Properties

Label 804.2.ba.b.41.18
Level 804
Weight 2
Character 804.41
Analytic conductor 6.420
Analytic rank 0
Dimension 440
CM no
Inner twists 4

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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 41.18
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.18

$q$-expansion

\(f(q)\) \(=\) \(q+(1.44123 - 0.960654i) q^{3} +(0.412679 - 2.87025i) q^{5} +(-0.273979 - 2.86924i) q^{7} +(1.15429 - 2.76905i) q^{9} +O(q^{10})\) \(q+(1.44123 - 0.960654i) q^{3} +(0.412679 - 2.87025i) q^{5} +(-0.273979 - 2.86924i) q^{7} +(1.15429 - 2.76905i) q^{9} +(-4.55535 + 1.82369i) q^{11} +(1.25875 + 1.32014i) q^{13} +(-2.16255 - 4.53313i) q^{15} +(1.49442 - 0.517223i) q^{17} +(3.17757 + 0.303421i) q^{19} +(-3.15121 - 3.87203i) q^{21} +(-5.20992 + 0.248179i) q^{23} +(-3.27055 - 0.960320i) q^{25} +(-0.996499 - 5.09970i) q^{27} +(0.761179 - 0.439467i) q^{29} +(-2.73430 + 2.86765i) q^{31} +(-4.81338 + 7.00447i) q^{33} +(-8.34848 - 0.397687i) q^{35} +(-2.86589 + 4.96387i) q^{37} +(3.08236 + 0.693403i) q^{39} +(6.58885 + 1.26990i) q^{41} +(6.45298 + 5.59154i) q^{43} +(-7.47150 - 4.45582i) q^{45} +(4.64743 - 9.01475i) q^{47} +(-1.28395 + 0.247462i) q^{49} +(1.65693 - 2.18106i) q^{51} +(-4.94001 - 5.70108i) q^{53} +(3.35454 + 13.8276i) q^{55} +(4.87109 - 2.61524i) q^{57} +(0.523482 + 1.78282i) q^{59} +(4.12990 - 10.3160i) q^{61} +(-8.26130 - 2.55327i) q^{63} +(4.30860 - 3.06814i) q^{65} +(3.34986 - 7.46850i) q^{67} +(-7.27028 + 5.36261i) q^{69} +(-4.94506 - 1.71150i) q^{71} +(6.17224 + 2.47099i) q^{73} +(-5.63615 + 1.75782i) q^{75} +(6.48066 + 12.5707i) q^{77} +(11.3480 - 2.75300i) q^{79} +(-6.33524 - 6.39256i) q^{81} +(0.0980278 - 0.124653i) q^{83} +(-0.867843 - 4.50280i) q^{85} +(0.674859 - 1.36460i) q^{87} +(1.62244 - 2.52457i) q^{89} +(3.44293 - 3.97335i) q^{91} +(-1.18594 + 6.75966i) q^{93} +(2.18221 - 8.99519i) q^{95} +(6.23550 + 3.60007i) q^{97} +(-0.208315 + 14.7191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

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
\(3\) 1.44123 0.960654i 0.832095 0.554634i
\(4\) 0 0
\(5\) 0.412679 2.87025i 0.184556 1.28361i −0.661267 0.750150i \(-0.729981\pi\)
0.845823 0.533463i \(-0.179110\pi\)
\(6\) 0 0
\(7\) −0.273979 2.86924i −0.103554 1.08447i −0.886610 0.462518i \(-0.846946\pi\)
0.783056 0.621952i \(-0.213660\pi\)
\(8\) 0 0
\(9\) 1.15429 2.76905i 0.384763 0.923015i
\(10\) 0 0
\(11\) −4.55535 + 1.82369i −1.37349 + 0.549863i −0.936837 0.349767i \(-0.886261\pi\)
−0.436654 + 0.899629i \(0.643837\pi\)
\(12\) 0 0
\(13\) 1.25875 + 1.32014i 0.349116 + 0.366142i 0.874755 0.484566i \(-0.161022\pi\)
−0.525639 + 0.850708i \(0.676174\pi\)
\(14\) 0 0
\(15\) −2.16255 4.53313i −0.558367 1.17045i
\(16\) 0 0
\(17\) 1.49442 0.517223i 0.362450 0.125445i −0.139773 0.990184i \(-0.544637\pi\)
0.502222 + 0.864739i \(0.332516\pi\)
\(18\) 0 0
\(19\) 3.17757 + 0.303421i 0.728984 + 0.0696096i 0.452947 0.891537i \(-0.350373\pi\)
0.276037 + 0.961147i \(0.410979\pi\)
\(20\) 0 0
\(21\) −3.15121 3.87203i −0.687650 0.844946i
\(22\) 0 0
\(23\) −5.20992 + 0.248179i −1.08634 + 0.0517489i −0.583103 0.812398i \(-0.698162\pi\)
−0.503240 + 0.864147i \(0.667859\pi\)
\(24\) 0 0
\(25\) −3.27055 0.960320i −0.654110 0.192064i
\(26\) 0 0
\(27\) −0.996499 5.09970i −0.191776 0.981439i
\(28\) 0 0
\(29\) 0.761179 0.439467i 0.141347 0.0816070i −0.427659 0.903940i \(-0.640661\pi\)
0.569006 + 0.822333i \(0.307328\pi\)
\(30\) 0 0
\(31\) −2.73430 + 2.86765i −0.491095 + 0.515045i −0.921915 0.387392i \(-0.873376\pi\)
0.430820 + 0.902438i \(0.358224\pi\)
\(32\) 0 0
\(33\) −4.81338 + 7.00447i −0.837902 + 1.21932i
\(34\) 0 0
\(35\) −8.34848 0.397687i −1.41115 0.0672214i
\(36\) 0 0
\(37\) −2.86589 + 4.96387i −0.471150 + 0.816055i −0.999455 0.0329989i \(-0.989494\pi\)
0.528306 + 0.849054i \(0.322828\pi\)
\(38\) 0 0
\(39\) 3.08236 + 0.693403i 0.493572 + 0.111033i
\(40\) 0 0
\(41\) 6.58885 + 1.26990i 1.02900 + 0.198324i 0.675695 0.737182i \(-0.263844\pi\)
0.353310 + 0.935506i \(0.385056\pi\)
\(42\) 0 0
\(43\) 6.45298 + 5.59154i 0.984070 + 0.852702i 0.989094 0.147286i \(-0.0470537\pi\)
−0.00502389 + 0.999987i \(0.501599\pi\)
\(44\) 0 0
\(45\) −7.47150 4.45582i −1.11378 0.664235i
\(46\) 0 0
\(47\) 4.64743 9.01475i 0.677897 1.31494i −0.259185 0.965828i \(-0.583454\pi\)
0.937082 0.349109i \(-0.113516\pi\)
\(48\) 0 0
\(49\) −1.28395 + 0.247462i −0.183422 + 0.0353517i
\(50\) 0 0
\(51\) 1.65693 2.18106i 0.232016 0.305409i
\(52\) 0 0
\(53\) −4.94001 5.70108i −0.678563 0.783103i 0.307128 0.951668i \(-0.400632\pi\)
−0.985691 + 0.168565i \(0.946087\pi\)
\(54\) 0 0
\(55\) 3.35454 + 13.8276i 0.452326 + 1.86451i
\(56\) 0 0
\(57\) 4.87109 2.61524i 0.645192 0.346398i
\(58\) 0 0
\(59\) 0.523482 + 1.78282i 0.0681516 + 0.232103i 0.986525 0.163613i \(-0.0523148\pi\)
−0.918373 + 0.395716i \(0.870497\pi\)
\(60\) 0 0
\(61\) 4.12990 10.3160i 0.528780 1.32083i −0.388082 0.921625i \(-0.626862\pi\)
0.916862 0.399204i \(-0.130713\pi\)
\(62\) 0 0
\(63\) −8.26130 2.55327i −1.04083 0.321681i
\(64\) 0 0
\(65\) 4.30860 3.06814i 0.534416 0.380556i
\(66\) 0 0
\(67\) 3.34986 7.46850i 0.409251 0.912422i
\(68\) 0 0
\(69\) −7.27028 + 5.36261i −0.875239 + 0.645583i
\(70\) 0 0
\(71\) −4.94506 1.71150i −0.586871 0.203118i 0.0174653 0.999847i \(-0.494440\pi\)
−0.604336 + 0.796730i \(0.706562\pi\)
\(72\) 0 0
\(73\) 6.17224 + 2.47099i 0.722406 + 0.289208i 0.703581 0.710615i \(-0.251583\pi\)
0.0188251 + 0.999823i \(0.494007\pi\)
\(74\) 0 0
\(75\) −5.63615 + 1.75782i −0.650806 + 0.202976i
\(76\) 0 0
\(77\) 6.48066 + 12.5707i 0.738540 + 1.43257i
\(78\) 0 0
\(79\) 11.3480 2.75300i 1.27675 0.309736i 0.460617 0.887599i \(-0.347628\pi\)
0.816134 + 0.577863i \(0.196113\pi\)
\(80\) 0 0
\(81\) −6.33524 6.39256i −0.703915 0.710284i
\(82\) 0 0
\(83\) 0.0980278 0.124653i 0.0107600 0.0136824i −0.780643 0.624977i \(-0.785108\pi\)
0.791403 + 0.611294i \(0.209351\pi\)
\(84\) 0 0
\(85\) −0.867843 4.50280i −0.0941308 0.488397i
\(86\) 0 0
\(87\) 0.674859 1.36460i 0.0723524 0.146301i
\(88\) 0 0
\(89\) 1.62244 2.52457i 0.171978 0.267603i −0.744556 0.667560i \(-0.767339\pi\)
0.916534 + 0.399957i \(0.130975\pi\)
\(90\) 0 0
\(91\) 3.44293 3.97335i 0.360917 0.416521i
\(92\) 0 0
\(93\) −1.18594 + 6.75966i −0.122976 + 0.700944i
\(94\) 0 0
\(95\) 2.18221 8.99519i 0.223890 0.922887i
\(96\) 0 0
\(97\) 6.23550 + 3.60007i 0.633119 + 0.365532i 0.781959 0.623330i \(-0.214221\pi\)
−0.148840 + 0.988861i \(0.547554\pi\)
\(98\) 0 0
\(99\) −0.208315 + 14.7191i −0.0209364 + 1.47932i
\(100\) 0 0
\(101\) 3.85442 5.41278i 0.383530 0.538592i −0.577009 0.816738i \(-0.695780\pi\)
0.960539 + 0.278146i \(0.0897198\pi\)
\(102\) 0 0
\(103\) 4.53815 + 4.32712i 0.447157 + 0.426364i 0.879904 0.475152i \(-0.157607\pi\)
−0.432746 + 0.901516i \(0.642455\pi\)
\(104\) 0 0
\(105\) −12.4141 + 7.44684i −1.21149 + 0.726737i
\(106\) 0 0
\(107\) −15.9522 + 2.29358i −1.54215 + 0.221728i −0.860311 0.509770i \(-0.829730\pi\)
−0.681843 + 0.731498i \(0.738821\pi\)
\(108\) 0 0
\(109\) −0.0633795 + 0.215851i −0.00607066 + 0.0206748i −0.962473 0.271379i \(-0.912520\pi\)
0.956402 + 0.292054i \(0.0943386\pi\)
\(110\) 0 0
\(111\) 0.638151 + 9.90721i 0.0605706 + 0.940351i
\(112\) 0 0
\(113\) −9.32118 + 7.33026i −0.876863 + 0.689572i −0.951503 0.307638i \(-0.900461\pi\)
0.0746407 + 0.997210i \(0.476219\pi\)
\(114\) 0 0
\(115\) −1.43769 + 15.0562i −0.134065 + 1.40400i
\(116\) 0 0
\(117\) 5.10850 1.96172i 0.472281 0.181361i
\(118\) 0 0
\(119\) −1.89347 4.14613i −0.173574 0.380075i
\(120\) 0 0
\(121\) 9.46434 9.02423i 0.860394 0.820384i
\(122\) 0 0
\(123\) 10.7160 4.49939i 0.966227 0.405696i
\(124\) 0 0
\(125\) 1.91698 4.19760i 0.171460 0.375445i
\(126\) 0 0
\(127\) −11.0452 + 1.05469i −0.980103 + 0.0935885i −0.572792 0.819701i \(-0.694140\pi\)
−0.407311 + 0.913289i \(0.633534\pi\)
\(128\) 0 0
\(129\) 14.6718 + 1.85961i 1.29178 + 0.163730i
\(130\) 0 0
\(131\) 7.68105 + 11.9519i 0.671096 + 1.04425i 0.995165 + 0.0982128i \(0.0313126\pi\)
−0.324069 + 0.946033i \(0.605051\pi\)
\(132\) 0 0
\(133\) 9.20033i 0.797770i
\(134\) 0 0
\(135\) −15.0486 + 0.755657i −1.29518 + 0.0650366i
\(136\) 0 0
\(137\) 11.7097 7.52537i 1.00043 0.642936i 0.0655291 0.997851i \(-0.479126\pi\)
0.934899 + 0.354915i \(0.115490\pi\)
\(138\) 0 0
\(139\) −14.8993 2.14219i −1.26374 0.181698i −0.522325 0.852746i \(-0.674935\pi\)
−0.741414 + 0.671048i \(0.765844\pi\)
\(140\) 0 0
\(141\) −1.96204 17.4569i −0.165234 1.47014i
\(142\) 0 0
\(143\) −8.14160 3.71814i −0.680835 0.310927i
\(144\) 0 0
\(145\) −0.947256 2.36613i −0.0786653 0.196496i
\(146\) 0 0
\(147\) −1.61275 + 1.59008i −0.133017 + 0.131148i
\(148\) 0 0
\(149\) 15.7275 7.18251i 1.28845 0.588414i 0.350946 0.936396i \(-0.385860\pi\)
0.937502 + 0.347981i \(0.113133\pi\)
\(150\) 0 0
\(151\) −5.00929 14.4734i −0.407650 1.17783i −0.942883 0.333123i \(-0.891897\pi\)
0.535233 0.844704i \(-0.320224\pi\)
\(152\) 0 0
\(153\) 0.292775 4.73514i 0.0236694 0.382813i
\(154\) 0 0
\(155\) 7.10248 + 9.03154i 0.570485 + 0.725430i
\(156\) 0 0
\(157\) 0.742429 + 15.5855i 0.0592522 + 1.24386i 0.811253 + 0.584695i \(0.198786\pi\)
−0.752001 + 0.659162i \(0.770911\pi\)
\(158\) 0 0
\(159\) −12.5965 3.47092i −0.998964 0.275262i
\(160\) 0 0
\(161\) 2.13949 + 14.8805i 0.168616 + 1.17275i
\(162\) 0 0
\(163\) 8.90024 + 15.4157i 0.697121 + 1.20745i 0.969460 + 0.245248i \(0.0788693\pi\)
−0.272340 + 0.962201i \(0.587797\pi\)
\(164\) 0 0
\(165\) 18.1182 + 16.7062i 1.41050 + 1.30058i
\(166\) 0 0
\(167\) 8.27884 + 5.89534i 0.640636 + 0.456195i 0.853645 0.520855i \(-0.174387\pi\)
−0.213009 + 0.977050i \(0.568326\pi\)
\(168\) 0 0
\(169\) 0.460248 9.66180i 0.0354037 0.743216i
\(170\) 0 0
\(171\) 4.50802 8.44860i 0.344737 0.646081i
\(172\) 0 0
\(173\) 13.3638 + 3.24203i 1.01603 + 0.246487i 0.708997 0.705211i \(-0.249148\pi\)
0.307036 + 0.951698i \(0.400663\pi\)
\(174\) 0 0
\(175\) −1.85932 + 9.64709i −0.140552 + 0.729251i
\(176\) 0 0
\(177\) 2.46713 + 2.06656i 0.185441 + 0.155332i
\(178\) 0 0
\(179\) −2.93658 1.88723i −0.219490 0.141058i 0.426275 0.904593i \(-0.359825\pi\)
−0.645766 + 0.763535i \(0.723462\pi\)
\(180\) 0 0
\(181\) 13.6951 + 7.06029i 1.01795 + 0.524787i 0.884634 0.466287i \(-0.154409\pi\)
0.133312 + 0.991074i \(0.457439\pi\)
\(182\) 0 0
\(183\) −3.95796 18.8351i −0.292581 1.39233i
\(184\) 0 0
\(185\) 13.0648 + 10.2743i 0.960546 + 0.755382i
\(186\) 0 0
\(187\) −5.86435 + 5.08149i −0.428844 + 0.371595i
\(188\) 0 0
\(189\) −14.3592 + 4.25640i −1.04448 + 0.309608i
\(190\) 0 0
\(191\) −19.9911 + 10.3061i −1.44650 + 0.745725i −0.989608 0.143795i \(-0.954070\pi\)
−0.456897 + 0.889520i \(0.651039\pi\)
\(192\) 0 0
\(193\) −18.7628 + 5.50926i −1.35058 + 0.396565i −0.875431 0.483342i \(-0.839423\pi\)
−0.475145 + 0.879907i \(0.657604\pi\)
\(194\) 0 0
\(195\) 3.26226 8.56097i 0.233616 0.613064i
\(196\) 0 0
\(197\) −7.60523 + 21.9739i −0.541850 + 1.56557i 0.258482 + 0.966016i \(0.416778\pi\)
−0.800332 + 0.599557i \(0.795343\pi\)
\(198\) 0 0
\(199\) 11.7674 + 16.5251i 0.834172 + 1.17143i 0.983188 + 0.182596i \(0.0584499\pi\)
−0.149016 + 0.988835i \(0.547611\pi\)
\(200\) 0 0
\(201\) −2.34671 13.9819i −0.165524 0.986206i
\(202\) 0 0
\(203\) −1.46948 2.06360i −0.103137 0.144836i
\(204\) 0 0
\(205\) 6.36399 18.3876i 0.444481 1.28424i
\(206\) 0 0
\(207\) −5.32653 + 14.7130i −0.370220 + 1.02262i
\(208\) 0 0
\(209\) −15.0283 + 4.41271i −1.03953 + 0.305233i
\(210\) 0 0
\(211\) 7.21754 3.72090i 0.496876 0.256157i −0.191525 0.981488i \(-0.561343\pi\)
0.688401 + 0.725330i \(0.258313\pi\)
\(212\) 0 0
\(213\) −8.77113 + 2.28382i −0.600988 + 0.156485i
\(214\) 0 0
\(215\) 18.7121 16.2141i 1.27616 1.10579i
\(216\) 0 0
\(217\) 8.97711 + 7.05968i 0.609406 + 0.479242i
\(218\) 0 0
\(219\) 11.2694 2.36812i 0.761515 0.160023i
\(220\) 0 0
\(221\) 2.56391 + 1.32179i 0.172467 + 0.0889132i
\(222\) 0 0
\(223\) −17.6132 11.3193i −1.17946 0.757995i −0.204176 0.978934i \(-0.565452\pi\)
−0.975288 + 0.220939i \(0.929088\pi\)
\(224\) 0 0
\(225\) −6.43433 + 7.94782i −0.428955 + 0.529854i
\(226\) 0 0
\(227\) −3.70345 + 19.2153i −0.245806 + 1.27536i 0.623787 + 0.781595i \(0.285593\pi\)
−0.869593 + 0.493769i \(0.835619\pi\)
\(228\) 0 0
\(229\) 25.8908 + 6.28104i 1.71091 + 0.415063i 0.967317 0.253569i \(-0.0816044\pi\)
0.743594 + 0.668631i \(0.233120\pi\)
\(230\) 0 0
\(231\) 21.4163 + 11.8916i 1.40909 + 0.782413i
\(232\) 0 0
\(233\) 0.0573869 1.20470i 0.00375954 0.0789225i −0.996208 0.0870060i \(-0.972270\pi\)
0.999967 + 0.00808354i \(0.00257310\pi\)
\(234\) 0 0
\(235\) −23.9567 17.0595i −1.56276 1.11284i
\(236\) 0 0
\(237\) 13.7104 14.8692i 0.890587 0.965859i
\(238\) 0 0
\(239\) 5.73202 + 9.92816i 0.370774 + 0.642199i 0.989685 0.143262i \(-0.0457592\pi\)
−0.618911 + 0.785461i \(0.712426\pi\)
\(240\) 0 0
\(241\) 4.19075 + 29.1473i 0.269950 + 1.87754i 0.448752 + 0.893656i \(0.351869\pi\)
−0.178802 + 0.983885i \(0.557222\pi\)
\(242\) 0 0
\(243\) −15.2716 3.12718i −0.979671 0.200609i
\(244\) 0 0
\(245\) 0.180415 + 3.78738i 0.0115263 + 0.241967i
\(246\) 0 0
\(247\) 3.59922 + 4.57678i 0.229013 + 0.291214i
\(248\) 0 0
\(249\) 0.0215327 0.273824i 0.00136458 0.0173529i
\(250\) 0 0
\(251\) 8.82263 + 25.4913i 0.556880 + 1.60900i 0.774230 + 0.632904i \(0.218137\pi\)
−0.217350 + 0.976094i \(0.569741\pi\)
\(252\) 0 0
\(253\) 23.2804 10.6318i 1.46363 0.668416i
\(254\) 0 0
\(255\) −5.57639 5.65587i −0.349207 0.354184i
\(256\) 0 0
\(257\) 0.387194 + 0.967163i 0.0241525 + 0.0603299i 0.939954 0.341301i \(-0.110868\pi\)
−0.915802 + 0.401631i \(0.868443\pi\)
\(258\) 0 0
\(259\) 15.0277 + 6.86293i 0.933777 + 0.426442i
\(260\) 0 0
\(261\) −0.338284 2.61501i −0.0209393 0.161865i
\(262\) 0 0
\(263\) −16.2766 2.34022i −1.00366 0.144304i −0.379161 0.925331i \(-0.623787\pi\)
−0.624498 + 0.781026i \(0.714697\pi\)
\(264\) 0 0
\(265\) −18.4021 + 11.8263i −1.13043 + 0.726486i
\(266\) 0 0
\(267\) −0.0869244 5.19708i −0.00531968 0.318056i
\(268\) 0 0
\(269\) 0.773869i 0.0471836i −0.999722 0.0235918i \(-0.992490\pi\)
0.999722 0.0235918i \(-0.00751021\pi\)
\(270\) 0 0
\(271\) −14.5273 22.6050i −0.882472 1.37315i −0.927364 0.374161i \(-0.877931\pi\)
0.0448918 0.998992i \(-0.485706\pi\)
\(272\) 0 0
\(273\) 1.14504 9.03398i 0.0693009 0.546762i
\(274\) 0 0
\(275\) 16.6498 1.58987i 1.00402 0.0958725i
\(276\) 0 0
\(277\) −2.01847 + 4.41983i −0.121278 + 0.265562i −0.960528 0.278184i \(-0.910267\pi\)
0.839250 + 0.543746i \(0.182995\pi\)
\(278\) 0 0
\(279\) 4.78449 + 10.8815i 0.286440 + 0.651458i
\(280\) 0 0
\(281\) 1.48895 1.41971i 0.0888232 0.0846927i −0.644367 0.764716i \(-0.722879\pi\)
0.733190 + 0.680024i \(0.238031\pi\)
\(282\) 0 0
\(283\) −6.63031 14.5184i −0.394131 0.863027i −0.997832 0.0658158i \(-0.979035\pi\)
0.603701 0.797211i \(-0.293692\pi\)
\(284\) 0 0
\(285\) −5.49620 15.0605i −0.325567 0.892107i
\(286\) 0 0
\(287\) 1.83843 19.2529i 0.108519 1.13646i
\(288\) 0 0
\(289\) −11.3971 + 8.96281i −0.670420 + 0.527224i
\(290\) 0 0
\(291\) 12.4452 0.801631i 0.729551 0.0469924i
\(292\) 0 0
\(293\) 3.34108 11.3787i 0.195188 0.664749i −0.802492 0.596663i \(-0.796493\pi\)
0.997679 0.0680855i \(-0.0216891\pi\)
\(294\) 0 0
\(295\) 5.33315 0.766792i 0.310508 0.0446443i
\(296\) 0 0
\(297\) 13.8397 + 21.4137i 0.803060 + 1.24255i
\(298\) 0 0
\(299\) −6.88564 6.56544i −0.398207 0.379689i
\(300\) 0 0
\(301\) 14.2755 20.0471i 0.822824 1.15549i
\(302\) 0 0
\(303\) 0.355303 11.5038i 0.0204116 0.660878i
\(304\) 0 0
\(305\) −27.9051 16.1110i −1.59784 0.922516i
\(306\) 0 0
\(307\) −3.62873 + 14.9578i −0.207102 + 0.853688i 0.769502 + 0.638644i \(0.220505\pi\)
−0.976604 + 0.215044i \(0.931011\pi\)
\(308\) 0 0
\(309\) 10.6974 + 1.87678i 0.608553 + 0.106766i
\(310\) 0 0
\(311\) −9.56540 + 11.0391i −0.542404 + 0.625968i −0.959096 0.283080i \(-0.908644\pi\)
0.416692 + 0.909048i \(0.363189\pi\)
\(312\) 0 0
\(313\) 10.2057 15.8803i 0.576858 0.897609i −0.423106 0.906080i \(-0.639060\pi\)
0.999964 + 0.00847122i \(0.00269650\pi\)
\(314\) 0 0
\(315\) −10.7378 + 22.6583i −0.605005 + 1.27665i
\(316\) 0 0
\(317\) −2.53662 13.1612i −0.142471 0.739208i −0.980948 0.194271i \(-0.937766\pi\)
0.838477 0.544937i \(-0.183446\pi\)
\(318\) 0 0
\(319\) −2.66599 + 3.39008i −0.149267 + 0.189808i
\(320\) 0 0
\(321\) −20.7874 + 18.6301i −1.16024 + 1.03983i
\(322\) 0 0
\(323\) 4.90555 1.19007i 0.272952 0.0662175i
\(324\) 0 0
\(325\) −2.84906 5.52640i −0.158037 0.306550i
\(326\) 0 0
\(327\) 0.116013 + 0.371977i 0.00641556 + 0.0205703i
\(328\) 0 0
\(329\) −27.1388 10.8647i −1.49621 0.598991i
\(330\) 0 0
\(331\) −2.04960 0.709374i −0.112656 0.0389907i 0.270158 0.962816i \(-0.412924\pi\)
−0.382815 + 0.923825i \(0.625045\pi\)
\(332\) 0 0
\(333\) 10.4371 + 13.6655i 0.571951 + 0.748866i
\(334\) 0 0
\(335\) −20.0540 12.6970i −1.09567 0.693713i
\(336\) 0 0
\(337\) −18.1955 + 12.9570i −0.991172 + 0.705810i −0.955938 0.293569i \(-0.905157\pi\)
−0.0352341 + 0.999379i \(0.511218\pi\)
\(338\) 0 0
\(339\) −6.39213 + 19.5190i −0.347173 + 1.06013i
\(340\) 0 0
\(341\) 7.22600 18.0497i 0.391310 0.977445i
\(342\) 0 0
\(343\) −4.62244 15.7426i −0.249588 0.850019i
\(344\) 0 0
\(345\) 12.3917 + 23.0805i 0.667148 + 1.24261i
\(346\) 0 0
\(347\) 2.68001 + 11.0472i 0.143870 + 0.593042i 0.997404 + 0.0720047i \(0.0229397\pi\)
−0.853534 + 0.521037i \(0.825545\pi\)
\(348\) 0 0
\(349\) −8.47039 9.77535i −0.453409 0.523262i 0.482313 0.875999i \(-0.339797\pi\)
−0.935723 + 0.352736i \(0.885251\pi\)
\(350\) 0 0
\(351\) 5.47799 7.73480i 0.292394 0.412853i
\(352\) 0 0
\(353\) −6.92313 + 1.33432i −0.368481 + 0.0710189i −0.370130 0.928980i \(-0.620687\pi\)
0.00164965 + 0.999999i \(0.499475\pi\)
\(354\) 0 0
\(355\) −6.95316 + 13.4872i −0.369035 + 0.715829i
\(356\) 0 0
\(357\) −6.71193 4.15655i −0.355233 0.219988i
\(358\) 0 0
\(359\) 8.77136 + 7.60043i 0.462935 + 0.401135i 0.854857 0.518863i \(-0.173644\pi\)
−0.391923 + 0.919998i \(0.628190\pi\)
\(360\) 0 0
\(361\) −8.65176 1.66749i −0.455356 0.0877627i
\(362\) 0 0
\(363\) 4.97113 22.0979i 0.260917 1.15984i
\(364\) 0 0
\(365\) 9.63951 16.6961i 0.504555 0.873915i
\(366\) 0 0
\(367\) −5.33054 0.253925i −0.278252 0.0132548i −0.0920077 0.995758i \(-0.529328\pi\)
−0.186244 + 0.982504i \(0.559631\pi\)
\(368\) 0 0
\(369\) 11.1218 16.7790i 0.578979 0.873479i
\(370\) 0 0
\(371\) −15.0043 + 15.7360i −0.778984 + 0.816975i
\(372\) 0 0
\(373\) −21.4669 + 12.3939i −1.11151 + 0.641733i −0.939221 0.343313i \(-0.888451\pi\)
−0.172293 + 0.985046i \(0.555117\pi\)
\(374\) 0 0
\(375\) −1.26963 7.89127i −0.0655635 0.407503i
\(376\) 0 0
\(377\) 1.53830 + 0.451685i 0.0792263 + 0.0232629i
\(378\) 0 0
\(379\) 0.240410 0.0114521i 0.0123490 0.000588257i −0.0414065 0.999142i \(-0.513184\pi\)
0.0537555 + 0.998554i \(0.482881\pi\)
\(380\) 0 0
\(381\) −14.9055 + 12.1307i −0.763631 + 0.621473i
\(382\) 0 0
\(383\) 13.7852 + 1.31633i 0.704392 + 0.0672613i 0.441104 0.897456i \(-0.354587\pi\)
0.263288 + 0.964717i \(0.415193\pi\)
\(384\) 0 0
\(385\) 38.7556 13.4134i 1.97517 0.683612i
\(386\) 0 0
\(387\) 22.9318 11.4143i 1.16569 0.580224i
\(388\) 0 0
\(389\) 0.683887 + 0.717241i 0.0346745 + 0.0363655i 0.740843 0.671678i \(-0.234426\pi\)
−0.706168 + 0.708044i \(0.749578\pi\)
\(390\) 0 0
\(391\) −7.65743 + 3.06557i −0.387253 + 0.155033i
\(392\) 0 0
\(393\) 22.5518 + 9.84667i 1.13759 + 0.496699i
\(394\) 0 0
\(395\) −3.21869 33.7077i −0.161950 1.69602i
\(396\) 0 0
\(397\) −0.0894249 + 0.621964i −0.00448810 + 0.0312155i −0.991942 0.126689i \(-0.959565\pi\)
0.987454 + 0.157905i \(0.0504739\pi\)
\(398\) 0 0
\(399\) −8.83833 13.2598i −0.442470 0.663820i
\(400\) 0 0
\(401\) 17.7271 0.885249 0.442624 0.896707i \(-0.354048\pi\)
0.442624 + 0.896707i \(0.354048\pi\)
\(402\) 0 0
\(403\) −7.22752 −0.360029
\(404\) 0 0
\(405\) −20.9626 + 15.5456i −1.04164 + 0.772468i
\(406\) 0 0
\(407\) 4.00260 27.8387i 0.198401 1.37991i
\(408\) 0 0
\(409\) −1.27676 13.3708i −0.0631315 0.661143i −0.970548 0.240910i \(-0.922554\pi\)
0.907416 0.420234i \(-0.138052\pi\)
\(410\) 0 0
\(411\) 9.64711 22.0948i 0.475857 1.08985i
\(412\) 0 0
\(413\) 4.97190 1.99045i 0.244651 0.0979436i
\(414\) 0 0
\(415\) −0.317329 0.332806i −0.0155771 0.0163368i
\(416\) 0 0
\(417\) −23.5312 + 11.2256i −1.15233 + 0.549722i
\(418\) 0 0
\(419\) −6.59427 + 2.28230i −0.322151 + 0.111498i −0.483357 0.875423i \(-0.660583\pi\)
0.161206 + 0.986921i \(0.448462\pi\)
\(420\) 0 0
\(421\) 25.9279 + 2.47581i 1.26365 + 0.120664i 0.705279 0.708930i \(-0.250822\pi\)
0.558368 + 0.829593i \(0.311428\pi\)
\(422\) 0 0
\(423\) −19.5978 23.2746i −0.952877 1.13165i
\(424\) 0 0
\(425\) −5.38427 + 0.256484i −0.261175 + 0.0124413i
\(426\) 0 0
\(427\) −30.7306 9.02330i −1.48716 0.436668i
\(428\) 0 0
\(429\) −15.3058 + 2.46256i −0.738970 + 0.118893i
\(430\) 0 0
\(431\) 24.2306 13.9896i 1.16715 0.673853i 0.214141 0.976803i \(-0.431305\pi\)
0.953007 + 0.302950i \(0.0979714\pi\)
\(432\) 0 0
\(433\) 16.5700 17.3781i 0.796301 0.835137i −0.192974 0.981204i \(-0.561813\pi\)
0.989275 + 0.146067i \(0.0466617\pi\)
\(434\) 0 0
\(435\) −3.63825 2.50015i −0.174441 0.119873i
\(436\) 0 0
\(437\) −16.6302 0.792193i −0.795530 0.0378957i
\(438\) 0 0
\(439\) 6.66863 11.5504i 0.318276 0.551270i −0.661852 0.749634i \(-0.730229\pi\)
0.980128 + 0.198364i \(0.0635627\pi\)
\(440\) 0 0
\(441\) −0.796819 + 3.84097i −0.0379438 + 0.182903i
\(442\) 0 0
\(443\) 28.3444 + 5.46294i 1.34668 + 0.259552i 0.811089 0.584923i \(-0.198875\pi\)
0.535595 + 0.844475i \(0.320088\pi\)
\(444\) 0 0
\(445\) −6.57658 5.69864i −0.311760 0.270141i
\(446\) 0 0
\(447\) 15.7671 25.4603i 0.745756 1.20423i
\(448\) 0 0
\(449\) 1.16700 2.26366i 0.0550741 0.106829i −0.859692 0.510813i \(-0.829345\pi\)
0.914766 + 0.403984i \(0.132375\pi\)
\(450\) 0 0
\(451\) −32.3304 + 6.23118i −1.52238 + 0.293415i
\(452\) 0 0
\(453\) −21.1235 16.0473i −0.992466 0.753968i
\(454\) 0 0
\(455\) −9.98368 11.5218i −0.468042 0.540150i
\(456\) 0 0
\(457\) −8.37612 34.5268i −0.391818 1.61510i −0.736541 0.676393i \(-0.763542\pi\)
0.344723 0.938705i \(-0.387973\pi\)
\(458\) 0 0
\(459\) −4.12687 7.10568i −0.192626 0.331665i
\(460\) 0 0
\(461\) 1.46906 + 5.00315i 0.0684208 + 0.233020i 0.986603 0.163138i \(-0.0521615\pi\)
−0.918182 + 0.396158i \(0.870343\pi\)
\(462\) 0 0
\(463\) 13.5553 33.8596i 0.629970 1.57359i −0.177785 0.984069i \(-0.556893\pi\)
0.807754 0.589519i \(-0.200683\pi\)
\(464\) 0 0
\(465\) 18.9125 + 6.19350i 0.877046 + 0.287217i
\(466\) 0 0
\(467\) −30.8962 + 22.0011i −1.42971 + 1.01809i −0.436754 + 0.899581i \(0.643872\pi\)
−0.992953 + 0.118509i \(0.962189\pi\)
\(468\) 0 0
\(469\) −22.3467 7.56534i −1.03187 0.349335i
\(470\) 0 0
\(471\) 16.0423 + 21.7491i 0.739189 + 1.00214i
\(472\) 0 0
\(473\) −39.5928 13.7032i −1.82048 0.630074i
\(474\) 0 0
\(475\) −10.1010 4.04384i −0.463466 0.185544i
\(476\) 0 0
\(477\) −21.4888 + 7.09844i −0.983902 + 0.325015i
\(478\) 0 0
\(479\) −15.8205 30.6876i −0.722859 1.40215i −0.907801 0.419402i \(-0.862240\pi\)
0.184941 0.982750i \(-0.440790\pi\)
\(480\) 0 0
\(481\) −10.1605 + 2.46490i −0.463278 + 0.112390i
\(482\) 0 0
\(483\) 17.3785 + 19.3909i 0.790749 + 0.882317i
\(484\) 0 0
\(485\) 12.9063 16.4118i 0.586047 0.745219i
\(486\) 0 0
\(487\) 7.59904 + 39.4276i 0.344346 + 1.78663i 0.579810 + 0.814752i \(0.303127\pi\)
−0.235465 + 0.971883i \(0.575661\pi\)
\(488\) 0 0
\(489\) 27.6364 + 13.6675i 1.24976 + 0.618065i
\(490\) 0 0
\(491\) −11.4876 + 17.8750i −0.518427 + 0.806688i −0.997469 0.0711041i \(-0.977348\pi\)
0.479042 + 0.877792i \(0.340984\pi\)
\(492\) 0 0
\(493\) 0.910217 1.05045i 0.0409941 0.0473097i
\(494\) 0 0
\(495\) 42.1613 + 6.67216i 1.89501 + 0.299891i
\(496\) 0 0
\(497\) −3.55586 + 14.6575i −0.159502 + 0.657477i
\(498\) 0 0
\(499\) 27.2460 + 15.7305i 1.21970 + 0.704194i 0.964854 0.262788i \(-0.0846419\pi\)
0.254846 + 0.966982i \(0.417975\pi\)
\(500\) 0 0
\(501\) 17.5951 + 0.543436i 0.786091 + 0.0242789i
\(502\) 0 0
\(503\) 24.3950 34.2579i 1.08772 1.52749i 0.260609 0.965444i \(-0.416077\pi\)
0.827109 0.562042i \(-0.189984\pi\)
\(504\) 0 0
\(505\) −13.9454 13.2969i −0.620561 0.591704i
\(506\) 0 0
\(507\) −8.61832 14.3670i −0.382753 0.638062i
\(508\) 0 0
\(509\) −22.8411 + 3.28406i −1.01242 + 0.145563i −0.628504 0.777806i \(-0.716332\pi\)
−0.383912 + 0.923370i \(0.625423\pi\)
\(510\) 0 0
\(511\) 5.39880 18.3866i 0.238829 0.813376i
\(512\) 0 0
\(513\) −1.61909 16.5070i −0.0714845 0.728803i
\(514\) 0 0
\(515\) 14.2927 11.2399i 0.629811 0.495289i
\(516\) 0 0
\(517\) −4.73058 + 49.5409i −0.208051 + 2.17880i
\(518\) 0 0
\(519\) 22.3748 8.16550i 0.982146 0.358426i
\(520\) 0 0
\(521\) 10.1543 + 22.2347i 0.444866 + 0.974121i 0.990679 + 0.136214i \(0.0434934\pi\)
−0.545813 + 0.837907i \(0.683779\pi\)
\(522\) 0 0
\(523\) −19.2841 + 18.3873i −0.843234 + 0.804022i −0.982506 0.186232i \(-0.940372\pi\)
0.139272 + 0.990254i \(0.455524\pi\)
\(524\) 0 0
\(525\) 6.58780 + 15.6898i 0.287515 + 0.684761i
\(526\) 0 0
\(527\) −2.60297 + 5.69971i −0.113387 + 0.248283i
\(528\) 0 0
\(529\) 4.18581 0.399697i 0.181992 0.0173781i
\(530\) 0 0
\(531\) 5.54095 + 0.608338i 0.240457 + 0.0263996i
\(532\) 0 0
\(533\) 6.61729 + 10.2967i 0.286627 + 0.446000i
\(534\) 0 0
\(535\) 46.7332i 2.02045i
\(536\) 0 0
\(537\) −6.04526 + 0.101111i −0.260872 + 0.00436325i
\(538\) 0 0
\(539\) 5.39757 3.46881i 0.232490 0.149412i
\(540\) 0 0
\(541\) −14.4964 2.08427i −0.623249 0.0896097i −0.176547 0.984292i \(-0.556493\pi\)
−0.446702 + 0.894683i \(0.647402\pi\)
\(542\) 0 0
\(543\) 26.5202 2.98070i 1.13809 0.127914i
\(544\) 0 0
\(545\) 0.593390 + 0.270992i 0.0254180 + 0.0116080i
\(546\) 0 0
\(547\) −13.2130 33.0045i −0.564948 1.41117i −0.885811 0.464046i \(-0.846397\pi\)
0.320863 0.947126i \(-0.396027\pi\)
\(548\) 0 0
\(549\) −23.7984 23.3435i −1.01569 0.996278i
\(550\) 0 0
\(551\) 2.55204 1.16548i 0.108721 0.0496511i
\(552\) 0 0
\(553\) −11.0081 31.8058i −0.468112 1.35252i
\(554\) 0 0
\(555\) 28.6995 + 2.25685i 1.21823 + 0.0957979i
\(556\) 0 0
\(557\) 6.36471 + 8.09338i 0.269681 + 0.342928i 0.901965 0.431809i \(-0.142125\pi\)
−0.632284 + 0.774737i \(0.717882\pi\)
\(558\) 0 0
\(559\) 0.741082 + 15.5572i 0.0313444 + 0.658001i
\(560\) 0 0
\(561\) −3.57033 + 12.9572i −0.150739 + 0.547053i
\(562\) 0 0
\(563\) −1.76420 12.2703i −0.0743520 0.517130i −0.992629 0.121191i \(-0.961329\pi\)
0.918277 0.395938i \(-0.129581\pi\)
\(564\) 0 0
\(565\) 17.1930 + 29.7791i 0.723314 + 1.25282i
\(566\) 0 0
\(567\) −16.6060 + 19.9287i −0.697388 + 0.836927i
\(568\) 0 0
\(569\) 14.4597 + 10.2967i 0.606180 + 0.431659i 0.841499 0.540259i \(-0.181674\pi\)
−0.235318 + 0.971918i \(0.575613\pi\)
\(570\) 0 0
\(571\) −0.852971 + 17.9061i −0.0356957 + 0.749345i 0.908088 + 0.418780i \(0.137542\pi\)
−0.943783 + 0.330565i \(0.892761\pi\)
\(572\) 0 0
\(573\) −18.9111 + 34.0580i −0.790025 + 1.42279i
\(574\) 0 0
\(575\) 17.2776 + 4.19151i 0.720527 + 0.174798i
\(576\) 0 0
\(577\) 4.51436 23.4227i 0.187935 0.975100i −0.758370 0.651825i \(-0.774004\pi\)
0.946305 0.323276i \(-0.104784\pi\)
\(578\) 0 0
\(579\) −21.7490 + 25.9647i −0.903859 + 1.07906i
\(580\) 0 0
\(581\) −0.384515 0.247113i −0.0159524 0.0102520i
\(582\) 0 0
\(583\) 32.9005 + 16.9614i 1.36260 + 0.702469i
\(584\) 0 0
\(585\) −3.52245 15.4722i −0.145636 0.639698i
\(586\) 0 0
\(587\) 21.0887 + 16.5843i 0.870423 + 0.684508i 0.949976 0.312323i \(-0.101107\pi\)
−0.0795534 + 0.996831i \(0.525349\pi\)
\(588\) 0 0
\(589\) −9.55853 + 8.28252i −0.393853 + 0.341275i
\(590\) 0 0
\(591\) 10.1484 + 38.9754i 0.417449 + 1.60323i
\(592\) 0 0
\(593\) −10.4172 + 5.37044i −0.427783 + 0.220538i −0.658653 0.752447i \(-0.728873\pi\)
0.230869 + 0.972985i \(0.425843\pi\)
\(594\) 0 0
\(595\) −12.6818 + 3.72372i −0.519904 + 0.152658i
\(596\) 0 0
\(597\) 32.8345 + 12.5120i 1.34382 + 0.512081i
\(598\) 0 0
\(599\) 7.04181 20.3460i 0.287721 0.831315i −0.704818 0.709388i \(-0.748972\pi\)
0.992539 0.121927i \(-0.0389073\pi\)
\(600\) 0 0
\(601\) −14.3803 20.1943i −0.586584 0.823743i 0.409485 0.912317i \(-0.365708\pi\)
−0.996070 + 0.0885743i \(0.971769\pi\)
\(602\) 0 0
\(603\) −16.8139 17.8967i −0.684715 0.728811i
\(604\) 0 0
\(605\) −21.9960 30.8891i −0.894266 1.25582i
\(606\) 0 0
\(607\) −11.2024 + 32.3671i −0.454690 + 1.31374i 0.452027 + 0.892004i \(0.350701\pi\)
−0.906718 + 0.421738i \(0.861420\pi\)
\(608\) 0 0
\(609\) −4.10026 1.56246i −0.166151 0.0633139i
\(610\) 0 0
\(611\) 17.7507 5.21209i 0.718118 0.210858i
\(612\) 0 0
\(613\) −23.0170 + 11.8661i −0.929647 + 0.479266i −0.855397 0.517973i \(-0.826687\pi\)
−0.0742502 + 0.997240i \(0.523656\pi\)
\(614\) 0 0
\(615\) −8.49209 32.6143i −0.342434 1.31514i
\(616\) 0 0
\(617\) −11.7828 + 10.2099i −0.474358 + 0.411034i −0.858955 0.512051i \(-0.828886\pi\)
0.384597 + 0.923085i \(0.374341\pi\)
\(618\) 0 0
\(619\) 13.0161 + 10.2360i 0.523160 + 0.411418i 0.844508 0.535544i \(-0.179893\pi\)
−0.321347 + 0.946961i \(0.604136\pi\)
\(620\) 0 0
\(621\) 6.45732 + 26.3217i 0.259123 + 1.05626i
\(622\) 0 0
\(623\) −7.68809 3.96348i −0.308017 0.158794i
\(624\) 0 0
\(625\) −25.5946 16.4487i −1.02379 0.657947i
\(626\) 0 0
\(627\) −17.4202 + 20.7967i −0.695694 + 0.830541i
\(628\) 0 0
\(629\) −1.71541 + 8.90040i −0.0683980 + 0.354882i
\(630\) 0 0
\(631\) −12.6793 3.07597i −0.504756 0.122452i −0.0247079 0.999695i \(-0.507866\pi\)
−0.480048 + 0.877242i \(0.659381\pi\)
\(632\) 0 0
\(633\) 6.82764 12.2962i 0.271374 0.488731i
\(634\) 0 0
\(635\) −1.53091 + 32.1377i −0.0607522 + 1.27535i
\(636\) 0 0
\(637\) −1.94287 1.38351i −0.0769791 0.0548166i
\(638\) 0 0
\(639\) −10.4473 + 11.7175i −0.413287 + 0.463538i
\(640\) 0 0
\(641\) −18.7729 32.5157i −0.741487 1.28429i −0.951818 0.306663i \(-0.900788\pi\)
0.210332 0.977630i \(-0.432546\pi\)
\(642\) 0 0
\(643\) −0.929880 6.46746i −0.0366709 0.255052i 0.963237 0.268655i \(-0.0865790\pi\)
−0.999907 + 0.0136029i \(0.995670\pi\)
\(644\) 0 0
\(645\) 11.3923 41.3442i 0.448571 1.62792i
\(646\) 0 0
\(647\) 1.31497 + 27.6046i 0.0516969 + 1.08525i 0.864475 + 0.502677i \(0.167651\pi\)
−0.812778 + 0.582574i \(0.802046\pi\)
\(648\) 0 0
\(649\) −5.63595 7.16669i −0.221230 0.281317i
\(650\) 0 0
\(651\) 19.7200 + 1.55072i 0.772887 + 0.0607777i
\(652\) 0 0
\(653\) 0.0497588 + 0.143769i 0.00194721 + 0.00562611i 0.945970 0.324253i \(-0.105113\pi\)
−0.944023 + 0.329880i \(0.892992\pi\)
\(654\) 0 0
\(655\) 37.4748 17.1142i 1.46426 0.668707i
\(656\) 0 0
\(657\) 13.9668 14.2390i 0.544898 0.555516i
\(658\) 0 0
\(659\) 14.5115 + 36.2480i 0.565289 + 1.41202i 0.885483 + 0.464671i \(0.153827\pi\)
−0.320195 + 0.947352i \(0.603748\pi\)
\(660\) 0 0
\(661\) −28.9799 13.2347i −1.12719 0.514769i −0.237521 0.971382i \(-0.576335\pi\)
−0.889665 + 0.456613i \(0.849062\pi\)
\(662\) 0 0
\(663\) 4.96497 0.558031i 0.192823 0.0216721i
\(664\) 0 0
\(665\) −26.4072 3.79678i −1.02403 0.147233i
\(666\) 0 0
\(667\) −3.85662 + 2.47850i −0.149329 + 0.0959678i
\(668\) 0 0
\(669\) −36.2585 + 0.606446i −1.40184 + 0.0234466i
\(670\) 0 0
\(671\) 54.5247i 2.10490i
\(672\) 0 0
\(673\) 11.2718 + 17.5392i 0.434495 + 0.676087i 0.987594 0.157028i \(-0.0501914\pi\)
−0.553099 + 0.833115i \(0.686555\pi\)
\(674\) 0 0
\(675\) −1.63825 + 17.6358i −0.0630562 + 0.678802i
\(676\) 0 0
\(677\) 7.29459 0.696549i 0.280354 0.0267706i 0.0460681 0.998938i \(-0.485331\pi\)
0.234286 + 0.972168i \(0.424725\pi\)
\(678\) 0 0
\(679\) 8.62105 18.8775i 0.330846 0.724451i
\(680\) 0 0
\(681\) 13.1217 + 31.2514i 0.502826 + 1.19756i
\(682\) 0 0
\(683\) 19.8958 18.9706i 0.761292 0.725891i −0.206278 0.978493i \(-0.566135\pi\)
0.967570 + 0.252603i \(0.0812866\pi\)
\(684\) 0 0
\(685\) −16.7673 36.7153i −0.640646 1.40282i
\(686\) 0 0
\(687\) 43.3485 15.8197i 1.65385 0.603558i
\(688\) 0 0
\(689\) 1.30798 13.6978i 0.0498301 0.521844i
\(690\) 0 0
\(691\) 5.01612 3.94472i 0.190822 0.150064i −0.518177 0.855273i \(-0.673389\pi\)
0.708999 + 0.705209i \(0.249147\pi\)
\(692\) 0 0
\(693\) 42.2895 3.43500i 1.60645 0.130485i
\(694\) 0 0
\(695\) −12.2972 + 41.8805i −0.466461 + 1.58862i
\(696\) 0 0
\(697\) 10.5033 1.51015i 0.397841 0.0572009i
\(698\) 0 0
\(699\) −1.07459 1.79138i −0.0406448 0.0677561i
\(700\) 0 0
\(701\) 10.2133 + 9.73839i 0.385752 + 0.367814i 0.857998 0.513653i \(-0.171708\pi\)
−0.472246 + 0.881467i \(0.656557\pi\)
\(702\) 0 0
\(703\) −10.6127 + 14.9035i −0.400266 + 0.562095i
\(704\) 0 0
\(705\) −50.9153 1.57255i −1.91758 0.0592258i
\(706\) 0 0
\(707\) −16.5866 9.57627i −0.623803 0.360153i
\(708\) 0 0
\(709\) −7.75370 + 31.9612i −0.291196 + 1.20033i 0.618745 + 0.785592i \(0.287641\pi\)
−0.909942 + 0.414736i \(0.863874\pi\)
\(710\) 0 0
\(711\) 5.47570 34.6009i 0.205355 1.29764i
\(712\) 0 0
\(713\) 13.5338 15.6188i 0.506844 0.584930i
\(714\) 0 0
\(715\) −14.0319 + 21.8340i −0.524762 + 0.816546i
\(716\) 0 0
\(717\) 17.7987 + 8.80227i 0.664704 + 0.328727i
\(718\) 0 0
\(719\) 2.79908 + 14.5230i 0.104388 + 0.541617i 0.996041 + 0.0888971i \(0.0283342\pi\)
−0.891653 + 0.452720i \(0.850454\pi\)
\(720\) 0 0
\(721\) 11.1722 14.2066i 0.416073 0.529080i
\(722\) 0 0
\(723\) 34.0403 + 37.9821i 1.26597 + 1.41257i
\(724\) 0 0
\(725\) −2.91150 + 0.706323i −0.108130 + 0.0262322i
\(726\) 0 0
\(727\) −6.31770 12.2546i −0.234310 0.454499i 0.742139 0.670246i \(-0.233812\pi\)
−0.976449 + 0.215747i \(0.930781\pi\)
\(728\) 0 0
\(729\) −25.0140 + 10.1637i −0.926444 + 0.376434i
\(730\) 0 0
\(731\) 12.5355 + 5.01847i 0.463643 + 0.185615i
\(732\) 0 0
\(733\) −4.69450 1.62478i −0.173395 0.0600127i 0.238991 0.971022i \(-0.423183\pi\)
−0.412386 + 0.911009i \(0.635305\pi\)
\(734\) 0 0
\(735\) 3.89838 + 5.28517i 0.143794 + 0.194947i
\(736\) 0 0
\(737\) −1.63960 + 40.1307i −0.0603955 + 1.47824i
\(738\) 0 0
\(739\) 7.24093 5.15624i 0.266362 0.189675i −0.439071 0.898453i \(-0.644692\pi\)
0.705432 + 0.708777i \(0.250753\pi\)
\(740\) 0 0
\(741\) 9.58400 + 3.13859i 0.352077 + 0.115299i
\(742\) 0 0
\(743\) 14.1770 35.4125i 0.520104 1.29916i −0.403209 0.915108i \(-0.632105\pi\)
0.923313 0.384049i \(-0.125471\pi\)
\(744\) 0 0
\(745\) −14.1252 48.1059i −0.517506 1.76246i
\(746\) 0 0
\(747\) −0.232016 0.415329i −0.00848903 0.0151961i
\(748\) 0 0
\(749\) 10.9514 + 45.1421i 0.400154 + 1.64946i
\(750\) 0 0
\(751\) 8.03102 + 9.26829i 0.293056 + 0.338205i 0.883116 0.469155i \(-0.155441\pi\)
−0.590060 + 0.807359i \(0.700896\pi\)
\(752\) 0 0
\(753\) 37.2038 + 28.2634i 1.35578 + 1.02997i
\(754\) 0 0
\(755\) −43.6094 + 8.40503i −1.58711 + 0.305890i
\(756\) 0 0
\(757\) 3.74952 7.27305i 0.136279 0.264343i −0.810814 0.585304i \(-0.800975\pi\)
0.947093 + 0.320960i \(0.104006\pi\)
\(758\) 0 0
\(759\) 23.3390 37.6873i 0.847151 1.36796i
\(760\) 0 0
\(761\) −19.6756 17.0490i −0.713240 0.618026i 0.220748 0.975331i \(-0.429150\pi\)
−0.933988 + 0.357305i \(0.883696\pi\)
\(762\) 0 0
\(763\) 0.636692 + 0.122712i 0.0230498 + 0.00444248i
\(764\) 0 0
\(765\) −13.4702 2.79443i −0.487016 0.101033i
\(766\) 0 0
\(767\) −1.69464 + 2.93520i −0.0611898 + 0.105984i
\(768\) 0 0
\(769\) −14.9664 0.712936i −0.539701 0.0257091i −0.224038 0.974580i \(-0.571924\pi\)
−0.315663 + 0.948871i \(0.602227\pi\)
\(770\) 0 0
\(771\) 1.48714 + 1.02195i 0.0535582 + 0.0368045i
\(772\) 0 0
\(773\) −14.5862 + 15.2976i −0.524630 + 0.550216i −0.931723 0.363171i \(-0.881694\pi\)
0.407092 + 0.913387i \(0.366543\pi\)