Properties

Label 50.3.f.a.13.2
Level $50$
Weight $3$
Character 50.13
Analytic conductor $1.362$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [50,3,Mod(3,50)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(50, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([7]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("50.3");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 50.f (of order \(20\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.36240132180\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{20})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 13.2
Root \(-3.40366i\) of defining polynomial
Character \(\chi\) \(=\) 50.13
Dual form 50.3.f.a.27.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39680 + 0.221232i) q^{2} +(0.252608 - 0.495771i) q^{3} +(1.90211 - 0.618034i) q^{4} +(3.68015 + 3.38474i) q^{5} +(-0.243163 + 0.748380i) q^{6} +(7.20385 - 7.20385i) q^{7} +(-2.52015 + 1.28408i) q^{8} +(5.10809 + 7.03068i) q^{9} +O(q^{10})\) \(q+(-1.39680 + 0.221232i) q^{2} +(0.252608 - 0.495771i) q^{3} +(1.90211 - 0.618034i) q^{4} +(3.68015 + 3.38474i) q^{5} +(-0.243163 + 0.748380i) q^{6} +(7.20385 - 7.20385i) q^{7} +(-2.52015 + 1.28408i) q^{8} +(5.10809 + 7.03068i) q^{9} +(-5.88926 - 3.91365i) q^{10} +(4.56901 + 3.31958i) q^{11} +(0.174086 - 1.09913i) q^{12} +(-22.6344 - 3.58493i) q^{13} +(-8.46863 + 11.6561i) q^{14} +(2.60770 - 0.969500i) q^{15} +(3.23607 - 2.35114i) q^{16} +(-8.10888 - 15.9146i) q^{17} +(-8.69040 - 8.69040i) q^{18} +(-13.6027 - 4.41978i) q^{19} +(9.09195 + 4.16371i) q^{20} +(-1.75171 - 5.39121i) q^{21} +(-7.11641 - 3.62599i) q^{22} +(4.05981 + 25.6327i) q^{23} +1.57379i q^{24} +(2.08702 + 24.9127i) q^{25} +32.4088 q^{26} +(9.72206 - 1.53982i) q^{27} +(9.25031 - 18.1548i) q^{28} +(-14.8092 + 4.81180i) q^{29} +(-3.42795 + 1.93110i) q^{30} +(10.7392 - 33.0518i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(2.79992 - 1.42663i) q^{33} +(14.8473 + 20.4356i) q^{34} +(50.8944 - 2.12806i) q^{35} +(14.0614 + 10.2162i) q^{36} +(2.42751 - 15.3267i) q^{37} +(19.9781 + 3.16422i) q^{38} +(-7.49493 + 10.3159i) q^{39} +(-13.6208 - 3.80445i) q^{40} +(-37.3476 + 27.1346i) q^{41} +(3.63950 + 7.14292i) q^{42} +(-31.8617 - 31.8617i) q^{43} +(10.7424 + 3.49042i) q^{44} +(-4.99852 + 43.1635i) q^{45} +(-11.3415 - 34.9056i) q^{46} +(8.16953 + 4.16259i) q^{47} +(-0.348171 - 2.19827i) q^{48} -54.7908i q^{49} +(-8.42664 - 34.3364i) q^{50} -9.93836 q^{51} +(-45.2687 + 7.16986i) q^{52} +(-12.8896 + 25.2972i) q^{53} +(-13.2391 + 4.30166i) q^{54} +(5.57872 + 27.6815i) q^{55} +(-8.90444 + 27.4051i) q^{56} +(-5.62735 + 5.62735i) q^{57} +(19.6210 - 9.99739i) q^{58} +(-23.3065 - 32.0786i) q^{59} +(4.36095 - 3.45574i) q^{60} +(11.5211 + 8.37057i) q^{61} +(-7.68840 + 48.5426i) q^{62} +(87.4458 + 13.8501i) q^{63} +(4.70228 - 6.47214i) q^{64} +(-71.1638 - 89.8046i) q^{65} +(-3.59532 + 2.61216i) q^{66} +(24.8631 + 48.7966i) q^{67} +(-25.2597 - 25.2597i) q^{68} +(13.7335 + 4.46228i) q^{69} +(-70.6186 + 14.2319i) q^{70} +(-23.8910 - 73.5289i) q^{71} +(-21.9011 - 11.1592i) q^{72} +(15.4792 + 97.7321i) q^{73} +21.9454i q^{74} +(12.8782 + 5.25848i) q^{75} -28.6054 q^{76} +(56.8282 - 9.00071i) q^{77} +(8.18674 - 16.0674i) q^{78} +(110.397 - 35.8702i) q^{79} +(19.8672 + 2.30071i) q^{80} +(-22.4769 + 69.1767i) q^{81} +(46.1642 - 46.1642i) q^{82} +(-13.6584 + 6.95931i) q^{83} +(-6.66390 - 9.17208i) q^{84} +(24.0249 - 86.0145i) q^{85} +(51.5533 + 37.4556i) q^{86} +(-1.35537 + 8.55747i) q^{87} +(-15.7772 - 2.49886i) q^{88} +(43.0149 - 59.2049i) q^{89} +(-2.56720 - 61.3968i) q^{90} +(-188.880 + 137.229i) q^{91} +(23.5641 + 46.2471i) q^{92} +(-13.6733 - 13.6733i) q^{93} +(-12.3321 - 4.00695i) q^{94} +(-35.1001 - 62.3071i) q^{95} +(0.972653 + 2.99352i) q^{96} +(67.9854 + 34.6403i) q^{97} +(12.1215 + 76.5319i) q^{98} +49.0800i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9} + 10 q^{10} + 32 q^{11} + 4 q^{12} - 8 q^{13} - 30 q^{14} + 16 q^{16} - 62 q^{17} - 16 q^{18} + 30 q^{19} - 20 q^{20} - 68 q^{21} - 48 q^{22} - 18 q^{23} + 70 q^{25} - 56 q^{26} - 40 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} + 132 q^{31} - 64 q^{32} - 36 q^{33} + 100 q^{34} + 150 q^{35} + 48 q^{36} + 138 q^{37} + 20 q^{38} - 320 q^{39} - 88 q^{41} - 8 q^{42} - 78 q^{43} + 40 q^{44} - 20 q^{45} - 26 q^{46} - 22 q^{47} - 8 q^{48} - 20 q^{50} - 168 q^{51} - 16 q^{52} + 182 q^{53} + 80 q^{54} + 280 q^{55} + 48 q^{56} + 280 q^{57} - 120 q^{58} - 350 q^{59} - 140 q^{60} + 372 q^{61} - 158 q^{62} + 22 q^{63} - 910 q^{65} - 202 q^{66} - 112 q^{67} - 196 q^{68} - 30 q^{69} - 20 q^{70} + 122 q^{71} - 132 q^{72} - 248 q^{73} - 80 q^{75} + 40 q^{76} + 16 q^{77} + 438 q^{78} + 760 q^{79} + 80 q^{80} - 144 q^{81} + 352 q^{82} + 132 q^{83} - 20 q^{84} - 30 q^{85} + 264 q^{86} + 770 q^{87} + 116 q^{88} + 550 q^{89} - 140 q^{90} - 798 q^{91} + 384 q^{92} + 54 q^{93} + 190 q^{94} + 40 q^{95} - 16 q^{96} - 292 q^{97} - 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).

\(n\) \(27\)
\(\chi(n)\) \(e\left(\frac{19}{20}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39680 + 0.221232i −0.698401 + 0.110616i
\(3\) 0.252608 0.495771i 0.0842027 0.165257i −0.845066 0.534663i \(-0.820439\pi\)
0.929268 + 0.369406i \(0.120439\pi\)
\(4\) 1.90211 0.618034i 0.475528 0.154508i
\(5\) 3.68015 + 3.38474i 0.736030 + 0.676949i
\(6\) −0.243163 + 0.748380i −0.0405272 + 0.124730i
\(7\) 7.20385 7.20385i 1.02912 1.02912i 0.0295578 0.999563i \(-0.490590\pi\)
0.999563 0.0295578i \(-0.00940991\pi\)
\(8\) −2.52015 + 1.28408i −0.315018 + 0.160510i
\(9\) 5.10809 + 7.03068i 0.567565 + 0.781187i
\(10\) −5.88926 3.91365i −0.588926 0.391365i
\(11\) 4.56901 + 3.31958i 0.415365 + 0.301780i 0.775770 0.631016i \(-0.217362\pi\)
−0.360405 + 0.932796i \(0.617362\pi\)
\(12\) 0.174086 1.09913i 0.0145071 0.0915945i
\(13\) −22.6344 3.58493i −1.74111 0.275764i −0.796659 0.604429i \(-0.793401\pi\)
−0.944446 + 0.328666i \(0.893401\pi\)
\(14\) −8.46863 + 11.6561i −0.604902 + 0.832576i
\(15\) 2.60770 0.969500i 0.173846 0.0646333i
\(16\) 3.23607 2.35114i 0.202254 0.146946i
\(17\) −8.10888 15.9146i −0.476993 0.936151i −0.996651 0.0817767i \(-0.973941\pi\)
0.519658 0.854374i \(-0.326059\pi\)
\(18\) −8.69040 8.69040i −0.482800 0.482800i
\(19\) −13.6027 4.41978i −0.715931 0.232620i −0.0716731 0.997428i \(-0.522834\pi\)
−0.644258 + 0.764808i \(0.722834\pi\)
\(20\) 9.09195 + 4.16371i 0.454597 + 0.208185i
\(21\) −1.75171 5.39121i −0.0834148 0.256724i
\(22\) −7.11641 3.62599i −0.323473 0.164818i
\(23\) 4.05981 + 25.6327i 0.176514 + 1.11446i 0.903745 + 0.428071i \(0.140807\pi\)
−0.727232 + 0.686392i \(0.759193\pi\)
\(24\) 1.57379i 0.0655744i
\(25\) 2.08702 + 24.9127i 0.0834807 + 0.996509i
\(26\) 32.4088 1.24649
\(27\) 9.72206 1.53982i 0.360076 0.0570305i
\(28\) 9.25031 18.1548i 0.330368 0.648384i
\(29\) −14.8092 + 4.81180i −0.510662 + 0.165924i −0.553003 0.833179i \(-0.686518\pi\)
0.0423415 + 0.999103i \(0.486518\pi\)
\(30\) −3.42795 + 1.93110i −0.114265 + 0.0643701i
\(31\) 10.7392 33.0518i 0.346425 1.06619i −0.614392 0.789001i \(-0.710598\pi\)
0.960817 0.277185i \(-0.0894015\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) 2.79992 1.42663i 0.0848462 0.0432313i
\(34\) 14.8473 + 20.4356i 0.436686 + 0.601046i
\(35\) 50.8944 2.12806i 1.45413 0.0608018i
\(36\) 14.0614 + 10.2162i 0.390593 + 0.283783i
\(37\) 2.42751 15.3267i 0.0656084 0.414235i −0.932924 0.360074i \(-0.882752\pi\)
0.998532 0.0541612i \(-0.0172485\pi\)
\(38\) 19.9781 + 3.16422i 0.525739 + 0.0832688i
\(39\) −7.49493 + 10.3159i −0.192178 + 0.264510i
\(40\) −13.6208 3.80445i −0.340520 0.0951112i
\(41\) −37.3476 + 27.1346i −0.910917 + 0.661820i −0.941247 0.337720i \(-0.890344\pi\)
0.0303297 + 0.999540i \(0.490344\pi\)
\(42\) 3.63950 + 7.14292i 0.0866548 + 0.170070i
\(43\) −31.8617 31.8617i −0.740969 0.740969i 0.231796 0.972765i \(-0.425540\pi\)
−0.972765 + 0.231796i \(0.925540\pi\)
\(44\) 10.7424 + 3.49042i 0.244145 + 0.0793276i
\(45\) −4.99852 + 43.1635i −0.111078 + 0.959190i
\(46\) −11.3415 34.9056i −0.246555 0.758817i
\(47\) 8.16953 + 4.16259i 0.173820 + 0.0885657i 0.538736 0.842475i \(-0.318902\pi\)
−0.364916 + 0.931041i \(0.618902\pi\)
\(48\) −0.348171 2.19827i −0.00725357 0.0457972i
\(49\) 54.7908i 1.11818i
\(50\) −8.42664 34.3364i −0.168533 0.686729i
\(51\) −9.93836 −0.194870
\(52\) −45.2687 + 7.16986i −0.870553 + 0.137882i
\(53\) −12.8896 + 25.2972i −0.243199 + 0.477305i −0.980050 0.198750i \(-0.936312\pi\)
0.736851 + 0.676055i \(0.236312\pi\)
\(54\) −13.2391 + 4.30166i −0.245169 + 0.0796603i
\(55\) 5.57872 + 27.6815i 0.101431 + 0.503300i
\(56\) −8.90444 + 27.4051i −0.159008 + 0.489376i
\(57\) −5.62735 + 5.62735i −0.0987255 + 0.0987255i
\(58\) 19.6210 9.99739i 0.338293 0.172369i
\(59\) −23.3065 32.0786i −0.395025 0.543706i 0.564461 0.825459i \(-0.309084\pi\)
−0.959487 + 0.281754i \(0.909084\pi\)
\(60\) 4.36095 3.45574i 0.0726825 0.0575957i
\(61\) 11.5211 + 8.37057i 0.188871 + 0.137223i 0.678202 0.734875i \(-0.262759\pi\)
−0.489332 + 0.872098i \(0.662759\pi\)
\(62\) −7.68840 + 48.5426i −0.124006 + 0.782946i
\(63\) 87.4458 + 13.8501i 1.38803 + 0.219842i
\(64\) 4.70228 6.47214i 0.0734732 0.101127i
\(65\) −71.1638 89.8046i −1.09483 1.38161i
\(66\) −3.59532 + 2.61216i −0.0544746 + 0.0395781i
\(67\) 24.8631 + 48.7966i 0.371091 + 0.728308i 0.998740 0.0501893i \(-0.0159825\pi\)
−0.627648 + 0.778497i \(0.715982\pi\)
\(68\) −25.2597 25.2597i −0.371467 0.371467i
\(69\) 13.7335 + 4.46228i 0.199036 + 0.0646707i
\(70\) −70.6186 + 14.2319i −1.00884 + 0.203313i
\(71\) −23.8910 73.5289i −0.336493 1.03562i −0.965982 0.258609i \(-0.916736\pi\)
0.629489 0.777009i \(-0.283264\pi\)
\(72\) −21.9011 11.1592i −0.304182 0.154988i
\(73\) 15.4792 + 97.7321i 0.212044 + 1.33880i 0.832269 + 0.554371i \(0.187041\pi\)
−0.620225 + 0.784424i \(0.712959\pi\)
\(74\) 21.9454i 0.296559i
\(75\) 12.8782 + 5.25848i 0.171710 + 0.0701130i
\(76\) −28.6054 −0.376387
\(77\) 56.8282 9.00071i 0.738029 0.116892i
\(78\) 8.18674 16.0674i 0.104958 0.205992i
\(79\) 110.397 35.8702i 1.39743 0.454053i 0.489073 0.872243i \(-0.337335\pi\)
0.908360 + 0.418189i \(0.137335\pi\)
\(80\) 19.8672 + 2.30071i 0.248340 + 0.0287589i
\(81\) −22.4769 + 69.1767i −0.277492 + 0.854033i
\(82\) 46.1642 46.1642i 0.562978 0.562978i
\(83\) −13.6584 + 6.95931i −0.164559 + 0.0838471i −0.534330 0.845276i \(-0.679436\pi\)
0.369771 + 0.929123i \(0.379436\pi\)
\(84\) −6.66390 9.17208i −0.0793322 0.109191i
\(85\) 24.0249 86.0145i 0.282645 1.01194i
\(86\) 51.5533 + 37.4556i 0.599456 + 0.435531i
\(87\) −1.35537 + 8.55747i −0.0155790 + 0.0983617i
\(88\) −15.7772 2.49886i −0.179286 0.0283962i
\(89\) 43.0149 59.2049i 0.483314 0.665224i −0.495824 0.868423i \(-0.665134\pi\)
0.979137 + 0.203199i \(0.0651339\pi\)
\(90\) −2.56720 61.3968i −0.0285245 0.682186i
\(91\) −188.880 + 137.229i −2.07560 + 1.50801i
\(92\) 23.5641 + 46.2471i 0.256131 + 0.502686i
\(93\) −13.6733 13.6733i −0.147025 0.147025i
\(94\) −12.3321 4.00695i −0.131193 0.0426271i
\(95\) −35.1001 62.3071i −0.369475 0.655864i
\(96\) 0.972653 + 2.99352i 0.0101318 + 0.0311825i
\(97\) 67.9854 + 34.6403i 0.700880 + 0.357116i 0.767842 0.640639i \(-0.221331\pi\)
−0.0669620 + 0.997756i \(0.521331\pi\)
\(98\) 12.1215 + 76.5319i 0.123688 + 0.780938i
\(99\) 49.0800i 0.495758i
\(100\) 19.3667 + 46.0970i 0.193667 + 0.460970i
\(101\) 156.192 1.54646 0.773228 0.634128i \(-0.218641\pi\)
0.773228 + 0.634128i \(0.218641\pi\)
\(102\) 13.8819 2.19868i 0.136097 0.0215557i
\(103\) 73.4520 144.158i 0.713127 1.39959i −0.194962 0.980811i \(-0.562458\pi\)
0.908088 0.418779i \(-0.137542\pi\)
\(104\) 61.6453 20.0298i 0.592743 0.192594i
\(105\) 11.8013 25.7696i 0.112393 0.245424i
\(106\) 12.4076 38.1868i 0.117053 0.360252i
\(107\) −125.552 + 125.552i −1.17338 + 1.17338i −0.191981 + 0.981399i \(0.561491\pi\)
−0.981399 + 0.191981i \(0.938509\pi\)
\(108\) 17.5408 8.93748i 0.162415 0.0827544i
\(109\) 52.2004 + 71.8476i 0.478902 + 0.659153i 0.978294 0.207224i \(-0.0664429\pi\)
−0.499391 + 0.866377i \(0.666443\pi\)
\(110\) −13.9164 37.4314i −0.126513 0.340286i
\(111\) −6.98533 5.07514i −0.0629309 0.0457220i
\(112\) 6.37488 40.2494i 0.0569186 0.359370i
\(113\) 23.7002 + 3.75375i 0.209736 + 0.0332190i 0.260418 0.965496i \(-0.416139\pi\)
−0.0506820 + 0.998715i \(0.516139\pi\)
\(114\) 6.61535 9.10525i 0.0580294 0.0798706i
\(115\) −71.8192 + 108.073i −0.624515 + 0.939769i
\(116\) −25.1949 + 18.3052i −0.217197 + 0.157803i
\(117\) −90.4138 177.447i −0.772768 1.51664i
\(118\) 39.6514 + 39.6514i 0.336029 + 0.336029i
\(119\) −173.061 56.2310i −1.45430 0.472529i
\(120\) −5.32686 + 5.79177i −0.0443905 + 0.0482647i
\(121\) −27.5348 84.7434i −0.227560 0.700359i
\(122\) −17.9445 9.14320i −0.147086 0.0749443i
\(123\) 4.01826 + 25.3703i 0.0326688 + 0.206263i
\(124\) 69.5054i 0.560527i
\(125\) −76.6427 + 98.7466i −0.613142 + 0.789973i
\(126\) −125.209 −0.993719
\(127\) −30.8349 + 4.88376i −0.242794 + 0.0384548i −0.276645 0.960972i \(-0.589223\pi\)
0.0338513 + 0.999427i \(0.489223\pi\)
\(128\) −5.13632 + 10.0806i −0.0401275 + 0.0787546i
\(129\) −23.8446 + 7.74759i −0.184842 + 0.0600588i
\(130\) 119.269 + 109.696i 0.917457 + 0.843812i
\(131\) 39.8145 122.536i 0.303928 0.935393i −0.676148 0.736766i \(-0.736352\pi\)
0.980075 0.198627i \(-0.0636481\pi\)
\(132\) 4.44407 4.44407i 0.0336672 0.0336672i
\(133\) −129.831 + 66.1523i −0.976174 + 0.497386i
\(134\) −45.5242 62.6587i −0.339733 0.467602i
\(135\) 40.9905 + 27.2399i 0.303634 + 0.201777i
\(136\) 40.8711 + 29.6946i 0.300523 + 0.218343i
\(137\) −4.80456 + 30.3348i −0.0350698 + 0.221422i −0.998999 0.0447377i \(-0.985755\pi\)
0.963929 + 0.266159i \(0.0857548\pi\)
\(138\) −20.1702 3.19464i −0.146161 0.0231496i
\(139\) −100.363 + 138.137i −0.722034 + 0.993794i 0.277420 + 0.960749i \(0.410521\pi\)
−0.999454 + 0.0330456i \(0.989479\pi\)
\(140\) 95.4917 35.5023i 0.682084 0.253588i
\(141\) 4.12738 2.99872i 0.0292722 0.0212675i
\(142\) 49.6379 + 97.4199i 0.349563 + 0.686056i
\(143\) −91.5163 91.5163i −0.639974 0.639974i
\(144\) 33.0602 + 10.7419i 0.229585 + 0.0745967i
\(145\) −70.7867 32.4172i −0.488184 0.223567i
\(146\) −43.2429 133.088i −0.296184 0.911561i
\(147\) −27.1637 13.8406i −0.184787 0.0941538i
\(148\) −4.85502 30.6534i −0.0328042 0.207117i
\(149\) 23.7099i 0.159127i 0.996830 + 0.0795635i \(0.0253527\pi\)
−0.996830 + 0.0795635i \(0.974647\pi\)
\(150\) −19.1517 4.49598i −0.127678 0.0299732i
\(151\) 207.294 1.37281 0.686403 0.727222i \(-0.259189\pi\)
0.686403 + 0.727222i \(0.259189\pi\)
\(152\) 39.9561 6.32843i 0.262869 0.0416344i
\(153\) 70.4694 138.304i 0.460584 0.903948i
\(154\) −77.3866 + 25.1444i −0.502510 + 0.163275i
\(155\) 151.394 85.2862i 0.976733 0.550233i
\(156\) −7.88064 + 24.2541i −0.0505169 + 0.155475i
\(157\) 25.6746 25.6746i 0.163533 0.163533i −0.620597 0.784130i \(-0.713110\pi\)
0.784130 + 0.620597i \(0.213110\pi\)
\(158\) −146.267 + 74.5270i −0.925743 + 0.471690i
\(159\) 9.28562 + 12.7806i 0.0584001 + 0.0803808i
\(160\) −28.2596 + 1.18163i −0.176622 + 0.00738517i
\(161\) 213.900 + 155.407i 1.32857 + 0.965263i
\(162\) 16.0917 101.599i 0.0993312 0.627153i
\(163\) 81.5666 + 12.9189i 0.500408 + 0.0792569i 0.401536 0.915843i \(-0.368476\pi\)
0.0988723 + 0.995100i \(0.468476\pi\)
\(164\) −54.2692 + 74.6952i −0.330910 + 0.455458i
\(165\) 15.1329 + 4.22680i 0.0917147 + 0.0256170i
\(166\) 17.5385 12.7424i 0.105653 0.0767617i
\(167\) 23.8290 + 46.7671i 0.142689 + 0.280043i 0.951280 0.308328i \(-0.0997695\pi\)
−0.808591 + 0.588371i \(0.799770\pi\)
\(168\) 11.3373 + 11.3373i 0.0674840 + 0.0674840i
\(169\) 338.734 + 110.061i 2.00434 + 0.651251i
\(170\) −14.5288 + 125.460i −0.0854637 + 0.738002i
\(171\) −38.4097 118.213i −0.224618 0.691303i
\(172\) −80.2961 40.9129i −0.466838 0.237866i
\(173\) −6.98501 44.1016i −0.0403758 0.254923i 0.959241 0.282588i \(-0.0911928\pi\)
−0.999617 + 0.0276651i \(0.991193\pi\)
\(174\) 12.2529i 0.0704192i
\(175\) 194.502 + 164.433i 1.11144 + 0.939617i
\(176\) 22.5904 0.128355
\(177\) −21.7911 + 3.45137i −0.123113 + 0.0194993i
\(178\) −46.9853 + 92.2138i −0.263962 + 0.518055i
\(179\) −310.306 + 100.824i −1.73355 + 0.563265i −0.993955 0.109787i \(-0.964983\pi\)
−0.739596 + 0.673051i \(0.764983\pi\)
\(180\) 17.1688 + 85.1912i 0.0953821 + 0.473284i
\(181\) 25.5973 78.7805i 0.141422 0.435251i −0.855112 0.518444i \(-0.826512\pi\)
0.996534 + 0.0831923i \(0.0265116\pi\)
\(182\) 233.468 233.468i 1.28279 1.28279i
\(183\) 7.06022 3.59736i 0.0385804 0.0196577i
\(184\) −43.1457 59.3849i −0.234487 0.322744i
\(185\) 60.8105 48.1880i 0.328706 0.260476i
\(186\) 22.1239 + 16.0740i 0.118946 + 0.0864191i
\(187\) 15.7802 99.6320i 0.0843859 0.532791i
\(188\) 18.1120 + 2.86866i 0.0963404 + 0.0152588i
\(189\) 58.9436 81.1289i 0.311871 0.429253i
\(190\) 62.8123 + 79.2655i 0.330591 + 0.417187i
\(191\) 112.018 81.3859i 0.586482 0.426104i −0.254573 0.967053i \(-0.581935\pi\)
0.841055 + 0.540950i \(0.181935\pi\)
\(192\) −2.02087 3.96617i −0.0105253 0.0206571i
\(193\) −14.7833 14.7833i −0.0765975 0.0765975i 0.667770 0.744368i \(-0.267249\pi\)
−0.744368 + 0.667770i \(0.767249\pi\)
\(194\) −102.626 33.3451i −0.528998 0.171882i
\(195\) −62.4991 + 12.5956i −0.320508 + 0.0645928i
\(196\) −33.8626 104.218i −0.172768 0.531726i
\(197\) −5.58697 2.84670i −0.0283602 0.0144503i 0.439753 0.898119i \(-0.355066\pi\)
−0.468113 + 0.883669i \(0.655066\pi\)
\(198\) −10.8581 68.5551i −0.0548387 0.346238i
\(199\) 244.037i 1.22632i 0.789961 + 0.613158i \(0.210101\pi\)
−0.789961 + 0.613158i \(0.789899\pi\)
\(200\) −37.2495 60.1039i −0.186248 0.300519i
\(201\) 30.4726 0.151605
\(202\) −218.169 + 34.5546i −1.08005 + 0.171063i
\(203\) −72.0197 + 141.347i −0.354777 + 0.696288i
\(204\) −18.9039 + 6.14224i −0.0926661 + 0.0301090i
\(205\) −229.288 26.5526i −1.11848 0.129525i
\(206\) −70.7057 + 217.610i −0.343232 + 1.05636i
\(207\) −159.477 + 159.477i −0.770421 + 0.770421i
\(208\) −81.6750 + 41.6155i −0.392668 + 0.200075i
\(209\) −47.4791 65.3493i −0.227173 0.312676i
\(210\) −10.7831 + 38.6058i −0.0513479 + 0.183837i
\(211\) −128.663 93.4793i −0.609778 0.443030i 0.239558 0.970882i \(-0.422998\pi\)
−0.849336 + 0.527852i \(0.822998\pi\)
\(212\) −8.88288 + 56.0843i −0.0419004 + 0.264549i
\(213\) −42.4886 6.72953i −0.199477 0.0315940i
\(214\) 147.595 203.147i 0.689695 0.949284i
\(215\) −9.41215 225.099i −0.0437774 1.04697i
\(216\) −22.5238 + 16.3645i −0.104277 + 0.0757614i
\(217\) −160.737 315.463i −0.740721 1.45375i
\(218\) −88.8086 88.8086i −0.407379 0.407379i
\(219\) 52.3629 + 17.0138i 0.239100 + 0.0776884i
\(220\) 27.7195 + 49.2055i 0.125998 + 0.223661i
\(221\) 126.487 + 389.286i 0.572338 + 1.76147i
\(222\) 10.8799 + 5.54359i 0.0490086 + 0.0249711i
\(223\) −59.4523 375.367i −0.266602 1.68326i −0.650203 0.759761i \(-0.725316\pi\)
0.383601 0.923499i \(-0.374684\pi\)
\(224\) 57.6308i 0.257280i
\(225\) −164.493 + 141.930i −0.731079 + 0.630798i
\(226\) −33.9350 −0.150155
\(227\) 178.162 28.2180i 0.784853 0.124309i 0.248870 0.968537i \(-0.419941\pi\)
0.535983 + 0.844228i \(0.319941\pi\)
\(228\) −7.22597 + 14.1818i −0.0316928 + 0.0622007i
\(229\) 24.3355 7.90707i 0.106268 0.0345287i −0.255400 0.966835i \(-0.582207\pi\)
0.361669 + 0.932307i \(0.382207\pi\)
\(230\) 76.4080 166.846i 0.332209 0.725417i
\(231\) 9.89298 30.4475i 0.0428268 0.131807i
\(232\) 31.1426 31.1426i 0.134235 0.134235i
\(233\) −244.770 + 124.717i −1.05052 + 0.535265i −0.891974 0.452088i \(-0.850679\pi\)
−0.158542 + 0.987352i \(0.550679\pi\)
\(234\) 165.547 + 227.856i 0.707467 + 0.973744i
\(235\) 15.9758 + 42.9707i 0.0679823 + 0.182854i
\(236\) −64.1573 46.6130i −0.271853 0.197513i
\(237\) 10.1038 63.7929i 0.0426321 0.269168i
\(238\) 254.172 + 40.2570i 1.06795 + 0.169147i
\(239\) 63.7205 87.7038i 0.266613 0.366962i −0.654630 0.755950i \(-0.727175\pi\)
0.921243 + 0.388988i \(0.127175\pi\)
\(240\) 6.15925 9.26843i 0.0256635 0.0386184i
\(241\) −299.048 + 217.271i −1.24086 + 0.901541i −0.997656 0.0684333i \(-0.978200\pi\)
−0.243209 + 0.969974i \(0.578200\pi\)
\(242\) 57.2086 + 112.278i 0.236399 + 0.463959i
\(243\) 91.2600 + 91.2600i 0.375556 + 0.375556i
\(244\) 27.0877 + 8.80134i 0.111015 + 0.0360711i
\(245\) 185.453 201.638i 0.756950 0.823014i
\(246\) −11.2254 34.5483i −0.0456318 0.140440i
\(247\) 292.044 + 148.804i 1.18236 + 0.602444i
\(248\) 15.3768 + 97.0853i 0.0620032 + 0.391473i
\(249\) 8.52943i 0.0342547i
\(250\) 85.2088 154.885i 0.340835 0.619541i
\(251\) −20.6897 −0.0824293 −0.0412146 0.999150i \(-0.513123\pi\)
−0.0412146 + 0.999150i \(0.513123\pi\)
\(252\) 174.892 27.7001i 0.694015 0.109921i
\(253\) −66.5404 + 130.593i −0.263005 + 0.516177i
\(254\) 41.9898 13.6433i 0.165314 0.0537138i
\(255\) −36.5747 33.6388i −0.143430 0.131917i
\(256\) 4.94427 15.2169i 0.0193136 0.0594410i
\(257\) −57.5934 + 57.5934i −0.224099 + 0.224099i −0.810222 0.586123i \(-0.800653\pi\)
0.586123 + 0.810222i \(0.300653\pi\)
\(258\) 31.5922 16.0970i 0.122450 0.0623916i
\(259\) −92.9237 127.899i −0.358779 0.493817i
\(260\) −190.864 126.837i −0.734092 0.487834i
\(261\) −109.477 79.5396i −0.419452 0.304749i
\(262\) −28.5040 + 179.967i −0.108794 + 0.686898i
\(263\) 86.6150 + 13.7185i 0.329335 + 0.0521615i 0.318912 0.947784i \(-0.396682\pi\)
0.0104222 + 0.999946i \(0.496682\pi\)
\(264\) −5.22431 + 7.19065i −0.0197891 + 0.0272373i
\(265\) −133.060 + 49.4696i −0.502113 + 0.186678i
\(266\) 166.713 121.124i 0.626742 0.455355i
\(267\) −18.4862 36.2812i −0.0692367 0.135885i
\(268\) 77.4504 + 77.4504i 0.288994 + 0.288994i
\(269\) −79.3898 25.7953i −0.295129 0.0958934i 0.157710 0.987485i \(-0.449589\pi\)
−0.452839 + 0.891592i \(0.649589\pi\)
\(270\) −63.2820 28.9803i −0.234378 0.107335i
\(271\) 33.5180 + 103.158i 0.123683 + 0.380656i 0.993659 0.112438i \(-0.0358658\pi\)
−0.869976 + 0.493094i \(0.835866\pi\)
\(272\) −63.6583 32.4355i −0.234038 0.119248i
\(273\) 20.3217 + 128.306i 0.0744386 + 0.469987i
\(274\) 43.4346i 0.158520i
\(275\) −73.1643 + 120.755i −0.266052 + 0.439108i
\(276\) 28.8805 0.104639
\(277\) −55.6330 + 8.81141i −0.200841 + 0.0318101i −0.256044 0.966665i \(-0.582419\pi\)
0.0552032 + 0.998475i \(0.482419\pi\)
\(278\) 109.626 215.154i 0.394340 0.773935i
\(279\) 287.233 93.3277i 1.02951 0.334508i
\(280\) −125.529 + 70.7155i −0.448317 + 0.252555i
\(281\) 98.2119 302.265i 0.349509 1.07568i −0.609617 0.792696i \(-0.708677\pi\)
0.959126 0.282981i \(-0.0913233\pi\)
\(282\) −5.10172 + 5.10172i −0.0180912 + 0.0180912i
\(283\) 426.824 217.478i 1.50821 0.768472i 0.512300 0.858807i \(-0.328794\pi\)
0.995911 + 0.0903348i \(0.0287937\pi\)
\(284\) −90.8867 125.095i −0.320024 0.440475i
\(285\) −39.7567 + 1.66236i −0.139497 + 0.00583283i
\(286\) 148.076 + 107.584i 0.517750 + 0.376167i
\(287\) −73.5727 + 464.520i −0.256351 + 1.61854i
\(288\) −48.5551 7.69037i −0.168594 0.0267027i
\(289\) −17.6497 + 24.2927i −0.0610716 + 0.0840579i
\(290\) 106.047 + 29.6201i 0.365679 + 0.102138i
\(291\) 34.3473 24.9548i 0.118032 0.0857553i
\(292\) 89.8450 + 176.331i 0.307688 + 0.603872i
\(293\) 385.350 + 385.350i 1.31519 + 1.31519i 0.917536 + 0.397652i \(0.130175\pi\)
0.397652 + 0.917536i \(0.369825\pi\)
\(294\) 41.0043 + 13.3231i 0.139470 + 0.0453167i
\(295\) 22.8066 196.941i 0.0773104 0.667596i
\(296\) 13.5630 + 41.7426i 0.0458210 + 0.141022i
\(297\) 49.5318 + 25.2377i 0.166774 + 0.0849754i
\(298\) −5.24539 33.1181i −0.0176020 0.111135i
\(299\) 594.733i 1.98907i
\(300\) 27.7457 + 2.04304i 0.0924858 + 0.00681013i
\(301\) −459.053 −1.52509
\(302\) −289.548 + 45.8599i −0.958769 + 0.151854i
\(303\) 39.4554 77.4356i 0.130216 0.255563i
\(304\) −54.4108 + 17.6791i −0.178983 + 0.0581550i
\(305\) 14.0672 + 69.8010i 0.0461218 + 0.228856i
\(306\) −67.8346 + 208.773i −0.221682 + 0.682266i
\(307\) 40.8331 40.8331i 0.133007 0.133007i −0.637469 0.770476i \(-0.720019\pi\)
0.770476 + 0.637469i \(0.220019\pi\)
\(308\) 102.531 52.2422i 0.332893 0.169617i
\(309\) −52.9147 72.8308i −0.171245 0.235699i
\(310\) −192.599 + 152.621i −0.621287 + 0.492326i
\(311\) −419.194 304.562i −1.34789 0.979299i −0.999114 0.0420933i \(-0.986597\pi\)
−0.348776 0.937206i \(-0.613403\pi\)
\(312\) 5.64191 35.6216i 0.0180831 0.114172i
\(313\) −199.049 31.5263i −0.635940 0.100723i −0.169864 0.985468i \(-0.554333\pi\)
−0.466076 + 0.884745i \(0.654333\pi\)
\(314\) −30.1823 + 41.5424i −0.0961221 + 0.132301i
\(315\) 274.935 + 346.952i 0.872809 + 1.10144i
\(316\) 187.819 136.458i 0.594364 0.431831i
\(317\) 215.645 + 423.227i 0.680268 + 1.33510i 0.930277 + 0.366857i \(0.119566\pi\)
−0.250009 + 0.968243i \(0.580434\pi\)
\(318\) −15.7976 15.7976i −0.0496781 0.0496781i
\(319\) −83.6366 27.1752i −0.262184 0.0851886i
\(320\) 39.2116 7.90241i 0.122536 0.0246950i
\(321\) 30.5295 + 93.9603i 0.0951076 + 0.292711i
\(322\) −333.157 169.752i −1.03465 0.527180i
\(323\) 39.9636 + 252.321i 0.123726 + 0.781178i
\(324\) 145.473i 0.448992i
\(325\) 42.0721 571.366i 0.129453 1.75805i
\(326\) −116.790 −0.358253
\(327\) 48.8062 7.73015i 0.149255 0.0236396i
\(328\) 59.2784 116.340i 0.180727 0.354697i
\(329\) 88.8387 28.8654i 0.270026 0.0877369i
\(330\) −22.0728 2.55613i −0.0668873 0.00774583i
\(331\) −128.800 + 396.407i −0.389125 + 1.19760i 0.544318 + 0.838879i \(0.316789\pi\)
−0.933443 + 0.358725i \(0.883211\pi\)
\(332\) −21.6787 + 21.6787i −0.0652974 + 0.0652974i
\(333\) 120.157 61.2231i 0.360832 0.183853i
\(334\) −43.6308 60.0527i −0.130631 0.179798i
\(335\) −73.6640 + 263.734i −0.219893 + 0.787266i
\(336\) −18.3442 13.3278i −0.0545957 0.0396661i
\(337\) 33.4503 211.197i 0.0992591 0.626697i −0.887035 0.461702i \(-0.847239\pi\)
0.986294 0.164996i \(-0.0527610\pi\)
\(338\) −497.494 78.7953i −1.47188 0.233122i
\(339\) 7.84787 10.8017i 0.0231501 0.0318633i
\(340\) −7.46190 178.457i −0.0219468 0.524875i
\(341\) 158.786 115.364i 0.465647 0.338312i
\(342\) 79.8032 + 156.623i 0.233343 + 0.457961i
\(343\) −41.7160 41.7160i −0.121621 0.121621i
\(344\) 121.209 + 39.3832i 0.352352 + 0.114486i
\(345\) 35.4376 + 62.9062i 0.102718 + 0.182337i
\(346\) 19.5133 + 60.0559i 0.0563970 + 0.173572i
\(347\) −113.136 57.6455i −0.326039 0.166125i 0.283307 0.959029i \(-0.408568\pi\)
−0.609347 + 0.792904i \(0.708568\pi\)
\(348\) 2.71074 + 17.1149i 0.00778949 + 0.0491809i
\(349\) 117.679i 0.337189i −0.985686 0.168594i \(-0.946077\pi\)
0.985686 0.168594i \(-0.0539228\pi\)
\(350\) −308.059 186.650i −0.880168 0.533287i
\(351\) −225.573 −0.642657
\(352\) −31.5544 + 4.99772i −0.0896432 + 0.0141981i
\(353\) −24.8731 + 48.8161i −0.0704619 + 0.138289i −0.923551 0.383477i \(-0.874727\pi\)
0.853089 + 0.521766i \(0.174727\pi\)
\(354\) 29.6743 9.64176i 0.0838256 0.0272366i
\(355\) 160.954 351.462i 0.453392 0.990035i
\(356\) 45.2285 139.199i 0.127046 0.391009i
\(357\) −71.5944 + 71.5944i −0.200545 + 0.200545i
\(358\) 411.130 209.481i 1.14841 0.585143i
\(359\) 269.868 + 371.442i 0.751723 + 1.03466i 0.997858 + 0.0654220i \(0.0208394\pi\)
−0.246135 + 0.969236i \(0.579161\pi\)
\(360\) −42.8284 115.197i −0.118968 0.319992i
\(361\) −126.556 91.9485i −0.350571 0.254705i
\(362\) −18.3257 + 115.704i −0.0506234 + 0.319624i
\(363\) −48.9689 7.75591i −0.134900 0.0213661i
\(364\) −274.458 + 377.760i −0.754007 + 1.03780i
\(365\) −273.832 + 412.062i −0.750225 + 1.12894i
\(366\) −9.06588 + 6.58674i −0.0247702 + 0.0179966i
\(367\) −254.971 500.410i −0.694745 1.36351i −0.921045 0.389456i \(-0.872663\pi\)
0.226300 0.974058i \(-0.427337\pi\)
\(368\) 73.4038 + 73.4038i 0.199467 + 0.199467i
\(369\) −381.550 123.973i −1.03401 0.335970i
\(370\) −74.2796 + 80.7624i −0.200756 + 0.218277i
\(371\) 89.3826 + 275.091i 0.240924 + 0.741486i
\(372\) −34.4588 17.5576i −0.0926311 0.0471979i
\(373\) −29.4686 186.058i −0.0790044 0.498814i −0.995182 0.0980422i \(-0.968742\pi\)
0.916178 0.400772i \(-0.131258\pi\)
\(374\) 142.657i 0.381437i
\(375\) 29.5952 + 62.9415i 0.0789205 + 0.167844i
\(376\) −25.9335 −0.0689721
\(377\) 352.447 55.8220i 0.934871 0.148069i
\(378\) −64.3842 + 126.361i −0.170329 + 0.334289i
\(379\) −22.7930 + 7.40589i −0.0601398 + 0.0195406i −0.338932 0.940811i \(-0.610066\pi\)
0.278793 + 0.960351i \(0.410066\pi\)
\(380\) −105.272 96.8221i −0.277032 0.254795i
\(381\) −5.36791 + 16.5207i −0.0140890 + 0.0433615i
\(382\) −138.462 + 138.462i −0.362466 + 0.362466i
\(383\) −14.2210 + 7.24595i −0.0371305 + 0.0189189i −0.472457 0.881354i \(-0.656633\pi\)
0.435327 + 0.900273i \(0.356633\pi\)
\(384\) 3.70019 + 5.09288i 0.00963592 + 0.0132627i
\(385\) 239.602 + 159.225i 0.622342 + 0.413572i
\(386\) 23.9199 + 17.3788i 0.0619687 + 0.0450229i
\(387\) 61.2570 386.761i 0.158287 0.999383i
\(388\) 150.725 + 23.8724i 0.388466 + 0.0615269i
\(389\) 143.389 197.358i 0.368610 0.507348i −0.583913 0.811817i \(-0.698479\pi\)
0.952522 + 0.304469i \(0.0984789\pi\)
\(390\) 84.5124 31.4204i 0.216698 0.0805650i
\(391\) 375.012 272.462i 0.959110 0.696834i
\(392\) 70.3557 + 138.081i 0.179479 + 0.352247i
\(393\) −50.6926 50.6926i −0.128989 0.128989i
\(394\) 8.43367 + 2.74026i 0.0214052 + 0.00695499i
\(395\) 527.690 + 241.658i 1.33592 + 0.611794i
\(396\) 30.3331 + 93.3557i 0.0765988 + 0.235747i
\(397\) 191.548 + 97.5985i 0.482488 + 0.245840i 0.678277 0.734806i \(-0.262727\pi\)
−0.195789 + 0.980646i \(0.562727\pi\)
\(398\) −53.9887 340.871i −0.135650 0.856460i
\(399\) 81.0772i 0.203201i
\(400\) 65.3271 + 75.7124i 0.163318 + 0.189281i
\(401\) 517.832 1.29135 0.645676 0.763612i \(-0.276576\pi\)
0.645676 + 0.763612i \(0.276576\pi\)
\(402\) −42.5642 + 6.74150i −0.105881 + 0.0167699i
\(403\) −361.563 + 709.607i −0.897178 + 1.76081i
\(404\) 297.095 96.5320i 0.735384 0.238941i
\(405\) −316.864 + 178.502i −0.782379 + 0.440746i
\(406\) 69.3269 213.366i 0.170756 0.525533i
\(407\) 61.9696 61.9696i 0.152259 0.152259i
\(408\) 25.0461 12.7616i 0.0613876 0.0312785i
\(409\) −111.733 153.787i −0.273186 0.376008i 0.650276 0.759698i \(-0.274653\pi\)
−0.923462 + 0.383690i \(0.874653\pi\)
\(410\) 326.145 13.6372i 0.795476 0.0332615i
\(411\) 13.8254 + 10.0448i 0.0336386 + 0.0244398i
\(412\) 50.6197 319.600i 0.122863 0.775729i
\(413\) −398.986 63.1932i −0.966068 0.153010i
\(414\) 187.477 258.039i 0.452842 0.623284i
\(415\) −73.8205 20.6189i −0.177881 0.0496841i
\(416\) 104.877 76.1977i 0.252109 0.183168i
\(417\) 43.1321 + 84.6516i 0.103434 + 0.203001i
\(418\) 80.7762 + 80.7762i 0.193245 + 0.193245i
\(419\) −101.900 33.1094i −0.243199 0.0790200i 0.184882 0.982761i \(-0.440810\pi\)
−0.428080 + 0.903741i \(0.640810\pi\)
\(420\) 6.52096 56.3102i 0.0155261 0.134072i
\(421\) 113.217 + 348.447i 0.268925 + 0.827666i 0.990763 + 0.135604i \(0.0432975\pi\)
−0.721838 + 0.692062i \(0.756703\pi\)
\(422\) 200.398 + 102.108i 0.474876 + 0.241961i
\(423\) 12.4649 + 78.7002i 0.0294678 + 0.186053i
\(424\) 80.3039i 0.189396i
\(425\) 379.552 235.228i 0.893064 0.553478i
\(426\) 60.8369 0.142810
\(427\) 143.297 22.6960i 0.335589 0.0531521i
\(428\) −161.218 + 316.409i −0.376678 + 0.739272i
\(429\) −68.4889 + 22.2534i −0.159648 + 0.0518727i
\(430\) 62.9460 + 312.337i 0.146386 + 0.726365i
\(431\) 28.4314 87.5029i 0.0659662 0.203023i −0.912640 0.408763i \(-0.865960\pi\)
0.978607 + 0.205740i \(0.0659602\pi\)
\(432\) 27.8409 27.8409i 0.0644465 0.0644465i
\(433\) −38.7505 + 19.7444i −0.0894932 + 0.0455990i −0.498164 0.867083i \(-0.665992\pi\)
0.408671 + 0.912682i \(0.365992\pi\)
\(434\) 294.308 + 405.080i 0.678128 + 0.933363i
\(435\) −33.9528 + 26.9052i −0.0780525 + 0.0618510i
\(436\) 143.695 + 104.401i 0.329576 + 0.239451i
\(437\) 58.0664 366.617i 0.132875 0.838940i
\(438\) −76.9047 12.1805i −0.175581 0.0278094i
\(439\) −452.403 + 622.679i −1.03053 + 1.41840i −0.125982 + 0.992033i \(0.540208\pi\)
−0.904548 + 0.426371i \(0.859792\pi\)
\(440\) −49.6044 62.5980i −0.112737 0.142268i
\(441\) 385.217 279.876i 0.873507 0.634640i
\(442\) −262.799 515.773i −0.594569 1.16691i
\(443\) −479.183 479.183i −1.08168 1.08168i −0.996353 0.0853248i \(-0.972807\pi\)
−0.0853248 0.996353i \(-0.527193\pi\)
\(444\) −16.4235 5.33632i −0.0369898 0.0120187i
\(445\) 358.695 72.2886i 0.806056 0.162446i
\(446\) 166.086 + 511.161i 0.372390 + 1.14610i
\(447\) 11.7547 + 5.98932i 0.0262969 + 0.0133989i
\(448\) −12.7498 80.4988i −0.0284593 0.179685i
\(449\) 889.585i 1.98126i 0.136578 + 0.990629i \(0.456390\pi\)
−0.136578 + 0.990629i \(0.543610\pi\)
\(450\) 198.365 234.639i 0.440810 0.521419i
\(451\) −260.717 −0.578087
\(452\) 47.4004 7.50749i 0.104868 0.0166095i
\(453\) 52.3641 102.770i 0.115594 0.226866i
\(454\) −242.614 + 78.8300i −0.534392 + 0.173634i
\(455\) −1159.59 134.286i −2.54855 0.295133i
\(456\) 6.95579 21.4077i 0.0152539 0.0469468i
\(457\) 46.1201 46.1201i 0.100919 0.100919i −0.654844 0.755764i \(-0.727266\pi\)
0.755764 + 0.654844i \(0.227266\pi\)
\(458\) −32.2425 + 16.4284i −0.0703985 + 0.0358698i
\(459\) −103.341 142.236i −0.225143 0.309883i
\(460\) −69.8153 + 249.955i −0.151772 + 0.543380i
\(461\) −625.212 454.243i −1.35621 0.985343i −0.998676 0.0514415i \(-0.983618\pi\)
−0.357532 0.933901i \(-0.616382\pi\)
\(462\) −7.08259 + 44.7177i −0.0153303 + 0.0967916i
\(463\) −449.918 71.2599i −0.971744 0.153909i −0.349675 0.936871i \(-0.613708\pi\)
−0.622069 + 0.782962i \(0.713708\pi\)
\(464\) −36.6103 + 50.3898i −0.0789016 + 0.108599i
\(465\) −4.03919 96.6006i −0.00868643 0.207743i
\(466\) 314.304 228.355i 0.674473 0.490033i
\(467\) −158.701 311.468i −0.339830 0.666955i 0.656333 0.754472i \(-0.272107\pi\)
−0.996163 + 0.0875169i \(0.972107\pi\)
\(468\) −281.646 281.646i −0.601807 0.601807i
\(469\) 530.633 + 172.413i 1.13141 + 0.367619i
\(470\) −31.8216 56.4872i −0.0677055 0.120186i
\(471\) −6.24313 19.2144i −0.0132551 0.0407949i
\(472\) 99.9273 + 50.9155i 0.211710 + 0.107872i
\(473\) −39.8090 251.344i −0.0841627 0.531382i
\(474\) 91.3413i 0.192703i
\(475\) 81.7198 348.105i 0.172042 0.732852i
\(476\) −363.935 −0.764569
\(477\) −243.698 + 38.5979i −0.510896 + 0.0809180i
\(478\) −69.6021 + 136.602i −0.145611 + 0.285778i
\(479\) 49.6354 16.1275i 0.103623 0.0336692i −0.256747 0.966479i \(-0.582651\pi\)
0.360370 + 0.932810i \(0.382651\pi\)
\(480\) −6.55278 + 14.3088i −0.0136516 + 0.0298100i
\(481\) −109.890 + 338.207i −0.228462 + 0.703134i
\(482\) 369.644 369.644i 0.766896 0.766896i
\(483\) 131.079 66.7883i 0.271386 0.138278i
\(484\) −104.749 144.174i −0.216423 0.297880i
\(485\) 132.948 + 357.594i 0.274119 + 0.737308i
\(486\) −147.662 107.283i −0.303831 0.220746i
\(487\) −93.1133 + 587.894i −0.191198 + 1.20718i 0.686200 + 0.727413i \(0.259277\pi\)
−0.877398 + 0.479763i \(0.840723\pi\)
\(488\) −39.7834 6.30106i −0.0815233 0.0129120i
\(489\) 27.0092 37.1750i 0.0552335 0.0760224i
\(490\) −214.432 + 322.677i −0.437617 + 0.658524i
\(491\) −109.988 + 79.9113i −0.224009 + 0.162752i −0.694129 0.719850i \(-0.744210\pi\)
0.470120 + 0.882602i \(0.344210\pi\)
\(492\) 23.3229 + 45.7737i 0.0474042 + 0.0930361i
\(493\) 196.664 + 196.664i 0.398912 + 0.398912i
\(494\) −440.847 143.240i −0.892404 0.289960i
\(495\) −166.123 + 180.622i −0.335603 + 0.364893i
\(496\) −42.9567 132.207i −0.0866062 0.266547i
\(497\) −701.798 357.584i −1.41207 0.719485i
\(498\) −1.88698 11.9139i −0.00378912 0.0239235i
\(499\) 483.808i 0.969555i −0.874637 0.484778i \(-0.838901\pi\)
0.874637 0.484778i \(-0.161099\pi\)
\(500\) −84.7543 + 235.195i −0.169509 + 0.470390i
\(501\) 29.2052 0.0582938
\(502\) 28.8995 4.57723i 0.0575687 0.00911799i
\(503\) −141.234 + 277.188i −0.280784 + 0.551070i −0.987725 0.156203i \(-0.950075\pi\)
0.706941 + 0.707273i \(0.250075\pi\)
\(504\) −238.161 + 77.3832i −0.472542 + 0.153538i
\(505\) 574.810 + 528.670i 1.13824 + 1.04687i
\(506\) 64.0525 197.133i 0.126586 0.389591i
\(507\) 140.132 140.132i 0.276395 0.276395i
\(508\) −55.6331 + 28.3465i −0.109514 + 0.0558001i
\(509\) −177.828 244.759i −0.349367 0.480862i 0.597781 0.801659i \(-0.296049\pi\)
−0.947148 + 0.320797i \(0.896049\pi\)
\(510\) 58.5295 + 38.8953i 0.114764 + 0.0762652i
\(511\) 815.557 + 592.537i 1.59600 + 1.15956i
\(512\) −3.53971 + 22.3488i −0.00691349 + 0.0436501i
\(513\) −139.052 22.0237i −0.271056 0.0429311i
\(514\) 67.7051 93.1881i 0.131722 0.181300i
\(515\) 758.252 281.906i 1.47233 0.547390i
\(516\) −40.5669 + 29.4736i −0.0786180 + 0.0571193i
\(517\) 23.5087 + 46.1384i 0.0454713 + 0.0892425i
\(518\) 158.091 + 158.091i 0.305196 + 0.305196i
\(519\) −23.6288 7.67746i −0.0455275 0.0147928i
\(520\) 294.659 + 134.941i 0.566653 + 0.259502i
\(521\) −114.065 351.056i −0.218935 0.673813i −0.998851 0.0479282i \(-0.984738\pi\)
0.779916 0.625885i \(-0.215262\pi\)
\(522\) 170.514 + 86.8813i 0.326656 + 0.166439i
\(523\) 47.6107 + 300.602i 0.0910338 + 0.574765i 0.990472 + 0.137716i \(0.0439762\pi\)
−0.899438 + 0.437049i \(0.856024\pi\)
\(524\) 257.685i 0.491765i
\(525\) 130.654 54.8915i 0.248865 0.104555i
\(526\) −124.019 −0.235777
\(527\) −613.087 + 97.1035i −1.16335 + 0.184257i
\(528\) 5.70653 11.1997i 0.0108078 0.0212116i
\(529\) −137.442 + 44.6576i −0.259815 + 0.0844189i
\(530\) 174.914 98.5364i 0.330027 0.185918i
\(531\) 106.483 327.721i 0.200533 0.617177i
\(532\) −206.069 + 206.069i −0.387348 + 0.387348i
\(533\) 942.615 480.286i 1.76851 0.901100i
\(534\) 33.8481 + 46.5879i 0.0633860 + 0.0872433i
\(535\) −887.009 + 37.0888i −1.65796 + 0.0693248i
\(536\) −125.317 91.0484i −0.233801 0.169866i
\(537\) −28.3999 + 179.310i −0.0528862 + 0.333910i
\(538\) 116.599 + 18.4674i 0.216726 + 0.0343260i
\(539\) 181.883 250.340i 0.337445 0.464453i
\(540\) 94.8038 + 26.4798i 0.175563 + 0.0490367i
\(541\) 724.924 526.688i 1.33997 0.973545i 0.340525 0.940235i \(-0.389395\pi\)
0.999445 0.0333098i \(-0.0106048\pi\)
\(542\) −69.6399 136.676i −0.128487 0.252170i
\(543\) −32.5910 32.5910i −0.0600203 0.0600203i
\(544\) 96.0938 + 31.2228i 0.176643 + 0.0573948i
\(545\) −51.0807 + 441.095i −0.0937260 + 0.809349i
\(546\) −56.7709 174.723i −0.103976 0.320005i
\(547\) 524.755 + 267.376i 0.959333 + 0.488804i 0.862256 0.506473i \(-0.169051\pi\)
0.0970765 + 0.995277i \(0.469051\pi\)
\(548\) 9.60912 + 60.6696i 0.0175349 + 0.110711i
\(549\) 123.759i 0.225426i
\(550\) 75.4813 184.857i 0.137239 0.336103i
\(551\) 222.712 0.404196
\(552\) −40.3403 + 6.38928i −0.0730803 + 0.0115748i
\(553\) 536.881 1053.69i 0.970852 1.90540i
\(554\) 75.7590 24.6156i 0.136749 0.0444325i
\(555\) −8.52902 42.3208i −0.0153676 0.0762537i
\(556\) −105.528 + 324.781i −0.189798 + 0.584138i
\(557\) −136.133 + 136.133i −0.244404 + 0.244404i −0.818669 0.574265i \(-0.805288\pi\)
0.574265 + 0.818669i \(0.305288\pi\)
\(558\) −380.561 + 193.905i −0.682009 + 0.347501i
\(559\) 606.947 + 835.390i 1.08577 + 1.49444i
\(560\) 159.694 126.547i 0.285169 0.225976i
\(561\) −45.4085 32.9912i −0.0809421 0.0588079i
\(562\) −70.3120 + 443.932i −0.125110 + 0.789915i
\(563\) 931.083 + 147.469i 1.65379 + 0.261934i 0.912448 0.409194i \(-0.134190\pi\)
0.741341 + 0.671128i \(0.234190\pi\)
\(564\) 5.99744 8.25476i 0.0106338 0.0146361i
\(565\) 74.5149 + 94.0335i 0.131885 + 0.166431i
\(566\) −548.075 + 398.200i −0.968331 + 0.703534i
\(567\) 336.418 + 660.258i 0.593330 + 1.16448i
\(568\) 154.626 + 154.626i 0.272228 + 0.272228i
\(569\) −333.782 108.452i −0.586611 0.190602i 0.000648813 1.00000i \(-0.499793\pi\)
−0.587260 + 0.809398i \(0.699793\pi\)
\(570\) 55.1644 11.1174i 0.0967797 0.0195042i
\(571\) 136.304 + 419.502i 0.238712 + 0.734679i 0.996607 + 0.0823034i \(0.0262277\pi\)
−0.757896 + 0.652376i \(0.773772\pi\)
\(572\) −230.634 117.514i −0.403207 0.205444i
\(573\) −12.0521 76.0941i −0.0210334 0.132799i
\(574\) 665.119i 1.15874i
\(575\) −630.107 + 154.637i −1.09584 + 0.268934i
\(576\) 69.5232 0.120700
\(577\) 86.6592 13.7255i 0.150189 0.0237876i −0.0808870 0.996723i \(-0.525775\pi\)
0.231076 + 0.972936i \(0.425775\pi\)
\(578\) 19.2788 37.8368i 0.0333544 0.0654616i
\(579\) −11.0635 + 3.59476i −0.0191080 + 0.00620857i
\(580\) −154.679 17.9125i −0.266688 0.0308836i
\(581\) −48.2593 + 148.527i −0.0830625 + 0.255640i
\(582\) −42.4556 + 42.4556i −0.0729478 + 0.0729478i
\(583\) −142.869 + 72.7953i −0.245058 + 0.124863i
\(584\) −164.506 226.423i −0.281688 0.387710i
\(585\) 267.877 959.060i 0.457909 1.63942i
\(586\) −623.510 453.006i −1.06401 0.773048i
\(587\) 106.732 673.879i 0.181826 1.14801i −0.712859 0.701308i \(-0.752600\pi\)
0.894685 0.446698i \(-0.147400\pi\)
\(588\) −60.2224 9.53829i −0.102419 0.0162216i
\(589\) −292.163 + 402.128i −0.496033 + 0.682731i
\(590\) 11.7133 + 280.133i 0.0198530 + 0.474801i
\(591\) −2.82263 + 2.05076i −0.00477602 + 0.00346998i
\(592\) −28.1796 55.3056i −0.0476007 0.0934217i
\(593\) 526.775 + 526.775i 0.888322 + 0.888322i 0.994362 0.106039i \(-0.0338170\pi\)
−0.106039 + 0.994362i \(0.533817\pi\)
\(594\) −74.7695 24.2941i −0.125875 0.0408991i
\(595\) −446.564 792.706i −0.750527 1.33228i
\(596\) 14.6535 + 45.0990i 0.0245865 + 0.0756694i
\(597\) 120.986 + 61.6457i 0.202657 + 0.103259i
\(598\) 131.574 + 830.724i 0.220023 + 1.38917i
\(599\) 586.777i 0.979594i −0.871836 0.489797i \(-0.837071\pi\)
0.871836 0.489797i \(-0.162929\pi\)
\(600\) −39.2073 + 3.28452i −0.0653455 + 0.00547420i
\(601\) −664.202 −1.10516 −0.552581 0.833459i \(-0.686357\pi\)
−0.552581 + 0.833459i \(0.686357\pi\)
\(602\) 641.206 101.557i 1.06513 0.168700i
\(603\) −216.070 + 424.062i −0.358326 + 0.703254i
\(604\) 394.296 128.114i 0.652808 0.212110i
\(605\) 185.502 405.067i 0.306616 0.669532i
\(606\) −37.9802 + 116.891i −0.0626736 + 0.192889i
\(607\) −90.2350 + 90.2350i −0.148657 + 0.148657i −0.777518 0.628861i \(-0.783522\pi\)
0.628861 + 0.777518i \(0.283522\pi\)
\(608\) 72.0899 36.7316i 0.118569 0.0604139i
\(609\) 51.8828 + 71.4106i 0.0851935 + 0.117259i
\(610\) −35.0912 94.3860i −0.0575266 0.154731i
\(611\) −169.990 123.505i −0.278215 0.202135i
\(612\) 48.5642 306.622i 0.0793533 0.501017i
\(613\) −773.095 122.446i −1.26117 0.199749i −0.510180 0.860067i \(-0.670421\pi\)
−0.750986 + 0.660318i \(0.770421\pi\)
\(614\) −48.0021 + 66.0693i −0.0781794 + 0.107605i
\(615\) −71.0842 + 106.967i −0.115584 + 0.173931i
\(616\) −131.658 + 95.6551i −0.213730 + 0.155284i
\(617\) 305.103 + 598.799i 0.494495 + 0.970500i 0.994526 + 0.104493i \(0.0333219\pi\)
−0.500031 + 0.866008i \(0.666678\pi\)
\(618\) 90.0239 + 90.0239i 0.145670 + 0.145670i
\(619\) 318.118 + 103.363i 0.513922 + 0.166983i 0.554485 0.832194i \(-0.312915\pi\)
−0.0405633 + 0.999177i \(0.512915\pi\)
\(620\) 235.258 255.790i 0.379448 0.412565i
\(621\) 78.9395 + 242.951i 0.127117 + 0.391225i
\(622\) 652.910 + 332.674i 1.04969 + 0.534846i
\(623\) −116.630 736.376i −0.187208 1.18198i
\(624\) 51.0046i 0.0817381i
\(625\) −616.289 + 103.987i −0.986062 + 0.166379i
\(626\) 285.007 0.455283
\(627\) −44.3919 + 7.03099i −0.0708005 + 0.0112137i
\(628\) 32.9683 64.7039i 0.0524972 0.103032i
\(629\) −263.602 + 85.6495i −0.419081 + 0.136168i
\(630\) −460.787 423.799i −0.731407 0.672697i
\(631\) 27.3879 84.2913i 0.0434040 0.133584i −0.927006 0.375046i \(-0.877627\pi\)
0.970410 + 0.241462i \(0.0776270\pi\)
\(632\) −232.157 + 232.157i −0.367337 + 0.367337i
\(633\) −78.8458 + 40.1739i −0.124559 + 0.0634659i
\(634\) −394.845 543.457i −0.622783 0.857188i
\(635\) −130.007 86.3951i −0.204736 0.136055i
\(636\) 25.5611 + 18.5712i 0.0401904 + 0.0292000i
\(637\) −196.421 + 1240.15i −0.308354 + 1.94687i
\(638\) 122.836 + 19.4553i 0.192533 + 0.0304942i
\(639\) 394.921 543.562i 0.618030 0.850645i
\(640\) −53.0226 + 19.7130i −0.0828479 + 0.0308015i
\(641\) −763.194 + 554.493i −1.19063 + 0.865044i −0.993331 0.115299i \(-0.963217\pi\)
−0.197300 + 0.980343i \(0.563217\pi\)
\(642\) −63.4307 124.490i −0.0988018 0.193909i
\(643\) 81.8654 + 81.8654i 0.127318 + 0.127318i 0.767894 0.640576i \(-0.221305\pi\)
−0.640576 + 0.767894i \(0.721305\pi\)
\(644\) 502.909 + 163.405i 0.780915 + 0.253735i
\(645\) −113.975 52.1956i −0.176706 0.0809235i
\(646\) −111.643 343.601i −0.172821 0.531890i
\(647\) −989.616 504.234i −1.52955 0.779342i −0.531827 0.846853i \(-0.678494\pi\)
−0.997719 + 0.0675110i \(0.978494\pi\)
\(648\) −32.1833 203.197i −0.0496656 0.313576i
\(649\) 223.936i 0.345047i
\(650\) 67.6378 + 807.393i 0.104058 + 1.24214i
\(651\) −197.001 −0.302613
\(652\) 163.133 25.8377i 0.250204 0.0396284i
\(653\) 278.161 545.922i 0.425975 0.836022i −0.573880 0.818940i \(-0.694562\pi\)
0.999854 0.0170824i \(-0.00543777\pi\)
\(654\) −66.4625 + 21.5950i −0.101625 + 0.0330199i
\(655\) 561.278 316.191i 0.856913 0.482734i
\(656\) −57.0620 + 175.619i −0.0869848 + 0.267712i
\(657\) −608.054 + 608.054i −0.925500 + 0.925500i
\(658\) −117.704 + 59.9733i −0.178882 + 0.0911448i
\(659\) 306.794 + 422.266i 0.465545 + 0.640768i 0.975647 0.219346i \(-0.0703924\pi\)
−0.510102 + 0.860114i \(0.670392\pi\)
\(660\) 31.3969 1.31281i 0.0475710 0.00198910i
\(661\) 119.230 + 86.6259i 0.180379 + 0.131053i 0.674311 0.738448i \(-0.264441\pi\)
−0.493932 + 0.869501i \(0.664441\pi\)
\(662\) 92.2109 582.197i 0.139291 0.879452i
\(663\) 224.948 + 35.6283i 0.339289 + 0.0537381i
\(664\) 25.4849 35.0769i 0.0383809 0.0528267i
\(665\) −701.707 195.995i −1.05520 0.294729i
\(666\) −154.291 + 112.099i −0.231668 + 0.168317i
\(667\) −183.462 360.064i −0.275055 0.539826i
\(668\) 74.2292 + 74.2292i 0.111122 + 0.111122i
\(669\) −201.114 65.3460i −0.300619 0.0976771i
\(670\) 44.5477 384.681i 0.0664891 0.574151i
\(671\) 24.8533 + 76.4905i 0.0370392 + 0.113995i
\(672\) 28.5717 + 14.5580i 0.0425174 + 0.0216637i
\(673\) 38.7807 + 244.852i 0.0576236 + 0.363821i 0.999604 + 0.0281522i \(0.00896230\pi\)
−0.941980 + 0.335669i \(0.891038\pi\)
\(674\) 302.401i 0.448666i
\(675\) 58.6513 + 238.989i 0.0868908 + 0.354058i
\(676\) 712.332 1.05375
\(677\) −301.786 + 47.7981i −0.445769 + 0.0706029i −0.375284 0.926910i \(-0.622455\pi\)
−0.0704851 + 0.997513i \(0.522455\pi\)
\(678\) −8.57225 + 16.8240i −0.0126434 + 0.0248141i
\(679\) 739.299 240.213i 1.08881 0.353774i
\(680\) 49.9033 + 247.619i 0.0733871 + 0.364146i
\(681\) 31.0154 95.4556i 0.0455439 0.140170i
\(682\) −196.270 + 196.270i −0.287786 + 0.287786i
\(683\) −241.102 + 122.848i −0.353005 + 0.179865i −0.621496 0.783417i \(-0.713475\pi\)
0.268491 + 0.963282i \(0.413475\pi\)
\(684\) −146.119 201.116i −0.213624 0.294029i
\(685\) −120.357 + 95.3744i −0.175704 + 0.139233i
\(686\) 67.4979 + 49.0401i 0.0983935 + 0.0714870i
\(687\) 2.22724 14.0622i 0.00324197 0.0204690i
\(688\) −178.018 28.1952i −0.258747 0.0409815i
\(689\) 382.436 526.378i 0.555059 0.763973i
\(690\) −63.4162 80.0276i −0.0919075 0.115982i
\(691\) −432.755 + 314.415i −0.626274 + 0.455014i −0.855107 0.518451i \(-0.826509\pi\)
0.228834 + 0.973466i \(0.426509\pi\)
\(692\) −40.5426 79.5693i −0.0585875 0.114984i
\(693\) 353.565 + 353.565i 0.510195 + 0.510195i
\(694\) 170.781 + 55.4902i 0.246082 + 0.0799570i
\(695\) −836.910 + 168.664i −1.20419 + 0.242683i
\(696\) −7.57274 23.3065i −0.0108804 0.0334863i
\(697\) 734.683 + 374.340i 1.05406 + 0.537073i
\(698\) 26.0343 + 164.374i 0.0372984 + 0.235493i
\(699\) 152.855i 0.218676i
\(700\) 471.590 + 192.561i 0.673700 + 0.275087i
\(701\) −617.860 −0.881397 −0.440699 0.897655i \(-0.645269\pi\)
−0.440699 + 0.897655i \(0.645269\pi\)
\(702\) 315.081 49.9039i 0.448833 0.0710881i
\(703\) −100.761 + 197.755i −0.143330 + 0.281302i
\(704\) 42.9696 13.9617i 0.0610363 0.0198319i
\(705\) 25.3393 + 2.93440i 0.0359422 + 0.00416226i
\(706\) 23.9431 73.6892i 0.0339137 0.104376i
\(707\) 1125.18 1125.18i 1.59149 1.59149i
\(708\) −39.3160 + 20.0325i −0.0555311 + 0.0282945i
\(709\) −718.310 988.668i −1.01313 1.39445i −0.916910 0.399095i \(-0.869325\pi\)
−0.0962207 0.995360i \(-0.530675\pi\)
\(710\) −147.066 + 526.531i −0.207136 + 0.741594i
\(711\) 816.111 + 592.939i 1.14784 + 0.833951i
\(712\) −32.3801 + 204.440i −0.0454776 + 0.287134i
\(713\) 890.804 + 141.089i 1.24937 + 0.197881i
\(714\) 84.1643 115.842i 0.117877 0.162244i
\(715\) −27.0345 646.553i −0.0378105 0.904270i
\(716\) −527.923 + 383.559i −0.737323 + 0.535697i
\(717\) −27.3847 53.7455i −0.0381935 0.0749589i
\(718\) −459.128 459.128i −0.639454 0.639454i
\(719\) 552.407 + 179.488i 0.768299 + 0.249635i 0.666837 0.745204i \(-0.267648\pi\)
0.101462 + 0.994839i \(0.467648\pi\)
\(720\) 85.3080 + 151.432i 0.118483 + 0.210323i
\(721\) −509.353 1567.63i −0.706454 2.17424i
\(722\) 197.116 + 100.436i 0.273014 + 0.139108i
\(723\) 32.1749 + 203.144i 0.0445019 + 0.280974i
\(724\) 165.669i 0.228825i
\(725\) −150.782 358.895i −0.207975 0.495028i
\(726\) 70.1157 0.0965781
\(727\) −353.383 + 55.9703i −0.486083 + 0.0769880i −0.394666 0.918825i \(-0.629140\pi\)
−0.0914173 + 0.995813i \(0.529140\pi\)
\(728\) 299.792 588.374i 0.411802 0.808206i
\(729\) −554.293 + 180.101i −0.760347 + 0.247052i
\(730\) 291.328 636.149i 0.399080 0.871438i
\(731\) −248.702 + 765.427i −0.340222 + 1.04710i
\(732\) 11.2060 11.2060i 0.0153088 0.0153088i
\(733\) −1280.53 + 652.460i −1.74697 + 0.890123i −0.783886 + 0.620904i \(0.786766\pi\)
−0.963079 + 0.269219i \(0.913234\pi\)
\(734\) 466.851 + 642.566i 0.636037 + 0.875430i
\(735\) −53.1197 142.878i −0.0722716 0.194391i
\(736\) −118.770 86.2914i −0.161372 0.117244i
\(737\) −48.3845 + 305.488i −0.0656506 + 0.414501i
\(738\) 560.376 + 88.7549i 0.759317 + 0.120264i
\(739\) −125.167 + 172.278i −0.169373 + 0.233123i −0.885263 0.465091i \(-0.846022\pi\)
0.715889 + 0.698214i \(0.246022\pi\)
\(740\) 85.8867 129.242i 0.116063 0.174651i
\(741\) 147.545 107.198i 0.199116 0.144667i
\(742\) −185.709 364.474i −0.250281 0.491205i
\(743\) −775.885 775.885i −1.04426 1.04426i −0.998974 0.0452854i \(-0.985580\pi\)
−0.0452854 0.998974i \(-0.514420\pi\)
\(744\) 52.0164 + 16.9012i 0.0699145 + 0.0227166i
\(745\) −80.2521 + 87.2561i −0.107721 + 0.117122i
\(746\) 82.3237 + 253.366i 0.110354 + 0.339633i
\(747\) −118.697 60.4792i −0.158898 0.0809627i
\(748\) −31.5603 199.264i −0.0421929 0.266396i
\(749\) 1808.91i 2.41510i
\(750\) −55.2633 81.3694i −0.0736844 0.108493i
\(751\) 738.937 0.983938 0.491969 0.870613i \(-0.336277\pi\)
0.491969 + 0.870613i \(0.336277\pi\)
\(752\) 36.2240 5.73732i 0.0481702 0.00762941i
\(753\) −5.22640 + 10.2574i −0.00694077 + 0.0136220i
\(754\) −479.949 + 155.945i −0.636537 + 0.206823i
\(755\) 762.872 + 701.636i 1.01043 + 0.929319i
\(756\) 61.9769 190.745i 0.0819801 0.252309i
\(757\) 821.816 821.816i 1.08562 1.08562i 0.0896488 0.995973i \(-0.471426\pi\)
0.995973 0.0896488i \(-0.0285745\pi\)
\(758\) 30.1989 15.3871i 0.0398402 0.0202996i
\(759\) 47.9356 + 65.9776i 0.0631562 + 0.0869271i
\(760\) 168.465 + 111.952i 0.221664 + 0.147305i
\(761\) 972.054 + 706.239i 1.27734 + 0.928040i 0.999469 0.0325787i \(-0.0103719\pi\)
0.277869 + 0.960619i \(0.410372\pi\)
\(762\) 3.84300 24.2637i 0.00504330 0.0318422i
\(763\) 893.623 + 141.536i 1.17120 + 0.185499i
\(764\) 162.772 224.036i 0.213052 0.293241i
\(765\) 727.462 270.459i 0.950930 0.353541i
\(766\) 18.2609 13.2673i 0.0238392 0.0173202i
\(767\) 412.528 + 809.632i 0.537846 + 1.05558i
\(768\) −6.29514 6.29514i −0.00819680 0.00819680i
\(769\) 596.588 + 193.843i 0.775797 + 0.252072i 0.670045 0.742321i \(-0.266275\pi\)
0.105753 + 0.994392i \(0.466275\pi\)
\(770\) −369.902 169.398i −0.480392 0.219998i
\(771\) 14.0046 + 43.1017i 0.0181642 + 0.0559037i
\(772\) −37.2561 18.9829i −0.0482592 0.0245893i
\(773\) −119.204 752.625i −0.154210 0.973641i −0.936485 0.350708i \(-0.885941\pi\)
0.782275 0.622933i \(-0.214059\pi\)
\(774\) 553.781i 0.715480i
\(775\) 845.823 + 198.563i 1.09138 + 0.256210i
\(776\) −215.814 −0.278111
\(777\) −86.8817 + 13.7607i −0.111817 + 0.0177101i
\(778\) −156.624 + 307.393i −0.201317 + 0.395106i
\(779\) 627.957 204.036i 0.806107 0.261920i
\(780\) −111.096 + 62.5848i −0.142431 + 0.0802370i
\(781\) 134.927 415.263i 0.172762 0.531706i
\(782\) −463.540 + 463.540i −0.592763 + 0.592763i
\(783\) −136.566 + 69.5841i −0.174414 + 0.0888686i
\(784\) −128.821 177.307i −0.164312 0.226157i
\(785\) 181.389 7.58446i 0.231068 0.00966173i
\(786\) 82.0223 + 59.5927i 0.104354 + 0.0758177i
\(787\) 172.436 1088.72i 0.219105 1.38338i −0.595497 0.803357i \(-0.703045\pi\)
0.814603 0.580019i \(-0.196955\pi\)
\(788\) −12.3864 1.96181i −0.0157188 0.00248961i
\(789\) 28.6809 39.4758i 0.0363509 0.0500327i
\(790\) −790.541 220.807i −1.00068 0.279503i
\(791\) 197.774 143.691i 0.250031 0.181658i
\(792\) −63.0226 123.689i −0.0795740 0.156173i
\(793\) −230.765 230.765i −0.291003 0.291003i
\(794\) −289.146 93.9493i −0.364164 0.118324i
\(795\) −9.08644 + 78.4638i −0.0114295 + 0.0986966i
\(796\) 150.823 + 464.185i 0.189476 + 0.583148i
\(797\) −932.407 475.085i −1.16990 0.596091i −0.242492 0.970154i \(-0.577965\pi\)
−0.927404 + 0.374062i \(0.877965\pi\)
\(798\) −17.9368 113.249i −0.0224773 0.141916i
\(799\) 163.769i 0.204967i
\(800\) −107.999 91.3029i −0.134999 0.114129i
\(801\) 635.975 0.793976
\(802\) −723.309 + 114.561i −0.901881 + 0.142844i
\(803\) −253.705 + 497.924i −0.315946 + 0.620079i
\(804\) 57.9623 18.8331i 0.0720924 0.0234242i
\(805\) 261.170 + 1295.92i 0.324434 + 1.60984i
\(806\) 348.044 1071.17i 0.431816 1.32899i
\(807\) −32.8431 + 32.8431i −0.0406978 + 0.0406978i
\(808\) −393.627 + 200.563i −0.487162 + 0.248222i
\(809\) −476.312 655.588i −0.588767 0.810368i 0.405855 0.913937i \(-0.366974\pi\)
−0.994622 + 0.103569i \(0.966974\pi\)
\(810\) 403.105 319.432i 0.497661 0.394361i
\(811\) −288.711 209.761i −0.355994 0.258644i 0.395385 0.918515i \(-0.370611\pi\)
−0.751379 + 0.659871i \(0.770611\pi\)
\(812\) −49.6326 + 313.368i −0.0611239 + 0.385921i
\(813\) 59.6097 + 9.44124i 0.0733206 + 0.0116128i
\(814\) −72.8496 + 100.269i −0.0894958 + 0.123180i
\(815\) 256.450 + 323.625i 0.314663 + 0.397086i
\(816\) −32.1612 + 23.3665i −0.0394132 + 0.0286354i
\(817\) 292.583 + 574.226i 0.358119 + 0.702847i
\(818\) 190.091 + 190.091i 0.232386 + 0.232386i
\(819\) −1929.63 626.975i −2.35608 0.765537i
\(820\) −452.543 + 91.2021i −0.551882 + 0.111222i
\(821\) −456.889 1406.16i −0.556503 1.71274i −0.691941 0.721954i \(-0.743244\pi\)
0.135438 0.990786i \(-0.456756\pi\)
\(822\) −21.5336 10.9719i −0.0261966 0.0133479i
\(823\) −32.3733 204.397i −0.0393357 0.248356i 0.960183 0.279371i \(-0.0901259\pi\)
−0.999519 + 0.0310153i \(0.990126\pi\)
\(824\) 457.617i 0.555360i
\(825\) 41.3848 + 66.7764i 0.0501634 + 0.0809411i
\(826\) 571.285 0.691628
\(827\) 415.905 65.8728i 0.502908 0.0796528i 0.100174 0.994970i \(-0.468060\pi\)
0.402734 + 0.915317i \(0.368060\pi\)
\(828\) −204.781 + 401.906i −0.247320 + 0.485393i
\(829\) −1383.10 + 449.395i −1.66839 + 0.542093i −0.982605 0.185709i \(-0.940542\pi\)
−0.685787 + 0.727802i \(0.740542\pi\)
\(830\) 107.674 + 12.4691i 0.129728 + 0.0150230i
\(831\) −9.68491 + 29.8071i −0.0116545 + 0.0358690i
\(832\) −129.635 + 129.635i −0.155812 + 0.155812i
\(833\) −871.972 + 444.292i −1.04679 + 0.533364i
\(834\) −78.9747 108.699i −0.0946939 0.130335i
\(835\) −70.6003 + 252.765i −0.0845512 + 0.302713i
\(836\) −130.699 94.9581i −0.156338 0.113586i
\(837\) 53.5130 337.868i 0.0639343 0.403665i
\(838\) 149.659 + 23.7037i 0.178591 + 0.0282860i
\(839\) −342.847 + 471.888i −0.408638 + 0.562441i −0.962885 0.269910i \(-0.913006\pi\)
0.554248 + 0.832352i \(0.313006\pi\)
\(840\) 3.34912 + 80.0969i 0.00398704 + 0.0953535i
\(841\) −484.225 + 351.810i −0.575772 + 0.418323i
\(842\) −235.230 461.665i −0.279370 0.548295i
\(843\) −125.045 125.045i −0.148334 0.148334i
\(844\) −302.505 98.2900i −0.358419 0.116457i
\(845\) 874.063 + 1551.57i 1.03439 + 1.83618i
\(846\) −34.8220 107.171i −0.0411607 0.126680i
\(847\) −808.835 412.122i −0.954941 0.486567i
\(848\) 17.7658 + 112.169i 0.0209502 + 0.132274i
\(849\) 266.544i 0.313950i
\(850\) −478.119 + 412.536i −0.562493 + 0.485337i
\(851\) 402.719 0.473230
\(852\) −84.9772 + 13.4591i −0.0997385 + 0.0157970i
\(853\) 335.123 657.717i 0.392876 0.771063i −0.606842 0.794823i \(-0.707564\pi\)
0.999718 + 0.0237600i \(0.00756377\pi\)
\(854\) −195.136 + 63.4035i −0.228496 + 0.0742430i
\(855\) 258.767 565.048i 0.302651 0.660875i
\(856\) 155.190 477.627i 0.181297 0.557975i
\(857\) 189.288 189.288i 0.220873 0.220873i −0.587993 0.808866i \(-0.700082\pi\)
0.808866 + 0.587993i \(0.200082\pi\)
\(858\) 90.7423 46.2355i 0.105760 0.0538875i
\(859\) −689.325 948.775i −0.802474 1.10451i −0.992441 0.122720i \(-0.960838\pi\)
0.189967 0.981790i \(-0.439162\pi\)
\(860\) −157.022 422.347i −0.182584 0.491101i
\(861\) 211.711 + 153.817i 0.245889 + 0.178649i
\(862\) −20.3547 + 128.514i −0.0236133 + 0.149088i
\(863\) 238.733 + 37.8116i 0.276631 + 0.0438141i 0.293209 0.956048i \(-0.405277\pi\)
−0.0165773 + 0.999863i \(0.505277\pi\)
\(864\) −32.7289 + 45.0475i −0.0378807 + 0.0521383i
\(865\) 123.567 185.943i 0.142852 0.214963i
\(866\) 49.7588 36.1519i 0.0574582 0.0417458i
\(867\) 7.58518 + 14.8868i 0.00874877 + 0.0171704i
\(868\) −500.706 500.706i −0.576850 0.576850i
\(869\) 623.481 + 202.581i 0.717469 + 0.233120i
\(870\) 41.4731 45.0927i 0.0476702 0.0518307i
\(871\) −387.828 1193.61i −0.445268 1.37039i
\(872\) −223.811 114.037i −0.256664 0.130777i
\(873\) 103.731 + 654.929i 0.118821 + 0.750205i
\(874\) 524.937i 0.600615i
\(875\) 159.233 + 1263.48i 0.181981 + 1.44397i
\(876\) 110.115 0.125702
\(877\) 338.646 53.6362i 0.386141 0.0611587i 0.0396540 0.999213i \(-0.487374\pi\)
0.346487 + 0.938055i \(0.387374\pi\)
\(878\) 494.161 969.845i 0.562826 1.10461i
\(879\) 288.388 93.7030i 0.328087 0.106602i
\(880\) 83.1363 + 76.4629i 0.0944730 + 0.0868896i
\(881\) 66.8030 205.598i 0.0758263 0.233369i −0.905958 0.423367i \(-0.860848\pi\)
0.981785 + 0.189998i \(0.0608481\pi\)
\(882\) −476.154 + 476.154i −0.539857 + 0.539857i
\(883\) −305.211 + 155.513i −0.345653 + 0.176119i −0.618195 0.786025i \(-0.712136\pi\)
0.272542 + 0.962144i \(0.412136\pi\)
\(884\) 481.184 + 662.293i 0.544326 + 0.749200i
\(885\) −91.8765 61.0557i −0.103815 0.0689895i
\(886\) 775.335 + 563.314i 0.875096 + 0.635794i
\(887\) 18.6058 117.473i 0.0209761 0.132438i −0.974978 0.222302i \(-0.928643\pi\)
0.995954 + 0.0898635i \(0.0286431\pi\)
\(888\) 24.1209 + 3.82038i 0.0271632 + 0.00430223i
\(889\) −186.948 + 257.311i −0.210290 + 0.289439i
\(890\) −485.033 + 180.328i −0.544981 + 0.202615i
\(891\) −332.335 + 241.455i −0.372991 + 0.270994i
\(892\) −345.074 677.247i −0.386855 0.759245i
\(893\) −92.7300 92.7300i −0.103841 0.103841i
\(894\) −17.7440 5.76539i −0.0198479 0.00644898i
\(895\) −1483.24 679.256i −1.65725 0.758945i
\(896\) 35.6178 + 109.620i 0.0397520 + 0.122344i
\(897\) −294.852 150.234i −0.328709 0.167485i
\(898\) −196.804 1242.57i −0.219159 1.38371i
\(899\) 541.145i 0.601941i
\(900\) −225.167 + 371.628i −0.250185 + 0.412920i
\(901\) 507.114 0.562834
\(902\) 364.171 57.6789i 0.403737 0.0639456i
\(903\) −115.961 + 227.585i −0.128417 + 0.252033i
\(904\) −64.5481 + 20.9730i −0.0714028 + 0.0232002i
\(905\) 360.854 203.284i 0.398734 0.224623i
\(906\) −50.4062 + 155.134i −0.0556360 + 0.171230i
\(907\) −102.765 + 102.765i −0.113302 + 0.113302i −0.761485 0.648183i \(-0.775529\pi\)
0.648183 + 0.761485i \(0.275529\pi\)
\(908\) 321.444 163.784i 0.354013 0.180379i
\(909\) 797.843 + 1098.14i 0.877715 + 1.20807i
\(910\) 1649.43 68.9681i 1.81256 0.0757891i
\(911\) −107.266 77.9334i −0.117745 0.0855471i 0.527354 0.849646i \(-0.323184\pi\)
−0.645100 + 0.764099i \(0.723184\pi\)
\(912\) −4.97980 + 31.4412i −0.00546030 + 0.0344750i
\(913\) −85.5075 13.5431i −0.0936555 0.0148336i
\(914\) −54.2175 + 74.6239i −0.0593189 + 0.0816454i
\(915\) 38.1588 + 10.6582i 0.0417036 + 0.0116483i
\(916\) 41.4020 30.0803i 0.0451986 0.0328387i
\(917\) −595.916 1169.55i −0.649854 1.27541i
\(918\) 175.814 + 175.814i 0.191518 + 0.191518i
\(919\) 1104.79 + 358.968i 1.20217 + 0.390607i 0.840557 0.541723i \(-0.182228\pi\)
0.361609 + 0.932330i \(0.382228\pi\)
\(920\) 42.2202 364.583i 0.0458915 0.396285i
\(921\) −9.92910 30.5586i −0.0107808 0.0331798i
\(922\) 973.790 + 496.171i 1.05617 + 0.538146i
\(923\) 277.161 + 1749.93i 0.300283 + 1.89591i
\(924\) 64.0287i 0.0692952i
\(925\) 386.896 + 28.4888i 0.418266 + 0.0307987i
\(926\) 644.211 0.695692
\(927\) 1388.73 219.953i 1.49809 0.237274i
\(928\) 39.9896 78.4839i 0.0430922 0.0845732i
\(929\) 68.6295 22.2991i 0.0738746 0.0240033i −0.271847 0.962341i \(-0.587634\pi\)
0.345721 + 0.938337i \(0.387634\pi\)
\(930\) 27.0131 + 134.038i 0.0290463 + 0.144127i
\(931\) −242.163 + 745.303i −0.260111 + 0.800540i
\(932\) −388.501 + 388.501i −0.416847 + 0.416847i
\(933\) −256.885 + 130.889i −0.275332 + 0.140289i
\(934\) 290.580 + 399.949i 0.311114 + 0.428211i
\(935\) 395.302 313.249i 0.422783 0.335026i
\(936\) 455.712 + 331.094i 0.486872 + 0.353733i
\(937\) 1.09335 6.90314i 0.00116686 0.00736728i −0.987098 0.160117i \(-0.948813\pi\)
0.988265 + 0.152750i \(0.0488128\pi\)
\(938\) −779.333 123.434i −0.830845 0.131593i
\(939\) −65.9113 + 90.7191i −0.0701931 + 0.0966125i
\(940\) 56.9452 + 71.8616i 0.0605800 + 0.0764485i
\(941\) −895.131 + 650.351i −0.951255 + 0.691127i −0.951103 0.308873i \(-0.900048\pi\)
−0.000151406 1.00000i \(0.500048\pi\)
\(942\) 12.9712 + 25.4575i 0.0137699 + 0.0270250i
\(943\) −847.156 847.156i −0.898363 0.898363i
\(944\) −150.843 49.0118i −0.159791 0.0519193i
\(945\) 491.522 99.0575i 0.520129 0.104823i
\(946\) 111.210 + 342.271i 0.117559 + 0.361808i
\(947\) 553.987 + 282.271i 0.584992 + 0.298068i 0.721327 0.692595i \(-0.243532\pi\)
−0.136335 + 0.990663i \(0.543532\pi\)
\(948\) −20.2076 127.586i −0.0213160 0.134584i
\(949\) 2267.60i 2.38946i
\(950\) −37.1347 + 504.312i −0.0390892 + 0.530855i
\(951\) 264.298 0.277915
\(952\) 508.345 80.5139i 0.533976 0.0845734i
\(953\) 757.601 1486.88i 0.794965 1.56021i −0.0330196 0.999455i \(-0.510512\pi\)
0.827984 0.560751i \(-0.189488\pi\)
\(954\) 331.858 107.827i 0.347860 0.113026i
\(955\) 687.713 + 79.6401i 0.720119 + 0.0833928i
\(956\) 66.9997 206.204i 0.0700834 0.215695i
\(957\) −34.5999 + 34.5999i −0.0361546 + 0.0361546i
\(958\) −65.7630 + 33.5079i −0.0686461 + 0.0349769i
\(959\) 183.916 + 253.138i 0.191779 + 0.263961i
\(960\) 5.98739 21.4362i 0.00623686 0.0223294i
\(961\) −199.625 145.036i −0.207726 0.150922i
\(962\) 78.6727 496.720i 0.0817804 0.516341i
\(963\) −1524.04 241.385i −1.58260 0.250659i
\(964\) −434.543 + 598.097i −0.450770 + 0.620432i
\(965\) −4.36709 104.443i −0.00452548 0.108231i
\(966\) −168.316 + 122.289i −0.174241 + 0.126593i
\(967\) 289.998 + 569.153i 0.299894 + 0.588576i 0.990951 0.134225i \(-0.0428545\pi\)
−0.691057 + 0.722801i \(0.742854\pi\)
\(968\) 178.209 + 178.209i 0.184100 + 0.184100i
\(969\) 135.188 + 43.9254i 0.139513 + 0.0453306i
\(970\) −264.813 470.076i −0.273003 0.484615i
\(971\) −108.279 333.249i −0.111513 0.343201i 0.879691 0.475546i \(-0.157749\pi\)
−0.991204 + 0.132345i \(0.957749\pi\)
\(972\) 229.989 + 117.185i 0.236614 + 0.120561i
\(973\) 272.123 + 1718.12i 0.279674 + 1.76579i
\(974\) 841.772i 0.864242i
\(975\) −272.639 165.190i −0.279630 0.169425i
\(976\) 56.9635 0.0583642
\(977\) −960.639 + 152.150i −0.983253 + 0.155732i −0.627305 0.778774i \(-0.715842\pi\)
−0.355948 + 0.934506i \(0.615842\pi\)
\(978\) −29.5022 + 57.9013i −0.0301659 + 0.0592038i
\(979\) 393.071 127.717i 0.401503 0.130456i
\(980\) 228.133 498.155i 0.232789 0.508322i
\(981\) −238.494 + 734.008i −0.243113 + 0.748225i
\(982\) 135.953 135.953i 0.138445 0.138445i
\(983\) 731.267 372.599i 0.743913 0.379043i −0.0405830 0.999176i \(-0.512922\pi\)
0.784496 + 0.620133i \(0.212922\pi\)
\(984\) −42.7041 58.7771i −0.0433984 0.0597328i
\(985\) −10.9255 29.3867i −0.0110919 0.0298343i
\(986\) −318.208 231.192i −0.322727 0.234475i
\(987\) 8.13072 51.3353i 0.00823781 0.0520115i
\(988\) 647.466 + 102.549i 0.655330 + 0.103794i
\(989\) 687.347 946.051i 0.694991 0.956574i
\(990\) 192.082 289.045i 0.194022 0.291964i
\(991\) 280.178 203.561i 0.282722 0.205410i −0.437382 0.899276i \(-0.644094\pi\)
0.720104 + 0.693866i \(0.244094\pi\)
\(992\) 89.2504 + 175.164i 0.0899702 + 0.176576i
\(993\) 163.991 + 163.991i 0.165147 + 0.165147i
\(994\) 1059.38 + 344.214i 1.06578 + 0.346292i
\(995\) −826.002 + 898.092i −0.830153 + 0.902605i
\(996\) 5.27148 + 16.2239i 0.00529265 + 0.0162891i
\(997\) 1161.91 + 592.022i 1.16540 + 0.593803i 0.926151 0.377154i \(-0.123097\pi\)
0.239254 + 0.970957i \(0.423097\pi\)
\(998\) 107.034 + 675.784i 0.107248 + 0.677138i
\(999\) 152.745i 0.152898i
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 50.3.f.a.13.2 16
4.3 odd 2 400.3.bg.a.113.1 16
5.2 odd 4 250.3.f.a.207.1 16
5.3 odd 4 250.3.f.c.207.2 16
5.4 even 2 250.3.f.b.43.1 16
25.2 odd 20 inner 50.3.f.a.27.2 yes 16
25.11 even 5 250.3.f.a.93.1 16
25.14 even 10 250.3.f.c.93.2 16
25.23 odd 20 250.3.f.b.157.1 16
100.27 even 20 400.3.bg.a.177.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
50.3.f.a.13.2 16 1.1 even 1 trivial
50.3.f.a.27.2 yes 16 25.2 odd 20 inner
250.3.f.a.93.1 16 25.11 even 5
250.3.f.a.207.1 16 5.2 odd 4
250.3.f.b.43.1 16 5.4 even 2
250.3.f.b.157.1 16 25.23 odd 20
250.3.f.c.93.2 16 25.14 even 10
250.3.f.c.207.2 16 5.3 odd 4
400.3.bg.a.113.1 16 4.3 odd 2
400.3.bg.a.177.1 16 100.27 even 20