Properties

Label 162.2.g.b.97.3
Level $162$
Weight $2$
Character 162.97
Analytic conductor $1.294$
Analytic rank $0$
Dimension $90$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,2,Mod(7,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.g (of order \(27\), degree \(18\), 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: \(1.29357651274\)
Analytic rank: \(0\)
Dimension: \(90\)
Relative dimension: \(5\) over \(\Q(\zeta_{27})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 97.3
Character \(\chi\) \(=\) 162.97
Dual form 162.2.g.b.157.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.973045 + 0.230616i) q^{2} +(0.190350 + 1.72156i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.06995 + 1.43719i) q^{5} +(-0.211800 + 1.71905i) q^{6} +(-0.983264 - 0.646703i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-2.92753 + 0.655396i) q^{9} +O(q^{10})\) \(q+(0.973045 + 0.230616i) q^{2} +(0.190350 + 1.72156i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.06995 + 1.43719i) q^{5} +(-0.211800 + 1.71905i) q^{6} +(-0.983264 - 0.646703i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-2.92753 + 0.655396i) q^{9} +(-1.37255 + 1.15170i) q^{10} +(3.61528 - 0.422566i) q^{11} +(-0.602532 + 1.62387i) q^{12} +(1.84593 - 6.16584i) q^{13} +(-0.807620 - 0.856027i) q^{14} +(-2.67787 - 1.56841i) q^{15} +(0.597159 + 0.802123i) q^{16} +(0.461322 + 2.61629i) q^{17} +(-2.99977 - 0.0374058i) q^{18} +(-0.128292 + 0.727580i) q^{19} +(-1.60115 + 0.804128i) q^{20} +(0.926174 - 1.81585i) q^{21} +(3.61528 + 0.422566i) q^{22} +(3.51483 - 2.31174i) q^{23} +(-0.960781 + 1.44115i) q^{24} +(0.513291 + 1.71451i) q^{25} +(3.21811 - 5.57394i) q^{26} +(-1.68556 - 4.91517i) q^{27} +(-0.588437 - 1.01920i) q^{28} +(-1.71661 + 1.81950i) q^{29} +(-2.24399 - 2.14369i) q^{30} +(-0.374563 - 6.43100i) q^{31} +(0.396080 + 0.918216i) q^{32} +(1.41564 + 6.14349i) q^{33} +(-0.154470 + 2.65215i) q^{34} +(1.98148 - 0.721198i) q^{35} +(-2.91028 - 0.728191i) q^{36} +(-7.73114 - 2.81391i) q^{37} +(-0.292625 + 0.678382i) q^{38} +(10.9662 + 2.00421i) q^{39} +(-1.74344 + 0.413202i) q^{40} +(-9.76678 + 2.31477i) q^{41} +(1.31997 - 1.55331i) q^{42} +(2.11947 - 4.91348i) q^{43} +(3.42038 + 1.24492i) q^{44} +(2.19038 - 4.90866i) q^{45} +(3.95321 - 1.43885i) q^{46} +(-0.160028 + 2.74758i) q^{47} +(-1.26723 + 1.18073i) q^{48} +(-2.22397 - 5.15575i) q^{49} +(0.104062 + 1.78667i) q^{50} +(-4.41628 + 1.29220i) q^{51} +(4.41681 - 4.68154i) q^{52} +(4.71775 + 8.17138i) q^{53} +(-0.506608 - 5.17140i) q^{54} +(-3.26086 + 5.64797i) q^{55} +(-0.337531 - 1.12743i) q^{56} +(-1.27699 - 0.0823677i) q^{57} +(-2.08995 + 1.37458i) q^{58} +(-9.18819 - 1.07395i) q^{59} +(-1.68913 - 2.60341i) q^{60} +(-10.4142 + 5.23023i) q^{61} +(1.11862 - 6.34403i) q^{62} +(3.30239 + 1.24882i) q^{63} +(0.173648 + 0.984808i) q^{64} +(6.88643 + 9.25008i) q^{65} +(-0.0393048 + 6.30436i) q^{66} +(1.44376 + 1.53030i) q^{67} +(-0.761935 + 2.54504i) q^{68} +(4.64885 + 5.61095i) q^{69} +(2.09438 - 0.244798i) q^{70} +(8.87851 - 7.44995i) q^{71} +(-2.66390 - 1.37972i) q^{72} +(6.70365 + 5.62503i) q^{73} +(-6.87382 - 4.52098i) q^{74} +(-2.85393 + 1.21002i) q^{75} +(-0.441183 + 0.592612i) q^{76} +(-3.82805 - 1.92252i) q^{77} +(10.2084 + 4.47918i) q^{78} +(5.84449 + 1.38517i) q^{79} -1.79173 q^{80} +(8.14091 - 3.83739i) q^{81} -10.0373 q^{82} +(-0.953883 - 0.226074i) q^{83} +(1.64261 - 1.20703i) q^{84} +(-4.25369 - 2.13628i) q^{85} +(3.19546 - 4.29225i) q^{86} +(-3.45914 - 2.60891i) q^{87} +(3.04109 + 2.00015i) q^{88} +(-4.23002 - 3.54941i) q^{89} +(3.26335 - 4.27121i) q^{90} +(-5.80250 + 4.86888i) q^{91} +(4.17847 - 0.488394i) q^{92} +(11.0001 - 1.86897i) q^{93} +(-0.789350 + 2.63661i) q^{94} +(-0.908405 - 0.962853i) q^{95} +(-1.50537 + 0.856657i) q^{96} +(10.4945 + 14.0966i) q^{97} +(-0.975029 - 5.52966i) q^{98} +(-10.3069 + 3.60652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 90 q - 9 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{2}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.973045 + 0.230616i 0.688047 + 0.163070i
\(3\) 0.190350 + 1.72156i 0.109898 + 0.993943i
\(4\) 0.893633 + 0.448799i 0.446816 + 0.224400i
\(5\) −1.06995 + 1.43719i −0.478495 + 0.642731i −0.974180 0.225772i \(-0.927510\pi\)
0.495685 + 0.868502i \(0.334917\pi\)
\(6\) −0.211800 + 1.71905i −0.0864671 + 0.701800i
\(7\) −0.983264 0.646703i −0.371639 0.244431i 0.349926 0.936777i \(-0.386207\pi\)
−0.721565 + 0.692347i \(0.756577\pi\)
\(8\) 0.766044 + 0.642788i 0.270838 + 0.227260i
\(9\) −2.92753 + 0.655396i −0.975845 + 0.218465i
\(10\) −1.37255 + 1.15170i −0.434037 + 0.364200i
\(11\) 3.61528 0.422566i 1.09005 0.127408i 0.447971 0.894048i \(-0.352147\pi\)
0.642077 + 0.766640i \(0.278073\pi\)
\(12\) −0.602532 + 1.62387i −0.173936 + 0.468771i
\(13\) 1.84593 6.16584i 0.511969 1.71010i −0.176030 0.984385i \(-0.556326\pi\)
0.687999 0.725711i \(-0.258489\pi\)
\(14\) −0.807620 0.856027i −0.215846 0.228783i
\(15\) −2.67787 1.56841i −0.691423 0.404962i
\(16\) 0.597159 + 0.802123i 0.149290 + 0.200531i
\(17\) 0.461322 + 2.61629i 0.111887 + 0.634543i 0.988245 + 0.152882i \(0.0488553\pi\)
−0.876358 + 0.481661i \(0.840034\pi\)
\(18\) −2.99977 0.0374058i −0.707052 0.00881663i
\(19\) −0.128292 + 0.727580i −0.0294322 + 0.166918i −0.995981 0.0895643i \(-0.971453\pi\)
0.966549 + 0.256483i \(0.0825637\pi\)
\(20\) −1.60115 + 0.804128i −0.358028 + 0.179808i
\(21\) 0.926174 1.81585i 0.202108 0.396250i
\(22\) 3.61528 + 0.422566i 0.770780 + 0.0900913i
\(23\) 3.51483 2.31174i 0.732893 0.482031i −0.127387 0.991853i \(-0.540659\pi\)
0.860280 + 0.509822i \(0.170289\pi\)
\(24\) −0.960781 + 1.44115i −0.196119 + 0.294173i
\(25\) 0.513291 + 1.71451i 0.102658 + 0.342902i
\(26\) 3.21811 5.57394i 0.631124 1.09314i
\(27\) −1.68556 4.91517i −0.324386 0.945925i
\(28\) −0.588437 1.01920i −0.111204 0.192611i
\(29\) −1.71661 + 1.81950i −0.318767 + 0.337873i −0.866867 0.498540i \(-0.833870\pi\)
0.548100 + 0.836413i \(0.315351\pi\)
\(30\) −2.24399 2.14369i −0.409694 0.391383i
\(31\) −0.374563 6.43100i −0.0672735 1.15504i −0.847939 0.530093i \(-0.822157\pi\)
0.780666 0.624949i \(-0.214880\pi\)
\(32\) 0.396080 + 0.918216i 0.0700177 + 0.162319i
\(33\) 1.41564 + 6.14349i 0.246431 + 1.06944i
\(34\) −0.154470 + 2.65215i −0.0264914 + 0.454840i
\(35\) 1.98148 0.721198i 0.334931 0.121905i
\(36\) −2.91028 0.728191i −0.485047 0.121365i
\(37\) −7.73114 2.81391i −1.27099 0.462603i −0.383549 0.923521i \(-0.625298\pi\)
−0.887443 + 0.460917i \(0.847520\pi\)
\(38\) −0.292625 + 0.678382i −0.0474701 + 0.110048i
\(39\) 10.9662 + 2.00421i 1.75600 + 0.320931i
\(40\) −1.74344 + 0.413202i −0.275661 + 0.0653329i
\(41\) −9.76678 + 2.31477i −1.52532 + 0.361506i −0.905878 0.423540i \(-0.860787\pi\)
−0.619438 + 0.785046i \(0.712639\pi\)
\(42\) 1.31997 1.55331i 0.203676 0.239681i
\(43\) 2.11947 4.91348i 0.323216 0.749299i −0.676699 0.736260i \(-0.736590\pi\)
0.999915 0.0130390i \(-0.00415056\pi\)
\(44\) 3.42038 + 1.24492i 0.515642 + 0.187678i
\(45\) 2.19038 4.90866i 0.326523 0.731740i
\(46\) 3.95321 1.43885i 0.582869 0.212147i
\(47\) −0.160028 + 2.74758i −0.0233425 + 0.400775i 0.966318 + 0.257349i \(0.0828490\pi\)
−0.989661 + 0.143426i \(0.954188\pi\)
\(48\) −1.26723 + 1.18073i −0.182909 + 0.170423i
\(49\) −2.22397 5.15575i −0.317711 0.736536i
\(50\) 0.104062 + 1.78667i 0.0147165 + 0.252673i
\(51\) −4.41628 + 1.29220i −0.618403 + 0.180945i
\(52\) 4.41681 4.68154i 0.612501 0.649213i
\(53\) 4.71775 + 8.17138i 0.648033 + 1.12243i 0.983592 + 0.180407i \(0.0577413\pi\)
−0.335559 + 0.942019i \(0.608925\pi\)
\(54\) −0.506608 5.17140i −0.0689406 0.703738i
\(55\) −3.26086 + 5.64797i −0.439694 + 0.761572i
\(56\) −0.337531 1.12743i −0.0451045 0.150660i
\(57\) −1.27699 0.0823677i −0.169142 0.0109099i
\(58\) −2.08995 + 1.37458i −0.274424 + 0.180491i
\(59\) −9.18819 1.07395i −1.19620 0.139816i −0.505415 0.862876i \(-0.668661\pi\)
−0.690785 + 0.723060i \(0.742735\pi\)
\(60\) −1.68913 2.60341i −0.218066 0.336099i
\(61\) −10.4142 + 5.23023i −1.33341 + 0.669662i −0.965549 0.260220i \(-0.916205\pi\)
−0.367857 + 0.929882i \(0.619909\pi\)
\(62\) 1.11862 6.34403i 0.142065 0.805693i
\(63\) 3.30239 + 1.24882i 0.416061 + 0.157336i
\(64\) 0.173648 + 0.984808i 0.0217060 + 0.123101i
\(65\) 6.88643 + 9.25008i 0.854156 + 1.14733i
\(66\) −0.0393048 + 6.30436i −0.00483808 + 0.776013i
\(67\) 1.44376 + 1.53030i 0.176383 + 0.186955i 0.809534 0.587073i \(-0.199720\pi\)
−0.633150 + 0.774029i \(0.718239\pi\)
\(68\) −0.761935 + 2.54504i −0.0923982 + 0.308631i
\(69\) 4.64885 + 5.61095i 0.559655 + 0.675479i
\(70\) 2.09438 0.244798i 0.250327 0.0292590i
\(71\) 8.87851 7.44995i 1.05369 0.884147i 0.0602090 0.998186i \(-0.480823\pi\)
0.993476 + 0.114039i \(0.0363789\pi\)
\(72\) −2.66390 1.37972i −0.313944 0.162602i
\(73\) 6.70365 + 5.62503i 0.784603 + 0.658360i 0.944403 0.328789i \(-0.106641\pi\)
−0.159800 + 0.987149i \(0.551085\pi\)
\(74\) −6.87382 4.52098i −0.799065 0.525553i
\(75\) −2.85393 + 1.21002i −0.329543 + 0.139721i
\(76\) −0.441183 + 0.592612i −0.0506072 + 0.0679773i
\(77\) −3.82805 1.92252i −0.436247 0.219091i
\(78\) 10.2084 + 4.47918i 1.15588 + 0.507167i
\(79\) 5.84449 + 1.38517i 0.657556 + 0.155844i 0.545831 0.837895i \(-0.316214\pi\)
0.111726 + 0.993739i \(0.464362\pi\)
\(80\) −1.79173 −0.200322
\(81\) 8.14091 3.83739i 0.904546 0.426377i
\(82\) −10.0373 −1.10844
\(83\) −0.953883 0.226074i −0.104702 0.0248149i 0.177931 0.984043i \(-0.443060\pi\)
−0.282633 + 0.959228i \(0.591208\pi\)
\(84\) 1.64261 1.20703i 0.179223 0.131698i
\(85\) −4.25369 2.13628i −0.461377 0.231712i
\(86\) 3.19546 4.29225i 0.344576 0.462846i
\(87\) −3.45914 2.60891i −0.370859 0.279704i
\(88\) 3.04109 + 2.00015i 0.324181 + 0.213217i
\(89\) −4.23002 3.54941i −0.448381 0.376236i 0.390454 0.920623i \(-0.372318\pi\)
−0.838835 + 0.544386i \(0.816763\pi\)
\(90\) 3.26335 4.27121i 0.343988 0.450225i
\(91\) −5.80250 + 4.86888i −0.608268 + 0.510397i
\(92\) 4.17847 0.488394i 0.435636 0.0509186i
\(93\) 11.0001 1.86897i 1.14065 0.193803i
\(94\) −0.789350 + 2.63661i −0.0814152 + 0.271946i
\(95\) −0.908405 0.962853i −0.0932004 0.0987866i
\(96\) −1.50537 + 0.856657i −0.153641 + 0.0874322i
\(97\) 10.4945 + 14.0966i 1.06556 + 1.43129i 0.895065 + 0.445936i \(0.147129\pi\)
0.170494 + 0.985359i \(0.445464\pi\)
\(98\) −0.975029 5.52966i −0.0984928 0.558580i
\(99\) −10.3069 + 3.60652i −1.03588 + 0.362469i
\(100\) −0.310778 + 1.76251i −0.0310778 + 0.176251i
\(101\) −7.07386 + 3.55263i −0.703876 + 0.353500i −0.764467 0.644663i \(-0.776998\pi\)
0.0605912 + 0.998163i \(0.480701\pi\)
\(102\) −4.59524 + 0.238906i −0.454997 + 0.0236553i
\(103\) 8.41247 + 0.983277i 0.828905 + 0.0968851i 0.519956 0.854193i \(-0.325948\pi\)
0.308950 + 0.951078i \(0.400023\pi\)
\(104\) 5.37739 3.53676i 0.527296 0.346808i
\(105\) 1.61876 + 3.27395i 0.157975 + 0.319505i
\(106\) 2.70613 + 9.03911i 0.262843 + 0.877956i
\(107\) −5.50285 + 9.53121i −0.531980 + 0.921417i 0.467323 + 0.884087i \(0.345219\pi\)
−0.999303 + 0.0373303i \(0.988115\pi\)
\(108\) 0.699654 5.14883i 0.0673242 0.495447i
\(109\) 1.31433 + 2.27648i 0.125890 + 0.218047i 0.922080 0.386998i \(-0.126488\pi\)
−0.796191 + 0.605046i \(0.793155\pi\)
\(110\) −4.47547 + 4.74372i −0.426719 + 0.452296i
\(111\) 3.37269 13.8452i 0.320121 1.31413i
\(112\) −0.0684291 1.17488i −0.00646595 0.111016i
\(113\) 0.121350 + 0.281321i 0.0114156 + 0.0264644i 0.923829 0.382806i \(-0.125042\pi\)
−0.912413 + 0.409271i \(0.865783\pi\)
\(114\) −1.22358 0.374642i −0.114598 0.0350885i
\(115\) −0.438277 + 7.52492i −0.0408695 + 0.701702i
\(116\) −2.35061 + 0.855553i −0.218249 + 0.0794361i
\(117\) −1.36296 + 19.2605i −0.126005 + 1.78064i
\(118\) −8.69285 3.16394i −0.800242 0.291264i
\(119\) 1.23836 2.87084i 0.113520 0.263169i
\(120\) −1.04321 2.92277i −0.0952319 0.266812i
\(121\) 2.18820 0.518613i 0.198927 0.0471467i
\(122\) −11.3397 + 2.68756i −1.02665 + 0.243320i
\(123\) −5.84412 16.3735i −0.526946 1.47635i
\(124\) 2.55151 5.91506i 0.229132 0.531188i
\(125\) −11.4317 4.16078i −1.02248 0.372152i
\(126\) 2.92537 + 1.97674i 0.260613 + 0.176102i
\(127\) 5.43508 1.97821i 0.482285 0.175538i −0.0894241 0.995994i \(-0.528503\pi\)
0.571710 + 0.820456i \(0.306280\pi\)
\(128\) −0.0581448 + 0.998308i −0.00513933 + 0.0882388i
\(129\) 8.86229 + 2.71351i 0.780281 + 0.238911i
\(130\) 4.56759 + 10.5889i 0.400604 + 0.928705i
\(131\) −1.07690 18.4897i −0.0940894 1.61545i −0.633728 0.773556i \(-0.718476\pi\)
0.539639 0.841897i \(-0.318561\pi\)
\(132\) −1.49213 + 6.12536i −0.129873 + 0.533144i
\(133\) 0.596673 0.632437i 0.0517381 0.0548392i
\(134\) 1.05193 + 1.82200i 0.0908731 + 0.157397i
\(135\) 8.86749 + 2.83651i 0.763192 + 0.244128i
\(136\) −1.32832 + 2.30072i −0.113903 + 0.197285i
\(137\) −1.37081 4.57884i −0.117117 0.391197i 0.879250 0.476360i \(-0.158044\pi\)
−0.996367 + 0.0851632i \(0.972859\pi\)
\(138\) 3.22956 + 6.53180i 0.274918 + 0.556024i
\(139\) −16.2013 + 10.6558i −1.37418 + 0.903812i −0.999725 0.0234336i \(-0.992540\pi\)
−0.374454 + 0.927246i \(0.622170\pi\)
\(140\) 2.09438 + 0.244798i 0.177008 + 0.0206892i
\(141\) −4.76058 + 0.247502i −0.400913 + 0.0208435i
\(142\) 10.3573 5.20161i 0.869162 0.436510i
\(143\) 4.06809 23.0713i 0.340191 1.92932i
\(144\) −2.27391 1.95687i −0.189493 0.163072i
\(145\) −0.778285 4.41387i −0.0646330 0.366552i
\(146\) 5.22573 + 7.01938i 0.432485 + 0.580928i
\(147\) 8.45260 4.81010i 0.697159 0.396730i
\(148\) −5.64592 5.98433i −0.464092 0.491909i
\(149\) 5.34018 17.8374i 0.437484 1.46130i −0.400851 0.916143i \(-0.631285\pi\)
0.838335 0.545156i \(-0.183529\pi\)
\(150\) −3.05605 + 0.519240i −0.249525 + 0.0423958i
\(151\) −6.76364 + 0.790556i −0.550417 + 0.0643345i −0.386756 0.922182i \(-0.626404\pi\)
−0.163661 + 0.986517i \(0.552330\pi\)
\(152\) −0.565957 + 0.474894i −0.0459052 + 0.0385190i
\(153\) −3.06524 7.35692i −0.247810 0.594772i
\(154\) −3.28150 2.75351i −0.264431 0.221884i
\(155\) 9.64333 + 6.34252i 0.774571 + 0.509443i
\(156\) 8.90029 + 6.71267i 0.712594 + 0.537443i
\(157\) 14.4791 19.4488i 1.15556 1.55218i 0.375085 0.926990i \(-0.377613\pi\)
0.780471 0.625192i \(-0.214979\pi\)
\(158\) 5.36751 + 2.69566i 0.427016 + 0.214456i
\(159\) −13.1695 + 9.67731i −1.04441 + 0.767460i
\(160\) −1.74344 0.413202i −0.137831 0.0326665i
\(161\) −4.95102 −0.390195
\(162\) 8.80644 1.85653i 0.691899 0.145863i
\(163\) 12.0798 0.946163 0.473082 0.881019i \(-0.343142\pi\)
0.473082 + 0.881019i \(0.343142\pi\)
\(164\) −9.76678 2.31477i −0.762658 0.180753i
\(165\) −10.3440 4.53867i −0.805280 0.353335i
\(166\) −0.876034 0.439961i −0.0679935 0.0341476i
\(167\) −11.4508 + 15.3811i −0.886090 + 1.19023i 0.0947675 + 0.995499i \(0.469789\pi\)
−0.980858 + 0.194726i \(0.937618\pi\)
\(168\) 1.87669 0.795687i 0.144790 0.0613886i
\(169\) −23.7488 15.6198i −1.82683 1.20152i
\(170\) −3.64637 3.05967i −0.279664 0.234666i
\(171\) −0.101274 2.21410i −0.00774463 0.169316i
\(172\) 4.09919 3.43963i 0.312560 0.262269i
\(173\) 2.67346 0.312482i 0.203259 0.0237576i −0.0138540 0.999904i \(-0.504410\pi\)
0.217113 + 0.976146i \(0.430336\pi\)
\(174\) −2.76424 3.33632i −0.209557 0.252926i
\(175\) 0.604079 2.01776i 0.0456641 0.152529i
\(176\) 2.49785 + 2.64756i 0.188282 + 0.199567i
\(177\) 0.0998925 16.0224i 0.00750838 1.20432i
\(178\) −3.29745 4.42924i −0.247154 0.331986i
\(179\) 2.19379 + 12.4416i 0.163972 + 0.929931i 0.950118 + 0.311890i \(0.100962\pi\)
−0.786146 + 0.618040i \(0.787927\pi\)
\(180\) 4.16040 3.40350i 0.310098 0.253682i
\(181\) 1.55173 8.80030i 0.115339 0.654121i −0.871243 0.490853i \(-0.836685\pi\)
0.986582 0.163268i \(-0.0522036\pi\)
\(182\) −6.76894 + 3.39949i −0.501747 + 0.251987i
\(183\) −10.9865 16.9332i −0.812145 1.25174i
\(184\) 4.17847 + 0.488394i 0.308041 + 0.0360049i
\(185\) 12.3160 8.10038i 0.905493 0.595552i
\(186\) 11.1346 + 0.718194i 0.816426 + 0.0526605i
\(187\) 2.77336 + 9.26367i 0.202808 + 0.677427i
\(188\) −1.37612 + 2.38350i −0.100364 + 0.173835i
\(189\) −1.52131 + 5.92296i −0.110659 + 0.430832i
\(190\) −0.661869 1.14639i −0.0480171 0.0831680i
\(191\) 16.0171 16.9771i 1.15895 1.22842i 0.189838 0.981815i \(-0.439204\pi\)
0.969116 0.246605i \(-0.0793149\pi\)
\(192\) −1.66235 + 0.486403i −0.119970 + 0.0351031i
\(193\) 0.783836 + 13.4579i 0.0564217 + 0.968724i 0.901144 + 0.433519i \(0.142728\pi\)
−0.844722 + 0.535205i \(0.820235\pi\)
\(194\) 6.96076 + 16.1368i 0.499753 + 1.15856i
\(195\) −14.6137 + 13.6161i −1.04651 + 0.975072i
\(196\) 0.326481 5.60547i 0.0233201 0.400391i
\(197\) −15.4354 + 5.61801i −1.09972 + 0.400267i −0.827214 0.561886i \(-0.810076\pi\)
−0.272509 + 0.962153i \(0.587854\pi\)
\(198\) −10.8608 + 1.13237i −0.771844 + 0.0804738i
\(199\) −1.00917 0.367309i −0.0715384 0.0260378i 0.306003 0.952031i \(-0.401008\pi\)
−0.377541 + 0.925993i \(0.623230\pi\)
\(200\) −0.708863 + 1.64333i −0.0501242 + 0.116201i
\(201\) −2.35968 + 2.77681i −0.166439 + 0.195861i
\(202\) −7.70248 + 1.82552i −0.541945 + 0.128443i
\(203\) 2.86456 0.678914i 0.201053 0.0476504i
\(204\) −4.52647 0.827269i −0.316916 0.0579204i
\(205\) 7.12319 16.5134i 0.497505 1.15335i
\(206\) 7.95895 + 2.89682i 0.554526 + 0.201831i
\(207\) −8.77468 + 9.07131i −0.609882 + 0.630499i
\(208\) 6.04808 2.20132i 0.419359 0.152634i
\(209\) −0.156361 + 2.68462i −0.0108157 + 0.185699i
\(210\) 0.820100 + 3.55901i 0.0565923 + 0.245595i
\(211\) 9.19140 + 21.3081i 0.632762 + 1.46691i 0.868800 + 0.495164i \(0.164892\pi\)
−0.236037 + 0.971744i \(0.575849\pi\)
\(212\) 0.548625 + 9.41954i 0.0376798 + 0.646936i
\(213\) 14.5156 + 13.8668i 0.994590 + 0.950137i
\(214\) −7.55257 + 8.00525i −0.516283 + 0.547228i
\(215\) 4.79388 + 8.30325i 0.326940 + 0.566277i
\(216\) 1.86820 4.84869i 0.127115 0.329912i
\(217\) −3.79065 + 6.56560i −0.257326 + 0.445702i
\(218\) 0.753907 + 2.51822i 0.0510610 + 0.170556i
\(219\) −8.40779 + 12.6115i −0.568146 + 0.852204i
\(220\) −5.44881 + 3.58374i −0.367359 + 0.241616i
\(221\) 16.9832 + 1.98505i 1.14241 + 0.133529i
\(222\) 6.47471 12.6943i 0.434554 0.851982i
\(223\) 0.407187 0.204497i 0.0272673 0.0136941i −0.435113 0.900376i \(-0.643292\pi\)
0.462381 + 0.886682i \(0.346995\pi\)
\(224\) 0.204362 1.15899i 0.0136545 0.0774386i
\(225\) −2.62636 4.68288i −0.175091 0.312192i
\(226\) 0.0532019 + 0.301723i 0.00353893 + 0.0200703i
\(227\) −3.04738 4.09334i −0.202262 0.271685i 0.689406 0.724375i \(-0.257872\pi\)
−0.891668 + 0.452691i \(0.850464\pi\)
\(228\) −1.10420 0.646720i −0.0731272 0.0428301i
\(229\) −12.2467 12.9808i −0.809285 0.857792i 0.182827 0.983145i \(-0.441475\pi\)
−0.992112 + 0.125353i \(0.959994\pi\)
\(230\) −2.16183 + 7.22101i −0.142547 + 0.476139i
\(231\) 2.58106 6.95617i 0.169821 0.457682i
\(232\) −2.48456 + 0.290403i −0.163119 + 0.0190659i
\(233\) −1.21666 + 1.02090i −0.0797058 + 0.0668811i −0.681770 0.731567i \(-0.738790\pi\)
0.602064 + 0.798448i \(0.294345\pi\)
\(234\) −5.76800 + 18.4270i −0.377066 + 1.20461i
\(235\) −3.77757 3.16976i −0.246421 0.206772i
\(236\) −7.72888 5.08336i −0.503107 0.330899i
\(237\) −1.27216 + 10.3253i −0.0826354 + 0.670700i
\(238\) 1.86704 2.50787i 0.121022 0.162561i
\(239\) 0.320055 + 0.160738i 0.0207026 + 0.0103972i 0.459120 0.888374i \(-0.348165\pi\)
−0.438418 + 0.898771i \(0.644461\pi\)
\(240\) −0.341055 3.08457i −0.0220150 0.199108i
\(241\) 9.12041 + 2.16158i 0.587497 + 0.139239i 0.513605 0.858027i \(-0.328310\pi\)
0.0738924 + 0.997266i \(0.476458\pi\)
\(242\) 2.24882 0.144560
\(243\) 8.15591 + 13.2846i 0.523202 + 0.852209i
\(244\) −11.6538 −0.746060
\(245\) 9.78933 + 2.32011i 0.625417 + 0.148227i
\(246\) −1.91060 17.2799i −0.121816 1.10172i
\(247\) 4.24932 + 2.13409i 0.270378 + 0.135789i
\(248\) 3.84684 5.16720i 0.244274 0.328117i
\(249\) 0.207629 1.68520i 0.0131580 0.106795i
\(250\) −10.1640 6.68495i −0.642826 0.422793i
\(251\) 12.8852 + 10.8119i 0.813304 + 0.682443i 0.951394 0.307977i \(-0.0996518\pi\)
−0.138090 + 0.990420i \(0.544096\pi\)
\(252\) 2.39065 + 2.59809i 0.150597 + 0.163664i
\(253\) 11.7302 9.84284i 0.737474 0.618814i
\(254\) 5.74478 0.671469i 0.360460 0.0421317i
\(255\) 2.86805 7.72962i 0.179604 0.484048i
\(256\) −0.286803 + 0.957990i −0.0179252 + 0.0598743i
\(257\) 12.9520 + 13.7283i 0.807923 + 0.856348i 0.991957 0.126572i \(-0.0403974\pi\)
−0.184035 + 0.982920i \(0.558916\pi\)
\(258\) 7.99763 + 4.68415i 0.497910 + 0.291623i
\(259\) 5.78199 + 7.76656i 0.359276 + 0.482591i
\(260\) 2.00251 + 11.3568i 0.124190 + 0.704319i
\(261\) 3.83295 6.45172i 0.237253 0.399351i
\(262\) 3.21614 18.2397i 0.198694 1.12685i
\(263\) 0.0777083 0.0390266i 0.00479170 0.00240648i −0.446402 0.894833i \(-0.647295\pi\)
0.451193 + 0.892426i \(0.350998\pi\)
\(264\) −2.86451 + 5.61614i −0.176299 + 0.345649i
\(265\) −16.7916 1.96265i −1.03150 0.120565i
\(266\) 0.726440 0.477787i 0.0445409 0.0292950i
\(267\) 5.30533 7.95786i 0.324681 0.487013i
\(268\) 0.603395 + 2.01548i 0.0368582 + 0.123115i
\(269\) −13.9803 + 24.2145i −0.852392 + 1.47639i 0.0266520 + 0.999645i \(0.491515\pi\)
−0.879044 + 0.476741i \(0.841818\pi\)
\(270\) 7.97432 + 4.80503i 0.485302 + 0.292425i
\(271\) 8.66520 + 15.0086i 0.526373 + 0.911705i 0.999528 + 0.0307258i \(0.00978186\pi\)
−0.473155 + 0.880979i \(0.656885\pi\)
\(272\) −1.82310 + 1.93238i −0.110542 + 0.117167i
\(273\) −9.48657 9.06257i −0.574153 0.548491i
\(274\) −0.277911 4.77155i −0.0167892 0.288260i
\(275\) 2.58019 + 5.98154i 0.155591 + 0.360701i
\(276\) 1.63617 + 7.10053i 0.0984858 + 0.427402i
\(277\) −0.361549 + 6.20756i −0.0217234 + 0.372976i 0.969873 + 0.243609i \(0.0783314\pi\)
−0.991597 + 0.129367i \(0.958706\pi\)
\(278\) −18.2220 + 6.63227i −1.09288 + 0.397777i
\(279\) 5.31140 + 18.5815i 0.317985 + 1.11244i
\(280\) 1.98148 + 0.721198i 0.118416 + 0.0430998i
\(281\) −7.21907 + 16.7357i −0.430653 + 0.998367i 0.555346 + 0.831619i \(0.312586\pi\)
−0.986000 + 0.166748i \(0.946673\pi\)
\(282\) −4.68934 0.857034i −0.279246 0.0510357i
\(283\) 8.73861 2.07109i 0.519456 0.123113i 0.0374796 0.999297i \(-0.488067\pi\)
0.481977 + 0.876184i \(0.339919\pi\)
\(284\) 11.2777 2.67285i 0.669206 0.158605i
\(285\) 1.48469 1.74715i 0.0879457 0.103492i
\(286\) 9.27903 21.5112i 0.548681 1.27198i
\(287\) 11.1003 + 4.04018i 0.655230 + 0.238484i
\(288\) −1.76133 2.42852i −0.103788 0.143102i
\(289\) 9.34264 3.40044i 0.549567 0.200026i
\(290\) 0.260603 4.47438i 0.0153031 0.262745i
\(291\) −22.2705 + 20.7503i −1.30552 + 1.21640i
\(292\) 3.46609 + 8.03531i 0.202838 + 0.470231i
\(293\) −0.0639623 1.09819i −0.00373672 0.0641570i 0.995924 0.0901933i \(-0.0287485\pi\)
−0.999661 + 0.0260363i \(0.991711\pi\)
\(294\) 9.33405 2.73114i 0.544373 0.159283i
\(295\) 11.3743 12.0561i 0.662240 0.701933i
\(296\) −4.11366 7.12506i −0.239101 0.414136i
\(297\) −8.17075 17.0575i −0.474115 0.989774i
\(298\) 9.30983 16.1251i 0.539304 0.934101i
\(299\) −7.76568 25.9392i −0.449101 1.50010i
\(300\) −3.09342 0.199530i −0.178599 0.0115198i
\(301\) −5.26156 + 3.46058i −0.303271 + 0.199465i
\(302\) −6.76364 0.790556i −0.389204 0.0454914i
\(303\) −7.46257 11.5018i −0.428713 0.660763i
\(304\) −0.660220 + 0.331575i −0.0378662 + 0.0190171i
\(305\) 3.62587 20.5633i 0.207616 1.17745i
\(306\) −1.28599 7.86551i −0.0735154 0.449641i
\(307\) −4.44355 25.2006i −0.253607 1.43828i −0.799624 0.600502i \(-0.794968\pi\)
0.546017 0.837774i \(-0.316143\pi\)
\(308\) −2.55805 3.43605i −0.145758 0.195787i
\(309\) −0.0914590 + 14.6697i −0.00520292 + 0.834532i
\(310\) 7.92071 + 8.39546i 0.449866 + 0.476830i
\(311\) −6.83294 + 22.8236i −0.387460 + 1.29421i 0.512670 + 0.858586i \(0.328657\pi\)
−0.900130 + 0.435622i \(0.856529\pi\)
\(312\) 7.11234 + 8.58427i 0.402657 + 0.485989i
\(313\) −24.6494 + 2.88110i −1.39327 + 0.162849i −0.779383 0.626548i \(-0.784467\pi\)
−0.613883 + 0.789397i \(0.710393\pi\)
\(314\) 18.5740 15.5854i 1.04819 0.879537i
\(315\) −5.32817 + 3.40998i −0.300208 + 0.192131i
\(316\) 4.60116 + 3.86083i 0.258836 + 0.217189i
\(317\) −12.8790 8.47067i −0.723359 0.475760i 0.133672 0.991026i \(-0.457323\pi\)
−0.857031 + 0.515265i \(0.827693\pi\)
\(318\) −15.0463 + 6.37936i −0.843752 + 0.357737i
\(319\) −5.43718 + 7.30340i −0.304424 + 0.408912i
\(320\) −1.60115 0.804128i −0.0895070 0.0449521i
\(321\) −17.4560 7.65922i −0.974300 0.427496i
\(322\) −4.81756 1.14178i −0.268472 0.0636291i
\(323\) −1.96274 −0.109210
\(324\) 8.99720 + 0.224417i 0.499845 + 0.0124676i
\(325\) 11.5189 0.638954
\(326\) 11.7542 + 2.78579i 0.651004 + 0.154291i
\(327\) −3.66892 + 2.69602i −0.202892 + 0.149090i
\(328\) −8.96970 4.50475i −0.495269 0.248733i
\(329\) 1.93422 2.59810i 0.106637 0.143238i
\(330\) −9.01850 6.80182i −0.496452 0.374428i
\(331\) −18.9769 12.4813i −1.04306 0.686034i −0.0922311 0.995738i \(-0.529400\pi\)
−0.950833 + 0.309703i \(0.899770\pi\)
\(332\) −0.750959 0.630129i −0.0412142 0.0345828i
\(333\) 24.4774 + 3.17084i 1.34135 + 0.173761i
\(334\) −14.6893 + 12.3258i −0.803761 + 0.674436i
\(335\) −3.74407 + 0.437619i −0.204560 + 0.0239097i
\(336\) 2.00961 0.341443i 0.109633 0.0186273i
\(337\) 3.49968 11.6897i 0.190639 0.636780i −0.808213 0.588890i \(-0.799565\pi\)
0.998853 0.0478901i \(-0.0152497\pi\)
\(338\) −19.5064 20.6756i −1.06101 1.12461i
\(339\) −0.461211 + 0.262460i −0.0250496 + 0.0142549i
\(340\) −2.84247 3.81811i −0.154155 0.207066i
\(341\) −4.07167 23.0916i −0.220493 1.25048i
\(342\) 0.412062 2.17777i 0.0222818 0.117760i
\(343\) −2.57802 + 14.6207i −0.139200 + 0.789443i
\(344\) 4.78193 2.40158i 0.257824 0.129484i
\(345\) −13.0380 + 0.677846i −0.701944 + 0.0364940i
\(346\) 2.67346 + 0.312482i 0.143726 + 0.0167992i
\(347\) 2.40626 1.58262i 0.129175 0.0849597i −0.483277 0.875467i \(-0.660554\pi\)
0.612452 + 0.790508i \(0.290183\pi\)
\(348\) −1.92032 3.88387i −0.102940 0.208197i
\(349\) 1.42792 + 4.76957i 0.0764346 + 0.255309i 0.987664 0.156591i \(-0.0500504\pi\)
−0.911229 + 0.411900i \(0.864865\pi\)
\(350\) 1.05312 1.82407i 0.0562919 0.0975004i
\(351\) −33.4176 + 1.31982i −1.78370 + 0.0704468i
\(352\) 1.81995 + 3.15224i 0.0970035 + 0.168015i
\(353\) 17.1705 18.1997i 0.913896 0.968673i −0.0857222 0.996319i \(-0.527320\pi\)
0.999618 + 0.0276463i \(0.00880123\pi\)
\(354\) 3.79223 15.5675i 0.201555 0.827404i
\(355\) 1.20745 + 20.7312i 0.0640849 + 1.10030i
\(356\) −2.18711 5.07029i −0.115917 0.268725i
\(357\) 5.17804 + 1.58545i 0.274051 + 0.0839107i
\(358\) −0.734576 + 12.6122i −0.0388235 + 0.666575i
\(359\) −12.8993 + 4.69497i −0.680800 + 0.247791i −0.659191 0.751976i \(-0.729101\pi\)
−0.0216088 + 0.999767i \(0.506879\pi\)
\(360\) 4.83316 2.35230i 0.254730 0.123977i
\(361\) 17.3412 + 6.31170i 0.912697 + 0.332195i
\(362\) 3.53939 8.20523i 0.186026 0.431257i
\(363\) 1.30935 + 3.66840i 0.0687229 + 0.192541i
\(364\) −7.37045 + 1.74683i −0.386317 + 0.0915588i
\(365\) −15.2568 + 3.61593i −0.798577 + 0.189266i
\(366\) −6.78530 19.0104i −0.354673 0.993689i
\(367\) 10.8698 25.1991i 0.567400 1.31538i −0.357052 0.934084i \(-0.616218\pi\)
0.924452 0.381297i \(-0.124523\pi\)
\(368\) 3.95321 + 1.43885i 0.206075 + 0.0750053i
\(369\) 27.0755 13.1777i 1.40949 0.686003i
\(370\) 13.8521 5.04176i 0.720138 0.262109i
\(371\) 0.645663 11.0856i 0.0335212 0.575536i
\(372\) 10.6688 + 3.26664i 0.553152 + 0.169367i
\(373\) −6.48302 15.0293i −0.335678 0.778189i −0.999540 0.0303339i \(-0.990343\pi\)
0.663862 0.747855i \(-0.268916\pi\)
\(374\) 0.562255 + 9.65355i 0.0290735 + 0.499173i
\(375\) 4.98702 20.4723i 0.257529 1.05718i
\(376\) −1.88870 + 2.00190i −0.0974022 + 0.103240i
\(377\) 8.05001 + 13.9430i 0.414597 + 0.718103i
\(378\) −2.84623 + 5.41247i −0.146394 + 0.278388i
\(379\) −9.26188 + 16.0420i −0.475751 + 0.824024i −0.999614 0.0277779i \(-0.991157\pi\)
0.523863 + 0.851802i \(0.324490\pi\)
\(380\) −0.379653 1.26813i −0.0194758 0.0650536i
\(381\) 4.44017 + 8.98026i 0.227477 + 0.460073i
\(382\) 19.5005 12.8257i 0.997733 0.656219i
\(383\) 26.9481 + 3.14979i 1.37699 + 0.160947i 0.772169 0.635418i \(-0.219172\pi\)
0.604817 + 0.796364i \(0.293246\pi\)
\(384\) −1.72971 + 0.0899278i −0.0882691 + 0.00458911i
\(385\) 6.85884 3.44464i 0.349559 0.175555i
\(386\) −2.34091 + 13.2759i −0.119149 + 0.675728i
\(387\) −2.98454 + 15.7735i −0.151713 + 0.801811i
\(388\) 3.05172 + 17.3071i 0.154927 + 0.878637i
\(389\) −3.51381 4.71987i −0.178157 0.239307i 0.704070 0.710131i \(-0.251364\pi\)
−0.882227 + 0.470824i \(0.843957\pi\)
\(390\) −17.3599 + 9.87896i −0.879054 + 0.500241i
\(391\) 7.66964 + 8.12935i 0.387871 + 0.411119i
\(392\) 1.61039 5.37908i 0.0813370 0.271685i
\(393\) 31.6261 5.37346i 1.59533 0.271055i
\(394\) −16.3149 + 1.90694i −0.821933 + 0.0960702i
\(395\) −8.24405 + 6.91758i −0.414803 + 0.348061i
\(396\) −10.8292 1.40283i −0.544187 0.0704949i
\(397\) 17.9372 + 15.0511i 0.900243 + 0.755393i 0.970238 0.242154i \(-0.0778539\pi\)
−0.0699952 + 0.997547i \(0.522298\pi\)
\(398\) −0.897263 0.590139i −0.0449757 0.0295810i
\(399\) 1.20235 + 0.906824i 0.0601930 + 0.0453980i
\(400\) −1.06873 + 1.43556i −0.0534367 + 0.0717779i
\(401\) 3.31607 + 1.66539i 0.165597 + 0.0831657i 0.529667 0.848206i \(-0.322317\pi\)
−0.364070 + 0.931371i \(0.618613\pi\)
\(402\) −2.93645 + 2.15778i −0.146457 + 0.107620i
\(403\) −40.3439 9.56169i −2.00968 0.476302i
\(404\) −7.91585 −0.393828
\(405\) −3.19529 + 15.8058i −0.158775 + 0.785399i
\(406\) 2.94392 0.146104
\(407\) −29.1393 6.90614i −1.44438 0.342325i
\(408\) −4.21368 1.84885i −0.208608 0.0915315i
\(409\) 9.23834 + 4.63967i 0.456807 + 0.229417i 0.662296 0.749243i \(-0.269582\pi\)
−0.205489 + 0.978659i \(0.565879\pi\)
\(410\) 10.7394 14.4256i 0.530383 0.712428i
\(411\) 7.62181 3.23152i 0.375956 0.159399i
\(412\) 7.07636 + 4.65420i 0.348627 + 0.229296i
\(413\) 8.33989 + 6.99800i 0.410379 + 0.344349i
\(414\) −10.6301 + 6.80321i −0.522443 + 0.334359i
\(415\) 1.34552 1.12902i 0.0660488 0.0554215i
\(416\) 6.39271 0.747200i 0.313428 0.0366345i
\(417\) −21.4285 25.8632i −1.04936 1.26653i
\(418\) −0.771262 + 2.57619i −0.0377237 + 0.126006i
\(419\) −9.51027 10.0803i −0.464607 0.492455i 0.452127 0.891954i \(-0.350666\pi\)
−0.916734 + 0.399499i \(0.869184\pi\)
\(420\) −0.0227698 + 3.65221i −0.00111105 + 0.178209i
\(421\) 5.20311 + 6.98898i 0.253584 + 0.340622i 0.910626 0.413232i \(-0.135600\pi\)
−0.657042 + 0.753854i \(0.728193\pi\)
\(422\) 4.02967 + 22.8534i 0.196161 + 1.11249i
\(423\) −1.33226 8.14851i −0.0647769 0.396194i
\(424\) −1.63846 + 9.29215i −0.0795705 + 0.451267i
\(425\) −4.24886 + 2.13386i −0.206100 + 0.103507i
\(426\) 10.9264 + 16.8405i 0.529385 + 0.815926i
\(427\) 13.6223 + 1.59222i 0.659232 + 0.0770531i
\(428\) −9.19513 + 6.04773i −0.444463 + 0.292328i
\(429\) 40.4929 + 2.61185i 1.95502 + 0.126101i
\(430\) 2.74980 + 9.18498i 0.132607 + 0.442939i
\(431\) 10.7815 18.6742i 0.519328 0.899503i −0.480420 0.877039i \(-0.659516\pi\)
0.999748 0.0224638i \(-0.00715106\pi\)
\(432\) 2.93603 4.28716i 0.141260 0.206266i
\(433\) −3.07025 5.31783i −0.147547 0.255558i 0.782773 0.622307i \(-0.213804\pi\)
−0.930320 + 0.366748i \(0.880471\pi\)
\(434\) −5.20261 + 5.51444i −0.249733 + 0.264702i
\(435\) 7.45060 2.18004i 0.357229 0.104525i
\(436\) 0.152843 + 2.62421i 0.00731984 + 0.125677i
\(437\) 1.23105 + 2.85390i 0.0588892 + 0.136521i
\(438\) −11.0896 + 10.3325i −0.529880 + 0.493708i
\(439\) −0.719298 + 12.3499i −0.0343302 + 0.589427i 0.936650 + 0.350267i \(0.113909\pi\)
−0.970980 + 0.239160i \(0.923128\pi\)
\(440\) −6.12840 + 2.23056i −0.292160 + 0.106338i
\(441\) 9.88982 + 13.6361i 0.470944 + 0.649336i
\(442\) 16.0676 + 5.84813i 0.764258 + 0.278167i
\(443\) 6.40801 14.8554i 0.304454 0.705803i −0.695465 0.718560i \(-0.744802\pi\)
0.999919 + 0.0127572i \(0.00406086\pi\)
\(444\) 9.22768 10.8589i 0.437926 0.515341i
\(445\) 9.62707 2.28166i 0.456367 0.108161i
\(446\) 0.443372 0.105081i 0.0209943 0.00497573i
\(447\) 31.7247 + 5.79808i 1.50053 + 0.274240i
\(448\) 0.466136 1.08062i 0.0220229 0.0510547i
\(449\) −12.4608 4.53535i −0.588060 0.214036i 0.0308157 0.999525i \(-0.490189\pi\)
−0.618876 + 0.785489i \(0.712412\pi\)
\(450\) −1.47562 5.16234i −0.0695614 0.243355i
\(451\) −34.3315 + 12.4957i −1.61661 + 0.588397i
\(452\) −0.0178143 + 0.305859i −0.000837912 + 0.0143864i
\(453\) −2.64844 11.4935i −0.124435 0.540013i
\(454\) −2.02125 4.68578i −0.0948618 0.219914i
\(455\) −0.789124 13.5487i −0.0369947 0.635175i
\(456\) −0.925288 0.883933i −0.0433306 0.0413939i
\(457\) −1.21778 + 1.29077i −0.0569654 + 0.0603798i −0.755230 0.655460i \(-0.772475\pi\)
0.698264 + 0.715840i \(0.253956\pi\)
\(458\) −8.92303 15.4551i −0.416946 0.722171i
\(459\) 12.0819 6.67738i 0.563935 0.311673i
\(460\) −3.76884 + 6.52782i −0.175723 + 0.304361i
\(461\) −0.0152579 0.0509649i −0.000710630 0.00237367i 0.957633 0.287990i \(-0.0929869\pi\)
−0.958344 + 0.285616i \(0.907802\pi\)
\(462\) 4.11569 6.17343i 0.191479 0.287214i
\(463\) −8.70742 + 5.72696i −0.404668 + 0.266154i −0.735486 0.677540i \(-0.763046\pi\)
0.330817 + 0.943695i \(0.392676\pi\)
\(464\) −2.48456 0.290403i −0.115343 0.0134816i
\(465\) −9.08342 + 17.8089i −0.421234 + 0.825866i
\(466\) −1.41930 + 0.712797i −0.0657476 + 0.0330197i
\(467\) −5.23134 + 29.6684i −0.242078 + 1.37289i 0.585105 + 0.810957i \(0.301053\pi\)
−0.827183 + 0.561933i \(0.810058\pi\)
\(468\) −9.86209 + 16.6001i −0.455875 + 0.767341i
\(469\) −0.429950 2.43837i −0.0198532 0.112593i
\(470\) −2.94475 3.95548i −0.135831 0.182453i
\(471\) 36.2383 + 21.2245i 1.66977 + 0.977975i
\(472\) −6.34824 6.72874i −0.292202 0.309716i
\(473\) 5.58621 18.6592i 0.256854 0.857952i
\(474\) −3.61904 + 9.75360i −0.166228 + 0.447998i
\(475\) −1.31330 + 0.153502i −0.0602581 + 0.00704317i
\(476\) 2.39507 2.00970i 0.109778 0.0921145i
\(477\) −19.1669 20.8300i −0.877591 0.953740i
\(478\) 0.274359 + 0.230215i 0.0125489 + 0.0105298i
\(479\) 2.50288 + 1.64617i 0.114359 + 0.0752154i 0.605400 0.795921i \(-0.293013\pi\)
−0.491041 + 0.871137i \(0.663383\pi\)
\(480\) 0.379489 3.08008i 0.0173212 0.140586i
\(481\) −31.6212 + 42.4747i −1.44180 + 1.93668i
\(482\) 8.37608 + 4.20662i 0.381520 + 0.191606i
\(483\) −0.942424 8.52347i −0.0428818 0.387831i
\(484\) 2.18820 + 0.518613i 0.0994637 + 0.0235733i
\(485\) −31.4881 −1.42980
\(486\) 4.87243 + 14.8074i 0.221018 + 0.671678i
\(487\) 5.17613 0.234553 0.117276 0.993099i \(-0.462584\pi\)
0.117276 + 0.993099i \(0.462584\pi\)
\(488\) −11.3397 2.68756i −0.513324 0.121660i
\(489\) 2.29939 + 20.7961i 0.103982 + 0.940432i
\(490\) 8.99040 + 4.51515i 0.406145 + 0.203974i
\(491\) −23.8549 + 32.0427i −1.07656 + 1.44607i −0.190966 + 0.981597i \(0.561162\pi\)
−0.885589 + 0.464469i \(0.846245\pi\)
\(492\) 2.12591 17.2547i 0.0958435 0.777903i
\(493\) −5.55225 3.65177i −0.250061 0.164468i
\(494\) 3.64263 + 3.05653i 0.163890 + 0.137520i
\(495\) 5.84461 18.6718i 0.262696 0.839234i
\(496\) 4.93478 4.14077i 0.221578 0.185926i
\(497\) −13.5478 + 1.58351i −0.607703 + 0.0710303i
\(498\) 0.590666 1.59189i 0.0264684 0.0713344i
\(499\) 4.79308 16.0100i 0.214568 0.716706i −0.781157 0.624335i \(-0.785370\pi\)
0.995725 0.0923714i \(-0.0294447\pi\)
\(500\) −8.34835 8.84873i −0.373349 0.395727i
\(501\) −28.6591 16.7855i −1.28040 0.749919i
\(502\) 10.0444 + 13.4920i 0.448305 + 0.602178i
\(503\) −0.0162598 0.0922139i −0.000724989 0.00411162i 0.984443 0.175704i \(-0.0562200\pi\)
−0.985168 + 0.171592i \(0.945109\pi\)
\(504\) 1.72705 + 3.07938i 0.0769289 + 0.137167i
\(505\) 2.46287 13.9676i 0.109596 0.621550i
\(506\) 13.6840 6.87234i 0.608326 0.305513i
\(507\) 22.3699 43.8581i 0.993480 1.94781i
\(508\) 5.74478 + 0.671469i 0.254884 + 0.0297916i
\(509\) −24.4077 + 16.0532i −1.08185 + 0.711545i −0.959717 0.280968i \(-0.909344\pi\)
−0.122135 + 0.992513i \(0.538974\pi\)
\(510\) 4.57332 6.85985i 0.202510 0.303759i
\(511\) −2.95374 9.86617i −0.130666 0.436453i
\(512\) −0.500000 + 0.866025i −0.0220971 + 0.0382733i
\(513\) 3.79242 0.595802i 0.167440 0.0263053i
\(514\) 9.43690 + 16.3452i 0.416244 + 0.720955i
\(515\) −10.4141 + 11.0383i −0.458898 + 0.486404i
\(516\) 6.70181 + 6.40227i 0.295031 + 0.281844i
\(517\) 0.582485 + 10.0009i 0.0256177 + 0.439839i
\(518\) 3.83505 + 8.89064i 0.168502 + 0.390632i
\(519\) 1.04685 + 4.54304i 0.0459516 + 0.199417i
\(520\) −0.670526 + 11.5125i −0.0294045 + 0.504856i
\(521\) 13.5587 4.93498i 0.594019 0.216205i −0.0274771 0.999622i \(-0.508747\pi\)
0.621496 + 0.783417i \(0.286525\pi\)
\(522\) 5.21750 5.39387i 0.228364 0.236083i
\(523\) −31.0775 11.3113i −1.35893 0.494609i −0.443204 0.896421i \(-0.646158\pi\)
−0.915722 + 0.401812i \(0.868380\pi\)
\(524\) 7.33581 17.0063i 0.320466 0.742924i
\(525\) 3.58869 + 0.655877i 0.156623 + 0.0286248i
\(526\) 0.0846138 0.0200538i 0.00368934 0.000874389i
\(527\) 16.6526 3.94673i 0.725397 0.171922i
\(528\) −4.08247 + 4.80415i −0.177667 + 0.209074i
\(529\) −2.09994 + 4.86822i −0.0913019 + 0.211662i
\(530\) −15.8863 5.78215i −0.690058 0.251161i
\(531\) 27.6026 2.87789i 1.19785 0.124890i
\(532\) 0.817044 0.297380i 0.0354233 0.0128930i
\(533\) −3.75631 + 64.4933i −0.162704 + 2.79352i
\(534\) 6.99754 6.51986i 0.302813 0.282142i
\(535\) −7.81040 18.1065i −0.337673 0.782814i
\(536\) 0.122329 + 2.10030i 0.00528380 + 0.0907194i
\(537\) −21.0014 + 6.14500i −0.906278 + 0.265177i
\(538\) −19.1877 + 20.3378i −0.827240 + 0.876823i
\(539\) −10.2189 17.6997i −0.440161 0.762381i
\(540\) 6.65126 + 6.51452i 0.286224 + 0.280340i
\(541\) 13.8125 23.9240i 0.593846 1.02857i −0.399863 0.916575i \(-0.630942\pi\)
0.993709 0.111996i \(-0.0357245\pi\)
\(542\) 4.97041 + 16.6023i 0.213498 + 0.713131i
\(543\) 15.4456 + 0.996262i 0.662834 + 0.0427537i
\(544\) −2.21960 + 1.45985i −0.0951644 + 0.0625906i
\(545\) −4.67800 0.546779i −0.200383 0.0234215i
\(546\) −7.14088 11.0060i −0.305602 0.471015i
\(547\) 29.3813 14.7559i 1.25626 0.630915i 0.308899 0.951095i \(-0.400040\pi\)
0.947357 + 0.320180i \(0.103743\pi\)
\(548\) 0.829975 4.70702i 0.0354548 0.201074i
\(549\) 27.0602 22.1371i 1.15490 0.944789i
\(550\) 1.13120 + 6.41534i 0.0482344 + 0.273551i
\(551\) −1.10361 1.48240i −0.0470152 0.0631524i
\(552\) −0.0454277 + 7.28646i −0.00193353 + 0.310132i
\(553\) −4.85088 5.14164i −0.206281 0.218645i
\(554\) −1.78336 + 5.95685i −0.0757679 + 0.253082i
\(555\) 16.2896 + 19.6609i 0.691457 + 0.834558i
\(556\) −19.2603 + 2.25121i −0.816821 + 0.0954727i
\(557\) 11.2025 9.40005i 0.474667 0.398293i −0.373827 0.927499i \(-0.621954\pi\)
0.848494 + 0.529206i \(0.177510\pi\)
\(558\) 0.883046 + 19.3055i 0.0373823 + 0.817268i
\(559\) −26.3833 22.1382i −1.11590 0.936348i
\(560\) 1.76175 + 1.15872i 0.0744473 + 0.0489648i
\(561\) −15.4201 + 6.53784i −0.651035 + 0.276028i
\(562\) −10.8840 + 14.6197i −0.459113 + 0.616696i
\(563\) 12.5877 + 6.32179i 0.530509 + 0.266432i 0.693827 0.720142i \(-0.255923\pi\)
−0.163318 + 0.986573i \(0.552220\pi\)
\(564\) −4.36529 1.91537i −0.183812 0.0806516i
\(565\) −0.534149 0.126596i −0.0224718 0.00532592i
\(566\) 8.98069 0.377486
\(567\) −10.4863 1.49158i −0.440384 0.0626406i
\(568\) 11.5901 0.486309
\(569\) 22.1272 + 5.24425i 0.927621 + 0.219850i 0.666542 0.745467i \(-0.267774\pi\)
0.261079 + 0.965318i \(0.415922\pi\)
\(570\) 1.84759 1.35766i 0.0773872 0.0568662i
\(571\) 11.3254 + 5.68783i 0.473953 + 0.238028i 0.669708 0.742625i \(-0.266419\pi\)
−0.195755 + 0.980653i \(0.562716\pi\)
\(572\) 13.9897 18.7915i 0.584940 0.785711i
\(573\) 32.2759 + 24.3428i 1.34835 + 1.01693i
\(574\) 9.86936 + 6.49118i 0.411939 + 0.270936i
\(575\) 5.76764 + 4.83962i 0.240527 + 0.201826i
\(576\) −1.15380 2.76925i −0.0480750 0.115385i
\(577\) 1.95448 1.64000i 0.0813660 0.0682742i −0.601197 0.799100i \(-0.705309\pi\)
0.682564 + 0.730826i \(0.260865\pi\)
\(578\) 9.87500 1.15422i 0.410746 0.0480093i
\(579\) −23.0194 + 3.91113i −0.956656 + 0.162541i
\(580\) 1.28544 4.29367i 0.0533750 0.178285i
\(581\) 0.791716 + 0.839170i 0.0328459 + 0.0348146i
\(582\) −26.4556 + 15.0550i −1.09662 + 0.624050i
\(583\) 20.5089 + 27.5483i 0.849393 + 1.14093i
\(584\) 1.51960 + 8.61805i 0.0628813 + 0.356618i
\(585\) −26.2227 22.5666i −1.08418 0.933013i
\(586\) 0.191022 1.08334i 0.00789104 0.0447523i
\(587\) −2.66520 + 1.33851i −0.110005 + 0.0552464i −0.502951 0.864315i \(-0.667752\pi\)
0.392946 + 0.919562i \(0.371456\pi\)
\(588\) 9.71229 0.504942i 0.400528 0.0208234i
\(589\) 4.72712 + 0.552522i 0.194778 + 0.0227663i
\(590\) 13.8481 9.10802i 0.570116 0.374971i
\(591\) −12.6099 25.5035i −0.518700 1.04907i
\(592\) −2.35962 7.88168i −0.0969798 0.323935i
\(593\) 20.6292 35.7308i 0.847140 1.46729i −0.0366105 0.999330i \(-0.511656\pi\)
0.883750 0.467959i \(-0.155011\pi\)
\(594\) −4.01679 18.4820i −0.164811 0.758325i
\(595\) 2.80096 + 4.85140i 0.114828 + 0.198888i
\(596\) 12.7776 13.5434i 0.523390 0.554761i
\(597\) 0.440248 1.80727i 0.0180182 0.0739666i
\(598\) −1.57437 27.0309i −0.0643808 1.10538i
\(599\) −5.96114 13.8195i −0.243565 0.564648i 0.751953 0.659217i \(-0.229112\pi\)
−0.995518 + 0.0945686i \(0.969853\pi\)
\(600\) −2.96402 0.907543i −0.121006 0.0370503i
\(601\) −1.13397 + 19.4696i −0.0462558 + 0.794181i 0.892808 + 0.450438i \(0.148732\pi\)
−0.939064 + 0.343743i \(0.888305\pi\)
\(602\) −5.91780 + 2.15390i −0.241191 + 0.0877865i
\(603\) −5.22960 3.53376i −0.212966 0.143906i
\(604\) −6.39901 2.32905i −0.260372 0.0947676i
\(605\) −1.59592 + 3.69975i −0.0648832 + 0.150416i
\(606\) −4.60891 12.9128i −0.187224 0.524546i
\(607\) −11.6570 + 2.76275i −0.473141 + 0.112137i −0.460267 0.887781i \(-0.652246\pi\)
−0.0128744 + 0.999917i \(0.504098\pi\)
\(608\) −0.718890 + 0.170380i −0.0291548 + 0.00690982i
\(609\) 1.71406 + 4.80228i 0.0694571 + 0.194598i
\(610\) 8.27036 19.1728i 0.334857 0.776286i
\(611\) 16.6457 + 6.05855i 0.673414 + 0.245103i
\(612\) 0.562581 7.95006i 0.0227410 0.321362i
\(613\) −18.2405 + 6.63900i −0.736727 + 0.268147i −0.683010 0.730409i \(-0.739329\pi\)
−0.0537175 + 0.998556i \(0.517107\pi\)
\(614\) 1.48789 25.5461i 0.0600464 1.03096i
\(615\) 29.7847 + 9.11967i 1.20103 + 0.367741i
\(616\) −1.69669 3.93336i −0.0683614 0.158480i
\(617\) 0.236895 + 4.06733i 0.00953704 + 0.163745i 0.999714 + 0.0239233i \(0.00761576\pi\)
−0.990177 + 0.139821i \(0.955347\pi\)
\(618\) −3.47207 + 14.2532i −0.139667 + 0.573348i
\(619\) 30.8347 32.6828i 1.23935 1.31363i 0.307163 0.951657i \(-0.400620\pi\)
0.932187 0.361977i \(-0.117898\pi\)
\(620\) 5.77108 + 9.99580i 0.231772 + 0.401441i
\(621\) −17.2871 13.3794i −0.693705 0.536897i
\(622\) −11.9122 + 20.6326i −0.477637 + 0.827292i
\(623\) 1.86381 + 6.22557i 0.0746721 + 0.249422i
\(624\) 4.94095 + 9.99310i 0.197796 + 0.400044i
\(625\) 10.7348 7.06036i 0.429390 0.282414i
\(626\) −24.6494 2.88110i −0.985188 0.115152i
\(627\) −4.65149 + 0.241831i −0.185763 + 0.00965780i
\(628\) 21.6676 10.8819i 0.864631 0.434234i
\(629\) 3.79544 21.5250i 0.151334 0.858258i
\(630\) −5.97094 + 2.08931i −0.237888 + 0.0832400i
\(631\) −7.98428 45.2811i −0.317849 1.80261i −0.555780 0.831330i \(-0.687580\pi\)
0.237931 0.971282i \(-0.423531\pi\)
\(632\) 3.58677 + 4.81787i 0.142674 + 0.191644i
\(633\) −34.9335 + 19.8795i −1.38848 + 0.790140i
\(634\) −10.5784 11.2125i −0.420122 0.445304i
\(635\) −2.97219 + 9.92782i −0.117948 + 0.393973i
\(636\) −16.1119 + 2.73750i −0.638877 + 0.108549i
\(637\) −35.8948 + 4.19551i −1.42221 + 0.166232i
\(638\) −6.97490 + 5.85263i −0.276139 + 0.231708i
\(639\) −21.1095 + 27.6289i −0.835078 + 1.09298i
\(640\) −1.37255 1.15170i −0.0542546 0.0455251i
\(641\) 20.1660 + 13.2634i 0.796510 + 0.523873i 0.881318 0.472524i \(-0.156657\pi\)
−0.0848075 + 0.996397i \(0.527028\pi\)
\(642\) −15.2191 11.4784i −0.600652 0.453016i
\(643\) 13.9752 18.7719i 0.551127 0.740292i −0.436050 0.899922i \(-0.643623\pi\)
0.987177 + 0.159631i \(0.0510304\pi\)
\(644\) −4.42439 2.22201i −0.174345 0.0875595i
\(645\) −13.3820 + 9.83347i −0.526916 + 0.387193i
\(646\) −1.90984 0.452640i −0.0751415 0.0178089i
\(647\) 11.2246 0.441285 0.220643 0.975355i \(-0.429185\pi\)
0.220643 + 0.975355i \(0.429185\pi\)
\(648\) 8.70293 + 2.29327i 0.341883 + 0.0900880i
\(649\) −33.6717 −1.32173
\(650\) 11.2084 + 2.65644i 0.439630 + 0.104194i
\(651\) −12.0246 5.27608i −0.471282 0.206786i
\(652\) 10.7949 + 5.42141i 0.422761 + 0.212319i
\(653\) −5.07586 + 6.81807i −0.198634 + 0.266812i −0.890269 0.455436i \(-0.849483\pi\)
0.691635 + 0.722247i \(0.256891\pi\)
\(654\) −4.19177 + 1.77724i −0.163911 + 0.0694955i
\(655\) 27.7254 + 18.2353i 1.08332 + 0.712512i
\(656\) −7.68905 6.45188i −0.300207 0.251904i
\(657\) −23.3118 12.0739i −0.909480 0.471049i
\(658\) 2.48124 2.08201i 0.0967289 0.0811652i
\(659\) −35.8975 + 4.19582i −1.39837 + 0.163446i −0.781640 0.623730i \(-0.785617\pi\)
−0.616729 + 0.787176i \(0.711543\pi\)
\(660\) −7.20680 8.69829i −0.280524 0.338580i
\(661\) −6.73818 + 22.5071i −0.262085 + 0.875425i 0.721103 + 0.692828i \(0.243635\pi\)
−0.983188 + 0.182597i \(0.941550\pi\)
\(662\) −15.5870 16.5212i −0.605805 0.642116i
\(663\) −0.184638 + 29.6154i −0.00717076 + 1.15017i
\(664\) −0.585399 0.786327i −0.0227179 0.0305154i
\(665\) 0.270522 + 1.53421i 0.0104904 + 0.0594940i
\(666\) 23.0864 + 8.73025i 0.894579 + 0.338290i
\(667\) −1.82738 + 10.3636i −0.0707566 + 0.401281i
\(668\) −17.1358 + 8.60594i −0.663006 + 0.332974i
\(669\) 0.429562 + 0.662071i 0.0166078 + 0.0255972i
\(670\) −3.74407 0.437619i −0.144646 0.0169067i
\(671\) −35.4403 + 23.3094i −1.36816 + 0.899851i
\(672\) 2.03418 + 0.131207i 0.0784701 + 0.00506143i
\(673\) 12.6137 + 42.1326i 0.486221 + 1.62409i 0.751368 + 0.659884i \(0.229394\pi\)
−0.265147 + 0.964208i \(0.585420\pi\)
\(674\) 6.10118 10.5676i 0.235009 0.407047i
\(675\) 7.56193 5.41282i 0.291059 0.208340i
\(676\) −14.2125 24.6168i −0.546635 0.946800i
\(677\) −17.6888 + 18.7490i −0.679836 + 0.720584i −0.971790 0.235848i \(-0.924213\pi\)
0.291954 + 0.956432i \(0.405695\pi\)
\(678\) −0.509307 + 0.149023i −0.0195598 + 0.00572319i
\(679\) −1.20258 20.6475i −0.0461509 0.792380i
\(680\) −1.88534 4.37071i −0.0722995 0.167609i
\(681\) 6.46686 6.02541i 0.247811 0.230894i
\(682\) 1.36337 23.4082i 0.0522061 0.896345i
\(683\) 8.21143 2.98872i 0.314202 0.114360i −0.180106 0.983647i \(-0.557644\pi\)
0.494307 + 0.869287i \(0.335422\pi\)
\(684\) 0.903183 2.02404i 0.0345341 0.0773912i
\(685\) 8.04736 + 2.92900i 0.307474 + 0.111911i
\(686\) −5.88029 + 13.6320i −0.224511 + 0.520474i
\(687\) 20.0160 23.5543i 0.763657 0.898653i
\(688\) 5.20688 1.23405i 0.198510 0.0470478i
\(689\) 59.0921 14.0051i 2.25123 0.533551i
\(690\) −12.8429 2.34720i −0.488921 0.0893564i
\(691\) 14.5352 33.6963i 0.552943 1.28187i −0.381043 0.924557i \(-0.624435\pi\)
0.933986 0.357309i \(-0.116306\pi\)
\(692\) 2.52933 + 0.920601i 0.0961507 + 0.0349960i
\(693\) 12.4668 + 3.11935i 0.473573 + 0.118494i
\(694\) 2.70638 0.985041i 0.102733 0.0373917i
\(695\) 2.02020 34.6855i 0.0766306 1.31570i
\(696\) −0.972880 4.22203i −0.0368769 0.160036i
\(697\) −10.5617 24.4849i −0.400054 0.927430i
\(698\) 0.289488 + 4.97031i 0.0109573 + 0.188129i
\(699\) −1.98912 1.90022i −0.0752355 0.0718729i
\(700\) 1.44540 1.53203i 0.0546308 0.0579053i
\(701\) 4.33269 + 7.50444i 0.163643 + 0.283439i 0.936173 0.351540i \(-0.114342\pi\)
−0.772529 + 0.634979i \(0.781009\pi\)
\(702\) −32.8212 6.42238i −1.23876 0.242397i
\(703\) 3.03919 5.26402i 0.114625 0.198536i
\(704\) 1.04393 + 3.48698i 0.0393447 + 0.131420i
\(705\) 4.73787 7.10667i 0.178438 0.267653i
\(706\) 20.9048 13.7493i 0.786764 0.517463i
\(707\) 9.25297 + 1.08152i 0.347994 + 0.0406746i
\(708\) 7.28012 14.2733i 0.273604 0.536425i
\(709\) 13.8097 6.93551i 0.518636 0.260469i −0.170170 0.985415i \(-0.554432\pi\)
0.688806 + 0.724946i \(0.258135\pi\)
\(710\) −3.60603 + 20.4508i −0.135332 + 0.767505i
\(711\) −18.0178 0.224674i −0.675719 0.00842592i
\(712\) −0.958867 5.43801i −0.0359351 0.203798i
\(713\) −16.1833 21.7380i −0.606071 0.814094i
\(714\) 4.67284 + 2.73685i 0.174877 + 0.102424i
\(715\) 28.8051 + 30.5317i 1.07725 + 1.14182i
\(716\) −3.62334 + 12.1028i −0.135411 + 0.452303i
\(717\) −0.215797 + 0.581590i −0.00805908 + 0.0217199i
\(718\) −13.6343 + 1.59363i −0.508829 + 0.0594736i
\(719\) 11.5092 9.65734i 0.429220 0.360158i −0.402438 0.915447i \(-0.631837\pi\)
0.831657 + 0.555289i \(0.187393\pi\)
\(720\) 5.24536 1.17429i 0.195483 0.0437634i
\(721\) −7.63579 6.40719i −0.284372 0.238616i
\(722\) 15.4182 + 10.1407i 0.573807 + 0.377399i
\(723\) −1.98522 + 16.1128i −0.0738310 + 0.599241i
\(724\) 5.33624 7.16782i 0.198320 0.266390i
\(725\) −4.00068 2.00922i −0.148582 0.0746205i
\(726\) 0.428062 + 3.87147i 0.0158869 + 0.143684i
\(727\) 16.5338 + 3.91859i 0.613205 + 0.145332i 0.525471 0.850812i \(-0.323889\pi\)
0.0877345 + 0.996144i \(0.472037\pi\)
\(728\) −7.57463 −0.280734
\(729\) −21.3178 + 16.5696i −0.789548 + 0.613689i
\(730\) −15.6794 −0.580322
\(731\) 13.8328 + 3.27844i 0.511626 + 0.121258i
\(732\) −2.21830 20.0628i −0.0819908 0.741541i
\(733\) −25.3695 12.7410i −0.937043 0.470600i −0.0863505 0.996265i \(-0.527521\pi\)
−0.850692 + 0.525664i \(0.823817\pi\)
\(734\) 16.3881 22.0131i 0.604897 0.812518i
\(735\) −2.13082 + 17.2946i −0.0785965 + 0.637919i
\(736\) 3.51483 + 2.31174i 0.129558 + 0.0852119i
\(737\) 5.86625 + 4.92236i 0.216086 + 0.181318i
\(738\) 29.3847 6.57844i 1.08166 0.242156i
\(739\) 1.59783 1.34074i 0.0587771 0.0493198i −0.612926 0.790140i \(-0.710008\pi\)
0.671703 + 0.740821i \(0.265563\pi\)
\(740\) 14.6415 1.71134i 0.538231 0.0629101i
\(741\) −2.86511 + 7.72169i −0.105252 + 0.283663i
\(742\) 3.18478 10.6379i 0.116917 0.390529i
\(743\) 17.6295 + 18.6862i 0.646764 + 0.685529i 0.964931 0.262505i \(-0.0845487\pi\)
−0.318167 + 0.948035i \(0.603067\pi\)
\(744\) 9.62788 + 5.63898i 0.352975 + 0.206735i
\(745\) 19.9221 + 26.7600i 0.729888 + 0.980409i
\(746\) −2.84227 16.1193i −0.104063 0.590169i
\(747\) 2.94069 + 0.0366691i 0.107594 + 0.00134165i
\(748\) −1.67916 + 9.52300i −0.0613963 + 0.348195i
\(749\) 11.5746 5.81299i 0.422927 0.212402i
\(750\) 9.57383 18.7704i 0.349587 0.685397i
\(751\) −49.3806 5.77176i −1.80192 0.210614i −0.852094 0.523388i \(-0.824668\pi\)
−0.949828 + 0.312774i \(0.898742\pi\)
\(752\) −2.29946 + 1.51238i −0.0838526 + 0.0551507i
\(753\) −16.1607 + 24.2406i −0.588929 + 0.883377i
\(754\) 4.61754 + 15.4237i 0.168161 + 0.561697i
\(755\) 6.10056 10.5665i 0.222022 0.384554i
\(756\) −4.01771 + 4.61019i −0.146123 + 0.167671i
\(757\) −3.58950 6.21720i −0.130463 0.225968i 0.793392 0.608711i \(-0.208313\pi\)
−0.923855 + 0.382743i \(0.874980\pi\)
\(758\) −12.7118 + 13.4737i −0.461712 + 0.489387i
\(759\) 19.1779 + 18.3207i 0.696113 + 0.665000i
\(760\) −0.0769686 1.32150i −0.00279194 0.0479358i
\(761\) −12.0807 28.0062i −0.437924 1.01522i −0.984110 0.177559i \(-0.943180\pi\)
0.546186 0.837664i \(-0.316079\pi\)
\(762\) 2.24949 + 9.76217i 0.0814904 + 0.353646i
\(763\) 0.179877 3.08836i 0.00651197 0.111806i
\(764\) 21.9327 7.98284i 0.793497 0.288809i
\(765\) 13.8529 + 3.46619i 0.500854 + 0.125320i
\(766\) 25.4954 + 9.27955i 0.921185 + 0.335284i
\(767\) −23.5825 + 54.6705i −0.851516 + 1.97404i
\(768\) −1.70383 0.311396i −0.0614816 0.0112365i
\(769\) 17.6258 4.17739i 0.635602 0.150641i 0.0998320 0.995004i \(-0.468169\pi\)
0.535770 + 0.844364i \(0.320021\pi\)
\(770\) 7.46835 1.77003i 0.269140 0.0637875i
\(771\) −21.1687 + 24.9108i −0.762372 + 0.897140i
\(772\) −5.33945 + 12.3782i −0.192171 + 0.445503i
\(773\) −42.8857 15.6091i −1.54249 0.561421i −0.575850 0.817555i \(-0.695329\pi\)
−0.966641 + 0.256135i \(0.917551\pi\)
\(774\) −6.54170 + 14.6600i −0.235137 + 0.526943i
\(775\) 10.8338 3.94317i 0.389160 0.141643i
\(776\) −1.02184 + 17.5444i −0.0366821 + 0.629807i
\(777\) −12.2700 + 11.4324i −0.440184 + 0.410135i
\(778\) −2.33062 5.40298i −0.0835567 0.193706i
\(779\) −0.431181 7.40308i −0.0154486 0.265243i
\(780\) −19.1702 + 5.60920i −0.686404 + 0.200842i
\(781\) 28.9502 30.6854i 1.03592 1.09801i
\(782\) 5.58815 + 9.67896i 0.199832 + 0.346119i
\(783\) 11.8366 + 5.37056i 0.423006 + 0.191928i
\(784\) 2.80748 4.86270i 0.100267 0.173668i
\(785\) 12.4597 + 41.6184i 0.444707 + 1.48542i
\(786\) 32.0128 + 2.06487i 1.14186 + 0.0736515i
\(787\) 28.4320 18.7000i 1.01349 0.666583i 0.0698503 0.997557i \(-0.477748\pi\)
0.943640 + 0.330975i \(0.107377\pi\)
\(788\) −16.3149 1.90694i −0.581194 0.0679319i
\(789\) 0.0819783 + 0.126351i 0.00291851 + 0.00449821i
\(790\) −9.61713 + 4.82991i −0.342162 + 0.171840i
\(791\) 0.0626119 0.355090i 0.00222622 0.0126255i
\(792\) −10.2138 3.86240i −0.362931 0.137244i
\(793\) 13.0248 + 73.8672i 0.462523 + 2.62310i
\(794\) 13.9827 + 18.7820i 0.496227 + 0.666548i
\(795\) 0.182555 29.2813i 0.00647457 1.03850i
\(796\) −0.736982 0.781155i −0.0261216 0.0276873i
\(797\) 7.05051 23.5504i 0.249742 0.834196i −0.737552 0.675291i \(-0.764018\pi\)
0.987294 0.158906i \(-0.0507966\pi\)
\(798\) 0.960816 + 1.15966i 0.0340125 + 0.0410516i
\(799\) −7.26228 + 0.848838i −0.256921 + 0.0300297i
\(800\) −1.37099 + 1.15040i −0.0484717 + 0.0406726i
\(801\) 14.7098 + 7.61867i 0.519745 + 0.269193i
\(802\) 2.84262 + 2.38524i 0.100376 + 0.0842257i
\(803\) 26.6125 + 17.5033i 0.939136 + 0.617680i
\(804\) −3.35491 + 1.42243i −0.118319 + 0.0501651i
\(805\) 5.29733 7.11555i 0.186706 0.250790i
\(806\) −37.0514 18.6079i −1.30508 0.655436i
\(807\) −44.3479 19.4586i −1.56112 0.684976i
\(808\) −7.70248 1.82552i −0.270972 0.0642216i
\(809\) 18.6098 0.654287 0.327144 0.944975i \(-0.393914\pi\)
0.327144 + 0.944975i \(0.393914\pi\)
\(810\) −6.75424 + 14.6429i −0.237320 + 0.514499i
\(811\) −0.841099 −0.0295350 −0.0147675 0.999891i \(-0.504701\pi\)
−0.0147675 + 0.999891i \(0.504701\pi\)
\(812\) 2.86456 + 0.678914i 0.100526 + 0.0238252i
\(813\) −24.1887 + 17.7745i −0.848335 + 0.623380i
\(814\) −26.7612 13.4400i −0.937979 0.471071i
\(815\) −12.9248 + 17.3610i −0.452735 + 0.608128i
\(816\) −3.67373 2.77075i −0.128606 0.0969957i
\(817\) 3.30304 + 2.17244i 0.115559 + 0.0760042i
\(818\) 7.91934 + 6.64511i 0.276893 + 0.232341i
\(819\) 13.7960 18.0567i 0.482071 0.630954i
\(820\) 13.7767 11.5600i 0.481104 0.403694i
\(821\) 8.91103 1.04155i 0.310997 0.0363503i 0.0408371 0.999166i \(-0.486998\pi\)
0.270160 + 0.962815i \(0.412923\pi\)
\(822\) 8.16160 1.38670i 0.284669 0.0483668i
\(823\) −13.4350 + 44.8760i −0.468314 + 1.56428i 0.319018 + 0.947749i \(0.396647\pi\)
−0.787332 + 0.616529i \(0.788538\pi\)
\(824\) 5.81229 + 6.16066i 0.202481 + 0.214617i
\(825\) −9.80644 + 5.58053i −0.341417 + 0.194289i
\(826\) 6.50124 + 8.73268i 0.226207 + 0.303849i
\(827\) −0.976710 5.53920i −0.0339635 0.192617i 0.963105 0.269124i \(-0.0867342\pi\)
−0.997069 + 0.0765074i \(0.975623\pi\)
\(828\) −11.9125 + 4.16835i −0.413989 + 0.144860i
\(829\) −1.17419 + 6.65918i −0.0407814 + 0.231283i −0.998385 0.0568054i \(-0.981909\pi\)
0.957604 + 0.288088i \(0.0930196\pi\)
\(830\) 1.56962 0.788292i 0.0544823 0.0273620i
\(831\) −10.7555 + 0.559178i −0.373104 + 0.0193977i
\(832\) 6.39271 + 0.747200i 0.221627 + 0.0259045i
\(833\) 12.4630 8.19702i 0.431816 0.284010i
\(834\) −14.8864 30.1078i −0.515474 1.04255i
\(835\) −9.85379 32.9140i −0.341005 1.13903i
\(836\) −1.34458 + 2.32889i −0.0465034 + 0.0805463i
\(837\) −30.9781 + 12.6809i −1.07076 + 0.438315i
\(838\) −6.92924 12.0018i −0.239367 0.414595i
\(839\) −6.12368 + 6.49072i −0.211413 + 0.224084i −0.824399 0.566009i \(-0.808487\pi\)
0.612986 + 0.790094i \(0.289968\pi\)
\(840\) −0.864412 + 3.54851i −0.0298251 + 0.122435i
\(841\) 1.32237 + 22.7042i 0.0455989 + 0.782902i
\(842\) 3.45109 + 8.00051i 0.118932 + 0.275716i
\(843\) −30.1856 9.24242i −1.03965 0.318326i
\(844\) −1.34931 + 23.1667i −0.0464450 + 0.797430i
\(845\) 47.8586 17.4191i 1.64638 0.599235i
\(846\) 0.582823 8.23611i 0.0200379 0.283163i
\(847\) −2.48697 0.905182i −0.0854532 0.0311024i
\(848\) −3.73721 + 8.66383i −0.128336 + 0.297517i
\(849\) 5.22889 + 14.6498i 0.179455 + 0.502780i
\(850\) −4.62643 + 1.09649i −0.158685 + 0.0376091i
\(851\) −33.6787 + 7.98199i −1.15449 + 0.273619i
\(852\) 6.74818 + 18.9064i 0.231189 + 0.647722i
\(853\) −4.25012 + 9.85289i −0.145521 + 0.337356i −0.975351 0.220661i \(-0.929179\pi\)
0.829829 + 0.558017i \(0.188438\pi\)
\(854\) 12.8880 + 4.69084i 0.441017 + 0.160517i
\(855\) 3.29044 + 2.22342i 0.112531 + 0.0760393i
\(856\) −10.3420 + 3.76417i −0.353481 + 0.128657i
\(857\) 0.209079 3.58975i 0.00714201 0.122624i −0.992853 0.119347i \(-0.961920\pi\)
0.999995 0.00327672i \(-0.00104301\pi\)
\(858\) 38.7991 + 11.8798i 1.32458 + 0.405568i
\(859\) 2.50399 + 5.80491i 0.0854351 + 0.198061i 0.955578 0.294739i \(-0.0952327\pi\)
−0.870143 + 0.492800i \(0.835973\pi\)
\(860\) 0.557479 + 9.57154i 0.0190099 + 0.326387i
\(861\) −4.84247 + 19.8789i −0.165031 + 0.677470i
\(862\) 14.7975 15.6844i 0.504004 0.534213i
\(863\) −7.18055 12.4371i −0.244429 0.423363i 0.717542 0.696515i \(-0.245267\pi\)
−0.961971 + 0.273152i \(0.911934\pi\)
\(864\) 3.84557 3.49451i 0.130829 0.118886i
\(865\) −2.41136 + 4.17661i −0.0819889 + 0.142009i
\(866\) −1.76111 5.88253i −0.0598451 0.199897i
\(867\) 7.63243 + 15.4366i 0.259211 + 0.524255i
\(868\) −6.33409 + 4.16600i −0.214993 + 0.141403i
\(869\) 21.7148 + 2.53810i 0.736624 + 0.0860990i
\(870\) 7.75252 0.403053i 0.262835 0.0136648i
\(871\) 12.1006 6.07717i 0.410014 0.205917i
\(872\) −0.456461 + 2.58872i −0.0154577 + 0.0876651i
\(873\) −39.9620 34.3902i −1.35251 1.16393i
\(874\) 0.539714 + 3.06087i 0.0182561 + 0.103536i
\(875\) 8.54955 + 11.4840i 0.289027 + 0.388231i
\(876\) −13.1735 + 7.49660i −0.445091 + 0.253287i
\(877\) 1.78773 + 1.89488i 0.0603674 + 0.0639857i 0.756853 0.653585i \(-0.226736\pi\)
−0.696486 + 0.717570i \(0.745254\pi\)
\(878\) −3.54798 + 11.8511i −0.119739 + 0.399955i
\(879\) 1.87843 0.319155i 0.0633577 0.0107648i
\(880\) −6.47761 + 0.757124i −0.218360 + 0.0255227i
\(881\) −16.5522 + 13.8889i −0.557656 + 0.467929i −0.877524 0.479533i \(-0.840806\pi\)
0.319868 + 0.947462i \(0.396362\pi\)
\(882\) 6.47855 + 15.5492i 0.218144 + 0.523570i
\(883\) −26.7029 22.4064i −0.898625 0.754036i 0.0712965 0.997455i \(-0.477286\pi\)
−0.969921 + 0.243420i \(0.921731\pi\)
\(884\) 14.2858 + 9.39594i 0.480484 + 0.316020i
\(885\) 22.9204 + 17.2867i 0.770461 + 0.581087i
\(886\) 9.66117 12.9772i 0.324574 0.435978i
\(887\) −8.39071 4.21398i −0.281733 0.141491i 0.302322 0.953206i \(-0.402238\pi\)
−0.584054 + 0.811714i \(0.698535\pi\)
\(888\) 11.4832 8.43815i 0.385350 0.283166i
\(889\) −6.62343 1.56978i −0.222143 0.0526488i
\(890\) 9.89376 0.331640
\(891\) 27.8101 17.3133i 0.931674 0.580018i
\(892\) 0.455654 0.0152564
\(893\) −1.97855 0.468926i −0.0662098 0.0156920i
\(894\) 29.5324 + 12.9580i 0.987712 + 0.433381i
\(895\) −20.2282 10.1590i −0.676155 0.339578i
\(896\) 0.702780 0.943998i 0.0234782 0.0315368i
\(897\) 43.1777 18.3066i 1.44166 0.611240i
\(898\) −11.0790 7.28675i −0.369710 0.243162i
\(899\) 12.3442 + 10.3580i 0.411702 + 0.345459i
\(900\) −0.245329 5.36349i −0.00817763 0.178783i
\(901\) −19.2023 + 16.1126i −0.639721 + 0.536789i
\(902\) −36.2878 + 4.24144i −1.20825 + 0.141224i
\(903\) −6.95913 8.39937i −0.231585 0.279513i
\(904\) −0.0878700 + 0.293506i −0.00292251 + 0.00976187i
\(905\) 10.9874 + 11.6460i 0.365234 + 0.387126i
\(906\) 0.0735332 11.7945i 0.00244298 0.391845i
\(907\) 24.3257 + 32.6751i 0.807722 + 1.08496i 0.994723 + 0.102599i \(0.0327158\pi\)
−0.187001 + 0.982360i \(0.559877\pi\)
\(908\) −0.886150 5.02560i −0.0294079 0.166781i
\(909\) 18.3806 15.0366i 0.609646 0.498733i
\(910\) 2.35670 13.3655i 0.0781239 0.443063i
\(911\) 33.1845 16.6659i 1.09945 0.552165i 0.195891 0.980626i \(-0.437240\pi\)
0.903560 + 0.428461i \(0.140944\pi\)
\(912\) −0.696498 1.07349i −0.0230634 0.0355469i
\(913\) −3.54409 0.414244i −0.117292 0.0137095i
\(914\) −1.48263 + 0.975140i −0.0490410 + 0.0322548i
\(915\) 36.0911 + 2.32793i 1.19314 + 0.0769589i
\(916\) −5.11831 17.0963i −0.169114 0.564879i
\(917\) −10.8985 + 18.8767i −0.359899 + 0.623363i
\(918\) 13.2961 3.71111i 0.438838 0.122485i
\(919\) −15.7608 27.2985i −0.519900 0.900494i −0.999732 0.0231334i \(-0.992636\pi\)
0.479832 0.877360i \(-0.340698\pi\)
\(920\) −5.17266 + 5.48270i −0.170538 + 0.180759i
\(921\) 42.5386 12.4468i 1.40169 0.410135i
\(922\) −0.00309329 0.0531098i −0.000101872 0.00174908i
\(923\) −29.5461 68.4956i −0.972522 2.25456i
\(924\) 5.42844 5.05788i 0.178583 0.166392i
\(925\) 0.856148 14.6995i 0.0281500 0.483316i
\(926\) −9.79344 + 3.56452i −0.321832 + 0.117137i
\(927\) −25.2722 + 2.63493i −0.830049 + 0.0865423i
\(928\) −2.35061 0.855553i −0.0771626 0.0280849i
\(929\) 19.1028 44.2852i 0.626742 1.45295i −0.248192 0.968711i \(-0.579837\pi\)
0.874935 0.484241i \(-0.160904\pi\)
\(930\) −12.9456 + 15.2340i −0.424502 + 0.499544i
\(931\) 4.03654 0.956678i 0.132292 0.0313539i
\(932\) −1.54542 + 0.366271i −0.0506219 + 0.0119976i
\(933\) −40.5928 7.41885i −1.32895 0.242882i
\(934\) −11.9323 + 27.6623i −0.390438 + 0.905137i
\(935\) −16.2810 5.92580i −0.532446 0.193794i
\(936\) −13.4245 + 13.8783i −0.438794 + 0.453627i
\(937\) −28.3897 + 10.3330i −0.927450 + 0.337564i −0.761198 0.648519i \(-0.775389\pi\)
−0.166252 + 0.986083i \(0.553166\pi\)
\(938\) 0.143966 2.47179i 0.00470064 0.0807069i
\(939\) −9.65199 41.8870i −0.314981 1.36693i
\(940\) −1.95317 4.52797i −0.0637055 0.147686i
\(941\) 0.0770951 + 1.32367i 0.00251323 + 0.0431504i 0.999332 0.0365560i \(-0.0116387\pi\)
−0.996818 + 0.0797065i \(0.974602\pi\)
\(942\) 30.3668 + 29.0096i 0.989404 + 0.945182i
\(943\) −28.9774 + 30.7143i −0.943635 + 1.00019i
\(944\) −4.62537 8.01138i −0.150543 0.260748i
\(945\) −6.88471 8.52367i −0.223959 0.277275i
\(946\) 9.73874 16.8680i 0.316634 0.548426i
\(947\) −5.81151 19.4118i −0.188849 0.630798i −0.999006 0.0445853i \(-0.985803\pi\)
0.810157 0.586213i \(-0.199382\pi\)
\(948\) −5.77083 + 8.65608i −0.187428 + 0.281137i
\(949\) 47.0575 30.9502i 1.52755 1.00469i
\(950\) −1.31330 0.153502i −0.0426089 0.00498027i
\(951\) 12.1313 23.7844i 0.393383 0.771262i
\(952\) 2.79398 1.40319i 0.0905533 0.0454776i
\(953\) −1.69939 + 9.63772i −0.0550486 + 0.312196i −0.999882 0.0153547i \(-0.995112\pi\)
0.944833 + 0.327551i \(0.106223\pi\)
\(954\) −13.8465 24.6887i −0.448297 0.799327i
\(955\) 7.26188 + 41.1842i 0.234989 + 1.33269i
\(956\) 0.213872 + 0.287281i 0.00691713 + 0.00929132i
\(957\) −13.6082 7.97023i −0.439891 0.257641i
\(958\) 2.05578 + 2.17900i 0.0664192 + 0.0704003i
\(959\) −1.61328 + 5.38872i −0.0520954 + 0.174011i
\(960\) 1.07958 2.90954i 0.0348431 0.0939050i
\(961\) −10.4271 + 1.21875i −0.336358 + 0.0393147i
\(962\) −40.5642 + 34.0374i −1.30784 + 1.09741i
\(963\) 9.86305 31.5095i 0.317832 1.01538i
\(964\) 7.18018 + 6.02489i 0.231258 + 0.194049i
\(965\) −20.1803 13.2728i −0.649626 0.427266i
\(966\) 1.04863 8.51105i 0.0337390 0.273839i
\(967\) 21.9660 29.5055i 0.706380 0.948833i −0.293595 0.955930i \(-0.594852\pi\)
0.999975 + 0.00709668i \(0.00225896\pi\)
\(968\) 2.00962 + 1.00927i 0.0645915 + 0.0324391i
\(969\) −0.373607 3.37898i −0.0120020 0.108548i
\(970\) −30.6394 7.26166i −0.983770 0.233158i
\(971\) 43.6991 1.40237 0.701185 0.712979i \(-0.252655\pi\)
0.701185 + 0.712979i \(0.252655\pi\)
\(972\) 1.32627 + 15.5319i 0.0425400 + 0.498187i
\(973\) 22.8213 0.731618
\(974\) 5.03661 + 1.19370i 0.161383 + 0.0382485i
\(975\) 2.19262 + 19.8305i 0.0702200 + 0.635083i
\(976\) −10.4142 5.23023i −0.333352 0.167416i
\(977\) 4.79772 6.44446i 0.153493 0.206176i −0.718725 0.695295i \(-0.755274\pi\)
0.872218 + 0.489118i \(0.162681\pi\)
\(978\) −2.55851 + 20.7658i −0.0818120 + 0.664017i
\(979\) −16.7926 11.0446i −0.536693 0.352988i
\(980\) 7.70680 + 6.46677i 0.246185 + 0.206574i
\(981\) −5.33974 5.80307i −0.170485 0.185278i
\(982\) −30.6014 + 25.6776i −0.976531 + 0.819406i
\(983\) −24.8115 + 2.90005i −0.791364 + 0.0924972i −0.502165 0.864772i \(-0.667463\pi\)
−0.289199 + 0.957269i \(0.593389\pi\)
\(984\) 6.04782 16.2993i 0.192797 0.519604i
\(985\) 8.44088 28.1945i 0.268949 0.898352i
\(986\) −4.56043 4.83378i −0.145234 0.153939i
\(987\) 4.84097 + 2.83532i 0.154090 + 0.0902493i
\(988\) 2.83956 + 3.81419i 0.0903383 + 0.121345i
\(989\) −3.90912 22.1697i −0.124303 0.704956i
\(990\) 9.99307 16.8206i 0.317601 0.534594i
\(991\) −5.49412 + 31.1587i −0.174526 + 0.989788i 0.764163 + 0.645024i \(0.223152\pi\)
−0.938689 + 0.344765i \(0.887959\pi\)
\(992\) 5.75669 2.89112i 0.182775 0.0917932i
\(993\) 17.8751 35.0457i 0.567248 1.11214i
\(994\) −13.5478 1.58351i −0.429711 0.0502260i
\(995\) 1.60766 1.05737i 0.0509661 0.0335209i
\(996\) 0.941860 1.41277i 0.0298440 0.0447652i
\(997\) 1.53861 + 5.13931i 0.0487282 + 0.162763i 0.978891 0.204385i \(-0.0655194\pi\)
−0.930162 + 0.367148i \(0.880334\pi\)
\(998\) 8.35604 14.4731i 0.264506 0.458138i
\(999\) −0.799529 + 42.7429i −0.0252960 + 1.35232i
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 162.2.g.b.97.3 90
3.2 odd 2 486.2.g.b.451.4 90
81.5 odd 54 486.2.g.b.361.4 90
81.76 even 27 inner 162.2.g.b.157.3 yes 90
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.2.g.b.97.3 90 1.1 even 1 trivial
162.2.g.b.157.3 yes 90 81.76 even 27 inner
486.2.g.b.361.4 90 81.5 odd 54
486.2.g.b.451.4 90 3.2 odd 2