Properties

Label 126.3.r.a.11.3
Level $126$
Weight $3$
Character 126.11
Analytic conductor $3.433$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [126,3,Mod(11,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("126.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.r (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.43325133094\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.3
Character \(\chi\) \(=\) 126.11
Dual form 126.3.r.a.23.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.41421i q^{2} +(-0.991189 - 2.83153i) q^{3} -2.00000 q^{4} +(-6.36825 - 3.67671i) q^{5} +(-4.00438 + 1.40175i) q^{6} +(2.82364 + 6.40524i) q^{7} +2.82843i q^{8} +(-7.03509 + 5.61316i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(-0.991189 - 2.83153i) q^{3} -2.00000 q^{4} +(-6.36825 - 3.67671i) q^{5} +(-4.00438 + 1.40175i) q^{6} +(2.82364 + 6.40524i) q^{7} +2.82843i q^{8} +(-7.03509 + 5.61316i) q^{9} +(-5.19965 + 9.00606i) q^{10} +(3.62186 - 2.09108i) q^{11} +(1.98238 + 5.66305i) q^{12} +(-0.596138 - 1.03254i) q^{13} +(9.05837 - 3.99323i) q^{14} +(-4.09856 + 21.6762i) q^{15} +4.00000 q^{16} +(-17.8385 - 10.2991i) q^{17} +(7.93820 + 9.94912i) q^{18} +(-9.10890 - 15.7771i) q^{19} +(12.7365 + 7.35342i) q^{20} +(15.3378 - 14.3440i) q^{21} +(-2.95724 - 5.12208i) q^{22} +(-21.6941 - 12.5251i) q^{23} +(8.00877 - 2.80351i) q^{24} +(14.5364 + 25.1777i) q^{25} +(-1.46023 + 0.843066i) q^{26} +(22.8669 + 14.3563i) q^{27} +(-5.64728 - 12.8105i) q^{28} +(-2.85906 - 1.65068i) q^{29} +(30.6547 + 5.79624i) q^{30} -51.9558 q^{31} -5.65685i q^{32} +(-9.51090 - 8.18274i) q^{33} +(-14.5651 + 25.2275i) q^{34} +(5.56856 - 51.1718i) q^{35} +(14.0702 - 11.2263i) q^{36} +(9.43150 + 16.3358i) q^{37} +(-22.3122 + 12.8819i) q^{38} +(-2.33278 + 2.71142i) q^{39} +(10.3993 - 18.0121i) q^{40} +(66.2491 - 38.2490i) q^{41} +(-20.2855 - 21.6910i) q^{42} +(25.6345 - 44.4002i) q^{43} +(-7.24372 + 4.18216i) q^{44} +(65.4391 - 9.87999i) q^{45} +(-17.7131 + 30.6801i) q^{46} -59.3465i q^{47} +(-3.96476 - 11.3261i) q^{48} +(-33.0541 + 36.1722i) q^{49} +(35.6067 - 20.5575i) q^{50} +(-11.4808 + 60.7186i) q^{51} +(1.19228 + 2.06508i) q^{52} +(1.33008 + 0.767921i) q^{53} +(20.3029 - 32.3387i) q^{54} -30.7532 q^{55} +(-18.1167 + 7.98646i) q^{56} +(-35.6446 + 41.4302i) q^{57} +(-2.33441 + 4.04332i) q^{58} +32.0345i q^{59} +(8.19713 - 43.3523i) q^{60} +111.784 q^{61} +73.4766i q^{62} +(-55.8181 - 29.2119i) q^{63} -8.00000 q^{64} +8.76730i q^{65} +(-11.5721 + 13.4504i) q^{66} -28.1640 q^{67} +(35.6770 + 20.5982i) q^{68} +(-13.9622 + 73.8421i) q^{69} +(-72.3679 - 7.87514i) q^{70} +75.9807i q^{71} +(-15.8764 - 19.8982i) q^{72} +(31.0717 - 53.8177i) q^{73} +(23.1024 - 13.3382i) q^{74} +(56.8831 - 66.1160i) q^{75} +(18.2178 + 31.5542i) q^{76} +(23.6207 + 17.2944i) q^{77} +(3.83453 + 3.29905i) q^{78} -67.1229 q^{79} +(-25.4730 - 14.7068i) q^{80} +(17.9850 - 78.9781i) q^{81} +(-54.0922 - 93.6904i) q^{82} +(-64.7785 - 37.3999i) q^{83} +(-30.6757 + 28.6880i) q^{84} +(75.7334 + 131.174i) q^{85} +(-62.7914 - 36.2526i) q^{86} +(-1.84007 + 9.73165i) q^{87} +(5.91447 + 10.2442i) q^{88} +(-95.3059 + 55.0249i) q^{89} +(-13.9724 - 92.5449i) q^{90} +(4.93039 - 6.73393i) q^{91} +(43.3882 + 25.0502i) q^{92} +(51.4980 + 147.114i) q^{93} -83.9287 q^{94} +133.963i q^{95} +(-16.0175 + 5.60701i) q^{96} +(14.0865 - 24.3986i) q^{97} +(51.1552 + 46.7456i) q^{98} +(-13.7425 + 35.0410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27} - 4 q^{28} + 36 q^{29} + 76 q^{30} + 16 q^{31} - 40 q^{33} - 90 q^{35} + 40 q^{36} + 22 q^{37} + 46 q^{39} + 72 q^{41} + 120 q^{42} + 16 q^{43} + 72 q^{44} + 464 q^{45} - 12 q^{46} + 2 q^{49} - 288 q^{50} - 286 q^{51} - 20 q^{52} - 72 q^{53} - 160 q^{54} - 24 q^{55} - 72 q^{56} - 282 q^{57} - 24 q^{58} - 20 q^{60} + 124 q^{61} + 66 q^{63} - 256 q^{64} - 16 q^{66} - 140 q^{67} + 108 q^{68} + 218 q^{69} + 72 q^{70} + 196 q^{73} + 216 q^{74} + 658 q^{75} - 56 q^{76} + 486 q^{77} + 32 q^{78} + 76 q^{79} - 380 q^{81} - 56 q^{84} + 60 q^{85} - 144 q^{86} - 740 q^{87} - 486 q^{89} + 296 q^{90} - 122 q^{91} + 252 q^{92} + 238 q^{93} - 336 q^{94} + 32 q^{96} - 38 q^{97} + 288 q^{98} + 394 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) −0.991189 2.83153i −0.330396 0.943842i
\(4\) −2.00000 −0.500000
\(5\) −6.36825 3.67671i −1.27365 0.735342i −0.297976 0.954573i \(-0.596312\pi\)
−0.975673 + 0.219232i \(0.929645\pi\)
\(6\) −4.00438 + 1.40175i −0.667397 + 0.233625i
\(7\) 2.82364 + 6.40524i 0.403377 + 0.915034i
\(8\) 2.82843i 0.353553i
\(9\) −7.03509 + 5.61316i −0.781677 + 0.623684i
\(10\) −5.19965 + 9.00606i −0.519965 + 0.900606i
\(11\) 3.62186 2.09108i 0.329260 0.190098i −0.326253 0.945283i \(-0.605786\pi\)
0.655513 + 0.755184i \(0.272453\pi\)
\(12\) 1.98238 + 5.66305i 0.165198 + 0.471921i
\(13\) −0.596138 1.03254i −0.0458568 0.0794262i 0.842186 0.539187i \(-0.181268\pi\)
−0.888043 + 0.459761i \(0.847935\pi\)
\(14\) 9.05837 3.99323i 0.647027 0.285231i
\(15\) −4.09856 + 21.6762i −0.273238 + 1.44508i
\(16\) 4.00000 0.250000
\(17\) −17.8385 10.2991i −1.04932 0.605828i −0.126865 0.991920i \(-0.540491\pi\)
−0.922460 + 0.386092i \(0.873825\pi\)
\(18\) 7.93820 + 9.94912i 0.441011 + 0.552729i
\(19\) −9.10890 15.7771i −0.479416 0.830373i 0.520305 0.853980i \(-0.325818\pi\)
−0.999721 + 0.0236075i \(0.992485\pi\)
\(20\) 12.7365 + 7.35342i 0.636825 + 0.367671i
\(21\) 15.3378 14.3440i 0.730373 0.683048i
\(22\) −2.95724 5.12208i −0.134420 0.232822i
\(23\) −21.6941 12.5251i −0.943221 0.544569i −0.0522525 0.998634i \(-0.516640\pi\)
−0.890969 + 0.454065i \(0.849973\pi\)
\(24\) 8.00877 2.80351i 0.333699 0.116813i
\(25\) 14.5364 + 25.1777i 0.581455 + 1.00711i
\(26\) −1.46023 + 0.843066i −0.0561628 + 0.0324256i
\(27\) 22.8669 + 14.3563i 0.846922 + 0.531717i
\(28\) −5.64728 12.8105i −0.201689 0.457517i
\(29\) −2.85906 1.65068i −0.0985884 0.0569200i 0.449895 0.893081i \(-0.351461\pi\)
−0.548484 + 0.836161i \(0.684795\pi\)
\(30\) 30.6547 + 5.79624i 1.02182 + 0.193208i
\(31\) −51.9558 −1.67599 −0.837996 0.545676i \(-0.816273\pi\)
−0.837996 + 0.545676i \(0.816273\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −9.51090 8.18274i −0.288209 0.247962i
\(34\) −14.5651 + 25.2275i −0.428385 + 0.741985i
\(35\) 5.56856 51.1718i 0.159102 1.46205i
\(36\) 14.0702 11.2263i 0.390838 0.311842i
\(37\) 9.43150 + 16.3358i 0.254905 + 0.441509i 0.964870 0.262728i \(-0.0846223\pi\)
−0.709964 + 0.704238i \(0.751289\pi\)
\(38\) −22.3122 + 12.8819i −0.587162 + 0.338998i
\(39\) −2.33278 + 2.71142i −0.0598149 + 0.0695237i
\(40\) 10.3993 18.0121i 0.259983 0.450303i
\(41\) 66.2491 38.2490i 1.61583 0.932901i 0.627850 0.778334i \(-0.283935\pi\)
0.987982 0.154567i \(-0.0493984\pi\)
\(42\) −20.2855 21.6910i −0.482988 0.516452i
\(43\) 25.6345 44.4002i 0.596151 1.03256i −0.397233 0.917718i \(-0.630029\pi\)
0.993383 0.114845i \(-0.0366372\pi\)
\(44\) −7.24372 + 4.18216i −0.164630 + 0.0950492i
\(45\) 65.4391 9.87999i 1.45420 0.219555i
\(46\) −17.7131 + 30.6801i −0.385068 + 0.666958i
\(47\) 59.3465i 1.26269i −0.775501 0.631346i \(-0.782503\pi\)
0.775501 0.631346i \(-0.217497\pi\)
\(48\) −3.96476 11.3261i −0.0825991 0.235961i
\(49\) −33.0541 + 36.1722i −0.674574 + 0.738207i
\(50\) 35.6067 20.5575i 0.712134 0.411151i
\(51\) −11.4808 + 60.7186i −0.225113 + 1.19056i
\(52\) 1.19228 + 2.06508i 0.0229284 + 0.0397131i
\(53\) 1.33008 + 0.767921i 0.0250958 + 0.0144891i 0.512495 0.858690i \(-0.328721\pi\)
−0.487400 + 0.873179i \(0.662054\pi\)
\(54\) 20.3029 32.3387i 0.375980 0.598865i
\(55\) −30.7532 −0.559149
\(56\) −18.1167 + 7.98646i −0.323513 + 0.142615i
\(57\) −35.6446 + 41.4302i −0.625344 + 0.726845i
\(58\) −2.33441 + 4.04332i −0.0402485 + 0.0697125i
\(59\) 32.0345i 0.542958i 0.962444 + 0.271479i \(0.0875128\pi\)
−0.962444 + 0.271479i \(0.912487\pi\)
\(60\) 8.19713 43.3523i 0.136619 0.722539i
\(61\) 111.784 1.83253 0.916265 0.400572i \(-0.131188\pi\)
0.916265 + 0.400572i \(0.131188\pi\)
\(62\) 73.4766i 1.18511i
\(63\) −55.8181 29.2119i −0.886002 0.463681i
\(64\) −8.00000 −0.125000
\(65\) 8.76730i 0.134882i
\(66\) −11.5721 + 13.4504i −0.175335 + 0.203795i
\(67\) −28.1640 −0.420358 −0.210179 0.977663i \(-0.567405\pi\)
−0.210179 + 0.977663i \(0.567405\pi\)
\(68\) 35.6770 + 20.5982i 0.524662 + 0.302914i
\(69\) −13.9622 + 73.8421i −0.202350 + 1.07018i
\(70\) −72.3679 7.87514i −1.03383 0.112502i
\(71\) 75.9807i 1.07015i 0.844804 + 0.535075i \(0.179717\pi\)
−0.844804 + 0.535075i \(0.820283\pi\)
\(72\) −15.8764 19.8982i −0.220506 0.276364i
\(73\) 31.0717 53.8177i 0.425639 0.737228i −0.570841 0.821061i \(-0.693383\pi\)
0.996480 + 0.0838323i \(0.0267160\pi\)
\(74\) 23.1024 13.3382i 0.312194 0.180245i
\(75\) 56.8831 66.1160i 0.758442 0.881547i
\(76\) 18.2178 + 31.5542i 0.239708 + 0.415186i
\(77\) 23.6207 + 17.2944i 0.306762 + 0.224603i
\(78\) 3.83453 + 3.29905i 0.0491607 + 0.0422955i
\(79\) −67.1229 −0.849656 −0.424828 0.905274i \(-0.639665\pi\)
−0.424828 + 0.905274i \(0.639665\pi\)
\(80\) −25.4730 14.7068i −0.318412 0.183835i
\(81\) 17.9850 78.9781i 0.222036 0.975038i
\(82\) −54.0922 93.6904i −0.659661 1.14257i
\(83\) −64.7785 37.3999i −0.780464 0.450601i 0.0561309 0.998423i \(-0.482124\pi\)
−0.836595 + 0.547822i \(0.815457\pi\)
\(84\) −30.6757 + 28.6880i −0.365187 + 0.341524i
\(85\) 75.7334 + 131.174i 0.890981 + 1.54322i
\(86\) −62.7914 36.2526i −0.730132 0.421542i
\(87\) −1.84007 + 9.73165i −0.0211503 + 0.111858i
\(88\) 5.91447 + 10.2442i 0.0672099 + 0.116411i
\(89\) −95.3059 + 55.0249i −1.07085 + 0.618257i −0.928414 0.371546i \(-0.878828\pi\)
−0.142439 + 0.989804i \(0.545494\pi\)
\(90\) −13.9724 92.5449i −0.155249 1.02828i
\(91\) 4.93039 6.73393i 0.0541801 0.0739992i
\(92\) 43.3882 + 25.0502i 0.471611 + 0.272284i
\(93\) 51.4980 + 147.114i 0.553742 + 1.58187i
\(94\) −83.9287 −0.892858
\(95\) 133.963i 1.41014i
\(96\) −16.0175 + 5.60701i −0.166849 + 0.0584064i
\(97\) 14.0865 24.3986i 0.145222 0.251531i −0.784234 0.620465i \(-0.786944\pi\)
0.929456 + 0.368934i \(0.120277\pi\)
\(98\) 51.1552 + 46.7456i 0.521991 + 0.476996i
\(99\) −13.7425 + 35.0410i −0.138814 + 0.353950i
\(100\) −29.0727 50.3555i −0.290727 0.503555i
\(101\) −106.654 + 61.5768i −1.05598 + 0.609672i −0.924318 0.381623i \(-0.875365\pi\)
−0.131664 + 0.991294i \(0.542032\pi\)
\(102\) 85.8690 + 16.2363i 0.841853 + 0.159179i
\(103\) 42.3146 73.2910i 0.410821 0.711563i −0.584159 0.811639i \(-0.698575\pi\)
0.994980 + 0.100077i \(0.0319088\pi\)
\(104\) 2.92047 1.68613i 0.0280814 0.0162128i
\(105\) −150.414 + 34.9534i −1.43251 + 0.332890i
\(106\) 1.08600 1.88101i 0.0102453 0.0177454i
\(107\) 132.511 76.5054i 1.23842 0.715004i 0.269651 0.962958i \(-0.413092\pi\)
0.968772 + 0.247954i \(0.0797583\pi\)
\(108\) −45.7338 28.7127i −0.423461 0.265858i
\(109\) 54.8712 95.0398i 0.503406 0.871925i −0.496586 0.867987i \(-0.665413\pi\)
0.999992 0.00393721i \(-0.00125326\pi\)
\(110\) 43.4916i 0.395378i
\(111\) 36.9070 42.8975i 0.332495 0.386464i
\(112\) 11.2946 + 25.6209i 0.100844 + 0.228758i
\(113\) −111.093 + 64.1393i −0.983120 + 0.567604i −0.903211 0.429198i \(-0.858796\pi\)
−0.0799092 + 0.996802i \(0.525463\pi\)
\(114\) 58.5911 + 50.4091i 0.513957 + 0.442185i
\(115\) 92.1022 + 159.526i 0.800888 + 1.38718i
\(116\) 5.71812 + 3.30136i 0.0492942 + 0.0284600i
\(117\) 9.98970 + 3.91780i 0.0853820 + 0.0334855i
\(118\) 45.3037 0.383930
\(119\) 15.5985 143.341i 0.131080 1.20454i
\(120\) −61.3095 11.5925i −0.510912 0.0966041i
\(121\) −51.7548 + 89.6419i −0.427725 + 0.740842i
\(122\) 158.087i 1.29580i
\(123\) −173.968 149.674i −1.41438 1.21686i
\(124\) 103.912 0.837996
\(125\) 29.9486i 0.239588i
\(126\) −41.3118 + 78.9388i −0.327872 + 0.626498i
\(127\) 184.511 1.45284 0.726422 0.687249i \(-0.241182\pi\)
0.726422 + 0.687249i \(0.241182\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −151.129 28.5757i −1.17154 0.221517i
\(130\) 12.3988 0.0953757
\(131\) −22.0979 12.7582i −0.168686 0.0973908i 0.413280 0.910604i \(-0.364383\pi\)
−0.581966 + 0.813213i \(0.697716\pi\)
\(132\) 19.0218 + 16.3655i 0.144105 + 0.123981i
\(133\) 75.3357 102.893i 0.566434 0.773635i
\(134\) 39.8299i 0.297238i
\(135\) −92.8380 175.500i −0.687689 1.30000i
\(136\) 29.1302 50.4550i 0.214193 0.370992i
\(137\) 155.974 90.0518i 1.13850 0.657313i 0.192440 0.981309i \(-0.438360\pi\)
0.946058 + 0.323996i \(0.105026\pi\)
\(138\) 104.429 + 19.7455i 0.756728 + 0.143083i
\(139\) −90.7540 157.191i −0.652906 1.13087i −0.982414 0.186714i \(-0.940216\pi\)
0.329508 0.944153i \(-0.393117\pi\)
\(140\) −11.1371 + 102.344i −0.0795509 + 0.731026i
\(141\) −168.041 + 58.8236i −1.19178 + 0.417189i
\(142\) 107.453 0.756711
\(143\) −4.31826 2.49315i −0.0301976 0.0174346i
\(144\) −28.1404 + 22.4526i −0.195419 + 0.155921i
\(145\) 12.1381 + 21.0239i 0.0837113 + 0.144992i
\(146\) −76.1097 43.9419i −0.521299 0.300972i
\(147\) 135.185 + 57.7402i 0.919628 + 0.392790i
\(148\) −18.8630 32.6717i −0.127453 0.220755i
\(149\) −8.10894 4.68170i −0.0544224 0.0314208i 0.472542 0.881308i \(-0.343337\pi\)
−0.526964 + 0.849887i \(0.676670\pi\)
\(150\) −93.5022 80.4449i −0.623348 0.536299i
\(151\) −4.14530 7.17987i −0.0274523 0.0475488i 0.851973 0.523586i \(-0.175406\pi\)
−0.879425 + 0.476037i \(0.842073\pi\)
\(152\) 44.6243 25.7639i 0.293581 0.169499i
\(153\) 183.306 27.6755i 1.19808 0.180886i
\(154\) 24.4580 33.4047i 0.158818 0.216914i
\(155\) 330.867 + 191.026i 2.13463 + 1.23243i
\(156\) 4.66556 5.42285i 0.0299075 0.0347618i
\(157\) 256.152 1.63154 0.815771 0.578375i \(-0.196313\pi\)
0.815771 + 0.578375i \(0.196313\pi\)
\(158\) 94.9260i 0.600798i
\(159\) 0.856030 4.52731i 0.00538384 0.0284736i
\(160\) −20.7986 + 36.0242i −0.129991 + 0.225151i
\(161\) 18.9699 174.322i 0.117825 1.08275i
\(162\) −111.692 25.4346i −0.689456 0.157004i
\(163\) −100.951 174.853i −0.619334 1.07272i −0.989607 0.143795i \(-0.954069\pi\)
0.370273 0.928923i \(-0.379264\pi\)
\(164\) −132.498 + 76.4979i −0.807916 + 0.466451i
\(165\) 30.4822 + 87.0785i 0.184741 + 0.527749i
\(166\) −52.8914 + 91.6106i −0.318623 + 0.551871i
\(167\) −240.071 + 138.605i −1.43755 + 0.829970i −0.997679 0.0680908i \(-0.978309\pi\)
−0.439871 + 0.898061i \(0.644976\pi\)
\(168\) 40.5710 + 43.3820i 0.241494 + 0.258226i
\(169\) 83.7892 145.127i 0.495794 0.858741i
\(170\) 185.508 107.103i 1.09122 0.630019i
\(171\) 152.641 + 59.8635i 0.892639 + 0.350079i
\(172\) −51.2689 + 88.8004i −0.298075 + 0.516282i
\(173\) 61.0699i 0.353005i 0.984300 + 0.176503i \(0.0564784\pi\)
−0.984300 + 0.176503i \(0.943522\pi\)
\(174\) 13.7626 + 2.60226i 0.0790956 + 0.0149555i
\(175\) −120.224 + 164.202i −0.686994 + 0.938296i
\(176\) 14.4874 8.36433i 0.0823150 0.0475246i
\(177\) 90.7067 31.7523i 0.512467 0.179391i
\(178\) 77.8169 + 134.783i 0.437174 + 0.757207i
\(179\) −27.5108 15.8834i −0.153692 0.0887338i 0.421182 0.906976i \(-0.361615\pi\)
−0.574873 + 0.818242i \(0.694949\pi\)
\(180\) −130.878 + 19.7600i −0.727101 + 0.109778i
\(181\) −72.7677 −0.402031 −0.201016 0.979588i \(-0.564424\pi\)
−0.201016 + 0.979588i \(0.564424\pi\)
\(182\) −9.52321 6.97263i −0.0523253 0.0383111i
\(183\) −110.799 316.521i −0.605461 1.72962i
\(184\) 35.4263 61.3601i 0.192534 0.333479i
\(185\) 138.708i 0.749770i
\(186\) 208.051 72.8292i 1.11855 0.391555i
\(187\) −86.1448 −0.460668
\(188\) 118.693i 0.631346i
\(189\) −27.3879 + 187.005i −0.144910 + 0.989445i
\(190\) 189.452 0.997118
\(191\) 308.310i 1.61419i 0.590422 + 0.807095i \(0.298961\pi\)
−0.590422 + 0.807095i \(0.701039\pi\)
\(192\) 7.92951 + 22.6522i 0.0412995 + 0.117980i
\(193\) −35.4668 −0.183766 −0.0918830 0.995770i \(-0.529289\pi\)
−0.0918830 + 0.995770i \(0.529289\pi\)
\(194\) −34.5048 19.9213i −0.177860 0.102687i
\(195\) 24.8248 8.69005i 0.127307 0.0445644i
\(196\) 66.1082 72.3443i 0.337287 0.369104i
\(197\) 83.3940i 0.423320i −0.977343 0.211660i \(-0.932113\pi\)
0.977343 0.211660i \(-0.0678869\pi\)
\(198\) 49.5555 + 19.4349i 0.250280 + 0.0981560i
\(199\) −103.081 + 178.541i −0.517993 + 0.897190i 0.481789 + 0.876287i \(0.339987\pi\)
−0.999782 + 0.0209024i \(0.993346\pi\)
\(200\) −71.2134 + 41.1151i −0.356067 + 0.205575i
\(201\) 27.9159 + 79.7472i 0.138885 + 0.396752i
\(202\) 87.0828 + 150.832i 0.431103 + 0.746692i
\(203\) 2.50004 22.9739i 0.0123155 0.113172i
\(204\) 22.9615 121.437i 0.112557 0.595280i
\(205\) −562.521 −2.74401
\(206\) −103.649 59.8418i −0.503151 0.290494i
\(207\) 222.925 33.6572i 1.07693 0.162595i
\(208\) −2.38455 4.13016i −0.0114642 0.0198566i
\(209\) −65.9824 38.0949i −0.315705 0.182272i
\(210\) 49.4316 + 212.717i 0.235389 + 1.01294i
\(211\) −130.471 225.982i −0.618345 1.07100i −0.989788 0.142549i \(-0.954470\pi\)
0.371443 0.928456i \(-0.378863\pi\)
\(212\) −2.66016 1.53584i −0.0125479 0.00724454i
\(213\) 215.141 75.3112i 1.01005 0.353574i
\(214\) −108.195 187.399i −0.505584 0.875697i
\(215\) −326.493 + 188.501i −1.51857 + 0.876749i
\(216\) −40.6059 + 64.6774i −0.187990 + 0.299432i
\(217\) −146.704 332.789i −0.676057 1.53359i
\(218\) −134.407 77.5996i −0.616544 0.355962i
\(219\) −183.184 34.6367i −0.836457 0.158159i
\(220\) 61.5064 0.279575
\(221\) 24.5587i 0.111125i
\(222\) −60.6662 52.1943i −0.273271 0.235110i
\(223\) −39.9500 + 69.1954i −0.179148 + 0.310293i −0.941589 0.336764i \(-0.890667\pi\)
0.762441 + 0.647058i \(0.224001\pi\)
\(224\) 36.2335 15.9729i 0.161757 0.0713077i
\(225\) −243.591 95.5327i −1.08263 0.424590i
\(226\) 90.7067 + 157.109i 0.401357 + 0.695171i
\(227\) 21.4405 12.3787i 0.0944515 0.0545316i −0.452030 0.892003i \(-0.649300\pi\)
0.546482 + 0.837471i \(0.315967\pi\)
\(228\) 71.2892 82.8604i 0.312672 0.363423i
\(229\) −34.1974 + 59.2317i −0.149334 + 0.258654i −0.930981 0.365067i \(-0.881046\pi\)
0.781648 + 0.623720i \(0.214380\pi\)
\(230\) 225.603 130.252i 0.980884 0.566314i
\(231\) 25.5570 84.0247i 0.110636 0.363743i
\(232\) 4.66883 8.08665i 0.0201243 0.0348562i
\(233\) 87.0618 50.2652i 0.373656 0.215730i −0.301399 0.953498i \(-0.597453\pi\)
0.675054 + 0.737768i \(0.264120\pi\)
\(234\) 5.54061 14.1276i 0.0236778 0.0603742i
\(235\) −218.200 + 377.933i −0.928510 + 1.60823i
\(236\) 64.0691i 0.271479i
\(237\) 66.5314 + 190.060i 0.280723 + 0.801942i
\(238\) −202.715 22.0596i −0.851742 0.0926873i
\(239\) 65.7064 37.9356i 0.274922 0.158726i −0.356200 0.934410i \(-0.615928\pi\)
0.631122 + 0.775683i \(0.282595\pi\)
\(240\) −16.3943 + 86.7047i −0.0683094 + 0.361270i
\(241\) 200.746 + 347.701i 0.832969 + 1.44274i 0.895673 + 0.444713i \(0.146694\pi\)
−0.0627043 + 0.998032i \(0.519973\pi\)
\(242\) 126.773 + 73.1923i 0.523854 + 0.302447i
\(243\) −241.455 + 27.3573i −0.993642 + 0.112582i
\(244\) −223.569 −0.916265
\(245\) 343.491 108.823i 1.40201 0.444175i
\(246\) −211.671 + 246.028i −0.860453 + 1.00012i
\(247\) −10.8603 + 18.8106i −0.0439689 + 0.0761564i
\(248\) 146.953i 0.592553i
\(249\) −41.6910 + 220.492i −0.167434 + 0.885512i
\(250\) −42.3536 −0.169415
\(251\) 230.144i 0.916910i −0.888718 0.458455i \(-0.848403\pi\)
0.888718 0.458455i \(-0.151597\pi\)
\(252\) 111.636 + 58.4238i 0.443001 + 0.231840i
\(253\) −104.764 −0.414087
\(254\) 260.938i 1.02732i
\(255\) 296.357 344.459i 1.16218 1.35082i
\(256\) 16.0000 0.0625000
\(257\) 216.346 + 124.907i 0.841813 + 0.486021i 0.857880 0.513850i \(-0.171781\pi\)
−0.0160667 + 0.999871i \(0.505114\pi\)
\(258\) −40.4122 + 213.729i −0.156636 + 0.828406i
\(259\) −78.0038 + 106.538i −0.301173 + 0.411342i
\(260\) 17.5346i 0.0674408i
\(261\) 29.3793 4.43568i 0.112564 0.0169949i
\(262\) −18.0428 + 31.2511i −0.0688657 + 0.119279i
\(263\) −39.4454 + 22.7738i −0.149982 + 0.0865924i −0.573113 0.819476i \(-0.694264\pi\)
0.423131 + 0.906069i \(0.360931\pi\)
\(264\) 23.1443 26.9009i 0.0876677 0.101897i
\(265\) −5.64684 9.78062i −0.0213088 0.0369080i
\(266\) −145.513 106.541i −0.547043 0.400529i
\(267\) 250.271 + 215.321i 0.937343 + 0.806446i
\(268\) 56.3280 0.210179
\(269\) −141.279 81.5677i −0.525202 0.303226i 0.213858 0.976865i \(-0.431397\pi\)
−0.739060 + 0.673639i \(0.764730\pi\)
\(270\) −248.194 + 131.293i −0.919237 + 0.486269i
\(271\) 124.879 + 216.297i 0.460808 + 0.798143i 0.999001 0.0446784i \(-0.0142263\pi\)
−0.538193 + 0.842821i \(0.680893\pi\)
\(272\) −71.3541 41.1963i −0.262331 0.151457i
\(273\) −23.9542 7.28594i −0.0877445 0.0266884i
\(274\) −127.353 220.581i −0.464790 0.805040i
\(275\) 105.297 + 60.7935i 0.382900 + 0.221067i
\(276\) 27.9244 147.684i 0.101175 0.535088i
\(277\) 110.900 + 192.085i 0.400363 + 0.693449i 0.993770 0.111454i \(-0.0355508\pi\)
−0.593407 + 0.804903i \(0.702217\pi\)
\(278\) −222.301 + 128.346i −0.799644 + 0.461675i
\(279\) 365.514 291.636i 1.31008 1.04529i
\(280\) 144.736 + 15.7503i 0.516913 + 0.0562510i
\(281\) −45.2239 26.1100i −0.160939 0.0929183i 0.417367 0.908738i \(-0.362953\pi\)
−0.578306 + 0.815820i \(0.696286\pi\)
\(282\) 83.1892 + 237.646i 0.294997 + 0.842717i
\(283\) −221.358 −0.782185 −0.391093 0.920351i \(-0.627903\pi\)
−0.391093 + 0.920351i \(0.627903\pi\)
\(284\) 151.961i 0.535075i
\(285\) 379.320 132.783i 1.33095 0.465904i
\(286\) −3.52584 + 6.10694i −0.0123281 + 0.0213529i
\(287\) 432.057 + 316.340i 1.50543 + 1.10223i
\(288\) 31.7528 + 39.7965i 0.110253 + 0.138182i
\(289\) 67.6419 + 117.159i 0.234055 + 0.405395i
\(290\) 29.7323 17.1659i 0.102525 0.0591928i
\(291\) −83.0476 15.7028i −0.285387 0.0539614i
\(292\) −62.1433 + 107.635i −0.212820 + 0.368614i
\(293\) 85.2950 49.2451i 0.291109 0.168072i −0.347333 0.937742i \(-0.612913\pi\)
0.638442 + 0.769670i \(0.279579\pi\)
\(294\) 81.6570 191.181i 0.277745 0.650275i
\(295\) 117.782 204.004i 0.399260 0.691538i
\(296\) −46.2047 + 26.6763i −0.156097 + 0.0901227i
\(297\) 112.841 + 4.18010i 0.379936 + 0.0140744i
\(298\) −6.62092 + 11.4678i −0.0222179 + 0.0384825i
\(299\) 29.8667i 0.0998887i
\(300\) −113.766 + 132.232i −0.379221 + 0.440773i
\(301\) 356.776 + 38.8247i 1.18530 + 0.128986i
\(302\) −10.1539 + 5.86234i −0.0336221 + 0.0194117i
\(303\) 280.071 + 240.960i 0.924326 + 0.795247i
\(304\) −36.4356 63.1083i −0.119854 0.207593i
\(305\) −711.870 410.999i −2.33400 1.34754i
\(306\) −39.1391 259.234i −0.127905 0.847169i
\(307\) 64.4159 0.209824 0.104912 0.994482i \(-0.466544\pi\)
0.104912 + 0.994482i \(0.466544\pi\)
\(308\) −47.2414 34.5888i −0.153381 0.112301i
\(309\) −249.467 47.1696i −0.807337 0.152652i
\(310\) 270.152 467.917i 0.871458 1.50941i
\(311\) 137.494i 0.442102i 0.975262 + 0.221051i \(0.0709488\pi\)
−0.975262 + 0.221051i \(0.929051\pi\)
\(312\) −7.66906 6.59811i −0.0245803 0.0211478i
\(313\) 58.0528 0.185472 0.0927360 0.995691i \(-0.470439\pi\)
0.0927360 + 0.995691i \(0.470439\pi\)
\(314\) 362.254i 1.15367i
\(315\) 248.060 + 391.256i 0.787492 + 1.24208i
\(316\) 134.246 0.424828
\(317\) 250.573i 0.790451i −0.918584 0.395226i \(-0.870666\pi\)
0.918584 0.395226i \(-0.129334\pi\)
\(318\) −6.40258 1.21061i −0.0201339 0.00380695i
\(319\) −13.8068 −0.0432816
\(320\) 50.9460 + 29.4137i 0.159206 + 0.0919177i
\(321\) −347.971 299.378i −1.08402 0.932641i
\(322\) −246.529 26.8275i −0.765617 0.0833151i
\(323\) 375.253i 1.16177i
\(324\) −35.9699 + 157.956i −0.111018 + 0.487519i
\(325\) 17.3314 30.0188i 0.0533273 0.0923655i
\(326\) −247.280 + 142.767i −0.758526 + 0.437935i
\(327\) −323.495 61.1670i −0.989283 0.187055i
\(328\) 108.184 + 187.381i 0.329830 + 0.571283i
\(329\) 380.129 167.573i 1.15541 0.509341i
\(330\) 123.148 43.1084i 0.373175 0.130631i
\(331\) 9.70718 0.0293268 0.0146634 0.999892i \(-0.495332\pi\)
0.0146634 + 0.999892i \(0.495332\pi\)
\(332\) 129.557 + 74.7998i 0.390232 + 0.225300i
\(333\) −158.047 61.9836i −0.474616 0.186137i
\(334\) 196.017 + 339.512i 0.586877 + 1.01650i
\(335\) 179.355 + 103.551i 0.535389 + 0.309107i
\(336\) 61.3514 57.3760i 0.182593 0.170762i
\(337\) −161.035 278.920i −0.477848 0.827656i 0.521830 0.853050i \(-0.325250\pi\)
−0.999678 + 0.0253933i \(0.991916\pi\)
\(338\) −205.241 118.496i −0.607222 0.350580i
\(339\) 291.726 + 250.987i 0.860548 + 0.740376i
\(340\) −151.467 262.348i −0.445491 0.771612i
\(341\) −188.177 + 108.644i −0.551837 + 0.318604i
\(342\) 84.6598 215.867i 0.247543 0.631191i
\(343\) −325.024 109.582i −0.947592 0.319482i
\(344\) 125.583 + 72.5052i 0.365066 + 0.210771i
\(345\) 360.410 418.910i 1.04467 1.21423i
\(346\) 86.3659 0.249612
\(347\) 540.407i 1.55737i −0.627415 0.778685i \(-0.715887\pi\)
0.627415 0.778685i \(-0.284113\pi\)
\(348\) 3.68015 19.4633i 0.0105751 0.0559290i
\(349\) 64.0391 110.919i 0.183493 0.317820i −0.759575 0.650420i \(-0.774593\pi\)
0.943068 + 0.332601i \(0.107926\pi\)
\(350\) 232.216 + 170.022i 0.663475 + 0.485778i
\(351\) 1.19169 32.1694i 0.00339512 0.0916506i
\(352\) −11.8289 20.4883i −0.0336050 0.0582055i
\(353\) −391.328 + 225.933i −1.10858 + 0.640038i −0.938461 0.345386i \(-0.887748\pi\)
−0.170118 + 0.985424i \(0.554415\pi\)
\(354\) −44.9045 128.279i −0.126849 0.362369i
\(355\) 279.359 483.864i 0.786926 1.36300i
\(356\) 190.612 110.050i 0.535426 0.309129i
\(357\) −421.334 + 97.9104i −1.18021 + 0.274259i
\(358\) −22.4625 + 38.9061i −0.0627443 + 0.108676i
\(359\) 328.357 189.577i 0.914643 0.528069i 0.0327206 0.999465i \(-0.489583\pi\)
0.881922 + 0.471395i \(0.156250\pi\)
\(360\) 27.9448 + 185.090i 0.0776245 + 0.514138i
\(361\) 14.5557 25.2113i 0.0403206 0.0698374i
\(362\) 102.909i 0.284279i
\(363\) 305.122 + 57.6930i 0.840557 + 0.158934i
\(364\) −9.86078 + 13.4679i −0.0270901 + 0.0369996i
\(365\) −395.744 + 228.483i −1.08423 + 0.625980i
\(366\) −447.628 + 156.694i −1.22303 + 0.428126i
\(367\) −239.155 414.229i −0.651650 1.12869i −0.982722 0.185085i \(-0.940744\pi\)
0.331073 0.943605i \(-0.392589\pi\)
\(368\) −86.7763 50.1003i −0.235805 0.136142i
\(369\) −251.371 + 640.952i −0.681223 + 1.73700i
\(370\) −196.162 −0.530168
\(371\) −1.16306 + 10.6878i −0.00313492 + 0.0288081i
\(372\) −102.996 294.228i −0.276871 0.790936i
\(373\) 112.582 194.997i 0.301828 0.522781i −0.674722 0.738072i \(-0.735737\pi\)
0.976550 + 0.215291i \(0.0690700\pi\)
\(374\) 121.827i 0.325741i
\(375\) −84.8001 + 29.6847i −0.226134 + 0.0791591i
\(376\) 167.857 0.446429
\(377\) 3.93613i 0.0104407i
\(378\) 264.465 + 38.7324i 0.699643 + 0.102467i
\(379\) −88.5871 −0.233739 −0.116869 0.993147i \(-0.537286\pi\)
−0.116869 + 0.993147i \(0.537286\pi\)
\(380\) 267.926i 0.705069i
\(381\) −182.885 522.448i −0.480014 1.37125i
\(382\) 436.016 1.14140
\(383\) 37.1766 + 21.4639i 0.0970669 + 0.0560416i 0.547748 0.836644i \(-0.315485\pi\)
−0.450681 + 0.892685i \(0.648819\pi\)
\(384\) 32.0351 11.2140i 0.0834247 0.0292032i
\(385\) −86.8359 196.982i −0.225548 0.511640i
\(386\) 50.1577i 0.129942i
\(387\) 68.8845 + 456.250i 0.177996 + 1.17894i
\(388\) −28.1730 + 48.7971i −0.0726109 + 0.125766i
\(389\) 120.250 69.4262i 0.309125 0.178473i −0.337410 0.941358i \(-0.609551\pi\)
0.646535 + 0.762884i \(0.276217\pi\)
\(390\) −12.2896 35.1076i −0.0315118 0.0900196i
\(391\) 257.994 + 446.858i 0.659830 + 1.14286i
\(392\) −102.310 93.4912i −0.260996 0.238498i
\(393\) −14.2220 + 75.2164i −0.0361884 + 0.191390i
\(394\) −117.937 −0.299332
\(395\) 427.455 + 246.791i 1.08216 + 0.624788i
\(396\) 27.4851 70.0820i 0.0694068 0.176975i
\(397\) 232.398 + 402.525i 0.585385 + 1.01392i 0.994827 + 0.101581i \(0.0323900\pi\)
−0.409442 + 0.912336i \(0.634277\pi\)
\(398\) 252.495 + 145.778i 0.634409 + 0.366276i
\(399\) −366.018 111.328i −0.917337 0.279018i
\(400\) 58.1455 + 100.711i 0.145364 + 0.251777i
\(401\) −42.7264 24.6681i −0.106550 0.0615165i 0.445778 0.895143i \(-0.352927\pi\)
−0.552328 + 0.833627i \(0.686260\pi\)
\(402\) 112.780 39.4790i 0.280546 0.0982064i
\(403\) 30.9728 + 53.6465i 0.0768556 + 0.133118i
\(404\) 213.308 123.154i 0.527991 0.304836i
\(405\) −404.912 + 436.827i −0.999783 + 1.07858i
\(406\) −32.4900 3.53559i −0.0800246 0.00870835i
\(407\) 68.3192 + 39.4441i 0.167860 + 0.0969142i
\(408\) −171.738 32.4725i −0.420927 0.0795895i
\(409\) −124.959 −0.305523 −0.152761 0.988263i \(-0.548817\pi\)
−0.152761 + 0.988263i \(0.548817\pi\)
\(410\) 795.525i 1.94030i
\(411\) −409.584 352.387i −0.996555 0.857390i
\(412\) −84.6291 + 146.582i −0.205410 + 0.355781i
\(413\) −205.189 + 90.4540i −0.496825 + 0.219017i
\(414\) −47.5985 315.264i −0.114972 0.761506i
\(415\) 275.017 + 476.343i 0.662691 + 1.14782i
\(416\) −5.84093 + 3.37226i −0.0140407 + 0.00810641i
\(417\) −355.135 + 412.778i −0.851642 + 0.989875i
\(418\) −53.8744 + 93.3131i −0.128886 + 0.223237i
\(419\) −584.499 + 337.461i −1.39499 + 0.805395i −0.993862 0.110628i \(-0.964714\pi\)
−0.401124 + 0.916024i \(0.631380\pi\)
\(420\) 300.828 69.9068i 0.716257 0.166445i
\(421\) 7.77481 13.4664i 0.0184675 0.0319866i −0.856644 0.515908i \(-0.827455\pi\)
0.875111 + 0.483921i \(0.160788\pi\)
\(422\) −319.587 + 184.513i −0.757314 + 0.437236i
\(423\) 333.121 + 417.508i 0.787521 + 0.987017i
\(424\) −2.17201 + 3.76203i −0.00512266 + 0.00887271i
\(425\) 598.845i 1.40905i
\(426\) −106.506 304.256i −0.250014 0.714216i
\(427\) 315.639 + 716.006i 0.739201 + 1.67683i
\(428\) −265.022 + 153.011i −0.619211 + 0.357502i
\(429\) −2.77920 + 14.6984i −0.00647833 + 0.0342621i
\(430\) 266.581 + 461.731i 0.619955 + 1.07379i
\(431\) 257.966 + 148.937i 0.598530 + 0.345561i 0.768463 0.639894i \(-0.221022\pi\)
−0.169933 + 0.985456i \(0.554355\pi\)
\(432\) 91.4676 + 57.4254i 0.211731 + 0.132929i
\(433\) 193.183 0.446151 0.223076 0.974801i \(-0.428390\pi\)
0.223076 + 0.974801i \(0.428390\pi\)
\(434\) −470.635 + 207.471i −1.08441 + 0.478044i
\(435\) 47.4985 55.2081i 0.109192 0.126915i
\(436\) −109.742 + 190.080i −0.251703 + 0.435962i
\(437\) 456.359i 1.04430i
\(438\) −48.9837 + 259.061i −0.111835 + 0.591464i
\(439\) −787.361 −1.79353 −0.896767 0.442503i \(-0.854090\pi\)
−0.896767 + 0.442503i \(0.854090\pi\)
\(440\) 86.9832i 0.197689i
\(441\) 29.4987 440.012i 0.0668906 0.997760i
\(442\) 34.7312 0.0785774
\(443\) 303.517i 0.685140i −0.939492 0.342570i \(-0.888703\pi\)
0.939492 0.342570i \(-0.111297\pi\)
\(444\) −73.8139 + 85.7949i −0.166248 + 0.193232i
\(445\) 809.242 1.81852
\(446\) 97.8571 + 56.4978i 0.219410 + 0.126677i
\(447\) −5.21887 + 27.6011i −0.0116753 + 0.0617475i
\(448\) −22.5891 51.2419i −0.0504221 0.114379i
\(449\) 195.191i 0.434723i 0.976091 + 0.217362i \(0.0697451\pi\)
−0.976091 + 0.217362i \(0.930255\pi\)
\(450\) −135.104 + 344.490i −0.300230 + 0.765533i
\(451\) 159.963 277.065i 0.354686 0.614334i
\(452\) 222.185 128.279i 0.491560 0.283802i
\(453\) −16.2212 + 18.8541i −0.0358085 + 0.0416206i
\(454\) −17.5061 30.3214i −0.0385597 0.0667873i
\(455\) −56.1566 + 24.7557i −0.123421 + 0.0544081i
\(456\) −117.182 100.818i −0.256979 0.221092i
\(457\) −808.848 −1.76991 −0.884954 0.465678i \(-0.845810\pi\)
−0.884954 + 0.465678i \(0.845810\pi\)
\(458\) 83.7662 + 48.3624i 0.182896 + 0.105595i
\(459\) −260.055 491.604i −0.566568 1.07103i
\(460\) −184.204 319.051i −0.400444 0.693590i
\(461\) −29.3032 16.9182i −0.0635643 0.0366989i 0.467881 0.883791i \(-0.345018\pi\)
−0.531445 + 0.847093i \(0.678351\pi\)
\(462\) −118.829 36.1431i −0.257205 0.0782318i
\(463\) −266.892 462.270i −0.576440 0.998424i −0.995884 0.0906421i \(-0.971108\pi\)
0.419443 0.907781i \(-0.362225\pi\)
\(464\) −11.4362 6.60272i −0.0246471 0.0142300i
\(465\) 212.944 1126.20i 0.457944 2.42194i
\(466\) −71.0857 123.124i −0.152544 0.264215i
\(467\) 311.027 179.571i 0.666010 0.384521i −0.128553 0.991703i \(-0.541033\pi\)
0.794563 + 0.607182i \(0.207700\pi\)
\(468\) −19.9794 7.83561i −0.0426910 0.0167427i
\(469\) −79.5250 180.397i −0.169563 0.384642i
\(470\) 534.478 + 308.581i 1.13719 + 0.656556i
\(471\) −253.895 725.301i −0.539055 1.53992i
\(472\) −90.6074 −0.191965
\(473\) 214.415i 0.453309i
\(474\) 268.786 94.0896i 0.567058 0.198501i
\(475\) 264.821 458.683i 0.557517 0.965649i
\(476\) −31.1969 + 286.682i −0.0655398 + 0.602272i
\(477\) −13.6677 + 2.06354i −0.0286534 + 0.00432609i
\(478\) −53.6490 92.9228i −0.112236 0.194399i
\(479\) −185.500 + 107.099i −0.387266 + 0.223588i −0.680975 0.732307i \(-0.738444\pi\)
0.293709 + 0.955895i \(0.405110\pi\)
\(480\) 122.619 + 23.1850i 0.255456 + 0.0483020i
\(481\) 11.2449 19.4768i 0.0233783 0.0404924i
\(482\) 491.724 283.897i 1.02017 0.588998i
\(483\) −512.400 + 119.072i −1.06087 + 0.246527i
\(484\) 103.510 179.284i 0.213863 0.370421i
\(485\) −179.413 + 103.584i −0.369923 + 0.213575i
\(486\) 38.6891 + 341.469i 0.0796072 + 0.702611i
\(487\) 368.143 637.643i 0.755941 1.30933i −0.188965 0.981984i \(-0.560513\pi\)
0.944905 0.327344i \(-0.106153\pi\)
\(488\) 316.174i 0.647898i
\(489\) −395.039 + 459.159i −0.807851 + 0.938976i
\(490\) −153.899 485.770i −0.314079 0.991367i
\(491\) −120.218 + 69.4081i −0.244844 + 0.141361i −0.617401 0.786649i \(-0.711814\pi\)
0.372557 + 0.928009i \(0.378481\pi\)
\(492\) 347.937 + 299.349i 0.707188 + 0.608432i
\(493\) 34.0010 + 58.8914i 0.0689675 + 0.119455i
\(494\) 26.6023 + 15.3588i 0.0538507 + 0.0310907i
\(495\) 216.351 172.622i 0.437074 0.348732i
\(496\) −207.823 −0.418998
\(497\) −486.674 + 214.542i −0.979224 + 0.431674i
\(498\) 311.823 + 58.9600i 0.626151 + 0.118394i
\(499\) −0.603448 + 1.04520i −0.00120931 + 0.00209459i −0.866629 0.498952i \(-0.833718\pi\)
0.865420 + 0.501047i \(0.167052\pi\)
\(500\) 59.8971i 0.119794i
\(501\) 630.419 + 542.383i 1.25832 + 1.08260i
\(502\) −325.473 −0.648353
\(503\) 35.0159i 0.0696142i −0.999394 0.0348071i \(-0.988918\pi\)
0.999394 0.0348071i \(-0.0110817\pi\)
\(504\) 82.6237 157.878i 0.163936 0.313249i
\(505\) 905.600 1.79327
\(506\) 148.159i 0.292803i
\(507\) −493.983 93.4030i −0.974325 0.184227i
\(508\) −369.022 −0.726422
\(509\) 458.447 + 264.684i 0.900681 + 0.520009i 0.877421 0.479721i \(-0.159262\pi\)
0.0232602 + 0.999729i \(0.492595\pi\)
\(510\) −487.139 419.112i −0.955175 0.821788i
\(511\) 432.450 + 47.0596i 0.846282 + 0.0920931i
\(512\) 22.6274i 0.0441942i
\(513\) 18.2088 491.544i 0.0354948 0.958175i
\(514\) 176.646 305.960i 0.343669 0.595252i
\(515\) −538.939 + 311.157i −1.04648 + 0.604187i
\(516\) 302.258 + 57.1514i 0.585771 + 0.110759i
\(517\) −124.098 214.945i −0.240036 0.415754i
\(518\) 150.667 + 110.314i 0.290863 + 0.212961i
\(519\) 172.921 60.5318i 0.333181 0.116632i
\(520\) −24.7977 −0.0476878
\(521\) −578.118 333.776i −1.10963 0.640646i −0.170897 0.985289i \(-0.554667\pi\)
−0.938734 + 0.344643i \(0.888000\pi\)
\(522\) −6.27300 41.5486i −0.0120172 0.0795950i
\(523\) −16.1523 27.9766i −0.0308839 0.0534925i 0.850170 0.526508i \(-0.176499\pi\)
−0.881054 + 0.473015i \(0.843166\pi\)
\(524\) 44.1957 + 25.5164i 0.0843429 + 0.0486954i
\(525\) 584.106 + 177.662i 1.11258 + 0.338404i
\(526\) 32.2070 + 55.7842i 0.0612301 + 0.106054i
\(527\) 926.814 + 535.096i 1.75866 + 1.01536i
\(528\) −38.0436 32.7310i −0.0720523 0.0619904i
\(529\) 49.2555 + 85.3131i 0.0931106 + 0.161272i
\(530\) −13.8319 + 7.98584i −0.0260979 + 0.0150676i
\(531\) −179.815 225.366i −0.338634 0.424418i
\(532\) −150.671 + 205.787i −0.283217 + 0.386818i
\(533\) −78.9872 45.6033i −0.148194 0.0855597i
\(534\) 304.510 353.936i 0.570244 0.662802i
\(535\) −1125.15 −2.10309
\(536\) 79.6599i 0.148619i
\(537\) −17.7058 + 93.6409i −0.0329716 + 0.174378i
\(538\) −115.354 + 199.799i −0.214413 + 0.371374i
\(539\) −44.0785 + 200.129i −0.0817783 + 0.371298i
\(540\) 185.676 + 350.999i 0.343844 + 0.649999i
\(541\) 227.423 + 393.908i 0.420375 + 0.728110i 0.995976 0.0896201i \(-0.0285653\pi\)
−0.575601 + 0.817730i \(0.695232\pi\)
\(542\) 305.890 176.606i 0.564372 0.325840i
\(543\) 72.1265 + 206.044i 0.132830 + 0.379454i
\(544\) −58.2604 + 100.910i −0.107096 + 0.185496i
\(545\) −698.867 + 403.491i −1.28232 + 0.740351i
\(546\) −10.3039 + 33.8764i −0.0188716 + 0.0620447i
\(547\) −42.6443 + 73.8621i −0.0779604 + 0.135031i −0.902370 0.430963i \(-0.858174\pi\)
0.824409 + 0.565994i \(0.191507\pi\)
\(548\) −311.949 + 180.104i −0.569249 + 0.328656i
\(549\) −786.413 + 627.463i −1.43245 + 1.14292i
\(550\) 85.9750 148.913i 0.156318 0.270751i
\(551\) 60.1436i 0.109153i
\(552\) −208.857 39.4910i −0.378364 0.0715417i
\(553\) −189.531 429.938i −0.342732 0.777464i
\(554\) 271.650 156.837i 0.490342 0.283099i
\(555\) −392.754 + 137.485i −0.707665 + 0.247721i
\(556\) 181.508 + 314.381i 0.326453 + 0.565434i
\(557\) 880.083 + 508.116i 1.58004 + 0.912237i 0.994852 + 0.101340i \(0.0323131\pi\)
0.585189 + 0.810897i \(0.301020\pi\)
\(558\) −412.435 516.914i −0.739132 0.926369i
\(559\) −61.1267 −0.109350
\(560\) 22.2742 204.687i 0.0397754 0.365513i
\(561\) 85.3858 + 243.921i 0.152203 + 0.434798i
\(562\) −36.9252 + 63.9563i −0.0657031 + 0.113801i
\(563\) 992.663i 1.76317i −0.472029 0.881583i \(-0.656478\pi\)
0.472029 0.881583i \(-0.343522\pi\)
\(564\) 336.083 117.647i 0.595891 0.208594i
\(565\) 943.286 1.66953
\(566\) 313.048i 0.553088i
\(567\) 556.657 107.808i 0.981758 0.190137i
\(568\) −214.906 −0.378355
\(569\) 68.0794i 0.119647i −0.998209 0.0598237i \(-0.980946\pi\)
0.998209 0.0598237i \(-0.0190539\pi\)
\(570\) −187.783 536.440i −0.329444 0.941122i
\(571\) 850.229 1.48902 0.744509 0.667613i \(-0.232684\pi\)
0.744509 + 0.667613i \(0.232684\pi\)
\(572\) 8.63651 + 4.98629i 0.0150988 + 0.00871729i
\(573\) 872.988 305.594i 1.52354 0.533322i
\(574\) 447.373 611.021i 0.779395 1.06450i
\(575\) 728.277i 1.26657i
\(576\) 56.2807 44.9052i 0.0977096 0.0779605i
\(577\) 239.703 415.178i 0.415431 0.719547i −0.580043 0.814586i \(-0.696964\pi\)
0.995474 + 0.0950391i \(0.0302976\pi\)
\(578\) 165.688 95.6601i 0.286658 0.165502i
\(579\) 35.1543 + 100.425i 0.0607156 + 0.173446i
\(580\) −24.2763 42.0478i −0.0418557 0.0724961i
\(581\) 56.6440 520.525i 0.0974940 0.895913i
\(582\) −22.2071 + 117.447i −0.0381565 + 0.201799i
\(583\) 6.42314 0.0110174
\(584\) 152.219 + 87.8839i 0.260650 + 0.150486i
\(585\) −49.2122 61.6787i −0.0841235 0.105434i
\(586\) −69.6431 120.625i −0.118845 0.205845i
\(587\) −317.341 183.217i −0.540615 0.312124i 0.204713 0.978822i \(-0.434374\pi\)
−0.745328 + 0.666698i \(0.767707\pi\)
\(588\) −270.371 115.480i −0.459814 0.196395i
\(589\) 473.260 + 819.711i 0.803498 + 1.39170i
\(590\) −288.505 166.568i −0.488992 0.282319i
\(591\) −236.132 + 82.6592i −0.399547 + 0.139863i
\(592\) 37.7260 + 65.3434i 0.0637264 + 0.110377i
\(593\) 418.142 241.415i 0.705130 0.407107i −0.104125 0.994564i \(-0.533204\pi\)
0.809255 + 0.587457i \(0.199871\pi\)
\(594\) 5.91156 159.581i 0.00995212 0.268655i
\(595\) −626.357 + 855.479i −1.05270 + 1.43778i
\(596\) 16.2179 + 9.36340i 0.0272112 + 0.0157104i
\(597\) 607.715 + 114.908i 1.01795 + 0.192475i
\(598\) 42.2379 0.0706319
\(599\) 455.755i 0.760860i −0.924810 0.380430i \(-0.875776\pi\)
0.924810 0.380430i \(-0.124224\pi\)
\(600\) 187.004 + 160.890i 0.311674 + 0.268150i
\(601\) 285.550 494.587i 0.475125 0.822940i −0.524469 0.851429i \(-0.675736\pi\)
0.999594 + 0.0284892i \(0.00906962\pi\)
\(602\) 54.9064 504.558i 0.0912067 0.838136i
\(603\) 198.136 158.089i 0.328584 0.262171i
\(604\) 8.29060 + 14.3597i 0.0137262 + 0.0237744i
\(605\) 659.174 380.574i 1.08954 0.629048i
\(606\) 340.769 396.080i 0.562325 0.653597i
\(607\) −77.8517 + 134.843i −0.128256 + 0.222147i −0.923001 0.384797i \(-0.874271\pi\)
0.794745 + 0.606944i \(0.207605\pi\)
\(608\) −89.2487 + 51.5277i −0.146791 + 0.0847496i
\(609\) −67.5292 + 15.6925i −0.110885 + 0.0257677i
\(610\) −581.240 + 1006.74i −0.952852 + 1.65039i
\(611\) −61.2777 + 35.3787i −0.100291 + 0.0579030i
\(612\) −366.612 + 55.3510i −0.599039 + 0.0904428i
\(613\) −383.832 + 664.817i −0.626154 + 1.08453i 0.362163 + 0.932115i \(0.382038\pi\)
−0.988317 + 0.152415i \(0.951295\pi\)
\(614\) 91.0978i 0.148368i
\(615\) 557.565 + 1592.79i 0.906609 + 2.58991i
\(616\) −48.9160 + 66.8094i −0.0794091 + 0.108457i
\(617\) 252.306 145.669i 0.408924 0.236093i −0.281403 0.959590i \(-0.590800\pi\)
0.690327 + 0.723497i \(0.257466\pi\)
\(618\) −66.7079 + 352.800i −0.107942 + 0.570873i
\(619\) 275.150 + 476.575i 0.444508 + 0.769911i 0.998018 0.0629322i \(-0.0200452\pi\)
−0.553510 + 0.832843i \(0.686712\pi\)
\(620\) −661.734 382.052i −1.06731 0.616214i
\(621\) −316.262 597.858i −0.509279 0.962734i
\(622\) 194.446 0.312613
\(623\) −621.557 455.087i −0.997684 0.730476i
\(624\) −9.33113 + 10.8457i −0.0149537 + 0.0173809i
\(625\) 253.297 438.724i 0.405275 0.701958i
\(626\) 82.0990i 0.131149i
\(627\) −42.4658 + 224.590i −0.0677286 + 0.358198i
\(628\) −512.304 −0.815771
\(629\) 388.543i 0.617715i
\(630\) 553.319 350.810i 0.878284 0.556841i
\(631\) −599.999 −0.950870 −0.475435 0.879751i \(-0.657709\pi\)
−0.475435 + 0.879751i \(0.657709\pi\)
\(632\) 189.852i 0.300399i
\(633\) −510.553 + 593.422i −0.806560 + 0.937476i
\(634\) −354.364 −0.558934
\(635\) −1175.01 678.393i −1.85041 1.06834i
\(636\) −1.71206 + 9.05461i −0.00269192 + 0.0142368i
\(637\) 57.0540 + 12.5661i 0.0895668 + 0.0197271i
\(638\) 19.5258i 0.0306047i
\(639\) −426.492 534.531i −0.667436 0.836512i
\(640\) 41.5972 72.0485i 0.0649956 0.112576i
\(641\) 193.598 111.774i 0.302025 0.174374i −0.341327 0.939945i \(-0.610876\pi\)
0.643352 + 0.765570i \(0.277543\pi\)
\(642\) −423.384 + 492.105i −0.659477 + 0.766519i
\(643\) −34.9542 60.5424i −0.0543611 0.0941562i 0.837564 0.546339i \(-0.183979\pi\)
−0.891925 + 0.452183i \(0.850646\pi\)
\(644\) −37.9398 + 348.644i −0.0589127 + 0.541373i
\(645\) 857.362 + 737.634i 1.32924 + 1.14362i
\(646\) 530.688 0.821499
\(647\) −81.4441 47.0218i −0.125880 0.0726767i 0.435738 0.900074i \(-0.356487\pi\)
−0.561618 + 0.827397i \(0.689821\pi\)
\(648\) 223.384 + 50.8691i 0.344728 + 0.0785018i
\(649\) 66.9869 + 116.025i 0.103216 + 0.178774i
\(650\) −42.4530 24.5102i −0.0653123 0.0377081i
\(651\) −796.889 + 745.254i −1.22410 + 1.14478i
\(652\) 201.903 + 349.706i 0.309667 + 0.536359i
\(653\) 445.768 + 257.364i 0.682647 + 0.394126i 0.800851 0.598863i \(-0.204381\pi\)
−0.118205 + 0.992989i \(0.537714\pi\)
\(654\) −86.5032 + 457.492i −0.132268 + 0.699528i
\(655\) 93.8164 + 162.495i 0.143231 + 0.248084i
\(656\) 264.997 152.996i 0.403958 0.233225i
\(657\) 83.4952 + 553.022i 0.127086 + 0.841738i
\(658\) −236.984 537.583i −0.360158 0.816996i
\(659\) 451.104 + 260.445i 0.684529 + 0.395213i 0.801559 0.597916i \(-0.204004\pi\)
−0.117030 + 0.993128i \(0.537338\pi\)
\(660\) −60.9645 174.157i −0.0923704 0.263874i
\(661\) −867.089 −1.31178 −0.655892 0.754855i \(-0.727707\pi\)
−0.655892 + 0.754855i \(0.727707\pi\)
\(662\) 13.7280i 0.0207372i
\(663\) 69.5385 24.3423i 0.104885 0.0367154i
\(664\) 105.783 183.221i 0.159311 0.275936i
\(665\) −858.066 + 378.264i −1.29032 + 0.568817i
\(666\) −87.6580 + 223.512i −0.131619 + 0.335604i
\(667\) 41.3498 + 71.6200i 0.0619937 + 0.107376i
\(668\) 480.142 277.210i 0.718775 0.414985i
\(669\) 235.527 + 44.5337i 0.352058 + 0.0665676i
\(670\) 146.443 253.647i 0.218572 0.378577i
\(671\) 404.867 233.750i 0.603379 0.348361i
\(672\) −81.1420 86.7639i −0.120747 0.129113i
\(673\) −329.187 + 570.169i −0.489134 + 0.847205i −0.999922 0.0125020i \(-0.996020\pi\)
0.510788 + 0.859707i \(0.329354\pi\)
\(674\) −394.453 + 227.737i −0.585241 + 0.337889i
\(675\) −29.0584 + 784.426i −0.0430495 + 1.16211i
\(676\) −167.578 + 290.254i −0.247897 + 0.429370i
\(677\) 610.254i 0.901409i −0.892673 0.450705i \(-0.851173\pi\)
0.892673 0.450705i \(-0.148827\pi\)
\(678\) 354.950 412.563i 0.523525 0.608500i
\(679\) 196.054 + 21.3347i 0.288739 + 0.0314208i
\(680\) −371.016 + 214.206i −0.545612 + 0.315009i
\(681\) −56.3021 48.4397i −0.0826757 0.0711303i
\(682\) 153.646 + 266.122i 0.225287 + 0.390208i
\(683\) 120.639 + 69.6512i 0.176632 + 0.101978i 0.585709 0.810521i \(-0.300816\pi\)
−0.409077 + 0.912500i \(0.634149\pi\)
\(684\) −305.282 119.727i −0.446319 0.175039i
\(685\) −1324.38 −1.93340
\(686\) −154.973 + 459.654i −0.225908 + 0.670049i
\(687\) 201.612 + 38.1211i 0.293467 + 0.0554893i
\(688\) 102.538 177.601i 0.149038 0.258141i
\(689\) 1.83115i 0.00265769i
\(690\) −592.428 509.697i −0.858591 0.738692i
\(691\) 861.604 1.24689 0.623447 0.781866i \(-0.285732\pi\)
0.623447 + 0.781866i \(0.285732\pi\)
\(692\) 122.140i 0.176503i
\(693\) −263.250 + 10.9190i −0.379870 + 0.0157561i
\(694\) −764.251 −1.10123
\(695\) 1334.70i 1.92044i
\(696\) −27.5253 5.20452i −0.0395478 0.00747776i
\(697\) −1575.72 −2.26071
\(698\) −156.863 90.5650i −0.224732 0.129749i
\(699\) −228.622 196.696i −0.327070 0.281396i
\(700\) 240.448 328.403i 0.343497 0.469148i
\(701\) 562.653i 0.802643i −0.915937 0.401322i \(-0.868551\pi\)
0.915937 0.401322i \(-0.131449\pi\)
\(702\) −45.4944 1.68530i −0.0648068 0.00240072i
\(703\) 171.821 297.603i 0.244411 0.423333i
\(704\) −28.9749 + 16.7287i −0.0411575 + 0.0237623i
\(705\) 1286.41 + 243.236i 1.82469 + 0.345015i
\(706\) 319.518 + 553.422i 0.452575 + 0.783883i
\(707\) −695.567 509.275i −0.983829 0.720332i
\(708\) −181.413 + 63.5046i −0.256234 + 0.0896957i
\(709\) −1189.60 −1.67786 −0.838929 0.544241i \(-0.816818\pi\)
−0.838929 + 0.544241i \(0.816818\pi\)
\(710\) −684.287 395.073i −0.963784 0.556441i
\(711\) 472.215 376.771i 0.664156 0.529917i
\(712\) −155.634 269.566i −0.218587 0.378604i
\(713\) 1127.13 + 650.751i 1.58083 + 0.912694i
\(714\) 138.466 + 595.857i 0.193930 + 0.834533i
\(715\) 18.3331 + 31.7539i 0.0256408 + 0.0444111i
\(716\) 55.0216 + 31.7667i 0.0768458 + 0.0443669i
\(717\) −172.543 148.448i −0.240646 0.207040i
\(718\) −268.102 464.366i −0.373401 0.646750i
\(719\) 172.791 99.7608i 0.240321 0.138749i −0.375003 0.927023i \(-0.622358\pi\)
0.615324 + 0.788274i \(0.289025\pi\)
\(720\) 261.756 39.5199i 0.363551 0.0548888i
\(721\) 588.927 + 64.0875i 0.816820 + 0.0888870i
\(722\) −35.6541 20.5849i −0.0493825 0.0285110i
\(723\) 785.549 913.054i 1.08651 1.26287i
\(724\) 145.535 0.201016
\(725\) 95.9796i 0.132386i
\(726\) 81.5902 431.508i 0.112383 0.594363i
\(727\) 282.658 489.578i 0.388800 0.673422i −0.603488 0.797372i \(-0.706223\pi\)
0.992288 + 0.123950i \(0.0395563\pi\)
\(728\) 19.0464 + 13.9453i 0.0261627 + 0.0191556i
\(729\) 316.791 + 656.570i 0.434555 + 0.900645i
\(730\) 323.123 + 559.666i 0.442635 + 0.766666i
\(731\) −914.562 + 528.023i −1.25111 + 0.722329i
\(732\) 221.599 + 633.041i 0.302731 + 0.864810i
\(733\) 113.152 195.985i 0.154369 0.267374i −0.778460 0.627694i \(-0.783999\pi\)
0.932829 + 0.360319i \(0.117332\pi\)
\(734\) −585.809 + 338.217i −0.798105 + 0.460786i
\(735\) −648.599 864.741i −0.882448 1.17652i
\(736\) −70.8526 + 122.720i −0.0962671 + 0.166739i
\(737\) −102.006 + 58.8933i −0.138407 + 0.0799094i
\(738\) 906.442 + 355.493i 1.22824 + 0.481697i
\(739\) 262.119 454.004i 0.354694 0.614349i −0.632371 0.774665i \(-0.717918\pi\)
0.987066 + 0.160317i \(0.0512516\pi\)
\(740\) 277.415i 0.374885i
\(741\) 64.0274 + 12.1064i 0.0864068 + 0.0163379i
\(742\) 15.1148 + 1.64481i 0.0203704 + 0.00221672i
\(743\) 474.032 273.683i 0.637998 0.368348i −0.145845 0.989307i \(-0.546590\pi\)
0.783843 + 0.620959i \(0.213257\pi\)
\(744\) −416.102 + 145.658i −0.559277 + 0.195777i
\(745\) 34.4265 + 59.6284i 0.0462101 + 0.0800382i
\(746\) −275.768 159.215i −0.369662 0.213424i
\(747\) 665.654 100.500i 0.891103 0.134539i
\(748\) 172.290 0.230334
\(749\) 864.199 + 632.742i 1.15380 + 0.844783i
\(750\) 41.9805 + 119.925i 0.0559740 + 0.159901i
\(751\) −183.600 + 318.004i −0.244474 + 0.423441i −0.961984 0.273107i \(-0.911949\pi\)
0.717510 + 0.696549i \(0.245282\pi\)
\(752\) 237.386i 0.315673i
\(753\) −651.660 + 228.117i −0.865418 + 0.302944i
\(754\) 5.56653 0.00738267
\(755\) 60.9643i 0.0807474i
\(756\) 54.7758 374.010i 0.0724548 0.494722i
\(757\) −519.753 −0.686596 −0.343298 0.939227i \(-0.611544\pi\)
−0.343298 + 0.939227i \(0.611544\pi\)
\(758\) 125.281i 0.165278i
\(759\) 103.841 + 296.642i 0.136813 + 0.390833i
\(760\) −378.905 −0.498559
\(761\) 856.816 + 494.683i 1.12591 + 0.650043i 0.942902 0.333069i \(-0.108084\pi\)
0.183005 + 0.983112i \(0.441418\pi\)
\(762\) −738.853 + 258.639i −0.969624 + 0.339421i
\(763\) 763.689 + 83.1053i 1.00090 + 0.108919i
\(764\) 616.620i 0.807095i
\(765\) −1269.09 497.718i −1.65894 0.650612i
\(766\) 30.3546 52.5757i 0.0396274 0.0686366i
\(767\) 33.0770 19.0970i 0.0431251 0.0248983i
\(768\) −15.8590 45.3044i −0.0206498 0.0589901i
\(769\) 497.717 + 862.071i 0.647226 + 1.12103i 0.983783 + 0.179365i \(0.0574043\pi\)
−0.336557 + 0.941663i \(0.609262\pi\)
\(770\) −278.574 + 122.805i −0.361784 + 0.159486i
\(771\) 139.239 736.397i 0.180595 0.955119i
\(772\) 70.9337 0.0918830
\(773\) 1104.94 + 637.935i 1.42941 + 0.825272i 0.997074 0.0764392i \(-0.0243551\pi\)
0.432339 + 0.901711i \(0.357688\pi\)
\(774\) 645.235 97.4174i 0.833636 0.125862i
\(775\) −755.248 1308.13i −0.974514 1.68791i
\(776\) 69.0095 + 39.8427i 0.0889298 + 0.0513436i
\(777\) 378.980 + 115.271i 0.487748 + 0.148354i
\(778\) −98.1835 170.059i −0.126200 0.218584i
\(779\) −1206.91 696.812i −1.54931 0.894496i
\(780\) −49.6497 + 17.3801i −0.0636535 + 0.0222822i
\(781\) 158.882 + 275.192i 0.203434 + 0.352358i
\(782\) 631.953 364.858i 0.808124 0.466570i
\(783\) −41.6802 78.7916i −0.0532314 0.100628i
\(784\) −132.216 + 144.689i −0.168643 + 0.184552i
\(785\) −1631.24 941.796i −2.07801 1.19974i
\(786\) 106.372 + 20.1130i 0.135333 + 0.0255891i
\(787\) −253.914 −0.322635 −0.161317 0.986903i \(-0.551574\pi\)
−0.161317 + 0.986903i \(0.551574\pi\)
\(788\) 166.788i 0.211660i
\(789\) 103.582 + 89.1175i 0.131283 + 0.112950i
\(790\) 349.015 604.512i 0.441792 0.765206i
\(791\) −724.513 530.468i −0.915945 0.670629i
\(792\) −99.1110 38.8698i −0.125140 0.0490780i
\(793\) −66.6389 115.422i −0.0840339 0.145551i
\(794\) 569.256 328.660i 0.716947 0.413930i
\(795\) −22.0970 + 25.6836i −0.0277950 + 0.0323065i
\(796\) 206.161 357.082i 0.258996 0.448595i
\(797\) −179.472 + 103.618i −0.225185 + 0.130011i −0.608349 0.793670i \(-0.708168\pi\)
0.383164 + 0.923680i \(0.374834\pi\)
\(798\) −157.442 + 517.627i −0.197296 + 0.648655i
\(799\) −611.214 + 1058.65i −0.764974 + 1.32497i
\(800\) 142.427 82.2301i 0.178033 0.102788i
\(801\) 361.622 922.072i 0.451463 1.15115i
\(802\) −34.8860 + 60.4243i −0.0434987 + 0.0753420i
\(803\) 259.893i 0.323653i
\(804\) −55.8317 159.494i −0.0694424 0.198376i
\(805\) −761.736 + 1040.38i −0.946256 + 1.29240i
\(806\) 75.8676 43.8022i 0.0941285 0.0543451i
\(807\) −90.9265 + 480.885i −0.112672 + 0.595893i
\(808\) −174.166 301.664i −0.215551 0.373346i
\(809\) 725.129 + 418.654i 0.896328 + 0.517495i 0.876007 0.482298i \(-0.160198\pi\)
0.0203210 + 0.999794i \(0.493531\pi\)
\(810\) 617.766 + 572.632i 0.762674 + 0.706953i
\(811\) −125.310 −0.154513 −0.0772566 0.997011i \(-0.524616\pi\)
−0.0772566 + 0.997011i \(0.524616\pi\)
\(812\) −5.00008 + 45.9478i −0.00615773 + 0.0565860i
\(813\) 488.671 567.989i 0.601072 0.698634i
\(814\) 55.7824 96.6179i 0.0685287 0.118695i
\(815\) 1484.68i 1.82169i
\(816\) −45.9231 + 242.874i −0.0562783 + 0.297640i
\(817\) −934.008 −1.14322
\(818\) 176.718i 0.216037i
\(819\) 3.11284 + 75.0488i 0.00380078 + 0.0916347i
\(820\) 1125.04 1.37200
\(821\) 919.053i 1.11943i 0.828685 + 0.559716i \(0.189090\pi\)
−0.828685 + 0.559716i \(0.810910\pi\)
\(822\) −498.351 + 579.240i −0.606266 + 0.704671i
\(823\) 204.382 0.248338 0.124169 0.992261i \(-0.460374\pi\)
0.124169 + 0.992261i \(0.460374\pi\)
\(824\) 207.298 + 119.684i 0.251575 + 0.145247i
\(825\) 67.7688 358.410i 0.0821440 0.434437i
\(826\) 127.921 + 290.181i 0.154868 + 0.351309i
\(827\) 496.263i 0.600076i −0.953927 0.300038i \(-0.903001\pi\)
0.953927 0.300038i \(-0.0969994\pi\)
\(828\) −445.850 + 67.3144i −0.538466 + 0.0812976i
\(829\) 594.038 1028.90i 0.716571 1.24114i −0.245779 0.969326i \(-0.579044\pi\)
0.962350 0.271812i \(-0.0876229\pi\)
\(830\) 673.651 388.933i 0.811628 0.468594i
\(831\) 433.971 504.410i 0.522228 0.606992i
\(832\) 4.76910 + 8.26033i 0.00573209 + 0.00992828i
\(833\) 962.176 304.831i 1.15507 0.365943i
\(834\) 583.756 + 502.237i 0.699947 + 0.602202i
\(835\) 2038.44 2.44125
\(836\) 131.965 + 76.1899i 0.157853 + 0.0911362i
\(837\) −1188.07 745.895i −1.41944 0.891153i
\(838\) 477.241 + 826.606i 0.569501 + 0.986404i
\(839\) −122.938 70.9782i −0.146529 0.0845986i 0.424943 0.905220i \(-0.360294\pi\)
−0.571472 + 0.820622i \(0.693627\pi\)
\(840\) −98.8632 425.435i −0.117694 0.506470i
\(841\) −415.051 718.889i −0.493520 0.854802i
\(842\) −19.0443 10.9952i −0.0226179 0.0130585i
\(843\) −29.1058 + 153.933i −0.0345265 + 0.182601i
\(844\) 260.941 + 451.964i 0.309172 + 0.535502i
\(845\) −1067.18 + 616.137i −1.26294 + 0.729156i
\(846\) 590.446 471.105i 0.697926 0.556861i
\(847\) −720.314 78.3852i −0.850430 0.0925445i
\(848\) 5.32031 + 3.07168i 0.00627395 + 0.00362227i
\(849\) 219.408 + 626.782i 0.258431 + 0.738259i
\(850\) −846.894 −0.996346
\(851\) 472.521i 0.555254i
\(852\) −430.283 + 150.622i −0.505027 + 0.176787i
\(853\) 324.476 562.008i 0.380393 0.658861i −0.610725 0.791843i \(-0.709122\pi\)
0.991118 + 0.132982i \(0.0424553\pi\)
\(854\) 1012.58 446.381i 1.18570 0.522694i
\(855\) −751.956 942.443i −0.879481 1.10227i
\(856\) 216.390 + 374.798i 0.252792 + 0.437849i
\(857\) 730.115 421.532i 0.851943 0.491869i −0.00936302 0.999956i \(-0.502980\pi\)
0.861306 + 0.508087i \(0.169647\pi\)
\(858\) 20.7867 + 3.93039i 0.0242270 + 0.00458087i
\(859\) −140.397 + 243.175i −0.163442 + 0.283090i −0.936101 0.351731i \(-0.885593\pi\)
0.772659 + 0.634822i \(0.218926\pi\)
\(860\) 652.987 377.002i 0.759287 0.438374i
\(861\) 467.475 1536.93i 0.542945 1.78506i
\(862\) 210.629 364.820i 0.244349 0.423225i
\(863\) 711.247 410.638i 0.824156 0.475827i −0.0276915 0.999617i \(-0.508816\pi\)
0.851848 + 0.523790i \(0.175482\pi\)
\(864\) 81.2118 129.355i 0.0939951 0.149716i
\(865\) 224.536 388.908i 0.259579 0.449605i
\(866\) 273.203i 0.315477i
\(867\) 264.694 307.657i 0.305298 0.354852i
\(868\) 293.409 + 665.578i 0.338028 + 0.766795i
\(869\) −243.110 + 140.359i −0.279758 + 0.161518i
\(870\) −78.0760 67.1730i −0.0897426 0.0772103i
\(871\) 16.7896 + 29.0805i 0.0192763 + 0.0333875i
\(872\) 268.813 + 155.199i 0.308272 + 0.177981i
\(873\) 37.8530 + 250.716i 0.0433597 + 0.287189i
\(874\) 645.389 0.738432
\(875\) 191.828 84.5639i 0.219232 0.0966445i
\(876\) 366.368 + 69.2735i 0.418228 + 0.0790793i
\(877\) 138.403 239.720i 0.157814 0.273341i −0.776266 0.630405i \(-0.782889\pi\)
0.934080 + 0.357064i \(0.116222\pi\)
\(878\) 1113.50i 1.26822i
\(879\) −223.982 192.704i −0.254815 0.219231i
\(880\) −123.013 −0.139787
\(881\) 1353.04i 1.53580i 0.640568 + 0.767901i \(0.278699\pi\)
−0.640568 + 0.767901i \(0.721301\pi\)
\(882\) −622.271 41.7175i −0.705523 0.0472988i
\(883\) 1338.00 1.51529 0.757647 0.652665i \(-0.226349\pi\)
0.757647 + 0.652665i \(0.226349\pi\)
\(884\) 49.1173i 0.0555626i
\(885\) −694.386 131.296i −0.784617 0.148357i
\(886\) −429.238 −0.484467
\(887\) 248.517 + 143.481i 0.280177 + 0.161760i 0.633504 0.773740i \(-0.281616\pi\)
−0.353327 + 0.935500i \(0.614950\pi\)
\(888\) 121.332 + 104.389i 0.136635 + 0.117555i
\(889\) 520.993 + 1181.84i 0.586044 + 1.32940i
\(890\) 1144.44i 1.28589i
\(891\) −100.011 323.656i −0.112245 0.363250i
\(892\) 79.9000 138.391i 0.0895739 0.155147i
\(893\) −936.315 + 540.582i −1.04851 + 0.605355i
\(894\) 39.0339 + 7.38059i 0.0436621 + 0.00825570i
\(895\) 116.797 + 202.298i 0.130499 + 0.226032i
\(896\) −72.4670 + 31.9458i −0.0808783 + 0.0356538i
\(897\) 84.5684 29.6036i 0.0942791 0.0330028i
\(898\) 276.041 0.307396
\(899\) 148.545 + 85.7624i 0.165233 + 0.0953975i
\(900\) 487.182 + 191.065i 0.541314 + 0.212295i
\(901\) −15.8178 27.3972i −0.0175558 0.0304075i
\(902\) −391.829 226.222i −0.434400 0.250801i
\(903\) −243.700 1048.70i −0.269878 1.16136i
\(904\) −181.413 314.217i −0.200678 0.347585i
\(905\) 463.402 + 267.546i 0.512047 + 0.295630i
\(906\) 26.6638 + 22.9403i 0.0294302 + 0.0253204i
\(907\) −847.762 1468.37i −0.934688 1.61893i −0.775189 0.631730i \(-0.782345\pi\)
−0.159500 0.987198i \(-0.550988\pi\)
\(908\) −42.8810 + 24.7574i −0.0472258 + 0.0272658i
\(909\) 404.681 1031.87i 0.445194 1.13517i
\(910\) 35.0098 + 79.4175i 0.0384723 + 0.0872720i
\(911\) −172.108 99.3667i −0.188922 0.109074i 0.402556 0.915395i \(-0.368122\pi\)
−0.591478 + 0.806321i \(0.701455\pi\)
\(912\) −142.578 + 165.721i −0.156336 + 0.181711i
\(913\) −312.825 −0.342634
\(914\) 1143.88i 1.25151i
\(915\) −458.155 + 2423.06i −0.500716 + 2.64815i
\(916\) 68.3948 118.463i 0.0746668 0.129327i
\(917\) 19.3229 177.567i 0.0210719 0.193639i
\(918\) −695.233 + 367.773i −0.757334 + 0.400624i
\(919\) −425.209 736.484i −0.462687 0.801397i 0.536407 0.843960i \(-0.319781\pi\)
−0.999094 + 0.0425622i \(0.986448\pi\)
\(920\) −451.207 + 260.504i −0.490442 + 0.283157i
\(921\) −63.8483 182.395i −0.0693250 0.198040i
\(922\) −23.9259 + 41.4409i −0.0259500 + 0.0449468i
\(923\) 78.4532 45.2950i 0.0849980 0.0490736i
\(924\) −51.1140 + 168.049i −0.0553182 + 0.181872i
\(925\) −274.200 + 474.928i −0.296432 + 0.513435i
\(926\) −653.749 + 377.442i −0.705992 + 0.407605i
\(927\) 113.707 + 753.127i 0.122661 + 0.812434i
\(928\) −9.33766 + 16.1733i −0.0100621 + 0.0174281i
\(929\) 812.786i 0.874904i −0.899242 0.437452i \(-0.855881\pi\)
0.899242 0.437452i \(-0.144119\pi\)
\(930\) −1592.69 301.148i −1.71257 0.323815i
\(931\) 871.778 + 192.009i 0.936389 + 0.206240i
\(932\) −174.124 + 100.530i −0.186828 + 0.107865i
\(933\) 389.317 136.282i 0.417275 0.146069i
\(934\) −253.952 439.858i −0.271897 0.470940i
\(935\) 548.592 + 316.729i 0.586729 + 0.338748i
\(936\) −11.0812 + 28.2551i −0.0118389 + 0.0301871i
\(937\) −1288.17 −1.37478 −0.687391 0.726288i \(-0.741244\pi\)
−0.687391 + 0.726288i \(0.741244\pi\)
\(938\) −255.120 + 112.465i −0.271983 + 0.119899i
\(939\) −57.5413 164.378i −0.0612793 0.175056i
\(940\) 436.400 755.867i 0.464255 0.804113i
\(941\) 1029.51i 1.09406i −0.837112 0.547032i \(-0.815758\pi\)
0.837112 0.547032i \(-0.184242\pi\)
\(942\) −1025.73 + 359.062i −1.08889 + 0.381170i
\(943\) −1916.29 −2.03212
\(944\) 128.138i 0.135740i
\(945\) 861.976 1090.20i 0.912144 1.15365i
\(946\) −303.229 −0.320538
\(947\) 339.125i 0.358104i 0.983840 + 0.179052i \(0.0573031\pi\)
−0.983840 + 0.179052i \(0.942697\pi\)
\(948\) −133.063 380.120i −0.140362 0.400971i
\(949\) −74.0919 −0.0780737
\(950\) −648.676 374.513i −0.682817 0.394224i
\(951\) −709.504 + 248.365i −0.746061 + 0.261162i
\(952\) 405.429 + 44.1191i 0.425871 + 0.0463436i
\(953\) 1756.40i 1.84303i 0.388348 + 0.921513i \(0.373046\pi\)
−0.388348 + 0.921513i \(0.626954\pi\)
\(954\) 2.91829 + 19.3290i 0.00305901 + 0.0202610i
\(955\) 1133.57 1963.39i 1.18698 2.05591i
\(956\) −131.413 + 75.8712i −0.137461 + 0.0793631i
\(957\) 13.6852 + 39.0944i 0.0143001 + 0.0408510i
\(958\) 151.460 + 262.337i 0.158101 + 0.273838i
\(959\) 1017.22 + 744.779i 1.06071 + 0.776620i
\(960\) 32.7885 173.409i 0.0341547 0.180635i
\(961\) 1738.40 1.80895
\(962\) −27.5444 15.9028i −0.0286324 0.0165309i
\(963\) −502.792 + 1282.03i −0.522110 + 1.33129i
\(964\) −401.491 695.403i −0.416485 0.721372i
\(965\) 225.862 + 130.401i 0.234053 + 0.135131i
\(966\) 168.394 + 724.644i 0.174321 + 0.750149i
\(967\) 193.430 + 335.031i 0.200031 + 0.346464i 0.948538 0.316663i \(-0.102562\pi\)
−0.748507 + 0.663127i \(0.769229\pi\)
\(968\) −253.545 146.385i −0.261927 0.151224i
\(969\) 1062.54 371.947i 1.09653 0.383846i
\(970\) 146.490 + 253.728i 0.151021 + 0.261575i
\(971\) −940.140 + 542.790i −0.968218 + 0.559001i −0.898693 0.438579i \(-0.855482\pi\)
−0.0695257 + 0.997580i \(0.522149\pi\)
\(972\) 482.910 54.7147i 0.496821 0.0562908i
\(973\) 750.586 1025.15i 0.771414 1.05360i
\(974\) −901.763 520.633i −0.925834 0.534531i
\(975\) −102.178 19.3199i −0.104798 0.0198153i
\(976\) 447.138 0.458133
\(977\) 1211.94i 1.24047i 0.784416 + 0.620236i \(0.212963\pi\)
−0.784416 + 0.620236i \(0.787037\pi\)
\(978\) 649.349 + 558.670i 0.663956 + 0.571237i
\(979\) −230.123 + 398.585i −0.235059 + 0.407135i
\(980\) −686.983 + 217.646i −0.701003 + 0.222087i
\(981\) 147.449 + 976.614i 0.150305 + 0.995529i
\(982\) 98.1579 + 170.014i 0.0999571 + 0.173131i
\(983\) −498.045 + 287.547i −0.506658 + 0.292519i −0.731459 0.681885i \(-0.761160\pi\)
0.224801 + 0.974405i \(0.427827\pi\)
\(984\) 423.343 492.057i 0.430226 0.500058i
\(985\) −306.615 + 531.073i −0.311285 + 0.539161i
\(986\) 83.2850 48.0846i 0.0844676 0.0487674i
\(987\) −851.267 910.248i −0.862480 0.922237i
\(988\) 21.7206 37.6213i 0.0219845 0.0380782i
\(989\) −1112.23 + 642.148i −1.12460 + 0.649290i
\(990\) −244.125 305.967i −0.246591 0.309058i
\(991\) −747.247 + 1294.27i −0.754033 + 1.30602i 0.191821 + 0.981430i \(0.438561\pi\)
−0.945854 + 0.324593i \(0.894773\pi\)
\(992\) 293.906i 0.296276i
\(993\) −9.62165 27.4861i −0.00968947 0.0276799i
\(994\) 303.408 + 688.262i 0.305240 + 0.692416i
\(995\) 1312.88 757.994i 1.31948 0.761803i
\(996\) 83.3821 440.985i 0.0837170 0.442756i
\(997\) −841.538 1457.59i −0.844070 1.46197i −0.886426 0.462870i \(-0.846820\pi\)
0.0423555 0.999103i \(-0.486514\pi\)
\(998\) 1.47814 + 0.853405i 0.00148110 + 0.000855115i
\(999\) −18.8537 + 508.952i −0.0188726 + 0.509461i
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 126.3.r.a.11.3 yes 32
3.2 odd 2 378.3.r.a.305.16 32
7.2 even 3 126.3.i.a.65.8 32
9.4 even 3 378.3.i.a.179.16 32
9.5 odd 6 126.3.i.a.95.8 yes 32
21.2 odd 6 378.3.i.a.359.9 32
63.23 odd 6 inner 126.3.r.a.23.11 yes 32
63.58 even 3 378.3.r.a.233.8 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.3.i.a.65.8 32 7.2 even 3
126.3.i.a.95.8 yes 32 9.5 odd 6
126.3.r.a.11.3 yes 32 1.1 even 1 trivial
126.3.r.a.23.11 yes 32 63.23 odd 6 inner
378.3.i.a.179.16 32 9.4 even 3
378.3.i.a.359.9 32 21.2 odd 6
378.3.r.a.233.8 32 63.58 even 3
378.3.r.a.305.16 32 3.2 odd 2