Properties

Label 675.2.e.a.451.1
Level $675$
Weight $2$
Character 675.451
Analytic conductor $5.390$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 675.451
Dual form 675.2.e.a.226.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{7} -3.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{7} -3.00000 q^{8} +(-1.00000 + 1.73205i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(0.500000 - 0.866025i) q^{16} +4.00000 q^{17} -8.00000 q^{19} +(-1.00000 - 1.73205i) q^{22} +(-1.50000 - 2.59808i) q^{23} +2.00000 q^{26} -3.00000 q^{28} +(-0.500000 + 0.866025i) q^{29} +(-2.50000 - 4.33013i) q^{32} +(-2.00000 + 3.46410i) q^{34} +4.00000 q^{37} +(4.00000 - 6.92820i) q^{38} +(2.50000 + 4.33013i) q^{41} +(-4.00000 + 6.92820i) q^{43} -2.00000 q^{44} +3.00000 q^{46} +(-3.50000 + 6.06218i) q^{47} +(-1.00000 - 1.73205i) q^{49} +(1.00000 - 1.73205i) q^{52} -2.00000 q^{53} +(4.50000 - 7.79423i) q^{56} +(-0.500000 - 0.866025i) q^{58} +(-7.00000 - 12.1244i) q^{59} +(-3.50000 + 6.06218i) q^{61} +7.00000 q^{64} +(-1.50000 - 2.59808i) q^{67} +(2.00000 + 3.46410i) q^{68} -2.00000 q^{71} -4.00000 q^{73} +(-2.00000 + 3.46410i) q^{74} +(-4.00000 - 6.92820i) q^{76} +(-3.00000 - 5.19615i) q^{77} +(3.00000 - 5.19615i) q^{79} -5.00000 q^{82} +(-4.50000 + 7.79423i) q^{83} +(-4.00000 - 6.92820i) q^{86} +(3.00000 - 5.19615i) q^{88} +15.0000 q^{89} +6.00000 q^{91} +(1.50000 - 2.59808i) q^{92} +(-3.50000 - 6.06218i) q^{94} +(1.00000 - 1.73205i) q^{97} +2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{4} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + q^{4} - 3 q^{7} - 6 q^{8} - 2 q^{11} - 2 q^{13} - 3 q^{14} + q^{16} + 8 q^{17} - 16 q^{19} - 2 q^{22} - 3 q^{23} + 4 q^{26} - 6 q^{28} - q^{29} - 5 q^{32} - 4 q^{34} + 8 q^{37} + 8 q^{38} + 5 q^{41} - 8 q^{43} - 4 q^{44} + 6 q^{46} - 7 q^{47} - 2 q^{49} + 2 q^{52} - 4 q^{53} + 9 q^{56} - q^{58} - 14 q^{59} - 7 q^{61} + 14 q^{64} - 3 q^{67} + 4 q^{68} - 4 q^{71} - 8 q^{73} - 4 q^{74} - 8 q^{76} - 6 q^{77} + 6 q^{79} - 10 q^{82} - 9 q^{83} - 8 q^{86} + 6 q^{88} + 30 q^{89} + 12 q^{91} + 3 q^{92} - 7 q^{94} + 2 q^{97} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i −0.986869 0.161521i \(-0.948360\pi\)
0.633316 + 0.773893i \(0.281693\pi\)
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −1.50000 + 2.59808i −0.566947 + 0.981981i 0.429919 + 0.902867i \(0.358542\pi\)
−0.996866 + 0.0791130i \(0.974791\pi\)
\(8\) −3.00000 −1.06066
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −1.50000 2.59808i −0.400892 0.694365i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) −8.00000 −1.83533 −0.917663 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.00000 1.73205i −0.213201 0.369274i
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) −3.00000 −0.566947
\(29\) −0.500000 + 0.866025i −0.0928477 + 0.160817i −0.908708 0.417432i \(-0.862930\pi\)
0.815861 + 0.578249i \(0.196264\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) −2.50000 4.33013i −0.441942 0.765466i
\(33\) 0 0
\(34\) −2.00000 + 3.46410i −0.342997 + 0.594089i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 4.00000 6.92820i 0.648886 1.12390i
\(39\) 0 0
\(40\) 0 0
\(41\) 2.50000 + 4.33013i 0.390434 + 0.676252i 0.992507 0.122189i \(-0.0389915\pi\)
−0.602072 + 0.798441i \(0.705658\pi\)
\(42\) 0 0
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) −3.50000 + 6.06218i −0.510527 + 0.884260i 0.489398 + 0.872060i \(0.337217\pi\)
−0.999926 + 0.0121990i \(0.996117\pi\)
\(48\) 0 0
\(49\) −1.00000 1.73205i −0.142857 0.247436i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 4.50000 7.79423i 0.601338 1.04155i
\(57\) 0 0
\(58\) −0.500000 0.866025i −0.0656532 0.113715i
\(59\) −7.00000 12.1244i −0.911322 1.57846i −0.812198 0.583382i \(-0.801729\pi\)
−0.0991242 0.995075i \(-0.531604\pi\)
\(60\) 0 0
\(61\) −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i \(-0.981243\pi\)
0.550135 + 0.835076i \(0.314576\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i \(-0.225330\pi\)
−0.942987 + 0.332830i \(0.891996\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) 0 0
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) −2.00000 + 3.46410i −0.232495 + 0.402694i
\(75\) 0 0
\(76\) −4.00000 6.92820i −0.458831 0.794719i
\(77\) −3.00000 5.19615i −0.341882 0.592157i
\(78\) 0 0
\(79\) 3.00000 5.19615i 0.337526 0.584613i −0.646440 0.762964i \(-0.723743\pi\)
0.983967 + 0.178352i \(0.0570765\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −5.00000 −0.552158
\(83\) −4.50000 + 7.79423i −0.493939 + 0.855528i −0.999976 0.00698436i \(-0.997777\pi\)
0.506036 + 0.862512i \(0.331110\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) 0 0
\(88\) 3.00000 5.19615i 0.319801 0.553912i
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) 1.50000 2.59808i 0.156386 0.270868i
\(93\) 0 0
\(94\) −3.50000 6.06218i −0.360997 0.625266i
\(95\) 0 0
\(96\) 0 0
\(97\) 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) 2.00000 0.202031
\(99\) 0 0
\(100\) 0 0
\(101\) −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i \(0.519872\pi\)
−0.833143 + 0.553058i \(0.813461\pi\)
\(102\) 0 0
\(103\) 4.00000 + 6.92820i 0.394132 + 0.682656i 0.992990 0.118199i \(-0.0377120\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(104\) 3.00000 + 5.19615i 0.294174 + 0.509525i
\(105\) 0 0
\(106\) 1.00000 1.73205i 0.0971286 0.168232i
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 0 0
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.50000 + 2.59808i 0.141737 + 0.245495i
\(113\) 4.00000 + 6.92820i 0.376288 + 0.651751i 0.990519 0.137376i \(-0.0438669\pi\)
−0.614231 + 0.789127i \(0.710534\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.00000 −0.0928477
\(117\) 0 0
\(118\) 14.0000 1.28880
\(119\) −6.00000 + 10.3923i −0.550019 + 0.952661i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −3.50000 6.06218i −0.316875 0.548844i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 1.50000 2.59808i 0.132583 0.229640i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 0 0
\(133\) 12.0000 20.7846i 1.04053 1.80225i
\(134\) 3.00000 0.259161
\(135\) 0 0
\(136\) −12.0000 −1.02899
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) 8.00000 + 13.8564i 0.678551 + 1.17529i 0.975417 + 0.220366i \(0.0707252\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.00000 1.73205i 0.0839181 0.145350i
\(143\) 4.00000 0.334497
\(144\) 0 0
\(145\) 0 0
\(146\) 2.00000 3.46410i 0.165521 0.286691i
\(147\) 0 0
\(148\) 2.00000 + 3.46410i 0.164399 + 0.284747i
\(149\) 8.50000 + 14.7224i 0.696347 + 1.20611i 0.969724 + 0.244202i \(0.0785259\pi\)
−0.273377 + 0.961907i \(0.588141\pi\)
\(150\) 0 0
\(151\) 1.00000 1.73205i 0.0813788 0.140952i −0.822464 0.568818i \(-0.807401\pi\)
0.903842 + 0.427865i \(0.140734\pi\)
\(152\) 24.0000 1.94666
\(153\) 0 0
\(154\) 6.00000 0.483494
\(155\) 0 0
\(156\) 0 0
\(157\) 7.00000 + 12.1244i 0.558661 + 0.967629i 0.997609 + 0.0691164i \(0.0220180\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) 3.00000 + 5.19615i 0.238667 + 0.413384i
\(159\) 0 0
\(160\) 0 0
\(161\) 9.00000 0.709299
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −2.50000 + 4.33013i −0.195217 + 0.338126i
\(165\) 0 0
\(166\) −4.50000 7.79423i −0.349268 0.604949i
\(167\) 4.50000 + 7.79423i 0.348220 + 0.603136i 0.985933 0.167139i \(-0.0534527\pi\)
−0.637713 + 0.770274i \(0.720119\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) 0 0
\(172\) −8.00000 −0.609994
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 + 1.73205i 0.0753778 + 0.130558i
\(177\) 0 0
\(178\) −7.50000 + 12.9904i −0.562149 + 0.973670i
\(179\) 2.00000 0.149487 0.0747435 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) −3.00000 + 5.19615i −0.222375 + 0.385164i
\(183\) 0 0
\(184\) 4.50000 + 7.79423i 0.331744 + 0.574598i
\(185\) 0 0
\(186\) 0 0
\(187\) −4.00000 + 6.92820i −0.292509 + 0.506640i
\(188\) −7.00000 −0.510527
\(189\) 0 0
\(190\) 0 0
\(191\) 4.00000 6.92820i 0.289430 0.501307i −0.684244 0.729253i \(-0.739868\pi\)
0.973674 + 0.227946i \(0.0732010\pi\)
\(192\) 0 0
\(193\) −5.00000 8.66025i −0.359908 0.623379i 0.628037 0.778183i \(-0.283859\pi\)
−0.987945 + 0.154805i \(0.950525\pi\)
\(194\) 1.00000 + 1.73205i 0.0717958 + 0.124354i
\(195\) 0 0
\(196\) 1.00000 1.73205i 0.0714286 0.123718i
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −9.00000 15.5885i −0.633238 1.09680i
\(203\) −1.50000 2.59808i −0.105279 0.182349i
\(204\) 0 0
\(205\) 0 0
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) −2.00000 −0.138675
\(209\) 8.00000 13.8564i 0.553372 0.958468i
\(210\) 0 0
\(211\) 11.0000 + 19.0526i 0.757271 + 1.31163i 0.944237 + 0.329266i \(0.106801\pi\)
−0.186966 + 0.982366i \(0.559865\pi\)
\(212\) −1.00000 1.73205i −0.0686803 0.118958i
\(213\) 0 0
\(214\) −1.50000 + 2.59808i −0.102538 + 0.177601i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −2.50000 + 4.33013i −0.169321 + 0.293273i
\(219\) 0 0
\(220\) 0 0
\(221\) −4.00000 6.92820i −0.269069 0.466041i
\(222\) 0 0
\(223\) −9.50000 + 16.4545i −0.636167 + 1.10187i 0.350100 + 0.936713i \(0.386148\pi\)
−0.986267 + 0.165161i \(0.947186\pi\)
\(224\) 15.0000 1.00223
\(225\) 0 0
\(226\) −8.00000 −0.532152
\(227\) 2.00000 3.46410i 0.132745 0.229920i −0.791989 0.610535i \(-0.790954\pi\)
0.924734 + 0.380615i \(0.124288\pi\)
\(228\) 0 0
\(229\) −7.50000 12.9904i −0.495614 0.858429i 0.504373 0.863486i \(-0.331724\pi\)
−0.999987 + 0.00505719i \(0.998390\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.50000 2.59808i 0.0984798 0.170572i
\(233\) 24.0000 1.57229 0.786146 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 7.00000 12.1244i 0.455661 0.789228i
\(237\) 0 0
\(238\) −6.00000 10.3923i −0.388922 0.673633i
\(239\) −4.00000 6.92820i −0.258738 0.448148i 0.707166 0.707048i \(-0.249973\pi\)
−0.965904 + 0.258900i \(0.916640\pi\)
\(240\) 0 0
\(241\) 5.50000 9.52628i 0.354286 0.613642i −0.632709 0.774389i \(-0.718057\pi\)
0.986996 + 0.160748i \(0.0513906\pi\)
\(242\) −7.00000 −0.449977
\(243\) 0 0
\(244\) −7.00000 −0.448129
\(245\) 0 0
\(246\) 0 0
\(247\) 8.00000 + 13.8564i 0.509028 + 0.881662i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) −2.50000 + 4.33013i −0.156864 + 0.271696i
\(255\) 0 0
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) 0 0
\(259\) −6.00000 + 10.3923i −0.372822 + 0.645746i
\(260\) 0 0
\(261\) 0 0
\(262\) 6.00000 0.370681
\(263\) 8.00000 13.8564i 0.493301 0.854423i −0.506669 0.862141i \(-0.669123\pi\)
0.999970 + 0.00771799i \(0.00245674\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 12.0000 + 20.7846i 0.735767 + 1.27439i
\(267\) 0 0
\(268\) 1.50000 2.59808i 0.0916271 0.158703i
\(269\) −25.0000 −1.52428 −0.762138 0.647414i \(-0.775850\pi\)
−0.762138 + 0.647414i \(0.775850\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 2.00000 3.46410i 0.121268 0.210042i
\(273\) 0 0
\(274\) −6.00000 10.3923i −0.362473 0.627822i
\(275\) 0 0
\(276\) 0 0
\(277\) 6.00000 10.3923i 0.360505 0.624413i −0.627539 0.778585i \(-0.715938\pi\)
0.988044 + 0.154172i \(0.0492710\pi\)
\(278\) −16.0000 −0.959616
\(279\) 0 0
\(280\) 0 0
\(281\) −7.50000 + 12.9904i −0.447412 + 0.774941i −0.998217 0.0596933i \(-0.980988\pi\)
0.550804 + 0.834634i \(0.314321\pi\)
\(282\) 0 0
\(283\) 10.5000 + 18.1865i 0.624160 + 1.08108i 0.988703 + 0.149890i \(0.0478921\pi\)
−0.364542 + 0.931187i \(0.618775\pi\)
\(284\) −1.00000 1.73205i −0.0593391 0.102778i
\(285\) 0 0
\(286\) −2.00000 + 3.46410i −0.118262 + 0.204837i
\(287\) −15.0000 −0.885422
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) −2.00000 3.46410i −0.117041 0.202721i
\(293\) −6.00000 10.3923i −0.350524 0.607125i 0.635818 0.771839i \(-0.280663\pi\)
−0.986341 + 0.164714i \(0.947330\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −12.0000 −0.697486
\(297\) 0 0
\(298\) −17.0000 −0.984784
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 0 0
\(301\) −12.0000 20.7846i −0.691669 1.19800i
\(302\) 1.00000 + 1.73205i 0.0575435 + 0.0996683i
\(303\) 0 0
\(304\) −4.00000 + 6.92820i −0.229416 + 0.397360i
\(305\) 0 0
\(306\) 0 0
\(307\) −7.00000 −0.399511 −0.199756 0.979846i \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) 3.00000 5.19615i 0.170941 0.296078i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) 0 0
\(313\) 7.00000 12.1244i 0.395663 0.685309i −0.597522 0.801852i \(-0.703848\pi\)
0.993186 + 0.116543i \(0.0371814\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 6.00000 0.337526
\(317\) 17.0000 29.4449i 0.954815 1.65379i 0.220024 0.975494i \(-0.429386\pi\)
0.734791 0.678294i \(-0.237280\pi\)
\(318\) 0 0
\(319\) −1.00000 1.73205i −0.0559893 0.0969762i
\(320\) 0 0
\(321\) 0 0
\(322\) −4.50000 + 7.79423i −0.250775 + 0.434355i
\(323\) −32.0000 −1.78053
\(324\) 0 0
\(325\) 0 0
\(326\) −2.00000 + 3.46410i −0.110770 + 0.191859i
\(327\) 0 0
\(328\) −7.50000 12.9904i −0.414118 0.717274i
\(329\) −10.5000 18.1865i −0.578884 1.00266i
\(330\) 0 0
\(331\) 3.00000 5.19615i 0.164895 0.285606i −0.771723 0.635959i \(-0.780605\pi\)
0.936618 + 0.350352i \(0.113938\pi\)
\(332\) −9.00000 −0.493939
\(333\) 0 0
\(334\) −9.00000 −0.492458
\(335\) 0 0
\(336\) 0 0
\(337\) −4.00000 6.92820i −0.217894 0.377403i 0.736270 0.676688i \(-0.236585\pi\)
−0.954164 + 0.299285i \(0.903252\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 12.0000 20.7846i 0.646997 1.12063i
\(345\) 0 0
\(346\) 0 0
\(347\) −2.00000 3.46410i −0.107366 0.185963i 0.807337 0.590091i \(-0.200908\pi\)
−0.914702 + 0.404128i \(0.867575\pi\)
\(348\) 0 0
\(349\) 2.50000 4.33013i 0.133822 0.231786i −0.791325 0.611396i \(-0.790608\pi\)
0.925147 + 0.379610i \(0.123942\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.0000 0.533002
\(353\) −12.0000 + 20.7846i −0.638696 + 1.10625i 0.347024 + 0.937856i \(0.387192\pi\)
−0.985719 + 0.168397i \(0.946141\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 7.50000 + 12.9904i 0.397499 + 0.688489i
\(357\) 0 0
\(358\) −1.00000 + 1.73205i −0.0528516 + 0.0915417i
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) 3.50000 6.06218i 0.183956 0.318621i
\(363\) 0 0
\(364\) 3.00000 + 5.19615i 0.157243 + 0.272352i
\(365\) 0 0
\(366\) 0 0
\(367\) 12.0000 20.7846i 0.626395 1.08495i −0.361874 0.932227i \(-0.617863\pi\)
0.988269 0.152721i \(-0.0488036\pi\)
\(368\) −3.00000 −0.156386
\(369\) 0 0
\(370\) 0 0
\(371\) 3.00000 5.19615i 0.155752 0.269771i
\(372\) 0 0
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) −4.00000 6.92820i −0.206835 0.358249i
\(375\) 0 0
\(376\) 10.5000 18.1865i 0.541496 0.937899i
\(377\) 2.00000 0.103005
\(378\) 0 0
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 4.00000 + 6.92820i 0.204658 + 0.354478i
\(383\) −18.0000 31.1769i −0.919757 1.59307i −0.799783 0.600289i \(-0.795052\pi\)
−0.119974 0.992777i \(-0.538281\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) 0 0
\(388\) 2.00000 0.101535
\(389\) 16.5000 28.5788i 0.836583 1.44900i −0.0561516 0.998422i \(-0.517883\pi\)
0.892735 0.450582i \(-0.148784\pi\)
\(390\) 0 0
\(391\) −6.00000 10.3923i −0.303433 0.525561i
\(392\) 3.00000 + 5.19615i 0.151523 + 0.262445i
\(393\) 0 0
\(394\) 6.00000 10.3923i 0.302276 0.523557i
\(395\) 0 0
\(396\) 0 0
\(397\) −34.0000 −1.70641 −0.853206 0.521575i \(-0.825345\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −2.00000 + 3.46410i −0.100251 + 0.173640i
\(399\) 0 0
\(400\) 0 0
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −18.0000 −0.895533
\(405\) 0 0
\(406\) 3.00000 0.148888
\(407\) −4.00000 + 6.92820i −0.198273 + 0.343418i
\(408\) 0 0
\(409\) −7.00000 12.1244i −0.346128 0.599511i 0.639430 0.768849i \(-0.279170\pi\)
−0.985558 + 0.169338i \(0.945837\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.00000 + 6.92820i −0.197066 + 0.341328i
\(413\) 42.0000 2.06668
\(414\) 0 0
\(415\) 0 0
\(416\) −5.00000 + 8.66025i −0.245145 + 0.424604i
\(417\) 0 0
\(418\) 8.00000 + 13.8564i 0.391293 + 0.677739i
\(419\) 13.0000 + 22.5167i 0.635092 + 1.10001i 0.986496 + 0.163787i \(0.0523710\pi\)
−0.351404 + 0.936224i \(0.614296\pi\)
\(420\) 0 0
\(421\) −17.0000 + 29.4449i −0.828529 + 1.43505i 0.0706626 + 0.997500i \(0.477489\pi\)
−0.899192 + 0.437555i \(0.855845\pi\)
\(422\) −22.0000 −1.07094
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) −10.5000 18.1865i −0.508131 0.880108i
\(428\) 1.50000 + 2.59808i 0.0725052 + 0.125583i
\(429\) 0 0
\(430\) 0 0
\(431\) 30.0000 1.44505 0.722525 0.691345i \(-0.242982\pi\)
0.722525 + 0.691345i \(0.242982\pi\)
\(432\) 0 0
\(433\) −28.0000 −1.34559 −0.672797 0.739827i \(-0.734907\pi\)
−0.672797 + 0.739827i \(0.734907\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.50000 + 4.33013i 0.119728 + 0.207375i
\(437\) 12.0000 + 20.7846i 0.574038 + 0.994263i
\(438\) 0 0
\(439\) −14.0000 + 24.2487i −0.668184 + 1.15733i 0.310228 + 0.950662i \(0.399595\pi\)
−0.978412 + 0.206666i \(0.933739\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 8.00000 0.380521
\(443\) −7.50000 + 12.9904i −0.356336 + 0.617192i −0.987346 0.158583i \(-0.949307\pi\)
0.631010 + 0.775775i \(0.282641\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −9.50000 16.4545i −0.449838 0.779142i
\(447\) 0 0
\(448\) −10.5000 + 18.1865i −0.496078 + 0.859233i
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) 0 0
\(451\) −10.0000 −0.470882
\(452\) −4.00000 + 6.92820i −0.188144 + 0.325875i
\(453\) 0 0
\(454\) 2.00000 + 3.46410i 0.0938647 + 0.162578i
\(455\) 0 0
\(456\) 0 0
\(457\) −10.0000 + 17.3205i −0.467780 + 0.810219i −0.999322 0.0368128i \(-0.988279\pi\)
0.531542 + 0.847032i \(0.321613\pi\)
\(458\) 15.0000 0.700904
\(459\) 0 0
\(460\) 0 0
\(461\) 4.50000 7.79423i 0.209586 0.363013i −0.741998 0.670402i \(-0.766122\pi\)
0.951584 + 0.307388i \(0.0994551\pi\)
\(462\) 0 0
\(463\) −18.0000 31.1769i −0.836531 1.44891i −0.892778 0.450497i \(-0.851247\pi\)
0.0562469 0.998417i \(-0.482087\pi\)
\(464\) 0.500000 + 0.866025i 0.0232119 + 0.0402042i
\(465\) 0 0
\(466\) −12.0000 + 20.7846i −0.555889 + 0.962828i
\(467\) 20.0000 0.925490 0.462745 0.886492i \(-0.346865\pi\)
0.462745 + 0.886492i \(0.346865\pi\)
\(468\) 0 0
\(469\) 9.00000 0.415581
\(470\) 0 0
\(471\) 0 0
\(472\) 21.0000 + 36.3731i 0.966603 + 1.67421i
\(473\) −8.00000 13.8564i −0.367840 0.637118i
\(474\) 0 0
\(475\) 0 0
\(476\) −12.0000 −0.550019
\(477\) 0 0
\(478\) 8.00000 0.365911
\(479\) −9.00000 + 15.5885i −0.411220 + 0.712255i −0.995023 0.0996406i \(-0.968231\pi\)
0.583803 + 0.811895i \(0.301564\pi\)
\(480\) 0 0
\(481\) −4.00000 6.92820i −0.182384 0.315899i
\(482\) 5.50000 + 9.52628i 0.250518 + 0.433910i
\(483\) 0 0
\(484\) −3.50000 + 6.06218i −0.159091 + 0.275554i
\(485\) 0 0
\(486\) 0 0
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) 10.5000 18.1865i 0.475313 0.823266i
\(489\) 0 0
\(490\) 0 0
\(491\) 10.0000 + 17.3205i 0.451294 + 0.781664i 0.998467 0.0553560i \(-0.0176294\pi\)
−0.547173 + 0.837020i \(0.684296\pi\)
\(492\) 0 0
\(493\) −2.00000 + 3.46410i −0.0900755 + 0.156015i
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) 0 0
\(497\) 3.00000 5.19615i 0.134568 0.233079i
\(498\) 0 0
\(499\) 16.0000 + 27.7128i 0.716258 + 1.24060i 0.962472 + 0.271380i \(0.0874801\pi\)
−0.246214 + 0.969216i \(0.579187\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −7.00000 −0.312115 −0.156057 0.987748i \(-0.549878\pi\)
−0.156057 + 0.987748i \(0.549878\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −3.00000 + 5.19615i −0.133366 + 0.230997i
\(507\) 0 0
\(508\) 2.50000 + 4.33013i 0.110920 + 0.192118i
\(509\) 21.5000 + 37.2391i 0.952971 + 1.65059i 0.738945 + 0.673766i \(0.235324\pi\)
0.214026 + 0.976828i \(0.431342\pi\)
\(510\) 0 0
\(511\) 6.00000 10.3923i 0.265424 0.459728i
\(512\) −11.0000 −0.486136
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) 0 0
\(516\) 0 0
\(517\) −7.00000 12.1244i −0.307860 0.533229i
\(518\) −6.00000 10.3923i −0.263625 0.456612i
\(519\) 0 0
\(520\) 0 0
\(521\) −11.0000 −0.481919 −0.240959 0.970535i \(-0.577462\pi\)
−0.240959 + 0.970535i \(0.577462\pi\)
\(522\) 0 0
\(523\) 29.0000 1.26808 0.634041 0.773300i \(-0.281395\pi\)
0.634041 + 0.773300i \(0.281395\pi\)
\(524\) 3.00000 5.19615i 0.131056 0.226995i
\(525\) 0 0
\(526\) 8.00000 + 13.8564i 0.348817 + 0.604168i
\(527\) 0 0
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 0 0
\(532\) 24.0000 1.04053
\(533\) 5.00000 8.66025i 0.216574 0.375117i
\(534\) 0 0
\(535\) 0 0
\(536\) 4.50000 + 7.79423i 0.194370 + 0.336659i
\(537\) 0 0
\(538\) 12.5000 21.6506i 0.538913 0.933425i
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −39.0000 −1.67674 −0.838370 0.545101i \(-0.816491\pi\)
−0.838370 + 0.545101i \(0.816491\pi\)
\(542\) 4.00000 6.92820i 0.171815 0.297592i
\(543\) 0 0
\(544\) −10.0000 17.3205i −0.428746 0.742611i
\(545\) 0 0
\(546\) 0 0
\(547\) −14.5000 + 25.1147i −0.619975 + 1.07383i 0.369514 + 0.929225i \(0.379524\pi\)
−0.989490 + 0.144604i \(0.953809\pi\)
\(548\) −12.0000 −0.512615
\(549\) 0 0
\(550\) 0 0
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) 0 0
\(553\) 9.00000 + 15.5885i 0.382719 + 0.662889i
\(554\) 6.00000 + 10.3923i 0.254916 + 0.441527i
\(555\) 0 0
\(556\) −8.00000 + 13.8564i −0.339276 + 0.587643i
\(557\) −30.0000 −1.27114 −0.635570 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 0 0
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) −7.50000 12.9904i −0.316368 0.547966i
\(563\) 10.5000 + 18.1865i 0.442522 + 0.766471i 0.997876 0.0651433i \(-0.0207504\pi\)
−0.555354 + 0.831614i \(0.687417\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −21.0000 −0.882696
\(567\) 0 0
\(568\) 6.00000 0.251754
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 2.00000 + 3.46410i 0.0836242 + 0.144841i
\(573\) 0 0
\(574\) 7.50000 12.9904i 0.313044 0.542208i
\(575\) 0 0
\(576\) 0 0
\(577\) 10.0000 0.416305 0.208153 0.978096i \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) 0.500000 0.866025i 0.0207973 0.0360219i
\(579\) 0 0
\(580\) 0 0
\(581\) −13.5000 23.3827i −0.560074 0.970077i
\(582\) 0 0
\(583\) 2.00000 3.46410i 0.0828315 0.143468i
\(584\) 12.0000 0.496564
\(585\) 0 0
\(586\) 12.0000 0.495715
\(587\) 16.5000 28.5788i 0.681028 1.17957i −0.293640 0.955916i \(-0.594867\pi\)
0.974668 0.223659i \(-0.0718001\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 2.00000 3.46410i 0.0821995 0.142374i
\(593\) 20.0000 0.821302 0.410651 0.911793i \(-0.365302\pi\)
0.410651 + 0.911793i \(0.365302\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −8.50000 + 14.7224i −0.348174 + 0.603054i
\(597\) 0 0
\(598\) −3.00000 5.19615i −0.122679 0.212486i
\(599\) −5.00000 8.66025i −0.204294 0.353848i 0.745613 0.666379i \(-0.232157\pi\)
−0.949908 + 0.312531i \(0.898823\pi\)
\(600\) 0 0
\(601\) −1.00000 + 1.73205i −0.0407909 + 0.0706518i −0.885700 0.464258i \(-0.846321\pi\)
0.844909 + 0.534910i \(0.179654\pi\)
\(602\) 24.0000 0.978167
\(603\) 0 0
\(604\) 2.00000 0.0813788
\(605\) 0 0
\(606\) 0 0
\(607\) −20.5000 35.5070i −0.832069 1.44119i −0.896394 0.443257i \(-0.853823\pi\)
0.0643251 0.997929i \(-0.479511\pi\)
\(608\) 20.0000 + 34.6410i 0.811107 + 1.40488i
\(609\) 0 0
\(610\) 0 0
\(611\) 14.0000 0.566379
\(612\) 0 0
\(613\) 44.0000 1.77714 0.888572 0.458738i \(-0.151698\pi\)
0.888572 + 0.458738i \(0.151698\pi\)
\(614\) 3.50000 6.06218i 0.141249 0.244650i
\(615\) 0 0
\(616\) 9.00000 + 15.5885i 0.362620 + 0.628077i
\(617\) 18.0000 + 31.1769i 0.724653 + 1.25514i 0.959117 + 0.283011i \(0.0913331\pi\)
−0.234464 + 0.972125i \(0.575334\pi\)
\(618\) 0 0
\(619\) 2.00000 3.46410i 0.0803868 0.139234i −0.823029 0.567999i \(-0.807718\pi\)
0.903416 + 0.428765i \(0.141051\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −22.5000 + 38.9711i −0.901443 + 1.56135i
\(624\) 0 0
\(625\) 0 0
\(626\) 7.00000 + 12.1244i 0.279776 + 0.484587i
\(627\) 0 0
\(628\) −7.00000 + 12.1244i −0.279330 + 0.483814i
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) −9.00000 + 15.5885i −0.358001 + 0.620076i
\(633\) 0 0
\(634\) 17.0000 + 29.4449i 0.675156 + 1.16940i
\(635\) 0 0
\(636\) 0 0
\(637\) −2.00000 + 3.46410i −0.0792429 + 0.137253i
\(638\) 2.00000 0.0791808
\(639\) 0 0
\(640\) 0 0
\(641\) 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) 0 0
\(643\) −4.50000 7.79423i −0.177463 0.307374i 0.763548 0.645751i \(-0.223456\pi\)
−0.941011 + 0.338377i \(0.890122\pi\)
\(644\) 4.50000 + 7.79423i 0.177325 + 0.307136i
\(645\) 0 0
\(646\) 16.0000 27.7128i 0.629512 1.09035i
\(647\) −17.0000 −0.668339 −0.334169 0.942513i \(-0.608456\pi\)
−0.334169 + 0.942513i \(0.608456\pi\)
\(648\) 0 0
\(649\) 28.0000 1.09910
\(650\) 0 0
\(651\) 0 0
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) 2.00000 + 3.46410i 0.0782660 + 0.135561i 0.902502 0.430686i \(-0.141728\pi\)
−0.824236 + 0.566247i \(0.808395\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 5.00000 0.195217
\(657\) 0 0
\(658\) 21.0000 0.818665
\(659\) −4.00000 + 6.92820i −0.155818 + 0.269884i −0.933357 0.358951i \(-0.883135\pi\)
0.777539 + 0.628835i \(0.216468\pi\)
\(660\) 0 0
\(661\) 7.00000 + 12.1244i 0.272268 + 0.471583i 0.969442 0.245319i \(-0.0788928\pi\)
−0.697174 + 0.716902i \(0.745559\pi\)
\(662\) 3.00000 + 5.19615i 0.116598 + 0.201954i
\(663\) 0 0
\(664\) 13.5000 23.3827i 0.523902 0.907424i
\(665\) 0 0
\(666\) 0 0
\(667\) 3.00000 0.116160
\(668\) −4.50000 + 7.79423i −0.174110 + 0.301568i
\(669\) 0 0
\(670\) 0 0
\(671\) −7.00000 12.1244i −0.270232 0.468056i
\(672\) 0 0
\(673\) 3.00000 5.19615i 0.115642 0.200297i −0.802395 0.596794i \(-0.796441\pi\)
0.918036 + 0.396497i \(0.129774\pi\)
\(674\) 8.00000 0.308148
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) 21.0000 36.3731i 0.807096 1.39793i −0.107772 0.994176i \(-0.534372\pi\)
0.914867 0.403755i \(-0.132295\pi\)
\(678\) 0 0
\(679\) 3.00000 + 5.19615i 0.115129 + 0.199410i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 7.50000 12.9904i 0.286351 0.495975i
\(687\) 0 0
\(688\) 4.00000 + 6.92820i 0.152499 + 0.264135i
\(689\) 2.00000 + 3.46410i 0.0761939 + 0.131972i
\(690\) 0 0
\(691\) 7.00000 12.1244i 0.266293 0.461232i −0.701609 0.712562i \(-0.747535\pi\)
0.967901 + 0.251330i \(0.0808679\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) 0 0
\(696\) 0 0
\(697\) 10.0000 + 17.3205i 0.378777 + 0.656061i
\(698\) 2.50000 + 4.33013i 0.0946264 + 0.163898i
\(699\) 0 0
\(700\) 0 0
\(701\) −23.0000 −0.868698 −0.434349 0.900745i \(-0.643022\pi\)
−0.434349 + 0.900745i \(0.643022\pi\)
\(702\) 0 0
\(703\) −32.0000 −1.20690
\(704\) −7.00000 + 12.1244i −0.263822 + 0.456954i
\(705\) 0 0
\(706\) −12.0000 20.7846i −0.451626 0.782239i
\(707\) −27.0000 46.7654i −1.01544 1.75879i
\(708\) 0 0
\(709\) 20.5000 35.5070i 0.769894 1.33349i −0.167727 0.985834i \(-0.553643\pi\)
0.937620 0.347661i \(-0.113024\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −45.0000 −1.68645
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.00000 + 1.73205i 0.0373718 + 0.0647298i
\(717\) 0 0
\(718\) 12.0000 20.7846i 0.447836 0.775675i
\(719\) −6.00000 −0.223762 −0.111881 0.993722i \(-0.535688\pi\)
−0.111881 + 0.993722i \(0.535688\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) −22.5000 + 38.9711i −0.837363 + 1.45036i
\(723\) 0 0
\(724\) −3.50000 6.06218i −0.130076 0.225299i
\(725\) 0 0
\(726\) 0 0
\(727\) 11.5000 19.9186i 0.426511 0.738739i −0.570049 0.821611i \(-0.693076\pi\)
0.996560 + 0.0828714i \(0.0264091\pi\)
\(728\) −18.0000 −0.667124
\(729\) 0 0
\(730\) 0 0
\(731\) −16.0000 + 27.7128i −0.591781 + 1.02500i
\(732\) 0 0
\(733\) −17.0000 29.4449i −0.627909 1.08757i −0.987971 0.154642i \(-0.950578\pi\)
0.360061 0.932929i \(-0.382756\pi\)
\(734\) 12.0000 + 20.7846i 0.442928 + 0.767174i
\(735\) 0 0
\(736\) −7.50000 + 12.9904i −0.276454 + 0.478832i
\(737\) 6.00000 0.221013
\(738\) 0 0
\(739\) −2.00000 −0.0735712 −0.0367856 0.999323i \(-0.511712\pi\)
−0.0367856 + 0.999323i \(0.511712\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 3.00000 + 5.19615i 0.110133 + 0.190757i
\(743\) 14.5000 + 25.1147i 0.531953 + 0.921370i 0.999304 + 0.0372984i \(0.0118752\pi\)
−0.467351 + 0.884072i \(0.654791\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −10.0000 −0.366126
\(747\) 0 0
\(748\) −8.00000 −0.292509
\(749\) −4.50000 + 7.79423i −0.164426 + 0.284795i
\(750\) 0 0
\(751\) −5.00000 8.66025i −0.182453 0.316017i 0.760263 0.649616i \(-0.225070\pi\)
−0.942715 + 0.333599i \(0.891737\pi\)
\(752\) 3.50000 + 6.06218i 0.127632 + 0.221065i
\(753\) 0 0
\(754\) −1.00000 + 1.73205i −0.0364179 + 0.0630776i
\(755\) 0 0
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 13.0000 22.5167i 0.472181 0.817842i
\(759\) 0 0
\(760\) 0 0
\(761\) 7.50000 + 12.9904i 0.271875 + 0.470901i 0.969342 0.245716i \(-0.0790230\pi\)
−0.697467 + 0.716617i \(0.745690\pi\)
\(762\) 0 0
\(763\) −7.50000 + 12.9904i −0.271518 + 0.470283i
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) 36.0000 1.30073
\(767\) −14.0000 + 24.2487i −0.505511 + 0.875570i
\(768\) 0 0
\(769\) −2.50000 4.33013i −0.0901523 0.156148i 0.817423 0.576038i \(-0.195402\pi\)
−0.907575 + 0.419890i \(0.862069\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 5.00000 8.66025i 0.179954 0.311689i
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −3.00000 + 5.19615i −0.107694 + 0.186531i
\(777\) 0 0
\(778\) 16.5000 + 28.5788i 0.591554 + 1.02460i
\(779\) −20.0000 34.6410i −0.716574 1.24114i
\(780\) 0 0
\(781\) 2.00000 3.46410i 0.0715656 0.123955i
\(782\) 12.0000 0.429119
\(783\) 0 0
\(784\) −2.00000 −0.0714286
\(785\) 0 0
\(786\) 0 0
\(787\) 14.0000 + 24.2487i 0.499046 + 0.864373i 0.999999 0.00110111i \(-0.000350496\pi\)
−0.500953 + 0.865474i \(0.667017\pi\)
\(788\) −6.00000 10.3923i −0.213741 0.370211i
\(789\) 0 0
\(790\) 0 0
\(791\) −24.0000 −0.853342
\(792\) 0 0
\(793\) 14.0000 0.497155
\(794\) 17.0000 29.4449i 0.603307 1.04496i