Properties

Label 350.4.j.d.249.1
Level $350$
Weight $4$
Character 350.249
Analytic conductor $20.651$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

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

Self dual: no
Analytic conductor: \(20.6506685020\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
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 249.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 350.249
Dual form 350.4.j.d.149.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.73205 + 1.00000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.00000 - 3.46410i) q^{4} +2.00000 q^{6} +(15.5885 - 10.0000i) q^{7} +8.00000i q^{8} +(-13.0000 - 22.5167i) q^{9} +O(q^{10})\) \(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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 0.414346 0.910119i \(-0.364010\pi\)
−0.581013 + 0.813894i \(0.697344\pi\)
\(4\) 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 −0.999728 0.0233099i \(-0.992580\pi\)
0.520051 + 0.854135i \(0.325913\pi\)
\(12\) −3.46410 + 2.00000i −0.0833333 + 0.0481125i
\(13\) 66.0000i 1.40809i −0.710158 0.704043i \(-0.751376\pi\)
0.710158 0.704043i \(-0.248624\pi\)
\(14\) −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 0.0890757 0.996025i \(-0.471609\pi\)
−0.818045 + 0.575154i \(0.804942\pi\)
\(18\) 45.0333 + 26.0000i 0.589692 + 0.340459i
\(19\) 68.5000 + 118.645i 0.827104 + 1.43259i 0.900301 + 0.435269i \(0.143347\pi\)
−0.0731965 + 0.997318i \(0.523320\pi\)
\(20\) 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 −0.472269 0.881455i \(-0.656565\pi\)
0.527228 + 0.849724i \(0.323232\pi\)
\(24\) 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 −0.953971 0.299900i \(-0.903047\pi\)
0.736706 + 0.676213i \(0.236380\pi\)
\(32\) 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 −0.478687 0.877986i \(-0.658887\pi\)
0.521014 + 0.853548i \(0.325554\pi\)
\(38\) −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 \(-0.847476\pi\)
0.887378 0.461042i \(-0.152524\pi\)
\(44\) 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 −0.711876 0.702305i \(-0.752154\pi\)
0.252276 + 0.967655i \(0.418821\pi\)
\(48\) 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 −0.0472619 0.998883i \(-0.515050\pi\)
−0.888689 + 0.458511i \(0.848383\pi\)
\(54\) −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 −0.875251 0.483669i \(-0.839304\pi\)
0.856495 + 0.516155i \(0.172637\pi\)
\(60\) 0 0
\(61\) −25.5000 44.1673i −0.0535236 0.0927056i 0.838022 0.545636i \(-0.183712\pi\)
−0.891546 + 0.452930i \(0.850379\pi\)
\(62\) 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 0.111585 0.993755i \(-0.464407\pi\)
−0.804824 + 0.593513i \(0.797740\pi\)
\(68\) −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 0.690621 0.723217i \(-0.257337\pi\)
−0.281013 + 0.959704i \(0.590671\pi\)
\(74\) −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 0.634203 0.773166i \(-0.281328\pi\)
−0.986683 + 0.162653i \(0.947995\pi\)
\(80\) 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 \(-0.788644\pi\)
0.787537 0.616267i \(-0.211356\pi\)
\(84\) −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 −0.999733 0.0231042i \(-0.992645\pi\)
0.479858 0.877346i \(-0.340688\pi\)
\(90\) 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 \(-0.951500\pi\)
0.988415 0.151779i \(-0.0485001\pi\)
\(98\) 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 −0.464726 0.885454i \(-0.653847\pi\)
0.999189 0.0402627i \(-0.0128195\pi\)
\(102\) −102.191 59.0000i −0.0992002 0.0572732i
\(103\) −1344.94 + 776.500i −1.28661 + 0.742823i −0.978048 0.208381i \(-0.933181\pi\)
−0.308560 + 0.951205i \(0.599847\pi\)
\(104\) 528.000 0.497833
\(105\) 0 0
\(106\) 834.000 0.764200
\(107\) 111.717 64.5000i 0.100936 0.0582752i −0.448682 0.893691i \(-0.648107\pi\)
0.549618 + 0.835416i \(0.314773\pi\)
\(108\) 183.597 + 106.000i 0.163580 + 0.0944431i
\(109\) −482.500 + 835.715i −0.423992 + 0.734376i −0.996326 0.0856452i \(-0.972705\pi\)
0.572334 + 0.820021i \(0.306038\pi\)
\(110\) 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 \(0.00662527\pi\)
−0.999783 + 0.0208124i \(0.993375\pi\)
\(114\) 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 \(0.106036\pi\)
−0.945026 + 0.326994i \(0.893964\pi\)
\(128\) 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 0.964014 0.265851i \(-0.0856529\pi\)
−0.712241 + 0.701935i \(0.752320\pi\)
\(132\) 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 0.975541 0.219817i \(-0.0705461\pi\)
0.297403 + 0.954752i \(0.403879\pi\)
\(138\) 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 0.987364 + 0.158467i \(0.0506551\pi\)
−0.356446 + 0.934316i \(0.616012\pi\)
\(150\) 0 0
\(151\) 554.500 960.422i 0.298838 0.517603i −0.677032 0.735953i \(-0.736734\pi\)
0.975870 + 0.218350i \(0.0700676\pi\)
\(152\) −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 0.115911 0.993260i \(-0.463021\pi\)
−0.802232 + 0.597012i \(0.796354\pi\)
\(158\) 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 0.0478115 0.998856i \(-0.484775\pi\)
0.888941 + 0.458022i \(0.151442\pi\)
\(164\) −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 \(0.223532\pi\)
−0.763393 + 0.645934i \(0.776468\pi\)
\(168\) −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 −0.769418 0.638746i \(-0.779454\pi\)
0.168461 + 0.985708i \(0.446120\pi\)
\(174\) −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 −0.488186 0.872740i \(-0.662341\pi\)
0.999908 0.0135883i \(-0.00432541\pi\)
\(180\) 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 0.961144 0.276048i \(-0.0890249\pi\)
−0.719637 + 0.694351i \(0.755692\pi\)
\(192\) 55.4256 + 32.0000i 0.0208333 + 0.0120281i
\(193\) 30.3109 + 17.5000i 0.0113048 + 0.00652683i 0.505642 0.862744i \(-0.331256\pi\)
−0.494337 + 0.869270i \(0.664589\pi\)
\(194\) 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 \(-0.835392\pi\)
0.869241 0.494389i \(-0.164608\pi\)
\(198\) −1576.17 + 910.000i −0.565724 + 0.326621i
\(199\) 1121.50 1942.49i 0.399503 0.691959i −0.594162 0.804345i \(-0.702516\pi\)
0.993665 + 0.112387i \(0.0358495\pi\)
\(200\) 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 \(-0.901713\pi\)
0.952706 0.303895i \(-0.0982871\pi\)
\(224\) 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 0.137827 0.990456i \(-0.455988\pi\)
−0.788847 + 0.614590i \(0.789321\pi\)
\(228\) −474.582 274.000i −0.137851 0.0795881i
\(229\) 447.500 + 775.093i 0.129134 + 0.223666i 0.923341 0.383980i \(-0.125447\pi\)
−0.794207 + 0.607647i \(0.792114\pi\)
\(230\) 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 −0.701531 0.712639i \(-0.747500\pi\)
0.266398 + 0.963863i \(0.414166\pi\)
\(234\) 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 −0.439420 0.898282i \(-0.644816\pi\)
0.997645 0.0685917i \(-0.0218506\pi\)
\(242\) −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 −0.672426 0.740164i \(-0.734748\pi\)
0.304788 + 0.952420i \(0.401414\pi\)
\(258\) 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 −0.0283689 0.999598i \(-0.509031\pi\)
−0.879861 + 0.475231i \(0.842365\pi\)
\(264\) 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 −0.732141 0.681153i \(-0.761479\pi\)
0.955966 + 0.293476i \(0.0948122\pi\)
\(270\) 0 0
\(271\) 4219.50 + 7308.39i 0.945817 + 1.63820i 0.754107 + 0.656751i \(0.228070\pi\)
0.191710 + 0.981452i \(0.438597\pi\)
\(272\) 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 0.449684 0.893188i \(-0.351537\pi\)
−0.548681 + 0.836032i \(0.684870\pi\)
\(278\) 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 −0.447745 0.894161i \(-0.647773\pi\)
−0.998239 + 0.0593220i \(0.981106\pi\)
\(284\) −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 \(-0.989907\pi\)
0.999497 0.0317027i \(-0.0100930\pi\)
\(294\) 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 \(-0.727203\pi\)
0.654696 0.755892i \(-0.272797\pi\)
\(308\) 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 −0.820568 0.571549i \(-0.806343\pi\)
0.905260 + 0.424858i \(0.139676\pi\)
\(312\) −457.261 264.000i −0.0829722 0.0479040i
\(313\) 180.999 104.500i 0.0326859 0.0188712i −0.483568 0.875307i \(-0.660659\pi\)
0.516254 + 0.856436i \(0.327326\pi\)
\(314\) 3118.00 0.560379
\(315\) 0 0
\(316\) −1980.00 −0.352480
\(317\) 6175.63 3565.50i 1.09419 0.631730i 0.159500 0.987198i \(-0.449012\pi\)
0.934689 + 0.355468i \(0.115678\pi\)
\(318\) −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 0.998570 + 0.0534583i \(0.0170244\pi\)
−0.452989 + 0.891516i \(0.649642\pi\)
\(332\) −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 \(-0.622636\pi\)
0.375813 0.926696i \(-0.377364\pi\)
\(338\) 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 0.982081 0.188459i \(-0.0603491\pi\)
0.327831 + 0.944737i \(0.393682\pi\)
\(348\) 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 0.958592 0.284783i \(-0.0919214\pi\)
0.232667 + 0.972556i \(0.425255\pi\)
\(354\) −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 0.992968 + 0.118385i \(0.0377716\pi\)
−0.393960 + 0.919128i \(0.628895\pi\)
\(360\) 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 −0.232660 0.972558i \(-0.574743\pi\)
−0.958590 + 0.284790i \(0.908076\pi\)
\(368\) −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 −0.232248 0.972657i \(-0.574608\pi\)
0.726221 + 0.687461i \(0.241275\pi\)
\(374\) −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 −0.910360 0.413818i \(-0.864195\pi\)
−0.0968028 + 0.995304i \(0.530862\pi\)
\(384\) −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 −0.860665 0.509171i \(-0.829952\pi\)
0.871288 + 0.490772i \(0.163285\pi\)
\(390\) 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 −0.444316 0.895870i \(-0.646553\pi\)
0.553689 + 0.832724i \(0.313220\pi\)
\(398\) 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 0.801143 + 0.598474i \(0.204226\pi\)
0.117722 + 0.993047i \(0.462441\pi\)
\(402\) −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 −0.870017 0.493021i \(-0.835892\pi\)
0.861978 + 0.506946i \(0.169226\pi\)
\(410\) 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 −0.0310213 0.999519i \(-0.509876\pi\)
0.881119 0.472894i \(-0.156791\pi\)
\(432\) 734.390 424.000i 0.0817901 0.0472215i
\(433\) 1378.00i 0.152939i 0.997072 + 0.0764693i \(0.0243647\pi\)
−0.997072 + 0.0764693i \(0.975635\pi\)
\(434\) −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 0.781104 0.624401i \(-0.214657\pi\)
−0.931299 + 0.364256i \(0.881323\pi\)
\(440\) 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 −0.746399 0.665499i \(-0.768219\pi\)
0.203140 + 0.979150i \(0.434885\pi\)
\(444\) −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 0.108700 0.994075i \(-0.465331\pi\)
0.915244 + 0.402901i \(0.131998\pi\)
\(458\) −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 \(0.170321\pi\)
−0.860229 + 0.509908i \(0.829679\pi\)
\(464\) 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 −0.555030 0.831831i \(-0.687293\pi\)
0.442872 + 0.896585i \(0.353960\pi\)
\(468\) 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 0.0124559 0.999922i \(-0.496035\pi\)
0.859730 0.510748i \(-0.170632\pi\)
\(480\) 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 0.961650 0.274281i \(-0.0884398\pi\)
0.243291 + 0.969953i \(0.421773\pi\)
\(488\) 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 0.714900 0.699226i \(-0.246472\pi\)
−0.962998 + 0.269509i \(0.913139\pi\)
\(500\) 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 \(-0.878568\pi\)
0.928111 0.372304i \(-0.121432\pi\)
\(504\) 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 0.809421 0.587228i \(-0.199781\pi\)
−0.913265 + 0.407365i \(0.866448\pi\)
\(510\) 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 −0.606910 0.794771i \(-0.707591\pi\)
0.991747 + 0.128214i \(0.0409243\pi\)
\(522\) −4773.53 2756.00i −0.400253 0.231086i
\(523\) 11957.2 6903.50i 0.999718 0.577187i 0.0915530 0.995800i \(-0.470817\pi\)
0.908165 + 0.418613i \(0.137484\pi\)
\(524\) 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 0.656645 0.754200i \(-0.271975\pi\)
−0.981479 + 0.191571i \(0.938642\pi\)
\(542\) −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 \(0.0582477\pi\)
−0.983304 + 0.181971i \(0.941752\pi\)
\(548\) 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 0.251261 0.967919i \(-0.419155\pi\)
−0.712612 + 0.701558i \(0.752488\pi\)
\(558\) −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 −0.303612 0.952796i \(-0.598193\pi\)
−0.976951 + 0.213462i \(0.931526\pi\)
\(564\) 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 0.710569 0.703628i \(-0.248438\pi\)
−0.964644 + 0.263557i \(0.915104\pi\)
\(570\) 0 0
\(571\) −12457.5 + 21577.0i −0.913013 + 1.58138i −0.103227 + 0.994658i \(0.532917\pi\)
−0.809785 + 0.586726i \(0.800416\pi\)
\(572\) 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 0.496027 0.868307i \(-0.334792\pi\)
−0.503962 + 0.863726i \(0.668125\pi\)
\(578\) 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 \(0.102998\pi\)
−0.948104 + 0.317961i \(0.897002\pi\)
\(588\) 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 −0.143532 0.989646i \(-0.545846\pi\)
0.785292 + 0.619125i \(0.212513\pi\)
\(594\) 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 −0.255722 0.966750i \(-0.582313\pi\)
0.965091 0.261913i \(-0.0843533\pi\)
\(600\) 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 −0.299028 0.954244i \(-0.596662\pi\)
0.676886 + 0.736088i \(0.263329\pi\)
\(608\) 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 0.863619 0.504145i \(-0.168192\pi\)
−0.00479285 + 0.999989i \(0.501526\pi\)
\(614\) 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 \(0.118508\pi\)
−0.931492 + 0.363762i \(0.881492\pi\)
\(618\) −2689.87 + 1553.00i −0.175085 + 0.101085i
\(619\) 1707.50 2957.48i 0.110873 0.192037i −0.805250 0.592936i \(-0.797969\pi\)
0.916122 + 0.400899i \(0.131302\pi\)
\(620\) 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 −0.652660 0.757651i \(-0.726347\pi\)
0.982475 + 0.186395i \(0.0596805\pi\)
\(642\) 223.435 129.000i 0.0137356 0.00793026i
\(643\) 6860.00i 0.420734i −0.977622 0.210367i \(-0.932534\pi\)
0.977622 0.210367i \(-0.0674659\pi\)
\(644\) −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 0.0686008 0.997644i \(-0.478147\pi\)
−0.829685 + 0.558232i \(0.811480\pi\)
\(648\) −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 −0.647063 0.762436i \(-0.724003\pi\)
0.336758 + 0.941591i \(0.390670\pi\)
\(654\) −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 −0.993001 0.118102i \(-0.962319\pi\)
0.598780 + 0.800914i \(0.295652\pi\)
\(662\) −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 \(-0.679531\pi\)
0.534582 0.845117i \(-0.320469\pi\)
\(674\) 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 −0.976538 0.215344i \(-0.930913\pi\)
−0.301776 + 0.953379i \(0.597579\pi\)
\(678\) 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 0.270954 0.962592i \(-0.412661\pi\)
−0.698152 + 0.715949i \(0.745994\pi\)
\(684\) −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 −0.926211 0.377004i \(-0.876954\pi\)
0.136610 0.990625i \(-0.456379\pi\)
\(692\) 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 0.882216 0.470845i \(-0.156051\pi\)
−0.848871 + 0.528599i \(0.822717\pi\)
\(710\) 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 0.996511 0.0834645i \(-0.0265985\pi\)
−0.570538 + 0.821271i \(0.693265\pi\)
\(720\) 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 \(-0.950829\pi\)
0.988092 0.153861i \(-0.0491709\pi\)
\(728\) 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 −0.794251 0.607589i \(-0.792137\pi\)
0.129062 + 0.991636i \(0.458803\pi\)
\(734\) 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 −0.963583 0.267411i \(-0.913832\pi\)
0.713376 + 0.700782i \(0.247165\pi\)
\(740\) 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 \(-0.794373\pi\)
0.798501 0.601993i \(-0.205627\pi\)
\(744\) 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 0.690216 0.723603i \(-0.257515\pi\)
−0.971767 + 0.235943i \(0.924182\pi\)
\(752\) 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 \(0.113676\pi\)
−0.936906 + 0.349581i \(0.886324\pi\)
\(758\) −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 0.998777 + 0.0494360i \(0.0157424\pi\)
−0.456576 + 0.889684i \(0.650924\pi\)
\(762\) 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 −0.150849 0.988557i \(-0.548201\pi\)
−0.931540 + 0.363639i \(0.881534\pi\)
\(774\) 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