Properties

Label 315.2.p.e.307.8
Level 315
Weight 2
Character 315.307
Analytic conductor 2.515
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.8
Root \(-0.517174 + 1.31626i\) of \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
Character \(\chi\) \(=\) 315.307
Dual form 315.2.p.e.118.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.86147 + 1.86147i) q^{2} +4.93012i q^{4} +(1.50619 - 1.65269i) q^{5} +(-2.20563 + 1.46123i) q^{7} +(-5.45433 + 5.45433i) q^{8} +O(q^{10})\) \(q+(1.86147 + 1.86147i) q^{2} +4.93012i q^{4} +(1.50619 - 1.65269i) q^{5} +(-2.20563 + 1.46123i) q^{7} +(-5.45433 + 5.45433i) q^{8} +(5.88016 - 0.272713i) q^{10} +1.46279 q^{11} +(0.887844 + 0.887844i) q^{13} +(-6.82574 - 1.38567i) q^{14} -10.4459 q^{16} +(2.10614 - 2.10614i) q^{17} -3.95987 q^{19} +(8.14798 + 7.42570i) q^{20} +(2.72294 + 2.72294i) q^{22} +(4.13007 - 4.13007i) q^{23} +(-0.462789 - 4.97854i) q^{25} +3.30539i q^{26} +(-7.20405 - 10.8740i) q^{28} -5.18572i q^{29} -6.10346i q^{31} +(-8.53599 - 8.53599i) q^{32} +7.84104 q^{34} +(-0.907129 + 5.84612i) q^{35} +(2.25560 + 2.25560i) q^{37} +(-7.37117 - 7.37117i) q^{38} +(0.799082 + 17.2296i) q^{40} -0.769968i q^{41} +(-5.18572 + 5.18572i) q^{43} +7.21173i q^{44} +15.3760 q^{46} +(-8.57041 + 8.57041i) q^{47} +(2.72961 - 6.44587i) q^{49} +(8.40592 - 10.1289i) q^{50} +(-4.37718 + 4.37718i) q^{52} +(0.544449 - 0.544449i) q^{53} +(2.20324 - 2.41754i) q^{55} +(4.06020 - 20.0003i) q^{56} +(9.65306 - 9.65306i) q^{58} +3.19633 q^{59} +1.42064i q^{61} +(11.3614 - 11.3614i) q^{62} -10.8872i q^{64} +(2.80460 - 0.130073i) q^{65} +(-5.93012 - 5.93012i) q^{67} +(10.3835 + 10.3835i) q^{68} +(-12.5710 + 9.19377i) q^{70} -7.62611 q^{71} +(6.81378 + 6.81378i) q^{73} +8.39746i q^{74} -19.5226i q^{76} +(-3.22637 + 2.13747i) q^{77} +4.52029i q^{79} +(-15.7335 + 17.2638i) q^{80} +(1.43327 - 1.43327i) q^{82} +(6.75794 + 6.75794i) q^{83} +(-0.308559 - 6.65306i) q^{85} -19.3061 q^{86} +(-7.97854 + 7.97854i) q^{88} -1.19991 q^{89} +(-3.25560 - 0.660910i) q^{91} +(20.3618 + 20.3618i) q^{92} -31.9071 q^{94} +(-5.96431 + 6.54445i) q^{95} +(-8.68829 + 8.68829i) q^{97} +(17.0799 - 6.91770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{7} - 24q^{8} + O(q^{10}) \) \( 16q - 8q^{7} - 24q^{8} + 16q^{11} - 48q^{16} - 16q^{22} + 40q^{23} + 24q^{28} - 48q^{32} + 8q^{35} + 32q^{37} - 16q^{43} + 64q^{46} + 72q^{50} - 24q^{53} - 24q^{56} + 32q^{58} - 40q^{65} - 32q^{67} - 40q^{70} - 64q^{71} + 24q^{77} + 48q^{85} - 64q^{86} - 64q^{88} - 48q^{91} + 40q^{92} + 72q^{95} + 96q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.86147 + 1.86147i 1.31626 + 1.31626i 0.916715 + 0.399541i \(0.130831\pi\)
0.399541 + 0.916715i \(0.369169\pi\)
\(3\) 0 0
\(4\) 4.93012i 2.46506i
\(5\) 1.50619 1.65269i 0.673588 0.739107i
\(6\) 0 0
\(7\) −2.20563 + 1.46123i −0.833650 + 0.552293i
\(8\) −5.45433 + 5.45433i −1.92840 + 1.92840i
\(9\) 0 0
\(10\) 5.88016 0.272713i 1.85947 0.0862394i
\(11\) 1.46279 0.441048 0.220524 0.975382i \(-0.429223\pi\)
0.220524 + 0.975382i \(0.429223\pi\)
\(12\) 0 0
\(13\) 0.887844 + 0.887844i 0.246244 + 0.246244i 0.819427 0.573183i \(-0.194292\pi\)
−0.573183 + 0.819427i \(0.694292\pi\)
\(14\) −6.82574 1.38567i −1.82426 0.370337i
\(15\) 0 0
\(16\) −10.4459 −2.61147
\(17\) 2.10614 2.10614i 0.510815 0.510815i −0.403961 0.914776i \(-0.632367\pi\)
0.914776 + 0.403961i \(0.132367\pi\)
\(18\) 0 0
\(19\) −3.95987 −0.908456 −0.454228 0.890885i \(-0.650085\pi\)
−0.454228 + 0.890885i \(0.650085\pi\)
\(20\) 8.14798 + 7.42570i 1.82194 + 1.66044i
\(21\) 0 0
\(22\) 2.72294 + 2.72294i 0.580532 + 0.580532i
\(23\) 4.13007 4.13007i 0.861180 0.861180i −0.130295 0.991475i \(-0.541593\pi\)
0.991475 + 0.130295i \(0.0415926\pi\)
\(24\) 0 0
\(25\) −0.462789 4.97854i −0.0925579 0.995707i
\(26\) 3.30539i 0.648240i
\(27\) 0 0
\(28\) −7.20405 10.8740i −1.36144 2.05500i
\(29\) 5.18572i 0.962965i −0.876456 0.481482i \(-0.840099\pi\)
0.876456 0.481482i \(-0.159901\pi\)
\(30\) 0 0
\(31\) 6.10346i 1.09621i −0.836408 0.548107i \(-0.815349\pi\)
0.836408 0.548107i \(-0.184651\pi\)
\(32\) −8.53599 8.53599i −1.50896 1.50896i
\(33\) 0 0
\(34\) 7.84104 1.34473
\(35\) −0.907129 + 5.84612i −0.153333 + 0.988175i
\(36\) 0 0
\(37\) 2.25560 + 2.25560i 0.370819 + 0.370819i 0.867775 0.496957i \(-0.165549\pi\)
−0.496957 + 0.867775i \(0.665549\pi\)
\(38\) −7.37117 7.37117i −1.19576 1.19576i
\(39\) 0 0
\(40\) 0.799082 + 17.2296i 0.126346 + 2.72424i
\(41\) 0.769968i 0.120249i −0.998191 0.0601244i \(-0.980850\pi\)
0.998191 0.0601244i \(-0.0191497\pi\)
\(42\) 0 0
\(43\) −5.18572 + 5.18572i −0.790816 + 0.790816i −0.981627 0.190811i \(-0.938888\pi\)
0.190811 + 0.981627i \(0.438888\pi\)
\(44\) 7.21173i 1.08721i
\(45\) 0 0
\(46\) 15.3760 2.26707
\(47\) −8.57041 + 8.57041i −1.25012 + 1.25012i −0.294459 + 0.955664i \(0.595139\pi\)
−0.955664 + 0.294459i \(0.904861\pi\)
\(48\) 0 0
\(49\) 2.72961 6.44587i 0.389944 0.920839i
\(50\) 8.40592 10.1289i 1.18878 1.43244i
\(51\) 0 0
\(52\) −4.37718 + 4.37718i −0.607006 + 0.607006i
\(53\) 0.544449 0.544449i 0.0747859 0.0747859i −0.668724 0.743510i \(-0.733159\pi\)
0.743510 + 0.668724i \(0.233159\pi\)
\(54\) 0 0
\(55\) 2.20324 2.41754i 0.297084 0.325981i
\(56\) 4.06020 20.0003i 0.542567 2.67265i
\(57\) 0 0
\(58\) 9.65306 9.65306i 1.26751 1.26751i
\(59\) 3.19633 0.416127 0.208063 0.978115i \(-0.433284\pi\)
0.208063 + 0.978115i \(0.433284\pi\)
\(60\) 0 0
\(61\) 1.42064i 0.181894i 0.995856 + 0.0909472i \(0.0289894\pi\)
−0.995856 + 0.0909472i \(0.971011\pi\)
\(62\) 11.3614 11.3614i 1.44290 1.44290i
\(63\) 0 0
\(64\) 10.8872i 1.36090i
\(65\) 2.80460 0.130073i 0.347867 0.0161336i
\(66\) 0 0
\(67\) −5.93012 5.93012i −0.724480 0.724480i 0.245034 0.969514i \(-0.421201\pi\)
−0.969514 + 0.245034i \(0.921201\pi\)
\(68\) 10.3835 + 10.3835i 1.25919 + 1.25919i
\(69\) 0 0
\(70\) −12.5710 + 9.19377i −1.50252 + 1.09887i
\(71\) −7.62611 −0.905053 −0.452526 0.891751i \(-0.649477\pi\)
−0.452526 + 0.891751i \(0.649477\pi\)
\(72\) 0 0
\(73\) 6.81378 + 6.81378i 0.797493 + 0.797493i 0.982700 0.185207i \(-0.0592955\pi\)
−0.185207 + 0.982700i \(0.559296\pi\)
\(74\) 8.39746i 0.976185i
\(75\) 0 0
\(76\) 19.5226i 2.23940i
\(77\) −3.22637 + 2.13747i −0.367679 + 0.243588i
\(78\) 0 0
\(79\) 4.52029i 0.508573i 0.967129 + 0.254286i \(0.0818405\pi\)
−0.967129 + 0.254286i \(0.918159\pi\)
\(80\) −15.7335 + 17.2638i −1.75905 + 1.93015i
\(81\) 0 0
\(82\) 1.43327 1.43327i 0.158278 0.158278i
\(83\) 6.75794 + 6.75794i 0.741781 + 0.741781i 0.972921 0.231140i \(-0.0742455\pi\)
−0.231140 + 0.972921i \(0.574246\pi\)
\(84\) 0 0
\(85\) −0.308559 6.65306i −0.0334679 0.721626i
\(86\) −19.3061 −2.08183
\(87\) 0 0
\(88\) −7.97854 + 7.97854i −0.850515 + 0.850515i
\(89\) −1.19991 −0.127190 −0.0635950 0.997976i \(-0.520257\pi\)
−0.0635950 + 0.997976i \(0.520257\pi\)
\(90\) 0 0
\(91\) −3.25560 0.660910i −0.341280 0.0692822i
\(92\) 20.3618 + 20.3618i 2.12286 + 2.12286i
\(93\) 0 0
\(94\) −31.9071 −3.29096
\(95\) −5.96431 + 6.54445i −0.611925 + 0.671446i
\(96\) 0 0
\(97\) −8.68829 + 8.68829i −0.882162 + 0.882162i −0.993754 0.111592i \(-0.964405\pi\)
0.111592 + 0.993754i \(0.464405\pi\)
\(98\) 17.0799 6.91770i 1.72533 0.698794i
\(99\) 0 0
\(100\) 24.5448 2.28161i 2.45448 0.228161i
\(101\) 15.3420i 1.52659i −0.646050 0.763295i \(-0.723580\pi\)
0.646050 0.763295i \(-0.276420\pi\)
\(102\) 0 0
\(103\) 8.30776 + 8.30776i 0.818588 + 0.818588i 0.985903 0.167316i \(-0.0535099\pi\)
−0.167316 + 0.985903i \(0.553510\pi\)
\(104\) −9.68519 −0.949711
\(105\) 0 0
\(106\) 2.02695 0.196875
\(107\) −4.39022 4.39022i −0.424418 0.424418i 0.462303 0.886722i \(-0.347023\pi\)
−0.886722 + 0.462303i \(0.847023\pi\)
\(108\) 0 0
\(109\) 7.44587i 0.713185i 0.934260 + 0.356593i \(0.116062\pi\)
−0.934260 + 0.356593i \(0.883938\pi\)
\(110\) 8.60143 0.398921i 0.820114 0.0380357i
\(111\) 0 0
\(112\) 23.0397 15.2638i 2.17705 1.44230i
\(113\) −2.54445 + 2.54445i −0.239362 + 0.239362i −0.816586 0.577224i \(-0.804136\pi\)
0.577224 + 0.816586i \(0.304136\pi\)
\(114\) 0 0
\(115\) −0.605073 13.0464i −0.0564233 1.21658i
\(116\) 25.5663 2.37377
\(117\) 0 0
\(118\) 5.94986 + 5.94986i 0.547729 + 0.547729i
\(119\) −1.56781 + 7.72294i −0.143721 + 0.707960i
\(120\) 0 0
\(121\) −8.86025 −0.805477
\(122\) −2.64448 + 2.64448i −0.239420 + 0.239420i
\(123\) 0 0
\(124\) 30.0908 2.70223
\(125\) −8.92504 6.73377i −0.798280 0.602287i
\(126\) 0 0
\(127\) 7.86025 + 7.86025i 0.697484 + 0.697484i 0.963867 0.266383i \(-0.0858286\pi\)
−0.266383 + 0.963867i \(0.585829\pi\)
\(128\) 3.19418 3.19418i 0.282329 0.282329i
\(129\) 0 0
\(130\) 5.46279 + 4.97854i 0.479118 + 0.436647i
\(131\) 6.18216i 0.540138i −0.962841 0.270069i \(-0.912953\pi\)
0.962841 0.270069i \(-0.0870465\pi\)
\(132\) 0 0
\(133\) 8.73401 5.78628i 0.757334 0.501735i
\(134\) 22.0775i 1.90720i
\(135\) 0 0
\(136\) 22.9752i 1.97011i
\(137\) −9.05565 9.05565i −0.773677 0.773677i 0.205071 0.978747i \(-0.434258\pi\)
−0.978747 + 0.205071i \(0.934258\pi\)
\(138\) 0 0
\(139\) −11.9913 −1.01709 −0.508544 0.861036i \(-0.669816\pi\)
−0.508544 + 0.861036i \(0.669816\pi\)
\(140\) −28.8221 4.47226i −2.43591 0.377975i
\(141\) 0 0
\(142\) −14.1958 14.1958i −1.19128 1.19128i
\(143\) 1.29873 + 1.29873i 0.108605 + 0.108605i
\(144\) 0 0
\(145\) −8.57041 7.81068i −0.711734 0.648642i
\(146\) 25.3673i 2.09941i
\(147\) 0 0
\(148\) −11.1204 + 11.1204i −0.914091 + 0.914091i
\(149\) 0.0968261i 0.00793230i 0.999992 + 0.00396615i \(0.00126247\pi\)
−0.999992 + 0.00396615i \(0.998738\pi\)
\(150\) 0 0
\(151\) −13.4550 −1.09495 −0.547475 0.836822i \(-0.684411\pi\)
−0.547475 + 0.836822i \(0.684411\pi\)
\(152\) 21.5984 21.5984i 1.75186 1.75186i
\(153\) 0 0
\(154\) −9.98463 2.02695i −0.804584 0.163336i
\(155\) −10.0871 9.19296i −0.810219 0.738397i
\(156\) 0 0
\(157\) 1.64757 1.64757i 0.131491 0.131491i −0.638298 0.769789i \(-0.720361\pi\)
0.769789 + 0.638298i \(0.220361\pi\)
\(158\) −8.41438 + 8.41438i −0.669412 + 0.669412i
\(159\) 0 0
\(160\) −26.9642 + 1.25056i −2.13171 + 0.0988653i
\(161\) −3.07442 + 15.1444i −0.242298 + 1.19355i
\(162\) 0 0
\(163\) −10.2746 + 10.2746i −0.804771 + 0.804771i −0.983837 0.179066i \(-0.942692\pi\)
0.179066 + 0.983837i \(0.442692\pi\)
\(164\) 3.79604 0.296421
\(165\) 0 0
\(166\) 25.1594i 1.95275i
\(167\) −0.293008 + 0.293008i −0.0226737 + 0.0226737i −0.718353 0.695679i \(-0.755104\pi\)
0.695679 + 0.718353i \(0.255104\pi\)
\(168\) 0 0
\(169\) 11.4235i 0.878728i
\(170\) 11.8101 12.9588i 0.905792 0.993897i
\(171\) 0 0
\(172\) −25.5663 25.5663i −1.94941 1.94941i
\(173\) 3.45189 + 3.45189i 0.262442 + 0.262442i 0.826046 0.563603i \(-0.190585\pi\)
−0.563603 + 0.826046i \(0.690585\pi\)
\(174\) 0 0
\(175\) 8.29554 + 10.3046i 0.627084 + 0.778952i
\(176\) −15.2801 −1.15178
\(177\) 0 0
\(178\) −2.23359 2.23359i −0.167415 0.167415i
\(179\) 1.99756i 0.149305i 0.997210 + 0.0746523i \(0.0237847\pi\)
−0.997210 + 0.0746523i \(0.976215\pi\)
\(180\) 0 0
\(181\) 8.48528i 0.630706i −0.948974 0.315353i \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) −4.82993 7.29046i −0.358019 0.540405i
\(183\) 0 0
\(184\) 45.0536i 3.32139i
\(185\) 7.12518 0.330455i 0.523854 0.0242955i
\(186\) 0 0
\(187\) 3.08084 3.08084i 0.225294 0.225294i
\(188\) −42.2532 42.2532i −3.08163 3.08163i
\(189\) 0 0
\(190\) −23.2847 + 1.07991i −1.68925 + 0.0783447i
\(191\) 7.83424 0.566866 0.283433 0.958992i \(-0.408527\pi\)
0.283433 + 0.958992i \(0.408527\pi\)
\(192\) 0 0
\(193\) 13.5617 13.5617i 0.976194 0.976194i −0.0235293 0.999723i \(-0.507490\pi\)
0.999723 + 0.0235293i \(0.00749029\pi\)
\(194\) −32.3459 −2.32230
\(195\) 0 0
\(196\) 31.7789 + 13.4573i 2.26992 + 0.961236i
\(197\) 11.4791 + 11.4791i 0.817853 + 0.817853i 0.985797 0.167943i \(-0.0537126\pi\)
−0.167943 + 0.985797i \(0.553713\pi\)
\(198\) 0 0
\(199\) 20.1468 1.42817 0.714084 0.700061i \(-0.246844\pi\)
0.714084 + 0.700061i \(0.246844\pi\)
\(200\) 29.6788 + 24.6304i 2.09861 + 1.74163i
\(201\) 0 0
\(202\) 28.5587 28.5587i 2.00938 2.00938i
\(203\) 7.57754 + 11.4378i 0.531839 + 0.802775i
\(204\) 0 0
\(205\) −1.27252 1.15972i −0.0888767 0.0809981i
\(206\) 30.9292i 2.15494i
\(207\) 0 0
\(208\) −9.27431 9.27431i −0.643057 0.643057i
\(209\) −5.79246 −0.400673
\(210\) 0 0
\(211\) 11.9662 0.823785 0.411892 0.911233i \(-0.364868\pi\)
0.411892 + 0.911233i \(0.364868\pi\)
\(212\) 2.68420 + 2.68420i 0.184352 + 0.184352i
\(213\) 0 0
\(214\) 16.3445i 1.11729i
\(215\) 0.759730 + 16.3811i 0.0518132 + 1.11718i
\(216\) 0 0
\(217\) 8.91857 + 13.4620i 0.605432 + 0.913858i
\(218\) −13.8602 + 13.8602i −0.938734 + 0.938734i
\(219\) 0 0
\(220\) 11.9188 + 10.8622i 0.803564 + 0.732332i
\(221\) 3.73985 0.251570
\(222\) 0 0
\(223\) −0.660910 0.660910i −0.0442578 0.0442578i 0.684632 0.728889i \(-0.259963\pi\)
−0.728889 + 0.684632i \(0.759963\pi\)
\(224\) 31.3003 + 6.35418i 2.09134 + 0.424557i
\(225\) 0 0
\(226\) −9.47282 −0.630123
\(227\) 17.3487 17.3487i 1.15147 1.15147i 0.165216 0.986257i \(-0.447168\pi\)
0.986257 0.165216i \(-0.0528323\pi\)
\(228\) 0 0
\(229\) −25.0782 −1.65721 −0.828607 0.559831i \(-0.810866\pi\)
−0.828607 + 0.559831i \(0.810866\pi\)
\(230\) 23.1592 25.4118i 1.52707 1.67560i
\(231\) 0 0
\(232\) 28.2847 + 28.2847i 1.85698 + 1.85698i
\(233\) −2.24138 + 2.24138i −0.146837 + 0.146837i −0.776704 0.629866i \(-0.783110\pi\)
0.629866 + 0.776704i \(0.283110\pi\)
\(234\) 0 0
\(235\) 1.25560 + 27.0729i 0.0819064 + 1.76604i
\(236\) 15.7583i 1.02578i
\(237\) 0 0
\(238\) −17.2944 + 11.4576i −1.12103 + 0.742684i
\(239\) 21.3769i 1.38276i 0.722492 + 0.691380i \(0.242997\pi\)
−0.722492 + 0.691380i \(0.757003\pi\)
\(240\) 0 0
\(241\) 0.624129i 0.0402037i −0.999798 0.0201018i \(-0.993601\pi\)
0.999798 0.0201018i \(-0.00639905\pi\)
\(242\) −16.4931 16.4931i −1.06021 1.06021i
\(243\) 0 0
\(244\) −7.00393 −0.448381
\(245\) −6.54174 14.2199i −0.417937 0.908476i
\(246\) 0 0
\(247\) −3.51575 3.51575i −0.223702 0.223702i
\(248\) 33.2903 + 33.2903i 2.11394 + 2.11394i
\(249\) 0 0
\(250\) −4.07899 29.1484i −0.257978 1.84350i
\(251\) 16.3443i 1.03164i −0.856696 0.515822i \(-0.827487\pi\)
0.856696 0.515822i \(-0.172513\pi\)
\(252\) 0 0
\(253\) 6.04143 6.04143i 0.379821 0.379821i
\(254\) 29.2632i 1.83614i
\(255\) 0 0
\(256\) −9.88265 −0.617666
\(257\) −21.3054 + 21.3054i −1.32900 + 1.32900i −0.422749 + 0.906247i \(0.638935\pi\)
−0.906247 + 0.422749i \(0.861065\pi\)
\(258\) 0 0
\(259\) −8.27098 1.67907i −0.513933 0.104332i
\(260\) 0.641275 + 13.8270i 0.0397702 + 0.857514i
\(261\) 0 0
\(262\) 11.5079 11.5079i 0.710960 0.710960i
\(263\) 16.3449 16.3449i 1.00787 1.00787i 0.00789784 0.999969i \(-0.497486\pi\)
0.999969 0.00789784i \(-0.00251399\pi\)
\(264\) 0 0
\(265\) −0.0797641 1.71985i −0.00489987 0.105650i
\(266\) 27.0291 + 5.48709i 1.65726 + 0.336435i
\(267\) 0 0
\(268\) 29.2362 29.2362i 1.78589 1.78589i
\(269\) 16.5903 1.01153 0.505764 0.862672i \(-0.331211\pi\)
0.505764 + 0.862672i \(0.331211\pi\)
\(270\) 0 0
\(271\) 7.78033i 0.472621i 0.971678 + 0.236311i \(0.0759383\pi\)
−0.971678 + 0.236311i \(0.924062\pi\)
\(272\) −22.0005 + 22.0005i −1.33398 + 1.33398i
\(273\) 0 0
\(274\) 33.7136i 2.03671i
\(275\) −0.676964 7.28255i −0.0408224 0.439154i
\(276\) 0 0
\(277\) 21.3107 + 21.3107i 1.28043 + 1.28043i 0.940421 + 0.340013i \(0.110431\pi\)
0.340013 + 0.940421i \(0.389569\pi\)
\(278\) −22.3214 22.3214i −1.33875 1.33875i
\(279\) 0 0
\(280\) −26.9389 36.8344i −1.60991 2.20128i
\(281\) 21.1519 1.26182 0.630908 0.775858i \(-0.282683\pi\)
0.630908 + 0.775858i \(0.282683\pi\)
\(282\) 0 0
\(283\) 2.65471 + 2.65471i 0.157806 + 0.157806i 0.781594 0.623788i \(-0.214407\pi\)
−0.623788 + 0.781594i \(0.714407\pi\)
\(284\) 37.5977i 2.23101i
\(285\) 0 0
\(286\) 4.83508i 0.285905i
\(287\) 1.12510 + 1.69826i 0.0664126 + 0.100245i
\(288\) 0 0
\(289\) 8.12832i 0.478136i
\(290\) −1.41421 30.4929i −0.0830455 1.79060i
\(291\) 0 0
\(292\) −33.5928 + 33.5928i −1.96587 + 1.96587i
\(293\) 1.56714 + 1.56714i 0.0915536 + 0.0915536i 0.751400 0.659847i \(-0.229379\pi\)
−0.659847 + 0.751400i \(0.729379\pi\)
\(294\) 0 0
\(295\) 4.81428 5.28255i 0.280298 0.307562i
\(296\) −24.6056 −1.43017
\(297\) 0 0
\(298\) −0.180239 + 0.180239i −0.0104409 + 0.0104409i
\(299\) 7.33372 0.424120
\(300\) 0 0
\(301\) 3.86025 19.0153i 0.222501 1.09603i
\(302\) −25.0460 25.0460i −1.44123 1.44123i
\(303\) 0 0
\(304\) 41.3643 2.37240
\(305\) 2.34788 + 2.13975i 0.134439 + 0.122522i
\(306\) 0 0
\(307\) −17.3551 + 17.3551i −0.990510 + 0.990510i −0.999955 0.00944588i \(-0.996993\pi\)
0.00944588 + 0.999955i \(0.496993\pi\)
\(308\) −10.5380 15.9064i −0.600459 0.906352i
\(309\) 0 0
\(310\) −1.66449 35.8893i −0.0945368 2.03838i
\(311\) 31.0648i 1.76153i −0.473558 0.880763i \(-0.657030\pi\)
0.473558 0.880763i \(-0.342970\pi\)
\(312\) 0 0
\(313\) 5.72426 + 5.72426i 0.323554 + 0.323554i 0.850129 0.526575i \(-0.176524\pi\)
−0.526575 + 0.850129i \(0.676524\pi\)
\(314\) 6.13381 0.346151
\(315\) 0 0
\(316\) −22.2856 −1.25366
\(317\) −0.752579 0.752579i −0.0422691 0.0422691i 0.685656 0.727925i \(-0.259515\pi\)
−0.727925 + 0.685656i \(0.759515\pi\)
\(318\) 0 0
\(319\) 7.58562i 0.424713i
\(320\) −17.9932 16.3982i −1.00585 0.916686i
\(321\) 0 0
\(322\) −33.9138 + 22.4679i −1.88994 + 1.25209i
\(323\) −8.34005 + 8.34005i −0.464053 + 0.464053i
\(324\) 0 0
\(325\) 4.00928 4.83105i 0.222395 0.267978i
\(326\) −38.2518 −2.11857
\(327\) 0 0
\(328\) 4.19966 + 4.19966i 0.231887 + 0.231887i
\(329\) 6.37980 31.4265i 0.351730 1.73260i
\(330\) 0 0
\(331\) 15.8082 0.868899 0.434449 0.900696i \(-0.356943\pi\)
0.434449 + 0.900696i \(0.356943\pi\)
\(332\) −33.3175 + 33.3175i −1.82853 + 1.82853i
\(333\) 0 0
\(334\) −1.09085 −0.0596887
\(335\) −18.7326 + 0.868788i −1.02347 + 0.0474670i
\(336\) 0 0
\(337\) −20.0460 20.0460i −1.09197 1.09197i −0.995318 0.0966558i \(-0.969185\pi\)
−0.0966558 0.995318i \(-0.530815\pi\)
\(338\) 21.2644 21.2644i 1.15663 1.15663i
\(339\) 0 0
\(340\) 32.8004 1.52123i 1.77885 0.0825005i
\(341\) 8.92808i 0.483482i
\(342\) 0 0
\(343\) 3.39840 + 18.2058i 0.183497 + 0.983020i
\(344\) 56.5693i 3.05001i
\(345\) 0 0
\(346\) 12.8512i 0.690883i
\(347\) 20.0847 + 20.0847i 1.07820 + 1.07820i 0.996671 + 0.0815328i \(0.0259815\pi\)
0.0815328 + 0.996671i \(0.474018\pi\)
\(348\) 0 0
\(349\) 14.7663 0.790420 0.395210 0.918591i \(-0.370672\pi\)
0.395210 + 0.918591i \(0.370672\pi\)
\(350\) −3.73975 + 34.6235i −0.199898 + 1.85070i
\(351\) 0 0
\(352\) −12.4864 12.4864i −0.665525 0.665525i
\(353\) 12.4890 + 12.4890i 0.664724 + 0.664724i 0.956490 0.291766i \(-0.0942429\pi\)
−0.291766 + 0.956490i \(0.594243\pi\)
\(354\) 0 0
\(355\) −11.4864 + 12.6036i −0.609633 + 0.668931i
\(356\) 5.91570i 0.313531i
\(357\) 0 0
\(358\) −3.71839 + 3.71839i −0.196523 + 0.196523i
\(359\) 10.5372i 0.556133i 0.960562 + 0.278066i \(0.0896935\pi\)
−0.960562 + 0.278066i \(0.910306\pi\)
\(360\) 0 0
\(361\) −3.31943 −0.174707
\(362\) 15.7951 15.7951i 0.830171 0.830171i
\(363\) 0 0
\(364\) 3.25837 16.0505i 0.170785 0.841276i
\(365\) 21.5239 0.998247i 1.12661 0.0522507i
\(366\) 0 0
\(367\) 11.1910 11.1910i 0.584163 0.584163i −0.351881 0.936045i \(-0.614458\pi\)
0.936045 + 0.351881i \(0.114458\pi\)
\(368\) −43.1422 + 43.1422i −2.24894 + 2.24894i
\(369\) 0 0
\(370\) 13.8784 + 12.6482i 0.721505 + 0.657546i
\(371\) −0.405287 + 1.99642i −0.0210415 + 0.103649i
\(372\) 0 0
\(373\) 17.2746 17.2746i 0.894446 0.894446i −0.100492 0.994938i \(-0.532042\pi\)
0.994938 + 0.100492i \(0.0320416\pi\)
\(374\) 11.4698 0.593088
\(375\) 0 0
\(376\) 93.4917i 4.82147i
\(377\) 4.60412 4.60412i 0.237124 0.237124i
\(378\) 0 0
\(379\) 17.6237i 0.905267i 0.891697 + 0.452634i \(0.149515\pi\)
−0.891697 + 0.452634i \(0.850485\pi\)
\(380\) −32.2649 29.4048i −1.65516 1.50843i
\(381\) 0 0
\(382\) 14.5832 + 14.5832i 0.746141 + 0.746141i
\(383\) −16.1249 16.1249i −0.823942 0.823942i 0.162729 0.986671i \(-0.447970\pi\)
−0.986671 + 0.162729i \(0.947970\pi\)
\(384\) 0 0
\(385\) −1.32694 + 8.55164i −0.0676270 + 0.435832i
\(386\) 50.4894 2.56984
\(387\) 0 0
\(388\) −42.8343 42.8343i −2.17458 2.17458i
\(389\) 15.4011i 0.780865i −0.920632 0.390432i \(-0.872326\pi\)
0.920632 0.390432i \(-0.127674\pi\)
\(390\) 0 0
\(391\) 17.3971i 0.879807i
\(392\) 20.2697 + 50.0461i 1.02378 + 2.52771i
\(393\) 0 0
\(394\) 42.7360i 2.15301i
\(395\) 7.47066 + 6.80841i 0.375889 + 0.342568i
\(396\) 0 0
\(397\) 16.1781 16.1781i 0.811955 0.811955i −0.172972 0.984927i \(-0.555337\pi\)
0.984927 + 0.172972i \(0.0553370\pi\)
\(398\) 37.5026 + 37.5026i 1.87983 + 1.87983i
\(399\) 0 0
\(400\) 4.83424 + 52.0051i 0.241712 + 2.60026i
\(401\) 0.977595 0.0488188 0.0244094 0.999702i \(-0.492229\pi\)
0.0244094 + 0.999702i \(0.492229\pi\)
\(402\) 0 0
\(403\) 5.41892 5.41892i 0.269936 0.269936i
\(404\) 75.6382 3.76314
\(405\) 0 0
\(406\) −7.18572 + 35.3964i −0.356622 + 1.75670i
\(407\) 3.29947 + 3.29947i 0.163549 + 0.163549i
\(408\) 0 0
\(409\) 24.3171 1.20241 0.601203 0.799097i \(-0.294688\pi\)
0.601203 + 0.799097i \(0.294688\pi\)
\(410\) −0.209980 4.52753i −0.0103702 0.223599i
\(411\) 0 0
\(412\) −40.9583 + 40.9583i −2.01787 + 2.01787i
\(413\) −7.04992 + 4.67058i −0.346904 + 0.229824i
\(414\) 0 0
\(415\) 21.3475 0.990067i 1.04791 0.0486005i
\(416\) 15.1573i 0.743146i
\(417\) 0 0
\(418\) −10.7825 10.7825i −0.527388 0.527388i
\(419\) −15.9893 −0.781127 −0.390563 0.920576i \(-0.627720\pi\)
−0.390563 + 0.920576i \(0.627720\pi\)
\(420\) 0 0
\(421\) 14.7000 0.716433 0.358216 0.933639i \(-0.383385\pi\)
0.358216 + 0.933639i \(0.383385\pi\)
\(422\) 22.2746 + 22.2746i 1.08431 + 1.08431i
\(423\) 0 0
\(424\) 5.93921i 0.288434i
\(425\) −11.4602 9.51081i −0.555902 0.461342i
\(426\) 0 0
\(427\) −2.07588 3.13341i −0.100459 0.151636i
\(428\) 21.6443 21.6443i 1.04622 1.04622i
\(429\) 0 0
\(430\) −29.0787 + 31.9071i −1.40230 + 1.53870i
\(431\) −22.2722 −1.07281 −0.536407 0.843960i \(-0.680219\pi\)
−0.536407 + 0.843960i \(0.680219\pi\)
\(432\) 0 0
\(433\) −28.0171 28.0171i −1.34642 1.34642i −0.889520 0.456896i \(-0.848961\pi\)
−0.456896 0.889520i \(-0.651039\pi\)
\(434\) −8.45741 + 41.6606i −0.405968 + 1.99978i
\(435\) 0 0
\(436\) −36.7091 −1.75805
\(437\) −16.3545 + 16.3545i −0.782344 + 0.782344i
\(438\) 0 0
\(439\) −2.35656 −0.112473 −0.0562363 0.998417i \(-0.517910\pi\)
−0.0562363 + 0.998417i \(0.517910\pi\)
\(440\) 1.16889 + 25.2033i 0.0557246 + 1.20152i
\(441\) 0 0
\(442\) 6.96162 + 6.96162i 0.331130 + 0.331130i
\(443\) 5.47247 5.47247i 0.260005 0.260005i −0.565051 0.825056i \(-0.691144\pi\)
0.825056 + 0.565051i \(0.191144\pi\)
\(444\) 0 0
\(445\) −1.80729 + 1.98308i −0.0856737 + 0.0940071i
\(446\) 2.46053i 0.116509i
\(447\) 0 0
\(448\) 15.9087 + 24.0131i 0.751616 + 1.13451i
\(449\) 1.20020i 0.0566410i 0.999599 + 0.0283205i \(0.00901591\pi\)
−0.999599 + 0.0283205i \(0.990984\pi\)
\(450\) 0 0
\(451\) 1.12630i 0.0530354i
\(452\) −12.5444 12.5444i −0.590041 0.590041i
\(453\) 0 0
\(454\) 64.5881 3.03127
\(455\) −5.99583 + 4.38505i −0.281089 + 0.205575i
\(456\) 0 0
\(457\) −21.0775 21.0775i −0.985962 0.985962i 0.0139406 0.999903i \(-0.495562\pi\)
−0.999903 + 0.0139406i \(0.995562\pi\)
\(458\) −46.6823 46.6823i −2.18132 2.18132i
\(459\) 0 0
\(460\) 64.3204 2.98308i 2.99896 0.139087i
\(461\) 21.9670i 1.02311i 0.859252 + 0.511553i \(0.170929\pi\)
−0.859252 + 0.511553i \(0.829071\pi\)
\(462\) 0 0
\(463\) −21.6776 + 21.6776i −1.00744 + 1.00744i −0.00746987 + 0.999972i \(0.502378\pi\)
−0.999972 + 0.00746987i \(0.997622\pi\)
\(464\) 54.1694i 2.51475i
\(465\) 0 0
\(466\) −8.34450 −0.386551
\(467\) −7.11299 + 7.11299i −0.329150 + 0.329150i −0.852263 0.523113i \(-0.824770\pi\)
0.523113 + 0.852263i \(0.324770\pi\)
\(468\) 0 0
\(469\) 21.7449 + 4.41438i 1.00409 + 0.203837i
\(470\) −48.0581 + 52.7326i −2.21676 + 2.43237i
\(471\) 0 0
\(472\) −17.4338 + 17.4338i −0.802457 + 0.802457i
\(473\) −7.58562 + 7.58562i −0.348787 + 0.348787i
\(474\) 0 0
\(475\) 1.83259 + 19.7144i 0.0840848 + 0.904557i
\(476\) −38.0750 7.72950i −1.74517 0.354281i
\(477\) 0 0
\(478\) −39.7925 + 39.7925i −1.82007 + 1.82007i
\(479\) −31.7749 −1.45183 −0.725917 0.687782i \(-0.758584\pi\)
−0.725917 + 0.687782i \(0.758584\pi\)
\(480\) 0 0
\(481\) 4.00524i 0.182623i
\(482\) 1.16180 1.16180i 0.0529184 0.0529184i
\(483\) 0 0
\(484\) 43.6821i 1.98555i
\(485\) 1.27287 + 27.4453i 0.0577981 + 1.24623i
\(486\) 0 0
\(487\) −4.81428 4.81428i −0.218156 0.218156i 0.589565 0.807721i \(-0.299299\pi\)
−0.807721 + 0.589565i \(0.799299\pi\)
\(488\) −7.74864 7.74864i −0.350765 0.350765i
\(489\) 0 0
\(490\) 14.2926 38.6471i 0.645676 1.74590i
\(491\) −28.3401 −1.27897 −0.639484 0.768804i \(-0.720852\pi\)
−0.639484 + 0.768804i \(0.720852\pi\)
\(492\) 0 0
\(493\) −10.9219 10.9219i −0.491897 0.491897i
\(494\) 13.0889i 0.588897i
\(495\) 0 0
\(496\) 63.7559i 2.86273i
\(497\) 16.8204 11.1435i 0.754497 0.499855i
\(498\) 0 0
\(499\) 3.39197i 0.151845i 0.997114 + 0.0759227i \(0.0241902\pi\)
−0.997114 + 0.0759227i \(0.975810\pi\)
\(500\) 33.1983 44.0016i 1.48467 1.96781i
\(501\) 0 0
\(502\) 30.4244 30.4244i 1.35791 1.35791i
\(503\) 8.32921 + 8.32921i 0.371381 + 0.371381i 0.867980 0.496599i \(-0.165418\pi\)
−0.496599 + 0.867980i \(0.665418\pi\)
\(504\) 0 0
\(505\) −25.3557 23.1080i −1.12831 1.02829i
\(506\) 22.4918 0.999884
\(507\) 0 0
\(508\) −38.7520 + 38.7520i −1.71934 + 1.71934i
\(509\) 38.9452 1.72622 0.863108 0.505020i \(-0.168515\pi\)
0.863108 + 0.505020i \(0.168515\pi\)
\(510\) 0 0
\(511\) −24.9852 5.07217i −1.10528 0.224380i
\(512\) −24.7846 24.7846i −1.09534 1.09534i
\(513\) 0 0
\(514\) −79.3187 −3.49860
\(515\) 26.2432 1.21712i 1.15641 0.0536328i
\(516\) 0 0
\(517\) −12.5367 + 12.5367i −0.551364 + 0.551364i
\(518\) −12.2706 18.5217i −0.539140 0.813796i
\(519\) 0 0
\(520\) −14.5877 + 16.0066i −0.639714 + 0.701938i
\(521\) 7.06726i 0.309622i 0.987944 + 0.154811i \(0.0494769\pi\)
−0.987944 + 0.154811i \(0.950523\pi\)
\(522\) 0 0
\(523\) 14.5887 + 14.5887i 0.637921 + 0.637921i 0.950042 0.312121i \(-0.101040\pi\)
−0.312121 + 0.950042i \(0.601040\pi\)
\(524\) 30.4788 1.33147
\(525\) 0 0
\(526\) 60.8508 2.65322
\(527\) −12.8548 12.8548i −0.559962 0.559962i
\(528\) 0 0
\(529\) 11.1150i 0.483261i
\(530\) 3.05297 3.34993i 0.132613 0.145511i
\(531\) 0 0
\(532\) 28.5271 + 43.0597i 1.23681 + 1.86688i
\(533\) 0.683611 0.683611i 0.0296105 0.0296105i
\(534\) 0 0
\(535\) −13.8682 + 0.643185i −0.599574 + 0.0278073i
\(536\) 64.6897 2.79417
\(537\) 0 0
\(538\) 30.8823 + 30.8823i 1.33143 + 1.33143i
\(539\) 3.99284 9.42895i 0.171984 0.406134i
\(540\) 0 0
\(541\) 18.6013 0.799731 0.399865 0.916574i \(-0.369057\pi\)
0.399865 + 0.916574i \(0.369057\pi\)
\(542\) −14.4828 + 14.4828i −0.622091 + 0.622091i
\(543\) 0 0
\(544\) −35.9560 −1.54160
\(545\) 12.3057 + 11.2149i 0.527120 + 0.480393i
\(546\) 0 0
\(547\) −7.22715 7.22715i −0.309011 0.309011i 0.535515 0.844526i \(-0.320118\pi\)
−0.844526 + 0.535515i \(0.820118\pi\)
\(548\) 44.6455 44.6455i 1.90716 1.90716i
\(549\) 0 0
\(550\) 12.2961 14.8164i 0.524307 0.631772i
\(551\) 20.5348i 0.874812i
\(552\) 0 0
\(553\) −6.60519 9.97009i −0.280881 0.423971i
\(554\) 79.3382i 3.37076i
\(555\) 0 0
\(556\) 59.1185i 2.50718i
\(557\) 0.558927 + 0.558927i 0.0236825 + 0.0236825i 0.718849 0.695166i \(-0.244669\pi\)
−0.695166 + 0.718849i \(0.744669\pi\)
\(558\) 0 0
\(559\) −9.20823 −0.389467
\(560\) 9.47575 61.0678i 0.400423 2.58059i
\(561\) 0 0
\(562\) 39.3736 + 39.3736i 1.66087 + 1.66087i
\(563\) −0.702475 0.702475i −0.0296058 0.0296058i 0.692149 0.721755i \(-0.256664\pi\)
−0.721755 + 0.692149i \(0.756664\pi\)
\(564\) 0 0
\(565\) 0.372772 + 8.03762i 0.0156827 + 0.338145i
\(566\) 9.88333i 0.415427i
\(567\) 0 0
\(568\) 41.5953 41.5953i 1.74530 1.74530i
\(569\) 9.72049i 0.407504i −0.979023 0.203752i \(-0.934686\pi\)
0.979023 0.203752i \(-0.0653137\pi\)
\(570\) 0 0
\(571\) −0.986684 −0.0412914 −0.0206457 0.999787i \(-0.506572\pi\)
−0.0206457 + 0.999787i \(0.506572\pi\)
\(572\) −6.40289 + 6.40289i −0.267718 + 0.267718i
\(573\) 0 0
\(574\) −1.06692 + 5.25560i −0.0445326 + 0.219365i
\(575\) −22.4731 18.6504i −0.937192 0.777774i
\(576\) 0 0
\(577\) −10.3510 + 10.3510i −0.430917 + 0.430917i −0.888940 0.458024i \(-0.848558\pi\)
0.458024 + 0.888940i \(0.348558\pi\)
\(578\) −15.1306 + 15.1306i −0.629350 + 0.629350i
\(579\) 0 0
\(580\) 38.5076 42.2532i 1.59894 1.75447i
\(581\) −24.7804 5.03060i −1.02807 0.208705i
\(582\) 0 0
\(583\) 0.796415 0.796415i 0.0329841 0.0329841i
\(584\) −74.3292 −3.07576
\(585\) 0 0
\(586\) 5.83438i 0.241016i
\(587\) 21.1413 21.1413i 0.872594 0.872594i −0.120160 0.992755i \(-0.538341\pi\)
0.992755 + 0.120160i \(0.0383409\pi\)
\(588\) 0 0
\(589\) 24.1689i 0.995862i
\(590\) 18.7949 0.871680i 0.773774 0.0358865i
\(591\) 0 0
\(592\) −23.5617 23.5617i −0.968381 0.968381i
\(593\) −7.07816 7.07816i −0.290665 0.290665i 0.546678 0.837343i \(-0.315892\pi\)
−0.837343 + 0.546678i \(0.815892\pi\)
\(594\) 0 0
\(595\) 10.4022 + 14.2233i 0.426450 + 0.583099i
\(596\) −0.477365 −0.0195536
\(597\) 0 0
\(598\) 13.6515 + 13.6515i 0.558251 + 0.558251i
\(599\) 7.13847i 0.291670i 0.989309 + 0.145835i \(0.0465869\pi\)
−0.989309 + 0.145835i \(0.953413\pi\)
\(600\) 0 0
\(601\) 35.0829i 1.43106i 0.698580 + 0.715532i \(0.253815\pi\)
−0.698580 + 0.715532i \(0.746185\pi\)
\(602\) 42.5822 28.2107i 1.73552 1.14978i
\(603\) 0 0
\(604\) 66.3346i 2.69912i
\(605\) −13.3452 + 14.6433i −0.542560 + 0.595334i
\(606\) 0 0
\(607\) −5.36385 + 5.36385i −0.217712 + 0.217712i −0.807533 0.589822i \(-0.799198\pi\)
0.589822 + 0.807533i \(0.299198\pi\)
\(608\) 33.8014 + 33.8014i 1.37083 + 1.37083i
\(609\) 0 0
\(610\) 0.387427 + 8.35359i 0.0156865 + 0.338227i
\(611\) −15.2184 −0.615670
\(612\) 0 0
\(613\) −10.4888 + 10.4888i −0.423639 + 0.423639i −0.886454 0.462816i \(-0.846839\pi\)
0.462816 + 0.886454i \(0.346839\pi\)
\(614\) −64.6120 −2.60753
\(615\) 0 0
\(616\) 5.93921 29.2562i 0.239298 1.17877i
\(617\) −19.7986 19.7986i −0.797060 0.797060i 0.185571 0.982631i \(-0.440586\pi\)
−0.982631 + 0.185571i \(0.940586\pi\)
\(618\) 0 0
\(619\) −12.0675 −0.485034 −0.242517 0.970147i \(-0.577973\pi\)
−0.242517 + 0.970147i \(0.577973\pi\)
\(620\) 45.3224 49.7309i 1.82019 1.99724i
\(621\) 0 0
\(622\) 57.8262 57.8262i 2.31862 2.31862i
\(623\) 2.64655 1.75334i 0.106032 0.0702462i
\(624\) 0 0
\(625\) −24.5717 + 4.60803i −0.982866 + 0.184321i
\(626\) 21.3110i 0.851761i
\(627\) 0 0
\(628\) 8.12275 + 8.12275i 0.324133 + 0.324133i
\(629\) 9.50124 0.378839
\(630\) 0 0
\(631\) 30.4435 1.21194 0.605969 0.795488i \(-0.292786\pi\)
0.605969 + 0.795488i \(0.292786\pi\)
\(632\) −24.6552 24.6552i −0.980730 0.980730i
\(633\) 0 0
\(634\) 2.80180i 0.111274i
\(635\) 24.8296 1.15156i 0.985332 0.0456982i
\(636\) 0 0
\(637\) 8.14639 3.29946i 0.322772 0.130729i
\(638\) 14.1204 14.1204i 0.559032 0.559032i
\(639\) 0 0
\(640\) −0.467961 10.0901i −0.0184978 0.398844i
\(641\) −36.5929 −1.44533 −0.722666 0.691198i \(-0.757083\pi\)
−0.722666 + 0.691198i \(0.757083\pi\)
\(642\) 0 0
\(643\) −12.1140 12.1140i −0.477731 0.477731i 0.426675 0.904405i \(-0.359685\pi\)
−0.904405 + 0.426675i \(0.859685\pi\)
\(644\) −74.6638 15.1573i −2.94217 0.597280i
\(645\) 0 0
\(646\) −31.0495 −1.22163
\(647\) 19.0978 19.0978i 0.750814 0.750814i −0.223817 0.974631i \(-0.571852\pi\)
0.974631 + 0.223817i \(0.0718519\pi\)
\(648\) 0 0
\(649\) 4.67556 0.183532
\(650\) 16.4560 1.52970i 0.645457 0.0599997i
\(651\) 0 0
\(652\) −50.6552 50.6552i −1.98381 1.98381i
\(653\) −20.3709 + 20.3709i −0.797173 + 0.797173i −0.982649 0.185476i \(-0.940617\pi\)
0.185476 + 0.982649i \(0.440617\pi\)
\(654\) 0 0
\(655\) −10.2172 9.31151i −0.399220 0.363831i
\(656\) 8.04298i 0.314026i
\(657\) 0 0
\(658\) 70.3752 46.6236i 2.74351 1.81758i
\(659\) 31.4882i 1.22661i −0.789847 0.613304i \(-0.789840\pi\)
0.789847 0.613304i \(-0.210160\pi\)
\(660\) 0 0
\(661\) 48.1880i 1.87430i 0.348931 + 0.937149i \(0.386545\pi\)
−0.348931 + 0.937149i \(0.613455\pi\)
\(662\) 29.4265 + 29.4265i 1.14369 + 1.14369i
\(663\) 0 0
\(664\) −73.7201 −2.86089
\(665\) 3.59211 23.1499i 0.139296 0.897714i
\(666\) 0 0
\(667\) −21.4174 21.4174i −0.829286 0.829286i
\(668\) −1.44457 1.44457i −0.0558920 0.0558920i
\(669\) 0 0
\(670\) −36.4873 33.2528i −1.40963 1.28467i
\(671\) 2.07810i 0.0802241i
\(672\) 0 0
\(673\) −30.6900 + 30.6900i −1.18301 + 1.18301i −0.204055 + 0.978960i \(0.565412\pi\)
−0.978960 + 0.204055i \(0.934588\pi\)
\(674\) 74.6299i 2.87463i
\(675\) 0 0
\(676\) 56.3191 2.16612
\(677\) 1.54060 1.54060i 0.0592101 0.0592101i −0.676882 0.736092i \(-0.736669\pi\)
0.736092 + 0.676882i \(0.236669\pi\)
\(678\) 0 0
\(679\) 6.46755 31.8587i 0.248202 1.22263i
\(680\) 37.9710 + 34.6050i 1.45612 + 1.32704i
\(681\) 0 0
\(682\) 16.6193 16.6193i 0.636387 0.636387i
\(683\) −14.2154 + 14.2154i −0.543936 + 0.543936i −0.924680 0.380744i \(-0.875668\pi\)
0.380744 + 0.924680i \(0.375668\pi\)
\(684\) 0 0
\(685\) −28.6057 + 1.32669i −1.09297 + 0.0506903i
\(686\) −27.5635 + 40.2155i −1.05238 + 1.53544i
\(687\) 0 0
\(688\) 54.1694 54.1694i 2.06519 2.06519i
\(689\) 0.966772 0.0368311
\(690\) 0 0
\(691\) 10.2887i 0.391401i −0.980664 0.195700i \(-0.937302\pi\)
0.980664 0.195700i \(-0.0626980\pi\)
\(692\) −17.0182 + 17.0182i −0.646937 + 0.646937i
\(693\) 0 0
\(694\) 74.7741i 2.83838i
\(695\) −18.0611 + 19.8179i −0.685098 + 0.751736i
\(696\) 0 0
\(697\) −1.62166 1.62166i −0.0614248 0.0614248i
\(698\) 27.4869 + 27.4869i 1.04040 + 1.04040i
\(699\) 0 0
\(700\) −50.8028 + 40.8980i −1.92016 + 1.54580i
\(701\) 44.3183 1.67388 0.836939 0.547297i \(-0.184343\pi\)
0.836939 + 0.547297i \(0.184343\pi\)
\(702\) 0 0
\(703\) −8.93189 8.93189i −0.336872 0.336872i
\(704\) 15.9257i 0.600222i
\(705\) 0 0
\(706\) 46.4958i 1.74989i
\(707\) 22.4183 + 33.8389i 0.843126 + 1.27264i
\(708\) 0 0
\(709\) 0.817976i 0.0307197i −0.999882 0.0153599i \(-0.995111\pi\)
0.999882 0.0153599i \(-0.00488939\pi\)
\(710\) −44.8427 + 2.07974i −1.68292 + 0.0780512i
\(711\) 0 0
\(712\) 6.54470 6.54470i 0.245273 0.245273i
\(713\) −25.2077 25.2077i −0.944037 0.944037i
\(714\) 0 0
\(715\) 4.10253 0.190269i 0.153426 0.00711567i
\(716\) −9.84821 −0.368045
\(717\) 0 0
\(718\) −19.6147 + 19.6147i −0.732013 + 0.732013i
\(719\) −0.00762056 −0.000284199 −0.000142099 1.00000i \(-0.500045\pi\)
−0.000142099 1.00000i \(0.500045\pi\)
\(720\) 0 0
\(721\) −30.4634 6.18428i −1.13452 0.230315i
\(722\) −6.17902 6.17902i −0.229959 0.229959i
\(723\) 0 0
\(724\) 41.8335 1.55473
\(725\) −25.8173 + 2.39990i −0.958831 + 0.0891300i
\(726\) 0 0
\(727\) 28.5738 28.5738i 1.05974 1.05974i 0.0616465 0.998098i \(-0.480365\pi\)
0.998098 0.0616465i \(-0.0196352\pi\)
\(728\) 21.3619 14.1523i 0.791726 0.524519i
\(729\) 0 0
\(730\) 41.9243 + 38.2079i 1.55169 + 1.41414i
\(731\) 21.8438i 0.807921i
\(732\) 0 0
\(733\) −24.1522 24.1522i −0.892083 0.892083i 0.102636 0.994719i \(-0.467272\pi\)
−0.994719 + 0.102636i \(0.967272\pi\)
\(734\) 41.6632 1.53782
\(735\) 0 0
\(736\) −70.5085 −2.59898
\(737\) −8.67452 8.67452i −0.319530 0.319530i
\(738\) 0 0
\(739\) 37.9522i 1.39609i −0.716052 0.698047i \(-0.754053\pi\)
0.716052 0.698047i \(-0.245947\pi\)
\(740\) 1.62918 + 35.1280i 0.0598900 + 1.29133i
\(741\) 0 0
\(742\) −4.47070 + 2.96184i −0.164125 + 0.108733i
\(743\) 18.8022 18.8022i 0.689784 0.689784i −0.272400 0.962184i \(-0.587817\pi\)
0.962184 + 0.272400i \(0.0878174\pi\)
\(744\) 0 0
\(745\) 0.160024 + 0.145838i 0.00586282 + 0.00534311i
\(746\) 64.3123 2.35464
\(747\) 0 0
\(748\) 15.1889 + 15.1889i 0.555363 + 0.555363i
\(749\) 16.0983 + 3.26807i 0.588220 + 0.119413i
\(750\) 0 0
\(751\) 0.105915 0.00386490 0.00193245 0.999998i \(-0.499385\pi\)
0.00193245 + 0.999998i \(0.499385\pi\)
\(752\) 89.5254 89.5254i 3.26466 3.26466i
\(753\) 0 0
\(754\) 17.1408 0.624232
\(755\) −20.2657 + 22.2369i −0.737545 + 0.809284i
\(756\) 0 0
\(757\) 3.14514 + 3.14514i 0.114312 + 0.114312i 0.761949 0.647637i \(-0.224243\pi\)
−0.647637 + 0.761949i \(0.724243\pi\)
\(758\) −32.8059 + 32.8059i −1.19156 + 1.19156i
\(759\) 0 0
\(760\) −3.16426 68.2269i −0.114780 2.47485i
\(761\) 35.1123i 1.27282i −0.771351 0.636410i \(-0.780419\pi\)
0.771351 0.636410i \(-0.219581\pi\)
\(762\) 0 0
\(763\) −10.8801 16.4228i −0.393887 0.594547i
\(764\) 38.6238i 1.39736i
\(765\) 0 0
\(766\) 60.0318i 2.16904i
\(767\) 2.83784 + 2.83784i 0.102469 + 0.102469i
\(768\) 0 0
\(769\) 8.16835 0.294558 0.147279 0.989095i \(-0.452948\pi\)
0.147279 + 0.989095i \(0.452948\pi\)
\(770\) −18.3887 + 13.4486i −0.662681 + 0.484652i
\(771\) 0 0
\(772\) 66.8609 + 66.8609i 2.40638 + 2.40638i
\(773\) 2.51166 + 2.51166i 0.0903382 + 0.0903382i 0.750832 0.660494i \(-0.229653\pi\)
−0.660494 + 0.750832i \(0.729653\pi\)
\(774\) 0 0
\(775\) −30.3863 + 2.82462i −1.09151 + 0.101463i
\(776\) 94.7776i 3.40232i
\(777\) 0 0
\(778\) 28.6686 28.6686i 1.02782 1.02782i
\(779\) 3.04897i 0.109241i
\(780\) 0 0
\(781\) −11.1554 −0.399171
\(782\) 32.3840 32.3840i 1.15805 1.15805i
\(783\) 0 0
\(784\) −28.5131 + 67.3327i −1.01833 + 2.40474i
\(785\) −0.241377 5.20449i −0.00861510 0.185756i