Properties

Label 350.4.j.d.149.1
Level $350$
Weight $4$
Character 350.149
Analytic conductor $20.651$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [350,4,Mod(149,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.149");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 350.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(20.6506685020\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 149.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 350.149
Dual form 350.4.j.d.249.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.73205 - 1.00000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.00000 + 3.46410i) q^{4} +2.00000 q^{6} +(15.5885 + 10.0000i) q^{7} -8.00000i q^{8} +(-13.0000 + 22.5167i) q^{9} +O(q^{10})\) \(q+(-1.73205 - 1.00000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.00000 + 3.46410i) q^{4} +2.00000 q^{6} +(15.5885 + 10.0000i) q^{7} -8.00000i q^{8} +(-13.0000 + 22.5167i) q^{9} +(-17.5000 - 30.3109i) q^{11} +(-3.46410 - 2.00000i) q^{12} +66.0000i q^{13} +(-17.0000 - 32.9090i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-51.0955 + 29.5000i) q^{17} +(45.0333 - 26.0000i) q^{18} +(68.5000 - 118.645i) q^{19} +(-18.5000 - 0.866025i) q^{21} +70.0000i q^{22} +(6.06218 + 3.50000i) q^{23} +(4.00000 + 6.92820i) q^{24} +(66.0000 - 114.315i) q^{26} -53.0000i q^{27} +(-3.46410 + 74.0000i) q^{28} -106.000 q^{29} +(-37.5000 - 64.9519i) q^{31} +(27.7128 - 16.0000i) q^{32} +(30.3109 + 17.5000i) q^{33} +118.000 q^{34} -104.000 q^{36} +(9.52628 + 5.50000i) q^{37} +(-237.291 + 137.000i) q^{38} +(-33.0000 - 57.1577i) q^{39} -498.000 q^{41} +(31.1769 + 20.0000i) q^{42} +260.000i q^{43} +(70.0000 - 121.244i) q^{44} +(-7.00000 - 12.1244i) q^{46} +(-148.090 - 85.5000i) q^{47} -16.0000i q^{48} +(143.000 + 311.769i) q^{49} +(29.5000 - 51.0955i) q^{51} +(-228.631 + 132.000i) q^{52} +(-361.133 + 208.500i) q^{53} +(-53.0000 + 91.7987i) q^{54} +(80.0000 - 124.708i) q^{56} +137.000i q^{57} +(183.597 + 106.000i) q^{58} +(-8.50000 - 14.7224i) q^{59} +(-25.5000 + 44.1673i) q^{61} +150.000i q^{62} +(-427.817 + 221.000i) q^{63} -64.0000 q^{64} +(-35.0000 - 60.6218i) q^{66} +(-380.185 + 219.500i) q^{67} +(-204.382 - 118.000i) q^{68} -7.00000 q^{69} -784.000 q^{71} +(180.133 + 104.000i) q^{72} +(255.477 - 147.500i) q^{73} +(-11.0000 - 19.0526i) q^{74} +548.000 q^{76} +(30.3109 - 647.500i) q^{77} +132.000i q^{78} +(-247.500 + 428.683i) q^{79} +(-324.500 - 562.050i) q^{81} +(862.561 + 498.000i) q^{82} +932.000i q^{83} +(-34.0000 - 65.8179i) q^{84} +(260.000 - 450.333i) q^{86} +(91.7987 - 53.0000i) q^{87} +(-242.487 + 140.000i) q^{88} +(-436.500 + 756.040i) q^{89} +(-660.000 + 1028.84i) q^{91} +28.0000i q^{92} +(64.9519 + 37.5000i) q^{93} +(171.000 + 296.181i) q^{94} +(-16.0000 + 27.7128i) q^{96} +290.000i q^{97} +(64.0859 - 683.000i) q^{98} +910.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{4} + 8 q^{6} - 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{4} + 8 q^{6} - 52 q^{9} - 70 q^{11} - 68 q^{14} - 32 q^{16} + 274 q^{19} - 74 q^{21} + 16 q^{24} + 264 q^{26} - 424 q^{29} - 150 q^{31} + 472 q^{34} - 416 q^{36} - 132 q^{39} - 1992 q^{41} + 280 q^{44} - 28 q^{46} + 572 q^{49} + 118 q^{51} - 212 q^{54} + 320 q^{56} - 34 q^{59} - 102 q^{61} - 256 q^{64} - 140 q^{66} - 28 q^{69} - 3136 q^{71} - 44 q^{74} + 2192 q^{76} - 990 q^{79} - 1298 q^{81} - 136 q^{84} + 1040 q^{86} - 1746 q^{89} - 2640 q^{91} + 684 q^{94} - 64 q^{96} + 3640 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73205 1.00000i −0.612372 0.353553i
\(3\) −0.866025 + 0.500000i −0.166667 + 0.0962250i −0.581013 0.813894i \(-0.697344\pi\)
0.414346 + 0.910119i \(0.364010\pi\)
\(4\) 2.00000 + 3.46410i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 2.00000 0.136083
\(7\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(8\) 8.00000i 0.353553i
\(9\) −13.0000 + 22.5167i −0.481481 + 0.833950i
\(10\) 0 0
\(11\) −17.5000 30.3109i −0.479677 0.830825i 0.520051 0.854135i \(-0.325913\pi\)
−0.999728 + 0.0233099i \(0.992580\pi\)
\(12\) −3.46410 2.00000i −0.0833333 0.0481125i
\(13\) 66.0000i 1.40809i 0.710158 + 0.704043i \(0.248624\pi\)
−0.710158 + 0.704043i \(0.751376\pi\)
\(14\) −17.0000 32.9090i −0.324532 0.628235i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −51.0955 + 29.5000i −0.728969 + 0.420871i −0.818045 0.575154i \(-0.804942\pi\)
0.0890757 + 0.996025i \(0.471609\pi\)
\(18\) 45.0333 26.0000i 0.589692 0.340459i
\(19\) 68.5000 118.645i 0.827104 1.43259i −0.0731965 0.997318i \(-0.523320\pi\)
0.900301 0.435269i \(-0.143347\pi\)
\(20\) 0 0
\(21\) −18.5000 0.866025i −0.192240 0.00899915i
\(22\) 70.0000i 0.678366i
\(23\) 6.06218 + 3.50000i 0.0549588 + 0.0317305i 0.527228 0.849724i \(-0.323232\pi\)
−0.472269 + 0.881455i \(0.656565\pi\)
\(24\) 4.00000 + 6.92820i 0.0340207 + 0.0589256i
\(25\) 0 0
\(26\) 66.0000 114.315i 0.497833 0.862273i
\(27\) 53.0000i 0.377772i
\(28\) −3.46410 + 74.0000i −0.0233805 + 0.499453i
\(29\) −106.000 −0.678748 −0.339374 0.940651i \(-0.610215\pi\)
−0.339374 + 0.940651i \(0.610215\pi\)
\(30\) 0 0
\(31\) −37.5000 64.9519i −0.217264 0.376313i 0.736706 0.676213i \(-0.236380\pi\)
−0.953971 + 0.299900i \(0.903047\pi\)
\(32\) 27.7128 16.0000i 0.153093 0.0883883i
\(33\) 30.3109 + 17.5000i 0.159892 + 0.0923139i
\(34\) 118.000 0.595201
\(35\) 0 0
\(36\) −104.000 −0.481481
\(37\) 9.52628 + 5.50000i 0.0423273 + 0.0244377i 0.521014 0.853548i \(-0.325554\pi\)
−0.478687 + 0.877986i \(0.658887\pi\)
\(38\) −237.291 + 137.000i −1.01299 + 0.584851i
\(39\) −33.0000 57.1577i −0.135493 0.234681i
\(40\) 0 0
\(41\) −498.000 −1.89694 −0.948470 0.316867i \(-0.897369\pi\)
−0.948470 + 0.316867i \(0.897369\pi\)
\(42\) 31.1769 + 20.0000i 0.114541 + 0.0734778i
\(43\) 260.000i 0.922084i 0.887378 + 0.461042i \(0.152524\pi\)
−0.887378 + 0.461042i \(0.847476\pi\)
\(44\) 70.0000 121.244i 0.239839 0.415413i
\(45\) 0 0
\(46\) −7.00000 12.1244i −0.0224368 0.0388617i
\(47\) −148.090 85.5000i −0.459600 0.265350i 0.252276 0.967655i \(-0.418821\pi\)
−0.711876 + 0.702305i \(0.752154\pi\)
\(48\) 16.0000i 0.0481125i
\(49\) 143.000 + 311.769i 0.416910 + 0.908948i
\(50\) 0 0
\(51\) 29.5000 51.0955i 0.0809966 0.140290i
\(52\) −228.631 + 132.000i −0.609719 + 0.352021i
\(53\) −361.133 + 208.500i −0.935951 + 0.540371i −0.888689 0.458511i \(-0.848383\pi\)
−0.0472619 + 0.998883i \(0.515050\pi\)
\(54\) −53.0000 + 91.7987i −0.133563 + 0.231337i
\(55\) 0 0
\(56\) 80.0000 124.708i 0.190901 0.297585i
\(57\) 137.000i 0.318353i
\(58\) 183.597 + 106.000i 0.415647 + 0.239974i
\(59\) −8.50000 14.7224i −0.0187560 0.0324864i 0.856495 0.516155i \(-0.172637\pi\)
−0.875251 + 0.483669i \(0.839304\pi\)
\(60\) 0 0
\(61\) −25.5000 + 44.1673i −0.0535236 + 0.0927056i −0.891546 0.452930i \(-0.850379\pi\)
0.838022 + 0.545636i \(0.183712\pi\)
\(62\) 150.000i 0.307258i
\(63\) −427.817 + 221.000i −0.855553 + 0.441958i
\(64\) −64.0000 −0.125000
\(65\) 0 0
\(66\) −35.0000 60.6218i −0.0652758 0.113061i
\(67\) −380.185 + 219.500i −0.693239 + 0.400242i −0.804824 0.593513i \(-0.797740\pi\)
0.111585 + 0.993755i \(0.464407\pi\)
\(68\) −204.382 118.000i −0.364485 0.210435i
\(69\) −7.00000 −0.0122131
\(70\) 0 0
\(71\) −784.000 −1.31047 −0.655237 0.755423i \(-0.727431\pi\)
−0.655237 + 0.755423i \(0.727431\pi\)
\(72\) 180.133 + 104.000i 0.294846 + 0.170229i
\(73\) 255.477 147.500i 0.409608 0.236487i −0.281013 0.959704i \(-0.590671\pi\)
0.690621 + 0.723217i \(0.257337\pi\)
\(74\) −11.0000 19.0526i −0.0172801 0.0299299i
\(75\) 0 0
\(76\) 548.000 0.827104
\(77\) 30.3109 647.500i 0.0448603 0.958305i
\(78\) 132.000i 0.191616i
\(79\) −247.500 + 428.683i −0.352480 + 0.610513i −0.986683 0.162653i \(-0.947995\pi\)
0.634203 + 0.773166i \(0.281328\pi\)
\(80\) 0 0
\(81\) −324.500 562.050i −0.445130 0.770988i
\(82\) 862.561 + 498.000i 1.16163 + 0.670670i
\(83\) 932.000i 1.23253i 0.787537 + 0.616267i \(0.211356\pi\)
−0.787537 + 0.616267i \(0.788644\pi\)
\(84\) −34.0000 65.8179i −0.0441631 0.0854920i
\(85\) 0 0
\(86\) 260.000 450.333i 0.326006 0.564659i
\(87\) 91.7987 53.0000i 0.113125 0.0653126i
\(88\) −242.487 + 140.000i −0.293741 + 0.169591i
\(89\) −436.500 + 756.040i −0.519875 + 0.900451i 0.479858 + 0.877346i \(0.340688\pi\)
−0.999733 + 0.0231042i \(0.992645\pi\)
\(90\) 0 0
\(91\) −660.000 + 1028.84i −0.760294 + 1.18518i
\(92\) 28.0000i 0.0317305i
\(93\) 64.9519 + 37.5000i 0.0724215 + 0.0418126i
\(94\) 171.000 + 296.181i 0.187631 + 0.324986i
\(95\) 0 0
\(96\) −16.0000 + 27.7128i −0.0170103 + 0.0294628i
\(97\) 290.000i 0.303557i 0.988415 + 0.151779i \(0.0485001\pi\)
−0.988415 + 0.151779i \(0.951500\pi\)
\(98\) 64.0859 683.000i 0.0660577 0.704014i
\(99\) 910.000 0.923823
\(100\) 0 0
\(101\) 542.500 + 939.638i 0.534463 + 0.925717i 0.999189 + 0.0402627i \(0.0128195\pi\)
−0.464726 + 0.885454i \(0.653847\pi\)
\(102\) −102.191 + 59.0000i −0.0992002 + 0.0572732i
\(103\) −1344.94 776.500i −1.28661 0.742823i −0.308560 0.951205i \(-0.599847\pi\)
−0.978048 + 0.208381i \(0.933181\pi\)
\(104\) 528.000 0.497833
\(105\) 0 0
\(106\) 834.000 0.764200
\(107\) 111.717 + 64.5000i 0.100936 + 0.0582752i 0.549618 0.835416i \(-0.314773\pi\)
−0.448682 + 0.893691i \(0.648107\pi\)
\(108\) 183.597 106.000i 0.163580 0.0944431i
\(109\) −482.500 835.715i −0.423992 0.734376i 0.572334 0.820021i \(-0.306038\pi\)
−0.996326 + 0.0856452i \(0.972705\pi\)
\(110\) 0 0
\(111\) −11.0000 −0.00940607
\(112\) −263.272 + 136.000i −0.222115 + 0.114739i
\(113\) 50.0000i 0.0416248i −0.999783 0.0208124i \(-0.993375\pi\)
0.999783 0.0208124i \(-0.00662527\pi\)
\(114\) 137.000 237.291i 0.112555 0.194950i
\(115\) 0 0
\(116\) −212.000 367.195i −0.169687 0.293907i
\(117\) −1486.10 858.000i −1.17427 0.677967i
\(118\) 34.0000i 0.0265250i
\(119\) −1091.50 51.0955i −0.840821 0.0393606i
\(120\) 0 0
\(121\) 53.0000 91.7987i 0.0398197 0.0689697i
\(122\) 88.3346 51.0000i 0.0655528 0.0378469i
\(123\) 431.281 249.000i 0.316157 0.182533i
\(124\) 150.000 259.808i 0.108632 0.188157i
\(125\) 0 0
\(126\) 962.000 + 45.0333i 0.680173 + 0.0318404i
\(127\) 936.000i 0.653989i −0.945026 0.326994i \(-0.893964\pi\)
0.945026 0.326994i \(-0.106036\pi\)
\(128\) 110.851 + 64.0000i 0.0765466 + 0.0441942i
\(129\) −130.000 225.167i −0.0887276 0.153681i
\(130\) 0 0
\(131\) 377.500 653.849i 0.251773 0.436084i −0.712241 0.701935i \(-0.752320\pi\)
0.964014 + 0.265851i \(0.0856529\pi\)
\(132\) 140.000i 0.0923139i
\(133\) 2254.26 1164.50i 1.46970 0.759210i
\(134\) 878.000 0.566027
\(135\) 0 0
\(136\) 236.000 + 408.764i 0.148800 + 0.257730i
\(137\) 2041.22 1178.50i 1.27294 0.734935i 0.297403 0.954752i \(-0.403879\pi\)
0.975541 + 0.219817i \(0.0705461\pi\)
\(138\) 12.1244 + 7.00000i 0.00747894 + 0.00431797i
\(139\) −28.0000 −0.0170858 −0.00854291 0.999964i \(-0.502719\pi\)
−0.00854291 + 0.999964i \(0.502719\pi\)
\(140\) 0 0
\(141\) 171.000 0.102133
\(142\) 1357.93 + 784.000i 0.802498 + 0.463323i
\(143\) 2000.52 1155.00i 1.16987 0.675426i
\(144\) −208.000 360.267i −0.120370 0.208488i
\(145\) 0 0
\(146\) −590.000 −0.334443
\(147\) −279.726 198.500i −0.156948 0.111374i
\(148\) 44.0000i 0.0244377i
\(149\) 1147.50 1987.53i 0.630919 1.09278i −0.356446 0.934316i \(-0.616012\pi\)
0.987364 0.158467i \(-0.0506551\pi\)
\(150\) 0 0
\(151\) 554.500 + 960.422i 0.298838 + 0.517603i 0.975870 0.218350i \(-0.0700676\pi\)
−0.677032 + 0.735953i \(0.736734\pi\)
\(152\) −949.164 548.000i −0.506496 0.292425i
\(153\) 1534.00i 0.810566i
\(154\) −700.000 + 1091.19i −0.366283 + 0.570979i
\(155\) 0 0
\(156\) 132.000 228.631i 0.0677465 0.117340i
\(157\) −1350.13 + 779.500i −0.686321 + 0.396248i −0.802232 0.597012i \(-0.796354\pi\)
0.115911 + 0.993260i \(0.463021\pi\)
\(158\) 857.365 495.000i 0.431698 0.249241i
\(159\) 208.500 361.133i 0.103995 0.180124i
\(160\) 0 0
\(161\) 59.5000 + 115.181i 0.0291258 + 0.0563824i
\(162\) 1298.00i 0.629509i
\(163\) 1949.42 + 1125.50i 0.936752 + 0.540834i 0.888941 0.458022i \(-0.151442\pi\)
0.0478115 + 0.998856i \(0.484775\pi\)
\(164\) −996.000 1725.12i −0.474235 0.821399i
\(165\) 0 0
\(166\) 932.000 1614.27i 0.435766 0.754770i
\(167\) 2788.00i 1.29187i −0.763393 0.645934i \(-0.776468\pi\)
0.763393 0.645934i \(-0.223532\pi\)
\(168\) −6.92820 + 148.000i −0.00318168 + 0.0679670i
\(169\) −2159.00 −0.982704
\(170\) 0 0
\(171\) 1781.00 + 3084.78i 0.796471 + 1.37953i
\(172\) −900.666 + 520.000i −0.399274 + 0.230521i
\(173\) −1367.45 789.500i −0.600957 0.346963i 0.168461 0.985708i \(-0.446120\pi\)
−0.769418 + 0.638746i \(0.779454\pi\)
\(174\) −212.000 −0.0923660
\(175\) 0 0
\(176\) 560.000 0.239839
\(177\) 14.7224 + 8.50000i 0.00625201 + 0.00360960i
\(178\) 1512.08 873.000i 0.636715 0.367607i
\(179\) 1225.50 + 2122.63i 0.511722 + 0.886328i 0.999908 + 0.0135883i \(0.00432541\pi\)
−0.488186 + 0.872740i \(0.662341\pi\)
\(180\) 0 0
\(181\) −1170.00 −0.480472 −0.240236 0.970715i \(-0.577225\pi\)
−0.240236 + 0.970715i \(0.577225\pi\)
\(182\) 2171.99 1122.00i 0.884608 0.456968i
\(183\) 51.0000i 0.0206012i
\(184\) 28.0000 48.4974i 0.0112184 0.0194309i
\(185\) 0 0
\(186\) −75.0000 129.904i −0.0295660 0.0512097i
\(187\) 1788.34 + 1032.50i 0.699340 + 0.403764i
\(188\) 684.000i 0.265350i
\(189\) 530.000 826.188i 0.203978 0.317970i
\(190\) 0 0
\(191\) 637.500 1104.18i 0.241507 0.418303i −0.719637 0.694351i \(-0.755692\pi\)
0.961144 + 0.276048i \(0.0890249\pi\)
\(192\) 55.4256 32.0000i 0.0208333 0.0120281i
\(193\) 30.3109 17.5000i 0.0113048 0.00652683i −0.494337 0.869270i \(-0.664589\pi\)
0.505642 + 0.862744i \(0.331256\pi\)
\(194\) 290.000 502.295i 0.107324 0.185890i
\(195\) 0 0
\(196\) −794.000 + 1118.90i −0.289359 + 0.407764i
\(197\) 2734.00i 0.988779i 0.869241 + 0.494389i \(0.164608\pi\)
−0.869241 + 0.494389i \(0.835392\pi\)
\(198\) −1576.17 910.000i −0.565724 0.326621i
\(199\) 1121.50 + 1942.49i 0.399503 + 0.691959i 0.993665 0.112387i \(-0.0358495\pi\)
−0.594162 + 0.804345i \(0.702516\pi\)
\(200\) 0 0
\(201\) 219.500 380.185i 0.0770265 0.133414i
\(202\) 2170.00i 0.755845i
\(203\) −1652.38 1060.00i −0.571301 0.366490i
\(204\) 236.000 0.0809966
\(205\) 0 0
\(206\) 1553.00 + 2689.87i 0.525256 + 0.909769i
\(207\) −157.617 + 91.0000i −0.0529232 + 0.0305553i
\(208\) −914.523 528.000i −0.304859 0.176011i
\(209\) −4795.00 −1.58697
\(210\) 0 0
\(211\) 1172.00 0.382388 0.191194 0.981552i \(-0.438764\pi\)
0.191194 + 0.981552i \(0.438764\pi\)
\(212\) −1444.53 834.000i −0.467975 0.270186i
\(213\) 678.964 392.000i 0.218412 0.126100i
\(214\) −129.000 223.435i −0.0412068 0.0713723i
\(215\) 0 0
\(216\) −424.000 −0.133563
\(217\) 64.9519 1387.50i 0.0203190 0.434054i
\(218\) 1930.00i 0.599615i
\(219\) −147.500 + 255.477i −0.0455120 + 0.0788291i
\(220\) 0 0
\(221\) −1947.00 3372.30i −0.592622 1.02645i
\(222\) 19.0526 + 11.0000i 0.00576002 + 0.00332555i
\(223\) 2024.00i 0.607790i 0.952706 + 0.303895i \(0.0982871\pi\)
−0.952706 + 0.303895i \(0.901713\pi\)
\(224\) 592.000 + 27.7128i 0.176583 + 0.00826625i
\(225\) 0 0
\(226\) −50.0000 + 86.6025i −0.0147166 + 0.0254899i
\(227\) −2226.55 + 1285.50i −0.651019 + 0.375866i −0.788847 0.614590i \(-0.789321\pi\)
0.137827 + 0.990456i \(0.455988\pi\)
\(228\) −474.582 + 274.000i −0.137851 + 0.0795881i
\(229\) 447.500 775.093i 0.129134 0.223666i −0.794207 0.607647i \(-0.792114\pi\)
0.923341 + 0.383980i \(0.125447\pi\)
\(230\) 0 0
\(231\) 297.500 + 575.907i 0.0847362 + 0.164034i
\(232\) 848.000i 0.239974i
\(233\) −1547.59 893.500i −0.435132 0.251224i 0.266398 0.963863i \(-0.414166\pi\)
−0.701531 + 0.712639i \(0.747500\pi\)
\(234\) 1716.00 + 2972.20i 0.479395 + 0.830336i
\(235\) 0 0
\(236\) 34.0000 58.8897i 0.00937801 0.0162432i
\(237\) 495.000i 0.135670i
\(238\) 1839.44 + 1180.00i 0.500979 + 0.321378i
\(239\) 5100.00 1.38030 0.690150 0.723667i \(-0.257545\pi\)
0.690150 + 0.723667i \(0.257545\pi\)
\(240\) 0 0
\(241\) 2088.50 + 3617.39i 0.558225 + 0.966873i 0.997645 + 0.0685917i \(0.0218506\pi\)
−0.439420 + 0.898282i \(0.644816\pi\)
\(242\) −183.597 + 106.000i −0.0487690 + 0.0281568i
\(243\) 1801.33 + 1040.00i 0.475537 + 0.274552i
\(244\) −204.000 −0.0535236
\(245\) 0 0
\(246\) −996.000 −0.258141
\(247\) 7830.60 + 4521.00i 2.01720 + 1.16463i
\(248\) −519.615 + 300.000i −0.133047 + 0.0768146i
\(249\) −466.000 807.136i −0.118601 0.205422i
\(250\) 0 0
\(251\) −4680.00 −1.17689 −0.588444 0.808538i \(-0.700259\pi\)
−0.588444 + 0.808538i \(0.700259\pi\)
\(252\) −1621.20 1040.00i −0.405262 0.259976i
\(253\) 245.000i 0.0608815i
\(254\) −936.000 + 1621.20i −0.231220 + 0.400485i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −1514.68 874.500i −0.367638 0.212256i 0.304788 0.952420i \(-0.401414\pi\)
−0.672426 + 0.740164i \(0.734748\pi\)
\(258\) 520.000i 0.125480i
\(259\) 93.5000 + 180.999i 0.0224317 + 0.0434237i
\(260\) 0 0
\(261\) 1378.00 2386.77i 0.326805 0.566043i
\(262\) −1307.70 + 755.000i −0.308358 + 0.178031i
\(263\) −3873.73 + 2236.50i −0.908230 + 0.524367i −0.879861 0.475231i \(-0.842365\pi\)
−0.0283689 + 0.999598i \(0.509031\pi\)
\(264\) 140.000 242.487i 0.0326379 0.0565305i
\(265\) 0 0
\(266\) −5069.00 237.291i −1.16842 0.0546964i
\(267\) 873.000i 0.200100i
\(268\) −1520.74 878.000i −0.346619 0.200121i
\(269\) 987.500 + 1710.40i 0.223825 + 0.387676i 0.955966 0.293476i \(-0.0948122\pi\)
−0.732141 + 0.681153i \(0.761479\pi\)
\(270\) 0 0
\(271\) 4219.50 7308.39i 0.945817 1.63820i 0.191710 0.981452i \(-0.438597\pi\)
0.754107 0.656751i \(-0.228070\pi\)
\(272\) 944.000i 0.210435i
\(273\) 57.1577 1221.00i 0.0126716 0.270690i
\(274\) −4714.00 −1.03935
\(275\) 0 0
\(276\) −14.0000 24.2487i −0.00305326 0.00528841i
\(277\) −456.395 + 263.500i −0.0989969 + 0.0571559i −0.548681 0.836032i \(-0.684870\pi\)
0.449684 + 0.893188i \(0.351537\pi\)
\(278\) 48.4974 + 28.0000i 0.0104629 + 0.00604075i
\(279\) 1950.00 0.418435
\(280\) 0 0
\(281\) −202.000 −0.0428837 −0.0214418 0.999770i \(-0.506826\pi\)
−0.0214418 + 0.999770i \(0.506826\pi\)
\(282\) −296.181 171.000i −0.0625436 0.0361096i
\(283\) −6884.04 + 3974.50i −1.44598 + 0.834839i −0.998239 0.0593220i \(-0.981106\pi\)
−0.447745 + 0.894161i \(0.647773\pi\)
\(284\) −1568.00 2715.86i −0.327619 0.567452i
\(285\) 0 0
\(286\) −4620.00 −0.955197
\(287\) −7763.05 4980.00i −1.59665 1.02425i
\(288\) 832.000i 0.170229i
\(289\) −716.000 + 1240.15i −0.145736 + 0.252422i
\(290\) 0 0
\(291\) −145.000 251.147i −0.0292098 0.0505929i
\(292\) 1021.91 + 590.000i 0.204804 + 0.118244i
\(293\) 318.000i 0.0634053i 0.999497 + 0.0317027i \(0.0100930\pi\)
−0.999497 + 0.0317027i \(0.989907\pi\)
\(294\) 286.000 + 623.538i 0.0567342 + 0.123692i
\(295\) 0 0
\(296\) 44.0000 76.2102i 0.00864003 0.0149650i
\(297\) −1606.48 + 927.500i −0.313863 + 0.181209i
\(298\) −3975.06 + 2295.00i −0.772714 + 0.446127i
\(299\) −231.000 + 400.104i −0.0446792 + 0.0773866i
\(300\) 0 0
\(301\) −2600.00 + 4053.00i −0.497879 + 0.776116i
\(302\) 2218.00i 0.422621i
\(303\) −939.638 542.500i −0.178154 0.102857i
\(304\) 1096.00 + 1898.33i 0.206776 + 0.358147i
\(305\) 0 0
\(306\) −1534.00 + 2656.97i −0.286578 + 0.496368i
\(307\) 8132.00i 1.51178i 0.654696 + 0.755892i \(0.272797\pi\)
−0.654696 + 0.755892i \(0.727203\pi\)
\(308\) 2303.63 1190.00i 0.426173 0.220151i
\(309\) 1553.00 0.285913
\(310\) 0 0
\(311\) 464.500 + 804.538i 0.0846925 + 0.146692i 0.905260 0.424858i \(-0.139676\pi\)
−0.820568 + 0.571549i \(0.806343\pi\)
\(312\) −457.261 + 264.000i −0.0829722 + 0.0479040i
\(313\) 180.999 + 104.500i 0.0326859 + 0.0188712i 0.516254 0.856436i \(-0.327326\pi\)
−0.483568 + 0.875307i \(0.660659\pi\)
\(314\) 3118.00 0.560379
\(315\) 0 0
\(316\) −1980.00 −0.352480
\(317\) 6175.63 + 3565.50i 1.09419 + 0.631730i 0.934689 0.355468i \(-0.115678\pi\)
0.159500 + 0.987198i \(0.449012\pi\)
\(318\) −722.265 + 417.000i −0.127367 + 0.0735352i
\(319\) 1855.00 + 3212.95i 0.325580 + 0.563921i
\(320\) 0 0
\(321\) −129.000 −0.0224301
\(322\) 12.1244 259.000i 0.00209834 0.0448246i
\(323\) 8083.00i 1.39242i
\(324\) 1298.00 2248.20i 0.222565 0.385494i
\(325\) 0 0
\(326\) −2251.00 3898.85i −0.382427 0.662384i
\(327\) 835.715 + 482.500i 0.141331 + 0.0815973i
\(328\) 3984.00i 0.670670i
\(329\) −1453.50 2813.72i −0.243569 0.471505i
\(330\) 0 0
\(331\) 3285.50 5690.65i 0.545581 0.944975i −0.452989 0.891516i \(-0.649642\pi\)
0.998570 0.0534583i \(-0.0170244\pi\)
\(332\) −3228.54 + 1864.00i −0.533703 + 0.308133i
\(333\) −247.683 + 143.000i −0.0407596 + 0.0235326i
\(334\) −2788.00 + 4828.96i −0.456744 + 0.791104i
\(335\) 0 0
\(336\) 160.000 249.415i 0.0259783 0.0404962i
\(337\) 11466.0i 1.85339i 0.375813 + 0.926696i \(0.377364\pi\)
−0.375813 + 0.926696i \(0.622636\pi\)
\(338\) 3739.50 + 2159.00i 0.601781 + 0.347438i
\(339\) 25.0000 + 43.3013i 0.00400535 + 0.00693747i
\(340\) 0 0
\(341\) −1312.50 + 2273.32i −0.208434 + 0.361018i
\(342\) 7124.00i 1.12638i
\(343\) −888.542 + 6290.00i −0.139874 + 0.990169i
\(344\) 2080.00 0.326006
\(345\) 0 0
\(346\) 1579.00 + 2734.91i 0.245340 + 0.424941i
\(347\) 8467.13 4888.50i 1.30991 0.756278i 0.327831 0.944737i \(-0.393682\pi\)
0.982081 + 0.188459i \(0.0603491\pi\)
\(348\) 367.195 + 212.000i 0.0565624 + 0.0326563i
\(349\) −11914.0 −1.82734 −0.913670 0.406456i \(-0.866764\pi\)
−0.913670 + 0.406456i \(0.866764\pi\)
\(350\) 0 0
\(351\) 3498.00 0.531936
\(352\) −969.948 560.000i −0.146871 0.0847957i
\(353\) 7900.75 4561.50i 1.19126 0.687774i 0.232667 0.972556i \(-0.425255\pi\)
0.958592 + 0.284783i \(0.0919214\pi\)
\(354\) −17.0000 29.4449i −0.00255237 0.00442084i
\(355\) 0 0
\(356\) −3492.00 −0.519875
\(357\) 970.814 501.500i 0.143924 0.0743479i
\(358\) 4902.00i 0.723684i
\(359\) 4074.50 7057.24i 0.599008 1.03751i −0.393960 0.919128i \(-0.628895\pi\)
0.992968 0.118385i \(-0.0377716\pi\)
\(360\) 0 0
\(361\) −5955.00 10314.4i −0.868202 1.50377i
\(362\) 2026.50 + 1170.00i 0.294228 + 0.169872i
\(363\) 106.000i 0.0153266i
\(364\) −4884.00 228.631i −0.703272 0.0329217i
\(365\) 0 0
\(366\) −51.0000 + 88.3346i −0.00728364 + 0.0126156i
\(367\) −8375.33 + 4835.50i −1.19125 + 0.687769i −0.958590 0.284790i \(-0.908076\pi\)
−0.232660 + 0.972558i \(0.574743\pi\)
\(368\) −96.9948 + 56.0000i −0.0137397 + 0.00793261i
\(369\) 6474.00 11213.3i 0.913341 1.58195i
\(370\) 0 0
\(371\) −7714.50 361.133i −1.07956 0.0505366i
\(372\) 300.000i 0.0418126i
\(373\) 3558.50 + 2054.50i 0.493973 + 0.285196i 0.726221 0.687461i \(-0.241275\pi\)
−0.232248 + 0.972657i \(0.574608\pi\)
\(374\) −2065.00 3576.68i −0.285504 0.494508i
\(375\) 0 0
\(376\) −684.000 + 1184.72i −0.0938154 + 0.162493i
\(377\) 6996.00i 0.955736i
\(378\) −1744.18 + 901.000i −0.237330 + 0.122599i
\(379\) 3488.00 0.472735 0.236367 0.971664i \(-0.424043\pi\)
0.236367 + 0.971664i \(0.424043\pi\)
\(380\) 0 0
\(381\) 468.000 + 810.600i 0.0629301 + 0.108998i
\(382\) −2208.36 + 1275.00i −0.295785 + 0.170771i
\(383\) −7549.14 4358.50i −1.00716 0.581485i −0.0968028 0.995304i \(-0.530862\pi\)
−0.910360 + 0.413818i \(0.864195\pi\)
\(384\) −128.000 −0.0170103
\(385\) 0 0
\(386\) −70.0000 −0.00923033
\(387\) −5854.33 3380.00i −0.768973 0.443967i
\(388\) −1004.59 + 580.000i −0.131444 + 0.0758893i
\(389\) 81.5000 + 141.162i 0.0106227 + 0.0183990i 0.871288 0.490772i \(-0.163285\pi\)
−0.860665 + 0.509171i \(0.829952\pi\)
\(390\) 0 0
\(391\) −413.000 −0.0534177
\(392\) 2494.15 1144.00i 0.321362 0.147400i
\(393\) 755.000i 0.0969077i
\(394\) 2734.00 4735.43i 0.349586 0.605501i
\(395\) 0 0
\(396\) 1820.00 + 3152.33i 0.230956 + 0.400027i
\(397\) 865.159 + 499.500i 0.109373 + 0.0631466i 0.553689 0.832724i \(-0.313220\pi\)
−0.444316 + 0.895870i \(0.646553\pi\)
\(398\) 4486.00i 0.564982i
\(399\) −1370.00 + 2135.62i −0.171894 + 0.267957i
\(400\) 0 0
\(401\) 7378.50 12779.9i 0.918865 1.59152i 0.117722 0.993047i \(-0.462441\pi\)
0.801143 0.598474i \(-0.204226\pi\)
\(402\) −760.370 + 439.000i −0.0943379 + 0.0544660i
\(403\) 4286.83 2475.00i 0.529881 0.305927i
\(404\) −2170.00 + 3758.55i −0.267232 + 0.462859i
\(405\) 0 0
\(406\) 1802.00 + 3488.35i 0.220275 + 0.426414i
\(407\) 385.000i 0.0468888i
\(408\) −408.764 236.000i −0.0496001 0.0286366i
\(409\) −66.5000 115.181i −0.00803964 0.0139251i 0.861978 0.506946i \(-0.169226\pi\)
−0.870017 + 0.493021i \(0.835892\pi\)
\(410\) 0 0
\(411\) −1178.50 + 2041.22i −0.141438 + 0.244978i
\(412\) 6212.00i 0.742823i
\(413\) 14.7224 314.500i 0.00175410 0.0374710i
\(414\) 364.000 0.0432117
\(415\) 0 0
\(416\) 1056.00 + 1829.05i 0.124458 + 0.215568i
\(417\) 24.2487 14.0000i 0.00284764 0.00164408i
\(418\) 8305.18 + 4795.00i 0.971818 + 0.561079i
\(419\) 6420.00 0.748538 0.374269 0.927320i \(-0.377894\pi\)
0.374269 + 0.927320i \(0.377894\pi\)
\(420\) 0 0
\(421\) 10266.0 1.18844 0.594221 0.804302i \(-0.297460\pi\)
0.594221 + 0.804302i \(0.297460\pi\)
\(422\) −2029.96 1172.00i −0.234164 0.135194i
\(423\) 3850.35 2223.00i 0.442578 0.255522i
\(424\) 1668.00 + 2889.06i 0.191050 + 0.330908i
\(425\) 0 0
\(426\) −1568.00 −0.178333
\(427\) −839.179 + 433.500i −0.0951070 + 0.0491301i
\(428\) 516.000i 0.0582752i
\(429\) −1155.00 + 2000.52i −0.129986 + 0.225142i
\(430\) 0 0
\(431\) 7606.50 + 13174.8i 0.850098 + 1.47241i 0.881119 + 0.472894i \(0.156791\pi\)
−0.0310213 + 0.999519i \(0.509876\pi\)
\(432\) 734.390 + 424.000i 0.0817901 + 0.0472215i
\(433\) 1378.00i 0.152939i −0.997072 0.0764693i \(-0.975635\pi\)
0.997072 0.0764693i \(-0.0243647\pi\)
\(434\) −1500.00 + 2338.27i −0.165904 + 0.258619i
\(435\) 0 0
\(436\) 1930.00 3342.86i 0.211996 0.367188i
\(437\) 830.518 479.500i 0.0909132 0.0524888i
\(438\) 510.955 295.000i 0.0557406 0.0321818i
\(439\) −1381.50 + 2392.83i −0.150195 + 0.260145i −0.931299 0.364256i \(-0.881323\pi\)
0.781104 + 0.624401i \(0.214657\pi\)
\(440\) 0 0
\(441\) −8879.00 833.116i −0.958752 0.0899597i
\(442\) 7788.00i 0.838094i
\(443\) −5065.38 2924.50i −0.543259 0.313651i 0.203140 0.979150i \(-0.434885\pi\)
−0.746399 + 0.665499i \(0.768219\pi\)
\(444\) −22.0000 38.1051i −0.00235152 0.00407295i
\(445\) 0 0
\(446\) 2024.00 3505.67i 0.214886 0.372194i
\(447\) 2295.00i 0.242841i
\(448\) −997.661 640.000i −0.105212 0.0674937i
\(449\) −4582.00 −0.481599 −0.240799 0.970575i \(-0.577410\pi\)
−0.240799 + 0.970575i \(0.577410\pi\)
\(450\) 0 0
\(451\) 8715.00 + 15094.8i 0.909919 + 1.57603i
\(452\) 173.205 100.000i 0.0180241 0.0104062i
\(453\) −960.422 554.500i −0.0996127 0.0575114i
\(454\) 5142.00 0.531555
\(455\) 0 0
\(456\) 1096.00 0.112555
\(457\) 10003.5 + 5775.50i 1.02394 + 0.591174i 0.915244 0.402901i \(-0.131998\pi\)
0.108700 + 0.994075i \(0.465331\pi\)
\(458\) −1550.19 + 895.000i −0.158156 + 0.0913114i
\(459\) 1563.50 + 2708.06i 0.158993 + 0.275384i
\(460\) 0 0
\(461\) −9494.00 −0.959175 −0.479587 0.877494i \(-0.659214\pi\)
−0.479587 + 0.877494i \(0.659214\pi\)
\(462\) 60.6218 1295.00i 0.00610472 0.130409i
\(463\) 10160.0i 1.01982i −0.860229 0.509908i \(-0.829679\pi\)
0.860229 0.509908i \(-0.170321\pi\)
\(464\) 848.000 1468.78i 0.0848436 0.146953i
\(465\) 0 0
\(466\) 1787.00 + 3095.17i 0.177642 + 0.307685i
\(467\) −1131.90 653.500i −0.112158 0.0647545i 0.442872 0.896585i \(-0.353960\pi\)
−0.555030 + 0.831831i \(0.687293\pi\)
\(468\) 6864.00i 0.677967i
\(469\) −8121.50 380.185i −0.799608 0.0374314i
\(470\) 0 0
\(471\) 779.500 1350.13i 0.0762579 0.132083i
\(472\) −117.779 + 68.0000i −0.0114857 + 0.00663126i
\(473\) 7880.83 4550.00i 0.766091 0.442303i
\(474\) −495.000 + 857.365i −0.0479665 + 0.0830803i
\(475\) 0 0
\(476\) −2006.00 3883.26i −0.193161 0.373926i
\(477\) 10842.0i 1.04072i
\(478\) −8833.46 5100.00i −0.845257 0.488010i
\(479\) 9143.50 + 15837.0i 0.872186 + 1.51067i 0.859730 + 0.510748i \(0.170632\pi\)
0.0124559 + 0.999922i \(0.496035\pi\)
\(480\) 0 0
\(481\) −363.000 + 628.734i −0.0344103 + 0.0596005i
\(482\) 8354.00i 0.789449i
\(483\) −109.119 70.0000i −0.0102797 0.00659443i
\(484\) 424.000 0.0398197
\(485\) 0 0
\(486\) −2080.00 3602.67i −0.194137 0.336256i
\(487\) 12949.7 7476.50i 1.20494 0.695673i 0.243291 0.969953i \(-0.421773\pi\)
0.961650 + 0.274281i \(0.0884398\pi\)
\(488\) 353.338 + 204.000i 0.0327764 + 0.0189235i
\(489\) −2251.00 −0.208167
\(490\) 0 0
\(491\) 14352.0 1.31914 0.659569 0.751644i \(-0.270739\pi\)
0.659569 + 0.751644i \(0.270739\pi\)
\(492\) 1725.12 + 996.000i 0.158078 + 0.0912666i
\(493\) 5416.12 3127.00i 0.494787 0.285665i
\(494\) −9042.00 15661.2i −0.823520 1.42638i
\(495\) 0 0
\(496\) 1200.00 0.108632
\(497\) −12221.4 7840.00i −1.10302 0.707590i
\(498\) 1864.00i 0.167727i
\(499\) −2765.50 + 4789.99i −0.248098 + 0.429718i −0.962998 0.269509i \(-0.913139\pi\)
0.714900 + 0.699226i \(0.246472\pi\)
\(500\) 0 0
\(501\) 1394.00 + 2414.48i 0.124310 + 0.215311i
\(502\) 8106.00 + 4680.00i 0.720694 + 0.416093i
\(503\) 8400.00i 0.744607i 0.928111 + 0.372304i \(0.121432\pi\)
−0.928111 + 0.372304i \(0.878568\pi\)
\(504\) 1768.00 + 3422.53i 0.156256 + 0.302484i
\(505\) 0 0
\(506\) −245.000 + 424.352i −0.0215249 + 0.0372821i
\(507\) 1869.75 1079.50i 0.163784 0.0945607i
\(508\) 3242.40 1872.00i 0.283185 0.163497i
\(509\) −1192.50 + 2065.47i −0.103844 + 0.179863i −0.913265 0.407365i \(-0.866448\pi\)
0.809421 + 0.587228i \(0.199781\pi\)
\(510\) 0 0
\(511\) 5457.50 + 255.477i 0.472457 + 0.0221167i
\(512\) 512.000i 0.0441942i
\(513\) −6288.21 3630.50i −0.541192 0.312457i
\(514\) 1749.00 + 3029.36i 0.150088 + 0.259960i
\(515\) 0 0
\(516\) 520.000 900.666i 0.0443638 0.0768404i
\(517\) 5985.00i 0.509130i
\(518\) 19.0526 407.000i 0.00161606 0.0345223i
\(519\) 1579.00 0.133546
\(520\) 0 0
\(521\) 4576.50 + 7926.73i 0.384837 + 0.666557i 0.991747 0.128214i \(-0.0409243\pi\)
−0.606910 + 0.794771i \(0.707591\pi\)
\(522\) −4773.53 + 2756.00i −0.400253 + 0.231086i
\(523\) 11957.2 + 6903.50i 0.999718 + 0.577187i 0.908165 0.418613i \(-0.137484\pi\)
0.0915530 + 0.995800i \(0.470817\pi\)
\(524\) 3020.00 0.251773
\(525\) 0 0
\(526\) 8946.00 0.741567
\(527\) 3832.16 + 2212.50i 0.316758 + 0.182880i
\(528\) −484.974 + 280.000i −0.0399731 + 0.0230785i
\(529\) −6059.00 10494.5i −0.497986 0.862538i
\(530\) 0 0
\(531\) 442.000 0.0361227
\(532\) 8542.47 + 5480.00i 0.696172 + 0.446594i
\(533\) 32868.0i 2.67105i
\(534\) −873.000 + 1512.08i −0.0707461 + 0.122536i
\(535\) 0 0
\(536\) 1756.00 + 3041.48i 0.141507 + 0.245097i
\(537\) −2122.63 1225.50i −0.170574 0.0984809i
\(538\) 3950.00i 0.316536i
\(539\) 6947.50 9790.42i 0.555195 0.782381i
\(540\) 0 0
\(541\) −4087.50 + 7079.76i −0.324834 + 0.562629i −0.981479 0.191571i \(-0.938642\pi\)
0.656645 + 0.754200i \(0.271975\pi\)
\(542\) −14616.8 + 8439.00i −1.15838 + 0.668794i
\(543\) 1013.25 585.000i 0.0800787 0.0462334i
\(544\) −944.000 + 1635.06i −0.0744001 + 0.128865i
\(545\) 0 0
\(546\) −1320.00 + 2057.68i −0.103463 + 0.161283i
\(547\) 4656.00i 0.363942i −0.983304 0.181971i \(-0.941752\pi\)
0.983304 0.181971i \(-0.0582477\pi\)
\(548\) 8164.89 + 4714.00i 0.636472 + 0.367467i
\(549\) −663.000 1148.35i −0.0515413 0.0892721i
\(550\) 0 0
\(551\) −7261.00 + 12576.4i −0.561396 + 0.972366i
\(552\) 56.0000i 0.00431797i
\(553\) −8144.97 + 4207.50i −0.626328 + 0.323546i
\(554\) 1054.00 0.0808306
\(555\) 0 0
\(556\) −56.0000 96.9948i −0.00427146 0.00739838i
\(557\) −6064.78 + 3501.50i −0.461352 + 0.266361i −0.712612 0.701558i \(-0.752488\pi\)
0.251261 + 0.967919i \(0.419155\pi\)
\(558\) −3377.50 1950.00i −0.256238 0.147939i
\(559\) −17160.0 −1.29837
\(560\) 0 0
\(561\) −2065.00 −0.155409
\(562\) 349.874 + 202.000i 0.0262608 + 0.0151617i
\(563\) −17106.6 + 9876.50i −1.28056 + 0.739334i −0.976951 0.213462i \(-0.931526\pi\)
−0.303612 + 0.952796i \(0.598193\pi\)
\(564\) 342.000 + 592.361i 0.0255333 + 0.0442250i
\(565\) 0 0
\(566\) 15898.0 1.18064
\(567\) 562.050 12006.5i 0.0416295 0.889287i
\(568\) 6272.00i 0.463323i
\(569\) −3448.50 + 5972.98i −0.254075 + 0.440071i −0.964644 0.263557i \(-0.915104\pi\)
0.710569 + 0.703628i \(0.248438\pi\)
\(570\) 0 0
\(571\) −12457.5 21577.0i −0.913013 1.58138i −0.809785 0.586726i \(-0.800416\pi\)
−0.103227 0.994658i \(-0.532917\pi\)
\(572\) 8002.07 + 4620.00i 0.584936 + 0.337713i
\(573\) 1275.00i 0.0929562i
\(574\) 8466.00 + 16388.7i 0.615617 + 1.19172i
\(575\) 0 0
\(576\) 832.000 1441.07i 0.0601852 0.104244i
\(577\) −109.985 + 63.5000i −0.00793543 + 0.00458152i −0.503962 0.863726i \(-0.668125\pi\)
0.496027 + 0.868307i \(0.334792\pi\)
\(578\) 2480.30 1432.00i 0.178489 0.103051i
\(579\) −17.5000 + 30.3109i −0.00125609 + 0.00217561i
\(580\) 0 0
\(581\) −9320.00 + 14528.4i −0.665506 + 1.03742i
\(582\) 580.000i 0.0413089i
\(583\) 12639.6 + 7297.50i 0.897908 + 0.518407i
\(584\) −1180.00 2043.82i −0.0836109 0.144818i
\(585\) 0 0
\(586\) 318.000 550.792i 0.0224172 0.0388277i
\(587\) 9044.00i 0.635921i −0.948104 0.317961i \(-0.897002\pi\)
0.948104 0.317961i \(-0.102998\pi\)
\(588\) 128.172 1366.00i 0.00898931 0.0958042i
\(589\) −10275.0 −0.718801
\(590\) 0 0
\(591\) −1367.00 2367.71i −0.0951453 0.164796i
\(592\) −152.420 + 88.0000i −0.0105818 + 0.00610942i
\(593\) 9267.34 + 5350.50i 0.641760 + 0.370521i 0.785292 0.619125i \(-0.212513\pi\)
−0.143532 + 0.989646i \(0.545846\pi\)
\(594\) 3710.00 0.256268
\(595\) 0 0
\(596\) 9180.00 0.630919
\(597\) −1942.49 1121.50i −0.133168 0.0768843i
\(598\) 800.207 462.000i 0.0547206 0.0315930i
\(599\) 10399.5 + 18012.5i 0.709369 + 1.22866i 0.965091 + 0.261913i \(0.0843533\pi\)
−0.255722 + 0.966750i \(0.582313\pi\)
\(600\) 0 0
\(601\) −1402.00 −0.0951560 −0.0475780 0.998868i \(-0.515150\pi\)
−0.0475780 + 0.998868i \(0.515150\pi\)
\(602\) 8556.33 4420.00i 0.579286 0.299245i
\(603\) 11414.0i 0.770836i
\(604\) −2218.00 + 3841.69i −0.149419 + 0.258801i
\(605\) 0 0
\(606\) 1085.00 + 1879.28i 0.0727312 + 0.125974i
\(607\) 5650.82 + 3262.50i 0.377858 + 0.218156i 0.676886 0.736088i \(-0.263329\pi\)
−0.299028 + 0.954244i \(0.596662\pi\)
\(608\) 4384.00i 0.292425i
\(609\) 1961.00 + 91.7987i 0.130482 + 0.00610816i
\(610\) 0 0
\(611\) 5643.00 9773.96i 0.373636 0.647156i
\(612\) 5313.93 3068.00i 0.350985 0.202641i
\(613\) 13034.5 7525.50i 0.858826 0.495844i −0.00479285 0.999989i \(-0.501526\pi\)
0.863619 + 0.504145i \(0.168192\pi\)
\(614\) 8132.00 14085.0i 0.534496 0.925775i
\(615\) 0 0
\(616\) −5180.00 242.487i −0.338812 0.0158605i
\(617\) 11150.0i 0.727524i −0.931492 0.363762i \(-0.881492\pi\)
0.931492 0.363762i \(-0.118508\pi\)
\(618\) −2689.87 1553.00i −0.175085 0.101085i
\(619\) 1707.50 + 2957.48i 0.110873 + 0.192037i 0.916122 0.400899i \(-0.131302\pi\)
−0.805250 + 0.592936i \(0.797969\pi\)
\(620\) 0 0
\(621\) 185.500 321.295i 0.0119869 0.0207619i
\(622\) 1858.00i 0.119773i
\(623\) −14364.8 + 7420.50i −0.923775 + 0.477201i
\(624\) 1056.00 0.0677465
\(625\) 0 0
\(626\) −209.000 361.999i −0.0133440 0.0231124i
\(627\) 4152.59 2397.50i 0.264495 0.152706i
\(628\) −5400.53 3118.00i −0.343160 0.198124i
\(629\) −649.000 −0.0411404
\(630\) 0 0
\(631\) −21184.0 −1.33648 −0.668242 0.743944i \(-0.732953\pi\)
−0.668242 + 0.743944i \(0.732953\pi\)
\(632\) 3429.46 + 1980.00i 0.215849 + 0.124621i
\(633\) −1014.98 + 586.000i −0.0637313 + 0.0367953i
\(634\) −7131.00 12351.3i −0.446701 0.773708i
\(635\) 0 0
\(636\) 1668.00 0.103995
\(637\) −20576.8 + 9438.00i −1.27988 + 0.587044i
\(638\) 7420.00i 0.460440i
\(639\) 10192.0 17653.1i 0.630969 1.09287i
\(640\) 0 0
\(641\) 5352.50 + 9270.80i 0.329814 + 0.571255i 0.982475 0.186395i \(-0.0596805\pi\)
−0.652660 + 0.757651i \(0.726347\pi\)
\(642\) 223.435 + 129.000i 0.0137356 + 0.00793026i
\(643\) 6860.00i 0.420734i 0.977622 + 0.210367i \(0.0674659\pi\)
−0.977622 + 0.210367i \(0.932534\pi\)
\(644\) −280.000 + 436.477i −0.0171328 + 0.0267074i
\(645\) 0 0
\(646\) 8083.00 14000.2i 0.492293 0.852677i
\(647\) −12525.3 + 7231.50i −0.761084 + 0.439412i −0.829685 0.558232i \(-0.811480\pi\)
0.0686008 + 0.997644i \(0.478147\pi\)
\(648\) −4496.40 + 2596.00i −0.272586 + 0.157377i
\(649\) −297.500 + 515.285i −0.0179937 + 0.0311660i
\(650\) 0 0
\(651\) 637.500 + 1234.09i 0.0383803 + 0.0742975i
\(652\) 9004.00i 0.540834i
\(653\) −5177.97 2989.50i −0.310305 0.179155i 0.336758 0.941591i \(-0.390670\pi\)
−0.647063 + 0.762436i \(0.724003\pi\)
\(654\) −965.000 1671.43i −0.0576980 0.0999359i
\(655\) 0 0
\(656\) 3984.00 6900.49i 0.237117 0.410700i
\(657\) 7670.00i 0.455457i
\(658\) −296.181 + 6327.00i −0.0175476 + 0.374851i
\(659\) 6940.00 0.410234 0.205117 0.978737i \(-0.434243\pi\)
0.205117 + 0.978737i \(0.434243\pi\)
\(660\) 0 0
\(661\) −6699.50 11603.9i −0.394221 0.682812i 0.598780 0.800914i \(-0.295652\pi\)
−0.993001 + 0.118102i \(0.962319\pi\)
\(662\) −11381.3 + 6571.00i −0.668198 + 0.385784i
\(663\) 3372.30 + 1947.00i 0.197541 + 0.114050i
\(664\) 7456.00 0.435766
\(665\) 0 0
\(666\) 572.000 0.0332801
\(667\) −642.591 371.000i −0.0373032 0.0215370i
\(668\) 9657.92 5576.00i 0.559395 0.322967i
\(669\) −1012.00 1752.84i −0.0584846 0.101298i
\(670\) 0 0
\(671\) 1785.00 0.102696
\(672\) −526.543 + 272.000i −0.0302260 + 0.0156140i
\(673\) 29510.0i 1.69023i 0.534582 + 0.845117i \(0.320469\pi\)
−0.534582 + 0.845117i \(0.679531\pi\)
\(674\) 11466.0 19859.7i 0.655273 1.13497i
\(675\) 0 0
\(676\) −4318.00 7479.00i −0.245676 0.425523i
\(677\) −22517.5 13000.5i −1.27831 0.738035i −0.301776 0.953379i \(-0.597579\pi\)
−0.976538 + 0.215344i \(0.930913\pi\)
\(678\) 100.000i 0.00566442i
\(679\) −2900.00 + 4520.65i −0.163905 + 0.255503i
\(680\) 0 0
\(681\) 1285.50 2226.55i 0.0723355 0.125289i
\(682\) 4546.63 2625.00i 0.255278 0.147385i
\(683\) −7625.35 + 4402.50i −0.427198 + 0.246643i −0.698152 0.715949i \(-0.745994\pi\)
0.270954 + 0.962592i \(0.412661\pi\)
\(684\) −7124.00 + 12339.1i −0.398235 + 0.689764i
\(685\) 0 0
\(686\) 7829.00 10006.1i 0.435733 0.556899i
\(687\) 895.000i 0.0497036i
\(688\) −3602.67 2080.00i −0.199637 0.115261i
\(689\) −13761.0 23834.8i −0.760889 1.31790i
\(690\) 0 0
\(691\) −14342.5 + 24841.9i −0.789601 + 1.36763i 0.136610 + 0.990625i \(0.456379\pi\)
−0.926211 + 0.377004i \(0.876954\pi\)
\(692\) 6316.00i 0.346963i
\(693\) 14185.5 + 9100.00i 0.777579 + 0.498817i
\(694\) −19554.0 −1.06954
\(695\) 0 0
\(696\) −424.000 734.390i −0.0230915 0.0399956i
\(697\) 25445.6 14691.0i 1.38281 0.798366i
\(698\) 20635.7 + 11914.0i 1.11901 + 0.646062i
\(699\) 1787.00 0.0966961
\(700\) 0 0
\(701\) −3146.00 −0.169505 −0.0847523 0.996402i \(-0.527010\pi\)
−0.0847523 + 0.996402i \(0.527010\pi\)
\(702\) −6058.71 3498.00i −0.325743 0.188068i
\(703\) 1305.10 753.500i 0.0700182 0.0404250i
\(704\) 1120.00 + 1939.90i 0.0599596 + 0.103853i
\(705\) 0 0
\(706\) −18246.0 −0.972659
\(707\) −939.638 + 20072.5i −0.0499840 + 1.06776i
\(708\) 68.0000i 0.00360960i
\(709\) 629.500 1090.33i 0.0333447 0.0577547i −0.848871 0.528599i \(-0.822717\pi\)
0.882216 + 0.470845i \(0.156051\pi\)
\(710\) 0 0
\(711\) −6435.00 11145.7i −0.339425 0.587902i
\(712\) 6048.32 + 3492.00i 0.318357 + 0.183804i
\(713\) 525.000i 0.0275756i
\(714\) −2183.00 102.191i −0.114421 0.00535631i
\(715\) 0 0
\(716\) −4902.00 + 8490.51i −0.255861 + 0.443164i
\(717\) −4416.73 + 2550.00i −0.230050 + 0.132819i
\(718\) −14114.5 + 8149.00i −0.733632 + 0.423563i
\(719\) 8212.50 14224.5i 0.425973 0.737807i −0.570538 0.821271i \(-0.693265\pi\)
0.996511 + 0.0834645i \(0.0265985\pi\)
\(720\) 0 0
\(721\) −13200.5 25553.8i −0.681848 1.31994i
\(722\) 23820.0i 1.22782i
\(723\) −3617.39 2088.50i −0.186075 0.107430i
\(724\) −2340.00 4053.00i −0.120118 0.208050i
\(725\) 0 0
\(726\) 106.000 183.597i 0.00541877 0.00938559i
\(727\) 6032.00i 0.307723i 0.988092 + 0.153861i \(0.0491709\pi\)
−0.988092 + 0.153861i \(0.950829\pi\)
\(728\) 8230.71 + 5280.00i 0.419025 + 0.268805i
\(729\) 15443.0 0.784586
\(730\) 0 0
\(731\) −7670.00 13284.8i −0.388078 0.672171i
\(732\) 176.669 102.000i 0.00892060 0.00515031i
\(733\) −13200.8 7621.50i −0.665189 0.384047i 0.129062 0.991636i \(-0.458803\pi\)
−0.794251 + 0.607589i \(0.792137\pi\)
\(734\) 19342.0 0.972652
\(735\) 0 0
\(736\) 224.000 0.0112184
\(737\) 13306.5 + 7682.50i 0.665062 + 0.383974i
\(738\) −22426.6 + 12948.0i −1.11861 + 0.645830i
\(739\) −5026.50 8706.15i −0.250207 0.433371i 0.713376 0.700782i \(-0.247165\pi\)
−0.963583 + 0.267411i \(0.913832\pi\)
\(740\) 0 0
\(741\) −9042.00 −0.448267
\(742\) 13000.8 + 8340.00i 0.643226 + 0.412629i
\(743\) 24384.0i 1.20399i 0.798501 + 0.601993i \(0.205627\pi\)
−0.798501 + 0.601993i \(0.794373\pi\)
\(744\) 300.000 519.615i 0.0147830 0.0256049i
\(745\) 0 0
\(746\) −4109.00 7117.00i −0.201664 0.349292i
\(747\) −20985.5 12116.0i −1.02787 0.593442i
\(748\) 8260.00i 0.403764i
\(749\) 1096.50 + 2122.63i 0.0534916 + 0.103550i
\(750\) 0 0
\(751\) −5794.50 + 10036.4i −0.281550 + 0.487660i −0.971767 0.235943i \(-0.924182\pi\)
0.690216 + 0.723603i \(0.257515\pi\)
\(752\) 2369.45 1368.00i 0.114900 0.0663375i
\(753\) 4053.00 2340.00i 0.196148 0.113246i
\(754\) −6996.00 + 12117.4i −0.337904 + 0.585266i
\(755\) 0 0
\(756\) 3922.00 + 183.597i 0.188680 + 0.00883250i
\(757\) 14562.0i 0.699161i −0.936906 0.349581i \(-0.886324\pi\)
0.936906 0.349581i \(-0.113676\pi\)
\(758\) −6041.39 3488.00i −0.289490 0.167137i
\(759\) 122.500 + 212.176i 0.00585832 + 0.0101469i
\(760\) 0 0
\(761\) 11382.5 19715.1i 0.542201 0.939120i −0.456576 0.889684i \(-0.650924\pi\)
0.998777 0.0494360i \(-0.0157424\pi\)
\(762\) 1872.00i 0.0889966i
\(763\) 835.715 17852.5i 0.0396526 0.847056i
\(764\) 5100.00 0.241507
\(765\) 0 0
\(766\) 8717.00 + 15098.3i 0.411172 + 0.712171i
\(767\) 971.681 561.000i 0.0457436 0.0264101i
\(768\) 221.703 + 128.000i 0.0104167 + 0.00601407i
\(769\) −3766.00 −0.176600 −0.0883000 0.996094i \(-0.528143\pi\)
−0.0883000 + 0.996094i \(0.528143\pi\)
\(770\) 0 0
\(771\) 1749.00 0.0816974
\(772\) 121.244 + 70.0000i 0.00565240 + 0.00326341i
\(773\) −23262.3 + 13430.5i −1.08239 + 0.624918i −0.931540 0.363639i \(-0.881534\pi\)
−0.150849 + 0.988557i \(0.548201\pi\)
\(774\) 6760.00 + 11708.7i 0.313932 + 0.543746i
\(775\) 0 0
\(776\) 2320.00 0.107324
\(777\) −171.473 110.000i −0.00791707 0.00507880i
\(778\) 326.000i 0.0150227i
\(779\) −34113.0 + 59085.4i −1.56897 + 2.71753i
\(780\) 0 0
\(781\) 13720.0 + 23763.7i 0.628605 + 1.08878i
\(782\) 715.337 + 413.000i 0.0327115 + 0.0188860i
\(783\) 5618.00i 0.256412i
\(784\) −5464.00 512.687i −0.248907 0.0233549i
\(785\) 0 0
\(786\) 755.000 1307.70i 0.0342620 0.0593436i
\(787\) 1816.06 1048.50i 0.0822559 0.0474905i −0.458308 0.888793i \(-0.651544\pi\)
0.540564 + 0.841303i \(0.318211\pi\)
\(788\) −9470.85 + 5468.00i −0.428154 + 0.247195i
\(789\) 2236.50 3873.73i 0.100914 0.174789i
\(790\) 0 0
\(791\) 500.000 779.423i 0.0224753 0.0350355i
\(792\) 7280.00i 0.326621i
\(793\) −2915.04 1683.00i −0.130537 0.0753658i
\(794\) −999.000 1730.32i −0.0446514 0.0773384i
\(795\) 0 0
\(796\) −4486.00 + 7769.98i −0.199751 + 0.345979i
\(797\) 35334.0i 1.57038i 0.619254 + 0.785191i \(0.287435\pi\)
−0.619254 + 0.785191i \(0.712565\pi\)
\(798\) 4508.53 2329.00i 0.200000 0.103315i
\(799\) 10089.0 0.446712
\(800\) 0 0
\(801\) −11349.0 19657.0i −0.500621 0.867101i
\(802\) −25559.9 + 14757.0i −1.12537 + 0.649735i
\(803\) −8941.71 5162.50i −0.392959 0.226875i
\(804\) 1756.00 0.0770265
\(805\) 0 0
\(806\) −9900.00 −0.432646
\(807\) −1710.40 987.500i −0.0746083 0.0430752i
\(808\) 7517.10 4340.00i 0.327290 0.188961i
\(809\) 21267.5 + 36836.4i 0.924259 + 1.60086i 0.792749 + 0.609549i \(0.208649\pi\)
0.131510 + 0.991315i \(0.458017\pi\)
\(810\) 0 0
\(811\) 30676.0 1.32821 0.664106 0.747638i \(-0.268812\pi\)
0.664106 + 0.747638i \(0.268812\pi\)
\(812\) 367.195 7844.00i 0.0158695 0.339003i
\(813\) 8439.00i 0.364045i
\(814\) −385.000 + 666.840i −0.0165777 + 0.0287134i
\(815\) 0 0
\(816\) 472.000 + 817.528i 0.0202491 + 0.0350726i
\(817\) 30847.8 + 17810.0i 1.32097 + 0.762660i
\(818\) 266.000i 0.0113698i
\(819\) −14586.0 28235.9i −0.622315 1.20469i
\(820\) 0 0
\(821\) −18671.5 + 32340.0i −0.793715 + 1.37475i 0.129937 + 0.991522i \(0.458522\pi\)
−0.923652 + 0.383232i \(0.874811\pi\)
\(822\) 4082.44 2357.00i 0.173226 0.100012i
\(823\) 2437.86 1407.50i 0.103255 0.0596141i −0.447483 0.894292i \(-0.647680\pi\)
0.550738 + 0.834678i \(0.314346\pi\)
\(824\) −6212.00 + 10759.5i −0.262628 + 0.454885i
\(825\) 0 0
\(826\) −340.000 + 530.008i −0.0143222 + 0.0223261i
\(827\) 9276.00i 0.390034i 0.980800 + 0.195017i \(0.0624762\pi\)
−0.980800 + 0.195017i \(0.937524\pi\)
\(828\) −630.466 364.000i −0.0264616 0.0152776i
\(829\) 9285.50 + 16083.0i 0.389021 + 0.673805i 0.992318 0.123712i \(-0.0394799\pi\)
−0.603297 + 0.797517i \(0.706147\pi\)
\(830\) 0 0
\(831\) 263.500 456.395i 0.0109997 0.0190520i
\(832\) 4224.00i 0.176011i
\(833\) −16503.8 11711.5i −0.686464 0.487130i
\(834\) −56.0000 −0.00232509
\(835\) 0 0
\(836\) −9590.00 16610.4i −0.396743 0.687179i
\(837\) −3442.45 + 1987.50i −0.142161 + 0.0820765i
\(838\) −11119.8 6420.00i −0.458384 0.264648i
\(839\) −29048.0 −1.19529 −0.597645 0.801761i \(-0.703897\pi\)
−0.597645 + 0.801761i \(0.703897\pi\)
\(840\) 0 0
\(841\) −13153.0 −0.539301
\(842\) −17781.2 10266.0i −0.727769 0.420178i
\(843\) 174.937 101.000i 0.00714728 0.00412648i
\(844\) 2344.00 + 4059.93i 0.0955969 + 0.165579i
\(845\) 0 0
\(846\) −8892.00 −0.361363
\(847\) 1744.18 901.000i 0.0707563 0.0365510i
\(848\) 6672.00i 0.270186i
\(849\) 3974.50 6884.04i 0.160665 0.278280i
\(850\) 0 0
\(851\) 38.5000 + 66.6840i 0.00155084 + 0.00268613i
\(852\) 2715.86 + 1568.00i 0.109206 + 0.0630502i
\(853\) 32090.0i 1.28809i 0.764988 + 0.644045i \(0.222745\pi\)
−0.764988 + 0.644045i \(0.777255\pi\)
\(854\) 1887.00 + 88.3346i 0.0756110 + 0.00353952i
\(855\) 0 0
\(856\) 516.000 893.738i 0.0206034 0.0356861i
\(857\) 21249.7 12268.5i 0.846995 0.489013i −0.0126408 0.999920i \(-0.504024\pi\)
0.859636 + 0.510907i \(0.170690\pi\)
\(858\) 4001.04 2310.00i 0.159199 0.0919139i
\(859\) 10412.5 18035.0i 0.413585 0.716351i −0.581693 0.813408i \(-0.697610\pi\)
0.995279 + 0.0970571i \(0.0309430\pi\)
\(860\) 0 0
\(861\) 9213.00 + 431.281i 0.364667 + 0.0170709i
\(862\) 30426.0i 1.20222i
\(863\) 19786.1 + 11423.5i 0.780447 + 0.450591i 0.836589 0.547831i \(-0.184546\pi\)
−0.0561414 + 0.998423i \(0.517880\pi\)
\(864\) −848.000 1468.78i −0.0333907 0.0578344i
\(865\) 0 0
\(866\) −1378.00 + 2386.77i −0.0540720 + 0.0936554i
\(867\) 1432.00i 0.0560937i
\(868\) 4936.34 2550.00i 0.193030 0.0997150i
\(869\) 17325.0 0.676307
\(870\) 0 0
\(871\) −14487.0 25092.2i −0.563574 0.976139i
\(872\) −6685.72 + 3860.00i −0.259641 + 0.149904i
\(873\) −6529.83 3770.00i −0.253152 0.146157i
\(874\) −1918.00 −0.0742303
\(875\) 0 0
\(876\) −1180.00 −0.0455120
\(877\) −37011.3 21368.5i −1.42507 0.822763i −0.428341 0.903617i \(-0.640902\pi\)
−0.996726 + 0.0808543i \(0.974235\pi\)
\(878\) 4785.66 2763.00i 0.183950 0.106204i
\(879\) −159.000 275.396i −0.00610118 0.0105676i
\(880\) 0 0
\(881\) 6162.00 0.235645 0.117822 0.993035i \(-0.462409\pi\)
0.117822 + 0.993035i \(0.462409\pi\)
\(882\) 14545.8 + 10322.0i 0.555308 + 0.394059i
\(883\) 7748.00i 0.295290i 0.989040 + 0.147645i \(0.0471693\pi\)
−0.989040 + 0.147645i \(0.952831\pi\)
\(884\) 7788.00 13489.2i 0.296311 0.513225i
\(885\) 0 0
\(886\) 5849.00 + 10130.8i 0.221784 + 0.384142i
\(887\) −22450.0 12961.5i −0.849827 0.490648i 0.0107656 0.999942i \(-0.496573\pi\)
−0.860592 + 0.509294i \(0.829906\pi\)
\(888\) 88.0000i 0.00332555i
\(889\) 9360.00 14590.8i 0.353121 0.550461i
\(890\) 0 0
\(891\) −11357.5 + 19671.8i −0.427038 + 0.739651i
\(892\) −7011.34 + 4048.00i −0.263181 + 0.151947i
\(893\) −20288.4 + 11713.5i −0.760274 + 0.438944i
\(894\) 2295.00 3975.06i 0.0858571 0.148709i
\(895\) 0 0
\(896\) 1088.00 + 2106.17i 0.0405664 + 0.0785294i
\(897\) 462.000i 0.0171970i
\(898\) 7936.26 + 4582.00i 0.294918 + 0.170271i
\(899\) 3975.00 + 6884.90i 0.147468 + 0.255422i
\(900\) 0 0
\(901\) 12301.5 21306.8i 0.454853 0.787828i
\(902\) 34860.0i 1.28682i
\(903\) 225.167 4810.00i 0.00829798 0.177261i
\(904\) −400.000 −0.0147166
\(905\) 0 0
\(906\) 1109.00 + 1920.84i 0.0406667 + 0.0704368i
\(907\) −27656.5 + 15967.5i −1.01248 + 0.584556i −0.911917 0.410375i \(-0.865398\pi\)
−0.100563 + 0.994931i \(0.532065\pi\)
\(908\) −8906.21 5142.00i −0.325510 0.187933i
\(909\) −28210.0 −1.02934
\(910\) 0 0
\(911\) 3408.00 0.123943 0.0619715 0.998078i \(-0.480261\pi\)
0.0619715 + 0.998078i \(0.480261\pi\)
\(912\) −1898.33 1096.00i −0.0689253 0.0397941i
\(913\) 28249.7 16310.0i 1.02402 0.591218i
\(914\) −11551.0 20006.9i −0.418023 0.724037i
\(915\) 0 0
\(916\) 3580.00 0.129134
\(917\) 12423.1 6417.50i 0.447381 0.231106i
\(918\) 6254.00i 0.224850i
\(919\) 6954.50 12045.5i 0.249628 0.432368i −0.713795 0.700355i \(-0.753025\pi\)
0.963423 + 0.267987i \(0.0863585\pi\)
\(920\) 0 0
\(921\) −4066.00 7042.52i −0.145472 0.251964i
\(922\) 16444.1 + 9494.00i 0.587372 + 0.339120i
\(923\) 51744.0i 1.84526i
\(924\) −1400.00 + 2182.38i −0.0498448 + 0.0777004i
\(925\) 0 0
\(926\) −10160.0 + 17597.6i −0.360560 + 0.624508i
\(927\) 34968.4 20189.0i 1.23896 0.715311i
\(928\) −2937.56 + 1696.00i −0.103912 + 0.0599935i
\(929\) −12268.5 + 21249.7i −0.433279 + 0.750462i −0.997153 0.0753990i \(-0.975977\pi\)
0.563874 + 0.825861i \(0.309310\pi\)
\(930\) 0 0
\(931\) 46785.5 + 4389.88i 1.64697 + 0.154536i
\(932\) 7148.00i 0.251224i
\(933\) −804.538 464.500i −0.0282308 0.0162991i
\(934\) 1307.00 + 2263.79i 0.0457884 + 0.0793078i
\(935\) 0 0
\(936\) −6864.00 + 11888.8i −0.239697 + 0.415168i
\(937\) 32758.0i 1.14211i 0.820912 + 0.571055i \(0.193466\pi\)
−0.820912 + 0.571055i \(0.806534\pi\)
\(938\) 13686.7 + 8780.00i 0.476424 + 0.305626i
\(939\) −209.000 −0.00726353
\(940\) 0 0
\(941\) 19280.5 + 33394.8i 0.667934 + 1.15690i 0.978481 + 0.206338i \(0.0661547\pi\)
−0.310546 + 0.950558i \(0.600512\pi\)
\(942\) −2700.27 + 1559.00i −0.0933965 + 0.0539225i
\(943\) −3018.96 1743.00i −0.104253 0.0601908i
\(944\) 272.000 0.00937801
\(945\) 0 0
\(946\) −18200.0 −0.625511
\(947\) 34347.4 + 19830.5i 1.17861 + 0.680470i 0.955692 0.294368i \(-0.0951092\pi\)
0.222916 + 0.974838i \(0.428443\pi\)
\(948\) 1714.73 990.000i 0.0587467 0.0339174i
\(949\) 9735.00 + 16861.5i 0.332994 + 0.576763i
\(950\) 0 0
\(951\) −7131.00 −0.243153
\(952\) −408.764 + 8732.00i −0.0139161 + 0.297275i
\(953\) 46618.0i 1.58458i −0.610144 0.792290i \(-0.708889\pi\)
0.610144 0.792290i \(-0.291111\pi\)
\(954\) −10842.0 + 18778.9i −0.367948 + 0.637305i
\(955\) 0 0
\(956\) 10200.0 + 17666.9i 0.345075 + 0.597687i
\(957\) −3212.95 1855.00i −0.108527 0.0626579i
\(958\) 36574.0i 1.23346i
\(959\) 43604.5 + 2041.22i 1.46826 + 0.0687325i
\(960\) 0 0
\(961\) 12083.0 20928.4i 0.405592 0.702506i
\(962\) 1257.47 726.000i 0.0421439 0.0243318i
\(963\) −2904.65 + 1677.00i −0.0971973 + 0.0561169i
\(964\) −8354.00 + 14469.6i −0.279112 + 0.483437i
\(965\) 0 0
\(966\) 119.000 + 230.363i 0.00396352 + 0.00767267i
\(967\) 14816.0i 0.492710i −0.969180 0.246355i \(-0.920767\pi\)
0.969180 0.246355i \(-0.0792329\pi\)
\(968\) −734.390 424.000i −0.0243845 0.0140784i
\(969\) −4041.50 7000.08i −0.133985 0.232069i
\(970\) 0 0
\(971\) 8437.50 14614.2i 0.278859 0.482998i −0.692242 0.721665i \(-0.743377\pi\)
0.971102 + 0.238667i \(0.0767104\pi\)
\(972\) 8320.00i 0.274552i
\(973\) −436.477 280.000i −0.0143811 0.00922548i
\(974\) −29906.0 −0.983830
\(975\) 0 0
\(976\) −408.000 706.677i −0.0133809 0.0231764i
\(977\) 13715.2 7918.50i 0.449119 0.259299i −0.258339 0.966054i \(-0.583175\pi\)
0.707458 + 0.706755i \(0.249842\pi\)
\(978\) 3898.85 + 2251.00i 0.127476 + 0.0735982i
\(979\) 30555.0 0.997489
\(980\) 0 0
\(981\) 25090.0 0.816577
\(982\) −24858.4 14352.0i −0.807804 0.466386i
\(983\) 8586.64 4957.50i 0.278608 0.160854i −0.354185 0.935175i \(-0.615242\pi\)
0.632793 + 0.774321i \(0.281908\pi\)
\(984\) −1992.00 3450.25i −0.0645352 0.111778i
\(985\) 0 0
\(986\) −12508.0 −0.403992
\(987\) 2665.63 + 1710.00i 0.0859654 + 0.0551468i
\(988\) 36168.0i 1.16463i
\(989\) −910.000 + 1576.17i −0.0292582 + 0.0506766i
\(990\) 0 0
\(991\) 21840.5 + 37828.9i 0.700087 + 1.21259i 0.968435 + 0.249265i \(0.0801889\pi\)
−0.268348 + 0.963322i \(0.586478\pi\)
\(992\) −2078.46 1200.00i −0.0665234 0.0384073i
\(993\) 6571.00i 0.209994i
\(994\) 13328.0 + 25800.6i 0.425290 + 0.823286i
\(995\) 0 0
\(996\) 1864.00 3228.54i 0.0593003 0.102711i
\(997\) 40801.1 23556.5i 1.29607 0.748287i 0.316348 0.948643i \(-0.397543\pi\)
0.979723 + 0.200357i \(0.0642101\pi\)
\(998\) 9579.97 5531.00i 0.303856 0.175432i
\(999\) 291.500 504.893i 0.00923188 0.0159901i
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 350.4.j.d.149.1 4
5.2 odd 4 14.4.c.b.9.1 2
5.3 odd 4 350.4.e.b.51.1 2
5.4 even 2 inner 350.4.j.d.149.2 4
7.4 even 3 inner 350.4.j.d.249.2 4
15.2 even 4 126.4.g.c.37.1 2
20.7 even 4 112.4.i.b.65.1 2
35.2 odd 12 98.4.a.b.1.1 1
35.4 even 6 inner 350.4.j.d.249.1 4
35.12 even 12 98.4.a.c.1.1 1
35.17 even 12 98.4.c.e.67.1 2
35.18 odd 12 350.4.e.b.151.1 2
35.23 odd 12 2450.4.a.bh.1.1 1
35.27 even 4 98.4.c.e.79.1 2
35.32 odd 12 14.4.c.b.11.1 yes 2
35.33 even 12 2450.4.a.bf.1.1 1
40.27 even 4 448.4.i.d.65.1 2
40.37 odd 4 448.4.i.c.65.1 2
105.2 even 12 882.4.a.k.1.1 1
105.17 odd 12 882.4.g.d.361.1 2
105.32 even 12 126.4.g.c.109.1 2
105.47 odd 12 882.4.a.p.1.1 1
105.62 odd 4 882.4.g.d.667.1 2
140.47 odd 12 784.4.a.j.1.1 1
140.67 even 12 112.4.i.b.81.1 2
140.107 even 12 784.4.a.l.1.1 1
280.67 even 12 448.4.i.d.193.1 2
280.277 odd 12 448.4.i.c.193.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.4.c.b.9.1 2 5.2 odd 4
14.4.c.b.11.1 yes 2 35.32 odd 12
98.4.a.b.1.1 1 35.2 odd 12
98.4.a.c.1.1 1 35.12 even 12
98.4.c.e.67.1 2 35.17 even 12
98.4.c.e.79.1 2 35.27 even 4
112.4.i.b.65.1 2 20.7 even 4
112.4.i.b.81.1 2 140.67 even 12
126.4.g.c.37.1 2 15.2 even 4
126.4.g.c.109.1 2 105.32 even 12
350.4.e.b.51.1 2 5.3 odd 4
350.4.e.b.151.1 2 35.18 odd 12
350.4.j.d.149.1 4 1.1 even 1 trivial
350.4.j.d.149.2 4 5.4 even 2 inner
350.4.j.d.249.1 4 35.4 even 6 inner
350.4.j.d.249.2 4 7.4 even 3 inner
448.4.i.c.65.1 2 40.37 odd 4
448.4.i.c.193.1 2 280.277 odd 12
448.4.i.d.65.1 2 40.27 even 4
448.4.i.d.193.1 2 280.67 even 12
784.4.a.j.1.1 1 140.47 odd 12
784.4.a.l.1.1 1 140.107 even 12
882.4.a.k.1.1 1 105.2 even 12
882.4.a.p.1.1 1 105.47 odd 12
882.4.g.d.361.1 2 105.17 odd 12
882.4.g.d.667.1 2 105.62 odd 4
2450.4.a.bf.1.1 1 35.33 even 12
2450.4.a.bh.1.1 1 35.23 odd 12