Properties

Label 3330.2.d.p.1999.3
Level $3330$
Weight $2$
Character 3330.1999
Analytic conductor $26.590$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.5901838731\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 51 x^{6} - 124 x^{5} + 154 x^{4} - 46 x^{3} + x^{2} + 4 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 370)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1999.3
Root \(-0.282359 - 0.282359i\) of defining polynomial
Character \(\chi\) \(=\) 3330.1999
Dual form 3330.2.d.p.1999.8

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-1.70518 - 1.44650i) q^{5} -1.83227i q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-1.70518 - 1.44650i) q^{5} -1.83227i q^{7} +1.00000i q^{8} +(-1.44650 + 1.70518i) q^{10} -4.19017 q^{11} +0.369454i q^{13} -1.83227 q^{14} +1.00000 q^{16} +5.08317i q^{17} -3.55963 q^{19} +(1.70518 + 1.44650i) q^{20} +4.19017i q^{22} +5.62036i q^{23} +(0.815273 + 4.93309i) q^{25} +0.369454 q^{26} +1.83227i q^{28} +1.20681 q^{29} +10.1030 q^{31} -1.00000i q^{32} +5.08317 q^{34} +(-2.65038 + 3.12434i) q^{35} +1.00000i q^{37} +3.55963i q^{38} +(1.44650 - 1.70518i) q^{40} +8.01447 q^{41} +2.27264i q^{43} +4.19017 q^{44} +5.62036 q^{46} -10.9154i q^{47} +3.64280 q^{49} +(4.93309 - 0.815273i) q^{50} -0.369454i q^{52} -9.94355i q^{53} +(7.14499 + 6.06108i) q^{55} +1.83227 q^{56} -1.20681i q^{58} -5.34563 q^{59} -9.79428 q^{61} -10.1030i q^{62} -1.00000 q^{64} +(0.534415 - 0.629985i) q^{65} +1.85073i q^{67} -5.08317i q^{68} +(3.12434 + 2.65038i) q^{70} -2.86038 q^{71} +8.09942i q^{73} +1.00000 q^{74} +3.55963 q^{76} +7.67751i q^{77} -6.06361 q^{79} +(-1.70518 - 1.44650i) q^{80} -8.01447i q^{82} -8.93200i q^{83} +(7.35281 - 8.66772i) q^{85} +2.27264 q^{86} -4.19017i q^{88} +11.4773 q^{89} +0.676938 q^{91} -5.62036i q^{92} -10.9154 q^{94} +(6.06980 + 5.14900i) q^{95} +6.05864i q^{97} -3.64280i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{4} - 6 q^{5} + O(q^{10}) \) \( 10 q - 10 q^{4} - 6 q^{5} + 2 q^{10} - 6 q^{11} - 2 q^{14} + 10 q^{16} - 8 q^{19} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 22 q^{29} + 46 q^{31} - 18 q^{34} - 32 q^{35} - 2 q^{40} + 14 q^{41} + 6 q^{44} + 12 q^{46} - 60 q^{49} - 8 q^{50} + 42 q^{55} + 2 q^{56} + 40 q^{59} - 18 q^{61} - 10 q^{64} - 4 q^{65} - 6 q^{70} - 12 q^{71} + 10 q^{74} + 8 q^{76} - 40 q^{79} - 6 q^{80} + 36 q^{85} + 34 q^{86} + 24 q^{89} + 32 q^{91} - 24 q^{94} - 12 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −1.70518 1.44650i −0.762579 0.646895i
\(6\) 0 0
\(7\) 1.83227i 0.692532i −0.938136 0.346266i \(-0.887449\pi\)
0.938136 0.346266i \(-0.112551\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.44650 + 1.70518i −0.457424 + 0.539225i
\(11\) −4.19017 −1.26338 −0.631692 0.775219i \(-0.717639\pi\)
−0.631692 + 0.775219i \(0.717639\pi\)
\(12\) 0 0
\(13\) 0.369454i 0.102468i 0.998687 + 0.0512340i \(0.0163154\pi\)
−0.998687 + 0.0512340i \(0.983685\pi\)
\(14\) −1.83227 −0.489694
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 5.08317i 1.23285i 0.787414 + 0.616425i \(0.211420\pi\)
−0.787414 + 0.616425i \(0.788580\pi\)
\(18\) 0 0
\(19\) −3.55963 −0.816634 −0.408317 0.912840i \(-0.633884\pi\)
−0.408317 + 0.912840i \(0.633884\pi\)
\(20\) 1.70518 + 1.44650i 0.381290 + 0.323447i
\(21\) 0 0
\(22\) 4.19017i 0.893348i
\(23\) 5.62036i 1.17193i 0.810338 + 0.585963i \(0.199284\pi\)
−0.810338 + 0.585963i \(0.800716\pi\)
\(24\) 0 0
\(25\) 0.815273 + 4.93309i 0.163055 + 0.986617i
\(26\) 0.369454 0.0724559
\(27\) 0 0
\(28\) 1.83227i 0.346266i
\(29\) 1.20681 0.224100 0.112050 0.993703i \(-0.464258\pi\)
0.112050 + 0.993703i \(0.464258\pi\)
\(30\) 0 0
\(31\) 10.1030 1.81455 0.907276 0.420535i \(-0.138158\pi\)
0.907276 + 0.420535i \(0.138158\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 5.08317 0.871757
\(35\) −2.65038 + 3.12434i −0.447995 + 0.528111i
\(36\) 0 0
\(37\) 1.00000i 0.164399i
\(38\) 3.55963i 0.577447i
\(39\) 0 0
\(40\) 1.44650 1.70518i 0.228712 0.269613i
\(41\) 8.01447 1.25165 0.625825 0.779964i \(-0.284762\pi\)
0.625825 + 0.779964i \(0.284762\pi\)
\(42\) 0 0
\(43\) 2.27264i 0.346575i 0.984871 + 0.173287i \(0.0554389\pi\)
−0.984871 + 0.173287i \(0.944561\pi\)
\(44\) 4.19017 0.631692
\(45\) 0 0
\(46\) 5.62036 0.828677
\(47\) 10.9154i 1.59218i −0.605178 0.796090i \(-0.706898\pi\)
0.605178 0.796090i \(-0.293102\pi\)
\(48\) 0 0
\(49\) 3.64280 0.520400
\(50\) 4.93309 0.815273i 0.697644 0.115297i
\(51\) 0 0
\(52\) 0.369454i 0.0512340i
\(53\) 9.94355i 1.36585i −0.730488 0.682926i \(-0.760707\pi\)
0.730488 0.682926i \(-0.239293\pi\)
\(54\) 0 0
\(55\) 7.14499 + 6.06108i 0.963431 + 0.817276i
\(56\) 1.83227 0.244847
\(57\) 0 0
\(58\) 1.20681i 0.158463i
\(59\) −5.34563 −0.695941 −0.347971 0.937505i \(-0.613129\pi\)
−0.347971 + 0.937505i \(0.613129\pi\)
\(60\) 0 0
\(61\) −9.79428 −1.25403 −0.627015 0.779008i \(-0.715723\pi\)
−0.627015 + 0.779008i \(0.715723\pi\)
\(62\) 10.1030i 1.28308i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.534415 0.629985i 0.0662861 0.0781401i
\(66\) 0 0
\(67\) 1.85073i 0.226103i 0.993589 + 0.113052i \(0.0360625\pi\)
−0.993589 + 0.113052i \(0.963937\pi\)
\(68\) 5.08317i 0.616425i
\(69\) 0 0
\(70\) 3.12434 + 2.65038i 0.373431 + 0.316780i
\(71\) −2.86038 −0.339464 −0.169732 0.985490i \(-0.554290\pi\)
−0.169732 + 0.985490i \(0.554290\pi\)
\(72\) 0 0
\(73\) 8.09942i 0.947966i 0.880534 + 0.473983i \(0.157184\pi\)
−0.880534 + 0.473983i \(0.842816\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) 3.55963 0.408317
\(77\) 7.67751i 0.874934i
\(78\) 0 0
\(79\) −6.06361 −0.682209 −0.341105 0.940025i \(-0.610801\pi\)
−0.341105 + 0.940025i \(0.610801\pi\)
\(80\) −1.70518 1.44650i −0.190645 0.161724i
\(81\) 0 0
\(82\) 8.01447i 0.885050i
\(83\) 8.93200i 0.980414i −0.871606 0.490207i \(-0.836921\pi\)
0.871606 0.490207i \(-0.163079\pi\)
\(84\) 0 0
\(85\) 7.35281 8.66772i 0.797524 0.940146i
\(86\) 2.27264 0.245065
\(87\) 0 0
\(88\) 4.19017i 0.446674i
\(89\) 11.4773 1.21659 0.608295 0.793711i \(-0.291854\pi\)
0.608295 + 0.793711i \(0.291854\pi\)
\(90\) 0 0
\(91\) 0.676938 0.0709624
\(92\) 5.62036i 0.585963i
\(93\) 0 0
\(94\) −10.9154 −1.12584
\(95\) 6.06980 + 5.14900i 0.622748 + 0.528276i
\(96\) 0 0
\(97\) 6.05864i 0.615162i 0.951522 + 0.307581i \(0.0995195\pi\)
−0.951522 + 0.307581i \(0.900480\pi\)
\(98\) 3.64280i 0.367978i
\(99\) 0 0
\(100\) −0.815273 4.93309i −0.0815273 0.493309i
\(101\) −4.96528 −0.494064 −0.247032 0.969007i \(-0.579455\pi\)
−0.247032 + 0.969007i \(0.579455\pi\)
\(102\) 0 0
\(103\) 7.33338i 0.722579i 0.932454 + 0.361289i \(0.117663\pi\)
−0.932454 + 0.361289i \(0.882337\pi\)
\(104\) −0.369454 −0.0362279
\(105\) 0 0
\(106\) −9.94355 −0.965803
\(107\) 8.21182i 0.793867i 0.917847 + 0.396933i \(0.129926\pi\)
−0.917847 + 0.396933i \(0.870074\pi\)
\(108\) 0 0
\(109\) 20.5503 1.96836 0.984179 0.177175i \(-0.0566960\pi\)
0.984179 + 0.177175i \(0.0566960\pi\)
\(110\) 6.06108 7.14499i 0.577902 0.681248i
\(111\) 0 0
\(112\) 1.83227i 0.173133i
\(113\) 0.652984i 0.0614276i −0.999528 0.0307138i \(-0.990222\pi\)
0.999528 0.0307138i \(-0.00977804\pi\)
\(114\) 0 0
\(115\) 8.12985 9.58372i 0.758113 0.893686i
\(116\) −1.20681 −0.112050
\(117\) 0 0
\(118\) 5.34563i 0.492105i
\(119\) 9.31373 0.853788
\(120\) 0 0
\(121\) 6.55754 0.596140
\(122\) 9.79428i 0.886733i
\(123\) 0 0
\(124\) −10.1030 −0.907276
\(125\) 5.74552 9.59109i 0.513895 0.857853i
\(126\) 0 0
\(127\) 19.2856i 1.71132i −0.517539 0.855660i \(-0.673152\pi\)
0.517539 0.855660i \(-0.326848\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −0.629985 0.534415i −0.0552534 0.0468713i
\(131\) 8.82072 0.770670 0.385335 0.922777i \(-0.374086\pi\)
0.385335 + 0.922777i \(0.374086\pi\)
\(132\) 0 0
\(133\) 6.52218i 0.565545i
\(134\) 1.85073 0.159879
\(135\) 0 0
\(136\) −5.08317 −0.435878
\(137\) 4.66126i 0.398239i −0.979975 0.199119i \(-0.936192\pi\)
0.979975 0.199119i \(-0.0638081\pi\)
\(138\) 0 0
\(139\) −16.4050 −1.39145 −0.695727 0.718306i \(-0.744918\pi\)
−0.695727 + 0.718306i \(0.744918\pi\)
\(140\) 2.65038 3.12434i 0.223998 0.264055i
\(141\) 0 0
\(142\) 2.86038i 0.240037i
\(143\) 1.54808i 0.129457i
\(144\) 0 0
\(145\) −2.05784 1.74566i −0.170894 0.144969i
\(146\) 8.09942 0.670313
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) −5.86259 −0.480282 −0.240141 0.970738i \(-0.577194\pi\)
−0.240141 + 0.970738i \(0.577194\pi\)
\(150\) 0 0
\(151\) 13.1460 1.06981 0.534903 0.844913i \(-0.320348\pi\)
0.534903 + 0.844913i \(0.320348\pi\)
\(152\) 3.55963i 0.288724i
\(153\) 0 0
\(154\) 7.67751 0.618672
\(155\) −17.2274 14.6140i −1.38374 1.17382i
\(156\) 0 0
\(157\) 7.33629i 0.585500i −0.956189 0.292750i \(-0.905430\pi\)
0.956189 0.292750i \(-0.0945704\pi\)
\(158\) 6.06361i 0.482395i
\(159\) 0 0
\(160\) −1.44650 + 1.70518i −0.114356 + 0.134806i
\(161\) 10.2980 0.811596
\(162\) 0 0
\(163\) 18.7968i 1.47228i 0.676831 + 0.736138i \(0.263353\pi\)
−0.676831 + 0.736138i \(0.736647\pi\)
\(164\) −8.01447 −0.625825
\(165\) 0 0
\(166\) −8.93200 −0.693257
\(167\) 5.92772i 0.458700i 0.973344 + 0.229350i \(0.0736601\pi\)
−0.973344 + 0.229350i \(0.926340\pi\)
\(168\) 0 0
\(169\) 12.8635 0.989500
\(170\) −8.66772 7.35281i −0.664784 0.563935i
\(171\) 0 0
\(172\) 2.27264i 0.173287i
\(173\) 5.78242i 0.439629i 0.975542 + 0.219815i \(0.0705453\pi\)
−0.975542 + 0.219815i \(0.929455\pi\)
\(174\) 0 0
\(175\) 9.03873 1.49380i 0.683264 0.112921i
\(176\) −4.19017 −0.315846
\(177\) 0 0
\(178\) 11.4773i 0.860259i
\(179\) 7.13581 0.533355 0.266678 0.963786i \(-0.414074\pi\)
0.266678 + 0.963786i \(0.414074\pi\)
\(180\) 0 0
\(181\) 11.5365 0.857503 0.428752 0.903422i \(-0.358954\pi\)
0.428752 + 0.903422i \(0.358954\pi\)
\(182\) 0.676938i 0.0501780i
\(183\) 0 0
\(184\) −5.62036 −0.414338
\(185\) 1.44650 1.70518i 0.106349 0.125367i
\(186\) 0 0
\(187\) 21.2994i 1.55756i
\(188\) 10.9154i 0.796090i
\(189\) 0 0
\(190\) 5.14900 6.06980i 0.373548 0.440350i
\(191\) 20.6048 1.49091 0.745456 0.666555i \(-0.232232\pi\)
0.745456 + 0.666555i \(0.232232\pi\)
\(192\) 0 0
\(193\) 26.1663i 1.88349i 0.336321 + 0.941747i \(0.390817\pi\)
−0.336321 + 0.941747i \(0.609183\pi\)
\(194\) 6.05864 0.434985
\(195\) 0 0
\(196\) −3.64280 −0.260200
\(197\) 14.6067i 1.04069i −0.853957 0.520343i \(-0.825804\pi\)
0.853957 0.520343i \(-0.174196\pi\)
\(198\) 0 0
\(199\) −5.81275 −0.412055 −0.206027 0.978546i \(-0.566054\pi\)
−0.206027 + 0.978546i \(0.566054\pi\)
\(200\) −4.93309 + 0.815273i −0.348822 + 0.0576485i
\(201\) 0 0
\(202\) 4.96528i 0.349356i
\(203\) 2.21121i 0.155196i
\(204\) 0 0
\(205\) −13.6661 11.5929i −0.954482 0.809685i
\(206\) 7.33338 0.510940
\(207\) 0 0
\(208\) 0.369454i 0.0256170i
\(209\) 14.9154 1.03172
\(210\) 0 0
\(211\) 16.0976 1.10821 0.554104 0.832448i \(-0.313061\pi\)
0.554104 + 0.832448i \(0.313061\pi\)
\(212\) 9.94355i 0.682926i
\(213\) 0 0
\(214\) 8.21182 0.561349
\(215\) 3.28738 3.87526i 0.224197 0.264291i
\(216\) 0 0
\(217\) 18.5114i 1.25664i
\(218\) 20.5503i 1.39184i
\(219\) 0 0
\(220\) −7.14499 6.06108i −0.481715 0.408638i
\(221\) −1.87800 −0.126328
\(222\) 0 0
\(223\) 25.3608i 1.69828i −0.528164 0.849142i \(-0.677119\pi\)
0.528164 0.849142i \(-0.322881\pi\)
\(224\) −1.83227 −0.122423
\(225\) 0 0
\(226\) −0.652984 −0.0434359
\(227\) 5.57339i 0.369919i 0.982746 + 0.184960i \(0.0592154\pi\)
−0.982746 + 0.184960i \(0.940785\pi\)
\(228\) 0 0
\(229\) −9.02035 −0.596081 −0.298041 0.954553i \(-0.596333\pi\)
−0.298041 + 0.954553i \(0.596333\pi\)
\(230\) −9.58372 8.12985i −0.631932 0.536067i
\(231\) 0 0
\(232\) 1.20681i 0.0792313i
\(233\) 11.8100i 0.773696i 0.922144 + 0.386848i \(0.126436\pi\)
−0.922144 + 0.386848i \(0.873564\pi\)
\(234\) 0 0
\(235\) −15.7892 + 18.6128i −1.02997 + 1.21416i
\(236\) 5.34563 0.347971
\(237\) 0 0
\(238\) 9.31373i 0.603719i
\(239\) 0.907160 0.0586793 0.0293396 0.999569i \(-0.490660\pi\)
0.0293396 + 0.999569i \(0.490660\pi\)
\(240\) 0 0
\(241\) −4.15616 −0.267722 −0.133861 0.991000i \(-0.542738\pi\)
−0.133861 + 0.991000i \(0.542738\pi\)
\(242\) 6.55754i 0.421534i
\(243\) 0 0
\(244\) 9.79428 0.627015
\(245\) −6.21162 5.26931i −0.396846 0.336644i
\(246\) 0 0
\(247\) 1.31512i 0.0836789i
\(248\) 10.1030i 0.641541i
\(249\) 0 0
\(250\) −9.59109 5.74552i −0.606594 0.363379i
\(251\) −9.31888 −0.588203 −0.294101 0.955774i \(-0.595020\pi\)
−0.294101 + 0.955774i \(0.595020\pi\)
\(252\) 0 0
\(253\) 23.5503i 1.48059i
\(254\) −19.2856 −1.21009
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 13.6312i 0.850294i 0.905124 + 0.425147i \(0.139778\pi\)
−0.905124 + 0.425147i \(0.860222\pi\)
\(258\) 0 0
\(259\) 1.83227 0.113852
\(260\) −0.534415 + 0.629985i −0.0331430 + 0.0390700i
\(261\) 0 0
\(262\) 8.82072i 0.544946i
\(263\) 27.2170i 1.67827i 0.543921 + 0.839137i \(0.316939\pi\)
−0.543921 + 0.839137i \(0.683061\pi\)
\(264\) 0 0
\(265\) −14.3833 + 16.9555i −0.883562 + 1.04157i
\(266\) 6.52218 0.399901
\(267\) 0 0
\(268\) 1.85073i 0.113052i
\(269\) 23.0550 1.40569 0.702845 0.711343i \(-0.251913\pi\)
0.702845 + 0.711343i \(0.251913\pi\)
\(270\) 0 0
\(271\) 22.9320 1.39302 0.696510 0.717547i \(-0.254735\pi\)
0.696510 + 0.717547i \(0.254735\pi\)
\(272\) 5.08317i 0.308213i
\(273\) 0 0
\(274\) −4.66126 −0.281597
\(275\) −3.41613 20.6705i −0.206001 1.24648i
\(276\) 0 0
\(277\) 11.7534i 0.706192i −0.935587 0.353096i \(-0.885129\pi\)
0.935587 0.353096i \(-0.114871\pi\)
\(278\) 16.4050i 0.983906i
\(279\) 0 0
\(280\) −3.12434 2.65038i −0.186715 0.158390i
\(281\) 29.0962 1.73573 0.867865 0.496799i \(-0.165492\pi\)
0.867865 + 0.496799i \(0.165492\pi\)
\(282\) 0 0
\(283\) 10.1829i 0.605311i 0.953100 + 0.302655i \(0.0978731\pi\)
−0.953100 + 0.302655i \(0.902127\pi\)
\(284\) 2.86038 0.169732
\(285\) 0 0
\(286\) −1.54808 −0.0915396
\(287\) 14.6846i 0.866807i
\(288\) 0 0
\(289\) −8.83864 −0.519920
\(290\) −1.74566 + 2.05784i −0.102509 + 0.120840i
\(291\) 0 0
\(292\) 8.09942i 0.473983i
\(293\) 18.1243i 1.05883i 0.848363 + 0.529415i \(0.177589\pi\)
−0.848363 + 0.529415i \(0.822411\pi\)
\(294\) 0 0
\(295\) 9.11525 + 7.73245i 0.530711 + 0.450201i
\(296\) −1.00000 −0.0581238
\(297\) 0 0
\(298\) 5.86259i 0.339611i
\(299\) −2.07646 −0.120085
\(300\) 0 0
\(301\) 4.16409 0.240014
\(302\) 13.1460i 0.756467i
\(303\) 0 0
\(304\) −3.55963 −0.204159
\(305\) 16.7010 + 14.1674i 0.956297 + 0.811225i
\(306\) 0 0
\(307\) 6.15561i 0.351319i −0.984451 0.175660i \(-0.943794\pi\)
0.984451 0.175660i \(-0.0562058\pi\)
\(308\) 7.67751i 0.437467i
\(309\) 0 0
\(310\) −14.6140 + 17.2274i −0.830019 + 0.978452i
\(311\) 29.4512 1.67002 0.835011 0.550234i \(-0.185461\pi\)
0.835011 + 0.550234i \(0.185461\pi\)
\(312\) 0 0
\(313\) 13.0102i 0.735378i −0.929949 0.367689i \(-0.880149\pi\)
0.929949 0.367689i \(-0.119851\pi\)
\(314\) −7.33629 −0.414011
\(315\) 0 0
\(316\) 6.06361 0.341105
\(317\) 7.39826i 0.415528i 0.978179 + 0.207764i \(0.0666186\pi\)
−0.978179 + 0.207764i \(0.933381\pi\)
\(318\) 0 0
\(319\) −5.05676 −0.283124
\(320\) 1.70518 + 1.44650i 0.0953224 + 0.0808618i
\(321\) 0 0
\(322\) 10.2980i 0.573885i
\(323\) 18.0942i 1.00679i
\(324\) 0 0
\(325\) −1.82255 + 0.301206i −0.101097 + 0.0167079i
\(326\) 18.7968 1.04106
\(327\) 0 0
\(328\) 8.01447i 0.442525i
\(329\) −20.0000 −1.10264
\(330\) 0 0
\(331\) 33.2545 1.82783 0.913916 0.405903i \(-0.133043\pi\)
0.913916 + 0.405903i \(0.133043\pi\)
\(332\) 8.93200i 0.490207i
\(333\) 0 0
\(334\) 5.92772 0.324350
\(335\) 2.67709 3.15583i 0.146265 0.172422i
\(336\) 0 0
\(337\) 22.6288i 1.23267i 0.787485 + 0.616334i \(0.211383\pi\)
−0.787485 + 0.616334i \(0.788617\pi\)
\(338\) 12.8635i 0.699682i
\(339\) 0 0
\(340\) −7.35281 + 8.66772i −0.398762 + 0.470073i
\(341\) −42.3333 −2.29248
\(342\) 0 0
\(343\) 19.5004i 1.05293i
\(344\) −2.27264 −0.122533
\(345\) 0 0
\(346\) 5.78242 0.310865
\(347\) 24.1396i 1.29588i 0.761691 + 0.647941i \(0.224370\pi\)
−0.761691 + 0.647941i \(0.775630\pi\)
\(348\) 0 0
\(349\) 10.3702 0.555102 0.277551 0.960711i \(-0.410477\pi\)
0.277551 + 0.960711i \(0.410477\pi\)
\(350\) −1.49380 9.03873i −0.0798469 0.483140i
\(351\) 0 0
\(352\) 4.19017i 0.223337i
\(353\) 3.92699i 0.209013i −0.994524 0.104506i \(-0.966674\pi\)
0.994524 0.104506i \(-0.0333262\pi\)
\(354\) 0 0
\(355\) 4.87745 + 4.13753i 0.258868 + 0.219598i
\(356\) −11.4773 −0.608295
\(357\) 0 0
\(358\) 7.13581i 0.377139i
\(359\) −9.85179 −0.519957 −0.259979 0.965614i \(-0.583716\pi\)
−0.259979 + 0.965614i \(0.583716\pi\)
\(360\) 0 0
\(361\) −6.32907 −0.333109
\(362\) 11.5365i 0.606346i
\(363\) 0 0
\(364\) −0.676938 −0.0354812
\(365\) 11.7158 13.8110i 0.613234 0.722899i
\(366\) 0 0
\(367\) 33.2559i 1.73594i 0.496614 + 0.867972i \(0.334577\pi\)
−0.496614 + 0.867972i \(0.665423\pi\)
\(368\) 5.62036i 0.292981i
\(369\) 0 0
\(370\) −1.70518 1.44650i −0.0886481 0.0752000i
\(371\) −18.2192 −0.945896
\(372\) 0 0
\(373\) 28.5387i 1.47768i 0.673882 + 0.738839i \(0.264625\pi\)
−0.673882 + 0.738839i \(0.735375\pi\)
\(374\) −21.2994 −1.10136
\(375\) 0 0
\(376\) 10.9154 0.562921
\(377\) 0.445862i 0.0229631i
\(378\) 0 0
\(379\) −0.476554 −0.0244789 −0.0122395 0.999925i \(-0.503896\pi\)
−0.0122395 + 0.999925i \(0.503896\pi\)
\(380\) −6.06980 5.14900i −0.311374 0.264138i
\(381\) 0 0
\(382\) 20.6048i 1.05423i
\(383\) 7.13962i 0.364818i 0.983223 + 0.182409i \(0.0583895\pi\)
−0.983223 + 0.182409i \(0.941611\pi\)
\(384\) 0 0
\(385\) 11.1055 13.0915i 0.565990 0.667206i
\(386\) 26.1663 1.33183
\(387\) 0 0
\(388\) 6.05864i 0.307581i
\(389\) −24.2060 −1.22729 −0.613646 0.789581i \(-0.710298\pi\)
−0.613646 + 0.789581i \(0.710298\pi\)
\(390\) 0 0
\(391\) −28.5693 −1.44481
\(392\) 3.64280i 0.183989i
\(393\) 0 0
\(394\) −14.6067 −0.735876
\(395\) 10.3395 + 8.77101i 0.520239 + 0.441318i
\(396\) 0 0
\(397\) 20.7491i 1.04137i 0.853750 + 0.520684i \(0.174323\pi\)
−0.853750 + 0.520684i \(0.825677\pi\)
\(398\) 5.81275i 0.291367i
\(399\) 0 0
\(400\) 0.815273 + 4.93309i 0.0407637 + 0.246654i
\(401\) 34.8410 1.73988 0.869939 0.493159i \(-0.164158\pi\)
0.869939 + 0.493159i \(0.164158\pi\)
\(402\) 0 0
\(403\) 3.73259i 0.185934i
\(404\) 4.96528 0.247032
\(405\) 0 0
\(406\) −2.21121 −0.109740
\(407\) 4.19017i 0.207699i
\(408\) 0 0
\(409\) −25.2132 −1.24671 −0.623356 0.781938i \(-0.714231\pi\)
−0.623356 + 0.781938i \(0.714231\pi\)
\(410\) −11.5929 + 13.6661i −0.572534 + 0.674921i
\(411\) 0 0
\(412\) 7.33338i 0.361289i
\(413\) 9.79462i 0.481962i
\(414\) 0 0
\(415\) −12.9201 + 15.2307i −0.634225 + 0.747644i
\(416\) 0.369454 0.0181140
\(417\) 0 0
\(418\) 14.9154i 0.729538i
\(419\) 5.69695 0.278314 0.139157 0.990270i \(-0.455561\pi\)
0.139157 + 0.990270i \(0.455561\pi\)
\(420\) 0 0
\(421\) 3.38092 0.164776 0.0823880 0.996600i \(-0.473745\pi\)
0.0823880 + 0.996600i \(0.473745\pi\)
\(422\) 16.0976i 0.783621i
\(423\) 0 0
\(424\) 9.94355 0.482901
\(425\) −25.0757 + 4.14417i −1.21635 + 0.201022i
\(426\) 0 0
\(427\) 17.9457i 0.868455i
\(428\) 8.21182i 0.396933i
\(429\) 0 0
\(430\) −3.87526 3.28738i −0.186882 0.158531i
\(431\) 0.381731 0.0183873 0.00919367 0.999958i \(-0.497074\pi\)
0.00919367 + 0.999958i \(0.497074\pi\)
\(432\) 0 0
\(433\) 21.6393i 1.03992i 0.854192 + 0.519958i \(0.174052\pi\)
−0.854192 + 0.519958i \(0.825948\pi\)
\(434\) −18.5114 −0.888575
\(435\) 0 0
\(436\) −20.5503 −0.984179
\(437\) 20.0064i 0.957035i
\(438\) 0 0
\(439\) −26.4663 −1.26317 −0.631583 0.775308i \(-0.717595\pi\)
−0.631583 + 0.775308i \(0.717595\pi\)
\(440\) −6.06108 + 7.14499i −0.288951 + 0.340624i
\(441\) 0 0
\(442\) 1.87800i 0.0893273i
\(443\) 4.65489i 0.221161i −0.993867 0.110580i \(-0.964729\pi\)
0.993867 0.110580i \(-0.0352709\pi\)
\(444\) 0 0
\(445\) −19.5708 16.6019i −0.927746 0.787005i
\(446\) −25.3608 −1.20087
\(447\) 0 0
\(448\) 1.83227i 0.0865665i
\(449\) −26.5531 −1.25312 −0.626558 0.779375i \(-0.715537\pi\)
−0.626558 + 0.779375i \(0.715537\pi\)
\(450\) 0 0
\(451\) −33.5820 −1.58131
\(452\) 0.652984i 0.0307138i
\(453\) 0 0
\(454\) 5.57339 0.261572
\(455\) −1.15430 0.979192i −0.0541145 0.0459052i
\(456\) 0 0
\(457\) 4.27264i 0.199866i 0.994994 + 0.0999329i \(0.0318628\pi\)
−0.994994 + 0.0999329i \(0.968137\pi\)
\(458\) 9.02035i 0.421493i
\(459\) 0 0
\(460\) −8.12985 + 9.58372i −0.379056 + 0.446843i
\(461\) −32.1873 −1.49911 −0.749555 0.661942i \(-0.769733\pi\)
−0.749555 + 0.661942i \(0.769733\pi\)
\(462\) 0 0
\(463\) 18.4014i 0.855186i −0.903971 0.427593i \(-0.859362\pi\)
0.903971 0.427593i \(-0.140638\pi\)
\(464\) 1.20681 0.0560250
\(465\) 0 0
\(466\) 11.8100 0.547086
\(467\) 3.06777i 0.141959i 0.997478 + 0.0709797i \(0.0226125\pi\)
−0.997478 + 0.0709797i \(0.977387\pi\)
\(468\) 0 0
\(469\) 3.39104 0.156584
\(470\) 18.6128 + 15.7892i 0.858544 + 0.728301i
\(471\) 0 0
\(472\) 5.34563i 0.246052i
\(473\) 9.52276i 0.437857i
\(474\) 0 0
\(475\) −2.90207 17.5599i −0.133156 0.805705i
\(476\) −9.31373 −0.426894
\(477\) 0 0
\(478\) 0.907160i 0.0414925i
\(479\) 8.78798 0.401533 0.200767 0.979639i \(-0.435657\pi\)
0.200767 + 0.979639i \(0.435657\pi\)
\(480\) 0 0
\(481\) −0.369454 −0.0168457
\(482\) 4.15616i 0.189308i
\(483\) 0 0
\(484\) −6.55754 −0.298070
\(485\) 8.76383 10.3311i 0.397945 0.469110i
\(486\) 0 0
\(487\) 22.4814i 1.01873i −0.860550 0.509366i \(-0.829880\pi\)
0.860550 0.509366i \(-0.170120\pi\)
\(488\) 9.79428i 0.443366i
\(489\) 0 0
\(490\) −5.26931 + 6.21162i −0.238043 + 0.280613i
\(491\) 0.0441752 0.00199360 0.000996799 1.00000i \(-0.499683\pi\)
0.000996799 1.00000i \(0.499683\pi\)
\(492\) 0 0
\(493\) 6.13445i 0.276282i
\(494\) −1.31512 −0.0591699
\(495\) 0 0
\(496\) 10.1030 0.453638
\(497\) 5.24097i 0.235090i
\(498\) 0 0
\(499\) −28.2445 −1.26440 −0.632199 0.774806i \(-0.717847\pi\)
−0.632199 + 0.774806i \(0.717847\pi\)
\(500\) −5.74552 + 9.59109i −0.256948 + 0.428926i
\(501\) 0 0
\(502\) 9.31888i 0.415922i
\(503\) 19.7713i 0.881560i −0.897615 0.440780i \(-0.854702\pi\)
0.897615 0.440780i \(-0.145298\pi\)
\(504\) 0 0
\(505\) 8.46670 + 7.18229i 0.376763 + 0.319608i
\(506\) −23.5503 −1.04694
\(507\) 0 0
\(508\) 19.2856i 0.855660i
\(509\) 43.4809 1.92726 0.963628 0.267247i \(-0.0861141\pi\)
0.963628 + 0.267247i \(0.0861141\pi\)
\(510\) 0 0
\(511\) 14.8403 0.656496
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 13.6312 0.601249
\(515\) 10.6077 12.5047i 0.467432 0.551024i
\(516\) 0 0
\(517\) 45.7376i 2.01154i
\(518\) 1.83227i 0.0805052i
\(519\) 0 0
\(520\) 0.629985 + 0.534415i 0.0276267 + 0.0234357i
\(521\) 18.0325 0.790019 0.395009 0.918677i \(-0.370741\pi\)
0.395009 + 0.918677i \(0.370741\pi\)
\(522\) 0 0
\(523\) 31.6788i 1.38522i −0.721313 0.692610i \(-0.756461\pi\)
0.721313 0.692610i \(-0.243539\pi\)
\(524\) −8.82072 −0.385335
\(525\) 0 0
\(526\) 27.2170 1.18672
\(527\) 51.3553i 2.23707i
\(528\) 0 0
\(529\) −8.58844 −0.373410
\(530\) 16.9555 + 14.3833i 0.736501 + 0.624773i
\(531\) 0 0
\(532\) 6.52218i 0.282773i
\(533\) 2.96098i 0.128254i
\(534\) 0 0
\(535\) 11.8784 14.0026i 0.513548 0.605387i
\(536\) −1.85073 −0.0799395
\(537\) 0 0
\(538\) 23.0550i 0.993973i
\(539\) −15.2639 −0.657465
\(540\) 0 0
\(541\) 9.39442 0.403898 0.201949 0.979396i \(-0.435273\pi\)
0.201949 + 0.979396i \(0.435273\pi\)
\(542\) 22.9320i 0.985014i
\(543\) 0 0
\(544\) 5.08317 0.217939
\(545\) −35.0419 29.7260i −1.50103 1.27332i
\(546\) 0 0
\(547\) 24.7824i 1.05962i 0.848117 + 0.529809i \(0.177737\pi\)
−0.848117 + 0.529809i \(0.822263\pi\)
\(548\) 4.66126i 0.199119i
\(549\) 0 0
\(550\) −20.6705 + 3.41613i −0.881392 + 0.145664i
\(551\) −4.29581 −0.183008
\(552\) 0 0
\(553\) 11.1102i 0.472452i
\(554\) −11.7534 −0.499353
\(555\) 0 0
\(556\) 16.4050 0.695727
\(557\) 22.1627i 0.939062i 0.882916 + 0.469531i \(0.155577\pi\)
−0.882916 + 0.469531i \(0.844423\pi\)
\(558\) 0 0
\(559\) −0.839637 −0.0355128
\(560\) −2.65038 + 3.12434i −0.111999 + 0.132028i
\(561\) 0 0
\(562\) 29.0962i 1.22735i
\(563\) 6.46846i 0.272613i 0.990667 + 0.136306i \(0.0435232\pi\)
−0.990667 + 0.136306i \(0.956477\pi\)
\(564\) 0 0
\(565\) −0.944542 + 1.11346i −0.0397372 + 0.0468434i
\(566\) 10.1829 0.428019
\(567\) 0 0
\(568\) 2.86038i 0.120019i
\(569\) 8.26550 0.346508 0.173254 0.984877i \(-0.444572\pi\)
0.173254 + 0.984877i \(0.444572\pi\)
\(570\) 0 0
\(571\) 34.5179 1.44453 0.722264 0.691618i \(-0.243102\pi\)
0.722264 + 0.691618i \(0.243102\pi\)
\(572\) 1.54808i 0.0647283i
\(573\) 0 0
\(574\) −14.6846 −0.612925
\(575\) −27.7257 + 4.58213i −1.15624 + 0.191088i
\(576\) 0 0
\(577\) 3.05347i 0.127117i −0.997978 0.0635587i \(-0.979755\pi\)
0.997978 0.0635587i \(-0.0202450\pi\)
\(578\) 8.83864i 0.367639i
\(579\) 0 0
\(580\) 2.05784 + 1.74566i 0.0854470 + 0.0724845i
\(581\) −16.3658 −0.678968
\(582\) 0 0
\(583\) 41.6652i 1.72559i
\(584\) −8.09942 −0.335156
\(585\) 0 0
\(586\) 18.1243 0.748706
\(587\) 35.1344i 1.45015i 0.688668 + 0.725076i \(0.258196\pi\)
−0.688668 + 0.725076i \(0.741804\pi\)
\(588\) 0 0
\(589\) −35.9629 −1.48183
\(590\) 7.73245 9.11525i 0.318340 0.375269i
\(591\) 0 0
\(592\) 1.00000i 0.0410997i
\(593\) 12.0400i 0.494424i −0.968961 0.247212i \(-0.920486\pi\)
0.968961 0.247212i \(-0.0795144\pi\)
\(594\) 0 0
\(595\) −15.8816 13.4723i −0.651081 0.552311i
\(596\) 5.86259 0.240141
\(597\) 0 0
\(598\) 2.07646i 0.0849129i
\(599\) −17.4701 −0.713810 −0.356905 0.934141i \(-0.616168\pi\)
−0.356905 + 0.934141i \(0.616168\pi\)
\(600\) 0 0
\(601\) 38.7044 1.57878 0.789392 0.613890i \(-0.210396\pi\)
0.789392 + 0.613890i \(0.210396\pi\)
\(602\) 4.16409i 0.169716i
\(603\) 0 0
\(604\) −13.1460 −0.534903
\(605\) −11.1818 9.48548i −0.454604 0.385639i
\(606\) 0 0
\(607\) 28.7903i 1.16856i −0.811551 0.584282i \(-0.801376\pi\)
0.811551 0.584282i \(-0.198624\pi\)
\(608\) 3.55963i 0.144362i
\(609\) 0 0
\(610\) 14.1674 16.7010i 0.573623 0.676204i
\(611\) 4.03275 0.163148
\(612\) 0 0
\(613\) 7.66539i 0.309602i 0.987946 + 0.154801i \(0.0494737\pi\)
−0.987946 + 0.154801i \(0.950526\pi\)
\(614\) −6.15561 −0.248420
\(615\) 0 0
\(616\) −7.67751 −0.309336
\(617\) 36.5388i 1.47100i −0.677527 0.735498i \(-0.736948\pi\)
0.677527 0.735498i \(-0.263052\pi\)
\(618\) 0 0
\(619\) 45.8085 1.84120 0.920599 0.390510i \(-0.127701\pi\)
0.920599 + 0.390510i \(0.127701\pi\)
\(620\) 17.2274 + 14.6140i 0.691870 + 0.586912i
\(621\) 0 0
\(622\) 29.4512i 1.18088i
\(623\) 21.0294i 0.842527i
\(624\) 0 0
\(625\) −23.6707 + 8.04362i −0.946826 + 0.321745i
\(626\) −13.0102 −0.519991
\(627\) 0 0
\(628\) 7.33629i 0.292750i
\(629\) −5.08317 −0.202679
\(630\) 0 0
\(631\) 3.42682 0.136420 0.0682098 0.997671i \(-0.478271\pi\)
0.0682098 + 0.997671i \(0.478271\pi\)
\(632\) 6.06361i 0.241197i
\(633\) 0 0
\(634\) 7.39826 0.293823
\(635\) −27.8966 + 32.8854i −1.10704 + 1.30502i
\(636\) 0 0
\(637\) 1.34585i 0.0533244i
\(638\) 5.05676i 0.200199i
\(639\) 0 0
\(640\) 1.44650 1.70518i 0.0571779 0.0674031i
\(641\) −38.3241 −1.51371 −0.756855 0.653583i \(-0.773265\pi\)
−0.756855 + 0.653583i \(0.773265\pi\)
\(642\) 0 0
\(643\) 1.36660i 0.0538935i −0.999637 0.0269468i \(-0.991422\pi\)
0.999637 0.0269468i \(-0.00857846\pi\)
\(644\) −10.2980 −0.405798
\(645\) 0 0
\(646\) −18.0942 −0.711906
\(647\) 11.2690i 0.443028i −0.975157 0.221514i \(-0.928900\pi\)
0.975157 0.221514i \(-0.0710999\pi\)
\(648\) 0 0
\(649\) 22.3991 0.879241
\(650\) 0.301206 + 1.82255i 0.0118143 + 0.0714862i
\(651\) 0 0
\(652\) 18.7968i 0.736138i
\(653\) 29.5439i 1.15614i −0.815987 0.578070i \(-0.803806\pi\)
0.815987 0.578070i \(-0.196194\pi\)
\(654\) 0 0
\(655\) −15.0409 12.7592i −0.587697 0.498542i
\(656\) 8.01447 0.312912
\(657\) 0 0
\(658\) 20.0000i 0.779681i
\(659\) −49.9126 −1.94432 −0.972159 0.234324i \(-0.924712\pi\)
−0.972159 + 0.234324i \(0.924712\pi\)
\(660\) 0 0
\(661\) 25.9950 1.01109 0.505545 0.862800i \(-0.331292\pi\)
0.505545 + 0.862800i \(0.331292\pi\)
\(662\) 33.2545i 1.29247i
\(663\) 0 0
\(664\) 8.93200 0.346629
\(665\) 9.43434 11.1215i 0.365848 0.431273i
\(666\) 0 0
\(667\) 6.78273i 0.262628i
\(668\) 5.92772i 0.229350i
\(669\) 0 0
\(670\) −3.15583 2.67709i −0.121920 0.103425i
\(671\) 41.0397 1.58432
\(672\) 0 0
\(673\) 6.91054i 0.266382i −0.991090 0.133191i \(-0.957478\pi\)
0.991090 0.133191i \(-0.0425223\pi\)
\(674\) 22.6288 0.871627
\(675\) 0 0
\(676\) −12.8635 −0.494750
\(677\) 15.6913i 0.603065i 0.953456 + 0.301532i \(0.0974982\pi\)
−0.953456 + 0.301532i \(0.902502\pi\)
\(678\) 0 0
\(679\) 11.1011 0.426019
\(680\) 8.66772 + 7.35281i 0.332392 + 0.281967i
\(681\) 0 0
\(682\) 42.3333i 1.62103i
\(683\) 18.2002i 0.696412i −0.937418 0.348206i \(-0.886791\pi\)
0.937418 0.348206i \(-0.113209\pi\)
\(684\) 0 0
\(685\) −6.74252 + 7.94829i −0.257618 + 0.303689i
\(686\) −19.5004 −0.744531
\(687\) 0 0
\(688\) 2.27264i 0.0866437i
\(689\) 3.67368 0.139956
\(690\) 0 0
\(691\) −2.58658 −0.0983982 −0.0491991 0.998789i \(-0.515667\pi\)
−0.0491991 + 0.998789i \(0.515667\pi\)
\(692\) 5.78242i 0.219815i
\(693\) 0 0
\(694\) 24.1396 0.916327
\(695\) 27.9735 + 23.7298i 1.06109 + 0.900124i
\(696\) 0 0
\(697\) 40.7389i 1.54310i
\(698\) 10.3702i 0.392516i
\(699\) 0 0
\(700\) −9.03873 + 1.49380i −0.341632 + 0.0564603i
\(701\) 26.5092 1.00124 0.500620 0.865667i \(-0.333105\pi\)
0.500620 + 0.865667i \(0.333105\pi\)
\(702\) 0 0
\(703\) 3.55963i 0.134254i
\(704\) 4.19017 0.157923
\(705\) 0 0
\(706\) −3.92699 −0.147794
\(707\) 9.09773i 0.342155i
\(708\) 0 0
\(709\) 25.0474 0.940674 0.470337 0.882487i \(-0.344132\pi\)
0.470337 + 0.882487i \(0.344132\pi\)
\(710\) 4.13753 4.87745i 0.155279 0.183048i
\(711\) 0 0
\(712\) 11.4773i 0.430129i
\(713\) 56.7825i 2.12652i
\(714\) 0 0
\(715\) −2.23929 + 2.63975i −0.0837448 + 0.0987209i
\(716\) −7.13581 −0.266678
\(717\) 0 0
\(718\) 9.85179i 0.367665i
\(719\) 24.9551 0.930668 0.465334 0.885135i \(-0.345934\pi\)
0.465334 + 0.885135i \(0.345934\pi\)
\(720\) 0 0
\(721\) 13.4367 0.500409
\(722\) 6.32907i 0.235544i
\(723\) 0 0
\(724\) −11.5365 −0.428752
\(725\) 0.983883 + 5.95332i 0.0365405 + 0.221101i
\(726\) 0 0
\(727\) 21.6774i 0.803970i −0.915646 0.401985i \(-0.868320\pi\)
0.915646 0.401985i \(-0.131680\pi\)
\(728\) 0.676938i 0.0250890i
\(729\) 0 0
\(730\) −13.8110 11.7158i −0.511167 0.433622i
\(731\) −11.5522 −0.427275
\(732\) 0 0
\(733\) 6.33267i 0.233903i −0.993138 0.116951i \(-0.962688\pi\)
0.993138 0.116951i \(-0.0373122\pi\)
\(734\) 33.2559 1.22750
\(735\) 0 0
\(736\) 5.62036 0.207169
\(737\) 7.75489i 0.285655i
\(738\) 0 0
\(739\) −12.8076 −0.471136 −0.235568 0.971858i \(-0.575695\pi\)
−0.235568 + 0.971858i \(0.575695\pi\)
\(740\) −1.44650 + 1.70518i −0.0531744 + 0.0626836i
\(741\) 0 0
\(742\) 18.2192i 0.668849i
\(743\) 11.0694i 0.406097i 0.979169 + 0.203048i \(0.0650848\pi\)
−0.979169 + 0.203048i \(0.934915\pi\)
\(744\) 0 0
\(745\) 9.99677 + 8.48024i 0.366253 + 0.310692i
\(746\) 28.5387 1.04488
\(747\) 0 0
\(748\) 21.2994i 0.778782i
\(749\) 15.0463 0.549778
\(750\) 0 0
\(751\) −46.5316 −1.69796 −0.848981 0.528423i \(-0.822784\pi\)
−0.848981 + 0.528423i \(0.822784\pi\)
\(752\) 10.9154i 0.398045i
\(753\) 0 0
\(754\) 0.445862 0.0162374
\(755\) −22.4163 19.0157i −0.815812 0.692052i
\(756\) 0 0
\(757\) 32.9872i 1.19894i 0.800397 + 0.599470i \(0.204622\pi\)
−0.800397 + 0.599470i \(0.795378\pi\)
\(758\) 0.476554i 0.0173092i
\(759\) 0 0
\(760\) −5.14900 + 6.06980i −0.186774 + 0.220175i
\(761\) −28.7913 −1.04369 −0.521843 0.853042i \(-0.674755\pi\)
−0.521843 + 0.853042i \(0.674755\pi\)
\(762\) 0 0
\(763\) 37.6536i 1.36315i
\(764\) −20.6048 −0.745456
\(765\) 0 0
\(766\) 7.13962 0.257965
\(767\) 1.97496i 0.0713118i
\(768\) 0 0
\(769\) −41.9025 −1.51104 −0.755521 0.655124i \(-0.772616\pi\)
−0.755521 + 0.655124i \(0.772616\pi\)
\(770\) −13.0915 11.1055i −0.471786 0.400215i
\(771\) 0 0
\(772\) 26.1663i 0.941747i
\(773\) 31.0931i 1.11834i 0.829052 + 0.559171i \(0.188881\pi\)
−0.829052 + 0.559171i \(0.811119\pi\)
\(774\) 0 0
\(775\) 8.23670 + 49.8390i 0.295871 + 1.79027i
\(776\) −6.05864 −0.217493
\(777\) 0 0
\(778\) 24.2060i 0.867827i
\(779\) −28.5285 −1.02214
\(780\) 0 0
\(781\) 11.9855 0.428874
\(782\) 28.5693i 1.02163i
\(783\) 0 0
\(784\) 3.64280 0.130100
\(785\) −10.6120 + 12.5097i −0.378757 + 0.446490i
\(786\) 0 0
\(787\) 18.2842i 0.651760i −0.945411 0.325880i \(-0.894339\pi\)
0.945411 0.325880i \(-0.105661\pi\)
\(788\) 14.6067i 0.520343i
\(789\) 0 0
\(790\) 8.77101 10.3395i 0.312059 0.367864i
\(791\) −1.19644 −0.0425406
\(792\) 0 0
\(793\) 3.61854i 0.128498i
\(794\) 20.7491 0.736358
\(795\) 0 0
\(796\) 5.81275 0.206027
\(797\) 40.6025i 1.43821i 0.694900 + 0.719106i \(0.255449\pi\)