Properties

Label 804.2.q.b.25.4
Level 804
Weight 2
Character 804.25
Analytic conductor 6.420
Analytic rank 0
Dimension 60
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.q (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 25.4
Character \(\chi\) = 804.25
Dual form 804.2.q.b.193.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.654861 - 0.755750i) q^{3} +(1.12656 - 0.723994i) q^{5} +(-0.202268 - 1.40680i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\) \(q+(0.654861 - 0.755750i) q^{3} +(1.12656 - 0.723994i) q^{5} +(-0.202268 - 1.40680i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(-2.52874 + 1.62512i) q^{11} +(1.08620 - 2.37844i) q^{13} +(0.190580 - 1.32551i) q^{15} +(2.15851 + 0.633795i) q^{17} +(1.08664 - 7.55774i) q^{19} +(-1.19565 - 0.768395i) q^{21} +(5.68168 - 6.55701i) q^{23} +(-1.33211 + 2.91692i) q^{25} +(-0.841254 - 0.540641i) q^{27} -3.39419 q^{29} +(1.49181 + 3.26660i) q^{31} +(-0.427787 + 2.97532i) q^{33} +(-1.24638 - 1.43840i) q^{35} -6.63386 q^{37} +(-1.08620 - 2.37844i) q^{39} +(1.86302 + 0.547031i) q^{41} +(-8.87900 - 2.60711i) q^{43} +(-0.876951 - 1.01206i) q^{45} +(-0.660772 + 0.762571i) q^{47} +(4.77827 - 1.40303i) q^{49} +(1.89251 - 1.21624i) q^{51} +(11.0069 - 3.23191i) q^{53} +(-1.67219 + 3.66158i) q^{55} +(-5.00016 - 5.77049i) q^{57} +(3.66918 + 8.03438i) q^{59} +(8.80650 + 5.65959i) q^{61} +(-1.36370 + 0.400417i) q^{63} +(-0.498313 - 3.46584i) q^{65} +(0.105510 - 8.18467i) q^{67} +(-1.23475 - 8.58786i) q^{69} +(-3.96022 + 1.16283i) q^{71} +(-6.59618 - 4.23911i) q^{73} +(1.33211 + 2.91692i) q^{75} +(2.79770 + 3.22872i) q^{77} +(3.97765 - 8.70984i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-7.38873 + 4.74845i) q^{83} +(2.89055 - 0.848742i) q^{85} +(-2.22272 + 2.56516i) q^{87} +(7.60486 + 8.77648i) q^{89} +(-3.56569 - 1.04698i) q^{91} +(3.44566 + 1.01174i) q^{93} +(-4.24760 - 9.30095i) q^{95} -5.54010 q^{97} +(1.96846 + 2.27172i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} - 11q^{11} - 2q^{13} + 9q^{15} + 21q^{17} + 10q^{19} - 2q^{21} - 10q^{23} - 36q^{25} + 6q^{27} + 4q^{29} - 24q^{31} - 32q^{35} + 2q^{37} + 2q^{39} + 10q^{41} + 23q^{43} + 2q^{45} + 66q^{47} + 34q^{49} + 23q^{51} - 13q^{53} + 27q^{55} + q^{57} + 35q^{59} + 56q^{61} - 9q^{63} + 48q^{65} + 13q^{67} + 10q^{69} + 76q^{71} - q^{73} + 36q^{75} - 38q^{77} - 46q^{79} - 6q^{81} - 26q^{83} + 42q^{85} + 7q^{87} + 58q^{89} - 40q^{91} - 9q^{93} - 29q^{95} - 46q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{11}\right)\) \(1\)

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
\(3\) 0.654861 0.755750i 0.378084 0.436332i
\(4\) 0 0
\(5\) 1.12656 0.723994i 0.503812 0.323780i −0.263928 0.964543i \(-0.585018\pi\)
0.767739 + 0.640762i \(0.221382\pi\)
\(6\) 0 0
\(7\) −0.202268 1.40680i −0.0764499 0.531721i −0.991674 0.128775i \(-0.958895\pi\)
0.915224 0.402946i \(-0.132014\pi\)
\(8\) 0 0
\(9\) −0.142315 0.989821i −0.0474383 0.329940i
\(10\) 0 0
\(11\) −2.52874 + 1.62512i −0.762443 + 0.489992i −0.863165 0.504922i \(-0.831521\pi\)
0.100722 + 0.994915i \(0.467885\pi\)
\(12\) 0 0
\(13\) 1.08620 2.37844i 0.301256 0.659660i −0.697100 0.716974i \(-0.745527\pi\)
0.998356 + 0.0573146i \(0.0182538\pi\)
\(14\) 0 0
\(15\) 0.190580 1.32551i 0.0492075 0.342245i
\(16\) 0 0
\(17\) 2.15851 + 0.633795i 0.523515 + 0.153718i 0.532804 0.846239i \(-0.321138\pi\)
−0.00928835 + 0.999957i \(0.502957\pi\)
\(18\) 0 0
\(19\) 1.08664 7.55774i 0.249292 1.73386i −0.353030 0.935612i \(-0.614849\pi\)
0.602323 0.798253i \(-0.294242\pi\)
\(20\) 0 0
\(21\) −1.19565 0.768395i −0.260911 0.167678i
\(22\) 0 0
\(23\) 5.68168 6.55701i 1.18471 1.36723i 0.270135 0.962823i \(-0.412932\pi\)
0.914578 0.404409i \(-0.132523\pi\)
\(24\) 0 0
\(25\) −1.33211 + 2.91692i −0.266422 + 0.583384i
\(26\) 0 0
\(27\) −0.841254 0.540641i −0.161899 0.104046i
\(28\) 0 0
\(29\) −3.39419 −0.630286 −0.315143 0.949044i \(-0.602052\pi\)
−0.315143 + 0.949044i \(0.602052\pi\)
\(30\) 0 0
\(31\) 1.49181 + 3.26660i 0.267936 + 0.586699i 0.995000 0.0998707i \(-0.0318429\pi\)
−0.727064 + 0.686570i \(0.759116\pi\)
\(32\) 0 0
\(33\) −0.427787 + 2.97532i −0.0744681 + 0.517937i
\(34\) 0 0
\(35\) −1.24638 1.43840i −0.210677 0.243134i
\(36\) 0 0
\(37\) −6.63386 −1.09060 −0.545300 0.838241i \(-0.683584\pi\)
−0.545300 + 0.838241i \(0.683584\pi\)
\(38\) 0 0
\(39\) −1.08620 2.37844i −0.173930 0.380855i
\(40\) 0 0
\(41\) 1.86302 + 0.547031i 0.290954 + 0.0854319i 0.423953 0.905684i \(-0.360642\pi\)
−0.132998 + 0.991116i \(0.542461\pi\)
\(42\) 0 0
\(43\) −8.87900 2.60711i −1.35403 0.397581i −0.477379 0.878698i \(-0.658413\pi\)
−0.876656 + 0.481117i \(0.840231\pi\)
\(44\) 0 0
\(45\) −0.876951 1.01206i −0.130728 0.150868i
\(46\) 0 0
\(47\) −0.660772 + 0.762571i −0.0963835 + 0.111232i −0.801892 0.597469i \(-0.796173\pi\)
0.705509 + 0.708701i \(0.250719\pi\)
\(48\) 0 0
\(49\) 4.77827 1.40303i 0.682610 0.200432i
\(50\) 0 0
\(51\) 1.89251 1.21624i 0.265005 0.170308i
\(52\) 0 0
\(53\) 11.0069 3.23191i 1.51191 0.443937i 0.582453 0.812864i \(-0.302093\pi\)
0.929458 + 0.368927i \(0.120275\pi\)
\(54\) 0 0
\(55\) −1.67219 + 3.66158i −0.225478 + 0.493728i
\(56\) 0 0
\(57\) −5.00016 5.77049i −0.662288 0.764321i
\(58\) 0 0
\(59\) 3.66918 + 8.03438i 0.477687 + 1.04599i 0.983093 + 0.183106i \(0.0586152\pi\)
−0.505407 + 0.862881i \(0.668657\pi\)
\(60\) 0 0
\(61\) 8.80650 + 5.65959i 1.12756 + 0.724637i 0.965049 0.262071i \(-0.0844053\pi\)
0.162508 + 0.986707i \(0.448042\pi\)
\(62\) 0 0
\(63\) −1.36370 + 0.400417i −0.171810 + 0.0504479i
\(64\) 0 0
\(65\) −0.498313 3.46584i −0.0618081 0.429885i
\(66\) 0 0
\(67\) 0.105510 8.18467i 0.0128902 0.999917i
\(68\) 0 0
\(69\) −1.23475 8.58786i −0.148646 1.03386i
\(70\) 0 0
\(71\) −3.96022 + 1.16283i −0.469992 + 0.138002i −0.508148 0.861270i \(-0.669670\pi\)
0.0381560 + 0.999272i \(0.487852\pi\)
\(72\) 0 0
\(73\) −6.59618 4.23911i −0.772024 0.496150i 0.0943538 0.995539i \(-0.469922\pi\)
−0.866378 + 0.499389i \(0.833558\pi\)
\(74\) 0 0
\(75\) 1.33211 + 2.91692i 0.153819 + 0.336817i
\(76\) 0 0
\(77\) 2.79770 + 3.22872i 0.318828 + 0.367947i
\(78\) 0 0
\(79\) 3.97765 8.70984i 0.447521 0.979934i −0.542635 0.839968i \(-0.682573\pi\)
0.990156 0.139966i \(-0.0446992\pi\)
\(80\) 0 0
\(81\) −0.959493 + 0.281733i −0.106610 + 0.0313036i
\(82\) 0 0
\(83\) −7.38873 + 4.74845i −0.811018 + 0.521210i −0.879194 0.476463i \(-0.841918\pi\)
0.0681759 + 0.997673i \(0.478282\pi\)
\(84\) 0 0
\(85\) 2.89055 0.848742i 0.313524 0.0920589i
\(86\) 0 0
\(87\) −2.22272 + 2.56516i −0.238301 + 0.275014i
\(88\) 0 0
\(89\) 7.60486 + 8.77648i 0.806113 + 0.930305i 0.998700 0.0509754i \(-0.0162330\pi\)
−0.192586 + 0.981280i \(0.561688\pi\)
\(90\) 0 0
\(91\) −3.56569 1.04698i −0.373786 0.109753i
\(92\) 0 0
\(93\) 3.44566 + 1.01174i 0.357298 + 0.104912i
\(94\) 0 0
\(95\) −4.24760 9.30095i −0.435795 0.954257i
\(96\) 0 0
\(97\) −5.54010 −0.562512 −0.281256 0.959633i \(-0.590751\pi\)
−0.281256 + 0.959633i \(0.590751\pi\)
\(98\) 0 0
\(99\) 1.96846 + 2.27172i 0.197837 + 0.228316i
\(100\) 0 0
\(101\) −1.94942 + 13.5585i −0.193974 + 1.34912i 0.627385 + 0.778709i \(0.284125\pi\)
−0.821360 + 0.570411i \(0.806784\pi\)
\(102\) 0 0
\(103\) −5.86913 12.8516i −0.578303 1.26631i −0.942257 0.334890i \(-0.891301\pi\)
0.363955 0.931417i \(-0.381426\pi\)
\(104\) 0 0
\(105\) −1.90328 −0.185741
\(106\) 0 0
\(107\) 11.6790 + 7.50566i 1.12905 + 0.725600i 0.965363 0.260912i \(-0.0840232\pi\)
0.163692 + 0.986511i \(0.447660\pi\)
\(108\) 0 0
\(109\) −0.953650 + 2.08820i −0.0913431 + 0.200013i −0.949789 0.312890i \(-0.898703\pi\)
0.858446 + 0.512904i \(0.171430\pi\)
\(110\) 0 0
\(111\) −4.34426 + 5.01354i −0.412339 + 0.475864i
\(112\) 0 0
\(113\) 11.3583 + 7.29951i 1.06849 + 0.686680i 0.951872 0.306497i \(-0.0991568\pi\)
0.116623 + 0.993176i \(0.462793\pi\)
\(114\) 0 0
\(115\) 1.65350 11.5004i 0.154190 1.07241i
\(116\) 0 0
\(117\) −2.50881 0.736653i −0.231940 0.0681036i
\(118\) 0 0
\(119\) 0.455028 3.16479i 0.0417124 0.290116i
\(120\) 0 0
\(121\) −0.816068 + 1.78694i −0.0741880 + 0.162449i
\(122\) 0 0
\(123\) 1.63343 1.04974i 0.147282 0.0946523i
\(124\) 0 0
\(125\) 1.56403 + 10.8781i 0.139891 + 0.972964i
\(126\) 0 0
\(127\) 1.92871 + 13.4145i 0.171146 + 1.19034i 0.876469 + 0.481459i \(0.159893\pi\)
−0.705323 + 0.708886i \(0.749198\pi\)
\(128\) 0 0
\(129\) −7.78483 + 5.00301i −0.685416 + 0.440490i
\(130\) 0 0
\(131\) 9.57774 11.0533i 0.836811 0.965731i −0.162971 0.986631i \(-0.552108\pi\)
0.999782 + 0.0208995i \(0.00665300\pi\)
\(132\) 0 0
\(133\) −10.8520 −0.940991
\(134\) 0 0
\(135\) −1.33914 −0.115255
\(136\) 0 0
\(137\) 3.72372 4.29740i 0.318139 0.367152i −0.574045 0.818823i \(-0.694627\pi\)
0.892184 + 0.451672i \(0.149172\pi\)
\(138\) 0 0
\(139\) −11.7701 + 7.56419i −0.998328 + 0.641587i −0.934347 0.356365i \(-0.884016\pi\)
−0.0639811 + 0.997951i \(0.520380\pi\)
\(140\) 0 0
\(141\) 0.143599 + 0.998756i 0.0120933 + 0.0841104i
\(142\) 0 0
\(143\) 1.11854 + 7.77964i 0.0935373 + 0.650566i
\(144\) 0 0
\(145\) −3.82375 + 2.45738i −0.317545 + 0.204074i
\(146\) 0 0
\(147\) 2.06877 4.52997i 0.170629 0.373625i
\(148\) 0 0
\(149\) −3.09970 + 21.5589i −0.253938 + 1.76617i 0.320137 + 0.947371i \(0.396271\pi\)
−0.574074 + 0.818803i \(0.694638\pi\)
\(150\) 0 0
\(151\) 9.93981 + 2.91859i 0.808890 + 0.237512i 0.659926 0.751331i \(-0.270588\pi\)
0.148965 + 0.988843i \(0.452406\pi\)
\(152\) 0 0
\(153\) 0.320156 2.22674i 0.0258831 0.180021i
\(154\) 0 0
\(155\) 4.04561 + 2.59995i 0.324951 + 0.208833i
\(156\) 0 0
\(157\) 1.48075 1.70888i 0.118177 0.136383i −0.693578 0.720381i \(-0.743967\pi\)
0.811755 + 0.583998i \(0.198512\pi\)
\(158\) 0 0
\(159\) 4.76546 10.4349i 0.377925 0.827541i
\(160\) 0 0
\(161\) −10.3736 6.66673i −0.817557 0.525412i
\(162\) 0 0
\(163\) 16.1499 1.26496 0.632479 0.774577i \(-0.282037\pi\)
0.632479 + 0.774577i \(0.282037\pi\)
\(164\) 0 0
\(165\) 1.67219 + 3.66158i 0.130180 + 0.285054i
\(166\) 0 0
\(167\) −0.874032 + 6.07902i −0.0676346 + 0.470409i 0.927653 + 0.373443i \(0.121823\pi\)
−0.995288 + 0.0969660i \(0.969086\pi\)
\(168\) 0 0
\(169\) 4.03605 + 4.65785i 0.310465 + 0.358296i
\(170\) 0 0
\(171\) −7.63546 −0.583898
\(172\) 0 0
\(173\) 2.01439 + 4.41090i 0.153151 + 0.335355i 0.970620 0.240619i \(-0.0773504\pi\)
−0.817468 + 0.575974i \(0.804623\pi\)
\(174\) 0 0
\(175\) 4.37297 + 1.28402i 0.330565 + 0.0970627i
\(176\) 0 0
\(177\) 8.47478 + 2.48842i 0.637004 + 0.187041i
\(178\) 0 0
\(179\) −14.9942 17.3042i −1.12072 1.29338i −0.951449 0.307806i \(-0.900405\pi\)
−0.169267 0.985570i \(-0.554140\pi\)
\(180\) 0 0
\(181\) −7.12283 + 8.22018i −0.529435 + 0.611001i −0.955968 0.293471i \(-0.905190\pi\)
0.426532 + 0.904472i \(0.359735\pi\)
\(182\) 0 0
\(183\) 10.0443 2.94926i 0.742493 0.218016i
\(184\) 0 0
\(185\) −7.47343 + 4.80288i −0.549457 + 0.353115i
\(186\) 0 0
\(187\) −6.48830 + 1.90514i −0.474471 + 0.139317i
\(188\) 0 0
\(189\) −0.590416 + 1.29283i −0.0429464 + 0.0940396i
\(190\) 0 0
\(191\) 10.8396 + 12.5095i 0.784323 + 0.905157i 0.997414 0.0718758i \(-0.0228985\pi\)
−0.213091 + 0.977032i \(0.568353\pi\)
\(192\) 0 0
\(193\) 4.01603 + 8.79387i 0.289080 + 0.632997i 0.997335 0.0729601i \(-0.0232446\pi\)
−0.708255 + 0.705957i \(0.750517\pi\)
\(194\) 0 0
\(195\) −2.94564 1.89305i −0.210941 0.135564i
\(196\) 0 0
\(197\) 4.17889 1.22703i 0.297734 0.0874226i −0.129454 0.991585i \(-0.541322\pi\)
0.427188 + 0.904163i \(0.359504\pi\)
\(198\) 0 0
\(199\) 2.24247 + 15.5967i 0.158964 + 1.10562i 0.900547 + 0.434759i \(0.143166\pi\)
−0.741582 + 0.670862i \(0.765924\pi\)
\(200\) 0 0
\(201\) −6.11647 5.43956i −0.431422 0.383677i
\(202\) 0 0
\(203\) 0.686535 + 4.77495i 0.0481853 + 0.335136i
\(204\) 0 0
\(205\) 2.49484 0.732551i 0.174247 0.0511636i
\(206\) 0 0
\(207\) −7.29886 4.69069i −0.507306 0.326026i
\(208\) 0 0
\(209\) 9.53442 + 20.8775i 0.659510 + 1.44412i
\(210\) 0 0
\(211\) −9.34056 10.7796i −0.643031 0.742097i 0.336877 0.941549i \(-0.390629\pi\)
−0.979908 + 0.199451i \(0.936084\pi\)
\(212\) 0 0
\(213\) −1.71459 + 3.75443i −0.117482 + 0.257249i
\(214\) 0 0
\(215\) −11.8902 + 3.49129i −0.810907 + 0.238104i
\(216\) 0 0
\(217\) 4.29372 2.75940i 0.291476 0.187321i
\(218\) 0 0
\(219\) −7.52328 + 2.20903i −0.508376 + 0.149273i
\(220\) 0 0
\(221\) 3.85201 4.44545i 0.259114 0.299033i
\(222\) 0 0
\(223\) 14.7457 + 17.0174i 0.987444 + 1.13957i 0.990212 + 0.139575i \(0.0445736\pi\)
−0.00276766 + 0.999996i \(0.500881\pi\)
\(224\) 0 0
\(225\) 3.07681 + 0.903432i 0.205120 + 0.0602288i
\(226\) 0 0
\(227\) −9.14491 2.68519i −0.606969 0.178222i −0.0362160 0.999344i \(-0.511530\pi\)
−0.570753 + 0.821122i \(0.693349\pi\)
\(228\) 0 0
\(229\) −2.91562 6.38432i −0.192670 0.421888i 0.788500 0.615034i \(-0.210858\pi\)
−0.981170 + 0.193147i \(0.938131\pi\)
\(230\) 0 0
\(231\) 4.27221 0.281091
\(232\) 0 0
\(233\) 6.11516 + 7.05727i 0.400617 + 0.462337i 0.919835 0.392305i \(-0.128322\pi\)
−0.519218 + 0.854642i \(0.673777\pi\)
\(234\) 0 0
\(235\) −0.192300 + 1.33748i −0.0125443 + 0.0872473i
\(236\) 0 0
\(237\) −3.97765 8.70984i −0.258376 0.565765i
\(238\) 0 0
\(239\) −26.4821 −1.71299 −0.856493 0.516158i \(-0.827362\pi\)
−0.856493 + 0.516158i \(0.827362\pi\)
\(240\) 0 0
\(241\) −18.3896 11.8182i −1.18458 0.761280i −0.208353 0.978054i \(-0.566810\pi\)
−0.976222 + 0.216773i \(0.930447\pi\)
\(242\) 0 0
\(243\) −0.415415 + 0.909632i −0.0266489 + 0.0583529i
\(244\) 0 0
\(245\) 4.36721 5.04003i 0.279011 0.321996i
\(246\) 0 0
\(247\) −16.7953 10.7937i −1.06866 0.686786i
\(248\) 0 0
\(249\) −1.24995 + 8.69360i −0.0792124 + 0.550935i
\(250\) 0 0
\(251\) −8.16027 2.39607i −0.515072 0.151239i 0.0138586 0.999904i \(-0.495589\pi\)
−0.528930 + 0.848665i \(0.677407\pi\)
\(252\) 0 0
\(253\) −3.71155 + 25.8144i −0.233343 + 1.62294i
\(254\) 0 0
\(255\) 1.25147 2.74034i 0.0783701 0.171607i
\(256\) 0 0
\(257\) 10.2447 6.58389i 0.639049 0.410692i −0.180601 0.983556i \(-0.557804\pi\)
0.819650 + 0.572865i \(0.194168\pi\)
\(258\) 0 0
\(259\) 1.34182 + 9.33253i 0.0833763 + 0.579895i
\(260\) 0 0
\(261\) 0.483044 + 3.35964i 0.0298997 + 0.207957i
\(262\) 0 0
\(263\) 8.47112 5.44406i 0.522352 0.335695i −0.252750 0.967532i \(-0.581335\pi\)
0.775102 + 0.631837i \(0.217699\pi\)
\(264\) 0 0
\(265\) 10.0600 11.6099i 0.617981 0.713188i
\(266\) 0 0
\(267\) 11.6129 0.710700
\(268\) 0 0
\(269\) 14.3381 0.874208 0.437104 0.899411i \(-0.356004\pi\)
0.437104 + 0.899411i \(0.356004\pi\)
\(270\) 0 0
\(271\) 1.12115 1.29388i 0.0681050 0.0785974i −0.720675 0.693273i \(-0.756168\pi\)
0.788780 + 0.614676i \(0.210713\pi\)
\(272\) 0 0
\(273\) −3.12629 + 2.00914i −0.189211 + 0.121599i
\(274\) 0 0
\(275\) −1.37178 9.54096i −0.0827217 0.575342i
\(276\) 0 0
\(277\) 0.214899 + 1.49466i 0.0129120 + 0.0898052i 0.995258 0.0972657i \(-0.0310097\pi\)
−0.982346 + 0.187071i \(0.940101\pi\)
\(278\) 0 0
\(279\) 3.02105 1.94151i 0.180865 0.116235i
\(280\) 0 0
\(281\) 2.61728 5.73104i 0.156134 0.341885i −0.815359 0.578956i \(-0.803460\pi\)
0.971492 + 0.237071i \(0.0761875\pi\)
\(282\) 0 0
\(283\) 2.63994 18.3612i 0.156928 1.09146i −0.747324 0.664460i \(-0.768662\pi\)
0.904252 0.426999i \(-0.140429\pi\)
\(284\) 0 0
\(285\) −9.81077 2.88070i −0.581140 0.170638i
\(286\) 0 0
\(287\) 0.392736 2.73154i 0.0231825 0.161238i
\(288\) 0 0
\(289\) −10.0438 6.45479i −0.590814 0.379693i
\(290\) 0 0
\(291\) −3.62799 + 4.18693i −0.212677 + 0.245442i
\(292\) 0 0
\(293\) −2.59390 + 5.67986i −0.151537 + 0.331821i −0.970142 0.242536i \(-0.922021\pi\)
0.818605 + 0.574357i \(0.194748\pi\)
\(294\) 0 0
\(295\) 9.95039 + 6.39473i 0.579334 + 0.372315i
\(296\) 0 0
\(297\) 3.00592 0.174421
\(298\) 0 0
\(299\) −9.42402 20.6357i −0.545005 1.19339i
\(300\) 0 0
\(301\) −1.87175 + 13.0183i −0.107886 + 0.750364i
\(302\) 0 0
\(303\) 8.97022 + 10.3522i 0.515326 + 0.594718i
\(304\) 0 0
\(305\) 14.0185 0.802699
\(306\) 0 0
\(307\) 8.79483 + 19.2580i 0.501948 + 1.09911i 0.975831 + 0.218524i \(0.0701243\pi\)
−0.473884 + 0.880587i \(0.657148\pi\)
\(308\) 0 0
\(309\) −13.5561 3.98042i −0.771177 0.226438i
\(310\) 0 0
\(311\) 11.5887 + 3.40276i 0.657137 + 0.192953i 0.593268 0.805005i \(-0.297838\pi\)
0.0638697 + 0.997958i \(0.479656\pi\)
\(312\) 0 0
\(313\) 9.62902 + 11.1125i 0.544265 + 0.628115i 0.959537 0.281582i \(-0.0908592\pi\)
−0.415273 + 0.909697i \(0.636314\pi\)
\(314\) 0 0
\(315\) −1.24638 + 1.43840i −0.0702257 + 0.0810448i
\(316\) 0 0
\(317\) −27.7406 + 8.14537i −1.55807 + 0.457490i −0.943499 0.331375i \(-0.892487\pi\)
−0.614567 + 0.788865i \(0.710669\pi\)
\(318\) 0 0
\(319\) 8.58302 5.51597i 0.480557 0.308835i
\(320\) 0 0
\(321\) 13.3205 3.91126i 0.743480 0.218305i
\(322\) 0 0
\(323\) 7.13558 15.6247i 0.397034 0.869384i
\(324\) 0 0
\(325\) 5.49077 + 6.33669i 0.304573 + 0.351496i
\(326\) 0 0
\(327\) 0.953650 + 2.08820i 0.0527370 + 0.115478i
\(328\) 0 0
\(329\) 1.20644 + 0.775331i 0.0665132 + 0.0427454i
\(330\) 0 0
\(331\) −15.3580 + 4.50953i −0.844154 + 0.247866i −0.675087 0.737738i \(-0.735894\pi\)
−0.169068 + 0.985604i \(0.554076\pi\)
\(332\) 0 0
\(333\) 0.944097 + 6.56634i 0.0517362 + 0.359833i
\(334\) 0 0
\(335\) −5.80679 9.29689i −0.317259 0.507943i
\(336\) 0 0
\(337\) −2.75983 19.1950i −0.150337 1.04562i −0.915654 0.401966i \(-0.868327\pi\)
0.765317 0.643654i \(-0.222582\pi\)
\(338\) 0 0
\(339\) 12.9547 3.80384i 0.703601 0.206596i
\(340\) 0 0
\(341\) −9.08101 5.83601i −0.491764 0.316038i
\(342\) 0 0
\(343\) −7.07318 15.4881i −0.381916 0.836279i
\(344\) 0 0
\(345\) −7.60858 8.78076i −0.409632 0.472740i
\(346\) 0 0
\(347\) 7.53963 16.5095i 0.404749 0.886276i −0.592018 0.805925i \(-0.701669\pi\)
0.996767 0.0803511i \(-0.0256041\pi\)
\(348\) 0 0
\(349\) 18.6250 5.46879i 0.996973 0.292738i 0.257760 0.966209i \(-0.417016\pi\)
0.739213 + 0.673471i \(0.235198\pi\)
\(350\) 0 0
\(351\) −2.19965 + 1.41363i −0.117408 + 0.0754538i
\(352\) 0 0
\(353\) 4.25790 1.25023i 0.226625 0.0665432i −0.166448 0.986050i \(-0.553230\pi\)
0.393074 + 0.919507i \(0.371412\pi\)
\(354\) 0 0
\(355\) −3.61954 + 4.17717i −0.192105 + 0.221701i
\(356\) 0 0
\(357\) −2.09381 2.41638i −0.110816 0.127889i
\(358\) 0 0
\(359\) −5.39866 1.58519i −0.284930 0.0836631i 0.136144 0.990689i \(-0.456529\pi\)
−0.421075 + 0.907026i \(0.638347\pi\)
\(360\) 0 0
\(361\) −37.7083 11.0722i −1.98465 0.582745i
\(362\) 0 0
\(363\) 0.816068 + 1.78694i 0.0428325 + 0.0937900i
\(364\) 0 0
\(365\) −10.5001 −0.549598
\(366\) 0 0
\(367\) −10.2868 11.8716i −0.536966 0.619692i 0.420830 0.907139i \(-0.361739\pi\)
−0.957796 + 0.287447i \(0.907193\pi\)
\(368\) 0 0
\(369\) 0.276328 1.92190i 0.0143851 0.100050i
\(370\) 0 0
\(371\) −6.77299 14.8308i −0.351636 0.769976i
\(372\) 0 0
\(373\) 13.5332 0.700723 0.350361 0.936615i \(-0.386059\pi\)
0.350361 + 0.936615i \(0.386059\pi\)
\(374\) 0 0
\(375\) 9.24532 + 5.94161i 0.477426 + 0.306823i
\(376\) 0 0
\(377\) −3.68676 + 8.07287i −0.189878 + 0.415774i
\(378\) 0 0
\(379\) 12.5546 14.4888i 0.644886 0.744238i −0.335345 0.942096i \(-0.608853\pi\)
0.980231 + 0.197857i \(0.0633982\pi\)
\(380\) 0 0
\(381\) 11.4010 + 7.32701i 0.584093 + 0.375374i
\(382\) 0 0
\(383\) −4.66462 + 32.4431i −0.238351 + 1.65777i 0.421840 + 0.906670i \(0.361384\pi\)
−0.660191 + 0.751097i \(0.729525\pi\)
\(384\) 0 0
\(385\) 5.48935 + 1.61182i 0.279763 + 0.0821459i
\(386\) 0 0
\(387\) −1.31696 + 9.15966i −0.0669448 + 0.465611i
\(388\) 0 0
\(389\) −2.93841 + 6.43422i −0.148983 + 0.326228i −0.969379 0.245568i \(-0.921026\pi\)
0.820396 + 0.571795i \(0.193753\pi\)
\(390\) 0 0
\(391\) 16.4198 10.5523i 0.830383 0.533655i
\(392\) 0 0
\(393\) −2.08144 14.4767i −0.104995 0.730255i
\(394\) 0 0
\(395\) −1.82482 12.6919i −0.0918169 0.638601i
\(396\) 0 0
\(397\) −0.325544 + 0.209214i −0.0163386 + 0.0105002i −0.548785 0.835964i \(-0.684909\pi\)
0.532446 + 0.846464i \(0.321273\pi\)
\(398\) 0 0
\(399\) −7.10657 + 8.20142i −0.355774 + 0.410585i
\(400\) 0 0
\(401\) 9.41238 0.470032 0.235016 0.971992i \(-0.424486\pi\)
0.235016 + 0.971992i \(0.424486\pi\)
\(402\) 0 0
\(403\) 9.38980 0.467739
\(404\) 0 0
\(405\) −0.876951 + 1.01206i −0.0435760 + 0.0502894i
\(406\) 0 0
\(407\) 16.7753 10.7808i 0.831521 0.534386i
\(408\) 0 0
\(409\) 0.104187 + 0.724633i 0.00515169 + 0.0358308i 0.992235 0.124376i \(-0.0396929\pi\)
−0.987083 + 0.160207i \(0.948784\pi\)
\(410\) 0 0
\(411\) −0.809241 5.62840i −0.0399169 0.277628i
\(412\) 0 0
\(413\) 10.5606 6.78690i 0.519654 0.333962i
\(414\) 0 0
\(415\) −4.88598 + 10.6988i −0.239843 + 0.525183i
\(416\) 0 0
\(417\) −1.99115 + 13.8488i −0.0975070 + 0.678176i
\(418\) 0 0
\(419\) −20.3895 5.98689i −0.996091 0.292479i −0.257240 0.966348i \(-0.582813\pi\)
−0.738851 + 0.673869i \(0.764631\pi\)
\(420\) 0 0
\(421\) 4.74139 32.9771i 0.231081 1.60721i −0.462359 0.886693i \(-0.652997\pi\)
0.693441 0.720514i \(-0.256094\pi\)
\(422\) 0 0
\(423\) 0.848847 + 0.545521i 0.0412724 + 0.0265241i
\(424\) 0 0
\(425\) −4.72410 + 5.45191i −0.229153 + 0.264456i
\(426\) 0 0
\(427\) 6.18066 13.5337i 0.299103 0.654944i
\(428\) 0 0
\(429\) 6.61195 + 4.24924i 0.319228 + 0.205155i
\(430\) 0 0
\(431\) 18.1531 0.874402 0.437201 0.899364i \(-0.355970\pi\)
0.437201 + 0.899364i \(0.355970\pi\)
\(432\) 0 0
\(433\) −4.44435 9.73177i −0.213582 0.467679i 0.772271 0.635294i \(-0.219121\pi\)
−0.985853 + 0.167614i \(0.946394\pi\)
\(434\) 0 0
\(435\) −0.646864 + 4.49904i −0.0310148 + 0.215712i
\(436\) 0 0
\(437\) −43.3823 50.0658i −2.07525 2.39497i
\(438\) 0 0
\(439\) 13.5190 0.645229 0.322614 0.946531i \(-0.395438\pi\)
0.322614 + 0.946531i \(0.395438\pi\)
\(440\) 0 0
\(441\) −2.06877 4.52997i −0.0985127 0.215713i
\(442\) 0 0
\(443\) −3.50537 1.02927i −0.166545 0.0489020i 0.197397 0.980324i \(-0.436751\pi\)
−0.363942 + 0.931422i \(0.618569\pi\)
\(444\) 0 0
\(445\) 14.9214 + 4.38133i 0.707344 + 0.207695i
\(446\) 0 0
\(447\) 14.2633 + 16.4607i 0.674629 + 0.778564i
\(448\) 0 0
\(449\) 22.3267 25.7664i 1.05366 1.21599i 0.0779464 0.996958i \(-0.475164\pi\)
0.975717 0.219035i \(-0.0702908\pi\)
\(450\) 0 0
\(451\) −5.60007 + 1.64433i −0.263697 + 0.0774284i
\(452\) 0 0
\(453\) 8.71492 5.60074i 0.409462 0.263146i
\(454\) 0 0
\(455\) −4.77496 + 1.40206i −0.223854 + 0.0657294i
\(456\) 0 0
\(457\) 9.00452 19.7172i 0.421214 0.922330i −0.573458 0.819235i \(-0.694398\pi\)
0.994672 0.103094i \(-0.0328744\pi\)
\(458\) 0 0
\(459\) −1.47320 1.70016i −0.0687630 0.0793567i
\(460\) 0 0
\(461\) −7.24083 15.8552i −0.337239 0.738450i 0.662707 0.748879i \(-0.269408\pi\)
−0.999946 + 0.0104288i \(0.996680\pi\)
\(462\) 0 0
\(463\) 32.5779 + 20.9366i 1.51402 + 0.973004i 0.992826 + 0.119569i \(0.0381512\pi\)
0.521198 + 0.853436i \(0.325485\pi\)
\(464\) 0 0
\(465\) 4.61422 1.35486i 0.213980 0.0628301i
\(466\) 0 0
\(467\) −4.81787 33.5091i −0.222945 1.55061i −0.726814 0.686834i \(-0.759000\pi\)
0.503869 0.863780i \(-0.331909\pi\)
\(468\) 0 0
\(469\) −11.5356 + 1.50706i −0.532662 + 0.0695896i
\(470\) 0 0
\(471\) −0.321798 2.23815i −0.0148277 0.103129i
\(472\) 0 0
\(473\) 26.6895 7.83675i 1.22719 0.360334i
\(474\) 0 0
\(475\) 20.5978 + 13.2374i 0.945091 + 0.607373i
\(476\) 0 0
\(477\) −4.76546 10.4349i −0.218195 0.477781i
\(478\) 0 0
\(479\) −6.59804 7.61455i −0.301472 0.347918i 0.584720 0.811235i \(-0.301204\pi\)
−0.886192 + 0.463318i \(0.846659\pi\)
\(480\) 0 0
\(481\) −7.20567 + 15.7782i −0.328550 + 0.719425i
\(482\) 0 0
\(483\) −11.8317 + 3.47409i −0.538359 + 0.158077i
\(484\) 0 0
\(485\) −6.24124 + 4.01100i −0.283400 + 0.182130i
\(486\) 0 0
\(487\) −27.1679 + 7.97722i −1.23110 + 0.361482i −0.831663 0.555280i \(-0.812611\pi\)
−0.399433 + 0.916763i \(0.630793\pi\)
\(488\) 0 0
\(489\) 10.5759 12.2053i 0.478260 0.551942i
\(490\) 0 0
\(491\) −22.6326 26.1194i −1.02139 1.17875i −0.983765 0.179460i \(-0.942565\pi\)
−0.0376286 0.999292i \(-0.511980\pi\)
\(492\) 0 0
\(493\) −7.32639 2.15122i −0.329964 0.0968862i
\(494\) 0 0
\(495\) 3.86229 + 1.13407i 0.173597 + 0.0509727i
\(496\) 0 0
\(497\) 2.43689 + 5.33605i 0.109310 + 0.239354i
\(498\) 0 0
\(499\) 1.49914 0.0671108 0.0335554 0.999437i \(-0.489317\pi\)
0.0335554 + 0.999437i \(0.489317\pi\)
\(500\) 0 0
\(501\) 4.02185 + 4.64146i 0.179683 + 0.207365i
\(502\) 0 0
\(503\) 1.10404 7.67875i 0.0492266 0.342379i −0.950292 0.311360i \(-0.899216\pi\)
0.999519 0.0310191i \(-0.00987526\pi\)
\(504\) 0 0
\(505\) 7.62014 + 16.6858i 0.339092 + 0.742507i
\(506\) 0 0
\(507\) 6.16322 0.273718
\(508\) 0 0
\(509\) 7.04353 + 4.52660i 0.312199 + 0.200638i 0.687351 0.726325i \(-0.258773\pi\)
−0.375152 + 0.926963i \(0.622410\pi\)
\(510\) 0 0
\(511\) −4.62939 + 10.1369i −0.204792 + 0.448432i
\(512\) 0 0
\(513\) −5.00016 + 5.77049i −0.220763 + 0.254774i
\(514\) 0 0
\(515\) −15.9164 10.2289i −0.701360 0.450737i
\(516\) 0 0
\(517\) 0.431648 3.00218i 0.0189839 0.132036i
\(518\) 0 0
\(519\) 4.65268 + 1.36615i 0.204230 + 0.0599674i
\(520\) 0 0
\(521\) −4.66783 + 32.4655i −0.204502 + 1.42234i 0.586214 + 0.810156i \(0.300618\pi\)
−0.790716 + 0.612183i \(0.790291\pi\)
\(522\) 0 0
\(523\) −2.29293 + 5.02082i −0.100263 + 0.219545i −0.953116 0.302606i \(-0.902143\pi\)
0.852853 + 0.522152i \(0.174870\pi\)
\(524\) 0 0
\(525\) 3.83408 2.46401i 0.167333 0.107538i
\(526\) 0 0
\(527\) 1.14972 + 7.99649i 0.0500827 + 0.348333i
\(528\) 0 0
\(529\) −7.43964 51.7438i −0.323463 2.24973i
\(530\) 0 0
\(531\) 7.43043 4.77524i 0.322453 0.207228i
\(532\) 0 0
\(533\) 3.32468 3.83688i 0.144008 0.166194i
\(534\) 0 0
\(535\) 18.5912 0.803766
\(536\) 0 0
\(537\) −22.8967 −0.988067
\(538\) 0 0
\(539\) −9.80291 + 11.3132i −0.422241 + 0.487292i
\(540\) 0 0
\(541\) −25.5915 + 16.4466i −1.10026 + 0.707096i −0.959150 0.282898i \(-0.908704\pi\)
−0.141112 + 0.989994i \(0.545068\pi\)
\(542\) 0 0
\(543\) 1.54794 + 10.7661i 0.0664284 + 0.462020i
\(544\) 0 0
\(545\) 0.437505 + 3.04292i 0.0187407 + 0.130344i
\(546\) 0 0
\(547\) −18.3111 + 11.7678i −0.782924 + 0.503155i −0.870003 0.493047i \(-0.835883\pi\)
0.0870789 + 0.996201i \(0.472247\pi\)
\(548\) 0 0
\(549\) 4.34869 9.52231i 0.185598 0.406402i
\(550\) 0 0
\(551\) −3.68826 + 25.6524i −0.157125 + 1.09283i
\(552\) 0 0
\(553\) −13.0576 3.83405i −0.555264 0.163040i
\(554\) 0 0
\(555\) −1.26428 + 8.79326i −0.0536657 + 0.373253i
\(556\) 0 0
\(557\) −22.9401 14.7427i −0.972004 0.624669i −0.0447088 0.999000i \(-0.514236\pi\)
−0.927295 + 0.374331i \(0.877872\pi\)
\(558\) 0 0
\(559\) −15.8452 + 18.2863i −0.670180 + 0.773428i
\(560\) 0 0
\(561\) −2.80913 + 6.15113i −0.118601 + 0.259701i
\(562\) 0 0
\(563\) −11.7296 7.53816i −0.494344 0.317695i 0.269607 0.962971i \(-0.413106\pi\)
−0.763950 + 0.645275i \(0.776743\pi\)
\(564\) 0 0
\(565\) 18.0805 0.760653
\(566\) 0 0
\(567\) 0.590416 + 1.29283i 0.0247951 + 0.0542938i
\(568\) 0 0
\(569\) 0.736629 5.12337i 0.0308811 0.214783i −0.968538 0.248866i \(-0.919942\pi\)
0.999419 + 0.0340833i \(0.0108512\pi\)
\(570\) 0 0
\(571\) 4.73028 + 5.45904i 0.197956 + 0.228454i 0.846045 0.533111i \(-0.178977\pi\)
−0.648089 + 0.761564i \(0.724432\pi\)
\(572\) 0 0
\(573\) 16.5525 0.691489
\(574\) 0 0
\(575\) 11.5576 + 25.3077i 0.481986 + 1.05540i
\(576\) 0 0
\(577\) 21.1778 + 6.21837i 0.881645 + 0.258874i 0.691061 0.722797i \(-0.257144\pi\)
0.190584 + 0.981671i \(0.438962\pi\)
\(578\) 0 0
\(579\) 9.27590 + 2.72365i 0.385493 + 0.113191i
\(580\) 0 0
\(581\) 8.17462 + 9.43402i 0.339140 + 0.391389i
\(582\) 0 0
\(583\) −22.5813 + 26.0602i −0.935221 + 1.07930i
\(584\) 0 0
\(585\) −3.35965 + 0.986482i −0.138904 + 0.0407860i
\(586\) 0 0
\(587\) −8.22817 + 5.28793i −0.339613 + 0.218256i −0.699319 0.714810i \(-0.746513\pi\)
0.359706 + 0.933066i \(0.382877\pi\)
\(588\) 0 0
\(589\) 26.3092 7.72507i 1.08405 0.318306i
\(590\) 0 0
\(591\) 1.80926 3.96173i 0.0744231 0.162964i
\(592\) 0 0
\(593\) −14.3954 16.6132i −0.591148 0.682221i 0.378816 0.925472i \(-0.376331\pi\)
−0.969963 + 0.243252i \(0.921786\pi\)
\(594\) 0 0
\(595\) −1.77867 3.89475i −0.0729186 0.159669i
\(596\) 0 0
\(597\) 13.2557 + 8.51892i 0.542520 + 0.348656i
\(598\) 0 0
\(599\) −41.6630 + 12.2334i −1.70230 + 0.499841i −0.981201 0.192988i \(-0.938182\pi\)
−0.721102 + 0.692829i \(0.756364\pi\)
\(600\) 0 0
\(601\) −0.313733 2.18206i −0.0127974 0.0890080i 0.982422 0.186675i \(-0.0597711\pi\)
−0.995219 + 0.0976669i \(0.968862\pi\)
\(602\) 0 0
\(603\) −8.11638 + 1.06036i −0.330525 + 0.0431814i
\(604\) 0 0
\(605\) 0.374387 + 2.60392i 0.0152210 + 0.105864i
\(606\) 0 0
\(607\) 34.4626 10.1191i 1.39879 0.410723i 0.506525 0.862226i \(-0.330930\pi\)
0.892270 + 0.451502i \(0.149112\pi\)
\(608\) 0 0
\(609\) 4.05825 + 2.60808i 0.164449 + 0.105685i
\(610\) 0 0
\(611\) 1.09600 + 2.39991i 0.0443394 + 0.0970898i
\(612\) 0 0
\(613\) −1.28231 1.47986i −0.0517918 0.0597710i 0.729263 0.684234i \(-0.239863\pi\)
−0.781054 + 0.624463i \(0.785318\pi\)
\(614\) 0 0
\(615\) 1.08015 2.36519i 0.0435558 0.0953738i
\(616\) 0 0
\(617\) 8.62792 2.53339i 0.347347 0.101990i −0.103405 0.994639i \(-0.532974\pi\)
0.450752 + 0.892649i \(0.351156\pi\)
\(618\) 0 0
\(619\) 7.30225 4.69287i 0.293502 0.188622i −0.385600 0.922666i \(-0.626006\pi\)
0.679102 + 0.734044i \(0.262369\pi\)
\(620\) 0 0
\(621\) −8.32472 + 2.44436i −0.334060 + 0.0980888i
\(622\) 0 0
\(623\) 10.8085 12.4737i 0.433035 0.499749i
\(624\) 0 0
\(625\) −0.862081 0.994895i −0.0344833 0.0397958i
\(626\) 0 0
\(627\) 22.0219 + 6.46620i 0.879468 + 0.258235i
\(628\) 0 0
\(629\) −14.3193 4.20451i −0.570946 0.167645i
\(630\) 0 0
\(631\) 6.08155 + 13.3167i 0.242103 + 0.530131i 0.991207 0.132321i \(-0.0422431\pi\)
−0.749104 + 0.662452i \(0.769516\pi\)
\(632\) 0 0
\(633\) −14.2634 −0.566921
\(634\) 0 0
\(635\) 11.8848 + 13.7158i 0.471635 + 0.544296i
\(636\) 0 0
\(637\) 1.85313 12.8888i 0.0734236 0.510672i
\(638\) 0 0
\(639\) 1.71459 + 3.75443i 0.0678281 + 0.148523i
\(640\) 0 0
\(641\) 11.8875 0.469526 0.234763 0.972053i \(-0.424569\pi\)
0.234763 + 0.972053i \(0.424569\pi\)
\(642\) 0 0
\(643\) 29.4878 + 18.9507i 1.16288 + 0.747341i 0.972164 0.234303i \(-0.0752809\pi\)
0.190721 + 0.981644i \(0.438917\pi\)
\(644\) 0 0
\(645\) −5.14791 + 11.2723i −0.202699 + 0.443848i
\(646\) 0 0
\(647\) −29.7892 + 34.3785i −1.17113 + 1.35156i −0.247219 + 0.968960i \(0.579517\pi\)
−0.923914 + 0.382600i \(0.875029\pi\)
\(648\) 0 0
\(649\) −22.3352 14.3540i −0.876735 0.563443i
\(650\) 0 0
\(651\) 0.726368 5.05200i 0.0284686 0.198003i
\(652\) 0 0
\(653\) 42.0184 + 12.3377i 1.64431 + 0.482812i 0.967399 0.253256i \(-0.0815013\pi\)
0.676908 + 0.736068i \(0.263320\pi\)
\(654\) 0 0
\(655\) 2.78734 19.3864i 0.108911 0.757490i
\(656\) 0 0
\(657\) −3.25722 + 7.13232i −0.127076 + 0.278258i
\(658\) 0 0
\(659\) −11.3357 + 7.28503i −0.441577 + 0.283785i −0.742477 0.669871i \(-0.766349\pi\)
0.300900 + 0.953656i \(0.402713\pi\)
\(660\) 0 0
\(661\) −4.48663 31.2052i −0.174510 1.21374i −0.869210 0.494443i \(-0.835372\pi\)
0.694700 0.719299i \(-0.255537\pi\)
\(662\) 0 0
\(663\) −0.837121 5.82230i −0.0325111 0.226119i
\(664\) 0 0
\(665\) −12.2254 + 7.85681i −0.474082 + 0.304674i
\(666\) 0 0
\(667\) −19.2847 + 22.2558i −0.746707 + 0.861746i
\(668\) 0 0
\(669\) 22.5173 0.870568
\(670\) 0 0
\(671\) −31.4669 −1.21476
\(672\) 0 0
\(673\) −27.0163 + 31.1784i −1.04140 + 1.20184i −0.0623859 + 0.998052i \(0.519871\pi\)
−0.979015 + 0.203789i \(0.934674\pi\)
\(674\) 0 0
\(675\) 2.69765 1.73367i 0.103833 0.0667291i
\(676\) 0 0
\(677\) −7.19945 50.0733i −0.276697 1.92447i −0.370399 0.928873i \(-0.620779\pi\)
0.0937016 0.995600i \(-0.470130\pi\)
\(678\) 0 0
\(679\) 1.12058 + 7.79382i 0.0430040 + 0.299099i
\(680\) 0 0
\(681\) −8.01797 + 5.15284i −0.307249 + 0.197457i
\(682\) 0 0
\(683\) −13.2896 + 29.1002i −0.508512 + 1.11349i 0.465096 + 0.885260i \(0.346020\pi\)
−0.973608 + 0.228226i \(0.926707\pi\)
\(684\) 0 0
\(685\) 1.08369 7.53722i 0.0414056 0.287982i
\(686\) 0 0
\(687\) −6.73427 1.97736i −0.256928 0.0754410i
\(688\) 0 0
\(689\) 4.26873 29.6897i 0.162626 1.13109i
\(690\) 0 0
\(691\) −29.2522 18.7993i −1.11281 0.715158i −0.150904 0.988548i \(-0.548219\pi\)
−0.961903 + 0.273390i \(0.911855\pi\)
\(692\) 0 0
\(693\) 2.79770 3.22872i 0.106276 0.122649i
\(694\) 0 0
\(695\) −7.78327 + 17.0430i −0.295236 + 0.646478i
\(696\) 0 0
\(697\) 3.67463 + 2.36154i 0.139187 + 0.0894498i
\(698\) 0 0
\(699\) 9.33811 0.353200
\(700\) 0 0
\(701\) −4.30651 9.42994i −0.162655 0.356164i 0.810702 0.585458i \(-0.199085\pi\)
−0.973357 + 0.229294i \(0.926358\pi\)
\(702\) 0 0
\(703\) −7.20862 + 50.1370i −0.271878 + 1.89095i
\(704\) 0 0
\(705\) 0.884867 + 1.02119i 0.0333260 + 0.0384603i
\(706\) 0 0
\(707\) 19.4684 0.732185
\(708\) 0 0
\(709\) 7.78656 + 17.0502i 0.292431 + 0.640334i 0.997640 0.0686658i \(-0.0218742\pi\)
−0.705209 + 0.708999i \(0.749147\pi\)
\(710\) 0 0
\(711\) −9.18727 2.69763i −0.344550 0.101169i
\(712\) 0 0
\(713\) 29.8951 + 8.77800i 1.11958 + 0.328739i
\(714\) 0 0
\(715\) 6.89252 + 7.95439i 0.257766 + 0.297477i
\(716\) 0 0
\(717\) −17.3421 + 20.0139i −0.647653 + 0.747431i
\(718\) 0 0
\(719\) 2.89873 0.851145i 0.108104 0.0317423i −0.227233 0.973840i \(-0.572968\pi\)
0.335337 + 0.942098i \(0.391150\pi\)
\(720\) 0 0
\(721\) −16.8925 + 10.8562i −0.629110 + 0.404305i
\(722\) 0 0
\(723\) −20.9742 + 6.15859i −0.780040 + 0.229040i
\(724\) 0 0
\(725\) 4.52144 9.90058i 0.167922 0.367698i
\(726\) 0 0
\(727\) 19.9419 + 23.0141i 0.739603 + 0.853547i 0.993517 0.113680i \(-0.0362638\pi\)
−0.253915 + 0.967227i \(0.581718\pi\)
\(728\) 0 0
\(729\) 0.415415 + 0.909632i 0.0153857 + 0.0336901i
\(730\) 0 0
\(731\) −17.5130 11.2549i −0.647743 0.416279i
\(732\) 0 0
\(733\) 4.42962 1.30065i 0.163612 0.0480408i −0.198901 0.980020i \(-0.563737\pi\)
0.362513 + 0.931979i \(0.381919\pi\)
\(734\) 0 0
\(735\) −0.949086 6.60104i −0.0350076 0.243483i
\(736\) 0 0
\(737\) 13.0343 + 20.8684i 0.480124 + 0.768696i
\(738\) 0 0
\(739\) 4.41634 + 30.7163i 0.162458 + 1.12992i 0.893982 + 0.448103i \(0.147900\pi\)
−0.731524 + 0.681815i \(0.761191\pi\)
\(740\) 0 0
\(741\) −19.1559 + 5.62468i −0.703710 + 0.206628i
\(742\) 0 0
\(743\) 4.00743 + 2.57542i 0.147018 + 0.0944830i 0.612082 0.790794i \(-0.290332\pi\)
−0.465064 + 0.885277i \(0.653969\pi\)
\(744\) 0 0
\(745\) 12.1165 + 26.5315i 0.443916 + 0.972039i
\(746\) 0 0
\(747\) 5.75164 + 6.63775i 0.210442 + 0.242862i
\(748\) 0 0
\(749\) 8.19668 17.9482i 0.299500 0.655814i
\(750\) 0 0
\(751\) 18.2482 5.35816i 0.665886 0.195522i 0.0687160 0.997636i \(-0.478110\pi\)
0.597170 + 0.802114i \(0.296292\pi\)
\(752\) 0 0
\(753\) −7.15467 + 4.59803i −0.260731 + 0.167561i
\(754\) 0 0
\(755\) 13.3108 3.90841i 0.484430 0.142241i
\(756\) 0 0
\(757\) −3.76964 + 4.35040i −0.137010 + 0.158118i −0.820108 0.572209i \(-0.806087\pi\)
0.683098 + 0.730327i \(0.260632\pi\)
\(758\) 0 0
\(759\) 17.0787 + 19.7098i 0.619916 + 0.715422i
\(760\) 0 0
\(761\) −25.5030 7.48836i −0.924483 0.271453i −0.215358 0.976535i \(-0.569092\pi\)
−0.709125 + 0.705083i \(0.750910\pi\)
\(762\) 0 0
\(763\) 3.13058 + 0.919221i 0.113335 + 0.0332780i
\(764\) 0 0
\(765\) −1.25147 2.74034i −0.0452470 0.0990771i
\(766\) 0 0
\(767\) 23.0947 0.833902
\(768\) 0 0
\(769\) 10.0105 + 11.5528i 0.360989 + 0.416604i 0.906971 0.421193i \(-0.138389\pi\)
−0.545982 + 0.837797i \(0.683843\pi\)
\(770\) 0 0
\(771\) 1.73310 12.0540i 0.0624161 0.434113i
\(772\) 0 0
\(773\) −12.4743 27.3149i −0.448669 0.982447i −0.989925 0.141590i \(-0.954779\pi\)
0.541257 0.840857i \(-0.317949\pi\)
\(774\) 0 0
\(775\) −11.5157 −0.413655
\(776\) 0 0
\(777\) 7.93176 + 5.09743i 0.284550 + 0.182869i
\(778\) 0 0
\(779\) 6.15874 13.4858i 0.220660 0.483178i
\(780\) 0 0
\(781\) 8.12464 9.37633i 0.290722 0.335511i
\(782\) 0