Properties

Label 349.2.e.a.123.5
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.5
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.85370 + 1.07024i) q^{2} +(1.18706 - 2.05605i) q^{3} +(1.29081 - 2.23575i) q^{4} +(1.34675 - 2.33263i) q^{5} +5.08174i q^{6} +(2.87980 - 1.66266i) q^{7} +1.24494i q^{8} +(-1.31823 - 2.28323i) q^{9} +O(q^{10})\) \(q+(-1.85370 + 1.07024i) q^{2} +(1.18706 - 2.05605i) q^{3} +(1.29081 - 2.23575i) q^{4} +(1.34675 - 2.33263i) q^{5} +5.08174i q^{6} +(2.87980 - 1.66266i) q^{7} +1.24494i q^{8} +(-1.31823 - 2.28323i) q^{9} +5.76535i q^{10} +0.545693i q^{11} +(-3.06454 - 5.30794i) q^{12} +(0.131290 - 0.0758002i) q^{13} +(-3.55887 + 6.16414i) q^{14} +(-3.19734 - 5.53795i) q^{15} +(1.24924 + 2.16374i) q^{16} -2.30327 q^{17} +(4.88720 + 2.82163i) q^{18} +(-2.50657 + 4.34151i) q^{19} +(-3.47679 - 6.02197i) q^{20} -7.89469i q^{21} +(-0.584020 - 1.01155i) q^{22} +(-2.56604 - 4.44452i) q^{23} +(2.55966 + 1.47782i) q^{24} +(-1.12745 - 1.95280i) q^{25} +(-0.162248 + 0.281022i) q^{26} +0.863107 q^{27} -8.58470i q^{28} +(-2.81549 + 4.87657i) q^{29} +(11.8538 + 6.84382i) q^{30} +2.33848 q^{31} +(-6.78774 - 3.91890i) q^{32} +(1.12197 + 0.647770i) q^{33} +(4.26959 - 2.46505i) q^{34} -8.95671i q^{35} -6.80632 q^{36} -3.26599 q^{37} -10.7305i q^{38} -0.359918i q^{39} +(2.90400 + 1.67662i) q^{40} +10.0059 q^{41} +(8.44919 + 14.6344i) q^{42} +(6.94329 + 4.00871i) q^{43} +(1.22003 + 0.704386i) q^{44} -7.10126 q^{45} +(9.51336 + 5.49254i) q^{46} +3.68216i q^{47} +5.93169 q^{48} +(2.02885 - 3.51407i) q^{49} +(4.17992 + 2.41328i) q^{50} +(-2.73413 + 4.73565i) q^{51} -0.391375i q^{52} -7.63103i q^{53} +(-1.59994 + 0.923728i) q^{54} +(1.27290 + 0.734910i) q^{55} +(2.06991 + 3.58519i) q^{56} +(5.95091 + 10.3073i) q^{57} -12.0529i q^{58} +(-2.78764 - 1.60944i) q^{59} -16.5086 q^{60} -8.03093i q^{61} +(-4.33486 + 2.50273i) q^{62} +(-7.59247 - 4.38351i) q^{63} +11.7796 q^{64} -0.408335i q^{65} -2.77307 q^{66} +8.84653 q^{67} +(-2.97309 + 5.14954i) q^{68} -12.1842 q^{69} +(9.58579 + 16.6031i) q^{70} +(-13.5642 + 7.83131i) q^{71} +(2.84250 - 1.64112i) q^{72} +(-7.17140 + 12.4212i) q^{73} +(6.05418 - 3.49538i) q^{74} -5.35342 q^{75} +(6.47102 + 11.2081i) q^{76} +(0.907299 + 1.57149i) q^{77} +(0.385197 + 0.667181i) q^{78} -0.708893i q^{79} +6.72963 q^{80} +(4.97924 - 8.62429i) q^{81} +(-18.5480 + 10.7087i) q^{82} +(-3.54508 - 6.14026i) q^{83} +(-17.6506 - 10.1906i) q^{84} +(-3.10193 + 5.37269i) q^{85} -17.1611 q^{86} +(6.68431 + 11.5776i) q^{87} -0.679356 q^{88} +(-12.3681 - 7.14073i) q^{89} +(13.1636 - 7.60003i) q^{90} +(0.252059 - 0.436580i) q^{91} -13.2491 q^{92} +(2.77592 - 4.80804i) q^{93} +(-3.94078 - 6.82563i) q^{94} +(6.75143 + 11.6938i) q^{95} +(-16.1149 + 9.30395i) q^{96} +(2.04436 - 1.18031i) q^{97} +8.68540i q^{98} +(1.24594 - 0.719346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.85370 + 1.07024i −1.31077 + 0.756771i −0.982223 0.187718i \(-0.939891\pi\)
−0.328543 + 0.944489i \(0.606558\pi\)
\(3\) 1.18706 2.05605i 0.685350 1.18706i −0.287977 0.957637i \(-0.592983\pi\)
0.973327 0.229423i \(-0.0736840\pi\)
\(4\) 1.29081 2.23575i 0.645405 1.11787i
\(5\) 1.34675 2.33263i 0.602283 1.04319i −0.390191 0.920734i \(-0.627591\pi\)
0.992475 0.122451i \(-0.0390756\pi\)
\(6\) 5.08174i 2.07461i
\(7\) 2.87980 1.66266i 1.08846 0.628425i 0.155297 0.987868i \(-0.450367\pi\)
0.933167 + 0.359443i \(0.117033\pi\)
\(8\) 1.24494i 0.440154i
\(9\) −1.31823 2.28323i −0.439409 0.761078i
\(10\) 5.76535i 1.82316i
\(11\) 0.545693i 0.164533i 0.996610 + 0.0822663i \(0.0262158\pi\)
−0.996610 + 0.0822663i \(0.973784\pi\)
\(12\) −3.06454 5.30794i −0.884657 1.53227i
\(13\) 0.131290 0.0758002i 0.0364133 0.0210232i −0.481683 0.876346i \(-0.659974\pi\)
0.518096 + 0.855322i \(0.326641\pi\)
\(14\) −3.55887 + 6.16414i −0.951148 + 1.64744i
\(15\) −3.19734 5.53795i −0.825549 1.42989i
\(16\) 1.24924 + 2.16374i 0.312309 + 0.540936i
\(17\) −2.30327 −0.558626 −0.279313 0.960200i \(-0.590107\pi\)
−0.279313 + 0.960200i \(0.590107\pi\)
\(18\) 4.88720 + 2.82163i 1.15192 + 0.665064i
\(19\) −2.50657 + 4.34151i −0.575047 + 0.996011i 0.420989 + 0.907066i \(0.361683\pi\)
−0.996037 + 0.0889452i \(0.971650\pi\)
\(20\) −3.47679 6.02197i −0.777434 1.34655i
\(21\) 7.89469i 1.72276i
\(22\) −0.584020 1.01155i −0.124513 0.215664i
\(23\) −2.56604 4.44452i −0.535057 0.926746i −0.999161 0.0409649i \(-0.986957\pi\)
0.464104 0.885781i \(-0.346377\pi\)
\(24\) 2.55966 + 1.47782i 0.522489 + 0.301659i
\(25\) −1.12745 1.95280i −0.225490 0.390561i
\(26\) −0.162248 + 0.281022i −0.0318195 + 0.0551130i
\(27\) 0.863107 0.166105
\(28\) 8.58470i 1.62235i
\(29\) −2.81549 + 4.87657i −0.522823 + 0.905556i 0.476824 + 0.878999i \(0.341788\pi\)
−0.999647 + 0.0265573i \(0.991546\pi\)
\(30\) 11.8538 + 6.84382i 2.16420 + 1.24950i
\(31\) 2.33848 0.420004 0.210002 0.977701i \(-0.432653\pi\)
0.210002 + 0.977701i \(0.432653\pi\)
\(32\) −6.78774 3.91890i −1.19991 0.692771i
\(33\) 1.12197 + 0.647770i 0.195310 + 0.112762i
\(34\) 4.26959 2.46505i 0.732228 0.422752i
\(35\) 8.95671i 1.51396i
\(36\) −6.80632 −1.13439
\(37\) −3.26599 −0.536925 −0.268463 0.963290i \(-0.586516\pi\)
−0.268463 + 0.963290i \(0.586516\pi\)
\(38\) 10.7305i 1.74072i
\(39\) 0.359918i 0.0576330i
\(40\) 2.90400 + 1.67662i 0.459162 + 0.265097i
\(41\) 10.0059 1.56266 0.781330 0.624118i \(-0.214541\pi\)
0.781330 + 0.624118i \(0.214541\pi\)
\(42\) 8.44919 + 14.6344i 1.30374 + 2.25814i
\(43\) 6.94329 + 4.00871i 1.05884 + 0.611322i 0.925112 0.379695i \(-0.123971\pi\)
0.133730 + 0.991018i \(0.457305\pi\)
\(44\) 1.22003 + 0.704386i 0.183927 + 0.106190i
\(45\) −7.10126 −1.05859
\(46\) 9.51336 + 5.49254i 1.40267 + 0.809831i
\(47\) 3.68216i 0.537098i 0.963266 + 0.268549i \(0.0865442\pi\)
−0.963266 + 0.268549i \(0.913456\pi\)
\(48\) 5.93169 0.856165
\(49\) 2.02885 3.51407i 0.289836 0.502010i
\(50\) 4.17992 + 2.41328i 0.591130 + 0.341289i
\(51\) −2.73413 + 4.73565i −0.382854 + 0.663123i
\(52\) 0.391375i 0.0542739i
\(53\) 7.63103i 1.04820i −0.851656 0.524101i \(-0.824401\pi\)
0.851656 0.524101i \(-0.175599\pi\)
\(54\) −1.59994 + 0.923728i −0.217725 + 0.125703i
\(55\) 1.27290 + 0.734910i 0.171638 + 0.0990952i
\(56\) 2.06991 + 3.58519i 0.276604 + 0.479092i
\(57\) 5.95091 + 10.3073i 0.788217 + 1.36523i
\(58\) 12.0529i 1.58263i
\(59\) −2.78764 1.60944i −0.362919 0.209532i 0.307441 0.951567i \(-0.400527\pi\)
−0.670361 + 0.742035i \(0.733861\pi\)
\(60\) −16.5086 −2.13126
\(61\) 8.03093i 1.02826i −0.857714 0.514128i \(-0.828116\pi\)
0.857714 0.514128i \(-0.171884\pi\)
\(62\) −4.33486 + 2.50273i −0.550527 + 0.317847i
\(63\) −7.59247 4.38351i −0.956561 0.552271i
\(64\) 11.7796 1.47246
\(65\) 0.408335i 0.0506477i
\(66\) −2.77307 −0.341341
\(67\) 8.84653 1.08078 0.540388 0.841416i \(-0.318278\pi\)
0.540388 + 0.841416i \(0.318278\pi\)
\(68\) −2.97309 + 5.14954i −0.360540 + 0.624474i
\(69\) −12.1842 −1.46680
\(70\) 9.58579 + 16.6031i 1.14572 + 1.98445i
\(71\) −13.5642 + 7.83131i −1.60978 + 0.929405i −0.620358 + 0.784319i \(0.713013\pi\)
−0.989419 + 0.145087i \(0.953654\pi\)
\(72\) 2.84250 1.64112i 0.334991 0.193407i
\(73\) −7.17140 + 12.4212i −0.839349 + 1.45379i 0.0510915 + 0.998694i \(0.483730\pi\)
−0.890440 + 0.455100i \(0.849603\pi\)
\(74\) 6.05418 3.49538i 0.703784 0.406330i
\(75\) −5.35342 −0.618159
\(76\) 6.47102 + 11.2081i 0.742277 + 1.28566i
\(77\) 0.907299 + 1.57149i 0.103396 + 0.179088i
\(78\) 0.385197 + 0.667181i 0.0436150 + 0.0755434i
\(79\) 0.708893i 0.0797567i −0.999205 0.0398783i \(-0.987303\pi\)
0.999205 0.0398783i \(-0.0126970\pi\)
\(80\) 6.72963 0.752395
\(81\) 4.97924 8.62429i 0.553249 0.958255i
\(82\) −18.5480 + 10.7087i −2.04828 + 1.18258i
\(83\) −3.54508 6.14026i −0.389123 0.673981i 0.603209 0.797584i \(-0.293889\pi\)
−0.992332 + 0.123602i \(0.960555\pi\)
\(84\) −17.6506 10.1906i −1.92583 1.11188i
\(85\) −3.10193 + 5.37269i −0.336451 + 0.582750i
\(86\) −17.1611 −1.85052
\(87\) 6.68431 + 11.5776i 0.716633 + 1.24125i
\(88\) −0.679356 −0.0724196
\(89\) −12.3681 7.14073i −1.31102 0.756915i −0.328752 0.944416i \(-0.606628\pi\)
−0.982264 + 0.187501i \(0.939961\pi\)
\(90\) 13.1636 7.60003i 1.38757 0.801113i
\(91\) 0.252059 0.436580i 0.0264230 0.0457660i
\(92\) −13.2491 −1.38131
\(93\) 2.77592 4.80804i 0.287850 0.498570i
\(94\) −3.94078 6.82563i −0.406461 0.704010i
\(95\) 6.75143 + 11.6938i 0.692683 + 1.19976i
\(96\) −16.1149 + 9.30395i −1.64472 + 0.949580i
\(97\) 2.04436 1.18031i 0.207573 0.119843i −0.392610 0.919705i \(-0.628428\pi\)
0.600183 + 0.799863i \(0.295094\pi\)
\(98\) 8.68540i 0.877358i
\(99\) 1.24594 0.719346i 0.125222 0.0722970i
\(100\) −5.82131 −0.582131
\(101\) 19.9091i 1.98103i 0.137402 + 0.990515i \(0.456125\pi\)
−0.137402 + 0.990515i \(0.543875\pi\)
\(102\) 11.7046i 1.15893i
\(103\) 1.32750i 0.130802i −0.997859 0.0654012i \(-0.979167\pi\)
0.997859 0.0654012i \(-0.0208327\pi\)
\(104\) 0.0943670 + 0.163448i 0.00925344 + 0.0160274i
\(105\) −18.4154 10.6322i −1.79716 1.03759i
\(106\) 8.16700 + 14.1457i 0.793249 + 1.37395i
\(107\) −3.90280 + 2.25329i −0.377298 + 0.217833i −0.676642 0.736312i \(-0.736566\pi\)
0.299344 + 0.954145i \(0.403232\pi\)
\(108\) 1.11411 1.92969i 0.107205 0.185685i
\(109\) 4.43872 7.68809i 0.425152 0.736386i −0.571282 0.820754i \(-0.693554\pi\)
0.996435 + 0.0843680i \(0.0268871\pi\)
\(110\) −3.14611 −0.299970
\(111\) −3.87693 + 6.71504i −0.367982 + 0.637363i
\(112\) 7.19512 + 4.15411i 0.679875 + 0.392526i
\(113\) 10.9736 6.33560i 1.03231 0.596003i 0.114662 0.993405i \(-0.463421\pi\)
0.917645 + 0.397402i \(0.130088\pi\)
\(114\) −22.0624 12.7377i −2.06634 1.19300i
\(115\) −13.8232 −1.28902
\(116\) 7.26852 + 12.5894i 0.674865 + 1.16890i
\(117\) −0.346139 0.199844i −0.0320006 0.0184756i
\(118\) 6.88993 0.634270
\(119\) −6.63298 + 3.82955i −0.608044 + 0.351055i
\(120\) 6.89444 3.98050i 0.629373 0.363369i
\(121\) 10.7022 0.972929
\(122\) 8.59500 + 14.8870i 0.778154 + 1.34780i
\(123\) 11.8776 20.5726i 1.07097 1.85497i
\(124\) 3.01854 5.22826i 0.271073 0.469512i
\(125\) 7.39390 0.661330
\(126\) 18.7656 1.67177
\(127\) 15.6113i 1.38528i 0.721284 + 0.692640i \(0.243552\pi\)
−0.721284 + 0.692640i \(0.756448\pi\)
\(128\) −8.26050 + 4.76920i −0.730132 + 0.421542i
\(129\) 16.4842 9.51716i 1.45135 0.837939i
\(130\) 0.437015 + 0.756931i 0.0383287 + 0.0663873i
\(131\) 16.0664i 1.40373i 0.712310 + 0.701865i \(0.247649\pi\)
−0.712310 + 0.701865i \(0.752351\pi\)
\(132\) 2.89650 1.67230i 0.252108 0.145555i
\(133\) 16.6703i 1.44550i
\(134\) −16.3988 + 9.46787i −1.41664 + 0.817900i
\(135\) 1.16239 2.01331i 0.100042 0.173278i
\(136\) 2.86744i 0.245881i
\(137\) 3.90723 + 2.25584i 0.333818 + 0.192730i 0.657535 0.753424i \(-0.271599\pi\)
−0.323717 + 0.946154i \(0.604933\pi\)
\(138\) 22.5859 13.0400i 1.92264 1.11004i
\(139\) −3.43043 −0.290966 −0.145483 0.989361i \(-0.546474\pi\)
−0.145483 + 0.989361i \(0.546474\pi\)
\(140\) −20.0249 11.5614i −1.69242 0.977117i
\(141\) 7.57071 + 4.37095i 0.637568 + 0.368100i
\(142\) 16.7627 29.0338i 1.40669 2.43647i
\(143\) 0.0413636 + 0.0716439i 0.00345900 + 0.00599117i
\(144\) 3.29356 5.70461i 0.274463 0.475384i
\(145\) 7.58350 + 13.1350i 0.629775 + 1.09080i
\(146\) 30.7004i 2.54078i
\(147\) −4.81674 8.34284i −0.397278 0.688106i
\(148\) −4.21577 + 7.30193i −0.346534 + 0.600215i
\(149\) 14.6945 8.48388i 1.20382 0.695026i 0.242418 0.970172i \(-0.422059\pi\)
0.961403 + 0.275145i \(0.0887260\pi\)
\(150\) 9.92364 5.72942i 0.810262 0.467805i
\(151\) 6.54280 11.3325i 0.532445 0.922222i −0.466837 0.884343i \(-0.654607\pi\)
0.999282 0.0378788i \(-0.0120601\pi\)
\(152\) −5.40493 3.12054i −0.438398 0.253109i
\(153\) 3.03624 + 5.25891i 0.245465 + 0.425158i
\(154\) −3.36373 1.94205i −0.271057 0.156495i
\(155\) 3.14935 5.45483i 0.252961 0.438142i
\(156\) −0.804686 0.464586i −0.0644265 0.0371966i
\(157\) 11.9336 20.6695i 0.952402 1.64961i 0.212197 0.977227i \(-0.431938\pi\)
0.740205 0.672382i \(-0.234729\pi\)
\(158\) 0.758683 + 1.31408i 0.0603576 + 0.104542i
\(159\) −15.6898 9.05849i −1.24428 0.718385i
\(160\) −18.2827 + 10.5555i −1.44538 + 0.834488i
\(161\) −14.7794 8.53289i −1.16478 0.672486i
\(162\) 21.3158i 1.67473i
\(163\) 11.8530i 0.928402i 0.885730 + 0.464201i \(0.153658\pi\)
−0.885730 + 0.464201i \(0.846342\pi\)
\(164\) 12.9157 22.3707i 1.00855 1.74686i
\(165\) 3.02202 1.74476i 0.235264 0.135830i
\(166\) 13.1431 + 7.58815i 1.02010 + 0.588955i
\(167\) 4.69956i 0.363663i −0.983330 0.181832i \(-0.941797\pi\)
0.983330 0.181832i \(-0.0582026\pi\)
\(168\) 9.82844 0.758281
\(169\) −6.48851 + 11.2384i −0.499116 + 0.864494i
\(170\) 13.2792i 1.01847i
\(171\) 13.2169 1.01072
\(172\) 17.9249 10.3490i 1.36676 0.789101i
\(173\) 3.72588 2.15114i 0.283273 0.163548i −0.351631 0.936139i \(-0.614373\pi\)
0.634904 + 0.772591i \(0.281040\pi\)
\(174\) −24.7815 14.3076i −1.87868 1.08465i
\(175\) −6.49368 3.74913i −0.490876 0.283408i
\(176\) −1.18074 + 0.681700i −0.0890016 + 0.0513851i
\(177\) −6.61819 + 3.82101i −0.497453 + 0.287205i
\(178\) 30.5690 2.29125
\(179\) 0.731822i 0.0546990i 0.999626 + 0.0273495i \(0.00870669\pi\)
−0.999626 + 0.0273495i \(0.991293\pi\)
\(180\) −9.16639 + 15.8766i −0.683222 + 1.18338i
\(181\) −21.5060 −1.59853 −0.799266 0.600978i \(-0.794778\pi\)
−0.799266 + 0.600978i \(0.794778\pi\)
\(182\) 1.07905i 0.0799847i
\(183\) −16.5120 9.53321i −1.22060 0.704715i
\(184\) 5.53317 3.19458i 0.407911 0.235507i
\(185\) −4.39846 + 7.61836i −0.323381 + 0.560113i
\(186\) 11.8836i 0.871346i
\(187\) 1.25688i 0.0919122i
\(188\) 8.23239 + 4.75297i 0.600409 + 0.346646i
\(189\) 2.48558 1.43505i 0.180799 0.104385i
\(190\) −25.0303 14.4513i −1.81589 1.04840i
\(191\) −0.550318 0.953179i −0.0398196 0.0689696i 0.845429 0.534088i \(-0.179345\pi\)
−0.885248 + 0.465119i \(0.846012\pi\)
\(192\) 13.9832 24.2195i 1.00915 1.74789i
\(193\) 6.78851 + 3.91935i 0.488648 + 0.282121i 0.724013 0.689786i \(-0.242295\pi\)
−0.235366 + 0.971907i \(0.575629\pi\)
\(194\) −2.52643 + 4.37590i −0.181387 + 0.314171i
\(195\) −0.839556 0.484718i −0.0601219 0.0347114i
\(196\) −5.23772 9.07200i −0.374123 0.648000i
\(197\) 16.4978 + 9.52503i 1.17542 + 0.678630i 0.954951 0.296763i \(-0.0959073\pi\)
0.220471 + 0.975394i \(0.429241\pi\)
\(198\) −1.53974 + 2.66691i −0.109425 + 0.189529i
\(199\) −15.7666 + 9.10283i −1.11766 + 0.645283i −0.940803 0.338954i \(-0.889927\pi\)
−0.176859 + 0.984236i \(0.556594\pi\)
\(200\) 2.43113 1.40361i 0.171907 0.0992504i
\(201\) 10.5014 18.1889i 0.740709 1.28295i
\(202\) −21.3075 36.9056i −1.49919 2.59667i
\(203\) 18.7248i 1.31422i
\(204\) 7.05848 + 12.2256i 0.494192 + 0.855966i
\(205\) 13.4754 23.3401i 0.941164 1.63014i
\(206\) 1.42074 + 2.46079i 0.0989874 + 0.171451i
\(207\) −6.76525 + 11.7178i −0.470217 + 0.814440i
\(208\) 0.328025 + 0.189385i 0.0227444 + 0.0131315i
\(209\) −2.36913 1.36782i −0.163876 0.0946140i
\(210\) 45.5157 3.14088
\(211\) −9.64710 + 5.56975i −0.664134 + 0.383438i −0.793850 0.608113i \(-0.791927\pi\)
0.129717 + 0.991551i \(0.458593\pi\)
\(212\) −17.0611 9.85021i −1.17176 0.676515i
\(213\) 37.1850i 2.54787i
\(214\) 4.82309 8.35384i 0.329700 0.571057i
\(215\) 18.7017 10.7974i 1.27545 0.736379i
\(216\) 1.07452i 0.0731117i
\(217\) 6.73438 3.88809i 0.457159 0.263941i
\(218\) 19.0019i 1.28697i
\(219\) 17.0258 + 29.4895i 1.15049 + 1.99272i
\(220\) 3.28615 1.89726i 0.221552 0.127913i
\(221\) −0.302397 + 0.174589i −0.0203414 + 0.0117441i
\(222\) 16.5969i 1.11391i
\(223\) −4.73226 −0.316896 −0.158448 0.987367i \(-0.550649\pi\)
−0.158448 + 0.987367i \(0.550649\pi\)
\(224\) −26.0631 −1.74142
\(225\) −2.97247 + 5.14847i −0.198165 + 0.343232i
\(226\) −13.5612 + 23.4886i −0.902075 + 1.56244i
\(227\) 9.56248 + 16.5627i 0.634684 + 1.09930i 0.986582 + 0.163266i \(0.0522030\pi\)
−0.351898 + 0.936038i \(0.614464\pi\)
\(228\) 30.7260 2.03488
\(229\) 11.3029 6.52576i 0.746919 0.431234i −0.0776603 0.996980i \(-0.524745\pi\)
0.824580 + 0.565746i \(0.191412\pi\)
\(230\) 25.6242 14.7941i 1.68961 0.975496i
\(231\) 4.30808 0.283451
\(232\) −6.07105 3.50512i −0.398584 0.230122i
\(233\) 4.97511 + 8.61714i 0.325930 + 0.564528i 0.981700 0.190433i \(-0.0609892\pi\)
−0.655770 + 0.754961i \(0.727656\pi\)
\(234\) 0.855520 0.0559271
\(235\) 8.58913 + 4.95894i 0.560293 + 0.323485i
\(236\) −7.19662 + 4.15497i −0.468460 + 0.270466i
\(237\) −1.45752 0.841499i −0.0946760 0.0546612i
\(238\) 8.19705 14.1977i 0.531336 0.920301i
\(239\) −13.4507 −0.870051 −0.435026 0.900418i \(-0.643261\pi\)
−0.435026 + 0.900418i \(0.643261\pi\)
\(240\) 7.98848 13.8364i 0.515654 0.893139i
\(241\) 10.0761 17.4523i 0.649058 1.12420i −0.334290 0.942470i \(-0.608497\pi\)
0.983348 0.181731i \(-0.0581700\pi\)
\(242\) −19.8387 + 11.4539i −1.27528 + 0.736285i
\(243\) −10.5267 18.2327i −0.675285 1.16963i
\(244\) −17.9552 10.3664i −1.14946 0.663642i
\(245\) −5.46470 9.46513i −0.349127 0.604705i
\(246\) 50.8474i 3.24191i
\(247\) 0.759995i 0.0483573i
\(248\) 2.91128i 0.184866i
\(249\) −16.8329 −1.06674
\(250\) −13.7061 + 7.91321i −0.866849 + 0.500476i
\(251\) 15.4563i 0.975593i 0.872957 + 0.487796i \(0.162199\pi\)
−0.872957 + 0.487796i \(0.837801\pi\)
\(252\) −19.6009 + 11.3166i −1.23474 + 0.712877i
\(253\) 2.42534 1.40027i 0.152480 0.0880343i
\(254\) −16.7078 28.9387i −1.04834 1.81578i
\(255\) 7.36435 + 12.7554i 0.461173 + 0.798776i
\(256\) −1.57131 + 2.72159i −0.0982068 + 0.170099i
\(257\) −19.5280 −1.21812 −0.609061 0.793123i \(-0.708454\pi\)
−0.609061 + 0.793123i \(0.708454\pi\)
\(258\) −20.3712 + 35.2840i −1.26826 + 2.19668i
\(259\) −9.40541 + 5.43022i −0.584424 + 0.337417i
\(260\) −0.912934 0.527083i −0.0566178 0.0326883i
\(261\) 14.8458 0.918932
\(262\) −17.1949 29.7824i −1.06230 1.83996i
\(263\) 14.8779 0.917410 0.458705 0.888589i \(-0.348313\pi\)
0.458705 + 0.888589i \(0.348313\pi\)
\(264\) −0.806437 + 1.39679i −0.0496328 + 0.0859665i
\(265\) −17.8004 10.2771i −1.09347 0.631315i
\(266\) −17.8411 30.9017i −1.09391 1.89471i
\(267\) −29.3634 + 16.9530i −1.79701 + 1.03750i
\(268\) 11.4192 19.7786i 0.697538 1.20817i
\(269\) −5.42046 −0.330491 −0.165246 0.986252i \(-0.552842\pi\)
−0.165246 + 0.986252i \(0.552842\pi\)
\(270\) 4.97611i 0.302836i
\(271\) −14.1788 24.5584i −0.861302 1.49182i −0.870673 0.491863i \(-0.836316\pi\)
0.00937068 0.999956i \(-0.497017\pi\)
\(272\) −2.87734 4.98369i −0.174464 0.302181i
\(273\) −0.598420 1.03649i −0.0362180 0.0627314i
\(274\) −9.65714 −0.583409
\(275\) 1.06563 0.615242i 0.0642600 0.0371005i
\(276\) −15.7275 + 27.2408i −0.946683 + 1.63970i
\(277\) −16.5475 + 9.55371i −0.994244 + 0.574027i −0.906540 0.422120i \(-0.861286\pi\)
−0.0877038 + 0.996147i \(0.527953\pi\)
\(278\) 6.35900 3.67137i 0.381388 0.220194i
\(279\) −3.08265 5.33931i −0.184553 0.319656i
\(280\) 11.1506 0.666375
\(281\) 11.4041 19.7525i 0.680314 1.17834i −0.294571 0.955630i \(-0.595177\pi\)
0.974885 0.222709i \(-0.0714899\pi\)
\(282\) −18.7118 −1.11427
\(283\) −7.38519 −0.439004 −0.219502 0.975612i \(-0.570443\pi\)
−0.219502 + 0.975612i \(0.570443\pi\)
\(284\) 40.4349i 2.39937i
\(285\) 32.0574 1.89892
\(286\) −0.153352 0.0885377i −0.00906788 0.00523534i
\(287\) 28.8151 16.6364i 1.70090 0.982015i
\(288\) 20.6640i 1.21764i
\(289\) −11.6949 −0.687937
\(290\) −28.1151 16.2323i −1.65098 0.953191i
\(291\) 5.60441i 0.328536i
\(292\) 18.5138 + 32.0669i 1.08344 + 1.87657i
\(293\) 14.5160 + 25.1424i 0.848033 + 1.46884i 0.882961 + 0.469446i \(0.155546\pi\)
−0.0349283 + 0.999390i \(0.511120\pi\)
\(294\) 17.8576 + 10.3101i 1.04148 + 0.601297i
\(295\) −7.50848 + 4.33502i −0.437161 + 0.252395i
\(296\) 4.06597i 0.236330i
\(297\) 0.470991i 0.0273297i
\(298\) −18.1595 + 31.4532i −1.05195 + 1.82203i
\(299\) −0.673791 0.389013i −0.0389663 0.0224972i
\(300\) −6.91024 + 11.9689i −0.398963 + 0.691024i
\(301\) 26.6604 1.53668
\(302\) 28.0093i 1.61176i
\(303\) 40.9341 + 23.6333i 2.35160 + 1.35770i
\(304\) −12.5252 −0.718371
\(305\) −18.7332 10.8156i −1.07266 0.619301i
\(306\) −11.2566 6.49898i −0.643495 0.371522i
\(307\) −10.4670 18.1294i −0.597385 1.03470i −0.993206 0.116374i \(-0.962873\pi\)
0.395820 0.918328i \(-0.370460\pi\)
\(308\) 4.68461 0.266930
\(309\) −2.72940 1.57582i −0.155270 0.0896454i
\(310\) 13.4822i 0.765736i
\(311\) 16.5490i 0.938407i −0.883090 0.469203i \(-0.844541\pi\)
0.883090 0.469203i \(-0.155459\pi\)
\(312\) 0.448077 0.0253674
\(313\) −3.00317 −0.169749 −0.0848747 0.996392i \(-0.527049\pi\)
−0.0848747 + 0.996392i \(0.527049\pi\)
\(314\) 51.0869i 2.88300i
\(315\) −20.4503 + 11.8070i −1.15224 + 0.665247i
\(316\) −1.58491 0.915046i −0.0891580 0.0514754i
\(317\) −15.2838 8.82411i −0.858424 0.495611i 0.00506015 0.999987i \(-0.498389\pi\)
−0.863484 + 0.504376i \(0.831723\pi\)
\(318\) 38.7789 2.17461
\(319\) −2.66111 1.53639i −0.148993 0.0860214i
\(320\) 15.8642 27.4776i 0.886836 1.53604i
\(321\) 10.6991i 0.597168i
\(322\) 36.5288 2.03567
\(323\) 5.77332 9.99969i 0.321236 0.556398i
\(324\) −12.8545 22.2647i −0.714139 1.23693i
\(325\) −0.296046 0.170922i −0.0164217 0.00948106i
\(326\) −12.6856 21.9720i −0.702588 1.21692i
\(327\) −10.5381 18.2525i −0.582756 1.00936i
\(328\) 12.4568i 0.687811i
\(329\) 6.12217 + 10.6039i 0.337526 + 0.584612i
\(330\) −3.73462 + 6.46855i −0.205584 + 0.356082i
\(331\) −7.02727 4.05720i −0.386254 0.223004i 0.294282 0.955719i \(-0.404920\pi\)
−0.680536 + 0.732715i \(0.738253\pi\)
\(332\) −18.3041 −1.00457
\(333\) 4.30531 + 7.45702i 0.235930 + 0.408642i
\(334\) 5.02964 + 8.71160i 0.275210 + 0.476677i
\(335\) 11.9140 20.6357i 0.650933 1.12745i
\(336\) 17.0821 9.86235i 0.931905 0.538035i
\(337\) −2.20795 3.82428i −0.120275 0.208322i 0.799601 0.600531i \(-0.205044\pi\)
−0.919876 + 0.392210i \(0.871711\pi\)
\(338\) 27.7769i 1.51087i
\(339\) 30.0829i 1.63388i
\(340\) 8.00800 + 13.8703i 0.434295 + 0.752220i
\(341\) 1.27609i 0.0691044i
\(342\) −24.5002 + 14.1452i −1.32482 + 0.764886i
\(343\) 9.78406i 0.528290i
\(344\) −4.99061 + 8.64400i −0.269076 + 0.466053i
\(345\) −16.4090 + 28.4213i −0.883432 + 1.53015i
\(346\) −4.60445 + 7.97513i −0.247537 + 0.428746i
\(347\) −1.18322 + 0.683131i −0.0635185 + 0.0366724i −0.531423 0.847107i \(-0.678342\pi\)
0.467904 + 0.883779i \(0.345009\pi\)
\(348\) 34.5127 1.85008
\(349\) 18.6790 + 0.308348i 0.999864 + 0.0165055i
\(350\) 16.0498 0.857899
\(351\) 0.113317 0.0654237i 0.00604842 0.00349206i
\(352\) 2.13852 3.70402i 0.113983 0.197425i
\(353\) 8.51907 14.7555i 0.453424 0.785354i −0.545172 0.838324i \(-0.683536\pi\)
0.998596 + 0.0529706i \(0.0168690\pi\)
\(354\) 8.17877 14.1660i 0.434697 0.752917i
\(355\) 42.1871i 2.23906i
\(356\) −31.9297 + 18.4346i −1.69227 + 0.977034i
\(357\) 18.1836i 0.962381i
\(358\) −0.783222 1.35658i −0.0413946 0.0716975i
\(359\) 13.6052i 0.718055i −0.933327 0.359027i \(-0.883108\pi\)
0.933327 0.359027i \(-0.116892\pi\)
\(360\) 8.84067i 0.465944i
\(361\) −3.06581 5.31014i −0.161358 0.279481i
\(362\) 39.8658 23.0165i 2.09530 1.20972i
\(363\) 12.7042 22.0043i 0.666797 1.15493i
\(364\) −0.650722 1.12708i −0.0341071 0.0590752i
\(365\) 19.3161 + 33.4565i 1.01105 + 1.75119i
\(366\) 40.8111 2.13323
\(367\) −17.1081 9.87738i −0.893037 0.515595i −0.0181021 0.999836i \(-0.505762\pi\)
−0.874935 + 0.484241i \(0.839096\pi\)
\(368\) 6.41120 11.1045i 0.334207 0.578863i
\(369\) −13.1900 22.8458i −0.686647 1.18931i
\(370\) 18.8296i 0.978902i
\(371\) −12.6878 21.9759i −0.658716 1.14093i
\(372\) −7.16638 12.4125i −0.371559 0.643560i
\(373\) −20.1239 11.6185i −1.04198 0.601585i −0.121584 0.992581i \(-0.538797\pi\)
−0.920392 + 0.390996i \(0.872131\pi\)
\(374\) 1.34516 + 2.32988i 0.0695565 + 0.120475i
\(375\) 8.77700 15.2022i 0.453243 0.785039i
\(376\) −4.58408 −0.236406
\(377\) 0.853658i 0.0439656i
\(378\) −3.07168 + 5.32031i −0.157990 + 0.273647i
\(379\) 0.807071 + 0.465963i 0.0414564 + 0.0239349i 0.520585 0.853810i \(-0.325714\pi\)
−0.479129 + 0.877745i \(0.659047\pi\)
\(380\) 34.8593 1.78824
\(381\) 32.0976 + 18.5316i 1.64441 + 0.949401i
\(382\) 2.04025 + 1.17794i 0.104388 + 0.0602687i
\(383\) −12.8462 + 7.41678i −0.656412 + 0.378980i −0.790908 0.611934i \(-0.790392\pi\)
0.134497 + 0.990914i \(0.457058\pi\)
\(384\) 22.6453i 1.15561i
\(385\) 4.88761 0.249096
\(386\) −16.7785 −0.854004
\(387\) 21.1375i 1.07448i
\(388\) 6.09424i 0.309388i
\(389\) 10.4362 + 6.02533i 0.529135 + 0.305496i 0.740664 0.671875i \(-0.234511\pi\)
−0.211529 + 0.977372i \(0.567844\pi\)
\(390\) 2.07505 0.105074
\(391\) 5.91030 + 10.2369i 0.298897 + 0.517704i
\(392\) 4.37482 + 2.52580i 0.220962 + 0.127572i
\(393\) 33.0333 + 19.0718i 1.66631 + 0.962046i
\(394\) −40.7761 −2.05427
\(395\) −1.65359 0.954699i −0.0832010 0.0480361i
\(396\) 3.71416i 0.186644i
\(397\) 33.0092 1.65669 0.828343 0.560222i \(-0.189284\pi\)
0.828343 + 0.560222i \(0.189284\pi\)
\(398\) 19.4844 33.7479i 0.976663 1.69163i
\(399\) 34.2749 + 19.7886i 1.71589 + 0.990670i
\(400\) 2.81691 4.87903i 0.140846 0.243952i
\(401\) 23.7136i 1.18420i 0.805865 + 0.592099i \(0.201701\pi\)
−0.805865 + 0.592099i \(0.798299\pi\)
\(402\) 44.9558i 2.24219i
\(403\) 0.307019 0.177258i 0.0152937 0.00882983i
\(404\) 44.5118 + 25.6989i 2.21454 + 1.27857i
\(405\) −13.4115 23.2295i −0.666425 1.15428i
\(406\) −20.0399 34.7101i −0.994564 1.72263i
\(407\) 1.78223i 0.0883417i
\(408\) −5.89561 3.40383i −0.291876 0.168515i
\(409\) −15.5294 −0.767881 −0.383941 0.923358i \(-0.625433\pi\)
−0.383941 + 0.923358i \(0.625433\pi\)
\(410\) 57.6875i 2.84898i
\(411\) 9.27625 5.35564i 0.457564 0.264174i
\(412\) −2.96795 1.71355i −0.146221 0.0844205i
\(413\) −10.7038 −0.526699
\(414\) 28.9617i 1.42339i
\(415\) −19.0973 −0.937450
\(416\) −1.18821 −0.0582570
\(417\) −4.07213 + 7.05314i −0.199413 + 0.345394i
\(418\) 5.85555 0.286404
\(419\) 18.6327 + 32.2728i 0.910267 + 1.57663i 0.813687 + 0.581304i \(0.197457\pi\)
0.0965806 + 0.995325i \(0.469209\pi\)
\(420\) −47.5417 + 27.4482i −2.31980 + 1.33933i
\(421\) 5.92803 3.42255i 0.288914 0.166805i −0.348538 0.937295i \(-0.613322\pi\)
0.637452 + 0.770490i \(0.279988\pi\)
\(422\) 11.9219 20.6493i 0.580349 1.00519i
\(423\) 8.40724 4.85392i 0.408774 0.236006i
\(424\) 9.50019 0.461370
\(425\) 2.59683 + 4.49784i 0.125965 + 0.218177i
\(426\) −39.7967 68.9299i −1.92816 3.33966i
\(427\) −13.3527 23.1275i −0.646182 1.11922i
\(428\) 11.6343i 0.562363i
\(429\) 0.196405 0.00948250
\(430\) −23.1116 + 40.0305i −1.11454 + 1.93044i
\(431\) −13.9570 + 8.05807i −0.672285 + 0.388144i −0.796942 0.604056i \(-0.793550\pi\)
0.124657 + 0.992200i \(0.460217\pi\)
\(432\) 1.07823 + 1.86754i 0.0518762 + 0.0898522i
\(433\) −11.3754 6.56757i −0.546665 0.315617i 0.201111 0.979568i \(-0.435545\pi\)
−0.747776 + 0.663951i \(0.768878\pi\)
\(434\) −8.32236 + 14.4147i −0.399486 + 0.691930i
\(435\) 36.0083 1.72646
\(436\) −11.4591 19.8477i −0.548791 0.950534i
\(437\) 25.7279 1.23073
\(438\) −63.1214 36.4432i −3.01606 1.74132i
\(439\) −28.7553 + 16.6019i −1.37242 + 0.792364i −0.991232 0.132135i \(-0.957817\pi\)
−0.381184 + 0.924499i \(0.624483\pi\)
\(440\) −0.914921 + 1.58469i −0.0436171 + 0.0755471i
\(441\) −10.6979 −0.509426
\(442\) 0.373702 0.647271i 0.0177752 0.0307876i
\(443\) 2.61699 + 4.53275i 0.124337 + 0.215358i 0.921474 0.388441i \(-0.126986\pi\)
−0.797137 + 0.603799i \(0.793653\pi\)
\(444\) 10.0088 + 17.3357i 0.474995 + 0.822715i
\(445\) −33.3134 + 19.2335i −1.57921 + 0.911755i
\(446\) 8.77221 5.06464i 0.415376 0.239818i
\(447\) 40.2835i 1.90534i
\(448\) 33.9231 19.5855i 1.60272 0.925328i
\(449\) −6.81397 −0.321571 −0.160786 0.986989i \(-0.551403\pi\)
−0.160786 + 0.986989i \(0.551403\pi\)
\(450\) 12.7250i 0.599862i
\(451\) 5.46015i 0.257109i
\(452\) 32.7122i 1.53865i
\(453\) −15.5334 26.9046i −0.729822 1.26409i
\(454\) −35.4520 20.4682i −1.66384 0.960621i
\(455\) −0.678920 1.17592i −0.0318283 0.0551282i
\(456\) −12.8320 + 7.40854i −0.600912 + 0.346937i
\(457\) 12.8648 22.2825i 0.601791 1.04233i −0.390759 0.920493i \(-0.627787\pi\)
0.992550 0.121840i \(-0.0388794\pi\)
\(458\) −13.9682 + 24.1936i −0.652691 + 1.13049i
\(459\) −1.98797 −0.0927906
\(460\) −17.8432 + 30.9053i −0.831942 + 1.44097i
\(461\) 21.7770 + 12.5729i 1.01425 + 0.585580i 0.912435 0.409223i \(-0.134200\pi\)
0.101820 + 0.994803i \(0.467533\pi\)
\(462\) −7.98590 + 4.61066i −0.371538 + 0.214507i
\(463\) 6.54872 + 3.78090i 0.304345 + 0.175714i 0.644393 0.764694i \(-0.277110\pi\)
−0.340048 + 0.940408i \(0.610443\pi\)
\(464\) −14.0689 −0.653130
\(465\) −7.47693 12.9504i −0.346734 0.600561i
\(466\) −18.4447 10.6491i −0.854436 0.493309i
\(467\) 0.873460 0.0404189 0.0202095 0.999796i \(-0.493567\pi\)
0.0202095 + 0.999796i \(0.493567\pi\)
\(468\) −0.893601 + 0.515921i −0.0413067 + 0.0238484i
\(469\) 25.4763 14.7087i 1.17639 0.679186i
\(470\) −21.2289 −0.979218
\(471\) −28.3317 49.0720i −1.30546 2.26112i
\(472\) 2.00366 3.47045i 0.0922261 0.159740i
\(473\) −2.18752 + 3.78890i −0.100582 + 0.174214i
\(474\) 3.60241 0.165464
\(475\) 11.3042 0.518670
\(476\) 19.7729i 0.906290i
\(477\) −17.4234 + 10.0594i −0.797764 + 0.460589i
\(478\) 24.9335 14.3954i 1.14043 0.658430i
\(479\) −15.7140 27.2174i −0.717990 1.24359i −0.961795 0.273770i \(-0.911729\pi\)
0.243806 0.969824i \(-0.421604\pi\)
\(480\) 50.1202i 2.28767i
\(481\) −0.428791 + 0.247563i −0.0195512 + 0.0112879i
\(482\) 43.1352i 1.96475i
\(483\) −35.0881 + 20.2581i −1.59656 + 0.921777i
\(484\) 13.8145 23.9275i 0.627933 1.08761i
\(485\) 6.35832i 0.288717i
\(486\) 39.0266 + 22.5320i 1.77028 + 1.02207i
\(487\) 2.09840 1.21151i 0.0950876 0.0548988i −0.451702 0.892169i \(-0.649183\pi\)
0.546790 + 0.837270i \(0.315850\pi\)
\(488\) 9.99805 0.452591
\(489\) 24.3704 + 14.0703i 1.10207 + 0.636280i
\(490\) 20.2598 + 11.6970i 0.915247 + 0.528418i
\(491\) −9.13356 + 15.8198i −0.412192 + 0.713937i −0.995129 0.0985799i \(-0.968570\pi\)
0.582937 + 0.812517i \(0.301903\pi\)
\(492\) −30.6635 53.1108i −1.38242 2.39442i
\(493\) 6.48484 11.2321i 0.292062 0.505867i
\(494\) −0.813374 1.40881i −0.0365954 0.0633851i
\(495\) 3.87511i 0.174173i
\(496\) 2.92132 + 5.05988i 0.131171 + 0.227195i
\(497\) −26.0415 + 45.1053i −1.16812 + 2.02325i
\(498\) 31.2032 18.0152i 1.39825 0.807280i
\(499\) −23.5856 + 13.6171i −1.05583 + 0.609586i −0.924277 0.381722i \(-0.875331\pi\)
−0.131557 + 0.991309i \(0.541998\pi\)
\(500\) 9.54412 16.5309i 0.426826 0.739284i
\(501\) −9.66253 5.57867i −0.431690 0.249236i
\(502\) −16.5419 28.6514i −0.738301 1.27877i
\(503\) 1.15067 + 0.664340i 0.0513059 + 0.0296215i 0.525434 0.850835i \(-0.323903\pi\)
−0.474128 + 0.880456i \(0.657236\pi\)
\(504\) 5.45722 9.45219i 0.243084 0.421034i
\(505\) 46.4407 + 26.8125i 2.06658 + 1.19314i
\(506\) −2.99724 + 5.19137i −0.133244 + 0.230785i
\(507\) 15.4045 + 26.6814i 0.684138 + 1.18496i
\(508\) 34.9030 + 20.1512i 1.54857 + 0.894067i
\(509\) 27.5488 15.9053i 1.22108 0.704991i 0.255932 0.966695i \(-0.417618\pi\)
0.965148 + 0.261703i \(0.0842843\pi\)
\(510\) −27.3026 15.7632i −1.20898 0.698005i
\(511\) 47.6943i 2.10987i
\(512\) 25.8035i 1.14036i
\(513\) −2.16344 + 3.74719i −0.0955182 + 0.165442i
\(514\) 36.1991 20.8996i 1.59667 0.921840i
\(515\) −3.09657 1.78780i −0.136451 0.0787801i
\(516\) 49.1394i 2.16324i
\(517\) −2.00933 −0.0883702
\(518\) 11.6232 20.1320i 0.510695 0.884550i
\(519\) 10.2141i 0.448350i
\(520\) 0.508353 0.0222928
\(521\) −11.2082 + 6.47108i −0.491042 + 0.283503i −0.725007 0.688742i \(-0.758163\pi\)
0.233965 + 0.972245i \(0.424830\pi\)
\(522\) −27.5197 + 15.8885i −1.20450 + 0.695421i
\(523\) −15.8896 9.17388i −0.694805 0.401146i 0.110605 0.993864i \(-0.464721\pi\)
−0.805410 + 0.592719i \(0.798055\pi\)
\(524\) 35.9205 + 20.7387i 1.56919 + 0.905974i
\(525\) −15.4168 + 8.90089i −0.672844 + 0.388467i
\(526\) −27.5792 + 15.9229i −1.20251 + 0.694269i
\(527\) −5.38617 −0.234625
\(528\) 3.23688i 0.140867i
\(529\) −1.66915 + 2.89106i −0.0725719 + 0.125698i
\(530\) 43.9955 1.91104
\(531\) 8.48644i 0.368280i
\(532\) 37.2705 + 21.5182i 1.61588 + 0.932930i
\(533\) 1.31367 0.758450i 0.0569016 0.0328521i
\(534\) 36.2873 62.8515i 1.57031 2.71985i
\(535\) 12.1384i 0.524790i
\(536\) 11.0134i 0.475707i
\(537\) 1.50466 + 0.868717i 0.0649310 + 0.0374879i
\(538\) 10.0479 5.80117i 0.433197 0.250106i
\(539\) 1.91760 + 1.10713i 0.0825971 + 0.0476874i
\(540\) −3.00084 5.19761i −0.129136 0.223669i
\(541\) 8.86271 15.3507i 0.381038 0.659977i −0.610173 0.792268i \(-0.708900\pi\)
0.991211 + 0.132291i \(0.0422335\pi\)
\(542\) 52.5667 + 30.3494i 2.25793 + 1.30362i
\(543\) −25.5290 + 44.2175i −1.09555 + 1.89755i
\(544\) 15.6340 + 9.02630i 0.670303 + 0.387000i
\(545\) −11.9557 20.7078i −0.512124 0.887026i
\(546\) 2.21859 + 1.28090i 0.0949467 + 0.0548175i
\(547\) −16.8807 + 29.2383i −0.721768 + 1.25014i 0.238523 + 0.971137i \(0.423337\pi\)
−0.960291 + 0.279002i \(0.909996\pi\)
\(548\) 10.0870 5.82373i 0.430895 0.248777i
\(549\) −18.3365 + 10.5866i −0.782583 + 0.451825i
\(550\) −1.31691 + 2.28095i −0.0561532 + 0.0972602i
\(551\) −14.1144 24.4469i −0.601296 1.04147i
\(552\) 15.1686i 0.645620i
\(553\) −1.17865 2.04147i −0.0501211 0.0868123i
\(554\) 20.4495 35.4195i 0.868814 1.50483i
\(555\) 10.4425 + 18.0869i 0.443258 + 0.767746i
\(556\) −4.42804 + 7.66959i −0.187791 + 0.325263i
\(557\) −10.7250 6.19206i −0.454432 0.262366i 0.255268 0.966870i \(-0.417836\pi\)
−0.709700 + 0.704504i \(0.751169\pi\)
\(558\) 11.4286 + 6.59833i 0.483813 + 0.279329i
\(559\) 1.21544 0.0514078
\(560\) 19.3800 11.1891i 0.818955 0.472824i
\(561\) −2.58421 1.49199i −0.109105 0.0629920i
\(562\) 48.8205i 2.05937i
\(563\) −8.98229 + 15.5578i −0.378558 + 0.655682i −0.990853 0.134948i \(-0.956913\pi\)
0.612295 + 0.790630i \(0.290247\pi\)
\(564\) 19.5447 11.2841i 0.822980 0.475148i
\(565\) 34.1298i 1.43585i
\(566\) 13.6900 7.90390i 0.575432 0.332226i
\(567\) 33.1150i 1.39070i
\(568\) −9.74953 16.8867i −0.409081 0.708550i
\(569\) −31.5138 + 18.1945i −1.32113 + 0.762754i −0.983909 0.178672i \(-0.942820\pi\)
−0.337220 + 0.941426i \(0.609487\pi\)
\(570\) −59.4250 + 34.3090i −2.48904 + 1.43705i
\(571\) 14.0268i 0.587003i 0.955959 + 0.293502i \(0.0948206\pi\)
−0.955959 + 0.293502i \(0.905179\pi\)
\(572\) 0.213570 0.00892983
\(573\) −2.61304 −0.109161
\(574\) −35.6097 + 61.6778i −1.48632 + 2.57438i
\(575\) −5.78618 + 10.0220i −0.241300 + 0.417945i
\(576\) −15.5282 26.8957i −0.647010 1.12065i
\(577\) −24.5499 −1.02203 −0.511013 0.859573i \(-0.670730\pi\)
−0.511013 + 0.859573i \(0.670730\pi\)
\(578\) 21.6789 12.5163i 0.901724 0.520611i
\(579\) 16.1167 9.30501i 0.669789 0.386703i
\(580\) 39.1554 1.62584
\(581\) −20.4183 11.7885i −0.847093 0.489070i
\(582\) 5.99804 + 10.3889i 0.248627 + 0.430634i
\(583\) 4.16420 0.172463
\(584\) −15.4637 8.92798i −0.639893 0.369442i
\(585\) −0.932324 + 0.538278i −0.0385469 + 0.0222550i
\(586\) −53.8167 31.0711i −2.22315 1.28353i
\(587\) 20.9862 36.3491i 0.866192 1.50029i 0.000333499 1.00000i \(-0.499894\pi\)
0.865859 0.500289i \(-0.166773\pi\)
\(588\) −24.8700 −1.02562
\(589\) −5.86158 + 10.1526i −0.241522 + 0.418329i
\(590\) 9.27899 16.0717i 0.382010 0.661661i
\(591\) 39.1679 22.6136i 1.61115 0.930198i
\(592\) −4.08000 7.06676i −0.167687 0.290442i
\(593\) −24.1573 13.9472i −0.992021 0.572744i −0.0861435 0.996283i \(-0.527454\pi\)
−0.905878 + 0.423539i \(0.860788\pi\)
\(594\) −0.504072 0.873078i −0.0206823 0.0358228i
\(595\) 20.6297i 0.845737i
\(596\) 43.8043i 1.79429i
\(597\) 43.2225i 1.76898i
\(598\) 1.66534 0.0681010
\(599\) −16.1054 + 9.29847i −0.658050 + 0.379925i −0.791533 0.611126i \(-0.790717\pi\)
0.133484 + 0.991051i \(0.457384\pi\)
\(600\) 6.66470i 0.272085i
\(601\) 6.42472 3.70931i 0.262070 0.151306i −0.363209 0.931708i \(-0.618319\pi\)
0.625278 + 0.780402i \(0.284985\pi\)
\(602\) −49.4205 + 28.5329i −2.01423 + 1.16292i
\(603\) −11.6617 20.1987i −0.474902 0.822555i
\(604\) −16.8910 29.2561i −0.687286 1.19041i
\(605\) 14.4132 24.9644i 0.585979 1.01495i
\(606\) −101.173 −4.10987
\(607\) 7.81867 13.5423i 0.317350 0.549666i −0.662584 0.748987i \(-0.730540\pi\)
0.979934 + 0.199321i \(0.0638737\pi\)
\(608\) 34.0279 19.6460i 1.38001 0.796751i
\(609\) 38.4990 + 22.2274i 1.56006 + 0.900700i
\(610\) 46.3011 1.87468
\(611\) 0.279109 + 0.483430i 0.0112915 + 0.0195575i
\(612\) 15.6768 0.633698
\(613\) −14.9829 + 25.9512i −0.605154 + 1.04816i 0.386873 + 0.922133i \(0.373555\pi\)
−0.992027 + 0.126025i \(0.959778\pi\)
\(614\) 38.8056 + 22.4044i 1.56606 + 0.904168i
\(615\) −31.9923 55.4123i −1.29005 2.23444i
\(616\) −1.95641 + 1.12954i −0.0788262 + 0.0455103i
\(617\) −1.30545 + 2.26111i −0.0525555 + 0.0910288i −0.891106 0.453795i \(-0.850070\pi\)
0.838551 + 0.544823i \(0.183403\pi\)
\(618\) 6.74600 0.271364
\(619\) 3.08230i 0.123888i 0.998080 + 0.0619440i \(0.0197300\pi\)
−0.998080 + 0.0619440i \(0.980270\pi\)
\(620\) −8.13041 14.0823i −0.326525 0.565558i
\(621\) −2.21477 3.83609i −0.0888756 0.153937i
\(622\) 17.7113 + 30.6769i 0.710159 + 1.23003i
\(623\) −47.4903 −1.90266
\(624\) 0.778770 0.449623i 0.0311758 0.0179993i
\(625\) 15.5950 27.0113i 0.623799 1.08045i
\(626\) 5.56699 3.21410i 0.222502 0.128461i
\(627\) −5.62460 + 3.24737i −0.224625 + 0.129687i
\(628\) −30.8079 53.3609i −1.22937 2.12933i
\(629\) 7.52247 0.299940
\(630\) 25.2725 43.7732i 1.00688 1.74397i
\(631\) 11.6553 0.463991 0.231995 0.972717i \(-0.425475\pi\)
0.231995 + 0.972717i \(0.425475\pi\)
\(632\) 0.882531 0.0351052
\(633\) 26.4465i 1.05116i
\(634\) 37.7755 1.50026
\(635\) 36.4155 + 21.0245i 1.44510 + 0.834331i
\(636\) −40.5050 + 23.3856i −1.60613 + 0.927299i
\(637\) 0.615150i 0.0243731i
\(638\) 6.57720 0.260394
\(639\) 35.7614 + 20.6469i 1.41470 + 0.816778i
\(640\) 25.6916i 1.01555i
\(641\) −5.25790 9.10696i −0.207675 0.359703i 0.743307 0.668951i \(-0.233256\pi\)
−0.950982 + 0.309247i \(0.899923\pi\)
\(642\) −11.4506 19.8330i −0.451920 0.782748i
\(643\) −28.5085 16.4594i −1.12427 0.649095i −0.181779 0.983339i \(-0.558186\pi\)
−0.942486 + 0.334245i \(0.891519\pi\)
\(644\) −38.1548 + 22.0287i −1.50351 + 0.868052i
\(645\) 51.2688i 2.01871i
\(646\) 24.7153i 0.972409i
\(647\) −13.9890 + 24.2297i −0.549965 + 0.952568i 0.448311 + 0.893878i \(0.352026\pi\)
−0.998276 + 0.0586902i \(0.981308\pi\)
\(648\) 10.7368 + 6.19887i 0.421779 + 0.243515i
\(649\) 0.878261 1.52119i 0.0344748 0.0597120i
\(650\) 0.731709 0.0287000
\(651\) 18.4616i 0.723568i
\(652\) 26.5004 + 15.3000i 1.03784 + 0.599195i
\(653\) −13.4927 −0.528009 −0.264005 0.964521i \(-0.585043\pi\)
−0.264005 + 0.964521i \(0.585043\pi\)
\(654\) 39.0689 + 22.5564i 1.52771 + 0.882026i
\(655\) 37.4771 + 21.6374i 1.46435 + 0.845443i
\(656\) 12.4998 + 21.6502i 0.488034 + 0.845299i
\(657\) 37.8141 1.47527
\(658\) −22.6974 13.1043i −0.884835 0.510860i
\(659\) 8.01200i 0.312103i 0.987749 + 0.156052i \(0.0498766\pi\)
−0.987749 + 0.156052i \(0.950123\pi\)
\(660\) 9.00864i 0.350661i
\(661\) 26.2209 1.01987 0.509936 0.860212i \(-0.329669\pi\)
0.509936 + 0.860212i \(0.329669\pi\)
\(662\) 17.3686 0.675051
\(663\) 0.828990i 0.0321953i
\(664\) 7.64428 4.41342i 0.296655 0.171274i
\(665\) 38.8856 + 22.4506i 1.50792 + 0.870598i
\(666\) −15.9615 9.21540i −0.618497 0.357090i
\(667\) 28.8986 1.11896
\(668\) −10.5070 6.06624i −0.406530 0.234710i
\(669\) −5.61749 + 9.72977i −0.217185 + 0.376175i
\(670\) 51.0033i 1.97043i
\(671\) 4.38242 0.169182
\(672\) −30.9385 + 53.5871i −1.19348 + 2.06717i
\(673\) 11.7245 + 20.3074i 0.451947 + 0.782795i 0.998507 0.0546252i \(-0.0173964\pi\)
−0.546560 + 0.837420i \(0.684063\pi\)
\(674\) 8.18576 + 4.72605i 0.315304 + 0.182041i
\(675\) −0.973112 1.68548i −0.0374551 0.0648741i
\(676\) 16.7509 + 29.0134i 0.644264 + 1.11590i
\(677\) 32.5105i 1.24948i −0.780832 0.624741i \(-0.785205\pi\)
0.780832 0.624741i \(-0.214795\pi\)
\(678\) 32.1959 + 55.7649i 1.23647 + 2.14164i
\(679\) 3.92491 6.79814i 0.150624 0.260889i
\(680\) −6.68870 3.86172i −0.256500 0.148090i
\(681\) 45.4050 1.73992
\(682\) −1.36572 2.36550i −0.0522962 0.0905796i
\(683\) −11.9471 20.6930i −0.457144 0.791797i 0.541664 0.840595i \(-0.317794\pi\)
−0.998809 + 0.0487975i \(0.984461\pi\)
\(684\) 17.0605 29.5497i 0.652326 1.12986i
\(685\) 10.5241 6.07610i 0.402105 0.232156i
\(686\) −10.4713 18.1367i −0.399794 0.692464i
\(687\) 30.9859i 1.18218i
\(688\) 20.0313i 0.763687i
\(689\) −0.578434 1.00188i −0.0220366 0.0381684i
\(690\) 70.2461i 2.67422i
\(691\) 3.87792 2.23892i 0.147523 0.0851726i −0.424421 0.905465i \(-0.639523\pi\)
0.571945 + 0.820292i \(0.306189\pi\)
\(692\) 11.1068i 0.422218i
\(693\) 2.39205 4.14315i 0.0908665 0.157385i
\(694\) 1.46222 2.53264i 0.0555052 0.0961379i
\(695\) −4.61992 + 8.00194i −0.175244 + 0.303531i
\(696\) −14.4134 + 8.32158i −0.546339 + 0.315429i
\(697\) −23.0464 −0.872943
\(698\) −34.9553 + 19.4193i −1.32308 + 0.735033i
\(699\) 23.6230 0.893505
\(700\) −16.7642 + 9.67883i −0.633628 + 0.365825i
\(701\) 18.0656 31.2906i 0.682329 1.18183i −0.291940 0.956437i \(-0.594301\pi\)
0.974268 0.225391i \(-0.0723661\pi\)
\(702\) −0.140038 + 0.242552i −0.00528538 + 0.00915455i
\(703\) 8.18644 14.1793i 0.308757 0.534783i
\(704\) 6.42807i 0.242267i
\(705\) 20.3916 11.7731i 0.767994 0.443401i
\(706\) 36.4696i 1.37255i
\(707\) 33.1020 + 57.3344i 1.24493 + 2.15628i
\(708\) 19.7288i 0.741454i
\(709\) 28.9871i 1.08863i −0.838879 0.544317i \(-0.816789\pi\)
0.838879 0.544317i \(-0.183211\pi\)
\(710\) −45.1502 78.2024i −1.69446 2.93489i
\(711\) −1.61857 + 0.934481i −0.0607011 + 0.0350458i
\(712\) 8.88980 15.3976i 0.333159 0.577049i
\(713\) −6.00065 10.3934i −0.224726 0.389237i
\(714\) −19.4608 33.7071i −0.728302 1.26146i
\(715\) 0.222825 0.00833319
\(716\) 1.63617 + 0.944644i 0.0611466 + 0.0353030i
\(717\) −15.9668 + 27.6552i −0.596289 + 1.03280i
\(718\) 14.5608 + 25.2200i 0.543403 + 0.941202i
\(719\) 10.8238i 0.403659i 0.979421 + 0.201830i \(0.0646887\pi\)
−0.979421 + 0.201830i \(0.935311\pi\)
\(720\) −8.87117 15.3653i −0.330609 0.572632i
\(721\) −2.20717 3.82294i −0.0821995 0.142374i
\(722\) 11.3662 + 6.56228i 0.423006 + 0.244223i
\(723\) −23.9219 41.4339i −0.889663 1.54094i
\(724\) −27.7602 + 48.0821i −1.03170 + 1.78696i
\(725\) 12.6973 0.471566
\(726\) 54.3859i 2.01845i
\(727\) 26.1171 45.2361i 0.968628 1.67771i 0.269093 0.963114i \(-0.413276\pi\)
0.699535 0.714599i \(-0.253391\pi\)
\(728\) 0.543517 + 0.313800i 0.0201441 + 0.0116302i
\(729\) −20.1077 −0.744729
\(730\) −71.6127 41.3456i −2.65050 1.53027i
\(731\) −15.9923 9.23316i −0.591496 0.341501i
\(732\) −42.6277 + 24.6111i −1.57557 + 0.909653i
\(733\) 30.0239i 1.10896i 0.832198 + 0.554478i \(0.187082\pi\)
−0.832198 + 0.554478i \(0.812918\pi\)
\(734\) 42.2845 1.56075
\(735\) −25.9477 −0.957095
\(736\) 40.2243i 1.48269i
\(737\) 4.82749i 0.177823i
\(738\) 48.9009 + 28.2329i 1.80007 + 1.03927i
\(739\) 24.5199 0.901979 0.450990 0.892529i \(-0.351071\pi\)
0.450990 + 0.892529i \(0.351071\pi\)
\(740\) 11.3552 + 19.6677i 0.417424 + 0.722999i
\(741\) 1.56259 + 0.902160i 0.0574031 + 0.0331417i
\(742\) 47.0387 + 27.1578i 1.72685 + 0.996995i
\(743\) −6.60204 −0.242205 −0.121103 0.992640i \(-0.538643\pi\)
−0.121103 + 0.992640i \(0.538643\pi\)
\(744\) 5.98573 + 3.45586i 0.219448 + 0.126698i
\(745\) 45.7025i 1.67441i
\(746\) 49.7383 1.82105
\(747\) −9.34644 + 16.1885i −0.341968 + 0.592307i
\(748\) −2.81007 1.62239i −0.102746 0.0593206i
\(749\) −7.49288 + 12.9780i −0.273784 + 0.474207i
\(750\) 37.5739i 1.37200i
\(751\) 14.3601i 0.524008i −0.965067 0.262004i \(-0.915617\pi\)
0.965067 0.262004i \(-0.0843833\pi\)
\(752\) −7.96725 + 4.59990i −0.290536 + 0.167741i
\(753\) 31.7789 + 18.3476i 1.15809 + 0.668622i
\(754\) −0.913616 1.58243i −0.0332719 0.0576287i
\(755\) −17.6230 30.5239i −0.641366 1.11088i
\(756\) 7.40951i 0.269481i
\(757\) 5.78032 + 3.33727i 0.210089 + 0.121295i 0.601353 0.798983i \(-0.294629\pi\)
−0.391264 + 0.920279i \(0.627962\pi\)
\(758\) −1.99476 −0.0724529
\(759\) 6.64883i 0.241337i
\(760\) −14.5581 + 8.40515i −0.528079 + 0.304887i
\(761\) −33.3744 19.2687i −1.20982 0.698490i −0.247100 0.968990i \(-0.579477\pi\)
−0.962720 + 0.270501i \(0.912811\pi\)
\(762\) −79.3326 −2.87392
\(763\) 29.5203i 1.06871i
\(764\) −2.84142 −0.102799
\(765\) 16.3562 0.591358
\(766\) 15.8754 27.4970i 0.573602 0.993507i