Properties

Label 210.3.l.a.127.3
Level $210$
Weight $3$
Character 210.127
Analytic conductor $5.722$
Analytic rank $0$
Dimension $8$
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] = [210,3,Mod(43,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.43");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.l (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.12745506816.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 23x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.3
Root \(0.323042 + 0.323042i\) of defining polynomial
Character \(\chi\) \(=\) 210.127
Dual form 210.3.l.a.43.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(0.578661 - 4.96640i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(0.578661 - 4.96640i) q^{5} +2.44949 q^{6} +(-1.87083 - 1.87083i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(5.54506 - 4.38774i) q^{10} +19.5717 q^{11} +(2.44949 + 2.44949i) q^{12} +(8.03207 - 8.03207i) q^{13} -3.74166i q^{14} +(-5.37386 - 6.79129i) q^{15} -4.00000 q^{16} +(-2.19659 - 2.19659i) q^{17} +(3.00000 - 3.00000i) q^{18} -8.25097i q^{19} +(9.93280 + 1.15732i) q^{20} -4.58258 q^{21} +(19.5717 + 19.5717i) q^{22} +(-17.9068 + 17.9068i) q^{23} +4.89898i q^{24} +(-24.3303 - 5.74773i) q^{25} +16.0641 q^{26} +(-3.67423 - 3.67423i) q^{27} +(3.74166 - 3.74166i) q^{28} +19.7495i q^{29} +(1.41742 - 12.1652i) q^{30} +30.0043 q^{31} +(-4.00000 - 4.00000i) q^{32} +(23.9703 - 23.9703i) q^{33} -4.39319i q^{34} +(-10.3739 + 8.20871i) q^{35} +6.00000 q^{36} +(37.2346 + 37.2346i) q^{37} +(8.25097 - 8.25097i) q^{38} -19.6745i q^{39} +(8.77548 + 11.0901i) q^{40} -80.8620 q^{41} +(-4.58258 - 4.58258i) q^{42} +(-13.6780 + 13.6780i) q^{43} +39.1434i q^{44} +(-14.8992 - 1.73598i) q^{45} -35.8136 q^{46} +(-8.17549 - 8.17549i) q^{47} +(-4.89898 + 4.89898i) q^{48} +7.00000i q^{49} +(-18.5826 - 30.0780i) q^{50} -5.38053 q^{51} +(16.0641 + 16.0641i) q^{52} +(-38.8560 + 38.8560i) q^{53} -7.34847i q^{54} +(11.3254 - 97.2008i) q^{55} +7.48331 q^{56} +(-10.1053 - 10.1053i) q^{57} +(-19.7495 + 19.7495i) q^{58} +74.3773i q^{59} +(13.5826 - 10.7477i) q^{60} +97.8414 q^{61} +(30.0043 + 30.0043i) q^{62} +(-5.61249 + 5.61249i) q^{63} -8.00000i q^{64} +(-35.2426 - 44.5383i) q^{65} +47.9406 q^{66} +(-67.1712 - 67.1712i) q^{67} +(4.39319 - 4.39319i) q^{68} +43.8625i q^{69} +(-18.5826 - 2.16515i) q^{70} -13.3793 q^{71} +(6.00000 + 6.00000i) q^{72} +(-48.2738 + 48.2738i) q^{73} +74.4691i q^{74} +(-36.8379 + 22.7589i) q^{75} +16.5019 q^{76} +(-36.6153 - 36.6153i) q^{77} +(19.6745 - 19.6745i) q^{78} -40.2089i q^{79} +(-2.31464 + 19.8656i) q^{80} -9.00000 q^{81} +(-80.8620 - 80.8620i) q^{82} +(34.4137 - 34.4137i) q^{83} -9.16515i q^{84} +(-12.1803 + 9.63809i) q^{85} -27.3560 q^{86} +(24.1881 + 24.1881i) q^{87} +(-39.1434 + 39.1434i) q^{88} +157.941i q^{89} +(-13.1632 - 16.6352i) q^{90} -30.0532 q^{91} +(-35.8136 - 35.8136i) q^{92} +(36.7476 - 36.7476i) q^{93} -16.3510i q^{94} +(-40.9776 - 4.77451i) q^{95} -9.79796 q^{96} +(-73.2856 - 73.2856i) q^{97} +(-7.00000 + 7.00000i) q^{98} -58.7150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{2} - 16 q^{8} - 8 q^{11} + 8 q^{13} + 12 q^{15} - 32 q^{16} - 32 q^{17} + 24 q^{18} - 8 q^{22} - 40 q^{23} - 48 q^{25} + 16 q^{26} + 48 q^{30} + 144 q^{31} - 32 q^{32} + 120 q^{33} - 28 q^{35} + 48 q^{36} + 160 q^{37} - 320 q^{41} - 32 q^{43} - 80 q^{46} - 144 q^{47} - 112 q^{50} + 72 q^{51} + 16 q^{52} - 200 q^{53} + 184 q^{55} - 24 q^{57} - 64 q^{58} + 72 q^{60} + 288 q^{61} + 144 q^{62} + 24 q^{65} + 240 q^{66} + 80 q^{67} + 64 q^{68} - 112 q^{70} - 280 q^{71} + 48 q^{72} + 312 q^{73} - 56 q^{77} + 48 q^{78} - 72 q^{81} - 320 q^{82} - 320 q^{83} + 80 q^{85} - 64 q^{86} - 48 q^{87} + 16 q^{88} - 80 q^{92} + 48 q^{93} - 472 q^{95} - 24 q^{97} - 56 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) 0.578661 4.96640i 0.115732 0.993280i
\(6\) 2.44949 0.408248
\(7\) −1.87083 1.87083i −0.267261 0.267261i
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) 5.54506 4.38774i 0.554506 0.438774i
\(11\) 19.5717 1.77924 0.889622 0.456698i \(-0.150968\pi\)
0.889622 + 0.456698i \(0.150968\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) 8.03207 8.03207i 0.617851 0.617851i −0.327129 0.944980i \(-0.606081\pi\)
0.944980 + 0.327129i \(0.106081\pi\)
\(14\) 3.74166i 0.267261i
\(15\) −5.37386 6.79129i −0.358258 0.452753i
\(16\) −4.00000 −0.250000
\(17\) −2.19659 2.19659i −0.129211 0.129211i 0.639543 0.768755i \(-0.279123\pi\)
−0.768755 + 0.639543i \(0.779123\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) 8.25097i 0.434261i −0.976143 0.217131i \(-0.930330\pi\)
0.976143 0.217131i \(-0.0696698\pi\)
\(20\) 9.93280 + 1.15732i 0.496640 + 0.0578661i
\(21\) −4.58258 −0.218218
\(22\) 19.5717 + 19.5717i 0.889622 + 0.889622i
\(23\) −17.9068 + 17.9068i −0.778557 + 0.778557i −0.979585 0.201028i \(-0.935572\pi\)
0.201028 + 0.979585i \(0.435572\pi\)
\(24\) 4.89898i 0.204124i
\(25\) −24.3303 5.74773i −0.973212 0.229909i
\(26\) 16.0641 0.617851
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 3.74166 3.74166i 0.133631 0.133631i
\(29\) 19.7495i 0.681017i 0.940241 + 0.340508i \(0.110599\pi\)
−0.940241 + 0.340508i \(0.889401\pi\)
\(30\) 1.41742 12.1652i 0.0472475 0.405505i
\(31\) 30.0043 0.967881 0.483940 0.875101i \(-0.339205\pi\)
0.483940 + 0.875101i \(0.339205\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 23.9703 23.9703i 0.726373 0.726373i
\(34\) 4.39319i 0.129211i
\(35\) −10.3739 + 8.20871i −0.296396 + 0.234535i
\(36\) 6.00000 0.166667
\(37\) 37.2346 + 37.2346i 1.00634 + 1.00634i 0.999980 + 0.00635971i \(0.00202437\pi\)
0.00635971 + 0.999980i \(0.497976\pi\)
\(38\) 8.25097 8.25097i 0.217131 0.217131i
\(39\) 19.6745i 0.504473i
\(40\) 8.77548 + 11.0901i 0.219387 + 0.277253i
\(41\) −80.8620 −1.97224 −0.986122 0.166023i \(-0.946907\pi\)
−0.986122 + 0.166023i \(0.946907\pi\)
\(42\) −4.58258 4.58258i −0.109109 0.109109i
\(43\) −13.6780 + 13.6780i −0.318093 + 0.318093i −0.848034 0.529942i \(-0.822214\pi\)
0.529942 + 0.848034i \(0.322214\pi\)
\(44\) 39.1434i 0.889622i
\(45\) −14.8992 1.73598i −0.331093 0.0385774i
\(46\) −35.8136 −0.778557
\(47\) −8.17549 8.17549i −0.173947 0.173947i 0.614764 0.788711i \(-0.289251\pi\)
−0.788711 + 0.614764i \(0.789251\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 7.00000i 0.142857i
\(50\) −18.5826 30.0780i −0.371652 0.601561i
\(51\) −5.38053 −0.105501
\(52\) 16.0641 + 16.0641i 0.308926 + 0.308926i
\(53\) −38.8560 + 38.8560i −0.733132 + 0.733132i −0.971239 0.238107i \(-0.923473\pi\)
0.238107 + 0.971239i \(0.423473\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 11.3254 97.2008i 0.205916 1.76729i
\(56\) 7.48331 0.133631
\(57\) −10.1053 10.1053i −0.177287 0.177287i
\(58\) −19.7495 + 19.7495i −0.340508 + 0.340508i
\(59\) 74.3773i 1.26063i 0.776339 + 0.630316i \(0.217075\pi\)
−0.776339 + 0.630316i \(0.782925\pi\)
\(60\) 13.5826 10.7477i 0.226376 0.179129i
\(61\) 97.8414 1.60396 0.801979 0.597352i \(-0.203781\pi\)
0.801979 + 0.597352i \(0.203781\pi\)
\(62\) 30.0043 + 30.0043i 0.483940 + 0.483940i
\(63\) −5.61249 + 5.61249i −0.0890871 + 0.0890871i
\(64\) 8.00000i 0.125000i
\(65\) −35.2426 44.5383i −0.542194 0.685205i
\(66\) 47.9406 0.726373
\(67\) −67.1712 67.1712i −1.00255 1.00255i −0.999997 0.00255792i \(-0.999186\pi\)
−0.00255792 0.999997i \(-0.500814\pi\)
\(68\) 4.39319 4.39319i 0.0646057 0.0646057i
\(69\) 43.8625i 0.635689i
\(70\) −18.5826 2.16515i −0.265465 0.0309307i
\(71\) −13.3793 −0.188441 −0.0942203 0.995551i \(-0.530036\pi\)
−0.0942203 + 0.995551i \(0.530036\pi\)
\(72\) 6.00000 + 6.00000i 0.0833333 + 0.0833333i
\(73\) −48.2738 + 48.2738i −0.661285 + 0.661285i −0.955683 0.294398i \(-0.904881\pi\)
0.294398 + 0.955683i \(0.404881\pi\)
\(74\) 74.4691i 1.00634i
\(75\) −36.8379 + 22.7589i −0.491172 + 0.303452i
\(76\) 16.5019 0.217131
\(77\) −36.6153 36.6153i −0.475523 0.475523i
\(78\) 19.6745 19.6745i 0.252237 0.252237i
\(79\) 40.2089i 0.508973i −0.967076 0.254487i \(-0.918094\pi\)
0.967076 0.254487i \(-0.0819065\pi\)
\(80\) −2.31464 + 19.8656i −0.0289331 + 0.248320i
\(81\) −9.00000 −0.111111
\(82\) −80.8620 80.8620i −0.986122 0.986122i
\(83\) 34.4137 34.4137i 0.414623 0.414623i −0.468722 0.883346i \(-0.655285\pi\)
0.883346 + 0.468722i \(0.155285\pi\)
\(84\) 9.16515i 0.109109i
\(85\) −12.1803 + 9.63809i −0.143297 + 0.113389i
\(86\) −27.3560 −0.318093
\(87\) 24.1881 + 24.1881i 0.278024 + 0.278024i
\(88\) −39.1434 + 39.1434i −0.444811 + 0.444811i
\(89\) 157.941i 1.77462i 0.461176 + 0.887309i \(0.347428\pi\)
−0.461176 + 0.887309i \(0.652572\pi\)
\(90\) −13.1632 16.6352i −0.146258 0.184835i
\(91\) −30.0532 −0.330255
\(92\) −35.8136 35.8136i −0.389278 0.389278i
\(93\) 36.7476 36.7476i 0.395136 0.395136i
\(94\) 16.3510i 0.173947i
\(95\) −40.9776 4.77451i −0.431343 0.0502580i
\(96\) −9.79796 −0.102062
\(97\) −73.2856 73.2856i −0.755522 0.755522i 0.219982 0.975504i \(-0.429400\pi\)
−0.975504 + 0.219982i \(0.929400\pi\)
\(98\) −7.00000 + 7.00000i −0.0714286 + 0.0714286i
\(99\) 58.7150i 0.593081i
\(100\) 11.4955 48.6606i 0.114955 0.486606i
\(101\) 121.236 1.20035 0.600176 0.799868i \(-0.295097\pi\)
0.600176 + 0.799868i \(0.295097\pi\)
\(102\) −5.38053 5.38053i −0.0527503 0.0527503i
\(103\) 23.5614 23.5614i 0.228751 0.228751i −0.583419 0.812171i \(-0.698286\pi\)
0.812171 + 0.583419i \(0.198286\pi\)
\(104\) 32.1283i 0.308926i
\(105\) −2.65176 + 22.7589i −0.0252548 + 0.216752i
\(106\) −77.7120 −0.733132
\(107\) −14.4314 14.4314i −0.134873 0.134873i 0.636447 0.771320i \(-0.280403\pi\)
−0.771320 + 0.636447i \(0.780403\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 34.6374i 0.317775i −0.987297 0.158887i \(-0.949209\pi\)
0.987297 0.158887i \(-0.0507907\pi\)
\(110\) 108.526 85.8755i 0.986602 0.780686i
\(111\) 91.2057 0.821673
\(112\) 7.48331 + 7.48331i 0.0668153 + 0.0668153i
\(113\) −19.9430 + 19.9430i −0.176486 + 0.176486i −0.789822 0.613336i \(-0.789827\pi\)
0.613336 + 0.789822i \(0.289827\pi\)
\(114\) 20.2107i 0.177287i
\(115\) 78.5704 + 99.2944i 0.683221 + 0.863429i
\(116\) −39.4990 −0.340508
\(117\) −24.0962 24.0962i −0.205950 0.205950i
\(118\) −74.3773 + 74.3773i −0.630316 + 0.630316i
\(119\) 8.21890i 0.0690664i
\(120\) 24.3303 + 2.83485i 0.202753 + 0.0236237i
\(121\) 262.051 2.16571
\(122\) 97.8414 + 97.8414i 0.801979 + 0.801979i
\(123\) −99.0353 + 99.0353i −0.805165 + 0.805165i
\(124\) 60.0086i 0.483940i
\(125\) −42.6245 + 117.508i −0.340996 + 0.940065i
\(126\) −11.2250 −0.0890871
\(127\) 13.8950 + 13.8950i 0.109410 + 0.109410i 0.759692 0.650283i \(-0.225350\pi\)
−0.650283 + 0.759692i \(0.725350\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 33.5041i 0.259722i
\(130\) 9.29569 79.7809i 0.0715053 0.613700i
\(131\) 161.799 1.23511 0.617554 0.786528i \(-0.288124\pi\)
0.617554 + 0.786528i \(0.288124\pi\)
\(132\) 47.9406 + 47.9406i 0.363187 + 0.363187i
\(133\) −15.4361 + 15.4361i −0.116061 + 0.116061i
\(134\) 134.342i 1.00255i
\(135\) −20.3739 + 16.1216i −0.150918 + 0.119419i
\(136\) 8.78638 0.0646057
\(137\) −35.8023 35.8023i −0.261331 0.261331i 0.564264 0.825595i \(-0.309160\pi\)
−0.825595 + 0.564264i \(0.809160\pi\)
\(138\) −43.8625 + 43.8625i −0.317845 + 0.317845i
\(139\) 89.7460i 0.645654i −0.946458 0.322827i \(-0.895367\pi\)
0.946458 0.322827i \(-0.104633\pi\)
\(140\) −16.4174 20.7477i −0.117267 0.148198i
\(141\) −20.0258 −0.142027
\(142\) −13.3793 13.3793i −0.0942203 0.0942203i
\(143\) 157.201 157.201i 1.09931 1.09931i
\(144\) 12.0000i 0.0833333i
\(145\) 98.0839 + 11.4283i 0.676441 + 0.0788156i
\(146\) −96.5477 −0.661285
\(147\) 8.57321 + 8.57321i 0.0583212 + 0.0583212i
\(148\) −74.4691 + 74.4691i −0.503170 + 0.503170i
\(149\) 293.641i 1.97075i 0.170408 + 0.985374i \(0.445491\pi\)
−0.170408 + 0.985374i \(0.554509\pi\)
\(150\) −59.5968 14.0790i −0.397312 0.0938600i
\(151\) 231.725 1.53461 0.767303 0.641285i \(-0.221598\pi\)
0.767303 + 0.641285i \(0.221598\pi\)
\(152\) 16.5019 + 16.5019i 0.108565 + 0.108565i
\(153\) −6.58978 + 6.58978i −0.0430705 + 0.0430705i
\(154\) 73.2305i 0.475523i
\(155\) 17.3623 149.013i 0.112015 0.961377i
\(156\) 39.3489 0.252237
\(157\) 62.8204 + 62.8204i 0.400130 + 0.400130i 0.878279 0.478149i \(-0.158692\pi\)
−0.478149 + 0.878279i \(0.658692\pi\)
\(158\) 40.2089 40.2089i 0.254487 0.254487i
\(159\) 95.1774i 0.598600i
\(160\) −22.1803 + 17.5510i −0.138627 + 0.109694i
\(161\) 67.0011 0.416156
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 97.0117 97.0117i 0.595164 0.595164i −0.343858 0.939022i \(-0.611734\pi\)
0.939022 + 0.343858i \(0.111734\pi\)
\(164\) 161.724i 0.986122i
\(165\) −105.176 132.917i −0.637428 0.805557i
\(166\) 68.8275 0.414623
\(167\) −135.497 135.497i −0.811362 0.811362i 0.173476 0.984838i \(-0.444500\pi\)
−0.984838 + 0.173476i \(0.944500\pi\)
\(168\) 9.16515 9.16515i 0.0545545 0.0545545i
\(169\) 39.9718i 0.236520i
\(170\) −21.8183 2.54217i −0.128343 0.0149539i
\(171\) −24.7529 −0.144754
\(172\) −27.3560 27.3560i −0.159046 0.159046i
\(173\) −66.1772 + 66.1772i −0.382527 + 0.382527i −0.872012 0.489485i \(-0.837185\pi\)
0.489485 + 0.872012i \(0.337185\pi\)
\(174\) 48.3762i 0.278024i
\(175\) 34.7648 + 56.2708i 0.198656 + 0.321548i
\(176\) −78.2867 −0.444811
\(177\) 91.0932 + 91.0932i 0.514651 + 0.514651i
\(178\) −157.941 + 157.941i −0.887309 + 0.887309i
\(179\) 274.045i 1.53098i −0.643450 0.765488i \(-0.722497\pi\)
0.643450 0.765488i \(-0.277503\pi\)
\(180\) 3.47197 29.7984i 0.0192887 0.165547i
\(181\) −36.0493 −0.199167 −0.0995836 0.995029i \(-0.531751\pi\)
−0.0995836 + 0.995029i \(0.531751\pi\)
\(182\) −30.0532 30.0532i −0.165128 0.165128i
\(183\) 119.831 119.831i 0.654813 0.654813i
\(184\) 71.6272i 0.389278i
\(185\) 206.468 163.376i 1.11604 0.883111i
\(186\) 73.4952 0.395136
\(187\) −42.9910 42.9910i −0.229899 0.229899i
\(188\) 16.3510 16.3510i 0.0869733 0.0869733i
\(189\) 13.7477i 0.0727393i
\(190\) −36.2031 45.7521i −0.190543 0.240801i
\(191\) 133.194 0.697352 0.348676 0.937243i \(-0.386631\pi\)
0.348676 + 0.937243i \(0.386631\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) −236.565 + 236.565i −1.22573 + 1.22573i −0.260160 + 0.965566i \(0.583775\pi\)
−0.965566 + 0.260160i \(0.916225\pi\)
\(194\) 146.571i 0.755522i
\(195\) −97.7113 11.3848i −0.501084 0.0583838i
\(196\) −14.0000 −0.0714286
\(197\) −203.011 203.011i −1.03051 1.03051i −0.999520 0.0309909i \(-0.990134\pi\)
−0.0309909 0.999520i \(-0.509866\pi\)
\(198\) 58.7150 58.7150i 0.296541 0.296541i
\(199\) 102.932i 0.517244i −0.965979 0.258622i \(-0.916732\pi\)
0.965979 0.258622i \(-0.0832684\pi\)
\(200\) 60.1561 37.1652i 0.300780 0.185826i
\(201\) −164.535 −0.818582
\(202\) 121.236 + 121.236i 0.600176 + 0.600176i
\(203\) 36.9479 36.9479i 0.182009 0.182009i
\(204\) 10.7611i 0.0527503i
\(205\) −46.7917 + 401.593i −0.228252 + 1.95899i
\(206\) 47.1228 0.228751
\(207\) 53.7204 + 53.7204i 0.259519 + 0.259519i
\(208\) −32.1283 + 32.1283i −0.154463 + 0.154463i
\(209\) 161.485i 0.772657i
\(210\) −25.4107 + 20.1072i −0.121003 + 0.0957484i
\(211\) −216.191 −1.02460 −0.512301 0.858806i \(-0.671207\pi\)
−0.512301 + 0.858806i \(0.671207\pi\)
\(212\) −77.7120 77.7120i −0.366566 0.366566i
\(213\) −16.3862 + 16.3862i −0.0769306 + 0.0769306i
\(214\) 28.8629i 0.134873i
\(215\) 60.0154 + 75.8453i 0.279142 + 0.352769i
\(216\) 14.6969 0.0680414
\(217\) −56.1329 56.1329i −0.258677 0.258677i
\(218\) 34.6374 34.6374i 0.158887 0.158887i
\(219\) 118.246i 0.539937i
\(220\) 194.402 + 22.6507i 0.883644 + 0.102958i
\(221\) −35.2864 −0.159667
\(222\) 91.2057 + 91.2057i 0.410836 + 0.410836i
\(223\) 143.253 143.253i 0.642390 0.642390i −0.308752 0.951142i \(-0.599911\pi\)
0.951142 + 0.308752i \(0.0999114\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) −17.2432 + 72.9909i −0.0766364 + 0.324404i
\(226\) −39.8859 −0.176486
\(227\) 226.766 + 226.766i 0.998969 + 0.998969i 0.999999 0.00103000i \(-0.000327858\pi\)
−0.00103000 + 0.999999i \(0.500328\pi\)
\(228\) 20.2107 20.2107i 0.0886433 0.0886433i
\(229\) 48.9068i 0.213567i 0.994282 + 0.106783i \(0.0340552\pi\)
−0.994282 + 0.106783i \(0.965945\pi\)
\(230\) −20.7239 + 177.865i −0.0901041 + 0.773325i
\(231\) −89.6887 −0.388263
\(232\) −39.4990 39.4990i −0.170254 0.170254i
\(233\) −122.967 + 122.967i −0.527755 + 0.527755i −0.919902 0.392147i \(-0.871732\pi\)
0.392147 + 0.919902i \(0.371732\pi\)
\(234\) 48.1924i 0.205950i
\(235\) −45.3336 + 35.8719i −0.192909 + 0.152647i
\(236\) −148.755 −0.630316
\(237\) −49.2456 49.2456i −0.207787 0.207787i
\(238\) −8.21890 + 8.21890i −0.0345332 + 0.0345332i
\(239\) 359.392i 1.50373i 0.659317 + 0.751865i \(0.270846\pi\)
−0.659317 + 0.751865i \(0.729154\pi\)
\(240\) 21.4955 + 27.1652i 0.0895644 + 0.113188i
\(241\) −96.4510 −0.400212 −0.200106 0.979774i \(-0.564129\pi\)
−0.200106 + 0.979774i \(0.564129\pi\)
\(242\) 262.051 + 262.051i 1.08285 + 1.08285i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 195.683i 0.801979i
\(245\) 34.7648 + 4.05063i 0.141897 + 0.0165332i
\(246\) −198.071 −0.805165
\(247\) −66.2723 66.2723i −0.268309 0.268309i
\(248\) −60.0086 + 60.0086i −0.241970 + 0.241970i
\(249\) 84.2961i 0.338539i
\(250\) −160.133 + 74.8836i −0.640530 + 0.299534i
\(251\) −290.502 −1.15738 −0.578690 0.815548i \(-0.696436\pi\)
−0.578690 + 0.815548i \(0.696436\pi\)
\(252\) −11.2250 11.2250i −0.0445435 0.0445435i
\(253\) −350.466 + 350.466i −1.38524 + 1.38524i
\(254\) 27.7901i 0.109410i
\(255\) −3.11351 + 26.7219i −0.0122098 + 0.104792i
\(256\) 16.0000 0.0625000
\(257\) −225.583 225.583i −0.877755 0.877755i 0.115547 0.993302i \(-0.463138\pi\)
−0.993302 + 0.115547i \(0.963138\pi\)
\(258\) −33.5041 + 33.5041i −0.129861 + 0.129861i
\(259\) 139.319i 0.537911i
\(260\) 89.0766 70.4852i 0.342602 0.271097i
\(261\) 59.2485 0.227006
\(262\) 161.799 + 161.799i 0.617554 + 0.617554i
\(263\) 245.931 245.931i 0.935097 0.935097i −0.0629214 0.998018i \(-0.520042\pi\)
0.998018 + 0.0629214i \(0.0200417\pi\)
\(264\) 95.8813i 0.363187i
\(265\) 170.490 + 215.459i 0.643359 + 0.813053i
\(266\) −30.8723 −0.116061
\(267\) 193.437 + 193.437i 0.724485 + 0.724485i
\(268\) 134.342 134.342i 0.501277 0.501277i
\(269\) 306.198i 1.13828i −0.822240 0.569142i \(-0.807276\pi\)
0.822240 0.569142i \(-0.192724\pi\)
\(270\) −36.4955 4.25227i −0.135168 0.0157492i
\(271\) −370.284 −1.36636 −0.683180 0.730250i \(-0.739404\pi\)
−0.683180 + 0.730250i \(0.739404\pi\)
\(272\) 8.78638 + 8.78638i 0.0323029 + 0.0323029i
\(273\) −36.8075 + 36.8075i −0.134826 + 0.134826i
\(274\) 71.6046i 0.261331i
\(275\) −476.185 112.493i −1.73158 0.409064i
\(276\) −87.7251 −0.317845
\(277\) −161.817 161.817i −0.584176 0.584176i 0.351872 0.936048i \(-0.385545\pi\)
−0.936048 + 0.351872i \(0.885545\pi\)
\(278\) 89.7460 89.7460i 0.322827 0.322827i
\(279\) 90.0129i 0.322627i
\(280\) 4.33030 37.1652i 0.0154654 0.132733i
\(281\) −235.757 −0.838994 −0.419497 0.907757i \(-0.637793\pi\)
−0.419497 + 0.907757i \(0.637793\pi\)
\(282\) −20.0258 20.0258i −0.0710134 0.0710134i
\(283\) 2.26750 2.26750i 0.00801238 0.00801238i −0.703089 0.711102i \(-0.748197\pi\)
0.711102 + 0.703089i \(0.248197\pi\)
\(284\) 26.7586i 0.0942203i
\(285\) −56.0347 + 44.3396i −0.196613 + 0.155577i
\(286\) 314.402 1.09931
\(287\) 151.279 + 151.279i 0.527104 + 0.527104i
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) 279.350i 0.966609i
\(290\) 86.6556 + 109.512i 0.298813 + 0.377628i
\(291\) −179.512 −0.616881
\(292\) −96.5477 96.5477i −0.330643 0.330643i
\(293\) 199.403 199.403i 0.680556 0.680556i −0.279570 0.960125i \(-0.590192\pi\)
0.960125 + 0.279570i \(0.0901918\pi\)
\(294\) 17.1464i 0.0583212i
\(295\) 369.387 + 43.0392i 1.25216 + 0.145896i
\(296\) −148.938 −0.503170
\(297\) −71.9110 71.9110i −0.242124 0.242124i
\(298\) −293.641 + 293.641i −0.985374 + 0.985374i
\(299\) 287.657i 0.962065i
\(300\) −45.5178 73.6758i −0.151726 0.245586i
\(301\) 51.1783 0.170028
\(302\) 231.725 + 231.725i 0.767303 + 0.767303i
\(303\) 148.483 148.483i 0.490042 0.490042i
\(304\) 33.0039i 0.108565i
\(305\) 56.6170 485.920i 0.185630 1.59318i
\(306\) −13.1796 −0.0430705
\(307\) −381.514 381.514i −1.24272 1.24272i −0.958870 0.283847i \(-0.908389\pi\)
−0.283847 0.958870i \(-0.591611\pi\)
\(308\) 73.2305 73.2305i 0.237761 0.237761i
\(309\) 57.7134i 0.186775i
\(310\) 166.376 131.651i 0.536696 0.424681i
\(311\) −388.702 −1.24985 −0.624923 0.780686i \(-0.714870\pi\)
−0.624923 + 0.780686i \(0.714870\pi\)
\(312\) 39.3489 + 39.3489i 0.126118 + 0.126118i
\(313\) −50.5806 + 50.5806i −0.161599 + 0.161599i −0.783275 0.621675i \(-0.786452\pi\)
0.621675 + 0.783275i \(0.286452\pi\)
\(314\) 125.641i 0.400130i
\(315\) 24.6261 + 31.1216i 0.0781782 + 0.0987987i
\(316\) 80.4178 0.254487
\(317\) 54.9675 + 54.9675i 0.173399 + 0.173399i 0.788471 0.615072i \(-0.210873\pi\)
−0.615072 + 0.788471i \(0.710873\pi\)
\(318\) −95.1774 + 95.1774i −0.299300 + 0.299300i
\(319\) 386.531i 1.21169i
\(320\) −39.7312 4.62929i −0.124160 0.0144665i
\(321\) −35.3497 −0.110124
\(322\) 67.0011 + 67.0011i 0.208078 + 0.208078i
\(323\) −18.1240 + 18.1240i −0.0561115 + 0.0561115i
\(324\) 18.0000i 0.0555556i
\(325\) −241.589 + 149.256i −0.743350 + 0.459251i
\(326\) 194.023 0.595164
\(327\) −42.4220 42.4220i −0.129731 0.129731i
\(328\) 161.724 161.724i 0.493061 0.493061i
\(329\) 30.5899i 0.0929783i
\(330\) 27.7414 238.092i 0.0840648 0.721492i
\(331\) 195.576 0.590865 0.295433 0.955364i \(-0.404536\pi\)
0.295433 + 0.955364i \(0.404536\pi\)
\(332\) 68.8275 + 68.8275i 0.207312 + 0.207312i
\(333\) 111.704 111.704i 0.335446 0.335446i
\(334\) 270.995i 0.811362i
\(335\) −372.468 + 294.730i −1.11185 + 0.879790i
\(336\) 18.3303 0.0545545
\(337\) 420.206 + 420.206i 1.24690 + 1.24690i 0.957081 + 0.289822i \(0.0935961\pi\)
0.289822 + 0.957081i \(0.406404\pi\)
\(338\) −39.9718 + 39.9718i −0.118260 + 0.118260i
\(339\) 48.8501i 0.144101i
\(340\) −19.2762 24.3605i −0.0566946 0.0716485i
\(341\) 587.235 1.72210
\(342\) −24.7529 24.7529i −0.0723769 0.0723769i
\(343\) 13.0958 13.0958i 0.0381802 0.0381802i
\(344\) 54.7119i 0.159046i
\(345\) 217.839 + 25.3815i 0.631418 + 0.0735697i
\(346\) −132.354 −0.382527
\(347\) 21.4182 + 21.4182i 0.0617238 + 0.0617238i 0.737295 0.675571i \(-0.236103\pi\)
−0.675571 + 0.737295i \(0.736103\pi\)
\(348\) −48.3762 + 48.3762i −0.139012 + 0.139012i
\(349\) 244.156i 0.699588i −0.936827 0.349794i \(-0.886252\pi\)
0.936827 0.349794i \(-0.113748\pi\)
\(350\) −21.5060 + 91.0357i −0.0614458 + 0.260102i
\(351\) −59.0234 −0.168158
\(352\) −78.2867 78.2867i −0.222405 0.222405i
\(353\) 228.969 228.969i 0.648637 0.648637i −0.304026 0.952664i \(-0.598331\pi\)
0.952664 + 0.304026i \(0.0983311\pi\)
\(354\) 182.186i 0.514651i
\(355\) −7.74207 + 66.4469i −0.0218087 + 0.187174i
\(356\) −315.882 −0.887309
\(357\) 10.0661 + 10.0661i 0.0281962 + 0.0281962i
\(358\) 274.045 274.045i 0.765488 0.765488i
\(359\) 165.483i 0.460956i 0.973078 + 0.230478i \(0.0740290\pi\)
−0.973078 + 0.230478i \(0.925971\pi\)
\(360\) 33.2704 26.3264i 0.0924177 0.0731290i
\(361\) 292.922 0.811417
\(362\) −36.0493 36.0493i −0.0995836 0.0995836i
\(363\) 320.945 320.945i 0.884147 0.884147i
\(364\) 60.1065i 0.165128i
\(365\) 211.813 + 267.681i 0.580310 + 0.733374i
\(366\) 239.662 0.654813
\(367\) −225.601 225.601i −0.614715 0.614715i 0.329456 0.944171i \(-0.393135\pi\)
−0.944171 + 0.329456i \(0.893135\pi\)
\(368\) 71.6272 71.6272i 0.194639 0.194639i
\(369\) 242.586i 0.657415i
\(370\) 369.844 + 43.0924i 0.999577 + 0.116466i
\(371\) 145.386 0.391876
\(372\) 73.4952 + 73.4952i 0.197568 + 0.197568i
\(373\) 279.406 279.406i 0.749078 0.749078i −0.225228 0.974306i \(-0.572313\pi\)
0.974306 + 0.225228i \(0.0723128\pi\)
\(374\) 85.9821i 0.229899i
\(375\) 91.7133 + 196.122i 0.244569 + 0.522991i
\(376\) 32.7020 0.0869733
\(377\) 158.629 + 158.629i 0.420767 + 0.420767i
\(378\) −13.7477 + 13.7477i −0.0363696 + 0.0363696i
\(379\) 746.946i 1.97083i −0.170158 0.985417i \(-0.554428\pi\)
0.170158 0.985417i \(-0.445572\pi\)
\(380\) 9.54903 81.9553i 0.0251290 0.215672i
\(381\) 34.0357 0.0893327
\(382\) 133.194 + 133.194i 0.348676 + 0.348676i
\(383\) 359.176 359.176i 0.937797 0.937797i −0.0603788 0.998176i \(-0.519231\pi\)
0.998176 + 0.0603788i \(0.0192309\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −203.034 + 160.658i −0.527361 + 0.417294i
\(386\) −473.130 −1.22573
\(387\) 41.0339 + 41.0339i 0.106031 + 0.106031i
\(388\) 146.571 146.571i 0.377761 0.377761i
\(389\) 476.719i 1.22550i 0.790278 + 0.612749i \(0.209936\pi\)
−0.790278 + 0.612749i \(0.790064\pi\)
\(390\) −86.3264 109.096i −0.221350 0.279734i
\(391\) 78.6680 0.201197
\(392\) −14.0000 14.0000i −0.0357143 0.0357143i
\(393\) 198.163 198.163i 0.504231 0.504231i
\(394\) 406.021i 1.03051i
\(395\) −199.693 23.2673i −0.505553 0.0589046i
\(396\) 117.430 0.296541
\(397\) −137.315 137.315i −0.345883 0.345883i 0.512691 0.858573i \(-0.328649\pi\)
−0.858573 + 0.512691i \(0.828649\pi\)
\(398\) 102.932 102.932i 0.258622 0.258622i
\(399\) 37.8107i 0.0947636i
\(400\) 97.3212 + 22.9909i 0.243303 + 0.0574773i
\(401\) −691.294 −1.72392 −0.861962 0.506973i \(-0.830765\pi\)
−0.861962 + 0.506973i \(0.830765\pi\)
\(402\) −164.535 164.535i −0.409291 0.409291i
\(403\) 240.997 240.997i 0.598006 0.598006i
\(404\) 242.471i 0.600176i
\(405\) −5.20795 + 44.6976i −0.0128591 + 0.110364i
\(406\) 73.8958 0.182009
\(407\) 728.743 + 728.743i 1.79052 + 1.79052i
\(408\) 10.7611 10.7611i 0.0263752 0.0263752i
\(409\) 146.348i 0.357818i −0.983866 0.178909i \(-0.942743\pi\)
0.983866 0.178909i \(-0.0572568\pi\)
\(410\) −448.385 + 354.801i −1.09362 + 0.865369i
\(411\) −87.6974 −0.213376
\(412\) 47.1228 + 47.1228i 0.114376 + 0.114376i
\(413\) 139.147 139.147i 0.336918 0.336918i
\(414\) 107.441i 0.259519i
\(415\) −150.999 190.826i −0.363852 0.459823i
\(416\) −64.2565 −0.154463
\(417\) −109.916 109.916i −0.263587 0.263587i
\(418\) 161.485 161.485i 0.386329 0.386329i
\(419\) 19.1814i 0.0457790i 0.999738 + 0.0228895i \(0.00728659\pi\)
−0.999738 + 0.0228895i \(0.992713\pi\)
\(420\) −45.5178 5.30352i −0.108376 0.0126274i
\(421\) −343.060 −0.814870 −0.407435 0.913234i \(-0.633577\pi\)
−0.407435 + 0.913234i \(0.633577\pi\)
\(422\) −216.191 216.191i −0.512301 0.512301i
\(423\) −24.5265 + 24.5265i −0.0579822 + 0.0579822i
\(424\) 155.424i 0.366566i
\(425\) 40.8184 + 66.0692i 0.0960432 + 0.155457i
\(426\) −32.7724 −0.0769306
\(427\) −183.045 183.045i −0.428676 0.428676i
\(428\) 28.8629 28.8629i 0.0674366 0.0674366i
\(429\) 385.062i 0.897581i
\(430\) −15.8298 + 135.861i −0.0368136 + 0.315955i
\(431\) 251.794 0.584210 0.292105 0.956386i \(-0.405644\pi\)
0.292105 + 0.956386i \(0.405644\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) −125.195 + 125.195i −0.289133 + 0.289133i −0.836737 0.547604i \(-0.815540\pi\)
0.547604 + 0.836737i \(0.315540\pi\)
\(434\) 112.266i 0.258677i
\(435\) 134.124 106.131i 0.308332 0.243979i
\(436\) 69.2749 0.158887
\(437\) 147.749 + 147.749i 0.338097 + 0.338097i
\(438\) −118.246 + 118.246i −0.269969 + 0.269969i
\(439\) 37.5609i 0.0855601i 0.999085 + 0.0427801i \(0.0136215\pi\)
−0.999085 + 0.0427801i \(0.986379\pi\)
\(440\) 171.751 + 217.052i 0.390343 + 0.493301i
\(441\) 21.0000 0.0476190
\(442\) −35.2864 35.2864i −0.0798334 0.0798334i
\(443\) −583.967 + 583.967i −1.31821 + 1.31821i −0.403019 + 0.915192i \(0.632039\pi\)
−0.915192 + 0.403019i \(0.867961\pi\)
\(444\) 182.411i 0.410836i
\(445\) 784.398 + 91.3943i 1.76269 + 0.205380i
\(446\) 286.506 0.642390
\(447\) 359.636 + 359.636i 0.804554 + 0.804554i
\(448\) −14.9666 + 14.9666i −0.0334077 + 0.0334077i
\(449\) 595.556i 1.32640i −0.748440 0.663202i \(-0.769197\pi\)
0.748440 0.663202i \(-0.230803\pi\)
\(450\) −90.2341 + 55.7477i −0.200520 + 0.123884i
\(451\) −1582.61 −3.50910
\(452\) −39.8859 39.8859i −0.0882432 0.0882432i
\(453\) 283.805 283.805i 0.626500 0.626500i
\(454\) 453.532i 0.998969i
\(455\) −17.3906 + 149.256i −0.0382212 + 0.328036i
\(456\) 40.4213 0.0886433
\(457\) 300.505 + 300.505i 0.657560 + 0.657560i 0.954802 0.297242i \(-0.0960668\pi\)
−0.297242 + 0.954802i \(0.596067\pi\)
\(458\) −48.9068 + 48.9068i −0.106783 + 0.106783i
\(459\) 16.1416i 0.0351669i
\(460\) −198.589 + 157.141i −0.431715 + 0.341611i
\(461\) 565.424 1.22652 0.613258 0.789883i \(-0.289859\pi\)
0.613258 + 0.789883i \(0.289859\pi\)
\(462\) −89.6887 89.6887i −0.194131 0.194131i
\(463\) −247.619 + 247.619i −0.534815 + 0.534815i −0.922001 0.387186i \(-0.873447\pi\)
0.387186 + 0.922001i \(0.373447\pi\)
\(464\) 78.9979i 0.170254i
\(465\) −161.239 203.768i −0.346751 0.438211i
\(466\) −245.934 −0.527755
\(467\) −310.936 310.936i −0.665816 0.665816i 0.290929 0.956745i \(-0.406036\pi\)
−0.956745 + 0.290929i \(0.906036\pi\)
\(468\) 48.1924 48.1924i 0.102975 0.102975i
\(469\) 251.331i 0.535888i
\(470\) −81.2055 9.46167i −0.172778 0.0201312i
\(471\) 153.878 0.326705
\(472\) −148.755 148.755i −0.315158 0.315158i
\(473\) −267.701 + 267.701i −0.565964 + 0.565964i
\(474\) 98.4912i 0.207787i
\(475\) −47.4243 + 200.749i −0.0998407 + 0.422629i
\(476\) −16.4378 −0.0345332
\(477\) 116.568 + 116.568i 0.244377 + 0.244377i
\(478\) −359.392 + 359.392i −0.751865 + 0.751865i
\(479\) 337.547i 0.704692i 0.935870 + 0.352346i \(0.114616\pi\)
−0.935870 + 0.352346i \(0.885384\pi\)
\(480\) −5.66970 + 48.6606i −0.0118119 + 0.101376i
\(481\) 598.141 1.24354
\(482\) −96.4510 96.4510i −0.200106 0.200106i
\(483\) 82.0593 82.0593i 0.169895 0.169895i
\(484\) 524.101i 1.08285i
\(485\) −406.373 + 321.558i −0.837883 + 0.663007i
\(486\) −22.0454 −0.0453609
\(487\) 153.784 + 153.784i 0.315778 + 0.315778i 0.847143 0.531365i \(-0.178321\pi\)
−0.531365 + 0.847143i \(0.678321\pi\)
\(488\) −195.683 + 195.683i −0.400989 + 0.400989i
\(489\) 237.629i 0.485949i
\(490\) 30.7142 + 38.8154i 0.0626820 + 0.0792152i
\(491\) 320.910 0.653585 0.326792 0.945096i \(-0.394032\pi\)
0.326792 + 0.945096i \(0.394032\pi\)
\(492\) −198.071 198.071i −0.402583 0.402583i
\(493\) 43.3816 43.3816i 0.0879951 0.0879951i
\(494\) 132.545i 0.268309i
\(495\) −291.603 33.9761i −0.589096 0.0686386i
\(496\) −120.017 −0.241970
\(497\) 25.0304 + 25.0304i 0.0503629 + 0.0503629i
\(498\) 84.2961 84.2961i 0.169269 0.169269i
\(499\) 284.928i 0.570997i 0.958379 + 0.285499i \(0.0921592\pi\)
−0.958379 + 0.285499i \(0.907841\pi\)
\(500\) −235.016 85.2490i −0.470032 0.170498i
\(501\) −331.900 −0.662474
\(502\) −290.502 290.502i −0.578690 0.578690i
\(503\) −548.564 + 548.564i −1.09058 + 1.09058i −0.0951181 + 0.995466i \(0.530323\pi\)
−0.995466 + 0.0951181i \(0.969677\pi\)
\(504\) 22.4499i 0.0445435i
\(505\) 70.1543 602.105i 0.138919 1.19229i
\(506\) −700.933 −1.38524
\(507\) 48.9553 + 48.9553i 0.0965588 + 0.0965588i
\(508\) −27.7901 + 27.7901i −0.0547049 + 0.0547049i
\(509\) 558.480i 1.09721i −0.836081 0.548606i \(-0.815159\pi\)
0.836081 0.548606i \(-0.184841\pi\)
\(510\) −29.8354 + 23.6084i −0.0585008 + 0.0462910i
\(511\) 180.624 0.353472
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −30.3160 + 30.3160i −0.0590955 + 0.0590955i
\(514\) 451.166i 0.877755i
\(515\) −103.381 130.649i −0.200740 0.253688i
\(516\) −67.0081 −0.129861
\(517\) −160.008 160.008i −0.309493 0.309493i
\(518\) 139.319 139.319i 0.268956 0.268956i
\(519\) 162.100i 0.312332i
\(520\) 159.562 + 18.5914i 0.306850 + 0.0357526i
\(521\) 455.328 0.873949 0.436975 0.899474i \(-0.356050\pi\)
0.436975 + 0.899474i \(0.356050\pi\)
\(522\) 59.2485 + 59.2485i 0.113503 + 0.113503i
\(523\) 37.6920 37.6920i 0.0720687 0.0720687i −0.670154 0.742222i \(-0.733772\pi\)
0.742222 + 0.670154i \(0.233772\pi\)
\(524\) 323.598i 0.617554i
\(525\) 111.495 + 26.3394i 0.212372 + 0.0501703i
\(526\) 491.861 0.935097
\(527\) −65.9073 65.9073i −0.125061 0.125061i
\(528\) −95.8813 + 95.8813i −0.181593 + 0.181593i
\(529\) 112.308i 0.212302i
\(530\) −44.9689 + 385.949i −0.0848470 + 0.728206i
\(531\) 223.132 0.420211
\(532\) −30.8723 30.8723i −0.0580306 0.0580306i
\(533\) −649.489 + 649.489i −1.21855 + 1.21855i
\(534\) 386.875i 0.724485i
\(535\) −80.0233 + 63.3214i −0.149576 + 0.118358i
\(536\) 268.685 0.501277
\(537\) −335.635 335.635i −0.625019 0.625019i
\(538\) 306.198 306.198i 0.569142 0.569142i
\(539\) 137.002i 0.254178i
\(540\) −32.2432 40.7477i −0.0597096 0.0754588i
\(541\) 122.456 0.226352 0.113176 0.993575i \(-0.463898\pi\)
0.113176 + 0.993575i \(0.463898\pi\)
\(542\) −370.284 370.284i −0.683180 0.683180i
\(543\) −44.1512 + 44.1512i −0.0813097 + 0.0813097i
\(544\) 17.5728i 0.0323029i
\(545\) −172.023 20.0433i −0.315639 0.0367768i
\(546\) −73.6151 −0.134826
\(547\) 630.975 + 630.975i 1.15352 + 1.15352i 0.985842 + 0.167676i \(0.0536264\pi\)
0.167676 + 0.985842i \(0.446374\pi\)
\(548\) 71.6046 71.6046i 0.130665 0.130665i
\(549\) 293.524i 0.534653i
\(550\) −363.692 588.678i −0.661259 1.07032i
\(551\) 162.952 0.295739
\(552\) −87.7251 87.7251i −0.158922 0.158922i
\(553\) −75.2239 + 75.2239i −0.136029 + 0.136029i
\(554\) 323.634i 0.584176i
\(555\) 52.7772 452.964i 0.0950940 0.816151i
\(556\) 179.492 0.322827
\(557\) 89.6207 + 89.6207i 0.160899 + 0.160899i 0.782965 0.622066i \(-0.213706\pi\)
−0.622066 + 0.782965i \(0.713706\pi\)
\(558\) 90.0129 90.0129i 0.161313 0.161313i
\(559\) 219.725i 0.393068i
\(560\) 41.4955 32.8348i 0.0740990 0.0586337i
\(561\) −105.306 −0.187711
\(562\) −235.757 235.757i −0.419497 0.419497i
\(563\) −268.774 + 268.774i −0.477396 + 0.477396i −0.904298 0.426902i \(-0.859605\pi\)
0.426902 + 0.904298i \(0.359605\pi\)
\(564\) 40.0516i 0.0710134i
\(565\) 87.5046 + 110.585i 0.154875 + 0.195726i
\(566\) 4.53501 0.00801238
\(567\) 16.8375 + 16.8375i 0.0296957 + 0.0296957i
\(568\) 26.7586 26.7586i 0.0471102 0.0471102i
\(569\) 373.315i 0.656089i −0.944662 0.328045i \(-0.893610\pi\)
0.944662 0.328045i \(-0.106390\pi\)
\(570\) −100.374 11.6951i −0.176095 0.0205178i
\(571\) 93.3963 0.163566 0.0817831 0.996650i \(-0.473939\pi\)
0.0817831 + 0.996650i \(0.473939\pi\)
\(572\) 314.402 + 314.402i 0.549654 + 0.549654i
\(573\) 163.129 163.129i 0.284693 0.284693i
\(574\) 302.558i 0.527104i
\(575\) 538.602 332.755i 0.936698 0.578704i
\(576\) −24.0000 −0.0416667
\(577\) −356.401 356.401i −0.617679 0.617679i 0.327257 0.944936i \(-0.393876\pi\)
−0.944936 + 0.327257i \(0.893876\pi\)
\(578\) 279.350 279.350i 0.483304 0.483304i
\(579\) 579.464i 1.00080i
\(580\) −22.8565 + 196.168i −0.0394078 + 0.338220i
\(581\) −128.764 −0.221626
\(582\) −179.512 179.512i −0.308441 0.308441i
\(583\) −760.478 + 760.478i −1.30442 + 1.30442i
\(584\) 193.095i 0.330643i
\(585\) −133.615 + 105.728i −0.228402 + 0.180731i
\(586\) 398.806 0.680556
\(587\) −213.286 213.286i −0.363349 0.363349i 0.501695 0.865044i \(-0.332710\pi\)
−0.865044 + 0.501695i \(0.832710\pi\)
\(588\) −17.1464 + 17.1464i −0.0291606 + 0.0291606i
\(589\) 247.565i 0.420313i
\(590\) 326.348 + 412.427i 0.553133 + 0.699028i
\(591\) −497.272 −0.841408
\(592\) −148.938 148.938i −0.251585 0.251585i
\(593\) 118.172 118.172i 0.199279 0.199279i −0.600412 0.799691i \(-0.704997\pi\)
0.799691 + 0.600412i \(0.204997\pi\)
\(594\) 143.822i 0.242124i
\(595\) 40.8184 + 4.75596i 0.0686023 + 0.00799321i
\(596\) −587.283 −0.985374
\(597\) −126.065 126.065i −0.211164 0.211164i
\(598\) −287.657 + 287.657i −0.481032 + 0.481032i
\(599\) 210.890i 0.352071i 0.984384 + 0.176035i \(0.0563273\pi\)
−0.984384 + 0.176035i \(0.943673\pi\)
\(600\) 28.1580 119.194i 0.0469300 0.198656i
\(601\) −238.143 −0.396244 −0.198122 0.980177i \(-0.563484\pi\)
−0.198122 + 0.980177i \(0.563484\pi\)
\(602\) 51.1783 + 51.1783i 0.0850138 + 0.0850138i
\(603\) −201.513 + 201.513i −0.334185 + 0.334185i
\(604\) 463.451i 0.767303i
\(605\) 151.639 1301.45i 0.250642 2.15116i
\(606\) 296.965 0.490042
\(607\) 617.412 + 617.412i 1.01715 + 1.01715i 0.999850 + 0.0173035i \(0.00550814\pi\)
0.0173035 + 0.999850i \(0.494492\pi\)
\(608\) −33.0039 + 33.0039i −0.0542827 + 0.0542827i
\(609\) 90.5035i 0.148610i
\(610\) 542.537 429.303i 0.889405 0.703775i
\(611\) −131.332 −0.214946
\(612\) −13.1796 13.1796i −0.0215352 0.0215352i
\(613\) −765.627 + 765.627i −1.24898 + 1.24898i −0.292816 + 0.956169i \(0.594592\pi\)
−0.956169 + 0.292816i \(0.905408\pi\)
\(614\) 763.028i 1.24272i
\(615\) 434.541 + 549.157i 0.706571 + 0.892938i
\(616\) 146.461 0.237761
\(617\) 42.0185 + 42.0185i 0.0681012 + 0.0681012i 0.740337 0.672236i \(-0.234666\pi\)
−0.672236 + 0.740337i \(0.734666\pi\)
\(618\) 57.7134 57.7134i 0.0933874 0.0933874i
\(619\) 564.440i 0.911858i −0.890016 0.455929i \(-0.849307\pi\)
0.890016 0.455929i \(-0.150693\pi\)
\(620\) 298.027 + 34.7247i 0.480689 + 0.0560075i
\(621\) 131.588 0.211896
\(622\) −388.702 388.702i −0.624923 0.624923i
\(623\) 295.480 295.480i 0.474287 0.474287i
\(624\) 78.6978i 0.126118i
\(625\) 558.927 + 279.688i 0.894284 + 0.447501i
\(626\) −101.161 −0.161599
\(627\) −197.778 197.778i −0.315436 0.315436i
\(628\) −125.641 + 125.641i −0.200065 + 0.200065i
\(629\) 163.578i 0.260061i
\(630\) −6.49545 + 55.7477i −0.0103102 + 0.0884885i
\(631\) 498.286 0.789676 0.394838 0.918751i \(-0.370801\pi\)
0.394838 + 0.918751i \(0.370801\pi\)
\(632\) 80.4178 + 80.4178i 0.127243 + 0.127243i
\(633\) −264.779 + 264.779i −0.418292 + 0.418292i
\(634\) 109.935i 0.173399i
\(635\) 77.0489 60.9678i 0.121337 0.0960123i
\(636\) −190.355 −0.299300
\(637\) 56.2245 + 56.2245i 0.0882645 + 0.0882645i
\(638\) −386.531 + 386.531i −0.605847 + 0.605847i
\(639\) 40.1379i 0.0628136i
\(640\) −35.1019 44.3605i −0.0548468 0.0693133i
\(641\) 145.183 0.226494 0.113247 0.993567i \(-0.463875\pi\)
0.113247 + 0.993567i \(0.463875\pi\)
\(642\) −35.3497 35.3497i −0.0550618 0.0550618i
\(643\) 646.724 646.724i 1.00579 1.00579i 0.00580843 0.999983i \(-0.498151\pi\)
0.999983 0.00580843i \(-0.00184889\pi\)
\(644\) 134.002i 0.208078i
\(645\) 166.395 + 19.3875i 0.257976 + 0.0300581i
\(646\) −36.2481 −0.0561115
\(647\) 190.030 + 190.030i 0.293710 + 0.293710i 0.838544 0.544834i \(-0.183407\pi\)
−0.544834 + 0.838544i \(0.683407\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 1455.69i 2.24297i
\(650\) −390.845 92.3322i −0.601300 0.142050i
\(651\) −137.497 −0.211209
\(652\) 194.023 + 194.023i 0.297582 + 0.297582i
\(653\) 416.099 416.099i 0.637212 0.637212i −0.312655 0.949867i \(-0.601218\pi\)
0.949867 + 0.312655i \(0.101218\pi\)
\(654\) 84.8441i 0.129731i
\(655\) 93.6269 803.560i 0.142942 1.22681i
\(656\) 323.448 0.493061
\(657\) 144.822 + 144.822i 0.220428 + 0.220428i
\(658\) −30.5899 + 30.5899i −0.0464892 + 0.0464892i
\(659\) 615.296i 0.933682i −0.884341 0.466841i \(-0.845392\pi\)
0.884341 0.466841i \(-0.154608\pi\)
\(660\) 265.834 210.351i 0.402779 0.318714i
\(661\) −455.425 −0.688994 −0.344497 0.938787i \(-0.611951\pi\)
−0.344497 + 0.938787i \(0.611951\pi\)
\(662\) 195.576 + 195.576i 0.295433 + 0.295433i
\(663\) −43.2168 + 43.2168i −0.0651837 + 0.0651837i
\(664\) 137.655i 0.207312i
\(665\) 67.7298 + 85.5944i 0.101849 + 0.128713i
\(666\) 223.407 0.335446
\(667\) −353.650 353.650i −0.530210 0.530210i
\(668\) 270.995 270.995i 0.405681 0.405681i
\(669\) 350.897i 0.524509i
\(670\) −667.198 77.7387i −0.995818 0.116028i
\(671\) 1914.92 2.85383
\(672\) 18.3303 + 18.3303i 0.0272772 + 0.0272772i
\(673\) 156.161 156.161i 0.232037 0.232037i −0.581505 0.813543i \(-0.697536\pi\)
0.813543 + 0.581505i \(0.197536\pi\)
\(674\) 840.412i 1.24690i
\(675\) 68.2767 + 110.514i 0.101151 + 0.163724i
\(676\) −79.9437 −0.118260
\(677\) −567.709 567.709i −0.838566 0.838566i 0.150104 0.988670i \(-0.452039\pi\)
−0.988670 + 0.150104i \(0.952039\pi\)
\(678\) −48.8501 + 48.8501i −0.0720503 + 0.0720503i
\(679\) 274.210i 0.403843i
\(680\) 5.08433 43.6367i 0.00747696 0.0641716i
\(681\) 555.461 0.815655
\(682\) 587.235 + 587.235i 0.861048 + 0.861048i
\(683\) −124.523 + 124.523i −0.182317 + 0.182317i −0.792365 0.610047i \(-0.791150\pi\)
0.610047 + 0.792365i \(0.291150\pi\)
\(684\) 49.5058i 0.0723769i
\(685\) −198.526 + 157.091i −0.289819 + 0.229330i
\(686\) 26.1916 0.0381802
\(687\) 59.8984 + 59.8984i 0.0871883 + 0.0871883i
\(688\) 54.7119 54.7119i 0.0795231 0.0795231i
\(689\) 624.188i 0.905934i
\(690\) 192.457 + 243.221i 0.278924 + 0.352494i
\(691\) −1214.16 −1.75710 −0.878551 0.477648i \(-0.841489\pi\)
−0.878551 + 0.477648i \(0.841489\pi\)
\(692\) −132.354 132.354i −0.191263 0.191263i
\(693\) −109.846 + 109.846i −0.158508 + 0.158508i
\(694\) 42.8363i 0.0617238i
\(695\) −445.715 51.9325i −0.641316 0.0747230i
\(696\) −96.7523 −0.139012
\(697\) 177.621 + 177.621i 0.254836 + 0.254836i
\(698\) 244.156 244.156i 0.349794 0.349794i
\(699\) 301.206i 0.430910i
\(700\) −112.542 + 69.5296i −0.160774 + 0.0993280i
\(701\) −788.147 −1.12432 −0.562159 0.827029i \(-0.690029\pi\)
−0.562159 + 0.827029i \(0.690029\pi\)
\(702\) −59.0234 59.0234i −0.0840789 0.0840789i
\(703\) 307.221 307.221i 0.437014 0.437014i
\(704\) 156.573i 0.222405i
\(705\) −11.5881 + 99.4561i −0.0164371 + 0.141072i
\(706\) 457.938 0.648637
\(707\) −226.811 226.811i −0.320808 0.320808i
\(708\) −182.186 + 182.186i −0.257325 + 0.257325i
\(709\) 1230.75i 1.73589i −0.496660 0.867945i \(-0.665440\pi\)
0.496660 0.867945i \(-0.334560\pi\)
\(710\) −74.1890 + 58.7049i −0.104492 + 0.0826829i
\(711\) −120.627 −0.169658
\(712\) −315.882 315.882i −0.443654 0.443654i
\(713\) −537.281 + 537.281i −0.753550 + 0.753550i
\(714\) 20.1321i 0.0281962i
\(715\) −689.757 871.690i −0.964696 1.21915i
\(716\) 548.090 0.765488
\(717\) 440.163 + 440.163i 0.613895 + 0.613895i
\(718\) −165.483 + 165.483i −0.230478 + 0.230478i
\(719\) 251.624i 0.349963i −0.984572 0.174982i \(-0.944013\pi\)
0.984572 0.174982i \(-0.0559866\pi\)
\(720\) 59.5968 + 6.94393i 0.0827734 + 0.00964435i
\(721\) −88.1587 −0.122273
\(722\) 292.922 + 292.922i 0.405708 + 0.405708i
\(723\) −118.128 + 118.128i −0.163386 + 0.163386i
\(724\) 72.0985i 0.0995836i
\(725\) 113.515 480.511i 0.156572 0.662774i
\(726\) 641.891 0.884147
\(727\) 254.322 + 254.322i 0.349824 + 0.349824i 0.860044 0.510220i \(-0.170436\pi\)
−0.510220 + 0.860044i \(0.670436\pi\)
\(728\) 60.1065 60.1065i 0.0825638 0.0825638i
\(729\) 27.0000i 0.0370370i
\(730\) −55.8684 + 479.495i −0.0765320 + 0.656842i
\(731\) 60.0899 0.0822024
\(732\) 239.662 + 239.662i 0.327406 + 0.327406i
\(733\) −27.6831 + 27.6831i −0.0377668 + 0.0377668i −0.725738 0.687971i \(-0.758502\pi\)
0.687971 + 0.725738i \(0.258502\pi\)
\(734\) 451.201i 0.614715i
\(735\) 47.5390 37.6170i 0.0646789 0.0511797i
\(736\) 143.254 0.194639
\(737\) −1314.65 1314.65i −1.78379 1.78379i
\(738\) −242.586 + 242.586i −0.328707 + 0.328707i
\(739\) 434.621i 0.588121i 0.955787 + 0.294060i \(0.0950066\pi\)
−0.955787 + 0.294060i \(0.904993\pi\)
\(740\) 326.751 + 412.936i 0.441556 + 0.558022i
\(741\) −162.333 −0.219073
\(742\) 145.386 + 145.386i 0.195938 + 0.195938i
\(743\) 126.704 126.704i 0.170530 0.170530i −0.616682 0.787212i \(-0.711524\pi\)
0.787212 + 0.616682i \(0.211524\pi\)
\(744\) 146.990i 0.197568i
\(745\) 1458.34 + 169.919i 1.95750 + 0.228079i
\(746\) 558.812 0.749078
\(747\) −103.241 103.241i −0.138208 0.138208i
\(748\) 85.9821 85.9821i 0.114949 0.114949i
\(749\) 53.9975i 0.0720928i
\(750\) −104.408 + 287.835i −0.139211 + 0.383780i
\(751\) 735.755 0.979701 0.489851 0.871806i \(-0.337051\pi\)
0.489851 + 0.871806i \(0.337051\pi\)
\(752\) 32.7020 + 32.7020i 0.0434866 + 0.0434866i
\(753\) −355.791 + 355.791i −0.472498 + 0.472498i
\(754\) 317.258i 0.420767i
\(755\) 134.090 1150.84i 0.177603 1.52429i
\(756\) −27.4955 −0.0363696
\(757\) −255.322 255.322i −0.337281 0.337281i 0.518062 0.855343i \(-0.326654\pi\)
−0.855343 + 0.518062i \(0.826654\pi\)
\(758\) 746.946 746.946i 0.985417 0.985417i
\(759\) 858.464i 1.13105i
\(760\) 91.5043 72.4062i 0.120400 0.0952713i
\(761\) 783.231 1.02921 0.514606 0.857427i \(-0.327938\pi\)
0.514606 + 0.857427i \(0.327938\pi\)
\(762\) 34.0357 + 34.0357i 0.0446663 + 0.0446663i
\(763\) −64.8007 + 64.8007i −0.0849289 + 0.0849289i
\(764\) 266.389i 0.348676i
\(765\) 28.9143 + 36.5408i 0.0377964 + 0.0477657i
\(766\) 718.352 0.937797
\(767\) 597.403 + 597.403i 0.778883 + 0.778883i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 186.068i 0.241961i −0.992655 0.120980i \(-0.961396\pi\)
0.992655 0.120980i \(-0.0386038\pi\)
\(770\) −363.692 42.3757i −0.472328 0.0550333i
\(771\) −552.564 −0.716684
\(772\) −473.130 473.130i −0.612863 0.612863i
\(773\) −333.576 + 333.576i −0.431534 + 0.431534i −0.889150 0.457616i \(-0.848703\pi\)
0.457616 + 0.889150i \(0.348703\pi\)
\(774\) 82.0679i 0.106031i
\(775\) −730.014 172.457i −0.941953 0.222525i
\(776\) 293.143 0.377761
\(777\) −170.630 170.630i −0.219601 0.219601i
\(778\) −476.719 + 476.719i −0.612749 + 0.612749i
\(779\) 667.190i 0.856469i
\(780\) 22.7697 195.423i 0.0291919 0.250542i
\(781\) −261.855 −0.335282
\(782\) 78.6680 + 78.6680i 0.100598 + 0.100598i
\(783\) 72.5642 72.5642i 0.0926746 0.0926746i
\(784\) 28.0000i 0.0357143i
\(785\) 348.343 275.639i 0.443749 0.351133i
\(786\) 396.326 0.504231
\(787\) 431.752 + 431.752i 0.548605 + 0.548605i 0.926037 0.377432i \(-0.123193\pi\)
−0.377432 + 0.926037i \(0.623193\pi\)
\(788\) 406.021 406.021i 0.515255 0.515255i
\(789\) 602.404i 0.763504i
\(790\) −176.426 222.961i −0.223324 0.282229i
\(791\) 74.6197 0.0943360
\(792\) 117.430 + 117.430i 0.148270 + 0.148270i
\(793\) 785.869 785.869i 0.991007 0.991007i
\(794\) 274.631i 0.345883i
\(795\) 472.689 + 55.0755i 0.594578 + 0.0692773i
\(796\) 205.863 0.258622
\(797\) −67.9296 67.9296i −0.0852316 0.0852316i 0.663206 0.748437i \(-0.269195\pi\)
−0.748437 + 0.663206i \(0.769195\pi\)
\(798\) −37.8107 + 37.8107i −0.0473818 + 0.0473818i
\(799\) 35.9165i 0.0449518i
\(800\) 74.3303 + 120.312i 0.0929129 + 0.150390i
\(801\) 473.823 0.591539
\(802\) −691.294 691.294i −0.861962 0.861962i
\(803\) −944.800 + 944.800i −1.17659 + 1.17659i
\(804\) 329.070i 0.409291i
\(805\) 38.7710 332.755i 0.0481627 0.413360i
\(806\) 481.993 0.598006
\(807\) −375.015 375.015i −0.464702 0.464702i
\(808\) −242.471 + 242.471i −0.300088 + 0.300088i
\(809\) 375.281i 0.463883i 0.972730 + 0.231941i \(0.0745078\pi\)
−0.972730 + 0.231941i \(0.925492\pi\)
\(810\) −49.9056 + 39.4897i −0.0616118 + 0.0487527i
\(811\) 283.093 0.349066 0.174533 0.984651i \(-0.444158\pi\)
0.174533 + 0.984651i \(0.444158\pi\)
\(812\) 73.8958 + 73.8958i 0.0910047 + 0.0910047i
\(813\) −453.503 + 453.503i −0.557814 + 0.557814i
\(814\) 1457.49i 1.79052i
\(815\) −425.662 537.936i −0.522285 0.660044i
\(816\) 21.5221 0.0263752
\(817\) 112.857 + 112.857i 0.138135 + 0.138135i
\(818\) 146.348 146.348i 0.178909 0.178909i
\(819\) 90.1597i 0.110085i
\(820\) −803.186 93.5834i −0.979496 0.114126i
\(821\) 1325.60 1.61462 0.807308 0.590131i \(-0.200924\pi\)
0.807308 + 0.590131i \(0.200924\pi\)
\(822\) −87.6974 87.6974i −0.106688 0.106688i
\(823\) 794.494 794.494i 0.965363 0.965363i −0.0340566 0.999420i \(-0.510843\pi\)
0.999420 + 0.0340566i \(0.0108427\pi\)
\(824\) 94.2456i 0.114376i
\(825\) −720.980 + 445.430i −0.873915 + 0.539915i
\(826\) 278.294 0.336918
\(827\) 361.128 + 361.128i 0.436672 + 0.436672i 0.890890 0.454218i \(-0.150081\pi\)
−0.454218 + 0.890890i \(0.650081\pi\)
\(828\) −107.441 + 107.441i −0.129759 + 0.129759i
\(829\) 195.726i 0.236099i 0.993008 + 0.118049i \(0.0376641\pi\)
−0.993008 + 0.118049i \(0.962336\pi\)
\(830\) 39.8278 341.825i 0.0479853 0.411837i
\(831\) −396.368 −0.476978
\(832\) −64.2565 64.2565i −0.0772314 0.0772314i
\(833\) 15.3762 15.3762i 0.0184588 0.0184588i
\(834\) 219.832i 0.263587i
\(835\) −751.342 + 594.528i −0.899811 + 0.712009i
\(836\) 322.971 0.386329
\(837\) −110.243 110.243i −0.131712 0.131712i
\(838\) −19.1814 + 19.1814i −0.0228895 + 0.0228895i
\(839\) 10.5401i 0.0125627i −0.999980 0.00628133i \(-0.998001\pi\)
0.999980 0.00628133i \(-0.00199942\pi\)
\(840\) −40.2143 50.8213i −0.0478742 0.0605016i
\(841\) 450.958 0.536216
\(842\) −343.060 343.060i −0.407435 0.407435i
\(843\) −288.742 + 288.742i −0.342518 + 0.342518i
\(844\) 432.382i 0.512301i
\(845\) 198.516 + 23.1302i 0.234931 + 0.0273730i
\(846\) −49.0529 −0.0579822
\(847\) −490.252 490.252i −0.578810 0.578810i
\(848\) 155.424 155.424i 0.183283 0.183283i
\(849\) 5.55423i 0.00654208i
\(850\) −25.2508 + 106.888i −0.0297069 + 0.125750i
\(851\) −1333.50 −1.56699
\(852\) −32.7724 32.7724i −0.0384653 0.0384653i
\(853\) −950.696 + 950.696i −1.11453 + 1.11453i −0.122002 + 0.992530i \(0.538932\pi\)
−0.992530 + 0.122002i \(0.961068\pi\)
\(854\) 366.089i 0.428676i
\(855\) −14.3235 + 122.933i −0.0167527 + 0.143781i
\(856\) 57.7258 0.0674366
\(857\) 628.392 + 628.392i 0.733246 + 0.733246i 0.971261 0.238016i \(-0.0764969\pi\)
−0.238016 + 0.971261i \(0.576497\pi\)
\(858\) 385.062 385.062i 0.448791 0.448791i
\(859\) 832.998i 0.969730i −0.874589 0.484865i \(-0.838869\pi\)
0.874589 0.484865i \(-0.161131\pi\)
\(860\) −151.691 + 120.031i −0.176384 + 0.139571i
\(861\) 370.556 0.430379
\(862\) 251.794 + 251.794i 0.292105 + 0.292105i
\(863\) 802.913 802.913i 0.930374 0.930374i −0.0673547 0.997729i \(-0.521456\pi\)
0.997729 + 0.0673547i \(0.0214559\pi\)
\(864\) 29.3939i 0.0340207i
\(865\) 290.368 + 366.957i 0.335686 + 0.424227i
\(866\) −250.389 −0.289133
\(867\) −342.132 342.132i −0.394616 0.394616i
\(868\) 112.266 112.266i 0.129339 0.129339i
\(869\) 786.955i 0.905587i
\(870\) 240.255 + 27.9934i 0.276156 + 0.0321763i
\(871\) −1079.05 −1.23886
\(872\) 69.2749 + 69.2749i 0.0794437 + 0.0794437i
\(873\) −219.857 + 219.857i −0.251841 + 0.251841i
\(874\) 295.497i 0.338097i
\(875\) 299.581 140.094i 0.342378 0.160108i
\(876\) −236.493 −0.269969
\(877\) 483.085 + 483.085i 0.550838 + 0.550838i 0.926683 0.375845i \(-0.122647\pi\)
−0.375845 + 0.926683i \(0.622647\pi\)
\(878\) −37.5609 + 37.5609i −0.0427801 + 0.0427801i
\(879\) 488.435i 0.555671i
\(880\) −45.3015 + 388.803i −0.0514790 + 0.441822i
\(881\) −1190.88 −1.35174 −0.675868 0.737023i \(-0.736231\pi\)
−0.675868 + 0.737023i \(0.736231\pi\)
\(882\) 21.0000 + 21.0000i 0.0238095 + 0.0238095i
\(883\) −52.9133 + 52.9133i −0.0599245 + 0.0599245i −0.736434 0.676509i \(-0.763492\pi\)
0.676509 + 0.736434i \(0.263492\pi\)
\(884\) 70.5727i 0.0798334i
\(885\) 505.118 399.693i 0.570754 0.451631i
\(886\) −1167.93 −1.31821
\(887\) −393.366 393.366i −0.443479 0.443479i 0.449700 0.893180i \(-0.351531\pi\)
−0.893180 + 0.449700i \(0.851531\pi\)
\(888\) −182.411 + 182.411i −0.205418 + 0.205418i
\(889\) 51.9905i 0.0584820i
\(890\) 693.004 + 875.793i 0.778656 + 0.984037i
\(891\) −176.145 −0.197694
\(892\) 286.506 + 286.506i 0.321195 + 0.321195i
\(893\) −67.4557 + 67.4557i −0.0755383 + 0.0755383i
\(894\) 719.271i 0.804554i
\(895\) −1361.02 158.579i −1.52069 0.177183i
\(896\) −29.9333 −0.0334077
\(897\) 352.307 + 352.307i 0.392761 + 0.392761i
\(898\) 595.556 595.556i 0.663202 0.663202i
\(899\) 592.570i 0.659143i
\(900\) −145.982 34.4864i −0.162202 0.0383182i
\(901\) 170.702 0.189458
\(902\) −1582.61 1582.61i −1.75455 1.75455i
\(903\) 62.6804 62.6804i 0.0694135 0.0694135i
\(904\) 79.7719i 0.0882432i
\(905\) −20.8603 + 179.035i −0.0230501 + 0.197829i
\(906\) 567.609 0.626500
\(907\) 715.081 + 715.081i 0.788403 + 0.788403i 0.981232 0.192829i \(-0.0617664\pi\)
−0.192829 + 0.981232i \(0.561766\pi\)
\(908\) −453.532 + 453.532i −0.499485 + 0.499485i
\(909\) 363.707i 0.400118i
\(910\) −166.647 + 131.866i −0.183129 + 0.144908i
\(911\) −1440.70 −1.58145 −0.790727 0.612169i \(-0.790297\pi\)
−0.790727 + 0.612169i \(0.790297\pi\)
\(912\) 40.4213 + 40.4213i 0.0443216 + 0.0443216i
\(913\) 673.535 673.535i 0.737716 0.737716i
\(914\) 601.010i 0.657560i
\(915\) −525.786 664.469i −0.574630 0.726196i
\(916\) −97.8136 −0.106783
\(917\) −302.699 302.699i −0.330097 0.330097i
\(918\) −16.1416 + 16.1416i −0.0175834 + 0.0175834i
\(919\) 139.961i 0.152297i −0.997096 0.0761485i \(-0.975738\pi\)
0.997096 0.0761485i \(-0.0242623\pi\)
\(920\) −355.730 41.4479i −0.386663 0.0450521i
\(921\) −934.515 −1.01467
\(922\) 565.424 + 565.424i 0.613258 + 0.613258i
\(923\) −107.463 + 107.463i −0.116428 + 0.116428i
\(924\) 179.377i 0.194131i
\(925\) −691.914 1119.94i −0.748015 1.21075i
\(926\) −495.239 −0.534815
\(927\) −70.6842 70.6842i −0.0762505 0.0762505i
\(928\) 78.9979 78.9979i 0.0851271 0.0851271i
\(929\) 268.303i 0.288808i 0.989519 + 0.144404i \(0.0461265\pi\)
−0.989519 + 0.144404i \(0.953874\pi\)
\(930\) 42.5288 365.007i 0.0457299 0.392481i
\(931\) 57.7568 0.0620374
\(932\) −245.934 245.934i −0.263878 0.263878i
\(933\) −476.061 + 476.061i −0.510248 + 0.510248i
\(934\) 621.872i 0.665816i
\(935\) −238.388 + 188.634i −0.254960 + 0.201747i
\(936\) 96.3848 0.102975
\(937\) −750.288 750.288i −0.800734 0.800734i 0.182476 0.983210i \(-0.441589\pi\)
−0.983210 + 0.182476i \(0.941589\pi\)
\(938\) −251.331 + 251.331i −0.267944 + 0.267944i
\(939\) 123.897i 0.131945i
\(940\) −71.7439 90.6672i −0.0763233 0.0964545i
\(941\) 858.370 0.912189 0.456095 0.889931i \(-0.349248\pi\)
0.456095 + 0.889931i \(0.349248\pi\)
\(942\) 153.878 + 153.878i 0.163352 + 0.163352i
\(943\) 1447.98 1447.98i 1.53550 1.53550i
\(944\) 297.509i 0.315158i
\(945\) 68.2767 + 7.95527i 0.0722505 + 0.00841828i
\(946\) −535.402 −0.565964
\(947\) 1103.38 + 1103.38i 1.16513 + 1.16513i 0.983336 + 0.181798i \(0.0581917\pi\)
0.181798 + 0.983336i \(0.441808\pi\)
\(948\) 98.4912 98.4912i 0.103894 0.103894i
\(949\) 775.477i 0.817152i
\(950\) −248.173 + 153.324i −0.261235 + 0.161394i
\(951\) 134.642 0.141580
\(952\) −16.4378 16.4378i −0.0172666 0.0172666i
\(953\) −1277.56 + 1277.56i −1.34056 + 1.34056i −0.445064 + 0.895499i \(0.646819\pi\)
−0.895499 + 0.445064i \(0.853181\pi\)
\(954\) 233.136i 0.244377i
\(955\) 77.0743 661.496i 0.0807061 0.692666i
\(956\) −718.783 −0.751865
\(957\) 473.401 + 473.401i 0.494672 + 0.494672i
\(958\) −337.547 + 337.547i −0.352346 + 0.352346i
\(959\) 133.960i 0.139687i
\(960\) −54.3303 + 42.9909i −0.0565941 + 0.0447822i
\(961\) −60.7414 −0.0632064
\(962\) 598.141 + 598.141i 0.621768 + 0.621768i
\(963\) −43.2943 + 43.2943i −0.0449578 + 0.0449578i
\(964\) 192.902i 0.200106i
\(965\) 1037.99 + 1311.77i 1.07563 + 1.35935i
\(966\) 164.119 0.169895
\(967\) −478.601 478.601i −0.494933 0.494933i 0.414923 0.909857i \(-0.363808\pi\)
−0.909857 + 0.414923i \(0.863808\pi\)
\(968\) −524.101 + 524.101i −0.541427 + 0.541427i
\(969\) 44.3946i 0.0458149i
\(970\) −727.932 84.8151i −0.750445 0.0874382i
\(971\) 97.1677 0.100070 0.0500349 0.998747i \(-0.484067\pi\)
0.0500349 + 0.998747i \(0.484067\pi\)
\(972\) −22.0454 22.0454i −0.0226805 0.0226805i
\(973\) −167.899 + 167.899i −0.172558 + 0.172558i
\(974\) 307.568i 0.315778i
\(975\) −113.083 + 478.686i −0.115983 + 0.490960i
\(976\) −391.366 −0.400989
\(977\) −711.442 711.442i −0.728191 0.728191i 0.242068 0.970259i \(-0.422174\pi\)
−0.970259 + 0.242068i \(0.922174\pi\)
\(978\) 237.629 237.629i 0.242975 0.242975i
\(979\) 3091.17i 3.15748i
\(980\) −8.10125 + 69.5296i −0.00826659 + 0.0709486i
\(981\) −103.912 −0.105925
\(982\) 320.910 + 320.910i 0.326792 + 0.326792i
\(983\) −443.320 + 443.320i −0.450986 + 0.450986i −0.895682 0.444695i \(-0.853312\pi\)
0.444695 + 0.895682i \(0.353312\pi\)
\(984\) 396.141i 0.402583i
\(985\) −1125.71 + 890.758i −1.14285 + 0.904323i
\(986\) 86.7632 0.0879951
\(987\) 37.4648 + 37.4648i 0.0379583 + 0.0379583i
\(988\) 132.545 132.545i 0.134154 0.134154i
\(989\) 489.858i 0.495306i
\(990\) −257.626 325.579i −0.260229 0.328867i
\(991\) 1708.27 1.72378 0.861890 0.507095i \(-0.169281\pi\)
0.861890 + 0.507095i \(0.169281\pi\)
\(992\) −120.017 120.017i −0.120985 0.120985i
\(993\) 239.531 239.531i 0.241220 0.241220i
\(994\) 50.0607i 0.0503629i
\(995\) −511.200 59.5625i −0.513768 0.0598618i
\(996\) 168.592 0.169269
\(997\) 1363.41 + 1363.41i 1.36752 + 1.36752i 0.863967 + 0.503548i \(0.167972\pi\)
0.503548 + 0.863967i \(0.332028\pi\)
\(998\) −284.928 + 284.928i −0.285499 + 0.285499i
\(999\) 273.617i 0.273891i
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 210.3.l.a.127.3 yes 8
3.2 odd 2 630.3.o.b.127.2 8
5.2 odd 4 1050.3.l.b.43.2 8
5.3 odd 4 inner 210.3.l.a.43.3 8
5.4 even 2 1050.3.l.b.757.2 8
15.8 even 4 630.3.o.b.253.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.l.a.43.3 8 5.3 odd 4 inner
210.3.l.a.127.3 yes 8 1.1 even 1 trivial
630.3.o.b.127.2 8 3.2 odd 2
630.3.o.b.253.2 8 15.8 even 4
1050.3.l.b.43.2 8 5.2 odd 4
1050.3.l.b.757.2 8 5.4 even 2