Properties

Label 1323.2.o.e.440.7
Level $1323$
Weight $2$
Character 1323.440
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 440.7
Character \(\chi\) \(=\) 1323.440
Dual form 1323.2.o.e.881.7

$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

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

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 −0.180001 0.983667i \(-0.557610\pi\)
−0.941880 + 0.335948i \(0.890943\pi\)
\(3\) 0 0
\(4\) 0.678156 + 1.17460i 0.339078 + 0.587300i
\(5\) 0.322784 + 0.559079i 0.144353 + 0.250028i 0.929132 0.369749i \(-0.120556\pi\)
−0.784778 + 0.619777i \(0.787223\pi\)
\(6\) 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 −0.394983 0.918688i \(-0.629250\pi\)
−0.993099 + 0.117279i \(0.962583\pi\)
\(12\) 0 0
\(13\) −4.44045 + 2.56370i −1.23156 + 0.711041i −0.967355 0.253425i \(-0.918443\pi\)
−0.264205 + 0.964467i \(0.585110\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.43652 4.22018i 0.609130 1.05504i
\(17\) 1.62986 0.395299 0.197650 0.980273i \(-0.436669\pi\)
0.197650 + 0.980273i \(0.436669\pi\)
\(18\) 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 −0.361213 0.932483i \(-0.617637\pi\)
0.626947 + 0.779062i \(0.284304\pi\)
\(24\) 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 0.959569 0.281473i \(-0.0908229\pi\)
0.236022 + 0.971748i \(0.424156\pi\)
\(30\) 0 0
\(31\) 4.90799 2.83363i 0.881501 0.508935i 0.0103477 0.999946i \(-0.496706\pi\)
0.871153 + 0.491012i \(0.163373\pi\)
\(32\) −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 0.773628 + 0.633640i \(0.218440\pi\)
0.161934 + 0.986802i \(0.448227\pi\)
\(42\) 0 0
\(43\) −1.51281 + 2.62026i −0.230701 + 0.399586i −0.958015 0.286719i \(-0.907435\pi\)
0.727314 + 0.686305i \(0.240769\pi\)
\(44\) 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 \(-0.905535\pi\)
0.731397 + 0.681952i \(0.238869\pi\)
\(48\) 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 \(0.0518661\pi\)
−0.986754 + 0.162222i \(0.948134\pi\)
\(54\) 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 \(-0.104983\pi\)
−0.753529 + 0.657414i \(0.771650\pi\)
\(60\) 0 0
\(61\) 9.18018 + 5.30018i 1.17540 + 0.678618i 0.954946 0.296779i \(-0.0959124\pi\)
0.220455 + 0.975397i \(0.429246\pi\)
\(62\) −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 0.989428 + 0.145028i \(0.0463273\pi\)
−0.369116 + 0.929383i \(0.620339\pi\)
\(68\) 1.10530 + 1.91444i 0.134037 + 0.232159i
\(69\) 0 0
\(70\) 0 0
\(71\) 4.76597i 0.565617i 0.959176 + 0.282808i \(0.0912661\pi\)
−0.959176 + 0.282808i \(0.908734\pi\)
\(72\) 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 −0.992667 0.120881i \(-0.961428\pi\)
0.601019 + 0.799235i \(0.294762\pi\)
\(80\) 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 \(-0.707207\pi\)
0.991901 + 0.127016i \(0.0405399\pi\)
\(84\) 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 \(-0.426351\pi\)
0.229317 + 0.973352i \(0.426351\pi\)
\(90\) 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 \(-0.0136294\pi\)
0.462472 + 0.886634i \(0.346963\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 6.21631 0.621631
\(101\) 2.32577 4.02835i 0.231423 0.400836i −0.726804 0.686845i \(-0.758995\pi\)
0.958227 + 0.286009i \(0.0923286\pi\)
\(102\) 0 0
\(103\) 8.92382 5.15217i 0.879290 0.507658i 0.00886554 0.999961i \(-0.497178\pi\)
0.870424 + 0.492303i \(0.163845\pi\)
\(104\) −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 \(-0.995252\pi\)
0.999889 0.0149143i \(-0.00474756\pi\)
\(108\) 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 −0.817343 0.576151i \(-0.804554\pi\)
0.0902895 + 0.995916i \(0.471221\pi\)
\(114\) 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 \(-0.131351\pi\)
−0.805341 + 0.592812i \(0.798018\pi\)
\(132\) 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 0.454457 0.890769i \(-0.349833\pi\)
−0.544200 + 0.838956i \(0.683167\pi\)
\(138\) 0 0
\(139\) 6.11754 3.53196i 0.518883 0.299577i −0.217594 0.976039i \(-0.569821\pi\)
0.736478 + 0.676462i \(0.236488\pi\)
\(140\) 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 −0.725304 0.688428i \(-0.758301\pi\)
0.233544 + 0.972346i \(0.424968\pi\)
\(150\) 0 0
\(151\) −3.15939 + 5.47223i −0.257108 + 0.445323i −0.965466 0.260530i \(-0.916103\pi\)
0.708358 + 0.705853i \(0.249436\pi\)
\(152\) 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 \(-0.691974\pi\)
0.429640 + 0.903000i \(0.358640\pi\)
\(158\) 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 \(-0.183868\pi\)
−0.891767 + 0.452494i \(0.850534\pi\)
\(168\) 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 \(-0.739913\pi\)
0.973641 + 0.228085i \(0.0732464\pi\)
\(174\) 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 \(-0.887672\pi\)
0.938379 0.345609i \(-0.112328\pi\)
\(180\) 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 0.975081 0.221847i \(-0.0712087\pi\)
0.295415 + 0.955369i \(0.404542\pi\)
\(192\) 0 0
\(193\) 8.44583 + 14.6286i 0.607944 + 1.05299i 0.991579 + 0.129505i \(0.0413389\pi\)
−0.383634 + 0.923485i \(0.625328\pi\)
\(194\) −15.2255 26.3713i −1.09313 1.89335i
\(195\) 0 0
\(196\) 0 0
\(197\) 18.7102i 1.33305i −0.745484 0.666524i \(-0.767781\pi\)
0.745484 0.666524i \(-0.232219\pi\)
\(198\) 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 0.693057 0.720883i \(-0.256264\pi\)
−0.970831 + 0.239763i \(0.922930\pi\)
\(212\) −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 \(-0.0471671\pi\)
0.366662 + 0.930354i \(0.380500\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 16.3496 1.08756
\(227\) −7.22154 + 12.5081i −0.479310 + 0.830190i −0.999718 0.0237280i \(-0.992446\pi\)
0.520408 + 0.853918i \(0.325780\pi\)
\(228\) 0 0
\(229\) −11.3568 + 6.55685i −0.750479 + 0.433289i −0.825867 0.563865i \(-0.809314\pi\)
0.0753881 + 0.997154i \(0.475980\pi\)
\(230\) −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 \(0.0892922\pi\)
−0.960912 + 0.276855i \(0.910708\pi\)
\(234\) 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 0.569466 0.822015i \(-0.307150\pi\)
0.996619 0.0821642i \(-0.0261832\pi\)
\(240\) 0 0
\(241\) 19.4058 + 11.2039i 1.25004 + 0.721710i 0.971117 0.238605i \(-0.0766900\pi\)
0.278921 + 0.960314i \(0.410023\pi\)
\(242\) 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 \(-0.564696\pi\)
−0.201852 + 0.979416i \(0.564696\pi\)
\(252\) 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 \(-0.199627\pi\)
−0.913069 + 0.407806i \(0.866294\pi\)
\(258\) 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 −0.248559 0.968617i \(-0.579957\pi\)
−0.963126 + 0.269050i \(0.913290\pi\)
\(264\) 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 \(-0.526824\pi\)
−0.0841707 + 0.996451i \(0.526824\pi\)
\(270\) 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 −0.688814 0.724938i \(-0.741869\pi\)
0.972222 + 0.234062i \(0.0752019\pi\)
\(278\) −12.9413 −0.776167
\(279\) 0 0
\(280\) 0 0
\(281\) −4.57153 2.63938i −0.272715 0.157452i 0.357406 0.933949i \(-0.383661\pi\)
−0.630121 + 0.776497i \(0.716995\pi\)
\(282\) 0 0
\(283\) −17.0346 + 9.83496i −1.01260 + 0.584628i −0.911953 0.410294i \(-0.865426\pi\)
−0.100651 + 0.994922i \(0.532093\pi\)
\(284\) −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 0.999276 + 0.0380495i \(0.0121145\pi\)
−0.466686 + 0.884423i \(0.654552\pi\)
\(294\) 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 −0.918303 0.395878i \(-0.870440\pi\)
0.116311 0.993213i \(-0.462893\pi\)
\(312\) 0 0
\(313\) −4.82891 2.78797i −0.272946 0.157586i 0.357280 0.933998i \(-0.383704\pi\)
−0.630226 + 0.776412i \(0.717038\pi\)
\(314\) 3.64624 0.205769
\(315\) 0 0
\(316\) −9.44276 −0.531197
\(317\) −29.0708 16.7841i −1.63278 0.942686i −0.983230 0.182367i \(-0.941624\pi\)
−0.649550 0.760319i \(-0.725043\pi\)
\(318\) 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 −0.0595042 0.998228i \(-0.518952\pi\)
0.894243 0.447582i \(-0.147715\pi\)
\(332\) 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 0.912256 0.409620i \(-0.134339\pi\)
−0.810870 + 0.585227i \(0.801005\pi\)
\(338\) −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 −0.656629 0.754214i \(-0.728018\pi\)
0.324854 + 0.945764i \(0.394685\pi\)
\(348\) 0 0
\(349\) −13.2087 7.62607i −0.707047 0.408214i 0.102920 0.994690i \(-0.467182\pi\)
−0.809967 + 0.586476i \(0.800515\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 34.9206 1.86127
\(353\) −17.2359 + 29.8534i −0.917373 + 1.58894i −0.113985 + 0.993482i \(0.536362\pi\)
−0.803389 + 0.595455i \(0.796972\pi\)
\(354\) 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 \(0.0559415\pi\)
−0.984596 + 0.174842i \(0.944059\pi\)
\(360\) 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 \(-0.307575\pi\)
−0.428358 + 0.903609i \(0.640908\pi\)
\(368\) 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 0.712712 0.701457i \(-0.247467\pi\)
−0.963835 + 0.266499i \(0.914133\pi\)
\(374\) 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 0.987788 + 0.155804i \(0.0497970\pi\)
−0.358963 + 0.933352i \(0.616870\pi\)
\(384\) 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 0.352221 0.935917i \(-0.385427\pi\)
−0.634417 + 0.772991i \(0.718760\pi\)
\(390\) 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 −0.117653 0.993055i \(-0.537537\pi\)
0.801184 + 0.598418i \(0.204204\pi\)
\(402\) 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 \(-0.709437\pi\)
0.379477 + 0.925201i \(0.376104\pi\)
\(410\) 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 0.993072 + 0.117509i \(0.0374909\pi\)
−0.394770 + 0.918780i \(0.629176\pi\)
\(420\) 0 0
\(421\) 5.99347 10.3810i 0.292104 0.505939i −0.682203 0.731163i \(-0.738978\pi\)
0.974307 + 0.225224i \(0.0723113\pi\)
\(422\) 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 \(0.266274\pi\)
−0.670046 + 0.742320i \(0.733726\pi\)
\(432\) 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 \(-0.557634\pi\)
−0.941906 + 0.335877i \(0.890967\pi\)
\(440\) 4.04697 0.192932
\(441\) 0 0
\(442\) 15.3101 0.728228
\(443\) 4.63465 + 2.67582i 0.220199 + 0.127132i 0.606042 0.795432i \(-0.292756\pi\)
−0.385843 + 0.922564i \(0.626090\pi\)
\(444\) 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 \(0.299442\pi\)
−0.589204 + 0.807985i \(0.700558\pi\)
\(450\) 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 −0.618755 0.785584i \(-0.712363\pi\)
0.989713 + 0.143065i \(0.0456959\pi\)
\(458\) 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 \(-0.735328\pi\)
0.976825 + 0.214038i \(0.0686618\pi\)
\(462\) 0 0
\(463\) −6.01941 10.4259i −0.279746 0.484534i 0.691576 0.722304i \(-0.256917\pi\)
−0.971321 + 0.237770i \(0.923583\pi\)
\(464\) 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 \(-0.343986\pi\)
0.470743 + 0.882270i \(0.343986\pi\)
\(468\) 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 −0.442786 0.896627i \(-0.646010\pi\)
0.997895 0.0648499i \(-0.0206569\pi\)
\(480\) 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 −0.169185 0.985584i \(-0.554114\pi\)
0.768948 + 0.639311i \(0.220780\pi\)
\(492\) 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 0.958035 0.286650i \(-0.0925418\pi\)
−0.727264 + 0.686358i \(0.759208\pi\)
\(500\) 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 \(-0.314572\pi\)
0.550146 + 0.835068i \(0.314572\pi\)
\(504\) 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 \(-0.130101\pi\)
−0.803006 + 0.595971i \(0.796767\pi\)
\(510\) 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 \(-0.817267\pi\)
−0.839696 + 0.543058i \(0.817267\pi\)
\(522\) 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 −0.459125 0.888372i \(-0.651837\pi\)
0.998915 0.0465723i \(-0.0148298\pi\)
\(548\) 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 \(0.249069\pi\)
−0.709171 + 0.705036i \(0.750931\pi\)
\(558\) 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 0.984742 + 0.174023i \(0.0556767\pi\)
−0.341663 + 0.939823i \(0.610990\pi\)
\(564\) 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 0.191982 0.981398i \(-0.438509\pi\)
−0.753925 + 0.656960i \(0.771842\pi\)
\(570\) 0 0
\(571\) 12.2042 + 21.1384i 0.510731 + 0.884613i 0.999923 + 0.0124362i \(0.00395868\pi\)
−0.489191 + 0.872177i \(0.662708\pi\)
\(572\) 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 \(-0.674219\pi\)
0.999719 + 0.0237232i \(0.00755204\pi\)
\(588\) 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 \(-0.426729\pi\)
0.228160 + 0.973624i \(0.426729\pi\)
\(594\) 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 −0.196753 0.980453i \(-0.563040\pi\)
0.750721 + 0.660620i \(0.229706\pi\)
\(600\) 0 0
\(601\) 30.5665 + 17.6476i 1.24684 + 0.719861i 0.970477 0.241194i \(-0.0775390\pi\)
0.276358 + 0.961055i \(0.410872\pi\)
\(602\) 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 \(-0.378029\pi\)
0.990158 + 0.139955i \(0.0446959\pi\)
\(608\) 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 −0.525053 0.851070i \(-0.675955\pi\)
0.474521 + 0.880244i \(0.342621\pi\)
\(618\) 0 0
\(619\) −25.2590 14.5833i −1.01524 0.586152i −0.102522 0.994731i \(-0.532691\pi\)
−0.912723 + 0.408579i \(0.866024\pi\)
\(620\) 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 0.684770 0.728760i \(-0.259903\pi\)
−0.288740 + 0.957408i \(0.593236\pi\)
\(642\) 0 0
\(643\) −13.1240 + 7.57712i −0.517558 + 0.298812i −0.735935 0.677052i \(-0.763257\pi\)
0.218377 + 0.975865i \(0.429924\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.60370 + 6.24180i −0.141786 + 0.245580i
\(647\) 12.4411 0.489111 0.244556 0.969635i \(-0.421358\pi\)
0.244556 + 0.969635i \(0.421358\pi\)
\(648\) 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 −0.420303 0.907384i \(-0.638076\pi\)
0.575666 + 0.817685i \(0.304743\pi\)
\(654\) 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 0.164111 0.986442i \(-0.447525\pi\)
−0.772228 + 0.635345i \(0.780858\pi\)
\(660\) 0 0
\(661\) 0.554932 0.320390i 0.0215844 0.0124617i −0.489169 0.872189i \(-0.662700\pi\)
0.510753 + 0.859727i \(0.329367\pi\)
\(662\) −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 −0.996577 0.0826667i \(-0.973656\pi\)
0.569880 + 0.821728i \(0.306990\pi\)
\(674\) 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 \(-0.959114\pi\)
0.606815 + 0.794843i \(0.292447\pi\)
\(678\) 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 \(-0.868816\pi\)
0.916271 0.400558i \(-0.131184\pi\)
\(684\) 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 \(-0.342663\pi\)
−0.525165 + 0.851001i \(0.675996\pi\)
\(692\) 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 \(-0.795975\pi\)
0.801520 0.597967i \(-0.204025\pi\)
\(702\) 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 −0.995912 0.0903259i \(-0.971209\pi\)
0.576181 + 0.817322i \(0.304542\pi\)
\(710\) 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 \(-0.758403\pi\)
−0.725525 + 0.688195i \(0.758403\pi\)
\(720\) 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 \(-0.412282\pi\)
−0.697301 + 0.716779i \(0.745616\pi\)
\(728\) 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 \(-0.871382\pi\)
−0.119248 + 0.992865i \(0.538048\pi\)
\(734\) −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 −0.953398 0.301715i \(-0.902441\pi\)
−0.215406 + 0.976525i \(0.569108\pi\)
\(744\) 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 0.897473 0.441068i \(-0.145400\pi\)
−0.830713 + 0.556701i \(0.812067\pi\)
\(752\) 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 \(-0.0871381\pi\)
−0.715508 + 0.698604i \(0.753805\pi\)
\(762\) 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 \(-0.825107\pi\)
0.0258399 + 0.999666i \(0.491774\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −11.4552 + 19.8410i −0.412281 + 0.714092i
\(773\) −26.2218 −0.943132 −0.471566 0.881831i \(-0.656311\pi\)
−0.471566 + 0.881831i \(0.656311\pi\)
\(774\) 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 \(-0.493453\pi\)
0.876126 + 0.482082i \(0.160119\pi\)
\(788\) 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 0.751245 0.433731i