Properties

Label 60.3.l.a.23.11
Level $60$
Weight $3$
Character 60.23
Analytic conductor $1.635$
Analytic rank $0$
Dimension $40$
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] = [60,3,Mod(23,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.23");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 60.l (of order \(4\), 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: \(1.63488158616\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 23.11
Character \(\chi\) \(=\) 60.23
Dual form 60.3.l.a.47.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.141758 + 1.99497i) q^{2} +(2.17477 - 2.06649i) q^{3} +(-3.95981 + 0.565605i) q^{4} +(3.07600 + 3.94185i) q^{5} +(4.43087 + 4.04566i) q^{6} +(5.18766 + 5.18766i) q^{7} +(-1.68970 - 7.81952i) q^{8} +(0.459255 - 8.98827i) q^{9} +O(q^{10})\) \(q+(0.141758 + 1.99497i) q^{2} +(2.17477 - 2.06649i) q^{3} +(-3.95981 + 0.565605i) q^{4} +(3.07600 + 3.94185i) q^{5} +(4.43087 + 4.04566i) q^{6} +(5.18766 + 5.18766i) q^{7} +(-1.68970 - 7.81952i) q^{8} +(0.459255 - 8.98827i) q^{9} +(-7.42783 + 6.69532i) q^{10} -7.14796 q^{11} +(-7.44286 + 9.41296i) q^{12} +(-7.93751 - 7.93751i) q^{13} +(-9.61384 + 11.0846i) q^{14} +(14.8354 + 2.21611i) q^{15} +(15.3602 - 4.47938i) q^{16} +(-16.5858 - 16.5858i) q^{17} +(17.9964 - 0.357959i) q^{18} +12.1545 q^{19} +(-14.4099 - 13.8692i) q^{20} +(22.0022 + 0.561734i) q^{21} +(-1.01328 - 14.2600i) q^{22} +(-11.0852 - 11.0852i) q^{23} +(-19.8337 - 13.5139i) q^{24} +(-6.07643 + 24.2503i) q^{25} +(14.7099 - 16.9603i) q^{26} +(-17.5754 - 20.4965i) q^{27} +(-23.4763 - 17.6080i) q^{28} +26.1010 q^{29} +(-2.31804 + 29.9103i) q^{30} +8.74184i q^{31} +(11.1137 + 30.0081i) q^{32} +(-15.5452 + 14.7712i) q^{33} +(30.7369 - 35.4392i) q^{34} +(-4.49175 + 36.4063i) q^{35} +(3.26525 + 35.8516i) q^{36} +(-26.7167 + 26.7167i) q^{37} +(1.72299 + 24.2478i) q^{38} +(-33.6650 - 0.859495i) q^{39} +(25.6259 - 30.7134i) q^{40} +35.4164i q^{41} +(1.99834 + 43.9734i) q^{42} +(-24.6907 + 24.6907i) q^{43} +(28.3045 - 4.04292i) q^{44} +(36.8431 - 25.8376i) q^{45} +(20.5431 - 23.6860i) q^{46} +(58.6014 - 58.6014i) q^{47} +(24.1483 - 41.4833i) q^{48} +4.82369i q^{49} +(-49.2400 - 8.68463i) q^{50} +(-70.3445 - 1.79595i) q^{51} +(35.9205 + 26.9415i) q^{52} +(-20.4453 + 20.4453i) q^{53} +(38.3984 - 37.9679i) q^{54} +(-21.9871 - 28.1762i) q^{55} +(31.7994 - 49.3306i) q^{56} +(26.4332 - 25.1171i) q^{57} +(3.70002 + 52.0707i) q^{58} +59.4125i q^{59} +(-59.9988 - 0.384395i) q^{60} +7.42905 q^{61} +(-17.4397 + 1.23923i) q^{62} +(49.0106 - 44.2457i) q^{63} +(-58.2898 + 26.4253i) q^{64} +(6.87272 - 55.7043i) q^{65} +(-31.6717 - 28.9182i) q^{66} +(35.8479 + 35.8479i) q^{67} +(75.0574 + 56.2954i) q^{68} +(-47.0150 - 1.20033i) q^{69} +(-73.2661 - 3.80004i) q^{70} +46.2359 q^{71} +(-71.0600 + 11.5963i) q^{72} +(10.6280 + 10.6280i) q^{73} +(-57.0864 - 49.5118i) q^{74} +(36.8981 + 65.2957i) q^{75} +(-48.1294 + 6.87464i) q^{76} +(-37.0812 - 37.0812i) q^{77} +(-3.05762 - 67.2826i) q^{78} +68.3530 q^{79} +(64.9050 + 46.7690i) q^{80} +(-80.5782 - 8.25582i) q^{81} +(-70.6547 + 5.02056i) q^{82} +(-76.6461 - 76.6461i) q^{83} +(-87.4423 + 10.2202i) q^{84} +(14.3608 - 116.396i) q^{85} +(-52.7574 - 45.7572i) q^{86} +(56.7637 - 53.9374i) q^{87} +(12.0779 + 55.8936i) q^{88} +41.0916 q^{89} +(56.7681 + 69.8383i) q^{90} -82.3543i q^{91} +(50.1649 + 37.6253i) q^{92} +(18.0649 + 19.0115i) q^{93} +(125.215 + 108.601i) q^{94} +(37.3872 + 47.9112i) q^{95} +(86.1810 + 42.2945i) q^{96} +(81.7315 - 81.7315i) q^{97} +(-9.62311 + 0.683795i) q^{98} +(-3.28274 + 64.2478i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.141758 + 1.99497i 0.0708789 + 0.997485i
\(3\) 2.17477 2.06649i 0.724924 0.688829i
\(4\) −3.95981 + 0.565605i −0.989952 + 0.141401i
\(5\) 3.07600 + 3.94185i 0.615200 + 0.788371i
\(6\) 4.43087 + 4.04566i 0.738479 + 0.674277i
\(7\) 5.18766 + 5.18766i 0.741095 + 0.741095i 0.972789 0.231694i \(-0.0744268\pi\)
−0.231694 + 0.972789i \(0.574427\pi\)
\(8\) −1.68970 7.81952i −0.211212 0.977440i
\(9\) 0.459255 8.98827i 0.0510283 0.998697i
\(10\) −7.42783 + 6.69532i −0.742783 + 0.669532i
\(11\) −7.14796 −0.649814 −0.324907 0.945746i \(-0.605333\pi\)
−0.324907 + 0.945746i \(0.605333\pi\)
\(12\) −7.44286 + 9.41296i −0.620238 + 0.784413i
\(13\) −7.93751 7.93751i −0.610578 0.610578i 0.332519 0.943097i \(-0.392102\pi\)
−0.943097 + 0.332519i \(0.892102\pi\)
\(14\) −9.61384 + 11.0846i −0.686703 + 0.791759i
\(15\) 14.8354 + 2.21611i 0.989026 + 0.147741i
\(16\) 15.3602 4.47938i 0.960011 0.279961i
\(17\) −16.5858 16.5858i −0.975633 0.975633i 0.0240774 0.999710i \(-0.492335\pi\)
−0.999710 + 0.0240774i \(0.992335\pi\)
\(18\) 17.9964 0.357959i 0.999802 0.0198866i
\(19\) 12.1545 0.639709 0.319855 0.947467i \(-0.396366\pi\)
0.319855 + 0.947467i \(0.396366\pi\)
\(20\) −14.4099 13.8692i −0.720496 0.693459i
\(21\) 22.0022 + 0.561734i 1.04772 + 0.0267492i
\(22\) −1.01328 14.2600i −0.0460581 0.648180i
\(23\) −11.0852 11.0852i −0.481963 0.481963i 0.423795 0.905758i \(-0.360698\pi\)
−0.905758 + 0.423795i \(0.860698\pi\)
\(24\) −19.8337 13.5139i −0.826402 0.563080i
\(25\) −6.07643 + 24.2503i −0.243057 + 0.970012i
\(26\) 14.7099 16.9603i 0.565765 0.652319i
\(27\) −17.5754 20.4965i −0.650940 0.759129i
\(28\) −23.4763 17.6080i −0.838440 0.628857i
\(29\) 26.1010 0.900034 0.450017 0.893020i \(-0.351418\pi\)
0.450017 + 0.893020i \(0.351418\pi\)
\(30\) −2.31804 + 29.9103i −0.0772680 + 0.997010i
\(31\) 8.74184i 0.281995i 0.990010 + 0.140997i \(0.0450309\pi\)
−0.990010 + 0.140997i \(0.954969\pi\)
\(32\) 11.1137 + 30.0081i 0.347302 + 0.937753i
\(33\) −15.5452 + 14.7712i −0.471066 + 0.447611i
\(34\) 30.7369 35.4392i 0.904027 1.04233i
\(35\) −4.49175 + 36.4063i −0.128336 + 1.04018i
\(36\) 3.26525 + 35.8516i 0.0907015 + 0.995878i
\(37\) −26.7167 + 26.7167i −0.722074 + 0.722074i −0.969027 0.246953i \(-0.920571\pi\)
0.246953 + 0.969027i \(0.420571\pi\)
\(38\) 1.72299 + 24.2478i 0.0453419 + 0.638100i
\(39\) −33.6650 0.859495i −0.863206 0.0220383i
\(40\) 25.6259 30.7134i 0.640647 0.767835i
\(41\) 35.4164i 0.863815i 0.901918 + 0.431908i \(0.142159\pi\)
−0.901918 + 0.431908i \(0.857841\pi\)
\(42\) 1.99834 + 43.9734i 0.0475796 + 1.04699i
\(43\) −24.6907 + 24.6907i −0.574203 + 0.574203i −0.933300 0.359097i \(-0.883085\pi\)
0.359097 + 0.933300i \(0.383085\pi\)
\(44\) 28.3045 4.04292i 0.643285 0.0918846i
\(45\) 36.8431 25.8376i 0.818736 0.574170i
\(46\) 20.5431 23.6860i 0.446590 0.514912i
\(47\) 58.6014 58.6014i 1.24684 1.24684i 0.289728 0.957109i \(-0.406435\pi\)
0.957109 0.289728i \(-0.0935650\pi\)
\(48\) 24.1483 41.4833i 0.503089 0.864234i
\(49\) 4.82369i 0.0984426i
\(50\) −49.2400 8.68463i −0.984800 0.173693i
\(51\) −70.3445 1.79595i −1.37930 0.0352147i
\(52\) 35.9205 + 26.9415i 0.690779 + 0.518106i
\(53\) −20.4453 + 20.4453i −0.385761 + 0.385761i −0.873172 0.487411i \(-0.837941\pi\)
0.487411 + 0.873172i \(0.337941\pi\)
\(54\) 38.3984 37.9679i 0.711082 0.703109i
\(55\) −21.9871 28.1762i −0.399766 0.512295i
\(56\) 31.7994 49.3306i 0.567847 0.880904i
\(57\) 26.4332 25.1171i 0.463740 0.440651i
\(58\) 3.70002 + 52.0707i 0.0637935 + 0.897771i
\(59\) 59.4125i 1.00699i 0.863998 + 0.503496i \(0.167953\pi\)
−0.863998 + 0.503496i \(0.832047\pi\)
\(60\) −59.9988 0.384395i −0.999979 0.00640659i
\(61\) 7.42905 0.121788 0.0608939 0.998144i \(-0.480605\pi\)
0.0608939 + 0.998144i \(0.480605\pi\)
\(62\) −17.4397 + 1.23923i −0.281286 + 0.0199875i
\(63\) 49.0106 44.2457i 0.777946 0.702312i
\(64\) −58.2898 + 26.4253i −0.910779 + 0.412895i
\(65\) 6.87272 55.7043i 0.105734 0.856989i
\(66\) −31.6717 28.9182i −0.479874 0.438155i
\(67\) 35.8479 + 35.8479i 0.535044 + 0.535044i 0.922069 0.387025i \(-0.126497\pi\)
−0.387025 + 0.922069i \(0.626497\pi\)
\(68\) 75.0574 + 56.2954i 1.10379 + 0.827874i
\(69\) −47.0150 1.20033i −0.681377 0.0173961i
\(70\) −73.2661 3.80004i −1.04666 0.0542863i
\(71\) 46.2359 0.651210 0.325605 0.945506i \(-0.394432\pi\)
0.325605 + 0.945506i \(0.394432\pi\)
\(72\) −71.0600 + 11.5963i −0.986945 + 0.161060i
\(73\) 10.6280 + 10.6280i 0.145589 + 0.145589i 0.776144 0.630555i \(-0.217173\pi\)
−0.630555 + 0.776144i \(0.717173\pi\)
\(74\) −57.0864 49.5118i −0.771438 0.669078i
\(75\) 36.8981 + 65.2957i 0.491975 + 0.870609i
\(76\) −48.1294 + 6.87464i −0.633282 + 0.0904558i
\(77\) −37.0812 37.0812i −0.481574 0.481574i
\(78\) −3.05762 67.2826i −0.0392002 0.862597i
\(79\) 68.3530 0.865228 0.432614 0.901579i \(-0.357591\pi\)
0.432614 + 0.901579i \(0.357591\pi\)
\(80\) 64.9050 + 46.7690i 0.811312 + 0.584613i
\(81\) −80.5782 8.25582i −0.994792 0.101924i
\(82\) −70.6547 + 5.02056i −0.861643 + 0.0612263i
\(83\) −76.6461 76.6461i −0.923447 0.923447i 0.0738244 0.997271i \(-0.476480\pi\)
−0.997271 + 0.0738244i \(0.976480\pi\)
\(84\) −87.4423 + 10.2202i −1.04098 + 0.121669i
\(85\) 14.3608 116.396i 0.168951 1.36937i
\(86\) −52.7574 45.7572i −0.613458 0.532060i
\(87\) 56.7637 53.9374i 0.652456 0.619970i
\(88\) 12.0779 + 55.8936i 0.137249 + 0.635155i
\(89\) 41.0916 0.461703 0.230852 0.972989i \(-0.425849\pi\)
0.230852 + 0.972989i \(0.425849\pi\)
\(90\) 56.7681 + 69.8383i 0.630757 + 0.775981i
\(91\) 82.3543i 0.904992i
\(92\) 50.1649 + 37.6253i 0.545271 + 0.408970i
\(93\) 18.0649 + 19.0115i 0.194246 + 0.204425i
\(94\) 125.215 + 108.601i 1.33208 + 1.15533i
\(95\) 37.3872 + 47.9112i 0.393549 + 0.504328i
\(96\) 86.1810 + 42.2945i 0.897719 + 0.440568i
\(97\) 81.7315 81.7315i 0.842593 0.842593i −0.146602 0.989196i \(-0.546834\pi\)
0.989196 + 0.146602i \(0.0468338\pi\)
\(98\) −9.62311 + 0.683795i −0.0981950 + 0.00697750i
\(99\) −3.28274 + 64.2478i −0.0331589 + 0.648968i
\(100\) 10.3454 99.4634i 0.103454 0.994634i
\(101\) 125.873i 1.24626i 0.782117 + 0.623132i \(0.214140\pi\)
−0.782117 + 0.623132i \(0.785860\pi\)
\(102\) −6.38902 140.590i −0.0626374 1.37833i
\(103\) −46.2904 + 46.2904i −0.449421 + 0.449421i −0.895162 0.445741i \(-0.852940\pi\)
0.445741 + 0.895162i \(0.352940\pi\)
\(104\) −48.6555 + 75.4796i −0.467842 + 0.725765i
\(105\) 65.4646 + 88.4574i 0.623472 + 0.842452i
\(106\) −43.6861 37.8895i −0.412133 0.357448i
\(107\) −107.270 + 107.270i −1.00252 + 1.00252i −0.00252770 + 0.999997i \(0.500805\pi\)
−0.999997 + 0.00252770i \(0.999195\pi\)
\(108\) 81.1881 + 71.2214i 0.751742 + 0.659458i
\(109\) 22.8980i 0.210073i 0.994468 + 0.105037i \(0.0334960\pi\)
−0.994468 + 0.105037i \(0.966504\pi\)
\(110\) 53.0938 47.8579i 0.482671 0.435071i
\(111\) −2.89296 + 113.313i −0.0260627 + 1.02083i
\(112\) 102.921 + 56.4459i 0.918937 + 0.503982i
\(113\) 85.7431 85.7431i 0.758788 0.758788i −0.217314 0.976102i \(-0.569729\pi\)
0.976102 + 0.217314i \(0.0697294\pi\)
\(114\) 53.8549 + 49.1729i 0.472412 + 0.431341i
\(115\) 9.59812 77.7940i 0.0834619 0.676470i
\(116\) −103.355 + 14.7629i −0.890991 + 0.127266i
\(117\) −74.9899 + 67.6992i −0.640939 + 0.578626i
\(118\) −118.526 + 8.42219i −1.00446 + 0.0713745i
\(119\) 172.083i 1.44607i
\(120\) −7.73844 119.750i −0.0644870 0.997919i
\(121\) −69.9067 −0.577741
\(122\) 1.05313 + 14.8207i 0.00863219 + 0.121481i
\(123\) 73.1876 + 77.0226i 0.595021 + 0.626200i
\(124\) −4.94443 34.6160i −0.0398745 0.279162i
\(125\) −114.282 + 50.6415i −0.914258 + 0.405132i
\(126\) 95.2164 + 91.5025i 0.755686 + 0.726210i
\(127\) −77.5158 77.5158i −0.610361 0.610361i 0.332679 0.943040i \(-0.392047\pi\)
−0.943040 + 0.332679i \(0.892047\pi\)
\(128\) −60.9807 112.540i −0.476412 0.879222i
\(129\) −2.67358 + 104.720i −0.0207254 + 0.811781i
\(130\) 112.103 + 5.81434i 0.862328 + 0.0447257i
\(131\) −20.0258 −0.152869 −0.0764345 0.997075i \(-0.524354\pi\)
−0.0764345 + 0.997075i \(0.524354\pi\)
\(132\) 53.2013 67.2834i 0.403040 0.509723i
\(133\) 63.0533 + 63.0533i 0.474085 + 0.474085i
\(134\) −66.4338 + 76.5972i −0.495775 + 0.571621i
\(135\) 26.7322 132.327i 0.198017 0.980199i
\(136\) −101.668 + 157.718i −0.747557 + 1.15969i
\(137\) −8.45410 8.45410i −0.0617088 0.0617088i 0.675579 0.737288i \(-0.263894\pi\)
−0.737288 + 0.675579i \(0.763894\pi\)
\(138\) −4.27012 93.9637i −0.0309429 0.680896i
\(139\) −165.614 −1.19147 −0.595734 0.803182i \(-0.703139\pi\)
−0.595734 + 0.803182i \(0.703139\pi\)
\(140\) −2.80509 146.702i −0.0200364 1.04787i
\(141\) 6.34551 248.543i 0.0450036 1.76272i
\(142\) 6.55430 + 92.2392i 0.0461571 + 0.649572i
\(143\) 56.7370 + 56.7370i 0.396762 + 0.396762i
\(144\) −33.2076 140.119i −0.230609 0.973047i
\(145\) 80.2867 + 102.886i 0.553701 + 0.709561i
\(146\) −19.6960 + 22.7092i −0.134904 + 0.155542i
\(147\) 9.96809 + 10.4904i 0.0678101 + 0.0713633i
\(148\) 90.6821 120.904i 0.612717 0.816921i
\(149\) 26.8277 0.180052 0.0900259 0.995939i \(-0.471305\pi\)
0.0900259 + 0.995939i \(0.471305\pi\)
\(150\) −125.032 + 82.8668i −0.833549 + 0.552445i
\(151\) 6.88363i 0.0455870i −0.999740 0.0227935i \(-0.992744\pi\)
0.999740 0.0227935i \(-0.00725602\pi\)
\(152\) −20.5374 95.0422i −0.135115 0.625278i
\(153\) −156.694 + 141.460i −1.02415 + 0.924577i
\(154\) 68.7193 79.2324i 0.446229 0.514496i
\(155\) −34.4591 + 26.8899i −0.222317 + 0.173483i
\(156\) 133.793 15.6377i 0.857649 0.100242i
\(157\) −33.6577 + 33.6577i −0.214380 + 0.214380i −0.806125 0.591745i \(-0.798439\pi\)
0.591745 + 0.806125i \(0.298439\pi\)
\(158\) 9.68957 + 136.362i 0.0613264 + 0.863051i
\(159\) −2.21388 + 86.7139i −0.0139237 + 0.545371i
\(160\) −84.1020 + 136.113i −0.525637 + 0.850709i
\(161\) 115.012i 0.714361i
\(162\) 5.04752 161.921i 0.0311576 0.999514i
\(163\) −1.81560 + 1.81560i −0.0111386 + 0.0111386i −0.712654 0.701516i \(-0.752507\pi\)
0.701516 + 0.712654i \(0.252507\pi\)
\(164\) −20.0317 140.242i −0.122145 0.855136i
\(165\) −106.043 15.8407i −0.642683 0.0960040i
\(166\) 142.041 163.772i 0.855671 0.986577i
\(167\) −110.613 + 110.613i −0.662355 + 0.662355i −0.955935 0.293579i \(-0.905153\pi\)
0.293579 + 0.955935i \(0.405153\pi\)
\(168\) −32.7846 172.996i −0.195147 1.02974i
\(169\) 42.9918i 0.254389i
\(170\) 234.243 + 12.1493i 1.37790 + 0.0714665i
\(171\) 5.58200 109.248i 0.0326433 0.638876i
\(172\) 83.8054 111.736i 0.487241 0.649627i
\(173\) 58.8176 58.8176i 0.339986 0.339986i −0.516376 0.856362i \(-0.672719\pi\)
0.856362 + 0.516376i \(0.172719\pi\)
\(174\) 115.650 + 105.596i 0.664656 + 0.606872i
\(175\) −157.325 + 94.2799i −0.898999 + 0.538742i
\(176\) −109.794 + 32.0184i −0.623829 + 0.181923i
\(177\) 122.775 + 129.209i 0.693646 + 0.729992i
\(178\) 5.82505 + 81.9764i 0.0327250 + 0.460542i
\(179\) 221.072i 1.23504i −0.786555 0.617520i \(-0.788138\pi\)
0.786555 0.617520i \(-0.211862\pi\)
\(180\) −131.278 + 123.151i −0.729322 + 0.684171i
\(181\) 184.455 1.01909 0.509545 0.860444i \(-0.329814\pi\)
0.509545 + 0.860444i \(0.329814\pi\)
\(182\) 164.294 11.6744i 0.902716 0.0641449i
\(183\) 16.1565 15.3520i 0.0882868 0.0838910i
\(184\) −67.9500 + 105.411i −0.369294 + 0.572887i
\(185\) −187.494 23.1328i −1.01348 0.125042i
\(186\) −35.3665 + 38.7340i −0.190143 + 0.208247i
\(187\) 118.554 + 118.554i 0.633980 + 0.633980i
\(188\) −198.905 + 265.195i −1.05801 + 1.41061i
\(189\) 15.1537 197.504i 0.0801780 1.04499i
\(190\) −90.2814 + 81.3781i −0.475165 + 0.428306i
\(191\) 247.515 1.29589 0.647944 0.761688i \(-0.275629\pi\)
0.647944 + 0.761688i \(0.275629\pi\)
\(192\) −72.1595 + 177.924i −0.375831 + 0.926688i
\(193\) −218.501 218.501i −1.13213 1.13213i −0.989823 0.142305i \(-0.954549\pi\)
−0.142305 0.989823i \(-0.545451\pi\)
\(194\) 174.638 + 151.466i 0.900196 + 0.780752i
\(195\) −100.166 135.346i −0.513670 0.694085i
\(196\) −2.72830 19.1009i −0.0139199 0.0974534i
\(197\) 199.518 + 199.518i 1.01278 + 1.01278i 0.999917 + 0.0128655i \(0.00409532\pi\)
0.0128655 + 0.999917i \(0.495905\pi\)
\(198\) −128.638 + 2.55867i −0.649686 + 0.0129226i
\(199\) 278.384 1.39891 0.699457 0.714674i \(-0.253425\pi\)
0.699457 + 0.714674i \(0.253425\pi\)
\(200\) 199.893 + 6.53907i 0.999465 + 0.0326953i
\(201\) 152.040 + 3.88171i 0.756419 + 0.0193120i
\(202\) −251.112 + 17.8434i −1.24313 + 0.0883338i
\(203\) 135.403 + 135.403i 0.667011 + 0.667011i
\(204\) 279.567 32.6756i 1.37042 0.160174i
\(205\) −139.606 + 108.941i −0.681007 + 0.531419i
\(206\) −98.9099 85.7859i −0.480145 0.416436i
\(207\) −104.727 + 94.5455i −0.505929 + 0.456742i
\(208\) −157.477 86.3665i −0.757100 0.415224i
\(209\) −86.8797 −0.415692
\(210\) −167.190 + 143.139i −0.796142 + 0.681616i
\(211\) 85.1758i 0.403677i 0.979419 + 0.201838i \(0.0646916\pi\)
−0.979419 + 0.201838i \(0.935308\pi\)
\(212\) 69.3956 92.5236i 0.327338 0.436432i
\(213\) 100.552 95.5459i 0.472077 0.448572i
\(214\) −229.207 198.794i −1.07106 0.928945i
\(215\) −173.276 21.3786i −0.805935 0.0994351i
\(216\) −130.576 + 172.064i −0.604516 + 0.796593i
\(217\) −45.3497 + 45.3497i −0.208985 + 0.208985i
\(218\) −45.6808 + 3.24597i −0.209545 + 0.0148898i
\(219\) 45.0762 + 1.15083i 0.205827 + 0.00525494i
\(220\) 103.001 + 99.1364i 0.468188 + 0.450620i
\(221\) 263.299i 1.19140i
\(222\) −226.465 + 10.2916i −1.02011 + 0.0463585i
\(223\) 222.212 222.212i 0.996466 0.996466i −0.00352781 0.999994i \(-0.501123\pi\)
0.999994 + 0.00352781i \(0.00112294\pi\)
\(224\) −98.0181 + 213.326i −0.437581 + 0.952347i
\(225\) 215.178 + 65.7537i 0.956345 + 0.292239i
\(226\) 183.210 + 158.900i 0.810662 + 0.703098i
\(227\) 33.6138 33.6138i 0.148078 0.148078i −0.629181 0.777259i \(-0.716609\pi\)
0.777259 + 0.629181i \(0.216609\pi\)
\(228\) −90.4641 + 114.410i −0.396772 + 0.501797i
\(229\) 127.633i 0.557349i −0.960386 0.278675i \(-0.910105\pi\)
0.960386 0.278675i \(-0.0898951\pi\)
\(230\) 156.557 + 8.12004i 0.680684 + 0.0353045i
\(231\) −157.271 4.01525i −0.680827 0.0173820i
\(232\) −44.1029 204.097i −0.190098 0.879730i
\(233\) 190.936 190.936i 0.819467 0.819467i −0.166564 0.986031i \(-0.553267\pi\)
0.986031 + 0.166564i \(0.0532671\pi\)
\(234\) −145.688 140.006i −0.622599 0.598315i
\(235\) 411.256 + 50.7402i 1.75002 + 0.215916i
\(236\) −33.6040 235.262i −0.142390 0.996874i
\(237\) 148.652 141.251i 0.627224 0.595994i
\(238\) 343.300 24.3941i 1.44244 0.102496i
\(239\) 164.867i 0.689820i 0.938636 + 0.344910i \(0.112090\pi\)
−0.938636 + 0.344910i \(0.887910\pi\)
\(240\) 237.801 32.4135i 0.990838 0.135056i
\(241\) −20.3865 −0.0845915 −0.0422957 0.999105i \(-0.513467\pi\)
−0.0422957 + 0.999105i \(0.513467\pi\)
\(242\) −9.90982 139.462i −0.0409497 0.576288i
\(243\) −192.300 + 148.559i −0.791356 + 0.611355i
\(244\) −29.4176 + 4.20191i −0.120564 + 0.0172209i
\(245\) −19.0143 + 14.8377i −0.0776092 + 0.0605619i
\(246\) −143.283 + 156.926i −0.582451 + 0.637909i
\(247\) −96.4763 96.4763i −0.390592 0.390592i
\(248\) 68.3570 14.7711i 0.275633 0.0595609i
\(249\) −325.076 8.29945i −1.30553 0.0333311i
\(250\) −117.229 220.811i −0.468915 0.883243i
\(251\) 425.326 1.69452 0.847262 0.531175i \(-0.178249\pi\)
0.847262 + 0.531175i \(0.178249\pi\)
\(252\) −169.047 + 202.925i −0.670822 + 0.805258i
\(253\) 79.2362 + 79.2362i 0.313187 + 0.313187i
\(254\) 143.653 165.630i 0.565564 0.652087i
\(255\) −209.300 282.812i −0.820786 1.10907i
\(256\) 215.870 137.608i 0.843243 0.537532i
\(257\) −162.977 162.977i −0.634150 0.634150i 0.314956 0.949106i \(-0.398010\pi\)
−0.949106 + 0.314956i \(0.898010\pi\)
\(258\) −209.292 + 9.51114i −0.811209 + 0.0368649i
\(259\) −277.195 −1.07025
\(260\) 4.29200 + 224.466i 0.0165077 + 0.863330i
\(261\) 11.9870 234.603i 0.0459273 0.898862i
\(262\) −2.83882 39.9510i −0.0108352 0.152485i
\(263\) −216.217 216.217i −0.822117 0.822117i 0.164294 0.986411i \(-0.447465\pi\)
−0.986411 + 0.164294i \(0.947465\pi\)
\(264\) 141.770 + 96.5969i 0.537008 + 0.365898i
\(265\) −143.482 17.7027i −0.541443 0.0668025i
\(266\) −116.851 + 134.728i −0.439290 + 0.506495i
\(267\) 89.3647 84.9152i 0.334699 0.318035i
\(268\) −162.227 121.675i −0.605324 0.454012i
\(269\) −90.1584 −0.335161 −0.167581 0.985858i \(-0.553595\pi\)
−0.167581 + 0.985858i \(0.553595\pi\)
\(270\) 267.778 + 34.5716i 0.991769 + 0.128043i
\(271\) 406.310i 1.49930i 0.661836 + 0.749649i \(0.269777\pi\)
−0.661836 + 0.749649i \(0.730223\pi\)
\(272\) −329.054 180.466i −1.20976 0.663479i
\(273\) −170.184 179.102i −0.623385 0.656050i
\(274\) 15.6672 18.0641i 0.0571797 0.0659274i
\(275\) 43.4341 173.340i 0.157942 0.630328i
\(276\) 186.849 21.8389i 0.676991 0.0791263i
\(277\) −190.299 + 190.299i −0.687001 + 0.687001i −0.961568 0.274567i \(-0.911466\pi\)
0.274567 + 0.961568i \(0.411466\pi\)
\(278\) −23.4771 330.395i −0.0844500 1.18847i
\(279\) 78.5741 + 4.01474i 0.281628 + 0.0143897i
\(280\) 292.269 26.3923i 1.04382 0.0942582i
\(281\) 150.443i 0.535385i −0.963504 0.267692i \(-0.913739\pi\)
0.963504 0.267692i \(-0.0862611\pi\)
\(282\) 496.736 22.5739i 1.76148 0.0800492i
\(283\) −152.489 + 152.489i −0.538830 + 0.538830i −0.923185 0.384355i \(-0.874424\pi\)
0.384355 + 0.923185i \(0.374424\pi\)
\(284\) −183.085 + 26.1513i −0.644667 + 0.0920819i
\(285\) 180.316 + 26.9357i 0.632689 + 0.0945111i
\(286\) −105.146 + 121.232i −0.367642 + 0.423886i
\(287\) −183.728 + 183.728i −0.640169 + 0.640169i
\(288\) 274.825 86.1112i 0.954254 0.298997i
\(289\) 261.175i 0.903718i
\(290\) −193.874 + 174.755i −0.668531 + 0.602602i
\(291\) 8.85011 346.645i 0.0304128 1.19122i
\(292\) −48.0962 36.0737i −0.164713 0.123540i
\(293\) −132.745 + 132.745i −0.453054 + 0.453054i −0.896367 0.443313i \(-0.853803\pi\)
0.443313 + 0.896367i \(0.353803\pi\)
\(294\) −19.5150 + 21.3731i −0.0663775 + 0.0726977i
\(295\) −234.196 + 182.753i −0.793883 + 0.619502i
\(296\) 254.055 + 163.769i 0.858295 + 0.553273i
\(297\) 125.628 + 146.508i 0.422990 + 0.493293i
\(298\) 3.80304 + 53.5205i 0.0127619 + 0.179599i
\(299\) 175.977i 0.588552i
\(300\) −183.041 237.689i −0.610137 0.792296i
\(301\) −256.174 −0.851078
\(302\) 13.7326 0.975809i 0.0454723 0.00323115i
\(303\) 260.114 + 273.744i 0.858463 + 0.903446i
\(304\) 186.695 54.4445i 0.614128 0.179094i
\(305\) 22.8518 + 29.2842i 0.0749239 + 0.0960139i
\(306\) −304.422 292.548i −0.994842 0.956038i
\(307\) −88.3919 88.3919i −0.287922 0.287922i 0.548336 0.836258i \(-0.315261\pi\)
−0.836258 + 0.548336i \(0.815261\pi\)
\(308\) 167.808 + 125.861i 0.544830 + 0.408640i
\(309\) −5.01245 + 196.329i −0.0162215 + 0.635370i
\(310\) −58.5294 64.9330i −0.188805 0.209461i
\(311\) −514.733 −1.65509 −0.827545 0.561399i \(-0.810263\pi\)
−0.827545 + 0.561399i \(0.810263\pi\)
\(312\) 50.1630 + 264.697i 0.160779 + 0.848387i
\(313\) 387.047 + 387.047i 1.23657 + 1.23657i 0.961393 + 0.275179i \(0.0887372\pi\)
0.275179 + 0.961393i \(0.411263\pi\)
\(314\) −71.9174 62.3749i −0.229036 0.198646i
\(315\) 325.167 + 57.0929i 1.03228 + 0.181247i
\(316\) −270.665 + 38.6608i −0.856534 + 0.122344i
\(317\) −3.71813 3.71813i −0.0117291 0.0117291i 0.701218 0.712947i \(-0.252640\pi\)
−0.712947 + 0.701218i \(0.752640\pi\)
\(318\) −173.306 + 7.87577i −0.544986 + 0.0247666i
\(319\) −186.569 −0.584855
\(320\) −283.464 148.486i −0.885826 0.464018i
\(321\) −11.6155 + 454.960i −0.0361854 + 1.41732i
\(322\) 229.446 16.3039i 0.712564 0.0506331i
\(323\) −201.591 201.591i −0.624121 0.624121i
\(324\) 323.744 12.8840i 0.999209 0.0397653i
\(325\) 240.719 144.255i 0.740673 0.443862i
\(326\) −3.87944 3.36469i −0.0119001 0.0103211i
\(327\) 47.3184 + 49.7978i 0.144705 + 0.152287i
\(328\) 276.939 59.8431i 0.844328 0.182449i
\(329\) 608.008 1.84805
\(330\) 16.5692 213.798i 0.0502098 0.647872i
\(331\) 573.217i 1.73177i −0.500241 0.865886i \(-0.666755\pi\)
0.500241 0.865886i \(-0.333245\pi\)
\(332\) 346.855 + 260.152i 1.04474 + 0.783592i
\(333\) 227.868 + 252.407i 0.684287 + 0.757980i
\(334\) −236.351 204.990i −0.707636 0.613742i
\(335\) −31.0390 + 251.576i −0.0926538 + 0.750972i
\(336\) 340.474 89.9279i 1.01332 0.267643i
\(337\) 143.969 143.969i 0.427209 0.427209i −0.460468 0.887676i \(-0.652318\pi\)
0.887676 + 0.460468i \(0.152318\pi\)
\(338\) 85.7674 6.09443i 0.253750 0.0180309i
\(339\) 9.28449 363.659i 0.0273879 1.07274i
\(340\) 8.96830 + 469.030i 0.0263774 + 1.37950i
\(341\) 62.4863i 0.183244i
\(342\) 218.737 4.35080i 0.639583 0.0127216i
\(343\) 229.172 229.172i 0.668139 0.668139i
\(344\) 234.790 + 151.350i 0.682528 + 0.439970i
\(345\) −139.887 189.019i −0.405469 0.547880i
\(346\) 125.677 + 109.002i 0.363229 + 0.315033i
\(347\) 358.220 358.220i 1.03233 1.03233i 0.0328744 0.999459i \(-0.489534\pi\)
0.999459 0.0328744i \(-0.0104661\pi\)
\(348\) −194.266 + 245.688i −0.558236 + 0.705999i
\(349\) 153.076i 0.438613i 0.975656 + 0.219307i \(0.0703795\pi\)
−0.975656 + 0.219307i \(0.929621\pi\)
\(350\) −210.388 300.493i −0.601107 0.858553i
\(351\) −23.1862 + 302.196i −0.0660576 + 0.860957i
\(352\) −79.4399 214.497i −0.225682 0.609366i
\(353\) −199.291 + 199.291i −0.564563 + 0.564563i −0.930600 0.366037i \(-0.880714\pi\)
0.366037 + 0.930600i \(0.380714\pi\)
\(354\) −240.363 + 263.249i −0.678991 + 0.743642i
\(355\) 142.222 + 182.255i 0.400624 + 0.513395i
\(356\) −162.715 + 23.2416i −0.457064 + 0.0652854i
\(357\) −355.607 374.240i −0.996097 1.04829i
\(358\) 441.032 31.3387i 1.23193 0.0875383i
\(359\) 54.0713i 0.150616i 0.997160 + 0.0753082i \(0.0239941\pi\)
−0.997160 + 0.0753082i \(0.976006\pi\)
\(360\) −264.292 244.438i −0.734144 0.678994i
\(361\) −213.269 −0.590772
\(362\) 26.1480 + 367.983i 0.0722321 + 1.01653i
\(363\) −152.031 + 144.461i −0.418818 + 0.397965i
\(364\) 46.5800 + 326.107i 0.127967 + 0.895899i
\(365\) −9.20231 + 74.5859i −0.0252118 + 0.204345i
\(366\) 32.9172 + 30.0554i 0.0899376 + 0.0821187i
\(367\) 8.93510 + 8.93510i 0.0243463 + 0.0243463i 0.719175 0.694829i \(-0.244520\pi\)
−0.694829 + 0.719175i \(0.744520\pi\)
\(368\) −219.925 120.615i −0.597621 0.327759i
\(369\) 318.333 + 16.2652i 0.862690 + 0.0440791i
\(370\) 19.5704 377.325i 0.0528930 1.01980i
\(371\) −212.127 −0.571771
\(372\) −82.2866 65.0643i −0.221201 0.174904i
\(373\) −409.810 409.810i −1.09869 1.09869i −0.994565 0.104121i \(-0.966797\pi\)
−0.104121 0.994565i \(-0.533203\pi\)
\(374\) −219.706 + 253.318i −0.587450 + 0.677321i
\(375\) −143.888 + 346.297i −0.383700 + 0.923458i
\(376\) −557.253 359.216i −1.48206 0.955361i
\(377\) −207.177 207.177i −0.549541 0.549541i
\(378\) 396.163 + 2.23333i 1.04805 + 0.00590828i
\(379\) 5.84018 0.0154095 0.00770473 0.999970i \(-0.497547\pi\)
0.00770473 + 0.999970i \(0.497547\pi\)
\(380\) −175.145 168.573i −0.460908 0.443612i
\(381\) −328.765 8.39362i −0.862899 0.0220305i
\(382\) 35.0872 + 493.784i 0.0918512 + 1.29263i
\(383\) 137.693 + 137.693i 0.359513 + 0.359513i 0.863633 0.504121i \(-0.168183\pi\)
−0.504121 + 0.863633i \(0.668183\pi\)
\(384\) −365.183 118.734i −0.950996 0.309203i
\(385\) 32.1069 260.230i 0.0833945 0.675923i
\(386\) 404.928 466.876i 1.04904 1.20952i
\(387\) 210.588 + 233.266i 0.544155 + 0.602756i
\(388\) −277.414 + 369.869i −0.714983 + 0.953271i
\(389\) −34.5568 −0.0888349 −0.0444174 0.999013i \(-0.514143\pi\)
−0.0444174 + 0.999013i \(0.514143\pi\)
\(390\) 255.813 219.014i 0.655931 0.561574i
\(391\) 367.711i 0.940438i
\(392\) 37.7189 8.15058i 0.0962217 0.0207923i
\(393\) −43.5516 + 41.3832i −0.110818 + 0.105301i
\(394\) −369.750 + 426.316i −0.938451 + 1.08202i
\(395\) 210.254 + 269.437i 0.532288 + 0.682120i
\(396\) −23.3399 256.266i −0.0589391 0.647136i
\(397\) 446.029 446.029i 1.12350 1.12350i 0.132286 0.991212i \(-0.457768\pi\)
0.991212 0.132286i \(-0.0422318\pi\)
\(398\) 39.4631 + 555.368i 0.0991536 + 1.39540i
\(399\) 267.425 + 6.82759i 0.670239 + 0.0171117i
\(400\) 15.2912 + 399.708i 0.0382279 + 0.999269i
\(401\) 103.887i 0.259071i −0.991575 0.129535i \(-0.958651\pi\)
0.991575 0.129535i \(-0.0413486\pi\)
\(402\) 13.8090 + 303.866i 0.0343508 + 0.755886i
\(403\) 69.3885 69.3885i 0.172180 0.172180i
\(404\) −71.1942 498.432i −0.176223 1.23374i
\(405\) −215.315 343.022i −0.531643 0.846969i
\(406\) −250.931 + 289.320i −0.618056 + 0.712610i
\(407\) 190.970 190.970i 0.469214 0.469214i
\(408\) 104.818 + 553.095i 0.256906 + 1.35562i
\(409\) 583.243i 1.42602i −0.701153 0.713011i \(-0.747331\pi\)
0.701153 0.713011i \(-0.252669\pi\)
\(410\) −237.124 263.067i −0.578352 0.641628i
\(411\) −35.8560 0.915433i −0.0872409 0.00222733i
\(412\) 157.119 209.483i 0.381357 0.508454i
\(413\) −308.212 + 308.212i −0.746276 + 0.746276i
\(414\) −203.461 195.525i −0.491453 0.472283i
\(415\) 66.3643 537.891i 0.159914 1.29612i
\(416\) 149.975 326.404i 0.360517 0.784626i
\(417\) −360.173 + 342.240i −0.863724 + 0.820719i
\(418\) −12.3159 173.322i −0.0294638 0.414647i
\(419\) 231.688i 0.552954i −0.961021 0.276477i \(-0.910833\pi\)
0.961021 0.276477i \(-0.0891669\pi\)
\(420\) −309.259 313.247i −0.736332 0.745827i
\(421\) 252.861 0.600620 0.300310 0.953842i \(-0.402910\pi\)
0.300310 + 0.953842i \(0.402910\pi\)
\(422\) −169.923 + 12.0743i −0.402662 + 0.0286122i
\(423\) −499.812 553.638i −1.18159 1.30884i
\(424\) 194.419 + 125.326i 0.458536 + 0.295581i
\(425\) 502.992 301.427i 1.18351 0.709241i
\(426\) 204.865 + 187.055i 0.480905 + 0.439096i
\(427\) 38.5394 + 38.5394i 0.0902562 + 0.0902562i
\(428\) 364.097 485.442i 0.850693 1.13421i
\(429\) 240.636 + 6.14364i 0.560924 + 0.0143208i
\(430\) 18.0863 348.711i 0.0420612 0.810956i
\(431\) −122.832 −0.284993 −0.142496 0.989795i \(-0.545513\pi\)
−0.142496 + 0.989795i \(0.545513\pi\)
\(432\) −361.773 236.103i −0.837437 0.546534i
\(433\) 317.452 + 317.452i 0.733145 + 0.733145i 0.971241 0.238097i \(-0.0765235\pi\)
−0.238097 + 0.971241i \(0.576523\pi\)
\(434\) −96.9000 84.0427i −0.223272 0.193647i
\(435\) 387.219 + 57.8427i 0.890158 + 0.132972i
\(436\) −12.9512 90.6716i −0.0297046 0.207962i
\(437\) −134.734 134.734i −0.308316 0.308316i
\(438\) 4.09403 + 90.0888i 0.00934710 + 0.205682i
\(439\) 238.776 0.543908 0.271954 0.962310i \(-0.412330\pi\)
0.271954 + 0.962310i \(0.412330\pi\)
\(440\) −183.173 + 219.538i −0.416302 + 0.498950i
\(441\) 43.3566 + 2.21530i 0.0983143 + 0.00502336i
\(442\) −525.274 + 37.3247i −1.18840 + 0.0844451i
\(443\) 228.090 + 228.090i 0.514875 + 0.514875i 0.916016 0.401141i \(-0.131386\pi\)
−0.401141 + 0.916016i \(0.631386\pi\)
\(444\) −52.6346 450.333i −0.118547 1.01426i
\(445\) 126.398 + 161.977i 0.284040 + 0.363993i
\(446\) 474.806 + 411.806i 1.06459 + 0.923331i
\(447\) 58.3442 55.4392i 0.130524 0.124025i
\(448\) −439.473 165.303i −0.980967 0.368979i
\(449\) −483.206 −1.07618 −0.538091 0.842887i \(-0.680854\pi\)
−0.538091 + 0.842887i \(0.680854\pi\)
\(450\) −100.674 + 438.594i −0.223719 + 0.974654i
\(451\) 253.155i 0.561320i
\(452\) −291.030 + 388.023i −0.643871 + 0.858458i
\(453\) −14.2249 14.9703i −0.0314016 0.0330471i
\(454\) 71.8235 + 62.2934i 0.158202 + 0.137210i
\(455\) 324.629 253.322i 0.713469 0.556751i
\(456\) −241.068 164.255i −0.528657 0.360208i
\(457\) 48.6424 48.6424i 0.106438 0.106438i −0.651882 0.758320i \(-0.726020\pi\)
0.758320 + 0.651882i \(0.226020\pi\)
\(458\) 254.624 18.0930i 0.555947 0.0395043i
\(459\) −48.4486 + 631.451i −0.105552 + 1.37571i
\(460\) 5.99400 + 313.478i 0.0130304 + 0.681474i
\(461\) 436.442i 0.946728i 0.880867 + 0.473364i \(0.156960\pi\)
−0.880867 + 0.473364i \(0.843040\pi\)
\(462\) −14.2841 314.320i −0.0309179 0.680346i
\(463\) 31.1103 31.1103i 0.0671929 0.0671929i −0.672712 0.739905i \(-0.734871\pi\)
0.739905 + 0.672712i \(0.234871\pi\)
\(464\) 400.916 116.916i 0.864043 0.251975i
\(465\) −19.3729 + 129.689i −0.0416621 + 0.278900i
\(466\) 407.978 + 353.845i 0.875489 + 0.759323i
\(467\) 228.219 228.219i 0.488693 0.488693i −0.419201 0.907894i \(-0.637690\pi\)
0.907894 + 0.419201i \(0.137690\pi\)
\(468\) 258.655 310.491i 0.552681 0.663441i
\(469\) 371.934i 0.793036i
\(470\) −42.9263 + 827.636i −0.0913327 + 1.76093i
\(471\) −3.64455 + 142.751i −0.00773790 + 0.303081i
\(472\) 464.577 100.389i 0.984274 0.212689i
\(473\) 176.488 176.488i 0.373125 0.373125i
\(474\) 302.863 + 276.533i 0.638952 + 0.583403i
\(475\) −73.8559 + 294.750i −0.155486 + 0.620526i
\(476\) 97.3308 + 681.414i 0.204477 + 1.43154i
\(477\) 174.379 + 193.158i 0.365574 + 0.404943i
\(478\) −328.904 + 23.3712i −0.688085 + 0.0488937i
\(479\) 698.050i 1.45731i 0.684883 + 0.728653i \(0.259853\pi\)
−0.684883 + 0.728653i \(0.740147\pi\)
\(480\) 98.3741 + 469.811i 0.204946 + 0.978773i
\(481\) 424.129 0.881765
\(482\) −2.88995 40.6705i −0.00599575 0.0843787i
\(483\) −237.671 250.125i −0.492073 0.517857i
\(484\) 276.817 39.5396i 0.571936 0.0816934i
\(485\) 573.580 + 70.7675i 1.18264 + 0.145912i
\(486\) −323.631 362.572i −0.665908 0.746034i
\(487\) −521.267 521.267i −1.07036 1.07036i −0.997329 0.0730343i \(-0.976732\pi\)
−0.0730343 0.997329i \(-0.523268\pi\)
\(488\) −12.5529 58.0916i −0.0257231 0.119040i
\(489\) −0.196598 + 7.70043i −0.000402041 + 0.0157473i
\(490\) −32.2961 35.8295i −0.0659104 0.0731215i
\(491\) −423.603 −0.862736 −0.431368 0.902176i \(-0.641969\pi\)
−0.431368 + 0.902176i \(0.641969\pi\)
\(492\) −333.373 263.600i −0.677588 0.535771i
\(493\) −432.905 432.905i −0.878103 0.878103i
\(494\) 178.791 206.144i 0.361925 0.417295i
\(495\) −263.353 + 184.686i −0.532027 + 0.373104i
\(496\) 39.1580 + 134.276i 0.0789476 + 0.270718i
\(497\) 239.856 + 239.856i 0.482608 + 0.482608i
\(498\) −29.5249 649.693i −0.0592870 1.30460i
\(499\) −422.547 −0.846787 −0.423393 0.905946i \(-0.639161\pi\)
−0.423393 + 0.905946i \(0.639161\pi\)
\(500\) 423.893 265.169i 0.847786 0.530339i
\(501\) −11.9775 + 469.140i −0.0239072 + 0.936407i
\(502\) 60.2933 + 848.512i 0.120106 + 1.69026i
\(503\) −71.8560 71.8560i −0.142855 0.142855i 0.632063 0.774917i \(-0.282209\pi\)
−0.774917 + 0.632063i \(0.782209\pi\)
\(504\) −428.793 308.478i −0.850780 0.612059i
\(505\) −496.172 + 387.184i −0.982518 + 0.766702i
\(506\) −146.842 + 169.306i −0.290201 + 0.334597i
\(507\) −88.8421 93.4973i −0.175231 0.184413i
\(508\) 350.791 + 263.104i 0.690534 + 0.517922i
\(509\) −196.155 −0.385374 −0.192687 0.981260i \(-0.561720\pi\)
−0.192687 + 0.981260i \(0.561720\pi\)
\(510\) 534.532 457.639i 1.04810 0.897331i
\(511\) 110.269i 0.215791i
\(512\) 305.125 + 411.148i 0.595948 + 0.803023i
\(513\) −213.620 249.124i −0.416413 0.485622i
\(514\) 302.030 348.237i 0.587608 0.677503i
\(515\) −324.859 40.0807i −0.630795 0.0778265i
\(516\) −48.6432 416.183i −0.0942698 0.806556i
\(517\) −418.880 + 418.880i −0.810213 + 0.810213i
\(518\) −39.2946 552.995i −0.0758582 1.06756i
\(519\) 6.36893 249.461i 0.0122715 0.480657i
\(520\) −447.194 + 40.3822i −0.859988 + 0.0776580i
\(521\) 22.8866i 0.0439282i 0.999759 + 0.0219641i \(0.00699195\pi\)
−0.999759 + 0.0219641i \(0.993008\pi\)
\(522\) 469.725 9.34308i 0.899856 0.0178986i
\(523\) −665.171 + 665.171i −1.27184 + 1.27184i −0.326715 + 0.945123i \(0.605942\pi\)
−0.945123 + 0.326715i \(0.894058\pi\)
\(524\) 79.2985 11.3267i 0.151333 0.0216159i
\(525\) −147.317 + 530.147i −0.280604 + 1.00980i
\(526\) 400.696 461.997i 0.761779 0.878320i
\(527\) 144.990 144.990i 0.275124 0.275124i
\(528\) −172.611 + 296.521i −0.326915 + 0.561592i
\(529\) 283.239i 0.535423i
\(530\) 14.9765 288.752i 0.0282576 0.544816i
\(531\) 534.016 + 27.2855i 1.00568 + 0.0513851i
\(532\) −285.342 214.016i −0.536358 0.402285i
\(533\) 281.118 281.118i 0.527426 0.527426i
\(534\) 182.071 + 166.243i 0.340958 + 0.311316i
\(535\) −752.806 92.8802i −1.40711 0.173608i
\(536\) 219.741 340.886i 0.409965 0.635981i
\(537\) −456.843 480.781i −0.850731 0.895309i
\(538\) −12.7807 179.863i −0.0237559 0.334318i
\(539\) 34.4795i 0.0639694i
\(540\) −31.0098 + 539.109i −0.0574255 + 0.998350i
\(541\) 197.624 0.365294 0.182647 0.983179i \(-0.441533\pi\)
0.182647 + 0.983179i \(0.441533\pi\)
\(542\) −810.575 + 57.5976i −1.49553 + 0.106269i
\(543\) 401.148 381.175i 0.738763 0.701979i
\(544\) 313.379 682.036i 0.576064 1.25374i
\(545\) −90.2605 + 70.4342i −0.165616 + 0.129237i
\(546\) 333.177 364.901i 0.610215 0.668317i
\(547\) 547.610 + 547.610i 1.00111 + 1.00111i 0.999999 + 0.00111506i \(0.000354935\pi\)
0.00111506 + 0.999999i \(0.499645\pi\)
\(548\) 38.2583 + 28.6949i 0.0698144 + 0.0523630i
\(549\) 3.41183 66.7744i 0.00621463 0.121629i
\(550\) 351.965 + 62.0774i 0.639937 + 0.112868i
\(551\) 317.244 0.575760
\(552\) 70.0552 + 369.663i 0.126912 + 0.669679i
\(553\) 354.592 + 354.592i 0.641216 + 0.641216i
\(554\) −406.618 352.665i −0.733967 0.636579i
\(555\) −455.561 + 337.146i −0.820830 + 0.607471i
\(556\) 655.800 93.6722i 1.17950 0.168475i
\(557\) −13.7649 13.7649i −0.0247126 0.0247126i 0.694643 0.719355i \(-0.255563\pi\)
−0.719355 + 0.694643i \(0.755563\pi\)
\(558\) 3.12922 + 157.322i 0.00560792 + 0.281939i
\(559\) 391.966 0.701192
\(560\) 94.0833 + 579.327i 0.168006 + 1.03451i
\(561\) 502.819 + 12.8374i 0.896291 + 0.0228830i
\(562\) 300.130 21.3265i 0.534038 0.0379475i
\(563\) 50.4772 + 50.4772i 0.0896575 + 0.0896575i 0.750513 0.660856i \(-0.229806\pi\)
−0.660856 + 0.750513i \(0.729806\pi\)
\(564\) 115.450 + 987.774i 0.204699 + 1.75137i
\(565\) 601.733 + 74.2409i 1.06501 + 0.131400i
\(566\) −325.827 282.594i −0.575667 0.499283i
\(567\) −375.184 460.841i −0.661700 0.812770i
\(568\) −78.1248 361.543i −0.137544 0.636519i
\(569\) −981.959 −1.72576 −0.862882 0.505406i \(-0.831343\pi\)
−0.862882 + 0.505406i \(0.831343\pi\)
\(570\) −28.1745 + 363.544i −0.0494290 + 0.637797i
\(571\) 721.470i 1.26352i −0.775164 0.631760i \(-0.782333\pi\)
0.775164 0.631760i \(-0.217667\pi\)
\(572\) −256.758 192.577i −0.448878 0.336673i
\(573\) 538.288 511.486i 0.939420 0.892646i
\(574\) −392.578 340.488i −0.683933 0.593184i
\(575\) 336.177 201.460i 0.584655 0.350365i
\(576\) 210.748 + 536.061i 0.365882 + 0.930661i
\(577\) −581.890 + 581.890i −1.00847 + 1.00847i −0.00851059 + 0.999964i \(0.502709\pi\)
−0.999964 + 0.00851059i \(0.997291\pi\)
\(578\) −521.035 + 37.0236i −0.901445 + 0.0640546i
\(579\) −926.718 23.6598i −1.60055 0.0408633i
\(580\) −376.113 362.000i −0.648471 0.624137i
\(581\) 795.228i 1.36872i
\(582\) 692.800 31.4839i 1.19038 0.0540960i
\(583\) 146.142 146.142i 0.250673 0.250673i
\(584\) 65.1479 101.064i 0.111555 0.173055i
\(585\) −497.529 87.3564i −0.850477 0.149327i
\(586\) −283.640 246.005i −0.484027 0.419803i
\(587\) −681.614 + 681.614i −1.16118 + 1.16118i −0.176965 + 0.984217i \(0.556628\pi\)
−0.984217 + 0.176965i \(0.943372\pi\)
\(588\) −45.4052 35.9020i −0.0772197 0.0610579i
\(589\) 106.253i 0.180395i
\(590\) −397.786 441.306i −0.674213 0.747977i
\(591\) 846.208 + 21.6044i 1.43182 + 0.0365556i
\(592\) −290.700 + 530.048i −0.491047 + 0.895352i
\(593\) −428.337 + 428.337i −0.722322 + 0.722322i −0.969078 0.246756i \(-0.920635\pi\)
0.246756 + 0.969078i \(0.420635\pi\)
\(594\) −274.470 + 271.393i −0.462071 + 0.456891i
\(595\) 678.325 529.326i 1.14004 0.889624i
\(596\) −106.233 + 15.1739i −0.178243 + 0.0254596i
\(597\) 605.422 575.277i 1.01411 0.963614i
\(598\) −351.069 + 24.9461i −0.587072 + 0.0417159i
\(599\) 798.031i 1.33227i −0.745830 0.666136i \(-0.767947\pi\)
0.745830 0.666136i \(-0.232053\pi\)
\(600\) 448.235 398.856i 0.747058 0.664759i
\(601\) −20.9629 −0.0348801 −0.0174400 0.999848i \(-0.505552\pi\)
−0.0174400 + 0.999848i \(0.505552\pi\)
\(602\) −36.3147 511.060i −0.0603235 0.848937i
\(603\) 338.674 305.748i 0.561649 0.507044i
\(604\) 3.89342 + 27.2579i 0.00644606 + 0.0451289i
\(605\) −215.033 275.562i −0.355427 0.455474i
\(606\) −509.238 + 557.725i −0.840327 + 0.920339i
\(607\) 648.167 + 648.167i 1.06782 + 1.06782i 0.997526 + 0.0702937i \(0.0223936\pi\)
0.0702937 + 0.997526i \(0.477606\pi\)
\(608\) 135.081 + 364.733i 0.222172 + 0.599890i
\(609\) 574.280 + 14.6618i 0.942988 + 0.0240752i
\(610\) −55.1818 + 49.7399i −0.0904619 + 0.0815408i
\(611\) −930.298 −1.52258
\(612\) 540.469 648.783i 0.883120 1.06010i
\(613\) −394.049 394.049i −0.642821 0.642821i 0.308427 0.951248i \(-0.400197\pi\)
−0.951248 + 0.308427i \(0.900197\pi\)
\(614\) 163.809 188.870i 0.266790 0.307605i
\(615\) −78.4867 + 525.417i −0.127621 + 0.854336i
\(616\) −227.301 + 352.613i −0.368995 + 0.572424i
\(617\) 597.558 + 597.558i 0.968489 + 0.968489i 0.999518 0.0310296i \(-0.00987863\pi\)
−0.0310296 + 0.999518i \(0.509879\pi\)
\(618\) −392.382 + 17.8316i −0.634922 + 0.0288537i
\(619\) 541.863 0.875384 0.437692 0.899125i \(-0.355796\pi\)
0.437692 + 0.899125i \(0.355796\pi\)
\(620\) 121.242 125.969i 0.195552 0.203176i
\(621\) −32.3808 + 422.033i −0.0521430 + 0.679602i
\(622\) −72.9675 1026.88i −0.117311 1.65093i
\(623\) 213.169 + 213.169i 0.342166 + 0.342166i
\(624\) −520.951 + 137.596i −0.834858 + 0.220507i
\(625\) −551.154 294.711i −0.881846 0.471537i
\(626\) −717.280 + 827.014i −1.14582 + 1.32111i
\(627\) −188.943 + 179.536i −0.301345 + 0.286341i
\(628\) 114.241 152.315i 0.181913 0.242540i
\(629\) 886.235 1.40896
\(630\) −67.8036 + 656.791i −0.107625 + 1.04253i
\(631\) 941.798i 1.49255i 0.665638 + 0.746274i \(0.268159\pi\)
−0.665638 + 0.746274i \(0.731841\pi\)
\(632\) −115.496 534.488i −0.182747 0.845708i
\(633\) 176.015 + 185.238i 0.278064 + 0.292635i
\(634\) 6.89048 7.94463i 0.0108683 0.0125310i
\(635\) 67.1173 543.995i 0.105697 0.856685i
\(636\) −40.2793 344.623i −0.0633323 0.541860i
\(637\) 38.2881 38.2881i 0.0601068 0.0601068i
\(638\) −26.4476 372.199i −0.0414539 0.583384i
\(639\) 21.2341 415.581i 0.0332302 0.650361i
\(640\) 256.041 586.552i 0.400065 0.916487i
\(641\) 563.904i 0.879726i −0.898065 0.439863i \(-0.855027\pi\)
0.898065 0.439863i \(-0.144973\pi\)
\(642\) −909.279 + 41.3216i −1.41632 + 0.0643639i
\(643\) −41.5913 + 41.5913i −0.0646832 + 0.0646832i −0.738708 0.674025i \(-0.764564\pi\)
0.674025 + 0.738708i \(0.264564\pi\)
\(644\) 65.0514 + 455.426i 0.101012 + 0.707183i
\(645\) −421.014 + 311.579i −0.652735 + 0.483069i
\(646\) 373.591 430.745i 0.578315 0.666789i
\(647\) 28.6494 28.6494i 0.0442804 0.0442804i −0.684620 0.728900i \(-0.740032\pi\)
0.728900 + 0.684620i \(0.240032\pi\)
\(648\) 71.5963 + 644.033i 0.110488 + 0.993877i
\(649\) 424.678i 0.654358i
\(650\) 321.909 + 459.777i 0.495244 + 0.707350i
\(651\) −4.91059 + 192.340i −0.00754315 + 0.295453i
\(652\) 6.16252 8.21634i 0.00945171 0.0126018i
\(653\) −386.414 + 386.414i −0.591753 + 0.591753i −0.938105 0.346352i \(-0.887420\pi\)
0.346352 + 0.938105i \(0.387420\pi\)
\(654\) −92.6374 + 101.458i −0.141647 + 0.155135i
\(655\) −61.5995 78.9390i −0.0940451 0.120517i
\(656\) 158.644 + 544.003i 0.241835 + 0.829272i
\(657\) 100.409 90.6466i 0.152829 0.137970i
\(658\) 86.1899 + 1212.96i 0.130988 + 1.84340i
\(659\) 851.849i 1.29264i 0.763067 + 0.646320i \(0.223693\pi\)
−0.763067 + 0.646320i \(0.776307\pi\)
\(660\) 428.869 + 2.74764i 0.649801 + 0.00416309i
\(661\) −523.764 −0.792381 −0.396191 0.918168i \(-0.629668\pi\)
−0.396191 + 0.918168i \(0.629668\pi\)
\(662\) 1143.55 81.2580i 1.72742 0.122746i
\(663\) 544.105 + 572.616i 0.820671 + 0.863673i
\(664\) −469.827 + 728.845i −0.707571 + 1.09766i
\(665\) −54.5949 + 442.499i −0.0820976 + 0.665412i
\(666\) −471.243 + 490.370i −0.707572 + 0.736291i
\(667\) −289.334 289.334i −0.433784 0.433784i
\(668\) 375.444 500.571i 0.562042 0.749358i
\(669\) 24.0617 942.458i 0.0359667 1.40876i
\(670\) −506.286 26.2591i −0.755650 0.0391927i
\(671\) −53.1026 −0.0791394
\(672\) 227.668 + 666.488i 0.338792 + 0.991798i
\(673\) −319.629 319.629i −0.474931 0.474931i 0.428575 0.903506i \(-0.359016\pi\)
−0.903506 + 0.428575i \(0.859016\pi\)
\(674\) 307.623 + 266.806i 0.456414 + 0.395854i
\(675\) 603.841 301.663i 0.894580 0.446908i
\(676\) 24.3164 + 170.239i 0.0359710 + 0.251833i
\(677\) 509.574 + 509.574i 0.752694 + 0.752694i 0.974981 0.222288i \(-0.0713524\pi\)
−0.222288 + 0.974981i \(0.571352\pi\)
\(678\) 726.804 33.0292i 1.07198 0.0487156i
\(679\) 847.991 1.24888
\(680\) −934.430 + 84.3802i −1.37416 + 0.124089i
\(681\) 3.63979 142.565i 0.00534477 0.209346i
\(682\) 124.658 8.85793i 0.182784 0.0129882i
\(683\) 278.938 + 278.938i 0.408402 + 0.408402i 0.881181 0.472779i \(-0.156749\pi\)
−0.472779 + 0.881181i \(0.656749\pi\)
\(684\) 39.6875 + 435.758i 0.0580226 + 0.637073i
\(685\) 7.32001 59.3297i 0.0106861 0.0866126i
\(686\) 489.678 + 424.704i 0.713816 + 0.619102i
\(687\) −263.752 277.572i −0.383918 0.404035i
\(688\) −268.655 + 489.853i −0.390487 + 0.711996i
\(689\) 324.570 0.471074
\(690\) 357.256 305.865i 0.517763 0.443282i
\(691\) 108.692i 0.157297i 0.996902 + 0.0786483i \(0.0250604\pi\)
−0.996902 + 0.0786483i \(0.974940\pi\)
\(692\) −199.639 + 266.174i −0.288496 + 0.384645i
\(693\) −350.326 + 316.266i −0.505520 + 0.456373i
\(694\) 765.418 + 663.857i 1.10291 + 0.956567i
\(695\) −509.429 652.827i −0.732992 0.939319i
\(696\) −517.678 352.727i −0.743791 0.506791i
\(697\) 587.408 587.408i 0.842766 0.842766i
\(698\) −305.382 + 21.6997i −0.437510 + 0.0310884i
\(699\) 20.6751 809.808i 0.0295780 1.15852i
\(700\) 569.651 462.314i 0.813787 0.660449i
\(701\) 1299.56i 1.85387i −0.375224 0.926934i \(-0.622434\pi\)
0.375224 0.926934i \(-0.377566\pi\)
\(702\) −606.159 3.41716i −0.863474 0.00486775i
\(703\) −324.728 + 324.728i −0.461918 + 0.461918i
\(704\) 416.653 188.887i 0.591837 0.268305i
\(705\) 999.241 739.507i 1.41736 1.04895i
\(706\) −425.830 369.328i −0.603158 0.523127i
\(707\) −652.985 + 652.985i −0.923599 + 0.923599i
\(708\) −559.248 442.199i −0.789898 0.624575i
\(709\) 1025.36i 1.44620i 0.690743 + 0.723100i \(0.257283\pi\)
−0.690743 + 0.723100i \(0.742717\pi\)
\(710\) −343.433 + 309.564i −0.483708 + 0.436006i
\(711\) 31.3914 614.375i 0.0441511 0.864100i
\(712\) −69.4324 321.316i −0.0975174 0.451287i
\(713\) 96.9047 96.9047i 0.135911 0.135911i
\(714\) 696.188 762.476i 0.975053 1.06789i
\(715\) −49.1259 + 398.172i −0.0687076 + 0.556884i
\(716\) 125.040 + 875.403i 0.174636 + 1.22263i
\(717\) 340.695 + 358.548i 0.475168 + 0.500066i
\(718\) −107.871 + 7.66503i −0.150238 + 0.0106755i
\(719\) 873.333i 1.21465i −0.794454 0.607325i \(-0.792243\pi\)
0.794454 0.607325i \(-0.207757\pi\)
\(720\) 450.181 561.905i 0.625251 0.780424i
\(721\) −480.278 −0.666127
\(722\) −30.2325 425.465i −0.0418733 0.589286i
\(723\) −44.3361 + 42.1285i −0.0613224 + 0.0582691i
\(724\) −730.408 + 104.329i −1.00885 + 0.144101i
\(725\) −158.601 + 632.957i −0.218760 + 0.873044i
\(726\) −309.748 282.819i −0.426650 0.389558i
\(727\) 165.684 + 165.684i 0.227901 + 0.227901i 0.811815 0.583914i \(-0.198480\pi\)
−0.583914 + 0.811815i \(0.698480\pi\)
\(728\) −643.971 + 139.154i −0.884575 + 0.191146i
\(729\) −111.212 + 720.467i −0.152554 + 0.988295i
\(730\) −150.101 7.78518i −0.205618 0.0106646i
\(731\) 819.029 1.12042
\(732\) −55.2934 + 69.9294i −0.0755374 + 0.0955319i
\(733\) 896.646 + 896.646i 1.22325 + 1.22325i 0.966468 + 0.256786i \(0.0826637\pi\)
0.256786 + 0.966468i \(0.417336\pi\)
\(734\) −16.5586 + 19.0919i −0.0225594 + 0.0260107i
\(735\) −10.6898 + 71.5613i −0.0145440 + 0.0973623i
\(736\) 209.448 455.841i 0.284576 0.619349i
\(737\) −256.239 256.239i −0.347679 0.347679i
\(738\) 12.6776 + 637.370i 0.0171783 + 0.863644i
\(739\) −135.132 −0.182858 −0.0914290 0.995812i \(-0.529143\pi\)
−0.0914290 + 0.995812i \(0.529143\pi\)
\(740\) 755.526 14.4464i 1.02098 0.0195221i
\(741\) −409.181 10.4467i −0.552201 0.0140981i
\(742\) −30.0707 423.187i −0.0405265 0.570333i
\(743\) 472.574 + 472.574i 0.636035 + 0.636035i 0.949575 0.313540i \(-0.101515\pi\)
−0.313540 + 0.949575i \(0.601515\pi\)
\(744\) 118.137 173.383i 0.158786 0.233041i
\(745\) 82.5221 + 105.751i 0.110768 + 0.141948i
\(746\) 759.465 875.652i 1.01805 1.17380i
\(747\) −724.116 + 653.716i −0.969366 + 0.875122i
\(748\) −536.507 402.397i −0.717256 0.537964i
\(749\) −1112.96 −1.48593
\(750\) −711.249 237.961i −0.948331 0.317281i
\(751\) 643.372i 0.856687i −0.903616 0.428344i \(-0.859097\pi\)
0.903616 0.428344i \(-0.140903\pi\)
\(752\) 637.630 1162.63i 0.847912 1.54604i
\(753\) 924.986 878.930i 1.22840 1.16724i
\(754\) 383.943 442.681i 0.509208 0.587110i
\(755\) 27.1343 21.1741i 0.0359394 0.0280451i
\(756\) 51.7037 + 790.649i 0.0683912 + 1.04583i
\(757\) 205.600 205.600i 0.271598 0.271598i −0.558145 0.829743i \(-0.688487\pi\)
0.829743 + 0.558145i \(0.188487\pi\)
\(758\) 0.827892 + 11.6510i 0.00109221 + 0.0153707i
\(759\) 336.061 + 8.57991i 0.442768 + 0.0113042i
\(760\) 311.469 373.305i 0.409828 0.491191i
\(761\) 477.527i 0.627499i 0.949506 + 0.313750i \(0.101585\pi\)
−0.949506 + 0.313750i \(0.898415\pi\)
\(762\) −29.8599 657.065i −0.0391863 0.862290i
\(763\) −118.787 + 118.787i −0.155684 + 0.155684i
\(764\) −980.111 + 139.996i −1.28287 + 0.183240i
\(765\) −1039.61 182.535i −1.35896 0.238607i
\(766\) −255.175 + 294.213i −0.333126 + 0.384090i
\(767\) 471.588 471.588i 0.614847 0.614847i
\(768\) 185.103 745.360i 0.241019 0.970520i
\(769\) 743.814i 0.967249i 0.875276 + 0.483624i \(0.160680\pi\)
−0.875276 + 0.483624i \(0.839320\pi\)
\(770\) 523.703 + 27.1625i 0.680134 + 0.0352760i
\(771\) −691.226 17.6476i −0.896532 0.0228892i
\(772\) 988.806 + 741.636i 1.28084 + 0.960668i
\(773\) 357.445 357.445i 0.462412 0.462412i −0.437033 0.899445i \(-0.643971\pi\)
0.899445 + 0.437033i \(0.143971\pi\)
\(774\) −435.507 + 453.184i −0.562671 + 0.585509i
\(775\) −211.992 53.1192i −0.273538 0.0685409i
\(776\) −777.203 501.000i −1.00155 0.645618i
\(777\) −602.835 + 572.820i −0.775850 + 0.737220i
\(778\) −4.89869 68.9397i −0.00629652 0.0886114i
\(779\) 430.468i 0.552591i
\(780\) 473.190 + 479.292i 0.606654 + 0.614477i
\(781\) −330.492 −0.423165
\(782\) −733.573 + 52.1260i −0.938073 + 0.0666573i
\(783\) −458.735 534.979i −0.585869 0.683242i
\(784\) 21.6071 + 74.0927i 0.0275601 + 0.0945060i
\(785\) −236.205 29.1426i −0.300898 0.0371244i
\(786\) −88.7319 81.0178i −0.112891 0.103076i
\(787\) 188.018 + 188.018i 0.238905 + 0.238905i 0.816396 0.577492i \(-0.195968\pi\)
−0.577492 + 0.816396i \(0.695968\pi\)
\(788\) −902.903 677.205i −1.14582 0.859398i
\(789\) −917.032 23.4126i −1.16227 0.0296737i
\(790\) −507.715 + 457.645i −0.642677 + 0.579297i
\(791\) 889.612 1.12467
\(792\) 507.934 82.8901i 0.641331 0.104659i
\(793\) −58.9682 58.9682i −0.0743609 0.0743609i
\(794\) 953.042 + 826.586i 1.20030 + 1.04104i
\(795\) −348.624 + 258.005i −0.438520 + 0.324535i
\(796\) −1102.35 + 157.456i −1.38486 + 0.197808i
\(797\) −651.365 651.365i −0.817271 0.817271i 0.168441 0.985712i \(-0.446127\pi\)
−0.985712 + 0.168441i \(0.946127\pi\)
\(798\) 24.2888 + 534.474i 0.0304371 + 0.669766i
\(799\) −1943.90 −2.43291
\(800\) −795.237 + 87.1671i −0.994046 + 0.108959i
\(801\) 18.8715 369.342i 0.0235599 0.461102i
\(802\) 207.252 14.7269i 0.258419 0.0183627i
\(803\) −75.9686 75.9686i −0.0946060 0.0946060i
\(804\) −604.246 + 70.6240i −0.751550 + 0.0878408i
\(805\) 453.361 353.777i 0.563181 0.439475i
\(806\) 148.264 + 128.592i 0.183951 + 0.159543i
\(807\) −196.074 + 186.311i −0.242966 + 0.230869i
\(808\) 984.264 212.687i 1.21815 0.263226i
\(809\) 735.550 0.909209 0.454604 0.890694i \(-0.349781\pi\)
0.454604 + 0.890694i \(0.349781\pi\)
\(810\) 653.797 478.174i 0.807156 0.590338i
\(811\) 92.4709i 0.114021i −0.998374 0.0570104i \(-0.981843\pi\)
0.998374 0.0570104i \(-0.0181568\pi\)
\(812\) −612.756 459.586i −0.754625 0.565993i
\(813\) 839.634 + 883.630i 1.03276 + 1.08688i
\(814\) 408.051 + 353.908i 0.501291 + 0.434777i
\(815\) −12.7416 1.57204i −0.0156339 0.00192889i
\(816\) −1088.55 + 287.513i −1.33401 + 0.352345i
\(817\) −300.103 + 300.103i −0.367323 + 0.367323i
\(818\) 1163.55 82.6793i 1.42244 0.101075i
\(819\) −740.223 37.8216i −0.903813 0.0461802i
\(820\) 491.197 510.348i 0.599021 0.622375i
\(821\) 593.249i 0.722593i 0.932451 + 0.361296i \(0.117666\pi\)
−0.932451 + 0.361296i \(0.882334\pi\)
\(822\) −3.25661 71.6615i −0.00396182 0.0871794i
\(823\) 468.289 468.289i 0.569003 0.569003i −0.362846 0.931849i \(-0.618195\pi\)
0.931849 + 0.362846i \(0.118195\pi\)
\(824\) 440.185 + 283.752i 0.534206 + 0.344359i
\(825\) −263.746 466.731i −0.319692 0.565735i
\(826\) −658.565 571.182i −0.797295 0.691504i
\(827\) 337.326 337.326i 0.407891 0.407891i −0.473111 0.881003i \(-0.656869\pi\)
0.881003 + 0.473111i \(0.156869\pi\)
\(828\) 361.225 433.617i 0.436262 0.523691i
\(829\) 483.086i 0.582733i −0.956611 0.291367i \(-0.905890\pi\)
0.956611 0.291367i \(-0.0941099\pi\)
\(830\) 1082.48 + 56.1444i 1.30420 + 0.0676438i
\(831\) −20.6061 + 807.109i −0.0247968 + 0.971250i
\(832\) 672.427 + 252.925i 0.808206 + 0.303997i
\(833\) 80.0045 80.0045i 0.0960438 0.0960438i
\(834\) −733.815 670.019i −0.879874 0.803380i
\(835\) −776.268 95.7749i −0.929663 0.114700i
\(836\) 344.027 49.1396i 0.411516 0.0587794i
\(837\) 179.177 153.641i 0.214071 0.183562i
\(838\) 462.210 32.8435i 0.551563 0.0391928i
\(839\) 835.860i 0.996257i 0.867103 + 0.498129i \(0.165979\pi\)
−0.867103 + 0.498129i \(0.834021\pi\)
\(840\) 581.079 661.368i 0.691761 0.787343i
\(841\) −159.738 −0.189938
\(842\) 35.8451 + 504.450i 0.0425713 + 0.599110i
\(843\) −310.889 327.179i −0.368789 0.388113i
\(844\) −48.1759 337.280i −0.0570804 0.399621i
\(845\) 169.467 132.243i 0.200553 0.156500i
\(846\) 1033.64 1075.59i 1.22180 1.27139i
\(847\) −362.652 362.652i −0.428161 0.428161i
\(848\) −222.462 + 405.626i −0.262337 + 0.478333i
\(849\) −16.5119 + 646.745i −0.0194487 + 0.761773i
\(850\) 672.641 + 960.724i 0.791343 + 1.13026i
\(851\) 592.319 0.696026
\(852\) −344.127 + 435.217i −0.403905 + 0.510818i
\(853\) −306.961 306.961i −0.359861 0.359861i 0.503901 0.863762i \(-0.331898\pi\)
−0.863762 + 0.503901i \(0.831898\pi\)
\(854\) −71.4217 + 82.3482i −0.0836320 + 0.0964265i
\(855\) 447.809 314.043i 0.523753 0.367302i
\(856\) 1020.06 + 657.547i 1.19165 + 0.768162i
\(857\) 861.944 + 861.944i 1.00577 + 1.00577i 0.999983 + 0.00578611i \(0.00184179\pi\)
0.00578611 + 0.999983i \(0.498158\pi\)
\(858\) 21.8557 + 480.933i 0.0254729 + 0.560528i
\(859\) 518.926 0.604104 0.302052 0.953291i \(-0.402328\pi\)
0.302052 + 0.953291i \(0.402328\pi\)
\(860\) 698.232 13.3509i 0.811898 0.0155243i
\(861\) −19.8946 + 779.240i −0.0231064 + 0.905041i
\(862\) −17.4124 245.046i −0.0202000 0.284276i
\(863\) −284.726 284.726i −0.329926 0.329926i 0.522633 0.852558i \(-0.324950\pi\)
−0.852558 + 0.522633i \(0.824950\pi\)
\(864\) 419.734 755.195i 0.485803 0.874068i
\(865\) 412.774 + 50.9274i 0.477195 + 0.0588756i
\(866\) −588.305 + 678.308i −0.679336 + 0.783266i
\(867\) 539.714 + 567.995i 0.622508 + 0.655127i
\(868\) 153.926 205.226i 0.177334 0.236436i
\(869\) −488.584 −0.562237
\(870\) −60.5031 + 780.689i −0.0695438 + 0.897344i
\(871\) 569.087i 0.653372i
\(872\) 179.051 38.6907i 0.205334 0.0443701i
\(873\) −697.090 772.161i −0.798499 0.884492i
\(874\) 249.691 287.890i 0.285688 0.329394i
\(875\) −855.569 330.147i −0.977793 0.377310i
\(876\) −179.144 + 20.9383i −0.204502 + 0.0239021i
\(877\) −127.814 + 127.814i −0.145740 + 0.145740i −0.776212 0.630472i \(-0.782861\pi\)
0.630472 + 0.776212i \(0.282861\pi\)
\(878\) 33.8483 + 476.350i 0.0385516 + 0.542540i
\(879\) −14.3740 + 563.006i −0.0163527 + 0.640507i
\(880\) −463.938 334.303i −0.527202 0.379890i
\(881\) 833.425i 0.945999i 0.881063 + 0.472999i \(0.156829\pi\)
−0.881063 + 0.472999i \(0.843171\pi\)
\(882\) 1.72668 + 86.8092i 0.00195769 + 0.0984231i
\(883\) −314.080 + 314.080i −0.355696 + 0.355696i −0.862224 0.506527i \(-0.830929\pi\)
0.506527 + 0.862224i \(0.330929\pi\)
\(884\) −148.923 1042.61i −0.168465 1.17943i
\(885\) −131.665 + 881.408i −0.148774 + 0.995941i
\(886\) −422.698 + 487.365i −0.477086 + 0.550074i
\(887\) −341.814 + 341.814i −0.385359 + 0.385359i −0.873029 0.487669i \(-0.837847\pi\)
0.487669 + 0.873029i \(0.337847\pi\)
\(888\) 890.939 168.843i 1.00331 0.190138i
\(889\) 804.252i 0.904670i
\(890\) −305.221 + 275.121i −0.342945 + 0.309125i
\(891\) 575.969 + 59.0123i 0.646430 + 0.0662315i
\(892\) −754.233 + 1005.60i −0.845552 + 1.12736i
\(893\) 712.269 712.269i 0.797613 0.797613i
\(894\) 118.870 + 108.536i 0.132964 + 0.121405i
\(895\) 871.434 680.018i 0.973669 0.759797i
\(896\) 267.475 900.169i 0.298521 1.00465i
\(897\) 363.655 + 382.710i 0.405412 + 0.426655i
\(898\) −68.4982 963.981i −0.0762787 1.07348i
\(899\) 228.171i 0.253805i
\(900\) −889.253 138.667i −0.988059 0.154074i
\(901\) 678.202 0.752722
\(902\) 505.037 35.8867i 0.559908 0.0397857i
\(903\) −557.121 + 529.381i −0.616966 + 0.586247i
\(904\) −815.350 525.590i −0.901936 0.581405i
\(905\) 567.385 + 727.096i 0.626945 + 0.803421i
\(906\) 27.8488 30.5005i 0.0307382 0.0336650i
\(907\) −542.622 542.622i −0.598261 0.598261i 0.341589 0.939850i \(-0.389035\pi\)
−0.939850 + 0.341589i \(0.889035\pi\)
\(908\) −114.092 + 152.116i −0.125652 + 0.167529i
\(909\) 1131.38 + 57.8076i 1.24464 + 0.0635948i
\(910\) 551.388 + 611.714i 0.605921 + 0.672213i
\(911\) −695.346 −0.763277 −0.381639 0.924312i \(-0.624640\pi\)
−0.381639 + 0.924312i \(0.624640\pi\)
\(912\) 293.510 504.207i 0.321831 0.552859i
\(913\) 547.863 + 547.863i 0.600069 + 0.600069i
\(914\) 103.935 + 90.1446i 0.113715 + 0.0986265i
\(915\) 110.213 + 16.4636i 0.120451 + 0.0179930i
\(916\) 72.1899 + 505.402i 0.0788099 + 0.551749i
\(917\) −103.887 103.887i −0.113290 0.113290i
\(918\) −1266.59 7.14030i −1.37973 0.00777811i
\(919\) 718.456 0.781780 0.390890 0.920437i \(-0.372167\pi\)
0.390890 + 0.920437i \(0.372167\pi\)
\(920\) −624.530 + 56.3959i −0.678837 + 0.0612998i
\(921\) −374.893 9.57132i −0.407050 0.0103923i
\(922\) −870.688 + 61.8690i −0.944347 + 0.0671031i
\(923\) −366.998 366.998i −0.397614 0.397614i
\(924\) 625.034 73.0536i 0.676444 0.0790624i
\(925\) −485.547 810.232i −0.524915 0.875926i
\(926\) 66.4743 + 57.6540i 0.0717865 + 0.0622613i
\(927\) 394.812 + 437.330i 0.425902 + 0.471769i
\(928\) 290.077 + 783.242i 0.312583 + 0.844010i
\(929\) −832.286 −0.895895 −0.447947 0.894060i \(-0.647845\pi\)
−0.447947 + 0.894060i \(0.647845\pi\)
\(930\) −261.471 20.2639i −0.281152 0.0217892i
\(931\) 58.6294i 0.0629746i
\(932\) −648.075 + 864.064i −0.695360 + 0.927107i
\(933\) −1119.43 + 1063.69i −1.19981 + 1.14008i
\(934\) 487.643 + 422.939i 0.522102 + 0.452826i
\(935\) −102.651 + 831.997i −0.109787 + 0.889836i
\(936\) 656.086 + 471.994i 0.700946 + 0.504267i
\(937\) 1098.42 1098.42i 1.17227 1.17227i 0.190603 0.981667i \(-0.438956\pi\)
0.981667 0.190603i \(-0.0610442\pi\)
\(938\) −741.997 + 52.7245i −0.791041 + 0.0562095i
\(939\) 1641.57 + 41.9105i 1.74821 + 0.0446331i
\(940\) −1657.19 + 31.6871i −1.76297 + 0.0337097i
\(941\) 1235.22i 1.31267i −0.754470 0.656334i \(-0.772106\pi\)
0.754470 0.656334i \(-0.227894\pi\)
\(942\) −285.301 + 12.9653i −0.302867 + 0.0137636i
\(943\) 392.597 392.597i 0.416327 0.416327i
\(944\) 266.131 + 912.587i 0.281919 + 0.966724i
\(945\) 825.145 547.789i 0.873169 0.579671i
\(946\) 377.108 + 327.070i 0.398634 + 0.345740i
\(947\) 1168.65 1168.65i 1.23405 1.23405i 0.271656 0.962394i \(-0.412429\pi\)
0.962394 0.271656i \(-0.0875713\pi\)
\(948\) −508.742 + 643.404i −0.536647 + 0.678696i
\(949\) 168.720i 0.177787i
\(950\) −598.486 105.557i −0.629986 0.111113i
\(951\) −15.7696 0.402609i −0.0165821 0.000423354i
\(952\) −1345.60 + 290.768i −1.41345 + 0.305428i
\(953\) −756.942 + 756.942i −0.794273 + 0.794273i −0.982186 0.187913i \(-0.939828\pi\)
0.187913 + 0.982186i \(0.439828\pi\)
\(954\) −360.625 + 375.262i −0.378013 + 0.393356i
\(955\) 761.356 + 975.667i 0.797231 + 1.02164i
\(956\) −93.2496 652.841i −0.0975414 0.682888i
\(957\) −405.744 + 385.542i −0.423975 + 0.402865i
\(958\) −1392.59 + 98.9541i −1.45364 + 0.103292i
\(959\) 87.7140i 0.0914641i
\(960\) −923.314 + 262.853i −0.961785 + 0.273805i
\(961\) 884.580 0.920479
\(962\) 60.1236 + 846.124i 0.0624986 + 0.879547i
\(963\) 914.909 + 1013.44i 0.950061 + 1.05238i
\(964\) 80.7268 11.5307i 0.0837415 0.0119613i
\(965\) 189.189 1533.41i 0.196051 1.58902i
\(966\) 465.300 509.604i 0.481677 0.527540i
\(967\) −366.482 366.482i −0.378989 0.378989i 0.491749 0.870737i \(-0.336358\pi\)
−0.870737 + 0.491749i \(0.836358\pi\)
\(968\) 118.121 + 546.637i 0.122026 + 0.564708i
\(969\) −855.000 21.8288i −0.882353 0.0225272i
\(970\) −59.8695 + 1154.31i −0.0617212 + 1.19001i
\(971\) −1773.80 −1.82678 −0.913390 0.407086i \(-0.866545\pi\)
−0.913390 + 0.407086i \(0.866545\pi\)
\(972\) 677.444 697.032i 0.696959 0.717111i
\(973\) −859.150 859.150i −0.882991 0.882991i
\(974\) 966.018 1113.81i 0.991805 1.14354i
\(975\) 225.406 811.165i 0.231186 0.831964i
\(976\) 114.112 33.2775i 0.116918 0.0340958i
\(977\) −887.249 887.249i −0.908136 0.908136i 0.0879854 0.996122i \(-0.471957\pi\)
−0.996122 + 0.0879854i \(0.971957\pi\)
\(978\) −15.3900 + 0.699389i −0.0157362 + 0.000715122i
\(979\) −293.721 −0.300021
\(980\) 66.9006 69.5089i 0.0682659 0.0709274i
\(981\) 205.813 + 10.5160i 0.209799 + 0.0107197i
\(982\) −60.0491 845.076i −0.0611498 0.860566i
\(983\) −297.097 297.097i −0.302235 0.302235i 0.539653 0.841888i \(-0.318556\pi\)
−0.841888 + 0.539653i \(0.818556\pi\)
\(984\) 478.615 702.437i 0.486397 0.713859i
\(985\) −172.753 + 1400.19i −0.175384 + 1.42151i
\(986\) 802.264 925.000i 0.813656 0.938134i
\(987\) 1322.28 1256.44i 1.33969 1.27299i
\(988\) 436.595 + 327.460i 0.441898 + 0.331438i
\(989\) 547.401 0.553490
\(990\) −405.776 499.201i −0.409875 0.504243i
\(991\) 1518.20i 1.53198i 0.642850 + 0.765992i \(0.277752\pi\)
−0.642850 + 0.765992i \(0.722248\pi\)
\(992\) −262.326 + 97.1538i −0.264442 + 0.0979373i
\(993\) −1184.55 1246.61i −1.19290 1.25540i
\(994\) −444.504 + 512.507i −0.447188 + 0.515601i
\(995\) 856.310 + 1097.35i 0.860613 + 1.10286i
\(996\) 1291.93 151.000i 1.29712 0.151607i
\(997\) −566.238 + 566.238i −0.567942 + 0.567942i −0.931551 0.363610i \(-0.881544\pi\)
0.363610 + 0.931551i \(0.381544\pi\)
\(998\) −59.8993 842.968i −0.0600193 0.844657i
\(999\) 1017.16 + 78.0421i 1.01817 + 0.0781203i
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 60.3.l.a.23.11 yes 40
3.2 odd 2 inner 60.3.l.a.23.10 yes 40
4.3 odd 2 inner 60.3.l.a.23.20 yes 40
5.2 odd 4 inner 60.3.l.a.47.1 yes 40
5.3 odd 4 300.3.l.g.107.20 40
5.4 even 2 300.3.l.g.143.10 40
12.11 even 2 inner 60.3.l.a.23.1 40
15.2 even 4 inner 60.3.l.a.47.20 yes 40
15.8 even 4 300.3.l.g.107.1 40
15.14 odd 2 300.3.l.g.143.11 40
20.3 even 4 300.3.l.g.107.11 40
20.7 even 4 inner 60.3.l.a.47.10 yes 40
20.19 odd 2 300.3.l.g.143.1 40
60.23 odd 4 300.3.l.g.107.10 40
60.47 odd 4 inner 60.3.l.a.47.11 yes 40
60.59 even 2 300.3.l.g.143.20 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.3.l.a.23.1 40 12.11 even 2 inner
60.3.l.a.23.10 yes 40 3.2 odd 2 inner
60.3.l.a.23.11 yes 40 1.1 even 1 trivial
60.3.l.a.23.20 yes 40 4.3 odd 2 inner
60.3.l.a.47.1 yes 40 5.2 odd 4 inner
60.3.l.a.47.10 yes 40 20.7 even 4 inner
60.3.l.a.47.11 yes 40 60.47 odd 4 inner
60.3.l.a.47.20 yes 40 15.2 even 4 inner
300.3.l.g.107.1 40 15.8 even 4
300.3.l.g.107.10 40 60.23 odd 4
300.3.l.g.107.11 40 20.3 even 4
300.3.l.g.107.20 40 5.3 odd 4
300.3.l.g.143.1 40 20.19 odd 2
300.3.l.g.143.10 40 5.4 even 2
300.3.l.g.143.11 40 15.14 odd 2
300.3.l.g.143.20 40 60.59 even 2