Properties

Label 1470.2.g.k.589.4
Level $1470$
Weight $2$
Character 1470.589
Analytic conductor $11.738$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.1698758656.6
Defining polynomial: \(x^{8} + 18 x^{6} + 97 x^{4} + 176 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 589.4
Root \(-1.69230i\) of defining polynomial
Character \(\chi\) \(=\) 1470.589
Dual form 1470.2.g.k.589.8

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.18183 - 0.489528i) q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.18183 - 0.489528i) q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(-0.489528 - 2.18183i) q^{10} -2.39327 q^{11} -1.00000i q^{12} +3.80748i q^{13} +(0.489528 + 2.18183i) q^{15} +1.00000 q^{16} -1.97038i q^{17} +1.00000i q^{18} +4.17113 q^{19} +(-2.18183 + 0.489528i) q^{20} +2.39327i q^{22} +8.17113i q^{23} -1.00000 q^{24} +(4.52072 - 2.13613i) q^{25} +3.80748 q^{26} -1.00000i q^{27} +9.16246 q^{29} +(2.18183 - 0.489528i) q^{30} +1.60673 q^{31} -1.00000i q^{32} -2.39327i q^{33} -1.97038 q^{34} +1.00000 q^{36} -1.26358i q^{37} -4.17113i q^{38} -3.80748 q^{39} +(0.489528 + 2.18183i) q^{40} -3.19208 q^{41} +4.90755i q^{43} +2.39327 q^{44} +(-2.18183 + 0.489528i) q^{45} +8.17113 q^{46} -3.00868i q^{47} +1.00000i q^{48} +(-2.13613 - 4.52072i) q^{50} +1.97038 q^{51} -3.80748i q^{52} +12.1711i q^{53} -1.00000 q^{54} +(-5.22170 + 1.17157i) q^{55} +4.17113i q^{57} -9.16246i q^{58} -13.0414 q^{59} +(-0.489528 - 2.18183i) q^{60} +13.0910 q^{61} -1.60673i q^{62} -1.00000 q^{64} +(1.86387 + 8.30726i) q^{65} -2.39327 q^{66} +5.77786i q^{67} +1.97038i q^{68} -8.17113 q^{69} +6.94032 q^{71} -1.00000i q^{72} -0.506664i q^{73} -1.26358 q^{74} +(2.13613 + 4.52072i) q^{75} -4.17113 q^{76} +3.80748i q^{78} +12.4260 q^{79} +(2.18183 - 0.489528i) q^{80} +1.00000 q^{81} +3.19208i q^{82} -1.89887i q^{83} +(-0.964557 - 4.29903i) q^{85} +4.90755 q^{86} +9.16246i q^{87} -2.39327i q^{88} -1.97949 q^{89} +(0.489528 + 2.18183i) q^{90} -8.17113i q^{92} +1.60673i q^{93} -3.00868 q^{94} +(9.10069 - 2.04189i) q^{95} +1.00000 q^{96} -12.0624i q^{97} +2.39327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{4} + 4q^{5} + 8q^{6} - 8q^{9} + O(q^{10}) \) \( 8q - 8q^{4} + 4q^{5} + 8q^{6} - 8q^{9} + 8q^{16} - 24q^{19} - 4q^{20} - 8q^{24} + 4q^{25} + 16q^{29} + 4q^{30} + 32q^{31} - 8q^{34} + 8q^{36} + 24q^{41} - 4q^{45} + 8q^{46} - 4q^{50} + 8q^{51} - 8q^{54} - 40q^{59} + 24q^{61} - 8q^{64} + 28q^{65} - 8q^{69} - 40q^{71} + 16q^{74} + 4q^{75} + 24q^{76} + 16q^{79} + 4q^{80} + 8q^{81} + 28q^{85} + 8q^{86} - 88q^{89} - 24q^{94} + 24q^{95} + 8q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 2.18183 0.489528i 0.975742 0.218924i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −0.489528 2.18183i −0.154802 0.689954i
\(11\) −2.39327 −0.721598 −0.360799 0.932644i \(-0.617496\pi\)
−0.360799 + 0.932644i \(0.617496\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 3.80748i 1.05601i 0.849243 + 0.528003i \(0.177059\pi\)
−0.849243 + 0.528003i \(0.822941\pi\)
\(14\) 0 0
\(15\) 0.489528 + 2.18183i 0.126396 + 0.563345i
\(16\) 1.00000 0.250000
\(17\) 1.97038i 0.477888i −0.971033 0.238944i \(-0.923199\pi\)
0.971033 0.238944i \(-0.0768012\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.17113 0.956924 0.478462 0.878108i \(-0.341194\pi\)
0.478462 + 0.878108i \(0.341194\pi\)
\(20\) −2.18183 + 0.489528i −0.487871 + 0.109462i
\(21\) 0 0
\(22\) 2.39327i 0.510247i
\(23\) 8.17113i 1.70380i 0.523705 + 0.851900i \(0.324549\pi\)
−0.523705 + 0.851900i \(0.675451\pi\)
\(24\) −1.00000 −0.204124
\(25\) 4.52072 2.13613i 0.904145 0.427226i
\(26\) 3.80748 0.746709
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 9.16246 1.70143 0.850713 0.525631i \(-0.176171\pi\)
0.850713 + 0.525631i \(0.176171\pi\)
\(30\) 2.18183 0.489528i 0.398345 0.0893752i
\(31\) 1.60673 0.288577 0.144289 0.989536i \(-0.453911\pi\)
0.144289 + 0.989536i \(0.453911\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.39327i 0.416615i
\(34\) −1.97038 −0.337918
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 1.26358i 0.207732i −0.994591 0.103866i \(-0.966879\pi\)
0.994591 0.103866i \(-0.0331213\pi\)
\(38\) 4.17113i 0.676647i
\(39\) −3.80748 −0.609685
\(40\) 0.489528 + 2.18183i 0.0774012 + 0.344977i
\(41\) −3.19208 −0.498519 −0.249259 0.968437i \(-0.580187\pi\)
−0.249259 + 0.968437i \(0.580187\pi\)
\(42\) 0 0
\(43\) 4.90755i 0.748394i 0.927349 + 0.374197i \(0.122082\pi\)
−0.927349 + 0.374197i \(0.877918\pi\)
\(44\) 2.39327 0.360799
\(45\) −2.18183 + 0.489528i −0.325247 + 0.0729745i
\(46\) 8.17113 1.20477
\(47\) 3.00868i 0.438860i −0.975628 0.219430i \(-0.929580\pi\)
0.975628 0.219430i \(-0.0704198\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) −2.13613 4.52072i −0.302094 0.639327i
\(51\) 1.97038 0.275909
\(52\) 3.80748i 0.528003i
\(53\) 12.1711i 1.67183i 0.548856 + 0.835917i \(0.315064\pi\)
−0.548856 + 0.835917i \(0.684936\pi\)
\(54\) −1.00000 −0.136083
\(55\) −5.22170 + 1.17157i −0.704093 + 0.157975i
\(56\) 0 0
\(57\) 4.17113i 0.552480i
\(58\) 9.16246i 1.20309i
\(59\) −13.0414 −1.69785 −0.848926 0.528512i \(-0.822750\pi\)
−0.848926 + 0.528512i \(0.822750\pi\)
\(60\) −0.489528 2.18183i −0.0631978 0.281672i
\(61\) 13.0910 1.67612 0.838062 0.545574i \(-0.183688\pi\)
0.838062 + 0.545574i \(0.183688\pi\)
\(62\) 1.60673i 0.204055i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.86387 + 8.30726i 0.231185 + 1.03039i
\(66\) −2.39327 −0.294591
\(67\) 5.77786i 0.705878i 0.935646 + 0.352939i \(0.114818\pi\)
−0.935646 + 0.352939i \(0.885182\pi\)
\(68\) 1.97038i 0.238944i
\(69\) −8.17113 −0.983689
\(70\) 0 0
\(71\) 6.94032 0.823665 0.411832 0.911260i \(-0.364889\pi\)
0.411832 + 0.911260i \(0.364889\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 0.506664i 0.0593005i −0.999560 0.0296503i \(-0.990561\pi\)
0.999560 0.0296503i \(-0.00943935\pi\)
\(74\) −1.26358 −0.146889
\(75\) 2.13613 + 4.52072i 0.246659 + 0.522008i
\(76\) −4.17113 −0.478462
\(77\) 0 0
\(78\) 3.80748i 0.431113i
\(79\) 12.4260 1.39804 0.699020 0.715103i \(-0.253620\pi\)
0.699020 + 0.715103i \(0.253620\pi\)
\(80\) 2.18183 0.489528i 0.243935 0.0547309i
\(81\) 1.00000 0.111111
\(82\) 3.19208i 0.352506i
\(83\) 1.89887i 0.208429i −0.994555 0.104214i \(-0.966767\pi\)
0.994555 0.104214i \(-0.0332328\pi\)
\(84\) 0 0
\(85\) −0.964557 4.29903i −0.104621 0.466295i
\(86\) 4.90755 0.529195
\(87\) 9.16246i 0.982319i
\(88\) 2.39327i 0.255123i
\(89\) −1.97949 −0.209826 −0.104913 0.994481i \(-0.533456\pi\)
−0.104913 + 0.994481i \(0.533456\pi\)
\(90\) 0.489528 + 2.18183i 0.0516008 + 0.229985i
\(91\) 0 0
\(92\) 8.17113i 0.851900i
\(93\) 1.60673i 0.166610i
\(94\) −3.00868 −0.310321
\(95\) 9.10069 2.04189i 0.933711 0.209493i
\(96\) 1.00000 0.102062
\(97\) 12.0624i 1.22475i −0.790567 0.612375i \(-0.790214\pi\)
0.790567 0.612375i \(-0.209786\pi\)
\(98\) 0 0
\(99\) 2.39327 0.240533
\(100\) −4.52072 + 2.13613i −0.452072 + 0.213613i
\(101\) 7.86672 0.782768 0.391384 0.920227i \(-0.371996\pi\)
0.391384 + 0.920227i \(0.371996\pi\)
\(102\) 1.97038i 0.195097i
\(103\) 5.89887i 0.581233i 0.956840 + 0.290617i \(0.0938604\pi\)
−0.956840 + 0.290617i \(0.906140\pi\)
\(104\) −3.80748 −0.373354
\(105\) 0 0
\(106\) 12.1711 1.18217
\(107\) 3.75798i 0.363298i −0.983363 0.181649i \(-0.941857\pi\)
0.983363 0.181649i \(-0.0581434\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −7.14257 −0.684135 −0.342067 0.939675i \(-0.611127\pi\)
−0.342067 + 0.939675i \(0.611127\pi\)
\(110\) 1.17157 + 5.22170i 0.111705 + 0.497869i
\(111\) 1.26358 0.119934
\(112\) 0 0
\(113\) 17.3837i 1.63532i −0.575700 0.817661i \(-0.695270\pi\)
0.575700 0.817661i \(-0.304730\pi\)
\(114\) 4.17113 0.390663
\(115\) 4.00000 + 17.8280i 0.373002 + 1.66247i
\(116\) −9.16246 −0.850713
\(117\) 3.80748i 0.352002i
\(118\) 13.0414i 1.20056i
\(119\) 0 0
\(120\) −2.18183 + 0.489528i −0.199173 + 0.0446876i
\(121\) −5.27226 −0.479296
\(122\) 13.0910i 1.18520i
\(123\) 3.19208i 0.287820i
\(124\) −1.60673 −0.144289
\(125\) 8.81774 6.87368i 0.788682 0.614801i
\(126\) 0 0
\(127\) 18.4434i 1.63659i 0.574801 + 0.818293i \(0.305079\pi\)
−0.574801 + 0.818293i \(0.694921\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −4.90755 −0.432086
\(130\) 8.30726 1.86387i 0.728595 0.163472i
\(131\) 0.615405 0.0537682 0.0268841 0.999639i \(-0.491441\pi\)
0.0268841 + 0.999639i \(0.491441\pi\)
\(132\) 2.39327i 0.208307i
\(133\) 0 0
\(134\) 5.77786 0.499131
\(135\) −0.489528 2.18183i −0.0421319 0.187782i
\(136\) 1.97038 0.168959
\(137\) 7.82799i 0.668790i 0.942433 + 0.334395i \(0.108532\pi\)
−0.942433 + 0.334395i \(0.891468\pi\)
\(138\) 8.17113i 0.695573i
\(139\) 6.15378 0.521957 0.260979 0.965345i \(-0.415955\pi\)
0.260979 + 0.965345i \(0.415955\pi\)
\(140\) 0 0
\(141\) 3.00868 0.253376
\(142\) 6.94032i 0.582419i
\(143\) 9.11233i 0.762012i
\(144\) −1.00000 −0.0833333
\(145\) 19.9909 4.48528i 1.66015 0.372482i
\(146\) −0.506664 −0.0419318
\(147\) 0 0
\(148\) 1.26358i 0.103866i
\(149\) 7.53584 0.617360 0.308680 0.951166i \(-0.400113\pi\)
0.308680 + 0.951166i \(0.400113\pi\)
\(150\) 4.52072 2.13613i 0.369116 0.174414i
\(151\) 9.04145 0.735783 0.367891 0.929869i \(-0.380080\pi\)
0.367891 + 0.929869i \(0.380080\pi\)
\(152\) 4.17113i 0.338324i
\(153\) 1.97038i 0.159296i
\(154\) 0 0
\(155\) 3.50560 0.786540i 0.281577 0.0631764i
\(156\) 3.80748 0.304843
\(157\) 22.6640i 1.80879i 0.426700 + 0.904393i \(0.359676\pi\)
−0.426700 + 0.904393i \(0.640324\pi\)
\(158\) 12.4260i 0.988563i
\(159\) −12.1711 −0.965234
\(160\) −0.489528 2.18183i −0.0387006 0.172488i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 10.2039i 0.799232i 0.916683 + 0.399616i \(0.130856\pi\)
−0.916683 + 0.399616i \(0.869144\pi\)
\(164\) 3.19208 0.249259
\(165\) −1.17157 5.22170i −0.0912068 0.406509i
\(166\) −1.89887 −0.147381
\(167\) 25.2498i 1.95389i −0.213492 0.976945i \(-0.568484\pi\)
0.213492 0.976945i \(-0.431516\pi\)
\(168\) 0 0
\(169\) −1.49693 −0.115148
\(170\) −4.29903 + 0.964557i −0.329720 + 0.0739781i
\(171\) −4.17113 −0.318975
\(172\) 4.90755i 0.374197i
\(173\) 12.5348i 0.953002i −0.879174 0.476501i \(-0.841905\pi\)
0.879174 0.476501i \(-0.158095\pi\)
\(174\) 9.16246 0.694604
\(175\) 0 0
\(176\) −2.39327 −0.180399
\(177\) 13.0414i 0.980255i
\(178\) 1.97949i 0.148369i
\(179\) −22.9196 −1.71309 −0.856544 0.516074i \(-0.827393\pi\)
−0.856544 + 0.516074i \(0.827393\pi\)
\(180\) 2.18183 0.489528i 0.162624 0.0364873i
\(181\) 19.6181 1.45820 0.729102 0.684405i \(-0.239938\pi\)
0.729102 + 0.684405i \(0.239938\pi\)
\(182\) 0 0
\(183\) 13.0910i 0.967711i
\(184\) −8.17113 −0.602384
\(185\) −0.618560 2.75692i −0.0454774 0.202693i
\(186\) 1.60673 0.117811
\(187\) 4.71565i 0.344843i
\(188\) 3.00868i 0.219430i
\(189\) 0 0
\(190\) −2.04189 9.10069i −0.148134 0.660233i
\(191\) −19.7269 −1.42739 −0.713693 0.700459i \(-0.752979\pi\)
−0.713693 + 0.700459i \(0.752979\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 4.78654i 0.344543i −0.985050 0.172271i \(-0.944889\pi\)
0.985050 0.172271i \(-0.0551106\pi\)
\(194\) −12.0624 −0.866029
\(195\) −8.30726 + 1.86387i −0.594896 + 0.133475i
\(196\) 0 0
\(197\) 17.1997i 1.22543i −0.790305 0.612714i \(-0.790078\pi\)
0.790305 0.612714i \(-0.209922\pi\)
\(198\) 2.39327i 0.170082i
\(199\) −15.5056 −1.09916 −0.549582 0.835440i \(-0.685213\pi\)
−0.549582 + 0.835440i \(0.685213\pi\)
\(200\) 2.13613 + 4.52072i 0.151047 + 0.319663i
\(201\) −5.77786 −0.407539
\(202\) 7.86672i 0.553501i
\(203\) 0 0
\(204\) −1.97038 −0.137954
\(205\) −6.96456 + 1.56261i −0.486426 + 0.109138i
\(206\) 5.89887 0.410994
\(207\) 8.17113i 0.567933i
\(208\) 3.80748i 0.264001i
\(209\) −9.98265 −0.690514
\(210\) 0 0
\(211\) −23.8980 −1.64521 −0.822603 0.568616i \(-0.807479\pi\)
−0.822603 + 0.568616i \(0.807479\pi\)
\(212\) 12.1711i 0.835917i
\(213\) 6.94032i 0.475543i
\(214\) −3.75798 −0.256890
\(215\) 2.40238 + 10.7074i 0.163841 + 0.730240i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 7.14257i 0.483756i
\(219\) 0.506664 0.0342372
\(220\) 5.22170 1.17157i 0.352047 0.0789874i
\(221\) 7.50219 0.504652
\(222\) 1.26358i 0.0848062i
\(223\) 0.870315i 0.0582806i 0.999575 + 0.0291403i \(0.00927696\pi\)
−0.999575 + 0.0291403i \(0.990723\pi\)
\(224\) 0 0
\(225\) −4.52072 + 2.13613i −0.301382 + 0.142409i
\(226\) −17.3837 −1.15635
\(227\) 14.6854i 0.974705i −0.873205 0.487353i \(-0.837963\pi\)
0.873205 0.487353i \(-0.162037\pi\)
\(228\) 4.17113i 0.276240i
\(229\) −24.0379 −1.58847 −0.794233 0.607613i \(-0.792127\pi\)
−0.794233 + 0.607613i \(0.792127\pi\)
\(230\) 17.8280 4.00000i 1.17554 0.263752i
\(231\) 0 0
\(232\) 9.16246i 0.601545i
\(233\) 10.5445i 0.690794i 0.938457 + 0.345397i \(0.112256\pi\)
−0.938457 + 0.345397i \(0.887744\pi\)
\(234\) −3.80748 −0.248903
\(235\) −1.47283 6.56440i −0.0960769 0.428215i
\(236\) 13.0414 0.848926
\(237\) 12.4260i 0.807158i
\(238\) 0 0
\(239\) 4.01289 0.259572 0.129786 0.991542i \(-0.458571\pi\)
0.129786 + 0.991542i \(0.458571\pi\)
\(240\) 0.489528 + 2.18183i 0.0315989 + 0.140836i
\(241\) 0.543899 0.0350356 0.0175178 0.999847i \(-0.494424\pi\)
0.0175178 + 0.999847i \(0.494424\pi\)
\(242\) 5.27226i 0.338914i
\(243\) 1.00000i 0.0641500i
\(244\) −13.0910 −0.838062
\(245\) 0 0
\(246\) −3.19208 −0.203519
\(247\) 15.8815i 1.01052i
\(248\) 1.60673i 0.102027i
\(249\) 1.89887 0.120336
\(250\) −6.87368 8.81774i −0.434730 0.557683i
\(251\) −4.62829 −0.292135 −0.146068 0.989275i \(-0.546662\pi\)
−0.146068 + 0.989275i \(0.546662\pi\)
\(252\) 0 0
\(253\) 19.5557i 1.22946i
\(254\) 18.4434 1.15724
\(255\) 4.29903 0.964557i 0.269216 0.0604029i
\(256\) 1.00000 0.0625000
\(257\) 25.5671i 1.59483i −0.603429 0.797417i \(-0.706199\pi\)
0.603429 0.797417i \(-0.293801\pi\)
\(258\) 4.90755i 0.305531i
\(259\) 0 0
\(260\) −1.86387 8.30726i −0.115592 0.515195i
\(261\) −9.16246 −0.567142
\(262\) 0.615405i 0.0380199i
\(263\) 20.5972i 1.27008i 0.772481 + 0.635038i \(0.219016\pi\)
−0.772481 + 0.635038i \(0.780984\pi\)
\(264\) 2.39327 0.147296
\(265\) 5.95811 + 26.5553i 0.366004 + 1.63128i
\(266\) 0 0
\(267\) 1.97949i 0.121143i
\(268\) 5.77786i 0.352939i
\(269\) 2.23799 0.136453 0.0682263 0.997670i \(-0.478266\pi\)
0.0682263 + 0.997670i \(0.478266\pi\)
\(270\) −2.18183 + 0.489528i −0.132782 + 0.0297917i
\(271\) −19.1616 −1.16398 −0.581992 0.813195i \(-0.697726\pi\)
−0.581992 + 0.813195i \(0.697726\pi\)
\(272\) 1.97038i 0.119472i
\(273\) 0 0
\(274\) 7.82799 0.472906
\(275\) −10.8193 + 5.11233i −0.652429 + 0.308285i
\(276\) 8.17113 0.491844
\(277\) 3.67674i 0.220914i −0.993881 0.110457i \(-0.964769\pi\)
0.993881 0.110457i \(-0.0352314\pi\)
\(278\) 6.15378i 0.369079i
\(279\) −1.60673 −0.0961924
\(280\) 0 0
\(281\) −29.8280 −1.77939 −0.889694 0.456557i \(-0.849083\pi\)
−0.889694 + 0.456557i \(0.849083\pi\)
\(282\) 3.00868i 0.179164i
\(283\) 4.28961i 0.254991i −0.991839 0.127495i \(-0.959306\pi\)
0.991839 0.127495i \(-0.0406938\pi\)
\(284\) −6.94032 −0.411832
\(285\) 2.04189 + 9.10069i 0.120951 + 0.539078i
\(286\) −9.11233 −0.538824
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) 13.1176 0.771623
\(290\) −4.48528 19.9909i −0.263385 1.17391i
\(291\) 12.0624 0.707110
\(292\) 0.506664i 0.0296503i
\(293\) 24.5940i 1.43680i −0.695631 0.718399i \(-0.744875\pi\)
0.695631 0.718399i \(-0.255125\pi\)
\(294\) 0 0
\(295\) −28.4542 + 6.38416i −1.65667 + 0.371700i
\(296\) 1.26358 0.0734444
\(297\) 2.39327i 0.138872i
\(298\) 7.53584i 0.436540i
\(299\) −31.1115 −1.79922
\(300\) −2.13613 4.52072i −0.123330 0.261004i
\(301\) 0 0
\(302\) 9.04145i 0.520277i
\(303\) 7.86672i 0.451931i
\(304\) 4.17113 0.239231
\(305\) 28.5622 6.40839i 1.63547 0.366943i
\(306\) 1.97038 0.112639
\(307\) 2.14089i 0.122187i 0.998132 + 0.0610937i \(0.0194588\pi\)
−0.998132 + 0.0610937i \(0.980541\pi\)
\(308\) 0 0
\(309\) −5.89887 −0.335575
\(310\) −0.786540 3.50560i −0.0446724 0.199105i
\(311\) 13.9991 0.793817 0.396909 0.917858i \(-0.370083\pi\)
0.396909 + 0.917858i \(0.370083\pi\)
\(312\) 3.80748i 0.215556i
\(313\) 33.0727i 1.86938i −0.355463 0.934690i \(-0.615677\pi\)
0.355463 0.934690i \(-0.384323\pi\)
\(314\) 22.6640 1.27901
\(315\) 0 0
\(316\) −12.4260 −0.699020
\(317\) 7.38459i 0.414760i −0.978260 0.207380i \(-0.933506\pi\)
0.978260 0.207380i \(-0.0664937\pi\)
\(318\) 12.1711i 0.682523i
\(319\) −21.9282 −1.22775
\(320\) −2.18183 + 0.489528i −0.121968 + 0.0273655i
\(321\) 3.75798 0.209750
\(322\) 0 0
\(323\) 8.21872i 0.457302i
\(324\) −1.00000 −0.0555556
\(325\) 8.13328 + 17.2126i 0.451153 + 0.954782i
\(326\) 10.2039 0.565142
\(327\) 7.14257i 0.394985i
\(328\) 3.19208i 0.176253i
\(329\) 0 0
\(330\) −5.22170 + 1.17157i −0.287445 + 0.0644930i
\(331\) 21.5549 1.18476 0.592381 0.805658i \(-0.298188\pi\)
0.592381 + 0.805658i \(0.298188\pi\)
\(332\) 1.89887i 0.104214i
\(333\) 1.26358i 0.0692440i
\(334\) −25.2498 −1.38161
\(335\) 2.82843 + 12.6063i 0.154533 + 0.688755i
\(336\) 0 0
\(337\) 22.2549i 1.21230i 0.795350 + 0.606151i \(0.207287\pi\)
−0.795350 + 0.606151i \(0.792713\pi\)
\(338\) 1.49693i 0.0814222i
\(339\) 17.3837 0.944154
\(340\) 0.964557 + 4.29903i 0.0523104 + 0.233148i
\(341\) −3.84534 −0.208237
\(342\) 4.17113i 0.225549i
\(343\) 0 0
\(344\) −4.90755 −0.264597
\(345\) −17.8280 + 4.00000i −0.959827 + 0.215353i
\(346\) −12.5348 −0.673874
\(347\) 2.14089i 0.114929i 0.998348 + 0.0574646i \(0.0183016\pi\)
−0.998348 + 0.0574646i \(0.981698\pi\)
\(348\) 9.16246i 0.491159i
\(349\) 0.906929 0.0485468 0.0242734 0.999705i \(-0.492273\pi\)
0.0242734 + 0.999705i \(0.492273\pi\)
\(350\) 0 0
\(351\) 3.80748 0.203228
\(352\) 2.39327i 0.127562i
\(353\) 13.8866i 0.739109i −0.929209 0.369555i \(-0.879510\pi\)
0.929209 0.369555i \(-0.120490\pi\)
\(354\) −13.0414 −0.693145
\(355\) 15.1426 3.39748i 0.803684 0.180320i
\(356\) 1.97949 0.104913
\(357\) 0 0
\(358\) 22.9196i 1.21134i
\(359\) −18.8565 −0.995211 −0.497605 0.867404i \(-0.665787\pi\)
−0.497605 + 0.867404i \(0.665787\pi\)
\(360\) −0.489528 2.18183i −0.0258004 0.114992i
\(361\) −1.60164 −0.0842968
\(362\) 19.6181i 1.03111i
\(363\) 5.27226i 0.276722i
\(364\) 0 0
\(365\) −0.248026 1.10545i −0.0129823 0.0578620i
\(366\) 13.0910 0.684275
\(367\) 31.5722i 1.64806i −0.566549 0.824028i \(-0.691722\pi\)
0.566549 0.824028i \(-0.308278\pi\)
\(368\) 8.17113i 0.425950i
\(369\) 3.19208 0.166173
\(370\) −2.75692 + 0.618560i −0.143325 + 0.0321574i
\(371\) 0 0
\(372\) 1.60673i 0.0833051i
\(373\) 20.9075i 1.08255i −0.840845 0.541276i \(-0.817941\pi\)
0.840845 0.541276i \(-0.182059\pi\)
\(374\) 4.71565 0.243841
\(375\) 6.87368 + 8.81774i 0.354956 + 0.455346i
\(376\) 3.00868 0.155161
\(377\) 34.8859i 1.79672i
\(378\) 0 0
\(379\) 9.82440 0.504646 0.252323 0.967643i \(-0.418805\pi\)
0.252323 + 0.967643i \(0.418805\pi\)
\(380\) −9.10069 + 2.04189i −0.466855 + 0.104747i
\(381\) −18.4434 −0.944884
\(382\) 19.7269i 1.00931i
\(383\) 30.6647i 1.56689i 0.621461 + 0.783445i \(0.286540\pi\)
−0.621461 + 0.783445i \(0.713460\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −4.78654 −0.243628
\(387\) 4.90755i 0.249465i
\(388\) 12.0624i 0.612375i
\(389\) −23.4476 −1.18884 −0.594420 0.804154i \(-0.702618\pi\)
−0.594420 + 0.804154i \(0.702618\pi\)
\(390\) 1.86387 + 8.30726i 0.0943807 + 0.420655i
\(391\) 16.1002 0.814225
\(392\) 0 0
\(393\) 0.615405i 0.0310431i
\(394\) −17.1997 −0.866508
\(395\) 27.1115 6.08290i 1.36413 0.306064i
\(396\) −2.39327 −0.120266
\(397\) 35.3761i 1.77548i 0.460349 + 0.887738i \(0.347724\pi\)
−0.460349 + 0.887738i \(0.652276\pi\)
\(398\) 15.5056i 0.777226i
\(399\) 0 0
\(400\) 4.52072 2.13613i 0.226036 0.106806i
\(401\) −9.04145 −0.451508 −0.225754 0.974184i \(-0.572485\pi\)
−0.225754 + 0.974184i \(0.572485\pi\)
\(402\) 5.77786i 0.288174i
\(403\) 6.11760i 0.304739i
\(404\) −7.86672 −0.391384
\(405\) 2.18183 0.489528i 0.108416 0.0243248i
\(406\) 0 0
\(407\) 3.02410i 0.149899i
\(408\) 1.97038i 0.0975484i
\(409\) 15.4379 0.763354 0.381677 0.924296i \(-0.375347\pi\)
0.381677 + 0.924296i \(0.375347\pi\)
\(410\) 1.56261 + 6.96456i 0.0771719 + 0.343955i
\(411\) −7.82799 −0.386126
\(412\) 5.89887i 0.290617i
\(413\) 0 0
\(414\) −8.17113 −0.401589
\(415\) −0.929553 4.14301i −0.0456299 0.203373i
\(416\) 3.80748 0.186677
\(417\) 6.15378i 0.301352i
\(418\) 9.98265i 0.488267i
\(419\) 26.6274 1.30083 0.650417 0.759577i \(-0.274594\pi\)
0.650417 + 0.759577i \(0.274594\pi\)
\(420\) 0 0
\(421\) 5.04591 0.245923 0.122961 0.992411i \(-0.460761\pi\)
0.122961 + 0.992411i \(0.460761\pi\)
\(422\) 23.8980i 1.16334i
\(423\) 3.00868i 0.146287i
\(424\) −12.1711 −0.591083
\(425\) −4.20899 8.90755i −0.204166 0.432080i
\(426\) 6.94032 0.336260
\(427\) 0 0
\(428\) 3.75798i 0.181649i
\(429\) 9.11233 0.439948
\(430\) 10.7074 2.40238i 0.516357 0.115853i
\(431\) −25.2835 −1.21786 −0.608931 0.793223i \(-0.708401\pi\)
−0.608931 + 0.793223i \(0.708401\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 27.0063i 1.29784i 0.760857 + 0.648920i \(0.224779\pi\)
−0.760857 + 0.648920i \(0.775221\pi\)
\(434\) 0 0
\(435\) 4.48528 + 19.9909i 0.215053 + 0.958490i
\(436\) 7.14257 0.342067
\(437\) 34.0829i 1.63041i
\(438\) 0.506664i 0.0242093i
\(439\) −27.9316 −1.33310 −0.666552 0.745458i \(-0.732231\pi\)
−0.666552 + 0.745458i \(0.732231\pi\)
\(440\) −1.17157 5.22170i −0.0558525 0.248935i
\(441\) 0 0
\(442\) 7.50219i 0.356843i
\(443\) 10.7692i 0.511660i 0.966722 + 0.255830i \(0.0823487\pi\)
−0.966722 + 0.255830i \(0.917651\pi\)
\(444\) −1.26358 −0.0599671
\(445\) −4.31891 + 0.969018i −0.204736 + 0.0459359i
\(446\) 0.870315 0.0412106
\(447\) 7.53584i 0.356433i
\(448\) 0 0
\(449\) 15.1288 0.713973 0.356986 0.934110i \(-0.383804\pi\)
0.356986 + 0.934110i \(0.383804\pi\)
\(450\) 2.13613 + 4.52072i 0.100698 + 0.213109i
\(451\) 7.63950 0.359730
\(452\) 17.3837i 0.817661i
\(453\) 9.04145i 0.424804i
\(454\) −14.6854 −0.689221
\(455\) 0 0
\(456\) −4.17113 −0.195331
\(457\) 21.4711i 1.00437i −0.864759 0.502187i \(-0.832529\pi\)
0.864759 0.502187i \(-0.167471\pi\)
\(458\) 24.0379i 1.12322i
\(459\) −1.97038 −0.0919695
\(460\) −4.00000 17.8280i −0.186501 0.831234i
\(461\) −30.4465 −1.41804 −0.709019 0.705190i \(-0.750862\pi\)
−0.709019 + 0.705190i \(0.750862\pi\)
\(462\) 0 0
\(463\) 40.2005i 1.86828i −0.356913 0.934138i \(-0.616171\pi\)
0.356913 0.934138i \(-0.383829\pi\)
\(464\) 9.16246 0.425356
\(465\) 0.786540 + 3.50560i 0.0364749 + 0.162569i
\(466\) 10.5445 0.488465
\(467\) 7.84175i 0.362873i −0.983403 0.181437i \(-0.941925\pi\)
0.983403 0.181437i \(-0.0580747\pi\)
\(468\) 3.80748i 0.176001i
\(469\) 0 0
\(470\) −6.56440 + 1.47283i −0.302793 + 0.0679366i
\(471\) −22.6640 −1.04430
\(472\) 13.0414i 0.600281i
\(473\) 11.7451i 0.540040i
\(474\) 12.4260 0.570747
\(475\) 18.8565 8.91008i 0.865198 0.408823i
\(476\) 0 0
\(477\) 12.1711i 0.557278i
\(478\) 4.01289i 0.183545i
\(479\) −27.7745 −1.26905 −0.634524 0.772904i \(-0.718804\pi\)
−0.634524 + 0.772904i \(0.718804\pi\)
\(480\) 2.18183 0.489528i 0.0995863 0.0223438i
\(481\) 4.81108 0.219366
\(482\) 0.543899i 0.0247739i
\(483\) 0 0
\(484\) 5.27226 0.239648
\(485\) −5.90488 26.3180i −0.268127 1.19504i
\(486\) 1.00000 0.0453609
\(487\) 12.5263i 0.567620i −0.958880 0.283810i \(-0.908401\pi\)
0.958880 0.283810i \(-0.0915986\pi\)
\(488\) 13.0910i 0.592600i
\(489\) −10.2039 −0.461437
\(490\) 0 0
\(491\) −24.3924 −1.10081 −0.550407 0.834897i \(-0.685527\pi\)
−0.550407 + 0.834897i \(0.685527\pi\)
\(492\) 3.19208i 0.143910i
\(493\) 18.0535i 0.813090i
\(494\) 15.8815 0.714544
\(495\) 5.22170 1.17157i 0.234698 0.0526583i
\(496\) 1.60673 0.0721443
\(497\) 0 0
\(498\) 1.89887i 0.0850906i
\(499\) 23.6560 1.05899 0.529493 0.848314i \(-0.322382\pi\)
0.529493 + 0.848314i \(0.322382\pi\)
\(500\) −8.81774 + 6.87368i −0.394341 + 0.307400i
\(501\) 25.2498 1.12808
\(502\) 4.62829i 0.206571i
\(503\) 20.8496i 0.929636i −0.885406 0.464818i \(-0.846120\pi\)
0.885406 0.464818i \(-0.153880\pi\)
\(504\) 0 0
\(505\) 17.1638 3.85098i 0.763780 0.171366i
\(506\) −19.5557 −0.869358
\(507\) 1.49693i 0.0664810i
\(508\) 18.4434i 0.818293i
\(509\) −2.59490 −0.115017 −0.0575085 0.998345i \(-0.518316\pi\)
−0.0575085 + 0.998345i \(0.518316\pi\)
\(510\) −0.964557 4.29903i −0.0427113 0.190364i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 4.17113i 0.184160i
\(514\) −25.5671 −1.12772
\(515\) 2.88767 + 12.8703i 0.127246 + 0.567134i
\(516\) 4.90755 0.216043
\(517\) 7.20057i 0.316681i
\(518\) 0 0
\(519\) 12.5348 0.550216
\(520\) −8.30726 + 1.86387i −0.364298 + 0.0817361i
\(521\) 24.4884 1.07286 0.536429 0.843945i \(-0.319773\pi\)
0.536429 + 0.843945i \(0.319773\pi\)
\(522\) 9.16246i 0.401030i
\(523\) 21.6257i 0.945627i 0.881162 + 0.472814i \(0.156762\pi\)
−0.881162 + 0.472814i \(0.843238\pi\)
\(524\) −0.615405 −0.0268841
\(525\) 0 0
\(526\) 20.5972 0.898080
\(527\) 3.16587i 0.137907i
\(528\) 2.39327i 0.104154i
\(529\) −43.7674 −1.90293
\(530\) 26.5553 5.95811i 1.15349 0.258804i
\(531\) 13.0414 0.565951
\(532\) 0 0
\(533\) 12.1538i 0.526439i
\(534\) −1.97949 −0.0856611
\(535\) −1.83964 8.19926i −0.0795344 0.354485i
\(536\) −5.77786 −0.249566
\(537\) 22.9196i 0.989052i
\(538\) 2.23799i 0.0964865i
\(539\) 0 0
\(540\) 0.489528 + 2.18183i 0.0210659 + 0.0938908i
\(541\) 8.01735 0.344693 0.172346 0.985036i \(-0.444865\pi\)
0.172346 + 0.985036i \(0.444865\pi\)
\(542\) 19.1616i 0.823060i
\(543\) 19.6181i 0.841894i
\(544\) −1.97038 −0.0844794
\(545\) −15.5839 + 3.49649i −0.667539 + 0.149773i
\(546\) 0 0
\(547\) 43.0251i 1.83962i 0.392361 + 0.919811i \(0.371658\pi\)
−0.392361 + 0.919811i \(0.628342\pi\)
\(548\) 7.82799i 0.334395i
\(549\) −13.0910 −0.558708
\(550\) 5.11233 + 10.8193i 0.217991 + 0.461337i
\(551\) 38.2178 1.62814
\(552\) 8.17113i 0.347787i
\(553\) 0 0
\(554\) −3.67674 −0.156210
\(555\) 2.75692 0.618560i 0.117025 0.0262564i
\(556\) −6.15378 −0.260979
\(557\) 11.1823i 0.473811i −0.971533 0.236906i \(-0.923867\pi\)
0.971533 0.236906i \(-0.0761332\pi\)
\(558\) 1.60673i 0.0680183i
\(559\) −18.6854 −0.790309
\(560\) 0 0
\(561\) −4.71565 −0.199095
\(562\) 29.8280i 1.25822i
\(563\) 26.8694i 1.13241i −0.824264 0.566206i \(-0.808411\pi\)
0.824264 0.566206i \(-0.191589\pi\)
\(564\) −3.00868 −0.126688
\(565\) −8.50982 37.9282i −0.358011 1.59565i
\(566\) −4.28961 −0.180306
\(567\) 0 0
\(568\) 6.94032i 0.291210i
\(569\) 2.61453 0.109607 0.0548034 0.998497i \(-0.482547\pi\)
0.0548034 + 0.998497i \(0.482547\pi\)
\(570\) 9.10069 2.04189i 0.381186 0.0855253i
\(571\) 12.4607 0.521466 0.260733 0.965411i \(-0.416036\pi\)
0.260733 + 0.965411i \(0.416036\pi\)
\(572\) 9.11233i 0.381006i
\(573\) 19.7269i 0.824102i
\(574\) 0 0
\(575\) 17.4546 + 36.9394i 0.727907 + 1.54048i
\(576\) 1.00000 0.0416667
\(577\) 17.8195i 0.741835i −0.928666 0.370918i \(-0.879043\pi\)
0.928666 0.370918i \(-0.120957\pi\)
\(578\) 13.1176i 0.545620i
\(579\) 4.78654 0.198922
\(580\) −19.9909 + 4.48528i −0.830076 + 0.186241i
\(581\) 0 0
\(582\) 12.0624i 0.500002i
\(583\) 29.1288i 1.20639i
\(584\) 0.506664 0.0209659
\(585\) −1.86387 8.30726i −0.0770615 0.343463i
\(586\) −24.5940 −1.01597
\(587\) 9.55661i 0.394443i 0.980359 + 0.197222i \(0.0631919\pi\)
−0.980359 + 0.197222i \(0.936808\pi\)
\(588\) 0 0
\(589\) 6.70189 0.276146
\(590\) 6.38416 + 28.4542i 0.262832 + 1.17144i
\(591\) 17.1997 0.707501
\(592\) 1.26358i 0.0519330i
\(593\) 11.6619i 0.478898i −0.970909 0.239449i \(-0.923033\pi\)
0.970909 0.239449i \(-0.0769668\pi\)
\(594\) 2.39327 0.0981970
\(595\) 0 0
\(596\) −7.53584 −0.308680
\(597\) 15.5056i 0.634602i
\(598\) 31.1115i 1.27224i
\(599\) 33.0977 1.35234 0.676168 0.736748i \(-0.263640\pi\)
0.676168 + 0.736748i \(0.263640\pi\)
\(600\) −4.52072 + 2.13613i −0.184558 + 0.0872071i
\(601\) 15.2886 0.623633 0.311817 0.950142i \(-0.399063\pi\)
0.311817 + 0.950142i \(0.399063\pi\)
\(602\) 0 0
\(603\) 5.77786i 0.235293i
\(604\) −9.04145 −0.367891
\(605\) −11.5032 + 2.58092i −0.467670 + 0.104929i
\(606\) 7.86672 0.319564
\(607\) 40.1823i 1.63095i 0.578794 + 0.815474i \(0.303524\pi\)
−0.578794 + 0.815474i \(0.696476\pi\)
\(608\) 4.17113i 0.169162i
\(609\) 0 0
\(610\) −6.40839 28.5622i −0.259468 1.15645i
\(611\) 11.4555 0.463439
\(612\) 1.97038i 0.0796479i
\(613\) 24.8591i 1.00405i −0.864853 0.502024i \(-0.832589\pi\)
0.864853 0.502024i \(-0.167411\pi\)
\(614\) 2.14089 0.0863995
\(615\) −1.56261 6.96456i −0.0630106 0.280838i
\(616\) 0 0
\(617\) 22.7647i 0.916473i −0.888830 0.458237i \(-0.848481\pi\)
0.888830 0.458237i \(-0.151519\pi\)
\(618\) 5.89887i 0.237288i
\(619\) −17.8280 −0.716567 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(620\) −3.50560 + 0.786540i −0.140788 + 0.0315882i
\(621\) 8.17113 0.327896
\(622\) 13.9991i 0.561314i
\(623\) 0 0
\(624\) −3.80748 −0.152421
\(625\) 15.8739 19.3137i 0.634956 0.772548i
\(626\) −33.0727 −1.32185
\(627\) 9.98265i 0.398669i
\(628\) 22.6640i 0.904393i
\(629\) −2.48974 −0.0992725
\(630\) 0 0
\(631\) 0.580705 0.0231175 0.0115587 0.999933i \(-0.496321\pi\)
0.0115587 + 0.999933i \(0.496321\pi\)
\(632\) 12.4260i 0.494281i
\(633\) 23.8980i 0.949860i
\(634\) −7.38459 −0.293280
\(635\) 9.02856 + 40.2403i 0.358287 + 1.59689i
\(636\) 12.1711 0.482617
\(637\) 0 0
\(638\) 21.9282i 0.868147i
\(639\) −6.94032 −0.274555
\(640\) 0.489528 + 2.18183i 0.0193503 + 0.0862442i
\(641\) 18.0353 0.712352 0.356176 0.934419i \(-0.384080\pi\)
0.356176 + 0.934419i \(0.384080\pi\)
\(642\) 3.75798i 0.148316i
\(643\) 39.3664i 1.55246i −0.630451 0.776229i \(-0.717130\pi\)
0.630451 0.776229i \(-0.282870\pi\)
\(644\) 0 0
\(645\) −10.7074 + 2.40238i −0.421604 + 0.0945938i
\(646\) −8.21872 −0.323361
\(647\) 2.38038i 0.0935824i 0.998905 + 0.0467912i \(0.0148995\pi\)
−0.998905 + 0.0467912i \(0.985100\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 31.2117 1.22517
\(650\) 17.2126 8.13328i 0.675133 0.319013i
\(651\) 0 0
\(652\) 10.2039i 0.399616i
\(653\) 25.1115i 0.982687i −0.870966 0.491344i \(-0.836506\pi\)
0.870966 0.491344i \(-0.163494\pi\)
\(654\) −7.14257 −0.279297
\(655\) 1.34271 0.301258i 0.0524639 0.0117711i
\(656\) −3.19208 −0.124630
\(657\) 0.506664i 0.0197668i
\(658\) 0 0
\(659\) 7.17981 0.279686 0.139843 0.990174i \(-0.455340\pi\)
0.139843 + 0.990174i \(0.455340\pi\)
\(660\) 1.17157 + 5.22170i 0.0456034 + 0.203254i
\(661\) −25.0330 −0.973669 −0.486835 0.873494i \(-0.661849\pi\)
−0.486835 + 0.873494i \(0.661849\pi\)
\(662\) 21.5549i 0.837753i
\(663\) 7.50219i 0.291361i
\(664\) 1.89887 0.0736906
\(665\) 0 0
\(666\) 1.26358 0.0489629
\(667\) 74.8677i 2.89889i
\(668\) 25.2498i 0.976945i
\(669\) −0.870315 −0.0336483
\(670\) 12.6063 2.82843i 0.487024 0.109272i
\(671\) −31.3302 −1.20949
\(672\) 0 0
\(673\) 9.67062i 0.372775i −0.982476 0.186388i \(-0.940322\pi\)
0.982476 0.186388i \(-0.0596780\pi\)
\(674\) 22.2549 0.857227
\(675\) −2.13613 4.52072i −0.0822197 0.174003i
\(676\) 1.49693 0.0575742
\(677\) 27.6890i 1.06418i 0.846689 + 0.532088i \(0.178592\pi\)
−0.846689 + 0.532088i \(0.821408\pi\)
\(678\) 17.3837i 0.667618i
\(679\) 0 0
\(680\) 4.29903 0.964557i 0.164860 0.0369891i
\(681\) 14.6854 0.562746
\(682\) 3.84534i 0.147246i
\(683\) 26.1227i 0.999556i −0.866154 0.499778i \(-0.833415\pi\)
0.866154 0.499778i \(-0.166585\pi\)
\(684\) 4.17113 0.159487
\(685\) 3.83202 + 17.0793i 0.146414 + 0.652567i
\(686\) 0 0
\(687\) 24.0379i 0.917101i
\(688\) 4.90755i 0.187099i
\(689\) −46.3414 −1.76547
\(690\) 4.00000 + 17.8280i 0.152277 + 0.678700i
\(691\) 24.7901 0.943061 0.471530 0.881850i \(-0.343702\pi\)
0.471530 + 0.881850i \(0.343702\pi\)
\(692\) 12.5348i 0.476501i
\(693\) 0 0
\(694\) 2.14089 0.0812673
\(695\) 13.4265 3.01245i 0.509295 0.114269i
\(696\) −9.16246 −0.347302
\(697\) 6.28961i 0.238236i
\(698\) 0.906929i 0.0343278i
\(699\) −10.5445 −0.398830
\(700\) 0 0
\(701\) 37.8817 1.43077 0.715386 0.698730i \(-0.246251\pi\)
0.715386 + 0.698730i \(0.246251\pi\)
\(702\) 3.80748i 0.143704i
\(703\) 5.27058i 0.198784i
\(704\) 2.39327 0.0901997
\(705\) 6.56440 1.47283i 0.247230 0.0554700i
\(706\) −13.8866 −0.522629
\(707\) 0 0
\(708\) 13.0414i 0.490128i
\(709\) 30.9801 1.16348 0.581741 0.813374i \(-0.302372\pi\)
0.581741 + 0.813374i \(0.302372\pi\)
\(710\) −3.39748 15.1426i −0.127505 0.568291i
\(711\) −12.4260 −0.466013
\(712\) 1.97949i 0.0741847i
\(713\) 13.1288i 0.491678i
\(714\) 0 0
\(715\) −4.46074 19.8815i −0.166822 0.743527i
\(716\) 22.9196 0.856544
\(717\) 4.01289i 0.149864i
\(718\) 18.8565i 0.703720i
\(719\) 16.7028 0.622908 0.311454 0.950261i \(-0.399184\pi\)
0.311454 + 0.950261i \(0.399184\pi\)
\(720\) −2.18183 + 0.489528i −0.0813118 + 0.0182436i
\(721\) 0 0
\(722\) 1.60164i 0.0596068i
\(723\) 0.543899i 0.0202278i
\(724\) −19.6181 −0.729102
\(725\) 41.4210 19.5722i 1.53834 0.726893i
\(726\) −5.27226 −0.195672
\(727\) 36.1218i 1.33968i −0.742504 0.669842i \(-0.766362\pi\)
0.742504 0.669842i \(-0.233638\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −1.10545 + 0.248026i −0.0409146 + 0.00917986i
\(731\) 9.66974 0.357648
\(732\) 13.0910i 0.483856i
\(733\) 7.83860i 0.289525i −0.989466 0.144763i \(-0.953758\pi\)
0.989466 0.144763i \(-0.0462419\pi\)
\(734\) −31.5722 −1.16535
\(735\) 0 0
\(736\) 8.17113 0.301192
\(737\) 13.8280i 0.509361i
\(738\) 3.19208i 0.117502i
\(739\) 29.7969 1.09610 0.548048 0.836447i \(-0.315371\pi\)
0.548048 + 0.836447i \(0.315371\pi\)
\(740\) 0.618560 + 2.75692i 0.0227387 + 0.101346i
\(741\) −15.8815 −0.583422
\(742\) 0 0
\(743\) 11.7487i 0.431017i 0.976502 + 0.215509i \(0.0691409\pi\)
−0.976502 + 0.215509i \(0.930859\pi\)
\(744\) −1.60673 −0.0589056
\(745\) 16.4419 3.68901i 0.602384 0.135155i
\(746\) −20.9075 −0.765480
\(747\) 1.89887i 0.0694762i
\(748\) 4.71565i 0.172421i
\(749\) 0 0
\(750\) 8.81774 6.87368i 0.321978 0.250991i
\(751\) −2.43981 −0.0890299 −0.0445150 0.999009i \(-0.514174\pi\)
−0.0445150 + 0.999009i \(0.514174\pi\)
\(752\) 3.00868i 0.109715i
\(753\) 4.62829i 0.168664i
\(754\) 34.8859 1.27047
\(755\) 19.7269 4.42604i 0.717934 0.161080i
\(756\) 0 0
\(757\) 17.5039i 0.636188i −0.948059 0.318094i \(-0.896957\pi\)
0.948059 0.318094i \(-0.103043\pi\)
\(758\) 9.82440i 0.356838i
\(759\) 19.5557 0.709828
\(760\) 2.04189 + 9.10069i 0.0740670 + 0.330117i
\(761\) −6.06327 −0.219793 −0.109897 0.993943i \(-0.535052\pi\)
−0.109897 + 0.993943i \(0.535052\pi\)
\(762\) 18.4434i 0.668134i
\(763\) 0 0
\(764\) 19.7269 0.713693
\(765\) 0.964557 + 4.29903i 0.0348736 + 0.155432i
\(766\) 30.6647 1.10796
\(767\) 49.6551i 1.79294i
\(768\) 1.00000i 0.0360844i
\(769\) 6.94628 0.250489 0.125245 0.992126i \(-0.460028\pi\)
0.125245 + 0.992126i \(0.460028\pi\)
\(770\) 0 0
\(771\) 25.5671 0.920777
\(772\) 4.78654i 0.172271i
\(773\) 14.8597i 0.534466i 0.963632 + 0.267233i \(0.0861094\pi\)
−0.963632 + 0.267233i \(0.913891\pi\)
\(774\) −4.90755 −0.176398
\(775\) 7.26358 3.43218i 0.260916 0.123288i
\(776\) 12.0624 0.433015
\(777\) 0 0
\(778\) 23.4476i 0.840637i
\(779\) −13.3146 −0.477045
\(780\) 8.30726 1.86387i 0.297448 0.0667373i
\(781\) −16.6101 −0.594355
\(782\) 16.1002i 0.575744i
\(783\) 9.16246i 0.327440i
\(784\) 0 0
\(785\) 11.0947 + 49.4490i 0.395986 + 1.76491i
\(786\) 0.615405 0.0219508
\(787\) 16.7683i 0.597726i −0.954296 0.298863i \(-0.903393\pi\)
0.954296 0.298863i \(-0.0966073\pi\)
\(788\) 17.1997i 0.612714i
\(789\) −20.5972 −0.733279
\(790\) −6.08290 27.1115i −0.216420 0.964582i
\(791\) 0 0
\(792\) 2.39327i 0.0850411i
\(793\)