Properties

Label 456.2.bf.a.65.1
Level $456$
Weight $2$
Character 456.65
Analytic conductor $3.641$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.64117833217\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.1
Root \(-1.18614 + 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 456.65
Dual form 456.2.bf.a.449.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.18614 + 1.26217i) q^{3} +(0.686141 + 0.396143i) q^{5} -2.37228 q^{7} +(-0.186141 - 2.99422i) q^{9} +O(q^{10})\) \(q+(-1.18614 + 1.26217i) q^{3} +(0.686141 + 0.396143i) q^{5} -2.37228 q^{7} +(-0.186141 - 2.99422i) q^{9} +3.46410i q^{11} +(-2.87228 + 1.65831i) q^{13} +(-1.31386 + 0.396143i) q^{15} +(0.686141 + 0.396143i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(2.81386 - 2.99422i) q^{21} +(-6.43070 + 3.71277i) q^{23} +(-2.18614 - 3.78651i) q^{25} +(4.00000 + 3.31662i) q^{27} +(-2.68614 - 4.65253i) q^{29} -4.40387i q^{31} +(-4.37228 - 4.10891i) q^{33} +(-1.62772 - 0.939764i) q^{35} +7.86797i q^{37} +(1.31386 - 5.59230i) q^{39} +(-0.313859 + 0.543620i) q^{41} +(-0.127719 + 0.221215i) q^{43} +(1.05842 - 2.12819i) q^{45} +(-3.68614 + 2.12819i) q^{47} -1.37228 q^{49} +(-1.31386 + 0.396143i) q^{51} +(5.68614 + 9.84868i) q^{53} +(-1.37228 + 2.37686i) q^{55} +(6.93070 - 2.99422i) q^{57} +(-3.68614 + 6.38458i) q^{59} +(0.500000 + 0.866025i) q^{61} +(0.441578 + 7.10313i) q^{63} -2.62772 q^{65} +(10.2446 - 5.91470i) q^{67} +(2.94158 - 12.5205i) q^{69} +(-3.31386 + 5.73977i) q^{71} +(2.87228 - 4.97494i) q^{73} +(7.37228 + 1.73205i) q^{75} -8.21782i q^{77} +(9.98913 + 5.76722i) q^{79} +(-8.93070 + 1.11469i) q^{81} -3.46410i q^{83} +(0.313859 + 0.543620i) q^{85} +(9.05842 + 2.12819i) q^{87} +(3.68614 + 6.38458i) q^{89} +(6.81386 - 3.93398i) q^{91} +(5.55842 + 5.22360i) q^{93} +(-2.05842 - 2.77300i) q^{95} +(11.0584 + 6.38458i) q^{97} +(10.3723 - 0.644810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{3} - 3q^{5} + 2q^{7} + 5q^{9} + O(q^{10}) \) \( 4q + q^{3} - 3q^{5} + 2q^{7} + 5q^{9} - 11q^{15} - 3q^{17} - 16q^{19} + 17q^{21} + 3q^{23} - 3q^{25} + 16q^{27} - 5q^{29} - 6q^{33} - 18q^{35} + 11q^{39} - 7q^{41} - 12q^{43} - 13q^{45} - 9q^{47} + 6q^{49} - 11q^{51} + 17q^{53} + 6q^{55} - q^{57} - 9q^{59} + 2q^{61} + 19q^{63} - 22q^{65} + 18q^{67} + 29q^{69} - 19q^{71} + 18q^{75} - 6q^{79} - 7q^{81} + 7q^{85} + 19q^{87} + 9q^{89} + 33q^{91} + 5q^{93} + 9q^{95} + 27q^{97} + 30q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(343\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(1\)

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 0
\(3\) −1.18614 + 1.26217i −0.684819 + 0.728714i
\(4\) 0 0
\(5\) 0.686141 + 0.396143i 0.306851 + 0.177161i 0.645517 0.763746i \(-0.276642\pi\)
−0.338665 + 0.940907i \(0.609975\pi\)
\(6\) 0 0
\(7\) −2.37228 −0.896638 −0.448319 0.893874i \(-0.647977\pi\)
−0.448319 + 0.893874i \(0.647977\pi\)
\(8\) 0 0
\(9\) −0.186141 2.99422i −0.0620469 0.998073i
\(10\) 0 0
\(11\) 3.46410i 1.04447i 0.852803 + 0.522233i \(0.174901\pi\)
−0.852803 + 0.522233i \(0.825099\pi\)
\(12\) 0 0
\(13\) −2.87228 + 1.65831i −0.796628 + 0.459933i −0.842291 0.539024i \(-0.818793\pi\)
0.0456630 + 0.998957i \(0.485460\pi\)
\(14\) 0 0
\(15\) −1.31386 + 0.396143i −0.339237 + 0.102284i
\(16\) 0 0
\(17\) 0.686141 + 0.396143i 0.166414 + 0.0960789i 0.580894 0.813979i \(-0.302703\pi\)
−0.414480 + 0.910058i \(0.636037\pi\)
\(18\) 0 0
\(19\) −4.00000 1.73205i −0.917663 0.397360i
\(20\) 0 0
\(21\) 2.81386 2.99422i 0.614034 0.653392i
\(22\) 0 0
\(23\) −6.43070 + 3.71277i −1.34089 + 0.774166i −0.986939 0.161096i \(-0.948497\pi\)
−0.353956 + 0.935262i \(0.615164\pi\)
\(24\) 0 0
\(25\) −2.18614 3.78651i −0.437228 0.757301i
\(26\) 0 0
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) 0 0
\(29\) −2.68614 4.65253i −0.498804 0.863954i 0.501195 0.865334i \(-0.332894\pi\)
−0.999999 + 0.00138070i \(0.999561\pi\)
\(30\) 0 0
\(31\) 4.40387i 0.790958i −0.918475 0.395479i \(-0.870579\pi\)
0.918475 0.395479i \(-0.129421\pi\)
\(32\) 0 0
\(33\) −4.37228 4.10891i −0.761116 0.715270i
\(34\) 0 0
\(35\) −1.62772 0.939764i −0.275135 0.158849i
\(36\) 0 0
\(37\) 7.86797i 1.29349i 0.762708 + 0.646743i \(0.223869\pi\)
−0.762708 + 0.646743i \(0.776131\pi\)
\(38\) 0 0
\(39\) 1.31386 5.59230i 0.210386 0.895484i
\(40\) 0 0
\(41\) −0.313859 + 0.543620i −0.0490166 + 0.0848992i −0.889493 0.456949i \(-0.848942\pi\)
0.840476 + 0.541849i \(0.182275\pi\)
\(42\) 0 0
\(43\) −0.127719 + 0.221215i −0.0194769 + 0.0337350i −0.875600 0.483038i \(-0.839533\pi\)
0.856123 + 0.516773i \(0.172867\pi\)
\(44\) 0 0
\(45\) 1.05842 2.12819i 0.157780 0.317252i
\(46\) 0 0
\(47\) −3.68614 + 2.12819i −0.537679 + 0.310429i −0.744138 0.668026i \(-0.767139\pi\)
0.206459 + 0.978455i \(0.433806\pi\)
\(48\) 0 0
\(49\) −1.37228 −0.196040
\(50\) 0 0
\(51\) −1.31386 + 0.396143i −0.183977 + 0.0554712i
\(52\) 0 0
\(53\) 5.68614 + 9.84868i 0.781051 + 1.35282i 0.931330 + 0.364177i \(0.118650\pi\)
−0.150278 + 0.988644i \(0.548017\pi\)
\(54\) 0 0
\(55\) −1.37228 + 2.37686i −0.185038 + 0.320496i
\(56\) 0 0
\(57\) 6.93070 2.99422i 0.917994 0.396594i
\(58\) 0 0
\(59\) −3.68614 + 6.38458i −0.479895 + 0.831202i −0.999734 0.0230621i \(-0.992658\pi\)
0.519839 + 0.854264i \(0.325992\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 0 0
\(63\) 0.441578 + 7.10313i 0.0556336 + 0.894910i
\(64\) 0 0
\(65\) −2.62772 −0.325928
\(66\) 0 0
\(67\) 10.2446 5.91470i 1.25157 0.722596i 0.280151 0.959956i \(-0.409616\pi\)
0.971422 + 0.237360i \(0.0762822\pi\)
\(68\) 0 0
\(69\) 2.94158 12.5205i 0.354124 1.50729i
\(70\) 0 0
\(71\) −3.31386 + 5.73977i −0.393283 + 0.681186i −0.992880 0.119116i \(-0.961994\pi\)
0.599598 + 0.800302i \(0.295327\pi\)
\(72\) 0 0
\(73\) 2.87228 4.97494i 0.336175 0.582272i −0.647535 0.762036i \(-0.724200\pi\)
0.983710 + 0.179764i \(0.0575333\pi\)
\(74\) 0 0
\(75\) 7.37228 + 1.73205i 0.851278 + 0.200000i
\(76\) 0 0
\(77\) 8.21782i 0.936508i
\(78\) 0 0
\(79\) 9.98913 + 5.76722i 1.12386 + 0.648863i 0.942385 0.334531i \(-0.108578\pi\)
0.181480 + 0.983395i \(0.441911\pi\)
\(80\) 0 0
\(81\) −8.93070 + 1.11469i −0.992300 + 0.123855i
\(82\) 0 0
\(83\) 3.46410i 0.380235i −0.981761 0.190117i \(-0.939113\pi\)
0.981761 0.190117i \(-0.0608868\pi\)
\(84\) 0 0
\(85\) 0.313859 + 0.543620i 0.0340428 + 0.0589639i
\(86\) 0 0
\(87\) 9.05842 + 2.12819i 0.971165 + 0.228166i
\(88\) 0 0
\(89\) 3.68614 + 6.38458i 0.390730 + 0.676764i 0.992546 0.121870i \(-0.0388892\pi\)
−0.601816 + 0.798635i \(0.705556\pi\)
\(90\) 0 0
\(91\) 6.81386 3.93398i 0.714287 0.412394i
\(92\) 0 0
\(93\) 5.55842 + 5.22360i 0.576382 + 0.541662i
\(94\) 0 0
\(95\) −2.05842 2.77300i −0.211190 0.284504i
\(96\) 0 0
\(97\) 11.0584 + 6.38458i 1.12281 + 0.648256i 0.942117 0.335283i \(-0.108832\pi\)
0.180695 + 0.983539i \(0.442165\pi\)
\(98\) 0 0
\(99\) 10.3723 0.644810i 1.04245 0.0648059i
\(100\) 0 0
\(101\) 0.686141 0.396143i 0.0682735 0.0394178i −0.465475 0.885061i \(-0.654116\pi\)
0.533748 + 0.845643i \(0.320783\pi\)
\(102\) 0 0
\(103\) 0.644810i 0.0635350i 0.999495 + 0.0317675i \(0.0101136\pi\)
−0.999495 + 0.0317675i \(0.989886\pi\)
\(104\) 0 0
\(105\) 3.11684 0.939764i 0.304173 0.0917116i
\(106\) 0 0
\(107\) 16.7446 1.61876 0.809379 0.587287i \(-0.199804\pi\)
0.809379 + 0.587287i \(0.199804\pi\)
\(108\) 0 0
\(109\) 5.05842 + 2.92048i 0.484509 + 0.279731i 0.722294 0.691587i \(-0.243088\pi\)
−0.237785 + 0.971318i \(0.576421\pi\)
\(110\) 0 0
\(111\) −9.93070 9.33252i −0.942581 0.885803i
\(112\) 0 0
\(113\) −14.7446 −1.38705 −0.693526 0.720432i \(-0.743944\pi\)
−0.693526 + 0.720432i \(0.743944\pi\)
\(114\) 0 0
\(115\) −5.88316 −0.548607
\(116\) 0 0
\(117\) 5.50000 + 8.29156i 0.508475 + 0.766555i
\(118\) 0 0
\(119\) −1.62772 0.939764i −0.149213 0.0861480i
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) 0 0
\(123\) −0.313859 1.04095i −0.0282997 0.0938596i
\(124\) 0 0
\(125\) 7.42554i 0.664160i
\(126\) 0 0
\(127\) −16.8030 + 9.70121i −1.49102 + 0.860843i −0.999947 0.0102734i \(-0.996730\pi\)
−0.491077 + 0.871116i \(0.663396\pi\)
\(128\) 0 0
\(129\) −0.127719 0.423595i −0.0112450 0.0372955i
\(130\) 0 0
\(131\) 4.80298 + 2.77300i 0.419639 + 0.242279i 0.694923 0.719084i \(-0.255439\pi\)
−0.275284 + 0.961363i \(0.588772\pi\)
\(132\) 0 0
\(133\) 9.48913 + 4.10891i 0.822812 + 0.356288i
\(134\) 0 0
\(135\) 1.43070 + 3.86025i 0.123135 + 0.332237i
\(136\) 0 0
\(137\) −11.3139 + 6.53206i −0.966608 + 0.558072i −0.898201 0.439586i \(-0.855125\pi\)
−0.0684077 + 0.997657i \(0.521792\pi\)
\(138\) 0 0
\(139\) −8.24456 14.2800i −0.699295 1.21121i −0.968711 0.248190i \(-0.920164\pi\)
0.269417 0.963024i \(-0.413169\pi\)
\(140\) 0 0
\(141\) 1.68614 7.17687i 0.141999 0.604401i
\(142\) 0 0
\(143\) −5.74456 9.94987i −0.480384 0.832050i
\(144\) 0 0
\(145\) 4.25639i 0.353474i
\(146\) 0 0
\(147\) 1.62772 1.73205i 0.134252 0.142857i
\(148\) 0 0
\(149\) −2.05842 1.18843i −0.168632 0.0973600i 0.413308 0.910591i \(-0.364373\pi\)
−0.581941 + 0.813231i \(0.697706\pi\)
\(150\) 0 0
\(151\) 13.5615i 1.10362i −0.833971 0.551808i \(-0.813938\pi\)
0.833971 0.551808i \(-0.186062\pi\)
\(152\) 0 0
\(153\) 1.05842 2.12819i 0.0855683 0.172054i
\(154\) 0 0
\(155\) 1.74456 3.02167i 0.140127 0.242706i
\(156\) 0 0
\(157\) −10.2446 + 17.7441i −0.817605 + 1.41613i 0.0898370 + 0.995956i \(0.471365\pi\)
−0.907442 + 0.420177i \(0.861968\pi\)
\(158\) 0 0
\(159\) −19.1753 4.50506i −1.52070 0.357274i
\(160\) 0 0
\(161\) 15.2554 8.80773i 1.20230 0.694146i
\(162\) 0 0
\(163\) 9.62772 0.754101 0.377051 0.926193i \(-0.376938\pi\)
0.377051 + 0.926193i \(0.376938\pi\)
\(164\) 0 0
\(165\) −1.37228 4.55134i −0.106832 0.354322i
\(166\) 0 0
\(167\) −9.05842 15.6896i −0.700962 1.21410i −0.968129 0.250451i \(-0.919421\pi\)
0.267167 0.963650i \(-0.413912\pi\)
\(168\) 0 0
\(169\) −1.00000 + 1.73205i −0.0769231 + 0.133235i
\(170\) 0 0
\(171\) −4.44158 + 12.2993i −0.339656 + 0.940550i
\(172\) 0 0
\(173\) −7.43070 + 12.8704i −0.564946 + 0.978515i 0.432109 + 0.901821i \(0.357770\pi\)
−0.997055 + 0.0766935i \(0.975564\pi\)
\(174\) 0 0
\(175\) 5.18614 + 8.98266i 0.392035 + 0.679025i
\(176\) 0 0
\(177\) −3.68614 12.2255i −0.277067 0.918928i
\(178\) 0 0
\(179\) 21.4891 1.60617 0.803086 0.595863i \(-0.203190\pi\)
0.803086 + 0.595863i \(0.203190\pi\)
\(180\) 0 0
\(181\) 1.80298 1.04095i 0.134015 0.0773735i −0.431494 0.902116i \(-0.642013\pi\)
0.565508 + 0.824742i \(0.308680\pi\)
\(182\) 0 0
\(183\) −1.68614 0.396143i −0.124643 0.0292838i
\(184\) 0 0
\(185\) −3.11684 + 5.39853i −0.229155 + 0.396908i
\(186\) 0 0
\(187\) −1.37228 + 2.37686i −0.100351 + 0.173813i
\(188\) 0 0
\(189\) −9.48913 7.86797i −0.690232 0.572310i
\(190\) 0 0
\(191\) 6.63325i 0.479965i 0.970777 + 0.239983i \(0.0771417\pi\)
−0.970777 + 0.239983i \(0.922858\pi\)
\(192\) 0 0
\(193\) 13.5000 + 7.79423i 0.971751 + 0.561041i 0.899770 0.436365i \(-0.143734\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 0 0
\(195\) 3.11684 3.31662i 0.223202 0.237508i
\(196\) 0 0
\(197\) 16.4356i 1.17099i 0.810676 + 0.585496i \(0.199100\pi\)
−0.810676 + 0.585496i \(0.800900\pi\)
\(198\) 0 0
\(199\) −10.2446 17.7441i −0.726218 1.25785i −0.958471 0.285191i \(-0.907943\pi\)
0.232253 0.972655i \(-0.425390\pi\)
\(200\) 0 0
\(201\) −4.68614 + 19.9460i −0.330535 + 1.40688i
\(202\) 0 0
\(203\) 6.37228 + 11.0371i 0.447246 + 0.774654i
\(204\) 0 0
\(205\) −0.430703 + 0.248667i −0.0300816 + 0.0173676i
\(206\) 0 0
\(207\) 12.3139 + 18.5638i 0.855872 + 1.29028i
\(208\) 0 0
\(209\) 6.00000 13.8564i 0.415029 0.958468i
\(210\) 0 0
\(211\) −12.9891 7.49927i −0.894208 0.516271i −0.0188916 0.999822i \(-0.506014\pi\)
−0.875317 + 0.483550i \(0.839347\pi\)
\(212\) 0 0
\(213\) −3.31386 10.9908i −0.227062 0.753079i
\(214\) 0 0
\(215\) −0.175266 + 0.101190i −0.0119530 + 0.00690109i
\(216\) 0 0
\(217\) 10.4472i 0.709203i
\(218\) 0 0
\(219\) 2.87228 + 9.52628i 0.194091 + 0.643726i
\(220\) 0 0
\(221\) −2.62772 −0.176759
\(222\) 0 0
\(223\) −15.7337 9.08385i −1.05361 0.608300i −0.129949 0.991521i \(-0.541481\pi\)
−0.923657 + 0.383221i \(0.874815\pi\)
\(224\) 0 0
\(225\) −10.9307 + 7.25061i −0.728714 + 0.483374i
\(226\) 0 0
\(227\) −7.25544 −0.481560 −0.240780 0.970580i \(-0.577403\pi\)
−0.240780 + 0.970580i \(0.577403\pi\)
\(228\) 0 0
\(229\) −21.1168 −1.39544 −0.697720 0.716370i \(-0.745802\pi\)
−0.697720 + 0.716370i \(0.745802\pi\)
\(230\) 0 0
\(231\) 10.3723 + 9.74749i 0.682446 + 0.641338i
\(232\) 0 0
\(233\) 3.94158 + 2.27567i 0.258221 + 0.149084i 0.623523 0.781805i \(-0.285701\pi\)
−0.365302 + 0.930889i \(0.619034\pi\)
\(234\) 0 0
\(235\) −3.37228 −0.219983
\(236\) 0 0
\(237\) −19.1277 + 5.76722i −1.24248 + 0.374621i
\(238\) 0 0
\(239\) 10.3923i 0.672222i −0.941822 0.336111i \(-0.890888\pi\)
0.941822 0.336111i \(-0.109112\pi\)
\(240\) 0 0
\(241\) 0.383156 0.221215i 0.0246812 0.0142497i −0.487609 0.873062i \(-0.662131\pi\)
0.512290 + 0.858813i \(0.328797\pi\)
\(242\) 0 0
\(243\) 9.18614 12.5942i 0.589291 0.807921i
\(244\) 0 0
\(245\) −0.941578 0.543620i −0.0601552 0.0347306i
\(246\) 0 0
\(247\) 14.3614 1.65831i 0.913794 0.105516i
\(248\) 0 0
\(249\) 4.37228 + 4.10891i 0.277082 + 0.260392i
\(250\) 0 0
\(251\) 5.56930 3.21543i 0.351531 0.202956i −0.313828 0.949480i \(-0.601612\pi\)
0.665359 + 0.746523i \(0.268278\pi\)
\(252\) 0 0
\(253\) −12.8614 22.2766i −0.808590 1.40052i
\(254\) 0 0
\(255\) −1.05842 0.248667i −0.0662810 0.0155721i
\(256\) 0 0
\(257\) 0.941578 + 1.63086i 0.0587340 + 0.101730i 0.893897 0.448272i \(-0.147960\pi\)
−0.835163 + 0.550002i \(0.814627\pi\)
\(258\) 0 0
\(259\) 18.6650i 1.15979i
\(260\) 0 0
\(261\) −13.4307 + 8.90892i −0.831340 + 0.551448i
\(262\) 0 0
\(263\) −3.43070 1.98072i −0.211546 0.122136i 0.390484 0.920610i \(-0.372308\pi\)
−0.602030 + 0.798474i \(0.705641\pi\)
\(264\) 0 0
\(265\) 9.01011i 0.553487i
\(266\) 0 0
\(267\) −12.4307 2.92048i −0.760747 0.178731i
\(268\) 0 0
\(269\) 6.43070 11.1383i 0.392087 0.679114i −0.600638 0.799521i \(-0.705087\pi\)
0.992725 + 0.120407i \(0.0384199\pi\)
\(270\) 0 0
\(271\) −4.43070 + 7.67420i −0.269146 + 0.466175i −0.968642 0.248462i \(-0.920075\pi\)
0.699495 + 0.714637i \(0.253408\pi\)
\(272\) 0 0
\(273\) −3.11684 + 13.2665i −0.188640 + 0.802925i
\(274\) 0 0
\(275\) 13.1168 7.57301i 0.790975 0.456670i
\(276\) 0 0
\(277\) 3.48913 0.209641 0.104821 0.994491i \(-0.466573\pi\)
0.104821 + 0.994491i \(0.466573\pi\)
\(278\) 0 0
\(279\) −13.1861 + 0.819738i −0.789434 + 0.0490765i
\(280\) 0 0
\(281\) 12.8030 + 22.1754i 0.763762 + 1.32287i 0.940899 + 0.338688i \(0.109983\pi\)
−0.177137 + 0.984186i \(0.556683\pi\)
\(282\) 0 0
\(283\) −14.4307 + 24.9947i −0.857816 + 1.48578i 0.0161912 + 0.999869i \(0.494846\pi\)
−0.874007 + 0.485912i \(0.838487\pi\)
\(284\) 0 0
\(285\) 5.94158 + 0.691097i 0.351949 + 0.0409371i
\(286\) 0 0
\(287\) 0.744563 1.28962i 0.0439501 0.0761239i
\(288\) 0 0
\(289\) −8.18614 14.1788i −0.481538 0.834048i
\(290\) 0 0
\(291\) −21.1753 + 6.38458i −1.24132 + 0.374271i
\(292\) 0 0
\(293\) −9.25544 −0.540708 −0.270354 0.962761i \(-0.587141\pi\)
−0.270354 + 0.962761i \(0.587141\pi\)
\(294\) 0 0
\(295\) −5.05842 + 2.92048i −0.294513 + 0.170037i
\(296\) 0 0
\(297\) −11.4891 + 13.8564i −0.666667 + 0.804030i
\(298\) 0 0
\(299\) 12.3139 21.3282i 0.712129 1.23344i
\(300\) 0 0
\(301\) 0.302985 0.524785i 0.0174637 0.0302481i
\(302\) 0 0
\(303\) −0.313859 + 1.33591i −0.0180307 + 0.0767459i
\(304\) 0 0
\(305\) 0.792287i 0.0453662i
\(306\) 0 0
\(307\) 16.2921 + 9.40625i 0.929840 + 0.536843i 0.886761 0.462228i \(-0.152950\pi\)
0.0430789 + 0.999072i \(0.486283\pi\)
\(308\) 0 0
\(309\) −0.813859 0.764836i −0.0462988 0.0435100i
\(310\) 0 0
\(311\) 12.2718i 0.695872i −0.937518 0.347936i \(-0.886883\pi\)
0.937518 0.347936i \(-0.113117\pi\)
\(312\) 0 0
\(313\) −16.1753 28.0164i −0.914280 1.58358i −0.807952 0.589248i \(-0.799424\pi\)
−0.106328 0.994331i \(-0.533909\pi\)
\(314\) 0 0
\(315\) −2.51087 + 5.04868i −0.141472 + 0.284461i
\(316\) 0 0
\(317\) −10.6861 18.5089i −0.600193 1.03957i −0.992791 0.119855i \(-0.961757\pi\)
0.392598 0.919710i \(-0.371576\pi\)
\(318\) 0 0
\(319\) 16.1168 9.30506i 0.902370 0.520984i
\(320\) 0 0
\(321\) −19.8614 + 21.1345i −1.10856 + 1.17961i
\(322\) 0 0
\(323\) −2.05842 2.77300i −0.114534 0.154294i
\(324\) 0 0
\(325\) 12.5584 + 7.25061i 0.696616 + 0.402191i
\(326\) 0 0
\(327\) −9.68614 + 2.92048i −0.535645 + 0.161503i
\(328\) 0 0
\(329\) 8.74456 5.04868i 0.482103 0.278342i
\(330\) 0 0
\(331\) 19.5499i 1.07456i 0.843404 + 0.537280i \(0.180548\pi\)
−0.843404 + 0.537280i \(0.819452\pi\)
\(332\) 0 0
\(333\) 23.5584 1.46455i 1.29099 0.0802568i
\(334\) 0 0
\(335\) 9.37228 0.512062
\(336\) 0 0
\(337\) 9.73369 + 5.61975i 0.530228 + 0.306127i 0.741109 0.671385i \(-0.234300\pi\)
−0.210881 + 0.977512i \(0.567633\pi\)
\(338\) 0 0
\(339\) 17.4891 18.6101i 0.949879 1.01076i
\(340\) 0 0
\(341\) 15.2554 0.826128
\(342\) 0 0
\(343\) 19.8614 1.07242
\(344\) 0 0
\(345\) 6.97825 7.42554i 0.375696 0.399777i
\(346\) 0 0
\(347\) 7.54755 + 4.35758i 0.405174 + 0.233927i 0.688714 0.725033i \(-0.258176\pi\)
−0.283540 + 0.958960i \(0.591509\pi\)
\(348\) 0 0
\(349\) −30.6060 −1.63830 −0.819150 0.573579i \(-0.805554\pi\)
−0.819150 + 0.573579i \(0.805554\pi\)
\(350\) 0 0
\(351\) −16.9891 2.89303i −0.906812 0.154419i
\(352\) 0 0
\(353\) 35.3407i 1.88100i −0.339798 0.940499i \(-0.610359\pi\)
0.339798 0.940499i \(-0.389641\pi\)
\(354\) 0 0
\(355\) −4.54755 + 2.62553i −0.241359 + 0.139349i
\(356\) 0 0
\(357\) 3.11684 0.939764i 0.164961 0.0497376i
\(358\) 0 0
\(359\) −1.80298 1.04095i −0.0951579 0.0549394i 0.451666 0.892187i \(-0.350830\pi\)
−0.546824 + 0.837248i \(0.684163\pi\)
\(360\) 0 0
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) 0 0
\(363\) 1.18614 1.26217i 0.0622562 0.0662467i
\(364\) 0 0
\(365\) 3.94158 2.27567i 0.206312 0.119114i
\(366\) 0 0
\(367\) 9.61684 + 16.6569i 0.501995 + 0.869481i 0.999997 + 0.00230536i \(0.000733819\pi\)
−0.498002 + 0.867176i \(0.665933\pi\)
\(368\) 0 0
\(369\) 1.68614 + 0.838574i 0.0877770 + 0.0436544i
\(370\) 0 0
\(371\) −13.4891 23.3639i −0.700320 1.21299i
\(372\) 0 0
\(373\) 6.92820i 0.358729i −0.983783 0.179364i \(-0.942596\pi\)
0.983783 0.179364i \(-0.0574041\pi\)
\(374\) 0 0
\(375\) 9.37228 + 8.80773i 0.483983 + 0.454829i
\(376\) 0 0
\(377\) 15.4307 + 8.90892i 0.794722 + 0.458833i
\(378\) 0 0
\(379\) 10.7422i 0.551788i −0.961188 0.275894i \(-0.911026\pi\)
0.961188 0.275894i \(-0.0889738\pi\)
\(380\) 0 0
\(381\) 7.68614 32.7152i 0.393773 1.67605i
\(382\) 0 0
\(383\) −4.80298 + 8.31901i −0.245421 + 0.425082i −0.962250 0.272167i \(-0.912260\pi\)
0.716829 + 0.697249i \(0.245593\pi\)
\(384\) 0 0
\(385\) 3.25544 5.63858i 0.165912 0.287369i
\(386\) 0 0
\(387\) 0.686141 + 0.341241i 0.0348785 + 0.0173462i
\(388\) 0 0
\(389\) −26.6644 + 15.3947i −1.35194 + 0.780542i −0.988521 0.151084i \(-0.951723\pi\)
−0.363417 + 0.931626i \(0.618390\pi\)
\(390\) 0 0
\(391\) −5.88316 −0.297524
\(392\) 0 0
\(393\) −9.19702 + 2.77300i −0.463928 + 0.139880i
\(394\) 0 0
\(395\) 4.56930 + 7.91425i 0.229906 + 0.398209i
\(396\) 0 0
\(397\) −4.61684 + 7.99661i −0.231713 + 0.401338i −0.958312 0.285723i \(-0.907766\pi\)
0.726599 + 0.687061i \(0.241100\pi\)
\(398\) 0 0
\(399\) −16.4416 + 7.10313i −0.823108 + 0.355601i
\(400\) 0 0
\(401\) 9.17527 15.8920i 0.458191 0.793610i −0.540675 0.841232i \(-0.681831\pi\)
0.998865 + 0.0476219i \(0.0151643\pi\)
\(402\) 0 0
\(403\) 7.30298 + 12.6491i 0.363788 + 0.630099i
\(404\) 0 0
\(405\) −6.56930 2.77300i −0.326431 0.137792i
\(406\) 0 0
\(407\) −27.2554 −1.35100
\(408\) 0 0
\(409\) 31.2921 18.0665i 1.54730 0.893331i 0.548948 0.835856i \(-0.315028\pi\)
0.998347 0.0574750i \(-0.0183050\pi\)
\(410\) 0 0
\(411\) 5.17527 22.0279i 0.255277 1.08656i
\(412\) 0 0
\(413\) 8.74456 15.1460i 0.430292 0.745287i
\(414\) 0 0
\(415\) 1.37228 2.37686i 0.0673626 0.116676i
\(416\) 0 0
\(417\) 27.8030 + 6.53206i 1.36152 + 0.319876i
\(418\) 0 0
\(419\) 37.5152i 1.83274i 0.400335 + 0.916369i \(0.368894\pi\)
−0.400335 + 0.916369i \(0.631106\pi\)
\(420\) 0 0
\(421\) 25.2921 + 14.6024i 1.23266 + 0.711678i 0.967584 0.252549i \(-0.0812690\pi\)
0.265078 + 0.964227i \(0.414602\pi\)
\(422\) 0 0
\(423\) 7.05842 + 10.6410i 0.343192 + 0.517382i
\(424\) 0 0
\(425\) 3.46410i 0.168034i
\(426\) 0 0
\(427\) −1.18614 2.05446i −0.0574014 0.0994221i
\(428\) 0 0
\(429\) 19.3723 + 4.55134i 0.935303 + 0.219741i
\(430\) 0 0
\(431\) 18.4307 + 31.9229i 0.887776 + 1.53767i 0.842499 + 0.538698i \(0.181084\pi\)
0.0452769 + 0.998974i \(0.485583\pi\)
\(432\) 0 0
\(433\) 3.73369 2.15565i 0.179430 0.103594i −0.407595 0.913163i \(-0.633632\pi\)
0.587025 + 0.809569i \(0.300299\pi\)
\(434\) 0 0
\(435\) 5.37228 + 5.04868i 0.257581 + 0.242065i
\(436\) 0 0
\(437\) 32.1535 3.71277i 1.53811 0.177606i
\(438\) 0 0
\(439\) 4.50000 + 2.59808i 0.214773 + 0.123999i 0.603528 0.797342i \(-0.293761\pi\)
−0.388755 + 0.921341i \(0.627095\pi\)
\(440\) 0 0
\(441\) 0.255437 + 4.10891i 0.0121637 + 0.195662i
\(442\) 0 0
\(443\) −31.0367 + 17.9190i −1.47460 + 0.851359i −0.999590 0.0286234i \(-0.990888\pi\)
−0.475007 + 0.879982i \(0.657554\pi\)
\(444\) 0 0
\(445\) 5.84096i 0.276888i
\(446\) 0 0
\(447\) 3.94158 1.18843i 0.186430 0.0562108i
\(448\) 0 0
\(449\) −38.4674 −1.81539 −0.907694 0.419633i \(-0.862159\pi\)
−0.907694 + 0.419633i \(0.862159\pi\)
\(450\) 0 0
\(451\) −1.88316 1.08724i −0.0886744 0.0511962i
\(452\) 0 0
\(453\) 17.1168 + 16.0858i 0.804219 + 0.755776i
\(454\) 0 0
\(455\) 6.23369 0.292240
\(456\) 0 0
\(457\) 36.3723 1.70142 0.850712 0.525632i \(-0.176171\pi\)
0.850712 + 0.525632i \(0.176171\pi\)
\(458\) 0 0
\(459\) 1.43070 + 3.86025i 0.0667795 + 0.180181i
\(460\) 0 0
\(461\) 11.5693 + 6.67954i 0.538836 + 0.311097i 0.744607 0.667503i \(-0.232637\pi\)
−0.205771 + 0.978600i \(0.565970\pi\)
\(462\) 0 0
\(463\) 17.6277 0.819230 0.409615 0.912259i \(-0.365663\pi\)
0.409615 + 0.912259i \(0.365663\pi\)
\(464\) 0 0
\(465\) 1.74456 + 5.78606i 0.0809022 + 0.268322i
\(466\) 0 0
\(467\) 4.16381i 0.192678i 0.995349 + 0.0963392i \(0.0307133\pi\)
−0.995349 + 0.0963392i \(0.969287\pi\)
\(468\) 0 0
\(469\) −24.3030 + 14.0313i −1.12221 + 0.647907i
\(470\) 0 0
\(471\) −10.2446 33.9774i −0.472045 1.56559i
\(472\) 0 0
\(473\) −0.766312 0.442430i −0.0352351 0.0203430i
\(474\) 0 0
\(475\) 2.18614 + 18.9325i 0.100307 + 0.868684i
\(476\) 0 0
\(477\) 28.4307 18.8588i 1.30175 0.863485i
\(478\) 0 0
\(479\) −8.56930 + 4.94749i −0.391541 + 0.226056i −0.682828 0.730579i \(-0.739250\pi\)
0.291287 + 0.956636i \(0.405917\pi\)
\(480\) 0 0
\(481\) −13.0475 22.5990i −0.594917 1.03043i
\(482\) 0 0
\(483\) −6.97825 + 29.7021i −0.317521 + 1.35149i
\(484\) 0 0
\(485\) 5.05842 + 8.76144i 0.229691 + 0.397837i
\(486\) 0 0
\(487\) 0.294954i 0.0133656i 0.999978 + 0.00668281i \(0.00212722\pi\)
−0.999978 + 0.00668281i \(0.997873\pi\)
\(488\) 0 0
\(489\) −11.4198 + 12.1518i −0.516423 + 0.549524i
\(490\) 0 0
\(491\) −18.1753 10.4935i −0.820238 0.473565i 0.0302604 0.999542i \(-0.490366\pi\)
−0.850499 + 0.525977i \(0.823700\pi\)
\(492\) 0 0
\(493\) 4.25639i 0.191698i
\(494\) 0 0
\(495\) 7.37228 + 3.66648i 0.331359 + 0.164796i
\(496\) 0 0
\(497\) 7.86141 13.6164i 0.352632 0.610777i
\(498\) 0 0
\(499\) 11.8723 20.5634i 0.531476 0.920544i −0.467849 0.883809i \(-0.654971\pi\)
0.999325 0.0367354i \(-0.0116959\pi\)
\(500\) 0 0
\(501\) 30.5475 + 7.17687i 1.36476 + 0.320639i
\(502\) 0 0
\(503\) 36.6861 21.1808i 1.63575 0.944403i 0.653482 0.756942i \(-0.273307\pi\)
0.982272 0.187461i \(-0.0600259\pi\)
\(504\) 0 0
\(505\) 0.627719 0.0279331
\(506\) 0 0
\(507\) −1.00000 3.31662i −0.0444116 0.147296i
\(508\) 0 0
\(509\) −5.05842 8.76144i −0.224211 0.388344i 0.731872 0.681442i \(-0.238647\pi\)
−0.956082 + 0.293098i \(0.905314\pi\)
\(510\) 0 0
\(511\) −6.81386 + 11.8020i −0.301427 + 0.522088i
\(512\) 0 0
\(513\) −10.2554 20.1947i −0.452789 0.891618i
\(514\) 0 0
\(515\) −0.255437 + 0.442430i −0.0112559 + 0.0194958i
\(516\) 0 0
\(517\) −7.37228 12.7692i −0.324233 0.561587i
\(518\) 0 0
\(519\) −7.43070 24.6449i −0.326172 1.08179i
\(520\) 0 0
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 0 0
\(523\) 10.2446 5.91470i 0.447963 0.258632i −0.259006 0.965876i \(-0.583395\pi\)
0.706970 + 0.707244i \(0.250062\pi\)
\(524\) 0 0
\(525\) −17.4891 4.10891i −0.763288 0.179328i
\(526\) 0 0
\(527\) 1.74456 3.02167i 0.0759943 0.131626i
\(528\) 0 0
\(529\) 16.0693 27.8328i 0.698665 1.21012i
\(530\) 0 0
\(531\) 19.8030 + 9.84868i 0.859376 + 0.427397i
\(532\) 0 0
\(533\) 2.08191i 0.0901774i
\(534\) 0 0
\(535\) 11.4891 + 6.63325i 0.496718 + 0.286780i
\(536\) 0 0
\(537\) −25.4891 + 27.1229i −1.09994 + 1.17044i
\(538\) 0 0
\(539\) 4.75372i 0.204757i
\(540\) 0 0
\(541\) 7.98913 + 13.8376i 0.343479 + 0.594924i 0.985076 0.172118i \(-0.0550611\pi\)
−0.641597 + 0.767042i \(0.721728\pi\)
\(542\) 0 0
\(543\) −0.824734 + 3.51039i −0.0353927 + 0.150645i
\(544\) 0 0
\(545\) 2.31386 + 4.00772i 0.0991148 + 0.171672i
\(546\) 0 0
\(547\) −35.6168 + 20.5634i −1.52287 + 0.879227i −0.523232 + 0.852190i \(0.675274\pi\)
−0.999634 + 0.0270369i \(0.991393\pi\)
\(548\) 0 0
\(549\) 2.50000 1.65831i 0.106697 0.0707750i
\(550\) 0 0
\(551\) 2.68614 + 23.2627i 0.114433 + 0.991023i
\(552\) 0 0
\(553\) −23.6970 13.6815i −1.00770 0.581796i
\(554\) 0 0
\(555\) −3.11684 10.3374i −0.132303 0.438798i
\(556\) 0 0
\(557\) 27.4307 15.8371i 1.16228 0.671040i 0.210428 0.977609i \(-0.432514\pi\)
0.951848 + 0.306569i \(0.0991810\pi\)
\(558\) 0 0
\(559\) 0.847190i 0.0358323i
\(560\) 0 0
\(561\) −1.37228 4.55134i −0.0579378 0.192158i
\(562\) 0 0
\(563\) −43.7228 −1.84270 −0.921348 0.388738i \(-0.872911\pi\)
−0.921348 + 0.388738i \(0.872911\pi\)
\(564\) 0 0
\(565\) −10.1168 5.84096i −0.425619 0.245731i
\(566\) 0 0
\(567\) 21.1861 2.64436i 0.889734 0.111053i
\(568\) 0 0
\(569\) −38.7446 −1.62426 −0.812128 0.583479i \(-0.801691\pi\)
−0.812128 + 0.583479i \(0.801691\pi\)
\(570\) 0 0
\(571\) 9.62772 0.402907 0.201454 0.979498i \(-0.435433\pi\)
0.201454 + 0.979498i \(0.435433\pi\)
\(572\) 0 0
\(573\) −8.37228 7.86797i −0.349757 0.328689i
\(574\) 0 0
\(575\) 28.1168 + 16.2333i 1.17255 + 0.676974i
\(576\) 0 0
\(577\) −27.4891 −1.14439 −0.572194 0.820119i \(-0.693907\pi\)
−0.572194 + 0.820119i \(0.693907\pi\)
\(578\) 0 0
\(579\) −25.8505 + 7.79423i −1.07431 + 0.323917i
\(580\) 0 0
\(581\) 8.21782i 0.340933i
\(582\) 0 0
\(583\) −34.1168 + 19.6974i −1.41298 + 0.815782i
\(584\) 0 0
\(585\) 0.489125 + 7.86797i 0.0202228 + 0.325300i
\(586\) 0 0
\(587\) −38.3139 22.1205i −1.58138 0.913011i −0.994658 0.103225i \(-0.967084\pi\)
−0.586724 0.809787i \(-0.699583\pi\)
\(588\) 0 0
\(589\) −7.62772 + 17.6155i −0.314295 + 0.725832i
\(590\) 0 0
\(591\) −20.7446 19.4950i −0.853317 0.801917i
\(592\) 0 0
\(593\) 4.54755 2.62553i 0.186745 0.107817i −0.403713 0.914886i \(-0.632280\pi\)
0.590458 + 0.807068i \(0.298947\pi\)
\(594\) 0 0
\(595\) −0.744563 1.28962i −0.0305241 0.0528693i
\(596\) 0 0
\(597\) 34.5475 + 8.11663i 1.41394 + 0.332192i
\(598\) 0 0
\(599\) 0.0584220 + 0.101190i 0.00238706 + 0.00413451i 0.867216 0.497931i \(-0.165907\pi\)
−0.864829 + 0.502066i \(0.832574\pi\)
\(600\) 0 0
\(601\) 27.4728i 1.12064i −0.828277 0.560319i \(-0.810679\pi\)
0.828277 0.560319i \(-0.189321\pi\)
\(602\) 0 0
\(603\) −19.6168 29.5735i −0.798860 1.20433i
\(604\) 0 0
\(605\) −0.686141 0.396143i −0.0278956 0.0161055i
\(606\) 0 0
\(607\) 2.52434i 0.102460i 0.998687 + 0.0512299i \(0.0163141\pi\)
−0.998687 + 0.0512299i \(0.983686\pi\)
\(608\) 0 0
\(609\) −21.4891 5.04868i −0.870783 0.204583i
\(610\) 0 0
\(611\) 7.05842 12.2255i 0.285553 0.494593i
\(612\) 0 0
\(613\) −3.94158 + 6.82701i −0.159199 + 0.275740i −0.934580 0.355753i \(-0.884224\pi\)
0.775381 + 0.631494i \(0.217558\pi\)
\(614\) 0 0
\(615\) 0.197015 0.838574i 0.00794443 0.0338146i
\(616\) 0 0
\(617\) 3.94158 2.27567i 0.158682 0.0916151i −0.418556 0.908191i \(-0.637464\pi\)
0.577238 + 0.816576i \(0.304130\pi\)
\(618\) 0 0
\(619\) 31.8614 1.28062 0.640309 0.768117i \(-0.278806\pi\)
0.640309 + 0.768117i \(0.278806\pi\)
\(620\) 0 0
\(621\) −38.0367 6.47716i −1.52636 0.259919i
\(622\) 0 0
\(623\) −8.74456 15.1460i −0.350344 0.606813i
\(624\) 0 0
\(625\) −7.98913 + 13.8376i −0.319565 + 0.553503i
\(626\) 0 0
\(627\) 10.3723 + 24.0087i 0.414229 + 0.958814i
\(628\) 0 0
\(629\) −3.11684 + 5.39853i −0.124277 + 0.215254i
\(630\) 0 0
\(631\) −4.61684 7.99661i −0.183794 0.318340i 0.759376 0.650652i \(-0.225504\pi\)
−0.943169 + 0.332312i \(0.892171\pi\)
\(632\) 0 0
\(633\) 24.8723 7.49927i 0.988584 0.298069i
\(634\) 0 0
\(635\) −15.3723 −0.610030
\(636\) 0 0
\(637\) 3.94158 2.27567i 0.156171 0.0901654i
\(638\) 0 0
\(639\) 17.8030 + 8.85402i 0.704275 + 0.350260i
\(640\) 0 0
\(641\) −10.3139 + 17.8641i −0.407373 + 0.705591i −0.994594 0.103836i \(-0.966888\pi\)
0.587222 + 0.809426i \(0.300222\pi\)
\(642\) 0 0
\(643\) 1.50000 2.59808i 0.0591542 0.102458i −0.834932 0.550353i \(-0.814493\pi\)
0.894086 + 0.447895i \(0.147826\pi\)
\(644\) 0 0
\(645\) 0.0801714 0.341241i 0.00315675 0.0134363i
\(646\) 0 0
\(647\) 44.4434i 1.74725i 0.486599 + 0.873625i \(0.338237\pi\)
−0.486599 + 0.873625i \(0.661763\pi\)
\(648\) 0 0
\(649\) −22.1168 12.7692i −0.868162 0.501234i
\(650\) 0 0
\(651\) −13.1861 12.3919i −0.516806 0.485675i
\(652\) 0 0
\(653\) 22.0742i 0.863831i 0.901914 + 0.431916i \(0.142162\pi\)
−0.901914 + 0.431916i \(0.857838\pi\)
\(654\) 0 0
\(655\) 2.19702 + 3.80534i 0.0858445 + 0.148687i
\(656\) 0 0
\(657\) −15.4307 7.67420i −0.602009 0.299399i
\(658\) 0 0
\(659\) 19.5475 + 33.8573i 0.761464 + 1.31889i 0.942096 + 0.335344i \(0.108853\pi\)
−0.180631 + 0.983551i \(0.557814\pi\)
\(660\) 0 0
\(661\) −4.19702 + 2.42315i −0.163245 + 0.0942495i −0.579397 0.815046i \(-0.696712\pi\)
0.416152 + 0.909295i \(0.363378\pi\)
\(662\) 0 0
\(663\) 3.11684 3.31662i 0.121048 0.128807i
\(664\) 0 0
\(665\) 4.88316 + 6.57835i 0.189361 + 0.255097i
\(666\) 0 0
\(667\) 34.5475 + 19.9460i 1.33769 + 0.772314i
\(668\) 0 0
\(669\) 30.1277 9.08385i 1.16480 0.351202i
\(670\) 0 0
\(671\) −3.00000 + 1.73205i −0.115814 + 0.0668651i
\(672\) 0 0
\(673\) 21.1345i 0.814674i −0.913278 0.407337i \(-0.866457\pi\)
0.913278 0.407337i \(-0.133543\pi\)
\(674\) 0 0
\(675\) 3.81386 22.3966i 0.146796 0.862047i
\(676\) 0 0
\(677\) −26.7446 −1.02788 −0.513939 0.857827i \(-0.671814\pi\)
−0.513939 + 0.857827i \(0.671814\pi\)
\(678\) 0 0
\(679\) −26.2337 15.1460i −1.00676 0.581251i
\(680\) 0 0
\(681\) 8.60597 9.15759i 0.329781 0.350920i
\(682\) 0 0
\(683\) −4.74456 −0.181546 −0.0907728 0.995872i \(-0.528934\pi\)
−0.0907728 + 0.995872i \(0.528934\pi\)
\(684\) 0 0
\(685\) −10.3505 −0.395473
\(686\) 0 0
\(687\) 25.0475 26.6530i 0.955624 1.01688i
\(688\) 0 0
\(689\) −32.6644 18.8588i −1.24441 0.718463i
\(690\) 0 0
\(691\) −41.9565 −1.59610 −0.798050 0.602591i \(-0.794135\pi\)
−0.798050 + 0.602591i \(0.794135\pi\)
\(692\) 0 0
\(693\) −24.6060 + 1.52967i −0.934703 + 0.0581074i
\(694\) 0 0
\(695\) 13.0641i 0.495550i
\(696\) 0 0
\(697\) −0.430703 + 0.248667i −0.0163141 + 0.00941892i
\(698\) 0 0
\(699\) −7.54755 + 2.27567i −0.285474 + 0.0860738i
\(700\) 0 0
\(701\) −14.0584 8.11663i −0.530979 0.306561i 0.210436 0.977608i \(-0.432512\pi\)
−0.741415 + 0.671047i \(0.765845\pi\)
\(702\) 0 0
\(703\) 13.6277 31.4719i 0.513979 1.18698i
\(704\) 0 0
\(705\) 4.00000 4.25639i 0.150649 0.160305i
\(706\) 0 0
\(707\) −1.62772 + 0.939764i −0.0612167 + 0.0353435i
\(708\) 0 0
\(709\) −0.244563 0.423595i −0.00918474 0.0159084i 0.861397 0.507933i \(-0.169590\pi\)
−0.870581 + 0.492025i \(0.836257\pi\)
\(710\) 0 0
\(711\) 15.4090 30.9832i 0.577881 1.16196i
\(712\) 0 0
\(713\) 16.3505 + 28.3200i 0.612332 + 1.06059i
\(714\) 0 0
\(715\) 9.10268i 0.340421i
\(716\) 0 0
\(717\) 13.1168 + 12.3267i 0.489858 + 0.460350i
\(718\) 0 0
\(719\) 3.68614 + 2.12819i 0.137470 + 0.0793683i 0.567158 0.823609i \(-0.308043\pi\)
−0.429688 + 0.902978i \(0.641376\pi\)
\(720\) 0 0
\(721\) 1.52967i 0.0569679i
\(722\) 0 0
\(723\) −0.175266 + 0.746000i −0.00651821 + 0.0277440i
\(724\) 0 0
\(725\) −11.7446 + 20.3422i −0.436182 + 0.755490i
\(726\) 0 0
\(727\) −16.8723 + 29.2236i −0.625758 + 1.08385i 0.362635 + 0.931931i \(0.381877\pi\)
−0.988394 + 0.151914i \(0.951456\pi\)
\(728\) 0 0
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) 0 0
\(731\) −0.175266 + 0.101190i −0.00648245 + 0.00374264i
\(732\) 0 0
\(733\) −24.9783 −0.922593 −0.461296 0.887246i \(-0.652616\pi\)
−0.461296 + 0.887246i \(0.652616\pi\)
\(734\) 0 0
\(735\) 1.80298 0.543620i 0.0665041 0.0200517i
\(736\) 0 0
\(737\) 20.4891 + 35.4882i 0.754727 + 1.30722i
\(738\) 0 0
\(739\) −15.2446 + 26.4044i −0.560780 + 0.971300i 0.436648 + 0.899632i \(0.356165\pi\)
−0.997429 + 0.0716677i \(0.977168\pi\)
\(740\) 0 0
\(741\) −14.9416 + 20.0935i −0.548893 + 0.738154i
\(742\) 0 0
\(743\) −5.31386 + 9.20387i −0.194947 + 0.337657i −0.946883 0.321578i \(-0.895787\pi\)
0.751936 + 0.659236i \(0.229120\pi\)
\(744\) 0 0
\(745\) −0.941578 1.63086i −0.0344967 0.0597501i
\(746\) 0 0
\(747\) −10.3723 + 0.644810i −0.379502 + 0.0235924i
\(748\) 0 0
\(749\) −39.7228 −1.45144
\(750\) 0 0
\(751\) 24.9891 14.4275i 0.911866 0.526466i 0.0308350 0.999524i \(-0.490183\pi\)
0.881031 + 0.473058i \(0.156850\pi\)
\(752\) 0 0
\(753\) −2.54755 + 10.8434i −0.0928378 + 0.395154i
\(754\) 0 0
\(755\) 5.37228 9.30506i 0.195517 0.338646i
\(756\) 0 0
\(757\) 12.8723 22.2954i 0.467851 0.810342i −0.531474 0.847075i \(-0.678362\pi\)
0.999325 + 0.0367328i \(0.0116950\pi\)
\(758\) 0 0
\(759\) 43.3723 + 10.1899i 1.57431 + 0.369871i
\(760\) 0 0
\(761\) 33.4612i 1.21297i 0.795096 + 0.606484i \(0.207421\pi\)
−0.795096 + 0.606484i \(0.792579\pi\)
\(762\) 0 0
\(763\) −12.0000 6.92820i −0.434429 0.250818i
\(764\) 0 0
\(765\) 1.56930 1.04095i 0.0567380 0.0376358i
\(766\) 0 0
\(767\) 24.4511i 0.882878i
\(768\) 0 0
\(769\) 10.1277 + 17.5417i 0.365215 + 0.632571i 0.988811 0.149176i \(-0.0476622\pi\)
−0.623596 + 0.781747i \(0.714329\pi\)
\(770\) 0 0
\(771\) −3.17527 0.746000i −0.114354 0.0268665i
\(772\) 0 0
\(773\) 21.6861 + 37.5615i 0.779996 + 1.35099i 0.931943 + 0.362604i \(0.118112\pi\)
−0.151947 + 0.988389i \(0.548554\pi\)
\(774\) 0 0
\(775\) −16.6753 + 9.62747i −0.598993 + 0.345829i
\(776\) 0 0
\(777\) 23.5584 + 22.1394i 0.845154 + 0.794245i
\(778\) 0 0
\(779\) 2.19702 1.63086i 0.0787162 0.0584317i
\(780\) 0 0
\(781\) −19.8832 11.4795i −0.711475 0.410770i
\(782\) 0 0
\(783\) 4.68614 27.5190i 0.167469 0.983451i
\(784\) 0 0
\(785\) −14.0584 + 8.11663i −0.501767 + 0.289695i
\(786\) 0 0
\(787\) 7.57301i 0.269949i 0.990849 + 0.134974i \(0.0430952\pi\)
−0.990849 + 0.134974i \(0.956905\pi\)
\(788\) 0 0
\(789\) 6.56930 1.98072i 0.233873 0.0705154i
\(790\) 0 0
\(791\) 34.9783 1.24368
\(792\) 0 0
\(793\) −2.87228 1.65831i −0.101998 0.0588884i
\(794\) 0 0