Properties

Label 441.2.bg.a.278.3
Level $441$
Weight $2$
Character 441.278
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 278.3
Character \(\chi\) \(=\) 441.278
Dual form 441.2.bg.a.395.3

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{41}{42}\right)\) \(-1\)

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 \(-0.908747\pi\)
−0.510803 + 0.859698i \(0.670652\pi\)
\(3\) 0 0
\(4\) 2.18995 2.03198i 1.09498 1.01599i
\(5\) −2.05954 + 1.40417i −0.921054 + 0.627964i −0.928229 0.372010i \(-0.878669\pi\)
0.00717441 + 0.999974i \(0.497716\pi\)
\(6\) 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 −0.947313 0.320311i \(-0.896213\pi\)
0.999639 0.0268550i \(-0.00854922\pi\)
\(12\) 0 0
\(13\) 1.20405 + 0.960194i 0.333942 + 0.266310i 0.776076 0.630639i \(-0.217207\pi\)
−0.442134 + 0.896949i \(0.645779\pi\)
\(14\) 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 \(-0.492720\pi\)
0.582069 + 0.813140i \(0.302244\pi\)
\(18\) 0 0
\(19\) 0.129636 + 0.0748453i 0.0297405 + 0.0171707i 0.514797 0.857312i \(-0.327867\pi\)
−0.485056 + 0.874483i \(0.661201\pi\)
\(20\) −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 \(-0.863085\pi\)
0.985876 + 0.167476i \(0.0535617\pi\)
\(24\) 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 \(-0.404127\pi\)
−0.147069 + 0.989126i \(0.546984\pi\)
\(30\) 0 0
\(31\) 8.87043 5.12134i 1.59318 0.919820i 0.600418 0.799687i \(-0.295001\pi\)
0.992758 0.120134i \(-0.0383323\pi\)
\(32\) −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 0.834706 + 0.550695i \(0.185637\pi\)
0.611533 + 0.791219i \(0.290553\pi\)
\(38\) −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 \(-0.153873\pi\)
0.188656 + 0.982043i \(0.439587\pi\)
\(42\) 0 0
\(43\) −9.17465 + 4.41828i −1.39912 + 0.673781i −0.972983 0.230877i \(-0.925841\pi\)
−0.426138 + 0.904658i \(0.640126\pi\)
\(44\) −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 \(-0.0265905\pi\)
−0.787249 + 0.616635i \(0.788495\pi\)
\(48\) 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 \(-0.312342\pi\)
−0.870417 + 0.492314i \(0.836151\pi\)
\(54\) 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 \(-0.0631920\pi\)
0.174577 + 0.984644i \(0.444144\pi\)
\(60\) 0 0
\(61\) 2.83787 3.05850i 0.363352 0.391601i −0.524742 0.851261i \(-0.675838\pi\)
0.888095 + 0.459660i \(0.152029\pi\)
\(62\) −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 −0.999895 0.0144772i \(-0.995392\pi\)
0.487410 0.873173i \(-0.337942\pi\)
\(68\) 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 \(-0.235606\pi\)
0.957848 + 0.287275i \(0.0927492\pi\)
\(72\) 0 0
\(73\) 10.1462 + 3.98209i 1.18752 + 0.466068i 0.875131 0.483885i \(-0.160775\pi\)
0.312391 + 0.949954i \(0.398870\pi\)
\(74\) −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 −0.895338 0.445387i \(-0.853066\pi\)
0.833386 + 0.552692i \(0.186399\pi\)
\(80\) −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 \(-0.320188\pi\)
−0.942589 + 0.333956i \(0.891616\pi\)
\(84\) 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 \(-0.388143\pi\)
0.605669 + 0.795716i \(0.292905\pi\)
\(90\) 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 \(-0.836146\pi\)
0.870410 0.492328i \(-0.163854\pi\)
\(98\) −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 −0.911851 0.410521i \(-0.865347\pi\)
0.840482 0.541840i \(-0.182272\pi\)
\(102\) 0 0
\(103\) −7.09042 10.3997i −0.698640 1.02472i −0.997517 0.0704251i \(-0.977564\pi\)
0.298877 0.954292i \(-0.403388\pi\)
\(104\) −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 −0.939001 0.343915i \(-0.888247\pi\)
0.795913 0.605411i \(-0.206991\pi\)
\(108\) 0 0
\(109\) −9.55463 1.44013i −0.915168 0.137939i −0.325460 0.945556i \(-0.605519\pi\)
−0.589708 + 0.807617i \(0.700757\pi\)
\(110\) −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 \(-0.895891\pi\)
0.102489 + 0.994734i \(0.467319\pi\)
\(114\) 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 −0.859908 0.510449i \(-0.829479\pi\)
0.996226 0.0867987i \(-0.0276637\pi\)
\(128\) −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 0.779754 + 0.626086i \(0.215344\pi\)
−0.864358 + 0.502877i \(0.832275\pi\)
\(132\) 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 −0.198498 + 0.980101i \(0.563606\pi\)
−0.839831 + 0.542848i \(0.817346\pi\)
\(138\) 0 0
\(139\) −1.62745 + 3.37944i −0.138039 + 0.286640i −0.958516 0.285039i \(-0.907993\pi\)
0.820477 + 0.571679i \(0.193708\pi\)
\(140\) 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 \(-0.480276\pi\)
0.724262 + 0.689525i \(0.242181\pi\)
\(150\) 0 0
\(151\) 9.91135 9.19639i 0.806575 0.748392i −0.164703 0.986343i \(-0.552666\pi\)
0.971277 + 0.237951i \(0.0764759\pi\)
\(152\) −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 −0.248624 0.968600i \(-0.579978\pi\)
0.992477 0.122432i \(-0.0390692\pi\)
\(158\) 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 −0.989118 0.147121i \(-0.952999\pi\)
0.999998 + 0.00194228i \(0.000618246\pi\)
\(164\) 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 −0.772851 0.634588i \(-0.781170\pi\)
0.971652 0.236416i \(-0.0759730\pi\)
\(168\) 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 \(-0.348203\pi\)
−0.121215 + 0.992626i \(0.538679\pi\)
\(174\) 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 0.812146 + 0.583454i \(0.198299\pi\)
−0.342355 + 0.939571i \(0.611224\pi\)
\(180\) 0 0
\(181\) −7.58961 + 6.05251i −0.564132 + 0.449880i −0.863565 0.504237i \(-0.831774\pi\)
0.299434 + 0.954117i \(0.403202\pi\)
\(182\) 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 \(-0.00592315\pi\)
−0.382599 + 0.923915i \(0.624971\pi\)
\(192\) 0 0
\(193\) 0.567028 + 7.56646i 0.0408155 + 0.544645i 0.979707 + 0.200433i \(0.0642350\pi\)
−0.938892 + 0.344212i \(0.888146\pi\)
\(194\) 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 −0.477370 0.878703i \(-0.658410\pi\)
−0.341074 + 0.940036i \(0.610791\pi\)
\(200\) 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 0.959931 0.280238i \(-0.0904134\pi\)
−0.486817 + 0.873504i \(0.661842\pi\)
\(212\) −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 0.852799 0.522240i \(-0.174903\pi\)
0.994936 + 0.100506i \(0.0320462\pi\)
\(224\) −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 \(-0.153157\pi\)
−0.844031 + 0.536294i \(0.819824\pi\)
\(228\) 0 0
\(229\) −19.7036 1.47658i −1.30205 0.0975752i −0.594418 0.804156i \(-0.702618\pi\)
−0.707632 + 0.706581i \(0.750237\pi\)
\(230\) −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 \(-0.780720\pi\)
0.691591 + 0.722289i \(0.256910\pi\)
\(234\) 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 \(-0.268263\pi\)
−0.998498 + 0.0547961i \(0.982549\pi\)
\(240\) 0 0
\(241\) 11.4016 + 12.2880i 0.734443 + 0.791541i 0.984255 0.176753i \(-0.0565595\pi\)
−0.249813 + 0.968294i \(0.580369\pi\)
\(242\) −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 \(-0.318570\pi\)
0.994678 + 0.103037i \(0.0328560\pi\)
\(252\) 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 \(-0.0734133\pi\)
−0.155205 + 0.987882i \(0.549604\pi\)
\(258\) 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 \(-0.593105\pi\)
0.685069 + 0.728478i \(0.259772\pi\)
\(264\) 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 \(-0.998823\pi\)
0.735562 + 0.677458i \(0.236918\pi\)
\(270\) 0 0
\(271\) −1.31490 + 4.26279i −0.0798742 + 0.258946i −0.986698 0.162564i \(-0.948024\pi\)
0.906824 + 0.421510i \(0.138500\pi\)
\(272\) 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 −0.328562 0.944482i \(-0.606564\pi\)
0.260575 + 0.965453i \(0.416088\pi\)
\(278\) 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 −0.988249 0.152851i \(-0.951154\pi\)
−0.368925 0.929459i \(-0.620274\pi\)
\(282\) 0 0
\(283\) −0.0238140 + 0.157995i −0.00141559 + 0.00939185i −0.989527 0.144345i \(-0.953893\pi\)
0.988112 + 0.153737i \(0.0491307\pi\)
\(284\) 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 0.918223 0.396065i \(-0.129624\pi\)
−0.181811 + 0.983334i \(0.558196\pi\)
\(308\) −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 \(-0.751568\pi\)
−0.190751 + 0.981639i \(0.561092\pi\)
\(312\) 0 0
\(313\) 19.7180 + 11.3842i 1.11452 + 0.643471i 0.939998 0.341181i \(-0.110827\pi\)
0.174527 + 0.984652i \(0.444160\pi\)
\(314\) −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 \(-0.931615\pi\)
0.927338 + 0.374225i \(0.122091\pi\)
\(318\) 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 0.996199 + 0.0871010i \(0.0277603\pi\)
0.161304 + 0.986905i \(0.448430\pi\)
\(332\) −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 −0.848477 0.529232i \(-0.822480\pi\)
−0.115246 + 0.993337i \(0.536766\pi\)
\(338\) 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 \(-0.290663\pi\)
−0.834896 + 0.550407i \(0.814472\pi\)
\(348\) 0 0
\(349\) 0.995638 + 2.06746i 0.0532953 + 0.110669i 0.925916 0.377730i \(-0.123295\pi\)
−0.872620 + 0.488399i \(0.837581\pi\)
\(350\) 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 \(-0.0624311\pi\)
0.176930 + 0.984223i \(0.443383\pi\)
\(354\) 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 \(-0.791053\pi\)
−0.874290 + 0.485404i \(0.838672\pi\)
\(360\) 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 0.318320 0.947983i \(-0.396881\pi\)
−0.411448 + 0.911433i \(0.634977\pi\)
\(368\) 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 −0.875294 0.483592i \(-0.839332\pi\)
0.856450 + 0.516231i \(0.172665\pi\)
\(374\) 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 −0.900192 0.435493i \(-0.856574\pi\)
0.624886 + 0.780716i \(0.285145\pi\)
\(380\) −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 \(-0.358695\pi\)
0.676590 + 0.736360i \(0.263457\pi\)
\(384\) 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 \(-0.560343\pi\)
−0.0399637 + 0.999201i \(0.512724\pi\)
\(390\) 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 0.991510 + 0.130028i \(0.0415067\pi\)
−0.241200 + 0.970475i \(0.577541\pi\)
\(398\) 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 0.999198 + 0.0400316i \(0.0127459\pi\)
−0.943007 + 0.332772i \(0.892016\pi\)
\(402\) 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 0.865188 0.501448i \(-0.167199\pi\)
−0.997327 + 0.0730615i \(0.976723\pi\)
\(410\) 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 −0.999487 0.0320196i \(-0.989806\pi\)
0.886614 0.462510i \(-0.153051\pi\)
\(420\) 0 0
\(421\) −1.40068 + 6.13680i −0.0682652 + 0.299089i −0.997523 0.0703429i \(-0.977591\pi\)
0.929258 + 0.369432i \(0.120448\pi\)
\(422\) −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 0.0718526 0.997415i \(-0.477109\pi\)
0.902217 0.431282i \(-0.141939\pi\)
\(432\) 0 0
\(433\) −7.73903 + 16.0703i −0.371914 + 0.772287i −0.999983 0.00587067i \(-0.998131\pi\)
0.628069 + 0.778158i \(0.283846\pi\)
\(434\) 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 −0.350999 0.936376i \(-0.614158\pi\)
0.379597 + 0.925152i \(0.376063\pi\)
\(440\) −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 \(-0.829544\pi\)
−0.283357 + 0.959014i \(0.591448\pi\)
\(444\) 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 \(-0.859931\pi\)
0.897134 + 0.441760i \(0.145646\pi\)
\(450\) 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 0.923847 + 0.382763i \(0.125027\pi\)
−0.970576 + 0.240796i \(0.922592\pi\)
\(458\) 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 −0.701165 0.712999i \(-0.747337\pi\)
0.941087 0.338165i \(-0.109806\pi\)
\(462\) 0 0
\(463\) 0.200977 + 0.880537i 0.00934018 + 0.0409220i 0.979383 0.202011i \(-0.0647476\pi\)
−0.970043 + 0.242933i \(0.921891\pi\)
\(464\) −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 \(-0.369343\pi\)
−0.186823 + 0.982394i \(0.559819\pi\)
\(468\) 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 \(-0.216688\pi\)
0.557070 + 0.830466i \(0.311926\pi\)
\(480\) 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 −0.994047 0.108952i \(-0.965251\pi\)
0.966706 0.255890i \(-0.0823684\pi\)
\(488\) 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 −0.740931 0.671581i \(-0.765616\pi\)
−0.510062 + 0.860138i \(0.670377\pi\)
\(500\) −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 \(-0.674339\pi\)
0.948191 + 0.317700i \(0.102911\pi\)
\(504\) 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 0.483897 + 0.875125i \(0.339221\pi\)
−0.999829 + 0.0184959i \(0.994112\pi\)
\(510\) 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 −0.728662 0.684874i \(-0.759857\pi\)
−0.228787 0.973477i \(-0.573476\pi\)
\(522\) 0 0
\(523\) 2.70012 + 0.202346i 0.118068 + 0.00884796i 0.133633 0.991031i \(-0.457336\pi\)
−0.0155651 + 0.999879i \(0.504955\pi\)
\(524\) 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 1.00000 0.000210854i \(-6.71170e-5\pi\)
−0.733195 + 0.680018i \(0.761972\pi\)
\(542\) −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 0.508201 0.861238i \(-0.330311\pi\)
−0.356485 + 0.934301i \(0.616025\pi\)
\(548\) 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 \(-0.944950\pi\)
−0.343511 + 0.939149i \(0.611616\pi\)
\(558\) 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 0.0949374 + 0.995483i \(0.469735\pi\)
−0.746695 + 0.665167i \(0.768360\pi\)
\(564\) 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 \(-0.256013\pi\)
−0.277019 + 0.960864i \(0.589346\pi\)
\(570\) 0 0
\(571\) 13.1509 4.05652i 0.550348 0.169760i −0.00709536 0.999975i \(-0.502259\pi\)
0.557443 + 0.830215i \(0.311782\pi\)
\(572\) 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 −0.862826 0.505502i \(-0.831307\pi\)
0.973492 0.228721i \(-0.0734544\pi\)
\(578\) 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 −0.551965 0.833868i \(-0.686122\pi\)
0.574570 + 0.818455i \(0.305169\pi\)
\(594\) 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 −0.934886 0.354947i \(-0.884499\pi\)
0.997975 0.0636149i \(-0.0202629\pi\)
\(600\) 0 0
\(601\) −37.7417 30.0980i −1.53952 1.22772i −0.878904 0.476999i \(-0.841725\pi\)
−0.660614 0.750726i \(-0.729704\pi\)
\(602\) −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 −0.216880 0.976198i \(-0.569588\pi\)
−0.953853 + 0.300275i \(0.902921\pi\)
\(608\) 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 −0.829945 0.557845i \(-0.811628\pi\)
0.987824 + 0.155577i \(0.0497236\pi\)
\(614\) −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 \(-0.497014\pi\)
−0.425414 + 0.904999i \(0.639871\pi\)
\(618\) 0 0
\(619\) 19.2455 11.1114i 0.773542 0.446605i −0.0605948 0.998162i \(-0.519300\pi\)
0.834137 + 0.551558i \(0.185966\pi\)
\(620\) 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 −0.826312 0.563213i \(-0.809565\pi\)
−0.0748589 + 0.997194i \(0.523851\pi\)
\(632\) −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 \(-0.177641\pi\)
−0.591466 + 0.806330i \(0.701451\pi\)
\(642\) 0 0
\(643\) 0.0302707 + 0.0628578i 0.00119376 + 0.00247887i 0.901565 0.432644i \(-0.142419\pi\)
−0.900371 + 0.435123i \(0.856705\pi\)
\(644\) −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 \(-0.218303\pi\)
−0.306791 + 0.951777i \(0.599255\pi\)
\(648\) 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 \(-0.518268\pi\)
−0.205515 + 0.978654i \(0.565887\pi\)
\(654\) 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 \(-0.485662\pi\)
0.474014 + 0.880517i \(0.342805\pi\)
\(660\) 0 0
\(661\) −14.5956 5.72834i −0.567702 0.222807i 0.0640904 0.997944i \(-0.479585\pi\)
−0.631793 + 0.775137i \(0.717681\pi\)
\(662\) −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 0.237263 0.971446i \(-0.423750\pi\)
0.894293 0.447481i \(-0.147679\pi\)
\(674\) 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 \(-0.244972\pi\)
0.891386 + 0.453244i \(0.149734\pi\)
\(678\) 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 \(-0.671525\pi\)
−0.379507 + 0.925189i \(0.623906\pi\)
\(684\) 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 0.637371 0.770557i \(-0.280022\pi\)
−0.950149 + 0.311796i \(0.899069\pi\)
\(692\) 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 \(-0.530667\pi\)
0.949002 + 0.315270i \(0.102095\pi\)
\(702\) 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 0.183437 0.983031i \(-0.441278\pi\)
−0.402198 + 0.915553i \(0.631754\pi\)
\(710\) 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 0.984867 + 0.173314i \(0.0554476\pi\)
−0.999698 + 0.0245915i \(0.992171\pi\)
\(720\) 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 0.401281 + 0.915955i \(0.368565\pi\)
−0.966317 + 0.257354i \(0.917149\pi\)
\(728\) 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 0.561849 0.827240i \(-0.310090\pi\)
0.974530 + 0.224256i \(0.0719951\pi\)
\(734\) 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 0.0348413 0.999393i \(-0.488907\pi\)
0.999202 + 0.0399408i \(0.0127169\pi\)
\(740\) −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 −0.524006 0.851715i \(-0.675563\pi\)
0.992610 0.121351i \(-0.0387228\pi\)
\(744\) 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 −0.773002 0.634404i \(-0.781246\pi\)
0.858921 0.512108i \(-0.171135\pi\)
\(752\) −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 0.856576 + 0.516021i \(0.172587\pi\)
−0.547855 + 0.836573i \(0.684555\pi\)
\(758\) 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 \(-0.449633\pi\)
−0.426090 + 0.904681i \(0.640109\pi\)
\(762\) 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 −0.901867 0.432013i \(-0.857804\pi\)
0.220497 + 0.975388i \(0.429232\pi\)
\(770\) 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 \(-0.457357\pi\)
−0.164481 + 0.986380i \(0.552595\pi\)
\(774\) 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 0.486098 0.873904i \(-0.338420\pi\)
0.610918 + 0.791694i \(0.290801\pi\)