Properties

Label 675.2.u.b.274.2
Level $675$
Weight $2$
Character 675.274
Analytic conductor $5.390$
Analytic rank $0$
Dimension $24$
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] = [675,2,Mod(49,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.u (of order \(18\), degree \(6\), not 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: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 274.2
Character \(\chi\) \(=\) 675.274
Dual form 675.2.u.b.574.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.274138 + 0.753189i) q^{2} +(-0.386327 + 1.68842i) q^{3} +(1.03995 + 0.872619i) q^{4} +(-1.16579 - 0.753837i) q^{6} +(1.52780 + 1.82076i) q^{7} +(-2.33062 + 1.34559i) q^{8} +(-2.70150 - 1.30456i) q^{9} +O(q^{10})\) \(q+(-0.274138 + 0.753189i) q^{2} +(-0.386327 + 1.68842i) q^{3} +(1.03995 + 0.872619i) q^{4} +(-1.16579 - 0.753837i) q^{6} +(1.52780 + 1.82076i) q^{7} +(-2.33062 + 1.34559i) q^{8} +(-2.70150 - 1.30456i) q^{9} +(-0.0434396 - 0.246358i) q^{11} +(-1.87510 + 1.41875i) q^{12} +(0.893351 + 2.45446i) q^{13} +(-1.79020 + 0.651581i) q^{14} +(0.0969067 + 0.549585i) q^{16} +(0.254072 + 0.146688i) q^{17} +(1.72317 - 1.67711i) q^{18} +(-1.39237 - 2.41166i) q^{19} +(-3.66443 + 1.87615i) q^{21} +(0.197463 + 0.0348180i) q^{22} +(-4.30015 + 5.12472i) q^{23} +(-1.37153 - 4.45490i) q^{24} -2.09357 q^{26} +(3.24631 - 4.05728i) q^{27} +3.22668i q^{28} +(-0.333645 - 0.121437i) q^{29} +(2.11847 + 1.77761i) q^{31} +(-5.74108 - 1.01231i) q^{32} +(0.432738 + 0.0218307i) q^{33} +(-0.180135 + 0.151151i) q^{34} +(-1.67103 - 3.71406i) q^{36} +(6.05558 + 3.49619i) q^{37} +(2.19814 - 0.387591i) q^{38} +(-4.48928 + 0.560124i) q^{39} +(9.13156 - 3.32362i) q^{41} +(-0.408537 - 3.27434i) q^{42} +(0.256746 - 0.0452712i) q^{43} +(0.169802 - 0.294106i) q^{44} +(-2.68104 - 4.64370i) q^{46} +(-7.34421 - 8.75249i) q^{47} +(-0.965367 - 0.0487006i) q^{48} +(0.234540 - 1.33014i) q^{49} +(-0.345826 + 0.372309i) q^{51} +(-1.21277 + 3.33207i) q^{52} -5.43137i q^{53} +(2.16596 + 3.55734i) q^{54} +(-6.01071 - 2.18772i) q^{56} +(4.60980 - 1.41922i) q^{57} +(0.182930 - 0.218007i) q^{58} +(-1.03788 + 5.88612i) q^{59} +(-9.07515 + 7.61495i) q^{61} +(-1.91963 + 1.10830i) q^{62} +(-1.75206 - 6.91190i) q^{63} +(1.77824 - 3.08001i) q^{64} +(-0.135073 + 0.319949i) q^{66} +(-0.619160 - 1.70113i) q^{67} +(0.136218 + 0.374256i) q^{68} +(-6.99139 - 9.24026i) q^{69} +(0.185255 - 0.320871i) q^{71} +(8.05158 - 0.594663i) q^{72} +(-4.35333 + 2.51339i) q^{73} +(-4.29336 + 3.60255i) q^{74} +(0.656467 - 3.72301i) q^{76} +(0.382193 - 0.455479i) q^{77} +(0.808804 - 3.53483i) q^{78} +(0.754406 + 0.274581i) q^{79} +(5.59624 + 7.04855i) q^{81} +7.78892i q^{82} +(0.942488 - 2.58947i) q^{83} +(-5.44798 - 1.24655i) q^{84} +(-0.0362861 + 0.205789i) q^{86} +(0.333932 - 0.516417i) q^{87} +(0.432738 + 0.515717i) q^{88} +(5.22533 + 9.05054i) q^{89} +(-3.10412 + 5.37650i) q^{91} +(-8.94385 + 1.57704i) q^{92} +(-3.81976 + 2.89012i) q^{93} +(8.60560 - 3.13218i) q^{94} +(3.92713 - 9.30225i) q^{96} +(14.6092 - 2.57600i) q^{97} +(0.937552 + 0.541296i) q^{98} +(-0.204037 + 0.722208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.274138 + 0.753189i −0.193845 + 0.532585i −0.998094 0.0617072i \(-0.980346\pi\)
0.804249 + 0.594292i \(0.202568\pi\)
\(3\) −0.386327 + 1.68842i −0.223046 + 0.974808i
\(4\) 1.03995 + 0.872619i 0.519974 + 0.436310i
\(5\) 0 0
\(6\) −1.16579 0.753837i −0.475932 0.307753i
\(7\) 1.52780 + 1.82076i 0.577454 + 0.688183i 0.973143 0.230202i \(-0.0739386\pi\)
−0.395689 + 0.918385i \(0.629494\pi\)
\(8\) −2.33062 + 1.34559i −0.823999 + 0.475736i
\(9\) −2.70150 1.30456i −0.900501 0.434854i
\(10\) 0 0
\(11\) −0.0434396 0.246358i −0.0130975 0.0742798i 0.977558 0.210665i \(-0.0675628\pi\)
−0.990656 + 0.136385i \(0.956452\pi\)
\(12\) −1.87510 + 1.41875i −0.541296 + 0.409557i
\(13\) 0.893351 + 2.45446i 0.247771 + 0.680745i 0.999767 + 0.0215777i \(0.00686892\pi\)
−0.751996 + 0.659167i \(0.770909\pi\)
\(14\) −1.79020 + 0.651581i −0.478452 + 0.174142i
\(15\) 0 0
\(16\) 0.0969067 + 0.549585i 0.0242267 + 0.137396i
\(17\) 0.254072 + 0.146688i 0.0616215 + 0.0355772i 0.530494 0.847689i \(-0.322006\pi\)
−0.468873 + 0.883266i \(0.655340\pi\)
\(18\) 1.72317 1.67711i 0.406154 0.395299i
\(19\) −1.39237 2.41166i −0.319432 0.553273i 0.660937 0.750441i \(-0.270159\pi\)
−0.980370 + 0.197168i \(0.936825\pi\)
\(20\) 0 0
\(21\) −3.66443 + 1.87615i −0.799645 + 0.409410i
\(22\) 0.197463 + 0.0348180i 0.0420992 + 0.00742323i
\(23\) −4.30015 + 5.12472i −0.896643 + 1.06858i 0.100641 + 0.994923i \(0.467911\pi\)
−0.997284 + 0.0736543i \(0.976534\pi\)
\(24\) −1.37153 4.45490i −0.279962 0.909352i
\(25\) 0 0
\(26\) −2.09357 −0.410584
\(27\) 3.24631 4.05728i 0.624752 0.780823i
\(28\) 3.22668i 0.609786i
\(29\) −0.333645 0.121437i −0.0619562 0.0225502i 0.310856 0.950457i \(-0.399384\pi\)
−0.372812 + 0.927907i \(0.621606\pi\)
\(30\) 0 0
\(31\) 2.11847 + 1.77761i 0.380488 + 0.319268i 0.812894 0.582411i \(-0.197891\pi\)
−0.432406 + 0.901679i \(0.642335\pi\)
\(32\) −5.74108 1.01231i −1.01489 0.178952i
\(33\) 0.432738 + 0.0218307i 0.0753299 + 0.00380023i
\(34\) −0.180135 + 0.151151i −0.0308929 + 0.0259222i
\(35\) 0 0
\(36\) −1.67103 3.71406i −0.278506 0.619010i
\(37\) 6.05558 + 3.49619i 0.995531 + 0.574770i 0.906923 0.421297i \(-0.138425\pi\)
0.0886080 + 0.996067i \(0.471758\pi\)
\(38\) 2.19814 0.387591i 0.356585 0.0628756i
\(39\) −4.48928 + 0.560124i −0.718860 + 0.0896917i
\(40\) 0 0
\(41\) 9.13156 3.32362i 1.42611 0.519062i 0.490296 0.871556i \(-0.336888\pi\)
0.935814 + 0.352494i \(0.114666\pi\)
\(42\) −0.408537 3.27434i −0.0630386 0.505241i
\(43\) 0.256746 0.0452712i 0.0391534 0.00690379i −0.154037 0.988065i \(-0.549228\pi\)
0.193191 + 0.981161i \(0.438116\pi\)
\(44\) 0.169802 0.294106i 0.0255986 0.0443381i
\(45\) 0 0
\(46\) −2.68104 4.64370i −0.395298 0.684677i
\(47\) −7.34421 8.75249i −1.07126 1.27668i −0.959123 0.282989i \(-0.908674\pi\)
−0.112140 0.993692i \(-0.535770\pi\)
\(48\) −0.965367 0.0487006i −0.139339 0.00702933i
\(49\) 0.234540 1.33014i 0.0335057 0.190020i
\(50\) 0 0
\(51\) −0.345826 + 0.372309i −0.0484253 + 0.0521337i
\(52\) −1.21277 + 3.33207i −0.168181 + 0.462074i
\(53\) 5.43137i 0.746056i −0.927820 0.373028i \(-0.878320\pi\)
0.927820 0.373028i \(-0.121680\pi\)
\(54\) 2.16596 + 3.55734i 0.294750 + 0.484092i
\(55\) 0 0
\(56\) −6.01071 2.18772i −0.803215 0.292346i
\(57\) 4.60980 1.41922i 0.610583 0.187980i
\(58\) 0.182930 0.218007i 0.0240198 0.0286257i
\(59\) −1.03788 + 5.88612i −0.135121 + 0.766308i 0.839655 + 0.543121i \(0.182757\pi\)
−0.974776 + 0.223188i \(0.928354\pi\)
\(60\) 0 0
\(61\) −9.07515 + 7.61495i −1.16195 + 0.974995i −0.999930 0.0117924i \(-0.996246\pi\)
−0.162023 + 0.986787i \(0.551802\pi\)
\(62\) −1.91963 + 1.10830i −0.243793 + 0.140754i
\(63\) −1.75206 6.91190i −0.220739 0.870817i
\(64\) 1.77824 3.08001i 0.222281 0.385001i
\(65\) 0 0
\(66\) −0.135073 + 0.319949i −0.0166263 + 0.0393829i
\(67\) −0.619160 1.70113i −0.0756424 0.207826i 0.896108 0.443835i \(-0.146383\pi\)
−0.971751 + 0.236010i \(0.924160\pi\)
\(68\) 0.136218 + 0.374256i 0.0165189 + 0.0453852i
\(69\) −6.99139 9.24026i −0.841665 1.11240i
\(70\) 0 0
\(71\) 0.185255 0.320871i 0.0219857 0.0380804i −0.854823 0.518919i \(-0.826334\pi\)
0.876809 + 0.480839i \(0.159668\pi\)
\(72\) 8.05158 0.594663i 0.948888 0.0700817i
\(73\) −4.35333 + 2.51339i −0.509518 + 0.294171i −0.732636 0.680621i \(-0.761710\pi\)
0.223117 + 0.974792i \(0.428377\pi\)
\(74\) −4.29336 + 3.60255i −0.499093 + 0.418789i
\(75\) 0 0
\(76\) 0.656467 3.72301i 0.0753019 0.427059i
\(77\) 0.382193 0.455479i 0.0435549 0.0519067i
\(78\) 0.808804 3.53483i 0.0915790 0.400240i
\(79\) 0.754406 + 0.274581i 0.0848773 + 0.0308928i 0.384110 0.923287i \(-0.374508\pi\)
−0.299233 + 0.954180i \(0.596731\pi\)
\(80\) 0 0
\(81\) 5.59624 + 7.04855i 0.621804 + 0.783173i
\(82\) 7.78892i 0.860143i
\(83\) 0.942488 2.58947i 0.103452 0.284231i −0.877158 0.480201i \(-0.840564\pi\)
0.980610 + 0.195971i \(0.0627858\pi\)
\(84\) −5.44798 1.24655i −0.594424 0.136010i
\(85\) 0 0
\(86\) −0.0362861 + 0.205789i −0.00391283 + 0.0221908i
\(87\) 0.333932 0.516417i 0.0358012 0.0553657i
\(88\) 0.432738 + 0.515717i 0.0461300 + 0.0549756i
\(89\) 5.22533 + 9.05054i 0.553884 + 0.959356i 0.997989 + 0.0633809i \(0.0201883\pi\)
−0.444105 + 0.895975i \(0.646478\pi\)
\(90\) 0 0
\(91\) −3.10412 + 5.37650i −0.325401 + 0.563611i
\(92\) −8.94385 + 1.57704i −0.932461 + 0.164418i
\(93\) −3.81976 + 2.89012i −0.396091 + 0.299692i
\(94\) 8.60560 3.13218i 0.887600 0.323060i
\(95\) 0 0
\(96\) 3.92713 9.30225i 0.400811 0.949407i
\(97\) 14.6092 2.57600i 1.48334 0.261553i 0.627430 0.778673i \(-0.284107\pi\)
0.855913 + 0.517120i \(0.172996\pi\)
\(98\) 0.937552 + 0.541296i 0.0947070 + 0.0546791i
\(99\) −0.204037 + 0.722208i −0.0205065 + 0.0725846i
\(100\) 0 0
\(101\) 3.06826 2.57457i 0.305303 0.256180i −0.477244 0.878771i \(-0.658364\pi\)
0.782548 + 0.622591i \(0.213920\pi\)
\(102\) −0.185615 0.362537i −0.0183786 0.0358965i
\(103\) 5.82943 + 1.02789i 0.574391 + 0.101281i 0.453296 0.891360i \(-0.350248\pi\)
0.121095 + 0.992641i \(0.461359\pi\)
\(104\) −5.38475 4.51834i −0.528018 0.443060i
\(105\) 0 0
\(106\) 4.09085 + 1.48895i 0.397338 + 0.144619i
\(107\) 0.258978i 0.0250364i −0.999922 0.0125182i \(-0.996015\pi\)
0.999922 0.0125182i \(-0.00398477\pi\)
\(108\) 6.91645 1.38656i 0.665535 0.133422i
\(109\) 8.55787 0.819695 0.409848 0.912154i \(-0.365582\pi\)
0.409848 + 0.912154i \(0.365582\pi\)
\(110\) 0 0
\(111\) −8.24246 + 8.87367i −0.782340 + 0.842251i
\(112\) −0.852609 + 1.01610i −0.0805640 + 0.0960124i
\(113\) 3.07179 + 0.541640i 0.288970 + 0.0509532i 0.316254 0.948675i \(-0.397575\pi\)
−0.0272843 + 0.999628i \(0.508686\pi\)
\(114\) −0.194784 + 3.86111i −0.0182432 + 0.361626i
\(115\) 0 0
\(116\) −0.241005 0.417432i −0.0223767 0.0387576i
\(117\) 0.788606 7.79617i 0.0729066 0.720756i
\(118\) −4.14884 2.39533i −0.381932 0.220508i
\(119\) 0.121086 + 0.686714i 0.0111000 + 0.0629510i
\(120\) 0 0
\(121\) 10.2778 3.74082i 0.934347 0.340074i
\(122\) −3.24765 8.92285i −0.294029 0.807837i
\(123\) 2.08388 + 16.7019i 0.187897 + 1.50596i
\(124\) 0.651922 + 3.69724i 0.0585444 + 0.332022i
\(125\) 0 0
\(126\) 5.68627 + 0.575183i 0.506573 + 0.0512414i
\(127\) −15.9821 + 9.22726i −1.41818 + 0.818787i −0.996139 0.0877893i \(-0.972020\pi\)
−0.422042 + 0.906576i \(0.638686\pi\)
\(128\) −5.66210 6.74783i −0.500464 0.596430i
\(129\) −0.0227511 + 0.450983i −0.00200312 + 0.0397069i
\(130\) 0 0
\(131\) 10.8973 + 9.14396i 0.952105 + 0.798911i 0.979651 0.200709i \(-0.0643246\pi\)
−0.0275454 + 0.999621i \(0.508769\pi\)
\(132\) 0.430974 + 0.400318i 0.0375115 + 0.0348432i
\(133\) 2.26379 6.21971i 0.196295 0.539317i
\(134\) 1.45101 0.125348
\(135\) 0 0
\(136\) −0.789527 −0.0677014
\(137\) −6.73287 + 18.4984i −0.575228 + 1.58042i 0.220900 + 0.975296i \(0.429100\pi\)
−0.796128 + 0.605128i \(0.793122\pi\)
\(138\) 8.87627 2.73273i 0.755598 0.232626i
\(139\) 13.7206 + 11.5129i 1.16377 + 0.976515i 0.999950 0.00997617i \(-0.00317556\pi\)
0.163815 + 0.986491i \(0.447620\pi\)
\(140\) 0 0
\(141\) 17.6151 9.01876i 1.48346 0.759517i
\(142\) 0.190891 + 0.227495i 0.0160192 + 0.0190910i
\(143\) 0.565870 0.326705i 0.0473205 0.0273205i
\(144\) 0.455174 1.61113i 0.0379312 0.134261i
\(145\) 0 0
\(146\) −0.699647 3.96789i −0.0579032 0.328385i
\(147\) 2.15522 + 0.909870i 0.177760 + 0.0750449i
\(148\) 3.24664 + 8.92007i 0.266872 + 0.733225i
\(149\) 15.3071 5.57132i 1.25401 0.456421i 0.372252 0.928132i \(-0.378586\pi\)
0.881753 + 0.471711i \(0.156363\pi\)
\(150\) 0 0
\(151\) 2.47880 + 14.0580i 0.201722 + 1.14402i 0.902515 + 0.430659i \(0.141719\pi\)
−0.700793 + 0.713365i \(0.747170\pi\)
\(152\) 6.49019 + 3.74711i 0.526424 + 0.303931i
\(153\) −0.495012 0.727731i −0.0400193 0.0588336i
\(154\) 0.238288 + 0.412728i 0.0192018 + 0.0332585i
\(155\) 0 0
\(156\) −5.15739 3.33493i −0.412922 0.267008i
\(157\) 0.751757 + 0.132555i 0.0599968 + 0.0105790i 0.203566 0.979061i \(-0.434747\pi\)
−0.143569 + 0.989640i \(0.545858\pi\)
\(158\) −0.413623 + 0.492937i −0.0329061 + 0.0392159i
\(159\) 9.17041 + 2.09828i 0.727261 + 0.166405i
\(160\) 0 0
\(161\) −15.9006 −1.25315
\(162\) −6.84304 + 2.28275i −0.537640 + 0.179349i
\(163\) 5.12834i 0.401682i −0.979624 0.200841i \(-0.935632\pi\)
0.979624 0.200841i \(-0.0643675\pi\)
\(164\) 12.3966 + 4.51199i 0.968011 + 0.352327i
\(165\) 0 0
\(166\) 1.69198 + 1.41974i 0.131323 + 0.110193i
\(167\) 8.76590 + 1.54566i 0.678325 + 0.119607i 0.502188 0.864759i \(-0.332529\pi\)
0.176137 + 0.984366i \(0.443640\pi\)
\(168\) 6.01588 9.30341i 0.464135 0.717774i
\(169\) 4.73227 3.97085i 0.364021 0.305450i
\(170\) 0 0
\(171\) 0.615340 + 8.33154i 0.0470562 + 0.637129i
\(172\) 0.306507 + 0.176962i 0.0233709 + 0.0134932i
\(173\) −6.70776 + 1.18276i −0.509982 + 0.0899235i −0.422717 0.906262i \(-0.638924\pi\)
−0.0872644 + 0.996185i \(0.527812\pi\)
\(174\) 0.297416 + 0.393083i 0.0225470 + 0.0297996i
\(175\) 0 0
\(176\) 0.131185 0.0477476i 0.00988847 0.00359911i
\(177\) −9.53727 4.02635i −0.716865 0.302639i
\(178\) −8.24923 + 1.45456i −0.618306 + 0.109024i
\(179\) −9.17382 + 15.8895i −0.685684 + 1.18764i 0.287538 + 0.957769i \(0.407163\pi\)
−0.973221 + 0.229870i \(0.926170\pi\)
\(180\) 0 0
\(181\) −5.66282 9.80830i −0.420914 0.729045i 0.575115 0.818073i \(-0.304957\pi\)
−0.996029 + 0.0890276i \(0.971624\pi\)
\(182\) −3.19856 3.81190i −0.237093 0.282557i
\(183\) −9.35124 18.2645i −0.691264 1.35015i
\(184\) 3.12628 17.7300i 0.230472 1.30707i
\(185\) 0 0
\(186\) −1.12966 3.66930i −0.0828310 0.269046i
\(187\) 0.0251011 0.0689648i 0.00183558 0.00504321i
\(188\) 15.5108i 1.13124i
\(189\) 12.3470 0.287957i 0.898115 0.0209458i
\(190\) 0 0
\(191\) −6.44480 2.34571i −0.466329 0.169730i 0.0981596 0.995171i \(-0.468704\pi\)
−0.564489 + 0.825441i \(0.690927\pi\)
\(192\) 4.51336 + 4.19231i 0.325724 + 0.302554i
\(193\) 13.1211 15.6371i 0.944477 1.12558i −0.0474627 0.998873i \(-0.515114\pi\)
0.991940 0.126711i \(-0.0404420\pi\)
\(194\) −2.06474 + 11.7097i −0.148239 + 0.840707i
\(195\) 0 0
\(196\) 1.40462 1.17861i 0.100330 0.0841866i
\(197\) 2.62902 1.51786i 0.187310 0.108143i −0.403413 0.915018i \(-0.632176\pi\)
0.590723 + 0.806875i \(0.298843\pi\)
\(198\) −0.488024 0.351663i −0.0346824 0.0249916i
\(199\) −1.13124 + 1.95936i −0.0801912 + 0.138895i −0.903332 0.428942i \(-0.858886\pi\)
0.823141 + 0.567837i \(0.192220\pi\)
\(200\) 0 0
\(201\) 3.11141 0.388209i 0.219462 0.0273821i
\(202\) 1.09801 + 3.01677i 0.0772560 + 0.212259i
\(203\) −0.288635 0.793018i −0.0202582 0.0556589i
\(204\) −0.684525 + 0.0854077i −0.0479263 + 0.00597974i
\(205\) 0 0
\(206\) −2.37226 + 4.10888i −0.165283 + 0.286279i
\(207\) 18.3024 8.23463i 1.27210 0.572346i
\(208\) −1.26236 + 0.728826i −0.0875292 + 0.0505350i
\(209\) −0.533649 + 0.447784i −0.0369132 + 0.0309739i
\(210\) 0 0
\(211\) 4.41601 25.0445i 0.304011 1.72413i −0.324113 0.946018i \(-0.605066\pi\)
0.628124 0.778113i \(-0.283823\pi\)
\(212\) 4.73952 5.64834i 0.325511 0.387929i
\(213\) 0.470195 + 0.436749i 0.0322172 + 0.0299255i
\(214\) 0.195060 + 0.0709959i 0.0133340 + 0.00485318i
\(215\) 0 0
\(216\) −2.10650 + 13.8242i −0.143329 + 0.940615i
\(217\) 6.57305i 0.446208i
\(218\) −2.34604 + 6.44569i −0.158894 + 0.436557i
\(219\) −2.56185 8.32122i −0.173114 0.562296i
\(220\) 0 0
\(221\) −0.133066 + 0.754654i −0.00895097 + 0.0507635i
\(222\) −4.42398 8.64074i −0.296918 0.579929i
\(223\) 2.46274 + 2.93497i 0.164917 + 0.196540i 0.842174 0.539206i \(-0.181276\pi\)
−0.677257 + 0.735747i \(0.736831\pi\)
\(224\) −6.92805 11.9997i −0.462900 0.801766i
\(225\) 0 0
\(226\) −1.25005 + 2.16515i −0.0831523 + 0.144024i
\(227\) −2.47777 + 0.436897i −0.164455 + 0.0289979i −0.255269 0.966870i \(-0.582164\pi\)
0.0908142 + 0.995868i \(0.471053\pi\)
\(228\) 6.03238 + 2.54669i 0.399504 + 0.168659i
\(229\) −14.9783 + 5.45167i −0.989797 + 0.360257i −0.785642 0.618682i \(-0.787667\pi\)
−0.204155 + 0.978939i \(0.565445\pi\)
\(230\) 0 0
\(231\) 0.621388 + 0.821264i 0.0408843 + 0.0540352i
\(232\) 0.941003 0.165924i 0.0617799 0.0108935i
\(233\) 24.3598 + 14.0641i 1.59586 + 0.921372i 0.992273 + 0.124077i \(0.0395971\pi\)
0.603590 + 0.797295i \(0.293736\pi\)
\(234\) 5.65580 + 2.73120i 0.369731 + 0.178544i
\(235\) 0 0
\(236\) −6.21569 + 5.21558i −0.404607 + 0.339505i
\(237\) −0.755055 + 1.16767i −0.0490461 + 0.0758485i
\(238\) −0.550420 0.0970539i −0.0356784 0.00629107i
\(239\) 11.2653 + 9.45270i 0.728691 + 0.611444i 0.929774 0.368130i \(-0.120002\pi\)
−0.201083 + 0.979574i \(0.564446\pi\)
\(240\) 0 0
\(241\) −7.93378 2.88766i −0.511059 0.186010i 0.0736022 0.997288i \(-0.476550\pi\)
−0.584662 + 0.811277i \(0.698773\pi\)
\(242\) 8.76664i 0.563541i
\(243\) −14.0629 + 6.72574i −0.902134 + 0.431456i
\(244\) −16.0826 −1.02958
\(245\) 0 0
\(246\) −13.1509 3.00907i −0.838474 0.191851i
\(247\) 4.67545 5.57198i 0.297492 0.354537i
\(248\) −7.32927 1.29235i −0.465409 0.0820642i
\(249\) 4.00799 + 2.59169i 0.253996 + 0.164242i
\(250\) 0 0
\(251\) 11.6102 + 20.1095i 0.732832 + 1.26930i 0.955668 + 0.294447i \(0.0951354\pi\)
−0.222835 + 0.974856i \(0.571531\pi\)
\(252\) 4.20940 8.71689i 0.265168 0.549112i
\(253\) 1.44931 + 0.836762i 0.0911176 + 0.0526067i
\(254\) −2.56857 14.5671i −0.161166 0.914020i
\(255\) 0 0
\(256\) 13.3186 4.84758i 0.832413 0.302973i
\(257\) −2.34804 6.45118i −0.146466 0.402413i 0.844666 0.535294i \(-0.179799\pi\)
−0.991132 + 0.132881i \(0.957577\pi\)
\(258\) −0.333439 0.140768i −0.0207590 0.00876382i
\(259\) 2.88598 + 16.3672i 0.179326 + 1.01701i
\(260\) 0 0
\(261\) 0.742920 + 0.763321i 0.0459856 + 0.0472484i
\(262\) −9.87451 + 5.70105i −0.610049 + 0.352212i
\(263\) −2.15523 2.56850i −0.132897 0.158381i 0.695492 0.718534i \(-0.255187\pi\)
−0.828389 + 0.560154i \(0.810742\pi\)
\(264\) −1.03792 + 0.531406i −0.0638797 + 0.0327058i
\(265\) 0 0
\(266\) 4.06402 + 3.41012i 0.249181 + 0.209088i
\(267\) −17.2998 + 5.32607i −1.05873 + 0.325950i
\(268\) 0.840543 2.30937i 0.0513444 0.141067i
\(269\) −12.7416 −0.776869 −0.388434 0.921476i \(-0.626984\pi\)
−0.388434 + 0.921476i \(0.626984\pi\)
\(270\) 0 0
\(271\) −23.5566 −1.43096 −0.715481 0.698632i \(-0.753792\pi\)
−0.715481 + 0.698632i \(0.753792\pi\)
\(272\) −0.0559965 + 0.153849i −0.00339529 + 0.00932848i
\(273\) −7.87857 7.31814i −0.476833 0.442914i
\(274\) −12.0871 10.1422i −0.730206 0.612715i
\(275\) 0 0
\(276\) 0.792545 15.7102i 0.0477056 0.945643i
\(277\) 2.68763 + 3.20300i 0.161484 + 0.192450i 0.840719 0.541472i \(-0.182133\pi\)
−0.679235 + 0.733921i \(0.737688\pi\)
\(278\) −12.4328 + 7.17806i −0.745667 + 0.430511i
\(279\) −3.40406 7.56589i −0.203795 0.452958i
\(280\) 0 0
\(281\) −3.75705 21.3073i −0.224127 1.27109i −0.864347 0.502896i \(-0.832268\pi\)
0.640220 0.768192i \(-0.278843\pi\)
\(282\) 1.96386 + 15.7399i 0.116946 + 0.937297i
\(283\) 1.78785 + 4.91209i 0.106277 + 0.291993i 0.981420 0.191870i \(-0.0614553\pi\)
−0.875143 + 0.483864i \(0.839233\pi\)
\(284\) 0.472654 0.172032i 0.0280468 0.0102082i
\(285\) 0 0
\(286\) 0.0909441 + 0.515770i 0.00537764 + 0.0304981i
\(287\) 20.0027 + 11.5486i 1.18072 + 0.681690i
\(288\) 14.1889 + 10.2243i 0.836090 + 0.602475i
\(289\) −8.45697 14.6479i −0.497469 0.861641i
\(290\) 0 0
\(291\) −1.29457 + 25.6617i −0.0758893 + 1.50431i
\(292\) −6.72047 1.18500i −0.393285 0.0693468i
\(293\) −3.94811 + 4.70517i −0.230651 + 0.274879i −0.868940 0.494918i \(-0.835198\pi\)
0.638289 + 0.769797i \(0.279643\pi\)
\(294\) −1.27613 + 1.37386i −0.0744257 + 0.0801252i
\(295\) 0 0
\(296\) −18.8177 −1.09376
\(297\) −1.14056 0.623508i −0.0661821 0.0361796i
\(298\) 13.0564i 0.756339i
\(299\) −16.4200 5.97638i −0.949591 0.345623i
\(300\) 0 0
\(301\) 0.474684 + 0.398307i 0.0273603 + 0.0229580i
\(302\) −11.2679 1.98683i −0.648393 0.114329i
\(303\) 3.16160 + 6.17513i 0.181629 + 0.354752i
\(304\) 1.19048 0.998934i 0.0682789 0.0572928i
\(305\) 0 0
\(306\) 0.683821 0.173338i 0.0390914 0.00990909i
\(307\) −16.4578 9.50194i −0.939298 0.542304i −0.0495580 0.998771i \(-0.515781\pi\)
−0.889740 + 0.456467i \(0.849115\pi\)
\(308\) 0.794920 0.140166i 0.0452948 0.00798669i
\(309\) −3.98757 + 9.44541i −0.226845 + 0.537331i
\(310\) 0 0
\(311\) 20.2475 7.36948i 1.14813 0.417885i 0.303286 0.952900i \(-0.401916\pi\)
0.844843 + 0.535015i \(0.179694\pi\)
\(312\) 9.70912 7.34615i 0.549671 0.415894i
\(313\) −3.75568 + 0.662228i −0.212284 + 0.0374313i −0.278778 0.960355i \(-0.589930\pi\)
0.0664949 + 0.997787i \(0.478818\pi\)
\(314\) −0.305925 + 0.529877i −0.0172643 + 0.0299027i
\(315\) 0 0
\(316\) 0.544937 + 0.943859i 0.0306551 + 0.0530962i
\(317\) 2.73473 + 3.25913i 0.153598 + 0.183051i 0.837356 0.546658i \(-0.184100\pi\)
−0.683758 + 0.729709i \(0.739656\pi\)
\(318\) −4.09437 + 6.33183i −0.229601 + 0.355072i
\(319\) −0.0154235 + 0.0874713i −0.000863553 + 0.00489745i
\(320\) 0 0
\(321\) 0.437264 + 0.100050i 0.0244057 + 0.00558426i
\(322\) 4.35898 11.9762i 0.242916 0.667407i
\(323\) 0.816980i 0.0454580i
\(324\) −0.330912 + 12.2135i −0.0183840 + 0.678528i
\(325\) 0 0
\(326\) 3.86261 + 1.40587i 0.213930 + 0.0778642i
\(327\) −3.30614 + 14.4493i −0.182830 + 0.799046i
\(328\) −16.8100 + 20.0334i −0.928178 + 1.10616i
\(329\) 4.71570 26.7441i 0.259985 1.47445i
\(330\) 0 0
\(331\) −10.9497 + 9.18787i −0.601849 + 0.505011i −0.892039 0.451958i \(-0.850726\pi\)
0.290191 + 0.956969i \(0.406281\pi\)
\(332\) 3.23976 1.87047i 0.177805 0.102656i
\(333\) −11.7982 17.3448i −0.646536 0.950491i
\(334\) −3.56725 + 6.17865i −0.195191 + 0.338081i
\(335\) 0 0
\(336\) −1.38621 1.83211i −0.0756242 0.0999496i
\(337\) −12.2164 33.5644i −0.665472 1.82837i −0.550194 0.835037i \(-0.685446\pi\)
−0.115278 0.993333i \(-0.536776\pi\)
\(338\) 1.69350 + 4.65286i 0.0921143 + 0.253082i
\(339\) −2.10123 + 4.97721i −0.114123 + 0.270325i
\(340\) 0 0
\(341\) 0.345903 0.599121i 0.0187317 0.0324442i
\(342\) −6.44391 1.82053i −0.348447 0.0984429i
\(343\) 17.1890 9.92407i 0.928118 0.535849i
\(344\) −0.537461 + 0.450983i −0.0289780 + 0.0243154i
\(345\) 0 0
\(346\) 0.948013 5.37645i 0.0509655 0.289040i
\(347\) 12.4968 14.8931i 0.670862 0.799502i −0.318039 0.948078i \(-0.603024\pi\)
0.988901 + 0.148575i \(0.0474688\pi\)
\(348\) 0.797906 0.245651i 0.0427723 0.0131683i
\(349\) −7.53700 2.74324i −0.403446 0.146842i 0.132323 0.991207i \(-0.457756\pi\)
−0.535770 + 0.844364i \(0.679978\pi\)
\(350\) 0 0
\(351\) 12.8585 + 4.34336i 0.686337 + 0.231832i
\(352\) 1.45834i 0.0777296i
\(353\) −2.99398 + 8.22589i −0.159354 + 0.437820i −0.993515 0.113700i \(-0.963730\pi\)
0.834162 + 0.551520i \(0.185952\pi\)
\(354\) 5.64713 6.07959i 0.300142 0.323127i
\(355\) 0 0
\(356\) −2.46361 + 13.9718i −0.130571 + 0.740505i
\(357\) −1.20624 0.0608521i −0.0638409 0.00322063i
\(358\) −9.45292 11.2656i −0.499602 0.595403i
\(359\) −4.13896 7.16888i −0.218446 0.378359i 0.735887 0.677104i \(-0.236765\pi\)
−0.954333 + 0.298745i \(0.903432\pi\)
\(360\) 0 0
\(361\) 5.62260 9.73862i 0.295926 0.512559i
\(362\) 8.93990 1.57635i 0.469871 0.0828509i
\(363\) 2.34547 + 18.7984i 0.123105 + 0.986661i
\(364\) −7.91977 + 2.88256i −0.415108 + 0.151087i
\(365\) 0 0
\(366\) 16.3201 2.03625i 0.853068 0.106437i
\(367\) 14.5750 2.56997i 0.760809 0.134151i 0.220234 0.975447i \(-0.429318\pi\)
0.540575 + 0.841296i \(0.318207\pi\)
\(368\) −3.23318 1.86668i −0.168541 0.0973074i
\(369\) −29.0048 2.93392i −1.50993 0.152734i
\(370\) 0 0
\(371\) 9.88922 8.29804i 0.513423 0.430813i
\(372\) −6.49433 0.327625i −0.336715 0.0169865i
\(373\) −25.1455 4.43383i −1.30198 0.229575i −0.520694 0.853743i \(-0.674327\pi\)
−0.781290 + 0.624168i \(0.785438\pi\)
\(374\) 0.0450623 + 0.0378118i 0.00233012 + 0.00195520i
\(375\) 0 0
\(376\) 28.8938 + 10.5165i 1.49008 + 0.542346i
\(377\) 0.927403i 0.0477637i
\(378\) −3.16791 + 9.37859i −0.162940 + 0.482383i
\(379\) −20.1244 −1.03372 −0.516861 0.856070i \(-0.672899\pi\)
−0.516861 + 0.856070i \(0.672899\pi\)
\(380\) 0 0
\(381\) −9.40516 30.5492i −0.481841 1.56508i
\(382\) 3.53353 4.21110i 0.180791 0.215459i
\(383\) 23.4987 + 4.14346i 1.20073 + 0.211721i 0.738014 0.674785i \(-0.235764\pi\)
0.462716 + 0.886507i \(0.346875\pi\)
\(384\) 13.5806 6.95312i 0.693031 0.354825i
\(385\) 0 0
\(386\) 8.18070 + 14.1694i 0.416387 + 0.721203i
\(387\) −0.752659 0.212640i −0.0382598 0.0108091i
\(388\) 17.4407 + 10.0694i 0.885418 + 0.511196i
\(389\) −6.59400 37.3964i −0.334329 1.89607i −0.433760 0.901029i \(-0.642813\pi\)
0.0994307 0.995044i \(-0.468298\pi\)
\(390\) 0 0
\(391\) −1.84428 + 0.671264i −0.0932694 + 0.0339473i
\(392\) 1.24320 + 3.41565i 0.0627908 + 0.172516i
\(393\) −19.6487 + 14.8667i −0.991148 + 0.749926i
\(394\) 0.422524 + 2.39625i 0.0212864 + 0.120721i
\(395\) 0 0
\(396\) −0.842400 + 0.573011i −0.0423322 + 0.0287949i
\(397\) 17.6230 10.1747i 0.884474 0.510651i 0.0123433 0.999924i \(-0.496071\pi\)
0.872131 + 0.489272i \(0.162738\pi\)
\(398\) −1.16565 1.38917i −0.0584289 0.0696328i
\(399\) 9.62690 + 6.22506i 0.481948 + 0.311643i
\(400\) 0 0
\(401\) 5.32015 + 4.46414i 0.265676 + 0.222928i 0.765887 0.642975i \(-0.222300\pi\)
−0.500212 + 0.865903i \(0.666744\pi\)
\(402\) −0.560563 + 2.44990i −0.0279583 + 0.122190i
\(403\) −2.47053 + 6.78773i −0.123066 + 0.338121i
\(404\) 5.43745 0.270523
\(405\) 0 0
\(406\) 0.676418 0.0335701
\(407\) 0.598264 1.64372i 0.0296548 0.0814760i
\(408\) 0.305015 1.33305i 0.0151005 0.0659958i
\(409\) 8.35444 + 7.01021i 0.413101 + 0.346633i 0.825531 0.564356i \(-0.190876\pi\)
−0.412431 + 0.910989i \(0.635320\pi\)
\(410\) 0 0
\(411\) −28.6319 18.5143i −1.41231 0.913244i
\(412\) 5.16535 + 6.15582i 0.254478 + 0.303276i
\(413\) −12.3029 + 7.10308i −0.605386 + 0.349520i
\(414\) 1.18485 + 16.0426i 0.0582322 + 0.788449i
\(415\) 0 0
\(416\) −2.64413 14.9956i −0.129639 0.735220i
\(417\) −24.7393 + 18.7183i −1.21149 + 0.916640i
\(418\) −0.190973 0.524693i −0.00934078 0.0256636i
\(419\) −9.46194 + 3.44386i −0.462246 + 0.168244i −0.562637 0.826704i \(-0.690213\pi\)
0.100391 + 0.994948i \(0.467991\pi\)
\(420\) 0 0
\(421\) −0.539623 3.06035i −0.0262996 0.149152i 0.968830 0.247726i \(-0.0796832\pi\)
−0.995130 + 0.0985733i \(0.968572\pi\)
\(422\) 17.6526 + 10.1917i 0.859315 + 0.496126i
\(423\) 8.42224 + 33.2258i 0.409504 + 1.61550i
\(424\) 7.30837 + 12.6585i 0.354926 + 0.614750i
\(425\) 0 0
\(426\) −0.457853 + 0.234416i −0.0221830 + 0.0113575i
\(427\) −27.7300 4.88955i −1.34195 0.236622i
\(428\) 0.225990 0.269324i 0.0109236 0.0130183i
\(429\) 0.333004 + 1.08164i 0.0160776 + 0.0522221i
\(430\) 0 0
\(431\) −28.0701 −1.35209 −0.676044 0.736862i \(-0.736307\pi\)
−0.676044 + 0.736862i \(0.736307\pi\)
\(432\) 2.54441 + 1.39095i 0.122418 + 0.0669219i
\(433\) 19.5251i 0.938317i −0.883114 0.469158i \(-0.844557\pi\)
0.883114 0.469158i \(-0.155443\pi\)
\(434\) −4.95075 1.80193i −0.237644 0.0864952i
\(435\) 0 0
\(436\) 8.89973 + 7.46776i 0.426220 + 0.357641i
\(437\) 18.3465 + 3.23498i 0.877631 + 0.154750i
\(438\) 6.96975 + 0.351609i 0.333028 + 0.0168005i
\(439\) −11.2069 + 9.40371i −0.534876 + 0.448815i −0.869781 0.493437i \(-0.835740\pi\)
0.334905 + 0.942252i \(0.391296\pi\)
\(440\) 0 0
\(441\) −2.36886 + 3.28741i −0.112803 + 0.156543i
\(442\) −0.531918 0.307103i −0.0253008 0.0146074i
\(443\) 18.0771 3.18748i 0.858868 0.151442i 0.273165 0.961967i \(-0.411930\pi\)
0.585703 + 0.810526i \(0.300818\pi\)
\(444\) −16.3151 + 2.03562i −0.774278 + 0.0966062i
\(445\) 0 0
\(446\) −2.88572 + 1.05032i −0.136643 + 0.0497339i
\(447\) 3.49318 + 27.9971i 0.165222 + 1.32422i
\(448\) 8.32476 1.46788i 0.393308 0.0693508i
\(449\) 6.92969 12.0026i 0.327032 0.566437i −0.654889 0.755725i \(-0.727285\pi\)
0.981922 + 0.189288i \(0.0606180\pi\)
\(450\) 0 0
\(451\) −1.21547 2.10526i −0.0572344 0.0991328i
\(452\) 2.72185 + 3.24378i 0.128025 + 0.152575i
\(453\) −24.6934 1.24573i −1.16020 0.0585294i
\(454\) 0.350185 1.98600i 0.0164350 0.0932075i
\(455\) 0 0
\(456\) −8.83402 + 9.51053i −0.413691 + 0.445372i
\(457\) 6.03602 16.5838i 0.282353 0.775758i −0.714728 0.699403i \(-0.753449\pi\)
0.997081 0.0763555i \(-0.0243284\pi\)
\(458\) 12.7760i 0.596985i
\(459\) 1.41995 0.554644i 0.0662776 0.0258886i
\(460\) 0 0
\(461\) −24.0919 8.76872i −1.12207 0.408400i −0.286663 0.958032i \(-0.592546\pi\)
−0.835407 + 0.549631i \(0.814768\pi\)
\(462\) −0.788913 + 0.242882i −0.0367036 + 0.0112999i
\(463\) 11.7935 14.0549i 0.548090 0.653189i −0.418891 0.908037i \(-0.637581\pi\)
0.966981 + 0.254848i \(0.0820255\pi\)
\(464\) 0.0344074 0.195134i 0.00159732 0.00905888i
\(465\) 0 0
\(466\) −17.2709 + 14.4920i −0.800059 + 0.671329i
\(467\) −14.0832 + 8.13092i −0.651692 + 0.376254i −0.789104 0.614260i \(-0.789455\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(468\) 7.62319 7.41945i 0.352382 0.342964i
\(469\) 2.15139 3.72632i 0.0993421 0.172066i
\(470\) 0 0
\(471\) −0.514232 + 1.21807i −0.0236946 + 0.0561257i
\(472\) −5.50137 15.1149i −0.253221 0.695719i
\(473\) −0.0223059 0.0612849i −0.00102563 0.00281788i
\(474\) −0.672489 0.888803i −0.0308884 0.0408241i
\(475\) 0 0
\(476\) −0.473317 + 0.819809i −0.0216944 + 0.0375759i
\(477\) −7.08555 + 14.6729i −0.324425 + 0.671824i
\(478\) −10.2079 + 5.89354i −0.466899 + 0.269564i
\(479\) 7.25575 6.08830i 0.331524 0.278181i −0.461797 0.886986i \(-0.652795\pi\)
0.793320 + 0.608804i \(0.208351\pi\)
\(480\) 0 0
\(481\) −3.17151 + 17.9865i −0.144608 + 0.820114i
\(482\) 4.34990 5.18401i 0.198133 0.236125i
\(483\) 6.14284 26.8469i 0.279509 1.22158i
\(484\) 13.9527 + 5.07836i 0.634213 + 0.230835i
\(485\) 0 0
\(486\) −1.21058 12.4358i −0.0549129 0.564099i
\(487\) 0.467564i 0.0211874i −0.999944 0.0105937i \(-0.996628\pi\)
0.999944 0.0105937i \(-0.00337214\pi\)
\(488\) 10.9042 29.9590i 0.493608 1.35618i
\(489\) 8.65877 + 1.98121i 0.391563 + 0.0895936i
\(490\) 0 0
\(491\) 4.34936 24.6665i 0.196284 1.11318i −0.714294 0.699846i \(-0.753252\pi\)
0.910578 0.413337i \(-0.135637\pi\)
\(492\) −12.4073 + 19.1875i −0.559363 + 0.865040i
\(493\) −0.0669563 0.0797954i −0.00301556 0.00359380i
\(494\) 2.91504 + 5.04899i 0.131154 + 0.227165i
\(495\) 0 0
\(496\) −0.771653 + 1.33654i −0.0346482 + 0.0600125i
\(497\) 0.867261 0.152922i 0.0389020 0.00685947i
\(498\) −3.05078 + 2.30829i −0.136709 + 0.103437i
\(499\) −13.1878 + 4.79996i −0.590367 + 0.214876i −0.619891 0.784688i \(-0.712823\pi\)
0.0295240 + 0.999564i \(0.490601\pi\)
\(500\) 0 0
\(501\) −5.99623 + 14.2034i −0.267892 + 0.634559i
\(502\) −18.3291 + 3.23191i −0.818068 + 0.144247i
\(503\) 24.5186 + 14.1558i 1.09323 + 0.631176i 0.934434 0.356136i \(-0.115906\pi\)
0.158794 + 0.987312i \(0.449239\pi\)
\(504\) 13.3839 + 13.7515i 0.596168 + 0.612539i
\(505\) 0 0
\(506\) −1.02755 + 0.862218i −0.0456803 + 0.0383303i
\(507\) 4.87624 + 9.52410i 0.216562 + 0.422980i
\(508\) −24.6724 4.35041i −1.09466 0.193018i
\(509\) 21.9759 + 18.4399i 0.974063 + 0.817336i 0.983183 0.182622i \(-0.0584586\pi\)
−0.00912008 + 0.999958i \(0.502903\pi\)
\(510\) 0 0
\(511\) −11.2273 4.08640i −0.496666 0.180772i
\(512\) 6.25700i 0.276523i
\(513\) −14.3048 2.17975i −0.631574 0.0962382i
\(514\) 5.50264 0.242711
\(515\) 0 0
\(516\) −0.417197 + 0.449146i −0.0183661 + 0.0197725i
\(517\) −1.83722 + 2.18951i −0.0808008 + 0.0962946i
\(518\) −13.1188 2.31319i −0.576406 0.101636i
\(519\) 0.594397 11.7824i 0.0260911 0.517191i
\(520\) 0 0
\(521\) 12.4548 + 21.5724i 0.545655 + 0.945102i 0.998565 + 0.0535462i \(0.0170525\pi\)
−0.452910 + 0.891556i \(0.649614\pi\)
\(522\) −0.778588 + 0.350304i −0.0340779 + 0.0153324i
\(523\) −22.3995 12.9324i −0.979464 0.565494i −0.0773554 0.997004i \(-0.524648\pi\)
−0.902108 + 0.431510i \(0.857981\pi\)
\(524\) 3.35347 + 19.0185i 0.146497 + 0.830826i
\(525\) 0 0
\(526\) 2.52540 0.919169i 0.110113 0.0400777i
\(527\) 0.277489 + 0.762395i 0.0120876 + 0.0332104i
\(528\) 0.0299374 + 0.239942i 0.00130286 + 0.0104421i
\(529\) −3.77754 21.4235i −0.164241 0.931456i
\(530\) 0 0
\(531\) 10.4827 14.5474i 0.454908 0.631303i
\(532\) 7.78166 4.49274i 0.337378 0.194785i
\(533\) 16.3154 + 19.4439i 0.706698 + 0.842209i
\(534\) 0.730992 14.4901i 0.0316331 0.627047i
\(535\) 0 0
\(536\) 3.73204 + 3.13155i 0.161200 + 0.135262i
\(537\) −23.2841 21.6278i −1.00478 0.933308i
\(538\) 3.49296 9.59683i 0.150592 0.413749i
\(539\) −0.337880 −0.0145535
\(540\) 0 0
\(541\) −21.9158 −0.942232 −0.471116 0.882071i \(-0.656149\pi\)
−0.471116 + 0.882071i \(0.656149\pi\)
\(542\) 6.45777 17.7426i 0.277385 0.762109i
\(543\) 18.7482 5.77200i 0.804562 0.247700i
\(544\) −1.31015 1.09935i −0.0561723 0.0471342i
\(545\) 0 0
\(546\) 7.67176 3.92787i 0.328321 0.168097i
\(547\) −6.41248 7.64210i −0.274178 0.326752i 0.611331 0.791375i \(-0.290634\pi\)
−0.885509 + 0.464623i \(0.846190\pi\)
\(548\) −23.1439 + 13.3621i −0.988658 + 0.570802i
\(549\) 34.4507 8.73273i 1.47032 0.372704i
\(550\) 0 0
\(551\) 0.171694 + 0.973722i 0.00731439 + 0.0414820i
\(552\) 28.7278 + 12.1280i 1.22274 + 0.516203i
\(553\) 0.652634 + 1.79310i 0.0277528 + 0.0762502i
\(554\) −3.14925 + 1.14623i −0.133799 + 0.0486987i
\(555\) 0 0
\(556\) 4.22227 + 23.9457i 0.179064 + 1.01552i
\(557\) 16.0500 + 9.26650i 0.680062 + 0.392634i 0.799879 0.600162i \(-0.204897\pi\)
−0.119816 + 0.992796i \(0.538231\pi\)
\(558\) 6.63172 0.489797i 0.280743 0.0207348i
\(559\) 0.340480 + 0.589729i 0.0144008 + 0.0249429i
\(560\) 0 0
\(561\) 0.106744 + 0.0690241i 0.00450674 + 0.00291420i
\(562\) 17.0784 + 3.01138i 0.720408 + 0.127027i
\(563\) 28.0789 33.4632i 1.18339 1.41031i 0.292388 0.956300i \(-0.405550\pi\)
0.890999 0.454005i \(-0.150005\pi\)
\(564\) 26.1887 + 5.99225i 1.10274 + 0.252319i
\(565\) 0 0
\(566\) −4.18985 −0.176113
\(567\) −4.28380 + 20.9582i −0.179903 + 0.880161i
\(568\) 0.997105i 0.0418376i
\(569\) 12.7485 + 4.64008i 0.534446 + 0.194522i 0.595122 0.803635i \(-0.297104\pi\)
−0.0606766 + 0.998157i \(0.519326\pi\)
\(570\) 0 0
\(571\) 18.1926 + 15.2654i 0.761335 + 0.638836i 0.938474 0.345350i \(-0.112240\pi\)
−0.177139 + 0.984186i \(0.556684\pi\)
\(572\) 0.873565 + 0.154033i 0.0365256 + 0.00644044i
\(573\) 6.45034 9.97529i 0.269467 0.416724i
\(574\) −14.1818 + 11.8999i −0.591935 + 0.496693i
\(575\) 0 0
\(576\) −8.82200 + 6.00083i −0.367583 + 0.250034i
\(577\) 7.03128 + 4.05951i 0.292716 + 0.169000i 0.639166 0.769069i \(-0.279280\pi\)
−0.346450 + 0.938068i \(0.612613\pi\)
\(578\) 13.3510 2.35414i 0.555329 0.0979194i
\(579\) 21.3329 + 28.1949i 0.886566 + 1.17174i
\(580\) 0 0
\(581\) 6.15473 2.24014i 0.255341 0.0929366i
\(582\) −18.9732 8.00990i −0.786464 0.332021i
\(583\) −1.33806 + 0.235937i −0.0554169 + 0.00977150i
\(584\) 6.76397 11.7155i 0.279895 0.484793i
\(585\) 0 0
\(586\) −2.46156 4.26354i −0.101686 0.176125i
\(587\) −2.37317 2.82823i −0.0979511 0.116734i 0.714842 0.699286i \(-0.246499\pi\)
−0.812793 + 0.582552i \(0.802054\pi\)
\(588\) 1.44735 + 2.82691i 0.0596877 + 0.116580i
\(589\) 1.33729 7.58412i 0.0551019 0.312498i
\(590\) 0 0
\(591\) 1.54713 + 5.02527i 0.0636403 + 0.206712i
\(592\) −1.33463 + 3.66686i −0.0548529 + 0.150707i
\(593\) 29.4590i 1.20974i −0.796325 0.604869i \(-0.793226\pi\)
0.796325 0.604869i \(-0.206774\pi\)
\(594\) 0.782291 0.688131i 0.0320978 0.0282344i
\(595\) 0 0
\(596\) 20.7802 + 7.56338i 0.851190 + 0.309808i
\(597\) −2.87119 2.66695i −0.117510 0.109151i
\(598\) 9.00268 10.7290i 0.368147 0.438740i
\(599\) 3.79862 21.5431i 0.155207 0.880225i −0.803388 0.595455i \(-0.796972\pi\)
0.958596 0.284770i \(-0.0919172\pi\)
\(600\) 0 0
\(601\) 27.9764 23.4750i 1.14118 0.957566i 0.141706 0.989909i \(-0.454741\pi\)
0.999477 + 0.0323424i \(0.0102967\pi\)
\(602\) −0.430130 + 0.248335i −0.0175308 + 0.0101214i
\(603\) −0.546563 + 5.40333i −0.0222578 + 0.220041i
\(604\) −9.68946 + 16.7826i −0.394258 + 0.682876i
\(605\) 0 0
\(606\) −5.51775 + 0.688447i −0.224143 + 0.0279662i
\(607\) 2.25077 + 6.18395i 0.0913561 + 0.250999i 0.976953 0.213457i \(-0.0684722\pi\)
−0.885596 + 0.464456i \(0.846250\pi\)
\(608\) 5.55238 + 15.2550i 0.225179 + 0.618674i
\(609\) 1.45045 0.180972i 0.0587753 0.00733335i
\(610\) 0 0
\(611\) 14.9217 25.8451i 0.603667 1.04558i
\(612\) 0.120247 1.18876i 0.00486068 0.0480527i
\(613\) 6.19093 3.57434i 0.250049 0.144366i −0.369737 0.929136i \(-0.620552\pi\)
0.619787 + 0.784770i \(0.287219\pi\)
\(614\) 11.6685 9.79101i 0.470901 0.395133i
\(615\) 0 0
\(616\) −0.277860 + 1.57582i −0.0111953 + 0.0634917i
\(617\) −10.6301 + 12.6684i −0.427951 + 0.510012i −0.936330 0.351121i \(-0.885800\pi\)
0.508379 + 0.861133i \(0.330245\pi\)
\(618\) −6.02103 5.59274i −0.242202 0.224973i
\(619\) −1.40893 0.512808i −0.0566296 0.0206115i 0.313550 0.949572i \(-0.398482\pi\)
−0.370180 + 0.928960i \(0.620704\pi\)
\(620\) 0 0
\(621\) 6.83279 + 34.0833i 0.274190 + 1.36772i
\(622\) 17.2704i 0.692481i
\(623\) −8.49561 + 23.3415i −0.340369 + 0.935157i
\(624\) −0.742878 2.41296i −0.0297389 0.0965958i
\(625\) 0 0
\(626\) 0.530793 3.01028i 0.0212148 0.120315i
\(627\) −0.549884 1.07401i −0.0219602 0.0428919i
\(628\) 0.666118 + 0.793848i 0.0265810 + 0.0316780i
\(629\) 1.02570 + 1.77657i 0.0408974 + 0.0708363i
\(630\) 0 0
\(631\) 17.9456 31.0827i 0.714404 1.23738i −0.248785 0.968559i \(-0.580031\pi\)
0.963189 0.268826i \(-0.0866356\pi\)
\(632\) −2.12771 + 0.375172i −0.0846356 + 0.0149235i
\(633\) 40.5795 + 17.1314i 1.61289 + 0.680913i
\(634\) −3.20443 + 1.16632i −0.127264 + 0.0463204i
\(635\) 0 0
\(636\) 7.70574 + 10.1844i 0.305553 + 0.403837i
\(637\) 3.47431 0.612614i 0.137657 0.0242727i
\(638\) −0.0616542 0.0355961i −0.00244091 0.00140926i
\(639\) −0.919063 + 0.625157i −0.0363576 + 0.0247308i
\(640\) 0 0
\(641\) 30.0504 25.2152i 1.18692 0.995942i 0.187010 0.982358i \(-0.440120\pi\)
0.999908 0.0135840i \(-0.00432406\pi\)
\(642\) −0.195227 + 0.301914i −0.00770501 + 0.0119156i
\(643\) 10.2602 + 1.80915i 0.404624 + 0.0713461i 0.372256 0.928130i \(-0.378584\pi\)
0.0323674 + 0.999476i \(0.489695\pi\)
\(644\) −16.5358 13.8752i −0.651603 0.546760i
\(645\) 0 0
\(646\) 0.615340 + 0.223965i 0.0242102 + 0.00881180i
\(647\) 39.1517i 1.53921i −0.638519 0.769606i \(-0.720453\pi\)
0.638519 0.769606i \(-0.279547\pi\)
\(648\) −22.5271 8.89730i −0.884950 0.349519i
\(649\) 1.49518 0.0586910
\(650\) 0 0
\(651\) −11.0981 2.53935i −0.434967 0.0995248i
\(652\) 4.47509 5.33320i 0.175258 0.208864i
\(653\) −32.4099 5.71474i −1.26830 0.223635i −0.501294 0.865277i \(-0.667142\pi\)
−0.767004 + 0.641642i \(0.778253\pi\)
\(654\) −9.97668 6.45124i −0.390119 0.252263i
\(655\) 0 0
\(656\) 2.71152 + 4.69649i 0.105867 + 0.183367i
\(657\) 15.0394 1.11076i 0.586743 0.0433349i
\(658\) 18.8506 + 10.8834i 0.734873 + 0.424279i
\(659\) 3.74532 + 21.2407i 0.145897 + 0.827422i 0.966643 + 0.256128i \(0.0824470\pi\)
−0.820746 + 0.571293i \(0.806442\pi\)
\(660\) 0 0
\(661\) −24.7105 + 8.99389i −0.961127 + 0.349822i −0.774475 0.632604i \(-0.781986\pi\)
−0.186652 + 0.982426i \(0.559764\pi\)
\(662\) −3.91848 10.7659i −0.152296 0.418430i
\(663\) −1.22276 0.516213i −0.0474882 0.0200481i
\(664\) 1.28776 + 7.30326i 0.0499749 + 0.283422i
\(665\) 0 0
\(666\) 16.2983 4.13136i 0.631545 0.160087i
\(667\) 2.05705 1.18764i 0.0796493 0.0459855i
\(668\) 7.76729 + 9.25670i 0.300526 + 0.358152i
\(669\) −5.90688 + 3.02427i −0.228373 + 0.116925i
\(670\) 0 0
\(671\) 2.27023 + 1.90495i 0.0876412 + 0.0735397i
\(672\) 22.9370 7.06161i 0.884815 0.272408i
\(673\) −3.94080 + 10.8272i −0.151907 + 0.417360i −0.992182 0.124800i \(-0.960171\pi\)
0.840275 + 0.542160i \(0.182393\pi\)
\(674\) 28.6293 1.10276
\(675\) 0 0
\(676\) 8.38635 0.322552
\(677\) −11.6030 + 31.8791i −0.445941 + 1.22521i 0.489585 + 0.871955i \(0.337148\pi\)
−0.935526 + 0.353257i \(0.885074\pi\)
\(678\) −3.17275 2.94707i −0.121849 0.113181i
\(679\) 27.0103 + 22.6643i 1.03656 + 0.869776i
\(680\) 0 0
\(681\) 0.219563 4.35229i 0.00841369 0.166780i
\(682\) 0.356426 + 0.424772i 0.0136483 + 0.0162654i
\(683\) −31.8310 + 18.3777i −1.21798 + 0.703201i −0.964486 0.264135i \(-0.914913\pi\)
−0.253495 + 0.967337i \(0.581580\pi\)
\(684\) −6.63034 + 9.20132i −0.253518 + 0.351821i
\(685\) 0 0
\(686\) 2.76254 + 15.6671i 0.105474 + 0.598174i
\(687\) −3.41816 27.3958i −0.130411 1.04522i
\(688\) 0.0497608 + 0.136717i 0.00189711 + 0.00521227i
\(689\) 13.3311 4.85212i 0.507874 0.184851i
\(690\) 0 0
\(691\) 2.32309 + 13.1749i 0.0883744 + 0.501196i 0.996577 + 0.0826660i \(0.0263435\pi\)
−0.908203 + 0.418530i \(0.862545\pi\)
\(692\) −8.00781 4.62331i −0.304411 0.175752i
\(693\) −1.62670 + 0.731885i −0.0617930 + 0.0278020i
\(694\) 7.79146 + 13.4952i 0.295760 + 0.512271i
\(695\) 0 0
\(696\) −0.0833854 + 1.65291i −0.00316072 + 0.0626532i
\(697\) 2.80761 + 0.495057i 0.106346 + 0.0187516i
\(698\) 4.13236 4.92475i 0.156412 0.186405i
\(699\) −33.1570 + 35.6961i −1.25411 + 1.35015i
\(700\) 0 0
\(701\) 5.00452 0.189018 0.0945091 0.995524i \(-0.469872\pi\)
0.0945091 + 0.995524i \(0.469872\pi\)
\(702\) −6.79639 + 8.49421i −0.256513 + 0.320593i
\(703\) 19.4720i 0.734400i
\(704\) −0.836033 0.304291i −0.0315092 0.0114684i
\(705\) 0 0
\(706\) −5.37489 4.51007i −0.202287 0.169739i
\(707\) 9.37537 + 1.65313i 0.352597 + 0.0621724i
\(708\) −6.40479 12.5096i −0.240707 0.470139i
\(709\) −13.1330 + 11.0199i −0.493218 + 0.413859i −0.855178 0.518334i \(-0.826552\pi\)
0.361960 + 0.932194i \(0.382108\pi\)
\(710\) 0 0
\(711\) −1.67982 1.72595i −0.0629982 0.0647282i
\(712\) −24.3566 14.0623i −0.912800 0.527006i
\(713\) −18.2195 + 3.21258i −0.682324 + 0.120312i
\(714\) 0.376509 0.891844i 0.0140905 0.0333764i
\(715\) 0 0
\(716\) −23.4058 + 8.51902i −0.874716 + 0.318371i
\(717\) −20.3122 + 15.3687i −0.758572 + 0.573954i
\(718\) 6.53417 1.15215i 0.243853 0.0429979i
\(719\) −21.6760 + 37.5439i −0.808377 + 1.40015i 0.105610 + 0.994408i \(0.466320\pi\)
−0.913987 + 0.405742i \(0.867013\pi\)
\(720\) 0 0
\(721\) 7.03467 + 12.1844i 0.261985 + 0.453771i
\(722\) 5.79365 + 6.90461i 0.215617 + 0.256963i
\(723\) 7.94060 12.2799i 0.295314 0.456696i
\(724\) 2.66987 15.1416i 0.0992251 0.562733i
\(725\) 0 0
\(726\) −14.8017 3.38679i −0.549344 0.125695i
\(727\) −12.4303 + 34.1521i −0.461016 + 1.26663i 0.463706 + 0.885989i \(0.346519\pi\)
−0.924722 + 0.380642i \(0.875703\pi\)
\(728\) 16.7075i 0.619220i
\(729\) −5.92298 26.3423i −0.219370 0.975642i
\(730\) 0 0
\(731\) 0.0718726 + 0.0261595i 0.00265830 + 0.000967544i
\(732\) 6.21315 27.1542i 0.229645 1.00365i
\(733\) 2.49119 2.96889i 0.0920143 0.109658i −0.718073 0.695968i \(-0.754975\pi\)
0.810087 + 0.586310i \(0.199420\pi\)
\(734\) −2.05990 + 11.6823i −0.0760322 + 0.431200i
\(735\) 0 0
\(736\) 29.8753 25.0683i 1.10122 0.924031i
\(737\) −0.392191 + 0.226432i −0.0144465 + 0.00834071i
\(738\) 10.1611 21.0418i 0.374036 0.774559i
\(739\) 13.2241 22.9048i 0.486456 0.842567i −0.513422 0.858136i \(-0.671623\pi\)
0.999879 + 0.0155689i \(0.00495594\pi\)
\(740\) 0 0
\(741\) 7.60158 + 10.0467i 0.279251 + 0.369075i
\(742\) 3.53898 + 9.72326i 0.129920 + 0.356952i
\(743\) −4.60474 12.6514i −0.168932 0.464136i 0.826120 0.563494i \(-0.190543\pi\)
−0.995052 + 0.0993584i \(0.968321\pi\)
\(744\) 5.01352 11.8756i 0.183805 0.435381i
\(745\) 0 0
\(746\) 10.2329 17.7238i 0.374651 0.648915i
\(747\) −5.92425 + 5.76591i −0.216757 + 0.210964i
\(748\) 0.0862839 0.0498160i 0.00315485 0.00182145i
\(749\) 0.471538 0.395667i 0.0172296 0.0144574i
\(750\) 0 0
\(751\) 0.654359 3.71106i 0.0238779 0.135418i −0.970538 0.240946i \(-0.922542\pi\)
0.994416 + 0.105528i \(0.0336533\pi\)
\(752\) 4.09854 4.88444i 0.149458 0.178117i
\(753\) −38.4386 + 11.8341i −1.40078 + 0.431258i
\(754\) 0.698510 + 0.254237i 0.0254382 + 0.00925876i
\(755\) 0 0
\(756\) 13.0915 + 10.4748i 0.476135 + 0.380965i
\(757\) 33.7073i 1.22511i −0.790427 0.612556i \(-0.790141\pi\)
0.790427 0.612556i \(-0.209859\pi\)
\(758\) 5.51687 15.1575i 0.200382 0.550544i
\(759\) −1.97271 + 2.12378i −0.0716049 + 0.0770884i
\(760\) 0 0
\(761\) −1.67665 + 9.50874i −0.0607784 + 0.344692i 0.939221 + 0.343314i \(0.111550\pi\)
−0.999999 + 0.00137744i \(0.999562\pi\)
\(762\) 25.5876 + 1.29084i 0.926941 + 0.0467621i
\(763\) 13.0747 + 15.5818i 0.473336 + 0.564100i
\(764\) −4.65533 8.06327i −0.168424 0.291719i
\(765\) 0 0
\(766\) −9.56272 + 16.5631i −0.345515 + 0.598450i
\(767\) −15.3745 + 2.71093i −0.555139 + 0.0978861i
\(768\) 3.03939 + 24.3601i 0.109675 + 0.879019i
\(769\) 36.3764 13.2399i 1.31177 0.477445i 0.410957 0.911655i \(-0.365195\pi\)
0.900812 + 0.434210i \(0.142973\pi\)
\(770\) 0 0
\(771\) 11.7994 1.47220i 0.424944 0.0530200i
\(772\) 27.2905 4.81205i 0.982206 0.173189i
\(773\) 21.0478 + 12.1519i 0.757036 + 0.437075i 0.828231 0.560387i \(-0.189348\pi\)
−0.0711944 + 0.997462i \(0.522681\pi\)
\(774\) 0.366491 0.508601i 0.0131732 0.0182813i
\(775\) 0 0
\(776\) −30.5824 + 25.6617i −1.09784 + 0.921200i
\(777\) −28.7496 1.45036i −1.03139 0.0520312i
\(778\) 29.9742 + 5.28527i 1.07463 + 0.189486i
\(779\) −20.7300 17.3945i −0.742728 0.623223i
\(780\) 0 0
\(781\) −0.0870967 0.0317006i −0.00311656 0.00113434i
\(782\) 1.57311i 0.0562544i
\(783\) −1.57581 + 0.959467i −0.0563150 + 0.0342886i
\(784\) 0.753755 0.0269198
\(785\) 0 0
\(786\) −5.81096 18.8748i −0.207270 0.673240i
\(787\) −13.4604 + 16.0414i −0.479810 + 0.571816i −0.950596 0.310432i \(-0.899526\pi\)
0.470785 + 0.882248i \(0.343971\pi\)
\(788\) 4.05856 + 0.715633i 0.144580 + 0.0254934i
\(789\) 5.16932 2.64664i 0.184033 0.0942229i
\(790\) 0 0
\(791\) 3.70688 + 6.42051i 0.131802 + 0.228287i
\(792\) −0.496258 1.95774i −0.0176338 0.0695654i
\(793\) −26.7979 15.4718i −0.951621 0.549419i
\(794\) 2.83229 + 16.0627i 0.100514 + 0.570045i
\(795\) 0 0
\(796\) −2.88620 + 1.05049i −0.102299 + 0.0372337i
\(797\) −4.08261 11.2169i −0.144614 0.397322i 0.846146 0.532951i \(-0.178917\pi\)
−0.990760 + 0.135628i \(0.956695\pi\)
\(798\) −7.32775 + 5.54435i −0.259400 + 0.196268i
\(799\) −0.582068 3.30107i −0.0205921 0.116783i
\(800\) 0 0
\(801\) −2.30926 31.2668i −0.0815939 1.10476i
\(802\) −4.82080 + 2.78329i −0.170228 + 0.0982814i
\(803\) 0.808303 + 0.963297i 0.0285244 + 0.0339940i
\(804\) 3.57446 + 2.31136i 0.126062 + 0.0815154i
\(805\) 0 0
\(806\) −4.43518 3.72155i −0.156222 0.131086i
\(807\) 4.92242 21.5131i 0.173277 0.757298i
\(808\) −3.68664 + 10.1290i −0.129696 + 0.356336i
\(809\) −8.60808 −0.302644 −0.151322 0.988485i \(-0.548353\pi\)
−0.151322 + 0.988485i \(0.548353\pi\)
\(810\) 0 0
\(811\) 1.53770 0.0539958 0.0269979 0.999635i \(-0.491405\pi\)
0.0269979 + 0.999635i \(0.491405\pi\)
\(812\) 0.391837 1.07656i 0.0137508 0.0377800i
\(813\) 9.10055 39.7734i 0.319170 1.39491i
\(814\) 1.07402 + 0.901211i 0.0376444 + 0.0315874i
\(815\) 0 0
\(816\) −0.238129 0.153982i −0.00833617 0.00539043i
\(817\) −0.466665 0.556149i −0.0163265 0.0194572i
\(818\) −7.57029 + 4.37071i −0.264689 + 0.152818i
\(819\) 15.3998 10.4751i 0.538112 0.366030i
\(820\) 0 0
\(821\) 5.03168 + 28.5361i 0.175607 + 0.995915i 0.937441 + 0.348144i \(0.113188\pi\)
−0.761835 + 0.647772i \(0.775701\pi\)
\(822\) 21.7939 16.4898i 0.760149 0.575147i
\(823\) −3.85004 10.5779i −0.134204 0.368722i 0.854328 0.519734i \(-0.173969\pi\)
−0.988532 + 0.151012i \(0.951747\pi\)
\(824\) −14.9693 + 5.44838i −0.521481 + 0.189803i
\(825\) 0 0
\(826\) −1.97727 11.2136i −0.0687979 0.390172i
\(827\) −26.7844 15.4640i −0.931383 0.537734i −0.0441346 0.999026i \(-0.514053\pi\)
−0.887249 + 0.461291i \(0.847386\pi\)
\(828\) 26.2192 + 7.40742i 0.911180 + 0.257426i
\(829\) −4.91762 8.51757i −0.170796 0.295827i 0.767902 0.640567i \(-0.221301\pi\)
−0.938698 + 0.344739i \(0.887967\pi\)
\(830\) 0 0
\(831\) −6.44630 + 3.30044i −0.223620 + 0.114491i
\(832\) 9.14836 + 1.61310i 0.317162 + 0.0559243i
\(833\) 0.254706 0.303547i 0.00882505 0.0105173i
\(834\) −7.31644 23.7648i −0.253348 0.822906i
\(835\) 0 0
\(836\) −0.945711 −0.0327081
\(837\) 14.0894 2.82456i 0.487003 0.0976310i
\(838\) 8.07072i 0.278798i
\(839\) −12.3506 4.49524i −0.426389 0.155193i 0.119907 0.992785i \(-0.461740\pi\)
−0.546296 + 0.837592i \(0.683963\pi\)
\(840\) 0 0
\(841\) −22.1187 18.5598i −0.762714 0.639993i
\(842\) 2.45296 + 0.432522i 0.0845344 + 0.0149057i
\(843\) 37.4271 + 1.88811i 1.28906 + 0.0650301i
\(844\) 26.4467 22.1914i 0.910333 0.763860i
\(845\) 0 0
\(846\) −27.3342 2.76494i −0.939769 0.0950604i
\(847\) 22.5136 + 12.9982i 0.773575 + 0.446624i
\(848\) 2.98500 0.526336i 0.102505 0.0180745i
\(849\) −8.98435 + 1.12097i −0.308342 + 0.0384717i
\(850\) 0 0
\(851\) −43.9569 + 15.9990i −1.50682 + 0.548438i
\(852\) 0.107863 + 0.864497i 0.00369531 + 0.0296172i
\(853\) 15.2077 2.68153i 0.520703 0.0918139i 0.0928812 0.995677i \(-0.470392\pi\)
0.427821 + 0.903863i \(0.359281\pi\)
\(854\) 11.2846 19.5455i 0.386151 0.668834i
\(855\) 0 0
\(856\) 0.348478 + 0.603581i 0.0119107 + 0.0206300i
\(857\) 14.1302 + 16.8398i 0.482680 + 0.575235i 0.951340 0.308143i \(-0.0997076\pi\)
−0.468660 + 0.883378i \(0.655263\pi\)
\(858\) −0.905968 0.0457041i −0.0309293 0.00156031i
\(859\) −3.39772 + 19.2694i −0.115929 + 0.657464i 0.870358 + 0.492420i \(0.163888\pi\)
−0.986286 + 0.165044i \(0.947223\pi\)
\(860\) 0 0
\(861\) −27.2264 + 29.3114i −0.927873 + 0.998929i
\(862\) 7.69508 21.1421i 0.262095 0.720101i
\(863\) 21.8676i 0.744383i −0.928156 0.372191i \(-0.878607\pi\)
0.928156 0.372191i \(-0.121393\pi\)
\(864\) −22.7445 + 20.0069i −0.773784 + 0.680648i
\(865\) 0 0
\(866\) 14.7061 + 5.35258i 0.499733 + 0.181888i
\(867\) 27.9989 8.62001i 0.950893 0.292751i
\(868\) −5.73577 + 6.83563i −0.194685 + 0.232016i
\(869\) 0.0348743 0.197782i 0.00118303 0.00670929i
\(870\) 0 0
\(871\) 3.62223 3.03941i 0.122734 0.102986i
\(872\) −19.9452 + 11.5153i −0.675428 + 0.389959i
\(873\) −42.8275 12.0996i −1.44949 0.409508i
\(874\) −7.46602 + 12.9315i −0.252542 + 0.437416i
\(875\) 0 0
\(876\) 4.59707 10.8891i 0.155321 0.367910i
\(877\) 13.3729 + 36.7419i 0.451572 + 1.24068i 0.931617 + 0.363441i \(0.118398\pi\)
−0.480045 + 0.877244i \(0.659380\pi\)
\(878\) −4.01053 11.0188i −0.135349 0.371868i
\(879\) −6.41903 8.48379i −0.216509 0.286151i
\(880\) 0 0
\(881\) 3.65254 6.32639i 0.123057 0.213141i −0.797915 0.602771i \(-0.794063\pi\)
0.920972 + 0.389629i \(0.127397\pi\)
\(882\) −1.82665 2.68541i −0.0615063 0.0904223i
\(883\) 3.02496 1.74646i 0.101798 0.0587732i −0.448237 0.893915i \(-0.647948\pi\)
0.550035 + 0.835142i \(0.314614\pi\)
\(884\) −0.796907 + 0.668684i −0.0268029 + 0.0224903i
\(885\) 0 0
\(886\) −2.55485 + 14.4893i −0.0858318 + 0.486776i
\(887\) −18.2688 + 21.7720i −0.613408 + 0.731031i −0.979922 0.199381i \(-0.936107\pi\)
0.366514 + 0.930413i \(0.380551\pi\)
\(888\) 7.26978 31.7721i 0.243958 1.06620i
\(889\) −41.2181 15.0021i −1.38241 0.503156i
\(890\) 0 0
\(891\) 1.49337 1.68487i 0.0500298 0.0564452i
\(892\) 5.20125i 0.174151i
\(893\) −10.8821 + 29.8985i −0.364157 + 1.00051i
\(894\) −22.0447 5.04405i −0.737286 0.168698i
\(895\) 0 0
\(896\) 3.63563 20.6187i 0.121458 0.688821i
\(897\) 16.4341 25.4149i 0.548718 0.848579i
\(898\) 7.14052 + 8.50974i 0.238282 + 0.283974i
\(899\) −0.490949 0.850349i −0.0163741 0.0283607i
\(900\) 0 0
\(901\) 0.796719 1.37996i 0.0265426 0.0459731i
\(902\) 1.91887 0.338348i 0.0638913 0.0112658i
\(903\) −0.855892 + 0.647588i −0.0284823 + 0.0215504i
\(904\) −7.88800 + 2.87100i −0.262351 + 0.0954880i
\(905\) 0 0
\(906\) 7.70767 18.2573i 0.256070 0.606558i
\(907\) −52.3097 + 9.22362i −1.73692 + 0.306265i −0.950337 0.311224i \(-0.899261\pi\)
−0.786579 + 0.617489i \(0.788150\pi\)
\(908\) −2.95799 1.70780i −0.0981644 0.0566753i
\(909\) −11.6476 + 2.95249i −0.386327 + 0.0979279i
\(910\) 0 0
\(911\) −6.18649 + 5.19108i −0.204968 + 0.171988i −0.739493 0.673164i \(-0.764935\pi\)
0.534526 + 0.845152i \(0.320490\pi\)
\(912\) 1.22670 + 2.39595i 0.0406201 + 0.0793377i
\(913\) −0.678878 0.119704i −0.0224676 0.00396164i
\(914\) 10.8360 + 9.09252i 0.358424 + 0.300754i
\(915\) 0 0
\(916\) −20.3339 7.40094i −0.671852 0.244534i
\(917\) 33.8116i 1.11656i
\(918\) 0.0284888 + 1.22154i 0.000940269 + 0.0403168i
\(919\) 47.9961 1.58325 0.791623 0.611009i \(-0.209236\pi\)
0.791623 + 0.611009i \(0.209236\pi\)
\(920\) 0 0
\(921\) 22.4013 24.1168i 0.738149 0.794677i
\(922\) 13.2090 15.7419i 0.435016 0.518431i
\(923\) 0.953063 + 0.168051i 0.0313705 + 0.00553146i
\(924\) −0.0704406 + 1.39631i −0.00231732 + 0.0459351i
\(925\) 0 0
\(926\) 7.35298 + 12.7357i 0.241634 + 0.418522i
\(927\) −14.4073 10.3817i −0.473197 0.340979i
\(928\) 1.79255 + 1.03493i 0.0588433 + 0.0339732i
\(929\) 5.03474 + 28.5534i 0.165185 + 0.936808i 0.948874 + 0.315655i \(0.102224\pi\)
−0.783689 + 0.621153i \(0.786665\pi\)
\(930\) 0 0
\(931\) −3.53442 + 1.28642i −0.115836 + 0.0421608i
\(932\) 13.0603 + 35.8828i 0.427803 + 1.17538i
\(933\) 4.62061 + 37.0332i 0.151272 + 1.21241i
\(934\) −2.26338 12.8363i −0.0740602 0.420016i
\(935\) 0 0
\(936\) 8.65246 + 19.2311i 0.282815 + 0.628587i
\(937\) 4.35481 2.51425i 0.142265 0.0821369i −0.427178 0.904168i \(-0.640492\pi\)
0.569443 + 0.822031i \(0.307159\pi\)
\(938\) 2.21685 + 2.64193i 0.0723826 + 0.0862622i
\(939\) 0.332803 6.59699i 0.0108606 0.215285i
\(940\) 0 0
\(941\) −42.7767 35.8939i −1.39448 1.17011i −0.963487 0.267755i \(-0.913718\pi\)
−0.430995 0.902354i \(-0.641837\pi\)
\(942\) −0.776466 0.721234i −0.0252986 0.0234991i
\(943\) −22.2345 + 61.0887i −0.724054 + 1.98932i
\(944\) −3.33551 −0.108561
\(945\) 0 0
\(946\) 0.0522740 0.00169957
\(947\) 14.5459 39.9645i 0.472678 1.29867i −0.442914 0.896564i \(-0.646055\pi\)
0.915592 0.402109i \(-0.131723\pi\)
\(948\) −1.80415 + 0.555443i −0.0585961 + 0.0180400i
\(949\) −10.0581 8.43973i −0.326499 0.273965i
\(950\) 0 0
\(951\) −6.55926 + 3.35828i −0.212699 + 0.108900i
\(952\) −1.20624 1.43754i −0.0390944 0.0465909i
\(953\) −18.8922 + 10.9074i −0.611977 + 0.353325i −0.773739 0.633505i \(-0.781616\pi\)
0.161762 + 0.986830i \(0.448282\pi\)
\(954\) −9.10901 9.35916i −0.294915 0.303014i
\(955\) 0 0
\(956\) 3.46670 + 19.6606i 0.112121 + 0.635870i
\(957\) −0.141729 0.0598339i −0.00458146 0.00193415i
\(958\) 2.59656 + 7.13399i 0.0838910 + 0.230489i
\(959\) −43.9676 + 16.0029i −1.41979 + 0.516761i
\(960\) 0 0
\(961\) −4.05507 22.9974i −0.130809 0.741852i
\(962\) −12.6778 7.31954i −0.408749 0.235991i
\(963\) −0.337853 + 0.699631i −0.0108872 + 0.0225453i
\(964\) −5.73088 9.92618i −0.184579 0.319701i
\(965\) 0 0
\(966\) 18.5368 + 11.9865i 0.596412 + 0.385659i
\(967\) 4.55827 + 0.803746i 0.146584 + 0.0258467i 0.246459 0.969153i \(-0.420733\pi\)
−0.0998746 + 0.995000i \(0.531844\pi\)
\(968\) −18.9201 + 22.5481i −0.608115 + 0.724724i
\(969\) 1.37940 + 0.315621i 0.0443128 + 0.0101392i
\(970\) 0 0
\(971\) −21.6509 −0.694809 −0.347405 0.937715i \(-0.612937\pi\)
−0.347405 + 0.937715i \(0.612937\pi\)
\(972\) −20.4937 5.27712i −0.657334 0.169264i
\(973\) 42.5714i 1.36478i
\(974\) 0.352164 + 0.128177i 0.0112841 + 0.00410707i
\(975\) 0 0
\(976\) −5.06451 4.24963i −0.162111 0.136027i
\(977\) −21.7493 3.83499i −0.695822 0.122692i −0.185460 0.982652i \(-0.559377\pi\)
−0.510362 + 0.859960i \(0.670489\pi\)
\(978\) −3.86593 + 5.97856i −0.123619 + 0.191173i
\(979\) 2.00269 1.68046i 0.0640063 0.0537076i
\(980\) 0 0
\(981\) −23.1191 11.1643i −0.738137 0.356448i
\(982\) 17.3862 + 10.0379i 0.554815 + 0.320323i
\(983\) −13.6524 + 2.40729i −0.435445 + 0.0767807i −0.387074 0.922049i \(-0.626514\pi\)
−0.0483713 + 0.998829i \(0.515403\pi\)
\(984\) −27.3306 36.1217i −0.871266 1.15152i
\(985\) 0 0
\(986\) 0.0784563 0.0285558i 0.00249856 0.000909401i
\(987\) 43.3334 + 18.2940i 1.37932 + 0.582305i
\(988\) 9.72444 1.71468i 0.309376 0.0545513i
\(989\) −0.872042 + 1.51042i −0.0277293 + 0.0480286i
\(990\) 0 0
\(991\) −17.4112 30.1570i −0.553084 0.957970i −0.998050 0.0624224i \(-0.980117\pi\)
0.444966 0.895548i \(-0.353216\pi\)
\(992\) −10.3628 12.3499i −0.329020 0.392111i
\(993\) −11.2828 22.0371i −0.358049 0.699328i
\(994\) −0.122571 + 0.695133i −0.00388771 + 0.0220483i
\(995\) 0 0
\(996\) 1.90653 + 6.19267i 0.0604109 + 0.196222i
\(997\) −8.46492 + 23.2572i −0.268087 + 0.736562i 0.730475 + 0.682940i \(0.239299\pi\)
−0.998561 + 0.0536221i \(0.982923\pi\)
\(998\) 11.2488i 0.356073i
\(999\) 33.8433 13.2195i 1.07075 0.418245i
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 675.2.u.b.274.2 24
5.2 odd 4 675.2.l.c.301.1 12
5.3 odd 4 27.2.e.a.4.2 12
5.4 even 2 inner 675.2.u.b.274.3 24
15.8 even 4 81.2.e.a.64.1 12
20.3 even 4 432.2.u.c.193.2 12
27.7 even 9 inner 675.2.u.b.574.3 24
45.13 odd 12 243.2.e.d.109.1 12
45.23 even 12 243.2.e.a.109.2 12
45.38 even 12 243.2.e.b.28.2 12
45.43 odd 12 243.2.e.c.28.1 12
135.7 odd 36 675.2.l.c.601.1 12
135.13 odd 36 729.2.a.a.1.3 6
135.23 even 36 729.2.c.b.244.3 12
135.34 even 18 inner 675.2.u.b.574.2 24
135.38 even 36 243.2.e.b.217.2 12
135.43 odd 36 243.2.e.c.217.1 12
135.58 odd 36 729.2.c.e.244.4 12
135.68 even 36 729.2.a.d.1.4 6
135.83 even 36 243.2.e.a.136.2 12
135.88 odd 36 27.2.e.a.7.2 yes 12
135.103 odd 36 729.2.c.e.487.4 12
135.113 even 36 729.2.c.b.487.3 12
135.128 even 36 81.2.e.a.19.1 12
135.133 odd 36 243.2.e.d.136.1 12
540.223 even 36 432.2.u.c.385.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.4.2 12 5.3 odd 4
27.2.e.a.7.2 yes 12 135.88 odd 36
81.2.e.a.19.1 12 135.128 even 36
81.2.e.a.64.1 12 15.8 even 4
243.2.e.a.109.2 12 45.23 even 12
243.2.e.a.136.2 12 135.83 even 36
243.2.e.b.28.2 12 45.38 even 12
243.2.e.b.217.2 12 135.38 even 36
243.2.e.c.28.1 12 45.43 odd 12
243.2.e.c.217.1 12 135.43 odd 36
243.2.e.d.109.1 12 45.13 odd 12
243.2.e.d.136.1 12 135.133 odd 36
432.2.u.c.193.2 12 20.3 even 4
432.2.u.c.385.2 12 540.223 even 36
675.2.l.c.301.1 12 5.2 odd 4
675.2.l.c.601.1 12 135.7 odd 36
675.2.u.b.274.2 24 1.1 even 1 trivial
675.2.u.b.274.3 24 5.4 even 2 inner
675.2.u.b.574.2 24 135.34 even 18 inner
675.2.u.b.574.3 24 27.7 even 9 inner
729.2.a.a.1.3 6 135.13 odd 36
729.2.a.d.1.4 6 135.68 even 36
729.2.c.b.244.3 12 135.23 even 36
729.2.c.b.487.3 12 135.113 even 36
729.2.c.e.244.4 12 135.58 odd 36
729.2.c.e.487.4 12 135.103 odd 36