Properties

Label 1260.2.c.e.811.3
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 811.3
Root \(1.10145 - 0.887017i\) of defining polynomial
Character \(\chi\) \(=\) 1260.811
Dual form 1260.2.c.e.811.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.10145 - 0.887017i) q^{2} +(0.426402 + 1.95402i) q^{4} -1.00000i q^{5} +(-0.391948 + 2.61656i) q^{7} +(1.26358 - 2.53049i) q^{8} +O(q^{10})\) \(q+(-1.10145 - 0.887017i) q^{2} +(0.426402 + 1.95402i) q^{4} -1.00000i q^{5} +(-0.391948 + 2.61656i) q^{7} +(1.26358 - 2.53049i) q^{8} +(-0.887017 + 1.10145i) q^{10} +0.770756i q^{11} -5.60576i q^{13} +(2.75264 - 2.53435i) q^{14} +(-3.63636 + 1.66639i) q^{16} +0.503042i q^{17} -1.63506 q^{19} +(1.95402 - 0.426402i) q^{20} +(0.683673 - 0.848952i) q^{22} -1.42475i q^{23} -1.00000 q^{25} +(-4.97240 + 6.17449i) q^{26} +(-5.27993 + 0.349833i) q^{28} -5.03595 q^{29} +8.23212 q^{31} +(5.48341 + 1.39006i) q^{32} +(0.446206 - 0.554077i) q^{34} +(2.61656 + 0.391948i) q^{35} +10.1403 q^{37} +(1.80094 + 1.45033i) q^{38} +(-2.53049 - 1.26358i) q^{40} -5.07885i q^{41} -9.06204i q^{43} +(-1.50607 + 0.328652i) q^{44} +(-1.26378 + 1.56930i) q^{46} +4.64967 q^{47} +(-6.69275 - 2.05111i) q^{49} +(1.10145 + 0.887017i) q^{50} +(10.9537 - 2.39031i) q^{52} -0.455805 q^{53} +0.770756 q^{55} +(6.12590 + 4.29806i) q^{56} +(5.54687 + 4.46697i) q^{58} +10.4908 q^{59} -3.32394i q^{61} +(-9.06730 - 7.30202i) q^{62} +(-4.80671 - 6.39496i) q^{64} -5.60576 q^{65} -8.70791i q^{67} +(-0.982952 + 0.214498i) q^{68} +(-2.53435 - 2.75264i) q^{70} +10.8176i q^{71} +2.29564i q^{73} +(-11.1691 - 8.99464i) q^{74} +(-0.697193 - 3.19494i) q^{76} +(-2.01673 - 0.302096i) q^{77} +2.56336i q^{79} +(1.66639 + 3.63636i) q^{80} +(-4.50503 + 5.59412i) q^{82} +13.9979 q^{83} +0.503042 q^{85} +(-8.03818 + 9.98142i) q^{86} +(1.95039 + 0.973914i) q^{88} -2.98877i q^{89} +(14.6678 + 2.19717i) q^{91} +(2.78399 - 0.607518i) q^{92} +(-5.12139 - 4.12433i) q^{94} +1.63506i q^{95} -15.5818i q^{97} +(5.55239 + 8.19579i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} + O(q^{10}) \) \( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.10145 0.887017i −0.778846 0.627216i
\(3\) 0 0
\(4\) 0.426402 + 1.95402i 0.213201 + 0.977008i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −0.391948 + 2.61656i −0.148142 + 0.988966i
\(8\) 1.26358 2.53049i 0.446744 0.894662i
\(9\) 0 0
\(10\) −0.887017 + 1.10145i −0.280499 + 0.348310i
\(11\) 0.770756i 0.232392i 0.993226 + 0.116196i \(0.0370700\pi\)
−0.993226 + 0.116196i \(0.962930\pi\)
\(12\) 0 0
\(13\) 5.60576i 1.55476i −0.629032 0.777379i \(-0.716549\pi\)
0.629032 0.777379i \(-0.283451\pi\)
\(14\) 2.75264 2.53435i 0.735675 0.677335i
\(15\) 0 0
\(16\) −3.63636 + 1.66639i −0.909091 + 0.416598i
\(17\) 0.503042i 0.122005i 0.998138 + 0.0610027i \(0.0194298\pi\)
−0.998138 + 0.0610027i \(0.980570\pi\)
\(18\) 0 0
\(19\) −1.63506 −0.375109 −0.187554 0.982254i \(-0.560056\pi\)
−0.187554 + 0.982254i \(0.560056\pi\)
\(20\) 1.95402 0.426402i 0.436931 0.0953464i
\(21\) 0 0
\(22\) 0.683673 0.848952i 0.145760 0.180997i
\(23\) 1.42475i 0.297082i −0.988906 0.148541i \(-0.952542\pi\)
0.988906 0.148541i \(-0.0474577\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −4.97240 + 6.17449i −0.975169 + 1.21092i
\(27\) 0 0
\(28\) −5.27993 + 0.349833i −0.997812 + 0.0661123i
\(29\) −5.03595 −0.935152 −0.467576 0.883953i \(-0.654873\pi\)
−0.467576 + 0.883953i \(0.654873\pi\)
\(30\) 0 0
\(31\) 8.23212 1.47853 0.739266 0.673414i \(-0.235173\pi\)
0.739266 + 0.673414i \(0.235173\pi\)
\(32\) 5.48341 + 1.39006i 0.969338 + 0.245730i
\(33\) 0 0
\(34\) 0.446206 0.554077i 0.0765238 0.0950235i
\(35\) 2.61656 + 0.391948i 0.442279 + 0.0662513i
\(36\) 0 0
\(37\) 10.1403 1.66706 0.833530 0.552475i \(-0.186316\pi\)
0.833530 + 0.552475i \(0.186316\pi\)
\(38\) 1.80094 + 1.45033i 0.292152 + 0.235274i
\(39\) 0 0
\(40\) −2.53049 1.26358i −0.400105 0.199790i
\(41\) 5.07885i 0.793184i −0.917995 0.396592i \(-0.870193\pi\)
0.917995 0.396592i \(-0.129807\pi\)
\(42\) 0 0
\(43\) 9.06204i 1.38195i −0.722880 0.690974i \(-0.757182\pi\)
0.722880 0.690974i \(-0.242818\pi\)
\(44\) −1.50607 + 0.328652i −0.227049 + 0.0495461i
\(45\) 0 0
\(46\) −1.26378 + 1.56930i −0.186334 + 0.231381i
\(47\) 4.64967 0.678223 0.339112 0.940746i \(-0.389874\pi\)
0.339112 + 0.940746i \(0.389874\pi\)
\(48\) 0 0
\(49\) −6.69275 2.05111i −0.956108 0.293016i
\(50\) 1.10145 + 0.887017i 0.155769 + 0.125443i
\(51\) 0 0
\(52\) 10.9537 2.39031i 1.51901 0.331476i
\(53\) −0.455805 −0.0626096 −0.0313048 0.999510i \(-0.509966\pi\)
−0.0313048 + 0.999510i \(0.509966\pi\)
\(54\) 0 0
\(55\) 0.770756 0.103929
\(56\) 6.12590 + 4.29806i 0.818608 + 0.574352i
\(57\) 0 0
\(58\) 5.54687 + 4.46697i 0.728339 + 0.586542i
\(59\) 10.4908 1.36578 0.682890 0.730521i \(-0.260723\pi\)
0.682890 + 0.730521i \(0.260723\pi\)
\(60\) 0 0
\(61\) 3.32394i 0.425587i −0.977097 0.212794i \(-0.931744\pi\)
0.977097 0.212794i \(-0.0682562\pi\)
\(62\) −9.06730 7.30202i −1.15155 0.927358i
\(63\) 0 0
\(64\) −4.80671 6.39496i −0.600839 0.799370i
\(65\) −5.60576 −0.695309
\(66\) 0 0
\(67\) 8.70791i 1.06384i −0.846794 0.531920i \(-0.821471\pi\)
0.846794 0.531920i \(-0.178529\pi\)
\(68\) −0.982952 + 0.214498i −0.119200 + 0.0260117i
\(69\) 0 0
\(70\) −2.53435 2.75264i −0.302913 0.329004i
\(71\) 10.8176i 1.28382i 0.766781 + 0.641909i \(0.221857\pi\)
−0.766781 + 0.641909i \(0.778143\pi\)
\(72\) 0 0
\(73\) 2.29564i 0.268685i 0.990935 + 0.134342i \(0.0428922\pi\)
−0.990935 + 0.134342i \(0.957108\pi\)
\(74\) −11.1691 8.99464i −1.29838 1.04561i
\(75\) 0 0
\(76\) −0.697193 3.19494i −0.0799736 0.366484i
\(77\) −2.01673 0.302096i −0.229827 0.0344270i
\(78\) 0 0
\(79\) 2.56336i 0.288400i 0.989549 + 0.144200i \(0.0460609\pi\)
−0.989549 + 0.144200i \(0.953939\pi\)
\(80\) 1.66639 + 3.63636i 0.186309 + 0.406558i
\(81\) 0 0
\(82\) −4.50503 + 5.59412i −0.497497 + 0.617768i
\(83\) 13.9979 1.53646 0.768232 0.640171i \(-0.221137\pi\)
0.768232 + 0.640171i \(0.221137\pi\)
\(84\) 0 0
\(85\) 0.503042 0.0545625
\(86\) −8.03818 + 9.98142i −0.866779 + 1.07632i
\(87\) 0 0
\(88\) 1.95039 + 0.973914i 0.207912 + 0.103820i
\(89\) 2.98877i 0.316809i −0.987374 0.158404i \(-0.949365\pi\)
0.987374 0.158404i \(-0.0506349\pi\)
\(90\) 0 0
\(91\) 14.6678 + 2.19717i 1.53760 + 0.230326i
\(92\) 2.78399 0.607518i 0.290251 0.0633382i
\(93\) 0 0
\(94\) −5.12139 4.12433i −0.528231 0.425392i
\(95\) 1.63506i 0.167754i
\(96\) 0 0
\(97\) 15.5818i 1.58209i −0.611756 0.791046i \(-0.709537\pi\)
0.611756 0.791046i \(-0.290463\pi\)
\(98\) 5.55239 + 8.19579i 0.560876 + 0.827900i
\(99\) 0 0
\(100\) −0.426402 1.95402i −0.0426402 0.195402i
\(101\) 18.9661i 1.88719i −0.331097 0.943597i \(-0.607419\pi\)
0.331097 0.943597i \(-0.392581\pi\)
\(102\) 0 0
\(103\) −8.23760 −0.811675 −0.405837 0.913945i \(-0.633020\pi\)
−0.405837 + 0.913945i \(0.633020\pi\)
\(104\) −14.1853 7.08335i −1.39098 0.694579i
\(105\) 0 0
\(106\) 0.502048 + 0.404306i 0.0487632 + 0.0392697i
\(107\) 11.8042i 1.14115i −0.821244 0.570577i \(-0.806720\pi\)
0.821244 0.570577i \(-0.193280\pi\)
\(108\) 0 0
\(109\) −9.80783 −0.939419 −0.469710 0.882821i \(-0.655641\pi\)
−0.469710 + 0.882821i \(0.655641\pi\)
\(110\) −0.848952 0.683673i −0.0809444 0.0651857i
\(111\) 0 0
\(112\) −2.93495 10.1679i −0.277327 0.960776i
\(113\) 10.0104 0.941702 0.470851 0.882213i \(-0.343947\pi\)
0.470851 + 0.882213i \(0.343947\pi\)
\(114\) 0 0
\(115\) −1.42475 −0.132859
\(116\) −2.14734 9.84033i −0.199376 0.913652i
\(117\) 0 0
\(118\) −11.5551 9.30548i −1.06373 0.856638i
\(119\) −1.31624 0.197166i −0.120659 0.0180742i
\(120\) 0 0
\(121\) 10.4059 0.945994
\(122\) −2.94839 + 3.66117i −0.266935 + 0.331467i
\(123\) 0 0
\(124\) 3.51019 + 16.0857i 0.315225 + 1.44454i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 3.09530i 0.274663i 0.990525 + 0.137332i \(0.0438526\pi\)
−0.990525 + 0.137332i \(0.956147\pi\)
\(128\) −0.378061 + 11.3074i −0.0334162 + 0.999442i
\(129\) 0 0
\(130\) 6.17449 + 4.97240i 0.541538 + 0.436109i
\(131\) −17.5001 −1.52899 −0.764495 0.644630i \(-0.777011\pi\)
−0.764495 + 0.644630i \(0.777011\pi\)
\(132\) 0 0
\(133\) 0.640859 4.27823i 0.0555695 0.370970i
\(134\) −7.72407 + 9.59137i −0.667258 + 0.828568i
\(135\) 0 0
\(136\) 1.27294 + 0.635635i 0.109154 + 0.0545052i
\(137\) 15.6542 1.33742 0.668712 0.743521i \(-0.266846\pi\)
0.668712 + 0.743521i \(0.266846\pi\)
\(138\) 0 0
\(139\) −1.13095 −0.0959261 −0.0479630 0.998849i \(-0.515273\pi\)
−0.0479630 + 0.998849i \(0.515273\pi\)
\(140\) 0.349833 + 5.27993i 0.0295663 + 0.446235i
\(141\) 0 0
\(142\) 9.59542 11.9151i 0.805230 0.999895i
\(143\) 4.32067 0.361313
\(144\) 0 0
\(145\) 5.03595i 0.418213i
\(146\) 2.03627 2.52855i 0.168523 0.209264i
\(147\) 0 0
\(148\) 4.32386 + 19.8144i 0.355419 + 1.62873i
\(149\) −21.3643 −1.75023 −0.875117 0.483911i \(-0.839216\pi\)
−0.875117 + 0.483911i \(0.839216\pi\)
\(150\) 0 0
\(151\) 2.83045i 0.230339i 0.993346 + 0.115169i \(0.0367411\pi\)
−0.993346 + 0.115169i \(0.963259\pi\)
\(152\) −2.06604 + 4.13750i −0.167578 + 0.335595i
\(153\) 0 0
\(154\) 1.95337 + 2.12162i 0.157407 + 0.170965i
\(155\) 8.23212i 0.661219i
\(156\) 0 0
\(157\) 18.7903i 1.49963i −0.661649 0.749814i \(-0.730143\pi\)
0.661649 0.749814i \(-0.269857\pi\)
\(158\) 2.27374 2.82342i 0.180889 0.224619i
\(159\) 0 0
\(160\) 1.39006 5.48341i 0.109894 0.433501i
\(161\) 3.72795 + 0.558430i 0.293804 + 0.0440104i
\(162\) 0 0
\(163\) 7.40744i 0.580195i 0.956997 + 0.290098i \(0.0936878\pi\)
−0.956997 + 0.290098i \(0.906312\pi\)
\(164\) 9.92417 2.16563i 0.774947 0.169108i
\(165\) 0 0
\(166\) −15.4180 12.4163i −1.19667 0.963694i
\(167\) −2.96147 −0.229165 −0.114583 0.993414i \(-0.536553\pi\)
−0.114583 + 0.993414i \(0.536553\pi\)
\(168\) 0 0
\(169\) −18.4246 −1.41727
\(170\) −0.554077 0.446206i −0.0424958 0.0342225i
\(171\) 0 0
\(172\) 17.7074 3.86407i 1.35017 0.294633i
\(173\) 15.0215i 1.14206i −0.820928 0.571031i \(-0.806543\pi\)
0.820928 0.571031i \(-0.193457\pi\)
\(174\) 0 0
\(175\) 0.391948 2.61656i 0.0296285 0.197793i
\(176\) −1.28438 2.80275i −0.0968140 0.211265i
\(177\) 0 0
\(178\) −2.65109 + 3.29199i −0.198707 + 0.246745i
\(179\) 4.82936i 0.360963i 0.983578 + 0.180482i \(0.0577656\pi\)
−0.983578 + 0.180482i \(0.942234\pi\)
\(180\) 0 0
\(181\) 18.2050i 1.35316i 0.736367 + 0.676582i \(0.236540\pi\)
−0.736367 + 0.676582i \(0.763460\pi\)
\(182\) −14.2070 15.4307i −1.05309 1.14380i
\(183\) 0 0
\(184\) −3.60532 1.80030i −0.265788 0.132720i
\(185\) 10.1403i 0.745532i
\(186\) 0 0
\(187\) −0.387722 −0.0283531
\(188\) 1.98263 + 9.08552i 0.144598 + 0.662630i
\(189\) 0 0
\(190\) 1.45033 1.80094i 0.105218 0.130654i
\(191\) 5.65184i 0.408953i −0.978871 0.204476i \(-0.934451\pi\)
0.978871 0.204476i \(-0.0655492\pi\)
\(192\) 0 0
\(193\) −16.0978 −1.15874 −0.579372 0.815063i \(-0.696702\pi\)
−0.579372 + 0.815063i \(0.696702\pi\)
\(194\) −13.8213 + 17.1626i −0.992313 + 1.23221i
\(195\) 0 0
\(196\) 1.15410 13.9523i 0.0824355 0.996596i
\(197\) 12.2972 0.876141 0.438071 0.898941i \(-0.355662\pi\)
0.438071 + 0.898941i \(0.355662\pi\)
\(198\) 0 0
\(199\) 16.8234 1.19258 0.596290 0.802769i \(-0.296641\pi\)
0.596290 + 0.802769i \(0.296641\pi\)
\(200\) −1.26358 + 2.53049i −0.0893488 + 0.178932i
\(201\) 0 0
\(202\) −16.8232 + 20.8902i −1.18368 + 1.46983i
\(203\) 1.97383 13.1769i 0.138536 0.924834i
\(204\) 0 0
\(205\) −5.07885 −0.354723
\(206\) 9.07333 + 7.30689i 0.632169 + 0.509095i
\(207\) 0 0
\(208\) 9.34141 + 20.3846i 0.647710 + 1.41342i
\(209\) 1.26023i 0.0871721i
\(210\) 0 0
\(211\) 9.19446i 0.632973i 0.948597 + 0.316486i \(0.102503\pi\)
−0.948597 + 0.316486i \(0.897497\pi\)
\(212\) −0.194356 0.890650i −0.0133484 0.0611701i
\(213\) 0 0
\(214\) −10.4705 + 13.0018i −0.715749 + 0.888782i
\(215\) −9.06204 −0.618026
\(216\) 0 0
\(217\) −3.22656 + 21.5398i −0.219033 + 1.46222i
\(218\) 10.8029 + 8.69971i 0.731663 + 0.589219i
\(219\) 0 0
\(220\) 0.328652 + 1.50607i 0.0221577 + 0.101539i
\(221\) 2.81993 0.189689
\(222\) 0 0
\(223\) −22.8560 −1.53055 −0.765275 0.643704i \(-0.777397\pi\)
−0.765275 + 0.643704i \(0.777397\pi\)
\(224\) −5.78638 + 13.8028i −0.386619 + 0.922240i
\(225\) 0 0
\(226\) −11.0260 8.87942i −0.733440 0.590650i
\(227\) 17.4680 1.15939 0.579697 0.814832i \(-0.303171\pi\)
0.579697 + 0.814832i \(0.303171\pi\)
\(228\) 0 0
\(229\) 12.6233i 0.834169i −0.908868 0.417085i \(-0.863052\pi\)
0.908868 0.417085i \(-0.136948\pi\)
\(230\) 1.56930 + 1.26378i 0.103477 + 0.0833313i
\(231\) 0 0
\(232\) −6.36334 + 12.7434i −0.417774 + 0.836645i
\(233\) 3.89410 0.255111 0.127555 0.991831i \(-0.459287\pi\)
0.127555 + 0.991831i \(0.459287\pi\)
\(234\) 0 0
\(235\) 4.64967i 0.303311i
\(236\) 4.47328 + 20.4991i 0.291186 + 1.33438i
\(237\) 0 0
\(238\) 1.27489 + 1.38469i 0.0826386 + 0.0897564i
\(239\) 11.6497i 0.753559i −0.926303 0.376779i \(-0.877032\pi\)
0.926303 0.376779i \(-0.122968\pi\)
\(240\) 0 0
\(241\) 21.0259i 1.35440i 0.735799 + 0.677200i \(0.236807\pi\)
−0.735799 + 0.677200i \(0.763193\pi\)
\(242\) −11.4617 9.23024i −0.736783 0.593342i
\(243\) 0 0
\(244\) 6.49504 1.41734i 0.415802 0.0907357i
\(245\) −2.05111 + 6.69275i −0.131041 + 0.427584i
\(246\) 0 0
\(247\) 9.16576i 0.583203i
\(248\) 10.4020 20.8312i 0.660525 1.32279i
\(249\) 0 0
\(250\) 0.887017 1.10145i 0.0560999 0.0696621i
\(251\) 1.36484 0.0861478 0.0430739 0.999072i \(-0.486285\pi\)
0.0430739 + 0.999072i \(0.486285\pi\)
\(252\) 0 0
\(253\) 1.09814 0.0690393
\(254\) 2.74558 3.40933i 0.172273 0.213920i
\(255\) 0 0
\(256\) 10.4463 12.1192i 0.652891 0.757452i
\(257\) 4.44214i 0.277093i 0.990356 + 0.138547i \(0.0442431\pi\)
−0.990356 + 0.138547i \(0.955757\pi\)
\(258\) 0 0
\(259\) −3.97448 + 26.5328i −0.246962 + 1.64866i
\(260\) −2.39031 10.9537i −0.148241 0.679323i
\(261\) 0 0
\(262\) 19.2755 + 15.5229i 1.19085 + 0.959006i
\(263\) 4.92839i 0.303898i 0.988388 + 0.151949i \(0.0485549\pi\)
−0.988388 + 0.151949i \(0.951445\pi\)
\(264\) 0 0
\(265\) 0.455805i 0.0279999i
\(266\) −4.50074 + 4.14382i −0.275958 + 0.254074i
\(267\) 0 0
\(268\) 17.0154 3.71307i 1.03938 0.226812i
\(269\) 25.0193i 1.52546i 0.646719 + 0.762728i \(0.276141\pi\)
−0.646719 + 0.762728i \(0.723859\pi\)
\(270\) 0 0
\(271\) −12.1353 −0.737170 −0.368585 0.929594i \(-0.620158\pi\)
−0.368585 + 0.929594i \(0.620158\pi\)
\(272\) −0.838265 1.82924i −0.0508273 0.110914i
\(273\) 0 0
\(274\) −17.2423 13.8855i −1.04165 0.838854i
\(275\) 0.770756i 0.0464783i
\(276\) 0 0
\(277\) 19.4692 1.16979 0.584896 0.811108i \(-0.301135\pi\)
0.584896 + 0.811108i \(0.301135\pi\)
\(278\) 1.24569 + 1.00317i 0.0747116 + 0.0601663i
\(279\) 0 0
\(280\) 4.29806 6.12590i 0.256858 0.366093i
\(281\) 17.7452 1.05859 0.529296 0.848437i \(-0.322456\pi\)
0.529296 + 0.848437i \(0.322456\pi\)
\(282\) 0 0
\(283\) 29.4942 1.75325 0.876623 0.481177i \(-0.159791\pi\)
0.876623 + 0.481177i \(0.159791\pi\)
\(284\) −21.1378 + 4.61266i −1.25430 + 0.273711i
\(285\) 0 0
\(286\) −4.75902 3.83251i −0.281407 0.226621i
\(287\) 13.2891 + 1.99065i 0.784432 + 0.117504i
\(288\) 0 0
\(289\) 16.7469 0.985115
\(290\) 4.46697 5.54687i 0.262310 0.325723i
\(291\) 0 0
\(292\) −4.48573 + 0.978867i −0.262507 + 0.0572839i
\(293\) 19.8780i 1.16129i 0.814158 + 0.580643i \(0.197199\pi\)
−0.814158 + 0.580643i \(0.802801\pi\)
\(294\) 0 0
\(295\) 10.4908i 0.610795i
\(296\) 12.8131 25.6599i 0.744749 1.49145i
\(297\) 0 0
\(298\) 23.5318 + 18.9505i 1.36316 + 1.09777i
\(299\) −7.98683 −0.461890
\(300\) 0 0
\(301\) 23.7114 + 3.55185i 1.36670 + 0.204725i
\(302\) 2.51065 3.11761i 0.144472 0.179398i
\(303\) 0 0
\(304\) 5.94567 2.72466i 0.341008 0.156270i
\(305\) −3.32394 −0.190328
\(306\) 0 0
\(307\) −2.12425 −0.121238 −0.0606188 0.998161i \(-0.519307\pi\)
−0.0606188 + 0.998161i \(0.519307\pi\)
\(308\) −0.269636 4.06953i −0.0153639 0.231883i
\(309\) 0 0
\(310\) −7.30202 + 9.06730i −0.414727 + 0.514988i
\(311\) 10.2870 0.583323 0.291661 0.956522i \(-0.405792\pi\)
0.291661 + 0.956522i \(0.405792\pi\)
\(312\) 0 0
\(313\) 17.8800i 1.01064i 0.862932 + 0.505320i \(0.168626\pi\)
−0.862932 + 0.505320i \(0.831374\pi\)
\(314\) −16.6673 + 20.6966i −0.940590 + 1.16798i
\(315\) 0 0
\(316\) −5.00884 + 1.09302i −0.281769 + 0.0614872i
\(317\) −12.3840 −0.695557 −0.347778 0.937577i \(-0.613064\pi\)
−0.347778 + 0.937577i \(0.613064\pi\)
\(318\) 0 0
\(319\) 3.88149i 0.217322i
\(320\) −6.39496 + 4.80671i −0.357489 + 0.268703i
\(321\) 0 0
\(322\) −3.61083 3.92184i −0.201224 0.218556i
\(323\) 0.822503i 0.0457653i
\(324\) 0 0
\(325\) 5.60576i 0.310952i
\(326\) 6.57052 8.15895i 0.363908 0.451883i
\(327\) 0 0
\(328\) −12.8520 6.41756i −0.709631 0.354350i
\(329\) −1.82243 + 12.1661i −0.100474 + 0.670740i
\(330\) 0 0
\(331\) 21.3000i 1.17075i 0.810762 + 0.585376i \(0.199053\pi\)
−0.810762 + 0.585376i \(0.800947\pi\)
\(332\) 5.96872 + 27.3520i 0.327576 + 1.50114i
\(333\) 0 0
\(334\) 3.26192 + 2.62687i 0.178484 + 0.143736i
\(335\) −8.70791 −0.475764
\(336\) 0 0
\(337\) −0.875789 −0.0477073 −0.0238536 0.999715i \(-0.507594\pi\)
−0.0238536 + 0.999715i \(0.507594\pi\)
\(338\) 20.2938 + 16.3429i 1.10384 + 0.888936i
\(339\) 0 0
\(340\) 0.214498 + 0.982952i 0.0116328 + 0.0533080i
\(341\) 6.34495i 0.343598i
\(342\) 0 0
\(343\) 7.99006 16.7081i 0.431423 0.902150i
\(344\) −22.9314 11.4506i −1.23638 0.617377i
\(345\) 0 0
\(346\) −13.3243 + 16.5455i −0.716320 + 0.889491i
\(347\) 34.9081i 1.87396i 0.349379 + 0.936981i \(0.386392\pi\)
−0.349379 + 0.936981i \(0.613608\pi\)
\(348\) 0 0
\(349\) 21.1880i 1.13417i 0.823660 + 0.567084i \(0.191929\pi\)
−0.823660 + 0.567084i \(0.808071\pi\)
\(350\) −2.75264 + 2.53435i −0.147135 + 0.135467i
\(351\) 0 0
\(352\) −1.07140 + 4.22637i −0.0571056 + 0.225266i
\(353\) 7.69915i 0.409785i −0.978785 0.204892i \(-0.934316\pi\)
0.978785 0.204892i \(-0.0656844\pi\)
\(354\) 0 0
\(355\) 10.8176 0.574140
\(356\) 5.84010 1.27442i 0.309525 0.0675439i
\(357\) 0 0
\(358\) 4.28372 5.31931i 0.226402 0.281134i
\(359\) 2.14821i 0.113378i 0.998392 + 0.0566890i \(0.0180543\pi\)
−0.998392 + 0.0566890i \(0.981946\pi\)
\(360\) 0 0
\(361\) −16.3266 −0.859294
\(362\) 16.1481 20.0519i 0.848726 1.05391i
\(363\) 0 0
\(364\) 1.96108 + 29.5980i 0.102789 + 1.55136i
\(365\) 2.29564 0.120159
\(366\) 0 0
\(367\) −26.6962 −1.39353 −0.696764 0.717300i \(-0.745378\pi\)
−0.696764 + 0.717300i \(0.745378\pi\)
\(368\) 2.37420 + 5.18092i 0.123764 + 0.270074i
\(369\) 0 0
\(370\) −8.99464 + 11.1691i −0.467609 + 0.580654i
\(371\) 0.178652 1.19264i 0.00927513 0.0619187i
\(372\) 0 0
\(373\) −8.51430 −0.440854 −0.220427 0.975403i \(-0.570745\pi\)
−0.220427 + 0.975403i \(0.570745\pi\)
\(374\) 0.427058 + 0.343916i 0.0220826 + 0.0177835i
\(375\) 0 0
\(376\) 5.87524 11.7659i 0.302992 0.606781i
\(377\) 28.2303i 1.45394i
\(378\) 0 0
\(379\) 31.1693i 1.60106i −0.599295 0.800529i \(-0.704552\pi\)
0.599295 0.800529i \(-0.295448\pi\)
\(380\) −3.19494 + 0.697193i −0.163897 + 0.0357653i
\(381\) 0 0
\(382\) −5.01328 + 6.22524i −0.256502 + 0.318511i
\(383\) −33.7311 −1.72358 −0.861788 0.507268i \(-0.830655\pi\)
−0.861788 + 0.507268i \(0.830655\pi\)
\(384\) 0 0
\(385\) −0.302096 + 2.01673i −0.0153962 + 0.102782i
\(386\) 17.7310 + 14.2790i 0.902483 + 0.726783i
\(387\) 0 0
\(388\) 30.4471 6.64412i 1.54572 0.337304i
\(389\) −25.9912 −1.31780 −0.658902 0.752228i \(-0.728979\pi\)
−0.658902 + 0.752228i \(0.728979\pi\)
\(390\) 0 0
\(391\) 0.716711 0.0362456
\(392\) −13.6472 + 14.3442i −0.689285 + 0.724490i
\(393\) 0 0
\(394\) −13.5448 10.9078i −0.682379 0.549529i
\(395\) 2.56336 0.128977
\(396\) 0 0
\(397\) 1.63535i 0.0820760i 0.999158 + 0.0410380i \(0.0130665\pi\)
−0.999158 + 0.0410380i \(0.986934\pi\)
\(398\) −18.5302 14.9226i −0.928835 0.748004i
\(399\) 0 0
\(400\) 3.63636 1.66639i 0.181818 0.0833197i
\(401\) 11.7906 0.588797 0.294398 0.955683i \(-0.404881\pi\)
0.294398 + 0.955683i \(0.404881\pi\)
\(402\) 0 0
\(403\) 46.1473i 2.29876i
\(404\) 37.0600 8.08717i 1.84380 0.402352i
\(405\) 0 0
\(406\) −13.8622 + 12.7629i −0.687968 + 0.633411i
\(407\) 7.81571i 0.387411i
\(408\) 0 0
\(409\) 9.74926i 0.482070i −0.970516 0.241035i \(-0.922513\pi\)
0.970516 0.241035i \(-0.0774868\pi\)
\(410\) 5.59412 + 4.50503i 0.276274 + 0.222488i
\(411\) 0 0
\(412\) −3.51253 16.0964i −0.173050 0.793013i
\(413\) −4.11183 + 27.4497i −0.202330 + 1.35071i
\(414\) 0 0
\(415\) 13.9979i 0.687128i
\(416\) 7.79233 30.7387i 0.382051 1.50709i
\(417\) 0 0
\(418\) −1.11785 + 1.38809i −0.0546757 + 0.0678936i
\(419\) 15.3501 0.749902 0.374951 0.927045i \(-0.377659\pi\)
0.374951 + 0.927045i \(0.377659\pi\)
\(420\) 0 0
\(421\) 36.0738 1.75813 0.879064 0.476703i \(-0.158168\pi\)
0.879064 + 0.476703i \(0.158168\pi\)
\(422\) 8.15564 10.1273i 0.397011 0.492988i
\(423\) 0 0
\(424\) −0.575947 + 1.15341i −0.0279705 + 0.0560144i
\(425\) 0.503042i 0.0244011i
\(426\) 0 0
\(427\) 8.69729 + 1.30281i 0.420891 + 0.0630475i
\(428\) 23.0656 5.03333i 1.11492 0.243295i
\(429\) 0 0
\(430\) 9.98142 + 8.03818i 0.481347 + 0.387635i
\(431\) 20.9842i 1.01077i 0.862893 + 0.505387i \(0.168650\pi\)
−0.862893 + 0.505387i \(0.831350\pi\)
\(432\) 0 0
\(433\) 10.4424i 0.501828i 0.968009 + 0.250914i \(0.0807312\pi\)
−0.968009 + 0.250914i \(0.919269\pi\)
\(434\) 22.6601 20.8631i 1.08772 1.00146i
\(435\) 0 0
\(436\) −4.18208 19.1647i −0.200285 0.917821i
\(437\) 2.32956i 0.111438i
\(438\) 0 0
\(439\) −36.2996 −1.73249 −0.866243 0.499624i \(-0.833472\pi\)
−0.866243 + 0.499624i \(0.833472\pi\)
\(440\) 0.973914 1.95039i 0.0464295 0.0929810i
\(441\) 0 0
\(442\) −3.10602 2.50133i −0.147738 0.118976i
\(443\) 3.71212i 0.176368i 0.996104 + 0.0881842i \(0.0281064\pi\)
−0.996104 + 0.0881842i \(0.971894\pi\)
\(444\) 0 0
\(445\) −2.98877 −0.141681
\(446\) 25.1748 + 20.2736i 1.19206 + 0.959985i
\(447\) 0 0
\(448\) 18.6168 10.0706i 0.879559 0.475789i
\(449\) −8.56515 −0.404215 −0.202107 0.979363i \(-0.564779\pi\)
−0.202107 + 0.979363i \(0.564779\pi\)
\(450\) 0 0
\(451\) 3.91456 0.184329
\(452\) 4.26847 + 19.5605i 0.200772 + 0.920051i
\(453\) 0 0
\(454\) −19.2402 15.4944i −0.902989 0.727190i
\(455\) 2.19717 14.6678i 0.103005 0.687637i
\(456\) 0 0
\(457\) −14.6705 −0.686259 −0.343129 0.939288i \(-0.611487\pi\)
−0.343129 + 0.939288i \(0.611487\pi\)
\(458\) −11.1971 + 13.9040i −0.523204 + 0.649689i
\(459\) 0 0
\(460\) −0.607518 2.78399i −0.0283257 0.129804i
\(461\) 19.3683i 0.902072i −0.892506 0.451036i \(-0.851055\pi\)
0.892506 0.451036i \(-0.148945\pi\)
\(462\) 0 0
\(463\) 4.34277i 0.201826i 0.994895 + 0.100913i \(0.0321763\pi\)
−0.994895 + 0.100913i \(0.967824\pi\)
\(464\) 18.3125 8.39188i 0.850138 0.389583i
\(465\) 0 0
\(466\) −4.28917 3.45413i −0.198692 0.160009i
\(467\) −15.4501 −0.714943 −0.357472 0.933924i \(-0.616361\pi\)
−0.357472 + 0.933924i \(0.616361\pi\)
\(468\) 0 0
\(469\) 22.7848 + 3.41305i 1.05210 + 0.157600i
\(470\) −4.12433 + 5.12139i −0.190241 + 0.236232i
\(471\) 0 0
\(472\) 13.2559 26.5467i 0.610154 1.22191i
\(473\) 6.98462 0.321153
\(474\) 0 0
\(475\) 1.63506 0.0750217
\(476\) −0.175981 2.65602i −0.00806606 0.121739i
\(477\) 0 0
\(478\) −10.3335 + 12.8316i −0.472644 + 0.586906i
\(479\) −22.4129 −1.02407 −0.512035 0.858964i \(-0.671108\pi\)
−0.512035 + 0.858964i \(0.671108\pi\)
\(480\) 0 0
\(481\) 56.8442i 2.59187i
\(482\) 18.6504 23.1591i 0.849501 1.05487i
\(483\) 0 0
\(484\) 4.43711 + 20.3334i 0.201687 + 0.924244i
\(485\) −15.5818 −0.707533
\(486\) 0 0
\(487\) 14.7901i 0.670202i 0.942182 + 0.335101i \(0.108770\pi\)
−0.942182 + 0.335101i \(0.891230\pi\)
\(488\) −8.41119 4.20008i −0.380757 0.190129i
\(489\) 0 0
\(490\) 8.19579 5.55239i 0.370248 0.250832i
\(491\) 18.0235i 0.813388i 0.913565 + 0.406694i \(0.133318\pi\)
−0.913565 + 0.406694i \(0.866682\pi\)
\(492\) 0 0
\(493\) 2.53329i 0.114094i
\(494\) 8.13018 10.0957i 0.365794 0.454225i
\(495\) 0 0
\(496\) −29.9350 + 13.7179i −1.34412 + 0.615954i
\(497\) −28.3050 4.23995i −1.26965 0.190188i
\(498\) 0 0
\(499\) 13.6272i 0.610036i −0.952347 0.305018i \(-0.901338\pi\)
0.952347 0.305018i \(-0.0986625\pi\)
\(500\) −1.95402 + 0.426402i −0.0873863 + 0.0190693i
\(501\) 0 0
\(502\) −1.50331 1.21063i −0.0670959 0.0540333i
\(503\) −23.8378 −1.06287 −0.531436 0.847098i \(-0.678348\pi\)
−0.531436 + 0.847098i \(0.678348\pi\)
\(504\) 0 0
\(505\) −18.9661 −0.843979
\(506\) −1.20955 0.974067i −0.0537710 0.0433025i
\(507\) 0 0
\(508\) −6.04827 + 1.31984i −0.268348 + 0.0585585i
\(509\) 35.2475i 1.56232i −0.624332 0.781159i \(-0.714629\pi\)
0.624332 0.781159i \(-0.285371\pi\)
\(510\) 0 0
\(511\) −6.00668 0.899773i −0.265720 0.0398036i
\(512\) −22.2560 + 4.08276i −0.983587 + 0.180434i
\(513\) 0 0
\(514\) 3.94026 4.89282i 0.173797 0.215813i
\(515\) 8.23760i 0.362992i
\(516\) 0 0
\(517\) 3.58376i 0.157613i
\(518\) 27.9127 25.6992i 1.22641 1.12916i
\(519\) 0 0
\(520\) −7.08335 + 14.1853i −0.310625 + 0.622066i
\(521\) 5.38270i 0.235820i 0.993024 + 0.117910i \(0.0376195\pi\)
−0.993024 + 0.117910i \(0.962381\pi\)
\(522\) 0 0
\(523\) −0.0967711 −0.00423150 −0.00211575 0.999998i \(-0.500673\pi\)
−0.00211575 + 0.999998i \(0.500673\pi\)
\(524\) −7.46207 34.1954i −0.325982 1.49384i
\(525\) 0 0
\(526\) 4.37156 5.42839i 0.190609 0.236689i
\(527\) 4.14110i 0.180389i
\(528\) 0 0
\(529\) 20.9701 0.911742
\(530\) 0.404306 0.502048i 0.0175619 0.0218076i
\(531\) 0 0
\(532\) 8.63300 0.571999i 0.374288 0.0247993i
\(533\) −28.4708 −1.23321
\(534\) 0 0
\(535\) −11.8042 −0.510339
\(536\) −22.0352 11.0032i −0.951778 0.475265i
\(537\) 0 0
\(538\) 22.1926 27.5577i 0.956790 1.18810i
\(539\) 1.58090 5.15848i 0.0680944 0.222191i
\(540\) 0 0
\(541\) 2.76915 0.119055 0.0595275 0.998227i \(-0.481041\pi\)
0.0595275 + 0.998227i \(0.481041\pi\)
\(542\) 13.3665 + 10.7643i 0.574141 + 0.462364i
\(543\) 0 0
\(544\) −0.699257 + 2.75838i −0.0299804 + 0.118265i
\(545\) 9.80783i 0.420121i
\(546\) 0 0
\(547\) 25.1688i 1.07614i 0.842900 + 0.538071i \(0.180847\pi\)
−0.842900 + 0.538071i \(0.819153\pi\)
\(548\) 6.67497 + 30.5885i 0.285140 + 1.30668i
\(549\) 0 0
\(550\) −0.683673 + 0.848952i −0.0291519 + 0.0361994i
\(551\) 8.23408 0.350784
\(552\) 0 0
\(553\) −6.70717 1.00470i −0.285218 0.0427243i
\(554\) −21.4445 17.2695i −0.911088 0.733712i
\(555\) 0 0
\(556\) −0.482240 2.20990i −0.0204515 0.0937206i
\(557\) 39.1885 1.66047 0.830235 0.557413i \(-0.188206\pi\)
0.830235 + 0.557413i \(0.188206\pi\)
\(558\) 0 0
\(559\) −50.7996 −2.14859
\(560\) −10.1679 + 2.93495i −0.429672 + 0.124024i
\(561\) 0 0
\(562\) −19.5455 15.7403i −0.824479 0.663965i
\(563\) −23.3400 −0.983665 −0.491832 0.870690i \(-0.663673\pi\)
−0.491832 + 0.870690i \(0.663673\pi\)
\(564\) 0 0
\(565\) 10.0104i 0.421142i
\(566\) −32.4865 26.1618i −1.36551 1.09966i
\(567\) 0 0
\(568\) 27.3739 + 13.6690i 1.14858 + 0.573538i
\(569\) 35.0677 1.47011 0.735057 0.678005i \(-0.237155\pi\)
0.735057 + 0.678005i \(0.237155\pi\)
\(570\) 0 0
\(571\) 8.01227i 0.335303i 0.985846 + 0.167651i \(0.0536183\pi\)
−0.985846 + 0.167651i \(0.946382\pi\)
\(572\) 1.84234 + 8.44266i 0.0770323 + 0.353006i
\(573\) 0 0
\(574\) −12.8716 13.9803i −0.537251 0.583525i
\(575\) 1.42475i 0.0594164i
\(576\) 0 0
\(577\) 27.1156i 1.12884i −0.825489 0.564418i \(-0.809100\pi\)
0.825489 0.564418i \(-0.190900\pi\)
\(578\) −18.4460 14.8548i −0.767252 0.617879i
\(579\) 0 0
\(580\) −9.84033 + 2.14734i −0.408598 + 0.0891634i
\(581\) −5.48643 + 36.6262i −0.227615 + 1.51951i
\(582\) 0 0
\(583\) 0.351314i 0.0145499i
\(584\) 5.80909 + 2.90074i 0.240382 + 0.120033i
\(585\) 0 0
\(586\) 17.6321 21.8947i 0.728377 0.904463i
\(587\) −44.6409 −1.84253 −0.921264 0.388939i \(-0.872842\pi\)
−0.921264 + 0.388939i \(0.872842\pi\)
\(588\) 0 0
\(589\) −13.4600 −0.554610
\(590\) −9.30548 + 11.5551i −0.383100 + 0.475715i
\(591\) 0 0
\(592\) −36.8739 + 16.8978i −1.51551 + 0.694494i
\(593\) 42.8848i 1.76107i −0.473984 0.880534i \(-0.657184\pi\)
0.473984 0.880534i \(-0.342816\pi\)
\(594\) 0 0
\(595\) −0.197166 + 1.31624i −0.00808302 + 0.0539605i
\(596\) −9.10980 41.7463i −0.373152 1.70999i
\(597\) 0 0
\(598\) 8.79713 + 7.08445i 0.359741 + 0.289705i
\(599\) 17.8050i 0.727492i −0.931498 0.363746i \(-0.881498\pi\)
0.931498 0.363746i \(-0.118502\pi\)
\(600\) 0 0
\(601\) 7.15463i 0.291843i −0.989296 0.145922i \(-0.953385\pi\)
0.989296 0.145922i \(-0.0466148\pi\)
\(602\) −22.9664 24.9446i −0.936041 1.01666i
\(603\) 0 0
\(604\) −5.53074 + 1.20691i −0.225043 + 0.0491084i
\(605\) 10.4059i 0.423061i
\(606\) 0 0
\(607\) −11.8573 −0.481272 −0.240636 0.970615i \(-0.577356\pi\)
−0.240636 + 0.970615i \(0.577356\pi\)
\(608\) −8.96570 2.27283i −0.363607 0.0921754i
\(609\) 0 0
\(610\) 3.66117 + 2.94839i 0.148236 + 0.119377i
\(611\) 26.0649i 1.05447i
\(612\) 0 0
\(613\) −22.6111 −0.913254 −0.456627 0.889658i \(-0.650943\pi\)
−0.456627 + 0.889658i \(0.650943\pi\)
\(614\) 2.33977 + 1.88425i 0.0944254 + 0.0760421i
\(615\) 0 0
\(616\) −3.31275 + 4.72158i −0.133475 + 0.190238i
\(617\) −18.4097 −0.741146 −0.370573 0.928803i \(-0.620839\pi\)
−0.370573 + 0.928803i \(0.620839\pi\)
\(618\) 0 0
\(619\) 33.4715 1.34533 0.672667 0.739946i \(-0.265149\pi\)
0.672667 + 0.739946i \(0.265149\pi\)
\(620\) 16.0857 3.51019i 0.646017 0.140973i
\(621\) 0 0
\(622\) −11.3307 9.12475i −0.454318 0.365869i
\(623\) 7.82028 + 1.17144i 0.313313 + 0.0469328i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 15.8599 19.6941i 0.633889 0.787133i
\(627\) 0 0
\(628\) 36.7165 8.01221i 1.46515 0.319722i
\(629\) 5.10101i 0.203390i
\(630\) 0 0
\(631\) 43.0583i 1.71412i 0.515213 + 0.857062i \(0.327713\pi\)
−0.515213 + 0.857062i \(0.672287\pi\)
\(632\) 6.48654 + 3.23902i 0.258021 + 0.128841i
\(633\) 0 0
\(634\) 13.6404 + 10.9848i 0.541731 + 0.436264i
\(635\) 3.09530 0.122833
\(636\) 0 0
\(637\) −11.4980 + 37.5180i −0.455568 + 1.48652i
\(638\) −3.44294 + 4.27528i −0.136307 + 0.169260i
\(639\) 0 0
\(640\) 11.3074 + 0.378061i 0.446964 + 0.0149442i
\(641\) 12.3471 0.487681 0.243841 0.969815i \(-0.421593\pi\)
0.243841 + 0.969815i \(0.421593\pi\)
\(642\) 0 0
\(643\) 9.21215 0.363292 0.181646 0.983364i \(-0.441858\pi\)
0.181646 + 0.983364i \(0.441858\pi\)
\(644\) 0.498427 + 7.52260i 0.0196408 + 0.296432i
\(645\) 0 0
\(646\) −0.729574 + 0.905950i −0.0287047 + 0.0356441i
\(647\) −19.8210 −0.779243 −0.389622 0.920975i \(-0.627394\pi\)
−0.389622 + 0.920975i \(0.627394\pi\)
\(648\) 0 0
\(649\) 8.08581i 0.317396i
\(650\) 4.97240 6.17449i 0.195034 0.242183i
\(651\) 0 0
\(652\) −14.4743 + 3.15855i −0.566856 + 0.123698i
\(653\) 19.0538 0.745635 0.372817 0.927905i \(-0.378392\pi\)
0.372817 + 0.927905i \(0.378392\pi\)
\(654\) 0 0
\(655\) 17.5001i 0.683785i
\(656\) 8.46337 + 18.4686i 0.330439 + 0.721076i
\(657\) 0 0
\(658\) 12.7989 11.7839i 0.498952 0.459384i
\(659\) 10.4331i 0.406416i 0.979136 + 0.203208i \(0.0651367\pi\)
−0.979136 + 0.203208i \(0.934863\pi\)
\(660\) 0 0
\(661\) 9.84122i 0.382779i 0.981514 + 0.191389i \(0.0612994\pi\)
−0.981514 + 0.191389i \(0.938701\pi\)
\(662\) 18.8934 23.4609i 0.734314 0.911836i
\(663\) 0 0
\(664\) 17.6875 35.4214i 0.686406 1.37462i
\(665\) −4.27823 0.640859i −0.165903 0.0248514i
\(666\) 0 0
\(667\) 7.17499i 0.277817i
\(668\) −1.26278 5.78676i −0.0488583 0.223896i
\(669\) 0 0
\(670\) 9.59137 + 7.72407i 0.370547 + 0.298407i
\(671\) 2.56195 0.0989029
\(672\) 0 0
\(673\) 5.51471 0.212577 0.106288 0.994335i \(-0.466103\pi\)
0.106288 + 0.994335i \(0.466103\pi\)
\(674\) 0.964641 + 0.776840i 0.0371566 + 0.0299227i
\(675\) 0 0
\(676\) −7.85627 36.0019i −0.302164 1.38469i
\(677\) 44.8711i 1.72454i −0.506451 0.862269i \(-0.669043\pi\)
0.506451 0.862269i \(-0.330957\pi\)
\(678\) 0 0
\(679\) 40.7707 + 6.10726i 1.56464 + 0.234375i
\(680\) 0.635635 1.27294i 0.0243755 0.0488150i
\(681\) 0 0
\(682\) 5.62808 6.98867i 0.215510 0.267610i
\(683\) 34.0718i 1.30372i −0.758338 0.651862i \(-0.773988\pi\)
0.758338 0.651862i \(-0.226012\pi\)
\(684\) 0 0
\(685\) 15.6542i 0.598115i
\(686\) −23.6210 + 11.3158i −0.901854 + 0.432041i
\(687\) 0 0
\(688\) 15.1009 + 32.9529i 0.575717 + 1.25632i
\(689\) 2.55513i 0.0973428i
\(690\) 0 0
\(691\) 0.264224 0.0100515 0.00502577 0.999987i \(-0.498400\pi\)
0.00502577 + 0.999987i \(0.498400\pi\)
\(692\) 29.3522 6.40520i 1.11581 0.243489i
\(693\) 0 0
\(694\) 30.9640 38.4496i 1.17538 1.45953i
\(695\) 1.13095i 0.0428994i
\(696\) 0 0
\(697\) 2.55487 0.0967728
\(698\) 18.7941 23.3376i 0.711368 0.883342i
\(699\) 0 0
\(700\) 5.27993 0.349833i 0.199562 0.0132225i
\(701\) −17.5109 −0.661376 −0.330688 0.943740i \(-0.607281\pi\)
−0.330688 + 0.943740i \(0.607281\pi\)
\(702\) 0 0
\(703\) −16.5800 −0.625328
\(704\) 4.92895 3.70480i 0.185767 0.139630i
\(705\) 0 0
\(706\) −6.82928 + 8.48026i −0.257023 + 0.319159i
\(707\) 49.6258 + 7.43371i 1.86637 + 0.279573i
\(708\) 0 0
\(709\) −13.0797 −0.491219 −0.245610 0.969369i \(-0.578988\pi\)
−0.245610 + 0.969369i \(0.578988\pi\)
\(710\) −11.9151 9.59542i −0.447167 0.360110i
\(711\) 0 0
\(712\) −7.56303 3.77656i −0.283437 0.141532i
\(713\) 11.7287i 0.439245i
\(714\) 0 0
\(715\) 4.32067i 0.161584i
\(716\) −9.43664 + 2.05925i −0.352664 + 0.0769577i
\(717\) 0 0
\(718\) 1.90549 2.36615i 0.0711124 0.0883039i
\(719\) −16.9650 −0.632689 −0.316345 0.948644i \(-0.602456\pi\)
−0.316345 + 0.948644i \(0.602456\pi\)
\(720\) 0 0
\(721\) 3.22871 21.5542i 0.120243 0.802719i
\(722\) 17.9830 + 14.4819i 0.669257 + 0.538962i
\(723\) 0 0
\(724\) −35.5728 + 7.76264i −1.32205 + 0.288496i
\(725\) 5.03595 0.187030
\(726\) 0 0
\(727\) 32.4836 1.20475 0.602375 0.798213i \(-0.294221\pi\)
0.602375 + 0.798213i \(0.294221\pi\)
\(728\) 24.0939 34.3403i 0.892979 1.27274i
\(729\) 0 0
\(730\) −2.52855 2.03627i −0.0935857 0.0753659i
\(731\) 4.55858 0.168605
\(732\) 0 0
\(733\) 35.8223i 1.32313i −0.749890 0.661563i \(-0.769894\pi\)
0.749890 0.661563i \(-0.230106\pi\)
\(734\) 29.4046 + 23.6799i 1.08534 + 0.874043i
\(735\) 0 0
\(736\) 1.98049 7.81251i 0.0730019 0.287973i
\(737\) 6.71167 0.247228
\(738\) 0 0
\(739\) 21.8037i 0.802060i 0.916065 + 0.401030i \(0.131348\pi\)
−0.916065 + 0.401030i \(0.868652\pi\)
\(740\) 19.8144 4.32386i 0.728391 0.158948i
\(741\) 0 0
\(742\) −1.25467 + 1.15517i −0.0460603 + 0.0424076i
\(743\) 23.4618i 0.860731i −0.902655 0.430365i \(-0.858385\pi\)
0.902655 0.430365i \(-0.141615\pi\)
\(744\) 0 0
\(745\) 21.3643i 0.782729i
\(746\) 9.37811 + 7.55233i 0.343357 + 0.276510i
\(747\) 0 0
\(748\) −0.165326 0.757616i −0.00604490 0.0277012i
\(749\) 30.8863 + 4.62662i 1.12856 + 0.169053i
\(750\) 0 0
\(751\) 15.9484i 0.581965i −0.956728 0.290983i \(-0.906018\pi\)
0.956728 0.290983i \(-0.0939822\pi\)
\(752\) −16.9079 + 7.74817i −0.616567 + 0.282547i
\(753\) 0 0
\(754\) 25.0408 31.0944i 0.911931 1.13239i
\(755\) 2.83045 0.103011
\(756\) 0 0
\(757\) 27.9746 1.01675 0.508377 0.861135i \(-0.330246\pi\)
0.508377 + 0.861135i \(0.330246\pi\)
\(758\) −27.6477 + 34.3315i −1.00421 + 1.24698i
\(759\) 0 0
\(760\) 4.13750 + 2.06604i 0.150083 + 0.0749430i
\(761\) 17.5525i 0.636277i 0.948044 + 0.318138i \(0.103058\pi\)
−0.948044 + 0.318138i \(0.896942\pi\)
\(762\) 0 0
\(763\) 3.84416 25.6627i 0.139168 0.929054i
\(764\) 11.0438 2.40996i 0.399550 0.0871892i
\(765\) 0 0
\(766\) 37.1532 + 29.9200i 1.34240 + 1.08105i
\(767\) 58.8087i 2.12346i
\(768\) 0 0
\(769\) 5.74365i 0.207121i 0.994623 + 0.103561i \(0.0330236\pi\)
−0.994623 + 0.103561i \(0.966976\pi\)
\(770\) 2.12162 1.95337i 0.0764577 0.0703945i
\(771\) 0 0
\(772\) −6.86414 31.4554i −0.247046 1.13210i
\(773\) 46.0638i 1.65680i 0.560138 + 0.828399i \(0.310748\pi\)
−0.560138 + 0.828399i \(0.689252\pi\)
\(774\) 0 0
\(775\) −8.23212 −0.295706
\(776\) −39.4295 19.6889i −1.41544 0.706791i
\(777\) 0 0
\(778\) 28.6281 + 23.0546i 1.02637 + 0.826548i
\(779\) 8.30423i 0.297530i
\(780\) 0 0
\(781\) −8.33775 −0.298348
\(782\) −0.789424 0.635734i −0.0282297 0.0227338i
\(783\) 0 0
\(784\) 27.7552 3.69419i 0.991258 0.131935i
\(785\) −18.7903 −0.670654
\(786\) 0 0
\(787\) 26.5373 0.945951 0.472976 0.881075i \(-0.343180\pi\)
0.472976 + 0.881075i \(0.343180\pi\)
\(788\) 5.24356 + 24.0290i 0.186794 + 0.855997i
\(789\) 0 0
\(790\) −2.82342 2.27374i −0.100453 0.0808961i
\(791\) −3.92357 + 26.1929i −0.139506 + 0.931311i
\(792\) 0