Properties

Label 1323.2.o.e.881.8
Level $1323$
Weight $2$
Character 1323.881
Analytic conductor $10.564$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.8
Character \(\chi\) \(=\) 1323.881
Dual form 1323.2.o.e.440.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.58658 + 0.916012i) q^{2} +(0.678156 - 1.17460i) q^{4} +(-0.322784 + 0.559079i) q^{5} -1.17925i q^{8} +O(q^{10})\) \(q+(-1.58658 + 0.916012i) q^{2} +(0.678156 - 1.17460i) q^{4} +(-0.322784 + 0.559079i) q^{5} -1.17925i q^{8} -1.18270i q^{10} +(-4.60375 + 2.65797i) q^{11} +(4.44045 + 2.56370i) q^{13} +(2.43652 + 4.22018i) q^{16} -1.62986 q^{17} -2.41378i q^{19} +(0.437796 + 0.758285i) q^{20} +(4.86947 - 8.43418i) q^{22} +(1.27442 + 0.735784i) q^{23} +(2.29162 + 3.96920i) q^{25} -9.39351 q^{26} +(6.43846 - 3.71724i) q^{29} +(-4.90799 - 2.83363i) q^{31} +(-5.68894 - 3.28451i) q^{32} +(2.58590 - 1.49297i) q^{34} -7.99471 q^{37} +(2.21105 + 3.82965i) q^{38} +(0.659294 + 0.380644i) q^{40} +(-5.99052 + 10.3759i) q^{41} +(-1.51281 - 2.62026i) q^{43} +7.21009i q^{44} -2.69595 q^{46} +(1.54176 + 2.67041i) q^{47} +(-7.27168 - 4.19830i) q^{50} +(6.02264 - 3.47717i) q^{52} -2.36199i q^{53} -3.43181i q^{55} +(-6.81008 + 11.7954i) q^{58} +(-1.47918 + 2.56202i) q^{59} +(-9.18018 + 5.30018i) q^{61} +10.3825 q^{62} +2.28853 q^{64} +(-2.86662 + 1.65504i) q^{65} +(5.07747 - 8.79444i) q^{67} +(-1.10530 + 1.91444i) q^{68} -4.76597i q^{71} +11.8055i q^{73} +(12.6842 - 7.32325i) q^{74} +(-2.83523 - 1.63692i) q^{76} +(-3.48104 - 6.02934i) q^{79} -3.14588 q^{80} -21.9496i q^{82} +(-3.51618 - 6.09021i) q^{83} +(0.526093 - 0.911221i) q^{85} +(4.80038 + 2.77150i) q^{86} +(3.13442 + 5.42898i) q^{88} -4.32674 q^{89} +(1.72850 - 0.997953i) q^{92} +(-4.89226 - 2.82455i) q^{94} +(1.34949 + 0.779129i) q^{95} +(-14.3946 + 8.31075i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{4} + O(q^{10}) \) \( 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.58658 + 0.916012i −1.12188 + 0.647718i −0.941880 0.335948i \(-0.890943\pi\)
−0.180001 + 0.983667i \(0.557610\pi\)
\(3\) 0 0
\(4\) 0.678156 1.17460i 0.339078 0.587300i
\(5\) −0.322784 + 0.559079i −0.144353 + 0.250028i −0.929132 0.369749i \(-0.879444\pi\)
0.784778 + 0.619777i \(0.212777\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.17925i 0.416928i
\(9\) 0 0
\(10\) 1.18270i 0.374002i
\(11\) −4.60375 + 2.65797i −1.38808 + 0.801410i −0.993099 0.117279i \(-0.962583\pi\)
−0.394983 + 0.918688i \(0.629250\pi\)
\(12\) 0 0
\(13\) 4.44045 + 2.56370i 1.23156 + 0.711041i 0.967355 0.253425i \(-0.0815572\pi\)
0.264205 + 0.964467i \(0.414890\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.43652 + 4.22018i 0.609130 + 1.05504i
\(17\) −1.62986 −0.395299 −0.197650 0.980273i \(-0.563331\pi\)
−0.197650 + 0.980273i \(0.563331\pi\)
\(18\) 0 0
\(19\) 2.41378i 0.553759i −0.960905 0.276879i \(-0.910700\pi\)
0.960905 0.276879i \(-0.0893002\pi\)
\(20\) 0.437796 + 0.758285i 0.0978942 + 0.169558i
\(21\) 0 0
\(22\) 4.86947 8.43418i 1.03818 1.79817i
\(23\) 1.27442 + 0.735784i 0.265734 + 0.153422i 0.626947 0.779062i \(-0.284304\pi\)
−0.361213 + 0.932483i \(0.617637\pi\)
\(24\) 0 0
\(25\) 2.29162 + 3.96920i 0.458324 + 0.793841i
\(26\) −9.39351 −1.84222
\(27\) 0 0
\(28\) 0 0
\(29\) 6.43846 3.71724i 1.19559 0.690275i 0.236022 0.971748i \(-0.424156\pi\)
0.959569 + 0.281473i \(0.0908229\pi\)
\(30\) 0 0
\(31\) −4.90799 2.83363i −0.881501 0.508935i −0.0103477 0.999946i \(-0.503294\pi\)
−0.871153 + 0.491012i \(0.836627\pi\)
\(32\) −5.68894 3.28451i −1.00567 0.580625i
\(33\) 0 0
\(34\) 2.58590 1.49297i 0.443479 0.256043i
\(35\) 0 0
\(36\) 0 0
\(37\) −7.99471 −1.31432 −0.657161 0.753750i \(-0.728243\pi\)
−0.657161 + 0.753750i \(0.728243\pi\)
\(38\) 2.21105 + 3.82965i 0.358680 + 0.621251i
\(39\) 0 0
\(40\) 0.659294 + 0.380644i 0.104244 + 0.0601851i
\(41\) −5.99052 + 10.3759i −0.935562 + 1.62044i −0.161934 + 0.986802i \(0.551773\pi\)
−0.773628 + 0.633640i \(0.781560\pi\)
\(42\) 0 0
\(43\) −1.51281 2.62026i −0.230701 0.399586i 0.727314 0.686305i \(-0.240769\pi\)
−0.958015 + 0.286719i \(0.907435\pi\)
\(44\) 7.21009i 1.08696i
\(45\) 0 0
\(46\) −2.69595 −0.397496
\(47\) 1.54176 + 2.67041i 0.224889 + 0.389520i 0.956286 0.292432i \(-0.0944646\pi\)
−0.731397 + 0.681952i \(0.761131\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −7.27168 4.19830i −1.02837 0.593730i
\(51\) 0 0
\(52\) 6.02264 3.47717i 0.835190 0.482197i
\(53\) 2.36199i 0.324444i −0.986754 0.162222i \(-0.948134\pi\)
0.986754 0.162222i \(-0.0518661\pi\)
\(54\) 0 0
\(55\) 3.43181i 0.462745i
\(56\) 0 0
\(57\) 0 0
\(58\) −6.81008 + 11.7954i −0.894207 + 1.54881i
\(59\) −1.47918 + 2.56202i −0.192573 + 0.333546i −0.946102 0.323868i \(-0.895017\pi\)
0.753529 + 0.657414i \(0.228350\pi\)
\(60\) 0 0
\(61\) −9.18018 + 5.30018i −1.17540 + 0.678618i −0.954946 0.296779i \(-0.904088\pi\)
−0.220455 + 0.975397i \(0.570754\pi\)
\(62\) 10.3825 1.31859
\(63\) 0 0
\(64\) 2.28853 0.286066
\(65\) −2.86662 + 1.65504i −0.355560 + 0.205283i
\(66\) 0 0
\(67\) 5.07747 8.79444i 0.620312 1.07441i −0.369116 0.929383i \(-0.620339\pi\)
0.989428 0.145028i \(-0.0463273\pi\)
\(68\) −1.10530 + 1.91444i −0.134037 + 0.232159i
\(69\) 0 0
\(70\) 0 0
\(71\) 4.76597i 0.565617i −0.959176 0.282808i \(-0.908734\pi\)
0.959176 0.282808i \(-0.0912661\pi\)
\(72\) 0 0
\(73\) 11.8055i 1.38173i 0.722982 + 0.690867i \(0.242771\pi\)
−0.722982 + 0.690867i \(0.757229\pi\)
\(74\) 12.6842 7.32325i 1.47451 0.851311i
\(75\) 0 0
\(76\) −2.83523 1.63692i −0.325223 0.187767i
\(77\) 0 0
\(78\) 0 0
\(79\) −3.48104 6.02934i −0.391648 0.678354i 0.601019 0.799235i \(-0.294762\pi\)
−0.992667 + 0.120881i \(0.961428\pi\)
\(80\) −3.14588 −0.351720
\(81\) 0 0
\(82\) 21.9496i 2.42392i
\(83\) −3.51618 6.09021i −0.385951 0.668487i 0.605949 0.795503i \(-0.292793\pi\)
−0.991901 + 0.127016i \(0.959460\pi\)
\(84\) 0 0
\(85\) 0.526093 0.911221i 0.0570628 0.0988357i
\(86\) 4.80038 + 2.77150i 0.517638 + 0.298859i
\(87\) 0 0
\(88\) 3.13442 + 5.42898i 0.334130 + 0.578731i
\(89\) −4.32674 −0.458633 −0.229317 0.973352i \(-0.573649\pi\)
−0.229317 + 0.973352i \(0.573649\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.72850 0.997953i 0.180209 0.104044i
\(93\) 0 0
\(94\) −4.89226 2.82455i −0.504598 0.291330i
\(95\) 1.34949 + 0.779129i 0.138455 + 0.0799370i
\(96\) 0 0
\(97\) −14.3946 + 8.31075i −1.46156 + 0.843829i −0.999083 0.0428048i \(-0.986371\pi\)
−0.462472 + 0.886634i \(0.653037\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 6.21631 0.621631
\(101\) −2.32577 4.02835i −0.231423 0.400836i 0.726804 0.686845i \(-0.241005\pi\)
−0.958227 + 0.286009i \(0.907671\pi\)
\(102\) 0 0
\(103\) −8.92382 5.15217i −0.879290 0.507658i −0.00886554 0.999961i \(-0.502822\pi\)
−0.870424 + 0.492303i \(0.836155\pi\)
\(104\) 3.02324 5.23641i 0.296453 0.513472i
\(105\) 0 0
\(106\) 2.16361 + 3.74749i 0.210149 + 0.363988i
\(107\) 0.308550i 0.0298287i 0.999889 + 0.0149143i \(0.00474756\pi\)
−0.999889 + 0.0149143i \(0.995252\pi\)
\(108\) 0 0
\(109\) −6.28845 −0.602324 −0.301162 0.953573i \(-0.597375\pi\)
−0.301162 + 0.953573i \(0.597375\pi\)
\(110\) 3.14358 + 5.44484i 0.299728 + 0.519145i
\(111\) 0 0
\(112\) 0 0
\(113\) −7.72869 4.46216i −0.727054 0.419765i 0.0902895 0.995916i \(-0.471221\pi\)
−0.817343 + 0.576151i \(0.804554\pi\)
\(114\) 0 0
\(115\) −0.822722 + 0.474999i −0.0767192 + 0.0442939i
\(116\) 10.0835i 0.936228i
\(117\) 0 0
\(118\) 5.41979i 0.498932i
\(119\) 0 0
\(120\) 0 0
\(121\) 8.62966 14.9470i 0.784515 1.35882i
\(122\) 9.71006 16.8183i 0.879107 1.52266i
\(123\) 0 0
\(124\) −6.65676 + 3.84328i −0.597795 + 0.345137i
\(125\) −6.18664 −0.553350
\(126\) 0 0
\(127\) −2.49989 −0.221829 −0.110915 0.993830i \(-0.535378\pi\)
−0.110915 + 0.993830i \(0.535378\pi\)
\(128\) 7.74695 4.47270i 0.684740 0.395335i
\(129\) 0 0
\(130\) 3.03208 5.25171i 0.265931 0.460605i
\(131\) −1.26725 + 2.19494i −0.110720 + 0.191773i −0.916061 0.401039i \(-0.868649\pi\)
0.805341 + 0.592812i \(0.201982\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 18.6041i 1.60715i
\(135\) 0 0
\(136\) 1.92202i 0.164812i
\(137\) −1.05041 + 0.606456i −0.0897429 + 0.0518131i −0.544200 0.838956i \(-0.683167\pi\)
0.454457 + 0.890769i \(0.349833\pi\)
\(138\) 0 0
\(139\) −6.11754 3.53196i −0.518883 0.299577i 0.217594 0.976039i \(-0.430179\pi\)
−0.736478 + 0.676462i \(0.763512\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4.36569 + 7.56159i 0.366360 + 0.634555i
\(143\) −27.2570 −2.27934
\(144\) 0 0
\(145\) 4.79947i 0.398574i
\(146\) −10.8140 18.7304i −0.894974 1.55014i
\(147\) 0 0
\(148\) −5.42166 + 9.39060i −0.445658 + 0.771902i
\(149\) −6.00270 3.46566i −0.491760 0.283918i 0.233544 0.972346i \(-0.424968\pi\)
−0.725304 + 0.688428i \(0.758301\pi\)
\(150\) 0 0
\(151\) −3.15939 5.47223i −0.257108 0.445323i 0.708358 0.705853i \(-0.249436\pi\)
−0.965466 + 0.260530i \(0.916103\pi\)
\(152\) −2.84645 −0.230878
\(153\) 0 0
\(154\) 0 0
\(155\) 3.16844 1.82930i 0.254495 0.146933i
\(156\) 0 0
\(157\) 1.72363 + 0.995139i 0.137561 + 0.0794208i 0.567201 0.823579i \(-0.308026\pi\)
−0.429640 + 0.903000i \(0.641360\pi\)
\(158\) 11.0459 + 6.37735i 0.878765 + 0.507355i
\(159\) 0 0
\(160\) 3.67260 2.12038i 0.290345 0.167631i
\(161\) 0 0
\(162\) 0 0
\(163\) −5.98729 −0.468961 −0.234480 0.972121i \(-0.575339\pi\)
−0.234480 + 0.972121i \(0.575339\pi\)
\(164\) 8.12502 + 14.0729i 0.634457 + 1.09891i
\(165\) 0 0
\(166\) 11.1574 + 6.44173i 0.865983 + 0.499976i
\(167\) 0.697990 1.20895i 0.0540121 0.0935516i −0.837755 0.546046i \(-0.816132\pi\)
0.891767 + 0.452494i \(0.149466\pi\)
\(168\) 0 0
\(169\) 6.64508 + 11.5096i 0.511160 + 0.885355i
\(170\) 1.92763i 0.147843i
\(171\) 0 0
\(172\) −4.10368 −0.312903
\(173\) −3.80506 6.59055i −0.289293 0.501071i 0.684348 0.729156i \(-0.260087\pi\)
−0.973641 + 0.228085i \(0.926754\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −22.4343 12.9524i −1.69105 0.976326i
\(177\) 0 0
\(178\) 6.86471 3.96334i 0.514532 0.297065i
\(179\) 9.24786i 0.691218i 0.938379 + 0.345609i \(0.112328\pi\)
−0.938379 + 0.345609i \(0.887672\pi\)
\(180\) 0 0
\(181\) 11.9634i 0.889234i −0.895721 0.444617i \(-0.853340\pi\)
0.895721 0.444617i \(-0.146660\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.867674 1.50286i 0.0639658 0.110792i
\(185\) 2.58057 4.46967i 0.189727 0.328617i
\(186\) 0 0
\(187\) 7.50347 4.33213i 0.548708 0.316797i
\(188\) 4.18223 0.305020
\(189\) 0 0
\(190\) −2.85477 −0.207107
\(191\) 17.5586 10.1375i 1.27050 0.733521i 0.295415 0.955369i \(-0.404542\pi\)
0.975081 + 0.221847i \(0.0712087\pi\)
\(192\) 0 0
\(193\) 8.44583 14.6286i 0.607944 1.05299i −0.383634 0.923485i \(-0.625328\pi\)
0.991579 0.129505i \(-0.0413389\pi\)
\(194\) 15.2255 26.3713i 1.09313 1.89335i
\(195\) 0 0
\(196\) 0 0
\(197\) 18.7102i 1.33305i 0.745484 + 0.666524i \(0.232219\pi\)
−0.745484 + 0.666524i \(0.767781\pi\)
\(198\) 0 0
\(199\) 18.0446i 1.27915i −0.768729 0.639574i \(-0.779111\pi\)
0.768729 0.639574i \(-0.220889\pi\)
\(200\) 4.68069 2.70240i 0.330975 0.191088i
\(201\) 0 0
\(202\) 7.38004 + 4.26087i 0.519258 + 0.299794i
\(203\) 0 0
\(204\) 0 0
\(205\) −3.86729 6.69834i −0.270103 0.467833i
\(206\) 18.8778 1.31528
\(207\) 0 0
\(208\) 24.9860i 1.73247i
\(209\) 6.41576 + 11.1124i 0.443788 + 0.768663i
\(210\) 0 0
\(211\) −4.03491 + 6.98868i −0.277775 + 0.481120i −0.970831 0.239763i \(-0.922930\pi\)
0.693057 + 0.720883i \(0.256264\pi\)
\(212\) −2.77440 1.60180i −0.190546 0.110012i
\(213\) 0 0
\(214\) −0.282636 0.489540i −0.0193206 0.0334642i
\(215\) 1.95324 0.133210
\(216\) 0 0
\(217\) 0 0
\(218\) 9.97713 5.76030i 0.675736 0.390137i
\(219\) 0 0
\(220\) −4.03101 2.32730i −0.271770 0.156907i
\(221\) −7.23732 4.17847i −0.486835 0.281074i
\(222\) 0 0
\(223\) −20.2450 + 11.6884i −1.35570 + 0.782716i −0.989041 0.147638i \(-0.952833\pi\)
−0.366662 + 0.930354i \(0.619500\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 16.3496 1.08756
\(227\) 7.22154 + 12.5081i 0.479310 + 0.830190i 0.999718 0.0237280i \(-0.00755356\pi\)
−0.520408 + 0.853918i \(0.674220\pi\)
\(228\) 0 0
\(229\) 11.3568 + 6.55685i 0.750479 + 0.433289i 0.825867 0.563865i \(-0.190686\pi\)
−0.0753881 + 0.997154i \(0.524020\pi\)
\(230\) 0.870209 1.50725i 0.0573799 0.0993849i
\(231\) 0 0
\(232\) −4.38357 7.59256i −0.287795 0.498476i
\(233\) 8.45202i 0.553710i −0.960912 0.276855i \(-0.910708\pi\)
0.960912 0.276855i \(-0.0892922\pi\)
\(234\) 0 0
\(235\) −1.99063 −0.129854
\(236\) 2.00623 + 3.47489i 0.130594 + 0.226196i
\(237\) 0 0
\(238\) 0 0
\(239\) 24.2111 + 13.9783i 1.56608 + 0.904179i 0.996619 + 0.0821642i \(0.0261832\pi\)
0.569466 + 0.822015i \(0.307150\pi\)
\(240\) 0 0
\(241\) −19.4058 + 11.2039i −1.25004 + 0.721710i −0.971117 0.238605i \(-0.923310\pi\)
−0.278921 + 0.960314i \(0.589977\pi\)
\(242\) 31.6195i 2.03258i
\(243\) 0 0
\(244\) 14.3774i 0.920418i
\(245\) 0 0
\(246\) 0 0
\(247\) 6.18819 10.7183i 0.393745 0.681987i
\(248\) −3.34156 + 5.78775i −0.212189 + 0.367523i
\(249\) 0 0
\(250\) 9.81559 5.66703i 0.620792 0.358415i
\(251\) 6.39587 0.403704 0.201852 0.979416i \(-0.435304\pi\)
0.201852 + 0.979416i \(0.435304\pi\)
\(252\) 0 0
\(253\) −7.82278 −0.491814
\(254\) 3.96627 2.28993i 0.248866 0.143683i
\(255\) 0 0
\(256\) −10.4826 + 18.1565i −0.655165 + 1.13478i
\(257\) 1.65705 2.87009i 0.103364 0.179031i −0.809705 0.586837i \(-0.800373\pi\)
0.913069 + 0.407806i \(0.133706\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 4.48950i 0.278427i
\(261\) 0 0
\(262\) 4.64326i 0.286862i
\(263\) −19.6502 + 11.3451i −1.21169 + 0.699567i −0.963126 0.269050i \(-0.913290\pi\)
−0.248559 + 0.968617i \(0.579957\pi\)
\(264\) 0 0
\(265\) 1.32054 + 0.762413i 0.0811200 + 0.0468347i
\(266\) 0 0
\(267\) 0 0
\(268\) −6.88664 11.9280i −0.420668 0.728619i
\(269\) 2.76100 0.168341 0.0841707 0.996451i \(-0.473176\pi\)
0.0841707 + 0.996451i \(0.473176\pi\)
\(270\) 0 0
\(271\) 6.08922i 0.369894i 0.982749 + 0.184947i \(0.0592113\pi\)
−0.982749 + 0.184947i \(0.940789\pi\)
\(272\) −3.97119 6.87830i −0.240789 0.417058i
\(273\) 0 0
\(274\) 1.11104 1.92438i 0.0671205 0.116256i
\(275\) −21.1001 12.1821i −1.27238 0.734611i
\(276\) 0 0
\(277\) 4.71684 + 8.16980i 0.283407 + 0.490876i 0.972222 0.234062i \(-0.0752019\pi\)
−0.688814 + 0.724938i \(0.741869\pi\)
\(278\) 12.9413 0.776167
\(279\) 0 0
\(280\) 0 0
\(281\) −4.57153 + 2.63938i −0.272715 + 0.157452i −0.630121 0.776497i \(-0.716995\pi\)
0.357406 + 0.933949i \(0.383661\pi\)
\(282\) 0 0
\(283\) 17.0346 + 9.83496i 1.01260 + 0.584628i 0.911953 0.410294i \(-0.134574\pi\)
0.100651 + 0.994922i \(0.467907\pi\)
\(284\) −5.59811 3.23207i −0.332187 0.191788i
\(285\) 0 0
\(286\) 43.2453 24.9677i 2.55715 1.47637i
\(287\) 0 0
\(288\) 0 0
\(289\) −14.3436 −0.843738
\(290\) −4.39637 7.61474i −0.258164 0.447153i
\(291\) 0 0
\(292\) 13.8668 + 8.00600i 0.811493 + 0.468516i
\(293\) −9.11647 + 15.7902i −0.532590 + 0.922473i 0.466686 + 0.884423i \(0.345448\pi\)
−0.999276 + 0.0380495i \(0.987886\pi\)
\(294\) 0 0
\(295\) −0.954912 1.65396i −0.0555971 0.0962970i
\(296\) 9.42778i 0.547979i
\(297\) 0 0
\(298\) 12.6983 0.735595
\(299\) 3.77265 + 6.53443i 0.218178 + 0.377896i
\(300\) 0 0
\(301\) 0 0
\(302\) 10.0253 + 5.78808i 0.576888 + 0.333067i
\(303\) 0 0
\(304\) 10.1866 5.88122i 0.584240 0.337311i
\(305\) 6.84326i 0.391844i
\(306\) 0 0
\(307\) 26.0447i 1.48645i 0.669042 + 0.743224i \(0.266704\pi\)
−0.669042 + 0.743224i \(0.733296\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −3.35132 + 5.80466i −0.190342 + 0.329683i
\(311\) 14.1433 24.4969i 0.801992 1.38909i −0.116311 0.993213i \(-0.537107\pi\)
0.918303 0.395878i \(-0.129560\pi\)
\(312\) 0 0
\(313\) 4.82891 2.78797i 0.272946 0.157586i −0.357280 0.933998i \(-0.616296\pi\)
0.630226 + 0.776412i \(0.282962\pi\)
\(314\) −3.64624 −0.205769
\(315\) 0 0
\(316\) −9.44276 −0.531197
\(317\) −29.0708 + 16.7841i −1.63278 + 0.942686i −0.649550 + 0.760319i \(0.725043\pi\)
−0.983230 + 0.182367i \(0.941624\pi\)
\(318\) 0 0
\(319\) −19.7607 + 34.2265i −1.10639 + 1.91632i
\(320\) −0.738701 + 1.27947i −0.0412947 + 0.0715244i
\(321\) 0 0
\(322\) 0 0
\(323\) 3.93412i 0.218901i
\(324\) 0 0
\(325\) 23.5001i 1.30355i
\(326\) 9.49931 5.48443i 0.526118 0.303755i
\(327\) 0 0
\(328\) 12.2358 + 7.06433i 0.675608 + 0.390063i
\(329\) 0 0
\(330\) 0 0
\(331\) 15.1867 + 26.3042i 0.834739 + 1.44581i 0.894243 + 0.447582i \(0.147715\pi\)
−0.0595042 + 0.998228i \(0.518952\pi\)
\(332\) −9.53809 −0.523470
\(333\) 0 0
\(334\) 2.55747i 0.139938i
\(335\) 3.27785 + 5.67741i 0.179088 + 0.310190i
\(336\) 0 0
\(337\) 1.86121 3.22371i 0.101387 0.175607i −0.810870 0.585227i \(-0.801005\pi\)
0.912256 + 0.409620i \(0.134339\pi\)
\(338\) −21.0859 12.1739i −1.14692 0.662175i
\(339\) 0 0
\(340\) −0.713547 1.23590i −0.0386975 0.0670261i
\(341\) 30.1268 1.63146
\(342\) 0 0
\(343\) 0 0
\(344\) −3.08995 + 1.78398i −0.166599 + 0.0961858i
\(345\) 0 0
\(346\) 12.0741 + 6.97096i 0.649105 + 0.374761i
\(347\) −6.18028 3.56818i −0.331775 0.191550i 0.324854 0.945764i \(-0.394685\pi\)
−0.656629 + 0.754214i \(0.728018\pi\)
\(348\) 0 0
\(349\) 13.2087 7.62607i 0.707047 0.408214i −0.102920 0.994690i \(-0.532818\pi\)
0.809967 + 0.586476i \(0.199485\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 34.9206 1.86127
\(353\) 17.2359 + 29.8534i 0.917373 + 1.58894i 0.803389 + 0.595455i \(0.203028\pi\)
0.113985 + 0.993482i \(0.463638\pi\)
\(354\) 0 0
\(355\) 2.66455 + 1.53838i 0.141420 + 0.0816487i
\(356\) −2.93420 + 5.08219i −0.155512 + 0.269355i
\(357\) 0 0
\(358\) −8.47115 14.6725i −0.447714 0.775464i
\(359\) 6.62557i 0.349684i −0.984596 0.174842i \(-0.944059\pi\)
0.984596 0.174842i \(-0.0559415\pi\)
\(360\) 0 0
\(361\) 13.1737 0.693351
\(362\) 10.9586 + 18.9809i 0.575973 + 0.997614i
\(363\) 0 0
\(364\) 0 0
\(365\) −6.60022 3.81064i −0.345472 0.199458i
\(366\) 0 0
\(367\) −2.68222 + 1.54858i −0.140011 + 0.0808352i −0.568369 0.822774i \(-0.692425\pi\)
0.428358 + 0.903609i \(0.359092\pi\)
\(368\) 7.17101i 0.373815i
\(369\) 0 0
\(370\) 9.45532i 0.491559i
\(371\) 0 0
\(372\) 0 0
\(373\) −4.84999 + 8.40043i −0.251123 + 0.434958i −0.963835 0.266499i \(-0.914133\pi\)
0.712712 + 0.701457i \(0.247467\pi\)
\(374\) −7.93657 + 13.7465i −0.410390 + 0.710816i
\(375\) 0 0
\(376\) 3.14909 1.81813i 0.162402 0.0937628i
\(377\) 38.1195 1.96326
\(378\) 0 0
\(379\) 7.76103 0.398657 0.199329 0.979933i \(-0.436124\pi\)
0.199329 + 0.979933i \(0.436124\pi\)
\(380\) 1.83033 1.05674i 0.0938941 0.0542098i
\(381\) 0 0
\(382\) −18.5721 + 32.1678i −0.950231 + 1.64585i
\(383\) −12.3063 + 21.3152i −0.628825 + 1.08916i 0.358963 + 0.933352i \(0.383130\pi\)
−0.987788 + 0.155804i \(0.950203\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 30.9459i 1.57511i
\(387\) 0 0
\(388\) 22.5440i 1.14450i
\(389\) −5.56578 + 3.21340i −0.282196 + 0.162926i −0.634417 0.772991i \(-0.718760\pi\)
0.352221 + 0.935917i \(0.385427\pi\)
\(390\) 0 0
\(391\) −2.07712 1.19923i −0.105044 0.0606474i
\(392\) 0 0
\(393\) 0 0
\(394\) −17.1388 29.6852i −0.863439 1.49552i
\(395\) 4.49450 0.226143
\(396\) 0 0
\(397\) 13.2600i 0.665498i 0.943015 + 0.332749i \(0.107976\pi\)
−0.943015 + 0.332749i \(0.892024\pi\)
\(398\) 16.5291 + 28.6292i 0.828528 + 1.43505i
\(399\) 0 0
\(400\) −11.1672 + 19.3421i −0.558358 + 0.967105i
\(401\) 13.6877 + 7.90259i 0.683530 + 0.394636i 0.801184 0.598418i \(-0.204204\pi\)
−0.117653 + 0.993055i \(0.537537\pi\)
\(402\) 0 0
\(403\) −14.5291 25.1652i −0.723747 1.25357i
\(404\) −6.30894 −0.313882
\(405\) 0 0
\(406\) 0 0
\(407\) 36.8056 21.2497i 1.82439 1.05331i
\(408\) 0 0
\(409\) 4.69257 + 2.70926i 0.232033 + 0.133964i 0.611509 0.791237i \(-0.290563\pi\)
−0.379477 + 0.925201i \(0.623896\pi\)
\(410\) 12.2715 + 7.08497i 0.606048 + 0.349902i
\(411\) 0 0
\(412\) −12.1035 + 6.98795i −0.596296 + 0.344271i
\(413\) 0 0
\(414\) 0 0
\(415\) 4.53987 0.222854
\(416\) −16.8410 29.1694i −0.825697 1.43015i
\(417\) 0 0
\(418\) −20.3582 11.7538i −0.995754 0.574899i
\(419\) −12.2469 + 21.2123i −0.598302 + 1.03629i 0.394770 + 0.918780i \(0.370824\pi\)
−0.993072 + 0.117509i \(0.962509\pi\)
\(420\) 0 0
\(421\) 5.99347 + 10.3810i 0.292104 + 0.505939i 0.974307 0.225224i \(-0.0723113\pi\)
−0.682203 + 0.731163i \(0.738978\pi\)
\(422\) 14.7841i 0.719680i
\(423\) 0 0
\(424\) −2.78538 −0.135270
\(425\) −3.73502 6.46925i −0.181175 0.313805i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.362424 + 0.209245i 0.0175184 + 0.0101143i
\(429\) 0 0
\(430\) −3.09897 + 1.78919i −0.149446 + 0.0862825i
\(431\) 30.8219i 1.48464i −0.670046 0.742320i \(-0.733726\pi\)
0.670046 0.742320i \(-0.266274\pi\)
\(432\) 0 0
\(433\) 6.06173i 0.291308i −0.989336 0.145654i \(-0.953471\pi\)
0.989336 0.145654i \(-0.0465287\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.26455 + 7.38642i −0.204235 + 0.353745i
\(437\) 1.77602 3.07616i 0.0849585 0.147152i
\(438\) 0 0
\(439\) 23.5081 13.5724i 1.12198 0.647776i 0.180075 0.983653i \(-0.442366\pi\)
0.941906 + 0.335877i \(0.109033\pi\)
\(440\) −4.04697 −0.192932
\(441\) 0 0
\(442\) 15.3101 0.728228
\(443\) 4.63465 2.67582i 0.220199 0.127132i −0.385843 0.922564i \(-0.626090\pi\)
0.606042 + 0.795432i \(0.292756\pi\)
\(444\) 0 0
\(445\) 1.39660 2.41899i 0.0662053 0.114671i
\(446\) 21.4135 37.0893i 1.01396 1.75623i
\(447\) 0 0
\(448\) 0 0
\(449\) 34.2418i 1.61597i −0.589204 0.807985i \(-0.700558\pi\)
0.589204 0.807985i \(-0.299442\pi\)
\(450\) 0 0
\(451\) 63.6906i 2.99907i
\(452\) −10.4825 + 6.05208i −0.493056 + 0.284666i
\(453\) 0 0
\(454\) −22.9151 13.2300i −1.07546 0.620916i
\(455\) 0 0
\(456\) 0 0
\(457\) 7.93019 + 13.7355i 0.370958 + 0.642519i 0.989713 0.143065i \(-0.0456959\pi\)
−0.618755 + 0.785584i \(0.712363\pi\)
\(458\) −24.0246 −1.12260
\(459\) 0 0
\(460\) 1.28849i 0.0600763i
\(461\) −6.50676 11.2700i −0.303050 0.524898i 0.673775 0.738936i \(-0.264672\pi\)
−0.976825 + 0.214038i \(0.931338\pi\)
\(462\) 0 0
\(463\) −6.01941 + 10.4259i −0.279746 + 0.484534i −0.971321 0.237770i \(-0.923583\pi\)
0.691576 + 0.722304i \(0.256917\pi\)
\(464\) 31.3749 + 18.1143i 1.45654 + 0.840935i
\(465\) 0 0
\(466\) 7.74215 + 13.4098i 0.358648 + 0.621197i
\(467\) −20.3457 −0.941486 −0.470743 0.882270i \(-0.656014\pi\)
−0.470743 + 0.882270i \(0.656014\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 3.15829 1.82344i 0.145681 0.0841090i
\(471\) 0 0
\(472\) 3.02126 + 1.74433i 0.139065 + 0.0802891i
\(473\) 13.9292 + 8.04201i 0.640464 + 0.369772i
\(474\) 0 0
\(475\) 9.58078 5.53146i 0.439596 0.253801i
\(476\) 0 0
\(477\) 0 0
\(478\) −51.2171 −2.34261
\(479\) −12.1492 21.0430i −0.555109 0.961477i −0.997895 0.0648499i \(-0.979343\pi\)
0.442786 0.896627i \(-0.353990\pi\)
\(480\) 0 0
\(481\) −35.5001 20.4960i −1.61867 0.934538i
\(482\) 20.5259 35.5519i 0.934929 1.61934i
\(483\) 0 0
\(484\) −11.7045 20.2728i −0.532023 0.921491i
\(485\) 10.7303i 0.487239i
\(486\) 0 0
\(487\) −27.3091 −1.23749 −0.618747 0.785590i \(-0.712359\pi\)
−0.618747 + 0.785590i \(0.712359\pi\)
\(488\) 6.25025 + 10.8257i 0.282935 + 0.490058i
\(489\) 0 0
\(490\) 0 0
\(491\) 13.2899 + 7.67290i 0.599763 + 0.346273i 0.768948 0.639311i \(-0.220780\pi\)
−0.169185 + 0.985584i \(0.554114\pi\)
\(492\) 0 0
\(493\) −10.4938 + 6.05859i −0.472616 + 0.272865i
\(494\) 22.6738i 1.02014i
\(495\) 0 0
\(496\) 27.6168i 1.24003i
\(497\) 0 0
\(498\) 0 0
\(499\) 5.15504 8.92879i 0.230771 0.399707i −0.727264 0.686358i \(-0.759208\pi\)
0.958035 + 0.286650i \(0.0925418\pi\)
\(500\) −4.19551 + 7.26683i −0.187629 + 0.324982i
\(501\) 0 0
\(502\) −10.1476 + 5.85869i −0.452907 + 0.261486i
\(503\) −24.6770 −1.10029 −0.550146 0.835068i \(-0.685428\pi\)
−0.550146 + 0.835068i \(0.685428\pi\)
\(504\) 0 0
\(505\) 3.00289 0.133627
\(506\) 12.4115 7.16576i 0.551757 0.318557i
\(507\) 0 0
\(508\) −1.69531 + 2.93637i −0.0752174 + 0.130280i
\(509\) −2.58601 + 4.47911i −0.114623 + 0.198533i −0.917629 0.397438i \(-0.869899\pi\)
0.803006 + 0.595971i \(0.203233\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 20.5181i 0.906778i
\(513\) 0 0
\(514\) 6.07150i 0.267802i
\(515\) 5.76093 3.32608i 0.253857 0.146564i
\(516\) 0 0
\(517\) −14.1958 8.19594i −0.624330 0.360457i
\(518\) 0 0
\(519\) 0 0
\(520\) 1.95171 + 3.38046i 0.0855882 + 0.148243i
\(521\) 38.3328 1.67939 0.839696 0.543058i \(-0.182733\pi\)
0.839696 + 0.543058i \(0.182733\pi\)
\(522\) 0 0
\(523\) 27.3050i 1.19396i 0.802255 + 0.596982i \(0.203634\pi\)
−0.802255 + 0.596982i \(0.796366\pi\)
\(524\) 1.71878 + 2.97702i 0.0750855 + 0.130052i
\(525\) 0 0
\(526\) 20.7844 35.9997i 0.906245 1.56966i
\(527\) 7.99934 + 4.61842i 0.348457 + 0.201182i
\(528\) 0 0
\(529\) −10.4172 18.0432i −0.452924 0.784487i
\(530\) −2.79352 −0.121343
\(531\) 0 0
\(532\) 0 0
\(533\) −53.2012 + 30.7158i −2.30440 + 1.33045i
\(534\) 0 0
\(535\) −0.172504 0.0995952i −0.00745799 0.00430588i
\(536\) −10.3709 5.98762i −0.447953 0.258626i
\(537\) 0 0
\(538\) −4.38055 + 2.52911i −0.188859 + 0.109038i
\(539\) 0 0
\(540\) 0 0
\(541\) 19.5610 0.840995 0.420498 0.907294i \(-0.361856\pi\)
0.420498 + 0.907294i \(0.361856\pi\)
\(542\) −5.57779 9.66102i −0.239587 0.414977i
\(543\) 0 0
\(544\) 9.27219 + 5.35330i 0.397542 + 0.229521i
\(545\) 2.02981 3.51574i 0.0869476 0.150598i
\(546\) 0 0
\(547\) 12.6246 + 21.8665i 0.539790 + 0.934944i 0.998915 + 0.0465723i \(0.0148298\pi\)
−0.459125 + 0.888372i \(0.651837\pi\)
\(548\) 1.64509i 0.0702747i
\(549\) 0 0
\(550\) 44.6359 1.90328
\(551\) −8.97260 15.5410i −0.382246 0.662069i
\(552\) 0 0
\(553\) 0 0
\(554\) −14.9673 8.64136i −0.635898 0.367136i
\(555\) 0 0
\(556\) −8.29730 + 4.79045i −0.351884 + 0.203160i
\(557\) 33.2789i 1.41007i −0.709171 0.705036i \(-0.750931\pi\)
0.709171 0.705036i \(-0.249069\pi\)
\(558\) 0 0
\(559\) 15.5135i 0.656152i
\(560\) 0 0
\(561\) 0 0
\(562\) 4.83540 8.37516i 0.203969 0.353285i
\(563\) −15.2587 + 26.4289i −0.643079 + 1.11385i 0.341663 + 0.939823i \(0.389010\pi\)
−0.984742 + 0.174023i \(0.944323\pi\)
\(564\) 0 0
\(565\) 4.98940 2.88063i 0.209905 0.121189i
\(566\) −36.0358 −1.51470
\(567\) 0 0
\(568\) −5.62028 −0.235822
\(569\) −13.4044 + 7.73906i −0.561943 + 0.324438i −0.753925 0.656960i \(-0.771842\pi\)
0.191982 + 0.981398i \(0.438509\pi\)
\(570\) 0 0
\(571\) 12.2042 21.1384i 0.510731 0.884613i −0.489191 0.872177i \(-0.662708\pi\)
0.999923 0.0124362i \(-0.00395868\pi\)
\(572\) −18.4845 + 32.0160i −0.772875 + 1.33866i
\(573\) 0 0
\(574\) 0 0
\(575\) 6.74455i 0.281267i
\(576\) 0 0
\(577\) 14.6533i 0.610024i −0.952349 0.305012i \(-0.901340\pi\)
0.952349 0.305012i \(-0.0986605\pi\)
\(578\) 22.7572 13.1389i 0.946574 0.546505i
\(579\) 0 0
\(580\) 5.63746 + 3.25479i 0.234083 + 0.135148i
\(581\) 0 0
\(582\) 0 0
\(583\) 6.27811 + 10.8740i 0.260013 + 0.450355i
\(584\) 13.9217 0.576084
\(585\) 0 0
\(586\) 33.4032i 1.37987i
\(587\) −11.6129 20.1141i −0.479314 0.830197i 0.520404 0.853920i \(-0.325781\pi\)
−0.999719 + 0.0237232i \(0.992448\pi\)
\(588\) 0 0
\(589\) −6.83975 + 11.8468i −0.281827 + 0.488139i
\(590\) 3.03009 + 1.74942i 0.124747 + 0.0720225i
\(591\) 0 0
\(592\) −19.4793 33.7391i −0.800594 1.38667i
\(593\) −11.1121 −0.456319 −0.228160 0.973624i \(-0.573271\pi\)
−0.228160 + 0.973624i \(0.573271\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −8.14153 + 4.70051i −0.333490 + 0.192541i
\(597\) 0 0
\(598\) −11.9712 6.91159i −0.489540 0.282636i
\(599\) 13.5581 + 7.82776i 0.553968 + 0.319833i 0.750721 0.660620i \(-0.229706\pi\)
−0.196753 + 0.980453i \(0.563040\pi\)
\(600\) 0 0
\(601\) −30.5665 + 17.6476i −1.24684 + 0.719861i −0.970477 0.241194i \(-0.922461\pi\)
−0.276358 + 0.961055i \(0.589128\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −8.57024 −0.348718
\(605\) 5.57104 + 9.64932i 0.226495 + 0.392301i
\(606\) 0 0
\(607\) −33.6062 19.4025i −1.36403 0.787524i −0.373874 0.927479i \(-0.621971\pi\)
−0.990158 + 0.139955i \(0.955304\pi\)
\(608\) −7.92809 + 13.7318i −0.321526 + 0.556900i
\(609\) 0 0
\(610\) 6.26850 + 10.8574i 0.253804 + 0.439602i
\(611\) 15.8105i 0.639623i
\(612\) 0 0
\(613\) 31.7572 1.28266 0.641330 0.767265i \(-0.278383\pi\)
0.641330 + 0.767265i \(0.278383\pi\)
\(614\) −23.8572 41.3220i −0.962800 1.66762i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.25518 0.724680i −0.0505317 0.0291745i 0.474521 0.880244i \(-0.342621\pi\)
−0.525053 + 0.851070i \(0.675955\pi\)
\(618\) 0 0
\(619\) 25.2590 14.5833i 1.01524 0.586152i 0.102522 0.994731i \(-0.467309\pi\)
0.912723 + 0.408579i \(0.133976\pi\)
\(620\) 4.96220i 0.199287i
\(621\) 0 0
\(622\) 51.8217i 2.07786i
\(623\) 0 0
\(624\) 0 0
\(625\) −9.46116 + 16.3872i −0.378446 + 0.655488i
\(626\) −5.10764 + 8.84668i −0.204142 + 0.353585i
\(627\) 0 0
\(628\) 2.33778 1.34972i 0.0932877 0.0538597i
\(629\) 13.0303 0.519551
\(630\) 0 0
\(631\) 11.7428 0.467473 0.233736 0.972300i \(-0.424905\pi\)
0.233736 + 0.972300i \(0.424905\pi\)
\(632\) −7.11011 + 4.10503i −0.282825 + 0.163289i
\(633\) 0 0
\(634\) 30.7488 53.2585i 1.22119 2.11516i
\(635\) 0.806924 1.39763i 0.0320218 0.0554634i
\(636\) 0 0
\(637\) 0 0
\(638\) 72.4041i 2.86651i
\(639\) 0 0
\(640\) 5.77487i 0.228272i
\(641\) 10.0267 5.78891i 0.396030 0.228648i −0.288740 0.957408i \(-0.593236\pi\)
0.684770 + 0.728760i \(0.259903\pi\)
\(642\) 0 0
\(643\) 13.1240 + 7.57712i 0.517558 + 0.298812i 0.735935 0.677052i \(-0.236743\pi\)
−0.218377 + 0.975865i \(0.570076\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.60370 6.24180i −0.141786 0.245580i
\(647\) −12.4411 −0.489111 −0.244556 0.969635i \(-0.578642\pi\)
−0.244556 + 0.969635i \(0.578642\pi\)
\(648\) 0 0
\(649\) 15.7265i 0.617319i
\(650\) −21.5264 37.2847i −0.844333 1.46243i
\(651\) 0 0
\(652\) −4.06032 + 7.03268i −0.159014 + 0.275421i
\(653\) 3.97013 + 2.29216i 0.155363 + 0.0896990i 0.575666 0.817685i \(-0.304743\pi\)
−0.420303 + 0.907384i \(0.638076\pi\)
\(654\) 0 0
\(655\) −0.818096 1.41698i −0.0319656 0.0553661i
\(656\) −58.3841 −2.27952
\(657\) 0 0
\(658\) 0 0
\(659\) −15.6110 + 9.01301i −0.608118 + 0.351097i −0.772228 0.635345i \(-0.780858\pi\)
0.164111 + 0.986442i \(0.447525\pi\)
\(660\) 0 0
\(661\) −0.554932 0.320390i −0.0215844 0.0124617i 0.489169 0.872189i \(-0.337300\pi\)
−0.510753 + 0.859727i \(0.670633\pi\)
\(662\) −48.1899 27.8225i −1.87296 1.08135i
\(663\) 0 0
\(664\) −7.18189 + 4.14647i −0.278711 + 0.160914i
\(665\) 0 0
\(666\) 0 0
\(667\) 10.9404 0.423612
\(668\) −0.946692 1.63972i −0.0366286 0.0634426i
\(669\) 0 0
\(670\) −10.4012 6.00511i −0.401832 0.231998i
\(671\) 28.1755 48.8014i 1.08770 1.88396i
\(672\) 0 0
\(673\) −11.0695 19.1729i −0.426697 0.739061i 0.569880 0.821728i \(-0.306990\pi\)
−0.996577 + 0.0826667i \(0.973656\pi\)
\(674\) 6.81956i 0.262680i
\(675\) 0 0
\(676\) 18.0256 0.693292
\(677\) 10.0160 + 17.3482i 0.384947 + 0.666747i 0.991762 0.128096i \(-0.0408865\pi\)
−0.606815 + 0.794843i \(0.707553\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.07456 0.620397i −0.0412074 0.0237911i
\(681\) 0 0
\(682\) −47.7986 + 27.5966i −1.83030 + 1.05673i
\(683\) 20.9366i 0.801116i 0.916271 + 0.400558i \(0.131184\pi\)
−0.916271 + 0.400558i \(0.868816\pi\)
\(684\) 0 0
\(685\) 0.783018i 0.0299176i
\(686\) 0 0
\(687\) 0 0
\(688\) 7.37198 12.7686i 0.281054 0.486800i
\(689\) 6.05543 10.4883i 0.230693 0.399573i
\(690\) 0 0
\(691\) 1.33430 0.770358i 0.0507591 0.0293058i −0.474406 0.880306i \(-0.657337\pi\)
0.525165 + 0.851001i \(0.324004\pi\)
\(692\) −10.3217 −0.392372
\(693\) 0 0
\(694\) 13.0740 0.496282
\(695\) 3.94929 2.28012i 0.149805 0.0864900i
\(696\) 0 0
\(697\) 9.76372 16.9113i 0.369827 0.640560i
\(698\) −13.9711 + 24.1987i −0.528815 + 0.915935i
\(699\) 0 0
\(700\) 0 0
\(701\) 31.6641i 1.19593i 0.801520 + 0.597967i \(0.204025\pi\)
−0.801520 + 0.597967i \(0.795975\pi\)
\(702\) 0 0
\(703\) 19.2975i 0.727818i
\(704\) −10.5358 + 6.08286i −0.397083 + 0.229256i
\(705\) 0 0
\(706\) −54.6922 31.5766i −2.05837 1.18840i
\(707\) 0 0
\(708\) 0 0
\(709\) −11.1762 19.3578i −0.419732 0.726996i 0.576181 0.817322i \(-0.304542\pi\)
−0.995912 + 0.0903259i \(0.971209\pi\)
\(710\) −5.63670 −0.211542
\(711\) 0 0
\(712\) 5.10231i 0.191217i
\(713\) −4.16988 7.22244i −0.156163 0.270482i
\(714\) 0 0
\(715\) 8.79812 15.2388i 0.329031 0.569898i
\(716\) 10.8625 + 6.27149i 0.405952 + 0.234377i
\(717\) 0 0
\(718\) 6.06910 + 10.5120i 0.226497 + 0.392304i
\(719\) 38.9087 1.45105 0.725525 0.688195i \(-0.241597\pi\)
0.725525 + 0.688195i \(0.241597\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −20.9011 + 12.0672i −0.777858 + 0.449096i
\(723\) 0 0
\(724\) −14.0522 8.11306i −0.522247 0.301520i
\(725\) 29.5090 + 17.0370i 1.09594 + 0.632739i
\(726\) 0 0
\(727\) 11.4647 6.61915i 0.425202 0.245491i −0.272098 0.962269i \(-0.587718\pi\)
0.697301 + 0.716779i \(0.254384\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 13.9624 0.516771
\(731\) 2.46567 + 4.27066i 0.0911960 + 0.157956i
\(732\) 0 0
\(733\) 28.1222 + 16.2364i 1.03872 + 0.599704i 0.919470 0.393161i \(-0.128618\pi\)
0.119248 + 0.992865i \(0.461952\pi\)
\(734\) 2.83703 4.91389i 0.104717 0.181375i
\(735\) 0 0
\(736\) −4.83338 8.37167i −0.178161 0.308584i
\(737\) 53.9832i 1.98850i
\(738\) 0 0
\(739\) −13.8393 −0.509087 −0.254543 0.967061i \(-0.581925\pi\)
−0.254543 + 0.967061i \(0.581925\pi\)
\(740\) −3.50005 6.06227i −0.128665 0.222854i
\(741\) 0 0
\(742\) 0 0
\(743\) −31.8593 18.3940i −1.16880 0.674810i −0.215406 0.976525i \(-0.569108\pi\)
−0.953398 + 0.301715i \(0.902441\pi\)
\(744\) 0 0
\(745\) 3.87515 2.23732i 0.141975 0.0819690i
\(746\) 17.7706i 0.650628i
\(747\) 0 0
\(748\) 11.7514i 0.429675i
\(749\) 0 0
\(750\) 0 0
\(751\) 1.82952 3.16883i 0.0667602 0.115632i −0.830713 0.556701i \(-0.812067\pi\)
0.897473 + 0.441068i \(0.145400\pi\)
\(752\) −7.51308 + 13.0130i −0.273974 + 0.474537i
\(753\) 0 0
\(754\) −60.4797 + 34.9180i −2.20254 + 1.27164i
\(755\) 4.07921 0.148458
\(756\) 0 0
\(757\) 13.8901 0.504842 0.252421 0.967617i \(-0.418773\pi\)
0.252421 + 0.967617i \(0.418773\pi\)
\(758\) −12.3135 + 7.10920i −0.447246 + 0.258218i
\(759\) 0 0
\(760\) 0.918790 1.59139i 0.0333280 0.0577258i
\(761\) −6.82083 + 11.8140i −0.247255 + 0.428258i −0.962763 0.270346i \(-0.912862\pi\)
0.715508 + 0.698604i \(0.246195\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 27.4991i 0.994884i
\(765\) 0 0
\(766\) 45.0910i 1.62920i
\(767\) −13.1365 + 7.58434i −0.474330 + 0.273855i
\(768\) 0 0
\(769\) 22.9328 + 13.2402i 0.826976 + 0.477455i 0.852816 0.522211i \(-0.174893\pi\)
−0.0258399 + 0.999666i \(0.508226\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −11.4552 19.8410i −0.412281 0.714092i
\(773\) 26.2218 0.943132 0.471566 0.881831i \(-0.343689\pi\)
0.471566 + 0.881831i \(0.343689\pi\)
\(774\) 0 0
\(775\) 25.9744i 0.933028i
\(776\) 9.80047 + 16.9749i 0.351816 + 0.609364i
\(777\) 0 0
\(778\) 5.88703 10.1966i 0.211060 0.365567i
\(779\) 25.0451 + 14.4598i 0.897334 + 0.518076i
\(780\) 0 0
\(781\) 12.6678 + 21.9413i 0.453291 + 0.785123i
\(782\) 4.39402 0.157130
\(783\) 0 0
\(784\) 0 0
\(785\) −1.11272 + 0.642430i −0.0397148 + 0.0229293i
\(786\) 0 0
\(787\) −25.1554 14.5235i −0.896694 0.517706i −0.0205676 0.999788i \(-0.506547\pi\)
−0.876126 + 0.482082i \(0.839881\pi\)
\(788\) 21.9770 + 12.6884i 0.782899 + 0.452007i
\(789\) 0 0
\(790\) −7.13088 + 4.11702i −0.253705 + 0.146477i
\(791\) 0 0
\(792\) 0 0
\(793\) −54.3522 −1.93010
\(794\) −12.1463 21.0380i −0.431055 0.746610i
\(795\) 0 0
\(796\) −21.1952 12.2371i