Properties

Label 1260.2.c.e.811.12
Level $1260$
Weight $2$
Character 1260.811
Analytic conductor $10.061$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + 24 x^{7} - 28 x^{6} + 16 x^{5} + 48 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 811.12
Root \(-0.449546 + 1.34086i\) of defining polynomial
Character \(\chi\) \(=\) 1260.811
Dual form 1260.2.c.e.811.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.449546 + 1.34086i) q^{2} +(-1.59582 + 1.20556i) q^{4} -1.00000i q^{5} +(-1.40015 - 2.24490i) q^{7} +(-2.33388 - 1.59781i) q^{8} +O(q^{10})\) \(q+(0.449546 + 1.34086i) q^{2} +(-1.59582 + 1.20556i) q^{4} -1.00000i q^{5} +(-1.40015 - 2.24490i) q^{7} +(-2.33388 - 1.59781i) q^{8} +(1.34086 - 0.449546i) q^{10} +3.99156i q^{11} -2.50547i q^{13} +(2.38067 - 2.88659i) q^{14} +(1.09326 - 3.84770i) q^{16} +1.07705i q^{17} +7.78975 q^{19} +(1.20556 + 1.59582i) q^{20} +(-5.35213 + 1.79439i) q^{22} +8.10651i q^{23} -1.00000 q^{25} +(3.35948 - 1.12632i) q^{26} +(4.94074 + 1.89449i) q^{28} +5.99783 q^{29} +6.32559 q^{31} +(5.65070 - 0.263812i) q^{32} +(-1.44417 + 0.484184i) q^{34} +(-2.24490 + 1.40015i) q^{35} +3.05357 q^{37} +(3.50185 + 10.4450i) q^{38} +(-1.59781 + 2.33388i) q^{40} -9.32685i q^{41} +8.13000i q^{43} +(-4.81206 - 6.36980i) q^{44} +(-10.8697 + 3.64425i) q^{46} +9.01476 q^{47} +(-3.07916 + 6.28639i) q^{49} +(-0.449546 - 1.34086i) q^{50} +(3.02049 + 3.99827i) q^{52} -2.86521 q^{53} +3.99156 q^{55} +(-0.319153 + 7.47651i) q^{56} +(2.69630 + 8.04226i) q^{58} +9.68276 q^{59} +3.21235i q^{61} +(2.84365 + 8.48173i) q^{62} +(2.89399 + 7.45821i) q^{64} -2.50547 q^{65} -7.79060i q^{67} +(-1.29845 - 1.71877i) q^{68} +(-2.88659 - 2.38067i) q^{70} -5.84987i q^{71} -5.73252i q^{73} +(1.37272 + 4.09441i) q^{74} +(-12.4310 + 9.39100i) q^{76} +(8.96067 - 5.58879i) q^{77} -2.81801i q^{79} +(-3.84770 - 1.09326i) q^{80} +(12.5060 - 4.19285i) q^{82} -12.5103 q^{83} +1.07705 q^{85} +(-10.9012 + 3.65481i) q^{86} +(6.37777 - 9.31583i) q^{88} -3.51385i q^{89} +(-5.62453 + 3.50803i) q^{91} +(-9.77288 - 12.9365i) q^{92} +(4.05255 + 12.0875i) q^{94} -7.78975i q^{95} +12.0136i q^{97} +(-9.81341 - 1.30270i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} + O(q^{10}) \) \( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.449546 + 1.34086i 0.317877 + 0.948132i
\(3\) 0 0
\(4\) −1.59582 + 1.20556i −0.797908 + 0.602779i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −1.40015 2.24490i −0.529207 0.848493i
\(8\) −2.33388 1.59781i −0.825151 0.564912i
\(9\) 0 0
\(10\) 1.34086 0.449546i 0.424017 0.142159i
\(11\) 3.99156i 1.20350i 0.798684 + 0.601751i \(0.205530\pi\)
−0.798684 + 0.601751i \(0.794470\pi\)
\(12\) 0 0
\(13\) 2.50547i 0.694892i −0.937700 0.347446i \(-0.887049\pi\)
0.937700 0.347446i \(-0.112951\pi\)
\(14\) 2.38067 2.88659i 0.636260 0.771474i
\(15\) 0 0
\(16\) 1.09326 3.84770i 0.273315 0.961925i
\(17\) 1.07705i 0.261223i 0.991434 + 0.130611i \(0.0416940\pi\)
−0.991434 + 0.130611i \(0.958306\pi\)
\(18\) 0 0
\(19\) 7.78975 1.78709 0.893546 0.448973i \(-0.148210\pi\)
0.893546 + 0.448973i \(0.148210\pi\)
\(20\) 1.20556 + 1.59582i 0.269571 + 0.356835i
\(21\) 0 0
\(22\) −5.35213 + 1.79439i −1.14108 + 0.382566i
\(23\) 8.10651i 1.69033i 0.534509 + 0.845163i \(0.320496\pi\)
−0.534509 + 0.845163i \(0.679504\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 3.35948 1.12632i 0.658849 0.220890i
\(27\) 0 0
\(28\) 4.94074 + 1.89449i 0.933712 + 0.358025i
\(29\) 5.99783 1.11377 0.556885 0.830590i \(-0.311997\pi\)
0.556885 + 0.830590i \(0.311997\pi\)
\(30\) 0 0
\(31\) 6.32559 1.13611 0.568055 0.822991i \(-0.307696\pi\)
0.568055 + 0.822991i \(0.307696\pi\)
\(32\) 5.65070 0.263812i 0.998912 0.0466358i
\(33\) 0 0
\(34\) −1.44417 + 0.484184i −0.247674 + 0.0830368i
\(35\) −2.24490 + 1.40015i −0.379458 + 0.236668i
\(36\) 0 0
\(37\) 3.05357 0.502003 0.251002 0.967987i \(-0.419240\pi\)
0.251002 + 0.967987i \(0.419240\pi\)
\(38\) 3.50185 + 10.4450i 0.568076 + 1.69440i
\(39\) 0 0
\(40\) −1.59781 + 2.33388i −0.252636 + 0.369019i
\(41\) 9.32685i 1.45661i −0.685254 0.728305i \(-0.740309\pi\)
0.685254 0.728305i \(-0.259691\pi\)
\(42\) 0 0
\(43\) 8.13000i 1.23981i 0.784676 + 0.619906i \(0.212829\pi\)
−0.784676 + 0.619906i \(0.787171\pi\)
\(44\) −4.81206 6.36980i −0.725446 0.960284i
\(45\) 0 0
\(46\) −10.8697 + 3.64425i −1.60265 + 0.537316i
\(47\) 9.01476 1.31494 0.657469 0.753482i \(-0.271627\pi\)
0.657469 + 0.753482i \(0.271627\pi\)
\(48\) 0 0
\(49\) −3.07916 + 6.28639i −0.439880 + 0.898056i
\(50\) −0.449546 1.34086i −0.0635755 0.189626i
\(51\) 0 0
\(52\) 3.02049 + 3.99827i 0.418866 + 0.554460i
\(53\) −2.86521 −0.393566 −0.196783 0.980447i \(-0.563049\pi\)
−0.196783 + 0.980447i \(0.563049\pi\)
\(54\) 0 0
\(55\) 3.99156 0.538222
\(56\) −0.319153 + 7.47651i −0.0426486 + 0.999090i
\(57\) 0 0
\(58\) 2.69630 + 8.04226i 0.354042 + 1.05600i
\(59\) 9.68276 1.26059 0.630294 0.776356i \(-0.282934\pi\)
0.630294 + 0.776356i \(0.282934\pi\)
\(60\) 0 0
\(61\) 3.21235i 0.411299i 0.978626 + 0.205649i \(0.0659307\pi\)
−0.978626 + 0.205649i \(0.934069\pi\)
\(62\) 2.84365 + 8.48173i 0.361143 + 1.07718i
\(63\) 0 0
\(64\) 2.89399 + 7.45821i 0.361748 + 0.932276i
\(65\) −2.50547 −0.310765
\(66\) 0 0
\(67\) 7.79060i 0.951773i −0.879507 0.475887i \(-0.842127\pi\)
0.879507 0.475887i \(-0.157873\pi\)
\(68\) −1.29845 1.71877i −0.157460 0.208432i
\(69\) 0 0
\(70\) −2.88659 2.38067i −0.345014 0.284544i
\(71\) 5.84987i 0.694252i −0.937819 0.347126i \(-0.887158\pi\)
0.937819 0.347126i \(-0.112842\pi\)
\(72\) 0 0
\(73\) 5.73252i 0.670941i −0.942051 0.335470i \(-0.891105\pi\)
0.942051 0.335470i \(-0.108895\pi\)
\(74\) 1.37272 + 4.09441i 0.159575 + 0.475965i
\(75\) 0 0
\(76\) −12.4310 + 9.39100i −1.42593 + 1.07722i
\(77\) 8.96067 5.58879i 1.02116 0.636901i
\(78\) 0 0
\(79\) 2.81801i 0.317050i −0.987355 0.158525i \(-0.949326\pi\)
0.987355 0.158525i \(-0.0506739\pi\)
\(80\) −3.84770 1.09326i −0.430186 0.122230i
\(81\) 0 0
\(82\) 12.5060 4.19285i 1.38106 0.463023i
\(83\) −12.5103 −1.37318 −0.686590 0.727045i \(-0.740893\pi\)
−0.686590 + 0.727045i \(0.740893\pi\)
\(84\) 0 0
\(85\) 1.07705 0.116822
\(86\) −10.9012 + 3.65481i −1.17551 + 0.394108i
\(87\) 0 0
\(88\) 6.37777 9.31583i 0.679873 0.993071i
\(89\) 3.51385i 0.372467i −0.982505 0.186234i \(-0.940372\pi\)
0.982505 0.186234i \(-0.0596282\pi\)
\(90\) 0 0
\(91\) −5.62453 + 3.50803i −0.589611 + 0.367741i
\(92\) −9.77288 12.9365i −1.01889 1.34872i
\(93\) 0 0
\(94\) 4.05255 + 12.0875i 0.417989 + 1.24673i
\(95\) 7.78975i 0.799211i
\(96\) 0 0
\(97\) 12.0136i 1.21980i 0.792479 + 0.609899i \(0.208790\pi\)
−0.792479 + 0.609899i \(0.791210\pi\)
\(98\) −9.81341 1.30270i −0.991304 0.131593i
\(99\) 0 0
\(100\) 1.59582 1.20556i 0.159582 0.120556i
\(101\) 0.260498i 0.0259205i −0.999916 0.0129602i \(-0.995875\pi\)
0.999916 0.0129602i \(-0.00412549\pi\)
\(102\) 0 0
\(103\) −1.76484 −0.173895 −0.0869475 0.996213i \(-0.527711\pi\)
−0.0869475 + 0.996213i \(0.527711\pi\)
\(104\) −4.00327 + 5.84746i −0.392553 + 0.573391i
\(105\) 0 0
\(106\) −1.28804 3.84184i −0.125106 0.373153i
\(107\) 6.10229i 0.589930i 0.955508 + 0.294965i \(0.0953081\pi\)
−0.955508 + 0.294965i \(0.904692\pi\)
\(108\) 0 0
\(109\) 14.9561 1.43253 0.716265 0.697828i \(-0.245850\pi\)
0.716265 + 0.697828i \(0.245850\pi\)
\(110\) 1.79439 + 5.35213i 0.171089 + 0.510306i
\(111\) 0 0
\(112\) −10.1684 + 2.93310i −0.960826 + 0.277152i
\(113\) −11.8448 −1.11427 −0.557133 0.830423i \(-0.688099\pi\)
−0.557133 + 0.830423i \(0.688099\pi\)
\(114\) 0 0
\(115\) 8.10651 0.755936
\(116\) −9.57144 + 7.23074i −0.888686 + 0.671357i
\(117\) 0 0
\(118\) 4.35285 + 12.9832i 0.400712 + 1.19520i
\(119\) 2.41787 1.50803i 0.221646 0.138241i
\(120\) 0 0
\(121\) −4.93258 −0.448416
\(122\) −4.30731 + 1.44410i −0.389966 + 0.130743i
\(123\) 0 0
\(124\) −10.0945 + 7.62587i −0.906511 + 0.684823i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 5.49406i 0.487519i 0.969836 + 0.243760i \(0.0783808\pi\)
−0.969836 + 0.243760i \(0.921619\pi\)
\(128\) −8.69944 + 7.23324i −0.768929 + 0.639334i
\(129\) 0 0
\(130\) −1.12632 3.35948i −0.0987852 0.294646i
\(131\) −9.93971 −0.868436 −0.434218 0.900808i \(-0.642975\pi\)
−0.434218 + 0.900808i \(0.642975\pi\)
\(132\) 0 0
\(133\) −10.9068 17.4872i −0.945741 1.51633i
\(134\) 10.4461 3.50224i 0.902407 0.302547i
\(135\) 0 0
\(136\) 1.72092 2.51370i 0.147568 0.215548i
\(137\) −16.4345 −1.40409 −0.702046 0.712132i \(-0.747730\pi\)
−0.702046 + 0.712132i \(0.747730\pi\)
\(138\) 0 0
\(139\) −17.8065 −1.51033 −0.755164 0.655535i \(-0.772443\pi\)
−0.755164 + 0.655535i \(0.772443\pi\)
\(140\) 1.89449 4.94074i 0.160113 0.417569i
\(141\) 0 0
\(142\) 7.84386 2.62979i 0.658242 0.220687i
\(143\) 10.0007 0.836303
\(144\) 0 0
\(145\) 5.99783i 0.498093i
\(146\) 7.68651 2.57703i 0.636140 0.213277i
\(147\) 0 0
\(148\) −4.87293 + 3.68125i −0.400553 + 0.302597i
\(149\) 19.6876 1.61287 0.806434 0.591324i \(-0.201395\pi\)
0.806434 + 0.591324i \(0.201395\pi\)
\(150\) 0 0
\(151\) 13.2712i 1.08000i 0.841666 + 0.539998i \(0.181575\pi\)
−0.841666 + 0.539998i \(0.818425\pi\)
\(152\) −18.1803 12.4466i −1.47462 1.00955i
\(153\) 0 0
\(154\) 11.5220 + 9.50259i 0.928471 + 0.765740i
\(155\) 6.32559i 0.508083i
\(156\) 0 0
\(157\) 19.3395i 1.54346i −0.635951 0.771730i \(-0.719392\pi\)
0.635951 0.771730i \(-0.280608\pi\)
\(158\) 3.77855 1.26682i 0.300606 0.100783i
\(159\) 0 0
\(160\) −0.263812 5.65070i −0.0208562 0.446727i
\(161\) 18.1983 11.3503i 1.43423 0.894531i
\(162\) 0 0
\(163\) 2.74676i 0.215143i −0.994197 0.107572i \(-0.965693\pi\)
0.994197 0.107572i \(-0.0343075\pi\)
\(164\) 11.2441 + 14.8839i 0.878014 + 1.16224i
\(165\) 0 0
\(166\) −5.62394 16.7745i −0.436502 1.30196i
\(167\) 5.82171 0.450498 0.225249 0.974301i \(-0.427680\pi\)
0.225249 + 0.974301i \(0.427680\pi\)
\(168\) 0 0
\(169\) 6.72263 0.517125
\(170\) 0.484184 + 1.44417i 0.0371352 + 0.110763i
\(171\) 0 0
\(172\) −9.80118 12.9740i −0.747333 0.989257i
\(173\) 10.5651i 0.803253i −0.915804 0.401626i \(-0.868445\pi\)
0.915804 0.401626i \(-0.131555\pi\)
\(174\) 0 0
\(175\) 1.40015 + 2.24490i 0.105841 + 0.169699i
\(176\) 15.3583 + 4.36381i 1.15768 + 0.328935i
\(177\) 0 0
\(178\) 4.71158 1.57964i 0.353148 0.118399i
\(179\) 4.59887i 0.343736i −0.985120 0.171868i \(-0.945020\pi\)
0.985120 0.171868i \(-0.0549802\pi\)
\(180\) 0 0
\(181\) 9.42719i 0.700717i 0.936616 + 0.350359i \(0.113940\pi\)
−0.936616 + 0.350359i \(0.886060\pi\)
\(182\) −7.23227 5.96469i −0.536091 0.442132i
\(183\) 0 0
\(184\) 12.9527 18.9196i 0.954885 1.39477i
\(185\) 3.05357i 0.224503i
\(186\) 0 0
\(187\) −4.29911 −0.314382
\(188\) −14.3859 + 10.8678i −1.04920 + 0.792617i
\(189\) 0 0
\(190\) 10.4450 3.50185i 0.757758 0.254051i
\(191\) 5.02689i 0.363733i 0.983323 + 0.181866i \(0.0582139\pi\)
−0.983323 + 0.181866i \(0.941786\pi\)
\(192\) 0 0
\(193\) 15.8775 1.14288 0.571442 0.820642i \(-0.306384\pi\)
0.571442 + 0.820642i \(0.306384\pi\)
\(194\) −16.1086 + 5.40068i −1.15653 + 0.387746i
\(195\) 0 0
\(196\) −2.66484 13.7440i −0.190346 0.981717i
\(197\) 10.1289 0.721651 0.360826 0.932633i \(-0.382495\pi\)
0.360826 + 0.932633i \(0.382495\pi\)
\(198\) 0 0
\(199\) −1.13945 −0.0807737 −0.0403869 0.999184i \(-0.512859\pi\)
−0.0403869 + 0.999184i \(0.512859\pi\)
\(200\) 2.33388 + 1.59781i 0.165030 + 0.112982i
\(201\) 0 0
\(202\) 0.349291 0.117106i 0.0245760 0.00823953i
\(203\) −8.39786 13.4645i −0.589414 0.945025i
\(204\) 0 0
\(205\) −9.32685 −0.651415
\(206\) −0.793378 2.36641i −0.0552773 0.164875i
\(207\) 0 0
\(208\) −9.64029 2.73912i −0.668434 0.189924i
\(209\) 31.0933i 2.15077i
\(210\) 0 0
\(211\) 16.8644i 1.16099i 0.814263 + 0.580497i \(0.197142\pi\)
−0.814263 + 0.580497i \(0.802858\pi\)
\(212\) 4.57234 3.45417i 0.314030 0.237233i
\(213\) 0 0
\(214\) −8.18232 + 2.74326i −0.559332 + 0.187525i
\(215\) 8.13000 0.554461
\(216\) 0 0
\(217\) −8.85677 14.2003i −0.601237 0.963981i
\(218\) 6.72344 + 20.0540i 0.455369 + 1.35823i
\(219\) 0 0
\(220\) −6.36980 + 4.81206i −0.429452 + 0.324429i
\(221\) 2.69851 0.181522
\(222\) 0 0
\(223\) −1.84769 −0.123730 −0.0618652 0.998085i \(-0.519705\pi\)
−0.0618652 + 0.998085i \(0.519705\pi\)
\(224\) −8.50406 12.3159i −0.568201 0.822890i
\(225\) 0 0
\(226\) −5.32479 15.8822i −0.354200 1.05647i
\(227\) 26.0109 1.72640 0.863201 0.504861i \(-0.168456\pi\)
0.863201 + 0.504861i \(0.168456\pi\)
\(228\) 0 0
\(229\) 14.8172i 0.979146i −0.871962 0.489573i \(-0.837153\pi\)
0.871962 0.489573i \(-0.162847\pi\)
\(230\) 3.64425 + 10.8697i 0.240295 + 0.716727i
\(231\) 0 0
\(232\) −13.9982 9.58342i −0.919028 0.629182i
\(233\) 3.41871 0.223967 0.111983 0.993710i \(-0.464280\pi\)
0.111983 + 0.993710i \(0.464280\pi\)
\(234\) 0 0
\(235\) 9.01476i 0.588058i
\(236\) −15.4519 + 11.6731i −1.00583 + 0.759856i
\(237\) 0 0
\(238\) 3.10900 + 2.56410i 0.201527 + 0.166206i
\(239\) 2.84316i 0.183909i 0.995763 + 0.0919544i \(0.0293114\pi\)
−0.995763 + 0.0919544i \(0.970689\pi\)
\(240\) 0 0
\(241\) 20.0977i 1.29461i 0.762233 + 0.647303i \(0.224103\pi\)
−0.762233 + 0.647303i \(0.775897\pi\)
\(242\) −2.21742 6.61390i −0.142541 0.425158i
\(243\) 0 0
\(244\) −3.87267 5.12632i −0.247922 0.328179i
\(245\) 6.28639 + 3.07916i 0.401623 + 0.196720i
\(246\) 0 0
\(247\) 19.5170i 1.24183i
\(248\) −14.7632 10.1071i −0.937462 0.641802i
\(249\) 0 0
\(250\) −1.34086 + 0.449546i −0.0848035 + 0.0284318i
\(251\) −15.7417 −0.993607 −0.496803 0.867863i \(-0.665493\pi\)
−0.496803 + 0.867863i \(0.665493\pi\)
\(252\) 0 0
\(253\) −32.3577 −2.03431
\(254\) −7.36677 + 2.46983i −0.462232 + 0.154971i
\(255\) 0 0
\(256\) −13.6096 8.41306i −0.850598 0.525816i
\(257\) 7.43670i 0.463889i −0.972729 0.231944i \(-0.925491\pi\)
0.972729 0.231944i \(-0.0745087\pi\)
\(258\) 0 0
\(259\) −4.27545 6.85496i −0.265664 0.425946i
\(260\) 3.99827 3.02049i 0.247962 0.187323i
\(261\) 0 0
\(262\) −4.46836 13.3278i −0.276056 0.823392i
\(263\) 8.49327i 0.523718i 0.965106 + 0.261859i \(0.0843355\pi\)
−0.965106 + 0.261859i \(0.915665\pi\)
\(264\) 0 0
\(265\) 2.86521i 0.176008i
\(266\) 18.5448 22.4858i 1.13706 1.37869i
\(267\) 0 0
\(268\) 9.39202 + 12.4324i 0.573709 + 0.759428i
\(269\) 5.94512i 0.362480i −0.983439 0.181240i \(-0.941989\pi\)
0.983439 0.181240i \(-0.0580111\pi\)
\(270\) 0 0
\(271\) 11.2023 0.680490 0.340245 0.940337i \(-0.389490\pi\)
0.340245 + 0.940337i \(0.389490\pi\)
\(272\) 4.14416 + 1.17749i 0.251277 + 0.0713960i
\(273\) 0 0
\(274\) −7.38806 22.0363i −0.446329 1.33126i
\(275\) 3.99156i 0.240700i
\(276\) 0 0
\(277\) 2.17155 0.130476 0.0652378 0.997870i \(-0.479219\pi\)
0.0652378 + 0.997870i \(0.479219\pi\)
\(278\) −8.00485 23.8761i −0.480099 1.43199i
\(279\) 0 0
\(280\) 7.47651 + 0.319153i 0.446807 + 0.0190730i
\(281\) −1.72189 −0.102720 −0.0513598 0.998680i \(-0.516356\pi\)
−0.0513598 + 0.998680i \(0.516356\pi\)
\(282\) 0 0
\(283\) −6.51271 −0.387140 −0.193570 0.981086i \(-0.562007\pi\)
−0.193570 + 0.981086i \(0.562007\pi\)
\(284\) 7.05236 + 9.33532i 0.418481 + 0.553949i
\(285\) 0 0
\(286\) 4.49579 + 13.4096i 0.265842 + 0.792926i
\(287\) −20.9379 + 13.0590i −1.23592 + 0.770847i
\(288\) 0 0
\(289\) 15.8400 0.931763
\(290\) 8.04226 2.69630i 0.472258 0.158332i
\(291\) 0 0
\(292\) 6.91089 + 9.14805i 0.404429 + 0.535349i
\(293\) 9.20381i 0.537692i −0.963183 0.268846i \(-0.913358\pi\)
0.963183 0.268846i \(-0.0866423\pi\)
\(294\) 0 0
\(295\) 9.68276i 0.563752i
\(296\) −7.12666 4.87903i −0.414229 0.283588i
\(297\) 0 0
\(298\) 8.85047 + 26.3983i 0.512694 + 1.52921i
\(299\) 20.3106 1.17459
\(300\) 0 0
\(301\) 18.2510 11.3832i 1.05197 0.656117i
\(302\) −17.7949 + 5.96603i −1.02398 + 0.343306i
\(303\) 0 0
\(304\) 8.51621 29.9726i 0.488438 1.71905i
\(305\) 3.21235 0.183938
\(306\) 0 0
\(307\) −32.5750 −1.85916 −0.929578 0.368626i \(-0.879828\pi\)
−0.929578 + 0.368626i \(0.879828\pi\)
\(308\) −7.56197 + 19.7213i −0.430883 + 1.12372i
\(309\) 0 0
\(310\) 8.48173 2.84365i 0.481730 0.161508i
\(311\) −27.3621 −1.55156 −0.775781 0.631002i \(-0.782644\pi\)
−0.775781 + 0.631002i \(0.782644\pi\)
\(312\) 0 0
\(313\) 19.7088i 1.11401i 0.830510 + 0.557004i \(0.188049\pi\)
−0.830510 + 0.557004i \(0.811951\pi\)
\(314\) 25.9316 8.69400i 1.46340 0.490631i
\(315\) 0 0
\(316\) 3.39727 + 4.49702i 0.191111 + 0.252977i
\(317\) 0.854973 0.0480201 0.0240100 0.999712i \(-0.492357\pi\)
0.0240100 + 0.999712i \(0.492357\pi\)
\(318\) 0 0
\(319\) 23.9407i 1.34042i
\(320\) 7.45821 2.89399i 0.416926 0.161779i
\(321\) 0 0
\(322\) 23.4002 + 19.2989i 1.30404 + 1.07549i
\(323\) 8.38994i 0.466829i
\(324\) 0 0
\(325\) 2.50547i 0.138978i
\(326\) 3.68303 1.23480i 0.203984 0.0683891i
\(327\) 0 0
\(328\) −14.9026 + 21.7677i −0.822856 + 1.20192i
\(329\) −12.6220 20.2372i −0.695874 1.11572i
\(330\) 0 0
\(331\) 4.23740i 0.232909i −0.993196 0.116454i \(-0.962847\pi\)
0.993196 0.116454i \(-0.0371529\pi\)
\(332\) 19.9641 15.0818i 1.09567 0.827724i
\(333\) 0 0
\(334\) 2.61713 + 7.80611i 0.143203 + 0.427131i
\(335\) −7.79060 −0.425646
\(336\) 0 0
\(337\) 20.5956 1.12191 0.560956 0.827846i \(-0.310434\pi\)
0.560956 + 0.827846i \(0.310434\pi\)
\(338\) 3.02213 + 9.01411i 0.164382 + 0.490303i
\(339\) 0 0
\(340\) −1.71877 + 1.29845i −0.0932135 + 0.0704181i
\(341\) 25.2490i 1.36731i
\(342\) 0 0
\(343\) 18.4236 1.88948i 0.994782 0.102022i
\(344\) 12.9902 18.9744i 0.700385 1.02303i
\(345\) 0 0
\(346\) 14.1664 4.74952i 0.761590 0.255336i
\(347\) 13.8257i 0.742200i −0.928593 0.371100i \(-0.878981\pi\)
0.928593 0.371100i \(-0.121019\pi\)
\(348\) 0 0
\(349\) 8.06666i 0.431798i 0.976416 + 0.215899i \(0.0692683\pi\)
−0.976416 + 0.215899i \(0.930732\pi\)
\(350\) −2.38067 + 2.88659i −0.127252 + 0.154295i
\(351\) 0 0
\(352\) 1.05302 + 22.5551i 0.0561262 + 1.20219i
\(353\) 7.67694i 0.408602i −0.978908 0.204301i \(-0.934508\pi\)
0.978908 0.204301i \(-0.0654922\pi\)
\(354\) 0 0
\(355\) −5.84987 −0.310479
\(356\) 4.23615 + 5.60746i 0.224516 + 0.297195i
\(357\) 0 0
\(358\) 6.16645 2.06741i 0.325907 0.109266i
\(359\) 21.6267i 1.14141i −0.821154 0.570706i \(-0.806670\pi\)
0.821154 0.570706i \(-0.193330\pi\)
\(360\) 0 0
\(361\) 41.6802 2.19369
\(362\) −12.6405 + 4.23796i −0.664372 + 0.222742i
\(363\) 0 0
\(364\) 4.74658 12.3789i 0.248788 0.648829i
\(365\) −5.73252 −0.300054
\(366\) 0 0
\(367\) 6.62228 0.345680 0.172840 0.984950i \(-0.444706\pi\)
0.172840 + 0.984950i \(0.444706\pi\)
\(368\) 31.1914 + 8.86251i 1.62597 + 0.461990i
\(369\) 0 0
\(370\) 4.09441 1.37272i 0.212858 0.0713643i
\(371\) 4.01172 + 6.43210i 0.208278 + 0.333938i
\(372\) 0 0
\(373\) −31.1585 −1.61332 −0.806662 0.591013i \(-0.798728\pi\)
−0.806662 + 0.591013i \(0.798728\pi\)
\(374\) −1.93265 5.76451i −0.0999349 0.298076i
\(375\) 0 0
\(376\) −21.0394 14.4039i −1.08502 0.742825i
\(377\) 15.0274i 0.773949i
\(378\) 0 0
\(379\) 31.1885i 1.60204i −0.598635 0.801022i \(-0.704290\pi\)
0.598635 0.801022i \(-0.295710\pi\)
\(380\) 9.39100 + 12.4310i 0.481748 + 0.637697i
\(381\) 0 0
\(382\) −6.74036 + 2.25982i −0.344867 + 0.115622i
\(383\) 27.9907 1.43026 0.715128 0.698993i \(-0.246368\pi\)
0.715128 + 0.698993i \(0.246368\pi\)
\(384\) 0 0
\(385\) −5.58879 8.96067i −0.284831 0.456678i
\(386\) 7.13766 + 21.2895i 0.363297 + 1.08361i
\(387\) 0 0
\(388\) −14.4831 19.1715i −0.735269 0.973286i
\(389\) −15.7502 −0.798568 −0.399284 0.916827i \(-0.630741\pi\)
−0.399284 + 0.916827i \(0.630741\pi\)
\(390\) 0 0
\(391\) −8.73111 −0.441551
\(392\) 17.2309 9.75176i 0.870291 0.492538i
\(393\) 0 0
\(394\) 4.55339 + 13.5814i 0.229397 + 0.684221i
\(395\) −2.81801 −0.141789
\(396\) 0 0
\(397\) 11.3689i 0.570589i 0.958440 + 0.285294i \(0.0920914\pi\)
−0.958440 + 0.285294i \(0.907909\pi\)
\(398\) −0.512237 1.52785i −0.0256761 0.0765841i
\(399\) 0 0
\(400\) −1.09326 + 3.84770i −0.0546629 + 0.192385i
\(401\) −12.7623 −0.637319 −0.318659 0.947869i \(-0.603233\pi\)
−0.318659 + 0.947869i \(0.603233\pi\)
\(402\) 0 0
\(403\) 15.8486i 0.789473i
\(404\) 0.314045 + 0.415706i 0.0156243 + 0.0206822i
\(405\) 0 0
\(406\) 14.2788 17.3133i 0.708647 0.859245i
\(407\) 12.1885i 0.604162i
\(408\) 0 0
\(409\) 1.91649i 0.0947643i 0.998877 + 0.0473822i \(0.0150879\pi\)
−0.998877 + 0.0473822i \(0.984912\pi\)
\(410\) −4.19285 12.5060i −0.207070 0.617628i
\(411\) 0 0
\(412\) 2.81636 2.12762i 0.138752 0.104820i
\(413\) −13.5573 21.7368i −0.667112 1.06960i
\(414\) 0 0
\(415\) 12.5103i 0.614104i
\(416\) −0.660972 14.1576i −0.0324068 0.694136i
\(417\) 0 0
\(418\) −41.6918 + 13.9779i −2.03921 + 0.683680i
\(419\) −13.7105 −0.669800 −0.334900 0.942254i \(-0.608703\pi\)
−0.334900 + 0.942254i \(0.608703\pi\)
\(420\) 0 0
\(421\) 7.87629 0.383867 0.191933 0.981408i \(-0.438524\pi\)
0.191933 + 0.981408i \(0.438524\pi\)
\(422\) −22.6128 + 7.58133i −1.10077 + 0.369053i
\(423\) 0 0
\(424\) 6.68704 + 4.57806i 0.324752 + 0.222330i
\(425\) 1.07705i 0.0522446i
\(426\) 0 0
\(427\) 7.21140 4.49777i 0.348984 0.217662i
\(428\) −7.35666 9.73813i −0.355598 0.470710i
\(429\) 0 0
\(430\) 3.65481 + 10.9012i 0.176251 + 0.525702i
\(431\) 22.3788i 1.07795i −0.842322 0.538974i \(-0.818812\pi\)
0.842322 0.538974i \(-0.181188\pi\)
\(432\) 0 0
\(433\) 33.9772i 1.63284i −0.577460 0.816419i \(-0.695956\pi\)
0.577460 0.816419i \(-0.304044\pi\)
\(434\) 15.0591 18.2594i 0.722861 0.876479i
\(435\) 0 0
\(436\) −23.8671 + 18.0304i −1.14303 + 0.863499i
\(437\) 63.1477i 3.02076i
\(438\) 0 0
\(439\) 2.97475 0.141977 0.0709886 0.997477i \(-0.477385\pi\)
0.0709886 + 0.997477i \(0.477385\pi\)
\(440\) −9.31583 6.37777i −0.444115 0.304048i
\(441\) 0 0
\(442\) 1.21311 + 3.61833i 0.0577016 + 0.172106i
\(443\) 20.4095i 0.969684i 0.874602 + 0.484842i \(0.161123\pi\)
−0.874602 + 0.484842i \(0.838877\pi\)
\(444\) 0 0
\(445\) −3.51385 −0.166572
\(446\) −0.830622 2.47750i −0.0393311 0.117313i
\(447\) 0 0
\(448\) 12.6909 16.9393i 0.599590 0.800308i
\(449\) 11.0234 0.520226 0.260113 0.965578i \(-0.416240\pi\)
0.260113 + 0.965578i \(0.416240\pi\)
\(450\) 0 0
\(451\) 37.2287 1.75303
\(452\) 18.9021 14.2796i 0.889082 0.671656i
\(453\) 0 0
\(454\) 11.6931 + 34.8769i 0.548784 + 1.63686i
\(455\) 3.50803 + 5.62453i 0.164459 + 0.263682i
\(456\) 0 0
\(457\) 0.409340 0.0191481 0.00957406 0.999954i \(-0.496952\pi\)
0.00957406 + 0.999954i \(0.496952\pi\)
\(458\) 19.8678 6.66101i 0.928360 0.311248i
\(459\) 0 0
\(460\) −12.9365 + 9.77288i −0.603168 + 0.455663i
\(461\) 23.9577i 1.11582i 0.829901 + 0.557910i \(0.188397\pi\)
−0.829901 + 0.557910i \(0.811603\pi\)
\(462\) 0 0
\(463\) 10.1008i 0.469424i −0.972065 0.234712i \(-0.924585\pi\)
0.972065 0.234712i \(-0.0754147\pi\)
\(464\) 6.55718 23.0779i 0.304409 1.07136i
\(465\) 0 0
\(466\) 1.53687 + 4.58401i 0.0711940 + 0.212350i
\(467\) −38.6883 −1.79028 −0.895140 0.445785i \(-0.852924\pi\)
−0.895140 + 0.445785i \(0.852924\pi\)
\(468\) 0 0
\(469\) −17.4891 + 10.9080i −0.807573 + 0.503685i
\(470\) 12.0875 4.05255i 0.557557 0.186930i
\(471\) 0 0
\(472\) −22.5984 15.4712i −1.04018 0.712122i
\(473\) −32.4514 −1.49212
\(474\) 0 0
\(475\) −7.78975 −0.357418
\(476\) −2.04046 + 5.32142i −0.0935242 + 0.243907i
\(477\) 0 0
\(478\) −3.81228 + 1.27813i −0.174370 + 0.0584604i
\(479\) 7.91710 0.361742 0.180871 0.983507i \(-0.442108\pi\)
0.180871 + 0.983507i \(0.442108\pi\)
\(480\) 0 0
\(481\) 7.65062i 0.348838i
\(482\) −26.9482 + 9.03484i −1.22746 + 0.411526i
\(483\) 0 0
\(484\) 7.87149 5.94651i 0.357795 0.270296i
\(485\) 12.0136 0.545510
\(486\) 0 0
\(487\) 28.5984i 1.29592i 0.761676 + 0.647958i \(0.224377\pi\)
−0.761676 + 0.647958i \(0.775623\pi\)
\(488\) 5.13273 7.49723i 0.232348 0.339384i
\(489\) 0 0
\(490\) −1.30270 + 9.81341i −0.0588501 + 0.443325i
\(491\) 23.6318i 1.06649i 0.845961 + 0.533244i \(0.179027\pi\)
−0.845961 + 0.533244i \(0.820973\pi\)
\(492\) 0 0
\(493\) 6.45996i 0.290942i
\(494\) 26.1695 8.77378i 1.17742 0.394751i
\(495\) 0 0
\(496\) 6.91550 24.3390i 0.310515 1.09285i
\(497\) −13.1324 + 8.19069i −0.589068 + 0.367403i
\(498\) 0 0
\(499\) 0.663011i 0.0296805i −0.999890 0.0148402i \(-0.995276\pi\)
0.999890 0.0148402i \(-0.00472397\pi\)
\(500\) −1.20556 1.59582i −0.0539142 0.0713671i
\(501\) 0 0
\(502\) −7.07662 21.1074i −0.315845 0.942070i
\(503\) −19.7450 −0.880385 −0.440192 0.897904i \(-0.645090\pi\)
−0.440192 + 0.897904i \(0.645090\pi\)
\(504\) 0 0
\(505\) −0.260498 −0.0115920
\(506\) −14.5463 43.3871i −0.646661 1.92879i
\(507\) 0 0
\(508\) −6.62341 8.76751i −0.293866 0.388995i
\(509\) 24.6928i 1.09449i 0.836972 + 0.547245i \(0.184324\pi\)
−0.836972 + 0.547245i \(0.815676\pi\)
\(510\) 0 0
\(511\) −12.8689 + 8.02639i −0.569288 + 0.355066i
\(512\) 5.16261 22.0306i 0.228157 0.973624i
\(513\) 0 0
\(514\) 9.97158 3.34314i 0.439828 0.147460i
\(515\) 1.76484i 0.0777682i
\(516\) 0 0
\(517\) 35.9830i 1.58253i
\(518\) 7.26953 8.81441i 0.319405 0.387283i
\(519\) 0 0
\(520\) 5.84746 + 4.00327i 0.256428 + 0.175555i
\(521\) 13.0343i 0.571042i −0.958372 0.285521i \(-0.907833\pi\)
0.958372 0.285521i \(-0.0921666\pi\)
\(522\) 0 0
\(523\) −21.5279 −0.941348 −0.470674 0.882307i \(-0.655989\pi\)
−0.470674 + 0.882307i \(0.655989\pi\)
\(524\) 15.8619 11.9829i 0.692932 0.523475i
\(525\) 0 0
\(526\) −11.3883 + 3.81812i −0.496553 + 0.166478i
\(527\) 6.81297i 0.296778i
\(528\) 0 0
\(529\) −42.7156 −1.85720
\(530\) −3.84184 + 1.28804i −0.166879 + 0.0559490i
\(531\) 0 0
\(532\) 38.4871 + 14.7576i 1.66863 + 0.639822i
\(533\) −23.3681 −1.01219
\(534\) 0 0
\(535\) 6.10229 0.263825
\(536\) −12.4479 + 18.1823i −0.537668 + 0.785357i
\(537\) 0 0
\(538\) 7.97158 2.67261i 0.343679 0.115224i
\(539\) −25.0925 12.2907i −1.08081 0.529397i
\(540\) 0 0
\(541\) −17.3274 −0.744965 −0.372482 0.928039i \(-0.621493\pi\)
−0.372482 + 0.928039i \(0.621493\pi\)
\(542\) 5.03595 + 15.0207i 0.216312 + 0.645195i
\(543\) 0 0
\(544\) 0.284138 + 6.08608i 0.0121823 + 0.260939i
\(545\) 14.9561i 0.640647i
\(546\) 0 0
\(547\) 5.19581i 0.222157i 0.993812 + 0.111079i \(0.0354305\pi\)
−0.993812 + 0.111079i \(0.964569\pi\)
\(548\) 26.2264 19.8127i 1.12034 0.846357i
\(549\) 0 0
\(550\) 5.35213 1.79439i 0.228216 0.0765132i
\(551\) 46.7216 1.99041
\(552\) 0 0
\(553\) −6.32615 + 3.94563i −0.269015 + 0.167785i
\(554\) 0.976211 + 2.91174i 0.0414752 + 0.123708i
\(555\) 0 0
\(556\) 28.4159 21.4668i 1.20510 0.910395i
\(557\) −10.4597 −0.443190 −0.221595 0.975139i \(-0.571126\pi\)
−0.221595 + 0.975139i \(0.571126\pi\)
\(558\) 0 0
\(559\) 20.3694 0.861536
\(560\) 2.93310 + 10.1684i 0.123946 + 0.429695i
\(561\) 0 0
\(562\) −0.774071 2.30882i −0.0326522 0.0973917i
\(563\) 1.94438 0.0819459 0.0409730 0.999160i \(-0.486954\pi\)
0.0409730 + 0.999160i \(0.486954\pi\)
\(564\) 0 0
\(565\) 11.8448i 0.498315i
\(566\) −2.92777 8.73264i −0.123063 0.367060i
\(567\) 0 0
\(568\) −9.34700 + 13.6529i −0.392191 + 0.572863i
\(569\) 5.72219 0.239887 0.119943 0.992781i \(-0.461729\pi\)
0.119943 + 0.992781i \(0.461729\pi\)
\(570\) 0 0
\(571\) 42.2732i 1.76908i −0.466466 0.884539i \(-0.654473\pi\)
0.466466 0.884539i \(-0.345527\pi\)
\(572\) −15.9593 + 12.0565i −0.667293 + 0.504106i
\(573\) 0 0
\(574\) −26.9228 22.2041i −1.12374 0.926783i
\(575\) 8.10651i 0.338065i
\(576\) 0 0
\(577\) 0.216956i 0.00903200i −0.999990 0.00451600i \(-0.998563\pi\)
0.999990 0.00451600i \(-0.00143749\pi\)
\(578\) 7.12080 + 21.2392i 0.296186 + 0.883434i
\(579\) 0 0
\(580\) 7.23074 + 9.57144i 0.300240 + 0.397432i
\(581\) 17.5162 + 28.0843i 0.726696 + 1.16513i
\(582\) 0 0
\(583\) 11.4366i 0.473658i
\(584\) −9.15950 + 13.3790i −0.379023 + 0.553627i
\(585\) 0 0
\(586\) 12.3410 4.13754i 0.509803 0.170920i
\(587\) −6.61005 −0.272826 −0.136413 0.990652i \(-0.543557\pi\)
−0.136413 + 0.990652i \(0.543557\pi\)
\(588\) 0 0
\(589\) 49.2747 2.03033
\(590\) 12.9832 4.35285i 0.534511 0.179204i
\(591\) 0 0
\(592\) 3.33834 11.7492i 0.137205 0.482889i
\(593\) 19.2223i 0.789365i 0.918818 + 0.394682i \(0.129145\pi\)
−0.918818 + 0.394682i \(0.870855\pi\)
\(594\) 0 0
\(595\) −1.50803 2.41787i −0.0618232 0.0991230i
\(596\) −31.4177 + 23.7345i −1.28692 + 0.972203i
\(597\) 0 0
\(598\) 9.13056 + 27.2337i 0.373376 + 1.11367i
\(599\) 29.5976i 1.20933i 0.796481 + 0.604663i \(0.206692\pi\)
−0.796481 + 0.604663i \(0.793308\pi\)
\(600\) 0 0
\(601\) 42.7644i 1.74440i 0.489154 + 0.872198i \(0.337306\pi\)
−0.489154 + 0.872198i \(0.662694\pi\)
\(602\) 23.4680 + 19.3548i 0.956484 + 0.788844i
\(603\) 0 0
\(604\) −15.9992 21.1784i −0.650999 0.861738i
\(605\) 4.93258i 0.200538i
\(606\) 0 0
\(607\) 43.6339 1.77104 0.885522 0.464598i \(-0.153801\pi\)
0.885522 + 0.464598i \(0.153801\pi\)
\(608\) 44.0175 2.05503i 1.78515 0.0833424i
\(609\) 0 0
\(610\) 1.44410 + 4.30731i 0.0584699 + 0.174398i
\(611\) 22.5862i 0.913740i
\(612\) 0 0
\(613\) −41.2984 −1.66803 −0.834013 0.551744i \(-0.813963\pi\)
−0.834013 + 0.551744i \(0.813963\pi\)
\(614\) −14.6440 43.6786i −0.590983 1.76272i
\(615\) 0 0
\(616\) −29.8429 1.27392i −1.20241 0.0513276i
\(617\) 2.12487 0.0855439 0.0427719 0.999085i \(-0.486381\pi\)
0.0427719 + 0.999085i \(0.486381\pi\)
\(618\) 0 0
\(619\) −21.1221 −0.848970 −0.424485 0.905435i \(-0.639545\pi\)
−0.424485 + 0.905435i \(0.639545\pi\)
\(620\) 7.62587 + 10.0945i 0.306262 + 0.405404i
\(621\) 0 0
\(622\) −12.3005 36.6888i −0.493206 1.47109i
\(623\) −7.88825 + 4.91992i −0.316036 + 0.197112i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −26.4268 + 8.86002i −1.05623 + 0.354118i
\(627\) 0 0
\(628\) 23.3149 + 30.8623i 0.930365 + 1.23154i
\(629\) 3.28884i 0.131135i
\(630\) 0 0
\(631\) 3.20820i 0.127716i 0.997959 + 0.0638582i \(0.0203406\pi\)
−0.997959 + 0.0638582i \(0.979659\pi\)
\(632\) −4.50265 + 6.57689i −0.179106 + 0.261615i
\(633\) 0 0
\(634\) 0.384350 + 1.14640i 0.0152645 + 0.0455294i
\(635\) 5.49406 0.218025
\(636\) 0 0
\(637\) 15.7504 + 7.71474i 0.624052 + 0.305669i
\(638\) −32.1012 + 10.7625i −1.27090 + 0.426090i
\(639\) 0 0
\(640\) 7.23324 + 8.69944i 0.285919 + 0.343875i
\(641\) 14.2121 0.561345 0.280673 0.959804i \(-0.409442\pi\)
0.280673 + 0.959804i \(0.409442\pi\)
\(642\) 0 0
\(643\) 7.89830 0.311479 0.155739 0.987798i \(-0.450224\pi\)
0.155739 + 0.987798i \(0.450224\pi\)
\(644\) −15.3577 + 40.0522i −0.605178 + 1.57828i
\(645\) 0 0
\(646\) −11.2497 + 3.77167i −0.442615 + 0.148394i
\(647\) 0.910960 0.0358135 0.0179068 0.999840i \(-0.494300\pi\)
0.0179068 + 0.999840i \(0.494300\pi\)
\(648\) 0 0
\(649\) 38.6494i 1.51712i
\(650\) −3.35948 + 1.12632i −0.131770 + 0.0441781i
\(651\) 0 0
\(652\) 3.31138 + 4.38333i 0.129684 + 0.171664i
\(653\) −1.82376 −0.0713691 −0.0356846 0.999363i \(-0.511361\pi\)
−0.0356846 + 0.999363i \(0.511361\pi\)
\(654\) 0 0
\(655\) 9.93971i 0.388377i
\(656\) −35.8869 10.1967i −1.40115 0.398113i
\(657\) 0 0
\(658\) 21.4612 26.0219i 0.836643 1.01444i
\(659\) 6.38815i 0.248847i −0.992229 0.124423i \(-0.960292\pi\)
0.992229 0.124423i \(-0.0397081\pi\)
\(660\) 0 0
\(661\) 16.7429i 0.651222i −0.945504 0.325611i \(-0.894430\pi\)
0.945504 0.325611i \(-0.105570\pi\)
\(662\) 5.68177 1.90491i 0.220828 0.0740364i
\(663\) 0 0
\(664\) 29.1974 + 19.9891i 1.13308 + 0.775726i
\(665\) −17.4872 + 10.9068i −0.678125 + 0.422948i
\(666\) 0 0
\(667\) 48.6215i 1.88263i
\(668\) −9.29038 + 7.01841i −0.359456 + 0.271551i
\(669\) 0 0
\(670\) −3.50224 10.4461i −0.135303 0.403569i
\(671\) −12.8223 −0.494999
\(672\) 0 0
\(673\) −35.5295 −1.36956 −0.684782 0.728748i \(-0.740102\pi\)
−0.684782 + 0.728748i \(0.740102\pi\)
\(674\) 9.25866 + 27.6158i 0.356630 + 1.06372i
\(675\) 0 0
\(676\) −10.7281 + 8.10452i −0.412619 + 0.311712i
\(677\) 12.3173i 0.473391i 0.971584 + 0.236696i \(0.0760644\pi\)
−0.971584 + 0.236696i \(0.923936\pi\)
\(678\) 0 0
\(679\) 26.9694 16.8209i 1.03499 0.645525i
\(680\) −2.51370 1.72092i −0.0963961 0.0659944i
\(681\) 0 0
\(682\) −33.8554 + 11.3506i −1.29639 + 0.434637i
\(683\) 5.01785i 0.192003i 0.995381 + 0.0960014i \(0.0306053\pi\)
−0.995381 + 0.0960014i \(0.969395\pi\)
\(684\) 0 0
\(685\) 16.4345i 0.627929i
\(686\) 10.8158 + 23.8541i 0.412949 + 0.910754i
\(687\) 0 0
\(688\) 31.2818 + 8.88819i 1.19261 + 0.338859i
\(689\) 7.17868i 0.273486i
\(690\) 0 0
\(691\) −31.8714 −1.21245 −0.606224 0.795294i \(-0.707316\pi\)
−0.606224 + 0.795294i \(0.707316\pi\)
\(692\) 12.7369 + 16.8600i 0.484184 + 0.640922i
\(693\) 0 0
\(694\) 18.5383 6.21527i 0.703703 0.235928i
\(695\) 17.8065i 0.675440i
\(696\) 0 0
\(697\) 10.0455 0.380500
\(698\) −10.8163 + 3.62634i −0.409402 + 0.137259i
\(699\) 0 0
\(700\) −4.94074 1.89449i −0.186742 0.0716049i
\(701\) −20.4325 −0.771725 −0.385862 0.922556i \(-0.626096\pi\)
−0.385862 + 0.922556i \(0.626096\pi\)
\(702\) 0 0
\(703\) 23.7865 0.897126
\(704\) −29.7699 + 11.5515i −1.12200 + 0.435365i
\(705\) 0 0
\(706\) 10.2937 3.45114i 0.387409 0.129885i
\(707\) −0.584791 + 0.364735i −0.0219933 + 0.0137173i
\(708\) 0 0
\(709\) −42.4953 −1.59594 −0.797972 0.602695i \(-0.794094\pi\)
−0.797972 + 0.602695i \(0.794094\pi\)
\(710\) −2.62979 7.84386i −0.0986942 0.294375i
\(711\) 0 0
\(712\) −5.61448 + 8.20090i −0.210411 + 0.307342i
\(713\) 51.2785i 1.92039i
\(714\) 0 0
\(715\) 10.0007i 0.374006i
\(716\) 5.54421 + 7.33895i 0.207197 + 0.274270i
\(717\) 0 0
\(718\) 28.9984 9.72219i 1.08221 0.362829i
\(719\) −3.58392 −0.133658 −0.0668289 0.997764i \(-0.521288\pi\)
−0.0668289 + 0.997764i \(0.521288\pi\)
\(720\) 0 0
\(721\) 2.47104 + 3.96190i 0.0920264 + 0.147549i
\(722\) 18.7372 + 55.8873i 0.697326 + 2.07991i
\(723\) 0 0
\(724\) −11.3650 15.0441i −0.422378 0.559108i
\(725\) −5.99783 −0.222754
\(726\) 0 0
\(727\) −21.1835 −0.785652 −0.392826 0.919613i \(-0.628503\pi\)
−0.392826 + 0.919613i \(0.628503\pi\)
\(728\) 18.7321 + 0.799627i 0.694260 + 0.0296361i
\(729\) 0 0
\(730\) −2.57703 7.68651i −0.0953803 0.284491i
\(731\) −8.75641 −0.323867
\(732\) 0 0
\(733\) 27.6118i 1.01986i −0.860215 0.509932i \(-0.829670\pi\)
0.860215 0.509932i \(-0.170330\pi\)
\(734\) 2.97702 + 8.87956i 0.109884 + 0.327751i
\(735\) 0 0
\(736\) 2.13859 + 45.8075i 0.0788296 + 1.68849i
\(737\) 31.0967 1.14546
\(738\) 0 0
\(739\) 18.3419i 0.674716i 0.941376 + 0.337358i \(0.109533\pi\)
−0.941376 + 0.337358i \(0.890467\pi\)
\(740\) 3.68125 + 4.87293i 0.135326 + 0.179133i
\(741\) 0 0
\(742\) −6.82110 + 8.27068i −0.250411 + 0.303626i
\(743\) 47.9531i 1.75923i −0.475688 0.879614i \(-0.657801\pi\)
0.475688 0.879614i \(-0.342199\pi\)
\(744\) 0 0
\(745\) 19.6876i 0.721296i
\(746\) −14.0072 41.7792i −0.512839 1.52964i
\(747\) 0 0
\(748\) 6.86059 5.18283i 0.250848 0.189503i
\(749\) 13.6990 8.54411i 0.500552 0.312195i
\(750\) 0 0
\(751\) 51.3906i 1.87527i 0.347624 + 0.937634i \(0.386989\pi\)
−0.347624 + 0.937634i \(0.613011\pi\)
\(752\) 9.85546 34.6861i 0.359392 1.26487i
\(753\) 0 0
\(754\) 20.1496 6.75550i 0.733806 0.246021i
\(755\) 13.2712 0.482989
\(756\) 0 0
\(757\) −7.69109 −0.279537 −0.139769 0.990184i \(-0.544636\pi\)
−0.139769 + 0.990184i \(0.544636\pi\)
\(758\) 41.8194 14.0207i 1.51895 0.509253i
\(759\) 0 0
\(760\) −12.4466 + 18.1803i −0.451484 + 0.659470i
\(761\) 48.0926i 1.74336i 0.490080 + 0.871678i \(0.336968\pi\)
−0.490080 + 0.871678i \(0.663032\pi\)
\(762\) 0 0
\(763\) −20.9407 33.5749i −0.758105 1.21549i
\(764\) −6.06021 8.02199i −0.219251 0.290225i
\(765\) 0 0
\(766\) 12.5831 + 37.5316i 0.454646 + 1.35607i
\(767\) 24.2599i 0.875973i
\(768\) 0 0
\(769\) 46.2666i 1.66842i −0.551449 0.834209i \(-0.685925\pi\)
0.551449 0.834209i \(-0.314075\pi\)
\(770\) 9.50259 11.5220i 0.342450 0.415225i
\(771\) 0 0
\(772\) −25.3375 + 19.1412i −0.911917 + 0.688907i
\(773\) 37.7785i 1.35880i −0.733768 0.679400i \(-0.762240\pi\)
0.733768 0.679400i \(-0.237760\pi\)
\(774\) 0 0
\(775\) −6.32559 −0.227222
\(776\) 19.1955 28.0383i 0.689079 1.00652i
\(777\) 0 0
\(778\) −7.08046 21.1189i −0.253847 0.757148i
\(779\) 72.6538i 2.60309i
\(780\) 0 0
\(781\) 23.3501 0.835533
\(782\) −3.92504 11.7072i −0.140359 0.418649i
\(783\) 0 0
\(784\) 20.8218 + 18.7203i 0.743637 + 0.668584i
\(785\) −19.3395 −0.690256
\(786\) 0 0
\(787\) −11.0579 −0.394172 −0.197086 0.980386i \(-0.563148\pi\)
−0.197086 + 0.980386i \(0.563148\pi\)
\(788\) −16.1638 + 12.2109i −0.575811 + 0.434996i
\(789\) 0 0
\(790\) −1.26682 3.77855i −0.0450716 0.134435i
\(791\) 16.5845 + 26.5904i 0.589677 + 0.945447i
\(792\) 0 0