Properties

Label 804.2.s.b.5.15
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 5.15
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.15

$q$-expansion

\(f(q)\) \(=\) \(q+(0.650892 + 1.60510i) q^{3} +(-0.966140 + 0.283684i) q^{5} +(1.54930 + 1.34247i) q^{7} +(-2.15268 + 2.08949i) q^{9} +O(q^{10})\) \(q+(0.650892 + 1.60510i) q^{3} +(-0.966140 + 0.283684i) q^{5} +(1.54930 + 1.34247i) q^{7} +(-2.15268 + 2.08949i) q^{9} +(-2.68695 + 0.788959i) q^{11} +(0.303154 + 0.471717i) q^{13} +(-1.08419 - 1.36610i) q^{15} +(-2.99315 - 0.430350i) q^{17} +(3.48728 + 4.02453i) q^{19} +(-1.14638 + 3.36058i) q^{21} +(-1.38260 + 0.631411i) q^{23} +(-3.35332 + 2.15505i) q^{25} +(-4.75500 - 2.09523i) q^{27} +1.01679i q^{29} +(1.77218 - 2.75757i) q^{31} +(-3.01527 - 3.79929i) q^{33} +(-1.87767 - 0.857505i) q^{35} +0.414150 q^{37} +(-0.559831 + 0.793629i) q^{39} +(-0.649850 + 4.51980i) q^{41} +(0.863281 + 0.124121i) q^{43} +(1.48703 - 2.62942i) q^{45} +(-1.67750 + 0.766089i) q^{47} +(-0.398118 - 2.76897i) q^{49} +(-1.25746 - 5.08441i) q^{51} +(1.21708 + 8.46498i) q^{53} +(2.37215 - 1.52449i) q^{55} +(-4.18993 + 8.21696i) q^{57} +(-1.75024 + 2.72343i) q^{59} +(-0.230536 + 0.785133i) q^{61} +(-6.14022 + 0.347328i) q^{63} +(-0.426708 - 0.369744i) q^{65} +(8.16532 - 0.572263i) q^{67} +(-1.91340 - 1.80822i) q^{69} +(-2.98320 + 0.428919i) q^{71} +(-3.06133 - 0.898887i) q^{73} +(-5.64171 - 3.97970i) q^{75} +(-5.22203 - 2.38482i) q^{77} +(0.0461512 + 0.0718126i) q^{79} +(0.268052 - 8.99601i) q^{81} +(-3.01301 - 10.2614i) q^{83} +(3.01389 - 0.433331i) q^{85} +(-1.63205 + 0.661823i) q^{87} +(8.74397 + 3.99324i) q^{89} +(-0.163592 + 1.13781i) q^{91} +(5.57967 + 1.04965i) q^{93} +(-4.51089 - 2.89897i) q^{95} +3.47150i q^{97} +(4.13561 - 7.31273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

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
\(3\) 0.650892 + 1.60510i 0.375793 + 0.926704i
\(4\) 0 0
\(5\) −0.966140 + 0.283684i −0.432071 + 0.126867i −0.490534 0.871422i \(-0.663198\pi\)
0.0584631 + 0.998290i \(0.481380\pi\)
\(6\) 0 0
\(7\) 1.54930 + 1.34247i 0.585579 + 0.507407i 0.896509 0.443026i \(-0.146095\pi\)
−0.310930 + 0.950433i \(0.600640\pi\)
\(8\) 0 0
\(9\) −2.15268 + 2.08949i −0.717560 + 0.696497i
\(10\) 0 0
\(11\) −2.68695 + 0.788959i −0.810145 + 0.237880i −0.660467 0.750855i \(-0.729642\pi\)
−0.149678 + 0.988735i \(0.547824\pi\)
\(12\) 0 0
\(13\) 0.303154 + 0.471717i 0.0840798 + 0.130831i 0.880746 0.473588i \(-0.157042\pi\)
−0.796666 + 0.604419i \(0.793405\pi\)
\(14\) 0 0
\(15\) −1.08419 1.36610i −0.279938 0.352726i
\(16\) 0 0
\(17\) −2.99315 0.430350i −0.725946 0.104375i −0.230572 0.973055i \(-0.574060\pi\)
−0.495374 + 0.868680i \(0.664969\pi\)
\(18\) 0 0
\(19\) 3.48728 + 4.02453i 0.800036 + 0.923291i 0.998383 0.0568410i \(-0.0181028\pi\)
−0.198347 + 0.980132i \(0.563557\pi\)
\(20\) 0 0
\(21\) −1.14638 + 3.36058i −0.250160 + 0.733338i
\(22\) 0 0
\(23\) −1.38260 + 0.631411i −0.288292 + 0.131658i −0.554312 0.832309i \(-0.687018\pi\)
0.266020 + 0.963967i \(0.414291\pi\)
\(24\) 0 0
\(25\) −3.35332 + 2.15505i −0.670664 + 0.431009i
\(26\) 0 0
\(27\) −4.75500 2.09523i −0.915100 0.403227i
\(28\) 0 0
\(29\) 1.01679i 0.188814i 0.995534 + 0.0944069i \(0.0300955\pi\)
−0.995534 + 0.0944069i \(0.969905\pi\)
\(30\) 0 0
\(31\) 1.77218 2.75757i 0.318293 0.495274i −0.644833 0.764323i \(-0.723073\pi\)
0.963126 + 0.269049i \(0.0867095\pi\)
\(32\) 0 0
\(33\) −3.01527 3.79929i −0.524891 0.661371i
\(34\) 0 0
\(35\) −1.87767 0.857505i −0.317385 0.144945i
\(36\) 0 0
\(37\) 0.414150 0.0680858 0.0340429 0.999420i \(-0.489162\pi\)
0.0340429 + 0.999420i \(0.489162\pi\)
\(38\) 0 0
\(39\) −0.559831 + 0.793629i −0.0896448 + 0.127082i
\(40\) 0 0
\(41\) −0.649850 + 4.51980i −0.101489 + 0.705875i 0.874016 + 0.485898i \(0.161507\pi\)
−0.975505 + 0.219977i \(0.929402\pi\)
\(42\) 0 0
\(43\) 0.863281 + 0.124121i 0.131649 + 0.0189283i 0.207824 0.978166i \(-0.433362\pi\)
−0.0761752 + 0.997094i \(0.524271\pi\)
\(44\) 0 0
\(45\) 1.48703 2.62942i 0.221674 0.391971i
\(46\) 0 0
\(47\) −1.67750 + 0.766089i −0.244689 + 0.111746i −0.533985 0.845494i \(-0.679306\pi\)
0.289296 + 0.957240i \(0.406579\pi\)
\(48\) 0 0
\(49\) −0.398118 2.76897i −0.0568740 0.395568i
\(50\) 0 0
\(51\) −1.25746 5.08441i −0.176080 0.711960i
\(52\) 0 0
\(53\) 1.21708 + 8.46498i 0.167179 + 1.16275i 0.884681 + 0.466197i \(0.154376\pi\)
−0.717502 + 0.696557i \(0.754715\pi\)
\(54\) 0 0
\(55\) 2.37215 1.52449i 0.319861 0.205562i
\(56\) 0 0
\(57\) −4.18993 + 8.21696i −0.554969 + 1.08836i
\(58\) 0 0
\(59\) −1.75024 + 2.72343i −0.227862 + 0.354560i −0.936293 0.351220i \(-0.885767\pi\)
0.708431 + 0.705780i \(0.249403\pi\)
\(60\) 0 0
\(61\) −0.230536 + 0.785133i −0.0295171 + 0.100526i −0.972934 0.231083i \(-0.925773\pi\)
0.943417 + 0.331609i \(0.107591\pi\)
\(62\) 0 0
\(63\) −6.14022 + 0.347328i −0.773595 + 0.0437593i
\(64\) 0 0
\(65\) −0.426708 0.369744i −0.0529266 0.0458612i
\(66\) 0 0
\(67\) 8.16532 0.572263i 0.997553 0.0699131i
\(68\) 0 0
\(69\) −1.91340 1.80822i −0.230346 0.217685i
\(70\) 0 0
\(71\) −2.98320 + 0.428919i −0.354040 + 0.0509033i −0.317041 0.948412i \(-0.602689\pi\)
−0.0369996 + 0.999315i \(0.511780\pi\)
\(72\) 0 0
\(73\) −3.06133 0.898887i −0.358301 0.105207i 0.0976275 0.995223i \(-0.468875\pi\)
−0.455929 + 0.890016i \(0.650693\pi\)
\(74\) 0 0
\(75\) −5.64171 3.97970i −0.651449 0.459536i
\(76\) 0 0
\(77\) −5.22203 2.38482i −0.595106 0.271776i
\(78\) 0 0
\(79\) 0.0461512 + 0.0718126i 0.00519241 + 0.00807955i 0.843840 0.536595i \(-0.180290\pi\)
−0.838648 + 0.544674i \(0.816653\pi\)
\(80\) 0 0
\(81\) 0.268052 8.99601i 0.0297835 0.999556i
\(82\) 0 0
\(83\) −3.01301 10.2614i −0.330720 1.12633i −0.942195 0.335066i \(-0.891241\pi\)
0.611474 0.791264i \(-0.290577\pi\)
\(84\) 0 0
\(85\) 3.01389 0.433331i 0.326902 0.0470014i
\(86\) 0 0
\(87\) −1.63205 + 0.661823i −0.174975 + 0.0709549i
\(88\) 0 0
\(89\) 8.74397 + 3.99324i 0.926859 + 0.423282i 0.820890 0.571087i \(-0.193478\pi\)
0.105970 + 0.994369i \(0.466205\pi\)
\(90\) 0 0
\(91\) −0.163592 + 1.13781i −0.0171491 + 0.119274i
\(92\) 0 0
\(93\) 5.57967 + 1.04965i 0.578585 + 0.108843i
\(94\) 0 0
\(95\) −4.51089 2.89897i −0.462808 0.297428i
\(96\) 0 0
\(97\) 3.47150i 0.352477i 0.984347 + 0.176239i \(0.0563930\pi\)
−0.984347 + 0.176239i \(0.943607\pi\)
\(98\) 0 0
\(99\) 4.13561 7.31273i 0.415645 0.734957i
\(100\) 0 0
\(101\) 2.21410 + 2.55520i 0.220311 + 0.254252i 0.855136 0.518403i \(-0.173473\pi\)
−0.634825 + 0.772656i \(0.718928\pi\)
\(102\) 0 0
\(103\) 8.21404 + 5.27884i 0.809354 + 0.520140i 0.878656 0.477456i \(-0.158441\pi\)
−0.0693021 + 0.997596i \(0.522077\pi\)
\(104\) 0 0
\(105\) 0.154216 3.57200i 0.0150500 0.348591i
\(106\) 0 0
\(107\) 1.90540 6.48919i 0.184202 0.627334i −0.814673 0.579920i \(-0.803084\pi\)
0.998875 0.0474140i \(-0.0150980\pi\)
\(108\) 0 0
\(109\) 7.92724 + 12.3350i 0.759292 + 1.18148i 0.978589 + 0.205824i \(0.0659873\pi\)
−0.219297 + 0.975658i \(0.570376\pi\)
\(110\) 0 0
\(111\) 0.269567 + 0.664751i 0.0255861 + 0.0630953i
\(112\) 0 0
\(113\) 12.4656 + 3.66022i 1.17266 + 0.344324i 0.809340 0.587340i \(-0.199825\pi\)
0.363321 + 0.931664i \(0.381643\pi\)
\(114\) 0 0
\(115\) 1.15666 1.00225i 0.107859 0.0934606i
\(116\) 0 0
\(117\) −1.63824 0.382017i −0.151456 0.0353175i
\(118\) 0 0
\(119\) −4.05954 4.68496i −0.372138 0.429470i
\(120\) 0 0
\(121\) −2.65656 + 1.70727i −0.241505 + 0.155206i
\(122\) 0 0
\(123\) −7.67771 + 1.89883i −0.692276 + 0.171212i
\(124\) 0 0
\(125\) 5.92541 6.83828i 0.529985 0.611635i
\(126\) 0 0
\(127\) −1.39668 + 1.61186i −0.123936 + 0.143029i −0.814326 0.580408i \(-0.802893\pi\)
0.690391 + 0.723437i \(0.257439\pi\)
\(128\) 0 0
\(129\) 0.362676 + 1.46644i 0.0319319 + 0.129113i
\(130\) 0 0
\(131\) 7.30624 3.33665i 0.638349 0.291524i −0.0698282 0.997559i \(-0.522245\pi\)
0.708177 + 0.706035i \(0.249518\pi\)
\(132\) 0 0
\(133\) 10.9168i 0.946604i
\(134\) 0 0
\(135\) 5.18838 + 0.675363i 0.446544 + 0.0581260i
\(136\) 0 0
\(137\) 6.97149 + 15.2654i 0.595615 + 1.30421i 0.931989 + 0.362486i \(0.118072\pi\)
−0.336375 + 0.941728i \(0.609201\pi\)
\(138\) 0 0
\(139\) −2.28442 7.78001i −0.193762 0.659892i −0.997859 0.0653948i \(-0.979169\pi\)
0.804098 0.594497i \(-0.202649\pi\)
\(140\) 0 0
\(141\) −2.32152 2.19391i −0.195507 0.184761i
\(142\) 0 0
\(143\) −1.18672 1.02830i −0.0992389 0.0859910i
\(144\) 0 0
\(145\) −0.288448 0.982365i −0.0239543 0.0815809i
\(146\) 0 0
\(147\) 4.18534 2.44132i 0.345201 0.201357i
\(148\) 0 0
\(149\) 16.1494 13.9935i 1.32301 1.14640i 0.344825 0.938667i \(-0.387938\pi\)
0.978187 0.207729i \(-0.0666071\pi\)
\(150\) 0 0
\(151\) 0.189990 1.32141i 0.0154611 0.107535i −0.980629 0.195872i \(-0.937246\pi\)
0.996091 + 0.0883374i \(0.0281554\pi\)
\(152\) 0 0
\(153\) 7.34251 5.32776i 0.593606 0.430724i
\(154\) 0 0
\(155\) −0.929896 + 3.16694i −0.0746911 + 0.254374i
\(156\) 0 0
\(157\) 8.86174 + 19.4045i 0.707244 + 1.54865i 0.830961 + 0.556330i \(0.187791\pi\)
−0.123718 + 0.992317i \(0.539482\pi\)
\(158\) 0 0
\(159\) −12.7949 + 7.46332i −1.01470 + 0.591880i
\(160\) 0 0
\(161\) −2.98971 0.877857i −0.235622 0.0691848i
\(162\) 0 0
\(163\) −1.47744 −0.115722 −0.0578608 0.998325i \(-0.518428\pi\)
−0.0578608 + 0.998325i \(0.518428\pi\)
\(164\) 0 0
\(165\) 3.99097 + 2.81526i 0.310697 + 0.219167i
\(166\) 0 0
\(167\) −1.89688 + 1.64366i −0.146785 + 0.127190i −0.725158 0.688582i \(-0.758233\pi\)
0.578373 + 0.815773i \(0.303688\pi\)
\(168\) 0 0
\(169\) 5.26978 11.5392i 0.405368 0.887632i
\(170\) 0 0
\(171\) −15.9162 1.37689i −1.21714 0.105293i
\(172\) 0 0
\(173\) 6.75608 10.5127i 0.513655 0.799263i −0.483444 0.875375i \(-0.660614\pi\)
0.997099 + 0.0761122i \(0.0242507\pi\)
\(174\) 0 0
\(175\) −8.08838 1.16293i −0.611424 0.0879095i
\(176\) 0 0
\(177\) −5.51059 1.03665i −0.414201 0.0779194i
\(178\) 0 0
\(179\) 4.58992 10.0505i 0.343067 0.751212i −0.656929 0.753952i \(-0.728145\pi\)
0.999996 + 0.00274020i \(0.000872234\pi\)
\(180\) 0 0
\(181\) 0.387326 + 0.848125i 0.0287897 + 0.0630406i 0.923481 0.383645i \(-0.125331\pi\)
−0.894691 + 0.446686i \(0.852604\pi\)
\(182\) 0 0
\(183\) −1.41027 + 0.141004i −0.104250 + 0.0104233i
\(184\) 0 0
\(185\) −0.400126 + 0.117488i −0.0294179 + 0.00863787i
\(186\) 0 0
\(187\) 8.38197 1.20515i 0.612950 0.0881289i
\(188\) 0 0
\(189\) −4.55412 9.62959i −0.331263 0.700449i
\(190\) 0 0
\(191\) −3.97243 + 8.69841i −0.287435 + 0.629395i −0.997179 0.0750653i \(-0.976083\pi\)
0.709744 + 0.704460i \(0.248811\pi\)
\(192\) 0 0
\(193\) 20.1470 + 12.9477i 1.45021 + 0.931994i 0.999221 + 0.0394647i \(0.0125653\pi\)
0.450990 + 0.892529i \(0.351071\pi\)
\(194\) 0 0
\(195\) 0.315735 0.925572i 0.0226103 0.0662816i
\(196\) 0 0
\(197\) 1.49850 + 10.4223i 0.106764 + 0.742560i 0.970932 + 0.239356i \(0.0769363\pi\)
−0.864168 + 0.503204i \(0.832155\pi\)
\(198\) 0 0
\(199\) −7.29446 + 8.41826i −0.517091 + 0.596755i −0.952900 0.303284i \(-0.901917\pi\)
0.435809 + 0.900039i \(0.356462\pi\)
\(200\) 0 0
\(201\) 6.23328 + 12.7337i 0.439662 + 0.898163i
\(202\) 0 0
\(203\) −1.36502 + 1.57531i −0.0958055 + 0.110565i
\(204\) 0 0
\(205\) −0.654351 4.55111i −0.0457019 0.317864i
\(206\) 0 0
\(207\) 1.65696 4.24815i 0.115167 0.295267i
\(208\) 0 0
\(209\) −12.5453 8.06239i −0.867778 0.557687i
\(210\) 0 0
\(211\) 5.67188 12.4197i 0.390468 0.855006i −0.607680 0.794182i \(-0.707900\pi\)
0.998148 0.0608245i \(-0.0193730\pi\)
\(212\) 0 0
\(213\) −2.63020 4.50914i −0.180218 0.308961i
\(214\) 0 0
\(215\) −0.869261 + 0.124981i −0.0592831 + 0.00852362i
\(216\) 0 0
\(217\) 6.44760 1.89319i 0.437691 0.128518i
\(218\) 0 0
\(219\) −0.549793 5.49881i −0.0371515 0.371575i
\(220\) 0 0
\(221\) −0.704383 1.54238i −0.0473819 0.103752i
\(222\) 0 0
\(223\) 2.86676 6.27733i 0.191973 0.420361i −0.789030 0.614354i \(-0.789417\pi\)
0.981003 + 0.193993i \(0.0621439\pi\)
\(224\) 0 0
\(225\) 2.71567 11.6459i 0.181044 0.776390i
\(226\) 0 0
\(227\) 21.5035 + 3.09174i 1.42724 + 0.205206i 0.812240 0.583324i \(-0.198248\pi\)
0.614997 + 0.788529i \(0.289157\pi\)
\(228\) 0 0
\(229\) 9.34315 14.5382i 0.617413 0.960713i −0.381920 0.924195i \(-0.624737\pi\)
0.999333 0.0365175i \(-0.0116265\pi\)
\(230\) 0 0
\(231\) 0.428893 9.93414i 0.0282191 0.653618i
\(232\) 0 0
\(233\) 5.77365 12.6425i 0.378245 0.828240i −0.620776 0.783988i \(-0.713182\pi\)
0.999020 0.0442520i \(-0.0140905\pi\)
\(234\) 0 0
\(235\) 1.40337 1.21603i 0.0915460 0.0793250i
\(236\) 0 0
\(237\) −0.0852269 + 0.120819i −0.00553608 + 0.00784807i
\(238\) 0 0
\(239\) 3.28691 0.212613 0.106306 0.994333i \(-0.466098\pi\)
0.106306 + 0.994333i \(0.466098\pi\)
\(240\) 0 0
\(241\) −24.1310 7.08551i −1.55442 0.456418i −0.611999 0.790859i \(-0.709634\pi\)
−0.942417 + 0.334441i \(0.891453\pi\)
\(242\) 0 0
\(243\) 14.6139 5.42518i 0.937485 0.348026i
\(244\) 0 0
\(245\) 1.17015 + 2.56227i 0.0747583 + 0.163698i
\(246\) 0 0
\(247\) −0.841258 + 2.86506i −0.0535279 + 0.182299i
\(248\) 0 0
\(249\) 14.5093 11.5152i 0.919492 0.729747i
\(250\) 0 0
\(251\) 1.44108 10.0229i 0.0909599 0.632640i −0.892437 0.451172i \(-0.851006\pi\)
0.983397 0.181468i \(-0.0580848\pi\)
\(252\) 0 0
\(253\) 3.21681 2.78738i 0.202239 0.175241i
\(254\) 0 0
\(255\) 2.65725 + 4.55553i 0.166404 + 0.285278i
\(256\) 0 0
\(257\) −3.00280 10.2266i −0.187310 0.637919i −0.998581 0.0532489i \(-0.983042\pi\)
0.811271 0.584670i \(-0.198776\pi\)
\(258\) 0 0
\(259\) 0.641641 + 0.555985i 0.0398696 + 0.0345472i
\(260\) 0 0
\(261\) −2.12458 2.18883i −0.131508 0.135485i
\(262\) 0 0
\(263\) −5.74612 19.5695i −0.354321 1.20671i −0.923211 0.384292i \(-0.874445\pi\)
0.568891 0.822413i \(-0.307373\pi\)
\(264\) 0 0
\(265\) −3.57725 7.83308i −0.219749 0.481182i
\(266\) 0 0
\(267\) −0.718155 + 16.6341i −0.0439504 + 1.01799i
\(268\) 0 0
\(269\) 18.7758i 1.14478i 0.819980 + 0.572392i \(0.193984\pi\)
−0.819980 + 0.572392i \(0.806016\pi\)
\(270\) 0 0
\(271\) −10.3459 + 4.72482i −0.628470 + 0.287013i −0.704075 0.710125i \(-0.748638\pi\)
0.0756055 + 0.997138i \(0.475911\pi\)
\(272\) 0 0
\(273\) −1.93277 + 0.478008i −0.116977 + 0.0289304i
\(274\) 0 0
\(275\) 7.30995 8.43613i 0.440806 0.508718i
\(276\) 0 0
\(277\) −7.83597 + 9.04319i −0.470818 + 0.543353i −0.940639 0.339409i \(-0.889773\pi\)
0.469821 + 0.882762i \(0.344318\pi\)
\(278\) 0 0
\(279\) 1.94698 + 9.63912i 0.116563 + 0.577079i
\(280\) 0 0
\(281\) −3.01821 + 1.93968i −0.180051 + 0.115712i −0.627562 0.778567i \(-0.715947\pi\)
0.447511 + 0.894279i \(0.352311\pi\)
\(282\) 0 0
\(283\) −7.46491 8.61497i −0.443743 0.512107i 0.489180 0.872183i \(-0.337296\pi\)
−0.932923 + 0.360076i \(0.882751\pi\)
\(284\) 0 0
\(285\) 1.71703 9.12734i 0.101708 0.540657i
\(286\) 0 0
\(287\) −7.07452 + 6.13011i −0.417596 + 0.361849i
\(288\) 0 0
\(289\) −7.53763 2.21325i −0.443390 0.130191i
\(290\) 0 0
\(291\) −5.57209 + 2.25957i −0.326642 + 0.132458i
\(292\) 0 0
\(293\) 5.35113 + 8.32652i 0.312616 + 0.486441i 0.961635 0.274332i \(-0.0884567\pi\)
−0.649019 + 0.760772i \(0.724820\pi\)
\(294\) 0 0
\(295\) 0.918384 3.12773i 0.0534704 0.182103i
\(296\) 0 0
\(297\) 14.4295 + 1.87826i 0.837284 + 0.108988i
\(298\) 0 0
\(299\) −0.716988 0.460780i −0.0414645 0.0266476i
\(300\) 0 0
\(301\) 1.17085 + 1.35123i 0.0674866 + 0.0778837i
\(302\) 0 0
\(303\) −2.66022 + 5.21701i −0.152825 + 0.299709i
\(304\) 0 0
\(305\) 0.823948i 0.0471791i
\(306\) 0 0
\(307\) 5.18062 + 3.32938i 0.295674 + 0.190018i 0.680064 0.733153i \(-0.261952\pi\)
−0.384390 + 0.923171i \(0.625588\pi\)
\(308\) 0 0
\(309\) −3.12661 + 16.6203i −0.177866 + 0.945496i
\(310\) 0 0
\(311\) −4.81843 + 33.5129i −0.273228 + 1.90034i 0.140728 + 0.990048i \(0.455056\pi\)
−0.413957 + 0.910297i \(0.635853\pi\)
\(312\) 0 0
\(313\) −21.8275 9.96830i −1.23377 0.563442i −0.311591 0.950216i \(-0.600862\pi\)
−0.922174 + 0.386775i \(0.873589\pi\)
\(314\) 0 0
\(315\) 5.83378 2.07745i 0.328696 0.117051i
\(316\) 0 0
\(317\) −19.5268 + 2.80753i −1.09673 + 0.157687i −0.666846 0.745195i \(-0.732356\pi\)
−0.429888 + 0.902882i \(0.641447\pi\)
\(318\) 0 0
\(319\) −0.802209 2.73207i −0.0449151 0.152967i
\(320\) 0 0
\(321\) 11.6560 1.16541i 0.650574 0.0650470i
\(322\) 0 0
\(323\) −8.70599 13.5468i −0.484414 0.753763i
\(324\) 0 0
\(325\) −2.03314 0.928506i −0.112779 0.0515042i
\(326\) 0 0
\(327\) −14.6392 + 20.7528i −0.809547 + 1.14763i
\(328\) 0 0
\(329\) −3.62740 1.06510i −0.199985 0.0587209i
\(330\) 0 0
\(331\) −8.36891 + 1.20327i −0.459997 + 0.0661375i −0.368418 0.929660i \(-0.620100\pi\)
−0.0915788 + 0.995798i \(0.529191\pi\)
\(332\) 0 0
\(333\) −0.891531 + 0.865362i −0.0488556 + 0.0474216i
\(334\) 0 0
\(335\) −7.72650 + 2.86926i −0.422144 + 0.156764i
\(336\) 0 0
\(337\) −2.94419 2.55116i −0.160380 0.138970i 0.570974 0.820968i \(-0.306566\pi\)
−0.731354 + 0.681998i \(0.761111\pi\)
\(338\) 0 0
\(339\) 2.23873 + 22.3908i 0.121591 + 1.21610i
\(340\) 0 0
\(341\) −2.58615 + 8.80762i −0.140048 + 0.476959i
\(342\) 0 0
\(343\) 10.8587 16.8965i 0.586315 0.912325i
\(344\) 0 0
\(345\) 2.36158 + 1.20420i 0.127143 + 0.0648318i
\(346\) 0 0
\(347\) 9.66034 6.20832i 0.518594 0.333280i −0.255022 0.966935i \(-0.582083\pi\)
0.773616 + 0.633655i \(0.218446\pi\)
\(348\) 0 0
\(349\) 4.77161 + 33.1873i 0.255418 + 1.77647i 0.564494 + 0.825437i \(0.309071\pi\)
−0.309076 + 0.951037i \(0.600020\pi\)
\(350\) 0 0
\(351\) −0.453144 2.87819i −0.0241870 0.153626i
\(352\) 0 0
\(353\) 0.418454 + 2.91041i 0.0222721 + 0.154906i 0.997923 0.0644256i \(-0.0205215\pi\)
−0.975650 + 0.219331i \(0.929612\pi\)
\(354\) 0 0
\(355\) 2.76051 1.26068i 0.146512 0.0669100i
\(356\) 0 0
\(357\) 4.87750 9.56537i 0.258145 0.506253i
\(358\) 0 0
\(359\) −36.2740 5.21541i −1.91447 0.275259i −0.921016 0.389524i \(-0.872640\pi\)
−0.993450 + 0.114265i \(0.963549\pi\)
\(360\) 0 0
\(361\) −1.33177 + 9.26270i −0.0700934 + 0.487510i
\(362\) 0 0
\(363\) −4.46946 3.15279i −0.234586 0.165478i
\(364\) 0 0
\(365\) 3.21267 0.168159
\(366\) 0 0
\(367\) −15.0174 6.85821i −0.783901 0.357995i −0.0170778 0.999854i \(-0.505436\pi\)
−0.766823 + 0.641859i \(0.778164\pi\)
\(368\) 0 0
\(369\) −8.04517 11.0875i −0.418815 0.577194i
\(370\) 0 0
\(371\) −9.47838 + 14.7487i −0.492093 + 0.765712i
\(372\) 0 0
\(373\) 24.2146i 1.25378i 0.779106 + 0.626892i \(0.215673\pi\)
−0.779106 + 0.626892i \(0.784327\pi\)
\(374\) 0 0
\(375\) 14.8329 + 5.05987i 0.765969 + 0.261291i
\(376\) 0 0
\(377\) −0.479639 + 0.308245i −0.0247027 + 0.0158754i
\(378\) 0 0
\(379\) 3.71132 1.69490i 0.190638 0.0870612i −0.317809 0.948155i \(-0.602947\pi\)
0.508447 + 0.861093i \(0.330220\pi\)
\(380\) 0 0
\(381\) −3.49628 1.19267i −0.179120 0.0611022i
\(382\) 0 0
\(383\) −4.71606 5.44262i −0.240979 0.278105i 0.622357 0.782733i \(-0.286175\pi\)
−0.863337 + 0.504628i \(0.831630\pi\)
\(384\) 0 0
\(385\) 5.72175 + 0.822664i 0.291607 + 0.0419268i
\(386\) 0 0
\(387\) −2.11772 + 1.53663i −0.107650 + 0.0781111i
\(388\) 0 0
\(389\) 8.77788 + 13.6586i 0.445056 + 0.692521i 0.989217 0.146460i \(-0.0467881\pi\)
−0.544160 + 0.838981i \(0.683152\pi\)
\(390\) 0 0
\(391\) 4.41005 1.29491i 0.223026 0.0654863i
\(392\) 0 0
\(393\) 10.1112 + 9.55543i 0.510043 + 0.482008i
\(394\) 0 0
\(395\) −0.0649606 0.0562887i −0.00326852 0.00283219i
\(396\) 0 0
\(397\) −5.99947 + 1.76160i −0.301105 + 0.0884123i −0.428795 0.903402i \(-0.641062\pi\)
0.127690 + 0.991814i \(0.459244\pi\)
\(398\) 0 0
\(399\) −17.5225 + 7.10564i −0.877221 + 0.355727i
\(400\) 0 0
\(401\) −20.2313 −1.01030 −0.505152 0.863030i \(-0.668564\pi\)
−0.505152 + 0.863030i \(0.668564\pi\)
\(402\) 0 0
\(403\) 1.83804 0.0915591
\(404\) 0 0
\(405\) 2.29305 + 8.76744i 0.113943 + 0.435658i
\(406\) 0 0
\(407\) −1.11280 + 0.326747i −0.0551594 + 0.0161963i
\(408\) 0 0
\(409\) 0.00324140 + 0.00280869i 0.000160277 + 0.000138881i 0.654941 0.755680i \(-0.272694\pi\)
−0.654781 + 0.755819i \(0.727239\pi\)
\(410\) 0 0
\(411\) −19.9648 + 21.1261i −0.984792 + 1.04207i
\(412\) 0 0
\(413\) −6.36777 + 1.86975i −0.313338 + 0.0920042i
\(414\) 0 0
\(415\) 5.82197 + 9.05916i 0.285789 + 0.444697i
\(416\) 0 0
\(417\) 11.0008 8.73066i 0.538710 0.427542i
\(418\) 0 0
\(419\) 22.8438 + 3.28445i 1.11600 + 0.160456i 0.675543 0.737320i \(-0.263909\pi\)
0.440452 + 0.897776i \(0.354818\pi\)
\(420\) 0 0
\(421\) −3.60373 4.15892i −0.175635 0.202693i 0.661106 0.750293i \(-0.270087\pi\)
−0.836741 + 0.547599i \(0.815542\pi\)
\(422\) 0 0
\(423\) 2.01038 5.15427i 0.0977482 0.250609i
\(424\) 0 0
\(425\) 10.9644 5.00728i 0.531852 0.242889i
\(426\) 0 0
\(427\) −1.41119 + 0.906916i −0.0682922 + 0.0438887i
\(428\) 0 0
\(429\) 0.878097 2.57412i 0.0423949 0.124280i
\(430\) 0 0
\(431\) 33.0153i 1.59029i 0.606418 + 0.795146i \(0.292606\pi\)
−0.606418 + 0.795146i \(0.707394\pi\)
\(432\) 0 0
\(433\) 5.71980 8.90018i 0.274876 0.427716i −0.676179 0.736738i \(-0.736365\pi\)
0.951055 + 0.309022i \(0.100002\pi\)
\(434\) 0 0
\(435\) 1.38904 1.10240i 0.0665995 0.0528561i
\(436\) 0 0
\(437\) −7.36264 3.36240i −0.352203 0.160846i
\(438\) 0 0
\(439\) −28.9237 −1.38045 −0.690226 0.723593i \(-0.742489\pi\)
−0.690226 + 0.723593i \(0.742489\pi\)
\(440\) 0 0
\(441\) 6.64277 + 5.12885i 0.316322 + 0.244231i
\(442\) 0 0
\(443\) 2.62916 18.2862i 0.124915 0.868803i −0.826948 0.562279i \(-0.809925\pi\)
0.951863 0.306524i \(-0.0991661\pi\)
\(444\) 0 0
\(445\) −9.58071 1.37750i −0.454169 0.0652997i
\(446\) 0 0
\(447\) 32.9725 + 16.8131i 1.55955 + 0.795232i
\(448\) 0 0
\(449\) −16.1989 + 7.39779i −0.764473 + 0.349123i −0.759195 0.650863i \(-0.774407\pi\)
−0.00527804 + 0.999986i \(0.501680\pi\)
\(450\) 0 0
\(451\) −1.81983 12.6572i −0.0856924 0.596003i
\(452\) 0 0
\(453\) 2.24465 0.555142i 0.105463 0.0260828i
\(454\) 0 0
\(455\) −0.164725 1.14569i −0.00772243 0.0537107i
\(456\) 0 0
\(457\) −28.4659 + 18.2939i −1.33158 + 0.855754i −0.996265 0.0863520i \(-0.972479\pi\)
−0.335315 + 0.942106i \(0.608843\pi\)
\(458\) 0 0
\(459\) 13.3308 + 8.31764i 0.622226 + 0.388234i
\(460\) 0 0
\(461\) −2.94920 + 4.58905i −0.137358 + 0.213733i −0.903117 0.429394i \(-0.858727\pi\)
0.765759 + 0.643128i \(0.222364\pi\)
\(462\) 0 0
\(463\) 5.34889 18.2166i 0.248584 0.846599i −0.736780 0.676133i \(-0.763654\pi\)
0.985364 0.170466i \(-0.0545274\pi\)
\(464\) 0 0
\(465\) −5.68851 + 0.568759i −0.263798 + 0.0263756i
\(466\) 0 0
\(467\) 14.0193 + 12.1478i 0.648736 + 0.562133i 0.915844 0.401534i \(-0.131523\pi\)
−0.267108 + 0.963667i \(0.586068\pi\)
\(468\) 0 0
\(469\) 13.4188 + 10.0751i 0.619621 + 0.465226i
\(470\) 0 0
\(471\) −25.3781 + 26.8542i −1.16936 + 1.23738i
\(472\) 0 0
\(473\) −2.41752 + 0.347586i −0.111158 + 0.0159820i
\(474\) 0 0
\(475\) −20.3670 5.98029i −0.934502 0.274395i
\(476\) 0 0
\(477\) −20.3075 15.6793i −0.929816 0.717906i
\(478\) 0 0
\(479\) 24.8352 + 11.3419i 1.13475 + 0.518222i 0.892076 0.451886i \(-0.149249\pi\)
0.242673 + 0.970108i \(0.421976\pi\)
\(480\) 0 0
\(481\) 0.125551 + 0.195361i 0.00572464 + 0.00890771i
\(482\) 0 0
\(483\) −0.536930 5.37016i −0.0244312 0.244351i
\(484\) 0 0
\(485\) −0.984809 3.35395i −0.0447179 0.152295i
\(486\) 0 0
\(487\) 27.5010 3.95405i 1.24619 0.179175i 0.512516 0.858678i \(-0.328714\pi\)
0.733673 + 0.679503i \(0.237804\pi\)
\(488\) 0 0
\(489\) −0.961651 2.37143i −0.0434874 0.107240i
\(490\) 0 0
\(491\) −2.78595 1.27230i −0.125728 0.0574182i 0.351558 0.936166i \(-0.385652\pi\)
−0.477286 + 0.878748i \(0.658379\pi\)
\(492\) 0 0
\(493\) 0.437577 3.04342i 0.0197075 0.137069i
\(494\) 0 0
\(495\) −1.92107 + 8.23833i −0.0863458 + 0.370285i
\(496\) 0 0
\(497\) −5.19767 3.34034i −0.233147 0.149835i
\(498\) 0 0
\(499\) 33.7775i 1.51209i −0.654521 0.756044i \(-0.727130\pi\)
0.654521 0.756044i \(-0.272870\pi\)
\(500\) 0 0
\(501\) −3.87290 1.97484i −0.173028 0.0882293i
\(502\) 0 0
\(503\) −8.18125 9.44167i −0.364784 0.420983i 0.543453 0.839440i \(-0.317117\pi\)
−0.908237 + 0.418456i \(0.862571\pi\)
\(504\) 0 0
\(505\) −2.86400 1.84058i −0.127446 0.0819047i
\(506\) 0 0
\(507\) 21.9516 + 0.947733i 0.974906 + 0.0420903i
\(508\) 0 0
\(509\) −7.15954 + 24.3831i −0.317341 + 1.08076i 0.634181 + 0.773184i \(0.281337\pi\)
−0.951522 + 0.307580i \(0.900481\pi\)
\(510\) 0 0
\(511\) −3.53617 5.50239i −0.156431 0.243411i
\(512\) 0 0
\(513\) −8.14969 26.4433i −0.359818 1.16750i
\(514\) 0 0
\(515\) −9.43344 2.76991i −0.415687 0.122057i
\(516\) 0 0
\(517\) 3.90295 3.38192i 0.171651 0.148737i
\(518\) 0 0
\(519\) 21.2713 + 4.00156i 0.933708 + 0.175649i
\(520\) 0 0
\(521\) −8.55265 9.87029i −0.374699 0.432425i 0.536812 0.843702i \(-0.319628\pi\)
−0.911511 + 0.411277i \(0.865083\pi\)
\(522\) 0 0
\(523\) 19.5661 12.5744i 0.855567 0.549840i −0.0377395 0.999288i \(-0.512016\pi\)
0.893306 + 0.449448i \(0.148379\pi\)
\(524\) 0 0
\(525\) −3.39804 13.7396i −0.148303 0.599644i
\(526\) 0 0
\(527\) −6.49113 + 7.49116i −0.282758 + 0.326320i
\(528\) 0 0
\(529\) −13.5489 + 15.6363i −0.589083 + 0.679838i
\(530\) 0 0
\(531\) −1.92287 9.51978i −0.0834456 0.413123i
\(532\) 0 0
\(533\) −2.32907 + 1.06365i −0.100883 + 0.0460719i
\(534\) 0 0
\(535\) 6.81000i 0.294422i
\(536\) 0 0
\(537\) 19.1196 + 0.825465i 0.825073 + 0.0356215i
\(538\) 0 0
\(539\) 3.25433 + 7.12599i 0.140174 + 0.306938i
\(540\) 0 0
\(541\) −10.6811 36.3766i −0.459218 1.56395i −0.785612 0.618720i \(-0.787652\pi\)
0.326393 0.945234i \(-0.394167\pi\)
\(542\) 0 0
\(543\) −1.10922 + 1.17373i −0.0476010 + 0.0503697i
\(544\) 0 0
\(545\) −11.1581 9.66853i −0.477960 0.414154i
\(546\) 0 0
\(547\) 6.93535 + 23.6196i 0.296534 + 1.00990i 0.964141 + 0.265389i \(0.0855005\pi\)
−0.667607 + 0.744514i \(0.732681\pi\)
\(548\) 0 0
\(549\) −1.14426 2.17184i −0.0488358 0.0926920i
\(550\) 0 0
\(551\) −4.09212 + 3.54584i −0.174330 + 0.151058i
\(552\) 0 0
\(553\) −0.0249047 + 0.173216i −0.00105905 + 0.00736588i
\(554\) 0 0
\(555\) −0.449018 0.565770i −0.0190598 0.0240156i
\(556\) 0 0
\(557\) −0.197657 + 0.673158i −0.00837500 + 0.0285226i −0.963574 0.267440i \(-0.913822\pi\)
0.955199 + 0.295963i \(0.0956404\pi\)
\(558\) 0 0
\(559\) 0.203157 + 0.444852i 0.00859263 + 0.0188152i
\(560\) 0 0
\(561\) 7.39013 + 12.6695i 0.312012 + 0.534905i
\(562\) 0 0
\(563\) 3.72548 + 1.09390i 0.157010 + 0.0461024i 0.359293 0.933225i \(-0.383018\pi\)
−0.202283 + 0.979327i \(0.564836\pi\)
\(564\) 0 0
\(565\) −13.0818 −0.550356
\(566\) 0 0
\(567\) 12.4922 13.5776i 0.524623 0.570207i
\(568\) 0 0
\(569\) −10.8384 + 9.39154i −0.454370 + 0.393714i −0.851757 0.523937i \(-0.824463\pi\)
0.397387 + 0.917651i \(0.369917\pi\)
\(570\) 0 0
\(571\) 10.9314 23.9364i 0.457464 1.00171i −0.530594 0.847626i \(-0.678031\pi\)
0.988058 0.154081i \(-0.0492416\pi\)
\(572\) 0 0
\(573\) −16.5474 0.714413i −0.691278 0.0298450i
\(574\) 0 0
\(575\) 3.27557 5.09689i 0.136601 0.212555i
\(576\) 0 0
\(577\) −38.1561 5.48602i −1.58846 0.228386i −0.709297 0.704909i \(-0.750988\pi\)
−0.879162 + 0.476523i \(0.841897\pi\)
\(578\) 0 0
\(579\) −7.66878 + 40.7654i −0.318703 + 1.69415i
\(580\) 0 0
\(581\) 9.10755 19.9428i 0.377845 0.827365i
\(582\) 0 0
\(583\) −9.94875 21.7847i −0.412035 0.902231i
\(584\) 0 0
\(585\) 1.69114 0.0956613i 0.0699202 0.00395511i
\(586\) 0 0
\(587\) 23.3634 6.86013i 0.964313 0.283148i 0.238579 0.971123i \(-0.423318\pi\)
0.725734 + 0.687975i \(0.241500\pi\)
\(588\) 0 0
\(589\) 17.2780 2.48420i 0.711928 0.102360i
\(590\) 0 0
\(591\) −15.7535 + 9.18905i −0.648012 + 0.377987i
\(592\) 0 0
\(593\) 5.35922 11.7351i 0.220077 0.481901i −0.767101 0.641526i \(-0.778301\pi\)
0.987178 + 0.159626i \(0.0510287\pi\)
\(594\) 0 0
\(595\) 5.25114 + 3.37470i 0.215276 + 0.138349i
\(596\) 0 0
\(597\) −18.2600 6.22895i −0.747334 0.254934i
\(598\) 0 0
\(599\) 4.00325 + 27.8432i 0.163568 + 1.13764i 0.891839 + 0.452353i \(0.149415\pi\)
−0.728271 + 0.685290i \(0.759676\pi\)
\(600\) 0 0
\(601\) −16.3336 + 18.8499i −0.666260 + 0.768905i −0.983786 0.179345i \(-0.942602\pi\)
0.317526 + 0.948249i \(0.397148\pi\)
\(602\) 0 0
\(603\) −16.3816 + 18.2933i −0.667110 + 0.744960i
\(604\) 0 0
\(605\) 2.08228 2.40308i 0.0846567 0.0976991i
\(606\) 0 0
\(607\) 0.952491 + 6.62472i 0.0386604 + 0.268889i 0.999979 0.00655145i \(-0.00208541\pi\)
−0.961318 + 0.275440i \(0.911176\pi\)
\(608\) 0 0
\(609\) −3.41701 1.16563i −0.138464 0.0472336i
\(610\) 0 0
\(611\) −0.869919 0.559063i −0.0351931 0.0226173i
\(612\) 0 0
\(613\) 5.13198 11.2375i 0.207279 0.453877i −0.777229 0.629218i \(-0.783375\pi\)
0.984508 + 0.175340i \(0.0561026\pi\)
\(614\) 0 0
\(615\) 6.87907 4.01258i 0.277391 0.161803i
\(616\) 0 0
\(617\) −5.84688 + 0.840654i −0.235386 + 0.0338435i −0.258998 0.965878i \(-0.583392\pi\)
0.0236120 + 0.999721i \(0.492483\pi\)
\(618\) 0 0
\(619\) −39.7054 + 11.6586i −1.59590 + 0.468597i −0.954401 0.298529i \(-0.903504\pi\)
−0.641496 + 0.767127i \(0.721686\pi\)
\(620\) 0 0
\(621\) 7.89720 0.105505i 0.316904 0.00423376i
\(622\) 0 0
\(623\) 8.18619 + 17.9253i 0.327973 + 0.718160i
\(624\) 0 0
\(625\) 4.49457 9.84173i 0.179783 0.393669i
\(626\) 0 0
\(627\) 4.77527 25.3842i 0.190706 1.01375i
\(628\) 0 0
\(629\) −1.23961 0.178229i −0.0494266 0.00710647i
\(630\) 0 0
\(631\) 21.6056 33.6190i 0.860105 1.33835i −0.0797638 0.996814i \(-0.525417\pi\)
0.939869 0.341536i \(-0.110947\pi\)
\(632\) 0 0
\(633\) 23.6266 + 1.02005i 0.939073 + 0.0405432i
\(634\) 0 0
\(635\) 0.892132 1.95350i 0.0354032 0.0775222i
\(636\) 0 0
\(637\) 1.18548 1.02722i 0.0469705 0.0407001i
\(638\) 0 0
\(639\) 5.52564 7.15669i 0.218591 0.283114i
\(640\) 0 0
\(641\) 21.3864 0.844712 0.422356 0.906430i \(-0.361203\pi\)
0.422356 + 0.906430i \(0.361203\pi\)
\(642\) 0 0
\(643\) 16.2695 + 4.77715i 0.641606 + 0.188393i 0.586322 0.810078i \(-0.300575\pi\)
0.0552841 + 0.998471i \(0.482394\pi\)
\(644\) 0 0
\(645\) −0.766402 1.31390i −0.0301770 0.0517348i
\(646\) 0 0
\(647\) 4.74123 + 10.3819i 0.186397 + 0.408153i 0.979643 0.200749i \(-0.0643376\pi\)
−0.793246 + 0.608902i \(0.791610\pi\)
\(648\) 0 0
\(649\) 2.55413 8.69858i 0.100259 0.341449i
\(650\) 0 0
\(651\) 7.23544 + 9.11676i 0.283579 + 0.357314i
\(652\) 0 0
\(653\) 6.71761 46.7220i 0.262880 1.82837i −0.248045 0.968749i \(-0.579788\pi\)
0.510925 0.859625i \(-0.329303\pi\)
\(654\) 0 0
\(655\) −6.11229 + 5.29633i −0.238827 + 0.206945i
\(656\) 0 0
\(657\) 8.46827 4.46160i 0.330379 0.174064i
\(658\) 0 0
\(659\) −11.1587 38.0030i −0.434681 1.48039i −0.827865 0.560927i \(-0.810445\pi\)
0.393185 0.919459i \(-0.371373\pi\)
\(660\) 0 0
\(661\) 1.78336 + 1.54529i 0.0693648 + 0.0601049i 0.688853 0.724901i \(-0.258114\pi\)
−0.619488 + 0.785006i \(0.712660\pi\)
\(662\) 0 0
\(663\) 2.01720 2.13453i 0.0783415 0.0828982i
\(664\) 0 0
\(665\) −3.09691 10.5471i −0.120093 0.409000i
\(666\) 0 0
\(667\) −0.642015 1.40582i −0.0248589 0.0544335i
\(668\) 0 0
\(669\) 11.9417 + 0.515567i 0.461692 + 0.0199330i
\(670\) 0 0
\(671\) 2.29149i 0.0884622i
\(672\) 0 0
\(673\) −36.5482 + 16.6910i −1.40883 + 0.643391i −0.967249 0.253830i \(-0.918309\pi\)
−0.441581 + 0.897221i \(0.645582\pi\)
\(674\) 0 0
\(675\) 20.4603 3.22129i 0.787519 0.123987i
\(676\) 0 0
\(677\) 9.77120 11.2766i 0.375538 0.433393i −0.536248 0.844061i \(-0.680159\pi\)
0.911785 + 0.410667i \(0.134704\pi\)
\(678\) 0 0
\(679\) −4.66039 + 5.37838i −0.178849 + 0.206403i
\(680\) 0 0
\(681\) 9.03392 + 36.5276i 0.346180 + 1.39974i
\(682\) 0 0
\(683\) 29.6644 19.0642i 1.13508 0.729471i 0.168465 0.985708i \(-0.446119\pi\)
0.966614 + 0.256237i \(0.0824828\pi\)
\(684\) 0 0
\(685\) −11.0660 12.7708i −0.422810 0.487949i
\(686\) 0 0
\(687\) 29.4166 + 5.53385i 1.12232 + 0.211130i
\(688\) 0 0
\(689\) −3.62411 + 3.14031i −0.138068 + 0.119636i
\(690\) 0 0
\(691\) −1.16029 0.340691i −0.0441395 0.0129605i 0.259588 0.965719i \(-0.416413\pi\)
−0.303728 + 0.952759i \(0.598231\pi\)
\(692\) 0 0
\(693\) 16.2244 5.77764i 0.616315 0.219474i
\(694\) 0 0
\(695\) 4.41413 + 6.86852i 0.167438 + 0.260538i
\(696\) 0 0
\(697\) 3.89020 13.2488i 0.147352 0.501834i
\(698\) 0 0
\(699\) 24.0505 + 1.03835i 0.909675 + 0.0392740i
\(700\) 0 0
\(701\) −22.7655 14.6305i −0.859840 0.552585i 0.0347895 0.999395i \(-0.488924\pi\)
−0.894629 + 0.446809i \(0.852560\pi\)
\(702\) 0 0
\(703\) 1.44425 + 1.66676i 0.0544711 + 0.0628630i
\(704\) 0 0
\(705\) 2.86529 + 1.46105i 0.107913 + 0.0550262i
\(706\) 0 0
\(707\) 6.93114i 0.260672i
\(708\) 0 0
\(709\) −21.0873 13.5520i −0.791950 0.508956i 0.0810296 0.996712i \(-0.474179\pi\)
−0.872980 + 0.487756i \(0.837816\pi\)
\(710\) 0 0
\(711\) −0.249401 0.0581570i −0.00935325 0.00218106i
\(712\) 0 0
\(713\) −0.709055 + 4.93159i −0.0265543 + 0.184689i
\(714\) 0 0
\(715\) 1.43826 + 0.656829i 0.0537877 + 0.0245640i
\(716\) 0 0
\(717\) 2.13943 + 5.27582i 0.0798984 + 0.197029i
\(718\) 0 0
\(719\) 36.2245 5.20830i 1.35095 0.194237i 0.571447 0.820639i \(-0.306382\pi\)
0.779500 + 0.626402i \(0.215473\pi\)
\(720\) 0 0
\(721\) 5.63928 + 19.2056i 0.210018 + 0.715255i
\(722\) 0 0
\(723\) −4.33376 43.3446i −0.161174 1.61200i
\(724\) 0 0
\(725\) −2.19124 3.40963i −0.0813805 0.126631i
\(726\) 0 0
\(727\) 2.87291 + 1.31201i 0.106550 + 0.0486599i 0.467977 0.883741i \(-0.344983\pi\)
−0.361427 + 0.932401i \(0.617710\pi\)
\(728\) 0 0
\(729\) 18.2201 + 19.9256i 0.674817 + 0.737985i
\(730\) 0 0
\(731\) −2.53051 0.743026i −0.0935945 0.0274818i
\(732\) 0 0
\(733\) 1.93442 0.278128i 0.0714494 0.0102729i −0.106497 0.994313i \(-0.533964\pi\)
0.177947 + 0.984040i \(0.443054\pi\)
\(734\) 0 0
\(735\) −3.35106 + 3.54597i −0.123606 + 0.130795i
\(736\) 0 0
\(737\) −21.4883 + 7.97975i −0.791532 + 0.293938i
\(738\) 0 0
\(739\) −15.9300 13.8034i −0.585995 0.507768i 0.310646 0.950526i \(-0.399455\pi\)
−0.896641 + 0.442758i \(0.854000\pi\)
\(740\) 0 0
\(741\) −5.14627 + 0.514545i −0.189053 + 0.0189023i
\(742\) 0 0
\(743\) 6.85255 23.3376i 0.251396 0.856175i −0.733003 0.680225i \(-0.761882\pi\)
0.984399 0.175950i \(-0.0562998\pi\)
\(744\) 0 0
\(745\) −11.6328 + 18.1010i −0.426194 + 0.663171i
\(746\) 0 0
\(747\) 27.9270 + 15.7938i 1.02180 + 0.577863i
\(748\) 0 0
\(749\) 11.6636 7.49574i 0.426178 0.273888i
\(750\) 0 0
\(751\) 2.12290 + 14.7651i 0.0774656 + 0.538785i 0.991190 + 0.132450i \(0.0422844\pi\)
−0.913724 + 0.406335i \(0.866807\pi\)
\(752\) 0 0
\(753\) 17.0257 4.21076i 0.620452 0.153449i
\(754\) 0 0
\(755\) 0.191306 + 1.33056i 0.00696233 + 0.0484241i
\(756\) 0 0
\(757\) 1.05419 0.481431i 0.0383150 0.0174979i −0.396165 0.918179i \(-0.629659\pi\)
0.434480 + 0.900681i \(0.356932\pi\)
\(758\) 0 0
\(759\) 6.56782 + 3.34901i 0.238397 + 0.121561i
\(760\) 0 0
\(761\) 23.9508 + 3.44360i 0.868215 + 0.124830i 0.562005 0.827134i \(-0.310030\pi\)
0.306209 + 0.951964i \(0.400939\pi\)
\(762\) 0 0
\(763\) −4.27780 + 29.7527i −0.154867 + 1.07712i
\(764\) 0 0
\(765\) −5.58248 + 7.23031i −0.201835 + 0.261412i
\(766\) 0 0
\(767\) −1.81528 −0.0655460
\(768\) 0 0
\(769\) 15.4927 + 7.07527i 0.558680 + 0.255141i 0.674682 0.738108i \(-0.264281\pi\)
−0.116002 + 0.993249i \(0.537008\pi\)
\(770\) 0 0
\(771\) 14.4602 11.4762i 0.520772 0.413306i
\(772\) 0 0
\(773\) 14.4824 22.5351i 0.520897 0.810531i −0.476754 0.879037i \(-0.658187\pi\)
0.997651 + 0.0685055i \(0.0218231\pi\)
\(774\) 0 0
\(775\) 13.0661i 0.469350i
\(776\) 0