Properties

Label 42.4.e.c.25.1
Level $42$
Weight $4$
Character 42.25
Analytic conductor $2.478$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 42.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.47808022024\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{1345})\)
Defining polynomial: \(x^{4} - x^{3} + 337 x^{2} + 336 x + 112896\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 25.1
Root \(-8.91856 - 15.4474i\) of defining polynomial
Character \(\chi\) \(=\) 42.25
Dual form 42.4.e.c.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-10.4186 - 18.0455i) q^{5} +6.00000 q^{6} +(-18.3371 - 2.59808i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-10.4186 - 18.0455i) q^{5} +6.00000 q^{6} +(-18.3371 - 2.59808i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-20.8371 + 36.0910i) q^{10} +(-7.58144 + 13.1314i) q^{11} +(-6.00000 - 10.3923i) q^{12} +2.16288 q^{13} +(13.8371 + 34.3589i) q^{14} +62.5114 q^{15} +(-8.00000 - 13.8564i) q^{16} +(59.6742 - 103.359i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(16.7557 + 29.0217i) q^{19} +83.3485 q^{20} +(34.2557 - 43.7441i) q^{21} +30.3258 q^{22} +(-0.325758 - 0.564230i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-154.593 + 267.763i) q^{25} +(-2.16288 - 3.74622i) q^{26} +27.0000 q^{27} +(45.6742 - 58.3255i) q^{28} -163.208 q^{29} +(-62.5114 - 108.273i) q^{30} +(111.663 - 193.406i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-22.7443 - 39.3943i) q^{33} -238.697 q^{34} +(144.163 + 357.970i) q^{35} +36.0000 q^{36} +(-84.2670 - 145.955i) q^{37} +(33.5114 - 58.0434i) q^{38} +(-3.24432 + 5.61932i) q^{39} +(-83.3485 - 144.364i) q^{40} -323.023 q^{41} +(-110.023 - 15.5885i) q^{42} +221.557 q^{43} +(-30.3258 - 52.5258i) q^{44} +(-93.7670 + 162.409i) q^{45} +(-0.651517 + 1.12846i) q^{46} +(-254.023 - 439.980i) q^{47} +48.0000 q^{48} +(329.500 + 95.2825i) q^{49} +618.371 q^{50} +(179.023 + 310.076i) q^{51} +(-4.32576 + 7.49243i) q^{52} +(88.2557 - 152.863i) q^{53} +(-27.0000 - 46.7654i) q^{54} +315.951 q^{55} +(-146.697 - 20.7846i) q^{56} -100.534 q^{57} +(163.208 + 282.685i) q^{58} +(-227.464 + 393.979i) q^{59} +(-125.023 + 216.546i) q^{60} +(-19.3258 - 33.4732i) q^{61} -446.652 q^{62} +(62.2670 + 154.615i) q^{63} +64.0000 q^{64} +(-22.5341 - 39.0302i) q^{65} +(-45.4886 + 78.7886i) q^{66} +(-70.8958 + 122.795i) q^{67} +(238.697 + 413.435i) q^{68} +1.95455 q^{69} +(475.860 - 607.668i) q^{70} +602.742 q^{71} +(-36.0000 - 62.3538i) q^{72} +(551.150 - 954.619i) q^{73} +(-168.534 + 291.910i) q^{74} +(-463.778 - 803.288i) q^{75} -134.045 q^{76} +(173.138 - 221.096i) q^{77} +12.9773 q^{78} +(58.1515 + 100.721i) q^{79} +(-166.697 + 288.728i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(323.023 + 559.492i) q^{82} -568.928 q^{83} +(83.0227 + 206.153i) q^{84} -2486.88 q^{85} +(-221.557 - 383.748i) q^{86} +(244.812 - 424.028i) q^{87} +(-60.6515 + 105.052i) q^{88} +(191.580 + 331.825i) q^{89} +375.068 q^{90} +(-39.6610 - 5.61932i) q^{91} +2.60607 q^{92} +(334.989 + 580.217i) q^{93} +(-508.045 + 879.961i) q^{94} +(349.140 - 604.728i) q^{95} +(-48.0000 - 83.1384i) q^{96} +334.701 q^{97} +(-164.466 - 665.993i) q^{98} +136.466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 6q^{3} - 8q^{4} - 5q^{5} + 24q^{6} + 32q^{8} - 18q^{9} + O(q^{10}) \) \( 4q - 4q^{2} - 6q^{3} - 8q^{4} - 5q^{5} + 24q^{6} + 32q^{8} - 18q^{9} - 10q^{10} - 67q^{11} - 24q^{12} + 82q^{13} - 18q^{14} + 30q^{15} - 32q^{16} + 92q^{17} - 36q^{18} - 43q^{19} + 40q^{20} + 27q^{21} + 268q^{22} - 148q^{23} - 48q^{24} - 435q^{25} - 82q^{26} + 108q^{27} + 36q^{28} + 154q^{29} - 30q^{30} + 520q^{31} - 64q^{32} - 201q^{33} - 368q^{34} + 650q^{35} + 144q^{36} - 7q^{37} - 86q^{38} - 123q^{39} - 40q^{40} - 852q^{41} - 214q^{43} - 268q^{44} - 45q^{45} - 296q^{46} - 576q^{47} + 192q^{48} + 1318q^{49} + 1740q^{50} + 276q^{51} - 164q^{52} + 243q^{53} - 108q^{54} - 1010q^{55} + 258q^{57} - 154q^{58} + 7q^{59} - 60q^{60} - 224q^{61} - 2080q^{62} - 81q^{63} + 256q^{64} + 570q^{65} - 402q^{66} - 687q^{67} + 368q^{68} + 888q^{69} + 1390q^{70} + 944q^{71} - 144q^{72} + 921q^{73} - 14q^{74} - 1305q^{75} + 344q^{76} - 371q^{77} + 492q^{78} + 526q^{79} - 80q^{80} - 162q^{81} + 852q^{82} - 442q^{83} - 108q^{84} - 5840q^{85} + 214q^{86} - 231q^{87} - 536q^{88} - 774q^{89} + 180q^{90} + 1345q^{91} + 1184q^{92} + 1560q^{93} - 1152q^{94} + 1910q^{95} - 192q^{96} + 3906q^{97} - 1318q^{98} + 1206q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −10.4186 18.0455i −0.931864 1.61404i −0.780132 0.625615i \(-0.784848\pi\)
−0.151732 0.988422i \(-0.548485\pi\)
\(6\) 6.00000 0.408248
\(7\) −18.3371 2.59808i −0.990111 0.140283i
\(8\) 8.00000 0.353553
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −20.8371 + 36.0910i −0.658928 + 1.14130i
\(11\) −7.58144 + 13.1314i −0.207808 + 0.359934i −0.951024 0.309118i \(-0.899966\pi\)
0.743216 + 0.669052i \(0.233300\pi\)
\(12\) −6.00000 10.3923i −0.144338 0.250000i
\(13\) 2.16288 0.0461442 0.0230721 0.999734i \(-0.492655\pi\)
0.0230721 + 0.999734i \(0.492655\pi\)
\(14\) 13.8371 + 34.3589i 0.264152 + 0.655914i
\(15\) 62.5114 1.07602
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 59.6742 103.359i 0.851361 1.47460i −0.0286202 0.999590i \(-0.509111\pi\)
0.879981 0.475009i \(-0.157555\pi\)
\(18\) −9.00000 + 15.5885i −0.117851 + 0.204124i
\(19\) 16.7557 + 29.0217i 0.202317 + 0.350423i 0.949274 0.314449i \(-0.101820\pi\)
−0.746958 + 0.664871i \(0.768486\pi\)
\(20\) 83.3485 0.931864
\(21\) 34.2557 43.7441i 0.355962 0.454560i
\(22\) 30.3258 0.293885
\(23\) −0.325758 0.564230i −0.00295327 0.00511522i 0.864545 0.502555i \(-0.167607\pi\)
−0.867498 + 0.497440i \(0.834273\pi\)
\(24\) −12.0000 + 20.7846i −0.102062 + 0.176777i
\(25\) −154.593 + 267.763i −1.23674 + 2.14210i
\(26\) −2.16288 3.74622i −0.0163144 0.0282574i
\(27\) 27.0000 0.192450
\(28\) 45.6742 58.3255i 0.308272 0.393660i
\(29\) −163.208 −1.04507 −0.522535 0.852618i \(-0.675014\pi\)
−0.522535 + 0.852618i \(0.675014\pi\)
\(30\) −62.5114 108.273i −0.380432 0.658928i
\(31\) 111.663 193.406i 0.646943 1.12054i −0.336906 0.941538i \(-0.609380\pi\)
0.983849 0.179000i \(-0.0572863\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) −22.7443 39.3943i −0.119978 0.207808i
\(34\) −238.697 −1.20401
\(35\) 144.163 + 357.970i 0.696228 + 1.72880i
\(36\) 36.0000 0.166667
\(37\) −84.2670 145.955i −0.374417 0.648509i 0.615823 0.787885i \(-0.288824\pi\)
−0.990240 + 0.139376i \(0.955490\pi\)
\(38\) 33.5114 58.0434i 0.143059 0.247786i
\(39\) −3.24432 + 5.61932i −0.0133207 + 0.0230721i
\(40\) −83.3485 144.364i −0.329464 0.570648i
\(41\) −323.023 −1.23043 −0.615216 0.788359i \(-0.710931\pi\)
−0.615216 + 0.788359i \(0.710931\pi\)
\(42\) −110.023 15.5885i −0.404211 0.0572703i
\(43\) 221.557 0.785746 0.392873 0.919593i \(-0.371481\pi\)
0.392873 + 0.919593i \(0.371481\pi\)
\(44\) −30.3258 52.5258i −0.103904 0.179967i
\(45\) −93.7670 + 162.409i −0.310621 + 0.538012i
\(46\) −0.651517 + 1.12846i −0.00208828 + 0.00361701i
\(47\) −254.023 439.980i −0.788362 1.36548i −0.926970 0.375136i \(-0.877596\pi\)
0.138608 0.990347i \(-0.455737\pi\)
\(48\) 48.0000 0.144338
\(49\) 329.500 + 95.2825i 0.960641 + 0.277791i
\(50\) 618.371 1.74902
\(51\) 179.023 + 310.076i 0.491533 + 0.851361i
\(52\) −4.32576 + 7.49243i −0.0115361 + 0.0199810i
\(53\) 88.2557 152.863i 0.228733 0.396177i −0.728700 0.684833i \(-0.759875\pi\)
0.957433 + 0.288656i \(0.0932084\pi\)
\(54\) −27.0000 46.7654i −0.0680414 0.117851i
\(55\) 315.951 0.774596
\(56\) −146.697 20.7846i −0.350057 0.0495975i
\(57\) −100.534 −0.233615
\(58\) 163.208 + 282.685i 0.369488 + 0.639972i
\(59\) −227.464 + 393.979i −0.501920 + 0.869351i 0.498077 + 0.867133i \(0.334040\pi\)
−0.999998 + 0.00221868i \(0.999294\pi\)
\(60\) −125.023 + 216.546i −0.269006 + 0.465932i
\(61\) −19.3258 33.4732i −0.0405641 0.0702591i 0.845031 0.534718i \(-0.179582\pi\)
−0.885595 + 0.464459i \(0.846249\pi\)
\(62\) −446.652 −0.914916
\(63\) 62.2670 + 154.615i 0.124522 + 0.309201i
\(64\) 64.0000 0.125000
\(65\) −22.5341 39.0302i −0.0430001 0.0744784i
\(66\) −45.4886 + 78.7886i −0.0848373 + 0.146943i
\(67\) −70.8958 + 122.795i −0.129273 + 0.223908i −0.923395 0.383851i \(-0.874598\pi\)
0.794122 + 0.607758i \(0.207931\pi\)
\(68\) 238.697 + 413.435i 0.425680 + 0.737300i
\(69\) 1.95455 0.00341015
\(70\) 475.860 607.668i 0.812516 1.03757i
\(71\) 602.742 1.00750 0.503749 0.863850i \(-0.331954\pi\)
0.503749 + 0.863850i \(0.331954\pi\)
\(72\) −36.0000 62.3538i −0.0589256 0.102062i
\(73\) 551.150 954.619i 0.883660 1.53054i 0.0364183 0.999337i \(-0.488405\pi\)
0.847242 0.531207i \(-0.178262\pi\)
\(74\) −168.534 + 291.910i −0.264753 + 0.458565i
\(75\) −463.778 803.288i −0.714034 1.23674i
\(76\) −134.045 −0.202317
\(77\) 173.138 221.096i 0.256246 0.327223i
\(78\) 12.9773 0.0188383
\(79\) 58.1515 + 100.721i 0.0828172 + 0.143444i 0.904459 0.426561i \(-0.140275\pi\)
−0.821642 + 0.570004i \(0.806942\pi\)
\(80\) −166.697 + 288.728i −0.232966 + 0.403509i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 323.023 + 559.492i 0.435023 + 0.753482i
\(83\) −568.928 −0.752385 −0.376193 0.926542i \(-0.622767\pi\)
−0.376193 + 0.926542i \(0.622767\pi\)
\(84\) 83.0227 + 206.153i 0.107840 + 0.267776i
\(85\) −2486.88 −3.17341
\(86\) −221.557 383.748i −0.277803 0.481169i
\(87\) 244.812 424.028i 0.301686 0.522535i
\(88\) −60.6515 + 105.052i −0.0734713 + 0.127256i
\(89\) 191.580 + 331.825i 0.228173 + 0.395207i 0.957267 0.289207i \(-0.0933915\pi\)
−0.729094 + 0.684414i \(0.760058\pi\)
\(90\) 375.068 0.439285
\(91\) −39.6610 5.61932i −0.0456879 0.00647325i
\(92\) 2.60607 0.00295327
\(93\) 334.989 + 580.217i 0.373513 + 0.646943i
\(94\) −508.045 + 879.961i −0.557456 + 0.965543i
\(95\) 349.140 604.728i 0.377063 0.653093i
\(96\) −48.0000 83.1384i −0.0510310 0.0883883i
\(97\) 334.701 0.350348 0.175174 0.984538i \(-0.443951\pi\)
0.175174 + 0.984538i \(0.443951\pi\)
\(98\) −164.466 665.993i −0.169526 0.686484i
\(99\) 136.466 0.138539
\(100\) −618.371 1071.05i −0.618371 1.07105i
\(101\) 7.37121 12.7673i 0.00726201 0.0125782i −0.862372 0.506276i \(-0.831022\pi\)
0.869634 + 0.493698i \(0.164355\pi\)
\(102\) 358.045 620.153i 0.347566 0.602003i
\(103\) 420.710 + 728.691i 0.402464 + 0.697088i 0.994023 0.109174i \(-0.0348205\pi\)
−0.591559 + 0.806262i \(0.701487\pi\)
\(104\) 17.3030 0.0163144
\(105\) −1146.28 162.409i −1.06538 0.150948i
\(106\) −353.023 −0.323477
\(107\) 357.835 + 619.789i 0.323301 + 0.559974i 0.981167 0.193161i \(-0.0618739\pi\)
−0.657866 + 0.753135i \(0.728541\pi\)
\(108\) −54.0000 + 93.5307i −0.0481125 + 0.0833333i
\(109\) −300.009 + 519.632i −0.263630 + 0.456621i −0.967204 0.254001i \(-0.918253\pi\)
0.703574 + 0.710622i \(0.251587\pi\)
\(110\) −315.951 547.243i −0.273861 0.474341i
\(111\) 505.602 0.432339
\(112\) 110.697 + 274.871i 0.0933918 + 0.231901i
\(113\) 622.644 0.518349 0.259174 0.965831i \(-0.416550\pi\)
0.259174 + 0.965831i \(0.416550\pi\)
\(114\) 100.534 + 174.130i 0.0825954 + 0.143059i
\(115\) −6.78787 + 11.7569i −0.00550410 + 0.00953339i
\(116\) 326.417 565.370i 0.261267 0.452529i
\(117\) −9.73296 16.8580i −0.00769070 0.0133207i
\(118\) 909.856 0.709822
\(119\) −1362.79 + 1740.26i −1.04980 + 1.34059i
\(120\) 500.091 0.380432
\(121\) 550.544 + 953.569i 0.413632 + 0.716431i
\(122\) −38.6515 + 66.9464i −0.0286831 + 0.0496807i
\(123\) 484.534 839.238i 0.355195 0.615216i
\(124\) 446.652 + 773.623i 0.323472 + 0.560269i
\(125\) 3837.90 2.74618
\(126\) 205.534 262.465i 0.145321 0.185573i
\(127\) −180.076 −0.125820 −0.0629100 0.998019i \(-0.520038\pi\)
−0.0629100 + 0.998019i \(0.520038\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) −332.335 + 575.621i −0.226825 + 0.392873i
\(130\) −45.0682 + 78.0604i −0.0304057 + 0.0526642i
\(131\) −108.930 188.672i −0.0726508 0.125835i 0.827411 0.561596i \(-0.189813\pi\)
−0.900062 + 0.435761i \(0.856479\pi\)
\(132\) 181.955 0.119978
\(133\) −231.850 575.707i −0.151158 0.375339i
\(134\) 283.583 0.182820
\(135\) −281.301 487.228i −0.179337 0.310621i
\(136\) 477.394 826.871i 0.301001 0.521350i
\(137\) 1300.93 2253.27i 0.811283 1.40518i −0.100683 0.994919i \(-0.532103\pi\)
0.911966 0.410265i \(-0.134564\pi\)
\(138\) −1.95455 3.38538i −0.00120567 0.00208828i
\(139\) −2651.55 −1.61800 −0.808998 0.587811i \(-0.799990\pi\)
−0.808998 + 0.587811i \(0.799990\pi\)
\(140\) −1528.37 216.546i −0.922650 0.130725i
\(141\) 1524.14 0.910322
\(142\) −602.742 1043.98i −0.356204 0.616964i
\(143\) −16.3977 + 28.4017i −0.00958914 + 0.0166089i
\(144\) −72.0000 + 124.708i −0.0416667 + 0.0721688i
\(145\) 1700.40 + 2945.17i 0.973863 + 1.68678i
\(146\) −2204.60 −1.24968
\(147\) −741.801 + 713.142i −0.416209 + 0.400129i
\(148\) 674.136 0.374417
\(149\) −290.511 503.180i −0.159729 0.276659i 0.775042 0.631910i \(-0.217729\pi\)
−0.934771 + 0.355251i \(0.884395\pi\)
\(150\) −927.557 + 1606.58i −0.504898 + 0.874509i
\(151\) 307.695 532.943i 0.165827 0.287221i −0.771122 0.636688i \(-0.780304\pi\)
0.936949 + 0.349467i \(0.113637\pi\)
\(152\) 134.045 + 232.174i 0.0715297 + 0.123893i
\(153\) −1074.14 −0.567574
\(154\) −556.087 78.7886i −0.290979 0.0412271i
\(155\) −4653.47 −2.41145
\(156\) −12.9773 22.4773i −0.00666034 0.0115361i
\(157\) 153.466 265.811i 0.0780122 0.135121i −0.824380 0.566037i \(-0.808476\pi\)
0.902392 + 0.430916i \(0.141809\pi\)
\(158\) 116.303 201.443i 0.0585606 0.101430i
\(159\) 264.767 + 458.590i 0.132059 + 0.228733i
\(160\) 666.788 0.329464
\(161\) 4.50756 + 11.1927i 0.00220649 + 0.00547893i
\(162\) 162.000 0.0785674
\(163\) −1757.25 3043.65i −0.844408 1.46256i −0.886135 0.463428i \(-0.846619\pi\)
0.0417271 0.999129i \(-0.486714\pi\)
\(164\) 646.045 1118.98i 0.307608 0.532792i
\(165\) −473.926 + 820.864i −0.223607 + 0.387298i
\(166\) 568.928 + 985.412i 0.266008 + 0.460740i
\(167\) 1123.30 0.520502 0.260251 0.965541i \(-0.416195\pi\)
0.260251 + 0.965541i \(0.416195\pi\)
\(168\) 274.045 349.953i 0.125852 0.160711i
\(169\) −2192.32 −0.997871
\(170\) 2486.88 + 4307.40i 1.12197 + 1.94331i
\(171\) 150.801 261.195i 0.0674389 0.116808i
\(172\) −443.114 + 767.495i −0.196437 + 0.340238i
\(173\) −765.299 1325.54i −0.336327 0.582536i 0.647412 0.762141i \(-0.275852\pi\)
−0.983739 + 0.179605i \(0.942518\pi\)
\(174\) −979.250 −0.426648
\(175\) 3530.45 4508.35i 1.52501 1.94742i
\(176\) 242.606 0.103904
\(177\) −682.392 1181.94i −0.289784 0.501920i
\(178\) 383.159 663.651i 0.161343 0.279454i
\(179\) −1706.72 + 2956.12i −0.712659 + 1.23436i 0.251197 + 0.967936i \(0.419176\pi\)
−0.963856 + 0.266425i \(0.914157\pi\)
\(180\) −375.068 649.637i −0.155311 0.269006i
\(181\) 1286.71 0.528399 0.264200 0.964468i \(-0.414892\pi\)
0.264200 + 0.964468i \(0.414892\pi\)
\(182\) 29.9280 + 74.3142i 0.0121891 + 0.0302667i
\(183\) 115.955 0.0468394
\(184\) −2.60607 4.51384i −0.00104414 0.00180850i
\(185\) −1755.88 + 3041.28i −0.697811 + 1.20864i
\(186\) 669.977 1160.43i 0.264114 0.457458i
\(187\) 904.833 + 1567.22i 0.353839 + 0.612868i
\(188\) 2032.18 0.788362
\(189\) −495.102 70.1481i −0.190547 0.0269975i
\(190\) −1396.56 −0.533248
\(191\) −527.648 913.913i −0.199891 0.346222i 0.748602 0.663020i \(-0.230726\pi\)
−0.948493 + 0.316798i \(0.897392\pi\)
\(192\) −96.0000 + 166.277i −0.0360844 + 0.0625000i
\(193\) 2385.42 4131.67i 0.889670 1.54095i 0.0494044 0.998779i \(-0.484268\pi\)
0.840266 0.542175i \(-0.182399\pi\)
\(194\) −334.701 579.719i −0.123867 0.214543i
\(195\) 135.205 0.0496523
\(196\) −989.068 + 950.857i −0.360448 + 0.346522i
\(197\) 1622.31 0.586725 0.293363 0.956001i \(-0.405226\pi\)
0.293363 + 0.956001i \(0.405226\pi\)
\(198\) −136.466 236.366i −0.0489809 0.0848373i
\(199\) 1775.07 3074.51i 0.632318 1.09521i −0.354759 0.934958i \(-0.615437\pi\)
0.987077 0.160249i \(-0.0512296\pi\)
\(200\) −1236.74 + 2142.10i −0.437254 + 0.757347i
\(201\) −212.688 368.386i −0.0746359 0.129273i
\(202\) −29.4848 −0.0102700
\(203\) 2992.77 + 424.028i 1.03474 + 0.146605i
\(204\) −1432.18 −0.491533
\(205\) 3365.43 + 5829.10i 1.14659 + 1.98596i
\(206\) 841.420 1457.38i 0.284585 0.492916i
\(207\) −2.93183 + 5.07807i −0.000984425 + 0.00170507i
\(208\) −17.3030 29.9697i −0.00576803 0.00999051i
\(209\) −508.129 −0.168172
\(210\) 864.977 + 2147.82i 0.284234 + 0.705780i
\(211\) 4653.39 1.51826 0.759129 0.650941i \(-0.225625\pi\)
0.759129 + 0.650941i \(0.225625\pi\)
\(212\) 353.023 + 611.453i 0.114367 + 0.198089i
\(213\) −904.114 + 1565.97i −0.290840 + 0.503749i
\(214\) 715.670 1239.58i 0.228609 0.395962i
\(215\) −2308.30 3998.10i −0.732209 1.26822i
\(216\) 216.000 0.0680414
\(217\) −2550.06 + 3256.40i −0.797739 + 1.01870i
\(218\) 1200.04 0.372829
\(219\) 1653.45 + 2863.86i 0.510181 + 0.883660i
\(220\) −631.901 + 1094.49i −0.193649 + 0.335410i
\(221\) 129.068 223.553i 0.0392854 0.0680442i
\(222\) −505.602 875.729i −0.152855 0.264753i
\(223\) −4649.53 −1.39621 −0.698107 0.715993i \(-0.745974\pi\)
−0.698107 + 0.715993i \(0.745974\pi\)
\(224\) 365.394 466.604i 0.108991 0.139180i
\(225\) 2782.67 0.824495
\(226\) −622.644 1078.45i −0.183264 0.317423i
\(227\) −2075.86 + 3595.49i −0.606958 + 1.05128i 0.384780 + 0.923008i \(0.374277\pi\)
−0.991739 + 0.128274i \(0.959056\pi\)
\(228\) 201.068 348.260i 0.0584038 0.101158i
\(229\) −2131.82 3692.41i −0.615172 1.06551i −0.990354 0.138558i \(-0.955753\pi\)
0.375182 0.926951i \(-0.377580\pi\)
\(230\) 27.1515 0.00778398
\(231\) 314.716 + 781.470i 0.0896398 + 0.222584i
\(232\) −1305.67 −0.369488
\(233\) −1524.95 2641.29i −0.428768 0.742647i 0.567996 0.823031i \(-0.307719\pi\)
−0.996764 + 0.0803838i \(0.974385\pi\)
\(234\) −19.4659 + 33.7159i −0.00543815 + 0.00941915i
\(235\) −5293.10 + 9167.92i −1.46929 + 2.54489i
\(236\) −909.856 1575.92i −0.250960 0.434676i
\(237\) −348.909 −0.0956290
\(238\) 4377.02 + 620.153i 1.19210 + 0.168901i
\(239\) 3987.20 1.07912 0.539562 0.841946i \(-0.318590\pi\)
0.539562 + 0.841946i \(0.318590\pi\)
\(240\) −500.091 866.183i −0.134503 0.232966i
\(241\) 312.324 540.961i 0.0834795 0.144591i −0.821263 0.570550i \(-0.806730\pi\)
0.904742 + 0.425959i \(0.140063\pi\)
\(242\) 1101.09 1907.14i 0.292482 0.506593i
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) 154.606 0.0405641
\(245\) −1713.50 6938.69i −0.446822 1.80937i
\(246\) −1938.14 −0.502321
\(247\) 36.2405 + 62.7704i 0.00933574 + 0.0161700i
\(248\) 893.303 1547.25i 0.228729 0.396170i
\(249\) 853.392 1478.12i 0.217195 0.376193i
\(250\) −3837.90 6647.43i −0.970920 1.68168i
\(251\) −1328.78 −0.334152 −0.167076 0.985944i \(-0.553432\pi\)
−0.167076 + 0.985944i \(0.553432\pi\)
\(252\) −660.136 93.5307i −0.165019 0.0233805i
\(253\) 9.87887 0.00245486
\(254\) 180.076 + 311.900i 0.0444841 + 0.0770487i
\(255\) 3730.32 6461.10i 0.916085 1.58671i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 1613.09 + 2793.96i 0.391525 + 0.678141i 0.992651 0.121013i \(-0.0386144\pi\)
−0.601126 + 0.799154i \(0.705281\pi\)
\(258\) 1329.34 0.320780
\(259\) 1166.01 + 2895.32i 0.279740 + 0.694620i
\(260\) 180.273 0.0430001
\(261\) 734.437 + 1272.08i 0.174178 + 0.301686i
\(262\) −217.860 + 377.344i −0.0513719 + 0.0889787i
\(263\) −1625.31 + 2815.11i −0.381067 + 0.660028i −0.991215 0.132260i \(-0.957777\pi\)
0.610148 + 0.792288i \(0.291110\pi\)
\(264\) −181.955 315.155i −0.0424187 0.0734713i
\(265\) −3677.99 −0.852593
\(266\) −765.303 + 977.283i −0.176405 + 0.225267i
\(267\) −1149.48 −0.263471
\(268\) −283.583 491.181i −0.0646366 0.111954i
\(269\) −1413.02 + 2447.42i −0.320273 + 0.554729i −0.980544 0.196298i \(-0.937108\pi\)
0.660271 + 0.751027i \(0.270441\pi\)
\(270\) −562.602 + 974.456i −0.126811 + 0.219643i
\(271\) 1198.38 + 2075.66i 0.268622 + 0.465268i 0.968506 0.248989i \(-0.0800983\pi\)
−0.699884 + 0.714257i \(0.746765\pi\)
\(272\) −1909.58 −0.425680
\(273\) 74.0909 94.6133i 0.0164256 0.0209753i
\(274\) −5203.71 −1.14733
\(275\) −2344.07 4060.05i −0.514010 0.890292i
\(276\) −3.90910 + 6.77076i −0.000852537 + 0.00147664i
\(277\) −910.233 + 1576.57i −0.197439 + 0.341974i −0.947697 0.319170i \(-0.896596\pi\)
0.750258 + 0.661145i \(0.229929\pi\)
\(278\) 2651.55 + 4592.62i 0.572048 + 0.990816i
\(279\) −2009.93 −0.431296
\(280\) 1153.30 + 2863.76i 0.246154 + 0.611223i
\(281\) 3083.81 0.654679 0.327339 0.944907i \(-0.393848\pi\)
0.327339 + 0.944907i \(0.393848\pi\)
\(282\) −1524.14 2639.88i −0.321848 0.557456i
\(283\) −1277.38 + 2212.49i −0.268313 + 0.464732i −0.968426 0.249300i \(-0.919800\pi\)
0.700113 + 0.714032i \(0.253133\pi\)
\(284\) −1205.48 + 2087.96i −0.251875 + 0.436259i
\(285\) 1047.42 + 1814.19i 0.217698 + 0.377063i
\(286\) 65.5910 0.0135611
\(287\) 5923.31 + 839.238i 1.21826 + 0.172608i
\(288\) 288.000 0.0589256
\(289\) −4665.53 8080.94i −0.949630 1.64481i
\(290\) 3400.79 5890.34i 0.688625 1.19273i
\(291\) −502.051 + 869.578i −0.101137 + 0.175174i
\(292\) 2204.60 + 3818.48i 0.441830 + 0.765272i
\(293\) −1846.47 −0.368163 −0.184081 0.982911i \(-0.558931\pi\)
−0.184081 + 0.982911i \(0.558931\pi\)
\(294\) 1977.00 + 571.695i 0.392180 + 0.113408i
\(295\) 9479.39 1.87089
\(296\) −674.136 1167.64i −0.132376 0.229282i
\(297\) −204.699 + 354.549i −0.0399927 + 0.0692694i
\(298\) −581.023 + 1006.36i −0.112945 + 0.195627i
\(299\) −0.704576 1.22036i −0.000136277 0.000236038i
\(300\) 3710.23 0.714034
\(301\) −4062.71 575.621i −0.777977 0.110227i
\(302\) −1230.78 −0.234515
\(303\) 22.1136 + 38.3019i 0.00419272 + 0.00726201i
\(304\) 268.091 464.347i 0.0505792 0.0876057i
\(305\) −402.693 + 697.485i −0.0756005 + 0.130944i
\(306\) 1074.14 + 1860.46i 0.200668 + 0.347566i
\(307\) 7041.50 1.30905 0.654527 0.756039i \(-0.272868\pi\)
0.654527 + 0.756039i \(0.272868\pi\)
\(308\) 419.621 + 1041.96i 0.0776303 + 0.192764i
\(309\) −2524.26 −0.464726
\(310\) 4653.47 + 8060.04i 0.852578 + 1.47671i
\(311\) 1343.00 2326.14i 0.244869 0.424126i −0.717226 0.696841i \(-0.754588\pi\)
0.962095 + 0.272715i \(0.0879216\pi\)
\(312\) −25.9546 + 44.9546i −0.00470957 + 0.00815722i
\(313\) −1109.59 1921.87i −0.200377 0.347063i 0.748273 0.663391i \(-0.230883\pi\)
−0.948650 + 0.316328i \(0.897550\pi\)
\(314\) −613.864 −0.110326
\(315\) 2141.37 2734.50i 0.383024 0.489117i
\(316\) −465.212 −0.0828172
\(317\) −1110.63 1923.67i −0.196780 0.340833i 0.750703 0.660640i \(-0.229715\pi\)
−0.947483 + 0.319807i \(0.896382\pi\)
\(318\) 529.534 917.180i 0.0933799 0.161739i
\(319\) 1237.35 2143.16i 0.217174 0.376157i
\(320\) −666.788 1154.91i −0.116483 0.201755i
\(321\) −2147.01 −0.373316
\(322\) 14.8788 19.0000i 0.00257503 0.00328829i
\(323\) 3999.53 0.688978
\(324\) −162.000 280.592i −0.0277778 0.0481125i
\(325\) −334.366 + 579.138i −0.0570685 + 0.0988455i
\(326\) −3514.50 + 6087.29i −0.597086 + 1.03418i
\(327\) −900.028 1558.89i −0.152207 0.263630i
\(328\) −2584.18 −0.435023
\(329\) 3514.94 + 8727.94i 0.589012 + 1.46257i
\(330\) 1895.70 0.316228
\(331\) −2077.03 3597.52i −0.344906 0.597394i 0.640431 0.768016i \(-0.278756\pi\)
−0.985337 + 0.170622i \(0.945422\pi\)
\(332\) 1137.86 1970.82i 0.188096 0.325792i
\(333\) −758.403 + 1313.59i −0.124806 + 0.216170i
\(334\) −1123.30 1945.62i −0.184025 0.318741i
\(335\) 2954.53 0.481860
\(336\) −880.182 124.708i −0.142910 0.0202481i
\(337\) −254.167 −0.0410841 −0.0205420 0.999789i \(-0.506539\pi\)
−0.0205420 + 0.999789i \(0.506539\pi\)
\(338\) 2192.32 + 3797.21i 0.352801 + 0.611069i
\(339\) −933.966 + 1617.68i −0.149634 + 0.259174i
\(340\) 4973.76 8614.80i 0.793353 1.37413i
\(341\) 1693.13 + 2932.59i 0.268880 + 0.465714i
\(342\) −603.205 −0.0953730
\(343\) −5794.53 2603.27i −0.912173 0.409806i
\(344\) 1772.45 0.277803
\(345\) −20.3636 35.2708i −0.00317780 0.00550410i
\(346\) −1530.60 + 2651.07i −0.237819 + 0.411915i
\(347\) 3112.32 5390.69i 0.481493 0.833970i −0.518282 0.855210i \(-0.673428\pi\)
0.999774 + 0.0212401i \(0.00676143\pi\)
\(348\) 979.250 + 1696.11i 0.150843 + 0.261267i
\(349\) 9732.21 1.49270 0.746352 0.665552i \(-0.231804\pi\)
0.746352 + 0.665552i \(0.231804\pi\)
\(350\) −11339.1 1606.58i −1.73172 0.245357i
\(351\) 58.3977 0.00888046
\(352\) −242.606 420.206i −0.0367356 0.0636280i
\(353\) −712.807 + 1234.62i −0.107476 + 0.186153i −0.914747 0.404027i \(-0.867610\pi\)
0.807271 + 0.590180i \(0.200943\pi\)
\(354\) −1364.78 + 2363.88i −0.204908 + 0.354911i
\(355\) −6279.71 10876.8i −0.938852 1.62614i
\(356\) −1532.64 −0.228173
\(357\) −2477.16 6151.02i −0.367241 0.911896i
\(358\) 6826.86 1.00785
\(359\) 2883.25 + 4993.93i 0.423877 + 0.734177i 0.996315 0.0857714i \(-0.0273355\pi\)
−0.572438 + 0.819948i \(0.694002\pi\)
\(360\) −750.136 + 1299.27i −0.109821 + 0.190216i
\(361\) 2867.99 4967.51i 0.418136 0.724233i
\(362\) −1286.71 2228.64i −0.186817 0.323577i
\(363\) −3303.26 −0.477621
\(364\) 98.7879 126.151i 0.0142250 0.0181651i
\(365\) −22968.7 −3.29381
\(366\) −115.955 200.839i −0.0165602 0.0286831i
\(367\) −5772.67 + 9998.56i −0.821065 + 1.42213i 0.0838244 + 0.996481i \(0.473287\pi\)
−0.904890 + 0.425646i \(0.860047\pi\)
\(368\) −5.21213 + 9.02768i −0.000738319 + 0.00127881i
\(369\) 1453.60 + 2517.71i 0.205072 + 0.355195i
\(370\) 7023.53 0.986854
\(371\) −2015.51 + 2573.78i −0.282048 + 0.360172i
\(372\) −2679.91 −0.373513
\(373\) 3239.79 + 5611.47i 0.449731 + 0.778957i 0.998368 0.0571033i \(-0.0181864\pi\)
−0.548637 + 0.836061i \(0.684853\pi\)
\(374\) 1809.67 3134.43i 0.250202 0.433363i
\(375\) −5756.85 + 9971.15i −0.792753 + 1.37309i
\(376\) −2032.18 3519.84i −0.278728 0.482771i
\(377\) −353.000 −0.0482239
\(378\) 373.602 + 927.690i 0.0508360 + 0.126231i
\(379\) 611.996 0.0829449 0.0414725 0.999140i \(-0.486795\pi\)
0.0414725 + 0.999140i \(0.486795\pi\)
\(380\) 1396.56 + 2418.91i 0.188532 + 0.326546i
\(381\) 270.114 467.851i 0.0363211 0.0629100i
\(382\) −1055.30 + 1827.83i −0.141345 + 0.244816i
\(383\) −2180.41 3776.57i −0.290897 0.503848i 0.683125 0.730301i \(-0.260620\pi\)
−0.974022 + 0.226453i \(0.927287\pi\)
\(384\) 384.000 0.0510310
\(385\) −5793.63 820.864i −0.766937 0.108663i
\(386\) −9541.68 −1.25818
\(387\) −997.006 1726.86i −0.130958 0.226825i
\(388\) −669.402 + 1159.44i −0.0875869 + 0.151705i
\(389\) 6573.46 11385.6i 0.856781 1.48399i −0.0182021 0.999834i \(-0.505794\pi\)
0.874983 0.484154i \(-0.160872\pi\)
\(390\) −135.205 234.181i −0.0175547 0.0304057i
\(391\) −77.7575 −0.0100572
\(392\) 2636.00 + 762.260i 0.339638 + 0.0982141i
\(393\) 653.580 0.0838899
\(394\) −1622.31 2809.92i −0.207439 0.359294i
\(395\) 1211.71 2098.74i 0.154349 0.267340i
\(396\) −272.932 + 472.732i −0.0346347 + 0.0599891i
\(397\) 4239.02 + 7342.20i 0.535895 + 0.928198i 0.999119 + 0.0419565i \(0.0133591\pi\)
−0.463224 + 0.886241i \(0.653308\pi\)
\(398\) −7100.27 −0.894232
\(399\) 1843.51 + 261.195i 0.231305 + 0.0327722i
\(400\) 4946.97 0.618371
\(401\) −1401.50 2427.47i −0.174533 0.302299i 0.765467 0.643475i \(-0.222508\pi\)
−0.939999 + 0.341176i \(0.889175\pi\)
\(402\) −425.375 + 736.771i −0.0527756 + 0.0914100i
\(403\) 241.513 418.313i 0.0298527 0.0517064i
\(404\) 29.4848 + 51.0692i 0.00363100 + 0.00628908i
\(405\) 1687.81 0.207081
\(406\) −2258.33 5607.66i −0.276057 0.685476i
\(407\) 2555.46 0.311227
\(408\) 1432.18 + 2480.61i 0.173783 + 0.301001i
\(409\) 3192.69 5529.91i 0.385987 0.668548i −0.605919 0.795526i \(-0.707194\pi\)
0.991906 + 0.126978i \(0.0405278\pi\)
\(410\) 6730.86 11658.2i 0.810765 1.40429i
\(411\) 3902.78 + 6759.82i 0.468395 + 0.811283i
\(412\) −3365.68 −0.402464
\(413\) 5194.62 6633.48i 0.618912 0.790344i
\(414\) 11.7273 0.00139219
\(415\) 5927.41 + 10266.6i 0.701121 + 1.21438i
\(416\) −34.6061 + 59.9395i −0.00407861 + 0.00706436i
\(417\) 3977.32 6888.93i 0.467075 0.808998i
\(418\) 508.129 + 880.105i 0.0594579 + 0.102984i
\(419\) 4831.66 0.563346 0.281673 0.959510i \(-0.409111\pi\)
0.281673 + 0.959510i \(0.409111\pi\)
\(420\) 2855.16 3646.01i 0.331708 0.423588i
\(421\) 7475.37 0.865385 0.432693 0.901542i \(-0.357564\pi\)
0.432693 + 0.901542i \(0.357564\pi\)
\(422\) −4653.39 8059.90i −0.536785 0.929739i
\(423\) −2286.20 + 3959.82i −0.262787 + 0.455161i
\(424\) 706.045 1222.91i 0.0808693 0.140070i
\(425\) 18450.4 + 31957.1i 2.10583 + 3.64740i
\(426\) 3616.45 0.411309
\(427\) 267.413 + 664.012i 0.0303068 + 0.0752548i
\(428\) −2862.68 −0.323301
\(429\) −49.1932 85.2051i −0.00553630 0.00958914i
\(430\) −4616.61 + 7996.20i −0.517750 + 0.896769i
\(431\) −3495.97 + 6055.19i −0.390707 + 0.676725i −0.992543 0.121895i \(-0.961103\pi\)
0.601836 + 0.798620i \(0.294436\pi\)
\(432\) −216.000 374.123i −0.0240563 0.0416667i
\(433\) −7699.26 −0.854510 −0.427255 0.904131i \(-0.640519\pi\)
−0.427255 + 0.904131i \(0.640519\pi\)
\(434\) 8190.30 + 1160.43i 0.905869 + 0.128347i
\(435\) −10202.4 −1.12452
\(436\) −1200.04 2078.53i −0.131815 0.228310i
\(437\) 10.9166 18.9081i 0.00119499 0.00206979i
\(438\) 3306.90 5727.71i 0.360753 0.624842i
\(439\) −4706.16 8151.31i −0.511646 0.886198i −0.999909 0.0135008i \(-0.995702\pi\)
0.488262 0.872697i \(-0.337631\pi\)
\(440\) 2527.61 0.273861
\(441\) −740.097 2996.97i −0.0799154 0.323612i
\(442\) −516.273 −0.0555579
\(443\) 3129.09 + 5419.74i 0.335593 + 0.581263i 0.983598 0.180372i \(-0.0577301\pi\)
−0.648006 + 0.761635i \(0.724397\pi\)
\(444\) −1011.20 + 1751.46i −0.108085 + 0.187208i
\(445\) 3991.97 6914.29i 0.425252 0.736559i
\(446\) 4649.53 + 8053.23i 0.493636 + 0.855003i
\(447\) 1743.07 0.184439
\(448\) −1173.58 166.277i −0.123764 0.0175354i
\(449\) −11633.8 −1.22279 −0.611396 0.791325i \(-0.709392\pi\)
−0.611396 + 0.791325i \(0.709392\pi\)
\(450\) −2782.67 4819.73i −0.291503 0.504898i
\(451\) 2448.98 4241.75i 0.255694 0.442874i
\(452\) −1245.29 + 2156.90i −0.129587 + 0.224452i
\(453\) 923.085 + 1598.83i 0.0957402 + 0.165827i
\(454\) 8303.43 0.858369
\(455\) 311.807 + 774.246i 0.0321269 + 0.0797741i
\(456\) −804.273 −0.0825954
\(457\) 6552.31 + 11348.9i 0.670688 + 1.16167i 0.977709 + 0.209963i \(0.0673343\pi\)
−0.307022 + 0.951703i \(0.599332\pi\)
\(458\) −4263.63 + 7384.83i −0.434992 + 0.753429i
\(459\) 1611.20 2790.69i 0.163844 0.283787i
\(460\) −27.1515 47.0277i −0.00275205 0.00476669i
\(461\) −2594.63 −0.262134 −0.131067 0.991373i \(-0.541840\pi\)
−0.131067 + 0.991373i \(0.541840\pi\)
\(462\) 1038.83 1326.57i 0.104612 0.133588i
\(463\) −14136.2 −1.41893 −0.709465 0.704741i \(-0.751063\pi\)
−0.709465 + 0.704741i \(0.751063\pi\)
\(464\) 1305.67 + 2261.48i 0.130634 + 0.226264i
\(465\) 6980.20 12090.1i 0.696127 1.20573i
\(466\) −3049.90 + 5282.58i −0.303184 + 0.525131i
\(467\) −7795.12 13501.5i −0.772409 1.33785i −0.936239 0.351363i \(-0.885718\pi\)
0.163830 0.986489i \(-0.447615\pi\)
\(468\) 77.8637 0.00769070
\(469\) 1619.06 2067.52i 0.159405 0.203559i
\(470\) 21172.4 2.07789
\(471\) 460.398 + 797.432i 0.0450404 + 0.0780122i
\(472\) −1819.71 + 3151.83i −0.177456 + 0.307362i
\(473\) −1679.72 + 2909.36i −0.163285 + 0.282817i
\(474\) 348.909 + 604.328i 0.0338100 + 0.0585606i
\(475\) −10361.2 −1.00085
\(476\) −3302.88 8201.37i −0.318040 0.789725i
\(477\) −1588.60 −0.152489
\(478\) −3987.20 6906.04i −0.381528 0.660826i
\(479\) 4226.75 7320.95i 0.403184 0.698336i −0.590924 0.806727i \(-0.701237\pi\)
0.994108 + 0.108391i \(0.0345700\pi\)
\(480\) −1000.18 + 1732.37i −0.0951080 + 0.164732i
\(481\) −182.259 315.683i −0.0172772 0.0299249i
\(482\) −1249.30 −0.118058
\(483\) −35.8408 5.07807i −0.00337643 0.000478386i
\(484\) −4404.35 −0.413632
\(485\) −3487.10 6039.83i −0.326476 0.565474i
\(486\) −243.000 + 420.888i −0.0226805 + 0.0392837i
\(487\) 2005.53 3473.69i 0.186611 0.323219i −0.757507 0.652827i \(-0.773583\pi\)
0.944118 + 0.329607i \(0.106916\pi\)
\(488\) −154.606 267.786i −0.0143416 0.0248403i
\(489\) 10543.5 0.975038
\(490\) −10304.7 + 9906.56i −0.950035 + 0.913332i
\(491\) 13927.9 1.28016 0.640079 0.768309i \(-0.278902\pi\)
0.640079 + 0.768309i \(0.278902\pi\)
\(492\) 1938.14 + 3356.95i 0.177597 + 0.307608i
\(493\) −9739.33 + 16869.0i −0.889731 + 1.54106i
\(494\) 72.4810 125.541i 0.00660137 0.0114339i
\(495\) −1421.78 2462.59i −0.129099 0.223607i
\(496\) −3573.21 −0.323472
\(497\) −11052.6 1565.97i −0.997535 0.141335i
\(498\) −3413.57 −0.307160
\(499\) 1973.77 + 3418.68i 0.177071 + 0.306695i 0.940876 0.338751i \(-0.110005\pi\)
−0.763805 + 0.645447i \(0.776671\pi\)
\(500\) −7675.80 + 13294.9i −0.686544 + 1.18913i
\(501\) −1684.95 + 2918.43i −0.150256 + 0.260251i
\(502\) 1328.78 + 2301.52i 0.118141 + 0.204625i
\(503\) −13725.3 −1.21666 −0.608331 0.793684i \(-0.708161\pi\)
−0.608331 + 0.793684i \(0.708161\pi\)
\(504\) 498.136 + 1236.92i 0.0440253 + 0.109319i
\(505\) −307.190 −0.0270688
\(506\) −9.87887 17.1107i −0.000867924 0.00150329i
\(507\) 3288.48 5695.82i 0.288060 0.498935i
\(508\) 360.152 623.801i 0.0314550 0.0544817i
\(509\) −3915.05 6781.07i −0.340926 0.590502i 0.643679 0.765296i \(-0.277407\pi\)
−0.984605 + 0.174794i \(0.944074\pi\)
\(510\) −14921.3 −1.29554
\(511\) −12586.7 + 16073.0i −1.08963 + 1.39145i
\(512\) 512.000 0.0441942
\(513\) 452.403 + 783.586i 0.0389359 + 0.0674389i
\(514\) 3226.18 5587.91i 0.276850 0.479518i
\(515\) 8766.39 15183.8i 0.750084 1.29918i
\(516\) −1329.34 2302.49i −0.113413 0.196437i
\(517\) 7703.43 0.655312
\(518\) 3848.83 4914.92i 0.326463 0.416890i
\(519\) 4591.80 0.388357
\(520\) −180.273 312.241i −0.0152028 0.0263321i
\(521\) 2953.69 5115.95i 0.248376 0.430199i −0.714700 0.699431i \(-0.753437\pi\)
0.963075 + 0.269232i \(0.0867700\pi\)
\(522\) 1468.87 2544.17i 0.123163 0.213324i
\(523\) −3954.03 6848.58i −0.330588 0.572595i 0.652039 0.758185i \(-0.273914\pi\)
−0.982627 + 0.185590i \(0.940580\pi\)
\(524\) 871.439 0.0726508
\(525\) 6417.36 + 15934.9i 0.533479 + 1.32468i
\(526\) 6501.23 0.538911
\(527\) −13326.8 23082.7i −1.10156 1.90797i
\(528\) −363.909 + 630.309i −0.0299945 + 0.0519520i
\(529\) 6083.29 10536.6i 0.499983 0.865995i
\(530\) 3677.99 + 6370.46i 0.301437 + 0.522104i
\(531\) 4094.35 0.334613
\(532\) 2458.01 + 348.260i 0.200316 + 0.0283816i
\(533\) −698.659 −0.0567773
\(534\) 1149.48 + 1990.95i 0.0931512 + 0.161343i
\(535\) 7456.26 12914.6i 0.602546 1.04364i
\(536\) −567.167 + 982.362i −0.0457050 + 0.0791633i
\(537\) −5120.15 8868.36i −0.411454 0.712659i
\(538\) 5652.08 0.452934
\(539\) −3749.28 + 3604.43i −0.299616 + 0.288040i
\(540\) 2250.41 0.179337
\(541\) 1970.52 + 3413.04i 0.156598 + 0.271235i 0.933640 0.358214i \(-0.116614\pi\)
−0.777042 + 0.629449i \(0.783281\pi\)
\(542\) 2396.77 4151.33i 0.189945 0.328994i
\(543\) −1930.06 + 3342.97i −0.152536 + 0.264200i
\(544\) 1909.58 + 3307.48i 0.150501 + 0.260675i
\(545\) 12502.7 0.982670
\(546\) −237.966 33.7159i −0.0186520 0.00264269i
\(547\) −1828.71 −0.142943 −0.0714717 0.997443i \(-0.522770\pi\)
−0.0714717 + 0.997443i \(0.522770\pi\)
\(548\) 5203.71 + 9013.09i 0.405642 + 0.702592i
\(549\) −173.932 + 301.259i −0.0135214 + 0.0234197i
\(550\) −4688.14 + 8120.10i −0.363460 + 0.629532i
\(551\) −2734.67 4736.58i −0.211435 0.366216i
\(552\) 15.6364 0.00120567
\(553\) −804.650 1998.02i −0.0618756 0.153643i
\(554\) 3640.93 0.279221
\(555\) −5267.65 9123.83i −0.402881 0.697811i
\(556\) 5303.10 9185.24i 0.404499 0.700613i
\(557\) −11266.0 + 19513.3i −0.857011 + 1.48439i 0.0177556 + 0.999842i \(0.494348\pi\)
−0.874767 + 0.484544i \(0.838985\pi\)
\(558\) 2009.93 + 3481.30i 0.152486 + 0.264114i
\(559\) 479.201 0.0362577
\(560\) 3806.88 4861.34i 0.287268 0.366838i
\(561\) −5429.00 −0.408579
\(562\) −3083.81 5341.32i −0.231464 0.400907i
\(563\) −11677.9 + 20226.6i −0.874179 + 1.51412i −0.0165446 + 0.999863i \(0.505267\pi\)
−0.857635 + 0.514260i \(0.828067\pi\)
\(564\) −3048.27 + 5279.76i −0.227581 + 0.394181i
\(565\) −6487.05 11235.9i −0.483031 0.836634i
\(566\) 5109.54 0.379452
\(567\) 924.903 1181.09i 0.0685049 0.0874800i
\(568\) 4821.94 0.356204
\(569\) 10443.8 + 18089.2i 0.769468 + 1.33276i 0.937852 + 0.347036i \(0.112812\pi\)
−0.168384 + 0.985721i \(0.553855\pi\)
\(570\) 2094.84 3628.37i 0.153935 0.266624i
\(571\) −11872.6 + 20564.0i −0.870147 + 1.50714i −0.00830301 + 0.999966i \(0.502643\pi\)
−0.861844 + 0.507173i \(0.830690\pi\)
\(572\) −65.5910 113.607i −0.00479457 0.00830444i
\(573\) 3165.89 0.230815
\(574\) −4469.70 11098.7i −0.325021 0.807058i
\(575\) 201.440 0.0146098
\(576\) −288.000 498.831i −0.0208333 0.0360844i
\(577\) −1227.20 + 2125.57i −0.0885422 + 0.153360i −0.906895 0.421356i \(-0.861554\pi\)
0.818353 + 0.574716i \(0.194887\pi\)
\(578\) −9331.06 + 16161.9i −0.671490 + 1.16305i
\(579\) 7156.26 + 12395.0i 0.513651 + 0.889670i
\(580\) −13603.2 −0.973863
\(581\) 10432.5 + 1478.12i 0.744945 + 0.105547i
\(582\) 2008.20 0.143029
\(583\) 1338.21 + 2317.85i 0.0950652 + 0.164658i
\(584\) 4409.20 7636.95i 0.312421 0.541129i
\(585\) −202.807 + 351.272i −0.0143334 + 0.0248261i
\(586\) 1846.47 + 3198.17i 0.130165 + 0.225453i
\(587\) 18567.5 1.30556 0.652780 0.757547i \(-0.273603\pi\)
0.652780 + 0.757547i \(0.273603\pi\)
\(588\) −986.795 3995.96i −0.0692088 0.280256i
\(589\) 7483.95 0.523550
\(590\) −9479.39 16418.8i −0.661458 1.14568i
\(591\) −2433.47 + 4214.89i −0.169373 + 0.293363i
\(592\) −1348.27 + 2335.28i −0.0936042 + 0.162127i
\(593\) −8556.47 14820.2i −0.592533 1.02630i −0.993890 0.110375i \(-0.964795\pi\)
0.401357 0.915922i \(-0.368539\pi\)
\(594\) 818.795 0.0565582
\(595\) 45602.2 + 6461.10i 3.14203 + 0.445175i
\(596\) 2324.09 0.159729
\(597\) 5325.20 + 9223.52i 0.365069 + 0.632318i
\(598\) −1.40915 + 2.44072i −9.63621e−5 + 0.000166904i
\(599\) −11632.4 + 20147.9i −0.793469 + 1.37433i 0.130338 + 0.991470i \(0.458394\pi\)
−0.923807 + 0.382859i \(0.874940\pi\)
\(600\) −3710.23 6426.30i −0.252449 0.437254i
\(601\) 25322.3 1.71867 0.859334 0.511416i \(-0.170879\pi\)
0.859334 + 0.511416i \(0.170879\pi\)
\(602\) 3065.71 + 7612.45i 0.207556 + 0.515382i
\(603\) 1276.13 0.0861821
\(604\) 1230.78 + 2131.77i 0.0829135 + 0.143610i
\(605\) 11471.7 19869.6i 0.770897 1.33523i
\(606\) 44.2272 76.6038i 0.00296470 0.00513501i
\(607\) 10867.2 + 18822.5i 0.726665 + 1.25862i 0.958285 + 0.285814i \(0.0922639\pi\)
−0.231620 + 0.972806i \(0.574403\pi\)
\(608\) −1072.36 −0.0715297
\(609\) −5590.81 + 7139.41i −0.372005 + 0.475046i
\(610\) 1610.77 0.106915
\(611\) −549.420 951.624i −0.0363784 0.0630092i
\(612\) 2148.27 3720.92i 0.141893 0.245767i
\(613\) 6786.19 11754.0i 0.447131 0.774454i −0.551067 0.834461i \(-0.685779\pi\)
0.998198 + 0.0600072i \(0.0191124\pi\)
\(614\) −7041.50 12196.2i −0.462820 0.801628i
\(615\) −20192.6 −1.32397
\(616\) 1385.11 1768.76i 0.0905966 0.115691i
\(617\) −8497.12 −0.554427 −0.277213 0.960808i \(-0.589411\pi\)
−0.277213 + 0.960808i \(0.589411\pi\)
\(618\) 2524.26 + 4372.15i 0.164305 + 0.284585i
\(619\) 11491.5 19903.8i 0.746173 1.29241i −0.203472 0.979081i \(-0.565223\pi\)
0.949645 0.313329i \(-0.101444\pi\)
\(620\) 9306.93 16120.1i 0.602863 1.04419i
\(621\) −8.79548 15.2342i −0.000568358 0.000984425i
\(622\) −5371.98 −0.346297
\(623\) −2650.91 6582.46i −0.170476 0.423308i
\(624\) 103.818 0.00666034
\(625\) −20661.3 35786.4i −1.32232 2.29033i
\(626\) −2219.19 + 3843.75i −0.141688 + 0.245411i
\(627\) 762.193 1320.16i 0.0485471 0.0840861i
\(628\) 613.864 + 1063.24i 0.0390061 + 0.0675605i
\(629\) −20114.3 −1.27505
\(630\) −6877.67 974.456i −0.434941 0.0616242i
\(631\) −15717.9 −0.991635 −0.495817 0.868427i \(-0.665131\pi\)
−0.495817 + 0.868427i \(0.665131\pi\)
\(632\) 465.212 + 805.771i 0.0292803 + 0.0507150i
\(633\) −6980.08 + 12089.9i −0.438283 + 0.759129i
\(634\) −2221.26 + 3847.34i −0.139144 + 0.241005i
\(635\) 1876.13 + 3249.55i 0.117247 + 0.203078i
\(636\) −2118.14 −0.132059
\(637\) 712.669 + 206.084i 0.0443280 + 0.0128185i
\(638\) −4949.42 −0.307131
\(639\) −2712.34 4697.91i −0.167916 0.290840i
\(640\) −1333.58 + 2309.82i −0.0823660 + 0.142662i
\(641\) −14553.7 + 25207.7i −0.896780 + 1.55327i −0.0651930 + 0.997873i \(0.520766\pi\)
−0.831587 + 0.555395i \(0.812567\pi\)
\(642\) 2147.01 + 3718.73i 0.131987 + 0.228609i
\(643\) −3112.26 −0.190880 −0.0954398 0.995435i \(-0.530426\pi\)
−0.0954398 + 0.995435i \(0.530426\pi\)
\(644\) −47.7878 6.77076i −0.00292407 0.000414294i
\(645\) 13849.8 0.845482
\(646\) −3999.53 6927.39i −0.243590 0.421911i
\(647\) 3928.80 6804.87i 0.238728 0.413489i −0.721622 0.692288i \(-0.756603\pi\)
0.960349 + 0.278799i \(0.0899363\pi\)
\(648\) −324.000 + 561.184i −0.0196419 + 0.0340207i
\(649\) −3449.01 5973.86i −0.208606 0.361317i
\(650\) 1337.46 0.0807071
\(651\) −4635.28 11509.8i −0.279064 0.692944i
\(652\) 14058.0 0.844408
\(653\) 9761.01 + 16906.6i 0.584958 + 1.01318i 0.994881 + 0.101057i \(0.0322224\pi\)
−0.409923 + 0.912120i \(0.634444\pi\)
\(654\) −1800.06 + 3117.79i −0.107627 + 0.186415i
\(655\) −2269.79 + 3931.38i −0.135401 + 0.234522i
\(656\) 2584.18 + 4475.93i 0.153804 + 0.266396i
\(657\) −9920.69 −0.589107
\(658\) 11602.3 14816.0i 0.687393 0.877793i
\(659\) 664.061 0.0392536 0.0196268 0.999807i \(-0.493752\pi\)
0.0196268 + 0.999807i \(0.493752\pi\)
\(660\) −1895.70 3283.46i −0.111803 0.193649i
\(661\) −7960.82 + 13788.5i −0.468442 + 0.811365i −0.999349 0.0360650i \(-0.988518\pi\)
0.530908 + 0.847430i \(0.321851\pi\)
\(662\) −4154.06 + 7195.04i −0.243885 + 0.422422i
\(663\) 387.205 + 670.658i 0.0226814 + 0.0392854i
\(664\) −4551.42 −0.266008
\(665\) −7973.36 + 10181.9i −0.464953 + 0.593739i
\(666\) 3033.61 0.176502
\(667\) 53.1665 + 92.0870i 0.00308638 + 0.00534576i
\(668\) −2246.61 + 3891.24i −0.130125 + 0.225384i
\(669\) 6974.30 12079.8i 0.403052 0.698107i
\(670\) −2954.53 5117.40i −0.170363 0.295078i
\(671\) 586.068 0.0337182
\(672\) 664.182 + 1649.23i 0.0381270 + 0.0946731i
\(673\) 24631.0 1.41078 0.705391 0.708819i \(-0.250771\pi\)
0.705391 + 0.708819i \(0.250771\pi\)
\(674\) 254.167 + 440.230i 0.0145254 + 0.0251588i
\(675\) −4174.01 + 7229.59i −0.238011 + 0.412247i
\(676\) 4384.64 7594.43i 0.249468 0.432091i
\(677\) −8546.39 14802.8i −0.485177 0.840350i 0.514678 0.857383i \(-0.327911\pi\)
−0.999855 + 0.0170329i \(0.994578\pi\)
\(678\) 3735.86 0.211615
\(679\) −6137.45 869.578i −0.346883 0.0491478i
\(680\) −19895.0 −1.12197
\(681\) −6227.57 10786.5i −0.350428 0.606958i
\(682\) 3386.26 5865.18i 0.190127 0.329310i
\(683\) 9581.79 16596.1i 0.536804 0.929771i −0.462270 0.886739i \(-0.652965\pi\)
0.999074 0.0430322i \(-0.0137018\pi\)
\(684\) 603.205 + 1044.78i 0.0337194 + 0.0584038i
\(685\) −54215.2 −3.02402
\(686\) 1285.53 + 12639.7i 0.0715478 + 0.703478i
\(687\) 12790.9 0.710339
\(688\) −1772.45 3069.98i −0.0982183 0.170119i
\(689\) 190.886 330.625i 0.0105547 0.0182813i
\(690\) −40.7272 + 70.5416i −0.00224704 + 0.00389199i
\(691\) −4047.94 7011.23i −0.222852 0.385991i 0.732821 0.680422i \(-0.238203\pi\)
−0.955673 + 0.294431i \(0.904870\pi\)
\(692\) 6122.39 0.336327
\(693\) −2502.39 354.549i −0.137169 0.0194346i
\(694\) −12449.3 −0.680934
\(695\) 27625.3 + 47848.5i 1.50775 + 2.61150i
\(696\) 1958.50 3392.22i 0.106662 0.184744i
\(697\) −19276.1 + 33387.2i −1.04754 + 1.81439i
\(698\) −9732.21 16856.7i −0.527750 0.914090i
\(699\) 9149.70 0.495098
\(700\) 8556.48 + 21246.6i 0.462006 + 1.14721i
\(701\) 12354.7 0.665664 0.332832 0.942986i \(-0.391996\pi\)
0.332832 + 0.942986i \(0.391996\pi\)
\(702\) −58.3977 101.148i −0.00313972 0.00543815i
\(703\) 2823.90 4891.14i 0.151501 0.262408i
\(704\) −485.212 + 840.412i −0.0259760 + 0.0449918i
\(705\) −15879.3 27503.8i −0.848297 1.46929i
\(706\) 2851.23 0.151993
\(707\) −168.337 + 214.965i −0.00895470 + 0.0114350i
\(708\) 5459.14 0.289784
\(709\) −1914.41 3315.85i −0.101406 0.175641i 0.810858 0.585243i \(-0.199001\pi\)
−0.912264 + 0.409602i \(0.865668\pi\)
\(710\) −12559.4 + 21753.5i −0.663868 + 1.14985i
\(711\) 523.364 906.492i 0.0276057 0.0478145i
\(712\) 1532.64 + 2654.60i 0.0806713 + 0.139727i
\(713\) −145.500 −0.00764241
\(714\) −8176.73 + 10441.6i −0.428580 + 0.547292i
\(715\) 683.363 0.0357431
\(716\) −6826.86 11824.5i −0.356329 0.617181i
\(717\) −5980.81 + 10359.1i −0.311516 + 0.539562i
\(718\) 5766.49 9987.86i 0.299726 0.519141i
\(719\) −611.500 1059.15i −0.0317178 0.0549368i 0.849731 0.527217i \(-0.176764\pi\)
−0.881449 + 0.472280i \(0.843431\pi\)
\(720\) 3000.55 0.155311
\(721\) −5821.42 14455.1i −0.300695 0.746654i
\(722\) −11472.0 −0.591333
\(723\) 936.972 + 1622.88i 0.0481969 + 0.0834795i
\(724\) −2573.42 + 4457.29i −0.132100 + 0.228804i
\(725\) 25230.8 43701.1i 1.29248 2.23864i
\(726\) 3303.26 + 5721.42i 0.168864 + 0.292482i
\(727\) 6368.21 0.324875 0.162437 0.986719i \(-0.448064\pi\)
0.162437 + 0.986719i \(0.448064\pi\)
\(728\) −317.288 44.9546i −0.0161531 0.00228864i
\(729\) 729.000 0.0370370
\(730\) 22968.7 + 39783.0i 1.16454 + 2.01704i
\(731\) 13221.2 22899.9i 0.668954 1.15866i
\(732\) −231.909 + 401.678i −0.0117098 + 0.0202820i
\(733\) 12577.0 + 21784.0i 0.633753 + 1.09769i 0.986778 + 0.162079i \(0.0518199\pi\)
−0.353024 + 0.935614i \(0.614847\pi\)
\(734\) 23090.7 1.16116
\(735\) 20597.5 + 5956.24i 1.03367 + 0.298910i
\(736\) 20.8485 0.00104414
\(737\) −1074.98 1861.93i −0.0537281 0.0930597i
\(738\) 2907.20 5035.43i 0.145008 0.251161i
\(739\) 5369.55 9300.34i 0.267283 0.462948i −0.700876 0.713283i \(-0.747207\pi\)
0.968159 + 0.250335i \(0.0805408\pi\)
\(740\) −7023.53 12165.1i −0.348906 0.604322i
\(741\) −217.443 −0.0107800
\(742\) 6473.42 + 917.180i 0.320279 + 0.0453783i
\(743\) 28166.3 1.39074 0.695370 0.718652i \(-0.255240\pi\)
0.695370 + 0.718652i \(0.255240\pi\)
\(744\) 2679.91 + 4641.74i 0.132057 + 0.228729i
\(745\) −6053.42 + 10484.8i −0.297691 + 0.515617i
\(746\) 6479.57 11222.9i 0.318008 0.550806i
\(747\) 2560.18 + 4434.36i 0.125398 + 0.217195i
\(748\) −7238.67 −0.353839
\(749\) −4951.41 12294.8i −0.241549 0.599791i
\(750\) 23027.4 1.12112
\(751\) −14328.5 24817.7i −0.696211 1.20587i −0.969771 0.244018i \(-0.921534\pi\)
0.273559 0.961855i \(-0.411799\pi\)
\(752\) −4064.36 + 7039.68i −0.197091 + 0.341371i
\(753\) 1993.18 3452.28i 0.0964613 0.167076i
\(754\) 353.000 + 611.414i 0.0170497 + 0.0295310i
\(755\) −12823.0 −0.618113
\(756\) 1233.20 1574.79i 0.0593270 0.0757599i
\(757\) −23604.1 −1.13330 −0.566648 0.823960i \(-0.691760\pi\)
−0.566648 + 0.823960i \(0.691760\pi\)
\(758\) −611.996 1060.01i −0.0293255 0.0507932i
\(759\) −14.8183 + 25.6661i −0.000708657 + 0.00122743i
\(760\) 2793.12 4837.83i 0.133312 0.230903i
\(761\) −2315.48 4010.54i −0.110297 0.191041i 0.805593 0.592470i \(-0.201847\pi\)
−0.915890 + 0.401429i \(0.868514\pi\)
\(762\) −1080.45 −0.0513658
\(763\) 6851.35 8749.10i 0.325079 0.415123i
\(764\) 4221.18 0.199891
\(765\) 11191.0 + 19383.3i 0.528902 + 0.916085i
\(766\) −4360.81 + 7553.15i −0.205695 + 0.356274i
\(767\) −491.977 + 852.129i −0.0231607 + 0.0401155i
\(768\) −384.000 665.108i −0.0180422 0.0312500i
\(769\) 33276.8 1.56046 0.780228 0.625495i \(-0.215103\pi\)
0.780228 + 0.625495i \(0.215103\pi\)
\(770\) 4371.85 + 10855.7i 0.204611 + 0.508069i
\(771\) −9678.55 −0.452094
\(772\) 9541.68 + 16526.7i 0.444835 + 0.770477i
\(773\) 11469.4 19865.6i 0.533668 0.924340i −0.465558