Properties

Label 261.3.s.a.55.1
Level $261$
Weight $3$
Character 261.55
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.11173489980\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 55.1
Character \(\chi\) \(=\) 261.55
Dual form 261.3.s.a.19.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.42815 + 2.27289i) q^{2} +(-1.39088 - 2.88819i) q^{4} +(6.69994 - 1.52922i) q^{5} +(-4.78081 - 2.30231i) q^{7} +(-2.11889 - 0.238741i) q^{8} +O(q^{10})\) \(q+(-1.42815 + 2.27289i) q^{2} +(-1.39088 - 2.88819i) q^{4} +(6.69994 - 1.52922i) q^{5} +(-4.78081 - 2.30231i) q^{7} +(-2.11889 - 0.238741i) q^{8} +(-6.09279 + 17.4122i) q^{10} +(3.10194 - 0.349505i) q^{11} +(14.9316 + 11.9076i) q^{13} +(12.0606 - 7.57819i) q^{14} +(11.5635 - 14.5002i) q^{16} +(19.1156 + 19.1156i) q^{17} +(3.26204 + 1.14144i) q^{19} +(-13.7355 - 17.2238i) q^{20} +(-3.63566 + 7.54952i) q^{22} +(3.11691 - 13.6561i) q^{23} +(20.0264 - 9.64422i) q^{25} +(-48.3892 + 16.9321i) q^{26} +17.0101i q^{28} +(22.5579 + 18.2247i) q^{29} +(-30.9563 + 49.2666i) q^{31} +(13.6259 + 38.9405i) q^{32} +(-70.7477 + 16.1477i) q^{34} +(-35.5518 - 8.11447i) q^{35} +(23.4414 + 2.64121i) q^{37} +(-7.25305 + 5.78412i) q^{38} +(-14.5615 + 1.64069i) q^{40} +(-29.0869 + 29.0869i) q^{41} +(28.3964 - 17.8426i) q^{43} +(-5.32387 - 8.47289i) q^{44} +(26.5873 + 26.5873i) q^{46} +(-5.42166 - 48.1186i) q^{47} +(-12.9956 - 16.2959i) q^{49} +(-6.68052 + 59.2913i) q^{50} +(13.6233 - 59.6874i) q^{52} +(-2.93760 - 12.8705i) q^{53} +(20.2483 - 7.08520i) q^{55} +(9.58032 + 6.01972i) q^{56} +(-73.6390 + 25.2439i) q^{58} -11.7545 q^{59} +(-18.2928 - 52.2779i) q^{61} +(-67.7674 - 140.721i) q^{62} +(-35.6416 - 8.13496i) q^{64} +(118.250 + 56.9463i) q^{65} +(-6.83210 + 5.44842i) q^{67} +(28.6221 - 81.7971i) q^{68} +(69.2167 - 69.2167i) q^{70} +(49.1193 + 39.1713i) q^{71} +(33.0911 + 52.6641i) q^{73} +(-39.4811 + 49.5078i) q^{74} +(-1.24042 - 11.0090i) q^{76} +(-15.6344 - 5.47073i) q^{77} +(5.05536 - 44.8675i) q^{79} +(55.3008 - 114.833i) q^{80} +(-24.5708 - 107.652i) q^{82} +(123.603 - 59.5242i) q^{83} +(157.305 + 98.8415i) q^{85} +90.0238i q^{86} -6.65610 q^{88} +(-38.7651 + 61.6944i) q^{89} +(-43.9702 - 91.3050i) q^{91} +(-43.7766 + 9.99172i) q^{92} +(117.111 + 56.3978i) q^{94} +(23.6010 + 2.65919i) q^{95} +(16.9565 - 48.4590i) q^{97} +(55.5985 - 6.26444i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{19}{28}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.42815 + 2.27289i −0.714076 + 1.13645i 0.270708 + 0.962662i \(0.412742\pi\)
−0.984784 + 0.173784i \(0.944401\pi\)
\(3\) 0 0
\(4\) −1.39088 2.88819i −0.347720 0.722048i
\(5\) 6.69994 1.52922i 1.33999 0.305843i 0.508344 0.861154i \(-0.330258\pi\)
0.831643 + 0.555311i \(0.187401\pi\)
\(6\) 0 0
\(7\) −4.78081 2.30231i −0.682972 0.328902i 0.0600247 0.998197i \(-0.480882\pi\)
−0.742997 + 0.669295i \(0.766596\pi\)
\(8\) −2.11889 0.238741i −0.264861 0.0298426i
\(9\) 0 0
\(10\) −6.09279 + 17.4122i −0.609279 + 1.74122i
\(11\) 3.10194 0.349505i 0.281995 0.0317732i 0.0301656 0.999545i \(-0.490397\pi\)
0.251829 + 0.967772i \(0.418968\pi\)
\(12\) 0 0
\(13\) 14.9316 + 11.9076i 1.14859 + 0.915967i 0.997366 0.0725336i \(-0.0231085\pi\)
0.151220 + 0.988500i \(0.451680\pi\)
\(14\) 12.0606 7.57819i 0.861473 0.541300i
\(15\) 0 0
\(16\) 11.5635 14.5002i 0.722718 0.906260i
\(17\) 19.1156 + 19.1156i 1.12445 + 1.12445i 0.991065 + 0.133383i \(0.0425841\pi\)
0.133383 + 0.991065i \(0.457416\pi\)
\(18\) 0 0
\(19\) 3.26204 + 1.14144i 0.171686 + 0.0600756i 0.414753 0.909934i \(-0.363868\pi\)
−0.243067 + 0.970009i \(0.578154\pi\)
\(20\) −13.7355 17.2238i −0.686774 0.861188i
\(21\) 0 0
\(22\) −3.63566 + 7.54952i −0.165257 + 0.343160i
\(23\) 3.11691 13.6561i 0.135518 0.593742i −0.860870 0.508824i \(-0.830080\pi\)
0.996388 0.0849173i \(-0.0270626\pi\)
\(24\) 0 0
\(25\) 20.0264 9.64422i 0.801057 0.385769i
\(26\) −48.3892 + 16.9321i −1.86112 + 0.651235i
\(27\) 0 0
\(28\) 17.0101i 0.607505i
\(29\) 22.5579 + 18.2247i 0.777858 + 0.628440i
\(30\) 0 0
\(31\) −30.9563 + 49.2666i −0.998590 + 1.58925i −0.206864 + 0.978370i \(0.566326\pi\)
−0.791726 + 0.610877i \(0.790817\pi\)
\(32\) 13.6259 + 38.9405i 0.425808 + 1.21689i
\(33\) 0 0
\(34\) −70.7477 + 16.1477i −2.08082 + 0.474932i
\(35\) −35.5518 8.11447i −1.01577 0.231842i
\(36\) 0 0
\(37\) 23.4414 + 2.64121i 0.633552 + 0.0713842i 0.422899 0.906177i \(-0.361012\pi\)
0.210653 + 0.977561i \(0.432441\pi\)
\(38\) −7.25305 + 5.78412i −0.190870 + 0.152214i
\(39\) 0 0
\(40\) −14.5615 + 1.64069i −0.364037 + 0.0410171i
\(41\) −29.0869 + 29.0869i −0.709436 + 0.709436i −0.966417 0.256981i \(-0.917272\pi\)
0.256981 + 0.966417i \(0.417272\pi\)
\(42\) 0 0
\(43\) 28.3964 17.8426i 0.660380 0.414945i −0.159721 0.987162i \(-0.551060\pi\)
0.820102 + 0.572218i \(0.193917\pi\)
\(44\) −5.32387 8.47289i −0.120997 0.192566i
\(45\) 0 0
\(46\) 26.5873 + 26.5873i 0.577985 + 0.577985i
\(47\) −5.42166 48.1186i −0.115355 1.02380i −0.909395 0.415934i \(-0.863455\pi\)
0.794040 0.607865i \(-0.207974\pi\)
\(48\) 0 0
\(49\) −12.9956 16.2959i −0.265215 0.332570i
\(50\) −6.68052 + 59.2913i −0.133610 + 1.18583i
\(51\) 0 0
\(52\) 13.6233 59.6874i 0.261986 1.14783i
\(53\) −2.93760 12.8705i −0.0554265 0.242839i 0.939624 0.342208i \(-0.111175\pi\)
−0.995051 + 0.0993688i \(0.968318\pi\)
\(54\) 0 0
\(55\) 20.2483 7.08520i 0.368152 0.128822i
\(56\) 9.58032 + 6.01972i 0.171077 + 0.107495i
\(57\) 0 0
\(58\) −73.6390 + 25.2439i −1.26964 + 0.435240i
\(59\) −11.7545 −0.199228 −0.0996140 0.995026i \(-0.531761\pi\)
−0.0996140 + 0.995026i \(0.531761\pi\)
\(60\) 0 0
\(61\) −18.2928 52.2779i −0.299882 0.857014i −0.990951 0.134225i \(-0.957145\pi\)
0.691069 0.722789i \(-0.257140\pi\)
\(62\) −67.7674 140.721i −1.09302 2.26969i
\(63\) 0 0
\(64\) −35.6416 8.13496i −0.556900 0.127109i
\(65\) 118.250 + 56.9463i 1.81923 + 0.876096i
\(66\) 0 0
\(67\) −6.83210 + 5.44842i −0.101972 + 0.0813196i −0.673148 0.739507i \(-0.735058\pi\)
0.571177 + 0.820827i \(0.306487\pi\)
\(68\) 28.6221 81.7971i 0.420913 1.20290i
\(69\) 0 0
\(70\) 69.2167 69.2167i 0.988811 0.988811i
\(71\) 49.1193 + 39.1713i 0.691821 + 0.551709i 0.905056 0.425292i \(-0.139829\pi\)
−0.213235 + 0.977001i \(0.568400\pi\)
\(72\) 0 0
\(73\) 33.0911 + 52.6641i 0.453302 + 0.721426i 0.992698 0.120626i \(-0.0384902\pi\)
−0.539396 + 0.842052i \(0.681347\pi\)
\(74\) −39.4811 + 49.5078i −0.533529 + 0.669024i
\(75\) 0 0
\(76\) −1.24042 11.0090i −0.0163213 0.144855i
\(77\) −15.6344 5.47073i −0.203045 0.0710484i
\(78\) 0 0
\(79\) 5.05536 44.8675i 0.0639919 0.567943i −0.920277 0.391267i \(-0.872037\pi\)
0.984269 0.176676i \(-0.0565346\pi\)
\(80\) 55.3008 114.833i 0.691260 1.43542i
\(81\) 0 0
\(82\) −24.5708 107.652i −0.299644 1.31283i
\(83\) 123.603 59.5242i 1.48920 0.717159i 0.500312 0.865845i \(-0.333218\pi\)
0.988885 + 0.148686i \(0.0475042\pi\)
\(84\) 0 0
\(85\) 157.305 + 98.8415i 1.85065 + 1.16284i
\(86\) 90.0238i 1.04679i
\(87\) 0 0
\(88\) −6.65610 −0.0756375
\(89\) −38.7651 + 61.6944i −0.435563 + 0.693195i −0.990318 0.138819i \(-0.955669\pi\)
0.554754 + 0.832014i \(0.312812\pi\)
\(90\) 0 0
\(91\) −43.9702 91.3050i −0.483189 1.00335i
\(92\) −43.7766 + 9.99172i −0.475833 + 0.108606i
\(93\) 0 0
\(94\) 117.111 + 56.3978i 1.24586 + 0.599977i
\(95\) 23.6010 + 2.65919i 0.248431 + 0.0279915i
\(96\) 0 0
\(97\) 16.9565 48.4590i 0.174810 0.499577i −0.822827 0.568292i \(-0.807604\pi\)
0.997636 + 0.0687153i \(0.0218900\pi\)
\(98\) 55.5985 6.26444i 0.567331 0.0639229i
\(99\) 0 0
\(100\) −55.7087 44.4262i −0.557087 0.444262i
\(101\) −10.9319 + 6.86898i −0.108237 + 0.0680097i −0.585063 0.810988i \(-0.698930\pi\)
0.476826 + 0.878998i \(0.341787\pi\)
\(102\) 0 0
\(103\) −21.5998 + 27.0853i −0.209706 + 0.262964i −0.875550 0.483128i \(-0.839501\pi\)
0.665843 + 0.746092i \(0.268072\pi\)
\(104\) −28.7956 28.7956i −0.276880 0.276880i
\(105\) 0 0
\(106\) 33.4486 + 11.7042i 0.315552 + 0.110417i
\(107\) −87.5840 109.827i −0.818542 1.02642i −0.999081 0.0428518i \(-0.986356\pi\)
0.180539 0.983568i \(-0.442216\pi\)
\(108\) 0 0
\(109\) 13.2898 27.5965i 0.121925 0.253179i −0.831069 0.556169i \(-0.812271\pi\)
0.952994 + 0.302990i \(0.0979849\pi\)
\(110\) −12.8138 + 56.1410i −0.116489 + 0.510373i
\(111\) 0 0
\(112\) −88.6667 + 42.6996i −0.791667 + 0.381247i
\(113\) −28.9202 + 10.1196i −0.255931 + 0.0895541i −0.455195 0.890392i \(-0.650430\pi\)
0.199264 + 0.979946i \(0.436145\pi\)
\(114\) 0 0
\(115\) 96.2612i 0.837054i
\(116\) 21.2613 90.5000i 0.183287 0.780173i
\(117\) 0 0
\(118\) 16.7872 26.7166i 0.142264 0.226412i
\(119\) −47.3779 135.398i −0.398133 1.13780i
\(120\) 0 0
\(121\) −108.466 + 24.7567i −0.896416 + 0.204601i
\(122\) 144.947 + 33.0832i 1.18809 + 0.271174i
\(123\) 0 0
\(124\) 185.348 + 20.8837i 1.49474 + 0.168417i
\(125\) −14.8956 + 11.8789i −0.119165 + 0.0950311i
\(126\) 0 0
\(127\) 4.07151 0.458749i 0.0320591 0.00361220i −0.0959203 0.995389i \(-0.530579\pi\)
0.127979 + 0.991777i \(0.459151\pi\)
\(128\) −47.2969 + 47.2969i −0.369507 + 0.369507i
\(129\) 0 0
\(130\) −298.312 + 187.442i −2.29471 + 1.44186i
\(131\) 15.8863 + 25.2830i 0.121270 + 0.193000i 0.901842 0.432066i \(-0.142215\pi\)
−0.780572 + 0.625065i \(0.785072\pi\)
\(132\) 0 0
\(133\) −12.9672 12.9672i −0.0974980 0.0974980i
\(134\) −2.62638 23.3098i −0.0195999 0.173954i
\(135\) 0 0
\(136\) −35.9401 45.0675i −0.264266 0.331379i
\(137\) 13.7929 122.415i 0.100678 0.893542i −0.837276 0.546781i \(-0.815853\pi\)
0.937954 0.346761i \(-0.112718\pi\)
\(138\) 0 0
\(139\) 52.0026 227.838i 0.374119 1.63912i −0.340958 0.940079i \(-0.610751\pi\)
0.715077 0.699045i \(-0.246392\pi\)
\(140\) 26.0122 + 113.967i 0.185801 + 0.814049i
\(141\) 0 0
\(142\) −159.182 + 55.7002i −1.12100 + 0.392255i
\(143\) 50.4787 + 31.7179i 0.352998 + 0.221803i
\(144\) 0 0
\(145\) 179.006 + 87.6087i 1.23452 + 0.604198i
\(146\) −166.959 −1.14355
\(147\) 0 0
\(148\) −24.9759 71.3770i −0.168756 0.482277i
\(149\) −44.8786 93.1914i −0.301199 0.625446i 0.694356 0.719632i \(-0.255689\pi\)
−0.995555 + 0.0941861i \(0.969975\pi\)
\(150\) 0 0
\(151\) 17.1757 + 3.92024i 0.113746 + 0.0259618i 0.279015 0.960287i \(-0.409992\pi\)
−0.165269 + 0.986249i \(0.552849\pi\)
\(152\) −6.63938 3.19736i −0.0436801 0.0210352i
\(153\) 0 0
\(154\) 34.7627 27.7224i 0.225732 0.180015i
\(155\) −132.066 + 377.422i −0.852037 + 2.43498i
\(156\) 0 0
\(157\) 55.4971 55.4971i 0.353485 0.353485i −0.507920 0.861404i \(-0.669585\pi\)
0.861404 + 0.507920i \(0.169585\pi\)
\(158\) 94.7592 + 75.5679i 0.599742 + 0.478278i
\(159\) 0 0
\(160\) 150.841 + 240.062i 0.942755 + 1.50039i
\(161\) −46.3419 + 58.1109i −0.287838 + 0.360937i
\(162\) 0 0
\(163\) 18.1802 + 161.354i 0.111535 + 0.989899i 0.917445 + 0.397862i \(0.130248\pi\)
−0.805910 + 0.592037i \(0.798324\pi\)
\(164\) 124.465 + 43.5521i 0.758932 + 0.265562i
\(165\) 0 0
\(166\) −41.2323 + 365.947i −0.248387 + 2.20450i
\(167\) −71.6533 + 148.790i −0.429061 + 0.890955i 0.568600 + 0.822614i \(0.307485\pi\)
−0.997662 + 0.0683416i \(0.978229\pi\)
\(168\) 0 0
\(169\) 43.5570 + 190.836i 0.257734 + 1.12920i
\(170\) −449.312 + 216.377i −2.64301 + 1.27281i
\(171\) 0 0
\(172\) −91.0289 57.1972i −0.529238 0.332542i
\(173\) 41.6753i 0.240898i −0.992720 0.120449i \(-0.961567\pi\)
0.992720 0.120449i \(-0.0384334\pi\)
\(174\) 0 0
\(175\) −117.946 −0.673980
\(176\) 30.8014 49.0201i 0.175008 0.278523i
\(177\) 0 0
\(178\) −84.8621 176.218i −0.476753 0.989988i
\(179\) 93.6851 21.3830i 0.523380 0.119458i 0.0473352 0.998879i \(-0.484927\pi\)
0.476045 + 0.879421i \(0.342070\pi\)
\(180\) 0 0
\(181\) −141.858 68.3150i −0.783744 0.377431i −0.00117831 0.999999i \(-0.500375\pi\)
−0.782566 + 0.622568i \(0.786089\pi\)
\(182\) 270.323 + 30.4580i 1.48529 + 0.167352i
\(183\) 0 0
\(184\) −9.86463 + 28.1915i −0.0536121 + 0.153215i
\(185\) 161.095 18.1511i 0.870784 0.0981138i
\(186\) 0 0
\(187\) 65.9765 + 52.6145i 0.352815 + 0.281361i
\(188\) −131.435 + 82.5860i −0.699122 + 0.439287i
\(189\) 0 0
\(190\) −39.7498 + 49.8447i −0.209210 + 0.262340i
\(191\) −149.268 149.268i −0.781507 0.781507i 0.198578 0.980085i \(-0.436368\pi\)
−0.980085 + 0.198578i \(0.936368\pi\)
\(192\) 0 0
\(193\) −7.47034 2.61398i −0.0387064 0.0135440i 0.310856 0.950457i \(-0.399384\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(194\) 85.9255 + 107.747i 0.442915 + 0.555398i
\(195\) 0 0
\(196\) −28.9905 + 60.1993i −0.147911 + 0.307139i
\(197\) 83.3370 365.123i 0.423030 1.85342i −0.0912973 0.995824i \(-0.529101\pi\)
0.514328 0.857594i \(-0.328042\pi\)
\(198\) 0 0
\(199\) −320.598 + 154.392i −1.61105 + 0.775840i −0.999877 0.0156595i \(-0.995015\pi\)
−0.611170 + 0.791499i \(0.709301\pi\)
\(200\) −44.7362 + 15.6539i −0.223681 + 0.0782693i
\(201\) 0 0
\(202\) 34.6570i 0.171569i
\(203\) −65.8858 139.064i −0.324561 0.685046i
\(204\) 0 0
\(205\) −150.400 + 239.360i −0.733659 + 1.16761i
\(206\) −30.7141 87.7758i −0.149097 0.426096i
\(207\) 0 0
\(208\) 345.323 78.8178i 1.66021 0.378932i
\(209\) 10.5176 + 2.40057i 0.0503234 + 0.0114860i
\(210\) 0 0
\(211\) 231.167 + 26.0462i 1.09558 + 0.123442i 0.641205 0.767370i \(-0.278435\pi\)
0.454372 + 0.890812i \(0.349864\pi\)
\(212\) −33.0866 + 26.3857i −0.156069 + 0.124461i
\(213\) 0 0
\(214\) 374.708 42.2194i 1.75097 0.197287i
\(215\) 162.969 162.969i 0.757993 0.757993i
\(216\) 0 0
\(217\) 261.423 164.263i 1.20472 0.756973i
\(218\) 43.7441 + 69.6183i 0.200661 + 0.319350i
\(219\) 0 0
\(220\) −48.6264 48.6264i −0.221029 0.221029i
\(221\) 57.8066 + 513.047i 0.261568 + 2.32148i
\(222\) 0 0
\(223\) −193.421 242.542i −0.867359 1.08763i −0.995394 0.0958637i \(-0.969439\pi\)
0.128036 0.991770i \(-0.459133\pi\)
\(224\) 24.5106 217.538i 0.109422 0.971151i
\(225\) 0 0
\(226\) 18.3016 80.1848i 0.0809807 0.354800i
\(227\) −50.9304 223.141i −0.224363 0.982999i −0.954151 0.299326i \(-0.903238\pi\)
0.729788 0.683674i \(-0.239619\pi\)
\(228\) 0 0
\(229\) 17.7179 6.19978i 0.0773709 0.0270733i −0.291316 0.956627i \(-0.594093\pi\)
0.368687 + 0.929554i \(0.379807\pi\)
\(230\) 218.791 + 137.476i 0.951266 + 0.597720i
\(231\) 0 0
\(232\) −43.4466 44.0017i −0.187270 0.189662i
\(233\) −24.0314 −0.103139 −0.0515695 0.998669i \(-0.516422\pi\)
−0.0515695 + 0.998669i \(0.516422\pi\)
\(234\) 0 0
\(235\) −109.909 314.101i −0.467696 1.33660i
\(236\) 16.3490 + 33.9491i 0.0692756 + 0.143852i
\(237\) 0 0
\(238\) 375.408 + 85.6845i 1.57735 + 0.360019i
\(239\) 247.377 + 119.131i 1.03505 + 0.498454i 0.872689 0.488277i \(-0.162374\pi\)
0.162362 + 0.986731i \(0.448089\pi\)
\(240\) 0 0
\(241\) −230.544 + 183.853i −0.956615 + 0.762875i −0.971506 0.237014i \(-0.923831\pi\)
0.0148913 + 0.999889i \(0.495260\pi\)
\(242\) 98.6371 281.889i 0.407591 1.16483i
\(243\) 0 0
\(244\) −125.546 + 125.546i −0.514531 + 0.514531i
\(245\) −111.989 89.3085i −0.457099 0.364525i
\(246\) 0 0
\(247\) 35.1158 + 55.8864i 0.142169 + 0.226261i
\(248\) 77.3548 96.9998i 0.311914 0.391128i
\(249\) 0 0
\(250\) −5.72616 50.8210i −0.0229046 0.203284i
\(251\) −238.983 83.6236i −0.952122 0.333162i −0.190868 0.981616i \(-0.561130\pi\)
−0.761254 + 0.648454i \(0.775416\pi\)
\(252\) 0 0
\(253\) 4.89560 43.4497i 0.0193502 0.171738i
\(254\) −4.77205 + 9.90926i −0.0187876 + 0.0390128i
\(255\) 0 0
\(256\) −72.4934 317.614i −0.283177 1.24068i
\(257\) −177.185 + 85.3278i −0.689436 + 0.332015i −0.745588 0.666407i \(-0.767831\pi\)
0.0561518 + 0.998422i \(0.482117\pi\)
\(258\) 0 0
\(259\) −105.988 66.5967i −0.409220 0.257130i
\(260\) 420.735i 1.61821i
\(261\) 0 0
\(262\) −80.1535 −0.305929
\(263\) −244.782 + 389.569i −0.930731 + 1.48125i −0.0549801 + 0.998487i \(0.517510\pi\)
−0.875751 + 0.482763i \(0.839633\pi\)
\(264\) 0 0
\(265\) −39.3635 81.7392i −0.148542 0.308450i
\(266\) 47.9923 10.9539i 0.180422 0.0411802i
\(267\) 0 0
\(268\) 25.2387 + 12.1543i 0.0941743 + 0.0453519i
\(269\) −158.746 17.8864i −0.590136 0.0664923i −0.188153 0.982140i \(-0.560250\pi\)
−0.401982 + 0.915647i \(0.631679\pi\)
\(270\) 0 0
\(271\) −117.128 + 334.733i −0.432207 + 1.23518i 0.497690 + 0.867355i \(0.334182\pi\)
−0.929897 + 0.367821i \(0.880104\pi\)
\(272\) 498.223 56.1362i 1.83170 0.206383i
\(273\) 0 0
\(274\) 258.538 + 206.177i 0.943570 + 0.752472i
\(275\) 58.7501 36.9151i 0.213637 0.134237i
\(276\) 0 0
\(277\) 317.714 398.400i 1.14698 1.43827i 0.266721 0.963774i \(-0.414060\pi\)
0.880259 0.474494i \(-0.157369\pi\)
\(278\) 443.584 + 443.584i 1.59563 + 1.59563i
\(279\) 0 0
\(280\) 73.3930 + 25.6813i 0.262118 + 0.0917190i
\(281\) −53.3766 66.9321i −0.189952 0.238192i 0.677731 0.735310i \(-0.262963\pi\)
−0.867683 + 0.497117i \(0.834392\pi\)
\(282\) 0 0
\(283\) 44.3462 92.0859i 0.156700 0.325392i −0.807807 0.589447i \(-0.799346\pi\)
0.964508 + 0.264055i \(0.0850601\pi\)
\(284\) 44.8153 196.349i 0.157800 0.691369i
\(285\) 0 0
\(286\) −144.183 + 69.4347i −0.504135 + 0.242779i
\(287\) 206.026 72.0915i 0.717860 0.251190i
\(288\) 0 0
\(289\) 441.813i 1.52877i
\(290\) −454.773 + 281.743i −1.56818 + 0.971526i
\(291\) 0 0
\(292\) 106.078 168.823i 0.363282 0.578161i
\(293\) −24.9996 71.4447i −0.0853228 0.243838i 0.893315 0.449431i \(-0.148373\pi\)
−0.978638 + 0.205593i \(0.934088\pi\)
\(294\) 0 0
\(295\) −78.7541 + 17.9751i −0.266963 + 0.0609326i
\(296\) −49.0391 11.1929i −0.165673 0.0378137i
\(297\) 0 0
\(298\) 275.907 + 31.0873i 0.925864 + 0.104320i
\(299\) 209.151 166.792i 0.699501 0.557834i
\(300\) 0 0
\(301\) −176.837 + 19.9247i −0.587498 + 0.0661951i
\(302\) −33.4398 + 33.4398i −0.110728 + 0.110728i
\(303\) 0 0
\(304\) 54.2716 34.1011i 0.178525 0.112175i
\(305\) −202.505 322.285i −0.663951 1.05667i
\(306\) 0 0
\(307\) −36.5877 36.5877i −0.119178 0.119178i 0.645002 0.764181i \(-0.276856\pi\)
−0.764181 + 0.645002i \(0.776856\pi\)
\(308\) 5.94512 + 52.7644i 0.0193024 + 0.171313i
\(309\) 0 0
\(310\) −669.230 839.187i −2.15881 2.70706i
\(311\) −35.9242 + 318.836i −0.115512 + 1.02520i 0.793541 + 0.608516i \(0.208235\pi\)
−0.909053 + 0.416680i \(0.863193\pi\)
\(312\) 0 0
\(313\) −32.4462 + 142.156i −0.103662 + 0.454173i 0.896281 + 0.443487i \(0.146259\pi\)
−0.999943 + 0.0106861i \(0.996598\pi\)
\(314\) 46.8806 + 205.397i 0.149301 + 0.654131i
\(315\) 0 0
\(316\) −136.618 + 47.8045i −0.432334 + 0.151280i
\(317\) 73.0249 + 45.8846i 0.230362 + 0.144746i 0.642268 0.766480i \(-0.277994\pi\)
−0.411905 + 0.911227i \(0.635137\pi\)
\(318\) 0 0
\(319\) 76.3429 + 48.6480i 0.239319 + 0.152502i
\(320\) −251.236 −0.785114
\(321\) 0 0
\(322\) −65.8964 188.321i −0.204647 0.584848i
\(323\) 40.5366 + 84.1752i 0.125500 + 0.260604i
\(324\) 0 0
\(325\) 413.866 + 94.4622i 1.27343 + 0.290653i
\(326\) −392.703 189.116i −1.20461 0.580110i
\(327\) 0 0
\(328\) 68.5760 54.6875i 0.209073 0.166730i
\(329\) −84.8642 + 242.528i −0.257946 + 0.737167i
\(330\) 0 0
\(331\) −49.8314 + 49.8314i −0.150548 + 0.150548i −0.778363 0.627815i \(-0.783950\pi\)
0.627815 + 0.778363i \(0.283950\pi\)
\(332\) −343.835 274.199i −1.03565 0.825901i
\(333\) 0 0
\(334\) −235.851 375.354i −0.706140 1.12381i
\(335\) −37.4428 + 46.9518i −0.111770 + 0.140155i
\(336\) 0 0
\(337\) −34.9489 310.180i −0.103706 0.920414i −0.932576 0.360974i \(-0.882444\pi\)
0.828870 0.559441i \(-0.188984\pi\)
\(338\) −495.954 173.542i −1.46732 0.513438i
\(339\) 0 0
\(340\) 66.6804 591.805i 0.196119 1.74060i
\(341\) −78.8056 + 163.642i −0.231102 + 0.479887i
\(342\) 0 0
\(343\) 82.4682 + 361.317i 0.240432 + 1.05340i
\(344\) −64.4284 + 31.0271i −0.187292 + 0.0901950i
\(345\) 0 0
\(346\) 94.7234 + 59.5187i 0.273767 + 0.172019i
\(347\) 266.679i 0.768528i −0.923223 0.384264i \(-0.874455\pi\)
0.923223 0.384264i \(-0.125545\pi\)
\(348\) 0 0
\(349\) −132.806 −0.380532 −0.190266 0.981733i \(-0.560935\pi\)
−0.190266 + 0.981733i \(0.560935\pi\)
\(350\) 168.445 268.079i 0.481273 0.765941i
\(351\) 0 0
\(352\) 55.8765 + 116.029i 0.158740 + 0.329627i
\(353\) 325.525 74.2990i 0.922168 0.210479i 0.265022 0.964242i \(-0.414621\pi\)
0.657146 + 0.753763i \(0.271764\pi\)
\(354\) 0 0
\(355\) 388.998 + 187.331i 1.09577 + 0.527694i
\(356\) 232.103 + 26.1517i 0.651975 + 0.0734599i
\(357\) 0 0
\(358\) −85.1953 + 243.474i −0.237976 + 0.680095i
\(359\) −417.651 + 47.0579i −1.16337 + 0.131081i −0.672464 0.740130i \(-0.734764\pi\)
−0.490909 + 0.871211i \(0.663335\pi\)
\(360\) 0 0
\(361\) −272.903 217.633i −0.755964 0.602861i
\(362\) 357.867 224.863i 0.988583 0.621168i
\(363\) 0 0
\(364\) −202.549 + 253.989i −0.556454 + 0.697771i
\(365\) 302.243 + 302.243i 0.828063 + 0.828063i
\(366\) 0 0
\(367\) −658.212 230.319i −1.79349 0.627571i −0.999815 0.0192348i \(-0.993877\pi\)
−0.793680 0.608336i \(-0.791837\pi\)
\(368\) −161.973 203.107i −0.440143 0.551922i
\(369\) 0 0
\(370\) −188.813 + 392.074i −0.510305 + 1.05966i
\(371\) −15.5878 + 68.2946i −0.0420156 + 0.184082i
\(372\) 0 0
\(373\) −0.614583 + 0.295968i −0.00164768 + 0.000793479i −0.434707 0.900572i \(-0.643148\pi\)
0.433060 + 0.901365i \(0.357434\pi\)
\(374\) −213.812 + 74.8159i −0.571689 + 0.200042i
\(375\) 0 0
\(376\) 103.252i 0.274607i
\(377\) 119.813 + 540.735i 0.317807 + 1.43431i
\(378\) 0 0
\(379\) 56.7788 90.3630i 0.149812 0.238425i −0.763384 0.645945i \(-0.776464\pi\)
0.913196 + 0.407520i \(0.133606\pi\)
\(380\) −25.1459 71.8628i −0.0661733 0.189113i
\(381\) 0 0
\(382\) 552.446 126.092i 1.44619 0.330085i
\(383\) 427.991 + 97.6862i 1.11747 + 0.255055i 0.741087 0.671409i \(-0.234310\pi\)
0.376383 + 0.926464i \(0.377168\pi\)
\(384\) 0 0
\(385\) −113.116 12.7451i −0.293807 0.0331041i
\(386\) 16.6101 13.2461i 0.0430313 0.0343163i
\(387\) 0 0
\(388\) −163.543 + 18.4269i −0.421504 + 0.0474920i
\(389\) 139.368 139.368i 0.358272 0.358272i −0.504904 0.863176i \(-0.668472\pi\)
0.863176 + 0.504904i \(0.168472\pi\)
\(390\) 0 0
\(391\) 320.626 201.462i 0.820014 0.515249i
\(392\) 23.6456 + 37.6317i 0.0603204 + 0.0959993i
\(393\) 0 0
\(394\) 710.867 + 710.867i 1.80423 + 1.80423i
\(395\) −34.7416 308.340i −0.0879535 0.780609i
\(396\) 0 0
\(397\) 91.8303 + 115.152i 0.231311 + 0.290054i 0.883918 0.467642i \(-0.154896\pi\)
−0.652607 + 0.757696i \(0.726325\pi\)
\(398\) 106.947 949.181i 0.268711 2.38488i
\(399\) 0 0
\(400\) 91.7327 401.907i 0.229332 1.00477i
\(401\) 62.6107 + 274.315i 0.156136 + 0.684078i 0.991027 + 0.133662i \(0.0426738\pi\)
−0.834891 + 0.550416i \(0.814469\pi\)
\(402\) 0 0
\(403\) −1048.87 + 367.017i −2.60266 + 0.910711i
\(404\) 35.0439 + 22.0196i 0.0867424 + 0.0545039i
\(405\) 0 0
\(406\) 410.173 + 48.8538i 1.01028 + 0.120330i
\(407\) 73.6370 0.180926
\(408\) 0 0
\(409\) −142.774 408.025i −0.349081 0.997615i −0.975856 0.218415i \(-0.929911\pi\)
0.626775 0.779200i \(-0.284374\pi\)
\(410\) −329.246 683.686i −0.803038 1.66753i
\(411\) 0 0
\(412\) 108.270 + 24.7120i 0.262792 + 0.0599805i
\(413\) 56.1958 + 27.0625i 0.136067 + 0.0655265i
\(414\) 0 0
\(415\) 737.109 587.825i 1.77617 1.41645i
\(416\) −260.230 + 743.695i −0.625553 + 1.78773i
\(417\) 0 0
\(418\) −20.4770 + 20.4770i −0.0489879 + 0.0489879i
\(419\) −248.060 197.821i −0.592028 0.472126i 0.281060 0.959690i \(-0.409314\pi\)
−0.873087 + 0.487564i \(0.837886\pi\)
\(420\) 0 0
\(421\) 284.084 + 452.117i 0.674783 + 1.07391i 0.992083 + 0.125586i \(0.0400811\pi\)
−0.317299 + 0.948325i \(0.602776\pi\)
\(422\) −389.342 + 488.219i −0.922610 + 1.15692i
\(423\) 0 0
\(424\) 3.15173 + 27.9724i 0.00743333 + 0.0659727i
\(425\) 567.172 + 198.462i 1.33452 + 0.466970i
\(426\) 0 0
\(427\) −32.9057 + 292.046i −0.0770625 + 0.683949i
\(428\) −195.382 + 405.716i −0.456501 + 0.947934i
\(429\) 0 0
\(430\) 137.666 + 603.154i 0.320153 + 1.40268i
\(431\) −377.110 + 181.607i −0.874966 + 0.421361i −0.816783 0.576945i \(-0.804245\pi\)
−0.0581825 + 0.998306i \(0.518531\pi\)
\(432\) 0 0
\(433\) 385.889 + 242.470i 0.891198 + 0.559977i 0.897998 0.440000i \(-0.145021\pi\)
−0.00679946 + 0.999977i \(0.502164\pi\)
\(434\) 828.779i 1.90963i
\(435\) 0 0
\(436\) −98.1886 −0.225203
\(437\) 25.7550 40.9889i 0.0589359 0.0937960i
\(438\) 0 0
\(439\) −74.7895 155.302i −0.170363 0.353763i 0.798254 0.602321i \(-0.205757\pi\)
−0.968617 + 0.248558i \(0.920043\pi\)
\(440\) −44.5954 + 10.1786i −0.101353 + 0.0231332i
\(441\) 0 0
\(442\) −1248.66 601.322i −2.82502 1.36046i
\(443\) 462.876 + 52.1536i 1.04487 + 0.117728i 0.617676 0.786433i \(-0.288074\pi\)
0.427191 + 0.904161i \(0.359503\pi\)
\(444\) 0 0
\(445\) −165.380 + 472.629i −0.371640 + 1.06209i
\(446\) 827.507 93.2376i 1.85540 0.209053i
\(447\) 0 0
\(448\) 151.666 + 120.950i 0.338541 + 0.269977i
\(449\) 74.4790 46.7982i 0.165877 0.104228i −0.446535 0.894766i \(-0.647342\pi\)
0.612412 + 0.790539i \(0.290199\pi\)
\(450\) 0 0
\(451\) −80.0597 + 100.392i −0.177516 + 0.222598i
\(452\) 69.4519 + 69.4519i 0.153655 + 0.153655i
\(453\) 0 0
\(454\) 579.911 + 202.920i 1.27734 + 0.446960i
\(455\) −434.223 544.498i −0.954335 1.19670i
\(456\) 0 0
\(457\) −152.739 + 317.166i −0.334221 + 0.694018i −0.998573 0.0534021i \(-0.982993\pi\)
0.664352 + 0.747420i \(0.268708\pi\)
\(458\) −11.2125 + 49.1252i −0.0244814 + 0.107260i
\(459\) 0 0
\(460\) −278.021 + 133.888i −0.604393 + 0.291060i
\(461\) 265.537 92.9154i 0.576002 0.201552i −0.0265280 0.999648i \(-0.508445\pi\)
0.602530 + 0.798096i \(0.294159\pi\)
\(462\) 0 0
\(463\) 683.990i 1.47730i −0.674088 0.738651i \(-0.735463\pi\)
0.674088 0.738651i \(-0.264537\pi\)
\(464\) 525.110 116.351i 1.13170 0.250757i
\(465\) 0 0
\(466\) 34.3205 54.6207i 0.0736491 0.117212i
\(467\) 128.753 + 367.954i 0.275702 + 0.787911i 0.995589 + 0.0938199i \(0.0299078\pi\)
−0.719887 + 0.694091i \(0.755807\pi\)
\(468\) 0 0
\(469\) 45.2069 10.3182i 0.0963900 0.0220004i
\(470\) 870.883 + 198.773i 1.85294 + 0.422922i
\(471\) 0 0
\(472\) 24.9063 + 2.80627i 0.0527677 + 0.00594549i
\(473\) 81.8477 65.2714i 0.173040 0.137994i
\(474\) 0 0
\(475\) 76.3352 8.60092i 0.160706 0.0181072i
\(476\) −325.159 + 325.159i −0.683108 + 0.683108i
\(477\) 0 0
\(478\) −624.063 + 392.125i −1.30557 + 0.820345i
\(479\) −188.880 300.600i −0.394321 0.627558i 0.589278 0.807931i \(-0.299412\pi\)
−0.983598 + 0.180373i \(0.942270\pi\)
\(480\) 0 0
\(481\) 318.568 + 318.568i 0.662303 + 0.662303i
\(482\) −88.6253 786.572i −0.183870 1.63189i
\(483\) 0 0
\(484\) 222.366 + 278.838i 0.459434 + 0.576112i
\(485\) 39.5034 350.602i 0.0814503 0.722891i
\(486\) 0 0
\(487\) 122.134 535.104i 0.250788 1.09878i −0.679998 0.733214i \(-0.738020\pi\)
0.930787 0.365562i \(-0.119123\pi\)
\(488\) 26.2795 + 115.138i 0.0538515 + 0.235939i
\(489\) 0 0
\(490\) 362.926 126.993i 0.740666 0.259170i
\(491\) 14.6268 + 9.19065i 0.0297899 + 0.0187182i 0.546845 0.837234i \(-0.315829\pi\)
−0.517055 + 0.855952i \(0.672972\pi\)
\(492\) 0 0
\(493\) 82.8307 + 779.585i 0.168014 + 1.58131i
\(494\) −177.174 −0.358653
\(495\) 0 0
\(496\) 356.411 + 1018.57i 0.718571 + 2.05356i
\(497\) −144.645 300.359i −0.291036 0.604343i
\(498\) 0 0
\(499\) −274.548 62.6637i −0.550196 0.125579i −0.0616193 0.998100i \(-0.519626\pi\)
−0.488576 + 0.872521i \(0.662484\pi\)
\(500\) 55.0266 + 26.4994i 0.110053 + 0.0529988i
\(501\) 0 0
\(502\) 531.371 423.754i 1.05851 0.844132i
\(503\) 13.3525 38.1593i 0.0265457 0.0758634i −0.929848 0.367944i \(-0.880062\pi\)
0.956394 + 0.292081i \(0.0943475\pi\)
\(504\) 0 0
\(505\) −62.7390 + 62.7390i −0.124236 + 0.124236i
\(506\) 91.7647 + 73.1799i 0.181353 + 0.144624i
\(507\) 0 0
\(508\) −6.98794 11.1212i −0.0137558 0.0218922i
\(509\) 53.4784 67.0598i 0.105066 0.131748i −0.726519 0.687147i \(-0.758863\pi\)
0.831584 + 0.555399i \(0.187434\pi\)
\(510\) 0 0
\(511\) −36.9525 327.963i −0.0723142 0.641806i
\(512\) 572.897 + 200.465i 1.11894 + 0.391534i
\(513\) 0 0
\(514\) 59.1064 524.584i 0.114993 1.02059i
\(515\) −103.298 + 214.500i −0.200578 + 0.416505i
\(516\) 0 0
\(517\) −33.6354 147.366i −0.0650587 0.285041i
\(518\) 302.734 145.789i 0.584429 0.281446i
\(519\) 0 0
\(520\) −236.963 148.894i −0.455698 0.286334i
\(521\) 299.573i 0.574997i 0.957781 + 0.287498i \(0.0928236\pi\)
−0.957781 + 0.287498i \(0.907176\pi\)
\(522\) 0 0
\(523\) −691.011 −1.32124 −0.660622 0.750718i \(-0.729708\pi\)
−0.660622 + 0.750718i \(0.729708\pi\)
\(524\) 50.9261 81.0484i 0.0971872 0.154673i
\(525\) 0 0
\(526\) −535.861 1112.73i −1.01875 2.11545i
\(527\) −1533.51 + 350.014i −2.90989 + 0.664163i
\(528\) 0 0
\(529\) 299.840 + 144.395i 0.566805 + 0.272959i
\(530\) 242.001 + 27.2670i 0.456606 + 0.0514472i
\(531\) 0 0
\(532\) −19.4160 + 55.4877i −0.0364962 + 0.104300i
\(533\) −780.668 + 87.9601i −1.46467 + 0.165028i
\(534\) 0 0
\(535\) −754.757 601.898i −1.41076 1.12504i
\(536\) 15.7772 9.91347i 0.0294351 0.0184953i
\(537\) 0 0
\(538\) 267.368 335.269i 0.496967 0.623176i
\(539\) −46.0069 46.0069i −0.0853561 0.0853561i
\(540\) 0 0
\(541\) 163.211 + 57.1098i 0.301683 + 0.105563i 0.476876 0.878971i \(-0.341769\pi\)
−0.175193 + 0.984534i \(0.556055\pi\)
\(542\) −593.534 744.268i −1.09508 1.37319i
\(543\) 0 0
\(544\) −483.904 + 1004.84i −0.889530 + 1.84713i
\(545\) 46.8396 205.218i 0.0859443 0.376547i
\(546\) 0 0
\(547\) −608.085 + 292.838i −1.11167 + 0.535353i −0.897310 0.441401i \(-0.854482\pi\)
−0.214362 + 0.976754i \(0.568767\pi\)
\(548\) −372.743 + 130.428i −0.680188 + 0.238008i
\(549\) 0 0
\(550\) 186.253i 0.338642i
\(551\) 52.7823 + 85.1983i 0.0957937 + 0.154625i
\(552\) 0 0
\(553\) −127.468 + 202.864i −0.230502 + 0.366843i
\(554\) 451.777 + 1291.10i 0.815482 + 2.33051i
\(555\) 0 0
\(556\) −730.370 + 166.702i −1.31362 + 0.299824i
\(557\) 430.440 + 98.2451i 0.772782 + 0.176383i 0.590690 0.806899i \(-0.298856\pi\)
0.182093 + 0.983281i \(0.441713\pi\)
\(558\) 0 0
\(559\) 636.466 + 71.7124i 1.13858 + 0.128287i
\(560\) −528.764 + 421.676i −0.944222 + 0.752992i
\(561\) 0 0
\(562\) 228.359 25.7299i 0.406333 0.0457827i
\(563\) −505.628 + 505.628i −0.898096 + 0.898096i −0.995268 0.0971715i \(-0.969020\pi\)
0.0971715 + 0.995268i \(0.469020\pi\)
\(564\) 0 0
\(565\) −178.288 + 112.026i −0.315554 + 0.198276i
\(566\) 145.968 + 232.307i 0.257894 + 0.410436i
\(567\) 0 0
\(568\) −94.7263 94.7263i −0.166772 0.166772i
\(569\) −23.0557 204.625i −0.0405197 0.359622i −0.997568 0.0696949i \(-0.977797\pi\)
0.957049 0.289927i \(-0.0936311\pi\)
\(570\) 0 0
\(571\) 699.676 + 877.367i 1.22535 + 1.53654i 0.757655 + 0.652656i \(0.226345\pi\)
0.467698 + 0.883888i \(0.345083\pi\)
\(572\) 21.3975 189.908i 0.0374082 0.332007i
\(573\) 0 0
\(574\) −130.380 + 571.232i −0.227143 + 0.995177i
\(575\) −69.2815 303.542i −0.120490 0.527899i
\(576\) 0 0
\(577\) 648.576 226.947i 1.12405 0.393322i 0.296678 0.954978i \(-0.404121\pi\)
0.827371 + 0.561656i \(0.189836\pi\)
\(578\) −1004.19 630.977i −1.73736 1.09166i
\(579\) 0 0
\(580\) 4.05499 638.857i 0.00699136 1.10148i
\(581\) −727.967 −1.25296
\(582\) 0 0
\(583\) −13.6106 38.8968i −0.0233457 0.0667183i
\(584\) −57.5431 119.489i −0.0985327 0.204605i
\(585\) 0 0
\(586\) 198.089 + 45.2126i 0.338036 + 0.0771545i
\(587\) 95.7428 + 46.1073i 0.163105 + 0.0785474i 0.513655 0.857997i \(-0.328291\pi\)
−0.350550 + 0.936544i \(0.614005\pi\)
\(588\) 0 0
\(589\) −157.215 + 125.375i −0.266919 + 0.212861i
\(590\) 71.6174 204.671i 0.121385 0.346899i
\(591\) 0 0
\(592\) 309.363 309.363i 0.522572 0.522572i
\(593\) 338.480 + 269.929i 0.570793 + 0.455192i 0.865861 0.500284i \(-0.166771\pi\)
−0.295069 + 0.955476i \(0.595343\pi\)
\(594\) 0 0
\(595\) −524.482 834.708i −0.881482 1.40287i
\(596\) −206.734 + 259.236i −0.346869 + 0.434960i
\(597\) 0 0
\(598\) 80.4014 + 713.582i 0.134450 + 1.19328i
\(599\) 300.963 + 105.311i 0.502442 + 0.175812i 0.569587 0.821931i \(-0.307103\pi\)
−0.0671447 + 0.997743i \(0.521389\pi\)
\(600\) 0 0
\(601\) 90.6856 804.857i 0.150891 1.33920i −0.658791 0.752326i \(-0.728932\pi\)
0.809682 0.586869i \(-0.199640\pi\)
\(602\) 207.263 430.386i 0.344291 0.714927i
\(603\) 0 0
\(604\) −12.5669 55.0593i −0.0208062 0.0911577i
\(605\) −688.860 + 331.737i −1.13861 + 0.548326i
\(606\) 0 0
\(607\) 114.515 + 71.9543i 0.188657 + 0.118541i 0.623049 0.782183i \(-0.285894\pi\)
−0.434392 + 0.900724i \(0.643037\pi\)
\(608\) 142.578i 0.234504i
\(609\) 0 0
\(610\) 1021.73 1.67496
\(611\) 492.021 783.047i 0.805272 1.28158i
\(612\) 0 0
\(613\) 335.706 + 697.102i 0.547645 + 1.13720i 0.972708 + 0.232033i \(0.0745377\pi\)
−0.425063 + 0.905164i \(0.639748\pi\)
\(614\) 135.413 30.9071i 0.220542 0.0503372i
\(615\) 0 0
\(616\) 31.8215 + 15.3244i 0.0516583 + 0.0248773i
\(617\) 227.497 + 25.6327i 0.368714 + 0.0415441i 0.294378 0.955689i \(-0.404888\pi\)
0.0743364 + 0.997233i \(0.476316\pi\)
\(618\) 0 0
\(619\) −55.4200 + 158.381i −0.0895314 + 0.255866i −0.979939 0.199298i \(-0.936134\pi\)
0.890407 + 0.455164i \(0.150419\pi\)
\(620\) 1273.76 143.518i 2.05445 0.231480i
\(621\) 0 0
\(622\) −673.375 536.998i −1.08260 0.863341i
\(623\) 327.368 205.699i 0.525471 0.330175i
\(624\) 0 0
\(625\) −428.102 + 536.823i −0.684964 + 0.858917i
\(626\) −276.767 276.767i −0.442120 0.442120i
\(627\) 0 0
\(628\) −237.476 83.0965i −0.378147 0.132319i
\(629\) 397.609 + 498.586i 0.632129 + 0.792664i
\(630\) 0 0
\(631\) 366.946 761.972i 0.581531 1.20756i −0.377959 0.925822i \(-0.623374\pi\)
0.959491 0.281740i \(-0.0909116\pi\)
\(632\) −21.4234 + 93.8622i −0.0338979 + 0.148516i
\(633\) 0 0
\(634\) −208.581 + 100.447i −0.328993 + 0.158435i
\(635\) 26.5773 9.29981i 0.0418541 0.0146454i
\(636\) 0 0
\(637\) 398.070i 0.624913i
\(638\) −219.601 + 104.042i −0.344202 + 0.163076i
\(639\) 0 0
\(640\) −244.559 + 389.213i −0.382123 + 0.608146i
\(641\) −127.709 364.971i −0.199234 0.569377i 0.800310 0.599587i \(-0.204668\pi\)
−0.999544 + 0.0302093i \(0.990383\pi\)
\(642\) 0 0
\(643\) 190.043 43.3761i 0.295557 0.0674589i −0.0721713 0.997392i \(-0.522993\pi\)
0.367728 + 0.929933i \(0.380136\pi\)
\(644\) 232.291 + 53.0190i 0.360701 + 0.0823277i
\(645\) 0 0
\(646\) −249.213 28.0796i −0.385779 0.0434669i
\(647\) 420.130 335.042i 0.649350 0.517839i −0.242511 0.970149i \(-0.577971\pi\)
0.891861 + 0.452309i \(0.149400\pi\)
\(648\) 0 0
\(649\) −36.4616 + 4.10824i −0.0561812 + 0.00633010i
\(650\) −805.766 + 805.766i −1.23964 + 1.23964i
\(651\) 0 0
\(652\) 440.734 276.931i 0.675972 0.424742i
\(653\) −346.424 551.330i −0.530511 0.844304i 0.468726 0.883343i \(-0.344713\pi\)
−0.999238 + 0.0390396i \(0.987570\pi\)
\(654\) 0 0
\(655\) 145.101 + 145.101i 0.221528 + 0.221528i
\(656\) 85.4185 + 758.110i 0.130211 + 1.15566i
\(657\) 0 0
\(658\) −430.041 539.254i −0.653557 0.819535i
\(659\) 21.4040 189.966i 0.0324795 0.288264i −0.966964 0.254912i \(-0.917953\pi\)
0.999444 0.0333513i \(-0.0106180\pi\)
\(660\) 0 0
\(661\) 220.074 964.209i 0.332942 1.45871i −0.480463 0.877015i \(-0.659532\pi\)
0.813405 0.581698i \(-0.197611\pi\)
\(662\) −42.0946 184.428i −0.0635869 0.278593i
\(663\) 0 0
\(664\) −276.112 + 96.6158i −0.415832 + 0.145506i
\(665\) −106.709 67.0499i −0.160465 0.100827i
\(666\) 0 0
\(667\) 319.189 251.247i 0.478544 0.376682i
\(668\) 529.394 0.792506
\(669\) 0 0
\(670\) −53.2423 152.158i −0.0794661 0.227101i
\(671\) −75.0146 155.769i −0.111795 0.232145i
\(672\) 0 0
\(673\) 1093.28 + 249.533i 1.62448 + 0.370777i 0.935312 0.353823i \(-0.115118\pi\)
0.689169 + 0.724600i \(0.257976\pi\)
\(674\) 754.917 + 363.549i 1.12005 + 0.539390i
\(675\) 0 0
\(676\) 490.587 391.230i 0.725721 0.578743i
\(677\) 266.705 762.199i 0.393951 1.12585i −0.560673 0.828037i \(-0.689458\pi\)
0.954625 0.297811i \(-0.0962566\pi\)
\(678\) 0 0
\(679\) −192.634 + 192.634i −0.283702 + 0.283702i
\(680\) −309.714 246.989i −0.455462 0.363219i
\(681\) 0 0
\(682\) −259.393 412.822i −0.380342 0.605310i
\(683\) −172.817 + 216.706i −0.253027 + 0.317285i −0.892080 0.451877i \(-0.850755\pi\)
0.639054 + 0.769162i \(0.279326\pi\)
\(684\) 0 0
\(685\) −94.7880 841.266i −0.138377 1.22813i
\(686\) −939.011 328.574i −1.36882 0.478971i
\(687\) 0 0
\(688\) 69.6403 618.075i 0.101221 0.898364i
\(689\) 109.393 227.157i 0.158771 0.329691i
\(690\) 0 0
\(691\) −129.908 569.165i −0.188000 0.823683i −0.977669 0.210150i \(-0.932605\pi\)
0.789669 0.613533i \(-0.210252\pi\)
\(692\) −120.366 + 57.9654i −0.173940 + 0.0837650i
\(693\) 0 0
\(694\) 606.132 + 380.858i 0.873390 + 0.548787i
\(695\) 1606.02i 2.31083i
\(696\) 0 0
\(697\) −1112.03 −1.59545
\(698\) 189.667 301.853i 0.271729 0.432454i
\(699\) 0 0
\(700\) 164.049 + 340.652i 0.234356 + 0.486646i
\(701\) 1089.11 248.581i 1.55365 0.354610i 0.642366 0.766398i \(-0.277953\pi\)
0.911280 + 0.411788i \(0.135096\pi\)
\(702\) 0 0
\(703\) 73.4521 + 35.3727i 0.104484 + 0.0503167i
\(704\) −113.401 12.7773i −0.161081 0.0181495i
\(705\) 0 0
\(706\) −296.026 + 845.994i −0.419300 + 1.19829i
\(707\) 68.0779 7.67054i 0.0962913 0.0108494i
\(708\) 0 0
\(709\) −36.5193 29.1232i −0.0515082 0.0410764i 0.597397 0.801945i \(-0.296202\pi\)
−0.648906 + 0.760869i \(0.724773\pi\)
\(710\) −981.331 + 616.611i −1.38216 + 0.868467i
\(711\) 0 0
\(712\) 96.8679 121.468i 0.136050 0.170602i
\(713\) 576.300 + 576.300i 0.808275 + 0.808275i
\(714\) 0 0
\(715\) 386.708 + 135.315i 0.540850 + 0.189252i
\(716\) −192.063 240.839i −0.268244 0.336368i
\(717\) 0 0
\(718\) 489.511 1016.48i 0.681771 1.41571i
\(719\) −47.5410 + 208.291i −0.0661210 + 0.289695i −0.997168 0.0752038i \(-0.976039\pi\)
0.931047 + 0.364899i \(0.118896\pi\)
\(720\) 0 0
\(721\) 165.623 79.7599i 0.229713 0.110624i
\(722\) 884.403 309.466i 1.22494 0.428623i
\(723\) 0 0
\(724\) 504.730i 0.697141i
\(725\) 627.517 + 147.423i 0.865541 + 0.203342i
\(726\) 0 0
\(727\) 312.925 498.018i 0.430434 0.685031i −0.559138 0.829075i \(-0.688868\pi\)
0.989571 + 0.144044i \(0.0460105\pi\)
\(728\) 71.3695 + 203.962i 0.0980351 + 0.280168i
\(729\) 0 0
\(730\) −1118.61 + 255.316i −1.53235 + 0.349748i
\(731\) 883.886 + 201.741i 1.20915 + 0.275980i
\(732\) 0 0
\(733\) −208.812 23.5275i −0.284873 0.0320975i −0.0316283 0.999500i \(-0.510069\pi\)
−0.253245 + 0.967402i \(0.581498\pi\)
\(734\) 1463.52 1167.12i 1.99389 1.59008i
\(735\) 0 0
\(736\) 574.244 64.7017i 0.780222 0.0879100i
\(737\) −19.2885 + 19.2885i −0.0261717 + 0.0261717i
\(738\) 0 0
\(739\) 291.025 182.863i 0.393810 0.247447i −0.320541 0.947234i \(-0.603865\pi\)
0.714351 + 0.699788i \(0.246722\pi\)
\(740\) −276.488 440.028i −0.373632 0.594632i
\(741\) 0 0
\(742\) −132.964 132.964i −0.179197 0.179197i
\(743\) 26.4958 + 235.157i 0.0356605 + 0.316496i 0.998861 + 0.0477124i \(0.0151931\pi\)
−0.963201 + 0.268784i \(0.913378\pi\)
\(744\) 0 0
\(745\) −443.194 555.747i −0.594891 0.745970i
\(746\) 0.205016 1.81957i 0.000274820 0.00243910i
\(747\) 0 0
\(748\) 60.1954 263.733i 0.0804752 0.352585i
\(749\) 165.866 + 726.707i 0.221450 + 0.970236i
\(750\) 0 0
\(751\) 550.749 192.716i 0.733355 0.256612i 0.0623390 0.998055i \(-0.480144\pi\)
0.671016 + 0.741443i \(0.265858\pi\)
\(752\) −760.421 477.804i −1.01120 0.635378i
\(753\) 0 0
\(754\) −1400.14 499.928i −1.85695 0.663035i
\(755\) 121.071 0.160359
\(756\) 0 0
\(757\) 363.807 + 1039.70i 0.480590 + 1.37345i 0.887849 + 0.460135i \(0.152199\pi\)
−0.407259 + 0.913313i \(0.633515\pi\)
\(758\) 124.296 + 258.104i 0.163979 + 0.340507i
\(759\) 0 0
\(760\) −49.3729 11.2690i −0.0649643 0.0148277i
\(761\) −191.779 92.3558i −0.252009 0.121361i 0.303615 0.952795i \(-0.401806\pi\)
−0.555624 + 0.831434i \(0.687521\pi\)
\(762\) 0 0
\(763\) −127.072 + 101.336i −0.166542 + 0.132813i
\(764\) −223.501 + 638.728i −0.292540 + 0.836031i
\(765\) 0 0
\(766\) −833.267 + 833.267i −1.08782 + 1.08782i
\(767\) −175.513 139.967i −0.228830 0.182486i
\(768\) 0 0
\(769\) −122.480 194.927i −0.159272 0.253481i 0.757549 0.652779i \(-0.226397\pi\)
−0.916821 + 0.399298i \(0.869254\pi\)
\(770\) 190.515 238.898i 0.247422 0.310257i
\(771\) 0 0
\(772\) 2.84066 + 25.2115i 0.00367961 + 0.0326574i
\(773\) −889.330 311.190i −1.15049 0.402575i −0.313392 0.949624i \(-0.601465\pi\)
−0.837100 + 0.547049i \(0.815751\pi\)
\(774\) 0 0
\(775\) −144.805 + 1285.18i −0.186846 + 1.65830i
\(776\) −47.4981 + 98.6308i −0.0612089 + 0.127102i
\(777\) 0 0
\(778\) 117.729 + 515.806i 0.151323 + 0.662989i
\(779\) −128.083 + 61.6817i −0.164420 + 0.0791806i
\(780\) 0 0
\(781\) 166.056 + 104.340i 0.212619 + 0.133598i
\(782\) 1016.47i 1.29983i
\(783\) 0 0
\(784\) −386.567 −0.493070
\(785\) 286.960 456.694i 0.365554 0.581776i
\(786\) 0 0
\(787\) 493.293 + 1024.33i 0.626801 + 1.30157i 0.936479 + 0.350725i