Properties

Label 804.2.s.b.5.6
Level 804
Weight 2
Character 804.5
Analytic conductor 6.420
Analytic rank 0
Dimension 200
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.s (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(20\) over \(\Q(\zeta_{22})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.6
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.17979 - 1.26810i) q^{3} +(2.83063 - 0.831147i) q^{5} +(-2.86249 - 2.48036i) q^{7} +(-0.216176 + 2.99220i) q^{9} +O(q^{10})\) \(q+(-1.17979 - 1.26810i) q^{3} +(2.83063 - 0.831147i) q^{5} +(-2.86249 - 2.48036i) q^{7} +(-0.216176 + 2.99220i) q^{9} +(-3.88931 + 1.14200i) q^{11} +(-0.777890 - 1.21042i) q^{13} +(-4.39353 - 2.60895i) q^{15} +(-5.27916 - 0.759028i) q^{17} +(-0.130434 - 0.150529i) q^{19} +(0.231790 + 6.55625i) q^{21} +(0.694228 - 0.317043i) q^{23} +(3.11537 - 2.00213i) q^{25} +(4.04946 - 3.25605i) q^{27} +8.71464i q^{29} +(3.86518 - 6.01434i) q^{31} +(6.03676 + 3.58472i) q^{33} +(-10.1642 - 4.64183i) q^{35} -2.50144 q^{37} +(-0.617189 + 2.41449i) q^{39} +(-0.0416445 + 0.289644i) q^{41} +(-6.85998 - 0.986316i) q^{43} +(1.87505 + 8.64948i) q^{45} +(-6.89272 + 3.14780i) q^{47} +(1.04545 + 7.27129i) q^{49} +(5.26579 + 7.59001i) q^{51} +(-0.173569 - 1.20720i) q^{53} +(-10.0600 + 6.46518i) q^{55} +(-0.0370010 + 0.342996i) q^{57} +(0.206913 - 0.321963i) q^{59} +(3.48314 - 11.8625i) q^{61} +(8.04055 - 8.02896i) q^{63} +(-3.20795 - 2.77971i) q^{65} +(-8.15987 + 0.645356i) q^{67} +(-1.22109 - 0.506307i) q^{69} +(-0.756392 + 0.108753i) q^{71} +(-11.2432 - 3.30131i) q^{73} +(-6.21440 - 1.58852i) q^{75} +(13.9657 + 6.37792i) q^{77} +(8.00157 + 12.4507i) q^{79} +(-8.90654 - 1.29368i) q^{81} +(-3.51473 - 11.9701i) q^{83} +(-15.5742 + 2.23923i) q^{85} +(11.0511 - 10.2815i) q^{87} +(-0.0142974 - 0.00652940i) q^{89} +(-0.775578 + 5.39427i) q^{91} +(-12.1869 + 2.19423i) q^{93} +(-0.494321 - 0.317681i) q^{95} -15.9958i q^{97} +(-2.57633 - 11.8845i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{22}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.17979 1.26810i −0.681154 0.732140i
\(4\) 0 0
\(5\) 2.83063 0.831147i 1.26589 0.371700i 0.421209 0.906964i \(-0.361606\pi\)
0.844685 + 0.535263i \(0.179788\pi\)
\(6\) 0 0
\(7\) −2.86249 2.48036i −1.08192 0.937489i −0.0836625 0.996494i \(-0.526662\pi\)
−0.998258 + 0.0590050i \(0.981207\pi\)
\(8\) 0 0
\(9\) −0.216176 + 2.99220i −0.0720585 + 0.997400i
\(10\) 0 0
\(11\) −3.88931 + 1.14200i −1.17267 + 0.344327i −0.809344 0.587334i \(-0.800177\pi\)
−0.363327 + 0.931662i \(0.618359\pi\)
\(12\) 0 0
\(13\) −0.777890 1.21042i −0.215748 0.335710i 0.716464 0.697625i \(-0.245760\pi\)
−0.932211 + 0.361914i \(0.882123\pi\)
\(14\) 0 0
\(15\) −4.39353 2.60895i −1.13441 0.673627i
\(16\) 0 0
\(17\) −5.27916 0.759028i −1.28038 0.184091i −0.531651 0.846964i \(-0.678428\pi\)
−0.748732 + 0.662872i \(0.769337\pi\)
\(18\) 0 0
\(19\) −0.130434 0.150529i −0.0299236 0.0345336i 0.740591 0.671957i \(-0.234546\pi\)
−0.770514 + 0.637423i \(0.780000\pi\)
\(20\) 0 0
\(21\) 0.231790 + 6.55625i 0.0505807 + 1.43069i
\(22\) 0 0
\(23\) 0.694228 0.317043i 0.144756 0.0661081i −0.341720 0.939802i \(-0.611009\pi\)
0.486476 + 0.873694i \(0.338282\pi\)
\(24\) 0 0
\(25\) 3.11537 2.00213i 0.623074 0.400425i
\(26\) 0 0
\(27\) 4.04946 3.25605i 0.779320 0.626626i
\(28\) 0 0
\(29\) 8.71464i 1.61827i 0.587624 + 0.809134i \(0.300063\pi\)
−0.587624 + 0.809134i \(0.699937\pi\)
\(30\) 0 0
\(31\) 3.86518 6.01434i 0.694207 1.08021i −0.297873 0.954605i \(-0.596277\pi\)
0.992081 0.125602i \(-0.0400864\pi\)
\(32\) 0 0
\(33\) 6.03676 + 3.58472i 1.05087 + 0.624020i
\(34\) 0 0
\(35\) −10.1642 4.64183i −1.71806 0.784612i
\(36\) 0 0
\(37\) −2.50144 −0.411234 −0.205617 0.978633i \(-0.565920\pi\)
−0.205617 + 0.978633i \(0.565920\pi\)
\(38\) 0 0
\(39\) −0.617189 + 2.41449i −0.0988294 + 0.386628i
\(40\) 0 0
\(41\) −0.0416445 + 0.289644i −0.00650378 + 0.0452348i −0.992815 0.119660i \(-0.961819\pi\)
0.986311 + 0.164895i \(0.0527286\pi\)
\(42\) 0 0
\(43\) −6.85998 0.986316i −1.04614 0.150412i −0.402248 0.915531i \(-0.631771\pi\)
−0.643889 + 0.765119i \(0.722680\pi\)
\(44\) 0 0
\(45\) 1.87505 + 8.64948i 0.279515 + 1.28939i
\(46\) 0 0
\(47\) −6.89272 + 3.14780i −1.00541 + 0.459154i −0.848917 0.528526i \(-0.822745\pi\)
−0.156489 + 0.987680i \(0.550018\pi\)
\(48\) 0 0
\(49\) 1.04545 + 7.27129i 0.149351 + 1.03876i
\(50\) 0 0
\(51\) 5.26579 + 7.59001i 0.737357 + 1.06281i
\(52\) 0 0
\(53\) −0.173569 1.20720i −0.0238415 0.165821i 0.974422 0.224725i \(-0.0721485\pi\)
−0.998264 + 0.0589041i \(0.981239\pi\)
\(54\) 0 0
\(55\) −10.0600 + 6.46518i −1.35649 + 0.871764i
\(56\) 0 0
\(57\) −0.0370010 + 0.342996i −0.00490091 + 0.0454310i
\(58\) 0 0
\(59\) 0.206913 0.321963i 0.0269378 0.0419160i −0.827524 0.561431i \(-0.810251\pi\)
0.854461 + 0.519515i \(0.173887\pi\)
\(60\) 0 0
\(61\) 3.48314 11.8625i 0.445970 1.51883i −0.363456 0.931612i \(-0.618403\pi\)
0.809425 0.587223i \(-0.199779\pi\)
\(62\) 0 0
\(63\) 8.04055 8.02896i 1.01301 1.01155i
\(64\) 0 0
\(65\) −3.20795 2.77971i −0.397897 0.344780i
\(66\) 0 0
\(67\) −8.15987 + 0.645356i −0.996887 + 0.0788428i
\(68\) 0 0
\(69\) −1.22109 0.506307i −0.147002 0.0609523i
\(70\) 0 0
\(71\) −0.756392 + 0.108753i −0.0897672 + 0.0129066i −0.187052 0.982350i \(-0.559893\pi\)
0.0972849 + 0.995257i \(0.468984\pi\)
\(72\) 0 0
\(73\) −11.2432 3.30131i −1.31592 0.386390i −0.452903 0.891560i \(-0.649612\pi\)
−0.863020 + 0.505170i \(0.831430\pi\)
\(74\) 0 0
\(75\) −6.21440 1.58852i −0.717577 0.183426i
\(76\) 0 0
\(77\) 13.9657 + 6.37792i 1.59154 + 0.726832i
\(78\) 0 0
\(79\) 8.00157 + 12.4507i 0.900247 + 1.40081i 0.916105 + 0.400938i \(0.131316\pi\)
−0.0158579 + 0.999874i \(0.505048\pi\)
\(80\) 0 0
\(81\) −8.90654 1.29368i −0.989615 0.143742i
\(82\) 0 0
\(83\) −3.51473 11.9701i −0.385792 1.31389i −0.892219 0.451603i \(-0.850852\pi\)
0.506428 0.862282i \(-0.330966\pi\)
\(84\) 0 0
\(85\) −15.5742 + 2.23923i −1.68926 + 0.242878i
\(86\) 0 0
\(87\) 11.0511 10.2815i 1.18480 1.10229i
\(88\) 0 0
\(89\) −0.0142974 0.00652940i −0.00151552 0.000692115i 0.414657 0.909978i \(-0.363902\pi\)
−0.416173 + 0.909286i \(0.636629\pi\)
\(90\) 0 0
\(91\) −0.775578 + 5.39427i −0.0813027 + 0.565473i
\(92\) 0 0
\(93\) −12.1869 + 2.19423i −1.26373 + 0.227531i
\(94\) 0 0
\(95\) −0.494321 0.317681i −0.0507162 0.0325933i
\(96\) 0 0
\(97\) 15.9958i 1.62413i −0.583566 0.812066i \(-0.698343\pi\)
0.583566 0.812066i \(-0.301657\pi\)
\(98\) 0 0
\(99\) −2.57633 11.8845i −0.258931 1.19443i
\(100\) 0 0
\(101\) 9.07482 + 10.4729i 0.902979 + 1.04209i 0.998909 + 0.0467048i \(0.0148720\pi\)
−0.0959301 + 0.995388i \(0.530583\pi\)
\(102\) 0 0
\(103\) 0.156435 + 0.100534i 0.0154140 + 0.00990596i 0.548325 0.836265i \(-0.315266\pi\)
−0.532911 + 0.846171i \(0.678902\pi\)
\(104\) 0 0
\(105\) 6.10532 + 18.3656i 0.595818 + 1.79230i
\(106\) 0 0
\(107\) −3.20448 + 10.9135i −0.309789 + 1.05504i 0.646571 + 0.762854i \(0.276202\pi\)
−0.956360 + 0.292191i \(0.905616\pi\)
\(108\) 0 0
\(109\) −7.91640 12.3182i −0.758254 1.17987i −0.978866 0.204504i \(-0.934442\pi\)
0.220612 0.975362i \(-0.429195\pi\)
\(110\) 0 0
\(111\) 2.95118 + 3.17209i 0.280114 + 0.301081i
\(112\) 0 0
\(113\) 13.2015 + 3.87631i 1.24189 + 0.364653i 0.835726 0.549147i \(-0.185047\pi\)
0.406166 + 0.913799i \(0.366865\pi\)
\(114\) 0 0
\(115\) 1.70159 1.47444i 0.158674 0.137492i
\(116\) 0 0
\(117\) 3.78998 2.06594i 0.350384 0.190996i
\(118\) 0 0
\(119\) 13.2289 + 15.2669i 1.21269 + 1.39952i
\(120\) 0 0
\(121\) 4.56877 2.93617i 0.415343 0.266925i
\(122\) 0 0
\(123\) 0.416431 0.288911i 0.0375483 0.0260502i
\(124\) 0 0
\(125\) −2.50523 + 2.89118i −0.224074 + 0.258595i
\(126\) 0 0
\(127\) 2.59056 2.98967i 0.229875 0.265290i −0.629080 0.777340i \(-0.716568\pi\)
0.858956 + 0.512050i \(0.171114\pi\)
\(128\) 0 0
\(129\) 6.84261 + 9.86282i 0.602458 + 0.868372i
\(130\) 0 0
\(131\) 3.04712 1.39157i 0.266228 0.121582i −0.277829 0.960631i \(-0.589615\pi\)
0.544057 + 0.839048i \(0.316888\pi\)
\(132\) 0 0
\(133\) 0.754410i 0.0654157i
\(134\) 0 0
\(135\) 8.75627 12.5823i 0.753620 1.08292i
\(136\) 0 0
\(137\) −6.27585 13.7422i −0.536182 1.17407i −0.962942 0.269710i \(-0.913072\pi\)
0.426760 0.904365i \(-0.359655\pi\)
\(138\) 0 0
\(139\) −4.37634 14.9044i −0.371196 1.26418i −0.907464 0.420130i \(-0.861985\pi\)
0.536268 0.844048i \(-0.319834\pi\)
\(140\) 0 0
\(141\) 12.1237 + 5.02693i 1.02100 + 0.423344i
\(142\) 0 0
\(143\) 4.40776 + 3.81935i 0.368595 + 0.319390i
\(144\) 0 0
\(145\) 7.24315 + 24.6679i 0.601510 + 2.04856i
\(146\) 0 0
\(147\) 7.98733 9.90436i 0.658784 0.816898i
\(148\) 0 0
\(149\) 13.7776 11.9383i 1.12870 0.978026i 0.128795 0.991671i \(-0.458889\pi\)
0.999907 + 0.0136454i \(0.00434360\pi\)
\(150\) 0 0
\(151\) −0.470875 + 3.27501i −0.0383192 + 0.266516i −0.999970 0.00776115i \(-0.997530\pi\)
0.961651 + 0.274277i \(0.0884386\pi\)
\(152\) 0 0
\(153\) 3.41239 15.6322i 0.275875 1.26379i
\(154\) 0 0
\(155\) 5.94209 20.2369i 0.477280 1.62547i
\(156\) 0 0
\(157\) −4.94188 10.8212i −0.394405 0.863626i −0.997807 0.0661893i \(-0.978916\pi\)
0.603402 0.797437i \(-0.293811\pi\)
\(158\) 0 0
\(159\) −1.32607 + 1.64434i −0.105165 + 0.130405i
\(160\) 0 0
\(161\) −2.77360 0.814403i −0.218591 0.0641840i
\(162\) 0 0
\(163\) 17.8684 1.39956 0.699781 0.714357i \(-0.253281\pi\)
0.699781 + 0.714357i \(0.253281\pi\)
\(164\) 0 0
\(165\) 20.0672 + 5.12957i 1.56223 + 0.399336i
\(166\) 0 0
\(167\) 0.518218 0.449039i 0.0401009 0.0347477i −0.634580 0.772857i \(-0.718827\pi\)
0.674681 + 0.738110i \(0.264281\pi\)
\(168\) 0 0
\(169\) 4.54039 9.94207i 0.349261 0.764775i
\(170\) 0 0
\(171\) 0.478609 0.357744i 0.0366001 0.0273573i
\(172\) 0 0
\(173\) 11.6014 18.0521i 0.882037 1.37248i −0.0455864 0.998960i \(-0.514516\pi\)
0.927624 0.373516i \(-0.121848\pi\)
\(174\) 0 0
\(175\) −13.8837 1.99618i −1.04951 0.150897i
\(176\) 0 0
\(177\) −0.652398 + 0.117463i −0.0490372 + 0.00882903i
\(178\) 0 0
\(179\) −1.38815 + 3.03963i −0.103755 + 0.227192i −0.954389 0.298567i \(-0.903491\pi\)
0.850633 + 0.525759i \(0.176219\pi\)
\(180\) 0 0
\(181\) −1.03125 2.25813i −0.0766526 0.167846i 0.867426 0.497566i \(-0.165773\pi\)
−0.944079 + 0.329720i \(0.893046\pi\)
\(182\) 0 0
\(183\) −19.1522 + 9.57829i −1.41577 + 0.708047i
\(184\) 0 0
\(185\) −7.08064 + 2.07906i −0.520579 + 0.152856i
\(186\) 0 0
\(187\) 21.3991 3.07672i 1.56486 0.224992i
\(188\) 0 0
\(189\) −19.6677 0.723740i −1.43062 0.0526443i
\(190\) 0 0
\(191\) 2.31794 5.07558i 0.167720 0.367256i −0.807045 0.590491i \(-0.798934\pi\)
0.974765 + 0.223235i \(0.0716616\pi\)
\(192\) 0 0
\(193\) 17.2923 + 11.1131i 1.24473 + 0.799938i 0.986118 0.166044i \(-0.0530994\pi\)
0.258609 + 0.965982i \(0.416736\pi\)
\(194\) 0 0
\(195\) 0.259763 + 7.34749i 0.0186020 + 0.526165i
\(196\) 0 0
\(197\) −0.352396 2.45097i −0.0251072 0.174624i 0.973409 0.229072i \(-0.0735692\pi\)
−0.998517 + 0.0544480i \(0.982660\pi\)
\(198\) 0 0
\(199\) −3.29690 + 3.80483i −0.233711 + 0.269717i −0.860476 0.509492i \(-0.829833\pi\)
0.626764 + 0.779209i \(0.284379\pi\)
\(200\) 0 0
\(201\) 10.4453 + 9.58618i 0.736758 + 0.676157i
\(202\) 0 0
\(203\) 21.6155 24.9456i 1.51711 1.75084i
\(204\) 0 0
\(205\) 0.122857 + 0.854487i 0.00858068 + 0.0596800i
\(206\) 0 0
\(207\) 0.798582 + 2.14581i 0.0555053 + 0.149144i
\(208\) 0 0
\(209\) 0.679202 + 0.436497i 0.0469814 + 0.0301931i
\(210\) 0 0
\(211\) −9.04523 + 19.8063i −0.622699 + 1.36352i 0.290840 + 0.956772i \(0.406065\pi\)
−0.913540 + 0.406750i \(0.866662\pi\)
\(212\) 0 0
\(213\) 1.03030 + 0.830878i 0.0705947 + 0.0569308i
\(214\) 0 0
\(215\) −20.2378 + 2.90976i −1.38021 + 0.198444i
\(216\) 0 0
\(217\) −25.9818 + 7.62895i −1.76376 + 0.517887i
\(218\) 0 0
\(219\) 9.07830 + 18.1525i 0.613454 + 1.22663i
\(220\) 0 0
\(221\) 3.18786 + 6.98043i 0.214439 + 0.469555i
\(222\) 0 0
\(223\) 9.31921 20.4062i 0.624060 1.36650i −0.288469 0.957489i \(-0.593146\pi\)
0.912529 0.409012i \(-0.134127\pi\)
\(224\) 0 0
\(225\) 5.31730 + 9.75462i 0.354487 + 0.650308i
\(226\) 0 0
\(227\) −4.40653 0.633564i −0.292472 0.0420511i −0.00548275 0.999985i \(-0.501745\pi\)
−0.286989 + 0.957934i \(0.592654\pi\)
\(228\) 0 0
\(229\) 8.29963 12.9145i 0.548455 0.853413i −0.450775 0.892638i \(-0.648852\pi\)
0.999230 + 0.0392245i \(0.0124888\pi\)
\(230\) 0 0
\(231\) −8.38877 25.2346i −0.551941 1.66031i
\(232\) 0 0
\(233\) −5.70613 + 12.4947i −0.373821 + 0.818553i 0.625446 + 0.780267i \(0.284917\pi\)
−0.999267 + 0.0382859i \(0.987810\pi\)
\(234\) 0 0
\(235\) −16.8944 + 14.6391i −1.10207 + 0.954950i
\(236\) 0 0
\(237\) 6.34857 24.8361i 0.412384 1.61328i
\(238\) 0 0
\(239\) −23.3595 −1.51100 −0.755500 0.655148i \(-0.772606\pi\)
−0.755500 + 0.655148i \(0.772606\pi\)
\(240\) 0 0
\(241\) 2.15759 + 0.633526i 0.138983 + 0.0408090i 0.350484 0.936569i \(-0.386017\pi\)
−0.211501 + 0.977378i \(0.567835\pi\)
\(242\) 0 0
\(243\) 8.86735 + 12.8207i 0.568841 + 0.822448i
\(244\) 0 0
\(245\) 9.00280 + 19.7134i 0.575168 + 1.25944i
\(246\) 0 0
\(247\) −0.0807398 + 0.274974i −0.00513735 + 0.0174962i
\(248\) 0 0
\(249\) −11.0326 + 18.5792i −0.699165 + 1.17741i
\(250\) 0 0
\(251\) 2.12352 14.7694i 0.134035 0.932237i −0.806183 0.591666i \(-0.798470\pi\)
0.940219 0.340571i \(-0.110620\pi\)
\(252\) 0 0
\(253\) −2.33800 + 2.02589i −0.146989 + 0.127367i
\(254\) 0 0
\(255\) 21.2139 + 17.1078i 1.32846 + 1.07134i
\(256\) 0 0
\(257\) 3.22142 + 10.9711i 0.200947 + 0.684361i 0.996877 + 0.0789730i \(0.0251641\pi\)
−0.795930 + 0.605389i \(0.793018\pi\)
\(258\) 0 0
\(259\) 7.16035 + 6.20448i 0.444923 + 0.385528i
\(260\) 0 0
\(261\) −26.0760 1.88389i −1.61406 0.116610i
\(262\) 0 0
\(263\) −4.21240 14.3461i −0.259747 0.884619i −0.981337 0.192297i \(-0.938406\pi\)
0.721589 0.692321i \(-0.243412\pi\)
\(264\) 0 0
\(265\) −1.49466 3.27286i −0.0918165 0.201050i
\(266\) 0 0
\(267\) 0.00858801 + 0.0258339i 0.000525578 + 0.00158101i
\(268\) 0 0
\(269\) 20.8104i 1.26884i −0.772990 0.634418i \(-0.781240\pi\)
0.772990 0.634418i \(-0.218760\pi\)
\(270\) 0 0
\(271\) −26.4716 + 12.0892i −1.60804 + 0.734366i −0.998303 0.0582400i \(-0.981451\pi\)
−0.609734 + 0.792606i \(0.708724\pi\)
\(272\) 0 0
\(273\) 7.75551 5.38060i 0.469385 0.325649i
\(274\) 0 0
\(275\) −9.83020 + 11.3447i −0.592784 + 0.684109i
\(276\) 0 0
\(277\) −16.1014 + 18.5820i −0.967440 + 1.11648i 0.0257141 + 0.999669i \(0.491814\pi\)
−0.993154 + 0.116815i \(0.962731\pi\)
\(278\) 0 0
\(279\) 17.1606 + 12.8656i 1.02738 + 0.770241i
\(280\) 0 0
\(281\) −27.7394 + 17.8271i −1.65480 + 1.06347i −0.729681 + 0.683788i \(0.760331\pi\)
−0.925116 + 0.379685i \(0.876032\pi\)
\(282\) 0 0
\(283\) 3.38795 + 3.90990i 0.201393 + 0.232420i 0.847458 0.530863i \(-0.178132\pi\)
−0.646065 + 0.763282i \(0.723587\pi\)
\(284\) 0 0
\(285\) 0.180344 + 1.00165i 0.0106827 + 0.0593325i
\(286\) 0 0
\(287\) 0.837630 0.725810i 0.0494437 0.0428432i
\(288\) 0 0
\(289\) 10.9820 + 3.22460i 0.645999 + 0.189682i
\(290\) 0 0
\(291\) −20.2844 + 18.8718i −1.18909 + 1.10628i
\(292\) 0 0
\(293\) −1.03101 1.60428i −0.0602322 0.0937231i 0.809831 0.586663i \(-0.199559\pi\)
−0.870063 + 0.492940i \(0.835922\pi\)
\(294\) 0 0
\(295\) 0.318095 1.08333i 0.0185202 0.0630741i
\(296\) 0 0
\(297\) −12.0312 + 17.2883i −0.698121 + 1.00317i
\(298\) 0 0
\(299\) −0.923788 0.593682i −0.0534240 0.0343335i
\(300\) 0 0
\(301\) 17.1902 + 19.8386i 0.990827 + 1.14348i
\(302\) 0 0
\(303\) 2.57432 23.8637i 0.147891 1.37093i
\(304\) 0 0
\(305\) 36.4732i 2.08845i
\(306\) 0 0
\(307\) 2.28977 + 1.47155i 0.130684 + 0.0839857i 0.604350 0.796719i \(-0.293433\pi\)
−0.473665 + 0.880705i \(0.657069\pi\)
\(308\) 0 0
\(309\) −0.0570724 0.316985i −0.00324674 0.0180327i
\(310\) 0 0
\(311\) −0.224559 + 1.56184i −0.0127336 + 0.0885639i −0.995197 0.0978904i \(-0.968791\pi\)
0.982464 + 0.186454i \(0.0596996\pi\)
\(312\) 0 0
\(313\) 2.15289 + 0.983191i 0.121688 + 0.0555732i 0.475329 0.879808i \(-0.342329\pi\)
−0.353640 + 0.935381i \(0.615056\pi\)
\(314\) 0 0
\(315\) 16.0865 29.4098i 0.906374 1.65706i
\(316\) 0 0
\(317\) 1.60985 0.231462i 0.0904183 0.0130002i −0.0969572 0.995289i \(-0.530911\pi\)
0.187375 + 0.982288i \(0.440002\pi\)
\(318\) 0 0
\(319\) −9.95216 33.8939i −0.557214 1.89770i
\(320\) 0 0
\(321\) 17.6200 8.81201i 0.983454 0.491839i
\(322\) 0 0
\(323\) 0.574325 + 0.893667i 0.0319563 + 0.0497250i
\(324\) 0 0
\(325\) −4.84683 2.21347i −0.268854 0.122781i
\(326\) 0 0
\(327\) −6.28099 + 24.5717i −0.347340 + 1.35882i
\(328\) 0 0
\(329\) 27.5380 + 8.08590i 1.51822 + 0.445790i
\(330\) 0 0
\(331\) 28.3260 4.07266i 1.55694 0.223853i 0.690570 0.723265i \(-0.257360\pi\)
0.866365 + 0.499412i \(0.166450\pi\)
\(332\) 0 0
\(333\) 0.540750 7.48481i 0.0296329 0.410165i
\(334\) 0 0
\(335\) −22.5612 + 8.60881i −1.23265 + 0.470350i
\(336\) 0 0
\(337\) −15.2316 13.1983i −0.829719 0.718956i 0.132514 0.991181i \(-0.457695\pi\)
−0.962234 + 0.272225i \(0.912240\pi\)
\(338\) 0 0
\(339\) −10.6595 21.3141i −0.578943 1.15762i
\(340\) 0 0
\(341\) −8.16449 + 27.8057i −0.442132 + 1.50576i
\(342\) 0 0
\(343\) 0.708644 1.10267i 0.0382632 0.0595387i
\(344\) 0 0
\(345\) −3.87726 0.418263i −0.208745 0.0225185i
\(346\) 0 0
\(347\) 24.7044 15.8765i 1.32620 0.852297i 0.330399 0.943841i \(-0.392817\pi\)
0.995801 + 0.0915445i \(0.0291804\pi\)
\(348\) 0 0
\(349\) −2.66838 18.5590i −0.142835 0.993439i −0.927581 0.373622i \(-0.878116\pi\)
0.784746 0.619817i \(-0.212793\pi\)
\(350\) 0 0
\(351\) −7.09122 2.36871i −0.378501 0.126432i
\(352\) 0 0
\(353\) 1.25495 + 8.72836i 0.0667942 + 0.464564i 0.995578 + 0.0939411i \(0.0299465\pi\)
−0.928784 + 0.370623i \(0.879144\pi\)
\(354\) 0 0
\(355\) −2.05067 + 0.936511i −0.108838 + 0.0497048i
\(356\) 0 0
\(357\) 3.75272 34.7874i 0.198615 1.84115i
\(358\) 0 0
\(359\) 4.63866 + 0.666939i 0.244819 + 0.0351997i 0.263632 0.964623i \(-0.415080\pi\)
−0.0188128 + 0.999823i \(0.505989\pi\)
\(360\) 0 0
\(361\) 2.69834 18.7673i 0.142018 0.987755i
\(362\) 0 0
\(363\) −9.11358 2.32960i −0.478339 0.122272i
\(364\) 0 0
\(365\) −34.5693 −1.80944
\(366\) 0 0
\(367\) 10.3001 + 4.70390i 0.537661 + 0.245541i 0.665689 0.746229i \(-0.268138\pi\)
−0.128029 + 0.991770i \(0.540865\pi\)
\(368\) 0 0
\(369\) −0.857671 0.187223i −0.0446486 0.00974643i
\(370\) 0 0
\(371\) −2.49745 + 3.88610i −0.129661 + 0.201756i
\(372\) 0 0
\(373\) 27.8273i 1.44084i 0.693538 + 0.720420i \(0.256051\pi\)
−0.693538 + 0.720420i \(0.743949\pi\)
\(374\) 0 0
\(375\) 6.62197 0.234113i 0.341957 0.0120896i
\(376\) 0 0
\(377\) 10.5484 6.77903i 0.543269 0.349138i
\(378\) 0 0
\(379\) 33.4407 15.2718i 1.71773 0.784461i 0.722027 0.691865i \(-0.243210\pi\)
0.995704 0.0925970i \(-0.0295168\pi\)
\(380\) 0 0
\(381\) −6.84754 + 0.242088i −0.350810 + 0.0124025i
\(382\) 0 0
\(383\) 12.5766 + 14.5142i 0.642634 + 0.741639i 0.979838 0.199793i \(-0.0640269\pi\)
−0.337205 + 0.941431i \(0.609481\pi\)
\(384\) 0 0
\(385\) 44.8327 + 6.44597i 2.28488 + 0.328517i
\(386\) 0 0
\(387\) 4.43422 20.3132i 0.225404 1.03258i
\(388\) 0 0
\(389\) 10.8893 + 16.9441i 0.552109 + 0.859098i 0.999377 0.0353022i \(-0.0112394\pi\)
−0.447268 + 0.894400i \(0.647603\pi\)
\(390\) 0 0
\(391\) −3.90558 + 1.14678i −0.197514 + 0.0579952i
\(392\) 0 0
\(393\) −5.35963 2.22230i −0.270357 0.112100i
\(394\) 0 0
\(395\) 32.9978 + 28.5928i 1.66030 + 1.43866i
\(396\) 0 0
\(397\) −12.5930 + 3.69765i −0.632026 + 0.185580i −0.582027 0.813170i \(-0.697740\pi\)
−0.0499993 + 0.998749i \(0.515922\pi\)
\(398\) 0 0
\(399\) 0.956671 0.890048i 0.0478934 0.0445581i
\(400\) 0 0
\(401\) −30.6091 −1.52854 −0.764272 0.644894i \(-0.776901\pi\)
−0.764272 + 0.644894i \(0.776901\pi\)
\(402\) 0 0
\(403\) −10.2866 −0.512410
\(404\) 0 0
\(405\) −26.2863 + 3.74071i −1.30618 + 0.185877i
\(406\) 0 0
\(407\) 9.72888 2.85666i 0.482243 0.141599i
\(408\) 0 0
\(409\) 6.14065 + 5.32091i 0.303636 + 0.263102i 0.793329 0.608793i \(-0.208346\pi\)
−0.489694 + 0.871895i \(0.662891\pi\)
\(410\) 0 0
\(411\) −10.0223 + 24.1714i −0.494365 + 1.19229i
\(412\) 0 0
\(413\) −1.39087 + 0.408397i −0.0684404 + 0.0200959i
\(414\) 0 0
\(415\) −19.8978 30.9615i −0.976743 1.51984i
\(416\) 0 0
\(417\) −13.7372 + 23.1338i −0.672713 + 1.13287i
\(418\) 0 0
\(419\) −19.7307 2.83685i −0.963908 0.138589i −0.357649 0.933856i \(-0.616421\pi\)
−0.606259 + 0.795267i \(0.707331\pi\)
\(420\) 0 0
\(421\) −4.74306 5.47379i −0.231163 0.266776i 0.628304 0.777968i \(-0.283750\pi\)
−0.859467 + 0.511192i \(0.829204\pi\)
\(422\) 0 0
\(423\) −7.92881 21.3049i −0.385512 1.03588i
\(424\) 0 0
\(425\) −17.9662 + 8.20488i −0.871488 + 0.397995i
\(426\) 0 0
\(427\) −39.3937 + 25.3168i −1.90639 + 1.22517i
\(428\) 0 0
\(429\) −0.356918 10.0955i −0.0172322 0.487417i
\(430\) 0 0
\(431\) 10.6012i 0.510640i 0.966857 + 0.255320i \(0.0821809\pi\)
−0.966857 + 0.255320i \(0.917819\pi\)
\(432\) 0 0
\(433\) 12.1735 18.9423i 0.585021 0.910310i −0.414979 0.909831i \(-0.636211\pi\)
1.00000 0.000479079i \(-0.000152496\pi\)
\(434\) 0 0
\(435\) 22.7360 38.2881i 1.09011 1.83577i
\(436\) 0 0
\(437\) −0.138275 0.0631480i −0.00661458 0.00302078i
\(438\) 0 0
\(439\) −13.7539 −0.656438 −0.328219 0.944602i \(-0.606448\pi\)
−0.328219 + 0.944602i \(0.606448\pi\)
\(440\) 0 0
\(441\) −21.9832 + 1.55633i −1.04682 + 0.0741110i
\(442\) 0 0
\(443\) 2.76881 19.2575i 0.131550 0.914950i −0.811985 0.583678i \(-0.801613\pi\)
0.943535 0.331272i \(-0.107478\pi\)
\(444\) 0 0
\(445\) −0.0458975 0.00659906i −0.00217575 0.000312825i
\(446\) 0 0
\(447\) −31.3937 3.38663i −1.48487 0.160182i
\(448\) 0 0
\(449\) −38.1025 + 17.4008i −1.79817 + 0.821196i −0.836005 + 0.548722i \(0.815114\pi\)
−0.962163 + 0.272473i \(0.912158\pi\)
\(450\) 0 0
\(451\) −0.168806 1.17407i −0.00794878 0.0552850i
\(452\) 0 0
\(453\) 4.70858 3.26671i 0.221228 0.153483i
\(454\) 0 0
\(455\) 2.28805 + 15.9138i 0.107266 + 0.746049i
\(456\) 0 0
\(457\) −11.0054 + 7.07271i −0.514809 + 0.330848i −0.772115 0.635482i \(-0.780801\pi\)
0.257307 + 0.966330i \(0.417165\pi\)
\(458\) 0 0
\(459\) −23.8492 + 14.1155i −1.11318 + 0.658856i
\(460\) 0 0
\(461\) −11.9303 + 18.5639i −0.555649 + 0.864607i −0.999504 0.0314915i \(-0.989974\pi\)
0.443855 + 0.896099i \(0.353611\pi\)
\(462\) 0 0
\(463\) −11.2952 + 38.4680i −0.524934 + 1.78776i 0.0862514 + 0.996273i \(0.472511\pi\)
−0.611185 + 0.791488i \(0.709307\pi\)
\(464\) 0 0
\(465\) −32.6729 + 16.3402i −1.51517 + 0.757757i
\(466\) 0 0
\(467\) 17.4693 + 15.1372i 0.808382 + 0.700467i 0.957525 0.288349i \(-0.0931062\pi\)
−0.149144 + 0.988816i \(0.547652\pi\)
\(468\) 0 0
\(469\) 24.9583 + 18.3921i 1.15247 + 0.849269i
\(470\) 0 0
\(471\) −7.89202 + 19.0336i −0.363645 + 0.877022i
\(472\) 0 0
\(473\) 27.8070 3.99804i 1.27857 0.183830i
\(474\) 0 0
\(475\) −0.707727 0.207807i −0.0324727 0.00953486i
\(476\) 0 0
\(477\) 3.64969 0.258386i 0.167108 0.0118307i
\(478\) 0 0
\(479\) −23.8724 10.9021i −1.09076 0.498132i −0.212909 0.977072i \(-0.568294\pi\)
−0.877848 + 0.478940i \(0.841021\pi\)
\(480\) 0 0
\(481\) 1.94584 + 3.02779i 0.0887229 + 0.138055i
\(482\) 0 0
\(483\) 2.23953 + 4.47804i 0.101902 + 0.203758i
\(484\) 0 0
\(485\) −13.2949 45.2782i −0.603690 2.05598i
\(486\) 0 0
\(487\) −1.33732 + 0.192278i −0.0605997 + 0.00871293i −0.172548 0.985001i \(-0.555200\pi\)
0.111948 + 0.993714i \(0.464291\pi\)
\(488\) 0 0
\(489\) −21.0810 22.6590i −0.953318 1.02468i
\(490\) 0 0
\(491\) 29.2186 + 13.3437i 1.31862 + 0.602193i 0.945509 0.325595i \(-0.105565\pi\)
0.373109 + 0.927788i \(0.378292\pi\)
\(492\) 0 0
\(493\) 6.61466 46.0059i 0.297909 2.07200i
\(494\) 0 0
\(495\) −17.1704 31.4992i −0.771751 1.41578i
\(496\) 0 0
\(497\) 2.43491 + 1.56482i 0.109221 + 0.0701919i
\(498\) 0 0
\(499\) 12.9260i 0.578646i −0.957231 0.289323i \(-0.906570\pi\)
0.957231 0.289323i \(-0.0934302\pi\)
\(500\) 0 0
\(501\) −1.18082 0.127382i −0.0527551 0.00569100i
\(502\) 0 0
\(503\) 12.5972 + 14.5380i 0.561682 + 0.648215i 0.963565 0.267476i \(-0.0861895\pi\)
−0.401883 + 0.915691i \(0.631644\pi\)
\(504\) 0 0
\(505\) 34.3919 + 22.1024i 1.53042 + 0.983542i
\(506\) 0 0
\(507\) −17.9643 + 5.97190i −0.797823 + 0.265221i
\(508\) 0 0
\(509\) 5.63479 19.1903i 0.249758 0.850597i −0.735207 0.677842i \(-0.762915\pi\)
0.984965 0.172754i \(-0.0552666\pi\)
\(510\) 0 0
\(511\) 23.9952 + 37.3373i 1.06149 + 1.65171i
\(512\) 0 0
\(513\) −1.01832 0.184862i −0.0449597 0.00816186i
\(514\) 0 0
\(515\) 0.526367 + 0.154555i 0.0231945 + 0.00681052i
\(516\) 0 0
\(517\) 23.2131 20.1143i 1.02091 0.884625i
\(518\) 0 0
\(519\) −36.5792 + 6.58599i −1.60565 + 0.289093i
\(520\) 0 0
\(521\) 14.3488 + 16.5594i 0.628632 + 0.725480i 0.977322 0.211758i \(-0.0679189\pi\)
−0.348690 + 0.937238i \(0.613373\pi\)
\(522\) 0 0
\(523\) −1.74778 + 1.12323i −0.0764251 + 0.0491154i −0.578295 0.815828i \(-0.696282\pi\)
0.501870 + 0.864943i \(0.332645\pi\)
\(524\) 0 0
\(525\) 13.8486 + 19.9611i 0.604401 + 0.871173i
\(526\) 0 0
\(527\) −24.9700 + 28.8169i −1.08771 + 1.25528i
\(528\) 0 0
\(529\) −14.6804 + 16.9420i −0.638277 + 0.736610i
\(530\) 0 0
\(531\) 0.918649 + 0.688727i 0.0398660 + 0.0298882i
\(532\) 0 0
\(533\) 0.382986 0.174904i 0.0165890 0.00757592i
\(534\) 0 0
\(535\) 33.5553i 1.45072i
\(536\) 0 0
\(537\) 5.49229 1.82581i 0.237010 0.0787895i
\(538\) 0 0
\(539\) −12.3699 27.0864i −0.532811 1.16669i
\(540\) 0 0
\(541\) −10.1591 34.5988i −0.436775 1.48752i −0.824563 0.565770i \(-0.808579\pi\)
0.387788 0.921748i \(-0.373239\pi\)
\(542\) 0 0
\(543\) −1.64688 + 3.97187i −0.0706744 + 0.170449i
\(544\) 0 0
\(545\) −32.6466 28.2884i −1.39843 1.21174i
\(546\) 0 0
\(547\) 7.92881 + 27.0031i 0.339012 + 1.15457i 0.935907 + 0.352248i \(0.114583\pi\)
−0.596895 + 0.802319i \(0.703599\pi\)
\(548\) 0 0
\(549\) 34.7419 + 12.9866i 1.48275 + 0.554256i
\(550\) 0 0
\(551\) 1.31180 1.13668i 0.0558847 0.0484244i
\(552\) 0 0
\(553\) 7.97780 55.4868i 0.339251 2.35954i
\(554\) 0 0
\(555\) 10.9902 + 6.52612i 0.466506 + 0.277019i
\(556\) 0 0
\(557\) 6.49987 22.1365i 0.275409 0.937955i −0.699366 0.714764i \(-0.746534\pi\)
0.974775 0.223192i \(-0.0716476\pi\)
\(558\) 0 0
\(559\) 4.14245 + 9.07070i 0.175207 + 0.383650i
\(560\) 0 0
\(561\) −29.1481 23.5064i −1.23063 0.992440i
\(562\) 0 0
\(563\) −23.5092 6.90294i −0.990797 0.290924i −0.254123 0.967172i \(-0.581787\pi\)
−0.736674 + 0.676248i \(0.763605\pi\)
\(564\) 0 0
\(565\) 40.5903 1.70765
\(566\) 0 0
\(567\) 22.2861 + 25.7946i 0.935928 + 1.08327i
\(568\) 0 0
\(569\) 4.98397 4.31864i 0.208939 0.181047i −0.544104 0.839018i \(-0.683130\pi\)
0.753043 + 0.657971i \(0.228585\pi\)
\(570\) 0 0
\(571\) 8.65212 18.9455i 0.362080 0.792844i −0.637666 0.770313i \(-0.720100\pi\)
0.999746 0.0225316i \(-0.00717263\pi\)
\(572\) 0 0
\(573\) −9.17105 + 3.04875i −0.383126 + 0.127363i
\(574\) 0 0
\(575\) 1.52802 2.37764i 0.0637226 0.0991544i
\(576\) 0 0
\(577\) 20.2236 + 2.90771i 0.841918 + 0.121049i 0.549762 0.835321i \(-0.314718\pi\)
0.292156 + 0.956371i \(0.405627\pi\)
\(578\) 0 0
\(579\) −6.30879 35.0396i −0.262185 1.45620i
\(580\) 0 0
\(581\) −19.6292 + 42.9820i −0.814358 + 1.78319i
\(582\) 0 0
\(583\) 2.05369 + 4.49694i 0.0850550 + 0.186244i
\(584\) 0 0
\(585\) 9.01092 8.99793i 0.372556 0.372019i
\(586\) 0 0
\(587\) −13.5582 + 3.98104i −0.559606 + 0.164315i −0.549290 0.835632i \(-0.685102\pi\)
−0.0103159 + 0.999947i \(0.503284\pi\)
\(588\) 0 0
\(589\) −1.40948 + 0.202653i −0.0580767 + 0.00835017i
\(590\) 0 0
\(591\) −2.69233 + 3.33851i −0.110748 + 0.137328i
\(592\) 0 0
\(593\) 8.23739 18.0374i 0.338269 0.740706i −0.661690 0.749778i \(-0.730160\pi\)
0.999959 + 0.00907163i \(0.00288763\pi\)
\(594\) 0 0
\(595\) 50.1351 + 32.2198i 2.05534 + 1.32088i
\(596\) 0 0
\(597\) 8.71458 0.308095i 0.356664 0.0126095i
\(598\) 0 0
\(599\) −3.41470 23.7497i −0.139521 0.970388i −0.932508 0.361150i \(-0.882384\pi\)
0.792987 0.609239i \(-0.208525\pi\)
\(600\) 0 0
\(601\) −13.9003 + 16.0418i −0.567004 + 0.654358i −0.964759 0.263134i \(-0.915244\pi\)
0.397755 + 0.917492i \(0.369789\pi\)
\(602\) 0 0
\(603\) −0.167069 24.5555i −0.00680358 0.999977i
\(604\) 0 0
\(605\) 10.4921 12.1085i 0.426564 0.492281i
\(606\) 0 0
\(607\) 2.80749 + 19.5266i 0.113953 + 0.792558i 0.964010 + 0.265867i \(0.0856583\pi\)
−0.850057 + 0.526691i \(0.823433\pi\)
\(608\) 0 0
\(609\) −57.1354 + 2.01997i −2.31524 + 0.0818532i
\(610\) 0 0
\(611\) 9.17194 + 5.89445i 0.371057 + 0.238464i
\(612\) 0 0
\(613\) −3.16626 + 6.93315i −0.127884 + 0.280027i −0.962734 0.270451i \(-0.912827\pi\)
0.834850 + 0.550478i \(0.185555\pi\)
\(614\) 0 0
\(615\) 0.938633 1.16391i 0.0378493 0.0469335i
\(616\) 0 0
\(617\) 3.30061 0.474556i 0.132877 0.0191049i −0.0755552 0.997142i \(-0.524073\pi\)
0.208433 + 0.978037i \(0.433164\pi\)
\(618\) 0 0
\(619\) 45.2582 13.2890i 1.81908 0.534130i 0.819822 0.572619i \(-0.194072\pi\)
0.999259 + 0.0384883i \(0.0122542\pi\)
\(620\) 0 0
\(621\) 1.77894 3.54429i 0.0713865 0.142228i
\(622\) 0 0
\(623\) 0.0247309 + 0.0541531i 0.000990822 + 0.00216960i
\(624\) 0 0
\(625\) −12.3803 + 27.1090i −0.495211 + 1.08436i
\(626\) 0 0
\(627\) −0.247795 1.37627i −0.00989597 0.0549631i
\(628\) 0 0
\(629\) 13.2055 + 1.89866i 0.526537 + 0.0757046i
\(630\) 0 0
\(631\) −19.5180 + 30.3706i −0.776999 + 1.20903i 0.196537 + 0.980496i \(0.437031\pi\)
−0.973535 + 0.228537i \(0.926606\pi\)
\(632\) 0 0
\(633\) 35.7879 11.8970i 1.42244 0.472865i
\(634\) 0 0
\(635\) 4.84806 10.6158i 0.192389 0.421274i
\(636\) 0 0
\(637\) 7.98807 6.92170i 0.316499 0.274248i
\(638\) 0 0
\(639\) −0.161897 2.28679i −0.00640453 0.0904638i
\(640\) 0 0
\(641\) 19.0369 0.751914 0.375957 0.926637i \(-0.377314\pi\)
0.375957 + 0.926637i \(0.377314\pi\)
\(642\) 0 0
\(643\) −26.1566 7.68027i −1.03152 0.302880i −0.278189 0.960526i \(-0.589734\pi\)
−0.753327 + 0.657646i \(0.771552\pi\)
\(644\) 0 0
\(645\) 27.5663 + 22.2307i 1.08542 + 0.875334i
\(646\) 0 0
\(647\) 19.9666 + 43.7207i 0.784968 + 1.71884i 0.690524 + 0.723310i \(0.257380\pi\)
0.0944441 + 0.995530i \(0.469893\pi\)
\(648\) 0 0
\(649\) −0.437066 + 1.48851i −0.0171564 + 0.0584292i
\(650\) 0 0
\(651\) 40.3275 + 23.9471i 1.58056 + 0.938559i
\(652\) 0 0
\(653\) 1.49965 10.4303i 0.0586860 0.408170i −0.939210 0.343342i \(-0.888441\pi\)
0.997896 0.0648281i \(-0.0206499\pi\)
\(654\) 0 0
\(655\) 7.46865 6.47162i 0.291824 0.252867i
\(656\) 0 0
\(657\) 12.3087 32.9284i 0.480209 1.28466i
\(658\) 0 0
\(659\) 3.84876 + 13.1077i 0.149926 + 0.510602i 0.999868 0.0162753i \(-0.00518083\pi\)
−0.849941 + 0.526878i \(0.823363\pi\)
\(660\) 0 0
\(661\) −6.20052 5.37278i −0.241172 0.208977i 0.525885 0.850556i \(-0.323734\pi\)
−0.767057 + 0.641579i \(0.778280\pi\)
\(662\) 0 0
\(663\) 5.09090 12.2780i 0.197714 0.476838i
\(664\) 0 0
\(665\) 0.627026 + 2.13545i 0.0243150 + 0.0828093i
\(666\) 0 0
\(667\) 2.76292 + 6.04994i 0.106981 + 0.234255i
\(668\) 0 0
\(669\) −36.8719 + 12.2574i −1.42555 + 0.473898i
\(670\) 0 0
\(671\) 50.1146i 1.93465i
\(672\) 0 0
\(673\) 12.7092 5.80409i 0.489903 0.223731i −0.155118 0.987896i \(-0.549576\pi\)
0.645021 + 0.764165i \(0.276849\pi\)
\(674\) 0 0
\(675\) 6.09657 18.2513i 0.234657 0.702494i
\(676\) 0 0
\(677\) 1.10341 1.27340i 0.0424073 0.0489407i −0.734150 0.678988i \(-0.762419\pi\)
0.776557 + 0.630047i \(0.216964\pi\)
\(678\) 0 0
\(679\) −39.6755 + 45.7880i −1.52261 + 1.75718i
\(680\) 0 0
\(681\) 4.39537 + 6.33541i 0.168431 + 0.242774i
\(682\) 0 0
\(683\) 12.0221 7.72614i 0.460013 0.295633i −0.290035 0.957016i \(-0.593667\pi\)
0.750048 + 0.661384i \(0.230030\pi\)
\(684\) 0 0
\(685\) −29.1864 33.6828i −1.11515 1.28696i
\(686\) 0 0
\(687\) −26.1688 + 4.71162i −0.998400 + 0.179760i
\(688\) 0 0
\(689\) −1.32620 + 1.14916i −0.0505241 + 0.0437794i
\(690\) 0 0
\(691\) −16.0896 4.72433i −0.612077 0.179722i −0.0390213 0.999238i \(-0.512424\pi\)
−0.573056 + 0.819516i \(0.694242\pi\)
\(692\) 0 0
\(693\) −22.1031 + 40.4094i −0.839626 + 1.53503i
\(694\) 0 0
\(695\) −24.7755 38.5515i −0.939790 1.46234i
\(696\) 0 0
\(697\) 0.439696 1.49747i 0.0166547 0.0567206i
\(698\) 0 0
\(699\) 22.5766 7.50517i 0.853925 0.283872i
\(700\) 0 0
\(701\) 14.5696 + 9.36331i 0.550286 + 0.353647i 0.786050 0.618163i \(-0.212123\pi\)
−0.235764 + 0.971810i \(0.575759\pi\)
\(702\) 0 0
\(703\) 0.326272 + 0.376538i 0.0123056 + 0.0142014i
\(704\) 0 0
\(705\) 38.4958 + 4.15277i 1.44984 + 0.156403i
\(706\) 0 0
\(707\) 52.4875i 1.97399i
\(708\) 0 0
\(709\) 20.9318 + 13.4520i 0.786110 + 0.505202i 0.871056 0.491183i \(-0.163436\pi\)
−0.0849464 + 0.996386i \(0.527072\pi\)
\(710\) 0 0
\(711\) −38.9847 + 21.2508i −1.46204 + 0.796967i
\(712\) 0 0
\(713\) 0.776511 5.40075i 0.0290806 0.202260i
\(714\) 0 0
\(715\) 15.6512 + 7.14764i 0.585320 + 0.267307i
\(716\) 0 0
\(717\) 27.5594 + 29.6223i 1.02922 + 1.10626i
\(718\) 0 0
\(719\) −6.05908 + 0.871164i −0.225966 + 0.0324889i −0.254367 0.967108i \(-0.581867\pi\)
0.0284019 + 0.999597i \(0.490958\pi\)
\(720\) 0 0
\(721\) −0.198431 0.675794i −0.00738996 0.0251679i
\(722\) 0 0
\(723\) −1.74214 3.48348i −0.0647907 0.129552i
\(724\) 0 0
\(725\) 17.4478 + 27.1493i 0.647996 + 1.00830i
\(726\) 0 0
\(727\) −14.1305 6.45316i −0.524070 0.239335i 0.135771 0.990740i \(-0.456649\pi\)
−0.659840 + 0.751406i \(0.729376\pi\)
\(728\) 0 0
\(729\) 5.79633 26.3705i 0.214679 0.976685i
\(730\) 0 0
\(731\) 35.4663 + 10.4138i 1.31177 + 0.385169i
\(732\) 0 0
\(733\) −25.2314 + 3.62773i −0.931944 + 0.133993i −0.591531 0.806282i \(-0.701476\pi\)
−0.340414 + 0.940276i \(0.610567\pi\)
\(734\) 0 0
\(735\) 14.3772 34.6742i 0.530310 1.27898i
\(736\) 0 0
\(737\) 30.9993 11.8286i 1.14187 0.435712i
\(738\) 0 0
\(739\) −14.2599 12.3563i −0.524558 0.454532i 0.351881 0.936045i \(-0.385542\pi\)
−0.876439 + 0.481512i \(0.840088\pi\)
\(740\) 0 0
\(741\) 0.443952 0.222027i 0.0163090 0.00815635i
\(742\) 0 0
\(743\) 11.9043 40.5424i 0.436728 1.48736i −0.387910 0.921697i \(-0.626803\pi\)
0.824638 0.565661i \(-0.191379\pi\)
\(744\) 0 0
\(745\) 29.0766 45.2441i 1.06529 1.65762i
\(746\) 0 0
\(747\) 36.5766 7.92914i 1.33827 0.290112i
\(748\) 0 0
\(749\) 36.2422 23.2914i 1.32426 0.851050i
\(750\) 0 0
\(751\) 0.861200 + 5.98978i 0.0314256 + 0.218570i 0.999483 0.0321598i \(-0.0102385\pi\)
−0.968057 + 0.250730i \(0.919329\pi\)
\(752\) 0 0
\(753\) −21.2345 + 14.7320i −0.773827 + 0.536864i
\(754\) 0 0
\(755\) 1.38914 + 9.66168i 0.0505560 + 0.351625i
\(756\) 0 0
\(757\) 0.504090 0.230210i 0.0183215 0.00836714i −0.406233 0.913769i \(-0.633158\pi\)
0.424555 + 0.905402i \(0.360431\pi\)
\(758\) 0 0
\(759\) 5.32740 + 0.574698i 0.193372 + 0.0208602i
\(760\) 0 0
\(761\) 1.51723 + 0.218144i 0.0549995 + 0.00790773i 0.169760 0.985485i \(-0.445701\pi\)
−0.114760 + 0.993393i \(0.536610\pi\)
\(762\) 0 0
\(763\) −7.89288 + 54.8962i −0.285741 + 1.98738i
\(764\) 0 0
\(765\) −3.33347 47.0851i −0.120522 1.70237i
\(766\) 0 0
\(767\) −0.550666 −0.0198834
\(768\) 0 0
\(769\) 5.52872 + 2.52488i 0.199371 + 0.0910496i 0.512598 0.858629i \(-0.328683\pi\)
−0.313228 + 0.949678i \(0.601410\pi\)
\(770\) 0 0
\(771\) 10.1119 17.0288i 0.364173 0.613277i
\(772\) 0 0
\(773\) −16.8998 + 26.2967i −0.607845 + 0.945825i 0.391823 + 0.920041i \(0.371845\pi\)
−0.999668 + 0.0257841i \(0.991792\pi\)
\(774\) 0 0
\(775\) 26.4755i 0.951028i
\(776\) 0 0