Properties

Label 804.2.s.b.5.14
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 5.14
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.575290 - 1.63372i) q^{3} +(2.05430 - 0.603197i) q^{5} +(-2.91035 - 2.52183i) q^{7} +(-2.33808 - 1.87973i) q^{9} +O(q^{10})\) \(q+(0.575290 - 1.63372i) q^{3} +(2.05430 - 0.603197i) q^{5} +(-2.91035 - 2.52183i) q^{7} +(-2.33808 - 1.87973i) q^{9} +(5.36557 - 1.57547i) q^{11} +(3.44974 + 5.36790i) q^{13} +(0.196364 - 3.70316i) q^{15} +(-0.764837 - 0.109967i) q^{17} +(-5.19155 - 5.99137i) q^{19} +(-5.79426 + 3.30391i) q^{21} +(4.69664 - 2.14488i) q^{23} +(-0.349969 + 0.224911i) q^{25} +(-4.41602 + 2.73838i) q^{27} -8.43272i q^{29} +(-1.76539 + 2.74699i) q^{31} +(0.512878 - 9.67219i) q^{33} +(-7.49988 - 3.42508i) q^{35} -5.40444 q^{37} +(10.7543 - 2.54781i) q^{39} +(-1.28169 + 8.91433i) q^{41} +(0.443176 + 0.0637191i) q^{43} +(-5.93697 - 2.45120i) q^{45} +(3.17052 - 1.44793i) q^{47} +(1.11429 + 7.75005i) q^{49} +(-0.619659 + 1.18627i) q^{51} +(-0.119970 - 0.834409i) q^{53} +(10.0722 - 6.47299i) q^{55} +(-12.7749 + 5.03476i) q^{57} +(-6.01354 + 9.35726i) q^{59} +(2.74338 - 9.34309i) q^{61} +(2.06428 + 11.3669i) q^{63} +(10.3247 + 8.94641i) q^{65} +(7.35766 + 3.58676i) q^{67} +(-0.802207 - 8.90692i) q^{69} +(7.24102 - 1.04110i) q^{71} +(6.32300 + 1.85660i) q^{73} +(0.166108 + 0.701140i) q^{75} +(-19.5887 - 8.94588i) q^{77} +(1.27332 + 1.98132i) q^{79} +(1.93326 + 8.78991i) q^{81} +(-2.86458 - 9.75587i) q^{83} +(-1.63754 + 0.235442i) q^{85} +(-13.7767 - 4.85127i) q^{87} +(-3.49281 - 1.59511i) q^{89} +(3.49699 - 24.3221i) q^{91} +(3.47221 + 4.46447i) q^{93} +(-14.2790 - 9.17653i) q^{95} +1.22491i q^{97} +(-15.5066 - 6.40222i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

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
\(3\) 0.575290 1.63372i 0.332144 0.943229i
\(4\) 0 0
\(5\) 2.05430 0.603197i 0.918711 0.269758i 0.212007 0.977268i \(-0.432000\pi\)
0.706703 + 0.707510i \(0.250182\pi\)
\(6\) 0 0
\(7\) −2.91035 2.52183i −1.10001 0.953162i −0.100879 0.994899i \(-0.532166\pi\)
−0.999129 + 0.0417366i \(0.986711\pi\)
\(8\) 0 0
\(9\) −2.33808 1.87973i −0.779361 0.626576i
\(10\) 0 0
\(11\) 5.36557 1.57547i 1.61778 0.475023i 0.657360 0.753577i \(-0.271673\pi\)
0.960421 + 0.278554i \(0.0898551\pi\)
\(12\) 0 0
\(13\) 3.44974 + 5.36790i 0.956786 + 1.48879i 0.870292 + 0.492536i \(0.163930\pi\)
0.0864941 + 0.996252i \(0.472434\pi\)
\(14\) 0 0
\(15\) 0.196364 3.70316i 0.0507010 0.956153i
\(16\) 0 0
\(17\) −0.764837 0.109967i −0.185500 0.0266709i 0.0489385 0.998802i \(-0.484416\pi\)
−0.234439 + 0.972131i \(0.575325\pi\)
\(18\) 0 0
\(19\) −5.19155 5.99137i −1.19102 1.37451i −0.909893 0.414844i \(-0.863836\pi\)
−0.281130 0.959670i \(-0.590709\pi\)
\(20\) 0 0
\(21\) −5.79426 + 3.30391i −1.26441 + 0.720972i
\(22\) 0 0
\(23\) 4.69664 2.14488i 0.979316 0.447239i 0.139567 0.990213i \(-0.455429\pi\)
0.839750 + 0.542974i \(0.182702\pi\)
\(24\) 0 0
\(25\) −0.349969 + 0.224911i −0.0699937 + 0.0449822i
\(26\) 0 0
\(27\) −4.41602 + 2.73838i −0.849864 + 0.527002i
\(28\) 0 0
\(29\) 8.43272i 1.56592i −0.622074 0.782959i \(-0.713710\pi\)
0.622074 0.782959i \(-0.286290\pi\)
\(30\) 0 0
\(31\) −1.76539 + 2.74699i −0.317073 + 0.493375i −0.962808 0.270187i \(-0.912915\pi\)
0.645735 + 0.763561i \(0.276551\pi\)
\(32\) 0 0
\(33\) 0.512878 9.67219i 0.0892806 1.68371i
\(34\) 0 0
\(35\) −7.49988 3.42508i −1.26771 0.578944i
\(36\) 0 0
\(37\) −5.40444 −0.888484 −0.444242 0.895907i \(-0.646527\pi\)
−0.444242 + 0.895907i \(0.646527\pi\)
\(38\) 0 0
\(39\) 10.7543 2.54781i 1.72206 0.407976i
\(40\) 0 0
\(41\) −1.28169 + 8.91433i −0.200166 + 1.39218i 0.603623 + 0.797270i \(0.293723\pi\)
−0.803789 + 0.594915i \(0.797186\pi\)
\(42\) 0 0
\(43\) 0.443176 + 0.0637191i 0.0675837 + 0.00971707i 0.176024 0.984386i \(-0.443676\pi\)
−0.108440 + 0.994103i \(0.534586\pi\)
\(44\) 0 0
\(45\) −5.93697 2.45120i −0.885030 0.365403i
\(46\) 0 0
\(47\) 3.17052 1.44793i 0.462467 0.211202i −0.170535 0.985352i \(-0.554550\pi\)
0.633002 + 0.774150i \(0.281822\pi\)
\(48\) 0 0
\(49\) 1.11429 + 7.75005i 0.159184 + 1.10715i
\(50\) 0 0
\(51\) −0.619659 + 1.18627i −0.0867696 + 0.166111i
\(52\) 0 0
\(53\) −0.119970 0.834409i −0.0164791 0.114615i 0.979922 0.199384i \(-0.0638940\pi\)
−0.996401 + 0.0847686i \(0.972985\pi\)
\(54\) 0 0
\(55\) 10.0722 6.47299i 1.35813 0.872818i
\(56\) 0 0
\(57\) −12.7749 + 5.03476i −1.69207 + 0.666870i
\(58\) 0 0
\(59\) −6.01354 + 9.35726i −0.782897 + 1.21821i 0.188808 + 0.982014i \(0.439538\pi\)
−0.971705 + 0.236197i \(0.924099\pi\)
\(60\) 0 0
\(61\) 2.74338 9.34309i 0.351254 1.19626i −0.574618 0.818422i \(-0.694849\pi\)
0.925872 0.377838i \(-0.123332\pi\)
\(62\) 0 0
\(63\) 2.06428 + 11.3669i 0.260075 + 1.43209i
\(64\) 0 0
\(65\) 10.3247 + 8.94641i 1.28062 + 1.10967i
\(66\) 0 0
\(67\) 7.35766 + 3.58676i 0.898881 + 0.438192i
\(68\) 0 0
\(69\) −0.802207 8.90692i −0.0965744 1.07227i
\(70\) 0 0
\(71\) 7.24102 1.04110i 0.859351 0.123556i 0.301469 0.953476i \(-0.402523\pi\)
0.557882 + 0.829920i \(0.311614\pi\)
\(72\) 0 0
\(73\) 6.32300 + 1.85660i 0.740051 + 0.217298i 0.629965 0.776624i \(-0.283069\pi\)
0.110086 + 0.993922i \(0.464887\pi\)
\(74\) 0 0
\(75\) 0.166108 + 0.701140i 0.0191805 + 0.0809607i
\(76\) 0 0
\(77\) −19.5887 8.94588i −2.23234 1.01948i
\(78\) 0 0
\(79\) 1.27332 + 1.98132i 0.143259 + 0.222916i 0.905467 0.424417i \(-0.139521\pi\)
−0.762208 + 0.647332i \(0.775885\pi\)
\(80\) 0 0
\(81\) 1.93326 + 8.78991i 0.214806 + 0.976657i
\(82\) 0 0
\(83\) −2.86458 9.75587i −0.314429 1.07085i −0.953424 0.301635i \(-0.902468\pi\)
0.638995 0.769211i \(-0.279350\pi\)
\(84\) 0 0
\(85\) −1.63754 + 0.235442i −0.177616 + 0.0255373i
\(86\) 0 0
\(87\) −13.7767 4.85127i −1.47702 0.520110i
\(88\) 0 0
\(89\) −3.49281 1.59511i −0.370238 0.169082i 0.221603 0.975137i \(-0.428871\pi\)
−0.591840 + 0.806055i \(0.701598\pi\)
\(90\) 0 0
\(91\) 3.49699 24.3221i 0.366584 2.54965i
\(92\) 0 0
\(93\) 3.47221 + 4.46447i 0.360051 + 0.462944i
\(94\) 0 0
\(95\) −14.2790 9.17653i −1.46499 0.941493i
\(96\) 0 0
\(97\) 1.22491i 0.124371i 0.998065 + 0.0621853i \(0.0198070\pi\)
−0.998065 + 0.0621853i \(0.980193\pi\)
\(98\) 0 0
\(99\) −15.5066 6.40222i −1.55847 0.643447i
\(100\) 0 0
\(101\) −1.40427 1.62061i −0.139730 0.161257i 0.681571 0.731752i \(-0.261297\pi\)
−0.821301 + 0.570495i \(0.806752\pi\)
\(102\) 0 0
\(103\) −2.30070 1.47857i −0.226695 0.145688i 0.422364 0.906426i \(-0.361201\pi\)
−0.649058 + 0.760739i \(0.724837\pi\)
\(104\) 0 0
\(105\) −9.91023 + 10.2823i −0.967140 + 1.00345i
\(106\) 0 0
\(107\) 0.573320 1.95255i 0.0554249 0.188760i −0.927127 0.374746i \(-0.877730\pi\)
0.982552 + 0.185986i \(0.0595480\pi\)
\(108\) 0 0
\(109\) 8.11037 + 12.6200i 0.776832 + 1.20877i 0.973586 + 0.228322i \(0.0733237\pi\)
−0.196754 + 0.980453i \(0.563040\pi\)
\(110\) 0 0
\(111\) −3.10912 + 8.82934i −0.295105 + 0.838044i
\(112\) 0 0
\(113\) 18.3068 + 5.37535i 1.72216 + 0.505671i 0.985366 0.170451i \(-0.0545224\pi\)
0.736790 + 0.676121i \(0.236341\pi\)
\(114\) 0 0
\(115\) 8.35451 7.23922i 0.779062 0.675061i
\(116\) 0 0
\(117\) 2.02441 19.0352i 0.187157 1.75980i
\(118\) 0 0
\(119\) 1.94862 + 2.24883i 0.178630 + 0.206150i
\(120\) 0 0
\(121\) 17.0534 10.9596i 1.55031 0.996325i
\(122\) 0 0
\(123\) 13.8262 + 7.22225i 1.24666 + 0.651208i
\(124\) 0 0
\(125\) −7.59364 + 8.76353i −0.679196 + 0.783834i
\(126\) 0 0
\(127\) 2.98832 3.44871i 0.265171 0.306024i −0.607512 0.794310i \(-0.707832\pi\)
0.872683 + 0.488287i \(0.162378\pi\)
\(128\) 0 0
\(129\) 0.359054 0.687369i 0.0316130 0.0605195i
\(130\) 0 0
\(131\) 2.81078 1.28364i 0.245579 0.112152i −0.288824 0.957382i \(-0.593264\pi\)
0.534402 + 0.845230i \(0.320537\pi\)
\(132\) 0 0
\(133\) 30.5292i 2.64721i
\(134\) 0 0
\(135\) −7.42005 + 8.28919i −0.638616 + 0.713420i
\(136\) 0 0
\(137\) 3.57227 + 7.82217i 0.305199 + 0.668293i 0.998635 0.0522248i \(-0.0166312\pi\)
−0.693436 + 0.720518i \(0.743904\pi\)
\(138\) 0 0
\(139\) 4.95108 + 16.8618i 0.419945 + 1.43020i 0.849705 + 0.527259i \(0.176780\pi\)
−0.429759 + 0.902943i \(0.641402\pi\)
\(140\) 0 0
\(141\) −0.541539 6.01272i −0.0456058 0.506362i
\(142\) 0 0
\(143\) 26.9668 + 23.3669i 2.25508 + 1.95404i
\(144\) 0 0
\(145\) −5.08659 17.3233i −0.422418 1.43863i
\(146\) 0 0
\(147\) 13.3024 + 2.63809i 1.09717 + 0.217586i
\(148\) 0 0
\(149\) 10.0243 8.68614i 0.821226 0.711596i −0.139160 0.990270i \(-0.544440\pi\)
0.960386 + 0.278674i \(0.0898948\pi\)
\(150\) 0 0
\(151\) −1.31762 + 9.16424i −0.107226 + 0.745775i 0.863285 + 0.504717i \(0.168403\pi\)
−0.970511 + 0.241057i \(0.922506\pi\)
\(152\) 0 0
\(153\) 1.58154 + 1.69480i 0.127860 + 0.137016i
\(154\) 0 0
\(155\) −1.96965 + 6.70802i −0.158206 + 0.538802i
\(156\) 0 0
\(157\) 2.04478 + 4.47745i 0.163192 + 0.357340i 0.973508 0.228653i \(-0.0734321\pi\)
−0.810316 + 0.585992i \(0.800705\pi\)
\(158\) 0 0
\(159\) −1.43221 0.284030i −0.113582 0.0225251i
\(160\) 0 0
\(161\) −19.0779 5.60177i −1.50355 0.441481i
\(162\) 0 0
\(163\) 7.70377 0.603406 0.301703 0.953402i \(-0.402445\pi\)
0.301703 + 0.953402i \(0.402445\pi\)
\(164\) 0 0
\(165\) −4.78063 20.1789i −0.372172 1.57093i
\(166\) 0 0
\(167\) 13.1265 11.3742i 1.01576 0.880161i 0.0229352 0.999737i \(-0.492699\pi\)
0.992825 + 0.119576i \(0.0381534\pi\)
\(168\) 0 0
\(169\) −11.5133 + 25.2105i −0.885636 + 1.93927i
\(170\) 0 0
\(171\) 0.876135 + 23.7670i 0.0669997 + 1.81751i
\(172\) 0 0
\(173\) −2.04209 + 3.17755i −0.155257 + 0.241585i −0.910165 0.414246i \(-0.864045\pi\)
0.754908 + 0.655831i \(0.227682\pi\)
\(174\) 0 0
\(175\) 1.58572 + 0.227992i 0.119869 + 0.0172346i
\(176\) 0 0
\(177\) 11.8276 + 15.2076i 0.889017 + 1.14307i
\(178\) 0 0
\(179\) −2.71308 + 5.94082i −0.202785 + 0.444037i −0.983514 0.180833i \(-0.942121\pi\)
0.780729 + 0.624870i \(0.214848\pi\)
\(180\) 0 0
\(181\) −3.14530 6.88725i −0.233788 0.511925i 0.755982 0.654592i \(-0.227160\pi\)
−0.989771 + 0.142667i \(0.954432\pi\)
\(182\) 0 0
\(183\) −13.6858 9.85690i −1.01168 0.728643i
\(184\) 0 0
\(185\) −11.1023 + 3.25994i −0.816260 + 0.239675i
\(186\) 0 0
\(187\) −4.27704 + 0.614945i −0.312768 + 0.0449693i
\(188\) 0 0
\(189\) 19.7579 + 3.16681i 1.43718 + 0.230352i
\(190\) 0 0
\(191\) −1.20933 + 2.64807i −0.0875041 + 0.191607i −0.948325 0.317301i \(-0.897223\pi\)
0.860821 + 0.508908i \(0.169951\pi\)
\(192\) 0 0
\(193\) 4.28043 + 2.75087i 0.308112 + 0.198012i 0.685554 0.728021i \(-0.259560\pi\)
−0.377442 + 0.926033i \(0.623196\pi\)
\(194\) 0 0
\(195\) 20.5556 11.7209i 1.47202 0.839351i
\(196\) 0 0
\(197\) 0.0858349 + 0.596995i 0.00611548 + 0.0425341i 0.992651 0.121015i \(-0.0386149\pi\)
−0.986535 + 0.163549i \(0.947706\pi\)
\(198\) 0 0
\(199\) −6.87755 + 7.93711i −0.487536 + 0.562647i −0.945206 0.326475i \(-0.894139\pi\)
0.457669 + 0.889123i \(0.348684\pi\)
\(200\) 0 0
\(201\) 10.0925 9.95693i 0.711874 0.702308i
\(202\) 0 0
\(203\) −21.2659 + 24.5422i −1.49257 + 1.72252i
\(204\) 0 0
\(205\) 2.74413 + 19.0858i 0.191658 + 1.33301i
\(206\) 0 0
\(207\) −15.0129 3.81348i −1.04347 0.265055i
\(208\) 0 0
\(209\) −37.2949 23.9679i −2.57974 1.65790i
\(210\) 0 0
\(211\) 4.15574 9.09981i 0.286093 0.626457i −0.710955 0.703238i \(-0.751737\pi\)
0.997048 + 0.0767810i \(0.0244642\pi\)
\(212\) 0 0
\(213\) 2.46482 12.4287i 0.168887 0.851603i
\(214\) 0 0
\(215\) 0.948852 0.136424i 0.0647111 0.00930406i
\(216\) 0 0
\(217\) 12.0653 3.54270i 0.819049 0.240494i
\(218\) 0 0
\(219\) 6.67072 9.26192i 0.450766 0.625863i
\(220\) 0 0
\(221\) −2.04820 4.48493i −0.137777 0.301689i
\(222\) 0 0
\(223\) 4.61874 10.1136i 0.309294 0.677259i −0.689604 0.724186i \(-0.742216\pi\)
0.998898 + 0.0469270i \(0.0149428\pi\)
\(224\) 0 0
\(225\) 1.24103 + 0.131985i 0.0827351 + 0.00879897i
\(226\) 0 0
\(227\) 16.6970 + 2.40067i 1.10822 + 0.159338i 0.672035 0.740519i \(-0.265420\pi\)
0.436185 + 0.899857i \(0.356329\pi\)
\(228\) 0 0
\(229\) −9.00592 + 14.0135i −0.595128 + 0.926037i 0.404805 + 0.914403i \(0.367340\pi\)
−0.999932 + 0.0116336i \(0.996297\pi\)
\(230\) 0 0
\(231\) −25.8843 + 26.8560i −1.70306 + 1.76700i
\(232\) 0 0
\(233\) −5.65669 + 12.3864i −0.370582 + 0.811461i 0.628842 + 0.777533i \(0.283529\pi\)
−0.999424 + 0.0339285i \(0.989198\pi\)
\(234\) 0 0
\(235\) 5.63981 4.88692i 0.367900 0.318787i
\(236\) 0 0
\(237\) 3.96944 0.940408i 0.257843 0.0610861i
\(238\) 0 0
\(239\) −5.75934 −0.372540 −0.186270 0.982499i \(-0.559640\pi\)
−0.186270 + 0.982499i \(0.559640\pi\)
\(240\) 0 0
\(241\) −11.5227 3.38337i −0.742242 0.217942i −0.111316 0.993785i \(-0.535507\pi\)
−0.630926 + 0.775843i \(0.717325\pi\)
\(242\) 0 0
\(243\) 15.4724 + 1.89835i 0.992557 + 0.121779i
\(244\) 0 0
\(245\) 6.96389 + 15.2488i 0.444906 + 0.974209i
\(246\) 0 0
\(247\) 14.2516 48.5364i 0.906806 3.08830i
\(248\) 0 0
\(249\) −17.5863 0.932533i −1.11449 0.0590969i
\(250\) 0 0
\(251\) 0.484711 3.37124i 0.0305947 0.212791i −0.968789 0.247886i \(-0.920264\pi\)
0.999384 + 0.0350948i \(0.0111733\pi\)
\(252\) 0 0
\(253\) 21.8209 18.9079i 1.37187 1.18873i
\(254\) 0 0
\(255\) −0.557412 + 2.81072i −0.0349065 + 0.176014i
\(256\) 0 0
\(257\) 7.42734 + 25.2952i 0.463305 + 1.57787i 0.777736 + 0.628591i \(0.216368\pi\)
−0.314431 + 0.949280i \(0.601814\pi\)
\(258\) 0 0
\(259\) 15.7288 + 13.6291i 0.977339 + 0.846869i
\(260\) 0 0
\(261\) −15.8512 + 19.7164i −0.981166 + 1.22041i
\(262\) 0 0
\(263\) −6.36513 21.6777i −0.392491 1.33670i −0.884674 0.466210i \(-0.845619\pi\)
0.492183 0.870492i \(-0.336199\pi\)
\(264\) 0 0
\(265\) −0.749767 1.64176i −0.0460578 0.100853i
\(266\) 0 0
\(267\) −4.61535 + 4.78863i −0.282455 + 0.293059i
\(268\) 0 0
\(269\) 19.6323i 1.19700i −0.801123 0.598500i \(-0.795764\pi\)
0.801123 0.598500i \(-0.204236\pi\)
\(270\) 0 0
\(271\) −18.3397 + 8.37545i −1.11406 + 0.508773i −0.885445 0.464745i \(-0.846146\pi\)
−0.228612 + 0.973518i \(0.573419\pi\)
\(272\) 0 0
\(273\) −37.7237 19.7054i −2.28315 1.19262i
\(274\) 0 0
\(275\) −1.52344 + 1.75814i −0.0918669 + 0.106020i
\(276\) 0 0
\(277\) −2.81170 + 3.24488i −0.168939 + 0.194966i −0.833906 0.551907i \(-0.813900\pi\)
0.664967 + 0.746873i \(0.268446\pi\)
\(278\) 0 0
\(279\) 9.29122 3.10426i 0.556251 0.185847i
\(280\) 0 0
\(281\) −2.96094 + 1.90288i −0.176635 + 0.113516i −0.625971 0.779847i \(-0.715297\pi\)
0.449336 + 0.893363i \(0.351661\pi\)
\(282\) 0 0
\(283\) 2.64597 + 3.05361i 0.157286 + 0.181518i 0.828923 0.559362i \(-0.188954\pi\)
−0.671637 + 0.740880i \(0.734408\pi\)
\(284\) 0 0
\(285\) −23.2064 + 18.0487i −1.37463 + 1.06911i
\(286\) 0 0
\(287\) 26.2106 22.7116i 1.54716 1.34062i
\(288\) 0 0
\(289\) −15.7385 4.62124i −0.925794 0.271838i
\(290\) 0 0
\(291\) 2.00116 + 0.704678i 0.117310 + 0.0413089i
\(292\) 0 0
\(293\) 8.56693 + 13.3304i 0.500485 + 0.778771i 0.995955 0.0898548i \(-0.0286403\pi\)
−0.495469 + 0.868625i \(0.665004\pi\)
\(294\) 0 0
\(295\) −6.70935 + 22.8500i −0.390634 + 1.33038i
\(296\) 0 0
\(297\) −19.3802 + 21.6503i −1.12456 + 1.25628i
\(298\) 0 0
\(299\) 27.7157 + 17.8118i 1.60284 + 1.03008i
\(300\) 0 0
\(301\) −1.12911 1.30306i −0.0650807 0.0751071i
\(302\) 0 0
\(303\) −3.45549 + 1.36186i −0.198513 + 0.0782368i
\(304\) 0 0
\(305\) 20.8483i 1.19377i
\(306\) 0 0
\(307\) 8.05757 + 5.17828i 0.459870 + 0.295540i 0.749989 0.661450i \(-0.230059\pi\)
−0.290119 + 0.956990i \(0.593695\pi\)
\(308\) 0 0
\(309\) −3.73914 + 2.90809i −0.212712 + 0.165436i
\(310\) 0 0
\(311\) −2.80597 + 19.5159i −0.159112 + 1.10665i 0.741163 + 0.671325i \(0.234275\pi\)
−0.900275 + 0.435322i \(0.856634\pi\)
\(312\) 0 0
\(313\) 26.7398 + 12.2117i 1.51142 + 0.690245i 0.986927 0.161167i \(-0.0515259\pi\)
0.524498 + 0.851412i \(0.324253\pi\)
\(314\) 0 0
\(315\) 11.0971 + 22.1059i 0.625252 + 1.24552i
\(316\) 0 0
\(317\) −5.12090 + 0.736274i −0.287618 + 0.0413533i −0.284614 0.958642i \(-0.591865\pi\)
−0.00300432 + 0.999995i \(0.500956\pi\)
\(318\) 0 0
\(319\) −13.2855 45.2464i −0.743847 2.53331i
\(320\) 0 0
\(321\) −2.86009 2.05993i −0.159635 0.114974i
\(322\) 0 0
\(323\) 3.31184 + 5.15332i 0.184276 + 0.286738i
\(324\) 0 0
\(325\) −2.41460 1.10271i −0.133938 0.0611675i
\(326\) 0 0
\(327\) 25.2833 5.98992i 1.39817 0.331243i
\(328\) 0 0
\(329\) −12.8787 3.78154i −0.710027 0.208483i
\(330\) 0 0
\(331\) −26.9910 + 3.88072i −1.48356 + 0.213303i −0.836007 0.548719i \(-0.815116\pi\)
−0.647551 + 0.762022i \(0.724207\pi\)
\(332\) 0 0
\(333\) 12.6360 + 10.1589i 0.692449 + 0.556702i
\(334\) 0 0
\(335\) 17.2784 + 2.93016i 0.944017 + 0.160092i
\(336\) 0 0
\(337\) −17.4251 15.0990i −0.949207 0.822493i 0.0350227 0.999387i \(-0.488850\pi\)
−0.984230 + 0.176894i \(0.943395\pi\)
\(338\) 0 0
\(339\) 19.3135 26.8158i 1.04897 1.45643i
\(340\) 0 0
\(341\) −5.14449 + 17.5205i −0.278590 + 0.948789i
\(342\) 0 0
\(343\) 1.72751 2.68805i 0.0932766 0.145141i
\(344\) 0 0
\(345\) −7.02060 17.8136i −0.377976 0.959051i
\(346\) 0 0
\(347\) 10.3251 6.63554i 0.554280 0.356214i −0.233321 0.972400i \(-0.574959\pi\)
0.787601 + 0.616185i \(0.211323\pi\)
\(348\) 0 0
\(349\) −3.49322 24.2959i −0.186988 1.30053i −0.839754 0.542968i \(-0.817301\pi\)
0.652766 0.757560i \(-0.273609\pi\)
\(350\) 0 0
\(351\) −29.9335 14.2581i −1.59773 0.761039i
\(352\) 0 0
\(353\) −3.07084 21.3582i −0.163444 1.13678i −0.892079 0.451879i \(-0.850754\pi\)
0.728635 0.684902i \(-0.240155\pi\)
\(354\) 0 0
\(355\) 14.2472 6.50649i 0.756165 0.345329i
\(356\) 0 0
\(357\) 4.79499 1.88977i 0.253778 0.100017i
\(358\) 0 0
\(359\) −19.9608 2.86993i −1.05349 0.151469i −0.406255 0.913760i \(-0.633166\pi\)
−0.647235 + 0.762291i \(0.724075\pi\)
\(360\) 0 0
\(361\) −6.24031 + 43.4023i −0.328437 + 2.28433i
\(362\) 0 0
\(363\) −8.09421 34.1655i −0.424836 1.79322i
\(364\) 0 0
\(365\) 14.1092 0.738510
\(366\) 0 0
\(367\) 5.59358 + 2.55450i 0.291983 + 0.133344i 0.556021 0.831168i \(-0.312327\pi\)
−0.264039 + 0.964512i \(0.585055\pi\)
\(368\) 0 0
\(369\) 19.7532 18.4332i 1.02831 0.959595i
\(370\) 0 0
\(371\) −1.75508 + 2.73096i −0.0911194 + 0.141785i
\(372\) 0 0
\(373\) 9.15585i 0.474072i −0.971501 0.237036i \(-0.923824\pi\)
0.971501 0.237036i \(-0.0761759\pi\)
\(374\) 0 0
\(375\) 9.94861 + 17.4475i 0.513744 + 0.900983i
\(376\) 0 0
\(377\) 45.2660 29.0907i 2.33132 1.49825i
\(378\) 0 0
\(379\) 8.36305 3.81928i 0.429581 0.196183i −0.188877 0.982001i \(-0.560485\pi\)
0.618458 + 0.785818i \(0.287758\pi\)
\(380\) 0 0
\(381\) −3.91507 6.86610i −0.200575 0.351761i
\(382\) 0 0
\(383\) −13.2261 15.2638i −0.675824 0.779942i 0.309452 0.950915i \(-0.399854\pi\)
−0.985276 + 0.170973i \(0.945309\pi\)
\(384\) 0 0
\(385\) −45.6373 6.56165i −2.32589 0.334413i
\(386\) 0 0
\(387\) −0.916408 0.982031i −0.0465836 0.0499194i
\(388\) 0 0
\(389\) 3.16294 + 4.92163i 0.160367 + 0.249536i 0.912133 0.409893i \(-0.134434\pi\)
−0.751766 + 0.659430i \(0.770798\pi\)
\(390\) 0 0
\(391\) −3.82803 + 1.12401i −0.193592 + 0.0568437i
\(392\) 0 0
\(393\) −0.480093 5.33048i −0.0242175 0.268887i
\(394\) 0 0
\(395\) 3.81089 + 3.30216i 0.191747 + 0.166150i
\(396\) 0 0
\(397\) −1.73367 + 0.509053i −0.0870107 + 0.0255486i −0.324948 0.945732i \(-0.605347\pi\)
0.237937 + 0.971280i \(0.423529\pi\)
\(398\) 0 0
\(399\) 49.8761 + 17.5631i 2.49693 + 0.879256i
\(400\) 0 0
\(401\) 23.9896 1.19798 0.598992 0.800755i \(-0.295568\pi\)
0.598992 + 0.800755i \(0.295568\pi\)
\(402\) 0 0
\(403\) −20.8357 −1.03790
\(404\) 0 0
\(405\) 9.27353 + 16.8910i 0.460805 + 0.839319i
\(406\) 0 0
\(407\) −28.9979 + 8.51455i −1.43737 + 0.422050i
\(408\) 0 0
\(409\) 6.86757 + 5.95079i 0.339580 + 0.294247i 0.807910 0.589306i \(-0.200599\pi\)
−0.468330 + 0.883553i \(0.655144\pi\)
\(410\) 0 0
\(411\) 14.8343 1.33606i 0.731724 0.0659031i
\(412\) 0 0
\(413\) 41.0989 12.0677i 2.02235 0.593814i
\(414\) 0 0
\(415\) −11.7694 18.3136i −0.577738 0.898977i
\(416\) 0 0
\(417\) 30.3958 + 1.61177i 1.48849 + 0.0789287i
\(418\) 0 0
\(419\) −30.2736 4.35269i −1.47896 0.212643i −0.644880 0.764284i \(-0.723093\pi\)
−0.834082 + 0.551641i \(0.814002\pi\)
\(420\) 0 0
\(421\) 11.1131 + 12.8253i 0.541622 + 0.625065i 0.958910 0.283709i \(-0.0915651\pi\)
−0.417289 + 0.908774i \(0.637020\pi\)
\(422\) 0 0
\(423\) −10.1346 2.57433i −0.492763 0.125168i
\(424\) 0 0
\(425\) 0.292402 0.133535i 0.0141836 0.00647742i
\(426\) 0 0
\(427\) −31.5459 + 20.2733i −1.52661 + 0.981094i
\(428\) 0 0
\(429\) 53.6887 30.6135i 2.59211 1.47803i
\(430\) 0 0
\(431\) 15.4336i 0.743410i −0.928351 0.371705i \(-0.878773\pi\)
0.928351 0.371705i \(-0.121227\pi\)
\(432\) 0 0
\(433\) −12.6950 + 19.7538i −0.610084 + 0.949309i 0.389516 + 0.921020i \(0.372642\pi\)
−0.999600 + 0.0282893i \(0.990994\pi\)
\(434\) 0 0
\(435\) −31.2278 1.65588i −1.49726 0.0793935i
\(436\) 0 0
\(437\) −37.2336 17.0040i −1.78112 0.813412i
\(438\) 0 0
\(439\) −36.2970 −1.73236 −0.866180 0.499733i \(-0.833432\pi\)
−0.866180 + 0.499733i \(0.833432\pi\)
\(440\) 0 0
\(441\) 11.9627 20.2148i 0.569651 0.962610i
\(442\) 0 0
\(443\) −1.80487 + 12.5531i −0.0857518 + 0.596417i 0.900956 + 0.433911i \(0.142867\pi\)
−0.986708 + 0.162506i \(0.948042\pi\)
\(444\) 0 0
\(445\) −8.13745 1.16999i −0.385752 0.0554628i
\(446\) 0 0
\(447\) −8.42381 21.3740i −0.398433 1.01096i
\(448\) 0 0
\(449\) −9.35902 + 4.27412i −0.441680 + 0.201708i −0.623826 0.781563i \(-0.714423\pi\)
0.182147 + 0.983271i \(0.441695\pi\)
\(450\) 0 0
\(451\) 7.16731 + 49.8497i 0.337495 + 2.34733i
\(452\) 0 0
\(453\) 14.2138 + 7.42472i 0.667822 + 0.348844i
\(454\) 0 0
\(455\) −7.48715 52.0743i −0.351003 2.44128i
\(456\) 0 0
\(457\) −17.7520 + 11.4085i −0.830403 + 0.533668i −0.885406 0.464818i \(-0.846120\pi\)
0.0550027 + 0.998486i \(0.482483\pi\)
\(458\) 0 0
\(459\) 3.67867 1.60880i 0.171706 0.0750924i
\(460\) 0 0
\(461\) 19.4412 30.2511i 0.905468 1.40894i −0.00708430 0.999975i \(-0.502255\pi\)
0.912552 0.408960i \(-0.134109\pi\)
\(462\) 0 0
\(463\) 7.61122 25.9214i 0.353723 1.20467i −0.570011 0.821637i \(-0.693061\pi\)
0.923734 0.383034i \(-0.125121\pi\)
\(464\) 0 0
\(465\) 9.82591 + 7.07692i 0.455666 + 0.328185i
\(466\) 0 0
\(467\) −28.5506 24.7392i −1.32116 1.14479i −0.978707 0.205261i \(-0.934196\pi\)
−0.342457 0.939534i \(-0.611259\pi\)
\(468\) 0 0
\(469\) −12.3681 28.9935i −0.571108 1.33879i
\(470\) 0 0
\(471\) 8.49125 0.764769i 0.391256 0.0352387i
\(472\) 0 0
\(473\) 2.47828 0.356323i 0.113951 0.0163837i
\(474\) 0 0
\(475\) 3.16440 + 0.929153i 0.145193 + 0.0426325i
\(476\) 0 0
\(477\) −1.28796 + 2.17643i −0.0589717 + 0.0996518i
\(478\) 0 0
\(479\) 29.6370 + 13.5348i 1.35415 + 0.618420i 0.954490 0.298243i \(-0.0964005\pi\)
0.399661 + 0.916663i \(0.369128\pi\)
\(480\) 0 0
\(481\) −18.6439 29.0105i −0.850089 1.32276i
\(482\) 0 0
\(483\) −20.1270 + 27.9452i −0.915812 + 1.27155i
\(484\) 0 0
\(485\) 0.738860 + 2.51633i 0.0335499 + 0.114261i
\(486\) 0 0
\(487\) 2.23477 0.321312i 0.101267 0.0145600i −0.0914949 0.995806i \(-0.529165\pi\)
0.192762 + 0.981246i \(0.438255\pi\)
\(488\) 0 0
\(489\) 4.43191 12.5858i 0.200418 0.569150i
\(490\) 0 0
\(491\) −3.36878 1.53847i −0.152031 0.0694303i 0.337946 0.941165i \(-0.390268\pi\)
−0.489977 + 0.871735i \(0.662995\pi\)
\(492\) 0 0
\(493\) −0.927321 + 6.44966i −0.0417645 + 0.290478i
\(494\) 0 0
\(495\) −35.7170 3.79854i −1.60536 0.170732i
\(496\) 0 0
\(497\) −23.6994 15.2307i −1.06306 0.683188i
\(498\) 0 0
\(499\) 8.44924i 0.378240i 0.981954 + 0.189120i \(0.0605635\pi\)
−0.981954 + 0.189120i \(0.939436\pi\)
\(500\) 0 0
\(501\) −11.0307 27.9885i −0.492815 1.25043i
\(502\) 0 0
\(503\) −3.25435 3.75572i −0.145104 0.167459i 0.678545 0.734559i \(-0.262611\pi\)
−0.823649 + 0.567100i \(0.808065\pi\)
\(504\) 0 0
\(505\) −3.86234 2.48218i −0.171872 0.110455i
\(506\) 0 0
\(507\) 34.5635 + 33.3128i 1.53502 + 1.47948i
\(508\) 0 0
\(509\) −3.15472 + 10.7440i −0.139831 + 0.476219i −0.999394 0.0348099i \(-0.988917\pi\)
0.859563 + 0.511029i \(0.170736\pi\)
\(510\) 0 0
\(511\) −13.7201 21.3489i −0.606941 0.944418i
\(512\) 0 0
\(513\) 39.3327 + 12.2416i 1.73658 + 0.540478i
\(514\) 0 0
\(515\) −5.61819 1.64965i −0.247567 0.0726923i
\(516\) 0 0
\(517\) 14.7305 12.7640i 0.647845 0.561361i
\(518\) 0 0
\(519\) 4.01644 + 5.16421i 0.176302 + 0.226684i
\(520\) 0 0
\(521\) 2.87894 + 3.32248i 0.126129 + 0.145560i 0.815301 0.579037i \(-0.196571\pi\)
−0.689173 + 0.724597i \(0.742026\pi\)
\(522\) 0 0
\(523\) −5.19011 + 3.33548i −0.226948 + 0.145850i −0.649174 0.760640i \(-0.724885\pi\)
0.422226 + 0.906491i \(0.361249\pi\)
\(524\) 0 0
\(525\) 1.28472 2.45946i 0.0560699 0.107340i
\(526\) 0 0
\(527\) 1.65231 1.90687i 0.0719759 0.0830646i
\(528\) 0 0
\(529\) 2.39607 2.76522i 0.104177 0.120227i
\(530\) 0 0
\(531\) 31.6492 10.5742i 1.37346 0.458882i
\(532\) 0 0
\(533\) −52.2728 + 23.8722i −2.26418 + 1.03402i
\(534\) 0 0
\(535\) 4.35694i 0.188367i
\(536\) 0 0
\(537\) 8.14482 + 7.85011i 0.351475 + 0.338757i
\(538\) 0 0
\(539\) 18.1888 + 39.8279i 0.783447 + 1.71551i
\(540\) 0 0
\(541\) −4.93169 16.7958i −0.212030 0.722108i −0.994985 0.100029i \(-0.968107\pi\)
0.782955 0.622079i \(-0.213712\pi\)
\(542\) 0 0
\(543\) −13.0613 + 1.17637i −0.560514 + 0.0504830i
\(544\) 0 0
\(545\) 24.2734 + 21.0331i 1.03976 + 0.900957i
\(546\) 0 0
\(547\) −6.70920 22.8494i −0.286865 0.976971i −0.969270 0.245998i \(-0.920884\pi\)
0.682406 0.730974i \(-0.260934\pi\)
\(548\) 0 0
\(549\) −23.9767 + 16.6881i −1.02330 + 0.712231i
\(550\) 0 0
\(551\) −50.5235 + 43.7789i −2.15238 + 1.86504i
\(552\) 0 0
\(553\) 1.29076 8.97740i 0.0548885 0.381758i
\(554\) 0 0
\(555\) −1.06124 + 20.0135i −0.0450470 + 0.849526i
\(556\) 0 0
\(557\) 10.2018 34.7442i 0.432264 1.47216i −0.399347 0.916800i \(-0.630763\pi\)
0.831612 0.555358i \(-0.187419\pi\)
\(558\) 0 0
\(559\) 1.18681 + 2.59874i 0.0501965 + 0.109915i
\(560\) 0 0
\(561\) −1.45589 + 7.34126i −0.0614677 + 0.309948i
\(562\) 0 0
\(563\) −4.92173 1.44515i −0.207426 0.0609059i 0.176369 0.984324i \(-0.443565\pi\)
−0.383795 + 0.923418i \(0.625383\pi\)
\(564\) 0 0
\(565\) 40.8500 1.71857
\(566\) 0 0
\(567\) 16.5402 30.4570i 0.694624 1.27907i
\(568\) 0 0
\(569\) 24.4368 21.1746i 1.02445 0.887687i 0.0307191 0.999528i \(-0.490220\pi\)
0.993726 + 0.111841i \(0.0356748\pi\)
\(570\) 0 0
\(571\) −1.79742 + 3.93581i −0.0752198 + 0.164708i −0.943506 0.331355i \(-0.892494\pi\)
0.868286 + 0.496063i \(0.165222\pi\)
\(572\) 0 0
\(573\) 3.63048 + 3.49911i 0.151666 + 0.146178i
\(574\) 0 0
\(575\) −1.16127 + 1.80697i −0.0484282 + 0.0753557i
\(576\) 0 0
\(577\) 12.8650 + 1.84971i 0.535577 + 0.0770043i 0.404796 0.914407i \(-0.367342\pi\)
0.130781 + 0.991411i \(0.458252\pi\)
\(578\) 0 0
\(579\) 6.95664 5.41048i 0.289108 0.224852i
\(580\) 0 0
\(581\) −16.2657 + 35.6169i −0.674815 + 1.47764i
\(582\) 0 0
\(583\) −1.95830 4.28807i −0.0811044 0.177594i
\(584\) 0 0
\(585\) −7.32320 40.3251i −0.302777 1.66724i
\(586\) 0 0
\(587\) −10.5178 + 3.08830i −0.434116 + 0.127468i −0.491487 0.870885i \(-0.663546\pi\)
0.0573709 + 0.998353i \(0.481728\pi\)
\(588\) 0 0
\(589\) 25.6233 3.68408i 1.05579 0.151800i
\(590\) 0 0
\(591\) 1.02470 + 0.203215i 0.0421506 + 0.00835915i
\(592\) 0 0
\(593\) −6.86975 + 15.0427i −0.282107 + 0.617728i −0.996643 0.0818707i \(-0.973911\pi\)
0.714536 + 0.699599i \(0.246638\pi\)
\(594\) 0 0
\(595\) 5.35954 + 3.44437i 0.219720 + 0.141205i
\(596\) 0 0
\(597\) 9.01043 + 15.8021i 0.368773 + 0.646738i
\(598\) 0 0
\(599\) 5.87718 + 40.8767i 0.240135 + 1.67018i 0.651456 + 0.758686i \(0.274158\pi\)
−0.411321 + 0.911490i \(0.634933\pi\)
\(600\) 0 0
\(601\) −16.6168 + 19.1768i −0.677812 + 0.782236i −0.985577 0.169226i \(-0.945873\pi\)
0.307766 + 0.951462i \(0.400419\pi\)
\(602\) 0 0
\(603\) −10.4607 22.2165i −0.425992 0.904727i
\(604\) 0 0
\(605\) 28.4221 32.8008i 1.15552 1.33354i
\(606\) 0 0
\(607\) 2.41607 + 16.8041i 0.0980651 + 0.682058i 0.978250 + 0.207428i \(0.0665092\pi\)
−0.880185 + 0.474630i \(0.842582\pi\)
\(608\) 0 0
\(609\) 27.8609 + 48.8614i 1.12898 + 1.97996i
\(610\) 0 0
\(611\) 18.7098 + 12.0241i 0.756917 + 0.486441i
\(612\) 0 0
\(613\) 5.03209 11.0187i 0.203244 0.445043i −0.780372 0.625315i \(-0.784970\pi\)
0.983617 + 0.180272i \(0.0576978\pi\)
\(614\) 0 0
\(615\) 32.7595 + 6.49675i 1.32099 + 0.261974i
\(616\) 0 0
\(617\) 9.54492 1.37235i 0.384264 0.0552488i 0.0525240 0.998620i \(-0.483273\pi\)
0.331740 + 0.943371i \(0.392364\pi\)
\(618\) 0 0
\(619\) −38.3872 + 11.2715i −1.54291 + 0.453040i −0.938973 0.343990i \(-0.888221\pi\)
−0.603940 + 0.797030i \(0.706403\pi\)
\(620\) 0 0
\(621\) −14.8669 + 22.3330i −0.596590 + 0.896194i
\(622\) 0 0
\(623\) 6.14269 + 13.4506i 0.246102 + 0.538888i
\(624\) 0 0
\(625\) −9.44940 + 20.6913i −0.377976 + 0.827652i
\(626\) 0 0
\(627\) −60.6123 + 47.1408i −2.42062 + 1.88262i
\(628\) 0 0
\(629\) 4.13352 + 0.594310i 0.164814 + 0.0236967i
\(630\) 0 0
\(631\) −12.1271 + 18.8702i −0.482774 + 0.751210i −0.994134 0.108156i \(-0.965505\pi\)
0.511360 + 0.859366i \(0.329142\pi\)
\(632\) 0 0
\(633\) −12.4758 12.0244i −0.495868 0.477925i
\(634\) 0 0
\(635\) 4.05866 8.88723i 0.161063 0.352679i
\(636\) 0 0
\(637\) −37.7575 + 32.7171i −1.49601 + 1.29630i
\(638\) 0 0
\(639\) −18.8871 11.1770i −0.747162 0.442154i
\(640\) 0 0
\(641\) 44.6524 1.76366 0.881831 0.471565i \(-0.156311\pi\)
0.881831 + 0.471565i \(0.156311\pi\)
\(642\) 0 0
\(643\) −10.6277 3.12056i −0.419114 0.123063i 0.0653743 0.997861i \(-0.479176\pi\)
−0.484488 + 0.874798i \(0.660994\pi\)
\(644\) 0 0
\(645\) 0.322986 1.62864i 0.0127176 0.0641277i
\(646\) 0 0
\(647\) −6.78193 14.8504i −0.266625 0.583828i 0.728207 0.685357i \(-0.240354\pi\)
−0.994833 + 0.101529i \(0.967627\pi\)
\(648\) 0 0
\(649\) −17.5240 + 59.6812i −0.687877 + 2.34269i
\(650\) 0 0
\(651\) 1.15329 21.7495i 0.0452009 0.852429i
\(652\) 0 0
\(653\) −3.18187 + 22.1304i −0.124516 + 0.866029i 0.827823 + 0.560989i \(0.189579\pi\)
−0.952340 + 0.305040i \(0.901330\pi\)
\(654\) 0 0
\(655\) 4.99989 4.33243i 0.195362 0.169282i
\(656\) 0 0
\(657\) −11.2938 16.2264i −0.440612 0.633052i
\(658\) 0 0
\(659\) −10.0400 34.1930i −0.391101 1.33197i −0.886269 0.463171i \(-0.846712\pi\)
0.495168 0.868797i \(-0.335107\pi\)
\(660\) 0 0
\(661\) 3.86237 + 3.34676i 0.150229 + 0.130174i 0.726733 0.686920i \(-0.241038\pi\)
−0.576504 + 0.817094i \(0.695583\pi\)
\(662\) 0 0
\(663\) −8.50543 + 0.766047i −0.330323 + 0.0297508i
\(664\) 0 0
\(665\) 18.4151 + 62.7160i 0.714106 + 2.43202i
\(666\) 0 0
\(667\) −18.0872 39.6054i −0.700339 1.53353i
\(668\) 0 0
\(669\) −13.8657 13.3640i −0.536080 0.516683i
\(670\) 0 0
\(671\) 54.4531i 2.10214i
\(672\) 0 0
\(673\) −2.83398 + 1.29423i −0.109242 + 0.0498890i −0.469286 0.883046i \(-0.655489\pi\)
0.360045 + 0.932935i \(0.382761\pi\)
\(674\) 0 0
\(675\) 0.929577 1.95156i 0.0357794 0.0751156i
\(676\) 0 0
\(677\) −15.1871 + 17.5269i −0.583689 + 0.673613i −0.968394 0.249427i \(-0.919758\pi\)
0.384705 + 0.923040i \(0.374303\pi\)
\(678\) 0 0
\(679\) 3.08901 3.56491i 0.118545 0.136809i
\(680\) 0 0
\(681\) 13.5276 25.8972i 0.518381 0.992381i
\(682\) 0 0
\(683\) −22.4208 + 14.4090i −0.857909 + 0.551344i −0.894032 0.448003i \(-0.852135\pi\)
0.0361235 + 0.999347i \(0.488499\pi\)
\(684\) 0 0
\(685\) 12.0568 + 13.9143i 0.460667 + 0.531638i
\(686\) 0 0
\(687\) 17.7131 + 22.7750i 0.675796 + 0.868919i
\(688\) 0 0
\(689\) 4.06516 3.52248i 0.154870 0.134196i
\(690\) 0 0
\(691\) −37.8298 11.1078i −1.43911 0.422562i −0.533187 0.845997i \(-0.679006\pi\)
−0.905926 + 0.423435i \(0.860824\pi\)
\(692\) 0 0
\(693\) 28.9843 + 57.7377i 1.10102 + 2.19327i
\(694\) 0 0
\(695\) 20.3420 + 31.6528i 0.771616 + 1.20066i
\(696\) 0 0
\(697\) 1.96056 6.67707i 0.0742617 0.252912i
\(698\) 0 0
\(699\) 16.9817 + 16.3672i 0.642307 + 0.619066i
\(700\) 0 0
\(701\) −26.6339 17.1166i −1.00595 0.646483i −0.0696066 0.997575i \(-0.522174\pi\)
−0.936341 + 0.351091i \(0.885811\pi\)
\(702\) 0 0
\(703\) 28.0574 + 32.3800i 1.05820 + 1.22123i
\(704\) 0 0
\(705\) −4.73933 12.0253i −0.178494 0.452898i
\(706\) 0 0
\(707\) 8.25788i 0.310570i
\(708\) 0 0
\(709\) −27.0527 17.3857i −1.01599 0.652935i −0.0770512 0.997027i \(-0.524550\pi\)
−0.938936 + 0.344092i \(0.888187\pi\)
\(710\) 0 0
\(711\) 0.747219 7.02597i 0.0280229 0.263494i
\(712\) 0 0
\(713\) −2.39940 + 16.6882i −0.0898582 + 0.624977i
\(714\) 0 0
\(715\) 69.4927 + 31.7363i 2.59888 + 1.18687i
\(716\) 0 0
\(717\) −3.31329 + 9.40914i −0.123737 + 0.351391i
\(718\) 0 0
\(719\) −10.6376 + 1.52946i −0.396717 + 0.0570393i −0.337786 0.941223i \(-0.609678\pi\)
−0.0589305 + 0.998262i \(0.518769\pi\)
\(720\) 0 0
\(721\) 2.96713 + 10.1051i 0.110502 + 0.376334i
\(722\) 0 0
\(723\) −12.1564 + 16.8784i −0.452100 + 0.627716i
\(724\) 0 0
\(725\) 1.89661 + 2.95119i 0.0704385 + 0.109604i
\(726\) 0 0
\(727\) −4.85499 2.21720i −0.180062 0.0822314i 0.323344 0.946281i \(-0.395193\pi\)
−0.503406 + 0.864050i \(0.667920\pi\)
\(728\) 0 0
\(729\) 12.0025 24.1855i 0.444538 0.895760i
\(730\) 0 0
\(731\) −0.331951 0.0974695i −0.0122776 0.00360504i
\(732\) 0 0
\(733\) 27.6536 3.97598i 1.02141 0.146856i 0.388795 0.921324i \(-0.372891\pi\)
0.632613 + 0.774468i \(0.281982\pi\)
\(734\) 0 0
\(735\) 28.9185 2.60456i 1.06667 0.0960707i
\(736\) 0 0
\(737\) 45.1289 + 7.65321i 1.66234 + 0.281909i
\(738\) 0 0
\(739\) −10.7060 9.27680i −0.393826 0.341252i 0.435328 0.900272i \(-0.356632\pi\)
−0.829155 + 0.559019i \(0.811178\pi\)
\(740\) 0 0
\(741\) −71.0961 51.2056i −2.61178 1.88108i
\(742\) 0 0
\(743\) 11.1004 37.8045i 0.407234 1.38691i −0.459517 0.888169i \(-0.651977\pi\)
0.866751 0.498742i \(-0.166204\pi\)
\(744\) 0 0
\(745\) 15.3535 23.8906i 0.562510 0.875283i
\(746\) 0 0
\(747\) −11.6407 + 28.1946i −0.425912 + 1.03159i
\(748\) 0 0
\(749\) −6.59255 + 4.23677i −0.240887 + 0.154808i
\(750\) 0 0
\(751\) −1.92313 13.3756i −0.0701758 0.488084i −0.994353 0.106120i \(-0.966157\pi\)
0.924177 0.381963i \(-0.124752\pi\)
\(752\) 0 0
\(753\) −5.22882 2.73133i −0.190549 0.0995351i
\(754\) 0 0
\(755\) 2.82105 + 19.6209i 0.102669 + 0.714076i
\(756\) 0 0
\(757\) 36.5661 16.6992i 1.32902 0.606942i 0.380828 0.924646i \(-0.375639\pi\)
0.948190 + 0.317704i \(0.102912\pi\)
\(758\) 0 0
\(759\) −18.3369 46.5268i −0.665588 1.68882i
\(760\) 0 0
\(761\) −1.08944 0.156638i −0.0394923 0.00567813i 0.122540 0.992464i \(-0.460896\pi\)
−0.162033 + 0.986785i \(0.551805\pi\)
\(762\) 0 0
\(763\) 8.22145 57.1815i 0.297637 2.07011i
\(764\) 0 0
\(765\) 4.27126 + 2.52764i 0.154428 + 0.0913869i
\(766\) 0 0
\(767\) −70.9740 −2.56272
\(768\) 0 0
\(769\) 32.1287 + 14.6727i 1.15859 + 0.529111i 0.899577 0.436763i \(-0.143875\pi\)
0.259014 + 0.965874i \(0.416602\pi\)
\(770\) 0 0
\(771\) 45.5981 + 2.41789i 1.64218 + 0.0870781i
\(772\) 0 0
\(773\) 9.47518 14.7437i 0.340798 0.530293i −0.627977 0.778232i \(-0.716117\pi\)
0.968776 + 0.247939i \(0.0797533\pi\)
\(774\) 0 0
\(775\) 1.35842i 0.0487958i
\(776\) 0 0
\(777