Properties

Label 378.2.k.c.215.1
Level $378$
Weight $2$
Character 378.215
Analytic conductor $3.018$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.k (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 215.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 378.215
Dual form 378.2.k.c.269.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(2.00000 - 1.73205i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 1.50000i) q^{5} +(2.00000 - 1.73205i) q^{7} -1.00000i q^{8} +(1.50000 - 0.866025i) q^{10} +(-2.59808 + 0.500000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.73205 + 3.00000i) q^{17} +(6.00000 + 3.46410i) q^{19} -1.73205 q^{20} +(5.19615 + 3.00000i) q^{23} +(1.00000 + 1.73205i) q^{25} +(2.50000 + 0.866025i) q^{28} -9.00000i q^{29} +(3.00000 - 1.73205i) q^{31} +(0.866025 - 0.500000i) q^{32} -3.46410i q^{34} +(0.866025 + 4.50000i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(-3.46410 - 6.00000i) q^{38} +(1.50000 + 0.866025i) q^{40} +3.46410 q^{41} -8.00000 q^{43} +(-3.00000 - 5.19615i) q^{46} +(1.73205 - 3.00000i) q^{47} +(1.00000 - 6.92820i) q^{49} -2.00000i q^{50} +(2.59808 - 1.50000i) q^{53} +(-1.73205 - 2.00000i) q^{56} +(-4.50000 + 7.79423i) q^{58} +(6.06218 + 10.5000i) q^{59} +(3.00000 + 1.73205i) q^{61} -3.46410 q^{62} -1.00000 q^{64} +(-7.00000 - 12.1244i) q^{67} +(-1.73205 + 3.00000i) q^{68} +(1.50000 - 4.33013i) q^{70} +6.00000i q^{71} +(-10.5000 + 6.06218i) q^{73} +(3.46410 - 2.00000i) q^{74} +6.92820i q^{76} +(-5.50000 + 9.52628i) q^{79} +(-0.866025 - 1.50000i) q^{80} +(-3.00000 - 1.73205i) q^{82} -17.3205 q^{83} -6.00000 q^{85} +(6.92820 + 4.00000i) q^{86} +(5.19615 - 9.00000i) q^{89} +6.00000i q^{92} +(-3.00000 + 1.73205i) q^{94} +(-10.3923 + 6.00000i) q^{95} -6.92820i q^{97} +(-4.33013 + 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} + 8 q^{7} + 6 q^{10} - 2 q^{16} + 24 q^{19} + 4 q^{25} + 10 q^{28} + 12 q^{31} - 8 q^{37} + 6 q^{40} - 32 q^{43} - 12 q^{46} + 4 q^{49} - 18 q^{58} + 12 q^{61} - 4 q^{64} - 28 q^{67} + 6 q^{70} - 42 q^{73} - 22 q^{79} - 12 q^{82} - 24 q^{85} - 12 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.866025 + 1.50000i −0.387298 + 0.670820i −0.992085 0.125567i \(-0.959925\pi\)
0.604787 + 0.796387i \(0.293258\pi\)
\(6\) 0 0
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.50000 0.866025i 0.474342 0.273861i
\(11\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −2.59808 + 0.500000i −0.694365 + 0.133631i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.73205 + 3.00000i 0.420084 + 0.727607i 0.995947 0.0899392i \(-0.0286673\pi\)
−0.575863 + 0.817546i \(0.695334\pi\)
\(18\) 0 0
\(19\) 6.00000 + 3.46410i 1.37649 + 0.794719i 0.991736 0.128298i \(-0.0409513\pi\)
0.384759 + 0.923017i \(0.374285\pi\)
\(20\) −1.73205 −0.387298
\(21\) 0 0
\(22\) 0 0
\(23\) 5.19615 + 3.00000i 1.08347 + 0.625543i 0.931831 0.362892i \(-0.118211\pi\)
0.151642 + 0.988436i \(0.451544\pi\)
\(24\) 0 0
\(25\) 1.00000 + 1.73205i 0.200000 + 0.346410i
\(26\) 0 0
\(27\) 0 0
\(28\) 2.50000 + 0.866025i 0.472456 + 0.163663i
\(29\) 9.00000i 1.67126i −0.549294 0.835629i \(-0.685103\pi\)
0.549294 0.835629i \(-0.314897\pi\)
\(30\) 0 0
\(31\) 3.00000 1.73205i 0.538816 0.311086i −0.205783 0.978598i \(-0.565974\pi\)
0.744599 + 0.667512i \(0.232641\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 3.46410i 0.594089i
\(35\) 0.866025 + 4.50000i 0.146385 + 0.760639i
\(36\) 0 0
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) −3.46410 6.00000i −0.561951 0.973329i
\(39\) 0 0
\(40\) 1.50000 + 0.866025i 0.237171 + 0.136931i
\(41\) 3.46410 0.541002 0.270501 0.962720i \(-0.412811\pi\)
0.270501 + 0.962720i \(0.412811\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) 1.73205 3.00000i 0.252646 0.437595i −0.711608 0.702577i \(-0.752033\pi\)
0.964253 + 0.264982i \(0.0853660\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 2.00000i 0.282843i
\(51\) 0 0
\(52\) 0 0
\(53\) 2.59808 1.50000i 0.356873 0.206041i −0.310835 0.950464i \(-0.600609\pi\)
0.667708 + 0.744423i \(0.267275\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.73205 2.00000i −0.231455 0.267261i
\(57\) 0 0
\(58\) −4.50000 + 7.79423i −0.590879 + 1.02343i
\(59\) 6.06218 + 10.5000i 0.789228 + 1.36698i 0.926440 + 0.376442i \(0.122853\pi\)
−0.137212 + 0.990542i \(0.543814\pi\)
\(60\) 0 0
\(61\) 3.00000 + 1.73205i 0.384111 + 0.221766i 0.679605 0.733578i \(-0.262151\pi\)
−0.295495 + 0.955344i \(0.595484\pi\)
\(62\) −3.46410 −0.439941
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −7.00000 12.1244i −0.855186 1.48123i −0.876472 0.481452i \(-0.840109\pi\)
0.0212861 0.999773i \(-0.493224\pi\)
\(68\) −1.73205 + 3.00000i −0.210042 + 0.363803i
\(69\) 0 0
\(70\) 1.50000 4.33013i 0.179284 0.517549i
\(71\) 6.00000i 0.712069i 0.934473 + 0.356034i \(0.115871\pi\)
−0.934473 + 0.356034i \(0.884129\pi\)
\(72\) 0 0
\(73\) −10.5000 + 6.06218i −1.22893 + 0.709524i −0.966807 0.255510i \(-0.917757\pi\)
−0.262126 + 0.965034i \(0.584423\pi\)
\(74\) 3.46410 2.00000i 0.402694 0.232495i
\(75\) 0 0
\(76\) 6.92820i 0.794719i
\(77\) 0 0
\(78\) 0 0
\(79\) −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i \(0.379047\pi\)
−0.989705 + 0.143120i \(0.954286\pi\)
\(80\) −0.866025 1.50000i −0.0968246 0.167705i
\(81\) 0 0
\(82\) −3.00000 1.73205i −0.331295 0.191273i
\(83\) −17.3205 −1.90117 −0.950586 0.310460i \(-0.899517\pi\)
−0.950586 + 0.310460i \(0.899517\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) 6.92820 + 4.00000i 0.747087 + 0.431331i
\(87\) 0 0
\(88\) 0 0
\(89\) 5.19615 9.00000i 0.550791 0.953998i −0.447427 0.894321i \(-0.647659\pi\)
0.998218 0.0596775i \(-0.0190072\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.00000i 0.625543i
\(93\) 0 0
\(94\) −3.00000 + 1.73205i −0.309426 + 0.178647i
\(95\) −10.3923 + 6.00000i −1.06623 + 0.615587i
\(96\) 0 0
\(97\) 6.92820i 0.703452i −0.936103 0.351726i \(-0.885595\pi\)
0.936103 0.351726i \(-0.114405\pi\)
\(98\) −4.33013 + 5.50000i −0.437409 + 0.555584i
\(99\) 0 0
\(100\) −1.00000 + 1.73205i −0.100000 + 0.173205i
\(101\) −2.59808 4.50000i −0.258518 0.447767i 0.707327 0.706887i \(-0.249901\pi\)
−0.965845 + 0.259120i \(0.916568\pi\)
\(102\) 0 0
\(103\) 9.00000 + 5.19615i 0.886796 + 0.511992i 0.872893 0.487911i \(-0.162241\pi\)
0.0139031 + 0.999903i \(0.495574\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −3.00000 −0.291386
\(107\) −2.59808 1.50000i −0.251166 0.145010i 0.369132 0.929377i \(-0.379655\pi\)
−0.620298 + 0.784366i \(0.712988\pi\)
\(108\) 0 0
\(109\) −8.00000 13.8564i −0.766261 1.32720i −0.939577 0.342337i \(-0.888782\pi\)
0.173316 0.984866i \(-0.444552\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.500000 + 2.59808i 0.0472456 + 0.245495i
\(113\) 18.0000i 1.69330i −0.532152 0.846649i \(-0.678617\pi\)
0.532152 0.846649i \(-0.321383\pi\)
\(114\) 0 0
\(115\) −9.00000 + 5.19615i −0.839254 + 0.484544i
\(116\) 7.79423 4.50000i 0.723676 0.417815i
\(117\) 0 0
\(118\) 12.1244i 1.11614i
\(119\) 8.66025 + 3.00000i 0.793884 + 0.275010i
\(120\) 0 0
\(121\) −5.50000 + 9.52628i −0.500000 + 0.866025i
\(122\) −1.73205 3.00000i −0.156813 0.271607i
\(123\) 0 0
\(124\) 3.00000 + 1.73205i 0.269408 + 0.155543i
\(125\) −12.1244 −1.08444
\(126\) 0 0
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −5.19615 + 9.00000i −0.453990 + 0.786334i −0.998630 0.0523366i \(-0.983333\pi\)
0.544640 + 0.838670i \(0.316666\pi\)
\(132\) 0 0
\(133\) 18.0000 3.46410i 1.56080 0.300376i
\(134\) 14.0000i 1.20942i
\(135\) 0 0
\(136\) 3.00000 1.73205i 0.257248 0.148522i
\(137\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) 0 0
\(139\) 10.3923i 0.881464i −0.897639 0.440732i \(-0.854719\pi\)
0.897639 0.440732i \(-0.145281\pi\)
\(140\) −3.46410 + 3.00000i −0.292770 + 0.253546i
\(141\) 0 0
\(142\) 3.00000 5.19615i 0.251754 0.436051i
\(143\) 0 0
\(144\) 0 0
\(145\) 13.5000 + 7.79423i 1.12111 + 0.647275i
\(146\) 12.1244 1.00342
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) −12.9904 7.50000i −1.06421 0.614424i −0.137619 0.990485i \(-0.543945\pi\)
−0.926595 + 0.376061i \(0.877278\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 3.46410 6.00000i 0.280976 0.486664i
\(153\) 0 0
\(154\) 0 0
\(155\) 6.00000i 0.481932i
\(156\) 0 0
\(157\) 9.00000 5.19615i 0.718278 0.414698i −0.0958404 0.995397i \(-0.530554\pi\)
0.814119 + 0.580699i \(0.197221\pi\)
\(158\) 9.52628 5.50000i 0.757870 0.437557i
\(159\) 0 0
\(160\) 1.73205i 0.136931i
\(161\) 15.5885 3.00000i 1.22854 0.236433i
\(162\) 0 0
\(163\) −1.00000 + 1.73205i −0.0783260 + 0.135665i −0.902528 0.430632i \(-0.858291\pi\)
0.824202 + 0.566296i \(0.191624\pi\)
\(164\) 1.73205 + 3.00000i 0.135250 + 0.234261i
\(165\) 0 0
\(166\) 15.0000 + 8.66025i 1.16423 + 0.672166i
\(167\) 17.3205 1.34030 0.670151 0.742225i \(-0.266230\pi\)
0.670151 + 0.742225i \(0.266230\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 5.19615 + 3.00000i 0.398527 + 0.230089i
\(171\) 0 0
\(172\) −4.00000 6.92820i −0.304997 0.528271i
\(173\) 2.59808 4.50000i 0.197528 0.342129i −0.750198 0.661213i \(-0.770042\pi\)
0.947726 + 0.319084i \(0.103375\pi\)
\(174\) 0 0
\(175\) 5.00000 + 1.73205i 0.377964 + 0.130931i
\(176\) 0 0
\(177\) 0 0
\(178\) −9.00000 + 5.19615i −0.674579 + 0.389468i
\(179\) −12.9904 + 7.50000i −0.970947 + 0.560576i −0.899525 0.436870i \(-0.856087\pi\)
−0.0714220 + 0.997446i \(0.522754\pi\)
\(180\) 0 0
\(181\) 17.3205i 1.28742i 0.765268 + 0.643712i \(0.222606\pi\)
−0.765268 + 0.643712i \(0.777394\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) −3.46410 6.00000i −0.254686 0.441129i
\(186\) 0 0
\(187\) 0 0
\(188\) 3.46410 0.252646
\(189\) 0 0
\(190\) 12.0000 0.870572
\(191\) 5.19615 + 3.00000i 0.375980 + 0.217072i 0.676068 0.736839i \(-0.263683\pi\)
−0.300088 + 0.953912i \(0.597016\pi\)
\(192\) 0 0
\(193\) −5.00000 8.66025i −0.359908 0.623379i 0.628037 0.778183i \(-0.283859\pi\)
−0.987945 + 0.154805i \(0.950525\pi\)
\(194\) −3.46410 + 6.00000i −0.248708 + 0.430775i
\(195\) 0 0
\(196\) 6.50000 2.59808i 0.464286 0.185577i
\(197\) 3.00000i 0.213741i −0.994273 0.106871i \(-0.965917\pi\)
0.994273 0.106871i \(-0.0340831\pi\)
\(198\) 0 0
\(199\) 7.50000 4.33013i 0.531661 0.306955i −0.210032 0.977695i \(-0.567357\pi\)
0.741693 + 0.670740i \(0.234023\pi\)
\(200\) 1.73205 1.00000i 0.122474 0.0707107i
\(201\) 0 0
\(202\) 5.19615i 0.365600i
\(203\) −15.5885 18.0000i −1.09410 1.26335i
\(204\) 0 0
\(205\) −3.00000 + 5.19615i −0.209529 + 0.362915i
\(206\) −5.19615 9.00000i −0.362033 0.627060i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 16.0000 1.10149 0.550743 0.834675i \(-0.314345\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) 2.59808 + 1.50000i 0.178437 + 0.103020i
\(213\) 0 0
\(214\) 1.50000 + 2.59808i 0.102538 + 0.177601i
\(215\) 6.92820 12.0000i 0.472500 0.818393i
\(216\) 0 0
\(217\) 3.00000 8.66025i 0.203653 0.587896i
\(218\) 16.0000i 1.08366i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 15.5885i 1.04388i −0.852982 0.521940i \(-0.825208\pi\)
0.852982 0.521940i \(-0.174792\pi\)
\(224\) 0.866025 2.50000i 0.0578638 0.167038i
\(225\) 0 0
\(226\) −9.00000 + 15.5885i −0.598671 + 1.03693i
\(227\) 12.9904 + 22.5000i 0.862202 + 1.49338i 0.869799 + 0.493406i \(0.164248\pi\)
−0.00759708 + 0.999971i \(0.502418\pi\)
\(228\) 0 0
\(229\) −3.00000 1.73205i −0.198246 0.114457i 0.397591 0.917563i \(-0.369846\pi\)
−0.595837 + 0.803105i \(0.703180\pi\)
\(230\) 10.3923 0.685248
\(231\) 0 0
\(232\) −9.00000 −0.590879
\(233\) −25.9808 15.0000i −1.70206 0.982683i −0.943676 0.330870i \(-0.892658\pi\)
−0.758380 0.651813i \(-0.774009\pi\)
\(234\) 0 0
\(235\) 3.00000 + 5.19615i 0.195698 + 0.338960i
\(236\) −6.06218 + 10.5000i −0.394614 + 0.683492i
\(237\) 0 0
\(238\) −6.00000 6.92820i −0.388922 0.449089i
\(239\) 24.0000i 1.55243i −0.630468 0.776215i \(-0.717137\pi\)
0.630468 0.776215i \(-0.282863\pi\)
\(240\) 0 0
\(241\) 1.50000 0.866025i 0.0966235 0.0557856i −0.450910 0.892570i \(-0.648900\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 9.52628 5.50000i 0.612372 0.353553i
\(243\) 0 0
\(244\) 3.46410i 0.221766i
\(245\) 9.52628 + 7.50000i 0.608612 + 0.479157i
\(246\) 0 0
\(247\) 0 0
\(248\) −1.73205 3.00000i −0.109985 0.190500i
\(249\) 0 0
\(250\) 10.5000 + 6.06218i 0.664078 + 0.383406i
\(251\) −8.66025 −0.546630 −0.273315 0.961925i \(-0.588120\pi\)
−0.273315 + 0.961925i \(0.588120\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 6.06218 + 3.50000i 0.380375 + 0.219610i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.3923 + 18.0000i −0.648254 + 1.12281i 0.335285 + 0.942117i \(0.391167\pi\)
−0.983540 + 0.180693i \(0.942166\pi\)
\(258\) 0 0
\(259\) 2.00000 + 10.3923i 0.124274 + 0.645746i
\(260\) 0 0
\(261\) 0 0
\(262\) 9.00000 5.19615i 0.556022 0.321019i
\(263\) −15.5885 + 9.00000i −0.961225 + 0.554964i −0.896550 0.442943i \(-0.853935\pi\)
−0.0646755 + 0.997906i \(0.520601\pi\)
\(264\) 0 0
\(265\) 5.19615i 0.319197i
\(266\) −17.3205 6.00000i −1.06199 0.367884i
\(267\) 0 0
\(268\) 7.00000 12.1244i 0.427593 0.740613i
\(269\) 0.866025 + 1.50000i 0.0528025 + 0.0914566i 0.891219 0.453574i \(-0.149851\pi\)
−0.838416 + 0.545031i \(0.816518\pi\)
\(270\) 0 0
\(271\) 10.5000 + 6.06218i 0.637830 + 0.368251i 0.783778 0.621041i \(-0.213290\pi\)
−0.145948 + 0.989292i \(0.546623\pi\)
\(272\) −3.46410 −0.210042
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) −5.19615 + 9.00000i −0.311645 + 0.539784i
\(279\) 0 0
\(280\) 4.50000 0.866025i 0.268926 0.0517549i
\(281\) 18.0000i 1.07379i 0.843649 + 0.536895i \(0.180403\pi\)
−0.843649 + 0.536895i \(0.819597\pi\)
\(282\) 0 0
\(283\) 6.00000 3.46410i 0.356663 0.205919i −0.310953 0.950425i \(-0.600648\pi\)
0.667616 + 0.744506i \(0.267315\pi\)
\(284\) −5.19615 + 3.00000i −0.308335 + 0.178017i
\(285\) 0 0
\(286\) 0 0
\(287\) 6.92820 6.00000i 0.408959 0.354169i
\(288\) 0 0
\(289\) 2.50000 4.33013i 0.147059 0.254713i
\(290\) −7.79423 13.5000i −0.457693 0.792747i
\(291\) 0 0
\(292\) −10.5000 6.06218i −0.614466 0.354762i
\(293\) 29.4449 1.72019 0.860094 0.510136i \(-0.170405\pi\)
0.860094 + 0.510136i \(0.170405\pi\)
\(294\) 0 0
\(295\) −21.0000 −1.22267
\(296\) 3.46410 + 2.00000i 0.201347 + 0.116248i
\(297\) 0 0
\(298\) 7.50000 + 12.9904i 0.434463 + 0.752513i
\(299\) 0 0
\(300\) 0 0
\(301\) −16.0000 + 13.8564i −0.922225 + 0.798670i
\(302\) 8.00000i 0.460348i
\(303\) 0 0
\(304\) −6.00000 + 3.46410i −0.344124 + 0.198680i
\(305\) −5.19615 + 3.00000i −0.297531 + 0.171780i
\(306\) 0 0
\(307\) 6.92820i 0.395413i −0.980261 0.197707i \(-0.936651\pi\)
0.980261 0.197707i \(-0.0633494\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 3.00000 5.19615i 0.170389 0.295122i
\(311\) 6.92820 + 12.0000i 0.392862 + 0.680458i 0.992826 0.119570i \(-0.0381515\pi\)
−0.599963 + 0.800027i \(0.704818\pi\)
\(312\) 0 0
\(313\) −19.5000 11.2583i −1.10221 0.636358i −0.165406 0.986226i \(-0.552893\pi\)
−0.936799 + 0.349867i \(0.886227\pi\)
\(314\) −10.3923 −0.586472
\(315\) 0 0
\(316\) −11.0000 −0.618798
\(317\) −5.19615 3.00000i −0.291845 0.168497i 0.346929 0.937892i \(-0.387225\pi\)
−0.638774 + 0.769395i \(0.720558\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.866025 1.50000i 0.0484123 0.0838525i
\(321\) 0 0
\(322\) −15.0000 5.19615i −0.835917 0.289570i
\(323\) 24.0000i 1.33540i
\(324\) 0 0
\(325\) 0 0
\(326\) 1.73205 1.00000i 0.0959294 0.0553849i
\(327\) 0 0
\(328\) 3.46410i 0.191273i
\(329\) −1.73205 9.00000i −0.0954911 0.496186i
\(330\) 0 0
\(331\) −5.00000 + 8.66025i −0.274825 + 0.476011i −0.970091 0.242742i \(-0.921953\pi\)
0.695266 + 0.718752i \(0.255287\pi\)
\(332\) −8.66025 15.0000i −0.475293 0.823232i
\(333\) 0 0
\(334\) −15.0000 8.66025i −0.820763 0.473868i
\(335\) 24.2487 1.32485
\(336\) 0 0
\(337\) −23.0000 −1.25289 −0.626445 0.779466i \(-0.715491\pi\)
−0.626445 + 0.779466i \(0.715491\pi\)
\(338\) −11.2583 6.50000i −0.612372 0.353553i
\(339\) 0 0
\(340\) −3.00000 5.19615i −0.162698 0.281801i
\(341\) 0 0
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 8.00000i 0.431331i
\(345\) 0 0
\(346\) −4.50000 + 2.59808i −0.241921 + 0.139673i
\(347\) −28.5788 + 16.5000i −1.53419 + 0.885766i −0.535031 + 0.844833i \(0.679700\pi\)
−0.999162 + 0.0409337i \(0.986967\pi\)
\(348\) 0 0
\(349\) 3.46410i 0.185429i −0.995693 0.0927146i \(-0.970446\pi\)
0.995693 0.0927146i \(-0.0295544\pi\)
\(350\) −3.46410 4.00000i −0.185164 0.213809i
\(351\) 0 0
\(352\) 0 0
\(353\) 1.73205 + 3.00000i 0.0921878 + 0.159674i 0.908431 0.418034i \(-0.137281\pi\)
−0.816244 + 0.577708i \(0.803947\pi\)
\(354\) 0 0
\(355\) −9.00000 5.19615i −0.477670 0.275783i
\(356\) 10.3923 0.550791
\(357\) 0 0
\(358\) 15.0000 0.792775
\(359\) 20.7846 + 12.0000i 1.09697 + 0.633336i 0.935423 0.353529i \(-0.115019\pi\)
0.161546 + 0.986865i \(0.448352\pi\)
\(360\) 0 0
\(361\) 14.5000 + 25.1147i 0.763158 + 1.32183i
\(362\) 8.66025 15.0000i 0.455173 0.788382i
\(363\) 0 0
\(364\) 0 0
\(365\) 21.0000i 1.09919i
\(366\) 0 0
\(367\) −7.50000 + 4.33013i −0.391497 + 0.226031i −0.682808 0.730597i \(-0.739242\pi\)
0.291312 + 0.956628i \(0.405908\pi\)
\(368\) −5.19615 + 3.00000i −0.270868 + 0.156386i
\(369\) 0 0
\(370\) 6.92820i 0.360180i
\(371\) 2.59808 7.50000i 0.134885 0.389381i
\(372\) 0 0
\(373\) −7.00000 + 12.1244i −0.362446 + 0.627775i −0.988363 0.152115i \(-0.951392\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 1.73205i −0.154713 0.0893237i
\(377\) 0 0
\(378\) 0 0
\(379\) −14.0000 −0.719132 −0.359566 0.933120i \(-0.617075\pi\)
−0.359566 + 0.933120i \(0.617075\pi\)
\(380\) −10.3923 6.00000i −0.533114 0.307794i
\(381\) 0 0
\(382\) −3.00000 5.19615i −0.153493 0.265858i
\(383\) 8.66025 15.0000i 0.442518 0.766464i −0.555357 0.831612i \(-0.687419\pi\)
0.997876 + 0.0651476i \(0.0207518\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.0000i 0.508987i
\(387\) 0 0
\(388\) 6.00000 3.46410i 0.304604 0.175863i
\(389\) 18.1865 10.5000i 0.922094 0.532371i 0.0377914 0.999286i \(-0.487968\pi\)
0.884302 + 0.466915i \(0.154634\pi\)
\(390\) 0 0
\(391\) 20.7846i 1.05112i
\(392\) −6.92820 1.00000i −0.349927 0.0505076i
\(393\) 0 0
\(394\) −1.50000 + 2.59808i −0.0755689 + 0.130889i
\(395\) −9.52628 16.5000i −0.479319 0.830205i
\(396\) 0 0
\(397\) −24.0000 13.8564i −1.20453 0.695433i −0.242967 0.970034i \(-0.578121\pi\)
−0.961558 + 0.274601i \(0.911454\pi\)
\(398\) −8.66025 −0.434099
\(399\) 0 0
\(400\) −2.00000 −0.100000
\(401\) 5.19615 + 3.00000i 0.259483 + 0.149813i 0.624099 0.781345i \(-0.285466\pi\)
−0.364615 + 0.931158i \(0.618800\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 2.59808 4.50000i 0.129259 0.223883i
\(405\) 0 0
\(406\) 4.50000 + 23.3827i 0.223331 + 1.16046i
\(407\) 0 0
\(408\) 0 0
\(409\) −13.5000 + 7.79423i −0.667532 + 0.385400i −0.795141 0.606425i \(-0.792603\pi\)
0.127609 + 0.991825i \(0.459270\pi\)
\(410\) 5.19615 3.00000i 0.256620 0.148159i
\(411\) 0 0
\(412\) 10.3923i 0.511992i
\(413\) 30.3109 + 10.5000i 1.49150 + 0.516671i
\(414\) 0 0
\(415\) 15.0000 25.9808i 0.736321 1.27535i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.46410 −0.169232 −0.0846162 0.996414i \(-0.526966\pi\)
−0.0846162 + 0.996414i \(0.526966\pi\)
\(420\) 0 0
\(421\) 32.0000 1.55958 0.779792 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) −13.8564 8.00000i −0.674519 0.389434i
\(423\) 0 0
\(424\) −1.50000 2.59808i −0.0728464 0.126174i
\(425\) −3.46410 + 6.00000i −0.168034 + 0.291043i
\(426\) 0 0
\(427\) 9.00000 1.73205i 0.435541 0.0838198i
\(428\) 3.00000i 0.145010i
\(429\) 0 0
\(430\) −12.0000 + 6.92820i −0.578691 + 0.334108i
\(431\) 31.1769 18.0000i 1.50174 0.867029i 0.501741 0.865018i \(-0.332693\pi\)
0.999998 0.00201168i \(-0.000640338\pi\)
\(432\) 0 0
\(433\) 1.73205i 0.0832370i 0.999134 + 0.0416185i \(0.0132514\pi\)
−0.999134 + 0.0416185i \(0.986749\pi\)
\(434\) −6.92820 + 6.00000i −0.332564 + 0.288009i
\(435\) 0 0
\(436\) 8.00000 13.8564i 0.383131 0.663602i
\(437\) 20.7846 + 36.0000i 0.994263 + 1.72211i
\(438\) 0 0
\(439\) −27.0000 15.5885i −1.28864 0.743996i −0.310228 0.950662i \(-0.600405\pi\)
−0.978412 + 0.206666i \(0.933739\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −7.79423 4.50000i −0.370315 0.213801i 0.303281 0.952901i \(-0.401918\pi\)
−0.673596 + 0.739100i \(0.735251\pi\)
\(444\) 0 0
\(445\) 9.00000 + 15.5885i 0.426641 + 0.738964i
\(446\) −7.79423 + 13.5000i −0.369067 + 0.639244i
\(447\) 0 0
\(448\) −2.00000 + 1.73205i −0.0944911 + 0.0818317i
\(449\) 6.00000i 0.283158i 0.989927 + 0.141579i \(0.0452178\pi\)
−0.989927 + 0.141579i \(0.954782\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 15.5885 9.00000i 0.733219 0.423324i
\(453\) 0 0
\(454\) 25.9808i 1.21934i
\(455\) 0 0
\(456\) 0 0
\(457\) 20.5000 35.5070i 0.958950 1.66095i 0.233890 0.972263i \(-0.424854\pi\)
0.725059 0.688686i \(-0.241812\pi\)
\(458\) 1.73205 + 3.00000i 0.0809334 + 0.140181i
\(459\) 0 0
\(460\) −9.00000 5.19615i −0.419627 0.242272i
\(461\) −22.5167 −1.04871 −0.524353 0.851501i \(-0.675693\pi\)
−0.524353 + 0.851501i \(0.675693\pi\)
\(462\) 0 0
\(463\) 23.0000 1.06890 0.534450 0.845200i \(-0.320519\pi\)
0.534450 + 0.845200i \(0.320519\pi\)
\(464\) 7.79423 + 4.50000i 0.361838 + 0.208907i
\(465\) 0 0
\(466\) 15.0000 + 25.9808i 0.694862 + 1.20354i
\(467\) 2.59808 4.50000i 0.120225 0.208235i −0.799632 0.600491i \(-0.794972\pi\)
0.919856 + 0.392256i \(0.128305\pi\)
\(468\) 0 0
\(469\) −35.0000 12.1244i −1.61615 0.559851i
\(470\) 6.00000i 0.276759i
\(471\) 0 0
\(472\) 10.5000 6.06218i 0.483302 0.279034i
\(473\) 0 0
\(474\) 0 0
\(475\) 13.8564i 0.635776i
\(476\) 1.73205 + 9.00000i 0.0793884 + 0.412514i
\(477\) 0 0
\(478\) −12.0000 + 20.7846i −0.548867 + 0.950666i
\(479\) −6.92820 12.0000i −0.316558 0.548294i 0.663210 0.748434i \(-0.269194\pi\)
−0.979767 + 0.200140i \(0.935860\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.73205 −0.0788928
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 10.3923 + 6.00000i 0.471890 + 0.272446i
\(486\) 0 0
\(487\) −0.500000 0.866025i −0.0226572 0.0392434i 0.854475 0.519493i \(-0.173879\pi\)
−0.877132 + 0.480250i \(0.840546\pi\)
\(488\) 1.73205 3.00000i 0.0784063 0.135804i
\(489\) 0 0
\(490\) −4.50000 11.2583i −0.203289 0.508600i
\(491\) 3.00000i 0.135388i 0.997706 + 0.0676941i \(0.0215642\pi\)
−0.997706 + 0.0676941i \(0.978436\pi\)
\(492\) 0 0
\(493\) 27.0000 15.5885i 1.21602 0.702069i
\(494\) 0 0
\(495\) 0 0
\(496\) 3.46410i 0.155543i
\(497\) 10.3923 + 12.0000i 0.466159 + 0.538274i
\(498\) 0 0
\(499\) 7.00000 12.1244i 0.313363 0.542761i −0.665725 0.746197i \(-0.731878\pi\)
0.979088 + 0.203436i \(0.0652110\pi\)
\(500\) −6.06218 10.5000i −0.271109 0.469574i
\(501\) 0 0
\(502\) 7.50000 + 4.33013i 0.334741 + 0.193263i
\(503\) −27.7128 −1.23565 −0.617827 0.786314i \(-0.711987\pi\)
−0.617827 + 0.786314i \(0.711987\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) 0 0
\(507\) 0 0
\(508\) −3.50000 6.06218i −0.155287 0.268966i
\(509\) −17.3205 + 30.0000i −0.767718 + 1.32973i 0.171080 + 0.985257i \(0.445274\pi\)
−0.938798 + 0.344469i \(0.888059\pi\)
\(510\) 0 0
\(511\) −10.5000 + 30.3109i −0.464493 + 1.34087i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 18.0000 10.3923i 0.793946 0.458385i
\(515\) −15.5885 + 9.00000i −0.686909 + 0.396587i
\(516\) 0 0
\(517\) 0 0
\(518\) 3.46410 10.0000i 0.152204 0.439375i
\(519\) 0 0
\(520\) 0 0
\(521\) −1.73205 3.00000i −0.0758825 0.131432i 0.825587 0.564275i \(-0.190844\pi\)
−0.901470 + 0.432842i \(0.857511\pi\)
\(522\) 0 0
\(523\) 18.0000 + 10.3923i 0.787085 + 0.454424i 0.838935 0.544231i \(-0.183179\pi\)
−0.0518503 + 0.998655i \(0.516512\pi\)
\(524\) −10.3923 −0.453990
\(525\) 0 0
\(526\) 18.0000 0.784837
\(527\) 10.3923 + 6.00000i 0.452696 + 0.261364i
\(528\) 0 0
\(529\) 6.50000 + 11.2583i 0.282609 + 0.489493i
\(530\) 2.59808 4.50000i 0.112853 0.195468i
\(531\) 0 0
\(532\) 12.0000 + 13.8564i 0.520266 + 0.600751i
\(533\) 0 0
\(534\) 0 0
\(535\) 4.50000 2.59808i 0.194552 0.112325i
\(536\) −12.1244 + 7.00000i −0.523692 + 0.302354i
\(537\) 0 0
\(538\) 1.73205i 0.0746740i
\(539\) 0 0
\(540\) 0 0
\(541\) 17.0000 29.4449i 0.730887 1.26593i −0.225617 0.974216i \(-0.572440\pi\)
0.956504 0.291718i \(-0.0942267\pi\)
\(542\) −6.06218 10.5000i −0.260393 0.451014i
\(543\) 0 0
\(544\) 3.00000 + 1.73205i 0.128624 + 0.0742611i
\(545\) 27.7128 1.18709
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 31.1769 54.0000i 1.32818 2.30048i
\(552\) 0 0
\(553\) 5.50000 + 28.5788i 0.233884 + 1.21530i
\(554\) 8.00000i 0.339887i
\(555\) 0 0
\(556\) 9.00000 5.19615i 0.381685 0.220366i
\(557\) −15.5885 + 9.00000i −0.660504 + 0.381342i −0.792469 0.609912i \(-0.791205\pi\)
0.131965 + 0.991254i \(0.457871\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −4.33013 1.50000i −0.182981 0.0633866i
\(561\) 0 0
\(562\) 9.00000 15.5885i 0.379642 0.657559i
\(563\) −2.59808 4.50000i −0.109496 0.189652i 0.806070 0.591820i \(-0.201590\pi\)
−0.915566 + 0.402167i \(0.868257\pi\)
\(564\) 0 0
\(565\) 27.0000 + 15.5885i 1.13590 + 0.655811i
\(566\) −6.92820 −0.291214
\(567\) 0 0
\(568\) 6.00000 0.251754
\(569\) −36.3731 21.0000i −1.52484 0.880366i −0.999567 0.0294311i \(-0.990630\pi\)
−0.525271 0.850935i \(-0.676036\pi\)
\(570\) 0 0
\(571\) 20.0000 + 34.6410i 0.836974 + 1.44968i 0.892413 + 0.451219i \(0.149011\pi\)
−0.0554391 + 0.998462i \(0.517656\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −9.00000 + 1.73205i −0.375653 + 0.0722944i
\(575\) 12.0000i 0.500435i
\(576\) 0 0
\(577\) −13.5000 + 7.79423i −0.562012 + 0.324478i −0.753953 0.656929i \(-0.771855\pi\)
0.191940 + 0.981407i \(0.438522\pi\)
\(578\) −4.33013 + 2.50000i −0.180110 + 0.103986i
\(579\) 0 0
\(580\) 15.5885i 0.647275i
\(581\) −34.6410 + 30.0000i −1.43715 + 1.24461i
\(582\) 0 0
\(583\) 0 0
\(584\) 6.06218 + 10.5000i 0.250855 + 0.434493i
\(585\) 0 0
\(586\) −25.5000 14.7224i −1.05340 0.608178i
\(587\) −36.3731 −1.50128 −0.750639 0.660713i \(-0.770254\pi\)
−0.750639 + 0.660713i \(0.770254\pi\)
\(588\) 0 0
\(589\) 24.0000 0.988903
\(590\) 18.1865 + 10.5000i 0.748728 + 0.432278i
\(591\) 0 0
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) −12.1244 + 21.0000i −0.497888 + 0.862367i −0.999997 0.00243746i \(-0.999224\pi\)
0.502109 + 0.864804i \(0.332557\pi\)
\(594\) 0 0
\(595\) −12.0000 + 10.3923i −0.491952 + 0.426043i
\(596\) 15.0000i 0.614424i
\(597\) 0 0
\(598\) 0 0
\(599\) 20.7846 12.0000i 0.849236 0.490307i −0.0111569 0.999938i \(-0.503551\pi\)
0.860393 + 0.509631i \(0.170218\pi\)
\(600\) 0 0
\(601\) 1.73205i 0.0706518i −0.999376 0.0353259i \(-0.988753\pi\)
0.999376 0.0353259i \(-0.0112469\pi\)
\(602\) 20.7846 4.00000i 0.847117 0.163028i
\(603\) 0 0
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) −9.52628 16.5000i −0.387298 0.670820i
\(606\) 0 0
\(607\) −28.5000 16.4545i −1.15678 0.667867i −0.206249 0.978499i \(-0.566126\pi\)
−0.950530 + 0.310633i \(0.899459\pi\)
\(608\) 6.92820 0.280976
\(609\) 0 0
\(610\) 6.00000 0.242933
\(611\) 0 0
\(612\) 0 0
\(613\) −4.00000 6.92820i −0.161558 0.279827i 0.773869 0.633345i \(-0.218319\pi\)
−0.935428 + 0.353518i \(0.884985\pi\)
\(614\) −3.46410 + 6.00000i −0.139800 + 0.242140i
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000i 0.241551i −0.992680 0.120775i \(-0.961462\pi\)
0.992680 0.120775i \(-0.0385381\pi\)
\(618\) 0 0
\(619\) 18.0000 10.3923i 0.723481 0.417702i −0.0925515 0.995708i \(-0.529502\pi\)
0.816033 + 0.578006i \(0.196169\pi\)
\(620\) −5.19615 + 3.00000i −0.208683 + 0.120483i
\(621\) 0 0
\(622\) 13.8564i 0.555591i
\(623\) −5.19615 27.0000i −0.208179 1.08173i
\(624\) 0 0
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 11.2583 + 19.5000i 0.449973 + 0.779377i
\(627\) 0 0
\(628\) 9.00000 + 5.19615i 0.359139 + 0.207349i
\(629\) −13.8564 −0.552491
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 9.52628 + 5.50000i 0.378935 + 0.218778i
\(633\) 0 0
\(634\) 3.00000 + 5.19615i 0.119145 + 0.206366i
\(635\) 6.06218 10.5000i 0.240570 0.416680i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −1.50000 + 0.866025i −0.0592927 + 0.0342327i
\(641\) 10.3923 6.00000i 0.410471 0.236986i −0.280521 0.959848i \(-0.590507\pi\)
0.690992 + 0.722862i \(0.257174\pi\)
\(642\) 0 0
\(643\) 27.7128i 1.09289i 0.837496 + 0.546443i \(0.184019\pi\)
−0.837496 + 0.546443i \(0.815981\pi\)
\(644\) 10.3923 + 12.0000i 0.409514 + 0.472866i
\(645\) 0 0
\(646\) 12.0000 20.7846i 0.472134 0.817760i
\(647\) 5.19615 + 9.00000i 0.204282 + 0.353827i 0.949904 0.312543i \(-0.101181\pi\)
−0.745622 + 0.666369i \(0.767847\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −2.00000 −0.0783260
\(653\) 12.9904 + 7.50000i 0.508353 + 0.293498i 0.732156 0.681137i \(-0.238514\pi\)
−0.223803 + 0.974634i \(0.571847\pi\)
\(654\) 0 0
\(655\) −9.00000 15.5885i −0.351659 0.609091i
\(656\) −1.73205 + 3.00000i −0.0676252 + 0.117130i
\(657\) 0 0
\(658\) −3.00000 + 8.66025i −0.116952 + 0.337612i
\(659\) 27.0000i 1.05177i −0.850555 0.525885i \(-0.823734\pi\)
0.850555 0.525885i \(-0.176266\pi\)
\(660\) 0 0
\(661\) −12.0000 + 6.92820i −0.466746 + 0.269476i −0.714877 0.699251i \(-0.753517\pi\)
0.248131 + 0.968727i \(0.420184\pi\)
\(662\) 8.66025 5.00000i 0.336590 0.194331i
\(663\) 0 0
\(664\) 17.3205i 0.672166i
\(665\) −10.3923 + 30.0000i −0.402996 + 1.16335i
\(666\) 0 0
\(667\) 27.0000 46.7654i 1.04544 1.81076i
\(668\) 8.66025 + 15.0000i 0.335075 + 0.580367i
\(669\) 0 0
\(670\) −21.0000 12.1244i −0.811301 0.468405i
\(671\) 0 0
\(672\) 0 0
\(673\) −5.00000 −0.192736 −0.0963679 0.995346i \(-0.530723\pi\)
−0.0963679 + 0.995346i \(0.530723\pi\)
\(674\) 19.9186 + 11.5000i 0.767235 + 0.442963i
\(675\) 0 0
\(676\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(677\) −12.9904 + 22.5000i −0.499261 + 0.864745i −1.00000 0.000853228i \(-0.999728\pi\)
0.500739 + 0.865598i \(0.333062\pi\)
\(678\) 0 0
\(679\) −12.0000 13.8564i −0.460518 0.531760i
\(680\) 6.00000i 0.230089i
\(681\) 0 0
\(682\) 0 0
\(683\) −7.79423 + 4.50000i −0.298238 + 0.172188i −0.641651 0.766997i \(-0.721750\pi\)
0.343413 + 0.939184i \(0.388417\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.866025 + 18.5000i 0.0330650 + 0.706333i
\(687\) 0 0
\(688\) 4.00000 6.92820i 0.152499 0.264135i
\(689\) 0 0
\(690\) 0 0
\(691\) −24.0000 13.8564i −0.913003 0.527123i −0.0316069 0.999500i \(-0.510062\pi\)
−0.881396 + 0.472378i \(0.843396\pi\)
\(692\) 5.19615 0.197528
\(693\) 0 0
\(694\) 33.0000 1.25266
\(695\) 15.5885 + 9.00000i 0.591304 + 0.341389i
\(696\) 0 0
\(697\) 6.00000 + 10.3923i 0.227266 + 0.393637i
\(698\) −1.73205 + 3.00000i −0.0655591 + 0.113552i
\(699\) 0 0
\(700\) 1.00000 + 5.19615i 0.0377964 + 0.196396i
\(701\) 27.0000i 1.01978i −0.860241 0.509888i \(-0.829687\pi\)
0.860241 0.509888i \(-0.170313\pi\)
\(702\) 0 0
\(703\) −24.0000 + 13.8564i −0.905177 + 0.522604i
\(704\) 0 0
\(705\) 0 0
\(706\) 3.46410i 0.130373i
\(707\) −12.9904 4.50000i −0.488554 0.169240i
\(708\) 0 0
\(709\) −14.0000 + 24.2487i −0.525781 + 0.910679i 0.473768 + 0.880650i \(0.342894\pi\)
−0.999549 + 0.0300298i \(0.990440\pi\)
\(710\) 5.19615 + 9.00000i 0.195008 + 0.337764i
\(711\) 0 0
\(712\) −9.00000 5.19615i −0.337289 0.194734i
\(713\) 20.7846 0.778390
\(714\) 0 0
\(715\) 0 0
\(716\) −12.9904 7.50000i −0.485473 0.280288i
\(717\) 0 0
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) 24.2487 42.0000i 0.904324 1.56634i 0.0825027 0.996591i \(-0.473709\pi\)
0.821822 0.569745i \(-0.192958\pi\)
\(720\) 0 0
\(721\) 27.0000 5.19615i 1.00553 0.193515i
\(722\) 29.0000i 1.07927i
\(723\) 0 0
\(724\) −15.0000 + 8.66025i −0.557471 + 0.321856i
\(725\) 15.5885 9.00000i 0.578941 0.334252i
\(726\) 0 0
\(727\) 12.1244i 0.449667i 0.974397 + 0.224834i \(0.0721839\pi\)
−0.974397 + 0.224834i \(0.927816\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −10.5000 + 18.1865i −0.388622 + 0.673114i
\(731\) −13.8564 24.0000i −0.512498 0.887672i
\(732\) 0 0
\(733\) −6.00000 3.46410i −0.221615 0.127950i 0.385083 0.922882i \(-0.374173\pi\)
−0.606698 + 0.794933i \(0.707506\pi\)
\(734\) 8.66025 0.319656
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) 0 0
\(739\) 5.00000 + 8.66025i 0.183928 + 0.318573i 0.943215 0.332184i \(-0.107785\pi\)
−0.759287 + 0.650756i \(0.774452\pi\)
\(740\) 3.46410 6.00000i 0.127343 0.220564i
\(741\) 0 0
\(742\) −6.00000 + 5.19615i −0.220267 + 0.190757i
\(743\) 36.0000i 1.32071i −0.750953 0.660356i \(-0.770405\pi\)
0.750953 0.660356i \(-0.229595\pi\)
\(744\) 0 0
\(745\) 22.5000 12.9904i 0.824336 0.475931i
\(746\) 12.1244 7.00000i 0.443904 0.256288i
\(747\) 0 0
\(748\) 0 0
\(749\) −7.79423 + 1.50000i −0.284795 + 0.0548088i
\(750\) 0 0
\(751\) −3.50000 + 6.06218i −0.127717 + 0.221212i −0.922792 0.385299i \(-0.874098\pi\)
0.795075 + 0.606511i \(0.207432\pi\)
\(752\) 1.73205 + 3.00000i 0.0631614 + 0.109399i
\(753\) 0 0
\(754\) 0 0
\(755\) −13.8564 −0.504286
\(756\) 0 0
\(757\) −38.0000 −1.38113 −0.690567 0.723269i \(-0.742639\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) 12.1244 + 7.00000i 0.440376 + 0.254251i
\(759\) 0 0
\(760\) 6.00000 + 10.3923i 0.217643 + 0.376969i
\(761\) −17.3205 + 30.0000i −0.627868 + 1.08750i 0.360111 + 0.932910i \(0.382739\pi\)
−0.987979 + 0.154590i \(0.950594\pi\)
\(762\) 0 0
\(763\) −40.0000 13.8564i −1.44810 0.501636i
\(764\) 6.00000i 0.217072i
\(765\) 0 0
\(766\) −15.0000 + 8.66025i −0.541972 + 0.312908i
\(767\) 0 0
\(768\) 0 0
\(769\) 48.4974i 1.74886i −0.485150 0.874431i \(-0.661235\pi\)
0.485150 0.874431i \(-0.338765\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 5.00000 8.66025i 0.179954 0.311689i
\(773\) 6.92820 + 12.0000i 0.249190 + 0.431610i 0.963301 0.268422i \(-0.0865023\pi\)
−0.714111 + 0.700032i \(0.753169\pi\)
\(774\) 0 0
\(775\) 6.00000 + 3.46410i 0.215526 + 0.124434i
\(776\) −6.92820 −0.248708
\(777\) 0 0
\(778\) −21.0000 −0.752886
\(779\) 20.7846 + 12.0000i 0.744686 + 0.429945i
\(780\) 0 0
\(781\) 0 0
\(782\) 10.3923 18.0000i 0.371628 0.643679i
\(783\) 0 0
\(784\) 5.50000 + 4.33013i 0.196429 + 0.154647i
\(785\) 18.0000i 0.642448i
\(786\) 0 0
\(787\) 3.00000 1.73205i 0.106938 0.0617409i −0.445577 0.895244i \(-0.647001\pi\)
0.552515 + 0.833503i \(0.313668\pi\)
\(788\) 2.59808 1.50000i 0.0925526 0.0534353i
\(789\) 0 0
\(790\) 19.0526i 0.677860i
\(791\) −31.1769 36.0000i −1.10852