18.0358i) q^{95} +(4.67017 + 9.44284i) q^{96} +(2.17010 + 6.96411i) q^{97} +(4.61098 - 7.62749i) q^{98} +(15.4671 + 4.61072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1200 q - 26 q^{3} - 52 q^{4} - 20 q^{6} - 40 q^{7} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1200 q - 26 q^{3} - 52 q^{4} - 20 q^{6} - 40 q^{7} - 18 q^{9} - 52 q^{10} - 80 q^{12} - 12 q^{15} + 16 q^{16} + 12 q^{18} - 52 q^{19} - 26 q^{21} - 64 q^{22} + 18 q^{24} + 104 q^{25} - 26 q^{27} - 84 q^{28} - 34 q^{30} - 52 q^{31} - 26 q^{33} - 80 q^{34} - 26 q^{36} - 308 q^{37} + 52 q^{39} - 340 q^{40} - 26 q^{42} - 76 q^{43} - 52 q^{45} - 60 q^{46} - 130 q^{48} - 52 q^{49} - 26 q^{51} + 84 q^{52} - 246 q^{54} - 36 q^{55} - 26 q^{57} - 52 q^{58} + 14 q^{60} - 4 q^{61} - 46 q^{63} - 52 q^{64} - 22 q^{66} + 28 q^{67} - 72 q^{69} - 40 q^{70} + 46 q^{72} - 48 q^{73} - 46 q^{75} - 52 q^{76} + 146 q^{78} - 100 q^{79} + 58 q^{81} - 52 q^{82} - 156 q^{84} - 20 q^{85} + 12 q^{87} - 116 q^{88} - 26 q^{90} + 360 q^{91} - 310 q^{93} + 96 q^{94} + 176 q^{96} + 116 q^{97} - 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).

\(n\) \(158\) \(319\)
\(\chi(n)\) \(-1\) \(e\left(\frac{47}{52}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.76476 + 0.323404i −1.24787 + 0.228681i −0.763286 0.646061i \(-0.776415\pi\)
−0.484588 + 0.874742i \(0.661031\pi\)
\(3\) −0.748594 + 1.56192i −0.432201 + 0.901777i
\(4\) 1.13976 0.432253i 0.569879 0.216126i
\(5\) −1.29547 4.15732i −0.579353 1.85921i −0.507227 0.861812i \(-0.669330\pi\)
−0.0721252 0.997396i \(-0.522978\pi\)
\(6\) 0.815956 2.99852i 0.333113 1.22414i
\(7\) 1.29997 0.585071i 0.491344 0.221136i −0.149566 0.988752i \(-0.547788\pi\)
0.640910 + 0.767616i \(0.278557\pi\)
\(8\) 1.19919 0.724937i 0.423978 0.256304i
\(9\) −1.87921 2.33849i −0.626405 0.779498i
\(10\) 3.63069 + 6.91770i 1.14813 + 2.18757i
\(11\) −4.42757 + 3.05613i −1.33496 + 0.921458i −0.999786 0.0206978i \(-0.993411\pi\)
−0.335176 + 0.942155i \(0.608796\pi\)
\(12\) −0.178069 + 2.10380i −0.0514042 + 0.607314i
\(13\) 1.06451i 0.295242i −0.989044 0.147621i \(-0.952838\pi\)
0.989044 0.147621i \(-0.0471616\pi\)
\(14\) −2.10493 + 1.45293i −0.562566 + 0.388311i
\(15\) 7.46319 + 1.08871i 1.92699 + 0.281104i
\(16\) −3.70666 + 3.28382i −0.926666 + 0.820954i
\(17\) 0.783207 1.49228i 0.189956 0.361930i −0.771789 0.635879i \(-0.780638\pi\)
0.961744 + 0.273949i \(0.0883300\pi\)
\(18\) 4.07264 + 3.51914i 0.959931 + 0.829468i
\(19\) 4.02889 + 0.993033i 0.924292 + 0.227817i 0.672614 0.739994i \(-0.265171\pi\)
0.251678 + 0.967811i \(0.419018\pi\)
\(20\) −3.27354 4.17836i −0.731985 0.934309i
\(21\) −0.0593166 + 2.46844i −0.0129439 + 0.538658i
\(22\) 6.82523 6.82523i 1.45514 1.45514i
\(23\) −0.453506 + 7.49735i −0.0945626 + 1.56331i 0.573503 + 0.819203i \(0.305584\pi\)
−0.668066 + 0.744102i \(0.732877\pi\)
\(24\) 0.234588 + 2.41573i 0.0478851 + 0.493109i
\(25\) −11.4901 + 7.93104i −2.29802 + 1.58621i
\(26\) 0.344267 + 1.87860i 0.0675163 + 0.368425i
\(27\) 5.05932 1.18461i 0.973666 0.227978i
\(28\) 1.22876 1.22876i 0.232213 0.232213i
\(29\) 3.42698 + 1.06789i 0.636374 + 0.198302i 0.598682 0.800987i \(-0.295692\pi\)
0.0376927 + 0.999289i \(0.487999\pi\)
\(30\) −13.5228 + 0.492312i −2.46892 + 0.0898835i
\(31\) −3.35998 0.407976i −0.603471 0.0732746i −0.186902 0.982379i \(-0.559845\pi\)
−0.416569 + 0.909104i \(0.636768\pi\)
\(32\) 3.75098 4.78777i 0.663086 0.846366i
\(33\) −1.45899 9.20333i −0.253978 1.60209i
\(34\) −0.899564 + 2.88680i −0.154274 + 0.495083i
\(35\) −4.11640 4.64646i −0.695799 0.785395i
\(36\) −3.15267 1.85302i −0.525445 0.308837i
\(37\) −7.81338 + 4.10078i −1.28451 + 0.674163i −0.962167 0.272459i \(-0.912163\pi\)
−0.322344 + 0.946623i \(0.604471\pi\)
\(38\) −7.43119 0.449504i −1.20550 0.0729192i
\(39\) 1.66268 + 0.796886i 0.266242 + 0.127604i
\(40\) −4.56731 4.04628i −0.722155 0.639774i
\(41\) −0.384206 6.35168i −0.0600029 0.991966i −0.896232 0.443586i \(-0.853706\pi\)
0.836229 0.548380i \(-0.184755\pi\)
\(42\) −0.693625 4.37539i −0.107029 0.675137i
\(43\) −5.62635 2.53221i −0.858010 0.386159i −0.0668462 0.997763i \(-0.521294\pi\)
−0.791164 + 0.611604i \(0.790524\pi\)
\(44\) −3.72533 + 5.39708i −0.561615 + 0.813640i
\(45\) −7.28739 + 10.8419i −1.08634 + 1.61622i
\(46\) −1.62435 13.3777i −0.239497 1.97243i
\(47\) −2.52427 + 4.80960i −0.368203 + 0.701552i −0.997113 0.0759256i \(-0.975809\pi\)
0.628911 + 0.777478i \(0.283501\pi\)
\(48\) −2.35429 8.24777i −0.339812 1.19046i
\(49\) −3.29423 + 3.71842i −0.470605 + 0.531203i
\(50\) 17.7123 17.7123i 2.50490 2.50490i
\(51\) 1.74452 + 2.34042i 0.244281 + 0.327724i
\(52\) −0.460137 1.21328i −0.0638096 0.168252i
\(53\) −5.19968 + 3.14332i −0.714231 + 0.431768i −0.827256 0.561825i \(-0.810100\pi\)
0.113026 + 0.993592i \(0.463946\pi\)
\(54\) −8.54538 + 3.72675i −1.16288 + 0.507147i
\(55\) 18.4411 + 14.4477i 2.48660 + 1.94812i
\(56\) 1.13478 1.64401i 0.151641 0.219690i
\(57\) −4.56705 + 5.54945i −0.604920 + 0.735042i
\(58\) −6.39316 0.776270i −0.839463 0.101929i
\(59\) 6.76857 + 4.09174i 0.881192 + 0.532699i 0.884101 0.467296i \(-0.154772\pi\)
−0.00290838 + 0.999996i \(0.500926\pi\)
\(60\) 8.97683 1.98512i 1.15890 0.256278i
\(61\) 8.68773 5.25192i 1.11235 0.672439i 0.162990 0.986628i \(-0.447886\pi\)
0.949361 + 0.314188i \(0.101732\pi\)
\(62\) 6.06151 0.366654i 0.769812 0.0465651i
\(63\) −3.81111 1.94051i −0.480155 0.244481i
\(64\) −0.468527 + 0.892703i −0.0585659 + 0.111588i
\(65\) −4.42550 + 1.37904i −0.548916 + 0.171049i
\(66\) 5.55117 + 15.7698i 0.683301 + 1.94113i
\(67\) −1.74040 0.428971i −0.212624 0.0524071i 0.131565 0.991308i \(-0.458000\pi\)
−0.344189 + 0.938900i \(0.611846\pi\)
\(68\) 0.247625 2.03938i 0.0300289 0.247311i
\(69\) −11.3708 6.32081i −1.36888 0.760937i
\(70\) 8.76715 + 6.86862i 1.04787 + 0.820958i
\(71\) −1.69986 + 6.89662i −0.201737 + 0.818478i 0.779615 + 0.626259i \(0.215415\pi\)
−0.981352 + 0.192219i \(0.938432\pi\)
\(72\) −3.94880 1.44199i −0.465370 0.169940i
\(73\) 1.32575 + 2.94571i 0.155168 + 0.344769i 0.973042 0.230629i \(-0.0740782\pi\)
−0.817874 + 0.575397i \(0.804847\pi\)
\(74\) 12.4625 9.76377i 1.44874 1.13502i
\(75\) −3.78627 23.8838i −0.437201 2.75786i
\(76\) 5.02120 0.609685i 0.575972 0.0699356i
\(77\) −3.96767 + 6.56333i −0.452158 + 0.747961i
\(78\) −3.19195 0.868593i −0.361418 0.0983488i
\(79\) −1.34867 + 7.35946i −0.151737 + 0.828004i 0.816382 + 0.577513i \(0.195977\pi\)
−0.968119 + 0.250491i \(0.919408\pi\)
\(80\) 18.4537 + 11.1557i 2.06319 + 1.24724i
\(81\) −1.93711 + 8.78906i −0.215234 + 0.976562i
\(82\) 2.73219 + 11.0849i 0.301720 + 1.22413i
\(83\) 2.78649 + 3.55669i 0.305857 + 0.390397i 0.915526 0.402258i \(-0.131775\pi\)
−0.609669 + 0.792656i \(0.708698\pi\)
\(84\) 0.999384 + 2.83906i 0.109042 + 0.309767i
\(85\) −7.21848 1.32284i −0.782954 0.143482i
\(86\) 10.7481 + 2.64917i 1.15900 + 0.285667i
\(87\) −4.23338 + 4.55327i −0.453866 + 0.488161i
\(88\) −3.09400 + 6.87459i −0.329822 + 0.732834i
\(89\) −0.789216 0.0958282i −0.0836568 0.0101578i 0.0786012 0.996906i \(-0.474955\pi\)
−0.162258 + 0.986748i \(0.551878\pi\)
\(90\) 9.35417 21.4902i 0.986016 2.26527i
\(91\) −0.622814 1.38383i −0.0652886 0.145065i
\(92\) 2.72386 + 8.74119i 0.283983 + 0.911332i
\(93\) 3.15249 4.94263i 0.326898 0.512527i
\(94\) 2.89929 9.30415i 0.299039 0.959650i
\(95\) −1.09097 18.0358i −0.111931 1.85044i
\(96\) 4.67017 + 9.44284i 0.476648 + 0.963756i
\(97\) 2.17010 + 6.96411i 0.220341 + 0.707098i 0.997016 + 0.0771969i \(0.0245970\pi\)
−0.776675 + 0.629901i \(0.783095\pi\)
\(98\) 4.61098 7.62749i 0.465779 0.770493i
\(99\) 15.4671 + 4.61072i 1.55450 + 0.463395i
\(100\) −9.66771 + 14.0061i −0.966771 + 1.40061i
\(101\) −3.19518 2.20547i −0.317932 0.219453i 0.398401 0.917211i \(-0.369565\pi\)
−0.716333 + 0.697759i \(0.754181\pi\)
\(102\) −3.83556 3.56609i −0.379777 0.353096i
\(103\) 3.93552 + 5.02332i 0.387778 + 0.494962i 0.941158 0.337967i \(-0.109739\pi\)
−0.553380 + 0.832929i \(0.686662\pi\)
\(104\) −0.771702 1.27655i −0.0756716 0.125176i
\(105\) 10.3389 2.95120i 1.00898 0.288007i
\(106\) 8.15963 7.22880i 0.792533 0.702123i
\(107\) −3.71393 3.71393i −0.359040 0.359040i 0.504419 0.863459i \(-0.331707\pi\)
−0.863459 + 0.504419i \(0.831707\pi\)
\(108\) 5.25435 3.53707i 0.505600 0.340355i
\(109\) 0.844101 + 2.22571i 0.0808502 + 0.213184i 0.969346 0.245701i \(-0.0790181\pi\)
−0.888495 + 0.458885i \(0.848249\pi\)
\(110\) −37.2165 19.5327i −3.54846 1.86237i
\(111\) −0.556054 15.2737i −0.0527783 1.44972i
\(112\) −2.89730 + 6.43754i −0.273769 + 0.608290i
\(113\) −1.08681 0.750169i −0.102238 0.0705700i 0.515849 0.856680i \(-0.327477\pi\)
−0.618087 + 0.786110i \(0.712092\pi\)
\(114\) 6.26503 11.2705i 0.586774 1.05557i
\(115\) 31.7564 7.82724i 2.96130 0.729894i
\(116\) 4.36752 0.264187i 0.405514 0.0245291i
\(117\) −2.48935 + 2.00044i −0.230140 + 0.184941i
\(118\) −13.2682 5.03196i −1.22144 0.463229i
\(119\) 0.145061 2.39815i 0.0132978 0.219838i
\(120\) 9.73905 4.10477i 0.889049 0.374712i
\(121\) 6.36278 16.7773i 0.578434 1.52521i
\(122\) −13.6333 + 12.0780i −1.23430 + 1.09349i
\(123\) 10.2085 + 4.15473i 0.920466 + 0.374620i
\(124\) −4.00591 + 0.987369i −0.359742 + 0.0886684i
\(125\) 30.7181 + 24.0661i 2.74751 + 2.15254i
\(126\) 7.35327 + 2.19200i 0.655082 + 0.195279i
\(127\) −20.1505 + 2.44672i −1.78807 + 0.217111i −0.946426 0.322921i \(-0.895335\pi\)
−0.841644 + 0.540032i \(0.818412\pi\)
\(128\) −3.08078 + 9.88659i −0.272305 + 0.873859i
\(129\) 8.16698 6.89233i 0.719062 0.606836i
\(130\) 7.36396 3.86491i 0.645862 0.338975i
\(131\) 2.85478 0.523158i 0.249423 0.0457085i −0.0540887 0.998536i \(-0.517225\pi\)
0.303512 + 0.952828i \(0.401841\pi\)
\(132\) −5.64106 9.85890i −0.490991 0.858107i
\(133\) 5.81845 1.06627i 0.504524 0.0924574i
\(134\) 3.21012 + 0.194177i 0.277312 + 0.0167743i
\(135\) −11.4790 19.4986i −0.987954 1.67817i
\(136\) −0.142590 2.35730i −0.0122270 0.202137i
\(137\) −14.8196 + 11.6104i −1.26613 + 0.991946i −0.266521 + 0.963829i \(0.585874\pi\)
−0.999605 + 0.0281166i \(0.991049\pi\)
\(138\) 22.1109 + 7.47736i 1.88221 + 0.636515i
\(139\) −1.86030 1.12459i −0.157788 0.0953864i 0.436241 0.899830i \(-0.356310\pi\)
−0.594029 + 0.804444i \(0.702464\pi\)
\(140\) −6.70015 3.51651i −0.566266 0.297199i
\(141\) −5.62257 7.54316i −0.473506 0.635249i
\(142\) 0.769456 12.7206i 0.0645713 1.06749i
\(143\) 3.25328 + 4.71319i 0.272053 + 0.394137i
\(144\) 14.6448 + 2.49702i 1.22040 + 0.208085i
\(145\) 15.6305i 1.29804i
\(146\) −3.29229 4.76971i −0.272472 0.394744i
\(147\) −3.34185 7.92893i −0.275631 0.653967i
\(148\) −7.13278 + 8.05124i −0.586311 + 0.661808i
\(149\) 3.34350 + 5.53083i 0.273911 + 0.453103i 0.962204 0.272329i \(-0.0877938\pi\)
−0.688294 + 0.725432i \(0.741640\pi\)
\(150\) 14.4060 + 40.9247i 1.17624 + 3.34149i
\(151\) 6.73874 + 1.23492i 0.548391 + 0.100496i 0.447305 0.894381i \(-0.352384\pi\)
0.101085 + 0.994878i \(0.467768\pi\)
\(152\) 5.55130 1.72986i 0.450270 0.140310i
\(153\) −4.96149 + 0.972781i −0.401113 + 0.0786447i
\(154\) 4.87938 12.8659i 0.393192 1.03676i
\(155\) 2.65668 + 14.4970i 0.213390 + 1.16443i
\(156\) 2.23951 + 0.189556i 0.179304 + 0.0151767i
\(157\) −12.3519 2.10475i −0.985791 0.167977i
\(158\) 13.4239i 1.06794i
\(159\) −1.01717 10.4746i −0.0806669 0.830687i
\(160\) −24.7636 9.39158i −1.95773 0.742469i
\(161\) 3.79693 + 10.0117i 0.299240 + 0.789032i
\(162\) 0.576115 16.1371i 0.0452638 1.26785i
\(163\) 1.91762 10.4641i 0.150200 0.819613i −0.819085 0.573672i \(-0.805518\pi\)
0.969285 0.245941i \(-0.0790969\pi\)
\(164\) −3.18344 7.07330i −0.248585 0.552332i
\(165\) −36.3710 + 17.9881i −2.83148 + 1.40037i
\(166\) −6.06774 5.37554i −0.470948 0.417223i
\(167\) −22.4856 + 11.8014i −1.73999 + 0.913216i −0.783527 + 0.621358i \(0.786581\pi\)
−0.956462 + 0.291858i \(0.905726\pi\)
\(168\) 1.71833 + 3.00313i 0.132572 + 0.231697i
\(169\) 11.8668 0.912832
\(170\) 13.1667 1.00984
\(171\) −5.24895 11.2877i −0.401397 0.863190i
\(172\) −7.50723 0.454104i −0.572421 0.0346251i
\(173\) −16.5185 18.6456i −1.25588 1.41760i −0.868511 0.495671i \(-0.834922\pi\)
−0.387369 0.921925i \(-0.626616\pi\)
\(174\) 5.99836 9.40452i 0.454734 0.712955i
\(175\) −10.2966 + 17.0327i −0.778351 + 1.28755i
\(176\) 6.37573 25.8674i 0.480589 1.94983i
\(177\) −11.4579 + 7.50893i −0.861228 + 0.564406i
\(178\) 1.42377 0.0861222i 0.106716 0.00645513i
\(179\) −13.4917 13.4917i −1.00842 1.00842i −0.999964 0.00845578i \(-0.997308\pi\)
−0.00845578 0.999964i \(-0.502692\pi\)
\(180\) −3.61940 + 15.5072i −0.269774 + 1.15584i
\(181\) −2.64028 14.4076i −0.196251 1.07090i −0.923231 0.384246i \(-0.874461\pi\)
0.726980 0.686659i \(-0.240923\pi\)
\(182\) 1.54666 + 2.24072i 0.114646 + 0.166093i
\(183\) 1.69951 + 17.5011i 0.125632 + 1.29372i
\(184\) 4.89126 + 9.31952i 0.360589 + 0.687044i
\(185\) 27.1702 + 27.1702i 1.99759 + 1.99759i
\(186\) −3.96492 + 9.74209i −0.290722 + 0.714325i
\(187\) 1.09289 + 9.00073i 0.0799198 + 0.658199i
\(188\) −0.798095 + 6.57290i −0.0582070 + 0.479378i
\(189\) 5.88390 4.50002i 0.427991 0.327328i
\(190\) 7.75816 + 31.4761i 0.562836 + 2.28352i
\(191\) 2.14014 + 0.666895i 0.154855 + 0.0482548i 0.373951 0.927449i \(-0.378003\pi\)
−0.219095 + 0.975703i \(0.570311\pi\)
\(192\) −1.04360 1.40008i −0.0753152 0.101042i
\(193\) 16.8692 + 6.39765i 1.21427 + 0.460513i 0.876815 0.480828i \(-0.159664\pi\)
0.337458 + 0.941341i \(0.390433\pi\)
\(194\) −6.08194 11.5882i −0.436658 0.831982i
\(195\) 1.15895 7.94464i 0.0829938 0.568928i
\(196\) −2.14733 + 5.66204i −0.153381 + 0.404432i
\(197\) 10.0112 11.3003i 0.713266 0.805110i −0.274412 0.961612i \(-0.588483\pi\)
0.987678 + 0.156502i \(0.0500217\pi\)
\(198\) −28.7868 3.13469i −2.04579 0.222773i
\(199\) 1.47146 + 5.96994i 0.104309 + 0.423198i 0.999759 0.0219647i \(-0.00699215\pi\)
−0.895450 + 0.445162i \(0.853146\pi\)
\(200\) −8.02933 + 17.8404i −0.567759 + 1.26151i
\(201\) 1.97287 2.39725i 0.139156 0.169089i
\(202\) 6.35198 + 2.85880i 0.446924 + 0.201144i
\(203\) 5.07978 0.616796i 0.356530 0.0432906i
\(204\) 2.99998 + 1.91344i 0.210041 + 0.133967i
\(205\) −25.9082 + 9.82569i −1.80951 + 0.686256i
\(206\) −8.56981 7.59219i −0.597087 0.528973i
\(207\) 18.3847 13.0286i 1.27783 0.905551i
\(208\) 3.49566 + 3.94578i 0.242380 + 0.273591i
\(209\) −20.8730 + 7.91610i −1.44382 + 0.547568i
\(210\) −17.2913 + 8.55181i −1.19321 + 0.590131i
\(211\) −2.66149 + 2.08515i −0.183225 + 0.143547i −0.704140 0.710061i \(-0.748667\pi\)
0.520916 + 0.853608i \(0.325591\pi\)
\(212\) −4.56766 + 5.83019i −0.313708 + 0.400419i
\(213\) −9.49949 7.81783i −0.650894 0.535669i
\(214\) 7.75531 + 5.35310i 0.530142 + 0.365931i
\(215\) −3.23844 + 26.6709i −0.220859 + 1.81894i
\(216\) 5.20833 5.08826i 0.354382 0.346212i
\(217\) −4.60659 + 1.43547i −0.312715 + 0.0974461i
\(218\) −2.20944 3.65486i −0.149642 0.247538i
\(219\) −5.59342 0.134410i −0.377968 0.00908257i
\(220\) 27.2634 + 8.49562i 1.83810 + 0.572775i
\(221\) −1.58854 0.833731i −0.106857 0.0560828i
\(222\) 5.92089 + 26.7746i 0.397384 + 1.79700i
\(223\) −17.6616 + 7.94883i −1.18271 + 0.532293i −0.903771 0.428017i \(-0.859212\pi\)
−0.278936 + 0.960310i \(0.589982\pi\)
\(224\) 2.07499 8.41856i 0.138641 0.562489i
\(225\) 40.1391 + 11.9654i 2.67594 + 0.797694i
\(226\) 2.16056 + 0.972391i 0.143719 + 0.0646825i
\(227\) 8.48241 10.8270i 0.562998 0.718613i −0.418899 0.908033i \(-0.637584\pi\)
0.981896 + 0.189420i \(0.0606607\pi\)
\(228\) −2.80656 + 8.29915i −0.185869 + 0.549624i
\(229\) −0.696379 + 3.80002i −0.0460180 + 0.251112i −0.998583 0.0532244i \(-0.983050\pi\)
0.952565 + 0.304337i \(0.0984348\pi\)
\(230\) −53.5110 + 24.0833i −3.52841 + 1.58801i
\(231\) −7.28125 11.1105i −0.479071 0.731015i
\(232\) 4.88376 1.20374i 0.320634 0.0790293i
\(233\) −1.21116 9.97478i −0.0793455 0.653469i −0.977071 0.212914i \(-0.931705\pi\)
0.897725 0.440555i \(-0.145218\pi\)
\(234\) 3.74616 4.33537i 0.244894 0.283412i
\(235\) 23.2651 + 4.26350i 1.51765 + 0.278120i
\(236\) 9.48319 + 1.73786i 0.617303 + 0.113125i
\(237\) −10.4853 7.61577i −0.681094 0.494697i
\(238\) 0.519574 + 4.27908i 0.0336790 + 0.277371i
\(239\) 11.3489 2.79724i 0.734097 0.180939i 0.145492 0.989359i \(-0.453523\pi\)
0.588605 + 0.808421i \(0.299677\pi\)
\(240\) −31.2387 + 20.4723i −2.01645 + 1.32148i
\(241\) 11.6179 5.22881i 0.748377 0.336817i −8.06254e−5 1.00000i \(-0.500026\pi\)
0.748457 + 0.663183i \(0.230795\pi\)
\(242\) −5.80294 + 31.6656i −0.373027 + 2.03554i
\(243\) −12.2777 9.60506i −0.787617 0.616165i
\(244\) 7.63175 9.74121i 0.488573 0.623617i
\(245\) 19.7262 + 8.87806i 1.26026 + 0.567198i
\(246\) −19.3591 4.03065i −1.23429 0.256985i
\(247\) 1.05709 4.28880i 0.0672613 0.272890i
\(248\) −4.32502 + 1.94653i −0.274639 + 0.123605i
\(249\) −7.64123 + 1.68977i −0.484243 + 0.107085i
\(250\) −61.9931 32.5365i −3.92079 2.05779i
\(251\) −14.1832 4.41965i −0.895233 0.278966i −0.184838 0.982769i \(-0.559176\pi\)
−0.710395 + 0.703803i \(0.751484\pi\)
\(252\) −5.18254 0.564344i −0.326469 0.0355503i
\(253\) −20.9049 34.5810i −1.31428 2.17409i
\(254\) 34.7696 10.8346i 2.18164 0.679826i
\(255\) 7.46988 10.2845i 0.467782 0.644038i
\(256\) 2.48253 20.4455i 0.155158 1.27784i
\(257\) 22.4421 + 15.4907i 1.39990 + 0.966283i 0.998735 + 0.0502781i \(0.0160108\pi\)
0.401167 + 0.916005i \(0.368605\pi\)
\(258\) −12.1837 + 14.8045i −0.758527 + 0.921691i
\(259\) −7.75794 + 9.90228i −0.482055 + 0.615298i
\(260\) −4.44790 + 3.48471i −0.275847 + 0.216113i
\(261\) −3.94277 10.0208i −0.244052 0.620270i
\(262\) −4.86881 + 1.84650i −0.300796 + 0.114077i
\(263\) 4.94578 + 5.58263i 0.304970 + 0.344240i 0.880937 0.473233i \(-0.156913\pi\)
−0.575968 + 0.817472i \(0.695375\pi\)
\(264\) −8.42144 9.97888i −0.518304 0.614157i
\(265\) 19.8038 + 17.5446i 1.21654 + 1.07776i
\(266\) −9.92334 + 3.76343i −0.608439 + 0.230750i
\(267\) 0.740479 1.16096i 0.0453166 0.0710496i
\(268\) −2.16906 + 0.263372i −0.132496 + 0.0160880i
\(269\) −22.5664 10.1563i −1.37590 0.619242i −0.418555 0.908191i \(-0.637463\pi\)
−0.957345 + 0.288949i \(0.906694\pi\)
\(270\) 26.5636 + 30.6979i 1.61661 + 1.86822i
\(271\) 2.32560 5.16726i 0.141270 0.313889i −0.827658 0.561233i \(-0.810327\pi\)
0.968928 + 0.247344i \(0.0795579\pi\)
\(272\) 1.99728 + 8.10327i 0.121103 + 0.491333i
\(273\) 2.62768 + 0.0631431i 0.159034 + 0.00382159i
\(274\) 22.3982 25.2824i 1.35313 1.52736i
\(275\) 26.6349 70.2305i 1.60615 4.23506i
\(276\) −15.6921 2.28913i −0.944556 0.137790i
\(277\) 10.0883 + 19.2216i 0.606146 + 1.15491i 0.974322 + 0.225159i \(0.0722901\pi\)
−0.368176 + 0.929756i \(0.620018\pi\)
\(278\) 3.64668 + 1.38300i 0.218713 + 0.0829470i
\(279\) 5.36008 + 8.62398i 0.320899 + 0.516304i
\(280\) −8.30474 2.58786i −0.496303 0.154654i
\(281\) −2.23737 9.07736i −0.133470 0.541510i −0.999162 0.0409323i \(-0.986967\pi\)
0.865692 0.500577i \(-0.166879\pi\)
\(282\) 12.3620 + 11.4935i 0.736146 + 0.684428i
\(283\) 3.42987 28.2475i 0.203885 1.67914i −0.427766 0.903889i \(-0.640699\pi\)
0.631651 0.775253i \(-0.282378\pi\)
\(284\) 1.04365 + 8.59524i 0.0619293 + 0.510034i
\(285\) 28.9873 + 11.7975i 1.71706 + 0.698824i
\(286\) −7.26553 7.26553i −0.429620 0.429620i
\(287\) −4.21564 8.03223i −0.248841 0.474128i
\(288\) −18.2451 + 0.225603i −1.07510 + 0.0132938i
\(289\) 8.04363 + 11.6532i 0.473154 + 0.685483i
\(290\) 5.05496 + 27.5840i 0.296837 + 1.61979i
\(291\) −12.5019 1.82375i −0.732877 0.106910i
\(292\) 2.78433 + 2.78433i 0.162941 + 0.162941i
\(293\) 20.9347 1.26632i 1.22302 0.0739791i 0.563789 0.825919i \(-0.309343\pi\)
0.659231 + 0.751940i \(0.270882\pi\)
\(294\) 8.46181 + 12.9119i 0.493503 + 0.753037i
\(295\) 8.24217 33.4398i 0.479878 1.94694i
\(296\) −6.39693 + 10.5818i −0.371814 + 0.615056i
\(297\) −18.7802 + 20.7069i −1.08974 + 1.20153i
\(298\) −7.68918 8.67929i −0.445422 0.502778i
\(299\) 7.98100 + 0.482762i 0.461553 + 0.0279188i
\(300\) −14.6393 25.5851i −0.845199 1.47716i
\(301\) −8.79563 −0.506972
\(302\) −12.2916 −0.707304
\(303\) 5.83667 3.33962i 0.335308 0.191856i
\(304\) −18.1947 + 9.54931i −1.04354 + 0.547691i
\(305\) −33.0886 29.3139i −1.89465 1.67851i
\(306\) 8.44124 3.32129i 0.482554 0.189866i
\(307\) −9.35186 20.7790i −0.533739 1.18592i −0.959661 0.281159i \(-0.909281\pi\)
0.425922 0.904760i \(-0.359950\pi\)
\(308\) −1.68516 + 9.19564i −0.0960211 + 0.523970i
\(309\) −10.7921 + 2.38655i −0.613944 + 0.135766i
\(310\) −9.37681 24.7246i −0.532567 1.40426i
\(311\) −0.234512 0.0889386i −0.0132979 0.00504324i 0.347947 0.937514i \(-0.386879\pi\)
−0.361245 + 0.932471i \(0.617648\pi\)
\(312\) 2.57157 0.249722i 0.145586 0.0141377i
\(313\) 7.64939i 0.432369i 0.976353 + 0.216185i \(0.0693613\pi\)
−0.976353 + 0.216185i \(0.930639\pi\)
\(314\) 22.4789 0.280284i 1.26856 0.0158173i
\(315\) −3.13011 + 18.3579i −0.176362 + 1.03435i
\(316\) 1.64399 + 8.97097i 0.0924817 + 0.504656i
\(317\) −5.62993 + 14.8449i −0.316208 + 0.833773i 0.678831 + 0.734294i \(0.262487\pi\)
−0.995040 + 0.0994789i \(0.968282\pi\)
\(318\) 5.18259 + 18.1562i 0.290625 + 1.01815i
\(319\) −18.4368 + 5.74514i −1.03226 + 0.321666i
\(320\) 4.31821 + 0.791342i 0.241395 + 0.0442374i
\(321\) 8.58111 3.02066i 0.478951 0.168597i
\(322\) −9.93851 16.4403i −0.553851 0.916182i
\(323\) 4.63734 5.23447i 0.258028 0.291254i
\(324\) 1.59126 + 10.8547i 0.0884035 + 0.603040i
\(325\) 8.44267 + 12.2313i 0.468315 + 0.678472i
\(326\) 19.0868i 1.05712i
\(327\) −4.10828 0.347733i −0.227188 0.0192297i
\(328\) −5.06530 7.33836i −0.279685 0.405193i
\(329\) −0.467532 + 7.72923i −0.0257759 + 0.426126i
\(330\) 58.3687 43.5073i 3.21309 2.39500i
\(331\) 9.08388 + 4.76759i 0.499295 + 0.262050i 0.695518 0.718509i \(-0.255175\pi\)
−0.196222 + 0.980559i \(0.562867\pi\)
\(332\) 4.71331 + 2.84930i 0.258677 + 0.156375i
\(333\) 24.2726 + 10.5653i 1.33013 + 0.578975i
\(334\) 35.8651 28.0985i 1.96245 1.53748i
\(335\) 0.471276 + 7.79112i 0.0257486 + 0.425674i
\(336\) −7.88604 9.34447i −0.430219 0.509782i
\(337\) −12.1177 0.732983i −0.660091 0.0399281i −0.273063 0.961996i \(-0.588037\pi\)
−0.387028 + 0.922068i \(0.626498\pi\)
\(338\) −20.9421 + 3.83778i −1.13910 + 0.208748i
\(339\) 1.98529 1.13594i 0.107826 0.0616957i
\(340\) −8.79912 + 1.61250i −0.477199 + 0.0874500i
\(341\) 16.1234 8.46220i 0.873130 0.458254i
\(342\) 12.9136 + 18.2225i 0.698289 + 0.985360i
\(343\) −5.07565 + 16.2883i −0.274059 + 0.879488i
\(344\) −8.58276 + 1.04214i −0.462752 + 0.0561882i
\(345\) −11.5471 + 55.4604i −0.621673 + 2.98589i
\(346\) 35.1813 + 27.5628i 1.89136 + 1.48178i
\(347\) −9.23472 + 2.27615i −0.495746 + 0.122190i −0.479259 0.877674i \(-0.659094\pi\)
−0.0164870 + 0.999864i \(0.505248\pi\)
\(348\) −2.85686 + 7.01951i −0.153144 + 0.376285i
\(349\) −16.1390 + 14.2979i −0.863900 + 0.765348i −0.973514 0.228626i \(-0.926577\pi\)
0.109615 + 0.993974i \(0.465038\pi\)
\(350\) 12.6626 33.3886i 0.676845 1.78469i
\(351\) −1.26103 5.38569i −0.0673086 0.287467i
\(352\) −1.97567 + 32.6617i −0.105303 + 1.74087i
\(353\) −23.6301 8.96173i −1.25770 0.476985i −0.366429 0.930446i \(-0.619420\pi\)
−0.891276 + 0.453461i \(0.850189\pi\)
\(354\) 17.7920 16.9570i 0.945635 0.901255i
\(355\) 30.8735 1.86751i 1.63860 0.0991169i
\(356\) −0.940937 + 0.231920i −0.0498696 + 0.0122917i
\(357\) 3.63714 + 2.02182i 0.192498 + 0.107006i
\(358\) 28.1730 + 19.4464i 1.48899 + 1.02777i
\(359\) 6.61392 14.6955i 0.349070 0.775601i −0.650797 0.759252i \(-0.725565\pi\)
0.999866 0.0163488i \(-0.00520422\pi\)
\(360\) −0.879258 + 18.2845i −0.0463410 + 0.963676i
\(361\) −1.57779 0.828087i −0.0830415 0.0435835i
\(362\) 9.31893 + 24.5720i 0.489792 + 1.29148i
\(363\) 21.4417 + 22.4975i 1.12540 + 1.18081i
\(364\) −1.30802 1.30802i −0.0685590 0.0685590i
\(365\) 10.5288 9.32766i 0.551100 0.488232i
\(366\) −8.65918 30.3357i −0.452622 1.58567i
\(367\) −14.1795 23.4558i −0.740164 1.22438i −0.968066 0.250697i \(-0.919340\pi\)
0.227901 0.973684i \(-0.426814\pi\)
\(368\) −22.9389 29.2794i −1.19577 1.52629i
\(369\) −14.1314 + 12.8346i −0.735650 + 0.668144i
\(370\) −56.7359 39.1620i −2.94956 2.03593i
\(371\) −4.92038 + 7.12841i −0.255454 + 0.370088i
\(372\) 1.45661 6.99607i 0.0755216 0.362729i
\(373\) 10.6742 17.6573i 0.552688 0.914258i −0.447116 0.894476i \(-0.647549\pi\)
0.999804 0.0197824i \(-0.00629733\pi\)
\(374\) −4.83956 15.5307i −0.250248 0.803073i
\(375\) −60.5847 + 29.9636i −3.12858 + 1.54731i
\(376\) 0.459568 + 7.59757i 0.0237004 + 0.391815i
\(377\) 1.13678 3.64805i 0.0585471 0.187884i
\(378\) −8.92836 + 9.84433i −0.459225 + 0.506338i
\(379\) 4.45606 + 14.3000i 0.228892 + 0.734541i 0.995698 + 0.0926616i \(0.0295375\pi\)
−0.766805 + 0.641880i \(0.778155\pi\)
\(380\) −9.03948 20.0849i −0.463715 1.03033i
\(381\) 11.2630 33.3052i 0.577020 1.70628i
\(382\) −3.99251 0.484779i −0.204275 0.0248034i
\(383\) 6.13871 13.6397i 0.313673 0.696954i −0.685853 0.727740i \(-0.740571\pi\)
0.999526 + 0.0307869i \(0.00980131\pi\)
\(384\) −13.1358 12.2130i −0.670335 0.623242i
\(385\) 32.4258 + 7.99225i 1.65257 + 0.407323i
\(386\) −31.8392 5.83474i −1.62057 0.296981i
\(387\) 4.65154 + 17.9158i 0.236451 + 0.910709i
\(388\) 5.48365 + 6.99936i 0.278390 + 0.355339i
\(389\) −3.70178 15.0187i −0.187688 0.761478i −0.987021 0.160591i \(-0.948660\pi\)
0.799334 0.600888i \(-0.205186\pi\)
\(390\) 0.524071 + 14.3952i 0.0265374 + 0.728929i
\(391\) 10.8329 + 6.54873i 0.547845 + 0.331184i
\(392\) −1.25480 + 6.84721i −0.0633769 + 0.345836i
\(393\) −1.31994 + 4.85058i −0.0665821 + 0.244680i
\(394\) −14.0127 + 23.1799i −0.705952 + 1.16779i
\(395\) 32.3428 3.92712i 1.62734 0.197595i
\(396\) 19.6217 1.43059i 0.986029 0.0718899i
\(397\) −11.3617 + 8.90131i −0.570226 + 0.446744i −0.859958 0.510364i \(-0.829511\pi\)
0.289732 + 0.957108i \(0.406434\pi\)
\(398\) −4.52747 10.0596i −0.226942 0.504244i
\(399\) −2.69022 + 9.88619i −0.134680 + 0.494928i
\(400\) 16.5458 67.1291i 0.827292 3.35646i
\(401\) −3.04503 2.38563i −0.152062 0.119133i 0.537805 0.843069i \(-0.319254\pi\)
−0.689866 + 0.723937i \(0.742331\pi\)
\(402\) −2.70637 + 4.86861i −0.134981 + 0.242824i
\(403\) −0.434294 + 3.57673i −0.0216337 + 0.178170i
\(404\) −4.59505 1.13258i −0.228612 0.0563478i
\(405\) 39.0484 3.33280i 1.94033 0.165608i
\(406\) −8.76511 + 2.73132i −0.435005 + 0.135553i
\(407\) 22.0618 42.0352i 1.09356 2.08361i
\(408\) 3.78867 + 1.54195i 0.187567 + 0.0763377i
\(409\) 23.5629 1.42529i 1.16511 0.0704761i 0.533526 0.845784i \(-0.320867\pi\)
0.631584 + 0.775308i \(0.282405\pi\)
\(410\) 42.5441 25.7188i 2.10111 1.27016i
\(411\) −7.04073 31.8386i −0.347294 1.57048i
\(412\) 6.65688 + 4.02422i 0.327961 + 0.198259i
\(413\) 11.1929 + 1.35907i 0.550767 + 0.0668753i
\(414\) −28.2312 + 28.9381i −1.38749 + 1.42223i
\(415\) 11.1765 16.1919i 0.548631 0.794829i
\(416\) −5.09663 3.99295i −0.249883 0.195771i
\(417\) 3.14913 2.06378i 0.154214 0.101064i
\(418\) 34.2758 20.7205i 1.67649 1.01347i
\(419\) −1.21701 3.20900i −0.0594549 0.156770i 0.901997 0.431741i \(-0.142101\pi\)
−0.961452 + 0.274972i \(0.911331\pi\)
\(420\) 10.5082 7.83268i 0.512748 0.382196i
\(421\) −15.9265 + 15.9265i −0.776210 + 0.776210i −0.979184 0.202974i \(-0.934939\pi\)
0.202974 + 0.979184i \(0.434939\pi\)
\(422\) 4.02255 4.54052i 0.195815 0.221029i
\(423\) 15.9909 3.13527i 0.777503 0.152442i
\(424\) −3.95671 + 7.53887i −0.192155 + 0.366120i
\(425\) 2.83618 + 23.3581i 0.137575 + 1.13303i
\(426\) 19.2926 + 10.7244i 0.934731 + 0.519600i
\(427\) 8.22108 11.9103i 0.397846 0.576380i
\(428\) −5.83834 2.62763i −0.282207 0.127011i
\(429\) −9.79703 + 1.55311i −0.473005 + 0.0749849i
\(430\) −2.91043 48.1151i −0.140353 2.32032i
\(431\) 3.96818 + 3.51550i 0.191141 + 0.169336i 0.753266 0.657717i \(-0.228478\pi\)
−0.562125 + 0.827052i \(0.690016\pi\)
\(432\) −14.8632 + 21.0048i −0.715104 + 1.01059i
\(433\) 1.45441 + 0.0879756i 0.0698945 + 0.00422784i 0.0952887 0.995450i \(-0.469623\pi\)
−0.0253942 + 0.999678i \(0.508084\pi\)
\(434\) 7.66528 4.02305i 0.367945 0.193113i
\(435\) 24.4136 + 11.7009i 1.17054 + 0.561014i
\(436\) 1.92414 + 2.17191i 0.0921496 + 0.104015i
\(437\) −9.27225 + 29.7557i −0.443552 + 1.42341i
\(438\) 9.91452 1.57174i 0.473734 0.0751004i
\(439\) 9.28948 11.8571i 0.443363 0.565911i −0.512889 0.858455i \(-0.671425\pi\)
0.956252 + 0.292544i \(0.0945018\pi\)
\(440\) 32.5880 + 3.95690i 1.55357 + 0.188638i
\(441\) 14.8861 + 0.715838i 0.708861 + 0.0340875i
\(442\) 3.07303 + 0.957595i 0.146169 + 0.0455481i
\(443\) −16.1312 + 16.1312i −0.766415 + 0.766415i −0.977474 0.211058i \(-0.932309\pi\)
0.211058 + 0.977474i \(0.432309\pi\)
\(444\) −7.23588 17.1680i −0.343400 0.814756i
\(445\) 0.624020 + 3.40516i 0.0295814 + 0.161420i
\(446\) 28.5978 19.7396i 1.35414 0.934698i
\(447\) −11.1417 + 1.08195i −0.526983 + 0.0511746i
\(448\) −0.0867781 + 1.43461i −0.00409988 + 0.0677791i
\(449\) 1.66318 1.66318i 0.0784905 0.0784905i −0.666772 0.745262i \(-0.732324\pi\)
0.745262 + 0.666772i \(0.232324\pi\)
\(450\) −74.7055 8.13493i −3.52165 0.383484i
\(451\) 21.1127 + 26.9483i 0.994157 + 1.26895i
\(452\) −1.56296 0.385235i −0.0735155 0.0181199i
\(453\) −6.97343 + 9.60094i −0.327640 + 0.451092i
\(454\) −11.4679 + 21.8503i −0.538217 + 1.02549i
\(455\) −4.94620 + 4.38195i −0.231881 + 0.205429i
\(456\) −1.45377 + 9.96567i −0.0680790 + 0.466685i
\(457\) 3.58383 2.47374i 0.167644 0.115717i −0.481288 0.876562i \(-0.659831\pi\)
0.648933 + 0.760846i \(0.275216\pi\)
\(458\) 6.93133i 0.323880i
\(459\) 2.19473 8.47769i 0.102441 0.395705i
\(460\) 32.8112 22.6479i 1.52983 1.05597i
\(461\) 3.22663 + 6.14783i 0.150279 + 0.286333i 0.948945 0.315442i \(-0.102153\pi\)
−0.798666 + 0.601775i \(0.794460\pi\)
\(462\) 16.4428 + 17.2525i 0.764990 + 0.802660i
\(463\) −24.9738 + 15.0972i −1.16063 + 0.701626i −0.960537 0.278151i \(-0.910278\pi\)
−0.200093 + 0.979777i \(0.564124\pi\)
\(464\) −16.2094 + 7.29527i −0.752503 + 0.338674i
\(465\) −24.6320 6.70286i −1.14228 0.310838i
\(466\) 5.36329 + 17.2114i 0.248450 + 0.797303i
\(467\) −28.3566 + 10.7543i −1.31219 + 0.497648i −0.908743 0.417356i \(-0.862957\pi\)
−0.403446 + 0.915004i \(0.632188\pi\)
\(468\) −1.97256 + 3.35605i −0.0911815 + 0.155133i
\(469\) −2.51346 + 0.460608i −0.116061 + 0.0212689i
\(470\) −42.4362 −1.95744
\(471\) 12.5340 17.7172i 0.577538 0.816364i
\(472\) 11.0831 0.510139
\(473\) 32.6498 5.98330i 1.50124 0.275112i
\(474\) 20.9670 + 10.0490i 0.963048 + 0.461567i
\(475\) −54.1682 + 20.5433i −2.48541 + 0.942591i
\(476\) −0.871273 2.79601i −0.0399347 0.128155i
\(477\) 17.1219 + 6.25246i 0.783959 + 0.286280i
\(478\) −19.1234 + 8.60674i −0.874684 + 0.393663i
\(479\) −28.2948 + 17.1048i −1.29282 + 0.781538i −0.985436 0.170046i \(-0.945608\pi\)
−0.307386 + 0.951585i \(0.599454\pi\)
\(480\) 33.2068 31.6483i 1.51568 1.44454i
\(481\) 4.36532 + 8.31742i 0.199041 + 0.379241i
\(482\) −18.8118 + 12.9849i −0.856856 + 0.591445i
\(483\) −18.4799 1.56417i −0.840863 0.0711722i
\(484\) 21.8723i 0.994197i
\(485\) 26.1407 18.0436i 1.18699 0.819318i
\(486\) 24.7736 + 12.9800i 1.12375 + 0.588783i
\(487\) −22.0428 + 19.5282i −0.998854 + 0.884907i −0.993357 0.115077i \(-0.963288\pi\)
−0.00549752 + 0.999985i \(0.501750\pi\)
\(488\) 6.61095 12.5961i 0.299264 0.570199i
\(489\) 14.9086 + 10.8286i 0.674192 + 0.489684i
\(490\) −37.6833 9.28810i −1.70236 0.419593i
\(491\) 4.95326 + 6.32237i 0.223538 + 0.285325i 0.885917 0.463844i \(-0.153530\pi\)
−0.662379 + 0.749169i \(0.730453\pi\)
\(492\) 13.4311 + 0.322748i 0.605519 + 0.0145506i
\(493\) 4.27762 4.27762i 0.192654 0.192654i
\(494\) −0.478501 + 7.91057i −0.0215288 + 0.355913i
\(495\) −0.868957 70.2746i −0.0390567 3.15861i
\(496\) 13.7940 9.52134i 0.619371 0.427521i
\(497\) 1.82523 + 9.95996i 0.0818728 + 0.446765i
\(498\) 12.9385 5.45324i 0.579786 0.244366i
\(499\) −10.5005 + 10.5005i −0.470069 + 0.470069i −0.901937 0.431868i \(-0.857855\pi\)
0.431868 + 0.901937i \(0.357855\pi\)
\(500\) 45.4138 + 14.1515i 2.03097 + 0.632875i
\(501\) −1.60023 43.9552i −0.0714931 1.96378i
\(502\) 26.4592 + 3.21273i 1.18093 + 0.143391i
\(503\) −8.51880 + 10.8734i −0.379834 + 0.484823i −0.938846 0.344337i \(-0.888104\pi\)
0.559012 + 0.829160i \(0.311181\pi\)
\(504\) −5.97700 + 0.435775i −0.266237 + 0.0194109i
\(505\) −5.02958 + 16.1405i −0.223813 + 0.718242i
\(506\) 48.0759 + 54.2664i 2.13723 + 2.41244i
\(507\) −8.88343 + 18.5351i −0.394527 + 0.823171i
\(508\) −21.9091 + 11.4988i −0.972060 + 0.510176i
\(509\) 0.809067 + 0.0489396i 0.0358613 + 0.00216921i 0.0782994 0.996930i \(-0.475051\pi\)
−0.0424381 + 0.999099i \(0.513513\pi\)
\(510\) −9.85652 + 20.5654i −0.436454 + 0.910651i
\(511\) 3.44689 + 3.05368i 0.152482 + 0.135087i
\(512\) 0.980588 + 16.2111i 0.0433363 + 0.716434i
\(513\) 21.5598 + 0.251417i 0.951889 + 0.0111003i
\(514\) −44.6148 20.0795i −1.96787 0.885668i
\(515\) 15.7852 22.8688i 0.695577 1.00772i
\(516\) 6.32914 11.3858i 0.278625 0.501231i
\(517\) −3.52237 29.0093i −0.154914 1.27583i
\(518\) 10.4885 19.9841i 0.460837 0.878051i
\(519\) 41.4886 11.8427i 1.82115 0.519838i
\(520\) −4.30731 + 4.86195i −0.188888 + 0.213210i
\(521\) −12.8121 + 12.8121i −0.561307 + 0.561307i −0.929679 0.368372i \(-0.879915\pi\)
0.368372 + 0.929679i \(0.379915\pi\)
\(522\) 10.1988 + 16.4091i 0.446390 + 0.718209i
\(523\) −7.03789 18.5574i −0.307745 0.811458i −0.996274 0.0862483i \(-0.972512\pi\)
0.688528 0.725209i \(-0.258257\pi\)
\(524\) 3.02762 1.83026i 0.132262 0.0799553i
\(525\) −18.8958 28.8331i −0.824679 1.25838i
\(526\) −10.5336 8.25252i −0.459285 0.359827i
\(527\) −3.24037 + 4.69449i −0.141153 + 0.204495i
\(528\) 35.6300 + 29.3226i 1.55060 + 1.27610i
\(529\) −33.1723 4.02785i −1.44227 0.175124i
\(530\) −40.6230 24.5574i −1.76455 1.06671i
\(531\) −3.15107 23.5175i −0.136745 1.02057i
\(532\) 6.17073 3.73033i 0.267535 0.161730i
\(533\) −6.76143 + 0.408991i −0.292870 + 0.0177154i
\(534\) −0.931309 + 2.28829i −0.0403017 + 0.0990240i
\(535\) −10.6287 + 20.2513i −0.459519 + 0.875540i
\(536\) −2.39805 + 0.747263i −0.103580 + 0.0322769i
\(537\) 31.1729 10.9732i 1.34521 0.473530i
\(538\) 43.1090 + 10.6254i 1.85856 + 0.458094i
\(539\) 3.22147 26.5312i 0.138758 1.14278i
\(540\) −21.5116 17.2618i −0.925711 0.742830i
\(541\) −10.5867 8.29411i −0.455156 0.356592i 0.362806 0.931865i \(-0.381819\pi\)
−0.817961 + 0.575273i \(0.804896\pi\)
\(542\) −2.43300 + 9.87109i −0.104506 + 0.423999i
\(543\) 24.4800 + 6.66149i 1.05054 + 0.285872i
\(544\) −4.20688 9.34731i −0.180369 0.400763i
\(545\) 8.15947 6.39254i 0.349513 0.273826i
\(546\) −4.65765 + 0.738371i −0.199329 + 0.0315993i
\(547\) 13.7077 1.66442i 0.586101 0.0711655i 0.177885 0.984051i \(-0.443074\pi\)
0.408215 + 0.912886i \(0.366151\pi\)
\(548\) −11.8721 + 19.6389i −0.507152 + 0.838932i
\(549\) −28.6077 10.4467i −1.22095 0.445856i
\(550\) −24.2914 + 132.554i −1.03579 + 5.65211i
\(551\) 12.7465 + 7.70552i 0.543019 + 0.328266i
\(552\) −18.2180 + 0.663242i −0.775408 + 0.0282295i
\(553\) 2.55257 + 10.3562i 0.108546 + 0.440389i
\(554\) −24.0198 30.6590i −1.02050 1.30257i
\(555\) −62.7773 + 22.0984i −2.66475 + 0.938023i
\(556\) −2.60640 0.477640i −0.110536 0.0202564i
\(557\) −16.3029 4.01831i −0.690776 0.170261i −0.121726 0.992564i \(-0.538843\pi\)
−0.569050 + 0.822303i \(0.692689\pi\)
\(558\) −12.2483 13.4858i −0.518511 0.570899i
\(559\) −2.69557 + 5.98930i −0.114010 + 0.253320i
\(560\) 30.5162 + 3.70534i 1.28955 + 0.156579i
\(561\) −14.8766 5.03089i −0.628090 0.212404i
\(562\) 6.88408 + 15.2958i 0.290387 + 0.645214i
\(563\) −4.96886 15.9456i −0.209413 0.672029i −0.998343 0.0575460i \(-0.981672\pi\)
0.788930 0.614483i \(-0.210635\pi\)
\(564\) −9.66892 6.16700i −0.407135 0.259677i
\(565\) −1.71076 + 5.49003i −0.0719723 + 0.230967i
\(566\) 3.08248 + 50.9594i 0.129566 + 2.14198i
\(567\) 2.62403 + 12.5589i 0.110199 + 0.527424i
\(568\) 2.96115 + 9.50266i 0.124247 + 0.398723i
\(569\) −5.92882 + 9.80746i −0.248549 + 0.411150i −0.954997 0.296614i \(-0.904142\pi\)
0.706448 + 0.707765i \(0.250296\pi\)
\(570\) −54.9710 11.4452i −2.30248 0.479385i
\(571\) −0.385109 + 0.557926i −0.0161163 + 0.0233485i −0.830959 0.556333i \(-0.812208\pi\)
0.814843 + 0.579682i \(0.196823\pi\)
\(572\) 5.74524 + 3.96565i 0.240221 + 0.165812i
\(573\) −2.64374 + 2.84350i −0.110444 + 0.118789i
\(574\) 10.0373 + 12.8116i 0.418947 + 0.534746i
\(575\) −54.2510 89.7421i −2.26242 3.74250i
\(576\) 2.96804 0.581933i 0.123668 0.0242472i
\(577\) 1.18383 1.04878i 0.0492834 0.0436613i −0.638122 0.769936i \(-0.720288\pi\)
0.687405 + 0.726274i \(0.258750\pi\)
\(578\) −17.9638 17.9638i −0.747194 0.747194i
\(579\) −22.6208 + 21.5592i −0.940090 + 0.895970i
\(580\) −6.75631 17.8149i −0.280541 0.739725i
\(581\) 5.70328 + 2.99331i 0.236612 + 0.124183i
\(582\) 22.6527 0.824695i 0.938986 0.0341847i
\(583\) 13.4156 29.8081i 0.555615 1.23453i
\(584\) 3.72528 + 2.57138i 0.154153 + 0.106404i
\(585\) 11.5413 + 7.75750i 0.477176 + 0.320733i
\(586\) −36.5353 + 9.00513i −1.50926 + 0.371999i
\(587\) 19.9059 1.20408i 0.821603 0.0496978i 0.355774 0.934572i \(-0.384217\pi\)
0.465830 + 0.884874i \(0.345756\pi\)
\(588\) −7.23620 7.59254i −0.298416 0.313111i
\(589\) −13.1319 4.98027i −0.541090 0.205208i
\(590\) −3.73088 + 61.6788i −0.153598 + 2.53928i
\(591\) 10.1559 + 24.0960i 0.417756 + 0.991176i
\(592\) 15.4954 40.8579i 0.636855 1.67925i
\(593\) 14.6461 12.9753i 0.601444 0.532833i −0.306529 0.951861i \(-0.599168\pi\)
0.907973 + 0.419028i \(0.137629\pi\)
\(594\) 26.4458 42.6162i 1.08508 1.74857i
\(595\) −10.1578 + 2.50367i −0.416429 + 0.102641i
\(596\) 6.20150 + 4.85857i 0.254023 + 0.199015i
\(597\) −10.4261 2.17075i −0.426712 0.0888431i
\(598\) −14.2407 + 1.72913i −0.582345 + 0.0707095i
\(599\) 6.64884 21.3369i 0.271664 0.871801i −0.713569 0.700584i \(-0.752923\pi\)
0.985234 0.171216i \(-0.0547696\pi\)
\(600\) −21.8547 25.8965i −0.892215 1.05722i
\(601\) 11.3203 5.94133i 0.461763 0.242352i −0.217766 0.976001i \(-0.569877\pi\)
0.679528 + 0.733649i \(0.262184\pi\)
\(602\) 15.5222 2.84455i 0.632637 0.115935i
\(603\) 2.26744 + 4.87605i 0.0923374 + 0.198568i
\(604\) 8.21432 1.50533i 0.334236 0.0612510i
\(605\) −77.9912 4.71760i −3.17079 0.191798i
\(606\) −9.22028 + 7.78124i −0.374548 + 0.316091i
\(607\) 0.676292 + 11.1804i 0.0274499 + 0.453800i 0.985770 + 0.168102i \(0.0537639\pi\)
−0.958320 + 0.285698i \(0.907775\pi\)
\(608\) 19.8667 15.5646i 0.805702 0.631227i
\(609\) −2.83930 + 8.39595i −0.115054 + 0.340221i
\(610\) 67.8737 + 41.0311i 2.74813 + 1.66130i
\(611\) 5.11986 + 2.68711i 0.207128 + 0.108709i
\(612\) −5.23441 + 3.25335i −0.211588 + 0.131509i
\(613\) −1.61694 + 26.7313i −0.0653077 + 1.07967i 0.806950 + 0.590619i \(0.201116\pi\)
−0.872258 + 0.489046i \(0.837345\pi\)
\(614\) 23.2238 + 33.6455i 0.937237 + 1.35782i
\(615\) 4.04775 47.8221i 0.163221 1.92837i
\(616\) 10.7470i 0.433009i
\(617\) 15.6227 + 22.6333i 0.628945 + 0.911184i 0.999847 0.0174878i \(-0.00556683\pi\)
−0.370902 + 0.928672i \(0.620951\pi\)
\(618\) 18.2737 7.70193i 0.735077 0.309817i
\(619\) −25.4250 + 28.6989i −1.02192 + 1.15351i −0.0338599 + 0.999427i \(0.510780\pi\)
−0.988058 + 0.154081i \(0.950758\pi\)
\(620\) 9.29435 + 15.3747i 0.373270 + 0.617464i
\(621\) 6.58698 + 38.4687i 0.264326 + 1.54370i
\(622\) 0.442620 + 0.0811132i 0.0177475 + 0.00325234i
\(623\) −1.08203 + 0.337173i −0.0433505 + 0.0135086i
\(624\) −8.77984 + 2.50616i −0.351475 + 0.100327i
\(625\) 35.5017 93.6104i 1.42007 3.74442i
\(626\) −2.47385 13.4993i −0.0988748 0.539542i
\(627\) 3.26109 38.5281i 0.130235 1.53866i
\(628\) −14.9880 + 2.94025i −0.598086 + 0.117329i
\(629\) 14.8715i 0.592964i
\(630\) −0.413114 33.4095i −0.0164589 1.33107i
\(631\) −5.14514 1.95129i −0.204825 0.0776798i 0.250059 0.968231i \(-0.419550\pi\)
−0.454884 + 0.890551i \(0.650319\pi\)
\(632\) 3.71783 + 9.80311i 0.147887 + 0.389947i
\(633\) −1.26446 5.71797i −0.0502579 0.227269i
\(634\) 5.13457 28.0185i 0.203920 1.11276i
\(635\) 36.2762 + 80.6024i 1.43958 + 3.19861i
\(636\) −5.68699 11.4988i −0.225504 0.455957i
\(637\) 3.95830 + 3.50674i 0.156833 + 0.138942i
\(638\) 30.6785 16.1013i 1.21457 0.637458i
\(639\) 19.3221 8.98510i 0.764371 0.355445i
\(640\) 45.0927 1.78245
\(641\) −33.3219 −1.31614 −0.658069 0.752958i \(-0.728626\pi\)
−0.658069 + 0.752958i \(0.728626\pi\)
\(642\) −14.1667 + 8.10590i −0.559116 + 0.319914i
\(643\) −4.28778 0.259363i −0.169094 0.0102283i −0.0243852 0.999703i \(-0.507763\pi\)
−0.144708 + 0.989474i \(0.546224\pi\)
\(644\) 8.65517 + 9.76967i 0.341061 + 0.384979i
\(645\) −39.2337 25.0239i −1.54482 0.985314i
\(646\) −6.49094 + 10.7373i −0.255383 + 0.422454i
\(647\) −10.5362 + 42.7470i −0.414221 + 1.68056i 0.279365 + 0.960185i \(0.409876\pi\)
−0.693586 + 0.720374i \(0.743970\pi\)
\(648\) 4.04855 + 11.9441i 0.159042 + 0.469207i
\(649\) −42.4732 + 2.56915i −1.66722 + 0.100848i
\(650\) −18.8550 18.8550i −0.739553 0.739553i
\(651\) 1.20637 8.26972i 0.0472813 0.324116i
\(652\) −2.33752 12.7555i −0.0915445 0.499542i
\(653\) 11.5782 + 16.7739i 0.453088 + 0.656412i 0.981252 0.192731i \(-0.0617345\pi\)
−0.528163 + 0.849143i \(0.677119\pi\)
\(654\) 7.36259 0.714971i 0.287900 0.0279576i
\(655\) −5.87322 11.1905i −0.229486 0.437248i
\(656\) 22.2819 + 22.2819i 0.869962 + 0.869962i
\(657\) 4.39714 8.63588i 0.171549 0.336918i
\(658\) −1.67458 13.7914i −0.0652821 0.537646i
\(659\) −2.81778 + 23.2065i −0.109765 + 0.903998i 0.828954 + 0.559316i \(0.188936\pi\)
−0.938720 + 0.344682i \(0.887987\pi\)
\(660\) −33.6787 + 36.2236i −1.31094 + 1.41000i
\(661\) −4.82341 19.5694i −0.187609 0.761159i −0.987050 0.160415i \(-0.948717\pi\)
0.799441 0.600745i \(-0.205129\pi\)
\(662\) −17.5727 5.47589i −0.682984 0.212826i
\(663\) 2.49140 1.85706i 0.0967579 0.0721221i
\(664\) 5.91991 + 2.24513i 0.229737 + 0.0871278i
\(665\) −11.9705 22.8078i −0.464195 0.884449i
\(666\) −46.2523 10.7953i −1.79224 0.418311i
\(667\) −9.56050 + 25.2090i −0.370184 + 0.976095i
\(668\) −20.5270 + 23.1702i −0.794212 + 0.896480i
\(669\) 0.805881 33.5365i 0.0311572 1.29660i
\(670\) −3.35137 13.5970i −0.129475 0.525300i
\(671\) −22.4150 + 49.8041i −0.865321 + 1.92266i
\(672\) 11.5958 + 9.54306i 0.447319 + 0.368132i
\(673\) −28.5561 12.8520i −1.10076 0.495410i −0.223145 0.974785i \(-0.571632\pi\)
−0.877610 + 0.479375i \(0.840863\pi\)
\(674\) 21.6218 2.62536i 0.832841 0.101125i
\(675\) −48.7369 + 53.7369i −1.87588 + 2.06834i
\(676\) 13.5253 5.12947i 0.520204 0.197287i
\(677\) −7.32336 6.48793i −0.281459 0.249351i 0.510567 0.859838i \(-0.329435\pi\)
−0.792027 + 0.610487i \(0.790974\pi\)
\(678\) −3.13619 + 2.64671i −0.120444 + 0.101646i
\(679\) 6.89558 + 7.78350i 0.264628 + 0.298703i
\(680\) −9.61532 + 3.64661i −0.368731 + 0.139841i
\(681\) 10.5611 + 21.3539i 0.404701 + 0.818284i
\(682\) −25.7172 + 20.1481i −0.984762 + 0.771512i
\(683\) 23.9977 30.6307i 0.918245 1.17205i −0.0664543 0.997789i \(-0.521169\pi\)
0.984699 0.174263i \(-0.0557544\pi\)
\(684\) −10.8617 10.5963i −0.415306 0.405161i
\(685\) 67.4666 + 46.5688i 2.57777 + 1.77930i
\(686\) 3.68959 30.3865i 0.140869 1.16016i
\(687\) −5.41403 3.93236i −0.206558 0.150029i
\(688\) 29.1703 9.08984i 1.11211 0.346547i
\(689\) 3.34609 + 5.53511i 0.127476 + 0.210871i
\(690\) 2.44166 101.609i 0.0929523 3.86818i
\(691\) 36.4500 + 11.3583i 1.38662 + 0.432089i 0.897842 0.440318i \(-0.145134\pi\)
0.488780 + 0.872407i \(0.337442\pi\)
\(692\) −26.8867 14.1112i −1.02208 0.536428i
\(693\) 22.8044 3.05552i 0.866268 0.116070i
\(694\) 15.5609 7.00341i 0.590685 0.265846i
\(695\) −2.26531 + 9.19072i −0.0859280 + 0.348624i
\(696\) −1.77580 + 8.52917i −0.0673117 + 0.323297i
\(697\) −9.77938 4.40134i −0.370420 0.166713i
\(698\) 23.8574 30.4518i 0.903017 1.15262i
\(699\) 16.4865 + 5.57532i 0.623577 + 0.210878i
\(700\) −4.37321 + 23.8639i −0.165292 + 0.901969i
\(701\) 34.3481 15.4588i 1.29731 0.583871i 0.360189 0.932880i \(-0.382712\pi\)
0.937120 + 0.349009i \(0.113482\pi\)
\(702\) 3.96717 + 9.09664i 0.149731 + 0.343331i
\(703\) −35.5515 + 8.76265i −1.34085 + 0.330490i
\(704\) −0.653783 5.38438i −0.0246404 0.202932i
\(705\) −24.0754 + 33.1468i −0.906732 + 1.24838i
\(706\) 44.5998 + 8.17321i 1.67854 + 0.307603i
\(707\) −5.44400 0.997651i −0.204743 0.0375205i
\(708\) −9.81346 + 13.5111i −0.368813 + 0.507777i
\(709\) 1.77020 + 14.5789i 0.0664813 + 0.547523i 0.987455 + 0.157899i \(0.0504719\pi\)
−0.920974 + 0.389624i \(0.872605\pi\)
\(710\) −53.8804 + 13.2803i −2.02210 + 0.498402i
\(711\) 19.7445 10.6761i 0.740477 0.400387i
\(712\) −1.01589 + 0.457216i −0.0380721 + 0.0171349i
\(713\) 4.58251 25.0060i 0.171616 0.936480i
\(714\) −7.07254 2.39176i −0.264683 0.0895092i
\(715\) 15.3797 19.6307i 0.575167 0.734147i
\(716\) −21.2092 9.54547i −0.792623 0.356731i
\(717\) −4.12661 + 19.8201i −0.154111 + 0.740194i
\(718\) −6.91939 + 28.0731i −0.258229 + 1.04768i
\(719\) −4.22130 + 1.89985i −0.157428 + 0.0708526i −0.487595 0.873070i \(-0.662126\pi\)
0.330167 + 0.943923i \(0.392895\pi\)
\(720\) −8.59105 64.1179i −0.320169 2.38953i
\(721\) 8.05507 + 4.22762i 0.299986 + 0.157445i
\(722\) 3.05223 + 0.951112i 0.113592 + 0.0353967i
\(723\) −0.530115 + 22.0606i −0.0197152 + 0.820442i
\(724\) −9.23699 15.2798i −0.343290 0.567871i
\(725\) −47.8458 + 14.9094i −1.77695 + 0.553720i
\(726\) −45.1152 32.7684i −1.67438 1.21615i
\(727\) 3.72452 30.6742i 0.138135 1.13764i −0.744513 0.667607i \(-0.767318\pi\)
0.882648 0.470034i \(-0.155758\pi\)
\(728\) −1.75007 1.20798i −0.0648617 0.0447708i
\(729\) 24.1934 11.9866i 0.896052 0.443948i
\(730\) −15.5641 + 19.8661i −0.576054 + 0.735278i
\(731\) −8.18536 + 6.41282i −0.302746 + 0.237187i
\(732\) 9.50195 + 19.2124i 0.351202 + 0.710112i
\(733\) 42.9513 16.2893i 1.58644 0.601658i 0.605481 0.795860i \(-0.292981\pi\)
0.980962 + 0.194202i \(0.0622117\pi\)
\(734\) 32.6091 + 36.8081i 1.20363 + 1.35861i
\(735\) −28.6338 + 24.1648i −1.05617 + 0.891333i
\(736\) 34.1945 + 30.2937i 1.26043 + 1.11664i
\(737\) 9.01674 3.41960i 0.332136 0.125962i
\(738\) 20.7877 27.2202i 0.765206 1.00199i
\(739\) 10.4869 1.27333i 0.385765 0.0468404i 0.0746430 0.997210i \(-0.476218\pi\)
0.311122 + 0.950370i \(0.399295\pi\)
\(740\) 42.7119 + 19.2231i 1.57012 + 0.706654i
\(741\) 5.90744 + 4.86167i 0.217015 + 0.178598i
\(742\) 6.37794 14.1712i 0.234142 0.520241i
\(743\) −4.59939 18.6605i −0.168735 0.684586i −0.992973 0.118342i \(-0.962242\pi\)
0.824238 0.566244i \(-0.191604\pi\)
\(744\) 0.197347 8.21252i 0.00723508 0.301086i
\(745\) 18.6620 21.0650i 0.683723 0.771763i
\(746\) −13.1270 + 34.6129i −0.480612 + 1.26727i
\(747\) 3.08089 13.2000i 0.112724 0.482962i
\(748\) 5.13622 + 9.78625i 0.187799 + 0.357821i
\(749\) −7.00093 2.65510i −0.255809 0.0970154i
\(750\) 97.2272 72.4719i 3.55024 2.64630i
\(751\) 18.3179 + 5.70807i 0.668428 + 0.208291i 0.612893 0.790166i \(-0.290006\pi\)
0.0555353 + 0.998457i \(0.482313\pi\)
\(752\) −6.43722 26.1168i −0.234741 0.952382i
\(753\) 17.5206 18.8445i 0.638486 0.686731i
\(754\) −0.826347 + 6.80558i −0.0300938 + 0.247845i
\(755\) −3.59589 29.6149i −0.130868 1.07779i
\(756\) 4.76108 7.67226i 0.173159 0.279037i
\(757\) 3.32919 + 3.32919i 0.121002 + 0.121002i 0.765015 0.644013i \(-0.222732\pi\)
−0.644013 + 0.765015i \(0.722732\pi\)
\(758\) −12.4886 23.7950i −0.453605 0.864272i
\(759\) 69.6622 6.76480i 2.52858 0.245547i
\(760\) −14.3831 20.8375i −0.521730 0.755857i
\(761\) −0.911898 4.97607i −0.0330563 0.180382i 0.962948 0.269687i \(-0.0869202\pi\)
−0.996004 + 0.0893046i \(0.971536\pi\)
\(762\) −9.10542 + 62.4182i −0.329854 + 2.26117i
\(763\) 2.39951 + 2.39951i 0.0868680 + 0.0868680i
\(764\) 2.72751 0.164984i 0.0986778 0.00596891i
\(765\) 10.4716 + 19.3663i 0.378603 + 0.700189i
\(766\) −6.42223 + 26.0560i −0.232045 + 0.941442i
\(767\) 4.35570 7.20521i 0.157275 0.260165i
\(768\) 30.0759 + 19.1829i 1.08527 + 0.692202i
\(769\) −17.1048 19.3073i −0.616814 0.696239i 0.354225 0.935160i \(-0.384745\pi\)
−0.971039 + 0.238921i \(0.923206\pi\)
\(770\) −59.8086 3.61775i −2.15535 0.130375i
\(771\) −40.9953 + 23.4567i −1.47641 + 0.844772i
\(772\) 21.9922 0.791517
\(773\) −33.2220 −1.19491 −0.597456 0.801902i \(-0.703822\pi\)
−0.597456 + 0.801902i \(0.703822\pi\)
\(774\) −14.0029 30.1127i −0.503324 1.08238i
\(775\) 41.8422 21.9605i 1.50302 0.788844i
\(776\) 7.65091 + 6.77811i 0.274652 + 0.243320i
\(777\) −9.65906 19.5301i −0.346517 0.700639i
\(778\) 11.3899 + 25.3072i 0.408346 + 0.907308i
\(779\) 4.75951 25.9718i 0.170527 0.930536i
\(780\) −2.11318 9.55592i −0.0756639 0.342157i
\(781\) −13.5507 35.7302i −0.484882 1.27853i
\(782\) −21.2354 8.05353i −0.759377 0.287994i
\(783\) 18.6032 + 1.34317i 0.664825 + 0.0480011i
\(784\) 24.6006i 0.878593i
\(785\) 7.25145 + 54.0775i 0.258815 + 1.93011i
\(786\) 0.760676 8.98699i 0.0271324 0.320555i
\(787\) 2.69728 + 14.7186i 0.0961476 + 0.524660i 0.996067 + 0.0886040i \(0.0282406\pi\)
−0.899919 + 0.436056i \(0.856375\pi\)
\(788\) 6.52572 17.2069i 0.232469 0.612971i
\(789\) −12.4220 + 3.54581i −0.442236 + 0.126234i
\(790\) −55.8072 + 17.3902i −1.98553 + 0.618716i
\(791\) −1.85172 0.339341i −0.0658397 0.0120656i
\(792\) 21.8905 5.68352i 0.777845 0.201955i
\(793\) −5.59072 9.24818i −0.198532 0.328412i
\(794\) 17.1719 19.3831i 0.609409 0.687880i
\(795\) −42.2284 + 17.7982i −1.49769 + 0.631238i
\(796\) 4.25763 + 6.16824i 0.150908 + 0.218627i
\(797\) 16.1837i 0.573257i 0.958042 + 0.286629i \(0.0925346\pi\)
−0.958042 + 0.286629i \(0.907465\pi\)
\(798\) 1.55037 18.3168i 0.0548824 0.648407i
\(799\) 5.20022 + 7.53382i 0.183971 + 0.266527i
\(800\) −5.12710 + 84.7611i −0.181271 + 2.99676i
\(801\) 1.25901 + 2.02566i 0.0444850 + 0.0715732i
\(802\) 6.14528 + 3.22529i 0.216997 + 0.113889i
\(803\) −14.8723 8.99064i −0.524833 0.317273i
\(804\) 1.21238 3.58507i 0.0427573 0.126435i
\(805\) 36.7029 28.7549i 1.29361 1.01348i
\(806\) −0.390306 6.45253i −0.0137480 0.227281i
\(807\) 32.7565 27.6441i 1.15308 0.973118i
\(808\) −5.43046 0.328482i −0.191043 0.0115560i
\(809\) 43.3047 7.93589i 1.52251 0.279011i 0.647107 0.762399i \(-0.275979\pi\)
0.875406 + 0.483388i \(0.160594\pi\)
\(810\) −67.8332 + 18.5100i −2.38342 + 0.650376i
\(811\) 5.92797 1.08634i 0.208159 0.0381466i −0.0751635 0.997171i \(-0.523948\pi\)
0.283323 + 0.959025i \(0.408563\pi\)
\(812\) 5.52310 2.89875i 0.193823 0.101726i
\(813\) 6.32994 + 7.50058i 0.222001 + 0.263057i
\(814\) −25.3394 + 81.3169i −0.888144 + 2.85015i
\(815\) −45.9869 + 5.58382i −1.61085 + 0.195593i
\(816\) −14.1518 2.94647i −0.495414 0.103147i
\(817\) −20.1534 15.7892i −0.705078 0.552393i
\(818\) −41.1219 + 10.1356i −1.43779 + 0.354384i
\(819\) −2.06569 + 4.05697i −0.0721810 + 0.141762i
\(820\) −25.2819 + 22.3978i −0.882882 + 0.782165i
\(821\) −12.0140 + 31.6782i −0.419290 + 1.10558i 0.544464 + 0.838784i \(0.316733\pi\)
−0.963754 + 0.266792i \(0.914036\pi\)
\(822\) 22.7220 + 53.9105i 0.792519 + 1.88035i
\(823\) −1.80962 + 29.9165i −0.0630792 + 1.04282i 0.819627 + 0.572898i \(0.194181\pi\)
−0.882706 + 0.469926i \(0.844281\pi\)
\(824\) 8.36103 + 3.17092i 0.291270 + 0.110464i
\(825\) 89.7559 + 94.1758i 3.12490 + 3.27878i
\(826\) −20.1923 + 1.22141i −0.702582 + 0.0424984i
\(827\) 6.63488 1.63535i 0.230717 0.0568667i −0.122262 0.992498i \(-0.539015\pi\)
0.352979 + 0.935631i \(0.385169\pi\)
\(828\) 15.3225 22.7963i 0.532494 0.792226i
\(829\) −13.9964 9.66099i −0.486114 0.335540i 0.299668 0.954043i \(-0.403124\pi\)
−0.785782 + 0.618503i \(0.787739\pi\)
\(830\) −14.4873 + 32.1894i −0.502860 + 1.11731i
\(831\) −37.5747 + 1.36794i −1.30345 + 0.0474535i
\(832\) 0.950291 + 0.498751i 0.0329454 + 0.0172911i
\(833\) 2.96884 + 7.82820i 0.102864 + 0.271231i
\(834\) −4.89003 + 4.66053i −0.169328 + 0.161381i
\(835\) 78.1914 + 78.1914i 2.70593 + 2.70593i
\(836\) −20.3684 + 18.0449i −0.704457 + 0.624095i
\(837\) −17.4825 + 1.91618i −0.604284 + 0.0662328i
\(838\) 3.18554 + 5.26952i 0.110043 + 0.182033i
\(839\) 17.5542 + 22.4062i 0.606037 + 0.773549i 0.988630 0.150368i \(-0.0480457\pi\)
−0.382593 + 0.923917i \(0.624969\pi\)
\(840\) 10.2589 11.0341i 0.353967 0.380713i
\(841\) −13.2627 9.15460i −0.457336 0.315676i
\(842\) 22.9558 33.2572i 0.791108 1.14612i
\(843\) 15.8530 + 3.30066i 0.546007 + 0.113681i
\(844\) −2.13214 + 3.52700i −0.0733914 + 0.121404i
\(845\) −15.3731 49.3341i −0.528852 1.69714i
\(846\) −27.2061 + 10.7045i −0.935365 + 0.368029i
\(847\) −1.54444 25.5327i −0.0530677 0.877313i
\(848\) 8.95139 28.7260i 0.307392 0.986455i
\(849\) 41.5529 + 26.5031i 1.42609 + 0.909586i
\(850\) −12.5593 40.3041i −0.430780 1.38242i
\(851\) −27.2015 60.4394i −0.932457 2.07183i
\(852\) −14.2064 4.80424i −0.486703 0.164591i
\(853\) −54.5687 6.62584i −1.86840 0.226865i −0.893429 0.449205i \(-0.851707\pi\)
−0.974969 + 0.222340i \(0.928630\pi\)
\(854\) −10.6564 + 23.6776i −0.364655 + 0.810229i
\(855\) −40.1265 + 36.4444i −1.37230 + 1.24637i
\(856\) −7.14609 1.76135i −0.244248 0.0602018i
\(857\) 18.2621 + 3.34666i 0.623822 + 0.114320i 0.482863 0.875696i \(-0.339597\pi\)
0.140959 + 0.990015i \(0.454981\pi\)
\(858\) 16.7871 5.90927i 0.573103 0.201739i
\(859\) 6.09192 + 7.77576i 0.207854 + 0.265305i 0.879853 0.475246i \(-0.157641\pi\)
−0.671999 + 0.740552i \(0.734564\pi\)
\(860\) 7.83755 + 31.7982i 0.267258 + 1.08431i
\(861\) 15.7015 0.571630i 0.535107 0.0194811i
\(862\) −8.13982 4.92069i −0.277243 0.167599i
\(863\) 1.58318 8.63916i 0.0538922 0.294080i −0.945621 0.325270i \(-0.894545\pi\)
0.999513 + 0.0311894i \(0.00992950\pi\)
\(864\) 13.3058 28.6663i 0.452672 0.975247i
\(865\) −56.1162 + 92.8275i −1.90801 + 3.15623i
\(866\) −2.59514 + 0.315107i −0.0881864 + 0.0107078i
\(867\) −24.2228 + 3.84001i −0.822651 + 0.130414i
\(868\) −4.62990 + 3.62730i −0.157149 + 0.123119i
\(869\) −16.5201 36.7062i −0.560407 1.24517i
\(870\) −46.8683 12.7538i −1.58898 0.432393i
\(871\) −0.456643 + 1.85267i −0.0154728 + 0.0627755i
\(872\) 2.62574 + 2.05713i 0.0889187 + 0.0696634i
\(873\) 12.2074 18.1618i 0.413159 0.614685i
\(874\) 6.74018 55.5104i 0.227990 1.87767i
\(875\) 54.0130 + 13.3130i 1.82597 + 0.450062i
\(876\) −6.43324 + 2.26458i −0.217359 + 0.0765130i
\(877\) −11.4313 + 3.56214i −0.386008 + 0.120285i −0.484364 0.874866i \(-0.660949\pi\)
0.0983566 + 0.995151i \(0.468641\pi\)
\(878\) −12.5591 + 23.9293i −0.423848 + 0.807574i
\(879\) −13.6937 + 33.6464i −0.461878 + 1.13487i
\(880\) −115.798 + 7.00451i −3.90356 + 0.236122i
\(881\) 7.56967 4.57603i 0.255029 0.154170i −0.384048 0.923313i \(-0.625470\pi\)
0.639077 + 0.769143i \(0.279317\pi\)
\(882\) −26.5019 + 3.55094i −0.892364 + 0.119566i
\(883\) −6.26812 3.78921i −0.210939 0.127517i 0.407924 0.913016i \(-0.366253\pi\)
−0.618863 + 0.785499i \(0.712407\pi\)
\(884\) −2.17094 0.263599i −0.0730165 0.00886580i
\(885\) 46.0604 + 37.9065i 1.54830 + 1.27421i
\(886\) 23.2508 33.6846i 0.781125 1.13165i
\(887\) 32.1234 + 25.1671i 1.07860 + 0.845027i 0.988547 0.150910i \(-0.0482204\pi\)
0.0900499 + 0.995937i \(0.471297\pi\)
\(888\) −11.7393 17.9130i −0.393945 0.601121i
\(889\) −24.7637 + 14.9702i −0.830546 + 0.502083i
\(890\) −2.20249 5.80749i −0.0738276 0.194667i
\(891\) −18.2838 44.8342i −0.612531 1.50200i
\(892\) −16.6940 + 16.6940i −0.558957 + 0.558957i
\(893\) −14.9461 + 16.8707i −0.500153 + 0.564556i
\(894\) 19.3125 5.51265i 0.645906 0.184371i
\(895\) −38.6112 + 73.5676i −1.29063 + 2.45909i
\(896\) 1.77941 + 14.6548i 0.0594460 + 0.489582i
\(897\) −6.72857 + 12.1043i −0.224660 + 0.404152i
\(898\) −2.39724 + 3.47300i −0.0799970 + 0.115896i
\(899\) −11.0789 4.98622i −0.369503 0.166300i
\(900\) 50.9209 3.71257i 1.69736 0.123752i
\(901\) 0.618270 + 10.2212i 0.0205976 + 0.340518i
\(902\) −45.9740 40.7294i −1.53077 1.35614i
\(903\) 6.58436 13.7381i 0.219114 0.457176i
\(904\) −1.84712 0.111730i −0.0614342 0.00371608i
\(905\) −56.4763 + 29.6411i −1.87734 + 0.985302i
\(906\) 9.20144 19.1986i 0.305698 0.637831i
\(907\) 34.0235 + 38.4046i 1.12973 + 1.27520i 0.956953 + 0.290242i \(0.0937357\pi\)
0.172778 + 0.984961i \(0.444726\pi\)
\(908\) 4.98789 16.0067i 0.165529 0.531201i
\(909\) 0.846939 + 11.6165i 0.0280912 + 0.385294i
\(910\) 7.31172 9.33272i 0.242381 0.309377i
\(911\) 17.5428 + 2.13008i 0.581219 + 0.0705728i 0.405866 0.913933i \(-0.366970\pi\)
0.175354 + 0.984506i \(0.443893\pi\)
\(912\) −1.29486 35.5673i −0.0428772 1.17775i
\(913\) −23.2071 7.23162i −0.768042 0.239332i
\(914\) −5.52458 + 5.52458i −0.182737 + 0.182737i
\(915\) 70.5561 29.7376i 2.33251 0.983096i
\(916\) 0.848865 + 4.63211i 0.0280473 + 0.153049i
\(917\) 3.40506 2.35034i 0.112445 0.0776151i
\(918\) −1.13146 + 15.6709i −0.0373436 + 0.517216i
\(919\) 1.67722 27.7278i 0.0553264 0.914655i −0.859583 0.510996i \(-0.829277\pi\)
0.914910 0.403659i \(-0.132262\pi\)
\(920\) 32.4077 32.4077i 1.06845 1.06845i
\(921\) 39.4559 + 0.948125i 1.30012 + 0.0312418i
\(922\) −7.68246 9.80593i −0.253008 0.322941i
\(923\) 7.34152 + 1.80952i 0.241649 + 0.0595611i
\(924\) −13.1014 9.51590i −0.431004 0.313050i
\(925\) 57.2531 109.087i 1.88247 3.58674i
\(926\) 39.1903 34.7195i 1.28787 1.14096i
\(927\) 4.35132 18.6431i 0.142916 0.612319i
\(928\) 17.9673 12.4020i 0.589807 0.407114i
\(929\) 3.98666i 0.130798i 0.997859 + 0.0653990i \(0.0208320\pi\)
−0.997859 + 0.0653990i \(0.979168\pi\)
\(930\) 45.6374 + 3.86283i 1.49651 + 0.126667i
\(931\) −16.9646 + 11.7098i −0.555994 + 0.383775i
\(932\) −5.69205 10.8453i −0.186449 0.355250i
\(933\) 0.314469 0.299711i 0.0102953 0.00981209i
\(934\) 46.5647 28.1494i 1.52364 0.921075i
\(935\) 36.0031 16.2037i 1.17743 0.529917i
\(936\) −1.53501 + 4.20353i −0.0501735 + 0.137397i
\(937\) −12.2451 39.2960i −0.400031 1.28374i −0.906763 0.421641i \(-0.861454\pi\)
0.506732 0.862104i \(-0.330853\pi\)
\(938\) 4.28668 1.62572i 0.139965 0.0530818i
\(939\) −11.9478 5.72629i −0.389901 0.186870i
\(940\) 28.3595 5.19708i 0.924986 0.169510i
\(941\) −4.57722 −0.149213 −0.0746065 0.997213i \(-0.523770\pi\)
−0.0746065 + 0.997213i \(0.523770\pi\)
\(942\) −16.3898 + 35.3201i −0.534008 + 1.15079i
\(943\) 47.7950 1.55642
\(944\) −38.5253 + 7.06003i −1.25389 + 0.229784i
\(945\) −26.3304 18.6316i −0.856529 0.606086i
\(946\) −55.6841 + 21.1182i −1.81045 + 0.686611i
\(947\) −1.39042 4.46201i −0.0451825 0.144996i 0.929373 0.369142i \(-0.120348\pi\)
−0.974556 + 0.224146i \(0.928041\pi\)
\(948\) −15.2427 4.14782i −0.495058 0.134715i
\(949\) 3.13573 1.41128i 0.101790 0.0458120i
\(950\) 88.9501 53.7722i 2.88592 1.74460i
\(951\) −18.9721 19.9063i −0.615212 0.645507i
\(952\) −1.56455 2.98100i −0.0507074 0.0966149i
\(953\) −43.9656 + 30.3473i −1.42419 + 0.983045i −0.427306 + 0.904107i \(0.640537\pi\)
−0.996880 + 0.0789378i \(0.974847\pi\)
\(954\) −32.2382 5.49678i −1.04375 0.177965i
\(955\) 9.76118i 0.315864i
\(956\) 11.7258 8.09376i 0.379241 0.261771i
\(957\) 4.82821 33.0977i 0.156074 1.06990i
\(958\) 44.4018 39.3365i 1.43456 1.27091i
\(959\) −12.4722 + 23.7638i −0.402748 + 0.767372i
\(960\) −4.46860 + 6.15233i −0.144224 + 0.198565i
\(961\) −18.9762 4.67720i −0.612134 0.150877i
\(962\) −10.3936 13.2665i −0.335104 0.427729i
\(963\) −1.70574 + 15.6643i −0.0549666 + 0.504775i
\(964\) 10.9815 10.9815i 0.353689 0.353689i
\(965\) 4.74345 78.4186i 0.152697 2.52439i
\(966\) 33.1184 3.21608i 1.06557 0.103476i
\(967\) −24.9198 + 17.2009i −0.801367 + 0.553144i −0.896875 0.442285i \(-0.854168\pi\)
0.0955075 + 0.995429i \(0.469553\pi\)
\(968\) −4.53226 24.7318i −0.145672 0.794909i
\(969\) 4.70436 + 11.1617i 0.151126 + 0.358564i
\(970\) −40.2967 + 40.2967i −1.29385 + 1.29385i
\(971\) −26.3225 8.20241i −0.844728 0.263228i −0.155557 0.987827i \(-0.549717\pi\)
−0.689171 + 0.724599i \(0.742025\pi\)
\(972\) −18.1455 5.64035i −0.582016 0.180914i
\(973\) −3.07630 0.373531i −0.0986217 0.0119748i
\(974\) 32.5847 41.5913i 1.04408 1.33267i
\(975\) −25.4245 + 4.03052i −0.814237 + 0.129080i
\(976\) −14.9562 + 47.9960i −0.478735 + 1.53632i
\(977\) 21.2972 + 24.0396i 0.681359 + 0.769096i 0.982857 0.184371i \(-0.0590249\pi\)
−0.301497 + 0.953467i \(0.597486\pi\)
\(978\) −29.8122 14.2883i −0.953288 0.456889i
\(979\) 3.78717 1.98766i 0.121039 0.0635259i
\(980\) 26.3207 + 1.59211i 0.840784 + 0.0508580i
\(981\) 3.61857 6.15651i 0.115532 0.196562i
\(982\) −10.7860 9.55557i −0.344195 0.304930i
\(983\) 2.07269 + 34.2656i 0.0661085 + 1.09290i 0.868365 + 0.495925i \(0.165171\pi\)
−0.802257 + 0.596979i \(0.796368\pi\)
\(984\) 15.2538 2.41817i 0.486274 0.0770884i
\(985\) −59.9479 26.9804i −1.91010 0.859666i
\(986\) −6.16558 + 8.93238i −0.196352 + 0.284465i
\(987\) −11.7225 6.51631i −0.373131 0.207416i
\(988\) −0.649015 5.34512i −0.0206479 0.170051i
\(989\) 21.5365 41.0343i 0.684820 1.30482i
\(990\) 24.2606 + 123.737i 0.771053 + 3.93262i
\(991\) 20.9596 23.6585i 0.665804 0.751537i −0.314451 0.949274i \(-0.601821\pi\)
0.980255 + 0.197736i \(0.0633590\pi\)
\(992\) −14.5565 + 14.5565i −0.462170 + 0.462170i
\(993\) −14.2468 + 10.6193i −0.452107 + 0.336995i
\(994\) −6.44219 16.9867i −0.204334 0.538784i
\(995\) 22.9127 13.8512i 0.726381 0.439112i
\(996\) −7.97874 + 5.22887i −0.252816 + 0.165683i
\(997\) −0.199226 0.156084i −0.00630956 0.00494322i 0.613559 0.789649i \(-0.289737\pi\)
−0.619869 + 0.784706i \(0.712814\pi\)
\(998\) 15.1350 21.9269i 0.479091 0.694083i
\(999\) −34.6726 + 30.0029i −1.09699 + 0.949250i
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 471.2.s.a.2.11 1200
3.2 odd 2 inner 471.2.s.a.2.40 yes 1200
157.79 odd 52 inner 471.2.s.a.236.40 yes 1200
471.236 even 52 inner 471.2.s.a.236.11 yes 1200
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
471.2.s.a.2.11 1200 1.1 even 1 trivial
471.2.s.a.2.40 yes 1200 3.2 odd 2 inner
471.2.s.a.236.11 yes 1200 471.236 even 52 inner
471.2.s.a.236.40 yes 1200 157.79 odd 52 inner