Properties

Label 804.2.s.b.5.20
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 5.20
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.20

$q$-expansion

\(f(q)\) \(=\) \(q+(1.64768 - 0.533989i) q^{3} +(2.22357 - 0.652900i) q^{5} +(2.01808 + 1.74867i) q^{7} +(2.42971 - 1.75969i) q^{9} +O(q^{10})\) \(q+(1.64768 - 0.533989i) q^{3} +(2.22357 - 0.652900i) q^{5} +(2.01808 + 1.74867i) q^{7} +(2.42971 - 1.75969i) q^{9} +(0.819238 - 0.240550i) q^{11} +(1.65269 + 2.57164i) q^{13} +(3.31510 - 2.26314i) q^{15} +(-5.09528 - 0.732591i) q^{17} +(0.289069 + 0.333603i) q^{19} +(4.25892 + 1.80362i) q^{21} +(-7.43322 + 3.39464i) q^{23} +(0.311737 - 0.200341i) q^{25} +(3.06373 - 4.19685i) q^{27} -2.95311i q^{29} +(-0.121792 + 0.189512i) q^{31} +(1.22139 - 0.833814i) q^{33} +(5.62905 + 2.57070i) q^{35} +1.16503 q^{37} +(4.09634 + 3.35472i) q^{39} +(0.236280 - 1.64336i) q^{41} +(0.275166 + 0.0395630i) q^{43} +(4.25374 - 5.49916i) q^{45} +(-9.50691 + 4.34166i) q^{47} +(0.0185697 + 0.129155i) q^{49} +(-8.78660 + 1.51375i) q^{51} +(-0.673384 - 4.68349i) q^{53} +(1.66458 - 1.06976i) q^{55} +(0.654435 + 0.395313i) q^{57} +(5.71278 - 8.88926i) q^{59} +(0.773829 - 2.63542i) q^{61} +(7.98046 + 0.697581i) q^{63} +(5.35390 + 4.63918i) q^{65} +(-4.57523 - 6.78728i) q^{67} +(-10.4349 + 9.56254i) q^{69} +(9.96884 - 1.43330i) q^{71} +(-9.73985 - 2.85988i) q^{73} +(0.406664 - 0.496563i) q^{75} +(2.07393 + 0.947131i) q^{77} +(4.58257 + 7.13062i) q^{79} +(2.80699 - 8.55107i) q^{81} +(2.86539 + 9.75864i) q^{83} +(-11.8080 + 1.69774i) q^{85} +(-1.57693 - 4.86579i) q^{87} +(1.51223 + 0.690613i) q^{89} +(-1.16170 + 8.07977i) q^{91} +(-0.0994770 + 0.377291i) q^{93} +(0.860576 + 0.553059i) q^{95} -10.4721i q^{97} +(1.56722 - 2.02607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

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
\(3\) 1.64768 0.533989i 0.951290 0.308299i
\(4\) 0 0
\(5\) 2.22357 0.652900i 0.994413 0.291986i 0.256251 0.966610i \(-0.417512\pi\)
0.738161 + 0.674624i \(0.235694\pi\)
\(6\) 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
\(9\) 2.42971 1.75969i 0.809903 0.586563i
\(10\) 0 0
\(11\) 0.819238 0.240550i 0.247010 0.0725286i −0.155884 0.987775i \(-0.549823\pi\)
0.402894 + 0.915247i \(0.368004\pi\)
\(12\) 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
\(15\) 3.31510 2.26314i 0.855955 0.584340i
\(16\) 0 0
\(17\) −5.09528 0.732591i −1.23579 0.177679i −0.506714 0.862114i \(-0.669140\pi\)
−0.729074 + 0.684435i \(0.760049\pi\)
\(18\) 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
\(21\) 4.25892 + 1.80362i 0.929372 + 0.393583i
\(22\) 0 0
\(23\) −7.43322 + 3.39464i −1.54993 + 0.707830i −0.992483 0.122381i \(-0.960947\pi\)
−0.557449 + 0.830211i \(0.688220\pi\)
\(24\) 0 0
\(25\) 0.311737 0.200341i 0.0623475 0.0400683i
\(26\) 0 0
\(27\) 3.06373 4.19685i 0.589616 0.807684i
\(28\) 0 0
\(29\) 2.95311i 0.548379i −0.961676 0.274189i \(-0.911590\pi\)
0.961676 0.274189i \(-0.0884095\pi\)
\(30\) 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
\(33\) 1.22139 0.833814i 0.212617 0.145148i
\(34\) 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
\(39\) 4.09634 + 3.35472i 0.655939 + 0.537185i
\(40\) 0 0
\(41\) 0.236280 1.64336i 0.0369007 0.256650i −0.963018 0.269439i \(-0.913162\pi\)
0.999918 + 0.0127888i \(0.00407091\pi\)
\(42\) 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
\(45\) 4.25374 5.49916i 0.634110 0.819766i
\(46\) 0 0
\(47\) −9.50691 + 4.34166i −1.38673 + 0.633296i −0.962256 0.272146i \(-0.912267\pi\)
−0.424469 + 0.905442i \(0.639539\pi\)
\(48\) 0 0
\(49\) 0.0185697 + 0.129155i 0.00265282 + 0.0184508i
\(50\) 0 0
\(51\) −8.78660 + 1.51375i −1.23037 + 0.211967i
\(52\) 0 0
\(53\) −0.673384 4.68349i −0.0924965 0.643327i −0.982346 0.187073i \(-0.940100\pi\)
0.889850 0.456254i \(-0.150809\pi\)
\(54\) 0 0
\(55\) 1.66458 1.06976i 0.224452 0.144247i
\(56\) 0 0
\(57\) 0.654435 + 0.395313i 0.0866820 + 0.0523604i
\(58\) 0 0
\(59\) 5.71278 8.88926i 0.743741 1.15728i −0.238770 0.971076i \(-0.576744\pi\)
0.982511 0.186207i \(-0.0596195\pi\)
\(60\) 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
\(63\) 7.98046 + 0.697581i 1.00544 + 0.0878870i
\(64\) 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
\(69\) −10.4349 + 9.56254i −1.25621 + 1.15119i
\(70\) 0 0
\(71\) 9.96884 1.43330i 1.18308 0.170102i 0.477437 0.878666i \(-0.341566\pi\)
0.705646 + 0.708564i \(0.250657\pi\)
\(72\) 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
\(75\) 0.406664 0.496563i 0.0469575 0.0573382i
\(76\) 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
\(81\) 2.80699 8.55107i 0.311887 0.950119i
\(82\) 0 0
\(83\) 2.86539 + 9.75864i 0.314518 + 1.07115i 0.953366 + 0.301817i \(0.0975931\pi\)
−0.638848 + 0.769333i \(0.720589\pi\)
\(84\) 0 0
\(85\) −11.8080 + 1.69774i −1.28076 + 0.184146i
\(86\) 0 0
\(87\) −1.57693 4.86579i −0.169065 0.521667i
\(88\) 0 0
\(89\) 1.51223 + 0.690613i 0.160296 + 0.0732049i 0.493947 0.869492i \(-0.335553\pi\)
−0.333651 + 0.942697i \(0.608281\pi\)
\(90\) 0 0
\(91\) −1.16170 + 8.07977i −0.121779 + 0.846990i
\(92\) 0 0
\(93\) −0.0994770 + 0.377291i −0.0103153 + 0.0391233i
\(94\) 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
\(99\) 1.56722 2.02607i 0.157511 0.203628i
\(100\) 0 0
\(101\) 1.06665 + 1.23098i 0.106136 + 0.122487i 0.806332 0.591463i \(-0.201450\pi\)
−0.700196 + 0.713951i \(0.746904\pi\)
\(102\) 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 \(-0.799608\pi\)
0.998298 0.0583167i \(-0.0185733\pi\)
\(108\) 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
\(111\) 1.91960 0.622114i 0.182200 0.0590484i
\(112\) 0 0
\(113\) −11.7027 3.43621i −1.10089 0.323251i −0.319686 0.947524i \(-0.603577\pi\)
−0.781207 + 0.624272i \(0.785396\pi\)
\(114\) 0 0
\(115\) −14.3119 + 12.4014i −1.33460 + 1.15643i
\(116\) 0 0
\(117\) 8.54084 + 3.34011i 0.789601 + 0.308793i
\(118\) 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
\(123\) −0.488224 2.83391i −0.0440217 0.255525i
\(124\) 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
\(129\) 0.474513 0.0817488i 0.0417785 0.00719758i
\(130\) 0 0
\(131\) 8.34179 3.80957i 0.728826 0.332844i −0.0162095 0.999869i \(-0.505160\pi\)
0.745035 + 0.667025i \(0.232433\pi\)
\(132\) 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 \(0.140989\pi\)
−0.267762 + 0.963485i \(0.586284\pi\)
\(138\) 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
\(141\) −13.3460 + 12.2303i −1.12393 + 1.02997i
\(142\) 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
\(147\) 0.0995647 + 0.202891i 0.00821196 + 0.0167342i
\(148\) 0 0
\(149\) 12.0237 10.4186i 0.985021 0.853526i −0.00419440 0.999991i \(-0.501335\pi\)
0.989216 + 0.146465i \(0.0467897\pi\)
\(150\) 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
\(153\) −13.6692 + 7.18613i −1.10509 + 0.580964i
\(154\) 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
\(159\) −3.61046 7.35732i −0.286328 0.583474i
\(160\) 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
\(165\) 2.17146 2.65150i 0.169048 0.206419i
\(166\) 0 0
\(167\) 5.28474 4.57925i 0.408945 0.354353i −0.425964 0.904740i \(-0.640065\pi\)
0.834910 + 0.550387i \(0.185520\pi\)
\(168\) 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 −0.475220 0.879867i \(-0.657632\pi\)
0.997769 + 0.0667654i \(0.0212679\pi\)
\(174\) 0 0
\(175\) 0.979441 + 0.140822i 0.0740388 + 0.0106452i
\(176\) 0 0
\(177\) 4.66607 17.6972i 0.350724 1.33021i
\(178\) 0 0
\(179\) −9.73917 + 21.3258i −0.727940 + 1.59397i 0.0744916 + 0.997222i \(0.476267\pi\)
−0.802431 + 0.596744i \(0.796461\pi\)
\(180\) 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
\(183\) −0.132262 4.75555i −0.00977712 0.351540i
\(184\) 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
\(189\) 13.5218 3.11209i 0.983563 0.226371i
\(190\) 0 0
\(191\) −6.82175 + 14.9376i −0.493605 + 1.08084i 0.484891 + 0.874575i \(0.338859\pi\)
−0.978495 + 0.206269i \(0.933868\pi\)
\(192\) 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
\(195\) 11.2988 + 4.78497i 0.809124 + 0.342659i
\(196\) 0 0
\(197\) −0.451957 3.14343i −0.0322006 0.223960i 0.967366 0.253381i \(-0.0815427\pi\)
−0.999567 + 0.0294210i \(0.990634\pi\)
\(198\) 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
\(201\) −11.1629 8.74016i −0.787368 0.616483i
\(202\) 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
\(207\) −12.0871 + 21.3281i −0.840108 + 1.48241i
\(208\) 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
\(213\) 15.6601 7.68488i 1.07301 0.526559i
\(214\) 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
\(219\) −17.5753 + 0.488809i −1.18763 + 0.0330306i
\(220\) 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
\(225\) 0.404893 1.03533i 0.0269929 0.0690222i
\(226\) 0 0
\(227\) −4.27145 0.614142i −0.283506 0.0407621i −0.000905286 1.00000i \(-0.500288\pi\)
−0.282601 + 0.959238i \(0.591197\pi\)
\(228\) 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 \(0.391953\pi\)
−0.930670 + 0.365860i \(0.880775\pi\)
\(234\) 0 0
\(235\) −18.3047 + 15.8611i −1.19406 + 1.03466i
\(236\) 0 0
\(237\) 11.3583 + 9.30195i 0.737801 + 0.604227i
\(238\) 0 0
\(239\) 22.7021 1.46848 0.734239 0.678891i \(-0.237539\pi\)
0.734239 + 0.678891i \(0.237539\pi\)
\(240\) 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
\(243\) 0.0588374 15.5883i 0.00377442 0.999993i
\(244\) 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
\(249\) 9.93227 + 14.5490i 0.629432 + 0.922008i
\(250\) 0 0
\(251\) −1.96791 + 13.6871i −0.124214 + 0.863924i 0.828486 + 0.560010i \(0.189203\pi\)
−0.952699 + 0.303914i \(0.901706\pi\)
\(252\) 0 0
\(253\) −5.27299 + 4.56908i −0.331510 + 0.287255i
\(254\) 0 0
\(255\) −18.5493 + 9.10271i −1.16160 + 0.570034i
\(256\) 0 0
\(257\) −1.64284 5.59501i −0.102478 0.349007i 0.892252 0.451537i \(-0.149124\pi\)
−0.994730 + 0.102530i \(0.967306\pi\)
\(258\) 0 0
\(259\) 2.35112 + 2.03726i 0.146091 + 0.126589i
\(260\) 0 0
\(261\) −5.19656 7.17520i −0.321659 0.444134i
\(262\) 0 0
\(263\) −5.40171 18.3965i −0.333084 1.13438i −0.940443 0.339951i \(-0.889589\pi\)
0.607359 0.794427i \(-0.292229\pi\)
\(264\) 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 \(0.183324\pi\)
−0.838687 + 0.544614i \(0.816676\pi\)
\(270\) 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
\(273\) 2.40041 + 13.9332i 0.145279 + 0.843277i
\(274\) 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
\(279\) 0.0375631 + 0.674775i 0.00224884 + 0.0403977i
\(280\) 0 0
\(281\) 6.23786 4.00883i 0.372120 0.239147i −0.341192 0.939994i \(-0.610831\pi\)
0.713312 + 0.700847i \(0.247194\pi\)
\(282\) 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
\(285\) 1.71328 + 0.451726i 0.101486 + 0.0267580i
\(286\) 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
\(291\) −5.59199 17.2547i −0.327808 1.01149i
\(292\) 0 0
\(293\) 7.63596 + 11.8818i 0.446098 + 0.694141i 0.989371 0.145415i \(-0.0464516\pi\)
−0.543273 + 0.839556i \(0.682815\pi\)
\(294\) 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
\(303\) 2.41484 + 1.45869i 0.138729 + 0.0837994i
\(304\) 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
\(309\) 9.00545 + 2.37439i 0.512302 + 0.135074i
\(310\) 0 0
\(311\) −3.43808 + 23.9124i −0.194956 + 1.35595i 0.623700 + 0.781664i \(0.285629\pi\)
−0.818656 + 0.574284i \(0.805281\pi\)
\(312\) 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
\(315\) 18.2006 3.65932i 1.02549 0.206179i
\(316\) 0 0
\(317\) 15.0821 2.16848i 0.847095 0.121794i 0.294920 0.955522i \(-0.404707\pi\)
0.552175 + 0.833728i \(0.313798\pi\)
\(318\) 0 0
\(319\) −0.710371 2.41930i −0.0397731 0.135455i
\(320\) 0 0
\(321\) −0.335929 12.0785i −0.0187497 0.674154i
\(322\) 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
\(327\) −2.01105 1.64697i −0.111212 0.0910774i
\(328\) 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
\(333\) 2.83069 2.05009i 0.155121 0.112344i
\(334\) 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
\(339\) −21.1171 + 0.587315i −1.14693 + 0.0318986i
\(340\) 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
\(345\) −16.9593 + 28.0759i −0.913060 + 1.51156i
\(346\) 0 0
\(347\) −6.56322 + 4.21793i −0.352332 + 0.226430i −0.704820 0.709386i \(-0.748972\pi\)
0.352488 + 0.935816i \(0.385336\pi\)
\(348\) 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
\(351\) 15.8562 + 0.942720i 0.846340 + 0.0503187i
\(352\) 0 0
\(353\) 1.80519 + 12.5554i 0.0960806 + 0.668255i 0.979762 + 0.200166i \(0.0641482\pi\)
−0.883681 + 0.468089i \(0.844943\pi\)
\(354\) 0 0
\(355\) 21.2307 9.69571i 1.12681 0.514595i
\(356\) 0 0
\(357\) −20.3791 12.3100i −1.07857 0.651515i
\(358\) 0 0
\(359\) −2.24774 0.323176i −0.118631 0.0170566i 0.0827435 0.996571i \(-0.473632\pi\)
−0.201375 + 0.979514i \(0.564541\pi\)
\(360\) 0 0
\(361\) 2.67625 18.6137i 0.140855 0.979670i
\(362\) 0 0
\(363\) −11.2716 + 13.7634i −0.591606 + 0.722390i
\(364\) 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
\(369\) −2.31772 4.40867i −0.120655 0.229506i
\(370\) 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
\(375\) −7.24644 + 17.1111i −0.374205 + 0.883613i
\(376\) 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
\(381\) −2.39329 + 5.65130i −0.122612 + 0.289525i
\(382\) 0 0
\(383\) −10.0397 11.5864i −0.513003 0.592037i 0.438862 0.898554i \(-0.355382\pi\)
−0.951865 + 0.306517i \(0.900836\pi\)
\(384\) 0 0
\(385\) 5.22992 + 0.751948i 0.266541 + 0.0383228i
\(386\) 0 0
\(387\) 0.738193 0.388081i 0.0375245 0.0197273i
\(388\) 0 0
\(389\) 0.293311 + 0.456400i 0.0148714 + 0.0231404i 0.848610 0.529019i \(-0.177440\pi\)
−0.833738 + 0.552160i \(0.813804\pi\)
\(390\) 0 0
\(391\) 40.3612 11.8511i 2.04115 0.599337i
\(392\) 0 0
\(393\) 11.7104 10.7314i 0.590709 0.541327i
\(394\) 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
\(399\) 0.629426 + 1.94216i 0.0315107 + 0.0972297i
\(400\) 0 0
\(401\) 36.7151 1.83346 0.916732 0.399504i \(-0.130818\pi\)
0.916732 + 0.399504i \(0.130818\pi\)
\(402\) 0 0
\(403\) −0.688641 −0.0343036
\(404\) 0 0
\(405\) 0.658545 20.8466i 0.0327233 1.03588i
\(406\) 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
\(411\) 20.9613 + 22.8735i 1.03395 + 1.12827i
\(412\) 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
\(417\) 22.7059 + 33.2602i 1.11191 + 1.62876i
\(418\) 0 0
\(419\) 20.6344 + 2.96678i 1.00806 + 0.144937i 0.626511 0.779413i \(-0.284483\pi\)
0.381547 + 0.924350i \(0.375392\pi\)
\(420\) 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
\(423\) −15.4591 + 27.2782i −0.751645 + 1.32631i
\(424\) 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
\(429\) 4.16285 + 1.76294i 0.200984 + 0.0851156i
\(430\) 0 0
\(431\) 33.4433i 1.61091i −0.592657 0.805455i \(-0.701921\pi\)
0.592657 0.805455i \(-0.298079\pi\)
\(432\) 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
\(435\) −6.68329 9.78986i −0.320439 0.469388i
\(436\) 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
\(441\) 0.272393 + 0.281133i 0.0129711 + 0.0133873i
\(442\) 0 0
\(443\) 2.63553 18.3305i 0.125218 0.870908i −0.826282 0.563257i \(-0.809548\pi\)
0.951499 0.307651i \(-0.0995429\pi\)
\(444\) 0 0
\(445\) 3.81346 + 0.548293i 0.180775 + 0.0259916i
\(446\) 0 0
\(447\) 14.2478 23.5871i 0.673899 1.11563i
\(448\) 0 0
\(449\) 0.0867474 0.0396162i 0.00409386 0.00186960i −0.413367 0.910564i \(-0.635647\pi\)
0.417461 + 0.908695i \(0.362920\pi\)
\(450\) 0 0
\(451\) −0.201741 1.40314i −0.00949963 0.0660714i
\(452\) 0 0
\(453\) 1.38875 + 8.06103i 0.0652492 + 0.378740i
\(454\) 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
\(459\) −18.6852 + 19.1397i −0.872149 + 0.893363i
\(460\) 0 0
\(461\) −8.20038 + 12.7600i −0.381930 + 0.594295i −0.977992 0.208644i \(-0.933095\pi\)
0.596062 + 0.802939i \(0.296731\pi\)
\(462\) 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
\(465\) 0.0251390 + 0.903884i 0.00116579 + 0.0419166i
\(466\) 0 0
\(467\) −21.7502 18.8467i −1.00648 0.872119i −0.0146757 0.999892i \(-0.504672\pi\)
−0.991803 + 0.127773i \(0.959217\pi\)
\(468\) 0 0
\(469\) 2.63557 21.6978i 0.121699 1.00191i
\(470\) 0 0
\(471\) −4.44445 4.84989i −0.204789 0.223471i
\(472\) 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
\(477\) −9.87762 10.1946i −0.452265 0.466778i
\(478\) 0 0
\(479\) 13.2034 + 6.02980i 0.603279 + 0.275509i 0.693550 0.720409i \(-0.256046\pi\)
−0.0902702 + 0.995917i \(0.528773\pi\)
\(480\) 0 0
\(481\) 1.92543 + 2.99603i 0.0877922 + 0.136607i
\(482\) 0 0
\(483\) −37.7801 + 1.05075i −1.71905 + 0.0478107i
\(484\) 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
\(489\) −26.2748 + 8.51526i −1.18819 + 0.385073i
\(490\) 0 0
\(491\) −13.3009 6.07431i −0.600261 0.274130i 0.0920211 0.995757i \(-0.470667\pi\)
−0.692282 + 0.721627i \(0.743395\pi\)
\(492\) 0 0
\(493\) −2.16342 + 15.0469i −0.0974356 + 0.677680i
\(494\) 0 0
\(495\) 2.16200 5.52836i 0.0971748 0.248481i
\(496\) 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
\(501\) 6.26230 10.3671i 0.279779 0.463170i
\(502\) 0 0
\(503\) 25.6829 + 29.6397i 1.14515 + 1.32157i 0.939345 + 0.342974i \(0.111434\pi\)
0.205801 + 0.978594i \(0.434020\pi\)
\(504\) 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 \(0.211789\pi\)
−0.995570 + 0.0940184i \(0.970029\pi\)
\(510\) 0 0
\(511\) −14.6548 22.8033i −0.648289 1.00876i
\(512\) 0 0
\(513\) 2.28571 0.191107i 0.100917 0.00843756i
\(514\) 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
\(519\) 5.61376 21.2916i 0.246417 0.934596i
\(520\) 0 0
\(521\) 12.8160 + 14.7905i 0.561481 + 0.647983i 0.963519 0.267639i \(-0.0862436\pi\)
−0.402038 + 0.915623i \(0.631698\pi\)
\(522\) 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
\(525\) 1.68900 0.290981i 0.0737142 0.0126994i
\(526\) 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
\(531\) −1.76193 31.6510i −0.0764614 1.37354i
\(532\) 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
\(543\) −20.3156 22.1688i −0.871824 0.951355i
\(544\) 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
\(549\) −2.75734 7.76501i −0.117680 0.331402i
\(550\) 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
\(555\) 3.86219 2.63662i 0.163941 0.111918i
\(556\) 0 0
\(557\) 2.56898 8.74915i 0.108851 0.370713i −0.886993 0.461782i \(-0.847210\pi\)
0.995845 + 0.0910688i \(0.0290283\pi\)
\(558\) 0 0
\(559\) 0.353023 + 0.773014i 0.0149313 + 0.0326950i
\(560\) 0 0
\(561\) −6.83418 + 3.35374i −0.288540 + 0.141595i
\(562\) 0 0
\(563\) 14.3375 + 4.20987i 0.604253 + 0.177425i 0.569528 0.821972i \(-0.307126\pi\)
0.0347256 + 0.999397i \(0.488944\pi\)
\(564\) 0 0
\(565\) −28.2652 −1.18913
\(566\) 0 0
\(567\) 20.6177 12.3482i 0.865863 0.518576i
\(568\) 0 0
\(569\) 10.7257 9.29384i 0.449643 0.389618i −0.400392 0.916344i \(-0.631126\pi\)
0.850035 + 0.526726i \(0.176581\pi\)
\(570\) 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
\(579\) −30.6483 8.08077i −1.27370 0.335825i
\(580\) 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
\(585\) 21.1720 + 1.85067i 0.875353 + 0.0765156i
\(586\) 0 0
\(587\) −38.0598 + 11.1754i −1.57090 + 0.461257i −0.947262 0.320460i \(-0.896163\pi\)
−0.623634 + 0.781717i \(0.714344\pi\)
\(588\) 0 0
\(589\) −0.0984282 + 0.0141518i −0.00405566 + 0.000583116i
\(590\) 0 0
\(591\) −2.42324 4.93804i −0.0996788 0.203124i
\(592\) 0 0
\(593\) 4.07433 8.92153i 0.167313 0.366363i −0.807340 0.590086i \(-0.799094\pi\)
0.974653 + 0.223723i \(0.0718210\pi\)
\(594\) 0 0
\(595\) −26.7983 17.2222i −1.09862 0.706043i
\(596\) 0 0
\(597\) −3.17093 + 7.48756i −0.129778 + 0.306445i
\(598\) 0 0
\(599\) −5.18426 36.0573i −0.211823 1.47326i −0.767063 0.641572i \(-0.778282\pi\)
0.555239 0.831691i \(-0.312627\pi\)
\(600\) 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
\(603\) −23.0600 8.44015i −0.939076 0.343709i
\(604\) 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
\(609\) 5.32630 12.5771i 0.215833 0.509648i
\(610\) 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
\(615\) −2.93586 5.98264i −0.118385 0.241244i
\(616\) 0 0
\(617\) −47.8677 + 6.88234i −1.92708 + 0.277073i −0.996117 0.0880352i \(-0.971941\pi\)
−0.930965 + 0.365108i \(0.881032\pi\)
\(618\) 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
\(621\) −8.52662 + 41.5963i −0.342162 + 1.66920i
\(622\) 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
\(627\) 0.631230 + 0.166431i 0.0252089 + 0.00664661i
\(628\) 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
\(639\) 21.6992 21.0246i 0.858408 0.831719i
\(640\) 0 0
\(641\) −32.2874 −1.27528 −0.637639 0.770336i \(-0.720089\pi\)
−0.637639 + 0.770336i \(0.720089\pi\)
\(642\) 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
\(645\) 1.00174 0.491584i 0.0394435 0.0193561i
\(646\) 0 0
\(647\) −10.4040 22.7815i −0.409023 0.895635i −0.996275 0.0862309i \(-0.972518\pi\)
0.587253 0.809404i \(-0.300210\pi\)
\(648\) 0 0
\(649\) 2.54182 8.65663i 0.0997750 0.339802i
\(650\) 0 0
\(651\) −0.860511 + 0.587449i −0.0337261 + 0.0230240i
\(652\) 0 0
\(653\) 3.38879 23.5696i 0.132614 0.922348i −0.809516 0.587098i \(-0.800270\pi\)
0.942129 0.335250i \(-0.108821\pi\)
\(654\) 0 0
\(655\) 16.0613 13.9172i 0.627568 0.543791i
\(656\) 0 0
\(657\) −28.6975 + 10.1904i −1.11960 + 0.397567i
\(658\) 0 0
\(659\) 5.05336 + 17.2102i 0.196851 + 0.670413i 0.997460 + 0.0712260i \(0.0226911\pi\)
−0.800609 + 0.599187i \(0.795491\pi\)
\(660\) 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
\(663\) −18.4143 20.0942i −0.715154 0.780393i
\(664\) 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
\(675\) 0.114278 1.92211i 0.00439855 0.0739819i
\(676\) 0 0
\(677\) 17.5361 20.2377i 0.673967 0.777800i −0.311024 0.950402i \(-0.600672\pi\)
0.984992 + 0.172602i \(0.0552176\pi\)
\(678\) 0 0
\(679\) 18.3123 21.1335i 0.702760 0.811028i
\(680\) 0 0
\(681\) −7.36594 + 1.26900i −0.282264 + 0.0486282i
\(682\) 0 0
\(683\) −35.1796 + 22.6085i −1.34611 + 0.865092i −0.997395 0.0721370i \(-0.977018\pi\)
−0.348715 + 0.937229i \(0.613382\pi\)
\(684\) 0 0
\(685\) 27.1841 + 31.3721i 1.03865 + 1.19867i
\(686\) 0 0
\(687\) −1.87537 + 7.11280i −0.0715498 + 0.271370i
\(688\) 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
\(693\) 6.70570 1.34821i 0.254728 0.0512144i
\(694\) 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 0.677037 0.735949i \(-0.263264\pi\)
−0.388192 + 0.921579i \(0.626900\pi\)
\(702\) 0 0
\(703\) 0.336774 + 0.388658i 0.0127017 + 0.0146585i
\(704\) 0 0
\(705\) −21.6906 + 35.9085i −0.816915 + 1.35239i
\(706\) 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
\(711\) 23.6820 + 9.26144i 0.888145 + 0.347331i
\(712\) 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
\(717\) 37.4059 12.1227i 1.39695 0.452730i
\(718\) 0 0
\(719\) 34.6967 4.98863i 1.29397 0.186044i 0.539278 0.842128i \(-0.318697\pi\)
0.754689 + 0.656083i \(0.227788\pi\)
\(720\) 0 0
\(721\) 4.04515 + 13.7765i 0.150649 + 0.513065i
\(722\) 0 0
\(723\) −28.8251 + 0.801689i −1.07202 + 0.0298151i
\(724\) 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
\(729\) −8.22707 25.7161i −0.304706 0.952446i
\(730\) 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
\(735\) 0.353857 + 0.386137i 0.0130522 + 0.0142429i
\(736\) 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
\(741\) 0.0649776 + 2.33630i 0.00238701 + 0.0858260i
\(742\) 0 0
\(743\) 3.18990 10.8638i 0.117026 0.398554i −0.880058 0.474866i \(-0.842496\pi\)
0.997084 + 0.0763124i \(0.0243146\pi\)
\(744\) 0 0
\(745\) 19.9333 31.0169i 0.730300 1.13637i
\(746\) 0 0
\(747\) 24.1343 + 18.6685i 0.883026 + 0.683043i
\(748\) 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
\(753\) 4.06629 + 23.6029i 0.148184 + 0.860137i
\(754\) 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
\(759\) −6.24838 + 10.3441i −0.226802 + 0.375467i
\(760\) 0 0
\(761\) 18.3174 + 2.63364i 0.664004 + 0.0954693i 0.466072 0.884747i \(-0.345669\pi\)
0.197931 + 0.980216i \(0.436578\pi\)
\(762\) 0 0
\(763\) 0.570323 3.96668i 0.0206471 0.143604i
\(764\) 0 0
\(765\) −25.7026 + 24.9035i −0.929281 + 0.900389i
\(766\) 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
\(771\) −5.69456 8.34153i −0.205084 0.300413i
\(772\) 0 0
\(773\) −17.7219 + 27.5759i −0.637413 + 0.991835i 0.360832 + 0.932631i \(0.382493\pi\)
−0.998246 + 0.0592040i \(0.981144\pi\)
\(774\) 0 0
\(775\) 0.0834780i 0.00299862i
\(776\) 0 0