Properties

Label 1110.2.x.d.751.5
Level $1110$
Weight $2$
Character 1110.751
Analytic conductor $8.863$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 60 x^{14} + 1362 x^{12} + 15028 x^{10} + 86441 x^{8} + 260376 x^{6} + 382684 x^{4} + 224224 x^{2} + 38416\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.5
Root \(3.25684i\) of defining polynomial
Character \(\chi\) \(=\) 1110.751
Dual form 1110.2.x.d.841.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-1.62842 + 2.82051i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-1.62842 + 2.82051i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} -5.25915 q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.16873 - 1.82947i) q^{13} +3.25684i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.95448 + 1.12842i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.21087 - 1.85380i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-1.62842 - 2.82051i) q^{21} +(-4.55456 + 2.62957i) q^{22} +1.92689i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} -3.65894 q^{26} +1.00000 q^{27} +(1.62842 + 2.82051i) q^{28} -3.37764i q^{29} +(-0.500000 + 0.866025i) q^{30} +1.35672i q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.62957 - 4.55456i) q^{33} +(-1.12842 + 1.95448i) q^{34} +(-2.82051 + 1.62842i) q^{35} -1.00000 q^{36} +(-5.27288 - 3.03262i) q^{37} -3.70759 q^{38} +(3.16873 - 1.82947i) q^{39} +(0.500000 - 0.866025i) q^{40} +(2.73745 - 4.74141i) q^{41} +(-2.82051 - 1.62842i) q^{42} -3.28360i q^{43} +(-2.62957 + 4.55456i) q^{44} -1.00000i q^{45} +(0.963443 + 1.66873i) q^{46} +3.32765 q^{47} +1.00000 q^{48} +(-1.80351 - 3.12377i) q^{49} +(0.866025 + 0.500000i) q^{50} -2.25684i q^{51} +(-3.16873 + 1.82947i) q^{52} +(5.09487 + 8.82457i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-4.55456 - 2.62957i) q^{55} +(2.82051 + 1.62842i) q^{56} +(3.21087 - 1.85380i) q^{57} +(-1.68882 - 2.92512i) q^{58} +(-9.55745 + 5.51800i) q^{59} +1.00000i q^{60} +(-1.07094 - 0.618309i) q^{61} +(0.678359 + 1.17495i) q^{62} +3.25684 q^{63} -1.00000 q^{64} +(-1.82947 - 3.16873i) q^{65} -5.25915i q^{66} +(-6.93555 + 12.0127i) q^{67} +2.25684i q^{68} +(-1.66873 - 0.963443i) q^{69} +(-1.62842 + 2.82051i) q^{70} +(-0.215263 + 0.372847i) q^{71} +(-0.866025 + 0.500000i) q^{72} +4.23689 q^{73} +(-6.08275 + 0.0101124i) q^{74} -1.00000 q^{75} +(-3.21087 + 1.85380i) q^{76} +(8.56411 - 14.8335i) q^{77} +(1.82947 - 3.16873i) q^{78} +(6.26143 + 3.61504i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -5.47491i q^{82} +(6.83148 + 11.8325i) q^{83} -3.25684 q^{84} -2.25684 q^{85} +(-1.64180 - 2.84368i) q^{86} +(2.92512 + 1.68882i) q^{87} +5.25915i q^{88} +(-9.75521 + 5.63218i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(10.3201 - 5.95829i) q^{91} +(1.66873 + 0.963443i) q^{92} +(-1.17495 - 0.678359i) q^{93} +(2.88183 - 1.66383i) q^{94} +(-1.85380 - 3.21087i) q^{95} +(0.866025 - 0.500000i) q^{96} -4.69418i q^{97} +(-3.12377 - 1.80351i) q^{98} +(2.62957 + 4.55456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + O(q^{10}) \) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + 16q^{10} - 8q^{11} + 8q^{12} - 6q^{13} - 8q^{16} + 6q^{17} - 12q^{19} - 2q^{21} + 8q^{25} + 4q^{26} + 16q^{27} + 2q^{28} - 8q^{30} + 4q^{33} + 6q^{34} + 6q^{35} - 16q^{36} + 12q^{37} - 4q^{38} + 6q^{39} + 8q^{40} + 4q^{41} + 6q^{42} - 4q^{44} - 2q^{46} + 68q^{47} + 16q^{48} - 4q^{49} - 6q^{52} - 12q^{53} - 6q^{56} + 12q^{57} - 6q^{58} + 6q^{59} + 12q^{61} + 4q^{62} + 4q^{63} - 16q^{64} + 2q^{65} - 36q^{67} + 18q^{69} - 2q^{70} + 6q^{71} - 16q^{73} + 14q^{74} - 16q^{75} - 12q^{76} + 26q^{77} - 2q^{78} - 24q^{79} - 8q^{81} + 12q^{83} - 4q^{84} + 12q^{85} - 2q^{86} + 24q^{89} - 8q^{90} + 60q^{91} - 18q^{92} - 30q^{93} + 6q^{94} - 2q^{95} - 12q^{98} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.866025 + 0.500000i 0.387298 + 0.223607i
\(6\) 1.00000i 0.408248i
\(7\) −1.62842 + 2.82051i −0.615485 + 1.06605i 0.374814 + 0.927100i \(0.377707\pi\)
−0.990299 + 0.138952i \(0.955627\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.00000 0.316228
\(11\) −5.25915 −1.58569 −0.792846 0.609422i \(-0.791402\pi\)
−0.792846 + 0.609422i \(0.791402\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −3.16873 1.82947i −0.878848 0.507403i −0.00856971 0.999963i \(-0.502728\pi\)
−0.870278 + 0.492560i \(0.836061\pi\)
\(14\) 3.25684i 0.870428i
\(15\) −0.866025 + 0.500000i −0.223607 + 0.129099i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.95448 + 1.12842i −0.474032 + 0.273682i −0.717926 0.696119i \(-0.754908\pi\)
0.243894 + 0.969802i \(0.421575\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) −3.21087 1.85380i −0.736624 0.425290i 0.0842164 0.996447i \(-0.473161\pi\)
−0.820841 + 0.571157i \(0.806495\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) −1.62842 2.82051i −0.355351 0.615485i
\(22\) −4.55456 + 2.62957i −0.971035 + 0.560627i
\(23\) 1.92689i 0.401783i 0.979613 + 0.200892i \(0.0643839\pi\)
−0.979613 + 0.200892i \(0.935616\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) −3.65894 −0.717577
\(27\) 1.00000 0.192450
\(28\) 1.62842 + 2.82051i 0.307743 + 0.533026i
\(29\) 3.37764i 0.627212i −0.949553 0.313606i \(-0.898463\pi\)
0.949553 0.313606i \(-0.101537\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 1.35672i 0.243674i 0.992550 + 0.121837i \(0.0388785\pi\)
−0.992550 + 0.121837i \(0.961122\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 2.62957 4.55456i 0.457750 0.792846i
\(34\) −1.12842 + 1.95448i −0.193523 + 0.335191i
\(35\) −2.82051 + 1.62842i −0.476753 + 0.275253i
\(36\) −1.00000 −0.166667
\(37\) −5.27288 3.03262i −0.866855 0.498560i
\(38\) −3.70759 −0.601451
\(39\) 3.16873 1.82947i 0.507403 0.292949i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 2.73745 4.74141i 0.427518 0.740484i −0.569133 0.822245i \(-0.692721\pi\)
0.996652 + 0.0817615i \(0.0260546\pi\)
\(42\) −2.82051 1.62842i −0.435214 0.251271i
\(43\) 3.28360i 0.500745i −0.968150 0.250372i \(-0.919447\pi\)
0.968150 0.250372i \(-0.0805531\pi\)
\(44\) −2.62957 + 4.55456i −0.396423 + 0.686625i
\(45\) 1.00000i 0.149071i
\(46\) 0.963443 + 1.66873i 0.142052 + 0.246041i
\(47\) 3.32765 0.485388 0.242694 0.970103i \(-0.421969\pi\)
0.242694 + 0.970103i \(0.421969\pi\)
\(48\) 1.00000 0.144338
\(49\) −1.80351 3.12377i −0.257645 0.446254i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) 2.25684i 0.316021i
\(52\) −3.16873 + 1.82947i −0.439424 + 0.253702i
\(53\) 5.09487 + 8.82457i 0.699834 + 1.21215i 0.968524 + 0.248921i \(0.0800759\pi\)
−0.268690 + 0.963227i \(0.586591\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) −4.55456 2.62957i −0.614136 0.354572i
\(56\) 2.82051 + 1.62842i 0.376906 + 0.217607i
\(57\) 3.21087 1.85380i 0.425290 0.245541i
\(58\) −1.68882 2.92512i −0.221753 0.384087i
\(59\) −9.55745 + 5.51800i −1.24427 + 0.718382i −0.969962 0.243258i \(-0.921784\pi\)
−0.274313 + 0.961640i \(0.588450\pi\)
\(60\) 1.00000i 0.129099i
\(61\) −1.07094 0.618309i −0.137120 0.0791663i 0.429871 0.902890i \(-0.358559\pi\)
−0.566991 + 0.823724i \(0.691892\pi\)
\(62\) 0.678359 + 1.17495i 0.0861517 + 0.149219i
\(63\) 3.25684 0.410324
\(64\) −1.00000 −0.125000
\(65\) −1.82947 3.16873i −0.226918 0.393033i
\(66\) 5.25915i 0.647356i
\(67\) −6.93555 + 12.0127i −0.847312 + 1.46759i 0.0362858 + 0.999341i \(0.488447\pi\)
−0.883598 + 0.468246i \(0.844886\pi\)
\(68\) 2.25684i 0.273682i
\(69\) −1.66873 0.963443i −0.200892 0.115985i
\(70\) −1.62842 + 2.82051i −0.194634 + 0.337115i
\(71\) −0.215263 + 0.372847i −0.0255471 + 0.0442488i −0.878516 0.477712i \(-0.841466\pi\)
0.852969 + 0.521961i \(0.174799\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 4.23689 0.495891 0.247945 0.968774i \(-0.420245\pi\)
0.247945 + 0.968774i \(0.420245\pi\)
\(74\) −6.08275 + 0.0101124i −0.707106 + 0.00117555i
\(75\) −1.00000 −0.115470
\(76\) −3.21087 + 1.85380i −0.368312 + 0.212645i
\(77\) 8.56411 14.8335i 0.975971 1.69043i
\(78\) 1.82947 3.16873i 0.207147 0.358788i
\(79\) 6.26143 + 3.61504i 0.704466 + 0.406724i 0.809009 0.587797i \(-0.200004\pi\)
−0.104542 + 0.994520i \(0.533338\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 5.47491i 0.604602i
\(83\) 6.83148 + 11.8325i 0.749853 + 1.29878i 0.947893 + 0.318589i \(0.103209\pi\)
−0.198040 + 0.980194i \(0.563458\pi\)
\(84\) −3.25684 −0.355351
\(85\) −2.25684 −0.244789
\(86\) −1.64180 2.84368i −0.177040 0.306642i
\(87\) 2.92512 + 1.68882i 0.313606 + 0.181060i
\(88\) 5.25915i 0.560627i
\(89\) −9.75521 + 5.63218i −1.03405 + 0.597009i −0.918142 0.396251i \(-0.870311\pi\)
−0.115908 + 0.993260i \(0.536978\pi\)
\(90\) −0.500000 0.866025i −0.0527046 0.0912871i
\(91\) 10.3201 5.95829i 1.08184 0.624599i
\(92\) 1.66873 + 0.963443i 0.173977 + 0.100446i
\(93\) −1.17495 0.678359i −0.121837 0.0703426i
\(94\) 2.88183 1.66383i 0.297238 0.171611i
\(95\) −1.85380 3.21087i −0.190196 0.329428i
\(96\) 0.866025 0.500000i 0.0883883 0.0510310i
\(97\) 4.69418i 0.476622i −0.971189 0.238311i \(-0.923406\pi\)
0.971189 0.238311i \(-0.0765938\pi\)
\(98\) −3.12377 1.80351i −0.315549 0.182182i
\(99\) 2.62957 + 4.55456i 0.264282 + 0.457750i
\(100\) 1.00000 0.100000
\(101\) −9.91358 −0.986438 −0.493219 0.869905i \(-0.664180\pi\)
−0.493219 + 0.869905i \(0.664180\pi\)
\(102\) −1.12842 1.95448i −0.111730 0.193523i
\(103\) 11.0762i 1.09137i 0.837991 + 0.545684i \(0.183730\pi\)
−0.837991 + 0.545684i \(0.816270\pi\)
\(104\) −1.82947 + 3.16873i −0.179394 + 0.310720i
\(105\) 3.25684i 0.317835i
\(106\) 8.82457 + 5.09487i 0.857118 + 0.494857i
\(107\) −6.80147 + 11.7805i −0.657523 + 1.13886i 0.323732 + 0.946149i \(0.395062\pi\)
−0.981255 + 0.192714i \(0.938271\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) −6.42341 + 3.70856i −0.615251 + 0.355215i −0.775018 0.631939i \(-0.782259\pi\)
0.159767 + 0.987155i \(0.448926\pi\)
\(110\) −5.25915 −0.501440
\(111\) 5.26276 3.05013i 0.499519 0.289506i
\(112\) 3.25684 0.307743
\(113\) 0.273291 0.157785i 0.0257090 0.0148431i −0.487090 0.873352i \(-0.661942\pi\)
0.512799 + 0.858508i \(0.328608\pi\)
\(114\) 1.85380 3.21087i 0.173624 0.300726i
\(115\) −0.963443 + 1.66873i −0.0898415 + 0.155610i
\(116\) −2.92512 1.68882i −0.271591 0.156803i
\(117\) 3.65894i 0.338269i
\(118\) −5.51800 + 9.55745i −0.507973 + 0.879835i
\(119\) 7.35018i 0.673790i
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) 16.6586 1.51442
\(122\) −1.23662 −0.111958
\(123\) 2.73745 + 4.74141i 0.246828 + 0.427518i
\(124\) 1.17495 + 0.678359i 0.105514 + 0.0609185i
\(125\) 1.00000i 0.0894427i
\(126\) 2.82051 1.62842i 0.251271 0.145071i
\(127\) −7.33602 12.7064i −0.650966 1.12751i −0.982889 0.184200i \(-0.941031\pi\)
0.331923 0.943307i \(-0.392303\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 2.84368 + 1.64180i 0.250372 + 0.144553i
\(130\) −3.16873 1.82947i −0.277916 0.160455i
\(131\) −7.34599 + 4.24121i −0.641822 + 0.370556i −0.785316 0.619095i \(-0.787500\pi\)
0.143494 + 0.989651i \(0.454166\pi\)
\(132\) −2.62957 4.55456i −0.228875 0.396423i
\(133\) 10.4573 6.03753i 0.906763 0.523520i
\(134\) 13.8711i 1.19828i
\(135\) 0.866025 + 0.500000i 0.0745356 + 0.0430331i
\(136\) 1.12842 + 1.95448i 0.0967613 + 0.167596i
\(137\) 14.1845 1.21186 0.605931 0.795517i \(-0.292801\pi\)
0.605931 + 0.795517i \(0.292801\pi\)
\(138\) −1.92689 −0.164027
\(139\) −10.6538 18.4528i −0.903640 1.56515i −0.822733 0.568428i \(-0.807552\pi\)
−0.0809066 0.996722i \(-0.525782\pi\)
\(140\) 3.25684i 0.275253i
\(141\) −1.66383 + 2.88183i −0.140119 + 0.242694i
\(142\) 0.430527i 0.0361290i
\(143\) 16.6648 + 9.62144i 1.39358 + 0.804586i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 1.68882 2.92512i 0.140249 0.242918i
\(146\) 3.66926 2.11845i 0.303670 0.175324i
\(147\) 3.60702 0.297502
\(148\) −5.26276 + 3.05013i −0.432596 + 0.250720i
\(149\) 8.36723 0.685470 0.342735 0.939432i \(-0.388647\pi\)
0.342735 + 0.939432i \(0.388647\pi\)
\(150\) −0.866025 + 0.500000i −0.0707107 + 0.0408248i
\(151\) 6.96505 12.0638i 0.566808 0.981740i −0.430071 0.902795i \(-0.641512\pi\)
0.996879 0.0789449i \(-0.0251551\pi\)
\(152\) −1.85380 + 3.21087i −0.150363 + 0.260436i
\(153\) 1.95448 + 1.12842i 0.158011 + 0.0912275i
\(154\) 17.1282i 1.38023i
\(155\) −0.678359 + 1.17495i −0.0544871 + 0.0943745i
\(156\) 3.65894i 0.292949i
\(157\) −4.49155 7.77960i −0.358465 0.620880i 0.629240 0.777211i \(-0.283366\pi\)
−0.987705 + 0.156332i \(0.950033\pi\)
\(158\) 7.23008 0.575194
\(159\) −10.1897 −0.808098
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −5.43480 3.13778i −0.428322 0.247292i
\(162\) 1.00000i 0.0785674i
\(163\) 17.2881 9.98128i 1.35411 0.781794i 0.365286 0.930895i \(-0.380971\pi\)
0.988822 + 0.149101i \(0.0476380\pi\)
\(164\) −2.73745 4.74141i −0.213759 0.370242i
\(165\) 4.55456 2.62957i 0.354572 0.204712i
\(166\) 11.8325 + 6.83148i 0.918378 + 0.530226i
\(167\) −7.09782 4.09793i −0.549246 0.317107i 0.199572 0.979883i \(-0.436045\pi\)
−0.748818 + 0.662776i \(0.769378\pi\)
\(168\) −2.82051 + 1.62842i −0.217607 + 0.125635i
\(169\) 0.193909 + 0.335860i 0.0149161 + 0.0258354i
\(170\) −1.95448 + 1.12842i −0.149902 + 0.0865460i
\(171\) 3.70759i 0.283527i
\(172\) −2.84368 1.64180i −0.216829 0.125186i
\(173\) 7.96169 + 13.7901i 0.605316 + 1.04844i 0.992001 + 0.126227i \(0.0402868\pi\)
−0.386685 + 0.922212i \(0.626380\pi\)
\(174\) 3.37764 0.256058
\(175\) −3.25684 −0.246194
\(176\) 2.62957 + 4.55456i 0.198212 + 0.343313i
\(177\) 11.0360i 0.829516i
\(178\) −5.63218 + 9.75521i −0.422149 + 0.731184i
\(179\) 0.900657i 0.0673182i −0.999433 0.0336591i \(-0.989284\pi\)
0.999433 0.0336591i \(-0.0107161\pi\)
\(180\) −0.866025 0.500000i −0.0645497 0.0372678i
\(181\) 1.45760 2.52464i 0.108343 0.187655i −0.806756 0.590884i \(-0.798779\pi\)
0.915099 + 0.403229i \(0.132112\pi\)
\(182\) 5.95829 10.3201i 0.441658 0.764974i
\(183\) 1.07094 0.618309i 0.0791663 0.0457067i
\(184\) 1.92689 0.142052
\(185\) −3.05013 5.26276i −0.224250 0.386926i
\(186\) −1.35672 −0.0994794
\(187\) 10.2789 5.93453i 0.751669 0.433976i
\(188\) 1.66383 2.88183i 0.121347 0.210179i
\(189\) −1.62842 + 2.82051i −0.118450 + 0.205162i
\(190\) −3.21087 1.85380i −0.232941 0.134489i
\(191\) 27.0970i 1.96067i 0.197342 + 0.980335i \(0.436769\pi\)
−0.197342 + 0.980335i \(0.563231\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 16.6359i 1.19748i −0.800943 0.598740i \(-0.795668\pi\)
0.800943 0.598740i \(-0.204332\pi\)
\(194\) −2.34709 4.06528i −0.168511 0.291870i
\(195\) 3.65894 0.262022
\(196\) −3.60702 −0.257645
\(197\) −8.59600 14.8887i −0.612439 1.06078i −0.990828 0.135129i \(-0.956855\pi\)
0.378389 0.925647i \(-0.376478\pi\)
\(198\) 4.55456 + 2.62957i 0.323678 + 0.186876i
\(199\) 2.73511i 0.193887i −0.995290 0.0969433i \(-0.969093\pi\)
0.995290 0.0969433i \(-0.0309066\pi\)
\(200\) 0.866025 0.500000i 0.0612372 0.0353553i
\(201\) −6.93555 12.0127i −0.489196 0.847312i
\(202\) −8.58541 + 4.95679i −0.604067 + 0.348758i
\(203\) 9.52666 + 5.50022i 0.668640 + 0.386040i
\(204\) −1.95448 1.12842i −0.136841 0.0790053i
\(205\) 4.74141 2.73745i 0.331154 0.191192i
\(206\) 5.53809 + 9.59224i 0.385857 + 0.668323i
\(207\) 1.66873 0.963443i 0.115985 0.0669639i
\(208\) 3.65894i 0.253702i
\(209\) 16.8864 + 9.74939i 1.16806 + 0.674380i
\(210\) −1.62842 2.82051i −0.112372 0.194634i
\(211\) −18.8199 −1.29561 −0.647807 0.761804i \(-0.724314\pi\)
−0.647807 + 0.761804i \(0.724314\pi\)
\(212\) 10.1897 0.699834
\(213\) −0.215263 0.372847i −0.0147496 0.0255471i
\(214\) 13.6029i 0.929877i
\(215\) 1.64180 2.84368i 0.111970 0.193938i
\(216\) 1.00000i 0.0680414i
\(217\) −3.82664 2.20931i −0.259769 0.149978i
\(218\) −3.70856 + 6.42341i −0.251175 + 0.435048i
\(219\) −2.11845 + 3.66926i −0.143151 + 0.247945i
\(220\) −4.55456 + 2.62957i −0.307068 + 0.177286i
\(221\) 8.25764 0.555469
\(222\) 3.03262 5.27288i 0.203536 0.353892i
\(223\) 25.6392 1.71693 0.858466 0.512871i \(-0.171418\pi\)
0.858466 + 0.512871i \(0.171418\pi\)
\(224\) 2.82051 1.62842i 0.188453 0.108803i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) 0.157785 0.273291i 0.0104957 0.0181790i
\(227\) 14.0727 + 8.12488i 0.934039 + 0.539268i 0.888087 0.459676i \(-0.152034\pi\)
0.0459521 + 0.998944i \(0.485368\pi\)
\(228\) 3.70759i 0.245541i
\(229\) −5.87416 + 10.1743i −0.388176 + 0.672340i −0.992204 0.124623i \(-0.960228\pi\)
0.604029 + 0.796963i \(0.293561\pi\)
\(230\) 1.92689i 0.127055i
\(231\) 8.56411 + 14.8335i 0.563477 + 0.975971i
\(232\) −3.37764 −0.221753
\(233\) 10.3859 0.680403 0.340202 0.940353i \(-0.389505\pi\)
0.340202 + 0.940353i \(0.389505\pi\)
\(234\) 1.82947 + 3.16873i 0.119596 + 0.207147i
\(235\) 2.88183 + 1.66383i 0.187990 + 0.108536i
\(236\) 11.0360i 0.718382i
\(237\) −6.26143 + 3.61504i −0.406724 + 0.234822i
\(238\) −3.67509 6.36544i −0.238221 0.412610i
\(239\) 3.68278 2.12625i 0.238219 0.137536i −0.376139 0.926563i \(-0.622748\pi\)
0.614358 + 0.789027i \(0.289415\pi\)
\(240\) 0.866025 + 0.500000i 0.0559017 + 0.0322749i
\(241\) 5.12924 + 2.96137i 0.330403 + 0.190758i 0.656020 0.754743i \(-0.272239\pi\)
−0.325617 + 0.945502i \(0.605572\pi\)
\(242\) 14.4268 8.32932i 0.927390 0.535429i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −1.07094 + 0.618309i −0.0685601 + 0.0395832i
\(245\) 3.60702i 0.230444i
\(246\) 4.74141 + 2.73745i 0.302301 + 0.174534i
\(247\) 6.78293 + 11.7484i 0.431587 + 0.747531i
\(248\) 1.35672 0.0861517
\(249\) −13.6630 −0.865856
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 11.4250i 0.721137i 0.932733 + 0.360568i \(0.117417\pi\)
−0.932733 + 0.360568i \(0.882583\pi\)
\(252\) 1.62842 2.82051i 0.102581 0.177675i
\(253\) 10.1338i 0.637105i
\(254\) −12.7064 7.33602i −0.797267 0.460303i
\(255\) 1.12842 1.95448i 0.0706645 0.122394i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −20.3226 + 11.7333i −1.26769 + 0.731901i −0.974550 0.224169i \(-0.928033\pi\)
−0.293139 + 0.956070i \(0.594700\pi\)
\(258\) 3.28360 0.204428
\(259\) 17.1400 9.93381i 1.06503 0.617257i
\(260\) −3.65894 −0.226918
\(261\) −2.92512 + 1.68882i −0.181060 + 0.104535i
\(262\) −4.24121 + 7.34599i −0.262023 + 0.453837i
\(263\) 10.3985 18.0108i 0.641200 1.11059i −0.343965 0.938982i \(-0.611770\pi\)
0.985165 0.171609i \(-0.0548965\pi\)
\(264\) −4.55456 2.62957i −0.280314 0.161839i
\(265\) 10.1897i 0.625950i
\(266\) 6.03753 10.4573i 0.370184 0.641178i
\(267\) 11.2644i 0.689367i
\(268\) 6.93555 + 12.0127i 0.423656 + 0.733794i
\(269\) 20.4144 1.24469 0.622345 0.782743i \(-0.286180\pi\)
0.622345 + 0.782743i \(0.286180\pi\)
\(270\) 1.00000 0.0608581
\(271\) −9.87486 17.1038i −0.599855 1.03898i −0.992842 0.119435i \(-0.961892\pi\)
0.392987 0.919544i \(-0.371442\pi\)
\(272\) 1.95448 + 1.12842i 0.118508 + 0.0684206i
\(273\) 11.9166i 0.721224i
\(274\) 12.2841 7.09224i 0.742111 0.428458i
\(275\) −2.62957 4.55456i −0.158569 0.274650i
\(276\) −1.66873 + 0.963443i −0.100446 + 0.0579925i
\(277\) 0.559700 + 0.323143i 0.0336291 + 0.0194158i 0.516720 0.856154i \(-0.327153\pi\)
−0.483091 + 0.875570i \(0.660486\pi\)
\(278\) −18.4528 10.6538i −1.10673 0.638970i
\(279\) 1.17495 0.678359i 0.0703426 0.0406123i
\(280\) 1.62842 + 2.82051i 0.0973168 + 0.168558i
\(281\) −1.71343 + 0.989249i −0.102215 + 0.0590136i −0.550236 0.835009i \(-0.685462\pi\)
0.448021 + 0.894023i \(0.352129\pi\)
\(282\) 3.32765i 0.198159i
\(283\) −6.32516 3.65183i −0.375992 0.217079i 0.300081 0.953914i \(-0.402986\pi\)
−0.676073 + 0.736835i \(0.736320\pi\)
\(284\) 0.215263 + 0.372847i 0.0127735 + 0.0221244i
\(285\) 3.70759 0.219619
\(286\) 19.2429 1.13786
\(287\) 8.91546 + 15.4420i 0.526263 + 0.911514i
\(288\) 1.00000i 0.0589256i
\(289\) −5.95333 + 10.3115i −0.350196 + 0.606557i
\(290\) 3.37764i 0.198342i
\(291\) 4.06528 + 2.34709i 0.238311 + 0.137589i
\(292\) 2.11845 3.66926i 0.123973 0.214727i
\(293\) −5.66939 + 9.81967i −0.331209 + 0.573671i −0.982749 0.184943i \(-0.940790\pi\)
0.651540 + 0.758614i \(0.274123\pi\)
\(294\) 3.12377 1.80351i 0.182182 0.105183i
\(295\) −11.0360 −0.642541
\(296\) −3.03262 + 5.27288i −0.176267 + 0.306480i
\(297\) −5.25915 −0.305167
\(298\) 7.24623 4.18361i 0.419763 0.242350i
\(299\) 3.52518 6.10579i 0.203866 0.353107i
\(300\) −0.500000 + 0.866025i −0.0288675 + 0.0500000i
\(301\) 9.26143 + 5.34709i 0.533820 + 0.308201i
\(302\) 13.9301i 0.801587i
\(303\) 4.95679 8.58541i 0.284760 0.493219i
\(304\) 3.70759i 0.212645i
\(305\) −0.618309 1.07094i −0.0354043 0.0613220i
\(306\) 2.25684 0.129015
\(307\) −9.54245 −0.544616 −0.272308 0.962210i \(-0.587787\pi\)
−0.272308 + 0.962210i \(0.587787\pi\)
\(308\) −8.56411 14.8335i −0.487985 0.845215i
\(309\) −9.59224 5.53809i −0.545684 0.315051i
\(310\) 1.35672i 0.0770564i
\(311\) −11.7442 + 6.78050i −0.665951 + 0.384487i −0.794541 0.607211i \(-0.792288\pi\)
0.128590 + 0.991698i \(0.458955\pi\)
\(312\) −1.82947 3.16873i −0.103573 0.179394i
\(313\) 2.94389 1.69966i 0.166399 0.0960703i −0.414488 0.910055i \(-0.636039\pi\)
0.580887 + 0.813985i \(0.302706\pi\)
\(314\) −7.77960 4.49155i −0.439028 0.253473i
\(315\) 2.82051 + 1.62842i 0.158918 + 0.0917511i
\(316\) 6.26143 3.61504i 0.352233 0.203362i
\(317\) −9.98619 17.2966i −0.560880 0.971473i −0.997420 0.0717881i \(-0.977129\pi\)
0.436540 0.899685i \(-0.356204\pi\)
\(318\) −8.82457 + 5.09487i −0.494857 + 0.285706i
\(319\) 17.7635i 0.994565i
\(320\) −0.866025 0.500000i −0.0484123 0.0279508i
\(321\) −6.80147 11.7805i −0.379621 0.657523i
\(322\) −6.27556 −0.349724
\(323\) 8.36746 0.465578
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 3.65894i 0.202961i
\(326\) 9.98128 17.2881i 0.552812 0.957499i
\(327\) 7.41712i 0.410167i
\(328\) −4.74141 2.73745i −0.261801 0.151151i
\(329\) −5.41882 + 9.38567i −0.298749 + 0.517449i
\(330\) 2.62957 4.55456i 0.144753 0.250720i
\(331\) 8.55298 4.93807i 0.470114 0.271421i −0.246173 0.969226i \(-0.579173\pi\)
0.716288 + 0.697805i \(0.245840\pi\)
\(332\) 13.6630 0.749853
\(333\) 0.0101124 + 6.08275i 0.000554158 + 0.333333i
\(334\) −8.19586 −0.448457
\(335\) −12.0127 + 6.93555i −0.656325 + 0.378930i
\(336\) −1.62842 + 2.82051i −0.0888377 + 0.153871i
\(337\) −1.52567 + 2.64253i −0.0831084 + 0.143948i −0.904584 0.426296i \(-0.859818\pi\)
0.821475 + 0.570244i \(0.193151\pi\)
\(338\) 0.335860 + 0.193909i 0.0182684 + 0.0105473i
\(339\) 0.315569i 0.0171394i
\(340\) −1.12842 + 1.95448i −0.0611972 + 0.105997i
\(341\) 7.13518i 0.386392i
\(342\) 1.85380 + 3.21087i 0.100242 + 0.173624i
\(343\) −11.0504 −0.596665
\(344\) −3.28360 −0.177040
\(345\) −0.963443 1.66873i −0.0518700 0.0898415i
\(346\) 13.7901 + 7.96169i 0.741358 + 0.428023i
\(347\) 26.8643i 1.44215i 0.692855 + 0.721077i \(0.256353\pi\)
−0.692855 + 0.721077i \(0.743647\pi\)
\(348\) 2.92512 1.68882i 0.156803 0.0905302i
\(349\) −8.06293 13.9654i −0.431599 0.747551i 0.565412 0.824808i \(-0.308717\pi\)
−0.997011 + 0.0772571i \(0.975384\pi\)
\(350\) −2.82051 + 1.62842i −0.150763 + 0.0870428i
\(351\) −3.16873 1.82947i −0.169134 0.0976498i
\(352\) 4.55456 + 2.62957i 0.242759 + 0.140157i
\(353\) −15.0990 + 8.71739i −0.803636 + 0.463980i −0.844741 0.535175i \(-0.820246\pi\)
0.0411047 + 0.999155i \(0.486912\pi\)
\(354\) −5.51800 9.55745i −0.293278 0.507973i
\(355\) −0.372847 + 0.215263i −0.0197887 + 0.0114250i
\(356\) 11.2644i 0.597009i
\(357\) 6.36544 + 3.67509i 0.336895 + 0.194506i
\(358\) −0.450328 0.779992i −0.0238006 0.0412238i
\(359\) −5.13196 −0.270854 −0.135427 0.990787i \(-0.543241\pi\)
−0.135427 + 0.990787i \(0.543241\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −2.62687 4.54988i −0.138256 0.239467i
\(362\) 2.91520i 0.153220i
\(363\) −8.32932 + 14.4268i −0.437176 + 0.757211i
\(364\) 11.9166i 0.624599i
\(365\) 3.66926 + 2.11845i 0.192058 + 0.110885i
\(366\) 0.618309 1.07094i 0.0323195 0.0559791i
\(367\) −2.33684 + 4.04753i −0.121982 + 0.211279i −0.920549 0.390626i \(-0.872258\pi\)
0.798567 + 0.601906i \(0.205592\pi\)
\(368\) 1.66873 0.963443i 0.0869887 0.0502229i
\(369\) −5.47491 −0.285012
\(370\) −5.27288 3.03262i −0.274124 0.157658i
\(371\) −33.1864 −1.72295
\(372\) −1.17495 + 0.678359i −0.0609185 + 0.0351713i
\(373\) 13.4218 23.2473i 0.694956 1.20370i −0.275240 0.961376i \(-0.588757\pi\)
0.970196 0.242323i \(-0.0779093\pi\)
\(374\) 5.93453 10.2789i 0.306867 0.531510i
\(375\) −0.866025 0.500000i −0.0447214 0.0258199i
\(376\) 3.32765i 0.171611i
\(377\) −6.17928 + 10.7028i −0.318249 + 0.551224i
\(378\) 3.25684i 0.167514i
\(379\) −14.0580 24.3491i −0.722109 1.25073i −0.960153 0.279476i \(-0.909839\pi\)
0.238043 0.971255i \(-0.423494\pi\)
\(380\) −3.70759 −0.190196
\(381\) 14.6720 0.751671
\(382\) 13.5485 + 23.4667i 0.693201 + 1.20066i
\(383\) −22.9304 13.2389i −1.17169 0.676474i −0.217611 0.976036i \(-0.569826\pi\)
−0.954077 + 0.299561i \(0.903160\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 14.8335 8.56411i 0.755984 0.436467i
\(386\) −8.31797 14.4071i −0.423373 0.733304i
\(387\) −2.84368 + 1.64180i −0.144553 + 0.0834575i
\(388\) −4.06528 2.34709i −0.206383 0.119156i
\(389\) −24.6665 14.2412i −1.25064 0.722057i −0.279403 0.960174i \(-0.590136\pi\)
−0.971236 + 0.238117i \(0.923470\pi\)
\(390\) 3.16873 1.82947i 0.160455 0.0926387i
\(391\) −2.17434 3.76607i −0.109961 0.190458i
\(392\) −3.12377 + 1.80351i −0.157774 + 0.0910911i
\(393\) 8.48241i 0.427881i
\(394\) −14.8887 8.59600i −0.750082 0.433060i
\(395\) 3.61504 + 6.26143i 0.181892 + 0.315047i
\(396\) 5.25915 0.264282
\(397\) −21.6765 −1.08791 −0.543956 0.839114i \(-0.683074\pi\)
−0.543956 + 0.839114i \(0.683074\pi\)
\(398\) −1.36755 2.36867i −0.0685493 0.118731i
\(399\) 12.0751i 0.604509i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 8.46569i 0.422756i 0.977404 + 0.211378i \(0.0677951\pi\)
−0.977404 + 0.211378i \(0.932205\pi\)
\(402\) −12.0127 6.93555i −0.599140 0.345914i
\(403\) 2.48207 4.29908i 0.123641 0.214152i
\(404\) −4.95679 + 8.58541i −0.246609 + 0.427140i
\(405\) −0.866025 + 0.500000i −0.0430331 + 0.0248452i
\(406\) 11.0004 0.545942
\(407\) 27.7308 + 15.9490i 1.37457 + 0.790562i
\(408\) −2.25684 −0.111730
\(409\) −1.34173 + 0.774650i −0.0663445 + 0.0383040i −0.532805 0.846238i \(-0.678862\pi\)
0.466461 + 0.884542i \(0.345529\pi\)
\(410\) 2.73745 4.74141i 0.135193 0.234161i
\(411\) −7.09224 + 12.2841i −0.349834 + 0.605931i
\(412\) 9.59224 + 5.53809i 0.472576 + 0.272842i
\(413\) 35.9425i 1.76862i
\(414\) 0.963443 1.66873i 0.0473506 0.0820137i
\(415\) 13.6630i 0.670689i
\(416\) 1.82947 + 3.16873i 0.0896971 + 0.155360i
\(417\) 21.3075 1.04343
\(418\) 19.4988 0.953717
\(419\) −16.3095 28.2489i −0.796772 1.38005i −0.921708 0.387884i \(-0.873206\pi\)
0.124936 0.992165i \(-0.460127\pi\)
\(420\) −2.82051 1.62842i −0.137627 0.0794588i
\(421\) 2.38884i 0.116425i −0.998304 0.0582124i \(-0.981460\pi\)
0.998304 0.0582124i \(-0.0185401\pi\)
\(422\) −16.2985 + 9.40994i −0.793398 + 0.458069i
\(423\) −1.66383 2.88183i −0.0808980 0.140119i
\(424\) 8.82457 5.09487i 0.428559 0.247429i
\(425\) −1.95448 1.12842i −0.0948064 0.0547365i
\(426\) −0.372847 0.215263i −0.0180645 0.0104295i
\(427\) 3.48789 2.01373i 0.168791 0.0974515i
\(428\) 6.80147 + 11.7805i 0.328761 + 0.569431i
\(429\) −16.6648 + 9.62144i −0.804586 + 0.464528i
\(430\) 3.28360i 0.158349i
\(431\) 13.1116 + 7.56997i 0.631562 + 0.364633i 0.781357 0.624084i \(-0.214528\pi\)
−0.149795 + 0.988717i \(0.547861\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 33.0099 1.58635 0.793177 0.608991i \(-0.208425\pi\)
0.793177 + 0.608991i \(0.208425\pi\)
\(434\) −4.41862 −0.212100
\(435\) 1.68882 + 2.92512i 0.0809727 + 0.140249i
\(436\) 7.41712i 0.355215i
\(437\) 3.57206 6.18698i 0.170875 0.295963i
\(438\) 4.23689i 0.202447i
\(439\) 12.4278 + 7.17520i 0.593147 + 0.342454i 0.766341 0.642434i \(-0.222075\pi\)
−0.173194 + 0.984888i \(0.555409\pi\)
\(440\) −2.62957 + 4.55456i −0.125360 + 0.217130i
\(441\) −1.80351 + 3.12377i −0.0858815 + 0.148751i
\(442\) 7.15133 4.12882i 0.340154 0.196388i
\(443\) 2.18743 0.103928 0.0519639 0.998649i \(-0.483452\pi\)
0.0519639 + 0.998649i \(0.483452\pi\)
\(444\) −0.0101124 6.08275i −0.000479915 0.288675i
\(445\) −11.2644 −0.533981
\(446\) 22.2042 12.8196i 1.05140 0.607027i
\(447\) −4.18361 + 7.24623i −0.197878 + 0.342735i
\(448\) 1.62842 2.82051i 0.0769357 0.133257i
\(449\) −32.0199 18.4867i −1.51111 0.872441i −0.999916 0.0129764i \(-0.995869\pi\)
−0.511196 0.859464i \(-0.670797\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −14.3967 + 24.9358i −0.677913 + 1.17418i
\(452\) 0.315569i 0.0148431i
\(453\) 6.96505 + 12.0638i 0.327247 + 0.566808i
\(454\) 16.2498 0.762639
\(455\) 11.9166 0.558658
\(456\) −1.85380 3.21087i −0.0868120 0.150363i
\(457\) 13.9843 + 8.07387i 0.654160 + 0.377679i 0.790048 0.613045i \(-0.210055\pi\)
−0.135888 + 0.990724i \(0.543389\pi\)
\(458\) 11.7483i 0.548963i
\(459\) −1.95448 + 1.12842i −0.0912275 + 0.0526702i
\(460\) 0.963443 + 1.66873i 0.0449208 + 0.0778050i
\(461\) −18.0603 + 10.4271i −0.841152 + 0.485639i −0.857656 0.514224i \(-0.828080\pi\)
0.0165035 + 0.999864i \(0.494747\pi\)
\(462\) 14.8335 + 8.56411i 0.690116 + 0.398438i
\(463\) −32.8561 18.9695i −1.52695 0.881585i −0.999488 0.0320070i \(-0.989810\pi\)
−0.527463 0.849578i \(-0.676857\pi\)
\(464\) −2.92512 + 1.68882i −0.135795 + 0.0784014i
\(465\) −0.678359 1.17495i −0.0314582 0.0544871i
\(466\) 8.99446 5.19295i 0.416660 0.240559i
\(467\) 11.6625i 0.539676i −0.962906 0.269838i \(-0.913030\pi\)
0.962906 0.269838i \(-0.0869702\pi\)
\(468\) 3.16873 + 1.82947i 0.146475 + 0.0845672i
\(469\) −22.5880 39.1236i −1.04302 1.80656i
\(470\) 3.32765 0.153493
\(471\) 8.98311 0.413920
\(472\) 5.51800 + 9.55745i 0.253986 + 0.439917i
\(473\) 17.2690i 0.794028i
\(474\) −3.61504 + 6.26143i −0.166044 + 0.287597i
\(475\) 3.70759i 0.170116i
\(476\) −6.36544 3.67509i −0.291760 0.168448i
\(477\) 5.09487 8.82457i 0.233278 0.404049i
\(478\) 2.12625 3.68278i 0.0972526 0.168446i
\(479\) −32.7632 + 18.9158i −1.49699 + 0.864286i −0.999994 0.00346864i \(-0.998896\pi\)
−0.496993 + 0.867755i \(0.665563\pi\)
\(480\) 1.00000 0.0456435
\(481\) 11.1602 + 19.2561i 0.508864 + 0.878003i
\(482\) 5.92273 0.269773
\(483\) 5.43480 3.13778i 0.247292 0.142774i
\(484\) 8.32932 14.4268i 0.378605 0.655764i
\(485\) 2.34709 4.06528i 0.106576 0.184595i
\(486\) −0.866025 0.500000i −0.0392837 0.0226805i
\(487\) 34.0667i 1.54371i 0.635799 + 0.771855i \(0.280671\pi\)
−0.635799 + 0.771855i \(0.719329\pi\)
\(488\) −0.618309 + 1.07094i −0.0279895 + 0.0484793i
\(489\) 19.9626i 0.902738i
\(490\) −1.80351 3.12377i −0.0814744 0.141118i
\(491\) 33.6933 1.52056 0.760278 0.649598i \(-0.225063\pi\)
0.760278 + 0.649598i \(0.225063\pi\)
\(492\) 5.47491 0.246828
\(493\) 3.81140 + 6.60154i 0.171657 + 0.297318i
\(494\) 11.7484 + 6.78293i 0.528584 + 0.305178i
\(495\) 5.25915i 0.236381i
\(496\) 1.17495 0.678359i 0.0527569 0.0304592i
\(497\) −0.701079 1.21430i −0.0314477 0.0544690i
\(498\) −11.8325 + 6.83148i −0.530226 + 0.306126i
\(499\) −0.744312 0.429729i −0.0333200 0.0192373i 0.483247 0.875484i \(-0.339457\pi\)
−0.516567 + 0.856246i \(0.672790\pi\)
\(500\) 0.866025 + 0.500000i 0.0387298 + 0.0223607i
\(501\) 7.09782 4.09793i 0.317107 0.183082i
\(502\) 5.71248 + 9.89430i 0.254960 + 0.441604i
\(503\) 32.4710 18.7472i 1.44781 0.835895i 0.449461 0.893300i \(-0.351616\pi\)
0.998351 + 0.0574051i \(0.0182827\pi\)
\(504\) 3.25684i 0.145071i
\(505\) −8.58541 4.95679i −0.382046 0.220574i
\(506\) −5.06689 8.77611i −0.225251 0.390146i
\(507\) −0.387818 −0.0172236
\(508\) −14.6720 −0.650966
\(509\) 13.1662 + 22.8045i 0.583580 + 1.01079i 0.995051 + 0.0993671i \(0.0316818\pi\)
−0.411471 + 0.911423i \(0.634985\pi\)
\(510\) 2.25684i 0.0999347i
\(511\) −6.89945 + 11.9502i −0.305214 + 0.528646i
\(512\) 1.00000i 0.0441942i
\(513\) −3.21087 1.85380i −0.141763 0.0818471i
\(514\) −11.7333 + 20.3226i −0.517532 + 0.896392i
\(515\) −5.53809 + 9.59224i −0.244037 + 0.422685i
\(516\) 2.84368 1.64180i 0.125186 0.0722763i
\(517\) −17.5006 −0.769676
\(518\) 9.87676 17.1729i 0.433960 0.754535i
\(519\) −15.9234 −0.698959
\(520\) −3.16873 + 1.82947i −0.138958 + 0.0802275i
\(521\) 0.172543 0.298854i 0.00755926 0.0130930i −0.862221 0.506532i \(-0.830927\pi\)
0.869780 + 0.493439i \(0.164260\pi\)
\(522\) −1.68882 + 2.92512i −0.0739176 + 0.128029i
\(523\) 33.3875 + 19.2763i 1.45993 + 0.842893i 0.999007 0.0445455i \(-0.0141840\pi\)
0.460926 + 0.887439i \(0.347517\pi\)
\(524\) 8.48241i 0.370556i
\(525\) 1.62842 2.82051i 0.0710701 0.123097i
\(526\) 20.7970i 0.906794i
\(527\) −1.53095 2.65168i −0.0666892 0.115509i
\(528\) −5.25915 −0.228875
\(529\) 19.2871 0.838570
\(530\) 5.09487 + 8.82457i 0.221307 + 0.383315i
\(531\) 9.55745 + 5.51800i 0.414758 + 0.239461i
\(532\) 12.0751i 0.523520i
\(533\) −17.3485 + 10.0162i −0.751448 + 0.433848i
\(534\) −5.63218 9.75521i −0.243728 0.422149i
\(535\) −11.7805 + 6.80147i −0.509315 + 0.294053i
\(536\) 12.0127 + 6.93555i 0.518871 + 0.299570i
\(537\) 0.779992 + 0.450328i 0.0336591 + 0.0194331i
\(538\) 17.6794 10.2072i 0.762214 0.440064i
\(539\) 9.48494 + 16.4284i 0.408545 + 0.707621i
\(540\) 0.866025 0.500000i 0.0372678 0.0215166i
\(541\) 0.789062i 0.0339244i 0.999856 + 0.0169622i \(0.00539950\pi\)
−0.999856 + 0.0169622i \(0.994601\pi\)
\(542\) −17.1038 9.87486i −0.734669 0.424162i
\(543\) 1.45760 + 2.52464i 0.0625517 + 0.108343i
\(544\) 2.25684 0.0967613
\(545\) −7.41712 −0.317714
\(546\) 5.95829 + 10.3201i 0.254991 + 0.441658i
\(547\) 27.8104i 1.18909i 0.804063 + 0.594544i \(0.202668\pi\)
−0.804063 + 0.594544i \(0.797332\pi\)
\(548\) 7.09224 12.2841i 0.302965 0.524752i
\(549\) 1.23662i 0.0527776i
\(550\) −4.55456 2.62957i −0.194207 0.112125i
\(551\) −6.26145 + 10.8452i −0.266747 + 0.462019i
\(552\) −0.963443 + 1.66873i −0.0410069 + 0.0710260i
\(553\) −20.3925 + 11.7736i −0.867178 + 0.500665i
\(554\) 0.646286 0.0274581
\(555\) 6.08275 0.0101124i 0.258199 0.000429249i
\(556\) −21.3075 −0.903640
\(557\) 8.64914 4.99358i 0.366476 0.211585i −0.305442 0.952211i \(-0.598804\pi\)
0.671918 + 0.740626i \(0.265471\pi\)
\(558\) 0.678359 1.17495i 0.0287172 0.0497397i
\(559\) −6.00725 + 10.4049i −0.254080 + 0.440079i
\(560\) 2.82051 + 1.62842i 0.119188 + 0.0688134i
\(561\) 11.8691i 0.501113i
\(562\) −0.989249 + 1.71343i −0.0417289 + 0.0722766i
\(563\) 35.7694i 1.50750i 0.657161 + 0.753751i \(0.271757\pi\)
−0.657161 + 0.753751i \(0.728243\pi\)
\(564\) 1.66383 + 2.88183i 0.0700597 + 0.121347i
\(565\) 0.315569 0.0132761
\(566\) −7.30367 −0.306996
\(567\) −1.62842 2.82051i −0.0683873 0.118450i
\(568\) 0.372847 + 0.215263i 0.0156443 + 0.00903225i
\(569\) 1.94164i 0.0813977i 0.999171 + 0.0406989i \(0.0129584\pi\)
−0.999171 + 0.0406989i \(0.987042\pi\)
\(570\) 3.21087 1.85380i 0.134489 0.0776470i
\(571\) −12.2709 21.2539i −0.513523 0.889448i −0.999877 0.0156863i \(-0.995007\pi\)
0.486354 0.873762i \(-0.338327\pi\)
\(572\) 16.6648 9.62144i 0.696792 0.402293i
\(573\) −23.4667 13.5485i −0.980335 0.565996i
\(574\) 15.4420 + 8.91546i 0.644538 + 0.372124i
\(575\) −1.66873 + 0.963443i −0.0695909 + 0.0401783i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 16.6742 9.62685i 0.694156 0.400771i −0.111011 0.993819i \(-0.535409\pi\)
0.805167 + 0.593048i \(0.202076\pi\)
\(578\) 11.9067i 0.495252i
\(579\) 14.4071 + 8.31797i 0.598740 + 0.345683i
\(580\) −1.68882 2.92512i −0.0701244 0.121459i
\(581\) −44.4981 −1.84609
\(582\) 4.69418 0.194580
\(583\) −26.7947 46.4097i −1.10972 1.92209i
\(584\) 4.23689i 0.175324i
\(585\) −1.82947 + 3.16873i −0.0756392 + 0.131011i
\(586\) 11.3388i 0.468400i
\(587\) −0.346155 0.199853i −0.0142873 0.00824880i 0.492839 0.870120i \(-0.335959\pi\)
−0.507127 + 0.861872i \(0.669292\pi\)
\(588\) 1.80351 3.12377i 0.0743756 0.128822i
\(589\) 2.51508 4.35625i 0.103632 0.179496i
\(590\) −9.55745 + 5.51800i −0.393474 + 0.227172i
\(591\) 17.1920 0.707184
\(592\) 0.0101124 + 6.08275i 0.000415618 + 0.250000i
\(593\) −14.6432 −0.601325 −0.300663 0.953731i \(-0.597208\pi\)
−0.300663 + 0.953731i \(0.597208\pi\)
\(594\) −4.55456 + 2.62957i −0.186876 + 0.107893i
\(595\) 3.67509 6.36544i 0.150664 0.260958i
\(596\) 4.18361 7.24623i 0.171367 0.296817i
\(597\) 2.36867 + 1.36755i 0.0969433 + 0.0559702i
\(598\) 7.05035i 0.288310i
\(599\) 6.43257 11.1415i 0.262828 0.455231i −0.704165 0.710037i \(-0.748678\pi\)
0.966992 + 0.254806i \(0.0820116\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) 8.59490 + 14.8868i 0.350593 + 0.607246i 0.986354 0.164641i \(-0.0526466\pi\)
−0.635760 + 0.771887i \(0.719313\pi\)
\(602\) 10.6942 0.435862
\(603\) 13.8711 0.564875
\(604\) −6.96505 12.0638i −0.283404 0.490870i
\(605\) 14.4268 + 8.32932i 0.586533 + 0.338635i
\(606\) 9.91358i 0.402712i
\(607\) −42.1054 + 24.3095i −1.70900 + 0.986694i −0.773208 + 0.634152i \(0.781349\pi\)
−0.935796 + 0.352542i \(0.885317\pi\)
\(608\) 1.85380 + 3.21087i 0.0751814 + 0.130218i
\(609\) −9.52666 + 5.50022i −0.386040 + 0.222880i
\(610\) −1.07094 0.618309i −0.0433612 0.0250346i
\(611\) −10.5444 6.08783i −0.426582 0.246287i
\(612\) 1.95448 1.12842i 0.0790053 0.0456137i
\(613\) 14.6936 + 25.4501i 0.593471 + 1.02792i 0.993761 + 0.111533i \(0.0355761\pi\)
−0.400290 + 0.916389i \(0.631091\pi\)
\(614\) −8.26401 + 4.77123i −0.333508 + 0.192551i
\(615\) 5.47491i 0.220770i
\(616\) −14.8335 8.56411i −0.597658 0.345058i
\(617\) −7.39870 12.8149i −0.297860 0.515909i 0.677786 0.735259i \(-0.262940\pi\)
−0.975646 + 0.219350i \(0.929606\pi\)
\(618\) −11.0762 −0.445549
\(619\) −38.0010 −1.52739 −0.763694 0.645579i \(-0.776616\pi\)
−0.763694 + 0.645579i \(0.776616\pi\)
\(620\) 0.678359 + 1.17495i 0.0272436 + 0.0471872i
\(621\) 1.92689i 0.0773233i
\(622\) −6.78050 + 11.7442i −0.271873 + 0.470899i
\(623\) 36.6862i 1.46980i
\(624\) −3.16873 1.82947i −0.126851 0.0732373i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 1.69966 2.94389i 0.0679320 0.117662i
\(627\) −16.8864 + 9.74939i −0.674380 + 0.389353i
\(628\) −8.98311 −0.358465
\(629\) 13.7278 0.0228222i 0.547364 0.000909979i
\(630\) 3.25684 0.129756
\(631\) −42.9542 + 24.7996i −1.70998 + 0.987258i −0.775425 + 0.631440i \(0.782464\pi\)
−0.934555 + 0.355818i \(0.884202\pi\)
\(632\) 3.61504 6.26143i 0.143799 0.249066i
\(633\) 9.40994 16.2985i 0.374012 0.647807i
\(634\) −17.2966 9.98619i −0.686935 0.396602i
\(635\) 14.6720i 0.582242i
\(636\) −5.09487 + 8.82457i −0.202025 + 0.349917i
\(637\) 13.1979i 0.522919i
\(638\) 8.88175 + 15.3836i 0.351632 + 0.609044i
\(639\) 0.430527 0.0170314
\(640\) −1.00000 −0.0395285
\(641\) −16.7195 28.9590i −0.660379 1.14381i −0.980516 0.196439i \(-0.937062\pi\)
0.320137 0.947371i \(-0.396271\pi\)
\(642\) −11.7805 6.80147i −0.464939 0.268432i
\(643\) 33.3367i 1.31467i 0.753598 + 0.657336i \(0.228317\pi\)
−0.753598 + 0.657336i \(0.771683\pi\)
\(644\) −5.43480 + 3.13778i −0.214161 + 0.123646i
\(645\) 1.64180 + 2.84368i 0.0646459 + 0.111970i
\(646\) 7.24643 4.18373i 0.285107 0.164607i
\(647\) 14.3341 + 8.27578i 0.563530 + 0.325354i 0.754561 0.656230i \(-0.227850\pi\)
−0.191031 + 0.981584i \(0.561183\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 50.2641 29.0200i 1.97304 1.13913i
\(650\) −1.82947 3.16873i −0.0717577 0.124288i
\(651\) 3.82664 2.20931i 0.149978 0.0865897i
\(652\) 19.9626i 0.781794i
\(653\) 4.84180 + 2.79541i 0.189474 + 0.109393i 0.591736 0.806132i \(-0.298443\pi\)
−0.402262 + 0.915525i \(0.631776\pi\)
\(654\) −3.70856 6.42341i −0.145016 0.251175i
\(655\) −8.48241 −0.331435
\(656\) −5.47491 −0.213759
\(657\) −2.11845 3.66926i −0.0826485 0.143151i
\(658\) 10.8376i 0.422495i
\(659\) 9.79210 16.9604i 0.381446 0.660684i −0.609823 0.792538i \(-0.708759\pi\)
0.991269 + 0.131853i \(0.0420928\pi\)
\(660\) 5.25915i 0.204712i
\(661\) −9.20675 5.31552i −0.358101 0.206750i 0.310146 0.950689i \(-0.399622\pi\)
−0.668248 + 0.743939i \(0.732955\pi\)
\(662\) 4.93807 8.55298i 0.191923 0.332421i
\(663\) −4.12882 + 7.15133i −0.160350 + 0.277735i
\(664\) 11.8325 6.83148i 0.459189 0.265113i
\(665\) 12.0751 0.468250
\(666\) 3.05013 + 5.26276i 0.118190 + 0.203928i
\(667\) 6.50832 0.252003
\(668\) −7.09782 + 4.09793i −0.274623 + 0.158554i
\(669\) −12.8196 + 22.2042i −0.495635 + 0.858466i
\(670\) −6.93555 + 12.0127i −0.267944 + 0.464092i
\(671\) 5.63224 + 3.25178i 0.217430 + 0.125533i
\(672\) 3.25684i 0.125635i
\(673\) −11.6444 + 20.1688i −0.448860 + 0.777449i −0.998312 0.0580767i \(-0.981503\pi\)
0.549452 + 0.835525i \(0.314837\pi\)
\(674\) 3.05134i 0.117533i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 0.387818 0.0149161
\(677\) −19.3235 −0.742661 −0.371331 0.928501i \(-0.621098\pi\)
−0.371331 + 0.928501i \(0.621098\pi\)
\(678\) 0.157785 + 0.273291i 0.00605968 + 0.0104957i
\(679\) 13.2400 + 7.64411i 0.508104 + 0.293354i
\(680\) 2.25684i 0.0865460i
\(681\) −14.0727 + 8.12488i −0.539268 + 0.311346i
\(682\) −3.56759 6.17925i −0.136610 0.236616i
\(683\) 9.23123 5.32965i 0.353223 0.203933i −0.312881 0.949792i \(-0.601294\pi\)
0.666104 + 0.745859i \(0.267961\pi\)
\(684\) 3.21087 + 1.85380i 0.122771 + 0.0708817i
\(685\) 12.2841 + 7.09224i 0.469352 + 0.270981i
\(686\) −9.56992 + 5.52519i −0.365381 + 0.210953i
\(687\) −5.87416 10.1743i −0.224113 0.388176i
\(688\) −2.84368 + 1.64180i −0.108414 + 0.0625931i
\(689\) 37.2836i 1.42039i
\(690\) −1.66873 0.963443i −0.0635275 0.0366776i
\(691\) −15.6445 27.0971i −0.595146 1.03082i −0.993526 0.113603i \(-0.963761\pi\)
0.398380 0.917220i \(-0.369572\pi\)
\(692\) 15.9234 0.605316
\(693\) −17.1282 −0.650647
\(694\) 13.4322 + 23.2652i 0.509878 + 0.883135i
\(695\) 21.3075i 0.808240i
\(696\) 1.68882 2.92512i 0.0640145 0.110876i
\(697\) 12.3560i 0.468017i
\(698\) −13.9654 8.06293i −0.528599 0.305187i
\(699\) −5.19295 + 8.99446i −0.196415 + 0.340202i
\(700\) −1.62842 + 2.82051i −0.0615485 + 0.106605i
\(701\) 30.0642 17.3576i 1.13551 0.655586i 0.190194 0.981746i \(-0.439088\pi\)
0.945315 + 0.326160i \(0.105755\pi\)
\(702\) −3.65894 −0.138098
\(703\) 11.3087 + 19.5122i 0.426514 + 0.735916i
\(704\) 5.25915 0.198212
\(705\) −2.88183 + 1.66383i −0.108536 + 0.0626633i
\(706\) −8.71739 + 15.0990i −0.328083 + 0.568257i
\(707\) 16.1435 27.9613i 0.607138 1.05159i
\(708\) −9.55745 5.51800i −0.359191 0.207379i
\(709\) 14.9127i 0.560056i 0.959992 + 0.280028i \(0.0903438\pi\)
−0.959992 + 0.280028i \(0.909656\pi\)
\(710\) −0.215263 + 0.372847i −0.00807869 + 0.0139927i
\(711\) 7.23008i 0.271149i
\(712\) 5.63218 + 9.75521i 0.211075 + 0.365592i
\(713\) −2.61424 −0.0979041
\(714\) 7.35018 0.275074
\(715\) 9.62144 + 16.6648i 0.359822 + 0.623229i
\(716\) −0.779992 0.450328i −0.0291497 0.0168296i
\(717\) 4.25251i 0.158813i
\(718\) −4.44441 + 2.56598i −0.165864 + 0.0957615i
\(719\) 24.6771 + 42.7419i 0.920300 + 1.59401i 0.798951 + 0.601396i \(0.205388\pi\)
0.121348 + 0.992610i \(0.461278\pi\)
\(720\) −0.866025 + 0.500000i −0.0322749 + 0.0186339i
\(721\) −31.2404 18.0367i −1.16345 0.671721i
\(722\) −4.54988 2.62687i −0.169329 0.0977621i
\(723\) −5.12924 + 2.96137i −0.190758 + 0.110134i
\(724\) −1.45760 2.52464i −0.0541713 0.0938275i
\(725\) 2.92512 1.68882i 0.108636 0.0627212i
\(726\) 16.6586i 0.618260i
\(727\) −16.9389 9.77968i −0.628229 0.362708i 0.151837 0.988406i \(-0.451481\pi\)
−0.780066 + 0.625697i \(0.784815\pi\)
\(728\) −5.95829 10.3201i −0.220829 0.382487i
\(729\) 1.00000 0.0370370
\(730\) 4.23689 0.156814
\(731\) 3.70529 + 6.41775i 0.137045 + 0.237369i
\(732\) 1.23662i 0.0457067i
\(733\) −3.88876 + 6.73552i −0.143635 + 0.248782i −0.928863 0.370424i \(-0.879212\pi\)
0.785228 + 0.619207i \(0.212546\pi\)
\(734\) 4.67369i 0.172509i
\(735\) 3.12377 + 1.80351i 0.115222 + 0.0665235i
\(736\) 0.963443 1.66873i 0.0355130 0.0615103i
\(737\) 36.4751 63.1767i 1.34358 2.32714i
\(738\) −4.74141 + 2.73745i −0.174534 + 0.100767i
\(739\) 9.29956 0.342090 0.171045 0.985263i \(-0.445286\pi\)
0.171045 + 0.985263i \(0.445286\pi\)
\(740\) −6.08275 + 0.0101124i −0.223606 + 0.000371740i
\(741\) −13.5659 −0.498354
\(742\) −28.7402 + 16.5932i −1.05509 + 0.609155i
\(743\) 6.76607 11.7192i 0.248223 0.429935i −0.714810 0.699319i \(-0.753487\pi\)
0.963033 + 0.269384i \(0.0868201\pi\)
\(744\) −0.678359 + 1.17495i −0.0248699 + 0.0430759i
\(745\) 7.24623 + 4.18361i 0.265481 + 0.153276i
\(746\) 26.8436i 0.982816i
\(747\) 6.83148 11.8325i 0.249951 0.432928i
\(748\) 11.8691i 0.433976i
\(749\) −22.1513 38.3672i −0.809391 1.40191i
\(750\) −1.00000 −0.0365148
\(751\) −2.87915 −0.105062 −0.0525309 0.998619i \(-0.516729\pi\)
−0.0525309 + 0.998619i \(0.516729\pi\)
\(752\) −1.66383 2.88183i −0.0606735 0.105090i
\(753\) −9.89430 5.71248i −0.360568 0.208174i
\(754\) 12.3586i 0.450072i
\(755\) 12.0638 6.96505i 0.439047 0.253484i
\(756\) 1.62842 + 2.82051i 0.0592251 + 0.102581i
\(757\) −26.6459 + 15.3840i −0.968463 + 0.559143i −0.898767 0.438426i \(-0.855536\pi\)
−0.0696959 + 0.997568i \(0.522203\pi\)
\(758\) −24.3491 14.0580i −0.884400 0.510608i
\(759\) 8.77611 + 5.06689i 0.318553 + 0.183916i
\(760\) −3.21087 + 1.85380i −0.116471 + 0.0672443i
\(761\) 5.21225 + 9.02789i 0.188944 + 0.327261i 0.944898 0.327364i \(-0.106160\pi\)
−0.755954 + 0.654624i \(0.772827\pi\)
\(762\) 12.7064 7.33602i 0.460303 0.265756i
\(763\) 24.1564i 0.874520i
\(764\) 23.4667 + 13.5485i 0.848995 + 0.490167i
\(765\) 1.12842 + 1.95448i 0.0407982 + 0.0706645i
\(766\) −26.4777 −0.956679
\(767\) 40.3800 1.45804
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 10.2078i 0.368104i −0.982917 0.184052i \(-0.941079\pi\)
0.982917 0.184052i \(-0.0589214\pi\)
\(770\) 8.56411 14.8335i 0.308629 0.534561i
\(771\) 23.4665i 0.845126i
\(772\) −14.4071 8.31797i −0.518524 0.299370i
\(773\) −15.3580 + 26.6008i −0.552389 + 0.956765i 0.445713 + 0.895176i \(0.352950\pi\)
−0.998102 + 0.0615892i \(0.980383\pi\)
\(774\) −1.64180 + 2.84368i −0.0590134 + 0.102214i
\(775\) −1.17495 + 0.678359i −0.0422055 + 0.0243674i
\(776\) −4.69418 −0.168511
\(777\)