Properties

Label 693.2.m.k.631.6
Level 693
Weight 2
Character 693.631
Analytic conductor 5.534
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 693.m (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.53363286007\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{5})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 631.6
Character \(\chi\) = 693.631
Dual form 693.2.m.k.190.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.727975 + 0.528905i) q^{2} +(-0.367826 - 1.13205i) q^{4} +(-0.650418 + 0.472557i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.887104 - 2.73023i) q^{8} +O(q^{10})\) \(q+(0.727975 + 0.528905i) q^{2} +(-0.367826 - 1.13205i) q^{4} +(-0.650418 + 0.472557i) q^{5} +(0.309017 + 0.951057i) q^{7} +(0.887104 - 2.73023i) q^{8} -0.723426 q^{10} +(3.31060 - 0.199849i) q^{11} +(-2.38421 - 1.73223i) q^{13} +(-0.278062 + 0.855786i) q^{14} +(0.163856 - 0.119049i) q^{16} +(2.67299 - 1.94204i) q^{17} +(2.45327 - 7.55040i) q^{19} +(0.774200 + 0.562489i) q^{20} +(2.51574 + 1.60551i) q^{22} +7.53481 q^{23} +(-1.34535 + 4.14056i) q^{25} +(-0.819462 - 2.52205i) q^{26} +(0.962982 - 0.699647i) q^{28} +(0.0724492 + 0.222976i) q^{29} +(-3.22308 - 2.34171i) q^{31} -5.55921 q^{32} +2.97302 q^{34} +(-0.650418 - 0.472557i) q^{35} +(-0.165770 - 0.510186i) q^{37} +(5.77936 - 4.19895i) q^{38} +(0.713197 + 2.19500i) q^{40} +(1.47849 - 4.55032i) q^{41} +3.16645 q^{43} +(-1.44396 - 3.67426i) q^{44} +(5.48516 + 3.98520i) q^{46} +(3.40270 - 10.4724i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-3.16935 + 2.30267i) q^{50} +(-1.08400 + 3.33622i) q^{52} +(9.49116 + 6.89573i) q^{53} +(-2.05883 + 1.69443i) q^{55} +2.87073 q^{56} +(-0.0651917 + 0.200640i) q^{58} +(1.62342 + 4.99638i) q^{59} +(-2.95649 + 2.14802i) q^{61} +(-1.10778 - 3.40941i) q^{62} +(-4.37468 - 3.17839i) q^{64} +2.36931 q^{65} -13.6736 q^{67} +(-3.18169 - 2.31163i) q^{68} +(-0.223551 - 0.688019i) q^{70} +(-8.36286 + 6.07597i) q^{71} +(2.75315 + 8.47332i) q^{73} +(0.149164 - 0.459079i) q^{74} -9.44983 q^{76} +(1.21310 + 3.08681i) q^{77} +(6.77674 + 4.92359i) q^{79} +(-0.0503180 + 0.154863i) q^{80} +(3.48299 - 2.53054i) q^{82} +(-5.87535 + 4.26869i) q^{83} +(-0.820837 + 2.52628i) q^{85} +(2.30509 + 1.67475i) q^{86} +(2.39121 - 9.21597i) q^{88} -8.03460 q^{89} +(0.910689 - 2.80281i) q^{91} +(-2.77150 - 8.52980i) q^{92} +(8.01600 - 5.82396i) q^{94} +(1.97234 + 6.07023i) q^{95} +(-15.5907 - 11.3273i) q^{97} -0.899827 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 10q^{4} - 8q^{7} + O(q^{10}) \) \( 32q - 10q^{4} - 8q^{7} - 12q^{10} + 10q^{13} - 26q^{16} - 10q^{19} - 6q^{22} - 52q^{25} - 10q^{28} - 20q^{31} + 24q^{34} - 4q^{37} + 124q^{40} + 32q^{43} + 30q^{46} - 8q^{49} + 24q^{52} - 12q^{55} - 104q^{58} + 34q^{61} - 52q^{64} + 104q^{67} + 18q^{70} + 2q^{73} - 28q^{76} - 42q^{79} - 172q^{82} - 30q^{85} - 16q^{88} - 10q^{91} + 150q^{94} - 74q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.727975 + 0.528905i 0.514756 + 0.373992i 0.814625 0.579988i \(-0.196943\pi\)
−0.299869 + 0.953981i \(0.596943\pi\)
\(3\) 0 0
\(4\) −0.367826 1.13205i −0.183913 0.566027i
\(5\) −0.650418 + 0.472557i −0.290876 + 0.211334i −0.723647 0.690170i \(-0.757536\pi\)
0.432771 + 0.901504i \(0.357536\pi\)
\(6\) 0 0
\(7\) 0.309017 + 0.951057i 0.116797 + 0.359466i
\(8\) 0.887104 2.73023i 0.313639 0.965280i
\(9\) 0 0
\(10\) −0.723426 −0.228767
\(11\) 3.31060 0.199849i 0.998183 0.0602567i
\(12\) 0 0
\(13\) −2.38421 1.73223i −0.661262 0.480435i 0.205827 0.978588i \(-0.434012\pi\)
−0.867089 + 0.498154i \(0.834012\pi\)
\(14\) −0.278062 + 0.855786i −0.0743152 + 0.228719i
\(15\) 0 0
\(16\) 0.163856 0.119049i 0.0409641 0.0297621i
\(17\) 2.67299 1.94204i 0.648295 0.471014i −0.214395 0.976747i \(-0.568778\pi\)
0.862690 + 0.505733i \(0.168778\pi\)
\(18\) 0 0
\(19\) 2.45327 7.55040i 0.562819 1.73218i −0.111524 0.993762i \(-0.535573\pi\)
0.674344 0.738418i \(-0.264427\pi\)
\(20\) 0.774200 + 0.562489i 0.173116 + 0.125776i
\(21\) 0 0
\(22\) 2.51574 + 1.60551i 0.536357 + 0.342295i
\(23\) 7.53481 1.57112 0.785558 0.618788i \(-0.212376\pi\)
0.785558 + 0.618788i \(0.212376\pi\)
\(24\) 0 0
\(25\) −1.34535 + 4.14056i −0.269070 + 0.828113i
\(26\) −0.819462 2.52205i −0.160710 0.494614i
\(27\) 0 0
\(28\) 0.962982 0.699647i 0.181986 0.132221i
\(29\) 0.0724492 + 0.222976i 0.0134535 + 0.0414055i 0.957558 0.288241i \(-0.0930704\pi\)
−0.944104 + 0.329647i \(0.893070\pi\)
\(30\) 0 0
\(31\) −3.22308 2.34171i −0.578882 0.420583i 0.259439 0.965760i \(-0.416462\pi\)
−0.838321 + 0.545177i \(0.816462\pi\)
\(32\) −5.55921 −0.982738
\(33\) 0 0
\(34\) 2.97302 0.509869
\(35\) −0.650418 0.472557i −0.109941 0.0798766i
\(36\) 0 0
\(37\) −0.165770 0.510186i −0.0272523 0.0838741i 0.936505 0.350653i \(-0.114040\pi\)
−0.963758 + 0.266779i \(0.914040\pi\)
\(38\) 5.77936 4.19895i 0.937537 0.681160i
\(39\) 0 0
\(40\) 0.713197 + 2.19500i 0.112766 + 0.347059i
\(41\) 1.47849 4.55032i 0.230901 0.710641i −0.766737 0.641961i \(-0.778121\pi\)
0.997639 0.0686803i \(-0.0218788\pi\)
\(42\) 0 0
\(43\) 3.16645 0.482878 0.241439 0.970416i \(-0.422381\pi\)
0.241439 + 0.970416i \(0.422381\pi\)
\(44\) −1.44396 3.67426i −0.217686 0.553916i
\(45\) 0 0
\(46\) 5.48516 + 3.98520i 0.808742 + 0.587586i
\(47\) 3.40270 10.4724i 0.496334 1.52756i −0.318533 0.947912i \(-0.603190\pi\)
0.814867 0.579648i \(-0.196810\pi\)
\(48\) 0 0
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) −3.16935 + 2.30267i −0.448213 + 0.325646i
\(51\) 0 0
\(52\) −1.08400 + 3.33622i −0.150324 + 0.462650i
\(53\) 9.49116 + 6.89573i 1.30371 + 0.947201i 0.999985 0.00555811i \(-0.00176921\pi\)
0.303726 + 0.952759i \(0.401769\pi\)
\(54\) 0 0
\(55\) −2.05883 + 1.69443i −0.277613 + 0.228477i
\(56\) 2.87073 0.383617
\(57\) 0 0
\(58\) −0.0651917 + 0.200640i −0.00856010 + 0.0263453i
\(59\) 1.62342 + 4.99638i 0.211352 + 0.650474i 0.999393 + 0.0348508i \(0.0110956\pi\)
−0.788041 + 0.615623i \(0.788904\pi\)
\(60\) 0 0
\(61\) −2.95649 + 2.14802i −0.378540 + 0.275025i −0.760743 0.649053i \(-0.775165\pi\)
0.382203 + 0.924078i \(0.375165\pi\)
\(62\) −1.10778 3.40941i −0.140689 0.432995i
\(63\) 0 0
\(64\) −4.37468 3.17839i −0.546835 0.397299i
\(65\) 2.36931 0.293877
\(66\) 0 0
\(67\) −13.6736 −1.67050 −0.835250 0.549871i \(-0.814677\pi\)
−0.835250 + 0.549871i \(0.814677\pi\)
\(68\) −3.18169 2.31163i −0.385836 0.280326i
\(69\) 0 0
\(70\) −0.223551 0.688019i −0.0267195 0.0822340i
\(71\) −8.36286 + 6.07597i −0.992489 + 0.721085i −0.960465 0.278402i \(-0.910195\pi\)
−0.0320239 + 0.999487i \(0.510195\pi\)
\(72\) 0 0
\(73\) 2.75315 + 8.47332i 0.322232 + 0.991727i 0.972675 + 0.232172i \(0.0745832\pi\)
−0.650443 + 0.759555i \(0.725417\pi\)
\(74\) 0.149164 0.459079i 0.0173400 0.0533669i
\(75\) 0 0
\(76\) −9.44983 −1.08397
\(77\) 1.21310 + 3.08681i 0.138245 + 0.351775i
\(78\) 0 0
\(79\) 6.77674 + 4.92359i 0.762442 + 0.553947i 0.899658 0.436594i \(-0.143815\pi\)
−0.137216 + 0.990541i \(0.543815\pi\)
\(80\) −0.0503180 + 0.154863i −0.00562572 + 0.0173142i
\(81\) 0 0
\(82\) 3.48299 2.53054i 0.384632 0.279452i
\(83\) −5.87535 + 4.26869i −0.644904 + 0.468550i −0.861531 0.507704i \(-0.830494\pi\)
0.216628 + 0.976254i \(0.430494\pi\)
\(84\) 0 0
\(85\) −0.820837 + 2.52628i −0.0890323 + 0.274013i
\(86\) 2.30509 + 1.67475i 0.248565 + 0.180593i
\(87\) 0 0
\(88\) 2.39121 9.21597i 0.254904 0.982425i
\(89\) −8.03460 −0.851666 −0.425833 0.904802i \(-0.640019\pi\)
−0.425833 + 0.904802i \(0.640019\pi\)
\(90\) 0 0
\(91\) 0.910689 2.80281i 0.0954661 0.293814i
\(92\) −2.77150 8.52980i −0.288949 0.889293i
\(93\) 0 0
\(94\) 8.01600 5.82396i 0.826787 0.600696i
\(95\) 1.97234 + 6.07023i 0.202357 + 0.622792i
\(96\) 0 0
\(97\) −15.5907 11.3273i −1.58299 1.15011i −0.913163 0.407595i \(-0.866368\pi\)
−0.669829 0.742516i \(-0.733632\pi\)
\(98\) −0.899827 −0.0908963
\(99\) 0 0
\(100\) 5.18219 0.518219
\(101\) 13.9793 + 10.1566i 1.39099 + 1.01062i 0.995755 + 0.0920385i \(0.0293383\pi\)
0.395239 + 0.918578i \(0.370662\pi\)
\(102\) 0 0
\(103\) 4.43665 + 13.6546i 0.437156 + 1.34543i 0.890861 + 0.454277i \(0.150102\pi\)
−0.453704 + 0.891152i \(0.649898\pi\)
\(104\) −6.84443 + 4.97277i −0.671152 + 0.487620i
\(105\) 0 0
\(106\) 3.26214 + 10.0398i 0.316847 + 0.975156i
\(107\) −4.73420 + 14.5704i −0.457672 + 1.40857i 0.410297 + 0.911952i \(0.365425\pi\)
−0.867969 + 0.496618i \(0.834575\pi\)
\(108\) 0 0
\(109\) −5.50237 −0.527032 −0.263516 0.964655i \(-0.584882\pi\)
−0.263516 + 0.964655i \(0.584882\pi\)
\(110\) −2.39497 + 0.144576i −0.228352 + 0.0137848i
\(111\) 0 0
\(112\) 0.163856 + 0.119049i 0.0154830 + 0.0112490i
\(113\) 2.06880 6.36710i 0.194616 0.598967i −0.805365 0.592780i \(-0.798031\pi\)
0.999981 0.00618714i \(-0.00196944\pi\)
\(114\) 0 0
\(115\) −4.90078 + 3.56062i −0.457000 + 0.332030i
\(116\) 0.225772 0.164033i 0.0209624 0.0152300i
\(117\) 0 0
\(118\) −1.46080 + 4.49588i −0.134478 + 0.413880i
\(119\) 2.67299 + 1.94204i 0.245032 + 0.178026i
\(120\) 0 0
\(121\) 10.9201 1.32324i 0.992738 0.120294i
\(122\) −3.28835 −0.297713
\(123\) 0 0
\(124\) −1.46540 + 4.51004i −0.131597 + 0.405014i
\(125\) −2.32380 7.15192i −0.207847 0.639687i
\(126\) 0 0
\(127\) 9.33897 6.78516i 0.828700 0.602086i −0.0904914 0.995897i \(-0.528844\pi\)
0.919191 + 0.393812i \(0.128844\pi\)
\(128\) 1.93219 + 5.94666i 0.170783 + 0.525616i
\(129\) 0 0
\(130\) 1.72480 + 1.25314i 0.151275 + 0.109908i
\(131\) −21.2008 −1.85232 −0.926161 0.377128i \(-0.876912\pi\)
−0.926161 + 0.377128i \(0.876912\pi\)
\(132\) 0 0
\(133\) 7.93896 0.688395
\(134\) −9.95407 7.23205i −0.859900 0.624754i
\(135\) 0 0
\(136\) −2.93099 9.02065i −0.251330 0.773514i
\(137\) 0.659483 0.479143i 0.0563435 0.0409359i −0.559257 0.828994i \(-0.688914\pi\)
0.615601 + 0.788058i \(0.288914\pi\)
\(138\) 0 0
\(139\) 2.86540 + 8.81880i 0.243040 + 0.748001i 0.995953 + 0.0898801i \(0.0286484\pi\)
−0.752912 + 0.658121i \(0.771352\pi\)
\(140\) −0.295718 + 0.910127i −0.0249927 + 0.0769198i
\(141\) 0 0
\(142\) −9.30157 −0.780570
\(143\) −8.23936 5.25824i −0.689010 0.439716i
\(144\) 0 0
\(145\) −0.152491 0.110791i −0.0126637 0.00920070i
\(146\) −2.47736 + 7.62452i −0.205028 + 0.631010i
\(147\) 0 0
\(148\) −0.516583 + 0.375320i −0.0424629 + 0.0308511i
\(149\) 5.62143 4.08421i 0.460526 0.334592i −0.333212 0.942852i \(-0.608132\pi\)
0.793738 + 0.608260i \(0.208132\pi\)
\(150\) 0 0
\(151\) 4.33498 13.3417i 0.352776 1.08573i −0.604512 0.796596i \(-0.706632\pi\)
0.957288 0.289136i \(-0.0933681\pi\)
\(152\) −18.4380 13.3960i −1.49552 1.08656i
\(153\) 0 0
\(154\) −0.749523 + 2.88874i −0.0603983 + 0.232781i
\(155\) 3.20294 0.257266
\(156\) 0 0
\(157\) 0.226627 0.697487i 0.0180868 0.0556655i −0.941606 0.336717i \(-0.890683\pi\)
0.959693 + 0.281052i \(0.0906833\pi\)
\(158\) 2.32919 + 7.16850i 0.185300 + 0.570295i
\(159\) 0 0
\(160\) 3.61581 2.62704i 0.285855 0.207686i
\(161\) 2.32838 + 7.16603i 0.183502 + 0.564762i
\(162\) 0 0
\(163\) −2.39758 1.74195i −0.187793 0.136440i 0.489916 0.871769i \(-0.337027\pi\)
−0.677710 + 0.735330i \(0.737027\pi\)
\(164\) −5.69504 −0.444708
\(165\) 0 0
\(166\) −6.53485 −0.507203
\(167\) 6.50456 + 4.72584i 0.503338 + 0.365697i 0.810291 0.586028i \(-0.199309\pi\)
−0.306952 + 0.951725i \(0.599309\pi\)
\(168\) 0 0
\(169\) −1.33338 4.10371i −0.102567 0.315670i
\(170\) −1.93371 + 1.40492i −0.148309 + 0.107753i
\(171\) 0 0
\(172\) −1.16470 3.58458i −0.0888077 0.273322i
\(173\) −1.59317 + 4.90326i −0.121126 + 0.372788i −0.993175 0.116630i \(-0.962791\pi\)
0.872049 + 0.489418i \(0.162791\pi\)
\(174\) 0 0
\(175\) −4.35365 −0.329105
\(176\) 0.518671 0.426868i 0.0390963 0.0321764i
\(177\) 0 0
\(178\) −5.84899 4.24954i −0.438400 0.318516i
\(179\) −1.85804 + 5.71844i −0.138876 + 0.427417i −0.996173 0.0874061i \(-0.972142\pi\)
0.857297 + 0.514823i \(0.172142\pi\)
\(180\) 0 0
\(181\) −1.98246 + 1.44034i −0.147355 + 0.107060i −0.659020 0.752125i \(-0.729029\pi\)
0.511665 + 0.859185i \(0.329029\pi\)
\(182\) 2.14538 1.55871i 0.159026 0.115539i
\(183\) 0 0
\(184\) 6.68416 20.5717i 0.492763 1.51657i
\(185\) 0.348911 + 0.253499i 0.0256525 + 0.0186376i
\(186\) 0 0
\(187\) 8.46107 6.96351i 0.618735 0.509222i
\(188\) −13.1069 −0.955922
\(189\) 0 0
\(190\) −1.77476 + 5.46215i −0.128755 + 0.396266i
\(191\) 6.57422 + 20.2334i 0.475694 + 1.46404i 0.845019 + 0.534736i \(0.179589\pi\)
−0.369325 + 0.929300i \(0.620411\pi\)
\(192\) 0 0
\(193\) 6.79512 4.93695i 0.489124 0.355369i −0.315723 0.948851i \(-0.602247\pi\)
0.804847 + 0.593482i \(0.202247\pi\)
\(194\) −5.35856 16.4920i −0.384722 1.18405i
\(195\) 0 0
\(196\) 0.962982 + 0.699647i 0.0687844 + 0.0499748i
\(197\) −10.9646 −0.781194 −0.390597 0.920562i \(-0.627731\pi\)
−0.390597 + 0.920562i \(0.627731\pi\)
\(198\) 0 0
\(199\) 6.26130 0.443852 0.221926 0.975064i \(-0.428766\pi\)
0.221926 + 0.975064i \(0.428766\pi\)
\(200\) 10.1112 + 7.34622i 0.714970 + 0.519456i
\(201\) 0 0
\(202\) 4.80474 + 14.7875i 0.338060 + 1.04044i
\(203\) −0.189674 + 0.137807i −0.0133125 + 0.00967212i
\(204\) 0 0
\(205\) 1.18865 + 3.65828i 0.0830188 + 0.255506i
\(206\) −3.99222 + 12.2868i −0.278151 + 0.856061i
\(207\) 0 0
\(208\) −0.596888 −0.0413867
\(209\) 6.61286 25.4866i 0.457421 1.76295i
\(210\) 0 0
\(211\) −13.5270 9.82796i −0.931239 0.676585i 0.0150571 0.999887i \(-0.495207\pi\)
−0.946296 + 0.323302i \(0.895207\pi\)
\(212\) 4.31523 13.2809i 0.296371 0.912138i
\(213\) 0 0
\(214\) −11.1527 + 8.10293i −0.762384 + 0.553905i
\(215\) −2.05951 + 1.49632i −0.140458 + 0.102049i
\(216\) 0 0
\(217\) 1.23111 3.78896i 0.0835730 0.257211i
\(218\) −4.00559 2.91023i −0.271293 0.197106i
\(219\) 0 0
\(220\) 2.67548 + 1.70745i 0.180381 + 0.115116i
\(221\) −9.73704 −0.654984
\(222\) 0 0
\(223\) 4.04713 12.4558i 0.271016 0.834101i −0.719230 0.694772i \(-0.755505\pi\)
0.990246 0.139329i \(-0.0444947\pi\)
\(224\) −1.71789 5.28712i −0.114781 0.353261i
\(225\) 0 0
\(226\) 4.87363 3.54090i 0.324189 0.235537i
\(227\) 4.91414 + 15.1242i 0.326163 + 1.00383i 0.970913 + 0.239432i \(0.0769613\pi\)
−0.644750 + 0.764393i \(0.723039\pi\)
\(228\) 0 0
\(229\) −7.29405 5.29944i −0.482004 0.350197i 0.320097 0.947385i \(-0.396285\pi\)
−0.802101 + 0.597188i \(0.796285\pi\)
\(230\) −5.45088 −0.359420
\(231\) 0 0
\(232\) 0.673044 0.0441875
\(233\) 2.05652 + 1.49415i 0.134727 + 0.0978850i 0.653108 0.757265i \(-0.273465\pi\)
−0.518381 + 0.855150i \(0.673465\pi\)
\(234\) 0 0
\(235\) 2.73564 + 8.41942i 0.178453 + 0.549222i
\(236\) 5.05903 3.67560i 0.329315 0.239261i
\(237\) 0 0
\(238\) 0.918715 + 2.82751i 0.0595514 + 0.183281i
\(239\) −5.92537 + 18.2364i −0.383281 + 1.17962i 0.554439 + 0.832224i \(0.312933\pi\)
−0.937720 + 0.347392i \(0.887067\pi\)
\(240\) 0 0
\(241\) −7.50063 −0.483158 −0.241579 0.970381i \(-0.577665\pi\)
−0.241579 + 0.970381i \(0.577665\pi\)
\(242\) 8.64945 + 4.81242i 0.556008 + 0.309354i
\(243\) 0 0
\(244\) 3.51914 + 2.55681i 0.225290 + 0.163683i
\(245\) 0.248438 0.764613i 0.0158721 0.0488493i
\(246\) 0 0
\(247\) −18.9282 + 13.7521i −1.20437 + 0.875026i
\(248\) −9.25259 + 6.72240i −0.587540 + 0.426873i
\(249\) 0 0
\(250\) 2.09102 6.43549i 0.132248 0.407016i
\(251\) 11.8847 + 8.63475i 0.750157 + 0.545021i 0.895875 0.444305i \(-0.146549\pi\)
−0.145719 + 0.989326i \(0.546549\pi\)
\(252\) 0 0
\(253\) 24.9447 1.50582i 1.56826 0.0946703i
\(254\) 10.3872 0.651754
\(255\) 0 0
\(256\) −5.08059 + 15.6365i −0.317537 + 0.977279i
\(257\) −6.41213 19.7345i −0.399978 1.23101i −0.925016 0.379927i \(-0.875949\pi\)
0.525038 0.851079i \(-0.324051\pi\)
\(258\) 0 0
\(259\) 0.433990 0.315312i 0.0269668 0.0195926i
\(260\) −0.871496 2.68219i −0.0540479 0.166342i
\(261\) 0 0
\(262\) −15.4337 11.2132i −0.953495 0.692754i
\(263\) 27.3462 1.68624 0.843118 0.537729i \(-0.180717\pi\)
0.843118 + 0.537729i \(0.180717\pi\)
\(264\) 0 0
\(265\) −9.43185 −0.579394
\(266\) 5.77936 + 4.19895i 0.354356 + 0.257454i
\(267\) 0 0
\(268\) 5.02952 + 15.4793i 0.307227 + 0.945547i
\(269\) −1.27748 + 0.928141i −0.0778891 + 0.0565898i −0.626048 0.779784i \(-0.715329\pi\)
0.548159 + 0.836374i \(0.315329\pi\)
\(270\) 0 0
\(271\) 4.66658 + 14.3622i 0.283474 + 0.872444i 0.986852 + 0.161628i \(0.0516744\pi\)
−0.703377 + 0.710817i \(0.748326\pi\)
\(272\) 0.206789 0.636431i 0.0125384 0.0385893i
\(273\) 0 0
\(274\) 0.733509 0.0443129
\(275\) −3.62643 + 13.9766i −0.218682 + 0.842821i
\(276\) 0 0
\(277\) 13.1342 + 9.54256i 0.789158 + 0.573357i 0.907714 0.419590i \(-0.137826\pi\)
−0.118555 + 0.992947i \(0.537826\pi\)
\(278\) −2.57837 + 7.93540i −0.154640 + 0.475933i
\(279\) 0 0
\(280\) −1.86717 + 1.35658i −0.111585 + 0.0810713i
\(281\) 13.8234 10.0433i 0.824633 0.599131i −0.0934030 0.995628i \(-0.529774\pi\)
0.918036 + 0.396498i \(0.129774\pi\)
\(282\) 0 0
\(283\) −0.0355451 + 0.109397i −0.00211294 + 0.00650296i −0.952107 0.305764i \(-0.901088\pi\)
0.949994 + 0.312267i \(0.101088\pi\)
\(284\) 9.95440 + 7.23230i 0.590685 + 0.429158i
\(285\) 0 0
\(286\) −3.21694 8.18571i −0.190222 0.484031i
\(287\) 4.78449 0.282420
\(288\) 0 0
\(289\) −1.87994 + 5.78587i −0.110585 + 0.340345i
\(290\) −0.0524116 0.161306i −0.00307772 0.00947224i
\(291\) 0 0
\(292\) 8.57956 6.23342i 0.502081 0.364783i
\(293\) −5.76629 17.7468i −0.336870 1.03678i −0.965793 0.259313i \(-0.916504\pi\)
0.628923 0.777467i \(-0.283496\pi\)
\(294\) 0 0
\(295\) −3.41698 2.48258i −0.198944 0.144541i
\(296\) −1.53998 −0.0895094
\(297\) 0 0
\(298\) 6.25243 0.362193
\(299\) −17.9646 13.0520i −1.03892 0.754819i
\(300\) 0 0
\(301\) 0.978486 + 3.01147i 0.0563990 + 0.173578i
\(302\) 10.2123 7.41964i 0.587649 0.426952i
\(303\) 0 0
\(304\) −0.496880 1.52924i −0.0284980 0.0877078i
\(305\) 0.907897 2.79422i 0.0519860 0.159996i
\(306\) 0 0
\(307\) 13.9263 0.794817 0.397408 0.917642i \(-0.369910\pi\)
0.397408 + 0.917642i \(0.369910\pi\)
\(308\) 3.04822 2.50870i 0.173689 0.142947i
\(309\) 0 0
\(310\) 2.33166 + 1.69405i 0.132429 + 0.0962156i
\(311\) 3.13862 9.65969i 0.177975 0.547751i −0.821782 0.569802i \(-0.807020\pi\)
0.999757 + 0.0220516i \(0.00701980\pi\)
\(312\) 0 0
\(313\) −3.89853 + 2.83245i −0.220358 + 0.160099i −0.692488 0.721430i \(-0.743485\pi\)
0.472130 + 0.881529i \(0.343485\pi\)
\(314\) 0.533884 0.387889i 0.0301288 0.0218899i
\(315\) 0 0
\(316\) 3.08110 9.48265i 0.173325 0.533441i
\(317\) 6.53134 + 4.74530i 0.366837 + 0.266523i 0.755898 0.654689i \(-0.227201\pi\)
−0.389061 + 0.921212i \(0.627201\pi\)
\(318\) 0 0
\(319\) 0.284412 + 0.723704i 0.0159240 + 0.0405196i
\(320\) 4.34734 0.243024
\(321\) 0 0
\(322\) −2.09514 + 6.44819i −0.116758 + 0.359343i
\(323\) −8.10560 24.9465i −0.451008 1.38806i
\(324\) 0 0
\(325\) 10.3800 7.54153i 0.575780 0.418329i
\(326\) −0.824058 2.53619i −0.0456403 0.140467i
\(327\) 0 0
\(328\) −11.1118 8.07322i −0.613548 0.445769i
\(329\) 11.0114 0.607076
\(330\) 0 0
\(331\) 0.776780 0.0426957 0.0213479 0.999772i \(-0.493204\pi\)
0.0213479 + 0.999772i \(0.493204\pi\)
\(332\) 6.99350 + 5.08107i 0.383818 + 0.278860i
\(333\) 0 0
\(334\) 2.23564 + 6.88059i 0.122329 + 0.376489i
\(335\) 8.89358 6.46156i 0.485908 0.353033i
\(336\) 0 0
\(337\) 0.0647699 + 0.199341i 0.00352824 + 0.0108588i 0.952805 0.303583i \(-0.0981828\pi\)
−0.949277 + 0.314441i \(0.898183\pi\)
\(338\) 1.19981 3.69263i 0.0652610 0.200853i
\(339\) 0 0
\(340\) 3.16180 0.171473
\(341\) −11.1383 7.10832i −0.603173 0.384937i
\(342\) 0 0
\(343\) −0.809017 0.587785i −0.0436828 0.0317374i
\(344\) 2.80897 8.64511i 0.151449 0.466113i
\(345\) 0 0
\(346\) −3.75315 + 2.72682i −0.201770 + 0.146595i
\(347\) 18.4431 13.3997i 0.990079 0.719334i 0.0301406 0.999546i \(-0.490405\pi\)
0.959938 + 0.280211i \(0.0904045\pi\)
\(348\) 0 0
\(349\) −4.33532 + 13.3427i −0.232064 + 0.714220i 0.765433 + 0.643516i \(0.222525\pi\)
−0.997497 + 0.0707048i \(0.977475\pi\)
\(350\) −3.16935 2.30267i −0.169409 0.123083i
\(351\) 0 0
\(352\) −18.4043 + 1.11100i −0.980953 + 0.0592166i
\(353\) 22.3703 1.19065 0.595327 0.803484i \(-0.297023\pi\)
0.595327 + 0.803484i \(0.297023\pi\)
\(354\) 0 0
\(355\) 2.56812 7.90385i 0.136301 0.419493i
\(356\) 2.95534 + 9.09559i 0.156633 + 0.482065i
\(357\) 0 0
\(358\) −4.37712 + 3.18016i −0.231338 + 0.168077i
\(359\) 0.834999 + 2.56986i 0.0440695 + 0.135632i 0.970670 0.240414i \(-0.0772833\pi\)
−0.926601 + 0.376046i \(0.877283\pi\)
\(360\) 0 0
\(361\) −35.6186 25.8784i −1.87466 1.36202i
\(362\) −2.20499 −0.115892
\(363\) 0 0
\(364\) −3.50791 −0.183864
\(365\) −5.79482 4.21018i −0.303315 0.220371i
\(366\) 0 0
\(367\) 8.73963 + 26.8978i 0.456205 + 1.40405i 0.869715 + 0.493555i \(0.164303\pi\)
−0.413509 + 0.910500i \(0.635697\pi\)
\(368\) 1.23463 0.897008i 0.0643593 0.0467598i
\(369\) 0 0
\(370\) 0.119922 + 0.369082i 0.00623445 + 0.0191877i
\(371\) −3.62530 + 11.1575i −0.188216 + 0.579270i
\(372\) 0 0
\(373\) 8.53857 0.442110 0.221055 0.975261i \(-0.429050\pi\)
0.221055 + 0.975261i \(0.429050\pi\)
\(374\) 9.84249 0.594156i 0.508943 0.0307231i
\(375\) 0 0
\(376\) −25.5735 18.5802i −1.31885 0.958203i
\(377\) 0.213511 0.657120i 0.0109964 0.0338434i
\(378\) 0 0
\(379\) −28.0587 + 20.3858i −1.44128 + 1.04715i −0.453506 + 0.891253i \(0.649827\pi\)
−0.987773 + 0.155897i \(0.950173\pi\)
\(380\) 6.14634 4.46558i 0.315301 0.229079i
\(381\) 0 0
\(382\) −5.91566 + 18.2065i −0.302672 + 0.931528i
\(383\) 10.2885 + 7.47507i 0.525720 + 0.381958i 0.818754 0.574144i \(-0.194665\pi\)
−0.293034 + 0.956102i \(0.594665\pi\)
\(384\) 0 0
\(385\) −2.24771 1.43446i −0.114554 0.0731068i
\(386\) 7.55786 0.384685
\(387\) 0 0
\(388\) −7.08842 + 21.8159i −0.359860 + 1.10754i
\(389\) −0.768678 2.36575i −0.0389735 0.119948i 0.929677 0.368376i \(-0.120086\pi\)
−0.968650 + 0.248428i \(0.920086\pi\)
\(390\) 0 0
\(391\) 20.1404 14.6329i 1.01855 0.740017i
\(392\) 0.887104 + 2.73023i 0.0448055 + 0.137897i
\(393\) 0 0
\(394\) −7.98194 5.79922i −0.402124 0.292160i
\(395\) −6.73439 −0.338844
\(396\) 0 0
\(397\) 19.1634 0.961781 0.480891 0.876781i \(-0.340313\pi\)
0.480891 + 0.876781i \(0.340313\pi\)
\(398\) 4.55807 + 3.31163i 0.228476 + 0.165997i
\(399\) 0 0
\(400\) 0.272484 + 0.838619i 0.0136242 + 0.0419310i
\(401\) −7.41873 + 5.39002i −0.370474 + 0.269165i −0.757407 0.652943i \(-0.773534\pi\)
0.386934 + 0.922108i \(0.373534\pi\)
\(402\) 0 0
\(403\) 3.62813 + 11.1663i 0.180730 + 0.556231i
\(404\) 6.35582 19.5612i 0.316214 0.973206i
\(405\) 0 0
\(406\) −0.210965 −0.0104700
\(407\) −0.650756 1.65589i −0.0322568 0.0820795i
\(408\) 0 0
\(409\) 23.9765 + 17.4200i 1.18556 + 0.861361i 0.992788 0.119882i \(-0.0382516\pi\)
0.192774 + 0.981243i \(0.438252\pi\)
\(410\) −1.06958 + 3.29182i −0.0528227 + 0.162572i
\(411\) 0 0
\(412\) 13.8258 10.0451i 0.681150 0.494884i
\(413\) −4.25018 + 3.08794i −0.209138 + 0.151947i
\(414\) 0 0
\(415\) 1.80424 5.55287i 0.0885666 0.272580i
\(416\) 13.2543 + 9.62984i 0.649847 + 0.472142i
\(417\) 0 0
\(418\) 18.2940 15.0561i 0.894789 0.736415i
\(419\) −31.7616 −1.55166 −0.775828 0.630944i \(-0.782668\pi\)
−0.775828 + 0.630944i \(0.782668\pi\)
\(420\) 0 0
\(421\) 1.83822 5.65747i 0.0895895 0.275728i −0.896216 0.443617i \(-0.853695\pi\)
0.985806 + 0.167889i \(0.0536950\pi\)
\(422\) −4.64928 14.3090i −0.226324 0.696552i
\(423\) 0 0
\(424\) 27.2465 19.7958i 1.32321 0.961367i
\(425\) 4.44503 + 13.6804i 0.215616 + 0.663597i
\(426\) 0 0
\(427\) −2.95649 2.14802i −0.143075 0.103950i
\(428\) 18.2358 0.881460
\(429\) 0 0
\(430\) −2.29069 −0.110467
\(431\) 9.13425 + 6.63642i 0.439981 + 0.319665i 0.785628 0.618700i \(-0.212340\pi\)
−0.345646 + 0.938365i \(0.612340\pi\)
\(432\) 0 0
\(433\) 5.31293 + 16.3515i 0.255323 + 0.785804i 0.993766 + 0.111488i \(0.0355616\pi\)
−0.738443 + 0.674316i \(0.764438\pi\)
\(434\) 2.90022 2.10713i 0.139215 0.101145i
\(435\) 0 0
\(436\) 2.02392 + 6.22898i 0.0969281 + 0.298314i
\(437\) 18.4849 56.8908i 0.884254 2.72146i
\(438\) 0 0
\(439\) −33.6983 −1.60833 −0.804167 0.594404i \(-0.797388\pi\)
−0.804167 + 0.594404i \(0.797388\pi\)
\(440\) 2.79978 + 7.12422i 0.133474 + 0.339634i
\(441\) 0 0
\(442\) −7.08832 5.14997i −0.337157 0.244959i
\(443\) 0.427271 1.31500i 0.0203002 0.0624777i −0.940393 0.340089i \(-0.889543\pi\)
0.960693 + 0.277611i \(0.0895428\pi\)
\(444\) 0 0
\(445\) 5.22585 3.79680i 0.247729 0.179986i
\(446\) 9.53414 6.92696i 0.451455 0.328001i
\(447\) 0 0
\(448\) 1.67098 5.14274i 0.0789463 0.242972i
\(449\) −17.3559 12.6098i −0.819076 0.595094i 0.0973716 0.995248i \(-0.468956\pi\)
−0.916448 + 0.400154i \(0.868956\pi\)
\(450\) 0 0
\(451\) 3.98531 15.3598i 0.187661 0.723263i
\(452\) −7.96886 −0.374823
\(453\) 0 0
\(454\) −4.42187 + 13.6091i −0.207529 + 0.638708i
\(455\) 0.732158 + 2.25335i 0.0343241 + 0.105639i
\(456\) 0 0
\(457\) 2.86665 2.08274i 0.134096 0.0974266i −0.518715 0.854947i \(-0.673589\pi\)
0.652811 + 0.757521i \(0.273589\pi\)
\(458\) −2.50699 7.71572i −0.117144 0.360532i
\(459\) 0 0
\(460\) 5.83345 + 4.23825i 0.271986 + 0.197609i
\(461\) 20.0540 0.934006 0.467003 0.884256i \(-0.345334\pi\)
0.467003 + 0.884256i \(0.345334\pi\)
\(462\) 0 0
\(463\) −9.80547 −0.455699 −0.227849 0.973696i \(-0.573169\pi\)
−0.227849 + 0.973696i \(0.573169\pi\)
\(464\) 0.0384162 + 0.0279110i 0.00178343 + 0.00129574i
\(465\) 0 0
\(466\) 0.706833 + 2.17541i 0.0327434 + 0.100774i
\(467\) −14.6630 + 10.6533i −0.678520 + 0.492974i −0.872867 0.487959i \(-0.837742\pi\)
0.194346 + 0.980933i \(0.437742\pi\)
\(468\) 0 0
\(469\) −4.22538 13.0044i −0.195110 0.600487i
\(470\) −2.46160 + 7.57602i −0.113545 + 0.349456i
\(471\) 0 0
\(472\) 15.0814 0.694178
\(473\) 10.4828 0.632811i 0.482001 0.0290967i
\(474\) 0 0
\(475\) 27.9624 + 20.3159i 1.28300 + 0.932155i
\(476\) 1.21530 3.74030i 0.0557030 0.171436i
\(477\) 0 0
\(478\) −13.9589 + 10.1417i −0.638464 + 0.463871i
\(479\) −31.2418 + 22.6985i −1.42747 + 1.03712i −0.436992 + 0.899465i \(0.643956\pi\)
−0.990480 + 0.137654i \(0.956044\pi\)
\(480\) 0 0
\(481\) −0.488531 + 1.50354i −0.0222751 + 0.0685557i
\(482\) −5.46028 3.96712i −0.248709 0.180698i
\(483\) 0 0
\(484\) −5.51468 11.8754i −0.250667 0.539792i
\(485\) 15.4932 0.703511
\(486\) 0 0
\(487\) 5.07760 15.6272i 0.230088 0.708138i −0.767647 0.640873i \(-0.778573\pi\)
0.997735 0.0672654i \(-0.0214274\pi\)
\(488\) 3.24185 + 9.97740i 0.146752 + 0.451656i
\(489\) 0 0
\(490\) 0.585264 0.425219i 0.0264395 0.0192094i
\(491\) 8.06058 + 24.8079i 0.363769 + 1.11957i 0.950748 + 0.309964i \(0.100317\pi\)
−0.586979 + 0.809602i \(0.699683\pi\)
\(492\) 0 0
\(493\) 0.626683 + 0.455312i 0.0282244 + 0.0205062i
\(494\) −21.0528 −0.947210
\(495\) 0 0
\(496\) −0.806899 −0.0362308
\(497\) −8.36286 6.07597i −0.375125 0.272545i
\(498\) 0 0
\(499\) −10.1147 31.1299i −0.452797 1.39357i −0.873702 0.486462i \(-0.838287\pi\)
0.420904 0.907105i \(-0.361713\pi\)
\(500\) −7.24159 + 5.26133i −0.323854 + 0.235294i
\(501\) 0 0
\(502\) 4.08482 + 12.5718i 0.182314 + 0.561106i
\(503\) 5.76094 17.7304i 0.256868 0.790558i −0.736588 0.676342i \(-0.763564\pi\)
0.993456 0.114216i \(-0.0364356\pi\)
\(504\) 0 0
\(505\) −13.8920 −0.618184
\(506\) 18.9556 + 12.0972i 0.842678 + 0.537786i
\(507\) 0 0
\(508\) −11.1163 8.07645i −0.493205 0.358335i
\(509\) 7.38282 22.7220i 0.327238 1.00713i −0.643182 0.765713i \(-0.722386\pi\)
0.970420 0.241422i \(-0.0776137\pi\)
\(510\) 0 0
\(511\) −7.20783 + 5.23680i −0.318856 + 0.231662i
\(512\) −1.85168 + 1.34533i −0.0818337 + 0.0594557i
\(513\) 0 0
\(514\) 5.76981 17.7577i 0.254496 0.783257i
\(515\) −9.33826 6.78464i −0.411493 0.298967i
\(516\) 0 0
\(517\) 9.17206 35.3500i 0.403387 1.55469i
\(518\) 0.482705 0.0212088
\(519\) 0 0
\(520\) 2.10183 6.46876i 0.0921713 0.283674i
\(521\) 11.1315 + 34.2591i 0.487678 + 1.50092i 0.828064 + 0.560634i \(0.189443\pi\)
−0.340385 + 0.940286i \(0.610557\pi\)
\(522\) 0 0
\(523\) −22.9277 + 16.6579i −1.00256 + 0.728401i −0.962635 0.270802i \(-0.912711\pi\)
−0.0399225 + 0.999203i \(0.512711\pi\)
\(524\) 7.79821 + 24.0004i 0.340666 + 1.04846i
\(525\) 0 0
\(526\) 19.9073 + 14.4635i 0.868001 + 0.630640i
\(527\) −13.1629 −0.573387
\(528\) 0 0
\(529\) 33.7733 1.46841
\(530\) −6.86615 4.98855i −0.298247 0.216689i
\(531\) 0 0
\(532\) −2.92016 8.98732i −0.126605 0.389650i
\(533\) −11.4073 + 8.28785i −0.494103 + 0.358987i
\(534\) 0 0
\(535\) −3.80611 11.7140i −0.164553 0.506441i
\(536\) −12.1299 + 37.3321i −0.523933 + 1.61250i
\(537\) 0 0
\(538\) −1.42087 −0.0612581
\(539\) −2.56086 + 2.10760i −0.110304 + 0.0907808i
\(540\) 0 0
\(541\) −20.8075 15.1175i −0.894582 0.649952i 0.0424864 0.999097i \(-0.486472\pi\)
−0.937069 + 0.349145i \(0.886472\pi\)
\(542\) −4.19911 + 12.9235i −0.180367 + 0.555114i
\(543\) 0 0
\(544\) −14.8597 + 10.7962i −0.637104 + 0.462883i
\(545\) 3.57884 2.60018i 0.153301 0.111380i
\(546\) 0 0
\(547\) 10.2533 31.5563i 0.438398 1.34925i −0.451166 0.892440i \(-0.648992\pi\)
0.889564 0.456810i \(-0.151008\pi\)
\(548\) −0.784990 0.570329i −0.0335331 0.0243632i
\(549\) 0 0
\(550\) −10.0323 + 8.25659i −0.427777 + 0.352062i
\(551\) 1.86129 0.0792937
\(552\) 0 0
\(553\) −2.58848 + 7.96653i −0.110073 + 0.338771i
\(554\) 4.51427 + 13.8935i 0.191793 + 0.590278i
\(555\) 0 0
\(556\) 8.92938 6.48757i 0.378690 0.275134i
\(557\) −10.0097 30.8066i −0.424123 1.30532i −0.903832 0.427888i \(-0.859258\pi\)
0.479709 0.877428i \(-0.340742\pi\)
\(558\) 0 0
\(559\) −7.54948 5.48502i −0.319309 0.231992i
\(560\) −0.162832 −0.00688092
\(561\) 0 0
\(562\) 15.3750 0.648555
\(563\) −28.0446 20.3756i −1.18194 0.858728i −0.189549 0.981871i \(-0.560702\pi\)
−0.992389 + 0.123143i \(0.960702\pi\)
\(564\) 0 0
\(565\) 1.66323 + 5.11890i 0.0699727 + 0.215354i
\(566\) −0.0837365 + 0.0608381i −0.00351971 + 0.00255722i
\(567\) 0 0
\(568\) 9.17005 + 28.2225i 0.384767 + 1.18419i
\(569\) 5.70625 17.5620i 0.239218 0.736239i −0.757315 0.653049i \(-0.773489\pi\)
0.996534 0.0831893i \(-0.0265106\pi\)
\(570\) 0 0
\(571\) 14.2034 0.594394 0.297197 0.954816i \(-0.403948\pi\)
0.297197 + 0.954816i \(0.403948\pi\)
\(572\) −2.92196 + 11.2615i −0.122173 + 0.470867i
\(573\) 0 0
\(574\) 3.48299 + 2.53054i 0.145377 + 0.105623i
\(575\) −10.1370 + 31.1984i −0.422740 + 1.30106i
\(576\) 0 0
\(577\) −13.6734 + 9.93428i −0.569229 + 0.413569i −0.834825 0.550515i \(-0.814431\pi\)
0.265596 + 0.964084i \(0.414431\pi\)
\(578\) −4.42873 + 3.21766i −0.184211 + 0.133837i
\(579\) 0 0
\(580\) −0.0693313 + 0.213380i −0.00287882 + 0.00886011i
\(581\) −5.87535 4.26869i −0.243751 0.177095i
\(582\) 0 0
\(583\) 32.7995 + 20.9322i 1.35842 + 0.866923i
\(584\) 25.5764 1.05836
\(585\) 0 0
\(586\) 5.18866 15.9691i 0.214342 0.659676i
\(587\) −10.7356 33.0409i −0.443107 1.36374i −0.884547 0.466451i \(-0.845532\pi\)
0.441440 0.897291i \(-0.354468\pi\)
\(588\) 0 0
\(589\) −25.5879 + 18.5907i −1.05433 + 0.766016i
\(590\) −1.17443 3.61452i −0.0483504 0.148807i
\(591\) 0 0
\(592\) −0.0878993 0.0638626i −0.00361264 0.00262474i
\(593\) −2.43045 −0.0998068 −0.0499034 0.998754i \(-0.515891\pi\)
−0.0499034 + 0.998754i \(0.515891\pi\)
\(594\) 0 0
\(595\) −2.65628 −0.108897
\(596\) −6.69126 4.86148i −0.274084 0.199134i
\(597\) 0 0
\(598\) −6.17449 19.0031i −0.252494 0.777096i
\(599\) −13.5264 + 9.82750i −0.552674 + 0.401541i −0.828770 0.559589i \(-0.810959\pi\)
0.276097 + 0.961130i \(0.410959\pi\)
\(600\) 0 0
\(601\) 0.132866 + 0.408920i 0.00541972 + 0.0166802i 0.953730 0.300665i \(-0.0972086\pi\)
−0.948310 + 0.317345i \(0.897209\pi\)
\(602\) −0.880468 + 2.70980i −0.0358852 + 0.110443i
\(603\) 0 0
\(604\) −16.6980 −0.679433
\(605\) −6.47734 + 6.02103i −0.263341 + 0.244790i
\(606\) 0 0
\(607\) −9.33931 6.78541i −0.379071 0.275411i 0.381891 0.924207i \(-0.375273\pi\)
−0.760962 + 0.648796i \(0.775273\pi\)
\(608\) −13.6383 + 41.9742i −0.553104 + 1.70228i
\(609\) 0 0
\(610\) 2.13880 1.55393i 0.0865976 0.0629168i
\(611\) −26.2534 + 19.0742i −1.06210 + 0.771660i
\(612\) 0 0
\(613\) −5.56380 + 17.1236i −0.224720 + 0.691616i 0.773600 + 0.633674i \(0.218454\pi\)
−0.998320 + 0.0579424i \(0.981546\pi\)
\(614\) 10.1380 + 7.36570i 0.409137 + 0.297255i
\(615\) 0 0
\(616\) 9.50383 0.573712i 0.382920 0.0231155i
\(617\) −32.1061 −1.29254 −0.646272 0.763107i \(-0.723673\pi\)
−0.646272 + 0.763107i \(0.723673\pi\)
\(618\) 0 0
\(619\) −0.0866156 + 0.266575i −0.00348137 + 0.0107146i −0.952782 0.303655i \(-0.901793\pi\)
0.949301 + 0.314369i \(0.101793\pi\)
\(620\) −1.17813 3.62590i −0.0473147 0.145620i
\(621\) 0 0
\(622\) 7.39390 5.37198i 0.296468 0.215397i
\(623\) −2.48283 7.64136i −0.0994724 0.306144i
\(624\) 0 0
\(625\) −12.7197 9.24143i −0.508790 0.369657i
\(626\) −4.33613 −0.173307
\(627\) 0 0
\(628\) −0.872952 −0.0348346
\(629\) −1.43390 1.04179i −0.0571734 0.0415389i
\(630\) 0 0
\(631\) 9.37415 + 28.8507i 0.373179 + 1.14853i 0.944699 + 0.327938i \(0.106354\pi\)
−0.571520 + 0.820588i \(0.693646\pi\)
\(632\) 19.4542 14.1343i 0.773845 0.562231i
\(633\) 0 0
\(634\) 2.24484 + 6.90892i 0.0891542 + 0.274388i
\(635\) −2.86787 + 8.82639i −0.113808 + 0.350264i
\(636\) 0 0
\(637\) 2.94705 0.116766
\(638\) −0.175726 + 0.677265i −0.00695706 + 0.0268132i
\(639\) 0 0
\(640\) −4.06686 2.95475i −0.160757 0.116797i
\(641\) −1.21458 + 3.73810i −0.0479731 + 0.147646i −0.972174 0.234262i \(-0.924733\pi\)
0.924200 + 0.381908i \(0.124733\pi\)
\(642\) 0 0
\(643\) 11.1032 8.06695i 0.437867 0.318129i −0.346920 0.937895i \(-0.612772\pi\)
0.784787 + 0.619766i \(0.212772\pi\)
\(644\) 7.25588 5.27171i 0.285922 0.207734i
\(645\) 0 0
\(646\) 7.29364 22.4475i 0.286964 0.883185i
\(647\) −1.62640 1.18165i −0.0639403 0.0464553i 0.555356 0.831613i \(-0.312582\pi\)
−0.619296 + 0.785157i \(0.712582\pi\)
\(648\) 0 0
\(649\) 6.37303 + 16.2166i 0.250163 + 0.636556i
\(650\) 11.5452 0.452838
\(651\) 0 0
\(652\) −1.09008 + 3.35493i −0.0426909 + 0.131389i
\(653\) 0.245776 + 0.756421i 0.00961797 + 0.0296011i 0.955750 0.294179i \(-0.0950462\pi\)
−0.946132 + 0.323780i \(0.895046\pi\)
\(654\) 0 0
\(655\) 13.7894 10.0186i 0.538796 0.391458i
\(656\) −0.299450 0.921611i −0.0116915 0.0359829i
\(657\) 0 0
\(658\) 8.01600 + 5.82396i 0.312496 + 0.227042i
\(659\) 21.9135 0.853628 0.426814 0.904340i \(-0.359636\pi\)
0.426814 + 0.904340i \(0.359636\pi\)
\(660\) 0 0
\(661\) −19.4952 −0.758276 −0.379138 0.925340i \(-0.623779\pi\)
−0.379138 + 0.925340i \(0.623779\pi\)
\(662\) 0.565477 + 0.410843i 0.0219779 + 0.0159679i
\(663\) 0 0
\(664\) 6.44245 + 19.8278i 0.250015 + 0.769468i
\(665\) −5.16364 + 3.75161i −0.200237 + 0.145481i
\(666\) 0 0
\(667\) 0.545891 + 1.68008i 0.0211370 + 0.0650529i
\(668\) 2.95735 9.10180i 0.114423 0.352159i
\(669\) 0 0
\(670\) 9.89186 0.382156
\(671\) −9.35847 + 7.70207i −0.361280 + 0.297335i
\(672\) 0 0
\(673\) 5.66917 + 4.11889i 0.218530 + 0.158772i 0.691665 0.722219i \(-0.256878\pi\)
−0.473134 + 0.880990i \(0.656878\pi\)
\(674\) −0.0582818 + 0.179373i −0.00224493 + 0.00690918i
\(675\) 0 0
\(676\) −4.15517 + 3.01891i −0.159814 + 0.116112i
\(677\) −4.73782 + 3.44223i −0.182089 + 0.132296i −0.675096 0.737730i \(-0.735898\pi\)
0.493007 + 0.870026i \(0.335898\pi\)
\(678\) 0 0
\(679\) 5.95510 18.3279i 0.228536 0.703361i
\(680\) 6.16913 + 4.48214i 0.236576 + 0.171882i
\(681\) 0 0
\(682\) −4.34879 11.0658i −0.166524 0.423731i
\(683\) −34.2255 −1.30960 −0.654802 0.755801i \(-0.727248\pi\)
−0.654802 + 0.755801i \(0.727248\pi\)
\(684\) 0 0
\(685\) −0.202518 + 0.623286i −0.00773782 + 0.0238145i
\(686\) −0.278062 0.855786i −0.0106165 0.0326741i
\(687\) 0 0
\(688\) 0.518842 0.376961i 0.0197807 0.0143715i
\(689\) −10.6839 32.8818i −0.407026 1.25270i
\(690\) 0 0
\(691\) −12.1422 8.82184i −0.461912 0.335598i 0.332369 0.943149i \(-0.392152\pi\)
−0.794281 + 0.607551i \(0.792152\pi\)
\(692\) 6.13676 0.233285
\(693\) 0 0
\(694\) 20.5133 0.778675
\(695\) −6.03109 4.38184i −0.228772 0.166213i
\(696\) 0 0
\(697\) −4.88492 15.0342i −0.185030 0.569463i
\(698\) −10.2130 + 7.42021i −0.386570 + 0.280859i
\(699\) 0 0
\(700\) 1.60139 + 4.92856i 0.0605267 + 0.186282i
\(701\) −3.70534 + 11.4039i −0.139949 + 0.430718i −0.996327 0.0856309i \(-0.972709\pi\)
0.856378 + 0.516349i \(0.172709\pi\)
\(702\) 0 0
\(703\) −4.25878 −0.160623
\(704\) −15.1180 9.64810i −0.569781 0.363626i
\(705\) 0 0
\(706\) 16.2851 + 11.8318i 0.612896 + 0.445295i
\(707\) −5.33963 + 16.4337i −0.200817 + 0.618052i
\(708\) 0 0
\(709\) −32.0008 + 23.2499i −1.20181 + 0.873169i −0.994462 0.105098i \(-0.966485\pi\)
−0.207352 + 0.978266i \(0.566485\pi\)
\(710\) 6.04991 4.39552i 0.227049 0.164961i
\(711\) 0 0
\(712\) −7.12752 + 21.9363i −0.267115 + 0.822096i
\(713\) −24.2853 17.6443i −0.909492 0.660784i
\(714\) 0 0
\(715\) 7.84385 0.473505i 0.293343 0.0177081i
\(716\) 7.15702 0.267470
\(717\) 0 0
\(718\) −0.751355 + 2.31243i −0.0280403 + 0.0862992i
\(719\) 13.7145 + 42.2089i 0.511465 + 1.57413i 0.789623 + 0.613592i \(0.210276\pi\)
−0.278158 + 0.960535i \(0.589724\pi\)
\(720\) 0 0
\(721\) −11.6153 + 8.43902i −0.432577 + 0.314285i
\(722\) −12.2422 37.6777i −0.455609 1.40222i
\(723\) 0 0
\(724\) 2.35975 + 1.71446i 0.0876994 + 0.0637173i
\(725\) −1.02071 −0.0379084
\(726\) 0 0
\(727\) −45.1325 −1.67387 −0.836935 0.547302i \(-0.815655\pi\)
−0.836935 + 0.547302i \(0.815655\pi\)
\(728\) −6.84443 4.97277i −0.253671 0.184303i
\(729\) 0 0
\(730\) −1.99170 6.12982i −0.0737161 0.226875i
\(731\) 8.46387 6.14936i 0.313048 0.227442i
\(732\) 0 0
\(733\) 4.26354 + 13.1218i 0.157478 + 0.484666i 0.998404 0.0564840i \(-0.0179890\pi\)
−0.840926 + 0.541150i \(0.817989\pi\)
\(734\) −7.86416 + 24.2034i −0.290271 + 0.893364i
\(735\) 0 0
\(736\) −41.8876 −1.54400
\(737\) −45.2679 + 2.73266i −1.66746 + 0.100659i
\(738\) 0 0
\(739\) 13.5472 + 9.84263i 0.498342 + 0.362067i 0.808383 0.588656i \(-0.200343\pi\)
−0.310041 + 0.950723i \(0.600343\pi\)
\(740\) 0.158635 0.488230i 0.00583156 0.0179477i
\(741\) 0 0
\(742\) −8.54040 + 6.20496i −0.313528 + 0.227791i
\(743\) −8.81274 + 6.40283i −0.323308 + 0.234897i −0.737586 0.675253i \(-0.764034\pi\)
0.414278 + 0.910151i \(0.364034\pi\)
\(744\) 0 0
\(745\) −1.72626 + 5.31289i −0.0632454 + 0.194649i
\(746\) 6.21587 + 4.51609i 0.227579 + 0.165346i
\(747\) 0 0
\(748\) −10.9953 7.01702i −0.402027 0.256568i
\(749\) −15.3202 −0.559788
\(750\) 0 0
\(751\) −8.37184 + 25.7659i −0.305493 + 0.940210i 0.674000 + 0.738731i \(0.264575\pi\)
−0.979493 + 0.201479i \(0.935425\pi\)
\(752\) −0.689173 2.12106i −0.0251316 0.0773470i
\(753\) 0 0
\(754\) 0.502985 0.365440i 0.0183176 0.0133086i
\(755\) 3.48516 + 10.7262i 0.126838 + 0.390367i
\(756\) 0 0
\(757\) −24.4567 17.7688i −0.888894 0.645820i 0.0466951 0.998909i \(-0.485131\pi\)
−0.935590 + 0.353090i \(0.885131\pi\)
\(758\) −31.2082 −1.13353
\(759\) 0 0
\(760\) 18.3227 0.664636
\(761\) 31.2246 + 22.6860i 1.13189 + 0.822367i 0.985969 0.166930i \(-0.0533853\pi\)
0.145922 + 0.989296i \(0.453385\pi\)
\(762\) 0 0
\(763\) −1.70033 5.23307i −0.0615560 0.189450i
\(764\) 20.4871 14.8847i 0.741197 0.538511i
\(765\) 0 0
\(766\) 3.53621 + 10.8833i 0.127768 + 0.393231i
\(767\) 4.78431 14.7246i 0.172751 0.531674i
\(768\) 0 0
\(769\) 40.5122 1.46091 0.730454 0.682962i \(-0.239309\pi\)
0.730454 + 0.682962i \(0.239309\pi\)
\(770\) −0.877587 2.23308i −0.0316261 0.0804746i
\(771\) 0 0
\(772\) −8.08831 5.87650i −0.291105 0.211500i
\(773\) 6.85839 21.1079i 0.246679 0.759200i −0.748677 0.662935i \(-0.769310\pi\)
0.995356 0.0962647i \(-0.0306895\pi\)
\(774\) 0 0
\(775\) 14.0322 10.1950i 0.504050 0.366214i
\(776\) −44.7565 + 32.5175i −1.60667 + 1.16731i
\(777\) 0 0
\(778\) 0.691677 2.12876i 0.0247978 0.0763199i
\(779\) −30.7296 22.3264i