Properties

Label 432.2.k.b.325.2
Level $432$
Weight $2$
Character 432.325
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 325.2
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 432.325
Dual form 432.2.k.b.109.1

$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 \(-0.321783\pi\)
−0.847316 + 0.531089i \(0.821783\pi\)
\(6\) 0 0
\(7\) 3.00000i 1.13389i −0.823754 0.566947i \(-0.808125\pi\)
0.823754 0.566947i \(-0.191875\pi\)
\(8\) 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 0.997662 + 0.0683416i \(0.0217708\pi\)
0.0683416 + 0.997662i \(0.478229\pi\)
\(12\) 0 0
\(13\) 1.00000 1.00000i 0.277350 0.277350i −0.554700 0.832050i \(-0.687167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 4.24264 1.13389
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) 4.24264 1.02899 0.514496 0.857493i \(-0.327979\pi\)
0.514496 + 0.857493i \(0.327979\pi\)
\(18\) 0 0
\(19\) 4.00000 4.00000i 0.917663 0.917663i −0.0791961 0.996859i \(-0.525235\pi\)
0.996859 + 0.0791961i \(0.0252353\pi\)
\(20\) 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 \(-0.628881\pi\)
0.919145 + 0.393919i \(0.128881\pi\)
\(30\) 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 0.523331 0.852129i \(-0.324689\pi\)
−0.852129 + 0.523331i \(0.824689\pi\)
\(38\) 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 0.997551 + 0.0699387i \(0.0222804\pi\)
0.0699387 + 0.997551i \(0.477720\pi\)
\(44\) −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 \(-0.600137\pi\)
−0.309426 + 0.950923i \(0.600137\pi\)
\(48\) 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 \(-0.271879\pi\)
−0.754001 + 0.656873i \(0.771879\pi\)
\(54\) 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 \(-0.475627\pi\)
−0.997070 + 0.0764953i \(0.975627\pi\)
\(60\) 0 0
\(61\) 10.0000 10.0000i 1.28037 1.28037i 0.339911 0.940457i \(-0.389603\pi\)
0.940457 0.339911i \(-0.110397\pi\)
\(62\) 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 −0.643379 0.765548i \(-0.722468\pi\)
0.765548 + 0.643379i \(0.222468\pi\)
\(68\) −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 \(0.340995\pi\)
−0.479012 + 0.877809i \(0.659005\pi\)
\(74\) 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 \(-0.956309\pi\)
0.136829 + 0.990595i \(0.456309\pi\)
\(84\) 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 \(-0.363228\pi\)
−0.909099 + 0.416581i \(0.863228\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i −0.955312 0.295599i \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) −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 \(-0.0715515\pi\)
−0.222897 + 0.974842i \(0.571551\pi\)
\(108\) 0 0
\(109\) 10.0000 10.0000i 0.957826 0.957826i −0.0413197 0.999146i \(-0.513156\pi\)
0.999146 + 0.0413197i \(0.0131562\pi\)
\(110\) 7.07107 0.674200
\(111\) 0 0
\(112\) 12.0000i 1.13389i
\(113\) −8.48528 −0.798228 −0.399114 0.916901i \(-0.630682\pi\)
−0.399114 + 0.916901i \(0.630682\pi\)
\(114\) 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 \(-0.736090\pi\)
0.737322 + 0.675542i \(0.236090\pi\)
\(132\) 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 0.989907 0.141718i \(-0.0452627\pi\)
−0.141718 + 0.989907i \(0.545263\pi\)
\(140\) 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 \(-0.342569\pi\)
−0.880166 + 0.474667i \(0.842569\pi\)
\(150\) 0 0
\(151\) 21.0000i 1.70896i 0.519488 + 0.854478i \(0.326123\pi\)
−0.519488 + 0.854478i \(0.673877\pi\)
\(152\) −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 −0.782397 0.622780i \(-0.786003\pi\)
0.622780 + 0.782397i \(0.286003\pi\)
\(158\) 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 −0.875268 0.483638i \(-0.839315\pi\)
0.483638 + 0.875268i \(0.339315\pi\)
\(164\) 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 \(-0.887324\pi\)
0.346636 + 0.938000i \(0.387324\pi\)
\(174\) 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 \(-0.884852\pi\)
0.353911 + 0.935279i \(0.384852\pi\)
\(180\) 0 0
\(181\) 16.0000 + 16.0000i 1.18927 + 1.18927i 0.977269 + 0.212001i \(0.0679981\pi\)
0.212001 + 0.977269i \(0.432002\pi\)
\(182\) 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 \(-0.549052\pi\)
−0.153493 + 0.988150i \(0.549052\pi\)
\(192\) 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 0.984750 + 0.173973i \(0.0556605\pi\)
0.173973 + 0.984750i \(0.444340\pi\)
\(198\) 0 0
\(199\) 15.0000i 1.06332i −0.846957 0.531661i \(-0.821568\pi\)
0.846957 0.531661i \(-0.178432\pi\)
\(200\) −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 −0.555887 0.831258i \(-0.687621\pi\)
0.831258 + 0.555887i \(0.187621\pi\)
\(212\) 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 \(-0.642323\pi\)
0.901695 + 0.432372i \(0.142323\pi\)
\(228\) 0 0
\(229\) 7.00000 + 7.00000i 0.462573 + 0.462573i 0.899498 0.436925i \(-0.143932\pi\)
−0.436925 + 0.899498i \(0.643932\pi\)
\(230\) 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 \(-0.192130\pi\)
0.823301 + 0.567605i \(0.192130\pi\)
\(240\) 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 \(-0.229895\pi\)
−0.661065 + 0.750329i \(0.729895\pi\)
\(252\) 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 \(-0.877004\pi\)
−0.926270 + 0.376860i \(0.877004\pi\)
\(258\) 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 \(-0.587811\pi\)
0.962190 + 0.272381i \(0.0878110\pi\)
\(270\) 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 −0.973654 0.228029i \(-0.926772\pi\)
−0.228029 0.973654i \(-0.573228\pi\)
\(278\) −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 0.815928 0.578153i \(-0.196226\pi\)
−0.578153 + 0.815928i \(0.696226\pi\)
\(284\) 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 \(-0.0514059\pi\)
−0.160795 + 0.986988i \(0.551406\pi\)
\(294\) 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 −0.478549 0.878061i \(-0.658837\pi\)
0.878061 + 0.478549i \(0.158837\pi\)
\(308\) −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 \(-0.723694\pi\)
0.646322 0.763065i \(-0.276306\pi\)
\(314\) −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 −0.564799 + 0.825228i \(0.691046\pi\)
−0.825228 + 0.564799i \(0.808954\pi\)
\(318\) 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 0.872812 0.488057i \(-0.162294\pi\)
−0.488057 + 0.872812i \(0.662294\pi\)
\(332\) 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 \(-0.484150\pi\)
−0.998761 + 0.0497735i \(0.984150\pi\)
\(348\) 0 0
\(349\) 4.00000 4.00000i 0.214115 0.214115i −0.591898 0.806013i \(-0.701621\pi\)
0.806013 + 0.591898i \(0.201621\pi\)
\(350\) 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 0.732522 0.680744i \(-0.238343\pi\)
−0.680744 + 0.732522i \(0.738343\pi\)
\(374\) −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 0.653872 0.756605i \(-0.273143\pi\)
−0.756605 + 0.653872i \(0.773143\pi\)
\(380\) 11.3137 0.580381
\(381\) 0 0
\(382\) 6.00000i 0.306987i
\(383\) 4.24264 0.216789 0.108394 0.994108i \(-0.465429\pi\)
0.108394 + 0.994108i \(0.465429\pi\)
\(384\) 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 \(-0.356901\pi\)
−0.900640 + 0.434567i \(0.856901\pi\)
\(390\) 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 −0.821357 0.570414i \(-0.806783\pi\)
0.570414 + 0.821357i \(0.306783\pi\)
\(398\) 21.2132 1.06332
\(399\) 0 0
\(400\) 16.0000i 0.800000i
\(401\) −8.48528 −0.423735 −0.211867 0.977298i \(-0.567954\pi\)
−0.211867 + 0.977298i \(0.567954\pi\)
\(402\) 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 \(-0.976369\pi\)
0.997246 0.0741702i \(-0.0236308\pi\)
\(410\) −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 \(-0.671453\pi\)
0.858409 + 0.512965i \(0.171453\pi\)
\(420\) 0 0
\(421\) 16.0000 + 16.0000i 0.779792 + 0.779792i 0.979795 0.200003i \(-0.0640952\pi\)
−0.200003 + 0.979795i \(0.564095\pi\)
\(422\) 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 \(-0.467418\pi\)
0.102180 + 0.994766i \(0.467418\pi\)
\(432\) 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 \(-0.883474\pi\)
0.933739 0.357955i \(-0.116526\pi\)
\(440\) −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 \(-0.142081\pi\)
−0.431685 + 0.902024i \(0.642081\pi\)
\(444\) 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 \(-0.631145\pi\)
−0.400445 + 0.916321i \(0.631145\pi\)
\(450\) 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 \(0.0223532\pi\)
−0.997535 + 0.0701670i \(0.977647\pi\)
\(458\) −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 −0.166647 + 0.986017i \(0.553294\pi\)
−0.986017 + 0.166647i \(0.946706\pi\)
\(462\) 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 \(-0.786907\pi\)
0.620557 + 0.784162i \(0.286907\pi\)
\(468\) 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 \(-0.469099\pi\)
0.0969256 + 0.995292i \(0.469099\pi\)
\(480\) 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 \(0.0876473\pi\)
−0.962329 + 0.271886i \(0.912353\pi\)
\(488\) −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 \(-0.300489\pi\)
−0.809920 + 0.586541i \(0.800489\pi\)
\(492\) 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 −0.0300737 + 0.999548i \(0.509574\pi\)
−0.999548 + 0.0300737i \(0.990426\pi\)
\(500\) 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 \(-0.700419\pi\)
0.808243 + 0.588849i \(0.200419\pi\)
\(510\) 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 −0.999984 0.00573623i \(-0.998174\pi\)
−0.00573623 0.999984i \(-0.501826\pi\)
\(524\) −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 −0.748792 0.662805i \(-0.769366\pi\)
0.662805 + 0.748792i \(0.269366\pi\)
\(542\) 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 −0.805873 0.592088i \(-0.798304\pi\)
0.592088 + 0.805873i \(0.298304\pi\)
\(548\) 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 \(-0.661185\pi\)
0.874507 + 0.485013i \(0.161185\pi\)
\(558\) 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 \(-0.743292\pi\)
0.721850 + 0.692049i \(0.243292\pi\)
\(564\) 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 0.838241 0.545300i \(-0.183584\pi\)
−0.545300 + 0.838241i \(0.683584\pi\)
\(572\) −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 \(-0.177105\pi\)
−0.528126 + 0.849166i \(0.677105\pi\)
\(588\) 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 \(-0.291256\pi\)
0.609785 + 0.792567i \(0.291256\pi\)
\(594\) 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 \(-0.814370\pi\)
0.834719 0.550676i \(-0.185630\pi\)
\(602\) 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 0.727013 0.686624i \(-0.240908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) 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 0.726918 0.686724i \(-0.240952\pi\)
−0.686724 + 0.726918i \(0.740952\pi\)
\(620\) −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 \(0.0965097\pi\)
−0.954388 + 0.298570i \(0.903490\pi\)
\(632\) 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 \(-0.816200\pi\)
−0.837871 + 0.545868i \(0.816200\pi\)
\(642\) 0 0
\(643\) 10.0000 10.0000i 0.394362 0.394362i −0.481877 0.876239i \(-0.660045\pi\)
0.876239 + 0.481877i \(0.160045\pi\)
\(644\) −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 \(-0.542548\pi\)
0.991080 + 0.133272i \(0.0425482\pi\)
\(654\) 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 \(-0.668516\pi\)
0.863107 + 0.505022i \(0.168516\pi\)
\(660\) 0 0
\(661\) 16.0000 + 16.0000i 0.622328 + 0.622328i 0.946126 0.323798i \(-0.104960\pi\)
−0.323798 + 0.946126i \(0.604960\pi\)
\(662\) −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 \(-0.0391843\pi\)
−0.122790 + 0.992433i \(0.539184\pi\)
\(678\) 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 \(-0.349028\pi\)
−0.889616 + 0.456709i \(0.849028\pi\)
\(684\) 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 −0.333929 0.942598i \(-0.608375\pi\)
0.942598 + 0.333929i \(0.108375\pi\)
\(692\) 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 \(-0.743988\pi\)
0.720334 + 0.693627i \(0.243988\pi\)
\(702\) 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 0.986993 0.160765i \(-0.0513962\pi\)
−0.160765 + 0.986993i \(0.551396\pi\)
\(710\) 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 \(-0.602490\pi\)
−0.316448 + 0.948610i \(0.602490\pi\)
\(720\) 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 \(0.0533743\pi\)
−0.985975 + 0.166896i \(0.946626\pi\)
\(728\) −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 −0.999243 0.0389108i \(-0.987611\pi\)
0.0389108 + 0.999243i \(0.487611\pi\)
\(734\) 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 −0.0691779 + 0.997604i \(0.522038\pi\)
−0.997604 + 0.0691779i \(0.977962\pi\)
\(740\) 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 0.902721 0.430227i \(-0.141567\pi\)
−0.430227 + 0.902721i \(0.641567\pi\)
\(758\) 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 \(-0.307557\pi\)
−0.822743 + 0.568414i \(0.807557\pi\)
\(774\) 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 −0.997498 0.0706979i \(-0.977477\pi\)
0.0706979 + 0.997498i \(0.477477\pi\)
\(788\) −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
\(792\)