Properties

Label 384.2.j.b.97.1
Level $384$
Weight $2$
Character 384.97
Analytic conductor $3.066$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.18939904.2
Defining polynomial: \(x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 43 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 97.1
Root \(0.500000 + 2.10607i\) of defining polynomial
Character \(\chi\) \(=\) 384.97
Dual form 384.2.j.b.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{3} +(-1.27133 - 1.27133i) q^{5} -0.158942i q^{7} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{3} +(-1.27133 - 1.27133i) q^{5} -0.158942i q^{7} -1.00000i q^{9} +(3.79793 + 3.79793i) q^{11} +(4.21215 - 4.21215i) q^{13} +1.79793 q^{15} +3.05320 q^{17} +(2.15894 - 2.15894i) q^{19} +(0.112389 + 0.112389i) q^{21} +2.82843i q^{23} -1.76744i q^{25} +(0.707107 + 0.707107i) q^{27} +(-2.09976 + 2.09976i) q^{29} +4.15894 q^{31} -5.37109 q^{33} +(-0.202067 + 0.202067i) q^{35} +(5.98737 + 5.98737i) q^{37} +5.95687i q^{39} -2.60365i q^{41} +(-5.75481 - 5.75481i) q^{43} +(-1.27133 + 1.27133i) q^{45} -2.82843 q^{47} +6.97474 q^{49} +(-2.15894 + 2.15894i) q^{51} +(-3.55710 - 3.55710i) q^{53} -9.65685i q^{55} +3.05320i q^{57} +(-4.00000 - 4.00000i) q^{59} +(-3.66949 + 3.66949i) q^{61} -0.158942 q^{63} -10.7101 q^{65} +(-0.767438 + 0.767438i) q^{67} +(-2.00000 - 2.00000i) q^{69} +0.317883i q^{71} -1.33897i q^{73} +(1.24977 + 1.24977i) q^{75} +(0.603650 - 0.603650i) q^{77} -9.69382 q^{79} -1.00000 q^{81} +(-0.115816 + 0.115816i) q^{83} +(-3.88163 - 3.88163i) q^{85} -2.96951i q^{87} +14.3990i q^{89} +(-0.669485 - 0.669485i) q^{91} +(-2.94082 + 2.94082i) q^{93} -5.48946 q^{95} -0.571533 q^{97} +(3.79793 - 3.79793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 8q^{11} - 8q^{15} + 8q^{19} + 16q^{29} + 24q^{31} - 24q^{35} + 16q^{37} + 8q^{43} - 8q^{49} - 8q^{51} - 16q^{53} - 32q^{59} - 16q^{61} + 8q^{63} - 16q^{65} + 16q^{67} - 16q^{69} - 16q^{75} - 16q^{77} - 24q^{79} - 8q^{81} + 40q^{83} + 16q^{85} + 8q^{91} - 48q^{95} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 0 0
\(5\) −1.27133 1.27133i −0.568556 0.568556i 0.363168 0.931724i \(-0.381695\pi\)
−0.931724 + 0.363168i \(0.881695\pi\)
\(6\) 0 0
\(7\) 0.158942i 0.0600743i −0.999549 0.0300371i \(-0.990437\pi\)
0.999549 0.0300371i \(-0.00956256\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 3.79793 + 3.79793i 1.14512 + 1.14512i 0.987500 + 0.157620i \(0.0503821\pi\)
0.157620 + 0.987500i \(0.449618\pi\)
\(12\) 0 0
\(13\) 4.21215 4.21215i 1.16824 1.16824i 0.185617 0.982622i \(-0.440572\pi\)
0.982622 0.185617i \(-0.0594284\pi\)
\(14\) 0 0
\(15\) 1.79793 0.464224
\(16\) 0 0
\(17\) 3.05320 0.740511 0.370255 0.928930i \(-0.379270\pi\)
0.370255 + 0.928930i \(0.379270\pi\)
\(18\) 0 0
\(19\) 2.15894 2.15894i 0.495295 0.495295i −0.414675 0.909970i \(-0.636105\pi\)
0.909970 + 0.414675i \(0.136105\pi\)
\(20\) 0 0
\(21\) 0.112389 + 0.112389i 0.0245252 + 0.0245252i
\(22\) 0 0
\(23\) 2.82843i 0.589768i 0.955533 + 0.294884i \(0.0952810\pi\)
−0.955533 + 0.294884i \(0.904719\pi\)
\(24\) 0 0
\(25\) 1.76744i 0.353488i
\(26\) 0 0
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 0 0
\(29\) −2.09976 + 2.09976i −0.389915 + 0.389915i −0.874657 0.484742i \(-0.838913\pi\)
0.484742 + 0.874657i \(0.338913\pi\)
\(30\) 0 0
\(31\) 4.15894 0.746968 0.373484 0.927637i \(-0.378163\pi\)
0.373484 + 0.927637i \(0.378163\pi\)
\(32\) 0 0
\(33\) −5.37109 −0.934986
\(34\) 0 0
\(35\) −0.202067 + 0.202067i −0.0341556 + 0.0341556i
\(36\) 0 0
\(37\) 5.98737 + 5.98737i 0.984317 + 0.984317i 0.999879 0.0155615i \(-0.00495359\pi\)
−0.0155615 + 0.999879i \(0.504954\pi\)
\(38\) 0 0
\(39\) 5.95687i 0.953863i
\(40\) 0 0
\(41\) 2.60365i 0.406622i −0.979114 0.203311i \(-0.934830\pi\)
0.979114 0.203311i \(-0.0651702\pi\)
\(42\) 0 0
\(43\) −5.75481 5.75481i −0.877600 0.877600i 0.115686 0.993286i \(-0.463093\pi\)
−0.993286 + 0.115686i \(0.963093\pi\)
\(44\) 0 0
\(45\) −1.27133 + 1.27133i −0.189519 + 0.189519i
\(46\) 0 0
\(47\) −2.82843 −0.412568 −0.206284 0.978492i \(-0.566137\pi\)
−0.206284 + 0.978492i \(0.566137\pi\)
\(48\) 0 0
\(49\) 6.97474 0.996391
\(50\) 0 0
\(51\) −2.15894 + 2.15894i −0.302312 + 0.302312i
\(52\) 0 0
\(53\) −3.55710 3.55710i −0.488605 0.488605i 0.419261 0.907866i \(-0.362289\pi\)
−0.907866 + 0.419261i \(0.862289\pi\)
\(54\) 0 0
\(55\) 9.65685i 1.30213i
\(56\) 0 0
\(57\) 3.05320i 0.404407i
\(58\) 0 0
\(59\) −4.00000 4.00000i −0.520756 0.520756i 0.397044 0.917800i \(-0.370036\pi\)
−0.917800 + 0.397044i \(0.870036\pi\)
\(60\) 0 0
\(61\) −3.66949 + 3.66949i −0.469829 + 0.469829i −0.901859 0.432030i \(-0.857798\pi\)
0.432030 + 0.901859i \(0.357798\pi\)
\(62\) 0 0
\(63\) −0.158942 −0.0200248
\(64\) 0 0
\(65\) −10.7101 −1.32842
\(66\) 0 0
\(67\) −0.767438 + 0.767438i −0.0937575 + 0.0937575i −0.752430 0.658672i \(-0.771118\pi\)
0.658672 + 0.752430i \(0.271118\pi\)
\(68\) 0 0
\(69\) −2.00000 2.00000i −0.240772 0.240772i
\(70\) 0 0
\(71\) 0.317883i 0.0377258i 0.999822 + 0.0188629i \(0.00600460\pi\)
−0.999822 + 0.0188629i \(0.993995\pi\)
\(72\) 0 0
\(73\) 1.33897i 0.156715i −0.996925 0.0783573i \(-0.975032\pi\)
0.996925 0.0783573i \(-0.0249675\pi\)
\(74\) 0 0
\(75\) 1.24977 + 1.24977i 0.144311 + 0.144311i
\(76\) 0 0
\(77\) 0.603650 0.603650i 0.0687923 0.0687923i
\(78\) 0 0
\(79\) −9.69382 −1.09064 −0.545320 0.838228i \(-0.683592\pi\)
−0.545320 + 0.838228i \(0.683592\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) −0.115816 + 0.115816i −0.0127125 + 0.0127125i −0.713434 0.700722i \(-0.752861\pi\)
0.700722 + 0.713434i \(0.252861\pi\)
\(84\) 0 0
\(85\) −3.88163 3.88163i −0.421022 0.421022i
\(86\) 0 0
\(87\) 2.96951i 0.318364i
\(88\) 0 0
\(89\) 14.3990i 1.52629i 0.646225 + 0.763147i \(0.276347\pi\)
−0.646225 + 0.763147i \(0.723653\pi\)
\(90\) 0 0
\(91\) −0.669485 0.669485i −0.0701811 0.0701811i
\(92\) 0 0
\(93\) −2.94082 + 2.94082i −0.304948 + 0.304948i
\(94\) 0 0
\(95\) −5.48946 −0.563206
\(96\) 0 0
\(97\) −0.571533 −0.0580304 −0.0290152 0.999579i \(-0.509237\pi\)
−0.0290152 + 0.999579i \(0.509237\pi\)
\(98\) 0 0
\(99\) 3.79793 3.79793i 0.381707 0.381707i
\(100\) 0 0
\(101\) 7.15296 + 7.15296i 0.711746 + 0.711746i 0.966900 0.255154i \(-0.0821262\pi\)
−0.255154 + 0.966900i \(0.582126\pi\)
\(102\) 0 0
\(103\) 11.3507i 1.11841i −0.829028 0.559207i \(-0.811106\pi\)
0.829028 0.559207i \(-0.188894\pi\)
\(104\) 0 0
\(105\) 0.285766i 0.0278879i
\(106\) 0 0
\(107\) 0.722018 + 0.722018i 0.0698001 + 0.0698001i 0.741145 0.671345i \(-0.234283\pi\)
−0.671345 + 0.741145i \(0.734283\pi\)
\(108\) 0 0
\(109\) 1.44471 1.44471i 0.138378 0.138378i −0.634525 0.772903i \(-0.718804\pi\)
0.772903 + 0.634525i \(0.218804\pi\)
\(110\) 0 0
\(111\) −8.46742 −0.803692
\(112\) 0 0
\(113\) −3.53488 −0.332533 −0.166267 0.986081i \(-0.553171\pi\)
−0.166267 + 0.986081i \(0.553171\pi\)
\(114\) 0 0
\(115\) 3.59587 3.59587i 0.335316 0.335316i
\(116\) 0 0
\(117\) −4.21215 4.21215i −0.389413 0.389413i
\(118\) 0 0
\(119\) 0.485281i 0.0444857i
\(120\) 0 0
\(121\) 17.8486i 1.62260i
\(122\) 0 0
\(123\) 1.84106 + 1.84106i 0.166003 + 0.166003i
\(124\) 0 0
\(125\) −8.60365 + 8.60365i −0.769534 + 0.769534i
\(126\) 0 0
\(127\) −1.49791 −0.132918 −0.0664591 0.997789i \(-0.521170\pi\)
−0.0664591 + 0.997789i \(0.521170\pi\)
\(128\) 0 0
\(129\) 8.13853 0.716557
\(130\) 0 0
\(131\) −10.4243 + 10.4243i −0.910775 + 0.910775i −0.996333 0.0855585i \(-0.972733\pi\)
0.0855585 + 0.996333i \(0.472733\pi\)
\(132\) 0 0
\(133\) −0.343146 0.343146i −0.0297545 0.0297545i
\(134\) 0 0
\(135\) 1.79793i 0.154741i
\(136\) 0 0
\(137\) 13.7954i 1.17862i −0.807907 0.589309i \(-0.799400\pi\)
0.807907 0.589309i \(-0.200600\pi\)
\(138\) 0 0
\(139\) 2.42429 + 2.42429i 0.205626 + 0.205626i 0.802405 0.596779i \(-0.203553\pi\)
−0.596779 + 0.802405i \(0.703553\pi\)
\(140\) 0 0
\(141\) 2.00000 2.00000i 0.168430 0.168430i
\(142\) 0 0
\(143\) 31.9949 2.67555
\(144\) 0 0
\(145\) 5.33897 0.443377
\(146\) 0 0
\(147\) −4.93188 + 4.93188i −0.406775 + 0.406775i
\(148\) 0 0
\(149\) −2.92818 2.92818i −0.239886 0.239886i 0.576917 0.816803i \(-0.304256\pi\)
−0.816803 + 0.576917i \(0.804256\pi\)
\(150\) 0 0
\(151\) 22.6644i 1.84440i 0.386712 + 0.922201i \(0.373611\pi\)
−0.386712 + 0.922201i \(0.626389\pi\)
\(152\) 0 0
\(153\) 3.05320i 0.246837i
\(154\) 0 0
\(155\) −5.28739 5.28739i −0.424693 0.424693i
\(156\) 0 0
\(157\) 2.78007 2.78007i 0.221874 0.221874i −0.587413 0.809287i \(-0.699854\pi\)
0.809287 + 0.587413i \(0.199854\pi\)
\(158\) 0 0
\(159\) 5.03049 0.398944
\(160\) 0 0
\(161\) 0.449555 0.0354299
\(162\) 0 0
\(163\) 5.43692 5.43692i 0.425853 0.425853i −0.461360 0.887213i \(-0.652638\pi\)
0.887213 + 0.461360i \(0.152638\pi\)
\(164\) 0 0
\(165\) 6.82843 + 6.82843i 0.531592 + 0.531592i
\(166\) 0 0
\(167\) 3.95458i 0.306015i −0.988225 0.153007i \(-0.951104\pi\)
0.988225 0.153007i \(-0.0488958\pi\)
\(168\) 0 0
\(169\) 22.4844i 1.72957i
\(170\) 0 0
\(171\) −2.15894 2.15894i −0.165098 0.165098i
\(172\) 0 0
\(173\) 15.9814 15.9814i 1.21504 1.21504i 0.245695 0.969347i \(-0.420984\pi\)
0.969347 0.245695i \(-0.0790163\pi\)
\(174\) 0 0
\(175\) −0.280920 −0.0212355
\(176\) 0 0
\(177\) 5.65685 0.425195
\(178\) 0 0
\(179\) 12.2316 12.2316i 0.914235 0.914235i −0.0823670 0.996602i \(-0.526248\pi\)
0.996602 + 0.0823670i \(0.0262480\pi\)
\(180\) 0 0
\(181\) −5.76259 5.76259i −0.428330 0.428330i 0.459729 0.888059i \(-0.347946\pi\)
−0.888059 + 0.459729i \(0.847946\pi\)
\(182\) 0 0
\(183\) 5.18944i 0.383614i
\(184\) 0 0
\(185\) 15.2238i 1.11928i
\(186\) 0 0
\(187\) 11.5959 + 11.5959i 0.847974 + 0.847974i
\(188\) 0 0
\(189\) 0.112389 0.112389i 0.00817508 0.00817508i
\(190\) 0 0
\(191\) −16.1674 −1.16983 −0.584916 0.811094i \(-0.698873\pi\)
−0.584916 + 0.811094i \(0.698873\pi\)
\(192\) 0 0
\(193\) −22.1454 −1.59406 −0.797030 0.603940i \(-0.793597\pi\)
−0.797030 + 0.603940i \(0.793597\pi\)
\(194\) 0 0
\(195\) 7.57316 7.57316i 0.542325 0.542325i
\(196\) 0 0
\(197\) 14.2993 + 14.2993i 1.01878 + 1.01878i 0.999820 + 0.0189608i \(0.00603576\pi\)
0.0189608 + 0.999820i \(0.493964\pi\)
\(198\) 0 0
\(199\) 25.0075i 1.77274i 0.462981 + 0.886368i \(0.346780\pi\)
−0.462981 + 0.886368i \(0.653220\pi\)
\(200\) 0 0
\(201\) 1.08532i 0.0765527i
\(202\) 0 0
\(203\) 0.333739 + 0.333739i 0.0234239 + 0.0234239i
\(204\) 0 0
\(205\) −3.31010 + 3.31010i −0.231187 + 0.231187i
\(206\) 0 0
\(207\) 2.82843 0.196589
\(208\) 0 0
\(209\) 16.3990 1.13434
\(210\) 0 0
\(211\) −18.4243 + 18.4243i −1.26838 + 1.26838i −0.321456 + 0.946924i \(0.604172\pi\)
−0.946924 + 0.321456i \(0.895828\pi\)
\(212\) 0 0
\(213\) −0.224777 0.224777i −0.0154015 0.0154015i
\(214\) 0 0
\(215\) 14.6325i 0.997930i
\(216\) 0 0
\(217\) 0.661029i 0.0448736i
\(218\) 0 0
\(219\) 0.946795 + 0.946795i 0.0639785 + 0.0639785i
\(220\) 0 0
\(221\) 12.8605 12.8605i 0.865094 0.865094i
\(222\) 0 0
\(223\) 18.3465 1.22857 0.614286 0.789083i \(-0.289444\pi\)
0.614286 + 0.789083i \(0.289444\pi\)
\(224\) 0 0
\(225\) −1.76744 −0.117829
\(226\) 0 0
\(227\) 0.115816 0.115816i 0.00768697 0.00768697i −0.703253 0.710940i \(-0.748270\pi\)
0.710940 + 0.703253i \(0.248270\pi\)
\(228\) 0 0
\(229\) −2.84791 2.84791i −0.188195 0.188195i 0.606720 0.794916i \(-0.292485\pi\)
−0.794916 + 0.606720i \(0.792485\pi\)
\(230\) 0 0
\(231\) 0.853690i 0.0561687i
\(232\) 0 0
\(233\) 11.7211i 0.767874i 0.923359 + 0.383937i \(0.125432\pi\)
−0.923359 + 0.383937i \(0.874568\pi\)
\(234\) 0 0
\(235\) 3.59587 + 3.59587i 0.234568 + 0.234568i
\(236\) 0 0
\(237\) 6.85456 6.85456i 0.445252 0.445252i
\(238\) 0 0
\(239\) −13.6517 −0.883058 −0.441529 0.897247i \(-0.645564\pi\)
−0.441529 + 0.897247i \(0.645564\pi\)
\(240\) 0 0
\(241\) 2.13167 0.137313 0.0686565 0.997640i \(-0.478129\pi\)
0.0686565 + 0.997640i \(0.478129\pi\)
\(242\) 0 0
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 0 0
\(245\) −8.86720 8.86720i −0.566504 0.566504i
\(246\) 0 0
\(247\) 18.1876i 1.15725i
\(248\) 0 0
\(249\) 0.163788i 0.0103797i
\(250\) 0 0
\(251\) 4.43370 + 4.43370i 0.279853 + 0.279853i 0.833050 0.553198i \(-0.186593\pi\)
−0.553198 + 0.833050i \(0.686593\pi\)
\(252\) 0 0
\(253\) −10.7422 + 10.7422i −0.675355 + 0.675355i
\(254\) 0 0
\(255\) 5.48946 0.343763
\(256\) 0 0
\(257\) 15.0853 0.940997 0.470498 0.882401i \(-0.344074\pi\)
0.470498 + 0.882401i \(0.344074\pi\)
\(258\) 0 0
\(259\) 0.951642 0.951642i 0.0591322 0.0591322i
\(260\) 0 0
\(261\) 2.09976 + 2.09976i 0.129972 + 0.129972i
\(262\) 0 0
\(263\) 26.1706i 1.61375i −0.590722 0.806875i \(-0.701157\pi\)
0.590722 0.806875i \(-0.298843\pi\)
\(264\) 0 0
\(265\) 9.04449i 0.555599i
\(266\) 0 0
\(267\) −10.1817 10.1817i −0.623107 0.623107i
\(268\) 0 0
\(269\) −8.59700 + 8.59700i −0.524168 + 0.524168i −0.918828 0.394659i \(-0.870863\pi\)
0.394659 + 0.918828i \(0.370863\pi\)
\(270\) 0 0
\(271\) 10.6644 0.647815 0.323907 0.946089i \(-0.395003\pi\)
0.323907 + 0.946089i \(0.395003\pi\)
\(272\) 0 0
\(273\) 0.946795 0.0573027
\(274\) 0 0
\(275\) 6.71261 6.71261i 0.404786 0.404786i
\(276\) 0 0
\(277\) 2.66170 + 2.66170i 0.159926 + 0.159926i 0.782534 0.622608i \(-0.213927\pi\)
−0.622608 + 0.782534i \(0.713927\pi\)
\(278\) 0 0
\(279\) 4.15894i 0.248989i
\(280\) 0 0
\(281\) 10.4496i 0.623368i 0.950186 + 0.311684i \(0.100893\pi\)
−0.950186 + 0.311684i \(0.899107\pi\)
\(282\) 0 0
\(283\) 12.4853 + 12.4853i 0.742173 + 0.742173i 0.972996 0.230823i \(-0.0741418\pi\)
−0.230823 + 0.972996i \(0.574142\pi\)
\(284\) 0 0
\(285\) 3.88163 3.88163i 0.229928 0.229928i
\(286\) 0 0
\(287\) −0.413828 −0.0244275
\(288\) 0 0
\(289\) −7.67794 −0.451644
\(290\) 0 0
\(291\) 0.404135 0.404135i 0.0236908 0.0236908i
\(292\) 0 0
\(293\) −21.7410 21.7410i −1.27013 1.27013i −0.946022 0.324104i \(-0.894937\pi\)
−0.324104 0.946022i \(-0.605063\pi\)
\(294\) 0 0
\(295\) 10.1706i 0.592158i
\(296\) 0 0
\(297\) 5.37109i 0.311662i
\(298\) 0 0
\(299\) 11.9137 + 11.9137i 0.688990 + 0.688990i
\(300\) 0 0
\(301\) −0.914679 + 0.914679i −0.0527212 + 0.0527212i
\(302\) 0 0
\(303\) −10.1158 −0.581138
\(304\) 0 0
\(305\) 9.33026 0.534249
\(306\) 0 0
\(307\) −15.0601 + 15.0601i −0.859523 + 0.859523i −0.991282 0.131759i \(-0.957938\pi\)
0.131759 + 0.991282i \(0.457938\pi\)
\(308\) 0 0
\(309\) 8.02614 + 8.02614i 0.456591 + 0.456591i
\(310\) 0 0
\(311\) 1.77883i 0.100868i −0.998727 0.0504342i \(-0.983939\pi\)
0.998727 0.0504342i \(-0.0160605\pi\)
\(312\) 0 0
\(313\) 2.70320i 0.152794i −0.997077 0.0763971i \(-0.975658\pi\)
0.997077 0.0763971i \(-0.0243417\pi\)
\(314\) 0 0
\(315\) 0.202067 + 0.202067i 0.0113852 + 0.0113852i
\(316\) 0 0
\(317\) −15.6025 + 15.6025i −0.876325 + 0.876325i −0.993152 0.116828i \(-0.962728\pi\)
0.116828 + 0.993152i \(0.462728\pi\)
\(318\) 0 0
\(319\) −15.9495 −0.892999
\(320\) 0 0
\(321\) −1.02109 −0.0569916
\(322\) 0 0
\(323\) 6.59169 6.59169i 0.366771 0.366771i
\(324\) 0 0
\(325\) −7.44471 7.44471i −0.412958 0.412958i
\(326\) 0 0
\(327\) 2.04313i 0.112985i
\(328\) 0 0
\(329\) 0.449555i 0.0247848i
\(330\) 0 0
\(331\) −15.4454 15.4454i −0.848955 0.848955i 0.141048 0.990003i \(-0.454953\pi\)
−0.990003 + 0.141048i \(0.954953\pi\)
\(332\) 0 0
\(333\) 5.98737 5.98737i 0.328106 0.328106i
\(334\) 0 0
\(335\) 1.95133 0.106613
\(336\) 0 0
\(337\) −18.8738 −1.02812 −0.514062 0.857753i \(-0.671860\pi\)
−0.514062 + 0.857753i \(0.671860\pi\)
\(338\) 0 0
\(339\) 2.49954 2.49954i 0.135756 0.135756i
\(340\) 0 0
\(341\) 15.7954 + 15.7954i 0.855368 + 0.855368i
\(342\) 0 0
\(343\) 2.22117i 0.119932i
\(344\) 0 0
\(345\) 5.08532i 0.273785i
\(346\) 0 0
\(347\) −19.8337 19.8337i −1.06473 1.06473i −0.997755 0.0669717i \(-0.978666\pi\)
−0.0669717 0.997755i \(-0.521334\pi\)
\(348\) 0 0
\(349\) −11.9718 + 11.9718i −0.640836 + 0.640836i −0.950761 0.309925i \(-0.899696\pi\)
0.309925 + 0.950761i \(0.399696\pi\)
\(350\) 0 0
\(351\) 5.95687 0.317954
\(352\) 0 0
\(353\) −12.6202 −0.671705 −0.335853 0.941915i \(-0.609024\pi\)
−0.335853 + 0.941915i \(0.609024\pi\)
\(354\) 0 0
\(355\) 0.404135 0.404135i 0.0214492 0.0214492i
\(356\) 0 0
\(357\) 0.343146 + 0.343146i 0.0181612 + 0.0181612i
\(358\) 0 0
\(359\) 27.0867i 1.42958i −0.699339 0.714790i \(-0.746522\pi\)
0.699339 0.714790i \(-0.253478\pi\)
\(360\) 0 0
\(361\) 9.67794i 0.509365i
\(362\) 0 0
\(363\) −12.6209 12.6209i −0.662423 0.662423i
\(364\) 0 0
\(365\) −1.70227 + 1.70227i −0.0891011 + 0.0891011i
\(366\) 0 0
\(367\) −20.4937 −1.06976 −0.534882 0.844927i \(-0.679644\pi\)
−0.534882 + 0.844927i \(0.679644\pi\)
\(368\) 0 0
\(369\) −2.60365 −0.135541
\(370\) 0 0
\(371\) −0.565371 + 0.565371i −0.0293526 + 0.0293526i
\(372\) 0 0
\(373\) −1.03372 1.03372i −0.0535239 0.0535239i 0.679838 0.733362i \(-0.262050\pi\)
−0.733362 + 0.679838i \(0.762050\pi\)
\(374\) 0 0
\(375\) 12.1674i 0.628322i
\(376\) 0 0
\(377\) 17.6890i 0.911028i
\(378\) 0 0
\(379\) −17.6686 17.6686i −0.907573 0.907573i 0.0885032 0.996076i \(-0.471792\pi\)
−0.996076 + 0.0885032i \(0.971792\pi\)
\(380\) 0 0
\(381\) 1.05918 1.05918i 0.0542636 0.0542636i
\(382\) 0 0
\(383\) −31.0958 −1.58892 −0.794460 0.607316i \(-0.792246\pi\)
−0.794460 + 0.607316i \(0.792246\pi\)
\(384\) 0 0
\(385\) −1.53488 −0.0782245
\(386\) 0 0
\(387\) −5.75481 + 5.75481i −0.292533 + 0.292533i
\(388\) 0 0
\(389\) 2.56127 + 2.56127i 0.129862 + 0.129862i 0.769050 0.639188i \(-0.220730\pi\)
−0.639188 + 0.769050i \(0.720730\pi\)
\(390\) 0 0
\(391\) 8.63577i 0.436729i
\(392\) 0 0
\(393\) 14.7422i 0.743644i
\(394\) 0 0
\(395\) 12.3240 + 12.3240i 0.620090 + 0.620090i
\(396\) 0 0
\(397\) 5.09795 5.09795i 0.255859 0.255859i −0.567509 0.823367i \(-0.692093\pi\)
0.823367 + 0.567509i \(0.192093\pi\)
\(398\) 0 0
\(399\) 0.485281 0.0242945
\(400\) 0 0
\(401\) −15.2660 −0.762349 −0.381174 0.924503i \(-0.624480\pi\)
−0.381174 + 0.924503i \(0.624480\pi\)
\(402\) 0 0
\(403\) 17.5181 17.5181i 0.872637 0.872637i
\(404\) 0 0
\(405\) 1.27133 + 1.27133i 0.0631729 + 0.0631729i
\(406\) 0 0
\(407\) 45.4792i 2.25432i
\(408\) 0 0
\(409\) 11.3779i 0.562603i −0.959619 0.281302i \(-0.909234\pi\)
0.959619 0.281302i \(-0.0907661\pi\)
\(410\) 0 0
\(411\) 9.75481 + 9.75481i 0.481169 + 0.481169i
\(412\) 0 0
\(413\) −0.635767 + 0.635767i −0.0312840 + 0.0312840i
\(414\) 0 0
\(415\) 0.294481 0.0144555
\(416\) 0 0
\(417\) −3.42847 −0.167893
\(418\) 0 0
\(419\) −23.3075 + 23.3075i −1.13865 + 1.13865i −0.149955 + 0.988693i \(0.547913\pi\)
−0.988693 + 0.149955i \(0.952087\pi\)
\(420\) 0 0
\(421\) 17.6154 + 17.6154i 0.858520 + 0.858520i 0.991164 0.132644i \(-0.0423467\pi\)
−0.132644 + 0.991164i \(0.542347\pi\)
\(422\) 0 0
\(423\) 2.82843i 0.137523i
\(424\) 0 0
\(425\) 5.39635i 0.261761i
\(426\) 0 0
\(427\) 0.583234 + 0.583234i 0.0282247 + 0.0282247i
\(428\) 0 0
\(429\) −22.6238 + 22.6238i −1.09229 + 1.09229i
\(430\) 0 0
\(431\) 10.3211 0.497151 0.248576 0.968612i \(-0.420038\pi\)
0.248576 + 0.968612i \(0.420038\pi\)
\(432\) 0 0
\(433\) −15.3137 −0.735930 −0.367965 0.929840i \(-0.619945\pi\)
−0.367965 + 0.929840i \(0.619945\pi\)
\(434\) 0 0
\(435\) −3.77522 + 3.77522i −0.181008 + 0.181008i
\(436\) 0 0
\(437\) 6.10641 + 6.10641i 0.292109 + 0.292109i
\(438\) 0 0
\(439\) 22.5735i 1.07738i −0.842505 0.538688i \(-0.818920\pi\)
0.842505 0.538688i \(-0.181080\pi\)
\(440\) 0 0
\(441\) 6.97474i 0.332130i
\(442\) 0 0
\(443\) −23.7117 23.7117i −1.12658 1.12658i −0.990730 0.135846i \(-0.956625\pi\)
−0.135846 0.990730i \(-0.543375\pi\)
\(444\) 0 0
\(445\) 18.3059 18.3059i 0.867784 0.867784i
\(446\) 0 0
\(447\) 4.14108 0.195866
\(448\) 0 0
\(449\) −1.75506 −0.0828266 −0.0414133 0.999142i \(-0.513186\pi\)
−0.0414133 + 0.999142i \(0.513186\pi\)
\(450\) 0 0
\(451\) 9.88849 9.88849i 0.465631 0.465631i
\(452\) 0 0
\(453\) −16.0261 16.0261i −0.752974 0.752974i
\(454\) 0 0
\(455\) 1.70227i 0.0798039i
\(456\) 0 0
\(457\) 26.7422i 1.25095i 0.780246 + 0.625473i \(0.215094\pi\)
−0.780246 + 0.625473i \(0.784906\pi\)
\(458\) 0 0
\(459\) 2.15894 + 2.15894i 0.100771 + 0.100771i
\(460\) 0 0
\(461\) −9.23921 + 9.23921i −0.430313 + 0.430313i −0.888735 0.458422i \(-0.848415\pi\)
0.458422 + 0.888735i \(0.348415\pi\)
\(462\) 0 0
\(463\) 29.4474 1.36854 0.684268 0.729231i \(-0.260122\pi\)
0.684268 + 0.729231i \(0.260122\pi\)
\(464\) 0 0
\(465\) 7.47750 0.346761
\(466\) 0 0
\(467\) 19.5897 19.5897i 0.906503 0.906503i −0.0894848 0.995988i \(-0.528522\pi\)
0.995988 + 0.0894848i \(0.0285221\pi\)
\(468\) 0 0
\(469\) 0.121978 + 0.121978i 0.00563242 + 0.00563242i
\(470\) 0 0
\(471\) 3.93161i 0.181159i
\(472\) 0 0
\(473\) 43.7127i 2.00991i
\(474\) 0 0
\(475\) −3.81580 3.81580i −0.175081 0.175081i
\(476\) 0 0
\(477\) −3.55710 + 3.55710i −0.162868 + 0.162868i
\(478\) 0 0
\(479\) 35.5499 1.62432 0.812159 0.583436i \(-0.198292\pi\)
0.812159 + 0.583436i \(0.198292\pi\)
\(480\) 0 0
\(481\) 50.4393 2.29984
\(482\) 0 0
\(483\) −0.317883 + 0.317883i −0.0144642 + 0.0144642i
\(484\) 0 0
\(485\) 0.726607 + 0.726607i 0.0329935 + 0.0329935i
\(486\) 0 0
\(487\) 9.86632i 0.447086i 0.974694 + 0.223543i \(0.0717623\pi\)
−0.974694 + 0.223543i \(0.928238\pi\)
\(488\) 0 0
\(489\) 7.68897i 0.347707i
\(490\) 0 0
\(491\) 0.449555 + 0.449555i 0.0202881 + 0.0202881i 0.717178 0.696890i \(-0.245433\pi\)
−0.696890 + 0.717178i \(0.745433\pi\)
\(492\) 0 0
\(493\) −6.41099 + 6.41099i −0.288736 + 0.288736i
\(494\) 0 0
\(495\) −9.65685 −0.434043
\(496\) 0 0
\(497\) 0.0505249 0.00226635
\(498\) 0 0
\(499\) −2.70645 + 2.70645i −0.121157 + 0.121157i −0.765086 0.643928i \(-0.777303\pi\)
0.643928 + 0.765086i \(0.277303\pi\)
\(500\) 0 0
\(501\) 2.79631 + 2.79631i 0.124930 + 0.124930i
\(502\) 0 0
\(503\) 23.6719i 1.05548i −0.849407 0.527739i \(-0.823040\pi\)
0.849407 0.527739i \(-0.176960\pi\)
\(504\) 0 0
\(505\) 18.1876i 0.809336i
\(506\) 0 0
\(507\) 15.8988 + 15.8988i 0.706092 + 0.706092i
\(508\) 0 0
\(509\) 24.6052 24.6052i 1.09061 1.09061i 0.0951425 0.995464i \(-0.469669\pi\)
0.995464 0.0951425i \(-0.0303307\pi\)
\(510\) 0 0
\(511\) −0.212818 −0.00941453
\(512\) 0 0
\(513\) 3.05320 0.134802
\(514\) 0 0
\(515\) −14.4305 + 14.4305i −0.635882 + 0.635882i
\(516\) 0 0
\(517\) −10.7422 10.7422i −0.472440 0.472440i
\(518\) 0 0
\(519\) 22.6011i 0.992078i
\(520\) 0 0
\(521\) 14.4889i 0.634770i 0.948297 + 0.317385i \(0.102805\pi\)
−0.948297 + 0.317385i \(0.897195\pi\)
\(522\) 0 0
\(523\) 19.4979 + 19.4979i 0.852584 + 0.852584i 0.990451 0.137867i \(-0.0440245\pi\)
−0.137867 + 0.990451i \(0.544025\pi\)
\(524\) 0 0
\(525\) 0.198640 0.198640i 0.00866937 0.00866937i
\(526\) 0 0
\(527\) 12.6981 0.553138
\(528\) 0 0
\(529\) 15.0000 0.652174
\(530\) 0 0
\(531\) −4.00000 + 4.00000i −0.173585 + 0.173585i
\(532\) 0 0
\(533\) −10.9670 10.9670i −0.475031 0.475031i
\(534\) 0 0
\(535\) 1.83585i 0.0793706i
\(536\) 0 0
\(537\) 17.2981i 0.746470i
\(538\) 0 0
\(539\) 26.4896 + 26.4896i 1.14099 + 1.14099i
\(540\) 0 0
\(541\) 10.0396 10.0396i 0.431638 0.431638i −0.457547 0.889185i \(-0.651272\pi\)
0.889185 + 0.457547i \(0.151272\pi\)
\(542\) 0 0
\(543\) 8.14953 0.349730
\(544\) 0 0
\(545\) −3.67340 −0.157351
\(546\) 0 0
\(547\) 7.19884 7.19884i 0.307800 0.307800i −0.536255 0.844056i \(-0.680162\pi\)
0.844056 + 0.536255i \(0.180162\pi\)
\(548\) 0 0
\(549\) 3.66949 + 3.66949i 0.156610 + 0.156610i
\(550\) 0 0
\(551\) 9.06651i 0.386246i
\(552\) 0 0
\(553\) 1.54075i 0.0655194i
\(554\) 0 0
\(555\) 10.7649 + 10.7649i 0.456944 + 0.456944i
\(556\) 0 0
\(557\) −1.02129 + 1.02129i −0.0432735 + 0.0432735i −0.728412 0.685139i \(-0.759741\pi\)
0.685139 + 0.728412i \(0.259741\pi\)
\(558\) 0 0
\(559\) −48.4802 −2.05049
\(560\) 0 0
\(561\) −16.3990 −0.692368
\(562\) 0 0
\(563\) −6.70751 + 6.70751i −0.282688 + 0.282688i −0.834180 0.551492i \(-0.814059\pi\)
0.551492 + 0.834180i \(0.314059\pi\)
\(564\) 0 0
\(565\) 4.49400 + 4.49400i 0.189064 + 0.189064i
\(566\) 0 0
\(567\) 0.158942i 0.00667492i
\(568\) 0 0
\(569\) 8.98711i 0.376759i 0.982096 + 0.188380i \(0.0603235\pi\)
−0.982096 + 0.188380i \(0.939676\pi\)
\(570\) 0 0
\(571\) 9.17157 + 9.17157i 0.383818 + 0.383818i 0.872476 0.488657i \(-0.162513\pi\)
−0.488657 + 0.872476i \(0.662513\pi\)
\(572\) 0 0
\(573\) 11.4321 11.4321i 0.477582 0.477582i
\(574\) 0 0
\(575\) 4.99907 0.208476
\(576\) 0 0
\(577\) 29.5013 1.22815 0.614077 0.789246i \(-0.289528\pi\)
0.614077 + 0.789246i \(0.289528\pi\)
\(578\) 0 0
\(579\) 15.6591 15.6591i 0.650772 0.650772i
\(580\) 0 0
\(581\) 0.0184080 + 0.0184080i 0.000763692 + 0.000763692i
\(582\) 0 0
\(583\) 27.0192i 1.11902i
\(584\) 0 0
\(585\) 10.7101i 0.442806i
\(586\) 0 0
\(587\) −1.82425 1.82425i −0.0752950 0.0752950i 0.668456 0.743751i \(-0.266955\pi\)
−0.743751 + 0.668456i \(0.766955\pi\)
\(588\) 0 0
\(589\) 8.97891 8.97891i 0.369970 0.369970i
\(590\) 0 0
\(591\) −20.2222 −0.831831
\(592\) 0 0
\(593\) −35.4338 −1.45509 −0.727546 0.686058i \(-0.759339\pi\)
−0.727546 + 0.686058i \(0.759339\pi\)
\(594\) 0 0
\(595\) −0.616953 + 0.616953i −0.0252926 + 0.0252926i
\(596\) 0 0
\(597\) −17.6830 17.6830i −0.723717 0.723717i
\(598\) 0 0
\(599\) 27.1632i 1.10986i 0.831897 + 0.554930i \(0.187255\pi\)
−0.831897 + 0.554930i \(0.812745\pi\)
\(600\) 0 0
\(601\) 5.33897i 0.217781i −0.994054 0.108891i \(-0.965270\pi\)
0.994054 0.108891i \(-0.0347298\pi\)
\(602\) 0 0
\(603\) 0.767438 + 0.767438i 0.0312525 + 0.0312525i
\(604\) 0 0
\(605\) 22.6914 22.6914i 0.922539 0.922539i
\(606\) 0 0
\(607\) 16.1084 0.653820 0.326910 0.945055i \(-0.393993\pi\)
0.326910 + 0.945055i \(0.393993\pi\)
\(608\) 0 0
\(609\) −0.471978 −0.0191255
\(610\) 0 0
\(611\) −11.9137 + 11.9137i −0.481979 + 0.481979i
\(612\) 0 0
\(613\) −0.436924 0.436924i −0.0176472 0.0176472i 0.698228 0.715875i \(-0.253972\pi\)
−0.715875 + 0.698228i \(0.753972\pi\)
\(614\) 0 0
\(615\) 4.68119i 0.188764i
\(616\) 0 0
\(617\) 8.80641i 0.354533i −0.984163 0.177266i \(-0.943275\pi\)
0.984163 0.177266i \(-0.0567254\pi\)
\(618\) 0 0
\(619\) −1.92932 1.92932i −0.0775458 0.0775458i 0.667270 0.744816i \(-0.267463\pi\)
−0.744816 + 0.667270i \(0.767463\pi\)
\(620\) 0 0
\(621\) −2.00000 + 2.00000i −0.0802572 + 0.0802572i
\(622\) 0 0
\(623\) 2.28861 0.0916910
\(624\) 0 0
\(625\) 13.0390 0.521559
\(626\) 0 0
\(627\) −11.5959 + 11.5959i −0.463094 + 0.463094i
\(628\) 0 0
\(629\) 18.2807 + 18.2807i 0.728898 + 0.728898i
\(630\) 0 0
\(631\) 38.7864i 1.54406i −0.635586 0.772030i \(-0.719241\pi\)
0.635586 0.772030i \(-0.280759\pi\)
\(632\) 0 0
\(633\) 26.0559i 1.03563i
\(634\) 0 0
\(635\) 1.90434 + 1.90434i 0.0755715 + 0.0755715i
\(636\) 0 0
\(637\) 29.3786 29.3786i 1.16402 1.16402i
\(638\) 0 0
\(639\) 0.317883 0.0125753
\(640\) 0 0
\(641\) 33.1091 1.30773 0.653865 0.756611i \(-0.273146\pi\)
0.653865 + 0.756611i \(0.273146\pi\)
\(642\) 0 0
\(643\) 19.2897 19.2897i 0.760711 0.760711i −0.215740 0.976451i \(-0.569216\pi\)
0.976451 + 0.215740i \(0.0692164\pi\)
\(644\) 0 0
\(645\) −10.3468 10.3468i −0.407403 0.407403i
\(646\) 0 0
\(647\) 41.8477i 1.64520i 0.568620 + 0.822601i \(0.307478\pi\)
−0.568620 + 0.822601i \(0.692522\pi\)
\(648\) 0 0
\(649\) 30.3835i 1.19266i
\(650\) 0 0
\(651\) 0.467418 + 0.467418i 0.0183196 + 0.0183196i
\(652\) 0 0
\(653\) −14.7741 + 14.7741i −0.578155 + 0.578155i −0.934395 0.356240i \(-0.884059\pi\)
0.356240 + 0.934395i \(0.384059\pi\)
\(654\) 0 0
\(655\) 26.5054 1.03565
\(656\) 0 0
\(657\) −1.33897 −0.0522382
\(658\) 0 0
\(659\) 2.22839 2.22839i 0.0868056 0.0868056i −0.662371 0.749176i \(-0.730450\pi\)
0.749176 + 0.662371i \(0.230450\pi\)
\(660\) 0 0
\(661\) 18.0685 + 18.0685i 0.702784 + 0.702784i 0.965007 0.262223i \(-0.0844557\pi\)
−0.262223 + 0.965007i \(0.584456\pi\)
\(662\) 0 0
\(663\) 18.1876i 0.706346i
\(664\) 0 0
\(665\) 0.872503i 0.0338342i
\(666\) 0 0
\(667\) −5.93901 5.93901i −0.229959 0.229959i
\(668\) 0 0
\(669\) −12.9729 + 12.9729i −0.501563 + 0.501563i
\(670\) 0 0
\(671\) −27.8729 −1.07602
\(672\) 0 0
\(673\) 20.7981 0.801706 0.400853 0.916142i \(-0.368714\pi\)
0.400853 + 0.916142i \(0.368714\pi\)
\(674\) 0 0
\(675\) 1.24977 1.24977i 0.0481036 0.0481036i
\(676\) 0 0
\(677\) −29.0213 29.0213i −1.11538 1.11538i −0.992411 0.122968i \(-0.960759\pi\)
−0.122968 0.992411i \(-0.539241\pi\)
\(678\) 0 0
\(679\) 0.0908404i 0.00348613i
\(680\) 0 0
\(681\) 0.163788i 0.00627639i
\(682\) 0 0
\(683\) 18.7938 + 18.7938i 0.719123 + 0.719123i 0.968426 0.249303i \(-0.0802013\pi\)
−0.249303 + 0.968426i \(0.580201\pi\)
\(684\) 0 0
\(685\) −17.5385 + 17.5385i −0.670111 + 0.670111i
\(686\) 0 0
\(687\) 4.02756 0.153661
\(688\) 0 0
\(689\) −29.9660 −1.14161
\(690\) 0 0
\(691\) −10.4580 + 10.4580i −0.397841 + 0.397841i −0.877471 0.479630i \(-0.840771\pi\)
0.479630 + 0.877471i \(0.340771\pi\)
\(692\) 0 0
\(693\) −0.603650 0.603650i −0.0229308 0.0229308i
\(694\) 0 0
\(695\) 6.16415i 0.233820i
\(696\) 0 0
\(697\) 7.94948i 0.301108i
\(698\) 0 0
\(699\) −8.28806 8.28806i −0.313483 0.313483i
\(700\) 0 0
\(701\) −18.3314 + 18.3314i −0.692367 + 0.692367i −0.962752 0.270385i \(-0.912849\pi\)
0.270385 + 0.962752i \(0.412849\pi\)
\(702\) 0 0
\(703\) 25.8528 0.975055
\(704\) 0 0
\(705\) −5.08532 −0.191524
\(706\) 0 0
\(707\) 1.13690 1.13690i 0.0427577 0.0427577i
\(708\) 0 0
\(709\) −14.5722 14.5722i −0.547271 0.547271i 0.378380 0.925650i \(-0.376481\pi\)
−0.925650 + 0.378380i \(0.876481\pi\)
\(710\) 0 0
\(711\) 9.69382i 0.363547i
\(712\) 0 0
\(713\) 11.7633i 0.440538i
\(714\) 0 0
\(715\) −40.6761 40.6761i −1.52120 1.52120i
\(716\) 0 0
\(717\) 9.65324 9.65324i 0.360507 0.360507i
\(718\) 0 0
\(719\) 44.0949 1.64446 0.822230 0.569155i \(-0.192730\pi\)
0.822230 + 0.569155i \(0.192730\pi\)
\(720\) 0 0
\(721\) −1.80409 −0.0671880
\(722\) 0 0
\(723\) −1.50732 + 1.50732i −0.0560578 + 0.0560578i
\(724\) 0 0
\(725\) 3.71119 + 3.71119i 0.137830 + 0.137830i
\(726\) 0 0
\(727\) 9.23457i 0.342491i 0.985228 + 0.171246i \(0.0547792\pi\)
−0.985228 + 0.171246i \(0.945221\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −17.5706 17.5706i −0.649872 0.649872i
\(732\) 0 0
\(733\) −18.2764 + 18.2764i −0.675053 + 0.675053i −0.958877 0.283823i \(-0.908397\pi\)
0.283823 + 0.958877i \(0.408397\pi\)
\(734\) 0 0
\(735\) 12.5401 0.462549
\(736\) 0 0
\(737\) −5.82936 −0.214727
\(738\) 0 0
\(739\) −16.9991 + 16.9991i −0.625321 + 0.625321i −0.946887 0.321566i \(-0.895791\pi\)
0.321566 + 0.946887i \(0.395791\pi\)
\(740\) 0 0
\(741\) 12.8605 + 12.8605i 0.472444 + 0.472444i
\(742\) 0 0
\(743\) 17.8748i 0.655762i −0.944719 0.327881i \(-0.893665\pi\)
0.944719 0.327881i \(-0.106335\pi\)
\(744\) 0 0
\(745\) 7.44538i 0.272778i
\(746\) 0 0
\(747\) 0.115816 + 0.115816i 0.00423748 + 0.00423748i
\(748\) 0 0
\(749\) 0.114759 0.114759i 0.00419319 0.00419319i
\(750\) 0 0
\(751\) −35.0731 −1.27984 −0.639918 0.768443i \(-0.721032\pi\)
−0.639918 + 0.768443i \(0.721032\pi\)
\(752\) 0 0
\(753\) −6.27020 −0.228499
\(754\) 0 0
\(755\) 28.8139 28.8139i 1.04865 1.04865i
\(756\) 0 0
\(757\) 32.8071 + 32.8071i 1.19239 + 1.19239i 0.976393 + 0.216000i \(0.0693012\pi\)
0.216000 + 0.976393i \(0.430699\pi\)
\(758\) 0 0
\(759\) 15.1917i 0.551425i
\(760\) 0 0
\(761\) 10.5531i 0.382550i −0.981536 0.191275i \(-0.938738\pi\)
0.981536 0.191275i \(-0.0612623\pi\)
\(762\) 0 0
\(763\) −0.229624 0.229624i −0.00831296 0.00831296i
\(764\) 0 0
\(765\) −3.88163 + 3.88163i −0.140341 + 0.140341i
\(766\) 0 0
\(767\) −33.6972 −1.21673
\(768\) 0 0
\(769\) −35.2068 −1.26959 −0.634795 0.772681i \(-0.718915\pi\)
−0.634795 + 0.772681i \(0.718915\pi\)
\(770\) 0 0
\(771\) −10.6669 + 10.6669i −0.384160 + 0.384160i
\(772\) 0 0
\(773\) 19.3897 + 19.3897i 0.697399 + 0.697399i 0.963849 0.266450i \(-0.0858507\pi\)
−0.266450 + 0.963849i \(0.585851\pi\)
\(774\) 0 0
\(775\) 7.35067i 0.264044i
\(776\) 0 0
\(777\) 1.34583i 0.0482812i
\(778\) 0 0
\(779\) −5.62113 5.62113i −0.201398 0.201398i
\(780\) 0 0
\(781\) −1.20730 + 1.20730i −0.0432006 + 0.0432006i
\(782\) 0 0
\(783\) −2.96951 −0.106121
\(784\) 0 0
\(785\) −7.06877 −0.252295
\(786\) 0 0
\(787\) 6.68964 6.68964i 0.238460 0.238460i −0.577752 0.816212i \(-0.696070\pi\)
0.816212 + 0.577752i \(0.196070\pi\)
\(788\) 0 0
\(789\) 18.5054 + 18.5054i 0.658811 + 0.658811i
\(790\) 0 0
\(791\) 0.561839i 0.0199767i
\(792\) 0 0
\(793\) 30.9128i 1.09775i
\(794\) 0 0
\(795\) −6.39542 6.39542i −0.226822 0.226822i
\(796\) 0 0
\(797\) −13.5617 + 13.5617i −0.480380 + 0.480380i −0.905253 0.424873i \(-0.860319\pi\)
0.424873 + 0.905253i \(0.360319\pi\)
\(798\) 0 0
\(799\) −8.63577 </