Properties

Label 637.2.g.b.263.2
Level $637$
Weight $2$
Character 637.263
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 263.2
Root \(-0.309017 + 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 637.263
Dual form 637.2.g.b.373.2

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

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

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 −0.925615 0.378467i \(-0.876451\pi\)
0.790569 + 0.612372i \(0.209785\pi\)
\(3\) −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 0.820156 0.572140i \(-0.193887\pi\)
−0.905566 + 0.424206i \(0.860553\pi\)
\(6\) 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 −0.819394 0.573231i \(-0.805690\pi\)
−0.0867359 0.996231i \(-0.527644\pi\)
\(18\) 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 −0.999257 0.0385394i \(-0.987729\pi\)
0.533005 + 0.846112i \(0.321063\pi\)
\(24\) 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 0.991028 0.133658i \(-0.0426723\pi\)
−0.611265 + 0.791426i \(0.709339\pi\)
\(30\) −0.0557281 −0.0101745
\(31\) −4.35410 + 7.54153i −0.782020 + 1.35450i 0.148744 + 0.988876i \(0.452477\pi\)
−0.930763 + 0.365622i \(0.880856\pi\)
\(32\) −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 −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) −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 0.585895 0.810387i \(-0.300743\pi\)
−0.994763 + 0.102206i \(0.967410\pi\)
\(42\) 0 0
\(43\) 3.78115 6.54915i 0.576620 0.998736i −0.419243 0.907874i \(-0.637704\pi\)
0.995864 0.0908618i \(-0.0289622\pi\)
\(44\) −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 0.772890 0.634539i \(-0.218810\pi\)
−0.935973 + 0.352073i \(0.885477\pi\)
\(48\) 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 0.431333 + 0.902193i \(0.358043\pi\)
−0.996988 + 0.0775512i \(0.975290\pi\)
\(54\) −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 0.784024 0.620730i \(-0.213164\pi\)
−0.929580 + 0.368620i \(0.879830\pi\)
\(60\) −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 −0.999860 0.0167615i \(-0.994664\pi\)
0.514446 + 0.857523i \(0.327998\pi\)
\(72\) 4.20163 0.495166
\(73\) 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i \(-0.795992\pi\)
0.918594 + 0.395203i \(0.129326\pi\)
\(74\) −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 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 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 0.0259145 + 0.999664i \(0.491750\pi\)
−0.878692 + 0.477389i \(0.841583\pi\)
\(90\) −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 0.373484 + 0.927636i \(0.378163\pi\)
−0.990099 + 0.140371i \(0.955170\pi\)
\(98\) 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 0.726427 0.687243i \(-0.241179\pi\)
−0.958384 + 0.285483i \(0.907846\pi\)
\(104\) 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 −0.697703 0.716387i \(-0.745794\pi\)
0.969261 + 0.246035i \(0.0791278\pi\)
\(108\) 2.07295 + 3.59045i 0.199470 + 0.345492i
\(109\) −5.35410 + 9.27358i −0.512830 + 0.888248i 0.487059 + 0.873369i \(0.338070\pi\)
−0.999889 + 0.0148787i \(0.995264\pi\)
\(110\) −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 −0.635046 0.772475i \(-0.719019\pi\)
0.986505 + 0.163728i \(0.0523521\pi\)
\(114\) 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 0.988027 + 0.154278i \(0.0493053\pi\)
−0.360405 + 0.932796i \(0.617361\pi\)
\(128\) 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 0.858812 0.512292i \(-0.171203\pi\)
−0.873063 + 0.487607i \(0.837870\pi\)
\(132\) 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 0.874069 0.485803i \(-0.161473\pi\)
−0.857752 + 0.514064i \(0.828139\pi\)
\(138\) 0.326238 + 0.565061i 0.0277712 + 0.0481012i
\(139\) 7.78115 13.4774i 0.659989 1.14313i −0.320629 0.947205i \(-0.603894\pi\)
0.980618 0.195929i \(-0.0627723\pi\)
\(140\) 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 −0.394579 0.918862i \(-0.629110\pi\)
0.993047 0.117716i \(-0.0375571\pi\)
\(152\) −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 −0.981524 0.191340i \(-0.938717\pi\)
0.656467 + 0.754355i \(0.272050\pi\)
\(158\) 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 0.612961 0.790113i \(-0.289978\pi\)
−0.990739 + 0.135783i \(0.956645\pi\)
\(168\) 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 0.693034 0.720905i \(-0.256274\pi\)
−0.970839 + 0.239732i \(0.922940\pi\)
\(198\) −2.64590 + 4.58283i −0.188036 + 0.325688i
\(199\) −1.20820 2.09267i −0.0856473 0.148345i 0.820020 0.572336i \(-0.193962\pi\)
−0.905667 + 0.423990i \(0.860629\pi\)
\(200\) −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 0.976078 0.217419i \(-0.0697638\pi\)
−0.676330 + 0.736599i \(0.736430\pi\)
\(212\) −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 0.998005 0.0631310i \(-0.0201086\pi\)
−0.553676 + 0.832732i \(0.686775\pi\)
\(224\) 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 0.962963 0.269634i \(-0.0869027\pi\)
−0.714991 + 0.699133i \(0.753569\pi\)
\(228\) −1.71885 2.97713i −0.113833 0.197165i
\(229\) −13.5623 23.4906i −0.896222 1.55230i −0.832284 0.554349i \(-0.812967\pi\)
−0.0639380 0.997954i \(-0.520366\pi\)
\(230\) −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 0.859702 0.510796i \(-0.170649\pi\)
−0.872213 + 0.489125i \(0.837316\pi\)
\(234\) −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 0.785670 0.618646i \(-0.212319\pi\)
−0.928598 + 0.371087i \(0.878985\pi\)
\(242\) −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 −0.936744 0.350016i \(-0.886176\pi\)
0.771495 + 0.636236i \(0.219509\pi\)
\(252\) 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 −0.114815 0.993387i \(-0.536627\pi\)
0.917706 0.397261i \(-0.130039\pi\)
\(258\) −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 0.576882 0.816827i \(-0.304269\pi\)
−0.995834 + 0.0911812i \(0.970936\pi\)
\(270\) 0.326238 0.0198542
\(271\) −9.20820 + 15.9491i −0.559359 + 0.968837i 0.438192 + 0.898882i \(0.355619\pi\)
−0.997550 + 0.0699558i \(0.977714\pi\)
\(272\) 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 0.931305 0.364241i \(-0.118672\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) 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 −0.653947 0.756540i \(-0.726888\pi\)
0.982157 + 0.188065i \(0.0602216\pi\)
\(294\) 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 −0.636678 0.771129i \(-0.719692\pi\)
0.986157 + 0.165815i \(0.0530255\pi\)
\(312\) −1.40576 1.46091i −0.0795858 0.0827079i
\(313\) 7.56231 + 13.0983i 0.427447 + 0.740360i 0.996645 0.0818405i \(-0.0260798\pi\)
−0.569199 + 0.822200i \(0.692746\pi\)
\(314\) −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 −0.991040 0.133567i \(-0.957357\pi\)
0.379848 0.925049i \(-0.375976\pi\)
\(318\) 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 −0.754171 0.656679i \(-0.771961\pi\)
−0.191615 0.981470i \(-0.561373\pi\)
\(348\) 1.44834 2.50859i 0.0776390 0.134475i
\(349\) −3.64590 6.31488i −0.195160 0.338028i 0.751793 0.659400i \(-0.229189\pi\)
−0.946953 + 0.321372i \(0.895856\pi\)
\(350\) 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 0.973308 0.229502i \(-0.0737098\pi\)
−0.685409 + 0.728159i \(0.740376\pi\)
\(360\) −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 0.982538 0.186061i \(-0.0595722\pi\)
−0.652403 + 0.757872i \(0.726239\pi\)
\(380\) 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 0.386358 + 0.922349i \(0.373733\pi\)
−0.991957 + 0.126579i \(0.959600\pi\)
\(390\) 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 −0.489291 0.872121i \(-0.662744\pi\)
0.999924 0.0123222i \(-0.00392237\pi\)
\(402\) 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 −0.877110 0.480290i \(-0.840532\pi\)
0.0226119 0.999744i \(-0.492802\pi\)
\(410\) −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 0.784249 0.620447i \(-0.213049\pi\)
−0.929447 + 0.368956i \(0.879715\pi\)
\(420\) 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 −0.877790 0.479046i \(-0.840983\pi\)
0.853761 + 0.520665i \(0.174316\pi\)
\(434\) 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 −0.946701 0.322114i \(-0.895606\pi\)
0.752310 + 0.658810i \(0.228940\pi\)
\(440\) −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 0.874957 0.484201i \(-0.160890\pi\)
−0.856809 + 0.515634i \(0.827556\pi\)
\(444\) 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 0.305540 + 0.952179i \(0.401163\pi\)
−0.977381 + 0.211484i \(0.932170\pi\)
\(450\) −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 −0.701072 0.713091i \(-0.747295\pi\)
0.968090 + 0.250601i \(0.0806282\pi\)
\(458\) 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 −0.103702 + 0.994608i \(0.533069\pi\)
−0.809505 + 0.587113i \(0.800264\pi\)
\(462\) 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 −0.932734 0.360565i \(-0.882584\pi\)
0.154109 0.988054i \(-0.450749\pi\)
\(468\) −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 0.991726 0.128372i \(-0.0409752\pi\)
−0.607037 + 0.794674i \(0.707642\pi\)
\(488\) 8.83282 0.399843
\(489\) −3.70820 −0.167691
\(490\) 0 0
\(491\) −7.30902 12.6596i −0.329851 0.571319i 0.652631 0.757676i \(-0.273665\pi\)
−0.982482 + 0.186357i \(0.940332\pi\)
\(492\) −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 0.760343 0.649521i \(-0.225031\pi\)
−0.942674 + 0.333716i \(0.891697\pi\)
\(500\) −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 0.455126 + 0.890427i \(0.349594\pi\)
−0.998695 + 0.0510624i \(0.983739\pi\)
\(504\) 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 0.297467 + 0.954732i \(0.403858\pi\)
−0.975556 + 0.219752i \(0.929475\pi\)
\(510\) 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 −0.693520 0.720438i \(-0.743941\pi\)
0.970677 + 0.240387i \(0.0772743\pi\)
\(522\) 4.45898 0.195164
\(523\) 19.5623 33.8829i 0.855400 1.48160i −0.0208736 0.999782i \(-0.506645\pi\)
0.876274 0.481814i \(-0.160022\pi\)
\(524\) 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 0.846838 0.531852i \(-0.178504\pi\)
−0.884016 + 0.467457i \(0.845170\pi\)
\(542\) −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 0.905197 + 0.424992i \(0.139723\pi\)
−0.0845442 + 0.996420i \(0.526943\pi\)
\(564\) −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 −0.833517 0.552494i \(-0.813676\pi\)
0.895232 + 0.445600i \(0.147010\pi\)
\(570\) −0.270510 −0.0113304
\(571\) 17.8435 30.9058i 0.746726 1.29337i −0.202659 0.979249i \(-0.564958\pi\)
0.949384 0.314117i \(-0.101708\pi\)
\(572\) −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 −0.950028 0.312163i \(-0.898946\pi\)
0.745356 + 0.666667i \(0.232280\pi\)
\(578\) −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 0.985072 + 0.172141i \(0.0550683\pi\)
−0.343458 + 0.939168i \(0.611598\pi\)
\(588\) 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 0.598748 0.800937i \(-0.295665\pi\)
−0.993006 + 0.118062i \(0.962332\pi\)
\(594\) 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 −0.765955 0.642894i \(-0.777734\pi\)
0.939740 + 0.341890i \(0.111067\pi\)
\(600\) 1.36475 2.36381i 0.0557155 0.0965021i
\(601\) 16.6976 + 28.9210i 0.681108 + 1.17971i 0.974643 + 0.223765i \(0.0718348\pi\)
−0.293535 + 0.955948i \(0.594832\pi\)
\(602\) 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 −0.988159 0.153431i \(-0.950968\pi\)
0.626955 + 0.779056i \(0.284301\pi\)
\(618\) −0.686918 −0.0276319
\(619\) 8.70820 15.0831i 0.350012 0.606239i −0.636239 0.771492i \(-0.719511\pi\)
0.986251 + 0.165253i \(0.0528441\pi\)
\(620\) 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 −0.145360 0.989379i \(-0.546434\pi\)
0.929507 0.368804i \(-0.120233\pi\)
\(632\) 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 0.944411 0.328768i \(-0.106633\pi\)
−0.756927 + 0.653500i \(0.773300\pi\)
\(642\) −0.409830 0.709846i −0.0161747 0.0280154i
\(643\) 3.50000 6.06218i 0.138027 0.239069i −0.788723 0.614749i \(-0.789257\pi\)
0.926750 + 0.375680i \(0.122591\pi\)
\(644\) 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 −0.839275 0.543706i \(-0.817021\pi\)
0.890501 + 0.454981i \(0.150354\pi\)
\(654\) 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 −0.958266 0.285877i \(-0.907715\pi\)
0.726710 + 0.686944i \(0.241048\pi\)
\(660\) 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 −0.922826 0.385216i \(-0.874127\pi\)
0.127806 0.991799i \(-0.459207\pi\)
\(674\) −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 0.853692 0.520779i \(-0.174358\pi\)
−0.877854 + 0.478929i \(0.841025\pi\)
\(678\) −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 0.928609 0.371060i \(-0.121006\pi\)
−0.785652 + 0.618669i \(0.787672\pi\)
\(684\) −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 −0.874034 0.485865i \(-0.838505\pi\)
0.857788 + 0.514003i \(0.171838\pi\)
\(692\) −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 0.854055 0.520182i \(-0.174136\pi\)
−0.877519 + 0.479542i \(0.840803\pi\)
\(734\) −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 0.562981 0.826470i \(-0.309654\pi\)
−0.997234 + 0.0743213i \(0.976321\pi\)
\(744\) −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 −0.938255 0.345944i \(-0.887559\pi\)
0.768724 + 0.639581i \(0.220892\pi\)
\(752\) 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 −0.999948 0.0102362i \(-0.996742\pi\)
0.491109 0.871098i \(-0.336592\pi\)
\(758\) −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 0.780120 0.625630i \(-0.215158\pi\)
−0.931872 + 0.362788i \(0.881825\pi\)
\(770\) 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 0.985926 0.167184i \(-0.0534673\pi\)
−0.637748 + 0.770245i \(0.720134\pi\)
\(774\) −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