Properties

Label 441.2.z.a.142.21
Level $441$
Weight $2$
Character 441.142
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
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] = [441,2,Mod(4,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([14, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.z (of order \(21\), degree \(12\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 142.21
Character \(\chi\) \(=\) 441.142
Dual form 441.2.z.a.382.21

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.342957 + 0.873839i) q^{2} +(-1.22183 + 1.22765i) q^{3} +(0.820128 + 0.760968i) q^{4} +(-2.38974 + 1.15084i) q^{5} +(-0.653732 - 1.48872i) q^{6} +(0.937668 - 2.47402i) q^{7} +(-2.63776 + 1.27028i) q^{8} +(-0.0142463 - 2.99997i) q^{9} +O(q^{10})\) \(q+(-0.342957 + 0.873839i) q^{2} +(-1.22183 + 1.22765i) q^{3} +(0.820128 + 0.760968i) q^{4} +(-2.38974 + 1.15084i) q^{5} +(-0.653732 - 1.48872i) q^{6} +(0.937668 - 2.47402i) q^{7} +(-2.63776 + 1.27028i) q^{8} +(-0.0142463 - 2.99997i) q^{9} +(-0.186070 - 2.48294i) q^{10} +(-3.42545 - 4.29538i) q^{11} +(-1.93626 + 0.0770541i) q^{12} +(-1.37379 + 3.50035i) q^{13} +(1.84032 + 1.66785i) q^{14} +(1.50704 - 4.33990i) q^{15} +(-0.0381680 - 0.509317i) q^{16} +(-2.12354 + 1.97035i) q^{17} +(2.62637 + 1.01641i) q^{18} +(1.07915 - 1.86914i) q^{19} +(-2.83564 - 0.874680i) q^{20} +(1.89156 + 4.17397i) q^{21} +(4.92825 - 1.52016i) q^{22} +(1.11865 - 4.90111i) q^{23} +(1.66345 - 4.79032i) q^{24} +(1.26898 - 1.59125i) q^{25} +(-2.58759 - 2.40094i) q^{26} +(3.70031 + 3.64797i) q^{27} +(2.65166 - 1.31548i) q^{28} +(5.56428 + 1.71635i) q^{29} +(3.27552 + 2.80530i) q^{30} +(0.882100 - 1.52784i) q^{31} +(-5.13711 - 1.58459i) q^{32} +(9.45855 + 1.04299i) q^{33} +(-0.993491 - 2.53137i) q^{34} +(0.606415 + 6.99137i) q^{35} +(2.27119 - 2.47120i) q^{36} +(-9.91167 - 3.05734i) q^{37} +(1.26323 + 1.58404i) q^{38} +(-2.61867 - 5.96337i) q^{39} +(4.84168 - 6.07128i) q^{40} +(-3.64491 - 2.48505i) q^{41} +(-4.29610 + 0.221426i) q^{42} +(-8.40136 + 5.72795i) q^{43} +(0.459337 - 6.12942i) q^{44} +(3.48652 + 7.15274i) q^{45} +(3.89913 + 2.65838i) q^{46} +(0.573497 - 1.46125i) q^{47} +(0.671897 + 0.575443i) q^{48} +(-5.24156 - 4.63962i) q^{49} +(0.955291 + 1.65461i) q^{50} +(0.175704 - 5.01440i) q^{51} +(-3.79034 + 1.82533i) q^{52} +(3.11830 - 0.961867i) q^{53} +(-4.45678 + 1.98238i) q^{54} +(13.1292 + 6.32270i) q^{55} +(0.669353 + 7.71699i) q^{56} +(0.976109 + 3.60859i) q^{57} +(-3.40812 + 4.27365i) q^{58} +(-2.90904 + 1.98335i) q^{59} +(4.53849 - 2.41246i) q^{60} +(-3.65212 + 3.38867i) q^{61} +(1.03257 + 1.29480i) q^{62} +(-7.43534 - 2.77773i) q^{63} +(3.78337 - 4.74419i) q^{64} +(-0.745345 - 9.94593i) q^{65} +(-4.15527 + 7.90755i) q^{66} +(3.22362 - 5.58347i) q^{67} -3.24095 q^{68} +(4.65004 + 7.36164i) q^{69} +(-6.31731 - 1.86783i) q^{70} +(-2.06456 + 9.04545i) q^{71} +(3.84838 + 7.89511i) q^{72} +(-0.706030 - 0.106417i) q^{73} +(6.07090 - 7.61267i) q^{74} +(0.403016 + 3.50210i) q^{75} +(2.30740 - 0.711737i) q^{76} +(-13.8388 + 4.44700i) q^{77} +(6.10912 - 0.243114i) q^{78} +(-5.41351 - 9.37648i) q^{79} +(0.677353 + 1.17321i) q^{80} +(-8.99959 + 0.0854767i) q^{81} +(3.42158 - 2.33280i) q^{82} +(6.20131 + 15.8007i) q^{83} +(-1.62494 + 4.86260i) q^{84} +(2.80714 - 7.15248i) q^{85} +(-2.12401 - 9.30588i) q^{86} +(-8.90570 + 4.73389i) q^{87} +(14.4919 + 6.97892i) q^{88} +(-2.89643 - 7.37998i) q^{89} +(-7.44607 + 0.593577i) q^{90} +(7.37179 + 6.68094i) q^{91} +(4.64702 - 3.16828i) q^{92} +(0.797876 + 2.94968i) q^{93} +(1.08021 + 1.00229i) q^{94} +(-0.427807 + 5.70868i) q^{95} +(8.22201 - 4.37046i) q^{96} +(0.441981 - 0.765534i) q^{97} +(5.85191 - 2.98909i) q^{98} +(-12.8372 + 10.3374i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9} - 22 q^{10} - 5 q^{11} + 2 q^{12} - 4 q^{13} + 52 q^{14} - 4 q^{15} + 38 q^{16} - 37 q^{17} - 16 q^{18} - 14 q^{19} - 11 q^{20} - 6 q^{21} - q^{22} - 20 q^{23} - 26 q^{24} - 97 q^{25} - 44 q^{26} + 14 q^{27} - 22 q^{28} - 53 q^{29} - 9 q^{30} + 10 q^{31} - 10 q^{32} + 2 q^{33} - 7 q^{34} - 32 q^{35} - 22 q^{36} - 39 q^{37} + 59 q^{38} - 26 q^{39} - 19 q^{40} - 17 q^{41} - 83 q^{42} - q^{43} - 31 q^{44} + 81 q^{45} + 56 q^{46} + 50 q^{47} - 23 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} - 9 q^{52} + 50 q^{53} + 48 q^{54} + 20 q^{55} - 239 q^{56} + 33 q^{57} + 17 q^{58} - 37 q^{59} - 152 q^{60} - 105 q^{61} - 30 q^{62} + 6 q^{63} - 88 q^{64} - 5 q^{65} - 99 q^{66} + 13 q^{67} - 290 q^{68} + 64 q^{69} + 17 q^{70} - 19 q^{71} + 11 q^{72} - 40 q^{73} - 57 q^{74} + 69 q^{75} - 41 q^{76} + 19 q^{77} + 81 q^{78} + 13 q^{79} + 163 q^{80} - 179 q^{81} - 28 q^{82} + 73 q^{83} - 341 q^{84} - 10 q^{85} + 15 q^{86} + 13 q^{87} - 13 q^{88} - 104 q^{89} + 171 q^{90} - 49 q^{91} - 91 q^{92} - 275 q^{93} - 4 q^{94} - 29 q^{95} + 231 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.342957 + 0.873839i −0.242507 + 0.617897i −0.999363 0.0356839i \(-0.988639\pi\)
0.756856 + 0.653581i \(0.226734\pi\)
\(3\) −1.22183 + 1.22765i −0.705426 + 0.708784i
\(4\) 0.820128 + 0.760968i 0.410064 + 0.380484i
\(5\) −2.38974 + 1.15084i −1.06872 + 0.514670i −0.883695 0.468063i \(-0.844952\pi\)
−0.185029 + 0.982733i \(0.559238\pi\)
\(6\) −0.653732 1.48872i −0.266885 0.607766i
\(7\) 0.937668 2.47402i 0.354405 0.935092i
\(8\) −2.63776 + 1.27028i −0.932591 + 0.449112i
\(9\) −0.0142463 2.99997i −0.00474876 0.999989i
\(10\) −0.186070 2.48294i −0.0588406 0.785173i
\(11\) −3.42545 4.29538i −1.03281 1.29511i −0.954511 0.298176i \(-0.903622\pi\)
−0.0783016 0.996930i \(-0.524950\pi\)
\(12\) −1.93626 + 0.0770541i −0.558951 + 0.0222436i
\(13\) −1.37379 + 3.50035i −0.381020 + 0.970823i 0.603783 + 0.797149i \(0.293659\pi\)
−0.984803 + 0.173674i \(0.944436\pi\)
\(14\) 1.84032 + 1.66785i 0.491845 + 0.445752i
\(15\) 1.50704 4.33990i 0.389116 1.12056i
\(16\) −0.0381680 0.509317i −0.00954200 0.127329i
\(17\) −2.12354 + 1.97035i −0.515033 + 0.477881i −0.894339 0.447391i \(-0.852353\pi\)
0.379306 + 0.925271i \(0.376163\pi\)
\(18\) 2.62637 + 1.01641i 0.619042 + 0.239570i
\(19\) 1.07915 1.86914i 0.247574 0.428810i −0.715278 0.698840i \(-0.753700\pi\)
0.962852 + 0.270029i \(0.0870334\pi\)
\(20\) −2.83564 0.874680i −0.634069 0.195584i
\(21\) 1.89156 + 4.17397i 0.412771 + 0.910835i
\(22\) 4.92825 1.52016i 1.05071 0.324100i
\(23\) 1.11865 4.90111i 0.233254 1.02195i −0.713667 0.700485i \(-0.752967\pi\)
0.946921 0.321467i \(-0.104176\pi\)
\(24\) 1.66345 4.79032i 0.339550 0.977820i
\(25\) 1.26898 1.59125i 0.253796 0.318250i
\(26\) −2.58759 2.40094i −0.507469 0.470862i
\(27\) 3.70031 + 3.64797i 0.712126 + 0.702052i
\(28\) 2.65166 1.31548i 0.501116 0.248602i
\(29\) 5.56428 + 1.71635i 1.03326 + 0.318719i 0.764592 0.644514i \(-0.222940\pi\)
0.268668 + 0.963233i \(0.413417\pi\)
\(30\) 3.27552 + 2.80530i 0.598026 + 0.512176i
\(31\) 0.882100 1.52784i 0.158430 0.274409i −0.775873 0.630889i \(-0.782690\pi\)
0.934303 + 0.356481i \(0.116023\pi\)
\(32\) −5.13711 1.58459i −0.908121 0.280118i
\(33\) 9.45855 + 1.04299i 1.64652 + 0.181560i
\(34\) −0.993491 2.53137i −0.170382 0.434127i
\(35\) 0.606415 + 6.99137i 0.102503 + 1.18176i
\(36\) 2.27119 2.47120i 0.378532 0.411866i
\(37\) −9.91167 3.05734i −1.62947 0.502624i −0.660712 0.750640i \(-0.729746\pi\)
−0.968756 + 0.248015i \(0.920222\pi\)
\(38\) 1.26323 + 1.58404i 0.204922 + 0.256965i
\(39\) −2.61867 5.96337i −0.419322 0.954904i
\(40\) 4.84168 6.07128i 0.765537 0.959954i
\(41\) −3.64491 2.48505i −0.569239 0.388100i 0.244223 0.969719i \(-0.421467\pi\)
−0.813461 + 0.581619i \(0.802420\pi\)
\(42\) −4.29610 + 0.221426i −0.662902 + 0.0341667i
\(43\) −8.40136 + 5.72795i −1.28120 + 0.873505i −0.996374 0.0850759i \(-0.972887\pi\)
−0.284822 + 0.958581i \(0.591934\pi\)
\(44\) 0.459337 6.12942i 0.0692476 0.924045i
\(45\) 3.48652 + 7.15274i 0.519740 + 1.06627i
\(46\) 3.89913 + 2.65838i 0.574896 + 0.391957i
\(47\) 0.573497 1.46125i 0.0836531 0.213145i −0.882927 0.469511i \(-0.844430\pi\)
0.966580 + 0.256366i \(0.0825254\pi\)
\(48\) 0.671897 + 0.575443i 0.0969800 + 0.0830581i
\(49\) −5.24156 4.63962i −0.748794 0.662803i
\(50\) 0.955291 + 1.65461i 0.135099 + 0.233998i
\(51\) 0.175704 5.01440i 0.0246035 0.702157i
\(52\) −3.79034 + 1.82533i −0.525625 + 0.253128i
\(53\) 3.11830 0.961867i 0.428331 0.132123i −0.0730914 0.997325i \(-0.523286\pi\)
0.501422 + 0.865203i \(0.332810\pi\)
\(54\) −4.45678 + 1.98238i −0.606492 + 0.269768i
\(55\) 13.1292 + 6.32270i 1.77034 + 0.852553i
\(56\) 0.669353 + 7.71699i 0.0894460 + 1.03123i
\(57\) 0.976109 + 3.60859i 0.129289 + 0.477970i
\(58\) −3.40812 + 4.27365i −0.447508 + 0.561158i
\(59\) −2.90904 + 1.98335i −0.378725 + 0.258210i −0.737689 0.675141i \(-0.764083\pi\)
0.358963 + 0.933352i \(0.383130\pi\)
\(60\) 4.53849 2.41246i 0.585916 0.311448i
\(61\) −3.65212 + 3.38867i −0.467606 + 0.433875i −0.878453 0.477829i \(-0.841424\pi\)
0.410846 + 0.911705i \(0.365233\pi\)
\(62\) 1.03257 + 1.29480i 0.131136 + 0.164439i
\(63\) −7.43534 2.77773i −0.936764 0.349961i
\(64\) 3.78337 4.74419i 0.472921 0.593024i
\(65\) −0.745345 9.94593i −0.0924486 1.23364i
\(66\) −4.15527 + 7.90755i −0.511479 + 0.973352i
\(67\) 3.22362 5.58347i 0.393827 0.682129i −0.599123 0.800657i \(-0.704484\pi\)
0.992951 + 0.118528i \(0.0378175\pi\)
\(68\) −3.24095 −0.393023
\(69\) 4.65004 + 7.36164i 0.559799 + 0.886237i
\(70\) −6.31731 1.86783i −0.755062 0.223248i
\(71\) −2.06456 + 9.04545i −0.245019 + 1.07350i 0.691361 + 0.722509i \(0.257011\pi\)
−0.936380 + 0.350988i \(0.885846\pi\)
\(72\) 3.84838 + 7.89511i 0.453536 + 0.930447i
\(73\) −0.706030 0.106417i −0.0826345 0.0124552i 0.107595 0.994195i \(-0.465685\pi\)
−0.190229 + 0.981740i \(0.560923\pi\)
\(74\) 6.07090 7.61267i 0.705728 0.884954i
\(75\) 0.403016 + 3.50210i 0.0465362 + 0.404388i
\(76\) 2.30740 0.711737i 0.264676 0.0816419i
\(77\) −13.8388 + 4.44700i −1.57708 + 0.506782i
\(78\) 6.10912 0.243114i 0.691721 0.0275273i
\(79\) −5.41351 9.37648i −0.609068 1.05494i −0.991394 0.130909i \(-0.958210\pi\)
0.382326 0.924027i \(-0.375123\pi\)
\(80\) 0.677353 + 1.17321i 0.0757303 + 0.131169i
\(81\) −8.99959 + 0.0854767i −0.999955 + 0.00949741i
\(82\) 3.42158 2.33280i 0.377851 0.257614i
\(83\) 6.20131 + 15.8007i 0.680682 + 1.73435i 0.678770 + 0.734351i \(0.262513\pi\)
0.00191131 + 0.999998i \(0.499392\pi\)
\(84\) −1.62494 + 4.86260i −0.177295 + 0.530554i
\(85\) 2.80714 7.15248i 0.304477 0.775795i
\(86\) −2.12401 9.30588i −0.229037 1.00348i
\(87\) −8.90570 + 4.73389i −0.954791 + 0.507526i
\(88\) 14.4919 + 6.97892i 1.54484 + 0.743955i
\(89\) −2.89643 7.37998i −0.307021 0.782277i −0.998222 0.0596137i \(-0.981013\pi\)
0.691201 0.722663i \(-0.257082\pi\)
\(90\) −7.44607 + 0.593577i −0.784885 + 0.0625685i
\(91\) 7.37179 + 6.68094i 0.772773 + 0.700353i
\(92\) 4.64702 3.16828i 0.484485 0.330316i
\(93\) 0.797876 + 2.94968i 0.0827358 + 0.305868i
\(94\) 1.08021 + 1.00229i 0.111415 + 0.103378i
\(95\) −0.427807 + 5.70868i −0.0438920 + 0.585699i
\(96\) 8.22201 4.37046i 0.839155 0.446059i
\(97\) 0.441981 0.765534i 0.0448764 0.0777282i −0.842715 0.538360i \(-0.819044\pi\)
0.887591 + 0.460632i \(0.152377\pi\)
\(98\) 5.85191 2.98909i 0.591132 0.301944i
\(99\) −12.8372 + 10.3374i −1.29019 + 1.03895i
\(100\) 2.25162 0.339376i 0.225162 0.0339376i
\(101\) −17.8111 + 8.57736i −1.77227 + 0.853479i −0.807722 + 0.589564i \(0.799300\pi\)
−0.964546 + 0.263915i \(0.914986\pi\)
\(102\) 4.32152 + 1.87326i 0.427894 + 0.185480i
\(103\) −10.5642 + 5.08746i −1.04092 + 0.501282i −0.874628 0.484794i \(-0.838895\pi\)
−0.166295 + 0.986076i \(0.553180\pi\)
\(104\) −0.822702 10.9782i −0.0806726 1.07650i
\(105\) −9.32389 7.79782i −0.909918 0.760990i
\(106\) −0.228923 + 3.05477i −0.0222350 + 0.296705i
\(107\) 2.14152 + 5.45650i 0.207028 + 0.527500i 0.996241 0.0866197i \(-0.0276065\pi\)
−0.789213 + 0.614120i \(0.789511\pi\)
\(108\) 0.258744 + 5.80762i 0.0248977 + 0.558839i
\(109\) 3.75975 9.57968i 0.360118 0.917567i −0.629906 0.776671i \(-0.716907\pi\)
0.990024 0.140895i \(-0.0449982\pi\)
\(110\) −10.0278 + 9.30442i −0.956111 + 0.887141i
\(111\) 15.8638 8.43249i 1.50572 0.800376i
\(112\) −1.29585 0.383141i −0.122446 0.0362035i
\(113\) −12.1264 1.82777i −1.14076 0.171942i −0.448631 0.893717i \(-0.648088\pi\)
−0.692128 + 0.721775i \(0.743327\pi\)
\(114\) −3.48809 0.384629i −0.326690 0.0360238i
\(115\) 2.96711 + 12.9998i 0.276684 + 1.21223i
\(116\) 3.25733 + 5.64187i 0.302436 + 0.523834i
\(117\) 10.5205 + 4.07145i 0.972621 + 0.376405i
\(118\) −0.735455 3.22224i −0.0677041 0.296631i
\(119\) 2.88352 + 7.10121i 0.264332 + 0.650967i
\(120\) 1.53767 + 13.3620i 0.140370 + 1.21978i
\(121\) −4.26884 + 18.7030i −0.388077 + 1.70027i
\(122\) −1.70864 4.35353i −0.154693 0.394150i
\(123\) 7.50424 1.43834i 0.676635 0.129691i
\(124\) 1.88608 0.581777i 0.169375 0.0522451i
\(125\) 1.74983 7.66649i 0.156509 0.685711i
\(126\) 4.97728 5.54465i 0.443412 0.493956i
\(127\) 4.06811 + 17.8236i 0.360987 + 1.58159i 0.750696 + 0.660648i \(0.229718\pi\)
−0.389709 + 0.920938i \(0.627424\pi\)
\(128\) −2.52781 4.37830i −0.223429 0.386991i
\(129\) 3.23315 17.3125i 0.284663 1.52428i
\(130\) 8.94677 + 2.75971i 0.784683 + 0.242043i
\(131\) 0.790009 + 0.380448i 0.0690234 + 0.0332399i 0.468077 0.883688i \(-0.344947\pi\)
−0.399054 + 0.916928i \(0.630661\pi\)
\(132\) 6.96355 + 8.05304i 0.606099 + 0.700927i
\(133\) −3.61241 4.42247i −0.313236 0.383477i
\(134\) 3.77349 + 4.73181i 0.325980 + 0.408766i
\(135\) −13.0410 4.45924i −1.12239 0.383790i
\(136\) 3.09849 7.89481i 0.265693 0.676975i
\(137\) 9.50437 + 4.57706i 0.812013 + 0.391045i 0.793339 0.608781i \(-0.208341\pi\)
0.0186745 + 0.999826i \(0.494055\pi\)
\(138\) −8.02765 + 1.53867i −0.683359 + 0.130980i
\(139\) −16.3034 11.1155i −1.38284 0.942802i −0.999818 0.0190617i \(-0.993932\pi\)
−0.383019 0.923741i \(-0.625116\pi\)
\(140\) −4.82287 + 6.19528i −0.407607 + 0.523597i
\(141\) 1.09318 + 2.48945i 0.0920624 + 0.209650i
\(142\) −7.19621 4.90629i −0.603892 0.411727i
\(143\) 19.7412 6.08935i 1.65084 0.509217i
\(144\) −1.52739 + 0.121759i −0.127282 + 0.0101465i
\(145\) −15.2724 + 2.30195i −1.26831 + 0.191166i
\(146\) 0.335129 0.580460i 0.0277355 0.0480392i
\(147\) 12.1001 0.765952i 0.998002 0.0631746i
\(148\) −5.80230 10.0499i −0.476946 0.826095i
\(149\) 4.12913 + 5.17777i 0.338272 + 0.424179i 0.921651 0.388021i \(-0.126841\pi\)
−0.583379 + 0.812200i \(0.698270\pi\)
\(150\) −3.19849 0.848899i −0.261156 0.0693123i
\(151\) 3.91674 17.1604i 0.318740 1.39649i −0.521025 0.853541i \(-0.674450\pi\)
0.839765 0.542950i \(-0.182693\pi\)
\(152\) −0.472208 + 6.30117i −0.0383011 + 0.511093i
\(153\) 5.94125 + 6.34247i 0.480321 + 0.512758i
\(154\) 0.860146 13.6180i 0.0693125 1.09737i
\(155\) −0.349691 + 4.66630i −0.0280879 + 0.374806i
\(156\) 2.39029 6.88345i 0.191377 0.551117i
\(157\) −3.39357 + 2.31370i −0.270836 + 0.184653i −0.691121 0.722739i \(-0.742883\pi\)
0.420284 + 0.907392i \(0.361930\pi\)
\(158\) 10.0501 1.51481i 0.799546 0.120512i
\(159\) −2.62920 + 5.00342i −0.208509 + 0.396797i
\(160\) 14.1000 2.12523i 1.11470 0.168014i
\(161\) −11.0765 7.36316i −0.872952 0.580299i
\(162\) 3.01178 7.89351i 0.236628 0.620173i
\(163\) −11.0323 + 7.52171i −0.864119 + 0.589146i −0.912222 0.409696i \(-0.865635\pi\)
0.0481033 + 0.998842i \(0.484682\pi\)
\(164\) −1.09824 4.81172i −0.0857584 0.375732i
\(165\) −23.8038 + 8.39280i −1.85312 + 0.653378i
\(166\) −15.9340 −1.23672
\(167\) 5.64392 5.23679i 0.436740 0.405235i −0.430923 0.902389i \(-0.641812\pi\)
0.867663 + 0.497154i \(0.165621\pi\)
\(168\) −10.2916 8.60714i −0.794013 0.664055i
\(169\) −0.835495 0.775226i −0.0642688 0.0596328i
\(170\) 5.28739 + 4.90598i 0.405524 + 0.376271i
\(171\) −5.62273 3.21078i −0.429981 0.245535i
\(172\) −11.2490 1.69551i −0.857727 0.129282i
\(173\) −14.7497 + 4.54968i −1.12140 + 0.345906i −0.799379 0.600827i \(-0.794838\pi\)
−0.322020 + 0.946733i \(0.604362\pi\)
\(174\) −1.08239 9.40567i −0.0820555 0.713042i
\(175\) −2.74690 4.63155i −0.207646 0.350112i
\(176\) −2.05697 + 1.90859i −0.155050 + 0.143865i
\(177\) 1.11951 5.99461i 0.0841472 0.450583i
\(178\) 7.44227 0.557822
\(179\) 3.72412 3.45548i 0.278354 0.258275i −0.528624 0.848856i \(-0.677292\pi\)
0.806978 + 0.590581i \(0.201101\pi\)
\(180\) −2.58361 + 8.51930i −0.192571 + 0.634991i
\(181\) 6.37716 7.99671i 0.474011 0.594391i −0.486137 0.873882i \(-0.661595\pi\)
0.960148 + 0.279492i \(0.0901659\pi\)
\(182\) −8.36627 + 4.15048i −0.620149 + 0.307654i
\(183\) 0.302181 8.62392i 0.0223379 0.637498i
\(184\) 3.27506 + 14.3490i 0.241440 + 1.05782i
\(185\) 27.2048 4.10047i 2.00014 0.301472i
\(186\) −2.85118 0.314397i −0.209059 0.0230527i
\(187\) 15.7375 + 2.37204i 1.15084 + 0.173461i
\(188\) 1.58230 0.761997i 0.115401 0.0555743i
\(189\) 12.4948 5.73407i 0.908864 0.417092i
\(190\) −4.84175 2.33166i −0.351258 0.169157i
\(191\) 5.61114 + 3.82561i 0.406008 + 0.276811i 0.749056 0.662506i \(-0.230507\pi\)
−0.343049 + 0.939318i \(0.611460\pi\)
\(192\) 1.20156 + 10.4413i 0.0867152 + 0.753533i
\(193\) 0.0968417 1.29226i 0.00697082 0.0930191i −0.992633 0.121158i \(-0.961339\pi\)
0.999604 + 0.0281392i \(0.00895818\pi\)
\(194\) 0.517373 + 0.648765i 0.0371452 + 0.0465786i
\(195\) 13.1208 + 11.2373i 0.939601 + 0.804716i
\(196\) −0.768148 7.79374i −0.0548677 0.556696i
\(197\) 19.1026 1.36100 0.680502 0.732746i \(-0.261762\pi\)
0.680502 + 0.732746i \(0.261762\pi\)
\(198\) −4.63065 14.7629i −0.329086 1.04916i
\(199\) 9.17070 + 6.25248i 0.650093 + 0.443226i 0.842944 0.538002i \(-0.180821\pi\)
−0.192850 + 0.981228i \(0.561773\pi\)
\(200\) −1.32594 + 5.80930i −0.0937578 + 0.410780i
\(201\) 2.91582 + 10.7795i 0.205666 + 0.760330i
\(202\) −1.38681 18.5057i −0.0975755 1.30205i
\(203\) 9.46374 12.1568i 0.664224 0.853238i
\(204\) 3.95990 3.97875i 0.277248 0.278568i
\(205\) 11.5703 + 1.74394i 0.808103 + 0.121802i
\(206\) −0.822553 10.9762i −0.0573099 0.764748i
\(207\) −14.7191 3.28608i −1.02305 0.228398i
\(208\) 1.83522 + 0.566091i 0.127250 + 0.0392513i
\(209\) −11.7252 + 1.76730i −0.811052 + 0.122246i
\(210\) 10.0117 5.47326i 0.690875 0.377691i
\(211\) 10.9228 + 1.64635i 0.751959 + 0.113340i 0.513828 0.857893i \(-0.328227\pi\)
0.238131 + 0.971233i \(0.423465\pi\)
\(212\) 3.28935 + 1.58407i 0.225914 + 0.108794i
\(213\) −8.58208 13.5866i −0.588035 0.930938i
\(214\) −5.50255 −0.376147
\(215\) 13.4851 23.3569i 0.919678 1.59293i
\(216\) −14.3945 4.92205i −0.979422 0.334903i
\(217\) −2.95280 3.61494i −0.200449 0.245398i
\(218\) 7.08167 + 6.57083i 0.479631 + 0.445033i
\(219\) 0.993294 0.736733i 0.0671206 0.0497838i
\(220\) 5.95628 + 15.1763i 0.401572 + 1.02319i
\(221\) −3.97964 10.1400i −0.267700 0.682088i
\(222\) 1.92806 + 16.7543i 0.129403 + 1.12448i
\(223\) −7.55898 7.01371i −0.506187 0.469673i 0.385254 0.922811i \(-0.374114\pi\)
−0.891440 + 0.453138i \(0.850304\pi\)
\(224\) −8.73720 + 11.2235i −0.583779 + 0.749901i
\(225\) −4.79177 3.78423i −0.319452 0.252282i
\(226\) 5.75601 9.96971i 0.382884 0.663175i
\(227\) 3.04163 0.201880 0.100940 0.994893i \(-0.467815\pi\)
0.100940 + 0.994893i \(0.467815\pi\)
\(228\) −1.94549 + 3.70230i −0.128843 + 0.245191i
\(229\) 13.9645 + 6.72497i 0.922803 + 0.444398i 0.834071 0.551657i \(-0.186004\pi\)
0.0887319 + 0.996056i \(0.471719\pi\)
\(230\) −12.3773 1.86557i −0.816134 0.123012i
\(231\) 11.4493 22.4227i 0.753312 1.47530i
\(232\) −16.8575 + 2.54086i −1.10675 + 0.166816i
\(233\) 12.0981 + 3.73176i 0.792570 + 0.244476i 0.664499 0.747289i \(-0.268645\pi\)
0.128072 + 0.991765i \(0.459121\pi\)
\(234\) −7.16587 + 7.79690i −0.468447 + 0.509699i
\(235\) 0.311149 + 4.15200i 0.0202972 + 0.270847i
\(236\) −3.89506 0.587085i −0.253547 0.0382160i
\(237\) 18.1254 + 4.81060i 1.17737 + 0.312482i
\(238\) −7.19424 + 0.0843291i −0.466333 + 0.00546624i
\(239\) −0.207056 2.76297i −0.0133933 0.178722i −0.999889 0.0149314i \(-0.995247\pi\)
0.986495 0.163790i \(-0.0523720\pi\)
\(240\) −2.26790 0.601915i −0.146392 0.0388534i
\(241\) −5.04717 + 22.1131i −0.325117 + 1.42443i 0.503201 + 0.864170i \(0.332156\pi\)
−0.828317 + 0.560259i \(0.810701\pi\)
\(242\) −14.8794 10.1446i −0.956484 0.652120i
\(243\) 10.8911 11.1528i 0.698662 0.715451i
\(244\) −5.57388 −0.356831
\(245\) 17.8654 + 5.05530i 1.14138 + 0.322971i
\(246\) −1.31675 + 7.05079i −0.0839528 + 0.449542i
\(247\) 5.06013 + 6.34520i 0.321968 + 0.403735i
\(248\) −0.385984 + 5.15060i −0.0245100 + 0.327064i
\(249\) −26.9746 11.6928i −1.70945 0.740998i
\(250\) 6.09916 + 4.15834i 0.385745 + 0.262996i
\(251\) 2.30104 + 1.10812i 0.145240 + 0.0699439i 0.505092 0.863065i \(-0.331459\pi\)
−0.359852 + 0.933009i \(0.617173\pi\)
\(252\) −3.98417 7.93615i −0.250979 0.499930i
\(253\) −24.8840 + 11.9835i −1.56444 + 0.753396i
\(254\) −16.9701 2.55783i −1.06480 0.160493i
\(255\) 5.35088 + 12.1853i 0.335085 + 0.763074i
\(256\) 16.6934 2.51613i 1.04334 0.157258i
\(257\) −5.16918 22.6477i −0.322445 1.41272i −0.833188 0.552990i \(-0.813487\pi\)
0.510743 0.859733i \(-0.329370\pi\)
\(258\) 14.0195 + 8.76270i 0.872818 + 0.545542i
\(259\) −16.8578 + 21.6549i −1.04749 + 1.34557i
\(260\) 6.95726 8.72413i 0.431471 0.541047i
\(261\) 5.06973 16.7171i 0.313808 1.03476i
\(262\) −0.603389 + 0.559863i −0.0372775 + 0.0345885i
\(263\) 10.1329 0.624823 0.312412 0.949947i \(-0.398863\pi\)
0.312412 + 0.949947i \(0.398863\pi\)
\(264\) −26.2743 + 9.26386i −1.61707 + 0.570151i
\(265\) −6.34497 + 5.88727i −0.389768 + 0.361652i
\(266\) 5.10342 1.63995i 0.312911 0.100552i
\(267\) 12.5990 + 5.46131i 0.771046 + 0.334227i
\(268\) 6.89262 2.12609i 0.421034 0.129872i
\(269\) −28.0189 4.22317i −1.70834 0.257491i −0.779083 0.626921i \(-0.784315\pi\)
−0.929258 + 0.369430i \(0.879553\pi\)
\(270\) 8.36915 9.86642i 0.509330 0.600451i
\(271\) −12.3183 11.4297i −0.748281 0.694303i 0.210770 0.977536i \(-0.432403\pi\)
−0.959051 + 0.283232i \(0.908593\pi\)
\(272\) 1.08458 + 1.00635i 0.0657626 + 0.0610188i
\(273\) −17.2090 + 0.886968i −1.04153 + 0.0536817i
\(274\) −7.25920 + 6.73555i −0.438544 + 0.406910i
\(275\) −11.1818 −0.674291
\(276\) −1.78834 + 9.57602i −0.107645 + 0.576409i
\(277\) 4.07098 + 17.8361i 0.244602 + 1.07167i 0.936773 + 0.349937i \(0.113797\pi\)
−0.692171 + 0.721733i \(0.743346\pi\)
\(278\) 15.3045 10.4344i 0.917903 0.625815i
\(279\) −4.59604 2.62451i −0.275158 0.157125i
\(280\) −10.4806 17.6713i −0.626334 1.05606i
\(281\) 1.36560 0.205831i 0.0814649 0.0122789i −0.108183 0.994131i \(-0.534503\pi\)
0.189648 + 0.981852i \(0.439265\pi\)
\(282\) −2.55029 + 0.101490i −0.151868 + 0.00604362i
\(283\) 12.3893 1.86739i 0.736468 0.111005i 0.229912 0.973212i \(-0.426156\pi\)
0.506556 + 0.862207i \(0.330918\pi\)
\(284\) −8.57650 + 5.84736i −0.508922 + 0.346977i
\(285\) −6.48555 7.50026i −0.384171 0.444277i
\(286\) −1.44926 + 19.3390i −0.0856964 + 1.14354i
\(287\) −9.56579 + 6.68742i −0.564651 + 0.394746i
\(288\) −4.68052 + 15.4337i −0.275803 + 0.909441i
\(289\) −0.643299 + 8.58423i −0.0378411 + 0.504955i
\(290\) 3.22625 14.1351i 0.189452 0.830042i
\(291\) 0.399780 + 1.47795i 0.0234355 + 0.0866391i
\(292\) −0.498055 0.624542i −0.0291465 0.0365485i
\(293\) 2.75159 + 4.76589i 0.160750 + 0.278426i 0.935138 0.354284i \(-0.115276\pi\)
−0.774388 + 0.632711i \(0.781942\pi\)
\(294\) −3.48050 + 10.8363i −0.202987 + 0.631983i
\(295\) 4.66934 8.08753i 0.271859 0.470874i
\(296\) 30.0283 4.52604i 1.74536 0.263071i
\(297\) 2.99417 28.3902i 0.173739 1.64737i
\(298\) −5.94065 + 1.83245i −0.344133 + 0.106151i
\(299\) 15.6188 + 10.6487i 0.903259 + 0.615832i
\(300\) −2.33446 + 3.17886i −0.134780 + 0.183531i
\(301\) 6.29338 + 26.1561i 0.362745 + 1.50761i
\(302\) 13.6521 + 9.30786i 0.785592 + 0.535607i
\(303\) 11.2322 32.3459i 0.645271 1.85822i
\(304\) −0.993173 0.478287i −0.0569624 0.0274316i
\(305\) 4.82781 12.3010i 0.276439 0.704356i
\(306\) −7.57988 + 3.01650i −0.433313 + 0.172442i
\(307\) 6.75337 + 8.46846i 0.385435 + 0.483320i 0.936264 0.351298i \(-0.114260\pi\)
−0.550829 + 0.834618i \(0.685688\pi\)
\(308\) −14.7336 6.88377i −0.839525 0.392239i
\(309\) 6.66210 19.1852i 0.378993 1.09141i
\(310\) −3.95767 1.90591i −0.224780 0.108249i
\(311\) 8.23016 + 2.53867i 0.466690 + 0.143955i 0.519177 0.854667i \(-0.326239\pi\)
−0.0524871 + 0.998622i \(0.516715\pi\)
\(312\) 14.4826 + 12.4035i 0.819915 + 0.702212i
\(313\) −6.34935 10.9974i −0.358886 0.621609i 0.628889 0.777495i \(-0.283510\pi\)
−0.987775 + 0.155886i \(0.950177\pi\)
\(314\) −0.857952 3.75893i −0.0484170 0.212129i
\(315\) 20.9652 1.91882i 1.18126 0.108113i
\(316\) 2.69542 11.8094i 0.151629 0.664332i
\(317\) 13.8144 4.26116i 0.775891 0.239331i 0.118575 0.992945i \(-0.462168\pi\)
0.657317 + 0.753614i \(0.271691\pi\)
\(318\) −3.47048 4.01346i −0.194615 0.225063i
\(319\) −11.6878 29.7800i −0.654390 1.66736i
\(320\) −3.58147 + 15.6914i −0.200210 + 0.877177i
\(321\) −9.31525 4.03790i −0.519927 0.225374i
\(322\) 10.2330 7.15385i 0.570262 0.398669i
\(323\) 1.39126 + 6.09549i 0.0774115 + 0.339162i
\(324\) −7.44587 6.77830i −0.413659 0.376572i
\(325\) 3.82663 + 6.62791i 0.212263 + 0.367650i
\(326\) −2.78916 12.2201i −0.154477 0.676809i
\(327\) 7.16670 + 16.3204i 0.396320 + 0.902521i
\(328\) 12.7711 + 1.92494i 0.705167 + 0.106287i
\(329\) −3.07740 2.78901i −0.169663 0.153763i
\(330\) 0.829710 23.6790i 0.0456740 1.30349i
\(331\) 4.35570 4.04150i 0.239411 0.222141i −0.551337 0.834283i \(-0.685882\pi\)
0.790748 + 0.612141i \(0.209692\pi\)
\(332\) −6.93794 + 17.6776i −0.380769 + 0.970183i
\(333\) −9.03073 + 29.7782i −0.494881 + 1.63184i
\(334\) 2.64049 + 6.72787i 0.144481 + 0.368133i
\(335\) −1.27794 + 17.0529i −0.0698212 + 0.931699i
\(336\) 2.05367 1.12271i 0.112037 0.0612490i
\(337\) −0.567509 7.57289i −0.0309142 0.412521i −0.991096 0.133147i \(-0.957492\pi\)
0.960182 0.279375i \(-0.0901272\pi\)
\(338\) 0.963961 0.464219i 0.0524326 0.0252502i
\(339\) 17.0603 12.6538i 0.926591 0.687259i
\(340\) 7.74502 3.72981i 0.420033 0.202277i
\(341\) −9.58426 + 1.44459i −0.519017 + 0.0782292i
\(342\) 4.73406 3.81220i 0.255989 0.206140i
\(343\) −16.3934 + 8.61730i −0.885158 + 0.465290i
\(344\) 14.8847 25.7811i 0.802530 1.39002i
\(345\) −19.5844 12.2410i −1.05439 0.659031i
\(346\) 1.08282 14.4492i 0.0582126 0.776794i
\(347\) −5.65325 5.24545i −0.303483 0.281591i 0.513700 0.857970i \(-0.328275\pi\)
−0.817182 + 0.576379i \(0.804465\pi\)
\(348\) −10.9062 2.89456i −0.584631 0.155165i
\(349\) 8.94659 6.09968i 0.478900 0.326509i −0.299695 0.954035i \(-0.596885\pi\)
0.778595 + 0.627526i \(0.215933\pi\)
\(350\) 4.98929 0.811933i 0.266689 0.0433996i
\(351\) −17.8526 + 7.94086i −0.952902 + 0.423852i
\(352\) 10.7905 + 27.4937i 0.575136 + 1.46542i
\(353\) −19.9797 9.62173i −1.06341 0.512113i −0.181435 0.983403i \(-0.558074\pi\)
−0.881978 + 0.471290i \(0.843788\pi\)
\(354\) 4.85438 + 3.03416i 0.258008 + 0.161264i
\(355\) −5.47607 23.9922i −0.290640 1.27338i
\(356\) 3.24049 8.25662i 0.171745 0.437600i
\(357\) −12.2410 5.13654i −0.647861 0.271854i
\(358\) 1.74232 + 4.43936i 0.0920846 + 0.234628i
\(359\) 23.5832 16.0787i 1.24467 0.848603i 0.251799 0.967779i \(-0.418978\pi\)
0.992873 + 0.119176i \(0.0380253\pi\)
\(360\) −18.2826 14.4384i −0.963578 0.760970i
\(361\) 7.17088 + 12.4203i 0.377415 + 0.653701i
\(362\) 4.80075 + 8.31514i 0.252322 + 0.437034i
\(363\) −17.7449 28.0926i −0.931368 1.47448i
\(364\) 0.961827 + 11.0889i 0.0504134 + 0.581218i
\(365\) 1.80970 0.558217i 0.0947238 0.0292184i
\(366\) 7.43228 + 3.22169i 0.388492 + 0.168400i
\(367\) −14.2923 + 17.9220i −0.746054 + 0.935522i −0.999493 0.0318290i \(-0.989867\pi\)
0.253439 + 0.967351i \(0.418438\pi\)
\(368\) −2.53891 0.382679i −0.132350 0.0199485i
\(369\) −7.40315 + 10.9700i −0.385393 + 0.571075i
\(370\) −5.74692 + 25.1789i −0.298768 + 1.30899i
\(371\) 0.544248 8.61664i 0.0282559 0.447354i
\(372\) −1.59025 + 3.02627i −0.0824507 + 0.156905i
\(373\) −5.96644 −0.308930 −0.154465 0.987998i \(-0.549365\pi\)
−0.154465 + 0.987998i \(0.549365\pi\)
\(374\) −7.47006 + 12.9385i −0.386267 + 0.669035i
\(375\) 7.27376 + 11.5153i 0.375615 + 0.594650i
\(376\) 0.343443 + 4.58293i 0.0177117 + 0.236346i
\(377\) −13.6520 + 17.1190i −0.703112 + 0.881675i
\(378\) 0.725473 + 12.8850i 0.0373143 + 0.662733i
\(379\) 19.7555 + 24.7726i 1.01477 + 1.27249i 0.961761 + 0.273891i \(0.0883108\pi\)
0.0530124 + 0.998594i \(0.483118\pi\)
\(380\) −4.69498 + 4.35631i −0.240847 + 0.223474i
\(381\) −26.8517 16.7832i −1.37565 0.859830i
\(382\) −5.26734 + 3.59121i −0.269501 + 0.183742i
\(383\) −9.72641 + 12.1965i −0.496996 + 0.623214i −0.965549 0.260222i \(-0.916204\pi\)
0.468553 + 0.883436i \(0.344776\pi\)
\(384\) 8.46359 + 2.24629i 0.431906 + 0.114630i
\(385\) 27.9533 26.5534i 1.42463 1.35329i
\(386\) 1.09602 + 0.527814i 0.0557858 + 0.0268650i
\(387\) 17.3034 + 25.1222i 0.879579 + 1.27703i
\(388\) 0.945028 0.291502i 0.0479765 0.0147988i
\(389\) −21.6644 + 10.4330i −1.09843 + 0.528976i −0.893164 0.449731i \(-0.851520\pi\)
−0.205265 + 0.978706i \(0.565806\pi\)
\(390\) −14.3194 + 7.61158i −0.725092 + 0.385428i
\(391\) 7.28143 + 12.6118i 0.368238 + 0.637806i
\(392\) 19.7196 + 5.57998i 0.995991 + 0.281831i
\(393\) −1.43232 + 0.505010i −0.0722508 + 0.0254744i
\(394\) −6.55136 + 16.6926i −0.330053 + 0.840961i
\(395\) 23.7277 + 16.1773i 1.19387 + 0.813967i
\(396\) −18.3946 1.29067i −0.924363 0.0648588i
\(397\) −1.89226 + 25.2505i −0.0949699 + 1.26729i 0.722523 + 0.691347i \(0.242982\pi\)
−0.817493 + 0.575939i \(0.804637\pi\)
\(398\) −8.60881 + 5.86939i −0.431520 + 0.294206i
\(399\) 9.84300 + 0.968749i 0.492766 + 0.0484981i
\(400\) −0.858884 0.585577i −0.0429442 0.0292789i
\(401\) −1.35609 + 1.70048i −0.0677198 + 0.0849179i −0.814538 0.580111i \(-0.803009\pi\)
0.746818 + 0.665029i \(0.231581\pi\)
\(402\) −10.4196 1.14896i −0.519681 0.0573048i
\(403\) 4.13617 + 5.18659i 0.206037 + 0.258363i
\(404\) −21.1345 6.51912i −1.05148 0.324338i
\(405\) 21.4083 10.5613i 1.06379 0.524797i
\(406\) 7.37741 + 12.4390i 0.366135 + 0.617339i
\(407\) 20.8195 + 53.0472i 1.03198 + 2.62945i
\(408\) 5.90623 + 13.4500i 0.292402 + 0.665874i
\(409\) 19.9014 + 6.13877i 0.984061 + 0.303543i 0.744708 0.667390i \(-0.232589\pi\)
0.239353 + 0.970933i \(0.423065\pi\)
\(410\) −5.49202 + 9.51246i −0.271232 + 0.469787i
\(411\) −17.2318 + 6.07563i −0.849981 + 0.299688i
\(412\) −12.5354 3.86666i −0.617575 0.190497i
\(413\) 2.17914 + 9.05676i 0.107228 + 0.445654i
\(414\) 7.91951 11.7351i 0.389223 0.576750i
\(415\) −33.0035 30.6228i −1.62008 1.50321i
\(416\) 12.6039 15.8048i 0.617957 0.774894i
\(417\) 33.5660 6.43361i 1.64373 0.315055i
\(418\) 2.47692 10.8521i 0.121150 0.530792i
\(419\) 8.45391 2.60769i 0.413000 0.127394i −0.0812902 0.996690i \(-0.525904\pi\)
0.494291 + 0.869297i \(0.335428\pi\)
\(420\) −1.71289 13.4904i −0.0835805 0.658264i
\(421\) −36.6794 11.3141i −1.78765 0.551416i −0.789585 0.613642i \(-0.789704\pi\)
−0.998062 + 0.0622258i \(0.980180\pi\)
\(422\) −5.18470 + 8.98017i −0.252387 + 0.437148i
\(423\) −4.39186 1.69965i −0.213540 0.0826400i
\(424\) −7.00349 + 6.49829i −0.340120 + 0.315585i
\(425\) 0.440601 + 5.87941i 0.0213723 + 0.285193i
\(426\) 14.8158 2.83975i 0.717826 0.137586i
\(427\) 4.95917 + 12.2129i 0.239991 + 0.591022i
\(428\) −2.39590 + 6.10466i −0.115810 + 0.295080i
\(429\) −16.6448 + 31.6754i −0.803621 + 1.52930i
\(430\) 15.7854 + 19.7942i 0.761239 + 0.954563i
\(431\) −1.77820 23.7284i −0.0856529 1.14296i −0.860033 0.510238i \(-0.829557\pi\)
0.774380 0.632721i \(-0.218062\pi\)
\(432\) 1.71674 2.02387i 0.0825966 0.0973733i
\(433\) 0.0477097 0.0229758i 0.00229278 0.00110415i −0.432737 0.901520i \(-0.642452\pi\)
0.435030 + 0.900416i \(0.356738\pi\)
\(434\) 4.17156 1.34050i 0.200241 0.0643461i
\(435\) 15.8344 21.5618i 0.759200 1.03381i
\(436\) 10.3733 4.99552i 0.496791 0.239242i
\(437\) −7.95367 7.37993i −0.380476 0.353030i
\(438\) 0.303130 + 1.12065i 0.0144841 + 0.0535465i
\(439\) 13.9656 35.5837i 0.666540 1.69832i −0.0481187 0.998842i \(-0.515323\pi\)
0.714658 0.699474i \(-0.246582\pi\)
\(440\) −42.6634 −2.03390
\(441\) −13.8440 + 15.7906i −0.659240 + 0.751933i
\(442\) 10.2255 0.486379
\(443\) −10.0963 + 25.7250i −0.479691 + 1.22223i 0.462339 + 0.886703i \(0.347010\pi\)
−0.942030 + 0.335529i \(0.891085\pi\)
\(444\) 19.4272 + 5.15609i 0.921973 + 0.244697i
\(445\) 15.4149 + 14.3029i 0.730735 + 0.678023i
\(446\) 8.72125 4.19994i 0.412963 0.198873i
\(447\) −11.4016 1.25724i −0.539277 0.0594656i
\(448\) −8.18969 13.8086i −0.386926 0.652395i
\(449\) 6.92699 3.33586i 0.326905 0.157429i −0.263231 0.964733i \(-0.584788\pi\)
0.590136 + 0.807304i \(0.299074\pi\)
\(450\) 4.95017 2.88941i 0.233353 0.136208i
\(451\) 1.81119 + 24.1687i 0.0852857 + 1.13806i
\(452\) −8.55436 10.7268i −0.402363 0.504548i
\(453\) 16.2813 + 25.7755i 0.764963 + 1.21104i
\(454\) −1.04315 + 2.65789i −0.0489573 + 0.124741i
\(455\) −25.3053 7.48199i −1.18633 0.350761i
\(456\) −7.15867 8.27869i −0.335236 0.387685i
\(457\) 0.671924 + 8.96621i 0.0314313 + 0.419422i 0.990619 + 0.136652i \(0.0436342\pi\)
−0.959188 + 0.282770i \(0.908747\pi\)
\(458\) −10.6658 + 9.89639i −0.498379 + 0.462428i
\(459\) −15.0455 0.455669i −0.702265 0.0212688i
\(460\) −7.45898 + 12.9193i −0.347777 + 0.602367i
\(461\) −24.4101 7.52952i −1.13689 0.350685i −0.331516 0.943450i \(-0.607560\pi\)
−0.805376 + 0.592765i \(0.798036\pi\)
\(462\) 15.6672 + 17.6949i 0.728903 + 0.823241i
\(463\) −39.5955 + 12.2136i −1.84016 + 0.567614i −0.840491 + 0.541826i \(0.817733\pi\)
−0.999667 + 0.0257874i \(0.991791\pi\)
\(464\) 0.661789 2.89949i 0.0307228 0.134605i
\(465\) −5.30132 6.13074i −0.245843 0.284306i
\(466\) −7.41007 + 9.29193i −0.343265 + 0.430440i
\(467\) 6.89754 + 6.39998i 0.319180 + 0.296156i 0.823448 0.567391i \(-0.192047\pi\)
−0.504268 + 0.863547i \(0.668238\pi\)
\(468\) 5.52993 + 11.3449i 0.255621 + 0.524417i
\(469\) −10.7909 13.2107i −0.498279 0.610015i
\(470\) −3.73489 1.15206i −0.172278 0.0531406i
\(471\) 1.30597 6.99307i 0.0601759 0.322224i
\(472\) 5.15396 8.92692i 0.237230 0.410895i
\(473\) 53.3822 + 16.4662i 2.45452 + 0.757118i
\(474\) −10.4199 + 14.1889i −0.478603 + 0.651717i
\(475\) −1.60485 4.08909i −0.0736356 0.187621i
\(476\) −3.03893 + 8.01817i −0.139289 + 0.367512i
\(477\) −2.92999 9.34108i −0.134155 0.427699i
\(478\) 2.48540 + 0.766645i 0.113680 + 0.0350655i
\(479\) 6.49770 + 8.14786i 0.296888 + 0.372285i 0.907793 0.419418i \(-0.137766\pi\)
−0.610905 + 0.791704i \(0.709194\pi\)
\(480\) −14.6188 + 19.9065i −0.667252 + 0.908602i
\(481\) 24.3183 30.4942i 1.10882 1.39041i
\(482\) −17.5923 11.9942i −0.801308 0.546323i
\(483\) 22.5730 4.60153i 1.02711 0.209377i
\(484\) −17.7334 + 12.0904i −0.806064 + 0.549565i
\(485\) −0.175214 + 2.33807i −0.00795608 + 0.106167i
\(486\) 6.01057 + 13.3420i 0.272645 + 0.605204i
\(487\) −10.6115 7.23477i −0.480851 0.327839i 0.298518 0.954404i \(-0.403508\pi\)
−0.779369 + 0.626565i \(0.784460\pi\)
\(488\) 5.32887 13.5777i 0.241227 0.614635i
\(489\) 4.24564 22.7341i 0.191994 1.02807i
\(490\) −10.5446 + 13.8777i −0.476356 + 0.626933i
\(491\) −1.50514 2.60698i −0.0679262 0.117652i 0.830062 0.557671i \(-0.188305\pi\)
−0.897988 + 0.440019i \(0.854972\pi\)
\(492\) 7.24898 + 4.53086i 0.326809 + 0.204267i
\(493\) −15.1978 + 7.31886i −0.684473 + 0.329625i
\(494\) −7.28009 + 2.24561i −0.327547 + 0.101035i
\(495\) 18.7808 39.4773i 0.844136 1.77437i
\(496\) −0.811824 0.390954i −0.0364520 0.0175543i
\(497\) 20.4427 + 13.5894i 0.916982 + 0.609568i
\(498\) 19.4687 19.5614i 0.872414 0.876567i
\(499\) 9.06661 11.3692i 0.405877 0.508954i −0.536319 0.844015i \(-0.680186\pi\)
0.942196 + 0.335061i \(0.108757\pi\)
\(500\) 7.26903 4.95594i 0.325081 0.221636i
\(501\) −0.466985 + 13.3272i −0.0208633 + 0.595417i
\(502\) −1.75747 + 1.63070i −0.0784399 + 0.0727816i
\(503\) 0.486669 + 0.610264i 0.0216995 + 0.0272103i 0.792563 0.609790i \(-0.208746\pi\)
−0.770863 + 0.637001i \(0.780175\pi\)
\(504\) 23.1412 2.11797i 1.03079 0.0943420i
\(505\) 32.6927 40.9953i 1.45480 1.82427i
\(506\) −1.93752 25.8544i −0.0861333 1.14937i
\(507\) 1.97254 0.0784979i 0.0876036 0.00348621i
\(508\) −10.2268 + 17.7133i −0.453740 + 0.785902i
\(509\) −18.7822 −0.832506 −0.416253 0.909249i \(-0.636657\pi\)
−0.416253 + 0.909249i \(0.636657\pi\)
\(510\) −12.4831 + 0.496770i −0.552762 + 0.0219973i
\(511\) −0.925299 + 1.64695i −0.0409328 + 0.0728567i
\(512\) −1.27646 + 5.59253i −0.0564120 + 0.247157i
\(513\) 10.8118 2.97970i 0.477351 0.131557i
\(514\) 21.5632 + 3.25013i 0.951113 + 0.143357i
\(515\) 19.3909 24.3154i 0.854465 1.07146i
\(516\) 15.8259 11.7382i 0.696696 0.516744i
\(517\) −8.24109 + 2.54204i −0.362443 + 0.111799i
\(518\) −13.1414 22.1577i −0.577400 0.973553i
\(519\) 12.4363 23.6664i 0.545891 1.03884i
\(520\) 14.6002 + 25.2882i 0.640260 + 1.10896i
\(521\) 5.88222 + 10.1883i 0.257705 + 0.446358i 0.965627 0.259933i \(-0.0837005\pi\)
−0.707922 + 0.706291i \(0.750367\pi\)
\(522\) 12.8694 + 10.1634i 0.563276 + 0.444838i
\(523\) 33.7546 23.0135i 1.47599 1.00631i 0.484687 0.874688i \(-0.338934\pi\)
0.991300 0.131623i \(-0.0420188\pi\)
\(524\) 0.358400 + 0.913188i 0.0156568 + 0.0398928i
\(525\) 9.04217 + 2.28674i 0.394633 + 0.0998016i
\(526\) −3.47516 + 8.85455i −0.151524 + 0.386077i
\(527\) 1.13722 + 4.98248i 0.0495380 + 0.217040i
\(528\) 0.170196 4.85721i 0.00740682 0.211383i
\(529\) −2.04720 0.985878i −0.0890086 0.0428643i
\(530\) −2.96848 7.56355i −0.128942 0.328540i
\(531\) 5.99143 + 8.69878i 0.260006 + 0.377495i
\(532\) 0.402718 6.37592i 0.0174601 0.276431i
\(533\) 13.7059 9.34452i 0.593668 0.404756i
\(534\) −9.09321 + 9.13650i −0.393502 + 0.395375i
\(535\) −11.3972 10.5751i −0.492745 0.457200i
\(536\) −1.41057 + 18.8228i −0.0609274 + 0.813020i
\(537\) −0.308138 + 8.79394i −0.0132972 + 0.379486i
\(538\) 13.2996 23.0356i 0.573388 0.993136i
\(539\) −1.97423 + 38.4073i −0.0850363 + 1.65432i
\(540\) −7.30196 13.5809i −0.314227 0.584430i
\(541\) −25.3480 + 3.82059i −1.08979 + 0.164260i −0.669269 0.743020i \(-0.733393\pi\)
−0.420526 + 0.907280i \(0.638154\pi\)
\(542\) 14.2123 6.84429i 0.610471 0.293988i
\(543\) 2.02533 + 17.5996i 0.0869150 + 0.755270i
\(544\) 14.0310 6.75699i 0.601575 0.289703i
\(545\) 2.03984 + 27.2198i 0.0873772 + 1.16597i
\(546\) 5.12686 15.3420i 0.219409 0.656579i
\(547\) 2.14748 28.6561i 0.0918196 1.22525i −0.740924 0.671589i \(-0.765612\pi\)
0.832744 0.553658i \(-0.186769\pi\)
\(548\) 4.31180 + 10.9863i 0.184191 + 0.469311i
\(549\) 10.2179 + 10.9080i 0.436091 + 0.465541i
\(550\) 3.83489 9.77114i 0.163520 0.416643i
\(551\) 9.21279 8.54822i 0.392478 0.364166i
\(552\) −21.6171 13.5114i −0.920083 0.575084i
\(553\) −28.2737 + 4.60112i −1.20232 + 0.195659i
\(554\) −16.9821 2.55964i −0.721500 0.108749i
\(555\) −28.2058 + 38.4081i −1.19727 + 1.63033i
\(556\) −4.91237 21.5225i −0.208331 0.912757i
\(557\) −11.0704 19.1746i −0.469070 0.812452i 0.530305 0.847807i \(-0.322077\pi\)
−0.999375 + 0.0353544i \(0.988744\pi\)
\(558\) 3.86964 3.11611i 0.163815 0.131915i
\(559\) −8.50817 37.2767i −0.359857 1.57664i
\(560\) 3.53768 0.575704i 0.149494 0.0243279i
\(561\) −22.1406 + 16.4219i −0.934778 + 0.693332i
\(562\) −0.288479 + 1.26391i −0.0121687 + 0.0533147i
\(563\) −9.30794 23.7162i −0.392283 0.999520i −0.981486 0.191535i \(-0.938653\pi\)
0.589203 0.807985i \(-0.299442\pi\)
\(564\) −0.997845 + 2.87355i −0.0420169 + 0.120998i
\(565\) 31.0825 9.58768i 1.30765 0.403357i
\(566\) −2.61720 + 11.4667i −0.110009 + 0.481981i
\(567\) −8.22716 + 22.3453i −0.345508 + 0.938416i
\(568\) −6.04442 26.4823i −0.253618 1.11117i
\(569\) −5.57058 9.64852i −0.233531 0.404487i 0.725314 0.688418i \(-0.241695\pi\)
−0.958845 + 0.283931i \(0.908361\pi\)
\(570\) 8.77828 3.09507i 0.367682 0.129638i
\(571\) 25.2676 + 7.79403i 1.05742 + 0.326170i 0.774237 0.632896i \(-0.218134\pi\)
0.283181 + 0.959066i \(0.408610\pi\)
\(572\) 20.8241 + 10.0284i 0.870699 + 0.419307i
\(573\) −11.5524 + 2.21425i −0.482608 + 0.0925017i
\(574\) −2.56308 10.6525i −0.106981 0.444625i
\(575\) −6.37935 7.99945i −0.266037 0.333600i
\(576\) −14.2863 11.2824i −0.595263 0.470099i
\(577\) 2.90302 7.39677i 0.120854 0.307931i −0.857625 0.514275i \(-0.828061\pi\)
0.978480 + 0.206343i \(0.0661564\pi\)
\(578\) −7.28061 3.50616i −0.302834 0.145837i
\(579\) 1.46812 + 1.69782i 0.0610130 + 0.0705589i
\(580\) −14.2771 9.73393i −0.592822 0.404179i
\(581\) 44.9059 0.526376i 1.86301 0.0218378i
\(582\) −1.42860 0.157530i −0.0592173 0.00652984i
\(583\) −14.8132 10.0994i −0.613498 0.418276i
\(584\) 1.99752 0.616153i 0.0826580 0.0254966i
\(585\) −29.8268 + 2.37770i −1.23319 + 0.0983059i
\(586\) −5.10830 + 0.769952i −0.211022 + 0.0318064i
\(587\) −13.4088 + 23.2248i −0.553442 + 0.958590i 0.444581 + 0.895739i \(0.353353\pi\)
−0.998023 + 0.0628512i \(0.979981\pi\)
\(588\) 10.5065 + 8.57964i 0.433282 + 0.353818i
\(589\) −1.90383 3.29754i −0.0784461 0.135873i
\(590\) 5.46582 + 6.85392i 0.225024 + 0.282172i
\(591\) −23.3402 + 23.4513i −0.960088 + 0.964658i
\(592\) −1.17885 + 5.16487i −0.0484503 + 0.212275i
\(593\) 2.96818 39.6077i 0.121889 1.62649i −0.516158 0.856494i \(-0.672638\pi\)
0.638046 0.769998i \(-0.279743\pi\)
\(594\) 23.7816 + 12.3530i 0.975770 + 0.506851i
\(595\) −15.0632 13.6516i −0.617531 0.559660i
\(596\) −0.553697 + 7.38858i −0.0226803 + 0.302648i
\(597\) −18.8809 + 3.61892i −0.772744 + 0.148112i
\(598\) −14.6618 + 9.99628i −0.599568 + 0.408778i
\(599\) −17.4003 + 2.62268i −0.710959 + 0.107160i −0.494558 0.869145i \(-0.664670\pi\)
−0.216401 + 0.976305i \(0.569432\pi\)
\(600\) −5.51171 8.72578i −0.225015 0.356229i
\(601\) 29.3613 4.42551i 1.19767 0.180520i 0.480234 0.877141i \(-0.340552\pi\)
0.717440 + 0.696620i \(0.245314\pi\)
\(602\) −25.0145 3.47099i −1.01952 0.141467i
\(603\) −16.7961 9.59119i −0.683991 0.390584i
\(604\) 16.2707 11.0932i 0.662046 0.451376i
\(605\) −11.3227 49.6081i −0.460334 2.01686i
\(606\) 24.4129 + 20.9083i 0.991707 + 0.849343i
\(607\) −4.98826 −0.202467 −0.101234 0.994863i \(-0.532279\pi\)
−0.101234 + 0.994863i \(0.532279\pi\)
\(608\) −8.50552 + 7.89197i −0.344944 + 0.320061i
\(609\) 3.36114 + 26.4717i 0.136200 + 1.07269i
\(610\) 9.09341 + 8.43745i 0.368181 + 0.341622i
\(611\) 4.32701 + 4.01488i 0.175052 + 0.162425i
\(612\) 0.0461714 + 9.72273i 0.00186637 + 0.393018i
\(613\) −14.4855 2.18333i −0.585062 0.0881839i −0.150160 0.988662i \(-0.547979\pi\)
−0.434902 + 0.900478i \(0.643217\pi\)
\(614\) −9.71618 + 2.99704i −0.392113 + 0.120951i
\(615\) −16.2779 + 12.0734i −0.656388 + 0.486848i
\(616\) 30.8546 29.3093i 1.24317 1.18090i
\(617\) 19.9717 18.5311i 0.804032 0.746032i −0.166749 0.985999i \(-0.553327\pi\)
0.970781 + 0.239967i \(0.0771366\pi\)
\(618\) 14.4799 + 12.4013i 0.582469 + 0.498853i
\(619\) −32.0294 −1.28737 −0.643685 0.765290i \(-0.722595\pi\)
−0.643685 + 0.765290i \(0.722595\pi\)
\(620\) −3.83770 + 3.56086i −0.154126 + 0.143008i
\(621\) 22.0184 14.0548i 0.883569 0.564002i
\(622\) −5.04098 + 6.32118i −0.202125 + 0.253456i
\(623\) −20.9741 + 0.245854i −0.840311 + 0.00984991i
\(624\) −2.93730 + 1.56134i −0.117586 + 0.0625036i
\(625\) 6.90572 + 30.2560i 0.276229 + 1.21024i
\(626\) 11.7875 1.77668i 0.471123 0.0710104i
\(627\) 12.1567 16.5538i 0.485491 0.661096i
\(628\) −4.54381 0.684870i −0.181318 0.0273293i
\(629\) 27.0718 13.0371i 1.07942 0.519823i
\(630\) −5.51342 + 18.9783i −0.219660 + 0.756114i
\(631\) −18.6007 8.95761i −0.740481 0.356597i 0.0253160 0.999679i \(-0.491941\pi\)
−0.765797 + 0.643083i \(0.777655\pi\)
\(632\) 26.1903 + 17.8563i 1.04180 + 0.710284i
\(633\) −15.3670 + 11.3978i −0.610785 + 0.453024i
\(634\) −1.01415 + 13.5329i −0.0402771 + 0.537461i
\(635\) −30.2338 37.9120i −1.19979 1.50449i
\(636\) −5.96372 + 2.10270i −0.236477 + 0.0833777i
\(637\) 23.4411 11.9734i 0.928770 0.474405i
\(638\) 30.0313 1.18895
\(639\) 27.1654 + 6.06476i 1.07465 + 0.239918i
\(640\) 11.0795 + 7.55390i 0.437957 + 0.298594i
\(641\) −2.10585 + 9.22633i −0.0831761 + 0.364418i −0.999338 0.0363910i \(-0.988414\pi\)
0.916162 + 0.400809i \(0.131271\pi\)
\(642\) 6.72320 6.75520i 0.265344 0.266607i
\(643\) −1.92469 25.6832i −0.0759024 1.01285i −0.896992 0.442047i \(-0.854252\pi\)
0.821089 0.570799i \(-0.193367\pi\)
\(644\) −3.48104 14.4676i −0.137172 0.570104i
\(645\) 12.1975 + 45.0933i 0.480278 + 1.77555i
\(646\) −5.80362 0.874754i −0.228340 0.0344168i
\(647\) −0.987092 13.1718i −0.0388066 0.517838i −0.982407 0.186752i \(-0.940204\pi\)
0.943601 0.331086i \(-0.107415\pi\)
\(648\) 23.6302 11.6575i 0.928283 0.457949i
\(649\) 18.4840 + 5.70157i 0.725562 + 0.223806i
\(650\) −7.10409 + 1.07077i −0.278645 + 0.0419990i
\(651\) 8.04571 + 0.791860i 0.315336 + 0.0310354i
\(652\) −14.7717 2.22648i −0.578505 0.0871956i
\(653\) −35.6045 17.1462i −1.39331 0.670984i −0.421519 0.906820i \(-0.638503\pi\)
−0.971793 + 0.235836i \(0.924217\pi\)
\(654\) −16.7193 + 0.665349i −0.653776 + 0.0260172i
\(655\) −2.32575 −0.0908746
\(656\) −1.12656 + 1.95126i −0.0439848 + 0.0761839i
\(657\) −0.309189 + 2.11958i −0.0120626 + 0.0826928i
\(658\) 3.49256 1.73265i 0.136154 0.0675456i
\(659\) −25.2361 23.4157i −0.983058 0.912145i 0.0130826 0.999914i \(-0.495836\pi\)
−0.996141 + 0.0877697i \(0.972026\pi\)
\(660\) −25.9088 11.2307i −1.00850 0.437156i
\(661\) −0.719771 1.83395i −0.0279958 0.0713323i 0.916192 0.400739i \(-0.131247\pi\)
−0.944188 + 0.329407i \(0.893151\pi\)
\(662\) 2.03781 + 5.19224i 0.0792015 + 0.201802i
\(663\) 17.3108 + 7.50374i 0.672295 + 0.291421i
\(664\) −36.4289 33.8010i −1.41371 1.31174i
\(665\) 13.7223 + 6.41125i 0.532126 + 0.248618i
\(666\) −22.9242 18.1040i −0.888296 0.701517i
\(667\) 14.6365 25.3511i 0.566727 0.981600i
\(668\) 8.61377 0.333277
\(669\) 17.8462 0.710194i 0.689974 0.0274577i
\(670\) −14.4632 6.96511i −0.558762 0.269086i
\(671\) 27.0658 + 4.07951i 1.04486 + 0.157488i
\(672\) −3.10311 24.4395i −0.119705 0.942772i
\(673\) 5.65736 0.852709i 0.218075 0.0328695i −0.0390958 0.999235i \(-0.512448\pi\)
0.257171 + 0.966366i \(0.417210\pi\)
\(674\) 6.81212 + 2.10126i 0.262393 + 0.0809375i
\(675\) 10.5005 1.25892i 0.404163 0.0484560i
\(676\) −0.0952910 1.27157i −0.00366504 0.0489065i
\(677\) −12.2158 1.84123i −0.469490 0.0707643i −0.0899636 0.995945i \(-0.528675\pi\)
−0.379527 + 0.925181i \(0.623913\pi\)
\(678\) 5.20642 + 19.2477i 0.199951 + 0.739203i
\(679\) −1.47951 1.81129i −0.0567786 0.0695108i
\(680\) 1.68108 + 22.4324i 0.0644663 + 0.860244i
\(681\) −3.71636 + 3.73405i −0.142411 + 0.143089i
\(682\) 2.02464 8.87053i 0.0775275 0.339670i
\(683\) −19.3361 13.1831i −0.739874 0.504438i 0.133764 0.991013i \(-0.457293\pi\)
−0.873639 + 0.486576i \(0.838246\pi\)
\(684\) −2.16806 6.91197i −0.0828978 0.264286i
\(685\) −27.9804 −1.06908
\(686\) −1.90792 17.2805i −0.0728448 0.659773i
\(687\) −25.3182 + 8.92677i −0.965951 + 0.340578i
\(688\) 3.23800 + 4.06033i 0.123448 + 0.154799i
\(689\) −0.917002 + 12.2365i −0.0349350 + 0.466175i
\(690\) 17.4132 12.9155i 0.662911 0.491686i
\(691\) −0.990196 0.675104i −0.0376688 0.0256822i 0.544339 0.838865i \(-0.316780\pi\)
−0.582008 + 0.813183i \(0.697733\pi\)
\(692\) −15.5588 7.49272i −0.591457 0.284831i
\(693\) 13.5380 + 41.4526i 0.514266 + 1.57465i
\(694\) 6.52250 3.14107i 0.247591 0.119233i
\(695\) 51.7530 + 7.80051i 1.96310 + 0.295890i
\(696\) 17.4778 23.7996i 0.662493 0.902122i
\(697\) 12.6365 1.90465i 0.478642 0.0721437i
\(698\) 2.26185 + 9.90981i 0.0856123 + 0.375092i
\(699\) −19.3631 + 10.2926i −0.732380 + 0.389302i
\(700\) 1.27164 5.88877i 0.0480636 0.222574i
\(701\) −11.5612 + 14.4973i −0.436661 + 0.547555i −0.950660 0.310236i \(-0.899592\pi\)
0.513999 + 0.857791i \(0.328163\pi\)
\(702\) −0.816366 18.3237i −0.0308118 0.691583i
\(703\) −16.4108 + 15.2270i −0.618944 + 0.574296i
\(704\) −33.3378 −1.25647
\(705\) −5.47737 4.69107i −0.206290 0.176676i
\(706\) 15.2600 14.1592i 0.574318 0.532889i
\(707\) 4.51969 + 52.1077i 0.169981 + 1.95971i
\(708\) 5.47985 4.06444i 0.205945 0.152751i
\(709\) −15.6909 + 4.84001i −0.589285 + 0.181770i −0.575036 0.818128i \(-0.695012\pi\)
−0.0142489 + 0.999898i \(0.504536\pi\)
\(710\) 22.8434 + 3.44309i 0.857298 + 0.129217i
\(711\) −28.0520 + 16.3739i −1.05203 + 0.614071i
\(712\) 17.0148 + 15.7874i 0.637655 + 0.591657i
\(713\) −6.50136 6.03238i −0.243478 0.225915i
\(714\) 8.68663 8.93504i 0.325089 0.334385i
\(715\) −40.1684 + 37.2709i −1.50221 + 1.39385i
\(716\) 5.68377 0.212412
\(717\) 3.64495 + 3.12170i 0.136123 + 0.116582i
\(718\) 5.96222 + 26.1222i 0.222508 + 0.974872i
\(719\) −14.3763 + 9.80161i −0.536146 + 0.365538i −0.800919 0.598772i \(-0.795655\pi\)
0.264773 + 0.964311i \(0.414703\pi\)
\(720\) 3.50994 2.04875i 0.130808 0.0763524i
\(721\) 2.68075 + 30.9064i 0.0998363 + 1.15102i
\(722\) −13.3127 + 2.00656i −0.495446 + 0.0746765i
\(723\) −20.9803 33.2147i −0.780266 1.23527i
\(724\) 11.3153 1.70551i 0.420531 0.0633849i
\(725\) 9.79210 6.67614i 0.363669 0.247946i
\(726\) 30.6342 5.87167i 1.13694 0.217918i
\(727\) 1.16817 15.5882i 0.0433251 0.578134i −0.932725 0.360588i \(-0.882576\pi\)
0.976050 0.217545i \(-0.0698050\pi\)
\(728\) −27.9317 8.25852i −1.03522 0.306081i
\(729\) 0.384638 + 26.9973i 0.0142458 + 0.999899i
\(730\) −0.132855 + 1.77283i −0.00491719 + 0.0656153i
\(731\) 6.55451 28.7172i 0.242427 1.06214i
\(732\) 6.81035 6.84277i 0.251718 0.252916i
\(733\) 30.6426 + 38.4246i 1.13181 + 1.41925i 0.894075 + 0.447917i \(0.147834\pi\)
0.237736 + 0.971330i \(0.423595\pi\)
\(734\) −10.7593 18.6357i −0.397134 0.687856i
\(735\) −28.0347 + 15.7557i −1.03408 + 0.581159i
\(736\) −13.5128 + 23.4049i −0.498090 + 0.862717i
\(737\) −35.0254 + 5.27924i −1.29018 + 0.194463i
\(738\) −7.04705 10.2314i −0.259406 0.376623i
\(739\) 16.7758 5.17464i 0.617106 0.190352i 0.0295869 0.999562i \(-0.490581\pi\)
0.587519 + 0.809210i \(0.300105\pi\)
\(740\) 25.4318 + 17.3391i 0.934890 + 0.637397i
\(741\) −13.9723 1.54071i −0.513286 0.0565995i
\(742\) 7.34291 + 3.43072i 0.269567 + 0.125946i
\(743\) −40.0030 27.2736i −1.46757 1.00057i −0.992713 0.120506i \(-0.961548\pi\)
−0.474854 0.880064i \(-0.657499\pi\)
\(744\) −5.85153 6.76703i −0.214527 0.248092i
\(745\) −15.8263 7.62156i −0.579832 0.279232i
\(746\) 2.04623 5.21371i 0.0749178 0.190887i
\(747\) 47.3131 18.8288i 1.73110 0.688910i
\(748\) 11.1017 + 13.9211i 0.405919 + 0.509006i
\(749\) 15.5075 0.181775i 0.566633 0.00664193i
\(750\) −12.5571 + 2.40684i −0.458522 + 0.0878852i
\(751\) 22.4734 + 10.8226i 0.820065 + 0.394923i 0.796380 0.604797i \(-0.206746\pi\)
0.0236854 + 0.999719i \(0.492460\pi\)
\(752\) −0.766126 0.236319i −0.0279378 0.00861766i
\(753\) −4.17187 + 1.47093i −0.152031 + 0.0536035i
\(754\) −10.2772 17.8007i −0.374275 0.648263i
\(755\) 10.3888 + 45.5164i 0.378088 + 1.65651i
\(756\) 14.6108 + 4.80548i 0.531390 + 0.174774i
\(757\) 6.35628 27.8487i 0.231023 1.01218i −0.717770 0.696280i \(-0.754837\pi\)
0.948793 0.315898i \(-0.102306\pi\)
\(758\) −28.4226 + 8.76721i −1.03235 + 0.318439i
\(759\) 15.6926 45.1906i 0.569604 1.64032i
\(760\) −6.12318 15.6016i −0.222111 0.565929i
\(761\) −7.78382 + 34.1031i −0.282163 + 1.23624i 0.612850 + 0.790199i \(0.290023\pi\)
−0.895013 + 0.446039i \(0.852834\pi\)
\(762\) 23.8748 17.7081i 0.864892 0.641497i
\(763\) −20.1749 18.2843i −0.730382 0.661934i
\(764\) 1.69069 + 7.40738i 0.0611669 + 0.267990i
\(765\) −21.4972 8.31943i −0.777232 0.300790i
\(766\) −7.32207 12.6822i −0.264557 0.458226i
\(767\) −2.94602 12.9074i −0.106375 0.466058i
\(768\) −17.3076 + 23.5679i −0.624536 + 0.850435i
\(769\) −30.8926 4.65631i −1.11401 0.167911i −0.433861 0.900980i \(-0.642849\pi\)
−0.680154 + 0.733069i \(0.738087\pi\)
\(770\) 13.6166 + 33.5334i 0.490708 + 1.20846i
\(771\) 34.1193 + 21.3257i 1.22878 + 0.768028i
\(772\) 1.06279 0.986128i 0.0382508 0.0354915i
\(773\) 14.0972 35.9190i 0.507039 1.29192i −0.416752 0.909020i \(-0.636832\pi\)
0.923792 0.382895i \(-0.125073\pi\)
\(774\) −27.8871 + 6.50452i −1.00238 + 0.233800i
\(775\) −1.31181 3.34244i −0.0471217 0.120064i
\(776\) −0.193400 + 2.58074i −0.00694264 + 0.0926431i
\(777\) −5.98721 47.1541i −0.214790 1.69164i
\(778\) −1.68684 22.5093i −0.0604761 0.806997i
\(779\) −8.57831 + 4.13110i −0.307350 + 0.148012i
\(780\) 2.20956 + 19.2005i 0.0791149 + 0.687488i
\(781\) 45.9257 22.1166i 1.64335 0.791396i
\(782\) −13.5179 + 2.03750i −0.483399 + 0.0728607i
\(783\) 14.3284 + 26.6494i 0.512054 + 0.952370i
\(784\) −2.16298 + 2.84670i −0.0772491 + 0.101668i
\(785\) 5.44706 9.43459i 0.194414 0.336735i
\(786\) 0.0499252 1.42481i 0.00178077 0.0508213i
\(787\) −1.03968 + 13.8735i −0.0370604 + 0.494537i 0.947531 + 0.319665i \(0.103570\pi\)
−0.984591 + 0.174872i \(0.944049\pi\)
\(788\) 15.6666 + 14.5365i 0.558099 + 0.517840i
\(789\) −12.3808 + 12.4397i −0.440767 + 0.442865i
\(790\) −22.2739 + 15.1861i −0.792470 + 0.540297i
\(791\) −15.8925 + 28.2872i −0.565072 + 1.00578i
\(792\) 20.7301 43.5745i 0.736611 1.54835i
\(793\) −6.84431 17.4390i −0.243049 0.619278i
\(794\) −21.4159 10.3134i −0.760022 0.366007i
\(795\) 0.524990 14.9827i 0.0186195 0.531380i
\(796\) 2.76322 + 12.1064i 0.0979396 + 0.429101i
\(797\) −7.32423 + 18.6618i −0.259438 + 0.661036i −0.999939 0.0110184i \(-0.996493\pi\)
0.740502 + 0.672054i \(0.234588\pi\)
\(798\) −4.22225 + 8.26896i −0.149466 + 0.292718i
\(799\) 1.66133 + 4.23300i 0.0587736 + 0.149753i
\(800\) −9.04036 + 6.16361i −0.319625 + 0.217917i
\(801\) −22.0984 + 8.79433i −0.780810 + 0.310732i
\(802\) −1.02087 1.76819i −0.0360481 0.0624371i
\(803\) 1.96137 + 3.39719i 0.0692152 + 0.119884i
\(804\) −5.81154 + 11.0594i −0.204957 + 0.390037i
\(805\) 34.9438 + 4.84876i 1.23161 + 0.170896i
\(806\) −5.95077 + 1.83557i −0.209607 + 0.0646552i
\(807\) 39.4190 29.2374i 1.38761 1.02920i
\(808\) 36.0858 45.2501i 1.26949 1.59189i
\(809\) −30.5984 4.61196i −1.07578 0.162148i −0.412828 0.910809i \(-0.635459\pi\)
−0.662953 + 0.748661i \(0.730697\pi\)
\(810\) 1.88679 + 22.3295i 0.0662950 + 0.784579i
\(811\) 11.5093 50.4253i 0.404145 1.77067i −0.206172 0.978516i \(-0.566101\pi\)
0.610316 0.792158i \(-0.291042\pi\)
\(812\) 17.0124 2.76851i 0.597018 0.0971557i
\(813\) 29.0825 1.15735i 1.01997 0.0405899i
\(814\) −53.4949 −1.87499
\(815\) 17.7081 30.6714i 0.620288 1.07437i
\(816\) −2.56062 + 0.101901i −0.0896398 + 0.00356724i
\(817\) 1.64003 + 21.8846i 0.0573773 + 0.765647i
\(818\) −12.1896 + 15.2853i −0.426200 + 0.534438i
\(819\) 19.9376 22.2103i 0.696676 0.776090i
\(820\) 8.16203 + 10.2349i 0.285030 + 0.357417i
\(821\) −9.85456 + 9.14369i −0.343926 + 0.319117i −0.833156 0.553038i \(-0.813468\pi\)
0.489230 + 0.872155i \(0.337278\pi\)
\(822\) 0.600635 17.1415i 0.0209496 0.597878i
\(823\) −20.2172 + 13.7839i −0.704728 + 0.480475i −0.861888 0.507098i \(-0.830718\pi\)
0.157161 + 0.987573i \(0.449766\pi\)
\(824\) 21.4034 26.8390i 0.745623 0.934982i
\(825\) 13.6624 13.7274i 0.475662 0.477926i
\(826\) −8.66150 1.20186i −0.301372 0.0418180i
\(827\) −27.5911 13.2872i −0.959438 0.462041i −0.112453 0.993657i \(-0.535871\pi\)
−0.846985 + 0.531616i \(0.821585\pi\)
\(828\) −9.57095 13.8958i −0.332613 0.482911i
\(829\) −21.1629 + 6.52789i −0.735018 + 0.226723i −0.639593 0.768714i \(-0.720897\pi\)
−0.0954249 + 0.995437i \(0.530421\pi\)
\(830\) 38.0782 18.3375i 1.32171 0.636503i
\(831\) −26.8706 16.7951i −0.932131 0.582614i
\(832\) 11.4088 + 19.7606i 0.395529 + 0.685076i
\(833\) 20.2723 0.475320i 0.702394 0.0164689i
\(834\) −5.88972 + 31.5377i −0.203944 + 1.09206i
\(835\) −7.46080 + 19.0098i −0.258192 + 0.657862i
\(836\) −10.9611 7.47312i −0.379096 0.258463i
\(837\) 8.83757 2.43562i 0.305471 0.0841874i
\(838\) −0.620626 + 8.28168i −0.0214392 + 0.286086i
\(839\) 20.3381 13.8663i 0.702149 0.478717i −0.158864 0.987300i \(-0.550783\pi\)
0.861013 + 0.508584i \(0.169831\pi\)
\(840\) 34.4996 + 8.72487i 1.19035 + 0.301037i
\(841\) 4.05440 + 2.76425i 0.139807 + 0.0953188i
\(842\) 22.4662 28.1717i 0.774235 0.970860i
\(843\) −1.41585 + 1.92797i −0.0487644 + 0.0664029i
\(844\) 7.70531 + 9.66215i 0.265228 + 0.332585i
\(845\) 2.88878 + 0.891069i 0.0993769 + 0.0306537i
\(846\) 2.99144 3.25487i 0.102848 0.111905i
\(847\) 42.2689 + 28.0984i 1.45238 + 0.965474i
\(848\) −0.608914 1.55149i −0.0209102 0.0532783i
\(849\) −12.8452 + 17.4914i −0.440845 + 0.600302i
\(850\) −5.28877 1.63137i −0.181403 0.0559555i
\(851\) −26.0720 + 45.1581i −0.893737 + 1.54800i
\(852\) 3.30055 17.6734i 0.113075 0.605482i
\(853\) 18.3952 + 5.67417i 0.629839 + 0.194280i 0.593208 0.805049i \(-0.297861\pi\)
0.0366313 + 0.999329i \(0.488337\pi\)
\(854\) −12.3729 + 0.145032i −0.423391 + 0.00496288i
\(855\) 17.1320 + 1.20208i 0.585900 + 0.0411102i
\(856\) −12.5801 11.6726i −0.429979 0.398962i
\(857\) −19.7799 + 24.8032i −0.675667 + 0.847260i −0.994947 0.100401i \(-0.967988\pi\)
0.319280 + 0.947660i \(0.396559\pi\)
\(858\) −21.9708 25.4082i −0.750069 0.867422i
\(859\) −0.544235 + 2.38445i −0.0185691 + 0.0813564i −0.983363 0.181649i \(-0.941857\pi\)
0.964794 + 0.263005i \(0.0847137\pi\)
\(860\) 28.8334 8.89393i 0.983211 0.303280i
\(861\) 3.47800 19.9143i 0.118530 0.678679i
\(862\) 21.3447 + 6.58396i 0.727003 + 0.224251i
\(863\) −6.97566 + 12.0822i −0.237454 + 0.411283i −0.959983 0.280058i \(-0.909646\pi\)
0.722529 + 0.691341i \(0.242980\pi\)
\(864\) −13.2284 24.6035i −0.450038 0.837027i
\(865\) 30.0120 27.8471i 1.02044 0.946828i
\(866\) 0.00371478 + 0.0495703i 0.000126233 + 0.00168447i
\(867\) −9.75242 11.2782i −0.331210 0.383029i
\(868\) 0.329184 5.21170i 0.0111732 0.176897i
\(869\) −21.7318 + 55.3718i −0.737202 + 1.87836i
\(870\) 13.4110 + 21.2314i 0.454676 + 0.719813i
\(871\) 15.1155 + 18.9543i 0.512170 + 0.642241i
\(872\) 2.25155 + 30.0449i 0.0762472 + 1.01745i
\(873\) −2.30287 1.31502i −0.0779404 0.0445068i
\(874\) 9.17663 4.41923i 0.310404 0.149483i
\(875\) −17.3263 11.5177i −0.585735 0.389370i
\(876\) 1.37526 + 0.151648i 0.0464657 + 0.00512373i
\(877\) 33.9705 16.3593i 1.14710 0.552415i 0.238940 0.971034i \(-0.423200\pi\)
0.908162 + 0.418619i \(0.137486\pi\)
\(878\) 26.3048 + 24.4073i 0.887744 + 0.823706i
\(879\) −9.21283 2.44514i −0.310741 0.0824725i
\(880\) 2.71914 6.92826i 0.0916622 0.233551i
\(881\) 25.3012 0.852417 0.426209 0.904625i \(-0.359849\pi\)
0.426209 + 0.904625i \(0.359849\pi\)
\(882\) −9.05053 17.5129i −0.304747 0.589691i
\(883\) 12.8526 0.432523 0.216262 0.976335i \(-0.430614\pi\)
0.216262 + 0.976335i \(0.430614\pi\)
\(884\) 4.45237 11.3445i 0.149749 0.381555i
\(885\) 4.22350 + 15.6139i 0.141971 + 0.524857i
\(886\) −19.0169 17.6451i −0.638886 0.592800i
\(887\) −13.1602 + 6.33763i −0.441877 + 0.212797i −0.641574 0.767061i \(-0.721718\pi\)
0.199697 + 0.979858i \(0.436004\pi\)
\(888\) −31.1332 + 42.3943i −1.04476 + 1.42266i
\(889\) 47.9104 + 6.64800i 1.60686 + 0.222967i
\(890\) −17.7851 + 8.56484i −0.596157 + 0.287094i
\(891\) 31.1948 + 38.3639i 1.04507 + 1.28524i
\(892\) −0.862127 11.5043i −0.0288661 0.385192i
\(893\) −2.11239 2.64885i −0.0706883 0.0886403i
\(894\) 5.00888 9.53198i 0.167522 0.318797i
\(895\) −4.92299 + 12.5436i −0.164557 + 0.419285i
\(896\) −13.2023 + 2.14847i −0.441057 + 0.0717754i
\(897\) −32.1565 + 6.16346i −1.07367 + 0.205792i
\(898\) 0.539351 + 7.19713i 0.0179984 + 0.240171i
\(899\) 7.53057 6.98735i 0.251159 0.233041i
\(900\) −1.05020 6.74994i −0.0350065 0.224998i
\(901\) −4.72660 + 8.18671i −0.157466 + 0.272739i
\(902\) −21.7407 6.70612i −0.723886 0.223289i
\(903\) −39.7999 24.2323i −1.32446 0.806400i
\(904\) 34.3085 10.5828i 1.14108 0.351977i
\(905\) −6.03684 + 26.4491i −0.200671 + 0.879199i
\(906\) −28.1074 + 5.38737i −0.933807 + 0.178983i
\(907\) 1.03926 1.30319i 0.0345080 0.0432717i −0.764278 0.644887i \(-0.776904\pi\)
0.798786 + 0.601615i \(0.205476\pi\)
\(908\) 2.49452 + 2.31458i 0.0827837 + 0.0768120i
\(909\) 25.9855 + 53.3104i 0.861886 + 1.76819i
\(910\) 15.2167 19.5468i 0.504428 0.647970i
\(911\) 37.3226 + 11.5125i 1.23655 + 0.381426i 0.843018 0.537885i \(-0.180776\pi\)
0.393533 + 0.919310i \(0.371253\pi\)
\(912\) 1.80066 0.634881i 0.0596258 0.0210230i
\(913\) 46.6276 80.7614i 1.54315 2.67281i
\(914\) −8.06546 2.48787i −0.266782 0.0822913i
\(915\) 9.20260 + 20.9567i 0.304229 + 0.692807i
\(916\) 6.33523 + 16.1419i 0.209322 + 0.533344i
\(917\) 1.68200 1.59776i 0.0555446 0.0527628i
\(918\) 5.55815 12.9911i 0.183446 0.428770i
\(919\) 38.1581 + 11.7702i 1.25872 + 0.388263i 0.851155 0.524914i \(-0.175903\pi\)
0.407563 + 0.913177i \(0.366379\pi\)
\(920\) −24.3399 30.5212i −0.802461 1.00625i
\(921\) −18.6478 2.05627i −0.614465 0.0677565i
\(922\) 14.9512 18.7482i 0.492391 0.617439i
\(923\) −28.8260 19.6532i −0.948818 0.646893i
\(924\) 26.4529 9.67689i 0.870236 0.318346i
\(925\) −17.4427 + 11.8922i −0.573512 + 0.391014i
\(926\) 2.90682 38.7888i 0.0955240 1.27468i
\(927\) 15.4127 + 31.6198i 0.506220 + 1.03853i
\(928\) −25.8646 17.6342i −0.849046 0.578870i
\(929\) 5.55165 14.1454i 0.182144 0.464095i −0.810416 0.585855i \(-0.800759\pi\)
0.992560 + 0.121760i \(0.0388539\pi\)
\(930\) 7.17540 2.52992i 0.235291 0.0829594i
\(931\) −14.3285 + 4.79037i −0.469598 + 0.156998i
\(932\) 7.08222 + 12.2668i 0.231986 + 0.401811i
\(933\) −13.1725 + 7.00192i −0.431248 + 0.229233i
\(934\) −7.95811 + 3.83242i −0.260397 + 0.125401i
\(935\) −40.3383 + 12.4427i −1.31920 + 0.406921i
\(936\) −32.9225 + 2.62448i −1.07611 + 0.0857837i
\(937\) 26.1577 + 12.5969i 0.854536 + 0.411523i 0.809259 0.587452i \(-0.199869\pi\)
0.0452769 + 0.998974i \(0.485583\pi\)
\(938\) 15.2449 4.89883i 0.497763 0.159952i
\(939\) 21.2588 + 5.64221i 0.693754 + 0.184127i
\(940\) −2.90436 + 3.64195i −0.0947297 + 0.118787i
\(941\) 4.68510 3.19425i 0.152730 0.104129i −0.484544 0.874767i \(-0.661014\pi\)
0.637274 + 0.770637i \(0.280062\pi\)
\(942\) 5.66293 + 3.53953i 0.184508 + 0.115324i
\(943\) −16.2569 + 15.0842i −0.529397 + 0.491208i
\(944\) 1.12119 + 1.40592i 0.0364915 + 0.0457589i
\(945\) −23.2604 + 28.0824i −0.756660 + 0.913522i
\(946\) −32.6966 + 41.0002i −1.06306 + 1.33303i
\(947\) 3.50908 + 46.8254i 0.114030 + 1.52162i 0.701671 + 0.712501i \(0.252437\pi\)
−0.587642 + 0.809121i \(0.699943\pi\)
\(948\) 11.2045 + 17.7382i 0.363905 + 0.576110i
\(949\) 1.34243 2.32516i 0.0435772 0.0754778i
\(950\) 4.12360 0.133787
\(951\) −11.6476 + 22.1656i −0.377700 + 0.718769i
\(952\) −16.6266 15.0684i −0.538871 0.488371i
\(953\) 3.88193 17.0079i 0.125748 0.550939i −0.872327 0.488923i \(-0.837390\pi\)
0.998075 0.0620159i \(-0.0197529\pi\)
\(954\) 9.16746 + 0.643243i 0.296808 + 0.0208258i
\(955\) −17.8118 2.68470i −0.576377 0.0868748i
\(956\) 1.93272 2.42355i 0.0625086 0.0783833i
\(957\) 50.8399 + 22.0377i 1.64342 + 0.712377i
\(958\) −9.34835 + 2.88358i −0.302031 + 0.0931644i
\(959\) 20.2357 19.2222i 0.653445 0.620719i
\(960\) −14.8876 23.5691i −0.480496 0.760689i
\(961\) 13.9438 + 24.1514i 0.449800 + 0.779076i
\(962\) 18.3069 + 31.7085i 0.590238 + 1.02232i
\(963\) 16.3388 6.50222i 0.526511 0.209531i
\(964\) −20.9667 + 14.2948i −0.675291 + 0.460406i
\(965\) 1.25576 + 3.19962i 0.0404243 + 0.102999i
\(966\) −3.72058 + 21.3033i −0.119708 + 0.685424i
\(967\) −0.528310 + 1.34611i −0.0169893 + 0.0432881i −0.939117 0.343598i \(-0.888354\pi\)
0.922127 + 0.386886i \(0.126449\pi\)
\(968\) −12.4979 54.7568i −0.401697 1.75995i
\(969\) −9.18301 5.73970i −0.295001 0.184386i
\(970\) −1.98301 0.954967i −0.0636706 0.0306622i
\(971\) 2.96550 + 7.55596i 0.0951673 + 0.242482i 0.970528 0.240988i \(-0.0774714\pi\)
−0.875361 + 0.483470i \(0.839376\pi\)
\(972\) 17.4190 0.858961i 0.558714 0.0275512i
\(973\) −42.7871 + 29.9123i −1.37169 + 0.958946i
\(974\) 9.96130 6.79150i 0.319180 0.217614i
\(975\) −12.8123 3.40045i −0.410320 0.108901i
\(976\) 1.86530 + 1.73075i 0.0597069 + 0.0553999i
\(977\) −0.0739733 + 0.987105i −0.00236661 + 0.0315803i −0.998262 0.0589306i \(-0.981231\pi\)
0.995895 + 0.0905109i \(0.0288500\pi\)
\(978\) 18.4099 + 11.5068i 0.588683 + 0.367947i
\(979\) −21.7783 + 37.7210i −0.696036 + 1.20557i
\(980\) 10.8050 + 17.7410i 0.345153 + 0.566715i
\(981\) −28.7923 11.1426i −0.919267 0.355757i
\(982\) 2.79428 0.421171i 0.0891692 0.0134401i
\(983\) 26.6551 12.8364i 0.850164 0.409417i 0.0425256 0.999095i \(-0.486460\pi\)
0.807638 + 0.589678i \(0.200745\pi\)
\(984\) −17.9673 + 13.3265i −0.572778 + 0.424834i
\(985\) −45.6503 + 21.9840i −1.45454 + 0.700469i
\(986\) −1.18333 15.7904i −0.0376849 0.502870i
\(987\) 7.18400 0.370271i 0.228669 0.0117859i
\(988\) −0.678539 + 9.05447i −0.0215872 + 0.288061i
\(989\) 18.6752 + 47.5835i 0.593836 + 1.51307i
\(990\) 28.0558 + 29.9504i 0.891672 + 0.951887i
\(991\) −16.5142 + 42.0775i −0.524591 + 1.33664i 0.385683 + 0.922631i \(0.373966\pi\)
−0.910274 + 0.414005i \(0.864129\pi\)
\(992\) −6.95244 + 6.45093i −0.220740 + 0.204817i
\(993\) −0.360396 + 10.2853i −0.0114368 + 0.326395i
\(994\) −18.8859 + 13.2031i −0.599025 + 0.418777i
\(995\) −29.1112 4.38780i −0.922886 0.139103i
\(996\) −13.2249 30.1164i −0.419046 0.954275i
\(997\) −8.67899 38.0251i −0.274866 1.20427i −0.904192 0.427126i \(-0.859526\pi\)
0.629326 0.777142i \(-0.283331\pi\)
\(998\) 6.82537 + 11.8219i 0.216053 + 0.374215i
\(999\) −25.5232 47.4706i −0.807518 1.50190i
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 441.2.z.a.142.21 yes 648
9.4 even 3 441.2.y.a.436.21 yes 648
49.39 even 21 441.2.y.a.88.21 648
441.382 even 21 inner 441.2.z.a.382.21 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.y.a.88.21 648 49.39 even 21
441.2.y.a.436.21 yes 648 9.4 even 3
441.2.z.a.142.21 yes 648 1.1 even 1 trivial
441.2.z.a.382.21 yes 648 441.382 even 21 inner