Properties

Label 675.2.e.b.451.2
Level $675$
Weight $2$
Character 675.451
Analytic conductor $5.390$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.954288.1
Defining polynomial: \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.2
Root \(-1.62241 + 0.606458i\) of defining polynomial
Character \(\chi\) \(=\) 675.451
Dual form 675.2.e.b.226.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.285997 + 0.495361i) q^{2} +(0.836412 + 1.44871i) q^{4} +(0.714003 - 1.23669i) q^{7} -2.10083 q^{8} +O(q^{10})\) \(q+(-0.285997 + 0.495361i) q^{2} +(0.836412 + 1.44871i) q^{4} +(0.714003 - 1.23669i) q^{7} -2.10083 q^{8} +(1.33641 - 2.31473i) q^{11} +(2.33641 + 4.04678i) q^{13} +(0.408405 + 0.707378i) q^{14} +(-1.07199 + 1.85675i) q^{16} +2.67282 q^{17} +4.67282 q^{19} +(0.764419 + 1.32401i) q^{22} +(2.95882 + 5.12483i) q^{23} -2.67282 q^{26} +2.38880 q^{28} +(-4.74482 + 8.21826i) q^{29} +(-3.48040 - 6.02823i) q^{31} +(-2.71400 - 4.70079i) q^{32} +(-0.764419 + 1.32401i) q^{34} +1.81681 q^{37} +(-1.33641 + 2.31473i) q^{38} +(-0.735581 - 1.27406i) q^{41} +(0.235581 - 0.408039i) q^{43} +4.47116 q^{44} -3.38485 q^{46} +(-3.47842 + 6.02480i) q^{47} +(2.48040 + 4.29618i) q^{49} +(-3.90841 + 6.76956i) q^{52} -1.14399 q^{53} +(-1.50000 + 2.59808i) q^{56} +(-2.71400 - 4.70079i) q^{58} +(-0.571993 - 0.990721i) q^{59} +(1.26442 - 2.19004i) q^{61} +3.98153 q^{62} -1.18319 q^{64} +(-3.29523 - 5.70751i) q^{67} +(2.23558 + 3.87214i) q^{68} +12.8745 q^{71} +1.71203 q^{73} +(-0.519602 + 0.899976i) q^{74} +(3.90841 + 6.76956i) q^{76} +(-1.90841 - 3.30545i) q^{77} +(0.143987 - 0.249392i) q^{79} +0.841495 q^{82} +(2.14201 - 3.71007i) q^{83} +(0.134751 + 0.233396i) q^{86} +(-2.80757 + 4.86286i) q^{88} +3.00000 q^{89} +6.67282 q^{91} +(-4.94958 + 8.57293i) q^{92} +(-1.98963 - 3.44615i) q^{94} +(3.91764 - 6.78555i) q^{97} -2.83754 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 5 q^{4} + 5 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 5 q^{4} + 5 q^{7} + 6 q^{8} - 2 q^{11} + 4 q^{13} - 9 q^{14} - 5 q^{16} - 4 q^{17} + 8 q^{19} - 4 q^{22} - 3 q^{23} + 4 q^{26} - 10 q^{28} - 7 q^{29} - 8 q^{31} - 17 q^{32} + 4 q^{34} - 12 q^{37} + 2 q^{38} - 13 q^{41} + 10 q^{43} + 44 q^{44} - 6 q^{46} - 13 q^{47} + 2 q^{49} - 12 q^{52} - 4 q^{53} - 9 q^{56} - 17 q^{58} - 2 q^{59} - q^{61} + 84 q^{62} - 30 q^{64} + 11 q^{67} + 22 q^{68} + 20 q^{71} + 16 q^{73} - 16 q^{74} + 12 q^{76} - 2 q^{79} + 58 q^{82} + 15 q^{83} + 28 q^{86} - 24 q^{88} + 18 q^{89} + 20 q^{91} - 39 q^{92} + 31 q^{94} - 18 q^{97} - 80 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.285997 + 0.495361i −0.202230 + 0.350273i −0.949247 0.314533i \(-0.898152\pi\)
0.747017 + 0.664805i \(0.231486\pi\)
\(3\) 0 0
\(4\) 0.836412 + 1.44871i 0.418206 + 0.724354i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.714003 1.23669i 0.269868 0.467425i −0.698960 0.715161i \(-0.746353\pi\)
0.968828 + 0.247736i \(0.0796866\pi\)
\(8\) −2.10083 −0.742756
\(9\) 0 0
\(10\) 0 0
\(11\) 1.33641 2.31473i 0.402943 0.697918i −0.591136 0.806572i \(-0.701321\pi\)
0.994080 + 0.108653i \(0.0346538\pi\)
\(12\) 0 0
\(13\) 2.33641 + 4.04678i 0.648004 + 1.12238i 0.983599 + 0.180370i \(0.0577294\pi\)
−0.335595 + 0.942006i \(0.608937\pi\)
\(14\) 0.408405 + 0.707378i 0.109151 + 0.189055i
\(15\) 0 0
\(16\) −1.07199 + 1.85675i −0.267998 + 0.464187i
\(17\) 2.67282 0.648255 0.324127 0.946013i \(-0.394929\pi\)
0.324127 + 0.946013i \(0.394929\pi\)
\(18\) 0 0
\(19\) 4.67282 1.07202 0.536010 0.844212i \(-0.319931\pi\)
0.536010 + 0.844212i \(0.319931\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.764419 + 1.32401i 0.162975 + 0.282280i
\(23\) 2.95882 + 5.12483i 0.616957 + 1.06860i 0.990038 + 0.140802i \(0.0449680\pi\)
−0.373081 + 0.927799i \(0.621699\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −2.67282 −0.524184
\(27\) 0 0
\(28\) 2.38880 0.451441
\(29\) −4.74482 + 8.21826i −0.881090 + 1.52609i −0.0309603 + 0.999521i \(0.509857\pi\)
−0.850130 + 0.526573i \(0.823477\pi\)
\(30\) 0 0
\(31\) −3.48040 6.02823i −0.625098 1.08270i −0.988522 0.151078i \(-0.951726\pi\)
0.363424 0.931624i \(-0.381608\pi\)
\(32\) −2.71400 4.70079i −0.479773 0.830990i
\(33\) 0 0
\(34\) −0.764419 + 1.32401i −0.131097 + 0.227066i
\(35\) 0 0
\(36\) 0 0
\(37\) 1.81681 0.298682 0.149341 0.988786i \(-0.452285\pi\)
0.149341 + 0.988786i \(0.452285\pi\)
\(38\) −1.33641 + 2.31473i −0.216795 + 0.375499i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.735581 1.27406i −0.114879 0.198975i 0.802853 0.596177i \(-0.203315\pi\)
−0.917731 + 0.397202i \(0.869981\pi\)
\(42\) 0 0
\(43\) 0.235581 0.408039i 0.0359258 0.0622254i −0.847503 0.530790i \(-0.821895\pi\)
0.883429 + 0.468565i \(0.155229\pi\)
\(44\) 4.47116 0.674053
\(45\) 0 0
\(46\) −3.38485 −0.499069
\(47\) −3.47842 + 6.02480i −0.507380 + 0.878808i 0.492584 + 0.870265i \(0.336053\pi\)
−0.999964 + 0.00854274i \(0.997281\pi\)
\(48\) 0 0
\(49\) 2.48040 + 4.29618i 0.354343 + 0.613739i
\(50\) 0 0
\(51\) 0 0
\(52\) −3.90841 + 6.76956i −0.541998 + 0.938769i
\(53\) −1.14399 −0.157139 −0.0785693 0.996909i \(-0.525035\pi\)
−0.0785693 + 0.996909i \(0.525035\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.50000 + 2.59808i −0.200446 + 0.347183i
\(57\) 0 0
\(58\) −2.71400 4.70079i −0.356366 0.617244i
\(59\) −0.571993 0.990721i −0.0744672 0.128981i 0.826387 0.563102i \(-0.190392\pi\)
−0.900854 + 0.434121i \(0.857059\pi\)
\(60\) 0 0
\(61\) 1.26442 2.19004i 0.161892 0.280406i −0.773655 0.633607i \(-0.781574\pi\)
0.935547 + 0.353201i \(0.114907\pi\)
\(62\) 3.98153 0.505655
\(63\) 0 0
\(64\) −1.18319 −0.147899
\(65\) 0 0
\(66\) 0 0
\(67\) −3.29523 5.70751i −0.402577 0.697283i 0.591459 0.806335i \(-0.298552\pi\)
−0.994036 + 0.109051i \(0.965219\pi\)
\(68\) 2.23558 + 3.87214i 0.271104 + 0.469566i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.8745 1.52792 0.763960 0.645263i \(-0.223252\pi\)
0.763960 + 0.645263i \(0.223252\pi\)
\(72\) 0 0
\(73\) 1.71203 0.200378 0.100189 0.994968i \(-0.468055\pi\)
0.100189 + 0.994968i \(0.468055\pi\)
\(74\) −0.519602 + 0.899976i −0.0604025 + 0.104620i
\(75\) 0 0
\(76\) 3.90841 + 6.76956i 0.448325 + 0.776521i
\(77\) −1.90841 3.30545i −0.217483 0.376692i
\(78\) 0 0
\(79\) 0.143987 0.249392i 0.0161998 0.0280588i −0.857812 0.513964i \(-0.828177\pi\)
0.874012 + 0.485905i \(0.161510\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0.841495 0.0929276
\(83\) 2.14201 3.71007i 0.235116 0.407233i −0.724190 0.689600i \(-0.757786\pi\)
0.959306 + 0.282367i \(0.0911196\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.134751 + 0.233396i 0.0145306 + 0.0251677i
\(87\) 0 0
\(88\) −2.80757 + 4.86286i −0.299288 + 0.518383i
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) 0 0
\(91\) 6.67282 0.699502
\(92\) −4.94958 + 8.57293i −0.516030 + 0.893790i
\(93\) 0 0
\(94\) −1.98963 3.44615i −0.205215 0.355443i
\(95\) 0 0
\(96\) 0 0
\(97\) 3.91764 6.78555i 0.397776 0.688968i −0.595675 0.803225i \(-0.703115\pi\)
0.993451 + 0.114257i \(0.0364487\pi\)
\(98\) −2.83754 −0.286635
\(99\) 0 0
\(100\) 0 0
\(101\) −2.10083 + 3.63875i −0.209040 + 0.362069i −0.951413 0.307919i \(-0.900367\pi\)
0.742372 + 0.669988i \(0.233701\pi\)
\(102\) 0 0
\(103\) −0.908405 1.57340i −0.0895078 0.155032i 0.817795 0.575509i \(-0.195196\pi\)
−0.907303 + 0.420477i \(0.861863\pi\)
\(104\) −4.90841 8.50161i −0.481309 0.833651i
\(105\) 0 0
\(106\) 0.327176 0.566686i 0.0317782 0.0550414i
\(107\) 11.9176 1.15212 0.576061 0.817407i \(-0.304589\pi\)
0.576061 + 0.817407i \(0.304589\pi\)
\(108\) 0 0
\(109\) −16.6521 −1.59498 −0.797491 0.603331i \(-0.793840\pi\)
−0.797491 + 0.603331i \(0.793840\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.53081 + 2.65145i 0.144648 + 0.250538i
\(113\) −10.0616 17.4272i −0.946518 1.63942i −0.752682 0.658384i \(-0.771240\pi\)
−0.193836 0.981034i \(-0.562093\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −15.8745 −1.47391
\(117\) 0 0
\(118\) 0.654353 0.0602380
\(119\) 1.90841 3.30545i 0.174943 0.303011i
\(120\) 0 0
\(121\) 1.92801 + 3.33941i 0.175273 + 0.303582i
\(122\) 0.723239 + 1.25269i 0.0654790 + 0.113413i
\(123\) 0 0
\(124\) 5.82209 10.0842i 0.522839 0.905584i
\(125\) 0 0
\(126\) 0 0
\(127\) −2.18714 −0.194078 −0.0970388 0.995281i \(-0.530937\pi\)
−0.0970388 + 0.995281i \(0.530937\pi\)
\(128\) 5.76640 9.98769i 0.509682 0.882795i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 0 0
\(133\) 3.33641 5.77883i 0.289304 0.501089i
\(134\) 3.76970 0.325653
\(135\) 0 0
\(136\) −5.61515 −0.481495
\(137\) 5.10083 8.83490i 0.435793 0.754816i −0.561567 0.827431i \(-0.689801\pi\)
0.997360 + 0.0726153i \(0.0231345\pi\)
\(138\) 0 0
\(139\) −4.00000 6.92820i −0.339276 0.587643i 0.645021 0.764165i \(-0.276849\pi\)
−0.984297 + 0.176522i \(0.943515\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.68206 + 6.37751i −0.308992 + 0.535189i
\(143\) 12.4896 1.04444
\(144\) 0 0
\(145\) 0 0
\(146\) −0.489634 + 0.848071i −0.0405224 + 0.0701868i
\(147\) 0 0
\(148\) 1.51960 + 2.63203i 0.124910 + 0.216351i
\(149\) −10.0381 17.3865i −0.822351 1.42435i −0.903927 0.427687i \(-0.859329\pi\)
0.0815762 0.996667i \(-0.474005\pi\)
\(150\) 0 0
\(151\) −1.51960 + 2.63203i −0.123663 + 0.214191i −0.921210 0.389066i \(-0.872798\pi\)
0.797546 + 0.603258i \(0.206131\pi\)
\(152\) −9.81681 −0.796248
\(153\) 0 0
\(154\) 2.18319 0.175926
\(155\) 0 0
\(156\) 0 0
\(157\) 0.100830 + 0.174643i 0.00804714 + 0.0139381i 0.870021 0.493015i \(-0.164105\pi\)
−0.861974 + 0.506953i \(0.830772\pi\)
\(158\) 0.0823593 + 0.142651i 0.00655216 + 0.0113487i
\(159\) 0 0
\(160\) 0 0
\(161\) 8.45043 0.665987
\(162\) 0 0
\(163\) −17.8168 −1.39552 −0.697760 0.716331i \(-0.745820\pi\)
−0.697760 + 0.716331i \(0.745820\pi\)
\(164\) 1.23050 2.13129i 0.0960858 0.166425i
\(165\) 0 0
\(166\) 1.22522 + 2.12214i 0.0950952 + 0.164710i
\(167\) −7.05042 12.2117i −0.545578 0.944968i −0.998570 0.0534538i \(-0.982977\pi\)
0.452993 0.891514i \(-0.350356\pi\)
\(168\) 0 0
\(169\) −4.41764 + 7.65158i −0.339819 + 0.588583i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.788172 0.0600976
\(173\) −2.18319 + 3.78140i −0.165985 + 0.287494i −0.937005 0.349317i \(-0.886414\pi\)
0.771020 + 0.636811i \(0.219747\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.86525 + 4.96276i 0.215976 + 0.374082i
\(177\) 0 0
\(178\) −0.857990 + 1.48608i −0.0643091 + 0.111387i
\(179\) 15.1625 1.13330 0.566648 0.823960i \(-0.308240\pi\)
0.566648 + 0.823960i \(0.308240\pi\)
\(180\) 0 0
\(181\) 3.20166 0.237978 0.118989 0.992896i \(-0.462035\pi\)
0.118989 + 0.992896i \(0.462035\pi\)
\(182\) −1.90841 + 3.30545i −0.141460 + 0.245017i
\(183\) 0 0
\(184\) −6.21598 10.7664i −0.458248 0.793709i
\(185\) 0 0
\(186\) 0 0
\(187\) 3.57199 6.18687i 0.261210 0.452429i
\(188\) −11.6376 −0.848757
\(189\) 0 0
\(190\) 0 0
\(191\) −1.41877 + 2.45738i −0.102659 + 0.177810i −0.912779 0.408453i \(-0.866068\pi\)
0.810121 + 0.586263i \(0.199402\pi\)
\(192\) 0 0
\(193\) −9.39409 16.2710i −0.676201 1.17121i −0.976116 0.217249i \(-0.930292\pi\)
0.299915 0.953966i \(-0.403042\pi\)
\(194\) 2.24086 + 3.88129i 0.160885 + 0.278660i
\(195\) 0 0
\(196\) −4.14927 + 7.18675i −0.296376 + 0.513339i
\(197\) 5.83528 0.415747 0.207873 0.978156i \(-0.433346\pi\)
0.207873 + 0.978156i \(0.433346\pi\)
\(198\) 0 0
\(199\) 13.0761 0.926943 0.463472 0.886112i \(-0.346604\pi\)
0.463472 + 0.886112i \(0.346604\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −1.20166 2.08134i −0.0845486 0.146442i
\(203\) 6.77563 + 11.7357i 0.475556 + 0.823687i
\(204\) 0 0
\(205\) 0 0
\(206\) 1.03920 0.0724047
\(207\) 0 0
\(208\) −10.0185 −0.694656
\(209\) 6.24482 10.8163i 0.431963 0.748182i
\(210\) 0 0
\(211\) −4.19243 7.26149i −0.288618 0.499902i 0.684862 0.728673i \(-0.259863\pi\)
−0.973480 + 0.228771i \(0.926529\pi\)
\(212\) −0.956844 1.65730i −0.0657163 0.113824i
\(213\) 0 0
\(214\) −3.40841 + 5.90353i −0.232994 + 0.403557i
\(215\) 0 0
\(216\) 0 0
\(217\) −9.94006 −0.674776
\(218\) 4.76244 8.24879i 0.322553 0.558679i
\(219\) 0 0
\(220\) 0 0
\(221\) 6.24482 + 10.8163i 0.420072 + 0.727586i
\(222\) 0 0
\(223\) 4.58321 7.93834i 0.306914 0.531591i −0.670772 0.741664i \(-0.734037\pi\)
0.977686 + 0.210073i \(0.0673702\pi\)
\(224\) −7.75123 −0.517901
\(225\) 0 0
\(226\) 11.5104 0.765658
\(227\) 1.33641 2.31473i 0.0887008 0.153634i −0.818261 0.574846i \(-0.805062\pi\)
0.906962 + 0.421212i \(0.138395\pi\)
\(228\) 0 0
\(229\) −1.27365 2.20603i −0.0841654 0.145779i 0.820870 0.571115i \(-0.193489\pi\)
−0.905035 + 0.425336i \(0.860156\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 9.96806 17.2652i 0.654435 1.13351i
\(233\) −6.22013 −0.407494 −0.203747 0.979024i \(-0.565312\pi\)
−0.203747 + 0.979024i \(0.565312\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.956844 1.65730i 0.0622852 0.107881i
\(237\) 0 0
\(238\) 1.09159 + 1.89070i 0.0707576 + 0.122556i
\(239\) 4.06163 + 7.03494i 0.262725 + 0.455053i 0.966965 0.254909i \(-0.0820455\pi\)
−0.704240 + 0.709962i \(0.748712\pi\)
\(240\) 0 0
\(241\) 13.1821 22.8320i 0.849131 1.47074i −0.0328536 0.999460i \(-0.510460\pi\)
0.881985 0.471278i \(-0.156207\pi\)
\(242\) −2.20561 −0.141782
\(243\) 0 0
\(244\) 4.23030 0.270817
\(245\) 0 0
\(246\) 0 0
\(247\) 10.9176 + 18.9099i 0.694673 + 1.20321i
\(248\) 7.31173 + 12.6643i 0.464295 + 0.804183i
\(249\) 0 0
\(250\) 0 0
\(251\) 0.549569 0.0346885 0.0173443 0.999850i \(-0.494479\pi\)
0.0173443 + 0.999850i \(0.494479\pi\)
\(252\) 0 0
\(253\) 15.8168 0.994394
\(254\) 0.625515 1.08342i 0.0392483 0.0679801i
\(255\) 0 0
\(256\) 2.11515 + 3.66355i 0.132197 + 0.228972i
\(257\) 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 0 0
\(259\) 1.29721 2.24683i 0.0806046 0.139611i
\(260\) 0 0
\(261\) 0 0
\(262\) 3.43196 0.212027
\(263\) −5.94761 + 10.3016i −0.366745 + 0.635221i −0.989055 0.147550i \(-0.952861\pi\)
0.622309 + 0.782771i \(0.286195\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.90841 + 3.30545i 0.117012 + 0.202670i
\(267\) 0 0
\(268\) 5.51234 9.54766i 0.336720 0.583216i
\(269\) −28.5737 −1.74217 −0.871084 0.491134i \(-0.836583\pi\)
−0.871084 + 0.491134i \(0.836583\pi\)
\(270\) 0 0
\(271\) −23.3641 −1.41927 −0.709635 0.704570i \(-0.751140\pi\)
−0.709635 + 0.704570i \(0.751140\pi\)
\(272\) −2.86525 + 4.96276i −0.173731 + 0.300911i
\(273\) 0 0
\(274\) 2.91764 + 5.05350i 0.176261 + 0.305293i
\(275\) 0 0
\(276\) 0 0
\(277\) −7.53807 + 13.0563i −0.452919 + 0.784479i −0.998566 0.0535366i \(-0.982951\pi\)
0.545647 + 0.838015i \(0.316284\pi\)
\(278\) 4.57595 0.274447
\(279\) 0 0
\(280\) 0 0
\(281\) 3.32605 5.76088i 0.198415 0.343665i −0.749599 0.661892i \(-0.769754\pi\)
0.948015 + 0.318226i \(0.103087\pi\)
\(282\) 0 0
\(283\) 13.4485 + 23.2934i 0.799428 + 1.38465i 0.919989 + 0.391943i \(0.128197\pi\)
−0.120562 + 0.992706i \(0.538470\pi\)
\(284\) 10.7684 + 18.6514i 0.638985 + 1.10675i
\(285\) 0 0
\(286\) −3.57199 + 6.18687i −0.211216 + 0.365838i
\(287\) −2.10083 −0.124008
\(288\) 0 0
\(289\) −9.85601 −0.579765
\(290\) 0 0
\(291\) 0 0
\(292\) 1.43196 + 2.48023i 0.0837991 + 0.145144i
\(293\) −6.19243 10.7256i −0.361765 0.626596i 0.626486 0.779433i \(-0.284493\pi\)
−0.988251 + 0.152837i \(0.951159\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −3.81681 −0.221848
\(297\) 0 0
\(298\) 11.4834 0.665217
\(299\) −13.8260 + 23.9474i −0.799581 + 1.38491i
\(300\) 0 0
\(301\) −0.336412 0.582682i −0.0193905 0.0335853i
\(302\) −0.869202 1.50550i −0.0500169 0.0866319i
\(303\) 0 0
\(304\) −5.00924 + 8.67625i −0.287299 + 0.497617i
\(305\) 0 0
\(306\) 0 0
\(307\) 2.49359 0.142317 0.0711583 0.997465i \(-0.477330\pi\)
0.0711583 + 0.997465i \(0.477330\pi\)
\(308\) 3.19243 5.52944i 0.181905 0.315069i
\(309\) 0 0
\(310\) 0 0
\(311\) −12.1101 20.9752i −0.686699 1.18940i −0.972900 0.231228i \(-0.925726\pi\)
0.286201 0.958170i \(-0.407608\pi\)
\(312\) 0 0
\(313\) −17.5420 + 30.3837i −0.991534 + 1.71739i −0.383315 + 0.923618i \(0.625218\pi\)
−0.608219 + 0.793770i \(0.708116\pi\)
\(314\) −0.115349 −0.00650950
\(315\) 0 0
\(316\) 0.481728 0.0270993
\(317\) 5.23558 9.06829i 0.294060 0.509326i −0.680706 0.732557i \(-0.738327\pi\)
0.974766 + 0.223231i \(0.0716603\pi\)
\(318\) 0 0
\(319\) 12.6821 + 21.9660i 0.710059 + 1.22986i
\(320\) 0 0
\(321\) 0 0
\(322\) −2.41679 + 4.18601i −0.134683 + 0.233277i
\(323\) 12.4896 0.694942
\(324\) 0 0
\(325\) 0 0
\(326\) 5.09555 8.82575i 0.282216 0.488813i
\(327\) 0 0
\(328\) 1.54533 + 2.67659i 0.0853267 + 0.147790i
\(329\) 4.96721 + 8.60346i 0.273851 + 0.474324i
\(330\) 0 0
\(331\) −8.38880 + 14.5298i −0.461090 + 0.798632i −0.999016 0.0443606i \(-0.985875\pi\)
0.537925 + 0.842993i \(0.319208\pi\)
\(332\) 7.16641 0.393308
\(333\) 0 0
\(334\) 8.06558 0.441329
\(335\) 0 0
\(336\) 0 0
\(337\) −13.5905 23.5394i −0.740320 1.28227i −0.952350 0.305008i \(-0.901341\pi\)
0.212030 0.977263i \(-0.431993\pi\)
\(338\) −2.52686 4.37665i −0.137443 0.238058i
\(339\) 0 0
\(340\) 0 0
\(341\) −18.6050 −1.00752
\(342\) 0 0
\(343\) 17.0801 0.922239
\(344\) −0.494917 + 0.857221i −0.0266841 + 0.0462182i
\(345\) 0 0
\(346\) −1.24877 2.16293i −0.0671343 0.116280i
\(347\) 11.7829 + 20.4086i 0.632539 + 1.09559i 0.987031 + 0.160530i \(0.0513204\pi\)
−0.354492 + 0.935059i \(0.615346\pi\)
\(348\) 0 0
\(349\) 5.35601 9.27689i 0.286701 0.496580i −0.686319 0.727300i \(-0.740775\pi\)
0.973020 + 0.230720i \(0.0741081\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −14.5081 −0.773285
\(353\) −13.6336 + 23.6141i −0.725644 + 1.25685i 0.233064 + 0.972461i \(0.425125\pi\)
−0.958708 + 0.284392i \(0.908208\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 2.50924 + 4.34612i 0.132989 + 0.230344i
\(357\) 0 0
\(358\) −4.33641 + 7.51089i −0.229186 + 0.396963i
\(359\) 10.6807 0.563707 0.281854 0.959457i \(-0.409051\pi\)
0.281854 + 0.959457i \(0.409051\pi\)
\(360\) 0 0
\(361\) 2.83528 0.149225
\(362\) −0.915664 + 1.58598i −0.0481262 + 0.0833571i
\(363\) 0 0
\(364\) 5.58123 + 9.66697i 0.292536 + 0.506687i
\(365\) 0 0
\(366\) 0 0
\(367\) −4.23558 + 7.33624i −0.221096 + 0.382949i −0.955141 0.296152i \(-0.904297\pi\)
0.734045 + 0.679100i \(0.237630\pi\)
\(368\) −12.6873 −0.661373
\(369\) 0 0
\(370\) 0 0
\(371\) −0.816810 + 1.41476i −0.0424067 + 0.0734505i
\(372\) 0 0
\(373\) 5.06163 + 8.76700i 0.262081 + 0.453938i 0.966795 0.255554i \(-0.0822579\pi\)
−0.704714 + 0.709492i \(0.748925\pi\)
\(374\) 2.04316 + 3.53885i 0.105649 + 0.182990i
\(375\) 0 0
\(376\) 7.30757 12.6571i 0.376859 0.652740i
\(377\) −44.3434 −2.28380
\(378\) 0 0
\(379\) 11.9216 0.612371 0.306186 0.951972i \(-0.400947\pi\)
0.306186 + 0.951972i \(0.400947\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −0.811528 1.40561i −0.0415214 0.0719171i
\(383\) −4.90841 8.50161i −0.250808 0.434412i 0.712941 0.701224i \(-0.247363\pi\)
−0.963748 + 0.266813i \(0.914030\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.7467 0.546993
\(387\) 0 0
\(388\) 13.1070 0.665409
\(389\) 4.61007 7.98487i 0.233740 0.404849i −0.725166 0.688574i \(-0.758237\pi\)
0.958906 + 0.283725i \(0.0915703\pi\)
\(390\) 0 0
\(391\) 7.90841 + 13.6978i 0.399945 + 0.692725i
\(392\) −5.21090 9.02554i −0.263190 0.455858i
\(393\) 0 0
\(394\) −1.66887 + 2.89057i −0.0840765 + 0.145625i
\(395\) 0 0
\(396\) 0 0
\(397\) 22.9793 1.15330 0.576648 0.816993i \(-0.304360\pi\)
0.576648 + 0.816993i \(0.304360\pi\)
\(398\) −3.73973 + 6.47741i −0.187456 + 0.324683i
\(399\) 0 0
\(400\) 0 0
\(401\) −5.53279 9.58307i −0.276294 0.478556i 0.694167 0.719814i \(-0.255773\pi\)
−0.970461 + 0.241259i \(0.922440\pi\)
\(402\) 0 0
\(403\) 16.2633 28.1688i 0.810132 1.40319i
\(404\) −7.02864 −0.349688
\(405\) 0 0
\(406\) −7.75123 −0.384687
\(407\) 2.42801 4.20543i 0.120352 0.208455i
\(408\) 0 0
\(409\) 8.81681 + 15.2712i 0.435963 + 0.755110i 0.997374 0.0724270i \(-0.0230744\pi\)
−0.561411 + 0.827537i \(0.689741\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.51960 2.63203i 0.0748654 0.129671i
\(413\) −1.63362 −0.0803852
\(414\) 0 0
\(415\) 0 0
\(416\) 12.6821 21.9660i 0.621789 1.07697i
\(417\) 0 0
\(418\) 3.57199 + 6.18687i 0.174712 + 0.302610i
\(419\) 18.5173 + 32.0730i 0.904631 + 1.56687i 0.821411 + 0.570336i \(0.193187\pi\)
0.0832199 + 0.996531i \(0.473480\pi\)
\(420\) 0 0
\(421\) −2.52884 + 4.38007i −0.123248 + 0.213472i −0.921047 0.389452i \(-0.872664\pi\)
0.797799 + 0.602924i \(0.205998\pi\)
\(422\) 4.79608 0.233469
\(423\) 0 0
\(424\) 2.40332 0.116716
\(425\) 0 0
\(426\) 0 0
\(427\) −1.80560 3.12739i −0.0873790 0.151345i
\(428\) 9.96806 + 17.2652i 0.481824 + 0.834544i
\(429\) 0 0
\(430\) 0 0
\(431\) 5.23030 0.251935 0.125967 0.992034i \(-0.459797\pi\)
0.125967 + 0.992034i \(0.459797\pi\)
\(432\) 0 0
\(433\) −34.3434 −1.65044 −0.825219 0.564813i \(-0.808948\pi\)
−0.825219 + 0.564813i \(0.808948\pi\)
\(434\) 2.84283 4.92392i 0.136460 0.236356i
\(435\) 0 0
\(436\) −13.9280 24.1240i −0.667031 1.15533i
\(437\) 13.8260 + 23.9474i 0.661389 + 1.14556i
\(438\) 0 0
\(439\) 9.77365 16.9285i 0.466471 0.807952i −0.532796 0.846244i \(-0.678859\pi\)
0.999267 + 0.0382924i \(0.0121918\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −7.14399 −0.339805
\(443\) −5.25208 + 9.09686i −0.249534 + 0.432205i −0.963396 0.268081i \(-0.913611\pi\)
0.713863 + 0.700286i \(0.246944\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 2.62156 + 4.54068i 0.124135 + 0.215007i
\(447\) 0 0
\(448\) −0.844801 + 1.46324i −0.0399131 + 0.0691315i
\(449\) −22.8560 −1.07864 −0.539321 0.842100i \(-0.681319\pi\)
−0.539321 + 0.842100i \(0.681319\pi\)
\(450\) 0 0
\(451\) −3.93216 −0.185158
\(452\) 16.8313 29.1527i 0.791679 1.37123i
\(453\) 0 0
\(454\) 0.764419 + 1.32401i 0.0358759 + 0.0621390i
\(455\) 0 0
\(456\) 0 0
\(457\) −7.01319 + 12.1472i −0.328063 + 0.568222i −0.982127 0.188217i \(-0.939729\pi\)
0.654064 + 0.756439i \(0.273063\pi\)
\(458\) 1.45704 0.0680832
\(459\) 0 0
\(460\) 0 0
\(461\) −12.0513 + 20.8734i −0.561283 + 0.972171i 0.436102 + 0.899897i \(0.356359\pi\)
−0.997385 + 0.0722736i \(0.976975\pi\)
\(462\) 0 0
\(463\) −16.9700 29.3930i −0.788664 1.36601i −0.926785 0.375591i \(-0.877440\pi\)
0.138121 0.990415i \(-0.455894\pi\)
\(464\) −10.1728 17.6198i −0.472261 0.817981i
\(465\) 0 0
\(466\) 1.77894 3.08121i 0.0824077 0.142734i
\(467\) −27.3720 −1.26663 −0.633313 0.773896i \(-0.718305\pi\)
−0.633313 + 0.773896i \(0.718305\pi\)
\(468\) 0 0
\(469\) −9.41123 −0.434570
\(470\) 0 0
\(471\) 0 0
\(472\) 1.20166 + 2.08134i 0.0553109 + 0.0958013i
\(473\) −0.629668 1.09062i −0.0289521 0.0501466i
\(474\) 0 0
\(475\) 0 0
\(476\) 6.38485 0.292649
\(477\) 0 0
\(478\) −4.64645 −0.212524
\(479\) 2.61515 4.52957i 0.119489 0.206961i −0.800076 0.599898i \(-0.795208\pi\)
0.919565 + 0.392937i \(0.128541\pi\)
\(480\) 0 0
\(481\) 4.24482 + 7.35224i 0.193547 + 0.335233i
\(482\) 7.54005 + 13.0597i 0.343440 + 0.594855i
\(483\) 0 0
\(484\) −3.22522 + 5.58624i −0.146601 + 0.253920i
\(485\) 0 0
\(486\) 0 0
\(487\) 24.0185 1.08838 0.544190 0.838962i \(-0.316837\pi\)
0.544190 + 0.838962i \(0.316837\pi\)
\(488\) −2.65633 + 4.60090i −0.120246 + 0.208273i
\(489\) 0 0
\(490\) 0 0
\(491\) 7.38880 + 12.7978i 0.333452 + 0.577556i 0.983186 0.182606i \(-0.0584531\pi\)
−0.649734 + 0.760161i \(0.725120\pi\)
\(492\) 0 0
\(493\) −12.6821 + 21.9660i −0.571171 + 0.989298i
\(494\) −12.4896 −0.561935
\(495\) 0 0
\(496\) 14.9239 0.670101
\(497\) 9.19243 15.9217i 0.412337 0.714188i
\(498\) 0 0
\(499\) −12.4280 21.5259i −0.556354 0.963633i −0.997797 0.0663440i \(-0.978867\pi\)
0.441443 0.897289i \(-0.354467\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −0.157175 + 0.272235i −0.00701506 + 0.0121504i
\(503\) 38.9154 1.73515 0.867576 0.497305i \(-0.165677\pi\)
0.867576 + 0.497305i \(0.165677\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −4.52355 + 7.83503i −0.201097 + 0.348309i
\(507\) 0 0
\(508\) −1.82935 3.16853i −0.0811644 0.140581i
\(509\) 1.01037 + 1.75001i 0.0447837 + 0.0775676i 0.887548 0.460715i \(-0.152407\pi\)
−0.842765 + 0.538282i \(0.819073\pi\)
\(510\) 0 0
\(511\) 1.22239 2.11725i 0.0540755 0.0936615i
\(512\) 20.6459 0.912428
\(513\) 0 0
\(514\) −10.2959 −0.454132
\(515\) 0 0
\(516\) 0 0
\(517\) 9.29721 + 16.1032i 0.408891 + 0.708220i
\(518\) 0.741995 + 1.28517i 0.0326014 + 0.0564672i
\(519\) 0 0
\(520\) 0 0
\(521\) 23.0290 1.00892 0.504460 0.863435i \(-0.331692\pi\)
0.504460 + 0.863435i \(0.331692\pi\)
\(522\) 0 0
\(523\) 41.1170 1.79792 0.898961 0.438028i \(-0.144323\pi\)
0.898961 + 0.438028i \(0.144323\pi\)
\(524\) 5.01847 8.69225i 0.219233 0.379723i
\(525\) 0 0
\(526\) −3.40199 5.89242i −0.148334 0.256922i
\(527\) −9.30249 16.1124i −0.405223 0.701867i
\(528\) 0 0
\(529\) −6.00924 + 10.4083i −0.261271 + 0.452535i
\(530\) 0 0
\(531\) 0 0
\(532\) 11.1625 0.483954
\(533\) 3.43724 5.95348i 0.148883 0.257874i
\(534\) 0 0
\(535\) 0 0
\(536\) 6.92272 + 11.9905i 0.299016 + 0.517911i
\(537\) 0 0
\(538\) 8.17198 14.1543i 0.352319 0.610234i
\(539\) 13.2593 0.571120
\(540\) 0 0
\(541\) 5.20957 0.223977 0.111988 0.993710i \(-0.464278\pi\)
0.111988 + 0.993710i \(0.464278\pi\)
\(542\) 6.68206 11.5737i 0.287019 0.497132i
\(543\) 0 0
\(544\) −7.25405 12.5644i −0.311015 0.538694i
\(545\) 0 0
\(546\) 0 0
\(547\) 20.0204 34.6764i 0.856013 1.48266i −0.0196900 0.999806i \(-0.506268\pi\)
0.875702 0.482851i \(-0.160399\pi\)
\(548\) 17.0656 0.729005
\(549\) 0 0
\(550\) 0 0
\(551\) −22.1717 + 38.4025i −0.944546 + 1.63600i
\(552\) 0 0
\(553\) −0.205614 0.356133i −0.00874359 0.0151443i
\(554\) −4.31173 7.46813i −0.183188 0.317290i
\(555\) 0 0
\(556\) 6.69129 11.5897i 0.283774 0.491511i
\(557\) −14.4033 −0.610288 −0.305144 0.952306i \(-0.598705\pi\)
−0.305144 + 0.952306i \(0.598705\pi\)
\(558\) 0 0
\(559\) 2.20166 0.0931203
\(560\) 0 0
\(561\) 0 0
\(562\) 1.90248 + 3.29518i 0.0802511 + 0.138999i
\(563\) −14.6840 25.4335i −0.618858 1.07189i −0.989694 0.143196i \(-0.954262\pi\)
0.370836 0.928698i \(-0.379071\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −15.3849 −0.646674
\(567\) 0 0
\(568\) −27.0471 −1.13487
\(569\) 23.4033 40.5357i 0.981118 1.69935i 0.323062 0.946378i \(-0.395288\pi\)
0.658056 0.752969i \(-0.271379\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 10.4465 + 18.0938i 0.436789 + 0.756541i
\(573\) 0 0
\(574\) 0.600830 1.04067i 0.0250782 0.0434367i
\(575\) 0 0
\(576\) 0 0
\(577\) −28.2386 −1.17559 −0.587794 0.809010i \(-0.700004\pi\)
−0.587794 + 0.809010i \(0.700004\pi\)
\(578\) 2.81879 4.88228i 0.117246 0.203076i
\(579\) 0 0
\(580\) 0 0
\(581\) −3.05880 5.29801i −0.126901 0.219798i
\(582\) 0 0
\(583\) −1.52884 + 2.64802i −0.0633180 + 0.109670i
\(584\) −3.59668 −0.148832
\(585\) 0 0
\(586\) 7.08405 0.292639
\(587\) −9.04118 + 15.6598i −0.373169 + 0.646348i −0.990051 0.140707i \(-0.955062\pi\)
0.616882 + 0.787056i \(0.288396\pi\)
\(588\) 0 0
\(589\) −16.2633 28.1688i −0.670117 1.16068i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.94761 + 3.37336i −0.0800462 + 0.138644i
\(593\) −7.73840 −0.317778 −0.158889 0.987296i \(-0.550791\pi\)
−0.158889 + 0.987296i \(0.550791\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 16.7919 29.0845i 0.687824 1.19135i
\(597\) 0 0
\(598\) −7.90841 13.6978i −0.323399 0.560143i
\(599\) −13.9608 24.1808i −0.570423 0.988001i −0.996522 0.0833249i \(-0.973446\pi\)
0.426100 0.904676i \(-0.359887\pi\)
\(600\) 0 0
\(601\) −19.2201 + 33.2902i −0.784006 + 1.35794i 0.145586 + 0.989346i \(0.453493\pi\)
−0.929591 + 0.368592i \(0.879840\pi\)
\(602\) 0.384851 0.0156853
\(603\) 0 0
\(604\) −5.08405 −0.206867
\(605\) 0 0
\(606\) 0 0
\(607\) −0.319917 0.554113i −0.0129850 0.0224907i 0.859460 0.511203i \(-0.170800\pi\)
−0.872445 + 0.488712i \(0.837467\pi\)
\(608\) −12.6821 21.9660i −0.514325 0.890838i
\(609\) 0 0
\(610\) 0 0
\(611\) −32.5081 −1.31514
\(612\) 0 0
\(613\) −42.7467 −1.72652 −0.863262 0.504757i \(-0.831582\pi\)
−0.863262 + 0.504757i \(0.831582\pi\)
\(614\) −0.713157 + 1.23522i −0.0287807 + 0.0498496i
\(615\) 0 0
\(616\) 4.00924 + 6.94420i 0.161537 + 0.279790i
\(617\) −10.5513 18.2753i −0.424778 0.735737i 0.571622 0.820517i \(-0.306314\pi\)
−0.996400 + 0.0847805i \(0.972981\pi\)
\(618\) 0 0
\(619\) 6.82605 11.8231i 0.274362 0.475209i −0.695612 0.718418i \(-0.744867\pi\)
0.969974 + 0.243209i \(0.0782000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 13.8538 0.555485
\(623\) 2.14201 3.71007i 0.0858178 0.148641i
\(624\) 0 0
\(625\) 0 0
\(626\) −10.0339 17.3793i −0.401036 0.694615i
\(627\) 0 0
\(628\) −0.168672 + 0.292148i −0.00673073 + 0.0116580i
\(629\) 4.85601 0.193622
\(630\) 0 0
\(631\) 33.2593 1.32403 0.662017 0.749489i \(-0.269701\pi\)
0.662017 + 0.749489i \(0.269701\pi\)
\(632\) −0.302491 + 0.523930i −0.0120325 + 0.0208408i
\(633\) 0 0
\(634\) 2.99472 + 5.18700i 0.118935 + 0.206002i
\(635\) 0 0
\(636\) 0 0
\(637\) −11.5905 + 20.0753i −0.459231 + 0.795411i
\(638\) −14.5081 −0.574381
\(639\) 0 0
\(640\) 0 0
\(641\) 13.1429 22.7641i 0.519112 0.899128i −0.480642 0.876917i \(-0.659596\pi\)
0.999753 0.0222106i \(-0.00707044\pi\)
\(642\) 0 0
\(643\) 10.2913 + 17.8250i 0.405848 + 0.702950i 0.994420 0.105495i \(-0.0336427\pi\)
−0.588571 + 0.808445i \(0.700309\pi\)
\(644\) 7.06804 + 12.2422i 0.278520 + 0.482410i
\(645\) 0 0
\(646\) −3.57199 + 6.18687i −0.140538 + 0.243419i
\(647\) 23.2527 0.914159 0.457079 0.889426i \(-0.348896\pi\)
0.457079 + 0.889426i \(0.348896\pi\)
\(648\) 0 0
\(649\) −3.05767 −0.120024
\(650\) 0 0
\(651\) 0 0
\(652\) −14.9022 25.8114i −0.583615 1.01085i
\(653\) −9.37957 16.2459i −0.367051 0.635751i 0.622052 0.782976i \(-0.286299\pi\)
−0.989103 + 0.147225i \(0.952966\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.15415 0.123149
\(657\) 0 0
\(658\) −5.68242 −0.221524
\(659\) −0.140034 + 0.242545i −0.00545494 + 0.00944823i −0.868740 0.495268i \(-0.835070\pi\)
0.863285 + 0.504717i \(0.168403\pi\)
\(660\) 0 0
\(661\) 19.8930 + 34.4556i 0.773746 + 1.34017i 0.935496 + 0.353336i \(0.114953\pi\)
−0.161750 + 0.986832i \(0.551714\pi\)
\(662\) −4.79834 8.31097i −0.186493 0.323015i
\(663\) 0 0
\(664\) −4.50000 + 7.79423i −0.174634 + 0.302475i
\(665\) 0 0
\(666\) 0 0
\(667\) −56.1562 −2.17438
\(668\) 11.7941 20.4280i 0.456327 0.790382i
\(669\) 0 0
\(670\) 0 0
\(671\) −3.37957 5.85358i −0.130467 0.225975i
\(672\) 0 0
\(673\) 16.7644 29.0368i 0.646221 1.11929i −0.337797 0.941219i \(-0.609682\pi\)
0.984018 0.178068i \(-0.0569848\pi\)
\(674\) 15.5473 0.598860
\(675\) 0 0
\(676\) −14.7799 −0.568456
\(677\) −13.7437 + 23.8048i −0.528213 + 0.914891i 0.471246 + 0.882002i \(0.343804\pi\)
−0.999459 + 0.0328897i \(0.989529\pi\)
\(678\) 0 0
\(679\) −5.59442 9.68981i −0.214694 0.371861i
\(680\) 0 0
\(681\) 0 0
\(682\) 5.32096 9.21618i 0.203750 0.352906i
\(683\) −34.5865 −1.32342 −0.661708 0.749762i \(-0.730168\pi\)
−0.661708 + 0.749762i \(0.730168\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −4.88485 + 8.46081i −0.186504 + 0.323035i
\(687\) 0 0
\(688\) 0.505083 + 0.874830i 0.0192561 + 0.0333526i
\(689\) −2.67282 4.62947i −0.101826 0.176369i
\(690\) 0 0
\(691\) −20.3641 + 35.2717i −0.774688 + 1.34180i 0.160282 + 0.987071i \(0.448760\pi\)
−0.934970 + 0.354727i \(0.884574\pi\)
\(692\) −7.30418 −0.277663
\(693\) 0 0
\(694\) −13.4795 −0.511674
\(695\) 0 0
\(696\) 0 0
\(697\) −1.96608 3.40535i −0.0744706 0.128987i
\(698\) 3.06360 + 5.30632i 0.115959 + 0.200847i
\(699\) 0 0
\(700\) 0 0
\(701\) 19.4712 0.735416 0.367708 0.929941i \(-0.380143\pi\)
0.367708 + 0.929941i \(0.380143\pi\)
\(702\) 0 0
\(703\) 8.48963 0.320193
\(704\) −1.58123 + 2.73877i −0.0595948 + 0.103221i
\(705\) 0 0
\(706\) −7.79834 13.5071i −0.293494 0.508347i
\(707\) 3.00000 + 5.19615i 0.112827 + 0.195421i
\(708\) 0 0
\(709\) −7.54316 + 13.0651i −0.283289 + 0.490671i −0.972193 0.234182i \(-0.924759\pi\)
0.688904 + 0.724853i \(0.258092\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −6.30249 −0.236196
\(713\) 20.5957 35.6729i 0.771317 1.33596i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.6821 + 21.9660i 0.473951 + 0.820907i
\(717\) 0 0
\(718\) −3.05465 + 5.29081i −0.113999 + 0.197451i
\(719\) 3.43196 0.127990 0.0639952 0.997950i \(-0.479616\pi\)
0.0639952 + 0.997950i \(0.479616\pi\)
\(720\) 0 0
\(721\) −2.59442 −0.0966211
\(722\) −0.810881 + 1.40449i −0.0301779 + 0.0522696i
\(723\) 0 0
\(724\) 2.67791 + 4.63827i 0.0995236 + 0.172380i
\(725\) 0 0
\(726\) 0 0
\(727\) −17.8857 + 30.9789i −0.663344 + 1.14895i 0.316388 + 0.948630i \(0.397530\pi\)
−0.979732 + 0.200315i \(0.935803\pi\)
\(728\) −14.0185 −0.519559
\(729\) 0 0
\(730\) 0 0
\(731\) 0.629668 1.09062i 0.0232891 0.0403379i
\(732\) 0 0
\(733\) −11.0000 19.0526i −0.406294 0.703722i 0.588177 0.808732i \(-0.299846\pi\)
−0.994471 + 0.105010i \(0.966513\pi\)
\(734\) −2.42272 4.19628i −0.0894244 0.154888i
\(735\) 0 0
\(736\) 16.0605 27.8176i 0.591998 1.02537i
\(737\) −17.6151 −0.648862
\(738\) 0 0
\(739\) 6.08631 0.223889 0.111944 0.993714i \(-0.464292\pi\)
0.111944 + 0.993714i \(0.464292\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.467210 0.809231i −0.0171518 0.0297078i
\(743\) 12.7509 + 22.0853i 0.467787 + 0.810231i 0.999322 0.0368054i \(-0.0117182\pi\)
−0.531536 + 0.847036i \(0.678385\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −5.79043 −0.212003
\(747\) 0 0
\(748\) 11.9506 0.436958
\(749\) 8.50924 14.7384i 0.310921 0.538530i
\(750\) 0 0
\(751\) 9.19638 + 15.9286i 0.335581 + 0.581243i 0.983596 0.180384i \(-0.0577342\pi\)
−0.648016 + 0.761627i \(0.724401\pi\)
\(752\) −7.45769 12.9171i −0.271954 0.471038i
\(753\) 0 0
\(754\) 12.6821 21.9660i 0.461853 0.799953i
\(755\) 0 0
\(756\) 0 0
\(757\) 41.8986 1.52283 0.761415 0.648264i \(-0.224505\pi\)
0.761415 + 0.648264i \(0.224505\pi\)
\(758\) −3.40954 + 5.90549i −0.123840 + 0.214497i
\(759\) 0 0
\(760\) 0 0
\(761\) −3.98568 6.90340i −0.144481 0.250248i 0.784698 0.619878i \(-0.212818\pi\)
−0.929179 + 0.369630i \(0.879485\pi\)
\(762\) 0 0
\(763\) −11.8896 + 20.5935i −0.430434 + 0.745534i
\(764\) −4.74671 −0.171730
\(765\) 0 0
\(766\) 5.61515 0.202884
\(767\) 2.67282 4.62947i 0.0965101 0.167160i
\(768\) 0 0
\(769\) −3.01432 5.22095i −0.108699 0.188272i 0.806544 0.591174i \(-0.201335\pi\)
−0.915244 + 0.402901i \(0.868002\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 15.7147 27.2186i 0.565583 0.979618i
\(773\) 44.4033 1.59708 0.798538 0.601944i \(-0.205607\pi\)
0.798538 + 0.601944i \(0.205607\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −8.23030 + 14.2553i −0.295451 + 0.511735i
\(777\) 0 0
\(778\) 2.63693 + 4.56729i 0.0945384 + 0.163745i
\(779\) −3.43724 5.95348i −0.123152 0.213305i
\(780\) 0 0
\(781\) 17.2056 29.8010i 0.615665 1.06636i
\(782\) −9.04711 −0.323524
\(783\) 0 0
\(784\) −10.6359 −0.379853
\(785\) 0 0
\(786\) 0 0
\(787\) 8.41877 + 14.5817i 0.300097 + 0.519783i 0.976158 0.217063i \(-0.0696477\pi\)
−0.676061 + 0.736846i \(0.736314\pi\)
\(788\) 4.88070 + 8.45362i 0.173868 + 0.301148i
\(789\) 0 0
\(790\) 0 0
\(791\) −28.7361 −1.02174
\(792\) 0 0
\(793\) 11.8168 0.419627
\(794\) −6.57199 + 11.3830i −0.233231 + 0.403968i