Properties

Label 804.2.ba.b.41.4
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 41.4
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.47255 + 0.911919i) q^{3} +(-0.412679 + 2.87025i) q^{5} +(-0.273979 - 2.86924i) q^{7} +(1.33681 - 2.68569i) q^{9} +O(q^{10})\) \(q+(-1.47255 + 0.911919i) q^{3} +(-0.412679 + 2.87025i) q^{5} +(-0.273979 - 2.86924i) q^{7} +(1.33681 - 2.68569i) q^{9} +(4.55535 - 1.82369i) q^{11} +(1.25875 + 1.32014i) q^{13} +(-2.00974 - 4.60291i) q^{15} +(-1.49442 + 0.517223i) q^{17} +(3.17757 + 0.303421i) q^{19} +(3.01996 + 3.97525i) q^{21} +(5.20992 - 0.248179i) q^{23} +(-3.27055 - 0.960320i) q^{25} +(0.480619 + 5.17388i) q^{27} +(-0.761179 + 0.439467i) q^{29} +(-2.73430 + 2.86765i) q^{31} +(-5.04493 + 6.83959i) q^{33} +(8.34848 + 0.397687i) q^{35} +(-2.86589 + 4.96387i) q^{37} +(-3.05744 - 0.796095i) q^{39} +(-6.58885 - 1.26990i) q^{41} +(6.45298 + 5.59154i) q^{43} +(7.15693 + 4.94530i) q^{45} +(-4.64743 + 9.01475i) q^{47} +(-1.28395 + 0.247462i) q^{49} +(1.72894 - 2.12442i) q^{51} +(4.94001 + 5.70108i) q^{53} +(3.35454 + 13.8276i) q^{55} +(-4.95583 + 2.45088i) q^{57} +(-0.523482 - 1.78282i) q^{59} +(4.12990 - 10.3160i) q^{61} +(-8.07214 - 3.09979i) q^{63} +(-4.30860 + 3.06814i) q^{65} +(3.34986 - 7.46850i) q^{67} +(-7.44555 + 5.11648i) q^{69} +(4.94506 + 1.71150i) q^{71} +(6.17224 + 2.47099i) q^{73} +(5.69178 - 1.56836i) q^{75} +(-6.48066 - 12.5707i) q^{77} +(11.3480 - 2.75300i) q^{79} +(-5.42589 - 7.18051i) q^{81} +(-0.0980278 + 0.124653i) q^{83} +(-0.867843 - 4.50280i) q^{85} +(0.720116 - 1.34127i) q^{87} +(-1.62244 + 2.52457i) q^{89} +(3.44293 - 3.97335i) q^{91} +(1.41133 - 6.71622i) q^{93} +(-2.18221 + 8.99519i) q^{95} +(6.23550 + 3.60007i) q^{97} +(1.19176 - 14.6722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

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
\(3\) −1.47255 + 0.911919i −0.850177 + 0.526497i
\(4\) 0 0
\(5\) −0.412679 + 2.87025i −0.184556 + 1.28361i 0.661267 + 0.750150i \(0.270019\pi\)
−0.845823 + 0.533463i \(0.820890\pi\)
\(6\) 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
\(9\) 1.33681 2.68569i 0.445602 0.895231i
\(10\) 0 0
\(11\) 4.55535 1.82369i 1.37349 0.549863i 0.436654 0.899629i \(-0.356163\pi\)
0.936837 + 0.349767i \(0.113739\pi\)
\(12\) 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
\(15\) −2.00974 4.60291i −0.518913 1.18847i
\(16\) 0 0
\(17\) −1.49442 + 0.517223i −0.362450 + 0.125445i −0.502222 0.864739i \(-0.667484\pi\)
0.139773 + 0.990184i \(0.455363\pi\)
\(18\) 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
\(21\) 3.01996 + 3.97525i 0.659009 + 0.867470i
\(22\) 0 0
\(23\) 5.20992 0.248179i 1.08634 0.0517489i 0.503240 0.864147i \(-0.332141\pi\)
0.583103 + 0.812398i \(0.301838\pi\)
\(24\) 0 0
\(25\) −3.27055 0.960320i −0.654110 0.192064i
\(26\) 0 0
\(27\) 0.480619 + 5.17388i 0.0924951 + 0.995713i
\(28\) 0 0
\(29\) −0.761179 + 0.439467i −0.141347 + 0.0816070i −0.569006 0.822333i \(-0.692672\pi\)
0.427659 + 0.903940i \(0.359339\pi\)
\(30\) 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
\(33\) −5.04493 + 6.83959i −0.878210 + 1.19062i
\(34\) 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
\(39\) −3.05744 0.796095i −0.489583 0.127477i
\(40\) 0 0
\(41\) −6.58885 1.26990i −1.02900 0.198324i −0.353310 0.935506i \(-0.614944\pi\)
−0.675695 + 0.737182i \(0.736156\pi\)
\(42\) 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
\(45\) 7.15693 + 4.94530i 1.06689 + 0.737201i
\(46\) 0 0
\(47\) −4.64743 + 9.01475i −0.677897 + 1.31494i 0.259185 + 0.965828i \(0.416546\pi\)
−0.937082 + 0.349109i \(0.886484\pi\)
\(48\) 0 0
\(49\) −1.28395 + 0.247462i −0.183422 + 0.0353517i
\(50\) 0 0
\(51\) 1.72894 2.12442i 0.242100 0.297479i
\(52\) 0 0
\(53\) 4.94001 + 5.70108i 0.678563 + 0.783103i 0.985691 0.168565i \(-0.0539133\pi\)
−0.307128 + 0.951668i \(0.599368\pi\)
\(54\) 0 0
\(55\) 3.35454 + 13.8276i 0.452326 + 1.86451i
\(56\) 0 0
\(57\) −4.95583 + 2.45088i −0.656415 + 0.324627i
\(58\) 0 0
\(59\) −0.523482 1.78282i −0.0681516 0.232103i 0.918373 0.395716i \(-0.129503\pi\)
−0.986525 + 0.163613i \(0.947685\pi\)
\(60\) 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
\(63\) −8.07214 3.09979i −1.01699 0.390537i
\(64\) 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
\(69\) −7.44555 + 5.11648i −0.896339 + 0.615952i
\(70\) 0 0
\(71\) 4.94506 + 1.71150i 0.586871 + 0.203118i 0.604336 0.796730i \(-0.293438\pi\)
−0.0174653 + 0.999847i \(0.505560\pi\)
\(72\) 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
\(75\) 5.69178 1.56836i 0.657230 0.181098i
\(76\) 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
\(81\) −5.42589 7.18051i −0.602877 0.797834i
\(82\) 0 0
\(83\) −0.0980278 + 0.124653i −0.0107600 + 0.0136824i −0.791403 0.611294i \(-0.790649\pi\)
0.780643 + 0.624977i \(0.214892\pi\)
\(84\) 0 0
\(85\) −0.867843 4.50280i −0.0941308 0.488397i
\(86\) 0 0
\(87\) 0.720116 1.34127i 0.0772045 0.143799i
\(88\) 0 0
\(89\) −1.62244 + 2.52457i −0.171978 + 0.267603i −0.916534 0.399957i \(-0.869025\pi\)
0.744556 + 0.667560i \(0.232661\pi\)
\(90\) 0 0
\(91\) 3.44293 3.97335i 0.360917 0.416521i
\(92\) 0 0
\(93\) 1.41133 6.71622i 0.146348 0.696440i
\(94\) 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
\(99\) 1.19176 14.6722i 0.119777 1.47461i
\(100\) 0 0
\(101\) −3.85442 + 5.41278i −0.383530 + 0.538592i −0.960539 0.278146i \(-0.910280\pi\)
0.577009 + 0.816738i \(0.304220\pi\)
\(102\) 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
\(105\) −12.6562 + 7.02753i −1.23512 + 0.685816i
\(106\) 0 0
\(107\) 15.9522 2.29358i 1.54215 0.221728i 0.681843 0.731498i \(-0.261179\pi\)
0.860311 + 0.509770i \(0.170270\pi\)
\(108\) 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
\(111\) −0.306479 9.92301i −0.0290897 0.941851i
\(112\) 0 0
\(113\) 9.32118 7.33026i 0.876863 0.689572i −0.0746407 0.997210i \(-0.523781\pi\)
0.951503 + 0.307638i \(0.0995386\pi\)
\(114\) 0 0
\(115\) −1.43769 + 15.0562i −0.134065 + 1.40400i
\(116\) 0 0
\(117\) 5.22821 1.61585i 0.483348 0.149385i
\(118\) 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
\(123\) 10.8604 4.13851i 0.979254 0.373157i
\(124\) 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
\(129\) −14.6014 2.34923i −1.28558 0.206838i
\(130\) 0 0
\(131\) −7.68105 11.9519i −0.671096 1.04425i −0.995165 0.0982128i \(-0.968687\pi\)
0.324069 0.946033i \(-0.394949\pi\)
\(132\) 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 −0.934899 0.354915i \(-0.884510\pi\)
−0.0655291 + 0.997851i \(0.520874\pi\)
\(138\) 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
\(141\) −1.37715 17.5128i −0.115977 1.47484i
\(142\) 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
\(147\) 1.66502 1.53526i 0.137328 0.126626i
\(148\) 0 0
\(149\) −15.7275 + 7.18251i −1.28845 + 0.588414i −0.937502 0.347981i \(-0.886867\pi\)
−0.350946 + 0.936396i \(0.614140\pi\)
\(150\) 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
\(153\) −0.608647 + 4.70497i −0.0492062 + 0.380375i
\(154\) 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
\(159\) −12.4733 3.89023i −0.989200 0.308516i
\(160\) 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
\(165\) −17.5494 17.3028i −1.36622 1.34702i
\(166\) 0 0
\(167\) −8.27884 5.89534i −0.640636 0.456195i 0.213009 0.977050i \(-0.431674\pi\)
−0.853645 + 0.520855i \(0.825613\pi\)
\(168\) 0 0
\(169\) 0.460248 9.66180i 0.0354037 0.743216i
\(170\) 0 0
\(171\) 5.06269 8.12836i 0.387154 0.621591i
\(172\) 0 0
\(173\) −13.3638 3.24203i −1.01603 0.246487i −0.307036 0.951698i \(-0.599337\pi\)
−0.708997 + 0.705211i \(0.750852\pi\)
\(174\) 0 0
\(175\) −1.85932 + 9.64709i −0.140552 + 0.729251i
\(176\) 0 0
\(177\) 2.39664 + 2.14791i 0.180142 + 0.161447i
\(178\) 0 0
\(179\) 2.93658 + 1.88723i 0.219490 + 0.141058i 0.645766 0.763535i \(-0.276538\pi\)
−0.426275 + 0.904593i \(0.640175\pi\)
\(180\) 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
\(183\) 3.32587 + 18.9570i 0.245855 + 1.40134i
\(184\) 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
\(189\) 14.7134 2.79654i 1.07024 0.203418i
\(190\) 0 0
\(191\) 19.9911 10.3061i 1.44650 0.745725i 0.456897 0.889520i \(-0.348961\pi\)
0.989608 + 0.143795i \(0.0459304\pi\)
\(192\) 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
\(195\) 3.54673 8.44708i 0.253987 0.604908i
\(196\) 0 0
\(197\) 7.60523 21.9739i 0.541850 1.56557i −0.258482 0.966016i \(-0.583222\pi\)
0.800332 0.599557i \(-0.204657\pi\)
\(198\) 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
\(201\) 1.87782 + 14.0525i 0.132451 + 0.991190i
\(202\) 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
\(207\) 6.29813 14.3240i 0.437750 0.995588i
\(208\) 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
\(213\) −8.84260 + 1.98922i −0.605885 + 0.136299i
\(214\) 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
\(219\) −11.3423 + 1.98992i −0.766440 + 0.134467i
\(220\) 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
\(225\) −6.95122 + 7.49993i −0.463415 + 0.499995i
\(226\) 0 0
\(227\) 3.70345 19.2153i 0.245806 1.27536i −0.623787 0.781595i \(-0.714407\pi\)
0.869593 0.493769i \(-0.164381\pi\)
\(228\) 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
\(231\) 21.0066 + 12.6012i 1.38213 + 0.829098i
\(232\) 0 0
\(233\) −0.0573869 + 1.20470i −0.00375954 + 0.0789225i −0.999967 0.00808354i \(-0.997427\pi\)
0.996208 + 0.0870060i \(0.0277299\pi\)
\(234\) 0 0
\(235\) −23.9567 17.0595i −1.56276 1.11284i
\(236\) 0 0
\(237\) −14.2000 + 14.4024i −0.922389 + 0.935536i
\(238\) 0 0
\(239\) −5.73202 9.92816i −0.370774 0.642199i 0.618911 0.785461i \(-0.287574\pi\)
−0.989685 + 0.143262i \(0.954241\pi\)
\(240\) 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
\(243\) 14.5379 + 5.62568i 0.932609 + 0.360888i
\(244\) 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
\(249\) 0.0306779 0.272951i 0.00194413 0.0172975i
\(250\) 0 0
\(251\) −8.82263 25.4913i −0.556880 1.60900i −0.774230 0.632904i \(-0.781863\pi\)
0.217350 0.976094i \(-0.430259\pi\)
\(252\) 0 0
\(253\) 23.2804 10.6318i 1.46363 0.668416i
\(254\) 0 0
\(255\) 5.38413 + 5.83919i 0.337167 + 0.365664i
\(256\) 0 0
\(257\) −0.387194 0.967163i −0.0241525 0.0603299i 0.915802 0.401631i \(-0.131557\pi\)
−0.939954 + 0.341301i \(0.889132\pi\)
\(258\) 0 0
\(259\) 15.0277 + 6.86293i 0.933777 + 0.426442i
\(260\) 0 0
\(261\) 0.162723 + 2.63178i 0.0100723 + 0.162903i
\(262\) 0 0
\(263\) 16.2766 + 2.34022i 1.00366 + 0.144304i 0.624498 0.781026i \(-0.285303\pi\)
0.379161 + 0.925331i \(0.376213\pi\)
\(264\) 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 \(0.00751021\pi\)
−0.999722 + 0.0235918i \(0.992490\pi\)
\(270\) 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
\(273\) −1.44651 + 8.99064i −0.0875468 + 0.544138i
\(274\) 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
\(279\) 4.04640 + 11.1770i 0.242252 + 0.669149i
\(280\) 0 0
\(281\) −1.48895 + 1.41971i −0.0888232 + 0.0846927i −0.733190 0.680024i \(-0.761969\pi\)
0.644367 + 0.764716i \(0.277121\pi\)
\(282\) 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
\(285\) −4.98947 15.2359i −0.295551 0.902495i
\(286\) 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
\(291\) −12.4651 + 0.384991i −0.730715 + 0.0225686i
\(292\) 0 0
\(293\) −3.34108 + 11.3787i −0.195188 + 0.664749i 0.802492 + 0.596663i \(0.203507\pi\)
−0.997679 + 0.0680855i \(0.978311\pi\)
\(294\) 0 0
\(295\) 5.33315 0.766792i 0.310508 0.0446443i
\(296\) 0 0
\(297\) 11.6249 + 22.6923i 0.674547 + 1.31674i
\(298\) 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
\(303\) 0.739814 11.4855i 0.0425012 0.659826i
\(304\) 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
\(309\) −10.6286 2.23347i −0.604642 0.127058i
\(310\) 0 0
\(311\) 9.56540 11.0391i 0.542404 0.625968i −0.416692 0.909048i \(-0.636811\pi\)
0.959096 + 0.283080i \(0.0913561\pi\)
\(312\) 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
\(315\) 12.2284 21.8898i 0.688991 1.23335i
\(316\) 0 0
\(317\) 2.53662 + 13.1612i 0.142471 + 0.739208i 0.980948 + 0.194271i \(0.0622342\pi\)
−0.838477 + 0.544937i \(0.816554\pi\)
\(318\) 0 0
\(319\) −2.66599 + 3.39008i −0.149267 + 0.189808i
\(320\) 0 0
\(321\) −21.3988 + 17.9245i −1.19436 + 1.00045i
\(322\) 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
\(327\) −0.103509 0.375648i −0.00572406 0.0207734i
\(328\) 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
\(333\) 9.50029 + 14.3326i 0.520613 + 0.785424i
\(334\) 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
\(339\) −7.04130 + 19.2943i −0.382431 + 1.04792i
\(340\) 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
\(345\) −11.6129 23.4820i −0.625220 1.26423i
\(346\) 0 0
\(347\) −2.68001 11.0472i −0.143870 0.593042i −0.997404 0.0720047i \(-0.977060\pi\)
0.853534 0.521037i \(-0.174455\pi\)
\(348\) 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
\(351\) −6.22528 + 7.14713i −0.332281 + 0.381485i
\(352\) 0 0
\(353\) 6.92313 1.33432i 0.368481 0.0710189i −0.00164965 0.999999i \(-0.500525\pi\)
0.370130 + 0.928980i \(0.379313\pi\)
\(354\) 0 0
\(355\) −6.95316 + 13.4872i −0.369035 + 0.715829i
\(356\) 0 0
\(357\) −6.56917 4.37869i −0.347677 0.231745i
\(358\) 0 0
\(359\) −8.77136 7.60043i −0.462935 0.401135i 0.391923 0.919998i \(-0.371810\pi\)
−0.854857 + 0.518863i \(0.826356\pi\)
\(360\) 0 0
\(361\) −8.65176 1.66749i −0.455356 0.0877627i
\(362\) 0 0
\(363\) −5.70735 + 21.9193i −0.299558 + 1.15047i
\(364\) 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
\(369\) −12.2186 + 15.9980i −0.636073 + 0.832823i
\(370\) 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
\(375\) −1.00502 7.92931i −0.0518992 0.409468i
\(376\) 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
\(381\) 15.3028 11.6254i 0.783987 0.595588i
\(382\) 0 0
\(383\) −13.7852 1.31633i −0.704392 0.0672613i −0.263288 0.964717i \(-0.584807\pi\)
−0.441104 + 0.897456i \(0.645413\pi\)
\(384\) 0 0
\(385\) 38.7556 13.4134i 1.97517 0.683612i
\(386\) 0 0
\(387\) 23.6435 9.85591i 1.20187 0.501004i
\(388\) 0 0
\(389\) −0.683887 0.717241i −0.0346745 0.0363655i 0.706168 0.708044i \(-0.250422\pi\)
−0.740843 + 0.671678i \(0.765574\pi\)
\(390\) 0 0
\(391\) −7.65743 + 3.06557i −0.387253 + 0.155033i
\(392\) 0 0
\(393\) 22.2099 + 10.5953i 1.12034 + 0.534464i
\(394\) 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
\(399\) 8.38996 + 13.5479i 0.420023 + 0.678246i
\(400\) 0 0
\(401\) −17.7271 −0.885249 −0.442624 0.896707i \(-0.645952\pi\)
−0.442624 + 0.896707i \(0.645952\pi\)
\(402\) 0 0
\(403\) −7.22752 −0.360029
\(404\) 0 0
\(405\) 22.8490 12.6104i 1.13538 0.626616i
\(406\) 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
\(411\) 10.3806 21.7598i 0.512037 1.07333i
\(412\) 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
\(417\) 23.8934 10.4324i 1.17007 0.510879i
\(418\) 0 0
\(419\) 6.59427 2.28230i 0.322151 0.111498i −0.161206 0.986921i \(-0.551538\pi\)
0.483357 + 0.875423i \(0.339417\pi\)
\(420\) 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
\(423\) 17.9981 + 24.5326i 0.875100 + 1.19281i
\(424\) 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
\(429\) −15.3796 + 1.94933i −0.742532 + 0.0941144i
\(430\) 0 0
\(431\) −24.2306 + 13.9896i −1.16715 + 0.673853i −0.953007 0.302950i \(-0.902029\pi\)
−0.214141 + 0.976803i \(0.568695\pi\)
\(432\) 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
\(435\) 3.55260 + 2.62043i 0.170334 + 0.125640i
\(436\) 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
\(441\) −1.05179 + 3.77911i −0.0500853 + 0.179958i
\(442\) 0 0
\(443\) −28.3444 5.46294i −1.34668 0.259552i −0.535595 0.844475i \(-0.679912\pi\)
−0.811089 + 0.584923i \(0.801125\pi\)
\(444\) 0 0
\(445\) −6.57658 5.69864i −0.311760 0.270141i
\(446\) 0 0
\(447\) 16.6097 24.9188i 0.785611 1.17862i
\(448\) 0 0
\(449\) −1.16700 + 2.26366i −0.0550741 + 0.106829i −0.914766 0.403984i \(-0.867625\pi\)
0.859692 + 0.510813i \(0.170655\pi\)
\(450\) 0 0
\(451\) −32.3304 + 6.23118i −1.52238 + 0.293415i
\(452\) 0 0
\(453\) 20.5750 + 16.7447i 0.966697 + 0.786736i
\(454\) 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
\(459\) −3.39429 7.48335i −0.158432 0.349293i
\(460\) 0 0
\(461\) −1.46906 5.00315i −0.0684208 0.233020i 0.918182 0.396158i \(-0.129657\pi\)
−0.986603 + 0.163138i \(0.947838\pi\)
\(462\) 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
\(465\) 18.6948 + 6.82250i 0.866950 + 0.316386i
\(466\) 0 0
\(467\) 30.8962 22.0011i 1.42971 1.01809i 0.436754 0.899581i \(-0.356128\pi\)
0.992953 0.118509i \(-0.0378115\pi\)
\(468\) 0 0
\(469\) −22.3467 7.56534i −1.03187 0.349335i
\(470\) 0 0
\(471\) −15.3060 22.2734i −0.705262 1.02630i
\(472\) 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
\(477\) 21.9152 5.64611i 1.00343 0.258518i
\(478\) 0 0
\(479\) 15.8205 + 30.6876i 0.722859 + 1.40215i 0.907801 + 0.419402i \(0.137760\pi\)
−0.184941 + 0.982750i \(0.559210\pi\)
\(480\) 0 0
\(481\) −10.1605 + 2.46490i −0.463278 + 0.112390i
\(482\) 0 0
\(483\) 16.7203 + 19.9612i 0.760801 + 0.908267i
\(484\) 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
\(489\) −27.1639 14.5841i −1.22839 0.659514i
\(490\) 0 0
\(491\) 11.4876 17.8750i 0.518427 0.806688i −0.479042 0.877792i \(-0.659016\pi\)
0.997469 + 0.0711041i \(0.0226522\pi\)
\(492\) 0 0
\(493\) 0.910217 1.05045i 0.0409941 0.0473097i
\(494\) 0 0
\(495\) 41.6210 + 9.47557i 1.87073 + 0.425895i
\(496\) 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
\(501\) 17.5671 + 1.13155i 0.784839 + 0.0505537i
\(502\) 0 0
\(503\) −24.3950 + 34.2579i −1.08772 + 1.52749i −0.260609 + 0.965444i \(0.583923\pi\)
−0.827109 + 0.562042i \(0.810016\pi\)
\(504\) 0 0
\(505\) −13.9454 13.2969i −0.620561 0.591704i
\(506\) 0 0
\(507\) 8.13304 + 14.6472i 0.361201 + 0.650505i
\(508\) 0 0
\(509\) 22.8411 3.28406i 1.01242 0.145563i 0.383912 0.923370i \(-0.374577\pi\)
0.628504 + 0.777806i \(0.283668\pi\)
\(510\) 0 0
\(511\) 5.39880 18.3866i 0.238829 0.813376i
\(512\) 0 0
\(513\) −0.0426641 + 16.5862i −0.00188367 + 0.732298i
\(514\) 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
\(519\) 22.6354 7.41268i 0.993583 0.325381i
\(520\) 0 0
\(521\) −10.1543 22.2347i −0.444866 0.974121i −0.990679 0.136214i \(-0.956507\pi\)
0.545813 0.837907i \(-0.316221\pi\)
\(522\) 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
\(525\) −6.05941 15.9014i −0.264455 0.693993i
\(526\) 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
\(531\) −5.48789 0.977370i −0.238154 0.0424142i
\(532\) 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
\(543\) −26.6051 + 2.09215i −1.14173 + 0.0897827i
\(544\) 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
\(549\) −22.1847 24.8822i −0.946821 1.06194i
\(550\) 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
\(555\) 28.6080 + 3.21535i 1.21434 + 0.136484i
\(556\) 0 0
\(557\) −6.36471 8.09338i −0.269681 0.342928i 0.632284 0.774737i \(-0.282118\pi\)
−0.901965 + 0.431809i \(0.857875\pi\)
\(558\) 0 0
\(559\) 0.741082 + 15.5572i 0.0313444 + 0.658001i
\(560\) 0 0
\(561\) 4.00164 12.8306i 0.168949 0.541706i
\(562\) 0 0
\(563\) 1.76420 + 12.2703i 0.0743520 + 0.517130i 0.992629 + 0.121191i \(0.0386715\pi\)
−0.918277 + 0.395938i \(0.870419\pi\)
\(564\) 0 0
\(565\) 17.1930 + 29.7791i 0.723314 + 1.25282i
\(566\) 0 0
\(567\) −19.1160 + 17.5355i −0.802796 + 0.736421i
\(568\) 0 0
\(569\) −14.4597 10.2967i −0.606180 0.431659i 0.235318 0.971918i \(-0.424387\pi\)
−0.841499 + 0.540259i \(0.818326\pi\)
\(570\) 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
\(573\) −20.0395 + 33.4065i −0.837164 + 1.39558i
\(574\) 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
\(579\) 22.6052 25.2228i 0.939439 1.04822i
\(580\) 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
\(585\) 2.48031 + 15.6731i 0.102548 + 0.648002i
\(586\) 0 0
\(587\) −21.0887 16.5843i −0.870423 0.684508i 0.0795534 0.996831i \(-0.474651\pi\)
−0.949976 + 0.312323i \(0.898893\pi\)
\(588\) 0 0
\(589\) −9.55853 + 8.28252i −0.393853 + 0.341275i
\(590\) 0 0
\(591\) 8.83931 + 39.2930i 0.363600 + 1.61630i
\(592\) 0 0
\(593\) 10.4172 5.37044i 0.427783 0.220538i −0.230869 0.972985i \(-0.574157\pi\)
0.658653 + 0.752447i \(0.271127\pi\)
\(594\) 0 0
\(595\) −12.6818 + 3.72372i −0.519904 + 0.152658i
\(596\) 0 0
\(597\) −32.3977 13.6030i −1.32595 0.556735i
\(598\) 0 0
\(599\) −7.04181 + 20.3460i −0.287721 + 0.831315i 0.704818 + 0.709388i \(0.251028\pi\)
−0.992539 + 0.121927i \(0.961093\pi\)
\(600\) 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
\(603\) −15.5800 18.9806i −0.634465 0.772951i
\(604\) 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
\(609\) −4.04572 1.69870i −0.163941 0.0688349i
\(610\) 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
\(615\) 7.39666 + 32.8800i 0.298262 + 1.32585i
\(616\) 0 0
\(617\) 11.7828 10.2099i 0.474358 0.411034i −0.384597 0.923085i \(-0.625659\pi\)
0.858955 + 0.512051i \(0.171114\pi\)
\(618\) 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
\(621\) 3.78803 + 26.8362i 0.152009 + 1.07690i
\(622\) 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
\(627\) −18.1059 + 20.2025i −0.723080 + 0.806811i
\(628\) 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
\(633\) −7.23503 + 12.0610i −0.287567 + 0.479383i
\(634\) 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
\(639\) 11.2072 10.9930i 0.443348 0.434875i
\(640\) 0 0
\(641\) 18.7729 + 32.5157i 0.741487 + 1.28429i 0.951818 + 0.306663i \(0.0992123\pi\)
−0.210332 + 0.977630i \(0.567454\pi\)
\(642\) 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
\(645\) 12.7685 40.9400i 0.502761 1.61201i
\(646\) 0 0
\(647\) −1.31497 27.6046i −0.0516969 1.08525i −0.864475 0.502677i \(-0.832349\pi\)
0.812778 0.582574i \(-0.197954\pi\)
\(648\) 0 0
\(649\) −5.63595 7.16669i −0.221230 0.281317i
\(650\) 0 0
\(651\) −19.6571 2.20933i −0.770422 0.0865905i
\(652\) 0 0
\(653\) −0.0497588 0.143769i −0.00194721 0.00562611i 0.944023 0.329880i \(-0.107008\pi\)
−0.945970 + 0.324253i \(0.894887\pi\)
\(654\) 0 0
\(655\) 37.4748 17.1142i 1.46426 0.668707i
\(656\) 0 0
\(657\) 14.8874 13.2735i 0.580814 0.517849i
\(658\) 0 0
\(659\) −14.5115 36.2480i −0.565289 1.41202i −0.885483 0.464671i \(-0.846173\pi\)
0.320195 0.947352i \(-0.396252\pi\)
\(660\) 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
\(663\) 4.98086 0.391681i 0.193440 0.0152116i
\(664\) 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
\(675\) 3.39669 17.3830i 0.130739 0.669071i
\(676\) 0 0
\(677\) −7.29459 + 0.696549i −0.280354 + 0.0267706i −0.234286 0.972168i \(-0.575275\pi\)
−0.0460681 + 0.998938i \(0.514669\pi\)
\(678\) 0 0
\(679\) 8.62105 18.8775i 0.330846 0.724451i
\(680\) 0 0
\(681\) 12.0693 + 31.6727i 0.462496 + 1.21370i
\(682\) 0 0
\(683\) −19.8958 + 18.9706i −0.761292 + 0.725891i −0.967570 0.252603i \(-0.918713\pi\)
0.206278 + 0.978493i \(0.433865\pi\)
\(684\) 0 0
\(685\) −16.7673 36.7153i −0.640646 1.40282i
\(686\) 0 0
\(687\) −43.8533 + 14.3612i −1.67311 + 0.547912i
\(688\) 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
\(693\) −42.4245 + 0.600423i −1.61157 + 0.0228082i
\(694\) 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
\(699\) −1.01408 1.82631i −0.0383561 0.0690775i
\(700\) 0 0
\(701\) −10.2133 9.73839i −0.385752 0.367814i 0.472246 0.881467i \(-0.343443\pi\)
−0.857998 + 0.513653i \(0.828292\pi\)
\(702\) 0 0
\(703\) −10.6127 + 14.9035i −0.400266 + 0.562095i
\(704\) 0 0
\(705\) 50.8342 + 3.27438i 1.91453 + 0.123320i
\(706\) 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
\(711\) 7.77639 34.1575i 0.291638 1.28101i
\(712\) 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
\(717\) 17.4944 + 9.39257i 0.653339 + 0.350772i
\(718\) 0 0
\(719\) −2.79908 14.5230i −0.104388 0.541617i −0.996041 0.0888971i \(-0.971666\pi\)
0.891653 0.452720i \(-0.149546\pi\)
\(720\) 0 0
\(721\) 11.1722 14.2066i 0.416073 0.529080i
\(722\) 0 0
\(723\) −32.7510 39.0992i −1.21802 1.45412i
\(724\) 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
\(729\) −26.5380 + 4.97332i −0.982889 + 0.184197i
\(730\) 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
\(735\) 3.71946 + 5.41259i 0.137194 + 0.199646i
\(736\) 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
\(741\) −9.47368 3.45734i −0.348024 0.127009i
\(742\) 0 0
\(743\) −14.1770 + 35.4125i −0.520104 + 1.29916i 0.403209 + 0.915108i \(0.367895\pi\)
−0.923313 + 0.384049i \(0.874529\pi\)
\(744\) 0 0
\(745\) −14.1252 48.1059i −0.517506 1.76246i
\(746\) 0 0
\(747\) 0.203734 + 0.429909i 0.00745424 + 0.0157295i
\(748\) 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
\(753\) 36.2378 + 29.4917i 1.32058 + 1.07474i
\(754\) 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
\(759\) −24.5862 + 36.8857i −0.892424 + 1.33887i
\(760\) 0 0
\(761\) 19.6756 + 17.0490i 0.713240 + 0.618026i 0.933988 0.357305i \(-0.116304\pi\)
−0.220748 + 0.975331i \(0.570850\pi\)
\(762\) 0 0
\(763\) 0.636692 + 0.122712i 0.0230498 + 0.00444248i
\(764\) 0 0
\(765\) −13.2533 3.68861i −0.479173 0.133362i
\(766\) 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
\(771\) 1.45214 + 1.07111i 0.0522974 + 0.0385749i
\(772\) 0 0
\(773\) 14.5862 15.2976i 0.524630 0.550216i −0.407092 0.913387i \(-0.633457\pi\)
0.931723 + 0.363171i \(0.118306\pi\)