Properties

Label 315.2.p.e.118.8
Level 315
Weight 2
Character 315.118
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 118.8
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 \(\chi\) \(=\) 315.118
Dual form 315.2.p.e.307.8

$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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 0.399541 0.916715i \(-0.369169\pi\)
0.916715 0.399541i \(-0.130831\pi\)
\(3\) 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 −0.573183 0.819427i \(-0.694292\pi\)
0.819427 + 0.573183i \(0.194292\pi\)
\(14\) −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 0.914776 0.403961i \(-0.132367\pi\)
−0.403961 + 0.914776i \(0.632367\pi\)
\(18\) 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 0.991475 0.130295i \(-0.0415926\pi\)
−0.130295 + 0.991475i \(0.541593\pi\)
\(24\) 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 \(0.159901\pi\)
−0.876456 + 0.481482i \(0.840099\pi\)
\(30\) 0 0
\(31\) 6.10346i 1.09621i 0.836408 + 0.548107i \(0.184651\pi\)
−0.836408 + 0.548107i \(0.815349\pi\)
\(32\) −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 −0.496957 0.867775i \(-0.665549\pi\)
0.867775 + 0.496957i \(0.165549\pi\)
\(38\) −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 \(0.0191497\pi\)
−0.998191 + 0.0601244i \(0.980850\pi\)
\(42\) 0 0
\(43\) −5.18572 5.18572i −0.790816 0.790816i 0.190811 0.981627i \(-0.438888\pi\)
−0.981627 + 0.190811i \(0.938888\pi\)
\(44\) 7.21173i 1.08721i
\(45\) 0 0
\(46\) 15.3760 2.26707
\(47\) −8.57041 8.57041i −1.25012 1.25012i −0.955664 0.294459i \(-0.904861\pi\)
−0.294459 0.955664i \(-0.595139\pi\)
\(48\) 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 0.743510 0.668724i \(-0.233159\pi\)
−0.668724 + 0.743510i \(0.733159\pi\)
\(54\) 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 \(-0.971011\pi\)
0.995856 0.0909472i \(-0.0289894\pi\)
\(62\) 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 −0.969514 0.245034i \(-0.921201\pi\)
0.245034 + 0.969514i \(0.421201\pi\)
\(68\) 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 −0.185207 0.982700i \(-0.559296\pi\)
0.982700 + 0.185207i \(0.0592955\pi\)
\(74\) 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 \(-0.918159\pi\)
0.967129 0.254286i \(-0.0818405\pi\)
\(80\) −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 −0.231140 0.972921i \(-0.574246\pi\)
0.972921 + 0.231140i \(0.0742455\pi\)
\(84\) 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 0.111592 0.993754i \(-0.464405\pi\)
−0.993754 + 0.111592i \(0.964405\pi\)
\(98\) 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 \(0.276420\pi\)
−0.646050 + 0.763295i \(0.723580\pi\)
\(102\) 0 0
\(103\) 8.30776 8.30776i 0.818588 0.818588i −0.167316 0.985903i \(-0.553510\pi\)
0.985903 + 0.167316i \(0.0535099\pi\)
\(104\) −9.68519 −0.949711
\(105\) 0 0
\(106\) 2.02695 0.196875
\(107\) −4.39022 + 4.39022i −0.424418 + 0.424418i −0.886722 0.462303i \(-0.847023\pi\)
0.462303 + 0.886722i \(0.347023\pi\)
\(108\) 0 0
\(109\) 7.44587i 0.713185i −0.934260 0.356593i \(-0.883938\pi\)
0.934260 0.356593i \(-0.116062\pi\)
\(110\) 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 0.577224 0.816586i \(-0.304136\pi\)
−0.816586 + 0.577224i \(0.804136\pi\)
\(114\) 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 −0.266383 0.963867i \(-0.585829\pi\)
0.963867 + 0.266383i \(0.0858286\pi\)
\(128\) 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 \(0.0870465\pi\)
−0.962841 + 0.270069i \(0.912953\pi\)
\(132\) 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 −0.978747 0.205071i \(-0.934258\pi\)
0.205071 + 0.978747i \(0.434258\pi\)
\(138\) 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 \(-0.998738\pi\)
0.999992 0.00396615i \(-0.00126247\pi\)
\(150\) 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 0.769789 0.638298i \(-0.220361\pi\)
−0.638298 + 0.769789i \(0.720361\pi\)
\(158\) −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 0.179066 0.983837i \(-0.442692\pi\)
−0.983837 + 0.179066i \(0.942692\pi\)
\(164\) 3.79604 0.296421
\(165\) 0 0
\(166\) 25.1594i 1.95275i
\(167\) −0.293008 0.293008i −0.0226737 0.0226737i 0.695679 0.718353i \(-0.255104\pi\)
−0.718353 + 0.695679i \(0.755104\pi\)
\(168\) 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 −0.563603 0.826046i \(-0.690585\pi\)
0.826046 + 0.563603i \(0.190585\pi\)
\(174\) 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 \(-0.976215\pi\)
0.997210 0.0746523i \(-0.0237847\pi\)
\(180\) 0 0
\(181\) 8.48528i 0.630706i 0.948974 + 0.315353i \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) −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 0.999723 0.0235293i \(-0.00749029\pi\)
−0.0235293 + 0.999723i \(0.507490\pi\)
\(194\) −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 −0.167943 0.985797i \(-0.553713\pi\)
0.985797 + 0.167943i \(0.0537126\pi\)
\(198\) 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 −0.728889 0.684632i \(-0.759963\pi\)
0.684632 + 0.728889i \(0.259963\pi\)
\(224\) 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 0.986257 + 0.165216i \(0.0528323\pi\)
0.165216 + 0.986257i \(0.447168\pi\)
\(228\) 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 0.629866 0.776704i \(-0.283110\pi\)
−0.776704 + 0.629866i \(0.783110\pi\)
\(234\) 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 \(-0.757003\pi\)
0.722492 0.691380i \(-0.242997\pi\)
\(240\) 0 0
\(241\) 0.624129i 0.0402037i 0.999798 + 0.0201018i \(0.00639905\pi\)
−0.999798 + 0.0201018i \(0.993601\pi\)
\(242\) −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 \(0.172513\pi\)
−0.856696 + 0.515822i \(0.827487\pi\)
\(252\) 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 −0.906247 0.422749i \(-0.861065\pi\)
−0.422749 0.906247i \(-0.638935\pi\)
\(258\) 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 0.999969 + 0.00789784i \(0.00251399\pi\)
0.00789784 + 0.999969i \(0.497486\pi\)
\(264\) 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 \(-0.924062\pi\)
0.971678 0.236311i \(-0.0759383\pi\)
\(272\) −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 0.340013 0.940421i \(-0.389569\pi\)
0.940421 0.340013i \(-0.110431\pi\)
\(278\) −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 −0.623788 0.781594i \(-0.714407\pi\)
0.781594 + 0.623788i \(0.214407\pi\)
\(284\) 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 −0.659847 0.751400i \(-0.729379\pi\)
0.751400 + 0.659847i \(0.229379\pi\)
\(294\) 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 0.00944588 0.999955i \(-0.496993\pi\)
−0.999955 + 0.00944588i \(0.996993\pi\)
\(308\) −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 \(0.342970\pi\)
−0.473558 + 0.880763i \(0.657030\pi\)
\(312\) 0 0
\(313\) 5.72426 5.72426i 0.323554 0.323554i −0.526575 0.850129i \(-0.676524\pi\)
0.850129 + 0.526575i \(0.176524\pi\)
\(314\) 6.13381 0.346151
\(315\) 0 0
\(316\) −22.2856 −1.25366
\(317\) −0.752579 + 0.752579i −0.0422691 + 0.0422691i −0.727925 0.685656i \(-0.759515\pi\)
0.685656 + 0.727925i \(0.259515\pi\)
\(318\) 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 −0.0966558 + 0.995318i \(0.530815\pi\)
−0.995318 + 0.0966558i \(0.969185\pi\)
\(338\) 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 0.0815328 0.996671i \(-0.474018\pi\)
0.996671 0.0815328i \(-0.0259815\pi\)
\(348\) 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 −0.291766 0.956490i \(-0.594243\pi\)
0.956490 + 0.291766i \(0.0942429\pi\)
\(354\) 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 \(-0.910306\pi\)
0.960562 0.278066i \(-0.0896935\pi\)
\(360\) 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 0.936045 0.351881i \(-0.114458\pi\)
−0.351881 + 0.936045i \(0.614458\pi\)
\(368\) −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 0.994938 0.100492i \(-0.0320416\pi\)
−0.100492 + 0.994938i \(0.532042\pi\)
\(374\) 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 \(-0.850485\pi\)
0.891697 0.452634i \(-0.149515\pi\)
\(380\) −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 −0.986671 0.162729i \(-0.947970\pi\)
0.162729 + 0.986671i \(0.447970\pi\)
\(384\) 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 \(0.127674\pi\)
−0.920632 + 0.390432i \(0.872326\pi\)
\(390\) 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 0.984927 0.172972i \(-0.0553370\pi\)
−0.172972 + 0.984927i \(0.555337\pi\)
\(398\) 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 −0.456896 + 0.889520i \(0.651039\pi\)
−0.889520 + 0.456896i \(0.848961\pi\)
\(434\) −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 0.825056 0.565051i \(-0.191144\pi\)
−0.565051 + 0.825056i \(0.691144\pi\)
\(444\) 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 \(-0.990984\pi\)
0.999599 0.0283205i \(-0.00901591\pi\)
\(450\) 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 −0.999903 0.0139406i \(-0.995562\pi\)
0.0139406 + 0.999903i \(0.495562\pi\)
\(458\) −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 \(-0.829071\pi\)
0.859252 0.511553i \(-0.170929\pi\)
\(462\) 0 0
\(463\) −21.6776 21.6776i −1.00744 1.00744i −0.999972 0.00746987i \(-0.997622\pi\)
−0.00746987 0.999972i \(-0.502378\pi\)
\(464\) 54.1694i 2.51475i
\(465\) 0 0
\(466\) −8.34450 −0.386551
\(467\) −7.11299 7.11299i −0.329150 0.329150i 0.523113 0.852263i \(-0.324770\pi\)
−0.852263 + 0.523113i \(0.824770\pi\)
\(468\) 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 −0.807721 0.589565i \(-0.799299\pi\)
0.589565 + 0.807721i \(0.299299\pi\)
\(488\) −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 \(-0.975810\pi\)
0.997114 0.0759227i \(-0.0241902\pi\)
\(500\) 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 −0.496599 0.867980i \(-0.665418\pi\)
0.867980 + 0.496599i \(0.165418\pi\)
\(504\) 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 \(-0.950523\pi\)
0.987944 0.154811i \(-0.0494769\pi\)
\(522\) 0 0
\(523\) 14.5887 14.5887i 0.637921 0.637921i −0.312121 0.950042i \(-0.601040\pi\)
0.950042 + 0.312121i \(0.101040\pi\)
\(524\) 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 −0.844526 0.535515i \(-0.820118\pi\)
0.535515 + 0.844526i \(0.320118\pi\)
\(548\) 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 −0.695166 0.718849i \(-0.744669\pi\)
0.718849 + 0.695166i \(0.244669\pi\)
\(558\) 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 −0.721755 0.692149i \(-0.756664\pi\)
0.692149 + 0.721755i \(0.256664\pi\)
\(564\) 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 \(0.0653137\pi\)
−0.979023 + 0.203752i \(0.934686\pi\)
\(570\) 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 0.458024 0.888940i \(-0.348558\pi\)
−0.888940 + 0.458024i \(0.848558\pi\)
\(578\) −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 0.992755 0.120160i \(-0.0383409\pi\)
−0.120160 + 0.992755i \(0.538341\pi\)
\(588\) 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 −0.837343 0.546678i \(-0.815892\pi\)
0.546678 + 0.837343i \(0.315892\pi\)
\(594\) 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 \(-0.953413\pi\)
0.989309 0.145835i \(-0.0465869\pi\)
\(600\) 0 0
\(601\) 35.0829i 1.43106i −0.698580 0.715532i \(-0.746185\pi\)
0.698580 0.715532i \(-0.253815\pi\)
\(602\) 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 0.589822 0.807533i \(-0.299198\pi\)
−0.807533 + 0.589822i \(0.799198\pi\)
\(608\) 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 0.462816 0.886454i \(-0.346839\pi\)
−0.886454 + 0.462816i \(0.846839\pi\)
\(614\) −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 −0.982631 0.185571i \(-0.940586\pi\)
0.185571 + 0.982631i \(0.440586\pi\)
\(618\) 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 −0.904405 0.426675i \(-0.859685\pi\)
0.426675 + 0.904405i \(0.359685\pi\)
\(644\) −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 0.974631 0.223817i \(-0.0718519\pi\)
−0.223817 + 0.974631i \(0.571852\pi\)
\(648\) 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 0.185476 0.982649i \(-0.440617\pi\)
−0.982649 + 0.185476i \(0.940617\pi\)
\(654\) 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 \(0.210160\pi\)
−0.789847 + 0.613304i \(0.789840\pi\)
\(660\) 0 0
\(661\) 48.1880i 1.87430i −0.348931 0.937149i \(-0.613455\pi\)
0.348931 0.937149i \(-0.386545\pi\)
\(662\) 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 −0.978960 0.204055i \(-0.934588\pi\)
−0.204055 0.978960i \(-0.565412\pi\)
\(674\) 74.6299i 2.87463i
\(675\) 0 0
\(676\) 56.3191 2.16612
\(677\) 1.54060 + 1.54060i 0.0592101 + 0.0592101i 0.736092 0.676882i \(-0.236669\pi\)
−0.676882 + 0.736092i \(0.736669\pi\)
\(678\) 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 0.380744 0.924680i \(-0.375668\pi\)
−0.924680 + 0.380744i \(0.875668\pi\)
\(684\) 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 \(0.0626980\pi\)
−0.980664 + 0.195700i \(0.937302\pi\)
\(692\) −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 \(0.00488939\pi\)
−0.999882 + 0.0153599i \(0.995111\pi\)
\(710\) −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 0.998098 + 0.0616465i \(0.0196352\pi\)
0.0616465 + 0.998098i \(0.480365\pi\)
\(728\) 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 −0.994719 0.102636i \(-0.967272\pi\)
0.102636 + 0.994719i \(0.467272\pi\)
\(734\) 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 \(0.245947\pi\)
−0.716052 + 0.698047i \(0.754053\pi\)
\(740\) 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 0.962184 0.272400i \(-0.0878174\pi\)
−0.272400 + 0.962184i \(0.587817\pi\)
\(744\) 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 −0.647637 0.761949i \(-0.724243\pi\)
0.761949 + 0.647637i \(0.224243\pi\)
\(758\) −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 \(0.219581\pi\)
−0.771351 + 0.636410i \(0.780419\pi\)
\(762\) 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 −0.660494 0.750832i \(-0.729653\pi\)
0.750832 + 0.660494i \(0.229653\pi\)
\(774\) 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