Properties

Label 845.2.l.c.654.1
Level $845$
Weight $2$
Character 845.654
Analytic conductor $6.747$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [845,2,Mod(654,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.654");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.l (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.49787136.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 654.1
Root \(-1.09445 + 0.895644i\) of defining polynomial
Character \(\chi\) \(=\) 845.654
Dual form 845.2.l.c.699.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.09445 + 1.89564i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.39564 - 2.41733i) q^{4} +(0.456850 - 2.18890i) q^{5} +(1.89564 - 1.09445i) q^{6} +(-0.866025 - 1.50000i) q^{7} +1.73205 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-1.09445 + 1.89564i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.39564 - 2.41733i) q^{4} +(0.456850 - 2.18890i) q^{5} +(1.89564 - 1.09445i) q^{6} +(-0.866025 - 1.50000i) q^{7} +1.73205 q^{8} +(-1.00000 - 1.73205i) q^{9} +(3.64938 + 3.26167i) q^{10} +(-2.29129 - 1.32288i) q^{11} +2.79129i q^{12} +3.79129 q^{14} +(-1.49009 + 1.66722i) q^{15} +(0.895644 - 1.55130i) q^{16} +(-3.96863 + 2.29129i) q^{17} +4.37780 q^{18} +(1.50000 - 0.866025i) q^{19} +(-5.92889 + 1.95057i) q^{20} +1.73205i q^{21} +(5.01540 - 2.89564i) q^{22} +(3.96863 + 2.29129i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(-4.58258 - 2.00000i) q^{25} +5.00000i q^{27} +(-2.41733 + 4.18693i) q^{28} +(-2.29129 + 3.96863i) q^{29} +(-1.52962 - 4.64938i) q^{30} +9.66930i q^{31} +(3.69253 + 6.39564i) q^{32} +(1.32288 + 2.29129i) q^{33} -10.0308i q^{34} +(-3.67900 + 1.21037i) q^{35} +(-2.79129 + 4.83465i) q^{36} +(-3.96863 + 6.87386i) q^{37} +3.79129i q^{38} +(0.791288 - 3.79129i) q^{40} +(2.29129 + 1.32288i) q^{41} +(-3.28335 - 1.89564i) q^{42} +(1.22753 - 0.708712i) q^{43} +7.38505i q^{44} +(-4.24814 + 1.39761i) q^{45} +(-8.68693 + 5.01540i) q^{46} -8.75560 q^{47} +(-1.55130 + 0.895644i) q^{48} +(2.00000 - 3.46410i) q^{49} +(8.80669 - 6.49803i) q^{50} +4.58258 q^{51} -1.58258i q^{53} +(-9.47822 - 5.47225i) q^{54} +(-3.94242 + 4.41105i) q^{55} +(-1.50000 - 2.59808i) q^{56} -1.73205 q^{57} +(-5.01540 - 8.68693i) q^{58} +(2.91742 - 1.68438i) q^{59} +(6.10985 + 1.27520i) q^{60} +(5.29129 + 9.16478i) q^{61} +(-18.3296 - 10.5826i) q^{62} +(-1.73205 + 3.00000i) q^{63} -12.5826 q^{64} -5.79129 q^{66} +(7.43273 - 12.8739i) q^{67} +(11.0776 + 6.39564i) q^{68} +(-2.29129 - 3.96863i) q^{69} +(1.73205 - 8.29875i) q^{70} +(3.08258 - 1.77973i) q^{71} +(-1.73205 - 3.00000i) q^{72} +(-8.68693 - 15.0462i) q^{74} +(2.96863 + 4.02334i) q^{75} +(-4.18693 - 2.41733i) q^{76} +4.58258i q^{77} +6.00000 q^{79} +(-2.98647 - 2.66919i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.01540 + 2.89564i) q^{82} -11.3060 q^{83} +(4.18693 - 2.41733i) q^{84} +(3.20233 + 9.73371i) q^{85} +3.10260i q^{86} +(3.96863 - 2.29129i) q^{87} +(-3.96863 - 2.29129i) q^{88} +(-3.70871 - 2.14123i) q^{89} +(2.00000 - 9.58258i) q^{90} -12.7913i q^{92} +(4.83465 - 8.37386i) q^{93} +(9.58258 - 16.5975i) q^{94} +(-1.21037 - 3.67900i) q^{95} -7.38505i q^{96} +(2.23658 + 3.87386i) q^{97} +(4.37780 + 7.58258i) q^{98} +5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{4} + 6 q^{6} - 8 q^{9} - 4 q^{10} + 12 q^{14} + 6 q^{15} - 2 q^{16} + 12 q^{19} - 24 q^{20} - 12 q^{24} - 10 q^{30} + 6 q^{35} - 4 q^{36} - 12 q^{40} - 12 q^{45} - 42 q^{46} + 16 q^{49} + 12 q^{50} - 30 q^{54} - 14 q^{55} - 12 q^{56} + 60 q^{59} + 24 q^{61} - 64 q^{64} - 28 q^{66} - 12 q^{71} - 42 q^{74} - 8 q^{75} - 6 q^{76} + 48 q^{79} - 18 q^{80} - 4 q^{81} + 6 q^{84} - 42 q^{85} - 48 q^{89} + 16 q^{90} + 40 q^{94} - 6 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09445 + 1.89564i −0.773893 + 1.34042i 0.161521 + 0.986869i \(0.448360\pi\)
−0.935414 + 0.353553i \(0.884973\pi\)
\(3\) −0.866025 0.500000i −0.500000 0.288675i 0.228714 0.973494i \(-0.426548\pi\)
−0.728714 + 0.684819i \(0.759881\pi\)
\(4\) −1.39564 2.41733i −0.697822 1.20866i
\(5\) 0.456850 2.18890i 0.204310 0.978906i
\(6\) 1.89564 1.09445i 0.773893 0.446808i
\(7\) −0.866025 1.50000i −0.327327 0.566947i 0.654654 0.755929i \(-0.272814\pi\)
−0.981981 + 0.188982i \(0.939481\pi\)
\(8\) 1.73205 0.612372
\(9\) −1.00000 1.73205i −0.333333 0.577350i
\(10\) 3.64938 + 3.26167i 1.15403 + 1.03143i
\(11\) −2.29129 1.32288i −0.690849 0.398862i 0.113081 0.993586i \(-0.463928\pi\)
−0.803930 + 0.594724i \(0.797261\pi\)
\(12\) 2.79129i 0.805775i
\(13\) 0 0
\(14\) 3.79129 1.01326
\(15\) −1.49009 + 1.66722i −0.384741 + 0.430474i
\(16\) 0.895644 1.55130i 0.223911 0.387825i
\(17\) −3.96863 + 2.29129i −0.962533 + 0.555719i −0.896952 0.442128i \(-0.854224\pi\)
−0.0655816 + 0.997847i \(0.520890\pi\)
\(18\) 4.37780 1.03186
\(19\) 1.50000 0.866025i 0.344124 0.198680i −0.317970 0.948101i \(-0.603001\pi\)
0.662094 + 0.749421i \(0.269668\pi\)
\(20\) −5.92889 + 1.95057i −1.32574 + 0.436161i
\(21\) 1.73205i 0.377964i
\(22\) 5.01540 2.89564i 1.06929 0.617353i
\(23\) 3.96863 + 2.29129i 0.827516 + 0.477767i 0.853001 0.521909i \(-0.174780\pi\)
−0.0254855 + 0.999675i \(0.508113\pi\)
\(24\) −1.50000 0.866025i −0.306186 0.176777i
\(25\) −4.58258 2.00000i −0.916515 0.400000i
\(26\) 0 0
\(27\) 5.00000i 0.962250i
\(28\) −2.41733 + 4.18693i −0.456832 + 0.791256i
\(29\) −2.29129 + 3.96863i −0.425481 + 0.736956i −0.996465 0.0840058i \(-0.973229\pi\)
0.570984 + 0.820961i \(0.306562\pi\)
\(30\) −1.52962 4.64938i −0.279269 0.848856i
\(31\) 9.66930i 1.73666i 0.495988 + 0.868329i \(0.334806\pi\)
−0.495988 + 0.868329i \(0.665194\pi\)
\(32\) 3.69253 + 6.39564i 0.652753 + 1.13060i
\(33\) 1.32288 + 2.29129i 0.230283 + 0.398862i
\(34\) 10.0308i 1.72027i
\(35\) −3.67900 + 1.21037i −0.621864 + 0.204590i
\(36\) −2.79129 + 4.83465i −0.465215 + 0.805775i
\(37\) −3.96863 + 6.87386i −0.652438 + 1.13006i 0.330091 + 0.943949i \(0.392920\pi\)
−0.982529 + 0.186107i \(0.940413\pi\)
\(38\) 3.79129i 0.615028i
\(39\) 0 0
\(40\) 0.791288 3.79129i 0.125114 0.599455i
\(41\) 2.29129 + 1.32288i 0.357839 + 0.206598i 0.668132 0.744042i \(-0.267094\pi\)
−0.310293 + 0.950641i \(0.600427\pi\)
\(42\) −3.28335 1.89564i −0.506632 0.292504i
\(43\) 1.22753 0.708712i 0.187196 0.108078i −0.403473 0.914991i \(-0.632197\pi\)
0.590669 + 0.806914i \(0.298864\pi\)
\(44\) 7.38505i 1.11334i
\(45\) −4.24814 + 1.39761i −0.633275 + 0.208344i
\(46\) −8.68693 + 5.01540i −1.28082 + 0.739481i
\(47\) −8.75560 −1.27714 −0.638568 0.769565i \(-0.720473\pi\)
−0.638568 + 0.769565i \(0.720473\pi\)
\(48\) −1.55130 + 0.895644i −0.223911 + 0.129275i
\(49\) 2.00000 3.46410i 0.285714 0.494872i
\(50\) 8.80669 6.49803i 1.24545 0.918960i
\(51\) 4.58258 0.641689
\(52\) 0 0
\(53\) 1.58258i 0.217383i −0.994076 0.108692i \(-0.965334\pi\)
0.994076 0.108692i \(-0.0346661\pi\)
\(54\) −9.47822 5.47225i −1.28982 0.744679i
\(55\) −3.94242 + 4.41105i −0.531596 + 0.594785i
\(56\) −1.50000 2.59808i −0.200446 0.347183i
\(57\) −1.73205 −0.229416
\(58\) −5.01540 8.68693i −0.658555 1.14065i
\(59\) 2.91742 1.68438i 0.379816 0.219287i −0.297922 0.954590i \(-0.596294\pi\)
0.677738 + 0.735303i \(0.262960\pi\)
\(60\) 6.10985 + 1.27520i 0.788779 + 0.164628i
\(61\) 5.29129 + 9.16478i 0.677480 + 1.17343i 0.975737 + 0.218944i \(0.0702613\pi\)
−0.298257 + 0.954485i \(0.596405\pi\)
\(62\) −18.3296 10.5826i −2.32786 1.34399i
\(63\) −1.73205 + 3.00000i −0.218218 + 0.377964i
\(64\) −12.5826 −1.57282
\(65\) 0 0
\(66\) −5.79129 −0.712858
\(67\) 7.43273 12.8739i 0.908052 1.57279i 0.0912856 0.995825i \(-0.470902\pi\)
0.816767 0.576968i \(-0.195764\pi\)
\(68\) 11.0776 + 6.39564i 1.34335 + 0.775586i
\(69\) −2.29129 3.96863i −0.275839 0.477767i
\(70\) 1.73205 8.29875i 0.207020 0.991891i
\(71\) 3.08258 1.77973i 0.365834 0.211215i −0.305803 0.952095i \(-0.598925\pi\)
0.671637 + 0.740880i \(0.265591\pi\)
\(72\) −1.73205 3.00000i −0.204124 0.353553i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) −8.68693 15.0462i −1.00984 1.74909i
\(75\) 2.96863 + 4.02334i 0.342788 + 0.464575i
\(76\) −4.18693 2.41733i −0.480274 0.277286i
\(77\) 4.58258i 0.522233i
\(78\) 0 0
\(79\) 6.00000 0.675053 0.337526 0.941316i \(-0.390410\pi\)
0.337526 + 0.941316i \(0.390410\pi\)
\(80\) −2.98647 2.66919i −0.333897 0.298424i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −5.01540 + 2.89564i −0.553859 + 0.319770i
\(83\) −11.3060 −1.24100 −0.620498 0.784208i \(-0.713069\pi\)
−0.620498 + 0.784208i \(0.713069\pi\)
\(84\) 4.18693 2.41733i 0.456832 0.263752i
\(85\) 3.20233 + 9.73371i 0.347342 + 1.05577i
\(86\) 3.10260i 0.334562i
\(87\) 3.96863 2.29129i 0.425481 0.245652i
\(88\) −3.96863 2.29129i −0.423057 0.244252i
\(89\) −3.70871 2.14123i −0.393123 0.226969i 0.290390 0.956909i \(-0.406215\pi\)
−0.683512 + 0.729939i \(0.739548\pi\)
\(90\) 2.00000 9.58258i 0.210819 1.01009i
\(91\) 0 0
\(92\) 12.7913i 1.33358i
\(93\) 4.83465 8.37386i 0.501330 0.868329i
\(94\) 9.58258 16.5975i 0.988367 1.71190i
\(95\) −1.21037 3.67900i −0.124181 0.377457i
\(96\) 7.38505i 0.753734i
\(97\) 2.23658 + 3.87386i 0.227090 + 0.393331i 0.956944 0.290271i \(-0.0937455\pi\)
−0.729854 + 0.683603i \(0.760412\pi\)
\(98\) 4.37780 + 7.58258i 0.442225 + 0.765956i
\(99\) 5.29150i 0.531816i
\(100\) 1.56099 + 13.8689i 0.156099 + 1.38689i
\(101\) −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i \(-0.981114\pi\)
0.550474 + 0.834853i \(0.314447\pi\)
\(102\) −5.01540 + 8.68693i −0.496599 + 0.860134i
\(103\) 15.1652i 1.49427i −0.664674 0.747133i \(-0.731430\pi\)
0.664674 0.747133i \(-0.268570\pi\)
\(104\) 0 0
\(105\) 3.79129 + 0.791288i 0.369992 + 0.0772218i
\(106\) 3.00000 + 1.73205i 0.291386 + 0.168232i
\(107\) −1.22753 0.708712i −0.118669 0.0685138i 0.439490 0.898247i \(-0.355159\pi\)
−0.558160 + 0.829733i \(0.688492\pi\)
\(108\) 12.0866 6.97822i 1.16304 0.671479i
\(109\) 2.74110i 0.262550i −0.991346 0.131275i \(-0.958093\pi\)
0.991346 0.131275i \(-0.0419071\pi\)
\(110\) −4.04699 12.3011i −0.385865 1.17286i
\(111\) 6.87386 3.96863i 0.652438 0.376685i
\(112\) −3.10260 −0.293168
\(113\) −14.3609 + 8.29129i −1.35096 + 0.779979i −0.988384 0.151975i \(-0.951437\pi\)
−0.362578 + 0.931953i \(0.618103\pi\)
\(114\) 1.89564 3.28335i 0.177543 0.307514i
\(115\) 6.82847 7.64016i 0.636758 0.712448i
\(116\) 12.7913 1.18764
\(117\) 0 0
\(118\) 7.37386i 0.678819i
\(119\) 6.87386 + 3.96863i 0.630126 + 0.363803i
\(120\) −2.58092 + 2.88771i −0.235605 + 0.263610i
\(121\) −2.00000 3.46410i −0.181818 0.314918i
\(122\) −23.1642 −2.09719
\(123\) −1.32288 2.29129i −0.119280 0.206598i
\(124\) 23.3739 13.4949i 2.09903 1.21188i
\(125\) −6.47135 + 9.11710i −0.578815 + 0.815459i
\(126\) −3.79129 6.56670i −0.337755 0.585008i
\(127\) −8.44178 4.87386i −0.749087 0.432485i 0.0762771 0.997087i \(-0.475697\pi\)
−0.825364 + 0.564601i \(0.809030\pi\)
\(128\) 6.38595 11.0608i 0.564444 0.977645i
\(129\) −1.41742 −0.124797
\(130\) 0 0
\(131\) 1.58258 0.138270 0.0691351 0.997607i \(-0.477976\pi\)
0.0691351 + 0.997607i \(0.477976\pi\)
\(132\) 3.69253 6.39564i 0.321393 0.556669i
\(133\) −2.59808 1.50000i −0.225282 0.130066i
\(134\) 16.2695 + 28.1796i 1.40547 + 2.43435i
\(135\) 10.9445 + 2.28425i 0.941953 + 0.196597i
\(136\) −6.87386 + 3.96863i −0.589429 + 0.340307i
\(137\) −0.0476751 0.0825757i −0.00407316 0.00705492i 0.863982 0.503523i \(-0.167963\pi\)
−0.868055 + 0.496468i \(0.834630\pi\)
\(138\) 10.0308 0.853879
\(139\) 2.87386 + 4.97768i 0.243758 + 0.422201i 0.961782 0.273817i \(-0.0882864\pi\)
−0.718024 + 0.696019i \(0.754953\pi\)
\(140\) 8.06042 + 7.20409i 0.681230 + 0.608857i
\(141\) 7.58258 + 4.37780i 0.638568 + 0.368677i
\(142\) 7.79129i 0.653830i
\(143\) 0 0
\(144\) −3.58258 −0.298548
\(145\) 7.64016 + 6.82847i 0.634480 + 0.567074i
\(146\) 0 0
\(147\) −3.46410 + 2.00000i −0.285714 + 0.164957i
\(148\) 22.1552 1.82114
\(149\) −8.45644 + 4.88233i −0.692778 + 0.399976i −0.804652 0.593747i \(-0.797648\pi\)
0.111874 + 0.993722i \(0.464315\pi\)
\(150\) −10.8758 + 1.22411i −0.888008 + 0.0999485i
\(151\) 6.20520i 0.504972i −0.967601 0.252486i \(-0.918752\pi\)
0.967601 0.252486i \(-0.0812482\pi\)
\(152\) 2.59808 1.50000i 0.210732 0.121666i
\(153\) 7.93725 + 4.58258i 0.641689 + 0.370479i
\(154\) −8.68693 5.01540i −0.700013 0.404153i
\(155\) 21.1652 + 4.41742i 1.70003 + 0.354816i
\(156\) 0 0
\(157\) 9.16515i 0.731459i 0.930721 + 0.365729i \(0.119180\pi\)
−0.930721 + 0.365729i \(0.880820\pi\)
\(158\) −6.56670 + 11.3739i −0.522419 + 0.904856i
\(159\) −0.791288 + 1.37055i −0.0627532 + 0.108692i
\(160\) 15.6864 5.16072i 1.24012 0.407991i
\(161\) 7.93725i 0.625543i
\(162\) −1.09445 1.89564i −0.0859882 0.148936i
\(163\) −5.33918 9.24773i −0.418197 0.724338i 0.577561 0.816347i \(-0.304004\pi\)
−0.995758 + 0.0920093i \(0.970671\pi\)
\(164\) 7.38505i 0.576676i
\(165\) 5.61976 1.84887i 0.437498 0.143934i
\(166\) 12.3739 21.4322i 0.960398 1.66346i
\(167\) −2.14123 + 3.70871i −0.165693 + 0.286989i −0.936901 0.349594i \(-0.886319\pi\)
0.771208 + 0.636583i \(0.219653\pi\)
\(168\) 3.00000i 0.231455i
\(169\) 0 0
\(170\) −21.9564 4.58258i −1.68398 0.351468i
\(171\) −3.00000 1.73205i −0.229416 0.132453i
\(172\) −3.42638 1.97822i −0.261259 0.150838i
\(173\) −6.42368 + 3.70871i −0.488383 + 0.281968i −0.723903 0.689901i \(-0.757654\pi\)
0.235520 + 0.971869i \(0.424321\pi\)
\(174\) 10.0308i 0.760433i
\(175\) 0.968627 + 8.60591i 0.0732213 + 0.650546i
\(176\) −4.10436 + 2.36965i −0.309377 + 0.178619i
\(177\) −3.36875 −0.253211
\(178\) 8.11800 4.68693i 0.608470 0.351300i
\(179\) −0.0825757 + 0.143025i −0.00617200 + 0.0106902i −0.869095 0.494645i \(-0.835298\pi\)
0.862923 + 0.505336i \(0.168631\pi\)
\(180\) 9.30738 + 8.31857i 0.693731 + 0.620029i
\(181\) −18.7477 −1.39351 −0.696754 0.717310i \(-0.745373\pi\)
−0.696754 + 0.717310i \(0.745373\pi\)
\(182\) 0 0
\(183\) 10.5826i 0.782287i
\(184\) 6.87386 + 3.96863i 0.506748 + 0.292571i
\(185\) 13.2331 + 11.8273i 0.972920 + 0.869557i
\(186\) 10.5826 + 18.3296i 0.775952 + 1.34399i
\(187\) 12.1244 0.886621
\(188\) 12.2197 + 21.1652i 0.891214 + 1.54363i
\(189\) 7.50000 4.33013i 0.545545 0.314970i
\(190\) 8.29875 + 1.73205i 0.602055 + 0.125656i
\(191\) 3.70871 + 6.42368i 0.268353 + 0.464801i 0.968437 0.249260i \(-0.0801873\pi\)
−0.700084 + 0.714061i \(0.746854\pi\)
\(192\) 10.8968 + 6.29129i 0.786411 + 0.454035i
\(193\) −0.504525 + 0.873864i −0.0363165 + 0.0629021i −0.883612 0.468219i \(-0.844896\pi\)
0.847296 + 0.531121i \(0.178229\pi\)
\(194\) −9.79129 −0.702973
\(195\) 0 0
\(196\) −11.1652 −0.797511
\(197\) −9.98313 + 17.2913i −0.711269 + 1.23195i 0.253113 + 0.967437i \(0.418546\pi\)
−0.964381 + 0.264516i \(0.914788\pi\)
\(198\) −10.0308 5.79129i −0.712858 0.411569i
\(199\) 0.708712 + 1.22753i 0.0502393 + 0.0870170i 0.890051 0.455860i \(-0.150668\pi\)
−0.839812 + 0.542877i \(0.817335\pi\)
\(200\) −7.93725 3.46410i −0.561249 0.244949i
\(201\) −12.8739 + 7.43273i −0.908052 + 0.524264i
\(202\) −9.85005 17.0608i −0.693047 1.20039i
\(203\) 7.93725 0.557086
\(204\) −6.39564 11.0776i −0.447785 0.775586i
\(205\) 3.94242 4.41105i 0.275351 0.308081i
\(206\) 28.7477 + 16.5975i 2.00295 + 1.15640i
\(207\) 9.16515i 0.637022i
\(208\) 0 0
\(209\) −4.58258 −0.316983
\(210\) −5.64938 + 6.32091i −0.389844 + 0.436184i
\(211\) −9.08258 + 15.7315i −0.625270 + 1.08300i 0.363218 + 0.931704i \(0.381678\pi\)
−0.988489 + 0.151296i \(0.951655\pi\)
\(212\) −3.82560 + 2.20871i −0.262743 + 0.151695i
\(213\) −3.55945 −0.243890
\(214\) 2.68693 1.55130i 0.183675 0.106045i
\(215\) −0.990505 3.01071i −0.0675519 0.205329i
\(216\) 8.66025i 0.589256i
\(217\) 14.5040 8.37386i 0.984593 0.568455i
\(218\) 5.19615 + 3.00000i 0.351928 + 0.203186i
\(219\) 0 0
\(220\) 16.1652 + 3.37386i 1.08985 + 0.227466i
\(221\) 0 0
\(222\) 17.3739i 1.16606i
\(223\) −4.33013 + 7.50000i −0.289967 + 0.502237i −0.973801 0.227400i \(-0.926978\pi\)
0.683835 + 0.729637i \(0.260311\pi\)
\(224\) 6.39564 11.0776i 0.427327 0.740152i
\(225\) 1.11847 + 9.93725i 0.0745649 + 0.662484i
\(226\) 36.2976i 2.41448i
\(227\) 3.05493 + 5.29129i 0.202763 + 0.351195i 0.949418 0.314016i \(-0.101675\pi\)
−0.746655 + 0.665212i \(0.768341\pi\)
\(228\) 2.41733 + 4.18693i 0.160091 + 0.277286i
\(229\) 5.48220i 0.362274i 0.983458 + 0.181137i \(0.0579778\pi\)
−0.983458 + 0.181137i \(0.942022\pi\)
\(230\) 7.00959 + 21.3061i 0.462199 + 1.40488i
\(231\) 2.29129 3.96863i 0.150756 0.261116i
\(232\) −3.96863 + 6.87386i −0.260553 + 0.451291i
\(233\) 21.1652i 1.38658i 0.720661 + 0.693288i \(0.243838\pi\)
−0.720661 + 0.693288i \(0.756162\pi\)
\(234\) 0 0
\(235\) −4.00000 + 19.1652i −0.260931 + 1.25020i
\(236\) −8.14337 4.70158i −0.530088 0.306047i
\(237\) −5.19615 3.00000i −0.337526 0.194871i
\(238\) −15.0462 + 8.68693i −0.975301 + 0.563090i
\(239\) 20.9753i 1.35678i 0.734702 + 0.678390i \(0.237322\pi\)
−0.734702 + 0.678390i \(0.762678\pi\)
\(240\) 1.25176 + 3.80482i 0.0808010 + 0.245600i
\(241\) 1.50000 0.866025i 0.0966235 0.0557856i −0.450910 0.892570i \(-0.648900\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 8.75560 0.562832
\(243\) 13.8564 8.00000i 0.888889 0.513200i
\(244\) 14.7695 25.5815i 0.945521 1.63769i
\(245\) −6.66888 5.96038i −0.426059 0.380795i
\(246\) 5.79129 0.369239
\(247\) 0 0
\(248\) 16.7477i 1.06348i
\(249\) 9.79129 + 5.65300i 0.620498 + 0.358244i
\(250\) −10.2002 22.2456i −0.645118 1.40694i
\(251\) −9.08258 15.7315i −0.573287 0.992962i −0.996225 0.0868039i \(-0.972335\pi\)
0.422938 0.906158i \(-0.360999\pi\)
\(252\) 9.66930 0.609109
\(253\) −6.06218 10.5000i −0.381126 0.660129i
\(254\) 18.4782 10.6684i 1.15943 0.669395i
\(255\) 2.09355 10.0308i 0.131103 0.628153i
\(256\) 1.39564 + 2.41733i 0.0872277 + 0.151083i
\(257\) 0.143025 + 0.0825757i 0.00892167 + 0.00515093i 0.504454 0.863438i \(-0.331694\pi\)
−0.495533 + 0.868589i \(0.665027\pi\)
\(258\) 1.55130 2.68693i 0.0965798 0.167281i
\(259\) 13.7477 0.854242
\(260\) 0 0
\(261\) 9.16515 0.567309
\(262\) −1.73205 + 3.00000i −0.107006 + 0.185341i
\(263\) −7.79423 4.50000i −0.480613 0.277482i 0.240059 0.970758i \(-0.422833\pi\)
−0.720672 + 0.693276i \(0.756167\pi\)
\(264\) 2.29129 + 3.96863i 0.141019 + 0.244252i
\(265\) −3.46410 0.723000i −0.212798 0.0444135i
\(266\) 5.68693 3.28335i 0.348688 0.201315i
\(267\) 2.14123 + 3.70871i 0.131041 + 0.226969i
\(268\) −41.4938 −2.53464
\(269\) −7.50000 12.9904i −0.457283 0.792038i 0.541533 0.840679i \(-0.317844\pi\)
−0.998816 + 0.0486418i \(0.984511\pi\)
\(270\) −16.3083 + 18.2469i −0.992494 + 1.11047i
\(271\) −7.50000 4.33013i −0.455593 0.263036i 0.254597 0.967047i \(-0.418057\pi\)
−0.710189 + 0.704011i \(0.751391\pi\)
\(272\) 8.20871i 0.497726i
\(273\) 0 0
\(274\) 0.208712 0.0126088
\(275\) 7.85425 + 10.6448i 0.473629 + 0.641903i
\(276\) −6.39564 + 11.0776i −0.384973 + 0.666792i
\(277\) 14.3609 8.29129i 0.862865 0.498175i −0.00210581 0.999998i \(-0.500670\pi\)
0.864971 + 0.501823i \(0.167337\pi\)
\(278\) −12.5812 −0.754571
\(279\) 16.7477 9.66930i 1.00266 0.578886i
\(280\) −6.37221 + 2.09642i −0.380812 + 0.125285i
\(281\) 17.5112i 1.04463i 0.852752 + 0.522316i \(0.174932\pi\)
−0.852752 + 0.522316i \(0.825068\pi\)
\(282\) −16.5975 + 9.58258i −0.988367 + 0.570634i
\(283\) 0.218475 + 0.126136i 0.0129870 + 0.00749803i 0.506479 0.862252i \(-0.330947\pi\)
−0.493492 + 0.869750i \(0.664280\pi\)
\(284\) −8.60436 4.96773i −0.510575 0.294780i
\(285\) −0.791288 + 3.79129i −0.0468718 + 0.224577i
\(286\) 0 0
\(287\) 4.58258i 0.270501i
\(288\) 7.38505 12.7913i 0.435168 0.753734i
\(289\) 2.00000 3.46410i 0.117647 0.203771i
\(290\) −21.3061 + 7.00959i −1.25114 + 0.411617i
\(291\) 4.47315i 0.262221i
\(292\) 0 0
\(293\) −11.7152 20.2913i −0.684408 1.18543i −0.973622 0.228165i \(-0.926727\pi\)
0.289214 0.957264i \(-0.406606\pi\)
\(294\) 8.75560i 0.510637i
\(295\) −2.35411 7.15546i −0.137061 0.416607i
\(296\) −6.87386 + 11.9059i −0.399535 + 0.692015i
\(297\) 6.61438 11.4564i 0.383805 0.664770i
\(298\) 21.3739i 1.23815i
\(299\) 0 0
\(300\) 5.58258 12.7913i 0.322310 0.738505i
\(301\) −2.12614 1.22753i −0.122548 0.0707534i
\(302\) 11.7629 + 6.79129i 0.676876 + 0.390795i
\(303\) 7.79423 4.50000i 0.447767 0.258518i
\(304\) 3.10260i 0.177946i
\(305\) 22.4781 7.39517i 1.28709 0.423446i
\(306\) −17.3739 + 10.0308i −0.993198 + 0.573423i
\(307\) 24.2487 1.38395 0.691974 0.721923i \(-0.256741\pi\)
0.691974 + 0.721923i \(0.256741\pi\)
\(308\) 11.0776 6.39564i 0.631204 0.364426i
\(309\) −7.58258 + 13.1334i −0.431358 + 0.747133i
\(310\) −31.5381 + 35.2869i −1.79124 + 2.00416i
\(311\) −1.58258 −0.0897396 −0.0448698 0.998993i \(-0.514287\pi\)
−0.0448698 + 0.998993i \(0.514287\pi\)
\(312\) 0 0
\(313\) 30.7477i 1.73796i −0.494843 0.868982i \(-0.664775\pi\)
0.494843 0.868982i \(-0.335225\pi\)
\(314\) −17.3739 10.0308i −0.980464 0.566071i
\(315\) 5.77542 + 5.16184i 0.325408 + 0.290837i
\(316\) −8.37386 14.5040i −0.471067 0.815911i
\(317\) 20.9753 1.17809 0.589045 0.808100i \(-0.299504\pi\)
0.589045 + 0.808100i \(0.299504\pi\)
\(318\) −1.73205 3.00000i −0.0971286 0.168232i
\(319\) 10.5000 6.06218i 0.587887 0.339417i
\(320\) −5.74835 + 27.5420i −0.321343 + 1.53965i
\(321\) 0.708712 + 1.22753i 0.0395565 + 0.0685138i
\(322\) 15.0462 + 8.68693i 0.838492 + 0.484104i
\(323\) −3.96863 + 6.87386i −0.220820 + 0.382472i
\(324\) 2.79129 0.155072
\(325\) 0 0
\(326\) 23.3739 1.29456
\(327\) −1.37055 + 2.37386i −0.0757916 + 0.131275i
\(328\) 3.96863 + 2.29129i 0.219131 + 0.126515i
\(329\) 7.58258 + 13.1334i 0.418041 + 0.724068i
\(330\) −2.64575 + 12.6766i −0.145644 + 0.697821i
\(331\) −9.87386 + 5.70068i −0.542717 + 0.313338i −0.746179 0.665745i \(-0.768114\pi\)
0.203463 + 0.979083i \(0.434780\pi\)
\(332\) 15.7792 + 27.3303i 0.865994 + 1.49995i
\(333\) 15.8745 0.869918
\(334\) −4.68693 8.11800i −0.256457 0.444197i
\(335\) −24.7840 22.1509i −1.35409 1.21023i
\(336\) 2.68693 + 1.55130i 0.146584 + 0.0846304i
\(337\) 3.25227i 0.177163i −0.996069 0.0885813i \(-0.971767\pi\)
0.996069 0.0885813i \(-0.0282333\pi\)
\(338\) 0 0
\(339\) 16.5826 0.900642
\(340\) 19.0602 21.3259i 1.03369 1.15656i
\(341\) 12.7913 22.1552i 0.692687 1.19977i
\(342\) 6.56670 3.79129i 0.355087 0.205009i
\(343\) −19.0526 −1.02874
\(344\) 2.12614 1.22753i 0.114634 0.0661837i
\(345\) −9.73371 + 3.20233i −0.524045 + 0.172408i
\(346\) 16.2360i 0.872853i
\(347\) −13.2764 + 7.66515i −0.712716 + 0.411487i −0.812066 0.583566i \(-0.801657\pi\)
0.0993497 + 0.995053i \(0.468324\pi\)
\(348\) −11.0776 6.39564i −0.593821 0.342843i
\(349\) −15.8739 9.16478i −0.849708 0.490579i 0.0108440 0.999941i \(-0.496548\pi\)
−0.860552 + 0.509362i \(0.829882\pi\)
\(350\) −17.3739 7.58258i −0.928672 0.405306i
\(351\) 0 0
\(352\) 19.5390i 1.04143i
\(353\) 8.70793 15.0826i 0.463476 0.802765i −0.535655 0.844437i \(-0.679935\pi\)
0.999131 + 0.0416724i \(0.0132686\pi\)
\(354\) 3.68693 6.38595i 0.195958 0.339410i
\(355\) −2.48737 7.56052i −0.132016 0.401271i
\(356\) 11.9536i 0.633537i
\(357\) −3.96863 6.87386i −0.210042 0.363803i
\(358\) −0.180750 0.313068i −0.00955294 0.0165462i
\(359\) 33.3857i 1.76203i −0.473088 0.881015i \(-0.656861\pi\)
0.473088 0.881015i \(-0.343139\pi\)
\(360\) −7.35799 + 2.42074i −0.387800 + 0.127584i
\(361\) −8.00000 + 13.8564i −0.421053 + 0.729285i
\(362\) 20.5185 35.5390i 1.07843 1.86789i
\(363\) 4.00000i 0.209946i
\(364\) 0 0
\(365\) 0 0
\(366\) 20.0608 + 11.5821i 1.04859 + 0.605406i
\(367\) 22.2982 + 12.8739i 1.16396 + 0.672010i 0.952249 0.305323i \(-0.0987644\pi\)
0.211707 + 0.977333i \(0.432098\pi\)
\(368\) 7.10895 4.10436i 0.370580 0.213954i
\(369\) 5.29150i 0.275465i
\(370\) −36.9033 + 12.1410i −1.91851 + 0.631179i
\(371\) −2.37386 + 1.37055i −0.123245 + 0.0711554i
\(372\) −26.9898 −1.39936
\(373\) −11.2583 + 6.50000i −0.582934 + 0.336557i −0.762299 0.647225i \(-0.775929\pi\)
0.179364 + 0.983783i \(0.442596\pi\)
\(374\) −13.2695 + 22.9835i −0.686150 + 1.18845i
\(375\) 10.1629 4.65997i 0.524810 0.240640i
\(376\) −15.1652 −0.782083
\(377\) 0 0
\(378\) 18.9564i 0.975014i
\(379\) −18.2477 10.5353i −0.937323 0.541164i −0.0482027 0.998838i \(-0.515349\pi\)
−0.889120 + 0.457674i \(0.848683\pi\)
\(380\) −7.20409 + 8.06042i −0.369562 + 0.413491i
\(381\) 4.87386 + 8.44178i 0.249696 + 0.432485i
\(382\) −16.2360 −0.830706
\(383\) −1.41823 2.45644i −0.0724680 0.125518i 0.827514 0.561444i \(-0.189754\pi\)
−0.899982 + 0.435926i \(0.856421\pi\)
\(384\) −11.0608 + 6.38595i −0.564444 + 0.325882i
\(385\) 10.0308 + 2.09355i 0.511217 + 0.106697i
\(386\) −1.10436 1.91280i −0.0562102 0.0973590i
\(387\) −2.45505 1.41742i −0.124797 0.0720517i
\(388\) 6.24293 10.8131i 0.316937 0.548950i
\(389\) −15.1652 −0.768904 −0.384452 0.923145i \(-0.625610\pi\)
−0.384452 + 0.923145i \(0.625610\pi\)
\(390\) 0 0
\(391\) −21.0000 −1.06202
\(392\) 3.46410 6.00000i 0.174964 0.303046i
\(393\) −1.37055 0.791288i −0.0691351 0.0399152i
\(394\) −21.8521 37.8489i −1.10089 1.90680i
\(395\) 2.74110 13.1334i 0.137920 0.660813i
\(396\) 12.7913 7.38505i 0.642786 0.371113i
\(397\) 13.6379 + 23.6216i 0.684468 + 1.18553i 0.973604 + 0.228245i \(0.0732989\pi\)
−0.289135 + 0.957288i \(0.593368\pi\)
\(398\) −3.10260 −0.155519
\(399\) 1.50000 + 2.59808i 0.0750939 + 0.130066i
\(400\) −7.20696 + 5.31767i −0.360348 + 0.265883i
\(401\) −10.8303 6.25288i −0.540840 0.312254i 0.204580 0.978850i \(-0.434417\pi\)
−0.745419 + 0.666596i \(0.767751\pi\)
\(402\) 32.5390i 1.62290i
\(403\) 0 0
\(404\) 25.1216 1.24985
\(405\) 1.66722 + 1.49009i 0.0828448 + 0.0740434i
\(406\) −8.68693 + 15.0462i −0.431125 + 0.746731i
\(407\) 18.1865 10.5000i 0.901473 0.520466i
\(408\) 7.93725 0.392953
\(409\) −7.50000 + 4.33013i −0.370851 + 0.214111i −0.673830 0.738886i \(-0.735352\pi\)
0.302979 + 0.952997i \(0.402019\pi\)
\(410\) 4.04699 + 12.3011i 0.199867 + 0.607508i
\(411\) 0.0953502i 0.00470328i
\(412\) −36.6591 + 21.1652i −1.80607 + 1.04273i
\(413\) −5.05313 2.91742i −0.248648 0.143557i
\(414\) 17.3739 + 10.0308i 0.853879 + 0.492987i
\(415\) −5.16515 + 24.7477i −0.253547 + 1.21482i
\(416\) 0 0
\(417\) 5.74773i 0.281467i
\(418\) 5.01540 8.68693i 0.245311 0.424892i
\(419\) −12.0826 + 20.9276i −0.590272 + 1.02238i 0.403923 + 0.914793i \(0.367646\pi\)
−0.994195 + 0.107589i \(0.965687\pi\)
\(420\) −3.37849 10.2691i −0.164853 0.501083i
\(421\) 26.2668i 1.28017i 0.768306 + 0.640083i \(0.221100\pi\)
−0.768306 + 0.640083i \(0.778900\pi\)
\(422\) −19.8809 34.4347i −0.967785 1.67625i
\(423\) 8.75560 + 15.1652i 0.425712 + 0.737355i
\(424\) 2.74110i 0.133120i
\(425\) 22.7691 2.56275i 1.10446 0.124311i
\(426\) 3.89564 6.74745i 0.188745 0.326915i
\(427\) 9.16478 15.8739i 0.443515 0.768190i
\(428\) 3.95644i 0.191242i
\(429\) 0 0
\(430\) 6.79129 + 1.41742i 0.327505 + 0.0683543i
\(431\) −25.6652 14.8178i −1.23625 0.713747i −0.267922 0.963441i \(-0.586337\pi\)
−0.968325 + 0.249693i \(0.919670\pi\)
\(432\) 7.75650 + 4.47822i 0.373185 + 0.215458i
\(433\) −15.3700 + 8.87386i −0.738634 + 0.426451i −0.821573 0.570104i \(-0.806903\pi\)
0.0829383 + 0.996555i \(0.473570\pi\)
\(434\) 36.6591i 1.75969i
\(435\) −3.20233 9.73371i −0.153540 0.466696i
\(436\) −6.62614 + 3.82560i −0.317334 + 0.183213i
\(437\) 7.93725 0.379690
\(438\) 0 0
\(439\) 20.2477 35.0701i 0.966371 1.67380i 0.260487 0.965477i \(-0.416117\pi\)
0.705885 0.708327i \(-0.250550\pi\)
\(440\) −6.82847 + 7.64016i −0.325535 + 0.364230i
\(441\) −8.00000 −0.380952
\(442\) 0 0
\(443\) 25.9129i 1.23116i −0.788075 0.615579i \(-0.788922\pi\)
0.788075 0.615579i \(-0.211078\pi\)
\(444\) −19.1869 11.0776i −0.910571 0.525719i
\(445\) −6.38126 + 7.13978i −0.302501 + 0.338458i
\(446\) −9.47822 16.4168i −0.448807 0.777356i
\(447\) 9.76465 0.461852
\(448\) 10.8968 + 18.8739i 0.514827 + 0.891706i
\(449\) −32.4564 + 18.7387i −1.53171 + 0.884336i −0.532431 + 0.846473i \(0.678721\pi\)
−0.999283 + 0.0378622i \(0.987945\pi\)
\(450\) −20.0616 8.75560i −0.945713 0.412743i
\(451\) −3.50000 6.06218i −0.164809 0.285457i
\(452\) 40.0855 + 23.1434i 1.88546 + 1.08857i
\(453\) −3.10260 + 5.37386i −0.145773 + 0.252486i
\(454\) −13.3739 −0.627667
\(455\) 0 0
\(456\) −3.00000 −0.140488
\(457\) 0.866025 1.50000i 0.0405110 0.0701670i −0.845059 0.534673i \(-0.820435\pi\)
0.885570 + 0.464506i \(0.153768\pi\)
\(458\) −10.3923 6.00000i −0.485601 0.280362i
\(459\) −11.4564 19.8431i −0.534741 0.926198i
\(460\) −27.9989 5.84370i −1.30545 0.272464i
\(461\) 1.03901 0.599876i 0.0483917 0.0279390i −0.475609 0.879657i \(-0.657772\pi\)
0.524001 + 0.851718i \(0.324439\pi\)
\(462\) 5.01540 + 8.68693i 0.233338 + 0.404153i
\(463\) −8.22330 −0.382169 −0.191085 0.981574i \(-0.561201\pi\)
−0.191085 + 0.981574i \(0.561201\pi\)
\(464\) 4.10436 + 7.10895i 0.190540 + 0.330025i
\(465\) −16.1208 14.4082i −0.747586 0.668163i
\(466\) −40.1216 23.1642i −1.85860 1.07306i
\(467\) 12.3303i 0.570578i −0.958441 0.285289i \(-0.907910\pi\)
0.958441 0.285289i \(-0.0920896\pi\)
\(468\) 0 0
\(469\) −25.7477 −1.18892
\(470\) −31.9525 28.5579i −1.47386 1.31728i
\(471\) 4.58258 7.93725i 0.211154 0.365729i
\(472\) 5.05313 2.91742i 0.232589 0.134285i
\(473\) −3.75015 −0.172432
\(474\) 11.3739 6.56670i 0.522419 0.301619i
\(475\) −8.60591 + 0.968627i −0.394866 + 0.0444437i
\(476\) 22.1552i 1.01548i
\(477\) −2.74110 + 1.58258i −0.125506 + 0.0724612i
\(478\) −39.7617 22.9564i −1.81866 1.05000i
\(479\) 28.0390 + 16.1883i 1.28114 + 0.739664i 0.977056 0.212983i \(-0.0683179\pi\)
0.304079 + 0.952647i \(0.401651\pi\)
\(480\) −16.1652 3.37386i −0.737835 0.153995i
\(481\) 0 0
\(482\) 3.79129i 0.172688i
\(483\) −3.96863 + 6.87386i −0.180579 + 0.312772i
\(484\) −5.58258 + 9.66930i −0.253753 + 0.439514i
\(485\) 9.50128 3.12587i 0.431431 0.141938i
\(486\) 35.0224i 1.58865i
\(487\) −10.5353 18.2477i −0.477401 0.826883i 0.522263 0.852784i \(-0.325088\pi\)
−0.999665 + 0.0259009i \(0.991755\pi\)
\(488\) 9.16478 + 15.8739i 0.414870 + 0.718576i
\(489\) 10.6784i 0.482892i
\(490\) 18.5975 6.11847i 0.840150 0.276404i
\(491\) −14.2913 + 24.7532i −0.644957 + 1.11710i 0.339355 + 0.940658i \(0.389791\pi\)
−0.984311 + 0.176439i \(0.943542\pi\)
\(492\) −3.69253 + 6.39564i −0.166472 + 0.288338i
\(493\) 21.0000i 0.945792i
\(494\) 0 0
\(495\) 11.5826 + 2.41742i 0.520598 + 0.108655i
\(496\) 15.0000 + 8.66025i 0.673520 + 0.388857i
\(497\) −5.33918 3.08258i −0.239495 0.138272i
\(498\) −21.4322 + 12.3739i −0.960398 + 0.554486i
\(499\) 16.5975i 0.743006i −0.928432 0.371503i \(-0.878842\pi\)
0.928432 0.371503i \(-0.121158\pi\)
\(500\) 31.0707 + 2.91914i 1.38952 + 0.130548i
\(501\) 3.70871 2.14123i 0.165693 0.0956629i
\(502\) 39.7617 1.77465
\(503\) −15.7315 + 9.08258i −0.701432 + 0.404972i −0.807881 0.589346i \(-0.799385\pi\)
0.106448 + 0.994318i \(0.466052\pi\)
\(504\) −3.00000 + 5.19615i −0.133631 + 0.231455i
\(505\) 15.0050 + 13.4109i 0.667712 + 0.596775i
\(506\) 26.5390 1.17980
\(507\) 0 0
\(508\) 27.2087i 1.20719i
\(509\) 25.6652 + 14.8178i 1.13759 + 0.656787i 0.945832 0.324656i \(-0.105249\pi\)
0.191756 + 0.981443i \(0.438582\pi\)
\(510\) 16.7235 + 14.9468i 0.740531 + 0.661857i
\(511\) 0 0
\(512\) 19.4340 0.858868
\(513\) 4.33013 + 7.50000i 0.191180 + 0.331133i
\(514\) −0.313068 + 0.180750i −0.0138088 + 0.00797254i
\(515\) −33.1950 6.92820i −1.46275 0.305293i
\(516\) 1.97822 + 3.42638i 0.0870863 + 0.150838i
\(517\) 20.0616 + 11.5826i 0.882309 + 0.509401i
\(518\) −15.0462 + 26.0608i −0.661092 + 1.14505i
\(519\) 7.41742 0.325589
\(520\) 0 0
\(521\) −27.4955 −1.20460 −0.602299 0.798271i \(-0.705748\pi\)
−0.602299 + 0.798271i \(0.705748\pi\)
\(522\) −10.0308 + 17.3739i −0.439036 + 0.760433i
\(523\) 15.7315 + 9.08258i 0.687890 + 0.397153i 0.802821 0.596220i \(-0.203331\pi\)
−0.114931 + 0.993373i \(0.536665\pi\)
\(524\) −2.20871 3.82560i −0.0964880 0.167122i
\(525\) 3.46410 7.93725i 0.151186 0.346410i
\(526\) 17.0608 9.85005i 0.743886 0.429483i
\(527\) −22.1552 38.3739i −0.965094 1.67159i
\(528\) 4.73930 0.206252
\(529\) −1.00000 1.73205i −0.0434783 0.0753066i
\(530\) 5.16184 5.77542i 0.224216 0.250868i
\(531\) −5.83485 3.36875i −0.253211 0.146191i
\(532\) 8.37386i 0.363053i
\(533\) 0 0
\(534\) −9.37386 −0.405647
\(535\) −2.11210 + 2.36316i −0.0913139 + 0.102168i
\(536\) 12.8739 22.2982i 0.556066 0.963135i
\(537\) 0.143025 0.0825757i 0.00617200 0.00356340i
\(538\) 32.8335 1.41555
\(539\) −9.16515 + 5.29150i −0.394771 + 0.227921i
\(540\) −9.75285 29.6444i −0.419696 1.27569i
\(541\) 10.3923i 0.446800i 0.974727 + 0.223400i \(0.0717156\pi\)
−0.974727 + 0.223400i \(0.928284\pi\)
\(542\) 16.4168 9.47822i 0.705160 0.407124i
\(543\) 16.2360 + 9.37386i 0.696754 + 0.402271i
\(544\) −29.3085 16.9213i −1.25659 0.725494i
\(545\) −6.00000 1.25227i −0.257012 0.0536415i
\(546\) 0 0
\(547\) 1.25227i 0.0535433i −0.999642 0.0267717i \(-0.991477\pi\)
0.999642 0.0267717i \(-0.00852270\pi\)
\(548\) −0.133075 + 0.230493i −0.00568468 + 0.00984615i
\(549\) 10.5826 18.3296i 0.451653 0.782287i
\(550\) −28.7747 + 3.23870i −1.22696 + 0.138099i
\(551\) 7.93725i 0.338138i
\(552\) −3.96863 6.87386i −0.168916 0.292571i
\(553\) −5.19615 9.00000i −0.220963 0.382719i
\(554\) 36.2976i 1.54214i
\(555\) −5.54661 16.8593i −0.235440 0.715636i
\(556\) 8.02178 13.8941i 0.340199 0.589242i
\(557\) 6.51903 11.2913i 0.276220 0.478427i −0.694222 0.719761i \(-0.744251\pi\)
0.970442 + 0.241334i \(0.0775848\pi\)
\(558\) 42.3303i 1.79198i
\(559\) 0 0
\(560\) −1.41742 + 6.79129i −0.0598971 + 0.286984i
\(561\) −10.5000 6.06218i −0.443310 0.255945i
\(562\) −33.1950 19.1652i −1.40025 0.808433i
\(563\) −7.79423 + 4.50000i −0.328488 + 0.189652i −0.655169 0.755482i \(-0.727403\pi\)
0.326682 + 0.945134i \(0.394069\pi\)
\(564\) 24.4394i 1.02908i
\(565\) 11.5880 + 35.2225i 0.487511 + 1.48182i
\(566\) −0.478220 + 0.276100i −0.0201011 + 0.0116054i
\(567\) 1.73205 0.0727393
\(568\) 5.33918 3.08258i 0.224027 0.129342i
\(569\) −9.87386 + 17.1020i −0.413934 + 0.716955i −0.995316 0.0966762i \(-0.969179\pi\)
0.581382 + 0.813631i \(0.302512\pi\)
\(570\) −6.32091 5.64938i −0.264754 0.236626i
\(571\) 29.0780 1.21688 0.608439 0.793601i \(-0.291796\pi\)
0.608439 + 0.793601i \(0.291796\pi\)
\(572\) 0 0
\(573\) 7.41742i 0.309867i
\(574\) 8.68693 + 5.01540i 0.362586 + 0.209339i
\(575\) −13.6040 18.4373i −0.567324 0.768887i
\(576\) 12.5826 + 21.7937i 0.524274 + 0.908069i
\(577\) −6.92820 −0.288425 −0.144212 0.989547i \(-0.546065\pi\)
−0.144212 + 0.989547i \(0.546065\pi\)
\(578\) 4.37780 + 7.58258i 0.182093 + 0.315394i
\(579\) 0.873864 0.504525i 0.0363165 0.0209674i
\(580\) 5.84370 27.9989i 0.242647 1.16259i
\(581\) 9.79129 + 16.9590i 0.406211 + 0.703578i
\(582\) 8.47950 + 4.89564i 0.351487 + 0.202931i
\(583\) −2.09355 + 3.62614i −0.0867060 + 0.150179i
\(584\) 0 0
\(585\) 0 0
\(586\) 51.2867 2.11864
\(587\) −9.35548 + 16.2042i −0.386142 + 0.668818i −0.991927 0.126811i \(-0.959526\pi\)
0.605785 + 0.795628i \(0.292859\pi\)
\(588\) 9.66930 + 5.58258i 0.398755 + 0.230222i
\(589\) 8.37386 + 14.5040i 0.345039 + 0.597625i
\(590\) 16.1407 + 3.36875i 0.664500 + 0.138689i
\(591\) 17.2913 9.98313i 0.711269 0.410651i
\(592\) 7.10895 + 12.3131i 0.292176 + 0.506064i
\(593\) 21.1660 0.869184 0.434592 0.900627i \(-0.356893\pi\)
0.434592 + 0.900627i \(0.356893\pi\)
\(594\) 14.4782 + 25.0770i 0.594049 + 1.02892i
\(595\) 11.8273 13.2331i 0.484870 0.542506i
\(596\) 23.6044 + 13.6280i 0.966872 + 0.558224i
\(597\) 1.41742i 0.0580113i
\(598\) 0 0
\(599\) 39.4955 1.61374 0.806870 0.590729i \(-0.201160\pi\)
0.806870 + 0.590729i \(0.201160\pi\)
\(600\) 5.14181 + 6.96863i 0.209914 + 0.284493i
\(601\) 14.4564 25.0393i 0.589690 1.02137i −0.404582 0.914502i \(-0.632583\pi\)
0.994273 0.106872i \(-0.0340836\pi\)
\(602\) 4.65390 2.68693i 0.189679 0.109511i
\(603\) −29.7309 −1.21074
\(604\) −15.0000 + 8.66025i −0.610341 + 0.352381i
\(605\) −8.49628 + 2.79523i −0.345423 + 0.113642i
\(606\) 19.7001i 0.800262i
\(607\) 17.1020 9.87386i 0.694150 0.400768i −0.111015 0.993819i \(-0.535410\pi\)
0.805165 + 0.593051i \(0.202077\pi\)
\(608\) 11.0776 + 6.39564i 0.449255 + 0.259378i
\(609\) −6.87386 3.96863i −0.278543 0.160817i
\(610\) −10.5826 + 50.7042i −0.428476 + 2.05295i
\(611\) 0 0
\(612\) 25.5826i 1.03411i
\(613\) −10.8968 + 18.8739i −0.440119 + 0.762308i −0.997698 0.0678157i \(-0.978397\pi\)
0.557579 + 0.830124i \(0.311730\pi\)
\(614\) −26.5390 + 45.9669i −1.07103 + 1.85507i
\(615\) −5.61976 + 1.84887i −0.226611 + 0.0745536i
\(616\) 7.93725i 0.319801i
\(617\) −1.68438 2.91742i −0.0678104 0.117451i 0.830127 0.557575i \(-0.188268\pi\)
−0.897937 + 0.440124i \(0.854935\pi\)
\(618\) −16.5975 28.7477i −0.667650 1.15640i
\(619\) 2.01810i 0.0811143i −0.999177 0.0405572i \(-0.987087\pi\)
0.999177 0.0405572i \(-0.0129133\pi\)
\(620\) −18.8607 57.3282i −0.757462 2.30236i
\(621\) −11.4564 + 19.8431i −0.459731 + 0.796278i
\(622\) 1.73205 3.00000i 0.0694489 0.120289i
\(623\) 7.41742i 0.297173i
\(624\) 0 0
\(625\) 17.0000 + 18.3303i 0.680000 + 0.733212i
\(626\) 58.2867 + 33.6519i 2.32961 + 1.34500i
\(627\) 3.96863 + 2.29129i 0.158492 + 0.0915052i
\(628\) 22.1552 12.7913i 0.884087 0.510428i
\(629\) 36.3731i 1.45029i
\(630\) −16.1059 + 5.29875i −0.641675 + 0.211107i
\(631\) 18.8739 10.8968i 0.751357 0.433796i −0.0748272 0.997197i \(-0.523841\pi\)
0.826184 + 0.563401i \(0.190507\pi\)
\(632\) 10.3923 0.413384
\(633\) 15.7315 9.08258i 0.625270 0.361000i
\(634\) −22.9564 + 39.7617i −0.911717 + 1.57914i
\(635\) −14.5250 + 16.2516i −0.576408 + 0.644925i
\(636\) 4.41742 0.175162
\(637\) 0 0
\(638\) 26.5390i 1.05069i
\(639\) −6.16515 3.55945i −0.243890 0.140810i
\(640\) −21.2936 19.0313i −0.841702 0.752280i
\(641\) 0.0825757 + 0.143025i 0.00326154 + 0.00564916i 0.867652 0.497173i \(-0.165628\pi\)
−0.864390 + 0.502822i \(0.832295\pi\)
\(642\) −3.10260 −0.122450
\(643\) −2.95958 5.12614i −0.116714 0.202155i 0.801749 0.597660i \(-0.203903\pi\)
−0.918464 + 0.395505i \(0.870570\pi\)
\(644\) −19.1869 + 11.0776i −0.756071 + 0.436518i
\(645\) −0.647551 + 3.10260i −0.0254973 + 0.122165i
\(646\) −8.68693 15.0462i −0.341783 0.591985i
\(647\) 23.3827 + 13.5000i 0.919268 + 0.530740i 0.883402 0.468617i \(-0.155247\pi\)
0.0358667 + 0.999357i \(0.488581\pi\)
\(648\) −0.866025 + 1.50000i −0.0340207 + 0.0589256i
\(649\) −8.91288 −0.349861
\(650\) 0 0
\(651\) −16.7477 −0.656395
\(652\) −14.9032 + 25.8131i −0.583654 + 1.01092i
\(653\) −42.2843 24.4129i −1.65471 0.955350i −0.975096 0.221784i \(-0.928812\pi\)
−0.679619 0.733566i \(-0.737855\pi\)
\(654\) −3.00000 5.19615i −0.117309 0.203186i
\(655\) 0.723000 3.46410i 0.0282500 0.135354i
\(656\) 4.10436 2.36965i 0.160248 0.0925193i
\(657\) 0 0
\(658\) −33.1950 −1.29408
\(659\) −12.2477 21.2137i −0.477104 0.826368i 0.522552 0.852607i \(-0.324980\pi\)
−0.999656 + 0.0262396i \(0.991647\pi\)
\(660\) −12.3125 11.0044i −0.479263 0.428347i
\(661\) −2.12614 1.22753i −0.0826971 0.0477452i 0.458081 0.888910i \(-0.348537\pi\)
−0.540778 + 0.841165i \(0.681870\pi\)
\(662\) 24.9564i 0.969960i
\(663\) 0 0
\(664\) −19.5826 −0.759951
\(665\) −4.47028 + 5.00166i −0.173350 + 0.193956i
\(666\) −17.3739 + 30.0924i −0.673224 + 1.16606i
\(667\) −18.1865 + 10.5000i −0.704185 + 0.406562i
\(668\) 11.9536 0.462497
\(669\) 7.50000 4.33013i 0.289967 0.167412i
\(670\) 69.1151 22.7385i 2.67015 0.878464i
\(671\) 27.9989i 1.08088i
\(672\) −11.0776 + 6.39564i −0.427327 + 0.246717i
\(673\) 5.05313 + 2.91742i 0.194784 + 0.112458i 0.594220 0.804302i \(-0.297461\pi\)
−0.399436 + 0.916761i \(0.630794\pi\)
\(674\) 6.16515 + 3.55945i 0.237473 + 0.137105i
\(675\) 10.0000 22.9129i 0.384900 0.881917i
\(676\) 0 0
\(677\) 21.1652i 0.813443i 0.913552 + 0.406721i \(0.133328\pi\)
−0.913552 + 0.406721i \(0.866672\pi\)
\(678\) −18.1488 + 31.4347i −0.697001 + 1.20724i
\(679\) 3.87386 6.70973i 0.148665 0.257496i
\(680\) 5.54661 + 16.8593i 0.212703 + 0.646524i
\(681\) 6.10985i 0.234130i
\(682\) 27.9989 + 48.4955i 1.07213 + 1.85699i
\(683\) 5.96683 + 10.3348i 0.228314 + 0.395452i 0.957309 0.289068i \(-0.0933453\pi\)
−0.728994 + 0.684520i \(0.760012\pi\)
\(684\) 9.66930i 0.369715i
\(685\) −0.202530 + 0.0666313i −0.00773829 + 0.00254585i
\(686\) 20.8521 36.1169i 0.796136 1.37895i
\(687\) 2.74110 4.74773i 0.104580 0.181137i
\(688\) 2.53901i 0.0967990i
\(689\) 0 0
\(690\) 4.58258 21.9564i 0.174456 0.835867i
\(691\) −30.8739 17.8250i −1.17450 0.678096i −0.219762 0.975554i \(-0.570528\pi\)
−0.954735 + 0.297457i \(0.903861\pi\)
\(692\) 17.9303 + 10.3521i 0.681609 + 0.393527i
\(693\) 7.93725 4.58258i 0.301511 0.174078i
\(694\) 33.5565i 1.27379i
\(695\) 12.2086 4.01655i 0.463097 0.152356i
\(696\) 6.87386 3.96863i 0.260553 0.150430i
\(697\) −12.1244 −0.459243
\(698\) 34.7463 20.0608i 1.31517 0.759312i
\(699\) 10.5826 18.3296i 0.400270 0.693288i
\(700\) 19.4514 14.3523i 0.735195 0.542465i
\(701\) −2.83485 −0.107071 −0.0535354 0.998566i \(-0.517049\pi\)
−0.0535354 + 0.998566i \(0.517049\pi\)
\(702\) 0 0
\(703\) 13.7477i 0.518505i
\(704\) 28.8303 + 16.6452i 1.08658 + 0.627339i
\(705\) 13.0467 14.5975i 0.491366 0.549774i
\(706\) 19.0608 + 33.0143i 0.717362 + 1.24251i
\(707\) 15.5885 0.586264
\(708\) 4.70158 + 8.14337i 0.176696 + 0.306047i
\(709\) −31.5000 + 18.1865i −1.18301 + 0.683010i −0.956708 0.291048i \(-0.905996\pi\)
−0.226299 + 0.974058i \(0.572663\pi\)
\(710\) 17.0544 + 3.55945i 0.640039 + 0.133584i
\(711\) −6.00000 10.3923i −0.225018 0.389742i
\(712\) −6.42368 3.70871i −0.240738 0.138990i
\(713\) −22.1552 + 38.3739i −0.829717 + 1.43711i
\(714\) 17.3739 0.650201
\(715\) 0 0
\(716\) 0.460985 0.0172278
\(717\) 10.4877 18.1652i 0.391669 0.678390i
\(718\) 63.2874 + 36.5390i 2.36187 + 1.36362i
\(719\) 15.2477 + 26.4098i 0.568644 + 0.984921i 0.996700 + 0.0811686i \(0.0258652\pi\)
−0.428056 + 0.903752i \(0.640801\pi\)
\(720\) −1.63670 + 7.84190i −0.0609962 + 0.292250i
\(721\) −22.7477 + 13.1334i −0.847170 + 0.489114i
\(722\) −17.5112 30.3303i −0.651700 1.12878i
\(723\) −1.73205 −0.0644157
\(724\) 26.1652 + 45.3194i 0.972420 + 1.68428i
\(725\) 18.4373 13.6040i 0.684742 0.505238i
\(726\) −7.58258 4.37780i −0.281416 0.162475i
\(727\) 42.7477i 1.58543i 0.609595 + 0.792713i \(0.291332\pi\)
−0.609595 + 0.792713i \(0.708668\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) −3.24773 + 5.62523i −0.120122 + 0.208057i
\(732\) −25.5815 + 14.7695i −0.945521 + 0.545897i
\(733\) −8.94630 −0.330439 −0.165220 0.986257i \(-0.552833\pi\)
−0.165220 + 0.986257i \(0.552833\pi\)
\(734\) −48.8085 + 28.1796i −1.80156 + 1.04013i
\(735\) 2.79523 + 8.49628i 0.103103 + 0.313390i
\(736\) 33.8426i 1.24745i
\(737\) −34.0610 + 19.6652i −1.25465 + 0.724375i
\(738\) 10.0308 + 5.79129i 0.369239 + 0.213180i
\(739\) 42.2477 + 24.3917i 1.55411 + 0.897265i 0.997801 + 0.0662878i \(0.0211156\pi\)
0.556307 + 0.830977i \(0.312218\pi\)
\(740\) 10.1216 48.4955i 0.372077 1.78273i
\(741\) 0 0
\(742\) 6.00000i 0.220267i
\(743\) 21.3845 37.0390i 0.784521 1.35883i −0.144764 0.989466i \(-0.546242\pi\)
0.929285 0.369364i \(-0.120424\pi\)
\(744\) 8.37386 14.5040i 0.307001 0.531741i
\(745\) 6.82361 + 20.7408i 0.249998 + 0.759884i
\(746\) 28.4557i 1.04184i
\(747\) 11.3060 + 19.5826i 0.413665 + 0.716489i
\(748\) −16.9213 29.3085i −0.618703 1.07163i
\(749\) 2.45505i 0.0897056i
\(750\) −2.28916 + 24.3654i −0.0835884 + 0.889697i
\(751\) 7.87386 13.6379i 0.287321 0.497655i −0.685848 0.727745i \(-0.740569\pi\)
0.973169 + 0.230090i \(0.0739019\pi\)
\(752\) −7.84190 + 13.5826i −0.285965 + 0.495306i
\(753\) 18.1652i 0.661975i
\(754\) 0 0
\(755\) −13.5826 2.83485i −0.494321 0.103171i
\(756\) −20.9347 12.0866i −0.761386 0.439587i
\(757\) −15.3700 8.87386i −0.558632 0.322526i 0.193965 0.981009i \(-0.437865\pi\)
−0.752596 + 0.658482i \(0.771199\pi\)
\(758\) 39.9425 23.0608i 1.45078 0.837606i
\(759\) 12.1244i 0.440086i
\(760\) −2.09642 6.37221i −0.0760451 0.231144i
\(761\) 35.2913 20.3754i 1.27931 0.738609i 0.302587 0.953122i \(-0.402150\pi\)
0.976721 + 0.214513i \(0.0688164\pi\)
\(762\) −21.3368 −0.772951
\(763\) −4.11165 + 2.37386i −0.148852 + 0.0859396i
\(764\) 10.3521 17.9303i 0.374525 0.648697i
\(765\) 13.6569 15.2803i 0.493768 0.552461i
\(766\) 6.20871 0.224330
\(767\) 0 0
\(768\) 2.79129i 0.100722i
\(769\) 13.5000 + 7.79423i 0.486822 + 0.281067i 0.723255 0.690581i \(-0.242645\pi\)
−0.236433 + 0.971648i \(0.575978\pi\)
\(770\) −14.9468 + 16.7235i −0.538647 + 0.602675i
\(771\) −0.0825757 0.143025i −0.00297389 0.00515093i
\(772\) 2.81655 0.101370
\(773\) −17.3682 30.0826i −0.624690 1.08200i −0.988601 0.150561i \(-0.951892\pi\)
0.363911 0.931434i \(-0.381441\pi\)
\(774\) 5.37386 3.10260i 0.193160 0.111521i
\(775\) 19.3386 44.3103i 0.694663 1.59167i
\(776\) 3.87386 + 6.70973i 0.139064 + 0.240865i
\(777\) −11.9059 6.87386i −0.427121 0.246598i
\(778\) 16.5975 28.7477i 0.595049 1.03066i
\(779\) 4.58258 0.164188
\(780\) 0 0
\(781\) −9.41742 −0.336982
\(782\) 22.9835 39.8085i 0.821887 1.42355i
\(783\) −19.8431 11.4564i −0.709136 0.409420i
\(784\) −3.58258 6.20520i −0.127949 0.221614i
\(785\) 20.0616 + 4.18710i 0.716030 + 0.149444i
\(786\) 3.00000 1.73205i 0.107006 0.0617802i
\(787\) 16.0930 + 27.8739i 0.573653 + 0.993596i 0.996187 + 0.0872487i \(0.0278075\pi\)
−0.422534 + 0.906347i \(0.638859\pi\)
\(788\) 55.7316 1.98536
\(789\) 4.50000 + 7.79423i 0.160204 + 0.277482i
\(790\) 21.8963 + 19.5700i 0.779034 + 0.696270i
\(791\) 24.8739 + 14.3609i 0.884413 + 0.510616i
\(792\) 9.16515i 0.325669i
\(793\) 0 0
\(794\) −59.7042 −2.11882
\(795\) 2.63850 + 2.35819i 0.0935779 + 0.0836363i
\(796\) 1.97822 3.42638i 0.0701161 0.121445i
\(797\) 17.3881 10.0390i 0.615918 0.355600i −0.159360 0.987220i \(-0.550943\pi\)
0.775278 + 0.631620i \(0.217610\pi\)
\(798\) −6.56670 −0.232459
\(799\) 34.7477 20.0616i 1.22929 0.709729i
\(800\) −4.13000 36.6936i −0.146017 1.29731i
\(801\) 8.56490i 0.302626i
\(802\) 23.7065 13.6869i 0.837104 0.483302i
\(803\) 0 0
\(804\) 35.9347 + 20.7469i 1.26732 + 0.731686i
\(805\) −17.3739 3.62614i −0.612348 0.127805i
\(806\) 0 0
\(807\) 15.0000i 0.528025i
\(808\) −7.79423 + 13.5000i −0.274200 + 0.474928i
\(809\) 18.4129 31.8920i 0.647362 1.12126i −0.336388 0.941723i \(-0.609205\pi\)
0.983750 0.179541i \(-0.0574613\pi\)
\(810\) −4.64938 + 1.52962i −0.163362 + 0.0537453i
\(811\) 18.7665i 0.658981i 0.944159 + 0.329491i \(0.106877\pi\)
−0.944159 + 0.329491i \(0.893123\pi\)
\(812\) −11.0776 19.1869i −0.388747 0.673329i
\(813\) 4.33013 + 7.50000i 0.151864 + 0.263036i
\(814\) 45.9669i 1.61114i
\(815\) −22.6816 + 7.46211i −0.794501 + 0.261386i
\(816\) 4.10436 7.10895i 0.143681 0.248863i
\(817\) 1.22753 2.12614i 0.0429457 0.0743841i
\(818\) 18.9564i 0.662796i
\(819\) 0 0
\(820\) −16.1652 3.37386i −0.564512 0.117820i
\(821\) −20.2913 11.7152i −0.708171 0.408863i 0.102213 0.994763i \(-0.467408\pi\)
−0.810383 + 0.585900i \(0.800741\pi\)
\(822\) −0.180750 0.104356i −0.00630438 0.00363984i
\(823\) −35.1455 + 20.2913i −1.22510 + 0.707310i −0.966000 0.258542i \(-0.916758\pi\)
−0.259096 + 0.965851i \(0.583425\pi\)
\(824\) 26.2668i 0.915048i
\(825\) −1.47960 13.1458i −0.0515131 0.457676i
\(826\) 11.0608 6.38595i 0.384854 0.222196i
\(827\) −31.5583 −1.09739 −0.548695 0.836023i \(-0.684875\pi\)
−0.548695 + 0.836023i \(0.684875\pi\)
\(828\) −22.1552 + 12.7913i −0.769945 + 0.444528i
\(829\) 1.66515 2.88413i 0.0578331 0.100170i −0.835659 0.549248i \(-0.814914\pi\)
0.893492 + 0.449078i \(0.148248\pi\)
\(830\) −41.2599 36.8765i −1.43215 1.28000i
\(831\) −16.5826 −0.575243
\(832\) 0 0
\(833\) 18.3303i 0.635107i
\(834\) 10.8956 + 6.29060i 0.377285 + 0.217826i
\(835\) 7.13978 + 6.38126i 0.247082 + 0.220833i
\(836\) 6.39564 + 11.0776i 0.221198 + 0.383126i
\(837\) −48.3465 −1.67110
\(838\) −26.4476 45.8085i −0.913616 1.58243i
\(839\) −1.16970 + 0.675325i −0.0403824 + 0.0233148i −0.520055 0.854133i \(-0.674089\pi\)
0.479673 + 0.877447i \(0.340755\pi\)
\(840\) 6.56670 + 1.37055i 0.226573 + 0.0472885i
\(841\) 4.00000 + 6.92820i 0.137931 + 0.238904i
\(842\) −49.7925 28.7477i −1.71596 0.990712i
\(843\) 8.75560 15.1652i 0.301559 0.522316i
\(844\) 50.7042 1.74531
\(845\) 0 0
\(846\) −38.3303 −1.31782
\(847\) −3.46410 + 6.00000i −0.119028 + 0.206162i
\(848\) −2.45505 1.41742i −0.0843068 0.0486746i
\(849\) −0.126136 0.218475i −0.00432899 0.00749803i
\(850\) −20.0616 + 45.9669i −0.688108 + 1.57665i
\(851\) −31.5000 + 18.1865i −1.07981 + 0.623426i
\(852\) 4.96773 + 8.60436i 0.170192 + 0.294780i
\(853\) −53.2566 −1.82347 −0.911736 0.410777i \(-0.865258\pi\)
−0.911736 + 0.410777i \(0.865258\pi\)
\(854\) 20.0608 + 34.7463i 0.686466 + 1.18899i
\(855\) −5.16184 + 5.77542i −0.176531 + 0.197515i
\(856\) −2.12614 1.22753i −0.0726698 0.0419560i
\(857\) 22.7477i 0.777048i −0.921439 0.388524i \(-0.872985\pi\)
0.921439 0.388524i \(-0.127015\pi\)
\(858\) 0 0
\(859\) −38.2432 −1.30484 −0.652420 0.757857i \(-0.726246\pi\)
−0.652420 + 0.757857i \(0.726246\pi\)
\(860\) −5.89547 + 6.59625i −0.201034 + 0.224930i
\(861\) −2.29129 + 3.96863i −0.0780869 + 0.135250i
\(862\) 56.1785 32.4347i 1.91345 1.10473i
\(863\) 34.8317 1.18569 0.592843 0.805318i \(-0.298006\pi\)
0.592843 + 0.805318i \(0.298006\pi\)
\(864\) −31.9782 + 18.4626i −1.08792 + 0.628112i
\(865\) 5.18335 + 15.7551i 0.176239 + 0.535690i
\(866\) 38.8480i 1.32011i
\(867\) −3.46410 + 2.00000i −0.117647 + 0.0679236i
\(868\) −40.4847 23.3739i −1.37414 0.793361i
\(869\) −13.7477 7.93725i −0.466360 0.269253i
\(870\) 21.9564 + 4.58258i 0.744393 + 0.155364i
\(871\) 0 0
\(872\) 4.74773i 0.160778i
\(873\) 4.47315 7.74773i 0.151393 0.262221i
\(874\) −8.68693 + 15.0462i −0.293840 + 0.508946i
\(875\) 19.2800 + 1.81139i 0.651783 + 0.0612360i
\(876\) 0 0
\(877\) 3.96863 + 6.87386i 0.134011 + 0.232114i 0.925219 0.379433i \(-0.123881\pi\)
−0.791208 + 0.611547i \(0.790548\pi\)
\(878\) 44.3203 + 76.7650i 1.49574 + 2.59069i
\(879\) 23.4304i 0.790286i
\(880\) 3.31186 + 10.0666i 0.111643 + 0.339345i
\(881\) 9.24773 16.0175i 0.311564 0.539644i −0.667137 0.744935i \(-0.732481\pi\)
0.978701 + 0.205290i \(0.0658139\pi\)
\(882\) 8.75560 15.1652i 0.294817 0.510637i
\(883\) 46.2432i 1.55621i −0.628136 0.778103i \(-0.716182\pi\)
0.628136 0.778103i \(-0.283818\pi\)
\(884\) 0 0
\(885\) −1.53901 + 7.37386i −0.0517334 + 0.247870i
\(886\) 49.1216 + 28.3604i 1.65027 + 0.952785i
\(887\) −0.429076 0.247727i −0.0144070 0.00831786i 0.492779 0.870154i \(-0.335981\pi\)
−0.507186 + 0.861837i \(0.669314\pi\)
\(888\) 11.9059 6.87386i 0.399535 0.230672i
\(889\) 16.8836i 0.566256i
\(890\) −6.55052 19.9107i −0.219574 0.667409i
\(891\) 2.29129 1.32288i 0.0767610 0.0443180i
\(892\) 24.1733 0.809381
\(893\) −13.1334 + 7.58258i −0.439493 + 0.253741i
\(894\) −10.6869 + 18.5103i −0.357424 + 0.619077i
\(895\) 0.275344 + 0.246091i 0.00920372 + 0.00822592i
\(896\) −22.1216 −0.739030
\(897\) 0 0
\(898\) 82.0345i 2.73753i
\(899\) −38.3739 22.1552i −1.27984 0.738916i
\(900\) 22.4606 16.5726i 0.748686 0.552419i
\(901\) 3.62614 + 6.28065i 0.120804 + 0.209239i
\(902\) 15.3223 0.510177
\(903\) 1.22753 + 2.12614i 0.0408495 + 0.0707534i
\(904\) −24.8739 + 14.3609i −0.827292 + 0.477637i
\(905\) −8.56490 + 41.0369i −0.284707 + 1.36411i
\(906\) −6.79129 11.7629i −0.225625 0.390795i
\(907\) −29.2264 16.8739i −0.970446 0.560287i −0.0710740 0.997471i \(-0.522643\pi\)
−0.899372 + 0.437184i \(0.855976\pi\)
\(908\) 8.52718 14.7695i 0.282984 0.490143i
\(909\) 18.0000 0.597022
\(910\) 0 0
\(911\) 37.9129 1.25611 0.628055 0.778169i \(-0.283851\pi\)
0.628055 + 0.778169i \(0.283851\pi\)
\(912\) −1.55130 + 2.68693i −0.0513687 + 0.0889732i
\(913\) 25.9053 + 14.9564i 0.857341 + 0.494986i
\(914\) 1.89564 + 3.28335i 0.0627023 + 0.108604i
\(915\) −23.1642 4.83465i −0.765785 0.159829i
\(916\) 13.2523 7.65120i 0.437867 0.252803i
\(917\) −1.37055 2.37386i −0.0452596 0.0783919i
\(918\) 50.1540 1.65533
\(919\) 17.9174 + 31.0339i 0.591041 + 1.02371i 0.994093 + 0.108536i \(0.0346163\pi\)
−0.403051 + 0.915177i \(0.632050\pi\)
\(920\) 11.8273 13.2331i 0.389933 0.436284i
\(921\) −21.0000 12.1244i −0.691974 0.399511i
\(922\) 2.62614i 0.0864872i
\(923\) 0 0
\(924\) −12.7913 −0.420802
\(925\) 31.9343 23.5627i 1.04999 0.774738i
\(926\) 9.00000 15.5885i 0.295758 0.512268i
\(927\) −26.2668 + 15.1652i −0.862715 + 0.498089i
\(928\) −33.8426 −1.11094
\(929\) 13.8303 7.98493i 0.453758 0.261977i −0.255658 0.966767i \(-0.582292\pi\)
0.709416 + 0.704790i \(0.248959\pi\)
\(930\) 44.9562 14.7903i 1.47417 0.484995i
\(931\) 6.92820i 0.227063i
\(932\) 51.1631 29.5390i 1.67590 0.967583i
\(933\) 1.37055 + 0.791288i 0.0448698 + 0.0259056i
\(934\) 23.3739 + 13.4949i 0.764816 + 0.441567i
\(935\) 5.53901 26.5390i 0.181145 0.867919i
\(936\) 0 0
\(937\) 23.4955i 0.767563i 0.923424 + 0.383782i \(0.125378\pi\)
−0.923424 + 0.383782i \(0.874622\pi\)
\(938\) 28.1796 48.8085i 0.920097 1.59365i
\(939\) −15.3739 + 26.6283i −0.501707 + 0.868982i
\(940\) 51.9110 17.0784i 1.69315 0.557037i
\(941\) 26.4575i 0.862490i −0.902235 0.431245i \(-0.858074\pi\)
0.902235 0.431245i \(-0.141926\pi\)
\(942\) 10.0308 + 17.3739i 0.326821 + 0.566071i
\(943\) 6.06218 + 10.5000i 0.197412 + 0.341927i
\(944\) 6.03440i 0.196403i
\(945\) −6.05184 18.3950i −0.196866 0.598389i
\(946\) 4.10436 7.10895i 0.133444 0.231132i
\(947\) −19.2909 + 33.4129i −0.626871 + 1.08577i 0.361305 + 0.932448i \(0.382331\pi\)
−0.988176 + 0.153325i \(0.951002\pi\)
\(948\) 16.7477i 0.543941i
\(949\) 0 0
\(950\) 7.58258 17.3739i 0.246011 0.563683i
\(951\) −18.1652 10.4877i −0.589045 0.340086i
\(952\) 11.9059 + 6.87386i 0.385872 + 0.222783i
\(953\) 48.5650 28.0390i 1.57317 0.908273i 0.577398 0.816463i \(-0.304068\pi\)
0.995777 0.0918100i \(-0.0292652\pi\)
\(954\) 6.92820i 0.224309i
\(955\) 15.7551 5.18335i 0.509824 0.167729i
\(956\) 50.7042 29.2741i 1.63989 0.946791i
\(957\) −12.1244 −0.391925
\(958\) −61.3746 + 35.4347i −1.98292 + 1.14484i
\(959\) −0.0825757 + 0.143025i −0.00266651 + 0.00461853i
\(960\) 18.7492 20.9779i 0.605129 0.677059i
\(961\) −62.4955 −2.01598
\(962\) 0 0
\(963\) 2.83485i 0.0913517i
\(964\) −4.18693 2.41733i −0.134852 0.0778568i
\(965\) 1.68231 + 1.50358i 0.0541554 + 0.0484020i
\(966\) −8.68693 15.0462i −0.279497 0.484104i
\(967\) −21.5076 −0.691638 −0.345819 0.938301i \(-0.612399\pi\)
−0.345819 + 0.938301i \(0.612399\pi\)
\(968\) −3.46410 6.00000i −0.111340 0.192847i
\(969\) 6.87386 3.96863i 0.220820 0.127491i
\(970\) −4.47315 + 21.4322i −0.143624 + 0.688145i
\(971\) −18.2477 31.6060i −0.585597 1.01428i −0.994801 0.101841i \(-0.967527\pi\)
0.409203 0.912443i \(-0.365807\pi\)
\(972\) −38.6772 22.3303i −1.24057 0.716245i
\(973\) 4.97768 8.62159i 0.159577 0.276396i
\(974\) 46.1216 1.47783
\(975\) 0 0
\(976\) 18.9564 0.606781
\(977\) 19.3863 33.5780i 0.620222 1.07426i −0.369222 0.929341i \(-0.620376\pi\)
0.989444 0.144915i \(-0.0462909\pi\)
\(978\) −20.2424 11.6869i −0.647279 0.373707i
\(979\) 5.66515 + 9.81233i 0.181059 + 0.313603i
\(980\) −5.10080 + 24.4394i −0.162939 + 0.780688i
\(981\) −4.74773 + 2.74110i −0.151583 + 0.0875166i
\(982\) −31.2822 54.1824i −0.998256 1.72903i
\(983\) −3.12250 −0.0995924 −0.0497962 0.998759i \(-0.515857\pi\)
−0.0497962 + 0.998759i \(0.515857\pi\)
\(984\) −2.29129 3.96863i −0.0730436 0.126515i
\(985\) 33.2881 + 29.7516i 1.06065 + 0.947965i
\(986\) 39.8085 + 22.9835i 1.26776 + 0.731943i
\(987\) 15.1652i 0.482712i
\(988\) 0 0
\(989\) 6.49545 0.206543
\(990\) −17.2591 + 19.3107i −0.548531 + 0.613734i
\(991\) 6.50000 11.2583i 0.206479 0.357633i −0.744124 0.668042i \(-0.767133\pi\)
0.950603 + 0.310409i \(0.100466\pi\)
\(992\) −61.8414 + 35.7042i −1.96347 + 1.13361i
\(993\) 11.4014 0.361811
\(994\) 11.6869 6.74745i 0.370687 0.214016i
\(995\) 3.01071 0.990505i 0.0954458 0.0314011i
\(996\) 31.5583i 0.999963i
\(997\) 15.7315 9.08258i 0.498221 0.287648i −0.229758 0.973248i \(-0.573793\pi\)
0.727979 + 0.685600i \(0.240460\pi\)
\(998\) 31.4630 + 18.1652i 0.995943 + 0.575008i
\(999\) −34.3693 19.8431i −1.08740 0.627809i
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 845.2.l.c.654.1 8
5.4 even 2 inner 845.2.l.c.654.4 8
13.2 odd 12 845.2.n.c.484.2 8
13.3 even 3 65.2.l.a.49.1 yes 8
13.4 even 6 845.2.d.c.844.2 8
13.5 odd 4 845.2.n.d.529.3 8
13.6 odd 12 845.2.b.f.339.2 8
13.7 odd 12 845.2.b.f.339.8 8
13.8 odd 4 845.2.n.c.529.1 8
13.9 even 3 845.2.d.c.844.8 8
13.10 even 6 inner 845.2.l.c.699.4 8
13.11 odd 12 845.2.n.d.484.4 8
13.12 even 2 65.2.l.a.4.4 yes 8
39.29 odd 6 585.2.bf.a.244.4 8
39.38 odd 2 585.2.bf.a.199.1 8
52.3 odd 6 1040.2.df.b.49.2 8
52.51 odd 2 1040.2.df.b.849.3 8
65.3 odd 12 325.2.n.b.101.1 4
65.4 even 6 845.2.d.c.844.7 8
65.7 even 12 4225.2.a.bk.1.1 4
65.9 even 6 845.2.d.c.844.1 8
65.12 odd 4 325.2.n.c.251.2 4
65.19 odd 12 845.2.b.f.339.7 8
65.24 odd 12 845.2.n.c.484.1 8
65.29 even 6 65.2.l.a.49.4 yes 8
65.32 even 12 4225.2.a.bk.1.4 4
65.33 even 12 4225.2.a.bj.1.4 4
65.34 odd 4 845.2.n.d.529.4 8
65.38 odd 4 325.2.n.b.251.1 4
65.42 odd 12 325.2.n.c.101.2 4
65.44 odd 4 845.2.n.c.529.2 8
65.49 even 6 inner 845.2.l.c.699.1 8
65.54 odd 12 845.2.n.d.484.3 8
65.58 even 12 4225.2.a.bj.1.1 4
65.59 odd 12 845.2.b.f.339.1 8
65.64 even 2 65.2.l.a.4.1 8
195.29 odd 6 585.2.bf.a.244.1 8
195.194 odd 2 585.2.bf.a.199.4 8
260.159 odd 6 1040.2.df.b.49.3 8
260.259 odd 2 1040.2.df.b.849.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.l.a.4.1 8 65.64 even 2
65.2.l.a.4.4 yes 8 13.12 even 2
65.2.l.a.49.1 yes 8 13.3 even 3
65.2.l.a.49.4 yes 8 65.29 even 6
325.2.n.b.101.1 4 65.3 odd 12
325.2.n.b.251.1 4 65.38 odd 4
325.2.n.c.101.2 4 65.42 odd 12
325.2.n.c.251.2 4 65.12 odd 4
585.2.bf.a.199.1 8 39.38 odd 2
585.2.bf.a.199.4 8 195.194 odd 2
585.2.bf.a.244.1 8 195.29 odd 6
585.2.bf.a.244.4 8 39.29 odd 6
845.2.b.f.339.1 8 65.59 odd 12
845.2.b.f.339.2 8 13.6 odd 12
845.2.b.f.339.7 8 65.19 odd 12
845.2.b.f.339.8 8 13.7 odd 12
845.2.d.c.844.1 8 65.9 even 6
845.2.d.c.844.2 8 13.4 even 6
845.2.d.c.844.7 8 65.4 even 6
845.2.d.c.844.8 8 13.9 even 3
845.2.l.c.654.1 8 1.1 even 1 trivial
845.2.l.c.654.4 8 5.4 even 2 inner
845.2.l.c.699.1 8 65.49 even 6 inner
845.2.l.c.699.4 8 13.10 even 6 inner
845.2.n.c.484.1 8 65.24 odd 12
845.2.n.c.484.2 8 13.2 odd 12
845.2.n.c.529.1 8 13.8 odd 4
845.2.n.c.529.2 8 65.44 odd 4
845.2.n.d.484.3 8 65.54 odd 12
845.2.n.d.484.4 8 13.11 odd 12
845.2.n.d.529.3 8 13.5 odd 4
845.2.n.d.529.4 8 65.34 odd 4
1040.2.df.b.49.2 8 52.3 odd 6
1040.2.df.b.49.3 8 260.159 odd 6
1040.2.df.b.849.2 8 260.259 odd 2
1040.2.df.b.849.3 8 52.51 odd 2
4225.2.a.bj.1.1 4 65.58 even 12
4225.2.a.bj.1.4 4 65.33 even 12
4225.2.a.bk.1.1 4 65.7 even 12
4225.2.a.bk.1.4 4 65.32 even 12