Properties

Label 289.2.d.f.134.2
Level $289$
Weight $2$
Character 289.134
Analytic conductor $2.308$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [289,2,Mod(110,289)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(289, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("289.110");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 289.d (of order \(8\), degree \(4\), 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: \(2.30767661842\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 134.2
Character \(\chi\) \(=\) 289.134
Dual form 289.2.d.f.110.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.08335 - 1.08335i) q^{2} +(0.515588 + 1.24474i) q^{3} +0.347296i q^{4} +(3.26322 - 1.35167i) q^{5} +(0.789927 - 1.90705i) q^{6} +(-0.320860 - 0.132905i) q^{7} +(-1.79046 + 1.79046i) q^{8} +(0.837775 - 0.837775i) q^{9} +O(q^{10})\) \(q+(-1.08335 - 1.08335i) q^{2} +(0.515588 + 1.24474i) q^{3} +0.347296i q^{4} +(3.26322 - 1.35167i) q^{5} +(0.789927 - 1.90705i) q^{6} +(-0.320860 - 0.132905i) q^{7} +(-1.79046 + 1.79046i) q^{8} +(0.837775 - 0.837775i) q^{9} +(-4.99955 - 2.07088i) q^{10} +(0.673052 - 1.62489i) q^{11} +(-0.432294 + 0.179062i) q^{12} +3.29086i q^{13} +(0.203622 + 0.491586i) q^{14} +(3.36496 + 3.36496i) q^{15} +4.57398 q^{16} -1.81521 q^{18} +(-1.08335 - 1.08335i) q^{19} +(0.469431 + 1.13331i) q^{20} -0.467911i q^{21} +(-2.48948 + 1.03118i) q^{22} +(1.07733 - 2.60091i) q^{23} +(-3.15179 - 1.30551i) q^{24} +(5.28608 - 5.28608i) q^{25} +(3.56515 - 3.56515i) q^{26} +(5.20898 + 2.15763i) q^{27} +(0.0461573 - 0.111434i) q^{28} +(1.09461 - 0.453400i) q^{29} -7.29086i q^{30} +(-2.71937 - 6.56515i) q^{31} +(-1.37431 - 1.37431i) q^{32} +2.36959 q^{33} -1.22668 q^{35} +(0.290956 + 0.290956i) q^{36} +(-1.50061 - 3.62279i) q^{37} +2.34730i q^{38} +(-4.09626 + 1.69673i) q^{39} +(-3.42255 + 8.26277i) q^{40} +(4.54666 + 1.88329i) q^{41} +(-0.506912 + 0.506912i) q^{42} +(-7.76789 + 7.76789i) q^{43} +(0.564319 + 0.233749i) q^{44} +(1.60145 - 3.86624i) q^{45} +(-3.98483 + 1.65057i) q^{46} +5.12061i q^{47} +(2.35829 + 5.69341i) q^{48} +(-4.86446 - 4.86446i) q^{49} -11.4534 q^{50} -1.14290 q^{52} +(5.91819 + 5.91819i) q^{53} +(-3.30568 - 7.98062i) q^{54} -6.21213i q^{55} +(0.812446 - 0.336526i) q^{56} +(0.789927 - 1.90705i) q^{57} +(-1.67703 - 0.694650i) q^{58} +(-7.68260 + 7.68260i) q^{59} +(-1.16864 + 1.16864i) q^{60} +(4.07567 + 1.68820i) q^{61} +(-4.16632 + 10.0584i) q^{62} +(-0.380153 + 0.157464i) q^{63} -6.17024i q^{64} +(4.44816 + 10.7388i) q^{65} +(-2.56709 - 2.56709i) q^{66} -8.07192 q^{67} +3.79292 q^{69} +(1.32893 + 1.32893i) q^{70} +(4.30479 + 10.3927i) q^{71} +3.00000i q^{72} +(1.57275 - 0.651455i) q^{73} +(-2.29906 + 5.55043i) q^{74} +(9.30524 + 3.85436i) q^{75} +(0.376244 - 0.376244i) q^{76} +(-0.431911 + 0.431911i) q^{77} +(6.27584 + 2.59954i) q^{78} +(-4.43213 + 10.7001i) q^{79} +(14.9259 - 6.18252i) q^{80} +4.04189i q^{81} +(-2.88537 - 6.96589i) q^{82} +(-1.51883 - 1.51883i) q^{83} +0.162504 q^{84} +16.8307 q^{86} +(1.12873 + 1.12873i) q^{87} +(1.70423 + 4.11437i) q^{88} +6.41921i q^{89} +(-5.92343 + 2.45356i) q^{90} +(0.437370 - 1.05591i) q^{91} +(0.903287 + 0.374154i) q^{92} +(6.76982 - 6.76982i) q^{93} +(5.54742 - 5.54742i) q^{94} +(-4.99955 - 2.07088i) q^{95} +(1.00208 - 2.41923i) q^{96} +(-3.77292 + 1.56279i) q^{97} +10.5398i q^{98} +(-0.797427 - 1.92516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 48 q^{16} - 72 q^{18} + 24 q^{35} - 168 q^{50} - 24 q^{52} + 72 q^{67} + 168 q^{69} + 24 q^{84} + 48 q^{86}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.08335 1.08335i −0.766044 0.766044i 0.211363 0.977408i \(-0.432210\pi\)
−0.977408 + 0.211363i \(0.932210\pi\)
\(3\) 0.515588 + 1.24474i 0.297675 + 0.718651i 0.999977 + 0.00677177i \(0.00215554\pi\)
−0.702302 + 0.711879i \(0.747844\pi\)
\(4\) 0.347296i 0.173648i
\(5\) 3.26322 1.35167i 1.45936 0.604486i 0.494954 0.868919i \(-0.335185\pi\)
0.964404 + 0.264433i \(0.0851848\pi\)
\(6\) 0.789927 1.90705i 0.322486 0.778551i
\(7\) −0.320860 0.132905i −0.121274 0.0502332i 0.321221 0.947004i \(-0.395907\pi\)
−0.442495 + 0.896771i \(0.645907\pi\)
\(8\) −1.79046 + 1.79046i −0.633022 + 0.633022i
\(9\) 0.837775 0.837775i 0.279258 0.279258i
\(10\) −4.99955 2.07088i −1.58100 0.654870i
\(11\) 0.673052 1.62489i 0.202933 0.489923i −0.789346 0.613948i \(-0.789580\pi\)
0.992279 + 0.124025i \(0.0395803\pi\)
\(12\) −0.432294 + 0.179062i −0.124792 + 0.0516907i
\(13\) 3.29086i 0.912720i 0.889795 + 0.456360i \(0.150847\pi\)
−0.889795 + 0.456360i \(0.849153\pi\)
\(14\) 0.203622 + 0.491586i 0.0544202 + 0.131382i
\(15\) 3.36496 + 3.36496i 0.868829 + 0.868829i
\(16\) 4.57398 1.14349
\(17\) 0 0
\(18\) −1.81521 −0.427849
\(19\) −1.08335 1.08335i −0.248538 0.248538i 0.571833 0.820370i \(-0.306233\pi\)
−0.820370 + 0.571833i \(0.806233\pi\)
\(20\) 0.469431 + 1.13331i 0.104968 + 0.253415i
\(21\) 0.467911i 0.102107i
\(22\) −2.48948 + 1.03118i −0.530759 + 0.219847i
\(23\) 1.07733 2.60091i 0.224640 0.542328i −0.770870 0.636993i \(-0.780178\pi\)
0.995509 + 0.0946652i \(0.0301780\pi\)
\(24\) −3.15179 1.30551i −0.643357 0.266487i
\(25\) 5.28608 5.28608i 1.05722 1.05722i
\(26\) 3.56515 3.56515i 0.699184 0.699184i
\(27\) 5.20898 + 2.15763i 1.00247 + 0.415236i
\(28\) 0.0461573 0.111434i 0.00872290 0.0210590i
\(29\) 1.09461 0.453400i 0.203263 0.0841944i −0.278729 0.960370i \(-0.589913\pi\)
0.481993 + 0.876175i \(0.339913\pi\)
\(30\) 7.29086i 1.33112i
\(31\) −2.71937 6.56515i −0.488414 1.17914i −0.955518 0.294933i \(-0.904703\pi\)
0.467104 0.884202i \(-0.345297\pi\)
\(32\) −1.37431 1.37431i −0.242945 0.242945i
\(33\) 2.36959 0.412492
\(34\) 0 0
\(35\) −1.22668 −0.207347
\(36\) 0.290956 + 0.290956i 0.0484927 + 0.0484927i
\(37\) −1.50061 3.62279i −0.246698 0.595582i 0.751222 0.660050i \(-0.229465\pi\)
−0.997920 + 0.0644679i \(0.979465\pi\)
\(38\) 2.34730i 0.380782i
\(39\) −4.09626 + 1.69673i −0.655927 + 0.271694i
\(40\) −3.42255 + 8.26277i −0.541153 + 1.30646i
\(41\) 4.54666 + 1.88329i 0.710070 + 0.294121i 0.708333 0.705878i \(-0.249447\pi\)
0.00173627 + 0.999998i \(0.499447\pi\)
\(42\) −0.506912 + 0.506912i −0.0782182 + 0.0782182i
\(43\) −7.76789 + 7.76789i −1.18459 + 1.18459i −0.206050 + 0.978541i \(0.566061\pi\)
−0.978541 + 0.206050i \(0.933939\pi\)
\(44\) 0.564319 + 0.233749i 0.0850743 + 0.0352389i
\(45\) 1.60145 3.86624i 0.238730 0.576346i
\(46\) −3.98483 + 1.65057i −0.587531 + 0.243363i
\(47\) 5.12061i 0.746918i 0.927647 + 0.373459i \(0.121828\pi\)
−0.927647 + 0.373459i \(0.878172\pi\)
\(48\) 2.35829 + 5.69341i 0.340390 + 0.821773i
\(49\) −4.86446 4.86446i −0.694923 0.694923i
\(50\) −11.4534 −1.61975
\(51\) 0 0
\(52\) −1.14290 −0.158492
\(53\) 5.91819 + 5.91819i 0.812926 + 0.812926i 0.985072 0.172146i \(-0.0550699\pi\)
−0.172146 + 0.985072i \(0.555070\pi\)
\(54\) −3.30568 7.98062i −0.449846 1.08602i
\(55\) 6.21213i 0.837644i
\(56\) 0.812446 0.336526i 0.108568 0.0449702i
\(57\) 0.789927 1.90705i 0.104628 0.252595i
\(58\) −1.67703 0.694650i −0.220205 0.0912120i
\(59\) −7.68260 + 7.68260i −1.00019 + 1.00019i −0.000189365 1.00000i \(0.500060\pi\)
−1.00000 0.000189365i \(0.999940\pi\)
\(60\) −1.16864 + 1.16864i −0.150871 + 0.150871i
\(61\) 4.07567 + 1.68820i 0.521836 + 0.216152i 0.628023 0.778195i \(-0.283864\pi\)
−0.106187 + 0.994346i \(0.533864\pi\)
\(62\) −4.16632 + 10.0584i −0.529124 + 1.27742i
\(63\) −0.380153 + 0.157464i −0.0478947 + 0.0198386i
\(64\) 6.17024i 0.771281i
\(65\) 4.44816 + 10.7388i 0.551727 + 1.33199i
\(66\) −2.56709 2.56709i −0.315987 0.315987i
\(67\) −8.07192 −0.986142 −0.493071 0.869989i \(-0.664126\pi\)
−0.493071 + 0.869989i \(0.664126\pi\)
\(68\) 0 0
\(69\) 3.79292 0.456614
\(70\) 1.32893 + 1.32893i 0.158837 + 0.158837i
\(71\) 4.30479 + 10.3927i 0.510885 + 1.23339i 0.943369 + 0.331744i \(0.107637\pi\)
−0.432484 + 0.901642i \(0.642363\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 1.57275 0.651455i 0.184077 0.0762470i −0.288741 0.957407i \(-0.593237\pi\)
0.472818 + 0.881160i \(0.343237\pi\)
\(74\) −2.29906 + 5.55043i −0.267261 + 0.645224i
\(75\) 9.30524 + 3.85436i 1.07448 + 0.445063i
\(76\) 0.376244 0.376244i 0.0431581 0.0431581i
\(77\) −0.431911 + 0.431911i −0.0492208 + 0.0492208i
\(78\) 6.27584 + 2.59954i 0.710599 + 0.294340i
\(79\) −4.43213 + 10.7001i −0.498654 + 1.20386i 0.451555 + 0.892243i \(0.350869\pi\)
−0.950209 + 0.311614i \(0.899131\pi\)
\(80\) 14.9259 6.18252i 1.66877 0.691226i
\(81\) 4.04189i 0.449099i
\(82\) −2.88537 6.96589i −0.318636 0.769254i
\(83\) −1.51883 1.51883i −0.166714 0.166714i 0.618820 0.785533i \(-0.287611\pi\)
−0.785533 + 0.618820i \(0.787611\pi\)
\(84\) 0.162504 0.0177306
\(85\) 0 0
\(86\) 16.8307 1.81490
\(87\) 1.12873 + 1.12873i 0.121013 + 0.121013i
\(88\) 1.70423 + 4.11437i 0.181671 + 0.438593i
\(89\) 6.41921i 0.680435i 0.940347 + 0.340218i \(0.110501\pi\)
−0.940347 + 0.340218i \(0.889499\pi\)
\(90\) −5.92343 + 2.45356i −0.624384 + 0.258628i
\(91\) 0.437370 1.05591i 0.0458489 0.110689i
\(92\) 0.903287 + 0.374154i 0.0941742 + 0.0390082i
\(93\) 6.76982 6.76982i 0.701998 0.701998i
\(94\) 5.54742 5.54742i 0.572173 0.572173i
\(95\) −4.99955 2.07088i −0.512943 0.212468i
\(96\) 1.00208 2.41923i 0.102274 0.246912i
\(97\) −3.77292 + 1.56279i −0.383082 + 0.158678i −0.565910 0.824467i \(-0.691475\pi\)
0.182828 + 0.983145i \(0.441475\pi\)
\(98\) 10.5398i 1.06468i
\(99\) −0.797427 1.92516i −0.0801445 0.193486i
\(100\) 1.83584 + 1.83584i 0.183584 + 0.183584i
\(101\) −5.26857 −0.524242 −0.262121 0.965035i \(-0.584422\pi\)
−0.262121 + 0.965035i \(0.584422\pi\)
\(102\) 0 0
\(103\) −18.4388 −1.81683 −0.908415 0.418069i \(-0.862707\pi\)
−0.908415 + 0.418069i \(0.862707\pi\)
\(104\) −5.89214 5.89214i −0.577772 0.577772i
\(105\) −0.632462 1.52690i −0.0617220 0.149010i
\(106\) 12.8229i 1.24547i
\(107\) 4.95370 2.05189i 0.478892 0.198364i −0.130161 0.991493i \(-0.541550\pi\)
0.609053 + 0.793129i \(0.291550\pi\)
\(108\) −0.749337 + 1.80906i −0.0721049 + 0.174077i
\(109\) −14.3363 5.93831i −1.37317 0.568787i −0.430525 0.902578i \(-0.641672\pi\)
−0.942647 + 0.333792i \(0.891672\pi\)
\(110\) −6.72992 + 6.72992i −0.641672 + 0.641672i
\(111\) 3.73573 3.73573i 0.354580 0.354580i
\(112\) −1.46761 0.607903i −0.138676 0.0574414i
\(113\) 2.68925 6.49242i 0.252983 0.610755i −0.745459 0.666551i \(-0.767770\pi\)
0.998442 + 0.0557962i \(0.0177697\pi\)
\(114\) −2.92177 + 1.21024i −0.273649 + 0.113349i
\(115\) 9.94356i 0.927242i
\(116\) 0.157464 + 0.380153i 0.0146202 + 0.0352963i
\(117\) 2.75700 + 2.75700i 0.254885 + 0.254885i
\(118\) 16.6459 1.53238
\(119\) 0 0
\(120\) −12.0496 −1.09998
\(121\) 5.59090 + 5.59090i 0.508264 + 0.508264i
\(122\) −2.58647 6.24429i −0.234168 0.565331i
\(123\) 6.63041i 0.597844i
\(124\) 2.28005 0.944429i 0.204755 0.0848122i
\(125\) 3.34627 8.07861i 0.299299 0.722573i
\(126\) 0.582427 + 0.241249i 0.0518868 + 0.0214922i
\(127\) 5.47599 5.47599i 0.485916 0.485916i −0.421099 0.907015i \(-0.638355\pi\)
0.907015 + 0.421099i \(0.138355\pi\)
\(128\) −9.43315 + 9.43315i −0.833781 + 0.833781i
\(129\) −13.6740 5.66397i −1.20393 0.498685i
\(130\) 6.81498 16.4528i 0.597713 1.44301i
\(131\) −17.2013 + 7.12501i −1.50288 + 0.622515i −0.974075 0.226225i \(-0.927361\pi\)
−0.528810 + 0.848740i \(0.677361\pi\)
\(132\) 0.822948i 0.0716285i
\(133\) 0.203622 + 0.491586i 0.0176562 + 0.0426259i
\(134\) 8.74472 + 8.74472i 0.755428 + 0.755428i
\(135\) 19.9145 1.71396
\(136\) 0 0
\(137\) 10.0719 0.860502 0.430251 0.902709i \(-0.358425\pi\)
0.430251 + 0.902709i \(0.358425\pi\)
\(138\) −4.10906 4.10906i −0.349786 0.349786i
\(139\) −3.27362 7.90321i −0.277665 0.670342i 0.722105 0.691783i \(-0.243175\pi\)
−0.999770 + 0.0214411i \(0.993175\pi\)
\(140\) 0.426022i 0.0360054i
\(141\) −6.37383 + 2.64013i −0.536773 + 0.222339i
\(142\) 6.59533 15.9225i 0.553468 1.33619i
\(143\) 5.34729 + 2.21492i 0.447163 + 0.185221i
\(144\) 3.83196 3.83196i 0.319330 0.319330i
\(145\) 2.95910 2.95910i 0.245739 0.245739i
\(146\) −2.40959 0.998087i −0.199419 0.0826022i
\(147\) 3.54693 8.56304i 0.292546 0.706268i
\(148\) 1.25818 0.521155i 0.103422 0.0428387i
\(149\) 11.8794i 0.973197i −0.873626 0.486599i \(-0.838237\pi\)
0.873626 0.486599i \(-0.161763\pi\)
\(150\) −5.90522 14.2565i −0.482159 1.16403i
\(151\) 4.63822 + 4.63822i 0.377453 + 0.377453i 0.870182 0.492730i \(-0.164001\pi\)
−0.492730 + 0.870182i \(0.664001\pi\)
\(152\) 3.87939 0.314660
\(153\) 0 0
\(154\) 0.935822 0.0754107
\(155\) −17.7479 17.7479i −1.42554 1.42554i
\(156\) −0.589267 1.42262i −0.0471791 0.113901i
\(157\) 8.88444i 0.709055i 0.935046 + 0.354528i \(0.115358\pi\)
−0.935046 + 0.354528i \(0.884642\pi\)
\(158\) 16.3935 6.79042i 1.30420 0.540217i
\(159\) −4.31526 + 10.4180i −0.342222 + 0.826197i
\(160\) −6.34228 2.62706i −0.501401 0.207687i
\(161\) −0.691346 + 0.691346i −0.0544857 + 0.0544857i
\(162\) 4.37878 4.37878i 0.344030 0.344030i
\(163\) 8.94320 + 3.70439i 0.700485 + 0.290150i 0.704361 0.709842i \(-0.251234\pi\)
−0.00387577 + 0.999992i \(0.501234\pi\)
\(164\) −0.654060 + 1.57904i −0.0510735 + 0.123302i
\(165\) 7.73249 3.20290i 0.601973 0.249346i
\(166\) 3.29086i 0.255420i
\(167\) −0.703179 1.69763i −0.0544137 0.131366i 0.894335 0.447398i \(-0.147649\pi\)
−0.948749 + 0.316032i \(0.897649\pi\)
\(168\) 0.837775 + 0.837775i 0.0646357 + 0.0646357i
\(169\) 2.17024 0.166942
\(170\) 0 0
\(171\) −1.81521 −0.138812
\(172\) −2.69776 2.69776i −0.205702 0.205702i
\(173\) 8.70976 + 21.0272i 0.662191 + 1.59867i 0.794363 + 0.607443i \(0.207805\pi\)
−0.132172 + 0.991227i \(0.542195\pi\)
\(174\) 2.44562i 0.185402i
\(175\) −2.39864 + 0.993548i −0.181320 + 0.0751052i
\(176\) 3.07853 7.43222i 0.232053 0.560225i
\(177\) −13.5239 5.60178i −1.01652 0.421056i
\(178\) 6.95426 6.95426i 0.521244 0.521244i
\(179\) 12.3922 12.3922i 0.926240 0.926240i −0.0712207 0.997461i \(-0.522689\pi\)
0.997461 + 0.0712207i \(0.0226895\pi\)
\(180\) 1.34273 + 0.556178i 0.100081 + 0.0414551i
\(181\) 1.74585 4.21485i 0.129768 0.313287i −0.845619 0.533786i \(-0.820769\pi\)
0.975387 + 0.220499i \(0.0707686\pi\)
\(182\) −1.61774 + 0.670090i −0.119915 + 0.0496704i
\(183\) 5.94356i 0.439361i
\(184\) 2.72790 + 6.58574i 0.201104 + 0.485507i
\(185\) −9.79363 9.79363i −0.720042 0.720042i
\(186\) −14.6682 −1.07552
\(187\) 0 0
\(188\) −1.77837 −0.129701
\(189\) −1.38459 1.38459i −0.100714 0.100714i
\(190\) 3.17277 + 7.65976i 0.230177 + 0.555697i
\(191\) 9.72462i 0.703649i −0.936066 0.351824i \(-0.885561\pi\)
0.936066 0.351824i \(-0.114439\pi\)
\(192\) 7.68035 3.18130i 0.554281 0.229591i
\(193\) −0.323101 + 0.780035i −0.0232573 + 0.0561481i −0.935082 0.354433i \(-0.884674\pi\)
0.911824 + 0.410581i \(0.134674\pi\)
\(194\) 5.78045 + 2.39434i 0.415012 + 0.171904i
\(195\) −11.0736 + 11.0736i −0.792997 + 0.792997i
\(196\) 1.68941 1.68941i 0.120672 0.120672i
\(197\) −15.7068 6.50598i −1.11906 0.463532i −0.255014 0.966937i \(-0.582080\pi\)
−0.864050 + 0.503406i \(0.832080\pi\)
\(198\) −1.22173 + 2.94952i −0.0868245 + 0.209613i
\(199\) 11.7291 4.85837i 0.831456 0.344401i 0.0739773 0.997260i \(-0.476431\pi\)
0.757479 + 0.652859i \(0.226431\pi\)
\(200\) 18.9290i 1.33848i
\(201\) −4.16178 10.0474i −0.293550 0.708691i
\(202\) 5.70771 + 5.70771i 0.401593 + 0.401593i
\(203\) −0.411474 −0.0288798
\(204\) 0 0
\(205\) 17.3824 1.21404
\(206\) 19.9757 + 19.9757i 1.39177 + 1.39177i
\(207\) −1.27642 3.08154i −0.0887171 0.214182i
\(208\) 15.0523i 1.04369i
\(209\) −2.48948 + 1.03118i −0.172201 + 0.0713279i
\(210\) −0.968988 + 2.33935i −0.0668666 + 0.161430i
\(211\) 21.7392 + 9.00467i 1.49659 + 0.619907i 0.972739 0.231904i \(-0.0744955\pi\)
0.523849 + 0.851811i \(0.324496\pi\)
\(212\) −2.05537 + 2.05537i −0.141163 + 0.141163i
\(213\) −10.7167 + 10.7167i −0.734296 + 0.734296i
\(214\) −7.58951 3.14368i −0.518808 0.214897i
\(215\) −14.8487 + 35.8480i −1.01267 + 2.44481i
\(216\) −13.1896 + 5.46331i −0.897438 + 0.371731i
\(217\) 2.46791i 0.167533i
\(218\) 9.09801 + 21.9645i 0.616195 + 1.48763i
\(219\) 1.62178 + 1.62178i 0.109590 + 0.109590i
\(220\) 2.15745 0.145455
\(221\) 0 0
\(222\) −8.09421 −0.543248
\(223\) −3.51496 3.51496i −0.235379 0.235379i 0.579554 0.814934i \(-0.303227\pi\)
−0.814934 + 0.579554i \(0.803227\pi\)
\(224\) 0.258308 + 0.623612i 0.0172590 + 0.0416668i
\(225\) 8.85710i 0.590473i
\(226\) −9.94696 + 4.12017i −0.661662 + 0.274069i
\(227\) −2.01166 + 4.85657i −0.133518 + 0.322342i −0.976472 0.215645i \(-0.930815\pi\)
0.842954 + 0.537986i \(0.180815\pi\)
\(228\) 0.662312 + 0.274339i 0.0438627 + 0.0181685i
\(229\) −17.1158 + 17.1158i −1.13104 + 1.13104i −0.141036 + 0.990004i \(0.545043\pi\)
−0.990004 + 0.141036i \(0.954957\pi\)
\(230\) −10.7724 + 10.7724i −0.710309 + 0.710309i
\(231\) −0.760305 0.314929i −0.0500244 0.0207208i
\(232\) −1.14805 + 2.77164i −0.0753732 + 0.181967i
\(233\) 26.5356 10.9914i 1.73841 0.720071i 0.739507 0.673149i \(-0.235059\pi\)
0.998899 0.0469221i \(-0.0149412\pi\)
\(234\) 5.97359i 0.390506i
\(235\) 6.92139 + 16.7097i 0.451502 + 1.09002i
\(236\) −2.66814 2.66814i −0.173681 0.173681i
\(237\) −15.6040 −1.01359
\(238\) 0 0
\(239\) −2.63310 −0.170321 −0.0851606 0.996367i \(-0.527140\pi\)
−0.0851606 + 0.996367i \(0.527140\pi\)
\(240\) 15.3912 + 15.3912i 0.993501 + 0.993501i
\(241\) −9.69478 23.4053i −0.624496 1.50767i −0.846373 0.532591i \(-0.821218\pi\)
0.221877 0.975075i \(-0.428782\pi\)
\(242\) 12.1138i 0.778705i
\(243\) 10.5958 4.38894i 0.679723 0.281550i
\(244\) −0.586305 + 1.41547i −0.0375343 + 0.0906159i
\(245\) −22.4490 9.29867i −1.43421 0.594070i
\(246\) 7.18306 7.18306i 0.457975 0.457975i
\(247\) 3.56515 3.56515i 0.226845 0.226845i
\(248\) 16.6235 + 6.88570i 1.05560 + 0.437242i
\(249\) 1.10746 2.67365i 0.0701824 0.169435i
\(250\) −12.3771 + 5.12678i −0.782799 + 0.324246i
\(251\) 10.6851i 0.674437i −0.941426 0.337219i \(-0.890514\pi\)
0.941426 0.337219i \(-0.109486\pi\)
\(252\) −0.0546868 0.132026i −0.00344494 0.00831683i
\(253\) −3.50110 3.50110i −0.220112 0.220112i
\(254\) −11.8648 −0.744466
\(255\) 0 0
\(256\) 8.09833 0.506145
\(257\) 2.64209 + 2.64209i 0.164809 + 0.164809i 0.784693 0.619884i \(-0.212820\pi\)
−0.619884 + 0.784693i \(0.712820\pi\)
\(258\) 8.67770 + 20.9498i 0.540250 + 1.30428i
\(259\) 1.36184i 0.0846209i
\(260\) −3.72955 + 1.54483i −0.231297 + 0.0958063i
\(261\) 0.537185 1.29688i 0.0332509 0.0802749i
\(262\) 26.3539 + 10.9162i 1.62815 + 0.674402i
\(263\) 7.21917 7.21917i 0.445153 0.445153i −0.448586 0.893739i \(-0.648072\pi\)
0.893739 + 0.448586i \(0.148072\pi\)
\(264\) −4.24264 + 4.24264i −0.261116 + 0.261116i
\(265\) 27.3118 + 11.3129i 1.67775 + 0.694948i
\(266\) 0.311966 0.753153i 0.0191279 0.0461788i
\(267\) −7.99025 + 3.30967i −0.488995 + 0.202549i
\(268\) 2.80335i 0.171242i
\(269\) −4.49239 10.8456i −0.273906 0.661267i 0.725738 0.687971i \(-0.241499\pi\)
−0.999643 + 0.0267048i \(0.991499\pi\)
\(270\) −21.5743 21.5743i −1.31297 1.31297i
\(271\) −17.0000 −1.03268 −0.516338 0.856385i \(-0.672705\pi\)
−0.516338 + 0.856385i \(0.672705\pi\)
\(272\) 0 0
\(273\) 1.53983 0.0931947
\(274\) −10.9114 10.9114i −0.659183 0.659183i
\(275\) −5.03150 12.1471i −0.303411 0.732499i
\(276\) 1.31727i 0.0792901i
\(277\) −22.4902 + 9.31573i −1.35130 + 0.559728i −0.936655 0.350254i \(-0.886095\pi\)
−0.414648 + 0.909982i \(0.636095\pi\)
\(278\) −5.01547 + 12.1084i −0.300808 + 0.726215i
\(279\) −7.77834 3.22189i −0.465677 0.192890i
\(280\) 2.19632 2.19632i 0.131255 0.131255i
\(281\) 4.09687 4.09687i 0.244399 0.244399i −0.574268 0.818667i \(-0.694713\pi\)
0.818667 + 0.574268i \(0.194713\pi\)
\(282\) 9.76528 + 4.04491i 0.581514 + 0.240871i
\(283\) 5.86269 14.1538i 0.348501 0.841356i −0.648297 0.761388i \(-0.724518\pi\)
0.996797 0.0799677i \(-0.0254817\pi\)
\(284\) −3.60934 + 1.49504i −0.214175 + 0.0887143i
\(285\) 7.29086i 0.431873i
\(286\) −3.39346 8.19253i −0.200659 0.484434i
\(287\) −1.20854 1.20854i −0.0713382 0.0713382i
\(288\) −2.30272 −0.135689
\(289\) 0 0
\(290\) −6.41147 −0.376495
\(291\) −3.89054 3.89054i −0.228068 0.228068i
\(292\) 0.226248 + 0.546211i 0.0132402 + 0.0319646i
\(293\) 2.98040i 0.174117i 0.996203 + 0.0870584i \(0.0277467\pi\)
−0.996203 + 0.0870584i \(0.972253\pi\)
\(294\) −13.1193 + 5.43421i −0.765136 + 0.316930i
\(295\) −14.6857 + 35.4544i −0.855034 + 2.06424i
\(296\) 9.17321 + 3.79967i 0.533182 + 0.220851i
\(297\) 7.01183 7.01183i 0.406868 0.406868i
\(298\) −12.8695 + 12.8695i −0.745512 + 0.745512i
\(299\) 8.55924 + 3.54535i 0.494993 + 0.205033i
\(300\) −1.33860 + 3.23168i −0.0772843 + 0.186581i
\(301\) 3.52479 1.46002i 0.203166 0.0841540i
\(302\) 10.0496i 0.578291i
\(303\) −2.71641 6.55800i −0.156054 0.376747i
\(304\) −4.95522 4.95522i −0.284201 0.284201i
\(305\) 15.5817 0.892207
\(306\) 0 0
\(307\) −3.26857 −0.186547 −0.0932736 0.995641i \(-0.529733\pi\)
−0.0932736 + 0.995641i \(0.529733\pi\)
\(308\) −0.150001 0.150001i −0.00854711 0.00854711i
\(309\) −9.50683 22.9515i −0.540825 1.30567i
\(310\) 38.4543i 2.18406i
\(311\) 3.26322 1.35167i 0.185040 0.0766463i −0.288239 0.957558i \(-0.593070\pi\)
0.473280 + 0.880912i \(0.343070\pi\)
\(312\) 4.29627 10.3721i 0.243228 0.587205i
\(313\) 1.36961 + 0.567313i 0.0774151 + 0.0320664i 0.421055 0.907035i \(-0.361660\pi\)
−0.343640 + 0.939102i \(0.611660\pi\)
\(314\) 9.62496 9.62496i 0.543168 0.543168i
\(315\) −1.02768 + 1.02768i −0.0579034 + 0.0579034i
\(316\) −3.71611 1.53926i −0.209048 0.0865903i
\(317\) 5.53505 13.3628i 0.310880 0.750530i −0.688793 0.724958i \(-0.741859\pi\)
0.999673 0.0255720i \(-0.00814071\pi\)
\(318\) 15.9612 6.61136i 0.895061 0.370747i
\(319\) 2.08378i 0.116669i
\(320\) −8.34015 20.1349i −0.466228 1.12557i
\(321\) 5.10813 + 5.10813i 0.285108 + 0.285108i
\(322\) 1.49794 0.0834770
\(323\) 0 0
\(324\) −1.40373 −0.0779852
\(325\) 17.3958 + 17.3958i 0.964943 + 0.964943i
\(326\) −5.67546 13.7018i −0.314335 0.758871i
\(327\) 20.9067i 1.15614i
\(328\) −11.5126 + 4.76866i −0.635675 + 0.263305i
\(329\) 0.680553 1.64300i 0.0375201 0.0905815i
\(330\) −11.8469 4.90713i −0.652148 0.270129i
\(331\) −6.38877 + 6.38877i −0.351158 + 0.351158i −0.860540 0.509382i \(-0.829874\pi\)
0.509382 + 0.860540i \(0.329874\pi\)
\(332\) 0.527486 0.527486i 0.0289495 0.0289495i
\(333\) −4.29225 1.77791i −0.235214 0.0974287i
\(334\) −1.07733 + 2.60091i −0.0589491 + 0.142316i
\(335\) −26.3405 + 10.9106i −1.43913 + 0.596109i
\(336\) 2.14022i 0.116758i
\(337\) 6.87523 + 16.5983i 0.374518 + 0.904166i 0.992972 + 0.118346i \(0.0377591\pi\)
−0.618455 + 0.785821i \(0.712241\pi\)
\(338\) −2.35114 2.35114i −0.127885 0.127885i
\(339\) 9.46791 0.514226
\(340\) 0 0
\(341\) −12.4979 −0.676801
\(342\) 1.96651 + 1.96651i 0.106336 + 0.106336i
\(343\) 1.84463 + 4.45334i 0.0996009 + 0.240458i
\(344\) 27.8161i 1.49975i
\(345\) 12.3771 5.12678i 0.666363 0.276017i
\(346\) 13.3441 32.2156i 0.717385 1.73192i
\(347\) −7.19125 2.97871i −0.386046 0.159906i 0.181215 0.983444i \(-0.441997\pi\)
−0.567261 + 0.823538i \(0.691997\pi\)
\(348\) −0.392004 + 0.392004i −0.0210136 + 0.0210136i
\(349\) 4.70227 4.70227i 0.251707 0.251707i −0.569963 0.821670i \(-0.693043\pi\)
0.821670 + 0.569963i \(0.193043\pi\)
\(350\) 3.67493 + 1.52220i 0.196433 + 0.0813652i
\(351\) −7.10045 + 17.1420i −0.378994 + 0.914973i
\(352\) −3.15808 + 1.30812i −0.168326 + 0.0697230i
\(353\) 4.14559i 0.220648i −0.993896 0.110324i \(-0.964811\pi\)
0.993896 0.110324i \(-0.0351888\pi\)
\(354\) 8.58242 + 20.7198i 0.456151 + 1.10125i
\(355\) 28.0950 + 28.0950i 1.49113 + 1.49113i
\(356\) −2.22937 −0.118156
\(357\) 0 0
\(358\) −26.8503 −1.41908
\(359\) 12.0752 + 12.0752i 0.637307 + 0.637307i 0.949890 0.312583i \(-0.101194\pi\)
−0.312583 + 0.949890i \(0.601194\pi\)
\(360\) 4.05502 + 9.78967i 0.213718 + 0.515961i
\(361\) 16.6527i 0.876458i
\(362\) −6.45752 + 2.67479i −0.339400 + 0.140584i
\(363\) −4.07661 + 9.84181i −0.213967 + 0.516561i
\(364\) 0.366712 + 0.151897i 0.0192209 + 0.00796157i
\(365\) 4.25169 4.25169i 0.222543 0.222543i
\(366\) 6.43896 6.43896i 0.336570 0.336570i
\(367\) −17.3973 7.20619i −0.908131 0.376160i −0.120790 0.992678i \(-0.538543\pi\)
−0.787341 + 0.616518i \(0.788543\pi\)
\(368\) 4.92770 11.8965i 0.256874 0.620149i
\(369\) 5.38685 2.23131i 0.280428 0.116157i
\(370\) 21.2199i 1.10317i
\(371\) −1.11236 2.68547i −0.0577506 0.139422i
\(372\) 2.35114 + 2.35114i 0.121901 + 0.121901i
\(373\) 11.7314 0.607430 0.303715 0.952763i \(-0.401773\pi\)
0.303715 + 0.952763i \(0.401773\pi\)
\(374\) 0 0
\(375\) 11.7811 0.608371
\(376\) −9.16824 9.16824i −0.472816 0.472816i
\(377\) 1.49208 + 3.60219i 0.0768459 + 0.185522i
\(378\) 3.00000i 0.154303i
\(379\) 7.54365 3.12468i 0.387491 0.160504i −0.180428 0.983588i \(-0.557748\pi\)
0.567920 + 0.823084i \(0.307748\pi\)
\(380\) 0.719210 1.73633i 0.0368947 0.0890716i
\(381\) 9.63954 + 3.99283i 0.493849 + 0.204559i
\(382\) −10.5352 + 10.5352i −0.539026 + 0.539026i
\(383\) −11.4933 + 11.4933i −0.587282 + 0.587282i −0.936894 0.349613i \(-0.886313\pi\)
0.349613 + 0.936894i \(0.386313\pi\)
\(384\) −16.6054 6.87820i −0.847393 0.351001i
\(385\) −0.825621 + 1.99323i −0.0420775 + 0.101584i
\(386\) 1.19508 0.495019i 0.0608281 0.0251958i
\(387\) 13.0155i 0.661614i
\(388\) −0.542753 1.31032i −0.0275541 0.0665215i
\(389\) −4.10650 4.10650i −0.208208 0.208208i 0.595298 0.803505i \(-0.297034\pi\)
−0.803505 + 0.595298i \(0.797034\pi\)
\(390\) 23.9932 1.21494
\(391\) 0 0
\(392\) 17.4192 0.879803
\(393\) −17.7376 17.7376i −0.894742 0.894742i
\(394\) 9.96773 + 24.0642i 0.502167 + 1.21234i
\(395\) 40.9077i 2.05829i
\(396\) 0.668601 0.276944i 0.0335985 0.0139169i
\(397\) 3.92314 9.47130i 0.196897 0.475351i −0.794336 0.607479i \(-0.792181\pi\)
0.991233 + 0.132128i \(0.0421810\pi\)
\(398\) −17.9701 7.44345i −0.900759 0.373106i
\(399\) −0.506912 + 0.506912i −0.0253773 + 0.0253773i
\(400\) 24.1784 24.1784i 1.20892 1.20892i
\(401\) −28.2357 11.6956i −1.41002 0.584051i −0.457691 0.889111i \(-0.651323\pi\)
−0.952333 + 0.305060i \(0.901323\pi\)
\(402\) −6.37622 + 15.3936i −0.318017 + 0.767761i
\(403\) 21.6050 8.94908i 1.07622 0.445785i
\(404\) 1.82976i 0.0910337i
\(405\) 5.46331 + 13.1896i 0.271474 + 0.655396i
\(406\) 0.445771 + 0.445771i 0.0221232 + 0.0221232i
\(407\) −6.89662 −0.341853
\(408\) 0 0
\(409\) 19.9736 0.987631 0.493815 0.869567i \(-0.335602\pi\)
0.493815 + 0.869567i \(0.335602\pi\)
\(410\) −18.8312 18.8312i −0.930007 0.930007i
\(411\) 5.19296 + 12.5369i 0.256150 + 0.618400i
\(412\) 6.40373i 0.315489i
\(413\) 3.48609 1.44399i 0.171539 0.0710539i
\(414\) −1.95558 + 4.72120i −0.0961117 + 0.232034i
\(415\) −7.00926 2.90333i −0.344071 0.142519i
\(416\) 4.52265 4.52265i 0.221741 0.221741i
\(417\) 8.14960 8.14960i 0.399088 0.399088i
\(418\) 3.81410 + 1.57985i 0.186554 + 0.0772731i
\(419\) 6.47845 15.6404i 0.316493 0.764082i −0.682942 0.730473i \(-0.739300\pi\)
0.999435 0.0336094i \(-0.0107002\pi\)
\(420\) 0.530286 0.219652i 0.0258753 0.0107179i
\(421\) 23.7297i 1.15651i 0.815855 + 0.578257i \(0.196267\pi\)
−0.815855 + 0.578257i \(0.803733\pi\)
\(422\) −13.7960 33.3064i −0.671577 1.62133i
\(423\) 4.28992 + 4.28992i 0.208583 + 0.208583i
\(424\) −21.1925 −1.02920
\(425\) 0 0
\(426\) 23.2199 1.12501
\(427\) −1.08335 1.08335i −0.0524270 0.0524270i
\(428\) 0.712614 + 1.72040i 0.0344455 + 0.0831587i
\(429\) 7.79797i 0.376490i
\(430\) 54.9223 22.7496i 2.64859 1.09708i
\(431\) 9.02832 21.7963i 0.434879 1.04989i −0.542814 0.839853i \(-0.682641\pi\)
0.977693 0.210038i \(-0.0673588\pi\)
\(432\) 23.8257 + 9.86895i 1.14632 + 0.474820i
\(433\) −8.97643 + 8.97643i −0.431380 + 0.431380i −0.889098 0.457718i \(-0.848667\pi\)
0.457718 + 0.889098i \(0.348667\pi\)
\(434\) 2.67361 2.67361i 0.128338 0.128338i
\(435\) 5.20898 + 2.15763i 0.249751 + 0.103450i
\(436\) 2.06235 4.97896i 0.0987687 0.238449i
\(437\) −3.98483 + 1.65057i −0.190620 + 0.0789575i
\(438\) 3.51392i 0.167902i
\(439\) −8.98181 21.6840i −0.428678 1.03492i −0.979707 0.200435i \(-0.935765\pi\)
0.551029 0.834486i \(-0.314235\pi\)
\(440\) 11.1226 + 11.1226i 0.530247 + 0.530247i
\(441\) −8.15064 −0.388126
\(442\) 0 0
\(443\) −19.4124 −0.922311 −0.461156 0.887319i \(-0.652565\pi\)
−0.461156 + 0.887319i \(0.652565\pi\)
\(444\) 1.29741 + 1.29741i 0.0615721 + 0.0615721i
\(445\) 8.67667 + 20.9473i 0.411314 + 0.992999i
\(446\) 7.61587i 0.360622i
\(447\) 14.7867 6.12487i 0.699389 0.289696i
\(448\) −0.820054 + 1.97978i −0.0387439 + 0.0935360i
\(449\) 16.2846 + 6.74529i 0.768517 + 0.318330i 0.732271 0.681013i \(-0.238460\pi\)
0.0362452 + 0.999343i \(0.488460\pi\)
\(450\) −9.59534 + 9.59534i −0.452329 + 0.452329i
\(451\) 6.12029 6.12029i 0.288193 0.288193i
\(452\) 2.25479 + 0.933966i 0.106057 + 0.0439301i
\(453\) −3.38196 + 8.16478i −0.158899 + 0.383615i
\(454\) 7.44069 3.08204i 0.349209 0.144647i
\(455\) 4.03684i 0.189250i
\(456\) 2.00016 + 4.82882i 0.0936663 + 0.226130i
\(457\) −26.2489 26.2489i −1.22787 1.22787i −0.964767 0.263104i \(-0.915254\pi\)
−0.263104 0.964767i \(-0.584746\pi\)
\(458\) 37.0847 1.73285
\(459\) 0 0
\(460\) 3.45336 0.161014
\(461\) −20.7941 20.7941i −0.968480 0.968480i 0.0310385 0.999518i \(-0.490119\pi\)
−0.999518 + 0.0310385i \(0.990119\pi\)
\(462\) 0.482499 + 1.16485i 0.0224479 + 0.0541940i
\(463\) 9.72462i 0.451942i −0.974134 0.225971i \(-0.927445\pi\)
0.974134 0.225971i \(-0.0725554\pi\)
\(464\) 5.00670 2.07384i 0.232430 0.0962758i
\(465\) 12.9409 31.2420i 0.600119 1.44881i
\(466\) −40.6549 16.8398i −1.88330 0.780089i
\(467\) −3.26872 + 3.26872i −0.151259 + 0.151259i −0.778680 0.627421i \(-0.784110\pi\)
0.627421 + 0.778680i \(0.284110\pi\)
\(468\) −0.957496 + 0.957496i −0.0442603 + 0.0442603i
\(469\) 2.58996 + 1.07279i 0.119593 + 0.0495371i
\(470\) 10.6042 25.6008i 0.489135 1.18088i
\(471\) −11.0588 + 4.58071i −0.509563 + 0.211068i
\(472\) 27.5107i 1.26628i
\(473\) 7.39378 + 17.8502i 0.339967 + 0.820752i
\(474\) 16.9046 + 16.9046i 0.776454 + 0.776454i
\(475\) −11.4534 −0.525516
\(476\) 0 0
\(477\) 9.91622 0.454033
\(478\) 2.85257 + 2.85257i 0.130474 + 0.130474i
\(479\) 2.61624 + 6.31616i 0.119539 + 0.288593i 0.972311 0.233691i \(-0.0750803\pi\)
−0.852772 + 0.522283i \(0.825080\pi\)
\(480\) 9.24897i 0.422156i
\(481\) 11.9221 4.93829i 0.543600 0.225166i
\(482\) −14.8533 + 35.8590i −0.676548 + 1.63333i
\(483\) −1.21700 0.504096i −0.0553752 0.0229372i
\(484\) −1.94170 + 1.94170i −0.0882591 + 0.0882591i
\(485\) −10.1995 + 10.1995i −0.463135 + 0.463135i
\(486\) −16.2338 6.72424i −0.736378 0.305018i
\(487\) 2.93243 7.07951i 0.132881 0.320803i −0.843408 0.537273i \(-0.819454\pi\)
0.976289 + 0.216470i \(0.0694544\pi\)
\(488\) −10.3200 + 4.27467i −0.467163 + 0.193505i
\(489\) 13.0419i 0.589775i
\(490\) 14.2464 + 34.3938i 0.643586 + 1.55375i
\(491\) 6.38139 + 6.38139i 0.287988 + 0.287988i 0.836284 0.548296i \(-0.184723\pi\)
−0.548296 + 0.836284i \(0.684723\pi\)
\(492\) −2.30272 −0.103815
\(493\) 0 0
\(494\) −7.72462 −0.347547
\(495\) −5.20437 5.20437i −0.233919 0.233919i
\(496\) −12.4384 30.0289i −0.558499 1.34834i
\(497\) 3.90673i 0.175241i
\(498\) −4.09626 + 1.69673i −0.183558 + 0.0760322i
\(499\) 10.2149 24.6610i 0.457282 1.10398i −0.512211 0.858859i \(-0.671174\pi\)
0.969493 0.245117i \(-0.0788264\pi\)
\(500\) 2.80567 + 1.16215i 0.125473 + 0.0519728i
\(501\) 1.75055 1.75055i 0.0782088 0.0782088i
\(502\) −11.5757 + 11.5757i −0.516649 + 0.516649i
\(503\) −11.9427 4.94682i −0.532497 0.220568i 0.100199 0.994967i \(-0.468052\pi\)
−0.632697 + 0.774400i \(0.718052\pi\)
\(504\) 0.398714 0.962580i 0.0177601 0.0428767i
\(505\) −17.1925 + 7.12138i −0.765058 + 0.316897i
\(506\) 7.58584i 0.337232i
\(507\) 1.11895 + 2.70139i 0.0496944 + 0.119973i
\(508\) 1.90179 + 1.90179i 0.0843784 + 0.0843784i
\(509\) 27.8753 1.23555 0.617775 0.786355i \(-0.288034\pi\)
0.617775 + 0.786355i \(0.288034\pi\)
\(510\) 0 0
\(511\) −0.591214 −0.0261538
\(512\) 10.0930 + 10.0930i 0.446051 + 0.446051i
\(513\) −3.30568 7.98062i −0.145949 0.352353i
\(514\) 5.72462i 0.252502i
\(515\) −60.1700 + 24.9232i −2.65141 + 1.09825i
\(516\) 1.96708 4.74894i 0.0865957 0.209060i
\(517\) 8.32045 + 3.44644i 0.365933 + 0.151574i
\(518\) 1.47535 1.47535i 0.0648234 0.0648234i
\(519\) −21.6828 + 21.6828i −0.951768 + 0.951768i
\(520\) −27.1916 11.2631i −1.19243 0.493921i
\(521\) −1.95890 + 4.72921i −0.0858211 + 0.207190i −0.960964 0.276675i \(-0.910768\pi\)
0.875143 + 0.483865i \(0.160768\pi\)
\(522\) −1.98694 + 0.823016i −0.0869658 + 0.0360224i
\(523\) 15.3182i 0.669818i −0.942250 0.334909i \(-0.891294\pi\)
0.942250 0.334909i \(-0.108706\pi\)
\(524\) −2.47449 5.97395i −0.108099 0.260973i
\(525\) −2.47342 2.47342i −0.107949 0.107949i
\(526\) −15.6418 −0.682014
\(527\) 0 0
\(528\) 10.8384 0.471682
\(529\) 10.6594 + 10.6594i 0.463450 + 0.463450i
\(530\) −17.3324 41.8442i −0.752872 1.81759i
\(531\) 12.8726i 0.558622i
\(532\) −0.170726 + 0.0707170i −0.00740191 + 0.00306597i
\(533\) −6.19764 + 14.9624i −0.268450 + 0.648095i
\(534\) 12.2418 + 5.07071i 0.529753 + 0.219431i
\(535\) 13.3915 13.3915i 0.578967 0.578967i
\(536\) 14.4524 14.4524i 0.624250 0.624250i
\(537\) 21.8144 + 9.03582i 0.941361 + 0.389925i
\(538\) −6.88273 + 16.6164i −0.296736 + 0.716383i
\(539\) −11.1783 + 4.63019i −0.481482 + 0.199436i
\(540\) 6.91622i 0.297627i
\(541\) −14.3302 34.5961i −0.616102 1.48740i −0.856195 0.516653i \(-0.827178\pi\)
0.240093 0.970750i \(-0.422822\pi\)
\(542\) 18.4170 + 18.4170i 0.791076 + 0.791076i
\(543\) 6.14653 0.263773
\(544\) 0 0
\(545\) −54.8093 −2.34777
\(546\) −1.66818 1.66818i −0.0713913 0.0713913i
\(547\) 10.4828 + 25.3077i 0.448211 + 1.08208i 0.972992 + 0.230840i \(0.0741473\pi\)
−0.524781 + 0.851237i \(0.675853\pi\)
\(548\) 3.49794i 0.149425i
\(549\) 4.82882 2.00016i 0.206089 0.0853649i
\(550\) −7.70871 + 18.6105i −0.328701 + 0.793553i
\(551\) −1.67703 0.694650i −0.0714440 0.0295931i
\(552\) −6.79106 + 6.79106i −0.289047 + 0.289047i
\(553\) 2.84419 2.84419i 0.120947 0.120947i
\(554\) 34.4569 + 14.2725i 1.46393 + 0.606382i
\(555\) 7.14104 17.2400i 0.303120 0.731797i
\(556\) 2.74476 1.13692i 0.116404 0.0482160i
\(557\) 9.07604i 0.384564i −0.981340 0.192282i \(-0.938411\pi\)
0.981340 0.192282i \(-0.0615888\pi\)
\(558\) 4.93623 + 11.9171i 0.208967 + 0.504491i
\(559\) −25.5630 25.5630i −1.08120 1.08120i
\(560\) −5.61081 −0.237100
\(561\) 0 0
\(562\) −8.87670 −0.374441
\(563\) 27.2161 + 27.2161i 1.14702 + 1.14702i 0.987135 + 0.159886i \(0.0511128\pi\)
0.159886 + 0.987135i \(0.448887\pi\)
\(564\) −0.916907 2.21361i −0.0386087 0.0932097i
\(565\) 24.8212i 1.04424i
\(566\) −21.6849 + 8.98217i −0.911483 + 0.377549i
\(567\) 0.537185 1.29688i 0.0225597 0.0544639i
\(568\) −26.3152 10.9001i −1.10416 0.457359i
\(569\) 31.9492 31.9492i 1.33938 1.33938i 0.442723 0.896658i \(-0.354012\pi\)
0.896658 0.442723i \(-0.145988\pi\)
\(570\) −7.89856 + 7.89856i −0.330834 + 0.330834i
\(571\) 28.1386 + 11.6554i 1.17756 + 0.487763i 0.883686 0.468081i \(-0.155054\pi\)
0.293877 + 0.955843i \(0.405054\pi\)
\(572\) −0.769234 + 1.85709i −0.0321633 + 0.0776490i
\(573\) 12.1046 5.01390i 0.505678 0.209459i
\(574\) 2.61856i 0.109296i
\(575\) −8.05377 19.4435i −0.335865 0.810851i
\(576\) −5.16928 5.16928i −0.215386 0.215386i
\(577\) 9.90167 0.412212 0.206106 0.978530i \(-0.433921\pi\)
0.206106 + 0.978530i \(0.433921\pi\)
\(578\) 0 0
\(579\) −1.13753 −0.0472740
\(580\) 1.02768 + 1.02768i 0.0426722 + 0.0426722i
\(581\) 0.285473 + 0.689193i 0.0118434 + 0.0285925i
\(582\) 8.42964i 0.349420i
\(583\) 13.5997 5.63317i 0.563241 0.233302i
\(584\) −1.64954 + 3.98235i −0.0682585 + 0.164791i
\(585\) 12.7233 + 5.27015i 0.526042 + 0.217894i
\(586\) 3.22882 3.22882i 0.133381 0.133381i
\(587\) 25.5508 25.5508i 1.05460 1.05460i 0.0561750 0.998421i \(-0.482110\pi\)
0.998421 0.0561750i \(-0.0178905\pi\)
\(588\) 2.97391 + 1.23184i 0.122642 + 0.0508000i
\(589\) −4.16632 + 10.0584i −0.171670 + 0.414449i
\(590\) 54.3193 22.4998i 2.23629 0.926302i
\(591\) 22.9053i 0.942198i
\(592\) −6.86374 16.5705i −0.282098 0.681045i
\(593\) −5.24428 5.24428i −0.215357 0.215357i 0.591182 0.806538i \(-0.298662\pi\)
−0.806538 + 0.591182i \(0.798662\pi\)
\(594\) −15.1925 −0.623357
\(595\) 0 0
\(596\) 4.12567 0.168994
\(597\) 12.0948 + 12.0948i 0.495007 + 0.495007i
\(598\) −5.43179 13.1135i −0.222123 0.536251i
\(599\) 7.61350i 0.311079i 0.987830 + 0.155540i \(0.0497116\pi\)
−0.987830 + 0.155540i \(0.950288\pi\)
\(600\) −23.5617 + 9.75957i −0.961902 + 0.398433i
\(601\) −12.4652 + 30.0937i −0.508466 + 1.22755i 0.436300 + 0.899801i \(0.356289\pi\)
−0.944766 + 0.327745i \(0.893711\pi\)
\(602\) −5.40029 2.23688i −0.220100 0.0911682i
\(603\) −6.76245 + 6.76245i −0.275388 + 0.275388i
\(604\) −1.61084 + 1.61084i −0.0655440 + 0.0655440i
\(605\) 25.8014 + 10.6873i 1.04898 + 0.434501i
\(606\) −4.16178 + 10.0474i −0.169061 + 0.408149i
\(607\) 2.78508 1.15362i 0.113043 0.0468239i −0.325445 0.945561i \(-0.605514\pi\)
0.438488 + 0.898737i \(0.355514\pi\)
\(608\) 2.97771i 0.120762i
\(609\) −0.212151 0.512178i −0.00859680 0.0207545i
\(610\) −16.8805 16.8805i −0.683470 0.683470i
\(611\) −16.8512 −0.681728
\(612\) 0 0
\(613\) 7.26857 0.293575 0.146787 0.989168i \(-0.453107\pi\)
0.146787 + 0.989168i \(0.453107\pi\)
\(614\) 3.54101 + 3.54101i 0.142903 + 0.142903i
\(615\) 8.96215 + 21.6365i 0.361389 + 0.872469i
\(616\) 1.54664i 0.0623158i
\(617\) −31.6381 + 13.1049i −1.27370 + 0.527585i −0.914088 0.405516i \(-0.867092\pi\)
−0.359615 + 0.933101i \(0.617092\pi\)
\(618\) −14.5653 + 35.1638i −0.585903 + 1.41449i
\(619\) 18.8745 + 7.81809i 0.758631 + 0.314235i 0.728258 0.685303i \(-0.240330\pi\)
0.0303735 + 0.999539i \(0.490330\pi\)
\(620\) 6.16377 6.16377i 0.247543 0.247543i
\(621\) 11.2236 11.2236i 0.450388 0.450388i
\(622\) −4.99955 2.07088i −0.200464 0.0830348i
\(623\) 0.853143 2.05967i 0.0341805 0.0825189i
\(624\) −18.7362 + 7.76079i −0.750049 + 0.310680i
\(625\) 6.49289i 0.259716i
\(626\) −0.869173 2.09837i −0.0347391 0.0838677i
\(627\) −2.56709 2.56709i −0.102520 0.102520i
\(628\) −3.08553 −0.123126
\(629\) 0 0
\(630\) 2.22668 0.0887131
\(631\) −10.9658 10.9658i −0.436543 0.436543i 0.454304 0.890847i \(-0.349888\pi\)
−0.890847 + 0.454304i \(0.849888\pi\)
\(632\) −11.2226 27.0936i −0.446409 1.07773i
\(633\) 31.7023i 1.26005i
\(634\) −20.4730 + 8.48019i −0.813087 + 0.336792i
\(635\) 10.4676 25.2711i 0.415396 1.00285i
\(636\) −3.61812 1.49867i −0.143468 0.0594263i
\(637\) 16.0083 16.0083i 0.634270 0.634270i
\(638\) −2.25746 + 2.25746i −0.0893738 + 0.0893738i
\(639\) 12.3132 + 5.10029i 0.487102 + 0.201764i
\(640\) −18.0320 + 43.5330i −0.712776 + 1.72079i
\(641\) −30.1134 + 12.4734i −1.18941 + 0.492669i −0.887562 0.460688i \(-0.847603\pi\)
−0.301846 + 0.953357i \(0.597603\pi\)
\(642\) 11.0678i 0.436811i
\(643\) 15.7696 + 38.0712i 0.621893 + 1.50138i 0.849478 + 0.527625i \(0.176917\pi\)
−0.227584 + 0.973758i \(0.573083\pi\)
\(644\) −0.240102 0.240102i −0.00946135 0.00946135i
\(645\) −52.2772 −2.05841
\(646\) 0 0
\(647\) 26.5131 1.04234 0.521169 0.853454i \(-0.325496\pi\)
0.521169 + 0.853454i \(0.325496\pi\)
\(648\) −7.23683 7.23683i −0.284290 0.284290i
\(649\) 7.31260 + 17.6542i 0.287045 + 0.692987i
\(650\) 37.6914i 1.47838i
\(651\) −3.07191 + 1.27243i −0.120398 + 0.0498703i
\(652\) −1.28652 + 3.10594i −0.0503841 + 0.121638i
\(653\) 13.1075 + 5.42931i 0.512937 + 0.212465i 0.624111 0.781335i \(-0.285461\pi\)
−0.111174 + 0.993801i \(0.535461\pi\)
\(654\) −22.6493 + 22.6493i −0.885658 + 0.885658i
\(655\) −46.5010 + 46.5010i −1.81695 + 1.81695i
\(656\) 20.7963 + 8.61413i 0.811961 + 0.336325i
\(657\) 0.771839 1.86338i 0.0301123 0.0726975i
\(658\) −2.51722 + 1.04267i −0.0981316 + 0.0406474i
\(659\) 28.3628i 1.10486i 0.833560 + 0.552428i \(0.186299\pi\)
−0.833560 + 0.552428i \(0.813701\pi\)
\(660\) 1.11236 + 2.68547i 0.0432984 + 0.104532i
\(661\) 20.6236 + 20.6236i 0.802164 + 0.802164i 0.983433 0.181270i \(-0.0580207\pi\)
−0.181270 + 0.983433i \(0.558021\pi\)
\(662\) 13.8425 0.538006
\(663\) 0 0
\(664\) 5.43882 0.211067
\(665\) 1.32893 + 1.32893i 0.0515335 + 0.0515335i
\(666\) 2.72391 + 6.57611i 0.105549 + 0.254819i
\(667\) 3.33544i 0.129149i
\(668\) 0.589579 0.244212i 0.0228115 0.00944883i
\(669\) 2.56294 6.18748i 0.0990889 0.239222i
\(670\) 40.3560 + 16.7160i 1.55909 + 0.645795i
\(671\) 5.48628 5.48628i 0.211795 0.211795i
\(672\) −0.643053 + 0.643053i −0.0248063 + 0.0248063i
\(673\) −27.1323 11.2386i −1.04587 0.433216i −0.207457 0.978244i \(-0.566519\pi\)
−0.838417 + 0.545029i \(0.816519\pi\)
\(674\) 10.5335 25.4300i 0.405734 0.979529i
\(675\) 38.9405 16.1297i 1.49882 0.620832i
\(676\) 0.753718i 0.0289892i
\(677\) 15.0694 + 36.3808i 0.579164 + 1.39823i 0.893564 + 0.448936i \(0.148197\pi\)
−0.314400 + 0.949291i \(0.601803\pi\)
\(678\) −10.2571 10.2571i −0.393920 0.393920i
\(679\) 1.41828 0.0544286
\(680\) 0 0
\(681\) −7.08235 −0.271396
\(682\) 13.5396 + 13.5396i 0.518460 + 0.518460i
\(683\) −10.3950 25.0957i −0.397754 0.960262i −0.988198 0.153184i \(-0.951047\pi\)
0.590444 0.807078i \(-0.298953\pi\)
\(684\) 0.630415i 0.0241045i
\(685\) 32.8669 13.6139i 1.25578 0.520161i
\(686\) 2.82614 6.82291i 0.107903 0.260500i
\(687\) −30.1293 12.4800i −1.14951 0.476141i
\(688\) −35.5301 + 35.5301i −1.35457 + 1.35457i
\(689\) −19.4759 + 19.4759i −0.741974 + 0.741974i
\(690\) −18.9629 7.85469i −0.721905 0.299023i
\(691\) −12.9539 + 31.2736i −0.492791 + 1.18970i 0.460502 + 0.887658i \(0.347669\pi\)
−0.953294 + 0.302045i \(0.902331\pi\)
\(692\) −7.30268 + 3.02487i −0.277606 + 0.114988i
\(693\) 0.723689i 0.0274907i
\(694\) 4.56365 + 11.0176i 0.173234 + 0.418223i
\(695\) −21.3651 21.3651i −0.810425 0.810425i
\(696\) −4.04189 −0.153207
\(697\) 0 0
\(698\) −10.1884 −0.385637
\(699\) 27.3629 + 27.3629i 1.03496 + 1.03496i
\(700\) −0.345056 0.833038i −0.0130419 0.0314859i
\(701\) 20.9540i 0.791421i 0.918375 + 0.395711i \(0.129502\pi\)
−0.918375 + 0.395711i \(0.870498\pi\)
\(702\) 26.2631 10.8785i 0.991236 0.410583i
\(703\) −2.29906 + 5.55043i −0.0867108 + 0.209338i
\(704\) −10.0260 4.15290i −0.377868 0.156518i
\(705\) −17.2307 + 17.2307i −0.648944 + 0.648944i
\(706\) −4.49113 + 4.49113i −0.169026 + 0.169026i
\(707\) 1.69047 + 0.700217i 0.0635768 + 0.0263344i
\(708\) 1.94548 4.69680i 0.0731155 0.176516i
\(709\) −28.9392 + 11.9870i −1.08683 + 0.450182i −0.852902 0.522071i \(-0.825160\pi\)
−0.233933 + 0.972253i \(0.575160\pi\)
\(710\) 60.8735i 2.28454i
\(711\) 5.25116 + 12.6774i 0.196934 + 0.475440i
\(712\) −11.4933 11.4933i −0.430731 0.430731i
\(713\) −20.0051 −0.749195
\(714\) 0 0
\(715\) 20.4433 0.764535
\(716\) 4.30378 + 4.30378i 0.160840 + 0.160840i
\(717\) −1.35760 3.27753i −0.0507004 0.122402i
\(718\) 26.1634i 0.976411i
\(719\) 41.0292 16.9949i 1.53013 0.633801i 0.550542 0.834807i \(-0.314421\pi\)
0.979590 + 0.201006i \(0.0644211\pi\)
\(720\) 7.32500 17.6841i 0.272987 0.659048i
\(721\) 5.91628 + 2.45060i 0.220334 + 0.0912652i
\(722\) −18.0407 + 18.0407i −0.671406 + 0.671406i
\(723\) 24.1350 24.1350i 0.897589 0.897589i
\(724\) 1.46380 + 0.606326i 0.0544017 + 0.0225339i
\(725\) 3.38946 8.18289i 0.125882 0.303905i
\(726\) 15.0785 6.24573i 0.559617 0.231801i
\(727\) 39.5354i 1.46629i 0.680074 + 0.733143i \(0.261947\pi\)
−0.680074 + 0.733143i \(0.738053\pi\)
\(728\) 1.10746 + 2.67365i 0.0410452 + 0.0990919i
\(729\) 19.5003 + 19.5003i 0.722234 + 0.722234i
\(730\) −9.21213 −0.340956
\(731\) 0 0
\(732\) −2.06418 −0.0762942
\(733\) −9.82807 9.82807i −0.363008 0.363008i 0.501911 0.864919i \(-0.332630\pi\)
−0.864919 + 0.501911i \(0.832630\pi\)
\(734\) 11.0405 + 26.6542i 0.407513 + 0.983824i
\(735\) 32.7374i 1.20754i
\(736\) −5.05504 + 2.09387i −0.186331 + 0.0771809i
\(737\) −5.43282 + 13.1160i −0.200121 + 0.483134i
\(738\) −8.25314 3.41856i −0.303802 0.125839i
\(739\) 8.06366 8.06366i 0.296626 0.296626i −0.543065 0.839691i \(-0.682736\pi\)
0.839691 + 0.543065i \(0.182736\pi\)
\(740\) 3.40129 3.40129i 0.125034 0.125034i
\(741\) 6.27584 + 2.59954i 0.230549 + 0.0954964i
\(742\) −1.70423 + 4.11437i −0.0625642 + 0.151043i
\(743\) −13.5080 + 5.59518i −0.495559 + 0.205267i −0.616443 0.787399i \(-0.711427\pi\)
0.120884 + 0.992667i \(0.461427\pi\)
\(744\) 24.2422i 0.888761i
\(745\) −16.0570 38.7651i −0.588284 1.42024i
\(746\) −12.7092 12.7092i −0.465319 0.465319i
\(747\) −2.54488 −0.0931124
\(748\) 0 0
\(749\) −1.86215 −0.0680414
\(750\) −12.7630 12.7630i −0.466039 0.466039i
\(751\) −10.7226 25.8867i −0.391275 0.944620i −0.989663 0.143414i \(-0.954192\pi\)
0.598388 0.801206i \(-0.295808\pi\)
\(752\) 23.4216i 0.854097i
\(753\) 13.3002 5.50911i 0.484685 0.200763i
\(754\) 2.28599 5.51888i 0.0832510 0.200986i
\(755\) 21.4049 + 8.86620i 0.779004 + 0.322674i
\(756\) 0.480864 0.480864i 0.0174889 0.0174889i
\(757\) −11.0440 + 11.0440i −0.401401 + 0.401401i −0.878726 0.477326i \(-0.841606\pi\)
0.477326 + 0.878726i \(0.341606\pi\)
\(758\) −11.5575 4.78729i −0.419789 0.173882i
\(759\) 2.55283 6.16308i 0.0926620 0.223706i
\(760\) 12.6593 5.24366i 0.459201 0.190207i
\(761\) 20.5868i 0.746270i −0.927777 0.373135i \(-0.878283\pi\)
0.927777 0.373135i \(-0.121717\pi\)
\(762\) −6.11737 14.7686i −0.221609 0.535011i
\(763\) 3.81073 + 3.81073i 0.137958 + 0.137958i
\(764\) 3.37733 0.122187
\(765\) 0 0
\(766\) 24.9026 0.899768
\(767\) −25.2824 25.2824i −0.912893 0.912893i
\(768\) 4.17540 + 10.0803i 0.150667 + 0.363742i
\(769\) 22.2249i 0.801451i 0.916198 + 0.400726i \(0.131242\pi\)
−0.916198 + 0.400726i \(0.868758\pi\)
\(770\) 3.05380 1.26492i 0.110051 0.0455847i
\(771\) −1.92649 + 4.65095i −0.0693807 + 0.167500i
\(772\) −0.270903 0.112212i −0.00975002 0.00403859i
\(773\) −19.0980 + 19.0980i −0.686908 + 0.686908i −0.961547 0.274639i \(-0.911442\pi\)
0.274639 + 0.961547i \(0.411442\pi\)
\(774\) 14.1003 14.1003i 0.506826 0.506826i
\(775\) −49.0788 20.3291i −1.76296 0.730243i
\(776\) 3.95713 9.55337i 0.142053 0.342946i
\(777\) −1.69514 + 0.702151i −0.0608129 + 0.0251895i
\(778\) 8.89756i 0.318993i
\(779\) −2.88537 6.96589i −0.103379 0.249579i
\(780\) −3.84582 3.84582i −0.137703 0.137703i
\(781\) 19.7844 0.707940
\(782\) 0 0
\(783\) 6.68004 0.238725
\(784\) −22.2499 22.2499i −0.794640 0.794640i
\(785\) 12.0088 + 28.9919i 0.428614 + 1.03477i
\(786\) 38.4320i 1.37082i
\(787\) −19.3839 + 8.02908i −0.690962 + 0.286206i −0.700401 0.713749i \(-0.746996\pi\)
0.00943877 + 0.999955i \(0.496996\pi\)
\(788\) 2.25950 5.45492i 0.0804914 0.194323i
\(789\) 12.7081 + 5.26387i 0.452420 + 0.187399i
\(790\) 44.3173 44.3173i 1.57674 1.57674i
\(791\) −1.72574 + 1.72574i −0.0613604 + 0.0613604i
\(792\) 4.87468 + 2.01916i 0.173214 + 0.0717476i
\(793\) −5.55562 + 13.4125i −0.197286 + 0.476290i
\(794\) −14.5109 + 6.01060i −0.514971 + 0.213308i
\(795\) 39.8289i 1.41259i
\(796\) 1.68729 + 4.07349i 0.0598045 + 0.144381i
\(797\) 24.3490 + 24.3490i 0.862486 + 0.862486i 0.991626 0.129140i \(-0.0412217\pi\)
−0.129140 + 0.991626i \(0.541222\pi\)
\(798\) 1.09833 0.0388803
\(799\) 0 0
\(800\) −14.5294 −0.513692
\(801\) 5.37786 + 5.37786i 0.190017 + 0.190017i
\(802\) 17.9187 + 43.2596i 0.632732 + 1.52755i
\(803\) 2.99401i 0.105656i
\(804\) 3.48944 1.44537i 0.123063 0.0509744i
\(805\) −1.32154 + 3.19049i −0.0465783 + 0.112450i
\(806\) −33.1008 13.7108i −1.16592 0.482942i
\(807\) 11.1837 11.1837i 0.393685 0.393685i
\(808\) 9.43315 9.43315i 0.331857 0.331857i
\(809\) 26.7228 + 11.0690i 0.939524 + 0.389164i 0.799284 0.600954i \(-0.205212\pi\)
0.140241 + 0.990117i \(0.455212\pi\)
\(810\) 8.37027 20.2076i 0.294101 0.710024i
\(811\) 35.6836 14.7806i 1.25302 0.519018i 0.345259 0.938507i \(-0.387791\pi\)
0.907760 + 0.419490i \(0.137791\pi\)
\(812\) 0.142903i 0.00501493i
\(813\) −8.76500 21.1606i −0.307402 0.742134i
\(814\) 7.47146 + 7.47146i 0.261874 + 0.261874i
\(815\) 34.1908 1.19765
\(816\) 0 0
\(817\) 16.8307 0.588831
\(818\) −21.6384 21.6384i −0.756569 0.756569i
\(819\) −0.518193 1.25103i −0.0181071 0.0437145i
\(820\) 6.03684i 0.210815i
\(821\) −4.98525 + 2.06496i −0.173986 + 0.0720675i −0.467976 0.883741i \(-0.655017\pi\)
0.293990 + 0.955808i \(0.405017\pi\)
\(822\) 7.95608 19.2077i 0.277500 0.669944i
\(823\) −28.3518 11.7437i −0.988282 0.409360i −0.170795 0.985307i \(-0.554634\pi\)
−0.817487 + 0.575947i \(0.804634\pi\)
\(824\) 33.0139 33.0139i 1.15009 1.15009i
\(825\) 12.5258 12.5258i 0.436093 0.436093i
\(826\) −5.34100 2.21232i −0.185837 0.0769763i
\(827\) 13.5998 32.8329i 0.472913 1.14171i −0.489957 0.871746i \(-0.662988\pi\)
0.962870 0.269965i \(-0.0870123\pi\)
\(828\) 1.07021 0.443295i 0.0371923 0.0154056i
\(829\) 3.17200i 0.110168i −0.998482 0.0550840i \(-0.982457\pi\)
0.998482 0.0550840i \(-0.0175427\pi\)
\(830\) 4.44816 + 10.7388i 0.154398 + 0.372750i
\(831\) −23.1913 23.1913i −0.804498 0.804498i
\(832\) 20.3054 0.703963
\(833\) 0 0
\(834\) −17.6578 −0.611438
\(835\) −4.58926 4.58926i −0.158818 0.158818i
\(836\) −0.358124 0.864587i −0.0123860 0.0299024i
\(837\) 40.0651i 1.38485i
\(838\) −23.9624 + 9.92557i −0.827769 + 0.342873i
\(839\) 14.0886 34.0128i 0.486391 1.17425i −0.470132 0.882596i \(-0.655794\pi\)
0.956523 0.291657i \(-0.0942064\pi\)
\(840\) 3.86624 + 1.60145i 0.133398 + 0.0552553i
\(841\) −19.5135 + 19.5135i −0.672880 + 0.672880i
\(842\) 25.7076 25.7076i 0.885941 0.885941i
\(843\) 7.21184 + 2.98724i 0.248389 + 0.102886i
\(844\) −3.12729 + 7.54994i −0.107646 + 0.259880i
\(845\) 7.08200 2.93346i 0.243628 0.100914i
\(846\) 9.29498i 0.319568i
\(847\) −1.05084 2.53695i −0.0361073 0.0871707i
\(848\) 27.0697 + 27.0697i 0.929576 + 0.929576i
\(849\) 20.6405 0.708381
\(850\) 0 0
\(851\) −11.0392 −0.378419
\(852\) −3.72187 3.72187i −0.127509 0.127509i
\(853\) −7.67859 18.5377i −0.262910 0.634720i 0.736206 0.676757i \(-0.236615\pi\)
−0.999116 + 0.0420369i \(0.986615\pi\)
\(854\) 2.34730i 0.0803228i
\(855\) −5.92343 + 2.45356i −0.202577 + 0.0839101i
\(856\) −5.19557 + 12.5432i −0.177581 + 0.428718i
\(857\) −18.4129 7.62686i −0.628972 0.260529i 0.0453444 0.998971i \(-0.485561\pi\)
−0.674316 + 0.738443i \(0.735561\pi\)
\(858\) 8.44794 8.44794i 0.288408 0.288408i
\(859\) 16.5128 16.5128i 0.563411 0.563411i −0.366864 0.930275i \(-0.619569\pi\)
0.930275 + 0.366864i \(0.119569\pi\)
\(860\) −12.4499 5.15691i −0.424537 0.175849i
\(861\) 0.881212 2.12743i 0.0300316 0.0725028i
\(862\) −33.3939 + 13.8322i −1.13740 + 0.471126i
\(863\) 44.3878i 1.51098i −0.655162 0.755488i \(-0.727400\pi\)
0.655162 0.755488i \(-0.272600\pi\)
\(864\) −4.19349 10.1240i −0.142665 0.344425i
\(865\) 56.8438 + 56.8438i 1.93275 + 1.93275i
\(866\) 19.4492 0.660912
\(867\) 0 0
\(868\) −0.857097 −0.0290918
\(869\) 14.4035 + 14.4035i 0.488604 + 0.488604i
\(870\) −3.30568 7.98062i −0.112073 0.270568i
\(871\) 26.5635i 0.900072i
\(872\) 36.3009 15.0363i 1.22930 0.509194i
\(873\) −1.85159 + 4.47013i −0.0626667 + 0.151291i
\(874\) 6.10511 + 2.52882i 0.206509 + 0.0855386i
\(875\) −2.14737 + 2.14737i −0.0725943 + 0.0725943i
\(876\) −0.563239 + 0.563239i −0.0190301 + 0.0190301i
\(877\) −8.45323 3.50144i −0.285445 0.118235i 0.235367 0.971907i \(-0.424371\pi\)
−0.520812 + 0.853671i \(0.674371\pi\)
\(878\) −13.7609 + 33.2218i −0.464409 + 1.12118i
\(879\) −3.70982 + 1.53666i −0.125129 + 0.0518302i
\(880\) 28.4142i 0.957841i
\(881\) −2.58998 6.25276i −0.0872586 0.210661i 0.874226 0.485519i \(-0.161369\pi\)
−0.961485 + 0.274858i \(0.911369\pi\)
\(882\) 8.83000 + 8.83000i 0.297322 + 0.297322i
\(883\) 47.9760 1.61452 0.807260 0.590196i \(-0.200950\pi\)
0.807260 + 0.590196i \(0.200950\pi\)
\(884\) 0 0
\(885\) −51.7033 −1.73799
\(886\) 21.0304 + 21.0304i 0.706531 + 0.706531i
\(887\) −15.9572 38.5241i −0.535791 1.29351i −0.927637 0.373483i \(-0.878163\pi\)
0.391846 0.920031i \(-0.371837\pi\)
\(888\) 13.3773i 0.448914i
\(889\) −2.48481 + 1.02924i −0.0833379 + 0.0345197i
\(890\) 13.2934 32.0932i 0.445597 1.07577i
\(891\) 6.56763 + 2.72040i 0.220024 + 0.0911369i
\(892\) 1.22073 1.22073i 0.0408732 0.0408732i
\(893\) 5.54742 5.54742i 0.185637 0.185637i
\(894\) −22.6546 9.38384i −0.757683 0.313843i
\(895\) 23.6884 57.1889i 0.791817 1.91162i
\(896\) 4.28043 1.77301i 0.142999 0.0592322i
\(897\) 12.4820i 0.416761i
\(898\) −10.3344 24.9494i −0.344863 0.832573i
\(899\) −5.95328 5.95328i −0.198553 0.198553i
\(900\) 3.07604 0.102535
\(901\) 0 0
\(902\) −13.2608 −0.441537
\(903\) 3.63468 + 3.63468i 0.120955 + 0.120955i
\(904\) 6.80941 + 16.4394i 0.226478 + 0.546766i
\(905\) 16.1138i 0.535641i
\(906\) 12.5092 5.18147i 0.415589 0.172143i
\(907\) 12.6037 30.4280i 0.418498 1.01034i −0.564285 0.825580i \(-0.690848\pi\)
0.982783 0.184764i \(-0.0591521\pi\)
\(908\) −1.68667 0.698641i −0.0559741 0.0231852i
\(909\) −4.41388 + 4.41388i −0.146399 + 0.146399i
\(910\) −4.37331 + 4.37331i −0.144974 + 0.144974i
\(911\) −17.0849 7.07680i −0.566048 0.234465i 0.0812605 0.996693i \(-0.474105\pi\)
−0.647308 + 0.762228i \(0.724105\pi\)
\(912\) 3.61311 8.72281i 0.119642 0.288841i
\(913\) −3.49020 + 1.44569i −0.115509 + 0.0478452i
\(914\) 56.8735i 1.88121i
\(915\) 8.03375 + 19.3952i 0.265587 + 0.641185i
\(916\) −5.94424 5.94424i −0.196403 0.196403i
\(917\) 6.46616 0.213531
\(918\) 0 0
\(919\) −13.3909 −0.441726 −0.220863 0.975305i \(-0.570887\pi\)
−0.220863 + 0.975305i \(0.570887\pi\)
\(920\) 17.8035 + 17.8035i 0.586965 + 0.586965i
\(921\) −1.68524 4.06852i −0.0555304 0.134062i
\(922\) 45.0547i 1.48380i
\(923\) −34.2009 + 14.1665i −1.12574 + 0.466295i
\(924\) 0.109374 0.264051i 0.00359813 0.00868665i
\(925\) −27.0827 11.2180i −0.890473 0.368846i
\(926\) −10.5352 + 10.5352i −0.346207 + 0.346207i
\(927\) −15.4476 + 15.4476i −0.507365 + 0.507365i
\(928\) −2.12743 0.881212i −0.0698365 0.0289272i
\(929\) −2.04336 + 4.93311i −0.0670404 + 0.161850i −0.953849 0.300288i \(-0.902917\pi\)
0.886808 + 0.462138i \(0.152917\pi\)
\(930\) −47.8656 + 19.8266i −1.56957 + 0.650139i
\(931\) 10.5398i 0.345429i
\(932\) 3.81728 + 9.21572i 0.125039 + 0.301871i
\(933\) 3.36496 + 3.36496i 0.110164 + 0.110164i
\(934\) 7.08235 0.231741
\(935\) 0 0
\(936\) −9.87258 −0.322695
\(937\) −29.2998 29.2998i −0.957182 0.957182i 0.0419385 0.999120i \(-0.486647\pi\)
−0.999120 + 0.0419385i \(0.986647\pi\)
\(938\) −1.64362 3.96804i −0.0536660 0.129561i
\(939\) 1.99731i 0.0651798i
\(940\) −5.80322 + 2.40377i −0.189280 + 0.0784025i
\(941\) −16.0957 + 38.8584i −0.524704 + 1.26675i 0.410248 + 0.911974i \(0.365442\pi\)
−0.934952 + 0.354774i \(0.884558\pi\)
\(942\) 16.9431 + 7.01805i 0.552035 + 0.228661i
\(943\) 9.79655 9.79655i 0.319019 0.319019i
\(944\) −35.1400 + 35.1400i −1.14371 + 1.14371i
\(945\) −6.38976 2.64672i −0.207859 0.0860979i
\(946\) 11.3279 27.3481i 0.368303 0.889162i
\(947\) 38.2735 15.8534i 1.24372 0.515167i 0.338846 0.940842i \(-0.389963\pi\)
0.904876 + 0.425675i \(0.139963\pi\)
\(948\) 5.41921i 0.176008i
\(949\) 2.14385 + 5.17570i 0.0695922 + 0.168010i
\(950\) 12.4080 + 12.4080i 0.402569 + 0.402569i
\(951\) 19.4870 0.631910
\(952\) 0 0
\(953\) 27.0719 0.876945 0.438473 0.898744i \(-0.355520\pi\)
0.438473 + 0.898744i \(0.355520\pi\)
\(954\) −10.7427 10.7427i −0.347809 0.347809i
\(955\) −13.1445 31.7336i −0.425346 1.02688i
\(956\) 0.914467i 0.0295760i
\(957\) 2.59376 1.07437i 0.0838444 0.0347295i
\(958\) 4.00831 9.67692i 0.129503 0.312647i
\(959\) −3.23168 1.33860i −0.104356 0.0432258i
\(960\) 20.7626 20.7626i 0.670111 0.670111i
\(961\) −13.7859 + 13.7859i −0.444706 + 0.444706i
\(962\) −18.2657 7.56589i −0.588909 0.243934i
\(963\) 2.43106 5.86910i 0.0783399 0.189129i
\(964\) 8.12857 3.36696i 0.261803 0.108443i
\(965\) 2.98215i 0.0959989i
\(966\) 0.772320 + 1.86455i 0.0248490 + 0.0599908i
\(967\) −30.6628 30.6628i −0.986048 0.986048i 0.0138557 0.999904i \(-0.495589\pi\)
−0.999904 + 0.0138557i \(0.995589\pi\)
\(968\) −20.0205 −0.643484
\(969\) 0 0
\(970\) 22.0993 0.709564
\(971\) 0.898916 + 0.898916i 0.0288476 + 0.0288476i 0.721383 0.692536i \(-0.243507\pi\)
−0.692536 + 0.721383i \(0.743507\pi\)
\(972\) 1.52426 + 3.67989i 0.0488907 + 0.118033i
\(973\) 2.97090i 0.0952428i
\(974\) −10.8464 + 4.49274i −0.347542 + 0.143957i
\(975\) −12.6841 + 30.6222i −0.406218 + 0.980696i
\(976\) 18.6420 + 7.72178i 0.596717 + 0.247168i
\(977\) −17.5109 + 17.5109i −0.560223 + 0.560223i −0.929371 0.369148i \(-0.879650\pi\)
0.369148 + 0.929371i \(0.379650\pi\)
\(978\) 14.1289 14.1289i 0.451794 0.451794i
\(979\) 10.4305 + 4.32047i 0.333361 + 0.138083i
\(980\) 3.22939 7.79645i 0.103159 0.249048i
\(981\) −16.9856 + 7.03566i −0.542308 + 0.224631i
\(982\) 13.8266i 0.441224i
\(983\) −15.1598 36.5990i −0.483522 1.16733i −0.957925 0.287018i \(-0.907336\pi\)
0.474403 0.880308i \(-0.342664\pi\)
\(984\) −11.8715 11.8715i −0.378449 0.378449i
\(985\) −60.0488 −1.91331
\(986\) 0 0
\(987\) 2.39599 0.0762653
\(988\) 1.23816 + 1.23816i 0.0393913 + 0.0393913i
\(989\) 11.8350 + 28.5722i 0.376331 + 0.908543i
\(990\) 11.2763i 0.358385i
\(991\) 30.7779 12.7486i 0.977692 0.404973i 0.164122 0.986440i \(-0.447521\pi\)
0.813570 + 0.581467i \(0.197521\pi\)
\(992\) −5.28527 + 12.7598i −0.167808 + 0.405123i
\(993\) −11.2463 4.65838i −0.356891 0.147829i
\(994\) −4.23235 + 4.23235i −0.134242 + 0.134242i
\(995\) 31.7079 31.7079i 1.00521 1.00521i
\(996\) 0.928547 + 0.384617i 0.0294221 + 0.0121871i
\(997\) −9.90989 + 23.9246i −0.313849 + 0.757700i 0.685706 + 0.727879i \(0.259494\pi\)
−0.999555 + 0.0298209i \(0.990506\pi\)
\(998\) −37.7828 + 15.6501i −1.19599 + 0.495397i
\(999\) 22.1088i 0.699490i
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 289.2.d.f.134.2 24
17.2 even 8 inner 289.2.d.f.179.6 24
17.3 odd 16 289.2.b.d.288.2 6
17.4 even 4 inner 289.2.d.f.155.6 24
17.5 odd 16 289.2.a.d.1.3 3
17.6 odd 16 289.2.c.d.251.2 12
17.7 odd 16 289.2.c.d.38.6 12
17.8 even 8 inner 289.2.d.f.110.2 24
17.9 even 8 inner 289.2.d.f.110.1 24
17.10 odd 16 289.2.c.d.38.5 12
17.11 odd 16 289.2.c.d.251.1 12
17.12 odd 16 289.2.a.e.1.3 yes 3
17.13 even 4 inner 289.2.d.f.155.5 24
17.14 odd 16 289.2.b.d.288.1 6
17.15 even 8 inner 289.2.d.f.179.5 24
17.16 even 2 inner 289.2.d.f.134.1 24
51.5 even 16 2601.2.a.x.1.1 3
51.29 even 16 2601.2.a.w.1.1 3
68.39 even 16 4624.2.a.bg.1.2 3
68.63 even 16 4624.2.a.bd.1.2 3
85.29 odd 16 7225.2.a.s.1.1 3
85.39 odd 16 7225.2.a.t.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.2.a.d.1.3 3 17.5 odd 16
289.2.a.e.1.3 yes 3 17.12 odd 16
289.2.b.d.288.1 6 17.14 odd 16
289.2.b.d.288.2 6 17.3 odd 16
289.2.c.d.38.5 12 17.10 odd 16
289.2.c.d.38.6 12 17.7 odd 16
289.2.c.d.251.1 12 17.11 odd 16
289.2.c.d.251.2 12 17.6 odd 16
289.2.d.f.110.1 24 17.9 even 8 inner
289.2.d.f.110.2 24 17.8 even 8 inner
289.2.d.f.134.1 24 17.16 even 2 inner
289.2.d.f.134.2 24 1.1 even 1 trivial
289.2.d.f.155.5 24 17.13 even 4 inner
289.2.d.f.155.6 24 17.4 even 4 inner
289.2.d.f.179.5 24 17.15 even 8 inner
289.2.d.f.179.6 24 17.2 even 8 inner
2601.2.a.w.1.1 3 51.29 even 16
2601.2.a.x.1.1 3 51.5 even 16
4624.2.a.bd.1.2 3 68.63 even 16
4624.2.a.bg.1.2 3 68.39 even 16
7225.2.a.s.1.1 3 85.29 odd 16
7225.2.a.t.1.1 3 85.39 odd 16