Properties

Label 342.2.s.b.107.1
Level $342$
Weight $2$
Character 342.107
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 107.1
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 342.107
Dual form 342.2.s.b.179.1

$q$-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 \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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 −0.748203 0.663470i \(-0.769083\pi\)
0.200480 + 0.979698i \(0.435750\pi\)
\(6\) 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 \(0.397534\pi\)
−0.316374 + 0.948634i \(0.602466\pi\)
\(12\) 0 0
\(13\) −2.17423 1.25529i −0.603024 0.348156i 0.167206 0.985922i \(-0.446525\pi\)
−0.770230 + 0.637766i \(0.779859\pi\)
\(14\) −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 −0.915448 0.402437i \(-0.868163\pi\)
−0.109203 + 0.994019i \(0.534830\pi\)
\(18\) 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 0.914540 0.404495i \(-0.132553\pi\)
0.106967 + 0.994263i \(0.465886\pi\)
\(24\) 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 −0.729616 0.683857i \(-0.760301\pi\)
0.957046 + 0.289938i \(0.0936346\pi\)
\(30\) 0 0
\(31\) 9.43879i 1.69526i −0.530590 0.847629i \(-0.678030\pi\)
0.530590 0.847629i \(-0.321970\pi\)
\(32\) 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 \(0.163411\pi\)
−0.871094 + 0.491117i \(0.836589\pi\)
\(38\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) 0 0
\(43\) 2.94949 + 5.10867i 0.449793 + 0.779064i 0.998372 0.0570343i \(-0.0181644\pi\)
−0.548579 + 0.836099i \(0.684831\pi\)
\(44\) −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 0.775405 0.631465i \(-0.217546\pi\)
−0.159162 + 0.987252i \(0.550879\pi\)
\(48\) 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 −0.983765 0.179463i \(-0.942564\pi\)
0.647302 + 0.762234i \(0.275897\pi\)
\(54\) 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 −0.989172 0.146762i \(-0.953115\pi\)
0.367487 0.930029i \(-0.380218\pi\)
\(60\) 0 0
\(61\) −0.724745 + 1.25529i −0.0927941 + 0.160724i −0.908686 0.417481i \(-0.862913\pi\)
0.815892 + 0.578205i \(0.196246\pi\)
\(62\) 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 0.812727 0.582645i \(-0.197982\pi\)
−0.0982223 + 0.995164i \(0.531316\pi\)
\(68\) 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 0.631260 0.775571i \(-0.282538\pi\)
−0.987294 + 0.158901i \(0.949205\pi\)
\(72\) 0 0
\(73\) 5.94949 + 10.3048i 0.696335 + 1.20609i 0.969729 + 0.244185i \(0.0785206\pi\)
−0.273393 + 0.961902i \(0.588146\pi\)
\(74\) −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 0.0361424 0.999347i \(-0.488493\pi\)
0.883531 + 0.468373i \(0.155160\pi\)
\(80\) 1.22474 + 0.707107i 0.136931 + 0.0790569i
\(81\) 0 0
\(82\) 0 0
\(83\) 8.97809i 0.985474i 0.870178 + 0.492737i \(0.164003\pi\)
−0.870178 + 0.492737i \(0.835997\pi\)
\(84\) 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 0.334221 + 0.942495i \(0.391527\pi\)
−0.983335 + 0.181803i \(0.941807\pi\)
\(90\) 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 −0.581495 0.813550i \(-0.697532\pi\)
0.413807 + 0.910364i \(0.364199\pi\)
\(98\) 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 0.789146 0.614206i \(-0.210524\pi\)
−0.137345 + 0.990523i \(0.543857\pi\)
\(102\) 0 0
\(103\) 10.9959i 1.08346i 0.840554 + 0.541728i \(0.182230\pi\)
−0.840554 + 0.541728i \(0.817770\pi\)
\(104\) 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 0.412544 0.910938i \(-0.364640\pi\)
0.995167 + 0.0981950i \(0.0313069\pi\)
\(110\) 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 0.137178 0.990546i \(-0.456197\pi\)
−0.789249 + 0.614073i \(0.789530\pi\)
\(128\) 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 −0.172714 0.984972i \(-0.555254\pi\)
0.766654 + 0.642060i \(0.221920\pi\)
\(132\) 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 0.523332 0.852129i \(-0.324689\pi\)
−0.476299 + 0.879283i \(0.658022\pi\)
\(138\) 0 0
\(139\) 3.50000 6.06218i 0.296866 0.514187i −0.678551 0.734553i \(-0.737392\pi\)
0.975417 + 0.220366i \(0.0707252\pi\)
\(140\) 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 −0.916462 0.400121i \(-0.868968\pi\)
−0.111716 + 0.993740i \(0.535635\pi\)
\(150\) 0 0
\(151\) 15.4135i 1.25433i 0.778886 + 0.627166i \(0.215785\pi\)
−0.778886 + 0.627166i \(0.784215\pi\)
\(152\) −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 0.909071 0.416641i \(-0.136793\pi\)
−0.815357 + 0.578958i \(0.803459\pi\)
\(158\) 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 −0.926502 0.376291i \(-0.877199\pi\)
0.789128 + 0.614228i \(0.210533\pi\)
\(168\) 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 0.533649 0.845706i \(-0.320820\pi\)
−0.999227 + 0.0393009i \(0.987487\pi\)
\(174\) 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 −0.440438 0.897783i \(-0.645177\pi\)
−0.997722 + 0.0674605i \(0.978510\pi\)
\(182\) 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 \(0.148627\pi\)
−0.892957 + 0.450143i \(0.851373\pi\)
\(192\) 0 0
\(193\) 0.151531 0.0874863i 0.0109074 0.00629740i −0.494536 0.869157i \(-0.664662\pi\)
0.505444 + 0.862860i \(0.331329\pi\)
\(194\) −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 \(0.00558842\pi\)
−0.999846 + 0.0175556i \(0.994412\pi\)
\(198\) 0 0
\(199\) 3.62372 6.27647i 0.256879 0.444927i −0.708525 0.705686i \(-0.750639\pi\)
0.965404 + 0.260758i \(0.0839725\pi\)
\(200\) 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 0.261973 0.965075i \(-0.415627\pi\)
0.966766 + 0.255662i \(0.0822935\pi\)
\(212\) −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 −0.316647 0.948543i \(-0.602557\pi\)
0.663139 + 0.748496i \(0.269224\pi\)
\(224\) −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 −0.771328 0.636438i \(-0.780407\pi\)
0.165507 + 0.986209i \(0.447074\pi\)
\(234\) 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 \(0.0900209\pi\)
−0.960275 + 0.279054i \(0.909979\pi\)
\(240\) 0 0
\(241\) 26.8485 + 15.5010i 1.72946 + 0.998505i 0.892058 + 0.451920i \(0.149261\pi\)
0.837404 + 0.546585i \(0.184072\pi\)
\(242\) −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 0.538154 0.842846i \(-0.319122\pi\)
−0.460849 + 0.887478i \(0.652455\pi\)
\(252\) 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 −0.615948 0.787787i \(-0.711227\pi\)
0.990217 + 0.139533i \(0.0445601\pi\)
\(258\) 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 0.208036 0.978121i \(-0.433293\pi\)
0.951096 + 0.308896i \(0.0999595\pi\)
\(264\) 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 0.525493 0.850798i \(-0.323881\pi\)
−0.999559 + 0.0296918i \(0.990547\pi\)
\(270\) 0 0
\(271\) 13.6969 + 23.7238i 0.832030 + 1.44112i 0.896426 + 0.443193i \(0.146155\pi\)
−0.0643963 + 0.997924i \(0.520512\pi\)
\(272\) 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 −0.982996 0.183629i \(-0.941215\pi\)
0.650525 + 0.759484i \(0.274549\pi\)
\(282\) 0 0
\(283\) 2.55051 + 4.41761i 0.151612 + 0.262600i 0.931820 0.362920i \(-0.118220\pi\)
−0.780208 + 0.625520i \(0.784887\pi\)
\(284\) 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 −0.461026 0.887387i \(-0.652518\pi\)
0.537987 + 0.842953i \(0.319185\pi\)
\(308\) 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 \(0.263150\pi\)
−0.677300 + 0.735707i \(0.736850\pi\)
\(312\) 0 0
\(313\) 3.34847 5.79972i 0.189267 0.327819i −0.755739 0.654873i \(-0.772722\pi\)
0.945006 + 0.327053i \(0.106056\pi\)
\(314\) −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 −0.744201 0.667955i \(-0.767170\pi\)
0.950567 + 0.310520i \(0.100503\pi\)
\(318\) 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 \(0.137546\pi\)
−0.908082 + 0.418792i \(0.862454\pi\)
\(332\) −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 0.753085 0.657924i \(-0.228565\pi\)
0.946321 0.323229i \(-0.104768\pi\)
\(338\) 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 0.391094 0.920351i \(-0.372097\pi\)
0.992594 + 0.121478i \(0.0387634\pi\)
\(348\) 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 \(0.153852\pi\)
−0.885447 + 0.464741i \(0.846148\pi\)
\(354\) 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 −0.218638 0.975806i \(-0.570161\pi\)
0.735754 + 0.677249i \(0.236828\pi\)
\(360\) 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 −0.870537 0.492103i \(-0.836228\pi\)
0.861442 + 0.507856i \(0.169562\pi\)
\(368\) 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 \(-0.726290\pi\)
0.652523 0.757769i \(-0.273710\pi\)
\(374\) 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 \(0.162759\pi\)
−0.872098 + 0.489332i \(0.837241\pi\)
\(380\) −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 0.879748 0.475441i \(-0.157712\pi\)
−0.851618 + 0.524163i \(0.824378\pi\)
\(384\) 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 0.129646 0.991560i \(-0.458616\pi\)
−0.793894 + 0.608057i \(0.791949\pi\)
\(390\) 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 −0.811037 0.584994i \(-0.801097\pi\)
−0.101101 0.994876i \(-0.532237\pi\)
\(398\) 7.24745 0.363282
\(399\) 0 0
\(400\) 3.00000 0.150000
\(401\) 12.1237 + 20.9989i 0.605430 + 1.04864i 0.991983 + 0.126368i \(0.0403321\pi\)
−0.386553 + 0.922267i \(0.626335\pi\)
\(402\) 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 0.890504 0.454976i \(-0.150352\pi\)
0.0512311 + 0.998687i \(0.483685\pi\)
\(410\) 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 \(-0.795448\pi\)
0.800530 0.599293i \(-0.204552\pi\)
\(420\) 0 0
\(421\) −13.3485 + 7.70674i −0.650565 + 0.375604i −0.788672 0.614814i \(-0.789231\pi\)
0.138108 + 0.990417i \(0.455898\pi\)
\(422\) 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 0.300887 + 0.953660i \(0.402717\pi\)
−0.976337 + 0.216254i \(0.930616\pi\)
\(432\) 0 0
\(433\) −4.19694 2.42310i −0.201692 0.116447i 0.395752 0.918357i \(-0.370484\pi\)
−0.597444 + 0.801910i \(0.703817\pi\)
\(434\) −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 −0.255232 0.966880i \(-0.582152\pi\)
0.709726 + 0.704478i \(0.248819\pi\)
\(440\) 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 0.986954 0.161003i \(-0.0514729\pi\)
0.354044 + 0.935229i \(0.384806\pi\)
\(444\) 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 −0.425490 0.904963i \(-0.639898\pi\)
0.570976 + 0.820967i \(0.306565\pi\)
\(462\) 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 \(-0.946621\pi\)
0.985972 0.166910i \(-0.0533791\pi\)
\(468\) 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 −0.235301 0.971923i \(-0.575608\pi\)
−0.959360 + 0.282185i \(0.908941\pi\)
\(480\) 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 \(0.171884\pi\)
−0.857713 + 0.514128i \(0.828116\pi\)
\(488\) 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 −0.304785 0.952421i \(-0.598585\pi\)
0.672428 + 0.740162i \(0.265251\pi\)
\(492\) 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 0.797954 0.602719i \(-0.205916\pi\)
−0.920947 + 0.389689i \(0.872583\pi\)
\(500\) 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 −0.994320 0.106430i \(-0.966058\pi\)
−0.589331 0.807891i \(-0.700609\pi\)
\(504\) 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 −0.880581 0.473896i \(-0.842847\pi\)
0.850696 + 0.525658i \(0.176181\pi\)
\(510\) 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 0.765222 0.643767i \(-0.222629\pi\)
−0.174908 + 0.984585i \(0.555963\pi\)
\(524\) 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 −0.983763 0.179470i \(-0.942562\pi\)
0.647307 + 0.762229i \(0.275895\pi\)
\(542\) −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 −0.347992 0.937497i \(-0.613136\pi\)
−0.985893 + 0.167379i \(0.946470\pi\)
\(548\) −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 0.808535 0.588448i \(-0.200261\pi\)
−0.105343 + 0.994436i \(0.533594\pi\)
\(558\) 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 −0.724652 0.689115i \(-0.757999\pi\)
0.234465 + 0.972124i \(0.424666\pi\)
\(588\) 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 0.197190 0.980365i \(-0.436818\pi\)
−0.750426 + 0.660954i \(0.770152\pi\)
\(594\) 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 −0.849263 0.527970i \(-0.822953\pi\)
0.881867 + 0.471499i \(0.156287\pi\)
\(600\) 0 0
\(601\) 6.75323i 0.275470i 0.990469 + 0.137735i \(0.0439822\pi\)
−0.990469 + 0.137735i \(0.956018\pi\)
\(602\) 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 \(0.304457\pi\)
−0.576399 + 0.817168i \(0.695543\pi\)
\(608\) 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 0.759376 0.650652i \(-0.225504\pi\)
−0.943169 + 0.332313i \(0.892171\pi\)
\(614\) 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 0.999533 + 0.0305482i \(0.00972531\pi\)
0.526222 + 0.850347i \(0.323608\pi\)
\(618\) 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 −0.992063 0.125742i \(-0.959869\pi\)
0.604927 + 0.796281i \(0.293202\pi\)
\(632\) −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 0.846080 0.533057i \(-0.178957\pi\)
−0.884680 + 0.466198i \(0.845623\pi\)
\(642\) 0 0
\(643\) −1.70204 2.94802i −0.0671219 0.116259i 0.830511 0.557002i \(-0.188048\pi\)
−0.897633 + 0.440743i \(0.854715\pi\)
\(644\) 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 \(-0.892687\pi\)
0.943707 0.330783i \(-0.107313\pi\)
\(648\) 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 \(0.0633636\pi\)
−0.980252 + 0.197750i \(0.936636\pi\)
\(654\) 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 0.128516 0.991707i \(-0.458979\pi\)
0.794586 0.607151i \(-0.207688\pi\)
\(660\) 0 0
\(661\) 5.69694 + 3.28913i 0.221585 + 0.127932i 0.606684 0.794943i \(-0.292499\pi\)
−0.385099 + 0.922875i \(0.625833\pi\)
\(662\) −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 \(0.119687\pi\)
−0.930138 + 0.367211i \(0.880313\pi\)
\(674\) 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 −0.223518 0.974700i \(-0.571754\pi\)
0.732356 + 0.680922i \(0.238421\pi\)
\(702\) 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 −0.776934 0.629582i \(-0.783226\pi\)
0.933701 + 0.358054i \(0.116560\pi\)
\(710\) 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 −0.144950 0.989439i \(-0.546302\pi\)
0.784404 + 0.620250i \(0.212969\pi\)
\(720\) 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 0.546963 0.837157i \(-0.315784\pi\)
−0.998481 + 0.0551057i \(0.982450\pi\)
\(728\) −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 0.957203 0.289418i \(-0.0934618\pi\)
−0.729245 + 0.684253i \(0.760128\pi\)
\(740\) 8.44949 0.310609
\(741\) 0 0
\(742\) 16.8990 0.620381
\(743\) −5.69694 9.86739i −0.209000 0.361999i 0.742400 0.669957i \(-0.233688\pi\)
−0.951400 + 0.307958i \(0.900354\pi\)
\(744\) 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 −0.0870120 0.996207i \(-0.527732\pi\)
−0.906247 + 0.422749i \(0.861065\pi\)
\(752\) 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 0.764903 0.644146i \(-0.222787\pi\)
−0.940298 + 0.340352i \(0.889454\pi\)
\(758\) −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 \(0.0188019\pi\)
−0.998256 + 0.0590335i \(0.981198\pi\)
\(762\) 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 0.320815 + 0.947142i \(0.396043\pi\)
−0.980656 + 0.195737i \(0.937290\pi\)
\(770\) −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 −0.105793 0.994388i \(-0.533738\pi\)
0.914062 0.405574i \(-0.132928\pi\)
\(774\) 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 \(0.0404066\pi\)
−0.991954 + 0.126600i \(0.959593\pi\)
\(788\) −0.426786 0.246405i −0.0152036 0.00877781i
\(789\) 0 0
\(790\)