Properties

Label 912.2.q.k.49.3
Level $912$
Weight $2$
Character 912.49
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 456)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.3
Root \(-0.766044 - 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 912.49
Dual form 912.2.q.k.577.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(1.87939 - 3.25519i) q^{5} -4.75877 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(1.87939 - 3.25519i) q^{5} -4.75877 q^{7} +(-0.500000 - 0.866025i) q^{9} +4.36959 q^{11} +(-0.500000 - 0.866025i) q^{13} +(1.87939 + 3.25519i) q^{15} +(-3.06418 + 5.30731i) q^{17} +(-0.694593 - 4.30320i) q^{19} +(2.37939 - 4.12122i) q^{21} +(-1.87939 - 3.25519i) q^{23} +(-4.56418 - 7.90539i) q^{25} +1.00000 q^{27} +(-2.69459 - 4.66717i) q^{29} -7.36959 q^{31} +(-2.18479 + 3.78417i) q^{33} +(-8.94356 + 15.4907i) q^{35} -7.12836 q^{37} +1.00000 q^{39} +(1.75877 - 3.04628i) q^{41} +(-0.379385 + 0.657115i) q^{43} -3.75877 q^{45} +(-3.00000 - 5.19615i) q^{47} +15.6459 q^{49} +(-3.06418 - 5.30731i) q^{51} +(-2.57398 - 4.45826i) q^{53} +(8.21213 - 14.2238i) q^{55} +(4.07398 + 1.55007i) q^{57} +(4.63816 - 8.03352i) q^{59} +(4.25877 + 7.37641i) q^{61} +(2.37939 + 4.12122i) q^{63} -3.75877 q^{65} +(0.684793 + 1.18610i) q^{67} +3.75877 q^{69} +(-5.82295 + 10.0856i) q^{71} +(-2.25877 + 3.91231i) q^{73} +9.12836 q^{75} -20.7939 q^{77} +(7.07398 - 12.2525i) q^{79} +(-0.500000 + 0.866025i) q^{81} -4.90673 q^{83} +(11.5175 + 19.9490i) q^{85} +5.38919 q^{87} +(-4.18479 - 7.24827i) q^{89} +(2.37939 + 4.12122i) q^{91} +(3.68479 - 6.38225i) q^{93} +(-15.3131 - 5.82634i) q^{95} +(5.82295 - 10.0856i) q^{97} +(-2.18479 - 3.78417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{3} - 6 q^{7} - 3 q^{9} + O(q^{10}) \) \( 6 q - 3 q^{3} - 6 q^{7} - 3 q^{9} + 12 q^{11} - 3 q^{13} + 3 q^{21} - 9 q^{25} + 6 q^{27} - 12 q^{29} - 30 q^{31} - 6 q^{33} - 24 q^{35} - 6 q^{37} + 6 q^{39} - 12 q^{41} + 9 q^{43} - 18 q^{47} + 12 q^{49} + 9 q^{57} - 6 q^{59} + 3 q^{61} + 3 q^{63} - 3 q^{67} + 6 q^{71} + 9 q^{73} + 18 q^{75} - 12 q^{77} + 27 q^{79} - 3 q^{81} + 24 q^{83} + 24 q^{85} + 24 q^{87} - 18 q^{89} + 3 q^{91} + 15 q^{93} - 48 q^{95} - 6 q^{97} - 6 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\)

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 0
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) 1.87939 3.25519i 0.840487 1.45577i −0.0489972 0.998799i \(-0.515603\pi\)
0.889484 0.456967i \(-0.151064\pi\)
\(6\) 0 0
\(7\) −4.75877 −1.79865 −0.899323 0.437285i \(-0.855940\pi\)
−0.899323 + 0.437285i \(0.855940\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 4.36959 1.31748 0.658740 0.752371i \(-0.271090\pi\)
0.658740 + 0.752371i \(0.271090\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) 1.87939 + 3.25519i 0.485255 + 0.840487i
\(16\) 0 0
\(17\) −3.06418 + 5.30731i −0.743172 + 1.28721i 0.207872 + 0.978156i \(0.433346\pi\)
−0.951044 + 0.309056i \(0.899987\pi\)
\(18\) 0 0
\(19\) −0.694593 4.30320i −0.159350 0.987222i
\(20\) 0 0
\(21\) 2.37939 4.12122i 0.519224 0.899323i
\(22\) 0 0
\(23\) −1.87939 3.25519i −0.391879 0.678754i 0.600818 0.799385i \(-0.294841\pi\)
−0.992697 + 0.120631i \(0.961508\pi\)
\(24\) 0 0
\(25\) −4.56418 7.90539i −0.912836 1.58108i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.69459 4.66717i −0.500373 0.866672i −1.00000 0.000431109i \(-0.999863\pi\)
0.499627 0.866241i \(-0.333471\pi\)
\(30\) 0 0
\(31\) −7.36959 −1.32362 −0.661808 0.749673i \(-0.730211\pi\)
−0.661808 + 0.749673i \(0.730211\pi\)
\(32\) 0 0
\(33\) −2.18479 + 3.78417i −0.380324 + 0.658740i
\(34\) 0 0
\(35\) −8.94356 + 15.4907i −1.51174 + 2.61841i
\(36\) 0 0
\(37\) −7.12836 −1.17189 −0.585947 0.810349i \(-0.699277\pi\)
−0.585947 + 0.810349i \(0.699277\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 1.75877 3.04628i 0.274674 0.475749i −0.695379 0.718643i \(-0.744763\pi\)
0.970053 + 0.242894i \(0.0780968\pi\)
\(42\) 0 0
\(43\) −0.379385 + 0.657115i −0.0578557 + 0.100209i −0.893503 0.449058i \(-0.851760\pi\)
0.835647 + 0.549267i \(0.185093\pi\)
\(44\) 0 0
\(45\) −3.75877 −0.560324
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) 15.6459 2.23513
\(50\) 0 0
\(51\) −3.06418 5.30731i −0.429071 0.743172i
\(52\) 0 0
\(53\) −2.57398 4.45826i −0.353563 0.612389i 0.633308 0.773900i \(-0.281697\pi\)
−0.986871 + 0.161511i \(0.948363\pi\)
\(54\) 0 0
\(55\) 8.21213 14.2238i 1.10732 1.91794i
\(56\) 0 0
\(57\) 4.07398 + 1.55007i 0.539612 + 0.205311i
\(58\) 0 0
\(59\) 4.63816 8.03352i 0.603836 1.04588i −0.388398 0.921492i \(-0.626971\pi\)
0.992234 0.124384i \(-0.0396953\pi\)
\(60\) 0 0
\(61\) 4.25877 + 7.37641i 0.545280 + 0.944452i 0.998589 + 0.0530990i \(0.0169099\pi\)
−0.453310 + 0.891353i \(0.649757\pi\)
\(62\) 0 0
\(63\) 2.37939 + 4.12122i 0.299774 + 0.519224i
\(64\) 0 0
\(65\) −3.75877 −0.466218
\(66\) 0 0
\(67\) 0.684793 + 1.18610i 0.0836607 + 0.144905i 0.904820 0.425795i \(-0.140005\pi\)
−0.821159 + 0.570699i \(0.806672\pi\)
\(68\) 0 0
\(69\) 3.75877 0.452503
\(70\) 0 0
\(71\) −5.82295 + 10.0856i −0.691057 + 1.19695i 0.280435 + 0.959873i \(0.409521\pi\)
−0.971492 + 0.237073i \(0.923812\pi\)
\(72\) 0 0
\(73\) −2.25877 + 3.91231i −0.264369 + 0.457901i −0.967398 0.253260i \(-0.918497\pi\)
0.703029 + 0.711161i \(0.251830\pi\)
\(74\) 0 0
\(75\) 9.12836 1.05405
\(76\) 0 0
\(77\) −20.7939 −2.36968
\(78\) 0 0
\(79\) 7.07398 12.2525i 0.795885 1.37851i −0.126391 0.991980i \(-0.540339\pi\)
0.922276 0.386532i \(-0.126327\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −4.90673 −0.538583 −0.269292 0.963059i \(-0.586790\pi\)
−0.269292 + 0.963059i \(0.586790\pi\)
\(84\) 0 0
\(85\) 11.5175 + 19.9490i 1.24925 + 2.16377i
\(86\) 0 0
\(87\) 5.38919 0.577781
\(88\) 0 0
\(89\) −4.18479 7.24827i −0.443587 0.768315i 0.554365 0.832273i \(-0.312961\pi\)
−0.997953 + 0.0639579i \(0.979628\pi\)
\(90\) 0 0
\(91\) 2.37939 + 4.12122i 0.249427 + 0.432021i
\(92\) 0 0
\(93\) 3.68479 6.38225i 0.382095 0.661808i
\(94\) 0 0
\(95\) −15.3131 5.82634i −1.57110 0.597770i
\(96\) 0 0
\(97\) 5.82295 10.0856i 0.591231 1.02404i −0.402836 0.915272i \(-0.631976\pi\)
0.994067 0.108770i \(-0.0346911\pi\)
\(98\) 0 0
\(99\) −2.18479 3.78417i −0.219580 0.380324i
\(100\) 0 0
\(101\) 2.06418 + 3.57526i 0.205393 + 0.355752i 0.950258 0.311464i \(-0.100819\pi\)
−0.744865 + 0.667216i \(0.767486\pi\)
\(102\) 0 0
\(103\) 6.75877 0.665961 0.332981 0.942934i \(-0.391946\pi\)
0.332981 + 0.942934i \(0.391946\pi\)
\(104\) 0 0
\(105\) −8.94356 15.4907i −0.872802 1.51174i
\(106\) 0 0
\(107\) 4.12836 0.399103 0.199552 0.979887i \(-0.436051\pi\)
0.199552 + 0.979887i \(0.436051\pi\)
\(108\) 0 0
\(109\) 0.0641778 0.111159i 0.00614712 0.0106471i −0.862935 0.505314i \(-0.831377\pi\)
0.869083 + 0.494667i \(0.164710\pi\)
\(110\) 0 0
\(111\) 3.56418 6.17334i 0.338297 0.585947i
\(112\) 0 0
\(113\) −2.40879 −0.226600 −0.113300 0.993561i \(-0.536142\pi\)
−0.113300 + 0.993561i \(0.536142\pi\)
\(114\) 0 0
\(115\) −14.1284 −1.31748
\(116\) 0 0
\(117\) −0.500000 + 0.866025i −0.0462250 + 0.0800641i
\(118\) 0 0
\(119\) 14.5817 25.2563i 1.33670 2.31524i
\(120\) 0 0
\(121\) 8.09327 0.735752
\(122\) 0 0
\(123\) 1.75877 + 3.04628i 0.158583 + 0.274674i
\(124\) 0 0
\(125\) −15.5175 −1.38793
\(126\) 0 0
\(127\) 0.241230 + 0.417822i 0.0214057 + 0.0370757i 0.876530 0.481348i \(-0.159853\pi\)
−0.855124 + 0.518423i \(0.826519\pi\)
\(128\) 0 0
\(129\) −0.379385 0.657115i −0.0334030 0.0578557i
\(130\) 0 0
\(131\) −1.69459 + 2.93512i −0.148057 + 0.256443i −0.930509 0.366268i \(-0.880635\pi\)
0.782452 + 0.622711i \(0.213969\pi\)
\(132\) 0 0
\(133\) 3.30541 + 20.4779i 0.286615 + 1.77566i
\(134\) 0 0
\(135\) 1.87939 3.25519i 0.161752 0.280162i
\(136\) 0 0
\(137\) 9.21213 + 15.9559i 0.787046 + 1.36320i 0.927769 + 0.373154i \(0.121724\pi\)
−0.140724 + 0.990049i \(0.544943\pi\)
\(138\) 0 0
\(139\) 0.00980018 + 0.0169744i 0.000831240 + 0.00143975i 0.866441 0.499280i \(-0.166402\pi\)
−0.865609 + 0.500720i \(0.833069\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) −2.18479 3.78417i −0.182702 0.316448i
\(144\) 0 0
\(145\) −20.2567 −1.68223
\(146\) 0 0
\(147\) −7.82295 + 13.5497i −0.645226 + 1.11756i
\(148\) 0 0
\(149\) −3.12061 + 5.40506i −0.255651 + 0.442800i −0.965072 0.261985i \(-0.915623\pi\)
0.709421 + 0.704785i \(0.248956\pi\)
\(150\) 0 0
\(151\) −0.739170 −0.0601528 −0.0300764 0.999548i \(-0.509575\pi\)
−0.0300764 + 0.999548i \(0.509575\pi\)
\(152\) 0 0
\(153\) 6.12836 0.495448
\(154\) 0 0
\(155\) −13.8503 + 23.9894i −1.11248 + 1.92688i
\(156\) 0 0
\(157\) 3.32295 5.75552i 0.265200 0.459340i −0.702416 0.711767i \(-0.747895\pi\)
0.967616 + 0.252427i \(0.0812286\pi\)
\(158\) 0 0
\(159\) 5.14796 0.408259
\(160\) 0 0
\(161\) 8.94356 + 15.4907i 0.704852 + 1.22084i
\(162\) 0 0
\(163\) 11.3696 0.890535 0.445267 0.895398i \(-0.353109\pi\)
0.445267 + 0.895398i \(0.353109\pi\)
\(164\) 0 0
\(165\) 8.21213 + 14.2238i 0.639314 + 1.10732i
\(166\) 0 0
\(167\) 1.49020 + 2.58110i 0.115315 + 0.199732i 0.917906 0.396799i \(-0.129879\pi\)
−0.802591 + 0.596530i \(0.796546\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) −3.37939 + 2.75314i −0.258428 + 0.210538i
\(172\) 0 0
\(173\) 2.69459 4.66717i 0.204866 0.354838i −0.745224 0.666814i \(-0.767657\pi\)
0.950090 + 0.311976i \(0.100991\pi\)
\(174\) 0 0
\(175\) 21.7199 + 37.6199i 1.64187 + 2.84380i
\(176\) 0 0
\(177\) 4.63816 + 8.03352i 0.348625 + 0.603836i
\(178\) 0 0
\(179\) −4.24123 −0.317004 −0.158502 0.987359i \(-0.550666\pi\)
−0.158502 + 0.987359i \(0.550666\pi\)
\(180\) 0 0
\(181\) −6.30541 10.9213i −0.468677 0.811773i 0.530682 0.847571i \(-0.321936\pi\)
−0.999359 + 0.0357984i \(0.988603\pi\)
\(182\) 0 0
\(183\) −8.51754 −0.629635
\(184\) 0 0
\(185\) −13.3969 + 23.2042i −0.984962 + 1.70600i
\(186\) 0 0
\(187\) −13.3892 + 23.1907i −0.979114 + 1.69588i
\(188\) 0 0
\(189\) −4.75877 −0.346150
\(190\) 0 0
\(191\) 22.6263 1.63718 0.818591 0.574377i \(-0.194756\pi\)
0.818591 + 0.574377i \(0.194756\pi\)
\(192\) 0 0
\(193\) −12.3229 + 21.3440i −0.887025 + 1.53637i −0.0436505 + 0.999047i \(0.513899\pi\)
−0.843375 + 0.537326i \(0.819435\pi\)
\(194\) 0 0
\(195\) 1.87939 3.25519i 0.134586 0.233109i
\(196\) 0 0
\(197\) 22.6655 1.61485 0.807425 0.589970i \(-0.200861\pi\)
0.807425 + 0.589970i \(0.200861\pi\)
\(198\) 0 0
\(199\) 6.96110 + 12.0570i 0.493460 + 0.854697i 0.999972 0.00753584i \(-0.00239875\pi\)
−0.506512 + 0.862233i \(0.669065\pi\)
\(200\) 0 0
\(201\) −1.36959 −0.0966031
\(202\) 0 0
\(203\) 12.8229 + 22.2100i 0.899995 + 1.55884i
\(204\) 0 0
\(205\) −6.61081 11.4503i −0.461719 0.799721i
\(206\) 0 0
\(207\) −1.87939 + 3.25519i −0.130626 + 0.226251i
\(208\) 0 0
\(209\) −3.03508 18.8032i −0.209941 1.30064i
\(210\) 0 0
\(211\) −1.00980 + 1.74903i −0.0695175 + 0.120408i −0.898689 0.438586i \(-0.855479\pi\)
0.829172 + 0.558994i \(0.188813\pi\)
\(212\) 0 0
\(213\) −5.82295 10.0856i −0.398982 0.691057i
\(214\) 0 0
\(215\) 1.42602 + 2.46994i 0.0972539 + 0.168449i
\(216\) 0 0
\(217\) 35.0702 2.38072
\(218\) 0 0
\(219\) −2.25877 3.91231i −0.152634 0.264369i
\(220\) 0 0
\(221\) 6.12836 0.412238
\(222\) 0 0
\(223\) 14.1827 24.5652i 0.949746 1.64501i 0.203789 0.979015i \(-0.434675\pi\)
0.745958 0.665993i \(-0.231992\pi\)
\(224\) 0 0
\(225\) −4.56418 + 7.90539i −0.304279 + 0.527026i
\(226\) 0 0
\(227\) −20.1830 −1.33960 −0.669798 0.742544i \(-0.733619\pi\)
−0.669798 + 0.742544i \(0.733619\pi\)
\(228\) 0 0
\(229\) 11.7784 0.778337 0.389168 0.921167i \(-0.372762\pi\)
0.389168 + 0.921167i \(0.372762\pi\)
\(230\) 0 0
\(231\) 10.3969 18.0080i 0.684068 1.18484i
\(232\) 0 0
\(233\) 0.0641778 0.111159i 0.00420443 0.00728228i −0.863916 0.503637i \(-0.831995\pi\)
0.868120 + 0.496354i \(0.165328\pi\)
\(234\) 0 0
\(235\) −22.5526 −1.47117
\(236\) 0 0
\(237\) 7.07398 + 12.2525i 0.459504 + 0.795885i
\(238\) 0 0
\(239\) −3.10876 −0.201089 −0.100544 0.994933i \(-0.532058\pi\)
−0.100544 + 0.994933i \(0.532058\pi\)
\(240\) 0 0
\(241\) −5.64796 9.78255i −0.363817 0.630149i 0.624769 0.780810i \(-0.285193\pi\)
−0.988586 + 0.150661i \(0.951860\pi\)
\(242\) 0 0
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 29.4047 50.9304i 1.87860 3.25382i
\(246\) 0 0
\(247\) −3.37939 + 2.75314i −0.215025 + 0.175178i
\(248\) 0 0
\(249\) 2.45336 4.24935i 0.155476 0.269292i
\(250\) 0 0
\(251\) −0.758770 1.31423i −0.0478932 0.0829534i 0.841085 0.540903i \(-0.181917\pi\)
−0.888978 + 0.457950i \(0.848584\pi\)
\(252\) 0 0
\(253\) −8.21213 14.2238i −0.516292 0.894245i
\(254\) 0 0
\(255\) −23.0351 −1.44251
\(256\) 0 0
\(257\) 6.09152 + 10.5508i 0.379979 + 0.658142i 0.991059 0.133427i \(-0.0425980\pi\)
−0.611080 + 0.791569i \(0.709265\pi\)
\(258\) 0 0
\(259\) 33.9222 2.10782
\(260\) 0 0
\(261\) −2.69459 + 4.66717i −0.166791 + 0.288891i
\(262\) 0 0
\(263\) −9.69459 + 16.7915i −0.597794 + 1.03541i 0.395352 + 0.918530i \(0.370623\pi\)
−0.993146 + 0.116880i \(0.962711\pi\)
\(264\) 0 0
\(265\) −19.3500 −1.18866
\(266\) 0 0
\(267\) 8.36959 0.512210
\(268\) 0 0
\(269\) −11.7023 + 20.2690i −0.713504 + 1.23582i 0.250030 + 0.968238i \(0.419560\pi\)
−0.963534 + 0.267587i \(0.913774\pi\)
\(270\) 0 0
\(271\) 0.482459 0.835644i 0.0293073 0.0507617i −0.851000 0.525166i \(-0.824003\pi\)
0.880307 + 0.474404i \(0.157337\pi\)
\(272\) 0 0
\(273\) −4.75877 −0.288014
\(274\) 0 0
\(275\) −19.9436 34.5433i −1.20264 2.08304i
\(276\) 0 0
\(277\) 15.3892 0.924647 0.462323 0.886711i \(-0.347016\pi\)
0.462323 + 0.886711i \(0.347016\pi\)
\(278\) 0 0
\(279\) 3.68479 + 6.38225i 0.220603 + 0.382095i
\(280\) 0 0
\(281\) −4.24897 7.35943i −0.253472 0.439027i 0.711007 0.703185i \(-0.248239\pi\)
−0.964479 + 0.264158i \(0.914906\pi\)
\(282\) 0 0
\(283\) −5.51754 + 9.55666i −0.327984 + 0.568085i −0.982112 0.188299i \(-0.939702\pi\)
0.654128 + 0.756384i \(0.273036\pi\)
\(284\) 0 0
\(285\) 12.7023 10.3484i 0.752421 0.612987i
\(286\) 0 0
\(287\) −8.36959 + 14.4965i −0.494041 + 0.855704i
\(288\) 0 0
\(289\) −10.2784 17.8027i −0.604610 1.04722i
\(290\) 0 0
\(291\) 5.82295 + 10.0856i 0.341347 + 0.591231i
\(292\) 0 0
\(293\) −1.03508 −0.0604701 −0.0302351 0.999543i \(-0.509626\pi\)
−0.0302351 + 0.999543i \(0.509626\pi\)
\(294\) 0 0
\(295\) −17.4338 30.1962i −1.01503 1.75809i
\(296\) 0 0
\(297\) 4.36959 0.253549
\(298\) 0 0
\(299\) −1.87939 + 3.25519i −0.108688 + 0.188253i
\(300\) 0 0
\(301\) 1.80541 3.12706i 0.104062 0.180241i
\(302\) 0 0
\(303\) −4.12836 −0.237168
\(304\) 0 0
\(305\) 32.0155 1.83320
\(306\) 0 0
\(307\) 7.43376 12.8757i 0.424267 0.734852i −0.572084 0.820195i \(-0.693865\pi\)
0.996352 + 0.0853423i \(0.0271984\pi\)
\(308\) 0 0
\(309\) −3.37939 + 5.85327i −0.192247 + 0.332981i
\(310\) 0 0
\(311\) 16.0547 0.910378 0.455189 0.890395i \(-0.349572\pi\)
0.455189 + 0.890395i \(0.349572\pi\)
\(312\) 0 0
\(313\) −17.5817 30.4524i −0.993777 1.72127i −0.593350 0.804945i \(-0.702195\pi\)
−0.400428 0.916328i \(-0.631138\pi\)
\(314\) 0 0
\(315\) 17.8871 1.00783
\(316\) 0 0
\(317\) −9.26857 16.0536i −0.520575 0.901662i −0.999714 0.0239230i \(-0.992384\pi\)
0.479139 0.877739i \(-0.340949\pi\)
\(318\) 0 0
\(319\) −11.7743 20.3936i −0.659232 1.14182i
\(320\) 0 0
\(321\) −2.06418 + 3.57526i −0.115211 + 0.199552i
\(322\) 0 0
\(323\) 24.9668 + 9.49935i 1.38919 + 0.528558i
\(324\) 0 0
\(325\) −4.56418 + 7.90539i −0.253175 + 0.438512i
\(326\) 0 0
\(327\) 0.0641778 + 0.111159i 0.00354904 + 0.00614712i
\(328\) 0 0
\(329\) 14.2763 + 24.7273i 0.787079 + 1.36326i
\(330\) 0 0
\(331\) 8.75877 0.481426 0.240713 0.970596i \(-0.422619\pi\)
0.240713 + 0.970596i \(0.422619\pi\)
\(332\) 0 0
\(333\) 3.56418 + 6.17334i 0.195316 + 0.338297i
\(334\) 0 0
\(335\) 5.14796 0.281263
\(336\) 0 0
\(337\) 10.6925 18.5200i 0.582459 1.00885i −0.412728 0.910855i \(-0.635424\pi\)
0.995187 0.0979947i \(-0.0312428\pi\)
\(338\) 0 0
\(339\) 1.20439 2.08607i 0.0654136 0.113300i
\(340\) 0 0
\(341\) −32.2020 −1.74384
\(342\) 0 0
\(343\) −41.1438 −2.22156
\(344\) 0 0
\(345\) 7.06418 12.2355i 0.380323 0.658738i
\(346\) 0 0
\(347\) 11.9632 20.7208i 0.642216 1.11235i −0.342721 0.939437i \(-0.611348\pi\)
0.984937 0.172914i \(-0.0553182\pi\)
\(348\) 0 0
\(349\) −23.0702 −1.23492 −0.617459 0.786603i \(-0.711838\pi\)
−0.617459 + 0.786603i \(0.711838\pi\)
\(350\) 0 0
\(351\) −0.500000 0.866025i −0.0266880 0.0462250i
\(352\) 0 0
\(353\) −28.4979 −1.51679 −0.758396 0.651794i \(-0.774017\pi\)
−0.758396 + 0.651794i \(0.774017\pi\)
\(354\) 0 0
\(355\) 21.8871 + 37.9096i 1.16165 + 2.01203i
\(356\) 0 0
\(357\) 14.5817 + 25.2563i 0.771746 + 1.33670i
\(358\) 0 0
\(359\) 2.48246 4.29975i 0.131019 0.226932i −0.793051 0.609156i \(-0.791508\pi\)
0.924070 + 0.382224i \(0.124842\pi\)
\(360\) 0 0
\(361\) −18.0351 + 5.97794i −0.949215 + 0.314629i
\(362\) 0 0
\(363\) −4.04664 + 7.00898i −0.212393 + 0.367876i
\(364\) 0 0
\(365\) 8.49020 + 14.7055i 0.444397 + 0.769719i
\(366\) 0 0
\(367\) 9.42396 + 16.3228i 0.491927 + 0.852042i 0.999957 0.00929712i \(-0.00295941\pi\)
−0.508030 + 0.861339i \(0.669626\pi\)
\(368\) 0 0
\(369\) −3.51754 −0.183116
\(370\) 0 0
\(371\) 12.2490 + 21.2158i 0.635935 + 1.10147i
\(372\) 0 0
\(373\) 35.9026 1.85897 0.929483 0.368864i \(-0.120253\pi\)
0.929483 + 0.368864i \(0.120253\pi\)
\(374\) 0 0
\(375\) 7.75877 13.4386i 0.400661 0.693966i
\(376\) 0 0
\(377\) −2.69459 + 4.66717i −0.138779 + 0.240372i
\(378\) 0 0
\(379\) 12.2763 0.630592 0.315296 0.948993i \(-0.397896\pi\)
0.315296 + 0.948993i \(0.397896\pi\)
\(380\) 0 0
\(381\) −0.482459 −0.0247171
\(382\) 0 0
\(383\) 7.20439 12.4784i 0.368127 0.637615i −0.621145 0.783695i \(-0.713332\pi\)
0.989273 + 0.146080i \(0.0466657\pi\)
\(384\) 0 0
\(385\) −39.0797 + 67.6880i −1.99168 + 3.44970i
\(386\) 0 0
\(387\) 0.758770 0.0385705
\(388\) 0 0
\(389\) −3.18479 5.51622i −0.161475 0.279684i 0.773923 0.633280i \(-0.218292\pi\)
−0.935398 + 0.353597i \(0.884959\pi\)
\(390\) 0 0
\(391\) 23.0351 1.16493
\(392\) 0 0
\(393\) −1.69459 2.93512i −0.0854809 0.148057i
\(394\) 0 0
\(395\) −26.5895 46.0543i −1.33786 2.31724i
\(396\) 0 0
\(397\) 5.27837 9.14241i 0.264914 0.458844i −0.702627 0.711558i \(-0.747990\pi\)
0.967541 + 0.252714i \(0.0813231\pi\)
\(398\) 0 0
\(399\) −19.3871 7.37641i −0.970570 0.369282i
\(400\) 0 0
\(401\) −10.7219 + 18.5709i −0.535428 + 0.927388i 0.463715 + 0.885985i \(0.346516\pi\)
−0.999143 + 0.0414036i \(0.986817\pi\)
\(402\) 0 0
\(403\) 3.68479 + 6.38225i 0.183553 + 0.317922i
\(404\) 0 0
\(405\) 1.87939 + 3.25519i 0.0933874 + 0.161752i
\(406\) 0 0
\(407\) −31.1480 −1.54395
\(408\) 0 0
\(409\) −3.32501 5.75908i −0.164411 0.284768i 0.772035 0.635580i \(-0.219239\pi\)
−0.936446 + 0.350812i \(0.885906\pi\)
\(410\) 0 0
\(411\) −18.4243 −0.908802
\(412\) 0 0
\(413\) −22.0719 + 38.2297i −1.08609 + 1.88116i
\(414\) 0 0
\(415\) −9.22163 + 15.9723i −0.452672 + 0.784051i
\(416\) 0 0
\(417\) −0.0196004 −0.000959834
\(418\) 0 0
\(419\) −5.84793 −0.285690 −0.142845 0.989745i \(-0.545625\pi\)
−0.142845 + 0.989745i \(0.545625\pi\)
\(420\) 0 0
\(421\) −0.714193 + 1.23702i −0.0348076 + 0.0602886i −0.882904 0.469553i \(-0.844415\pi\)
0.848097 + 0.529841i \(0.177749\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 55.9418 2.71358
\(426\) 0 0
\(427\) −20.2665 35.1026i −0.980765 1.69874i
\(428\) 0 0
\(429\) 4.36959 0.210966
\(430\) 0 0
\(431\) 0.389185 + 0.674089i 0.0187464 + 0.0324697i 0.875246 0.483677i \(-0.160699\pi\)
−0.856500 + 0.516147i \(0.827366\pi\)
\(432\) 0 0
\(433\) −13.3425 23.1100i −0.641202 1.11059i −0.985165 0.171611i \(-0.945103\pi\)
0.343963 0.938983i \(-0.388231\pi\)
\(434\) 0 0
\(435\) 10.1284 17.5428i 0.485617 0.841114i
\(436\) 0 0
\(437\) −12.7023 + 10.3484i −0.607635 + 0.495031i
\(438\) 0 0
\(439\) −14.2665 + 24.7103i −0.680903 + 1.17936i 0.293802 + 0.955866i \(0.405079\pi\)
−0.974706 + 0.223493i \(0.928254\pi\)
\(440\) 0 0
\(441\) −7.82295 13.5497i −0.372521 0.645226i
\(442\) 0 0
\(443\) −8.82295 15.2818i −0.419191 0.726060i 0.576667 0.816979i \(-0.304353\pi\)
−0.995858 + 0.0909191i \(0.971020\pi\)
\(444\) 0 0
\(445\) −31.4593 −1.49132
\(446\) 0 0
\(447\) −3.12061 5.40506i −0.147600 0.255651i
\(448\) 0 0
\(449\) −1.38919 −0.0655597 −0.0327799 0.999463i \(-0.510436\pi\)
−0.0327799 + 0.999463i \(0.510436\pi\)
\(450\) 0 0
\(451\) 7.68510 13.3110i 0.361877 0.626790i
\(452\) 0 0
\(453\) 0.369585 0.640140i 0.0173646 0.0300764i
\(454\) 0 0
\(455\) 17.8871 0.838561
\(456\) 0 0
\(457\) 24.6851 1.15472 0.577360 0.816490i \(-0.304083\pi\)
0.577360 + 0.816490i \(0.304083\pi\)
\(458\) 0 0
\(459\) −3.06418 + 5.30731i −0.143024 + 0.247724i
\(460\) 0 0
\(461\) −0.795607 + 1.37803i −0.0370551 + 0.0641813i −0.883958 0.467566i \(-0.845131\pi\)
0.846903 + 0.531747i \(0.178464\pi\)
\(462\) 0 0
\(463\) 21.7547 1.01102 0.505512 0.862819i \(-0.331304\pi\)
0.505512 + 0.862819i \(0.331304\pi\)
\(464\) 0 0
\(465\) −13.8503 23.9894i −0.642292 1.11248i
\(466\) 0 0
\(467\) −15.5175 −0.718066 −0.359033 0.933325i \(-0.616893\pi\)
−0.359033 + 0.933325i \(0.616893\pi\)
\(468\) 0 0
\(469\) −3.25877 5.64436i −0.150476 0.260632i
\(470\) 0 0
\(471\) 3.32295 + 5.75552i 0.153113 + 0.265200i
\(472\) 0 0
\(473\) −1.65776 + 2.87132i −0.0762237 + 0.132023i
\(474\) 0 0
\(475\) −30.8482 + 25.1316i −1.41541 + 1.15312i
\(476\) 0 0
\(477\) −2.57398 + 4.45826i −0.117854 + 0.204130i
\(478\) 0 0
\(479\) −5.82295 10.0856i −0.266057 0.460825i 0.701783 0.712391i \(-0.252388\pi\)
−0.967840 + 0.251566i \(0.919054\pi\)
\(480\) 0 0
\(481\) 3.56418 + 6.17334i 0.162513 + 0.281480i
\(482\) 0 0
\(483\) −17.8871 −0.813892
\(484\) 0 0
\(485\) −21.8871 37.9096i −0.993843 1.72139i
\(486\) 0 0
\(487\) −38.5526 −1.74699 −0.873493 0.486837i \(-0.838151\pi\)
−0.873493 + 0.486837i \(0.838151\pi\)
\(488\) 0 0
\(489\) −5.68479 + 9.84635i −0.257075 + 0.445267i
\(490\) 0 0
\(491\) 3.82295 6.62154i 0.172527 0.298826i −0.766776 0.641915i \(-0.778140\pi\)
0.939303 + 0.343089i \(0.111473\pi\)
\(492\) 0 0
\(493\) 33.0268 1.48745
\(494\) 0 0
\(495\) −16.4243 −0.738216
\(496\) 0 0
\(497\) 27.7101 47.9953i 1.24297 2.15288i
\(498\) 0 0
\(499\) 15.3152 26.5267i 0.685603 1.18750i −0.287644 0.957737i \(-0.592872\pi\)
0.973247 0.229762i \(-0.0737946\pi\)
\(500\) 0 0
\(501\) −2.98040 −0.133154
\(502\) 0 0
\(503\) −2.69459 4.66717i −0.120146 0.208099i 0.799679 0.600428i \(-0.205003\pi\)
−0.919825 + 0.392329i \(0.871670\pi\)
\(504\) 0 0
\(505\) 15.5175 0.690522
\(506\) 0 0
\(507\) 6.00000 + 10.3923i 0.266469 + 0.461538i
\(508\) 0 0
\(509\) 1.12836 + 1.95437i 0.0500135 + 0.0866259i 0.889948 0.456061i \(-0.150740\pi\)
−0.839935 + 0.542687i \(0.817407\pi\)
\(510\) 0 0
\(511\) 10.7490 18.6178i 0.475506 0.823601i
\(512\) 0 0
\(513\) −0.694593 4.30320i −0.0306670 0.189991i
\(514\) 0 0
\(515\) 12.7023 22.0011i 0.559732 0.969484i
\(516\) 0 0
\(517\) −13.1088 22.7050i −0.576522 0.998566i
\(518\) 0 0
\(519\) 2.69459 + 4.66717i 0.118279 + 0.204866i
\(520\) 0 0
\(521\) 37.2763 1.63310 0.816552 0.577271i \(-0.195882\pi\)
0.816552 + 0.577271i \(0.195882\pi\)
\(522\) 0 0
\(523\) −0.186852 0.323637i −0.00817046 0.0141517i 0.861911 0.507059i \(-0.169267\pi\)
−0.870082 + 0.492907i \(0.835934\pi\)
\(524\) 0 0
\(525\) −43.4397 −1.89587
\(526\) 0 0
\(527\) 22.5817 39.1127i 0.983675 1.70378i
\(528\) 0 0
\(529\) 4.43582 7.68307i 0.192862 0.334046i
\(530\) 0 0
\(531\) −9.27631 −0.402558
\(532\) 0 0
\(533\) −3.51754 −0.152362
\(534\) 0 0
\(535\) 7.75877 13.4386i 0.335441 0.581001i
\(536\) 0 0
\(537\) 2.12061 3.67301i 0.0915113 0.158502i
\(538\) 0 0
\(539\) 68.3661 2.94474
\(540\) 0 0
\(541\) 9.54458 + 16.5317i 0.410353 + 0.710753i 0.994928 0.100587i \(-0.0320720\pi\)
−0.584575 + 0.811340i \(0.698739\pi\)
\(542\) 0 0
\(543\) 12.6108 0.541182
\(544\) 0 0
\(545\) −0.241230 0.417822i −0.0103331 0.0178975i
\(546\) 0 0
\(547\) 21.8773 + 37.8926i 0.935407 + 1.62017i 0.773907 + 0.633300i \(0.218300\pi\)
0.161500 + 0.986873i \(0.448367\pi\)
\(548\) 0 0
\(549\) 4.25877 7.37641i 0.181760 0.314817i
\(550\) 0 0
\(551\) −18.2121 + 14.8372i −0.775863 + 0.632084i
\(552\) 0 0
\(553\) −33.6634 + 58.3068i −1.43151 + 2.47946i
\(554\) 0 0
\(555\) −13.3969 23.2042i −0.568668 0.984962i
\(556\) 0 0
\(557\) −15.9513 27.6285i −0.675878 1.17066i −0.976211 0.216821i \(-0.930431\pi\)
0.300333 0.953834i \(-0.402902\pi\)
\(558\) 0 0
\(559\) 0.758770 0.0320926
\(560\) 0 0
\(561\) −13.3892 23.1907i −0.565292 0.979114i
\(562\) 0 0
\(563\) 3.87164 0.163170 0.0815852 0.996666i \(-0.474002\pi\)
0.0815852 + 0.996666i \(0.474002\pi\)
\(564\) 0 0
\(565\) −4.52704 + 7.84106i −0.190454 + 0.329876i
\(566\) 0 0
\(567\) 2.37939 4.12122i 0.0999248 0.173075i
\(568\) 0 0
\(569\) −32.9959 −1.38326 −0.691630 0.722252i \(-0.743107\pi\)
−0.691630 + 0.722252i \(0.743107\pi\)
\(570\) 0 0
\(571\) 24.1789 1.01186 0.505928 0.862576i \(-0.331150\pi\)
0.505928 + 0.862576i \(0.331150\pi\)
\(572\) 0 0
\(573\) −11.3131 + 19.5949i −0.472614 + 0.818591i
\(574\) 0 0
\(575\) −17.1557 + 29.7145i −0.715442 + 1.23918i
\(576\) 0 0
\(577\) −3.16344 −0.131696 −0.0658478 0.997830i \(-0.520975\pi\)
−0.0658478 + 0.997830i \(0.520975\pi\)
\(578\) 0 0
\(579\) −12.3229 21.3440i −0.512124 0.887025i
\(580\) 0 0
\(581\) 23.3500 0.968721
\(582\) 0 0
\(583\) −11.2472 19.4807i −0.465812 0.806810i
\(584\) 0 0
\(585\) 1.87939 + 3.25519i 0.0777030 + 0.134586i
\(586\) 0 0
\(587\) −3.00774 + 5.20956i −0.124143 + 0.215022i −0.921398 0.388621i \(-0.872951\pi\)
0.797255 + 0.603643i \(0.206285\pi\)
\(588\) 0 0
\(589\) 5.11886 + 31.7128i 0.210919 + 1.30670i
\(590\) 0 0
\(591\) −11.3327 + 19.6289i −0.466167 + 0.807425i
\(592\) 0 0
\(593\) −11.4611 19.8512i −0.470651 0.815192i 0.528785 0.848756i \(-0.322648\pi\)
−0.999437 + 0.0335639i \(0.989314\pi\)
\(594\) 0 0
\(595\) −54.8093 94.9326i −2.24696 3.89186i
\(596\) 0 0
\(597\) −13.9222 −0.569798
\(598\) 0 0
\(599\) 17.2199 + 29.8257i 0.703585 + 1.21864i 0.967200 + 0.254017i \(0.0817519\pi\)
−0.263615 + 0.964628i \(0.584915\pi\)
\(600\) 0 0
\(601\) 24.1634 0.985647 0.492824 0.870129i \(-0.335965\pi\)
0.492824 + 0.870129i \(0.335965\pi\)
\(602\) 0 0
\(603\) 0.684793 1.18610i 0.0278869 0.0483015i
\(604\) 0 0
\(605\) 15.2104 26.3451i 0.618390 1.07108i
\(606\) 0 0
\(607\) 6.84793 0.277949 0.138974 0.990296i \(-0.455619\pi\)
0.138974 + 0.990296i \(0.455619\pi\)
\(608\) 0 0
\(609\) −25.6459 −1.03922
\(610\) 0 0
\(611\) −3.00000 + 5.19615i −0.121367 + 0.210214i
\(612\) 0 0
\(613\) −8.47296 + 14.6756i −0.342220 + 0.592742i −0.984845 0.173439i \(-0.944512\pi\)
0.642625 + 0.766181i \(0.277845\pi\)
\(614\) 0 0
\(615\) 13.2216 0.533148
\(616\) 0 0
\(617\) −21.1361 36.6088i −0.850907 1.47381i −0.880391 0.474249i \(-0.842720\pi\)
0.0294834 0.999565i \(-0.490614\pi\)
\(618\) 0 0
\(619\) −4.59121 −0.184536 −0.0922682 0.995734i \(-0.529412\pi\)
−0.0922682 + 0.995734i \(0.529412\pi\)
\(620\) 0 0
\(621\) −1.87939 3.25519i −0.0754171 0.130626i
\(622\) 0 0
\(623\) 19.9145 + 34.4929i 0.797856 + 1.38193i
\(624\) 0 0
\(625\) −6.34255 + 10.9856i −0.253702 + 0.439425i
\(626\) 0 0
\(627\) 17.8016 + 6.77314i 0.710927 + 0.270493i
\(628\) 0 0
\(629\) 21.8425 37.8324i 0.870919 1.50848i
\(630\) 0 0
\(631\) −18.7841 32.5349i −0.747781 1.29520i −0.948884 0.315625i \(-0.897786\pi\)
0.201103 0.979570i \(-0.435548\pi\)
\(632\) 0 0
\(633\) −1.00980 1.74903i −0.0401360 0.0695175i
\(634\) 0 0
\(635\) 1.81345 0.0719647
\(636\) 0 0
\(637\) −7.82295 13.5497i −0.309956 0.536860i
\(638\) 0 0
\(639\) 11.6459 0.460705
\(640\) 0 0
\(641\) 2.75877 4.77833i 0.108965 0.188733i −0.806386 0.591389i \(-0.798580\pi\)
0.915351 + 0.402656i \(0.131913\pi\)
\(642\) 0 0
\(643\) −17.5915 + 30.4694i −0.693742 + 1.20160i 0.276861 + 0.960910i \(0.410706\pi\)
−0.970603 + 0.240686i \(0.922628\pi\)
\(644\) 0 0
\(645\) −2.85204 −0.112299
\(646\) 0 0
\(647\) 3.57573 0.140577 0.0702883 0.997527i \(-0.477608\pi\)
0.0702883 + 0.997527i \(0.477608\pi\)
\(648\) 0 0
\(649\) 20.2668 35.1032i 0.795542 1.37792i
\(650\) 0 0
\(651\) −17.5351 + 30.3717i −0.687254 + 1.19036i
\(652\) 0 0
\(653\) 32.6418 1.27737 0.638686 0.769468i \(-0.279478\pi\)
0.638686 + 0.769468i \(0.279478\pi\)
\(654\) 0 0
\(655\) 6.36959 + 11.0324i 0.248880 + 0.431073i
\(656\) 0 0
\(657\) 4.51754 0.176246
\(658\) 0 0
\(659\) 24.4807 + 42.4018i 0.953633 + 1.65174i 0.737466 + 0.675384i \(0.236022\pi\)
0.216167 + 0.976356i \(0.430645\pi\)
\(660\) 0 0
\(661\) −17.7392 30.7251i −0.689974 1.19507i −0.971846 0.235618i \(-0.924289\pi\)
0.281872 0.959452i \(-0.409045\pi\)
\(662\) 0 0
\(663\) −3.06418 + 5.30731i −0.119003 + 0.206119i
\(664\) 0 0
\(665\) 72.8718 + 27.7262i 2.82585 + 1.07518i
\(666\) 0 0
\(667\) −10.1284 + 17.5428i −0.392171 + 0.679261i
\(668\) 0 0
\(669\) 14.1827 + 24.5652i 0.548336 + 0.949746i
\(670\) 0 0
\(671\) 18.6091 + 32.2318i 0.718395 + 1.24430i
\(672\) 0 0
\(673\) 2.68510 0.103503 0.0517514 0.998660i \(-0.483520\pi\)
0.0517514 + 0.998660i \(0.483520\pi\)
\(674\) 0 0
\(675\) −4.56418 7.90539i −0.175675 0.304279i
\(676\) 0 0
\(677\) 18.3351 0.704676 0.352338 0.935873i \(-0.385387\pi\)
0.352338 + 0.935873i \(0.385387\pi\)
\(678\) 0 0
\(679\) −27.7101 + 47.9953i −1.06342 + 1.84189i
\(680\) 0 0
\(681\) 10.0915 17.4790i 0.386708 0.669798i
\(682\) 0 0
\(683\) −4.07367 −0.155875 −0.0779374 0.996958i \(-0.524833\pi\)
−0.0779374 + 0.996958i \(0.524833\pi\)
\(684\) 0 0
\(685\) 69.2526 2.64601
\(686\) 0 0
\(687\) −5.88919 + 10.2004i −0.224686 + 0.389168i
\(688\) 0 0
\(689\) −2.57398 + 4.45826i −0.0980608 + 0.169846i
\(690\) 0 0
\(691\) −43.5485 −1.65666 −0.828332 0.560238i \(-0.810710\pi\)
−0.828332 + 0.560238i \(0.810710\pi\)
\(692\) 0 0
\(693\) 10.3969 + 18.0080i 0.394947 + 0.684068i
\(694\) 0 0
\(695\) 0.0736733 0.00279459
\(696\) 0 0
\(697\) 10.7784 + 18.6687i 0.408260 + 0.707127i
\(698\) 0 0
\(699\) 0.0641778 + 0.111159i 0.00242743 + 0.00420443i
\(700\) 0 0
\(701\) −15.6536 + 27.1129i −0.591230 + 1.02404i 0.402837 + 0.915272i \(0.368024\pi\)
−0.994067 + 0.108768i \(0.965309\pi\)
\(702\) 0 0
\(703\) 4.95130 + 30.6747i 0.186742 + 1.15692i
\(704\) 0 0
\(705\) 11.2763 19.5311i 0.424690 0.735585i
\(706\) 0 0
\(707\) −9.82295 17.0138i −0.369430 0.639872i
\(708\) 0 0
\(709\) −11.9047 20.6195i −0.447089 0.774381i 0.551106 0.834435i \(-0.314206\pi\)
−0.998195 + 0.0600541i \(0.980873\pi\)
\(710\) 0 0
\(711\) −14.1480 −0.530590
\(712\) 0 0
\(713\) 13.8503 + 23.9894i 0.518697 + 0.898410i
\(714\) 0 0
\(715\) −16.4243 −0.614233
\(716\) 0 0
\(717\) 1.55438 2.69226i 0.0580493 0.100544i
\(718\) 0 0
\(719\) 15.8949 27.5307i 0.592779 1.02672i −0.401078 0.916044i \(-0.631364\pi\)
0.993856 0.110678i \(-0.0353024\pi\)
\(720\) 0 0
\(721\) −32.1634 −1.19783
\(722\) 0 0
\(723\) 11.2959 0.420099
\(724\) 0 0
\(725\) −24.5972 + 42.6036i −0.913517 + 1.58226i
\(726\) 0 0
\(727\) −3.22193 + 5.58055i −0.119495 + 0.206971i −0.919568 0.392932i \(-0.871461\pi\)
0.800073 + 0.599903i \(0.204794\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −2.32501 4.02703i −0.0859935 0.148945i
\(732\) 0 0
\(733\) −33.9728 −1.25481 −0.627406 0.778692i \(-0.715884\pi\)
−0.627406 + 0.778692i \(0.715884\pi\)
\(734\) 0 0
\(735\) 29.4047 + 50.9304i 1.08461 + 1.87860i
\(736\) 0 0
\(737\) 2.99226 + 5.18274i 0.110221 + 0.190909i
\(738\) 0 0
\(739\) 11.4632 19.8548i 0.421679 0.730370i −0.574425 0.818557i \(-0.694774\pi\)
0.996104 + 0.0881876i \(0.0281075\pi\)
\(740\) 0 0
\(741\) −0.694593 4.30320i −0.0255165 0.158082i
\(742\) 0 0
\(743\) −3.98276 + 6.89835i −0.146113 + 0.253076i −0.929788 0.368096i \(-0.880010\pi\)
0.783674 + 0.621172i \(0.213343\pi\)
\(744\) 0 0
\(745\) 11.7297 + 20.3164i 0.429742 + 0.744335i
\(746\) 0 0
\(747\) 2.45336 + 4.24935i 0.0897639 + 0.155476i
\(748\) 0 0
\(749\) −19.6459 −0.717845
\(750\) 0 0
\(751\) −11.3794 19.7097i −0.415240 0.719216i 0.580214 0.814464i \(-0.302969\pi\)
−0.995454 + 0.0952479i \(0.969636\pi\)
\(752\) 0 0
\(753\) 1.51754 0.0553023
\(754\) 0 0
\(755\) −1.38919 + 2.40614i −0.0505576 + 0.0875684i
\(756\) 0 0
\(757\) −2.38713 + 4.13462i −0.0867616 + 0.150275i −0.906140 0.422977i \(-0.860985\pi\)
0.819379 + 0.573252i \(0.194318\pi\)
\(758\) 0 0
\(759\) 16.4243 0.596163
\(760\) 0 0
\(761\) 28.2222 1.02306 0.511528 0.859267i \(-0.329080\pi\)
0.511528 + 0.859267i \(0.329080\pi\)
\(762\) 0 0
\(763\) −0.305407 + 0.528981i −0.0110565 + 0.0191504i
\(764\) 0 0
\(765\) 11.5175 19.9490i 0.416418 0.721256i
\(766\) 0 0
\(767\) −9.27631 −0.334948
\(768\) 0 0
\(769\) −12.1108 20.9765i −0.436727 0.756434i 0.560708 0.828014i \(-0.310529\pi\)
−0.997435 + 0.0715802i \(0.977196\pi\)
\(770\) 0 0
\(771\) −12.1830 −0.438761
\(772\) 0 0
\(773\) −11.9804 20.7507i −0.430905 0.746349i 0.566046 0.824373i \(-0.308472\pi\)
−0.996951 + 0.0780239i \(0.975139\pi\)
\(774\) 0 0
\(775\) 33.6361 + 58.2594i 1.20824 + 2.09274i
\(776\) 0 0
\(777\) −16.9611 + 29.3775i −0.608476 + 1.05391i
\(778\) 0 0
\(779\) −14.3304 5.45242i −0.513439 0.195353i
\(780\) 0 0
\(781\) −25.4439 + 44.0701i −0.910453 + 1.57695i
\(782\) 0 0
\(783\) −2.69459 4.66717i −0.0962969 0.166791i
\(784\) 0 0
\(785\) −12.4902 21.6337i −0.445794 0.772138i
\(786\) 0 0
\(787\) 28.8871 1.02971 0.514857 0.857276i \(-0.327845\pi\)
0.514857 + 0.857276i \(0.327845\pi\)
\(788\) 0 0
\(789\) −9.69459 16.7915i −0.345137 0.597794i
\(790\) 0 0
\(791\) 11.4629 0.407572
\(792\) 0 0
\(793\) 4.25877 7.37641i 0.151233 0.261944i
\(794\) 0 0
\(795\) 9.67499 16.7576i 0.343137 0.594330i
\(796\) 0 0