Properties

Label 1050.2.o.k.949.2
Level $1050$
Weight $2$
Character 1050.949
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.949
Dual form 1050.2.o.k.499.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} +(0.866025 - 0.500000i) q^{12} -1.00000i q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(0.500000 + 0.866025i) q^{19} +(0.500000 - 2.59808i) q^{21} -4.00000i q^{22} +(1.73205 - 1.00000i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{26} +1.00000i q^{27} +(-2.59808 - 0.500000i) q^{28} -4.00000 q^{29} +(-0.866025 - 0.500000i) q^{32} +(3.46410 - 2.00000i) q^{33} -2.00000 q^{34} +1.00000 q^{36} +(2.59808 - 1.50000i) q^{37} +(0.866025 + 0.500000i) q^{38} +(0.500000 - 0.866025i) q^{39} +12.0000 q^{41} +(-0.866025 - 2.50000i) q^{42} -8.00000i q^{43} +(-2.00000 - 3.46410i) q^{44} +(1.00000 - 1.73205i) q^{46} +(-5.19615 + 3.00000i) q^{47} -1.00000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(1.73205 + 1.00000i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.50000 + 0.866025i) q^{56} +1.00000i q^{57} +(-3.46410 + 2.00000i) q^{58} +(3.00000 - 5.19615i) q^{59} +(6.50000 + 11.2583i) q^{61} +(1.73205 - 2.00000i) q^{63} -1.00000 q^{64} +(2.00000 - 3.46410i) q^{66} +(-2.59808 - 1.50000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +2.00000 q^{69} +16.0000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-9.52628 - 5.50000i) q^{73} +(1.50000 - 2.59808i) q^{74} +1.00000 q^{76} +(-10.3923 - 2.00000i) q^{77} -1.00000i q^{78} +(6.50000 + 11.2583i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(10.3923 - 6.00000i) q^{82} +6.00000i q^{83} +(-2.00000 - 1.73205i) q^{84} +(-4.00000 - 6.92820i) q^{86} +(-3.46410 - 2.00000i) q^{87} +(-3.46410 - 2.00000i) q^{88} +(-1.00000 - 1.73205i) q^{89} +(-2.50000 + 0.866025i) q^{91} -2.00000i q^{92} +(-3.00000 + 5.19615i) q^{94} +(-0.500000 - 0.866025i) q^{96} +17.0000i q^{97} +(-2.59808 + 6.50000i) q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} + 4q^{6} + 2q^{9} + 8q^{11} - 8q^{14} - 2q^{16} + 2q^{19} + 2q^{21} + 2q^{24} - 2q^{26} - 16q^{29} - 8q^{34} + 4q^{36} + 2q^{39} + 48q^{41} - 8q^{44} + 4q^{46} - 22q^{49} - 4q^{51} + 2q^{54} - 10q^{56} + 12q^{59} + 26q^{61} - 4q^{64} + 8q^{66} + 8q^{69} + 64q^{71} + 6q^{74} + 4q^{76} + 26q^{79} - 2q^{81} - 8q^{84} - 16q^{86} - 4q^{89} - 10q^{91} - 12q^{94} - 2q^{96} + 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) −0.866025 2.50000i −0.327327 0.944911i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 2.00000 3.46410i 0.603023 1.04447i −0.389338 0.921095i \(-0.627296\pi\)
0.992361 0.123371i \(-0.0393705\pi\)
\(12\) 0.866025 0.500000i 0.250000 0.144338i
\(13\) 1.00000i 0.277350i −0.990338 0.138675i \(-0.955716\pi\)
0.990338 0.138675i \(-0.0442844\pi\)
\(14\) −2.00000 1.73205i −0.534522 0.462910i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.73205 1.00000i −0.420084 0.242536i 0.275029 0.961436i \(-0.411312\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(18\) 0.866025 + 0.500000i 0.204124 + 0.117851i
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) 0.500000 2.59808i 0.109109 0.566947i
\(22\) 4.00000i 0.852803i
\(23\) 1.73205 1.00000i 0.361158 0.208514i −0.308431 0.951247i \(-0.599804\pi\)
0.669588 + 0.742732i \(0.266471\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0 0
\(26\) −0.500000 0.866025i −0.0980581 0.169842i
\(27\) 1.00000i 0.192450i
\(28\) −2.59808 0.500000i −0.490990 0.0944911i
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 3.46410 2.00000i 0.603023 0.348155i
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 2.59808 1.50000i 0.427121 0.246598i −0.270998 0.962580i \(-0.587354\pi\)
0.698119 + 0.715981i \(0.254020\pi\)
\(38\) 0.866025 + 0.500000i 0.140488 + 0.0811107i
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) 0 0
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) −0.866025 2.50000i −0.133631 0.385758i
\(43\) 8.00000i 1.21999i −0.792406 0.609994i \(-0.791172\pi\)
0.792406 0.609994i \(-0.208828\pi\)
\(44\) −2.00000 3.46410i −0.301511 0.522233i
\(45\) 0 0
\(46\) 1.00000 1.73205i 0.147442 0.255377i
\(47\) −5.19615 + 3.00000i −0.757937 + 0.437595i −0.828554 0.559908i \(-0.810836\pi\)
0.0706177 + 0.997503i \(0.477503\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −5.50000 + 4.33013i −0.785714 + 0.618590i
\(50\) 0 0
\(51\) −1.00000 1.73205i −0.140028 0.242536i
\(52\) −0.866025 0.500000i −0.120096 0.0693375i
\(53\) 1.73205 + 1.00000i 0.237915 + 0.137361i 0.614218 0.789136i \(-0.289471\pi\)
−0.376303 + 0.926497i \(0.622805\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −2.50000 + 0.866025i −0.334077 + 0.115728i
\(57\) 1.00000i 0.132453i
\(58\) −3.46410 + 2.00000i −0.454859 + 0.262613i
\(59\) 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0 0
\(61\) 6.50000 + 11.2583i 0.832240 + 1.44148i 0.896258 + 0.443533i \(0.146275\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 0 0
\(63\) 1.73205 2.00000i 0.218218 0.251976i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 2.00000 3.46410i 0.246183 0.426401i
\(67\) −2.59808 1.50000i −0.317406 0.183254i 0.332830 0.942987i \(-0.391996\pi\)
−0.650236 + 0.759733i \(0.725330\pi\)
\(68\) −1.73205 + 1.00000i −0.210042 + 0.121268i
\(69\) 2.00000 0.240772
\(70\) 0 0
\(71\) 16.0000 1.89885 0.949425 0.313993i \(-0.101667\pi\)
0.949425 + 0.313993i \(0.101667\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) −9.52628 5.50000i −1.11497 0.643726i −0.174855 0.984594i \(-0.555946\pi\)
−0.940111 + 0.340868i \(0.889279\pi\)
\(74\) 1.50000 2.59808i 0.174371 0.302020i
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) −10.3923 2.00000i −1.18431 0.227921i
\(78\) 1.00000i 0.113228i
\(79\) 6.50000 + 11.2583i 0.731307 + 1.26666i 0.956325 + 0.292306i \(0.0944227\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 10.3923 6.00000i 1.14764 0.662589i
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) −2.00000 1.73205i −0.218218 0.188982i
\(85\) 0 0
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) −3.46410 2.00000i −0.371391 0.214423i
\(88\) −3.46410 2.00000i −0.369274 0.213201i
\(89\) −1.00000 1.73205i −0.106000 0.183597i 0.808146 0.588982i \(-0.200471\pi\)
−0.914146 + 0.405385i \(0.867138\pi\)
\(90\) 0 0
\(91\) −2.50000 + 0.866025i −0.262071 + 0.0907841i
\(92\) 2.00000i 0.208514i
\(93\) 0 0
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 0 0
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 17.0000i 1.72609i 0.505128 + 0.863044i \(0.331445\pi\)
−0.505128 + 0.863044i \(0.668555\pi\)
\(98\) −2.59808 + 6.50000i −0.262445 + 0.656599i
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) −1.73205 1.00000i −0.171499 0.0990148i
\(103\) −6.06218 + 3.50000i −0.597324 + 0.344865i −0.767988 0.640464i \(-0.778742\pi\)
0.170664 + 0.985329i \(0.445409\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) 5.19615 3.00000i 0.502331 0.290021i −0.227345 0.973814i \(-0.573004\pi\)
0.729676 + 0.683793i \(0.239671\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) −9.50000 + 16.4545i −0.909935 + 1.57605i −0.0957826 + 0.995402i \(0.530535\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) 0 0
\(111\) 3.00000 0.284747
\(112\) −1.73205 + 2.00000i −0.163663 + 0.188982i
\(113\) 18.0000i 1.69330i −0.532152 0.846649i \(-0.678617\pi\)
0.532152 0.846649i \(-0.321383\pi\)
\(114\) 0.500000 + 0.866025i 0.0468293 + 0.0811107i
\(115\) 0 0
\(116\) −2.00000 + 3.46410i −0.185695 + 0.321634i
\(117\) 0.866025 0.500000i 0.0800641 0.0462250i
\(118\) 6.00000i 0.552345i
\(119\) −1.00000 + 5.19615i −0.0916698 + 0.476331i
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) 11.2583 + 6.50000i 1.01928 + 0.588482i
\(123\) 10.3923 + 6.00000i 0.937043 + 0.541002i
\(124\) 0 0
\(125\) 0 0
\(126\) 0.500000 2.59808i 0.0445435 0.231455i
\(127\) 1.00000i 0.0887357i −0.999015 0.0443678i \(-0.985873\pi\)
0.999015 0.0443678i \(-0.0141274\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 4.00000 6.92820i 0.352180 0.609994i
\(130\) 0 0
\(131\) −1.00000 1.73205i −0.0873704 0.151330i 0.819028 0.573753i \(-0.194513\pi\)
−0.906399 + 0.422423i \(0.861180\pi\)
\(132\) 4.00000i 0.348155i
\(133\) 1.73205 2.00000i 0.150188 0.173422i
\(134\) −3.00000 −0.259161
\(135\) 0 0
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) −8.66025 5.00000i −0.739895 0.427179i 0.0821359 0.996621i \(-0.473826\pi\)
−0.822031 + 0.569442i \(0.807159\pi\)
\(138\) 1.73205 1.00000i 0.147442 0.0851257i
\(139\) 13.0000 1.10265 0.551323 0.834292i \(-0.314123\pi\)
0.551323 + 0.834292i \(0.314123\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 13.8564 8.00000i 1.16280 0.671345i
\(143\) −3.46410 2.00000i −0.289683 0.167248i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) −11.0000 −0.910366
\(147\) −6.92820 + 1.00000i −0.571429 + 0.0824786i
\(148\) 3.00000i 0.246598i
\(149\) −8.00000 13.8564i −0.655386 1.13516i −0.981797 0.189933i \(-0.939173\pi\)
0.326411 0.945228i \(-0.394160\pi\)
\(150\) 0 0
\(151\) −9.50000 + 16.4545i −0.773099 + 1.33905i 0.162758 + 0.986666i \(0.447961\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) 0.866025 0.500000i 0.0702439 0.0405554i
\(153\) 2.00000i 0.161690i
\(154\) −10.0000 + 3.46410i −0.805823 + 0.279145i
\(155\) 0 0
\(156\) −0.500000 0.866025i −0.0400320 0.0693375i
\(157\) 18.1865 + 10.5000i 1.45144 + 0.837991i 0.998564 0.0535803i \(-0.0170633\pi\)
0.452880 + 0.891572i \(0.350397\pi\)
\(158\) 11.2583 + 6.50000i 0.895665 + 0.517112i
\(159\) 1.00000 + 1.73205i 0.0793052 + 0.137361i
\(160\) 0 0
\(161\) −4.00000 3.46410i −0.315244 0.273009i
\(162\) 1.00000i 0.0785674i
\(163\) −19.9186 + 11.5000i −1.56014 + 0.900750i −0.562902 + 0.826523i \(0.690315\pi\)
−0.997241 + 0.0742262i \(0.976351\pi\)
\(164\) 6.00000 10.3923i 0.468521 0.811503i
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) 10.0000i 0.773823i 0.922117 + 0.386912i \(0.126458\pi\)
−0.922117 + 0.386912i \(0.873542\pi\)
\(168\) −2.59808 0.500000i −0.200446 0.0385758i
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −0.500000 + 0.866025i −0.0382360 + 0.0662266i
\(172\) −6.92820 4.00000i −0.528271 0.304997i
\(173\) 5.19615 3.00000i 0.395056 0.228086i −0.289292 0.957241i \(-0.593420\pi\)
0.684349 + 0.729155i \(0.260087\pi\)
\(174\) −4.00000 −0.303239
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 5.19615 3.00000i 0.390567 0.225494i
\(178\) −1.73205 1.00000i −0.129823 0.0749532i
\(179\) −4.00000 + 6.92820i −0.298974 + 0.517838i −0.975901 0.218212i \(-0.929978\pi\)
0.676927 + 0.736050i \(0.263311\pi\)
\(180\) 0 0
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) −1.73205 + 2.00000i −0.128388 + 0.148250i
\(183\) 13.0000i 0.960988i
\(184\) −1.00000 1.73205i −0.0737210 0.127688i
\(185\) 0 0
\(186\) 0 0
\(187\) −6.92820 + 4.00000i −0.506640 + 0.292509i
\(188\) 6.00000i 0.437595i
\(189\) 2.50000 0.866025i 0.181848 0.0629941i
\(190\) 0 0
\(191\) −10.0000 17.3205i −0.723575 1.25327i −0.959558 0.281511i \(-0.909164\pi\)
0.235983 0.971757i \(-0.424169\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) −8.66025 5.00000i −0.623379 0.359908i 0.154805 0.987945i \(-0.450525\pi\)
−0.778183 + 0.628037i \(0.783859\pi\)
\(194\) 8.50000 + 14.7224i 0.610264 + 1.05701i
\(195\) 0 0
\(196\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 3.46410 2.00000i 0.246183 0.142134i
\(199\) 7.50000 12.9904i 0.531661 0.920864i −0.467656 0.883911i \(-0.654901\pi\)
0.999317 0.0369532i \(-0.0117652\pi\)
\(200\) 0 0
\(201\) −1.50000 2.59808i −0.105802 0.183254i
\(202\) 12.0000i 0.844317i
\(203\) 3.46410 + 10.0000i 0.243132 + 0.701862i
\(204\) −2.00000 −0.140028
\(205\) 0 0
\(206\) −3.50000 + 6.06218i −0.243857 + 0.422372i
\(207\) 1.73205 + 1.00000i 0.120386 + 0.0695048i
\(208\) −0.866025 + 0.500000i −0.0600481 + 0.0346688i
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) 3.00000 0.206529 0.103264 0.994654i \(-0.467071\pi\)
0.103264 + 0.994654i \(0.467071\pi\)
\(212\) 1.73205 1.00000i 0.118958 0.0686803i
\(213\) 13.8564 + 8.00000i 0.949425 + 0.548151i
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 19.0000i 1.28684i
\(219\) −5.50000 9.52628i −0.371656 0.643726i
\(220\) 0 0
\(221\) −1.00000 + 1.73205i −0.0672673 + 0.116510i
\(222\) 2.59808 1.50000i 0.174371 0.100673i
\(223\) 19.0000i 1.27233i 0.771551 + 0.636167i \(0.219481\pi\)
−0.771551 + 0.636167i \(0.780519\pi\)
\(224\) −0.500000 + 2.59808i −0.0334077 + 0.173591i
\(225\) 0 0
\(226\) −9.00000 15.5885i −0.598671 1.03693i
\(227\) 6.92820 + 4.00000i 0.459841 + 0.265489i 0.711977 0.702202i \(-0.247800\pi\)
−0.252136 + 0.967692i \(0.581133\pi\)
\(228\) 0.866025 + 0.500000i 0.0573539 + 0.0331133i
\(229\) −3.50000 6.06218i −0.231287 0.400600i 0.726900 0.686743i \(-0.240960\pi\)
−0.958187 + 0.286143i \(0.907627\pi\)
\(230\) 0 0
\(231\) −8.00000 6.92820i −0.526361 0.455842i
\(232\) 4.00000i 0.262613i
\(233\) 3.46410 2.00000i 0.226941 0.131024i −0.382219 0.924072i \(-0.624840\pi\)
0.609160 + 0.793047i \(0.291507\pi\)
\(234\) 0.500000 0.866025i 0.0326860 0.0566139i
\(235\) 0 0
\(236\) −3.00000 5.19615i −0.195283 0.338241i
\(237\) 13.0000i 0.844441i
\(238\) 1.73205 + 5.00000i 0.112272 + 0.324102i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −6.50000 + 11.2583i −0.418702 + 0.725213i −0.995809 0.0914555i \(-0.970848\pi\)
0.577107 + 0.816668i \(0.304181\pi\)
\(242\) −4.33013 2.50000i −0.278351 0.160706i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 13.0000 0.832240
\(245\) 0 0
\(246\) 12.0000 0.765092
\(247\) 0.866025 0.500000i 0.0551039 0.0318142i
\(248\) 0 0
\(249\) −3.00000 + 5.19615i −0.190117 + 0.329293i
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) −0.866025 2.50000i −0.0545545 0.157485i
\(253\) 8.00000i 0.502956i
\(254\) −0.500000 0.866025i −0.0313728 0.0543393i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.92820 + 4.00000i −0.432169 + 0.249513i −0.700270 0.713878i \(-0.746937\pi\)
0.268101 + 0.963391i \(0.413604\pi\)
\(258\) 8.00000i 0.498058i
\(259\) −6.00000 5.19615i −0.372822 0.322873i
\(260\) 0 0
\(261\) −2.00000 3.46410i −0.123797 0.214423i
\(262\) −1.73205 1.00000i −0.107006 0.0617802i
\(263\) 27.7128 + 16.0000i 1.70885 + 0.986602i 0.935995 + 0.352014i \(0.114503\pi\)
0.772851 + 0.634588i \(0.218830\pi\)
\(264\) −2.00000 3.46410i −0.123091 0.213201i
\(265\) 0 0
\(266\) 0.500000 2.59808i 0.0306570 0.159298i
\(267\) 2.00000i 0.122398i
\(268\) −2.59808 + 1.50000i −0.158703 + 0.0916271i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) 10.0000 + 17.3205i 0.607457 + 1.05215i 0.991658 + 0.128897i \(0.0411435\pi\)
−0.384201 + 0.923249i \(0.625523\pi\)
\(272\) 2.00000i 0.121268i
\(273\) −2.59808 0.500000i −0.157243 0.0302614i
\(274\) −10.0000 −0.604122
\(275\) 0 0
\(276\) 1.00000 1.73205i 0.0601929 0.104257i
\(277\) −0.866025 0.500000i −0.0520344 0.0300421i 0.473757 0.880656i \(-0.342897\pi\)
−0.525792 + 0.850613i \(0.676231\pi\)
\(278\) 11.2583 6.50000i 0.675230 0.389844i
\(279\) 0 0
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) −5.19615 + 3.00000i −0.309426 + 0.178647i
\(283\) 11.2583 + 6.50000i 0.669238 + 0.386385i 0.795788 0.605575i \(-0.207057\pi\)
−0.126550 + 0.991960i \(0.540390\pi\)
\(284\) 8.00000 13.8564i 0.474713 0.822226i
\(285\) 0 0
\(286\) −4.00000 −0.236525
\(287\) −10.3923 30.0000i −0.613438 1.77084i
\(288\) 1.00000i 0.0589256i
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) 0 0
\(291\) −8.50000 + 14.7224i −0.498279 + 0.863044i
\(292\) −9.52628 + 5.50000i −0.557483 + 0.321863i
\(293\) 12.0000i 0.701047i −0.936554 0.350524i \(-0.886004\pi\)
0.936554 0.350524i \(-0.113996\pi\)
\(294\) −5.50000 + 4.33013i −0.320767 + 0.252538i
\(295\) 0 0
\(296\) −1.50000 2.59808i −0.0871857 0.151010i
\(297\) 3.46410 + 2.00000i 0.201008 + 0.116052i
\(298\) −13.8564 8.00000i −0.802680 0.463428i
\(299\) −1.00000 1.73205i −0.0578315 0.100167i
\(300\) 0 0
\(301\) −20.0000 + 6.92820i −1.15278 + 0.399335i
\(302\) 19.0000i 1.09333i
\(303\) −10.3923 + 6.00000i −0.597022 + 0.344691i
\(304\) 0.500000 0.866025i 0.0286770 0.0496700i
\(305\) 0 0
\(306\) −1.00000 1.73205i −0.0571662 0.0990148i
\(307\) 20.0000i 1.14146i 0.821138 + 0.570730i \(0.193340\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(308\) −6.92820 + 8.00000i −0.394771 + 0.455842i
\(309\) −7.00000 −0.398216
\(310\) 0 0
\(311\) 7.00000 12.1244i 0.396934 0.687509i −0.596412 0.802678i \(-0.703408\pi\)
0.993346 + 0.115169i \(0.0367410\pi\)
\(312\) −0.866025 0.500000i −0.0490290 0.0283069i
\(313\) 15.5885 9.00000i 0.881112 0.508710i 0.0100869 0.999949i \(-0.496789\pi\)
0.871025 + 0.491239i \(0.163456\pi\)
\(314\) 21.0000 1.18510
\(315\) 0 0
\(316\) 13.0000 0.731307
\(317\) 19.0526 11.0000i 1.07010 0.617822i 0.141890 0.989882i \(-0.454682\pi\)
0.928208 + 0.372061i \(0.121349\pi\)
\(318\) 1.73205 + 1.00000i 0.0971286 + 0.0560772i
\(319\) −8.00000 + 13.8564i −0.447914 + 0.775810i
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) −5.19615 1.00000i −0.289570 0.0557278i
\(323\) 2.00000i 0.111283i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −11.5000 + 19.9186i −0.636926 + 1.10319i
\(327\) −16.4545 + 9.50000i −0.909935 + 0.525351i
\(328\) 12.0000i 0.662589i
\(329\) 12.0000 + 10.3923i 0.661581 + 0.572946i
\(330\) 0 0
\(331\) −10.5000 18.1865i −0.577132 0.999622i −0.995806 0.0914858i \(-0.970838\pi\)
0.418674 0.908137i \(-0.362495\pi\)
\(332\) 5.19615 + 3.00000i 0.285176 + 0.164646i
\(333\) 2.59808 + 1.50000i 0.142374 + 0.0821995i
\(334\) 5.00000 + 8.66025i 0.273588 + 0.473868i
\(335\) 0 0
\(336\) −2.50000 + 0.866025i −0.136386 + 0.0472456i
\(337\) 18.0000i 0.980522i −0.871576 0.490261i \(-0.836901\pi\)
0.871576 0.490261i \(-0.163099\pi\)
\(338\) 10.3923 6.00000i 0.565267 0.326357i
\(339\) 9.00000 15.5885i 0.488813 0.846649i
\(340\) 0 0
\(341\) 0 0
\(342\) 1.00000i 0.0540738i
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) 19.0526 + 11.0000i 1.02279 + 0.590511i 0.914912 0.403653i \(-0.132260\pi\)
0.107883 + 0.994164i \(0.465593\pi\)
\(348\) −3.46410 + 2.00000i −0.185695 + 0.107211i
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) −3.46410 + 2.00000i −0.184637 + 0.106600i
\(353\) −17.3205 10.0000i −0.921878 0.532246i −0.0376440 0.999291i \(-0.511985\pi\)
−0.884234 + 0.467045i \(0.845319\pi\)
\(354\) 3.00000 5.19615i 0.159448 0.276172i
\(355\) 0 0
\(356\) −2.00000 −0.106000
\(357\) −3.46410 + 4.00000i −0.183340 + 0.211702i
\(358\) 8.00000i 0.422813i
\(359\) −3.00000 5.19615i −0.158334 0.274242i 0.775934 0.630814i \(-0.217279\pi\)
−0.934268 + 0.356572i \(0.883946\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) −15.5885 + 9.00000i −0.819311 + 0.473029i
\(363\) 5.00000i 0.262432i
\(364\) −0.500000 + 2.59808i −0.0262071 + 0.136176i
\(365\) 0 0
\(366\) 6.50000 + 11.2583i 0.339760 + 0.588482i
\(367\) 6.92820 + 4.00000i 0.361649 + 0.208798i 0.669804 0.742538i \(-0.266378\pi\)
−0.308155 + 0.951336i \(0.599711\pi\)
\(368\) −1.73205 1.00000i −0.0902894 0.0521286i
\(369\) 6.00000 + 10.3923i 0.312348 + 0.541002i
\(370\) 0 0
\(371\) 1.00000 5.19615i 0.0519174 0.269771i
\(372\) 0 0
\(373\) −19.9186 + 11.5000i −1.03135 + 0.595447i −0.917370 0.398036i \(-0.869692\pi\)
−0.113975 + 0.993484i \(0.536359\pi\)
\(374\) −4.00000 + 6.92820i −0.206835 + 0.358249i
\(375\) 0 0
\(376\) 3.00000 + 5.19615i 0.154713 + 0.267971i
\(377\) 4.00000i 0.206010i
\(378\) 1.73205 2.00000i 0.0890871 0.102869i
\(379\) 5.00000 0.256833 0.128416 0.991720i \(-0.459011\pi\)
0.128416 + 0.991720i \(0.459011\pi\)
\(380\) 0 0
\(381\) 0.500000 0.866025i 0.0256158 0.0443678i
\(382\) −17.3205 10.0000i −0.886194 0.511645i
\(383\) 12.1244 7.00000i 0.619526 0.357683i −0.157159 0.987573i \(-0.550233\pi\)
0.776684 + 0.629890i \(0.216900\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 6.92820 4.00000i 0.352180 0.203331i
\(388\) 14.7224 + 8.50000i 0.747418 + 0.431522i
\(389\) −10.0000 + 17.3205i −0.507020 + 0.878185i 0.492947 + 0.870059i \(0.335920\pi\)
−0.999967 + 0.00812520i \(0.997414\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 4.33013 + 5.50000i 0.218704 + 0.277792i
\(393\) 2.00000i 0.100887i
\(394\) 0 0
\(395\) 0 0
\(396\) 2.00000 3.46410i 0.100504 0.174078i
\(397\) −15.5885 + 9.00000i −0.782362 + 0.451697i −0.837267 0.546795i \(-0.815848\pi\)
0.0549046 + 0.998492i \(0.482515\pi\)
\(398\) 15.0000i 0.751882i
\(399\) 2.50000 0.866025i 0.125157 0.0433555i
\(400\) 0 0
\(401\) −2.00000 3.46410i −0.0998752 0.172989i 0.811758 0.583994i \(-0.198511\pi\)
−0.911633 + 0.411005i \(0.865178\pi\)
\(402\) −2.59808 1.50000i −0.129580 0.0748132i
\(403\) 0 0
\(404\) 6.00000 + 10.3923i 0.298511 + 0.517036i
\(405\) 0 0
\(406\) 8.00000 + 6.92820i 0.397033 + 0.343841i
\(407\) 12.0000i 0.594818i
\(408\) −1.73205 + 1.00000i −0.0857493 + 0.0495074i
\(409\) −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i \(-0.921004\pi\)
0.697406 + 0.716677i \(0.254338\pi\)
\(410\) 0 0
\(411\) −5.00000 8.66025i −0.246632 0.427179i
\(412\) 7.00000i 0.344865i
\(413\) −15.5885 3.00000i −0.767058 0.147620i
\(414\) 2.00000 0.0982946
\(415\) 0 0
\(416\) −0.500000 + 0.866025i −0.0245145 + 0.0424604i
\(417\) 11.2583 + 6.50000i 0.551323 + 0.318306i
\(418\) 3.46410 2.00000i 0.169435 0.0978232i
\(419\) 16.0000 0.781651 0.390826 0.920465i \(-0.372190\pi\)
0.390826 + 0.920465i \(0.372190\pi\)
\(420\) 0 0
\(421\) 1.00000 0.0487370 0.0243685 0.999703i \(-0.492242\pi\)
0.0243685 + 0.999703i \(0.492242\pi\)
\(422\) 2.59808 1.50000i 0.126472 0.0730189i
\(423\) −5.19615 3.00000i −0.252646 0.145865i
\(424\) 1.00000 1.73205i 0.0485643 0.0841158i
\(425\) 0 0
\(426\) 16.0000 0.775203
\(427\) 22.5167 26.0000i 1.08966 1.25823i
\(428\) 6.00000i 0.290021i
\(429\) −2.00000 3.46410i −0.0965609 0.167248i
\(430\) 0 0
\(431\) −3.00000 + 5.19615i −0.144505 + 0.250290i −0.929188 0.369607i \(-0.879492\pi\)
0.784683 + 0.619897i \(0.212826\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 2.00000i 0.0961139i 0.998845 + 0.0480569i \(0.0153029\pi\)
−0.998845 + 0.0480569i \(0.984697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 9.50000 + 16.4545i 0.454967 + 0.788027i
\(437\) 1.73205 + 1.00000i 0.0828552 + 0.0478365i
\(438\) −9.52628 5.50000i −0.455183 0.262800i
\(439\) −11.5000 19.9186i −0.548865 0.950662i −0.998353 0.0573756i \(-0.981727\pi\)
0.449488 0.893287i \(-0.351607\pi\)
\(440\) 0 0
\(441\) −6.50000 2.59808i −0.309524 0.123718i
\(442\) 2.00000i 0.0951303i
\(443\) −5.19615 + 3.00000i −0.246877 + 0.142534i −0.618333 0.785916i \(-0.712192\pi\)
0.371457 + 0.928450i \(0.378858\pi\)
\(444\) 1.50000 2.59808i 0.0711868 0.123299i
\(445\) 0 0
\(446\) 9.50000 + 16.4545i 0.449838 + 0.779142i
\(447\) 16.0000i 0.756774i
\(448\) 0.866025 + 2.50000i 0.0409159 + 0.118114i
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) 24.0000 41.5692i 1.13012 1.95742i
\(452\) −15.5885 9.00000i −0.733219 0.423324i
\(453\) −16.4545 + 9.50000i −0.773099 + 0.446349i
\(454\) 8.00000 0.375459
\(455\) 0 0
\(456\) 1.00000 0.0468293
\(457\) 32.0429 18.5000i 1.49891 0.865393i 0.498906 0.866656i \(-0.333735\pi\)
0.999999 + 0.00126243i \(0.000401844\pi\)
\(458\) −6.06218 3.50000i −0.283267 0.163544i
\(459\) 1.00000 1.73205i 0.0466760 0.0808452i
\(460\) 0 0
\(461\) 26.0000 1.21094 0.605470 0.795868i \(-0.292985\pi\)
0.605470 + 0.795868i \(0.292985\pi\)
\(462\) −10.3923 2.00000i −0.483494 0.0930484i
\(463\) 3.00000i 0.139422i 0.997567 + 0.0697109i \(0.0222077\pi\)
−0.997567 + 0.0697109i \(0.977792\pi\)
\(464\) 2.00000 + 3.46410i 0.0928477 + 0.160817i
\(465\) 0 0
\(466\) 2.00000 3.46410i 0.0926482 0.160471i
\(467\) 25.9808 15.0000i 1.20225 0.694117i 0.241192 0.970477i \(-0.422462\pi\)
0.961054 + 0.276360i \(0.0891283\pi\)
\(468\) 1.00000i 0.0462250i
\(469\) −1.50000 + 7.79423i −0.0692636 + 0.359904i
\(470\) 0 0
\(471\) 10.5000 + 18.1865i 0.483814 + 0.837991i
\(472\) −5.19615 3.00000i −0.239172 0.138086i
\(473\) −27.7128 16.0000i −1.27424 0.735681i
\(474\) 6.50000 + 11.2583i 0.298555 + 0.517112i
\(475\) 0 0
\(476\) 4.00000 + 3.46410i 0.183340 + 0.158777i
\(477\) 2.00000i 0.0915737i
\(478\) 10.3923 6.00000i 0.475333 0.274434i
\(479\) −17.0000 + 29.4449i −0.776750 + 1.34537i 0.157056 + 0.987590i \(0.449800\pi\)
−0.933806 + 0.357780i \(0.883534\pi\)
\(480\) 0 0
\(481\) −1.50000 2.59808i −0.0683941 0.118462i
\(482\) 13.0000i 0.592134i
\(483\) −1.73205 5.00000i −0.0788110 0.227508i
\(484\) −5.00000 −0.227273
\(485\) 0 0
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) −34.6410 20.0000i −1.56973 0.906287i −0.996199 0.0871056i \(-0.972238\pi\)
−0.573535 0.819181i \(-0.694428\pi\)
\(488\) 11.2583 6.50000i 0.509641 0.294241i
\(489\) −23.0000 −1.04010
\(490\) 0 0
\(491\) 18.0000 0.812329 0.406164 0.913800i \(-0.366866\pi\)
0.406164 + 0.913800i \(0.366866\pi\)
\(492\) 10.3923 6.00000i 0.468521 0.270501i
\(493\) 6.92820 + 4.00000i 0.312031 + 0.180151i
\(494\) 0.500000 0.866025i 0.0224961 0.0389643i
\(495\) 0 0
\(496\) 0 0
\(497\) −13.8564 40.0000i −0.621545 1.79425i
\(498\) 6.00000i 0.268866i
\(499\) −13.5000 23.3827i −0.604343 1.04675i −0.992155 0.125014i \(-0.960102\pi\)
0.387812 0.921739i \(-0.373231\pi\)
\(500\) 0 0
\(501\) −5.00000 + 8.66025i −0.223384 + 0.386912i
\(502\) 20.7846 12.0000i 0.927663 0.535586i
\(503\) 4.00000i 0.178351i −0.996016 0.0891756i \(-0.971577\pi\)
0.996016 0.0891756i \(-0.0284232\pi\)
\(504\) −2.00000 1.73205i −0.0890871 0.0771517i
\(505\) 0 0
\(506\) −4.00000 6.92820i −0.177822 0.307996i
\(507\) 10.3923 + 6.00000i 0.461538 + 0.266469i
\(508\) −0.866025 0.500000i −0.0384237 0.0221839i
\(509\) −18.0000 31.1769i −0.797836 1.38189i −0.921023 0.389509i \(-0.872645\pi\)
0.123187 0.992384i \(-0.460689\pi\)
\(510\) 0 0
\(511\) −5.50000 + 28.5788i −0.243306 + 1.26425i
\(512\) 1.00000i 0.0441942i
\(513\) −0.866025 + 0.500000i −0.0382360 + 0.0220755i
\(514\) −4.00000 + 6.92820i −0.176432 + 0.305590i
\(515\) 0 0
\(516\) −4.00000 6.92820i −0.176090 0.304997i
\(517\) 24.0000i 1.05552i
\(518\) −7.79423 1.50000i −0.342459 0.0659062i
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −3.00000 + 5.19615i −0.131432 + 0.227648i −0.924229 0.381839i \(-0.875291\pi\)
0.792797 + 0.609486i \(0.208624\pi\)
\(522\) −3.46410 2.00000i −0.151620 0.0875376i
\(523\) −13.8564 + 8.00000i −0.605898 + 0.349816i −0.771358 0.636401i \(-0.780422\pi\)
0.165460 + 0.986216i \(0.447089\pi\)
\(524\) −2.00000 −0.0873704
\(525\) 0 0
\(526\) 32.0000 1.39527
\(527\) 0 0
\(528\) −3.46410 2.00000i −0.150756 0.0870388i
\(529\) −9.50000 + 16.4545i −0.413043 + 0.715412i
\(530\) 0 0
\(531\) 6.00000 0.260378
\(532\) −0.866025 2.50000i −0.0375470 0.108389i
\(533\) 12.0000i 0.519778i
\(534\) −1.00000 1.73205i −0.0432742 0.0749532i
\(535\) 0 0
\(536\) −1.50000 + 2.59808i −0.0647901 + 0.112220i
\(537\) −6.92820 + 4.00000i −0.298974 + 0.172613i
\(538\) 0 0
\(539\) 4.00000 + 27.7128i 0.172292 + 1.19368i
\(540\) 0 0
\(541\) −8.50000 14.7224i −0.365444 0.632967i 0.623404 0.781900i \(-0.285749\pi\)
−0.988847 + 0.148933i \(0.952416\pi\)
\(542\) 17.3205 + 10.0000i 0.743980 + 0.429537i
\(543\) −15.5885 9.00000i −0.668965 0.386227i
\(544\) 1.00000 + 1.73205i 0.0428746 + 0.0742611i
\(545\) 0 0
\(546\) −2.50000 + 0.866025i −0.106990 + 0.0370625i
\(547\) 12.0000i 0.513083i −0.966533 0.256541i \(-0.917417\pi\)
0.966533 0.256541i \(-0.0825830\pi\)
\(548\) −8.66025 + 5.00000i −0.369948 + 0.213589i
\(549\) −6.50000 + 11.2583i −0.277413 + 0.480494i
\(550\) 0 0
\(551\) −2.00000 3.46410i −0.0852029 0.147576i
\(552\) 2.00000i 0.0851257i
\(553\) 22.5167 26.0000i 0.957506 1.10563i
\(554\) −1.00000 −0.0424859
\(555\) 0 0
\(556\) 6.50000 11.2583i 0.275661 0.477460i
\(557\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) −8.00000 −0.337760
\(562\) −15.5885 + 9.00000i −0.657559 + 0.379642i
\(563\) −24.2487 14.0000i −1.02196 0.590030i −0.107290 0.994228i \(-0.534217\pi\)
−0.914671 + 0.404198i \(0.867551\pi\)
\(564\) −3.00000 + 5.19615i −0.126323 + 0.218797i
\(565\) 0 0
\(566\) 13.0000 0.546431
\(567\) 2.59808 + 0.500000i 0.109109 + 0.0209980i
\(568\) 16.0000i 0.671345i
\(569\) −20.0000 34.6410i −0.838444 1.45223i −0.891196 0.453619i \(-0.850133\pi\)
0.0527519 0.998608i \(-0.483201\pi\)
\(570\) 0 0
\(571\) 17.5000 30.3109i 0.732352 1.26847i −0.223523 0.974699i \(-0.571756\pi\)
0.955875 0.293773i \(-0.0949108\pi\)
\(572\) −3.46410 + 2.00000i −0.144841 + 0.0836242i
\(573\) 20.0000i 0.835512i
\(574\) −24.0000 20.7846i −1.00174 0.867533i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −19.0526 11.0000i −0.793168 0.457936i 0.0479084 0.998852i \(-0.484744\pi\)
−0.841077 + 0.540916i \(0.818078\pi\)
\(578\) −11.2583 6.50000i −0.468285 0.270364i
\(579\) −5.00000 8.66025i −0.207793 0.359908i
\(580\) 0 0
\(581\) 15.0000 5.19615i 0.622305 0.215573i
\(582\) 17.0000i 0.704673i
\(583\) 6.92820 4.00000i 0.286937 0.165663i
\(584\) −5.50000 + 9.52628i −0.227592 + 0.394200i
\(585\) 0 0
\(586\) −6.00000 10.3923i −0.247858 0.429302i
\(587\) 42.0000i 1.73353i −0.498721 0.866763i \(-0.666197\pi\)
0.498721 0.866763i \(-0.333803\pi\)
\(588\) −2.59808 + 6.50000i −0.107143 + 0.268055i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −2.59808 1.50000i −0.106780 0.0616496i
\(593\) −36.3731 + 21.0000i −1.49366 + 0.862367i −0.999974 0.00727173i \(-0.997685\pi\)
−0.493689 + 0.869638i \(0.664352\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) −16.0000 −0.655386
\(597\) 12.9904 7.50000i 0.531661 0.306955i
\(598\) −1.73205 1.00000i −0.0708288 0.0408930i
\(599\) −3.00000 + 5.19615i −0.122577 + 0.212309i −0.920783 0.390075i \(-0.872449\pi\)
0.798206 + 0.602384i \(0.205782\pi\)
\(600\) 0 0
\(601\) −29.0000 −1.18293 −0.591467 0.806329i \(-0.701451\pi\)
−0.591467 + 0.806329i \(0.701451\pi\)
\(602\) −13.8564 + 16.0000i −0.564745 + 0.652111i
\(603\) 3.00000i 0.122169i
\(604\) 9.50000 + 16.4545i 0.386550 + 0.669523i
\(605\) 0 0
\(606\) −6.00000 + 10.3923i −0.243733 + 0.422159i
\(607\) 0.866025 0.500000i 0.0351509 0.0202944i −0.482322 0.875994i \(-0.660206\pi\)
0.517472 + 0.855700i \(0.326873\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) −2.00000 + 10.3923i −0.0810441 + 0.421117i
\(610\) 0 0
\(611\) 3.00000 + 5.19615i 0.121367 + 0.210214i
\(612\) −1.73205 1.00000i −0.0700140 0.0404226i
\(613\) 5.19615 + 3.00000i 0.209871 + 0.121169i 0.601251 0.799060i \(-0.294669\pi\)
−0.391381 + 0.920229i \(0.628002\pi\)
\(614\) 10.0000 + 17.3205i 0.403567 + 0.698999i
\(615\) 0 0
\(616\) −2.00000 + 10.3923i −0.0805823 + 0.418718i
\(617\) 44.0000i 1.77137i 0.464283 + 0.885687i \(0.346312\pi\)
−0.464283 + 0.885687i \(0.653688\pi\)
\(618\) −6.06218 + 3.50000i −0.243857 + 0.140791i
\(619\) 22.0000 38.1051i 0.884255 1.53157i 0.0376891 0.999290i \(-0.488000\pi\)
0.846566 0.532284i \(-0.178666\pi\)
\(620\) 0 0
\(621\) 1.00000 + 1.73205i 0.0401286 + 0.0695048i
\(622\) 14.0000i 0.561349i
\(623\) −3.46410 + 4.00000i −0.138786 + 0.160257i
\(624\) −1.00000 −0.0400320
\(625\) 0 0
\(626\) 9.00000 15.5885i 0.359712 0.623040i
\(627\) 3.46410 + 2.00000i 0.138343 + 0.0798723i
\(628\) 18.1865 10.5000i 0.725722 0.418996i
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 17.0000 0.676759 0.338380 0.941010i \(-0.390121\pi\)
0.338380 + 0.941010i \(0.390121\pi\)
\(632\) 11.2583 6.50000i 0.447832 0.258556i
\(633\) 2.59808 + 1.50000i 0.103264 + 0.0596196i
\(634\) 11.0000 19.0526i 0.436866 0.756674i
\(635\) 0 0
\(636\) 2.00000 0.0793052
\(637\) 4.33013 + 5.50000i 0.171566 + 0.217918i
\(638\) 16.0000i 0.633446i
\(639\) 8.00000 + 13.8564i 0.316475 + 0.548151i
\(640\) 0 0
\(641\) −8.00000 + 13.8564i −0.315981 + 0.547295i −0.979646 0.200735i \(-0.935667\pi\)
0.663665 + 0.748030i \(0.269000\pi\)
\(642\) 5.19615 3.00000i 0.205076 0.118401i
\(643\) 11.0000i 0.433798i −0.976194 0.216899i \(-0.930406\pi\)
0.976194 0.216899i \(-0.0695942\pi\)
\(644\) −5.00000 + 1.73205i −0.197028 + 0.0682524i
\(645\) 0 0
\(646\) −1.00000 1.73205i −0.0393445 0.0681466i
\(647\) −10.3923 6.00000i −0.408564 0.235884i 0.281609 0.959529i \(-0.409132\pi\)
−0.690172 + 0.723645i \(0.742465\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −12.0000 20.7846i −0.471041 0.815867i
\(650\) 0 0
\(651\) 0 0
\(652\) 23.0000i 0.900750i
\(653\) 13.8564 8.00000i 0.542243 0.313064i −0.203744 0.979024i \(-0.565311\pi\)
0.745988 + 0.665960i \(0.231978\pi\)
\(654\) −9.50000 + 16.4545i −0.371479 + 0.643421i
\(655\) 0 0
\(656\) −6.00000 10.3923i −0.234261 0.405751i
\(657\) 11.0000i 0.429151i
\(658\) 15.5885 + 3.00000i 0.607701 + 0.116952i
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 12.5000 21.6506i 0.486194 0.842112i −0.513680 0.857982i \(-0.671718\pi\)
0.999874 + 0.0158695i \(0.00505163\pi\)
\(662\) −18.1865 10.5000i −0.706840 0.408094i
\(663\) −1.73205 + 1.00000i −0.0672673 + 0.0388368i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 3.00000 0.116248
\(667\) −6.92820 + 4.00000i −0.268261 + 0.154881i
\(668\) 8.66025 + 5.00000i 0.335075 + 0.193456i
\(669\) −9.50000 + 16.4545i −0.367291 + 0.636167i
\(670\) 0 0
\(671\) 52.0000 2.00744
\(672\) −1.73205 + 2.00000i −0.0668153 + 0.0771517i
\(673\) 9.00000i 0.346925i 0.984841 + 0.173462i \(0.0554955\pi\)
−0.984841 + 0.173462i \(0.944505\pi\)
\(674\) −9.00000 15.5885i −0.346667 0.600445i
\(675\) 0 0
\(676\) 6.00000 10.3923i 0.230769 0.399704i
\(677\) −1.73205 + 1.00000i −0.0665681 + 0.0384331i −0.532915 0.846169i \(-0.678903\pi\)
0.466347 + 0.884602i \(0.345570\pi\)
\(678\) 18.0000i 0.691286i
\(679\) 42.5000 14.7224i 1.63100 0.564995i
\(680\) 0 0
\(681\) 4.00000 + 6.92820i 0.153280 + 0.265489i
\(682\) 0 0
\(683\) 41.5692 + 24.0000i 1.59060 + 0.918334i 0.993204 + 0.116390i \(0.0371322\pi\)
0.597398 + 0.801945i \(0.296201\pi\)
\(684\) 0.500000 + 0.866025i 0.0191180 + 0.0331133i
\(685\) 0 0
\(686\) 18.5000 + 0.866025i 0.706333 + 0.0330650i
\(687\) 7.00000i 0.267067i
\(688\) −6.92820 + 4.00000i −0.264135 + 0.152499i
\(689\) 1.00000 1.73205i 0.0380970 0.0659859i
\(690\) 0 0
\(691\) 19.5000 + 33.7750i 0.741815 + 1.28486i 0.951668 + 0.307128i \(0.0993681\pi\)
−0.209853 + 0.977733i \(0.567299\pi\)
\(692\) 6.00000i 0.228086i
\(693\) −3.46410 10.0000i −0.131590 0.379869i
\(694\) 22.0000 0.835109
\(695\) 0 0
\(696\) −2.00000 + 3.46410i −0.0758098 + 0.131306i
\(697\) −20.7846 12.0000i −0.787273 0.454532i
\(698\) −1.73205 + 1.00000i −0.0655591 + 0.0378506i
\(699\) 4.00000 0.151294
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0.866025 0.500000i 0.0326860 0.0188713i
\(703\) 2.59808 + 1.50000i 0.0979883 + 0.0565736i
\(704\) −2.00000 + 3.46410i −0.0753778 + 0.130558i
\(705\) 0 0
\(706\) −20.0000 −0.752710
\(707\) 31.1769 + 6.00000i 1.17253 + 0.225653i
\(708\) 6.00000i 0.225494i
\(709\) −5.50000 9.52628i −0.206557 0.357767i 0.744071 0.668101i \(-0.232892\pi\)
−0.950628 + 0.310334i \(0.899559\pi\)
\(710\) 0 0
\(711\) −6.50000 + 11.2583i −0.243769 + 0.422220i
\(712\) −1.73205 + 1.00000i −0.0649113 + 0.0374766i
\(713\) 0 0
\(714\) −1.00000 + 5.19615i −0.0374241 + 0.194461i
\(715\) 0 0
\(716\) 4.00000 + 6.92820i 0.149487 + 0.258919i
\(717\) 10.3923 + 6.00000i 0.388108 + 0.224074i
\(718\) −5.19615 3.00000i −0.193919 0.111959i
\(719\) 4.00000 + 6.92820i 0.149175 + 0.258378i 0.930923 0.365216i \(-0.119005\pi\)
−0.781748 + 0.623595i \(0.785672\pi\)
\(720\) 0 0
\(721\) 14.0000 + 12.1244i 0.521387 + 0.451535i
\(722\) 18.0000i 0.669891i
\(723\) −11.2583 + 6.50000i −0.418702 + 0.241738i
\(724\) −9.00000 + 15.5885i −0.334482 + 0.579340i
\(725\) 0 0
\(726\) −2.50000 4.33013i −0.0927837 0.160706i
\(727\) 1.00000i 0.0370879i −0.999828 0.0185440i \(-0.994097\pi\)
0.999828 0.0185440i \(-0.00590307\pi\)
\(728\) 0.866025 + 2.50000i 0.0320970 + 0.0926562i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −8.00000 + 13.8564i −0.295891 + 0.512498i
\(732\) 11.2583 + 6.50000i 0.416120 + 0.240247i
\(733\) 30.3109 17.5000i 1.11956 0.646377i 0.178270 0.983982i \(-0.442950\pi\)
0.941288 + 0.337604i \(0.109617\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) −2.00000 −0.0737210
\(737\) −10.3923 + 6.00000i −0.382805 + 0.221013i
\(738\) 10.3923 + 6.00000i 0.382546 + 0.220863i
\(739\) −0.500000 + 0.866025i −0.0183928 + 0.0318573i −0.875075 0.483987i \(-0.839188\pi\)
0.856683 + 0.515844i \(0.172522\pi\)
\(740\) 0 0
\(741\) 1.00000 0.0367359
\(742\) −1.73205 5.00000i −0.0635856 0.183556i
\(743\) 6.00000i 0.220119i 0.993925 + 0.110059i \(0.0351041\pi\)
−0.993925 + 0.110059i \(0.964896\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −11.5000 + 19.9186i −0.421045 + 0.729271i
\(747\) −5.19615 + 3.00000i −0.190117 + 0.109764i
\(748\) 8.00000i 0.292509i
\(749\) −12.0000 10.3923i −0.438470 0.379727i
\(750\) 0 0
\(751\) −9.50000 16.4545i −0.346660 0.600433i 0.638994 0.769212i \(-0.279351\pi\)
−0.985654 + 0.168779i \(0.946018\pi\)
\(752\) 5.19615 + 3.00000i 0.189484 + 0.109399i
\(753\) 20.7846 + 12.0000i 0.757433 + 0.437304i
\(754\) 2.00000 + 3.46410i 0.0728357 + 0.126155i
\(755\) 0 0
\(756\) 0.500000 2.59808i 0.0181848 0.0944911i
\(757\) 1.00000i 0.0363456i 0.999835 + 0.0181728i \(0.00578490\pi\)
−0.999835 + 0.0181728i \(0.994215\pi\)
\(758\) 4.33013 2.50000i 0.157277 0.0908041i
\(759\) 4.00000 6.92820i 0.145191 0.251478i
\(760\) 0 0
\(761\) −17.0000 29.4449i −0.616250 1.06738i −0.990164 0.139912i \(-0.955318\pi\)
0.373914 0.927463i \(-0.378015\pi\)
\(762\) 1.00000i 0.0362262i
\(763\) 49.3634 + 9.50000i 1.78708 + 0.343923i
\(764\) −20.0000 −0.723575
\(765\) 0 0
\(766\) 7.00000 12.1244i 0.252920 0.438071i
\(767\) −5.19615 3.00000i −0.187622 0.108324i
\(768\) −0.866025 + 0.500000i −0.0312500 + 0.0180422i
\(769\) 50.0000 1.80305 0.901523 0.432731i \(-0.142450\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(770\) 0 0
\(771\) −8.00000 −0.288113
\(772\) −8.66025 + 5.00000i −0.311689 + 0.179954i
\(773\) −27.7128 16.0000i −0.996761 0.575480i −0.0894724 0.995989i \(-0.528518\pi\)
−0.907288 + 0.420509i \(0.861851\pi\)
\(774\) 4.00000 6.92820i 0.143777 0.249029i
\(775\) 0 0
\(776\) 17.0000 0.610264
\(777\) −2.59808 7.50000i −0.0932055 0.269061i
\(778\) 20.0000i 0.717035i
\(779\) 6.00000 + 10.3923i 0.214972 + 0.372343i
\(780\) 0 0
\(781\) 32.0000 55.4256i 1.14505 1.98328i
\(782\) −3.46410 + 2.00000i −0.123876 + 0.0715199i
\(783\) 4.00000i 0.142948i
\(784\) 6.50000 + 2.59808i 0.232143 + 0.0927884i