Properties

Label 1386.2.ba.a.989.1
Level $1386$
Weight $2$
Character 1386.989
Analytic conductor $11.067$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 989.1
Character \(\chi\) \(=\) 1386.989
Dual form 1386.2.ba.a.1187.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-3.19684 - 1.84570i) q^{5} +(-1.52985 - 2.15860i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-3.19684 - 1.84570i) q^{5} +(-1.52985 - 2.15860i) q^{7} +1.00000 q^{8} +(3.19684 - 1.84570i) q^{10} +(0.412474 + 3.29088i) q^{11} -5.60520i q^{13} +(2.63433 - 0.245585i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.39461 - 2.41554i) q^{17} +(-2.14631 - 1.23917i) q^{19} +3.69140i q^{20} +(-3.05622 - 1.28823i) q^{22} +(3.26215 + 1.88340i) q^{23} +(4.31321 + 7.47069i) q^{25} +(4.85424 + 2.80260i) q^{26} +(-1.10448 + 2.40419i) q^{28} -1.51011 q^{29} +(-1.70296 - 2.94961i) q^{31} +(-0.500000 - 0.866025i) q^{32} +2.78923 q^{34} +(0.906550 + 9.72435i) q^{35} +(2.85865 - 4.95132i) q^{37} +(2.14631 - 1.23917i) q^{38} +(-3.19684 - 1.84570i) q^{40} -6.24731 q^{41} +7.72006i q^{43} +(2.64375 - 2.00265i) q^{44} +(-3.26215 + 1.88340i) q^{46} +(8.98162 + 5.18554i) q^{47} +(-2.31914 + 6.60467i) q^{49} -8.62641 q^{50} +(-4.85424 + 2.80260i) q^{52} +(-9.27677 + 5.35595i) q^{53} +(4.75535 - 11.2817i) q^{55} +(-1.52985 - 2.15860i) q^{56} +(0.755057 - 1.30780i) q^{58} +(-11.6232 + 6.71066i) q^{59} +(-2.13230 - 1.23108i) q^{61} +3.40592 q^{62} +1.00000 q^{64} +(-10.3455 + 17.9189i) q^{65} +(5.66594 + 9.81369i) q^{67} +(-1.39461 + 2.41554i) q^{68} +(-8.87481 - 4.07708i) q^{70} +5.15087i q^{71} +(-4.53946 + 2.62086i) q^{73} +(2.85865 + 4.95132i) q^{74} +2.47835i q^{76} +(6.47267 - 5.92490i) q^{77} +(-0.250209 - 0.144458i) q^{79} +(3.19684 - 1.84570i) q^{80} +(3.12366 - 5.41033i) q^{82} -10.2522 q^{83} +10.2961i q^{85} +(-6.68577 - 3.86003i) q^{86} +(0.412474 + 3.29088i) q^{88} +(13.7391 + 7.93225i) q^{89} +(-12.0994 + 8.57509i) q^{91} -3.76681i q^{92} +(-8.98162 + 5.18554i) q^{94} +(4.57428 + 7.92289i) q^{95} +4.58628 q^{97} +(-4.56024 - 5.31076i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} + O(q^{10}) \) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} - 2q^{11} - 16q^{16} - 4q^{17} + 4q^{22} + 4q^{25} - 16q^{29} + 4q^{31} - 16q^{32} + 8q^{34} - 16q^{35} + 4q^{37} + 32q^{41} - 2q^{44} + 20q^{49} - 8q^{50} - 12q^{55} + 8q^{58} - 8q^{62} + 32q^{64} - 8q^{67} - 4q^{68} - 4q^{70} + 4q^{74} - 14q^{77} - 16q^{82} - 88q^{83} - 2q^{88} + 24q^{95} - 32q^{97} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −3.19684 1.84570i −1.42967 0.825421i −0.432577 0.901597i \(-0.642396\pi\)
−0.997094 + 0.0761754i \(0.975729\pi\)
\(6\) 0 0
\(7\) −1.52985 2.15860i −0.578228 0.815875i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 3.19684 1.84570i 1.01093 0.583661i
\(11\) 0.412474 + 3.29088i 0.124365 + 0.992236i
\(12\) 0 0
\(13\) 5.60520i 1.55460i −0.629129 0.777301i \(-0.716588\pi\)
0.629129 0.777301i \(-0.283412\pi\)
\(14\) 2.63433 0.245585i 0.704054 0.0656352i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.39461 2.41554i −0.338243 0.585855i 0.645859 0.763457i \(-0.276499\pi\)
−0.984102 + 0.177602i \(0.943166\pi\)
\(18\) 0 0
\(19\) −2.14631 1.23917i −0.492398 0.284286i 0.233171 0.972436i \(-0.425090\pi\)
−0.725569 + 0.688150i \(0.758423\pi\)
\(20\) 3.69140i 0.825421i
\(21\) 0 0
\(22\) −3.05622 1.28823i −0.651588 0.274651i
\(23\) 3.26215 + 1.88340i 0.680206 + 0.392717i 0.799933 0.600090i \(-0.204869\pi\)
−0.119727 + 0.992807i \(0.538202\pi\)
\(24\) 0 0
\(25\) 4.31321 + 7.47069i 0.862641 + 1.49414i
\(26\) 4.85424 + 2.80260i 0.951995 + 0.549635i
\(27\) 0 0
\(28\) −1.10448 + 2.40419i −0.208727 + 0.454349i
\(29\) −1.51011 −0.280421 −0.140210 0.990122i \(-0.544778\pi\)
−0.140210 + 0.990122i \(0.544778\pi\)
\(30\) 0 0
\(31\) −1.70296 2.94961i −0.305860 0.529766i 0.671592 0.740921i \(-0.265611\pi\)
−0.977453 + 0.211155i \(0.932277\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 2.78923 0.478348
\(35\) 0.906550 + 9.72435i 0.153235 + 1.64372i
\(36\) 0 0
\(37\) 2.85865 4.95132i 0.469959 0.813993i −0.529451 0.848340i \(-0.677602\pi\)
0.999410 + 0.0343479i \(0.0109354\pi\)
\(38\) 2.14631 1.23917i 0.348178 0.201021i
\(39\) 0 0
\(40\) −3.19684 1.84570i −0.505465 0.291831i
\(41\) −6.24731 −0.975666 −0.487833 0.872937i \(-0.662213\pi\)
−0.487833 + 0.872937i \(0.662213\pi\)
\(42\) 0 0
\(43\) 7.72006i 1.17730i 0.808389 + 0.588649i \(0.200340\pi\)
−0.808389 + 0.588649i \(0.799660\pi\)
\(44\) 2.64375 2.00265i 0.398560 0.301911i
\(45\) 0 0
\(46\) −3.26215 + 1.88340i −0.480978 + 0.277693i
\(47\) 8.98162 + 5.18554i 1.31010 + 0.756389i 0.982113 0.188292i \(-0.0602953\pi\)
0.327991 + 0.944681i \(0.393629\pi\)
\(48\) 0 0
\(49\) −2.31914 + 6.60467i −0.331305 + 0.943524i
\(50\) −8.62641 −1.21996
\(51\) 0 0
\(52\) −4.85424 + 2.80260i −0.673162 + 0.388650i
\(53\) −9.27677 + 5.35595i −1.27426 + 0.735696i −0.975787 0.218721i \(-0.929811\pi\)
−0.298475 + 0.954417i \(0.596478\pi\)
\(54\) 0 0
\(55\) 4.75535 11.2817i 0.641211 1.52123i
\(56\) −1.52985 2.15860i −0.204434 0.288456i
\(57\) 0 0
\(58\) 0.755057 1.30780i 0.0991438 0.171722i
\(59\) −11.6232 + 6.71066i −1.51321 + 0.873654i −0.513333 + 0.858190i \(0.671589\pi\)
−0.999880 + 0.0154644i \(0.995077\pi\)
\(60\) 0 0
\(61\) −2.13230 1.23108i −0.273013 0.157624i 0.357243 0.934011i \(-0.383717\pi\)
−0.630256 + 0.776387i \(0.717050\pi\)
\(62\) 3.40592 0.432552
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −10.3455 + 17.9189i −1.28320 + 2.22257i
\(66\) 0 0
\(67\) 5.66594 + 9.81369i 0.692204 + 1.19893i 0.971114 + 0.238616i \(0.0766936\pi\)
−0.278910 + 0.960317i \(0.589973\pi\)
\(68\) −1.39461 + 2.41554i −0.169122 + 0.292927i
\(69\) 0 0
\(70\) −8.87481 4.07708i −1.06074 0.487304i
\(71\) 5.15087i 0.611296i 0.952145 + 0.305648i \(0.0988730\pi\)
−0.952145 + 0.305648i \(0.901127\pi\)
\(72\) 0 0
\(73\) −4.53946 + 2.62086i −0.531303 + 0.306748i −0.741547 0.670901i \(-0.765908\pi\)
0.210244 + 0.977649i \(0.432574\pi\)
\(74\) 2.85865 + 4.95132i 0.332311 + 0.575580i
\(75\) 0 0
\(76\) 2.47835i 0.284286i
\(77\) 6.47267 5.92490i 0.737630 0.675205i
\(78\) 0 0
\(79\) −0.250209 0.144458i −0.0281507 0.0162528i 0.485859 0.874037i \(-0.338507\pi\)
−0.514009 + 0.857785i \(0.671840\pi\)
\(80\) 3.19684 1.84570i 0.357418 0.206355i
\(81\) 0 0
\(82\) 3.12366 5.41033i 0.344950 0.597471i
\(83\) −10.2522 −1.12533 −0.562664 0.826685i \(-0.690224\pi\)
−0.562664 + 0.826685i \(0.690224\pi\)
\(84\) 0 0
\(85\) 10.2961i 1.11677i
\(86\) −6.68577 3.86003i −0.720945 0.416238i
\(87\) 0 0
\(88\) 0.412474 + 3.29088i 0.0439698 + 0.350809i
\(89\) 13.7391 + 7.93225i 1.45634 + 0.840816i 0.998829 0.0483889i \(-0.0154087\pi\)
0.457508 + 0.889205i \(0.348742\pi\)
\(90\) 0 0
\(91\) −12.0994 + 8.57509i −1.26836 + 0.898914i
\(92\) 3.76681i 0.392717i
\(93\) 0 0
\(94\) −8.98162 + 5.18554i −0.926383 + 0.534848i
\(95\) 4.57428 + 7.92289i 0.469311 + 0.812871i
\(96\) 0 0
\(97\) 4.58628 0.465666 0.232833 0.972517i \(-0.425200\pi\)
0.232833 + 0.972517i \(0.425200\pi\)
\(98\) −4.56024 5.31076i −0.460654 0.536468i
\(99\) 0 0
\(100\) 4.31321 7.47069i 0.431321 0.747069i
\(101\) −1.45801 2.52536i −0.145078 0.251282i 0.784324 0.620351i \(-0.213010\pi\)
−0.929402 + 0.369069i \(0.879677\pi\)
\(102\) 0 0
\(103\) −4.61616 + 7.99543i −0.454844 + 0.787813i −0.998679 0.0513790i \(-0.983638\pi\)
0.543835 + 0.839192i \(0.316972\pi\)
\(104\) 5.60520i 0.549635i
\(105\) 0 0
\(106\) 10.7119i 1.04043i
\(107\) 1.81237 3.13911i 0.175208 0.303469i −0.765025 0.644000i \(-0.777274\pi\)
0.940233 + 0.340531i \(0.110607\pi\)
\(108\) 0 0
\(109\) 13.9355 8.04565i 1.33478 0.770634i 0.348749 0.937216i \(-0.386607\pi\)
0.986028 + 0.166583i \(0.0532732\pi\)
\(110\) 7.39258 + 9.75911i 0.704855 + 0.930495i
\(111\) 0 0
\(112\) 2.63433 0.245585i 0.248921 0.0232056i
\(113\) 18.8371i 1.77204i −0.463643 0.886022i \(-0.653458\pi\)
0.463643 0.886022i \(-0.346542\pi\)
\(114\) 0 0
\(115\) −6.95239 12.0419i −0.648314 1.12291i
\(116\) 0.755057 + 1.30780i 0.0701052 + 0.121426i
\(117\) 0 0
\(118\) 13.4213i 1.23553i
\(119\) −3.08065 + 6.70582i −0.282403 + 0.614722i
\(120\) 0 0
\(121\) −10.6597 + 2.71480i −0.969066 + 0.246800i
\(122\) 2.13230 1.23108i 0.193049 0.111457i
\(123\) 0 0
\(124\) −1.70296 + 2.94961i −0.152930 + 0.264883i
\(125\) 13.3865i 1.19733i
\(126\) 0 0
\(127\) 8.08283i 0.717235i −0.933485 0.358618i \(-0.883248\pi\)
0.933485 0.358618i \(-0.116752\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −10.3455 17.9189i −0.907361 1.57159i
\(131\) 7.83557 13.5716i 0.684597 1.18576i −0.288967 0.957339i \(-0.593312\pi\)
0.973563 0.228417i \(-0.0733549\pi\)
\(132\) 0 0
\(133\) 0.608644 + 6.52878i 0.0527761 + 0.566117i
\(134\) −11.3319 −0.978925
\(135\) 0 0
\(136\) −1.39461 2.41554i −0.119587 0.207131i
\(137\) −2.55426 + 1.47471i −0.218226 + 0.125993i −0.605128 0.796128i \(-0.706878\pi\)
0.386903 + 0.922120i \(0.373545\pi\)
\(138\) 0 0
\(139\) 4.00952i 0.340083i 0.985437 + 0.170042i \(0.0543902\pi\)
−0.985437 + 0.170042i \(0.945610\pi\)
\(140\) 7.96826 5.64727i 0.673441 0.477282i
\(141\) 0 0
\(142\) −4.46078 2.57543i −0.374341 0.216126i
\(143\) 18.4460 2.31200i 1.54253 0.193339i
\(144\) 0 0
\(145\) 4.82759 + 2.78721i 0.400910 + 0.231465i
\(146\) 5.24171i 0.433807i
\(147\) 0 0
\(148\) −5.71730 −0.469959
\(149\) 3.23457 5.60244i 0.264986 0.458969i −0.702574 0.711611i \(-0.747966\pi\)
0.967560 + 0.252641i \(0.0812993\pi\)
\(150\) 0 0
\(151\) −13.3957 + 7.73400i −1.09012 + 0.629384i −0.933610 0.358292i \(-0.883359\pi\)
−0.156515 + 0.987676i \(0.550026\pi\)
\(152\) −2.14631 1.23917i −0.174089 0.100510i
\(153\) 0 0
\(154\) 1.89478 + 8.56795i 0.152686 + 0.690425i
\(155\) 12.5726i 1.00985i
\(156\) 0 0
\(157\) 9.34257 + 16.1818i 0.745618 + 1.29145i 0.949905 + 0.312538i \(0.101179\pi\)
−0.204287 + 0.978911i \(0.565488\pi\)
\(158\) 0.250209 0.144458i 0.0199056 0.0114925i
\(159\) 0 0
\(160\) 3.69140i 0.291831i
\(161\) −0.925070 9.92301i −0.0729057 0.782043i
\(162\) 0 0
\(163\) 4.62801 8.01595i 0.362494 0.627858i −0.625877 0.779922i \(-0.715259\pi\)
0.988371 + 0.152064i \(0.0485920\pi\)
\(164\) 3.12366 + 5.41033i 0.243917 + 0.422476i
\(165\) 0 0
\(166\) 5.12612 8.87869i 0.397864 0.689120i
\(167\) 16.3875 1.26811 0.634053 0.773289i \(-0.281390\pi\)
0.634053 + 0.773289i \(0.281390\pi\)
\(168\) 0 0
\(169\) −18.4182 −1.41679
\(170\) −8.91672 5.14807i −0.683881 0.394839i
\(171\) 0 0
\(172\) 6.68577 3.86003i 0.509785 0.294325i
\(173\) −10.4622 + 18.1210i −0.795424 + 1.37771i 0.127146 + 0.991884i \(0.459418\pi\)
−0.922570 + 0.385831i \(0.873915\pi\)
\(174\) 0 0
\(175\) 9.52771 20.7395i 0.720228 1.56776i
\(176\) −3.05622 1.28823i −0.230371 0.0971036i
\(177\) 0 0
\(178\) −13.7391 + 7.93225i −1.02979 + 0.594547i
\(179\) −12.9584 + 7.48153i −0.968555 + 0.559196i −0.898795 0.438368i \(-0.855557\pi\)
−0.0697596 + 0.997564i \(0.522223\pi\)
\(180\) 0 0
\(181\) −10.1125 −0.751657 −0.375828 0.926689i \(-0.622642\pi\)
−0.375828 + 0.926689i \(0.622642\pi\)
\(182\) −1.37655 14.7659i −0.102037 1.09452i
\(183\) 0 0
\(184\) 3.26215 + 1.88340i 0.240489 + 0.138846i
\(185\) −18.2773 + 10.5524i −1.34377 + 0.775828i
\(186\) 0 0
\(187\) 7.37400 5.58584i 0.539240 0.408477i
\(188\) 10.3711i 0.756389i
\(189\) 0 0
\(190\) −9.14856 −0.663707
\(191\) −4.57254 2.63995i −0.330857 0.191020i 0.325364 0.945589i \(-0.394513\pi\)
−0.656222 + 0.754568i \(0.727846\pi\)
\(192\) 0 0
\(193\) 19.8361 11.4524i 1.42784 0.824362i 0.430886 0.902406i \(-0.358201\pi\)
0.996950 + 0.0780447i \(0.0248677\pi\)
\(194\) −2.29314 + 3.97184i −0.164638 + 0.285161i
\(195\) 0 0
\(196\) 6.87938 1.29390i 0.491384 0.0924215i
\(197\) 8.56673 0.610354 0.305177 0.952296i \(-0.401284\pi\)
0.305177 + 0.952296i \(0.401284\pi\)
\(198\) 0 0
\(199\) 2.28887 + 3.96444i 0.162254 + 0.281032i 0.935677 0.352859i \(-0.114790\pi\)
−0.773423 + 0.633890i \(0.781457\pi\)
\(200\) 4.31321 + 7.47069i 0.304990 + 0.528258i
\(201\) 0 0
\(202\) 2.91603 0.205171
\(203\) 2.31024 + 3.25974i 0.162147 + 0.228789i
\(204\) 0 0
\(205\) 19.9717 + 11.5307i 1.39488 + 0.805336i
\(206\) −4.61616 7.99543i −0.321623 0.557068i
\(207\) 0 0
\(208\) 4.85424 + 2.80260i 0.336581 + 0.194325i
\(209\) 3.19267 7.57437i 0.220842 0.523930i
\(210\) 0 0
\(211\) 10.0586i 0.692463i 0.938149 + 0.346231i \(0.112539\pi\)
−0.938149 + 0.346231i \(0.887461\pi\)
\(212\) 9.27677 + 5.35595i 0.637131 + 0.367848i
\(213\) 0 0
\(214\) 1.81237 + 3.13911i 0.123891 + 0.214585i
\(215\) 14.2489 24.6798i 0.971767 1.68315i
\(216\) 0 0
\(217\) −3.76177 + 8.18846i −0.255366 + 0.555869i
\(218\) 16.0913i 1.08984i
\(219\) 0 0
\(220\) −12.1479 + 1.52260i −0.819013 + 0.102654i
\(221\) −13.5396 + 7.81708i −0.910770 + 0.525834i
\(222\) 0 0
\(223\) 14.7430 0.987266 0.493633 0.869670i \(-0.335669\pi\)
0.493633 + 0.869670i \(0.335669\pi\)
\(224\) −1.10448 + 2.40419i −0.0737963 + 0.160637i
\(225\) 0 0
\(226\) 16.3134 + 9.41854i 1.08515 + 0.626512i
\(227\) −9.41469 16.3067i −0.624875 1.08232i −0.988565 0.150795i \(-0.951817\pi\)
0.363690 0.931520i \(-0.381517\pi\)
\(228\) 0 0
\(229\) −6.82233 + 11.8166i −0.450832 + 0.780865i −0.998438 0.0558720i \(-0.982206\pi\)
0.547606 + 0.836737i \(0.315539\pi\)
\(230\) 13.9048 0.916854
\(231\) 0 0
\(232\) −1.51011 −0.0991438
\(233\) −3.51518 + 6.08847i −0.230287 + 0.398869i −0.957893 0.287127i \(-0.907300\pi\)
0.727606 + 0.685996i \(0.240633\pi\)
\(234\) 0 0
\(235\) −19.1419 33.1547i −1.24868 2.16278i
\(236\) 11.6232 + 6.71066i 0.756607 + 0.436827i
\(237\) 0 0
\(238\) −4.26709 6.02083i −0.276594 0.390273i
\(239\) −10.3908 −0.672126 −0.336063 0.941840i \(-0.609095\pi\)
−0.336063 + 0.941840i \(0.609095\pi\)
\(240\) 0 0
\(241\) −9.24972 + 5.34033i −0.595827 + 0.344001i −0.767398 0.641171i \(-0.778449\pi\)
0.171571 + 0.985172i \(0.445116\pi\)
\(242\) 2.97878 10.5890i 0.191483 0.680687i
\(243\) 0 0
\(244\) 2.46216i 0.157624i
\(245\) 19.6041 16.8337i 1.25246 1.07546i
\(246\) 0 0
\(247\) −6.94581 + 12.0305i −0.441951 + 0.765482i
\(248\) −1.70296 2.94961i −0.108138 0.187300i
\(249\) 0 0
\(250\) 11.5931 + 6.69326i 0.733210 + 0.423319i
\(251\) 9.19949i 0.580667i −0.956926 0.290333i \(-0.906234\pi\)
0.956926 0.290333i \(-0.0937662\pi\)
\(252\) 0 0
\(253\) −4.85250 + 11.5122i −0.305074 + 0.723765i
\(254\) 6.99993 + 4.04141i 0.439215 + 0.253581i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −17.8743 10.3197i −1.11497 0.643728i −0.174858 0.984594i \(-0.555947\pi\)
−0.940112 + 0.340865i \(0.889280\pi\)
\(258\) 0 0
\(259\) −15.0612 + 1.40408i −0.935860 + 0.0872453i
\(260\) 20.6910 1.28320
\(261\) 0 0
\(262\) 7.83557 + 13.5716i 0.484083 + 0.838456i
\(263\) −13.1613 22.7960i −0.811561 1.40566i −0.911771 0.410698i \(-0.865285\pi\)
0.100211 0.994966i \(-0.468048\pi\)
\(264\) 0 0
\(265\) 39.5419 2.42904
\(266\) −5.95841 2.73729i −0.365334 0.167834i
\(267\) 0 0
\(268\) 5.66594 9.81369i 0.346102 0.599467i
\(269\) −7.04033 + 4.06473i −0.429256 + 0.247831i −0.699030 0.715093i \(-0.746385\pi\)
0.269773 + 0.962924i \(0.413051\pi\)
\(270\) 0 0
\(271\) 12.6065 + 7.27836i 0.765790 + 0.442129i 0.831371 0.555718i \(-0.187557\pi\)
−0.0655809 + 0.997847i \(0.520890\pi\)
\(272\) 2.78923 0.169122
\(273\) 0 0
\(274\) 2.94941i 0.178180i
\(275\) −22.8060 + 17.2757i −1.37526 + 1.04176i
\(276\) 0 0
\(277\) −25.9763 + 14.9974i −1.56077 + 0.901109i −0.563587 + 0.826057i \(0.690579\pi\)
−0.997180 + 0.0750526i \(0.976088\pi\)
\(278\) −3.47235 2.00476i −0.208258 0.120238i
\(279\) 0 0
\(280\) 0.906550 + 9.72435i 0.0541767 + 0.581141i
\(281\) 12.8423 0.766110 0.383055 0.923726i \(-0.374872\pi\)
0.383055 + 0.923726i \(0.374872\pi\)
\(282\) 0 0
\(283\) −6.35099 + 3.66675i −0.377527 + 0.217965i −0.676742 0.736220i \(-0.736609\pi\)
0.299215 + 0.954186i \(0.403275\pi\)
\(284\) 4.46078 2.57543i 0.264699 0.152824i
\(285\) 0 0
\(286\) −7.22076 + 17.1307i −0.426972 + 1.01296i
\(287\) 9.55743 + 13.4855i 0.564157 + 0.796022i
\(288\) 0 0
\(289\) 4.61011 7.98495i 0.271183 0.469703i
\(290\) −4.82759 + 2.78721i −0.283486 + 0.163671i
\(291\) 0 0
\(292\) 4.53946 + 2.62086i 0.265652 + 0.153374i
\(293\) −6.05343 −0.353645 −0.176823 0.984243i \(-0.556582\pi\)
−0.176823 + 0.984243i \(0.556582\pi\)
\(294\) 0 0
\(295\) 49.5434 2.88453
\(296\) 2.85865 4.95132i 0.166156 0.287790i
\(297\) 0 0
\(298\) 3.23457 + 5.60244i 0.187373 + 0.324540i
\(299\) 10.5569 18.2850i 0.610518 1.05745i
\(300\) 0 0
\(301\) 16.6646 11.8105i 0.960529 0.680747i
\(302\) 15.4680i 0.890083i
\(303\) 0 0
\(304\) 2.14631 1.23917i 0.123099 0.0710715i
\(305\) 4.54441 + 7.87116i 0.260212 + 0.450701i
\(306\) 0 0
\(307\) 6.24654i 0.356509i 0.983984 + 0.178255i \(0.0570450\pi\)
−0.983984 + 0.178255i \(0.942955\pi\)
\(308\) −8.36745 2.64305i −0.476780 0.150602i
\(309\) 0 0
\(310\) −10.8882 6.28629i −0.618407 0.357038i
\(311\) −8.45677 + 4.88252i −0.479539 + 0.276862i −0.720225 0.693741i \(-0.755961\pi\)
0.240685 + 0.970603i \(0.422628\pi\)
\(312\) 0 0
\(313\) −16.0158 + 27.7402i −0.905266 + 1.56797i −0.0847068 + 0.996406i \(0.526995\pi\)
−0.820559 + 0.571561i \(0.806338\pi\)
\(314\) −18.6851 −1.05446
\(315\) 0 0
\(316\) 0.288917i 0.0162528i
\(317\) −18.5774 10.7256i −1.04341 0.602412i −0.122612 0.992455i \(-0.539127\pi\)
−0.920797 + 0.390042i \(0.872460\pi\)
\(318\) 0 0
\(319\) −0.622882 4.96959i −0.0348747 0.278244i
\(320\) −3.19684 1.84570i −0.178709 0.103178i
\(321\) 0 0
\(322\) 9.05612 + 4.16037i 0.504678 + 0.231848i
\(323\) 6.91267i 0.384631i
\(324\) 0 0
\(325\) 41.8747 24.1764i 2.32279 1.34106i
\(326\) 4.62801 + 8.01595i 0.256322 + 0.443963i
\(327\) 0 0
\(328\) −6.24731 −0.344950
\(329\) −2.54698 27.3208i −0.140419 1.50625i
\(330\) 0 0
\(331\) 15.3327 26.5569i 0.842759 1.45970i −0.0447947 0.998996i \(-0.514263\pi\)
0.887553 0.460705i \(-0.152403\pi\)
\(332\) 5.12612 + 8.87869i 0.281332 + 0.487282i
\(333\) 0 0
\(334\) −8.19377 + 14.1920i −0.448343 + 0.776554i
\(335\) 41.8304i 2.28544i
\(336\) 0 0
\(337\) 33.3731i 1.81795i 0.416853 + 0.908974i \(0.363133\pi\)
−0.416853 + 0.908974i \(0.636867\pi\)
\(338\) 9.20911 15.9507i 0.500910 0.867601i
\(339\) 0 0
\(340\) 8.91672 5.14807i 0.483577 0.279193i
\(341\) 9.00438 6.82086i 0.487614 0.369370i
\(342\) 0 0
\(343\) 17.8048 5.09803i 0.961368 0.275268i
\(344\) 7.72006i 0.416238i
\(345\) 0 0
\(346\) −10.4622 18.1210i −0.562450 0.974191i
\(347\) 10.0767 + 17.4533i 0.540943 + 0.936941i 0.998850 + 0.0479408i \(0.0152659\pi\)
−0.457907 + 0.889000i \(0.651401\pi\)
\(348\) 0 0
\(349\) 25.8276i 1.38252i −0.722607 0.691259i \(-0.757056\pi\)
0.722607 0.691259i \(-0.242944\pi\)
\(350\) 13.1971 + 18.6210i 0.705414 + 0.995334i
\(351\) 0 0
\(352\) 2.64375 2.00265i 0.140912 0.106742i
\(353\) −8.21248 + 4.74148i −0.437106 + 0.252363i −0.702369 0.711813i \(-0.747875\pi\)
0.265263 + 0.964176i \(0.414541\pi\)
\(354\) 0 0
\(355\) 9.50695 16.4665i 0.504577 0.873952i
\(356\) 15.8645i 0.840816i
\(357\) 0 0
\(358\) 14.9631i 0.790822i
\(359\) −5.42112 + 9.38966i −0.286116 + 0.495567i −0.972879 0.231314i \(-0.925698\pi\)
0.686763 + 0.726881i \(0.259031\pi\)
\(360\) 0 0
\(361\) −6.42890 11.1352i −0.338363 0.586062i
\(362\) 5.05625 8.75769i 0.265751 0.460294i
\(363\) 0 0
\(364\) 13.4759 + 6.19084i 0.706331 + 0.324488i
\(365\) 19.3492 1.01279
\(366\) 0 0
\(367\) 4.46446 + 7.73268i 0.233043 + 0.403642i 0.958702 0.284412i \(-0.0917983\pi\)
−0.725659 + 0.688054i \(0.758465\pi\)
\(368\) −3.26215 + 1.88340i −0.170051 + 0.0981792i
\(369\) 0 0
\(370\) 21.1048i 1.09719i
\(371\) 25.7534 + 11.8311i 1.33705 + 0.614240i
\(372\) 0 0
\(373\) −12.8877 7.44073i −0.667301 0.385266i 0.127752 0.991806i \(-0.459224\pi\)
−0.795053 + 0.606540i \(0.792557\pi\)
\(374\) 1.15048 + 9.17900i 0.0594900 + 0.474635i
\(375\) 0 0
\(376\) 8.98162 + 5.18554i 0.463192 + 0.267424i
\(377\) 8.46448i 0.435943i
\(378\) 0 0
\(379\) 30.2827 1.55552 0.777759 0.628563i \(-0.216356\pi\)
0.777759 + 0.628563i \(0.216356\pi\)
\(380\) 4.57428 7.92289i 0.234656 0.406436i
\(381\) 0 0
\(382\) 4.57254 2.63995i 0.233951 0.135072i
\(383\) 18.4934 + 10.6772i 0.944969 + 0.545578i 0.891514 0.452992i \(-0.149643\pi\)
0.0534545 + 0.998570i \(0.482977\pi\)
\(384\) 0 0
\(385\) −31.6277 + 6.99438i −1.61190 + 0.356467i
\(386\) 22.9048i 1.16582i
\(387\) 0 0
\(388\) −2.29314 3.97184i −0.116417 0.201639i
\(389\) 6.05094 3.49351i 0.306795 0.177128i −0.338696 0.940896i \(-0.609986\pi\)
0.645491 + 0.763768i \(0.276653\pi\)
\(390\) 0 0
\(391\) 10.5065i 0.531335i
\(392\) −2.31914 + 6.60467i −0.117134 + 0.333586i
\(393\) 0 0
\(394\) −4.28337 + 7.41901i −0.215793 + 0.373764i
\(395\) 0.533253 + 0.923622i 0.0268309 + 0.0464725i
\(396\) 0 0
\(397\) −5.27929 + 9.14400i −0.264960 + 0.458924i −0.967553 0.252668i \(-0.918692\pi\)
0.702593 + 0.711592i \(0.252025\pi\)
\(398\) −4.57774 −0.229462
\(399\) 0 0
\(400\) −8.62641 −0.431321
\(401\) 8.21248 + 4.74148i 0.410112 + 0.236778i 0.690838 0.723010i \(-0.257242\pi\)
−0.280726 + 0.959788i \(0.590575\pi\)
\(402\) 0 0
\(403\) −16.5331 + 9.54542i −0.823575 + 0.475491i
\(404\) −1.45801 + 2.52536i −0.0725389 + 0.125641i
\(405\) 0 0
\(406\) −3.97813 + 0.370860i −0.197431 + 0.0184055i
\(407\) 17.4733 + 7.36517i 0.866120 + 0.365078i
\(408\) 0 0
\(409\) −1.48918 + 0.859778i −0.0736351 + 0.0425133i −0.536366 0.843986i \(-0.680203\pi\)
0.462730 + 0.886499i \(0.346870\pi\)
\(410\) −19.9717 + 11.5307i −0.986331 + 0.569459i
\(411\) 0 0
\(412\) 9.23233 0.454844
\(413\) 32.2674 + 14.8236i 1.58777 + 0.729422i
\(414\) 0 0
\(415\) 32.7748 + 18.9225i 1.60885 + 0.928870i
\(416\) −4.85424 + 2.80260i −0.237999 + 0.137409i
\(417\) 0 0
\(418\) 4.96326 + 6.55212i 0.242761 + 0.320475i
\(419\) 5.34038i 0.260895i 0.991455 + 0.130447i \(0.0416414\pi\)
−0.991455 + 0.130447i \(0.958359\pi\)
\(420\) 0 0
\(421\) −27.1036 −1.32095 −0.660475 0.750848i \(-0.729645\pi\)
−0.660475 + 0.750848i \(0.729645\pi\)
\(422\) −8.71101 5.02930i −0.424045 0.244823i
\(423\) 0 0
\(424\) −9.27677 + 5.35595i −0.450520 + 0.260108i
\(425\) 12.0305 20.8374i 0.583565 1.01076i
\(426\) 0 0
\(427\) 0.604670 + 6.48615i 0.0292620 + 0.313887i
\(428\) −3.62473 −0.175208
\(429\) 0 0
\(430\) 14.2489 + 24.6798i 0.687143 + 1.19017i
\(431\) 3.80062 + 6.58286i 0.183069 + 0.317085i 0.942924 0.333007i \(-0.108063\pi\)
−0.759855 + 0.650093i \(0.774730\pi\)
\(432\) 0 0
\(433\) −31.9514 −1.53549 −0.767744 0.640757i \(-0.778621\pi\)
−0.767744 + 0.640757i \(0.778621\pi\)
\(434\) −5.21053 7.35202i −0.250113 0.352908i
\(435\) 0 0
\(436\) −13.9355 8.04565i −0.667388 0.385317i
\(437\) −4.66773 8.08475i −0.223288 0.386746i
\(438\) 0 0
\(439\) −3.37246 1.94709i −0.160959 0.0929294i 0.417357 0.908743i \(-0.362956\pi\)
−0.578316 + 0.815813i \(0.696290\pi\)
\(440\) 4.75535 11.2817i 0.226702 0.537835i
\(441\) 0 0
\(442\) 15.6342i 0.743641i
\(443\) 4.84958 + 2.79991i 0.230410 + 0.133028i 0.610761 0.791815i \(-0.290863\pi\)
−0.380351 + 0.924842i \(0.624197\pi\)
\(444\) 0 0
\(445\) −29.2811 50.7163i −1.38806 2.40418i
\(446\) −7.37151 + 12.7678i −0.349051 + 0.604575i
\(447\) 0 0
\(448\) −1.52985 2.15860i −0.0722785 0.101984i
\(449\) 19.7608i 0.932570i 0.884635 + 0.466285i \(0.154408\pi\)
−0.884635 + 0.466285i \(0.845592\pi\)
\(450\) 0 0
\(451\) −2.57685 20.5591i −0.121339 0.968092i
\(452\) −16.3134 + 9.41854i −0.767318 + 0.443011i
\(453\) 0 0
\(454\) 18.8294 0.883707
\(455\) 54.5069 5.08139i 2.55532 0.238219i
\(456\) 0 0
\(457\) 16.7231 + 9.65507i 0.782272 + 0.451645i 0.837235 0.546843i \(-0.184171\pi\)
−0.0549627 + 0.998488i \(0.517504\pi\)
\(458\) −6.82233 11.8166i −0.318787 0.552155i
\(459\) 0 0
\(460\) −6.95239 + 12.0419i −0.324157 + 0.561456i
\(461\) 6.95967 0.324144 0.162072 0.986779i \(-0.448182\pi\)
0.162072 + 0.986779i \(0.448182\pi\)
\(462\) 0 0
\(463\) 16.2724 0.756243 0.378121 0.925756i \(-0.376570\pi\)
0.378121 + 0.925756i \(0.376570\pi\)
\(464\) 0.755057 1.30780i 0.0350526 0.0607129i
\(465\) 0 0
\(466\) −3.51518 6.08847i −0.162837 0.282043i
\(467\) −1.39696 0.806535i −0.0646436 0.0373220i 0.467330 0.884083i \(-0.345216\pi\)
−0.531973 + 0.846761i \(0.678549\pi\)
\(468\) 0 0
\(469\) 12.5158 27.2440i 0.577928 1.25801i
\(470\) 38.2838 1.76590
\(471\) 0 0
\(472\) −11.6232 + 6.71066i −0.535002 + 0.308883i
\(473\) −25.4058 + 3.18432i −1.16816 + 0.146415i
\(474\) 0 0
\(475\) 21.3792i 0.980947i
\(476\) 7.34774 0.684991i 0.336783 0.0313965i
\(477\) 0 0
\(478\) 5.19541 8.99871i 0.237632 0.411591i
\(479\) −16.9520 29.3616i −0.774555 1.34157i −0.935045 0.354530i \(-0.884641\pi\)
0.160490 0.987037i \(-0.448693\pi\)
\(480\) 0 0
\(481\) −27.7531 16.0233i −1.26543 0.730599i
\(482\) 10.6807i 0.486490i
\(483\) 0 0
\(484\) 7.68095 + 7.87420i 0.349134 + 0.357918i
\(485\) −14.6616 8.46489i −0.665750 0.384371i
\(486\) 0 0
\(487\) −1.52594 2.64300i −0.0691468 0.119766i 0.829379 0.558686i \(-0.188694\pi\)
−0.898526 + 0.438920i \(0.855361\pi\)
\(488\) −2.13230 1.23108i −0.0965246 0.0557285i
\(489\) 0 0
\(490\) 4.77630 + 25.3945i 0.215771 + 1.14721i
\(491\) −35.7449 −1.61315 −0.806573 0.591134i \(-0.798680\pi\)
−0.806573 + 0.591134i \(0.798680\pi\)
\(492\) 0 0
\(493\) 2.10602 + 3.64774i 0.0948505 + 0.164286i
\(494\) −6.94581 12.0305i −0.312507 0.541278i
\(495\) 0 0
\(496\) 3.40592 0.152930
\(497\) 11.1187 7.88004i 0.498741 0.353468i
\(498\) 0 0
\(499\) −3.75597 + 6.50553i −0.168140 + 0.291227i −0.937766 0.347268i \(-0.887109\pi\)
0.769626 + 0.638495i \(0.220443\pi\)
\(500\) −11.5931 + 6.69326i −0.518458 + 0.299332i
\(501\) 0 0
\(502\) 7.96699 + 4.59974i 0.355584 + 0.205297i
\(503\) −21.5419 −0.960507 −0.480253 0.877130i \(-0.659455\pi\)
−0.480253 + 0.877130i \(0.659455\pi\)
\(504\) 0 0
\(505\) 10.7642i 0.479002i
\(506\) −7.54360 9.95848i −0.335354 0.442709i
\(507\) 0 0
\(508\) −6.99993 + 4.04141i −0.310572 + 0.179309i
\(509\) −26.1028 15.0705i −1.15699 0.667986i −0.206406 0.978466i \(-0.566177\pi\)
−0.950580 + 0.310480i \(0.899510\pi\)
\(510\) 0 0
\(511\) 12.6021 + 5.78938i 0.557483 + 0.256107i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 17.8743 10.3197i 0.788403 0.455185i
\(515\) 29.5143 17.0401i 1.30056 0.750876i
\(516\) 0 0
\(517\) −13.3603 + 31.6963i −0.587585 + 1.39400i
\(518\) 6.31465 13.7455i 0.277450 0.603941i
\(519\) 0 0
\(520\) −10.3455 + 17.9189i −0.453680 + 0.785797i
\(521\) 27.8685 16.0899i 1.22094 0.704909i 0.255821 0.966724i \(-0.417654\pi\)
0.965118 + 0.261815i \(0.0843209\pi\)
\(522\) 0 0
\(523\) 3.03873 + 1.75441i 0.132874 + 0.0767149i 0.564964 0.825116i \(-0.308890\pi\)
−0.432089 + 0.901831i \(0.642224\pi\)
\(524\) −15.6711 −0.684597
\(525\) 0 0
\(526\) 26.3226 1.14772
\(527\) −4.74993 + 8.22713i −0.206910 + 0.358379i
\(528\) 0 0
\(529\) −4.40558 7.63068i −0.191547 0.331769i
\(530\) −19.7709 + 34.2443i −0.858794 + 1.48748i
\(531\) 0 0
\(532\) 5.34977 3.79149i 0.231942 0.164382i
\(533\) 35.0174i 1.51677i
\(534\) 0 0
\(535\) −11.5877 + 6.69016i −0.500980 + 0.289241i
\(536\) 5.66594 + 9.81369i 0.244731 + 0.423887i
\(537\) 0 0
\(538\) 8.12947i 0.350486i
\(539\) −22.6917 4.90774i −0.977401 0.211391i
\(540\) 0 0
\(541\) −3.92948 2.26869i −0.168942 0.0975385i 0.413145 0.910665i \(-0.364430\pi\)
−0.582087 + 0.813127i \(0.697764\pi\)
\(542\) −12.6065 + 7.27836i −0.541495 + 0.312632i
\(543\) 0 0
\(544\) −1.39461 + 2.41554i −0.0597935 + 0.103565i
\(545\) −59.3994 −2.54439
\(546\) 0 0
\(547\) 16.8271i 0.719477i −0.933053 0.359738i \(-0.882866\pi\)
0.933053 0.359738i \(-0.117134\pi\)
\(548\) 2.55426 + 1.47471i 0.109113 + 0.0629963i
\(549\) 0 0
\(550\) −3.55817 28.3884i −0.151721 1.21049i
\(551\) 3.24117 + 1.87129i 0.138079 + 0.0797197i
\(552\) 0 0
\(553\) 0.0709535 + 0.761102i 0.00301725 + 0.0323653i
\(554\) 29.9949i 1.27436i
\(555\) 0 0
\(556\) 3.47235 2.00476i 0.147260 0.0850208i
\(557\) −6.67157 11.5555i −0.282684 0.489622i 0.689361 0.724418i \(-0.257891\pi\)
−0.972045 + 0.234795i \(0.924558\pi\)
\(558\) 0 0
\(559\) 43.2725 1.83023
\(560\) −8.87481 4.07708i −0.375029 0.172288i
\(561\) 0 0
\(562\) −6.42117 + 11.1218i −0.270861 + 0.469144i
\(563\) 16.4049 + 28.4141i 0.691384 + 1.19751i 0.971385 + 0.237512i \(0.0763318\pi\)
−0.280001 + 0.960000i \(0.590335\pi\)
\(564\) 0 0
\(565\) −34.7676 + 60.2192i −1.46268 + 2.53344i
\(566\) 7.33349i 0.308250i
\(567\) 0 0
\(568\) 5.15087i 0.216126i
\(569\) 2.97076 5.14551i 0.124541 0.215711i −0.797012 0.603963i \(-0.793588\pi\)
0.921553 + 0.388252i \(0.126921\pi\)
\(570\) 0 0
\(571\) −31.8007 + 18.3601i −1.33082 + 0.768348i −0.985425 0.170110i \(-0.945588\pi\)
−0.345393 + 0.938458i \(0.612254\pi\)
\(572\) −11.2253 14.8187i −0.469351 0.619602i
\(573\) 0 0
\(574\) −16.4575 + 1.53424i −0.686922 + 0.0640381i
\(575\) 32.4940i 1.35510i
\(576\) 0 0
\(577\) 0.409992 + 0.710127i 0.0170682 + 0.0295630i 0.874433 0.485146i \(-0.161233\pi\)
−0.857365 + 0.514709i \(0.827900\pi\)
\(578\) 4.61011 + 7.98495i 0.191755 + 0.332130i
\(579\) 0 0
\(580\) 5.57443i 0.231465i
\(581\) 15.6843 + 22.1305i 0.650696 + 0.918128i
\(582\) 0 0
\(583\) −21.4522 28.3195i −0.888459 1.17287i
\(584\) −4.53946 + 2.62086i −0.187844 + 0.108452i
\(585\) 0 0
\(586\) 3.02672 5.24243i 0.125032 0.216563i
\(587\) 42.0341i 1.73493i −0.497494 0.867467i \(-0.665746\pi\)
0.497494 0.867467i \(-0.334254\pi\)
\(588\) 0 0
\(589\) 8.44105i 0.347807i
\(590\) −24.7717 + 42.9059i −1.01984 + 1.76641i
\(591\) 0 0
\(592\) 2.85865 + 4.95132i 0.117490 + 0.203498i
\(593\) −13.1169 + 22.7191i −0.538645 + 0.932960i 0.460333 + 0.887747i \(0.347730\pi\)
−0.998977 + 0.0452135i \(0.985603\pi\)
\(594\) 0 0
\(595\) 22.2253 15.7515i 0.911148 0.645749i
\(596\) −6.46913 −0.264986
\(597\) 0 0
\(598\) 10.5569 + 18.2850i 0.431702 + 0.747729i
\(599\) 22.7563 13.1384i 0.929798 0.536819i 0.0430501 0.999073i \(-0.486292\pi\)
0.886748 + 0.462254i \(0.152959\pi\)
\(600\) 0 0
\(601\) 37.0989i 1.51329i 0.653824 + 0.756647i \(0.273164\pi\)
−0.653824 + 0.756647i \(0.726836\pi\)
\(602\) 1.89593 + 20.3372i 0.0772722 + 0.828882i
\(603\) 0 0
\(604\) 13.3957 + 7.73400i 0.545062 + 0.314692i
\(605\) 39.0882 + 10.9959i 1.58916 + 0.447045i
\(606\) 0 0
\(607\) 1.72911 + 0.998300i 0.0701822 + 0.0405197i 0.534680 0.845054i \(-0.320432\pi\)
−0.464498 + 0.885574i \(0.653765\pi\)
\(608\) 2.47835i 0.100510i
\(609\) 0 0
\(610\) −9.08883 −0.367996
\(611\) 29.0660 50.3437i 1.17588 2.03669i
\(612\) 0 0
\(613\) −6.55742 + 3.78593i −0.264852 + 0.152912i −0.626546 0.779385i \(-0.715532\pi\)
0.361694 + 0.932297i \(0.382199\pi\)
\(614\) −5.40966 3.12327i −0.218316 0.126045i
\(615\) 0 0
\(616\) 6.47267 5.92490i 0.260792 0.238721i
\(617\) 17.2159i 0.693084i 0.938034 + 0.346542i \(0.112644\pi\)
−0.938034 + 0.346542i \(0.887356\pi\)
\(618\) 0 0
\(619\) −18.3426 31.7703i −0.737250 1.27695i −0.953729 0.300667i \(-0.902791\pi\)
0.216479 0.976287i \(-0.430543\pi\)
\(620\) 10.8882 6.28629i 0.437280 0.252464i
\(621\) 0 0
\(622\) 9.76504i 0.391542i
\(623\) −3.89607 41.7923i −0.156093 1.67437i
\(624\) 0 0
\(625\) −3.14145 + 5.44116i −0.125658 + 0.217646i
\(626\) −16.0158 27.7402i −0.640120 1.10872i
\(627\) 0 0
\(628\) 9.34257 16.1818i 0.372809 0.645725i
\(629\) −15.9468 −0.635842
\(630\) 0 0
\(631\) −47.4286 −1.88810 −0.944051 0.329801i \(-0.893019\pi\)
−0.944051 + 0.329801i \(0.893019\pi\)
\(632\) −0.250209 0.144458i −0.00995279 0.00574625i
\(633\) 0 0
\(634\) 18.5774 10.7256i 0.737802 0.425970i
\(635\) −14.9185 + 25.8395i −0.592021 + 1.02541i
\(636\) 0 0
\(637\) 37.0204 + 12.9992i 1.46680 + 0.515048i
\(638\) 4.61524 + 1.94537i 0.182719 + 0.0770178i
\(639\) 0 0
\(640\) 3.19684 1.84570i 0.126366 0.0729576i
\(641\) −28.5801 + 16.5007i −1.12884 + 0.651739i −0.943644 0.330962i \(-0.892627\pi\)
−0.185200 + 0.982701i \(0.559293\pi\)
\(642\) 0 0
\(643\) −41.8847 −1.65177 −0.825885 0.563838i \(-0.809324\pi\)
−0.825885 + 0.563838i \(0.809324\pi\)
\(644\) −8.13105 + 5.76264i −0.320408 + 0.227080i
\(645\) 0 0
\(646\) −5.98655 3.45634i −0.235538 0.135988i
\(647\) 17.9616 10.3701i 0.706142 0.407691i −0.103489 0.994631i \(-0.533001\pi\)
0.809631 + 0.586939i \(0.199667\pi\)
\(648\) 0 0
\(649\) −26.8782 35.4826i −1.05506 1.39281i
\(650\) 48.3527i 1.89655i
\(651\) 0 0
\(652\) −9.25602 −0.362494
\(653\) 6.73045 + 3.88583i 0.263383 + 0.152064i 0.625877 0.779922i \(-0.284741\pi\)
−0.362494 + 0.931986i \(0.618075\pi\)
\(654\) 0 0
\(655\) −50.0982 + 28.9242i −1.95750 + 1.13016i
\(656\) 3.12366 5.41033i 0.121958 0.211238i
\(657\) 0 0
\(658\) 24.9340 + 11.4547i 0.972029 + 0.446549i
\(659\) −44.6638 −1.73986 −0.869928 0.493180i \(-0.835835\pi\)
−0.869928 + 0.493180i \(0.835835\pi\)
\(660\) 0 0
\(661\) 3.14521 + 5.44767i 0.122335 + 0.211890i 0.920688 0.390300i \(-0.127629\pi\)
−0.798353 + 0.602189i \(0.794295\pi\)
\(662\) 15.3327 + 26.5569i 0.595920 + 1.03216i
\(663\) 0 0
\(664\) −10.2522 −0.397864
\(665\) 10.1044 21.9949i 0.391833 0.852924i
\(666\) 0 0
\(667\) −4.92622 2.84415i −0.190744 0.110126i
\(668\) −8.19377 14.1920i −0.317027 0.549106i
\(669\) 0 0
\(670\) 36.2262 + 20.9152i 1.39954 + 0.808025i
\(671\) 3.17182 7.52491i 0.122447 0.290496i
\(672\) 0 0
\(673\) 4.96695i 0.191462i 0.995407 + 0.0957309i \(0.0305188\pi\)
−0.995407 + 0.0957309i \(0.969481\pi\)
\(674\) −28.9019 16.6865i −1.11326 0.642742i
\(675\) 0 0
\(676\) 9.20911 + 15.9507i 0.354197 + 0.613487i
\(677\) −12.5168 + 21.6798i −0.481061 + 0.833222i −0.999764 0.0217327i \(-0.993082\pi\)
0.518703 + 0.854955i \(0.326415\pi\)
\(678\) 0 0
\(679\) −7.01631 9.89996i −0.269261 0.379926i
\(680\) 10.2961i 0.394839i
\(681\) 0 0
\(682\) 1.40485 + 11.2084i 0.0537945 + 0.429194i
\(683\) −37.1556 + 21.4518i −1.42172 + 0.820831i −0.996446 0.0842334i \(-0.973156\pi\)
−0.425275 + 0.905064i \(0.639823\pi\)
\(684\) 0 0
\(685\) 10.8874 0.415988
\(686\) −4.48737 + 17.9684i −0.171328 + 0.686037i
\(687\) 0 0
\(688\) −6.68577 3.86003i −0.254893 0.147162i
\(689\) 30.0211 + 51.9981i 1.14371 + 1.98097i
\(690\) 0 0
\(691\) −3.04518 + 5.27440i −0.115844 + 0.200648i −0.918117 0.396310i \(-0.870291\pi\)
0.802273 + 0.596958i \(0.203624\pi\)
\(692\) 20.9243 0.795424
\(693\) 0 0
\(694\) −20.1533 −0.765009
\(695\) 7.40037 12.8178i 0.280712 0.486207i
\(696\) 0 0
\(697\) 8.71258 + 15.0906i 0.330013 + 0.571599i
\(698\) 22.3673 + 12.9138i 0.846616 + 0.488794i
\(699\) 0 0
\(700\) −22.7248 + 2.11851i −0.858917 + 0.0800723i
\(701\) −49.6670 −1.87590 −0.937948 0.346777i \(-0.887276\pi\)
−0.937948 + 0.346777i \(0.887276\pi\)
\(702\) 0 0
\(703\) −12.2711 + 7.08472i −0.462813 + 0.267205i
\(704\) 0.412474 + 3.29088i 0.0155457 + 0.124030i
\(705\) 0 0
\(706\) 9.48296i 0.356896i
\(707\) −3.22070 + 7.01068i −0.121127 + 0.263664i
\(708\) 0 0
\(709\) −1.37833 + 2.38734i −0.0517643 + 0.0896584i −0.890746 0.454500i \(-0.849818\pi\)
0.838982 + 0.544159i \(0.183151\pi\)
\(710\) 9.50695 + 16.4665i 0.356789 + 0.617978i
\(711\) 0 0
\(712\) 13.7391 + 7.93225i 0.514893 + 0.297274i
\(713\) 12.8294i 0.480466i
\(714\) 0 0
\(715\) −63.2362 26.6547i −2.36490 0.996828i
\(716\) 12.9584 + 7.48153i 0.484278 + 0.279598i
\(717\) 0 0
\(718\) −5.42112 9.38966i −0.202314 0.350419i
\(719\) 34.4448 + 19.8867i 1.28457 + 0.741650i 0.977681 0.210094i \(-0.0673771\pi\)
0.306894 + 0.951744i \(0.400710\pi\)
\(720\) 0 0
\(721\) 24.3210 2.26732i 0.905761 0.0844393i
\(722\) 12.8578 0.478518
\(723\) 0 0
\(724\) 5.05625 + 8.75769i 0.187914 + 0.325477i
\(725\) −6.51343 11.2816i −0.241903 0.418988i
\(726\) 0 0
\(727\) 25.4901 0.945376 0.472688 0.881230i \(-0.343284\pi\)
0.472688 + 0.881230i \(0.343284\pi\)
\(728\) −12.0994 + 8.57509i −0.448433 + 0.317814i
\(729\) 0 0
\(730\) −9.67462 + 16.7569i −0.358074 + 0.620202i
\(731\) 18.6481 10.7665i 0.689726 0.398213i
\(732\) 0 0
\(733\) −42.1323 24.3251i −1.55619 0.898467i −0.997616 0.0690128i \(-0.978015\pi\)
−0.558575 0.829454i \(-0.688652\pi\)
\(734\) −8.92893 −0.329573
\(735\) 0 0
\(736\) 3.76681i 0.138846i
\(737\) −29.9586 + 22.6938i −1.10354 + 0.835936i
\(738\) 0 0
\(739\) 10.9783 6.33835i 0.403845 0.233160i −0.284297 0.958736i \(-0.591760\pi\)
0.688142 + 0.725576i \(0.258427\pi\)
\(740\) 18.2773 + 10.5524i 0.671887 + 0.387914i
\(741\) 0 0
\(742\) −23.1227 + 16.3876i −0.848862 + 0.601606i
\(743\) −18.4512 −0.676910 −0.338455 0.940983i \(-0.609904\pi\)
−0.338455 + 0.940983i \(0.609904\pi\)
\(744\) 0 0
\(745\) −20.6808 + 11.9401i −0.757686 + 0.437450i
\(746\) 12.8877 7.44073i 0.471853 0.272424i
\(747\) 0 0
\(748\) −8.52448 3.59315i −0.311686 0.131379i
\(749\) −9.54873 + 0.890178i −0.348903 + 0.0325264i
\(750\) 0 0
\(751\) 25.5428 44.2414i 0.932070 1.61439i 0.152293 0.988335i \(-0.451334\pi\)
0.779777 0.626057i \(-0.215332\pi\)
\(752\) −8.98162 + 5.18554i −0.327526 + 0.189097i
\(753\) 0 0
\(754\) −7.33046 4.23224i −0.266959 0.154129i
\(755\) 57.0985 2.07803
\(756\) 0 0
\(757\) 13.3898 0.486659 0.243329 0.969944i \(-0.421760\pi\)
0.243329 + 0.969944i \(0.421760\pi\)
\(758\) −15.1414 + 26.2256i −0.549959 + 0.952556i
\(759\) 0 0
\(760\) 4.57428 + 7.92289i 0.165927 + 0.287393i
\(761\) 3.48214 6.03125i 0.126228 0.218633i −0.795985 0.605317i \(-0.793046\pi\)
0.922212 + 0.386684i \(0.126380\pi\)
\(762\) 0 0
\(763\) −38.6865 17.7726i −1.40055 0.643410i
\(764\) 5.27991i 0.191020i
\(765\) 0 0
\(766\) −18.4934 + 10.6772i −0.668194 + 0.385782i
\(767\) 37.6146 + 65.1504i 1.35818 + 2.35244i
\(768\) 0 0
\(769\) 2.40816i 0.0868404i −0.999057 0.0434202i \(-0.986175\pi\)
0.999057 0.0434202i \(-0.0138254\pi\)
\(770\) 9.75654 30.8876i 0.351601 1.11311i
\(771\) 0 0
\(772\) −19.8361 11.4524i −0.713918 0.412181i
\(773\) 11.9339 6.89002i 0.429231 0.247817i −0.269788 0.962920i \(-0.586954\pi\)
0.699019 + 0.715103i \(0.253620\pi\)
\(774\) 0 0
\(775\) 14.6904 25.4445i 0.527695 0.913995i
\(776\) 4.58628 0.164638
\(777\) 0 0
\(778\) 6.98703i 0.250497i
\(779\) 13.4087 + 7.74151i 0.480416 + 0.277368i
\(780\) 0 0
\(781\) −16.9509 + 2.12460i −0.606550 + 0.0760241i
\(782\) 9.09888 + 5.25324i 0.325375 + 0.187855i
\(783\) 0 0
\(784\) −4.56024 5.31076i −0.162866 0.189670i
\(785\) 68.9743i 2.46180i
\(786\) 0 0
\(787\) 4.15993 2.40174i 0.148285 0.0856127i −0.424022 0.905652i \(-0.639382\pi\)
0.572307 + 0.820039i \(0.306049\pi\)
\(788\) −4.28337 7.41901i −0.152589 0.264291i
\(789\) 0 0
\(790\) −1.06651 −0.0379446
\(791\) −40.6618 + 28.8179i