Properties

Label 432.2.k.b.109.2
Level $432$
Weight $2$
Character 432.109
Analytic conductor $3.450$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 109.2
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 432.109
Dual form 432.2.k.b.325.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} -2.00000 q^{4} +(0.707107 - 0.707107i) q^{5} +3.00000i q^{7} -2.82843i q^{8} +O(q^{10})\) \(q+1.41421i q^{2} -2.00000 q^{4} +(0.707107 - 0.707107i) q^{5} +3.00000i q^{7} -2.82843i q^{8} +(1.00000 + 1.00000i) q^{10} +(-3.53553 + 3.53553i) q^{11} +(1.00000 + 1.00000i) q^{13} -4.24264 q^{14} +4.00000 q^{16} -4.24264 q^{17} +(4.00000 + 4.00000i) q^{19} +(-1.41421 + 1.41421i) q^{20} +(-5.00000 - 5.00000i) q^{22} +2.82843i q^{23} +4.00000i q^{25} +(-1.41421 + 1.41421i) q^{26} -6.00000i q^{28} +(-2.82843 - 2.82843i) q^{29} -7.00000 q^{31} +5.65685i q^{32} -6.00000i q^{34} +(2.12132 + 2.12132i) q^{35} +(-2.00000 + 2.00000i) q^{37} +(-5.65685 + 5.65685i) q^{38} +(-2.00000 - 2.00000i) q^{40} -5.65685i q^{41} +(7.00000 - 7.00000i) q^{43} +(7.07107 - 7.07107i) q^{44} -4.00000 q^{46} +4.24264 q^{47} -2.00000 q^{49} -5.65685 q^{50} +(-2.00000 - 2.00000i) q^{52} +(0.707107 - 0.707107i) q^{53} +5.00000i q^{55} +8.48528 q^{56} +(4.00000 - 4.00000i) q^{58} +(7.07107 - 7.07107i) q^{59} +(10.0000 + 10.0000i) q^{61} -9.89949i q^{62} -8.00000 q^{64} +1.41421 q^{65} +(1.00000 + 1.00000i) q^{67} +8.48528 q^{68} +(-3.00000 + 3.00000i) q^{70} +15.5563i q^{71} -15.0000i q^{73} +(-2.82843 - 2.82843i) q^{74} +(-8.00000 - 8.00000i) q^{76} +(-10.6066 - 10.6066i) q^{77} +2.00000 q^{79} +(2.82843 - 2.82843i) q^{80} +8.00000 q^{82} +(7.77817 + 7.77817i) q^{83} +(-3.00000 + 3.00000i) q^{85} +(9.89949 + 9.89949i) q^{86} +(10.0000 + 10.0000i) q^{88} -1.41421i q^{89} +(-3.00000 + 3.00000i) q^{91} -5.65685i q^{92} +6.00000i q^{94} +5.65685 q^{95} -7.00000 q^{97} -2.82843i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 8q^{4} + O(q^{10}) \) \( 4q - 8q^{4} + 4q^{10} + 4q^{13} + 16q^{16} + 16q^{19} - 20q^{22} - 28q^{31} - 8q^{37} - 8q^{40} + 28q^{43} - 16q^{46} - 8q^{49} - 8q^{52} + 16q^{58} + 40q^{61} - 32q^{64} + 4q^{67} - 12q^{70} - 32q^{76} + 8q^{79} + 32q^{82} - 12q^{85} + 40q^{88} - 12q^{91} - 28q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 1.00000i
\(3\) 0 0
\(4\) −2.00000 −1.00000
\(5\) 0.707107 0.707107i 0.316228 0.316228i −0.531089 0.847316i \(-0.678217\pi\)
0.847316 + 0.531089i \(0.178217\pi\)
\(6\) 0 0
\(7\) 3.00000i 1.13389i 0.823754 + 0.566947i \(0.191875\pi\)
−0.823754 + 0.566947i \(0.808125\pi\)
\(8\) 2.82843i 1.00000i
\(9\) 0 0
\(10\) 1.00000 + 1.00000i 0.316228 + 0.316228i
\(11\) −3.53553 + 3.53553i −1.06600 + 1.06600i −0.0683416 + 0.997662i \(0.521771\pi\)
−0.997662 + 0.0683416i \(0.978229\pi\)
\(12\) 0 0
\(13\) 1.00000 + 1.00000i 0.277350 + 0.277350i 0.832050 0.554700i \(-0.187167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −4.24264 −1.13389
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) −4.24264 −1.02899 −0.514496 0.857493i \(-0.672021\pi\)
−0.514496 + 0.857493i \(0.672021\pi\)
\(18\) 0 0
\(19\) 4.00000 + 4.00000i 0.917663 + 0.917663i 0.996859 0.0791961i \(-0.0252353\pi\)
−0.0791961 + 0.996859i \(0.525235\pi\)
\(20\) −1.41421 + 1.41421i −0.316228 + 0.316228i
\(21\) 0 0
\(22\) −5.00000 5.00000i −1.06600 1.06600i
\(23\) 2.82843i 0.589768i 0.955533 + 0.294884i \(0.0952810\pi\)
−0.955533 + 0.294884i \(0.904719\pi\)
\(24\) 0 0
\(25\) 4.00000i 0.800000i
\(26\) −1.41421 + 1.41421i −0.277350 + 0.277350i
\(27\) 0 0
\(28\) 6.00000i 1.13389i
\(29\) −2.82843 2.82843i −0.525226 0.525226i 0.393919 0.919145i \(-0.371119\pi\)
−0.919145 + 0.393919i \(0.871119\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 5.65685i 1.00000i
\(33\) 0 0
\(34\) 6.00000i 1.02899i
\(35\) 2.12132 + 2.12132i 0.358569 + 0.358569i
\(36\) 0 0
\(37\) −2.00000 + 2.00000i −0.328798 + 0.328798i −0.852129 0.523331i \(-0.824689\pi\)
0.523331 + 0.852129i \(0.324689\pi\)
\(38\) −5.65685 + 5.65685i −0.917663 + 0.917663i
\(39\) 0 0
\(40\) −2.00000 2.00000i −0.316228 0.316228i
\(41\) 5.65685i 0.883452i −0.897150 0.441726i \(-0.854366\pi\)
0.897150 0.441726i \(-0.145634\pi\)
\(42\) 0 0
\(43\) 7.00000 7.00000i 1.06749 1.06749i 0.0699387 0.997551i \(-0.477720\pi\)
0.997551 0.0699387i \(-0.0222804\pi\)
\(44\) 7.07107 7.07107i 1.06600 1.06600i
\(45\) 0 0
\(46\) −4.00000 −0.589768
\(47\) 4.24264 0.618853 0.309426 0.950923i \(-0.399863\pi\)
0.309426 + 0.950923i \(0.399863\pi\)
\(48\) 0 0
\(49\) −2.00000 −0.285714
\(50\) −5.65685 −0.800000
\(51\) 0 0
\(52\) −2.00000 2.00000i −0.277350 0.277350i
\(53\) 0.707107 0.707107i 0.0971286 0.0971286i −0.656873 0.754001i \(-0.728121\pi\)
0.754001 + 0.656873i \(0.228121\pi\)
\(54\) 0 0
\(55\) 5.00000i 0.674200i
\(56\) 8.48528 1.13389
\(57\) 0 0
\(58\) 4.00000 4.00000i 0.525226 0.525226i
\(59\) 7.07107 7.07107i 0.920575 0.920575i −0.0764953 0.997070i \(-0.524373\pi\)
0.997070 + 0.0764953i \(0.0243730\pi\)
\(60\) 0 0
\(61\) 10.0000 + 10.0000i 1.28037 + 1.28037i 0.940457 + 0.339911i \(0.110397\pi\)
0.339911 + 0.940457i \(0.389603\pi\)
\(62\) 9.89949i 1.25724i
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 1.41421 0.175412
\(66\) 0 0
\(67\) 1.00000 + 1.00000i 0.122169 + 0.122169i 0.765548 0.643379i \(-0.222468\pi\)
−0.643379 + 0.765548i \(0.722468\pi\)
\(68\) 8.48528 1.02899
\(69\) 0 0
\(70\) −3.00000 + 3.00000i −0.358569 + 0.358569i
\(71\) 15.5563i 1.84620i 0.384561 + 0.923099i \(0.374353\pi\)
−0.384561 + 0.923099i \(0.625647\pi\)
\(72\) 0 0
\(73\) 15.0000i 1.75562i −0.479012 0.877809i \(-0.659005\pi\)
0.479012 0.877809i \(-0.340995\pi\)
\(74\) −2.82843 2.82843i −0.328798 0.328798i
\(75\) 0 0
\(76\) −8.00000 8.00000i −0.917663 0.917663i
\(77\) −10.6066 10.6066i −1.20873 1.20873i
\(78\) 0 0
\(79\) 2.00000 0.225018 0.112509 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) 2.82843 2.82843i 0.316228 0.316228i
\(81\) 0 0
\(82\) 8.00000 0.883452
\(83\) 7.77817 + 7.77817i 0.853766 + 0.853766i 0.990595 0.136829i \(-0.0436911\pi\)
−0.136829 + 0.990595i \(0.543691\pi\)
\(84\) 0 0
\(85\) −3.00000 + 3.00000i −0.325396 + 0.325396i
\(86\) 9.89949 + 9.89949i 1.06749 + 1.06749i
\(87\) 0 0
\(88\) 10.0000 + 10.0000i 1.06600 + 1.06600i
\(89\) 1.41421i 0.149906i −0.997187 0.0749532i \(-0.976119\pi\)
0.997187 0.0749532i \(-0.0238807\pi\)
\(90\) 0 0
\(91\) −3.00000 + 3.00000i −0.314485 + 0.314485i
\(92\) 5.65685i 0.589768i
\(93\) 0 0
\(94\) 6.00000i 0.618853i
\(95\) 5.65685 0.580381
\(96\) 0 0
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 2.82843i 0.285714i
\(99\) 0 0
\(100\) 8.00000i 0.800000i
\(101\) 4.94975 4.94975i 0.492518 0.492518i −0.416581 0.909099i \(-0.636772\pi\)
0.909099 + 0.416581i \(0.136772\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i 0.955312 + 0.295599i \(0.0955191\pi\)
−0.955312 + 0.295599i \(0.904481\pi\)
\(104\) 2.82843 2.82843i 0.277350 0.277350i
\(105\) 0 0
\(106\) 1.00000 + 1.00000i 0.0971286 + 0.0971286i
\(107\) −7.77817 + 7.77817i −0.751945 + 0.751945i −0.974842 0.222897i \(-0.928449\pi\)
0.222897 + 0.974842i \(0.428449\pi\)
\(108\) 0 0
\(109\) 10.0000 + 10.0000i 0.957826 + 0.957826i 0.999146 0.0413197i \(-0.0131562\pi\)
−0.0413197 + 0.999146i \(0.513156\pi\)
\(110\) −7.07107 −0.674200
\(111\) 0 0
\(112\) 12.0000i 1.13389i
\(113\) 8.48528 0.798228 0.399114 0.916901i \(-0.369318\pi\)
0.399114 + 0.916901i \(0.369318\pi\)
\(114\) 0 0
\(115\) 2.00000 + 2.00000i 0.186501 + 0.186501i
\(116\) 5.65685 + 5.65685i 0.525226 + 0.525226i
\(117\) 0 0
\(118\) 10.0000 + 10.0000i 0.920575 + 0.920575i
\(119\) 12.7279i 1.16677i
\(120\) 0 0
\(121\) 14.0000i 1.27273i
\(122\) −14.1421 + 14.1421i −1.28037 + 1.28037i
\(123\) 0 0
\(124\) 14.0000 1.25724
\(125\) 6.36396 + 6.36396i 0.569210 + 0.569210i
\(126\) 0 0
\(127\) −13.0000 −1.15356 −0.576782 0.816898i \(-0.695692\pi\)
−0.576782 + 0.816898i \(0.695692\pi\)
\(128\) 11.3137i 1.00000i
\(129\) 0 0
\(130\) 2.00000i 0.175412i
\(131\) −0.707107 0.707107i −0.0617802 0.0617802i 0.675542 0.737322i \(-0.263910\pi\)
−0.737322 + 0.675542i \(0.763910\pi\)
\(132\) 0 0
\(133\) −12.0000 + 12.0000i −1.04053 + 1.04053i
\(134\) −1.41421 + 1.41421i −0.122169 + 0.122169i
\(135\) 0 0
\(136\) 12.0000i 1.02899i
\(137\) 18.3848i 1.57072i −0.619041 0.785359i \(-0.712479\pi\)
0.619041 0.785359i \(-0.287521\pi\)
\(138\) 0 0
\(139\) 10.0000 10.0000i 0.848189 0.848189i −0.141718 0.989907i \(-0.545263\pi\)
0.989907 + 0.141718i \(0.0452627\pi\)
\(140\) −4.24264 4.24264i −0.358569 0.358569i
\(141\) 0 0
\(142\) −22.0000 −1.84620
\(143\) −7.07107 −0.591312
\(144\) 0 0
\(145\) −4.00000 −0.332182
\(146\) 21.2132 1.75562
\(147\) 0 0
\(148\) 4.00000 4.00000i 0.328798 0.328798i
\(149\) 4.94975 4.94975i 0.405499 0.405499i −0.474667 0.880166i \(-0.657431\pi\)
0.880166 + 0.474667i \(0.157431\pi\)
\(150\) 0 0
\(151\) 21.0000i 1.70896i −0.519488 0.854478i \(-0.673877\pi\)
0.519488 0.854478i \(-0.326123\pi\)
\(152\) 11.3137 11.3137i 0.917663 0.917663i
\(153\) 0 0
\(154\) 15.0000 15.0000i 1.20873 1.20873i
\(155\) −4.94975 + 4.94975i −0.397573 + 0.397573i
\(156\) 0 0
\(157\) −2.00000 2.00000i −0.159617 0.159617i 0.622780 0.782397i \(-0.286003\pi\)
−0.782397 + 0.622780i \(0.786003\pi\)
\(158\) 2.82843i 0.225018i
\(159\) 0 0
\(160\) 4.00000 + 4.00000i 0.316228 + 0.316228i
\(161\) −8.48528 −0.668734
\(162\) 0 0
\(163\) −5.00000 5.00000i −0.391630 0.391630i 0.483638 0.875268i \(-0.339315\pi\)
−0.875268 + 0.483638i \(0.839315\pi\)
\(164\) 11.3137i 0.883452i
\(165\) 0 0
\(166\) −11.0000 + 11.0000i −0.853766 + 0.853766i
\(167\) 7.07107i 0.547176i 0.961847 + 0.273588i \(0.0882104\pi\)
−0.961847 + 0.273588i \(0.911790\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) −4.24264 4.24264i −0.325396 0.325396i
\(171\) 0 0
\(172\) −14.0000 + 14.0000i −1.06749 + 1.06749i
\(173\) 7.77817 + 7.77817i 0.591364 + 0.591364i 0.938000 0.346636i \(-0.112676\pi\)
−0.346636 + 0.938000i \(0.612676\pi\)
\(174\) 0 0
\(175\) −12.0000 −0.907115
\(176\) −14.1421 + 14.1421i −1.06600 + 1.06600i
\(177\) 0 0
\(178\) 2.00000 0.149906
\(179\) 7.77817 + 7.77817i 0.581368 + 0.581368i 0.935279 0.353911i \(-0.115148\pi\)
−0.353911 + 0.935279i \(0.615148\pi\)
\(180\) 0 0
\(181\) 16.0000 16.0000i 1.18927 1.18927i 0.212001 0.977269i \(-0.432002\pi\)
0.977269 0.212001i \(-0.0679981\pi\)
\(182\) −4.24264 4.24264i −0.314485 0.314485i
\(183\) 0 0
\(184\) 8.00000 0.589768
\(185\) 2.82843i 0.207950i
\(186\) 0 0
\(187\) 15.0000 15.0000i 1.09691 1.09691i
\(188\) −8.48528 −0.618853
\(189\) 0 0
\(190\) 8.00000i 0.580381i
\(191\) 4.24264 0.306987 0.153493 0.988150i \(-0.450948\pi\)
0.153493 + 0.988150i \(0.450948\pi\)
\(192\) 0 0
\(193\) −7.00000 −0.503871 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(194\) 9.89949i 0.710742i
\(195\) 0 0
\(196\) 4.00000 0.285714
\(197\) −16.2635 + 16.2635i −1.15872 + 1.15872i −0.173973 + 0.984750i \(0.555660\pi\)
−0.984750 + 0.173973i \(0.944340\pi\)
\(198\) 0 0
\(199\) 15.0000i 1.06332i 0.846957 + 0.531661i \(0.178432\pi\)
−0.846957 + 0.531661i \(0.821568\pi\)
\(200\) 11.3137 0.800000
\(201\) 0 0
\(202\) 7.00000 + 7.00000i 0.492518 + 0.492518i
\(203\) 8.48528 8.48528i 0.595550 0.595550i
\(204\) 0 0
\(205\) −4.00000 4.00000i −0.279372 0.279372i
\(206\) −8.48528 −0.591198
\(207\) 0 0
\(208\) 4.00000 + 4.00000i 0.277350 + 0.277350i
\(209\) −28.2843 −1.95646
\(210\) 0 0
\(211\) 4.00000 + 4.00000i 0.275371 + 0.275371i 0.831258 0.555887i \(-0.187621\pi\)
−0.555887 + 0.831258i \(0.687621\pi\)
\(212\) −1.41421 + 1.41421i −0.0971286 + 0.0971286i
\(213\) 0 0
\(214\) −11.0000 11.0000i −0.751945 0.751945i
\(215\) 9.89949i 0.675140i
\(216\) 0 0
\(217\) 21.0000i 1.42557i
\(218\) −14.1421 + 14.1421i −0.957826 + 0.957826i
\(219\) 0 0
\(220\) 10.0000i 0.674200i
\(221\) −4.24264 4.24264i −0.285391 0.285391i
\(222\) 0 0
\(223\) −22.0000 −1.47323 −0.736614 0.676313i \(-0.763577\pi\)
−0.736614 + 0.676313i \(0.763577\pi\)
\(224\) −16.9706 −1.13389
\(225\) 0 0
\(226\) 12.0000i 0.798228i
\(227\) −7.07107 7.07107i −0.469323 0.469323i 0.432372 0.901695i \(-0.357677\pi\)
−0.901695 + 0.432372i \(0.857677\pi\)
\(228\) 0 0
\(229\) 7.00000 7.00000i 0.462573 0.462573i −0.436925 0.899498i \(-0.643932\pi\)
0.899498 + 0.436925i \(0.143932\pi\)
\(230\) −2.82843 + 2.82843i −0.186501 + 0.186501i
\(231\) 0 0
\(232\) −8.00000 + 8.00000i −0.525226 + 0.525226i
\(233\) 15.5563i 1.01913i 0.860432 + 0.509565i \(0.170194\pi\)
−0.860432 + 0.509565i \(0.829806\pi\)
\(234\) 0 0
\(235\) 3.00000 3.00000i 0.195698 0.195698i
\(236\) −14.1421 + 14.1421i −0.920575 + 0.920575i
\(237\) 0 0
\(238\) 18.0000 1.16677
\(239\) −25.4558 −1.64660 −0.823301 0.567605i \(-0.807870\pi\)
−0.823301 + 0.567605i \(0.807870\pi\)
\(240\) 0 0
\(241\) −4.00000 −0.257663 −0.128831 0.991667i \(-0.541123\pi\)
−0.128831 + 0.991667i \(0.541123\pi\)
\(242\) 19.7990 1.27273
\(243\) 0 0
\(244\) −20.0000 20.0000i −1.28037 1.28037i
\(245\) −1.41421 + 1.41421i −0.0903508 + 0.0903508i
\(246\) 0 0
\(247\) 8.00000i 0.509028i
\(248\) 19.7990i 1.25724i
\(249\) 0 0
\(250\) −9.00000 + 9.00000i −0.569210 + 0.569210i
\(251\) −1.41421 + 1.41421i −0.0892644 + 0.0892644i −0.750329 0.661065i \(-0.770105\pi\)
0.661065 + 0.750329i \(0.270105\pi\)
\(252\) 0 0
\(253\) −10.0000 10.0000i −0.628695 0.628695i
\(254\) 18.3848i 1.15356i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 29.6985 1.85254 0.926270 0.376860i \(-0.122996\pi\)
0.926270 + 0.376860i \(0.122996\pi\)
\(258\) 0 0
\(259\) −6.00000 6.00000i −0.372822 0.372822i
\(260\) −2.82843 −0.175412
\(261\) 0 0
\(262\) 1.00000 1.00000i 0.0617802 0.0617802i
\(263\) 5.65685i 0.348817i −0.984673 0.174408i \(-0.944199\pi\)
0.984673 0.174408i \(-0.0558013\pi\)
\(264\) 0 0
\(265\) 1.00000i 0.0614295i
\(266\) −16.9706 16.9706i −1.04053 1.04053i
\(267\) 0 0
\(268\) −2.00000 2.00000i −0.122169 0.122169i
\(269\) −11.3137 11.3137i −0.689809 0.689809i 0.272381 0.962190i \(-0.412189\pi\)
−0.962190 + 0.272381i \(0.912189\pi\)
\(270\) 0 0
\(271\) −13.0000 −0.789694 −0.394847 0.918747i \(-0.629202\pi\)
−0.394847 + 0.918747i \(0.629202\pi\)
\(272\) −16.9706 −1.02899
\(273\) 0 0
\(274\) 26.0000 1.57072
\(275\) −14.1421 14.1421i −0.852803 0.852803i
\(276\) 0 0
\(277\) −20.0000 + 20.0000i −1.20168 + 1.20168i −0.228029 + 0.973654i \(0.573228\pi\)
−0.973654 + 0.228029i \(0.926772\pi\)
\(278\) 14.1421 + 14.1421i 0.848189 + 0.848189i
\(279\) 0 0
\(280\) 6.00000 6.00000i 0.358569 0.358569i
\(281\) 24.0416i 1.43420i 0.696969 + 0.717102i \(0.254532\pi\)
−0.696969 + 0.717102i \(0.745468\pi\)
\(282\) 0 0
\(283\) 4.00000 4.00000i 0.237775 0.237775i −0.578153 0.815928i \(-0.696226\pi\)
0.815928 + 0.578153i \(0.196226\pi\)
\(284\) 31.1127i 1.84620i
\(285\) 0 0
\(286\) 10.0000i 0.591312i
\(287\) 16.9706 1.00174
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 5.65685i 0.332182i
\(291\) 0 0
\(292\) 30.0000i 1.75562i
\(293\) −14.1421 + 14.1421i −0.826192 + 0.826192i −0.986988 0.160795i \(-0.948594\pi\)
0.160795 + 0.986988i \(0.448594\pi\)
\(294\) 0 0
\(295\) 10.0000i 0.582223i
\(296\) 5.65685 + 5.65685i 0.328798 + 0.328798i
\(297\) 0 0
\(298\) 7.00000 + 7.00000i 0.405499 + 0.405499i
\(299\) −2.82843 + 2.82843i −0.163572 + 0.163572i
\(300\) 0 0
\(301\) 21.0000 + 21.0000i 1.21042 + 1.21042i
\(302\) 29.6985 1.70896
\(303\) 0 0
\(304\) 16.0000 + 16.0000i 0.917663 + 0.917663i
\(305\) 14.1421 0.809776
\(306\) 0 0
\(307\) 7.00000 + 7.00000i 0.399511 + 0.399511i 0.878061 0.478549i \(-0.158837\pi\)
−0.478549 + 0.878061i \(0.658837\pi\)
\(308\) 21.2132 + 21.2132i 1.20873 + 1.20873i
\(309\) 0 0
\(310\) −7.00000 7.00000i −0.397573 0.397573i
\(311\) 19.7990i 1.12270i 0.827579 + 0.561349i \(0.189717\pi\)
−0.827579 + 0.561349i \(0.810283\pi\)
\(312\) 0 0
\(313\) 27.0000i 1.52613i 0.646322 + 0.763065i \(0.276306\pi\)
−0.646322 + 0.763065i \(0.723694\pi\)
\(314\) 2.82843 2.82843i 0.159617 0.159617i
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 24.7487 + 24.7487i 1.39003 + 1.39003i 0.825228 + 0.564799i \(0.191046\pi\)
0.564799 + 0.825228i \(0.308954\pi\)
\(318\) 0 0
\(319\) 20.0000 1.11979
\(320\) −5.65685 + 5.65685i −0.316228 + 0.316228i
\(321\) 0 0
\(322\) 12.0000i 0.668734i
\(323\) −16.9706 16.9706i −0.944267 0.944267i
\(324\) 0 0
\(325\) −4.00000 + 4.00000i −0.221880 + 0.221880i
\(326\) 7.07107 7.07107i 0.391630 0.391630i
\(327\) 0 0
\(328\) −16.0000 −0.883452
\(329\) 12.7279i 0.701713i
\(330\) 0 0
\(331\) 7.00000 7.00000i 0.384755 0.384755i −0.488057 0.872812i \(-0.662294\pi\)
0.872812 + 0.488057i \(0.162294\pi\)
\(332\) −15.5563 15.5563i −0.853766 0.853766i
\(333\) 0 0
\(334\) −10.0000 −0.547176
\(335\) 1.41421 0.0772667
\(336\) 0 0
\(337\) 20.0000 1.08947 0.544735 0.838608i \(-0.316630\pi\)
0.544735 + 0.838608i \(0.316630\pi\)
\(338\) 15.5563 0.846154
\(339\) 0 0
\(340\) 6.00000 6.00000i 0.325396 0.325396i
\(341\) 24.7487 24.7487i 1.34022 1.34022i
\(342\) 0 0
\(343\) 15.0000i 0.809924i
\(344\) −19.7990 19.7990i −1.06749 1.06749i
\(345\) 0 0
\(346\) −11.0000 + 11.0000i −0.591364 + 0.591364i
\(347\) 17.6777 17.6777i 0.948987 0.948987i −0.0497735 0.998761i \(-0.515850\pi\)
0.998761 + 0.0497735i \(0.0158499\pi\)
\(348\) 0 0
\(349\) 4.00000 + 4.00000i 0.214115 + 0.214115i 0.806013 0.591898i \(-0.201621\pi\)
−0.591898 + 0.806013i \(0.701621\pi\)
\(350\) 16.9706i 0.907115i
\(351\) 0 0
\(352\) −20.0000 20.0000i −1.06600 1.06600i
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 11.0000 + 11.0000i 0.583819 + 0.583819i
\(356\) 2.82843i 0.149906i
\(357\) 0 0
\(358\) −11.0000 + 11.0000i −0.581368 + 0.581368i
\(359\) 35.3553i 1.86598i −0.359898 0.932992i \(-0.617188\pi\)
0.359898 0.932992i \(-0.382812\pi\)
\(360\) 0 0
\(361\) 13.0000i 0.684211i
\(362\) 22.6274 + 22.6274i 1.18927 + 1.18927i
\(363\) 0 0
\(364\) 6.00000 6.00000i 0.314485 0.314485i
\(365\) −10.6066 10.6066i −0.555175 0.555175i
\(366\) 0 0
\(367\) 11.0000 0.574195 0.287098 0.957901i \(-0.407310\pi\)
0.287098 + 0.957901i \(0.407310\pi\)
\(368\) 11.3137i 0.589768i
\(369\) 0 0
\(370\) −4.00000 −0.207950
\(371\) 2.12132 + 2.12132i 0.110133 + 0.110133i
\(372\) 0 0
\(373\) 1.00000 1.00000i 0.0517780 0.0517780i −0.680744 0.732522i \(-0.738343\pi\)
0.732522 + 0.680744i \(0.238343\pi\)
\(374\) 21.2132 + 21.2132i 1.09691 + 1.09691i
\(375\) 0 0
\(376\) 12.0000i 0.618853i
\(377\) 5.65685i 0.291343i
\(378\) 0 0
\(379\) −2.00000 + 2.00000i −0.102733 + 0.102733i −0.756605 0.653872i \(-0.773143\pi\)
0.653872 + 0.756605i \(0.273143\pi\)
\(380\) −11.3137 −0.580381
\(381\) 0 0
\(382\) 6.00000i 0.306987i
\(383\) −4.24264 −0.216789 −0.108394 0.994108i \(-0.534571\pi\)
−0.108394 + 0.994108i \(0.534571\pi\)
\(384\) 0 0
\(385\) −15.0000 −0.764471
\(386\) 9.89949i 0.503871i
\(387\) 0 0
\(388\) 14.0000 0.710742
\(389\) 9.19239 9.19239i 0.466073 0.466073i −0.434567 0.900640i \(-0.643099\pi\)
0.900640 + 0.434567i \(0.143099\pi\)
\(390\) 0 0
\(391\) 12.0000i 0.606866i
\(392\) 5.65685i 0.285714i
\(393\) 0 0
\(394\) −23.0000 23.0000i −1.15872 1.15872i
\(395\) 1.41421 1.41421i 0.0711568 0.0711568i
\(396\) 0 0
\(397\) −5.00000 5.00000i −0.250943 0.250943i 0.570414 0.821357i \(-0.306783\pi\)
−0.821357 + 0.570414i \(0.806783\pi\)
\(398\) −21.2132 −1.06332
\(399\) 0 0
\(400\) 16.0000i 0.800000i
\(401\) 8.48528 0.423735 0.211867 0.977298i \(-0.432046\pi\)
0.211867 + 0.977298i \(0.432046\pi\)
\(402\) 0 0
\(403\) −7.00000 7.00000i −0.348695 0.348695i
\(404\) −9.89949 + 9.89949i −0.492518 + 0.492518i
\(405\) 0 0
\(406\) 12.0000 + 12.0000i 0.595550 + 0.595550i
\(407\) 14.1421i 0.701000i
\(408\) 0 0
\(409\) 3.00000i 0.148340i 0.997246 + 0.0741702i \(0.0236308\pi\)
−0.997246 + 0.0741702i \(0.976369\pi\)
\(410\) 5.65685 5.65685i 0.279372 0.279372i
\(411\) 0 0
\(412\) 12.0000i 0.591198i
\(413\) 21.2132 + 21.2132i 1.04383 + 1.04383i
\(414\) 0 0
\(415\) 11.0000 0.539969
\(416\) −5.65685 + 5.65685i −0.277350 + 0.277350i
\(417\) 0 0
\(418\) 40.0000i 1.95646i
\(419\) −7.07107 7.07107i −0.345444 0.345444i 0.512965 0.858409i \(-0.328547\pi\)
−0.858409 + 0.512965i \(0.828547\pi\)
\(420\) 0 0
\(421\) 16.0000 16.0000i 0.779792 0.779792i −0.200003 0.979795i \(-0.564095\pi\)
0.979795 + 0.200003i \(0.0640952\pi\)
\(422\) −5.65685 + 5.65685i −0.275371 + 0.275371i
\(423\) 0 0
\(424\) −2.00000 2.00000i −0.0971286 0.0971286i
\(425\) 16.9706i 0.823193i
\(426\) 0 0
\(427\) −30.0000 + 30.0000i −1.45180 + 1.45180i
\(428\) 15.5563 15.5563i 0.751945 0.751945i
\(429\) 0 0
\(430\) 14.0000 0.675140
\(431\) −4.24264 −0.204361 −0.102180 0.994766i \(-0.532582\pi\)
−0.102180 + 0.994766i \(0.532582\pi\)
\(432\) 0 0
\(433\) 5.00000 0.240285 0.120142 0.992757i \(-0.461665\pi\)
0.120142 + 0.992757i \(0.461665\pi\)
\(434\) 29.6985 1.42557
\(435\) 0 0
\(436\) −20.0000 20.0000i −0.957826 0.957826i
\(437\) −11.3137 + 11.3137i −0.541208 + 0.541208i
\(438\) 0 0
\(439\) 15.0000i 0.715911i 0.933739 + 0.357955i \(0.116526\pi\)
−0.933739 + 0.357955i \(0.883474\pi\)
\(440\) 14.1421 0.674200
\(441\) 0 0
\(442\) 6.00000 6.00000i 0.285391 0.285391i
\(443\) −9.89949 + 9.89949i −0.470339 + 0.470339i −0.902024 0.431685i \(-0.857919\pi\)
0.431685 + 0.902024i \(0.357919\pi\)
\(444\) 0 0
\(445\) −1.00000 1.00000i −0.0474045 0.0474045i
\(446\) 31.1127i 1.47323i
\(447\) 0 0
\(448\) 24.0000i 1.13389i
\(449\) 16.9706 0.800890 0.400445 0.916321i \(-0.368855\pi\)
0.400445 + 0.916321i \(0.368855\pi\)
\(450\) 0 0
\(451\) 20.0000 + 20.0000i 0.941763 + 0.941763i
\(452\) −16.9706 −0.798228
\(453\) 0 0
\(454\) 10.0000 10.0000i 0.469323 0.469323i
\(455\) 4.24264i 0.198898i
\(456\) 0 0
\(457\) 3.00000i 0.140334i −0.997535 0.0701670i \(-0.977647\pi\)
0.997535 0.0701670i \(-0.0223532\pi\)
\(458\) 9.89949 + 9.89949i 0.462573 + 0.462573i
\(459\) 0 0
\(460\) −4.00000 4.00000i −0.186501 0.186501i
\(461\) 24.7487 + 24.7487i 1.15266 + 1.15266i 0.986017 + 0.166647i \(0.0532940\pi\)
0.166647 + 0.986017i \(0.446706\pi\)
\(462\) 0 0
\(463\) −7.00000 −0.325318 −0.162659 0.986682i \(-0.552007\pi\)
−0.162659 + 0.986682i \(0.552007\pi\)
\(464\) −11.3137 11.3137i −0.525226 0.525226i
\(465\) 0 0
\(466\) −22.0000 −1.01913
\(467\) 3.53553 + 3.53553i 0.163605 + 0.163605i 0.784162 0.620557i \(-0.213093\pi\)
−0.620557 + 0.784162i \(0.713093\pi\)
\(468\) 0 0
\(469\) −3.00000 + 3.00000i −0.138527 + 0.138527i
\(470\) 4.24264 + 4.24264i 0.195698 + 0.195698i
\(471\) 0 0
\(472\) −20.0000 20.0000i −0.920575 0.920575i
\(473\) 49.4975i 2.27590i
\(474\) 0 0
\(475\) −16.0000 + 16.0000i −0.734130 + 0.734130i
\(476\) 25.4558i 1.16677i
\(477\) 0 0
\(478\) 36.0000i 1.64660i
\(479\) −4.24264 −0.193851 −0.0969256 0.995292i \(-0.530901\pi\)
−0.0969256 + 0.995292i \(0.530901\pi\)
\(480\) 0 0
\(481\) −4.00000 −0.182384
\(482\) 5.65685i 0.257663i
\(483\) 0 0
\(484\) 28.0000i 1.27273i
\(485\) −4.94975 + 4.94975i −0.224756 + 0.224756i
\(486\) 0 0
\(487\) 12.0000i 0.543772i −0.962329 0.271886i \(-0.912353\pi\)
0.962329 0.271886i \(-0.0876473\pi\)
\(488\) 28.2843 28.2843i 1.28037 1.28037i
\(489\) 0 0
\(490\) −2.00000 2.00000i −0.0903508 0.0903508i
\(491\) 4.94975 4.94975i 0.223379 0.223379i −0.586541 0.809920i \(-0.699511\pi\)
0.809920 + 0.586541i \(0.199511\pi\)
\(492\) 0 0
\(493\) 12.0000 + 12.0000i 0.540453 + 0.540453i
\(494\) −11.3137 −0.509028
\(495\) 0 0
\(496\) −28.0000 −1.25724
\(497\) −46.6690 −2.09339
\(498\) 0 0
\(499\) −23.0000 23.0000i −1.02962 1.02962i −0.999548 0.0300737i \(-0.990426\pi\)
−0.0300737 0.999548i \(-0.509574\pi\)
\(500\) −12.7279 12.7279i −0.569210 0.569210i
\(501\) 0 0
\(502\) −2.00000 2.00000i −0.0892644 0.0892644i
\(503\) 22.6274i 1.00891i −0.863439 0.504453i \(-0.831694\pi\)
0.863439 0.504453i \(-0.168306\pi\)
\(504\) 0 0
\(505\) 7.00000i 0.311496i
\(506\) 14.1421 14.1421i 0.628695 0.628695i
\(507\) 0 0
\(508\) 26.0000 1.15356
\(509\) −4.94975 4.94975i −0.219394 0.219394i 0.588849 0.808243i \(-0.299581\pi\)
−0.808243 + 0.588849i \(0.799581\pi\)
\(510\) 0 0
\(511\) 45.0000 1.99068
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) 42.0000i 1.85254i
\(515\) 4.24264 + 4.24264i 0.186953 + 0.186953i
\(516\) 0 0
\(517\) −15.0000 + 15.0000i −0.659699 + 0.659699i
\(518\) 8.48528 8.48528i 0.372822 0.372822i
\(519\) 0 0
\(520\) 4.00000i 0.175412i
\(521\) 26.8701i 1.17720i −0.808425 0.588599i \(-0.799680\pi\)
0.808425 0.588599i \(-0.200320\pi\)
\(522\) 0 0
\(523\) −23.0000 + 23.0000i −1.00572 + 1.00572i −0.00573623 + 0.999984i \(0.501826\pi\)
−0.999984 + 0.00573623i \(0.998174\pi\)
\(524\) 1.41421 + 1.41421i 0.0617802 + 0.0617802i
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 29.6985 1.29369
\(528\) 0 0
\(529\) 15.0000 0.652174
\(530\) 1.41421 0.0614295
\(531\) 0 0
\(532\) 24.0000 24.0000i 1.04053 1.04053i
\(533\) 5.65685 5.65685i 0.245026 0.245026i
\(534\) 0 0
\(535\) 11.0000i 0.475571i
\(536\) 2.82843 2.82843i 0.122169 0.122169i
\(537\) 0 0
\(538\) 16.0000 16.0000i 0.689809 0.689809i
\(539\) 7.07107 7.07107i 0.304572 0.304572i
\(540\) 0 0
\(541\) −2.00000 2.00000i −0.0859867 0.0859867i 0.662805 0.748792i \(-0.269366\pi\)
−0.748792 + 0.662805i \(0.769366\pi\)
\(542\) 18.3848i 0.789694i
\(543\) 0 0
\(544\) 24.0000i 1.02899i
\(545\) 14.1421 0.605783
\(546\) 0 0
\(547\) −5.00000 5.00000i −0.213785 0.213785i 0.592088 0.805873i \(-0.298304\pi\)
−0.805873 + 0.592088i \(0.798304\pi\)
\(548\) 36.7696i 1.57072i
\(549\) 0 0
\(550\) 20.0000 20.0000i 0.852803 0.852803i
\(551\) 22.6274i 0.963960i
\(552\) 0 0
\(553\) 6.00000i 0.255146i
\(554\) −28.2843 28.2843i −1.20168 1.20168i
\(555\) 0 0
\(556\) −20.0000 + 20.0000i −0.848189 + 0.848189i
\(557\) −9.19239 9.19239i −0.389494 0.389494i 0.485013 0.874507i \(-0.338815\pi\)
−0.874507 + 0.485013i \(0.838815\pi\)
\(558\) 0 0
\(559\) 14.0000 0.592137
\(560\) 8.48528 + 8.48528i 0.358569 + 0.358569i
\(561\) 0 0
\(562\) −34.0000 −1.43420
\(563\) −0.707107 0.707107i −0.0298010 0.0298010i 0.692049 0.721850i \(-0.256708\pi\)
−0.721850 + 0.692049i \(0.756708\pi\)
\(564\) 0 0
\(565\) 6.00000 6.00000i 0.252422 0.252422i
\(566\) 5.65685 + 5.65685i 0.237775 + 0.237775i
\(567\) 0 0
\(568\) 44.0000 1.84620
\(569\) 5.65685i 0.237148i −0.992945 0.118574i \(-0.962168\pi\)
0.992945 0.118574i \(-0.0378322\pi\)
\(570\) 0 0
\(571\) 7.00000 7.00000i 0.292941 0.292941i −0.545300 0.838241i \(-0.683584\pi\)
0.838241 + 0.545300i \(0.183584\pi\)
\(572\) 14.1421 0.591312
\(573\) 0 0
\(574\) 24.0000i 1.00174i
\(575\) −11.3137 −0.471814
\(576\) 0 0
\(577\) 32.0000 1.33218 0.666089 0.745873i \(-0.267967\pi\)
0.666089 + 0.745873i \(0.267967\pi\)
\(578\) 1.41421i 0.0588235i
\(579\) 0 0
\(580\) 8.00000 0.332182
\(581\) −23.3345 + 23.3345i −0.968079 + 0.968079i
\(582\) 0 0
\(583\) 5.00000i 0.207079i
\(584\) −42.4264 −1.75562
\(585\) 0 0
\(586\) −20.0000 20.0000i −0.826192 0.826192i
\(587\) −7.77817 + 7.77817i −0.321040 + 0.321040i −0.849166 0.528126i \(-0.822895\pi\)
0.528126 + 0.849166i \(0.322895\pi\)
\(588\) 0 0
\(589\) −28.0000 28.0000i −1.15372 1.15372i
\(590\) 14.1421 0.582223
\(591\) 0 0
\(592\) −8.00000 + 8.00000i −0.328798 + 0.328798i
\(593\) −29.6985 −1.21957 −0.609785 0.792567i \(-0.708744\pi\)
−0.609785 + 0.792567i \(0.708744\pi\)
\(594\) 0 0
\(595\) −9.00000 9.00000i −0.368964 0.368964i
\(596\) −9.89949 + 9.89949i −0.405499 + 0.405499i
\(597\) 0 0
\(598\) −4.00000 4.00000i −0.163572 0.163572i
\(599\) 41.0122i 1.67571i 0.545891 + 0.837856i \(0.316191\pi\)
−0.545891 + 0.837856i \(0.683809\pi\)
\(600\) 0 0
\(601\) 27.0000i 1.10135i 0.834719 + 0.550676i \(0.185630\pi\)
−0.834719 + 0.550676i \(0.814370\pi\)
\(602\) −29.6985 + 29.6985i −1.21042 + 1.21042i
\(603\) 0 0
\(604\) 42.0000i 1.70896i
\(605\) −9.89949 9.89949i −0.402472 0.402472i
\(606\) 0 0
\(607\) 20.0000 0.811775 0.405887 0.913923i \(-0.366962\pi\)
0.405887 + 0.913923i \(0.366962\pi\)
\(608\) −22.6274 + 22.6274i −0.917663 + 0.917663i
\(609\) 0 0
\(610\) 20.0000i 0.809776i
\(611\) 4.24264 + 4.24264i 0.171639 + 0.171639i
\(612\) 0 0
\(613\) 1.00000 1.00000i 0.0403896 0.0403896i −0.686624 0.727013i \(-0.740908\pi\)
0.727013 + 0.686624i \(0.240908\pi\)
\(614\) −9.89949 + 9.89949i −0.399511 + 0.399511i
\(615\) 0 0
\(616\) −30.0000 + 30.0000i −1.20873 + 1.20873i
\(617\) 2.82843i 0.113868i 0.998378 + 0.0569341i \(0.0181325\pi\)
−0.998378 + 0.0569341i \(0.981868\pi\)
\(618\) 0 0
\(619\) 1.00000 1.00000i 0.0401934 0.0401934i −0.686724 0.726918i \(-0.740952\pi\)
0.726918 + 0.686724i \(0.240952\pi\)
\(620\) 9.89949 9.89949i 0.397573 0.397573i
\(621\) 0 0
\(622\) −28.0000 −1.12270
\(623\) 4.24264 0.169978
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) −38.1838 −1.52613
\(627\) 0 0
\(628\) 4.00000 + 4.00000i 0.159617 + 0.159617i
\(629\) 8.48528 8.48528i 0.338330 0.338330i
\(630\) 0 0
\(631\) 15.0000i 0.597141i −0.954388 0.298570i \(-0.903490\pi\)
0.954388 0.298570i \(-0.0965097\pi\)
\(632\) 5.65685i 0.225018i
\(633\) 0 0
\(634\) −35.0000 + 35.0000i −1.39003 + 1.39003i
\(635\) −9.19239 + 9.19239i −0.364789 + 0.364789i
\(636\) 0 0
\(637\) −2.00000 2.00000i −0.0792429 0.0792429i
\(638\) 28.2843i 1.11979i
\(639\) 0 0
\(640\) −8.00000 8.00000i −0.316228 0.316228i
\(641\) 42.4264 1.67574 0.837871 0.545868i \(-0.183800\pi\)
0.837871 + 0.545868i \(0.183800\pi\)
\(642\) 0 0
\(643\) 10.0000 + 10.0000i 0.394362 + 0.394362i 0.876239 0.481877i \(-0.160045\pi\)
−0.481877 + 0.876239i \(0.660045\pi\)
\(644\) 16.9706 0.668734
\(645\) 0 0
\(646\) 24.0000 24.0000i 0.944267 0.944267i
\(647\) 28.2843i 1.11197i 0.831193 + 0.555985i \(0.187659\pi\)
−0.831193 + 0.555985i \(0.812341\pi\)
\(648\) 0 0
\(649\) 50.0000i 1.96267i
\(650\) −5.65685 5.65685i −0.221880 0.221880i
\(651\) 0 0
\(652\) 10.0000 + 10.0000i 0.391630 + 0.391630i
\(653\) −21.9203 21.9203i −0.857808 0.857808i 0.133272 0.991080i \(-0.457452\pi\)
−0.991080 + 0.133272i \(0.957452\pi\)
\(654\) 0 0
\(655\) −1.00000 −0.0390732
\(656\) 22.6274i 0.883452i
\(657\) 0 0
\(658\) −18.0000 −0.701713
\(659\) −9.19239 9.19239i −0.358085 0.358085i 0.505022 0.863107i \(-0.331484\pi\)
−0.863107 + 0.505022i \(0.831484\pi\)
\(660\) 0 0
\(661\) 16.0000 16.0000i 0.622328 0.622328i −0.323798 0.946126i \(-0.604960\pi\)
0.946126 + 0.323798i \(0.104960\pi\)
\(662\) 9.89949 + 9.89949i 0.384755 + 0.384755i
\(663\) 0 0
\(664\) 22.0000 22.0000i 0.853766 0.853766i
\(665\) 16.9706i 0.658090i
\(666\) 0 0
\(667\) 8.00000 8.00000i 0.309761 0.309761i
\(668\) 14.1421i 0.547176i
\(669\) 0 0
\(670\) 2.00000i 0.0772667i
\(671\) −70.7107 −2.72976
\(672\) 0 0
\(673\) −7.00000 −0.269830 −0.134915 0.990857i \(-0.543076\pi\)
−0.134915 + 0.990857i \(0.543076\pi\)
\(674\) 28.2843i 1.08947i
\(675\) 0 0
\(676\) 22.0000i 0.846154i
\(677\) −22.6274 + 22.6274i −0.869642 + 0.869642i −0.992433 0.122790i \(-0.960816\pi\)
0.122790 + 0.992433i \(0.460816\pi\)
\(678\) 0 0
\(679\) 21.0000i 0.805906i
\(680\) 8.48528 + 8.48528i 0.325396 + 0.325396i
\(681\) 0 0
\(682\) 35.0000 + 35.0000i 1.34022 + 1.34022i
\(683\) 11.3137 11.3137i 0.432907 0.432907i −0.456709 0.889616i \(-0.650972\pi\)
0.889616 + 0.456709i \(0.150972\pi\)
\(684\) 0 0
\(685\) −13.0000 13.0000i −0.496704 0.496704i
\(686\) −21.2132 −0.809924
\(687\) 0 0
\(688\) 28.0000 28.0000i 1.06749 1.06749i
\(689\) 1.41421 0.0538772
\(690\) 0 0
\(691\) 16.0000 + 16.0000i 0.608669 + 0.608669i 0.942598 0.333929i \(-0.108375\pi\)
−0.333929 + 0.942598i \(0.608375\pi\)
\(692\) −15.5563 15.5563i −0.591364 0.591364i
\(693\) 0 0
\(694\) 25.0000 + 25.0000i 0.948987 + 0.948987i
\(695\) 14.1421i 0.536442i
\(696\) 0 0
\(697\) 24.0000i 0.909065i
\(698\) −5.65685 + 5.65685i −0.214115 + 0.214115i
\(699\) 0 0
\(700\) 24.0000 0.907115
\(701\) −0.707107 0.707107i −0.0267071 0.0267071i 0.693627 0.720334i \(-0.256012\pi\)
−0.720334 + 0.693627i \(0.756012\pi\)
\(702\) 0 0
\(703\) −16.0000 −0.603451
\(704\) 28.2843 28.2843i 1.06600 1.06600i
\(705\) 0 0
\(706\) 0 0
\(707\) 14.8492 + 14.8492i 0.558463 + 0.558463i
\(708\) 0 0
\(709\) 22.0000 22.0000i 0.826227 0.826227i −0.160765 0.986993i \(-0.551396\pi\)
0.986993 + 0.160765i \(0.0513962\pi\)
\(710\) −15.5563 + 15.5563i −0.583819 + 0.583819i
\(711\) 0 0
\(712\) −4.00000 −0.149906
\(713\) 19.7990i 0.741478i
\(714\) 0 0
\(715\) −5.00000 + 5.00000i −0.186989 + 0.186989i
\(716\) −15.5563 15.5563i −0.581368 0.581368i
\(717\) 0 0
\(718\) 50.0000 1.86598
\(719\) 16.9706 0.632895 0.316448 0.948610i \(-0.397510\pi\)
0.316448 + 0.948610i \(0.397510\pi\)
\(720\) 0 0
\(721\) −18.0000 −0.670355
\(722\) −18.3848 −0.684211
\(723\) 0 0
\(724\) −32.0000 + 32.0000i −1.18927 + 1.18927i
\(725\) 11.3137 11.3137i 0.420181 0.420181i
\(726\) 0 0
\(727\) 9.00000i 0.333792i −0.985975 0.166896i \(-0.946626\pi\)
0.985975 0.166896i \(-0.0533743\pi\)
\(728\) 8.48528 + 8.48528i 0.314485 + 0.314485i
\(729\) 0 0
\(730\) 15.0000 15.0000i 0.555175 0.555175i
\(731\) −29.6985 + 29.6985i −1.09844 + 1.09844i
\(732\) 0 0
\(733\) −26.0000 26.0000i −0.960332 0.960332i 0.0389108 0.999243i \(-0.487611\pi\)
−0.999243 + 0.0389108i \(0.987611\pi\)
\(734\) 15.5563i 0.574195i
\(735\) 0 0
\(736\) −16.0000 −0.589768
\(737\) −7.07107 −0.260466
\(738\) 0 0
\(739\) −29.0000 29.0000i −1.06678 1.06678i −0.997604 0.0691779i \(-0.977962\pi\)
−0.0691779 0.997604i \(-0.522038\pi\)
\(740\) 5.65685i 0.207950i
\(741\) 0 0
\(742\) −3.00000 + 3.00000i −0.110133 + 0.110133i
\(743\) 41.0122i 1.50459i 0.658826 + 0.752296i \(0.271054\pi\)
−0.658826 + 0.752296i \(0.728946\pi\)
\(744\) 0 0
\(745\) 7.00000i 0.256460i
\(746\) 1.41421 + 1.41421i 0.0517780 + 0.0517780i
\(747\) 0 0
\(748\) −30.0000 + 30.0000i −1.09691 + 1.09691i
\(749\) −23.3345 23.3345i −0.852625 0.852625i
\(750\) 0 0
\(751\) −1.00000 −0.0364905 −0.0182453 0.999834i \(-0.505808\pi\)
−0.0182453 + 0.999834i \(0.505808\pi\)
\(752\) 16.9706 0.618853
\(753\) 0 0
\(754\) 8.00000 0.291343
\(755\) −14.8492 14.8492i −0.540419 0.540419i
\(756\) 0 0
\(757\) 13.0000 13.0000i 0.472493 0.472493i −0.430227 0.902721i \(-0.641567\pi\)
0.902721 + 0.430227i \(0.141567\pi\)
\(758\) −2.82843 2.82843i −0.102733 0.102733i
\(759\) 0 0
\(760\) 16.0000i 0.580381i
\(761\) 31.1127i 1.12783i −0.825831 0.563917i \(-0.809294\pi\)
0.825831 0.563917i \(-0.190706\pi\)
\(762\) 0 0
\(763\) −30.0000 + 30.0000i −1.08607 + 1.08607i
\(764\) −8.48528 −0.306987
\(765\) 0 0
\(766\) 6.00000i 0.216789i
\(767\) 14.1421 0.510643
\(768\) 0 0
\(769\) 11.0000 0.396670 0.198335 0.980134i \(-0.436447\pi\)
0.198335 + 0.980134i \(0.436447\pi\)
\(770\) 21.2132i 0.764471i
\(771\) 0 0
\(772\) 14.0000 0.503871
\(773\) 7.07107 7.07107i 0.254329 0.254329i −0.568414 0.822743i \(-0.692443\pi\)
0.822743 + 0.568414i \(0.192443\pi\)
\(774\) 0 0
\(775\) 28.0000i 1.00579i
\(776\) 19.7990i 0.710742i
\(777\) 0 0
\(778\) 13.0000 + 13.0000i 0.466073 + 0.466073i
\(779\) 22.6274 22.6274i 0.810711 0.810711i
\(780\) 0 0
\(781\) −55.0000 55.0000i −1.96805 1.96805i
\(782\) 16.9706 0.606866
\(783\) 0 0
\(784\) −8.00000 −0.285714
\(785\) −2.82843 −0.100951
\(786\) 0 0
\(787\) −26.0000 26.0000i −0.926800 0.926800i 0.0706979 0.997498i \(-0.477477\pi\)
−0.997498 + 0.0706979i \(0.977477\pi\)
\(788\) 32.5269 32.5269i 1.15872 1.15872i
\(789\) 0 0
\(790\) 2.00000 + 2.00000i 0.0711568 + 0.0711568i
\(791\) 25.4558i 0.905106i
\