Properties

Label 25.4.d.a.16.3
Level $25$
Weight $4$
Character 25.16
Analytic conductor $1.475$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [25,4,Mod(6,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.6");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 25.d (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.47504775014\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 16.3
Character \(\chi\) \(=\) 25.16
Dual form 25.4.d.a.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.51671 - 1.10196i) q^{2} +(-0.496278 - 1.52739i) q^{3} +(-1.38603 - 4.26575i) q^{4} +(2.00572 - 10.9990i) q^{5} +(-0.930402 + 2.86348i) q^{6} -5.91678 q^{7} +(-7.23313 + 22.2613i) q^{8} +(19.7568 - 14.3542i) q^{9} +O(q^{10})\) \(q+(-1.51671 - 1.10196i) q^{2} +(-0.496278 - 1.52739i) q^{3} +(-1.38603 - 4.26575i) q^{4} +(2.00572 - 10.9990i) q^{5} +(-0.930402 + 2.86348i) q^{6} -5.91678 q^{7} +(-7.23313 + 22.2613i) q^{8} +(19.7568 - 14.3542i) q^{9} +(-15.1625 + 14.4720i) q^{10} +(46.2426 + 33.5972i) q^{11} +(-5.82760 + 4.23400i) q^{12} +(-23.8943 + 17.3602i) q^{13} +(8.97406 + 6.52004i) q^{14} +(-17.7951 + 2.39503i) q^{15} +(6.47220 - 4.70233i) q^{16} +(16.1964 - 49.8475i) q^{17} -45.7831 q^{18} +(28.8671 - 88.8439i) q^{19} +(-49.6988 + 6.68896i) q^{20} +(2.93637 + 9.03722i) q^{21} +(-33.1141 - 101.915i) q^{22} +(101.186 + 73.5160i) q^{23} +37.5912 q^{24} +(-116.954 - 44.1216i) q^{25} +55.3710 q^{26} +(-66.8097 - 48.5401i) q^{27} +(8.20082 + 25.2395i) q^{28} +(42.2327 + 129.979i) q^{29} +(29.6292 + 15.9768i) q^{30} +(-22.0658 + 67.9115i) q^{31} +172.257 q^{32} +(28.3668 - 87.3040i) q^{33} +(-79.4951 + 57.7566i) q^{34} +(-11.8674 + 65.0785i) q^{35} +(-88.6149 - 64.3825i) q^{36} +(-149.002 + 108.256i) q^{37} +(-141.685 + 102.940i) q^{38} +(38.3741 + 27.8804i) q^{39} +(230.343 + 124.207i) q^{40} +(-28.3279 + 20.5814i) q^{41} +(5.50499 - 16.9426i) q^{42} +185.374 q^{43} +(79.2239 - 243.826i) q^{44} +(-118.254 - 246.095i) q^{45} +(-72.4588 - 223.005i) q^{46} +(130.295 + 401.007i) q^{47} +(-10.3943 - 7.55189i) q^{48} -307.992 q^{49} +(128.766 + 195.798i) q^{50} -84.1744 q^{51} +(107.173 + 77.8655i) q^{52} +(-214.260 - 659.426i) q^{53} +(47.8420 + 147.243i) q^{54} +(462.284 - 441.234i) q^{55} +(42.7968 - 131.715i) q^{56} -150.025 q^{57} +(79.1762 - 243.679i) q^{58} +(-466.375 + 338.841i) q^{59} +(34.8811 + 72.5897i) q^{60} +(29.5121 + 21.4418i) q^{61} +(108.303 - 78.6867i) q^{62} +(-116.897 + 84.9306i) q^{63} +(-313.042 - 227.438i) q^{64} +(143.019 + 297.633i) q^{65} +(-139.229 + 101.156i) q^{66} +(-48.1248 + 148.113i) q^{67} -235.086 q^{68} +(62.0710 - 191.035i) q^{69} +(89.7130 - 85.6279i) q^{70} +(120.884 + 372.044i) q^{71} +(176.639 + 543.638i) q^{72} +(946.113 + 687.392i) q^{73} +345.287 q^{74} +(-9.34899 + 200.531i) q^{75} -418.997 q^{76} +(-273.608 - 198.788i) q^{77} +(-27.4794 - 84.5730i) q^{78} +(323.388 + 995.287i) q^{79} +(-38.7393 - 80.6190i) q^{80} +(162.771 - 500.956i) q^{81} +65.6451 q^{82} +(289.936 - 892.333i) q^{83} +(34.4806 - 25.0517i) q^{84} +(-515.785 - 278.124i) q^{85} +(-281.159 - 204.274i) q^{86} +(177.569 - 129.011i) q^{87} +(-1082.40 + 786.407i) q^{88} +(-378.143 - 274.737i) q^{89} +(-91.8280 + 503.567i) q^{90} +(141.378 - 102.717i) q^{91} +(173.354 - 533.530i) q^{92} +114.678 q^{93} +(244.272 - 751.791i) q^{94} +(-919.291 - 495.704i) q^{95} +(-85.4873 - 263.103i) q^{96} +(-529.272 - 1628.93i) q^{97} +(467.135 + 339.393i) q^{98} +1395.87 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.51671 1.10196i −0.536239 0.389600i 0.286447 0.958096i \(-0.407526\pi\)
−0.822686 + 0.568496i \(0.807526\pi\)
\(3\) −0.496278 1.52739i −0.0955088 0.293946i 0.891877 0.452278i \(-0.149388\pi\)
−0.987386 + 0.158332i \(0.949388\pi\)
\(4\) −1.38603 4.26575i −0.173253 0.533219i
\(5\) 2.00572 10.9990i 0.179397 0.983777i
\(6\) −0.930402 + 2.86348i −0.0633059 + 0.194835i
\(7\) −5.91678 −0.319476 −0.159738 0.987159i \(-0.551065\pi\)
−0.159738 + 0.987159i \(0.551065\pi\)
\(8\) −7.23313 + 22.2613i −0.319662 + 0.983819i
\(9\) 19.7568 14.3542i 0.731735 0.531636i
\(10\) −15.1625 + 14.4720i −0.479479 + 0.457646i
\(11\) 46.2426 + 33.5972i 1.26752 + 0.920904i 0.999101 0.0423993i \(-0.0135002\pi\)
0.268415 + 0.963303i \(0.413500\pi\)
\(12\) −5.82760 + 4.23400i −0.140190 + 0.101854i
\(13\) −23.8943 + 17.3602i −0.509777 + 0.370374i −0.812739 0.582628i \(-0.802024\pi\)
0.302962 + 0.953003i \(0.402024\pi\)
\(14\) 8.97406 + 6.52004i 0.171316 + 0.124468i
\(15\) −17.7951 + 2.39503i −0.306311 + 0.0412264i
\(16\) 6.47220 4.70233i 0.101128 0.0734739i
\(17\) 16.1964 49.8475i 0.231071 0.711165i −0.766547 0.642188i \(-0.778027\pi\)
0.997618 0.0689764i \(-0.0219733\pi\)
\(18\) −45.7831 −0.599510
\(19\) 28.8671 88.8439i 0.348557 1.07275i −0.611096 0.791557i \(-0.709271\pi\)
0.959652 0.281190i \(-0.0907291\pi\)
\(20\) −49.6988 + 6.68896i −0.555650 + 0.0747848i
\(21\) 2.93637 + 9.03722i 0.0305128 + 0.0939087i
\(22\) −33.1141 101.915i −0.320907 0.987649i
\(23\) 101.186 + 73.5160i 0.917338 + 0.666485i 0.942860 0.333189i \(-0.108125\pi\)
−0.0255223 + 0.999674i \(0.508125\pi\)
\(24\) 37.5912 0.319720
\(25\) −116.954 44.1216i −0.935634 0.352973i
\(26\) 55.3710 0.417660
\(27\) −66.8097 48.5401i −0.476205 0.345983i
\(28\) 8.20082 + 25.2395i 0.0553503 + 0.170351i
\(29\) 42.2327 + 129.979i 0.270428 + 0.832293i 0.990393 + 0.138282i \(0.0441580\pi\)
−0.719965 + 0.694011i \(0.755842\pi\)
\(30\) 29.6292 + 15.9768i 0.180318 + 0.0972317i
\(31\) −22.0658 + 67.9115i −0.127843 + 0.393460i −0.994408 0.105603i \(-0.966323\pi\)
0.866565 + 0.499064i \(0.166323\pi\)
\(32\) 172.257 0.951594
\(33\) 28.3668 87.3040i 0.149637 0.460535i
\(34\) −79.4951 + 57.7566i −0.400979 + 0.291329i
\(35\) −11.8674 + 65.0785i −0.0573131 + 0.314293i
\(36\) −88.6149 64.3825i −0.410254 0.298067i
\(37\) −149.002 + 108.256i −0.662048 + 0.481006i −0.867354 0.497692i \(-0.834181\pi\)
0.205306 + 0.978698i \(0.434181\pi\)
\(38\) −141.685 + 102.940i −0.604852 + 0.439451i
\(39\) 38.3741 + 27.8804i 0.157558 + 0.114473i
\(40\) 230.343 + 124.207i 0.910512 + 0.490970i
\(41\) −28.3279 + 20.5814i −0.107904 + 0.0783971i −0.640429 0.768017i \(-0.721243\pi\)
0.532525 + 0.846415i \(0.321243\pi\)
\(42\) 5.50499 16.9426i 0.0202247 0.0622453i
\(43\) 185.374 0.657425 0.328712 0.944430i \(-0.393385\pi\)
0.328712 + 0.944430i \(0.393385\pi\)
\(44\) 79.2239 243.826i 0.271442 0.835413i
\(45\) −118.254 246.095i −0.391741 0.815238i
\(46\) −72.4588 223.005i −0.232249 0.714790i
\(47\) 130.295 + 401.007i 0.404372 + 1.24453i 0.921419 + 0.388571i \(0.127031\pi\)
−0.517047 + 0.855957i \(0.672969\pi\)
\(48\) −10.3943 7.55189i −0.0312560 0.0227088i
\(49\) −307.992 −0.897935
\(50\) 128.766 + 195.798i 0.364205 + 0.553801i
\(51\) −84.1744 −0.231113
\(52\) 107.173 + 77.8655i 0.285811 + 0.207654i
\(53\) −214.260 659.426i −0.555301 1.70904i −0.695148 0.718867i \(-0.744661\pi\)
0.139847 0.990173i \(-0.455339\pi\)
\(54\) 47.8420 + 147.243i 0.120564 + 0.371059i
\(55\) 462.284 441.234i 1.13335 1.08175i
\(56\) 42.7968 131.715i 0.102124 0.314307i
\(57\) −150.025 −0.348620
\(58\) 79.1762 243.679i 0.179247 0.551667i
\(59\) −466.375 + 338.841i −1.02910 + 0.747684i −0.968128 0.250455i \(-0.919420\pi\)
−0.0609711 + 0.998140i \(0.519420\pi\)
\(60\) 34.8811 + 72.5897i 0.0750521 + 0.156188i
\(61\) 29.5121 + 21.4418i 0.0619448 + 0.0450056i 0.618327 0.785921i \(-0.287811\pi\)
−0.556382 + 0.830927i \(0.687811\pi\)
\(62\) 108.303 78.6867i 0.221847 0.161181i
\(63\) −116.897 + 84.9306i −0.233772 + 0.169845i
\(64\) −313.042 227.438i −0.611410 0.444215i
\(65\) 143.019 + 297.633i 0.272913 + 0.567950i
\(66\) −139.229 + 101.156i −0.259666 + 0.188658i
\(67\) −48.1248 + 148.113i −0.0877519 + 0.270073i −0.985297 0.170850i \(-0.945349\pi\)
0.897545 + 0.440923i \(0.145349\pi\)
\(68\) −235.086 −0.419240
\(69\) 62.0710 191.035i 0.108297 0.333303i
\(70\) 89.7130 85.6279i 0.153182 0.146207i
\(71\) 120.884 + 372.044i 0.202061 + 0.621880i 0.999821 + 0.0189054i \(0.00601814\pi\)
−0.797760 + 0.602975i \(0.793982\pi\)
\(72\) 176.639 + 543.638i 0.289126 + 0.889838i
\(73\) 946.113 + 687.392i 1.51691 + 1.10210i 0.962994 + 0.269523i \(0.0868659\pi\)
0.553913 + 0.832575i \(0.313134\pi\)
\(74\) 345.287 0.542416
\(75\) −9.34899 + 200.531i −0.0143937 + 0.308738i
\(76\) −418.997 −0.632397
\(77\) −273.608 198.788i −0.404941 0.294207i
\(78\) −27.4794 84.5730i −0.0398902 0.122769i
\(79\) 323.388 + 995.287i 0.460557 + 1.41745i 0.864485 + 0.502659i \(0.167645\pi\)
−0.403927 + 0.914791i \(0.632355\pi\)
\(80\) −38.7393 80.6190i −0.0541398 0.112668i
\(81\) 162.771 500.956i 0.223279 0.687183i
\(82\) 65.6451 0.0884060
\(83\) 289.936 892.333i 0.383430 1.18007i −0.554184 0.832395i \(-0.686969\pi\)
0.937613 0.347680i \(-0.113031\pi\)
\(84\) 34.4806 25.0517i 0.0447875 0.0325400i
\(85\) −515.785 278.124i −0.658174 0.354903i
\(86\) −281.159 204.274i −0.352537 0.256133i
\(87\) 177.569 129.011i 0.218821 0.158983i
\(88\) −1082.40 + 786.407i −1.31118 + 0.952628i
\(89\) −378.143 274.737i −0.450371 0.327214i 0.339371 0.940653i \(-0.389786\pi\)
−0.789742 + 0.613439i \(0.789786\pi\)
\(90\) −91.8280 + 503.567i −0.107550 + 0.589784i
\(91\) 141.378 102.717i 0.162862 0.118326i
\(92\) 173.354 533.530i 0.196451 0.604613i
\(93\) 114.678 0.127866
\(94\) 244.272 751.791i 0.268029 0.824908i
\(95\) −919.291 495.704i −0.992813 0.535349i
\(96\) −85.4873 263.103i −0.0908856 0.279717i
\(97\) −529.272 1628.93i −0.554014 1.70508i −0.698532 0.715579i \(-0.746163\pi\)
0.144518 0.989502i \(-0.453837\pi\)
\(98\) 467.135 + 339.393i 0.481508 + 0.349836i
\(99\) 1395.87 1.41707
\(100\) −26.1103 + 560.051i −0.0261103 + 0.560051i
\(101\) 1054.59 1.03896 0.519482 0.854482i \(-0.326125\pi\)
0.519482 + 0.854482i \(0.326125\pi\)
\(102\) 127.668 + 92.7565i 0.123932 + 0.0900418i
\(103\) 28.4548 + 87.5749i 0.0272207 + 0.0837768i 0.963744 0.266829i \(-0.0859758\pi\)
−0.936523 + 0.350606i \(0.885976\pi\)
\(104\) −213.631 657.487i −0.201425 0.619922i
\(105\) 105.290 14.1709i 0.0978591 0.0131708i
\(106\) −401.687 + 1236.26i −0.368069 + 1.13280i
\(107\) −66.9507 −0.0604894 −0.0302447 0.999543i \(-0.509629\pi\)
−0.0302447 + 0.999543i \(0.509629\pi\)
\(108\) −114.460 + 352.271i −0.101981 + 0.313864i
\(109\) −160.237 + 116.419i −0.140806 + 0.102302i −0.655958 0.754797i \(-0.727735\pi\)
0.515152 + 0.857099i \(0.327735\pi\)
\(110\) −1187.37 + 159.808i −1.02920 + 0.138519i
\(111\) 239.296 + 173.858i 0.204621 + 0.148666i
\(112\) −38.2946 + 27.8227i −0.0323080 + 0.0234732i
\(113\) −1326.05 + 963.435i −1.10394 + 0.802056i −0.981698 0.190445i \(-0.939007\pi\)
−0.122237 + 0.992501i \(0.539007\pi\)
\(114\) 227.545 + 165.321i 0.186943 + 0.135822i
\(115\) 1011.55 965.490i 0.820240 0.782890i
\(116\) 495.922 360.309i 0.396942 0.288395i
\(117\) −222.884 + 685.967i −0.176117 + 0.542032i
\(118\) 1080.74 0.843141
\(119\) −95.8308 + 294.937i −0.0738218 + 0.227200i
\(120\) 75.3974 413.464i 0.0573568 0.314533i
\(121\) 598.304 + 1841.39i 0.449515 + 1.38346i
\(122\) −21.1334 65.0420i −0.0156830 0.0482675i
\(123\) 45.4944 + 33.0536i 0.0333503 + 0.0242304i
\(124\) 320.277 0.231950
\(125\) −719.869 + 1197.88i −0.515096 + 0.857132i
\(126\) 270.889 0.191529
\(127\) −404.153 293.635i −0.282384 0.205164i 0.437572 0.899183i \(-0.355838\pi\)
−0.719957 + 0.694019i \(0.755838\pi\)
\(128\) −201.675 620.692i −0.139263 0.428609i
\(129\) −91.9971 283.138i −0.0627898 0.193247i
\(130\) 111.059 609.024i 0.0749269 0.410884i
\(131\) 80.0952 246.508i 0.0534195 0.164408i −0.920787 0.390065i \(-0.872453\pi\)
0.974207 + 0.225656i \(0.0724527\pi\)
\(132\) −411.734 −0.271491
\(133\) −170.801 + 525.670i −0.111356 + 0.342717i
\(134\) 236.205 171.613i 0.152276 0.110635i
\(135\) −667.891 + 637.479i −0.425800 + 0.406411i
\(136\) 992.519 + 721.107i 0.625792 + 0.454665i
\(137\) 123.196 89.5073i 0.0768275 0.0558184i −0.548709 0.836014i \(-0.684880\pi\)
0.625536 + 0.780195i \(0.284880\pi\)
\(138\) −304.656 + 221.345i −0.187928 + 0.136537i
\(139\) −1835.62 1333.66i −1.12011 0.813809i −0.135885 0.990725i \(-0.543388\pi\)
−0.984226 + 0.176916i \(0.943388\pi\)
\(140\) 294.057 39.5771i 0.177517 0.0238920i
\(141\) 547.830 398.022i 0.327203 0.237727i
\(142\) 226.629 697.493i 0.133932 0.412200i
\(143\) −1688.19 −0.987229
\(144\) 60.3721 185.806i 0.0349376 0.107527i
\(145\) 1514.34 203.815i 0.867304 0.116730i
\(146\) −677.506 2085.15i −0.384047 1.18197i
\(147\) 152.850 + 470.423i 0.0857607 + 0.263944i
\(148\) 668.315 + 485.559i 0.371184 + 0.269681i
\(149\) 1563.68 0.859744 0.429872 0.902890i \(-0.358559\pi\)
0.429872 + 0.902890i \(0.358559\pi\)
\(150\) 235.156 293.846i 0.128003 0.159949i
\(151\) −2328.94 −1.25514 −0.627571 0.778559i \(-0.715951\pi\)
−0.627571 + 0.778559i \(0.715951\pi\)
\(152\) 1768.98 + 1285.24i 0.943968 + 0.685833i
\(153\) −395.530 1217.32i −0.208998 0.643230i
\(154\) 195.929 + 603.007i 0.102522 + 0.315530i
\(155\) 702.698 + 378.912i 0.364142 + 0.196354i
\(156\) 65.7433 202.337i 0.0337415 0.103846i
\(157\) −290.519 −0.147681 −0.0738406 0.997270i \(-0.523526\pi\)
−0.0738406 + 0.997270i \(0.523526\pi\)
\(158\) 606.275 1865.92i 0.305270 0.939525i
\(159\) −900.866 + 654.517i −0.449329 + 0.326457i
\(160\) 345.499 1894.65i 0.170713 0.936156i
\(161\) −598.696 434.978i −0.293068 0.212926i
\(162\) −798.908 + 580.441i −0.387458 + 0.281505i
\(163\) 1590.13 1155.30i 0.764102 0.555153i −0.136064 0.990700i \(-0.543445\pi\)
0.900166 + 0.435547i \(0.143445\pi\)
\(164\) 127.059 + 92.3135i 0.0604976 + 0.0439541i
\(165\) −903.357 487.112i −0.426220 0.229828i
\(166\) −1423.06 + 1033.91i −0.665367 + 0.483418i
\(167\) −634.745 + 1953.54i −0.294120 + 0.905208i 0.689396 + 0.724385i \(0.257876\pi\)
−0.983516 + 0.180823i \(0.942124\pi\)
\(168\) −222.419 −0.102143
\(169\) −409.350 + 1259.85i −0.186322 + 0.573440i
\(170\) 475.817 + 990.207i 0.214668 + 0.446738i
\(171\) −704.958 2169.64i −0.315260 0.970271i
\(172\) −256.933 790.759i −0.113901 0.350551i
\(173\) 1034.32 + 751.479i 0.454555 + 0.330254i 0.791392 0.611310i \(-0.209357\pi\)
−0.336836 + 0.941563i \(0.609357\pi\)
\(174\) −411.486 −0.179280
\(175\) 691.993 + 261.058i 0.298913 + 0.112767i
\(176\) 457.276 0.195844
\(177\) 748.994 + 544.176i 0.318067 + 0.231089i
\(178\) 270.786 + 833.393i 0.114024 + 0.350930i
\(179\) 144.118 + 443.549i 0.0601781 + 0.185209i 0.976626 0.214944i \(-0.0689569\pi\)
−0.916448 + 0.400153i \(0.868957\pi\)
\(180\) −885.877 + 845.538i −0.366830 + 0.350126i
\(181\) 360.349 1109.04i 0.147981 0.455439i −0.849401 0.527748i \(-0.823037\pi\)
0.997382 + 0.0723088i \(0.0230367\pi\)
\(182\) −327.619 −0.133432
\(183\) 18.1037 55.7175i 0.00731292 0.0225069i
\(184\) −2368.45 + 1720.78i −0.948938 + 0.689444i
\(185\) 891.850 + 1856.00i 0.354433 + 0.737598i
\(186\) −173.933 126.370i −0.0685667 0.0498167i
\(187\) 2423.70 1760.92i 0.947801 0.688618i
\(188\) 1530.00 1111.61i 0.593547 0.431237i
\(189\) 395.298 + 287.201i 0.152136 + 0.110533i
\(190\) 848.056 + 1764.86i 0.323813 + 0.673875i
\(191\) −1809.34 + 1314.56i −0.685440 + 0.498001i −0.875158 0.483837i \(-0.839243\pi\)
0.189718 + 0.981839i \(0.439243\pi\)
\(192\) −192.030 + 591.009i −0.0721802 + 0.222148i
\(193\) 1902.42 0.709530 0.354765 0.934956i \(-0.384561\pi\)
0.354765 + 0.934956i \(0.384561\pi\)
\(194\) −992.257 + 3053.85i −0.367216 + 1.13017i
\(195\) 383.623 366.154i 0.140881 0.134466i
\(196\) 426.885 + 1313.82i 0.155570 + 0.478796i
\(197\) 559.983 + 1723.45i 0.202524 + 0.623304i 0.999806 + 0.0196971i \(0.00627019\pi\)
−0.797282 + 0.603607i \(0.793730\pi\)
\(198\) −2117.13 1538.19i −0.759889 0.552091i
\(199\) −3011.24 −1.07267 −0.536335 0.844005i \(-0.680192\pi\)
−0.536335 + 0.844005i \(0.680192\pi\)
\(200\) 1828.15 2284.41i 0.646348 0.807662i
\(201\) 250.109 0.0877678
\(202\) −1599.50 1162.11i −0.557132 0.404780i
\(203\) −249.882 769.058i −0.0863954 0.265898i
\(204\) 116.668 + 359.067i 0.0400411 + 0.123234i
\(205\) 169.557 + 352.858i 0.0577675 + 0.120218i
\(206\) 53.3459 164.182i 0.0180427 0.0555296i
\(207\) 3054.38 1.02558
\(208\) −73.0153 + 224.718i −0.0243399 + 0.0749105i
\(209\) 4319.80 3138.52i 1.42970 1.03874i
\(210\) −175.310 94.5313i −0.0576072 0.0310632i
\(211\) −3153.40 2291.08i −1.02886 0.747509i −0.0607784 0.998151i \(-0.519358\pi\)
−0.968080 + 0.250642i \(0.919358\pi\)
\(212\) −2515.98 + 1827.96i −0.815085 + 0.592194i
\(213\) 508.263 369.275i 0.163501 0.118790i
\(214\) 101.545 + 73.7767i 0.0324368 + 0.0235667i
\(215\) 371.808 2038.92i 0.117940 0.646759i
\(216\) 1563.81 1136.17i 0.492609 0.357901i
\(217\) 130.558 401.818i 0.0408428 0.125701i
\(218\) 371.321 0.115362
\(219\) 580.378 1786.22i 0.179079 0.551148i
\(220\) −2522.93 1360.43i −0.773164 0.416909i
\(221\) 478.362 + 1472.25i 0.145602 + 0.448118i
\(222\) −171.358 527.387i −0.0518055 0.159441i
\(223\) −2941.83 2137.36i −0.883406 0.641832i 0.0507445 0.998712i \(-0.483841\pi\)
−0.934150 + 0.356880i \(0.883841\pi\)
\(224\) −1019.21 −0.304012
\(225\) −2943.98 + 807.078i −0.872289 + 0.239134i
\(226\) 3072.90 0.904454
\(227\) −562.815 408.909i −0.164561 0.119561i 0.502457 0.864602i \(-0.332430\pi\)
−0.667018 + 0.745042i \(0.732430\pi\)
\(228\) 207.939 + 639.970i 0.0603995 + 0.185891i
\(229\) −1706.92 5253.37i −0.492562 1.51595i −0.820722 0.571328i \(-0.806428\pi\)
0.328160 0.944622i \(-0.393572\pi\)
\(230\) −2598.16 + 349.686i −0.744859 + 0.100250i
\(231\) −167.840 + 516.559i −0.0478055 + 0.147130i
\(232\) −3198.97 −0.905271
\(233\) −1653.81 + 5089.90i −0.464998 + 1.43112i 0.393986 + 0.919116i \(0.371096\pi\)
−0.858985 + 0.512001i \(0.828904\pi\)
\(234\) 1093.96 794.806i 0.305616 0.222043i
\(235\) 4671.99 628.802i 1.29688 0.174547i
\(236\) 2091.82 + 1519.80i 0.576974 + 0.419196i
\(237\) 1359.70 987.879i 0.372666 0.270758i
\(238\) 470.355 341.733i 0.128103 0.0930726i
\(239\) 4030.36 + 2928.23i 1.09081 + 0.792517i 0.979535 0.201273i \(-0.0645079\pi\)
0.111271 + 0.993790i \(0.464508\pi\)
\(240\) −103.911 + 99.1793i −0.0279476 + 0.0266750i
\(241\) 1105.03 802.852i 0.295358 0.214590i −0.430230 0.902719i \(-0.641568\pi\)
0.725588 + 0.688129i \(0.241568\pi\)
\(242\) 1121.68 3452.17i 0.297951 0.916998i
\(243\) −3075.63 −0.811941
\(244\) 50.5608 155.610i 0.0132657 0.0408275i
\(245\) −617.745 + 3387.59i −0.161087 + 0.883368i
\(246\) −32.5783 100.266i −0.00844355 0.0259866i
\(247\) 852.591 + 2624.01i 0.219632 + 0.675957i
\(248\) −1352.19 982.425i −0.346227 0.251549i
\(249\) −1506.83 −0.383499
\(250\) 2411.84 1023.57i 0.610154 0.258946i
\(251\) −56.3223 −0.0141635 −0.00708174 0.999975i \(-0.502254\pi\)
−0.00708174 + 0.999975i \(0.502254\pi\)
\(252\) 524.315 + 380.937i 0.131066 + 0.0952254i
\(253\) 2209.18 + 6799.15i 0.548971 + 1.68956i
\(254\) 289.412 + 890.719i 0.0714934 + 0.220034i
\(255\) −168.830 + 925.831i −0.0414610 + 0.227364i
\(256\) −1334.66 + 4107.67i −0.325845 + 1.00285i
\(257\) −587.079 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(258\) −172.472 + 530.815i −0.0416188 + 0.128090i
\(259\) 881.612 640.529i 0.211509 0.153670i
\(260\) 1071.40 1022.61i 0.255559 0.243922i
\(261\) 2700.13 + 1961.76i 0.640359 + 0.465248i
\(262\) −393.122 + 285.620i −0.0926991 + 0.0673498i
\(263\) 388.238 282.072i 0.0910258 0.0661341i −0.541341 0.840803i \(-0.682083\pi\)
0.632367 + 0.774669i \(0.282083\pi\)
\(264\) 1738.32 + 1262.96i 0.405250 + 0.294431i
\(265\) −7682.74 + 1034.02i −1.78093 + 0.239696i
\(266\) 838.321 609.076i 0.193236 0.140394i
\(267\) −231.966 + 713.916i −0.0531688 + 0.163637i
\(268\) 698.515 0.159211
\(269\) 1495.78 4603.53i 0.339030 1.04343i −0.625673 0.780086i \(-0.715175\pi\)
0.964703 0.263342i \(-0.0848246\pi\)
\(270\) 1715.47 230.885i 0.386668 0.0520416i
\(271\) 1441.77 + 4437.32i 0.323179 + 0.994643i 0.972256 + 0.233920i \(0.0751553\pi\)
−0.649077 + 0.760723i \(0.724845\pi\)
\(272\) −129.573 398.784i −0.0288842 0.0888964i
\(273\) −227.051 164.962i −0.0503361 0.0365713i
\(274\) −285.486 −0.0629448
\(275\) −3925.90 5969.64i −0.860876 1.30903i
\(276\) −900.939 −0.196486
\(277\) −6762.05 4912.91i −1.46676 1.06566i −0.981537 0.191271i \(-0.938739\pi\)
−0.485221 0.874392i \(-0.661261\pi\)
\(278\) 1314.48 + 4045.55i 0.283587 + 0.872791i
\(279\) 538.864 + 1658.45i 0.115631 + 0.355874i
\(280\) −1362.89 734.904i −0.290887 0.156853i
\(281\) 1708.18 5257.23i 0.362638 1.11609i −0.588809 0.808272i \(-0.700403\pi\)
0.951447 0.307813i \(-0.0995970\pi\)
\(282\) −1269.50 −0.268077
\(283\) −161.101 + 495.817i −0.0338390 + 0.104146i −0.966549 0.256481i \(-0.917437\pi\)
0.932710 + 0.360626i \(0.117437\pi\)
\(284\) 1419.50 1031.33i 0.296591 0.215486i
\(285\) −300.908 + 1650.12i −0.0625413 + 0.342964i
\(286\) 2560.50 + 1860.31i 0.529390 + 0.384625i
\(287\) 167.610 121.776i 0.0344729 0.0250460i
\(288\) 3403.25 2472.61i 0.696314 0.505902i
\(289\) 1752.25 + 1273.08i 0.356656 + 0.259126i
\(290\) −2521.41 1359.61i −0.510560 0.275307i
\(291\) −2225.34 + 1616.81i −0.448288 + 0.325700i
\(292\) 1620.90 4988.63i 0.324850 0.999786i
\(293\) −2209.70 −0.440587 −0.220294 0.975434i \(-0.570702\pi\)
−0.220294 + 0.975434i \(0.570702\pi\)
\(294\) 286.556 881.929i 0.0568445 0.174949i
\(295\) 2791.48 + 5809.26i 0.550937 + 1.14654i
\(296\) −1332.17 4100.01i −0.261591 0.805094i
\(297\) −1458.64 4489.24i −0.284980 0.877078i
\(298\) −2371.66 1723.11i −0.461028 0.334957i
\(299\) −3694.03 −0.714486
\(300\) 868.373 238.061i 0.167118 0.0458148i
\(301\) −1096.82 −0.210032
\(302\) 3532.33 + 2566.39i 0.673056 + 0.489004i
\(303\) −523.368 1610.76i −0.0992301 0.305399i
\(304\) −230.939 710.758i −0.0435700 0.134095i
\(305\) 295.030 281.596i 0.0553881 0.0528660i
\(306\) −741.524 + 2282.18i −0.138530 + 0.426351i
\(307\) 10095.6 1.87683 0.938413 0.345516i \(-0.112296\pi\)
0.938413 + 0.345516i \(0.112296\pi\)
\(308\) −468.751 + 1442.67i −0.0867193 + 0.266895i
\(309\) 119.639 86.9230i 0.0220260 0.0160028i
\(310\) −648.246 1349.04i −0.118767 0.247163i
\(311\) −4497.20 3267.41i −0.819977 0.595748i 0.0967289 0.995311i \(-0.469162\pi\)
−0.916706 + 0.399563i \(0.869162\pi\)
\(312\) −898.217 + 652.593i −0.162986 + 0.118416i
\(313\) 4746.67 3448.66i 0.857180 0.622778i −0.0699360 0.997551i \(-0.522279\pi\)
0.927116 + 0.374773i \(0.122279\pi\)
\(314\) 440.634 + 320.139i 0.0791923 + 0.0575366i
\(315\) 699.686 + 1456.09i 0.125152 + 0.260449i
\(316\) 3797.42 2758.99i 0.676018 0.491156i
\(317\) −98.5888 + 303.425i −0.0174678 + 0.0537604i −0.959410 0.282013i \(-0.908998\pi\)
0.941943 + 0.335774i \(0.108998\pi\)
\(318\) 2087.60 0.368135
\(319\) −2413.98 + 7429.47i −0.423690 + 1.30398i
\(320\) −3129.46 + 2986.96i −0.546694 + 0.521800i
\(321\) 33.2262 + 102.260i 0.00577727 + 0.0177806i
\(322\) 428.723 + 1319.47i 0.0741982 + 0.228358i
\(323\) −3961.10 2877.91i −0.682358 0.495762i
\(324\) −2362.56 −0.405103
\(325\) 3560.50 976.097i 0.607696 0.166597i
\(326\) −3684.86 −0.626029
\(327\) 257.338 + 186.967i 0.0435194 + 0.0316187i
\(328\) −253.270 779.484i −0.0426356 0.131219i
\(329\) −770.927 2372.67i −0.129187 0.397597i
\(330\) 833.356 + 1734.27i 0.139014 + 0.289298i
\(331\) 904.957 2785.17i 0.150275 0.462498i −0.847377 0.530992i \(-0.821819\pi\)
0.997652 + 0.0684939i \(0.0218194\pi\)
\(332\) −4208.33 −0.695669
\(333\) −1389.88 + 4277.60i −0.228723 + 0.703938i
\(334\) 3115.44 2263.50i 0.510388 0.370818i
\(335\) 1532.56 + 826.395i 0.249949 + 0.134779i
\(336\) 61.5007 + 44.6829i 0.00998554 + 0.00725492i
\(337\) −4174.94 + 3033.27i −0.674848 + 0.490306i −0.871644 0.490139i \(-0.836946\pi\)
0.196797 + 0.980444i \(0.436946\pi\)
\(338\) 2009.16 1459.74i 0.323326 0.234910i
\(339\) 2129.63 + 1547.27i 0.341196 + 0.247894i
\(340\) −471.516 + 2585.70i −0.0752104 + 0.412439i
\(341\) −3302.02 + 2399.06i −0.524382 + 0.380986i
\(342\) −1321.63 + 4067.55i −0.208963 + 0.643123i
\(343\) 3851.78 0.606345
\(344\) −1340.83 + 4126.66i −0.210154 + 0.646787i
\(345\) −1976.69 1065.88i −0.308467 0.166333i
\(346\) −740.672 2279.55i −0.115083 0.354190i
\(347\) 540.620 + 1663.86i 0.0836369 + 0.257408i 0.984126 0.177470i \(-0.0567914\pi\)
−0.900489 + 0.434878i \(0.856791\pi\)
\(348\) −796.446 578.652i −0.122684 0.0891351i
\(349\) −1775.11 −0.272262 −0.136131 0.990691i \(-0.543467\pi\)
−0.136131 + 0.990691i \(0.543467\pi\)
\(350\) −761.879 1158.50i −0.116355 0.176926i
\(351\) 2439.04 0.370901
\(352\) 7965.61 + 5787.35i 1.20616 + 0.876327i
\(353\) 101.976 + 313.851i 0.0153758 + 0.0473218i 0.958450 0.285260i \(-0.0920801\pi\)
−0.943074 + 0.332582i \(0.892080\pi\)
\(354\) −536.350 1650.72i −0.0805274 0.247838i
\(355\) 4334.56 583.388i 0.648041 0.0872197i
\(356\) −647.843 + 1993.86i −0.0964484 + 0.296838i
\(357\) 498.042 0.0738352
\(358\) 270.186 831.548i 0.0398877 0.122762i
\(359\) −3398.46 + 2469.12i −0.499620 + 0.362995i −0.808872 0.587985i \(-0.799921\pi\)
0.309252 + 0.950980i \(0.399921\pi\)
\(360\) 6333.74 852.457i 0.927271 0.124801i
\(361\) −1510.88 1097.72i −0.220277 0.160040i
\(362\) −1768.66 + 1285.01i −0.256792 + 0.186570i
\(363\) 2515.59 1827.68i 0.363731 0.264266i
\(364\) −634.118 460.713i −0.0913099 0.0663405i
\(365\) 9458.23 9027.55i 1.35635 1.29458i
\(366\) −88.8563 + 64.5579i −0.0126901 + 0.00921993i
\(367\) −3499.21 + 10769.5i −0.497704 + 1.53177i 0.314997 + 0.949093i \(0.397997\pi\)
−0.812700 + 0.582682i \(0.802003\pi\)
\(368\) 1000.59 0.141738
\(369\) −264.240 + 813.248i −0.0372786 + 0.114732i
\(370\) 692.548 3797.79i 0.0973077 0.533616i
\(371\) 1267.73 + 3901.68i 0.177405 + 0.545998i
\(372\) −158.947 489.188i −0.0221532 0.0681806i
\(373\) −6524.79 4740.54i −0.905740 0.658059i 0.0341938 0.999415i \(-0.489114\pi\)
−0.939934 + 0.341357i \(0.889114\pi\)
\(374\) −5616.52 −0.776533
\(375\) 2186.88 + 505.038i 0.301147 + 0.0695468i
\(376\) −9869.36 −1.35365
\(377\) −3265.59 2372.59i −0.446118 0.324124i
\(378\) −283.071 871.203i −0.0385175 0.118545i
\(379\) 804.469 + 2475.90i 0.109031 + 0.335563i 0.990655 0.136389i \(-0.0435496\pi\)
−0.881624 + 0.471952i \(0.843550\pi\)
\(380\) −840.389 + 4608.53i −0.113450 + 0.622138i
\(381\) −247.921 + 763.023i −0.0333370 + 0.102601i
\(382\) 4192.83 0.561581
\(383\) 2941.06 9051.66i 0.392380 1.20762i −0.538604 0.842559i \(-0.681048\pi\)
0.930984 0.365061i \(-0.118952\pi\)
\(384\) −847.950 + 616.072i −0.112687 + 0.0818718i
\(385\) −2735.24 + 2610.69i −0.362079 + 0.345592i
\(386\) −2885.42 2096.38i −0.380477 0.276433i
\(387\) 3662.40 2660.89i 0.481061 0.349511i
\(388\) −6215.03 + 4515.48i −0.813197 + 0.590822i
\(389\) −3945.71 2866.72i −0.514281 0.373647i 0.300164 0.953888i \(-0.402959\pi\)
−0.814445 + 0.580241i \(0.802959\pi\)
\(390\) −985.331 + 132.616i −0.127934 + 0.0172186i
\(391\) 5303.45 3853.18i 0.685951 0.498373i
\(392\) 2227.74 6856.29i 0.287036 0.883405i
\(393\) −416.262 −0.0534291
\(394\) 1049.83 3231.06i 0.134238 0.413143i
\(395\) 11595.7 1560.67i 1.47708 0.198800i
\(396\) −1934.71 5954.43i −0.245512 0.755609i
\(397\) 230.334 + 708.897i 0.0291188 + 0.0896184i 0.964560 0.263865i \(-0.0849972\pi\)
−0.935441 + 0.353483i \(0.884997\pi\)
\(398\) 4567.19 + 3318.26i 0.575207 + 0.417912i
\(399\) 887.666 0.111376
\(400\) −964.425 + 264.393i −0.120553 + 0.0330491i
\(401\) 14597.9 1.81792 0.908960 0.416883i \(-0.136878\pi\)
0.908960 + 0.416883i \(0.136878\pi\)
\(402\) −379.343 275.609i −0.0470645 0.0341944i
\(403\) −651.713 2005.77i −0.0805562 0.247926i
\(404\) −1461.69 4498.60i −0.180004 0.553995i
\(405\) −5183.53 2795.08i −0.635979 0.342936i
\(406\) −468.469 + 1441.80i −0.0572653 + 0.176244i
\(407\) −10527.4 −1.28212
\(408\) 608.844 1873.83i 0.0738781 0.227374i
\(409\) −1138.26 + 826.991i −0.137612 + 0.0999807i −0.654461 0.756095i \(-0.727105\pi\)
0.516850 + 0.856076i \(0.327105\pi\)
\(410\) 131.666 722.028i 0.0158598 0.0869718i
\(411\) −197.852 143.748i −0.0237453 0.0172520i
\(412\) 334.134 242.762i 0.0399553 0.0290292i
\(413\) 2759.44 2004.85i 0.328773 0.238867i
\(414\) −4632.62 3365.79i −0.549953 0.399564i
\(415\) −9233.20 4978.77i −1.09214 0.588911i
\(416\) −4115.96 + 2990.42i −0.485100 + 0.352446i
\(417\) −1126.03 + 3465.57i −0.132235 + 0.406978i
\(418\) −10010.4 −1.17135
\(419\) −1471.61 + 4529.15i −0.171582 + 0.528075i −0.999461 0.0328318i \(-0.989547\pi\)
0.827879 + 0.560907i \(0.189547\pi\)
\(420\) −206.384 429.498i −0.0239774 0.0498984i
\(421\) −1185.64 3649.02i −0.137255 0.422429i 0.858679 0.512515i \(-0.171286\pi\)
−0.995934 + 0.0900856i \(0.971286\pi\)
\(422\) 2258.13 + 6949.82i 0.260484 + 0.801687i
\(423\) 8330.34 + 6052.34i 0.957529 + 0.695686i
\(424\) 16229.4 1.85889
\(425\) −4093.60 + 5115.26i −0.467220 + 0.583828i
\(426\) −1177.81 −0.133956
\(427\) −174.617 126.866i −0.0197899 0.0143782i
\(428\) 92.7955 + 285.595i 0.0104800 + 0.0322541i
\(429\) 837.813 + 2578.52i 0.0942890 + 0.290192i
\(430\) −2810.73 + 2682.74i −0.315222 + 0.300868i
\(431\) −901.448 + 2774.37i −0.100745 + 0.310062i −0.988708 0.149853i \(-0.952120\pi\)
0.887963 + 0.459915i \(0.152120\pi\)
\(432\) −660.657 −0.0735784
\(433\) 648.396 1995.56i 0.0719629 0.221479i −0.908606 0.417655i \(-0.862852\pi\)
0.980569 + 0.196175i \(0.0628522\pi\)
\(434\) −640.805 + 465.572i −0.0708747 + 0.0514935i
\(435\) −1062.84 2211.84i −0.117148 0.243792i
\(436\) 718.705 + 522.170i 0.0789443 + 0.0573564i
\(437\) 9452.40 6867.57i 1.03471 0.751763i
\(438\) −2848.60 + 2069.63i −0.310757 + 0.225778i
\(439\) 92.6878 + 67.3416i 0.0100769 + 0.00732127i 0.592812 0.805341i \(-0.298018\pi\)
−0.582735 + 0.812662i \(0.698018\pi\)
\(440\) 6478.67 + 13482.5i 0.701951 + 1.46081i
\(441\) −6084.94 + 4420.97i −0.657050 + 0.477375i
\(442\) 896.814 2760.11i 0.0965093 0.297025i
\(443\) 251.202 0.0269413 0.0134706 0.999909i \(-0.495712\pi\)
0.0134706 + 0.999909i \(0.495712\pi\)
\(444\) 409.967 1261.75i 0.0438202 0.134865i
\(445\) −3780.27 + 3608.13i −0.402701 + 0.384364i
\(446\) 2106.63 + 6483.53i 0.223659 + 0.688350i
\(447\) −776.022 2388.35i −0.0821131 0.252718i
\(448\) 1852.20 + 1345.70i 0.195331 + 0.141916i
\(449\) 9890.92 1.03960 0.519801 0.854287i \(-0.326006\pi\)
0.519801 + 0.854287i \(0.326006\pi\)
\(450\) 5354.53 + 2020.03i 0.560922 + 0.211611i
\(451\) −2001.44 −0.208967
\(452\) 5947.72 + 4321.27i 0.618932 + 0.449680i
\(453\) 1155.80 + 3557.19i 0.119877 + 0.368944i
\(454\) 403.029 + 1240.39i 0.0416632 + 0.128226i
\(455\) −846.215 1761.03i −0.0871893 0.181447i
\(456\) 1085.15 3339.75i 0.111440 0.342978i
\(457\) −3340.55 −0.341935 −0.170967 0.985277i \(-0.554689\pi\)
−0.170967 + 0.985277i \(0.554689\pi\)
\(458\) −3200.07 + 9848.81i −0.326484 + 1.00481i
\(459\) −3501.68 + 2544.12i −0.356088 + 0.258713i
\(460\) −5520.58 2976.83i −0.559561 0.301729i
\(461\) 9858.66 + 7162.73i 0.996016 + 0.723648i 0.961230 0.275747i \(-0.0889251\pi\)
0.0347857 + 0.999395i \(0.488925\pi\)
\(462\) 823.790 598.518i 0.0829571 0.0602719i
\(463\) −8431.33 + 6125.72i −0.846301 + 0.614873i −0.924124 0.382094i \(-0.875203\pi\)
0.0778229 + 0.996967i \(0.475203\pi\)
\(464\) 884.542 + 642.658i 0.0884997 + 0.0642988i
\(465\) 230.012 1261.34i 0.0229388 0.125792i
\(466\) 8117.20 5897.49i 0.806914 0.586257i
\(467\) 4094.04 12600.2i 0.405673 1.24853i −0.514658 0.857395i \(-0.672081\pi\)
0.920332 0.391139i \(-0.127919\pi\)
\(468\) 3235.09 0.319534
\(469\) 284.744 876.352i 0.0280347 0.0862818i
\(470\) −7778.98 4194.61i −0.763441 0.411666i
\(471\) 144.178 + 443.735i 0.0141048 + 0.0434102i
\(472\) −4169.69 12833.0i −0.406622 1.25145i
\(473\) 8572.18 + 6228.05i 0.833296 + 0.605425i
\(474\) −3150.87 −0.305325
\(475\) −7296.07 + 9117.00i −0.704772 + 0.880667i
\(476\) 1390.95 0.133937
\(477\) −13698.6 9952.64i −1.31492 0.955346i
\(478\) −2886.12 8882.57i −0.276168 0.849957i
\(479\) 232.883 + 716.739i 0.0222144 + 0.0683688i 0.961549 0.274633i \(-0.0885563\pi\)
−0.939335 + 0.343002i \(0.888556\pi\)
\(480\) −3065.32 + 412.561i −0.291484 + 0.0392308i
\(481\) 1680.95 5173.42i 0.159344 0.490411i
\(482\) −2560.72 −0.241987
\(483\) −367.260 + 1130.31i −0.0345982 + 0.106482i
\(484\) 7025.65 5104.43i 0.659810 0.479380i
\(485\) −18978.1 + 2554.26i −1.77681 + 0.239140i
\(486\) 4664.84 + 3389.21i 0.435394 + 0.316332i
\(487\) −1593.20 + 1157.53i −0.148244 + 0.107705i −0.659435 0.751762i \(-0.729204\pi\)
0.511191 + 0.859467i \(0.329204\pi\)
\(488\) −690.786 + 501.886i −0.0640787 + 0.0465559i
\(489\) −2553.73 1855.40i −0.236163 0.171583i
\(490\) 4669.91 4457.27i 0.430541 0.410936i
\(491\) −12244.4 + 8896.07i −1.12542 + 0.817666i −0.985022 0.172429i \(-0.944838\pi\)
−0.140398 + 0.990095i \(0.544838\pi\)
\(492\) 77.9420 239.881i 0.00714207 0.0219810i
\(493\) 7163.15 0.654386
\(494\) 1598.40 4919.38i 0.145578 0.448043i
\(495\) 2799.72 15353.1i 0.254218 1.39408i
\(496\) 176.528 + 543.297i 0.0159805 + 0.0491830i
\(497\) −715.247 2201.30i −0.0645538 0.198676i
\(498\) 2285.42 + 1660.46i 0.205647 + 0.149411i
\(499\) 12081.3 1.08384 0.541918 0.840431i \(-0.317698\pi\)
0.541918 + 0.840431i \(0.317698\pi\)
\(500\) 6107.61 + 1410.49i 0.546281 + 0.126158i
\(501\) 3298.83 0.294173
\(502\) 85.4248 + 62.0647i 0.00759501 + 0.00551810i
\(503\) −1951.30 6005.48i −0.172970 0.532348i 0.826565 0.562842i \(-0.190292\pi\)
−0.999535 + 0.0304937i \(0.990292\pi\)
\(504\) −1045.13 3216.59i −0.0923689 0.284282i
\(505\) 2115.20 11599.4i 0.186387 1.02211i
\(506\) 4141.67 12746.8i 0.363873 1.11989i
\(507\) 2127.43 0.186356
\(508\) −692.405 + 2131.00i −0.0604734 + 0.186118i
\(509\) −1730.89 + 1257.57i −0.150728 + 0.109510i −0.660593 0.750744i \(-0.729695\pi\)
0.509865 + 0.860254i \(0.329695\pi\)
\(510\) 1276.29 1218.18i 0.110814 0.105768i
\(511\) −5597.95 4067.15i −0.484616 0.352094i
\(512\) 2326.83 1690.54i 0.200845 0.145922i
\(513\) −6241.09 + 4534.42i −0.537136 + 0.390252i
\(514\) 890.430 + 646.935i 0.0764108 + 0.0555157i
\(515\) 1020.30 137.323i 0.0873010 0.0117498i
\(516\) −1080.29 + 784.873i −0.0921646 + 0.0669615i
\(517\) −7447.53 + 22921.1i −0.633544 + 1.94985i
\(518\) −2042.99 −0.173289
\(519\) 634.488 1952.75i 0.0536627 0.165157i
\(520\) −7660.16 + 1030.98i −0.646000 + 0.0869451i
\(521\) 3873.88 + 11922.6i 0.325754 + 1.00257i 0.971099 + 0.238677i \(0.0767137\pi\)
−0.645345 + 0.763891i \(0.723286\pi\)
\(522\) −1933.55 5950.84i −0.162125 0.498968i
\(523\) 4612.96 + 3351.51i 0.385680 + 0.280213i 0.763683 0.645591i \(-0.223389\pi\)
−0.378003 + 0.925804i \(0.623389\pi\)
\(524\) −1162.56 −0.0969207
\(525\) 55.3160 1186.50i 0.00459845 0.0986343i
\(526\) −899.676 −0.0745774
\(527\) 3027.83 + 2199.85i 0.250274 + 0.181835i
\(528\) −226.936 698.438i −0.0187048 0.0575675i
\(529\) 1074.22 + 3306.10i 0.0882893 + 0.271727i
\(530\) 12792.0 + 6897.74i 1.04839 + 0.565318i
\(531\) −4350.31 + 13388.9i −0.355531 + 1.09421i
\(532\) 2479.11 0.202036
\(533\) 319.578 983.559i 0.0259708 0.0799300i
\(534\) 1138.53 827.190i 0.0922640 0.0670337i
\(535\) −134.284 + 736.388i −0.0108516 + 0.0595081i
\(536\) −2949.09 2142.64i −0.237652 0.172664i
\(537\) 605.949 440.248i 0.0486939 0.0353782i
\(538\) −7341.55 + 5333.95i −0.588321 + 0.427440i
\(539\) −14242.3 10347.7i −1.13815 0.826912i
\(540\) 3645.04 + 1965.50i 0.290477 + 0.156632i
\(541\) 13794.1 10022.0i 1.09622 0.796448i 0.115778 0.993275i \(-0.463064\pi\)
0.980438 + 0.196827i \(0.0630638\pi\)
\(542\) 2702.98 8318.91i 0.214212 0.659276i
\(543\) −1872.77 −0.148008
\(544\) 2789.95 8586.58i 0.219886 0.676740i
\(545\) 959.094 + 1995.94i 0.0753818 + 0.156874i
\(546\) 162.590 + 500.400i 0.0127440 + 0.0392219i
\(547\) 2044.23 + 6291.50i 0.159790 + 0.491783i 0.998615 0.0526188i \(-0.0167568\pi\)
−0.838825 + 0.544401i \(0.816757\pi\)
\(548\) −552.569 401.465i −0.0430741 0.0312951i
\(549\) 890.845 0.0692538
\(550\) −623.810 + 13380.4i −0.0483624 + 1.03735i
\(551\) 12767.0 0.987099
\(552\) 3803.71 + 2763.56i 0.293291 + 0.213088i
\(553\) −1913.42 5888.90i −0.147137 0.452842i
\(554\) 4842.26 + 14903.0i 0.371350 + 1.14290i
\(555\) 2392.22 2283.29i 0.182962 0.174631i
\(556\) −3144.83 + 9678.80i −0.239875 + 0.738260i
\(557\) 567.016 0.0431333 0.0215667 0.999767i \(-0.493135\pi\)
0.0215667 + 0.999767i \(0.493135\pi\)
\(558\) 1010.24 3109.20i 0.0766432 0.235883i
\(559\) −4429.39 + 3218.14i −0.335140 + 0.243493i
\(560\) 229.212 + 477.005i 0.0172964 + 0.0359949i
\(561\) −3892.45 2828.03i −0.292940 0.212833i
\(562\) −8384.05 + 6091.37i −0.629288 + 0.457204i
\(563\) −13555.5 + 9848.62i −1.01473 + 0.737247i −0.965197 0.261526i \(-0.915774\pi\)
−0.0495366 + 0.998772i \(0.515774\pi\)
\(564\) −2457.17 1785.24i −0.183449 0.133284i
\(565\) 7937.09 + 16517.6i 0.591001 + 1.22991i
\(566\) 790.712 574.486i 0.0587210 0.0426633i
\(567\) −963.079 + 2964.05i −0.0713324 + 0.219539i
\(568\) −9156.55 −0.676409
\(569\) 1889.04 5813.88i 0.139179 0.428349i −0.857038 0.515254i \(-0.827698\pi\)
0.996217 + 0.0869048i \(0.0276976\pi\)
\(570\) 2274.75 2171.17i 0.167156 0.159544i
\(571\) −3930.14 12095.7i −0.288041 0.886499i −0.985471 0.169846i \(-0.945673\pi\)
0.697430 0.716653i \(-0.254327\pi\)
\(572\) 2339.88 + 7201.41i 0.171041 + 0.526409i
\(573\) 2905.78 + 2111.17i 0.211851 + 0.153919i
\(574\) −388.408 −0.0282436
\(575\) −8590.49 13062.5i −0.623041 0.947381i
\(576\) −9449.40 −0.683551
\(577\) 8937.40 + 6493.40i 0.644833 + 0.468499i 0.861507 0.507745i \(-0.169521\pi\)
−0.216674 + 0.976244i \(0.569521\pi\)
\(578\) −1254.78 3861.80i −0.0902972 0.277906i
\(579\) −944.130 2905.73i −0.0677663 0.208563i
\(580\) −2968.34 6177.31i −0.212506 0.442239i
\(581\) −1715.49 + 5279.74i −0.122497 + 0.377006i
\(582\) 5156.85 0.367282
\(583\) 12246.9 37692.1i 0.870009 2.67761i
\(584\) −22145.6 + 16089.7i −1.56916 + 1.14006i
\(585\) 7097.88 + 3827.35i 0.501643 + 0.270498i
\(586\) 3351.48 + 2434.99i 0.236260 + 0.171653i
\(587\) −6410.81 + 4657.73i −0.450771 + 0.327504i −0.789900 0.613236i \(-0.789868\pi\)
0.339129 + 0.940740i \(0.389868\pi\)
\(588\) 1794.85 1304.04i 0.125882 0.0914584i
\(589\) 5396.55 + 3920.82i 0.377523 + 0.274286i
\(590\) 2167.67 11887.1i 0.151257 0.829463i
\(591\) 2354.47 1710.62i 0.163875 0.119062i
\(592\) −455.314 + 1401.31i −0.0316103 + 0.0972864i
\(593\) 14752.2 1.02158 0.510792 0.859704i \(-0.329352\pi\)
0.510792 + 0.859704i \(0.329352\pi\)
\(594\) −2734.60 + 8416.24i −0.188892 + 0.581351i
\(595\) 3051.79 + 1645.60i 0.210271 + 0.113383i
\(596\) −2167.31 6670.28i −0.148954 0.458432i
\(597\) 1494.41 + 4599.33i 0.102449 + 0.315307i
\(598\) 5602.78 + 4070.66i 0.383135 + 0.278364i
\(599\) −610.057 −0.0416131 −0.0208065 0.999784i \(-0.506623\pi\)
−0.0208065 + 0.999784i \(0.506623\pi\)
\(600\) −4396.45 1658.59i −0.299141 0.112853i
\(601\) −16775.8 −1.13860 −0.569300 0.822130i \(-0.692786\pi\)
−0.569300 + 0.822130i \(0.692786\pi\)
\(602\) 1663.56 + 1208.64i 0.112627 + 0.0818284i
\(603\) 1175.25 + 3617.04i 0.0793693 + 0.244274i
\(604\) 3227.97 + 9934.68i 0.217458 + 0.669266i
\(605\) 21453.4 2887.41i 1.44166 0.194033i
\(606\) −981.190 + 3019.79i −0.0657725 + 0.202427i
\(607\) 10205.9 0.682445 0.341222 0.939983i \(-0.389159\pi\)
0.341222 + 0.939983i \(0.389159\pi\)
\(608\) 4972.56 15304.0i 0.331684 1.02082i
\(609\) −1050.64 + 763.333i −0.0699080 + 0.0507912i
\(610\) −757.782 + 101.990i −0.0502979 + 0.00676959i
\(611\) −10074.9 7319.83i −0.667080 0.484662i
\(612\) −4644.55 + 3374.47i −0.306773 + 0.222883i
\(613\) −7211.16 + 5239.22i −0.475132 + 0.345204i −0.799438 0.600749i \(-0.794869\pi\)
0.324306 + 0.945952i \(0.394869\pi\)
\(614\) −15312.1 11124.9i −1.00643 0.731212i
\(615\) 454.804 434.094i 0.0298203 0.0284624i
\(616\) 6404.30 4653.00i 0.418891 0.304342i
\(617\) 5702.91 17551.7i 0.372108 1.14523i −0.573302 0.819344i \(-0.694338\pi\)
0.945409 0.325885i \(-0.105662\pi\)
\(618\) −277.244 −0.0180459
\(619\) 5256.38 16177.5i 0.341312 1.05045i −0.622217 0.782845i \(-0.713768\pi\)
0.963529 0.267605i \(-0.0862321\pi\)
\(620\) 642.386 3522.72i 0.0416110 0.228187i
\(621\) −3191.74 9823.16i −0.206248 0.634766i
\(622\) 3220.42 + 9911.43i 0.207600 + 0.638927i
\(623\) 2237.39 + 1625.56i 0.143883 + 0.104537i
\(624\) 379.467 0.0243443
\(625\) 11731.6 + 10320.4i 0.750820 + 0.660507i
\(626\) −10999.6 −0.702288
\(627\) −6937.56 5040.43i −0.441881 0.321045i
\(628\) 402.667 + 1239.28i 0.0255862 + 0.0787464i
\(629\) 2983.01 + 9180.75i 0.189094 + 0.581972i
\(630\) 543.327 2979.49i 0.0343598 0.188422i
\(631\) 6272.07 19303.5i 0.395701 1.21784i −0.532713 0.846296i \(-0.678828\pi\)
0.928414 0.371547i \(-0.121172\pi\)
\(632\) −24495.5 −1.54174
\(633\) −1934.40 + 5953.48i −0.121462 + 0.373822i
\(634\) 483.892 351.568i 0.0303120 0.0220230i
\(635\) −4040.29 + 3856.32i −0.252495 + 0.240997i
\(636\) 4040.63 + 2935.69i 0.251921 + 0.183031i
\(637\) 7359.25 5346.81i 0.457746 0.332572i
\(638\) 11848.3 8608.27i 0.735231 0.534177i
\(639\) 7728.68 + 5615.22i 0.478470 + 0.347628i
\(640\) −7231.47 + 973.282i −0.446639 + 0.0601131i
\(641\) −13946.6 + 10132.8i −0.859371 + 0.624370i −0.927714 0.373292i \(-0.878229\pi\)
0.0683428 + 0.997662i \(0.478229\pi\)
\(642\) 62.2911 191.712i 0.00382934 0.0117855i
\(643\) 1616.35 0.0991331 0.0495666 0.998771i \(-0.484216\pi\)
0.0495666 + 0.998771i \(0.484216\pi\)
\(644\) −1025.70 + 3156.78i −0.0627613 + 0.193159i
\(645\) −3298.74 + 443.977i −0.201376 + 0.0271032i
\(646\) 2836.52 + 8729.92i 0.172758 + 0.531694i
\(647\) −1752.03 5392.20i −0.106460 0.327649i 0.883611 0.468223i \(-0.155105\pi\)
−0.990070 + 0.140573i \(0.955105\pi\)
\(648\) 9974.59 + 7246.96i 0.604690 + 0.439333i
\(649\) −32950.5 −1.99295
\(650\) −6475.88 2443.06i −0.390777 0.147423i
\(651\) −678.524 −0.0408502
\(652\) −7132.18 5181.83i −0.428401 0.311252i
\(653\) −7617.70 23444.9i −0.456514 1.40501i −0.869349 0.494199i \(-0.835461\pi\)
0.412835 0.910806i \(-0.364539\pi\)
\(654\) −184.278 567.151i −0.0110181 0.0339103i
\(655\) −2550.68 1375.39i −0.152158 0.0820472i
\(656\) −86.5632 + 266.414i −0.00515202 + 0.0158563i
\(657\) 28559.2 1.69589
\(658\) −1445.30 + 4448.18i −0.0856288 + 0.263538i
\(659\) 1095.83 796.169i 0.0647763 0.0470627i −0.554926 0.831900i \(-0.687253\pi\)
0.619702 + 0.784837i \(0.287253\pi\)
\(660\) −825.823 + 4528.65i −0.0487047 + 0.267087i
\(661\) −7325.16 5322.04i −0.431037 0.313167i 0.351026 0.936366i \(-0.385833\pi\)
−0.782064 + 0.623199i \(0.785833\pi\)
\(662\) −4441.70 + 3227.08i −0.260773 + 0.189462i
\(663\) 2011.29 1461.29i 0.117816 0.0855984i
\(664\) 17767.3 + 12908.7i 1.03841 + 0.754450i
\(665\) 5439.25 + 2932.97i 0.317180 + 0.171031i
\(666\) 6821.77 4956.31i 0.396905 0.288368i
\(667\) −5282.17 + 16256.9i −0.306636 + 0.943730i
\(668\) 9213.10 0.533631
\(669\) −1804.62 + 5554.04i −0.104291 + 0.320974i
\(670\) −1413.81 2942.22i −0.0815225 0.169654i
\(671\) 644.331 + 1983.05i 0.0370703 + 0.114091i
\(672\) 505.810 + 1556.72i 0.0290358 + 0.0893630i
\(673\) −6967.78 5062.39i −0.399091 0.289956i 0.370080 0.929000i \(-0.379330\pi\)
−0.769171 + 0.639044i \(0.779330\pi\)
\(674\) 9674.72 0.552903
\(675\) 5672.00 + 8624.71i 0.323430 + 0.491801i
\(676\) 5941.57 0.338050
\(677\) 6541.98 + 4753.03i 0.371387 + 0.269828i 0.757786 0.652503i \(-0.226281\pi\)
−0.386399 + 0.922332i \(0.626281\pi\)
\(678\) −1525.02 4693.52i −0.0863833 0.265860i
\(679\) 3131.59 + 9638.03i 0.176994 + 0.544733i
\(680\) 9922.14 9470.33i 0.559554 0.534075i
\(681\) −345.250 + 1062.57i −0.0194273 + 0.0597911i
\(682\) 7651.86 0.429626
\(683\) −10597.5 + 32615.7i −0.593706 + 1.82724i −0.0326425 + 0.999467i \(0.510392\pi\)
−0.561064 + 0.827773i \(0.689608\pi\)
\(684\) −8278.05 + 6014.35i −0.462747 + 0.336206i
\(685\) −737.390 1534.56i −0.0411303 0.0855948i
\(686\) −5842.04 4244.49i −0.325146 0.236232i
\(687\) −7176.82 + 5214.27i −0.398563 + 0.289573i
\(688\) 1199.78 871.689i 0.0664841 0.0483035i
\(689\) 16567.4 + 12036.9i 0.916064 + 0.665559i
\(690\) 1823.51 + 3794.85i 0.100609 + 0.209373i
\(691\) −8077.57 + 5868.70i −0.444697 + 0.323091i −0.787498 0.616317i \(-0.788624\pi\)
0.342802 + 0.939408i \(0.388624\pi\)
\(692\) 1772.02 5453.73i 0.0973443 0.299595i
\(693\) −8259.05 −0.452721
\(694\) 1013.53 3119.33i 0.0554368 0.170617i
\(695\) −18350.6 + 17515.0i −1.00155 + 0.955945i
\(696\) 1587.58 + 4886.07i 0.0864613 + 0.266101i
\(697\) 567.122 + 1745.42i 0.0308196 + 0.0948531i
\(698\) 2692.33 + 1956.09i 0.145997 + 0.106073i
\(699\) 8595.00 0.465082
\(700\) 154.489 3313.70i 0.00834161 0.178923i
\(701\) 2668.87 0.143797 0.0718987 0.997412i \(-0.477094\pi\)
0.0718987 + 0.997412i \(0.477094\pi\)
\(702\) −3699.32 2687.71i −0.198892 0.144503i
\(703\) 5316.65 + 16363.0i 0.285236 + 0.877867i
\(704\) −6834.58 21034.7i −0.365892 1.12610i
\(705\) −3279.03 6823.88i −0.175171 0.364542i
\(706\) 191.181 588.395i 0.0101915 0.0313662i
\(707\) −6239.76 −0.331924
\(708\) 1283.19 3949.26i 0.0681149 0.209636i
\(709\) 11300.0 8209.94i 0.598563 0.434881i −0.246806 0.969065i \(-0.579381\pi\)
0.845368 + 0.534184i \(0.179381\pi\)
\(710\) −7217.14 3891.66i −0.381485 0.205706i
\(711\) 20675.7 + 15021.8i 1.09057 + 0.792348i
\(712\) 8851.15 6430.74i 0.465886 0.338486i
\(713\) −7225.33 + 5249.51i −0.379510 + 0.275730i
\(714\) −755.386 548.820i −0.0395933 0.0287662i
\(715\) −3386.04 + 18568.4i −0.177106 + 0.971213i
\(716\) 1692.32 1229.54i 0.0883310 0.0641762i
\(717\) 2472.36 7609.14i 0.128775 0.396330i
\(718\) 7875.35 0.409339
\(719\) 8185.68 25192.9i 0.424582 1.30673i −0.478812 0.877917i \(-0.658933\pi\)
0.903394 0.428811i \(-0.141067\pi\)
\(720\) −1922.59 1036.71i −0.0995146 0.0536607i
\(721\) −168.361 518.162i −0.00869638 0.0267647i
\(722\) 1081.93 + 3329.84i 0.0557691 + 0.171640i
\(723\) −1774.67 1289.37i −0.0912872 0.0663240i
\(724\) −5230.35 −0.268487
\(725\) 795.589 17065.0i 0.0407551 0.874175i
\(726\) −5829.46 −0.298005
\(727\) −13903.6 10101.6i −0.709295 0.515333i 0.173651 0.984807i \(-0.444444\pi\)
−0.882946 + 0.469474i \(0.844444\pi\)
\(728\) 1264.01 + 3890.21i 0.0643505 + 0.198050i
\(729\) −2868.44 8828.15i −0.145732 0.448516i
\(730\) −24293.4 + 3269.64i −1.23170 + 0.165774i
\(731\) 3002.40 9240.43i 0.151912 0.467537i
\(732\) −262.769 −0.0132681
\(733\) −3541.75 + 10900.4i −0.178469 + 0.549270i −0.999775 0.0212175i \(-0.993246\pi\)
0.821306 + 0.570488i \(0.193246\pi\)
\(734\) 17174.8 12478.2i 0.863668 0.627491i
\(735\) 5480.73 737.651i 0.275047 0.0370186i
\(736\) 17430.0 + 12663.6i 0.872933 + 0.634223i
\(737\) −7201.60 + 5232.27i −0.359938 + 0.261510i
\(738\) 1296.94 942.282i 0.0646898 0.0469999i
\(739\) −30512.3 22168.5i −1.51883 1.10349i −0.962066 0.272818i \(-0.912044\pi\)
−0.556760 0.830673i \(-0.687956\pi\)
\(740\) 6681.10 6376.87i 0.331895 0.316782i
\(741\) 3584.75 2604.47i 0.177718 0.129120i
\(742\) 2376.69 7314.71i 0.117589 0.361902i
\(743\) −31924.8 −1.57632 −0.788160 0.615470i \(-0.788966\pi\)
−0.788160 + 0.615470i \(0.788966\pi\)
\(744\) −829.480 + 2552.88i −0.0408739 + 0.125797i
\(745\) 3136.31 17198.9i 0.154235 0.845796i
\(746\) 4672.37 + 14380.1i 0.229313 + 0.705753i
\(747\) −7080.48 21791.5i −0.346802 1.06735i
\(748\) −10871.0 7898.23i −0.531394 0.386080i
\(749\) 396.133 0.0193249
\(750\) −2760.34 3175.84i −0.134391 0.154620i
\(751\) 26464.6 1.28589 0.642946 0.765911i \(-0.277712\pi\)
0.642946 + 0.765911i \(0.277712\pi\)
\(752\) 2728.96 + 1982.70i 0.132334 + 0.0961460i
\(753\) 27.9516 + 86.0260i 0.00135274 + 0.00416330i
\(754\) 2338.47 + 7197.07i 0.112947 + 0.347615i
\(755\) −4671.20 + 25615.9i −0.225169 + 1.23478i
\(756\) 677.234 2084.31i 0.0325804 0.100272i
\(757\) −10652.8 −0.511470 −0.255735 0.966747i \(-0.582317\pi\)
−0.255735 + 0.966747i \(0.582317\pi\)
\(758\) 1508.19 4641.72i 0.0722688 0.222421i
\(759\) 9288.56 6748.54i 0.444207 0.322736i
\(760\) 17684.4 16879.1i 0.844051 0.805617i
\(761\) −9424.61 6847.38i −0.448938 0.326173i 0.340238 0.940339i \(-0.389492\pi\)
−0.789176 + 0.614167i \(0.789492\pi\)
\(762\) 1216.84 884.088i 0.0578498 0.0420304i
\(763\) 948.085 688.824i 0.0449842 0.0326830i
\(764\) 8115.38 + 5896.17i 0.384299 + 0.279209i
\(765\) −14182.5 + 1908.83i −0.670288 + 0.0902140i
\(766\) −14435.3 + 10487.8i −0.680898 + 0.494701i
\(767\) 5261.35 16192.8i 0.247688 0.762304i
\(768\) 6936.37 0.325904
\(769\) −3694.13 + 11369.4i −0.173230 + 0.533147i −0.999548 0.0300565i \(-0.990431\pi\)
0.826318 + 0.563203i \(0.190431\pi\)
\(770\) 7025.43 945.551i 0.328804 0.0442536i
\(771\) 291.354 + 896.697i 0.0136094 + 0.0418855i
\(772\) −2636.81 8115.25i −0.122928 0.378335i
\(773\) −16241.6 11800.2i −0.755717 0.549061i 0.141877 0.989884i \(-0.454686\pi\)
−0.897594 + 0.440824i \(0.854686\pi\)
\(774\) −8487.00 −0.394133
\(775\) 5577.05 6968.96i 0.258495 0.323009i
\(776\) 40090.4 1.85459
\(777\) −1415.86 1028.68i −0.0653716 0.0474952i
\(778\) 2825.50 + 8695.99i 0.130204 + 0.400728i
\(779\) 1010.79 + 3110.89i 0.0464895 + 0.143080i
\(780\) −2093.64 1128.94i −0.0961079 0.0518237i
\(781\) −6909.64 + 21265.7i −0.316576 + 0.974322i
\(782\) −12289.8 −0.562000
\(783\) 3487.63 10733.8i 0.159180 0.489905i
\(784\) −1993.38 + 1448.28i −0.0908064 + 0.0659747i
\(785\) −582.699 + 3195.41i −0.0264935 + 0.145285i
\(786\) 631.350 + 458.703i 0.0286508 + 0.0208160i
\(787\) 22616.7 16432.0i 1.02439 0.744266i 0.0572147 0.998362i \(-0.481778\pi\)
0.967179 + 0.254096i \(0.0817780\pi\)
\(788\) 6575.66 4777.50i 0.297269 0.215979i
\(789\) −623.507 453.004i −0.0281336 0.0204403i
\(790\) −19307.2 10410.9i −0.869518 0.468866i
\(791\) 7845.98 5700.43i 0.352681 0.256238i
\(792\) −10096.5 + 31073.8i −0.452984 + 1.39414i
\(793\) −1077.41 −0.0482469
\(794\) 431.822 1329.01i 0.0193007 0.0594015i
\(795\) 5392.13 + 11221.4i 0.240552 + 0.500605i
\(796\) 4173.66 + 12845.2i 0.185844 + 0.571968i
\(797\) 9441.64 + 29058.4i 0.419624 + 1.29147i 0.908049 + 0.418863i \(0.137571\pi\)
−0.488426 + 0.872605i \(0.662429\pi\)
\(798\) −1346.33 978.169i −0.0597240 0.0433920i
\(799\) 22099.5 0.978503
\(800\) −20146.2 7600.25i −0.890343 0.335887i
\(801\) −11414.5 −0.503511
\(802\) −22140.9 16086.3i −0.974839 0.708262i
\(803\) 20656.3 + 63573.6i 0.907777 + 2.79385i
\(804\) −346.658 1066.90i −0.0152061 0.0467995i
\(805\) −5985.13 + 5712.59i −0.262047 + 0.250115i
\(806\) −1221.81 + 3760.33i −0.0533949 + 0.164332i
\(807\) −7773.69 −0.339091
\(808\) −7627.96 + 23476.4i −0.332117 + 1.02215i
\(809\) 2550.54 1853.08i 0.110843 0.0805324i −0.530983 0.847383i \(-0.678177\pi\)
0.641826 + 0.766850i \(0.278177\pi\)
\(810\) 4781.86 + 9951.36i 0.207429 + 0.431673i
\(811\) −292.128 212.243i −0.0126486 0.00918973i 0.581443 0.813587i \(-0.302488\pi\)
−0.594092 + 0.804397i \(0.702488\pi\)
\(812\) −2934.27 + 2131.87i −0.126813 + 0.0921354i
\(813\) 6061.99 4404.29i 0.261505 0.189994i
\(814\) 15967.0 + 11600.7i 0.687521 + 0.499513i
\(815\) −9517.72 19807.0i −0.409069 0.851299i
\(816\) −544.793 + 395.816i −0.0233720 + 0.0169808i
\(817\) 5351.21 16469.3i 0.229150 0.705250i
\(818\) 2637.71 0.112745
\(819\) 1318.76 4058.72i 0.0562651 0.173166i
\(820\) 1270.20 1212.36i 0.0540941 0.0516309i
\(821\) −5224.35 16078.9i −0.222084 0.683505i −0.998574 0.0533758i \(-0.983002\pi\)
0.776490 0.630129i \(-0.216998\pi\)
\(822\) 141.681 + 436.048i 0.00601178 + 0.0185023i
\(823\) 10939.7 + 7948.18i 0.463348 + 0.336642i 0.794843 0.606815i \(-0.207553\pi\)
−0.331495 + 0.943457i \(0.607553\pi\)
\(824\) −2155.35 −0.0911226
\(825\) −7169.61 + 8958.97i −0.302562 + 0.378075i
\(826\) −6394.53 −0.269364
\(827\) 26154.0 + 19002.0i 1.09971 + 0.798988i 0.981013 0.193942i \(-0.0621273\pi\)
0.118700 + 0.992930i \(0.462127\pi\)
\(828\) −4233.45 13029.2i −0.177684 0.546856i
\(829\) −8942.80 27523.1i −0.374664 1.15310i −0.943705 0.330787i \(-0.892686\pi\)
0.569042 0.822309i \(-0.307314\pi\)
\(830\) 8517.72 + 17725.9i 0.356210 + 0.741297i
\(831\) −4148.07 + 12766.4i −0.173159 + 0.532928i
\(832\) 11428.3 0.476208
\(833\) −4988.37 + 15352.6i −0.207487 + 0.638580i
\(834\) 5526.77 4015.44i 0.229468 0.166718i
\(835\) 20213.8 + 10899.8i 0.837758 + 0.451740i
\(836\) −19375.5 14077.1i −0.801574 0.582377i
\(837\) 4770.64 3466.07i 0.197010 0.143136i
\(838\) 7222.93 5247.77i 0.297747 0.216326i
\(839\) 16807.4 + 12211.3i 0.691603 + 0.502479i 0.877187 0.480150i \(-0.159418\pi\)
−0.185584 + 0.982628i \(0.559418\pi\)
\(840\) −446.110 + 2446.38i −0.0183241 + 0.100486i
\(841\) 4620.18 3356.76i 0.189437 0.137634i
\(842\) −2222.79 + 6841.04i −0.0909767 + 0.279998i
\(843\) −8877.55 −0.362704
\(844\) −5402.48 + 16627.1i −0.220333 + 0.678115i
\(845\) 13036.0 + 7029.32i 0.530712 + 0.286173i
\(846\) −5965.31 18359.3i −0.242425 0.746107i
\(847\) −3540.04 10895.1i −0.143609 0.441984i
\(848\) −4487.57 3260.41i −0.181726 0.132032i
\(849\) 837.255 0.0338451
\(850\) 11845.6 3247.42i 0.478001 0.131042i
\(851\) −23035.5 −0.927905
\(852\) −2279.70 1656.30i −0.0916681 0.0666008i
\(853\) −10310.8 31733.5i −0.413877 1.27378i −0.913252 0.407395i \(-0.866437\pi\)
0.499375 0.866386i \(-0.333563\pi\)
\(854\) 125.042 + 384.840i 0.00501036 + 0.0154203i
\(855\) −25277.7 + 3402.12i −1.01109 + 0.136082i
\(856\) 484.263 1490.41i 0.0193362 0.0595106i
\(857\) −25175.7 −1.00348 −0.501742 0.865017i \(-0.667307\pi\)
−0.501742 + 0.865017i \(0.667307\pi\)
\(858\) 1570.70 4834.11i 0.0624974 0.192347i
\(859\) −5184.10 + 3766.47i −0.205913 + 0.149604i −0.685963 0.727637i \(-0.740619\pi\)
0.480050 + 0.877241i \(0.340619\pi\)
\(860\) −9212.87 + 1239.96i −0.365298 + 0.0491654i
\(861\) −269.180 195.571i −0.0106546 0.00774104i
\(862\) 4424.47 3214.57i 0.174824 0.127017i
\(863\) 39146.1 28441.3i 1.54409 1.12185i 0.596386 0.802698i \(-0.296603\pi\)
0.947704 0.319149i \(-0.103397\pi\)
\(864\) −11508.4 8361.36i −0.453153 0.329235i
\(865\) 10340.0 9869.21i 0.406442 0.387934i
\(866\) −3182.45 + 2312.18i −0.124878 + 0.0907289i
\(867\) 1074.89 3308.17i 0.0421051 0.129586i
\(868\) −1895.01 −0.0741024
\(869\) −18484.6 + 56889.6i −0.721572 + 2.22077i
\(870\) −825.325 + 4525.92i −0.0321622 + 0.176371i
\(871\) −1421.37 4374.52i −0.0552941 0.170178i
\(872\) −1432.62 4409.14i −0.0556359 0.171230i
\(873\) −33838.7 24585.3i −1.31187 0.953133i
\(874\) −21904.3 −0.847741
\(875\) 4259.31 7087.59i 0.164561 0.273833i
\(876\) −8423.99 −0.324909
\(877\) 21739.2 + 15794.5i 0.837036 + 0.608142i 0.921541 0.388281i \(-0.126931\pi\)
−0.0845052 + 0.996423i \(0.526931\pi\)
\(878\) −66.3732 204.276i −0.00255124 0.00785190i
\(879\) 1096.63 + 3375.07i 0.0420800 + 0.129509i
\(880\) 917.168 5029.57i 0.0351338 0.192667i
\(881\) 11453.8 35251.1i 0.438011 1.34806i −0.451959 0.892039i \(-0.649275\pi\)
0.889970 0.456020i \(-0.150725\pi\)
\(882\) 14100.8 0.538321
\(883\) −656.803 + 2021.43i −0.0250319 + 0.0770403i −0.962792 0.270243i \(-0.912896\pi\)
0.937760 + 0.347284i \(0.112896\pi\)
\(884\) 5617.22 4081.15i 0.213719 0.155276i
\(885\) 7487.64 7146.69i 0.284400 0.271450i
\(886\) −381.001 276.814i −0.0144469 0.0104963i
\(887\) 1712.00 1243.84i 0.0648065 0.0470847i −0.554910 0.831910i \(-0.687247\pi\)
0.619717 + 0.784825i \(0.287247\pi\)
\(888\) −5601.17 + 4069.49i −0.211670 + 0.153787i
\(889\) 2391.29 + 1737.37i 0.0902151 + 0.0655451i
\(890\) 9709.58 1306.81i 0.365692 0.0492184i
\(891\) 24357.7 17696.9i 0.915840 0.665397i
\(892\) −5040.01 + 15511.6i −0.189184 + 0.582248i
\(893\) 39388.2 1.47601
\(894\) −1454.85 + 4477.58i −0.0544268 + 0.167509i
\(895\) 5167.64 695.512i 0.193000 0.0259759i
\(896\) 1193.27 + 3672.50i 0.0444914 + 0.136930i
\(897\) 1833.27 + 5642.22i 0.0682397 + 0.210020i
\(898\) −15001.7 10899.4i −0.557475 0.405029i
\(899\) −9758.97 −0.362046
\(900\) 7523.22 + 11439.6i 0.278638 + 0.423690i
\(901\) −36341.0 −1.34372
\(902\) 3035.60 + 2205.49i 0.112056 + 0.0814135i
\(903\) 544.327 + 1675.27i 0.0200599 + 0.0617379i
\(904\) −11855.8 36488.3i −0.436191 1.34246i
\(905\) −11475.5 6187.89i −0.421503 0.227285i
\(906\) 2166.85 6668.88i 0.0794579 0.244546i
\(907\) −4188.50 −0.153337 −0.0766687 0.997057i \(-0.524428\pi\)
−0.0766687 + 0.997057i \(0.524428\pi\)
\(908\) −964.228 + 2967.59i −0.0352412 + 0.108461i
\(909\) 20835.3 15137.7i 0.760246 0.552351i
\(910\) −657.110 + 3603.46i −0.0239374 + 0.131268i
\(911\) 11515.9 + 8366.82i 0.418815 + 0.304287i 0.777161 0.629302i \(-0.216659\pi\)
−0.358346 + 0.933589i \(0.616659\pi\)
\(912\) −970.992 + 705.467i −0.0352552 + 0.0256144i
\(913\) 43387.3 31522.7i 1.57274 1.14266i
\(914\) 5066.65 + 3681.14i 0.183359 + 0.133218i
\(915\) −576.523 310.875i −0.0208298 0.0112319i
\(916\) −20043.7 + 14562.6i −0.722995 + 0.525287i
\(917\) −473.906 + 1458.53i −0.0170663 + 0.0525245i
\(918\) 8114.55 0.291743
\(919\) −9951.33 + 30627.0i −0.357197 + 1.09934i 0.597528 + 0.801848i \(0.296150\pi\)
−0.954725 + 0.297491i \(0.903850\pi\)
\(920\) 14176.4 + 29501.9i 0.508022 + 1.05723i
\(921\) −5010.22 15419.9i −0.179253 0.551685i
\(922\) −7059.73 21727.6i −0.252169 0.776096i
\(923\) −9347.23 6791.16i −0.333335 0.242182i
\(924\) 2436.14 0.0867350
\(925\) 22202.8 6086.81i 0.789216 0.216360i
\(926\) 19538.2 0.693374
\(927\) 1819.24 + 1321.76i 0.0644572 + 0.0468309i
\(928\) 7274.88 + 22389.8i 0.257338 + 0.792005i
\(929\) −4869.12 14985.6i −0.171960 0.529238i 0.827522 0.561434i \(-0.189750\pi\)
−0.999482 + 0.0321958i \(0.989750\pi\)
\(930\) −1738.80 + 1659.62i −0.0613091 + 0.0585174i
\(931\) −8890.84 + 27363.2i −0.312981 + 0.963257i
\(932\) 24004.5 0.843662
\(933\) −2758.73 + 8490.51i −0.0968027 + 0.297928i
\(934\) −20094.3 + 14599.4i −0.703967 + 0.511462i
\(935\) −14507.1 30190.1i −0.507414 1.05596i
\(936\) −13658.4 9923.38i −0.476963 0.346534i
\(937\) −31461.7 + 22858.3i −1.09692 + 0.796956i −0.980554 0.196251i \(-0.937123\pi\)
−0.116362 + 0.993207i \(0.537123\pi\)
\(938\) −1397.58 + 1015.40i −0.0486487 + 0.0353454i
\(939\) −7623.10 5538.51i −0.264931 0.192484i
\(940\) −9157.82 19058.0i −0.317761 0.661281i
\(941\) −32883.6 + 23891.4i −1.13919 + 0.827669i −0.987006 0.160684i \(-0.948630\pi\)
−0.152182 + 0.988352i \(0.548630\pi\)
\(942\) 270.299 831.896i 0.00934908 0.0287735i
\(943\) −4379.46 −0.151235
\(944\) −1425.13 + 4386.10i −0.0491356 + 0.151224i
\(945\) 3951.77 3771.83i 0.136033 0.129839i
\(946\) −6138.49 18892.3i −0.210972 0.649305i
\(947\) 6376.19 + 19623.9i 0.218794 + 0.673380i 0.998862 + 0.0476852i \(0.0151844\pi\)
−0.780068 + 0.625695i \(0.784816\pi\)
\(948\) −6098.62 4430.91i −0.208939 0.151803i
\(949\) −34540.0 −1.18147
\(950\) 21112.6 5787.92i 0.721034 0.197668i
\(951\) 512.375 0.0174710
\(952\) −5872.52 4266.63i −0.199926 0.145255i
\(953\) −6682.98 20568.1i −0.227160 0.699125i −0.998065 0.0621759i \(-0.980196\pi\)
0.770906 0.636949i \(-0.219804\pi\)
\(954\) 9809.51 + 30190.6i 0.332908 + 1.02459i
\(955\) 10829.8 + 22537.5i 0.366956 + 0.763660i
\(956\) 6904.91 21251.1i 0.233599 0.718945i
\(957\) 12545.7 0.423766
\(958\) 436.599 1343.71i 0.0147243 0.0453167i
\(959\) −728.926 + 529.595i −0.0245446 + 0.0178327i
\(960\) 6115.32 + 3297.53i 0.205595 + 0.110862i
\(961\) 19976.4 + 14513.7i 0.670550 + 0.487183i
\(962\) −8250.40 + 5994.26i −0.276511 + 0.200897i
\(963\) −1322.73 + 961.023i −0.0442622 + 0.0321584i
\(964\) −4956.37 3601.01i −0.165595 0.120312i
\(965\) 3815.72 20924.6i 0.127287 0.698019i
\(966\) 1802.58 1309.65i 0.0600384 0.0436205i
\(967\) −9371.85 + 28843.6i −0.311663 + 0.959201i 0.665443 + 0.746449i \(0.268243\pi\)
−0.977106 + 0.212752i \(0.931757\pi\)
\(968\) −45319.3 −1.50477
\(969\) −2429.87 + 7478.38i −0.0805560 + 0.247926i
\(970\) 31599.0 + 17039.0i 1.04596 + 0.564008i
\(971\) 10840.7 + 33364.3i 0.358285 + 1.10269i 0.954080 + 0.299552i \(0.0968372\pi\)
−0.595795 + 0.803137i \(0.703163\pi\)
\(972\) 4262.90 + 13119.9i 0.140672 + 0.432942i
\(973\) 10861.0 + 7890.97i 0.357849 + 0.259993i
\(974\) 3691.96 0.121456
\(975\) −3257.88 4953.85i −0.107011 0.162718i
\(976\) 291.834 0.00957110
\(977\) 36271.9 + 26353.1i 1.18776 + 0.862958i 0.993026 0.117899i \(-0.0376158\pi\)
0.194733 + 0.980856i \(0.437616\pi\)
\(978\) 1828.71 + 5628.21i 0.0597913 + 0.184019i
\(979\) −8255.92 25409.1i −0.269520 0.829498i
\(980\) 15306.8 2060.14i 0.498937 0.0671519i
\(981\) −1494.67 + 4600.13i −0.0486455 + 0.149715i
\(982\) 28374.3 0.922057
\(983\) 6943.28 21369.2i 0.225286 0.693359i −0.772976 0.634435i \(-0.781233\pi\)
0.998262 0.0589243i \(-0.0187671\pi\)
\(984\) −1064.88 + 773.682i −0.0344992 + 0.0250651i
\(985\) 20079.3 2702.47i 0.649524 0.0874193i
\(986\) −10864.4 7893.48i −0.350907 0.254949i
\(987\) −3241.39 + 2355.01i −0.104534 + 0.0759481i
\(988\) 10011.6 7273.88i 0.322381 0.234224i
\(989\) 18757.3 + 13628.0i 0.603081 + 0.438164i
\(990\) −21164.8 + 20201.1i −0.679456 + 0.648517i
\(991\) 27174.0 19743.1i 0.871049 0.632854i −0.0598190 0.998209i \(-0.519052\pi\)
0.930868 + 0.365355i \(0.119052\pi\)
\(992\) −3800.98 + 11698.2i −0.121655 + 0.374414i
\(993\) −4703.15 −0.150302
\(994\) −1340.92 + 4126.92i −0.0427880 + 0.131688i
\(995\) −6039.70 + 33120.5i −0.192434 + 1.05527i
\(996\) 2088.50 + 6427.75i 0.0664425 + 0.204489i
\(997\) −16212.5 49896.8i −0.514999 1.58500i −0.783284 0.621664i \(-0.786457\pi\)
0.268285 0.963339i \(-0.413543\pi\)
\(998\) −18323.9 13313.1i −0.581195 0.422263i
\(999\) 15209.5 0.481690
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 25.4.d.a.16.3 yes 28
3.2 odd 2 225.4.h.b.91.5 28
5.2 odd 4 125.4.e.b.49.9 56
5.3 odd 4 125.4.e.b.49.6 56
5.4 even 2 125.4.d.a.76.5 28
25.2 odd 20 125.4.e.b.74.6 56
25.6 even 5 625.4.a.c.1.9 14
25.11 even 5 inner 25.4.d.a.11.3 28
25.14 even 10 125.4.d.a.51.5 28
25.19 even 10 625.4.a.d.1.6 14
25.23 odd 20 125.4.e.b.74.9 56
75.11 odd 10 225.4.h.b.136.5 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.4.d.a.11.3 28 25.11 even 5 inner
25.4.d.a.16.3 yes 28 1.1 even 1 trivial
125.4.d.a.51.5 28 25.14 even 10
125.4.d.a.76.5 28 5.4 even 2
125.4.e.b.49.6 56 5.3 odd 4
125.4.e.b.49.9 56 5.2 odd 4
125.4.e.b.74.6 56 25.2 odd 20
125.4.e.b.74.9 56 25.23 odd 20
225.4.h.b.91.5 28 3.2 odd 2
225.4.h.b.136.5 28 75.11 odd 10
625.4.a.c.1.9 14 25.6 even 5
625.4.a.d.1.6 14 25.19 even 10