Properties

Label 342.2.s.b.179.1
Level $342$
Weight $2$
Character 342.179
Analytic conductor $2.731$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 342.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.73088374913\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 179.1
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 342.179
Dual form 342.2.s.b.107.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 - 0.707107i) q^{5} -3.44949 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 - 0.707107i) q^{5} -3.44949 q^{7} -1.00000 q^{8} +(-1.22474 + 0.707107i) q^{10} -6.29253i q^{11} +(-2.17423 + 1.25529i) q^{13} +(-1.72474 + 2.98735i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.22474 - 2.43916i) q^{17} +(4.00000 + 1.73205i) q^{19} +1.41421i q^{20} +(-5.44949 - 3.14626i) q^{22} +(4.89898 - 2.82843i) q^{23} +(-1.50000 - 2.59808i) q^{25} +2.51059i q^{26} +(1.72474 + 2.98735i) q^{28} +(1.22474 + 2.12132i) q^{29} +9.43879i q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.22474 + 2.43916i) q^{34} +(4.22474 + 2.43916i) q^{35} -5.97469i q^{37} +(3.50000 - 2.59808i) q^{38} +(1.22474 + 0.707107i) q^{40} +(2.94949 - 5.10867i) q^{43} +(-5.44949 + 3.14626i) q^{44} -5.65685i q^{46} +(4.22474 - 2.43916i) q^{47} +4.89898 q^{49} -3.00000 q^{50} +(2.17423 + 1.25529i) q^{52} +(-2.44949 - 4.24264i) q^{53} +(-4.44949 + 7.70674i) q^{55} +3.44949 q^{56} +2.44949 q^{58} +(-4.77526 + 8.27098i) q^{59} +(-0.724745 - 1.25529i) q^{61} +(8.17423 + 4.71940i) q^{62} +1.00000 q^{64} +3.55051 q^{65} +(5.84847 - 3.37662i) q^{67} +4.87832i q^{68} +(4.22474 - 2.43916i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(5.94949 - 10.3048i) q^{73} +(-5.17423 - 2.98735i) q^{74} +(-0.500000 - 4.33013i) q^{76} +21.7060i q^{77} +(8.17423 + 4.71940i) q^{79} +(1.22474 - 0.707107i) q^{80} -8.97809i q^{83} +(3.44949 + 5.97469i) q^{85} +(-2.94949 - 5.10867i) q^{86} +6.29253i q^{88} +(-6.12372 - 10.6066i) q^{89} +(7.50000 - 4.33013i) q^{91} +(-4.89898 - 2.82843i) q^{92} -4.87832i q^{94} +(-3.67423 - 4.94975i) q^{95} +(-1.65153 - 0.953512i) q^{97} +(2.44949 - 4.24264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} - 4q^{7} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} - 4q^{7} - 4q^{8} + 6q^{13} - 2q^{14} - 2q^{16} - 12q^{17} + 16q^{19} - 12q^{22} - 6q^{25} + 2q^{28} + 2q^{32} - 12q^{34} + 12q^{35} + 14q^{38} + 2q^{43} - 12q^{44} + 12q^{47} - 12q^{50} - 6q^{52} - 8q^{55} + 4q^{56} - 24q^{59} + 2q^{61} + 18q^{62} + 4q^{64} + 24q^{65} - 6q^{67} + 12q^{70} - 12q^{71} + 14q^{73} - 6q^{74} - 2q^{76} + 18q^{79} + 4q^{85} - 2q^{86} + 30q^{91} - 36q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.22474 0.707107i −0.547723 0.316228i 0.200480 0.979698i \(-0.435750\pi\)
−0.748203 + 0.663470i \(0.769083\pi\)
\(6\) 0 0
\(7\) −3.44949 −1.30378 −0.651892 0.758312i \(-0.726025\pi\)
−0.651892 + 0.758312i \(0.726025\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.22474 + 0.707107i −0.387298 + 0.223607i
\(11\) 6.29253i 1.89727i −0.316374 0.948634i \(-0.602466\pi\)
0.316374 0.948634i \(-0.397534\pi\)
\(12\) 0 0
\(13\) −2.17423 + 1.25529i −0.603024 + 0.348156i −0.770230 0.637766i \(-0.779859\pi\)
0.167206 + 0.985922i \(0.446525\pi\)
\(14\) −1.72474 + 2.98735i −0.460957 + 0.798402i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −4.22474 2.43916i −1.02465 0.591583i −0.109203 0.994019i \(-0.534830\pi\)
−0.915448 + 0.402437i \(0.868163\pi\)
\(18\) 0 0
\(19\) 4.00000 + 1.73205i 0.917663 + 0.397360i
\(20\) 1.41421i 0.316228i
\(21\) 0 0
\(22\) −5.44949 3.14626i −1.16184 0.670786i
\(23\) 4.89898 2.82843i 1.02151 0.589768i 0.106967 0.994263i \(-0.465886\pi\)
0.914540 + 0.404495i \(0.132553\pi\)
\(24\) 0 0
\(25\) −1.50000 2.59808i −0.300000 0.519615i
\(26\) 2.51059i 0.492367i
\(27\) 0 0
\(28\) 1.72474 + 2.98735i 0.325946 + 0.564555i
\(29\) 1.22474 + 2.12132i 0.227429 + 0.393919i 0.957046 0.289938i \(-0.0936346\pi\)
−0.729616 + 0.683857i \(0.760301\pi\)
\(30\) 0 0
\(31\) 9.43879i 1.69526i 0.530590 + 0.847629i \(0.321970\pi\)
−0.530590 + 0.847629i \(0.678030\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −4.22474 + 2.43916i −0.724538 + 0.418312i
\(35\) 4.22474 + 2.43916i 0.714112 + 0.412293i
\(36\) 0 0
\(37\) 5.97469i 0.982233i −0.871094 0.491117i \(-0.836589\pi\)
0.871094 0.491117i \(-0.163411\pi\)
\(38\) 3.50000 2.59808i 0.567775 0.421464i
\(39\) 0 0
\(40\) 1.22474 + 0.707107i 0.193649 + 0.111803i
\(41\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) 0 0
\(43\) 2.94949 5.10867i 0.449793 0.779064i −0.548579 0.836099i \(-0.684831\pi\)
0.998372 + 0.0570343i \(0.0181644\pi\)
\(44\) −5.44949 + 3.14626i −0.821541 + 0.474317i
\(45\) 0 0
\(46\) 5.65685i 0.834058i
\(47\) 4.22474 2.43916i 0.616242 0.355788i −0.159162 0.987252i \(-0.550879\pi\)
0.775405 + 0.631465i \(0.217546\pi\)
\(48\) 0 0
\(49\) 4.89898 0.699854
\(50\) −3.00000 −0.424264
\(51\) 0 0
\(52\) 2.17423 + 1.25529i 0.301512 + 0.174078i
\(53\) −2.44949 4.24264i −0.336463 0.582772i 0.647302 0.762234i \(-0.275897\pi\)
−0.983765 + 0.179463i \(0.942564\pi\)
\(54\) 0 0
\(55\) −4.44949 + 7.70674i −0.599969 + 1.03918i
\(56\) 3.44949 0.460957
\(57\) 0 0
\(58\) 2.44949 0.321634
\(59\) −4.77526 + 8.27098i −0.621685 + 1.07679i 0.367487 + 0.930029i \(0.380218\pi\)
−0.989172 + 0.146762i \(0.953115\pi\)
\(60\) 0 0
\(61\) −0.724745 1.25529i −0.0927941 0.160724i 0.815892 0.578205i \(-0.196246\pi\)
−0.908686 + 0.417481i \(0.862913\pi\)
\(62\) 8.17423 + 4.71940i 1.03813 + 0.599364i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.55051 0.440387
\(66\) 0 0
\(67\) 5.84847 3.37662i 0.714504 0.412519i −0.0982223 0.995164i \(-0.531316\pi\)
0.812727 + 0.582645i \(0.197982\pi\)
\(68\) 4.87832i 0.591583i
\(69\) 0 0
\(70\) 4.22474 2.43916i 0.504954 0.291535i
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 0 0
\(73\) 5.94949 10.3048i 0.696335 1.20609i −0.273393 0.961902i \(-0.588146\pi\)
0.969729 0.244185i \(-0.0785206\pi\)
\(74\) −5.17423 2.98735i −0.601493 0.347272i
\(75\) 0 0
\(76\) −0.500000 4.33013i −0.0573539 0.496700i
\(77\) 21.7060i 2.47363i
\(78\) 0 0
\(79\) 8.17423 + 4.71940i 0.919673 + 0.530974i 0.883531 0.468373i \(-0.155160\pi\)
0.0361424 + 0.999347i \(0.488493\pi\)
\(80\) 1.22474 0.707107i 0.136931 0.0790569i
\(81\) 0 0
\(82\) 0 0
\(83\) 8.97809i 0.985474i −0.870178 0.492737i \(-0.835997\pi\)
0.870178 0.492737i \(-0.164003\pi\)
\(84\) 0 0
\(85\) 3.44949 + 5.97469i 0.374150 + 0.648046i
\(86\) −2.94949 5.10867i −0.318052 0.550882i
\(87\) 0 0
\(88\) 6.29253i 0.670786i
\(89\) −6.12372 10.6066i −0.649113 1.12430i −0.983335 0.181803i \(-0.941807\pi\)
0.334221 0.942495i \(-0.391527\pi\)
\(90\) 0 0
\(91\) 7.50000 4.33013i 0.786214 0.453921i
\(92\) −4.89898 2.82843i −0.510754 0.294884i
\(93\) 0 0
\(94\) 4.87832i 0.503160i
\(95\) −3.67423 4.94975i −0.376969 0.507833i
\(96\) 0 0
\(97\) −1.65153 0.953512i −0.167688 0.0968144i 0.413807 0.910364i \(-0.364199\pi\)
−0.581495 + 0.813550i \(0.697532\pi\)
\(98\) 2.44949 4.24264i 0.247436 0.428571i
\(99\) 0 0
\(100\) −1.50000 + 2.59808i −0.150000 + 0.259808i
\(101\) 6.55051 3.78194i 0.651800 0.376317i −0.137345 0.990523i \(-0.543857\pi\)
0.789146 + 0.614206i \(0.210524\pi\)
\(102\) 0 0
\(103\) 10.9959i 1.08346i −0.840554 0.541728i \(-0.817770\pi\)
0.840554 0.541728i \(-0.182230\pi\)
\(104\) 2.17423 1.25529i 0.213201 0.123092i
\(105\) 0 0
\(106\) −4.89898 −0.475831
\(107\) 3.79796 0.367163 0.183581 0.983005i \(-0.441231\pi\)
0.183581 + 0.983005i \(0.441231\pi\)
\(108\) 0 0
\(109\) 14.6969 + 8.48528i 1.40771 + 0.812743i 0.995167 0.0981950i \(-0.0313069\pi\)
0.412544 + 0.910938i \(0.364640\pi\)
\(110\) 4.44949 + 7.70674i 0.424242 + 0.734809i
\(111\) 0 0
\(112\) 1.72474 2.98735i 0.162973 0.282278i
\(113\) −17.1464 −1.61300 −0.806500 0.591234i \(-0.798641\pi\)
−0.806500 + 0.591234i \(0.798641\pi\)
\(114\) 0 0
\(115\) −8.00000 −0.746004
\(116\) 1.22474 2.12132i 0.113715 0.196960i
\(117\) 0 0
\(118\) 4.77526 + 8.27098i 0.439598 + 0.761406i
\(119\) 14.5732 + 8.41385i 1.33592 + 0.771296i
\(120\) 0 0
\(121\) −28.5959 −2.59963
\(122\) −1.44949 −0.131231
\(123\) 0 0
\(124\) 8.17423 4.71940i 0.734068 0.423814i
\(125\) 11.3137i 1.01193i
\(126\) 0 0
\(127\) −7.34847 + 4.24264i −0.652071 + 0.376473i −0.789249 0.614073i \(-0.789530\pi\)
0.137178 + 0.990546i \(0.456197\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 1.77526 3.07483i 0.155700 0.269681i
\(131\) 6.79796 + 3.92480i 0.593940 + 0.342912i 0.766654 0.642060i \(-0.221920\pi\)
−0.172714 + 0.984972i \(0.555254\pi\)
\(132\) 0 0
\(133\) −13.7980 5.97469i −1.19643 0.518071i
\(134\) 6.75323i 0.583390i
\(135\) 0 0
\(136\) 4.22474 + 2.43916i 0.362269 + 0.209156i
\(137\) 0.550510 0.317837i 0.0470333 0.0271547i −0.476299 0.879283i \(-0.658022\pi\)
0.523332 + 0.852129i \(0.324689\pi\)
\(138\) 0 0
\(139\) 3.50000 + 6.06218i 0.296866 + 0.514187i 0.975417 0.220366i \(-0.0707252\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 4.87832i 0.412293i
\(141\) 0 0
\(142\) 3.00000 + 5.19615i 0.251754 + 0.436051i
\(143\) 7.89898 + 13.6814i 0.660546 + 1.14410i
\(144\) 0 0
\(145\) 3.46410i 0.287678i
\(146\) −5.94949 10.3048i −0.492383 0.852833i
\(147\) 0 0
\(148\) −5.17423 + 2.98735i −0.425319 + 0.245558i
\(149\) −12.5505 7.24604i −1.02818 0.593619i −0.111716 0.993740i \(-0.535635\pi\)
−0.916462 + 0.400121i \(0.868968\pi\)
\(150\) 0 0
\(151\) 15.4135i 1.25433i −0.778886 0.627166i \(-0.784215\pi\)
0.778886 0.627166i \(-0.215785\pi\)
\(152\) −4.00000 1.73205i −0.324443 0.140488i
\(153\) 0 0
\(154\) 18.7980 + 10.8530i 1.51478 + 0.874560i
\(155\) 6.67423 11.5601i 0.536087 0.928531i
\(156\) 0 0
\(157\) 1.17423 2.03383i 0.0937141 0.162318i −0.815357 0.578958i \(-0.803459\pi\)
0.909071 + 0.416641i \(0.136793\pi\)
\(158\) 8.17423 4.71940i 0.650307 0.375455i
\(159\) 0 0
\(160\) 1.41421i 0.111803i
\(161\) −16.8990 + 9.75663i −1.33183 + 0.768930i
\(162\) 0 0
\(163\) −21.6969 −1.69944 −0.849718 0.527238i \(-0.823228\pi\)
−0.849718 + 0.527238i \(0.823228\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −7.77526 4.48905i −0.603477 0.348418i
\(167\) −1.77526 3.07483i −0.137373 0.237938i 0.789128 0.614228i \(-0.210533\pi\)
−0.926502 + 0.376291i \(0.877199\pi\)
\(168\) 0 0
\(169\) −3.34847 + 5.79972i −0.257575 + 0.446132i
\(170\) 6.89898 0.529128
\(171\) 0 0
\(172\) −5.89898 −0.449793
\(173\) −6.12372 + 10.6066i −0.465578 + 0.806405i −0.999227 0.0393009i \(-0.987487\pi\)
0.533649 + 0.845706i \(0.320820\pi\)
\(174\) 0 0
\(175\) 5.17423 + 8.96204i 0.391135 + 0.677466i
\(176\) 5.44949 + 3.14626i 0.410771 + 0.237159i
\(177\) 0 0
\(178\) −12.2474 −0.917985
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −19.3485 + 11.1708i −1.43816 + 0.830322i −0.997722 0.0674605i \(-0.978510\pi\)
−0.440438 + 0.897783i \(0.645177\pi\)
\(182\) 8.66025i 0.641941i
\(183\) 0 0
\(184\) −4.89898 + 2.82843i −0.361158 + 0.208514i
\(185\) −4.22474 + 7.31747i −0.310609 + 0.537991i
\(186\) 0 0
\(187\) −15.3485 + 26.5843i −1.12239 + 1.94404i
\(188\) −4.22474 2.43916i −0.308121 0.177894i
\(189\) 0 0
\(190\) −6.12372 + 0.707107i −0.444262 + 0.0512989i
\(191\) 12.4422i 0.900285i −0.892957 0.450143i \(-0.851373\pi\)
0.892957 0.450143i \(-0.148627\pi\)
\(192\) 0 0
\(193\) 0.151531 + 0.0874863i 0.0109074 + 0.00629740i 0.505444 0.862860i \(-0.331329\pi\)
−0.494536 + 0.869157i \(0.664662\pi\)
\(194\) −1.65153 + 0.953512i −0.118573 + 0.0684582i
\(195\) 0 0
\(196\) −2.44949 4.24264i −0.174964 0.303046i
\(197\) 0.492810i 0.0351113i −0.999846 0.0175556i \(-0.994412\pi\)
0.999846 0.0175556i \(-0.00558842\pi\)
\(198\) 0 0
\(199\) 3.62372 + 6.27647i 0.256879 + 0.444927i 0.965404 0.260758i \(-0.0839725\pi\)
−0.708525 + 0.705686i \(0.750639\pi\)
\(200\) 1.50000 + 2.59808i 0.106066 + 0.183712i
\(201\) 0 0
\(202\) 7.56388i 0.532193i
\(203\) −4.22474 7.31747i −0.296519 0.513586i
\(204\) 0 0
\(205\) 0 0
\(206\) −9.52270 5.49794i −0.663478 0.383059i
\(207\) 0 0
\(208\) 2.51059i 0.174078i
\(209\) 10.8990 25.1701i 0.753898 1.74105i
\(210\) 0 0
\(211\) 17.8485 + 10.3048i 1.22874 + 0.709413i 0.966766 0.255662i \(-0.0822935\pi\)
0.261973 + 0.965075i \(0.415627\pi\)
\(212\) −2.44949 + 4.24264i −0.168232 + 0.291386i
\(213\) 0 0
\(214\) 1.89898 3.28913i 0.129812 0.224840i
\(215\) −7.22474 + 4.17121i −0.492724 + 0.284474i
\(216\) 0 0
\(217\) 32.5590i 2.21025i
\(218\) 14.6969 8.48528i 0.995402 0.574696i
\(219\) 0 0
\(220\) 8.89898 0.599969
\(221\) 12.2474 0.823853
\(222\) 0 0
\(223\) 5.17423 + 2.98735i 0.346492 + 0.200047i 0.663139 0.748496i \(-0.269224\pi\)
−0.316647 + 0.948543i \(0.602557\pi\)
\(224\) −1.72474 2.98735i −0.115239 0.199600i
\(225\) 0 0
\(226\) −8.57321 + 14.8492i −0.570282 + 0.987757i
\(227\) −11.1464 −0.739814 −0.369907 0.929069i \(-0.620611\pi\)
−0.369907 + 0.929069i \(0.620611\pi\)
\(228\) 0 0
\(229\) 5.24745 0.346761 0.173381 0.984855i \(-0.444531\pi\)
0.173381 + 0.984855i \(0.444531\pi\)
\(230\) −4.00000 + 6.92820i −0.263752 + 0.456832i
\(231\) 0 0
\(232\) −1.22474 2.12132i −0.0804084 0.139272i
\(233\) −9.24745 5.33902i −0.605821 0.349771i 0.165507 0.986209i \(-0.447074\pi\)
−0.771328 + 0.636438i \(0.780407\pi\)
\(234\) 0 0
\(235\) −6.89898 −0.450040
\(236\) 9.55051 0.621685
\(237\) 0 0
\(238\) 14.5732 8.41385i 0.944641 0.545389i
\(239\) 8.62815i 0.558108i −0.960275 0.279054i \(-0.909979\pi\)
0.960275 0.279054i \(-0.0900209\pi\)
\(240\) 0 0
\(241\) 26.8485 15.5010i 1.72946 0.998505i 0.837404 0.546585i \(-0.184072\pi\)
0.892058 0.451920i \(-0.149261\pi\)
\(242\) −14.2980 + 24.7648i −0.919108 + 1.59194i
\(243\) 0 0
\(244\) −0.724745 + 1.25529i −0.0463970 + 0.0803620i
\(245\) −6.00000 3.46410i −0.383326 0.221313i
\(246\) 0 0
\(247\) −10.8712 + 1.25529i −0.691716 + 0.0798725i
\(248\) 9.43879i 0.599364i
\(249\) 0 0
\(250\) 9.79796 + 5.65685i 0.619677 + 0.357771i
\(251\) 1.22474 0.707107i 0.0773052 0.0446322i −0.460849 0.887478i \(-0.652455\pi\)
0.538154 + 0.842846i \(0.319122\pi\)
\(252\) 0 0
\(253\) −17.7980 30.8270i −1.11895 1.93807i
\(254\) 8.48528i 0.532414i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.00000 + 10.3923i 0.374270 + 0.648254i 0.990217 0.139533i \(-0.0445601\pi\)
−0.615948 + 0.787787i \(0.711227\pi\)
\(258\) 0 0
\(259\) 20.6096i 1.28062i
\(260\) −1.77526 3.07483i −0.110097 0.190693i
\(261\) 0 0
\(262\) 6.79796 3.92480i 0.419979 0.242475i
\(263\) 18.7980 + 10.8530i 1.15913 + 0.669225i 0.951096 0.308896i \(-0.0999595\pi\)
0.208036 + 0.978121i \(0.433293\pi\)
\(264\) 0 0
\(265\) 6.92820i 0.425596i
\(266\) −12.0732 + 8.96204i −0.740256 + 0.549498i
\(267\) 0 0
\(268\) −5.84847 3.37662i −0.357252 0.206260i
\(269\) −7.77526 + 13.4671i −0.474066 + 0.821106i −0.999559 0.0296918i \(-0.990547\pi\)
0.525493 + 0.850798i \(0.323881\pi\)
\(270\) 0 0
\(271\) 13.6969 23.7238i 0.832030 1.44112i −0.0643963 0.997924i \(-0.520512\pi\)
0.896426 0.443193i \(-0.146155\pi\)
\(272\) 4.22474 2.43916i 0.256163 0.147896i
\(273\) 0 0
\(274\) 0.635674i 0.0384025i
\(275\) −16.3485 + 9.43879i −0.985850 + 0.569181i
\(276\) 0 0
\(277\) 18.8990 1.13553 0.567765 0.823191i \(-0.307808\pi\)
0.567765 + 0.823191i \(0.307808\pi\)
\(278\) 7.00000 0.419832
\(279\) 0 0
\(280\) −4.22474 2.43916i −0.252477 0.145768i
\(281\) −5.57321 9.65309i −0.332470 0.575855i 0.650525 0.759484i \(-0.274549\pi\)
−0.982996 + 0.183629i \(0.941215\pi\)
\(282\) 0 0
\(283\) 2.55051 4.41761i 0.151612 0.262600i −0.780208 0.625520i \(-0.784887\pi\)
0.931820 + 0.362920i \(0.118220\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) 15.7980 0.934153
\(287\) 0 0
\(288\) 0 0
\(289\) 3.39898 + 5.88721i 0.199940 + 0.346306i
\(290\) −3.00000 1.73205i −0.176166 0.101710i
\(291\) 0 0
\(292\) −11.8990 −0.696335
\(293\) 25.3485 1.48087 0.740437 0.672126i \(-0.234619\pi\)
0.740437 + 0.672126i \(0.234619\pi\)
\(294\) 0 0
\(295\) 11.6969 6.75323i 0.681022 0.393188i
\(296\) 5.97469i 0.347272i
\(297\) 0 0
\(298\) −12.5505 + 7.24604i −0.727032 + 0.419752i
\(299\) −7.10102 + 12.2993i −0.410663 + 0.711289i
\(300\) 0 0
\(301\) −10.1742 + 17.6223i −0.586433 + 1.01573i
\(302\) −13.3485 7.70674i −0.768118 0.443473i
\(303\) 0 0
\(304\) −3.50000 + 2.59808i −0.200739 + 0.149010i
\(305\) 2.04989i 0.117376i
\(306\) 0 0
\(307\) 1.34847 + 0.778539i 0.0769612 + 0.0444336i 0.537987 0.842953i \(-0.319185\pi\)
−0.461026 + 0.887387i \(0.652518\pi\)
\(308\) 18.7980 10.8530i 1.07111 0.618407i
\(309\) 0 0
\(310\) −6.67423 11.5601i −0.379071 0.656570i
\(311\) 25.9487i 1.47141i −0.677300 0.735707i \(-0.736850\pi\)
0.677300 0.735707i \(-0.263150\pi\)
\(312\) 0 0
\(313\) 3.34847 + 5.79972i 0.189267 + 0.327819i 0.945006 0.327053i \(-0.106056\pi\)
−0.755739 + 0.654873i \(0.772722\pi\)
\(314\) −1.17423 2.03383i −0.0662659 0.114776i
\(315\) 0 0
\(316\) 9.43879i 0.530974i
\(317\) 3.67423 + 6.36396i 0.206366 + 0.357436i 0.950567 0.310520i \(-0.100503\pi\)
−0.744201 + 0.667955i \(0.767170\pi\)
\(318\) 0 0
\(319\) 13.3485 7.70674i 0.747371 0.431495i
\(320\) −1.22474 0.707107i −0.0684653 0.0395285i
\(321\) 0 0
\(322\) 19.5133i 1.08743i
\(323\) −12.6742 17.0741i −0.705213 0.950029i
\(324\) 0 0
\(325\) 6.52270 + 3.76588i 0.361815 + 0.208894i
\(326\) −10.8485 + 18.7901i −0.600841 + 1.04069i
\(327\) 0 0
\(328\) 0 0
\(329\) −14.5732 + 8.41385i −0.803447 + 0.463871i
\(330\) 0 0
\(331\) 15.2385i 0.837584i −0.908082 0.418792i \(-0.862454\pi\)
0.908082 0.418792i \(-0.137546\pi\)
\(332\) −7.77526 + 4.48905i −0.426723 + 0.246368i
\(333\) 0 0
\(334\) −3.55051 −0.194275
\(335\) −9.55051 −0.521800
\(336\) 0 0
\(337\) 31.1969 + 18.0116i 1.69941 + 0.981152i 0.946321 + 0.323229i \(0.104768\pi\)
0.753085 + 0.657924i \(0.228565\pi\)
\(338\) 3.34847 + 5.79972i 0.182133 + 0.315463i
\(339\) 0 0
\(340\) 3.44949 5.97469i 0.187075 0.324023i
\(341\) 59.3939 3.21636
\(342\) 0 0
\(343\) 7.24745 0.391325
\(344\) −2.94949 + 5.10867i −0.159026 + 0.275441i
\(345\) 0 0
\(346\) 6.12372 + 10.6066i 0.329213 + 0.570214i
\(347\) 25.7753 + 14.8814i 1.38369 + 0.798873i 0.992594 0.121478i \(-0.0387634\pi\)
0.391094 + 0.920351i \(0.372097\pi\)
\(348\) 0 0
\(349\) −1.24745 −0.0667744 −0.0333872 0.999442i \(-0.510629\pi\)
−0.0333872 + 0.999442i \(0.510629\pi\)
\(350\) 10.3485 0.553149
\(351\) 0 0
\(352\) 5.44949 3.14626i 0.290459 0.167696i
\(353\) 17.4634i 0.929482i −0.885447 0.464741i \(-0.846148\pi\)
0.885447 0.464741i \(-0.153852\pi\)
\(354\) 0 0
\(355\) 7.34847 4.24264i 0.390016 0.225176i
\(356\) −6.12372 + 10.6066i −0.324557 + 0.562149i
\(357\) 0 0
\(358\) 6.00000 10.3923i 0.317110 0.549250i
\(359\) 9.79796 + 5.65685i 0.517116 + 0.298557i 0.735754 0.677249i \(-0.236828\pi\)
−0.218638 + 0.975806i \(0.570161\pi\)
\(360\) 0 0
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) 22.3417i 1.17425i
\(363\) 0 0
\(364\) −7.50000 4.33013i −0.393107 0.226960i
\(365\) −14.5732 + 8.41385i −0.762797 + 0.440401i
\(366\) 0 0
\(367\) −0.174235 0.301783i −0.00909497 0.0157530i 0.861442 0.507856i \(-0.169562\pi\)
−0.870537 + 0.492103i \(0.836228\pi\)
\(368\) 5.65685i 0.294884i
\(369\) 0 0
\(370\) 4.22474 + 7.31747i 0.219634 + 0.380417i
\(371\) 8.44949 + 14.6349i 0.438676 + 0.759809i
\(372\) 0 0
\(373\) 29.2699i 1.51554i 0.652523 + 0.757769i \(0.273710\pi\)
−0.652523 + 0.757769i \(0.726290\pi\)
\(374\) 15.3485 + 26.5843i 0.793650 + 1.37464i
\(375\) 0 0
\(376\) −4.22474 + 2.43916i −0.217875 + 0.125790i
\(377\) −5.32577 3.07483i −0.274291 0.158362i
\(378\) 0 0
\(379\) 19.0526i 0.978664i −0.872098 0.489332i \(-0.837241\pi\)
0.872098 0.489332i \(-0.162759\pi\)
\(380\) −2.44949 + 5.65685i −0.125656 + 0.290191i
\(381\) 0 0
\(382\) −10.7753 6.22110i −0.551310 0.318299i
\(383\) 0.550510 0.953512i 0.0281298 0.0487222i −0.851618 0.524163i \(-0.824378\pi\)
0.879748 + 0.475441i \(0.157712\pi\)
\(384\) 0 0
\(385\) 15.3485 26.5843i 0.782230 1.35486i
\(386\) 0.151531 0.0874863i 0.00771271 0.00445294i
\(387\) 0 0
\(388\) 1.90702i 0.0968144i
\(389\) −13.1010 + 7.56388i −0.664248 + 0.383504i −0.793894 0.608057i \(-0.791949\pi\)
0.129646 + 0.991560i \(0.458616\pi\)
\(390\) 0 0
\(391\) −27.5959 −1.39559
\(392\) −4.89898 −0.247436
\(393\) 0 0
\(394\) −0.426786 0.246405i −0.0215012 0.0124137i
\(395\) −6.67423 11.5601i −0.335817 0.581652i
\(396\) 0 0
\(397\) −18.1742 + 31.4787i −0.912139 + 1.57987i −0.101101 + 0.994876i \(0.532237\pi\)
−0.811037 + 0.584994i \(0.801097\pi\)
\(398\) 7.24745 0.363282
\(399\) 0 0
\(400\) 3.00000 0.150000
\(401\) 12.1237 20.9989i 0.605430 1.04864i −0.386553 0.922267i \(-0.626335\pi\)
0.991983 0.126368i \(-0.0403321\pi\)
\(402\) 0 0
\(403\) −11.8485 20.5222i −0.590214 1.02228i
\(404\) −6.55051 3.78194i −0.325900 0.188158i
\(405\) 0 0
\(406\) −8.44949 −0.419341
\(407\) −37.5959 −1.86356
\(408\) 0 0
\(409\) 19.0454 10.9959i 0.941735 0.543711i 0.0512311 0.998687i \(-0.483685\pi\)
0.890504 + 0.454976i \(0.150352\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −9.52270 + 5.49794i −0.469150 + 0.270864i
\(413\) 16.4722 28.5307i 0.810544 1.40390i
\(414\) 0 0
\(415\) −6.34847 + 10.9959i −0.311634 + 0.539766i
\(416\) −2.17423 1.25529i −0.106601 0.0615459i
\(417\) 0 0
\(418\) −16.3485 22.0239i −0.799630 1.07722i
\(419\) 24.5344i 1.19859i 0.800530 + 0.599293i \(0.204552\pi\)
−0.800530 + 0.599293i \(0.795448\pi\)
\(420\) 0 0
\(421\) −13.3485 7.70674i −0.650565 0.375604i 0.138108 0.990417i \(-0.455898\pi\)
−0.788672 + 0.614814i \(0.789231\pi\)
\(422\) 17.8485 10.3048i 0.868850 0.501631i
\(423\) 0 0
\(424\) 2.44949 + 4.24264i 0.118958 + 0.206041i
\(425\) 14.6349i 0.709899i
\(426\) 0 0
\(427\) 2.50000 + 4.33013i 0.120983 + 0.209550i
\(428\) −1.89898 3.28913i −0.0917906 0.158986i
\(429\) 0 0
\(430\) 8.34242i 0.402307i
\(431\) −14.0227 24.2880i −0.675450 1.16991i −0.976337 0.216254i \(-0.930616\pi\)
0.300887 0.953660i \(-0.402717\pi\)
\(432\) 0 0
\(433\) −4.19694 + 2.42310i −0.201692 + 0.116447i −0.597444 0.801910i \(-0.703817\pi\)
0.395752 + 0.918357i \(0.370484\pi\)
\(434\) −28.1969 16.2795i −1.35350 0.781441i
\(435\) 0 0
\(436\) 16.9706i 0.812743i
\(437\) 24.4949 2.82843i 1.17175 0.135302i
\(438\) 0 0
\(439\) 9.52270 + 5.49794i 0.454494 + 0.262402i 0.709726 0.704478i \(-0.248819\pi\)
−0.255232 + 0.966880i \(0.582152\pi\)
\(440\) 4.44949 7.70674i 0.212121 0.367405i
\(441\) 0 0
\(442\) 6.12372 10.6066i 0.291276 0.504505i
\(443\) 28.2247 16.2956i 1.34100 0.774226i 0.354044 0.935229i \(-0.384806\pi\)
0.986954 + 0.161003i \(0.0514729\pi\)
\(444\) 0 0
\(445\) 17.3205i 0.821071i
\(446\) 5.17423 2.98735i 0.245007 0.141455i
\(447\) 0 0
\(448\) −3.44949 −0.162973
\(449\) −6.24745 −0.294835 −0.147418 0.989074i \(-0.547096\pi\)
−0.147418 + 0.989074i \(0.547096\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 8.57321 + 14.8492i 0.403250 + 0.698450i
\(453\) 0 0
\(454\) −5.57321 + 9.65309i −0.261564 + 0.453042i
\(455\) −12.2474 −0.574169
\(456\) 0 0
\(457\) −9.69694 −0.453604 −0.226802 0.973941i \(-0.572827\pi\)
−0.226802 + 0.973941i \(0.572827\pi\)
\(458\) 2.62372 4.54442i 0.122599 0.212347i
\(459\) 0 0
\(460\) 4.00000 + 6.92820i 0.186501 + 0.323029i
\(461\) 3.12372 + 1.80348i 0.145486 + 0.0839966i 0.570976 0.820967i \(-0.306565\pi\)
−0.425490 + 0.904963i \(0.639898\pi\)
\(462\) 0 0
\(463\) 5.85357 0.272039 0.136019 0.990706i \(-0.456569\pi\)
0.136019 + 0.990706i \(0.456569\pi\)
\(464\) −2.44949 −0.113715
\(465\) 0 0
\(466\) −9.24745 + 5.33902i −0.428380 + 0.247325i
\(467\) 7.21393i 0.333821i 0.985972 + 0.166910i \(0.0533791\pi\)
−0.985972 + 0.166910i \(0.946621\pi\)
\(468\) 0 0
\(469\) −20.1742 + 11.6476i −0.931560 + 0.537836i
\(470\) −3.44949 + 5.97469i −0.159113 + 0.275592i
\(471\) 0 0
\(472\) 4.77526 8.27098i 0.219799 0.380703i
\(473\) −32.1464 18.5597i −1.47809 0.853378i
\(474\) 0 0
\(475\) −1.50000 12.9904i −0.0688247 0.596040i
\(476\) 16.8277i 0.771296i
\(477\) 0 0
\(478\) −7.47219 4.31407i −0.341770 0.197321i
\(479\) −26.1464 + 15.0956i −1.19466 + 0.689738i −0.959360 0.282185i \(-0.908941\pi\)
−0.235301 + 0.971923i \(0.575608\pi\)
\(480\) 0 0
\(481\) 7.50000 + 12.9904i 0.341971 + 0.592310i
\(482\) 31.0019i 1.41210i
\(483\) 0 0
\(484\) 14.2980 + 24.7648i 0.649907 + 1.12567i
\(485\) 1.34847 + 2.33562i 0.0612308 + 0.106055i
\(486\) 0 0
\(487\) 22.6916i 1.02826i −0.857713 0.514128i \(-0.828116\pi\)
0.857713 0.514128i \(-0.171884\pi\)
\(488\) 0.724745 + 1.25529i 0.0328077 + 0.0568245i
\(489\) 0 0
\(490\) −6.00000 + 3.46410i −0.271052 + 0.156492i
\(491\) 8.14643 + 4.70334i 0.367643 + 0.212259i 0.672428 0.740162i \(-0.265251\pi\)
−0.304785 + 0.952421i \(0.598585\pi\)
\(492\) 0 0
\(493\) 11.9494i 0.538173i
\(494\) −4.34847 + 10.0424i −0.195647 + 0.451827i
\(495\) 0 0
\(496\) −8.17423 4.71940i −0.367034 0.211907i
\(497\) 10.3485 17.9241i 0.464192 0.804005i
\(498\) 0 0
\(499\) −2.74745 + 4.75872i −0.122993 + 0.213030i −0.920947 0.389689i \(-0.872583\pi\)
0.797954 + 0.602719i \(0.205916\pi\)
\(500\) 9.79796 5.65685i 0.438178 0.252982i
\(501\) 0 0
\(502\) 1.41421i 0.0631194i
\(503\) −35.5176 + 20.5061i −1.58365 + 0.914322i −0.589331 + 0.807891i \(0.700609\pi\)
−0.994320 + 0.106430i \(0.966058\pi\)
\(504\) 0 0
\(505\) −10.6969 −0.476008
\(506\) −35.5959 −1.58243
\(507\) 0 0
\(508\) 7.34847 + 4.24264i 0.326036 + 0.188237i
\(509\) −0.674235 1.16781i −0.0298849 0.0517622i 0.850696 0.525658i \(-0.176181\pi\)
−0.880581 + 0.473896i \(0.842847\pi\)
\(510\) 0 0
\(511\) −20.5227 + 35.5464i −0.907871 + 1.57248i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 12.0000 0.529297
\(515\) −7.77526 + 13.4671i −0.342619 + 0.593433i
\(516\) 0 0
\(517\) −15.3485 26.5843i −0.675025 1.16918i
\(518\) 17.8485 + 10.3048i 0.784217 + 0.452768i
\(519\) 0 0
\(520\) −3.55051 −0.155700
\(521\) 27.7980 1.21785 0.608925 0.793228i \(-0.291601\pi\)
0.608925 + 0.793228i \(0.291601\pi\)
\(522\) 0 0
\(523\) 13.5000 7.79423i 0.590314 0.340818i −0.174908 0.984585i \(-0.555963\pi\)
0.765222 + 0.643767i \(0.222629\pi\)
\(524\) 7.84961i 0.342912i
\(525\) 0 0
\(526\) 18.7980 10.8530i 0.819630 0.473214i
\(527\) 23.0227 39.8765i 1.00288 1.73705i
\(528\) 0 0
\(529\) 4.50000 7.79423i 0.195652 0.338880i
\(530\) 6.00000 + 3.46410i 0.260623 + 0.150471i
\(531\) 0 0
\(532\) 1.72474 + 14.9367i 0.0747772 + 0.647589i
\(533\) 0 0
\(534\) 0 0
\(535\) −4.65153 2.68556i −0.201103 0.116107i
\(536\) −5.84847 + 3.37662i −0.252615 + 0.145848i
\(537\) 0 0
\(538\) 7.77526 + 13.4671i 0.335215 + 0.580610i
\(539\) 30.8270i 1.32781i
\(540\) 0 0
\(541\) −7.82577 13.5546i −0.336456 0.582759i 0.647307 0.762229i \(-0.275895\pi\)
−0.983763 + 0.179470i \(0.942562\pi\)
\(542\) −13.6969 23.7238i −0.588334 1.01902i
\(543\) 0 0
\(544\) 4.87832i 0.209156i
\(545\) −12.0000 20.7846i −0.514024 0.890315i
\(546\) 0 0
\(547\) −31.1969 + 18.0116i −1.33388 + 0.770119i −0.985893 0.167379i \(-0.946470\pi\)
−0.347992 + 0.937497i \(0.613136\pi\)
\(548\) −0.550510 0.317837i −0.0235166 0.0135773i
\(549\) 0 0
\(550\) 18.8776i 0.804943i
\(551\) 1.22474 + 10.6066i 0.0521759 + 0.451856i
\(552\) 0 0
\(553\) −28.1969 16.2795i −1.19906 0.692275i
\(554\) 9.44949 16.3670i 0.401470 0.695367i
\(555\) 0 0
\(556\) 3.50000 6.06218i 0.148433 0.257094i
\(557\) 16.5959 9.58166i 0.703192 0.405988i −0.105343 0.994436i \(-0.533594\pi\)
0.808535 + 0.588448i \(0.200261\pi\)
\(558\) 0 0
\(559\) 14.8099i 0.626393i
\(560\) −4.22474 + 2.43916i −0.178528 + 0.103073i
\(561\) 0 0
\(562\) −11.1464 −0.470184
\(563\) −13.5959 −0.573000 −0.286500 0.958080i \(-0.592492\pi\)
−0.286500 + 0.958080i \(0.592492\pi\)
\(564\) 0 0
\(565\) 21.0000 + 12.1244i 0.883477 + 0.510075i
\(566\) −2.55051 4.41761i −0.107206 0.185686i
\(567\) 0 0
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) −40.8990 −1.71457 −0.857287 0.514838i \(-0.827852\pi\)
−0.857287 + 0.514838i \(0.827852\pi\)
\(570\) 0 0
\(571\) 25.6969 1.07538 0.537692 0.843142i \(-0.319296\pi\)
0.537692 + 0.843142i \(0.319296\pi\)
\(572\) 7.89898 13.6814i 0.330273 0.572049i
\(573\) 0 0
\(574\) 0 0
\(575\) −14.6969 8.48528i −0.612905 0.353861i
\(576\) 0 0
\(577\) −13.7980 −0.574417 −0.287208 0.957868i \(-0.592727\pi\)
−0.287208 + 0.957868i \(0.592727\pi\)
\(578\) 6.79796 0.282758
\(579\) 0 0
\(580\) −3.00000 + 1.73205i −0.124568 + 0.0719195i
\(581\) 30.9698i 1.28485i
\(582\) 0 0
\(583\) −26.6969 + 15.4135i −1.10567 + 0.638361i
\(584\) −5.94949 + 10.3048i −0.246192 + 0.426416i
\(585\) 0 0
\(586\) 12.6742 21.9524i 0.523568 0.906846i
\(587\) −11.8763 6.85677i −0.490186 0.283009i 0.234465 0.972124i \(-0.424666\pi\)
−0.724652 + 0.689115i \(0.757999\pi\)
\(588\) 0 0
\(589\) −16.3485 + 37.7552i −0.673627 + 1.55567i
\(590\) 13.5065i 0.556052i
\(591\) 0 0
\(592\) 5.17423 + 2.98735i 0.212660 + 0.122779i
\(593\) −13.4722 + 7.77817i −0.553237 + 0.319411i −0.750426 0.660954i \(-0.770152\pi\)
0.197190 + 0.980365i \(0.436818\pi\)
\(594\) 0 0
\(595\) −11.8990 20.6096i −0.487811 0.844913i
\(596\) 14.4921i 0.593619i
\(597\) 0 0
\(598\) 7.10102 + 12.2993i 0.290382 + 0.502957i
\(599\) 0.797959 + 1.38211i 0.0326037 + 0.0564713i 0.881867 0.471499i \(-0.156287\pi\)
−0.849263 + 0.527970i \(0.822953\pi\)
\(600\) 0 0
\(601\) 6.75323i 0.275470i −0.990469 0.137735i \(-0.956018\pi\)
0.990469 0.137735i \(-0.0439822\pi\)
\(602\) 10.1742 + 17.6223i 0.414671 + 0.718231i
\(603\) 0 0
\(604\) −13.3485 + 7.70674i −0.543142 + 0.313583i
\(605\) 35.0227 + 20.2204i 1.42388 + 0.822075i
\(606\) 0 0
\(607\) 40.2658i 1.63434i −0.576399 0.817168i \(-0.695543\pi\)
0.576399 0.817168i \(-0.304457\pi\)
\(608\) 0.500000 + 4.33013i 0.0202777 + 0.175610i
\(609\) 0 0
\(610\) 1.77526 + 1.02494i 0.0718780 + 0.0414988i
\(611\) −6.12372 + 10.6066i −0.247739 + 0.429097i
\(612\) 0 0
\(613\) −4.55051 + 7.88171i −0.183793 + 0.318339i −0.943169 0.332313i \(-0.892171\pi\)
0.759376 + 0.650652i \(0.225504\pi\)
\(614\) 1.34847 0.778539i 0.0544198 0.0314193i
\(615\) 0 0
\(616\) 21.7060i 0.874560i
\(617\) 37.8990 21.8810i 1.52576 0.880895i 0.526222 0.850347i \(-0.323608\pi\)
0.999533 0.0305482i \(-0.00972531\pi\)
\(618\) 0 0
\(619\) 22.3939 0.900086 0.450043 0.893007i \(-0.351409\pi\)
0.450043 + 0.893007i \(0.351409\pi\)
\(620\) −13.3485 −0.536087
\(621\) 0 0
\(622\) −22.4722 12.9743i −0.901053 0.520223i
\(623\) 21.1237 + 36.5874i 0.846304 + 1.46584i
\(624\) 0 0
\(625\) 0.500000 0.866025i 0.0200000 0.0346410i
\(626\) 6.69694 0.267663
\(627\) 0 0
\(628\) −2.34847 −0.0937141
\(629\) −14.5732 + 25.2415i −0.581072 + 1.00645i
\(630\) 0 0
\(631\) −9.72474 16.8438i −0.387136 0.670539i 0.604927 0.796281i \(-0.293202\pi\)
−0.992063 + 0.125742i \(0.959869\pi\)
\(632\) −8.17423 4.71940i −0.325154 0.187728i
\(633\) 0 0
\(634\) 7.34847 0.291845
\(635\) 12.0000 0.476205
\(636\) 0 0
\(637\) −10.6515 + 6.14966i −0.422029 + 0.243659i
\(638\) 15.4135i 0.610226i
\(639\) 0 0
\(640\) −1.22474 + 0.707107i −0.0484123 + 0.0279508i
\(641\) −0.977296 + 1.69273i −0.0386009 + 0.0668587i −0.884680 0.466198i \(-0.845623\pi\)
0.846080 + 0.533057i \(0.178957\pi\)
\(642\) 0 0
\(643\) −1.70204 + 2.94802i −0.0671219 + 0.116259i −0.897633 0.440743i \(-0.854715\pi\)
0.830511 + 0.557002i \(0.188048\pi\)
\(644\) 16.8990 + 9.75663i 0.665913 + 0.384465i
\(645\) 0 0
\(646\) −21.1237 + 2.43916i −0.831102 + 0.0959674i
\(647\) 16.8277i 0.661565i 0.943707 + 0.330783i \(0.107313\pi\)
−0.943707 + 0.330783i \(0.892687\pi\)
\(648\) 0 0
\(649\) 52.0454 + 30.0484i 2.04296 + 1.17950i
\(650\) 6.52270 3.76588i 0.255841 0.147710i
\(651\) 0 0
\(652\) 10.8485 + 18.7901i 0.424859 + 0.735877i
\(653\) 10.1066i 0.395501i −0.980252 0.197750i \(-0.936636\pi\)
0.980252 0.197750i \(-0.0633636\pi\)
\(654\) 0 0
\(655\) −5.55051 9.61377i −0.216876 0.375641i
\(656\) 0 0
\(657\) 0 0
\(658\) 16.8277i 0.656012i
\(659\) 23.6969 + 41.0443i 0.923102 + 1.59886i 0.794586 + 0.607151i \(0.207688\pi\)
0.128516 + 0.991707i \(0.458979\pi\)
\(660\) 0 0
\(661\) 5.69694 3.28913i 0.221585 0.127932i −0.385099 0.922875i \(-0.625833\pi\)
0.606684 + 0.794943i \(0.292499\pi\)
\(662\) −13.1969 7.61926i −0.512914 0.296131i
\(663\) 0 0
\(664\) 8.97809i 0.348418i
\(665\) 12.6742 + 17.0741i 0.491486 + 0.662105i
\(666\) 0 0
\(667\) 12.0000 + 6.92820i 0.464642 + 0.268261i
\(668\) −1.77526 + 3.07483i −0.0686867 + 0.118969i
\(669\) 0 0
\(670\) −4.77526 + 8.27098i −0.184484 + 0.319536i
\(671\) −7.89898 + 4.56048i −0.304937 + 0.176055i
\(672\) 0 0
\(673\) 19.0526i 0.734422i −0.930138 0.367211i \(-0.880313\pi\)
0.930138 0.367211i \(-0.119687\pi\)
\(674\) 31.1969 18.0116i 1.20166 0.693779i
\(675\) 0 0
\(676\) 6.69694 0.257575
\(677\) −22.6515 −0.870569 −0.435285 0.900293i \(-0.643352\pi\)
−0.435285 + 0.900293i \(0.643352\pi\)
\(678\) 0 0
\(679\) 5.69694 + 3.28913i 0.218628 + 0.126225i
\(680\) −3.44949 5.97469i −0.132282 0.229119i
\(681\) 0 0
\(682\) 29.6969 51.4366i 1.13715 1.96961i
\(683\) −16.0454 −0.613960 −0.306980 0.951716i \(-0.599319\pi\)
−0.306980 + 0.951716i \(0.599319\pi\)
\(684\) 0 0
\(685\) −0.898979 −0.0343482
\(686\) 3.62372 6.27647i 0.138354 0.239637i
\(687\) 0 0
\(688\) 2.94949 + 5.10867i 0.112448 + 0.194766i
\(689\) 10.6515 + 6.14966i 0.405791 + 0.234284i
\(690\) 0 0
\(691\) 28.6969 1.09168 0.545841 0.837888i \(-0.316210\pi\)
0.545841 + 0.837888i \(0.316210\pi\)
\(692\) 12.2474 0.465578
\(693\) 0 0
\(694\) 25.7753 14.8814i 0.978415 0.564888i
\(695\) 9.89949i 0.375509i
\(696\) 0 0
\(697\) 0 0
\(698\) −0.623724 + 1.08032i −0.0236083 + 0.0408908i
\(699\) 0 0
\(700\) 5.17423 8.96204i 0.195568 0.338733i
\(701\) 13.4722 + 7.77817i 0.508838 + 0.293778i 0.732356 0.680922i \(-0.238421\pi\)
−0.223518 + 0.974700i \(0.571754\pi\)
\(702\) 0 0
\(703\) 10.3485 23.8988i 0.390300 0.901359i
\(704\) 6.29253i 0.237159i
\(705\) 0 0
\(706\) −15.1237 8.73169i −0.569189 0.328621i
\(707\) −22.5959 + 13.0458i −0.849807 + 0.490636i
\(708\) 0 0
\(709\) 4.17423 + 7.22999i 0.156767 + 0.271528i 0.933701 0.358054i \(-0.116560\pi\)
−0.776934 + 0.629582i \(0.783226\pi\)
\(710\) 8.48528i 0.318447i
\(711\) 0 0
\(712\) 6.12372 + 10.6066i 0.229496 + 0.397499i
\(713\) 26.6969 + 46.2405i 0.999808 + 1.73172i
\(714\) 0 0
\(715\) 22.3417i 0.835532i
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) 0 0
\(718\) 9.79796 5.65685i 0.365657 0.211112i
\(719\) 17.1464 + 9.89949i 0.639454 + 0.369189i 0.784404 0.620250i \(-0.212969\pi\)
−0.144950 + 0.989439i \(0.546302\pi\)
\(720\) 0 0
\(721\) 37.9301i 1.41259i
\(722\) 18.5000 4.33013i 0.688499 0.161151i
\(723\) 0 0
\(724\) 19.3485 + 11.1708i 0.719080 + 0.415161i
\(725\) 3.67423 6.36396i 0.136458 0.236352i
\(726\) 0 0
\(727\) −12.1742 + 21.0864i −0.451517 + 0.782051i −0.998481 0.0551057i \(-0.982450\pi\)
0.546963 + 0.837157i \(0.315784\pi\)
\(728\) −7.50000 + 4.33013i −0.277968 + 0.160485i
\(729\) 0 0
\(730\) 16.8277i 0.622821i
\(731\) −24.9217 + 14.3885i −0.921762 + 0.532179i
\(732\) 0 0
\(733\) −1.30306 −0.0481297 −0.0240648 0.999710i \(-0.507661\pi\)
−0.0240648 + 0.999710i \(0.507661\pi\)
\(734\) −0.348469 −0.0128622
\(735\) 0 0
\(736\) 4.89898 + 2.82843i 0.180579 + 0.104257i
\(737\) −21.2474 36.8017i −0.782660 1.35561i
\(738\) 0 0
\(739\) 6.19694 10.7334i 0.227958 0.394835i −0.729245 0.684253i \(-0.760128\pi\)
0.957203 + 0.289418i \(0.0934618\pi\)
\(740\) 8.44949 0.310609
\(741\) 0 0
\(742\) 16.8990 0.620381
\(743\) −5.69694 + 9.86739i −0.209000 + 0.361999i −0.951400 0.307958i \(-0.900354\pi\)
0.742400 + 0.669957i \(0.233688\pi\)
\(744\) 0 0
\(745\) 10.2474 + 17.7491i 0.375437 + 0.650277i
\(746\) 25.3485 + 14.6349i 0.928073 + 0.535823i
\(747\) 0 0
\(748\) 30.6969 1.12239
\(749\) −13.1010 −0.478701
\(750\) 0 0
\(751\) −27.2196 + 15.7153i −0.993259 + 0.573458i −0.906247 0.422749i \(-0.861065\pi\)
−0.0870120 + 0.996207i \(0.527732\pi\)
\(752\) 4.87832i 0.177894i
\(753\) 0 0
\(754\) −5.32577 + 3.07483i −0.193953 + 0.111979i
\(755\) −10.8990 + 18.8776i −0.396654 + 0.687026i
\(756\) 0 0
\(757\) −4.82577 + 8.35847i −0.175395 + 0.303794i −0.940298 0.340352i \(-0.889454\pi\)
0.764903 + 0.644146i \(0.222787\pi\)
\(758\) −16.5000 9.52628i −0.599307 0.346010i
\(759\) 0 0
\(760\) 3.67423 + 4.94975i 0.133278 + 0.179546i
\(761\) 3.25702i 0.118067i −0.998256 0.0590335i \(-0.981198\pi\)
0.998256 0.0590335i \(-0.0188019\pi\)
\(762\) 0 0
\(763\) −50.6969 29.2699i −1.83535 1.05964i
\(764\) −10.7753 + 6.22110i −0.389835 + 0.225071i
\(765\) 0 0
\(766\) −0.550510 0.953512i −0.0198907 0.0344518i
\(767\) 23.9774i 0.865774i
\(768\) 0 0
\(769\) −18.2980 31.6930i −0.659841 1.14288i −0.980656 0.195737i \(-0.937290\pi\)
0.320815 0.947142i \(-0.396043\pi\)
\(770\) −15.3485 26.5843i −0.553120 0.958033i
\(771\) 0 0
\(772\) 0.174973i 0.00629740i
\(773\) 22.4722 + 38.9230i 0.808269 + 1.39996i 0.914062 + 0.405574i \(0.132928\pi\)
−0.105793 + 0.994388i \(0.533738\pi\)
\(774\) 0 0
\(775\) 24.5227 14.1582i 0.880882 0.508577i
\(776\) 1.65153 + 0.953512i 0.0592865 + 0.0342291i
\(777\) 0 0
\(778\) 15.1278i 0.542356i
\(779\) 0 0
\(780\) 0 0
\(781\) 32.6969 + 18.8776i 1.16999 + 0.675493i
\(782\) −13.7980 + 23.8988i −0.493414 + 0.854618i
\(783\) 0 0
\(784\) −2.44949 + 4.24264i −0.0874818 + 0.151523i
\(785\) −2.87628 + 1.66062i −0.102659 + 0.0592700i
\(786\) 0 0
\(787\) 7.10318i 0.253201i −0.991954 0.126600i \(-0.959593\pi\)
0.991954 0.126600i \(-0.0404066\pi\)
\(788\) −0.426786 + 0.246405i −0.0152036 + 0.00877781i
\(789\) 0 0