Properties

Label 819.2.fm.e.496.1
Level $819$
Weight $2$
Character 819.496
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 496.1
Character \(\chi\) \(=\) 819.496
Dual form 819.2.fm.e.748.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.37607 - 0.636667i) q^{2} +(3.50833 + 2.02554i) q^{4} +(0.498430 + 0.498430i) q^{5} +(-2.62820 - 0.304236i) q^{7} +(-3.56765 - 3.56765i) q^{8} +O(q^{10})\) \(q+(-2.37607 - 0.636667i) q^{2} +(3.50833 + 2.02554i) q^{4} +(0.498430 + 0.498430i) q^{5} +(-2.62820 - 0.304236i) q^{7} +(-3.56765 - 3.56765i) q^{8} +(-0.866973 - 1.50164i) q^{10} +(-0.184478 + 0.688480i) q^{11} +(-3.17894 + 1.70127i) q^{13} +(6.05110 + 2.39618i) q^{14} +(2.15452 + 3.73174i) q^{16} +(2.27300 - 3.93695i) q^{17} +(3.25000 - 0.870835i) q^{19} +(0.739070 + 2.75825i) q^{20} +(0.876665 - 1.51843i) q^{22} +(1.67026 - 0.964326i) q^{23} -4.50313i q^{25} +(8.63655 - 2.01842i) q^{26} +(-8.60436 - 6.39088i) q^{28} +(-0.185925 - 0.322032i) q^{29} +(3.53994 + 3.53994i) q^{31} +(-0.131724 - 0.491600i) q^{32} +(-7.90735 + 7.90735i) q^{34} +(-1.15833 - 1.46162i) q^{35} +(-0.545727 + 2.03668i) q^{37} -8.27667 q^{38} -3.55645i q^{40} +(-3.11983 + 11.6434i) q^{41} +(6.38504 + 3.68640i) q^{43} +(-2.04175 + 2.04175i) q^{44} +(-4.58262 + 1.22791i) q^{46} +(3.55898 - 3.55898i) q^{47} +(6.81488 + 1.59919i) q^{49} +(-2.86700 + 10.6998i) q^{50} +(-14.5988 - 0.470438i) q^{52} +4.97712 q^{53} +(-0.435109 + 0.251210i) q^{55} +(8.29109 + 10.4619i) q^{56} +(0.236745 + 0.883543i) q^{58} +(1.03416 + 3.85953i) q^{59} +(10.0720 + 5.81509i) q^{61} +(-6.15739 - 10.6649i) q^{62} -7.36614i q^{64} +(-2.43245 - 0.736516i) q^{65} +(-12.5870 - 3.37267i) q^{67} +(15.9489 - 9.20809i) q^{68} +(1.82173 + 4.21038i) q^{70} +(-2.10681 - 7.86274i) q^{71} +(0.608899 - 0.608899i) q^{73} +(2.59337 - 4.49186i) q^{74} +(13.1660 + 3.52781i) q^{76} +(0.694305 - 1.75334i) q^{77} +9.81537 q^{79} +(-0.786133 + 2.93389i) q^{80} +(14.8259 - 25.6792i) q^{82} +(2.25452 + 2.25452i) q^{83} +(3.09523 - 0.829364i) q^{85} +(-12.8243 - 12.8243i) q^{86} +(3.11441 - 1.79810i) q^{88} +(17.5524 + 4.70315i) q^{89} +(8.87249 - 3.50413i) q^{91} +7.81311 q^{92} +(-10.7223 + 6.19052i) q^{94} +(2.05395 + 1.18585i) q^{95} +(8.73810 - 2.34137i) q^{97} +(-15.1745 - 8.13860i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37607 0.636667i −1.68014 0.450192i −0.712322 0.701852i \(-0.752357\pi\)
−0.967816 + 0.251661i \(0.919023\pi\)
\(3\) 0 0
\(4\) 3.50833 + 2.02554i 1.75417 + 1.01277i
\(5\) 0.498430 + 0.498430i 0.222905 + 0.222905i 0.809721 0.586816i \(-0.199619\pi\)
−0.586816 + 0.809721i \(0.699619\pi\)
\(6\) 0 0
\(7\) −2.62820 0.304236i −0.993367 0.114991i
\(8\) −3.56765 3.56765i −1.26135 1.26135i
\(9\) 0 0
\(10\) −0.866973 1.50164i −0.274161 0.474861i
\(11\) −0.184478 + 0.688480i −0.0556221 + 0.207585i −0.988144 0.153528i \(-0.950936\pi\)
0.932522 + 0.361113i \(0.117603\pi\)
\(12\) 0 0
\(13\) −3.17894 + 1.70127i −0.881680 + 0.471848i
\(14\) 6.05110 + 2.39618i 1.61723 + 0.640405i
\(15\) 0 0
\(16\) 2.15452 + 3.73174i 0.538630 + 0.932934i
\(17\) 2.27300 3.93695i 0.551284 0.954852i −0.446898 0.894585i \(-0.647471\pi\)
0.998182 0.0602669i \(-0.0191952\pi\)
\(18\) 0 0
\(19\) 3.25000 0.870835i 0.745601 0.199783i 0.134035 0.990977i \(-0.457207\pi\)
0.611566 + 0.791193i \(0.290540\pi\)
\(20\) 0.739070 + 2.75825i 0.165261 + 0.616763i
\(21\) 0 0
\(22\) 0.876665 1.51843i 0.186906 0.323730i
\(23\) 1.67026 0.964326i 0.348274 0.201076i −0.315651 0.948875i \(-0.602223\pi\)
0.663925 + 0.747799i \(0.268890\pi\)
\(24\) 0 0
\(25\) 4.50313i 0.900627i
\(26\) 8.63655 2.01842i 1.69377 0.395845i
\(27\) 0 0
\(28\) −8.60436 6.39088i −1.62607 1.20776i
\(29\) −0.185925 0.322032i −0.0345254 0.0597998i 0.848246 0.529602i \(-0.177659\pi\)
−0.882772 + 0.469802i \(0.844325\pi\)
\(30\) 0 0
\(31\) 3.53994 + 3.53994i 0.635792 + 0.635792i 0.949515 0.313723i \(-0.101576\pi\)
−0.313723 + 0.949515i \(0.601576\pi\)
\(32\) −0.131724 0.491600i −0.0232857 0.0869034i
\(33\) 0 0
\(34\) −7.90735 + 7.90735i −1.35610 + 1.35610i
\(35\) −1.15833 1.46162i −0.195794 0.247058i
\(36\) 0 0
\(37\) −0.545727 + 2.03668i −0.0897169 + 0.334828i −0.996166 0.0874879i \(-0.972116\pi\)
0.906449 + 0.422316i \(0.138783\pi\)
\(38\) −8.27667 −1.34265
\(39\) 0 0
\(40\) 3.55645i 0.562324i
\(41\) −3.11983 + 11.6434i −0.487236 + 1.81839i 0.0825406 + 0.996588i \(0.473697\pi\)
−0.569776 + 0.821800i \(0.692970\pi\)
\(42\) 0 0
\(43\) 6.38504 + 3.68640i 0.973709 + 0.562171i 0.900365 0.435136i \(-0.143300\pi\)
0.0733440 + 0.997307i \(0.476633\pi\)
\(44\) −2.04175 + 2.04175i −0.307805 + 0.307805i
\(45\) 0 0
\(46\) −4.58262 + 1.22791i −0.675671 + 0.181045i
\(47\) 3.55898 3.55898i 0.519131 0.519131i −0.398177 0.917308i \(-0.630357\pi\)
0.917308 + 0.398177i \(0.130357\pi\)
\(48\) 0 0
\(49\) 6.81488 + 1.59919i 0.973554 + 0.228455i
\(50\) −2.86700 + 10.6998i −0.405455 + 1.51318i
\(51\) 0 0
\(52\) −14.5988 0.470438i −2.02449 0.0652380i
\(53\) 4.97712 0.683660 0.341830 0.939762i \(-0.388953\pi\)
0.341830 + 0.939762i \(0.388953\pi\)
\(54\) 0 0
\(55\) −0.435109 + 0.251210i −0.0586700 + 0.0338732i
\(56\) 8.29109 + 10.4619i 1.10794 + 1.39803i
\(57\) 0 0
\(58\) 0.236745 + 0.883543i 0.0310861 + 0.116015i
\(59\) 1.03416 + 3.85953i 0.134636 + 0.502467i 0.999999 + 0.00132252i \(0.000420972\pi\)
−0.865363 + 0.501145i \(0.832912\pi\)
\(60\) 0 0
\(61\) 10.0720 + 5.81509i 1.28959 + 0.744546i 0.978581 0.205860i \(-0.0659992\pi\)
0.311011 + 0.950406i \(0.399333\pi\)
\(62\) −6.15739 10.6649i −0.781990 1.35445i
\(63\) 0 0
\(64\) 7.36614i 0.920767i
\(65\) −2.43245 0.736516i −0.301708 0.0913536i
\(66\) 0 0
\(67\) −12.5870 3.37267i −1.53774 0.412037i −0.612207 0.790697i \(-0.709718\pi\)
−0.925536 + 0.378660i \(0.876385\pi\)
\(68\) 15.9489 9.20809i 1.93409 1.11665i
\(69\) 0 0
\(70\) 1.82173 + 4.21038i 0.217738 + 0.503237i
\(71\) −2.10681 7.86274i −0.250033 0.933135i −0.970787 0.239944i \(-0.922871\pi\)
0.720754 0.693191i \(-0.243796\pi\)
\(72\) 0 0
\(73\) 0.608899 0.608899i 0.0712663 0.0712663i −0.670575 0.741842i \(-0.733953\pi\)
0.741842 + 0.670575i \(0.233953\pi\)
\(74\) 2.59337 4.49186i 0.301474 0.522168i
\(75\) 0 0
\(76\) 13.1660 + 3.52781i 1.51024 + 0.404668i
\(77\) 0.694305 1.75334i 0.0791234 0.199812i
\(78\) 0 0
\(79\) 9.81537 1.10432 0.552158 0.833740i \(-0.313805\pi\)
0.552158 + 0.833740i \(0.313805\pi\)
\(80\) −0.786133 + 2.93389i −0.0878924 + 0.328019i
\(81\) 0 0
\(82\) 14.8259 25.6792i 1.63725 2.83579i
\(83\) 2.25452 + 2.25452i 0.247465 + 0.247465i 0.819930 0.572464i \(-0.194012\pi\)
−0.572464 + 0.819930i \(0.694012\pi\)
\(84\) 0 0
\(85\) 3.09523 0.829364i 0.335725 0.0899572i
\(86\) −12.8243 12.8243i −1.38288 1.38288i
\(87\) 0 0
\(88\) 3.11441 1.79810i 0.331997 0.191678i
\(89\) 17.5524 + 4.70315i 1.86055 + 0.498533i 0.999942 0.0107329i \(-0.00341645\pi\)
0.860609 + 0.509266i \(0.170083\pi\)
\(90\) 0 0
\(91\) 8.87249 3.50413i 0.930089 0.367333i
\(92\) 7.81311 0.814573
\(93\) 0 0
\(94\) −10.7223 + 6.19052i −1.10592 + 0.638503i
\(95\) 2.05395 + 1.18585i 0.210731 + 0.121665i
\(96\) 0 0
\(97\) 8.73810 2.34137i 0.887220 0.237730i 0.213700 0.976899i \(-0.431448\pi\)
0.673520 + 0.739169i \(0.264782\pi\)
\(98\) −15.1745 8.13860i −1.53286 0.822123i
\(99\) 0 0
\(100\) 9.12126 15.7985i 0.912126 1.57985i
\(101\) 6.77353 + 11.7321i 0.673991 + 1.16739i 0.976763 + 0.214324i \(0.0687547\pi\)
−0.302772 + 0.953063i \(0.597912\pi\)
\(102\) 0 0
\(103\) 16.4565 1.62151 0.810756 0.585385i \(-0.199056\pi\)
0.810756 + 0.585385i \(0.199056\pi\)
\(104\) 17.4109 + 5.27181i 1.70728 + 0.516943i
\(105\) 0 0
\(106\) −11.8260 3.16877i −1.14864 0.307778i
\(107\) −8.35835 14.4771i −0.808033 1.39955i −0.914225 0.405208i \(-0.867199\pi\)
0.106192 0.994346i \(-0.466134\pi\)
\(108\) 0 0
\(109\) 1.77768 1.77768i 0.170271 0.170271i −0.616827 0.787099i \(-0.711582\pi\)
0.787099 + 0.616827i \(0.211582\pi\)
\(110\) 1.19379 0.319874i 0.113823 0.0304988i
\(111\) 0 0
\(112\) −4.52718 10.4632i −0.427778 0.988683i
\(113\) 2.96252 5.13124i 0.278691 0.482706i −0.692369 0.721544i \(-0.743433\pi\)
0.971060 + 0.238837i \(0.0767662\pi\)
\(114\) 0 0
\(115\) 1.31316 + 0.351860i 0.122453 + 0.0328111i
\(116\) 1.50639i 0.139865i
\(117\) 0 0
\(118\) 9.82893i 0.904826i
\(119\) −7.17167 + 9.65558i −0.657426 + 0.885125i
\(120\) 0 0
\(121\) 9.08631 + 5.24598i 0.826028 + 0.476907i
\(122\) −20.2296 20.2296i −1.83150 1.83150i
\(123\) 0 0
\(124\) 5.24901 + 19.5896i 0.471375 + 1.75919i
\(125\) 4.73665 4.73665i 0.423659 0.423659i
\(126\) 0 0
\(127\) −17.4169 + 10.0556i −1.54550 + 0.892293i −0.547019 + 0.837120i \(0.684238\pi\)
−0.998477 + 0.0551724i \(0.982429\pi\)
\(128\) −4.95322 + 18.4857i −0.437807 + 1.63392i
\(129\) 0 0
\(130\) 5.31076 + 3.29868i 0.465784 + 0.289313i
\(131\) 12.0796i 1.05540i −0.849430 0.527702i \(-0.823054\pi\)
0.849430 0.527702i \(-0.176946\pi\)
\(132\) 0 0
\(133\) −8.80659 + 1.29996i −0.763628 + 0.112721i
\(134\) 27.7603 + 16.0274i 2.39813 + 1.38456i
\(135\) 0 0
\(136\) −22.1549 + 5.93640i −1.89977 + 0.509042i
\(137\) 13.9883 3.74816i 1.19510 0.320227i 0.394202 0.919024i \(-0.371021\pi\)
0.800901 + 0.598797i \(0.204354\pi\)
\(138\) 0 0
\(139\) −6.95647 4.01632i −0.590040 0.340660i 0.175073 0.984555i \(-0.443984\pi\)
−0.765113 + 0.643896i \(0.777317\pi\)
\(140\) −1.10327 7.47408i −0.0932430 0.631675i
\(141\) 0 0
\(142\) 20.0238i 1.68036i
\(143\) −0.584848 2.50248i −0.0489074 0.209268i
\(144\) 0 0
\(145\) 0.0678396 0.253181i 0.00563378 0.0210255i
\(146\) −1.83446 + 1.05912i −0.151821 + 0.0876537i
\(147\) 0 0
\(148\) −6.03996 + 6.03996i −0.496481 + 0.496481i
\(149\) 2.13325 + 7.96140i 0.174763 + 0.652223i 0.996592 + 0.0824894i \(0.0262870\pi\)
−0.821829 + 0.569734i \(0.807046\pi\)
\(150\) 0 0
\(151\) −4.15300 4.15300i −0.337966 0.337966i 0.517635 0.855601i \(-0.326812\pi\)
−0.855601 + 0.517635i \(0.826812\pi\)
\(152\) −14.7017 8.48802i −1.19246 0.688469i
\(153\) 0 0
\(154\) −2.76601 + 3.72402i −0.222892 + 0.300090i
\(155\) 3.52883i 0.283442i
\(156\) 0 0
\(157\) 14.6163i 1.16651i 0.812291 + 0.583253i \(0.198220\pi\)
−0.812291 + 0.583253i \(0.801780\pi\)
\(158\) −23.3220 6.24912i −1.85540 0.497154i
\(159\) 0 0
\(160\) 0.179373 0.310684i 0.0141807 0.0245617i
\(161\) −4.68317 + 2.02629i −0.369085 + 0.159694i
\(162\) 0 0
\(163\) 7.35195 1.96995i 0.575849 0.154298i 0.0408715 0.999164i \(-0.486987\pi\)
0.534978 + 0.844866i \(0.320320\pi\)
\(164\) −34.5294 + 34.5294i −2.69630 + 2.69630i
\(165\) 0 0
\(166\) −3.92152 6.79228i −0.304369 0.527183i
\(167\) −7.60079 2.03663i −0.588167 0.157599i −0.0475517 0.998869i \(-0.515142\pi\)
−0.540615 + 0.841270i \(0.681809\pi\)
\(168\) 0 0
\(169\) 7.21135 10.8165i 0.554719 0.832038i
\(170\) −7.88252 −0.604562
\(171\) 0 0
\(172\) 14.9339 + 25.8662i 1.13870 + 1.97228i
\(173\) −5.36019 + 9.28412i −0.407528 + 0.705859i −0.994612 0.103667i \(-0.966942\pi\)
0.587084 + 0.809526i \(0.300276\pi\)
\(174\) 0 0
\(175\) −1.37002 + 11.8351i −0.103564 + 0.894653i
\(176\) −2.96669 + 0.794922i −0.223623 + 0.0599195i
\(177\) 0 0
\(178\) −38.7115 22.3501i −2.90155 1.67521i
\(179\) −8.63169 + 4.98351i −0.645163 + 0.372485i −0.786601 0.617462i \(-0.788161\pi\)
0.141438 + 0.989947i \(0.454828\pi\)
\(180\) 0 0
\(181\) −3.96508 −0.294722 −0.147361 0.989083i \(-0.547078\pi\)
−0.147361 + 0.989083i \(0.547078\pi\)
\(182\) −23.3127 + 2.67726i −1.72805 + 0.198452i
\(183\) 0 0
\(184\) −9.39929 2.51853i −0.692925 0.185669i
\(185\) −1.28715 + 0.743136i −0.0946331 + 0.0546365i
\(186\) 0 0
\(187\) 2.29120 + 2.29120i 0.167549 + 0.167549i
\(188\) 19.6949 5.27724i 1.43640 0.384882i
\(189\) 0 0
\(190\) −4.12534 4.12534i −0.299284 0.299284i
\(191\) 9.17881 15.8982i 0.664155 1.15035i −0.315358 0.948973i \(-0.602125\pi\)
0.979514 0.201378i \(-0.0645420\pi\)
\(192\) 0 0
\(193\) 4.24786 15.8532i 0.305767 1.14114i −0.626515 0.779409i \(-0.715519\pi\)
0.932283 0.361731i \(-0.117814\pi\)
\(194\) −22.2531 −1.59768
\(195\) 0 0
\(196\) 20.6696 + 19.4143i 1.47640 + 1.38673i
\(197\) −5.69553 1.52611i −0.405790 0.108731i 0.0501498 0.998742i \(-0.484030\pi\)
−0.455940 + 0.890011i \(0.650697\pi\)
\(198\) 0 0
\(199\) −9.61483 + 16.6534i −0.681578 + 1.18053i 0.292922 + 0.956136i \(0.405372\pi\)
−0.974499 + 0.224391i \(0.927961\pi\)
\(200\) −16.0656 + 16.0656i −1.13601 + 1.13601i
\(201\) 0 0
\(202\) −8.62496 32.1888i −0.606850 2.26480i
\(203\) 0.390675 + 0.902929i 0.0274200 + 0.0633732i
\(204\) 0 0
\(205\) −7.35842 + 4.24839i −0.513935 + 0.296720i
\(206\) −39.1020 10.4773i −2.72436 0.729991i
\(207\) 0 0
\(208\) −13.1978 8.19756i −0.915102 0.568398i
\(209\) 2.39821i 0.165888i
\(210\) 0 0
\(211\) −4.61920 8.00070i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980070 + 0.198650i \(0.936344\pi\)
\(212\) 17.4614 + 10.0813i 1.19925 + 0.692389i
\(213\) 0 0
\(214\) 10.6430 + 39.7201i 0.727539 + 2.71521i
\(215\) 1.34508 + 5.01991i 0.0917338 + 0.342355i
\(216\) 0 0
\(217\) −8.22669 10.3807i −0.558464 0.704684i
\(218\) −5.35570 + 3.09212i −0.362734 + 0.209425i
\(219\) 0 0
\(220\) −2.03534 −0.137223
\(221\) −0.527913 + 16.3823i −0.0355112 + 1.10200i
\(222\) 0 0
\(223\) 0.482353 1.80016i 0.0323007 0.120548i −0.947893 0.318589i \(-0.896791\pi\)
0.980194 + 0.198041i \(0.0634578\pi\)
\(224\) 0.196634 + 1.33210i 0.0131382 + 0.0890046i
\(225\) 0 0
\(226\) −10.3061 + 10.3061i −0.685549 + 0.685549i
\(227\) −5.38143 + 1.44195i −0.357178 + 0.0957056i −0.432946 0.901420i \(-0.642526\pi\)
0.0757678 + 0.997125i \(0.475859\pi\)
\(228\) 0 0
\(229\) 0.153144 0.153144i 0.0101200 0.0101200i −0.702029 0.712149i \(-0.747722\pi\)
0.712149 + 0.702029i \(0.247722\pi\)
\(230\) −2.89615 1.67209i −0.190966 0.110254i
\(231\) 0 0
\(232\) −0.485580 + 1.81221i −0.0318799 + 0.118977i
\(233\) 19.7822i 1.29598i 0.761650 + 0.647989i \(0.224390\pi\)
−0.761650 + 0.647989i \(0.775610\pi\)
\(234\) 0 0
\(235\) 3.54781 0.231434
\(236\) −4.18944 + 15.6352i −0.272710 + 1.01777i
\(237\) 0 0
\(238\) 23.1878 18.3764i 1.50304 1.19116i
\(239\) 0.636908 0.636908i 0.0411982 0.0411982i −0.686208 0.727406i \(-0.740726\pi\)
0.727406 + 0.686208i \(0.240726\pi\)
\(240\) 0 0
\(241\) −5.16499 19.2760i −0.332706 1.24168i −0.906335 0.422561i \(-0.861131\pi\)
0.573629 0.819116i \(-0.305535\pi\)
\(242\) −18.2498 18.2498i −1.17314 1.17314i
\(243\) 0 0
\(244\) 23.5574 + 40.8025i 1.50811 + 2.61212i
\(245\) 2.59966 + 4.19383i 0.166086 + 0.267934i
\(246\) 0 0
\(247\) −8.85003 + 8.29746i −0.563114 + 0.527955i
\(248\) 25.2585i 1.60392i
\(249\) 0 0
\(250\) −14.2703 + 8.23896i −0.902533 + 0.521078i
\(251\) 14.0053 24.2580i 0.884010 1.53115i 0.0371651 0.999309i \(-0.488167\pi\)
0.846845 0.531840i \(-0.178499\pi\)
\(252\) 0 0
\(253\) 0.355793 + 1.32784i 0.0223685 + 0.0834805i
\(254\) 47.7858 12.8042i 2.99835 0.803405i
\(255\) 0 0
\(256\) 16.1723 28.0113i 1.01077 1.75070i
\(257\) −4.51978 7.82849i −0.281936 0.488328i 0.689925 0.723880i \(-0.257643\pi\)
−0.971862 + 0.235553i \(0.924310\pi\)
\(258\) 0 0
\(259\) 2.05391 5.18677i 0.127624 0.322290i
\(260\) −7.04199 7.51095i −0.436726 0.465809i
\(261\) 0 0
\(262\) −7.69071 + 28.7021i −0.475134 + 1.77322i
\(263\) 11.6573 + 20.1910i 0.718819 + 1.24503i 0.961468 + 0.274917i \(0.0886503\pi\)
−0.242649 + 0.970114i \(0.578016\pi\)
\(264\) 0 0
\(265\) 2.48075 + 2.48075i 0.152391 + 0.152391i
\(266\) 21.7527 + 2.51806i 1.33375 + 0.154392i
\(267\) 0 0
\(268\) −37.3278 37.3278i −2.28016 2.28016i
\(269\) 24.9574 + 14.4092i 1.52168 + 0.878543i 0.999672 + 0.0256040i \(0.00815089\pi\)
0.522010 + 0.852939i \(0.325182\pi\)
\(270\) 0 0
\(271\) −11.9008 3.18880i −0.722920 0.193706i −0.121446 0.992598i \(-0.538753\pi\)
−0.601474 + 0.798892i \(0.705420\pi\)
\(272\) 19.5889 1.18775
\(273\) 0 0
\(274\) −35.6236 −2.15210
\(275\) 3.10032 + 0.830728i 0.186956 + 0.0500948i
\(276\) 0 0
\(277\) −12.3959 7.15677i −0.744797 0.430009i 0.0790140 0.996874i \(-0.474823\pi\)
−0.823811 + 0.566865i \(0.808156\pi\)
\(278\) 13.9720 + 13.9720i 0.837987 + 0.837987i
\(279\) 0 0
\(280\) −1.08200 + 9.34706i −0.0646619 + 0.558594i
\(281\) 10.7886 + 10.7886i 0.643591 + 0.643591i 0.951437 0.307845i \(-0.0996078\pi\)
−0.307845 + 0.951437i \(0.599608\pi\)
\(282\) 0 0
\(283\) −6.96923 12.0711i −0.414278 0.717550i 0.581075 0.813850i \(-0.302632\pi\)
−0.995352 + 0.0963004i \(0.969299\pi\)
\(284\) 8.53485 31.8525i 0.506450 1.89010i
\(285\) 0 0
\(286\) −0.203609 + 6.31844i −0.0120396 + 0.373617i
\(287\) 11.7419 29.6519i 0.693101 1.75030i
\(288\) 0 0
\(289\) −1.83307 3.17497i −0.107828 0.186763i
\(290\) −0.322384 + 0.558385i −0.0189310 + 0.0327895i
\(291\) 0 0
\(292\) 3.36957 0.902873i 0.197189 0.0528367i
\(293\) 4.49081 + 16.7599i 0.262356 + 0.979126i 0.963849 + 0.266450i \(0.0858506\pi\)
−0.701493 + 0.712677i \(0.747483\pi\)
\(294\) 0 0
\(295\) −1.40825 + 2.43916i −0.0819915 + 0.142013i
\(296\) 9.21312 5.31920i 0.535502 0.309172i
\(297\) 0 0
\(298\) 20.2750i 1.17450i
\(299\) −3.66909 + 5.90711i −0.212189 + 0.341617i
\(300\) 0 0
\(301\) −15.6596 11.6312i −0.902606 0.670409i
\(302\) 7.22375 + 12.5119i 0.415680 + 0.719980i
\(303\) 0 0
\(304\) 10.2519 + 10.2519i 0.587988 + 0.587988i
\(305\) 2.12179 + 7.91863i 0.121493 + 0.453419i
\(306\) 0 0
\(307\) −14.5281 + 14.5281i −0.829164 + 0.829164i −0.987401 0.158237i \(-0.949419\pi\)
0.158237 + 0.987401i \(0.449419\pi\)
\(308\) 5.98730 4.74495i 0.341158 0.270369i
\(309\) 0 0
\(310\) 2.24669 8.38475i 0.127603 0.476222i
\(311\) −7.52888 −0.426924 −0.213462 0.976951i \(-0.568474\pi\)
−0.213462 + 0.976951i \(0.568474\pi\)
\(312\) 0 0
\(313\) 7.90713i 0.446938i 0.974711 + 0.223469i \(0.0717381\pi\)
−0.974711 + 0.223469i \(0.928262\pi\)
\(314\) 9.30570 34.7293i 0.525151 1.95989i
\(315\) 0 0
\(316\) 34.4356 + 19.8814i 1.93715 + 1.11842i
\(317\) −12.2598 + 12.2598i −0.688580 + 0.688580i −0.961918 0.273338i \(-0.911872\pi\)
0.273338 + 0.961918i \(0.411872\pi\)
\(318\) 0 0
\(319\) 0.256011 0.0685980i 0.0143339 0.00384075i
\(320\) 3.67151 3.67151i 0.205243 0.205243i
\(321\) 0 0
\(322\) 12.4176 1.83299i 0.692007 0.102149i
\(323\) 3.95882 14.7745i 0.220274 0.822075i
\(324\) 0 0
\(325\) 7.66105 + 14.3152i 0.424959 + 0.794065i
\(326\) −18.7230 −1.03697
\(327\) 0 0
\(328\) 52.6699 30.4090i 2.90821 1.67905i
\(329\) −10.4365 + 8.27095i −0.575383 + 0.455992i
\(330\) 0 0
\(331\) 1.27846 + 4.77126i 0.0702703 + 0.262252i 0.992119 0.125297i \(-0.0399884\pi\)
−0.921849 + 0.387549i \(0.873322\pi\)
\(332\) 3.34299 + 12.4762i 0.183470 + 0.684720i
\(333\) 0 0
\(334\) 16.7634 + 9.67835i 0.917252 + 0.529576i
\(335\) −4.59269 7.95477i −0.250925 0.434615i
\(336\) 0 0
\(337\) 7.35624i 0.400720i 0.979722 + 0.200360i \(0.0642112\pi\)
−0.979722 + 0.200360i \(0.935789\pi\)
\(338\) −24.0212 + 21.1095i −1.30658 + 1.14821i
\(339\) 0 0
\(340\) 12.5390 + 3.35982i 0.680023 + 0.182212i
\(341\) −3.09022 + 1.78414i −0.167345 + 0.0966165i
\(342\) 0 0
\(343\) −17.4243 6.27632i −0.940826 0.338890i
\(344\) −9.62778 35.9314i −0.519095 1.93729i
\(345\) 0 0
\(346\) 18.6471 18.6471i 1.00247 1.00247i
\(347\) −1.58494 + 2.74519i −0.0850839 + 0.147370i −0.905427 0.424502i \(-0.860449\pi\)
0.820343 + 0.571872i \(0.193782\pi\)
\(348\) 0 0
\(349\) −26.0697 6.98534i −1.39548 0.373917i −0.518758 0.854921i \(-0.673605\pi\)
−0.876718 + 0.481004i \(0.840272\pi\)
\(350\) 10.7903 27.2489i 0.576766 1.45652i
\(351\) 0 0
\(352\) 0.362757 0.0193350
\(353\) 1.36374 5.08954i 0.0725845 0.270889i −0.920090 0.391706i \(-0.871885\pi\)
0.992675 + 0.120817i \(0.0385516\pi\)
\(354\) 0 0
\(355\) 2.86893 4.96913i 0.152267 0.263734i
\(356\) 52.0533 + 52.0533i 2.75882 + 2.75882i
\(357\) 0 0
\(358\) 23.6824 6.34567i 1.25165 0.335379i
\(359\) −17.8470 17.8470i −0.941927 0.941927i 0.0564767 0.998404i \(-0.482013\pi\)
−0.998404 + 0.0564767i \(0.982013\pi\)
\(360\) 0 0
\(361\) −6.65034 + 3.83958i −0.350018 + 0.202083i
\(362\) 9.42133 + 2.52444i 0.495174 + 0.132682i
\(363\) 0 0
\(364\) 38.2254 + 5.67788i 2.00355 + 0.297602i
\(365\) 0.606988 0.0317712
\(366\) 0 0
\(367\) 28.6206 16.5241i 1.49398 0.862551i 0.494006 0.869458i \(-0.335532\pi\)
0.999976 + 0.00690739i \(0.00219871\pi\)
\(368\) 7.19723 + 4.15532i 0.375181 + 0.216611i
\(369\) 0 0
\(370\) 3.53149 0.946261i 0.183594 0.0491938i
\(371\) −13.0809 1.51422i −0.679125 0.0786144i
\(372\) 0 0
\(373\) 13.8983 24.0726i 0.719627 1.24643i −0.241521 0.970396i \(-0.577646\pi\)
0.961148 0.276035i \(-0.0890204\pi\)
\(374\) −3.98532 6.90278i −0.206076 0.356934i
\(375\) 0 0
\(376\) −25.3944 −1.30962
\(377\) 1.13891 + 0.707411i 0.0586567 + 0.0364335i
\(378\) 0 0
\(379\) 14.6943 + 3.93733i 0.754797 + 0.202247i 0.615645 0.788024i \(-0.288896\pi\)
0.139152 + 0.990271i \(0.455562\pi\)
\(380\) 4.80395 + 8.32069i 0.246438 + 0.426843i
\(381\) 0 0
\(382\) −31.9314 + 31.9314i −1.63375 + 1.63375i
\(383\) −8.30637 + 2.22568i −0.424436 + 0.113727i −0.464713 0.885461i \(-0.653842\pi\)
0.0402774 + 0.999189i \(0.487176\pi\)
\(384\) 0 0
\(385\) 1.21998 0.527855i 0.0621759 0.0269020i
\(386\) −20.1864 + 34.9639i −1.02746 + 1.77962i
\(387\) 0 0
\(388\) 35.3987 + 9.48505i 1.79710 + 0.481530i
\(389\) 11.3461i 0.575268i −0.957740 0.287634i \(-0.907131\pi\)
0.957740 0.287634i \(-0.0928686\pi\)
\(390\) 0 0
\(391\) 8.76766i 0.443400i
\(392\) −18.6078 30.0184i −0.939834 1.51616i
\(393\) 0 0
\(394\) 12.5614 + 7.25232i 0.632833 + 0.365366i
\(395\) 4.89228 + 4.89228i 0.246157 + 0.246157i
\(396\) 0 0
\(397\) −4.16966 15.5614i −0.209269 0.781003i −0.988106 0.153776i \(-0.950856\pi\)
0.778836 0.627227i \(-0.215810\pi\)
\(398\) 33.4482 33.4482i 1.67661 1.67661i
\(399\) 0 0
\(400\) 16.8045 9.70209i 0.840226 0.485105i
\(401\) 9.35796 34.9244i 0.467314 1.74404i −0.181787 0.983338i \(-0.558188\pi\)
0.649101 0.760702i \(-0.275145\pi\)
\(402\) 0 0
\(403\) −17.2757 5.23087i −0.860562 0.260568i
\(404\) 54.8801i 2.73039i
\(405\) 0 0
\(406\) −0.353407 2.39416i −0.0175393 0.118820i
\(407\) −1.30154 0.751444i −0.0645149 0.0372477i
\(408\) 0 0
\(409\) 13.9857 3.74745i 0.691547 0.185300i 0.104106 0.994566i \(-0.466802\pi\)
0.587441 + 0.809267i \(0.300135\pi\)
\(410\) 20.1890 5.40962i 0.997062 0.267162i
\(411\) 0 0
\(412\) 57.7350 + 33.3333i 2.84440 + 1.64221i
\(413\) −1.54376 10.4582i −0.0759637 0.514616i
\(414\) 0 0
\(415\) 2.24744i 0.110322i
\(416\) 1.25509 + 1.33867i 0.0615357 + 0.0656337i
\(417\) 0 0
\(418\) 1.52686 5.69832i 0.0746812 0.278714i
\(419\) −19.0889 + 11.0210i −0.932553 + 0.538410i −0.887618 0.460580i \(-0.847641\pi\)
−0.0449347 + 0.998990i \(0.514308\pi\)
\(420\) 0 0
\(421\) −7.69603 + 7.69603i −0.375082 + 0.375082i −0.869324 0.494243i \(-0.835445\pi\)
0.494243 + 0.869324i \(0.335445\pi\)
\(422\) 5.88179 + 21.9511i 0.286321 + 1.06856i
\(423\) 0 0
\(424\) −17.7566 17.7566i −0.862338 0.862338i
\(425\) −17.7286 10.2356i −0.859965 0.496501i
\(426\) 0 0
\(427\) −24.7022 18.3475i −1.19542 0.887898i
\(428\) 67.7206i 3.27340i
\(429\) 0 0
\(430\) 12.7840i 0.616502i
\(431\) 26.2932 + 7.04525i 1.26650 + 0.339358i 0.828689 0.559709i \(-0.189087\pi\)
0.437812 + 0.899067i \(0.355754\pi\)
\(432\) 0 0
\(433\) −6.55214 + 11.3486i −0.314876 + 0.545381i −0.979411 0.201876i \(-0.935296\pi\)
0.664535 + 0.747257i \(0.268629\pi\)
\(434\) 12.9382 + 29.9029i 0.621054 + 1.43538i
\(435\) 0 0
\(436\) 9.83747 2.63594i 0.471129 0.126239i
\(437\) 4.58858 4.58858i 0.219502 0.219502i
\(438\) 0 0
\(439\) 19.9333 + 34.5255i 0.951364 + 1.64781i 0.742477 + 0.669872i \(0.233651\pi\)
0.208887 + 0.977940i \(0.433016\pi\)
\(440\) 2.44854 + 0.656085i 0.116730 + 0.0312776i
\(441\) 0 0
\(442\) 11.6845 38.5896i 0.555773 1.83552i
\(443\) −23.0066 −1.09308 −0.546539 0.837433i \(-0.684055\pi\)
−0.546539 + 0.837433i \(0.684055\pi\)
\(444\) 0 0
\(445\) 6.40446 + 11.0928i 0.303600 + 0.525851i
\(446\) −2.29221 + 3.97023i −0.108539 + 0.187996i
\(447\) 0 0
\(448\) −2.24105 + 19.3597i −0.105880 + 0.914659i
\(449\) −15.6281 + 4.18754i −0.737536 + 0.197622i −0.607983 0.793950i \(-0.708021\pi\)
−0.129553 + 0.991572i \(0.541354\pi\)
\(450\) 0 0
\(451\) −7.44068 4.29588i −0.350368 0.202285i
\(452\) 20.7870 12.0014i 0.977739 0.564498i
\(453\) 0 0
\(454\) 13.7047 0.643194
\(455\) 6.16888 + 2.67575i 0.289202 + 0.125441i
\(456\) 0 0
\(457\) 0.658952 + 0.176566i 0.0308245 + 0.00825939i 0.274198 0.961673i \(-0.411588\pi\)
−0.243374 + 0.969933i \(0.578254\pi\)
\(458\) −0.461383 + 0.266380i −0.0215590 + 0.0124471i
\(459\) 0 0
\(460\) 3.89429 + 3.89429i 0.181572 + 0.181572i
\(461\) −8.08252 + 2.16570i −0.376440 + 0.100867i −0.442078 0.896977i \(-0.645759\pi\)
0.0656375 + 0.997844i \(0.479092\pi\)
\(462\) 0 0
\(463\) 22.3879 + 22.3879i 1.04045 + 1.04045i 0.999146 + 0.0413082i \(0.0131525\pi\)
0.0413082 + 0.999146i \(0.486847\pi\)
\(464\) 0.801158 1.38765i 0.0371928 0.0644199i
\(465\) 0 0
\(466\) 12.5947 47.0041i 0.583438 2.17742i
\(467\) 13.5832 0.628554 0.314277 0.949331i \(-0.398238\pi\)
0.314277 + 0.949331i \(0.398238\pi\)
\(468\) 0 0
\(469\) 32.0550 + 12.6935i 1.48016 + 0.586130i
\(470\) −8.42986 2.25877i −0.388840 0.104189i
\(471\) 0 0
\(472\) 10.0799 17.4589i 0.463966 0.803613i
\(473\) −3.71591 + 3.71591i −0.170858 + 0.170858i
\(474\) 0 0
\(475\) −3.92148 14.6352i −0.179930 0.671508i
\(476\) −44.7183 + 19.3485i −2.04966 + 0.886836i
\(477\) 0 0
\(478\) −1.91884 + 1.10784i −0.0877656 + 0.0506715i
\(479\) 4.03229 + 1.08045i 0.184240 + 0.0493669i 0.349759 0.936840i \(-0.386263\pi\)
−0.165519 + 0.986207i \(0.552930\pi\)
\(480\) 0 0
\(481\) −1.73011 7.40292i −0.0788863 0.337544i
\(482\) 49.0896i 2.23597i
\(483\) 0 0
\(484\) 21.2518 + 36.8093i 0.965993 + 1.67315i
\(485\) 5.52235 + 3.18833i 0.250757 + 0.144775i
\(486\) 0 0
\(487\) 4.28159 + 15.9791i 0.194018 + 0.724083i 0.992519 + 0.122090i \(0.0389598\pi\)
−0.798501 + 0.601993i \(0.794374\pi\)
\(488\) −15.1873 56.6797i −0.687496 2.56577i
\(489\) 0 0
\(490\) −3.50691 11.6200i −0.158426 0.524936i
\(491\) −27.7156 + 16.0016i −1.25079 + 0.722143i −0.971266 0.237996i \(-0.923510\pi\)
−0.279523 + 0.960139i \(0.590176\pi\)
\(492\) 0 0
\(493\) −1.69043 −0.0761332
\(494\) 26.3111 14.0809i 1.18379 0.633528i
\(495\) 0 0
\(496\) −5.58326 + 20.8370i −0.250696 + 0.935609i
\(497\) 3.14500 + 21.3058i 0.141073 + 0.955697i
\(498\) 0 0
\(499\) −14.4246 + 14.4246i −0.645734 + 0.645734i −0.951959 0.306225i \(-0.900934\pi\)
0.306225 + 0.951959i \(0.400934\pi\)
\(500\) 26.2120 7.02348i 1.17224 0.314100i
\(501\) 0 0
\(502\) −48.7220 + 48.7220i −2.17457 + 2.17457i
\(503\) −23.6349 13.6456i −1.05383 0.608427i −0.130109 0.991500i \(-0.541533\pi\)
−0.923718 + 0.383072i \(0.874866\pi\)
\(504\) 0 0
\(505\) −2.47150 + 9.22376i −0.109980 + 0.410452i
\(506\) 3.38157i 0.150329i
\(507\) 0 0
\(508\) −81.4721 −3.61474
\(509\) −8.17110 + 30.4949i −0.362177 + 1.35166i 0.509030 + 0.860749i \(0.330004\pi\)
−0.871207 + 0.490916i \(0.836662\pi\)
\(510\) 0 0
\(511\) −1.78556 + 1.41506i −0.0789885 + 0.0625986i
\(512\) −29.1956 + 29.1956i −1.29027 + 1.29027i
\(513\) 0 0
\(514\) 5.75519 + 21.4787i 0.253851 + 0.947383i
\(515\) 8.20244 + 8.20244i 0.361443 + 0.361443i
\(516\) 0 0
\(517\) 1.79374 + 3.10684i 0.0788884 + 0.136639i
\(518\) −8.18249 + 11.0165i −0.359518 + 0.484037i
\(519\) 0 0
\(520\) 6.05048 + 11.3057i 0.265331 + 0.495790i
\(521\) 13.1042i 0.574107i −0.957915 0.287054i \(-0.907324\pi\)
0.957915 0.287054i \(-0.0926758\pi\)
\(522\) 0 0
\(523\) 7.44365 4.29760i 0.325488 0.187921i −0.328348 0.944557i \(-0.606492\pi\)
0.653836 + 0.756636i \(0.273159\pi\)
\(524\) 24.4678 42.3794i 1.06888 1.85135i
\(525\) 0 0
\(526\) −14.8436 55.3971i −0.647212 2.41543i
\(527\) 21.9829 5.89029i 0.957589 0.256585i
\(528\) 0 0
\(529\) −9.64015 + 16.6972i −0.419137 + 0.725966i
\(530\) −4.31503 7.47385i −0.187433 0.324643i
\(531\) 0 0
\(532\) −33.5295 13.2774i −1.45369 0.575647i
\(533\) −9.89076 42.3213i −0.428417 1.83314i
\(534\) 0 0
\(535\) 3.04977 11.3819i 0.131853 0.492082i
\(536\) 32.8734 + 56.9384i 1.41991 + 2.45936i
\(537\) 0 0
\(538\) −50.1269 50.1269i −2.16112 2.16112i
\(539\) −2.35820 + 4.39689i −0.101575 + 0.189388i
\(540\) 0 0
\(541\) 6.09190 + 6.09190i 0.261911 + 0.261911i 0.825830 0.563919i \(-0.190707\pi\)
−0.563919 + 0.825830i \(0.690707\pi\)
\(542\) 26.2469 + 15.1537i 1.12740 + 0.650905i
\(543\) 0 0
\(544\) −2.23482 0.598817i −0.0958169 0.0256741i
\(545\) 1.77210 0.0759086
\(546\) 0 0
\(547\) 30.2438 1.29313 0.646566 0.762858i \(-0.276205\pi\)
0.646566 + 0.762858i \(0.276205\pi\)
\(548\) 56.6677 + 15.1841i 2.42072 + 0.648631i
\(549\) 0 0
\(550\) −6.83769 3.94774i −0.291560 0.168332i
\(551\) −0.884692 0.884692i −0.0376892 0.0376892i
\(552\) 0 0
\(553\) −25.7968 2.98619i −1.09699 0.126986i
\(554\) 24.8971 + 24.8971i 1.05778 + 1.05778i
\(555\) 0 0
\(556\) −16.2704 28.1812i −0.690019 1.19515i
\(557\) 11.7586 43.8837i 0.498228 1.85941i −0.0129131 0.999917i \(-0.504110\pi\)
0.511141 0.859497i \(-0.329223\pi\)
\(558\) 0 0
\(559\) −26.5692 0.856180i −1.12376 0.0362126i
\(560\) 2.95871 7.47168i 0.125028 0.315736i
\(561\) 0 0
\(562\) −18.7657 32.5031i −0.791583 1.37106i
\(563\) 12.5992 21.8224i 0.530992 0.919704i −0.468354 0.883541i \(-0.655153\pi\)
0.999346 0.0361636i \(-0.0115137\pi\)
\(564\) 0 0
\(565\) 4.03418 1.08095i 0.169719 0.0454761i
\(566\) 8.87415 + 33.1188i 0.373009 + 1.39209i
\(567\) 0 0
\(568\) −20.5351 + 35.5679i −0.861634 + 1.49239i
\(569\) −13.9572 + 8.05819i −0.585116 + 0.337817i −0.763164 0.646205i \(-0.776355\pi\)
0.178048 + 0.984022i \(0.443022\pi\)
\(570\) 0 0
\(571\) 13.5825i 0.568409i −0.958764 0.284204i \(-0.908271\pi\)
0.958764 0.284204i \(-0.0917294\pi\)
\(572\) 3.01703 9.96418i 0.126149 0.416623i
\(573\) 0 0
\(574\) −46.7780 + 62.9795i −1.95247 + 2.62871i
\(575\) −4.34249 7.52142i −0.181094 0.313665i
\(576\) 0 0
\(577\) 33.5657 + 33.5657i 1.39736 + 1.39736i 0.807528 + 0.589829i \(0.200805\pi\)
0.589829 + 0.807528i \(0.299195\pi\)
\(578\) 2.33411 + 8.71103i 0.0970863 + 0.362331i
\(579\) 0 0
\(580\) 0.750831 0.750831i 0.0311766 0.0311766i
\(581\) −5.23942 6.61123i −0.217368 0.274280i
\(582\) 0 0
\(583\) −0.918168 + 3.42665i −0.0380266 + 0.141917i
\(584\) −4.34468 −0.179784
\(585\) 0 0
\(586\) 42.6820i 1.76318i
\(587\) 6.29368 23.4883i 0.259768 0.969467i −0.705607 0.708603i \(-0.749326\pi\)
0.965375 0.260864i \(-0.0840076\pi\)
\(588\) 0 0
\(589\) 14.5875 + 8.42210i 0.601067 + 0.347026i
\(590\) 4.89904 4.89904i 0.201690 0.201690i
\(591\) 0 0
\(592\) −8.77613 + 2.35156i −0.360697 + 0.0966484i
\(593\) 10.0628 10.0628i 0.413231 0.413231i −0.469631 0.882863i \(-0.655613\pi\)
0.882863 + 0.469631i \(0.155613\pi\)
\(594\) 0 0
\(595\) −8.38721 + 1.23805i −0.343842 + 0.0507553i
\(596\) −8.64195 + 32.2522i −0.353988 + 1.32110i
\(597\) 0 0
\(598\) 12.4789 11.6997i 0.510299 0.478438i
\(599\) −15.7719 −0.644422 −0.322211 0.946668i \(-0.604426\pi\)
−0.322211 + 0.946668i \(0.604426\pi\)
\(600\) 0 0
\(601\) 18.2565 10.5404i 0.744698 0.429952i −0.0790767 0.996869i \(-0.525197\pi\)
0.823775 + 0.566917i \(0.191864\pi\)
\(602\) 29.8032 + 37.6065i 1.21469 + 1.53273i
\(603\) 0 0
\(604\) −6.15805 22.9821i −0.250567 0.935130i
\(605\) 1.91413 + 7.14365i 0.0778206 + 0.290431i
\(606\) 0 0
\(607\) −14.6360 8.45008i −0.594056 0.342978i 0.172644 0.984984i \(-0.444769\pi\)
−0.766700 + 0.642006i \(0.778102\pi\)
\(608\) −0.856205 1.48299i −0.0347237 0.0601432i
\(609\) 0 0
\(610\) 20.1661i 0.816502i
\(611\) −5.25901 + 17.3686i −0.212757 + 0.702658i
\(612\) 0 0
\(613\) 17.4644 + 4.67958i 0.705381 + 0.189006i 0.593640 0.804731i \(-0.297690\pi\)
0.111742 + 0.993737i \(0.464357\pi\)
\(614\) 43.7695 25.2703i 1.76639 1.01983i
\(615\) 0 0
\(616\) −8.73233 + 3.77826i −0.351836 + 0.152230i
\(617\) −5.54500 20.6942i −0.223233 0.833118i −0.983105 0.183045i \(-0.941405\pi\)
0.759871 0.650074i \(-0.225262\pi\)
\(618\) 0 0
\(619\) 19.4756 19.4756i 0.782790 0.782790i −0.197511 0.980301i \(-0.563286\pi\)
0.980301 + 0.197511i \(0.0632857\pi\)
\(620\) −7.14777 + 12.3803i −0.287061 + 0.497205i
\(621\) 0 0
\(622\) 17.8892 + 4.79339i 0.717291 + 0.192197i
\(623\) −44.7004 17.7009i −1.79088 0.709172i
\(624\) 0 0
\(625\) −17.7939 −0.711756
\(626\) 5.03421 18.7879i 0.201208 0.750917i
\(627\) 0 0
\(628\) −29.6058 + 51.2787i −1.18140 + 2.04624i
\(629\) 6.77788 + 6.77788i 0.270252 + 0.270252i
\(630\) 0 0
\(631\) −20.8332 + 5.58224i −0.829356 + 0.222225i −0.648433 0.761272i \(-0.724575\pi\)
−0.180923 + 0.983497i \(0.557909\pi\)
\(632\) −35.0178 35.0178i −1.39293 1.39293i
\(633\) 0 0
\(634\) 36.9357 21.3248i 1.46690 0.846916i
\(635\) −13.6931 3.66906i −0.543395 0.145602i
\(636\) 0 0
\(637\) −24.3848 + 6.51023i −0.966160 + 0.257945i
\(638\) −0.651976 −0.0258120
\(639\) 0 0
\(640\) −11.6827 + 6.74499i −0.461798 + 0.266619i
\(641\) −25.3468 14.6340i −1.00114 0.578006i −0.0925521 0.995708i \(-0.529502\pi\)
−0.908584 + 0.417701i \(0.862836\pi\)
\(642\) 0 0
\(643\) 12.4873 3.34595i 0.492449 0.131951i −0.00404423 0.999992i \(-0.501287\pi\)
0.496494 + 0.868040i \(0.334621\pi\)
\(644\) −20.5344 2.37703i −0.809170 0.0936682i
\(645\) 0 0
\(646\) −18.8129 + 32.5849i −0.740183 + 1.28203i
\(647\) 18.8428 + 32.6368i 0.740788 + 1.28308i 0.952137 + 0.305672i \(0.0988813\pi\)
−0.211348 + 0.977411i \(0.567785\pi\)
\(648\) 0 0
\(649\) −2.84798 −0.111793
\(650\) −9.08921 38.8915i −0.356508 1.52545i
\(651\) 0 0
\(652\) 29.7833 + 7.98041i 1.16640 + 0.312537i
\(653\) 20.0158 + 34.6685i 0.783280 + 1.35668i 0.930021 + 0.367507i \(0.119788\pi\)
−0.146740 + 0.989175i \(0.546878\pi\)
\(654\) 0 0
\(655\) 6.02086 6.02086i 0.235255 0.235255i
\(656\) −50.1717 + 13.4435i −1.95888 + 0.524879i
\(657\) 0 0
\(658\) 30.0637 13.0078i 1.17201 0.507097i
\(659\) −15.0023 + 25.9848i −0.584407 + 1.01222i 0.410542 + 0.911842i \(0.365340\pi\)
−0.994949 + 0.100381i \(0.967994\pi\)
\(660\) 0 0
\(661\) −19.0751 5.11115i −0.741934 0.198801i −0.131996 0.991250i \(-0.542139\pi\)
−0.609937 + 0.792450i \(0.708805\pi\)
\(662\) 12.1508i 0.472255i
\(663\) 0 0
\(664\) 16.0866i 0.624283i
\(665\) −5.03741 3.74153i −0.195342 0.145090i
\(666\) 0 0
\(667\) −0.621087 0.358585i −0.0240486 0.0138845i
\(668\) −22.5408 22.5408i −0.872131 0.872131i
\(669\) 0 0
\(670\) 5.84803 + 21.8251i 0.225929 + 0.843178i
\(671\) −5.86164 + 5.86164i −0.226286 + 0.226286i
\(672\) 0 0
\(673\) −39.4906 + 22.7999i −1.52225 + 0.878872i −0.522597 + 0.852580i \(0.675037\pi\)
−0.999654 + 0.0262924i \(0.991630\pi\)
\(674\) 4.68348 17.4790i 0.180401 0.673265i
\(675\) 0 0
\(676\) 47.2090 23.3410i 1.81573 0.897730i
\(677\) 6.55217i 0.251821i −0.992042 0.125910i \(-0.959815\pi\)
0.992042 0.125910i \(-0.0401851\pi\)
\(678\) 0 0
\(679\) −23.6778 + 3.49514i −0.908672 + 0.134131i
\(680\) −14.0016 8.08381i −0.536936 0.310000i
\(681\) 0 0
\(682\) 8.47849 2.27180i 0.324658 0.0869919i
\(683\) −42.6432 + 11.4262i −1.63170 + 0.437212i −0.954408 0.298504i \(-0.903512\pi\)
−0.677290 + 0.735716i \(0.736846\pi\)
\(684\) 0 0
\(685\) 8.84040 + 5.10401i 0.337774 + 0.195014i
\(686\) 37.4056 + 26.0065i 1.42815 + 0.992933i
\(687\) 0 0
\(688\) 31.7697i 1.21121i
\(689\) −15.8220 + 8.46743i −0.602769 + 0.322584i
\(690\) 0 0
\(691\) 8.50701 31.7486i 0.323622 1.20777i −0.592068 0.805888i \(-0.701688\pi\)
0.915690 0.401885i \(-0.131645\pi\)
\(692\) −37.6106 + 21.7145i −1.42974 + 0.825462i
\(693\) 0 0
\(694\) 5.51370 5.51370i 0.209297 0.209297i
\(695\) −1.46546 5.46917i −0.0555881 0.207457i
\(696\) 0 0
\(697\) 38.7480 + 38.7480i 1.46769 + 1.46769i
\(698\) 57.4961 + 33.1954i 2.17626 + 1.25646i
\(699\) 0 0
\(700\) −28.7790 + 38.7466i −1.08774 + 1.46448i
\(701\) 8.83206i 0.333582i −0.985992 0.166791i \(-0.946659\pi\)
0.985992 0.166791i \(-0.0533406\pi\)
\(702\) 0 0
\(703\) 7.09444i 0.267572i
\(704\) 5.07144 + 1.35889i 0.191137 + 0.0512150i
\(705\) 0 0
\(706\) −6.48069 + 11.2249i −0.243904 + 0.422454i
\(707\) −14.2329 32.8950i −0.535282 1.23715i
\(708\) 0 0
\(709\) 28.7065 7.69188i 1.07809 0.288874i 0.324279 0.945961i \(-0.394878\pi\)
0.753815 + 0.657087i \(0.228212\pi\)
\(710\) −9.98046 + 9.98046i −0.374560 + 0.374560i
\(711\) 0 0
\(712\) −45.8416 79.4000i −1.71799 2.97564i
\(713\) 9.32628 + 2.49897i 0.349272 + 0.0935872i
\(714\) 0 0
\(715\) 0.955809 1.53882i 0.0357452 0.0575486i
\(716\) −40.3771 −1.50896
\(717\) 0 0
\(718\) 31.0431 + 53.7683i 1.15852 + 2.00662i
\(719\) 18.6597 32.3196i 0.695890 1.20532i −0.273990 0.961733i \(-0.588343\pi\)
0.969880 0.243584i \(-0.0783233\pi\)
\(720\) 0 0
\(721\) −43.2511 5.00668i −1.61076 0.186458i
\(722\) 18.2462 4.88907i 0.679055 0.181952i
\(723\) 0 0
\(724\) −13.9108 8.03142i −0.516992 0.298485i
\(725\) −1.45015 + 0.837245i −0.0538573 + 0.0310945i
\(726\) 0 0
\(727\) −9.88660 −0.366674 −0.183337 0.983050i \(-0.558690\pi\)
−0.183337 + 0.983050i \(0.558690\pi\)
\(728\) −44.1554 19.1524i −1.63651 0.709835i
\(729\) 0 0
\(730\) −1.44225 0.386449i −0.0533800 0.0143031i
\(731\) 29.0264 16.7584i 1.07358 0.619832i
\(732\) 0 0
\(733\) 14.5543 + 14.5543i 0.537577 + 0.537577i 0.922817 0.385240i \(-0.125881\pi\)
−0.385240 + 0.922817i \(0.625881\pi\)
\(734\) −78.5250 + 21.0407i −2.89841 + 0.776626i
\(735\) 0 0
\(736\) −0.694076 0.694076i −0.0255840 0.0255840i
\(737\) 4.64403 8.04370i 0.171065 0.296293i
\(738\) 0 0
\(739\) 13.1964 49.2497i 0.485438 1.81168i −0.0926405 0.995700i \(-0.529531\pi\)
0.578079 0.815981i \(-0.303803\pi\)
\(740\) −6.02100 −0.221336
\(741\) 0 0
\(742\) 30.1171 + 11.9261i 1.10563 + 0.437820i
\(743\) 13.4007 + 3.59070i 0.491623 + 0.131730i 0.496109 0.868260i \(-0.334761\pi\)
−0.00448658 + 0.999990i \(0.501428\pi\)
\(744\) 0 0
\(745\) −2.90493 + 5.03148i −0.106428 + 0.184339i
\(746\) −48.3496 + 48.3496i −1.77020 + 1.77020i
\(747\) 0 0
\(748\) 3.39737 + 12.6792i 0.124220 + 0.463597i
\(749\) 17.5630 + 40.5916i 0.641737 + 1.48319i
\(750\) 0 0
\(751\) −7.39608 + 4.27013i −0.269887 + 0.155819i −0.628836 0.777538i \(-0.716468\pi\)
0.358949 + 0.933357i \(0.383135\pi\)
\(752\) 20.9491 + 5.61329i 0.763935 + 0.204696i
\(753\) 0 0
\(754\) −2.25574 2.40597i −0.0821494 0.0876201i
\(755\) 4.13996i 0.150669i
\(756\) 0 0
\(757\) −5.08375 8.80531i −0.184772 0.320034i 0.758728 0.651408i \(-0.225821\pi\)
−0.943500 + 0.331374i \(0.892488\pi\)
\(758\) −32.4080 18.7108i −1.17711 0.679606i
\(759\) 0 0
\(760\) −3.09708 11.5585i −0.112343 0.419269i
\(761\) −0.975866 3.64198i −0.0353751 0.132022i 0.945980 0.324225i \(-0.105103\pi\)
−0.981355 + 0.192203i \(0.938437\pi\)
\(762\) 0 0
\(763\) −5.21295 + 4.13128i −0.188721 + 0.149562i
\(764\) 64.4046 37.1840i 2.33008 1.34527i
\(765\) 0 0
\(766\) 21.1536 0.764309
\(767\) −9.85363 10.5098i −0.355794 0.379488i
\(768\) 0 0
\(769\) −1.12134 + 4.18491i −0.0404367 + 0.150912i −0.983192 0.182572i \(-0.941558\pi\)
0.942756 + 0.333484i \(0.108224\pi\)
\(770\) −3.23483 + 0.477501i −0.116575 + 0.0172079i
\(771\) 0 0
\(772\) 47.0142 47.0142i 1.69208 1.69208i
\(773\) −14.9644 + 4.00970i −0.538233 + 0.144219i −0.517687 0.855570i \(-0.673207\pi\)
−0.0205453 + 0.999789i \(0.506540\pi\)
\(774\) 0 0
\(775\) 15.9408 15.9408i 0.572611 0.572611i
\(776\) −39.5277 22.8213i −1.41896 0.819237i
\(777\) 0 0
\(778\) −7.22366 + 26.9591i −0.258981 + 0.966529i
\(779\) 40.5578i 1.45313i
\(780\) 0 0
\(781\) 5.80200 0.207612
\(782\) −5.58208 + 20.8326i −0.199615 + 0.744973i
\(783\) 0 0
\(784\) 8.71504 + 28.8768i 0.311252 + 1.03132i
\(785\) −7.28519 + 7.28519i −0.260020 + 0.260020i
\(786\) 0 0
\(787\) 11.1122 + 41.4712i 0.396106 + 1.47829i 0.819888 + 0.572524i \(0.194036\pi\)
−0.423782 + 0.905764i \(0.639298\pi\)
\(788\) −16.8906 16.8906i −0.601703