Properties

Label 804.2.ba.b.41.17
Level 804
Weight 2
Character 804.41
Analytic conductor 6.420
Analytic rank 0
Dimension 440
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{66})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 41.17
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.17

$q$-expansion

\(f(q)\) \(=\) \(q+(1.08756 + 1.34804i) q^{3} +(0.177548 - 1.23488i) q^{5} +(0.271050 + 2.83857i) q^{7} +(-0.634425 + 2.93215i) q^{9} +O(q^{10})\) \(q+(1.08756 + 1.34804i) q^{3} +(0.177548 - 1.23488i) q^{5} +(0.271050 + 2.83857i) q^{7} +(-0.634425 + 2.93215i) q^{9} +(-5.62239 + 2.25086i) q^{11} +(0.830910 + 0.871434i) q^{13} +(1.85776 - 1.10366i) q^{15} +(-4.76535 + 1.64930i) q^{17} +(-3.22750 - 0.308189i) q^{19} +(-3.53172 + 3.45250i) q^{21} +(4.74225 - 0.225901i) q^{23} +(3.30407 + 0.970163i) q^{25} +(-4.64263 + 2.33366i) q^{27} +(7.03437 - 4.06129i) q^{29} +(-6.90458 + 7.24131i) q^{31} +(-9.14894 - 5.13125i) q^{33} +(3.55340 + 0.169269i) q^{35} +(3.38398 - 5.86123i) q^{37} +(-0.271063 + 2.06784i) q^{39} +(4.19811 + 0.809119i) q^{41} +(4.51548 + 3.91269i) q^{43} +(3.50820 + 1.30403i) q^{45} +(-2.74131 + 5.31740i) q^{47} +(-1.11049 + 0.214029i) q^{49} +(-7.40594 - 4.63017i) q^{51} +(6.19918 + 7.15424i) q^{53} +(1.78129 + 7.34258i) q^{55} +(-3.09465 - 4.68597i) q^{57} +(-1.03031 - 3.50891i) q^{59} +(0.285957 - 0.714285i) q^{61} +(-8.49506 - 1.00610i) q^{63} +(1.22364 - 0.871349i) q^{65} +(6.77031 - 4.60032i) q^{67} +(5.46201 + 6.14706i) q^{69} +(-13.6640 - 4.72917i) q^{71} +(-7.42126 - 2.97103i) q^{73} +(2.28556 + 5.50913i) q^{75} +(-7.91317 - 15.3494i) q^{77} +(5.89134 - 1.42922i) q^{79} +(-8.19501 - 3.72046i) q^{81} +(4.48418 - 5.70210i) q^{83} +(1.19061 + 6.17745i) q^{85} +(13.1251 + 5.06571i) q^{87} +(-8.56425 + 13.3262i) q^{89} +(-2.24840 + 2.59480i) q^{91} +(-17.2707 - 1.43228i) q^{93} +(-0.953612 + 3.93084i) q^{95} +(4.86960 + 2.81147i) q^{97} +(-3.03289 - 17.9137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{53}{66}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.08756 + 1.34804i 0.627903 + 0.778291i
\(4\) 0 0
\(5\) 0.177548 1.23488i 0.0794020 0.552253i −0.910826 0.412792i \(-0.864554\pi\)
0.990228 0.139461i \(-0.0445371\pi\)
\(6\) 0 0
\(7\) 0.271050 + 2.83857i 0.102447 + 1.07288i 0.889793 + 0.456365i \(0.150849\pi\)
−0.787345 + 0.616512i \(0.788545\pi\)
\(8\) 0 0
\(9\) −0.634425 + 2.93215i −0.211475 + 0.977383i
\(10\) 0 0
\(11\) −5.62239 + 2.25086i −1.69521 + 0.678661i −0.999224 0.0393914i \(-0.987458\pi\)
−0.695989 + 0.718052i \(0.745034\pi\)
\(12\) 0 0
\(13\) 0.830910 + 0.871434i 0.230453 + 0.241692i 0.828800 0.559545i \(-0.189024\pi\)
−0.598347 + 0.801237i \(0.704176\pi\)
\(14\) 0 0
\(15\) 1.85776 1.10366i 0.479671 0.284964i
\(16\) 0 0
\(17\) −4.76535 + 1.64930i −1.15577 + 0.400015i −0.836670 0.547707i \(-0.815501\pi\)
−0.319098 + 0.947722i \(0.603380\pi\)
\(18\) 0 0
\(19\) −3.22750 0.308189i −0.740439 0.0707034i −0.281982 0.959420i \(-0.590992\pi\)
−0.458457 + 0.888716i \(0.651598\pi\)
\(20\) 0 0
\(21\) −3.53172 + 3.45250i −0.770684 + 0.753397i
\(22\) 0 0
\(23\) 4.74225 0.225901i 0.988828 0.0471037i 0.453070 0.891475i \(-0.350329\pi\)
0.535758 + 0.844371i \(0.320026\pi\)
\(24\) 0 0
\(25\) 3.30407 + 0.970163i 0.660814 + 0.194033i
\(26\) 0 0
\(27\) −4.64263 + 2.33366i −0.893475 + 0.449113i
\(28\) 0 0
\(29\) 7.03437 4.06129i 1.30625 0.754163i 0.324781 0.945789i \(-0.394709\pi\)
0.981468 + 0.191626i \(0.0613760\pi\)
\(30\) 0 0
\(31\) −6.90458 + 7.24131i −1.24010 + 1.30058i −0.302378 + 0.953188i \(0.597780\pi\)
−0.937721 + 0.347390i \(0.887068\pi\)
\(32\) 0 0
\(33\) −9.14894 5.13125i −1.59263 0.893236i
\(34\) 0 0
\(35\) 3.55340 + 0.169269i 0.600634 + 0.0286117i
\(36\) 0 0
\(37\) 3.38398 5.86123i 0.556323 0.963580i −0.441476 0.897273i \(-0.645545\pi\)
0.997799 0.0663071i \(-0.0211217\pi\)
\(38\) 0 0
\(39\) −0.271063 + 2.06784i −0.0434048 + 0.331119i
\(40\) 0 0
\(41\) 4.19811 + 0.809119i 0.655634 + 0.126363i 0.506210 0.862410i \(-0.331046\pi\)
0.149424 + 0.988773i \(0.452258\pi\)
\(42\) 0 0
\(43\) 4.51548 + 3.91269i 0.688604 + 0.596679i 0.927257 0.374426i \(-0.122160\pi\)
−0.238652 + 0.971105i \(0.576706\pi\)
\(44\) 0 0
\(45\) 3.50820 + 1.30403i 0.522971 + 0.194394i
\(46\) 0 0
\(47\) −2.74131 + 5.31740i −0.399861 + 0.775623i −0.999700 0.0244981i \(-0.992201\pi\)
0.599838 + 0.800121i \(0.295232\pi\)
\(48\) 0 0
\(49\) −1.11049 + 0.214029i −0.158641 + 0.0305755i
\(50\) 0 0
\(51\) −7.40594 4.63017i −1.03704 0.648353i
\(52\) 0 0
\(53\) 6.19918 + 7.15424i 0.851523 + 0.982710i 0.999981 0.00620868i \(-0.00197630\pi\)
−0.148458 + 0.988919i \(0.547431\pi\)
\(54\) 0 0
\(55\) 1.78129 + 7.34258i 0.240189 + 0.990073i
\(56\) 0 0
\(57\) −3.09465 4.68597i −0.409896 0.620672i
\(58\) 0 0
\(59\) −1.03031 3.50891i −0.134135 0.456821i 0.864842 0.502044i \(-0.167418\pi\)
−0.998977 + 0.0452228i \(0.985600\pi\)
\(60\) 0 0
\(61\) 0.285957 0.714285i 0.0366130 0.0914548i −0.908935 0.416939i \(-0.863103\pi\)
0.945548 + 0.325484i \(0.105527\pi\)
\(62\) 0 0
\(63\) −8.49506 1.00610i −1.07028 0.126756i
\(64\) 0 0
\(65\) 1.22364 0.871349i 0.151774 0.108078i
\(66\) 0 0
\(67\) 6.77031 4.60032i 0.827125 0.562018i
\(68\) 0 0
\(69\) 5.46201 + 6.14706i 0.657549 + 0.740020i
\(70\) 0 0
\(71\) −13.6640 4.72917i −1.62162 0.561250i −0.642814 0.766022i \(-0.722233\pi\)
−0.978810 + 0.204772i \(0.934355\pi\)
\(72\) 0 0
\(73\) −7.42126 2.97103i −0.868593 0.347732i −0.105810 0.994386i \(-0.533743\pi\)
−0.762783 + 0.646654i \(0.776168\pi\)
\(74\) 0 0
\(75\) 2.28556 + 5.50913i 0.263914 + 0.636140i
\(76\) 0 0
\(77\) −7.91317 15.3494i −0.901790 1.74923i
\(78\) 0 0
\(79\) 5.89134 1.42922i 0.662827 0.160800i 0.109788 0.993955i \(-0.464983\pi\)
0.553040 + 0.833155i \(0.313468\pi\)
\(80\) 0 0
\(81\) −8.19501 3.72046i −0.910557 0.413385i
\(82\) 0 0
\(83\) 4.48418 5.70210i 0.492203 0.625887i −0.474971 0.880001i \(-0.657542\pi\)
0.967174 + 0.254114i \(0.0817840\pi\)
\(84\) 0 0
\(85\) 1.19061 + 6.17745i 0.129139 + 0.670038i
\(86\) 0 0
\(87\) 13.1251 + 5.06571i 1.40716 + 0.543101i
\(88\) 0 0
\(89\) −8.56425 + 13.3262i −0.907809 + 1.41258i 0.00311057 + 0.999995i \(0.499010\pi\)
−0.910920 + 0.412584i \(0.864626\pi\)
\(90\) 0 0
\(91\) −2.24840 + 2.59480i −0.235697 + 0.272009i
\(92\) 0 0
\(93\) −17.2707 1.43228i −1.79089 0.148521i
\(94\) 0 0
\(95\) −0.953612 + 3.93084i −0.0978385 + 0.403296i
\(96\) 0 0
\(97\) 4.86960 + 2.81147i 0.494433 + 0.285461i 0.726412 0.687260i \(-0.241187\pi\)
−0.231979 + 0.972721i \(0.574520\pi\)
\(98\) 0 0
\(99\) −3.03289 17.9137i −0.304817 1.80039i
\(100\) 0 0
\(101\) −4.60755 + 6.47040i −0.458468 + 0.643829i −0.977502 0.210925i \(-0.932352\pi\)
0.519034 + 0.854754i \(0.326292\pi\)
\(102\) 0 0
\(103\) −0.947981 0.903898i −0.0934073 0.0890637i 0.641937 0.766757i \(-0.278131\pi\)
−0.735344 + 0.677694i \(0.762980\pi\)
\(104\) 0 0
\(105\) 3.63635 + 4.97422i 0.354872 + 0.485434i
\(106\) 0 0
\(107\) −1.97204 + 0.283536i −0.190644 + 0.0274105i −0.236975 0.971516i \(-0.576156\pi\)
0.0463313 + 0.998926i \(0.485247\pi\)
\(108\) 0 0
\(109\) −0.666913 + 2.27130i −0.0638787 + 0.217551i −0.985247 0.171141i \(-0.945255\pi\)
0.921368 + 0.388692i \(0.127073\pi\)
\(110\) 0 0
\(111\) 11.5815 1.81270i 1.09926 0.172053i
\(112\) 0 0
\(113\) 16.4421 12.9302i 1.54674 1.21637i 0.662779 0.748815i \(-0.269377\pi\)
0.883963 0.467557i \(-0.154866\pi\)
\(114\) 0 0
\(115\) 0.563019 5.89620i 0.0525017 0.549823i
\(116\) 0 0
\(117\) −3.08233 + 1.88349i −0.284961 + 0.174129i
\(118\) 0 0
\(119\) −5.97331 13.0797i −0.547572 1.19902i
\(120\) 0 0
\(121\) 18.5838 17.7196i 1.68943 1.61087i
\(122\) 0 0
\(123\) 3.47497 + 6.53918i 0.313327 + 0.589618i
\(124\) 0 0
\(125\) 4.37597 9.58203i 0.391398 0.857043i
\(126\) 0 0
\(127\) 9.97022 0.952041i 0.884714 0.0844800i 0.357202 0.934027i \(-0.383731\pi\)
0.527513 + 0.849547i \(0.323125\pi\)
\(128\) 0 0
\(129\) −0.363601 + 10.3423i −0.0320133 + 0.910592i
\(130\) 0 0
\(131\) 12.1678 + 18.9335i 1.06311 + 1.65423i 0.685138 + 0.728414i \(0.259742\pi\)
0.377972 + 0.925817i \(0.376622\pi\)
\(132\) 0 0
\(133\) 9.24501i 0.801644i
\(134\) 0 0
\(135\) 2.05749 + 6.14741i 0.177080 + 0.529085i
\(136\) 0 0
\(137\) −1.42346 + 0.914800i −0.121614 + 0.0781566i −0.600034 0.799975i \(-0.704846\pi\)
0.478420 + 0.878131i \(0.341210\pi\)
\(138\) 0 0
\(139\) 19.3972 + 2.78890i 1.64525 + 0.236551i 0.901772 0.432211i \(-0.142267\pi\)
0.743476 + 0.668762i \(0.233176\pi\)
\(140\) 0 0
\(141\) −10.1494 + 2.08760i −0.854735 + 0.175807i
\(142\) 0 0
\(143\) −6.63318 3.02927i −0.554694 0.253320i
\(144\) 0 0
\(145\) −3.76625 9.40764i −0.312770 0.781262i
\(146\) 0 0
\(147\) −1.49624 1.26421i −0.123408 0.104270i
\(148\) 0 0
\(149\) −7.36263 + 3.36240i −0.603170 + 0.275459i −0.693504 0.720453i \(-0.743934\pi\)
0.0903335 + 0.995912i \(0.471207\pi\)
\(150\) 0 0
\(151\) 4.84507 + 13.9989i 0.394286 + 1.13922i 0.951181 + 0.308633i \(0.0998714\pi\)
−0.556895 + 0.830583i \(0.688007\pi\)
\(152\) 0 0
\(153\) −1.81275 15.0191i −0.146552 1.21422i
\(154\) 0 0
\(155\) 7.71622 + 9.81197i 0.619782 + 0.788117i
\(156\) 0 0
\(157\) −0.180626 3.79180i −0.0144155 0.302619i −0.994548 0.104277i \(-0.966747\pi\)
0.980133 0.198342i \(-0.0635557\pi\)
\(158\) 0 0
\(159\) −2.90222 + 16.1374i −0.230161 + 1.27978i
\(160\) 0 0
\(161\) 1.92662 + 13.4000i 0.151839 + 1.05606i
\(162\) 0 0
\(163\) 3.69900 + 6.40685i 0.289728 + 0.501823i 0.973745 0.227643i \(-0.0731019\pi\)
−0.684017 + 0.729466i \(0.739769\pi\)
\(164\) 0 0
\(165\) −7.96083 + 10.3868i −0.619750 + 0.808608i
\(166\) 0 0
\(167\) 7.94281 + 5.65605i 0.614633 + 0.437678i 0.844509 0.535542i \(-0.179893\pi\)
−0.229876 + 0.973220i \(0.573832\pi\)
\(168\) 0 0
\(169\) 0.549580 11.5371i 0.0422754 0.887470i
\(170\) 0 0
\(171\) 2.95126 9.26799i 0.225689 0.708741i
\(172\) 0 0
\(173\) −8.60933 2.08860i −0.654555 0.158793i −0.105290 0.994442i \(-0.533577\pi\)
−0.549265 + 0.835648i \(0.685092\pi\)
\(174\) 0 0
\(175\) −1.85830 + 9.64179i −0.140474 + 0.728851i
\(176\) 0 0
\(177\) 3.60963 5.20505i 0.271316 0.391235i
\(178\) 0 0
\(179\) −15.4083 9.90233i −1.15167 0.740135i −0.181700 0.983354i \(-0.558160\pi\)
−0.969971 + 0.243219i \(0.921797\pi\)
\(180\) 0 0
\(181\) 4.72348 + 2.43512i 0.351094 + 0.181001i 0.624747 0.780827i \(-0.285202\pi\)
−0.273654 + 0.961828i \(0.588232\pi\)
\(182\) 0 0
\(183\) 1.27388 0.391347i 0.0941679 0.0289292i
\(184\) 0 0
\(185\) −6.63707 5.21945i −0.487967 0.383741i
\(186\) 0 0
\(187\) 23.0803 19.9992i 1.68780 1.46249i
\(188\) 0 0
\(189\) −7.88263 12.5459i −0.573377 0.912578i
\(190\) 0 0
\(191\) 11.9859 6.17917i 0.867271 0.447109i 0.0336417 0.999434i \(-0.489290\pi\)
0.833629 + 0.552325i \(0.186259\pi\)
\(192\) 0 0
\(193\) 1.59036 0.466972i 0.114477 0.0336134i −0.223992 0.974591i \(-0.571909\pi\)
0.338469 + 0.940977i \(0.390091\pi\)
\(194\) 0 0
\(195\) 2.50539 + 0.701870i 0.179415 + 0.0502619i
\(196\) 0 0
\(197\) 0.0834813 0.241203i 0.00594779 0.0171850i −0.941988 0.335647i \(-0.891045\pi\)
0.947936 + 0.318462i \(0.103166\pi\)
\(198\) 0 0
\(199\) −3.88124 5.45044i −0.275134 0.386371i 0.653770 0.756694i \(-0.273187\pi\)
−0.928903 + 0.370322i \(0.879247\pi\)
\(200\) 0 0
\(201\) 13.5645 + 4.12353i 0.956768 + 0.290851i
\(202\) 0 0
\(203\) 13.4349 + 18.8667i 0.942946 + 1.32418i
\(204\) 0 0
\(205\) 1.74453 5.04048i 0.121843 0.352042i
\(206\) 0 0
\(207\) −2.34623 + 14.0483i −0.163074 + 0.976425i
\(208\) 0 0
\(209\) 18.8399 5.53191i 1.30319 0.382650i
\(210\) 0 0
\(211\) 1.54063 0.794251i 0.106061 0.0546785i −0.404380 0.914591i \(-0.632512\pi\)
0.510441 + 0.859913i \(0.329482\pi\)
\(212\) 0 0
\(213\) −8.48536 23.5629i −0.581407 1.61451i
\(214\) 0 0
\(215\) 5.63340 4.88136i 0.384194 0.332906i
\(216\) 0 0
\(217\) −22.4264 17.6363i −1.52240 1.19723i
\(218\) 0 0
\(219\) −4.06601 13.2353i −0.274755 0.894361i
\(220\) 0 0
\(221\) −5.39684 2.78227i −0.363031 0.187155i
\(222\) 0 0
\(223\) −20.0793 12.9042i −1.34461 0.864130i −0.347326 0.937745i \(-0.612910\pi\)
−0.997287 + 0.0736148i \(0.976546\pi\)
\(224\) 0 0
\(225\) −4.94085 + 9.07254i −0.329390 + 0.604836i
\(226\) 0 0
\(227\) 3.87856 20.1239i 0.257429 1.33567i −0.591134 0.806574i \(-0.701319\pi\)
0.848563 0.529095i \(-0.177468\pi\)
\(228\) 0 0
\(229\) −5.04776 1.22457i −0.333565 0.0809220i 0.0654785 0.997854i \(-0.479143\pi\)
−0.399044 + 0.916932i \(0.630658\pi\)
\(230\) 0 0
\(231\) 12.0856 27.3607i 0.795173 1.80020i
\(232\) 0 0
\(233\) −0.778718 + 16.3473i −0.0510155 + 1.07095i 0.817703 + 0.575641i \(0.195247\pi\)
−0.868718 + 0.495307i \(0.835056\pi\)
\(234\) 0 0
\(235\) 6.07961 + 4.32927i 0.396590 + 0.282411i
\(236\) 0 0
\(237\) 8.33384 + 6.38740i 0.541341 + 0.414906i
\(238\) 0 0
\(239\) 1.49234 + 2.58480i 0.0965313 + 0.167197i 0.910247 0.414066i \(-0.135892\pi\)
−0.813715 + 0.581264i \(0.802559\pi\)
\(240\) 0 0
\(241\) −3.09140 21.5012i −0.199135 1.38501i −0.806802 0.590821i \(-0.798804\pi\)
0.607668 0.794191i \(-0.292105\pi\)
\(242\) 0 0
\(243\) −3.89724 15.0934i −0.250008 0.968244i
\(244\) 0 0
\(245\) 0.0671338 + 1.40931i 0.00428902 + 0.0900376i
\(246\) 0 0
\(247\) −2.41320 3.06863i −0.153548 0.195252i
\(248\) 0 0
\(249\) 12.5635 0.156521i 0.796178 0.00991910i
\(250\) 0 0
\(251\) −4.13319 11.9421i −0.260885 0.753776i −0.997034 0.0769577i \(-0.975479\pi\)
0.736150 0.676819i \(-0.236642\pi\)
\(252\) 0 0
\(253\) −26.1543 + 11.9443i −1.64431 + 0.750930i
\(254\) 0 0
\(255\) −7.03259 + 8.32333i −0.440398 + 0.521227i
\(256\) 0 0
\(257\) −0.837662 2.09238i −0.0522519 0.130519i 0.899945 0.436003i \(-0.143606\pi\)
−0.952197 + 0.305484i \(0.901182\pi\)
\(258\) 0 0
\(259\) 17.5547 + 8.01697i 1.09080 + 0.498150i
\(260\) 0 0
\(261\) 7.44554 + 23.2024i 0.460868 + 1.43619i
\(262\) 0 0
\(263\) −12.2448 1.76054i −0.755047 0.108559i −0.245967 0.969278i \(-0.579105\pi\)
−0.509081 + 0.860719i \(0.670015\pi\)
\(264\) 0 0
\(265\) 9.93524 6.38499i 0.610317 0.392227i
\(266\) 0 0
\(267\) −27.2785 + 2.94813i −1.66941 + 0.180423i
\(268\) 0 0
\(269\) 26.0117i 1.58596i 0.609246 + 0.792981i \(0.291472\pi\)
−0.609246 + 0.792981i \(0.708528\pi\)
\(270\) 0 0
\(271\) 5.96421 + 9.28049i 0.362300 + 0.563749i 0.973775 0.227514i \(-0.0730599\pi\)
−0.611475 + 0.791264i \(0.709423\pi\)
\(272\) 0 0
\(273\) −5.94316 0.208942i −0.359697 0.0126457i
\(274\) 0 0
\(275\) −20.7605 + 1.98238i −1.25190 + 0.119542i
\(276\) 0 0
\(277\) 12.6487 27.6969i 0.759990 1.66414i 0.0124546 0.999922i \(-0.496035\pi\)
0.747535 0.664223i \(-0.231237\pi\)
\(278\) 0 0
\(279\) −16.8522 24.8393i −1.00891 1.48709i
\(280\) 0 0
\(281\) 1.23763 1.18007i 0.0738306 0.0703973i −0.652265 0.757991i \(-0.726181\pi\)
0.726096 + 0.687593i \(0.241333\pi\)
\(282\) 0 0
\(283\) 6.29421 + 13.7824i 0.374152 + 0.819278i 0.999250 + 0.0387317i \(0.0123318\pi\)
−0.625098 + 0.780546i \(0.714941\pi\)
\(284\) 0 0
\(285\) −6.33604 + 2.98952i −0.375315 + 0.177084i
\(286\) 0 0
\(287\) −1.15884 + 12.1359i −0.0684041 + 0.716360i
\(288\) 0 0
\(289\) 6.62548 5.21034i 0.389734 0.306490i
\(290\) 0 0
\(291\) 1.50602 + 9.62206i 0.0882842 + 0.564055i
\(292\) 0 0
\(293\) −4.96968 + 16.9252i −0.290332 + 0.988779i 0.677152 + 0.735844i \(0.263214\pi\)
−0.967483 + 0.252935i \(0.918604\pi\)
\(294\) 0 0
\(295\) −4.51599 + 0.649302i −0.262931 + 0.0378038i
\(296\) 0 0
\(297\) 20.8499 23.5707i 1.20984 1.36771i
\(298\) 0 0
\(299\) 4.13724 + 3.94485i 0.239263 + 0.228137i
\(300\) 0 0
\(301\) −9.88250 + 13.8780i −0.569618 + 0.799916i
\(302\) 0 0
\(303\) −13.7333 + 0.825785i −0.788960 + 0.0474401i
\(304\) 0 0
\(305\) −0.831282 0.479941i −0.0475991 0.0274813i
\(306\) 0 0
\(307\) 2.13694 8.80857i 0.121961 0.502732i −0.877759 0.479102i \(-0.840963\pi\)
0.999721 0.0236299i \(-0.00752233\pi\)
\(308\) 0 0
\(309\) 0.187504 2.26096i 0.0106668 0.128621i
\(310\) 0 0
\(311\) 15.3682 17.7358i 0.871450 1.00571i −0.128452 0.991716i \(-0.541001\pi\)
0.999902 0.0139911i \(-0.00445366\pi\)
\(312\) 0 0
\(313\) −1.83055 + 2.84839i −0.103469 + 0.161000i −0.889127 0.457660i \(-0.848688\pi\)
0.785659 + 0.618660i \(0.212324\pi\)
\(314\) 0 0
\(315\) −2.75069 + 10.3117i −0.154984 + 0.580999i
\(316\) 0 0
\(317\) 1.89899 + 9.85288i 0.106658 + 0.553393i 0.995466 + 0.0951144i \(0.0303217\pi\)
−0.888809 + 0.458279i \(0.848466\pi\)
\(318\) 0 0
\(319\) −30.4085 + 38.6676i −1.70255 + 2.16497i
\(320\) 0 0
\(321\) −2.52693 2.35002i −0.141039 0.131166i
\(322\) 0 0
\(323\) 15.8885 3.85450i 0.884058 0.214470i
\(324\) 0 0
\(325\) 1.89995 + 3.68540i 0.105391 + 0.204429i
\(326\) 0 0
\(327\) −3.78711 + 1.57115i −0.209428 + 0.0868847i
\(328\) 0 0
\(329\) −15.8368 6.34011i −0.873113 0.349542i
\(330\) 0 0
\(331\) 23.5013 + 8.13388i 1.29175 + 0.447079i 0.884629 0.466296i \(-0.154412\pi\)
0.407120 + 0.913375i \(0.366533\pi\)
\(332\) 0 0
\(333\) 15.0391 + 13.6409i 0.824139 + 0.747514i
\(334\) 0 0
\(335\) −4.47876 9.17727i −0.244701 0.501408i
\(336\) 0 0
\(337\) −27.8821 + 19.8548i −1.51884 + 1.08156i −0.549598 + 0.835429i \(0.685219\pi\)
−0.969237 + 0.246129i \(0.920841\pi\)
\(338\) 0 0
\(339\) 35.3122 + 8.10223i 1.91790 + 0.440053i
\(340\) 0 0
\(341\) 22.5210 56.2547i 1.21958 3.04636i
\(342\) 0 0
\(343\) 4.71495 + 16.0576i 0.254583 + 0.867031i
\(344\) 0 0
\(345\) 8.56063 5.65350i 0.460889 0.304374i
\(346\) 0 0
\(347\) 3.60288 + 14.8513i 0.193413 + 0.797258i 0.982998 + 0.183617i \(0.0587806\pi\)
−0.789585 + 0.613641i \(0.789704\pi\)
\(348\) 0 0
\(349\) 12.8926 + 14.8788i 0.690123 + 0.796445i 0.987383 0.158352i \(-0.0506181\pi\)
−0.297259 + 0.954797i \(0.596073\pi\)
\(350\) 0 0
\(351\) −5.89124 2.10668i −0.314451 0.112447i
\(352\) 0 0
\(353\) −5.06534 + 0.976265i −0.269601 + 0.0519613i −0.322260 0.946651i \(-0.604442\pi\)
0.0526590 + 0.998613i \(0.483230\pi\)
\(354\) 0 0
\(355\) −8.26597 + 16.0337i −0.438712 + 0.850982i
\(356\) 0 0
\(357\) 11.1357 22.2772i 0.589362 1.17904i
\(358\) 0 0
\(359\) −14.2243 12.3254i −0.750730 0.650511i 0.193011 0.981197i \(-0.438175\pi\)
−0.943741 + 0.330685i \(0.892720\pi\)
\(360\) 0 0
\(361\) −8.33487 1.60641i −0.438677 0.0845481i
\(362\) 0 0
\(363\) 44.0977 + 5.78055i 2.31453 + 0.303400i
\(364\) 0 0
\(365\) −4.98648 + 8.63683i −0.261004 + 0.452073i
\(366\) 0 0
\(367\) −24.4248 1.16350i −1.27497 0.0607341i −0.600851 0.799361i \(-0.705172\pi\)
−0.674115 + 0.738627i \(0.735475\pi\)
\(368\) 0 0
\(369\) −5.03584 + 11.7962i −0.262155 + 0.614083i
\(370\) 0 0
\(371\) −18.6275 + 19.5359i −0.967091 + 1.01426i
\(372\) 0 0
\(373\) −12.1758 + 7.02967i −0.630437 + 0.363983i −0.780921 0.624630i \(-0.785250\pi\)
0.150485 + 0.988612i \(0.451917\pi\)
\(374\) 0 0
\(375\) 17.6761 4.52206i 0.912789 0.233518i
\(376\) 0 0
\(377\) 9.38408 + 2.75541i 0.483305 + 0.141911i
\(378\) 0 0
\(379\) 15.7523 0.750375i 0.809142 0.0385442i 0.361067 0.932540i \(-0.382413\pi\)
0.448075 + 0.893996i \(0.352110\pi\)
\(380\) 0 0
\(381\) 12.1266 + 12.4049i 0.621265 + 0.635520i
\(382\) 0 0
\(383\) 12.6317 + 1.20618i 0.645447 + 0.0616327i 0.412646 0.910892i \(-0.364605\pi\)
0.232801 + 0.972524i \(0.425211\pi\)
\(384\) 0 0
\(385\) −20.3596 + 7.04652i −1.03762 + 0.359124i
\(386\) 0 0
\(387\) −14.3373 + 10.7578i −0.728807 + 0.546848i
\(388\) 0 0
\(389\) −16.4064 17.2065i −0.831837 0.872406i 0.161591 0.986858i \(-0.448337\pi\)
−0.993429 + 0.114452i \(0.963489\pi\)
\(390\) 0 0
\(391\) −22.2259 + 8.89792i −1.12401 + 0.449987i
\(392\) 0 0
\(393\) −12.2899 + 36.9941i −0.619944 + 1.86611i
\(394\) 0 0
\(395\) −0.718915 7.52882i −0.0361726 0.378816i
\(396\) 0 0
\(397\) −2.30702 + 16.0457i −0.115786 + 0.805311i 0.846328 + 0.532663i \(0.178809\pi\)
−0.962114 + 0.272648i \(0.912101\pi\)
\(398\) 0 0
\(399\) 12.4626 10.0545i 0.623912 0.503355i
\(400\) 0 0
\(401\) 9.84306 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(402\) 0 0
\(403\) −12.0474 −0.600124
\(404\) 0 0
\(405\) −6.04931 + 9.45925i −0.300593 + 0.470034i
\(406\) 0 0
\(407\) −5.83323 + 40.5710i −0.289142 + 2.01103i
\(408\) 0 0
\(409\) −0.952292 9.97285i −0.0470878 0.493126i −0.987998 0.154469i \(-0.950633\pi\)
0.940910 0.338657i \(-0.109973\pi\)
\(410\) 0 0
\(411\) −2.78128 0.923977i −0.137191 0.0455764i
\(412\) 0 0
\(413\) 9.68100 3.87569i 0.476371 0.190710i
\(414\) 0 0
\(415\) −6.24522 6.54980i −0.306566 0.321517i
\(416\) 0 0
\(417\) 17.3361 + 29.1813i 0.848951 + 1.42901i
\(418\) 0 0
\(419\) −9.38589 + 3.24849i −0.458531 + 0.158699i −0.546562 0.837419i \(-0.684064\pi\)
0.0880313 + 0.996118i \(0.471942\pi\)
\(420\) 0 0
\(421\) 26.5655 + 2.53670i 1.29472 + 0.123631i 0.719573 0.694417i \(-0.244338\pi\)
0.575150 + 0.818048i \(0.304944\pi\)
\(422\) 0 0
\(423\) −13.8523 11.4114i −0.673520 0.554843i
\(424\) 0 0
\(425\) −17.3452 + 0.826252i −0.841364 + 0.0400791i
\(426\) 0 0
\(427\) 2.10505 + 0.618100i 0.101871 + 0.0299119i
\(428\) 0 0
\(429\) −3.13040 12.2363i −0.151137 0.590774i
\(430\) 0 0
\(431\) −6.87919 + 3.97170i −0.331359 + 0.191310i −0.656444 0.754375i \(-0.727940\pi\)
0.325085 + 0.945685i \(0.394607\pi\)
\(432\) 0 0
\(433\) −8.68654 + 9.11018i −0.417448 + 0.437807i −0.898559 0.438853i \(-0.855385\pi\)
0.481111 + 0.876660i \(0.340234\pi\)
\(434\) 0 0
\(435\) 8.58586 15.3084i 0.411660 0.733983i
\(436\) 0 0
\(437\) −15.3752 0.732413i −0.735497 0.0350361i
\(438\) 0 0
\(439\) −2.96472 + 5.13504i −0.141498 + 0.245082i −0.928061 0.372428i \(-0.878525\pi\)
0.786563 + 0.617510i \(0.211859\pi\)
\(440\) 0 0
\(441\) 0.0769563 3.39190i 0.00366459 0.161519i
\(442\) 0 0
\(443\) −9.59946 1.85014i −0.456084 0.0879030i −0.0439651 0.999033i \(-0.513999\pi\)
−0.412119 + 0.911130i \(0.635211\pi\)
\(444\) 0 0
\(445\) 14.9357 + 12.9418i 0.708019 + 0.613502i
\(446\) 0 0
\(447\) −12.5400 6.26831i −0.593120 0.296481i
\(448\) 0 0
\(449\) 12.6532 24.5438i 0.597141 1.15829i −0.375683 0.926748i \(-0.622592\pi\)
0.972824 0.231544i \(-0.0743778\pi\)
\(450\) 0 0
\(451\) −25.4246 + 4.90019i −1.19720 + 0.230741i
\(452\) 0 0
\(453\) −13.6018 + 21.7560i −0.639068 + 1.02219i
\(454\) 0 0
\(455\) 2.80505 + 3.23720i 0.131503 + 0.151762i
\(456\) 0 0
\(457\) −6.78293 27.9596i −0.317292 1.30790i −0.877513 0.479552i \(-0.840799\pi\)
0.560221 0.828343i \(-0.310716\pi\)
\(458\) 0 0
\(459\) 18.2749 18.7778i 0.852998 0.876474i
\(460\) 0 0
\(461\) 7.46037 + 25.4077i 0.347464 + 1.18335i 0.929077 + 0.369888i \(0.120604\pi\)
−0.581613 + 0.813466i \(0.697578\pi\)
\(462\) 0 0
\(463\) −5.24553 + 13.1027i −0.243781 + 0.608935i −0.998912 0.0466391i \(-0.985149\pi\)
0.755131 + 0.655574i \(0.227573\pi\)
\(464\) 0 0
\(465\) −4.83508 + 21.0729i −0.224221 + 0.977232i
\(466\) 0 0
\(467\) 21.5349 15.3349i 0.996516 0.709616i 0.0393712 0.999225i \(-0.487465\pi\)
0.957145 + 0.289609i \(0.0935251\pi\)
\(468\) 0 0
\(469\) 14.8934 + 17.9711i 0.687713 + 0.829826i
\(470\) 0 0
\(471\) 4.91506 4.36730i 0.226474 0.201235i
\(472\) 0 0
\(473\) −34.1947 11.8349i −1.57227 0.544169i
\(474\) 0 0
\(475\) −10.3649 4.14948i −0.475574 0.190391i
\(476\) 0 0
\(477\) −24.9102 + 13.6381i −1.14056 + 0.624446i
\(478\) 0 0
\(479\) 14.2559 + 27.6526i 0.651368 + 1.26348i 0.950932 + 0.309401i \(0.100129\pi\)
−0.299563 + 0.954076i \(0.596841\pi\)
\(480\) 0 0
\(481\) 7.91946 1.92124i 0.361096 0.0876010i
\(482\) 0 0
\(483\) −15.9684 + 17.1704i −0.726586 + 0.781282i
\(484\) 0 0
\(485\) 4.33640 5.51418i 0.196906 0.250386i
\(486\) 0 0
\(487\) 1.33028 + 6.90213i 0.0602806 + 0.312765i 0.999536 0.0304531i \(-0.00969504\pi\)
−0.939256 + 0.343218i \(0.888483\pi\)
\(488\) 0 0
\(489\) −4.61381 + 11.9542i −0.208644 + 0.540589i
\(490\) 0 0
\(491\) −9.07689 + 14.1239i −0.409634 + 0.637403i −0.983365 0.181641i \(-0.941859\pi\)
0.573731 + 0.819044i \(0.305496\pi\)
\(492\) 0 0
\(493\) −26.8229 + 30.9553i −1.20804 + 1.39416i
\(494\) 0 0
\(495\) −22.6596 + 0.564693i −1.01848 + 0.0253811i
\(496\) 0 0
\(497\) 9.72043 40.0681i 0.436021 1.79730i
\(498\) 0 0
\(499\) −28.5971 16.5105i −1.28018 0.739113i −0.303300 0.952895i \(-0.598089\pi\)
−0.976881 + 0.213782i \(0.931422\pi\)
\(500\) 0 0
\(501\) 1.01370 + 16.8585i 0.0452889 + 0.753183i
\(502\) 0 0
\(503\) 2.49099 3.49810i 0.111068 0.155973i −0.755300 0.655379i \(-0.772509\pi\)
0.866368 + 0.499406i \(0.166448\pi\)
\(504\) 0 0
\(505\) 7.17207 + 6.83856i 0.319153 + 0.304312i
\(506\) 0 0
\(507\) 16.1502 11.8064i 0.717255 0.524343i
\(508\) 0 0
\(509\) 21.5661 3.10074i 0.955903 0.137438i 0.353327 0.935500i \(-0.385050\pi\)
0.602576 + 0.798062i \(0.294141\pi\)
\(510\) 0 0
\(511\) 6.42192 21.8710i 0.284089 0.967518i
\(512\) 0 0
\(513\) 15.7033 6.10108i 0.693318 0.269369i
\(514\) 0 0
\(515\) −1.28451 + 1.01015i −0.0566024 + 0.0445126i
\(516\) 0 0
\(517\) 3.44396 36.0668i 0.151465 1.58622i
\(518\) 0 0
\(519\) −6.54764 13.8772i −0.287410 0.609141i
\(520\) 0 0
\(521\) 4.00476 + 8.76920i 0.175452 + 0.384186i 0.976844 0.213954i \(-0.0686342\pi\)
−0.801392 + 0.598139i \(0.795907\pi\)
\(522\) 0 0
\(523\) −6.02032 + 5.74036i −0.263250 + 0.251009i −0.810195 0.586160i \(-0.800639\pi\)
0.546945 + 0.837168i \(0.315791\pi\)
\(524\) 0 0
\(525\) −15.0185 + 7.98096i −0.655462 + 0.348318i
\(526\) 0 0
\(527\) 20.9596 45.8952i 0.913015 1.99922i
\(528\) 0 0
\(529\) −0.457938 + 0.0437278i −0.0199104 + 0.00190121i
\(530\) 0 0
\(531\) 10.9423 0.794879i 0.474856 0.0344948i
\(532\) 0 0
\(533\) 2.78316 + 4.33068i 0.120552 + 0.187582i
\(534\) 0 0
\(535\) 2.48556i 0.107460i
\(536\) 0 0
\(537\) −3.40874 31.5404i −0.147098 1.36107i
\(538\) 0 0
\(539\) 5.76183 3.70290i 0.248180 0.159495i
\(540\) 0 0
\(541\) −2.16925 0.311891i −0.0932634 0.0134092i 0.0955251 0.995427i \(-0.469547\pi\)
−0.188788 + 0.982018i \(0.560456\pi\)
\(542\) 0 0
\(543\) 1.85443 + 9.01579i 0.0795810 + 0.386905i
\(544\) 0 0
\(545\) 2.68636 + 1.22682i 0.115071 + 0.0525512i
\(546\) 0 0
\(547\) −9.88563 24.6931i −0.422679 1.05580i −0.975007 0.222174i \(-0.928685\pi\)
0.552328 0.833627i \(-0.313740\pi\)
\(548\) 0 0
\(549\) 1.91297 + 1.29163i 0.0816437 + 0.0551254i
\(550\) 0 0
\(551\) −23.9551 + 10.9399i −1.02052 + 0.466056i
\(552\) 0 0
\(553\) 5.65379 + 16.3356i 0.240424 + 0.694659i
\(554\) 0 0
\(555\) −0.182185 14.6235i −0.00773333 0.620733i
\(556\) 0 0
\(557\) 5.97109 + 7.59286i 0.253003 + 0.321720i 0.895919 0.444217i \(-0.146518\pi\)
−0.642916 + 0.765937i \(0.722276\pi\)
\(558\) 0 0
\(559\) 0.342313 + 7.18603i 0.0144783 + 0.303937i
\(560\) 0 0
\(561\) 52.0609 + 9.36284i 2.19801 + 0.395300i
\(562\) 0 0
\(563\) −1.64096 11.4132i −0.0691584 0.481007i −0.994738 0.102454i \(-0.967331\pi\)
0.925579 0.378553i \(-0.123578\pi\)
\(564\) 0 0
\(565\) −13.0479 22.5997i −0.548930 0.950775i
\(566\) 0 0
\(567\) 8.33951 24.2705i 0.350227 1.01927i
\(568\) 0 0
\(569\) 11.1066 + 7.90898i 0.465613 + 0.331562i 0.788669 0.614818i \(-0.210771\pi\)
−0.323056 + 0.946380i \(0.604710\pi\)
\(570\) 0 0
\(571\) −0.284062 + 5.96320i −0.0118876 + 0.249552i 0.985100 + 0.171985i \(0.0550182\pi\)
−0.996987 + 0.0775669i \(0.975285\pi\)
\(572\) 0 0
\(573\) 21.3652 + 9.43728i 0.892543 + 0.394248i
\(574\) 0 0
\(575\) 15.8879 + 3.85436i 0.662571 + 0.160738i
\(576\) 0 0
\(577\) 4.96863 25.7797i 0.206847 1.07322i −0.718910 0.695103i \(-0.755359\pi\)
0.925757 0.378119i \(-0.123429\pi\)
\(578\) 0 0
\(579\) 2.35911 + 1.63601i 0.0980414 + 0.0679903i
\(580\) 0 0
\(581\) 17.4012 + 11.1831i 0.721924 + 0.463953i
\(582\) 0 0
\(583\) −50.9574 26.2704i −2.11044 1.08801i
\(584\) 0 0
\(585\) 1.77862 + 4.14070i 0.0735369 + 0.171197i
\(586\) 0 0
\(587\) 23.1431 + 18.1999i 0.955217 + 0.751191i 0.968576 0.248720i \(-0.0800098\pi\)
−0.0133582 + 0.999911i \(0.504252\pi\)
\(588\) 0 0
\(589\) 24.5162 21.2434i 1.01017 0.875320i
\(590\) 0 0
\(591\) 0.415943 0.149787i 0.0171096 0.00616141i
\(592\) 0 0
\(593\) −33.4171 + 17.2277i −1.37227 + 0.707457i −0.977424 0.211288i \(-0.932234\pi\)
−0.394851 + 0.918745i \(0.629204\pi\)
\(594\) 0 0
\(595\) −17.2124 + 5.05401i −0.705639 + 0.207194i
\(596\) 0 0
\(597\) 3.12633 11.1597i 0.127952 0.456738i
\(598\) 0 0
\(599\) 1.91514 5.53343i 0.0782505 0.226090i −0.899090 0.437764i \(-0.855770\pi\)
0.977340 + 0.211674i \(0.0678916\pi\)
\(600\) 0 0
\(601\) −6.08524 8.54552i −0.248222 0.348579i 0.671601 0.740913i \(-0.265607\pi\)
−0.919823 + 0.392334i \(0.871668\pi\)
\(602\) 0 0
\(603\) 9.19356 + 22.7701i 0.374391 + 0.927271i
\(604\) 0 0
\(605\) −18.5820 26.0947i −0.755464 1.06090i
\(606\) 0 0
\(607\) −13.1542 + 38.0064i −0.533911 + 1.54263i 0.279027 + 0.960283i \(0.409988\pi\)
−0.812938 + 0.582350i \(0.802133\pi\)
\(608\) 0 0
\(609\) −10.8218 + 38.6295i −0.438521 + 1.56535i
\(610\) 0 0
\(611\) −6.91155 + 2.02941i −0.279611 + 0.0821013i
\(612\) 0 0
\(613\) 1.05817 0.545524i 0.0427390 0.0220335i −0.436725 0.899595i \(-0.643862\pi\)
0.479464 + 0.877562i \(0.340831\pi\)
\(614\) 0 0
\(615\) 8.69205 3.13013i 0.350497 0.126219i
\(616\) 0 0
\(617\) −6.20162 + 5.37373i −0.249668 + 0.216338i −0.770699 0.637199i \(-0.780093\pi\)
0.521031 + 0.853537i \(0.325547\pi\)
\(618\) 0 0
\(619\) −30.7540 24.1852i −1.23611 0.972086i −1.00000 0.000359445i \(-0.999886\pi\)
−0.236108 0.971727i \(-0.575872\pi\)
\(620\) 0 0
\(621\) −21.4894 + 12.1156i −0.862338 + 0.486181i
\(622\) 0 0
\(623\) −40.1488 20.6981i −1.60853 0.829253i
\(624\) 0 0
\(625\) 3.42887 + 2.20360i 0.137155 + 0.0881440i
\(626\) 0 0
\(627\) 27.9468 + 19.3807i 1.11609 + 0.773991i
\(628\) 0 0
\(629\) −6.45892 + 33.5120i −0.257534 + 1.33621i
\(630\) 0 0
\(631\) −2.77883 0.674138i −0.110624 0.0268370i 0.180065 0.983655i \(-0.442369\pi\)
−0.290689 + 0.956818i \(0.593884\pi\)
\(632\) 0 0
\(633\) 2.74621 + 1.21304i 0.109152 + 0.0482139i
\(634\) 0 0
\(635\) 0.594544 12.4810i 0.0235938 0.495294i
\(636\) 0 0
\(637\) −1.10923 0.789876i −0.0439491 0.0312960i
\(638\) 0 0
\(639\) 22.5355 37.0647i 0.891489 1.46626i
\(640\) 0 0
\(641\) 17.5025 + 30.3151i 0.691305 + 1.19738i 0.971410 + 0.237407i \(0.0762974\pi\)
−0.280105 + 0.959969i \(0.590369\pi\)
\(642\) 0 0
\(643\) −3.61977 25.1761i −0.142750 0.992848i −0.927710 0.373301i \(-0.878226\pi\)
0.784960 0.619546i \(-0.212683\pi\)
\(644\) 0 0
\(645\) 12.7069 + 2.28527i 0.500335 + 0.0899822i
\(646\) 0 0
\(647\) 0.0372958 + 0.782935i 0.00146625 + 0.0307804i 0.999482 0.0321861i \(-0.0102469\pi\)
−0.998016 + 0.0629665i \(0.979944\pi\)
\(648\) 0 0
\(649\) 13.6909 + 17.4094i 0.537414 + 0.683377i
\(650\) 0 0
\(651\) −0.615598 49.4123i −0.0241272 1.93662i
\(652\) 0 0
\(653\) 4.66960 + 13.4919i 0.182735 + 0.527979i 0.998746 0.0500571i \(-0.0159403\pi\)
−0.816011 + 0.578036i \(0.803819\pi\)
\(654\) 0 0
\(655\) 25.5409 11.6642i 0.997967 0.455756i
\(656\) 0 0
\(657\) 13.4197 19.8754i 0.523554 0.775412i
\(658\) 0 0
\(659\) −6.02945 15.0608i −0.234874 0.586687i 0.763368 0.645964i \(-0.223545\pi\)
−0.998242 + 0.0592776i \(0.981120\pi\)
\(660\) 0 0
\(661\) 19.7598 + 9.02398i 0.768566 + 0.350992i 0.760807 0.648978i \(-0.224803\pi\)
0.00775838 + 0.999970i \(0.497530\pi\)
\(662\) 0 0
\(663\) −2.11878 10.3010i −0.0822868 0.400059i
\(664\) 0 0
\(665\) −11.4164 1.64143i −0.442710 0.0636521i
\(666\) 0 0
\(667\) 32.4413 20.8488i 1.25613 0.807267i
\(668\) 0 0
\(669\) −4.44210 41.1019i −0.171742 1.58909i
\(670\) 0 0
\(671\) 4.65964i 0.179883i
\(672\) 0 0
\(673\) 18.9480 + 29.4836i 0.730391 + 1.13651i 0.985513 + 0.169602i \(0.0542482\pi\)
−0.255121 + 0.966909i \(0.582115\pi\)
\(674\) 0 0
\(675\) −17.6036 + 3.20647i −0.677564 + 0.123417i
\(676\) 0 0
\(677\) 44.6510 4.26366i 1.71608 0.163866i 0.809845 0.586644i \(-0.199551\pi\)
0.906233 + 0.422778i \(0.138945\pi\)
\(678\) 0 0
\(679\) −6.66062 + 14.5847i −0.255611 + 0.559710i
\(680\) 0 0
\(681\) 31.3460 16.6575i 1.20118 0.638316i
\(682\) 0 0
\(683\) 4.89897 4.67116i 0.187454 0.178737i −0.590541 0.807008i \(-0.701085\pi\)
0.777995 + 0.628271i \(0.216237\pi\)
\(684\) 0 0
\(685\) 0.876931 + 1.92021i 0.0335058 + 0.0733675i
\(686\) 0 0
\(687\) −3.83897 8.13637i −0.146466 0.310422i
\(688\) 0 0
\(689\) −1.08348 + 11.3467i −0.0412773 + 0.432275i
\(690\) 0 0
\(691\) 16.3921 12.8909i 0.623583 0.490391i −0.255658 0.966767i \(-0.582292\pi\)
0.879242 + 0.476376i \(0.158050\pi\)
\(692\) 0 0
\(693\) 50.0271 13.4646i 1.90037 0.511476i
\(694\) 0 0
\(695\) 6.88788 23.4580i 0.261272 0.889811i
\(696\) 0 0
\(697\) −21.3399 + 3.06822i −0.808308 + 0.116217i
\(698\) 0 0
\(699\) −22.8837 + 16.7289i −0.865542 + 0.632746i
\(700\) 0 0
\(701\) −25.8412 24.6396i −0.976009 0.930623i 0.0215972 0.999767i \(-0.493125\pi\)
−0.997607 + 0.0691436i \(0.977973\pi\)
\(702\) 0 0
\(703\) −12.7282 + 17.8742i −0.480052 + 0.674139i
\(704\) 0 0
\(705\) 0.775912 + 12.9039i 0.0292225 + 0.485989i
\(706\) 0 0
\(707\) −19.6155 11.3250i −0.737718 0.425922i
\(708\) 0 0
\(709\) 5.74258 23.6712i 0.215667 0.888992i −0.756366 0.654148i \(-0.773027\pi\)
0.972033 0.234843i \(-0.0754577\pi\)
\(710\) 0 0
\(711\) 0.453083 + 18.1810i 0.0169919 + 0.681842i
\(712\) 0 0
\(713\) −31.1074 + 35.8999i −1.16498 + 1.34446i
\(714\) 0 0
\(715\) −4.91848 + 7.65330i −0.183941 + 0.286217i
\(716\) 0 0
\(717\) −1.86141 + 4.82286i −0.0695158 + 0.180113i
\(718\) 0 0
\(719\) −0.787928 4.08816i −0.0293847 0.152463i 0.964273 0.264911i \(-0.0853427\pi\)
−0.993658 + 0.112449i \(0.964131\pi\)
\(720\) 0 0
\(721\) 2.30882 2.93591i 0.0859850 0.109339i
\(722\) 0 0
\(723\) 25.6224 27.5512i 0.952906 1.02464i
\(724\) 0 0
\(725\) 27.1822 6.59432i 1.00952 0.244907i
\(726\) 0 0
\(727\) −5.16258 10.0140i −0.191470 0.371399i 0.773486 0.633814i \(-0.218511\pi\)
−0.964955 + 0.262415i \(0.915481\pi\)
\(728\) 0 0
\(729\) 16.1081 21.6686i 0.596595 0.802542i
\(730\) 0 0
\(731\) −27.9711 11.1979i −1.03455 0.414170i
\(732\) 0 0
\(733\) 5.54878 + 1.92045i 0.204949 + 0.0709336i 0.427614 0.903962i \(-0.359354\pi\)
−0.222665 + 0.974895i \(0.571476\pi\)
\(734\) 0 0
\(735\) −1.82680 + 1.62321i −0.0673824 + 0.0598730i
\(736\) 0 0
\(737\) −27.7106 + 41.1038i −1.02073 + 1.51408i
\(738\) 0 0
\(739\) −11.0929 + 7.89920i −0.408058 + 0.290577i −0.765596 0.643322i \(-0.777556\pi\)
0.357538 + 0.933899i \(0.383616\pi\)
\(740\) 0 0
\(741\) 1.51214 6.59041i 0.0555498 0.242105i
\(742\) 0 0
\(743\) −7.33380 + 18.3190i −0.269051 + 0.672057i −0.999946 0.0104334i \(-0.996679\pi\)
0.730894 + 0.682490i \(0.239103\pi\)
\(744\) 0 0
\(745\) 2.84492 + 9.68892i 0.104230 + 0.354975i
\(746\) 0 0
\(747\) 13.8745 + 16.7658i 0.507643 + 0.613430i
\(748\) 0 0
\(749\) −1.33936 5.52091i −0.0489391 0.201730i
\(750\) 0 0
\(751\) −24.5196 28.2972i −0.894734 1.03258i −0.999276 0.0380577i \(-0.987883\pi\)
0.104541 0.994521i \(-0.466663\pi\)
\(752\) 0 0
\(753\) 11.6033 18.5594i 0.422847 0.676343i
\(754\) 0 0
\(755\) 18.1471 3.49758i 0.660442 0.127290i
\(756\) 0 0
\(757\) 9.05969 17.5733i 0.329280 0.638714i −0.664842 0.746984i \(-0.731501\pi\)
0.994121 + 0.108270i \(0.0345313\pi\)
\(758\) 0 0
\(759\) −44.5457 22.2669i −1.61691 0.808238i
\(760\) 0 0
\(761\) −10.5028 9.10074i −0.380727 0.329902i 0.443382 0.896333i \(-0.353778\pi\)
−0.824109 + 0.566431i \(0.808324\pi\)
\(762\) 0 0
\(763\) −6.62800 1.27744i −0.239950 0.0462465i
\(764\) 0 0
\(765\) −18.8686 0.428095i −0.682194 0.0154778i
\(766\) 0 0
\(767\) 2.20169 3.81344i 0.0794983 0.137695i
\(768\) 0 0
\(769\) −0.686755 0.0327142i −0.0247650 0.00117970i 0.0351958 0.999380i \(-0.488795\pi\)
−0.0599608 + 0.998201i \(0.519098\pi\)
\(770\) 0 0
\(771\) 1.90960 3.40479i 0.0687726 0.122620i
\(772\) 0 0
\(773\) 15.8781 16.6525i 0.571095 0.598947i −0.373320 0.927703i \(-0.621781\pi\)
0.944415 + 0.328755i \(0.106629\pi\)