Properties

Label 210.3.v.b.163.3
Level $210$
Weight $3$
Character 210.163
Analytic conductor $5.722$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,3,Mod(37,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.37");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.v (of order \(12\), 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: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 163.3
Character \(\chi\) \(=\) 210.163
Dual form 210.3.v.b.67.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.366025 - 1.36603i) q^{2} +(-0.448288 + 1.67303i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.65824 - 4.71702i) q^{5} +2.44949 q^{6} +(-6.62205 + 2.26902i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(-0.366025 - 1.36603i) q^{2} +(-0.448288 + 1.67303i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.65824 - 4.71702i) q^{5} +2.44949 q^{6} +(-6.62205 + 2.26902i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(-7.05052 - 0.538651i) q^{10} +(-1.33229 - 2.30759i) q^{11} +(-0.896575 - 3.34607i) q^{12} +(-9.16064 - 9.16064i) q^{13} +(5.52338 + 8.21537i) q^{14} +(7.14835 + 4.88887i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-2.70344 - 0.724383i) q^{17} +(-1.09808 + 4.09808i) q^{18} +(-16.5863 - 9.57608i) q^{19} +(1.84486 + 9.82835i) q^{20} +(-0.827557 - 12.0961i) q^{21} +(-2.66457 + 2.66457i) q^{22} +(-34.9499 + 9.36480i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-19.5005 - 15.6439i) q^{25} +(-9.16064 + 15.8667i) q^{26} +(3.67423 - 3.67423i) q^{27} +(9.20071 - 10.5521i) q^{28} -12.4700i q^{29} +(4.06184 - 11.5543i) q^{30} +(5.33782 + 9.24538i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(4.45791 - 1.19449i) q^{33} +3.95810i q^{34} +(-0.277956 + 34.9989i) q^{35} +6.00000 q^{36} +(-5.88355 - 21.9577i) q^{37} +(-7.01018 + 26.1623i) q^{38} +(19.4326 - 11.2194i) q^{39} +(12.7505 - 6.11755i) q^{40} -1.17994 q^{41} +(-16.2206 + 5.55794i) q^{42} +(2.70577 + 2.70577i) q^{43} +(4.61517 + 2.66457i) q^{44} +(-11.3838 + 9.76781i) q^{45} +(25.5851 + 44.3147i) q^{46} +(19.2185 + 71.7245i) q^{47} +(4.89898 + 4.89898i) q^{48} +(38.7031 - 30.0511i) q^{49} +(-14.2323 + 32.3642i) q^{50} +(2.42383 - 4.19820i) q^{51} +(25.0273 + 6.70605i) q^{52} +(-2.09960 + 7.83581i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(-13.0942 + 2.45788i) q^{55} +(-17.7821 - 8.70607i) q^{56} +(23.4565 - 23.4565i) q^{57} +(-17.0343 + 4.56433i) q^{58} +(93.6121 - 54.0470i) q^{59} +(-17.2702 - 1.31942i) q^{60} +(35.0235 - 60.6625i) q^{61} +(10.6756 - 10.6756i) q^{62} +(20.6081 + 4.03799i) q^{63} +8.00000i q^{64} +(-58.4014 + 28.0203i) q^{65} +(-3.26342 - 5.65241i) q^{66} +(-16.8687 - 4.51996i) q^{67} +(5.40687 - 1.44877i) q^{68} -62.6705i q^{69} +(47.9111 - 12.4308i) q^{70} +66.2750 q^{71} +(-2.19615 - 8.19615i) q^{72} +(9.37151 - 34.9749i) q^{73} +(-27.8413 + 16.0742i) q^{74} +(34.9146 - 25.6120i) q^{75} +38.3043 q^{76} +(14.0584 + 12.2580i) q^{77} +(-22.4389 - 22.4389i) q^{78} +(-83.6148 - 48.2750i) q^{79} +(-13.0237 - 15.1783i) q^{80} +(4.50000 + 7.79423i) q^{81} +(0.431888 + 1.61183i) q^{82} +(-83.4979 - 83.4979i) q^{83} +(13.5295 + 20.1235i) q^{84} +(-7.89987 + 11.5509i) q^{85} +(2.70577 - 4.68654i) q^{86} +(20.8627 + 5.59014i) q^{87} +(1.95060 - 7.27974i) q^{88} +(125.762 + 72.6089i) q^{89} +(17.5098 + 11.9752i) q^{90} +(81.4478 + 39.8765i) q^{91} +(51.1702 - 51.1702i) q^{92} +(-17.8607 + 4.78576i) q^{93} +(90.9430 - 52.5060i) q^{94} +(-72.6745 + 62.3582i) q^{95} +(4.89898 - 8.48528i) q^{96} +(-43.6910 + 43.6910i) q^{97} +(-55.2169 - 41.8700i) q^{98} +7.99371i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8} + 12 q^{10} + 16 q^{11} + 32 q^{13} + 48 q^{15} + 64 q^{16} - 56 q^{17} + 48 q^{18} + 16 q^{20} + 32 q^{22} - 28 q^{25} + 32 q^{26} + 72 q^{28} + 36 q^{30} + 112 q^{31} - 64 q^{32} + 12 q^{33} - 112 q^{35} + 192 q^{36} - 52 q^{37} - 8 q^{40} - 336 q^{41} - 312 q^{43} + 12 q^{45} - 212 q^{47} + 96 q^{50} - 144 q^{51} - 32 q^{52} - 96 q^{53} - 312 q^{55} + 96 q^{56} + 48 q^{57} - 96 q^{58} - 24 q^{60} + 216 q^{61} + 224 q^{62} + 36 q^{63} + 248 q^{65} - 24 q^{66} + 128 q^{67} + 112 q^{68} - 264 q^{70} - 848 q^{71} + 96 q^{72} + 84 q^{73} - 144 q^{75} - 324 q^{77} + 48 q^{78} + 32 q^{80} + 144 q^{81} - 168 q^{82} - 416 q^{83} + 536 q^{85} - 312 q^{86} - 72 q^{87} + 32 q^{88} - 24 q^{90} + 504 q^{91} + 168 q^{93} + 168 q^{95} + 488 q^{97} - 328 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 1.36603i −0.183013 0.683013i
\(3\) −0.448288 + 1.67303i −0.149429 + 0.557678i
\(4\) −1.73205 + 1.00000i −0.433013 + 0.250000i
\(5\) 1.65824 4.71702i 0.331648 0.943403i
\(6\) 2.44949 0.408248
\(7\) −6.62205 + 2.26902i −0.946007 + 0.324145i
\(8\) 2.00000 + 2.00000i 0.250000 + 0.250000i
\(9\) −2.59808 1.50000i −0.288675 0.166667i
\(10\) −7.05052 0.538651i −0.705052 0.0538651i
\(11\) −1.33229 2.30759i −0.121117 0.209781i 0.799092 0.601209i \(-0.205314\pi\)
−0.920208 + 0.391429i \(0.871981\pi\)
\(12\) −0.896575 3.34607i −0.0747146 0.278839i
\(13\) −9.16064 9.16064i −0.704664 0.704664i 0.260744 0.965408i \(-0.416032\pi\)
−0.965408 + 0.260744i \(0.916032\pi\)
\(14\) 5.52338 + 8.21537i 0.394527 + 0.586812i
\(15\) 7.14835 + 4.88887i 0.476557 + 0.325925i
\(16\) 2.00000 3.46410i 0.125000 0.216506i
\(17\) −2.70344 0.724383i −0.159026 0.0426108i 0.178428 0.983953i \(-0.442899\pi\)
−0.337453 + 0.941342i \(0.609566\pi\)
\(18\) −1.09808 + 4.09808i −0.0610042 + 0.227671i
\(19\) −16.5863 9.57608i −0.872961 0.504004i −0.00462986 0.999989i \(-0.501474\pi\)
−0.868331 + 0.495985i \(0.834807\pi\)
\(20\) 1.84486 + 9.82835i 0.0922430 + 0.491418i
\(21\) −0.827557 12.0961i −0.0394075 0.576004i
\(22\) −2.66457 + 2.66457i −0.121117 + 0.121117i
\(23\) −34.9499 + 9.36480i −1.51956 + 0.407165i −0.919597 0.392862i \(-0.871485\pi\)
−0.599964 + 0.800027i \(0.704818\pi\)
\(24\) −4.24264 + 2.44949i −0.176777 + 0.102062i
\(25\) −19.5005 15.6439i −0.780019 0.625756i
\(26\) −9.16064 + 15.8667i −0.352332 + 0.610257i
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) 9.20071 10.5521i 0.328597 0.376861i
\(29\) 12.4700i 0.429999i −0.976614 0.215000i \(-0.931025\pi\)
0.976614 0.215000i \(-0.0689750\pi\)
\(30\) 4.06184 11.5543i 0.135395 0.385143i
\(31\) 5.33782 + 9.24538i 0.172188 + 0.298238i 0.939184 0.343413i \(-0.111583\pi\)
−0.766997 + 0.641651i \(0.778250\pi\)
\(32\) −5.46410 1.46410i −0.170753 0.0457532i
\(33\) 4.45791 1.19449i 0.135088 0.0361968i
\(34\) 3.95810i 0.116415i
\(35\) −0.277956 + 34.9989i −0.00794159 + 0.999968i
\(36\) 6.00000 0.166667
\(37\) −5.88355 21.9577i −0.159015 0.593452i −0.998728 0.0504215i \(-0.983944\pi\)
0.839713 0.543030i \(-0.182723\pi\)
\(38\) −7.01018 + 26.1623i −0.184478 + 0.688483i
\(39\) 19.4326 11.2194i 0.498273 0.287678i
\(40\) 12.7505 6.11755i 0.318763 0.152939i
\(41\) −1.17994 −0.0287791 −0.0143895 0.999896i \(-0.504580\pi\)
−0.0143895 + 0.999896i \(0.504580\pi\)
\(42\) −16.2206 + 5.55794i −0.386206 + 0.132332i
\(43\) 2.70577 + 2.70577i 0.0629250 + 0.0629250i 0.737869 0.674944i \(-0.235832\pi\)
−0.674944 + 0.737869i \(0.735832\pi\)
\(44\) 4.61517 + 2.66457i 0.104890 + 0.0605584i
\(45\) −11.3838 + 9.76781i −0.252972 + 0.217062i
\(46\) 25.5851 + 44.3147i 0.556198 + 0.963363i
\(47\) 19.2185 + 71.7245i 0.408905 + 1.52605i 0.796739 + 0.604324i \(0.206557\pi\)
−0.387834 + 0.921729i \(0.626777\pi\)
\(48\) 4.89898 + 4.89898i 0.102062 + 0.102062i
\(49\) 38.7031 30.0511i 0.789859 0.613288i
\(50\) −14.2323 + 32.3642i −0.284646 + 0.647284i
\(51\) 2.42383 4.19820i 0.0475262 0.0823177i
\(52\) 25.0273 + 6.70605i 0.481295 + 0.128963i
\(53\) −2.09960 + 7.83581i −0.0396151 + 0.147845i −0.982901 0.184137i \(-0.941051\pi\)
0.943285 + 0.331983i \(0.107718\pi\)
\(54\) −6.36396 3.67423i −0.117851 0.0680414i
\(55\) −13.0942 + 2.45788i −0.238076 + 0.0446887i
\(56\) −17.7821 8.70607i −0.317538 0.155465i
\(57\) 23.4565 23.4565i 0.411518 0.411518i
\(58\) −17.0343 + 4.56433i −0.293695 + 0.0786953i
\(59\) 93.6121 54.0470i 1.58665 0.916050i 0.592791 0.805356i \(-0.298026\pi\)
0.993855 0.110694i \(-0.0353072\pi\)
\(60\) −17.2702 1.31942i −0.287836 0.0219903i
\(61\) 35.0235 60.6625i 0.574156 0.994467i −0.421977 0.906606i \(-0.638664\pi\)
0.996133 0.0878604i \(-0.0280029\pi\)
\(62\) 10.6756 10.6756i 0.172188 0.172188i
\(63\) 20.6081 + 4.03799i 0.327113 + 0.0640951i
\(64\) 8.00000i 0.125000i
\(65\) −58.4014 + 28.0203i −0.898483 + 0.431082i
\(66\) −3.26342 5.65241i −0.0494457 0.0856425i
\(67\) −16.8687 4.51996i −0.251772 0.0674620i 0.130726 0.991419i \(-0.458269\pi\)
−0.382497 + 0.923957i \(0.624936\pi\)
\(68\) 5.40687 1.44877i 0.0795128 0.0213054i
\(69\) 62.6705i 0.908267i
\(70\) 47.9111 12.4308i 0.684445 0.177583i
\(71\) 66.2750 0.933450 0.466725 0.884402i \(-0.345434\pi\)
0.466725 + 0.884402i \(0.345434\pi\)
\(72\) −2.19615 8.19615i −0.0305021 0.113835i
\(73\) 9.37151 34.9749i 0.128377 0.479109i −0.871561 0.490288i \(-0.836892\pi\)
0.999938 + 0.0111788i \(0.00355839\pi\)
\(74\) −27.8413 + 16.0742i −0.376233 + 0.217218i
\(75\) 34.9146 25.6120i 0.465528 0.341493i
\(76\) 38.3043 0.504004
\(77\) 14.0584 + 12.2580i 0.182577 + 0.159194i
\(78\) −22.4389 22.4389i −0.287678 0.287678i
\(79\) −83.6148 48.2750i −1.05841 0.611076i −0.133421 0.991059i \(-0.542596\pi\)
−0.924993 + 0.379983i \(0.875930\pi\)
\(80\) −13.0237 15.1783i −0.162797 0.189729i
\(81\) 4.50000 + 7.79423i 0.0555556 + 0.0962250i
\(82\) 0.431888 + 1.61183i 0.00526693 + 0.0196565i
\(83\) −83.4979 83.4979i −1.00600 1.00600i −0.999982 0.00601630i \(-0.998085\pi\)
−0.00601630 0.999982i \(-0.501915\pi\)
\(84\) 13.5295 + 20.1235i 0.161065 + 0.239565i
\(85\) −7.89987 + 11.5509i −0.0929397 + 0.135894i
\(86\) 2.70577 4.68654i 0.0314625 0.0544946i
\(87\) 20.8627 + 5.59014i 0.239801 + 0.0642544i
\(88\) 1.95060 7.27974i 0.0221659 0.0827243i
\(89\) 125.762 + 72.6089i 1.41306 + 0.815830i 0.995675 0.0928996i \(-0.0296136\pi\)
0.417384 + 0.908730i \(0.362947\pi\)
\(90\) 17.5098 + 11.9752i 0.194554 + 0.133058i
\(91\) 81.4478 + 39.8765i 0.895031 + 0.438204i
\(92\) 51.1702 51.1702i 0.556198 0.556198i
\(93\) −17.8607 + 4.78576i −0.192051 + 0.0514598i
\(94\) 90.9430 52.5060i 0.967479 0.558574i
\(95\) −72.6745 + 62.3582i −0.764995 + 0.656402i
\(96\) 4.89898 8.48528i 0.0510310 0.0883883i
\(97\) −43.6910 + 43.6910i −0.450422 + 0.450422i −0.895495 0.445072i \(-0.853178\pi\)
0.445072 + 0.895495i \(0.353178\pi\)
\(98\) −55.2169 41.8700i −0.563438 0.427245i
\(99\) 7.99371i 0.0807446i
\(100\) 49.4197 + 7.59554i 0.494197 + 0.0759554i
\(101\) 41.1858 + 71.3359i 0.407780 + 0.706296i 0.994641 0.103392i \(-0.0329697\pi\)
−0.586861 + 0.809688i \(0.699636\pi\)
\(102\) −6.62204 1.77437i −0.0649219 0.0173958i
\(103\) 68.0759 18.2409i 0.660931 0.177096i 0.0872648 0.996185i \(-0.472187\pi\)
0.573666 + 0.819089i \(0.305521\pi\)
\(104\) 36.6425i 0.352332i
\(105\) −58.4297 16.1546i −0.556473 0.153853i
\(106\) 11.4724 0.108230
\(107\) 32.6260 + 121.762i 0.304916 + 1.13796i 0.933017 + 0.359831i \(0.117166\pi\)
−0.628101 + 0.778132i \(0.716168\pi\)
\(108\) −2.68973 + 10.0382i −0.0249049 + 0.0929463i
\(109\) −187.044 + 107.990i −1.71600 + 0.990731i −0.790079 + 0.613006i \(0.789960\pi\)
−0.925918 + 0.377725i \(0.876706\pi\)
\(110\) 8.15032 + 16.9873i 0.0740939 + 0.154430i
\(111\) 39.3735 0.354716
\(112\) −5.38399 + 27.4775i −0.0480714 + 0.245335i
\(113\) −30.7458 30.7458i −0.272087 0.272087i 0.557853 0.829940i \(-0.311625\pi\)
−0.829940 + 0.557853i \(0.811625\pi\)
\(114\) −40.6279 23.4565i −0.356385 0.205759i
\(115\) −13.7814 + 180.388i −0.119839 + 1.56859i
\(116\) 12.4700 + 21.5986i 0.107500 + 0.186195i
\(117\) 10.0591 + 37.5410i 0.0859750 + 0.320863i
\(118\) −108.094 108.094i −0.916050 0.916050i
\(119\) 19.5459 1.33724i 0.164251 0.0112373i
\(120\) 4.51896 + 24.0744i 0.0376580 + 0.200620i
\(121\) 56.9500 98.6403i 0.470661 0.815209i
\(122\) −95.6860 25.6390i −0.784311 0.210156i
\(123\) 0.528953 1.97408i 0.00430043 0.0160494i
\(124\) −18.4908 10.6756i −0.149119 0.0860939i
\(125\) −106.129 + 66.0427i −0.849032 + 0.528342i
\(126\) −2.02709 29.6292i −0.0160880 0.235153i
\(127\) −144.611 + 144.611i −1.13867 + 1.13867i −0.149980 + 0.988689i \(0.547921\pi\)
−0.988689 + 0.149980i \(0.952079\pi\)
\(128\) 10.9282 2.92820i 0.0853766 0.0228766i
\(129\) −5.73981 + 3.31388i −0.0444947 + 0.0256890i
\(130\) 59.6529 + 69.5216i 0.458868 + 0.534782i
\(131\) 76.1519 131.899i 0.581312 1.00686i −0.414012 0.910271i \(-0.635873\pi\)
0.995324 0.0965906i \(-0.0307938\pi\)
\(132\) −6.52684 + 6.52684i −0.0494457 + 0.0494457i
\(133\) 131.563 + 25.7788i 0.989198 + 0.193825i
\(134\) 24.6975i 0.184310i
\(135\) −11.2387 23.4242i −0.0832493 0.173512i
\(136\) −3.95810 6.85564i −0.0291037 0.0504091i
\(137\) −236.953 63.4914i −1.72959 0.463441i −0.749498 0.662007i \(-0.769705\pi\)
−0.980088 + 0.198566i \(0.936372\pi\)
\(138\) −85.6094 + 22.9390i −0.620358 + 0.166224i
\(139\) 137.703i 0.990670i −0.868702 0.495335i \(-0.835045\pi\)
0.868702 0.495335i \(-0.164955\pi\)
\(140\) −34.5175 60.8978i −0.246553 0.434984i
\(141\) −128.613 −0.912148
\(142\) −24.2583 90.5333i −0.170833 0.637558i
\(143\) −8.93437 + 33.3435i −0.0624781 + 0.233172i
\(144\) −10.3923 + 6.00000i −0.0721688 + 0.0416667i
\(145\) −58.8211 20.6782i −0.405663 0.142608i
\(146\) −51.2069 −0.350732
\(147\) 32.9264 + 78.2231i 0.223989 + 0.532130i
\(148\) 32.1483 + 32.1483i 0.217218 + 0.217218i
\(149\) −150.312 86.7825i −1.00880 0.582433i −0.0979622 0.995190i \(-0.531232\pi\)
−0.910841 + 0.412757i \(0.864566\pi\)
\(150\) −47.7662 38.3196i −0.318441 0.255464i
\(151\) 115.430 + 199.931i 0.764440 + 1.32405i 0.940542 + 0.339677i \(0.110318\pi\)
−0.176102 + 0.984372i \(0.556349\pi\)
\(152\) −14.0204 52.3247i −0.0922392 0.344241i
\(153\) 5.93716 + 5.93716i 0.0388049 + 0.0388049i
\(154\) 11.5990 23.6909i 0.0753179 0.153837i
\(155\) 52.4620 9.84754i 0.338465 0.0635325i
\(156\) −22.4389 + 38.8653i −0.143839 + 0.249136i
\(157\) −190.802 51.1253i −1.21530 0.325639i −0.406461 0.913668i \(-0.633237\pi\)
−0.808840 + 0.588029i \(0.799904\pi\)
\(158\) −35.3398 + 131.890i −0.223669 + 0.834745i
\(159\) −12.1683 7.02539i −0.0765304 0.0441849i
\(160\) −15.9670 + 23.3464i −0.0997936 + 0.145915i
\(161\) 210.191 141.316i 1.30553 0.877740i
\(162\) 9.00000 9.00000i 0.0555556 0.0555556i
\(163\) 56.2117 15.0619i 0.344857 0.0924042i −0.0822332 0.996613i \(-0.526205\pi\)
0.427091 + 0.904209i \(0.359539\pi\)
\(164\) 2.04372 1.17994i 0.0124617 0.00719476i
\(165\) 1.75784 23.0088i 0.0106536 0.139447i
\(166\) −83.4979 + 144.623i −0.502999 + 0.871220i
\(167\) 133.293 133.293i 0.798159 0.798159i −0.184646 0.982805i \(-0.559114\pi\)
0.982805 + 0.184646i \(0.0591138\pi\)
\(168\) 22.5370 25.8473i 0.134149 0.153853i
\(169\) 1.16549i 0.00689640i
\(170\) 18.6704 + 6.56349i 0.109826 + 0.0386088i
\(171\) 28.7282 + 49.7588i 0.168001 + 0.290987i
\(172\) −7.39231 1.98076i −0.0429786 0.0115161i
\(173\) 152.287 40.8051i 0.880270 0.235868i 0.209746 0.977756i \(-0.432736\pi\)
0.670523 + 0.741888i \(0.266070\pi\)
\(174\) 30.5451i 0.175546i
\(175\) 164.629 + 59.3477i 0.940740 + 0.339130i
\(176\) −10.6583 −0.0605584
\(177\) 48.4572 + 180.845i 0.273769 + 1.02172i
\(178\) 53.1534 198.371i 0.298615 1.11445i
\(179\) −99.0632 + 57.1941i −0.553425 + 0.319520i −0.750502 0.660868i \(-0.770188\pi\)
0.197077 + 0.980388i \(0.436855\pi\)
\(180\) 9.94944 28.3021i 0.0552747 0.157234i
\(181\) −138.045 −0.762680 −0.381340 0.924435i \(-0.624537\pi\)
−0.381340 + 0.924435i \(0.624537\pi\)
\(182\) 24.6604 125.856i 0.135497 0.691515i
\(183\) 85.7897 + 85.7897i 0.468796 + 0.468796i
\(184\) −88.6294 51.1702i −0.481682 0.278099i
\(185\) −113.331 8.65836i −0.612601 0.0468019i
\(186\) 13.0749 + 22.6465i 0.0702954 + 0.121755i
\(187\) 1.93017 + 7.20350i 0.0103218 + 0.0385214i
\(188\) −105.012 105.012i −0.558574 0.558574i
\(189\) −15.9941 + 32.6679i −0.0846247 + 0.172846i
\(190\) 111.784 + 76.4506i 0.588335 + 0.402371i
\(191\) 58.2285 100.855i 0.304861 0.528035i −0.672369 0.740216i \(-0.734723\pi\)
0.977230 + 0.212181i \(0.0680567\pi\)
\(192\) −13.3843 3.58630i −0.0697097 0.0186787i
\(193\) 68.1361 254.287i 0.353037 1.31755i −0.529900 0.848060i \(-0.677771\pi\)
0.882937 0.469491i \(-0.155563\pi\)
\(194\) 75.6750 + 43.6910i 0.390077 + 0.225211i
\(195\) −20.6983 110.269i −0.106145 0.565480i
\(196\) −36.9846 + 90.7532i −0.188697 + 0.463026i
\(197\) 87.0401 87.0401i 0.441828 0.441828i −0.450798 0.892626i \(-0.648861\pi\)
0.892626 + 0.450798i \(0.148861\pi\)
\(198\) 10.9196 2.92590i 0.0551496 0.0147773i
\(199\) −327.885 + 189.304i −1.64766 + 0.951278i −0.669664 + 0.742664i \(0.733562\pi\)
−0.977998 + 0.208615i \(0.933105\pi\)
\(200\) −7.71318 70.2887i −0.0385659 0.351444i
\(201\) 15.1241 26.1957i 0.0752441 0.130327i
\(202\) 82.3716 82.3716i 0.407780 0.407780i
\(203\) 28.2946 + 82.5768i 0.139382 + 0.406782i
\(204\) 9.69534i 0.0475262i
\(205\) −1.95663 + 5.56580i −0.00954452 + 0.0271502i
\(206\) −49.8350 86.3168i −0.241918 0.419013i
\(207\) 104.850 + 28.0944i 0.506520 + 0.135722i
\(208\) −50.0546 + 13.4121i −0.240647 + 0.0644813i
\(209\) 51.0323i 0.244174i
\(210\) −0.680850 + 85.7294i −0.00324214 + 0.408235i
\(211\) −282.104 −1.33698 −0.668492 0.743719i \(-0.733060\pi\)
−0.668492 + 0.743719i \(0.733060\pi\)
\(212\) −4.19920 15.6716i −0.0198075 0.0739227i
\(213\) −29.7102 + 110.880i −0.139485 + 0.520564i
\(214\) 154.388 89.1360i 0.721440 0.416523i
\(215\) 17.2500 8.27636i 0.0802326 0.0384947i
\(216\) 14.6969 0.0680414
\(217\) −56.3253 49.1118i −0.259563 0.226322i
\(218\) 215.979 + 215.979i 0.990731 + 0.990731i
\(219\) 54.3131 + 31.3577i 0.248005 + 0.143186i
\(220\) 20.2219 17.3513i 0.0919177 0.0788697i
\(221\) 18.1294 + 31.4010i 0.0820334 + 0.142086i
\(222\) −14.4117 53.7852i −0.0649176 0.242276i
\(223\) −284.006 284.006i −1.27357 1.27357i −0.944203 0.329365i \(-0.893165\pi\)
−0.329365 0.944203i \(-0.606835\pi\)
\(224\) 39.5056 2.70279i 0.176364 0.0120660i
\(225\) 27.1979 + 69.8947i 0.120880 + 0.310643i
\(226\) −30.7458 + 53.2533i −0.136043 + 0.235634i
\(227\) 251.195 + 67.3074i 1.10658 + 0.296508i 0.765443 0.643504i \(-0.222520\pi\)
0.341141 + 0.940012i \(0.389187\pi\)
\(228\) −17.1714 + 64.0844i −0.0753130 + 0.281072i
\(229\) 70.9480 + 40.9618i 0.309817 + 0.178873i 0.646844 0.762622i \(-0.276088\pi\)
−0.337028 + 0.941495i \(0.609422\pi\)
\(230\) 251.459 47.2009i 1.09330 0.205221i
\(231\) −26.8102 + 18.0251i −0.116061 + 0.0780307i
\(232\) 24.9400 24.9400i 0.107500 0.107500i
\(233\) 0.0719192 0.0192707i 0.000308666 8.27069e-5i −0.258665 0.965967i \(-0.583282\pi\)
0.258973 + 0.965884i \(0.416616\pi\)
\(234\) 47.6001 27.4819i 0.203419 0.117444i
\(235\) 370.195 + 28.2824i 1.57530 + 0.120351i
\(236\) −108.094 + 187.224i −0.458025 + 0.793323i
\(237\) 118.249 118.249i 0.498941 0.498941i
\(238\) −8.98101 26.2108i −0.0377353 0.110129i
\(239\) 214.333i 0.896789i −0.893836 0.448395i \(-0.851996\pi\)
0.893836 0.448395i \(-0.148004\pi\)
\(240\) 31.2322 14.9849i 0.130134 0.0624370i
\(241\) 8.97579 + 15.5465i 0.0372439 + 0.0645084i 0.884047 0.467399i \(-0.154809\pi\)
−0.846803 + 0.531907i \(0.821475\pi\)
\(242\) −155.590 41.6903i −0.642935 0.172274i
\(243\) −15.0573 + 4.03459i −0.0619642 + 0.0166032i
\(244\) 140.094i 0.574156i
\(245\) −77.5725 232.395i −0.316622 0.948552i
\(246\) −2.89025 −0.0117490
\(247\) 64.2177 + 239.664i 0.259991 + 0.970298i
\(248\) −7.81512 + 29.1664i −0.0315126 + 0.117606i
\(249\) 177.126 102.264i 0.711348 0.410697i
\(250\) 129.062 + 120.802i 0.516248 + 0.483206i
\(251\) 199.148 0.793420 0.396710 0.917944i \(-0.370152\pi\)
0.396710 + 0.917944i \(0.370152\pi\)
\(252\) −39.7323 + 13.6141i −0.157668 + 0.0540242i
\(253\) 68.1733 + 68.1733i 0.269460 + 0.269460i
\(254\) 250.473 + 144.611i 0.986116 + 0.569334i
\(255\) −15.7837 18.3949i −0.0618968 0.0721368i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −8.44926 31.5331i −0.0328765 0.122697i 0.947537 0.319645i \(-0.103564\pi\)
−0.980414 + 0.196948i \(0.936897\pi\)
\(258\) 6.62777 + 6.62777i 0.0256890 + 0.0256890i
\(259\) 88.7836 + 132.055i 0.342794 + 0.509866i
\(260\) 73.1339 106.934i 0.281284 0.411285i
\(261\) −18.7050 + 32.3979i −0.0716665 + 0.124130i
\(262\) −208.051 55.7470i −0.794087 0.212775i
\(263\) −16.2941 + 60.8104i −0.0619547 + 0.231218i −0.989960 0.141350i \(-0.954856\pi\)
0.928005 + 0.372568i \(0.121523\pi\)
\(264\) 11.3048 + 6.52684i 0.0428213 + 0.0247229i
\(265\) 33.4800 + 22.8975i 0.126340 + 0.0864056i
\(266\) −12.9411 189.155i −0.0486506 0.711107i
\(267\) −177.855 + 177.855i −0.666123 + 0.666123i
\(268\) 33.7374 9.03991i 0.125886 0.0337310i
\(269\) 254.691 147.046i 0.946807 0.546639i 0.0547192 0.998502i \(-0.482574\pi\)
0.892088 + 0.451863i \(0.149240\pi\)
\(270\) −27.8844 + 23.9261i −0.103276 + 0.0886153i
\(271\) −137.975 + 238.979i −0.509132 + 0.881843i 0.490812 + 0.871266i \(0.336700\pi\)
−0.999944 + 0.0105773i \(0.996633\pi\)
\(272\) −7.91621 + 7.91621i −0.0291037 + 0.0291037i
\(273\) −103.227 + 118.389i −0.378120 + 0.433658i
\(274\) 346.924i 1.26614i
\(275\) −10.1194 + 65.8412i −0.0367979 + 0.239422i
\(276\) 62.6705 + 108.548i 0.227067 + 0.393291i
\(277\) 320.716 + 85.9356i 1.15782 + 0.310237i 0.786095 0.618106i \(-0.212100\pi\)
0.371725 + 0.928343i \(0.378766\pi\)
\(278\) −188.106 + 50.4029i −0.676641 + 0.181305i
\(279\) 32.0269i 0.114792i
\(280\) −70.5537 + 69.4419i −0.251978 + 0.248007i
\(281\) −386.157 −1.37423 −0.687113 0.726551i \(-0.741122\pi\)
−0.687113 + 0.726551i \(0.741122\pi\)
\(282\) 47.0756 + 175.688i 0.166935 + 0.623009i
\(283\) 40.3806 150.703i 0.142688 0.532518i −0.857160 0.515051i \(-0.827773\pi\)
0.999847 0.0174672i \(-0.00556027\pi\)
\(284\) −114.792 + 66.2750i −0.404196 + 0.233363i
\(285\) −71.7482 149.541i −0.251748 0.524706i
\(286\) 48.8183 0.170693
\(287\) 7.81363 2.67731i 0.0272252 0.00932860i
\(288\) 12.0000 + 12.0000i 0.0416667 + 0.0416667i
\(289\) −243.498 140.583i −0.842552 0.486448i
\(290\) −6.71696 + 87.9198i −0.0231619 + 0.303172i
\(291\) −53.5103 92.6825i −0.183884 0.318497i
\(292\) 18.7430 + 69.9499i 0.0641884 + 0.239554i
\(293\) 86.2939 + 86.2939i 0.294519 + 0.294519i 0.838862 0.544344i \(-0.183221\pi\)
−0.544344 + 0.838862i \(0.683221\pi\)
\(294\) 94.8029 73.6099i 0.322459 0.250374i
\(295\) −99.7091 531.192i −0.337997 1.80065i
\(296\) 32.1483 55.6825i 0.108609 0.188117i
\(297\) −13.3737 3.58348i −0.0450294 0.0120656i
\(298\) −63.5292 + 237.094i −0.213185 + 0.795618i
\(299\) 405.951 + 234.376i 1.35770 + 0.783866i
\(300\) −34.8618 + 79.2758i −0.116206 + 0.264253i
\(301\) −24.0572 11.7783i −0.0799243 0.0391306i
\(302\) 230.861 230.861i 0.764440 0.764440i
\(303\) −137.810 + 36.9262i −0.454820 + 0.121869i
\(304\) −66.3450 + 38.3043i −0.218240 + 0.126001i
\(305\) −228.069 265.799i −0.747766 0.871473i
\(306\) 5.93716 10.2835i 0.0194025 0.0336061i
\(307\) 216.926 216.926i 0.706601 0.706601i −0.259218 0.965819i \(-0.583465\pi\)
0.965819 + 0.259218i \(0.0834648\pi\)
\(308\) −36.6079 7.17301i −0.118857 0.0232890i
\(309\) 122.070i 0.395050i
\(310\) −32.6544 68.0600i −0.105337 0.219548i
\(311\) −118.412 205.096i −0.380748 0.659474i 0.610422 0.792077i \(-0.291000\pi\)
−0.991169 + 0.132603i \(0.957667\pi\)
\(312\) 61.3042 + 16.4264i 0.196488 + 0.0526487i
\(313\) 350.504 93.9171i 1.11982 0.300055i 0.349009 0.937119i \(-0.386518\pi\)
0.770810 + 0.637065i \(0.219852\pi\)
\(314\) 279.354i 0.889662i
\(315\) 53.2205 90.5129i 0.168954 0.287342i
\(316\) 193.100 0.611076
\(317\) 108.374 + 404.457i 0.341874 + 1.27589i 0.896222 + 0.443606i \(0.146301\pi\)
−0.554348 + 0.832285i \(0.687032\pi\)
\(318\) −5.14294 + 19.1937i −0.0161728 + 0.0603576i
\(319\) −28.7755 + 16.6136i −0.0902055 + 0.0520801i
\(320\) 37.7361 + 13.2659i 0.117925 + 0.0414560i
\(321\) −218.338 −0.680180
\(322\) −269.977 235.401i −0.838437 0.731059i
\(323\) 37.9031 + 37.9031i 0.117347 + 0.117347i
\(324\) −15.5885 9.00000i −0.0481125 0.0277778i
\(325\) 35.3288 + 321.945i 0.108704 + 0.990599i
\(326\) −41.1499 71.2736i −0.126227 0.218631i
\(327\) −96.8209 361.340i −0.296088 1.10502i
\(328\) −2.35988 2.35988i −0.00719476 0.00719476i
\(329\) −290.010 431.356i −0.881490 1.31111i
\(330\) −32.0740 + 6.02055i −0.0971940 + 0.0182441i
\(331\) 137.911 238.870i 0.416651 0.721660i −0.578949 0.815364i \(-0.696537\pi\)
0.995600 + 0.0937031i \(0.0298704\pi\)
\(332\) 228.120 + 61.1247i 0.687110 + 0.184110i
\(333\) −17.6507 + 65.8731i −0.0530050 + 0.197817i
\(334\) −230.870 133.293i −0.691226 0.399080i
\(335\) −49.2931 + 72.0748i −0.147143 + 0.215149i
\(336\) −43.5572 21.3254i −0.129634 0.0634685i
\(337\) 353.069 353.069i 1.04768 1.04768i 0.0488767 0.998805i \(-0.484436\pi\)
0.998805 0.0488767i \(-0.0155642\pi\)
\(338\) −1.59209 + 0.426600i −0.00471033 + 0.00126213i
\(339\) 65.2217 37.6558i 0.192394 0.111079i
\(340\) 2.13204 27.9067i 0.00627069 0.0820785i
\(341\) 14.2230 24.6350i 0.0417097 0.0722433i
\(342\) 57.4565 57.4565i 0.168001 0.168001i
\(343\) −188.107 + 286.818i −0.548418 + 0.836204i
\(344\) 10.8231i 0.0314625i
\(345\) −295.618 103.923i −0.856862 0.301225i
\(346\) −111.482 193.092i −0.322201 0.558069i
\(347\) −574.723 153.997i −1.65626 0.443794i −0.694906 0.719100i \(-0.744554\pi\)
−0.961357 + 0.275306i \(0.911221\pi\)
\(348\) −41.7254 + 11.1803i −0.119900 + 0.0321272i
\(349\) 455.965i 1.30649i 0.757147 + 0.653245i \(0.226593\pi\)
−0.757147 + 0.653245i \(0.773407\pi\)
\(350\) 20.8119 246.611i 0.0594626 0.704602i
\(351\) −67.3167 −0.191785
\(352\) 3.90120 + 14.5595i 0.0110830 + 0.0413622i
\(353\) −73.5143 + 274.359i −0.208256 + 0.777221i 0.780177 + 0.625559i \(0.215129\pi\)
−0.988432 + 0.151662i \(0.951537\pi\)
\(354\) 229.302 132.387i 0.647745 0.373976i
\(355\) 109.900 312.620i 0.309577 0.880620i
\(356\) −290.436 −0.815830
\(357\) −6.52495 + 33.3004i −0.0182772 + 0.0932786i
\(358\) 114.388 + 114.388i 0.319520 + 0.319520i
\(359\) −270.053 155.915i −0.752237 0.434304i 0.0742647 0.997239i \(-0.476339\pi\)
−0.826502 + 0.562934i \(0.809672\pi\)
\(360\) −42.3031 3.23190i −0.117509 0.00897751i
\(361\) 2.90262 + 5.02749i 0.00804050 + 0.0139266i
\(362\) 50.5280 + 188.573i 0.139580 + 0.520920i
\(363\) 139.499 + 139.499i 0.384293 + 0.384293i
\(364\) −180.948 + 12.3796i −0.497111 + 0.0340100i
\(365\) −149.437 102.202i −0.409417 0.280007i
\(366\) 85.7897 148.592i 0.234398 0.405989i
\(367\) −223.110 59.7822i −0.607930 0.162894i −0.0582952 0.998299i \(-0.518566\pi\)
−0.549635 + 0.835405i \(0.685233\pi\)
\(368\) −37.4592 + 139.800i −0.101791 + 0.379890i
\(369\) 3.06558 + 1.76991i 0.00830780 + 0.00479651i
\(370\) 29.6546 + 157.983i 0.0801475 + 0.426980i
\(371\) −3.87594 56.6531i −0.0104473 0.152704i
\(372\) 26.1499 26.1499i 0.0702954 0.0702954i
\(373\) 523.306 140.219i 1.40296 0.375923i 0.523556 0.851991i \(-0.324605\pi\)
0.879409 + 0.476068i \(0.157938\pi\)
\(374\) 9.13367 5.27332i 0.0244216 0.0140998i
\(375\) −62.9153 207.163i −0.167774 0.552436i
\(376\) −105.012 + 181.886i −0.279287 + 0.483739i
\(377\) −114.233 + 114.233i −0.303005 + 0.303005i
\(378\) 50.4794 + 9.89102i 0.133543 + 0.0261667i
\(379\) 454.147i 1.19828i 0.800645 + 0.599139i \(0.204490\pi\)
−0.800645 + 0.599139i \(0.795510\pi\)
\(380\) 63.5178 180.682i 0.167152 0.475479i
\(381\) −177.111 306.766i −0.464860 0.805160i
\(382\) −159.083 42.6262i −0.416448 0.111587i
\(383\) −190.725 + 51.1047i −0.497977 + 0.133433i −0.499061 0.866567i \(-0.666322\pi\)
0.00108386 + 0.999999i \(0.499655\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 81.1333 45.9871i 0.210736 0.119447i
\(386\) −372.303 −0.964514
\(387\) −2.97115 11.0885i −0.00767738 0.0286524i
\(388\) 31.9840 119.366i 0.0824330 0.307644i
\(389\) 39.8246 22.9928i 0.102377 0.0591074i −0.447937 0.894065i \(-0.647841\pi\)
0.550314 + 0.834958i \(0.314508\pi\)
\(390\) −143.054 + 68.6355i −0.366804 + 0.175988i
\(391\) 101.269 0.258999
\(392\) 137.508 + 17.3040i 0.350787 + 0.0441429i
\(393\) 186.533 + 186.533i 0.474639 + 0.474639i
\(394\) −150.758 87.0401i −0.382634 0.220914i
\(395\) −366.367 + 314.361i −0.927512 + 0.795850i
\(396\) −7.99371 13.8455i −0.0201861 0.0349634i
\(397\) −151.527 565.506i −0.381680 1.42445i −0.843335 0.537388i \(-0.819411\pi\)
0.461655 0.887059i \(-0.347256\pi\)
\(398\) 378.609 + 378.609i 0.951278 + 0.951278i
\(399\) −102.107 + 208.553i −0.255907 + 0.522690i
\(400\) −93.1930 + 36.2639i −0.232982 + 0.0906596i
\(401\) −203.933 + 353.222i −0.508561 + 0.880853i 0.491390 + 0.870940i \(0.336489\pi\)
−0.999951 + 0.00991335i \(0.996844\pi\)
\(402\) −41.3197 11.0716i −0.102785 0.0275413i
\(403\) 35.7957 133.591i 0.0888231 0.331492i
\(404\) −142.672 82.3716i −0.353148 0.203890i
\(405\) 44.2276 8.30187i 0.109204 0.0204984i
\(406\) 102.445 68.8764i 0.252329 0.169646i
\(407\) −42.8307 + 42.8307i −0.105235 + 0.105235i
\(408\) 13.2441 3.54874i 0.0324610 0.00869789i
\(409\) 273.205 157.735i 0.667983 0.385660i −0.127329 0.991861i \(-0.540640\pi\)
0.795312 + 0.606201i \(0.207307\pi\)
\(410\) 8.31920 + 0.635576i 0.0202907 + 0.00155019i
\(411\) 212.446 367.968i 0.516901 0.895299i
\(412\) −99.6700 + 99.6700i −0.241918 + 0.241918i
\(413\) −497.270 + 570.309i −1.20404 + 1.38089i
\(414\) 153.511i 0.370799i
\(415\) −532.320 + 255.401i −1.28270 + 0.615425i
\(416\) 36.6425 + 63.4667i 0.0880830 + 0.152564i
\(417\) 230.382 + 61.7307i 0.552475 + 0.148035i
\(418\) 69.7114 18.6791i 0.166774 0.0446869i
\(419\) 661.489i 1.57873i 0.613922 + 0.789367i \(0.289591\pi\)
−0.613922 + 0.789367i \(0.710409\pi\)
\(420\) 117.358 30.4491i 0.279423 0.0724978i
\(421\) −392.108 −0.931372 −0.465686 0.884950i \(-0.654192\pi\)
−0.465686 + 0.884950i \(0.654192\pi\)
\(422\) 103.257 + 385.361i 0.244685 + 0.913177i
\(423\) 57.6556 215.173i 0.136302 0.508684i
\(424\) −19.8708 + 11.4724i −0.0468651 + 0.0270576i
\(425\) 41.3861 + 56.4181i 0.0973791 + 0.132748i
\(426\) 162.340 0.381079
\(427\) −94.2831 + 481.179i −0.220804 + 1.12688i
\(428\) −178.272 178.272i −0.416523 0.416523i
\(429\) −51.7797 29.8950i −0.120698 0.0696853i
\(430\) −17.6197 20.5346i −0.0409759 0.0477549i
\(431\) 21.8126 + 37.7805i 0.0506093 + 0.0876579i 0.890220 0.455530i \(-0.150550\pi\)
−0.839611 + 0.543188i \(0.817217\pi\)
\(432\) −5.37945 20.0764i −0.0124524 0.0464731i
\(433\) 527.265 + 527.265i 1.21770 + 1.21770i 0.968434 + 0.249268i \(0.0801901\pi\)
0.249268 + 0.968434i \(0.419810\pi\)
\(434\) −46.4714 + 94.9179i −0.107077 + 0.218705i
\(435\) 60.9641 89.1398i 0.140147 0.204919i
\(436\) 215.979 374.087i 0.495365 0.857998i
\(437\) 669.366 + 179.356i 1.53173 + 0.410426i
\(438\) 22.9554 85.6708i 0.0524096 0.195595i
\(439\) −307.063 177.283i −0.699459 0.403833i 0.107687 0.994185i \(-0.465656\pi\)
−0.807146 + 0.590352i \(0.798989\pi\)
\(440\) −31.1041 21.2726i −0.0706911 0.0483468i
\(441\) −145.630 + 20.0204i −0.330227 + 0.0453977i
\(442\) 36.2588 36.2588i 0.0820334 0.0820334i
\(443\) 582.736 156.144i 1.31543 0.352469i 0.468167 0.883640i \(-0.344915\pi\)
0.847265 + 0.531171i \(0.178248\pi\)
\(444\) −68.1969 + 39.3735i −0.153597 + 0.0886790i
\(445\) 551.042 472.820i 1.23830 1.06252i
\(446\) −284.006 + 491.912i −0.636784 + 1.10294i
\(447\) 212.573 212.573i 0.475554 0.475554i
\(448\) −18.1521 52.9764i −0.0405182 0.118251i
\(449\) 304.047i 0.677165i −0.940937 0.338583i \(-0.890053\pi\)
0.940937 0.338583i \(-0.109947\pi\)
\(450\) 85.5229 62.7363i 0.190051 0.139414i
\(451\) 1.57202 + 2.72282i 0.00348563 + 0.00603728i
\(452\) 83.9991 + 22.5075i 0.185839 + 0.0497954i
\(453\) −386.238 + 103.492i −0.852622 + 0.228459i
\(454\) 367.774i 0.810076i
\(455\) 323.158 318.066i 0.710238 0.699046i
\(456\) 93.8260 0.205759
\(457\) 66.4786 + 248.101i 0.145467 + 0.542891i 0.999734 + 0.0230567i \(0.00733981\pi\)
−0.854267 + 0.519835i \(0.825994\pi\)
\(458\) 29.9861 111.910i 0.0654719 0.244345i
\(459\) −12.5946 + 7.27150i −0.0274392 + 0.0158421i
\(460\) −156.518 326.223i −0.340257 0.709181i
\(461\) −528.700 −1.14685 −0.573427 0.819257i \(-0.694386\pi\)
−0.573427 + 0.819257i \(0.694386\pi\)
\(462\) 34.4359 + 30.0258i 0.0745367 + 0.0649909i
\(463\) −415.206 415.206i −0.896773 0.896773i 0.0983763 0.995149i \(-0.468635\pi\)
−0.995149 + 0.0983763i \(0.968635\pi\)
\(464\) −43.1973 24.9400i −0.0930975 0.0537499i
\(465\) −7.04283 + 92.1852i −0.0151459 + 0.198248i
\(466\) −0.0526485 0.0911900i −0.000112980 0.000195687i
\(467\) 109.764 + 409.645i 0.235041 + 0.877185i 0.978130 + 0.207993i \(0.0666930\pi\)
−0.743089 + 0.669192i \(0.766640\pi\)
\(468\) −54.9638 54.9638i −0.117444 0.117444i
\(469\) 121.961 8.34402i 0.260045 0.0177911i
\(470\) −96.8662 516.047i −0.206098 1.09797i
\(471\) 171.069 296.300i 0.363203 0.629086i
\(472\) 295.318 + 79.1302i 0.625674 + 0.167649i
\(473\) 2.63894 9.84867i 0.00557916 0.0208217i
\(474\) −204.813 118.249i −0.432096 0.249471i
\(475\) 173.633 + 446.212i 0.365543 + 0.939393i
\(476\) −32.5173 + 21.8621i −0.0683137 + 0.0459288i
\(477\) 17.2086 17.2086i 0.0360768 0.0360768i
\(478\) −292.784 + 78.4512i −0.612518 + 0.164124i
\(479\) 225.668 130.289i 0.471123 0.272003i −0.245587 0.969375i \(-0.578981\pi\)
0.716710 + 0.697372i \(0.245647\pi\)
\(480\) −31.9015 37.1792i −0.0664615 0.0774567i
\(481\) −147.250 + 255.044i −0.306132 + 0.530236i
\(482\) 17.9516 17.9516i 0.0372439 0.0372439i
\(483\) 142.200 + 415.007i 0.294411 + 0.859228i
\(484\) 227.800i 0.470661i
\(485\) 133.641 + 278.541i 0.275548 + 0.574312i
\(486\) 11.0227 + 19.0919i 0.0226805 + 0.0392837i
\(487\) −457.565 122.604i −0.939558 0.251754i −0.243632 0.969868i \(-0.578339\pi\)
−0.695925 + 0.718114i \(0.745006\pi\)
\(488\) 191.372 51.2780i 0.392156 0.105078i
\(489\) 100.796i 0.206127i
\(490\) −289.064 + 191.029i −0.589927 + 0.389854i
\(491\) 149.141 0.303750 0.151875 0.988400i \(-0.451469\pi\)
0.151875 + 0.988400i \(0.451469\pi\)
\(492\) 1.05791 + 3.94816i 0.00215022 + 0.00802471i
\(493\) −9.03304 + 33.7118i −0.0183226 + 0.0683809i
\(494\) 303.881 175.446i 0.615144 0.355154i
\(495\) 37.7065 + 13.2555i 0.0761747 + 0.0267788i
\(496\) 42.7026 0.0860939
\(497\) −438.876 + 150.379i −0.883050 + 0.302574i
\(498\) −204.527 204.527i −0.410697 0.410697i
\(499\) 298.044 + 172.076i 0.597282 + 0.344841i 0.767971 0.640484i \(-0.221266\pi\)
−0.170690 + 0.985325i \(0.554600\pi\)
\(500\) 117.778 220.518i 0.235556 0.441037i
\(501\) 163.249 + 282.756i 0.325847 + 0.564384i
\(502\) −72.8933 272.042i −0.145206 0.541916i
\(503\) −392.676 392.676i −0.780667 0.780667i 0.199276 0.979943i \(-0.436141\pi\)
−0.979943 + 0.199276i \(0.936141\pi\)
\(504\) 33.1403 + 49.2922i 0.0657545 + 0.0978020i
\(505\) 404.788 75.9820i 0.801561 0.150459i
\(506\) 68.1733 118.080i 0.134730 0.233359i
\(507\) 1.94991 + 0.522476i 0.00384597 + 0.00103052i
\(508\) 105.863 395.084i 0.208391 0.777725i
\(509\) −4.48117 2.58721i −0.00880388 0.00508292i 0.495592 0.868556i \(-0.334951\pi\)
−0.504395 + 0.863473i \(0.668285\pi\)
\(510\) −19.3507 + 28.2939i −0.0379425 + 0.0554783i
\(511\) 17.3002 + 252.870i 0.0338556 + 0.494853i
\(512\) −16.0000 + 16.0000i −0.0312500 + 0.0312500i
\(513\) −96.1266 + 25.7570i −0.187381 + 0.0502086i
\(514\) −39.9823 + 23.0838i −0.0777866 + 0.0449101i
\(515\) 26.8437 351.363i 0.0521236 0.682258i
\(516\) 6.62777 11.4796i 0.0128445 0.0222473i
\(517\) 139.906 139.906i 0.270611 0.270611i
\(518\) 147.894 169.616i 0.285509 0.327445i
\(519\) 273.073i 0.526152i
\(520\) −172.843 60.7621i −0.332391 0.116850i
\(521\) 330.348 + 572.180i 0.634065 + 1.09823i 0.986712 + 0.162477i \(0.0519484\pi\)
−0.352647 + 0.935756i \(0.614718\pi\)
\(522\) 51.1029 + 13.6930i 0.0978983 + 0.0262318i
\(523\) −615.606 + 164.951i −1.17707 + 0.315394i −0.793763 0.608228i \(-0.791881\pi\)
−0.383305 + 0.923622i \(0.625214\pi\)
\(524\) 304.607i 0.581312i
\(525\) −173.092 + 248.826i −0.329699 + 0.473953i
\(526\) 89.0325 0.169263
\(527\) −7.73326 28.8609i −0.0146741 0.0547646i
\(528\) 4.77798 17.8317i 0.00904920 0.0337721i
\(529\) 675.669 390.098i 1.27726 0.737425i
\(530\) 19.0240 54.1156i 0.0358944 0.102105i
\(531\) −324.282 −0.610700
\(532\) −253.653 + 86.9132i −0.476792 + 0.163371i
\(533\) 10.8090 + 10.8090i 0.0202796 + 0.0202796i
\(534\) 308.054 + 177.855i 0.576879 + 0.333061i
\(535\) 628.455 + 48.0132i 1.17468 + 0.0897442i
\(536\) −24.6975 42.7773i −0.0460774 0.0798084i
\(537\) −51.2789 191.375i −0.0954914 0.356379i
\(538\) −294.092 294.092i −0.546639 0.546639i
\(539\) −120.909 49.2741i −0.224321 0.0914176i
\(540\) 42.8901 + 29.3332i 0.0794261 + 0.0543208i
\(541\) 363.828 630.169i 0.672511 1.16482i −0.304679 0.952455i \(-0.598549\pi\)
0.977190 0.212368i \(-0.0681175\pi\)
\(542\) 376.954 + 101.005i 0.695488 + 0.186355i
\(543\) 61.8839 230.954i 0.113967 0.425330i
\(544\) 13.7113 + 7.91621i 0.0252046 + 0.0145519i
\(545\) 199.226 + 1061.36i 0.365552 + 1.94745i
\(546\) 199.506 + 97.6772i 0.365395 + 0.178896i
\(547\) −157.847 + 157.847i −0.288568 + 0.288568i −0.836514 0.547946i \(-0.815410\pi\)
0.547946 + 0.836514i \(0.315410\pi\)
\(548\) 473.906 126.983i 0.864793 0.231720i
\(549\) −181.987 + 105.070i −0.331489 + 0.191385i
\(550\) 93.6447 10.2762i 0.170263 0.0186839i
\(551\) −119.413 + 206.830i −0.216721 + 0.375372i
\(552\) 125.341 125.341i 0.227067 0.227067i
\(553\) 663.238 + 129.956i 1.19935 + 0.235002i
\(554\) 469.561i 0.847583i
\(555\) 65.2907 185.725i 0.117641 0.334640i
\(556\) 137.703 + 238.509i 0.247668 + 0.428973i
\(557\) 251.964 + 67.5136i 0.452359 + 0.121209i 0.477803 0.878467i \(-0.341433\pi\)
−0.0254439 + 0.999676i \(0.508100\pi\)
\(558\) −43.7496 + 11.7227i −0.0784043 + 0.0210084i
\(559\) 49.5732i 0.0886820i
\(560\) 120.684 + 70.9607i 0.215507 + 0.126715i
\(561\) −12.9170 −0.0230249
\(562\) 141.343 + 527.501i 0.251501 + 0.938613i
\(563\) 261.631 976.421i 0.464709 1.73432i −0.193142 0.981171i \(-0.561868\pi\)
0.657851 0.753148i \(-0.271466\pi\)
\(564\) 222.764 128.613i 0.394972 0.228037i
\(565\) −196.012 + 94.0446i −0.346925 + 0.166451i
\(566\) −220.644 −0.389830
\(567\) −47.4845 41.4032i −0.0837469 0.0730215i
\(568\) 132.550 + 132.550i 0.233363 + 0.233363i
\(569\) −232.943 134.490i −0.409391 0.236362i 0.281137 0.959668i \(-0.409288\pi\)
−0.690528 + 0.723306i \(0.742622\pi\)
\(570\) −178.015 + 152.746i −0.312308 + 0.267975i
\(571\) 30.3033 + 52.4869i 0.0530706 + 0.0919209i 0.891340 0.453335i \(-0.149766\pi\)
−0.838270 + 0.545256i \(0.816433\pi\)
\(572\) −17.8687 66.6871i −0.0312391 0.116586i
\(573\) 142.630 + 142.630i 0.248918 + 0.248918i
\(574\) −6.51726 9.69365i −0.0113541 0.0168879i
\(575\) 828.042 + 364.134i 1.44007 + 0.633277i
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) 173.023 + 46.3613i 0.299866 + 0.0803488i 0.405615 0.914044i \(-0.367057\pi\)
−0.105749 + 0.994393i \(0.533724\pi\)
\(578\) −102.914 + 384.081i −0.178052 + 0.664500i
\(579\) 394.886 + 227.988i 0.682015 + 0.393761i
\(580\) 122.559 23.0054i 0.211309 0.0396644i
\(581\) 742.385 + 363.469i 1.27777 + 0.625592i
\(582\) −107.021 + 107.021i −0.183884 + 0.183884i
\(583\) 20.8791 5.59453i 0.0358131 0.00959610i
\(584\) 88.6929 51.2069i 0.151871 0.0876830i
\(585\) 193.762 + 14.8031i 0.331217 + 0.0253045i
\(586\) 86.2939 149.465i 0.147259 0.255061i
\(587\) 9.92331 9.92331i 0.0169051 0.0169051i −0.698604 0.715509i \(-0.746195\pi\)
0.715509 + 0.698604i \(0.246195\pi\)
\(588\) −135.253 102.560i −0.230022 0.174422i
\(589\) 204.462i 0.347134i
\(590\) −689.126 + 330.635i −1.16801 + 0.560398i
\(591\) 106.602 + 184.640i 0.180375 + 0.312419i
\(592\) −87.8309 23.5342i −0.148363 0.0397537i
\(593\) −237.396 + 63.6101i −0.400331 + 0.107268i −0.453366 0.891324i \(-0.649777\pi\)
0.0530356 + 0.998593i \(0.483110\pi\)
\(594\) 19.5805i 0.0329638i
\(595\) 26.1041 94.4159i 0.0438724 0.158682i
\(596\) 347.130 0.582433
\(597\) −169.726 633.425i −0.284298 1.06101i
\(598\) 171.575 640.327i 0.286915 1.07078i
\(599\) −415.536 + 239.910i −0.693715 + 0.400517i −0.805002 0.593272i \(-0.797836\pi\)
0.111287 + 0.993788i \(0.464503\pi\)
\(600\) 121.053 + 18.6052i 0.201755 + 0.0310086i
\(601\) 425.170 0.707437 0.353719 0.935352i \(-0.384917\pi\)
0.353719 + 0.935352i \(0.384917\pi\)
\(602\) −7.28393 + 37.1739i −0.0120996 + 0.0617507i
\(603\) 37.0462 + 37.0462i 0.0614366 + 0.0614366i
\(604\) −399.863 230.861i −0.662024 0.382220i
\(605\) −370.851 432.204i −0.612977 0.714386i
\(606\) 100.884 + 174.736i 0.166476 + 0.288344i
\(607\) −263.511 983.437i −0.434120 1.62016i −0.743163 0.669111i \(-0.766675\pi\)
0.309042 0.951048i \(-0.399992\pi\)
\(608\) 76.6086 + 76.6086i 0.126001 + 0.126001i
\(609\) −150.838 + 10.3196i −0.247681 + 0.0169452i
\(610\) −279.610 + 408.837i −0.458377 + 0.670224i
\(611\) 480.988 833.096i 0.787215 1.36350i
\(612\) −16.2206 4.34630i −0.0265043 0.00710180i
\(613\) −139.188 + 519.456i −0.227060 + 0.847400i 0.754509 + 0.656290i \(0.227875\pi\)
−0.981569 + 0.191110i \(0.938791\pi\)
\(614\) −375.728 216.926i −0.611934 0.353300i
\(615\) −8.43463 5.76858i −0.0137149 0.00937980i
\(616\) 3.60089 + 52.6328i 0.00584560 + 0.0854428i
\(617\) 260.554 260.554i 0.422292 0.422292i −0.463700 0.885992i \(-0.653479\pi\)
0.885992 + 0.463700i \(0.153479\pi\)
\(618\) 166.751 44.6808i 0.269824 0.0722991i
\(619\) −208.960 + 120.643i −0.337577 + 0.194900i −0.659200 0.751967i \(-0.729105\pi\)
0.321623 + 0.946868i \(0.395772\pi\)
\(620\) −81.0193 + 69.5184i −0.130676 + 0.112127i
\(621\) −94.0057 + 162.823i −0.151378 + 0.262194i
\(622\) −236.825 + 236.825i −0.380748 + 0.380748i
\(623\) −997.555 195.463i −1.60121 0.313745i
\(624\) 89.7555i 0.143839i
\(625\) 135.537 + 610.127i 0.216860 + 0.976203i
\(626\) −256.586 444.421i −0.409882 0.709937i
\(627\) −85.3787 22.8771i −0.136170 0.0364867i
\(628\) 381.604 102.251i 0.607650 0.162819i
\(629\) 63.6232i 0.101150i
\(630\) −143.123 39.5705i −0.227179 0.0628104i
\(631\) −477.838 −0.757271 −0.378635 0.925546i \(-0.623607\pi\)
−0.378635 + 0.925546i \(0.623607\pi\)
\(632\) −70.6795 263.780i −0.111835 0.417373i
\(633\) 126.464 471.969i 0.199785 0.745606i
\(634\) 512.831 296.083i 0.808882 0.467008i
\(635\) 442.332 + 921.932i 0.696586 + 1.45186i
\(636\) 28.1016 0.0441849
\(637\) −629.832 79.2579i −0.988748 0.124424i
\(638\) 33.2271 + 33.2271i 0.0520801 + 0.0520801i
\(639\) −172.187 99.4124i −0.269464 0.155575i
\(640\) 4.30920 56.4042i 0.00673313 0.0881315i
\(641\) 353.417 + 612.135i 0.551352 + 0.954969i 0.998177 + 0.0603483i \(0.0192212\pi\)
−0.446825 + 0.894621i \(0.647446\pi\)
\(642\) 79.9172 + 298.255i 0.124482 + 0.464571i
\(643\) −473.054 473.054i −0.735698 0.735698i 0.236044 0.971742i \(-0.424149\pi\)
−0.971742 + 0.236044i \(0.924149\pi\)
\(644\) −222.746 + 454.958i −0.345878 + 0.706456i
\(645\) 6.11365 + 32.5700i 0.00947853 + 0.0504961i
\(646\) 37.9031 65.6501i 0.0586736 0.101626i
\(647\) −820.431 219.834i −1.26805 0.339774i −0.438769 0.898600i \(-0.644586\pi\)
−0.829285 + 0.558825i \(0.811252\pi\)
\(648\) −6.58846 + 24.5885i −0.0101674 + 0.0379452i
\(649\) −249.436 144.012i −0.384339 0.221898i
\(650\) 426.854 166.100i 0.656698 0.255538i
\(651\) 107.416 72.2178i 0.165001 0.110934i
\(652\) −82.2997 + 82.2997i −0.126227 + 0.126227i
\(653\) 342.981 91.9014i 0.525238 0.140737i 0.0135498 0.999908i \(-0.495687\pi\)
0.511689 + 0.859171i \(0.329020\pi\)
\(654\) −458.161 + 264.520i −0.700553 + 0.404464i
\(655\) −495.891 577.930i −0.757086 0.882335i
\(656\) −2.35988 + 4.08744i −0.00359738 + 0.00623085i
\(657\) −76.8103 + 76.8103i −0.116911 + 0.116911i
\(658\) −483.092 + 554.049i −0.734183 + 0.842019i
\(659\) 477.254i 0.724210i −0.932137 0.362105i \(-0.882058\pi\)
0.932137 0.362105i \(-0.117942\pi\)
\(660\) 19.9641 + 41.6103i 0.0302487 + 0.0630459i
\(661\) −34.1279 59.1113i −0.0516308 0.0894271i 0.839055 0.544047i \(-0.183109\pi\)
−0.890686 + 0.454620i \(0.849775\pi\)
\(662\) −376.781 100.958i −0.569156 0.152505i
\(663\) −60.6621 + 16.2544i −0.0914964 + 0.0245164i
\(664\) 333.991i 0.502999i
\(665\) 339.762 577.839i 0.510921 0.868931i
\(666\) 96.4450 0.144812
\(667\) 116.779 + 435.824i 0.175081 + 0.653410i
\(668\) −97.5770 + 364.162i −0.146073 + 0.545153i
\(669\) 602.467 347.834i 0.900548 0.519932i
\(670\) 116.498 + 40.9544i 0.173878 + 0.0611259i
\(671\) −186.645 −0.278160
\(672\) −13.1880 + 67.3058i −0.0196250 + 0.100157i
\(673\) −425.308 425.308i −0.631958 0.631958i 0.316601 0.948559i \(-0.397458\pi\)
−0.948559 + 0.316601i \(0.897458\pi\)
\(674\) −611.533 353.069i −0.907319 0.523841i
\(675\) −129.129 + 14.1700i −0.191302 + 0.0209926i
\(676\) 1.16549 + 2.01869i 0.00172410 + 0.00298623i
\(677\) −158.366 591.029i −0.233923 0.873012i −0.978631 0.205622i \(-0.934078\pi\)
0.744709 0.667390i \(-0.232588\pi\)
\(678\) −75.3116 75.3116i −0.111079 0.111079i
\(679\) 190.188 388.459i 0.280100 0.572105i
\(680\) −38.9016 + 7.30215i −0.0572083 + 0.0107385i
\(681\) −225.215 + 390.084i −0.330712 + 0.572810i
\(682\) −38.8580 10.4120i −0.0569765 0.0152668i
\(683\) 108.101 403.439i 0.158274 0.590687i −0.840529 0.541767i \(-0.817755\pi\)
0.998803 0.0489198i \(-0.0155779\pi\)
\(684\) −99.5175 57.4565i −0.145493 0.0840007i
\(685\) −692.415 + 1012.43i −1.01083 + 1.47800i
\(686\) 460.653 + 151.977i 0.671506 + 0.221541i
\(687\) −100.336 + 100.336i −0.146049 + 0.146049i
\(688\) 14.7846 3.96153i 0.0214893 0.00575804i
\(689\) 91.0146 52.5473i 0.132097 0.0762661i
\(690\) −33.7575 + 441.859i −0.0489239 + 0.640376i
\(691\) −303.668 + 525.968i −0.439462 + 0.761170i −0.997648 0.0685458i \(-0.978164\pi\)
0.558186 + 0.829716i \(0.311497\pi\)
\(692\) −222.963 + 222.963i −0.322201 + 0.322201i
\(693\) −18.1379 52.9348i −0.0261730 0.0763849i
\(694\) 841.453i 1.21247i
\(695\) −649.548 228.345i −0.934602 0.328554i
\(696\) 30.5451 + 52.9056i 0.0438866 + 0.0760138i
\(697\) 3.18989 + 0.854730i 0.00457661 + 0.00122630i
\(698\) 622.860 166.895i 0.892349 0.239104i
\(699\) 0.128962i 0.000184495i
\(700\) −344.494 + 61.8362i −0.492135 + 0.0883374i
\(701\) 483.579 0.689842 0.344921 0.938632i \(-0.387906\pi\)
0.344921 + 0.938632i \(0.387906\pi\)
\(702\) 24.6396 + 91.9563i 0.0350992 + 0.130992i
\(703\) −112.683 + 420.538i −0.160288 + 0.598204i
\(704\) 18.4607 10.6583i 0.0262226 0.0151396i
\(705\) −213.271 + 606.669i −0.302512 + 0.860523i
\(706\) 401.690 0.568966
\(707\) −434.597 378.938i −0.614705 0.535981i
\(708\) −264.775 264.775i −0.373976 0.373976i
\(709\) 744.478 + 429.824i 1.05004 + 0.606240i 0.922660 0.385614i \(-0.126010\pi\)
0.127379 + 0.991854i \(0.459344\pi\)
\(710\) −467.273 35.6990i −0.658131 0.0502803i
\(711\) 144.825 + 250.844i 0.203692 + 0.352805i
\(712\) 106.307 + 396.742i 0.149307 + 0.557223i
\(713\) −273.138 273.138i −0.383082 0.383082i
\(714\) 47.8775 3.27556i 0.0670554 0.00458762i
\(715\) 142.467 + 97.4352i 0.199254 + 0.136273i
\(716\) 114.388 198.126i 0.159760 0.276713i
\(717\) 358.585 + 96.0827i 0.500119 + 0.134007i
\(718\) −114.138 + 425.968i −0.158966 + 0.593271i
\(719\) 488.623 + 282.107i 0.679587 + 0.392360i 0.799699 0.600401i \(-0.204992\pi\)
−0.120112 + 0.992760i \(0.538326\pi\)
\(720\) 11.0692 + 58.9701i 0.0153738 + 0.0819029i
\(721\) −409.413 + 275.257i −0.567841 + 0.381772i
\(722\) 5.80524 5.80524i 0.00804050 0.00804050i
\(723\) −30.0336 + 8.04747i −0.0415402 + 0.0111307i
\(724\) 239.101 138.045i 0.330250 0.190670i
\(725\) −195.079 + 243.170i −0.269074 + 0.335408i
\(726\) 139.499 241.619i 0.192147 0.332808i
\(727\) 445.432 445.432i 0.612699 0.612699i −0.330949 0.943649i \(-0.607369\pi\)
0.943649 + 0.330949i \(0.107369\pi\)
\(728\) 83.1426 + 242.649i 0.114207 + 0.333309i
\(729\) 27.0000i 0.0370370i
\(730\) −84.9133 + 241.544i −0.116320 + 0.330882i
\(731\) −5.35487 9.27490i −0.00732540 0.0126880i
\(732\) −234.382 62.8024i −0.320194 0.0857957i
\(733\) −786.415 + 210.719i −1.07287 + 0.287475i −0.751672 0.659537i \(-0.770753\pi\)
−0.321199 + 0.947012i \(0.604086\pi\)
\(734\) 326.656i 0.445036i
\(735\) 423.579 25.6014i 0.576299 0.0348319i
\(736\) 204.681 0.278099
\(737\) 12.0437 + 44.9479i 0.0163416 + 0.0609876i
\(738\) 1.29567 4.83549i 0.00175564 0.00655215i
\(739\) −1181.31 + 682.028i −1.59852 + 0.922906i −0.606747 + 0.794895i \(0.707526\pi\)
−0.991773 + 0.128011i \(0.959141\pi\)
\(740\) 204.954 98.3345i 0.276965 0.132884i
\(741\) −429.753 −0.579964
\(742\) −75.9709 + 26.0311i −0.102387 + 0.0350824i
\(743\) −355.898 355.898i −0.479002 0.479002i 0.425810 0.904812i \(-0.359989\pi\)
−0.904812 + 0.425810i \(0.859989\pi\)
\(744\) −45.2929 26.1499i −0.0608776 0.0351477i
\(745\) −658.607 + 565.116i −0.884037 + 0.758545i
\(746\) −383.086 663.525i −0.513521 0.889444i
\(747\) 91.6870 + 342.181i 0.122740 + 0.458073i
\(748\) −10.5466 10.5466i −0.0140998 0.0140998i
\(749\) −492.332 732.285i −0.657319 0.977684i
\(750\) −259.962 + 161.771i −0.346616 + 0.215695i
\(751\) −52.5404 + 91.0027i −0.0699606 + 0.121175i −0.898884 0.438187i \(-0.855621\pi\)
0.828923 + 0.559363i \(0.188954\pi\)
\(752\) 286.898 + 76.8741i 0.381513 + 0.102226i
\(753\) −89.2757 + 333.182i −0.118560 + 0.442472i
\(754\) 197.857 + 114.233i 0.262410 + 0.151503i
\(755\) 1134.49 212.953i 1.50264 0.282057i
\(756\) −4.96534 72.5765i −0.00656792 0.0960006i
\(757\) 352.398 352.398i 0.465519 0.465519i −0.434940 0.900459i \(-0.643231\pi\)
0.900459 + 0.434940i \(0.143231\pi\)
\(758\) 620.377 166.229i 0.818439 0.219300i
\(759\) −144.617 + 83.4949i −0.190537 + 0.110006i
\(760\) −270.065 20.6326i −0.355349 0.0271482i
\(761\) 210.153 363.996i 0.276154 0.478313i −0.694271 0.719713i \(-0.744273\pi\)
0.970426 + 0.241400i \(0.0776066\pi\)
\(762\) −354.223 + 354.223i −0.464860 + 0.464860i
\(763\) 993.582 1139.52i 1.30220 1.49347i
\(764\) 232.914i 0.304861i
\(765\) 37.8509 18.1604i 0.0494783 0.0237391i
\(766\) 139.621 + 241.830i 0.182272 + 0.315705i
\(767\) −1352.65 362.442i −1.76356 0.472545i
\(768\) 26.7685 7.17260i 0.0348548 0.00933933i
\(769\) 187.682i 0.244059i −0.992526 0.122030i \(-0.961060\pi\)
0.992526 0.122030i \(-0.0389403\pi\)
\(770\) −92.5164 93.9977i −0.120151 0.122075i
\(771\) 56.5435 0.0733379
\(772\) 136.272 + 508.575i 0.176518 + 0.658776i
\(773\) 25.9771 96.9480i 0.0336056 0.125418i −0.947085 0.320982i \(-0.895987\pi\)
0.980691 + 0.195564i \(0.0626538\pi\)
\(774\) −14.0596 + 8.11732i −0.0181649 + 0.0104875i
\(775\) 40.5436 263.794i 0.0523144 0.340379i
\(776\) −174.764 −0.225211
\(777\) −260.733 + 89.3392i −0.335564 + 0.114980i
\(778\) −45.9855 45.9855i −0.0591074 0.0591074i
\(779\) 19.5708 + 11.2992i 0.0251230 + 0.0145048i
\(780\) 146.119 + 170.293i 0.187332 + 0.218324i
\(781\) −88.2971 152.935i −0.113057 0.195820i
\(782\) −37.0669 138.335i −0.0474001 0.176899i
\(783\) −45.8176 45.8176i −0.0585155 0.0585155i
\(784\) −26.6939 194.174i −0.0340483 0.247671i
\(785\) −557.555 + 815.239i −0.710261 + 1.03852i
\(786\) 186.533 323.085i 0.237320 0.411050i
\(787\) 96.9040 + 25.9653i 0.123131 + 0.0329928i 0.319858 0.947465i \(-0.396365\pi\)
−0.196727 + 0.980458i \(0.563031\pi\)
\(788\) −63.7177 + 237.798i −0.0808601 + 0.301774i
\(789\) −94.4333 54.5211i −0.119687 0.0691015i
\(790\) 563.524 + 385.403i 0.713322 + 0.487852i
\(791\) 273.363 + 133.838i 0.345592 + 0.169200i
\(792\) −15.9874 + 15.9874i −0.0201861 + 0.0201861i
\(793\) −876.544 + 234.869i −1.10535 + 0.296178i
\(794\) −717.032 + 413.979i −0.903064 + 0.521384i
\(795\) −53.3169 + 45.7485i −0.0670653 + 0.0575452i
\(796\) 378.609 655.770i 0.475639 0.823831i
\(797\) 583.267 583.267i 0.731828 0.731828i −0.239154 0.970982i \(-0.576870\pi\)
0.970982 + 0.239154i \(0.0768700\pi\)
\(798\) 322.263 + 63.1448i 0.403838 + 0.0791289i
\(799\) 207.824i 0.260105i
\(800\) 83.6484 + 114.030i 0.104560 + 0.142538i
\(801\) −217.827 377.287i −0.271943 0.471020i
\(802\) 557.155 + 149.289i 0.694707 + 0.186146i
\(803\) −93.1932 + 24.9711i −0.116056 + 0.0310972i
\(804\) 60.4963i 0.0752441i
\(805\) −318.043 1225.81i −0.395085 1.52275i
\(806\) −195.591 −0.242669
\(807\) 131.838 + 492.025i 0.163368 + 0.609697i
\(808\) −60.3002 + 225.043i −0.0746289 + 0.278519i
\(809\) 400.303 231.115i 0.494812 0.285680i −0.231757 0.972774i \(-0.574447\pi\)
0.726569 + 0.687094i \(0.241114\pi\)
\(810\) −27.5290 57.3773i −0.0339864 0.0708362i
\(811\) 727.161 0.896622 0.448311 0.893878i \(-0.352026\pi\)
0.448311 + 0.893878i \(0.352026\pi\)
\(812\) −131.584 114.733i −0.162050 0.141296i
\(813\) −337.968 337.968i −0.415705 0.415705i
\(814\) 74.1850 + 42.8307i 0.0911364 + 0.0526176i
\(815\) 22.1654 290.128i 0.0271968 0.355985i
\(816\) −9.69534 16.7928i −0.0118815 0.0205794i
\(817\) −18.9680 70.7894i −0.0232166 0.0866455i
\(818\) −315.470 315.470i −0.385660 0.385660i
\(819\) −151.793 225.774i −0.185339 0.275670i
\(820\) −2.17683 11.5969i −0.00265467 0.0141425i
\(821\) 174.689 302.569i 0.212775 0.368538i −0.739807 0.672819i \(-0.765083\pi\)
0.952582 + 0.304282i \(0.0984164\pi\)
\(822\) −580.414 155.522i −0.706100 0.189199i
\(823\) −331.498 + 1237.17i −0.402792 + 1.50324i 0.405301 + 0.914183i \(0.367167\pi\)
−0.808093 + 0.589056i \(0.799500\pi\)
\(824\) 172.634 + 99.6700i 0.209507 + 0.120959i
\(825\) −105.618 46.4459i −0.128022 0.0562981i
\(826\) 961.070 + 470.536i 1.16352 + 0.569657i
\(827\) −66.3759 + 66.3759i −0.0802611 + 0.0802611i −0.746098 0.665837i \(-0.768075\pi\)
0.665837 + 0.746098i \(0.268075\pi\)
\(828\) −209.699 + 56.1888i −0.253260 + 0.0678609i
\(829\) −723.468 + 417.694i −0.872699 + 0.503853i −0.868244 0.496137i \(-0.834751\pi\)
−0.00445501 + 0.999990i \(0.501418\pi\)
\(830\) 543.727 + 633.680i 0.655093 + 0.763469i
\(831\) −287.546 + 498.044i −0.346024 + 0.599332i
\(832\) 73.2851 73.2851i 0.0880830 0.0880830i
\(833\) −126.400 + 53.2053i −0.151741 + 0.0638720i
\(834\) 337.303i 0.404440i
\(835\) −407.712 849.774i −0.488278 1.01769i
\(836\) −51.0323 88.3905i −0.0610434 0.105730i
\(837\) 53.5821 + 14.3573i 0.0640169 + 0.0171533i
\(838\) 903.611 242.122i 1.07829 0.288928i
\(839\) 1320.93i 1.57441i −0.616689 0.787207i \(-0.711527\pi\)
0.616689 0.787207i \(-0.288473\pi\)
\(840\) −84.5502 149.169i −0.100655 0.177582i
\(841\) 685.500 0.815101
\(842\) 143.521 + 535.629i 0.170453 + 0.636139i
\(843\) 173.110 646.054i 0.205349 0.766375i
\(844\) 488.618 282.104i 0.578931 0.334246i
\(845\) −5.49765 1.93267i −0.00650609 0.00228718i
\(846\) −315.036 −0.372383
\(847\) −153.309 + 782.422i −0.181003 + 0.923757i
\(848\) 22.9448 + 22.9448i 0.0270576 + 0.0270576i
\(849\) 234.028 + 135.116i 0.275652 + 0.159148i
\(850\) 61.9202 77.1849i 0.0728472 0.0908058i
\(851\) 411.259 + 712.322i 0.483266 + 0.837041i
\(852\) −59.4205 221.760i −0.0697424 0.260282i
\(853\) −98.5485 98.5485i −0.115532 0.115532i 0.646977 0.762509i \(-0.276033\pi\)
−0.762509 + 0.646977i \(0.776033\pi\)
\(854\) 691.813 47.3306i 0.810085 0.0554222i
\(855\) 282.351 52.9996i 0.330235 0.0619878i
\(856\) −178.272 + 308.776i −0.208262 + 0.360720i
\(857\) 216.854 + 58.1059i 0.253039 + 0.0678016i 0.383109 0.923703i \(-0.374853\pi\)
−0.130070 + 0.991505i \(0.541520\pi\)
\(858\) −21.8847 + 81.6747i −0.0255066 + 0.0951919i
\(859\) 1277.65 + 737.654i 1.48737 + 0.858736i 0.999896 0.0144001i \(-0.00458386\pi\)
0.487477 + 0.873136i \(0.337917\pi\)
\(860\) −21.6015 + 31.5851i −0.0251181 + 0.0367268i
\(861\) 0.976469 + 14.2727i 0.00113411 + 0.0165768i
\(862\) 43.6252 43.6252i 0.0506093 0.0506093i
\(863\) 150.980 40.4550i 0.174948 0.0468771i −0.170282 0.985395i \(-0.554468\pi\)
0.345229 + 0.938518i \(0.387801\pi\)
\(864\) −25.4558 + 14.6969i −0.0294628 + 0.0170103i
\(865\) 60.0496 786.003i 0.0694215 0.908674i
\(866\) 527.265 913.250i 0.608851 1.05456i
\(867\) 344.357 344.357i 0.397183 0.397183i
\(868\) 146.670 + 28.7388i 0.168975 + 0.0331092i
\(869\) 257.264i 0.296046i
\(870\) −144.082 50.6511i −0.165611 0.0582196i
\(871\) 113.122 + 195.934i 0.129876 + 0.224953i
\(872\) −590.067 158.108i −0.676682 0.181316i
\(873\) 179.049 47.9760i 0.205096 0.0549553i
\(874\) 980.020i 1.12130i
\(875\) 552.939 678.147i 0.631931 0.775025i
\(876\) −125.431 −0.143186
\(877\) 299.481 + 1117.68i 0.341483 + 1.27443i 0.896668 + 0.442705i \(0.145981\pi\)
−0.555185 + 0.831727i \(0.687352\pi\)
\(878\) −129.780 + 484.345i −0.147813 + 0.551646i
\(879\) −183.057 + 105.688i −0.208256 + 0.120237i
\(880\) −17.6740 + 50.2753i −0.0200841 + 0.0571310i
\(881\) −126.852 −0.143986 −0.0719929 0.997405i \(-0.522936\pi\)
−0.0719929 + 0.997405i \(0.522936\pi\)
\(882\) 80.6528 + 191.607i 0.0914430 + 0.217241i
\(883\) 268.615 + 268.615i 0.304207 + 0.304207i 0.842657 0.538450i \(-0.180990\pi\)
−0.538450 + 0.842657i \(0.680990\pi\)
\(884\) −62.8020 36.2588i −0.0710430 0.0410167i
\(885\) 933.401 + 71.3106i 1.05469 + 0.0805769i
\(886\) −426.592 738.880i −0.481481 0.833950i
\(887\) 147.404 + 550.121i 0.166183 + 0.620204i 0.997886 + 0.0649835i \(0.0206995\pi\)
−0.831703 + 0.555220i \(0.812634\pi\)
\(888\) 78.7470 + 78.7470i 0.0886790 + 0.0886790i
\(889\) 629.496 1285.75i 0.708095 1.44628i
\(890\) −847.579 579.673i −0.952336 0.651318i
\(891\) 11.9906 20.7683i 0.0134574 0.0233089i
\(892\) 775.918 + 207.907i 0.869863 + 0.233079i
\(893\) 368.076 1373.68i 0.412179 1.53827i
\(894\) −368.187 212.573i −0.411842 0.237777i
\(895\) 105.515 + 562.124i 0.117894 + 0.628072i
\(896\) −65.7230 + 44.1870i −0.0733515 + 0.0493159i
\(897\) −574.101 + 574.101i −0.640024 + 0.640024i
\(898\) −415.336 + 111.289i −0.462512 + 0.123930i
\(899\) 115.290 66.5625i 0.128242 0.0740406i
\(900\) −117.003 93.8633i −0.130003 0.104293i
\(901\) 11.3523 19.6627i 0.0125996 0.0218232i
\(902\) 3.14404 3.14404i 0.00348563 0.00348563i
\(903\) 30.4901 34.9684i 0.0337653 0.0387247i
\(904\) 122.983i 0.136043i
\(905\) −228.912 + 651.161i −0.252941 + 0.719515i
\(906\) 282.746 + 489.730i 0.312081 + 0.540541i
\(907\) 738.355 + 197.842i 0.814063 + 0.218128i 0.641749 0.766915i \(-0.278209\pi\)
0.172314 + 0.985042i \(0.444876\pi\)
\(908\) −502.389 + 134.615i −0.553292 + 0.148254i
\(909\) 247.115i 0.271853i
\(910\) −552.770 325.022i −0.607440 0.357167i
\(911\) 1309.05 1.43693 0.718467 0.695561i \(-0.244844\pi\)
0.718467 + 0.695561i \(0.244844\pi\)
\(912\) −34.3427 128.169i −0.0376565 0.140536i
\(913\) −81.4355 + 303.921i −0.0891955 + 0.332882i
\(914\) 314.580 181.623i 0.344179 0.198712i
\(915\) 546.931 262.411i 0.597739 0.286788i
\(916\) −163.847 −0.178873
\(917\) −205.001 + 1046.23i −0.223556 + 1.14093i
\(918\) 14.5430 + 14.5430i 0.0158421 + 0.0158421i
\(919\) 17.4000 + 10.0459i 0.0189336 + 0.0109313i 0.509437 0.860508i \(-0.329854\pi\)
−0.490503 + 0.871439i \(0.663187\pi\)
\(920\) −388.340 + 333.214i −0.422108 + 0.362189i
\(921\) 265.680 + 460.170i 0.288469 + 0.499642i
\(922\) 193.518 + 722.217i 0.209889 + 0.783316i
\(923\) −607.121 607.121i −0.657769 0.657769i
\(924\) 28.4115 58.0306i 0.0307484 0.0628037i
\(925\) −228.772 + 520.228i −0.247321 + 0.562408i
\(926\) −415.206 + 719.158i −0.448386 + 0.776628i
\(927\) −204.228 54.7226i −0.220310 0.0590320i
\(928\) −18.2573 + 68.1372i −0.0196738 + 0.0734237i
\(929\) −593.913 342.896i −0.639304 0.369102i 0.145042 0.989425i \(-0.453668\pi\)
−0.784346 + 0.620323i \(0.787001\pi\)
\(930\) 128.505 24.1214i 0.138178 0.0259370i
\(931\) −929.712 + 127.811i −0.998616 + 0.137284i
\(932\) −0.105297 + 0.105297i −0.000112980 + 0.000112980i
\(933\) 396.216 106.166i 0.424669 0.113790i
\(934\) 519.409 299.881i 0.556113 0.321072i
\(935\) 37.1797 + 2.84048i 0.0397644 + 0.00303795i
\(936\) −54.9638 + 95.2001i −0.0587220 + 0.101710i
\(937\) 950.723 950.723i 1.01465 1.01465i 0.0147549 0.999891i \(-0.495303\pi\)
0.999891 0.0147549i \(-0.00469679\pi\)
\(938\) −56.0391 163.548i −0.0597431 0.174358i
\(939\) 628.506i 0.669335i
\(940\) −669.478 + 321.208i −0.712211 + 0.341711i
\(941\) −593.868 1028.61i −0.631103 1.09310i −0.987327 0.158701i \(-0.949269\pi\)
0.356224 0.934401i \(-0.384064\pi\)
\(942\) −467.368 125.231i −0.496144 0.132942i
\(943\) 41.2388 11.0499i 0.0437315 0.0117178i
\(944\) 432.376i 0.458025i
\(945\) 127.573 + 129.615i 0.134998 + 0.137159i
\(946\) −14.4195 −0.0152426
\(947\) −59.4273 221.786i −0.0627532 0.234198i 0.927425 0.374009i \(-0.122017\pi\)
−0.990178 + 0.139811i \(0.955350\pi\)
\(948\) −86.5644 + 323.063i −0.0913126 + 0.340783i
\(949\) −406.242 + 234.544i −0.428074 + 0.247148i
\(950\) 545.983 400.512i 0.574718 0.421591i
\(951\) −725.253 −0.762621
\(952\) 41.7663 + 36.4174i 0.0438722 + 0.0382535i
\(953\) 1044.99 + 1044.99i 1.09653 + 1.09653i 0.994813 + 0.101717i \(0.0324337\pi\)
0.101717 + 0.994813i \(0.467566\pi\)
\(954\) −29.8062 17.2086i −0.0312434 0.0180384i
\(955\) −379.176 441.906i −0.397043 0.462729i
\(956\) 214.333 + 371.235i 0.224197 + 0.388321i
\(957\) −14.8953 55.5901i −0.0155646 0.0580879i
\(958\) −260.579 260.579i −0.272003 0.272003i
\(959\) 1713.18 117.208i 1.78642 0.122219i
\(960\) −39.1110 + 57.1868i −0.0407406 + 0.0595696i
\(961\) 423.515 733.550i 0.440703 0.763319i
\(962\) 402.293 + 107.794i 0.418184 + 0.112052i
\(963\) 97.8781 365.286i 0.101639 0.379321i
\(964\) −31.0930 17.9516i −0.0322542 0.0186220i
\(965\) −1086.49 743.069i −1.12590 0.770019i
\(966\) 514.861 346.152i 0.532982 0.358336i
\(967\) 12.1019 12.1019i 0.0125149 0.0125149i −0.700822 0.713337i \(-0.747183\pi\)
0.713337 + 0.700822i \(0.247183\pi\)
\(968\) 311.181 83.3806i 0.321468 0.0861370i
\(969\) −80.4047 + 46.4217i −0.0829770 + 0.0479068i
\(970\) 331.578 284.510i 0.341833 0.293309i
\(971\) 157.069 272.051i 0.161760 0.280176i −0.773740 0.633503i \(-0.781616\pi\)
0.935500 + 0.353327i \(0.114950\pi\)
\(972\) 22.0454 22.0454i 0.0226805 0.0226805i
\(973\) 312.451 + 911.878i 0.321121 + 0.937181i
\(974\) 669.921i 0.687804i
\(975\) −554.462 85.2177i −0.568679 0.0874027i
\(976\) −140.094 242.650i −0.143539 0.248617i
\(977\) 1553.68 + 416.307i 1.59025 + 0.426107i 0.942081 0.335387i \(-0.108867\pi\)
0.648172 + 0.761494i \(0.275534\pi\)
\(978\) 137.690 36.8939i 0.140787 0.0377239i
\(979\) 386.943i 0.395243i
\(980\) 366.755 + 324.948i 0.374239 + 0.331579i
\(981\) 647.938 0.660487
\(982\) −54.5894 203.730i −0.0555900 0.207465i
\(983\) −264.896 + 988.604i −0.269477 + 1.00570i 0.689976 + 0.723832i \(0.257621\pi\)
−0.959453 + 0.281869i \(0.909046\pi\)
\(984\) 5.00607 2.89025i 0.00508747 0.00293725i
\(985\) −266.236 554.903i −0.270290 0.563353i
\(986\) 49.3575 0.0500583
\(987\) 851.681 291.825i 0.862899 0.295669i
\(988\) −350.892 350.892i −0.355154 0.355154i
\(989\) −119.906 69.2275i −0.121239 0.0699975i
\(990\) 4.30582 56.3598i 0.00434931 0.0569291i
\(991\) −128.671 222.864i −0.129839 0.224888i 0.793775 0.608211i \(-0.208113\pi\)
−0.923614 + 0.383324i \(0.874779\pi\)
\(992\) −15.6302 58.3328i −0.0157563 0.0588032i
\(993\) 337.813 + 337.813i 0.340194 + 0.340194i
\(994\) 366.061 + 544.473i 0.368271 + 0.547760i
\(995\) 349.240 + 1860.55i 0.350995 + 1.86990i
\(996\) −204.527 + 354.251i −0.205349 + 0.355674i
\(997\) 268.636 + 71.9807i 0.269444 + 0.0721973i 0.391011 0.920386i \(-0.372125\pi\)
−0.121567 + 0.992583i \(0.538792\pi\)
\(998\) 125.968 470.119i 0.126220 0.471061i
\(999\) −102.295 59.0602i −0.102398 0.0591194i
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 210.3.v.b.163.3 yes 32
5.2 odd 4 inner 210.3.v.b.37.7 32
7.4 even 3 inner 210.3.v.b.193.7 yes 32
35.32 odd 12 inner 210.3.v.b.67.3 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.v.b.37.7 32 5.2 odd 4 inner
210.3.v.b.67.3 yes 32 35.32 odd 12 inner
210.3.v.b.163.3 yes 32 1.1 even 1 trivial
210.3.v.b.193.7 yes 32 7.4 even 3 inner