Properties

Label 3330.2.d.p.1999.4
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 1999.4
Root \(0.478560 + 0.478560i\) of defining polynomial
Character \(\chi\) \(=\) 3330.1999
Dual form 3330.2.d.p.1999.9

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(1.10390 + 1.94458i) q^{5} +3.51336i q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(1.10390 + 1.94458i) q^{5} +3.51336i q^{7} +1.00000i q^{8} +(1.94458 - 1.10390i) q^{10} +0.290044 q^{11} +7.12558i q^{13} +3.51336 q^{14} +1.00000 q^{16} -6.17921i q^{17} -5.83553 q^{19} +(-1.10390 - 1.94458i) q^{20} -0.290044i q^{22} +6.45973i q^{23} +(-2.56279 + 4.29326i) q^{25} +7.12558 q^{26} -3.51336i q^{28} -1.18043 q^{29} +9.77838 q^{31} -1.00000i q^{32} -6.17921 q^{34} +(-6.83201 + 3.87841i) q^{35} +1.00000i q^{37} +5.83553i q^{38} +(-1.94458 + 1.10390i) q^{40} -1.64077 q^{41} -5.34889i q^{43} -0.290044 q^{44} +6.45973 q^{46} +5.69256i q^{47} -5.34367 q^{49} +(4.29326 + 2.56279i) q^{50} -7.12558i q^{52} -9.32034i q^{53} +(0.320181 + 0.564014i) q^{55} -3.51336 q^{56} +1.18043i q^{58} +5.94279 q^{59} -1.27699 q^{61} -9.77838i q^{62} -1.00000 q^{64} +(-13.8563 + 7.86596i) q^{65} -6.04334i q^{67} +6.17921i q^{68} +(3.87841 + 6.83201i) q^{70} -13.4995 q^{71} +1.71348i q^{73} +1.00000 q^{74} +5.83553 q^{76} +1.01903i q^{77} -8.25422 q^{79} +(1.10390 + 1.94458i) q^{80} +1.64077i q^{82} -2.41807i q^{83} +(12.0160 - 6.82126i) q^{85} -5.34889 q^{86} +0.290044i q^{88} -10.2797 q^{89} -25.0347 q^{91} -6.45973i q^{92} +5.69256 q^{94} +(-6.44187 - 11.3477i) q^{95} -15.1272i q^{97} +5.34367i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{4} - 6q^{5} + O(q^{10}) \) \( 10q - 10q^{4} - 6q^{5} + 2q^{10} - 6q^{11} - 2q^{14} + 10q^{16} - 8q^{19} + 6q^{20} + 4q^{25} + 12q^{26} + 22q^{29} + 46q^{31} - 18q^{34} - 32q^{35} - 2q^{40} + 14q^{41} + 6q^{44} + 12q^{46} - 60q^{49} - 8q^{50} + 42q^{55} + 2q^{56} + 40q^{59} - 18q^{61} - 10q^{64} - 4q^{65} - 6q^{70} - 12q^{71} + 10q^{74} + 8q^{76} - 40q^{79} - 6q^{80} + 36q^{85} + 34q^{86} + 24q^{89} + 32q^{91} - 24q^{94} - 12q^{95} + O(q^{100}) \)

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
\(5\) 1.10390 + 1.94458i 0.493681 + 0.869643i
\(6\) 0 0
\(7\) 3.51336i 1.32792i 0.747766 + 0.663962i \(0.231126\pi\)
−0.747766 + 0.663962i \(0.768874\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.94458 1.10390i 0.614930 0.349085i
\(11\) 0.290044 0.0874516 0.0437258 0.999044i \(-0.486077\pi\)
0.0437258 + 0.999044i \(0.486077\pi\)
\(12\) 0 0
\(13\) 7.12558i 1.97628i 0.153559 + 0.988140i \(0.450927\pi\)
−0.153559 + 0.988140i \(0.549073\pi\)
\(14\) 3.51336 0.938984
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 6.17921i 1.49868i −0.662187 0.749339i \(-0.730372\pi\)
0.662187 0.749339i \(-0.269628\pi\)
\(18\) 0 0
\(19\) −5.83553 −1.33876 −0.669381 0.742919i \(-0.733441\pi\)
−0.669381 + 0.742919i \(0.733441\pi\)
\(20\) −1.10390 1.94458i −0.246841 0.434821i
\(21\) 0 0
\(22\) 0.290044i 0.0618376i
\(23\) 6.45973i 1.34695i 0.739212 + 0.673473i \(0.235198\pi\)
−0.739212 + 0.673473i \(0.764802\pi\)
\(24\) 0 0
\(25\) −2.56279 + 4.29326i −0.512558 + 0.858653i
\(26\) 7.12558 1.39744
\(27\) 0 0
\(28\) 3.51336i 0.663962i
\(29\) −1.18043 −0.219201 −0.109600 0.993976i \(-0.534957\pi\)
−0.109600 + 0.993976i \(0.534957\pi\)
\(30\) 0 0
\(31\) 9.77838 1.75625 0.878124 0.478433i \(-0.158795\pi\)
0.878124 + 0.478433i \(0.158795\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −6.17921 −1.05972
\(35\) −6.83201 + 3.87841i −1.15482 + 0.655571i
\(36\) 0 0
\(37\) 1.00000i 0.164399i
\(38\) 5.83553i 0.946648i
\(39\) 0 0
\(40\) −1.94458 + 1.10390i −0.307465 + 0.174543i
\(41\) −1.64077 −0.256245 −0.128123 0.991758i \(-0.540895\pi\)
−0.128123 + 0.991758i \(0.540895\pi\)
\(42\) 0 0
\(43\) 5.34889i 0.815698i −0.913049 0.407849i \(-0.866279\pi\)
0.913049 0.407849i \(-0.133721\pi\)
\(44\) −0.290044 −0.0437258
\(45\) 0 0
\(46\) 6.45973 0.952435
\(47\) 5.69256i 0.830346i 0.909743 + 0.415173i \(0.136279\pi\)
−0.909743 + 0.415173i \(0.863721\pi\)
\(48\) 0 0
\(49\) −5.34367 −0.763382
\(50\) 4.29326 + 2.56279i 0.607159 + 0.362433i
\(51\) 0 0
\(52\) 7.12558i 0.988140i
\(53\) 9.32034i 1.28025i −0.768272 0.640123i \(-0.778883\pi\)
0.768272 0.640123i \(-0.221117\pi\)
\(54\) 0 0
\(55\) 0.320181 + 0.564014i 0.0431732 + 0.0760517i
\(56\) −3.51336 −0.469492
\(57\) 0 0
\(58\) 1.18043i 0.154998i
\(59\) 5.94279 0.773686 0.386843 0.922146i \(-0.373566\pi\)
0.386843 + 0.922146i \(0.373566\pi\)
\(60\) 0 0
\(61\) −1.27699 −0.163502 −0.0817512 0.996653i \(-0.526051\pi\)
−0.0817512 + 0.996653i \(0.526051\pi\)
\(62\) 9.77838i 1.24185i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −13.8563 + 7.86596i −1.71866 + 0.975652i
\(66\) 0 0
\(67\) 6.04334i 0.738312i −0.929368 0.369156i \(-0.879647\pi\)
0.929368 0.369156i \(-0.120353\pi\)
\(68\) 6.17921i 0.749339i
\(69\) 0 0
\(70\) 3.87841 + 6.83201i 0.463559 + 0.816581i
\(71\) −13.4995 −1.60210 −0.801050 0.598597i \(-0.795725\pi\)
−0.801050 + 0.598597i \(0.795725\pi\)
\(72\) 0 0
\(73\) 1.71348i 0.200548i 0.994960 + 0.100274i \(0.0319719\pi\)
−0.994960 + 0.100274i \(0.968028\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) 5.83553 0.669381
\(77\) 1.01903i 0.116129i
\(78\) 0 0
\(79\) −8.25422 −0.928672 −0.464336 0.885659i \(-0.653707\pi\)
−0.464336 + 0.885659i \(0.653707\pi\)
\(80\) 1.10390 + 1.94458i 0.123420 + 0.217411i
\(81\) 0 0
\(82\) 1.64077i 0.181193i
\(83\) 2.41807i 0.265418i −0.991155 0.132709i \(-0.957632\pi\)
0.991155 0.132709i \(-0.0423676\pi\)
\(84\) 0 0
\(85\) 12.0160 6.82126i 1.30331 0.739869i
\(86\) −5.34889 −0.576785
\(87\) 0 0
\(88\) 0.290044i 0.0309188i
\(89\) −10.2797 −1.08965 −0.544823 0.838551i \(-0.683403\pi\)
−0.544823 + 0.838551i \(0.683403\pi\)
\(90\) 0 0
\(91\) −25.0347 −2.62435
\(92\) 6.45973i 0.673473i
\(93\) 0 0
\(94\) 5.69256 0.587143
\(95\) −6.44187 11.3477i −0.660922 1.16425i
\(96\) 0 0
\(97\) 15.1272i 1.53594i −0.640489 0.767968i \(-0.721268\pi\)
0.640489 0.767968i \(-0.278732\pi\)
\(98\) 5.34367i 0.539793i
\(99\) 0 0
\(100\) 2.56279 4.29326i 0.256279 0.429326i
\(101\) −2.63730 −0.262421 −0.131210 0.991355i \(-0.541886\pi\)
−0.131210 + 0.991355i \(0.541886\pi\)
\(102\) 0 0
\(103\) 1.72469i 0.169939i −0.996384 0.0849695i \(-0.972921\pi\)
0.996384 0.0849695i \(-0.0270793\pi\)
\(104\) −7.12558 −0.698720
\(105\) 0 0
\(106\) −9.32034 −0.905271
\(107\) 10.0279i 0.969438i 0.874670 + 0.484719i \(0.161078\pi\)
−0.874670 + 0.484719i \(0.838922\pi\)
\(108\) 0 0
\(109\) −4.87361 −0.466807 −0.233403 0.972380i \(-0.574986\pi\)
−0.233403 + 0.972380i \(0.574986\pi\)
\(110\) 0.564014 0.320181i 0.0537767 0.0305281i
\(111\) 0 0
\(112\) 3.51336i 0.331981i
\(113\) 15.9290i 1.49847i 0.662303 + 0.749236i \(0.269579\pi\)
−0.662303 + 0.749236i \(0.730421\pi\)
\(114\) 0 0
\(115\) −12.5615 + 7.13092i −1.17136 + 0.664962i
\(116\) 1.18043 0.109600
\(117\) 0 0
\(118\) 5.94279i 0.547078i
\(119\) 21.7098 1.99013
\(120\) 0 0
\(121\) −10.9159 −0.992352
\(122\) 1.27699i 0.115614i
\(123\) 0 0
\(124\) −9.77838 −0.878124
\(125\) −11.1777 0.244192i −0.999761 0.0218412i
\(126\) 0 0
\(127\) 1.31265i 0.116479i −0.998303 0.0582395i \(-0.981451\pi\)
0.998303 0.0582395i \(-0.0185487\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 7.86596 + 13.8563i 0.689890 + 1.21527i
\(131\) −2.41562 −0.211054 −0.105527 0.994416i \(-0.533653\pi\)
−0.105527 + 0.994416i \(0.533653\pi\)
\(132\) 0 0
\(133\) 20.5023i 1.77778i
\(134\) −6.04334 −0.522065
\(135\) 0 0
\(136\) 6.17921 0.529862
\(137\) 6.87366i 0.587256i 0.955920 + 0.293628i \(0.0948627\pi\)
−0.955920 + 0.293628i \(0.905137\pi\)
\(138\) 0 0
\(139\) 9.80616 0.831748 0.415874 0.909422i \(-0.363476\pi\)
0.415874 + 0.909422i \(0.363476\pi\)
\(140\) 6.83201 3.87841i 0.577410 0.327786i
\(141\) 0 0
\(142\) 13.4995i 1.13286i
\(143\) 2.06673i 0.172829i
\(144\) 0 0
\(145\) −1.30308 2.29545i −0.108215 0.190626i
\(146\) 1.71348 0.141809
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) −9.07687 −0.743606 −0.371803 0.928312i \(-0.621260\pi\)
−0.371803 + 0.928312i \(0.621260\pi\)
\(150\) 0 0
\(151\) 20.1964 1.64356 0.821780 0.569805i \(-0.192981\pi\)
0.821780 + 0.569805i \(0.192981\pi\)
\(152\) 5.83553i 0.473324i
\(153\) 0 0
\(154\) 1.01903 0.0821157
\(155\) 10.7944 + 19.0148i 0.867027 + 1.52731i
\(156\) 0 0
\(157\) 17.2677i 1.37811i 0.724707 + 0.689057i \(0.241975\pi\)
−0.724707 + 0.689057i \(0.758025\pi\)
\(158\) 8.25422i 0.656670i
\(159\) 0 0
\(160\) 1.94458 1.10390i 0.153733 0.0872713i
\(161\) −22.6953 −1.78864
\(162\) 0 0
\(163\) 16.6901i 1.30727i 0.756810 + 0.653634i \(0.226757\pi\)
−0.756810 + 0.653634i \(0.773243\pi\)
\(164\) 1.64077 0.128123
\(165\) 0 0
\(166\) −2.41807 −0.187679
\(167\) 1.47354i 0.114026i 0.998373 + 0.0570130i \(0.0181577\pi\)
−0.998373 + 0.0570130i \(0.981842\pi\)
\(168\) 0 0
\(169\) −37.7738 −2.90568
\(170\) −6.82126 12.0160i −0.523166 0.921582i
\(171\) 0 0
\(172\) 5.34889i 0.407849i
\(173\) 13.8432i 1.05248i −0.850336 0.526240i \(-0.823601\pi\)
0.850336 0.526240i \(-0.176399\pi\)
\(174\) 0 0
\(175\) −15.0838 9.00399i −1.14023 0.680637i
\(176\) 0.290044 0.0218629
\(177\) 0 0
\(178\) 10.2797i 0.770496i
\(179\) 21.7817 1.62804 0.814020 0.580836i \(-0.197274\pi\)
0.814020 + 0.580836i \(0.197274\pi\)
\(180\) 0 0
\(181\) 2.03100 0.150963 0.0754817 0.997147i \(-0.475951\pi\)
0.0754817 + 0.997147i \(0.475951\pi\)
\(182\) 25.0347i 1.85569i
\(183\) 0 0
\(184\) −6.45973 −0.476217
\(185\) −1.94458 + 1.10390i −0.142968 + 0.0811607i
\(186\) 0 0
\(187\) 1.79224i 0.131062i
\(188\) 5.69256i 0.415173i
\(189\) 0 0
\(190\) −11.3477 + 6.44187i −0.823246 + 0.467343i
\(191\) 8.44668 0.611180 0.305590 0.952163i \(-0.401146\pi\)
0.305590 + 0.952163i \(0.401146\pi\)
\(192\) 0 0
\(193\) 3.64159i 0.262127i 0.991374 + 0.131064i \(0.0418392\pi\)
−0.991374 + 0.131064i \(0.958161\pi\)
\(194\) −15.1272 −1.08607
\(195\) 0 0
\(196\) 5.34367 0.381691
\(197\) 10.1939i 0.726288i 0.931733 + 0.363144i \(0.118297\pi\)
−0.931733 + 0.363144i \(0.881703\pi\)
\(198\) 0 0
\(199\) 5.25299 0.372375 0.186187 0.982514i \(-0.440387\pi\)
0.186187 + 0.982514i \(0.440387\pi\)
\(200\) −4.29326 2.56279i −0.303580 0.181216i
\(201\) 0 0
\(202\) 2.63730i 0.185560i
\(203\) 4.14728i 0.291082i
\(204\) 0 0
\(205\) −1.81125 3.19061i −0.126504 0.222842i
\(206\) −1.72469 −0.120165
\(207\) 0 0
\(208\) 7.12558i 0.494070i
\(209\) −1.69256 −0.117077
\(210\) 0 0
\(211\) −4.81998 −0.331821 −0.165910 0.986141i \(-0.553056\pi\)
−0.165910 + 0.986141i \(0.553056\pi\)
\(212\) 9.32034i 0.640123i
\(213\) 0 0
\(214\) 10.0279 0.685496
\(215\) 10.4013 5.90466i 0.709366 0.402695i
\(216\) 0 0
\(217\) 34.3549i 2.33216i
\(218\) 4.87361i 0.330082i
\(219\) 0 0
\(220\) −0.320181 0.564014i −0.0215866 0.0380258i
\(221\) 44.0304 2.96180
\(222\) 0 0
\(223\) 3.70392i 0.248033i 0.992280 + 0.124017i \(0.0395776\pi\)
−0.992280 + 0.124017i \(0.960422\pi\)
\(224\) 3.51336 0.234746
\(225\) 0 0
\(226\) 15.9290 1.05958
\(227\) 6.31512i 0.419149i 0.977793 + 0.209575i \(0.0672079\pi\)
−0.977793 + 0.209575i \(0.932792\pi\)
\(228\) 0 0
\(229\) 20.5548 1.35830 0.679150 0.734000i \(-0.262349\pi\)
0.679150 + 0.734000i \(0.262349\pi\)
\(230\) 7.13092 + 12.5615i 0.470199 + 0.828278i
\(231\) 0 0
\(232\) 1.18043i 0.0774992i
\(233\) 21.4393i 1.40453i −0.711914 0.702267i \(-0.752171\pi\)
0.711914 0.702267i \(-0.247829\pi\)
\(234\) 0 0
\(235\) −11.0696 + 6.28405i −0.722104 + 0.409926i
\(236\) −5.94279 −0.386843
\(237\) 0 0
\(238\) 21.7098i 1.40723i
\(239\) −20.7479 −1.34207 −0.671034 0.741426i \(-0.734150\pi\)
−0.671034 + 0.741426i \(0.734150\pi\)
\(240\) 0 0
\(241\) 10.7731 0.693957 0.346978 0.937873i \(-0.387208\pi\)
0.346978 + 0.937873i \(0.387208\pi\)
\(242\) 10.9159i 0.701699i
\(243\) 0 0
\(244\) 1.27699 0.0817512
\(245\) −5.89891 10.3912i −0.376867 0.663870i
\(246\) 0 0
\(247\) 41.5815i 2.64577i
\(248\) 9.77838i 0.620927i
\(249\) 0 0
\(250\) −0.244192 + 11.1777i −0.0154440 + 0.706938i
\(251\) 4.46812 0.282025 0.141013 0.990008i \(-0.454964\pi\)
0.141013 + 0.990008i \(0.454964\pi\)
\(252\) 0 0
\(253\) 1.87361i 0.117793i
\(254\) −1.31265 −0.0823631
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 1.24594i 0.0777194i −0.999245 0.0388597i \(-0.987627\pi\)
0.999245 0.0388597i \(-0.0123725\pi\)
\(258\) 0 0
\(259\) −3.51336 −0.218309
\(260\) 13.8563 7.86596i 0.859329 0.487826i
\(261\) 0 0
\(262\) 2.41562i 0.149237i
\(263\) 16.3230i 1.00652i −0.864135 0.503259i \(-0.832134\pi\)
0.864135 0.503259i \(-0.167866\pi\)
\(264\) 0 0
\(265\) 18.1241 10.2888i 1.11336 0.632034i
\(266\) −20.5023 −1.25708
\(267\) 0 0
\(268\) 6.04334i 0.369156i
\(269\) −18.5763 −1.13262 −0.566309 0.824193i \(-0.691629\pi\)
−0.566309 + 0.824193i \(0.691629\pi\)
\(270\) 0 0
\(271\) 16.4181 0.997327 0.498663 0.866796i \(-0.333824\pi\)
0.498663 + 0.866796i \(0.333824\pi\)
\(272\) 6.17921i 0.374669i
\(273\) 0 0
\(274\) 6.87366 0.415253
\(275\) −0.743322 + 1.24524i −0.0448240 + 0.0750906i
\(276\) 0 0
\(277\) 15.6104i 0.937937i −0.883215 0.468968i \(-0.844626\pi\)
0.883215 0.468968i \(-0.155374\pi\)
\(278\) 9.80616i 0.588134i
\(279\) 0 0
\(280\) −3.87841 6.83201i −0.231779 0.408290i
\(281\) 21.8665 1.30445 0.652224 0.758026i \(-0.273836\pi\)
0.652224 + 0.758026i \(0.273836\pi\)
\(282\) 0 0
\(283\) 2.24778i 0.133616i −0.997766 0.0668082i \(-0.978718\pi\)
0.997766 0.0668082i \(-0.0212816\pi\)
\(284\) 13.4995 0.801050
\(285\) 0 0
\(286\) 2.06673 0.122208
\(287\) 5.76461i 0.340274i
\(288\) 0 0
\(289\) −21.1826 −1.24603
\(290\) −2.29545 + 1.30308i −0.134793 + 0.0765198i
\(291\) 0 0
\(292\) 1.71348i 0.100274i
\(293\) 26.8794i 1.57031i 0.619297 + 0.785157i \(0.287418\pi\)
−0.619297 + 0.785157i \(0.712582\pi\)
\(294\) 0 0
\(295\) 6.56028 + 11.5562i 0.381954 + 0.672830i
\(296\) −1.00000 −0.0581238
\(297\) 0 0
\(298\) 9.07687i 0.525809i
\(299\) −46.0293 −2.66194
\(300\) 0 0
\(301\) 18.7926 1.08318
\(302\) 20.1964i 1.16217i
\(303\) 0 0
\(304\) −5.83553 −0.334691
\(305\) −1.40968 2.48322i −0.0807181 0.142189i
\(306\) 0 0
\(307\) 23.9979i 1.36963i 0.728717 + 0.684815i \(0.240117\pi\)
−0.728717 + 0.684815i \(0.759883\pi\)
\(308\) 1.01903i 0.0580645i
\(309\) 0 0
\(310\) 19.0148 10.7944i 1.07997 0.613081i
\(311\) 5.07563 0.287812 0.143906 0.989591i \(-0.454034\pi\)
0.143906 + 0.989591i \(0.454034\pi\)
\(312\) 0 0
\(313\) 8.96950i 0.506986i 0.967337 + 0.253493i \(0.0815795\pi\)
−0.967337 + 0.253493i \(0.918420\pi\)
\(314\) 17.2677 0.974474
\(315\) 0 0
\(316\) 8.25422 0.464336
\(317\) 22.0181i 1.23666i 0.785918 + 0.618330i \(0.212191\pi\)
−0.785918 + 0.618330i \(0.787809\pi\)
\(318\) 0 0
\(319\) −0.342377 −0.0191695
\(320\) −1.10390 1.94458i −0.0617102 0.108705i
\(321\) 0 0
\(322\) 22.6953i 1.26476i
\(323\) 36.0589i 2.00637i
\(324\) 0 0
\(325\) −30.5920 18.2613i −1.69694 1.01296i
\(326\) 16.6901 0.924379
\(327\) 0 0
\(328\) 1.64077i 0.0905964i
\(329\) −20.0000 −1.10264
\(330\) 0 0
\(331\) −10.7134 −0.588864 −0.294432 0.955672i \(-0.595130\pi\)
−0.294432 + 0.955672i \(0.595130\pi\)
\(332\) 2.41807i 0.132709i
\(333\) 0 0
\(334\) 1.47354 0.0806286
\(335\) 11.7518 6.67127i 0.642067 0.364491i
\(336\) 0 0
\(337\) 1.34097i 0.0730471i 0.999333 + 0.0365235i \(0.0116284\pi\)
−0.999333 + 0.0365235i \(0.988372\pi\)
\(338\) 37.7738i 2.05463i
\(339\) 0 0
\(340\) −12.0160 + 6.82126i −0.651657 + 0.369935i
\(341\) 2.83616 0.153587
\(342\) 0 0
\(343\) 5.81926i 0.314211i
\(344\) 5.34889 0.288393
\(345\) 0 0
\(346\) −13.8432 −0.744216
\(347\) 0.883744i 0.0474419i −0.999719 0.0237209i \(-0.992449\pi\)
0.999719 0.0237209i \(-0.00755131\pi\)
\(348\) 0 0
\(349\) 9.00521 0.482038 0.241019 0.970520i \(-0.422518\pi\)
0.241019 + 0.970520i \(0.422518\pi\)
\(350\) −9.00399 + 15.0838i −0.481283 + 0.806261i
\(351\) 0 0
\(352\) 0.290044i 0.0154594i
\(353\) 6.79030i 0.361411i 0.983537 + 0.180706i \(0.0578381\pi\)
−0.983537 + 0.180706i \(0.942162\pi\)
\(354\) 0 0
\(355\) −14.9022 26.2509i −0.790927 1.39326i
\(356\) 10.2797 0.544823
\(357\) 0 0
\(358\) 21.7817i 1.15120i
\(359\) −10.2263 −0.539722 −0.269861 0.962899i \(-0.586978\pi\)
−0.269861 + 0.962899i \(0.586978\pi\)
\(360\) 0 0
\(361\) 15.0534 0.792286
\(362\) 2.03100i 0.106747i
\(363\) 0 0
\(364\) 25.0347 1.31217
\(365\) −3.33200 + 1.89152i −0.174405 + 0.0990067i
\(366\) 0 0
\(367\) 17.1583i 0.895657i 0.894119 + 0.447829i \(0.147802\pi\)
−0.894119 + 0.447829i \(0.852198\pi\)
\(368\) 6.45973i 0.336737i
\(369\) 0 0
\(370\) 1.10390 + 1.94458i 0.0573893 + 0.101094i
\(371\) 32.7457 1.70007
\(372\) 0 0
\(373\) 17.1601i 0.888515i −0.895899 0.444257i \(-0.853468\pi\)
0.895899 0.444257i \(-0.146532\pi\)
\(374\) −1.79224 −0.0926747
\(375\) 0 0
\(376\) −5.69256 −0.293571
\(377\) 8.41126i 0.433202i
\(378\) 0 0
\(379\) 27.5435 1.41482 0.707408 0.706805i \(-0.249864\pi\)
0.707408 + 0.706805i \(0.249864\pi\)
\(380\) 6.44187 + 11.3477i 0.330461 + 0.582123i
\(381\) 0 0
\(382\) 8.44668i 0.432170i
\(383\) 3.49954i 0.178818i −0.995995 0.0894091i \(-0.971502\pi\)
0.995995 0.0894091i \(-0.0284979\pi\)
\(384\) 0 0
\(385\) −1.98158 + 1.12491i −0.100991 + 0.0573308i
\(386\) 3.64159 0.185352
\(387\) 0 0
\(388\) 15.1272i 0.767968i
\(389\) −13.0015 −0.659203 −0.329602 0.944120i \(-0.606914\pi\)
−0.329602 + 0.944120i \(0.606914\pi\)
\(390\) 0 0
\(391\) 39.9160 2.01864
\(392\) 5.34367i 0.269896i
\(393\) 0 0
\(394\) 10.1939 0.513563
\(395\) −9.11187 16.0510i −0.458468 0.807613i
\(396\) 0 0
\(397\) 26.6658i 1.33832i 0.743118 + 0.669160i \(0.233346\pi\)
−0.743118 + 0.669160i \(0.766654\pi\)
\(398\) 5.25299i 0.263309i
\(399\) 0 0
\(400\) −2.56279 + 4.29326i −0.128139 + 0.214663i
\(401\) −20.3546 −1.01646 −0.508231 0.861221i \(-0.669700\pi\)
−0.508231 + 0.861221i \(0.669700\pi\)
\(402\) 0 0
\(403\) 69.6766i 3.47084i
\(404\) 2.63730 0.131210
\(405\) 0 0
\(406\) −4.14728 −0.205826
\(407\) 0.290044i 0.0143770i
\(408\) 0 0
\(409\) −29.9603 −1.48144 −0.740720 0.671814i \(-0.765515\pi\)
−0.740720 + 0.671814i \(0.765515\pi\)
\(410\) −3.19061 + 1.81125i −0.157573 + 0.0894515i
\(411\) 0 0
\(412\) 1.72469i 0.0849695i
\(413\) 20.8791i 1.02740i
\(414\) 0 0
\(415\) 4.70214 2.66932i 0.230819 0.131032i
\(416\) 7.12558 0.349360
\(417\) 0 0
\(418\) 1.69256i 0.0827859i
\(419\) 23.3149 1.13901 0.569504 0.821988i \(-0.307135\pi\)
0.569504 + 0.821988i \(0.307135\pi\)
\(420\) 0 0
\(421\) 24.0289 1.17110 0.585548 0.810638i \(-0.300880\pi\)
0.585548 + 0.810638i \(0.300880\pi\)
\(422\) 4.81998i 0.234633i
\(423\) 0 0
\(424\) 9.32034 0.452636
\(425\) 26.5290 + 15.8360i 1.28684 + 0.768158i
\(426\) 0 0
\(427\) 4.48654i 0.217119i
\(428\) 10.0279i 0.484719i
\(429\) 0 0
\(430\) −5.90466 10.4013i −0.284748 0.501597i
\(431\) 19.2917 0.929247 0.464624 0.885508i \(-0.346190\pi\)
0.464624 + 0.885508i \(0.346190\pi\)
\(432\) 0 0
\(433\) 12.5816i 0.604634i −0.953207 0.302317i \(-0.902240\pi\)
0.953207 0.302317i \(-0.0977601\pi\)
\(434\) 34.3549 1.64909
\(435\) 0 0
\(436\) 4.87361 0.233403
\(437\) 37.6959i 1.80324i
\(438\) 0 0
\(439\) −14.0428 −0.670225 −0.335113 0.942178i \(-0.608774\pi\)
−0.335113 + 0.942178i \(0.608774\pi\)
\(440\) −0.564014 + 0.320181i −0.0268883 + 0.0152640i
\(441\) 0 0
\(442\) 44.0304i 2.09431i
\(443\) 24.5696i 1.16734i 0.811992 + 0.583668i \(0.198383\pi\)
−0.811992 + 0.583668i \(0.801617\pi\)
\(444\) 0 0
\(445\) −11.3478 19.9897i −0.537938 0.947603i
\(446\) 3.70392 0.175386
\(447\) 0 0
\(448\) 3.51336i 0.165990i
\(449\) −12.7574 −0.602061 −0.301030 0.953615i \(-0.597331\pi\)
−0.301030 + 0.953615i \(0.597331\pi\)
\(450\) 0 0
\(451\) −0.475896 −0.0224091
\(452\) 15.9290i 0.749236i
\(453\) 0 0
\(454\) 6.31512 0.296383
\(455\) −27.6359 48.6820i −1.29559 2.28225i
\(456\) 0 0
\(457\) 3.34889i 0.156654i −0.996928 0.0783272i \(-0.975042\pi\)
0.996928 0.0783272i \(-0.0249579\pi\)
\(458\) 20.5548i 0.960463i
\(459\) 0 0
\(460\) 12.5615 7.13092i 0.585681 0.332481i
\(461\) 0.859501 0.0400310 0.0200155 0.999800i \(-0.493628\pi\)
0.0200155 + 0.999800i \(0.493628\pi\)
\(462\) 0 0
\(463\) 13.8711i 0.644643i 0.946630 + 0.322321i \(0.104463\pi\)
−0.946630 + 0.322321i \(0.895537\pi\)
\(464\) −1.18043 −0.0548002
\(465\) 0 0
\(466\) −21.4393 −0.993155
\(467\) 40.9281i 1.89392i 0.321344 + 0.946962i \(0.395865\pi\)
−0.321344 + 0.946962i \(0.604135\pi\)
\(468\) 0 0
\(469\) 21.2324 0.980422
\(470\) 6.28405 + 11.0696i 0.289861 + 0.510605i
\(471\) 0 0
\(472\) 5.94279i 0.273539i
\(473\) 1.55141i 0.0713341i
\(474\) 0 0
\(475\) 14.9552 25.0535i 0.686193 1.14953i
\(476\) −21.7098 −0.995065
\(477\) 0 0
\(478\) 20.7479i 0.948986i
\(479\) 8.58990 0.392483 0.196241 0.980556i \(-0.437126\pi\)
0.196241 + 0.980556i \(0.437126\pi\)
\(480\) 0 0
\(481\) −7.12558 −0.324898
\(482\) 10.7731i 0.490702i
\(483\) 0 0
\(484\) 10.9159 0.496176
\(485\) 29.4161 16.6990i 1.33572 0.758263i
\(486\) 0 0
\(487\) 25.8389i 1.17087i −0.810718 0.585436i \(-0.800923\pi\)
0.810718 0.585436i \(-0.199077\pi\)
\(488\) 1.27699i 0.0578068i
\(489\) 0 0
\(490\) −10.3912 + 5.89891i −0.469427 + 0.266486i
\(491\) −11.4864 −0.518376 −0.259188 0.965827i \(-0.583455\pi\)
−0.259188 + 0.965827i \(0.583455\pi\)
\(492\) 0 0
\(493\) 7.29413i 0.328511i
\(494\) −41.5815 −1.87084
\(495\) 0 0
\(496\) 9.77838 0.439062
\(497\) 47.4287i 2.12747i
\(498\) 0 0
\(499\) 9.74599 0.436290 0.218145 0.975916i \(-0.429999\pi\)
0.218145 + 0.975916i \(0.429999\pi\)
\(500\) 11.1777 + 0.244192i 0.499881 + 0.0109206i
\(501\) 0 0
\(502\) 4.46812i 0.199422i
\(503\) 17.4803i 0.779408i −0.920940 0.389704i \(-0.872577\pi\)
0.920940 0.389704i \(-0.127423\pi\)
\(504\) 0 0
\(505\) −2.91133 5.12844i −0.129552 0.228212i
\(506\) 1.87361 0.0832920
\(507\) 0 0
\(508\) 1.31265i 0.0582395i
\(509\) −16.3273 −0.723695 −0.361847 0.932237i \(-0.617854\pi\)
−0.361847 + 0.932237i \(0.617854\pi\)
\(510\) 0 0
\(511\) −6.02007 −0.266312
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −1.24594 −0.0549559
\(515\) 3.35380 1.90390i 0.147786 0.0838957i
\(516\) 0 0
\(517\) 1.65109i 0.0726151i
\(518\) 3.51336i 0.154368i
\(519\) 0 0
\(520\) −7.86596 13.8563i −0.344945 0.607637i
\(521\) 4.78335 0.209562 0.104781 0.994495i \(-0.466586\pi\)
0.104781 + 0.994495i \(0.466586\pi\)
\(522\) 0 0
\(523\) 24.1224i 1.05480i −0.849618 0.527399i \(-0.823167\pi\)
0.849618 0.527399i \(-0.176833\pi\)
\(524\) 2.41562 0.105527
\(525\) 0 0
\(526\) −16.3230 −0.711716
\(527\) 60.4226i 2.63205i
\(528\) 0 0
\(529\) −18.7281 −0.814264
\(530\) −10.2888 18.1241i −0.446915 0.787263i
\(531\) 0 0
\(532\) 20.5023i 0.888888i
\(533\) 11.6914i 0.506412i
\(534\) 0 0
\(535\) −19.5001 + 11.0699i −0.843064 + 0.478593i
\(536\) 6.04334 0.261033
\(537\) 0 0
\(538\) 18.5763i 0.800881i
\(539\) −1.54990 −0.0667590
\(540\) 0 0
\(541\) 4.11745 0.177023 0.0885115 0.996075i \(-0.471789\pi\)
0.0885115 + 0.996075i \(0.471789\pi\)
\(542\) 16.4181i 0.705217i
\(543\) 0 0
\(544\) −6.17921 −0.264931
\(545\) −5.38000 9.47712i −0.230454 0.405955i
\(546\) 0 0
\(547\) 9.22742i 0.394536i −0.980350 0.197268i \(-0.936793\pi\)
0.980350 0.197268i \(-0.0632069\pi\)
\(548\) 6.87366i 0.293628i
\(549\) 0 0
\(550\) 1.24524 + 0.743322i 0.0530971 + 0.0316953i
\(551\) 6.88845 0.293458
\(552\) 0 0
\(553\) 29.0000i 1.23321i
\(554\) −15.6104 −0.663222
\(555\) 0 0
\(556\) −9.80616 −0.415874
\(557\) 2.25125i 0.0953885i −0.998862 0.0476943i \(-0.984813\pi\)
0.998862 0.0476943i \(-0.0151873\pi\)
\(558\) 0 0
\(559\) 38.1139 1.61205
\(560\) −6.83201 + 3.87841i −0.288705 + 0.163893i
\(561\) 0 0
\(562\) 21.8665i 0.922384i
\(563\) 5.79316i 0.244153i 0.992521 + 0.122076i \(0.0389553\pi\)
−0.992521 + 0.122076i \(0.961045\pi\)
\(564\) 0 0
\(565\) −30.9752 + 17.5841i −1.30314 + 0.739768i
\(566\) −2.24778 −0.0944811
\(567\) 0 0
\(568\) 13.4995i 0.566428i
\(569\) −34.4807 −1.44551 −0.722753 0.691106i \(-0.757124\pi\)
−0.722753 + 0.691106i \(0.757124\pi\)
\(570\) 0 0
\(571\) −19.2152 −0.804133 −0.402066 0.915611i \(-0.631708\pi\)
−0.402066 + 0.915611i \(0.631708\pi\)
\(572\) 2.06673i 0.0864144i
\(573\) 0 0
\(574\) −5.76461 −0.240610
\(575\) −27.7333 16.5549i −1.15656 0.690387i
\(576\) 0 0
\(577\) 6.33354i 0.263669i 0.991272 + 0.131834i \(0.0420867\pi\)
−0.991272 + 0.131834i \(0.957913\pi\)
\(578\) 21.1826i 0.881079i
\(579\) 0 0
\(580\) 1.30308 + 2.29545i 0.0541077 + 0.0953132i
\(581\) 8.49555 0.352455
\(582\) 0 0
\(583\) 2.70331i 0.111960i
\(584\) −1.71348 −0.0709044
\(585\) 0 0
\(586\) 26.8794 1.11038
\(587\) 21.9099i 0.904320i 0.891937 + 0.452160i \(0.149346\pi\)
−0.891937 + 0.452160i \(0.850654\pi\)
\(588\) 0 0
\(589\) −57.0620 −2.35120
\(590\) 11.5562 6.56028i 0.475763 0.270082i
\(591\) 0 0
\(592\) 1.00000i 0.0410997i
\(593\) 9.40482i 0.386210i −0.981178 0.193105i \(-0.938144\pi\)
0.981178 0.193105i \(-0.0618557\pi\)
\(594\) 0 0
\(595\) 23.9655 + 42.2164i 0.982490 + 1.73070i
\(596\) 9.07687 0.371803
\(597\) 0 0
\(598\) 46.0293i 1.88228i
\(599\) 16.4095 0.670474 0.335237 0.942134i \(-0.391184\pi\)
0.335237 + 0.942134i \(0.391184\pi\)
\(600\) 0 0
\(601\) −7.01392 −0.286104 −0.143052 0.989715i \(-0.545692\pi\)
−0.143052 + 0.989715i \(0.545692\pi\)
\(602\) 18.7926i 0.765927i
\(603\) 0 0
\(604\) −20.1964 −0.821780
\(605\) −12.0501 21.2268i −0.489906 0.862992i
\(606\) 0 0
\(607\) 16.5621i 0.672234i 0.941820 + 0.336117i \(0.109114\pi\)
−0.941820 + 0.336117i \(0.890886\pi\)
\(608\) 5.83553i 0.236662i
\(609\) 0 0
\(610\) −2.48322 + 1.40968i −0.100543 + 0.0570763i
\(611\) −40.5628 −1.64099
\(612\) 0 0
\(613\) 23.9370i 0.966804i −0.875398 0.483402i \(-0.839401\pi\)
0.875398 0.483402i \(-0.160599\pi\)
\(614\) 23.9979 0.968475
\(615\) 0 0
\(616\) −1.01903 −0.0410578
\(617\) 13.9489i 0.561563i 0.959772 + 0.280781i \(0.0905936\pi\)
−0.959772 + 0.280781i \(0.909406\pi\)
\(618\) 0 0
\(619\) −21.6942 −0.871964 −0.435982 0.899955i \(-0.643599\pi\)
−0.435982 + 0.899955i \(0.643599\pi\)
\(620\) −10.7944 19.0148i −0.433513 0.763654i
\(621\) 0 0
\(622\) 5.07563i 0.203514i
\(623\) 36.1163i 1.44697i
\(624\) 0 0
\(625\) −11.8642 22.0055i −0.474570 0.880218i
\(626\) 8.96950 0.358493
\(627\) 0 0
\(628\) 17.2677i 0.689057i
\(629\) 6.17921 0.246381
\(630\) 0 0
\(631\) −32.4902 −1.29342 −0.646708 0.762738i \(-0.723855\pi\)
−0.646708 + 0.762738i \(0.723855\pi\)
\(632\) 8.25422i 0.328335i
\(633\) 0 0
\(634\) 22.0181 0.874451
\(635\) 2.55256 1.44904i 0.101295 0.0575035i
\(636\) 0 0
\(637\) 38.0768i 1.50866i
\(638\) 0.342377i 0.0135549i
\(639\) 0 0
\(640\) −1.94458 + 1.10390i −0.0768663 + 0.0436357i
\(641\) 28.1621 1.11234 0.556168 0.831070i \(-0.312271\pi\)
0.556168 + 0.831070i \(0.312271\pi\)
\(642\) 0 0
\(643\) 8.32452i 0.328287i −0.986436 0.164144i \(-0.947514\pi\)
0.986436 0.164144i \(-0.0524860\pi\)
\(644\) 22.6953 0.894321
\(645\) 0 0
\(646\) 36.0589 1.41872
\(647\) 1.75827i 0.0691249i −0.999403 0.0345624i \(-0.988996\pi\)
0.999403 0.0345624i \(-0.0110038\pi\)
\(648\) 0 0
\(649\) 1.72367 0.0676600
\(650\) −18.2613 + 30.5920i −0.716269 + 1.19992i
\(651\) 0 0
\(652\) 16.6901i 0.653634i
\(653\) 24.7416i 0.968213i 0.875009 + 0.484106i \(0.160855\pi\)
−0.875009 + 0.484106i \(0.839145\pi\)
\(654\) 0 0
\(655\) −2.66661 4.69737i −0.104193 0.183541i
\(656\) −1.64077 −0.0640613
\(657\) 0 0
\(658\) 20.0000i 0.779681i
\(659\) 18.2640 0.711466 0.355733 0.934588i \(-0.384231\pi\)
0.355733 + 0.934588i \(0.384231\pi\)
\(660\) 0 0
\(661\) 2.61857 0.101851 0.0509253 0.998702i \(-0.483783\pi\)
0.0509253 + 0.998702i \(0.483783\pi\)
\(662\) 10.7134i 0.416390i
\(663\) 0 0
\(664\) 2.41807 0.0938394
\(665\) 39.8684 22.6326i 1.54603 0.877654i
\(666\) 0 0
\(667\) 7.62527i 0.295252i
\(668\) 1.47354i 0.0570130i
\(669\) 0 0
\(670\) −6.67127 11.7518i −0.257734 0.454010i
\(671\) −0.370385 −0.0142986
\(672\) 0 0
\(673\) 48.4181i 1.86638i 0.359384 + 0.933190i \(0.382987\pi\)
−0.359384 + 0.933190i \(0.617013\pi\)
\(674\) 1.34097 0.0516521
\(675\) 0 0
\(676\) 37.7738 1.45284
\(677\) 7.49862i 0.288195i 0.989563 + 0.144098i \(0.0460280\pi\)
−0.989563 + 0.144098i \(0.953972\pi\)
\(678\) 0 0
\(679\) 53.1473 2.03961
\(680\) 6.82126 + 12.0160i 0.261583 + 0.460791i
\(681\) 0 0
\(682\) 2.83616i 0.108602i
\(683\) 33.2987i 1.27414i −0.770806 0.637070i \(-0.780146\pi\)
0.770806 0.637070i \(-0.219854\pi\)
\(684\) 0 0
\(685\) −13.3664 + 7.58787i −0.510703 + 0.289917i
\(686\) 5.81926 0.222181
\(687\) 0 0
\(688\) 5.34889i 0.203924i
\(689\) 66.4128 2.53012
\(690\) 0 0
\(691\) 38.3695 1.45964 0.729822 0.683638i \(-0.239603\pi\)
0.729822 + 0.683638i \(0.239603\pi\)
\(692\) 13.8432i 0.526240i
\(693\) 0 0
\(694\) −0.883744 −0.0335465
\(695\) 10.8251 + 19.0689i 0.410618 + 0.723324i
\(696\) 0 0
\(697\) 10.1387i 0.384029i
\(698\) 9.00521i 0.340852i
\(699\) 0 0
\(700\) 15.0838 + 9.00399i 0.570113 + 0.340319i
\(701\) 40.6339 1.53472 0.767360 0.641217i \(-0.221570\pi\)
0.767360 + 0.641217i \(0.221570\pi\)
\(702\) 0 0
\(703\) 5.83553i 0.220091i
\(704\) −0.290044 −0.0109315
\(705\) 0 0
\(706\) 6.79030 0.255556
\(707\) 9.26577i 0.348475i
\(708\) 0 0
\(709\) −11.1957 −0.420464 −0.210232 0.977651i \(-0.567422\pi\)
−0.210232 + 0.977651i \(0.567422\pi\)
\(710\) −26.2509 + 14.9022i −0.985180 + 0.559270i
\(711\) 0 0
\(712\) 10.2797i 0.385248i
\(713\) 63.1656i 2.36557i
\(714\) 0 0
\(715\) −4.01893 + 2.28148i −0.150299 + 0.0853223i
\(716\) −21.7817 −0.814020
\(717\) 0 0
\(718\) 10.2263i 0.381641i
\(719\) 30.2226 1.12711 0.563556 0.826078i \(-0.309433\pi\)
0.563556 + 0.826078i \(0.309433\pi\)
\(720\) 0 0
\(721\) 6.05946 0.225666
\(722\) 15.0534i 0.560231i
\(723\) 0 0
\(724\) −2.03100 −0.0754817
\(725\) 3.02520 5.06791i 0.112353 0.188217i
\(726\) 0 0
\(727\) 19.1911i 0.711758i −0.934532 0.355879i \(-0.884182\pi\)
0.934532 0.355879i \(-0.115818\pi\)
\(728\) 25.0347i 0.927847i
\(729\) 0 0
\(730\) 1.89152 + 3.33200i 0.0700083 + 0.123323i
\(731\) −33.0519 −1.22247
\(732\) 0 0
\(733\) 5.39567i 0.199294i −0.995023 0.0996468i \(-0.968229\pi\)
0.995023 0.0996468i \(-0.0317713\pi\)
\(734\) 17.1583 0.633325
\(735\) 0 0
\(736\) 6.45973 0.238109
\(737\) 1.75284i 0.0645665i
\(738\) 0 0
\(739\) −24.7127 −0.909072 −0.454536 0.890728i \(-0.650195\pi\)
−0.454536 + 0.890728i \(0.650195\pi\)
\(740\) 1.94458 1.10390i 0.0714842 0.0405804i
\(741\) 0 0
\(742\) 32.7457i 1.20213i
\(743\) 45.4537i 1.66753i 0.552116 + 0.833767i \(0.313820\pi\)
−0.552116 + 0.833767i \(0.686180\pi\)
\(744\) 0 0
\(745\) −10.0200 17.6507i −0.367104 0.646672i
\(746\) −17.1601 −0.628275
\(747\) 0 0
\(748\) 1.79224i 0.0655309i
\(749\) −35.2317 −1.28734
\(750\) 0 0
\(751\) 49.6360 1.81124 0.905621 0.424088i \(-0.139405\pi\)
0.905621 + 0.424088i \(0.139405\pi\)
\(752\) 5.69256i 0.207586i
\(753\) 0 0
\(754\) −8.41126 −0.306320
\(755\) 22.2949 + 39.2735i 0.811395 + 1.42931i
\(756\) 0 0
\(757\) 27.9481i 1.01579i −0.861419 0.507896i \(-0.830424\pi\)
0.861419 0.507896i \(-0.169576\pi\)
\(758\) 27.5435i 1.00043i
\(759\) 0 0
\(760\) 11.3477 6.44187i 0.411623 0.233671i
\(761\) 53.4744 1.93844 0.969222 0.246188i \(-0.0791781\pi\)
0.969222 + 0.246188i \(0.0791781\pi\)
\(762\) 0 0
\(763\) 17.1227i 0.619884i
\(764\) −8.44668 −0.305590
\(765\) 0 0
\(766\) −3.49954 −0.126444
\(767\) 42.3458i 1.52902i
\(768\) 0 0
\(769\) 8.46659 0.305313 0.152657 0.988279i \(-0.451217\pi\)
0.152657 + 0.988279i \(0.451217\pi\)
\(770\) 1.12491 + 1.98158i 0.0405390 + 0.0714113i
\(771\) 0 0
\(772\) 3.64159i 0.131064i
\(773\) 0.530866i 0.0190939i −0.999954 0.00954697i \(-0.996961\pi\)
0.999954 0.00954697i \(-0.00303894\pi\)
\(774\) 0 0
\(775\) −25.0599 + 41.9811i −0.900178 + 1.50801i
\(776\) 15.1272 0.543035
\(777\) 0 0
\(778\) 13.0015i 0.466127i
\(779\) 9.57477 0.343052
\(780\) 0 0
\(781\) −3.91546 −0.140106
\(782\) 39.9160i 1.42739i
\(783\) 0 0
\(784\) −5.34367 −0.190846
\(785\) −33.5785 + 19.0619i −1.19847 + 0.680349i
\(786\) 0 0
\(787\) 2.16917i 0.0773227i −0.999252 0.0386613i \(-0.987691\pi\)
0.999252 0.0386613i \(-0.0123094\pi\)
\(788\) 10.1939i 0.363144i
\(789\) 0 0
\(790\) −16.0510 + 9.11187i −0.571069 + 0.324186i
\(791\) −55.9642 −1.98986
\(792\) 0 0
\(793\) 9.09932i 0.323126i
\(794\) 26.6658 0.946336
\(795\) 0 0
\(796\) −5.25299 −0.186187
\(797\) 26.2510i 0.929857i −0.885348 0.464928i \(-0.846080\pi\)