Properties

Label 1064.2.q.n.305.3
Level $1064$
Weight $2$
Character 1064.305
Analytic conductor $8.496$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.49608277506\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + 4560 x^{6} + 1376 x^{5} + 4688 x^{4} + 736 x^{3} + 1280 x^{2} - 128 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 305.3
Root \(-0.456148 + 0.790072i\) of defining polynomial
Character \(\chi\) \(=\) 1064.305
Dual form 1064.2.q.n.457.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.456148 + 0.790072i) q^{3} +(0.832641 + 1.44218i) q^{5} +(-0.462738 + 2.60497i) q^{7} +(1.08386 + 1.87730i) q^{9} +O(q^{10})\) \(q+(-0.456148 + 0.790072i) q^{3} +(0.832641 + 1.44218i) q^{5} +(-0.462738 + 2.60497i) q^{7} +(1.08386 + 1.87730i) q^{9} +(0.121120 - 0.209787i) q^{11} -5.76999 q^{13} -1.51923 q^{15} +(-2.88319 + 4.99382i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(-1.84704 - 1.55385i) q^{21} +(-3.30773 - 5.72915i) q^{23} +(1.11342 - 1.92850i) q^{25} -4.71449 q^{27} +8.91381 q^{29} +(2.96642 - 5.13799i) q^{31} +(0.110498 + 0.191388i) q^{33} +(-4.14212 + 1.50166i) q^{35} +(4.90185 + 8.49026i) q^{37} +(2.63197 - 4.55870i) q^{39} -2.00000 q^{41} -7.83237 q^{43} +(-1.80493 + 3.12623i) q^{45} +(-0.789589 - 1.36761i) q^{47} +(-6.57175 - 2.41084i) q^{49} +(-2.63032 - 4.55585i) q^{51} +(-3.24073 + 5.61311i) q^{53} +0.403399 q^{55} +0.912296 q^{57} +(-0.537488 + 0.930957i) q^{59} +(-4.55454 - 7.88869i) q^{61} +(-5.39185 + 1.95472i) q^{63} +(-4.80433 - 8.32134i) q^{65} +(-4.01270 + 6.95021i) q^{67} +6.03525 q^{69} +1.22955 q^{71} +(-0.400685 + 0.694007i) q^{73} +(1.01577 + 1.75936i) q^{75} +(0.490441 + 0.412591i) q^{77} +(3.79101 + 6.56622i) q^{79} +(-1.10107 + 1.90711i) q^{81} -8.91292 q^{83} -9.60264 q^{85} +(-4.06602 + 7.04255i) q^{87} +(6.55732 + 11.3576i) q^{89} +(2.66999 - 15.0307i) q^{91} +(2.70625 + 4.68737i) q^{93} +(0.832641 - 1.44218i) q^{95} +1.11664 q^{97} +0.525109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + q^{5} + 5 q^{7} - 6 q^{9} + O(q^{10}) \) \( 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times\).

\(n\) \(533\) \(799\) \(913\) \(1009\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.456148 + 0.790072i −0.263357 + 0.456148i −0.967132 0.254275i \(-0.918163\pi\)
0.703775 + 0.710423i \(0.251496\pi\)
\(4\) 0 0
\(5\) 0.832641 + 1.44218i 0.372368 + 0.644961i 0.989929 0.141562i \(-0.0452125\pi\)
−0.617561 + 0.786523i \(0.711879\pi\)
\(6\) 0 0
\(7\) −0.462738 + 2.60497i −0.174898 + 0.984586i
\(8\) 0 0
\(9\) 1.08386 + 1.87730i 0.361286 + 0.625766i
\(10\) 0 0
\(11\) 0.121120 0.209787i 0.0365192 0.0632531i −0.847188 0.531293i \(-0.821706\pi\)
0.883707 + 0.468040i \(0.155040\pi\)
\(12\) 0 0
\(13\) −5.76999 −1.60031 −0.800154 0.599795i \(-0.795249\pi\)
−0.800154 + 0.599795i \(0.795249\pi\)
\(14\) 0 0
\(15\) −1.51923 −0.392264
\(16\) 0 0
\(17\) −2.88319 + 4.99382i −0.699275 + 1.21118i 0.269443 + 0.963016i \(0.413160\pi\)
−0.968718 + 0.248164i \(0.920173\pi\)
\(18\) 0 0
\(19\) −0.500000 0.866025i −0.114708 0.198680i
\(20\) 0 0
\(21\) −1.84704 1.55385i −0.403056 0.339077i
\(22\) 0 0
\(23\) −3.30773 5.72915i −0.689709 1.19461i −0.971932 0.235262i \(-0.924405\pi\)
0.282224 0.959349i \(-0.408928\pi\)
\(24\) 0 0
\(25\) 1.11342 1.92850i 0.222684 0.385699i
\(26\) 0 0
\(27\) −4.71449 −0.907303
\(28\) 0 0
\(29\) 8.91381 1.65525 0.827627 0.561279i \(-0.189690\pi\)
0.827627 + 0.561279i \(0.189690\pi\)
\(30\) 0 0
\(31\) 2.96642 5.13799i 0.532785 0.922810i −0.466483 0.884530i \(-0.654479\pi\)
0.999267 0.0382794i \(-0.0121877\pi\)
\(32\) 0 0
\(33\) 0.110498 + 0.191388i 0.0192352 + 0.0333163i
\(34\) 0 0
\(35\) −4.14212 + 1.50166i −0.700147 + 0.253826i
\(36\) 0 0
\(37\) 4.90185 + 8.49026i 0.805860 + 1.39579i 0.915709 + 0.401842i \(0.131630\pi\)
−0.109849 + 0.993948i \(0.535037\pi\)
\(38\) 0 0
\(39\) 2.63197 4.55870i 0.421452 0.729977i
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) −7.83237 −1.19443 −0.597213 0.802083i \(-0.703725\pi\)
−0.597213 + 0.802083i \(0.703725\pi\)
\(44\) 0 0
\(45\) −1.80493 + 3.12623i −0.269063 + 0.466031i
\(46\) 0 0
\(47\) −0.789589 1.36761i −0.115173 0.199486i 0.802676 0.596416i \(-0.203409\pi\)
−0.917849 + 0.396930i \(0.870076\pi\)
\(48\) 0 0
\(49\) −6.57175 2.41084i −0.938821 0.344405i
\(50\) 0 0
\(51\) −2.63032 4.55585i −0.368318 0.637946i
\(52\) 0 0
\(53\) −3.24073 + 5.61311i −0.445148 + 0.771019i −0.998063 0.0622187i \(-0.980182\pi\)
0.552914 + 0.833238i \(0.313516\pi\)
\(54\) 0 0
\(55\) 0.403399 0.0543944
\(56\) 0 0
\(57\) 0.912296 0.120837
\(58\) 0 0
\(59\) −0.537488 + 0.930957i −0.0699750 + 0.121200i −0.898890 0.438174i \(-0.855625\pi\)
0.828915 + 0.559375i \(0.188959\pi\)
\(60\) 0 0
\(61\) −4.55454 7.88869i −0.583149 1.01004i −0.995103 0.0988387i \(-0.968487\pi\)
0.411955 0.911204i \(-0.364846\pi\)
\(62\) 0 0
\(63\) −5.39185 + 1.95472i −0.679309 + 0.246272i
\(64\) 0 0
\(65\) −4.80433 8.32134i −0.595904 1.03214i
\(66\) 0 0
\(67\) −4.01270 + 6.95021i −0.490230 + 0.849103i −0.999937 0.0112451i \(-0.996421\pi\)
0.509707 + 0.860348i \(0.329754\pi\)
\(68\) 0 0
\(69\) 6.03525 0.726559
\(70\) 0 0
\(71\) 1.22955 0.145921 0.0729606 0.997335i \(-0.476755\pi\)
0.0729606 + 0.997335i \(0.476755\pi\)
\(72\) 0 0
\(73\) −0.400685 + 0.694007i −0.0468966 + 0.0812274i −0.888521 0.458836i \(-0.848266\pi\)
0.841624 + 0.540064i \(0.181600\pi\)
\(74\) 0 0
\(75\) 1.01577 + 1.75936i 0.117291 + 0.203153i
\(76\) 0 0
\(77\) 0.490441 + 0.412591i 0.0558910 + 0.0470192i
\(78\) 0 0
\(79\) 3.79101 + 6.56622i 0.426522 + 0.738758i 0.996561 0.0828597i \(-0.0264053\pi\)
−0.570039 + 0.821617i \(0.693072\pi\)
\(80\) 0 0
\(81\) −1.10107 + 1.90711i −0.122341 + 0.211901i
\(82\) 0 0
\(83\) −8.91292 −0.978320 −0.489160 0.872194i \(-0.662697\pi\)
−0.489160 + 0.872194i \(0.662697\pi\)
\(84\) 0 0
\(85\) −9.60264 −1.04155
\(86\) 0 0
\(87\) −4.06602 + 7.04255i −0.435923 + 0.755041i
\(88\) 0 0
\(89\) 6.55732 + 11.3576i 0.695074 + 1.20390i 0.970156 + 0.242483i \(0.0779618\pi\)
−0.275082 + 0.961421i \(0.588705\pi\)
\(90\) 0 0
\(91\) 2.66999 15.0307i 0.279891 1.57564i
\(92\) 0 0
\(93\) 2.70625 + 4.68737i 0.280625 + 0.486057i
\(94\) 0 0
\(95\) 0.832641 1.44218i 0.0854272 0.147964i
\(96\) 0 0
\(97\) 1.11664 0.113377 0.0566886 0.998392i \(-0.481946\pi\)
0.0566886 + 0.998392i \(0.481946\pi\)
\(98\) 0 0
\(99\) 0.525109 0.0527755
\(100\) 0 0
\(101\) −6.51382 + 11.2823i −0.648149 + 1.12263i 0.335416 + 0.942070i \(0.391123\pi\)
−0.983565 + 0.180557i \(0.942210\pi\)
\(102\) 0 0
\(103\) 6.86294 + 11.8870i 0.676226 + 1.17126i 0.976109 + 0.217282i \(0.0697190\pi\)
−0.299883 + 0.953976i \(0.596948\pi\)
\(104\) 0 0
\(105\) 0.703005 3.95755i 0.0686063 0.386217i
\(106\) 0 0
\(107\) −1.88424 3.26359i −0.182156 0.315503i 0.760459 0.649386i \(-0.224974\pi\)
−0.942614 + 0.333883i \(0.891641\pi\)
\(108\) 0 0
\(109\) 0.337127 0.583921i 0.0322909 0.0559295i −0.849428 0.527704i \(-0.823053\pi\)
0.881719 + 0.471774i \(0.156386\pi\)
\(110\) 0 0
\(111\) −8.94388 −0.848916
\(112\) 0 0
\(113\) 10.1480 0.954646 0.477323 0.878728i \(-0.341607\pi\)
0.477323 + 0.878728i \(0.341607\pi\)
\(114\) 0 0
\(115\) 5.50830 9.54065i 0.513651 0.889670i
\(116\) 0 0
\(117\) −6.25385 10.8320i −0.578169 1.00142i
\(118\) 0 0
\(119\) −11.6746 9.82145i −1.07021 0.900330i
\(120\) 0 0
\(121\) 5.47066 + 9.47546i 0.497333 + 0.861406i
\(122\) 0 0
\(123\) 0.912296 1.58014i 0.0822590 0.142477i
\(124\) 0 0
\(125\) 12.0347 1.07642
\(126\) 0 0
\(127\) 18.5974 1.65025 0.825126 0.564949i \(-0.191104\pi\)
0.825126 + 0.564949i \(0.191104\pi\)
\(128\) 0 0
\(129\) 3.57272 6.18813i 0.314561 0.544835i
\(130\) 0 0
\(131\) −3.98570 6.90344i −0.348233 0.603157i 0.637703 0.770282i \(-0.279885\pi\)
−0.985936 + 0.167126i \(0.946551\pi\)
\(132\) 0 0
\(133\) 2.48734 0.901743i 0.215680 0.0781910i
\(134\) 0 0
\(135\) −3.92548 6.79912i −0.337851 0.585175i
\(136\) 0 0
\(137\) 0.159382 0.276057i 0.0136169 0.0235852i −0.859137 0.511746i \(-0.828999\pi\)
0.872754 + 0.488161i \(0.162332\pi\)
\(138\) 0 0
\(139\) −5.80115 −0.492047 −0.246024 0.969264i \(-0.579124\pi\)
−0.246024 + 0.969264i \(0.579124\pi\)
\(140\) 0 0
\(141\) 1.44068 0.121327
\(142\) 0 0
\(143\) −0.698864 + 1.21047i −0.0584419 + 0.101224i
\(144\) 0 0
\(145\) 7.42201 + 12.8553i 0.616364 + 1.06757i
\(146\) 0 0
\(147\) 4.90242 4.09245i 0.404345 0.337540i
\(148\) 0 0
\(149\) −6.83503 11.8386i −0.559948 0.969858i −0.997500 0.0706649i \(-0.977488\pi\)
0.437552 0.899193i \(-0.355845\pi\)
\(150\) 0 0
\(151\) −5.51411 + 9.55072i −0.448732 + 0.777226i −0.998304 0.0582201i \(-0.981457\pi\)
0.549572 + 0.835446i \(0.314791\pi\)
\(152\) 0 0
\(153\) −12.4999 −1.01055
\(154\) 0 0
\(155\) 9.87985 0.793568
\(156\) 0 0
\(157\) −8.92830 + 15.4643i −0.712556 + 1.23418i 0.251339 + 0.967899i \(0.419129\pi\)
−0.963895 + 0.266283i \(0.914204\pi\)
\(158\) 0 0
\(159\) −2.95650 5.12081i −0.234466 0.406107i
\(160\) 0 0
\(161\) 16.4549 5.96544i 1.29683 0.470142i
\(162\) 0 0
\(163\) −5.59851 9.69690i −0.438509 0.759520i 0.559066 0.829123i \(-0.311160\pi\)
−0.997575 + 0.0696035i \(0.977827\pi\)
\(164\) 0 0
\(165\) −0.184010 + 0.318714i −0.0143251 + 0.0248119i
\(166\) 0 0
\(167\) 1.44712 0.111981 0.0559906 0.998431i \(-0.482168\pi\)
0.0559906 + 0.998431i \(0.482168\pi\)
\(168\) 0 0
\(169\) 20.2928 1.56098
\(170\) 0 0
\(171\) 1.08386 1.87730i 0.0828847 0.143560i
\(172\) 0 0
\(173\) −5.94705 10.3006i −0.452146 0.783140i 0.546373 0.837542i \(-0.316008\pi\)
−0.998519 + 0.0544023i \(0.982675\pi\)
\(174\) 0 0
\(175\) 4.50846 + 3.79281i 0.340807 + 0.286709i
\(176\) 0 0
\(177\) −0.490348 0.849308i −0.0368568 0.0638379i
\(178\) 0 0
\(179\) −12.5864 + 21.8003i −0.940751 + 1.62943i −0.176708 + 0.984263i \(0.556545\pi\)
−0.764043 + 0.645165i \(0.776788\pi\)
\(180\) 0 0
\(181\) 18.7410 1.39301 0.696503 0.717554i \(-0.254738\pi\)
0.696503 + 0.717554i \(0.254738\pi\)
\(182\) 0 0
\(183\) 8.31017 0.614305
\(184\) 0 0
\(185\) −8.16297 + 14.1387i −0.600154 + 1.03950i
\(186\) 0 0
\(187\) 0.698425 + 1.20971i 0.0510739 + 0.0884626i
\(188\) 0 0
\(189\) 2.18157 12.2811i 0.158686 0.893319i
\(190\) 0 0
\(191\) −0.178001 0.308307i −0.0128797 0.0223083i 0.859514 0.511113i \(-0.170767\pi\)
−0.872393 + 0.488804i \(0.837433\pi\)
\(192\) 0 0
\(193\) −8.54939 + 14.8080i −0.615398 + 1.06590i 0.374916 + 0.927059i \(0.377671\pi\)
−0.990314 + 0.138842i \(0.955662\pi\)
\(194\) 0 0
\(195\) 8.76594 0.627742
\(196\) 0 0
\(197\) 13.1088 0.933964 0.466982 0.884267i \(-0.345341\pi\)
0.466982 + 0.884267i \(0.345341\pi\)
\(198\) 0 0
\(199\) −2.38489 + 4.13074i −0.169060 + 0.292821i −0.938090 0.346393i \(-0.887407\pi\)
0.769030 + 0.639213i \(0.220740\pi\)
\(200\) 0 0
\(201\) −3.66077 6.34065i −0.258211 0.447235i
\(202\) 0 0
\(203\) −4.12476 + 23.2202i −0.289501 + 1.62974i
\(204\) 0 0
\(205\) −1.66528 2.88435i −0.116308 0.201452i
\(206\) 0 0
\(207\) 7.17021 12.4192i 0.498364 0.863192i
\(208\) 0 0
\(209\) −0.242241 −0.0167561
\(210\) 0 0
\(211\) 22.0442 1.51759 0.758794 0.651331i \(-0.225789\pi\)
0.758794 + 0.651331i \(0.225789\pi\)
\(212\) 0 0
\(213\) −0.560858 + 0.971435i −0.0384294 + 0.0665616i
\(214\) 0 0
\(215\) −6.52156 11.2957i −0.444766 0.770358i
\(216\) 0 0
\(217\) 12.0116 + 10.1050i 0.815403 + 0.685970i
\(218\) 0 0
\(219\) −0.365543 0.633140i −0.0247011 0.0427836i
\(220\) 0 0
\(221\) 16.6360 28.8143i 1.11906 1.93826i
\(222\) 0 0
\(223\) 19.5836 1.31142 0.655708 0.755014i \(-0.272370\pi\)
0.655708 + 0.755014i \(0.272370\pi\)
\(224\) 0 0
\(225\) 4.82715 0.321810
\(226\) 0 0
\(227\) 2.89414 5.01280i 0.192091 0.332712i −0.753852 0.657044i \(-0.771806\pi\)
0.945943 + 0.324333i \(0.105140\pi\)
\(228\) 0 0
\(229\) 9.55372 + 16.5475i 0.631328 + 1.09349i 0.987281 + 0.158988i \(0.0508231\pi\)
−0.355953 + 0.934504i \(0.615844\pi\)
\(230\) 0 0
\(231\) −0.549691 + 0.199281i −0.0361670 + 0.0131117i
\(232\) 0 0
\(233\) 3.08563 + 5.34446i 0.202146 + 0.350127i 0.949220 0.314614i \(-0.101875\pi\)
−0.747074 + 0.664741i \(0.768542\pi\)
\(234\) 0 0
\(235\) 1.31489 2.27745i 0.0857739 0.148565i
\(236\) 0 0
\(237\) −6.91705 −0.449311
\(238\) 0 0
\(239\) 26.1425 1.69101 0.845507 0.533964i \(-0.179298\pi\)
0.845507 + 0.533964i \(0.179298\pi\)
\(240\) 0 0
\(241\) 9.79581 16.9668i 0.631003 1.09293i −0.356344 0.934355i \(-0.615977\pi\)
0.987347 0.158575i \(-0.0506899\pi\)
\(242\) 0 0
\(243\) −8.07623 13.9884i −0.518091 0.897359i
\(244\) 0 0
\(245\) −1.99506 11.4850i −0.127459 0.733749i
\(246\) 0 0
\(247\) 2.88499 + 4.99696i 0.183568 + 0.317949i
\(248\) 0 0
\(249\) 4.06561 7.04184i 0.257647 0.446259i
\(250\) 0 0
\(251\) −6.39080 −0.403384 −0.201692 0.979449i \(-0.564644\pi\)
−0.201692 + 0.979449i \(0.564644\pi\)
\(252\) 0 0
\(253\) −1.60253 −0.100750
\(254\) 0 0
\(255\) 4.38022 7.58677i 0.274300 0.475102i
\(256\) 0 0
\(257\) −10.9371 18.9436i −0.682238 1.18167i −0.974296 0.225271i \(-0.927673\pi\)
0.292058 0.956401i \(-0.405660\pi\)
\(258\) 0 0
\(259\) −24.3852 + 8.84043i −1.51522 + 0.549317i
\(260\) 0 0
\(261\) 9.66131 + 16.7339i 0.598020 + 1.03580i
\(262\) 0 0
\(263\) 14.8618 25.7414i 0.916420 1.58729i 0.111611 0.993752i \(-0.464399\pi\)
0.804809 0.593534i \(-0.202268\pi\)
\(264\) 0 0
\(265\) −10.7935 −0.663037
\(266\) 0 0
\(267\) −11.9644 −0.732211
\(268\) 0 0
\(269\) −6.69279 + 11.5923i −0.408067 + 0.706792i −0.994673 0.103080i \(-0.967130\pi\)
0.586606 + 0.809872i \(0.300464\pi\)
\(270\) 0 0
\(271\) 12.8866 + 22.3202i 0.782805 + 1.35586i 0.930301 + 0.366796i \(0.119545\pi\)
−0.147496 + 0.989063i \(0.547121\pi\)
\(272\) 0 0
\(273\) 10.6574 + 8.96569i 0.645014 + 0.542628i
\(274\) 0 0
\(275\) −0.269715 0.467161i −0.0162644 0.0281708i
\(276\) 0 0
\(277\) 1.48701 2.57558i 0.0893458 0.154751i −0.817889 0.575376i \(-0.804856\pi\)
0.907235 + 0.420625i \(0.138189\pi\)
\(278\) 0 0
\(279\) 12.8607 0.769950
\(280\) 0 0
\(281\) −18.8947 −1.12716 −0.563582 0.826060i \(-0.690577\pi\)
−0.563582 + 0.826060i \(0.690577\pi\)
\(282\) 0 0
\(283\) −11.4150 + 19.7713i −0.678551 + 1.17528i 0.296867 + 0.954919i \(0.404058\pi\)
−0.975417 + 0.220365i \(0.929275\pi\)
\(284\) 0 0
\(285\) 0.759615 + 1.31569i 0.0449957 + 0.0779349i
\(286\) 0 0
\(287\) 0.925475 5.20994i 0.0546291 0.307533i
\(288\) 0 0
\(289\) −8.12552 14.0738i −0.477972 0.827872i
\(290\) 0 0
\(291\) −0.509351 + 0.882222i −0.0298587 + 0.0517168i
\(292\) 0 0
\(293\) 11.3710 0.664299 0.332150 0.943227i \(-0.392226\pi\)
0.332150 + 0.943227i \(0.392226\pi\)
\(294\) 0 0
\(295\) −1.79014 −0.104226
\(296\) 0 0
\(297\) −0.571021 + 0.989037i −0.0331340 + 0.0573897i
\(298\) 0 0
\(299\) 19.0855 + 33.0571i 1.10375 + 1.91174i
\(300\) 0 0
\(301\) 3.62433 20.4031i 0.208903 1.17602i
\(302\) 0 0
\(303\) −5.94253 10.2928i −0.341389 0.591304i
\(304\) 0 0
\(305\) 7.58459 13.1369i 0.434292 0.752216i
\(306\) 0 0
\(307\) −3.87636 −0.221236 −0.110618 0.993863i \(-0.535283\pi\)
−0.110618 + 0.993863i \(0.535283\pi\)
\(308\) 0 0
\(309\) −12.5221 −0.712356
\(310\) 0 0
\(311\) −11.0281 + 19.1012i −0.625344 + 1.08313i 0.363130 + 0.931738i \(0.381708\pi\)
−0.988474 + 0.151389i \(0.951625\pi\)
\(312\) 0 0
\(313\) 15.5322 + 26.9025i 0.877930 + 1.52062i 0.853609 + 0.520914i \(0.174409\pi\)
0.0243207 + 0.999704i \(0.492258\pi\)
\(314\) 0 0
\(315\) −7.30853 6.14841i −0.411789 0.346424i
\(316\) 0 0
\(317\) −16.6431 28.8268i −0.934772 1.61907i −0.775040 0.631912i \(-0.782271\pi\)
−0.159731 0.987161i \(-0.551063\pi\)
\(318\) 0 0
\(319\) 1.07965 1.87000i 0.0604485 0.104700i
\(320\) 0 0
\(321\) 3.43796 0.191888
\(322\) 0 0
\(323\) 5.76637 0.320850
\(324\) 0 0
\(325\) −6.42441 + 11.1274i −0.356362 + 0.617237i
\(326\) 0 0
\(327\) 0.307560 + 0.532709i 0.0170081 + 0.0294589i
\(328\) 0 0
\(329\) 3.92795 1.42401i 0.216555 0.0785084i
\(330\) 0 0
\(331\) −4.18690 7.25192i −0.230133 0.398601i 0.727714 0.685880i \(-0.240583\pi\)
−0.957847 + 0.287279i \(0.907249\pi\)
\(332\) 0 0
\(333\) −10.6258 + 18.4045i −0.582292 + 1.00856i
\(334\) 0 0
\(335\) −13.3646 −0.730184
\(336\) 0 0
\(337\) −1.87908 −0.102360 −0.0511799 0.998689i \(-0.516298\pi\)
−0.0511799 + 0.998689i \(0.516298\pi\)
\(338\) 0 0
\(339\) −4.62900 + 8.01767i −0.251413 + 0.435460i
\(340\) 0 0
\(341\) −0.718588 1.24463i −0.0389137 0.0674005i
\(342\) 0 0
\(343\) 9.32115 16.0036i 0.503295 0.864115i
\(344\) 0 0
\(345\) 5.02520 + 8.70390i 0.270548 + 0.468602i
\(346\) 0 0
\(347\) 3.06863 5.31502i 0.164733 0.285325i −0.771828 0.635832i \(-0.780657\pi\)
0.936560 + 0.350506i \(0.113991\pi\)
\(348\) 0 0
\(349\) −18.9103 −1.01225 −0.506123 0.862461i \(-0.668922\pi\)
−0.506123 + 0.862461i \(0.668922\pi\)
\(350\) 0 0
\(351\) 27.2025 1.45196
\(352\) 0 0
\(353\) 4.97227 8.61222i 0.264647 0.458382i −0.702824 0.711364i \(-0.748078\pi\)
0.967471 + 0.252982i \(0.0814112\pi\)
\(354\) 0 0
\(355\) 1.02378 + 1.77323i 0.0543364 + 0.0941134i
\(356\) 0 0
\(357\) 13.0850 4.74374i 0.692531 0.251066i
\(358\) 0 0
\(359\) −9.19502 15.9262i −0.485295 0.840555i 0.514562 0.857453i \(-0.327954\pi\)
−0.999857 + 0.0168977i \(0.994621\pi\)
\(360\) 0 0
\(361\) −0.500000 + 0.866025i −0.0263158 + 0.0455803i
\(362\) 0 0
\(363\) −9.98172 −0.523905
\(364\) 0 0
\(365\) −1.33451 −0.0698513
\(366\) 0 0
\(367\) 7.10761 12.3107i 0.371014 0.642616i −0.618707 0.785621i \(-0.712343\pi\)
0.989722 + 0.143006i \(0.0456767\pi\)
\(368\) 0 0
\(369\) −2.16772 3.75459i −0.112847 0.195456i
\(370\) 0 0
\(371\) −13.1224 11.0394i −0.681280 0.573137i
\(372\) 0 0
\(373\) −12.8008 22.1716i −0.662800 1.14800i −0.979877 0.199604i \(-0.936034\pi\)
0.317076 0.948400i \(-0.397299\pi\)
\(374\) 0 0
\(375\) −5.48961 + 9.50829i −0.283482 + 0.491006i
\(376\) 0 0
\(377\) −51.4326 −2.64891
\(378\) 0 0
\(379\) −8.51685 −0.437481 −0.218741 0.975783i \(-0.570195\pi\)
−0.218741 + 0.975783i \(0.570195\pi\)
\(380\) 0 0
\(381\) −8.48316 + 14.6933i −0.434606 + 0.752759i
\(382\) 0 0
\(383\) 5.00847 + 8.67492i 0.255921 + 0.443268i 0.965145 0.261715i \(-0.0842881\pi\)
−0.709224 + 0.704983i \(0.750955\pi\)
\(384\) 0 0
\(385\) −0.186668 + 1.05084i −0.00951348 + 0.0535559i
\(386\) 0 0
\(387\) −8.48918 14.7037i −0.431529 0.747431i
\(388\) 0 0
\(389\) 10.1401 17.5631i 0.514123 0.890487i −0.485743 0.874102i \(-0.661451\pi\)
0.999866 0.0163851i \(-0.00521577\pi\)
\(390\) 0 0
\(391\) 38.1472 1.92918
\(392\) 0 0
\(393\) 7.27229 0.366838
\(394\) 0 0
\(395\) −6.31310 + 10.9346i −0.317647 + 0.550180i
\(396\) 0 0
\(397\) 13.4137 + 23.2333i 0.673216 + 1.16604i 0.976987 + 0.213300i \(0.0684211\pi\)
−0.303770 + 0.952745i \(0.598246\pi\)
\(398\) 0 0
\(399\) −0.422154 + 2.37650i −0.0211341 + 0.118974i
\(400\) 0 0
\(401\) 6.92911 + 12.0016i 0.346023 + 0.599330i 0.985539 0.169448i \(-0.0541985\pi\)
−0.639516 + 0.768778i \(0.720865\pi\)
\(402\) 0 0
\(403\) −17.1162 + 29.6461i −0.852619 + 1.47678i
\(404\) 0 0
\(405\) −3.66719 −0.182224
\(406\) 0 0
\(407\) 2.37486 0.117717
\(408\) 0 0
\(409\) 3.09715 5.36442i 0.153144 0.265253i −0.779238 0.626729i \(-0.784393\pi\)
0.932382 + 0.361475i \(0.117727\pi\)
\(410\) 0 0
\(411\) 0.145403 + 0.251846i 0.00717222 + 0.0124226i
\(412\) 0 0
\(413\) −2.17640 1.83093i −0.107094 0.0900942i
\(414\) 0 0
\(415\) −7.42126 12.8540i −0.364295 0.630978i
\(416\) 0 0
\(417\) 2.64618 4.58333i 0.129584 0.224446i
\(418\) 0 0
\(419\) 14.4938 0.708068 0.354034 0.935233i \(-0.384810\pi\)
0.354034 + 0.935233i \(0.384810\pi\)
\(420\) 0 0
\(421\) 29.8753 1.45603 0.728016 0.685560i \(-0.240443\pi\)
0.728016 + 0.685560i \(0.240443\pi\)
\(422\) 0 0
\(423\) 1.71161 2.96459i 0.0832211 0.144143i
\(424\) 0 0
\(425\) 6.42038 + 11.1204i 0.311434 + 0.539420i
\(426\) 0 0
\(427\) 22.6574 8.21404i 1.09647 0.397505i
\(428\) 0 0
\(429\) −0.637570 1.10430i −0.0307822 0.0533163i
\(430\) 0 0
\(431\) −10.9304 + 18.9321i −0.526501 + 0.911926i 0.473023 + 0.881050i \(0.343163\pi\)
−0.999523 + 0.0308754i \(0.990170\pi\)
\(432\) 0 0
\(433\) −11.1847 −0.537500 −0.268750 0.963210i \(-0.586611\pi\)
−0.268750 + 0.963210i \(0.586611\pi\)
\(434\) 0 0
\(435\) −13.5421 −0.649296
\(436\) 0 0
\(437\) −3.30773 + 5.72915i −0.158230 + 0.274062i
\(438\) 0 0
\(439\) 7.70936 + 13.3530i 0.367948 + 0.637304i 0.989245 0.146271i \(-0.0467272\pi\)
−0.621297 + 0.783575i \(0.713394\pi\)
\(440\) 0 0
\(441\) −2.59699 14.9501i −0.123666 0.711911i
\(442\) 0 0
\(443\) 0.469742 + 0.813616i 0.0223181 + 0.0386561i 0.876969 0.480547i \(-0.159562\pi\)
−0.854651 + 0.519203i \(0.826229\pi\)
\(444\) 0 0
\(445\) −10.9198 + 18.9136i −0.517647 + 0.896591i
\(446\) 0 0
\(447\) 12.4711 0.589865
\(448\) 0 0
\(449\) −28.2058 −1.33112 −0.665558 0.746346i \(-0.731806\pi\)
−0.665558 + 0.746346i \(0.731806\pi\)
\(450\) 0 0
\(451\) −0.242241 + 0.419573i −0.0114067 + 0.0197569i
\(452\) 0 0
\(453\) −5.03050 8.71308i −0.236353 0.409376i
\(454\) 0 0
\(455\) 23.9000 8.66454i 1.12045 0.406200i
\(456\) 0 0
\(457\) −0.388913 0.673617i −0.0181926 0.0315105i 0.856786 0.515672i \(-0.172458\pi\)
−0.874978 + 0.484162i \(0.839125\pi\)
\(458\) 0 0
\(459\) 13.5927 23.5433i 0.634455 1.09891i
\(460\) 0 0
\(461\) −19.3614 −0.901751 −0.450875 0.892587i \(-0.648888\pi\)
−0.450875 + 0.892587i \(0.648888\pi\)
\(462\) 0 0
\(463\) 34.5688 1.60655 0.803275 0.595608i \(-0.203089\pi\)
0.803275 + 0.595608i \(0.203089\pi\)
\(464\) 0 0
\(465\) −4.50667 + 7.80579i −0.208992 + 0.361985i
\(466\) 0 0
\(467\) 14.9272 + 25.8547i 0.690750 + 1.19641i 0.971593 + 0.236660i \(0.0760527\pi\)
−0.280843 + 0.959754i \(0.590614\pi\)
\(468\) 0 0
\(469\) −16.2483 13.6691i −0.750275 0.631180i
\(470\) 0 0
\(471\) −8.14525 14.1080i −0.375313 0.650062i
\(472\) 0 0
\(473\) −0.948660 + 1.64313i −0.0436194 + 0.0755511i
\(474\) 0 0
\(475\) −2.22684 −0.102174
\(476\) 0 0
\(477\) −14.0500 −0.643303
\(478\) 0 0
\(479\) 13.9432 24.1504i 0.637082 1.10346i −0.348987 0.937127i \(-0.613474\pi\)
0.986070 0.166332i \(-0.0531923\pi\)
\(480\) 0 0
\(481\) −28.2836 48.9887i −1.28962 2.23369i
\(482\) 0 0
\(483\) −2.79274 + 15.7217i −0.127074 + 0.715360i
\(484\) 0 0
\(485\) 0.929757 + 1.61039i 0.0422181 + 0.0731238i
\(486\) 0 0
\(487\) −5.81119 + 10.0653i −0.263330 + 0.456101i −0.967125 0.254302i \(-0.918154\pi\)
0.703795 + 0.710404i \(0.251488\pi\)
\(488\) 0 0
\(489\) 10.2150 0.461938
\(490\) 0 0
\(491\) −25.4037 −1.14645 −0.573225 0.819398i \(-0.694308\pi\)
−0.573225 + 0.819398i \(0.694308\pi\)
\(492\) 0 0
\(493\) −25.7002 + 44.5140i −1.15748 + 2.00481i
\(494\) 0 0
\(495\) 0.437228 + 0.757300i 0.0196519 + 0.0340381i
\(496\) 0 0
\(497\) −0.568961 + 3.20295i −0.0255214 + 0.143672i
\(498\) 0 0
\(499\) −1.33920 2.31956i −0.0599509 0.103838i 0.834492 0.551020i \(-0.185761\pi\)
−0.894443 + 0.447182i \(0.852428\pi\)
\(500\) 0 0
\(501\) −0.660099 + 1.14333i −0.0294911 + 0.0510800i
\(502\) 0 0
\(503\) −37.0893 −1.65373 −0.826866 0.562399i \(-0.809879\pi\)
−0.826866 + 0.562399i \(0.809879\pi\)
\(504\) 0 0
\(505\) −21.6947 −0.965401
\(506\) 0 0
\(507\) −9.25651 + 16.0327i −0.411096 + 0.712039i
\(508\) 0 0
\(509\) −7.41214 12.8382i −0.328537 0.569043i 0.653685 0.756767i \(-0.273222\pi\)
−0.982222 + 0.187724i \(0.939889\pi\)
\(510\) 0 0
\(511\) −1.62246 1.36492i −0.0717732 0.0603803i
\(512\) 0 0
\(513\) 2.35724 + 4.08287i 0.104075 + 0.180263i
\(514\) 0 0
\(515\) −11.4287 + 19.7951i −0.503610 + 0.872279i
\(516\) 0 0
\(517\) −0.382542 −0.0168242
\(518\) 0 0
\(519\) 10.8509 0.476303
\(520\) 0 0
\(521\) 5.24608 9.08648i 0.229835 0.398086i −0.727924 0.685658i \(-0.759515\pi\)
0.957759 + 0.287572i \(0.0928480\pi\)
\(522\) 0 0
\(523\) 7.73787 + 13.4024i 0.338353 + 0.586045i 0.984123 0.177487i \(-0.0567968\pi\)
−0.645770 + 0.763532i \(0.723463\pi\)
\(524\) 0 0
\(525\) −5.05311 + 1.83192i −0.220536 + 0.0799516i
\(526\) 0 0
\(527\) 17.1055 + 29.6275i 0.745126 + 1.29060i
\(528\) 0 0
\(529\) −10.3821 + 17.9823i −0.451396 + 0.781840i
\(530\) 0 0
\(531\) −2.33024 −0.101124
\(532\) 0 0
\(533\) 11.5400 0.499852
\(534\) 0 0
\(535\) 3.13778 5.43480i 0.135658 0.234967i
\(536\) 0 0
\(537\) −11.4825 19.8883i −0.495507 0.858243i
\(538\) 0 0
\(539\) −1.30173 + 1.08666i −0.0560697 + 0.0468059i
\(540\) 0 0
\(541\) 9.39634 + 16.2749i 0.403980 + 0.699715i 0.994202 0.107527i \(-0.0342931\pi\)
−0.590222 + 0.807241i \(0.700960\pi\)
\(542\) 0 0
\(543\) −8.54865 + 14.8067i −0.366858 + 0.635416i
\(544\) 0 0
\(545\) 1.12282 0.0480965
\(546\) 0 0
\(547\) −0.809060 −0.0345929 −0.0172965 0.999850i \(-0.505506\pi\)
−0.0172965 + 0.999850i \(0.505506\pi\)
\(548\) 0 0
\(549\) 9.87294 17.1004i 0.421367 0.729829i
\(550\) 0 0
\(551\) −4.45691 7.71959i −0.189871 0.328866i
\(552\) 0 0
\(553\) −18.8591 + 6.83703i −0.801969 + 0.290740i
\(554\) 0 0
\(555\) −7.44705 12.8987i −0.316109 0.547518i
\(556\) 0 0
\(557\) 8.72680 15.1153i 0.369767 0.640455i −0.619762 0.784790i \(-0.712771\pi\)
0.989529 + 0.144335i \(0.0461043\pi\)
\(558\) 0 0
\(559\) 45.1927 1.91145
\(560\) 0 0
\(561\) −1.27434 −0.0538027
\(562\) 0 0
\(563\) 1.84187 3.19022i 0.0776257 0.134452i −0.824599 0.565717i \(-0.808599\pi\)
0.902225 + 0.431265i \(0.141933\pi\)
\(564\) 0 0
\(565\) 8.44967 + 14.6353i 0.355480 + 0.615710i
\(566\) 0 0
\(567\) −4.45846 3.75075i −0.187238 0.157517i
\(568\) 0 0
\(569\) 4.56612 + 7.90875i 0.191422 + 0.331552i 0.945722 0.324978i \(-0.105357\pi\)
−0.754300 + 0.656530i \(0.772024\pi\)
\(570\) 0 0
\(571\) −10.5623 + 18.2945i −0.442020 + 0.765601i −0.997839 0.0657023i \(-0.979071\pi\)
0.555820 + 0.831303i \(0.312405\pi\)
\(572\) 0 0
\(573\) 0.324779 0.0135678
\(574\) 0 0
\(575\) −14.7315 −0.614347
\(576\) 0 0
\(577\) −2.62137 + 4.54035i −0.109129 + 0.189017i −0.915418 0.402505i \(-0.868140\pi\)
0.806289 + 0.591522i \(0.201473\pi\)
\(578\) 0 0
\(579\) −7.79957 13.5093i −0.324139 0.561425i
\(580\) 0 0
\(581\) 4.12434 23.2179i 0.171106 0.963240i
\(582\) 0 0
\(583\) 0.785037 + 1.35972i 0.0325129 + 0.0563140i
\(584\) 0 0
\(585\) 10.4144 18.0383i 0.430583 0.745792i
\(586\) 0 0
\(587\) −3.26045 −0.134573 −0.0672865 0.997734i \(-0.521434\pi\)
−0.0672865 + 0.997734i \(0.521434\pi\)
\(588\) 0 0
\(589\) −5.93284 −0.244458
\(590\) 0 0
\(591\) −5.97956 + 10.3569i −0.245966 + 0.426026i
\(592\) 0 0
\(593\) −9.96152 17.2539i −0.409070 0.708531i 0.585715 0.810517i \(-0.300814\pi\)
−0.994786 + 0.101986i \(0.967480\pi\)
\(594\) 0 0
\(595\) 4.44350 25.0146i 0.182166 1.02550i
\(596\) 0 0
\(597\) −2.17572 3.76846i −0.0890464 0.154233i
\(598\) 0 0
\(599\) −22.2325 + 38.5077i −0.908394 + 1.57338i −0.0920976 + 0.995750i \(0.529357\pi\)
−0.816296 + 0.577634i \(0.803976\pi\)
\(600\) 0 0
\(601\) 22.3392 0.911233 0.455617 0.890176i \(-0.349419\pi\)
0.455617 + 0.890176i \(0.349419\pi\)
\(602\) 0 0
\(603\) −17.3968 −0.708453
\(604\) 0 0
\(605\) −9.11019 + 15.7793i −0.370382 + 0.641520i
\(606\) 0 0
\(607\) −17.2044 29.7989i −0.698306 1.20950i −0.969053 0.246851i \(-0.920604\pi\)
0.270747 0.962651i \(-0.412729\pi\)
\(608\) 0 0
\(609\) −16.4641 13.8507i −0.667161 0.561259i
\(610\) 0 0
\(611\) 4.55592 + 7.89109i 0.184313 + 0.319239i
\(612\) 0 0
\(613\) 12.1470 21.0392i 0.490613 0.849766i −0.509329 0.860572i \(-0.670106\pi\)
0.999942 + 0.0108056i \(0.00343961\pi\)
\(614\) 0 0
\(615\) 3.03846 0.122523
\(616\) 0 0
\(617\) −17.0255 −0.685422 −0.342711 0.939441i \(-0.611345\pi\)
−0.342711 + 0.939441i \(0.611345\pi\)
\(618\) 0 0
\(619\) −14.3397 + 24.8372i −0.576363 + 0.998290i 0.419529 + 0.907742i \(0.362195\pi\)
−0.995892 + 0.0905479i \(0.971138\pi\)
\(620\) 0 0
\(621\) 15.5942 + 27.0100i 0.625775 + 1.08387i
\(622\) 0 0
\(623\) −32.6205 + 11.8260i −1.30691 + 0.473800i
\(624\) 0 0
\(625\) 4.45351 + 7.71371i 0.178141 + 0.308548i
\(626\) 0 0
\(627\) 0.110498 0.191388i 0.00441285 0.00764328i
\(628\) 0 0
\(629\) −56.5318 −2.25407
\(630\) 0 0
\(631\) −29.4675 −1.17308 −0.586542 0.809919i \(-0.699511\pi\)
−0.586542 + 0.809919i \(0.699511\pi\)
\(632\) 0 0
\(633\) −10.0554 + 17.4165i −0.399668 + 0.692244i
\(634\) 0 0
\(635\) 15.4849 + 26.8207i 0.614501 + 1.06435i
\(636\) 0 0
\(637\) 37.9189 + 13.9105i 1.50240 + 0.551154i
\(638\) 0 0
\(639\) 1.33266 + 2.30824i 0.0527193 + 0.0913124i
\(640\) 0 0
\(641\) 8.06837 13.9748i 0.318681 0.551972i −0.661532 0.749917i \(-0.730093\pi\)
0.980213 + 0.197945i \(0.0634266\pi\)
\(642\) 0 0
\(643\) 22.8353 0.900535 0.450267 0.892894i \(-0.351329\pi\)
0.450267 + 0.892894i \(0.351329\pi\)
\(644\) 0 0
\(645\) 11.8992 0.468530
\(646\) 0 0
\(647\) −10.3699 + 17.9613i −0.407685 + 0.706131i −0.994630 0.103496i \(-0.966997\pi\)
0.586945 + 0.809627i \(0.300330\pi\)
\(648\) 0 0
\(649\) 0.130202 + 0.225516i 0.00511086 + 0.00885227i
\(650\) 0 0
\(651\) −13.4627 + 4.88069i −0.527646 + 0.191289i
\(652\) 0 0
\(653\) 9.68834 + 16.7807i 0.379134 + 0.656679i 0.990936 0.134331i \(-0.0428886\pi\)
−0.611802 + 0.791011i \(0.709555\pi\)
\(654\) 0 0
\(655\) 6.63732 11.4962i 0.259342 0.449193i
\(656\) 0 0
\(657\) −1.73714 −0.0677724
\(658\) 0 0
\(659\) 7.33347 0.285672 0.142836 0.989746i \(-0.454378\pi\)
0.142836 + 0.989746i \(0.454378\pi\)
\(660\) 0 0
\(661\) 18.8535 32.6552i 0.733315 1.27014i −0.222144 0.975014i \(-0.571306\pi\)
0.955459 0.295124i \(-0.0953611\pi\)
\(662\) 0 0
\(663\) 15.1769 + 26.2872i 0.589422 + 1.02091i
\(664\) 0 0
\(665\) 3.37153 + 2.83636i 0.130742 + 0.109989i
\(666\) 0 0
\(667\) −29.4845 51.0686i −1.14164 1.97738i
\(668\) 0 0
\(669\) −8.93303 + 15.4725i −0.345371 + 0.598200i
\(670\) 0 0
\(671\) −2.20659 −0.0851844
\(672\) 0 0
\(673\) 48.4005 1.86570 0.932851 0.360263i \(-0.117313\pi\)
0.932851 + 0.360263i \(0.117313\pi\)
\(674\) 0 0
\(675\) −5.24919 + 9.09187i −0.202042 + 0.349946i
\(676\) 0 0
\(677\) −7.93290 13.7402i −0.304886 0.528078i 0.672350 0.740233i \(-0.265285\pi\)
−0.977236 + 0.212155i \(0.931952\pi\)
\(678\) 0 0
\(679\) −0.516709 + 2.90880i −0.0198295 + 0.111630i
\(680\) 0 0
\(681\) 2.64032 + 4.57316i 0.101177 + 0.175244i
\(682\) 0 0
\(683\) −8.63354 + 14.9537i −0.330353 + 0.572189i −0.982581 0.185834i \(-0.940501\pi\)
0.652228 + 0.758023i \(0.273835\pi\)
\(684\) 0 0
\(685\) 0.530831 0.0202820
\(686\) 0 0
\(687\) −17.4316 −0.665059
\(688\) 0 0
\(689\) 18.6990 32.3876i 0.712374 1.23387i
\(690\) 0 0
\(691\) 24.6306 + 42.6614i 0.936992 + 1.62292i 0.771043 + 0.636783i \(0.219735\pi\)
0.165949 + 0.986134i \(0.446931\pi\)
\(692\) 0 0
\(693\) −0.242988 + 1.36789i −0.00923034 + 0.0519620i
\(694\) 0 0
\(695\) −4.83028 8.36629i −0.183223 0.317351i
\(696\) 0 0
\(697\) 5.76637 9.98765i 0.218417 0.378309i
\(698\) 0 0
\(699\) −5.63001 −0.212947
\(700\) 0 0
\(701\) 10.1609 0.383770 0.191885 0.981417i \(-0.438540\pi\)
0.191885 + 0.981417i \(0.438540\pi\)
\(702\) 0 0
\(703\) 4.90185 8.49026i 0.184877 0.320216i
\(704\) 0 0
\(705\) 1.19957 + 2.07771i 0.0451784 + 0.0782512i
\(706\) 0 0
\(707\) −26.3758 22.1890i −0.991963 0.834504i
\(708\) 0 0
\(709\) −3.86510 6.69454i −0.145157 0.251419i 0.784275 0.620414i \(-0.213035\pi\)
−0.929431 + 0.368995i \(0.879702\pi\)
\(710\) 0 0
\(711\) −8.21783 + 14.2337i −0.308193 + 0.533806i
\(712\) 0 0
\(713\) −39.2484 −1.46986
\(714\) 0 0
\(715\) −2.32761 −0.0870477
\(716\) 0 0
\(717\) −11.9248 + 20.6544i −0.445341 + 0.771353i
\(718\) 0 0
\(719\) −12.6604 21.9284i −0.472152 0.817791i 0.527340 0.849654i \(-0.323189\pi\)
−0.999492 + 0.0318632i \(0.989856\pi\)
\(720\) 0 0
\(721\) −34.1409 + 12.3772i −1.27148 + 0.460952i
\(722\) 0 0
\(723\) 8.93667 + 15.4788i 0.332358 + 0.575662i
\(724\) 0 0
\(725\) 9.92480 17.1903i 0.368598 0.638430i
\(726\) 0 0
\(727\) 24.5601 0.910884 0.455442 0.890266i \(-0.349481\pi\)
0.455442 + 0.890266i \(0.349481\pi\)
\(728\) 0 0
\(729\) 8.12941 0.301089
\(730\) 0 0
\(731\) 22.5822 39.1135i 0.835232 1.44666i
\(732\) 0 0
\(733\) 13.6516 + 23.6453i 0.504235 + 0.873361i 0.999988 + 0.00489700i \(0.00155877\pi\)
−0.495753 + 0.868464i \(0.665108\pi\)
\(734\) 0 0
\(735\) 9.98400 + 3.66261i 0.368265 + 0.135098i
\(736\) 0 0
\(737\) 0.972041 + 1.68362i 0.0358056 + 0.0620171i
\(738\) 0 0
\(739\) −24.0188 + 41.6017i −0.883544 + 1.53034i −0.0361706 + 0.999346i \(0.511516\pi\)
−0.847373 + 0.530998i \(0.821817\pi\)
\(740\) 0 0
\(741\) −5.26394 −0.193376
\(742\) 0 0
\(743\) 10.8539 0.398190 0.199095 0.979980i \(-0.436200\pi\)
0.199095 + 0.979980i \(0.436200\pi\)
\(744\) 0 0
\(745\) 11.3823 19.7146i 0.417014 0.722289i
\(746\) 0 0
\(747\) −9.66033 16.7322i −0.353453 0.612199i
\(748\) 0 0
\(749\) 9.37347 3.39819i 0.342499 0.124167i
\(750\) 0 0
\(751\) −8.95718 15.5143i −0.326852 0.566125i 0.655033 0.755600i \(-0.272655\pi\)
−0.981885 + 0.189475i \(0.939321\pi\)
\(752\) 0 0
\(753\) 2.91515 5.04919i 0.106234 0.184003i
\(754\) 0 0
\(755\) −18.3651 −0.668374
\(756\) 0 0
\(757\) 19.7888 0.719235 0.359617 0.933100i \(-0.382907\pi\)
0.359617 + 0.933100i \(0.382907\pi\)
\(758\) 0 0
\(759\) 0.730992 1.26612i 0.0265333 0.0459571i
\(760\) 0 0
\(761\) −25.7301 44.5659i −0.932717 1.61551i −0.778655 0.627452i \(-0.784098\pi\)
−0.154062 0.988061i \(-0.549235\pi\)
\(762\) 0 0
\(763\) 1.36510 + 1.14841i 0.0494198 + 0.0415752i
\(764\) 0 0
\(765\) −10.4079 18.0270i −0.376298 0.651768i
\(766\) 0 0
\(767\) 3.10130 5.37161i 0.111981 0.193958i
\(768\) 0 0
\(769\) −26.2468 −0.946485 −0.473243 0.880932i \(-0.656917\pi\)
−0.473243 + 0.880932i \(0.656917\pi\)
\(770\) 0 0
\(771\) 19.9558 0.718689
\(772\) 0 0
\(773\) −3.02611 + 5.24138i −0.108842 + 0.188519i −0.915301 0.402770i \(-0.868048\pi\)
0.806460 + 0.591289i \(0.201381\pi\)
\(774\) 0 0
\(775\) −6.60573 11.4415i −0.237285 0.410989i
\(776\) 0 0
\(777\) 4.13867 23.2986i 0.148474 0.835831i
\(778\) 0 0
\(779\) 1.00000 + 1.73205i 0.0358287 + 0.0620572i
\(780\) 0 0
\(781\) 0.148924 0.257944i 0.00532892 0.00922996i
\(782\) 0 0
\(783\) −42.0241 −1.50182
\(784\) 0 0
\(785\) −29.7363 −1.06133
\(786\) 0 0
\(787\) 6.22879 10.7886i 0.222032 0.384571i −0.733393 0.679805i \(-0.762064\pi\)
0.955425 + 0.295234i \(0.0953976\pi\)
\(788\) 0 0
\(789\) 13.5584 + 23.4838i 0.482691 + 0.836046i
\(790\) 0 0
\(791\) −4.69587 + 26.4353i −0.166966 + 0.939932i
\(792\) 0 0
\(793\) 26.2796 + 45.5176i 0.933217 + 1.61638i
\(794\) 0 0
\(795\) 4.92341 8.52760i 0.174615 0.302443i
\(796\) 0 0
\(797\) 7.13423 0.252707