Properties

Label 950.2.e.l.201.3
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.39075800976.1
Defining polynomial: \(x^{8} - x^{7} + 12 x^{6} - 13 x^{5} + 125 x^{4} - 116 x^{3} + 232 x^{2} + 96 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.3
Root \(0.851703 - 1.47519i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.l.501.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.851703 - 1.47519i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.851703 + 1.47519i) q^{6} -3.74324 q^{7} +1.00000 q^{8} +(0.0492032 + 0.0852224i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.851703 - 1.47519i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.851703 + 1.47519i) q^{6} -3.74324 q^{7} +1.00000 q^{8} +(0.0492032 + 0.0852224i) q^{9} +3.64483 q^{11} -1.70341 q^{12} +(3.01991 + 5.23065i) q^{13} +(1.87162 - 3.24174i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.04920 - 3.54932i) q^{17} -0.0984064 q^{18} +(-0.697500 - 4.30273i) q^{19} +(-3.18813 + 5.52200i) q^{21} +(-1.82241 + 3.15651i) q^{22} +(-2.34233 - 4.05703i) q^{23} +(0.851703 - 1.47519i) q^{24} -6.03983 q^{26} +5.27785 q^{27} +(1.87162 + 3.24174i) q^{28} +(3.32241 + 5.75459i) q^{29} +10.8416 q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.10431 - 5.37683i) q^{33} +(2.04920 + 3.54932i) q^{34} +(0.0492032 - 0.0852224i) q^{36} -7.75505 q^{37} +(4.07502 + 1.54731i) q^{38} +10.2883 q^{39} +(3.99653 - 6.92220i) q^{41} +(-3.18813 - 5.52200i) q^{42} +(2.19403 - 3.80018i) q^{43} +(-1.82241 - 3.15651i) q^{44} +4.68466 q^{46} +(-0.871618 - 1.50969i) q^{47} +(0.851703 + 1.47519i) q^{48} +7.01181 q^{49} +(-3.49063 - 6.04594i) q^{51} +(3.01991 - 5.23065i) q^{52} +(0.871618 + 1.50969i) q^{53} +(-2.63892 + 4.57075i) q^{54} -3.74324 q^{56} +(-6.94142 - 2.63570i) q^{57} -6.64483 q^{58} +(3.67412 - 6.36376i) q^{59} +(-1.15420 - 1.99914i) q^{61} +(-5.42082 + 9.38914i) q^{62} +(-0.184179 - 0.319008i) q^{63} +1.00000 q^{64} +(3.10431 + 5.37683i) q^{66} +(3.37162 + 5.83981i) q^{67} -4.09841 q^{68} -7.97988 q^{69} +(0.994093 - 1.72182i) q^{71} +(0.0492032 + 0.0852224i) q^{72} +(4.59494 - 7.95867i) q^{73} +(3.87752 - 6.71607i) q^{74} +(-3.37752 + 2.75542i) q^{76} -13.6435 q^{77} +(-5.14414 + 8.90992i) q^{78} +(-3.07849 + 5.33210i) q^{79} +(4.34755 - 7.53017i) q^{81} +(3.99653 + 6.92220i) q^{82} -5.69159 q^{83} +6.37625 q^{84} +(2.19403 + 3.80018i) q^{86} +11.3188 q^{87} +3.64483 q^{88} +(5.53983 + 9.59527i) q^{89} +(-11.3043 - 19.5795i) q^{91} +(-2.34233 + 4.05703i) q^{92} +(9.23386 - 15.9935i) q^{93} +1.74324 q^{94} -1.70341 q^{96} +(0.752610 - 1.30356i) q^{97} +(-3.50591 + 6.07241i) q^{98} +(0.179337 + 0.310621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} + q^{3} - 4q^{4} + q^{6} + 12q^{7} + 8q^{8} - 11q^{9} + O(q^{10}) \) \( 8q - 4q^{2} + q^{3} - 4q^{4} + q^{6} + 12q^{7} + 8q^{8} - 11q^{9} + 10q^{11} - 2q^{12} + 9q^{13} - 6q^{14} - 4q^{16} + 5q^{17} + 22q^{18} - q^{21} - 5q^{22} + 6q^{23} + q^{24} - 18q^{26} + 16q^{27} - 6q^{28} + 17q^{29} + 22q^{31} - 4q^{32} - 4q^{33} + 5q^{34} - 11q^{36} - 8q^{37} - 36q^{39} + 7q^{41} - q^{42} - 13q^{43} - 5q^{44} - 12q^{46} + 14q^{47} + q^{48} + 44q^{49} - 9q^{51} + 9q^{52} - 14q^{53} - 8q^{54} + 12q^{56} - 48q^{57} - 34q^{58} + 14q^{59} - 9q^{61} - 11q^{62} - 45q^{63} + 8q^{64} - 4q^{66} + 6q^{67} - 10q^{68} + 54q^{69} + 14q^{71} - 11q^{72} - 11q^{73} + 4q^{74} - 10q^{77} + 18q^{78} - 17q^{79} - 36q^{81} + 7q^{82} - 46q^{83} + 2q^{84} - 13q^{86} - 2q^{87} + 10q^{88} + 14q^{89} - 25q^{91} + 6q^{92} + 13q^{93} - 28q^{94} - 2q^{96} - 17q^{97} - 22q^{98} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.851703 1.47519i 0.491731 0.851703i −0.508224 0.861225i \(-0.669698\pi\)
0.999955 + 0.00952194i \(0.00303097\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0.851703 + 1.47519i 0.347706 + 0.602245i
\(7\) −3.74324 −1.41481 −0.707405 0.706808i \(-0.750134\pi\)
−0.707405 + 0.706808i \(0.750134\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.0492032 + 0.0852224i 0.0164011 + 0.0284075i
\(10\) 0 0
\(11\) 3.64483 1.09896 0.549479 0.835508i \(-0.314826\pi\)
0.549479 + 0.835508i \(0.314826\pi\)
\(12\) −1.70341 −0.491731
\(13\) 3.01991 + 5.23065i 0.837574 + 1.45072i 0.891918 + 0.452198i \(0.149360\pi\)
−0.0543441 + 0.998522i \(0.517307\pi\)
\(14\) 1.87162 3.24174i 0.500211 0.866391i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.04920 3.54932i 0.497005 0.860838i −0.502989 0.864293i \(-0.667766\pi\)
0.999994 + 0.00345514i \(0.00109981\pi\)
\(18\) −0.0984064 −0.0231946
\(19\) −0.697500 4.30273i −0.160017 0.987114i
\(20\) 0 0
\(21\) −3.18813 + 5.52200i −0.695706 + 1.20500i
\(22\) −1.82241 + 3.15651i −0.388540 + 0.672971i
\(23\) −2.34233 4.05703i −0.488409 0.845950i 0.511502 0.859282i \(-0.329089\pi\)
−0.999911 + 0.0133324i \(0.995756\pi\)
\(24\) 0.851703 1.47519i 0.173853 0.301123i
\(25\) 0 0
\(26\) −6.03983 −1.18451
\(27\) 5.27785 1.01572
\(28\) 1.87162 + 3.24174i 0.353703 + 0.612631i
\(29\) 3.32241 + 5.75459i 0.616957 + 1.06860i 0.990038 + 0.140802i \(0.0449681\pi\)
−0.373081 + 0.927799i \(0.621699\pi\)
\(30\) 0 0
\(31\) 10.8416 1.94722 0.973608 0.228226i \(-0.0732925\pi\)
0.973608 + 0.228226i \(0.0732925\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 3.10431 5.37683i 0.540392 0.935986i
\(34\) 2.04920 + 3.54932i 0.351435 + 0.608704i
\(35\) 0 0
\(36\) 0.0492032 0.0852224i 0.00820053 0.0142037i
\(37\) −7.75505 −1.27492 −0.637461 0.770483i \(-0.720015\pi\)
−0.637461 + 0.770483i \(0.720015\pi\)
\(38\) 4.07502 + 1.54731i 0.661056 + 0.251007i
\(39\) 10.2883 1.64744
\(40\) 0 0
\(41\) 3.99653 6.92220i 0.624154 1.08107i −0.364550 0.931184i \(-0.618777\pi\)
0.988704 0.149882i \(-0.0478894\pi\)
\(42\) −3.18813 5.52200i −0.491939 0.852062i
\(43\) 2.19403 3.80018i 0.334587 0.579521i −0.648819 0.760943i \(-0.724737\pi\)
0.983405 + 0.181422i \(0.0580699\pi\)
\(44\) −1.82241 3.15651i −0.274739 0.475863i
\(45\) 0 0
\(46\) 4.68466 0.690715
\(47\) −0.871618 1.50969i −0.127139 0.220210i 0.795428 0.606048i \(-0.207246\pi\)
−0.922567 + 0.385837i \(0.873913\pi\)
\(48\) 0.851703 + 1.47519i 0.122933 + 0.212926i
\(49\) 7.01181 1.00169
\(50\) 0 0
\(51\) −3.49063 6.04594i −0.488785 0.846601i
\(52\) 3.01991 5.23065i 0.418787 0.725360i
\(53\) 0.871618 + 1.50969i 0.119726 + 0.207371i 0.919659 0.392718i \(-0.128465\pi\)
−0.799933 + 0.600089i \(0.795132\pi\)
\(54\) −2.63892 + 4.57075i −0.359112 + 0.622000i
\(55\) 0 0
\(56\) −3.74324 −0.500211
\(57\) −6.94142 2.63570i −0.919414 0.349107i
\(58\) −6.64483 −0.872509
\(59\) 3.67412 6.36376i 0.478329 0.828491i −0.521362 0.853336i \(-0.674576\pi\)
0.999691 + 0.0248448i \(0.00790917\pi\)
\(60\) 0 0
\(61\) −1.15420 1.99914i −0.147781 0.255963i 0.782626 0.622492i \(-0.213880\pi\)
−0.930407 + 0.366528i \(0.880546\pi\)
\(62\) −5.42082 + 9.38914i −0.688445 + 1.19242i
\(63\) −0.184179 0.319008i −0.0232044 0.0401912i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.10431 + 5.37683i 0.382115 + 0.661842i
\(67\) 3.37162 + 5.83981i 0.411909 + 0.713447i 0.995098 0.0988892i \(-0.0315289\pi\)
−0.583190 + 0.812336i \(0.698196\pi\)
\(68\) −4.09841 −0.497005
\(69\) −7.97988 −0.960664
\(70\) 0 0
\(71\) 0.994093 1.72182i 0.117977 0.204342i −0.800989 0.598679i \(-0.795692\pi\)
0.918966 + 0.394337i \(0.129026\pi\)
\(72\) 0.0492032 + 0.0852224i 0.00579865 + 0.0100436i
\(73\) 4.59494 7.95867i 0.537797 0.931492i −0.461225 0.887283i \(-0.652590\pi\)
0.999022 0.0442086i \(-0.0140766\pi\)
\(74\) 3.87752 6.71607i 0.450753 0.780727i
\(75\) 0 0
\(76\) −3.37752 + 2.75542i −0.387429 + 0.316068i
\(77\) −13.6435 −1.55482
\(78\) −5.14414 + 8.90992i −0.582459 + 1.00885i
\(79\) −3.07849 + 5.33210i −0.346357 + 0.599909i −0.985599 0.169097i \(-0.945915\pi\)
0.639242 + 0.769006i \(0.279248\pi\)
\(80\) 0 0
\(81\) 4.34755 7.53017i 0.483061 0.836686i
\(82\) 3.99653 + 6.92220i 0.441343 + 0.764429i
\(83\) −5.69159 −0.624734 −0.312367 0.949962i \(-0.601122\pi\)
−0.312367 + 0.949962i \(0.601122\pi\)
\(84\) 6.37625 0.695706
\(85\) 0 0
\(86\) 2.19403 + 3.80018i 0.236589 + 0.409783i
\(87\) 11.3188 1.21351
\(88\) 3.64483 0.388540
\(89\) 5.53983 + 9.59527i 0.587221 + 1.01710i 0.994595 + 0.103835i \(0.0331113\pi\)
−0.407374 + 0.913261i \(0.633555\pi\)
\(90\) 0 0
\(91\) −11.3043 19.5795i −1.18501 2.05249i
\(92\) −2.34233 + 4.05703i −0.244205 + 0.422975i
\(93\) 9.23386 15.9935i 0.957507 1.65845i
\(94\) 1.74324 0.179801
\(95\) 0 0
\(96\) −1.70341 −0.173853
\(97\) 0.752610 1.30356i 0.0764159 0.132356i −0.825285 0.564716i \(-0.808986\pi\)
0.901701 + 0.432360i \(0.142319\pi\)
\(98\) −3.50591 + 6.07241i −0.354150 + 0.613406i
\(99\) 0.179337 + 0.310621i 0.0180241 + 0.0312186i
\(100\) 0 0
\(101\) 3.91735 + 6.78506i 0.389791 + 0.675138i 0.992421 0.122883i \(-0.0392138\pi\)
−0.602630 + 0.798021i \(0.705880\pi\)
\(102\) 6.98125 0.691247
\(103\) 13.6036 1.34041 0.670203 0.742178i \(-0.266207\pi\)
0.670203 + 0.742178i \(0.266207\pi\)
\(104\) 3.01991 + 5.23065i 0.296127 + 0.512907i
\(105\) 0 0
\(106\) −1.74324 −0.169318
\(107\) 7.24845 0.700735 0.350367 0.936612i \(-0.386057\pi\)
0.350367 + 0.936612i \(0.386057\pi\)
\(108\) −2.63892 4.57075i −0.253930 0.439820i
\(109\) −2.24392 + 3.88659i −0.214929 + 0.372268i −0.953251 0.302181i \(-0.902285\pi\)
0.738322 + 0.674449i \(0.235619\pi\)
\(110\) 0 0
\(111\) −6.60500 + 11.4402i −0.626919 + 1.08586i
\(112\) 1.87162 3.24174i 0.176851 0.306315i
\(113\) −13.2813 −1.24940 −0.624702 0.780863i \(-0.714780\pi\)
−0.624702 + 0.780863i \(0.714780\pi\)
\(114\) 5.75330 4.69360i 0.538846 0.439596i
\(115\) 0 0
\(116\) 3.32241 5.75459i 0.308478 0.534300i
\(117\) −0.297179 + 0.514729i −0.0274742 + 0.0475867i
\(118\) 3.67412 + 6.36376i 0.338230 + 0.585831i
\(119\) −7.67065 + 13.2860i −0.703167 + 1.21792i
\(120\) 0 0
\(121\) 2.28478 0.207707
\(122\) 2.30841 0.208993
\(123\) −6.80772 11.7913i −0.613831 1.06319i
\(124\) −5.42082 9.38914i −0.486804 0.843169i
\(125\) 0 0
\(126\) 0.368358 0.0328160
\(127\) −1.72332 2.98488i −0.152920 0.264865i 0.779380 0.626552i \(-0.215534\pi\)
−0.932300 + 0.361687i \(0.882201\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −3.73733 6.47324i −0.329053 0.569937i
\(130\) 0 0
\(131\) −8.26315 + 14.3122i −0.721955 + 1.25046i 0.238260 + 0.971201i \(0.423423\pi\)
−0.960215 + 0.279261i \(0.909911\pi\)
\(132\) −6.20863 −0.540392
\(133\) 2.61091 + 16.1061i 0.226394 + 1.39658i
\(134\) −6.74324 −0.582527
\(135\) 0 0
\(136\) 2.04920 3.54932i 0.175718 0.304352i
\(137\) 11.1560 + 19.3227i 0.953118 + 1.65085i 0.738618 + 0.674124i \(0.235479\pi\)
0.214499 + 0.976724i \(0.431188\pi\)
\(138\) 3.98994 6.91078i 0.339646 0.588284i
\(139\) 0.880992 + 1.52592i 0.0747248 + 0.129427i 0.900967 0.433889i \(-0.142859\pi\)
−0.826242 + 0.563316i \(0.809526\pi\)
\(140\) 0 0
\(141\) −2.96944 −0.250072
\(142\) 0.994093 + 1.72182i 0.0834225 + 0.144492i
\(143\) 11.0071 + 19.0648i 0.920458 + 1.59428i
\(144\) −0.0984064 −0.00820053
\(145\) 0 0
\(146\) 4.59494 + 7.95867i 0.380280 + 0.658664i
\(147\) 5.97198 10.3438i 0.492561 0.853141i
\(148\) 3.87752 + 6.71607i 0.318731 + 0.552057i
\(149\) 1.80713 3.13005i 0.148046 0.256424i −0.782459 0.622702i \(-0.786035\pi\)
0.930505 + 0.366278i \(0.119368\pi\)
\(150\) 0 0
\(151\) −18.1711 −1.47875 −0.739373 0.673296i \(-0.764878\pi\)
−0.739373 + 0.673296i \(0.764878\pi\)
\(152\) −0.697500 4.30273i −0.0565747 0.348998i
\(153\) 0.403309 0.0326056
\(154\) 6.82173 11.8156i 0.549710 0.952126i
\(155\) 0 0
\(156\) −5.14414 8.90992i −0.411861 0.713364i
\(157\) 3.89153 6.74033i 0.310578 0.537937i −0.667910 0.744242i \(-0.732811\pi\)
0.978488 + 0.206305i \(0.0661440\pi\)
\(158\) −3.07849 5.33210i −0.244912 0.424199i
\(159\) 2.96944 0.235492
\(160\) 0 0
\(161\) 8.76789 + 15.1864i 0.691007 + 1.19686i
\(162\) 4.34755 + 7.53017i 0.341576 + 0.591626i
\(163\) 5.46539 0.428082 0.214041 0.976825i \(-0.431337\pi\)
0.214041 + 0.976825i \(0.431337\pi\)
\(164\) −7.99307 −0.624154
\(165\) 0 0
\(166\) 2.84580 4.92906i 0.220877 0.382570i
\(167\) 9.19994 + 15.9348i 0.711913 + 1.23307i 0.964138 + 0.265400i \(0.0855042\pi\)
−0.252226 + 0.967668i \(0.581163\pi\)
\(168\) −3.18813 + 5.52200i −0.245969 + 0.426031i
\(169\) −11.7398 + 20.3339i −0.903059 + 1.56414i
\(170\) 0 0
\(171\) 0.332370 0.271151i 0.0254170 0.0207354i
\(172\) −4.38806 −0.334587
\(173\) −9.74914 + 16.8860i −0.741214 + 1.28382i 0.210729 + 0.977544i \(0.432416\pi\)
−0.951943 + 0.306275i \(0.900917\pi\)
\(174\) −5.65942 + 9.80241i −0.429040 + 0.743119i
\(175\) 0 0
\(176\) −1.82241 + 3.15651i −0.137370 + 0.237931i
\(177\) −6.25852 10.8401i −0.470419 0.814789i
\(178\) −11.0797 −0.830456
\(179\) −23.5661 −1.76142 −0.880708 0.473660i \(-0.842932\pi\)
−0.880708 + 0.473660i \(0.842932\pi\)
\(180\) 0 0
\(181\) −7.86746 13.6268i −0.584784 1.01288i −0.994902 0.100843i \(-0.967846\pi\)
0.410118 0.912032i \(-0.365487\pi\)
\(182\) 22.6085 1.67585
\(183\) −3.93215 −0.290673
\(184\) −2.34233 4.05703i −0.172679 0.299088i
\(185\) 0 0
\(186\) 9.23386 + 15.9935i 0.677060 + 1.17270i
\(187\) 7.46900 12.9367i 0.546187 0.946024i
\(188\) −0.871618 + 1.50969i −0.0635693 + 0.110105i
\(189\) −19.7562 −1.43705
\(190\) 0 0
\(191\) 6.64483 0.480803 0.240401 0.970674i \(-0.422721\pi\)
0.240401 + 0.970674i \(0.422721\pi\)
\(192\) 0.851703 1.47519i 0.0614664 0.106463i
\(193\) −3.99931 + 6.92701i −0.287877 + 0.498617i −0.973303 0.229525i \(-0.926283\pi\)
0.685426 + 0.728142i \(0.259616\pi\)
\(194\) 0.752610 + 1.30356i 0.0540342 + 0.0935900i
\(195\) 0 0
\(196\) −3.50591 6.07241i −0.250422 0.433743i
\(197\) 0.481593 0.0343121 0.0171560 0.999853i \(-0.494539\pi\)
0.0171560 + 0.999853i \(0.494539\pi\)
\(198\) −0.358674 −0.0254899
\(199\) −11.6793 20.2292i −0.827926 1.43401i −0.899662 0.436587i \(-0.856187\pi\)
0.0717359 0.997424i \(-0.477146\pi\)
\(200\) 0 0
\(201\) 11.4865 0.810193
\(202\) −7.83471 −0.551248
\(203\) −12.4366 21.5408i −0.872877 1.51187i
\(204\) −3.49063 + 6.04594i −0.244393 + 0.423301i
\(205\) 0 0
\(206\) −6.80181 + 11.7811i −0.473905 + 0.820827i
\(207\) 0.230500 0.399238i 0.0160209 0.0277490i
\(208\) −6.03983 −0.418787
\(209\) −2.54227 15.6827i −0.175852 1.08480i
\(210\) 0 0
\(211\) 2.91491 5.04878i 0.200671 0.347572i −0.748074 0.663616i \(-0.769021\pi\)
0.948745 + 0.316043i \(0.102354\pi\)
\(212\) 0.871618 1.50969i 0.0598630 0.103686i
\(213\) −1.69335 2.93296i −0.116026 0.200963i
\(214\) −3.62423 + 6.27735i −0.247747 + 0.429111i
\(215\) 0 0
\(216\) 5.27785 0.359112
\(217\) −40.5828 −2.75494
\(218\) −2.24392 3.88659i −0.151978 0.263233i
\(219\) −7.82705 13.5568i −0.528903 0.916087i
\(220\) 0 0
\(221\) 24.7537 1.66511
\(222\) −6.60500 11.4402i −0.443299 0.767816i
\(223\) 8.36224 14.4838i 0.559977 0.969909i −0.437520 0.899209i \(-0.644143\pi\)
0.997498 0.0707005i \(-0.0225235\pi\)
\(224\) 1.87162 + 3.24174i 0.125053 + 0.216598i
\(225\) 0 0
\(226\) 6.64067 11.5020i 0.441731 0.765101i
\(227\) −4.16186 −0.276232 −0.138116 0.990416i \(-0.544105\pi\)
−0.138116 + 0.990416i \(0.544105\pi\)
\(228\) 1.18813 + 7.32930i 0.0786856 + 0.485395i
\(229\) −5.49828 −0.363337 −0.181668 0.983360i \(-0.558150\pi\)
−0.181668 + 0.983360i \(0.558150\pi\)
\(230\) 0 0
\(231\) −11.6202 + 20.1267i −0.764551 + 1.32424i
\(232\) 3.32241 + 5.75459i 0.218127 + 0.377807i
\(233\) −6.59738 + 11.4270i −0.432209 + 0.748607i −0.997063 0.0765832i \(-0.975599\pi\)
0.564855 + 0.825190i \(0.308932\pi\)
\(234\) −0.297179 0.514729i −0.0194272 0.0336489i
\(235\) 0 0
\(236\) −7.34824 −0.478329
\(237\) 5.24392 + 9.08274i 0.340629 + 0.589987i
\(238\) −7.67065 13.2860i −0.497214 0.861201i
\(239\) 8.47720 0.548345 0.274172 0.961681i \(-0.411596\pi\)
0.274172 + 0.961681i \(0.411596\pi\)
\(240\) 0 0
\(241\) −10.5146 18.2118i −0.677304 1.17313i −0.975790 0.218711i \(-0.929815\pi\)
0.298485 0.954414i \(-0.403519\pi\)
\(242\) −1.14239 + 1.97868i −0.0734356 + 0.127194i
\(243\) 0.511126 + 0.885296i 0.0327887 + 0.0567918i
\(244\) −1.15420 + 1.99914i −0.0738903 + 0.127982i
\(245\) 0 0
\(246\) 13.6154 0.868089
\(247\) 20.3997 16.6423i 1.29800 1.05892i
\(248\) 10.8416 0.688445
\(249\) −4.84755 + 8.39620i −0.307201 + 0.532088i
\(250\) 0 0
\(251\) −13.6183 23.5876i −0.859581 1.48884i −0.872329 0.488919i \(-0.837391\pi\)
0.0127485 0.999919i \(-0.495942\pi\)
\(252\) −0.184179 + 0.319008i −0.0116022 + 0.0200956i
\(253\) −8.53739 14.7872i −0.536741 0.929663i
\(254\) 3.44664 0.216262
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −8.32705 14.4229i −0.519427 0.899674i −0.999745 0.0225796i \(-0.992812\pi\)
0.480318 0.877094i \(-0.340521\pi\)
\(258\) 7.47466 0.465352
\(259\) 29.0290 1.80377
\(260\) 0 0
\(261\) −0.326947 + 0.566288i −0.0202375 + 0.0350524i
\(262\) −8.26315 14.3122i −0.510499 0.884210i
\(263\) 0.994093 1.72182i 0.0612984 0.106172i −0.833748 0.552146i \(-0.813809\pi\)
0.895046 + 0.445974i \(0.147143\pi\)
\(264\) 3.10431 5.37683i 0.191057 0.330921i
\(265\) 0 0
\(266\) −15.2538 5.79196i −0.935269 0.355128i
\(267\) 18.8732 1.15502
\(268\) 3.37162 5.83981i 0.205954 0.356723i
\(269\) −3.57224 + 6.18731i −0.217804 + 0.377247i −0.954136 0.299373i \(-0.903223\pi\)
0.736333 + 0.676620i \(0.236556\pi\)
\(270\) 0 0
\(271\) −5.47940 + 9.49060i −0.332850 + 0.576513i −0.983069 0.183234i \(-0.941344\pi\)
0.650220 + 0.759746i \(0.274677\pi\)
\(272\) 2.04920 + 3.54932i 0.124251 + 0.215209i
\(273\) −38.5115 −2.33082
\(274\) −22.3119 −1.34791
\(275\) 0 0
\(276\) 3.98994 + 6.91078i 0.240166 + 0.415980i
\(277\) 12.2686 0.737147 0.368574 0.929599i \(-0.379846\pi\)
0.368574 + 0.929599i \(0.379846\pi\)
\(278\) −1.76198 −0.105677
\(279\) 0.533443 + 0.923951i 0.0319364 + 0.0553155i
\(280\) 0 0
\(281\) 8.53983 + 14.7914i 0.509443 + 0.882382i 0.999940 + 0.0109390i \(0.00348205\pi\)
−0.490497 + 0.871443i \(0.663185\pi\)
\(282\) 1.48472 2.57161i 0.0884138 0.153137i
\(283\) −15.0064 + 25.9918i −0.892037 + 1.54505i −0.0546077 + 0.998508i \(0.517391\pi\)
−0.837429 + 0.546546i \(0.815943\pi\)
\(284\) −1.98819 −0.117977
\(285\) 0 0
\(286\) −22.0141 −1.30172
\(287\) −14.9600 + 25.9114i −0.883059 + 1.52950i
\(288\) 0.0492032 0.0852224i 0.00289933 0.00502178i
\(289\) 0.101533 + 0.175860i 0.00597251 + 0.0103447i
\(290\) 0 0
\(291\) −1.28200 2.22049i −0.0751522 0.130167i
\(292\) −9.18988 −0.537797
\(293\) 22.4677 1.31258 0.656289 0.754509i \(-0.272125\pi\)
0.656289 + 0.754509i \(0.272125\pi\)
\(294\) 5.97198 + 10.3438i 0.348293 + 0.603261i
\(295\) 0 0
\(296\) −7.75505 −0.450753
\(297\) 19.2368 1.11624
\(298\) 1.80713 + 3.13005i 0.104684 + 0.181319i
\(299\) 14.1473 24.5038i 0.818158 1.41709i
\(300\) 0 0
\(301\) −8.21278 + 14.2250i −0.473377 + 0.819913i
\(302\) 9.08556 15.7367i 0.522816 0.905543i
\(303\) 13.3457 0.766690
\(304\) 4.07502 + 1.54731i 0.233719 + 0.0887445i
\(305\) 0 0
\(306\) −0.201655 + 0.349276i −0.0115278 + 0.0199668i
\(307\) −8.19578 + 14.1955i −0.467758 + 0.810181i −0.999321 0.0368378i \(-0.988271\pi\)
0.531563 + 0.847019i \(0.321605\pi\)
\(308\) 6.82173 + 11.8156i 0.388704 + 0.673255i
\(309\) 11.5863 20.0680i 0.659119 1.14163i
\(310\) 0 0
\(311\) −18.0197 −1.02180 −0.510902 0.859639i \(-0.670688\pi\)
−0.510902 + 0.859639i \(0.670688\pi\)
\(312\) 10.2883 0.582459
\(313\) −9.00522 15.5975i −0.509005 0.881623i −0.999946 0.0104296i \(-0.996680\pi\)
0.490941 0.871193i \(-0.336653\pi\)
\(314\) 3.89153 + 6.74033i 0.219612 + 0.380379i
\(315\) 0 0
\(316\) 6.15698 0.346357
\(317\) −11.6277 20.1398i −0.653076 1.13116i −0.982372 0.186935i \(-0.940145\pi\)
0.329296 0.944227i \(-0.393189\pi\)
\(318\) −1.48472 + 2.57161i −0.0832589 + 0.144209i
\(319\) 12.1096 + 20.9745i 0.678009 + 1.17435i
\(320\) 0 0
\(321\) 6.17353 10.6929i 0.344573 0.596818i
\(322\) −17.5358 −0.977231
\(323\) −16.7011 6.34152i −0.929274 0.352851i
\(324\) −8.69510 −0.483061
\(325\) 0 0
\(326\) −2.73270 + 4.73317i −0.151350 + 0.262146i
\(327\) 3.82231 + 6.62044i 0.211374 + 0.366111i
\(328\) 3.99653 6.92220i 0.220672 0.382214i
\(329\) 3.26267 + 5.65111i 0.179877 + 0.311556i
\(330\) 0 0
\(331\) 7.38319 0.405817 0.202908 0.979198i \(-0.434961\pi\)
0.202908 + 0.979198i \(0.434961\pi\)
\(332\) 2.84580 + 4.92906i 0.156183 + 0.270518i
\(333\) −0.381573 0.660904i −0.0209101 0.0362173i
\(334\) −18.3999 −1.00680
\(335\) 0 0
\(336\) −3.18813 5.52200i −0.173927 0.301250i
\(337\) 15.4400 26.7429i 0.841073 1.45678i −0.0479153 0.998851i \(-0.515258\pi\)
0.888988 0.457930i \(-0.151409\pi\)
\(338\) −11.7398 20.3339i −0.638559 1.10602i
\(339\) −11.3118 + 19.5926i −0.614371 + 1.06412i
\(340\) 0 0
\(341\) 39.5159 2.13991
\(342\) 0.0686384 + 0.423416i 0.00371154 + 0.0228957i
\(343\) −0.0442191 −0.00238761
\(344\) 2.19403 3.80018i 0.118294 0.204892i
\(345\) 0 0
\(346\) −9.74914 16.8860i −0.524117 0.907797i
\(347\) 4.55974 7.89771i 0.244780 0.423971i −0.717290 0.696775i \(-0.754618\pi\)
0.962070 + 0.272804i \(0.0879510\pi\)
\(348\) −5.65942 9.80241i −0.303377 0.525464i
\(349\) −14.2508 −0.762827 −0.381414 0.924404i \(-0.624563\pi\)
−0.381414 + 0.924404i \(0.624563\pi\)
\(350\) 0 0
\(351\) 15.9386 + 27.6065i 0.850742 + 1.47353i
\(352\) −1.82241 3.15651i −0.0971350 0.168243i
\(353\) 7.77613 0.413882 0.206941 0.978353i \(-0.433649\pi\)
0.206941 + 0.978353i \(0.433649\pi\)
\(354\) 12.5170 0.665273
\(355\) 0 0
\(356\) 5.53983 9.59527i 0.293610 0.508548i
\(357\) 13.0662 + 22.6314i 0.691539 + 1.19778i
\(358\) 11.7831 20.4089i 0.622754 1.07864i
\(359\) −2.90437 + 5.03052i −0.153287 + 0.265501i −0.932434 0.361340i \(-0.882319\pi\)
0.779147 + 0.626841i \(0.215653\pi\)
\(360\) 0 0
\(361\) −18.0270 + 6.00231i −0.948789 + 0.315911i
\(362\) 15.7349 0.827009
\(363\) 1.94595 3.37049i 0.102136 0.176905i
\(364\) −11.3043 + 19.5795i −0.592504 + 1.02625i
\(365\) 0 0
\(366\) 1.96608 3.40535i 0.102769 0.178000i
\(367\) −11.1414 19.2974i −0.581574 1.00732i −0.995293 0.0969115i \(-0.969104\pi\)
0.413719 0.910405i \(-0.364230\pi\)
\(368\) 4.68466 0.244205
\(369\) 0.786568 0.0409471
\(370\) 0 0
\(371\) −3.26267 5.65111i −0.169389 0.293391i
\(372\) −18.4677 −0.957507
\(373\) −17.0609 −0.883380 −0.441690 0.897168i \(-0.645621\pi\)
−0.441690 + 0.897168i \(0.645621\pi\)
\(374\) 7.46900 + 12.9367i 0.386213 + 0.668940i
\(375\) 0 0
\(376\) −0.871618 1.50969i −0.0449503 0.0778561i
\(377\) −20.0668 + 34.7567i −1.03349 + 1.79006i
\(378\) 9.87811 17.1094i 0.508075 0.880012i
\(379\) −10.0329 −0.515355 −0.257678 0.966231i \(-0.582957\pi\)
−0.257678 + 0.966231i \(0.582957\pi\)
\(380\) 0 0
\(381\) −5.87103 −0.300782
\(382\) −3.32241 + 5.75459i −0.169990 + 0.294430i
\(383\) 0.994093 1.72182i 0.0507958 0.0879809i −0.839510 0.543345i \(-0.817158\pi\)
0.890305 + 0.455364i \(0.150491\pi\)
\(384\) 0.851703 + 1.47519i 0.0434633 + 0.0752806i
\(385\) 0 0
\(386\) −3.99931 6.92701i −0.203560 0.352576i
\(387\) 0.431814 0.0219503
\(388\) −1.50522 −0.0764159
\(389\) −4.43854 7.68778i −0.225043 0.389786i 0.731289 0.682067i \(-0.238919\pi\)
−0.956332 + 0.292282i \(0.905586\pi\)
\(390\) 0 0
\(391\) −19.1996 −0.970967
\(392\) 7.01181 0.354150
\(393\) 14.0755 + 24.3795i 0.710015 + 1.22978i
\(394\) −0.240797 + 0.417072i −0.0121312 + 0.0210118i
\(395\) 0 0
\(396\) 0.179337 0.310621i 0.00901203 0.0156093i
\(397\) −10.5563 + 18.2840i −0.529804 + 0.917648i 0.469591 + 0.882884i \(0.344401\pi\)
−0.999396 + 0.0347640i \(0.988932\pi\)
\(398\) 23.3587 1.17086
\(399\) 25.9834 + 9.86606i 1.30080 + 0.493921i
\(400\) 0 0
\(401\) −14.9806 + 25.9471i −0.748094 + 1.29574i 0.200642 + 0.979665i \(0.435697\pi\)
−0.948735 + 0.316072i \(0.897636\pi\)
\(402\) −5.74324 + 9.94758i −0.286447 + 0.496140i
\(403\) 32.7408 + 56.7088i 1.63094 + 2.82487i
\(404\) 3.91735 6.78506i 0.194896 0.337569i
\(405\) 0 0
\(406\) 24.8732 1.23443
\(407\) −28.2658 −1.40109
\(408\) −3.49063 6.04594i −0.172812 0.299319i
\(409\) 2.09772 + 3.63336i 0.103726 + 0.179658i 0.913217 0.407474i \(-0.133590\pi\)
−0.809491 + 0.587132i \(0.800257\pi\)
\(410\) 0 0
\(411\) 38.0063 1.87471
\(412\) −6.80181 11.7811i −0.335101 0.580412i
\(413\) −13.7531 + 23.8210i −0.676745 + 1.17216i
\(414\) 0.230500 + 0.399238i 0.0113285 + 0.0196215i
\(415\) 0 0
\(416\) 3.01991 5.23065i 0.148063 0.256453i
\(417\) 3.00137 0.146978
\(418\) 14.8528 + 5.63969i 0.726473 + 0.275846i
\(419\) 12.5326 0.612255 0.306128 0.951990i \(-0.400967\pi\)
0.306128 + 0.951990i \(0.400967\pi\)
\(420\) 0 0
\(421\) 13.2883 23.0160i 0.647631 1.12173i −0.336056 0.941842i \(-0.609093\pi\)
0.983687 0.179888i \(-0.0575736\pi\)
\(422\) 2.91491 + 5.04878i 0.141896 + 0.245771i
\(423\) 0.0857727 0.148563i 0.00417041 0.00722337i
\(424\) 0.871618 + 1.50969i 0.0423295 + 0.0733169i
\(425\) 0 0
\(426\) 3.38669 0.164086
\(427\) 4.32045 + 7.48325i 0.209081 + 0.362140i
\(428\) −3.62423 6.27735i −0.175184 0.303427i
\(429\) 37.4990 1.81047
\(430\) 0 0
\(431\) 0.0903049 + 0.156413i 0.00434983 + 0.00753413i 0.868192 0.496228i \(-0.165282\pi\)
−0.863842 + 0.503762i \(0.831949\pi\)
\(432\) −2.63892 + 4.57075i −0.126965 + 0.219910i
\(433\) −6.00522 10.4013i −0.288592 0.499857i 0.684882 0.728654i \(-0.259854\pi\)
−0.973474 + 0.228798i \(0.926521\pi\)
\(434\) 20.2914 35.1458i 0.974019 1.68705i
\(435\) 0 0
\(436\) 4.48785 0.214929
\(437\) −15.8225 + 12.9082i −0.756895 + 0.617483i
\(438\) 15.6541 0.747982
\(439\) 14.2544 24.6893i 0.680324 1.17835i −0.294559 0.955633i \(-0.595173\pi\)
0.974882 0.222722i \(-0.0714941\pi\)
\(440\) 0 0
\(441\) 0.345004 + 0.597564i 0.0164287 + 0.0284554i
\(442\) −12.3768 + 21.4373i −0.588706 + 1.01967i
\(443\) 4.27321 + 7.40142i 0.203026 + 0.351652i 0.949502 0.313761i \(-0.101589\pi\)
−0.746476 + 0.665413i \(0.768256\pi\)
\(444\) 13.2100 0.626919
\(445\) 0 0
\(446\) 8.36224 + 14.4838i 0.395964 + 0.685829i
\(447\) −3.07828 5.33174i −0.145598 0.252183i
\(448\) −3.74324 −0.176851
\(449\) −4.24612 −0.200387 −0.100193 0.994968i \(-0.531946\pi\)
−0.100193 + 0.994968i \(0.531946\pi\)
\(450\) 0 0
\(451\) 14.5667 25.2302i 0.685918 1.18805i
\(452\) 6.64067 + 11.5020i 0.312351 + 0.541008i
\(453\) −15.4764 + 26.8059i −0.727145 + 1.25945i
\(454\) 2.08093 3.60428i 0.0976629 0.169157i
\(455\) 0 0
\(456\) −6.94142 2.63570i −0.325062 0.123428i
\(457\) −18.2204 −0.852316 −0.426158 0.904649i \(-0.640133\pi\)
−0.426158 + 0.904649i \(0.640133\pi\)
\(458\) 2.74914 4.76165i 0.128459 0.222497i
\(459\) 10.8154 18.7328i 0.504819 0.874371i
\(460\) 0 0
\(461\) −15.0140 + 26.0050i −0.699272 + 1.21117i 0.269447 + 0.963015i \(0.413159\pi\)
−0.968719 + 0.248160i \(0.920174\pi\)
\(462\) −11.6202 20.1267i −0.540619 0.936380i
\(463\) 10.1656 0.472434 0.236217 0.971700i \(-0.424092\pi\)
0.236217 + 0.971700i \(0.424092\pi\)
\(464\) −6.64483 −0.308478
\(465\) 0 0
\(466\) −6.59738 11.4270i −0.305618 0.529345i
\(467\) 13.6129 0.629930 0.314965 0.949103i \(-0.398007\pi\)
0.314965 + 0.949103i \(0.398007\pi\)
\(468\) 0.594358 0.0274742
\(469\) −12.6208 21.8598i −0.582773 1.00939i
\(470\) 0 0
\(471\) −6.62886 11.4815i −0.305442 0.529041i
\(472\) 3.67412 6.36376i 0.169115 0.292916i
\(473\) 7.99687 13.8510i 0.367697 0.636869i
\(474\) −10.4878 −0.481723
\(475\) 0 0
\(476\) 15.3413 0.703167
\(477\) −0.0857727 + 0.148563i −0.00392726 + 0.00680222i
\(478\) −4.23860 + 7.34147i −0.193869 + 0.335791i
\(479\) −2.71463 4.70188i −0.124035 0.214835i 0.797320 0.603556i \(-0.206250\pi\)
−0.921355 + 0.388722i \(0.872917\pi\)
\(480\) 0 0
\(481\) −23.4196 40.5639i −1.06784 1.84956i
\(482\) 21.0292 0.957853
\(483\) 29.8706 1.35916
\(484\) −1.14239 1.97868i −0.0519268 0.0899399i
\(485\) 0 0
\(486\) −1.02225 −0.0463703
\(487\) 32.5569 1.47529 0.737646 0.675188i \(-0.235937\pi\)
0.737646 + 0.675188i \(0.235937\pi\)
\(488\) −1.15420 1.99914i −0.0522483 0.0904968i
\(489\) 4.65489 8.06251i 0.210501 0.364599i
\(490\) 0 0
\(491\) −15.3410 + 26.5713i −0.692328 + 1.19915i 0.278746 + 0.960365i \(0.410081\pi\)
−0.971073 + 0.238782i \(0.923252\pi\)
\(492\) −6.80772 + 11.7913i −0.306916 + 0.531594i
\(493\) 27.2332 1.22652
\(494\) 4.21278 + 25.9878i 0.189542 + 1.16924i
\(495\) 0 0
\(496\) −5.42082 + 9.38914i −0.243402 + 0.421585i
\(497\) −3.72113 + 6.44518i −0.166915 + 0.289106i
\(498\) −4.84755 8.39620i −0.217224 0.376243i
\(499\) 4.91213 8.50807i 0.219897 0.380873i −0.734879 0.678198i \(-0.762761\pi\)
0.954776 + 0.297325i \(0.0960944\pi\)
\(500\) 0 0
\(501\) 31.3425 1.40028
\(502\) 27.2366 1.21563
\(503\) −7.57502 13.1203i −0.337754 0.585006i 0.646256 0.763121i \(-0.276334\pi\)
−0.984010 + 0.178114i \(0.943000\pi\)
\(504\) −0.184179 0.319008i −0.00820399 0.0142097i
\(505\) 0 0
\(506\) 17.0748 0.759067
\(507\) 19.9976 + 34.6369i 0.888124 + 1.53828i
\(508\) −1.72332 + 2.98488i −0.0764600 + 0.132433i
\(509\) 1.12110 + 1.94180i 0.0496919 + 0.0860690i 0.889801 0.456348i \(-0.150843\pi\)
−0.840110 + 0.542417i \(0.817509\pi\)
\(510\) 0 0
\(511\) −17.1999 + 29.7912i −0.760881 + 1.31788i
\(512\) 1.00000 0.0441942
\(513\) −3.68130 22.7091i −0.162533 1.00263i
\(514\) 16.6541 0.734581
\(515\) 0 0
\(516\) −3.73733 + 6.47324i −0.164527 + 0.284969i
\(517\) −3.17690 5.50255i −0.139720 0.242002i
\(518\) −14.5145 + 25.1398i −0.637730 + 1.10458i
\(519\) 16.6068 + 28.7637i 0.728956 + 1.26259i
\(520\) 0 0
\(521\) −7.06785 −0.309648 −0.154824 0.987942i \(-0.549481\pi\)
−0.154824 + 0.987942i \(0.549481\pi\)
\(522\) −0.326947 0.566288i −0.0143101 0.0247858i
\(523\) 17.4970 + 30.3057i 0.765091 + 1.32518i 0.940199 + 0.340627i \(0.110639\pi\)
−0.175108 + 0.984549i \(0.556027\pi\)
\(524\) 16.5263 0.721955
\(525\) 0 0
\(526\) 0.994093 + 1.72182i 0.0433445 + 0.0750749i
\(527\) 22.2167 38.4805i 0.967776 1.67624i
\(528\) 3.10431 + 5.37683i 0.135098 + 0.233996i
\(529\) 0.526988 0.912769i 0.0229125 0.0396856i
\(530\) 0 0
\(531\) 0.723113 0.0313804
\(532\) 12.6429 10.3142i 0.548138 0.447176i
\(533\) 48.2767 2.09110
\(534\) −9.43658 + 16.3446i −0.408361 + 0.707302i
\(535\) 0 0
\(536\) 3.37162 + 5.83981i 0.145632 + 0.252242i
\(537\) −20.0713 + 34.7646i −0.866143 + 1.50020i
\(538\) −3.57224 6.18731i −0.154010 0.266754i
\(539\) 25.5569 1.10081
\(540\) 0 0
\(541\) 14.4090 + 24.9571i 0.619492 + 1.07299i 0.989579 + 0.143994i \(0.0459946\pi\)
−0.370087 + 0.928997i \(0.620672\pi\)
\(542\) −5.47940 9.49060i −0.235360 0.407656i
\(543\) −26.8030 −1.15023
\(544\) −4.09841 −0.175718
\(545\) 0 0
\(546\) 19.2557 33.3519i 0.824069 1.42733i
\(547\) −16.0375 27.7778i −0.685715 1.18769i −0.973211 0.229912i \(-0.926156\pi\)
0.287496 0.957782i \(-0.407177\pi\)
\(548\) 11.1560 19.3227i 0.476559 0.825424i
\(549\) 0.113581 0.196728i 0.00484752 0.00839615i
\(550\) 0 0
\(551\) 22.4431 18.3093i 0.956107 0.780002i
\(552\) −7.97988 −0.339646
\(553\) 11.5235 19.9593i 0.490030 0.848757i
\(554\) −6.13429 + 10.6249i −0.260621 + 0.451409i
\(555\) 0 0
\(556\) 0.880992 1.52592i 0.0373624 0.0647135i
\(557\) 5.18813 + 8.98610i 0.219828 + 0.380753i 0.954755 0.297393i \(-0.0961171\pi\)
−0.734927 + 0.678146i \(0.762784\pi\)
\(558\) −1.06689 −0.0451649
\(559\) 26.5032 1.12096
\(560\) 0 0
\(561\) −12.7227 22.0364i −0.537154 0.930379i
\(562\) −17.0797 −0.720462
\(563\) −8.44664 −0.355984 −0.177992 0.984032i \(-0.556960\pi\)
−0.177992 + 0.984032i \(0.556960\pi\)
\(564\) 1.48472 + 2.57161i 0.0625180 + 0.108284i
\(565\) 0 0
\(566\) −15.0064 25.9918i −0.630765 1.09252i
\(567\) −16.2739 + 28.1872i −0.683440 + 1.18375i
\(568\) 0.994093 1.72182i 0.0417112 0.0722460i
\(569\) 1.80181 0.0755359 0.0377680 0.999287i \(-0.487975\pi\)
0.0377680 + 0.999287i \(0.487975\pi\)
\(570\) 0 0
\(571\) 2.70574 0.113232 0.0566158 0.998396i \(-0.481969\pi\)
0.0566158 + 0.998396i \(0.481969\pi\)
\(572\) 11.0071 19.0648i 0.460229 0.797140i
\(573\) 5.65942 9.80241i 0.236426 0.409501i
\(574\) −14.9600 25.9114i −0.624417 1.08152i
\(575\) 0 0
\(576\) 0.0492032 + 0.0852224i 0.00205013 + 0.00355093i
\(577\) −6.61544 −0.275404 −0.137702 0.990474i \(-0.543972\pi\)
−0.137702 + 0.990474i \(0.543972\pi\)
\(578\) −0.203065 −0.00844640
\(579\) 6.81246 + 11.7995i 0.283116 + 0.490371i
\(580\) 0 0
\(581\) 21.3050 0.883879
\(582\) 2.56400 0.106281
\(583\) 3.17690 + 5.50255i 0.131574 + 0.227892i
\(584\) 4.59494 7.95867i 0.190140 0.329332i
\(585\) 0 0
\(586\) −11.2339 + 19.4576i −0.464067 + 0.803787i
\(587\) 7.21463 12.4961i 0.297780 0.515770i −0.677848 0.735202i \(-0.737087\pi\)
0.975628 + 0.219432i \(0.0704205\pi\)
\(588\) −11.9440 −0.492561
\(589\) −7.56204 46.6487i −0.311589 1.92212i
\(590\) 0 0
\(591\) 0.410174 0.710443i 0.0168723 0.0292237i
\(592\) 3.87752 6.71607i 0.159365 0.276029i
\(593\) 10.3722 + 17.9652i 0.425935 + 0.737742i 0.996507 0.0835060i \(-0.0266118\pi\)
−0.570572 + 0.821248i \(0.693278\pi\)
\(594\) −9.61842 + 16.6596i −0.394649 + 0.683552i
\(595\) 0 0
\(596\) −3.61427 −0.148046
\(597\) −39.7893 −1.62847
\(598\) 14.1473 + 24.5038i 0.578525 + 1.00203i
\(599\) 9.41389 + 16.3053i 0.384641 + 0.666218i 0.991719 0.128424i \(-0.0409919\pi\)
−0.607078 + 0.794642i \(0.707659\pi\)
\(600\) 0 0
\(601\) −23.0999 −0.942263 −0.471131 0.882063i \(-0.656154\pi\)
−0.471131 + 0.882063i \(0.656154\pi\)
\(602\) −8.21278 14.2250i −0.334728 0.579766i
\(603\) −0.331789 + 0.574675i −0.0135115 + 0.0234026i
\(604\) 9.08556 + 15.7367i 0.369686 + 0.640316i
\(605\) 0 0
\(606\) −6.67285 + 11.5577i −0.271066 + 0.469500i
\(607\) 28.6025 1.16094 0.580470 0.814281i \(-0.302869\pi\)
0.580470 + 0.814281i \(0.302869\pi\)
\(608\) −3.37752 + 2.75542i −0.136977 + 0.111747i
\(609\) −42.3691 −1.71688
\(610\) 0 0
\(611\) 5.26442 9.11825i 0.212976 0.368885i
\(612\) −0.201655 0.349276i −0.00815141 0.0141186i
\(613\) −3.72507 + 6.45202i −0.150454 + 0.260594i −0.931395 0.364011i \(-0.881407\pi\)
0.780940 + 0.624606i \(0.214740\pi\)
\(614\) −8.19578 14.1955i −0.330755 0.572884i
\(615\) 0 0
\(616\) −13.6435 −0.549710
\(617\) −15.6711 27.1432i −0.630896 1.09274i −0.987369 0.158438i \(-0.949354\pi\)
0.356473 0.934306i \(-0.383979\pi\)
\(618\) 11.5863 + 20.0680i 0.466067 + 0.807252i
\(619\) 1.60012 0.0643143 0.0321572 0.999483i \(-0.489762\pi\)
0.0321572 + 0.999483i \(0.489762\pi\)
\(620\) 0 0
\(621\) −12.3625 21.4124i −0.496088 0.859250i
\(622\) 9.00985 15.6055i 0.361262 0.625724i
\(623\) −20.7369 35.9173i −0.830806 1.43900i
\(624\) −5.14414 + 8.90992i −0.205930 + 0.356682i
\(625\) 0 0
\(626\) 18.0104 0.719842
\(627\) −25.3003 9.60669i −1.01040 0.383654i
\(628\) −7.78306 −0.310578
\(629\) −15.8917 + 27.5252i −0.633642 + 1.09750i
\(630\) 0 0
\(631\) 6.44386 + 11.1611i 0.256526 + 0.444316i 0.965309 0.261111i \(-0.0840887\pi\)
−0.708783 + 0.705427i \(0.750755\pi\)
\(632\) −3.07849 + 5.33210i −0.122456 + 0.212100i
\(633\) −4.96528 8.60012i −0.197352 0.341824i
\(634\) 23.2554 0.923590
\(635\) 0 0
\(636\) −1.48472 2.57161i −0.0588730 0.101971i
\(637\) 21.1751 + 36.6763i 0.838987 + 1.45317i
\(638\) −24.2193 −0.958850
\(639\) 0.195650 0.00773980
\(640\) 0 0
\(641\) 13.9086 24.0903i 0.549355 0.951511i −0.448964 0.893550i \(-0.648207\pi\)
0.998319 0.0579612i \(-0.0184600\pi\)
\(642\) 6.17353 + 10.6929i 0.243650 + 0.422014i
\(643\) −8.50292 + 14.7275i −0.335322 + 0.580795i −0.983547 0.180654i \(-0.942179\pi\)
0.648224 + 0.761449i \(0.275512\pi\)
\(644\) 8.76789 15.1864i 0.345503 0.598429i
\(645\) 0 0
\(646\) 13.8425 11.2928i 0.544625 0.444310i
\(647\) −42.3379 −1.66447 −0.832237 0.554420i \(-0.812940\pi\)
−0.832237 + 0.554420i \(0.812940\pi\)
\(648\) 4.34755 7.53017i 0.170788 0.295813i
\(649\) 13.3915 23.1948i 0.525664 0.910476i
\(650\) 0 0
\(651\) −34.5645 + 59.8675i −1.35469 + 2.34639i
\(652\) −2.73270 4.73317i −0.107021 0.185365i
\(653\) −48.6365 −1.90329 −0.951647 0.307194i \(-0.900610\pi\)
−0.951647 + 0.307194i \(0.900610\pi\)
\(654\) −7.64463 −0.298929
\(655\) 0 0
\(656\) 3.99653 + 6.92220i 0.156038 + 0.270266i
\(657\) 0.904342 0.0352818
\(658\) −6.52534 −0.254384
\(659\) −5.47593 9.48459i −0.213312 0.369467i 0.739437 0.673226i \(-0.235092\pi\)
−0.952749 + 0.303758i \(0.901758\pi\)
\(660\) 0 0
\(661\) 12.3214 + 21.3413i 0.479246 + 0.830079i 0.999717 0.0238007i \(-0.00757670\pi\)
−0.520470 + 0.853880i \(0.674243\pi\)
\(662\) −3.69159 + 6.39403i −0.143478 + 0.248511i
\(663\) 21.0828 36.5165i 0.818788 1.41818i
\(664\) −5.69159 −0.220877
\(665\) 0 0
\(666\) 0.763146 0.0295713
\(667\) 15.5644 26.9583i 0.602655 1.04383i
\(668\) 9.19994 15.9348i 0.355956 0.616534i
\(669\) −14.2443 24.6719i −0.550716 0.953869i
\(670\) 0 0
\(671\) −4.20687 7.28652i −0.162405 0.281293i
\(672\) 6.37625 0.245969
\(673\) 5.18012 0.199679 0.0998395 0.995004i \(-0.468167\pi\)
0.0998395 + 0.995004i \(0.468167\pi\)
\(674\) 15.4400 + 26.7429i 0.594728 + 1.03010i
\(675\) 0 0
\(676\) 23.4795 0.903059
\(677\) −45.4548 −1.74697 −0.873485 0.486851i \(-0.838146\pi\)
−0.873485 + 0.486851i \(0.838146\pi\)
\(678\) −11.3118 19.5926i −0.434426 0.752448i
\(679\) −2.81720 + 4.87953i −0.108114 + 0.187259i
\(680\) 0 0
\(681\) −3.54467 + 6.13955i −0.135832 + 0.235268i
\(682\) −19.7580 + 34.2218i −0.756572 + 1.31042i
\(683\) 3.24495 0.124165 0.0620823 0.998071i \(-0.480226\pi\)
0.0620823 + 0.998071i \(0.480226\pi\)
\(684\) −0.401008 0.152265i −0.0153329 0.00582201i
\(685\) 0 0
\(686\) 0.0221096 0.0382949i 0.000844147 0.00146211i
\(687\) −4.68291 + 8.11103i −0.178664 + 0.309455i
\(688\) 2.19403 + 3.80018i 0.0836467 + 0.144880i
\(689\) −5.26442 + 9.11825i −0.200559 + 0.347378i
\(690\) 0 0
\(691\) 44.0806 1.67691 0.838453 0.544974i \(-0.183461\pi\)
0.838453 + 0.544974i \(0.183461\pi\)
\(692\) 19.4983 0.741214
\(693\) −0.671301 1.16273i −0.0255006 0.0441684i
\(694\) 4.55974 + 7.89771i 0.173086 + 0.299793i
\(695\) 0 0
\(696\) 11.3188 0.429040
\(697\) −16.3794 28.3700i −0.620415 1.07459i
\(698\) 7.12539 12.3415i 0.269700 0.467134i
\(699\) 11.2380 + 19.4648i 0.425061 + 0.736227i
\(700\) 0 0
\(701\) −25.7667 + 44.6292i −0.973193 + 1.68562i −0.287420 + 0.957805i \(0.592797\pi\)
−0.685773 + 0.727815i \(0.740536\pi\)
\(702\) −31.8773 −1.20313
\(703\) 5.40915 + 33.3679i 0.204010 + 1.25849i
\(704\) 3.64483 0.137370
\(705\) 0 0
\(706\) −3.88806 + 6.73433i −0.146329 + 0.253450i
\(707\) −14.6636 25.3981i −0.551481 0.955192i
\(708\) −6.25852 + 10.8401i −0.235209 + 0.407395i
\(709\) −4.42556 7.66530i −0.166205 0.287876i 0.770877 0.636984i \(-0.219818\pi\)
−0.937083 + 0.349107i \(0.886485\pi\)
\(710\) 0 0
\(711\) −0.605886 −0.0227225
\(712\) 5.53983 + 9.59527i 0.207614 + 0.359598i
\(713\) −25.3947 43.9849i −0.951039 1.64725i
\(714\) −26.1325 −0.977983
\(715\) 0 0
\(716\) 11.7831 + 20.4089i 0.440354 + 0.762715i
\(717\) 7.22006 12.5055i 0.269638 0.467027i
\(718\) −2.90437 5.03052i −0.108390 0.187737i
\(719\) −23.5785 + 40.8392i −0.879331 + 1.52305i −0.0272540 + 0.999629i \(0.508676\pi\)
−0.852077 + 0.523417i \(0.824657\pi\)
\(720\) 0 0
\(721\) −50.9216 −1.89642
\(722\) 3.81534 18.6130i 0.141992 0.692704i
\(723\) −35.8213 −1.33221
\(724\) −7.86746 + 13.6268i −0.292392 + 0.506438i
\(725\) 0 0
\(726\) 1.94595 + 3.37049i 0.0722212 + 0.125091i
\(727\) −6.52177 + 11.2960i −0.241879 + 0.418947i −0.961250 0.275680i \(-0.911097\pi\)
0.719371 + 0.694627i \(0.244430\pi\)
\(728\) −11.3043 19.5795i −0.418963 0.725666i
\(729\) 27.8266 1.03061
\(730\) 0 0
\(731\) −8.99204 15.5747i −0.332582 0.576050i
\(732\) 1.96608 + 3.40535i 0.0726683 + 0.125865i
\(733\) 13.9861 0.516590 0.258295 0.966066i \(-0.416839\pi\)
0.258295 + 0.966066i \(0.416839\pi\)
\(734\) 22.2827 0.822470
\(735\) 0 0
\(736\) −2.34233 + 4.05703i −0.0863394 + 0.149544i
\(737\) 12.2890 + 21.2851i 0.452670 + 0.784048i
\(738\) −0.393284 + 0.681188i −0.0144770 + 0.0250749i
\(739\) −0.534508 + 0.925795i −0.0196622 + 0.0340559i −0.875689 0.482875i \(-0.839592\pi\)
0.856027 + 0.516931i \(0.172926\pi\)
\(740\) 0 0
\(741\) −7.17608 44.2677i −0.263620 1.62622i
\(742\) 6.52534 0.239553
\(743\) 5.00591 8.67048i 0.183649 0.318089i −0.759472 0.650541i \(-0.774542\pi\)
0.943120 + 0.332451i \(0.107876\pi\)
\(744\) 9.23386 15.9935i 0.338530 0.586351i
\(745\) 0 0
\(746\) 8.53046 14.7752i 0.312322 0.540958i
\(747\) −0.280045 0.485051i −0.0102463 0.0177471i
\(748\) −14.9380 −0.546187
\(749\) −27.1327 −0.991406
\(750\) 0 0
\(751\) −17.3070 29.9767i −0.631543 1.09386i −0.987236 0.159261i \(-0.949089\pi\)
0.355694 0.934603i \(-0.384245\pi\)
\(752\) 1.74324 0.0635693
\(753\) −46.3951 −1.69073
\(754\) −20.0668 34.7567i −0.730790 1.26577i
\(755\) 0 0
\(756\) 9.87811 + 17.1094i 0.359263 + 0.622262i
\(757\) −1.67642 + 2.90364i −0.0609305 + 0.105535i −0.894882 0.446304i \(-0.852740\pi\)
0.833951 + 0.551838i \(0.186073\pi\)
\(758\) 5.01645 8.68874i 0.182206 0.315589i
\(759\) −29.0853 −1.05573
\(760\) 0 0
\(761\) 27.5087 0.997190 0.498595 0.866835i \(-0.333849\pi\)
0.498595 + 0.866835i \(0.333849\pi\)
\(762\) 2.93552 5.08446i 0.106343 0.184191i
\(763\) 8.39953 14.5484i 0.304083 0.526688i
\(764\) −3.32241 5.75459i −0.120201 0.208194i
\(765\) 0 0
\(766\) 0.994093 + 1.72182i 0.0359181 + 0.0622119i
\(767\) 44.3821 1.60254
\(768\) −1.70341 −0.0614664
\(769\) 17.1306 + 29.6711i 0.617746 + 1.06997i 0.989896 + 0.141795i \(0.0452872\pi\)
−0.372150 + 0.928172i \(0.621379\pi\)
\(770\) 0 0
\(771\) −28.3687 −1.02167
\(772\) 7.99863 0.287877
\(773\) 5.98184 + 10.3608i 0.215152 + 0.372654i 0.953320 0.301963i \(-0.0976421\pi\)
−0.738168 + 0.674617i \(0.764309\pi\)
\(774\) −0.215907 + 0.373961i −0.00776061 + 0.0134418i
\(775\) 0 0
\(776\) 0.752610 1.30356i 0.0270171 0.0467950i
\(777\) 24.7241 42.8233i 0.886971 1.53628i
\(778\) 8.87708 0.318259
\(779\) −32.5719 12.3678i −1.16701 0.443121i
\(780\) 0 0
\(781\) 3.62330 6.27574i 0.129652 0.224564i
\(782\) 9.59982 16.6274i 0.343289 0.594594i
\(783\) 17.5352 + 30.3718i 0.626657 + 1.08540i
\(784\) −3.50591 + 6.07241i −0.125211 + 0.216872i
\(785\) 0 0
\(786\)