Properties

Label 324.3.f.h.55.1
Level $324$
Weight $3$
Character 324.55
Analytic conductor $8.828$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 55.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 324.55
Dual form 324.3.f.h.271.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} +(7.50000 + 4.33013i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} +(7.50000 + 4.33013i) q^{7} -8.00000 q^{8} +(-7.00000 + 12.1244i) q^{10} +(7.50000 + 4.33013i) q^{11} +(-10.0000 - 17.3205i) q^{13} +17.3205i q^{14} +(-8.00000 - 13.8564i) q^{16} +8.00000 q^{17} +10.3923i q^{19} -28.0000 q^{20} +17.3205i q^{22} +(3.00000 - 1.73205i) q^{23} +(-12.0000 + 20.7846i) q^{25} +(20.0000 - 34.6410i) q^{26} +(-30.0000 + 17.3205i) q^{28} +(5.00000 - 8.66025i) q^{29} +(-46.5000 + 26.8468i) q^{31} +(16.0000 - 27.7128i) q^{32} +(8.00000 + 13.8564i) q^{34} +60.6218i q^{35} -10.0000 q^{37} +(-18.0000 + 10.3923i) q^{38} +(-28.0000 - 48.4974i) q^{40} +(-25.0000 - 43.3013i) q^{41} +(-15.0000 - 8.66025i) q^{43} +(-30.0000 + 17.3205i) q^{44} +(6.00000 + 3.46410i) q^{46} +(75.0000 + 43.3013i) q^{47} +(13.0000 + 22.5167i) q^{49} -48.0000 q^{50} +80.0000 q^{52} +47.0000 q^{53} +60.6218i q^{55} +(-60.0000 - 34.6410i) q^{56} +20.0000 q^{58} +(30.0000 - 17.3205i) q^{59} +(32.0000 - 55.4256i) q^{61} +(-93.0000 - 53.6936i) q^{62} +64.0000 q^{64} +(70.0000 - 121.244i) q^{65} +(75.0000 - 43.3013i) q^{67} +(-16.0000 + 27.7128i) q^{68} +(-105.000 + 60.6218i) q^{70} -55.0000 q^{73} +(-10.0000 - 17.3205i) q^{74} +(-36.0000 - 20.7846i) q^{76} +(37.5000 + 64.9519i) q^{77} +(-6.00000 - 3.46410i) q^{79} +(56.0000 - 96.9948i) q^{80} +(50.0000 - 86.6025i) q^{82} +(25.5000 + 14.7224i) q^{83} +(28.0000 + 48.4974i) q^{85} -34.6410i q^{86} +(-60.0000 - 34.6410i) q^{88} -10.0000 q^{89} -173.205i q^{91} +13.8564i q^{92} +173.205i q^{94} +(-63.0000 + 36.3731i) q^{95} +(12.5000 - 21.6506i) q^{97} +(-26.0000 + 45.0333i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 4 q^{4} + 7 q^{5} + 15 q^{7} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 4 q^{4} + 7 q^{5} + 15 q^{7} - 16 q^{8} - 14 q^{10} + 15 q^{11} - 20 q^{13} - 16 q^{16} + 16 q^{17} - 56 q^{20} + 6 q^{23} - 24 q^{25} + 40 q^{26} - 60 q^{28} + 10 q^{29} - 93 q^{31} + 32 q^{32} + 16 q^{34} - 20 q^{37} - 36 q^{38} - 56 q^{40} - 50 q^{41} - 30 q^{43} - 60 q^{44} + 12 q^{46} + 150 q^{47} + 26 q^{49} - 96 q^{50} + 160 q^{52} + 94 q^{53} - 120 q^{56} + 40 q^{58} + 60 q^{59} + 64 q^{61} - 186 q^{62} + 128 q^{64} + 140 q^{65} + 150 q^{67} - 32 q^{68} - 210 q^{70} - 110 q^{73} - 20 q^{74} - 72 q^{76} + 75 q^{77} - 12 q^{79} + 112 q^{80} + 100 q^{82} + 51 q^{83} + 56 q^{85} - 120 q^{88} - 20 q^{89} - 126 q^{95} + 25 q^{97} - 52 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(5\) 3.50000 + 6.06218i 0.700000 + 1.21244i 0.968466 + 0.249146i \(0.0801500\pi\)
−0.268466 + 0.963289i \(0.586517\pi\)
\(6\) 0 0
\(7\) 7.50000 + 4.33013i 1.07143 + 0.618590i 0.928571 0.371154i \(-0.121038\pi\)
0.142857 + 0.989743i \(0.454371\pi\)
\(8\) −8.00000 −1.00000
\(9\) 0 0
\(10\) −7.00000 + 12.1244i −0.700000 + 1.21244i
\(11\) 7.50000 + 4.33013i 0.681818 + 0.393648i 0.800540 0.599280i \(-0.204546\pi\)
−0.118722 + 0.992928i \(0.537880\pi\)
\(12\) 0 0
\(13\) −10.0000 17.3205i −0.769231 1.33235i −0.937981 0.346688i \(-0.887306\pi\)
0.168750 0.985659i \(-0.446027\pi\)
\(14\) 17.3205i 1.23718i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.500000 0.866025i
\(17\) 8.00000 0.470588 0.235294 0.971924i \(-0.424395\pi\)
0.235294 + 0.971924i \(0.424395\pi\)
\(18\) 0 0
\(19\) 10.3923i 0.546963i 0.961877 + 0.273482i \(0.0881753\pi\)
−0.961877 + 0.273482i \(0.911825\pi\)
\(20\) −28.0000 −1.40000
\(21\) 0 0
\(22\) 17.3205i 0.787296i
\(23\) 3.00000 1.73205i 0.130435 0.0753066i −0.433363 0.901220i \(-0.642673\pi\)
0.563798 + 0.825913i \(0.309340\pi\)
\(24\) 0 0
\(25\) −12.0000 + 20.7846i −0.480000 + 0.831384i
\(26\) 20.0000 34.6410i 0.769231 1.33235i
\(27\) 0 0
\(28\) −30.0000 + 17.3205i −1.07143 + 0.618590i
\(29\) 5.00000 8.66025i 0.172414 0.298629i −0.766849 0.641827i \(-0.778177\pi\)
0.939263 + 0.343198i \(0.111510\pi\)
\(30\) 0 0
\(31\) −46.5000 + 26.8468i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(32\) 16.0000 27.7128i 0.500000 0.866025i
\(33\) 0 0
\(34\) 8.00000 + 13.8564i 0.235294 + 0.407541i
\(35\) 60.6218i 1.73205i
\(36\) 0 0
\(37\) −10.0000 −0.270270 −0.135135 0.990827i \(-0.543147\pi\)
−0.135135 + 0.990827i \(0.543147\pi\)
\(38\) −18.0000 + 10.3923i −0.473684 + 0.273482i
\(39\) 0 0
\(40\) −28.0000 48.4974i −0.700000 1.21244i
\(41\) −25.0000 43.3013i −0.609756 1.05613i −0.991280 0.131770i \(-0.957934\pi\)
0.381524 0.924359i \(-0.375399\pi\)
\(42\) 0 0
\(43\) −15.0000 8.66025i −0.348837 0.201401i 0.315336 0.948980i \(-0.397883\pi\)
−0.664173 + 0.747579i \(0.731216\pi\)
\(44\) −30.0000 + 17.3205i −0.681818 + 0.393648i
\(45\) 0 0
\(46\) 6.00000 + 3.46410i 0.130435 + 0.0753066i
\(47\) 75.0000 + 43.3013i 1.59574 + 0.921304i 0.992294 + 0.123903i \(0.0395412\pi\)
0.603450 + 0.797401i \(0.293792\pi\)
\(48\) 0 0
\(49\) 13.0000 + 22.5167i 0.265306 + 0.459524i
\(50\) −48.0000 −0.960000
\(51\) 0 0
\(52\) 80.0000 1.53846
\(53\) 47.0000 0.886792 0.443396 0.896326i \(-0.353773\pi\)
0.443396 + 0.896326i \(0.353773\pi\)
\(54\) 0 0
\(55\) 60.6218i 1.10221i
\(56\) −60.0000 34.6410i −1.07143 0.618590i
\(57\) 0 0
\(58\) 20.0000 0.344828
\(59\) 30.0000 17.3205i 0.508475 0.293568i −0.223732 0.974651i \(-0.571824\pi\)
0.732206 + 0.681083i \(0.238491\pi\)
\(60\) 0 0
\(61\) 32.0000 55.4256i 0.524590 0.908617i −0.475000 0.879986i \(-0.657552\pi\)
0.999590 0.0286310i \(-0.00911476\pi\)
\(62\) −93.0000 53.6936i −1.50000 0.866025i
\(63\) 0 0
\(64\) 64.0000 1.00000
\(65\) 70.0000 121.244i 1.07692 1.86529i
\(66\) 0 0
\(67\) 75.0000 43.3013i 1.11940 0.646288i 0.178155 0.984003i \(-0.442987\pi\)
0.941248 + 0.337715i \(0.109654\pi\)
\(68\) −16.0000 + 27.7128i −0.235294 + 0.407541i
\(69\) 0 0
\(70\) −105.000 + 60.6218i −1.50000 + 0.866025i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −55.0000 −0.753425 −0.376712 0.926330i \(-0.622945\pi\)
−0.376712 + 0.926330i \(0.622945\pi\)
\(74\) −10.0000 17.3205i −0.135135 0.234061i
\(75\) 0 0
\(76\) −36.0000 20.7846i −0.473684 0.273482i
\(77\) 37.5000 + 64.9519i 0.487013 + 0.843531i
\(78\) 0 0
\(79\) −6.00000 3.46410i −0.0759494 0.0438494i 0.461544 0.887117i \(-0.347296\pi\)
−0.537494 + 0.843268i \(0.680629\pi\)
\(80\) 56.0000 96.9948i 0.700000 1.21244i
\(81\) 0 0
\(82\) 50.0000 86.6025i 0.609756 1.05613i
\(83\) 25.5000 + 14.7224i 0.307229 + 0.177379i 0.645686 0.763603i \(-0.276572\pi\)
−0.338457 + 0.940982i \(0.609905\pi\)
\(84\) 0 0
\(85\) 28.0000 + 48.4974i 0.329412 + 0.570558i
\(86\) 34.6410i 0.402803i
\(87\) 0 0
\(88\) −60.0000 34.6410i −0.681818 0.393648i
\(89\) −10.0000 −0.112360 −0.0561798 0.998421i \(-0.517892\pi\)
−0.0561798 + 0.998421i \(0.517892\pi\)
\(90\) 0 0
\(91\) 173.205i 1.90335i
\(92\) 13.8564i 0.150613i
\(93\) 0 0
\(94\) 173.205i 1.84261i
\(95\) −63.0000 + 36.3731i −0.663158 + 0.382874i
\(96\) 0 0
\(97\) 12.5000 21.6506i 0.128866 0.223202i −0.794372 0.607432i \(-0.792200\pi\)
0.923237 + 0.384230i \(0.125533\pi\)
\(98\) −26.0000 + 45.0333i −0.265306 + 0.459524i
\(99\) 0 0
\(100\) −48.0000 83.1384i −0.480000 0.831384i
\(101\) −77.5000 + 134.234i −0.767327 + 1.32905i 0.171681 + 0.985153i \(0.445080\pi\)
−0.939008 + 0.343896i \(0.888253\pi\)
\(102\) 0 0
\(103\) 120.000 69.2820i 1.16505 0.672641i 0.212540 0.977152i \(-0.431826\pi\)
0.952509 + 0.304511i \(0.0984931\pi\)
\(104\) 80.0000 + 138.564i 0.769231 + 1.33235i
\(105\) 0 0
\(106\) 47.0000 + 81.4064i 0.443396 + 0.767985i
\(107\) 129.904i 1.21405i 0.794681 + 0.607027i \(0.207638\pi\)
−0.794681 + 0.607027i \(0.792362\pi\)
\(108\) 0 0
\(109\) 134.000 1.22936 0.614679 0.788777i \(-0.289286\pi\)
0.614679 + 0.788777i \(0.289286\pi\)
\(110\) −105.000 + 60.6218i −0.954545 + 0.551107i
\(111\) 0 0
\(112\) 138.564i 1.23718i
\(113\) −37.0000 64.0859i −0.327434 0.567132i 0.654568 0.756003i \(-0.272850\pi\)
−0.982002 + 0.188871i \(0.939517\pi\)
\(114\) 0 0
\(115\) 21.0000 + 12.1244i 0.182609 + 0.105429i
\(116\) 20.0000 + 34.6410i 0.172414 + 0.298629i
\(117\) 0 0
\(118\) 60.0000 + 34.6410i 0.508475 + 0.293568i
\(119\) 60.0000 + 34.6410i 0.504202 + 0.291101i
\(120\) 0 0
\(121\) −23.0000 39.8372i −0.190083 0.329233i
\(122\) 128.000 1.04918
\(123\) 0 0
\(124\) 214.774i 1.73205i
\(125\) 7.00000 0.0560000
\(126\) 0 0
\(127\) 25.9808i 0.204573i −0.994755 0.102286i \(-0.967384\pi\)
0.994755 0.102286i \(-0.0326158\pi\)
\(128\) 64.0000 + 110.851i 0.500000 + 0.866025i
\(129\) 0 0
\(130\) 280.000 2.15385
\(131\) 142.500 82.2724i 1.08779 0.628034i 0.154800 0.987946i \(-0.450527\pi\)
0.932986 + 0.359912i \(0.117193\pi\)
\(132\) 0 0
\(133\) −45.0000 + 77.9423i −0.338346 + 0.586032i
\(134\) 150.000 + 86.6025i 1.11940 + 0.646288i
\(135\) 0 0
\(136\) −64.0000 −0.470588
\(137\) −31.0000 + 53.6936i −0.226277 + 0.391924i −0.956702 0.291070i \(-0.905989\pi\)
0.730425 + 0.682993i \(0.239322\pi\)
\(138\) 0 0
\(139\) −150.000 + 86.6025i −1.07914 + 0.623040i −0.930663 0.365877i \(-0.880769\pi\)
−0.148473 + 0.988916i \(0.547436\pi\)
\(140\) −210.000 121.244i −1.50000 0.866025i
\(141\) 0 0
\(142\) 0 0
\(143\) 173.205i 1.21122i
\(144\) 0 0
\(145\) 70.0000 0.482759
\(146\) −55.0000 95.2628i −0.376712 0.652485i
\(147\) 0 0
\(148\) 20.0000 34.6410i 0.135135 0.234061i
\(149\) 57.5000 + 99.5929i 0.385906 + 0.668409i 0.991894 0.127065i \(-0.0405556\pi\)
−0.605988 + 0.795473i \(0.707222\pi\)
\(150\) 0 0
\(151\) −37.5000 21.6506i −0.248344 0.143382i 0.370662 0.928768i \(-0.379131\pi\)
−0.619006 + 0.785386i \(0.712464\pi\)
\(152\) 83.1384i 0.546963i
\(153\) 0 0
\(154\) −75.0000 + 129.904i −0.487013 + 0.843531i
\(155\) −325.500 187.928i −2.10000 1.21244i
\(156\) 0 0
\(157\) −10.0000 17.3205i −0.0636943 0.110322i 0.832420 0.554146i \(-0.186955\pi\)
−0.896114 + 0.443824i \(0.853622\pi\)
\(158\) 13.8564i 0.0876988i
\(159\) 0 0
\(160\) 224.000 1.40000
\(161\) 30.0000 0.186335
\(162\) 0 0
\(163\) 103.923i 0.637565i 0.947828 + 0.318782i \(0.103274\pi\)
−0.947828 + 0.318782i \(0.896726\pi\)
\(164\) 200.000 1.21951
\(165\) 0 0
\(166\) 58.8897i 0.354757i
\(167\) −213.000 + 122.976i −1.27545 + 0.736381i −0.976008 0.217734i \(-0.930133\pi\)
−0.299441 + 0.954115i \(0.596800\pi\)
\(168\) 0 0
\(169\) −115.500 + 200.052i −0.683432 + 1.18374i
\(170\) −56.0000 + 96.9948i −0.329412 + 0.570558i
\(171\) 0 0
\(172\) 60.0000 34.6410i 0.348837 0.201401i
\(173\) 63.5000 109.985i 0.367052 0.635753i −0.622051 0.782977i \(-0.713700\pi\)
0.989103 + 0.147224i \(0.0470338\pi\)
\(174\) 0 0
\(175\) −180.000 + 103.923i −1.02857 + 0.593846i
\(176\) 138.564i 0.787296i
\(177\) 0 0
\(178\) −10.0000 17.3205i −0.0561798 0.0973062i
\(179\) 233.827i 1.30630i −0.757231 0.653148i \(-0.773448\pi\)
0.757231 0.653148i \(-0.226552\pi\)
\(180\) 0 0
\(181\) 56.0000 0.309392 0.154696 0.987962i \(-0.450560\pi\)
0.154696 + 0.987962i \(0.450560\pi\)
\(182\) 300.000 173.205i 1.64835 0.951676i
\(183\) 0 0
\(184\) −24.0000 + 13.8564i −0.130435 + 0.0753066i
\(185\) −35.0000 60.6218i −0.189189 0.327685i
\(186\) 0 0
\(187\) 60.0000 + 34.6410i 0.320856 + 0.185246i
\(188\) −300.000 + 173.205i −1.59574 + 0.921304i
\(189\) 0 0
\(190\) −126.000 72.7461i −0.663158 0.382874i
\(191\) 30.0000 + 17.3205i 0.157068 + 0.0906833i 0.576474 0.817116i \(-0.304428\pi\)
−0.419406 + 0.907799i \(0.637762\pi\)
\(192\) 0 0
\(193\) −32.5000 56.2917i −0.168394 0.291667i 0.769462 0.638693i \(-0.220525\pi\)
−0.937855 + 0.347027i \(0.887191\pi\)
\(194\) 50.0000 0.257732
\(195\) 0 0
\(196\) −104.000 −0.530612
\(197\) −253.000 −1.28426 −0.642132 0.766594i \(-0.721950\pi\)
−0.642132 + 0.766594i \(0.721950\pi\)
\(198\) 0 0
\(199\) 129.904i 0.652783i −0.945235 0.326391i \(-0.894167\pi\)
0.945235 0.326391i \(-0.105833\pi\)
\(200\) 96.0000 166.277i 0.480000 0.831384i
\(201\) 0 0
\(202\) −310.000 −1.53465
\(203\) 75.0000 43.3013i 0.369458 0.213307i
\(204\) 0 0
\(205\) 175.000 303.109i 0.853659 1.47858i
\(206\) 240.000 + 138.564i 1.16505 + 0.672641i
\(207\) 0 0
\(208\) −160.000 + 277.128i −0.769231 + 1.33235i
\(209\) −45.0000 + 77.9423i −0.215311 + 0.372930i
\(210\) 0 0
\(211\) 129.000 74.4782i 0.611374 0.352977i −0.162129 0.986770i \(-0.551836\pi\)
0.773503 + 0.633792i \(0.218503\pi\)
\(212\) −94.0000 + 162.813i −0.443396 + 0.767985i
\(213\) 0 0
\(214\) −225.000 + 129.904i −1.05140 + 0.607027i
\(215\) 121.244i 0.563924i
\(216\) 0 0
\(217\) −465.000 −2.14286
\(218\) 134.000 + 232.095i 0.614679 + 1.06466i
\(219\) 0 0
\(220\) −210.000 121.244i −0.954545 0.551107i
\(221\) −80.0000 138.564i −0.361991 0.626987i
\(222\) 0 0
\(223\) 30.0000 + 17.3205i 0.134529 + 0.0776704i 0.565754 0.824574i \(-0.308585\pi\)
−0.431225 + 0.902244i \(0.641918\pi\)
\(224\) 240.000 138.564i 1.07143 0.618590i
\(225\) 0 0
\(226\) 74.0000 128.172i 0.327434 0.567132i
\(227\) −78.0000 45.0333i −0.343612 0.198385i 0.318256 0.948005i \(-0.396903\pi\)
−0.661868 + 0.749620i \(0.730236\pi\)
\(228\) 0 0
\(229\) −73.0000 126.440i −0.318777 0.552138i 0.661456 0.749984i \(-0.269939\pi\)
−0.980233 + 0.197846i \(0.936606\pi\)
\(230\) 48.4974i 0.210858i
\(231\) 0 0
\(232\) −40.0000 + 69.2820i −0.172414 + 0.298629i
\(233\) −334.000 −1.43348 −0.716738 0.697342i \(-0.754366\pi\)
−0.716738 + 0.697342i \(0.754366\pi\)
\(234\) 0 0
\(235\) 606.218i 2.57965i
\(236\) 138.564i 0.587136i
\(237\) 0 0
\(238\) 138.564i 0.582202i
\(239\) −15.0000 + 8.66025i −0.0627615 + 0.0362354i −0.531052 0.847339i \(-0.678203\pi\)
0.468291 + 0.883574i \(0.344870\pi\)
\(240\) 0 0
\(241\) −67.0000 + 116.047i −0.278008 + 0.481524i −0.970890 0.239527i \(-0.923008\pi\)
0.692881 + 0.721052i \(0.256341\pi\)
\(242\) 46.0000 79.6743i 0.190083 0.329233i
\(243\) 0 0
\(244\) 128.000 + 221.703i 0.524590 + 0.908617i
\(245\) −91.0000 + 157.617i −0.371429 + 0.643333i
\(246\) 0 0
\(247\) 180.000 103.923i 0.728745 0.420741i
\(248\) 372.000 214.774i 1.50000 0.866025i
\(249\) 0 0
\(250\) 7.00000 + 12.1244i 0.0280000 + 0.0484974i
\(251\) 207.846i 0.828072i 0.910260 + 0.414036i \(0.135881\pi\)
−0.910260 + 0.414036i \(0.864119\pi\)
\(252\) 0 0
\(253\) 30.0000 0.118577
\(254\) 45.0000 25.9808i 0.177165 0.102286i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.500000 + 0.866025i
\(257\) 134.000 + 232.095i 0.521401 + 0.903093i 0.999690 + 0.0248904i \(0.00792367\pi\)
−0.478289 + 0.878202i \(0.658743\pi\)
\(258\) 0 0
\(259\) −75.0000 43.3013i −0.289575 0.167186i
\(260\) 280.000 + 484.974i 1.07692 + 1.86529i
\(261\) 0 0
\(262\) 285.000 + 164.545i 1.08779 + 0.628034i
\(263\) −375.000 216.506i −1.42586 0.823218i −0.429065 0.903274i \(-0.641157\pi\)
−0.996790 + 0.0800555i \(0.974490\pi\)
\(264\) 0 0
\(265\) 164.500 + 284.922i 0.620755 + 1.07518i
\(266\) −180.000 −0.676692
\(267\) 0 0
\(268\) 346.410i 1.29258i
\(269\) 350.000 1.30112 0.650558 0.759457i \(-0.274535\pi\)
0.650558 + 0.759457i \(0.274535\pi\)
\(270\) 0 0
\(271\) 36.3731i 0.134218i −0.997746 0.0671090i \(-0.978622\pi\)
0.997746 0.0671090i \(-0.0213775\pi\)
\(272\) −64.0000 110.851i −0.235294 0.407541i
\(273\) 0 0
\(274\) −124.000 −0.452555
\(275\) −180.000 + 103.923i −0.654545 + 0.377902i
\(276\) 0 0
\(277\) 260.000 450.333i 0.938628 1.62575i 0.170595 0.985341i \(-0.445431\pi\)
0.768033 0.640410i \(-0.221236\pi\)
\(278\) −300.000 173.205i −1.07914 0.623040i
\(279\) 0 0
\(280\) 484.974i 1.73205i
\(281\) −220.000 + 381.051i −0.782918 + 1.35605i 0.147317 + 0.989089i \(0.452936\pi\)
−0.930235 + 0.366965i \(0.880397\pi\)
\(282\) 0 0
\(283\) −285.000 + 164.545i −1.00707 + 0.581430i −0.910332 0.413880i \(-0.864173\pi\)
−0.0967355 + 0.995310i \(0.530840\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 300.000 173.205i 1.04895 0.605612i
\(287\) 433.013i 1.50876i
\(288\) 0 0
\(289\) −225.000 −0.778547
\(290\) 70.0000 + 121.244i 0.241379 + 0.418081i
\(291\) 0 0
\(292\) 110.000 190.526i 0.376712 0.652485i
\(293\) −109.000 188.794i −0.372014 0.644347i 0.617862 0.786287i \(-0.287999\pi\)
−0.989875 + 0.141940i \(0.954666\pi\)
\(294\) 0 0
\(295\) 210.000 + 121.244i 0.711864 + 0.410995i
\(296\) 80.0000 0.270270
\(297\) 0 0
\(298\) −115.000 + 199.186i −0.385906 + 0.668409i
\(299\) −60.0000 34.6410i −0.200669 0.115856i
\(300\) 0 0
\(301\) −75.0000 129.904i −0.249169 0.431574i
\(302\) 86.6025i 0.286763i
\(303\) 0 0
\(304\) 144.000 83.1384i 0.473684 0.273482i
\(305\) 448.000 1.46885
\(306\) 0 0
\(307\) 207.846i 0.677023i −0.940962 0.338512i \(-0.890077\pi\)
0.940962 0.338512i \(-0.109923\pi\)
\(308\) −300.000 −0.974026
\(309\) 0 0
\(310\) 751.710i 2.42487i
\(311\) 255.000 147.224i 0.819936 0.473390i −0.0304586 0.999536i \(-0.509697\pi\)
0.850394 + 0.526146i \(0.176363\pi\)
\(312\) 0 0
\(313\) −242.500 + 420.022i −0.774760 + 1.34192i 0.160169 + 0.987090i \(0.448796\pi\)
−0.934929 + 0.354835i \(0.884537\pi\)
\(314\) 20.0000 34.6410i 0.0636943 0.110322i
\(315\) 0 0
\(316\) 24.0000 13.8564i 0.0759494 0.0438494i
\(317\) 108.500 187.928i 0.342271 0.592831i −0.642583 0.766216i \(-0.722137\pi\)
0.984854 + 0.173385i \(0.0554705\pi\)
\(318\) 0 0
\(319\) 75.0000 43.3013i 0.235110 0.135741i
\(320\) 224.000 + 387.979i 0.700000 + 1.21244i
\(321\) 0 0
\(322\) 30.0000 + 51.9615i 0.0931677 + 0.161371i
\(323\) 83.1384i 0.257395i
\(324\) 0 0
\(325\) 480.000 1.47692
\(326\) −180.000 + 103.923i −0.552147 + 0.318782i
\(327\) 0 0
\(328\) 200.000 + 346.410i 0.609756 + 1.05613i
\(329\) 375.000 + 649.519i 1.13982 + 1.97422i
\(330\) 0 0
\(331\) −375.000 216.506i −1.13293 0.654098i −0.188260 0.982119i \(-0.560285\pi\)
−0.944670 + 0.328021i \(0.893618\pi\)
\(332\) −102.000 + 58.8897i −0.307229 + 0.177379i
\(333\) 0 0
\(334\) −426.000 245.951i −1.27545 0.736381i
\(335\) 525.000 + 303.109i 1.56716 + 0.904803i
\(336\) 0 0
\(337\) 155.000 + 268.468i 0.459941 + 0.796641i 0.998957 0.0456545i \(-0.0145373\pi\)
−0.539017 + 0.842295i \(0.681204\pi\)
\(338\) −462.000 −1.36686
\(339\) 0 0
\(340\) −224.000 −0.658824
\(341\) −465.000 −1.36364
\(342\) 0 0
\(343\) 199.186i 0.580717i
\(344\) 120.000 + 69.2820i 0.348837 + 0.201401i
\(345\) 0 0
\(346\) 254.000 0.734104
\(347\) 187.500 108.253i 0.540346 0.311969i −0.204873 0.978789i \(-0.565678\pi\)
0.745219 + 0.666820i \(0.232345\pi\)
\(348\) 0 0
\(349\) −37.0000 + 64.0859i −0.106017 + 0.183627i −0.914153 0.405369i \(-0.867143\pi\)
0.808136 + 0.588996i \(0.200477\pi\)
\(350\) −360.000 207.846i −1.02857 0.593846i
\(351\) 0 0
\(352\) 240.000 138.564i 0.681818 0.393648i
\(353\) 197.000 341.214i 0.558074 0.966612i −0.439584 0.898202i \(-0.644874\pi\)
0.997657 0.0684103i \(-0.0217927\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 20.0000 34.6410i 0.0561798 0.0973062i
\(357\) 0 0
\(358\) 405.000 233.827i 1.13128 0.653148i
\(359\) 571.577i 1.59214i 0.605207 + 0.796068i \(0.293090\pi\)
−0.605207 + 0.796068i \(0.706910\pi\)
\(360\) 0 0
\(361\) 253.000 0.700831
\(362\) 56.0000 + 96.9948i 0.154696 + 0.267942i
\(363\) 0 0
\(364\) 600.000 + 346.410i 1.64835 + 0.951676i
\(365\) −192.500 333.420i −0.527397 0.913479i
\(366\) 0 0
\(367\) −487.500 281.458i −1.32834 0.766916i −0.343295 0.939228i \(-0.611543\pi\)
−0.985043 + 0.172311i \(0.944877\pi\)
\(368\) −48.0000 27.7128i −0.130435 0.0753066i
\(369\) 0 0
\(370\) 70.0000 121.244i 0.189189 0.327685i
\(371\) 352.500 + 203.516i 0.950135 + 0.548561i
\(372\) 0 0
\(373\) 20.0000 + 34.6410i 0.0536193 + 0.0928714i 0.891589 0.452845i \(-0.149591\pi\)
−0.837970 + 0.545716i \(0.816258\pi\)
\(374\) 138.564i 0.370492i
\(375\) 0 0
\(376\) −600.000 346.410i −1.59574 0.921304i
\(377\) −200.000 −0.530504
\(378\) 0 0
\(379\) 685.892i 1.80974i −0.425686 0.904871i \(-0.639967\pi\)
0.425686 0.904871i \(-0.360033\pi\)
\(380\) 290.985i 0.765749i
\(381\) 0 0
\(382\) 69.2820i 0.181367i
\(383\) −312.000 + 180.133i −0.814621 + 0.470322i −0.848558 0.529102i \(-0.822529\pi\)
0.0339368 + 0.999424i \(0.489196\pi\)
\(384\) 0 0
\(385\) −262.500 + 454.663i −0.681818 + 1.18094i
\(386\) 65.0000 112.583i 0.168394 0.291667i
\(387\) 0 0
\(388\) 50.0000 + 86.6025i 0.128866 + 0.223202i
\(389\) 237.500 411.362i 0.610540 1.05749i −0.380610 0.924736i \(-0.624286\pi\)
0.991150 0.132750i \(-0.0423808\pi\)
\(390\) 0 0
\(391\) 24.0000 13.8564i 0.0613811 0.0354384i
\(392\) −104.000 180.133i −0.265306 0.459524i
\(393\) 0 0
\(394\) −253.000 438.209i −0.642132 1.11221i
\(395\) 48.4974i 0.122778i
\(396\) 0 0
\(397\) 260.000 0.654912 0.327456 0.944866i \(-0.393809\pi\)
0.327456 + 0.944866i \(0.393809\pi\)
\(398\) 225.000 129.904i 0.565327 0.326391i
\(399\) 0 0
\(400\) 384.000 0.960000
\(401\) −370.000 640.859i −0.922693 1.59815i −0.795230 0.606308i \(-0.792650\pi\)
−0.127464 0.991843i \(-0.540684\pi\)
\(402\) 0 0
\(403\) 930.000 + 536.936i 2.30769 + 1.33235i
\(404\) −310.000 536.936i −0.767327 1.32905i
\(405\) 0 0
\(406\) 150.000 + 86.6025i 0.369458 + 0.213307i
\(407\) −75.0000 43.3013i −0.184275 0.106391i
\(408\) 0 0
\(409\) −329.500 570.711i −0.805623 1.39538i −0.915869 0.401476i \(-0.868497\pi\)
0.110246 0.993904i \(-0.464836\pi\)
\(410\) 700.000 1.70732
\(411\) 0 0
\(412\) 554.256i 1.34528i
\(413\) 300.000 0.726392
\(414\) 0 0
\(415\) 206.114i 0.496660i
\(416\) −640.000 −1.53846
\(417\) 0 0
\(418\) −180.000 −0.430622
\(419\) −510.000 + 294.449i −1.21718 + 0.702741i −0.964315 0.264759i \(-0.914708\pi\)
−0.252869 + 0.967500i \(0.581374\pi\)
\(420\) 0 0
\(421\) 248.000 429.549i 0.589074 1.02031i −0.405280 0.914192i \(-0.632826\pi\)
0.994354 0.106113i \(-0.0338405\pi\)
\(422\) 258.000 + 148.956i 0.611374 + 0.352977i
\(423\) 0 0
\(424\) −376.000 −0.886792
\(425\) −96.0000 + 166.277i −0.225882 + 0.391240i
\(426\) 0 0
\(427\) 480.000 277.128i 1.12412 0.649012i
\(428\) −450.000 259.808i −1.05140 0.607027i
\(429\) 0 0
\(430\) 210.000 121.244i 0.488372 0.281962i
\(431\) 571.577i 1.32616i 0.748547 + 0.663082i \(0.230752\pi\)
−0.748547 + 0.663082i \(0.769248\pi\)
\(432\) 0 0
\(433\) −235.000 −0.542725 −0.271363 0.962477i \(-0.587474\pi\)
−0.271363 + 0.962477i \(0.587474\pi\)
\(434\) −465.000 805.404i −1.07143 1.85577i
\(435\) 0 0
\(436\) −268.000 + 464.190i −0.614679 + 1.06466i
\(437\) 18.0000 + 31.1769i 0.0411899 + 0.0713431i
\(438\) 0 0
\(439\) 358.500 + 206.980i 0.816629 + 0.471481i 0.849253 0.527987i \(-0.177053\pi\)
−0.0326238 + 0.999468i \(0.510386\pi\)
\(440\) 484.974i 1.10221i
\(441\) 0 0
\(442\) 160.000 277.128i 0.361991 0.626987i
\(443\) 498.000 + 287.520i 1.12415 + 0.649030i 0.942458 0.334325i \(-0.108508\pi\)
0.181695 + 0.983355i \(0.441841\pi\)
\(444\) 0 0
\(445\) −35.0000 60.6218i −0.0786517 0.136229i
\(446\) 69.2820i 0.155341i
\(447\) 0 0
\(448\) 480.000 + 277.128i 1.07143 + 0.618590i
\(449\) 470.000 1.04677 0.523385 0.852096i \(-0.324669\pi\)
0.523385 + 0.852096i \(0.324669\pi\)
\(450\) 0 0
\(451\) 433.013i 0.960117i
\(452\) 296.000 0.654867
\(453\) 0 0
\(454\) 180.133i 0.396769i
\(455\) 1050.00 606.218i 2.30769 1.33235i
\(456\) 0 0
\(457\) 162.500 281.458i 0.355580 0.615882i −0.631637 0.775264i \(-0.717617\pi\)
0.987217 + 0.159382i \(0.0509501\pi\)
\(458\) 146.000 252.879i 0.318777 0.552138i
\(459\) 0 0
\(460\) −84.0000 + 48.4974i −0.182609 + 0.105429i
\(461\) 327.500 567.247i 0.710412 1.23047i −0.254290 0.967128i \(-0.581842\pi\)
0.964703 0.263342i \(-0.0848248\pi\)
\(462\) 0 0
\(463\) 142.500 82.2724i 0.307775 0.177694i −0.338155 0.941090i \(-0.609803\pi\)
0.645931 + 0.763396i \(0.276470\pi\)
\(464\) −160.000 −0.344828
\(465\) 0 0
\(466\) −334.000 578.505i −0.716738 1.24143i
\(467\) 57.1577i 0.122393i −0.998126 0.0611967i \(-0.980508\pi\)
0.998126 0.0611967i \(-0.0194917\pi\)
\(468\) 0 0
\(469\) 750.000 1.59915
\(470\) −1050.00 + 606.218i −2.23404 + 1.28983i
\(471\) 0 0
\(472\) −240.000 + 138.564i −0.508475 + 0.293568i
\(473\) −75.0000 129.904i −0.158562 0.274638i
\(474\) 0 0
\(475\) −216.000 124.708i −0.454737 0.262542i
\(476\) −240.000 + 138.564i −0.504202 + 0.291101i
\(477\) 0 0
\(478\) −30.0000 17.3205i −0.0627615 0.0362354i
\(479\) −285.000 164.545i −0.594990 0.343517i 0.172078 0.985083i \(-0.444952\pi\)
−0.767068 + 0.641566i \(0.778285\pi\)
\(480\) 0 0
\(481\) 100.000 + 173.205i 0.207900 + 0.360094i
\(482\) −268.000 −0.556017
\(483\) 0 0
\(484\) 184.000 0.380165
\(485\) 175.000 0.360825
\(486\) 0 0
\(487\) 519.615i 1.06697i 0.845809 + 0.533486i \(0.179118\pi\)
−0.845809 + 0.533486i \(0.820882\pi\)
\(488\) −256.000 + 443.405i −0.524590 + 0.908617i
\(489\) 0 0
\(490\) −364.000 −0.742857
\(491\) 187.500 108.253i 0.381874 0.220475i −0.296759 0.954952i \(-0.595906\pi\)
0.678633 + 0.734477i \(0.262573\pi\)
\(492\) 0 0
\(493\) 40.0000 69.2820i 0.0811359 0.140532i
\(494\) 360.000 + 207.846i 0.728745 + 0.420741i
\(495\) 0 0
\(496\) 744.000 + 429.549i 1.50000 + 0.866025i
\(497\) 0 0
\(498\) 0 0
\(499\) 39.0000 22.5167i 0.0781563 0.0451236i −0.460413 0.887705i \(-0.652299\pi\)
0.538569 + 0.842581i \(0.318965\pi\)
\(500\) −14.0000 + 24.2487i −0.0280000 + 0.0484974i
\(501\) 0 0
\(502\) −360.000 + 207.846i −0.717131 + 0.414036i
\(503\) 384.515i 0.764444i 0.924071 + 0.382222i \(0.124841\pi\)
−0.924071 + 0.382222i \(0.875159\pi\)
\(504\) 0 0
\(505\) −1085.00 −2.14851
\(506\) 30.0000 + 51.9615i 0.0592885 + 0.102691i
\(507\) 0 0
\(508\) 90.0000 + 51.9615i 0.177165 + 0.102286i
\(509\) 132.500 + 229.497i 0.260314 + 0.450878i 0.966325 0.257323i \(-0.0828405\pi\)
−0.706011 + 0.708201i \(0.749507\pi\)
\(510\) 0 0
\(511\) −412.500 238.157i −0.807241 0.466061i
\(512\) −512.000 −1.00000
\(513\) 0 0
\(514\) −268.000 + 464.190i −0.521401 + 0.903093i
\(515\) 840.000 + 484.974i 1.63107 + 0.941698i
\(516\) 0 0
\(517\) 375.000 + 649.519i 0.725338 + 1.25632i
\(518\) 173.205i 0.334373i
\(519\) 0 0
\(520\) −560.000 + 969.948i −1.07692 + 1.86529i
\(521\) 380.000 0.729367 0.364683 0.931132i \(-0.381177\pi\)
0.364683 + 0.931132i \(0.381177\pi\)
\(522\) 0 0
\(523\) 623.538i 1.19223i 0.802898 + 0.596117i \(0.203291\pi\)
−0.802898 + 0.596117i \(0.796709\pi\)
\(524\) 658.179i 1.25607i
\(525\) 0 0
\(526\) 866.025i 1.64644i
\(527\) −372.000 + 214.774i −0.705882 + 0.407541i
\(528\) 0 0
\(529\) −258.500 + 447.735i −0.488658 + 0.846380i
\(530\) −329.000 + 569.845i −0.620755 + 1.07518i
\(531\) 0 0
\(532\) −180.000 311.769i −0.338346 0.586032i
\(533\) −500.000 + 866.025i −0.938086 + 1.62481i
\(534\) 0 0
\(535\) −787.500 + 454.663i −1.47196 + 0.849838i
\(536\) −600.000 + 346.410i −1.11940 + 0.646288i
\(537\) 0 0
\(538\) 350.000 + 606.218i 0.650558 + 1.12680i
\(539\) 225.167i 0.417749i
\(540\) 0 0
\(541\) −532.000 −0.983364 −0.491682 0.870775i \(-0.663618\pi\)
−0.491682 + 0.870775i \(0.663618\pi\)
\(542\) 63.0000 36.3731i 0.116236 0.0671090i
\(543\) 0 0
\(544\) 128.000 221.703i 0.235294 0.407541i
\(545\) 469.000 + 812.332i 0.860550 + 1.49052i
\(546\) 0 0
\(547\) −780.000 450.333i −1.42596 0.823278i −0.429161 0.903228i \(-0.641191\pi\)
−0.996799 + 0.0799498i \(0.974524\pi\)
\(548\) −124.000 214.774i −0.226277 0.391924i
\(549\) 0 0
\(550\) −360.000 207.846i −0.654545 0.377902i
\(551\) 90.0000 + 51.9615i 0.163339 + 0.0943040i
\(552\) 0 0
\(553\) −30.0000 51.9615i −0.0542495 0.0939630i
\(554\) 1040.00 1.87726
\(555\) 0 0
\(556\) 692.820i 1.24608i
\(557\) 89.0000 0.159785 0.0798923 0.996804i \(-0.474542\pi\)
0.0798923 + 0.996804i \(0.474542\pi\)
\(558\) 0 0
\(559\) 346.410i 0.619696i
\(560\) 840.000 484.974i 1.50000 0.866025i
\(561\) 0 0
\(562\) −880.000 −1.56584
\(563\) −262.500 + 151.554i −0.466252 + 0.269191i −0.714670 0.699462i \(-0.753423\pi\)
0.248417 + 0.968653i \(0.420090\pi\)
\(564\) 0 0
\(565\) 259.000 448.601i 0.458407 0.793984i
\(566\) −570.000 329.090i −1.00707 0.581430i
\(567\) 0 0
\(568\) 0 0
\(569\) 50.0000 86.6025i 0.0878735 0.152201i −0.818739 0.574166i \(-0.805326\pi\)
0.906612 + 0.421965i \(0.138660\pi\)
\(570\) 0 0
\(571\) −294.000 + 169.741i −0.514886 + 0.297270i −0.734840 0.678241i \(-0.762743\pi\)
0.219954 + 0.975510i \(0.429409\pi\)
\(572\) 600.000 + 346.410i 1.04895 + 0.605612i
\(573\) 0 0
\(574\) 750.000 433.013i 1.30662 0.754378i
\(575\) 83.1384i 0.144589i
\(576\) 0 0
\(577\) −730.000 −1.26516 −0.632582 0.774493i \(-0.718005\pi\)
−0.632582 + 0.774493i \(0.718005\pi\)
\(578\) −225.000 389.711i −0.389273 0.674241i
\(579\) 0 0
\(580\) −140.000 + 242.487i −0.241379 + 0.418081i
\(581\) 127.500 + 220.836i 0.219449 + 0.380097i
\(582\) 0 0
\(583\) 352.500 + 203.516i 0.604631 + 0.349084i
\(584\) 440.000 0.753425
\(585\) 0 0
\(586\) 218.000 377.587i 0.372014 0.644347i
\(587\) −694.500 400.970i −1.18313 0.683083i −0.226397 0.974035i \(-0.572695\pi\)
−0.956738 + 0.290952i \(0.906028\pi\)
\(588\) 0 0
\(589\) −279.000 483.242i −0.473684 0.820445i
\(590\) 484.974i 0.821990i
\(591\) 0 0
\(592\) 80.0000 + 138.564i 0.135135 + 0.234061i
\(593\) −982.000 −1.65599 −0.827993 0.560738i \(-0.810517\pi\)
−0.827993 + 0.560738i \(0.810517\pi\)
\(594\) 0 0
\(595\) 484.974i 0.815083i
\(596\) −460.000 −0.771812
\(597\) 0 0
\(598\) 138.564i 0.231712i
\(599\) −195.000 + 112.583i −0.325543 + 0.187952i −0.653860 0.756615i \(-0.726852\pi\)
0.328318 + 0.944567i \(0.393518\pi\)
\(600\) 0 0
\(601\) −125.500 + 217.372i −0.208819 + 0.361684i −0.951343 0.308135i \(-0.900295\pi\)
0.742524 + 0.669819i \(0.233629\pi\)
\(602\) 150.000 259.808i 0.249169 0.431574i
\(603\) 0 0
\(604\) 150.000 86.6025i 0.248344 0.143382i
\(605\) 161.000 278.860i 0.266116 0.460926i
\(606\) 0 0
\(607\) −330.000 + 190.526i −0.543657 + 0.313881i −0.746560 0.665318i \(-0.768296\pi\)
0.202903 + 0.979199i \(0.434963\pi\)
\(608\) 288.000 + 166.277i 0.473684 + 0.273482i
\(609\) 0 0
\(610\) 448.000 + 775.959i 0.734426 + 1.27206i
\(611\) 1732.05i 2.83478i
\(612\) 0 0
\(613\) 650.000 1.06036 0.530179 0.847885i \(-0.322125\pi\)
0.530179 + 0.847885i \(0.322125\pi\)
\(614\) 360.000 207.846i 0.586319 0.338512i
\(615\) 0 0
\(616\) −300.000 519.615i −0.487013 0.843531i
\(617\) −379.000 656.447i −0.614263 1.06393i −0.990513 0.137416i \(-0.956120\pi\)
0.376251 0.926518i \(-0.377213\pi\)
\(618\) 0 0
\(619\) −150.000 86.6025i −0.242326 0.139907i 0.373919 0.927461i \(-0.378014\pi\)
−0.616245 + 0.787554i \(0.711347\pi\)
\(620\) 1302.00 751.710i 2.10000 1.21244i
\(621\) 0 0
\(622\) 510.000 + 294.449i 0.819936 + 0.473390i
\(623\) −75.0000 43.3013i −0.120385 0.0695044i
\(624\) 0 0
\(625\) 324.500 + 562.050i 0.519200 + 0.899281i
\(626\) −970.000 −1.54952
\(627\) 0 0
\(628\) 80.0000 0.127389
\(629\) −80.0000 −0.127186
\(630\) 0 0
\(631\) 119.512i 0.189400i −0.995506 0.0947001i \(-0.969811\pi\)
0.995506 0.0947001i \(-0.0301892\pi\)
\(632\) 48.0000 + 27.7128i 0.0759494 + 0.0438494i
\(633\) 0 0
\(634\) 434.000 0.684543
\(635\) 157.500 90.9327i 0.248031 0.143201i
\(636\) 0 0
\(637\) 260.000 450.333i 0.408163 0.706960i
\(638\) 150.000 + 86.6025i 0.235110 + 0.135741i
\(639\) 0 0
\(640\) −448.000 + 775.959i −0.700000 + 1.21244i
\(641\) 455.000 788.083i 0.709828 1.22946i −0.255092 0.966917i \(-0.582106\pi\)
0.964921 0.262542i \(-0.0845609\pi\)
\(642\) 0 0
\(643\) 30.0000 17.3205i 0.0466563 0.0269370i −0.476490 0.879180i \(-0.658091\pi\)
0.523147 + 0.852243i \(0.324758\pi\)
\(644\) −60.0000 + 103.923i −0.0931677 + 0.161371i
\(645\) 0 0
\(646\) −144.000 + 83.1384i −0.222910 + 0.128697i
\(647\) 914.523i 1.41348i 0.707472 + 0.706741i \(0.249835\pi\)
−0.707472 + 0.706741i \(0.750165\pi\)
\(648\) 0 0
\(649\) 300.000 0.462250
\(650\) 480.000 + 831.384i 0.738462 + 1.27905i
\(651\) 0 0
\(652\) −360.000 207.846i −0.552147 0.318782i
\(653\) 51.5000 + 89.2006i 0.0788668 + 0.136601i 0.902761 0.430142i \(-0.141536\pi\)
−0.823894 + 0.566743i \(0.808203\pi\)
\(654\) 0 0
\(655\) 997.500 + 575.907i 1.52290 + 0.879247i
\(656\) −400.000 + 692.820i −0.609756 + 1.05613i
\(657\) 0 0
\(658\) −750.000 + 1299.04i −1.13982 + 1.97422i
\(659\) 52.5000 + 30.3109i 0.0796662 + 0.0459953i 0.539304 0.842111i \(-0.318687\pi\)
−0.459638 + 0.888106i \(0.652021\pi\)
\(660\) 0 0
\(661\) −289.000 500.563i −0.437216 0.757281i 0.560257 0.828319i \(-0.310702\pi\)
−0.997474 + 0.0710377i \(0.977369\pi\)
\(662\) 866.025i 1.30820i
\(663\) 0 0
\(664\) −204.000 117.779i −0.307229 0.177379i
\(665\) −630.000 −0.947368
\(666\) 0 0
\(667\) 34.6410i 0.0519356i
\(668\) 983.805i 1.47276i
\(669\) 0 0
\(670\) 1212.44i 1.80961i
\(671\) 480.000 277.128i 0.715350 0.413008i
\(672\) 0 0
\(673\) −422.500 + 731.791i −0.627786 + 1.08736i 0.360209 + 0.932872i \(0.382705\pi\)
−0.987995 + 0.154486i \(0.950628\pi\)
\(674\) −310.000 + 536.936i −0.459941 + 0.796641i
\(675\) 0 0
\(676\) −462.000 800.207i −0.683432 1.18374i
\(677\) −577.000 + 999.393i −0.852290 + 1.47621i 0.0268475 + 0.999640i \(0.491453\pi\)
−0.879137 + 0.476569i \(0.841880\pi\)
\(678\) 0 0
\(679\) 187.500 108.253i 0.276141 0.159430i
\(680\) −224.000 387.979i −0.329412 0.570558i
\(681\) 0 0
\(682\) −465.000 805.404i −0.681818 1.18094i
\(683\) 187.061i 0.273882i 0.990579 + 0.136941i \(0.0437271\pi\)
−0.990579 + 0.136941i \(0.956273\pi\)
\(684\) 0 0
\(685\) −434.000 −0.633577
\(686\) 345.000 199.186i 0.502915 0.290358i
\(687\) 0 0
\(688\) 277.128i 0.402803i
\(689\) −470.000 814.064i −0.682148 1.18152i
\(690\) 0 0
\(691\) 426.000 + 245.951i 0.616498 + 0.355935i 0.775504 0.631342i \(-0.217496\pi\)
−0.159006 + 0.987278i \(0.550829\pi\)
\(692\) 254.000 + 439.941i 0.367052 + 0.635753i
\(693\) 0 0
\(694\) 375.000 + 216.506i 0.540346 + 0.311969i
\(695\) −1050.00 606.218i −1.51079 0.872256i
\(696\) 0 0
\(697\) −200.000 346.410i −0.286944 0.497002i
\(698\) −148.000 −0.212034
\(699\) 0 0
\(700\) 831.384i 1.18769i
\(701\) 215.000 0.306705 0.153352 0.988172i \(-0.450993\pi\)
0.153352 + 0.988172i \(0.450993\pi\)
\(702\) 0 0
\(703\) 103.923i 0.147828i
\(704\) 480.000 + 277.128i 0.681818 + 0.393648i
\(705\) 0 0
\(706\) 788.000 1.11615
\(707\) −1162.50 + 671.170i −1.64427 + 0.949321i
\(708\) 0 0
\(709\) 266.000 460.726i 0.375176 0.649824i −0.615177 0.788389i \(-0.710916\pi\)
0.990353 + 0.138565i \(0.0442488\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 80.0000 0.112360
\(713\) −93.0000 + 161.081i −0.130435 + 0.225920i
\(714\) 0 0
\(715\) 1050.00 606.218i 1.46853 0.847857i
\(716\) 810.000 + 467.654i 1.13128 + 0.653148i
\(717\) 0 0
\(718\) −990.000 + 571.577i −1.37883 + 0.796068i
\(719\) 1143.15i 1.58992i −0.606661 0.794961i \(-0.707491\pi\)
0.606661 0.794961i \(-0.292509\pi\)
\(720\) 0 0
\(721\) 1200.00 1.66436
\(722\) 253.000 + 438.209i 0.350416 + 0.606937i
\(723\) 0 0
\(724\) −112.000 + 193.990i −0.154696 + 0.267942i
\(725\) 120.000 + 207.846i 0.165517 + 0.286684i
\(726\) 0 0
\(727\) −1072.50 619.208i −1.47524 0.851731i −0.475630 0.879645i \(-0.657780\pi\)
−0.999610 + 0.0279146i \(0.991113\pi\)
\(728\) 1385.64i 1.90335i
\(729\) 0 0
\(730\) 385.000 666.840i 0.527397 0.913479i
\(731\) −120.000 69.2820i −0.164159 0.0947771i
\(732\) 0 0
\(733\) −475.000 822.724i −0.648022 1.12241i −0.983595 0.180392i \(-0.942263\pi\)
0.335573 0.942014i \(-0.391070\pi\)
\(734\) 1125.83i 1.53383i
\(735\) 0 0
\(736\) 110.851i 0.150613i
\(737\) 750.000 1.01764
\(738\) 0 0
\(739\) 581.969i 0.787509i −0.919216 0.393754i \(-0.871176\pi\)
0.919216 0.393754i \(-0.128824\pi\)
\(740\) 280.000 0.378378
\(741\) 0 0
\(742\) 814.064i 1.09712i
\(743\) 750.000 433.013i 1.00942 0.582790i 0.0983991 0.995147i \(-0.468628\pi\)
0.911022 + 0.412357i \(0.135294\pi\)
\(744\) 0 0
\(745\) −402.500 + 697.150i −0.540268 + 0.935772i
\(746\) −40.0000 + 69.2820i −0.0536193 + 0.0928714i
\(747\) 0 0
\(748\) −240.000 + 138.564i −0.320856 + 0.185246i
\(749\) −562.500 + 974.279i −0.751001 + 1.30077i
\(750\) 0 0
\(751\) 151.500 87.4686i 0.201731 0.116469i −0.395732 0.918366i \(-0.629509\pi\)
0.597463 + 0.801897i \(0.296176\pi\)
\(752\) 1385.64i 1.84261i
\(753\) 0 0
\(754\) −200.000 346.410i −0.265252 0.459430i
\(755\) 303.109i 0.401469i
\(756\) 0 0
\(757\) 830.000 1.09643 0.548217 0.836336i \(-0.315307\pi\)
0.548217 + 0.836336i \(0.315307\pi\)
\(758\) 1188.00 685.892i 1.56728 0.904871i
\(759\) 0 0
\(760\) 504.000 290.985i 0.663158 0.382874i
\(761\) −280.000 484.974i −0.367937 0.637285i 0.621306 0.783568i \(-0.286602\pi\)
−0.989243 + 0.146283i \(0.953269\pi\)
\(762\) 0 0
\(763\) 1005.00 + 580.237i 1.31717 + 0.760468i
\(764\) −120.000 + 69.2820i −0.157068 + 0.0906833i
\(765\) 0 0
\(766\) −624.000 360.267i −0.814621 0.470322i
\(767\) −600.000 346.410i −0.782269 0.451643i
\(768\) 0 0
\(769\) 165.500 + 286.654i 0.215215 + 0.372763i 0.953339 0.301902i \(-0.0976216\pi\)
−0.738124 + 0.674665i \(0.764288\pi\)
\(770\) −1050.00 −1.36364
\(771\) 0 0
\(772\) 260.000 0.336788
\(773\) −298.000 −0.385511 −0.192755 0.981247i \(-0.561742\pi\)
−0.192755 + 0.981247i \(0.561742\pi\)
\(774\) 0 0
\(775\) 1288.65i 1.66277i
\(776\) −100.000 + 173.205i −0.128866 + 0.223202i
\(777\) 0 0
\(778\) 950.000 1.22108
\(779\) 450.000 259.808i 0.577664 0.333514i
\(780\) 0 0
\(781\) 0 0
\(782\) 48.0000 + 27.7128i 0.0613811 + 0.0354384i
\(783\) 0 0
\(784\) 208.000 360.267i 0.265306 0.459524i
\(785\) 70.0000 121.244i 0.0891720 0.154450i