Properties

Label 441.2.bg.a.395.3
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 395.3
Character \(\chi\) \(=\) 441.395
Dual form 441.2.bg.a.278.3

$q$-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 −0.510803 0.859698i \(-0.670652\pi\)
−0.959188 + 0.282769i \(0.908747\pi\)
\(3\) 0 0
\(4\) 2.18995 + 2.03198i 1.09498 + 1.01599i
\(5\) −2.05954 1.40417i −0.921054 0.627964i 0.00717441 0.999974i \(-0.497716\pi\)
−0.928229 + 0.372010i \(0.878669\pi\)
\(6\) 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 \(0.00854922\pi\)
−0.947313 + 0.320311i \(0.896213\pi\)
\(12\) 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 0.582069 0.813140i \(-0.302244\pi\)
0.0228697 + 0.999738i \(0.492720\pi\)
\(18\) 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 0.985876 0.167476i \(-0.0535617\pi\)
−0.908912 + 0.416989i \(0.863085\pi\)
\(24\) 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 −0.147069 0.989126i \(-0.546984\pi\)
0.296661 + 0.954983i \(0.404127\pi\)
\(30\) 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 0.188656 0.982043i \(-0.439587\pi\)
0.885418 + 0.464797i \(0.153873\pi\)
\(42\) 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 −0.787249 0.616635i \(-0.788495\pi\)
0.996513 + 0.0834395i \(0.0265905\pi\)
\(48\) 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 −0.870417 0.492314i \(-0.836151\pi\)
0.555984 + 0.831193i \(0.312342\pi\)
\(54\) 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 0.174577 0.984644i \(-0.444144\pi\)
0.980359 + 0.197222i \(0.0631920\pi\)
\(60\) 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 0.957848 0.287275i \(-0.0927492\pi\)
0.738348 + 0.674420i \(0.235606\pi\)
\(72\) 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 −0.942589 0.333956i \(-0.891616\pi\)
0.535329 + 0.844644i \(0.320188\pi\)
\(84\) 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 0.605669 0.795716i \(-0.292905\pi\)
0.344220 + 0.938889i \(0.388143\pi\)
\(90\) 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 \(0.182272\pi\)
−0.911851 + 0.410521i \(0.865347\pi\)
\(102\) 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 \(0.206991\pi\)
−0.939001 + 0.343915i \(0.888247\pi\)
\(108\) 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 0.102489 0.994734i \(-0.467319\pi\)
−0.946988 + 0.321268i \(0.895891\pi\)
\(114\) 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 \(-0.832275\pi\)
0.779754 0.626086i \(-0.215344\pi\)
\(132\) 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 \(-0.817346\pi\)
−0.198498 0.980101i \(-0.563606\pi\)
\(138\) 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 0.724262 0.689525i \(-0.242181\pi\)
0.0619256 + 0.998081i \(0.480276\pi\)
\(150\) 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 \(0.0759730\pi\)
−0.772851 + 0.634588i \(0.781170\pi\)
\(168\) 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 −0.121215 0.992626i \(-0.538679\pi\)
0.459014 + 0.888429i \(0.348203\pi\)
\(174\) 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 \(-0.611224\pi\)
0.812146 0.583454i \(-0.198299\pi\)
\(180\) 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 −0.382599 0.923915i \(-0.624971\pi\)
0.999827 + 0.0186070i \(0.00592315\pi\)
\(192\) 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 \(-0.848865\pi\)
0.889383 0.457164i \(-0.151135\pi\)
\(198\) 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 −0.844031 0.536294i \(-0.819824\pi\)
0.886460 + 0.462806i \(0.153157\pi\)
\(228\) 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 0.691591 0.722289i \(-0.256910\pi\)
−0.771952 + 0.635681i \(0.780720\pi\)
\(234\) 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 −0.998498 0.0547961i \(-0.982549\pi\)
0.665394 + 0.746492i \(0.268263\pi\)
\(240\) 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 0.994678 0.103037i \(-0.0328560\pi\)
0.539614 + 0.841913i \(0.318570\pi\)
\(252\) 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 −0.155205 0.987882i \(-0.549604\pi\)
0.973522 + 0.228595i \(0.0734133\pi\)
\(258\) 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 0.685069 0.728478i \(-0.259772\pi\)
−0.288346 + 0.957526i \(0.593105\pi\)
\(264\) 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 0.735562 0.677458i \(-0.236918\pi\)
−0.999993 + 0.00369739i \(0.998823\pi\)
\(270\) 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 \(0.620274\pi\)
−0.988249 + 0.152851i \(0.951154\pi\)
\(282\) 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 \(-0.803916\pi\)
−0.816186 + 0.577789i \(0.803916\pi\)
\(294\) 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 −0.190751 0.981639i \(-0.561092\pi\)
−0.710582 + 0.703614i \(0.751568\pi\)
\(312\) 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 0.927338 0.374225i \(-0.122091\pi\)
−0.977011 + 0.213189i \(0.931615\pi\)
\(318\) 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 −0.834896 0.550407i \(-0.814472\pi\)
0.611260 + 0.791430i \(0.290663\pi\)
\(348\) 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 0.176930 0.984223i \(-0.443383\pi\)
0.980827 + 0.194878i \(0.0624311\pi\)
\(354\) 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 −0.874290 0.485404i \(-0.838672\pi\)
−0.792179 + 0.610289i \(0.791053\pi\)
\(360\) 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 0.676590 0.736360i \(-0.263457\pi\)
0.429485 + 0.903074i \(0.358695\pi\)
\(384\) 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 −0.0399637 0.999201i \(-0.512724\pi\)
−0.188441 + 0.982085i \(0.560343\pi\)
\(390\) 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 \(-0.892016\pi\)
0.999198 0.0400316i \(-0.0127459\pi\)
\(402\) 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 \(0.153051\pi\)
−0.999487 + 0.0320196i \(0.989806\pi\)
\(420\) 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 \(0.141939\pi\)
0.0718526 + 0.997415i \(0.477109\pi\)
\(432\) 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 −0.283357 0.959014i \(-0.591448\pi\)
−0.860011 + 0.510275i \(0.829544\pi\)
\(444\) 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 0.897134 0.441760i \(-0.145646\pi\)
−0.904735 + 0.425975i \(0.859931\pi\)
\(450\) 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 \(0.109806\pi\)
−0.701165 + 0.712999i \(0.747337\pi\)
\(462\) 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 −0.186823 0.982394i \(-0.559819\pi\)
0.399041 + 0.916933i \(0.369343\pi\)
\(468\) 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 0.557070 0.830466i \(-0.311926\pi\)
0.777105 + 0.629371i \(0.216688\pi\)
\(480\) 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 \(0.245057\pi\)
−0.718001 + 0.696042i \(0.754943\pi\)
\(492\) 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 0.948191 0.317700i \(-0.102911\pi\)
−0.520727 + 0.853723i \(0.674339\pi\)
\(504\) 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 \(-0.994112\pi\)
0.483897 0.875125i \(-0.339221\pi\)
\(510\) 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 \(0.573476\pi\)
−0.728662 + 0.684874i \(0.759857\pi\)
\(522\) 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 −0.343511 0.939149i \(-0.611616\pi\)
−0.985082 + 0.172085i \(0.944950\pi\)
\(558\) 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 \(-0.768360\pi\)
0.0949374 0.995483i \(-0.469735\pi\)
\(564\) 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 −0.277019 0.960864i \(-0.589346\pi\)
0.693624 + 0.720338i \(0.256013\pi\)
\(570\) 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 \(-0.736550\pi\)
−0.676606 + 0.736345i \(0.736550\pi\)
\(588\) 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 0.574570 0.818455i \(-0.305169\pi\)
−0.551965 + 0.833868i \(0.686122\pi\)
\(594\) 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 \(0.0202629\pi\)
−0.934886 + 0.354947i \(0.884499\pi\)
\(600\) 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 −0.425414 0.904999i \(-0.639871\pi\)
0.00938006 + 0.999956i \(0.497014\pi\)
\(618\) 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 −0.591466 0.806330i \(-0.701451\pi\)
0.848275 + 0.529555i \(0.177641\pi\)
\(642\) 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 −0.306791 0.951777i \(-0.599255\pi\)
0.773901 + 0.633307i \(0.218303\pi\)
\(648\) 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 −0.205515 0.978654i \(-0.565887\pi\)
−0.0573585 + 0.998354i \(0.518268\pi\)
\(654\) 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 0.474014 0.880517i \(-0.342805\pi\)
0.0450293 + 0.998986i \(0.485662\pi\)
\(660\) 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 0.891386 0.453244i \(-0.149734\pi\)
0.718188 + 0.695849i \(0.244972\pi\)
\(678\) 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 −0.379507 0.925189i \(-0.623906\pi\)
−0.513160 + 0.858293i \(0.671525\pi\)
\(684\) 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 0.949002 0.315270i \(-0.102095\pi\)
−0.0961928 + 0.995363i \(0.530667\pi\)
\(702\) 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 \(-0.992171\pi\)
0.984867 0.173314i \(-0.0554476\pi\)
\(720\) 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 \(0.0387228\pi\)
−0.524006 + 0.851715i \(0.675563\pi\)
\(744\) 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 −0.426090 0.904681i \(-0.640109\pi\)
0.157573 + 0.987507i \(0.449633\pi\)
\(762\) 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 −0.164481 0.986380i \(-0.552595\pi\)
0.133567 + 0.991040i \(0.457357\pi\)
\(774\) 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