Properties

Label 432.2.be.a.335.5
Level $432$
Weight $2$
Character 432.335
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 335.5
Character \(\chi\) \(=\) 432.335
Dual form 432.2.be.a.383.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.873396 + 1.49572i) q^{3} +(-0.268878 + 0.738735i) q^{5} +(-3.49766 - 0.616732i) q^{7} +(-1.47436 + 2.61271i) q^{9} +O(q^{10})\) \(q+(0.873396 + 1.49572i) q^{3} +(-0.268878 + 0.738735i) q^{5} +(-3.49766 - 0.616732i) q^{7} +(-1.47436 + 2.61271i) q^{9} +(-4.77372 + 1.73749i) q^{11} +(-4.34250 + 3.64379i) q^{13} +(-1.33978 + 0.243043i) q^{15} +(6.45925 - 3.72925i) q^{17} +(2.31140 + 1.33449i) q^{19} +(-2.13239 - 5.77017i) q^{21} +(0.749727 + 4.25191i) q^{23} +(3.35679 + 2.81668i) q^{25} +(-5.19559 + 0.0767079i) q^{27} +(3.09583 - 3.68947i) q^{29} +(-2.76226 + 0.487060i) q^{31} +(-6.76815 - 5.62263i) q^{33} +(1.39604 - 2.41802i) q^{35} +(0.526507 + 0.911937i) q^{37} +(-9.24281 - 3.31269i) q^{39} +(-1.18342 - 1.41034i) q^{41} +(3.64664 + 10.0191i) q^{43} +(-1.53368 - 1.79166i) q^{45} +(1.36451 - 7.73852i) q^{47} +(5.27542 + 1.92010i) q^{49} +(11.2194 + 6.40412i) q^{51} +3.08817i q^{53} -3.99368i q^{55} +(0.0227487 + 4.62274i) q^{57} +(5.15076 + 1.87472i) q^{59} +(-1.62926 + 9.24000i) q^{61} +(6.76815 - 8.22910i) q^{63} +(-1.52419 - 4.18769i) q^{65} +(-6.27089 - 7.47336i) q^{67} +(-5.70486 + 4.83499i) q^{69} +(-1.72857 - 2.99398i) q^{71} +(-4.99284 + 8.64785i) q^{73} +(-1.28116 + 7.48089i) q^{75} +(17.7684 - 3.13305i) q^{77} +(-0.929972 + 1.10830i) q^{79} +(-4.65254 - 7.70415i) q^{81} +(1.12835 + 0.946797i) q^{83} +(1.01818 + 5.77438i) q^{85} +(8.22230 + 1.40813i) q^{87} +(-3.10319 - 1.79163i) q^{89} +(17.4358 - 10.0666i) q^{91} +(-3.14105 - 3.70617i) q^{93} +(-1.60732 + 1.34870i) q^{95} +(-2.87618 + 1.04684i) q^{97} +(2.49860 - 15.0340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 6q^{5} - 12q^{9} + O(q^{10}) \) \( 36q - 6q^{5} - 12q^{9} - 36q^{21} + 18q^{25} - 24q^{29} - 36q^{33} - 18q^{41} - 18q^{45} + 42q^{65} + 54q^{69} - 18q^{73} + 90q^{77} + 36q^{81} + 72q^{85} + 72q^{89} + 54q^{93} + 54q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.873396 + 1.49572i 0.504256 + 0.863554i
\(4\) 0 0
\(5\) −0.268878 + 0.738735i −0.120246 + 0.330372i −0.985183 0.171508i \(-0.945136\pi\)
0.864937 + 0.501880i \(0.167358\pi\)
\(6\) 0 0
\(7\) −3.49766 0.616732i −1.32199 0.233103i −0.532273 0.846573i \(-0.678662\pi\)
−0.789718 + 0.613470i \(0.789773\pi\)
\(8\) 0 0
\(9\) −1.47436 + 2.61271i −0.491453 + 0.870904i
\(10\) 0 0
\(11\) −4.77372 + 1.73749i −1.43933 + 0.523873i −0.939590 0.342302i \(-0.888793\pi\)
−0.499740 + 0.866176i \(0.666571\pi\)
\(12\) 0 0
\(13\) −4.34250 + 3.64379i −1.20439 + 1.01061i −0.204899 + 0.978783i \(0.565686\pi\)
−0.999494 + 0.0318218i \(0.989869\pi\)
\(14\) 0 0
\(15\) −1.33978 + 0.243043i −0.345929 + 0.0627534i
\(16\) 0 0
\(17\) 6.45925 3.72925i 1.56660 0.904476i 0.570036 0.821620i \(-0.306929\pi\)
0.996562 0.0828560i \(-0.0264042\pi\)
\(18\) 0 0
\(19\) 2.31140 + 1.33449i 0.530271 + 0.306152i 0.741127 0.671365i \(-0.234292\pi\)
−0.210856 + 0.977517i \(0.567625\pi\)
\(20\) 0 0
\(21\) −2.13239 5.77017i −0.465325 1.25915i
\(22\) 0 0
\(23\) 0.749727 + 4.25191i 0.156329 + 0.886585i 0.957561 + 0.288231i \(0.0930672\pi\)
−0.801232 + 0.598354i \(0.795822\pi\)
\(24\) 0 0
\(25\) 3.35679 + 2.81668i 0.671358 + 0.563336i
\(26\) 0 0
\(27\) −5.19559 + 0.0767079i −0.999891 + 0.0147624i
\(28\) 0 0
\(29\) 3.09583 3.68947i 0.574882 0.685117i −0.397744 0.917497i \(-0.630207\pi\)
0.972625 + 0.232379i \(0.0746511\pi\)
\(30\) 0 0
\(31\) −2.76226 + 0.487060i −0.496116 + 0.0874786i −0.416107 0.909316i \(-0.636606\pi\)
−0.0800087 + 0.996794i \(0.525495\pi\)
\(32\) 0 0
\(33\) −6.76815 5.62263i −1.17818 0.978774i
\(34\) 0 0
\(35\) 1.39604 2.41802i 0.235974 0.408720i
\(36\) 0 0
\(37\) 0.526507 + 0.911937i 0.0865573 + 0.149922i 0.906054 0.423163i \(-0.139080\pi\)
−0.819496 + 0.573084i \(0.805747\pi\)
\(38\) 0 0
\(39\) −9.24281 3.31269i −1.48003 0.530455i
\(40\) 0 0
\(41\) −1.18342 1.41034i −0.184818 0.220258i 0.665678 0.746239i \(-0.268143\pi\)
−0.850496 + 0.525981i \(0.823698\pi\)
\(42\) 0 0
\(43\) 3.64664 + 10.0191i 0.556107 + 1.52789i 0.825237 + 0.564787i \(0.191042\pi\)
−0.269130 + 0.963104i \(0.586736\pi\)
\(44\) 0 0
\(45\) −1.53368 1.79166i −0.228628 0.267085i
\(46\) 0 0
\(47\) 1.36451 7.73852i 0.199034 1.12878i −0.707521 0.706692i \(-0.750187\pi\)
0.906555 0.422087i \(-0.138702\pi\)
\(48\) 0 0
\(49\) 5.27542 + 1.92010i 0.753632 + 0.274300i
\(50\) 0 0
\(51\) 11.2194 + 6.40412i 1.57103 + 0.896755i
\(52\) 0 0
\(53\) 3.08817i 0.424192i 0.977249 + 0.212096i \(0.0680290\pi\)
−0.977249 + 0.212096i \(0.931971\pi\)
\(54\) 0 0
\(55\) 3.99368i 0.538508i
\(56\) 0 0
\(57\) 0.0227487 + 4.62274i 0.00301313 + 0.612297i
\(58\) 0 0
\(59\) 5.15076 + 1.87472i 0.670572 + 0.244068i 0.654794 0.755807i \(-0.272755\pi\)
0.0157780 + 0.999876i \(0.494977\pi\)
\(60\) 0 0
\(61\) −1.62926 + 9.24000i −0.208606 + 1.18306i 0.683058 + 0.730364i \(0.260649\pi\)
−0.891664 + 0.452698i \(0.850462\pi\)
\(62\) 0 0
\(63\) 6.76815 8.22910i 0.852706 1.03677i
\(64\) 0 0
\(65\) −1.52419 4.18769i −0.189053 0.519419i
\(66\) 0 0
\(67\) −6.27089 7.47336i −0.766111 0.913016i 0.232107 0.972690i \(-0.425438\pi\)
−0.998218 + 0.0596746i \(0.980994\pi\)
\(68\) 0 0
\(69\) −5.70486 + 4.83499i −0.686785 + 0.582064i
\(70\) 0 0
\(71\) −1.72857 2.99398i −0.205144 0.355320i 0.745035 0.667026i \(-0.232433\pi\)
−0.950179 + 0.311706i \(0.899100\pi\)
\(72\) 0 0
\(73\) −4.99284 + 8.64785i −0.584367 + 1.01215i 0.410587 + 0.911822i \(0.365324\pi\)
−0.994954 + 0.100332i \(0.968009\pi\)
\(74\) 0 0
\(75\) −1.28116 + 7.48089i −0.147935 + 0.863819i
\(76\) 0 0
\(77\) 17.7684 3.13305i 2.02490 0.357044i
\(78\) 0 0
\(79\) −0.929972 + 1.10830i −0.104630 + 0.124693i −0.815818 0.578309i \(-0.803713\pi\)
0.711188 + 0.703002i \(0.248157\pi\)
\(80\) 0 0
\(81\) −4.65254 7.70415i −0.516949 0.856016i
\(82\) 0 0
\(83\) 1.12835 + 0.946797i 0.123852 + 0.103925i 0.702610 0.711575i \(-0.252018\pi\)
−0.578758 + 0.815500i \(0.696462\pi\)
\(84\) 0 0
\(85\) 1.01818 + 5.77438i 0.110437 + 0.626320i
\(86\) 0 0
\(87\) 8.22230 + 1.40813i 0.881523 + 0.150967i
\(88\) 0 0
\(89\) −3.10319 1.79163i −0.328938 0.189912i 0.326432 0.945221i \(-0.394154\pi\)
−0.655369 + 0.755308i \(0.727487\pi\)
\(90\) 0 0
\(91\) 17.4358 10.0666i 1.82777 1.05526i
\(92\) 0 0
\(93\) −3.14105 3.70617i −0.325712 0.384312i
\(94\) 0 0
\(95\) −1.60732 + 1.34870i −0.164907 + 0.138374i
\(96\) 0 0
\(97\) −2.87618 + 1.04684i −0.292031 + 0.106291i −0.483882 0.875133i \(-0.660773\pi\)
0.191850 + 0.981424i \(0.438551\pi\)
\(98\) 0 0
\(99\) 2.49860 15.0340i 0.251119 1.51098i
\(100\) 0 0
\(101\) 9.66552 + 1.70429i 0.961755 + 0.169583i 0.632417 0.774628i \(-0.282063\pi\)
0.329339 + 0.944212i \(0.393174\pi\)
\(102\) 0 0
\(103\) 2.73206 7.50626i 0.269197 0.739614i −0.729268 0.684229i \(-0.760139\pi\)
0.998465 0.0553854i \(-0.0176387\pi\)
\(104\) 0 0
\(105\) 4.83598 0.0237980i 0.471943 0.00232245i
\(106\) 0 0
\(107\) 15.2633 1.47555 0.737777 0.675044i \(-0.235875\pi\)
0.737777 + 0.675044i \(0.235875\pi\)
\(108\) 0 0
\(109\) 1.31092 0.125563 0.0627817 0.998027i \(-0.480003\pi\)
0.0627817 + 0.998027i \(0.480003\pi\)
\(110\) 0 0
\(111\) −0.904154 + 1.58399i −0.0858185 + 0.150346i
\(112\) 0 0
\(113\) −0.0329085 + 0.0904152i −0.00309577 + 0.00850555i −0.941231 0.337764i \(-0.890329\pi\)
0.938135 + 0.346269i \(0.112552\pi\)
\(114\) 0 0
\(115\) −3.34262 0.589395i −0.311701 0.0549613i
\(116\) 0 0
\(117\) −3.11778 16.7179i −0.288239 1.54557i
\(118\) 0 0
\(119\) −24.8922 + 9.06002i −2.28186 + 0.830531i
\(120\) 0 0
\(121\) 11.3430 9.51791i 1.03118 0.865265i
\(122\) 0 0
\(123\) 1.07588 3.00184i 0.0970091 0.270667i
\(124\) 0 0
\(125\) −6.38745 + 3.68780i −0.571311 + 0.329847i
\(126\) 0 0
\(127\) 9.78038 + 5.64670i 0.867868 + 0.501064i 0.866639 0.498935i \(-0.166276\pi\)
0.00122880 + 0.999999i \(0.499609\pi\)
\(128\) 0 0
\(129\) −11.8007 + 14.2049i −1.03900 + 1.25068i
\(130\) 0 0
\(131\) 2.07281 + 11.7555i 0.181102 + 1.02708i 0.930862 + 0.365372i \(0.119058\pi\)
−0.749759 + 0.661711i \(0.769831\pi\)
\(132\) 0 0
\(133\) −7.26147 6.09310i −0.629649 0.528339i
\(134\) 0 0
\(135\) 1.34031 3.85879i 0.115355 0.332111i
\(136\) 0 0
\(137\) −3.22440 + 3.84269i −0.275479 + 0.328303i −0.885990 0.463705i \(-0.846520\pi\)
0.610511 + 0.792008i \(0.290964\pi\)
\(138\) 0 0
\(139\) −5.82044 + 1.02630i −0.493684 + 0.0870497i −0.414947 0.909846i \(-0.636200\pi\)
−0.0787369 + 0.996895i \(0.525089\pi\)
\(140\) 0 0
\(141\) 12.7664 4.71787i 1.07513 0.397316i
\(142\) 0 0
\(143\) 14.3988 24.9395i 1.20409 2.08554i
\(144\) 0 0
\(145\) 1.89314 + 3.27901i 0.157217 + 0.272307i
\(146\) 0 0
\(147\) 1.73561 + 9.56756i 0.143150 + 0.789119i
\(148\) 0 0
\(149\) −13.2535 15.7949i −1.08577 1.29397i −0.953048 0.302819i \(-0.902072\pi\)
−0.132723 0.991153i \(-0.542372\pi\)
\(150\) 0 0
\(151\) 1.71324 + 4.70708i 0.139421 + 0.383057i 0.989678 0.143312i \(-0.0457753\pi\)
−0.850256 + 0.526369i \(0.823553\pi\)
\(152\) 0 0
\(153\) 0.220216 + 22.3744i 0.0178034 + 1.80886i
\(154\) 0 0
\(155\) 0.382900 2.17154i 0.0307553 0.174422i
\(156\) 0 0
\(157\) −12.7218 4.63034i −1.01531 0.369542i −0.219838 0.975536i \(-0.570553\pi\)
−0.795469 + 0.605995i \(0.792775\pi\)
\(158\) 0 0
\(159\) −4.61903 + 2.69719i −0.366313 + 0.213901i
\(160\) 0 0
\(161\) 15.3341i 1.20850i
\(162\) 0 0
\(163\) 7.88546i 0.617637i 0.951121 + 0.308819i \(0.0999336\pi\)
−0.951121 + 0.308819i \(0.900066\pi\)
\(164\) 0 0
\(165\) 5.97343 3.48807i 0.465031 0.271546i
\(166\) 0 0
\(167\) 17.4302 + 6.34409i 1.34879 + 0.490920i 0.912571 0.408919i \(-0.134094\pi\)
0.436221 + 0.899839i \(0.356316\pi\)
\(168\) 0 0
\(169\) 3.32267 18.8438i 0.255590 1.44952i
\(170\) 0 0
\(171\) −6.89446 + 4.07151i −0.527233 + 0.311356i
\(172\) 0 0
\(173\) 6.11376 + 16.7974i 0.464820 + 1.27708i 0.921821 + 0.387617i \(0.126702\pi\)
−0.457000 + 0.889467i \(0.651076\pi\)
\(174\) 0 0
\(175\) −10.0038 11.9220i −0.756214 0.901221i
\(176\) 0 0
\(177\) 1.69459 + 9.34148i 0.127374 + 0.702149i
\(178\) 0 0
\(179\) −5.34490 9.25764i −0.399497 0.691949i 0.594167 0.804342i \(-0.297482\pi\)
−0.993664 + 0.112393i \(0.964148\pi\)
\(180\) 0 0
\(181\) −0.113154 + 0.195989i −0.00841069 + 0.0145678i −0.870200 0.492698i \(-0.836011\pi\)
0.861789 + 0.507266i \(0.169344\pi\)
\(182\) 0 0
\(183\) −15.2435 + 5.63327i −1.12683 + 0.416423i
\(184\) 0 0
\(185\) −0.815246 + 0.143750i −0.0599381 + 0.0105687i
\(186\) 0 0
\(187\) −24.3551 + 29.0253i −1.78102 + 2.12254i
\(188\) 0 0
\(189\) 18.2197 + 2.93599i 1.32529 + 0.213562i
\(190\) 0 0
\(191\) −13.7279 11.5191i −0.993319 0.833493i −0.00727404 0.999974i \(-0.502315\pi\)
−0.986045 + 0.166480i \(0.946760\pi\)
\(192\) 0 0
\(193\) 0.973127 + 5.51888i 0.0700472 + 0.397258i 0.999592 + 0.0285493i \(0.00908874\pi\)
−0.929545 + 0.368708i \(0.879800\pi\)
\(194\) 0 0
\(195\) 4.93238 5.93728i 0.353215 0.425177i
\(196\) 0 0
\(197\) 14.2915 + 8.25120i 1.01823 + 0.587873i 0.913590 0.406637i \(-0.133299\pi\)
0.104637 + 0.994510i \(0.466632\pi\)
\(198\) 0 0
\(199\) −7.43752 + 4.29405i −0.527231 + 0.304397i −0.739888 0.672730i \(-0.765122\pi\)
0.212657 + 0.977127i \(0.431788\pi\)
\(200\) 0 0
\(201\) 5.70108 15.9067i 0.402123 1.12197i
\(202\) 0 0
\(203\) −13.1036 + 10.9952i −0.919691 + 0.771713i
\(204\) 0 0
\(205\) 1.36006 0.495022i 0.0949908 0.0345738i
\(206\) 0 0
\(207\) −12.2144 4.31002i −0.848959 0.299567i
\(208\) 0 0
\(209\) −13.3526 2.35443i −0.923620 0.162859i
\(210\) 0 0
\(211\) 4.01203 11.0230i 0.276200 0.758852i −0.721585 0.692326i \(-0.756586\pi\)
0.997785 0.0665263i \(-0.0211916\pi\)
\(212\) 0 0
\(213\) 2.96842 5.20039i 0.203393 0.356325i
\(214\) 0 0
\(215\) −8.38192 −0.571642
\(216\) 0 0
\(217\) 9.96182 0.676253
\(218\) 0 0
\(219\) −17.2955 + 0.0851116i −1.16872 + 0.00575131i
\(220\) 0 0
\(221\) −14.4607 + 39.7304i −0.972730 + 2.67255i
\(222\) 0 0
\(223\) 23.3625 + 4.11943i 1.56447 + 0.275858i 0.887729 0.460367i \(-0.152282\pi\)
0.676737 + 0.736225i \(0.263393\pi\)
\(224\) 0 0
\(225\) −12.3083 + 4.61753i −0.820552 + 0.307835i
\(226\) 0 0
\(227\) 9.14518 3.32857i 0.606987 0.220925i −0.0201973 0.999796i \(-0.506429\pi\)
0.627184 + 0.778871i \(0.284207\pi\)
\(228\) 0 0
\(229\) −5.04383 + 4.23227i −0.333306 + 0.279677i −0.794045 0.607859i \(-0.792029\pi\)
0.460740 + 0.887535i \(0.347584\pi\)
\(230\) 0 0
\(231\) 20.2050 + 23.8402i 1.32939 + 1.56857i
\(232\) 0 0
\(233\) −18.4755 + 10.6669i −1.21037 + 0.698809i −0.962841 0.270070i \(-0.912953\pi\)
−0.247532 + 0.968880i \(0.579620\pi\)
\(234\) 0 0
\(235\) 5.34983 + 3.08873i 0.348984 + 0.201486i
\(236\) 0 0
\(237\) −2.46994 0.422995i −0.160440 0.0274765i
\(238\) 0 0
\(239\) 3.46984 + 19.6784i 0.224445 + 1.27289i 0.863743 + 0.503933i \(0.168114\pi\)
−0.639298 + 0.768959i \(0.720775\pi\)
\(240\) 0 0
\(241\) 4.53930 + 3.80892i 0.292402 + 0.245354i 0.777173 0.629287i \(-0.216653\pi\)
−0.484771 + 0.874641i \(0.661097\pi\)
\(242\) 0 0
\(243\) 7.45974 13.6877i 0.478542 0.878065i
\(244\) 0 0
\(245\) −2.83689 + 3.38087i −0.181242 + 0.215996i
\(246\) 0 0
\(247\) −14.8998 + 2.62724i −0.948054 + 0.167167i
\(248\) 0 0
\(249\) −0.430648 + 2.51462i −0.0272912 + 0.159358i
\(250\) 0 0
\(251\) −7.81361 + 13.5336i −0.493191 + 0.854232i −0.999969 0.00784478i \(-0.997503\pi\)
0.506778 + 0.862076i \(0.330836\pi\)
\(252\) 0 0
\(253\) −10.9666 18.9948i −0.689467 1.19419i
\(254\) 0 0
\(255\) −7.74759 + 6.56624i −0.485173 + 0.411194i
\(256\) 0 0
\(257\) −10.0813 12.0145i −0.628856 0.749441i 0.353710 0.935355i \(-0.384920\pi\)
−0.982566 + 0.185914i \(0.940476\pi\)
\(258\) 0 0
\(259\) −1.27912 3.51436i −0.0794808 0.218372i
\(260\) 0 0
\(261\) 5.07516 + 13.5281i 0.314145 + 0.837369i
\(262\) 0 0
\(263\) −5.24105 + 29.7235i −0.323177 + 1.83283i 0.199012 + 0.979997i \(0.436227\pi\)
−0.522189 + 0.852830i \(0.674884\pi\)
\(264\) 0 0
\(265\) −2.28134 0.830339i −0.140141 0.0510073i
\(266\) 0 0
\(267\) −0.0305415 6.20631i −0.00186911 0.379820i
\(268\) 0 0
\(269\) 6.99110i 0.426255i 0.977024 + 0.213127i \(0.0683649\pi\)
−0.977024 + 0.213127i \(0.931635\pi\)
\(270\) 0 0
\(271\) 21.8898i 1.32971i −0.746973 0.664855i \(-0.768493\pi\)
0.746973 0.664855i \(-0.231507\pi\)
\(272\) 0 0
\(273\) 30.2852 + 17.2870i 1.83294 + 1.04626i
\(274\) 0 0
\(275\) −20.9183 7.61364i −1.26142 0.459120i
\(276\) 0 0
\(277\) −0.365886 + 2.07504i −0.0219840 + 0.124677i −0.993825 0.110961i \(-0.964607\pi\)
0.971841 + 0.235639i \(0.0757182\pi\)
\(278\) 0 0
\(279\) 2.80001 7.93509i 0.167632 0.475061i
\(280\) 0 0
\(281\) −8.95821 24.6125i −0.534402 1.46826i −0.853782 0.520631i \(-0.825697\pi\)
0.319380 0.947627i \(-0.396525\pi\)
\(282\) 0 0
\(283\) −10.7458 12.8063i −0.638769 0.761255i 0.345406 0.938453i \(-0.387741\pi\)
−0.984175 + 0.177198i \(0.943297\pi\)
\(284\) 0 0
\(285\) −3.42110 1.22615i −0.202648 0.0726307i
\(286\) 0 0
\(287\) 3.26938 + 5.66274i 0.192986 + 0.334261i
\(288\) 0 0
\(289\) 19.3146 33.4538i 1.13615 1.96787i
\(290\) 0 0
\(291\) −4.07783 3.38765i −0.239046 0.198587i
\(292\) 0 0
\(293\) 13.7176 2.41877i 0.801388 0.141306i 0.242069 0.970259i \(-0.422174\pi\)
0.559319 + 0.828953i \(0.311063\pi\)
\(294\) 0 0
\(295\) −2.76985 + 3.30098i −0.161267 + 0.192190i
\(296\) 0 0
\(297\) 24.6690 9.39346i 1.43144 0.545064i
\(298\) 0 0
\(299\) −18.7488 15.7321i −1.08427 0.909810i
\(300\) 0 0
\(301\) −6.57563 37.2922i −0.379013 2.14949i
\(302\) 0 0
\(303\) 5.89269 + 15.9454i 0.338526 + 0.916042i
\(304\) 0 0
\(305\) −6.38784 3.68802i −0.365767 0.211176i
\(306\) 0 0
\(307\) 21.4253 12.3699i 1.22281 0.705988i 0.257292 0.966334i \(-0.417170\pi\)
0.965516 + 0.260346i \(0.0838365\pi\)
\(308\) 0 0
\(309\) 13.6134 2.46955i 0.774441 0.140488i
\(310\) 0 0
\(311\) 11.6982 9.81598i 0.663346 0.556613i −0.247742 0.968826i \(-0.579688\pi\)
0.911088 + 0.412213i \(0.135244\pi\)
\(312\) 0 0
\(313\) 14.3850 5.23571i 0.813088 0.295940i 0.0981890 0.995168i \(-0.468695\pi\)
0.714899 + 0.699228i \(0.246473\pi\)
\(314\) 0 0
\(315\) 4.25932 + 7.21249i 0.239986 + 0.406378i
\(316\) 0 0
\(317\) −26.1063 4.60325i −1.46628 0.258544i −0.617197 0.786809i \(-0.711732\pi\)
−0.849080 + 0.528265i \(0.822843\pi\)
\(318\) 0 0
\(319\) −8.36821 + 22.9915i −0.468530 + 1.28727i
\(320\) 0 0
\(321\) 13.3309 + 22.8296i 0.744057 + 1.27422i
\(322\) 0 0
\(323\) 19.9065 1.10763
\(324\) 0 0
\(325\) −24.8402 −1.37789
\(326\) 0 0
\(327\) 1.14495 + 1.96077i 0.0633161 + 0.108431i
\(328\) 0 0
\(329\) −9.54519 + 26.2252i −0.526243 + 1.44584i
\(330\) 0 0
\(331\) −10.9290 1.92707i −0.600710 0.105921i −0.134980 0.990848i \(-0.543097\pi\)
−0.465730 + 0.884927i \(0.654208\pi\)
\(332\) 0 0
\(333\) −3.15889 + 0.0310908i −0.173106 + 0.00170376i
\(334\) 0 0
\(335\) 7.20693 2.62311i 0.393757 0.143316i
\(336\) 0 0
\(337\) −6.52591 + 5.47589i −0.355489 + 0.298291i −0.802990 0.595993i \(-0.796759\pi\)
0.447501 + 0.894284i \(0.352314\pi\)
\(338\) 0 0
\(339\) −0.163978 + 0.0297465i −0.00890606 + 0.00161561i
\(340\) 0 0
\(341\) 12.3400 7.12448i 0.668247 0.385812i
\(342\) 0 0
\(343\) 4.26308 + 2.46129i 0.230185 + 0.132897i
\(344\) 0 0
\(345\) −2.03787 5.51440i −0.109715 0.296885i
\(346\) 0 0
\(347\) −2.54186 14.4156i −0.136454 0.773871i −0.973836 0.227252i \(-0.927026\pi\)
0.837382 0.546619i \(-0.184085\pi\)
\(348\) 0 0
\(349\) 2.11745 + 1.77675i 0.113345 + 0.0951075i 0.697699 0.716392i \(-0.254208\pi\)
−0.584354 + 0.811499i \(0.698652\pi\)
\(350\) 0 0
\(351\) 22.2823 19.2647i 1.18934 1.02827i
\(352\) 0 0
\(353\) −4.00818 + 4.77676i −0.213334 + 0.254242i −0.862090 0.506755i \(-0.830845\pi\)
0.648756 + 0.760996i \(0.275289\pi\)
\(354\) 0 0
\(355\) 2.67653 0.471945i 0.142056 0.0250482i
\(356\) 0 0
\(357\) −35.2920 29.3188i −1.86785 1.55171i
\(358\) 0 0
\(359\) 12.3686 21.4231i 0.652791 1.13067i −0.329652 0.944103i \(-0.606931\pi\)
0.982443 0.186564i \(-0.0597353\pi\)
\(360\) 0 0
\(361\) −5.93829 10.2854i −0.312541 0.541338i
\(362\) 0 0
\(363\) 24.1431 + 8.65305i 1.26718 + 0.454168i
\(364\) 0 0
\(365\) −5.04600 6.01359i −0.264120 0.314766i
\(366\) 0 0
\(367\) 0.425247 + 1.16836i 0.0221977 + 0.0609877i 0.950297 0.311346i \(-0.100780\pi\)
−0.928099 + 0.372334i \(0.878558\pi\)
\(368\) 0 0
\(369\) 5.42959 1.01258i 0.282653 0.0527128i
\(370\) 0 0
\(371\) 1.90457 10.8014i 0.0988804 0.560779i
\(372\) 0 0
\(373\) 22.0894 + 8.03989i 1.14375 + 0.416290i 0.843265 0.537498i \(-0.180631\pi\)
0.300481 + 0.953788i \(0.402853\pi\)
\(374\) 0 0
\(375\) −11.0947 6.33293i −0.572928 0.327031i
\(376\) 0 0
\(377\) 27.3021i 1.40613i
\(378\) 0 0
\(379\) 4.98764i 0.256198i 0.991761 + 0.128099i \(0.0408875\pi\)
−0.991761 + 0.128099i \(0.959112\pi\)
\(380\) 0 0
\(381\) 0.0962579 + 19.5605i 0.00493144 + 1.00212i
\(382\) 0 0
\(383\) 28.2451 + 10.2804i 1.44326 + 0.525302i 0.940699 0.339243i \(-0.110171\pi\)
0.502556 + 0.864544i \(0.332393\pi\)
\(384\) 0 0
\(385\) −2.46303 + 13.9686i −0.125528 + 0.711903i
\(386\) 0 0
\(387\) −31.5533 5.24405i −1.60395 0.266570i
\(388\) 0 0
\(389\) 3.00042 + 8.24360i 0.152128 + 0.417967i 0.992223 0.124471i \(-0.0397235\pi\)
−0.840096 + 0.542438i \(0.817501\pi\)
\(390\) 0 0
\(391\) 20.6991 + 24.6682i 1.04680 + 1.24753i
\(392\) 0 0
\(393\) −15.7726 + 13.3676i −0.795620 + 0.674304i
\(394\) 0 0
\(395\) −0.568690 0.985000i −0.0286139 0.0495607i
\(396\) 0 0
\(397\) −9.80757 + 16.9872i −0.492228 + 0.852563i −0.999960 0.00895158i \(-0.997151\pi\)
0.507732 + 0.861515i \(0.330484\pi\)
\(398\) 0 0
\(399\) 2.77143 16.1828i 0.138745 0.810154i
\(400\) 0 0
\(401\) 26.5005 4.67276i 1.32337 0.233346i 0.533075 0.846068i \(-0.321036\pi\)
0.790299 + 0.612722i \(0.209925\pi\)
\(402\) 0 0
\(403\) 10.2203 12.1801i 0.509112 0.606736i
\(404\) 0 0
\(405\) 6.94229 1.36552i 0.344965 0.0678533i
\(406\) 0 0
\(407\) −4.09788 3.43853i −0.203124 0.170442i
\(408\) 0 0
\(409\) −1.36327 7.73147i −0.0674092 0.382297i −0.999784 0.0208025i \(-0.993378\pi\)
0.932374 0.361494i \(-0.117733\pi\)
\(410\) 0 0
\(411\) −8.56377 1.46661i −0.422419 0.0723424i
\(412\) 0 0
\(413\) −16.8594 9.73379i −0.829598 0.478969i
\(414\) 0 0
\(415\) −1.00282 + 0.578978i −0.0492265 + 0.0284209i
\(416\) 0 0
\(417\) −6.61861 7.80939i −0.324115 0.382427i
\(418\) 0 0
\(419\) 11.5624 9.70203i 0.564861 0.473975i −0.315075 0.949067i \(-0.602030\pi\)
0.879936 + 0.475092i \(0.157585\pi\)
\(420\) 0 0
\(421\) −12.2598 + 4.46218i −0.597504 + 0.217474i −0.623027 0.782201i \(-0.714097\pi\)
0.0255229 + 0.999674i \(0.491875\pi\)
\(422\) 0 0
\(423\) 18.2068 + 14.9744i 0.885243 + 0.728081i
\(424\) 0 0
\(425\) 32.1864 + 5.67533i 1.56127 + 0.275294i
\(426\) 0 0
\(427\) 11.3972 31.3136i 0.551550 1.51537i
\(428\) 0 0
\(429\) 49.8783 0.245453i 2.40815 0.0118506i
\(430\) 0 0
\(431\) −3.23665 −0.155904 −0.0779519 0.996957i \(-0.524838\pi\)
−0.0779519 + 0.996957i \(0.524838\pi\)
\(432\) 0 0
\(433\) 9.26788 0.445386 0.222693 0.974889i \(-0.428515\pi\)
0.222693 + 0.974889i \(0.428515\pi\)
\(434\) 0 0
\(435\) −3.25103 + 5.69549i −0.155875 + 0.273078i
\(436\) 0 0
\(437\) −3.94121 + 10.8284i −0.188533 + 0.517991i
\(438\) 0 0
\(439\) −18.8470 3.32323i −0.899516 0.158609i −0.295277 0.955412i \(-0.595412\pi\)
−0.604240 + 0.796803i \(0.706523\pi\)
\(440\) 0 0
\(441\) −12.7945 + 10.9523i −0.609263 + 0.521536i
\(442\) 0 0
\(443\) 16.5782 6.03398i 0.787655 0.286683i 0.0832943 0.996525i \(-0.473456\pi\)
0.704361 + 0.709842i \(0.251234\pi\)
\(444\) 0 0
\(445\) 2.15792 1.81071i 0.102295 0.0858358i
\(446\) 0 0
\(447\) 12.0492 33.6188i 0.569909 1.59012i
\(448\) 0 0
\(449\) 1.70349 0.983512i 0.0803928 0.0464148i −0.459265 0.888299i \(-0.651887\pi\)
0.539658 + 0.841885i \(0.318554\pi\)
\(450\) 0 0
\(451\) 8.09974 + 4.67639i 0.381402 + 0.220203i
\(452\) 0 0
\(453\) −5.54414 + 6.67367i −0.260487 + 0.313557i
\(454\) 0 0
\(455\) 2.74843 + 15.5871i 0.128848 + 0.730736i
\(456\) 0 0
\(457\) −18.4817 15.5080i −0.864539 0.725434i 0.0984023 0.995147i \(-0.468627\pi\)
−0.962941 + 0.269713i \(0.913071\pi\)
\(458\) 0 0
\(459\) −33.2735 + 19.8711i −1.55307 + 0.927504i
\(460\) 0 0
\(461\) 0.876842 1.04498i 0.0408386 0.0486695i −0.745239 0.666798i \(-0.767664\pi\)
0.786077 + 0.618128i \(0.212109\pi\)
\(462\) 0 0
\(463\) 37.2025 6.55980i 1.72895 0.304860i 0.781293 0.624164i \(-0.214560\pi\)
0.947652 + 0.319305i \(0.103449\pi\)
\(464\) 0 0
\(465\) 3.58243 1.32390i 0.166131 0.0613944i
\(466\) 0 0
\(467\) −9.08669 + 15.7386i −0.420482 + 0.728296i −0.995987 0.0895025i \(-0.971472\pi\)
0.575505 + 0.817798i \(0.304806\pi\)
\(468\) 0 0
\(469\) 17.3244 + 30.0067i 0.799966 + 1.38558i
\(470\) 0 0
\(471\) −4.18544 23.0723i −0.192855 1.06312i
\(472\) 0 0
\(473\) −34.8160 41.4921i −1.60084 1.90781i
\(474\) 0 0
\(475\) 4.00006 + 10.9901i 0.183535 + 0.504259i
\(476\) 0 0
\(477\) −8.06849 4.55306i −0.369431 0.208470i
\(478\) 0 0
\(479\) −2.04750 + 11.6119i −0.0935526 + 0.530563i 0.901629 + 0.432511i \(0.142372\pi\)
−0.995181 + 0.0980521i \(0.968739\pi\)
\(480\) 0 0
\(481\) −5.60926 2.04161i −0.255760 0.0930892i
\(482\) 0 0
\(483\) 22.9356 13.3928i 1.04360 0.609392i
\(484\) 0 0
\(485\) 2.40620i 0.109260i
\(486\) 0 0
\(487\) 27.5642i 1.24905i 0.781003 + 0.624527i \(0.214708\pi\)
−0.781003 + 0.624527i \(0.785292\pi\)
\(488\) 0 0
\(489\) −11.7944 + 6.88713i −0.533363 + 0.311447i
\(490\) 0 0
\(491\) −3.63911 1.32453i −0.164231 0.0597752i 0.258596 0.965985i \(-0.416740\pi\)
−0.422827 + 0.906210i \(0.638962\pi\)
\(492\) 0 0
\(493\) 6.23780 35.3763i 0.280936 1.59327i
\(494\) 0 0
\(495\) 10.4344 + 5.88812i 0.468989 + 0.264651i
\(496\) 0 0
\(497\) 4.19949 + 11.5380i 0.188373 + 0.517550i
\(498\) 0 0
\(499\) −12.5019 14.8992i −0.559664 0.666981i 0.409812 0.912170i \(-0.365594\pi\)
−0.969475 + 0.245189i \(0.921150\pi\)
\(500\) 0 0
\(501\) 5.73453 + 31.6117i 0.256200 + 1.41230i
\(502\) 0 0
\(503\) −7.58734 13.1417i −0.338303 0.585958i 0.645811 0.763497i \(-0.276519\pi\)
−0.984114 + 0.177540i \(0.943186\pi\)
\(504\) 0 0
\(505\) −3.85786 + 6.68201i −0.171673 + 0.297346i
\(506\) 0 0
\(507\) 31.0870 11.4883i 1.38062 0.510214i
\(508\) 0 0
\(509\) 24.1974 4.26666i 1.07253 0.189116i 0.390621 0.920552i \(-0.372260\pi\)
0.681911 + 0.731436i \(0.261149\pi\)
\(510\) 0 0
\(511\) 22.7966 27.1680i 1.00846 1.20184i
\(512\) 0 0
\(513\) −12.1114 6.75614i −0.534733 0.298291i
\(514\) 0 0
\(515\) 4.81055 + 4.03653i 0.211978 + 0.177871i
\(516\) 0 0
\(517\) 6.93183 + 39.3123i 0.304861 + 1.72895i
\(518\) 0 0
\(519\) −19.7845 + 23.8153i −0.868443 + 1.04537i
\(520\) 0 0
\(521\) −15.3333 8.85266i −0.671762 0.387842i 0.124982 0.992159i \(-0.460113\pi\)
−0.796744 + 0.604317i \(0.793446\pi\)
\(522\) 0 0
\(523\) −15.4545 + 8.92267i −0.675779 + 0.390161i −0.798263 0.602309i \(-0.794247\pi\)
0.122484 + 0.992471i \(0.460914\pi\)
\(524\) 0 0
\(525\) 9.09476 25.3755i 0.396928 1.10748i
\(526\) 0 0
\(527\) −16.0257 + 13.4472i −0.698092 + 0.585769i
\(528\) 0 0
\(529\) 4.09625 1.49091i 0.178098 0.0648223i
\(530\) 0 0
\(531\) −12.4922 + 10.6935i −0.542115 + 0.464056i
\(532\) 0 0
\(533\) 10.2780 + 1.81228i 0.445188 + 0.0784986i
\(534\) 0 0
\(535\) −4.10395 + 11.2755i −0.177429 + 0.487482i
\(536\) 0 0
\(537\) 9.17862 16.0801i 0.396087 0.693906i
\(538\) 0 0
\(539\) −28.5195 −1.22842
\(540\) 0 0
\(541\) 8.91858 0.383440 0.191720 0.981450i \(-0.438593\pi\)
0.191720 + 0.981450i \(0.438593\pi\)
\(542\) 0 0
\(543\) −0.391973 + 0.00192891i −0.0168212 + 8.27776e-5i
\(544\) 0 0
\(545\) −0.352477 + 0.968423i −0.0150985 + 0.0414827i
\(546\) 0 0
\(547\) −1.30961 0.230919i −0.0559947 0.00987337i 0.145581 0.989346i \(-0.453495\pi\)
−0.201575 + 0.979473i \(0.564606\pi\)
\(548\) 0 0
\(549\) −21.7394 17.8799i −0.927814 0.763094i
\(550\) 0 0
\(551\) 12.0793 4.39649i 0.514594 0.187297i
\(552\) 0 0
\(553\) 3.93625 3.30291i 0.167386 0.140454i
\(554\) 0 0
\(555\) −0.927043 1.09383i −0.0393508 0.0464305i
\(556\) 0 0
\(557\) 24.3179 14.0399i 1.03038 0.594891i 0.113288 0.993562i \(-0.463862\pi\)
0.917094 + 0.398671i \(0.130528\pi\)
\(558\) 0 0
\(559\) −52.3428 30.2201i −2.21386 1.27818i
\(560\) 0 0
\(561\) −64.6853 11.0778i −2.73102 0.467707i
\(562\) 0 0
\(563\) −5.14982 29.2061i −0.217039 1.23089i −0.877333 0.479882i \(-0.840679\pi\)
0.660294 0.751007i \(-0.270432\pi\)
\(564\) 0 0
\(565\) −0.0579446 0.0486213i −0.00243775 0.00204551i
\(566\) 0 0
\(567\) 11.5216 + 29.8159i 0.483862 + 1.25215i
\(568\) 0 0
\(569\) −7.18324 + 8.56066i −0.301137 + 0.358881i −0.895300 0.445463i \(-0.853039\pi\)
0.594163 + 0.804345i \(0.297483\pi\)
\(570\) 0 0
\(571\) −37.3754 + 6.59029i −1.56411 + 0.275795i −0.887592 0.460630i \(-0.847624\pi\)
−0.676519 + 0.736425i \(0.736512\pi\)
\(572\) 0 0
\(573\) 5.23943 30.5939i 0.218880 1.27808i
\(574\) 0 0
\(575\) −9.45960 + 16.3845i −0.394493 + 0.683282i
\(576\) 0 0
\(577\) 19.7897 + 34.2768i 0.823856 + 1.42696i 0.902790 + 0.430081i \(0.141515\pi\)
−0.0789341 + 0.996880i \(0.525152\pi\)
\(578\) 0 0
\(579\) −7.40477 + 6.27569i −0.307732 + 0.260809i
\(580\) 0 0
\(581\) −3.36266 4.00746i −0.139507 0.166258i
\(582\) 0 0
\(583\) −5.36566 14.7420i −0.222223 0.610553i
\(584\) 0 0
\(585\) 13.1884 + 2.19187i 0.545275 + 0.0906226i
\(586\) 0 0
\(587\) −0.480765 + 2.72655i −0.0198433 + 0.112537i −0.993121 0.117096i \(-0.962641\pi\)
0.973277 + 0.229633i \(0.0737526\pi\)
\(588\) 0 0
\(589\) −7.03466 2.56041i −0.289858 0.105500i
\(590\) 0 0
\(591\) 0.140656 + 28.5826i 0.00578582 + 1.17573i
\(592\) 0 0
\(593\) 20.8421i 0.855881i −0.903807 0.427941i \(-0.859239\pi\)
0.903807 0.427941i \(-0.140761\pi\)
\(594\) 0 0
\(595\) 20.8248i 0.853733i
\(596\) 0 0
\(597\) −12.9186 7.37403i −0.528723 0.301799i
\(598\) 0 0
\(599\) −26.8393 9.76870i −1.09662 0.399138i −0.270553 0.962705i \(-0.587206\pi\)
−0.826070 + 0.563567i \(0.809429\pi\)
\(600\) 0 0
\(601\) −5.28624 + 29.9798i −0.215630 + 1.22290i 0.664179 + 0.747574i \(0.268781\pi\)
−0.879809 + 0.475327i \(0.842330\pi\)
\(602\) 0 0
\(603\) 28.7713 5.36564i 1.17166 0.218506i
\(604\) 0 0
\(605\) 3.98134 + 10.9386i 0.161864 + 0.444719i
\(606\) 0 0
\(607\) 23.6515 + 28.1868i 0.959985 + 1.14407i 0.989505 + 0.144502i \(0.0461579\pi\)
−0.0295193 + 0.999564i \(0.509398\pi\)
\(608\) 0 0
\(609\) −27.8904 9.99611i −1.13018 0.405063i
\(610\) 0 0
\(611\) 22.2722 + 38.5765i 0.901035 + 1.56064i
\(612\) 0 0
\(613\) −0.0873020 + 0.151211i −0.00352609 + 0.00610737i −0.867783 0.496943i \(-0.834456\pi\)
0.864257 + 0.503051i \(0.167789\pi\)
\(614\) 0 0
\(615\) 1.92829 + 1.60192i 0.0777560 + 0.0645957i
\(616\) 0 0
\(617\) 41.1918 7.26323i 1.65832 0.292407i 0.735468 0.677559i \(-0.236962\pi\)
0.922853 + 0.385152i \(0.125851\pi\)
\(618\) 0 0
\(619\) 2.93870 3.50220i 0.118116 0.140765i −0.703746 0.710451i \(-0.748491\pi\)
0.821862 + 0.569686i \(0.192935\pi\)
\(620\) 0 0
\(621\) −4.22143 22.0337i −0.169400 0.884181i
\(622\) 0 0
\(623\) 9.74896 + 8.18035i 0.390584 + 0.327739i
\(624\) 0 0
\(625\) 2.79775 + 15.8668i 0.111910 + 0.634673i
\(626\) 0 0
\(627\) −8.14057 22.0281i −0.325103 0.879719i
\(628\) 0 0
\(629\) 6.80168 + 3.92695i 0.271201 + 0.156578i
\(630\) 0 0
\(631\) −17.5521 + 10.1337i −0.698740 + 0.403418i −0.806878 0.590718i \(-0.798844\pi\)
0.108138 + 0.994136i \(0.465511\pi\)
\(632\) 0 0
\(633\) 19.9914 3.62654i 0.794585 0.144142i
\(634\) 0 0
\(635\) −6.80114 + 5.70683i −0.269895 + 0.226469i
\(636\) 0 0
\(637\) −29.9049 + 10.8845i −1.18488 + 0.431260i
\(638\) 0 0
\(639\) 10.3709 0.102074i 0.410268 0.00403798i
\(640\) 0 0
\(641\) 19.8935 + 3.50776i 0.785747 + 0.138548i 0.552105 0.833775i \(-0.313825\pi\)
0.233641 + 0.972323i \(0.424936\pi\)
\(642\) 0 0
\(643\) −14.5397 + 39.9476i −0.573392 + 1.57538i 0.225717 + 0.974193i \(0.427528\pi\)
−0.799108 + 0.601187i \(0.794695\pi\)
\(644\) 0 0
\(645\) −7.32074 12.5370i −0.288254 0.493644i
\(646\) 0 0
\(647\) −8.10818 −0.318765 −0.159383 0.987217i \(-0.550950\pi\)
−0.159383 + 0.987217i \(0.550950\pi\)
\(648\) 0 0
\(649\) −27.8456 −1.09304
\(650\) 0 0
\(651\) 8.70062 + 14.9001i 0.341004 + 0.583981i
\(652\) 0 0
\(653\) 0.613037 1.68431i 0.0239900 0.0659120i −0.927120 0.374766i \(-0.877723\pi\)
0.951110 + 0.308854i \(0.0999454\pi\)
\(654\) 0 0
\(655\) −9.24154 1.62953i −0.361097 0.0636711i
\(656\) 0 0
\(657\) −15.2331 25.7949i −0.594300 1.00635i
\(658\) 0 0
\(659\) 10.8091 3.93418i 0.421062 0.153254i −0.122795 0.992432i \(-0.539186\pi\)
0.543857 + 0.839178i \(0.316964\pi\)
\(660\) 0 0
\(661\) 12.1899 10.2285i 0.474131 0.397843i −0.374168 0.927361i \(-0.622072\pi\)
0.848299 + 0.529518i \(0.177627\pi\)
\(662\) 0 0
\(663\) −72.0554 + 13.0712i −2.79840 + 0.507645i
\(664\) 0 0
\(665\) 6.45363 3.72601i 0.250261 0.144488i
\(666\) 0 0
\(667\) 18.0083 + 10.3971i 0.697285 + 0.402578i
\(668\) 0 0
\(669\) 14.2432 + 38.5416i 0.550673 + 1.49010i
\(670\) 0 0
\(671\) −8.27679 46.9400i −0.319522 1.81210i
\(672\) 0 0
\(673\) 35.1997 + 29.5361i 1.35685 + 1.13853i 0.976941 + 0.213509i \(0.0684893\pi\)
0.379909 + 0.925024i \(0.375955\pi\)
\(674\) 0 0
\(675\) −17.6565 14.3768i −0.679601 0.553364i
\(676\) 0 0
\(677\) 33.3997 39.8042i 1.28366 1.52980i 0.599984 0.800012i \(-0.295173\pi\)
0.683672 0.729790i \(-0.260382\pi\)
\(678\) 0 0
\(679\) 10.7055 1.88767i 0.410840 0.0724421i
\(680\) 0 0
\(681\) 12.9660 + 10.7715i 0.496858 + 0.412764i
\(682\) 0 0
\(683\) −18.8480 + 32.6457i −0.721199 + 1.24915i 0.239321 + 0.970941i \(0.423075\pi\)
−0.960520 + 0.278212i \(0.910258\pi\)
\(684\) 0 0
\(685\) −1.97176 3.41519i −0.0753371 0.130488i
\(686\) 0 0
\(687\) −10.7356 3.84770i −0.409587 0.146799i
\(688\) 0 0
\(689\) −11.2526 13.4104i −0.428691 0.510894i
\(690\) 0 0
\(691\) 10.5475 + 28.9791i 0.401247 + 1.10242i 0.961670 + 0.274210i \(0.0884164\pi\)
−0.560423 + 0.828207i \(0.689361\pi\)
\(692\) 0 0
\(693\) −18.0112 + 51.0430i −0.684190 + 1.93896i
\(694\) 0 0
\(695\) 0.806822 4.57572i 0.0306045 0.173567i
\(696\) 0 0
\(697\) −12.9035 4.69648i −0.488754 0.177892i
\(698\) 0 0
\(699\) −32.0911 18.3178i −1.21380 0.692845i
\(700\) 0 0
\(701\) 3.12015i 0.117846i −0.998263 0.0589232i \(-0.981233\pi\)
0.998263 0.0589232i \(-0.0187667\pi\)
\(702\) 0 0
\(703\) 2.81047i 0.105999i
\(704\) 0 0
\(705\) 0.0526527 + 10.6995i 0.00198302 + 0.402968i
\(706\) 0 0
\(707\) −32.7556 11.9221i −1.23190 0.448376i
\(708\) 0 0
\(709\) −3.06472 + 17.3809i −0.115098 + 0.652753i 0.871604 + 0.490211i \(0.163080\pi\)
−0.986702 + 0.162542i \(0.948031\pi\)
\(710\) 0 0
\(711\) −1.52455 4.06378i −0.0571752 0.152404i
\(712\) 0 0
\(713\) −4.14188 11.3797i −0.155115 0.426174i
\(714\) 0 0
\(715\) 14.5521 + 17.3426i 0.544219 + 0.648575i
\(716\) 0 0
\(717\) −26.4029 + 22.3770i −0.986034 + 0.835684i
\(718\) 0 0
\(719\) 0.448200 + 0.776305i 0.0167150 + 0.0289513i 0.874262 0.485454i \(-0.161346\pi\)
−0.857547 + 0.514406i \(0.828013\pi\)
\(720\) 0 0
\(721\) −14.1852 + 24.5694i −0.528283 + 0.915013i
\(722\) 0 0
\(723\) −1.73248 + 10.1162i −0.0644315 + 0.376226i
\(724\) 0 0
\(725\) 20.7841 3.66480i 0.771902 0.136107i
\(726\) 0 0
\(727\) 29.2965 34.9142i 1.08655 1.29490i 0.133842 0.991003i \(-0.457268\pi\)
0.952706 0.303895i \(-0.0982871\pi\)
\(728\) 0 0
\(729\) 26.9882 0.797085i 0.999564 0.0295217i
\(730\) 0 0
\(731\) 60.9181 + 51.1163i 2.25314 + 1.89061i
\(732\) 0 0
\(733\) 4.21540 + 23.9067i 0.155699 + 0.883014i 0.958144 + 0.286287i \(0.0924212\pi\)
−0.802445 + 0.596727i \(0.796468\pi\)
\(734\) 0 0
\(735\) −7.53456 1.29035i −0.277916 0.0475952i
\(736\) 0 0
\(737\) 42.9203 + 24.7801i 1.58099 + 0.912786i
\(738\) 0 0
\(739\) −27.2841 + 15.7525i −1.00366 + 0.579464i −0.909330 0.416077i \(-0.863405\pi\)
−0.0943320 + 0.995541i \(0.530072\pi\)
\(740\) 0 0
\(741\) −16.9431 19.9914i −0.622420 0.734401i
\(742\) 0 0
\(743\) 22.7123 19.0578i 0.833232 0.699165i −0.122799 0.992432i \(-0.539187\pi\)
0.956031 + 0.293267i \(0.0947425\pi\)
\(744\) 0 0
\(745\) 15.2319 5.54394i 0.558052 0.203114i
\(746\) 0 0
\(747\) −4.13730 + 1.55213i −0.151376 + 0.0567896i
\(748\) 0 0
\(749\) −53.3857 9.41334i −1.95067 0.343956i
\(750\) 0 0
\(751\) −5.19638 + 14.2769i −0.189618 + 0.520972i −0.997676 0.0681305i \(-0.978297\pi\)
0.808058 + 0.589103i \(0.200519\pi\)
\(752\) 0 0
\(753\) −27.0668 + 0.133197i −0.986370 + 0.00485396i
\(754\) 0 0
\(755\) −3.93794 −0.143316
\(756\) 0 0
\(757\) 15.3617 0.558330 0.279165 0.960243i \(-0.409942\pi\)
0.279165 + 0.960243i \(0.409942\pi\)
\(758\) 0 0
\(759\) 18.8327 32.9930i 0.683582 1.19757i
\(760\) 0 0
\(761\) −16.5195 + 45.3870i −0.598832 + 1.64528i 0.154774 + 0.987950i \(0.450535\pi\)
−0.753606 + 0.657326i \(0.771687\pi\)
\(762\) 0 0
\(763\) −4.58516 0.808487i −0.165994 0.0292692i
\(764\) 0 0
\(765\) −16.5880 5.85329i −0.599739 0.211626i
\(766\) 0 0
\(767\) −29.1983 + 10.6273i −1.05429 + 0.383730i
\(768\) 0 0
\(769\) −1.83911 + 1.54319i −0.0663199 + 0.0556490i −0.675345 0.737502i \(-0.736005\pi\)
0.609025 + 0.793151i \(0.291561\pi\)
\(770\) 0 0
\(771\) 9.16527 25.5722i 0.330079 0.920961i
\(772\) 0 0
\(773\) −25.9787 + 14.9988i −0.934389 + 0.539470i −0.888197 0.459463i \(-0.848042\pi\)
−0.0461920 + 0.998933i \(0.514709\pi\)
\(774\) 0 0
\(775\) −10.6442 6.14543i −0.382351 0.220750i
\(776\) 0 0
\(777\) 4.13932 4.98264i 0.148497 0.178751i
\(778\) 0 0
\(779\) −0.853266 4.83911i −0.0305714 0.173379i
\(780\) 0 0
\(781\) 13.4537 + 11.2890i 0.481413 + 0.403953i
\(782\) 0 0
\(783\) −15.8017 + 19.4064i −0.564705 + 0.693529i
\(784\) 0 0
\(785\) 6.84119 8.15301i 0.244173 0.290994i
\(786\) 0 0
\(787\) 38.5152 6.79128i 1.37292 0.242083i 0.561950 0.827171i \(-0.310051\pi\)
0.810970 + 0.585088i \(0.198940\pi\)
\(788\) 0 0
\(789\) −49.0355 + 18.1212i −1.74571 + 0.645132i
\(790\) 0 0
\(791\) 0.170865 0.295946i 0.00607524 0.0105226i
\(792\) 0 0
\(793\) −26.5936 46.0614i −0.944365 1.63569i
\(794\) 0 0
\(795\) −0.750557 4.13746i −0.0266195 0.146740i