Properties

Label 637.2.g.b.373.2
Level $637$
Weight $2$
Character 637.373
Analytic conductor $5.086$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(1\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.2
Root \(-0.309017 - 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 637.373
Dual form 637.2.g.b.263.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.190983 - 0.330792i) q^{2} -0.381966 q^{3} +(0.927051 - 1.60570i) q^{4} +(-0.190983 + 0.330792i) q^{5} +(0.0729490 + 0.126351i) q^{6} -1.47214 q^{8} -2.85410 q^{9} +O(q^{10})\) \(q+(-0.190983 - 0.330792i) q^{2} -0.381966 q^{3} +(0.927051 - 1.60570i) q^{4} +(-0.190983 + 0.330792i) q^{5} +(0.0729490 + 0.126351i) q^{6} -1.47214 q^{8} -2.85410 q^{9} +0.145898 q^{10} -4.85410 q^{11} +(-0.354102 + 0.613323i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(0.0729490 - 0.126351i) q^{15} +(-1.57295 - 2.72443i) q^{16} +(-3.73607 + 6.47106i) q^{17} +(0.545085 + 0.944115i) q^{18} +4.85410 q^{19} +(0.354102 + 0.613323i) q^{20} +(0.927051 + 1.60570i) q^{22} +(-2.23607 - 3.87298i) q^{23} +0.562306 q^{24} +(2.42705 + 4.20378i) q^{25} +(1.33688 + 0.330792i) q^{26} +2.23607 q^{27} +(2.04508 - 3.54219i) q^{29} -0.0557281 q^{30} +(-4.35410 - 7.54153i) q^{31} +(-2.07295 + 3.59045i) q^{32} +1.85410 q^{33} +2.85410 q^{34} +(-2.64590 + 4.58283i) q^{36} +(-2.00000 - 3.46410i) q^{37} +(-0.927051 - 1.60570i) q^{38} +(0.954915 - 0.992377i) q^{39} +(0.281153 - 0.486971i) q^{40} +(-2.61803 + 4.53457i) q^{41} +(3.78115 + 6.54915i) q^{43} +(-4.50000 + 7.79423i) q^{44} +(0.545085 - 0.944115i) q^{45} +(-0.854102 + 1.47935i) q^{46} +(-1.11803 + 1.93649i) q^{47} +(0.600813 + 1.04064i) q^{48} +(0.927051 - 1.60570i) q^{50} +(1.42705 - 2.47172i) q^{51} +(1.85410 + 6.42280i) q^{52} +(-4.11803 - 7.13264i) q^{53} +(-0.427051 - 0.739674i) q^{54} +(0.927051 - 1.60570i) q^{55} -1.85410 q^{57} -1.56231 q^{58} +(-1.11803 + 1.93649i) q^{59} +(-0.135255 - 0.234268i) q^{60} -6.00000 q^{61} +(-1.66312 + 2.88061i) q^{62} -4.70820 q^{64} +(-0.381966 - 1.32317i) q^{65} +(-0.354102 - 0.613323i) q^{66} +0.708204 q^{67} +(6.92705 + 11.9980i) q^{68} +(0.854102 + 1.47935i) q^{69} +(-4.09017 - 7.08438i) q^{71} +4.20163 q^{72} +(1.00000 + 1.73205i) q^{73} +(-0.763932 + 1.32317i) q^{74} +(-0.927051 - 1.60570i) q^{75} +(4.50000 - 7.79423i) q^{76} +(-0.510643 - 0.126351i) q^{78} +(-2.00000 + 3.46410i) q^{79} +1.20163 q^{80} +7.70820 q^{81} +2.00000 q^{82} -6.70820 q^{83} +(-1.42705 - 2.47172i) q^{85} +(1.44427 - 2.50155i) q^{86} +(-0.781153 + 1.35300i) q^{87} +7.14590 q^{88} +(-8.04508 - 13.9345i) q^{89} -0.416408 q^{90} -8.29180 q^{92} +(1.66312 + 2.88061i) q^{93} +0.854102 q^{94} +(-0.927051 + 1.60570i) q^{95} +(0.791796 - 1.37143i) q^{96} +(-6.07295 - 10.5187i) q^{97} +13.8541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 3q^{2} - 6q^{3} - 3q^{4} - 3q^{5} + 7q^{6} + 12q^{8} + 2q^{9} + O(q^{10}) \) \( 4q - 3q^{2} - 6q^{3} - 3q^{4} - 3q^{5} + 7q^{6} + 12q^{8} + 2q^{9} + 14q^{10} - 6q^{11} + 12q^{12} - 10q^{13} + 7q^{15} - 13q^{16} - 6q^{17} - 9q^{18} + 6q^{19} - 12q^{20} - 3q^{22} - 38q^{24} + 3q^{25} + 21q^{26} - 3q^{29} - 36q^{30} - 4q^{31} - 15q^{32} - 6q^{33} - 2q^{34} - 24q^{36} - 8q^{37} + 3q^{38} + 15q^{39} - 19q^{40} - 6q^{41} - 5q^{43} - 18q^{44} - 9q^{45} + 10q^{46} + 27q^{48} - 3q^{50} - q^{51} - 6q^{52} - 12q^{53} + 5q^{54} - 3q^{55} + 6q^{57} + 34q^{58} + 33q^{60} - 24q^{61} + 9q^{62} + 8q^{64} - 6q^{65} + 12q^{66} - 24q^{67} + 21q^{68} - 10q^{69} + 6q^{71} + 66q^{72} + 4q^{73} - 12q^{74} + 3q^{75} + 18q^{76} - 49q^{78} - 8q^{79} + 54q^{80} + 4q^{81} + 8q^{82} + q^{85} - 30q^{86} + 17q^{87} + 42q^{88} - 21q^{89} + 52q^{90} - 60q^{92} - 9q^{93} - 10q^{94} + 3q^{95} + 30q^{96} - 31q^{97} + 42q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.190983 0.330792i −0.135045 0.233905i 0.790569 0.612372i \(-0.209785\pi\)
−0.925615 + 0.378467i \(0.876451\pi\)
\(3\) −0.381966 −0.220528 −0.110264 0.993902i \(-0.535170\pi\)
−0.110264 + 0.993902i \(0.535170\pi\)
\(4\) 0.927051 1.60570i 0.463525 0.802850i
\(5\) −0.190983 + 0.330792i −0.0854102 + 0.147935i −0.905566 0.424206i \(-0.860553\pi\)
0.820156 + 0.572140i \(0.193887\pi\)
\(6\) 0.0729490 + 0.126351i 0.0297813 + 0.0515827i
\(7\) 0 0
\(8\) −1.47214 −0.520479
\(9\) −2.85410 −0.951367
\(10\) 0.145898 0.0461370
\(11\) −4.85410 −1.46357 −0.731783 0.681537i \(-0.761312\pi\)
−0.731783 + 0.681537i \(0.761312\pi\)
\(12\) −0.354102 + 0.613323i −0.102220 + 0.177051i
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) 0 0
\(15\) 0.0729490 0.126351i 0.0188354 0.0326238i
\(16\) −1.57295 2.72443i −0.393237 0.681107i
\(17\) −3.73607 + 6.47106i −0.906130 + 1.56946i −0.0867359 + 0.996231i \(0.527644\pi\)
−0.819394 + 0.573231i \(0.805690\pi\)
\(18\) 0.545085 + 0.944115i 0.128478 + 0.222530i
\(19\) 4.85410 1.11361 0.556804 0.830644i \(-0.312028\pi\)
0.556804 + 0.830644i \(0.312028\pi\)
\(20\) 0.354102 + 0.613323i 0.0791796 + 0.137143i
\(21\) 0 0
\(22\) 0.927051 + 1.60570i 0.197648 + 0.342336i
\(23\) −2.23607 3.87298i −0.466252 0.807573i 0.533005 0.846112i \(-0.321063\pi\)
−0.999257 + 0.0385394i \(0.987729\pi\)
\(24\) 0.562306 0.114780
\(25\) 2.42705 + 4.20378i 0.485410 + 0.840755i
\(26\) 1.33688 + 0.330792i 0.262184 + 0.0648737i
\(27\) 2.23607 0.430331
\(28\) 0 0
\(29\) 2.04508 3.54219i 0.379763 0.657768i −0.611265 0.791426i \(-0.709339\pi\)
0.991028 + 0.133658i \(0.0426723\pi\)
\(30\) −0.0557281 −0.0101745
\(31\) −4.35410 7.54153i −0.782020 1.35450i −0.930763 0.365622i \(-0.880856\pi\)
0.148744 0.988876i \(-0.452477\pi\)
\(32\) −2.07295 + 3.59045i −0.366449 + 0.634708i
\(33\) 1.85410 0.322758
\(34\) 2.85410 0.489474
\(35\) 0 0
\(36\) −2.64590 + 4.58283i −0.440983 + 0.763805i
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) −0.927051 1.60570i −0.150388 0.260479i
\(39\) 0.954915 0.992377i 0.152909 0.158907i
\(40\) 0.281153 0.486971i 0.0444542 0.0769969i
\(41\) −2.61803 + 4.53457i −0.408868 + 0.708181i −0.994763 0.102206i \(-0.967410\pi\)
0.585895 + 0.810387i \(0.300743\pi\)
\(42\) 0 0
\(43\) 3.78115 + 6.54915i 0.576620 + 0.998736i 0.995864 + 0.0908618i \(0.0289622\pi\)
−0.419243 + 0.907874i \(0.637704\pi\)
\(44\) −4.50000 + 7.79423i −0.678401 + 1.17502i
\(45\) 0.545085 0.944115i 0.0812565 0.140740i
\(46\) −0.854102 + 1.47935i −0.125930 + 0.218118i
\(47\) −1.11803 + 1.93649i −0.163082 + 0.282466i −0.935973 0.352073i \(-0.885477\pi\)
0.772890 + 0.634539i \(0.218810\pi\)
\(48\) 0.600813 + 1.04064i 0.0867199 + 0.150203i
\(49\) 0 0
\(50\) 0.927051 1.60570i 0.131105 0.227080i
\(51\) 1.42705 2.47172i 0.199827 0.346111i
\(52\) 1.85410 + 6.42280i 0.257118 + 0.890682i
\(53\) −4.11803 7.13264i −0.565655 0.979744i −0.996988 0.0775512i \(-0.975290\pi\)
0.431333 0.902193i \(-0.358043\pi\)
\(54\) −0.427051 0.739674i −0.0581143 0.100657i
\(55\) 0.927051 1.60570i 0.125004 0.216512i
\(56\) 0 0
\(57\) −1.85410 −0.245582
\(58\) −1.56231 −0.205141
\(59\) −1.11803 + 1.93649i −0.145556 + 0.252110i −0.929580 0.368620i \(-0.879830\pi\)
0.784024 + 0.620730i \(0.213164\pi\)
\(60\) −0.135255 0.234268i −0.0174613 0.0302439i
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) −1.66312 + 2.88061i −0.211216 + 0.365837i
\(63\) 0 0
\(64\) −4.70820 −0.588525
\(65\) −0.381966 1.32317i −0.0473771 0.164119i
\(66\) −0.354102 0.613323i −0.0435869 0.0754948i
\(67\) 0.708204 0.0865209 0.0432604 0.999064i \(-0.486225\pi\)
0.0432604 + 0.999064i \(0.486225\pi\)
\(68\) 6.92705 + 11.9980i 0.840028 + 1.45497i
\(69\) 0.854102 + 1.47935i 0.102822 + 0.178093i
\(70\) 0 0
\(71\) −4.09017 7.08438i −0.485414 0.840761i 0.514446 0.857523i \(-0.327998\pi\)
−0.999860 + 0.0167615i \(0.994664\pi\)
\(72\) 4.20163 0.495166
\(73\) 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) −0.763932 + 1.32317i −0.0888053 + 0.153815i
\(75\) −0.927051 1.60570i −0.107047 0.185410i
\(76\) 4.50000 7.79423i 0.516185 0.894059i
\(77\) 0 0
\(78\) −0.510643 0.126351i −0.0578189 0.0143065i
\(79\) −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 1.20163 0.134346
\(81\) 7.70820 0.856467
\(82\) 2.00000 0.220863
\(83\) −6.70820 −0.736321 −0.368161 0.929762i \(-0.620012\pi\)
−0.368161 + 0.929762i \(0.620012\pi\)
\(84\) 0 0
\(85\) −1.42705 2.47172i −0.154785 0.268096i
\(86\) 1.44427 2.50155i 0.155740 0.269749i
\(87\) −0.781153 + 1.35300i −0.0837484 + 0.145056i
\(88\) 7.14590 0.761755
\(89\) −8.04508 13.9345i −0.852777 1.47705i −0.878692 0.477389i \(-0.841583\pi\)
0.0259145 0.999664i \(-0.491750\pi\)
\(90\) −0.416408 −0.0438932
\(91\) 0 0
\(92\) −8.29180 −0.864479
\(93\) 1.66312 + 2.88061i 0.172457 + 0.298705i
\(94\) 0.854102 0.0880939
\(95\) −0.927051 + 1.60570i −0.0951134 + 0.164741i
\(96\) 0.791796 1.37143i 0.0808123 0.139971i
\(97\) −6.07295 10.5187i −0.616615 1.06801i −0.990099 0.140371i \(-0.955170\pi\)
0.373484 0.927636i \(-0.378163\pi\)
\(98\) 0 0
\(99\) 13.8541 1.39239
\(100\) 9.00000 0.900000
\(101\) 8.56231 0.851981 0.425991 0.904728i \(-0.359926\pi\)
0.425991 + 0.904728i \(0.359926\pi\)
\(102\) −1.09017 −0.107943
\(103\) −2.35410 + 4.07742i −0.231957 + 0.401761i −0.958384 0.285483i \(-0.907846\pi\)
0.726427 + 0.687243i \(0.241179\pi\)
\(104\) 3.68034 3.82472i 0.360887 0.375045i
\(105\) 0 0
\(106\) −1.57295 + 2.72443i −0.152778 + 0.264620i
\(107\) 2.80902 + 4.86536i 0.271558 + 0.470352i 0.969261 0.246035i \(-0.0791278\pi\)
−0.697703 + 0.716387i \(0.745794\pi\)
\(108\) 2.07295 3.59045i 0.199470 0.345492i
\(109\) −5.35410 9.27358i −0.512830 0.888248i −0.999889 0.0148787i \(-0.995264\pi\)
0.487059 0.873369i \(-0.338070\pi\)
\(110\) −0.708204 −0.0675246
\(111\) 0.763932 + 1.32317i 0.0725092 + 0.125590i
\(112\) 0 0
\(113\) 3.73607 + 6.47106i 0.351460 + 0.608746i 0.986505 0.163728i \(-0.0523521\pi\)
−0.635046 + 0.772475i \(0.719019\pi\)
\(114\) 0.354102 + 0.613323i 0.0331647 + 0.0574429i
\(115\) 1.70820 0.159291
\(116\) −3.79180 6.56758i −0.352059 0.609785i
\(117\) 7.13525 7.41517i 0.659655 0.685533i
\(118\) 0.854102 0.0786265
\(119\) 0 0
\(120\) −0.107391 + 0.186006i −0.00980340 + 0.0169800i
\(121\) 12.5623 1.14203
\(122\) 1.14590 + 1.98475i 0.103745 + 0.179691i
\(123\) 1.00000 1.73205i 0.0901670 0.156174i
\(124\) −16.1459 −1.44994
\(125\) −3.76393 −0.336656
\(126\) 0 0
\(127\) 7.07295 12.2507i 0.627623 1.08707i −0.360405 0.932796i \(-0.617361\pi\)
0.988027 0.154278i \(-0.0493053\pi\)
\(128\) 5.04508 + 8.73834i 0.445927 + 0.772368i
\(129\) −1.44427 2.50155i −0.127161 0.220249i
\(130\) −0.364745 + 0.379054i −0.0319903 + 0.0332453i
\(131\) −0.163119 + 0.282530i −0.0142518 + 0.0246848i −0.873063 0.487607i \(-0.837870\pi\)
0.858812 + 0.512292i \(0.171203\pi\)
\(132\) 1.71885 2.97713i 0.149606 0.259126i
\(133\) 0 0
\(134\) −0.135255 0.234268i −0.0116842 0.0202377i
\(135\) −0.427051 + 0.739674i −0.0367547 + 0.0636610i
\(136\) 5.50000 9.52628i 0.471621 0.816872i
\(137\) 0.190983 0.330792i 0.0163168 0.0282615i −0.857752 0.514064i \(-0.828139\pi\)
0.874069 + 0.485803i \(0.161473\pi\)
\(138\) 0.326238 0.565061i 0.0277712 0.0481012i
\(139\) 7.78115 + 13.4774i 0.659989 + 1.14313i 0.980618 + 0.195929i \(0.0627723\pi\)
−0.320629 + 0.947205i \(0.603894\pi\)
\(140\) 0 0
\(141\) 0.427051 0.739674i 0.0359642 0.0622918i
\(142\) −1.56231 + 2.70599i −0.131106 + 0.227082i
\(143\) 12.1353 12.6113i 1.01480 1.05461i
\(144\) 4.48936 + 7.77579i 0.374113 + 0.647983i
\(145\) 0.781153 + 1.35300i 0.0648712 + 0.112360i
\(146\) 0.381966 0.661585i 0.0316117 0.0547531i
\(147\) 0 0
\(148\) −7.41641 −0.609625
\(149\) −4.85410 −0.397664 −0.198832 0.980034i \(-0.563715\pi\)
−0.198832 + 0.980034i \(0.563715\pi\)
\(150\) −0.354102 + 0.613323i −0.0289123 + 0.0500776i
\(151\) 7.35410 + 12.7377i 0.598468 + 1.03658i 0.993047 + 0.117716i \(0.0375571\pi\)
−0.394579 + 0.918862i \(0.629110\pi\)
\(152\) −7.14590 −0.579609
\(153\) 10.6631 18.4691i 0.862062 1.49314i
\(154\) 0 0
\(155\) 3.32624 0.267170
\(156\) −0.708204 2.45329i −0.0567017 0.196420i
\(157\) −4.07295 7.05455i −0.325057 0.563015i 0.656467 0.754355i \(-0.272050\pi\)
−0.981524 + 0.191340i \(0.938717\pi\)
\(158\) 1.52786 0.121550
\(159\) 1.57295 + 2.72443i 0.124743 + 0.216061i
\(160\) −0.791796 1.37143i −0.0625970 0.108421i
\(161\) 0 0
\(162\) −1.47214 2.54981i −0.115662 0.200332i
\(163\) 9.70820 0.760405 0.380203 0.924903i \(-0.375854\pi\)
0.380203 + 0.924903i \(0.375854\pi\)
\(164\) 4.85410 + 8.40755i 0.379042 + 0.656519i
\(165\) −0.354102 + 0.613323i −0.0275668 + 0.0477471i
\(166\) 1.28115 + 2.21902i 0.0994368 + 0.172230i
\(167\) −4.88197 + 8.45581i −0.377778 + 0.654330i −0.990739 0.135783i \(-0.956645\pi\)
0.612961 + 0.790113i \(0.289978\pi\)
\(168\) 0 0
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) −0.545085 + 0.944115i −0.0418061 + 0.0724103i
\(171\) −13.8541 −1.05945
\(172\) 14.0213 1.06911
\(173\) −9.00000 −0.684257 −0.342129 0.939653i \(-0.611148\pi\)
−0.342129 + 0.939653i \(0.611148\pi\)
\(174\) 0.596748 0.0452393
\(175\) 0 0
\(176\) 7.63525 + 13.2246i 0.575529 + 0.996845i
\(177\) 0.427051 0.739674i 0.0320991 0.0555973i
\(178\) −3.07295 + 5.32250i −0.230327 + 0.398939i
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) −1.01064 1.75049i −0.0753289 0.130473i
\(181\) −3.70820 −0.275629 −0.137814 0.990458i \(-0.544008\pi\)
−0.137814 + 0.990458i \(0.544008\pi\)
\(182\) 0 0
\(183\) 2.29180 0.169414
\(184\) 3.29180 + 5.70156i 0.242674 + 0.420324i
\(185\) 1.52786 0.112331
\(186\) 0.635255 1.10029i 0.0465792 0.0806775i
\(187\) 18.1353 31.4112i 1.32618 2.29701i
\(188\) 2.07295 + 3.59045i 0.151185 + 0.261861i
\(189\) 0 0
\(190\) 0.708204 0.0513785
\(191\) 23.6180 1.70894 0.854470 0.519500i \(-0.173882\pi\)
0.854470 + 0.519500i \(0.173882\pi\)
\(192\) 1.79837 0.129786
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) −2.31966 + 4.01777i −0.166542 + 0.288459i
\(195\) 0.145898 + 0.505406i 0.0104480 + 0.0361928i
\(196\) 0 0
\(197\) −3.89919 + 6.75359i −0.277806 + 0.481173i −0.970839 0.239732i \(-0.922940\pi\)
0.693034 + 0.720905i \(0.256274\pi\)
\(198\) −2.64590 4.58283i −0.188036 0.325688i
\(199\) −1.20820 + 2.09267i −0.0856473 + 0.148345i −0.905667 0.423990i \(-0.860629\pi\)
0.820020 + 0.572336i \(0.193962\pi\)
\(200\) −3.57295 6.18853i −0.252646 0.437595i
\(201\) −0.270510 −0.0190803
\(202\) −1.63525 2.83234i −0.115056 0.199283i
\(203\) 0 0
\(204\) −2.64590 4.58283i −0.185250 0.320862i
\(205\) −1.00000 1.73205i −0.0698430 0.120972i
\(206\) 1.79837 0.125299
\(207\) 6.38197 + 11.0539i 0.443577 + 0.768298i
\(208\) 11.0106 + 2.72443i 0.763451 + 0.188905i
\(209\) −23.5623 −1.62984
\(210\) 0 0
\(211\) 4.35410 7.54153i 0.299749 0.519180i −0.676330 0.736599i \(-0.736430\pi\)
0.976078 + 0.217419i \(0.0697638\pi\)
\(212\) −15.2705 −1.04878
\(213\) 1.56231 + 2.70599i 0.107047 + 0.185412i
\(214\) 1.07295 1.85840i 0.0733453 0.127038i
\(215\) −2.88854 −0.196997
\(216\) −3.29180 −0.223978
\(217\) 0 0
\(218\) −2.04508 + 3.54219i −0.138511 + 0.239907i
\(219\) −0.381966 0.661585i −0.0258109 0.0447057i
\(220\) −1.71885 2.97713i −0.115885 0.200718i
\(221\) −7.47214 25.8842i −0.502630 1.74116i
\(222\) 0.291796 0.505406i 0.0195841 0.0339206i
\(223\) 6.63525 11.4926i 0.444330 0.769601i −0.553676 0.832732i \(-0.686775\pi\)
0.998005 + 0.0631310i \(0.0201086\pi\)
\(224\) 0 0
\(225\) −6.92705 11.9980i −0.461803 0.799867i
\(226\) 1.42705 2.47172i 0.0949260 0.164417i
\(227\) 3.73607 6.47106i 0.247972 0.429499i −0.714991 0.699133i \(-0.753569\pi\)
0.962963 + 0.269634i \(0.0869027\pi\)
\(228\) −1.71885 + 2.97713i −0.113833 + 0.197165i
\(229\) −13.5623 + 23.4906i −0.896222 + 1.55230i −0.0639380 + 0.997954i \(0.520366\pi\)
−0.832284 + 0.554349i \(0.812967\pi\)
\(230\) −0.326238 0.565061i −0.0215115 0.0372590i
\(231\) 0 0
\(232\) −3.01064 + 5.21459i −0.197658 + 0.342354i
\(233\) −0.190983 + 0.330792i −0.0125117 + 0.0216709i −0.872213 0.489125i \(-0.837316\pi\)
0.859702 + 0.510796i \(0.170649\pi\)
\(234\) −3.81559 0.944115i −0.249433 0.0617187i
\(235\) −0.427051 0.739674i −0.0278577 0.0482510i
\(236\) 2.07295 + 3.59045i 0.134937 + 0.233719i
\(237\) 0.763932 1.32317i 0.0496227 0.0859491i
\(238\) 0 0
\(239\) −11.2918 −0.730406 −0.365203 0.930928i \(-0.619000\pi\)
−0.365203 + 0.930928i \(0.619000\pi\)
\(240\) −0.458980 −0.0296271
\(241\) −2.21885 + 3.84316i −0.142929 + 0.247559i −0.928598 0.371087i \(-0.878985\pi\)
0.785670 + 0.618646i \(0.212319\pi\)
\(242\) −2.39919 4.15551i −0.154226 0.267127i
\(243\) −9.65248 −0.619207
\(244\) −5.56231 + 9.63420i −0.356090 + 0.616766i
\(245\) 0 0
\(246\) −0.763932 −0.0487065
\(247\) −12.1353 + 12.6113i −0.772148 + 0.802440i
\(248\) 6.40983 + 11.1022i 0.407025 + 0.704987i
\(249\) 2.56231 0.162380
\(250\) 0.718847 + 1.24508i 0.0454639 + 0.0787457i
\(251\) −2.61803 4.53457i −0.165249 0.286219i 0.771495 0.636236i \(-0.219509\pi\)
−0.936744 + 0.350016i \(0.886176\pi\)
\(252\) 0 0
\(253\) 10.8541 + 18.7999i 0.682392 + 1.18194i
\(254\) −5.40325 −0.339030
\(255\) 0.545085 + 0.944115i 0.0341345 + 0.0591228i
\(256\) −2.78115 + 4.81710i −0.173822 + 0.301069i
\(257\) 12.8713 + 22.2938i 0.802891 + 1.39065i 0.917706 + 0.397261i \(0.130039\pi\)
−0.114815 + 0.993387i \(0.536627\pi\)
\(258\) −0.551663 + 0.955508i −0.0343450 + 0.0594873i
\(259\) 0 0
\(260\) −2.47871 0.613323i −0.153723 0.0380367i
\(261\) −5.83688 + 10.1098i −0.361294 + 0.625779i
\(262\) 0.124612 0.00769854
\(263\) 9.00000 0.554964 0.277482 0.960731i \(-0.410500\pi\)
0.277482 + 0.960731i \(0.410500\pi\)
\(264\) −2.72949 −0.167989
\(265\) 3.14590 0.193251
\(266\) 0 0
\(267\) 3.07295 + 5.32250i 0.188061 + 0.325732i
\(268\) 0.656541 1.13716i 0.0401046 0.0694633i
\(269\) −6.87132 + 11.9015i −0.418952 + 0.725646i −0.995834 0.0911812i \(-0.970936\pi\)
0.576882 + 0.816827i \(0.304269\pi\)
\(270\) 0.326238 0.0198542
\(271\) −9.20820 15.9491i −0.559359 0.968837i −0.997550 0.0699558i \(-0.977714\pi\)
0.438192 0.898882i \(-0.355619\pi\)
\(272\) 23.5066 1.42530
\(273\) 0 0
\(274\) −0.145898 −0.00881402
\(275\) −11.7812 20.4056i −0.710430 1.23050i
\(276\) 3.16718 0.190642
\(277\) 2.50000 4.33013i 0.150210 0.260172i −0.781094 0.624413i \(-0.785338\pi\)
0.931305 + 0.364241i \(0.118672\pi\)
\(278\) 2.97214 5.14789i 0.178257 0.308750i
\(279\) 12.4271 + 21.5243i 0.743988 + 1.28863i
\(280\) 0 0
\(281\) −2.18034 −0.130068 −0.0650341 0.997883i \(-0.520716\pi\)
−0.0650341 + 0.997883i \(0.520716\pi\)
\(282\) −0.326238 −0.0194272
\(283\) −13.4164 −0.797523 −0.398761 0.917055i \(-0.630560\pi\)
−0.398761 + 0.917055i \(0.630560\pi\)
\(284\) −15.1672 −0.900007
\(285\) 0.354102 0.613323i 0.0209752 0.0363301i
\(286\) −6.48936 1.60570i −0.383724 0.0949470i
\(287\) 0 0
\(288\) 5.91641 10.2475i 0.348628 0.603841i
\(289\) −19.4164 33.6302i −1.14214 1.97825i
\(290\) 0.298374 0.516799i 0.0175211 0.0303475i
\(291\) 2.31966 + 4.01777i 0.135981 + 0.235526i
\(292\) 3.70820 0.217006
\(293\) 5.61803 + 9.73072i 0.328209 + 0.568475i 0.982157 0.188065i \(-0.0602216\pi\)
−0.653947 + 0.756540i \(0.726888\pi\)
\(294\) 0 0
\(295\) −0.427051 0.739674i −0.0248639 0.0430655i
\(296\) 2.94427 + 5.09963i 0.171132 + 0.296410i
\(297\) −10.8541 −0.629819
\(298\) 0.927051 + 1.60570i 0.0537026 + 0.0930157i
\(299\) 15.6525 + 3.87298i 0.905206 + 0.223980i
\(300\) −3.43769 −0.198475
\(301\) 0 0
\(302\) 2.80902 4.86536i 0.161641 0.279970i
\(303\) −3.27051 −0.187886
\(304\) −7.63525 13.2246i −0.437912 0.758486i
\(305\) 1.14590 1.98475i 0.0656139 0.113647i
\(306\) −8.14590 −0.465670
\(307\) 1.85410 0.105819 0.0529096 0.998599i \(-0.483150\pi\)
0.0529096 + 0.998599i \(0.483150\pi\)
\(308\) 0 0
\(309\) 0.899187 1.55744i 0.0511530 0.0885995i
\(310\) −0.635255 1.10029i −0.0360801 0.0624925i
\(311\) 6.16312 + 10.6748i 0.349478 + 0.605314i 0.986157 0.165815i \(-0.0530255\pi\)
−0.636678 + 0.771129i \(0.719692\pi\)
\(312\) −1.40576 + 1.46091i −0.0795858 + 0.0827079i
\(313\) 7.56231 13.0983i 0.427447 0.740360i −0.569199 0.822200i \(-0.692746\pi\)
0.996645 + 0.0818405i \(0.0260798\pi\)
\(314\) −1.55573 + 2.69460i −0.0877948 + 0.152065i
\(315\) 0 0
\(316\) 3.70820 + 6.42280i 0.208603 + 0.361311i
\(317\) −10.8820 + 18.8481i −0.611192 + 1.05862i 0.379848 + 0.925049i \(0.375976\pi\)
−0.991040 + 0.133567i \(0.957357\pi\)
\(318\) 0.600813 1.04064i 0.0336919 0.0583561i
\(319\) −9.92705 + 17.1942i −0.555808 + 0.962688i
\(320\) 0.899187 1.55744i 0.0502661 0.0870634i
\(321\) −1.07295 1.85840i −0.0598862 0.103726i
\(322\) 0 0
\(323\) −18.1353 + 31.4112i −1.00907 + 1.74776i
\(324\) 7.14590 12.3771i 0.396994 0.687614i
\(325\) −16.9894 4.20378i −0.942400 0.233184i
\(326\) −1.85410 3.21140i −0.102689 0.177863i
\(327\) 2.04508 + 3.54219i 0.113093 + 0.195884i
\(328\) 3.85410 6.67550i 0.212807 0.368593i
\(329\) 0 0
\(330\) 0.270510 0.0148911
\(331\) −16.8541 −0.926385 −0.463193 0.886258i \(-0.653296\pi\)
−0.463193 + 0.886258i \(0.653296\pi\)
\(332\) −6.21885 + 10.7714i −0.341304 + 0.591155i
\(333\) 5.70820 + 9.88690i 0.312808 + 0.541799i
\(334\) 3.72949 0.204069
\(335\) −0.135255 + 0.234268i −0.00738977 + 0.0127994i
\(336\) 0 0
\(337\) 8.56231 0.466419 0.233209 0.972427i \(-0.425077\pi\)
0.233209 + 0.972427i \(0.425077\pi\)
\(338\) −4.20163 + 2.64634i −0.228538 + 0.143942i
\(339\) −1.42705 2.47172i −0.0775068 0.134246i
\(340\) −5.29180 −0.286988
\(341\) 21.1353 + 36.6073i 1.14454 + 1.98240i
\(342\) 2.64590 + 4.58283i 0.143074 + 0.247811i
\(343\) 0 0
\(344\) −5.56637 9.64124i −0.300119 0.519821i
\(345\) −0.652476 −0.0351281
\(346\) 1.71885 + 2.97713i 0.0924058 + 0.160052i
\(347\) −17.6180 + 30.5153i −0.945786 + 1.63815i −0.191615 + 0.981470i \(0.561373\pi\)
−0.754171 + 0.656679i \(0.771961\pi\)
\(348\) 1.44834 + 2.50859i 0.0776390 + 0.134475i
\(349\) −3.64590 + 6.31488i −0.195160 + 0.338028i −0.946953 0.321372i \(-0.895856\pi\)
0.751793 + 0.659400i \(0.229189\pi\)
\(350\) 0 0
\(351\) −5.59017 + 5.80948i −0.298381 + 0.310087i
\(352\) 10.0623 17.4284i 0.536323 0.928938i
\(353\) 28.8541 1.53575 0.767874 0.640600i \(-0.221314\pi\)
0.767874 + 0.640600i \(0.221314\pi\)
\(354\) −0.326238 −0.0173393
\(355\) 3.12461 0.165837
\(356\) −29.8328 −1.58114
\(357\) 0 0
\(358\) 1.71885 + 2.97713i 0.0908439 + 0.157346i
\(359\) 5.45492 9.44819i 0.287899 0.498656i −0.685409 0.728159i \(-0.740376\pi\)
0.973308 + 0.229502i \(0.0737098\pi\)
\(360\) −0.802439 + 1.38987i −0.0422923 + 0.0732523i
\(361\) 4.56231 0.240121
\(362\) 0.708204 + 1.22665i 0.0372224 + 0.0644710i
\(363\) −4.79837 −0.251849
\(364\) 0 0
\(365\) −0.763932 −0.0399860
\(366\) −0.437694 0.758108i −0.0228786 0.0396270i
\(367\) 25.4164 1.32673 0.663363 0.748298i \(-0.269129\pi\)
0.663363 + 0.748298i \(0.269129\pi\)
\(368\) −7.03444 + 12.1840i −0.366696 + 0.635135i
\(369\) 7.47214 12.9421i 0.388984 0.673740i
\(370\) −0.291796 0.505406i −0.0151698 0.0262748i
\(371\) 0 0
\(372\) 6.16718 0.319754
\(373\) −0.437694 −0.0226629 −0.0113315 0.999936i \(-0.503607\pi\)
−0.0113315 + 0.999936i \(0.503607\pi\)
\(374\) −13.8541 −0.716379
\(375\) 1.43769 0.0742422
\(376\) 1.64590 2.85078i 0.0848807 0.147018i
\(377\) 4.09017 + 14.1688i 0.210654 + 0.729728i
\(378\) 0 0
\(379\) 6.42705 11.1320i 0.330135 0.571811i −0.652403 0.757872i \(-0.726239\pi\)
0.982538 + 0.186061i \(0.0595722\pi\)
\(380\) 1.71885 + 2.97713i 0.0881750 + 0.152724i
\(381\) −2.70163 + 4.67935i −0.138408 + 0.239731i
\(382\) −4.51064 7.81266i −0.230785 0.399731i
\(383\) 24.9787 1.27635 0.638176 0.769890i \(-0.279689\pi\)
0.638176 + 0.769890i \(0.279689\pi\)
\(384\) −1.92705 3.33775i −0.0983394 0.170329i
\(385\) 0 0
\(386\) 1.14590 + 1.98475i 0.0583247 + 0.101021i
\(387\) −10.7918 18.6919i −0.548578 0.950165i
\(388\) −22.5197 −1.14327
\(389\) −11.9443 20.6881i −0.605599 1.04893i −0.991957 0.126579i \(-0.959600\pi\)
0.386358 0.922349i \(-0.373733\pi\)
\(390\) 0.139320 0.144786i 0.00705475 0.00733152i
\(391\) 33.4164 1.68994
\(392\) 0 0
\(393\) 0.0623059 0.107917i 0.00314292 0.00544369i
\(394\) 2.97871 0.150065
\(395\) −0.763932 1.32317i −0.0384376 0.0665759i
\(396\) 12.8435 22.2455i 0.645408 1.11788i
\(397\) −25.4164 −1.27561 −0.637806 0.770197i \(-0.720158\pi\)
−0.637806 + 0.770197i \(0.720158\pi\)
\(398\) 0.922986 0.0462651
\(399\) 0 0
\(400\) 7.63525 13.2246i 0.381763 0.661232i
\(401\) 10.2254 + 17.7110i 0.510633 + 0.884443i 0.999924 + 0.0123222i \(0.00392237\pi\)
−0.489291 + 0.872121i \(0.662744\pi\)
\(402\) 0.0516628 + 0.0894826i 0.00257671 + 0.00446298i
\(403\) 30.4787 + 7.54153i 1.51825 + 0.375670i
\(404\) 7.93769 13.7485i 0.394915 0.684013i
\(405\) −1.47214 + 2.54981i −0.0731510 + 0.126701i
\(406\) 0 0
\(407\) 9.70820 + 16.8151i 0.481218 + 0.833494i
\(408\) −2.10081 + 3.63871i −0.104006 + 0.180143i
\(409\) −17.2812 + 29.9318i −0.854498 + 1.48003i 0.0226119 + 0.999744i \(0.492802\pi\)
−0.877110 + 0.480290i \(0.840532\pi\)
\(410\) −0.381966 + 0.661585i −0.0188640 + 0.0326733i
\(411\) −0.0729490 + 0.126351i −0.00359831 + 0.00623246i
\(412\) 4.36475 + 7.55996i 0.215036 + 0.372453i
\(413\) 0 0
\(414\) 2.43769 4.22221i 0.119806 0.207510i
\(415\) 1.28115 2.21902i 0.0628893 0.108928i
\(416\) −4.14590 14.3618i −0.203269 0.704146i
\(417\) −2.97214 5.14789i −0.145546 0.252093i
\(418\) 4.50000 + 7.79423i 0.220102 + 0.381228i
\(419\) −2.97214 + 5.14789i −0.145198 + 0.251491i −0.929447 0.368956i \(-0.879715\pi\)
0.784249 + 0.620447i \(0.213049\pi\)
\(420\) 0 0
\(421\) −25.4164 −1.23872 −0.619360 0.785107i \(-0.712608\pi\)
−0.619360 + 0.785107i \(0.712608\pi\)
\(422\) −3.32624 −0.161919
\(423\) 3.19098 5.52694i 0.155151 0.268729i
\(424\) 6.06231 + 10.5002i 0.294412 + 0.509936i
\(425\) −36.2705 −1.75938
\(426\) 0.596748 1.03360i 0.0289125 0.0500780i
\(427\) 0 0
\(428\) 10.4164 0.503496
\(429\) −4.63525 + 4.81710i −0.223792 + 0.232572i
\(430\) 0.551663 + 0.955508i 0.0266035 + 0.0460787i
\(431\) −16.7984 −0.809149 −0.404575 0.914505i \(-0.632580\pi\)
−0.404575 + 0.914505i \(0.632580\pi\)
\(432\) −3.51722 6.09201i −0.169222 0.293102i
\(433\) −0.500000 0.866025i −0.0240285 0.0416185i 0.853761 0.520665i \(-0.174316\pi\)
−0.877790 + 0.479046i \(0.840983\pi\)
\(434\) 0 0
\(435\) −0.298374 0.516799i −0.0143059 0.0247786i
\(436\) −19.8541 −0.950839
\(437\) −10.8541 18.7999i −0.519222 0.899319i
\(438\) −0.145898 + 0.252703i −0.00697128 + 0.0120746i
\(439\) −4.07295 7.05455i −0.194391 0.336696i 0.752310 0.658810i \(-0.228940\pi\)
−0.946701 + 0.322114i \(0.895606\pi\)
\(440\) −1.36475 + 2.36381i −0.0650617 + 0.112690i
\(441\) 0 0
\(442\) −7.13525 + 7.41517i −0.339389 + 0.352704i
\(443\) 0.381966 0.661585i 0.0181478 0.0314328i −0.856809 0.515634i \(-0.827556\pi\)
0.874957 + 0.484201i \(0.160890\pi\)
\(444\) 2.83282 0.134439
\(445\) 6.14590 0.291344
\(446\) −5.06888 −0.240019
\(447\) 1.85410 0.0876960
\(448\) 0 0
\(449\) −14.2361 24.6576i −0.671842 1.16366i −0.977381 0.211484i \(-0.932170\pi\)
0.305540 0.952179i \(-0.401163\pi\)
\(450\) −2.64590 + 4.58283i −0.124729 + 0.216037i
\(451\) 12.7082 22.0113i 0.598406 1.03647i
\(452\) 13.8541 0.651642
\(453\) −2.80902 4.86536i −0.131979 0.228595i
\(454\) −2.85410 −0.133950
\(455\) 0 0
\(456\) 2.72949 0.127820
\(457\) 5.70820 + 9.88690i 0.267019 + 0.462490i 0.968090 0.250601i \(-0.0806282\pi\)
−0.701072 + 0.713091i \(0.747295\pi\)
\(458\) 10.3607 0.484123
\(459\) −8.35410 + 14.4697i −0.389936 + 0.675389i
\(460\) 1.58359 2.74286i 0.0738354 0.127887i
\(461\) −19.6074 33.9610i −0.913207 1.58172i −0.809505 0.587113i \(-0.800264\pi\)
−0.103702 0.994608i \(-0.533069\pi\)
\(462\) 0 0
\(463\) −6.70820 −0.311757 −0.155878 0.987776i \(-0.549821\pi\)
−0.155878 + 0.987776i \(0.549821\pi\)
\(464\) −12.8673 −0.597347
\(465\) −1.27051 −0.0589185
\(466\) 0.145898 0.00675860
\(467\) −16.8262 + 29.1439i −0.778625 + 1.34862i 0.154109 + 0.988054i \(0.450749\pi\)
−0.932734 + 0.360565i \(0.882584\pi\)
\(468\) −5.29180 18.3313i −0.244613 0.847366i
\(469\) 0 0
\(470\) −0.163119 + 0.282530i −0.00752412 + 0.0130322i
\(471\) 1.55573 + 2.69460i 0.0716842 + 0.124161i
\(472\) 1.64590 2.85078i 0.0757586 0.131218i
\(473\) −18.3541 31.7902i −0.843923 1.46172i
\(474\) −0.583592 −0.0268053
\(475\) 11.7812 + 20.4056i 0.540556 + 0.936271i
\(476\) 0 0
\(477\) 11.7533 + 20.3573i 0.538146 + 0.932096i
\(478\) 2.15654 + 3.73524i 0.0986379 + 0.170846i
\(479\) −21.9787 −1.00423 −0.502117 0.864800i \(-0.667445\pi\)
−0.502117 + 0.864800i \(0.667445\pi\)
\(480\) 0.302439 + 0.523840i 0.0138044 + 0.0239099i
\(481\) 14.0000 + 3.46410i 0.638345 + 0.157949i
\(482\) 1.69505 0.0772073
\(483\) 0 0
\(484\) 11.6459 20.1713i 0.529359 0.916877i
\(485\) 4.63932 0.210661
\(486\) 1.84346 + 3.19296i 0.0836210 + 0.144836i
\(487\) 8.48936 14.7040i 0.384689 0.666302i −0.607037 0.794674i \(-0.707642\pi\)
0.991726 + 0.128372i \(0.0409752\pi\)
\(488\) 8.83282 0.399843
\(489\) −3.70820 −0.167691
\(490\) 0 0
\(491\) −7.30902 + 12.6596i −0.329851 + 0.571319i −0.982482 0.186357i \(-0.940332\pi\)
0.652631 + 0.757676i \(0.273665\pi\)
\(492\) −1.85410 3.21140i −0.0835894 0.144781i
\(493\) 15.2812 + 26.4677i 0.688229 + 1.19205i
\(494\) 6.48936 + 1.60570i 0.291970 + 0.0722438i
\(495\) −2.64590 + 4.58283i −0.118924 + 0.205983i
\(496\) −13.6976 + 23.7249i −0.615039 + 1.06528i
\(497\) 0 0
\(498\) −0.489357 0.847591i −0.0219286 0.0379815i
\(499\) −4.07295 + 7.05455i −0.182330 + 0.315805i −0.942674 0.333716i \(-0.891697\pi\)
0.760343 + 0.649521i \(0.225031\pi\)
\(500\) −3.48936 + 6.04374i −0.156049 + 0.270284i
\(501\) 1.86475 3.22983i 0.0833107 0.144298i
\(502\) −1.00000 + 1.73205i −0.0446322 + 0.0773052i
\(503\) −12.1910 21.1154i −0.543569 0.941489i −0.998695 0.0510624i \(-0.983739\pi\)
0.455126 0.890427i \(-0.349594\pi\)
\(504\) 0 0
\(505\) −1.63525 + 2.83234i −0.0727679 + 0.126038i
\(506\) 4.14590 7.18091i 0.184308 0.319230i
\(507\) 0.190983 + 4.96188i 0.00848185 + 0.220365i
\(508\) −13.1140 22.7141i −0.581838 1.00777i
\(509\) −15.2984 26.4976i −0.678089 1.17448i −0.975556 0.219752i \(-0.929475\pi\)
0.297467 0.954732i \(-0.403858\pi\)
\(510\) 0.208204 0.360620i 0.00921943 0.0159685i
\(511\) 0 0
\(512\) 22.3050 0.985749
\(513\) 10.8541 0.479220
\(514\) 4.91641 8.51547i 0.216853 0.375601i
\(515\) −0.899187 1.55744i −0.0396229 0.0686289i
\(516\) −5.35565 −0.235770
\(517\) 5.42705 9.39993i 0.238681 0.413408i
\(518\) 0 0
\(519\) 3.43769 0.150898
\(520\) 0.562306 + 1.94788i 0.0246587 + 0.0854204i
\(521\) 6.32624 + 10.9574i 0.277158 + 0.480051i 0.970677 0.240387i \(-0.0772743\pi\)
−0.693520 + 0.720438i \(0.743941\pi\)
\(522\) 4.45898 0.195164
\(523\) 19.5623 + 33.8829i 0.855400 + 1.48160i 0.876274 + 0.481814i \(0.160022\pi\)
−0.0208736 + 0.999782i \(0.506645\pi\)
\(524\) 0.302439 + 0.523840i 0.0132121 + 0.0228841i
\(525\) 0 0
\(526\) −1.71885 2.97713i −0.0749453 0.129809i
\(527\) 65.0689 2.83445
\(528\) −2.91641 5.05137i −0.126920 0.219833i
\(529\) 1.50000 2.59808i 0.0652174 0.112960i
\(530\) −0.600813 1.04064i −0.0260977 0.0452025i
\(531\) 3.19098 5.52694i 0.138477 0.239849i
\(532\) 0 0
\(533\) −5.23607 18.1383i −0.226799 0.785656i
\(534\) 1.17376 2.03302i 0.0507937 0.0879772i
\(535\) −2.14590 −0.0927753
\(536\) −1.04257 −0.0450323
\(537\) 3.43769 0.148347
\(538\) 5.24922 0.226310
\(539\) 0 0
\(540\) 0.791796 + 1.37143i 0.0340735 + 0.0590170i
\(541\) −0.864745 + 1.49778i −0.0371783 + 0.0643947i −0.884016 0.467457i \(-0.845170\pi\)
0.846838 + 0.531852i \(0.178504\pi\)
\(542\) −3.51722 + 6.09201i −0.151078 + 0.261674i
\(543\) 1.41641 0.0607839
\(544\) −15.4894 26.8284i −0.664101 1.15026i
\(545\) 4.09017 0.175204
\(546\) 0 0
\(547\) −3.00000 −0.128271 −0.0641354 0.997941i \(-0.520429\pi\)
−0.0641354 + 0.997941i \(0.520429\pi\)
\(548\) −0.354102 0.613323i −0.0151265 0.0261998i
\(549\) 17.1246 0.730861
\(550\) −4.50000 + 7.79423i −0.191881 + 0.332347i
\(551\) 9.92705 17.1942i 0.422907 0.732496i
\(552\) −1.25735 2.17780i −0.0535165 0.0926934i
\(553\) 0 0
\(554\) −1.90983 −0.0811409
\(555\) −0.583592 −0.0247721
\(556\) 28.8541 1.22369
\(557\) 18.9787 0.804154 0.402077 0.915606i \(-0.368288\pi\)
0.402077 + 0.915606i \(0.368288\pi\)
\(558\) 4.74671 8.22154i 0.200944 0.348046i
\(559\) −26.4681 6.54915i −1.11948 0.276999i
\(560\) 0 0
\(561\) −6.92705 + 11.9980i −0.292460 + 0.506556i
\(562\) 0.416408 + 0.721240i 0.0175651 + 0.0304237i
\(563\) 19.4721 33.7267i 0.820653 1.42141i −0.0845442 0.996420i \(-0.526943\pi\)
0.905197 0.424992i \(-0.139723\pi\)
\(564\) −0.791796 1.37143i −0.0333406 0.0577477i
\(565\) −2.85410 −0.120073
\(566\) 2.56231 + 4.43804i 0.107702 + 0.186545i
\(567\) 0 0
\(568\) 6.02129 + 10.4292i 0.252648 + 0.437598i
\(569\) 1.47214 + 2.54981i 0.0617151 + 0.106894i 0.895232 0.445600i \(-0.147010\pi\)
−0.833517 + 0.552494i \(0.813676\pi\)
\(570\) −0.270510 −0.0113304
\(571\) 17.8435 + 30.9058i 0.746726 + 1.29337i 0.949384 + 0.314117i \(0.101708\pi\)
−0.202659 + 0.979249i \(0.564958\pi\)
\(572\) −9.00000 31.1769i −0.376309 1.30357i
\(573\) −9.02129 −0.376870
\(574\) 0 0
\(575\) 10.8541 18.7999i 0.452647 0.784008i
\(576\) 13.4377 0.559904
\(577\) −4.91641 8.51547i −0.204673 0.354504i 0.745356 0.666667i \(-0.232280\pi\)
−0.950028 + 0.312163i \(0.898946\pi\)
\(578\) −7.41641 + 12.8456i −0.308482 + 0.534306i
\(579\) 2.29180 0.0952438
\(580\) 2.89667 0.120278
\(581\) 0 0
\(582\) 0.886031 1.53465i 0.0367272 0.0636133i
\(583\) 19.9894 + 34.6226i 0.827875 + 1.43392i
\(584\) −1.47214 2.54981i −0.0609174 0.105512i
\(585\) 1.09017 + 3.77646i 0.0450730 + 0.156137i
\(586\) 2.14590 3.71680i 0.0886462 0.153540i
\(587\) 15.5451 26.9249i 0.641614 1.11131i −0.343458 0.939168i \(-0.611598\pi\)
0.985072 0.172141i \(-0.0550683\pi\)
\(588\) 0 0
\(589\) −21.1353 36.6073i −0.870863 1.50838i
\(590\) −0.163119 + 0.282530i −0.00671550 + 0.0116316i
\(591\) 1.48936 2.57964i 0.0612640 0.106112i
\(592\) −6.29180 + 10.8977i −0.258591 + 0.447893i
\(593\) −9.60081 + 16.6291i −0.394258 + 0.682875i −0.993006 0.118062i \(-0.962332\pi\)
0.598748 + 0.800937i \(0.295665\pi\)
\(594\) 2.07295 + 3.59045i 0.0850541 + 0.147318i
\(595\) 0 0
\(596\) −4.50000 + 7.79423i −0.184327 + 0.319264i
\(597\) 0.461493 0.799329i 0.0188876 0.0327144i
\(598\) −1.70820 5.91739i −0.0698537 0.241980i
\(599\) 4.25329 + 7.36691i 0.173785 + 0.301004i 0.939740 0.341890i \(-0.111067\pi\)
−0.765955 + 0.642894i \(0.777734\pi\)
\(600\) 1.36475 + 2.36381i 0.0557155 + 0.0965021i
\(601\) 16.6976 28.9210i 0.681108 1.17971i −0.293535 0.955948i \(-0.594832\pi\)
0.974643 0.223765i \(-0.0718348\pi\)
\(602\) 0 0
\(603\) −2.02129 −0.0823131
\(604\) 27.2705 1.10962
\(605\) −2.39919 + 4.15551i −0.0975408 + 0.168946i
\(606\) 0.624612 + 1.08186i 0.0253731 + 0.0439475i
\(607\) −23.0000 −0.933541 −0.466771 0.884378i \(-0.654583\pi\)
−0.466771 + 0.884378i \(0.654583\pi\)
\(608\) −10.0623 + 17.4284i −0.408080 + 0.706816i
\(609\) 0 0
\(610\) −0.875388 −0.0354434
\(611\) −2.23607 7.74597i −0.0904616 0.313368i
\(612\) −19.7705 34.2435i −0.799175 1.38421i
\(613\) 14.4377 0.583133 0.291566 0.956551i \(-0.405824\pi\)
0.291566 + 0.956551i \(0.405824\pi\)
\(614\) −0.354102 0.613323i −0.0142904 0.0247517i
\(615\) 0.381966 + 0.661585i 0.0154024 + 0.0266777i
\(616\) 0 0
\(617\) −8.97214 15.5402i −0.361205 0.625625i 0.626955 0.779056i \(-0.284301\pi\)
−0.988159 + 0.153431i \(0.950968\pi\)
\(618\) −0.686918 −0.0276319
\(619\) 8.70820 + 15.0831i 0.350012 + 0.606239i 0.986251 0.165253i \(-0.0528441\pi\)
−0.636239 + 0.771492i \(0.719511\pi\)
\(620\) 3.08359 5.34094i 0.123840 0.214497i
\(621\) −5.00000 8.66025i −0.200643 0.347524i
\(622\) 2.35410 4.07742i 0.0943909 0.163490i
\(623\) 0 0
\(624\) −4.20569 1.04064i −0.168362 0.0416589i
\(625\) −11.4164 + 19.7738i −0.456656 + 0.790952i
\(626\) −5.77709 −0.230899
\(627\) 9.00000 0.359425
\(628\) −15.1033 −0.602688
\(629\) 29.8885 1.19173
\(630\) 0 0
\(631\) 19.6976 + 34.1172i 0.784148 + 1.35818i 0.929507 + 0.368804i \(0.120233\pi\)
−0.145360 + 0.989379i \(0.546434\pi\)
\(632\) 2.94427 5.09963i 0.117117 0.202852i
\(633\) −1.66312 + 2.88061i −0.0661030 + 0.114494i
\(634\) 8.31308 0.330155
\(635\) 2.70163 + 4.67935i 0.107211 + 0.185694i
\(636\) 5.83282 0.231286
\(637\) 0 0
\(638\) 7.58359 0.300237
\(639\) 11.6738 + 20.2195i 0.461807 + 0.799873i
\(640\) −3.85410 −0.152347
\(641\) 4.74671 8.22154i 0.187484 0.324731i −0.756927 0.653500i \(-0.773300\pi\)
0.944411 + 0.328768i \(0.106633\pi\)
\(642\) −0.409830 + 0.709846i −0.0161747 + 0.0280154i
\(643\) 3.50000 + 6.06218i 0.138027 + 0.239069i 0.926750 0.375680i \(-0.122591\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) 0 0
\(645\) 1.10333 0.0434434
\(646\) 13.8541 0.545082
\(647\) 29.2361 1.14939 0.574694 0.818368i \(-0.305121\pi\)
0.574694 + 0.818368i \(0.305121\pi\)
\(648\) −11.3475 −0.445773
\(649\) 5.42705 9.39993i 0.213030 0.368979i
\(650\) 1.85410 + 6.42280i 0.0727239 + 0.251923i
\(651\) 0 0
\(652\) 9.00000 15.5885i 0.352467 0.610491i
\(653\) 1.30902 + 2.26728i 0.0512258 + 0.0887257i 0.890501 0.454981i \(-0.150354\pi\)
−0.839275 + 0.543706i \(0.817021\pi\)
\(654\) 0.781153 1.35300i 0.0305455 0.0529064i
\(655\) −0.0623059 0.107917i −0.00243449 0.00421667i
\(656\) 16.4721 0.643129
\(657\) −2.85410 4.94345i −0.111349 0.192862i
\(658\) 0 0
\(659\) −5.94427 10.2958i −0.231556 0.401067i 0.726710 0.686944i \(-0.241048\pi\)
−0.958266 + 0.285877i \(0.907715\pi\)
\(660\) 0.656541 + 1.13716i 0.0255558 + 0.0442640i
\(661\) 18.5410 0.721162 0.360581 0.932728i \(-0.382578\pi\)
0.360581 + 0.932728i \(0.382578\pi\)
\(662\) 3.21885 + 5.57521i 0.125104 + 0.216687i
\(663\) 2.85410 + 9.88690i 0.110844 + 0.383975i
\(664\) 9.87539 0.383239
\(665\) 0 0
\(666\) 2.18034 3.77646i 0.0844865 0.146335i
\(667\) −18.2918 −0.708261
\(668\) 9.05166 + 15.6779i 0.350219 + 0.606598i
\(669\) −2.53444 + 4.38978i −0.0979872 + 0.169719i
\(670\) 0.103326 0.00399181
\(671\) 29.1246 1.12434
\(672\) 0 0
\(673\) −20.6246 + 35.7229i −0.795020 + 1.37702i 0.127806 + 0.991799i \(0.459207\pi\)
−0.922826 + 0.385216i \(0.874127\pi\)
\(674\) −1.63525 2.83234i −0.0629877 0.109098i
\(675\) 5.42705 + 9.39993i 0.208887 + 0.361803i
\(676\) −21.3222 11.2399i −0.820084 0.432304i
\(677\) −0.628677 + 1.08890i −0.0241620 + 0.0418499i −0.877854 0.478929i \(-0.841025\pi\)
0.853692 + 0.520779i \(0.174358\pi\)
\(678\) −0.545085 + 0.944115i −0.0209339 + 0.0362585i
\(679\) 0 0
\(680\) 2.10081 + 3.63871i 0.0805625 + 0.139538i
\(681\) −1.42705 + 2.47172i −0.0546847 + 0.0947167i
\(682\) 8.07295 13.9828i 0.309129 0.535427i
\(683\) 3.73607 6.47106i 0.142957 0.247608i −0.785652 0.618669i \(-0.787672\pi\)
0.928609 + 0.371060i \(0.121006\pi\)
\(684\) −12.8435 + 22.2455i −0.491082 + 0.850579i
\(685\) 0.0729490 + 0.126351i 0.00278724 + 0.00482764i
\(686\) 0 0
\(687\) 5.18034 8.97261i 0.197642 0.342326i
\(688\) 11.8951 20.6030i 0.453497 0.785480i
\(689\) 28.8262 + 7.13264i 1.09819 + 0.271732i
\(690\) 0.124612 + 0.215834i 0.00474389 + 0.00821666i
\(691\) −0.427051 0.739674i −0.0162458 0.0281385i 0.857788 0.514003i \(-0.171838\pi\)
−0.874034 + 0.485865i \(0.838505\pi\)
\(692\) −8.34346 + 14.4513i −0.317171 + 0.549356i
\(693\) 0 0
\(694\) 13.4590 0.510896
\(695\) −5.94427 −0.225479
\(696\) 1.14996 1.99179i 0.0435892 0.0754988i
\(697\) −19.5623 33.8829i −0.740975 1.28341i
\(698\) 2.78522 0.105422
\(699\) 0.0729490 0.126351i 0.00275919 0.00477905i
\(700\) 0 0
\(701\) 6.76393 0.255470 0.127735 0.991808i \(-0.459229\pi\)
0.127735 + 0.991808i \(0.459229\pi\)
\(702\) 2.98936 + 0.739674i 0.112826 + 0.0279172i
\(703\) −9.70820 16.8151i −0.366152 0.634194i
\(704\) 22.8541 0.861346
\(705\) 0.163119 + 0.282530i 0.00614342 + 0.0106407i
\(706\) −5.51064 9.54471i −0.207396 0.359220i
\(707\) 0 0
\(708\) −0.791796 1.37143i −0.0297575 0.0515415i
\(709\) 3.43769 0.129105 0.0645527 0.997914i \(-0.479438\pi\)
0.0645527 + 0.997914i \(0.479438\pi\)
\(710\) −0.596748 1.03360i −0.0223955 0.0387902i
\(711\) 5.70820 9.88690i 0.214074 0.370788i
\(712\) 11.8435 + 20.5135i 0.443852 + 0.768775i
\(713\) −19.4721 + 33.7267i −0.729237 + 1.26308i
\(714\) 0 0
\(715\) 1.85410 + 6.42280i 0.0693395 + 0.240199i
\(716\) −8.34346 + 14.4513i −0.311810 + 0.540070i
\(717\) 4.31308 0.161075
\(718\) −4.16718 −0.155518
\(719\) −32.1246 −1.19805 −0.599023 0.800732i \(-0.704444\pi\)
−0.599023 + 0.800732i \(0.704444\pi\)
\(720\) −3.42956 −0.127812
\(721\) 0 0
\(722\) −0.871323 1.50918i −0.0324273 0.0561657i
\(723\) 0.847524 1.46795i 0.0315198 0.0545938i
\(724\) −3.43769 + 5.95426i −0.127761 + 0.221288i
\(725\) 19.8541 0.737363
\(726\) 0.916408 + 1.58726i 0.0340111 + 0.0589089i
\(727\) −17.2918 −0.641317 −0.320659 0.947195i \(-0.603904\pi\)
−0.320659 + 0.947195i \(0.603904\pi\)
\(728\) 0 0
\(729\) −19.4377 −0.719915
\(730\) 0.145898 + 0.252703i 0.00539993 + 0.00935295i
\(731\) −56.5066 −2.08997
\(732\) 2.12461 3.67994i 0.0785279 0.136014i
\(733\) −0.635255 + 1.10029i −0.0234637 + 0.0406403i −0.877519 0.479542i \(-0.840803\pi\)
0.854055 + 0.520182i \(0.174136\pi\)
\(734\) −4.85410 8.40755i −0.179168 0.310328i
\(735\) 0 0
\(736\) 18.5410 0.683431
\(737\) −3.43769 −0.126629
\(738\) −5.70820 −0.210122
\(739\) −47.1246 −1.73351 −0.866753 0.498737i \(-0.833797\pi\)
−0.866753 + 0.498737i \(0.833797\pi\)
\(740\) 1.41641 2.45329i 0.0520682 0.0901847i
\(741\) 4.63525 4.81710i 0.170280 0.176961i
\(742\) 0 0
\(743\) −11.8369 + 20.5021i −0.434253 + 0.752148i −0.997234 0.0743213i \(-0.976321\pi\)
0.562981 + 0.826470i \(0.309654\pi\)
\(744\) −2.44834 4.24064i −0.0897604 0.155470i
\(745\) 0.927051 1.60570i 0.0339645 0.0588283i
\(746\) 0.0835921 + 0.144786i 0.00306053 + 0.00530099i
\(747\) 19.1459 0.700512
\(748\) −33.6246 58.2395i −1.22944 2.12945i
\(749\) 0 0
\(750\) −0.274575 0.475578i −0.0100261 0.0173657i
\(751\) −4.64590 8.04693i −0.169531 0.293637i 0.768724 0.639581i \(-0.220892\pi\)
−0.938255 + 0.345944i \(0.887559\pi\)
\(752\) 7.03444 0.256520
\(753\) 1.00000 + 1.73205i 0.0364420 + 0.0631194i
\(754\) 3.90576 4.05899i 0.142240 0.147820i
\(755\) −5.61803 −0.204461
\(756\) 0 0
\(757\) −14.0000 + 24.2487i −0.508839 + 0.881334i 0.491109 + 0.871098i \(0.336592\pi\)
−0.999948 + 0.0102362i \(0.996742\pi\)
\(758\) −4.90983 −0.178333
\(759\) −4.14590 7.18091i −0.150487 0.260650i
\(760\) 1.36475 2.36381i 0.0495045 0.0857443i
\(761\) −22.1459 −0.802788 −0.401394 0.915905i \(-0.631474\pi\)
−0.401394 + 0.915905i \(0.631474\pi\)
\(762\) 2.06386 0.0747657
\(763\) 0 0
\(764\) 21.8951 37.9235i 0.792138 1.37202i
\(765\) 4.07295 + 7.05455i 0.147258 + 0.255058i
\(766\) −4.77051 8.26277i −0.172366 0.298546i
\(767\) −2.23607 7.74597i −0.0807397 0.279691i
\(768\) 1.06231 1.83997i 0.0383327 0.0663941i
\(769\) −4.20820 + 7.28882i −0.151752 + 0.262842i −0.931872 0.362788i \(-0.881825\pi\)
0.780120 + 0.625630i \(0.215158\pi\)
\(770\) 0 0
\(771\) −4.91641 8.51547i −0.177060 0.306677i
\(772\) −5.56231 + 9.63420i −0.200192 + 0.346742i
\(773\) 9.68034 16.7668i 0.348178 0.603061i −0.637748 0.770245i \(-0.720134\pi\)
0.985926 + 0.167184i \(0.0534673\pi\)
\(774\) −4.12210 + 7.13969i −0.148166 + 0.256631i
\(775\) 21.1353 36.6073i 0.759201 1.31497i
\(776\) 8.94021 + 15.4849i 0.320935 + 0.555875i
\(777\) 0 0
\(778\) −4.56231 + 7.90215i −0.163567 + 0.283306i
\(779\) −12.7082 + 22.0113i −0.455319 + 0.788635i
\(780\) 0.946784 + 0.234268i 0.0339003 + 0.00838815i