Properties

Label 403.2.h.b.118.17
Level 403
Weight 2
Character 403.118
Analytic conductor 3.218
Analytic rank 0
Dimension 34
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 118.17
Character \(\chi\) \(=\) 403.118
Dual form 403.2.h.b.222.17

$q$-expansion

\(f(q)\) \(=\) \(q+2.78699 q^{2} +(-0.467575 - 0.809863i) q^{3} +5.76734 q^{4} +(-2.03564 + 3.52583i) q^{5} +(-1.30313 - 2.25709i) q^{6} +(-0.420736 - 0.728737i) q^{7} +10.4996 q^{8} +(1.06275 - 1.84073i) q^{9} +O(q^{10})\) \(q+2.78699 q^{2} +(-0.467575 - 0.809863i) q^{3} +5.76734 q^{4} +(-2.03564 + 3.52583i) q^{5} +(-1.30313 - 2.25709i) q^{6} +(-0.420736 - 0.728737i) q^{7} +10.4996 q^{8} +(1.06275 - 1.84073i) q^{9} +(-5.67332 + 9.82648i) q^{10} +(0.129596 - 0.224467i) q^{11} +(-2.69666 - 4.67076i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-1.17259 - 2.03098i) q^{14} +3.80726 q^{15} +17.7275 q^{16} +(-2.06964 - 3.58471i) q^{17} +(2.96187 - 5.13011i) q^{18} +(1.04660 + 1.81277i) q^{19} +(-11.7402 + 20.3347i) q^{20} +(-0.393451 + 0.681478i) q^{21} +(0.361184 - 0.625589i) q^{22} -4.22515 q^{23} +(-4.90933 - 8.50320i) q^{24} +(-5.78767 - 10.0245i) q^{25} +(-1.39350 + 2.41361i) q^{26} -4.79311 q^{27} +(-2.42653 - 4.20287i) q^{28} -8.39075 q^{29} +10.6108 q^{30} +(-4.09017 + 3.77764i) q^{31} +28.4074 q^{32} -0.242384 q^{33} +(-5.76806 - 9.99058i) q^{34} +3.42587 q^{35} +(6.12922 - 10.6161i) q^{36} +(2.35547 + 4.07980i) q^{37} +(2.91687 + 5.05217i) q^{38} +0.935150 q^{39} +(-21.3733 + 37.0197i) q^{40} +(2.13010 - 3.68944i) q^{41} +(-1.09655 + 1.89928i) q^{42} +(-1.83814 - 3.18376i) q^{43} +(0.747425 - 1.29458i) q^{44} +(4.32675 + 7.49414i) q^{45} -11.7755 q^{46} -2.22737 q^{47} +(-8.28894 - 14.3569i) q^{48} +(3.14596 - 5.44897i) q^{49} +(-16.1302 - 27.9383i) q^{50} +(-1.93542 + 3.35225i) q^{51} +(-2.88367 + 4.99466i) q^{52} +(1.29878 - 2.24955i) q^{53} -13.3584 q^{54} +(0.527623 + 0.913870i) q^{55} +(-4.41754 - 7.65141i) q^{56} +(0.978728 - 1.69521i) q^{57} -23.3850 q^{58} +(3.65454 + 6.32984i) q^{59} +21.9578 q^{60} +13.7039 q^{61} +(-11.3993 + 10.5283i) q^{62} -1.78855 q^{63} +43.7162 q^{64} +(-2.03564 - 3.52583i) q^{65} -0.675522 q^{66} +(-2.02616 + 3.50942i) q^{67} +(-11.9363 - 20.6743i) q^{68} +(1.97557 + 3.42179i) q^{69} +9.54789 q^{70} +(-0.900818 + 1.56026i) q^{71} +(11.1584 - 19.3269i) q^{72} +(5.05129 - 8.74910i) q^{73} +(6.56469 + 11.3704i) q^{74} +(-5.41234 + 9.37445i) q^{75} +(6.03610 + 10.4548i) q^{76} -0.218103 q^{77} +2.60626 q^{78} +(8.05852 + 13.9578i) q^{79} +(-36.0869 + 62.5043i) q^{80} +(-0.947107 - 1.64044i) q^{81} +(5.93658 - 10.2825i) q^{82} +(-0.533088 + 0.923335i) q^{83} +(-2.26917 + 3.93031i) q^{84} +16.8521 q^{85} +(-5.12290 - 8.87312i) q^{86} +(3.92330 + 6.79536i) q^{87} +(1.36070 - 2.35681i) q^{88} -0.765428 q^{89} +(12.0586 + 20.8861i) q^{90} +0.841473 q^{91} -24.3679 q^{92} +(4.97183 + 1.54615i) q^{93} -6.20768 q^{94} -8.52201 q^{95} +(-13.2826 - 23.0061i) q^{96} +0.945784 q^{97} +(8.76778 - 15.1862i) q^{98} +(-0.275456 - 0.477104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} + O(q^{10}) \) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} - 7q^{10} - 5q^{11} - 28q^{12} - 17q^{13} - 7q^{14} + 8q^{15} + 18q^{16} - 8q^{17} + 6q^{18} + 3q^{19} - 8q^{20} + 13q^{21} + 12q^{22} - 14q^{23} - 6q^{24} - 26q^{25} - 3q^{26} + 28q^{27} - 7q^{28} - 18q^{29} - 60q^{30} - 9q^{31} + 58q^{32} - 14q^{33} - 15q^{34} + 50q^{35} - 49q^{36} - 6q^{37} + 2q^{38} + 4q^{39} - 29q^{40} - 5q^{41} + 8q^{42} - q^{43} - 22q^{44} + 13q^{45} + 34q^{46} + 16q^{47} - 49q^{48} + 3q^{49} - 35q^{51} - 17q^{52} + 30q^{53} - 2q^{54} + 21q^{55} - 7q^{56} + 34q^{58} - 9q^{59} - 38q^{60} - 28q^{61} - 62q^{62} + 88q^{63} + 56q^{64} - 5q^{65} + 140q^{66} - 31q^{67} - 39q^{68} + 5q^{69} + 56q^{70} + q^{71} - 32q^{72} - 10q^{73} - 39q^{74} - 2q^{75} - 16q^{76} + 76q^{77} - 23q^{79} - 22q^{80} - 29q^{81} - 10q^{82} + 3q^{83} + 52q^{84} - 32q^{85} + 4q^{86} + 18q^{87} - 10q^{88} + 26q^{89} + 35q^{90} + 4q^{91} - 94q^{92} - 41q^{93} + 70q^{94} + 28q^{95} - 23q^{96} + 32q^{97} - 38q^{98} - 70q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.78699 1.97070 0.985351 0.170537i \(-0.0545501\pi\)
0.985351 + 0.170537i \(0.0545501\pi\)
\(3\) −0.467575 0.809863i −0.269954 0.467575i 0.698895 0.715224i \(-0.253675\pi\)
−0.968850 + 0.247649i \(0.920342\pi\)
\(4\) 5.76734 2.88367
\(5\) −2.03564 + 3.52583i −0.910366 + 1.57680i −0.0968193 + 0.995302i \(0.530867\pi\)
−0.813547 + 0.581499i \(0.802466\pi\)
\(6\) −1.30313 2.25709i −0.532000 0.921451i
\(7\) −0.420736 0.728737i −0.159023 0.275437i 0.775493 0.631356i \(-0.217501\pi\)
−0.934517 + 0.355919i \(0.884168\pi\)
\(8\) 10.4996 3.71215
\(9\) 1.06275 1.84073i 0.354249 0.613578i
\(10\) −5.67332 + 9.82648i −1.79406 + 3.10741i
\(11\) 0.129596 0.224467i 0.0390747 0.0676794i −0.845827 0.533458i \(-0.820892\pi\)
0.884901 + 0.465778i \(0.154226\pi\)
\(12\) −2.69666 4.67076i −0.778459 1.34833i
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i
\(14\) −1.17259 2.03098i −0.313388 0.542804i
\(15\) 3.80726 0.983030
\(16\) 17.7275 4.43188
\(17\) −2.06964 3.58471i −0.501960 0.869421i −0.999997 0.00226526i \(-0.999279\pi\)
0.498037 0.867156i \(-0.334054\pi\)
\(18\) 2.96187 5.13011i 0.698120 1.20918i
\(19\) 1.04660 + 1.81277i 0.240107 + 0.415877i 0.960744 0.277435i \(-0.0894843\pi\)
−0.720638 + 0.693312i \(0.756151\pi\)
\(20\) −11.7402 + 20.3347i −2.62520 + 4.54697i
\(21\) −0.393451 + 0.681478i −0.0858581 + 0.148711i
\(22\) 0.361184 0.625589i 0.0770047 0.133376i
\(23\) −4.22515 −0.881004 −0.440502 0.897752i \(-0.645200\pi\)
−0.440502 + 0.897752i \(0.645200\pi\)
\(24\) −4.90933 8.50320i −1.00211 1.73571i
\(25\) −5.78767 10.0245i −1.15753 2.00491i
\(26\) −1.39350 + 2.41361i −0.273287 + 0.473347i
\(27\) −4.79311 −0.922434
\(28\) −2.42653 4.20287i −0.458571 0.794268i
\(29\) −8.39075 −1.55812 −0.779061 0.626948i \(-0.784304\pi\)
−0.779061 + 0.626948i \(0.784304\pi\)
\(30\) 10.6108 1.93726
\(31\) −4.09017 + 3.77764i −0.734616 + 0.678484i
\(32\) 28.4074 5.02176
\(33\) −0.242384 −0.0421936
\(34\) −5.76806 9.99058i −0.989215 1.71337i
\(35\) 3.42587 0.579078
\(36\) 6.12922 10.6161i 1.02154 1.76935i
\(37\) 2.35547 + 4.07980i 0.387237 + 0.670714i 0.992077 0.125633i \(-0.0400961\pi\)
−0.604840 + 0.796347i \(0.706763\pi\)
\(38\) 2.91687 + 5.05217i 0.473179 + 0.819570i
\(39\) 0.935150 0.149744
\(40\) −21.3733 + 37.0197i −3.37942 + 5.85332i
\(41\) 2.13010 3.68944i 0.332666 0.576194i −0.650368 0.759619i \(-0.725385\pi\)
0.983034 + 0.183425i \(0.0587186\pi\)
\(42\) −1.09655 + 1.89928i −0.169201 + 0.293065i
\(43\) −1.83814 3.18376i −0.280314 0.485519i 0.691148 0.722714i \(-0.257105\pi\)
−0.971462 + 0.237195i \(0.923772\pi\)
\(44\) 0.747425 1.29458i 0.112679 0.195165i
\(45\) 4.32675 + 7.49414i 0.644993 + 1.11716i
\(46\) −11.7755 −1.73620
\(47\) −2.22737 −0.324896 −0.162448 0.986717i \(-0.551939\pi\)
−0.162448 + 0.986717i \(0.551939\pi\)
\(48\) −8.28894 14.3569i −1.19641 2.07224i
\(49\) 3.14596 5.44897i 0.449423 0.778424i
\(50\) −16.1302 27.9383i −2.28116 3.95108i
\(51\) −1.93542 + 3.35225i −0.271013 + 0.469408i
\(52\) −2.88367 + 4.99466i −0.399893 + 0.692635i
\(53\) 1.29878 2.24955i 0.178401 0.309000i −0.762932 0.646479i \(-0.776241\pi\)
0.941333 + 0.337479i \(0.109574\pi\)
\(54\) −13.3584 −1.81784
\(55\) 0.527623 + 0.913870i 0.0711446 + 0.123226i
\(56\) −4.41754 7.65141i −0.590319 1.02246i
\(57\) 0.978728 1.69521i 0.129636 0.224536i
\(58\) −23.3850 −3.07060
\(59\) 3.65454 + 6.32984i 0.475780 + 0.824076i 0.999615 0.0277443i \(-0.00883241\pi\)
−0.523835 + 0.851820i \(0.675499\pi\)
\(60\) 21.9578 2.83473
\(61\) 13.7039 1.75460 0.877302 0.479939i \(-0.159341\pi\)
0.877302 + 0.479939i \(0.159341\pi\)
\(62\) −11.3993 + 10.5283i −1.44771 + 1.33709i
\(63\) −1.78855 −0.225336
\(64\) 43.7162 5.46452
\(65\) −2.03564 3.52583i −0.252490 0.437326i
\(66\) −0.675522 −0.0831510
\(67\) −2.02616 + 3.50942i −0.247535 + 0.428744i −0.962841 0.270068i \(-0.912954\pi\)
0.715306 + 0.698811i \(0.246287\pi\)
\(68\) −11.9363 20.6743i −1.44749 2.50712i
\(69\) 1.97557 + 3.42179i 0.237831 + 0.411935i
\(70\) 9.54789 1.14119
\(71\) −0.900818 + 1.56026i −0.106907 + 0.185169i −0.914516 0.404550i \(-0.867428\pi\)
0.807608 + 0.589719i \(0.200762\pi\)
\(72\) 11.1584 19.3269i 1.31503 2.27769i
\(73\) 5.05129 8.74910i 0.591209 1.02400i −0.402861 0.915261i \(-0.631984\pi\)
0.994070 0.108743i \(-0.0346825\pi\)
\(74\) 6.56469 + 11.3704i 0.763129 + 1.32178i
\(75\) −5.41234 + 9.37445i −0.624963 + 1.08247i
\(76\) 6.03610 + 10.4548i 0.692388 + 1.19925i
\(77\) −0.218103 −0.0248552
\(78\) 2.60626 0.295101
\(79\) 8.05852 + 13.9578i 0.906655 + 1.57037i 0.818680 + 0.574250i \(0.194706\pi\)
0.0879745 + 0.996123i \(0.471961\pi\)
\(80\) −36.0869 + 62.5043i −4.03463 + 6.98819i
\(81\) −0.947107 1.64044i −0.105234 0.182271i
\(82\) 5.93658 10.2825i 0.655585 1.13551i
\(83\) −0.533088 + 0.923335i −0.0585140 + 0.101349i −0.893799 0.448469i \(-0.851970\pi\)
0.835285 + 0.549818i \(0.185303\pi\)
\(84\) −2.26917 + 3.93031i −0.247586 + 0.428832i
\(85\) 16.8521 1.82787
\(86\) −5.12290 8.87312i −0.552416 0.956813i
\(87\) 3.92330 + 6.79536i 0.420622 + 0.728539i
\(88\) 1.36070 2.35681i 0.145051 0.251236i
\(89\) −0.765428 −0.0811352 −0.0405676 0.999177i \(-0.512917\pi\)
−0.0405676 + 0.999177i \(0.512917\pi\)
\(90\) 12.0586 + 20.8861i 1.27109 + 2.20159i
\(91\) 0.841473 0.0882103
\(92\) −24.3679 −2.54052
\(93\) 4.97183 + 1.54615i 0.515555 + 0.160328i
\(94\) −6.20768 −0.640273
\(95\) −8.52201 −0.874340
\(96\) −13.2826 23.0061i −1.35565 2.34805i
\(97\) 0.945784 0.0960299 0.0480149 0.998847i \(-0.484710\pi\)
0.0480149 + 0.998847i \(0.484710\pi\)
\(98\) 8.76778 15.1862i 0.885679 1.53404i
\(99\) −0.275456 0.477104i −0.0276844 0.0479508i
\(100\) −33.3795 57.8149i −3.33795 5.78149i
\(101\) −14.0197 −1.39501 −0.697507 0.716578i \(-0.745708\pi\)
−0.697507 + 0.716578i \(0.745708\pi\)
\(102\) −5.39400 + 9.34269i −0.534086 + 0.925064i
\(103\) −0.594676 + 1.03001i −0.0585951 + 0.101490i −0.893835 0.448396i \(-0.851995\pi\)
0.835240 + 0.549886i \(0.185329\pi\)
\(104\) −5.24978 + 9.09288i −0.514783 + 0.891630i
\(105\) −1.60185 2.77449i −0.156325 0.270762i
\(106\) 3.61969 6.26949i 0.351576 0.608947i
\(107\) 5.44753 + 9.43539i 0.526632 + 0.912154i 0.999518 + 0.0310304i \(0.00987887\pi\)
−0.472886 + 0.881124i \(0.656788\pi\)
\(108\) −27.6435 −2.65999
\(109\) 1.54109 0.147610 0.0738050 0.997273i \(-0.476486\pi\)
0.0738050 + 0.997273i \(0.476486\pi\)
\(110\) 1.47048 + 2.54695i 0.140205 + 0.242842i
\(111\) 2.20272 3.81522i 0.209073 0.362125i
\(112\) −7.45861 12.9187i −0.704772 1.22070i
\(113\) −4.75415 + 8.23443i −0.447233 + 0.774630i −0.998205 0.0598938i \(-0.980924\pi\)
0.550972 + 0.834524i \(0.314257\pi\)
\(114\) 2.72771 4.72453i 0.255473 0.442493i
\(115\) 8.60088 14.8972i 0.802037 1.38917i
\(116\) −48.3923 −4.49311
\(117\) 1.06275 + 1.84073i 0.0982510 + 0.170176i
\(118\) 10.1852 + 17.6412i 0.937621 + 1.62401i
\(119\) −1.74154 + 3.01644i −0.159647 + 0.276517i
\(120\) 39.9745 3.64916
\(121\) 5.46641 + 9.46810i 0.496946 + 0.860736i
\(122\) 38.1927 3.45780
\(123\) −3.98393 −0.359219
\(124\) −23.5894 + 21.7869i −2.11839 + 1.95652i
\(125\) 26.7701 2.39439
\(126\) −4.98467 −0.444069
\(127\) −2.54274 4.40416i −0.225632 0.390806i 0.730877 0.682509i \(-0.239111\pi\)
−0.956509 + 0.291703i \(0.905778\pi\)
\(128\) 65.0220 5.74719
\(129\) −1.71894 + 2.97729i −0.151344 + 0.262136i
\(130\) −5.67332 9.82648i −0.497583 0.861839i
\(131\) −6.05562 10.4886i −0.529082 0.916397i −0.999425 0.0339130i \(-0.989203\pi\)
0.470343 0.882484i \(-0.344130\pi\)
\(132\) −1.39791 −0.121672
\(133\) 0.880686 1.52539i 0.0763651 0.132268i
\(134\) −5.64691 + 9.78073i −0.487818 + 0.844926i
\(135\) 9.75704 16.8997i 0.839753 1.45449i
\(136\) −21.7303 37.6379i −1.86335 3.22742i
\(137\) 0.518866 0.898703i 0.0443297 0.0767814i −0.843009 0.537899i \(-0.819218\pi\)
0.887339 + 0.461118i \(0.152551\pi\)
\(138\) 5.50591 + 9.53652i 0.468694 + 0.811802i
\(139\) 17.8696 1.51568 0.757838 0.652443i \(-0.226256\pi\)
0.757838 + 0.652443i \(0.226256\pi\)
\(140\) 19.7582 1.66987
\(141\) 1.04146 + 1.80387i 0.0877071 + 0.151913i
\(142\) −2.51058 + 4.34845i −0.210683 + 0.364913i
\(143\) 0.129596 + 0.224467i 0.0108374 + 0.0187709i
\(144\) 18.8399 32.6316i 1.56999 2.71930i
\(145\) 17.0805 29.5844i 1.41846 2.45685i
\(146\) 14.0779 24.3837i 1.16510 2.01801i
\(147\) −5.88389 −0.485295
\(148\) 13.5848 + 23.5296i 1.11666 + 1.93412i
\(149\) −1.58004 2.73671i −0.129442 0.224200i 0.794019 0.607894i \(-0.207985\pi\)
−0.923461 + 0.383693i \(0.874652\pi\)
\(150\) −15.0842 + 26.1265i −1.23162 + 2.13322i
\(151\) −5.86679 −0.477433 −0.238716 0.971089i \(-0.576727\pi\)
−0.238716 + 0.971089i \(0.576727\pi\)
\(152\) 10.9888 + 19.0332i 0.891312 + 1.54380i
\(153\) −8.79800 −0.711276
\(154\) −0.607853 −0.0489822
\(155\) −4.99321 22.1112i −0.401064 1.77601i
\(156\) 5.39333 0.431812
\(157\) −2.51588 −0.200789 −0.100395 0.994948i \(-0.532011\pi\)
−0.100395 + 0.994948i \(0.532011\pi\)
\(158\) 22.4591 + 38.9002i 1.78675 + 3.09474i
\(159\) −2.42911 −0.192641
\(160\) −57.8272 + 100.160i −4.57164 + 7.91832i
\(161\) 1.77767 + 3.07902i 0.140100 + 0.242661i
\(162\) −2.63958 4.57189i −0.207385 0.359201i
\(163\) 1.72397 0.135031 0.0675157 0.997718i \(-0.478493\pi\)
0.0675157 + 0.997718i \(0.478493\pi\)
\(164\) 12.2850 21.2783i 0.959298 1.66155i
\(165\) 0.493406 0.854605i 0.0384116 0.0665309i
\(166\) −1.48571 + 2.57333i −0.115314 + 0.199729i
\(167\) −9.54056 16.5247i −0.738270 1.27872i −0.953274 0.302108i \(-0.902310\pi\)
0.215003 0.976613i \(-0.431024\pi\)
\(168\) −4.13106 + 7.15521i −0.318718 + 0.552037i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 46.9668 3.60219
\(171\) 4.44909 0.340230
\(172\) −10.6012 18.3618i −0.808334 1.40008i
\(173\) 4.01250 6.94985i 0.305064 0.528387i −0.672211 0.740359i \(-0.734655\pi\)
0.977276 + 0.211972i \(0.0679887\pi\)
\(174\) 10.9342 + 18.9386i 0.828921 + 1.43573i
\(175\) −4.87017 + 8.43538i −0.368150 + 0.637654i
\(176\) 2.29742 3.97925i 0.173174 0.299947i
\(177\) 3.41754 5.91935i 0.256878 0.444926i
\(178\) −2.13324 −0.159893
\(179\) 9.72409 + 16.8426i 0.726813 + 1.25888i 0.958224 + 0.286020i \(0.0923325\pi\)
−0.231411 + 0.972856i \(0.574334\pi\)
\(180\) 24.9538 + 43.2213i 1.85995 + 3.22152i
\(181\) −6.70159 + 11.6075i −0.498126 + 0.862779i −0.999998 0.00216311i \(-0.999311\pi\)
0.501872 + 0.864942i \(0.332645\pi\)
\(182\) 2.34518 0.173836
\(183\) −6.40760 11.0983i −0.473663 0.820409i
\(184\) −44.3622 −3.27042
\(185\) −19.1796 −1.41011
\(186\) 13.8565 + 4.30911i 1.01600 + 0.315959i
\(187\) −1.07287 −0.0784559
\(188\) −12.8460 −0.936893
\(189\) 2.01663 + 3.49291i 0.146688 + 0.254072i
\(190\) −23.7508 −1.72306
\(191\) −3.21016 + 5.56016i −0.232279 + 0.402319i −0.958478 0.285165i \(-0.907952\pi\)
0.726199 + 0.687484i \(0.241285\pi\)
\(192\) −20.4406 35.4041i −1.47517 2.55507i
\(193\) 7.50612 + 13.0010i 0.540302 + 0.935831i 0.998886 + 0.0471799i \(0.0150234\pi\)
−0.458584 + 0.888651i \(0.651643\pi\)
\(194\) 2.63590 0.189246
\(195\) −1.90363 + 3.29718i −0.136322 + 0.236116i
\(196\) 18.1438 31.4260i 1.29599 2.24472i
\(197\) 4.58822 7.94702i 0.326897 0.566202i −0.654998 0.755631i \(-0.727330\pi\)
0.981894 + 0.189429i \(0.0606637\pi\)
\(198\) −0.767695 1.32969i −0.0545577 0.0944967i
\(199\) 2.01214 3.48513i 0.142637 0.247054i −0.785852 0.618415i \(-0.787775\pi\)
0.928489 + 0.371360i \(0.121109\pi\)
\(200\) −60.7679 105.253i −4.29694 7.44252i
\(201\) 3.78953 0.267293
\(202\) −39.0729 −2.74916
\(203\) 3.53029 + 6.11464i 0.247778 + 0.429164i
\(204\) −11.1622 + 19.3335i −0.781512 + 1.35362i
\(205\) 8.67224 + 15.0208i 0.605696 + 1.04910i
\(206\) −1.65736 + 2.87063i −0.115474 + 0.200006i
\(207\) −4.49026 + 7.77737i −0.312095 + 0.540564i
\(208\) −8.86376 + 15.3525i −0.614591 + 1.06450i
\(209\) 0.542542 0.0375284
\(210\) −4.46435 7.73249i −0.308070 0.533592i
\(211\) −10.7226 18.5721i −0.738176 1.27856i −0.953316 0.301975i \(-0.902354\pi\)
0.215140 0.976583i \(-0.430979\pi\)
\(212\) 7.49051 12.9739i 0.514450 0.891054i
\(213\) 1.68480 0.115441
\(214\) 15.1822 + 26.2964i 1.03784 + 1.79758i
\(215\) 14.9672 1.02076
\(216\) −50.3255 −3.42421
\(217\) 4.47378 + 1.39126i 0.303700 + 0.0944452i
\(218\) 4.29502 0.290895
\(219\) −9.44743 −0.638398
\(220\) 3.04298 + 5.27059i 0.205158 + 0.355343i
\(221\) 4.13927 0.278438
\(222\) 6.13896 10.6330i 0.412020 0.713640i
\(223\) −5.78526 10.0204i −0.387410 0.671013i 0.604691 0.796460i \(-0.293297\pi\)
−0.992100 + 0.125447i \(0.959963\pi\)
\(224\) −11.9520 20.7015i −0.798578 1.38318i
\(225\) −24.6033 −1.64022
\(226\) −13.2498 + 22.9493i −0.881363 + 1.52657i
\(227\) −4.94543 + 8.56573i −0.328239 + 0.568527i −0.982163 0.188034i \(-0.939789\pi\)
0.653923 + 0.756561i \(0.273122\pi\)
\(228\) 5.64466 9.77683i 0.373827 0.647487i
\(229\) 8.58258 + 14.8655i 0.567153 + 0.982338i 0.996846 + 0.0793625i \(0.0252885\pi\)
−0.429693 + 0.902975i \(0.641378\pi\)
\(230\) 23.9706 41.5183i 1.58058 2.73764i
\(231\) 0.101980 + 0.176634i 0.00670977 + 0.0116217i
\(232\) −88.0991 −5.78399
\(233\) 19.7483 1.29376 0.646878 0.762594i \(-0.276074\pi\)
0.646878 + 0.762594i \(0.276074\pi\)
\(234\) 2.96187 + 5.13011i 0.193624 + 0.335366i
\(235\) 4.53414 7.85335i 0.295774 0.512296i
\(236\) 21.0770 + 36.5064i 1.37199 + 2.37636i
\(237\) 7.53593 13.0526i 0.489511 0.847858i
\(238\) −4.85367 + 8.40680i −0.314617 + 0.544932i
\(239\) −13.1299 + 22.7416i −0.849300 + 1.47103i 0.0325342 + 0.999471i \(0.489642\pi\)
−0.881834 + 0.471560i \(0.843691\pi\)
\(240\) 67.4932 4.35667
\(241\) −9.23442 15.9945i −0.594841 1.03029i −0.993569 0.113226i \(-0.963882\pi\)
0.398728 0.917069i \(-0.369452\pi\)
\(242\) 15.2349 + 26.3875i 0.979333 + 1.69626i
\(243\) −8.07534 + 13.9869i −0.518034 + 0.897261i
\(244\) 79.0350 5.05970
\(245\) 12.8081 + 22.1843i 0.818279 + 1.41730i
\(246\) −11.1032 −0.707913
\(247\) −2.09320 −0.133187
\(248\) −42.9449 + 39.6635i −2.72700 + 2.51863i
\(249\) 0.997034 0.0631845
\(250\) 74.6080 4.71863
\(251\) 5.60248 + 9.70379i 0.353626 + 0.612498i 0.986882 0.161445i \(-0.0516153\pi\)
−0.633256 + 0.773942i \(0.718282\pi\)
\(252\) −10.3151 −0.649793
\(253\) −0.547563 + 0.948407i −0.0344250 + 0.0596258i
\(254\) −7.08662 12.2744i −0.444654 0.770163i
\(255\) −7.87964 13.6479i −0.493442 0.854667i
\(256\) 93.7836 5.86148
\(257\) −2.36984 + 4.10468i −0.147826 + 0.256043i −0.930424 0.366485i \(-0.880561\pi\)
0.782597 + 0.622528i \(0.213894\pi\)
\(258\) −4.79068 + 8.29770i −0.298255 + 0.516592i
\(259\) 1.98206 3.43304i 0.123160 0.213319i
\(260\) −11.7402 20.3347i −0.728098 1.26110i
\(261\) −8.91724 + 15.4451i −0.551964 + 0.956029i
\(262\) −16.8770 29.2318i −1.04266 1.80595i
\(263\) 19.0671 1.17573 0.587865 0.808959i \(-0.299968\pi\)
0.587865 + 0.808959i \(0.299968\pi\)
\(264\) −2.54492 −0.156629
\(265\) 5.28770 + 9.15857i 0.324821 + 0.562606i
\(266\) 2.45447 4.25126i 0.150493 0.260661i
\(267\) 0.357895 + 0.619892i 0.0219028 + 0.0379368i
\(268\) −11.6856 + 20.2400i −0.713810 + 1.23635i
\(269\) 3.48183 6.03071i 0.212291 0.367699i −0.740140 0.672453i \(-0.765241\pi\)
0.952431 + 0.304754i \(0.0985742\pi\)
\(270\) 27.1928 47.0994i 1.65490 2.86638i
\(271\) 5.35133 0.325070 0.162535 0.986703i \(-0.448033\pi\)
0.162535 + 0.986703i \(0.448033\pi\)
\(272\) −36.6895 63.5481i −2.22463 3.85317i
\(273\) −0.393451 0.681478i −0.0238128 0.0412449i
\(274\) 1.44608 2.50468i 0.0873608 0.151313i
\(275\) −3.00024 −0.180921
\(276\) 11.3938 + 19.7346i 0.685826 + 1.18789i
\(277\) −0.0361715 −0.00217334 −0.00108667 0.999999i \(-0.500346\pi\)
−0.00108667 + 0.999999i \(0.500346\pi\)
\(278\) 49.8023 2.98695
\(279\) 2.60681 + 11.5436i 0.156065 + 0.691096i
\(280\) 35.9701 2.14963
\(281\) −10.3402 −0.616843 −0.308422 0.951250i \(-0.599801\pi\)
−0.308422 + 0.951250i \(0.599801\pi\)
\(282\) 2.90256 + 5.02737i 0.172845 + 0.299376i
\(283\) −29.7841 −1.77048 −0.885241 0.465132i \(-0.846007\pi\)
−0.885241 + 0.465132i \(0.846007\pi\)
\(284\) −5.19532 + 8.99857i −0.308286 + 0.533967i
\(285\) 3.98468 + 6.90167i 0.236032 + 0.408819i
\(286\) 0.361184 + 0.625589i 0.0213573 + 0.0369918i
\(287\) −3.58484 −0.211607
\(288\) 30.1899 52.2904i 1.77896 3.08124i
\(289\) −0.0667873 + 0.115679i −0.00392866 + 0.00680464i
\(290\) 47.6034 82.4515i 2.79537 4.84172i
\(291\) −0.442225 0.765956i −0.0259237 0.0449011i
\(292\) 29.1325 50.4590i 1.70485 2.95289i
\(293\) 4.01720 + 6.95800i 0.234687 + 0.406491i 0.959182 0.282790i \(-0.0912600\pi\)
−0.724494 + 0.689281i \(0.757927\pi\)
\(294\) −16.3984 −0.956373
\(295\) −29.7573 −1.73254
\(296\) 24.7314 + 42.8360i 1.43748 + 2.48979i
\(297\) −0.621168 + 1.07590i −0.0360438 + 0.0624298i
\(298\) −4.40357 7.62720i −0.255092 0.441832i
\(299\) 2.11257 3.65909i 0.122173 0.211610i
\(300\) −31.2148 + 54.0656i −1.80219 + 3.12148i
\(301\) −1.54675 + 2.67905i −0.0891531 + 0.154418i
\(302\) −16.3507 −0.940878
\(303\) 6.55527 + 11.3541i 0.376590 + 0.652274i
\(304\) 18.5536 + 32.1358i 1.06412 + 1.84312i
\(305\) −27.8962 + 48.3177i −1.59733 + 2.76666i
\(306\) −24.5200 −1.40171
\(307\) −2.32545 4.02780i −0.132720 0.229879i 0.792004 0.610516i \(-0.209038\pi\)
−0.924724 + 0.380637i \(0.875705\pi\)
\(308\) −1.25788 −0.0716741
\(309\) 1.11222 0.0632721
\(310\) −13.9160 61.6237i −0.790378 3.49999i
\(311\) −6.67669 −0.378600 −0.189300 0.981919i \(-0.560622\pi\)
−0.189300 + 0.981919i \(0.560622\pi\)
\(312\) 9.81865 0.555872
\(313\) −6.39968 11.0846i −0.361731 0.626537i 0.626515 0.779410i \(-0.284481\pi\)
−0.988246 + 0.152873i \(0.951148\pi\)
\(314\) −7.01175 −0.395696
\(315\) 3.64084 6.30612i 0.205138 0.355309i
\(316\) 46.4762 + 80.4992i 2.61449 + 4.52843i
\(317\) −5.06486 8.77260i −0.284471 0.492718i 0.688010 0.725701i \(-0.258485\pi\)
−0.972481 + 0.232983i \(0.925151\pi\)
\(318\) −6.76991 −0.379638
\(319\) −1.08741 + 1.88345i −0.0608832 + 0.105453i
\(320\) −88.9905 + 154.136i −4.97472 + 8.61647i
\(321\) 5.09425 8.82351i 0.284334 0.492480i
\(322\) 4.95436 + 8.58121i 0.276096 + 0.478212i
\(323\) 4.33216 7.50353i 0.241048 0.417508i
\(324\) −5.46228 9.46095i −0.303460 0.525609i
\(325\) 11.5753 0.642084
\(326\) 4.80468 0.266107
\(327\) −0.720577 1.24808i −0.0398480 0.0690187i
\(328\) 22.3651 38.7375i 1.23491 2.13892i
\(329\) 0.937137 + 1.62317i 0.0516661 + 0.0894882i
\(330\) 1.37512 2.38178i 0.0756979 0.131113i
\(331\) −0.693958 + 1.20197i −0.0381434 + 0.0660663i −0.884467 0.466603i \(-0.845478\pi\)
0.846323 + 0.532669i \(0.178811\pi\)
\(332\) −3.07450 + 5.32519i −0.168735 + 0.292258i
\(333\) 10.0131 0.548714
\(334\) −26.5895 46.0543i −1.45491 2.51998i
\(335\) −8.24908 14.2878i −0.450695 0.780627i
\(336\) −6.97492 + 12.0809i −0.380513 + 0.659068i
\(337\) 9.17340 0.499707 0.249853 0.968284i \(-0.419618\pi\)
0.249853 + 0.968284i \(0.419618\pi\)
\(338\) −1.39350 2.41361i −0.0757963 0.131283i
\(339\) 8.89168 0.482930
\(340\) 97.1920 5.27098
\(341\) 0.317886 + 1.40768i 0.0172145 + 0.0762299i
\(342\) 12.3996 0.670493
\(343\) −11.1848 −0.603922
\(344\) −19.2997 33.4280i −1.04057 1.80232i
\(345\) −16.0862 −0.866054
\(346\) 11.1828 19.3692i 0.601191 1.04129i
\(347\) −16.6974 28.9207i −0.896362 1.55254i −0.832110 0.554611i \(-0.812867\pi\)
−0.0642526 0.997934i \(-0.520466\pi\)
\(348\) 22.6270 + 39.1911i 1.21294 + 2.10087i
\(349\) 21.1587 1.13260 0.566299 0.824200i \(-0.308375\pi\)
0.566299 + 0.824200i \(0.308375\pi\)
\(350\) −13.5731 + 23.5093i −0.725514 + 1.25663i
\(351\) 2.39655 4.15095i 0.127919 0.221561i
\(352\) 3.68149 6.37653i 0.196224 0.339870i
\(353\) −4.29571 7.44040i −0.228638 0.396012i 0.728767 0.684762i \(-0.240094\pi\)
−0.957405 + 0.288750i \(0.906760\pi\)
\(354\) 9.52467 16.4972i 0.506230 0.876817i
\(355\) −3.66749 6.35227i −0.194650 0.337144i
\(356\) −4.41448 −0.233967
\(357\) 3.25721 0.172390
\(358\) 27.1010 + 46.9403i 1.43233 + 2.48087i
\(359\) 9.22732 15.9822i 0.486999 0.843508i −0.512889 0.858455i \(-0.671425\pi\)
0.999888 + 0.0149472i \(0.00475802\pi\)
\(360\) 45.4289 + 78.6851i 2.39431 + 4.14707i
\(361\) 7.30925 12.6600i 0.384698 0.666316i
\(362\) −18.6773 + 32.3500i −0.981657 + 1.70028i
\(363\) 5.11191 8.85409i 0.268306 0.464719i
\(364\) 4.85306 0.254369
\(365\) 20.5652 + 35.6200i 1.07643 + 1.86444i
\(366\) −17.8579 30.9309i −0.933449 1.61678i
\(367\) 5.55113 9.61483i 0.289766 0.501890i −0.683987 0.729494i \(-0.739756\pi\)
0.973754 + 0.227604i \(0.0730891\pi\)
\(368\) −74.9014 −3.90450
\(369\) −4.52752 7.84189i −0.235693 0.408233i
\(370\) −53.4534 −2.77891
\(371\) −2.18578 −0.113480
\(372\) 28.6742 + 8.91716i 1.48669 + 0.462333i
\(373\) −23.4406 −1.21371 −0.606853 0.794814i \(-0.707569\pi\)
−0.606853 + 0.794814i \(0.707569\pi\)
\(374\) −2.99008 −0.154613
\(375\) −12.5170 21.6801i −0.646376 1.11956i
\(376\) −23.3864 −1.20606
\(377\) 4.19537 7.26660i 0.216073 0.374249i
\(378\) 5.62035 + 9.73473i 0.289079 + 0.500700i
\(379\) −12.2716 21.2551i −0.630352 1.09180i −0.987480 0.157746i \(-0.949577\pi\)
0.357127 0.934056i \(-0.383756\pi\)
\(380\) −49.1493 −2.52131
\(381\) −2.37785 + 4.11855i −0.121821 + 0.211000i
\(382\) −8.94669 + 15.4961i −0.457753 + 0.792851i
\(383\) −18.0042 + 31.1842i −0.919973 + 1.59344i −0.120520 + 0.992711i \(0.538456\pi\)
−0.799453 + 0.600729i \(0.794877\pi\)
\(384\) −30.4027 52.6590i −1.55148 2.68724i
\(385\) 0.443980 0.768996i 0.0226273 0.0391917i
\(386\) 20.9195 + 36.2337i 1.06478 + 1.84424i
\(387\) −7.81393 −0.397205
\(388\) 5.45466 0.276918
\(389\) 2.97808 + 5.15818i 0.150994 + 0.261530i 0.931593 0.363502i \(-0.118419\pi\)
−0.780599 + 0.625032i \(0.785086\pi\)
\(390\) −5.30540 + 9.18923i −0.268650 + 0.465315i
\(391\) 8.74452 + 15.1459i 0.442229 + 0.765964i
\(392\) 33.0312 57.2117i 1.66833 2.88963i
\(393\) −5.66291 + 9.80845i −0.285656 + 0.494771i
\(394\) 12.7873 22.1483i 0.644217 1.11582i
\(395\) −65.6171 −3.30155
\(396\) −1.58865 2.75162i −0.0798326 0.138274i
\(397\) −9.66422 16.7389i −0.485033 0.840102i 0.514819 0.857299i \(-0.327859\pi\)
−0.999852 + 0.0171967i \(0.994526\pi\)
\(398\) 5.60783 9.71304i 0.281095 0.486871i
\(399\) −1.64715 −0.0824604
\(400\) −102.601 177.710i −5.13005 8.88551i
\(401\) 17.5378 0.875796 0.437898 0.899025i \(-0.355723\pi\)
0.437898 + 0.899025i \(0.355723\pi\)
\(402\) 10.5614 0.526755
\(403\) −1.22645 5.43101i −0.0610937 0.270538i
\(404\) −80.8565 −4.02276
\(405\) 7.71188 0.383206
\(406\) 9.83890 + 17.0415i 0.488297 + 0.845754i
\(407\) 1.22104 0.0605247
\(408\) −20.3210 + 35.1971i −1.00604 + 1.74251i
\(409\) 3.34471 + 5.79321i 0.165385 + 0.286456i 0.936792 0.349887i \(-0.113780\pi\)
−0.771407 + 0.636342i \(0.780447\pi\)
\(410\) 24.1695 + 41.8628i 1.19365 + 2.06746i
\(411\) −0.970436 −0.0478681
\(412\) −3.42969 + 5.94041i −0.168969 + 0.292663i
\(413\) 3.07519 5.32639i 0.151320 0.262095i
\(414\) −12.5143 + 21.6755i −0.615046 + 1.06529i
\(415\) −2.17035 3.75916i −0.106538 0.184530i
\(416\) −14.2037 + 24.6015i −0.696393 + 1.20619i
\(417\) −8.35535 14.4719i −0.409163 0.708692i
\(418\) 1.51206 0.0739573
\(419\) 30.3574 1.48306 0.741528 0.670922i \(-0.234101\pi\)
0.741528 + 0.670922i \(0.234101\pi\)
\(420\) −9.23842 16.0014i −0.450789 0.780789i
\(421\) 15.8850 27.5136i 0.774187 1.34093i −0.161064 0.986944i \(-0.551493\pi\)
0.935251 0.353986i \(-0.115174\pi\)
\(422\) −29.8839 51.7604i −1.45472 2.51966i
\(423\) −2.36714 + 4.10000i −0.115094 + 0.199349i
\(424\) 13.6366 23.6193i 0.662252 1.14705i
\(425\) −23.9567 + 41.4943i −1.16207 + 2.01277i
\(426\) 4.69553 0.227499
\(427\) −5.76573 9.98653i −0.279023 0.483282i
\(428\) 31.4177 + 54.4171i 1.51863 + 2.63035i
\(429\) 0.121192 0.209910i 0.00585120 0.0101346i
\(430\) 41.7135 2.01161
\(431\) −12.9211 22.3801i −0.622389 1.07801i −0.989040 0.147651i \(-0.952829\pi\)
0.366650 0.930359i \(-0.380505\pi\)
\(432\) −84.9698 −4.08811
\(433\) −27.9846 −1.34485 −0.672426 0.740164i \(-0.734748\pi\)
−0.672426 + 0.740164i \(0.734748\pi\)
\(434\) 12.4684 + 3.87745i 0.598503 + 0.186123i
\(435\) −31.9457 −1.53168
\(436\) 8.88801 0.425658
\(437\) −4.42204 7.65920i −0.211535 0.366389i
\(438\) −26.3299 −1.25809
\(439\) −3.22950 + 5.59365i −0.154135 + 0.266970i −0.932744 0.360540i \(-0.882593\pi\)
0.778608 + 0.627510i \(0.215926\pi\)
\(440\) 5.53980 + 9.59522i 0.264100 + 0.457434i
\(441\) −6.68673 11.5817i −0.318416 0.551512i
\(442\) 11.5361 0.548718
\(443\) 9.65475 16.7225i 0.458711 0.794511i −0.540182 0.841548i \(-0.681645\pi\)
0.998893 + 0.0470371i \(0.0149779\pi\)
\(444\) 12.7038 22.0037i 0.602897 1.04425i
\(445\) 1.55814 2.69877i 0.0738627 0.127934i
\(446\) −16.1235 27.9267i −0.763469 1.32237i
\(447\) −1.47758 + 2.55924i −0.0698869 + 0.121048i
\(448\) −18.3930 31.8576i −0.868987 1.50513i
\(449\) −17.6398 −0.832473 −0.416237 0.909256i \(-0.636651\pi\)
−0.416237 + 0.909256i \(0.636651\pi\)
\(450\) −68.5693 −3.23239
\(451\) −0.552106 0.956276i −0.0259977 0.0450293i
\(452\) −27.4188 + 47.4907i −1.28967 + 2.23378i
\(453\) 2.74316 + 4.75130i 0.128885 + 0.223236i
\(454\) −13.7829 + 23.8726i −0.646862 + 1.12040i
\(455\) −1.71294 + 2.96689i −0.0803037 + 0.139090i
\(456\) 10.2762 17.7989i 0.481227 0.833510i
\(457\) 33.2079 1.55340 0.776701 0.629870i \(-0.216892\pi\)
0.776701 + 0.629870i \(0.216892\pi\)
\(458\) 23.9196 + 41.4300i 1.11769 + 1.93590i
\(459\) 9.91998 + 17.1819i 0.463025 + 0.801983i
\(460\) 49.6042 85.9170i 2.31281 4.00590i
\(461\) 15.5365 0.723608 0.361804 0.932254i \(-0.382161\pi\)
0.361804 + 0.932254i \(0.382161\pi\)
\(462\) 0.284217 + 0.492278i 0.0132230 + 0.0229028i
\(463\) −15.1329 −0.703287 −0.351643 0.936134i \(-0.614377\pi\)
−0.351643 + 0.936134i \(0.614377\pi\)
\(464\) −148.747 −6.90541
\(465\) −15.5723 + 14.3824i −0.722149 + 0.666970i
\(466\) 55.0385 2.54961
\(467\) 3.92039 0.181414 0.0907069 0.995878i \(-0.471087\pi\)
0.0907069 + 0.995878i \(0.471087\pi\)
\(468\) 6.12922 + 10.6161i 0.283323 + 0.490731i
\(469\) 3.40992 0.157456
\(470\) 12.6366 21.8873i 0.582883 1.00958i
\(471\) 1.17636 + 2.03752i 0.0542040 + 0.0938840i
\(472\) 38.3710 + 66.4605i 1.76617 + 3.05909i
\(473\) −0.952866 −0.0438128
\(474\) 21.0026 36.3775i 0.964681 1.67088i
\(475\) 12.1148 20.9834i 0.555863 0.962783i
\(476\) −10.0441 + 17.3968i −0.460369 + 0.797382i
\(477\) −2.76055 4.78141i −0.126397 0.218926i
\(478\) −36.5928 + 63.3807i −1.67372 + 2.89896i
\(479\) 19.7978 + 34.2907i 0.904582 + 1.56678i 0.821477 + 0.570242i \(0.193151\pi\)
0.0831055 + 0.996541i \(0.473516\pi\)
\(480\) 108.154 4.93654
\(481\) −4.71094 −0.214801
\(482\) −25.7363 44.5765i −1.17225 2.03040i
\(483\) 1.66239 2.87934i 0.0756414 0.131015i
\(484\) 31.5266 + 54.6057i 1.43303 + 2.48208i
\(485\) −1.92528 + 3.33468i −0.0874224 + 0.151420i
\(486\) −22.5059 + 38.9814i −1.02089 + 1.76823i
\(487\) −0.338825 + 0.586863i −0.0153536 + 0.0265933i −0.873600 0.486644i \(-0.838221\pi\)
0.858246 + 0.513238i \(0.171554\pi\)
\(488\) 143.885 6.51336
\(489\) −0.806083 1.39618i −0.0364523 0.0631373i
\(490\) 35.6961 + 61.8275i 1.61259 + 2.79308i
\(491\) −9.36279 + 16.2168i −0.422537 + 0.731855i −0.996187 0.0872455i \(-0.972194\pi\)
0.573650 + 0.819100i \(0.305527\pi\)
\(492\) −22.9766 −1.03587
\(493\) 17.3658 + 30.0784i 0.782116 + 1.35466i
\(494\) −5.83374 −0.262472
\(495\) 2.24292 0.100812
\(496\) −72.5085 + 66.9681i −3.25573 + 3.00696i
\(497\) 1.51603 0.0680032
\(498\) 2.77873 0.124518
\(499\) 12.2804 + 21.2704i 0.549748 + 0.952192i 0.998291 + 0.0584307i \(0.0186097\pi\)
−0.448543 + 0.893761i \(0.648057\pi\)
\(500\) 154.392 6.90462
\(501\) −8.92185 + 15.4531i −0.398599 + 0.690393i
\(502\) 15.6141 + 27.0444i 0.696891 + 1.20705i
\(503\) −3.09597 5.36238i −0.138043 0.239097i 0.788713 0.614762i \(-0.210748\pi\)
−0.926756 + 0.375665i \(0.877414\pi\)
\(504\) −18.7789 −0.836480
\(505\) 28.5391 49.4312i 1.26997 2.19966i
\(506\) −1.52606 + 2.64321i −0.0678414 + 0.117505i
\(507\) −0.467575 + 0.809863i −0.0207657 + 0.0359673i
\(508\) −14.6649 25.4003i −0.650648 1.12696i
\(509\) −9.86807 + 17.0920i −0.437395 + 0.757590i −0.997488 0.0708400i \(-0.977432\pi\)
0.560093 + 0.828430i \(0.310765\pi\)
\(510\) −21.9605 38.0367i −0.972428 1.68429i
\(511\) −8.50105 −0.376064
\(512\) 131.330 5.80404
\(513\) −5.01647 8.68877i −0.221482 0.383619i
\(514\) −6.60472 + 11.4397i −0.291322 + 0.504584i
\(515\) −2.42109 4.19345i −0.106686 0.184786i
\(516\) −9.91371 + 17.1711i −0.436427 + 0.755913i
\(517\) −0.288659 + 0.499973i −0.0126952 + 0.0219888i
\(518\) 5.52400 9.56785i 0.242711 0.420387i
\(519\) −7.50457 −0.329414
\(520\) −21.3733 37.0197i −0.937282 1.62342i
\(521\) −18.3647 31.8085i −0.804571 1.39356i −0.916580 0.399850i \(-0.869062\pi\)
0.112010 0.993707i \(-0.464271\pi\)
\(522\) −24.8523 + 43.0455i −1.08776 + 1.88405i
\(523\) −6.90952 −0.302132 −0.151066 0.988524i \(-0.548271\pi\)
−0.151066 + 0.988524i \(0.548271\pi\)
\(524\) −34.9248 60.4915i −1.52570 2.64259i
\(525\) 9.10867 0.397535
\(526\) 53.1400 2.31702
\(527\) 22.0069 + 6.84375i 0.958636 + 0.298118i
\(528\) −4.29686 −0.186997
\(529\) −5.14813 −0.223832
\(530\) 14.7368 + 25.5249i 0.640126 + 1.10873i
\(531\) 15.5354 0.674179
\(532\) 5.07921 8.79745i 0.220212 0.381418i
\(533\) 2.13010 + 3.68944i 0.0922649 + 0.159807i
\(534\) 0.997451 + 1.72764i 0.0431639 + 0.0747621i
\(535\) −44.3568 −1.91771
\(536\) −21.2738 + 36.8473i −0.918888 + 1.59156i
\(537\) 9.09348 15.7504i 0.392413 0.679679i
\(538\) 9.70384 16.8075i 0.418362 0.724625i
\(539\) −0.815410 1.41233i −0.0351222 0.0608334i
\(540\) 56.2722 97.4663i 2.42157 4.19428i
\(541\) 7.91889 + 13.7159i 0.340460 + 0.589693i 0.984518 0.175283i \(-0.0560840\pi\)
−0.644059 + 0.764976i \(0.722751\pi\)
\(542\) 14.9141 0.640617
\(543\) 12.5340 0.537885
\(544\) −58.7929 101.832i −2.52073 4.36603i
\(545\) −3.13711 + 5.43364i −0.134379 + 0.232752i
\(546\) −1.09655 1.89928i −0.0469279 0.0812815i
\(547\) −14.0110 + 24.2678i −0.599069 + 1.03762i 0.393890 + 0.919158i \(0.371129\pi\)
−0.992959 + 0.118460i \(0.962204\pi\)
\(548\) 2.99248 5.18312i 0.127832 0.221412i
\(549\) 14.5638 25.2252i 0.621567 1.07659i
\(550\) −8.36165 −0.356542
\(551\) −8.78176 15.2105i −0.374116 0.647987i
\(552\) 20.7426 + 35.9273i 0.882865 + 1.52917i
\(553\) 6.78103 11.7451i 0.288359 0.499452i
\(554\) −0.100810 −0.00428300
\(555\) 8.96789 + 15.5328i 0.380666 + 0.659332i
\(556\) 103.060 4.37071
\(557\) −27.3296 −1.15799 −0.578996 0.815331i \(-0.696555\pi\)
−0.578996 + 0.815331i \(0.696555\pi\)
\(558\) 7.26515 + 32.1719i 0.307558 + 1.36194i
\(559\) 3.67629 0.155490
\(560\) 60.7322 2.56640
\(561\) 0.501646 + 0.868877i 0.0211795 + 0.0366840i
\(562\) −28.8180 −1.21562
\(563\) −0.831984 + 1.44104i −0.0350640 + 0.0607326i −0.883025 0.469326i \(-0.844497\pi\)
0.847961 + 0.530059i \(0.177830\pi\)
\(564\) 6.00648 + 10.4035i 0.252918 + 0.438067i
\(565\) −19.3555 33.5247i −0.814291 1.41039i
\(566\) −83.0082 −3.48909
\(567\) −0.796964 + 1.38038i −0.0334693 + 0.0579706i
\(568\) −9.45819 + 16.3821i −0.396857 + 0.687376i
\(569\) −15.7435 + 27.2685i −0.660001 + 1.14316i 0.320614 + 0.947210i \(0.396111\pi\)
−0.980615 + 0.195946i \(0.937222\pi\)
\(570\) 11.1053 + 19.2349i 0.465149 + 0.805662i
\(571\) 8.90650 15.4265i 0.372725 0.645579i −0.617258 0.786761i \(-0.711757\pi\)
0.989984 + 0.141181i \(0.0450900\pi\)
\(572\) 0.747425 + 1.29458i 0.0312514 + 0.0541290i
\(573\) 6.00396 0.250819
\(574\) −9.99094 −0.417014
\(575\) 24.4538 + 42.3552i 1.01979 + 1.76633i
\(576\) 46.4593 80.4698i 1.93580 3.35291i
\(577\) 1.03045 + 1.78479i 0.0428982 + 0.0743018i 0.886677 0.462389i \(-0.153008\pi\)
−0.843779 + 0.536691i \(0.819674\pi\)
\(578\) −0.186136 + 0.322397i −0.00774223 + 0.0134099i
\(579\) 7.01934 12.1579i 0.291714 0.505264i
\(580\) 98.5093 170.623i 4.09038 7.08474i
\(581\) 0.897158 0.0372204
\(582\) −1.23248 2.13472i −0.0510879 0.0884868i
\(583\) −0.336634 0.583067i −0.0139420 0.0241482i
\(584\) 53.0363 91.8616i 2.19466 3.80126i
\(585\) −8.65349 −0.357778
\(586\) 11.1959 + 19.3919i 0.462499 + 0.801072i
\(587\) 27.3716 1.12975 0.564873 0.825178i \(-0.308925\pi\)
0.564873 + 0.825178i \(0.308925\pi\)
\(588\) −33.9344 −1.39943
\(589\) −11.1287 3.46083i −0.458552 0.142601i
\(590\) −82.9335 −3.41432
\(591\) −8.58134 −0.352989
\(592\) 41.7567 + 72.3246i 1.71619 + 2.97252i
\(593\) 9.88958 0.406117 0.203058 0.979167i \(-0.434912\pi\)
0.203058 + 0.979167i \(0.434912\pi\)
\(594\) −1.73119 + 2.99851i −0.0710317 + 0.123031i
\(595\) −7.09031 12.2808i −0.290674 0.503463i
\(596\) −9.11263 15.7835i −0.373268 0.646519i
\(597\) −3.76331 −0.154022
\(598\) 5.88773 10.1979i 0.240767 0.417021i
\(599\) 18.0061 31.1874i 0.735709 1.27428i −0.218703 0.975791i \(-0.570183\pi\)
0.954412 0.298493i \(-0.0964840\pi\)
\(600\) −56.8271 + 98.4275i −2.31996 + 4.01828i
\(601\) −4.41298 7.64350i −0.180009 0.311785i 0.761874 0.647725i \(-0.224279\pi\)
−0.941883 + 0.335940i \(0.890946\pi\)
\(602\) −4.31078 + 7.46649i −0.175694 + 0.304311i
\(603\) 4.30660 + 7.45925i 0.175378 + 0.303764i
\(604\) −33.8358 −1.37676
\(605\) −44.5106 −1.80961
\(606\) 18.2695 + 31.6437i 0.742148 + 1.28544i
\(607\) −8.96622 + 15.5299i −0.363928 + 0.630341i −0.988603 0.150543i \(-0.951898\pi\)
0.624676 + 0.780884i \(0.285231\pi\)
\(608\) 29.7312 + 51.4959i 1.20576 + 2.08844i
\(609\) 3.30135 5.71811i 0.133778 0.231709i
\(610\) −77.7466 + 134.661i −3.14787 + 5.45227i
\(611\) 1.11369 1.92896i 0.0450550 0.0780375i
\(612\) −50.7411 −2.05109
\(613\) −13.4523 23.3000i −0.543333 0.941080i −0.998710 0.0507811i \(-0.983829\pi\)
0.455377 0.890299i \(-0.349504\pi\)
\(614\) −6.48102 11.2255i −0.261553 0.453022i
\(615\) 8.10984 14.0467i 0.327020 0.566416i
\(616\) −2.28999 −0.0922662
\(617\) 16.9002 + 29.2720i 0.680375 + 1.17844i 0.974866 + 0.222791i \(0.0715166\pi\)
−0.294491 + 0.955654i \(0.595150\pi\)
\(618\) 3.09975 0.124690
\(619\) −22.6135 −0.908912 −0.454456 0.890769i \(-0.650166\pi\)
−0.454456 + 0.890769i \(0.650166\pi\)
\(620\) −28.7975 127.523i −1.15654 5.12143i
\(621\) 20.2516 0.812668
\(622\) −18.6079 −0.746108
\(623\) 0.322043 + 0.557795i 0.0129024 + 0.0223476i
\(624\) 16.5779 0.663646
\(625\) −25.5559 + 44.2641i −1.02224 + 1.77057i
\(626\) −17.8359 30.8926i −0.712865 1.23472i
\(627\) −0.253679 0.439385i −0.0101310 0.0175473i
\(628\) −14.5099 −0.579010
\(629\) 9.74994 16.8874i 0.388755 0.673344i
\(630\) 10.1470 17.5751i 0.404266 0.700209i
\(631\) 16.8310 29.1522i 0.670032 1.16053i −0.307863 0.951431i \(-0.599614\pi\)
0.977895 0.209099i \(-0.0670529\pi\)
\(632\) 84.6109 + 146.550i 3.36564 + 5.82946i
\(633\) −10.0273 + 17.3677i −0.398548 + 0.690305i
\(634\) −14.1157 24.4492i −0.560608 0.971001i
\(635\) 20.7045 0.821632
\(636\) −14.0095 −0.555512
\(637\) 3.14596 + 5.44897i 0.124648 + 0.215896i
\(638\) −3.03060 + 5.24916i −0.119983 + 0.207816i
\(639\) 1.91469 + 3.31633i 0.0757438 + 0.131192i
\(640\) −132.362 + 229.257i −5.23205 + 9.06217i
\(641\) 1.64265 2.84515i 0.0648807 0.112377i −0.831760 0.555135i \(-0.812667\pi\)
0.896641 + 0.442758i \(0.146000\pi\)
\(642\) 14.1977 24.5911i 0.560337 0.970532i
\(643\) 24.7246 0.975041 0.487521 0.873111i \(-0.337901\pi\)
0.487521 + 0.873111i \(0.337901\pi\)
\(644\) 10.2524 + 17.7577i 0.404003 + 0.699753i
\(645\) −6.99829 12.1214i −0.275557 0.477280i
\(646\) 12.0737 20.9123i 0.475034 0.822783i
\(647\) −4.02193 −0.158118 −0.0790591 0.996870i \(-0.525192\pi\)
−0.0790591 + 0.996870i \(0.525192\pi\)
\(648\) −9.94419 17.2238i −0.390645 0.676617i
\(649\) 1.89446 0.0743639
\(650\) 32.2604 1.26536
\(651\) −0.965094 4.27367i −0.0378250 0.167499i
\(652\) 9.94269 0.389386
\(653\) −39.6923 −1.55328 −0.776640 0.629945i \(-0.783077\pi\)
−0.776640 + 0.629945i \(0.783077\pi\)
\(654\) −2.00824 3.47838i −0.0785285 0.136015i
\(655\) 49.3083 1.92663
\(656\) 37.7614 65.4046i 1.47433 2.55362i
\(657\) −10.7365 18.5962i −0.418871 0.725505i
\(658\) 2.61180 + 4.52376i 0.101818 + 0.176355i
\(659\) −17.6062 −0.685840 −0.342920 0.939365i \(-0.611416\pi\)
−0.342920 + 0.939365i \(0.611416\pi\)
\(660\) 2.84564 4.92880i 0.110766 0.191853i
\(661\) 10.4738 18.1411i 0.407383 0.705609i −0.587212 0.809433i \(-0.699775\pi\)
0.994596 + 0.103824i \(0.0331080\pi\)
\(662\) −1.93406 + 3.34988i −0.0751693 + 0.130197i
\(663\) −1.93542 3.35225i −0.0751655 0.130190i
\(664\) −5.59718 + 9.69460i −0.217213 + 0.376224i
\(665\) 3.58552 + 6.21030i 0.139041 + 0.240825i
\(666\) 27.9064 1.08135
\(667\) 35.4521 1.37271
\(668\) −55.0236 95.3037i −2.12893 3.68741i
\(669\) −5.41008 + 9.37054i −0.209166 + 0.362286i
\(670\) −22.9901 39.8201i −0.888187 1.53838i
\(671\) 1.77597 3.07608i 0.0685607 0.118751i
\(672\) −11.1769 + 19.3590i −0.431159 + 0.746790i
\(673\) 8.52900 14.7727i 0.328769 0.569445i −0.653499 0.756927i \(-0.726700\pi\)
0.982268 + 0.187483i \(0.0600329\pi\)
\(674\) 25.5662 0.984774
\(675\) 27.7409 + 48.0487i 1.06775 + 1.84939i
\(676\) −2.88367 4.99466i −0.110910 0.192102i
\(677\) 16.6304 28.8046i 0.639156 1.10705i −0.346462 0.938064i \(-0.612617\pi\)
0.985618 0.168987i \(-0.0540497\pi\)
\(678\) 24.7811 0.951711
\(679\) −0.397926 0.689228i −0.0152710 0.0264501i
\(680\) 176.940 6.78534
\(681\) 9.24943 0.354439
\(682\) 0.885946 + 3.92318i 0.0339246 + 0.150226i
\(683\) 5.19052 0.198610 0.0993049 0.995057i \(-0.468338\pi\)
0.0993049 + 0.995057i \(0.468338\pi\)
\(684\) 25.6594 0.981112
\(685\) 2.11245 + 3.65887i 0.0807126 + 0.139798i
\(686\) −31.1719 −1.19015
\(687\) 8.02600 13.9014i 0.306211 0.530373i
\(688\) −32.5857 56.4401i −1.24232 2.15176i
\(689\) 1.29878 + 2.24955i 0.0494796 + 0.0857012i
\(690\) −44.8322 −1.70673
\(691\) −24.0337 + 41.6276i −0.914286 + 1.58359i −0.106342 + 0.994330i \(0.533914\pi\)
−0.807943 + 0.589260i \(0.799419\pi\)
\(692\) 23.1414 40.0821i 0.879705 1.52369i
\(693\) −0.231789 + 0.401470i −0.00880493 + 0.0152506i
\(694\) −46.5355 80.6018i −1.76646 3.05960i
\(695\) −36.3760 + 63.0051i −1.37982 + 2.38992i
\(696\) 41.1929 + 71.3482i 1.56141 + 2.70445i
\(697\) −17.6341 −0.667940
\(698\) 58.9691 2.23201
\(699\) −9.23382 15.9934i −0.349255 0.604928i
\(700\) −28.0879 + 48.6497i −1.06162 + 1.83878i
\(701\) −11.3053 19.5814i −0.426996 0.739579i 0.569608 0.821916i \(-0.307095\pi\)
−0.996605 + 0.0823371i \(0.973762\pi\)
\(702\) 6.67918 11.5687i 0.252089 0.436632i
\(703\) −4.93048 + 8.53983i −0.185956 + 0.322086i
\(704\) 5.66545 9.81285i 0.213525 0.369836i
\(705\) −8.48019 −0.319383
\(706\) −11.9721 20.7363i −0.450577 0.780423i
\(707\) 5.89861 + 10.2167i 0.221840 + 0.384238i
\(708\) 19.7101 34.1389i 0.740751 1.28302i
\(709\) 19.0043 0.713720 0.356860 0.934158i \(-0.383847\pi\)
0.356860 + 0.934158i \(0.383847\pi\)
\(710\) −10.2213 17.7037i −0.383597 0.664410i
\(711\) 34.2567 1.28473
\(712\) −8.03665 −0.301186
\(713\) 17.2816 15.9611i 0.647199 0.597747i
\(714\) 9.07781 0.339729
\(715\) −1.05525 −0.0394639
\(716\) 56.0821 + 97.1371i 2.09589 + 3.63018i
\(717\) 24.5568 0.917089
\(718\) 25.7165 44.5423i 0.959731 1.66230i
\(719\) 14.2717 + 24.7193i 0.532245 + 0.921876i 0.999291 + 0.0376428i \(0.0119849\pi\)
−0.467046 + 0.884233i \(0.654682\pi\)
\(720\) 76.7024 + 132.853i 2.85853 + 4.95112i
\(721\) 1.00081 0.0372720
\(722\) 20.3709 35.2834i 0.758125 1.31311i
\(723\) −8.63556 + 14.9572i −0.321160 + 0.556265i
\(724\) −38.6504 + 66.9444i −1.43643 + 2.48797i
\(725\) 48.5629 + 84.1134i 1.80358 + 3.12389i
\(726\) 14.2469 24.6763i 0.528751 0.915823i
\(727\) −14.6916 25.4466i −0.544881 0.943761i −0.998614 0.0526239i \(-0.983242\pi\)
0.453734 0.891137i \(-0.350092\pi\)
\(728\) 8.83508 0.327450
\(729\) 9.42067 0.348914
\(730\) 57.3152 + 99.2729i 2.12133 + 3.67425i
\(731\) −7.60858 + 13.1784i −0.281414 + 0.487422i
\(732\) −36.9548 64.0076i −1.36589 2.36579i
\(733\) 21.7698 37.7063i 0.804085 1.39272i −0.112823 0.993615i \(-0.535989\pi\)
0.916907 0.399100i \(-0.130677\pi\)
\(734\) 15.4710 26.7965i 0.571043 0.989076i
\(735\) 11.9775 20.7456i 0.441796 0.765214i
\(736\) −120.025 −4.42419
\(737\) 0.525166 + 0.909614i 0.0193447 + 0.0335061i
\(738\) −12.6182 21.8553i −0.464481 0.804505i
\(739\) −12.4726 + 21.6033i −0.458814 + 0.794689i −0.998899 0.0469219i \(-0.985059\pi\)
0.540085 + 0.841611i \(0.318392\pi\)
\(740\) −110.615 −4.06629
\(741\) 0.978728 + 1.69521i 0.0359545 + 0.0622750i
\(742\) −6.09175 −0.223635
\(743\) −43.6974 −1.60310 −0.801552 0.597925i \(-0.795992\pi\)
−0.801552 + 0.597925i \(0.795992\pi\)
\(744\) 52.2020 + 16.2339i 1.91382 + 0.595162i
\(745\) 12.8656 0.471359
\(746\) −65.3288 −2.39186
\(747\) 1.13308 + 1.96254i 0.0414571 + 0.0718057i
\(748\) −6.18759 −0.226241
\(749\) 4.58394 7.93963i 0.167494 0.290108i
\(750\) −34.8848 60.4223i −1.27381 2.20631i
\(751\) 3.42892 + 5.93906i 0.125123 + 0.216719i 0.921781 0.387711i \(-0.126734\pi\)
−0.796658 + 0.604430i \(0.793401\pi\)
\(752\) −39.4858 −1.43990
\(753\) 5.23916 9.07449i 0.190926 0.330693i
\(754\) 11.6925 20.2520i 0.425815 0.737533i
\(755\) 11.9427 20.6853i 0.434639 0.752816i
\(756\) 11.6306 + 20.1448i 0.423001 + 0.732659i
\(757\) −3.81100 + 6.60085i −0.138513 + 0.239912i −0.926934 0.375224i \(-0.877566\pi\)
0.788421 + 0.615136i \(0.210899\pi\)
\(758\) −34.2010 59.2379i −1.24224 2.15162i
\(759\) 1.02411 0.0371727
\(760\) −89.4773 −3.24568
\(761\) −14.7629 25.5701i −0.535156 0.926917i −0.999156 0.0410815i \(-0.986920\pi\)
0.464000 0.885835i \(-0.346414\pi\)
\(762\) −6.62705 + 11.4784i −0.240073 + 0.415818i
\(763\) −0.648394 1.12305i −0.0234734 0.0406572i
\(764\) −18.5141 + 32.0673i −0.669815 + 1.16015i
\(765\) 17.9096 31.0203i 0.647522 1.12154i
\(766\) −50.1777 + 86.9103i −1.81299 + 3.14020i
\(767\) −7.30908 −0.263915
\(768\) −43.8509 75.9519i −1.58233 2.74068i
\(769\) 21.0746 + 36.5022i 0.759968 + 1.31630i 0.942866 + 0.333171i \(0.108119\pi\)
−0.182898 + 0.983132i \(0.558548\pi\)
\(770\) 1.23737 2.14319i 0.0445917 0.0772351i
\(771\) 4.43230 0.159626