Properties

Label 1050.3.h.a.349.4
Level $1050$
Weight $3$
Character 1050.349
Analytic conductor $28.610$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 349.4
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1050.349
Dual form 1050.3.h.a.349.8

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(6.63103 + 2.24264i) q^{7} +2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -2.44949i q^{6} +(6.63103 + 2.24264i) q^{7} +2.82843i q^{8} +3.00000 q^{9} -10.2426 q^{11} -3.46410 q^{12} -8.95743 q^{13} +(3.17157 - 9.37769i) q^{14} +4.00000 q^{16} -30.4085 q^{17} -4.24264i q^{18} -16.1318i q^{19} +(11.4853 + 3.88437i) q^{21} +14.4853i q^{22} -6.72792i q^{23} +4.89898i q^{24} +12.6677i q^{26} +5.19615 q^{27} +(-13.2621 - 4.48528i) q^{28} -30.0000 q^{29} -50.1785i q^{31} -5.65685i q^{32} -17.7408 q^{33} +43.0041i q^{34} -6.00000 q^{36} -30.9117i q^{37} -22.8138 q^{38} -15.5147 q^{39} +7.10228i q^{41} +(5.49333 - 16.2426i) q^{42} -74.4264i q^{43} +20.4853 q^{44} -9.51472 q^{46} +58.2954 q^{47} +6.92820 q^{48} +(38.9411 + 29.7420i) q^{49} -52.6690 q^{51} +17.9149 q^{52} -70.9706i q^{53} -7.34847i q^{54} +(-6.34315 + 18.7554i) q^{56} -27.9411i q^{57} +42.4264i q^{58} -0.492372i q^{59} -2.86976i q^{61} -70.9631 q^{62} +(19.8931 + 6.72792i) q^{63} -8.00000 q^{64} +25.0892i q^{66} -27.0294i q^{67} +60.8170 q^{68} -11.6531i q^{69} +50.6102 q^{71} +8.48528i q^{72} -70.6149 q^{73} -43.7157 q^{74} +32.2636i q^{76} +(-67.9193 - 22.9706i) q^{77} +21.9411i q^{78} -133.823 q^{79} +9.00000 q^{81} +10.0441 q^{82} -104.415 q^{83} +(-22.9706 - 7.76874i) q^{84} -105.255 q^{86} -51.9615 q^{87} -28.9706i q^{88} +144.970i q^{89} +(-59.3970 - 20.0883i) q^{91} +13.4558i q^{92} -86.9117i q^{93} -82.4421i q^{94} -9.79796i q^{96} +100.705 q^{97} +(42.0616 - 55.0711i) q^{98} -30.7279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 16 q^{4} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 16 q^{4} + 24 q^{9} - 48 q^{11} + 48 q^{14} + 32 q^{16} + 24 q^{21} - 240 q^{29} - 48 q^{36} - 192 q^{39} + 96 q^{44} - 144 q^{46} + 40 q^{49} - 48 q^{51} - 96 q^{56} - 64 q^{64} - 240 q^{71} - 576 q^{74} - 256 q^{79} + 72 q^{81} - 48 q^{84} - 480 q^{86} - 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 1.73205 0.577350
\(4\) −2.00000 −0.500000
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) 6.63103 + 2.24264i 0.947290 + 0.320377i
\(8\) 2.82843i 0.353553i
\(9\) 3.00000 0.333333
\(10\) 0 0
\(11\) −10.2426 −0.931149 −0.465575 0.885009i \(-0.654152\pi\)
−0.465575 + 0.885009i \(0.654152\pi\)
\(12\) −3.46410 −0.288675
\(13\) −8.95743 −0.689033 −0.344516 0.938780i \(-0.611957\pi\)
−0.344516 + 0.938780i \(0.611957\pi\)
\(14\) 3.17157 9.37769i 0.226541 0.669835i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) −30.4085 −1.78873 −0.894367 0.447333i \(-0.852374\pi\)
−0.894367 + 0.447333i \(0.852374\pi\)
\(18\) 4.24264i 0.235702i
\(19\) 16.1318i 0.849043i −0.905418 0.424521i \(-0.860442\pi\)
0.905418 0.424521i \(-0.139558\pi\)
\(20\) 0 0
\(21\) 11.4853 + 3.88437i 0.546918 + 0.184970i
\(22\) 14.4853i 0.658422i
\(23\) 6.72792i 0.292518i −0.989246 0.146259i \(-0.953277\pi\)
0.989246 0.146259i \(-0.0467233\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 0 0
\(26\) 12.6677i 0.487220i
\(27\) 5.19615 0.192450
\(28\) −13.2621 4.48528i −0.473645 0.160189i
\(29\) −30.0000 −1.03448 −0.517241 0.855840i \(-0.673041\pi\)
−0.517241 + 0.855840i \(0.673041\pi\)
\(30\) 0 0
\(31\) 50.1785i 1.61866i −0.587354 0.809330i \(-0.699830\pi\)
0.587354 0.809330i \(-0.300170\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −17.7408 −0.537599
\(34\) 43.0041i 1.26483i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 30.9117i 0.835451i −0.908573 0.417726i \(-0.862827\pi\)
0.908573 0.417726i \(-0.137173\pi\)
\(38\) −22.8138 −0.600364
\(39\) −15.5147 −0.397813
\(40\) 0 0
\(41\) 7.10228i 0.173226i 0.996242 + 0.0866132i \(0.0276044\pi\)
−0.996242 + 0.0866132i \(0.972396\pi\)
\(42\) 5.49333 16.2426i 0.130793 0.386730i
\(43\) 74.4264i 1.73085i −0.501041 0.865423i \(-0.667050\pi\)
0.501041 0.865423i \(-0.332950\pi\)
\(44\) 20.4853 0.465575
\(45\) 0 0
\(46\) −9.51472 −0.206842
\(47\) 58.2954 1.24033 0.620164 0.784472i \(-0.287066\pi\)
0.620164 + 0.784472i \(0.287066\pi\)
\(48\) 6.92820 0.144338
\(49\) 38.9411 + 29.7420i 0.794717 + 0.606980i
\(50\) 0 0
\(51\) −52.6690 −1.03273
\(52\) 17.9149 0.344516
\(53\) 70.9706i 1.33907i −0.742782 0.669534i \(-0.766494\pi\)
0.742782 0.669534i \(-0.233506\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 0 0
\(56\) −6.34315 + 18.7554i −0.113270 + 0.334918i
\(57\) 27.9411i 0.490195i
\(58\) 42.4264i 0.731490i
\(59\) 0.492372i 0.00834529i −0.999991 0.00417265i \(-0.998672\pi\)
0.999991 0.00417265i \(-0.00132820\pi\)
\(60\) 0 0
\(61\) 2.86976i 0.0470452i −0.999723 0.0235226i \(-0.992512\pi\)
0.999723 0.0235226i \(-0.00748816\pi\)
\(62\) −70.9631 −1.14457
\(63\) 19.8931 + 6.72792i 0.315763 + 0.106792i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 25.0892i 0.380140i
\(67\) 27.0294i 0.403424i −0.979445 0.201712i \(-0.935349\pi\)
0.979445 0.201712i \(-0.0646506\pi\)
\(68\) 60.8170 0.894367
\(69\) 11.6531i 0.168886i
\(70\) 0 0
\(71\) 50.6102 0.712819 0.356410 0.934330i \(-0.384001\pi\)
0.356410 + 0.934330i \(0.384001\pi\)
\(72\) 8.48528i 0.117851i
\(73\) −70.6149 −0.967328 −0.483664 0.875254i \(-0.660694\pi\)
−0.483664 + 0.875254i \(0.660694\pi\)
\(74\) −43.7157 −0.590753
\(75\) 0 0
\(76\) 32.2636i 0.424521i
\(77\) −67.9193 22.9706i −0.882068 0.298319i
\(78\) 21.9411i 0.281296i
\(79\) −133.823 −1.69397 −0.846983 0.531619i \(-0.821584\pi\)
−0.846983 + 0.531619i \(0.821584\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 10.0441 0.122490
\(83\) −104.415 −1.25802 −0.629009 0.777398i \(-0.716539\pi\)
−0.629009 + 0.777398i \(0.716539\pi\)
\(84\) −22.9706 7.76874i −0.273459 0.0924849i
\(85\) 0 0
\(86\) −105.255 −1.22389
\(87\) −51.9615 −0.597259
\(88\) 28.9706i 0.329211i
\(89\) 144.970i 1.62888i 0.580250 + 0.814438i \(0.302955\pi\)
−0.580250 + 0.814438i \(0.697045\pi\)
\(90\) 0 0
\(91\) −59.3970 20.0883i −0.652714 0.220750i
\(92\) 13.4558i 0.146259i
\(93\) 86.9117i 0.934534i
\(94\) 82.4421i 0.877044i
\(95\) 0 0
\(96\) 9.79796i 0.102062i
\(97\) 100.705 1.03820 0.519099 0.854714i \(-0.326268\pi\)
0.519099 + 0.854714i \(0.326268\pi\)
\(98\) 42.0616 55.0711i 0.429200 0.561950i
\(99\) −30.7279 −0.310383
\(100\) 0 0
\(101\) 138.882i 1.37507i 0.726150 + 0.687536i \(0.241308\pi\)
−0.726150 + 0.687536i \(0.758692\pi\)
\(102\) 74.4853i 0.730248i
\(103\) 78.8760 0.765787 0.382893 0.923793i \(-0.374928\pi\)
0.382893 + 0.923793i \(0.374928\pi\)
\(104\) 25.3354i 0.243610i
\(105\) 0 0
\(106\) −100.368 −0.946864
\(107\) 37.7574i 0.352873i 0.984312 + 0.176436i \(0.0564569\pi\)
−0.984312 + 0.176436i \(0.943543\pi\)
\(108\) −10.3923 −0.0962250
\(109\) −31.9411 −0.293038 −0.146519 0.989208i \(-0.546807\pi\)
−0.146519 + 0.989208i \(0.546807\pi\)
\(110\) 0 0
\(111\) 53.5406i 0.482348i
\(112\) 26.5241 + 8.97056i 0.236823 + 0.0800943i
\(113\) 106.971i 0.946642i −0.880890 0.473321i \(-0.843055\pi\)
0.880890 0.473321i \(-0.156945\pi\)
\(114\) −39.5147 −0.346620
\(115\) 0 0
\(116\) 60.0000 0.517241
\(117\) −26.8723 −0.229678
\(118\) −0.696320 −0.00590101
\(119\) −201.640 68.1953i −1.69445 0.573070i
\(120\) 0 0
\(121\) −16.0883 −0.132961
\(122\) −4.05845 −0.0332660
\(123\) 12.3015i 0.100012i
\(124\) 100.357i 0.809330i
\(125\) 0 0
\(126\) 9.51472 28.1331i 0.0755136 0.223278i
\(127\) 22.0589i 0.173692i −0.996222 0.0868460i \(-0.972321\pi\)
0.996222 0.0868460i \(-0.0276788\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 128.910i 0.999305i
\(130\) 0 0
\(131\) 70.9631i 0.541703i 0.962621 + 0.270852i \(0.0873052\pi\)
−0.962621 + 0.270852i \(0.912695\pi\)
\(132\) 35.4815 0.268800
\(133\) 36.1779 106.971i 0.272014 0.804290i
\(134\) −38.2254 −0.285264
\(135\) 0 0
\(136\) 86.0082i 0.632413i
\(137\) 105.765i 0.772004i 0.922498 + 0.386002i \(0.126144\pi\)
−0.922498 + 0.386002i \(0.873856\pi\)
\(138\) −16.4800 −0.119420
\(139\) 181.322i 1.30447i 0.758015 + 0.652237i \(0.226169\pi\)
−0.758015 + 0.652237i \(0.773831\pi\)
\(140\) 0 0
\(141\) 100.971 0.716103
\(142\) 71.5736i 0.504039i
\(143\) 91.7477 0.641592
\(144\) 12.0000 0.0833333
\(145\) 0 0
\(146\) 99.8646i 0.684004i
\(147\) 67.4480 + 51.5147i 0.458830 + 0.350440i
\(148\) 61.8234i 0.417726i
\(149\) −41.1472 −0.276156 −0.138078 0.990421i \(-0.544092\pi\)
−0.138078 + 0.990421i \(0.544092\pi\)
\(150\) 0 0
\(151\) 80.3675 0.532235 0.266118 0.963941i \(-0.414259\pi\)
0.266118 + 0.963941i \(0.414259\pi\)
\(152\) 45.6277 0.300182
\(153\) −91.2255 −0.596245
\(154\) −32.4853 + 96.0523i −0.210943 + 0.623716i
\(155\) 0 0
\(156\) 31.0294 0.198907
\(157\) 57.3106 0.365036 0.182518 0.983203i \(-0.441575\pi\)
0.182518 + 0.983203i \(0.441575\pi\)
\(158\) 189.255i 1.19782i
\(159\) 122.925i 0.773111i
\(160\) 0 0
\(161\) 15.0883 44.6131i 0.0937162 0.277100i
\(162\) 12.7279i 0.0785674i
\(163\) 174.912i 1.07308i −0.843876 0.536539i \(-0.819731\pi\)
0.843876 0.536539i \(-0.180269\pi\)
\(164\) 14.2046i 0.0866132i
\(165\) 0 0
\(166\) 147.666i 0.889552i
\(167\) −196.163 −1.17463 −0.587315 0.809359i \(-0.699815\pi\)
−0.587315 + 0.809359i \(0.699815\pi\)
\(168\) −10.9867 + 32.4853i −0.0653967 + 0.193365i
\(169\) −88.7645 −0.525234
\(170\) 0 0
\(171\) 48.3954i 0.283014i
\(172\) 148.853i 0.865423i
\(173\) −38.5254 −0.222690 −0.111345 0.993782i \(-0.535516\pi\)
−0.111345 + 0.993782i \(0.535516\pi\)
\(174\) 73.4847i 0.422326i
\(175\) 0 0
\(176\) −40.9706 −0.232787
\(177\) 0.852814i 0.00481816i
\(178\) 205.019 1.15179
\(179\) 191.095 1.06757 0.533786 0.845619i \(-0.320769\pi\)
0.533786 + 0.845619i \(0.320769\pi\)
\(180\) 0 0
\(181\) 120.793i 0.667367i −0.942685 0.333683i \(-0.891708\pi\)
0.942685 0.333683i \(-0.108292\pi\)
\(182\) −28.4091 + 84.0000i −0.156094 + 0.461538i
\(183\) 4.97056i 0.0271615i
\(184\) 19.0294 0.103421
\(185\) 0 0
\(186\) −122.912 −0.660816
\(187\) 311.463 1.66558
\(188\) −116.591 −0.620164
\(189\) 34.4558 + 11.6531i 0.182306 + 0.0616566i
\(190\) 0 0
\(191\) 112.066 0.586733 0.293367 0.956000i \(-0.405224\pi\)
0.293367 + 0.956000i \(0.405224\pi\)
\(192\) −13.8564 −0.0721688
\(193\) 22.9117i 0.118713i −0.998237 0.0593567i \(-0.981095\pi\)
0.998237 0.0593567i \(-0.0189049\pi\)
\(194\) 142.419i 0.734116i
\(195\) 0 0
\(196\) −77.8823 59.4841i −0.397358 0.303490i
\(197\) 116.059i 0.589131i 0.955631 + 0.294566i \(0.0951750\pi\)
−0.955631 + 0.294566i \(0.904825\pi\)
\(198\) 43.4558i 0.219474i
\(199\) 163.101i 0.819604i 0.912174 + 0.409802i \(0.134402\pi\)
−0.912174 + 0.409802i \(0.865598\pi\)
\(200\) 0 0
\(201\) 46.8164i 0.232917i
\(202\) 196.409 0.972323
\(203\) −198.931 67.2792i −0.979955 0.331425i
\(204\) 105.338 0.516363
\(205\) 0 0
\(206\) 111.548i 0.541493i
\(207\) 20.1838i 0.0975061i
\(208\) −35.8297 −0.172258
\(209\) 165.232i 0.790586i
\(210\) 0 0
\(211\) 106.426 0.504391 0.252195 0.967676i \(-0.418847\pi\)
0.252195 + 0.967676i \(0.418847\pi\)
\(212\) 141.941i 0.669534i
\(213\) 87.6594 0.411546
\(214\) 53.3970 0.249519
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 112.532 332.735i 0.518582 1.53334i
\(218\) 45.1716i 0.207209i
\(219\) −122.309 −0.558487
\(220\) 0 0
\(221\) 272.382 1.23250
\(222\) −75.7179 −0.341071
\(223\) −57.0047 −0.255627 −0.127813 0.991798i \(-0.540796\pi\)
−0.127813 + 0.991798i \(0.540796\pi\)
\(224\) 12.6863 37.5108i 0.0566352 0.167459i
\(225\) 0 0
\(226\) −151.279 −0.669377
\(227\) −287.418 −1.26616 −0.633080 0.774086i \(-0.718210\pi\)
−0.633080 + 0.774086i \(0.718210\pi\)
\(228\) 55.8823i 0.245098i
\(229\) 139.405i 0.608754i 0.952552 + 0.304377i \(0.0984482\pi\)
−0.952552 + 0.304377i \(0.901552\pi\)
\(230\) 0 0
\(231\) −117.640 39.7862i −0.509262 0.172235i
\(232\) 84.8528i 0.365745i
\(233\) 362.735i 1.55680i 0.627767 + 0.778401i \(0.283969\pi\)
−0.627767 + 0.778401i \(0.716031\pi\)
\(234\) 38.0031i 0.162407i
\(235\) 0 0
\(236\) 0.984744i 0.00417265i
\(237\) −231.789 −0.978012
\(238\) −96.4427 + 285.161i −0.405222 + 1.19816i
\(239\) −18.4781 −0.0773144 −0.0386572 0.999253i \(-0.512308\pi\)
−0.0386572 + 0.999253i \(0.512308\pi\)
\(240\) 0 0
\(241\) 178.104i 0.739021i 0.929227 + 0.369510i \(0.120475\pi\)
−0.929227 + 0.369510i \(0.879525\pi\)
\(242\) 22.7523i 0.0940178i
\(243\) 15.5885 0.0641500
\(244\) 5.73951i 0.0235226i
\(245\) 0 0
\(246\) 17.3970 0.0707194
\(247\) 144.500i 0.585018i
\(248\) 141.926 0.572283
\(249\) −180.853 −0.726317
\(250\) 0 0
\(251\) 50.6709i 0.201876i −0.994893 0.100938i \(-0.967816\pi\)
0.994893 0.100938i \(-0.0321844\pi\)
\(252\) −39.7862 13.4558i −0.157882 0.0533962i
\(253\) 68.9117i 0.272378i
\(254\) −31.1960 −0.122819
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) −187.584 −0.729898 −0.364949 0.931028i \(-0.618914\pi\)
−0.364949 + 0.931028i \(0.618914\pi\)
\(258\) −182.307 −0.706615
\(259\) 69.3238 204.976i 0.267659 0.791414i
\(260\) 0 0
\(261\) −90.0000 −0.344828
\(262\) 100.357 0.383042
\(263\) 402.978i 1.53223i −0.642701 0.766117i \(-0.722186\pi\)
0.642701 0.766117i \(-0.277814\pi\)
\(264\) 50.1785i 0.190070i
\(265\) 0 0
\(266\) −151.279 51.1632i −0.568719 0.192343i
\(267\) 251.095i 0.940432i
\(268\) 54.0589i 0.201712i
\(269\) 480.538i 1.78639i −0.449674 0.893193i \(-0.648460\pi\)
0.449674 0.893193i \(-0.351540\pi\)
\(270\) 0 0
\(271\) 37.3068i 0.137664i 0.997628 + 0.0688318i \(0.0219272\pi\)
−0.997628 + 0.0688318i \(0.978073\pi\)
\(272\) −121.634 −0.447184
\(273\) −102.879 34.7939i −0.376845 0.127450i
\(274\) 149.574 0.545889
\(275\) 0 0
\(276\) 23.3062i 0.0844428i
\(277\) 82.6762i 0.298470i 0.988802 + 0.149235i \(0.0476811\pi\)
−0.988802 + 0.149235i \(0.952319\pi\)
\(278\) 256.428 0.922403
\(279\) 150.535i 0.539554i
\(280\) 0 0
\(281\) −150.853 −0.536843 −0.268421 0.963302i \(-0.586502\pi\)
−0.268421 + 0.963302i \(0.586502\pi\)
\(282\) 142.794i 0.506361i
\(283\) 284.158 1.00409 0.502046 0.864841i \(-0.332581\pi\)
0.502046 + 0.864841i \(0.332581\pi\)
\(284\) −101.220 −0.356410
\(285\) 0 0
\(286\) 129.751i 0.453674i
\(287\) −15.9279 + 47.0955i −0.0554978 + 0.164096i
\(288\) 16.9706i 0.0589256i
\(289\) 635.676 2.19957
\(290\) 0 0
\(291\) 174.426 0.599403
\(292\) 141.230 0.483664
\(293\) −537.237 −1.83357 −0.916786 0.399379i \(-0.869226\pi\)
−0.916786 + 0.399379i \(0.869226\pi\)
\(294\) 72.8528 95.3859i 0.247799 0.324442i
\(295\) 0 0
\(296\) 87.4315 0.295377
\(297\) −53.2223 −0.179200
\(298\) 58.1909i 0.195272i
\(299\) 60.2649i 0.201555i
\(300\) 0 0
\(301\) 166.912 493.524i 0.554524 1.63961i
\(302\) 113.657i 0.376347i
\(303\) 240.551i 0.793899i
\(304\) 64.5273i 0.212261i
\(305\) 0 0
\(306\) 129.012i 0.421609i
\(307\) 34.7430 0.113169 0.0565847 0.998398i \(-0.481979\pi\)
0.0565847 + 0.998398i \(0.481979\pi\)
\(308\) 135.839 + 45.9411i 0.441034 + 0.149159i
\(309\) 136.617 0.442127
\(310\) 0 0
\(311\) 89.1664i 0.286709i 0.989671 + 0.143354i \(0.0457888\pi\)
−0.989671 + 0.143354i \(0.954211\pi\)
\(312\) 43.8823i 0.140648i
\(313\) 519.700 1.66038 0.830191 0.557479i \(-0.188231\pi\)
0.830191 + 0.557479i \(0.188231\pi\)
\(314\) 81.0495i 0.258119i
\(315\) 0 0
\(316\) 267.647 0.846983
\(317\) 542.029i 1.70987i −0.518736 0.854935i \(-0.673597\pi\)
0.518736 0.854935i \(-0.326403\pi\)
\(318\) −173.842 −0.546672
\(319\) 307.279 0.963258
\(320\) 0 0
\(321\) 65.3977i 0.203731i
\(322\) −63.0924 21.3381i −0.195939 0.0662674i
\(323\) 490.544i 1.51871i
\(324\) −18.0000 −0.0555556
\(325\) 0 0
\(326\) −247.362 −0.758781
\(327\) −55.3237 −0.169185
\(328\) −20.0883 −0.0612448
\(329\) 386.558 + 130.736i 1.17495 + 0.397373i
\(330\) 0 0
\(331\) 179.632 0.542696 0.271348 0.962481i \(-0.412531\pi\)
0.271348 + 0.962481i \(0.412531\pi\)
\(332\) 208.831 0.629009
\(333\) 92.7351i 0.278484i
\(334\) 277.417i 0.830588i
\(335\) 0 0
\(336\) 45.9411 + 15.5375i 0.136730 + 0.0462425i
\(337\) 291.823i 0.865945i −0.901407 0.432972i \(-0.857465\pi\)
0.901407 0.432972i \(-0.142535\pi\)
\(338\) 125.532i 0.371396i
\(339\) 185.278i 0.546544i
\(340\) 0 0
\(341\) 513.960i 1.50721i
\(342\) −68.4415 −0.200121
\(343\) 191.519 + 284.551i 0.558365 + 0.829596i
\(344\) 210.510 0.611947
\(345\) 0 0
\(346\) 54.4831i 0.157466i
\(347\) 452.080i 1.30283i −0.758724 0.651413i \(-0.774177\pi\)
0.758724 0.651413i \(-0.225823\pi\)
\(348\) 103.923 0.298629
\(349\) 235.067i 0.673543i 0.941586 + 0.336772i \(0.109335\pi\)
−0.941586 + 0.336772i \(0.890665\pi\)
\(350\) 0 0
\(351\) −46.5442 −0.132604
\(352\) 57.9411i 0.164605i
\(353\) −25.2458 −0.0715179 −0.0357590 0.999360i \(-0.511385\pi\)
−0.0357590 + 0.999360i \(0.511385\pi\)
\(354\) −1.20606 −0.00340695
\(355\) 0 0
\(356\) 289.940i 0.814438i
\(357\) −349.250 118.118i −0.978291 0.330862i
\(358\) 270.250i 0.754888i
\(359\) 106.243 0.295941 0.147970 0.988992i \(-0.452726\pi\)
0.147970 + 0.988992i \(0.452726\pi\)
\(360\) 0 0
\(361\) 100.765 0.279126
\(362\) −170.828 −0.471900
\(363\) −27.8658 −0.0767652
\(364\) 118.794 + 40.1766i 0.326357 + 0.110375i
\(365\) 0 0
\(366\) −7.02944 −0.0192061
\(367\) 286.416 0.780426 0.390213 0.920725i \(-0.372401\pi\)
0.390213 + 0.920725i \(0.372401\pi\)
\(368\) 26.9117i 0.0731296i
\(369\) 21.3068i 0.0577421i
\(370\) 0 0
\(371\) 159.161 470.608i 0.429007 1.26849i
\(372\) 173.823i 0.467267i
\(373\) 423.470i 1.13531i −0.823267 0.567654i \(-0.807851\pi\)
0.823267 0.567654i \(-0.192149\pi\)
\(374\) 440.476i 1.17774i
\(375\) 0 0
\(376\) 164.884i 0.438522i
\(377\) 268.723 0.712793
\(378\) 16.4800 48.7279i 0.0435978 0.128910i
\(379\) −101.103 −0.266761 −0.133381 0.991065i \(-0.542583\pi\)
−0.133381 + 0.991065i \(0.542583\pi\)
\(380\) 0 0
\(381\) 38.2071i 0.100281i
\(382\) 158.485i 0.414883i
\(383\) 220.394 0.575442 0.287721 0.957714i \(-0.407102\pi\)
0.287721 + 0.957714i \(0.407102\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −32.4020 −0.0839431
\(387\) 223.279i 0.576949i
\(388\) −201.410 −0.519099
\(389\) 383.470 0.985784 0.492892 0.870090i \(-0.335940\pi\)
0.492892 + 0.870090i \(0.335940\pi\)
\(390\) 0 0
\(391\) 204.586i 0.523238i
\(392\) −84.1232 + 110.142i −0.214600 + 0.280975i
\(393\) 122.912i 0.312752i
\(394\) 164.132 0.416579
\(395\) 0 0
\(396\) 61.4558 0.155192
\(397\) 485.178 1.22211 0.611056 0.791588i \(-0.290745\pi\)
0.611056 + 0.791588i \(0.290745\pi\)
\(398\) 230.660 0.579548
\(399\) 62.6619 185.278i 0.157047 0.464357i
\(400\) 0 0
\(401\) −253.176 −0.631361 −0.315680 0.948866i \(-0.602233\pi\)
−0.315680 + 0.948866i \(0.602233\pi\)
\(402\) −66.2083 −0.164697
\(403\) 449.470i 1.11531i
\(404\) 277.765i 0.687536i
\(405\) 0 0
\(406\) −95.1472 + 281.331i −0.234353 + 0.692933i
\(407\) 316.617i 0.777930i
\(408\) 148.971i 0.365124i
\(409\) 5.39135i 0.0131818i 0.999978 + 0.00659089i \(0.00209796\pi\)
−0.999978 + 0.00659089i \(0.997902\pi\)
\(410\) 0 0
\(411\) 183.189i 0.445717i
\(412\) −157.752 −0.382893
\(413\) 1.10421 3.26494i 0.00267364 0.00790541i
\(414\) −28.5442 −0.0689472
\(415\) 0 0
\(416\) 50.6709i 0.121805i
\(417\) 314.059i 0.753139i
\(418\) 233.674 0.559028
\(419\) 294.431i 0.702700i 0.936244 + 0.351350i \(0.114277\pi\)
−0.936244 + 0.351350i \(0.885723\pi\)
\(420\) 0 0
\(421\) −290.441 −0.689883 −0.344941 0.938624i \(-0.612101\pi\)
−0.344941 + 0.938624i \(0.612101\pi\)
\(422\) 150.510i 0.356658i
\(423\) 174.886 0.413442
\(424\) 200.735 0.473432
\(425\) 0 0
\(426\) 123.969i 0.291007i
\(427\) 6.43583 19.0294i 0.0150722 0.0445654i
\(428\) 75.5147i 0.176436i
\(429\) 158.912 0.370424
\(430\) 0 0
\(431\) 50.7136 0.117665 0.0588325 0.998268i \(-0.481262\pi\)
0.0588325 + 0.998268i \(0.481262\pi\)
\(432\) 20.7846 0.0481125
\(433\) −724.761 −1.67381 −0.836906 0.547347i \(-0.815638\pi\)
−0.836906 + 0.547347i \(0.815638\pi\)
\(434\) −470.558 159.145i −1.08424 0.366693i
\(435\) 0 0
\(436\) 63.8823 0.146519
\(437\) −108.534 −0.248361
\(438\) 172.971i 0.394910i
\(439\) 371.728i 0.846761i −0.905952 0.423381i \(-0.860843\pi\)
0.905952 0.423381i \(-0.139157\pi\)
\(440\) 0 0
\(441\) 116.823 + 89.2261i 0.264906 + 0.202327i
\(442\) 385.206i 0.871507i
\(443\) 229.258i 0.517512i −0.965943 0.258756i \(-0.916687\pi\)
0.965943 0.258756i \(-0.0833125\pi\)
\(444\) 107.081i 0.241174i
\(445\) 0 0
\(446\) 80.6168i 0.180755i
\(447\) −71.2690 −0.159439
\(448\) −53.0482 17.9411i −0.118411 0.0400472i
\(449\) 600.323 1.33702 0.668511 0.743702i \(-0.266932\pi\)
0.668511 + 0.743702i \(0.266932\pi\)
\(450\) 0 0
\(451\) 72.7461i 0.161300i
\(452\) 213.941i 0.473321i
\(453\) 139.201 0.307286
\(454\) 406.471i 0.895311i
\(455\) 0 0
\(456\) 79.0294 0.173310
\(457\) 483.823i 1.05869i −0.848405 0.529347i \(-0.822437\pi\)
0.848405 0.529347i \(-0.177563\pi\)
\(458\) 197.148 0.430454
\(459\) −158.007 −0.344242
\(460\) 0 0
\(461\) 274.661i 0.595794i −0.954598 0.297897i \(-0.903715\pi\)
0.954598 0.297897i \(-0.0962852\pi\)
\(462\) −56.2662 + 166.368i −0.121788 + 0.360103i
\(463\) 153.470i 0.331469i −0.986170 0.165734i \(-0.947001\pi\)
0.986170 0.165734i \(-0.0529995\pi\)
\(464\) −120.000 −0.258621
\(465\) 0 0
\(466\) 512.985 1.10083
\(467\) 61.7420 0.132210 0.0661049 0.997813i \(-0.478943\pi\)
0.0661049 + 0.997813i \(0.478943\pi\)
\(468\) 53.7446 0.114839
\(469\) 60.6173 179.233i 0.129248 0.382160i
\(470\) 0 0
\(471\) 99.2649 0.210754
\(472\) 1.39264 0.00295051
\(473\) 762.323i 1.61168i
\(474\) 327.799i 0.691559i
\(475\) 0 0
\(476\) 403.279 + 136.391i 0.847225 + 0.286535i
\(477\) 212.912i 0.446356i
\(478\) 26.1320i 0.0546695i
\(479\) 556.514i 1.16182i 0.813966 + 0.580912i \(0.197304\pi\)
−0.813966 + 0.580912i \(0.802696\pi\)
\(480\) 0 0
\(481\) 276.889i 0.575653i
\(482\) 251.877 0.522567
\(483\) 26.1337 77.2721i 0.0541071 0.159984i
\(484\) 32.1766 0.0664806
\(485\) 0 0
\(486\) 22.0454i 0.0453609i
\(487\) 325.220i 0.667804i 0.942608 + 0.333902i \(0.108365\pi\)
−0.942608 + 0.333902i \(0.891635\pi\)
\(488\) 8.11689 0.0166330
\(489\) 302.956i 0.619542i
\(490\) 0 0
\(491\) 643.477 1.31054 0.655272 0.755393i \(-0.272554\pi\)
0.655272 + 0.755393i \(0.272554\pi\)
\(492\) 24.6030i 0.0500062i
\(493\) 912.255 1.85042
\(494\) 204.353 0.413671
\(495\) 0 0
\(496\) 200.714i 0.404665i
\(497\) 335.598 + 113.500i 0.675247 + 0.228371i
\(498\) 255.765i 0.513583i
\(499\) −755.426 −1.51388 −0.756939 0.653485i \(-0.773306\pi\)
−0.756939 + 0.653485i \(0.773306\pi\)
\(500\) 0 0
\(501\) −339.765 −0.678173
\(502\) −71.6594 −0.142748
\(503\) −509.409 −1.01274 −0.506371 0.862316i \(-0.669013\pi\)
−0.506371 + 0.862316i \(0.669013\pi\)
\(504\) −19.0294 + 56.2662i −0.0377568 + 0.111639i
\(505\) 0 0
\(506\) 97.4558 0.192600
\(507\) −153.745 −0.303244
\(508\) 44.1177i 0.0868460i
\(509\) 769.433i 1.51166i −0.654770 0.755828i \(-0.727234\pi\)
0.654770 0.755828i \(-0.272766\pi\)
\(510\) 0 0
\(511\) −468.250 158.364i −0.916340 0.309910i
\(512\) 22.6274i 0.0441942i
\(513\) 83.8234i 0.163398i
\(514\) 265.283i 0.516116i
\(515\) 0 0
\(516\) 257.821i 0.499652i
\(517\) −597.099 −1.15493
\(518\) −289.880 98.0387i −0.559615 0.189264i
\(519\) −66.7279 −0.128570
\(520\) 0 0
\(521\) 535.207i 1.02727i −0.858009 0.513635i \(-0.828299\pi\)
0.858009 0.513635i \(-0.171701\pi\)
\(522\) 127.279i 0.243830i
\(523\) 839.466 1.60510 0.802549 0.596586i \(-0.203477\pi\)
0.802549 + 0.596586i \(0.203477\pi\)
\(524\) 141.926i 0.270852i
\(525\) 0 0
\(526\) −569.897 −1.08345
\(527\) 1525.85i 2.89535i
\(528\) −70.9631 −0.134400
\(529\) 483.735 0.914433
\(530\) 0 0
\(531\) 1.47712i 0.00278176i
\(532\) −72.3557 + 213.941i −0.136007 + 0.402145i
\(533\) 63.6182i 0.119359i
\(534\) 355.103 0.664986
\(535\) 0 0
\(536\) 76.4508 0.142632
\(537\) 330.987 0.616363
\(538\) −679.583 −1.26317
\(539\) −398.860 304.637i −0.740000 0.565189i
\(540\) 0 0
\(541\) 285.852 0.528377 0.264188 0.964471i \(-0.414896\pi\)
0.264188 + 0.964471i \(0.414896\pi\)
\(542\) 52.7598 0.0973428
\(543\) 209.220i 0.385305i
\(544\) 172.016i 0.316207i
\(545\) 0 0
\(546\) −49.2061 + 145.492i −0.0901210 + 0.266469i
\(547\) 741.470i 1.35552i 0.735283 + 0.677761i \(0.237049\pi\)
−0.735283 + 0.677761i \(0.762951\pi\)
\(548\) 211.529i 0.386002i
\(549\) 8.60927i 0.0156817i
\(550\) 0 0
\(551\) 483.954i 0.878320i
\(552\) 32.9600 0.0597101
\(553\) −887.387 300.118i −1.60468 0.542708i
\(554\) 116.922 0.211050
\(555\) 0 0
\(556\) 362.644i 0.652237i
\(557\) 834.853i 1.49884i −0.662096 0.749419i \(-0.730333\pi\)
0.662096 0.749419i \(-0.269667\pi\)
\(558\) −212.889 −0.381522
\(559\) 666.669i 1.19261i
\(560\) 0 0
\(561\) 539.470 0.961622
\(562\) 213.338i 0.379605i
\(563\) −417.781 −0.742062 −0.371031 0.928620i \(-0.620996\pi\)
−0.371031 + 0.928620i \(0.620996\pi\)
\(564\) −201.941 −0.358052
\(565\) 0 0
\(566\) 401.861i 0.710001i
\(567\) 59.6793 + 20.1838i 0.105254 + 0.0355975i
\(568\) 143.147i 0.252020i
\(569\) −673.029 −1.18283 −0.591414 0.806368i \(-0.701430\pi\)
−0.591414 + 0.806368i \(0.701430\pi\)
\(570\) 0 0
\(571\) −265.088 −0.464253 −0.232126 0.972686i \(-0.574568\pi\)
−0.232126 + 0.972686i \(0.574568\pi\)
\(572\) −183.495 −0.320796
\(573\) 194.104 0.338750
\(574\) 66.6030 + 22.5254i 0.116033 + 0.0392429i
\(575\) 0 0
\(576\) −24.0000 −0.0416667
\(577\) −468.740 −0.812375 −0.406188 0.913790i \(-0.633142\pi\)
−0.406188 + 0.913790i \(0.633142\pi\)
\(578\) 898.982i 1.55533i
\(579\) 39.6842i 0.0685392i
\(580\) 0 0
\(581\) −692.382 234.166i −1.19171 0.403040i
\(582\) 246.676i 0.423842i
\(583\) 726.926i 1.24687i
\(584\) 199.729i 0.342002i
\(585\) 0 0
\(586\) 759.767i 1.29653i
\(587\) 120.530 0.205332 0.102666 0.994716i \(-0.467263\pi\)
0.102666 + 0.994716i \(0.467263\pi\)
\(588\) −134.896 103.029i −0.229415 0.175220i
\(589\) −809.470 −1.37431
\(590\) 0 0
\(591\) 201.020i 0.340135i
\(592\) 123.647i 0.208863i
\(593\) 561.468 0.946826 0.473413 0.880841i \(-0.343022\pi\)
0.473413 + 0.880841i \(0.343022\pi\)
\(594\) 75.2677i 0.126713i
\(595\) 0 0
\(596\) 82.2944 0.138078
\(597\) 282.500i 0.473199i
\(598\) 85.2274 0.142521
\(599\) −940.109 −1.56946 −0.784732 0.619835i \(-0.787199\pi\)
−0.784732 + 0.619835i \(0.787199\pi\)
\(600\) 0 0
\(601\) 563.527i 0.937649i −0.883291 0.468824i \(-0.844678\pi\)
0.883291 0.468824i \(-0.155322\pi\)
\(602\) −697.948 236.049i −1.15938 0.392108i
\(603\) 81.0883i 0.134475i
\(604\) −160.735 −0.266118
\(605\) 0 0
\(606\) 340.191 0.561371
\(607\) 306.589 0.505089 0.252544 0.967585i \(-0.418733\pi\)
0.252544 + 0.967585i \(0.418733\pi\)
\(608\) −91.2553 −0.150091
\(609\) −344.558 116.531i −0.565777 0.191348i
\(610\) 0 0
\(611\) −522.177 −0.854626
\(612\) 182.451 0.298122
\(613\) 275.588i 0.449572i 0.974408 + 0.224786i \(0.0721684\pi\)
−0.974408 + 0.224786i \(0.927832\pi\)
\(614\) 49.1340i 0.0800228i
\(615\) 0 0
\(616\) 64.9706 192.105i 0.105472 0.311858i
\(617\) 461.294i 0.747639i −0.927501 0.373820i \(-0.878048\pi\)
0.927501 0.373820i \(-0.121952\pi\)
\(618\) 193.206i 0.312631i
\(619\) 374.904i 0.605660i −0.953045 0.302830i \(-0.902068\pi\)
0.953045 0.302830i \(-0.0979315\pi\)
\(620\) 0 0
\(621\) 34.9593i 0.0562952i
\(622\) 126.100 0.202734
\(623\) −325.116 + 961.301i −0.521855 + 1.54302i
\(624\) −62.0589 −0.0994533
\(625\) 0 0
\(626\) 734.966i 1.17407i
\(627\) 286.191i 0.456445i
\(628\) −114.621 −0.182518
\(629\) 939.978i 1.49440i
\(630\) 0 0
\(631\) −1127.32 −1.78656 −0.893282 0.449496i \(-0.851603\pi\)
−0.893282 + 0.449496i \(0.851603\pi\)
\(632\) 378.510i 0.598908i
\(633\) 184.336 0.291210
\(634\) −766.544 −1.20906
\(635\) 0 0
\(636\) 245.849i 0.386555i
\(637\) −348.812 266.412i −0.547586 0.418229i
\(638\) 434.558i 0.681126i
\(639\) 151.831 0.237606
\(640\) 0 0
\(641\) −884.352 −1.37964 −0.689822 0.723979i \(-0.742311\pi\)
−0.689822 + 0.723979i \(0.742311\pi\)
\(642\) 92.4863 0.144060
\(643\) −300.765 −0.467753 −0.233876 0.972266i \(-0.575141\pi\)
−0.233876 + 0.972266i \(0.575141\pi\)
\(644\) −30.1766 + 89.2261i −0.0468581 + 0.138550i
\(645\) 0 0
\(646\) 693.734 1.07389
\(647\) 940.604 1.45379 0.726896 0.686747i \(-0.240962\pi\)
0.726896 + 0.686747i \(0.240962\pi\)
\(648\) 25.4558i 0.0392837i
\(649\) 5.04319i 0.00777071i
\(650\) 0 0
\(651\) 194.912 576.314i 0.299404 0.885275i
\(652\) 349.823i 0.536539i
\(653\) 455.970i 0.698269i −0.937073 0.349135i \(-0.886476\pi\)
0.937073 0.349135i \(-0.113524\pi\)
\(654\) 78.2395i 0.119632i
\(655\) 0 0
\(656\) 28.4091i 0.0433066i
\(657\) −211.845 −0.322443
\(658\) 184.888 546.676i 0.280985 0.830815i
\(659\) −403.684 −0.612571 −0.306285 0.951940i \(-0.599086\pi\)
−0.306285 + 0.951940i \(0.599086\pi\)
\(660\) 0 0
\(661\) 1153.41i 1.74495i 0.488663 + 0.872473i \(0.337485\pi\)
−0.488663 + 0.872473i \(0.662515\pi\)
\(662\) 254.039i 0.383744i
\(663\) 471.779 0.711582
\(664\) 295.331i 0.444776i
\(665\) 0 0
\(666\) −131.147 −0.196918
\(667\) 201.838i 0.302605i
\(668\) 392.326 0.587315
\(669\) −98.7351 −0.147586
\(670\) 0 0
\(671\) 29.3939i 0.0438061i
\(672\) 21.9733 64.9706i 0.0326984 0.0966824i
\(673\) 607.440i 0.902585i −0.892376 0.451293i \(-0.850963\pi\)
0.892376 0.451293i \(-0.149037\pi\)
\(674\) −412.701 −0.612315
\(675\) 0 0
\(676\) 177.529 0.262617
\(677\) 1137.59 1.68034 0.840168 0.542326i \(-0.182456\pi\)
0.840168 + 0.542326i \(0.182456\pi\)
\(678\) −262.023 −0.386465
\(679\) 667.779 + 225.845i 0.983474 + 0.332615i
\(680\) 0 0
\(681\) −497.823 −0.731018
\(682\) 726.849 1.06576
\(683\) 818.111i 1.19782i −0.800817 0.598910i \(-0.795601\pi\)
0.800817 0.598910i \(-0.204399\pi\)
\(684\) 96.7909i 0.141507i
\(685\) 0 0
\(686\) 402.416 270.849i 0.586613 0.394823i
\(687\) 241.456i 0.351464i
\(688\) 297.706i 0.432712i
\(689\) 635.714i 0.922661i
\(690\) 0 0
\(691\) 204.280i 0.295630i −0.989015 0.147815i \(-0.952776\pi\)
0.989015 0.147815i \(-0.0472239\pi\)
\(692\) 77.0508 0.111345
\(693\) −203.758 68.9117i −0.294023 0.0994397i
\(694\) −639.338 −0.921236
\(695\) 0 0
\(696\) 146.969i 0.211163i
\(697\) 215.970i 0.309856i
\(698\) 332.434 0.476267
\(699\) 628.276i 0.898821i
\(700\) 0 0
\(701\) −318.853 −0.454854 −0.227427 0.973795i \(-0.573031\pi\)
−0.227427 + 0.973795i \(0.573031\pi\)
\(702\) 65.8234i 0.0937655i
\(703\) −498.662 −0.709334
\(704\) 81.9411 0.116394
\(705\) 0 0
\(706\) 35.7030i 0.0505708i
\(707\) −311.463 + 920.933i −0.440542 + 1.30259i
\(708\) 1.70563i 0.00240908i
\(709\) 217.647 0.306977 0.153489 0.988150i \(-0.450949\pi\)
0.153489 + 0.988150i \(0.450949\pi\)
\(710\) 0 0
\(711\) −401.470 −0.564656
\(712\) −410.037 −0.575895
\(713\) −337.597 −0.473488
\(714\) −167.044 + 493.914i −0.233955 + 0.691757i
\(715\) 0 0
\(716\) −382.191 −0.533786
\(717\) −32.0051 −0.0446375
\(718\) 150.250i 0.209262i
\(719\) 1207.36i 1.67922i 0.543192 + 0.839609i \(0.317216\pi\)
−0.543192 + 0.839609i \(0.682784\pi\)
\(720\) 0 0
\(721\) 523.029 + 176.891i 0.725422 + 0.245341i
\(722\) 142.503i 0.197372i
\(723\) 308.485i 0.426674i
\(724\) 241.587i 0.333683i
\(725\) 0 0
\(726\) 39.4082i 0.0542812i
\(727\) −123.231 −0.169506 −0.0847528 0.996402i \(-0.527010\pi\)
−0.0847528 + 0.996402i \(0.527010\pi\)
\(728\) 56.8183 168.000i 0.0780471 0.230769i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 2263.19i 3.09603i
\(732\) 9.94113i 0.0135808i
\(733\) −375.779 −0.512659 −0.256330 0.966589i \(-0.582513\pi\)
−0.256330 + 0.966589i \(0.582513\pi\)
\(734\) 405.054i 0.551844i
\(735\) 0 0
\(736\) −38.0589 −0.0517104
\(737\) 276.853i 0.375648i
\(738\) 30.1324 0.0408299
\(739\) −722.530 −0.977713 −0.488856 0.872364i \(-0.662586\pi\)
−0.488856 + 0.872364i \(0.662586\pi\)
\(740\) 0 0
\(741\) 250.281i 0.337761i
\(742\) −665.540 225.088i −0.896954 0.303354i
\(743\) 1268.48i 1.70724i 0.520899 + 0.853618i \(0.325597\pi\)
−0.520899 + 0.853618i \(0.674403\pi\)
\(744\) 245.823 0.330408
\(745\) 0 0
\(746\) −598.877 −0.802784
\(747\) −313.246 −0.419339
\(748\) −622.926 −0.832789
\(749\) −84.6762 + 250.370i −0.113052 + 0.334273i
\(750\) 0 0
\(751\) 439.161 0.584769 0.292384 0.956301i \(-0.405551\pi\)
0.292384 + 0.956301i \(0.405551\pi\)
\(752\) 233.182 0.310082
\(753\) 87.7645i 0.116553i
\(754\) 380.031i 0.504020i
\(755\) 0 0
\(756\) −68.9117 23.3062i −0.0911530 0.0308283i
\(757\) 668.530i 0.883131i 0.897229 + 0.441565i \(0.145577\pi\)
−0.897229 + 0.441565i \(0.854423\pi\)
\(758\) 142.981i 0.188629i
\(759\) 119.359i 0.157258i
\(760\) 0 0
\(761\) 880.116i 1.15653i −0.815851 0.578263i \(-0.803731\pi\)
0.815851 0.578263i \(-0.196269\pi\)
\(762\) −54.0330 −0.0709094
\(763\) −211.803 71.6325i −0.277592 0.0938827i
\(764\) −224.132 −0.293367
\(765\) 0 0
\(766\) 311.685i 0.406899i
\(767\) 4.41039i 0.00575018i
\(768\) 27.7128 0.0360844
\(769\) 1163.41i 1.51289i −0.654059 0.756444i \(-0.726935\pi\)
0.654059 0.756444i \(-0.273065\pi\)
\(770\) 0 0
\(771\) −324.905 −0.421407
\(772\) 45.8234i 0.0593567i
\(773\) 536.371 0.693883 0.346941 0.937887i \(-0.387220\pi\)
0.346941 + 0.937887i \(0.387220\pi\)
\(774\) −315.765 −0.407964
\(775\) 0 0
\(776\) 284.837i 0.367058i
\(777\) 120.072 355.029i 0.154533 0.456923i
\(778\) 542.309i 0.697055i
\(779\) 114.573 0.147077
\(780\) 0 0
\(781\) −518.382 −0.663741
\(782\) 289.328 0.369985
\(783\) −155.885 −0.199086
\(784\) 155.765 + 118.968i 0.198679 + 0.151745i
\(785\) 0 0
\(786\) 173.823 0.221149
\(787\) 83.9192 0.106632 0.0533159 0.998578i \(-0.483021\pi\)
0.0533159 + 0.998578i \(0.483021\pi\)
\(788\) 232.118i 0.294566i
\(789\) 697.978i 0.884636i
\(790\) 0 0
\(791\) 239.897 709.325i 0.303283 0.896745i