Properties

Label 804.2.s.b.5.17
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 5.17
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.17

$q$-expansion

\(f(q)\) \(=\) \(q+(1.48256 - 0.895546i) q^{3} +(-2.22357 + 0.652900i) q^{5} +(2.01808 + 1.74867i) q^{7} +(1.39599 - 2.65541i) q^{9} +O(q^{10})\) \(q+(1.48256 - 0.895546i) q^{3} +(-2.22357 + 0.652900i) q^{5} +(2.01808 + 1.74867i) q^{7} +(1.39599 - 2.65541i) q^{9} +(-0.819238 + 0.240550i) q^{11} +(1.65269 + 2.57164i) q^{13} +(-2.71189 + 2.95928i) q^{15} +(5.09528 + 0.732591i) q^{17} +(0.289069 + 0.333603i) q^{19} +(4.55794 + 0.785240i) q^{21} +(7.43322 - 3.39464i) q^{23} +(0.311737 - 0.200341i) q^{25} +(-0.308390 - 5.18699i) q^{27} +2.95311i q^{29} +(-0.121792 + 0.189512i) q^{31} +(-0.999150 + 1.09030i) q^{33} +(-5.62905 - 2.57070i) q^{35} +1.16503 q^{37} +(4.75324 + 2.33256i) q^{39} +(-0.236280 + 1.64336i) q^{41} +(0.275166 + 0.0395630i) q^{43} +(-1.37038 + 6.81595i) q^{45} +(9.50691 - 4.34166i) q^{47} +(0.0185697 + 0.129155i) q^{49} +(8.21015 - 3.47695i) q^{51} +(0.673384 + 4.68349i) q^{53} +(1.66458 - 1.06976i) q^{55} +(0.727321 + 0.235714i) q^{57} +(-5.71278 + 8.88926i) q^{59} +(0.773829 - 2.63542i) q^{61} +(7.46066 - 2.91768i) q^{63} +(-5.35390 - 4.63918i) q^{65} +(-4.57523 - 6.78728i) q^{67} +(7.98017 - 11.6896i) q^{69} +(-9.96884 + 1.43330i) q^{71} +(-9.73985 - 2.85988i) q^{73} +(0.282756 - 0.576194i) q^{75} +(-2.07393 - 0.947131i) q^{77} +(4.58257 + 7.13062i) q^{79} +(-5.10240 - 7.41387i) q^{81} +(-2.86539 - 9.75864i) q^{83} +(-11.8080 + 1.69774i) q^{85} +(2.64465 + 4.37818i) q^{87} +(-1.51223 - 0.690613i) q^{89} +(-1.16170 + 8.07977i) q^{91} +(-0.0108477 + 0.390034i) q^{93} +(-0.860576 - 0.553059i) q^{95} -10.4721i q^{97} +(-0.504893 + 2.51122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.48256 0.895546i 0.855959 0.517044i
\(4\) 0 0
\(5\) −2.22357 + 0.652900i −0.994413 + 0.291986i −0.738161 0.674624i \(-0.764306\pi\)
−0.256251 + 0.966610i \(0.582488\pi\)
\(6\) 0 0
\(7\) 2.01808 + 1.74867i 0.762761 + 0.660936i 0.946742 0.321994i \(-0.104353\pi\)
−0.183981 + 0.982930i \(0.558898\pi\)
\(8\) 0 0
\(9\) 1.39599 2.65541i 0.465331 0.885136i
\(10\) 0 0
\(11\) −0.819238 + 0.240550i −0.247010 + 0.0725286i −0.402894 0.915247i \(-0.631996\pi\)
0.155884 + 0.987775i \(0.450177\pi\)
\(12\) 0 0
\(13\) 1.65269 + 2.57164i 0.458374 + 0.713244i 0.991111 0.133037i \(-0.0424729\pi\)
−0.532737 + 0.846281i \(0.678837\pi\)
\(14\) 0 0
\(15\) −2.71189 + 2.95928i −0.700207 + 0.764083i
\(16\) 0 0
\(17\) 5.09528 + 0.732591i 1.23579 + 0.177679i 0.729074 0.684435i \(-0.239951\pi\)
0.506714 + 0.862114i \(0.330860\pi\)
\(18\) 0 0
\(19\) 0.289069 + 0.333603i 0.0663170 + 0.0765339i 0.787939 0.615754i \(-0.211148\pi\)
−0.721622 + 0.692288i \(0.756603\pi\)
\(20\) 0 0
\(21\) 4.55794 + 0.785240i 0.994625 + 0.171353i
\(22\) 0 0
\(23\) 7.43322 3.39464i 1.54993 0.707830i 0.557449 0.830211i \(-0.311780\pi\)
0.992483 + 0.122381i \(0.0390529\pi\)
\(24\) 0 0
\(25\) 0.311737 0.200341i 0.0623475 0.0400683i
\(26\) 0 0
\(27\) −0.308390 5.18699i −0.0593496 0.998237i
\(28\) 0 0
\(29\) 2.95311i 0.548379i 0.961676 + 0.274189i \(0.0884095\pi\)
−0.961676 + 0.274189i \(0.911590\pi\)
\(30\) 0 0
\(31\) −0.121792 + 0.189512i −0.0218745 + 0.0340374i −0.852019 0.523511i \(-0.824622\pi\)
0.830144 + 0.557549i \(0.188258\pi\)
\(32\) 0 0
\(33\) −0.999150 + 1.09030i −0.173930 + 0.189796i
\(34\) 0 0
\(35\) −5.62905 2.57070i −0.951483 0.434528i
\(36\) 0 0
\(37\) 1.16503 0.191530 0.0957649 0.995404i \(-0.469470\pi\)
0.0957649 + 0.995404i \(0.469470\pi\)
\(38\) 0 0
\(39\) 4.75324 + 2.33256i 0.761127 + 0.373508i
\(40\) 0 0
\(41\) −0.236280 + 1.64336i −0.0369007 + 0.256650i −0.999918 0.0127888i \(-0.995929\pi\)
0.963018 + 0.269439i \(0.0868382\pi\)
\(42\) 0 0
\(43\) 0.275166 + 0.0395630i 0.0419625 + 0.00603330i 0.163264 0.986582i \(-0.447798\pi\)
−0.121302 + 0.992616i \(0.538707\pi\)
\(44\) 0 0
\(45\) −1.37038 + 6.81595i −0.204284 + 1.01606i
\(46\) 0 0
\(47\) 9.50691 4.34166i 1.38673 0.633296i 0.424469 0.905442i \(-0.360461\pi\)
0.962256 + 0.272146i \(0.0877334\pi\)
\(48\) 0 0
\(49\) 0.0185697 + 0.129155i 0.00265282 + 0.0184508i
\(50\) 0 0
\(51\) 8.21015 3.47695i 1.14965 0.486870i
\(52\) 0 0
\(53\) 0.673384 + 4.68349i 0.0924965 + 0.643327i 0.982346 + 0.187073i \(0.0599001\pi\)
−0.889850 + 0.456254i \(0.849191\pi\)
\(54\) 0 0
\(55\) 1.66458 1.06976i 0.224452 0.144247i
\(56\) 0 0
\(57\) 0.727321 + 0.235714i 0.0963360 + 0.0312211i
\(58\) 0 0
\(59\) −5.71278 + 8.88926i −0.743741 + 1.15728i 0.238770 + 0.971076i \(0.423256\pi\)
−0.982511 + 0.186207i \(0.940381\pi\)
\(60\) 0 0
\(61\) 0.773829 2.63542i 0.0990787 0.337431i −0.895004 0.446058i \(-0.852827\pi\)
0.994083 + 0.108627i \(0.0346456\pi\)
\(62\) 0 0
\(63\) 7.46066 2.91768i 0.939955 0.367593i
\(64\) 0 0
\(65\) −5.35390 4.63918i −0.664070 0.575420i
\(66\) 0 0
\(67\) −4.57523 6.78728i −0.558954 0.829199i
\(68\) 0 0
\(69\) 7.98017 11.6896i 0.960699 1.40726i
\(70\) 0 0
\(71\) −9.96884 + 1.43330i −1.18308 + 0.170102i −0.705646 0.708564i \(-0.749343\pi\)
−0.477437 + 0.878666i \(0.658434\pi\)
\(72\) 0 0
\(73\) −9.73985 2.85988i −1.13996 0.334723i −0.343347 0.939209i \(-0.611561\pi\)
−0.796616 + 0.604485i \(0.793379\pi\)
\(74\) 0 0
\(75\) 0.282756 0.576194i 0.0326498 0.0665332i
\(76\) 0 0
\(77\) −2.07393 0.947131i −0.236346 0.107936i
\(78\) 0 0
\(79\) 4.58257 + 7.13062i 0.515580 + 0.802258i 0.997251 0.0740942i \(-0.0236065\pi\)
−0.481672 + 0.876352i \(0.659970\pi\)
\(80\) 0 0
\(81\) −5.10240 7.41387i −0.566933 0.823764i
\(82\) 0 0
\(83\) −2.86539 9.75864i −0.314518 1.07115i −0.953366 0.301817i \(-0.902407\pi\)
0.638848 0.769333i \(-0.279411\pi\)
\(84\) 0 0
\(85\) −11.8080 + 1.69774i −1.28076 + 0.184146i
\(86\) 0 0
\(87\) 2.64465 + 4.37818i 0.283536 + 0.469390i
\(88\) 0 0
\(89\) −1.51223 0.690613i −0.160296 0.0732049i 0.333651 0.942697i \(-0.391719\pi\)
−0.493947 + 0.869492i \(0.664447\pi\)
\(90\) 0 0
\(91\) −1.16170 + 8.07977i −0.121779 + 0.846990i
\(92\) 0 0
\(93\) −0.0108477 + 0.390034i −0.00112486 + 0.0404447i
\(94\) 0 0
\(95\) −0.860576 0.553059i −0.0882933 0.0567426i
\(96\) 0 0
\(97\) 10.4721i 1.06328i −0.846971 0.531640i \(-0.821576\pi\)
0.846971 0.531640i \(-0.178424\pi\)
\(98\) 0 0
\(99\) −0.504893 + 2.51122i −0.0507437 + 0.252387i
\(100\) 0 0
\(101\) −1.06665 1.23098i −0.106136 0.122487i 0.700196 0.713951i \(-0.253096\pi\)
−0.806332 + 0.591463i \(0.798550\pi\)
\(102\) 0 0
\(103\) 4.52340 + 2.90702i 0.445704 + 0.286437i 0.744178 0.667981i \(-0.232841\pi\)
−0.298474 + 0.954418i \(0.596478\pi\)
\(104\) 0 0
\(105\) −10.6476 + 1.22984i −1.03910 + 0.120020i
\(106\) 0 0
\(107\) −1.96542 + 6.69362i −0.190005 + 0.647097i 0.808293 + 0.588780i \(0.200392\pi\)
−0.998298 + 0.0583167i \(0.981427\pi\)
\(108\) 0 0
\(109\) −0.811372 1.26252i −0.0777153 0.120927i 0.800220 0.599706i \(-0.204716\pi\)
−0.877936 + 0.478779i \(0.841080\pi\)
\(110\) 0 0
\(111\) 1.72723 1.04334i 0.163942 0.0990292i
\(112\) 0 0
\(113\) 11.7027 + 3.43621i 1.10089 + 0.323251i 0.781207 0.624272i \(-0.214604\pi\)
0.319686 + 0.947524i \(0.396423\pi\)
\(114\) 0 0
\(115\) −14.3119 + 12.4014i −1.33460 + 1.15643i
\(116\) 0 0
\(117\) 9.13590 0.798579i 0.844614 0.0738287i
\(118\) 0 0
\(119\) 9.00160 + 10.3884i 0.825175 + 0.952303i
\(120\) 0 0
\(121\) −8.64050 + 5.55291i −0.785500 + 0.504810i
\(122\) 0 0
\(123\) 1.12141 + 2.64799i 0.101114 + 0.238761i
\(124\) 0 0
\(125\) 7.02566 8.10804i 0.628394 0.725205i
\(126\) 0 0
\(127\) −2.32037 + 2.67785i −0.205900 + 0.237621i −0.849302 0.527907i \(-0.822977\pi\)
0.643402 + 0.765528i \(0.277522\pi\)
\(128\) 0 0
\(129\) 0.443382 0.187770i 0.0390376 0.0165322i
\(130\) 0 0
\(131\) −8.34179 + 3.80957i −0.728826 + 0.332844i −0.745035 0.667025i \(-0.767567\pi\)
0.0162095 + 0.999869i \(0.494840\pi\)
\(132\) 0 0
\(133\) 1.17872i 0.102208i
\(134\) 0 0
\(135\) 4.07232 + 11.3323i 0.350489 + 0.975331i
\(136\) 0 0
\(137\) −7.44112 16.2938i −0.635738 1.39207i −0.903500 0.428587i \(-0.859011\pi\)
0.267762 0.963485i \(-0.413716\pi\)
\(138\) 0 0
\(139\) 6.55050 + 22.3090i 0.555606 + 1.89222i 0.437493 + 0.899222i \(0.355866\pi\)
0.118113 + 0.993000i \(0.462315\pi\)
\(140\) 0 0
\(141\) 10.2064 14.9507i 0.859538 1.25907i
\(142\) 0 0
\(143\) −1.97255 1.70923i −0.164953 0.142933i
\(144\) 0 0
\(145\) −1.92809 6.56646i −0.160119 0.545315i
\(146\) 0 0
\(147\) 0.143195 + 0.174851i 0.0118106 + 0.0144215i
\(148\) 0 0
\(149\) −12.0237 + 10.4186i −0.985021 + 0.853526i −0.989216 0.146465i \(-0.953210\pi\)
0.00419440 + 0.999991i \(0.498665\pi\)
\(150\) 0 0
\(151\) −0.672096 + 4.67453i −0.0546944 + 0.380408i 0.944028 + 0.329867i \(0.107004\pi\)
−0.998722 + 0.0505414i \(0.983905\pi\)
\(152\) 0 0
\(153\) 9.05831 12.5074i 0.732321 1.01116i
\(154\) 0 0
\(155\) 0.147081 0.500912i 0.0118138 0.0402342i
\(156\) 0 0
\(157\) −1.57775 3.45479i −0.125918 0.275722i 0.836165 0.548477i \(-0.184792\pi\)
−0.962083 + 0.272755i \(0.912065\pi\)
\(158\) 0 0
\(159\) 5.19262 + 6.34053i 0.411801 + 0.502837i
\(160\) 0 0
\(161\) 20.9369 + 6.14763i 1.65006 + 0.484501i
\(162\) 0 0
\(163\) −15.9465 −1.24903 −0.624513 0.781014i \(-0.714703\pi\)
−0.624513 + 0.781014i \(0.714703\pi\)
\(164\) 0 0
\(165\) 1.50983 3.07670i 0.117540 0.239521i
\(166\) 0 0
\(167\) −5.28474 + 4.57925i −0.408945 + 0.354353i −0.834910 0.550387i \(-0.814480\pi\)
0.425964 + 0.904740i \(0.359935\pi\)
\(168\) 0 0
\(169\) 1.51847 3.32498i 0.116805 0.255767i
\(170\) 0 0
\(171\) 1.28939 0.301888i 0.0986023 0.0230860i
\(172\) 0 0
\(173\) −6.87305 + 10.6947i −0.522549 + 0.813102i −0.997769 0.0667654i \(-0.978732\pi\)
0.475220 + 0.879867i \(0.342368\pi\)
\(174\) 0 0
\(175\) 0.979441 + 0.140822i 0.0740388 + 0.0106452i
\(176\) 0 0
\(177\) −0.508823 + 18.2950i −0.0382455 + 1.37513i
\(178\) 0 0
\(179\) 9.73917 21.3258i 0.727940 1.59397i −0.0744916 0.997222i \(-0.523733\pi\)
0.802431 0.596744i \(-0.203539\pi\)
\(180\) 0 0
\(181\) −7.21188 15.7918i −0.536055 1.17380i −0.962996 0.269517i \(-0.913136\pi\)
0.426940 0.904280i \(-0.359591\pi\)
\(182\) 0 0
\(183\) −1.21289 4.60018i −0.0896593 0.340055i
\(184\) 0 0
\(185\) −2.59053 + 0.760648i −0.190460 + 0.0559240i
\(186\) 0 0
\(187\) −4.35047 + 0.625504i −0.318138 + 0.0457414i
\(188\) 0 0
\(189\) 8.44800 11.0070i 0.614501 0.800643i
\(190\) 0 0
\(191\) 6.82175 14.9376i 0.493605 1.08084i −0.484891 0.874575i \(-0.661141\pi\)
0.978495 0.206269i \(-0.0661321\pi\)
\(192\) 0 0
\(193\) −15.3945 9.89347i −1.10812 0.712148i −0.147240 0.989101i \(-0.547039\pi\)
−0.960883 + 0.276953i \(0.910675\pi\)
\(194\) 0 0
\(195\) −12.0921 2.08322i −0.865934 0.149183i
\(196\) 0 0
\(197\) 0.451957 + 3.14343i 0.0322006 + 0.223960i 0.999567 0.0294210i \(-0.00936636\pi\)
−0.967366 + 0.253381i \(0.918457\pi\)
\(198\) 0 0
\(199\) −3.07432 + 3.54796i −0.217933 + 0.251508i −0.854180 0.519977i \(-0.825940\pi\)
0.636247 + 0.771485i \(0.280486\pi\)
\(200\) 0 0
\(201\) −12.8614 5.96525i −0.907174 0.420757i
\(202\) 0 0
\(203\) −5.16402 + 5.95960i −0.362443 + 0.418282i
\(204\) 0 0
\(205\) −0.547566 3.80840i −0.0382437 0.265991i
\(206\) 0 0
\(207\) 1.36258 24.4771i 0.0947059 1.70128i
\(208\) 0 0
\(209\) −0.317065 0.203765i −0.0219318 0.0140947i
\(210\) 0 0
\(211\) −8.80239 + 19.2745i −0.605981 + 1.32691i 0.319307 + 0.947651i \(0.396550\pi\)
−0.925289 + 0.379263i \(0.876178\pi\)
\(212\) 0 0
\(213\) −13.4959 + 11.0525i −0.924721 + 0.757306i
\(214\) 0 0
\(215\) −0.637684 + 0.0916851i −0.0434897 + 0.00625287i
\(216\) 0 0
\(217\) −0.577180 + 0.169475i −0.0391815 + 0.0115047i
\(218\) 0 0
\(219\) −17.0011 + 4.48253i −1.14883 + 0.302901i
\(220\) 0 0
\(221\) 6.53697 + 14.3140i 0.439724 + 0.962861i
\(222\) 0 0
\(223\) 0.563061 1.23293i 0.0377053 0.0825632i −0.889842 0.456269i \(-0.849186\pi\)
0.927547 + 0.373705i \(0.121913\pi\)
\(224\) 0 0
\(225\) −0.0968049 1.10747i −0.00645366 0.0738311i
\(226\) 0 0
\(227\) 4.27145 + 0.614142i 0.283506 + 0.0407621i 0.282601 0.959238i \(-0.408803\pi\)
0.000905286 1.00000i \(0.499712\pi\)
\(228\) 0 0
\(229\) −2.29606 + 3.57274i −0.151728 + 0.236093i −0.908794 0.417245i \(-0.862996\pi\)
0.757066 + 0.653338i \(0.226632\pi\)
\(230\) 0 0
\(231\) −3.92293 + 0.453115i −0.258110 + 0.0298128i
\(232\) 0 0
\(233\) 9.12364 19.9780i 0.597710 1.30880i −0.332960 0.942941i \(-0.608047\pi\)
0.930670 0.365860i \(-0.119225\pi\)
\(234\) 0 0
\(235\) −18.3047 + 15.8611i −1.19406 + 1.03466i
\(236\) 0 0
\(237\) 13.1798 + 6.46770i 0.856117 + 0.420122i
\(238\) 0 0
\(239\) −22.7021 −1.46848 −0.734239 0.678891i \(-0.762461\pi\)
−0.734239 + 0.678891i \(0.762461\pi\)
\(240\) 0 0
\(241\) −15.9742 4.69045i −1.02899 0.302139i −0.276690 0.960959i \(-0.589237\pi\)
−0.752300 + 0.658821i \(0.771056\pi\)
\(242\) 0 0
\(243\) −14.2041 6.42211i −0.911193 0.411979i
\(244\) 0 0
\(245\) −0.125617 0.275063i −0.00802537 0.0175731i
\(246\) 0 0
\(247\) −0.380165 + 1.29472i −0.0241893 + 0.0823813i
\(248\) 0 0
\(249\) −12.9874 11.9017i −0.823046 0.754241i
\(250\) 0 0
\(251\) 1.96791 13.6871i 0.124214 0.863924i −0.828486 0.560010i \(-0.810797\pi\)
0.952699 0.303914i \(-0.0982937\pi\)
\(252\) 0 0
\(253\) −5.27299 + 4.56908i −0.331510 + 0.287255i
\(254\) 0 0
\(255\) −15.9858 + 13.0917i −1.00107 + 0.819832i
\(256\) 0 0
\(257\) 1.64284 + 5.59501i 0.102478 + 0.349007i 0.994730 0.102530i \(-0.0326939\pi\)
−0.892252 + 0.451537i \(0.850876\pi\)
\(258\) 0 0
\(259\) 2.35112 + 2.03726i 0.146091 + 0.126589i
\(260\) 0 0
\(261\) 7.84172 + 4.12253i 0.485390 + 0.255178i
\(262\) 0 0
\(263\) 5.40171 + 18.3965i 0.333084 + 1.13438i 0.940443 + 0.339951i \(0.110411\pi\)
−0.607359 + 0.794427i \(0.707771\pi\)
\(264\) 0 0
\(265\) −4.55517 9.97444i −0.279822 0.612725i
\(266\) 0 0
\(267\) −2.86046 + 0.330395i −0.175057 + 0.0202198i
\(268\) 0 0
\(269\) 17.8647i 1.08923i −0.838687 0.544614i \(-0.816676\pi\)
0.838687 0.544614i \(-0.183324\pi\)
\(270\) 0 0
\(271\) 3.89142 1.77715i 0.236387 0.107954i −0.293700 0.955898i \(-0.594887\pi\)
0.530087 + 0.847943i \(0.322159\pi\)
\(272\) 0 0
\(273\) 5.51352 + 13.0191i 0.333693 + 0.787954i
\(274\) 0 0
\(275\) −0.207195 + 0.239116i −0.0124943 + 0.0144192i
\(276\) 0 0
\(277\) 16.5491 19.0987i 0.994342 1.14753i 0.00528681 0.999986i \(-0.498317\pi\)
0.989055 0.147546i \(-0.0471374\pi\)
\(278\) 0 0
\(279\) 0.333211 + 0.587965i 0.0199488 + 0.0352006i
\(280\) 0 0
\(281\) −6.23786 + 4.00883i −0.372120 + 0.239147i −0.713312 0.700847i \(-0.752806\pi\)
0.341192 + 0.939994i \(0.389169\pi\)
\(282\) 0 0
\(283\) 13.1467 + 15.1721i 0.781489 + 0.901886i 0.997216 0.0745676i \(-0.0237576\pi\)
−0.215727 + 0.976454i \(0.569212\pi\)
\(284\) 0 0
\(285\) −1.77115 0.0492596i −0.104914 0.00291789i
\(286\) 0 0
\(287\) −3.35053 + 2.90325i −0.197776 + 0.171374i
\(288\) 0 0
\(289\) 9.11383 + 2.67606i 0.536108 + 0.157415i
\(290\) 0 0
\(291\) −9.37824 15.5255i −0.549762 0.910124i
\(292\) 0 0
\(293\) −7.63596 11.8818i −0.446098 0.694141i 0.543273 0.839556i \(-0.317185\pi\)
−0.989371 + 0.145415i \(0.953548\pi\)
\(294\) 0 0
\(295\) 6.89899 23.4958i 0.401675 1.36798i
\(296\) 0 0
\(297\) 1.50038 + 4.17520i 0.0870606 + 0.242270i
\(298\) 0 0
\(299\) 21.0146 + 13.5052i 1.21530 + 0.781029i
\(300\) 0 0
\(301\) 0.486124 + 0.561017i 0.0280197 + 0.0323365i
\(302\) 0 0
\(303\) −2.68379 0.869775i −0.154179 0.0499673i
\(304\) 0 0
\(305\) 6.36529i 0.364475i
\(306\) 0 0
\(307\) 10.6764 + 6.86130i 0.609333 + 0.391595i 0.808607 0.588349i \(-0.200222\pi\)
−0.199274 + 0.979944i \(0.563858\pi\)
\(308\) 0 0
\(309\) 9.30960 + 0.258921i 0.529605 + 0.0147295i
\(310\) 0 0
\(311\) 3.43808 23.9124i 0.194956 1.35595i −0.623700 0.781664i \(-0.714371\pi\)
0.818656 0.574284i \(-0.194719\pi\)
\(312\) 0 0
\(313\) −10.0420 4.58604i −0.567609 0.259218i 0.110874 0.993834i \(-0.464635\pi\)
−0.678483 + 0.734616i \(0.737362\pi\)
\(314\) 0 0
\(315\) −14.6844 + 11.3587i −0.827371 + 0.639993i
\(316\) 0 0
\(317\) −15.0821 + 2.16848i −0.847095 + 0.121794i −0.552175 0.833728i \(-0.686202\pi\)
−0.294920 + 0.955522i \(0.595293\pi\)
\(318\) 0 0
\(319\) −0.710371 2.41930i −0.0397731 0.135455i
\(320\) 0 0
\(321\) 3.08058 + 11.6838i 0.171941 + 0.652129i
\(322\) 0 0
\(323\) 1.22849 + 1.91157i 0.0683552 + 0.106363i
\(324\) 0 0
\(325\) 1.03041 + 0.470573i 0.0571569 + 0.0261027i
\(326\) 0 0
\(327\) −2.33356 1.14515i −0.129046 0.0633267i
\(328\) 0 0
\(329\) 26.7778 + 7.86267i 1.47631 + 0.433483i
\(330\) 0 0
\(331\) 20.5531 2.95508i 1.12970 0.162426i 0.447982 0.894043i \(-0.352143\pi\)
0.681716 + 0.731617i \(0.261234\pi\)
\(332\) 0 0
\(333\) 1.62638 3.09363i 0.0891248 0.169530i
\(334\) 0 0
\(335\) 14.6048 + 12.1049i 0.797945 + 0.661359i
\(336\) 0 0
\(337\) 10.1591 + 8.80291i 0.553401 + 0.479525i 0.886091 0.463511i \(-0.153411\pi\)
−0.332690 + 0.943036i \(0.607956\pi\)
\(338\) 0 0
\(339\) 20.4272 5.38586i 1.10945 0.292520i
\(340\) 0 0
\(341\) 0.0541895 0.184553i 0.00293453 0.00999408i
\(342\) 0 0
\(343\) 9.91732 15.4317i 0.535485 0.833231i
\(344\) 0 0
\(345\) −10.1124 + 31.2028i −0.544432 + 1.67990i
\(346\) 0 0
\(347\) 6.56322 4.21793i 0.352332 0.226430i −0.352488 0.935816i \(-0.614664\pi\)
0.704820 + 0.709386i \(0.251028\pi\)
\(348\) 0 0
\(349\) −4.40747 30.6546i −0.235926 1.64090i −0.671682 0.740840i \(-0.734428\pi\)
0.435755 0.900065i \(-0.356481\pi\)
\(350\) 0 0
\(351\) 12.8294 9.36556i 0.684782 0.499897i
\(352\) 0 0
\(353\) −1.80519 12.5554i −0.0960806 0.668255i −0.979762 0.200166i \(-0.935852\pi\)
0.883681 0.468089i \(-0.155057\pi\)
\(354\) 0 0
\(355\) 21.2307 9.69571i 1.12681 0.514595i
\(356\) 0 0
\(357\) 22.6487 + 7.34013i 1.19870 + 0.388481i
\(358\) 0 0
\(359\) 2.24774 + 0.323176i 0.118631 + 0.0170566i 0.201375 0.979514i \(-0.435459\pi\)
−0.0827435 + 0.996571i \(0.526368\pi\)
\(360\) 0 0
\(361\) 2.67625 18.6137i 0.140855 0.979670i
\(362\) 0 0
\(363\) −7.83721 + 15.9705i −0.411347 + 0.838235i
\(364\) 0 0
\(365\) 23.5245 1.23133
\(366\) 0 0
\(367\) 19.6118 + 8.95640i 1.02373 + 0.467520i 0.855267 0.518188i \(-0.173393\pi\)
0.168460 + 0.985708i \(0.446121\pi\)
\(368\) 0 0
\(369\) 4.03395 + 2.92154i 0.209999 + 0.152089i
\(370\) 0 0
\(371\) −6.83095 + 10.6292i −0.354645 + 0.551839i
\(372\) 0 0
\(373\) 35.5582i 1.84113i 0.390587 + 0.920566i \(0.372272\pi\)
−0.390587 + 0.920566i \(0.627728\pi\)
\(374\) 0 0
\(375\) 3.15487 18.3125i 0.162917 0.945653i
\(376\) 0 0
\(377\) −7.59433 + 4.88058i −0.391128 + 0.251363i
\(378\) 0 0
\(379\) 6.58430 3.00695i 0.338213 0.154457i −0.239067 0.971003i \(-0.576842\pi\)
0.577280 + 0.816546i \(0.304114\pi\)
\(380\) 0 0
\(381\) −1.04196 + 6.04809i −0.0533813 + 0.309853i
\(382\) 0 0
\(383\) 10.0397 + 11.5864i 0.513003 + 0.592037i 0.951865 0.306517i \(-0.0991637\pi\)
−0.438862 + 0.898554i \(0.644618\pi\)
\(384\) 0 0
\(385\) 5.22992 + 0.751948i 0.266541 + 0.0383228i
\(386\) 0 0
\(387\) 0.489187 0.675450i 0.0248668 0.0343351i
\(388\) 0 0
\(389\) −0.293311 0.456400i −0.0148714 0.0231404i 0.833738 0.552160i \(-0.186196\pi\)
−0.848610 + 0.529019i \(0.822560\pi\)
\(390\) 0 0
\(391\) 40.3612 11.8511i 2.04115 0.599337i
\(392\) 0 0
\(393\) −8.95560 + 13.1184i −0.451750 + 0.661735i
\(394\) 0 0
\(395\) −14.8453 12.8635i −0.746947 0.647233i
\(396\) 0 0
\(397\) 30.3256 8.90441i 1.52200 0.446900i 0.589410 0.807834i \(-0.299360\pi\)
0.932591 + 0.360935i \(0.117542\pi\)
\(398\) 0 0
\(399\) 1.05560 + 1.74753i 0.0528462 + 0.0874861i
\(400\) 0 0
\(401\) −36.7151 −1.83346 −0.916732 0.399504i \(-0.869182\pi\)
−0.916732 + 0.399504i \(0.869182\pi\)
\(402\) 0 0
\(403\) −0.688641 −0.0343036
\(404\) 0 0
\(405\) 16.1861 + 13.1539i 0.804293 + 0.653625i
\(406\) 0 0
\(407\) −0.954437 + 0.280248i −0.0473097 + 0.0138914i
\(408\) 0 0
\(409\) 0.203823 + 0.176614i 0.0100784 + 0.00873298i 0.659885 0.751366i \(-0.270605\pi\)
−0.649807 + 0.760099i \(0.725150\pi\)
\(410\) 0 0
\(411\) −25.6238 17.4927i −1.26393 0.862852i
\(412\) 0 0
\(413\) −27.0732 + 7.94942i −1.33219 + 0.391165i
\(414\) 0 0
\(415\) 12.7428 + 19.8282i 0.625521 + 0.973330i
\(416\) 0 0
\(417\) 29.6903 + 27.2082i 1.45394 + 1.33239i
\(418\) 0 0
\(419\) −20.6344 2.96678i −1.00806 0.144937i −0.381547 0.924350i \(-0.624608\pi\)
−0.626511 + 0.779413i \(0.715517\pi\)
\(420\) 0 0
\(421\) −7.46031 8.60966i −0.363593 0.419609i 0.544247 0.838925i \(-0.316815\pi\)
−0.907840 + 0.419316i \(0.862270\pi\)
\(422\) 0 0
\(423\) 1.74271 31.3057i 0.0847334 1.52213i
\(424\) 0 0
\(425\) 1.73516 0.792420i 0.0841675 0.0384380i
\(426\) 0 0
\(427\) 6.17013 3.96530i 0.298594 0.191894i
\(428\) 0 0
\(429\) −4.45513 0.767528i −0.215096 0.0370566i
\(430\) 0 0
\(431\) 33.4433i 1.61091i 0.592657 + 0.805455i \(0.298079\pi\)
−0.592657 + 0.805455i \(0.701921\pi\)
\(432\) 0 0
\(433\) −15.3658 + 23.9097i −0.738434 + 1.14903i 0.245310 + 0.969445i \(0.421110\pi\)
−0.983743 + 0.179580i \(0.942526\pi\)
\(434\) 0 0
\(435\) −8.73908 8.00851i −0.419007 0.383979i
\(436\) 0 0
\(437\) 3.28117 + 1.49846i 0.156960 + 0.0716812i
\(438\) 0 0
\(439\) 33.0398 1.57690 0.788451 0.615097i \(-0.210883\pi\)
0.788451 + 0.615097i \(0.210883\pi\)
\(440\) 0 0
\(441\) 0.368884 + 0.130990i 0.0175659 + 0.00623762i
\(442\) 0 0
\(443\) −2.63553 + 18.3305i −0.125218 + 0.870908i 0.826282 + 0.563257i \(0.190452\pi\)
−0.951499 + 0.307651i \(0.900457\pi\)
\(444\) 0 0
\(445\) 3.81346 + 0.548293i 0.180775 + 0.0259916i
\(446\) 0 0
\(447\) −8.49559 + 26.2141i −0.401828 + 1.23988i
\(448\) 0 0
\(449\) −0.0867474 + 0.0396162i −0.00409386 + 0.00186960i −0.417461 0.908695i \(-0.637080\pi\)
0.413367 + 0.910564i \(0.364353\pi\)
\(450\) 0 0
\(451\) −0.201741 1.40314i −0.00949963 0.0660714i
\(452\) 0 0
\(453\) 3.18983 + 7.53219i 0.149871 + 0.353893i
\(454\) 0 0
\(455\) −2.69217 18.7244i −0.126211 0.877816i
\(456\) 0 0
\(457\) 21.0770 13.5453i 0.985939 0.633625i 0.0548801 0.998493i \(-0.482522\pi\)
0.931059 + 0.364868i \(0.118886\pi\)
\(458\) 0 0
\(459\) 2.22861 26.6551i 0.104023 1.24415i
\(460\) 0 0
\(461\) 8.20038 12.7600i 0.381930 0.594295i −0.596062 0.802939i \(-0.703269\pi\)
0.977992 + 0.208644i \(0.0669050\pi\)
\(462\) 0 0
\(463\) −4.69457 + 15.9882i −0.218175 + 0.743037i 0.775560 + 0.631274i \(0.217468\pi\)
−0.993735 + 0.111762i \(0.964350\pi\)
\(464\) 0 0
\(465\) −0.230533 0.874352i −0.0106907 0.0405471i
\(466\) 0 0
\(467\) 21.7502 + 18.8467i 1.00648 + 0.872119i 0.991803 0.127773i \(-0.0407830\pi\)
0.0146757 + 0.999892i \(0.495328\pi\)
\(468\) 0 0
\(469\) 2.63557 21.6978i 0.121699 1.00191i
\(470\) 0 0
\(471\) −5.43303 3.70900i −0.250341 0.170902i
\(472\) 0 0
\(473\) −0.234944 + 0.0337798i −0.0108027 + 0.00155320i
\(474\) 0 0
\(475\) 0.156948 + 0.0460842i 0.00720128 + 0.00211449i
\(476\) 0 0
\(477\) 13.3766 + 4.75002i 0.612474 + 0.217488i
\(478\) 0 0
\(479\) −13.2034 6.02980i −0.603279 0.275509i 0.0902702 0.995917i \(-0.471227\pi\)
−0.693550 + 0.720409i \(0.743954\pi\)
\(480\) 0 0
\(481\) 1.92543 + 2.99603i 0.0877922 + 0.136607i
\(482\) 0 0
\(483\) 36.5458 9.63570i 1.66289 0.438440i
\(484\) 0 0
\(485\) 6.83723 + 23.2855i 0.310463 + 1.05734i
\(486\) 0 0
\(487\) 22.7140 3.26578i 1.02927 0.147986i 0.393067 0.919510i \(-0.371414\pi\)
0.636201 + 0.771523i \(0.280505\pi\)
\(488\) 0 0
\(489\) −23.6417 + 14.2808i −1.06912 + 0.645801i
\(490\) 0 0
\(491\) 13.3009 + 6.07431i 0.600261 + 0.274130i 0.692282 0.721627i \(-0.256605\pi\)
−0.0920211 + 0.995757i \(0.529333\pi\)
\(492\) 0 0
\(493\) −2.16342 + 15.0469i −0.0974356 + 0.677680i
\(494\) 0 0
\(495\) −0.516909 5.91353i −0.0232333 0.265793i
\(496\) 0 0
\(497\) −22.6242 14.5397i −1.01484 0.652196i
\(498\) 0 0
\(499\) 9.86407i 0.441576i 0.975322 + 0.220788i \(0.0708629\pi\)
−0.975322 + 0.220788i \(0.929137\pi\)
\(500\) 0 0
\(501\) −3.73403 + 11.5218i −0.166824 + 0.514754i
\(502\) 0 0
\(503\) −25.6829 29.6397i −1.14515 1.32157i −0.939345 0.342974i \(-0.888566\pi\)
−0.205801 0.978594i \(-0.565980\pi\)
\(504\) 0 0
\(505\) 3.17549 + 2.04077i 0.141308 + 0.0908129i
\(506\) 0 0
\(507\) −0.726446 6.28935i −0.0322626 0.279320i
\(508\) 0 0
\(509\) 4.71240 16.0490i 0.208873 0.711358i −0.786697 0.617339i \(-0.788211\pi\)
0.995570 0.0940184i \(-0.0299713\pi\)
\(510\) 0 0
\(511\) −14.6548 22.8033i −0.648289 1.00876i
\(512\) 0 0
\(513\) 1.64125 1.60228i 0.0724631 0.0707423i
\(514\) 0 0
\(515\) −11.9561 3.51063i −0.526849 0.154697i
\(516\) 0 0
\(517\) −6.74404 + 5.84374i −0.296602 + 0.257007i
\(518\) 0 0
\(519\) −0.612166 + 22.0107i −0.0268711 + 0.966162i
\(520\) 0 0
\(521\) −12.8160 14.7905i −0.561481 0.647983i 0.402038 0.915623i \(-0.368302\pi\)
−0.963519 + 0.267639i \(0.913756\pi\)
\(522\) 0 0
\(523\) −25.6769 + 16.5016i −1.12277 + 0.721563i −0.964040 0.265759i \(-0.914378\pi\)
−0.158734 + 0.987321i \(0.550741\pi\)
\(524\) 0 0
\(525\) 1.57820 0.668356i 0.0688782 0.0291695i
\(526\) 0 0
\(527\) −0.759399 + 0.876394i −0.0330800 + 0.0381763i
\(528\) 0 0
\(529\) 28.6673 33.0839i 1.24641 1.43843i
\(530\) 0 0
\(531\) 15.6296 + 27.5791i 0.678268 + 1.19683i
\(532\) 0 0
\(533\) −4.61663 + 2.10834i −0.199968 + 0.0913225i
\(534\) 0 0
\(535\) 16.1670i 0.698960i
\(536\) 0 0
\(537\) −4.65930 40.3388i −0.201063 1.74075i
\(538\) 0 0
\(539\) −0.0462814 0.101342i −0.00199348 0.00436511i
\(540\) 0 0
\(541\) 12.3523 + 42.0681i 0.531067 + 1.80865i 0.586198 + 0.810168i \(0.300624\pi\)
−0.0551315 + 0.998479i \(0.517558\pi\)
\(542\) 0 0
\(543\) −24.8344 16.9538i −1.06575 0.727558i
\(544\) 0 0
\(545\) 2.62845 + 2.27756i 0.112590 + 0.0975600i
\(546\) 0 0
\(547\) −12.2118 41.5897i −0.522141 1.77825i −0.621743 0.783221i \(-0.713575\pi\)
0.0996027 0.995027i \(-0.468243\pi\)
\(548\) 0 0
\(549\) −5.91786 5.73386i −0.252568 0.244715i
\(550\) 0 0
\(551\) −0.985168 + 0.853653i −0.0419696 + 0.0363668i
\(552\) 0 0
\(553\) −3.22114 + 22.4036i −0.136977 + 0.952696i
\(554\) 0 0
\(555\) −3.15943 + 3.44765i −0.134110 + 0.146345i
\(556\) 0 0
\(557\) −2.56898 + 8.74915i −0.108851 + 0.370713i −0.995845 0.0910688i \(-0.970972\pi\)
0.886993 + 0.461782i \(0.152790\pi\)
\(558\) 0 0
\(559\) 0.353023 + 0.773014i 0.0149313 + 0.0326950i
\(560\) 0 0
\(561\) −5.88969 + 4.82340i −0.248663 + 0.203644i
\(562\) 0 0
\(563\) −14.3375 4.20987i −0.604253 0.177425i −0.0347256 0.999397i \(-0.511056\pi\)
−0.569528 + 0.821972i \(0.692874\pi\)
\(564\) 0 0
\(565\) −28.2652 −1.18913
\(566\) 0 0
\(567\) 2.66741 23.8842i 0.112021 1.00304i
\(568\) 0 0
\(569\) −10.7257 + 9.29384i −0.449643 + 0.389618i −0.850035 0.526726i \(-0.823419\pi\)
0.400392 + 0.916344i \(0.368874\pi\)
\(570\) 0 0
\(571\) 4.24451 9.29417i 0.177627 0.388949i −0.799787 0.600285i \(-0.795054\pi\)
0.977414 + 0.211336i \(0.0677813\pi\)
\(572\) 0 0
\(573\) −3.26358 28.2551i −0.136338 1.18037i
\(574\) 0 0
\(575\) 1.63712 2.54742i 0.0682728 0.106235i
\(576\) 0 0
\(577\) 22.1115 + 3.17915i 0.920514 + 0.132350i 0.586251 0.810130i \(-0.300603\pi\)
0.334263 + 0.942480i \(0.391512\pi\)
\(578\) 0 0
\(579\) −31.6835 0.881187i −1.31672 0.0366209i
\(580\) 0 0
\(581\) 11.2821 24.7043i 0.468059 1.02491i
\(582\) 0 0
\(583\) −1.67828 3.67491i −0.0695071 0.152199i
\(584\) 0 0
\(585\) −19.7930 + 7.74053i −0.818338 + 0.320032i
\(586\) 0 0
\(587\) 38.0598 11.1754i 1.57090 0.461257i 0.623634 0.781717i \(-0.285656\pi\)
0.947262 + 0.320460i \(0.103837\pi\)
\(588\) 0 0
\(589\) −0.0984282 + 0.0141518i −0.00405566 + 0.000583116i
\(590\) 0 0
\(591\) 3.48514 + 4.25559i 0.143360 + 0.175052i
\(592\) 0 0
\(593\) −4.07433 + 8.92153i −0.167313 + 0.366363i −0.974653 0.223723i \(-0.928179\pi\)
0.807340 + 0.590086i \(0.200906\pi\)
\(594\) 0 0
\(595\) −26.7983 17.2222i −1.09862 0.706043i
\(596\) 0 0
\(597\) −1.38052 + 8.01327i −0.0565010 + 0.327961i
\(598\) 0 0
\(599\) 5.18426 + 36.0573i 0.211823 + 1.47326i 0.767063 + 0.641572i \(0.221718\pi\)
−0.555239 + 0.831691i \(0.687373\pi\)
\(600\) 0 0
\(601\) 24.1318 27.8496i 0.984356 1.13601i −0.00634899 0.999980i \(-0.502021\pi\)
0.990705 0.136028i \(-0.0434336\pi\)
\(602\) 0 0
\(603\) −24.4100 + 2.67411i −0.994053 + 0.108898i
\(604\) 0 0
\(605\) 15.5873 17.9887i 0.633714 0.731345i
\(606\) 0 0
\(607\) −2.89566 20.1398i −0.117531 0.817448i −0.960260 0.279109i \(-0.909961\pi\)
0.842728 0.538339i \(-0.180948\pi\)
\(608\) 0 0
\(609\) −2.31890 + 13.4601i −0.0939666 + 0.545431i
\(610\) 0 0
\(611\) 26.8772 + 17.2729i 1.08733 + 0.698787i
\(612\) 0 0
\(613\) −12.0272 + 26.3359i −0.485775 + 1.06370i 0.495060 + 0.868859i \(0.335146\pi\)
−0.980835 + 0.194840i \(0.937581\pi\)
\(614\) 0 0
\(615\) −4.22240 5.15583i −0.170264 0.207903i
\(616\) 0 0
\(617\) 47.8677 6.88234i 1.92708 0.277073i 0.930965 0.365108i \(-0.118968\pi\)
0.996117 + 0.0880352i \(0.0280588\pi\)
\(618\) 0 0
\(619\) −11.6821 + 3.43018i −0.469544 + 0.137871i −0.507941 0.861392i \(-0.669593\pi\)
0.0383967 + 0.999263i \(0.487775\pi\)
\(620\) 0 0
\(621\) −19.9003 37.5092i −0.798571 1.50519i
\(622\) 0 0
\(623\) −1.84414 4.03811i −0.0738840 0.161783i
\(624\) 0 0
\(625\) −11.0980 + 24.3013i −0.443921 + 0.972051i
\(626\) 0 0
\(627\) −0.652550 0.0181489i −0.0260603 0.000724796i
\(628\) 0 0
\(629\) 5.93616 + 0.853490i 0.236690 + 0.0340309i
\(630\) 0 0
\(631\) −1.12766 + 1.75467i −0.0448914 + 0.0698524i −0.862974 0.505248i \(-0.831401\pi\)
0.818082 + 0.575101i \(0.195037\pi\)
\(632\) 0 0
\(633\) 4.21113 + 36.4587i 0.167377 + 1.44910i
\(634\) 0 0
\(635\) 3.41115 7.46937i 0.135367 0.296413i
\(636\) 0 0
\(637\) −0.301451 + 0.261209i −0.0119439 + 0.0103495i
\(638\) 0 0
\(639\) −10.1104 + 28.4722i −0.399963 + 1.12634i
\(640\) 0 0
\(641\) 32.2874 1.27528 0.637639 0.770336i \(-0.279911\pi\)
0.637639 + 0.770336i \(0.279911\pi\)
\(642\) 0 0
\(643\) −27.9797 8.21557i −1.10341 0.323991i −0.321204 0.947010i \(-0.604088\pi\)
−0.782206 + 0.623019i \(0.785906\pi\)
\(644\) 0 0
\(645\) −0.863299 + 0.707004i −0.0339924 + 0.0278383i
\(646\) 0 0
\(647\) 10.4040 + 22.7815i 0.409023 + 0.895635i 0.996275 + 0.0862309i \(0.0274823\pi\)
−0.587253 + 0.809404i \(0.699790\pi\)
\(648\) 0 0
\(649\) 2.54182 8.65663i 0.0997750 0.339802i
\(650\) 0 0
\(651\) −0.703933 + 0.768149i −0.0275893 + 0.0301061i
\(652\) 0 0
\(653\) −3.38879 + 23.5696i −0.132614 + 0.922348i 0.809516 + 0.587098i \(0.199730\pi\)
−0.942129 + 0.335250i \(0.891179\pi\)
\(654\) 0 0
\(655\) 16.0613 13.9172i 0.627568 0.543791i
\(656\) 0 0
\(657\) −21.1909 + 21.8709i −0.826737 + 0.853266i
\(658\) 0 0
\(659\) −5.05336 17.2102i −0.196851 0.670413i −0.997460 0.0712260i \(-0.977309\pi\)
0.800609 0.599187i \(-0.204509\pi\)
\(660\) 0 0
\(661\) −3.39807 2.94445i −0.132170 0.114526i 0.586267 0.810118i \(-0.300597\pi\)
−0.718437 + 0.695592i \(0.755142\pi\)
\(662\) 0 0
\(663\) 22.5103 + 15.3672i 0.874227 + 0.596813i
\(664\) 0 0
\(665\) −0.769589 2.62098i −0.0298434 0.101637i
\(666\) 0 0
\(667\) 10.0247 + 21.9511i 0.388159 + 0.849950i
\(668\) 0 0
\(669\) −0.269373 2.33215i −0.0104146 0.0901660i
\(670\) 0 0
\(671\) 2.34518i 0.0905347i
\(672\) 0 0
\(673\) −6.05052 + 2.76318i −0.233230 + 0.106513i −0.528602 0.848870i \(-0.677284\pi\)
0.295372 + 0.955382i \(0.404556\pi\)
\(674\) 0 0
\(675\) −1.13531 1.55520i −0.0436980 0.0598595i
\(676\) 0 0
\(677\) −17.5361 + 20.2377i −0.673967 + 0.777800i −0.984992 0.172602i \(-0.944782\pi\)
0.311024 + 0.950402i \(0.399328\pi\)
\(678\) 0 0
\(679\) 18.3123 21.1335i 0.702760 0.811028i
\(680\) 0 0
\(681\) 6.88270 2.91478i 0.263746 0.111695i
\(682\) 0 0
\(683\) 35.1796 22.6085i 1.34611 0.865092i 0.348715 0.937229i \(-0.386618\pi\)
0.997395 + 0.0721370i \(0.0229819\pi\)
\(684\) 0 0
\(685\) 27.1841 + 31.3721i 1.03865 + 1.19867i
\(686\) 0 0
\(687\) −0.204504 + 7.35304i −0.00780232 + 0.280536i
\(688\) 0 0
\(689\) −10.9313 + 9.47206i −0.416451 + 0.360857i
\(690\) 0 0
\(691\) −29.0762 8.53754i −1.10611 0.324783i −0.322833 0.946456i \(-0.604635\pi\)
−0.783277 + 0.621673i \(0.786453\pi\)
\(692\) 0 0
\(693\) −5.41021 + 4.18494i −0.205517 + 0.158973i
\(694\) 0 0
\(695\) −29.1311 45.3288i −1.10500 1.71942i
\(696\) 0 0
\(697\) −2.40782 + 8.20030i −0.0912028 + 0.310608i
\(698\) 0 0
\(699\) −4.36482 37.7893i −0.165093 1.42932i
\(700\) 0 0
\(701\) −7.64757 4.91479i −0.288845 0.185629i 0.388192 0.921579i \(-0.373100\pi\)
−0.677037 + 0.735949i \(0.736736\pi\)
\(702\) 0 0
\(703\) 0.336774 + 0.388658i 0.0127017 + 0.0146585i
\(704\) 0 0
\(705\) −12.9335 + 39.9077i −0.487104 + 1.50301i
\(706\) 0 0
\(707\) 4.34945i 0.163578i
\(708\) 0 0
\(709\) −20.8810 13.4194i −0.784204 0.503977i 0.0862225 0.996276i \(-0.472520\pi\)
−0.870426 + 0.492299i \(0.836157\pi\)
\(710\) 0 0
\(711\) 25.3320 2.21430i 0.950023 0.0830426i
\(712\) 0 0
\(713\) −0.261982 + 1.82212i −0.00981129 + 0.0682390i
\(714\) 0 0
\(715\) 5.50208 + 2.51271i 0.205766 + 0.0939702i
\(716\) 0 0
\(717\) −33.6574 + 20.3308i −1.25696 + 0.759267i
\(718\) 0 0
\(719\) −34.6967 + 4.98863i −1.29397 + 0.186044i −0.754689 0.656083i \(-0.772212\pi\)
−0.539278 + 0.842128i \(0.681303\pi\)
\(720\) 0 0
\(721\) 4.04515 + 13.7765i 0.150649 + 0.513065i
\(722\) 0 0
\(723\) −27.8833 + 7.35175i −1.03699 + 0.273414i
\(724\) 0 0
\(725\) 0.591630 + 0.920595i 0.0219726 + 0.0341900i
\(726\) 0 0
\(727\) −32.5087 14.8462i −1.20568 0.550616i −0.291754 0.956493i \(-0.594239\pi\)
−0.913928 + 0.405877i \(0.866966\pi\)
\(728\) 0 0
\(729\) −26.8098 + 3.19923i −0.992955 + 0.118490i
\(730\) 0 0
\(731\) 1.37307 + 0.403169i 0.0507847 + 0.0149117i
\(732\) 0 0
\(733\) −39.4566 + 5.67300i −1.45736 + 0.209537i −0.824999 0.565135i \(-0.808824\pi\)
−0.632363 + 0.774672i \(0.717915\pi\)
\(734\) 0 0
\(735\) −0.432566 0.295302i −0.0159554 0.0108924i
\(736\) 0 0
\(737\) 5.38089 + 4.45983i 0.198208 + 0.164280i
\(738\) 0 0
\(739\) −16.8403 14.5922i −0.619480 0.536782i 0.287595 0.957752i \(-0.407144\pi\)
−0.907075 + 0.420970i \(0.861690\pi\)
\(740\) 0 0
\(741\) 0.595865 + 2.25997i 0.0218897 + 0.0830220i
\(742\) 0 0
\(743\) −3.18990 + 10.8638i −0.117026 + 0.398554i −0.997084 0.0763124i \(-0.975685\pi\)
0.880058 + 0.474866i \(0.157504\pi\)
\(744\) 0 0
\(745\) 19.9333 31.0169i 0.730300 1.13637i
\(746\) 0 0
\(747\) −29.9133 6.01421i −1.09447 0.220048i
\(748\) 0 0
\(749\) −15.6713 + 10.0713i −0.572618 + 0.367999i
\(750\) 0 0
\(751\) 3.83220 + 26.6535i 0.139839 + 0.972600i 0.932044 + 0.362345i \(0.118024\pi\)
−0.792205 + 0.610255i \(0.791067\pi\)
\(752\) 0 0
\(753\) −9.33990 22.0544i −0.340365 0.803708i
\(754\) 0 0
\(755\) −1.55755 10.8330i −0.0566850 0.394253i
\(756\) 0 0
\(757\) 16.5988 7.58043i 0.603295 0.275515i −0.0902614 0.995918i \(-0.528770\pi\)
0.693556 + 0.720403i \(0.256043\pi\)
\(758\) 0 0
\(759\) −3.72574 + 11.4962i −0.135236 + 0.417284i
\(760\) 0 0
\(761\) −18.3174 2.63364i −0.664004 0.0954693i −0.197931 0.980216i \(-0.563422\pi\)
−0.466072 + 0.884747i \(0.654331\pi\)
\(762\) 0 0
\(763\) 0.570323 3.96668i 0.0206471 0.143604i
\(764\) 0 0
\(765\) −11.9758 + 33.7252i −0.432985 + 1.21934i
\(766\) 0 0
\(767\) −32.3014 −1.16634
\(768\) 0 0
\(769\) 1.33843 + 0.611241i 0.0482651 + 0.0220419i 0.439401 0.898291i \(-0.355191\pi\)
−0.391136 + 0.920333i \(0.627918\pi\)
\(770\) 0 0
\(771\) 7.44621 + 6.82372i 0.268169 + 0.245750i
\(772\) 0 0
\(773\) 17.7219 27.5759i 0.637413 0.991835i −0.360832 0.932631i \(-0.617507\pi\)
0.998246 0.0592040i \(-0.0188562\pi\)
\(774\) 0 0
\(775\) 0.0834780i 0.00299862i
\(776\) 0 0