Properties

Label 430.2.g.b.257.12
Level $430$
Weight $2$
Character 430.257
Analytic conductor $3.434$
Analytic rank $0$
Dimension $40$
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] = [430,2,Mod(257,430)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(430, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("430.257");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 430.g (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: \(3.43356728692\)
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 257.12
Character \(\chi\) \(=\) 430.257
Dual form 430.2.g.b.343.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.91446 - 1.91446i) q^{3} -1.00000i q^{4} +(-2.21975 - 0.269648i) q^{5} -2.70746 q^{6} +(1.02061 - 1.02061i) q^{7} +(-0.707107 - 0.707107i) q^{8} +4.33033i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.91446 - 1.91446i) q^{3} -1.00000i q^{4} +(-2.21975 - 0.269648i) q^{5} -2.70746 q^{6} +(1.02061 - 1.02061i) q^{7} +(-0.707107 - 0.707107i) q^{8} +4.33033i q^{9} +(-1.76027 + 1.37893i) q^{10} -3.68947 q^{11} +(-1.91446 + 1.91446i) q^{12} +(-0.648955 + 0.648955i) q^{13} -1.44336i q^{14} +(3.73340 + 4.76586i) q^{15} -1.00000 q^{16} +(2.53300 + 2.53300i) q^{17} +(3.06201 + 3.06201i) q^{18} +0.0313512 q^{19} +(-0.269648 + 2.21975i) q^{20} -3.90784 q^{21} +(-2.60885 + 2.60885i) q^{22} +(2.32349 - 2.32349i) q^{23} +2.70746i q^{24} +(4.85458 + 1.19710i) q^{25} +0.917760i q^{26} +(2.54687 - 2.54687i) q^{27} +(-1.02061 - 1.02061i) q^{28} -7.48270 q^{29} +(6.00988 + 0.730061i) q^{30} -4.11398 q^{31} +(-0.707107 + 0.707107i) q^{32} +(7.06334 + 7.06334i) q^{33} +3.58221 q^{34} +(-2.54070 + 1.99029i) q^{35} +4.33033 q^{36} +(-2.60713 + 2.60713i) q^{37} +(0.0221686 - 0.0221686i) q^{38} +2.48480 q^{39} +(1.37893 + 1.76027i) q^{40} -10.1280 q^{41} +(-2.76326 + 2.76326i) q^{42} +(4.41676 - 4.84688i) q^{43} +3.68947i q^{44} +(1.16767 - 9.61226i) q^{45} -3.28591i q^{46} +(-6.32263 - 6.32263i) q^{47} +(1.91446 + 1.91446i) q^{48} +4.91671i q^{49} +(4.27919 - 2.58623i) q^{50} -9.69868i q^{51} +(0.648955 + 0.648955i) q^{52} +(3.09229 - 3.09229i) q^{53} -3.60182i q^{54} +(8.18969 + 0.994857i) q^{55} -1.44336 q^{56} +(-0.0600207 - 0.0600207i) q^{57} +(-5.29107 + 5.29107i) q^{58} -14.1930i q^{59} +(4.76586 - 3.73340i) q^{60} -7.52367i q^{61} +(-2.90902 + 2.90902i) q^{62} +(4.41958 + 4.41958i) q^{63} +1.00000i q^{64} +(1.61551 - 1.26553i) q^{65} +9.98908 q^{66} +(1.07630 + 1.07630i) q^{67} +(2.53300 - 2.53300i) q^{68} -8.89647 q^{69} +(-0.389199 + 3.20390i) q^{70} +4.73051i q^{71} +(3.06201 - 3.06201i) q^{72} +(-4.95201 - 4.95201i) q^{73} +3.68703i q^{74} +(-7.00210 - 11.5857i) q^{75} -0.0313512i q^{76} +(-3.76550 + 3.76550i) q^{77} +(1.75702 - 1.75702i) q^{78} -2.04141i q^{79} +(2.21975 + 0.269648i) q^{80} +3.23922 q^{81} +(-7.16159 + 7.16159i) q^{82} +(-4.90419 + 4.90419i) q^{83} +3.90784i q^{84} +(-4.93961 - 6.30565i) q^{85} +(-0.304139 - 6.55038i) q^{86} +(14.3253 + 14.3253i) q^{87} +(2.60885 + 2.60885i) q^{88} -9.71831 q^{89} +(-5.97123 - 7.62256i) q^{90} +1.32466i q^{91} +(-2.32349 - 2.32349i) q^{92} +(7.87606 + 7.87606i) q^{93} -8.94155 q^{94} +(-0.0695918 - 0.00845379i) q^{95} +2.70746 q^{96} +(-10.1116 - 10.1116i) q^{97} +(3.47664 + 3.47664i) q^{98} -15.9766i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 8 q^{10} + 16 q^{11} - 24 q^{13} + 8 q^{15} - 40 q^{16} - 12 q^{17} - 16 q^{21} + 44 q^{23} + 24 q^{25} + 32 q^{31} - 64 q^{35} + 48 q^{36} - 28 q^{38} - 4 q^{40} + 8 q^{41} - 16 q^{43} - 28 q^{47} + 24 q^{52} - 80 q^{53} + 24 q^{56} + 64 q^{57} + 12 q^{58} + 24 q^{67} - 12 q^{68} + 40 q^{78} - 120 q^{81} + 48 q^{83} + 28 q^{87} - 44 q^{92} - 16 q^{95} - 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/430\mathbb{Z}\right)^\times\).

\(n\) \(87\) \(261\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −1.91446 1.91446i −1.10532 1.10532i −0.993758 0.111557i \(-0.964416\pi\)
−0.111557 0.993758i \(-0.535584\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −2.21975 0.269648i −0.992702 0.120590i
\(6\) −2.70746 −1.10532
\(7\) 1.02061 1.02061i 0.385754 0.385754i −0.487416 0.873170i \(-0.662060\pi\)
0.873170 + 0.487416i \(0.162060\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 4.33033i 1.44344i
\(10\) −1.76027 + 1.37893i −0.556646 + 0.436056i
\(11\) −3.68947 −1.11242 −0.556208 0.831043i \(-0.687744\pi\)
−0.556208 + 0.831043i \(0.687744\pi\)
\(12\) −1.91446 + 1.91446i −0.552658 + 0.552658i
\(13\) −0.648955 + 0.648955i −0.179988 + 0.179988i −0.791350 0.611363i \(-0.790622\pi\)
0.611363 + 0.791350i \(0.290622\pi\)
\(14\) 1.44336i 0.385754i
\(15\) 3.73340 + 4.76586i 0.963959 + 1.23054i
\(16\) −1.00000 −0.250000
\(17\) 2.53300 + 2.53300i 0.614343 + 0.614343i 0.944075 0.329731i \(-0.106958\pi\)
−0.329731 + 0.944075i \(0.606958\pi\)
\(18\) 3.06201 + 3.06201i 0.721722 + 0.721722i
\(19\) 0.0313512 0.00719245 0.00359623 0.999994i \(-0.498855\pi\)
0.00359623 + 0.999994i \(0.498855\pi\)
\(20\) −0.269648 + 2.21975i −0.0602951 + 0.496351i
\(21\) −3.90784 −0.852760
\(22\) −2.60885 + 2.60885i −0.556208 + 0.556208i
\(23\) 2.32349 2.32349i 0.484481 0.484481i −0.422078 0.906559i \(-0.638699\pi\)
0.906559 + 0.422078i \(0.138699\pi\)
\(24\) 2.70746i 0.552658i
\(25\) 4.85458 + 1.19710i 0.970916 + 0.239421i
\(26\) 0.917760i 0.179988i
\(27\) 2.54687 2.54687i 0.490146 0.490146i
\(28\) −1.02061 1.02061i −0.192877 0.192877i
\(29\) −7.48270 −1.38950 −0.694751 0.719250i \(-0.744486\pi\)
−0.694751 + 0.719250i \(0.744486\pi\)
\(30\) 6.00988 + 0.730061i 1.09725 + 0.133290i
\(31\) −4.11398 −0.738892 −0.369446 0.929252i \(-0.620453\pi\)
−0.369446 + 0.929252i \(0.620453\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 7.06334 + 7.06334i 1.22957 + 1.22957i
\(34\) 3.58221 0.614343
\(35\) −2.54070 + 1.99029i −0.429457 + 0.336421i
\(36\) 4.33033 0.721722
\(37\) −2.60713 + 2.60713i −0.428609 + 0.428609i −0.888154 0.459545i \(-0.848012\pi\)
0.459545 + 0.888154i \(0.348012\pi\)
\(38\) 0.0221686 0.0221686i 0.00359623 0.00359623i
\(39\) 2.48480 0.397886
\(40\) 1.37893 + 1.76027i 0.218028 + 0.278323i
\(41\) −10.1280 −1.58173 −0.790866 0.611990i \(-0.790369\pi\)
−0.790866 + 0.611990i \(0.790369\pi\)
\(42\) −2.76326 + 2.76326i −0.426380 + 0.426380i
\(43\) 4.41676 4.84688i 0.673550 0.739142i
\(44\) 3.68947i 0.556208i
\(45\) 1.16767 9.61226i 0.174065 1.43291i
\(46\) 3.28591i 0.484481i
\(47\) −6.32263 6.32263i −0.922250 0.922250i 0.0749379 0.997188i \(-0.476124\pi\)
−0.997188 + 0.0749379i \(0.976124\pi\)
\(48\) 1.91446 + 1.91446i 0.276329 + 0.276329i
\(49\) 4.91671i 0.702388i
\(50\) 4.27919 2.58623i 0.605168 0.365748i
\(51\) 9.69868i 1.35809i
\(52\) 0.648955 + 0.648955i 0.0899938 + 0.0899938i
\(53\) 3.09229 3.09229i 0.424759 0.424759i −0.462080 0.886838i \(-0.652897\pi\)
0.886838 + 0.462080i \(0.152897\pi\)
\(54\) 3.60182i 0.490146i
\(55\) 8.18969 + 0.994857i 1.10430 + 0.134147i
\(56\) −1.44336 −0.192877
\(57\) −0.0600207 0.0600207i −0.00794993 0.00794993i
\(58\) −5.29107 + 5.29107i −0.694751 + 0.694751i
\(59\) 14.1930i 1.84777i −0.382674 0.923884i \(-0.624997\pi\)
0.382674 0.923884i \(-0.375003\pi\)
\(60\) 4.76586 3.73340i 0.615270 0.481979i
\(61\) 7.52367i 0.963307i −0.876362 0.481654i \(-0.840036\pi\)
0.876362 0.481654i \(-0.159964\pi\)
\(62\) −2.90902 + 2.90902i −0.369446 + 0.369446i
\(63\) 4.41958 + 4.41958i 0.556814 + 0.556814i
\(64\) 1.00000i 0.125000i
\(65\) 1.61551 1.26553i 0.200379 0.156969i
\(66\) 9.98908 1.22957
\(67\) 1.07630 + 1.07630i 0.131491 + 0.131491i 0.769789 0.638298i \(-0.220361\pi\)
−0.638298 + 0.769789i \(0.720361\pi\)
\(68\) 2.53300 2.53300i 0.307172 0.307172i
\(69\) −8.89647 −1.07101
\(70\) −0.389199 + 3.20390i −0.0465182 + 0.382939i
\(71\) 4.73051i 0.561408i 0.959794 + 0.280704i \(0.0905679\pi\)
−0.959794 + 0.280704i \(0.909432\pi\)
\(72\) 3.06201 3.06201i 0.360861 0.360861i
\(73\) −4.95201 4.95201i −0.579589 0.579589i 0.355201 0.934790i \(-0.384413\pi\)
−0.934790 + 0.355201i \(0.884413\pi\)
\(74\) 3.68703i 0.428609i
\(75\) −7.00210 11.5857i −0.808533 1.33780i
\(76\) 0.0313512i 0.00359623i
\(77\) −3.76550 + 3.76550i −0.429119 + 0.429119i
\(78\) 1.75702 1.75702i 0.198943 0.198943i
\(79\) 2.04141i 0.229677i −0.993384 0.114838i \(-0.963365\pi\)
0.993384 0.114838i \(-0.0366350\pi\)
\(80\) 2.21975 + 0.269648i 0.248176 + 0.0301476i
\(81\) 3.23922 0.359913
\(82\) −7.16159 + 7.16159i −0.790866 + 0.790866i
\(83\) −4.90419 + 4.90419i −0.538305 + 0.538305i −0.923031 0.384726i \(-0.874296\pi\)
0.384726 + 0.923031i \(0.374296\pi\)
\(84\) 3.90784i 0.426380i
\(85\) −4.93961 6.30565i −0.535776 0.683944i
\(86\) −0.304139 6.55038i −0.0327962 0.706346i
\(87\) 14.3253 + 14.3253i 1.53584 + 1.53584i
\(88\) 2.60885 + 2.60885i 0.278104 + 0.278104i
\(89\) −9.71831 −1.03014 −0.515070 0.857148i \(-0.672234\pi\)
−0.515070 + 0.857148i \(0.672234\pi\)
\(90\) −5.97123 7.62256i −0.629423 0.803488i
\(91\) 1.32466i 0.138862i
\(92\) −2.32349 2.32349i −0.242241 0.242241i
\(93\) 7.87606 + 7.87606i 0.816709 + 0.816709i
\(94\) −8.94155 −0.922250
\(95\) −0.0695918 0.00845379i −0.00713997 0.000867340i
\(96\) 2.70746 0.276329
\(97\) −10.1116 10.1116i −1.02668 1.02668i −0.999634 0.0270433i \(-0.991391\pi\)
−0.0270433 0.999634i \(-0.508609\pi\)
\(98\) 3.47664 + 3.47664i 0.351194 + 0.351194i
\(99\) 15.9766i 1.60571i
\(100\) 1.19710 4.85458i 0.119710 0.485458i
\(101\) 1.01624 0.101119 0.0505597 0.998721i \(-0.483899\pi\)
0.0505597 + 0.998721i \(0.483899\pi\)
\(102\) −6.85800 6.85800i −0.679043 0.679043i
\(103\) 12.2717 12.2717i 1.20917 1.20917i 0.237875 0.971296i \(-0.423549\pi\)
0.971296 0.237875i \(-0.0764510\pi\)
\(104\) 0.917760 0.0899938
\(105\) 8.67442 + 1.05374i 0.846537 + 0.102835i
\(106\) 4.37316i 0.424759i
\(107\) −6.96632 6.96632i −0.673460 0.673460i 0.285052 0.958512i \(-0.407989\pi\)
−0.958512 + 0.285052i \(0.907989\pi\)
\(108\) −2.54687 2.54687i −0.245073 0.245073i
\(109\) 1.28166i 0.122761i 0.998114 + 0.0613803i \(0.0195502\pi\)
−0.998114 + 0.0613803i \(0.980450\pi\)
\(110\) 6.49446 5.08752i 0.619222 0.485076i
\(111\) 9.98249 0.947496
\(112\) −1.02061 + 1.02061i −0.0964385 + 0.0964385i
\(113\) 8.83308 + 8.83308i 0.830946 + 0.830946i 0.987646 0.156700i \(-0.0500856\pi\)
−0.156700 + 0.987646i \(0.550086\pi\)
\(114\) −0.0848820 −0.00794993
\(115\) −5.78409 + 4.53104i −0.539369 + 0.422522i
\(116\) 7.48270i 0.694751i
\(117\) −2.81019 2.81019i −0.259802 0.259802i
\(118\) −10.0359 10.0359i −0.923884 0.923884i
\(119\) 5.17041 0.473971
\(120\) 0.730061 6.00988i 0.0666452 0.548625i
\(121\) 2.61216 0.237469
\(122\) −5.32004 5.32004i −0.481654 0.481654i
\(123\) 19.3897 + 19.3897i 1.74831 + 1.74831i
\(124\) 4.11398i 0.369446i
\(125\) −10.4532 3.96630i −0.934959 0.354756i
\(126\) 6.25023 0.556814
\(127\) 14.2953 + 14.2953i 1.26851 + 1.26851i 0.946859 + 0.321647i \(0.104237\pi\)
0.321647 + 0.946859i \(0.395763\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −17.7349 + 0.823444i −1.56147 + 0.0725002i
\(130\) 0.247472 2.03720i 0.0217048 0.178674i
\(131\) 16.6754i 1.45694i 0.685080 + 0.728468i \(0.259767\pi\)
−0.685080 + 0.728468i \(0.740233\pi\)
\(132\) 7.06334 7.06334i 0.614785 0.614785i
\(133\) 0.0319973 0.0319973i 0.00277452 0.00277452i
\(134\) 1.52212 0.131491
\(135\) −6.34018 + 4.96666i −0.545676 + 0.427462i
\(136\) 3.58221i 0.307172i
\(137\) 8.14514 8.14514i 0.695886 0.695886i −0.267634 0.963521i \(-0.586242\pi\)
0.963521 + 0.267634i \(0.0862420\pi\)
\(138\) −6.29075 + 6.29075i −0.535504 + 0.535504i
\(139\) 5.97569i 0.506851i 0.967355 + 0.253426i \(0.0815573\pi\)
−0.967355 + 0.253426i \(0.918443\pi\)
\(140\) 1.99029 + 2.54070i 0.168210 + 0.214729i
\(141\) 24.2089i 2.03875i
\(142\) 3.34497 + 3.34497i 0.280704 + 0.280704i
\(143\) 2.39430 2.39430i 0.200221 0.200221i
\(144\) 4.33033i 0.360861i
\(145\) 16.6097 + 2.01770i 1.37936 + 0.167560i
\(146\) −7.00321 −0.579589
\(147\) 9.41286 9.41286i 0.776360 0.776360i
\(148\) 2.60713 + 2.60713i 0.214305 + 0.214305i
\(149\) −3.51576 −0.288023 −0.144011 0.989576i \(-0.546000\pi\)
−0.144011 + 0.989576i \(0.546000\pi\)
\(150\) −13.1436 3.24111i −1.07317 0.264635i
\(151\) 10.6170i 0.863999i −0.901874 0.432000i \(-0.857808\pi\)
0.901874 0.432000i \(-0.142192\pi\)
\(152\) −0.0221686 0.0221686i −0.00179811 0.00179811i
\(153\) −10.9687 + 10.9687i −0.886770 + 0.886770i
\(154\) 5.32522i 0.429119i
\(155\) 9.13201 + 1.10933i 0.733500 + 0.0891033i
\(156\) 2.48480i 0.198943i
\(157\) −4.54306 + 4.54306i −0.362576 + 0.362576i −0.864760 0.502185i \(-0.832530\pi\)
0.502185 + 0.864760i \(0.332530\pi\)
\(158\) −1.44350 1.44350i −0.114838 0.114838i
\(159\) −11.8401 −0.938985
\(160\) 1.76027 1.37893i 0.139162 0.109014i
\(161\) 4.74275i 0.373781i
\(162\) 2.29047 2.29047i 0.179957 0.179957i
\(163\) −5.62978 5.62978i −0.440959 0.440959i 0.451376 0.892334i \(-0.350933\pi\)
−0.892334 + 0.451376i \(0.850933\pi\)
\(164\) 10.1280i 0.790866i
\(165\) −13.7742 17.5835i −1.07232 1.36887i
\(166\) 6.93557i 0.538305i
\(167\) −1.08392 1.08392i −0.0838759 0.0838759i 0.663924 0.747800i \(-0.268890\pi\)
−0.747800 + 0.663924i \(0.768890\pi\)
\(168\) 2.76326 + 2.76326i 0.213190 + 0.213190i
\(169\) 12.1577i 0.935209i
\(170\) −7.95160 0.965935i −0.609860 0.0740839i
\(171\) 0.135761i 0.0103819i
\(172\) −4.84688 4.41676i −0.369571 0.336775i
\(173\) −11.2690 + 11.2690i −0.856766 + 0.856766i −0.990956 0.134190i \(-0.957157\pi\)
0.134190 + 0.990956i \(0.457157\pi\)
\(174\) 20.2591 1.53584
\(175\) 6.17640 3.73285i 0.466892 0.282177i
\(176\) 3.68947 0.278104
\(177\) −27.1719 + 27.1719i −2.04237 + 2.04237i
\(178\) −6.87188 + 6.87188i −0.515070 + 0.515070i
\(179\) 20.4789 1.53067 0.765333 0.643634i \(-0.222574\pi\)
0.765333 + 0.643634i \(0.222574\pi\)
\(180\) −9.61226 1.16767i −0.716455 0.0870327i
\(181\) 5.42907 0.403540 0.201770 0.979433i \(-0.435331\pi\)
0.201770 + 0.979433i \(0.435331\pi\)
\(182\) 0.936675 + 0.936675i 0.0694309 + 0.0694309i
\(183\) −14.4038 + 14.4038i −1.06476 + 1.06476i
\(184\) −3.28591 −0.242241
\(185\) 6.49018 5.08416i 0.477167 0.373795i
\(186\) 11.1384 0.816709
\(187\) −9.34543 9.34543i −0.683405 0.683405i
\(188\) −6.32263 + 6.32263i −0.461125 + 0.461125i
\(189\) 5.19872i 0.378151i
\(190\) −0.0551866 + 0.0432311i −0.00400365 + 0.00313631i
\(191\) 11.5800i 0.837897i −0.908010 0.418948i \(-0.862399\pi\)
0.908010 0.418948i \(-0.137601\pi\)
\(192\) 1.91446 1.91446i 0.138164 0.138164i
\(193\) 15.1912 15.1912i 1.09349 1.09349i 0.0983333 0.995154i \(-0.468649\pi\)
0.995154 0.0983333i \(-0.0313511\pi\)
\(194\) −14.3000 −1.02668
\(195\) −5.51563 0.670021i −0.394982 0.0479812i
\(196\) 4.91671 0.351194
\(197\) 0.310153 + 0.310153i 0.0220975 + 0.0220975i 0.718069 0.695972i \(-0.245026\pi\)
−0.695972 + 0.718069i \(0.745026\pi\)
\(198\) −11.2972 11.2972i −0.802855 0.802855i
\(199\) 27.5168 1.95061 0.975307 0.220854i \(-0.0708845\pi\)
0.975307 + 0.220854i \(0.0708845\pi\)
\(200\) −2.58623 4.27919i −0.182874 0.302584i
\(201\) 4.12107i 0.290678i
\(202\) 0.718588 0.718588i 0.0505597 0.0505597i
\(203\) −7.63691 + 7.63691i −0.536006 + 0.536006i
\(204\) −9.69868 −0.679043
\(205\) 22.4817 + 2.73100i 1.57019 + 0.190741i
\(206\) 17.3549i 1.20917i
\(207\) 10.0615 + 10.0615i 0.699321 + 0.699321i
\(208\) 0.648955 0.648955i 0.0449969 0.0449969i
\(209\) −0.115669 −0.00800100
\(210\) 6.87885 5.38863i 0.474686 0.371851i
\(211\) 11.5577i 0.795667i −0.917458 0.397834i \(-0.869762\pi\)
0.917458 0.397834i \(-0.130238\pi\)
\(212\) −3.09229 3.09229i −0.212379 0.212379i
\(213\) 9.05638 9.05638i 0.620533 0.620533i
\(214\) −9.85187 −0.673460
\(215\) −11.1111 + 9.56789i −0.757768 + 0.652524i
\(216\) −3.60182 −0.245073
\(217\) −4.19876 + 4.19876i −0.285031 + 0.285031i
\(218\) 0.906269 + 0.906269i 0.0613803 + 0.0613803i
\(219\) 18.9609i 1.28126i
\(220\) 0.994857 8.18969i 0.0670733 0.552149i
\(221\) −3.28761 −0.221148
\(222\) 7.05869 7.05869i 0.473748 0.473748i
\(223\) −17.8690 17.8690i −1.19660 1.19660i −0.975178 0.221422i \(-0.928930\pi\)
−0.221422 0.975178i \(-0.571070\pi\)
\(224\) 1.44336i 0.0964385i
\(225\) −5.18385 + 21.0219i −0.345590 + 1.40146i
\(226\) 12.4919 0.830946
\(227\) 10.8185 10.8185i 0.718051 0.718051i −0.250155 0.968206i \(-0.580482\pi\)
0.968206 + 0.250155i \(0.0804816\pi\)
\(228\) −0.0600207 + 0.0600207i −0.00397497 + 0.00397497i
\(229\) 0.448544i 0.0296406i −0.999890 0.0148203i \(-0.995282\pi\)
0.999890 0.0148203i \(-0.00471763\pi\)
\(230\) −0.886040 + 7.29390i −0.0584237 + 0.480946i
\(231\) 14.4178 0.948623
\(232\) 5.29107 + 5.29107i 0.347376 + 0.347376i
\(233\) 13.4741 + 13.4741i 0.882716 + 0.882716i 0.993810 0.111094i \(-0.0354356\pi\)
−0.111094 + 0.993810i \(0.535436\pi\)
\(234\) −3.97421 −0.259802
\(235\) 12.3298 + 15.7395i 0.804306 + 1.02673i
\(236\) −14.1930 −0.923884
\(237\) −3.90821 + 3.90821i −0.253865 + 0.253865i
\(238\) 3.65603 3.65603i 0.236985 0.236985i
\(239\) 4.55977i 0.294947i 0.989066 + 0.147474i \(0.0471142\pi\)
−0.989066 + 0.147474i \(0.952886\pi\)
\(240\) −3.73340 4.76586i −0.240990 0.307635i
\(241\) 6.10070i 0.392981i 0.980506 + 0.196490i \(0.0629544\pi\)
−0.980506 + 0.196490i \(0.937046\pi\)
\(242\) 1.84707 1.84707i 0.118734 0.118734i
\(243\) −13.8420 13.8420i −0.887963 0.887963i
\(244\) −7.52367 −0.481654
\(245\) 1.32578 10.9139i 0.0847011 0.697262i
\(246\) 27.4212 1.74831
\(247\) −0.0203455 + 0.0203455i −0.00129455 + 0.00129455i
\(248\) 2.90902 + 2.90902i 0.184723 + 0.184723i
\(249\) 18.7778 1.18999
\(250\) −10.1961 + 4.58690i −0.644858 + 0.290101i
\(251\) −27.1856 −1.71594 −0.857970 0.513700i \(-0.828275\pi\)
−0.857970 + 0.513700i \(0.828275\pi\)
\(252\) 4.41958 4.41958i 0.278407 0.278407i
\(253\) −8.57244 + 8.57244i −0.538944 + 0.538944i
\(254\) 20.2167 1.26851
\(255\) −2.61523 + 21.5286i −0.163772 + 1.34818i
\(256\) 1.00000 0.0625000
\(257\) −10.5176 + 10.5176i −0.656068 + 0.656068i −0.954447 0.298379i \(-0.903554\pi\)
0.298379 + 0.954447i \(0.403554\pi\)
\(258\) −11.9582 + 13.1227i −0.744485 + 0.816985i
\(259\) 5.32172i 0.330675i
\(260\) −1.26553 1.61551i −0.0784847 0.100189i
\(261\) 32.4026i 2.00567i
\(262\) 11.7913 + 11.7913i 0.728468 + 0.728468i
\(263\) −16.2714 16.2714i −1.00334 1.00334i −0.999994 0.00334334i \(-0.998936\pi\)
−0.00334334 0.999994i \(-0.501064\pi\)
\(264\) 9.98908i 0.614785i
\(265\) −7.69794 + 6.03028i −0.472881 + 0.370437i
\(266\) 0.0452510i 0.00277452i
\(267\) 18.6053 + 18.6053i 1.13863 + 1.13863i
\(268\) 1.07630 1.07630i 0.0657455 0.0657455i
\(269\) 17.1705i 1.04690i −0.852055 0.523452i \(-0.824644\pi\)
0.852055 0.523452i \(-0.175356\pi\)
\(270\) −0.971224 + 7.99514i −0.0591068 + 0.486569i
\(271\) −14.9966 −0.910977 −0.455488 0.890242i \(-0.650535\pi\)
−0.455488 + 0.890242i \(0.650535\pi\)
\(272\) −2.53300 2.53300i −0.153586 0.153586i
\(273\) 2.53601 2.53601i 0.153486 0.153486i
\(274\) 11.5190i 0.695886i
\(275\) −17.9108 4.41667i −1.08006 0.266335i
\(276\) 8.89647i 0.535504i
\(277\) 13.1886 13.1886i 0.792426 0.792426i −0.189462 0.981888i \(-0.560674\pi\)
0.981888 + 0.189462i \(0.0606743\pi\)
\(278\) 4.22545 + 4.22545i 0.253426 + 0.253426i
\(279\) 17.8149i 1.06655i
\(280\) 3.20390 + 0.389199i 0.191469 + 0.0232591i
\(281\) −19.6850 −1.17431 −0.587154 0.809475i \(-0.699752\pi\)
−0.587154 + 0.809475i \(0.699752\pi\)
\(282\) 17.1183 + 17.1183i 1.01938 + 1.01938i
\(283\) −18.4977 + 18.4977i −1.09958 + 1.09958i −0.105116 + 0.994460i \(0.533522\pi\)
−0.994460 + 0.105116i \(0.966478\pi\)
\(284\) 4.73051 0.280704
\(285\) 0.117046 + 0.149415i 0.00693323 + 0.00885060i
\(286\) 3.38604i 0.200221i
\(287\) −10.3368 + 10.3368i −0.610159 + 0.610159i
\(288\) −3.06201 3.06201i −0.180431 0.180431i
\(289\) 4.16779i 0.245164i
\(290\) 13.1716 10.3181i 0.773461 0.605901i
\(291\) 38.7166i 2.26961i
\(292\) −4.95201 + 4.95201i −0.289795 + 0.289795i
\(293\) 23.4809 23.4809i 1.37177 1.37177i 0.513952 0.857819i \(-0.328181\pi\)
0.857819 0.513952i \(-0.171819\pi\)
\(294\) 13.3118i 0.776360i
\(295\) −3.82711 + 31.5048i −0.222823 + 1.83428i
\(296\) 3.68703 0.214305
\(297\) −9.39660 + 9.39660i −0.545246 + 0.545246i
\(298\) −2.48602 + 2.48602i −0.144011 + 0.144011i
\(299\) 3.01568i 0.174401i
\(300\) −11.5857 + 7.00210i −0.668902 + 0.404267i
\(301\) −0.438982 9.45455i −0.0253025 0.544951i
\(302\) −7.50735 7.50735i −0.432000 0.432000i
\(303\) −1.94555 1.94555i −0.111769 0.111769i
\(304\) −0.0313512 −0.00179811
\(305\) −2.02874 + 16.7007i −0.116165 + 0.956277i
\(306\) 15.5121i 0.886770i
\(307\) −9.55550 9.55550i −0.545361 0.545361i 0.379734 0.925096i \(-0.376015\pi\)
−0.925096 + 0.379734i \(0.876015\pi\)
\(308\) 3.76550 + 3.76550i 0.214559 + 0.214559i
\(309\) −46.9876 −2.67303
\(310\) 7.24172 5.67289i 0.411302 0.322199i
\(311\) 8.63845 0.489842 0.244921 0.969543i \(-0.421238\pi\)
0.244921 + 0.969543i \(0.421238\pi\)
\(312\) −1.75702 1.75702i −0.0994715 0.0994715i
\(313\) 12.9700 + 12.9700i 0.733109 + 0.733109i 0.971234 0.238126i \(-0.0765330\pi\)
−0.238126 + 0.971234i \(0.576533\pi\)
\(314\) 6.42486i 0.362576i
\(315\) −8.61863 11.0021i −0.485605 0.619897i
\(316\) −2.04141 −0.114838
\(317\) 4.42165 + 4.42165i 0.248345 + 0.248345i 0.820291 0.571946i \(-0.193811\pi\)
−0.571946 + 0.820291i \(0.693811\pi\)
\(318\) −8.37225 + 8.37225i −0.469492 + 0.469492i
\(319\) 27.6072 1.54570
\(320\) 0.269648 2.21975i 0.0150738 0.124088i
\(321\) 26.6735i 1.48877i
\(322\) −3.35363 3.35363i −0.186891 0.186891i
\(323\) 0.0794126 + 0.0794126i 0.00441864 + 0.00441864i
\(324\) 3.23922i 0.179957i
\(325\) −3.92727 + 2.37354i −0.217846 + 0.131660i
\(326\) −7.96171 −0.440959
\(327\) 2.45368 2.45368i 0.135689 0.135689i
\(328\) 7.16159 + 7.16159i 0.395433 + 0.395433i
\(329\) −12.9059 −0.711524
\(330\) −22.1732 2.69354i −1.22060 0.148274i
\(331\) 2.48208i 0.136427i 0.997671 + 0.0682137i \(0.0217300\pi\)
−0.997671 + 0.0682137i \(0.978270\pi\)
\(332\) 4.90419 + 4.90419i 0.269152 + 0.269152i
\(333\) −11.2897 11.2897i −0.618673 0.618673i
\(334\) −1.53289 −0.0838759
\(335\) −2.09889 2.67934i −0.114675 0.146388i
\(336\) 3.90784 0.213190
\(337\) −3.35893 3.35893i −0.182973 0.182973i 0.609677 0.792650i \(-0.291299\pi\)
−0.792650 + 0.609677i \(0.791299\pi\)
\(338\) 8.59680 + 8.59680i 0.467604 + 0.467604i
\(339\) 33.8212i 1.83692i
\(340\) −6.30565 + 4.93961i −0.341972 + 0.267888i
\(341\) 15.1784 0.821956
\(342\) 0.0959976 + 0.0959976i 0.00519095 + 0.00519095i
\(343\) 12.1623 + 12.1623i 0.656703 + 0.656703i
\(344\) −6.55038 + 0.304139i −0.353173 + 0.0163981i
\(345\) 19.7479 + 2.39892i 1.06319 + 0.129153i
\(346\) 15.9368i 0.856766i
\(347\) −3.16238 + 3.16238i −0.169766 + 0.169766i −0.786876 0.617111i \(-0.788303\pi\)
0.617111 + 0.786876i \(0.288303\pi\)
\(348\) 14.3253 14.3253i 0.767919 0.767919i
\(349\) 26.9669 1.44350 0.721751 0.692153i \(-0.243337\pi\)
0.721751 + 0.692153i \(0.243337\pi\)
\(350\) 1.72785 7.00690i 0.0923574 0.374535i
\(351\) 3.30561i 0.176440i
\(352\) 2.60885 2.60885i 0.139052 0.139052i
\(353\) 22.6884 22.6884i 1.20758 1.20758i 0.235773 0.971808i \(-0.424238\pi\)
0.971808 0.235773i \(-0.0757623\pi\)
\(354\) 38.4269i 2.04237i
\(355\) 1.27557 10.5005i 0.0677004 0.557311i
\(356\) 9.71831i 0.515070i
\(357\) −9.89856 9.89856i −0.523887 0.523887i
\(358\) 14.4808 14.4808i 0.765333 0.765333i
\(359\) 11.4906i 0.606452i −0.952919 0.303226i \(-0.901936\pi\)
0.952919 0.303226i \(-0.0980637\pi\)
\(360\) −7.62256 + 5.97123i −0.401744 + 0.314711i
\(361\) −18.9990 −0.999948
\(362\) 3.83893 3.83893i 0.201770 0.201770i
\(363\) −5.00087 5.00087i −0.262478 0.262478i
\(364\) 1.32466 0.0694309
\(365\) 9.65693 + 12.3275i 0.505467 + 0.645253i
\(366\) 20.3700i 1.06476i
\(367\) −7.66248 7.66248i −0.399978 0.399978i 0.478247 0.878225i \(-0.341272\pi\)
−0.878225 + 0.478247i \(0.841272\pi\)
\(368\) −2.32349 + 2.32349i −0.121120 + 0.121120i
\(369\) 43.8577i 2.28314i
\(370\) 0.994202 8.18429i 0.0516861 0.425481i
\(371\) 6.31204i 0.327705i
\(372\) 7.87606 7.87606i 0.408355 0.408355i
\(373\) −7.61855 7.61855i −0.394474 0.394474i 0.481805 0.876279i \(-0.339981\pi\)
−0.876279 + 0.481805i \(0.839981\pi\)
\(374\) −13.2164 −0.683405
\(375\) 12.4189 + 27.6055i 0.641307 + 1.42554i
\(376\) 8.94155i 0.461125i
\(377\) 4.85593 4.85593i 0.250093 0.250093i
\(378\) −3.67605 3.67605i −0.189076 0.189076i
\(379\) 20.6244i 1.05941i 0.848183 + 0.529703i \(0.177697\pi\)
−0.848183 + 0.529703i \(0.822303\pi\)
\(380\) −0.00845379 + 0.0695918i −0.000433670 + 0.00356998i
\(381\) 54.7358i 2.80420i
\(382\) −8.18827 8.18827i −0.418948 0.418948i
\(383\) −13.8575 13.8575i −0.708085 0.708085i 0.258047 0.966132i \(-0.416921\pi\)
−0.966132 + 0.258047i \(0.916921\pi\)
\(384\) 2.70746i 0.138164i
\(385\) 9.37383 7.34311i 0.477735 0.374240i
\(386\) 21.4836i 1.09349i
\(387\) 20.9886 + 19.1260i 1.06691 + 0.972231i
\(388\) −10.1116 + 10.1116i −0.513339 + 0.513339i
\(389\) 26.3733 1.33718 0.668590 0.743631i \(-0.266898\pi\)
0.668590 + 0.743631i \(0.266898\pi\)
\(390\) −4.37392 + 3.42636i −0.221482 + 0.173501i
\(391\) 11.7708 0.595276
\(392\) 3.47664 3.47664i 0.175597 0.175597i
\(393\) 31.9244 31.9244i 1.61037 1.61037i
\(394\) 0.438622 0.0220975
\(395\) −0.550463 + 4.53143i −0.0276968 + 0.228001i
\(396\) −15.9766 −0.802855
\(397\) 13.4243 + 13.4243i 0.673746 + 0.673746i 0.958578 0.284831i \(-0.0919376\pi\)
−0.284831 + 0.958578i \(0.591938\pi\)
\(398\) 19.4573 19.4573i 0.975307 0.975307i
\(399\) −0.122515 −0.00613344
\(400\) −4.85458 1.19710i −0.242729 0.0598551i
\(401\) −24.6103 −1.22898 −0.614490 0.788925i \(-0.710638\pi\)
−0.614490 + 0.788925i \(0.710638\pi\)
\(402\) −2.91404 2.91404i −0.145339 0.145339i
\(403\) 2.66979 2.66979i 0.132991 0.132991i
\(404\) 1.01624i 0.0505597i
\(405\) −7.19025 0.873449i −0.357287 0.0434020i
\(406\) 10.8002i 0.536006i
\(407\) 9.61890 9.61890i 0.476791 0.476791i
\(408\) −6.85800 + 6.85800i −0.339522 + 0.339522i
\(409\) 14.8243 0.733013 0.366506 0.930416i \(-0.380554\pi\)
0.366506 + 0.930416i \(0.380554\pi\)
\(410\) 17.8281 13.9658i 0.880465 0.689723i
\(411\) −31.1871 −1.53835
\(412\) −12.2717 12.2717i −0.604586 0.604586i
\(413\) −14.4855 14.4855i −0.712784 0.712784i
\(414\) 14.2291 0.699321
\(415\) 12.2085 9.56367i 0.599291 0.469462i
\(416\) 0.917760i 0.0449969i
\(417\) 11.4402 11.4402i 0.560231 0.560231i
\(418\) −0.0817904 + 0.0817904i −0.00400050 + 0.00400050i
\(419\) −28.8761 −1.41069 −0.705344 0.708865i \(-0.749208\pi\)
−0.705344 + 0.708865i \(0.749208\pi\)
\(420\) 1.05374 8.67442i 0.0514173 0.423268i
\(421\) 1.17333i 0.0571845i 0.999591 + 0.0285922i \(0.00910243\pi\)
−0.999591 + 0.0285922i \(0.990898\pi\)
\(422\) −8.17255 8.17255i −0.397834 0.397834i
\(423\) 27.3791 27.3791i 1.33122 1.33122i
\(424\) −4.37316 −0.212379
\(425\) 9.26440 + 15.3289i 0.449389 + 0.743562i
\(426\) 12.8077i 0.620533i
\(427\) −7.67873 7.67873i −0.371600 0.371600i
\(428\) −6.96632 + 6.96632i −0.336730 + 0.336730i
\(429\) −9.16758 −0.442615
\(430\) −1.09119 + 14.6222i −0.0526216 + 0.705146i
\(431\) −15.8267 −0.762345 −0.381173 0.924504i \(-0.624480\pi\)
−0.381173 + 0.924504i \(0.624480\pi\)
\(432\) −2.54687 + 2.54687i −0.122536 + 0.122536i
\(433\) −10.6823 10.6823i −0.513358 0.513358i 0.402195 0.915554i \(-0.368247\pi\)
−0.915554 + 0.402195i \(0.868247\pi\)
\(434\) 5.93795i 0.285031i
\(435\) −27.9359 35.6615i −1.33942 1.70984i
\(436\) 1.28166 0.0613803
\(437\) 0.0728442 0.0728442i 0.00348461 0.00348461i
\(438\) 13.4074 + 13.4074i 0.640629 + 0.640629i
\(439\) 5.26194i 0.251138i 0.992085 + 0.125569i \(0.0400757\pi\)
−0.992085 + 0.125569i \(0.959924\pi\)
\(440\) −5.08752 6.49446i −0.242538 0.309611i
\(441\) −21.2910 −1.01386
\(442\) −2.32469 + 2.32469i −0.110574 + 0.110574i
\(443\) 14.7566 14.7566i 0.701106 0.701106i −0.263542 0.964648i \(-0.584891\pi\)
0.964648 + 0.263542i \(0.0848906\pi\)
\(444\) 9.98249i 0.473748i
\(445\) 21.5722 + 2.62052i 1.02262 + 0.124225i
\(446\) −25.2707 −1.19660
\(447\) 6.73080 + 6.73080i 0.318356 + 0.318356i
\(448\) 1.02061 + 1.02061i 0.0482193 + 0.0482193i
\(449\) −2.33693 −0.110287 −0.0551433 0.998478i \(-0.517562\pi\)
−0.0551433 + 0.998478i \(0.517562\pi\)
\(450\) 11.1992 + 18.5303i 0.527936 + 0.873527i
\(451\) 37.3670 1.75954
\(452\) 8.83308 8.83308i 0.415473 0.415473i
\(453\) −20.3259 + 20.3259i −0.954992 + 0.954992i
\(454\) 15.2997i 0.718051i
\(455\) 0.357191 2.94041i 0.0167454 0.137849i
\(456\) 0.0848820i 0.00397497i
\(457\) 7.98362 7.98362i 0.373458 0.373458i −0.495277 0.868735i \(-0.664933\pi\)
0.868735 + 0.495277i \(0.164933\pi\)
\(458\) −0.317169 0.317169i −0.0148203 0.0148203i
\(459\) 12.9025 0.602236
\(460\) 4.53104 + 5.78409i 0.211261 + 0.269685i
\(461\) 16.7949 0.782216 0.391108 0.920345i \(-0.372092\pi\)
0.391108 + 0.920345i \(0.372092\pi\)
\(462\) 10.1949 10.1949i 0.474312 0.474312i
\(463\) −9.85334 9.85334i −0.457924 0.457924i 0.440050 0.897973i \(-0.354961\pi\)
−0.897973 + 0.440050i \(0.854961\pi\)
\(464\) 7.48270 0.347376
\(465\) −15.3591 19.6066i −0.712262 0.909236i
\(466\) 19.0552 0.882716
\(467\) 3.01945 3.01945i 0.139723 0.139723i −0.633785 0.773509i \(-0.718500\pi\)
0.773509 + 0.633785i \(0.218500\pi\)
\(468\) −2.81019 + 2.81019i −0.129901 + 0.129901i
\(469\) 2.19696 0.101446
\(470\) 19.8480 + 2.41107i 0.915520 + 0.111214i
\(471\) 17.3950 0.801521
\(472\) −10.0359 + 10.0359i −0.461942 + 0.461942i
\(473\) −16.2955 + 17.8824i −0.749267 + 0.822233i
\(474\) 5.52704i 0.253865i
\(475\) 0.152197 + 0.0375306i 0.00698327 + 0.00172202i
\(476\) 5.17041i 0.236985i
\(477\) 13.3906 + 13.3906i 0.613116 + 0.613116i
\(478\) 3.22425 + 3.22425i 0.147474 + 0.147474i
\(479\) 26.5511i 1.21315i −0.795026 0.606576i \(-0.792543\pi\)
0.795026 0.606576i \(-0.207457\pi\)
\(480\) −6.00988 0.730061i −0.274312 0.0333226i
\(481\) 3.38381i 0.154289i
\(482\) 4.31385 + 4.31385i 0.196490 + 0.196490i
\(483\) −9.07982 + 9.07982i −0.413146 + 0.413146i
\(484\) 2.61216i 0.118734i
\(485\) 19.7187 + 25.1718i 0.895378 + 1.14299i
\(486\) −19.5755 −0.887963
\(487\) −0.0809180 0.0809180i −0.00366674 0.00366674i 0.705271 0.708938i \(-0.250825\pi\)
−0.708938 + 0.705271i \(0.750825\pi\)
\(488\) −5.32004 + 5.32004i −0.240827 + 0.240827i
\(489\) 21.5560i 0.974796i
\(490\) −6.77981 8.65474i −0.306280 0.390982i
\(491\) 21.7824i 0.983025i −0.870870 0.491513i \(-0.836444\pi\)
0.870870 0.491513i \(-0.163556\pi\)
\(492\) 19.3897 19.3897i 0.874156 0.874156i
\(493\) −18.9537 18.9537i −0.853632 0.853632i
\(494\) 0.0287729i 0.00129455i
\(495\) −4.30806 + 35.4641i −0.193633 + 1.59399i
\(496\) 4.11398 0.184723
\(497\) 4.82800 + 4.82800i 0.216565 + 0.216565i
\(498\) 13.2779 13.2779i 0.594996 0.594996i
\(499\) 6.35752 0.284602 0.142301 0.989823i \(-0.454550\pi\)
0.142301 + 0.989823i \(0.454550\pi\)
\(500\) −3.96630 + 10.4532i −0.177378 + 0.467479i
\(501\) 4.15023i 0.185419i
\(502\) −19.2231 + 19.2231i −0.857970 + 0.857970i
\(503\) −23.1386 23.1386i −1.03170 1.03170i −0.999481 0.0322186i \(-0.989743\pi\)
−0.0322186 0.999481i \(-0.510257\pi\)
\(504\) 6.25023i 0.278407i
\(505\) −2.25579 0.274026i −0.100381 0.0121940i
\(506\) 12.1233i 0.538944i
\(507\) 23.2755 23.2755i 1.03370 1.03370i
\(508\) 14.2953 14.2953i 0.634253 0.634253i
\(509\) 37.8927i 1.67956i 0.542923 + 0.839782i \(0.317318\pi\)
−0.542923 + 0.839782i \(0.682682\pi\)
\(510\) 13.3738 + 17.0723i 0.592202 + 0.755974i
\(511\) −10.1081 −0.447158
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0.0798474 0.0798474i 0.00352535 0.00352535i
\(514\) 14.8741i 0.656068i
\(515\) −30.5493 + 23.9312i −1.34616 + 1.05453i
\(516\) 0.823444 + 17.7349i 0.0362501 + 0.780735i
\(517\) 23.3271 + 23.3271i 1.02593 + 1.02593i
\(518\) 3.76302 + 3.76302i 0.165338 + 0.165338i
\(519\) 43.1481 1.89399
\(520\) −2.03720 0.247472i −0.0893371 0.0108524i
\(521\) 44.0469i 1.92973i 0.262743 + 0.964866i \(0.415373\pi\)
−0.262743 + 0.964866i \(0.584627\pi\)
\(522\) −22.9121 22.9121i −1.00283 1.00283i
\(523\) 19.0964 + 19.0964i 0.835026 + 0.835026i 0.988199 0.153174i \(-0.0489494\pi\)
−0.153174 + 0.988199i \(0.548949\pi\)
\(524\) 16.6754 0.728468
\(525\) −18.9709 4.67808i −0.827958 0.204168i
\(526\) −23.0112 −1.00334
\(527\) −10.4207 10.4207i −0.453934 0.453934i
\(528\) −7.06334 7.06334i −0.307393 0.307393i
\(529\) 12.2028i 0.530556i
\(530\) −1.17921 + 9.70732i −0.0512218 + 0.421659i
\(531\) 61.4603 2.66715
\(532\) −0.0319973 0.0319973i −0.00138726 0.00138726i
\(533\) 6.57262 6.57262i 0.284692 0.284692i
\(534\) 26.3119 1.13863
\(535\) 13.5850 + 17.3420i 0.587333 + 0.749758i
\(536\) 1.52212i 0.0657455i
\(537\) −39.2061 39.2061i −1.69187 1.69187i
\(538\) −12.1414 12.1414i −0.523452 0.523452i
\(539\) 18.1400i 0.781347i
\(540\) 4.96666 + 6.34018i 0.213731 + 0.272838i
\(541\) −33.1678 −1.42599 −0.712997 0.701167i \(-0.752663\pi\)
−0.712997 + 0.701167i \(0.752663\pi\)
\(542\) −10.6042 + 10.6042i −0.455488 + 0.455488i
\(543\) −10.3938 10.3938i −0.446039 0.446039i
\(544\) −3.58221 −0.153586
\(545\) 0.345596 2.84496i 0.0148037 0.121865i
\(546\) 3.58646i 0.153486i
\(547\) −21.0500 21.0500i −0.900033 0.900033i 0.0954056 0.995438i \(-0.469585\pi\)
−0.995438 + 0.0954056i \(0.969585\pi\)
\(548\) −8.14514 8.14514i −0.347943 0.347943i
\(549\) 32.5800 1.39048
\(550\) −15.7879 + 9.54179i −0.673199 + 0.406864i
\(551\) −0.234591 −0.00999393
\(552\) 6.29075 + 6.29075i 0.267752 + 0.267752i
\(553\) −2.08348 2.08348i −0.0885988 0.0885988i
\(554\) 18.6515i 0.792426i
\(555\) −22.1586 2.69176i −0.940582 0.114259i
\(556\) 5.97569 0.253426
\(557\) 7.14577 + 7.14577i 0.302776 + 0.302776i 0.842099 0.539323i \(-0.181320\pi\)
−0.539323 + 0.842099i \(0.681320\pi\)
\(558\) −12.5970 12.5970i −0.533275 0.533275i
\(559\) 0.279127 + 6.01168i 0.0118058 + 0.254267i
\(560\) 2.54070 1.99029i 0.107364 0.0841052i
\(561\) 35.7829i 1.51076i
\(562\) −13.9194 + 13.9194i −0.587154 + 0.587154i
\(563\) 3.19095 3.19095i 0.134482 0.134482i −0.636661 0.771144i \(-0.719685\pi\)
0.771144 + 0.636661i \(0.219685\pi\)
\(564\) 24.2089 1.01938
\(565\) −17.2254 21.9890i −0.724678 0.925086i
\(566\) 26.1598i 1.09958i
\(567\) 3.30597 3.30597i 0.138838 0.138838i
\(568\) 3.34497 3.34497i 0.140352 0.140352i
\(569\) 21.8508i 0.916035i 0.888943 + 0.458018i \(0.151440\pi\)
−0.888943 + 0.458018i \(0.848560\pi\)
\(570\) 0.188417 + 0.0228883i 0.00789192 + 0.000958684i
\(571\) 23.7035i 0.991962i 0.868333 + 0.495981i \(0.165191\pi\)
−0.868333 + 0.495981i \(0.834809\pi\)
\(572\) −2.39430 2.39430i −0.100111 0.100111i
\(573\) −22.1694 + 22.1694i −0.926140 + 0.926140i
\(574\) 14.6184i 0.610159i
\(575\) 14.0610 8.49811i 0.586385 0.354396i
\(576\) −4.33033 −0.180431
\(577\) −2.26045 + 2.26045i −0.0941037 + 0.0941037i −0.752591 0.658488i \(-0.771196\pi\)
0.658488 + 0.752591i \(0.271196\pi\)
\(578\) −2.94707 2.94707i −0.122582 0.122582i
\(579\) −58.1660 −2.41730
\(580\) 2.01770 16.6097i 0.0837802 0.689681i
\(581\) 10.0105i 0.415306i
\(582\) 27.3767 + 27.3767i 1.13480 + 1.13480i
\(583\) −11.4089 + 11.4089i −0.472508 + 0.472508i
\(584\) 7.00321i 0.289795i
\(585\) 5.48015 + 6.99568i 0.226577 + 0.289236i
\(586\) 33.2071i 1.37177i
\(587\) 26.6723 26.6723i 1.10088 1.10088i 0.106579 0.994304i \(-0.466010\pi\)
0.994304 0.106579i \(-0.0339897\pi\)
\(588\) −9.41286 9.41286i −0.388180 0.388180i
\(589\) −0.128978 −0.00531445
\(590\) 19.5711 + 24.9835i 0.805730 + 1.02855i
\(591\) 1.18755i 0.0488493i
\(592\) 2.60713 2.60713i 0.107152 0.107152i
\(593\) 24.8475 + 24.8475i 1.02037 + 1.02037i 0.999788 + 0.0205776i \(0.00655051\pi\)
0.0205776 + 0.999788i \(0.493449\pi\)
\(594\) 13.2888i 0.545246i
\(595\) −11.4770 1.39419i −0.470512 0.0571563i
\(596\) 3.51576i 0.144011i
\(597\) −52.6799 52.6799i −2.15604 2.15604i
\(598\) 2.13241 + 2.13241i 0.0872006 + 0.0872006i
\(599\) 31.9194i 1.30419i 0.758137 + 0.652095i \(0.226110\pi\)
−0.758137 + 0.652095i \(0.773890\pi\)
\(600\) −3.24111 + 13.1436i −0.132318 + 0.536584i
\(601\) 24.5020i 0.999459i −0.866182 0.499729i \(-0.833433\pi\)
0.866182 0.499729i \(-0.166567\pi\)
\(602\) −6.99579 6.37497i −0.285127 0.259824i
\(603\) −4.66074 + 4.66074i −0.189800 + 0.189800i
\(604\) −10.6170 −0.432000
\(605\) −5.79833 0.704363i −0.235736 0.0286364i
\(606\) −2.75142 −0.111769
\(607\) −19.1505 + 19.1505i −0.777296 + 0.777296i −0.979370 0.202075i \(-0.935232\pi\)
0.202075 + 0.979370i \(0.435232\pi\)
\(608\) −0.0221686 + 0.0221686i −0.000899057 + 0.000899057i
\(609\) 29.2412 1.18491
\(610\) 10.3746 + 13.2437i 0.420056 + 0.536221i
\(611\) 8.20620 0.331987
\(612\) 10.9687 + 10.9687i 0.443385 + 0.443385i
\(613\) −12.1307 + 12.1307i −0.489956 + 0.489956i −0.908292 0.418336i \(-0.862613\pi\)
0.418336 + 0.908292i \(0.362613\pi\)
\(614\) −13.5135 −0.545361
\(615\) −37.8119 48.2687i −1.52472 1.94638i
\(616\) 5.32522 0.214559
\(617\) 30.3013 + 30.3013i 1.21988 + 1.21988i 0.967672 + 0.252211i \(0.0811578\pi\)
0.252211 + 0.967672i \(0.418842\pi\)
\(618\) −33.2252 + 33.2252i −1.33652 + 1.33652i
\(619\) 28.6337i 1.15089i 0.817842 + 0.575443i \(0.195170\pi\)
−0.817842 + 0.575443i \(0.804830\pi\)
\(620\) 1.10933 9.13201i 0.0445516 0.366750i
\(621\) 11.8353i 0.474933i
\(622\) 6.10831 6.10831i 0.244921 0.244921i
\(623\) −9.91860 + 9.91860i −0.397380 + 0.397380i
\(624\) −2.48480 −0.0994715
\(625\) 22.1339 + 11.6229i 0.885356 + 0.464914i
\(626\) 18.3424 0.733109
\(627\) 0.221444 + 0.221444i 0.00884363 + 0.00884363i
\(628\) 4.54306 + 4.54306i 0.181288 + 0.181288i
\(629\) −13.2077 −0.526626
\(630\) −13.8739 1.68536i −0.552751 0.0671464i
\(631\) 4.03917i 0.160797i −0.996763 0.0803983i \(-0.974381\pi\)
0.996763 0.0803983i \(-0.0256192\pi\)
\(632\) −1.44350 + 1.44350i −0.0574192 + 0.0574192i
\(633\) −22.1268 + 22.1268i −0.879463 + 0.879463i
\(634\) 6.25316 0.248345
\(635\) −27.8774 35.5868i −1.10628 1.41222i
\(636\) 11.8401i 0.469492i
\(637\) −3.19072 3.19072i −0.126421 0.126421i
\(638\) 19.5212 19.5212i 0.772852 0.772852i
\(639\) −20.4847 −0.810361
\(640\) −1.37893 1.76027i −0.0545070 0.0695808i
\(641\) 8.70502i 0.343828i −0.985112 0.171914i \(-0.945005\pi\)
0.985112 0.171914i \(-0.0549951\pi\)
\(642\) 18.8610 + 18.8610i 0.744386 + 0.744386i
\(643\) −14.1834 + 14.1834i −0.559340 + 0.559340i −0.929119 0.369780i \(-0.879433\pi\)
0.369780 + 0.929119i \(0.379433\pi\)
\(644\) −4.74275 −0.186891
\(645\) 39.5891 + 2.95434i 1.55882 + 0.116327i
\(646\) 0.112306 0.00441864
\(647\) −9.23223 + 9.23223i −0.362956 + 0.362956i −0.864900 0.501944i \(-0.832618\pi\)
0.501944 + 0.864900i \(0.332618\pi\)
\(648\) −2.29047 2.29047i −0.0899783 0.0899783i
\(649\) 52.3645i 2.05549i
\(650\) −1.09865 + 4.45534i −0.0430927 + 0.174753i
\(651\) 16.0768 0.630098
\(652\) −5.62978 + 5.62978i −0.220479 + 0.220479i
\(653\) 5.36237 + 5.36237i 0.209846 + 0.209846i 0.804202 0.594356i \(-0.202593\pi\)
−0.594356 + 0.804202i \(0.702593\pi\)
\(654\) 3.47003i 0.135689i
\(655\) 4.49649 37.0152i 0.175692 1.44630i
\(656\) 10.1280 0.395433
\(657\) 21.4439 21.4439i 0.836605 0.836605i
\(658\) −9.12583 + 9.12583i −0.355762 + 0.355762i
\(659\) 8.85409i 0.344906i 0.985018 + 0.172453i \(0.0551693\pi\)
−0.985018 + 0.172453i \(0.944831\pi\)
\(660\) −17.5835 + 13.7742i −0.684436 + 0.536162i
\(661\) 22.3457 0.869148 0.434574 0.900636i \(-0.356899\pi\)
0.434574 + 0.900636i \(0.356899\pi\)
\(662\) 1.75509 + 1.75509i 0.0682137 + 0.0682137i
\(663\) 6.29400 + 6.29400i 0.244439 + 0.244439i
\(664\) 6.93557 0.269152
\(665\) −0.0796540 + 0.0623980i −0.00308885 + 0.00241969i
\(666\) −15.9661 −0.618673
\(667\) −17.3860 + 17.3860i −0.673188 + 0.673188i
\(668\) −1.08392 + 1.08392i −0.0419379 + 0.0419379i
\(669\) 68.4192i 2.64524i
\(670\) −3.37872 0.410436i −0.130531 0.0158565i
\(671\) 27.7583i 1.07160i
\(672\) 2.76326 2.76326i 0.106595 0.106595i
\(673\) −20.2442 20.2442i −0.780358 0.780358i 0.199533 0.979891i \(-0.436057\pi\)
−0.979891 + 0.199533i \(0.936057\pi\)
\(674\) −4.75024 −0.182973
\(675\) 15.4129 9.31513i 0.593241 0.358539i
\(676\) 12.1577 0.467604
\(677\) 25.3721 25.3721i 0.975129 0.975129i −0.0245695 0.999698i \(-0.507822\pi\)
0.999698 + 0.0245695i \(0.00782151\pi\)
\(678\) −23.9152 23.9152i −0.918458 0.918458i
\(679\) −20.6400 −0.792090
\(680\) −0.965935 + 7.95160i −0.0370419 + 0.304930i
\(681\) −41.4233 −1.58735
\(682\) 10.7327 10.7327i 0.410978 0.410978i
\(683\) −8.18342 + 8.18342i −0.313130 + 0.313130i −0.846121 0.532991i \(-0.821068\pi\)
0.532991 + 0.846121i \(0.321068\pi\)
\(684\) 0.135761 0.00519095
\(685\) −20.2765 + 15.8838i −0.774725 + 0.606891i
\(686\) 17.2001 0.656703
\(687\) −0.858721 + 0.858721i −0.0327622 + 0.0327622i
\(688\) −4.41676 + 4.84688i −0.168387 + 0.184785i
\(689\) 4.01351i 0.152903i
\(690\) 15.6602 12.2676i 0.596173 0.467020i
\(691\) 43.2645i 1.64586i 0.568143 + 0.822930i \(0.307662\pi\)
−0.568143 + 0.822930i \(0.692338\pi\)
\(692\) 11.2690 + 11.2690i 0.428383 + 0.428383i
\(693\) −16.3059 16.3059i −0.619409 0.619409i
\(694\) 4.47229i 0.169766i
\(695\) 1.61133 13.2645i 0.0611214 0.503153i
\(696\) 20.2591i 0.767919i
\(697\) −25.6543 25.6543i −0.971726 0.971726i
\(698\) 19.0684 19.0684i 0.721751 0.721751i
\(699\) 51.5912i 1.95136i
\(700\) −3.73285 6.17640i −0.141089 0.233446i
\(701\) 7.64559 0.288770 0.144385 0.989522i \(-0.453880\pi\)
0.144385 + 0.989522i \(0.453880\pi\)
\(702\) 2.33742 + 2.33742i 0.0882201 + 0.0882201i
\(703\) −0.0817365 + 0.0817365i −0.00308275 + 0.00308275i
\(704\) 3.68947i 0.139052i
\(705\) 6.52788 53.7376i 0.245854 2.02388i
\(706\) 32.0862i 1.20758i
\(707\) 1.03718 1.03718i 0.0390072 0.0390072i
\(708\) 27.1719 + 27.1719i 1.02118 + 1.02118i
\(709\) 40.1277i 1.50703i −0.657433 0.753513i \(-0.728358\pi\)
0.657433 0.753513i \(-0.271642\pi\)
\(710\) −6.52304 8.32697i −0.244805 0.312506i
\(711\) 8.83999 0.331526
\(712\) 6.87188 + 6.87188i 0.257535 + 0.257535i
\(713\) −9.55879 + 9.55879i −0.357979 + 0.357979i
\(714\) −13.9987 −0.523887
\(715\) −5.96035 + 4.66912i −0.222905 + 0.174615i
\(716\) 20.4789i 0.765333i
\(717\) 8.72952 8.72952i 0.326010 0.326010i
\(718\) −8.12510 8.12510i −0.303226 0.303226i
\(719\) 28.6609i 1.06887i −0.845209 0.534436i \(-0.820524\pi\)
0.845209 0.534436i \(-0.179476\pi\)
\(720\) −1.16767 + 9.61226i −0.0435163 + 0.358228i
\(721\) 25.0493i 0.932885i
\(722\) −13.4343 + 13.4343i −0.499974 + 0.499974i
\(723\) 11.6796 11.6796i 0.434368 0.434368i
\(724\) 5.42907i 0.201770i
\(725\) −36.3254 8.95756i −1.34909 0.332675i
\(726\) −7.07230 −0.262478
\(727\) −16.4761 + 16.4761i −0.611066 + 0.611066i −0.943224 0.332158i \(-0.892223\pi\)
0.332158 + 0.943224i \(0.392223\pi\)
\(728\) 0.936675 0.936675i 0.0347155 0.0347155i
\(729\) 43.2822i 1.60305i
\(730\) 15.5454 + 1.88840i 0.575360 + 0.0698929i
\(731\) 23.4648 1.08949i 0.867878 0.0402962i
\(732\) 14.4038 + 14.4038i 0.532379 + 0.532379i
\(733\) −9.63596 9.63596i −0.355912 0.355912i 0.506391 0.862304i \(-0.330979\pi\)
−0.862304 + 0.506391i \(0.830979\pi\)
\(734\) −10.8364 −0.399978
\(735\) −23.4324 + 18.3560i −0.864316 + 0.677073i
\(736\) 3.28591i 0.121120i
\(737\) −3.97097 3.97097i −0.146273 0.146273i
\(738\) −31.0121 31.0121i −1.14157 1.14157i
\(739\) −44.4359 −1.63460 −0.817300 0.576212i \(-0.804530\pi\)
−0.817300 + 0.576212i \(0.804530\pi\)
\(740\) −5.08416 6.49018i −0.186898 0.238584i
\(741\) 0.0779014 0.00286178
\(742\) −4.46329 4.46329i −0.163852 0.163852i
\(743\) −0.0453056 0.0453056i −0.00166210 0.00166210i 0.706275 0.707937i \(-0.250374\pi\)
−0.707937 + 0.706275i \(0.750374\pi\)
\(744\) 11.1384i 0.408355i
\(745\) 7.80411 + 0.948019i 0.285921 + 0.0347327i
\(746\) −10.7743 −0.394474
\(747\) −21.2368 21.2368i −0.777013 0.777013i
\(748\) −9.34543 + 9.34543i −0.341703 + 0.341703i
\(749\) −14.2198 −0.519580
\(750\) 28.3015 + 10.7386i 1.03342 + 0.392118i
\(751\) 3.91932i 0.143018i −0.997440 0.0715091i \(-0.977219\pi\)
0.997440 0.0715091i \(-0.0227815\pi\)
\(752\) 6.32263 + 6.32263i 0.230563 + 0.230563i
\(753\) 52.0458 + 52.0458i 1.89665 + 1.89665i
\(754\) 6.86732i 0.250093i
\(755\) −2.86285 + 23.5671i −0.104190 + 0.857694i
\(756\) −5.19872 −0.189076
\(757\) 10.6675 10.6675i 0.387717 0.387717i −0.486156 0.873872i \(-0.661601\pi\)
0.873872 + 0.486156i \(0.161601\pi\)
\(758\) 14.5837 + 14.5837i 0.529703 + 0.529703i
\(759\) 32.8232 1.19141
\(760\) 0.0432311 + 0.0551866i 0.00156816 + 0.00200183i
\(761\) 51.5873i 1.87004i 0.354597 + 0.935019i \(0.384618\pi\)
−0.354597 + 0.935019i \(0.615382\pi\)
\(762\) −38.7041 38.7041i −1.40210 1.40210i
\(763\) 1.30807 + 1.30807i 0.0473554 + 0.0473554i
\(764\) −11.5800 −0.418948
\(765\) 27.3056 21.3902i 0.987235 0.773363i
\(766\) −19.5975 −0.708085
\(767\) 9.21059 + 9.21059i 0.332575 + 0.332575i
\(768\) −1.91446 1.91446i −0.0690822 0.0690822i
\(769\) 27.6619i 0.997512i −0.866742 0.498756i \(-0.833790\pi\)
0.866742 0.498756i \(-0.166210\pi\)
\(770\) 1.43594 11.8207i 0.0517476 0.425987i
\(771\) 40.2710 1.45032
\(772\) −15.1912 15.1912i −0.546743 0.546743i
\(773\) 18.4198 + 18.4198i 0.662514 + 0.662514i 0.955972 0.293458i \(-0.0948061\pi\)
−0.293458 + 0.955972i \(0.594806\pi\)
\(774\) 28.3653 1.31702i 1.01957 0.0473394i
\(775\) −19.9716 4.92486i −0.717402 0.176906i
\(776\) 14.3000i 0.513339i
\(777\) 10.1882 10.1882i 0.365501 0.365501i
\(778\) 18.6487 18.6487i 0.668590 0.668590i
\(779\) −0.317525 −0.0113765
\(780\) −0.670021 + 5.51563i −0.0239906 + 0.197491i
\(781\) 17.4530i 0.624519i
\(782\) 8.32322 8.32322i 0.297638 0.297638i
\(783\) −19.0575 + 19.0575i −0.681059 + 0.681059i
\(784\) 4.91671i 0.175597i
\(785\) 11.3095 8.85943i 0.403653 0.316207i
\(786\) 45.1479i 1.61037i
\(787\) 19.9428 + 19.9428i 0.710885 + 0.710885i 0.966720 0.255835i \(-0.0823505\pi\)
−0.255835 + 0.966720i \(0.582350\pi\)
\(788\) 0.310153 0.310153i 0.0110487 0.0110487i
\(789\) 62.3020i 2.21801i
\(790\) 2.81497 + 3.59344i 0.100152 + 0.127849i
\(791\) 18.0302 0.641082
\(792\) −11.2972 + 11.2972i −0.401428 + 0.401428i
\(793\) 4.88252 + 4.88252i 0.173383 + 0.173383i
\(794\) 18.9848 0.673746
\(795\) 26.2822 + 3.19267i 0.932132 + 0.113232i
\(796\) 27.5168i 0.975307i
\(797\) −6.01324 6.01324i −0.213000 0.213000i 0.592541 0.805541i \(-0.298125\pi\)
−0.805541 + 0.592541i \(0.798125\pi\)
\(798\) −0.0866314 + 0.0866314i −0.00306672 + 0.00306672i
\(799\) 32.0305i 1.13316i
\(800\) −4.27919 + 2.58623i −0.151292 + 0.0914369i
\(801\) 42.0835i 1.48695i
\(802\) −17.4021 + 17.4021i −0.614490 + 0.614490i
\(803\) 18.2703 + 18.2703i 0.644744 + 0.644744i
\(804\) −4.12107 −0.145339
\(805\) −1.27887 + 10.5277i −0.0450744 + 0.371053i
\(806\) 3.77565i 0.132991i
\(807\) −32.8723 + 32.8723i −1.15716 + 1.15716i
\(808\) −0.718588 0.718588i −0.0252798 0.0252798i
\(809\) 2.69059i 0.0945959i 0.998881 + 0.0472980i \(0.0150610\pi\)
−0.998881 + 0.0472980i \(0.984939\pi\)
\(810\) −5.70190 + 4.46665i −0.200344 + 0.156942i
\(811\) 1.60017i 0.0561897i 0.999605 + 0.0280948i \(0.00894404\pi\)
−0.999605 + 0.0280948i \(0.991056\pi\)
\(812\) 7.63691 + 7.63691i 0.268003 + 0.268003i
\(813\) 28.7104 + 28.7104i 1.00692 + 1.00692i
\(814\) 13.6032i 0.476791i
\(815\) 10.9786 + 14.0148i 0.384565 + 0.490916i
\(816\) 9.69868i 0.339522i
\(817\) 0.138471 0.151955i 0.00484448 0.00531625i
\(818\) 10.4823 10.4823i 0.366506 0.366506i
\(819\) −5.73621 −0.200439
\(820\) 2.73100 22.4817i 0.0953707 0.785094i
\(821\) −30.4124 −1.06140 −0.530700 0.847560i \(-0.678071\pi\)
−0.530700 + 0.847560i \(0.678071\pi\)
\(822\) −22.0526 + 22.0526i −0.769174 + 0.769174i
\(823\) 25.4456 25.4456i 0.886978 0.886978i −0.107253 0.994232i \(-0.534206\pi\)
0.994232 + 0.107253i \(0.0342056\pi\)
\(824\) −17.3549 −0.604586
\(825\) 25.8340 + 42.7451i 0.899425 + 1.48819i
\(826\) −20.4856 −0.712784
\(827\) 34.4225 + 34.4225i 1.19699 + 1.19699i 0.975064 + 0.221924i \(0.0712338\pi\)
0.221924 + 0.975064i \(0.428766\pi\)
\(828\) 10.0615 10.0615i 0.349661 0.349661i
\(829\) −48.6795 −1.69071 −0.845354 0.534207i \(-0.820610\pi\)
−0.845354 + 0.534207i \(0.820610\pi\)
\(830\) 1.87016 15.3952i 0.0649143 0.534376i
\(831\) −50.4982 −1.75176
\(832\) −0.648955 0.648955i −0.0224984 0.0224984i
\(833\) −12.4541 + 12.4541i −0.431507 + 0.431507i
\(834\) 16.1789i 0.560231i
\(835\) 2.11374 + 2.69830i 0.0731492 + 0.0933784i
\(836\) 0.115669i 0.00400050i
\(837\) −10.4778 + 10.4778i −0.362165 + 0.362165i
\(838\) −20.4185 + 20.4185i −0.705344 + 0.705344i
\(839\) −5.13321 −0.177218 −0.0886090 0.996066i \(-0.528242\pi\)
−0.0886090 + 0.996066i \(0.528242\pi\)
\(840\) −5.38863 6.87885i −0.185926 0.237343i
\(841\) 26.9908 0.930717
\(842\) 0.829667 + 0.829667i 0.0285922 + 0.0285922i
\(843\) 37.6862 + 37.6862i 1.29798 + 1.29798i
\(844\) −11.5577 −0.397834
\(845\) 3.27830 26.9871i 0.112777 0.928384i
\(846\) 38.7199i 1.33122i
\(847\) 2.66599 2.66599i 0.0916045 0.0916045i
\(848\) −3.09229 + 3.09229i −0.106190 + 0.106190i
\(849\) 70.8264 2.43076
\(850\) 17.3901 + 4.28827i 0.596476 + 0.147086i
\(851\) 12.1153i 0.415306i
\(852\) −9.05638 9.05638i −0.310266 0.310266i
\(853\) 15.1328 15.1328i 0.518137 0.518137i −0.398870 0.917007i \(-0.630598\pi\)
0.917007 + 0.398870i \(0.130598\pi\)
\(854\) −10.8594 −0.371600
\(855\) 0.0366077 0.301356i 0.00125196 0.0103061i
\(856\) 9.85187i 0.336730i
\(857\) −25.5613 25.5613i −0.873156 0.873156i 0.119659 0.992815i \(-0.461820\pi\)
−0.992815 + 0.119659i \(0.961820\pi\)
\(858\) −6.48246 + 6.48246i −0.221307 + 0.221307i
\(859\) 43.5692 1.48656 0.743281 0.668979i \(-0.233269\pi\)
0.743281 + 0.668979i \(0.233269\pi\)
\(860\) 9.56789 + 11.1111i 0.326262 + 0.378884i
\(861\) 39.5786 1.34884
\(862\) −11.1912 + 11.1912i −0.381173 + 0.381173i
\(863\) 18.0267 + 18.0267i 0.613637 + 0.613637i 0.943892 0.330255i \(-0.107135\pi\)
−0.330255 + 0.943892i \(0.607135\pi\)
\(864\) 3.60182i 0.122536i
\(865\) 28.0530 21.9757i 0.953831 0.747196i
\(866\) −15.1070 −0.513358
\(867\) −7.97908 + 7.97908i −0.270984 + 0.270984i
\(868\) 4.19876 + 4.19876i 0.142515 + 0.142515i
\(869\) 7.53172i 0.255496i
\(870\) −44.9701 5.46283i −1.52463 0.185207i
\(871\) −1.39694 −0.0473335
\(872\) 0.906269 0.906269i 0.0306901 0.0306901i
\(873\) 43.7866 43.7866i 1.48195 1.48195i
\(874\) 0.103017i 0.00348461i
\(875\) −14.7166 + 6.62055i −0.497513 + 0.223815i
\(876\) 18.9609 0.640629
\(877\) −10.0042 10.0042i −0.337818 0.337818i 0.517727 0.855546i \(-0.326778\pi\)
−0.855546 + 0.517727i \(0.826778\pi\)
\(878\) 3.72075 + 3.72075i 0.125569 + 0.125569i
\(879\) −89.9067 −3.03248
\(880\) −8.18969 0.994857i −0.276074 0.0335366i
\(881\) 35.4715 1.19506 0.597532 0.801845i \(-0.296148\pi\)
0.597532 + 0.801845i \(0.296148\pi\)
\(882\) −15.0550 + 15.0550i −0.506929 + 0.506929i
\(883\) −30.5919 + 30.5919i −1.02950 + 1.02950i −0.0299490 + 0.999551i \(0.509534\pi\)
−0.999551 + 0.0299490i \(0.990466\pi\)
\(884\) 3.28761i 0.110574i
\(885\) 67.6417 52.9880i 2.27375 1.78117i
\(886\) 20.8690i 0.701106i
\(887\) 3.08773 3.08773i 0.103676 0.103676i −0.653366 0.757042i \(-0.726644\pi\)
0.757042 + 0.653366i \(0.226644\pi\)
\(888\) −7.05869 7.05869i −0.236874 0.236874i
\(889\) 29.1799 0.978663
\(890\) 17.1069 13.4009i 0.573423 0.449198i
\(891\) −11.9510 −0.400373
\(892\) −17.8690 + 17.8690i −0.598300 + 0.598300i
\(893\) −0.198222 0.198222i −0.00663324 0.00663324i
\(894\) 9.51878 0.318356
\(895\) −45.4581 5.52210i −1.51950 0.184584i
\(896\) 1.44336 0.0482193
\(897\) 5.77340 5.77340i 0.192768 0.192768i
\(898\) −1.65246 + 1.65246i −0.0551433 + 0.0551433i
\(899\) 30.7837 1.02669
\(900\) 21.0219 + 5.18385i 0.700732 + 0.172795i
\(901\) 15.6656 0.521896
\(902\) 26.4224 26.4224i 0.879771 0.879771i
\(903\) −17.2600 + 18.9408i −0.574376 + 0.630310i
\(904\) 12.4919i 0.415473i
\(905\) −12.0512 1.46394i −0.400595 0.0486630i
\(906\) 28.7451i 0.954992i
\(907\) 12.6922 + 12.6922i 0.421436 + 0.421436i 0.885698 0.464262i \(-0.153680\pi\)
−0.464262 + 0.885698i \(0.653680\pi\)
\(908\) −10.8185 10.8185i −0.359025 0.359025i
\(909\) 4.40064i 0.145960i
\(910\) −1.82661 2.33176i −0.0605516 0.0772970i
\(911\) 17.3644i 0.575308i 0.957734 + 0.287654i \(0.0928752\pi\)
−0.957734 + 0.287654i \(0.907125\pi\)
\(912\) 0.0600207 + 0.0600207i 0.00198748 + 0.00198748i
\(913\) 18.0938 18.0938i 0.598819 0.598819i
\(914\) 11.2905i 0.373458i
\(915\) 35.8567 28.0888i 1.18539 0.928589i
\(916\) −0.448544 −0.0148203
\(917\) 17.0191 + 17.0191i 0.562019 + 0.562019i
\(918\) 9.12342 9.12342i 0.301118 0.301118i
\(919\) 48.4350i 1.59772i −0.601515 0.798862i \(-0.705436\pi\)
0.601515 0.798862i \(-0.294564\pi\)
\(920\) 7.29390 + 0.886040i 0.240473 + 0.0292119i
\(921\) 36.5873i 1.20559i
\(922\) 11.8758 11.8758i 0.391108 0.391108i
\(923\) −3.06988 3.06988i −0.101046 0.101046i
\(924\) 14.4178i 0.474312i
\(925\) −15.7775 + 9.53551i −0.518761 + 0.313526i
\(926\) −13.9347 −0.457924
\(927\) 53.1407 + 53.1407i 1.74537 + 1.74537i
\(928\) 5.29107 5.29107i 0.173688 0.173688i
\(929\) 5.86211 0.192330 0.0961649 0.995365i \(-0.469342\pi\)
0.0961649 + 0.995365i \(0.469342\pi\)
\(930\) −24.7245 3.00346i −0.810749 0.0984872i
\(931\) 0.154145i 0.00505189i
\(932\) 13.4741 13.4741i 0.441358 0.441358i
\(933\) −16.5380 16.5380i −0.541429 0.541429i
\(934\) 4.27014i 0.139723i
\(935\) 18.2245 + 23.2645i 0.596006 + 0.760830i
\(936\) 3.97421i 0.129901i
\(937\) −31.9484 + 31.9484i −1.04371 + 1.04371i −0.0447071 + 0.999000i \(0.514235\pi\)
−0.999000 + 0.0447071i \(0.985765\pi\)
\(938\) 1.55349 1.55349i 0.0507232 0.0507232i
\(939\) 49.6612i 1.62063i
\(940\) 15.7395 12.3298i 0.513367 0.402153i
\(941\) 37.5860 1.22527 0.612634 0.790367i \(-0.290110\pi\)
0.612634 + 0.790367i \(0.290110\pi\)
\(942\) 12.3001 12.3001i 0.400760 0.400760i
\(943\) −23.5324 + 23.5324i −0.766319 + 0.766319i
\(944\) 14.1930i 0.461942i
\(945\) −1.40183 + 11.5399i −0.0456014 + 0.375392i
\(946\) 1.12211 + 24.1674i 0.0364830 + 0.785750i
\(947\) 12.3138 + 12.3138i 0.400145 + 0.400145i 0.878284 0.478139i \(-0.158688\pi\)
−0.478139 + 0.878284i \(0.658688\pi\)
\(948\) 3.90821 + 3.90821i 0.126933 + 0.126933i
\(949\) 6.42726 0.208638
\(950\) 0.134158 0.0810813i 0.00435265 0.00263062i
\(951\) 16.9302i 0.548998i
\(952\) −3.65603 3.65603i −0.118493 0.118493i
\(953\) −30.8857 30.8857i −1.00048 1.00048i −1.00000 0.000484952i \(-0.999846\pi\)
−0.000484952 1.00000i \(-0.500154\pi\)
\(954\) 18.9372 0.613116
\(955\) −3.12252 + 25.7046i −0.101042 + 0.831782i
\(956\) 4.55977 0.147474
\(957\) −52.8529 52.8529i −1.70849 1.70849i
\(958\) −18.7745 18.7745i −0.606576 0.606576i
\(959\) 16.6260i 0.536882i
\(960\) −4.76586 + 3.73340i −0.153817 + 0.120495i
\(961\) −14.0752 −0.454038
\(962\) −2.39272 2.39272i −0.0771443 0.0771443i
\(963\) 30.1665 30.1665i 0.972102 0.972102i
\(964\) 6.10070 0.196490
\(965\) −37.8170 + 29.6244i −1.21737 + 0.953643i
\(966\) 12.8408i 0.413146i
\(967\) −16.6658 16.6658i −0.535935 0.535935i 0.386398 0.922332i \(-0.373719\pi\)
−0.922332 + 0.386398i \(0.873719\pi\)
\(968\) −1.84707 1.84707i −0.0593672 0.0593672i
\(969\) 0.304065i 0.00976798i
\(970\) 31.7423 + 3.85596i 1.01919 + 0.123807i
\(971\) −2.89870 −0.0930237 −0.0465119 0.998918i \(-0.514811\pi\)
−0.0465119 + 0.998918i \(0.514811\pi\)
\(972\) −13.8420 + 13.8420i −0.443982 + 0.443982i
\(973\) 6.09884 + 6.09884i 0.195520 + 0.195520i
\(974\) −0.114435 −0.00366674
\(975\) 12.0627 + 2.97456i 0.386314 + 0.0952621i
\(976\) 7.52367i 0.240827i
\(977\) 10.5011 + 10.5011i 0.335959 + 0.335959i 0.854844 0.518885i \(-0.173653\pi\)
−0.518885 + 0.854844i \(0.673653\pi\)
\(978\) 15.2424 + 15.2424i 0.487398 + 0.487398i
\(979\) 35.8554 1.14594
\(980\) −10.9139 1.32578i −0.348631 0.0423506i
\(981\) −5.55000 −0.177198
\(982\) −15.4025 15.4025i −0.491513 0.491513i
\(983\) −13.4594 13.4594i −0.429287 0.429287i 0.459099 0.888385i \(-0.348172\pi\)
−0.888385 + 0.459099i \(0.848172\pi\)
\(984\) 27.4212i 0.874156i
\(985\) −0.604829 0.772094i −0.0192715 0.0246009i
\(986\) −26.8046 −0.853632
\(987\) 24.7078 + 24.7078i 0.786458 + 0.786458i
\(988\) 0.0203455 + 0.0203455i 0.000647276 + 0.000647276i
\(989\) −0.999374 21.5240i −0.0317782 0.684422i
\(990\) 22.0306 + 28.1232i 0.700180 + 0.893813i
\(991\) 52.5804i 1.67027i −0.550045 0.835135i \(-0.685389\pi\)
0.550045 0.835135i \(-0.314611\pi\)
\(992\) 2.90902 2.90902i 0.0923616 0.0923616i
\(993\) 4.75184 4.75184i 0.150795 0.150795i
\(994\) 6.82782 0.216565
\(995\) −61.0804 7.41985i −1.93638 0.235225i
\(996\) 18.7778i 0.594996i
\(997\) 21.9441 21.9441i 0.694976 0.694976i −0.268346 0.963323i \(-0.586477\pi\)
0.963323 + 0.268346i \(0.0864771\pi\)
\(998\) 4.49545 4.49545i 0.142301 0.142301i
\(999\) 13.2800i 0.420162i
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 430.2.g.b.257.12 yes 40
5.3 odd 4 inner 430.2.g.b.343.9 yes 40
43.42 odd 2 inner 430.2.g.b.257.9 40
215.128 even 4 inner 430.2.g.b.343.12 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
430.2.g.b.257.9 40 43.42 odd 2 inner
430.2.g.b.257.12 yes 40 1.1 even 1 trivial
430.2.g.b.343.9 yes 40 5.3 odd 4 inner
430.2.g.b.343.12 yes 40 215.128 even 4 inner