Properties

Label 804.2.s.b.5.8
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 5.8
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.786808 - 1.54303i) q^{3} +(0.966140 - 0.283684i) q^{5} +(1.54930 + 1.34247i) q^{7} +(-1.76187 + 2.42813i) q^{9} +O(q^{10})\) \(q+(-0.786808 - 1.54303i) q^{3} +(0.966140 - 0.283684i) q^{5} +(1.54930 + 1.34247i) q^{7} +(-1.76187 + 2.42813i) q^{9} +(2.68695 - 0.788959i) q^{11} +(0.303154 + 0.471717i) q^{13} +(-1.19790 - 1.26757i) q^{15} +(2.99315 + 0.430350i) q^{17} +(3.48728 + 4.02453i) q^{19} +(0.852473 - 3.44688i) q^{21} +(1.38260 - 0.631411i) q^{23} +(-3.35332 + 2.15505i) q^{25} +(5.13293 + 0.808130i) q^{27} -1.01679i q^{29} +(1.77218 - 2.75757i) q^{31} +(-3.33150 - 3.52527i) q^{33} +(1.87767 + 0.857505i) q^{35} +0.414150 q^{37} +(0.489348 - 0.838926i) q^{39} +(0.649850 - 4.51980i) q^{41} +(0.863281 + 0.124121i) q^{43} +(-1.01338 + 2.84573i) q^{45} +(1.67750 - 0.766089i) q^{47} +(-0.398118 - 2.76897i) q^{49} +(-1.69099 - 4.95712i) q^{51} +(-1.21708 - 8.46498i) q^{53} +(2.37215 - 1.52449i) q^{55} +(3.46614 - 8.54750i) q^{57} +(1.75024 - 2.72343i) q^{59} +(-0.230536 + 0.785133i) q^{61} +(-5.98935 + 1.39664i) q^{63} +(0.426708 + 0.369744i) q^{65} +(8.16532 - 0.572263i) q^{67} +(-2.06212 - 1.63659i) q^{69} +(2.98320 - 0.428919i) q^{71} +(-3.06133 - 0.898887i) q^{73} +(5.96371 + 3.47865i) q^{75} +(5.22203 + 2.38482i) q^{77} +(0.0461512 + 0.0718126i) q^{79} +(-2.79166 - 8.55609i) q^{81} +(3.01301 + 10.2614i) q^{83} +(3.01389 - 0.433331i) q^{85} +(-1.56894 + 0.800022i) q^{87} +(-8.74397 - 3.99324i) q^{89} +(-0.163592 + 1.13781i) q^{91} +(-5.64937 - 0.564846i) q^{93} +(4.51089 + 2.89897i) q^{95} +3.47150i q^{97} +(-2.81834 + 7.91431i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

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
\(3\) −0.786808 1.54303i −0.454264 0.890867i
\(4\) 0 0
\(5\) 0.966140 0.283684i 0.432071 0.126867i −0.0584631 0.998290i \(-0.518620\pi\)
0.490534 + 0.871422i \(0.336802\pi\)
\(6\) 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
\(9\) −1.76187 + 2.42813i −0.587288 + 0.809378i
\(10\) 0 0
\(11\) 2.68695 0.788959i 0.810145 0.237880i 0.149678 0.988735i \(-0.452176\pi\)
0.660467 + 0.750855i \(0.270358\pi\)
\(12\) 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
\(15\) −1.19790 1.26757i −0.309296 0.327286i
\(16\) 0 0
\(17\) 2.99315 + 0.430350i 0.725946 + 0.104375i 0.495374 0.868680i \(-0.335031\pi\)
0.230572 + 0.973055i \(0.425940\pi\)
\(18\) 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
\(21\) 0.852473 3.44688i 0.186025 0.752170i
\(22\) 0 0
\(23\) 1.38260 0.631411i 0.288292 0.131658i −0.266020 0.963967i \(-0.585709\pi\)
0.554312 + 0.832309i \(0.312982\pi\)
\(24\) 0 0
\(25\) −3.35332 + 2.15505i −0.670664 + 0.431009i
\(26\) 0 0
\(27\) 5.13293 + 0.808130i 0.987832 + 0.155525i
\(28\) 0 0
\(29\) 1.01679i 0.188814i −0.995534 0.0944069i \(-0.969905\pi\)
0.995534 0.0944069i \(-0.0300955\pi\)
\(30\) 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
\(33\) −3.33150 3.52527i −0.579939 0.613671i
\(34\) 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
\(39\) 0.489348 0.838926i 0.0783584 0.134336i
\(40\) 0 0
\(41\) 0.649850 4.51980i 0.101489 0.705875i −0.874016 0.485898i \(-0.838493\pi\)
0.975505 0.219977i \(-0.0705982\pi\)
\(42\) 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
\(45\) −1.01338 + 2.84573i −0.151066 + 0.424216i
\(46\) 0 0
\(47\) 1.67750 0.766089i 0.244689 0.111746i −0.289296 0.957240i \(-0.593421\pi\)
0.533985 + 0.845494i \(0.320694\pi\)
\(48\) 0 0
\(49\) −0.398118 2.76897i −0.0568740 0.395568i
\(50\) 0 0
\(51\) −1.69099 4.95712i −0.236787 0.694135i
\(52\) 0 0
\(53\) −1.21708 8.46498i −0.167179 1.16275i −0.884681 0.466197i \(-0.845624\pi\)
0.717502 0.696557i \(-0.245285\pi\)
\(54\) 0 0
\(55\) 2.37215 1.52449i 0.319861 0.205562i
\(56\) 0 0
\(57\) 3.46614 8.54750i 0.459102 1.13214i
\(58\) 0 0
\(59\) 1.75024 2.72343i 0.227862 0.354560i −0.708431 0.705780i \(-0.750597\pi\)
0.936293 + 0.351220i \(0.114233\pi\)
\(60\) 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
\(63\) −5.98935 + 1.39664i −0.754588 + 0.175960i
\(64\) 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
\(69\) −2.06212 1.63659i −0.248251 0.197022i
\(70\) 0 0
\(71\) 2.98320 0.428919i 0.354040 0.0509033i 0.0369996 0.999315i \(-0.488220\pi\)
0.317041 + 0.948412i \(0.397311\pi\)
\(72\) 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
\(75\) 5.96371 + 3.47865i 0.688630 + 0.401680i
\(76\) 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
\(81\) −2.79166 8.55609i −0.310185 0.950676i
\(82\) 0 0
\(83\) 3.01301 + 10.2614i 0.330720 + 1.12633i 0.942195 + 0.335066i \(0.108759\pi\)
−0.611474 + 0.791264i \(0.709423\pi\)
\(84\) 0 0
\(85\) 3.01389 0.433331i 0.326902 0.0470014i
\(86\) 0 0
\(87\) −1.56894 + 0.800022i −0.168208 + 0.0857713i
\(88\) 0 0
\(89\) −8.74397 3.99324i −0.926859 0.423282i −0.105970 0.994369i \(-0.533795\pi\)
−0.820890 + 0.571087i \(0.806522\pi\)
\(90\) 0 0
\(91\) −0.163592 + 1.13781i −0.0171491 + 0.119274i
\(92\) 0 0
\(93\) −5.64937 0.564846i −0.585812 0.0585718i
\(94\) 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
\(99\) −2.81834 + 7.91431i −0.283254 + 0.795418i
\(100\) 0 0
\(101\) −2.21410 2.55520i −0.220311 0.254252i 0.634825 0.772656i \(-0.281072\pi\)
−0.855136 + 0.518403i \(0.826527\pi\)
\(102\) 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 \(0.196916\pi\)
−0.998875 + 0.0474140i \(0.984902\pi\)
\(108\) 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
\(111\) −0.325856 0.639044i −0.0309289 0.0606554i
\(112\) 0 0
\(113\) −12.4656 3.66022i −1.17266 0.344324i −0.363321 0.931664i \(-0.618357\pi\)
−0.809340 + 0.587340i \(0.800175\pi\)
\(114\) 0 0
\(115\) 1.15666 1.00225i 0.107859 0.0934606i
\(116\) 0 0
\(117\) −1.67951 0.0950032i −0.155271 0.00878305i
\(118\) 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
\(123\) −7.48549 + 2.55348i −0.674944 + 0.230240i
\(124\) 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
\(129\) −0.487714 1.42973i −0.0429409 0.125880i
\(130\) 0 0
\(131\) −7.30624 + 3.33665i −0.638349 + 0.291524i −0.708177 0.706035i \(-0.750482\pi\)
0.0698282 + 0.997559i \(0.477755\pi\)
\(132\) 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 \(-0.881928\pi\)
0.336375 0.941728i \(-0.390799\pi\)
\(138\) 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
\(141\) −2.50197 1.98566i −0.210704 0.167223i
\(142\) 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
\(147\) −3.95936 + 2.79296i −0.326562 + 0.230359i
\(148\) 0 0
\(149\) −16.1494 + 13.9935i −1.32301 + 1.14640i −0.344825 + 0.938667i \(0.612062\pi\)
−0.978187 + 0.207729i \(0.933393\pi\)
\(150\) 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
\(153\) −6.31848 + 6.50955i −0.510819 + 0.526266i
\(154\) 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
\(159\) −12.1041 + 8.53830i −0.959916 + 0.677131i
\(160\) 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
\(165\) −4.21876 2.46081i −0.328430 0.191574i
\(166\) 0 0
\(167\) 1.89688 1.64366i 0.146785 0.127190i −0.578373 0.815773i \(-0.696312\pi\)
0.725158 + 0.688582i \(0.241767\pi\)
\(168\) 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 −0.997099 0.0761122i \(-0.975749\pi\)
0.483444 + 0.875375i \(0.339386\pi\)
\(174\) 0 0
\(175\) −8.08838 1.16293i −0.611424 0.0879095i
\(176\) 0 0
\(177\) −5.57943 0.557853i −0.419376 0.0419308i
\(178\) 0 0
\(179\) −4.58992 + 10.0505i −0.343067 + 0.751212i −0.999996 0.00274020i \(-0.999128\pi\)
0.656929 + 0.753952i \(0.271855\pi\)
\(180\) 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
\(183\) 1.39287 0.262026i 0.102964 0.0193695i
\(184\) 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
\(189\) 6.86753 + 8.14285i 0.499539 + 0.592305i
\(190\) 0 0
\(191\) 3.97243 8.69841i 0.287435 0.629395i −0.709744 0.704460i \(-0.751189\pi\)
0.997179 + 0.0750653i \(0.0239165\pi\)
\(192\) 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
\(195\) 0.234788 0.949340i 0.0168135 0.0679836i
\(196\) 0 0
\(197\) −1.49850 10.4223i −0.106764 0.742560i −0.970932 0.239356i \(-0.923064\pi\)
0.864168 0.503204i \(-0.167845\pi\)
\(198\) 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
\(201\) −7.30756 12.1491i −0.515436 0.856928i
\(202\) 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
\(207\) −0.902801 + 4.46959i −0.0627490 + 0.310658i
\(208\) 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
\(213\) −3.00904 4.26568i −0.206176 0.292279i
\(214\) 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
\(219\) 1.02167 + 5.43096i 0.0690381 + 0.366990i
\(220\) 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
\(225\) 0.675354 11.9392i 0.0450236 0.795947i
\(226\) 0 0
\(227\) −21.5035 3.09174i −1.42724 0.205206i −0.614997 0.788529i \(-0.710843\pi\)
−0.812240 + 0.583324i \(0.801752\pi\)
\(228\) 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 \(0.286818\pi\)
−0.999020 + 0.0442520i \(0.985910\pi\)
\(234\) 0 0
\(235\) 1.40337 1.21603i 0.0915460 0.0793250i
\(236\) 0 0
\(237\) 0.0744967 0.127715i 0.00483908 0.00829600i
\(238\) 0 0
\(239\) −3.28691 −0.212613 −0.106306 0.994333i \(-0.533902\pi\)
−0.106306 + 0.994333i \(0.533902\pi\)
\(240\) 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
\(243\) −11.0058 + 11.0396i −0.706021 + 0.708191i
\(244\) 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
\(249\) 13.4629 12.7229i 0.853176 0.806279i
\(250\) 0 0
\(251\) −1.44108 + 10.0229i −0.0909599 + 0.632640i 0.892437 + 0.451172i \(0.148994\pi\)
−0.983397 + 0.181468i \(0.941915\pi\)
\(252\) 0 0
\(253\) 3.21681 2.78738i 0.202239 0.175241i
\(254\) 0 0
\(255\) −3.03999 4.30956i −0.190372 0.269875i
\(256\) 0 0
\(257\) 3.00280 + 10.2266i 0.187310 + 0.637919i 0.998581 + 0.0532489i \(0.0169577\pi\)
−0.811271 + 0.584670i \(0.801224\pi\)
\(258\) 0 0
\(259\) 0.641641 + 0.555985i 0.0398696 + 0.0345472i
\(260\) 0 0
\(261\) 2.46891 + 1.79145i 0.152822 + 0.110888i
\(262\) 0 0
\(263\) 5.74612 + 19.5695i 0.354321 + 1.20671i 0.923211 + 0.384292i \(0.125555\pi\)
−0.568891 + 0.822413i \(0.692627\pi\)
\(264\) 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 \(-0.806016\pi\)
0.819980 0.572392i \(-0.193984\pi\)
\(270\) 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
\(273\) 1.88438 0.642808i 0.114048 0.0389045i
\(274\) 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
\(279\) 3.57340 + 9.16156i 0.213934 + 0.548488i
\(280\) 0 0
\(281\) 3.01821 1.93968i 0.180051 0.115712i −0.447511 0.894279i \(-0.647689\pi\)
0.627562 + 0.778567i \(0.284053\pi\)
\(282\) 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
\(285\) 0.923988 9.24136i 0.0547323 0.547411i
\(286\) 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
\(291\) 5.35661 2.73140i 0.314010 0.160118i
\(292\) 0 0
\(293\) −5.35113 8.32652i −0.312616 0.486441i 0.649019 0.760772i \(-0.275180\pi\)
−0.961635 + 0.274332i \(0.911543\pi\)
\(294\) 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
\(303\) −2.20068 + 5.42687i −0.126426 + 0.311765i
\(304\) 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
\(309\) 1.68252 16.8279i 0.0957154 0.957308i
\(310\) 0 0
\(311\) 4.81843 33.5129i 0.273228 1.90034i −0.140728 0.990048i \(-0.544944\pi\)
0.413957 0.910297i \(-0.364147\pi\)
\(312\) 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
\(315\) −5.39035 + 3.04844i −0.303712 + 0.171760i
\(316\) 0 0
\(317\) 19.5268 2.80753i 1.09673 0.157687i 0.429888 0.902882i \(-0.358553\pi\)
0.666846 + 0.745195i \(0.267644\pi\)
\(318\) 0 0
\(319\) −0.802209 2.73207i −0.0449151 0.152967i
\(320\) 0 0
\(321\) 11.5122 2.16567i 0.642547 0.120876i
\(322\) 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
\(327\) 12.7961 21.9373i 0.707624 1.21313i
\(328\) 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
\(333\) −0.729676 + 1.00561i −0.0399860 + 0.0551071i
\(334\) 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
\(339\) 4.16019 + 22.1146i 0.225950 + 1.20110i
\(340\) 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
\(345\) −2.45657 0.996179i −0.132258 0.0536325i
\(346\) 0 0
\(347\) −9.66034 + 6.20832i −0.518594 + 0.333280i −0.773616 0.633655i \(-0.781554\pi\)
0.255022 + 0.966935i \(0.417917\pi\)
\(348\) 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
\(351\) 1.17486 + 2.66628i 0.0627093 + 0.142315i
\(352\) 0 0
\(353\) −0.418454 2.91041i −0.0222721 0.154906i 0.975650 0.219331i \(-0.0703876\pi\)
−0.997923 + 0.0644256i \(0.979478\pi\)
\(354\) 0 0
\(355\) 2.76051 1.26068i 0.146512 0.0669100i
\(356\) 0 0
\(357\) 4.03494 9.95016i 0.213552 0.526618i
\(358\) 0 0
\(359\) 36.2740 + 5.21541i 1.91447 + 0.275259i 0.993450 0.114265i \(-0.0364513\pi\)
0.921016 + 0.389524i \(0.127360\pi\)
\(360\) 0 0
\(361\) −1.33177 + 9.26270i −0.0700934 + 0.487510i
\(362\) 0 0
\(363\) 4.72456 + 2.75585i 0.247975 + 0.144645i
\(364\) 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
\(369\) 9.82974 + 9.54121i 0.511716 + 0.496695i
\(370\) 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
\(375\) 15.2138 + 3.76264i 0.785638 + 0.194302i
\(376\) 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
\(381\) 3.58606 + 0.886896i 0.183720 + 0.0454371i
\(382\) 0 0
\(383\) 4.71606 + 5.44262i 0.240979 + 0.278105i 0.863337 0.504628i \(-0.168370\pi\)
−0.622357 + 0.782733i \(0.713825\pi\)
\(384\) 0 0
\(385\) 5.72175 + 0.822664i 0.291607 + 0.0419268i
\(386\) 0 0
\(387\) −1.82237 + 1.87748i −0.0926361 + 0.0954375i
\(388\) 0 0
\(389\) −8.77788 13.6586i −0.445056 0.692521i 0.544160 0.838981i \(-0.316848\pi\)
−0.989217 + 0.146460i \(0.953212\pi\)
\(390\) 0 0
\(391\) 4.41005 1.29491i 0.223026 0.0654863i
\(392\) 0 0
\(393\) 10.8971 + 8.64842i 0.549688 + 0.436255i
\(394\) 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
\(399\) 16.8449 8.58940i 0.843298 0.430008i
\(400\) 0 0
\(401\) 20.2313 1.01030 0.505152 0.863030i \(-0.331436\pi\)
0.505152 + 0.863030i \(0.331436\pi\)
\(402\) 0 0
\(403\) 1.83804 0.0915591
\(404\) 0 0
\(405\) −5.12436 7.47442i −0.254632 0.371407i
\(406\) 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
\(411\) −18.0698 + 22.7682i −0.891315 + 1.12307i
\(412\) 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
\(417\) −10.2074 + 9.64630i −0.499857 + 0.472381i
\(418\) 0 0
\(419\) −22.8438 3.28445i −1.11600 0.160456i −0.440452 0.897776i \(-0.645182\pi\)
−0.675543 + 0.737320i \(0.736091\pi\)
\(420\) 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
\(423\) −1.09536 + 5.42294i −0.0532584 + 0.263672i
\(424\) 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
\(429\) 0.652974 2.64023i 0.0315259 0.127471i
\(430\) 0 0
\(431\) 33.0153i 1.59029i −0.606418 0.795146i \(-0.707394\pi\)
0.606418 0.795146i \(-0.292606\pi\)
\(432\) 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
\(435\) −1.28886 + 1.21802i −0.0617962 + 0.0583994i
\(436\) 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
\(441\) 7.42487 + 3.91187i 0.353565 + 0.186280i
\(442\) 0 0
\(443\) −2.62916 + 18.2862i −0.124915 + 0.868803i 0.826948 + 0.562279i \(0.190075\pi\)
−0.951863 + 0.306524i \(0.900834\pi\)
\(444\) 0 0
\(445\) −9.58071 1.37750i −0.454169 0.0652997i
\(446\) 0 0
\(447\) 34.2989 + 13.9087i 1.62228 + 0.657861i
\(448\) 0 0
\(449\) 16.1989 7.39779i 0.764473 0.349123i 0.00527804 0.999986i \(-0.498320\pi\)
0.759195 + 0.650863i \(0.225593\pi\)
\(450\) 0 0
\(451\) −1.81983 12.6572i −0.0856924 0.596003i
\(452\) 0 0
\(453\) −2.18845 + 0.746535i −0.102822 + 0.0350753i
\(454\) 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
\(459\) 15.0158 + 4.62781i 0.700879 + 0.216008i
\(460\) 0 0
\(461\) 2.94920 4.58905i 0.137358 0.213733i −0.765759 0.643128i \(-0.777636\pi\)
0.903117 + 0.429394i \(0.141273\pi\)
\(462\) 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
\(465\) −5.61832 + 1.05692i −0.260543 + 0.0490133i
\(466\) 0 0
\(467\) −14.0193 12.1478i −0.648736 0.562133i 0.267108 0.963667i \(-0.413932\pi\)
−0.915844 + 0.401534i \(0.868477\pi\)
\(468\) 0 0
\(469\) 13.4188 + 10.0751i 0.619621 + 0.465226i
\(470\) 0 0
\(471\) 22.9692 28.9415i 1.05836 1.33355i
\(472\) 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
\(477\) 22.6984 + 11.9589i 1.03929 + 0.547561i
\(478\) 0 0
\(479\) −24.8352 11.3419i −1.13475 0.518222i −0.242673 0.970108i \(-0.578024\pi\)
−0.892076 + 0.451886i \(0.850751\pi\)
\(480\) 0 0
\(481\) 0.125551 + 0.195361i 0.00572464 + 0.00890771i
\(482\) 0 0
\(483\) −0.997769 5.30390i −0.0454001 0.241336i
\(484\) 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
\(489\) 1.16246 + 2.27972i 0.0525682 + 0.103093i
\(490\) 0 0
\(491\) 2.78595 + 1.27230i 0.125728 + 0.0574182i 0.477286 0.878748i \(-0.341621\pi\)
−0.351558 + 0.936166i \(0.614348\pi\)
\(492\) 0 0
\(493\) 0.437577 3.04342i 0.0197075 0.137069i
\(494\) 0 0
\(495\) −0.477748 + 8.44584i −0.0214732 + 0.379612i
\(496\) 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
\(501\) −4.02869 1.63370i −0.179989 0.0729882i
\(502\) 0 0
\(503\) 8.18125 + 9.44167i 0.364784 + 0.420983i 0.908237 0.418456i \(-0.137429\pi\)
−0.543453 + 0.839440i \(0.682883\pi\)
\(504\) 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 \(-0.718663\pi\)
0.951522 0.307580i \(-0.0995191\pi\)
\(510\) 0 0
\(511\) −3.53617 5.50239i −0.156431 0.243411i
\(512\) 0 0
\(513\) 14.6476 + 23.4758i 0.646707 + 1.03648i
\(514\) 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
\(519\) 21.5371 + 2.15336i 0.945372 + 0.0945221i
\(520\) 0 0
\(521\) 8.55265 + 9.87029i 0.374699 + 0.432425i 0.911511 0.411277i \(-0.134917\pi\)
−0.536812 + 0.843702i \(0.680372\pi\)
\(522\) 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
\(525\) 4.56957 + 13.3956i 0.199432 + 0.584631i
\(526\) 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
\(531\) 3.52916 + 9.04813i 0.153152 + 0.392656i
\(532\) 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
\(543\) 1.00393 1.26497i 0.0430827 0.0542849i
\(544\) 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
\(549\) −1.50023 1.94307i −0.0640284 0.0829282i
\(550\) 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
\(555\) −0.496110 0.524966i −0.0210587 0.0222835i
\(556\) 0 0
\(557\) 0.197657 0.673158i 0.00837500 0.0285226i −0.955199 0.295963i \(-0.904360\pi\)
0.963574 + 0.267440i \(0.0861778\pi\)
\(558\) 0 0
\(559\) 0.203157 + 0.444852i 0.00859263 + 0.0188152i
\(560\) 0 0
\(561\) −8.45457 11.9854i −0.356952 0.506023i
\(562\) 0 0
\(563\) −3.72548 1.09390i −0.157010 0.0461024i 0.202283 0.979327i \(-0.435164\pi\)
−0.359293 + 0.933225i \(0.616982\pi\)
\(564\) 0 0
\(565\) −13.0818 −0.550356
\(566\) 0 0
\(567\) 7.16120 17.0036i 0.300742 0.714086i
\(568\) 0 0
\(569\) 10.8384 9.39154i 0.454370 0.393714i −0.397387 0.917651i \(-0.630083\pi\)
0.851757 + 0.523937i \(0.175537\pi\)
\(570\) 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
\(579\) 4.12680 41.2747i 0.171504 1.71532i
\(580\) 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
\(585\) −1.64959 + 0.384664i −0.0682022 + 0.0159039i
\(586\) 0 0
\(587\) −23.3634 + 6.86013i −0.964313 + 0.283148i −0.725734 0.687975i \(-0.758500\pi\)
−0.238579 + 0.971123i \(0.576682\pi\)
\(588\) 0 0
\(589\) 17.2780 2.48420i 0.711928 0.102360i
\(590\) 0 0
\(591\) −14.9029 + 10.5126i −0.613023 + 0.432431i
\(592\) 0 0
\(593\) −5.35922 + 11.7351i −0.220077 + 0.481901i −0.987178 0.159626i \(-0.948971\pi\)
0.767101 + 0.641526i \(0.221699\pi\)
\(594\) 0 0
\(595\) 5.25114 + 3.37470i 0.215276 + 0.138349i
\(596\) 0 0
\(597\) 18.7290 + 4.63200i 0.766525 + 0.189575i
\(598\) 0 0
\(599\) −4.00325 27.8432i −0.163568 1.13764i −0.891839 0.452353i \(-0.850585\pi\)
0.728271 0.685290i \(-0.240324\pi\)
\(600\) 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
\(603\) −12.9967 + 20.8347i −0.529265 + 0.848456i
\(604\) 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
\(609\) −3.50476 0.866789i −0.142020 0.0351241i
\(610\) 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
\(615\) −6.50764 + 4.59054i −0.262413 + 0.185108i
\(616\) 0 0
\(617\) 5.84688 0.840654i 0.235386 0.0338435i −0.0236120 0.999721i \(-0.507517\pi\)
0.258998 + 0.965878i \(0.416608\pi\)
\(618\) 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
\(621\) 7.60704 2.12367i 0.305260 0.0852199i
\(622\) 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
\(627\) 2.56972 25.7013i 0.102625 1.02641i
\(628\) 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
\(639\) −4.21452 + 7.99929i −0.166724 + 0.316447i
\(640\) 0 0
\(641\) −21.3864 −0.844712 −0.422356 0.906430i \(-0.638797\pi\)
−0.422356 + 0.906430i \(0.638797\pi\)
\(642\) 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
\(645\) −0.876791 1.24296i −0.0345236 0.0489414i
\(646\) 0 0
\(647\) −4.74123 10.3819i −0.186397 0.408153i 0.793246 0.608902i \(-0.208390\pi\)
−0.979643 + 0.200749i \(0.935662\pi\)
\(648\) 0 0
\(649\) 2.55413 8.69858i 0.100259 0.341449i
\(650\) 0 0
\(651\) −7.99426 8.45924i −0.313320 0.331544i
\(652\) 0 0
\(653\) −6.71761 + 46.7220i −0.262880 + 1.82837i 0.248045 + 0.968749i \(0.420212\pi\)
−0.510925 + 0.859625i \(0.670697\pi\)
\(654\) 0 0
\(655\) −6.11229 + 5.29633i −0.238827 + 0.206945i
\(656\) 0 0
\(657\) 7.57626 5.84959i 0.295578 0.228214i
\(658\) 0 0
\(659\) 11.1587 + 38.0030i 0.434681 + 1.48039i 0.827865 + 0.560927i \(0.189555\pi\)
−0.393185 + 0.919459i \(0.628627\pi\)
\(660\) 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
\(663\) 1.82572 2.30044i 0.0709052 0.0893417i
\(664\) 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
\(675\) −18.9539 + 8.35178i −0.729536 + 0.321460i
\(676\) 0 0
\(677\) −9.77120 + 11.2766i −0.375538 + 0.433393i −0.911785 0.410667i \(-0.865296\pi\)
0.536248 + 0.844061i \(0.319841\pi\)
\(678\) 0 0
\(679\) −4.66039 + 5.37838i −0.178849 + 0.206403i
\(680\) 0 0
\(681\) 12.1485 + 35.6131i 0.465531 + 1.36470i
\(682\) 0 0
\(683\) −29.6644 + 19.0642i −1.13508 + 0.729471i −0.966614 0.256237i \(-0.917517\pi\)
−0.168465 + 0.985708i \(0.553881\pi\)
\(684\) 0 0
\(685\) −11.0660 12.7708i −0.422810 0.487949i
\(686\) 0 0
\(687\) −29.7841 2.97794i −1.13634 0.113615i
\(688\) 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
\(693\) −14.9912 + 8.47806i −0.569468 + 0.322055i
\(694\) 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 0.894629 0.446809i \(-0.147440\pi\)
−0.0347895 + 0.999395i \(0.511076\pi\)
\(702\) 0 0
\(703\) 1.44425 + 1.66676i 0.0544711 + 0.0628630i
\(704\) 0 0
\(705\) −2.98055 1.20866i −0.112254 0.0455208i
\(706\) 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
\(711\) −0.255683 0.0144630i −0.00958885 0.000542404i
\(712\) 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
\(717\) 2.58617 + 5.07180i 0.0965824 + 0.189410i
\(718\) 0 0
\(719\) −36.2245 + 5.20830i −1.35095 + 0.194237i −0.779500 0.626402i \(-0.784527\pi\)
−0.571447 + 0.820639i \(0.693618\pi\)
\(720\) 0 0
\(721\) 5.63928 + 19.2056i 0.210018 + 0.715255i
\(722\) 0 0
\(723\) 8.05336 + 42.8098i 0.299508 + 1.59211i
\(724\) 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
\(729\) 25.6939 + 8.29615i 0.951624 + 0.307265i
\(730\) 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
\(735\) −3.03297 + 3.82160i −0.111873 + 0.140962i
\(736\) 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
\(741\) 5.08277 0.956170i 0.186720 0.0351258i
\(742\) 0 0
\(743\) −6.85255 + 23.3376i −0.251396 + 0.856175i 0.733003 + 0.680225i \(0.238118\pi\)
−0.984399 + 0.175950i \(0.943700\pi\)
\(744\) 0 0
\(745\) −11.6328 + 18.1010i −0.426194 + 0.663171i
\(746\) 0 0
\(747\) −30.2245 10.7631i −1.10585 0.393803i
\(748\) 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
\(753\) 16.5995 5.66248i 0.604918 0.206352i
\(754\) 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
\(759\) −6.83202 2.77049i −0.247987 0.100562i
\(760\) 0 0
\(761\) −23.9508 3.44360i −0.868215 0.124830i −0.306209 0.951964i \(-0.599061\pi\)
−0.562005 + 0.827134i \(0.689970\pi\)
\(762\) 0 0
\(763\) −4.27780 + 29.7527i −0.154867 + 1.07712i
\(764\) 0 0
\(765\) −4.25787 + 8.08159i −0.153944 + 0.292190i
\(766\) 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
\(771\) 13.4173 12.6798i 0.483213 0.456652i
\(772\) 0 0
\(773\) −14.4824 + 22.5351i −0.520897 + 0.810531i −0.997651 0.0685055i \(-0.978177\pi\)
0.476754 + 0.879037i \(0.341813\pi\)
\(774\) 0 0
\(775\) 13.0661i 0.469350i
\(776\) 0 0