Properties

Label 441.2.bg.a.395.16
Level $441$
Weight $2$
Character 441.395
Analytic conductor $3.521$
Analytic rank $0$
Dimension $216$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bg (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 395.16
Character \(\chi\) \(=\) 441.395
Dual form 441.2.bg.a.278.16

$q$-expansion

\(f(q)\) \(=\) \(q+(2.07888 + 0.815901i) q^{2} +(2.18995 + 2.03198i) q^{4} +(2.05954 + 1.40417i) q^{5} +(-1.91279 + 1.82790i) q^{7} +(0.956806 + 1.98683i) q^{8} +O(q^{10})\) \(q+(2.07888 + 0.815901i) q^{2} +(2.18995 + 2.03198i) q^{4} +(2.05954 + 1.40417i) q^{5} +(-1.91279 + 1.82790i) q^{7} +(0.956806 + 1.98683i) q^{8} +(3.13588 + 4.59948i) q^{10} +(-0.173548 - 1.15142i) q^{11} +(1.20405 - 0.960194i) q^{13} +(-5.46786 + 2.23934i) q^{14} +(-0.0784720 - 1.04714i) q^{16} +(-2.49422 - 0.769366i) q^{17} +(0.129636 - 0.0748453i) q^{19} +(1.65705 + 7.26000i) q^{20} +(0.578657 - 2.53526i) q^{22} +(-0.369109 - 1.19662i) q^{23} +(0.443305 + 1.12952i) q^{25} +(3.28649 - 1.01375i) q^{26} +(-7.90317 + 0.116256i) q^{28} +(-0.805580 + 0.183868i) q^{29} +(8.87043 + 5.12134i) q^{31} +(1.99122 - 6.45538i) q^{32} +(-4.55747 - 3.63446i) q^{34} +(-6.50616 + 1.07874i) q^{35} +(8.79713 - 8.16255i) q^{37} +(0.330564 - 0.0498245i) q^{38} +(-0.819266 + 5.43547i) q^{40} +(-6.87743 + 3.31199i) q^{41} +(-9.17465 - 4.41828i) q^{43} +(1.95959 - 2.87420i) q^{44} +(0.208991 - 2.78879i) q^{46} +(-1.43464 + 3.65541i) q^{47} +(0.317563 - 6.99279i) q^{49} +2.70984i q^{50} +(4.58789 + 0.343815i) q^{52} +(2.28911 - 2.46707i) q^{53} +(1.25936 - 2.61508i) q^{55} +(-5.46190 - 2.05145i) q^{56} +(-1.82472 - 0.275033i) q^{58} +(-8.87123 + 6.04830i) q^{59} +(2.83787 + 3.05850i) q^{61} +(14.2621 + 17.8841i) q^{62} +(8.09705 - 10.1534i) q^{64} +(3.82806 - 0.286873i) q^{65} +(-4.19487 + 7.26573i) q^{67} +(-3.89889 - 6.75308i) q^{68} +(-14.4057 - 3.06580i) q^{70} +(-14.2924 - 3.26215i) q^{71} +(10.1462 - 3.98209i) q^{73} +(24.9480 - 9.79138i) q^{74} +(0.435980 + 0.0995096i) q^{76} +(2.43664 + 1.88520i) q^{77} +(-0.550642 - 0.953740i) q^{79} +(1.30874 - 2.26681i) q^{80} +(-16.9996 + 1.27395i) q^{82} +(3.71031 - 4.65258i) q^{83} +(-4.05663 - 5.08686i) q^{85} +(-15.4681 - 16.6707i) q^{86} +(2.12162 - 1.44650i) q^{88} +(-8.96124 - 1.35069i) q^{89} +(-0.547952 + 4.03753i) q^{91} +(1.62318 - 3.37056i) q^{92} +(-5.96490 + 6.42863i) q^{94} +(0.372086 + 0.0278840i) q^{95} +9.69774i q^{97} +(6.36560 - 14.2781i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q - 16q^{4} + 2q^{7} + O(q^{10}) \) \( 216q - 16q^{4} + 2q^{7} + 12q^{10} + 12q^{16} - 6q^{19} + 44q^{22} + 26q^{25} + 84q^{28} - 6q^{31} - 112q^{34} + 60q^{37} - 304q^{40} + 20q^{43} - 20q^{46} - 86q^{49} - 168q^{52} - 84q^{55} - 120q^{58} - 2q^{61} + 32q^{64} + 22q^{67} - 136q^{70} - 6q^{73} + 84q^{76} + 2q^{79} - 104q^{82} + 96q^{85} - 12q^{88} + 58q^{91} + 52q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{42}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.07888 + 0.815901i 1.46999 + 0.576929i 0.959188 0.282769i \(-0.0912529\pi\)
0.510803 + 0.859698i \(0.329348\pi\)
\(3\) 0 0
\(4\) 2.18995 + 2.03198i 1.09498 + 1.01599i
\(5\) 2.05954 + 1.40417i 0.921054 + 0.627964i 0.928229 0.372010i \(-0.121331\pi\)
−0.00717441 + 0.999974i \(0.502284\pi\)
\(6\) 0 0
\(7\) −1.91279 + 1.82790i −0.722968 + 0.690881i
\(8\) 0.956806 + 1.98683i 0.338282 + 0.702450i
\(9\) 0 0
\(10\) 3.13588 + 4.59948i 0.991651 + 1.45448i
\(11\) −0.173548 1.15142i −0.0523268 0.347166i −0.999639 0.0268550i \(-0.991451\pi\)
0.947313 0.320311i \(-0.103787\pi\)
\(12\) 0 0
\(13\) 1.20405 0.960194i 0.333942 0.266310i −0.442134 0.896949i \(-0.645779\pi\)
0.776076 + 0.630639i \(0.217207\pi\)
\(14\) −5.46786 + 2.23934i −1.46135 + 0.598488i
\(15\) 0 0
\(16\) −0.0784720 1.04714i −0.0196180 0.261784i
\(17\) −2.49422 0.769366i −0.604938 0.186599i −0.0228697 0.999738i \(-0.507280\pi\)
−0.582069 + 0.813140i \(0.697756\pi\)
\(18\) 0 0
\(19\) 0.129636 0.0748453i 0.0297405 0.0171707i −0.485056 0.874483i \(-0.661201\pi\)
0.514797 + 0.857312i \(0.327867\pi\)
\(20\) 1.65705 + 7.26000i 0.370527 + 1.62339i
\(21\) 0 0
\(22\) 0.578657 2.53526i 0.123370 0.540519i
\(23\) −0.369109 1.19662i −0.0769645 0.249513i 0.908912 0.416989i \(-0.136915\pi\)
−0.985876 + 0.167476i \(0.946438\pi\)
\(24\) 0 0
\(25\) 0.443305 + 1.12952i 0.0886610 + 0.225904i
\(26\) 3.28649 1.01375i 0.644534 0.198812i
\(27\) 0 0
\(28\) −7.90317 + 0.116256i −1.49356 + 0.0219704i
\(29\) −0.805580 + 0.183868i −0.149592 + 0.0341435i −0.296661 0.954983i \(-0.595873\pi\)
0.147069 + 0.989126i \(0.453016\pi\)
\(30\) 0 0
\(31\) 8.87043 + 5.12134i 1.59318 + 0.919820i 0.992758 + 0.120134i \(0.0383323\pi\)
0.600418 + 0.799687i \(0.295001\pi\)
\(32\) 1.99122 6.45538i 0.352002 1.14116i
\(33\) 0 0
\(34\) −4.55747 3.63446i −0.781600 0.623305i
\(35\) −6.50616 + 1.07874i −1.09974 + 0.182341i
\(36\) 0 0
\(37\) 8.79713 8.16255i 1.44624 1.34191i 0.611533 0.791219i \(-0.290553\pi\)
0.834706 0.550695i \(-0.185637\pi\)
\(38\) 0.330564 0.0498245i 0.0536246 0.00808260i
\(39\) 0 0
\(40\) −0.819266 + 5.43547i −0.129537 + 0.859424i
\(41\) −6.87743 + 3.31199i −1.07407 + 0.517247i −0.885418 0.464797i \(-0.846127\pi\)
−0.188656 + 0.982043i \(0.560413\pi\)
\(42\) 0 0
\(43\) −9.17465 4.41828i −1.39912 0.673781i −0.426138 0.904658i \(-0.640126\pi\)
−0.972983 + 0.230877i \(0.925841\pi\)
\(44\) 1.95959 2.87420i 0.295420 0.433301i
\(45\) 0 0
\(46\) 0.208991 2.78879i 0.0308140 0.411185i
\(47\) −1.43464 + 3.65541i −0.209264 + 0.533196i −0.996513 0.0834395i \(-0.973409\pi\)
0.787249 + 0.616635i \(0.211505\pi\)
\(48\) 0 0
\(49\) 0.317563 6.99279i 0.0453662 0.998970i
\(50\) 2.70984i 0.383229i
\(51\) 0 0
\(52\) 4.58789 + 0.343815i 0.636226 + 0.0476786i
\(53\) 2.28911 2.46707i 0.314433 0.338879i −0.555984 0.831193i \(-0.687658\pi\)
0.870417 + 0.492314i \(0.163849\pi\)
\(54\) 0 0
\(55\) 1.25936 2.61508i 0.169812 0.352618i
\(56\) −5.46190 2.05145i −0.729877 0.274136i
\(57\) 0 0
\(58\) −1.82472 0.275033i −0.239598 0.0361136i
\(59\) −8.87123 + 6.04830i −1.15494 + 0.787422i −0.980359 0.197222i \(-0.936808\pi\)
−0.174577 + 0.984644i \(0.555856\pi\)
\(60\) 0 0
\(61\) 2.83787 + 3.05850i 0.363352 + 0.391601i 0.888095 0.459660i \(-0.152029\pi\)
−0.524742 + 0.851261i \(0.675838\pi\)
\(62\) 14.2621 + 17.8841i 1.81128 + 2.27128i
\(63\) 0 0
\(64\) 8.09705 10.1534i 1.01213 1.26917i
\(65\) 3.82806 0.286873i 0.474812 0.0355822i
\(66\) 0 0
\(67\) −4.19487 + 7.26573i −0.512485 + 0.887650i 0.487410 + 0.873173i \(0.337942\pi\)
−0.999895 + 0.0144772i \(0.995392\pi\)
\(68\) −3.89889 6.75308i −0.472810 0.818931i
\(69\) 0 0
\(70\) −14.4057 3.06580i −1.72181 0.366433i
\(71\) −14.2924 3.26215i −1.69620 0.387146i −0.738348 0.674420i \(-0.764394\pi\)
−0.957848 + 0.287275i \(0.907251\pi\)
\(72\) 0 0
\(73\) 10.1462 3.98209i 1.18752 0.466068i 0.312391 0.949954i \(-0.398870\pi\)
0.875131 + 0.483885i \(0.160775\pi\)
\(74\) 24.9480 9.79138i 2.90015 1.13822i
\(75\) 0 0
\(76\) 0.435980 + 0.0995096i 0.0500104 + 0.0114145i
\(77\) 2.43664 + 1.88520i 0.277681 + 0.214838i
\(78\) 0 0
\(79\) −0.550642 0.953740i −0.0619521 0.107304i 0.833386 0.552692i \(-0.186399\pi\)
−0.895338 + 0.445387i \(0.853066\pi\)
\(80\) 1.30874 2.26681i 0.146322 0.253437i
\(81\) 0 0
\(82\) −16.9996 + 1.27395i −1.87729 + 0.140684i
\(83\) 3.71031 4.65258i 0.407260 0.510687i −0.535329 0.844644i \(-0.679812\pi\)
0.942589 + 0.333956i \(0.108384\pi\)
\(84\) 0 0
\(85\) −4.05663 5.08686i −0.440004 0.551747i
\(86\) −15.4681 16.6707i −1.66797 1.79765i
\(87\) 0 0
\(88\) 2.12162 1.44650i 0.226165 0.154197i
\(89\) −8.96124 1.35069i −0.949889 0.143173i −0.344220 0.938889i \(-0.611857\pi\)
−0.605669 + 0.795716i \(0.707095\pi\)
\(90\) 0 0
\(91\) −0.547952 + 4.03753i −0.0574410 + 0.423248i
\(92\) 1.62318 3.37056i 0.169228 0.351405i
\(93\) 0 0
\(94\) −5.96490 + 6.42863i −0.615232 + 0.663063i
\(95\) 0.372086 + 0.0278840i 0.0381752 + 0.00286084i
\(96\) 0 0
\(97\) 9.69774i 0.984656i 0.870410 + 0.492328i \(0.163854\pi\)
−0.870410 + 0.492328i \(0.836146\pi\)
\(98\) 6.36560 14.2781i 0.643023 1.44230i
\(99\) 0 0
\(100\) −1.32435 + 3.37438i −0.132435 + 0.337438i
\(101\) 0.717255 9.57110i 0.0713695 0.952360i −0.840482 0.541840i \(-0.817728\pi\)
0.911851 0.410521i \(-0.134653\pi\)
\(102\) 0 0
\(103\) −7.09042 + 10.3997i −0.698640 + 1.02472i 0.298877 + 0.954292i \(0.403388\pi\)
−0.997517 + 0.0704251i \(0.977564\pi\)
\(104\) 3.05978 + 1.47351i 0.300036 + 0.144490i
\(105\) 0 0
\(106\) 6.77167 3.26107i 0.657723 0.316743i
\(107\) 1.48011 9.81990i 0.143088 0.949325i −0.795913 0.605411i \(-0.793009\pi\)
0.939001 0.343915i \(-0.111753\pi\)
\(108\) 0 0
\(109\) −9.55463 + 1.44013i −0.915168 + 0.137939i −0.589708 0.807617i \(-0.700757\pi\)
−0.325460 + 0.945556i \(0.605519\pi\)
\(110\) 4.75170 4.40894i 0.453057 0.420376i
\(111\) 0 0
\(112\) 2.06416 + 1.85952i 0.195045 + 0.175708i
\(113\) 8.97715 + 7.15904i 0.844500 + 0.673466i 0.946988 0.321268i \(-0.104109\pi\)
−0.102489 + 0.994734i \(0.532681\pi\)
\(114\) 0 0
\(115\) 0.920066 2.98278i 0.0857966 0.278146i
\(116\) −2.13780 1.23426i −0.198489 0.114598i
\(117\) 0 0
\(118\) −23.3770 + 5.33566i −2.15203 + 0.491187i
\(119\) 6.17726 3.08755i 0.566269 0.283036i
\(120\) 0 0
\(121\) 9.21566 2.84265i 0.837787 0.258423i
\(122\) 3.40417 + 8.67368i 0.308199 + 0.785278i
\(123\) 0 0
\(124\) 9.01934 + 29.2400i 0.809961 + 2.62583i
\(125\) 2.10032 9.20209i 0.187858 0.823060i
\(126\) 0 0
\(127\) 1.53622 + 6.73064i 0.136318 + 0.597248i 0.996226 + 0.0867987i \(0.0276637\pi\)
−0.859908 + 0.510449i \(0.829479\pi\)
\(128\) 13.4161 7.74577i 1.18582 0.684636i
\(129\) 0 0
\(130\) 8.19214 + 2.52694i 0.718498 + 0.221627i
\(131\) 0.968337 + 12.9216i 0.0846040 + 1.12896i 0.864358 + 0.502877i \(0.167725\pi\)
−0.779754 + 0.626086i \(0.784656\pi\)
\(132\) 0 0
\(133\) −0.111157 + 0.380125i −0.00963854 + 0.0329610i
\(134\) −14.6488 + 11.6820i −1.26546 + 1.00917i
\(135\) 0 0
\(136\) −0.857891 5.69173i −0.0735635 0.488062i
\(137\) 12.1533 + 17.8257i 1.03833 + 1.52295i 0.839831 + 0.542848i \(0.182654\pi\)
0.198498 + 0.980101i \(0.436394\pi\)
\(138\) 0 0
\(139\) −1.62745 3.37944i −0.138039 0.286640i 0.820477 0.571679i \(-0.193708\pi\)
−0.958516 + 0.285039i \(0.907993\pi\)
\(140\) −16.4401 10.8580i −1.38945 0.917666i
\(141\) 0 0
\(142\) −27.0506 18.4428i −2.27004 1.54769i
\(143\) −1.31455 1.21972i −0.109928 0.101998i
\(144\) 0 0
\(145\) −1.91731 0.752488i −0.159224 0.0624907i
\(146\) 24.3417 2.01454
\(147\) 0 0
\(148\) 35.8514 2.94697
\(149\) −9.59664 3.76640i −0.786188 0.308556i −0.0619256 0.998081i \(-0.519724\pi\)
−0.724262 + 0.689525i \(0.757819\pi\)
\(150\) 0 0
\(151\) 9.91135 + 9.19639i 0.806575 + 0.748392i 0.971277 0.237951i \(-0.0764759\pi\)
−0.164703 + 0.986343i \(0.552666\pi\)
\(152\) 0.272741 + 0.185952i 0.0221222 + 0.0150827i
\(153\) 0 0
\(154\) 3.52735 + 5.90716i 0.284242 + 0.476012i
\(155\) 11.0778 + 23.0032i 0.889787 + 1.84766i
\(156\) 0 0
\(157\) 9.32045 + 13.6706i 0.743853 + 1.09103i 0.992477 + 0.122432i \(0.0390692\pi\)
−0.248624 + 0.968600i \(0.579978\pi\)
\(158\) −0.366562 2.43198i −0.0291621 0.193478i
\(159\) 0 0
\(160\) 13.1655 10.4991i 1.04082 0.830027i
\(161\) 2.89333 + 1.61420i 0.228027 + 0.127216i
\(162\) 0 0
\(163\) 0.138902 + 1.85352i 0.0108797 + 0.145179i 0.999998 0.00194228i \(-0.000618246\pi\)
−0.989118 + 0.147121i \(0.952999\pi\)
\(164\) −21.7911 6.72167i −1.70160 0.524874i
\(165\) 0 0
\(166\) 11.5093 6.64492i 0.893299 0.515746i
\(167\) −2.56908 11.2559i −0.198801 0.871004i −0.971652 0.236416i \(-0.924027\pi\)
0.772851 0.634588i \(-0.218830\pi\)
\(168\) 0 0
\(169\) −2.36502 + 10.3618i −0.181925 + 0.797064i
\(170\) −4.28289 13.8848i −0.328483 1.06491i
\(171\) 0 0
\(172\) −11.1142 28.3185i −0.847449 2.15926i
\(173\) −4.44305 + 1.37050i −0.337799 + 0.104197i −0.459014 0.888429i \(-0.651797\pi\)
0.121215 + 0.992626i \(0.461321\pi\)
\(174\) 0 0
\(175\) −2.91260 1.35023i −0.220172 0.102068i
\(176\) −1.19207 + 0.272083i −0.0898559 + 0.0205090i
\(177\) 0 0
\(178\) −17.5273 10.1194i −1.31373 0.758481i
\(179\) −6.28538 + 20.3767i −0.469791 + 1.52303i 0.342355 + 0.939571i \(0.388776\pi\)
−0.812146 + 0.583454i \(0.801701\pi\)
\(180\) 0 0
\(181\) −7.58961 6.05251i −0.564132 0.449880i 0.299434 0.954117i \(-0.403202\pi\)
−0.863565 + 0.504237i \(0.831774\pi\)
\(182\) −4.43335 + 7.94647i −0.328622 + 0.589032i
\(183\) 0 0
\(184\) 2.02432 1.87829i 0.149235 0.138469i
\(185\) 29.5796 4.45841i 2.17474 0.327789i
\(186\) 0 0
\(187\) −0.452994 + 3.00542i −0.0331262 + 0.219778i
\(188\) −10.5695 + 5.09000i −0.770860 + 0.371227i
\(189\) 0 0
\(190\) 0.750772 + 0.361553i 0.0544667 + 0.0262298i
\(191\) −8.53026 + 12.5116i −0.617228 + 0.905308i −0.999827 0.0186070i \(-0.994077\pi\)
0.382599 + 0.923915i \(0.375029\pi\)
\(192\) 0 0
\(193\) 0.567028 7.56646i 0.0408155 0.544645i −0.938892 0.344212i \(-0.888146\pi\)
0.979707 0.200433i \(-0.0642350\pi\)
\(194\) −7.91239 + 20.1604i −0.568077 + 1.44744i
\(195\) 0 0
\(196\) 14.9046 14.6686i 1.06462 1.04776i
\(197\) 12.8332i 0.914327i 0.889383 + 0.457164i \(0.151135\pi\)
−0.889383 + 0.457164i \(0.848865\pi\)
\(198\) 0 0
\(199\) −11.5456 0.865220i −0.818443 0.0613339i −0.341074 0.940036i \(-0.610791\pi\)
−0.477370 + 0.878703i \(0.658410\pi\)
\(200\) −1.82001 + 1.96150i −0.128694 + 0.138699i
\(201\) 0 0
\(202\) 9.30016 19.3120i 0.654357 1.35879i
\(203\) 1.20482 1.82422i 0.0845615 0.128035i
\(204\) 0 0
\(205\) −18.8149 2.83590i −1.31409 0.198068i
\(206\) −23.2253 + 15.8347i −1.61818 + 1.10326i
\(207\) 0 0
\(208\) −1.09994 1.18545i −0.0762670 0.0821963i
\(209\) −0.108676 0.136276i −0.00751730 0.00942640i
\(210\) 0 0
\(211\) 6.87238 8.61769i 0.473114 0.593266i −0.486817 0.873504i \(-0.661842\pi\)
0.959931 + 0.280238i \(0.0904134\pi\)
\(212\) 10.0261 0.751350i 0.688593 0.0516029i
\(213\) 0 0
\(214\) 11.0890 19.2068i 0.758031 1.31295i
\(215\) −12.6915 21.9824i −0.865556 1.49919i
\(216\) 0 0
\(217\) −26.3286 + 6.41818i −1.78730 + 0.435694i
\(218\) −21.0379 4.80177i −1.42487 0.325217i
\(219\) 0 0
\(220\) 8.07172 3.16792i 0.544195 0.213581i
\(221\) −3.74190 + 1.46859i −0.251707 + 0.0987879i
\(222\) 0 0
\(223\) 27.5926 + 6.29782i 1.84774 + 0.421733i 0.994936 0.100506i \(-0.0320462\pi\)
0.852799 + 0.522240i \(0.174903\pi\)
\(224\) 7.99100 + 15.9876i 0.533921 + 1.06821i
\(225\) 0 0
\(226\) 12.8214 + 22.2073i 0.852865 + 1.47721i
\(227\) −0.639251 + 1.10722i −0.0424286 + 0.0734885i −0.886460 0.462806i \(-0.846843\pi\)
0.844031 + 0.536294i \(0.180176\pi\)
\(228\) 0 0
\(229\) −19.7036 + 1.47658i −1.30205 + 0.0975752i −0.707632 0.706581i \(-0.750237\pi\)
−0.594418 + 0.804156i \(0.702618\pi\)
\(230\) 4.34636 5.45016i 0.286591 0.359373i
\(231\) 0 0
\(232\) −1.13610 1.42462i −0.0745886 0.0935311i
\(233\) 1.22666 + 1.32202i 0.0803610 + 0.0866085i 0.771952 0.635681i \(-0.219280\pi\)
−0.691591 + 0.722289i \(0.743090\pi\)
\(234\) 0 0
\(235\) −8.08752 + 5.51398i −0.527571 + 0.359692i
\(236\) −31.7176 4.78065i −2.06464 0.311194i
\(237\) 0 0
\(238\) 15.3609 1.37862i 0.995701 0.0893629i
\(239\) 5.14965 10.6934i 0.333103 0.691696i −0.665394 0.746492i \(-0.731737\pi\)
0.998498 + 0.0547961i \(0.0174509\pi\)
\(240\) 0 0
\(241\) 11.4016 12.2880i 0.734443 0.791541i −0.249813 0.968294i \(-0.580369\pi\)
0.984255 + 0.176753i \(0.0565595\pi\)
\(242\) 21.4776 + 1.60952i 1.38063 + 0.103464i
\(243\) 0 0
\(244\) 12.4645i 0.797955i
\(245\) 10.4731 13.9560i 0.669102 0.891618i
\(246\) 0 0
\(247\) 0.0842215 0.214593i 0.00535889 0.0136542i
\(248\) −1.68795 + 22.5242i −0.107185 + 1.43029i
\(249\) 0 0
\(250\) 11.8743 17.4164i 0.750997 1.10151i
\(251\) −24.3077 11.7060i −1.53429 0.738876i −0.539614 0.841913i \(-0.681430\pi\)
−0.994678 + 0.103037i \(0.967144\pi\)
\(252\) 0 0
\(253\) −1.31375 + 0.632670i −0.0825950 + 0.0397756i
\(254\) −2.29791 + 15.2456i −0.144183 + 0.956595i
\(255\) 0 0
\(256\) 8.52697 1.28523i 0.532936 0.0803271i
\(257\) −13.1186 + 12.1723i −0.818317 + 0.759287i −0.973522 0.228595i \(-0.926587\pi\)
0.155205 + 0.987882i \(0.450396\pi\)
\(258\) 0 0
\(259\) −1.90679 + 31.6935i −0.118482 + 1.96934i
\(260\) 8.96617 + 7.15028i 0.556058 + 0.443442i
\(261\) 0 0
\(262\) −8.52966 + 27.6525i −0.526964 + 1.70838i
\(263\) −6.43376 3.71453i −0.396722 0.229048i 0.288346 0.957526i \(-0.406895\pi\)
−0.685069 + 0.728478i \(0.740228\pi\)
\(264\) 0 0
\(265\) 8.17870 1.86674i 0.502414 0.114673i
\(266\) −0.541227 + 0.699542i −0.0331847 + 0.0428917i
\(267\) 0 0
\(268\) −23.9504 + 7.38771i −1.46300 + 0.451276i
\(269\) 4.33700 + 11.0505i 0.264431 + 0.673760i 0.999993 0.00369739i \(-0.00117692\pi\)
−0.735562 + 0.677458i \(0.763082\pi\)
\(270\) 0 0
\(271\) −1.31490 4.26279i −0.0798742 0.258946i 0.906824 0.421510i \(-0.138500\pi\)
−0.986698 + 0.162564i \(0.948024\pi\)
\(272\) −0.609905 + 2.67217i −0.0369809 + 0.162024i
\(273\) 0 0
\(274\) 10.7214 + 46.9734i 0.647701 + 2.83776i
\(275\) 1.22362 0.706456i 0.0737869 0.0426009i
\(276\) 0 0
\(277\) −1.13152 0.349027i −0.0679863 0.0209710i 0.260575 0.965453i \(-0.416088\pi\)
−0.328562 + 0.944482i \(0.606564\pi\)
\(278\) −0.625993 8.35329i −0.0375446 0.500997i
\(279\) 0 0
\(280\) −8.36842 11.8945i −0.500108 0.710831i
\(281\) 22.7504 18.1428i 1.35717 1.08231i 0.368925 0.929459i \(-0.379726\pi\)
0.988249 0.152851i \(-0.0488456\pi\)
\(282\) 0 0
\(283\) −0.0238140 0.157995i −0.00141559 0.00939185i 0.988112 0.153737i \(-0.0491307\pi\)
−0.989527 + 0.144345i \(0.953893\pi\)
\(284\) −24.6710 36.1858i −1.46396 2.14723i
\(285\) 0 0
\(286\) −1.73761 3.60819i −0.102747 0.213357i
\(287\) 7.10111 18.9064i 0.419165 1.11601i
\(288\) 0 0
\(289\) −8.41683 5.73850i −0.495108 0.337559i
\(290\) −3.37190 3.12866i −0.198005 0.183722i
\(291\) 0 0
\(292\) 30.3112 + 11.8963i 1.77383 + 0.696176i
\(293\) 27.9417 1.63237 0.816186 0.577789i \(-0.196084\pi\)
0.816186 + 0.577789i \(0.196084\pi\)
\(294\) 0 0
\(295\) −26.7635 −1.55823
\(296\) 24.6347 + 9.66842i 1.43186 + 0.561966i
\(297\) 0 0
\(298\) −16.8773 15.6598i −0.977674 0.907149i
\(299\) −1.59341 1.08637i −0.0921494 0.0628264i
\(300\) 0 0
\(301\) 25.6254 8.31908i 1.47702 0.479504i
\(302\) 13.1012 + 27.2049i 0.753889 + 1.56547i
\(303\) 0 0
\(304\) −0.0885461 0.129873i −0.00507847 0.00744874i
\(305\) 1.55006 + 10.2840i 0.0887560 + 0.588858i
\(306\) 0 0
\(307\) 12.9030 10.2898i 0.736412 0.587269i −0.181811 0.983334i \(-0.558196\pi\)
0.918223 + 0.396065i \(0.129624\pi\)
\(308\) 1.50544 + 9.07968i 0.0857806 + 0.517363i
\(309\) 0 0
\(310\) 4.26101 + 56.8593i 0.242009 + 3.22939i
\(311\) 15.8952 + 4.90301i 0.901333 + 0.278024i 0.710582 0.703614i \(-0.248432\pi\)
0.190751 + 0.981639i \(0.438908\pi\)
\(312\) 0 0
\(313\) 19.7180 11.3842i 1.11452 0.643471i 0.174527 0.984652i \(-0.444160\pi\)
0.939998 + 0.341181i \(0.110827\pi\)
\(314\) 8.22226 + 36.0241i 0.464009 + 2.03296i
\(315\) 0 0
\(316\) 0.732099 3.20754i 0.0411838 0.180438i
\(317\) 0.884400 + 2.86715i 0.0496729 + 0.161035i 0.977011 0.213189i \(-0.0683851\pi\)
−0.927338 + 0.374225i \(0.877909\pi\)
\(318\) 0 0
\(319\) 0.351517 + 0.895650i 0.0196811 + 0.0501468i
\(320\) 30.9333 9.54165i 1.72922 0.533394i
\(321\) 0 0
\(322\) 4.69787 + 5.71639i 0.261802 + 0.318562i
\(323\) −0.380925 + 0.0869435i −0.0211952 + 0.00483767i
\(324\) 0 0
\(325\) 1.61832 + 0.934337i 0.0897682 + 0.0518277i
\(326\) −1.22353 + 3.96659i −0.0677650 + 0.219689i
\(327\) 0 0
\(328\) −13.1607 10.4953i −0.726680 0.579508i
\(329\) −3.93754 9.61442i −0.217084 0.530060i
\(330\) 0 0
\(331\) 21.0589 19.5398i 1.15750 1.07401i 0.161304 0.986905i \(-0.448430\pi\)
0.996199 0.0871010i \(-0.0277603\pi\)
\(332\) 17.5793 2.64966i 0.964792 0.145419i
\(333\) 0 0
\(334\) 3.84286 25.4957i 0.210272 1.39506i
\(335\) −18.8418 + 9.07375i −1.02944 + 0.495752i
\(336\) 0 0
\(337\) −17.6916 8.51983i −0.963723 0.464105i −0.115246 0.993337i \(-0.536766\pi\)
−0.848477 + 0.529232i \(0.822480\pi\)
\(338\) −13.3708 + 19.6114i −0.727277 + 1.06672i
\(339\) 0 0
\(340\) 1.45255 19.3829i 0.0787756 1.05119i
\(341\) 4.35736 11.1024i 0.235964 0.601227i
\(342\) 0 0
\(343\) 12.1747 + 13.9562i 0.657372 + 0.753567i
\(344\) 22.4559i 1.21074i
\(345\) 0 0
\(346\) −10.3548 0.775982i −0.556676 0.0417171i
\(347\) 4.16587 4.48974i 0.223636 0.241022i −0.611260 0.791430i \(-0.709337\pi\)
0.834896 + 0.550407i \(0.185528\pi\)
\(348\) 0 0
\(349\) 0.995638 2.06746i 0.0532953 0.110669i −0.872620 0.488399i \(-0.837581\pi\)
0.925916 + 0.377730i \(0.123295\pi\)
\(350\) −4.95331 5.18336i −0.264765 0.277062i
\(351\) 0 0
\(352\) −7.77842 1.17241i −0.414591 0.0624896i
\(353\) −21.7523 + 14.8305i −1.15776 + 0.789346i −0.980827 0.194878i \(-0.937569\pi\)
−0.176930 + 0.984223i \(0.556617\pi\)
\(354\) 0 0
\(355\) −24.8552 26.7875i −1.31918 1.42173i
\(356\) −16.8801 21.1670i −0.894643 1.12185i
\(357\) 0 0
\(358\) −29.6919 + 37.2325i −1.56927 + 1.96780i
\(359\) 31.5751 2.36623i 1.66647 0.124885i 0.792179 0.610289i \(-0.208947\pi\)
0.874290 + 0.485404i \(0.161328\pi\)
\(360\) 0 0
\(361\) −9.48880 + 16.4351i −0.499410 + 0.865004i
\(362\) −10.8397 18.7748i −0.569720 0.986783i
\(363\) 0 0
\(364\) −9.40415 + 7.72856i −0.492912 + 0.405087i
\(365\) 26.4880 + 6.04572i 1.38645 + 0.316448i
\(366\) 0 0
\(367\) −1.78408 + 0.700199i −0.0931280 + 0.0365501i −0.411448 0.911433i \(-0.634977\pi\)
0.318320 + 0.947983i \(0.396881\pi\)
\(368\) −1.22406 + 0.480408i −0.0638086 + 0.0250430i
\(369\) 0 0
\(370\) 65.1302 + 14.8655i 3.38596 + 0.772823i
\(371\) 0.130968 + 8.90327i 0.00679951 + 0.462235i
\(372\) 0 0
\(373\) −0.363940 0.630362i −0.0188441 0.0326389i 0.856450 0.516231i \(-0.172665\pi\)
−0.875294 + 0.483592i \(0.839332\pi\)
\(374\) −3.39384 + 5.87831i −0.175491 + 0.303960i
\(375\) 0 0
\(376\) −8.63534 + 0.647130i −0.445334 + 0.0333732i
\(377\) −0.793406 + 0.994899i −0.0408625 + 0.0512399i
\(378\) 0 0
\(379\) −5.35964 6.72077i −0.275306 0.345223i 0.624886 0.780716i \(-0.285145\pi\)
−0.900192 + 0.435493i \(0.856574\pi\)
\(380\) 0.758190 + 0.817135i 0.0388943 + 0.0419181i
\(381\) 0 0
\(382\) −27.9416 + 19.0503i −1.42962 + 0.974697i
\(383\) −21.6463 3.26266i −1.10608 0.166714i −0.429485 0.903074i \(-0.641305\pi\)
−0.676590 + 0.736360i \(0.736543\pi\)
\(384\) 0 0
\(385\) 2.37122 + 7.30410i 0.120848 + 0.372251i
\(386\) 7.35226 15.2671i 0.374220 0.777076i
\(387\) 0 0
\(388\) −19.7056 + 21.2376i −1.00040 + 1.07817i
\(389\) 4.50483 + 0.337591i 0.228404 + 0.0171165i 0.188441 0.982085i \(-0.439657\pi\)
0.0399637 + 0.999201i \(0.487276\pi\)
\(390\) 0 0
\(391\) 3.26862i 0.165301i
\(392\) 14.1973 6.05981i 0.717074 0.306066i
\(393\) 0 0
\(394\) −10.4706 + 26.6787i −0.527502 + 1.34405i
\(395\) 0.205144 2.73746i 0.0103219 0.137737i
\(396\) 0 0
\(397\) 14.9498 21.9274i 0.750311 1.10050i −0.241200 0.970475i \(-0.577541\pi\)
0.991510 0.130028i \(-0.0415067\pi\)
\(398\) −23.2959 11.2187i −1.16772 0.562344i
\(399\) 0 0
\(400\) 1.14798 0.552836i 0.0573988 0.0276418i
\(401\) −1.12523 + 7.46539i −0.0561911 + 0.372804i 0.943007 + 0.332772i \(0.107984\pi\)
−0.999198 + 0.0400316i \(0.987254\pi\)
\(402\) 0 0
\(403\) 15.5979 2.35100i 0.776986 0.117112i
\(404\) 21.0190 19.5028i 1.04573 0.970300i
\(405\) 0 0
\(406\) 3.99305 2.80933i 0.198172 0.139425i
\(407\) −10.9252 8.71258i −0.541544 0.431867i
\(408\) 0 0
\(409\) −2.67236 + 8.66359i −0.132140 + 0.428387i −0.997327 0.0730615i \(-0.976723\pi\)
0.865188 + 0.501448i \(0.167199\pi\)
\(410\) −36.8002 21.2466i −1.81743 1.04930i
\(411\) 0 0
\(412\) −36.6597 + 8.36734i −1.80609 + 0.412229i
\(413\) 5.91314 27.7849i 0.290967 1.36720i
\(414\) 0 0
\(415\) 14.1746 4.37227i 0.695802 0.214626i
\(416\) −3.80090 9.68453i −0.186354 0.474823i
\(417\) 0 0
\(418\) −0.114738 0.371971i −0.00561201 0.0181937i
\(419\) 2.31046 10.1228i 0.112873 0.494530i −0.886614 0.462510i \(-0.846949\pi\)
0.999487 0.0320196i \(-0.0101939\pi\)
\(420\) 0 0
\(421\) −1.40068 6.13680i −0.0682652 0.299089i 0.929258 0.369432i \(-0.120448\pi\)
−0.997523 + 0.0703429i \(0.977591\pi\)
\(422\) 21.3180 12.3080i 1.03775 0.599143i
\(423\) 0 0
\(424\) 7.09189 + 2.18756i 0.344412 + 0.106237i
\(425\) −0.236685 3.15835i −0.0114809 0.153202i
\(426\) 0 0
\(427\) −11.0189 0.662932i −0.533242 0.0320816i
\(428\) 23.1952 18.4975i 1.12118 0.894112i
\(429\) 0 0
\(430\) −8.44876 56.0538i −0.407435 2.70316i
\(431\) −20.2222 29.6605i −0.974070 1.42870i −0.902217 0.431282i \(-0.858061\pi\)
−0.0718526 0.997415i \(-0.522891\pi\)
\(432\) 0 0
\(433\) −7.73903 16.0703i −0.371914 0.772287i 0.628069 0.778158i \(-0.283846\pi\)
−0.999983 + 0.00587067i \(0.998131\pi\)
\(434\) −59.9706 8.13890i −2.87868 0.390680i
\(435\) 0 0
\(436\) −23.8505 16.2610i −1.14223 0.778760i
\(437\) −0.137411 0.127499i −0.00657327 0.00609910i
\(438\) 0 0
\(439\) 0.599199 + 0.235168i 0.0285982 + 0.0112240i 0.379597 0.925152i \(-0.376063\pi\)
−0.350999 + 0.936376i \(0.614158\pi\)
\(440\) 6.40069 0.305141
\(441\) 0 0
\(442\) −8.97719 −0.427001
\(443\) 24.0651 + 9.44487i 1.14337 + 0.448739i 0.860011 0.510275i \(-0.170456\pi\)
0.283357 + 0.959014i \(0.408552\pi\)
\(444\) 0 0
\(445\) −16.5594 15.3649i −0.784992 0.728366i
\(446\) 52.2233 + 35.6052i 2.47284 + 1.68596i
\(447\) 0 0
\(448\) 3.07137 + 34.2219i 0.145109 + 1.61683i
\(449\) 0.161075 + 0.334476i 0.00760160 + 0.0157849i 0.904735 0.425975i \(-0.140069\pi\)
−0.897134 + 0.441760i \(0.854354\pi\)
\(450\) 0 0
\(451\) 5.00706 + 7.34401i 0.235773 + 0.345816i
\(452\) 5.11251 + 33.9193i 0.240472 + 1.59543i
\(453\) 0 0
\(454\) −2.23230 + 1.78020i −0.104767 + 0.0835491i
\(455\) −6.79791 + 7.54603i −0.318691 + 0.353764i
\(456\) 0 0
\(457\) −0.998957 13.3302i −0.0467292 0.623558i −0.970576 0.240796i \(-0.922592\pi\)
0.923847 0.382763i \(-0.125027\pi\)
\(458\) −42.1662 13.0065i −1.97030 0.607756i
\(459\) 0 0
\(460\) 8.07584 4.66259i 0.376538 0.217394i
\(461\) −5.15133 22.5694i −0.239921 1.05116i −0.941087 0.338165i \(-0.890194\pi\)
0.701165 0.712999i \(-0.252663\pi\)
\(462\) 0 0
\(463\) 0.200977 0.880537i 0.00934018 0.0409220i −0.970043 0.242933i \(-0.921891\pi\)
0.979383 + 0.202011i \(0.0647476\pi\)
\(464\) 0.255751 + 0.829124i 0.0118729 + 0.0384911i
\(465\) 0 0
\(466\) 1.47144 + 3.74916i 0.0681629 + 0.173676i
\(467\) −4.58606 + 1.41461i −0.212218 + 0.0654605i −0.399041 0.916933i \(-0.630657\pi\)
0.186823 + 0.982394i \(0.440181\pi\)
\(468\) 0 0
\(469\) −5.25710 21.5657i −0.242750 0.995809i
\(470\) −21.3118 + 4.86429i −0.983042 + 0.224373i
\(471\) 0 0
\(472\) −20.5050 11.8386i −0.943819 0.544914i
\(473\) −3.49504 + 11.3306i −0.160702 + 0.520984i
\(474\) 0 0
\(475\) 0.142008 + 0.113247i 0.00651576 + 0.00519615i
\(476\) 19.8017 + 5.79047i 0.907611 + 0.265406i
\(477\) 0 0
\(478\) 19.4302 18.0286i 0.888718 0.824610i
\(479\) −29.1998 + 4.40117i −1.33417 + 0.201094i −0.777105 0.629371i \(-0.783312\pi\)
−0.557070 + 0.830466i \(0.688074\pi\)
\(480\) 0 0
\(481\) 2.75452 18.2750i 0.125595 0.833270i
\(482\) 33.7284 16.2427i 1.53629 0.739837i
\(483\) 0 0
\(484\) 25.9580 + 12.5007i 1.17991 + 0.568215i
\(485\) −13.6173 + 19.9729i −0.618329 + 0.906922i
\(486\) 0 0
\(487\) −0.603365 + 8.05135i −0.0273411 + 0.364842i 0.966706 + 0.255890i \(0.0823684\pi\)
−0.994047 + 0.108952i \(0.965251\pi\)
\(488\) −3.36142 + 8.56476i −0.152164 + 0.387709i
\(489\) 0 0
\(490\) 33.1591 20.4679i 1.49797 0.924646i
\(491\) 30.8465i 1.39208i −0.718001 0.696042i \(-0.754943\pi\)
0.718001 0.696042i \(-0.245057\pi\)
\(492\) 0 0
\(493\) 2.15076 + 0.161177i 0.0968653 + 0.00725905i
\(494\) 0.350173 0.377397i 0.0157550 0.0169799i
\(495\) 0 0
\(496\) 4.66666 9.69043i 0.209539 0.435113i
\(497\) 33.3013 19.8853i 1.49377 0.891976i
\(498\) 0 0
\(499\) −27.9451 4.21204i −1.25099 0.188557i −0.510062 0.860138i \(-0.670377\pi\)
−0.740931 + 0.671581i \(0.765616\pi\)
\(500\) 23.2980 15.8843i 1.04192 0.710369i
\(501\) 0 0
\(502\) −40.9820 44.1681i −1.82912 1.97132i
\(503\) −9.58702 12.0217i −0.427464 0.536023i 0.520727 0.853723i \(-0.325661\pi\)
−0.948191 + 0.317700i \(0.897089\pi\)
\(504\) 0 0
\(505\) 14.9167 18.7049i 0.663783 0.832358i
\(506\) −3.24733 + 0.243354i −0.144362 + 0.0108184i
\(507\) 0 0
\(508\) −10.3123 + 17.8613i −0.457532 + 0.792469i
\(509\) 11.6400 + 20.1610i 0.515932 + 0.893621i 0.999829 + 0.0184959i \(0.00588775\pi\)
−0.483897 + 0.875125i \(0.660779\pi\)
\(510\) 0 0
\(511\) −12.1287 + 26.1632i −0.536543 + 1.15739i
\(512\) −11.4311 2.60907i −0.505187 0.115306i
\(513\) 0 0
\(514\) −37.2034 + 14.6013i −1.64097 + 0.644034i
\(515\) −29.2060 + 11.4625i −1.28697 + 0.505099i
\(516\) 0 0
\(517\) 4.45788 + 1.01748i 0.196057 + 0.0447488i
\(518\) −29.8228 + 64.3314i −1.31034 + 2.82656i
\(519\) 0 0
\(520\) 4.23268 + 7.33121i 0.185615 + 0.321495i
\(521\) 21.8542 37.8525i 0.957449 1.65835i 0.228787 0.973477i \(-0.426524\pi\)
0.728662 0.684874i \(-0.240143\pi\)
\(522\) 0 0
\(523\) 2.70012 0.202346i 0.118068 0.00884796i −0.0155651 0.999879i \(-0.504955\pi\)
0.133633 + 0.991031i \(0.457336\pi\)
\(524\) −24.1357 + 30.2652i −1.05437 + 1.32214i
\(525\) 0 0
\(526\) −10.3443 12.9714i −0.451034 0.565579i
\(527\) −18.1846 19.5984i −0.792135 0.853719i
\(528\) 0 0
\(529\) 17.7078 12.0730i 0.769906 0.524913i
\(530\) 18.5256 + 2.79229i 0.804702 + 0.121289i
\(531\) 0 0
\(532\) −1.01583 + 0.606587i −0.0440420 + 0.0262989i
\(533\) −5.10058 + 10.5915i −0.220931 + 0.458767i
\(534\) 0 0
\(535\) 16.8372 18.1461i 0.727934 0.784526i
\(536\) −18.4494 1.38259i −0.796895 0.0597190i
\(537\) 0 0
\(538\) 26.5112i 1.14298i
\(539\) −8.10674 + 0.847940i −0.349182 + 0.0365233i
\(540\) 0 0
\(541\) 6.20572 15.8119i 0.266805 0.679807i −0.733195 0.680018i \(-0.761972\pi\)
1.00000 0.000210854i \(6.71170e-5\pi\)
\(542\) 0.744499 9.93465i 0.0319790 0.426730i
\(543\) 0 0
\(544\) −9.93311 + 14.5692i −0.425878 + 0.624649i
\(545\) −21.7003 10.4503i −0.929540 0.447643i
\(546\) 0 0
\(547\) 3.54836 1.70880i 0.151717 0.0730629i −0.356485 0.934301i \(-0.616025\pi\)
0.508201 + 0.861238i \(0.330311\pi\)
\(548\) −9.60615 + 63.7326i −0.410354 + 2.72252i
\(549\) 0 0
\(550\) 3.12015 0.470288i 0.133044 0.0200531i
\(551\) −0.0906704 + 0.0841299i −0.00386269 + 0.00358405i
\(552\) 0 0
\(553\) 2.79661 + 0.817790i 0.118924 + 0.0347760i
\(554\) −2.06752 1.64879i −0.0878404 0.0700504i
\(555\) 0 0
\(556\) 3.30290 10.7077i 0.140074 0.454110i
\(557\) 31.3559 + 18.1034i 1.32859 + 0.767064i 0.985082 0.172085i \(-0.0550504\pi\)
0.343511 + 0.939149i \(0.388384\pi\)
\(558\) 0 0
\(559\) −15.2891 + 3.48964i −0.646660 + 0.147596i
\(560\) 1.64014 + 6.72818i 0.0693087 + 0.284318i
\(561\) 0 0
\(562\) 62.0981 19.1547i 2.61945 0.807994i
\(563\) 15.4646 + 39.4033i 0.651757 + 1.66065i 0.746695 + 0.665167i \(0.231640\pi\)
−0.0949374 + 0.995483i \(0.530265\pi\)
\(564\) 0 0
\(565\) 8.43629 + 27.3498i 0.354917 + 1.15061i
\(566\) 0.0794022 0.347884i 0.00333752 0.0146226i
\(567\) 0 0
\(568\) −7.19373 31.5178i −0.301842 1.32246i
\(569\) −9.93757 + 5.73746i −0.416605 + 0.240527i −0.693624 0.720338i \(-0.743987\pi\)
0.277019 + 0.960864i \(0.410654\pi\)
\(570\) 0 0
\(571\) 13.1509 + 4.05652i 0.550348 + 0.169760i 0.557443 0.830215i \(-0.311782\pi\)
−0.00709536 + 0.999975i \(0.502259\pi\)
\(572\) −0.400346 5.34225i −0.0167393 0.223371i
\(573\) 0 0
\(574\) 30.1881 33.5104i 1.26003 1.39870i
\(575\) 1.18798 0.947384i 0.0495423 0.0395087i
\(576\) 0 0
\(577\) 2.65830 + 17.6366i 0.110666 + 0.734223i 0.973492 + 0.228721i \(0.0734544\pi\)
−0.862826 + 0.505502i \(0.831307\pi\)
\(578\) −12.8155 18.7970i −0.533056 0.781850i
\(579\) 0 0
\(580\) −2.66977 5.54383i −0.110856 0.230195i
\(581\) 1.40740 + 15.6815i 0.0583886 + 0.650579i
\(582\) 0 0
\(583\) −3.23790 2.20757i −0.134100 0.0914280i
\(584\) 17.6197 + 16.3487i 0.729108 + 0.676513i
\(585\) 0 0
\(586\) 58.0875 + 22.7977i 2.39957 + 0.941763i
\(587\) 32.7857 1.35321 0.676606 0.736345i \(-0.263450\pi\)
0.676606 + 0.736345i \(0.263450\pi\)
\(588\) 0 0
\(589\) 1.53323 0.0631758
\(590\) −55.6381 21.8364i −2.29059 0.898989i
\(591\) 0 0
\(592\) −9.23763 8.57126i −0.379664 0.352277i
\(593\) −0.550480 0.375311i −0.0226055 0.0154122i 0.551965 0.833868i \(-0.313878\pi\)
−0.574570 + 0.818455i \(0.694831\pi\)
\(594\) 0 0
\(595\) 17.0578 + 2.31499i 0.699300 + 0.0949054i
\(596\) −13.3629 27.7484i −0.547367 1.13662i
\(597\) 0 0
\(598\) −2.42615 3.55850i −0.0992125 0.145518i
\(599\) −1.54405 10.2441i −0.0630880 0.418562i −0.997975 0.0636149i \(-0.979737\pi\)
0.934886 0.354947i \(-0.115501\pi\)
\(600\) 0 0
\(601\) −37.7417 + 30.0980i −1.53952 + 1.22772i −0.660614 + 0.750726i \(0.729704\pi\)
−0.878904 + 0.476999i \(0.841725\pi\)
\(602\) 60.0597 + 3.61338i 2.44785 + 0.147271i
\(603\) 0 0
\(604\) 3.01852 + 40.2793i 0.122822 + 1.63894i
\(605\) 22.9716 + 7.08579i 0.933928 + 0.288079i
\(606\) 0 0
\(607\) −28.8438 + 16.6530i −1.17073 + 0.675923i −0.953853 0.300275i \(-0.902921\pi\)
−0.216880 + 0.976198i \(0.569588\pi\)
\(608\) −0.225021 0.985883i −0.00912582 0.0399828i
\(609\) 0 0
\(610\) −5.16831 + 22.6438i −0.209259 + 0.916822i
\(611\) 1.78253 + 5.77881i 0.0721133 + 0.233786i
\(612\) 0 0
\(613\) 3.90889 + 9.95969i 0.157879 + 0.402268i 0.987824 0.155577i \(-0.0497236\pi\)
−0.829945 + 0.557845i \(0.811628\pi\)
\(614\) 35.2192 10.8637i 1.42133 0.438423i
\(615\) 0 0
\(616\) −1.41417 + 6.64496i −0.0569786 + 0.267733i
\(617\) 10.3341 2.35868i 0.416033 0.0949569i −0.00938006 0.999956i \(-0.502986\pi\)
0.425414 + 0.904999i \(0.360129\pi\)
\(618\) 0 0
\(619\) 19.2455 + 11.1114i 0.773542 + 0.446605i 0.834137 0.551558i \(-0.185966\pi\)
−0.0605948 + 0.998162i \(0.519300\pi\)
\(620\) −22.4822 + 72.8856i −0.902908 + 2.92716i
\(621\) 0 0
\(622\) 29.0438 + 23.1617i 1.16455 + 0.928698i
\(623\) 19.6099 13.7967i 0.785655 0.552751i
\(624\) 0 0
\(625\) 21.6944 20.1295i 0.867777 0.805179i
\(626\) 50.2796 7.57844i 2.00958 0.302895i
\(627\) 0 0
\(628\) −7.36700 + 48.8768i −0.293975 + 1.95040i
\(629\) −28.2220 + 13.5910i −1.12528 + 0.541909i
\(630\) 0 0
\(631\) −22.6371 10.9015i −0.901170 0.433981i −0.0748589 0.997194i \(-0.523851\pi\)
−0.826312 + 0.563213i \(0.809565\pi\)
\(632\) 1.36806 2.00658i 0.0544185 0.0798173i
\(633\) 0 0
\(634\) −0.500751 + 6.68206i −0.0198874 + 0.265378i
\(635\) −6.28705 + 16.0191i −0.249494 + 0.635700i
\(636\) 0 0
\(637\) −6.33208 8.72456i −0.250886 0.345680i
\(638\) 2.14875i 0.0850699i
\(639\) 0 0
\(640\) 38.5073 + 2.88572i 1.52213 + 0.114068i
\(641\) −6.50188 + 7.00737i −0.256809 + 0.276774i −0.848275 0.529555i \(-0.822359\pi\)
0.591466 + 0.806330i \(0.298549\pi\)
\(642\) 0 0
\(643\) 0.0302707 0.0628578i 0.00119376 0.00247887i −0.900371 0.435123i \(-0.856705\pi\)
0.901565 + 0.432644i \(0.142419\pi\)
\(644\) 3.05625 + 9.41419i 0.120433 + 0.370971i
\(645\) 0 0
\(646\) −0.862834 0.130051i −0.0339478 0.00511680i
\(647\) −11.8815 + 8.10068i −0.467110 + 0.318471i −0.773901 0.633307i \(-0.781697\pi\)
0.306791 + 0.951777i \(0.400745\pi\)
\(648\) 0 0
\(649\) 8.50371 + 9.16482i 0.333800 + 0.359751i
\(650\) 2.60197 + 3.26277i 0.102058 + 0.127976i
\(651\) 0 0
\(652\) −3.46213 + 4.34137i −0.135587 + 0.170021i
\(653\) 6.71743 0.503402i 0.262873 0.0196996i 0.0573585 0.998354i \(-0.481732\pi\)
0.205515 + 0.978654i \(0.434113\pi\)
\(654\) 0 0
\(655\) −16.1498 + 27.9722i −0.631023 + 1.09296i
\(656\) 4.00780 + 6.94171i 0.156478 + 0.271028i
\(657\) 0 0
\(658\) −0.341273 23.1999i −0.0133042 0.904426i
\(659\) −13.3244 3.04120i −0.519043 0.118468i −0.0450293 0.998986i \(-0.514338\pi\)
−0.474014 + 0.880517i \(0.657195\pi\)
\(660\) 0 0
\(661\) −14.5956 + 5.72834i −0.567702 + 0.222807i −0.631793 0.775137i \(-0.717681\pi\)
0.0640904 + 0.997944i \(0.479585\pi\)
\(662\) 59.7216 23.4390i 2.32114 0.910982i
\(663\) 0 0
\(664\) 12.7939 + 2.92013i 0.496501 + 0.113323i
\(665\) −0.762693 + 0.626800i −0.0295760 + 0.0243062i
\(666\) 0 0
\(667\) 0.517367 + 0.896107i 0.0200325 + 0.0346974i
\(668\) 17.2455 29.8701i 0.667248 1.15571i
\(669\) 0 0
\(670\) −46.5732 + 3.49018i −1.79928 + 0.134837i
\(671\) 3.02910 3.79838i 0.116937 0.146635i
\(672\) 0 0
\(673\) 29.3551 + 36.8101i 1.13156 + 1.41893i 0.894293 + 0.447481i \(0.147679\pi\)
0.237263 + 0.971446i \(0.423750\pi\)
\(674\) −29.8274 32.1463i −1.14891 1.23823i
\(675\) 0 0
\(676\) −26.2343 + 17.8862i −1.00901 + 0.687932i
\(677\) −41.8799 6.31238i −1.60957 0.242604i −0.718188 0.695849i \(-0.755028\pi\)
−0.891386 + 0.453244i \(0.850266\pi\)
\(678\) 0 0
\(679\) −17.7265 18.5498i −0.680280 0.711875i
\(680\) 6.22530 12.9270i 0.238729 0.495727i
\(681\) 0 0
\(682\) 18.1169 19.5253i 0.693731 0.747664i
\(683\) 23.3292 + 1.74828i 0.892668 + 0.0668962i 0.513160 0.858293i \(-0.328475\pi\)
0.379507 + 0.925189i \(0.376094\pi\)
\(684\) 0 0
\(685\) 53.7780i 2.05475i
\(686\) 13.9228 + 38.9467i 0.531576 + 1.48699i
\(687\) 0 0
\(688\) −3.90659 + 9.95382i −0.148937 + 0.379486i
\(689\) 0.387322 5.16846i 0.0147558 0.196903i
\(690\) 0 0
\(691\) −8.22195 + 12.0594i −0.312778 + 0.458761i −0.950149 0.311796i \(-0.899069\pi\)
0.637371 + 0.770557i \(0.280022\pi\)
\(692\) −12.5149 6.02685i −0.475744 0.229106i
\(693\) 0 0
\(694\) 12.3235 5.93471i 0.467795 0.225278i
\(695\) 1.39351 9.24531i 0.0528587 0.350695i
\(696\) 0 0
\(697\) 19.7020 2.96960i 0.746266 0.112481i
\(698\) 3.75666 3.48567i 0.142192 0.131935i
\(699\) 0 0
\(700\) −3.63483 8.87527i −0.137384 0.335454i
\(701\) −22.5793 18.0064i −0.852809 0.680093i 0.0961928 0.995363i \(-0.469333\pi\)
−0.949002 + 0.315270i \(0.897905\pi\)
\(702\) 0 0
\(703\) 0.529496 1.71658i 0.0199703 0.0647422i
\(704\) −13.0960 7.56099i −0.493575 0.284965i
\(705\) 0 0
\(706\) −57.3206 + 13.0831i −2.15729 + 0.492387i
\(707\) 16.1231 + 19.6186i 0.606370 + 0.737834i
\(708\) 0 0
\(709\) −5.82495 + 1.79676i −0.218761 + 0.0674788i −0.402198 0.915553i \(-0.631754\pi\)
0.183437 + 0.983031i \(0.441278\pi\)
\(710\) −29.8150 75.9674i −1.11894 2.85100i
\(711\) 0 0
\(712\) −5.89058 19.0968i −0.220759 0.715683i
\(713\) 2.85415 12.5049i 0.106889 0.468311i
\(714\) 0 0
\(715\) −0.994664 4.35791i −0.0371983 0.162977i
\(716\) −55.1696 + 31.8522i −2.06179 + 1.19037i
\(717\) 0 0
\(718\) 67.5715 + 20.8430i 2.52174 + 0.777855i
\(719\) 0.397680 + 5.30667i 0.0148310 + 0.197906i 0.999698 + 0.0245915i \(0.00782851\pi\)
−0.984867 + 0.173314i \(0.944552\pi\)
\(720\) 0 0
\(721\) −5.44716 32.8531i −0.202863 1.22351i
\(722\) −33.1355 + 26.4247i −1.23317 + 0.983424i
\(723\) 0 0
\(724\) −4.32231 28.6766i −0.160637 1.06576i
\(725\) −0.564801 0.828411i −0.0209762 0.0307664i
\(726\) 0 0
\(727\) −15.2350 31.6359i −0.565036 1.17331i −0.966317 0.257354i \(-0.917149\pi\)
0.401281 0.915955i \(-0.368565\pi\)
\(728\) −8.54616 + 2.77445i −0.316742 + 0.102828i
\(729\) 0 0
\(730\) 50.1328 + 34.1799i 1.85550 + 1.26506i
\(731\) 19.4844 + 18.0788i 0.720655 + 0.668670i
\(732\) 0 0
\(733\) 41.5959 + 16.3252i 1.53638 + 0.602984i 0.974530 0.224256i \(-0.0719951\pi\)
0.561849 + 0.827240i \(0.310090\pi\)
\(734\) −4.28018 −0.157984
\(735\) 0 0
\(736\) −8.45962 −0.311826
\(737\) 9.09391 + 3.56910i 0.334978 + 0.131469i
\(738\) 0 0
\(739\) 28.1100 + 26.0823i 1.03404 + 0.959452i 0.999202 0.0399408i \(-0.0127169\pi\)
0.0348413 + 0.999393i \(0.488907\pi\)
\(740\) 73.8374 + 50.3415i 2.71432 + 1.85059i
\(741\) 0 0
\(742\) −6.99192 + 18.6157i −0.256681 + 0.683404i
\(743\) −12.7732 26.5239i −0.468604 0.973066i −0.992610 0.121351i \(-0.961277\pi\)
0.524006 0.851715i \(-0.324437\pi\)
\(744\) 0 0
\(745\) −14.4760 21.2324i −0.530359 0.777894i
\(746\) −0.242274 1.60739i −0.00887030 0.0588506i
\(747\) 0 0
\(748\) −7.09897 + 5.66124i −0.259564 + 0.206996i
\(749\) 15.1186 + 21.4889i 0.552423 + 0.785189i
\(750\) 0 0
\(751\) 2.35456 + 31.4194i 0.0859191 + 1.14651i 0.858921 + 0.512108i \(0.171135\pi\)
−0.773002 + 0.634404i \(0.781246\pi\)
\(752\) 3.94029 + 1.21542i 0.143688 + 0.0443217i
\(753\) 0 0
\(754\) −2.46114 + 1.42094i −0.0896293 + 0.0517475i
\(755\) 7.49953 + 32.8576i 0.272936 + 1.19581i
\(756\) 0 0
\(757\) 8.49403 37.2148i 0.308721 1.35259i −0.547855 0.836573i \(-0.684555\pi\)
0.856576 0.516021i \(-0.172587\pi\)
\(758\) −5.65857 18.3446i −0.205528 0.666307i
\(759\) 0 0
\(760\) 0.300614 + 0.765951i 0.0109044 + 0.0277840i
\(761\) 7.40735 2.28487i 0.268516 0.0828263i −0.157573 0.987507i \(-0.550367\pi\)
0.426090 + 0.904681i \(0.359891\pi\)
\(762\) 0 0
\(763\) 15.6436 20.2196i 0.566338 0.731998i
\(764\) −44.1041 + 10.0665i −1.59563 + 0.364193i
\(765\) 0 0
\(766\) −42.3381 24.4439i −1.52974 0.883195i
\(767\) −4.87382 + 15.8005i −0.175983 + 0.570524i
\(768\) 0 0
\(769\) −18.8950 15.0682i −0.681370 0.543375i 0.220497 0.975388i \(-0.429232\pi\)
−0.901867 + 0.432013i \(0.857804\pi\)
\(770\) −1.02994 + 17.1190i −0.0371163 + 0.616927i
\(771\) 0 0
\(772\) 16.6166 15.4180i 0.598046 0.554905i
\(773\) 0.859499 0.129549i 0.0309140 0.00465954i −0.133567 0.991040i \(-0.542643\pi\)
0.164481 + 0.986380i \(0.447405\pi\)
\(774\) 0 0
\(775\) −1.85237 + 12.2897i −0.0665390 + 0.441458i
\(776\) −19.2677 + 9.27886i −0.691672 + 0.333092i
\(777\) 0 0
\(778\) 9.08958 + 4.37731i 0.325877 + 0.156934i
\(779\) −0.643674 + 0.944097i −0.0230620 + 0.0338258i
\(780\) 0 0
\(781\) −1.27567 + 17.0227i −0.0456472 + 0.609119i
\(782\) −2.66687 + 6.79508i −0.0953671 + 0.242991i
\(783\) 0 0
\(784\) −7.34733 + 0.216207i −0.262405 + 0.00772166i
\(785\) 41.2426i 1.47201i
\(786\) 0 0
\(787\) 30.7752 + 2.30628i 1.09702 + 0.0822100i 0.610918 0.791694i \(-0.290801\pi\)
0.486098 + 0.873904i \(0.338420\pi\)
\(788\) −26.0768 <