Properties

Label 350.4.j.d.249.2
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 249.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 350.249
Dual form 350.4.j.d.149.2

$q$-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 0.581013 0.813894i \(-0.302656\pi\)
−0.414346 + 0.910119i \(0.635990\pi\)
\(4\) 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 \(0.248624\pi\)
−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 \(-0.195058\pi\)
−0.0890757 + 0.996025i \(0.528391\pi\)
\(18\) −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 −0.527228 0.849724i \(-0.676768\pi\)
0.472269 + 0.881455i \(0.343435\pi\)
\(24\) 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 −0.521014 0.853548i \(-0.674446\pi\)
0.478687 + 0.877986i \(0.341113\pi\)
\(38\) 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 \(-0.581179\pi\)
0.711876 + 0.702305i \(0.247846\pi\)
\(48\) 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 \(-0.151617\pi\)
0.0472619 + 0.998883i \(0.484950\pi\)
\(54\) −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 0.804824 0.593513i \(-0.202260\pi\)
−0.111585 + 0.993755i \(0.535593\pi\)
\(68\) 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 \(-0.409329\pi\)
−0.690621 + 0.723217i \(0.742663\pi\)
\(74\) −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 \(0.211356\pi\)
−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 −0.999733 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 \(0.0485001\pi\)
−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 −0.464726 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 0.308560 0.951205i \(-0.400153\pi\)
0.978048 + 0.208381i \(0.0668195\pi\)
\(104\) 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 \(-0.685227\pi\)
0.448682 + 0.893691i \(0.351893\pi\)
\(108\) −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 \(-0.993375\pi\)
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 0.964014 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 −0.297403 0.954752i \(-0.596121\pi\)
−0.975541 + 0.219817i \(0.929454\pi\)
\(138\) −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 0.802232 0.597012i \(-0.203646\pi\)
−0.115911 + 0.993260i \(0.536979\pi\)
\(158\) −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 \(-0.848558\pi\)
−0.0478115 + 0.998856i \(0.515225\pi\)
\(164\) −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 \(-0.553880\pi\)
0.769418 + 0.638746i \(0.220546\pi\)
\(174\) −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 0.494337 0.869270i \(-0.335411\pi\)
−0.505642 + 0.862744i \(0.668744\pi\)
\(194\) 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 −0.594162 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 \(0.0982871\pi\)
−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 \(-0.210679\pi\)
−0.137827 + 0.990456i \(0.544012\pi\)
\(228\) 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 −0.266398 0.963863i \(-0.585834\pi\)
0.701531 + 0.712639i \(0.252500\pi\)
\(234\) 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 −0.304788 0.952420i \(-0.598586\pi\)
0.672426 + 0.740164i \(0.265252\pi\)
\(258\) 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 \(-0.157635\pi\)
0.0283689 + 0.999598i \(0.490969\pi\)
\(264\) 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 0.548681 0.836032i \(-0.315130\pi\)
−0.449684 + 0.893188i \(0.648463\pi\)
\(278\) −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 \(-0.0188939\pi\)
0.447745 + 0.894161i \(0.352227\pi\)
\(284\) −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 −0.820568 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 −0.516254 0.856436i \(-0.672674\pi\)
0.483568 + 0.875307i \(0.339341\pi\)
\(314\) 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 \(-0.884322\pi\)
−0.159500 + 0.987198i \(0.550988\pi\)
\(318\) 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 \(0.377364\pi\)
−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 \(-0.606318\pi\)
−0.982081 + 0.188459i \(0.939651\pi\)
\(348\) −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 \(-0.574745\pi\)
−0.958592 + 0.284783i \(0.908079\pi\)
\(354\) −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 0.958590 0.284790i \(-0.0919237\pi\)
0.232660 + 0.972558i \(0.425257\pi\)
\(368\) 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 \(-0.758725\pi\)
0.232248 + 0.972657i \(0.425392\pi\)
\(374\) −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 \(-0.469138\pi\)
0.910360 + 0.413818i \(0.135805\pi\)
\(384\) −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 −0.553689 0.832724i \(-0.686780\pi\)
0.444316 + 0.895870i \(0.353447\pi\)
\(398\) 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 \(-0.975635\pi\)
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 0.781104 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 −0.203140 0.979150i \(-0.565115\pi\)
0.746399 + 0.665499i \(0.231781\pi\)
\(444\) −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 \(-0.868002\pi\)
−0.108700 + 0.994075i \(0.534669\pi\)
\(458\) 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 \(-0.646040\pi\)
0.555030 + 0.831831i \(0.312707\pi\)
\(468\) 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 −0.243291 0.969953i \(-0.578227\pi\)
−0.961650 + 0.274281i \(0.911560\pi\)
\(488\) −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 \(0.121432\pi\)
−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 0.809421 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 −0.908165 0.418613i \(-0.862516\pi\)
−0.0915530 + 0.995800i \(0.529183\pi\)
\(524\) 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 \(-0.941752\pi\)
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 \(-0.247512\pi\)
−0.251261 + 0.967919i \(0.580845\pi\)
\(558\) 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 \(-0.0684740\pi\)
0.303612 + 0.952796i \(0.401807\pi\)
\(564\) 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 0.503962 0.863726i \(-0.331875\pi\)
−0.496027 + 0.868307i \(0.665208\pi\)
\(578\) −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 \(-0.787487\pi\)
0.143532 + 0.989646i \(0.454154\pi\)
\(594\) 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 −0.676886 0.736088i \(-0.736671\pi\)
0.299028 + 0.954244i \(0.403338\pi\)
\(608\) 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 \(-0.498474\pi\)
−0.863619 + 0.504145i \(0.831808\pi\)
\(614\) 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 −0.805250 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 \(0.0674659\pi\)
−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 \(-0.188520\pi\)
−0.0686008 + 0.997644i \(0.521853\pi\)
\(648\) 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 \(-0.609330\pi\)
0.647063 + 0.762436i \(0.275997\pi\)
\(654\) −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 \(0.320469\pi\)
−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 \(-0.402421\pi\)
0.976538 + 0.215344i \(0.0690872\pi\)
\(678\) 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 \(-0.254006\pi\)
−0.270954 + 0.962592i \(0.587339\pi\)
\(684\) −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 \(0.0491709\pi\)
−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 \(-0.541197\pi\)
0.794251 + 0.607589i \(0.207863\pi\)
\(734\) 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 \(0.205627\pi\)
−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 0.690216 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 \(-0.886324\pi\)
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 0.998777 + 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 0.931540 0.363639i \(-0.118466\pi\)
0.150849 + 0.988557i \(0.451799\pi\)
\(774\) 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
\(778\)