Properties

Label 1260.2.c.d.811.14
Level $1260$
Weight $2$
Character 1260.811
Analytic conductor $10.061$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 811.14
Root \(-0.947441 + 1.04993i\) of defining polynomial
Character \(\chi\) \(=\) 1260.811
Dual form 1260.2.c.d.811.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.947441 + 1.04993i) q^{2} +(-0.204711 + 1.98950i) q^{4} -1.00000i q^{5} +(-2.29670 + 1.31346i) q^{7} +(-2.28279 + 1.67000i) q^{8} +O(q^{10})\) \(q+(0.947441 + 1.04993i) q^{2} +(-0.204711 + 1.98950i) q^{4} -1.00000i q^{5} +(-2.29670 + 1.31346i) q^{7} +(-2.28279 + 1.67000i) q^{8} +(1.04993 - 0.947441i) q^{10} +0.477147i q^{11} -2.96271i q^{13} +(-3.55503 - 1.16694i) q^{14} +(-3.91619 - 0.814543i) q^{16} +3.83353i q^{17} -5.31262 q^{19} +(1.98950 + 0.204711i) q^{20} +(-0.500972 + 0.452069i) q^{22} +7.60808i q^{23} -1.00000 q^{25} +(3.11064 - 2.80699i) q^{26} +(-2.14297 - 4.83815i) q^{28} -6.17752 q^{29} -3.38789 q^{31} +(-2.85514 - 4.88346i) q^{32} +(-4.02494 + 3.63204i) q^{34} +(1.31346 + 2.29670i) q^{35} -8.62867 q^{37} +(-5.03339 - 5.57788i) q^{38} +(1.67000 + 2.28279i) q^{40} -1.01125i q^{41} -6.85412i q^{43} +(-0.949282 - 0.0976772i) q^{44} +(-7.98796 + 7.20820i) q^{46} +6.21838 q^{47} +(3.54963 - 6.03325i) q^{49} +(-0.947441 - 1.04993i) q^{50} +(5.89430 + 0.606499i) q^{52} +9.30380 q^{53} +0.477147 q^{55} +(3.04938 - 6.83383i) q^{56} +(-5.85284 - 6.48597i) q^{58} -4.88854 q^{59} +4.75818i q^{61} +(-3.20982 - 3.55705i) q^{62} +(2.42221 - 7.62449i) q^{64} -2.96271 q^{65} +1.30610i q^{67} +(-7.62679 - 0.784764i) q^{68} +(-1.16694 + 3.55503i) q^{70} +9.18700i q^{71} -4.49766i q^{73} +(-8.17516 - 9.05951i) q^{74} +(1.08755 - 10.5694i) q^{76} +(-0.626715 - 1.09586i) q^{77} +8.80833i q^{79} +(-0.814543 + 3.91619i) q^{80} +(1.06174 - 0.958097i) q^{82} -10.9520 q^{83} +3.83353 q^{85} +(7.19635 - 6.49388i) q^{86} +(-0.796835 - 1.08922i) q^{88} +13.1208i q^{89} +(3.89141 + 6.80445i) q^{91} +(-15.1362 - 1.55746i) q^{92} +(5.89154 + 6.52887i) q^{94} +5.31262i q^{95} -1.60612i q^{97} +(9.69756 - 1.98928i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8} + O(q^{10}) \) \( 16 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 2 q^{8} + 2 q^{14} + 6 q^{16} - 24 q^{19} - 12 q^{22} - 16 q^{25} + 12 q^{26} + 14 q^{28} - 16 q^{29} + 8 q^{31} + 18 q^{32} + 24 q^{34} + 24 q^{37} - 28 q^{38} + 12 q^{40} + 8 q^{44} - 20 q^{46} - 16 q^{47} - 16 q^{49} + 2 q^{50} - 20 q^{52} + 32 q^{53} - 2 q^{56} - 32 q^{58} - 8 q^{59} - 16 q^{62} - 2 q^{64} + 8 q^{65} - 4 q^{68} + 4 q^{74} + 16 q^{76} + 8 q^{77} + 16 q^{80} - 4 q^{82} - 8 q^{83} - 64 q^{86} - 52 q^{88} + 16 q^{91} - 64 q^{92} + 16 q^{94} + 86 q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.947441 + 1.04993i 0.669942 + 0.742413i
\(3\) 0 0
\(4\) −0.204711 + 1.98950i −0.102355 + 0.994748i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −2.29670 + 1.31346i −0.868070 + 0.496442i
\(8\) −2.28279 + 1.67000i −0.807086 + 0.590433i
\(9\) 0 0
\(10\) 1.04993 0.947441i 0.332017 0.299607i
\(11\) 0.477147i 0.143865i 0.997409 + 0.0719326i \(0.0229167\pi\)
−0.997409 + 0.0719326i \(0.977083\pi\)
\(12\) 0 0
\(13\) 2.96271i 0.821708i −0.911701 0.410854i \(-0.865231\pi\)
0.911701 0.410854i \(-0.134769\pi\)
\(14\) −3.55503 1.16694i −0.950122 0.311879i
\(15\) 0 0
\(16\) −3.91619 0.814543i −0.979047 0.203636i
\(17\) 3.83353i 0.929767i 0.885372 + 0.464883i \(0.153904\pi\)
−0.885372 + 0.464883i \(0.846096\pi\)
\(18\) 0 0
\(19\) −5.31262 −1.21880 −0.609399 0.792864i \(-0.708589\pi\)
−0.609399 + 0.792864i \(0.708589\pi\)
\(20\) 1.98950 + 0.204711i 0.444865 + 0.0457747i
\(21\) 0 0
\(22\) −0.500972 + 0.452069i −0.106808 + 0.0963814i
\(23\) 7.60808i 1.58639i 0.608965 + 0.793197i \(0.291585\pi\)
−0.608965 + 0.793197i \(0.708415\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 3.11064 2.80699i 0.610047 0.550497i
\(27\) 0 0
\(28\) −2.14297 4.83815i −0.404983 0.914324i
\(29\) −6.17752 −1.14714 −0.573569 0.819158i \(-0.694441\pi\)
−0.573569 + 0.819158i \(0.694441\pi\)
\(30\) 0 0
\(31\) −3.38789 −0.608482 −0.304241 0.952595i \(-0.598403\pi\)
−0.304241 + 0.952595i \(0.598403\pi\)
\(32\) −2.85514 4.88346i −0.504723 0.863282i
\(33\) 0 0
\(34\) −4.02494 + 3.63204i −0.690271 + 0.622890i
\(35\) 1.31346 + 2.29670i 0.222016 + 0.388213i
\(36\) 0 0
\(37\) −8.62867 −1.41854 −0.709272 0.704935i \(-0.750976\pi\)
−0.709272 + 0.704935i \(0.750976\pi\)
\(38\) −5.03339 5.57788i −0.816524 0.904852i
\(39\) 0 0
\(40\) 1.67000 + 2.28279i 0.264050 + 0.360940i
\(41\) 1.01125i 0.157930i −0.996877 0.0789651i \(-0.974838\pi\)
0.996877 0.0789651i \(-0.0251616\pi\)
\(42\) 0 0
\(43\) 6.85412i 1.04524i −0.852565 0.522622i \(-0.824954\pi\)
0.852565 0.522622i \(-0.175046\pi\)
\(44\) −0.949282 0.0976772i −0.143110 0.0147254i
\(45\) 0 0
\(46\) −7.98796 + 7.20820i −1.17776 + 1.06279i
\(47\) 6.21838 0.907043 0.453522 0.891245i \(-0.350167\pi\)
0.453522 + 0.891245i \(0.350167\pi\)
\(48\) 0 0
\(49\) 3.54963 6.03325i 0.507090 0.861893i
\(50\) −0.947441 1.04993i −0.133988 0.148483i
\(51\) 0 0
\(52\) 5.89430 + 0.606499i 0.817392 + 0.0841063i
\(53\) 9.30380 1.27797 0.638987 0.769217i \(-0.279354\pi\)
0.638987 + 0.769217i \(0.279354\pi\)
\(54\) 0 0
\(55\) 0.477147 0.0643385
\(56\) 3.04938 6.83383i 0.407491 0.913209i
\(57\) 0 0
\(58\) −5.85284 6.48597i −0.768515 0.851650i
\(59\) −4.88854 −0.636433 −0.318217 0.948018i \(-0.603084\pi\)
−0.318217 + 0.948018i \(0.603084\pi\)
\(60\) 0 0
\(61\) 4.75818i 0.609222i 0.952477 + 0.304611i \(0.0985264\pi\)
−0.952477 + 0.304611i \(0.901474\pi\)
\(62\) −3.20982 3.55705i −0.407648 0.451745i
\(63\) 0 0
\(64\) 2.42221 7.62449i 0.302777 0.953061i
\(65\) −2.96271 −0.367479
\(66\) 0 0
\(67\) 1.30610i 0.159565i 0.996812 + 0.0797826i \(0.0254226\pi\)
−0.996812 + 0.0797826i \(0.974577\pi\)
\(68\) −7.62679 0.784764i −0.924884 0.0951667i
\(69\) 0 0
\(70\) −1.16694 + 3.55503i −0.139477 + 0.424907i
\(71\) 9.18700i 1.09030i 0.838340 + 0.545148i \(0.183527\pi\)
−0.838340 + 0.545148i \(0.816473\pi\)
\(72\) 0 0
\(73\) 4.49766i 0.526411i −0.964740 0.263206i \(-0.915220\pi\)
0.964740 0.263206i \(-0.0847797\pi\)
\(74\) −8.17516 9.05951i −0.950343 1.05315i
\(75\) 0 0
\(76\) 1.08755 10.5694i 0.124751 1.21240i
\(77\) −0.626715 1.09586i −0.0714208 0.124885i
\(78\) 0 0
\(79\) 8.80833i 0.991015i 0.868604 + 0.495507i \(0.165018\pi\)
−0.868604 + 0.495507i \(0.834982\pi\)
\(80\) −0.814543 + 3.91619i −0.0910686 + 0.437843i
\(81\) 0 0
\(82\) 1.06174 0.958097i 0.117249 0.105804i
\(83\) −10.9520 −1.20214 −0.601068 0.799198i \(-0.705258\pi\)
−0.601068 + 0.799198i \(0.705258\pi\)
\(84\) 0 0
\(85\) 3.83353 0.415804
\(86\) 7.19635 6.49388i 0.776003 0.700253i
\(87\) 0 0
\(88\) −0.796835 1.08922i −0.0849429 0.116112i
\(89\) 13.1208i 1.39080i 0.718621 + 0.695402i \(0.244774\pi\)
−0.718621 + 0.695402i \(0.755226\pi\)
\(90\) 0 0
\(91\) 3.89141 + 6.80445i 0.407931 + 0.713300i
\(92\) −15.1362 1.55746i −1.57806 0.162376i
\(93\) 0 0
\(94\) 5.89154 + 6.52887i 0.607666 + 0.673401i
\(95\) 5.31262i 0.545063i
\(96\) 0 0
\(97\) 1.60612i 0.163077i −0.996670 0.0815384i \(-0.974017\pi\)
0.996670 0.0815384i \(-0.0259833\pi\)
\(98\) 9.69756 1.98928i 0.979602 0.200948i
\(99\) 0 0
\(100\) 0.204711 1.98950i 0.0204711 0.198950i
\(101\) 6.17664i 0.614599i 0.951613 + 0.307299i \(0.0994253\pi\)
−0.951613 + 0.307299i \(0.900575\pi\)
\(102\) 0 0
\(103\) 16.8145 1.65678 0.828390 0.560151i \(-0.189257\pi\)
0.828390 + 0.560151i \(0.189257\pi\)
\(104\) 4.94772 + 6.76323i 0.485164 + 0.663189i
\(105\) 0 0
\(106\) 8.81480 + 9.76835i 0.856169 + 0.948786i
\(107\) 9.15824i 0.885360i −0.896680 0.442680i \(-0.854028\pi\)
0.896680 0.442680i \(-0.145972\pi\)
\(108\) 0 0
\(109\) −15.2477 −1.46046 −0.730230 0.683201i \(-0.760587\pi\)
−0.730230 + 0.683201i \(0.760587\pi\)
\(110\) 0.452069 + 0.500972i 0.0431031 + 0.0477658i
\(111\) 0 0
\(112\) 10.0642 3.27301i 0.950974 0.309270i
\(113\) 4.04995 0.380987 0.190493 0.981688i \(-0.438991\pi\)
0.190493 + 0.981688i \(0.438991\pi\)
\(114\) 0 0
\(115\) 7.60808 0.709457
\(116\) 1.26461 12.2902i 0.117416 1.14111i
\(117\) 0 0
\(118\) −4.63160 5.13263i −0.426373 0.472496i
\(119\) −5.03519 8.80445i −0.461576 0.807102i
\(120\) 0 0
\(121\) 10.7723 0.979303
\(122\) −4.99576 + 4.50809i −0.452295 + 0.408143i
\(123\) 0 0
\(124\) 0.693537 6.74018i 0.0622814 0.605286i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 12.9949i 1.15311i 0.817059 + 0.576554i \(0.195603\pi\)
−0.817059 + 0.576554i \(0.804397\pi\)
\(128\) 10.3001 4.68060i 0.910409 0.413710i
\(129\) 0 0
\(130\) −2.80699 3.11064i −0.246190 0.272821i
\(131\) 1.77552 0.155128 0.0775640 0.996987i \(-0.475286\pi\)
0.0775640 + 0.996987i \(0.475286\pi\)
\(132\) 0 0
\(133\) 12.2015 6.97792i 1.05800 0.605063i
\(134\) −1.37131 + 1.23745i −0.118463 + 0.106899i
\(135\) 0 0
\(136\) −6.40198 8.75112i −0.548965 0.750402i
\(137\) 15.1622 1.29539 0.647695 0.761900i \(-0.275733\pi\)
0.647695 + 0.761900i \(0.275733\pi\)
\(138\) 0 0
\(139\) −18.8544 −1.59921 −0.799607 0.600524i \(-0.794959\pi\)
−0.799607 + 0.600524i \(0.794959\pi\)
\(140\) −4.83815 + 2.14297i −0.408898 + 0.181114i
\(141\) 0 0
\(142\) −9.64571 + 8.70414i −0.809450 + 0.730435i
\(143\) 1.41365 0.118215
\(144\) 0 0
\(145\) 6.17752i 0.513015i
\(146\) 4.72223 4.26127i 0.390815 0.352665i
\(147\) 0 0
\(148\) 1.76638 17.1667i 0.145196 1.41109i
\(149\) 18.8439 1.54376 0.771878 0.635771i \(-0.219318\pi\)
0.771878 + 0.635771i \(0.219318\pi\)
\(150\) 0 0
\(151\) 18.6462i 1.51741i −0.651435 0.758704i \(-0.725833\pi\)
0.651435 0.758704i \(-0.274167\pi\)
\(152\) 12.1276 8.87206i 0.983675 0.719619i
\(153\) 0 0
\(154\) 0.556804 1.69627i 0.0448686 0.136690i
\(155\) 3.38789i 0.272121i
\(156\) 0 0
\(157\) 22.6941i 1.81118i 0.424149 + 0.905592i \(0.360573\pi\)
−0.424149 + 0.905592i \(0.639427\pi\)
\(158\) −9.24814 + 8.34538i −0.735743 + 0.663922i
\(159\) 0 0
\(160\) −4.88346 + 2.85514i −0.386071 + 0.225719i
\(161\) −9.99293 17.4734i −0.787553 1.37710i
\(162\) 0 0
\(163\) 9.17980i 0.719017i 0.933142 + 0.359509i \(0.117056\pi\)
−0.933142 + 0.359509i \(0.882944\pi\)
\(164\) 2.01187 + 0.207013i 0.157101 + 0.0161650i
\(165\) 0 0
\(166\) −10.3764 11.4988i −0.805362 0.892483i
\(167\) −14.8751 −1.15107 −0.575535 0.817777i \(-0.695206\pi\)
−0.575535 + 0.817777i \(0.695206\pi\)
\(168\) 0 0
\(169\) 4.22235 0.324796
\(170\) 3.63204 + 4.02494i 0.278565 + 0.308699i
\(171\) 0 0
\(172\) 13.6362 + 1.40311i 1.03975 + 0.106986i
\(173\) 18.2211i 1.38532i −0.721262 0.692662i \(-0.756438\pi\)
0.721262 0.692662i \(-0.243562\pi\)
\(174\) 0 0
\(175\) 2.29670 1.31346i 0.173614 0.0992885i
\(176\) 0.388657 1.86860i 0.0292961 0.140851i
\(177\) 0 0
\(178\) −13.7760 + 12.4312i −1.03255 + 0.931758i
\(179\) 5.02780i 0.375796i 0.982189 + 0.187898i \(0.0601674\pi\)
−0.982189 + 0.187898i \(0.939833\pi\)
\(180\) 0 0
\(181\) 14.6503i 1.08895i 0.838777 + 0.544476i \(0.183271\pi\)
−0.838777 + 0.544476i \(0.816729\pi\)
\(182\) −3.45732 + 10.5325i −0.256274 + 0.780723i
\(183\) 0 0
\(184\) −12.7055 17.3676i −0.936660 1.28036i
\(185\) 8.62867i 0.634393i
\(186\) 0 0
\(187\) −1.82916 −0.133761
\(188\) −1.27297 + 12.3714i −0.0928408 + 0.902279i
\(189\) 0 0
\(190\) −5.57788 + 5.03339i −0.404662 + 0.365161i
\(191\) 6.84692i 0.495426i −0.968833 0.247713i \(-0.920321\pi\)
0.968833 0.247713i \(-0.0796790\pi\)
\(192\) 0 0
\(193\) 7.47575 0.538116 0.269058 0.963124i \(-0.413288\pi\)
0.269058 + 0.963124i \(0.413288\pi\)
\(194\) 1.68632 1.52170i 0.121070 0.109252i
\(195\) 0 0
\(196\) 11.2765 + 8.29705i 0.805463 + 0.592646i
\(197\) 14.2749 1.01705 0.508523 0.861048i \(-0.330192\pi\)
0.508523 + 0.861048i \(0.330192\pi\)
\(198\) 0 0
\(199\) 1.60743 0.113948 0.0569739 0.998376i \(-0.481855\pi\)
0.0569739 + 0.998376i \(0.481855\pi\)
\(200\) 2.28279 1.67000i 0.161417 0.118087i
\(201\) 0 0
\(202\) −6.48505 + 5.85200i −0.456286 + 0.411745i
\(203\) 14.1879 8.11395i 0.995795 0.569487i
\(204\) 0 0
\(205\) −1.01125 −0.0706285
\(206\) 15.9307 + 17.6541i 1.10995 + 1.23002i
\(207\) 0 0
\(208\) −2.41325 + 11.6025i −0.167329 + 0.804491i
\(209\) 2.53490i 0.175343i
\(210\) 0 0
\(211\) 1.32588i 0.0912770i −0.998958 0.0456385i \(-0.985468\pi\)
0.998958 0.0456385i \(-0.0145322\pi\)
\(212\) −1.90459 + 18.5099i −0.130808 + 1.27126i
\(213\) 0 0
\(214\) 9.61552 8.67689i 0.657303 0.593140i
\(215\) −6.85412 −0.467447
\(216\) 0 0
\(217\) 7.78094 4.44986i 0.528205 0.302076i
\(218\) −14.4463 16.0090i −0.978424 1.08427i
\(219\) 0 0
\(220\) −0.0976772 + 0.949282i −0.00658539 + 0.0640006i
\(221\) 11.3576 0.763997
\(222\) 0 0
\(223\) −21.5307 −1.44180 −0.720902 0.693037i \(-0.756272\pi\)
−0.720902 + 0.693037i \(0.756272\pi\)
\(224\) 12.9716 + 7.46570i 0.866704 + 0.498823i
\(225\) 0 0
\(226\) 3.83709 + 4.25216i 0.255239 + 0.282850i
\(227\) 14.0514 0.932625 0.466313 0.884620i \(-0.345582\pi\)
0.466313 + 0.884620i \(0.345582\pi\)
\(228\) 0 0
\(229\) 17.1949i 1.13627i 0.822934 + 0.568136i \(0.192335\pi\)
−0.822934 + 0.568136i \(0.807665\pi\)
\(230\) 7.20820 + 7.98796i 0.475295 + 0.526710i
\(231\) 0 0
\(232\) 14.1020 10.3164i 0.925839 0.677308i
\(233\) 11.5500 0.756668 0.378334 0.925669i \(-0.376497\pi\)
0.378334 + 0.925669i \(0.376497\pi\)
\(234\) 0 0
\(235\) 6.21838i 0.405642i
\(236\) 1.00074 9.72572i 0.0651424 0.633091i
\(237\) 0 0
\(238\) 4.47351 13.6283i 0.289975 0.883392i
\(239\) 13.5047i 0.873549i 0.899571 + 0.436774i \(0.143879\pi\)
−0.899571 + 0.436774i \(0.856121\pi\)
\(240\) 0 0
\(241\) 6.07807i 0.391523i −0.980652 0.195761i \(-0.937282\pi\)
0.980652 0.195761i \(-0.0627178\pi\)
\(242\) 10.2061 + 11.3102i 0.656076 + 0.727048i
\(243\) 0 0
\(244\) −9.46637 0.974050i −0.606022 0.0623572i
\(245\) −6.03325 3.54963i −0.385450 0.226778i
\(246\) 0 0
\(247\) 15.7397i 1.00150i
\(248\) 7.73381 5.65776i 0.491098 0.359268i
\(249\) 0 0
\(250\) −1.04993 + 0.947441i −0.0664035 + 0.0599214i
\(251\) −25.9947 −1.64077 −0.820385 0.571812i \(-0.806241\pi\)
−0.820385 + 0.571812i \(0.806241\pi\)
\(252\) 0 0
\(253\) −3.63017 −0.228227
\(254\) −13.6437 + 12.3119i −0.856083 + 0.772516i
\(255\) 0 0
\(256\) 14.6730 + 6.37980i 0.917065 + 0.398738i
\(257\) 26.1382i 1.63045i 0.579141 + 0.815227i \(0.303388\pi\)
−0.579141 + 0.815227i \(0.696612\pi\)
\(258\) 0 0
\(259\) 19.8174 11.3334i 1.23140 0.704226i
\(260\) 0.606499 5.89430i 0.0376135 0.365549i
\(261\) 0 0
\(262\) 1.68220 + 1.86417i 0.103927 + 0.115169i
\(263\) 20.1419i 1.24200i 0.783809 + 0.621001i \(0.213274\pi\)
−0.783809 + 0.621001i \(0.786726\pi\)
\(264\) 0 0
\(265\) 9.30380i 0.571528i
\(266\) 18.8865 + 6.19953i 1.15801 + 0.380118i
\(267\) 0 0
\(268\) −2.59848 0.267372i −0.158727 0.0163324i
\(269\) 25.1731i 1.53483i 0.641151 + 0.767415i \(0.278457\pi\)
−0.641151 + 0.767415i \(0.721543\pi\)
\(270\) 0 0
\(271\) −9.13276 −0.554776 −0.277388 0.960758i \(-0.589469\pi\)
−0.277388 + 0.960758i \(0.589469\pi\)
\(272\) 3.12257 15.0128i 0.189334 0.910285i
\(273\) 0 0
\(274\) 14.3652 + 15.9192i 0.867836 + 0.961715i
\(275\) 0.477147i 0.0287731i
\(276\) 0 0
\(277\) −17.2069 −1.03386 −0.516931 0.856027i \(-0.672926\pi\)
−0.516931 + 0.856027i \(0.672926\pi\)
\(278\) −17.8635 19.7959i −1.07138 1.18728i
\(279\) 0 0
\(280\) −6.83383 3.04938i −0.408400 0.182236i
\(281\) −10.6360 −0.634490 −0.317245 0.948344i \(-0.602758\pi\)
−0.317245 + 0.948344i \(0.602758\pi\)
\(282\) 0 0
\(283\) 19.3615 1.15092 0.575462 0.817828i \(-0.304822\pi\)
0.575462 + 0.817828i \(0.304822\pi\)
\(284\) −18.2775 1.88068i −1.08457 0.111598i
\(285\) 0 0
\(286\) 1.33935 + 1.48423i 0.0791974 + 0.0877646i
\(287\) 1.32823 + 2.32253i 0.0784032 + 0.137094i
\(288\) 0 0
\(289\) 2.30407 0.135534
\(290\) −6.48597 + 5.85284i −0.380869 + 0.343690i
\(291\) 0 0
\(292\) 8.94807 + 0.920719i 0.523646 + 0.0538810i
\(293\) 24.5856i 1.43631i −0.695885 0.718153i \(-0.744988\pi\)
0.695885 0.718153i \(-0.255012\pi\)
\(294\) 0 0
\(295\) 4.88854i 0.284622i
\(296\) 19.6974 14.4099i 1.14489 0.837556i
\(297\) 0 0
\(298\) 17.8535 + 19.7848i 1.03423 + 1.14611i
\(299\) 22.5405 1.30355
\(300\) 0 0
\(301\) 9.00263 + 15.7418i 0.518903 + 0.907344i
\(302\) 19.5773 17.6662i 1.12654 1.01658i
\(303\) 0 0
\(304\) 20.8052 + 4.32735i 1.19326 + 0.248191i
\(305\) 4.75818 0.272452
\(306\) 0 0
\(307\) −3.23094 −0.184399 −0.0921997 0.995741i \(-0.529390\pi\)
−0.0921997 + 0.995741i \(0.529390\pi\)
\(308\) 2.30851 1.02251i 0.131539 0.0582630i
\(309\) 0 0
\(310\) −3.55705 + 3.20982i −0.202027 + 0.182306i
\(311\) −9.34597 −0.529962 −0.264981 0.964254i \(-0.585366\pi\)
−0.264981 + 0.964254i \(0.585366\pi\)
\(312\) 0 0
\(313\) 16.6495i 0.941085i −0.882377 0.470543i \(-0.844058\pi\)
0.882377 0.470543i \(-0.155942\pi\)
\(314\) −23.8272 + 21.5013i −1.34465 + 1.21339i
\(315\) 0 0
\(316\) −17.5241 1.80316i −0.985810 0.101436i
\(317\) −25.7874 −1.44836 −0.724182 0.689609i \(-0.757782\pi\)
−0.724182 + 0.689609i \(0.757782\pi\)
\(318\) 0 0
\(319\) 2.94759i 0.165033i
\(320\) −7.62449 2.42221i −0.426222 0.135406i
\(321\) 0 0
\(322\) 8.87821 27.0469i 0.494763 1.50727i
\(323\) 20.3661i 1.13320i
\(324\) 0 0
\(325\) 2.96271i 0.164342i
\(326\) −9.63816 + 8.69732i −0.533808 + 0.481700i
\(327\) 0 0
\(328\) 1.68878 + 2.30846i 0.0932473 + 0.127463i
\(329\) −14.2817 + 8.16760i −0.787377 + 0.450295i
\(330\) 0 0
\(331\) 33.4834i 1.84041i −0.391432 0.920207i \(-0.628020\pi\)
0.391432 0.920207i \(-0.371980\pi\)
\(332\) 2.24199 21.7889i 0.123045 1.19582i
\(333\) 0 0
\(334\) −14.0933 15.6178i −0.771151 0.854571i
\(335\) 1.30610 0.0713598
\(336\) 0 0
\(337\) −4.98366 −0.271477 −0.135739 0.990745i \(-0.543341\pi\)
−0.135739 + 0.990745i \(0.543341\pi\)
\(338\) 4.00042 + 4.43317i 0.217594 + 0.241133i
\(339\) 0 0
\(340\) −0.784764 + 7.62679i −0.0425598 + 0.413620i
\(341\) 1.61652i 0.0875395i
\(342\) 0 0
\(343\) −0.227975 + 18.5189i −0.0123095 + 0.999924i
\(344\) 11.4464 + 15.6465i 0.617147 + 0.843602i
\(345\) 0 0
\(346\) 19.1309 17.2634i 1.02848 0.928087i
\(347\) 2.96693i 0.159273i 0.996824 + 0.0796367i \(0.0253760\pi\)
−0.996824 + 0.0796367i \(0.974624\pi\)
\(348\) 0 0
\(349\) 15.7698i 0.844139i 0.906563 + 0.422070i \(0.138696\pi\)
−0.906563 + 0.422070i \(0.861304\pi\)
\(350\) 3.55503 + 1.16694i 0.190024 + 0.0623758i
\(351\) 0 0
\(352\) 2.33013 1.36232i 0.124196 0.0726121i
\(353\) 9.20491i 0.489928i −0.969532 0.244964i \(-0.921224\pi\)
0.969532 0.244964i \(-0.0787761\pi\)
\(354\) 0 0
\(355\) 9.18700 0.487595
\(356\) −26.1038 2.68597i −1.38350 0.142356i
\(357\) 0 0
\(358\) −5.27885 + 4.76355i −0.278996 + 0.251761i
\(359\) 20.9031i 1.10322i −0.834102 0.551611i \(-0.814013\pi\)
0.834102 0.551611i \(-0.185987\pi\)
\(360\) 0 0
\(361\) 9.22390 0.485468
\(362\) −15.3819 + 13.8803i −0.808452 + 0.729534i
\(363\) 0 0
\(364\) −14.3340 + 6.34900i −0.751308 + 0.332778i
\(365\) −4.49766 −0.235418
\(366\) 0 0
\(367\) 4.79845 0.250477 0.125239 0.992127i \(-0.460030\pi\)
0.125239 + 0.992127i \(0.460030\pi\)
\(368\) 6.19710 29.7947i 0.323046 1.55315i
\(369\) 0 0
\(370\) −9.05951 + 8.17516i −0.470982 + 0.425006i
\(371\) −21.3680 + 12.2202i −1.10937 + 0.634441i
\(372\) 0 0
\(373\) 28.9408 1.49850 0.749250 0.662287i \(-0.230414\pi\)
0.749250 + 0.662287i \(0.230414\pi\)
\(374\) −1.73302 1.92049i −0.0896122 0.0993061i
\(375\) 0 0
\(376\) −14.1952 + 10.3847i −0.732062 + 0.535549i
\(377\) 18.3022i 0.942612i
\(378\) 0 0
\(379\) 4.73908i 0.243430i −0.992565 0.121715i \(-0.961161\pi\)
0.992565 0.121715i \(-0.0388394\pi\)
\(380\) −10.5694 1.08755i −0.542200 0.0557901i
\(381\) 0 0
\(382\) 7.18880 6.48706i 0.367811 0.331907i
\(383\) 11.9795 0.612125 0.306063 0.952011i \(-0.400988\pi\)
0.306063 + 0.952011i \(0.400988\pi\)
\(384\) 0 0
\(385\) −1.09586 + 0.626715i −0.0558503 + 0.0319404i
\(386\) 7.08283 + 7.84902i 0.360507 + 0.399505i
\(387\) 0 0
\(388\) 3.19537 + 0.328790i 0.162220 + 0.0166918i
\(389\) −24.1871 −1.22633 −0.613167 0.789953i \(-0.710105\pi\)
−0.613167 + 0.789953i \(0.710105\pi\)
\(390\) 0 0
\(391\) −29.1658 −1.47498
\(392\) 1.97247 + 19.7005i 0.0996249 + 0.995025i
\(393\) 0 0
\(394\) 13.5246 + 14.9877i 0.681362 + 0.755069i
\(395\) 8.80833 0.443195
\(396\) 0 0
\(397\) 37.1405i 1.86403i −0.362420 0.932015i \(-0.618049\pi\)
0.362420 0.932015i \(-0.381951\pi\)
\(398\) 1.52295 + 1.68769i 0.0763384 + 0.0845964i
\(399\) 0 0
\(400\) 3.91619 + 0.814543i 0.195809 + 0.0407271i
\(401\) −20.4040 −1.01893 −0.509464 0.860492i \(-0.670156\pi\)
−0.509464 + 0.860492i \(0.670156\pi\)
\(402\) 0 0
\(403\) 10.0373i 0.499995i
\(404\) −12.2884 1.26442i −0.611371 0.0629075i
\(405\) 0 0
\(406\) 21.9613 + 7.20883i 1.08992 + 0.357768i
\(407\) 4.11715i 0.204079i
\(408\) 0 0
\(409\) 4.69204i 0.232007i 0.993249 + 0.116003i \(0.0370083\pi\)
−0.993249 + 0.116003i \(0.962992\pi\)
\(410\) −0.958097 1.06174i −0.0473170 0.0524356i
\(411\) 0 0
\(412\) −3.44211 + 33.4523i −0.169580 + 1.64808i
\(413\) 11.2275 6.42091i 0.552468 0.315952i
\(414\) 0 0
\(415\) 10.9520i 0.537612i
\(416\) −14.4683 + 8.45896i −0.709365 + 0.414735i
\(417\) 0 0
\(418\) 2.66147 2.40167i 0.130177 0.117469i
\(419\) 10.4551 0.510766 0.255383 0.966840i \(-0.417798\pi\)
0.255383 + 0.966840i \(0.417798\pi\)
\(420\) 0 0
\(421\) −29.0598 −1.41629 −0.708144 0.706068i \(-0.750467\pi\)
−0.708144 + 0.706068i \(0.750467\pi\)
\(422\) 1.39208 1.25619i 0.0677653 0.0611503i
\(423\) 0 0
\(424\) −21.2386 + 15.5373i −1.03144 + 0.754559i
\(425\) 3.83353i 0.185953i
\(426\) 0 0
\(427\) −6.24969 10.9281i −0.302444 0.528847i
\(428\) 18.2203 + 1.87479i 0.880710 + 0.0906214i
\(429\) 0 0
\(430\) −6.49388 7.19635i −0.313162 0.347039i
\(431\) 11.8497i 0.570779i 0.958412 + 0.285389i \(0.0921229\pi\)
−0.958412 + 0.285389i \(0.907877\pi\)
\(432\) 0 0
\(433\) 37.2566i 1.79044i −0.445625 0.895220i \(-0.647019\pi\)
0.445625 0.895220i \(-0.352981\pi\)
\(434\) 12.0440 + 3.95347i 0.578132 + 0.189773i
\(435\) 0 0
\(436\) 3.12136 30.3352i 0.149486 1.45279i
\(437\) 40.4188i 1.93349i
\(438\) 0 0
\(439\) 2.20068 0.105033 0.0525163 0.998620i \(-0.483276\pi\)
0.0525163 + 0.998620i \(0.483276\pi\)
\(440\) −1.08922 + 0.796835i −0.0519267 + 0.0379876i
\(441\) 0 0
\(442\) 10.7607 + 11.9247i 0.511834 + 0.567202i
\(443\) 5.86101i 0.278465i 0.990260 + 0.139233i \(0.0444636\pi\)
−0.990260 + 0.139233i \(0.955536\pi\)
\(444\) 0 0
\(445\) 13.1208 0.621987
\(446\) −20.3991 22.6058i −0.965925 1.07041i
\(447\) 0 0
\(448\) 4.45139 + 20.6926i 0.210309 + 0.977635i
\(449\) 11.2784 0.532259 0.266129 0.963937i \(-0.414255\pi\)
0.266129 + 0.963937i \(0.414255\pi\)
\(450\) 0 0
\(451\) 0.482513 0.0227207
\(452\) −0.829068 + 8.05735i −0.0389961 + 0.378986i
\(453\) 0 0
\(454\) 13.3129 + 14.7530i 0.624805 + 0.692394i
\(455\) 6.80445 3.89141i 0.318997 0.182432i
\(456\) 0 0
\(457\) 10.5671 0.494307 0.247153 0.968976i \(-0.420505\pi\)
0.247153 + 0.968976i \(0.420505\pi\)
\(458\) −18.0535 + 16.2912i −0.843584 + 0.761237i
\(459\) 0 0
\(460\) −1.55746 + 15.1362i −0.0726167 + 0.705731i
\(461\) 0.502682i 0.0234122i 0.999931 + 0.0117061i \(0.00372626\pi\)
−0.999931 + 0.0117061i \(0.996274\pi\)
\(462\) 0 0
\(463\) 16.5694i 0.770044i 0.922907 + 0.385022i \(0.125806\pi\)
−0.922907 + 0.385022i \(0.874194\pi\)
\(464\) 24.1923 + 5.03185i 1.12310 + 0.233598i
\(465\) 0 0
\(466\) 10.9430 + 12.1267i 0.506924 + 0.561761i
\(467\) 17.1182 0.792137 0.396069 0.918221i \(-0.370374\pi\)
0.396069 + 0.918221i \(0.370374\pi\)
\(468\) 0 0
\(469\) −1.71551 2.99971i −0.0792149 0.138514i
\(470\) 6.52887 5.89154i 0.301154 0.271757i
\(471\) 0 0
\(472\) 11.1595 8.16384i 0.513657 0.375771i
\(473\) 3.27042 0.150374
\(474\) 0 0
\(475\) 5.31262 0.243760
\(476\) 18.5472 8.21513i 0.850108 0.376540i
\(477\) 0 0
\(478\) −14.1790 + 12.7949i −0.648534 + 0.585227i
\(479\) −7.51289 −0.343272 −0.171636 0.985160i \(-0.554905\pi\)
−0.171636 + 0.985160i \(0.554905\pi\)
\(480\) 0 0
\(481\) 25.5643i 1.16563i
\(482\) 6.38155 5.75861i 0.290672 0.262298i
\(483\) 0 0
\(484\) −2.20521 + 21.4315i −0.100237 + 0.974159i
\(485\) −1.60612 −0.0729302
\(486\) 0 0
\(487\) 18.3725i 0.832537i −0.909242 0.416269i \(-0.863338\pi\)
0.909242 0.416269i \(-0.136662\pi\)
\(488\) −7.94614 10.8619i −0.359705 0.491695i
\(489\) 0 0
\(490\) −1.98928 9.69756i −0.0898666 0.438091i
\(491\) 12.3732i 0.558395i −0.960234 0.279197i \(-0.909932\pi\)
0.960234 0.279197i \(-0.0900684\pi\)
\(492\) 0 0
\(493\) 23.6817i 1.06657i
\(494\) −16.5257 + 14.9125i −0.743524 + 0.670944i
\(495\) 0 0
\(496\) 13.2676 + 2.75958i 0.595732 + 0.123909i
\(497\) −12.0668 21.0997i −0.541269 0.946453i
\(498\) 0 0
\(499\) 3.90928i 0.175003i 0.996164 + 0.0875017i \(0.0278883\pi\)
−0.996164 + 0.0875017i \(0.972112\pi\)
\(500\) −1.98950 0.204711i −0.0889730 0.00915495i
\(501\) 0 0
\(502\) −24.6284 27.2926i −1.09922 1.21813i
\(503\) 20.7397 0.924738 0.462369 0.886688i \(-0.347000\pi\)
0.462369 + 0.886688i \(0.347000\pi\)
\(504\) 0 0
\(505\) 6.17664 0.274857
\(506\) −3.43937 3.81143i −0.152899 0.169439i
\(507\) 0 0
\(508\) −25.8532 2.66019i −1.14705 0.118027i
\(509\) 19.9445i 0.884025i 0.897009 + 0.442012i \(0.145735\pi\)
−0.897009 + 0.442012i \(0.854265\pi\)
\(510\) 0 0
\(511\) 5.90751 + 10.3298i 0.261333 + 0.456962i
\(512\) 7.20349 + 21.4502i 0.318352 + 0.947972i
\(513\) 0 0
\(514\) −27.4433 + 24.7644i −1.21047 + 1.09231i
\(515\) 16.8145i 0.740935i
\(516\) 0 0
\(517\) 2.96708i 0.130492i
\(518\) 30.6752 + 10.0692i 1.34779 + 0.442414i
\(519\) 0 0
\(520\) 6.76323 4.94772i 0.296587 0.216972i
\(521\) 37.8103i 1.65650i 0.560361 + 0.828249i \(0.310662\pi\)
−0.560361 + 0.828249i \(0.689338\pi\)
\(522\) 0 0
\(523\) 16.5206 0.722398 0.361199 0.932489i \(-0.382368\pi\)
0.361199 + 0.932489i \(0.382368\pi\)
\(524\) −0.363468 + 3.53239i −0.0158782 + 0.154313i
\(525\) 0 0
\(526\) −21.1476 + 19.0833i −0.922080 + 0.832070i
\(527\) 12.9875i 0.565746i
\(528\) 0 0
\(529\) −34.8828 −1.51664
\(530\) 9.76835 8.81480i 0.424310 0.382890i
\(531\) 0 0
\(532\) 11.3848 + 25.7032i 0.493593 + 1.11438i
\(533\) −2.99603 −0.129773
\(534\) 0 0
\(535\) −9.15824 −0.395945
\(536\) −2.18118 2.98154i −0.0942127 0.128783i
\(537\) 0 0
\(538\) −26.4300 + 23.8500i −1.13948 + 1.02825i
\(539\) 2.87875 + 1.69370i 0.123996 + 0.0729527i
\(540\) 0 0
\(541\) −32.6251 −1.40266 −0.701331 0.712836i \(-0.747411\pi\)
−0.701331 + 0.712836i \(0.747411\pi\)
\(542\) −8.65275 9.58877i −0.371668 0.411873i
\(543\) 0 0
\(544\) 18.7209 10.9453i 0.802650 0.469274i
\(545\) 15.2477i 0.653138i
\(546\) 0 0
\(547\) 35.9526i 1.53722i −0.639716 0.768612i \(-0.720948\pi\)
0.639716 0.768612i \(-0.279052\pi\)
\(548\) −3.10386 + 30.1650i −0.132590 + 1.28859i
\(549\) 0 0
\(550\) 0.500972 0.452069i 0.0213615 0.0192763i
\(551\) 32.8188 1.39813
\(552\) 0 0
\(553\) −11.5694 20.2301i −0.491982 0.860270i
\(554\) −16.3025 18.0661i −0.692628 0.767553i
\(555\) 0 0
\(556\) 3.85971 37.5108i 0.163688 1.59081i
\(557\) 8.84229 0.374660 0.187330 0.982297i \(-0.440017\pi\)
0.187330 + 0.982297i \(0.440017\pi\)
\(558\) 0 0
\(559\) −20.3068 −0.858885
\(560\) −3.27301 10.0642i −0.138310 0.425289i
\(561\) 0 0
\(562\) −10.0770 11.1671i −0.425072 0.471054i
\(563\) 17.7594 0.748471 0.374235 0.927334i \(-0.377905\pi\)
0.374235 + 0.927334i \(0.377905\pi\)
\(564\) 0 0
\(565\) 4.04995i 0.170383i
\(566\) 18.3439 + 20.3283i 0.771052 + 0.854462i
\(567\) 0 0
\(568\) −15.3423 20.9719i −0.643747 0.879963i
\(569\) −36.7269 −1.53967 −0.769835 0.638243i \(-0.779661\pi\)
−0.769835 + 0.638243i \(0.779661\pi\)
\(570\) 0 0
\(571\) 17.1069i 0.715902i −0.933740 0.357951i \(-0.883476\pi\)
0.933740 0.357951i \(-0.116524\pi\)
\(572\) −0.289389 + 2.81245i −0.0121000 + 0.117594i
\(573\) 0 0
\(574\) −1.18007 + 3.59501i −0.0492551 + 0.150053i
\(575\) 7.60808i 0.317279i
\(576\) 0 0
\(577\) 37.9794i 1.58110i 0.612395 + 0.790552i \(0.290206\pi\)
−0.612395 + 0.790552i \(0.709794\pi\)
\(578\) 2.18297 + 2.41912i 0.0907998 + 0.100622i
\(579\) 0 0
\(580\) −12.2902 1.26461i −0.510321 0.0525099i
\(581\) 25.1534 14.3850i 1.04354 0.596792i
\(582\) 0 0
\(583\) 4.43928i 0.183856i
\(584\) 7.51108 + 10.2672i 0.310811 + 0.424859i
\(585\) 0 0
\(586\) 25.8132 23.2934i 1.06633 0.962242i
\(587\) −40.1743 −1.65817 −0.829085 0.559122i \(-0.811138\pi\)
−0.829085 + 0.559122i \(0.811138\pi\)
\(588\) 0 0
\(589\) 17.9985 0.741617
\(590\) −5.13263 + 4.63160i −0.211307 + 0.190680i
\(591\) 0 0
\(592\) 33.7915 + 7.02842i 1.38882 + 0.288866i
\(593\) 2.80855i 0.115333i 0.998336 + 0.0576667i \(0.0183661\pi\)
−0.998336 + 0.0576667i \(0.981634\pi\)
\(594\) 0 0
\(595\) −8.80445 + 5.03519i −0.360947 + 0.206423i
\(596\) −3.85756 + 37.4899i −0.158012 + 1.53565i
\(597\) 0 0
\(598\) 21.3558 + 23.6660i 0.873305 + 0.967775i
\(599\) 10.0933i 0.412399i −0.978510 0.206200i \(-0.933890\pi\)
0.978510 0.206200i \(-0.0661097\pi\)
\(600\) 0 0
\(601\) 8.17083i 0.333295i −0.986017 0.166648i \(-0.946706\pi\)
0.986017 0.166648i \(-0.0532942\pi\)
\(602\) −7.99838 + 24.3666i −0.325990 + 0.993109i
\(603\) 0 0
\(604\) 37.0966 + 3.81708i 1.50944 + 0.155315i
\(605\) 10.7723i 0.437958i
\(606\) 0 0
\(607\) −20.7112 −0.840642 −0.420321 0.907375i \(-0.638083\pi\)
−0.420321 + 0.907375i \(0.638083\pi\)
\(608\) 15.1683 + 25.9439i 0.615155 + 1.05217i
\(609\) 0 0
\(610\) 4.50809 + 4.99576i 0.182527 + 0.202272i
\(611\) 18.4232i 0.745325i
\(612\) 0 0
\(613\) 4.61369 0.186345 0.0931726 0.995650i \(-0.470299\pi\)
0.0931726 + 0.995650i \(0.470299\pi\)
\(614\) −3.06112 3.39226i −0.123537 0.136901i
\(615\) 0 0
\(616\) 3.26074 + 1.45501i 0.131379 + 0.0586238i
\(617\) −13.3799 −0.538655 −0.269328 0.963049i \(-0.586801\pi\)
−0.269328 + 0.963049i \(0.586801\pi\)
\(618\) 0 0
\(619\) 36.4215 1.46390 0.731951 0.681357i \(-0.238610\pi\)
0.731951 + 0.681357i \(0.238610\pi\)
\(620\) −6.74018 0.693537i −0.270692 0.0278531i
\(621\) 0 0
\(622\) −8.85476 9.81263i −0.355044 0.393451i
\(623\) −17.2337 30.1345i −0.690454 1.20732i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 17.4808 15.7744i 0.698674 0.630473i
\(627\) 0 0
\(628\) −45.1498 4.64572i −1.80167 0.185385i
\(629\) 33.0782i 1.31892i
\(630\) 0 0
\(631\) 23.3976i 0.931442i −0.884932 0.465721i \(-0.845795\pi\)
0.884932 0.465721i \(-0.154205\pi\)
\(632\) −14.7099 20.1075i −0.585128 0.799835i
\(633\) 0 0
\(634\) −24.4320 27.0750i −0.970320 1.07528i
\(635\) 12.9949 0.515686
\(636\) 0 0
\(637\) −17.8748 10.5165i −0.708224 0.416680i
\(638\) 3.09476 2.79267i 0.122523 0.110563i
\(639\) 0 0
\(640\) −4.68060 10.3001i −0.185017 0.407147i
\(641\) −14.4482 −0.570668 −0.285334 0.958428i \(-0.592104\pi\)
−0.285334 + 0.958428i \(0.592104\pi\)
\(642\) 0 0
\(643\) −14.1004 −0.556065 −0.278033 0.960572i \(-0.589682\pi\)
−0.278033 + 0.960572i \(0.589682\pi\)
\(644\) 36.8090 16.3039i 1.45048 0.642463i
\(645\) 0 0
\(646\) 21.3830 19.2956i 0.841301 0.759177i
\(647\) 13.1557 0.517205 0.258602 0.965984i \(-0.416738\pi\)
0.258602 + 0.965984i \(0.416738\pi\)
\(648\) 0 0
\(649\) 2.33255i 0.0915606i
\(650\) −3.11064 + 2.80699i −0.122009 + 0.110099i
\(651\) 0 0
\(652\) −18.2632 1.87920i −0.715241 0.0735953i
\(653\) −34.5944 −1.35378 −0.676892 0.736083i \(-0.736673\pi\)
−0.676892 + 0.736083i \(0.736673\pi\)
\(654\) 0 0
\(655\) 1.77552i 0.0693753i
\(656\) −0.823703 + 3.96023i −0.0321602 + 0.154621i
\(657\) 0 0
\(658\) −22.1065 7.25650i −0.861802 0.282888i
\(659\) 8.35962i 0.325644i 0.986655 + 0.162822i \(0.0520597\pi\)
−0.986655 + 0.162822i \(0.947940\pi\)
\(660\) 0 0
\(661\) 45.6469i 1.77546i −0.460366 0.887729i \(-0.652282\pi\)
0.460366 0.887729i \(-0.347718\pi\)
\(662\) 35.1553 31.7235i 1.36635 1.23297i
\(663\) 0 0
\(664\) 25.0010 18.2898i 0.970228 0.709782i
\(665\) −6.97792 12.2015i −0.270592 0.473153i
\(666\) 0 0
\(667\) 46.9991i 1.81981i
\(668\) 3.04510 29.5940i 0.117818 1.14503i
\(669\) 0 0
\(670\) 1.23745 + 1.37131i 0.0478069 + 0.0529784i
\(671\) −2.27035 −0.0876459
\(672\) 0 0
\(673\) −39.4155 −1.51936 −0.759678 0.650299i \(-0.774644\pi\)
−0.759678 + 0.650299i \(0.774644\pi\)
\(674\) −4.72173 5.23250i −0.181874 0.201548i
\(675\) 0 0
\(676\) −0.864360 + 8.40034i −0.0332446 + 0.323090i
\(677\) 19.6704i 0.755995i 0.925807 + 0.377997i \(0.123387\pi\)
−0.925807 + 0.377997i \(0.876613\pi\)
\(678\) 0 0
\(679\) 2.10958 + 3.68877i 0.0809582 + 0.141562i
\(680\) −8.75112 + 6.40198i −0.335590 + 0.245505i
\(681\) 0 0
\(682\) 1.69723 1.53156i 0.0649905 0.0586464i
\(683\) 5.27739i 0.201934i −0.994890 0.100967i \(-0.967806\pi\)
0.994890 0.100967i \(-0.0321936\pi\)
\(684\) 0 0
\(685\) 15.1622i 0.579316i
\(686\) −19.6595 + 17.3062i −0.750604 + 0.660753i
\(687\) 0 0
\(688\) −5.58297 + 26.8420i −0.212849 + 1.02334i
\(689\) 27.5645i 1.05012i
\(690\) 0 0
\(691\) −8.48775 −0.322889 −0.161445 0.986882i \(-0.551615\pi\)
−0.161445 + 0.986882i \(0.551615\pi\)
\(692\) 36.2508 + 3.73005i 1.37805 + 0.141795i
\(693\) 0 0
\(694\) −3.11508 + 2.81100i −0.118247 + 0.106704i
\(695\) 18.8544i 0.715190i
\(696\) 0 0
\(697\) 3.87664 0.146838
\(698\) −16.5572 + 14.9410i −0.626700 + 0.565524i
\(699\) 0 0
\(700\) 2.14297 + 4.83815i 0.0809967 + 0.182865i
\(701\) 10.1888 0.384825 0.192412 0.981314i \(-0.438369\pi\)
0.192412 + 0.981314i \(0.438369\pi\)
\(702\) 0 0
\(703\) 45.8408 1.72892
\(704\) 3.63800 + 1.15575i 0.137112 + 0.0435591i
\(705\) 0 0
\(706\) 9.66452 8.72111i 0.363729 0.328223i
\(707\) −8.11279 14.1859i −0.305113 0.533514i
\(708\) 0 0
\(709\) 3.99960 0.150208 0.0751041 0.997176i \(-0.476071\pi\)
0.0751041 + 0.997176i \(0.476071\pi\)
\(710\) 8.70414 + 9.64571i 0.326660 + 0.361997i
\(711\) 0 0
\(712\) −21.9117 29.9520i −0.821177 1.12250i
\(713\) 25.7753i 0.965292i
\(714\) 0 0
\(715\) 1.41365i 0.0528675i
\(716\) −10.0028 1.02925i −0.373822 0.0384647i
\(717\) 0 0
\(718\) 21.9468 19.8044i 0.819046 0.739094i
\(719\) 8.22659 0.306800 0.153400 0.988164i \(-0.450978\pi\)
0.153400 + 0.988164i \(0.450978\pi\)
\(720\) 0 0
\(721\) −38.6178 + 22.0852i −1.43820 + 0.822496i
\(722\) 8.73910 + 9.68446i 0.325236 + 0.360418i
\(723\) 0 0
\(724\) −29.1468 2.99908i −1.08323 0.111460i
\(725\) 6.17752 0.229427
\(726\) 0 0
\(727\) 2.05684 0.0762839 0.0381419 0.999272i \(-0.487856\pi\)
0.0381419 + 0.999272i \(0.487856\pi\)
\(728\) −20.2467 9.03444i −0.750391 0.334839i
\(729\) 0 0
\(730\) −4.26127 4.72223i −0.157717 0.174778i
\(731\) 26.2755 0.971833
\(732\) 0 0
\(733\) 24.8578i 0.918145i 0.888399 + 0.459072i \(0.151818\pi\)
−0.888399 + 0.459072i \(0.848182\pi\)
\(734\) 4.54625 + 5.03804i 0.167805 + 0.185958i
\(735\) 0 0
\(736\) 37.1537 21.7221i 1.36950 0.800689i
\(737\) −0.623201 −0.0229559
\(738\) 0 0
\(739\) 1.48614i 0.0546686i −0.999626 0.0273343i \(-0.991298\pi\)
0.999626 0.0273343i \(-0.00870186\pi\)
\(740\) −17.1667 1.76638i −0.631061 0.0649335i
\(741\) 0 0
\(742\) −33.0753 10.8570i −1.21423 0.398574i
\(743\) 4.73363i 0.173660i −0.996223 0.0868299i \(-0.972326\pi\)
0.996223 0.0868299i \(-0.0276737\pi\)
\(744\) 0 0
\(745\) 18.8439i 0.690389i
\(746\) 27.4197 + 30.3859i 1.00391 + 1.11251i
\(747\) 0 0
\(748\) 0.374448 3.63910i 0.0136912 0.133059i
\(749\) 12.0290 + 21.0337i 0.439530 + 0.768555i
\(750\) 0 0
\(751\) 49.1841i 1.79475i 0.441266 + 0.897376i \(0.354530\pi\)
−0.441266 + 0.897376i \(0.645470\pi\)
\(752\) −24.3523 5.06513i −0.888038 0.184706i
\(753\) 0 0
\(754\) −19.2161 + 17.3403i −0.699808 + 0.631495i
\(755\) −18.6462 −0.678606
\(756\) 0 0
\(757\) −6.41551 −0.233176 −0.116588 0.993180i \(-0.537196\pi\)
−0.116588 + 0.993180i \(0.537196\pi\)
\(758\) 4.97571 4.49000i 0.180726 0.163084i
\(759\) 0 0
\(760\) −8.87206 12.1276i −0.321823 0.439913i
\(761\) 1.23026i 0.0445970i 0.999751 + 0.0222985i \(0.00709843\pi\)
−0.999751 + 0.0222985i \(0.992902\pi\)
\(762\) 0 0
\(763\) 35.0192 20.0272i 1.26778 0.725035i
\(764\) 13.6219 + 1.40164i 0.492824 + 0.0507095i
\(765\) 0 0
\(766\) 11.3499 + 12.5777i 0.410088 + 0.454450i
\(767\) 14.4833i 0.522962i
\(768\) 0 0
\(769\) 28.9327i 1.04334i 0.853147 + 0.521670i \(0.174691\pi\)
−0.853147 + 0.521670i \(0.825309\pi\)
\(770\) −1.69627 0.556804i −0.0611294 0.0200658i
\(771\) 0 0
\(772\) −1.53037 + 14.8730i −0.0550791 + 0.535290i
\(773\) 12.9773i 0.466761i −0.972385 0.233380i \(-0.925021\pi\)
0.972385 0.233380i \(-0.0749788\pi\)
\(774\) 0 0
\(775\) 3.38789 0.121696
\(776\) 2.68222 + 3.66643i 0.0962860 + 0.131617i
\(777\) 0 0
\(778\) −22.9158 25.3948i −0.821573 0.910447i
\(779\) 5.37237i 0.192485i
\(780\) 0 0
\(781\) −4.38355 −0.156856
\(782\) −27.6328 30.6220i −0.988148 1.09504i
\(783\) 0 0
\(784\) −18.8154 + 20.7360i −0.671977 + 0.740572i
\(785\) 22.6941 0.809986
\(786\) 0 0
\(787\) −16.7024 −0.595377 −0.297688 0.954663i \(-0.596216\pi\)
−0.297688 + 0.954663i \(0.596216\pi\)
\(788\) −2.92223 + 28.3999i −0.104100 + 1.01170i
\(789\) 0 0
\(790\) 8.34538 + 9.24814i 0.296915 + 0.329034i
\(791\) −9.30150 + 5.31945i −0.330723 + 0.189138i
\(792\) 0