Properties

Label 48.3.l.a.43.8
Level $48$
Weight $3$
Character 48.43
Analytic conductor $1.308$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 48.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.30790526893\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.8
Root \(-1.96679 - 0.362960i\) of defining polynomial
Character \(\chi\) \(=\) 48.43
Dual form 48.3.l.a.19.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.96679 - 0.362960i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(3.73652 - 1.42773i) q^{4} +(1.69930 + 1.69930i) q^{5} +(-2.85335 - 1.96428i) q^{6} -5.74280 q^{7} +(6.83074 - 4.16426i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(1.96679 - 0.362960i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(3.73652 - 1.42773i) q^{4} +(1.69930 + 1.69930i) q^{5} +(-2.85335 - 1.96428i) q^{6} -5.74280 q^{7} +(6.83074 - 4.16426i) q^{8} +3.00000i q^{9} +(3.95895 + 2.72539i) q^{10} +(-5.59560 + 5.59560i) q^{11} +(-6.32489 - 2.82768i) q^{12} +(-13.5782 + 13.5782i) q^{13} +(-11.2949 + 2.08441i) q^{14} -4.16243i q^{15} +(11.9232 - 10.6695i) q^{16} +19.7023 q^{17} +(1.08888 + 5.90037i) q^{18} +(-21.6943 - 21.6943i) q^{19} +(8.77563 + 3.92333i) q^{20} +(7.03347 + 7.03347i) q^{21} +(-8.97439 + 13.0363i) q^{22} +24.9257 q^{23} +(-13.4661 - 3.26576i) q^{24} -19.2247i q^{25} +(-21.7771 + 31.6337i) q^{26} +(3.67423 - 3.67423i) q^{27} +(-21.4581 + 8.19918i) q^{28} +(1.50581 - 1.50581i) q^{29} +(-1.51080 - 8.18662i) q^{30} +2.20037i q^{31} +(19.5777 - 25.3123i) q^{32} +13.7064 q^{33} +(38.7504 - 7.15116i) q^{34} +(-9.75877 - 9.75877i) q^{35} +(4.28320 + 11.2096i) q^{36} +(27.6956 + 27.6956i) q^{37} +(-50.5423 - 34.7940i) q^{38} +33.2596 q^{39} +(18.6838 + 4.53116i) q^{40} -51.3127i q^{41} +(16.3862 + 11.2805i) q^{42} +(21.4400 - 21.4400i) q^{43} +(-12.9191 + 28.8971i) q^{44} +(-5.09791 + 5.09791i) q^{45} +(49.0236 - 9.04703i) q^{46} +76.5216i q^{47} +(-27.6702 - 1.53542i) q^{48} -16.0202 q^{49} +(-6.97781 - 37.8110i) q^{50} +(-24.1303 - 24.1303i) q^{51} +(-31.3491 + 70.1211i) q^{52} +(-56.5145 - 56.5145i) q^{53} +(5.89284 - 8.56005i) q^{54} -19.0173 q^{55} +(-39.2276 + 23.9145i) q^{56} +53.1400i q^{57} +(2.41506 - 3.50816i) q^{58} +(-48.0041 + 48.0041i) q^{59} +(-5.94283 - 15.5530i) q^{60} +(-51.5587 + 51.5587i) q^{61} +(0.798646 + 4.32766i) q^{62} -17.2284i q^{63} +(29.3180 - 56.8899i) q^{64} -46.1469 q^{65} +(26.9575 - 4.97486i) q^{66} +(63.4445 + 63.4445i) q^{67} +(73.6182 - 28.1297i) q^{68} +(-30.5276 - 30.5276i) q^{69} +(-22.7355 - 15.6514i) q^{70} +43.4856 q^{71} +(12.4928 + 20.4922i) q^{72} -73.9992i q^{73} +(64.5239 + 44.4190i) q^{74} +(-23.5454 + 23.5454i) q^{75} +(-112.035 - 50.0876i) q^{76} +(32.1344 - 32.1344i) q^{77} +(65.4146 - 12.0719i) q^{78} +4.12659i q^{79} +(38.3918 + 2.13036i) q^{80} -9.00000 q^{81} +(-18.6245 - 100.921i) q^{82} +(38.4428 + 38.4428i) q^{83} +(36.3226 + 16.2388i) q^{84} +(33.4803 + 33.4803i) q^{85} +(34.3862 - 49.9499i) q^{86} -3.68846 q^{87} +(-14.9206 + 61.5236i) q^{88} +52.9839i q^{89} +(-8.17618 + 11.8769i) q^{90} +(77.9767 - 77.9767i) q^{91} +(93.1353 - 35.5872i) q^{92} +(2.69489 - 2.69489i) q^{93} +(27.7743 + 150.502i) q^{94} -73.7305i q^{95} +(-54.9788 + 7.02335i) q^{96} +23.1008 q^{97} +(-31.5084 + 5.81471i) q^{98} +(-16.7868 - 16.7868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} - 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} - 12q^{8} - 56q^{10} + 32q^{11} - 24q^{12} - 44q^{14} + 32q^{16} + 12q^{18} - 32q^{19} + 80q^{20} + 32q^{22} - 128q^{23} + 36q^{24} - 100q^{26} - 120q^{28} + 32q^{29} + 72q^{30} + 160q^{32} + 96q^{34} + 96q^{35} + 12q^{36} - 96q^{37} + 168q^{38} + 48q^{40} - 60q^{42} + 160q^{43} + 88q^{44} + 136q^{46} - 144q^{48} + 112q^{49} - 236q^{50} - 96q^{51} - 48q^{52} - 160q^{53} - 36q^{54} - 256q^{55} - 224q^{56} + 144q^{58} - 128q^{59} - 72q^{60} - 32q^{61} - 276q^{62} - 408q^{64} - 32q^{65} + 72q^{66} + 320q^{67} - 448q^{68} + 96q^{69} - 384q^{70} + 512q^{71} + 60q^{72} + 348q^{74} + 192q^{75} + 72q^{76} + 224q^{77} + 396q^{78} + 552q^{80} - 144q^{81} - 40q^{82} - 160q^{83} + 72q^{84} + 160q^{85} + 528q^{86} + 480q^{88} - 24q^{90} - 480q^{91} + 496q^{92} + 312q^{94} - 480q^{96} - 440q^{98} + 96q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.96679 0.362960i 0.983395 0.181480i
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 3.73652 1.42773i 0.934130 0.356933i
\(5\) 1.69930 + 1.69930i 0.339861 + 0.339861i 0.856315 0.516454i \(-0.172748\pi\)
−0.516454 + 0.856315i \(0.672748\pi\)
\(6\) −2.85335 1.96428i −0.475558 0.327380i
\(7\) −5.74280 −0.820400 −0.410200 0.911996i \(-0.634541\pi\)
−0.410200 + 0.911996i \(0.634541\pi\)
\(8\) 6.83074 4.16426i 0.853842 0.520532i
\(9\) 3.00000i 0.333333i
\(10\) 3.95895 + 2.72539i 0.395895 + 0.272539i
\(11\) −5.59560 + 5.59560i −0.508691 + 0.508691i −0.914125 0.405434i \(-0.867121\pi\)
0.405434 + 0.914125i \(0.367121\pi\)
\(12\) −6.32489 2.82768i −0.527074 0.235640i
\(13\) −13.5782 + 13.5782i −1.04447 + 1.04447i −0.0455110 + 0.998964i \(0.514492\pi\)
−0.998964 + 0.0455110i \(0.985508\pi\)
\(14\) −11.2949 + 2.08441i −0.806777 + 0.148886i
\(15\) 4.16243i 0.277495i
\(16\) 11.9232 10.6695i 0.745198 0.666844i
\(17\) 19.7023 1.15896 0.579481 0.814986i \(-0.303255\pi\)
0.579481 + 0.814986i \(0.303255\pi\)
\(18\) 1.08888 + 5.90037i 0.0604933 + 0.327798i
\(19\) −21.6943 21.6943i −1.14181 1.14181i −0.988120 0.153687i \(-0.950885\pi\)
−0.153687 0.988120i \(-0.549115\pi\)
\(20\) 8.77563 + 3.92333i 0.438782 + 0.196167i
\(21\) 7.03347 + 7.03347i 0.334927 + 0.334927i
\(22\) −8.97439 + 13.0363i −0.407927 + 0.592561i
\(23\) 24.9257 1.08373 0.541863 0.840467i \(-0.317719\pi\)
0.541863 + 0.840467i \(0.317719\pi\)
\(24\) −13.4661 3.26576i −0.561086 0.136073i
\(25\) 19.2247i 0.768989i
\(26\) −21.7771 + 31.6337i −0.837580 + 1.21668i
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) −21.4581 + 8.19918i −0.766360 + 0.292828i
\(29\) 1.50581 1.50581i 0.0519245 0.0519245i −0.680668 0.732592i \(-0.738310\pi\)
0.732592 + 0.680668i \(0.238310\pi\)
\(30\) −1.51080 8.18662i −0.0503598 0.272887i
\(31\) 2.20037i 0.0709796i 0.999370 + 0.0354898i \(0.0112991\pi\)
−0.999370 + 0.0354898i \(0.988701\pi\)
\(32\) 19.5777 25.3123i 0.611805 0.791009i
\(33\) 13.7064 0.415344
\(34\) 38.7504 7.15116i 1.13972 0.210328i
\(35\) −9.75877 9.75877i −0.278822 0.278822i
\(36\) 4.28320 + 11.2096i 0.118978 + 0.311377i
\(37\) 27.6956 + 27.6956i 0.748530 + 0.748530i 0.974203 0.225673i \(-0.0724580\pi\)
−0.225673 + 0.974203i \(0.572458\pi\)
\(38\) −50.5423 34.7940i −1.33006 0.915631i
\(39\) 33.2596 0.852810
\(40\) 18.6838 + 4.53116i 0.467096 + 0.113279i
\(41\) 51.3127i 1.25153i −0.780012 0.625764i \(-0.784787\pi\)
0.780012 0.625764i \(-0.215213\pi\)
\(42\) 16.3862 + 11.2805i 0.390148 + 0.268583i
\(43\) 21.4400 21.4400i 0.498606 0.498606i −0.412398 0.911004i \(-0.635309\pi\)
0.911004 + 0.412398i \(0.135309\pi\)
\(44\) −12.9191 + 28.8971i −0.293615 + 0.656752i
\(45\) −5.09791 + 5.09791i −0.113287 + 0.113287i
\(46\) 49.0236 9.04703i 1.06573 0.196675i
\(47\) 76.5216i 1.62812i 0.580781 + 0.814060i \(0.302747\pi\)
−0.580781 + 0.814060i \(0.697253\pi\)
\(48\) −27.6702 1.53542i −0.576463 0.0319879i
\(49\) −16.0202 −0.326944
\(50\) −6.97781 37.8110i −0.139556 0.756220i
\(51\) −24.1303 24.1303i −0.473144 0.473144i
\(52\) −31.3491 + 70.1211i −0.602868 + 1.34848i
\(53\) −56.5145 56.5145i −1.06631 1.06631i −0.997639 0.0686712i \(-0.978124\pi\)
−0.0686712 0.997639i \(-0.521876\pi\)
\(54\) 5.89284 8.56005i 0.109127 0.158519i
\(55\) −19.0173 −0.345768
\(56\) −39.2276 + 23.9145i −0.700492 + 0.427044i
\(57\) 53.1400i 0.932281i
\(58\) 2.41506 3.50816i 0.0416390 0.0604855i
\(59\) −48.0041 + 48.0041i −0.813628 + 0.813628i −0.985176 0.171547i \(-0.945123\pi\)
0.171547 + 0.985176i \(0.445123\pi\)
\(60\) −5.94283 15.5530i −0.0990472 0.259217i
\(61\) −51.5587 + 51.5587i −0.845224 + 0.845224i −0.989533 0.144308i \(-0.953904\pi\)
0.144308 + 0.989533i \(0.453904\pi\)
\(62\) 0.798646 + 4.32766i 0.0128814 + 0.0698010i
\(63\) 17.2284i 0.273467i
\(64\) 29.3180 56.8899i 0.458093 0.888904i
\(65\) −46.1469 −0.709952
\(66\) 26.9575 4.97486i 0.408447 0.0753767i
\(67\) 63.4445 + 63.4445i 0.946934 + 0.946934i 0.998661 0.0517277i \(-0.0164728\pi\)
−0.0517277 + 0.998661i \(0.516473\pi\)
\(68\) 73.6182 28.1297i 1.08262 0.413672i
\(69\) −30.5276 30.5276i −0.442429 0.442429i
\(70\) −22.7355 15.6514i −0.324793 0.223591i
\(71\) 43.4856 0.612473 0.306237 0.951955i \(-0.400930\pi\)
0.306237 + 0.951955i \(0.400930\pi\)
\(72\) 12.4928 + 20.4922i 0.173511 + 0.284614i
\(73\) 73.9992i 1.01369i −0.862038 0.506844i \(-0.830812\pi\)
0.862038 0.506844i \(-0.169188\pi\)
\(74\) 64.5239 + 44.4190i 0.871944 + 0.600257i
\(75\) −23.5454 + 23.5454i −0.313939 + 0.313939i
\(76\) −112.035 50.0876i −1.47414 0.659047i
\(77\) 32.1344 32.1344i 0.417330 0.417330i
\(78\) 65.4146 12.0719i 0.838649 0.154768i
\(79\) 4.12659i 0.0522354i 0.999659 + 0.0261177i \(0.00831446\pi\)
−0.999659 + 0.0261177i \(0.991686\pi\)
\(80\) 38.3918 + 2.13036i 0.479898 + 0.0266295i
\(81\) −9.00000 −0.111111
\(82\) −18.6245 100.921i −0.227127 1.23075i
\(83\) 38.4428 + 38.4428i 0.463166 + 0.463166i 0.899692 0.436526i \(-0.143791\pi\)
−0.436526 + 0.899692i \(0.643791\pi\)
\(84\) 36.3226 + 16.2388i 0.432412 + 0.193319i
\(85\) 33.4803 + 33.4803i 0.393886 + 0.393886i
\(86\) 34.3862 49.9499i 0.399839 0.580813i
\(87\) −3.68846 −0.0423961
\(88\) −14.9206 + 61.5236i −0.169552 + 0.699132i
\(89\) 52.9839i 0.595325i 0.954671 + 0.297662i \(0.0962070\pi\)
−0.954671 + 0.297662i \(0.903793\pi\)
\(90\) −8.17618 + 11.8769i −0.0908465 + 0.131965i
\(91\) 77.9767 77.9767i 0.856887 0.856887i
\(92\) 93.1353 35.5872i 1.01234 0.386817i
\(93\) 2.69489 2.69489i 0.0289773 0.0289773i
\(94\) 27.7743 + 150.502i 0.295471 + 1.60108i
\(95\) 73.7305i 0.776111i
\(96\) −54.9788 + 7.02335i −0.572696 + 0.0731599i
\(97\) 23.1008 0.238153 0.119077 0.992885i \(-0.462007\pi\)
0.119077 + 0.992885i \(0.462007\pi\)
\(98\) −31.5084 + 5.81471i −0.321515 + 0.0593337i
\(99\) −16.7868 16.7868i −0.169564 0.169564i
\(100\) −27.4478 71.8336i −0.274478 0.718336i
\(101\) 16.1216 + 16.1216i 0.159619 + 0.159619i 0.782398 0.622779i \(-0.213996\pi\)
−0.622779 + 0.782398i \(0.713996\pi\)
\(102\) −56.2177 38.7010i −0.551153 0.379421i
\(103\) −98.8380 −0.959592 −0.479796 0.877380i \(-0.659289\pi\)
−0.479796 + 0.877380i \(0.659289\pi\)
\(104\) −36.2060 + 149.292i −0.348134 + 1.43550i
\(105\) 23.9040i 0.227657i
\(106\) −131.665 90.6395i −1.24212 0.855090i
\(107\) 15.6655 15.6655i 0.146406 0.146406i −0.630104 0.776511i \(-0.716988\pi\)
0.776511 + 0.630104i \(0.216988\pi\)
\(108\) 8.48303 18.9747i 0.0785466 0.175691i
\(109\) 84.6938 84.6938i 0.777008 0.777008i −0.202313 0.979321i \(-0.564846\pi\)
0.979321 + 0.202313i \(0.0648459\pi\)
\(110\) −37.4029 + 6.90250i −0.340027 + 0.0627500i
\(111\) 67.8401i 0.611172i
\(112\) −68.4724 + 61.2728i −0.611360 + 0.547079i
\(113\) 63.8537 0.565077 0.282538 0.959256i \(-0.408824\pi\)
0.282538 + 0.959256i \(0.408824\pi\)
\(114\) 19.2877 + 104.515i 0.169190 + 0.916800i
\(115\) 42.3563 + 42.3563i 0.368316 + 0.368316i
\(116\) 3.47659 7.77638i 0.0299706 0.0670377i
\(117\) −40.7345 40.7345i −0.348158 0.348158i
\(118\) −76.9903 + 111.837i −0.652461 + 0.947775i
\(119\) −113.147 −0.950812
\(120\) −17.3334 28.4325i −0.144445 0.236937i
\(121\) 58.3785i 0.482467i
\(122\) −82.6913 + 120.119i −0.677798 + 0.984580i
\(123\) −62.8449 + 62.8449i −0.510934 + 0.510934i
\(124\) 3.14154 + 8.22172i 0.0253350 + 0.0663042i
\(125\) 75.1513 75.1513i 0.601210 0.601210i
\(126\) −6.25322 33.8846i −0.0496288 0.268926i
\(127\) 36.8901i 0.290473i −0.989397 0.145237i \(-0.953606\pi\)
0.989397 0.145237i \(-0.0463944\pi\)
\(128\) 37.0135 122.532i 0.289168 0.957278i
\(129\) −52.5172 −0.407110
\(130\) −90.7612 + 16.7495i −0.698163 + 0.128842i
\(131\) −40.4136 40.4136i −0.308500 0.308500i 0.535827 0.844328i \(-0.320000\pi\)
−0.844328 + 0.535827i \(0.820000\pi\)
\(132\) 51.2141 19.5690i 0.387986 0.148250i
\(133\) 124.586 + 124.586i 0.936738 + 0.936738i
\(134\) 147.810 + 101.754i 1.10306 + 0.759360i
\(135\) 12.4873 0.0924984
\(136\) 134.582 82.0456i 0.989570 0.603276i
\(137\) 253.499i 1.85036i 0.379531 + 0.925179i \(0.376085\pi\)
−0.379531 + 0.925179i \(0.623915\pi\)
\(138\) −71.1217 48.9611i −0.515375 0.354790i
\(139\) 67.8065 67.8065i 0.487816 0.487816i −0.419800 0.907617i \(-0.637900\pi\)
0.907617 + 0.419800i \(0.137900\pi\)
\(140\) −50.3967 22.5309i −0.359977 0.160935i
\(141\) 93.7194 93.7194i 0.664677 0.664677i
\(142\) 85.5270 15.7835i 0.602303 0.111152i
\(143\) 151.956i 1.06263i
\(144\) 32.0085 + 35.7695i 0.222281 + 0.248399i
\(145\) 5.11766 0.0352942
\(146\) −26.8588 145.541i −0.183964 0.996856i
\(147\) 19.6207 + 19.6207i 0.133474 + 0.133474i
\(148\) 143.027 + 63.9433i 0.966400 + 0.432049i
\(149\) −43.9337 43.9337i −0.294857 0.294857i 0.544138 0.838996i \(-0.316857\pi\)
−0.838996 + 0.544138i \(0.816857\pi\)
\(150\) −37.7628 + 54.8549i −0.251752 + 0.365699i
\(151\) −223.084 −1.47738 −0.738688 0.674047i \(-0.764554\pi\)
−0.738688 + 0.674047i \(0.764554\pi\)
\(152\) −238.529 57.8475i −1.56927 0.380576i
\(153\) 59.1070i 0.386320i
\(154\) 51.5381 74.8651i 0.334663 0.486137i
\(155\) −3.73909 + 3.73909i −0.0241232 + 0.0241232i
\(156\) 124.275 47.4858i 0.796636 0.304396i
\(157\) −78.8526 + 78.8526i −0.502246 + 0.502246i −0.912135 0.409889i \(-0.865567\pi\)
0.409889 + 0.912135i \(0.365567\pi\)
\(158\) 1.49779 + 8.11614i 0.00947968 + 0.0513680i
\(159\) 138.432i 0.870639i
\(160\) 76.2818 9.74473i 0.476761 0.0609045i
\(161\) −143.143 −0.889089
\(162\) −17.7011 + 3.26664i −0.109266 + 0.0201644i
\(163\) 52.2425 + 52.2425i 0.320506 + 0.320506i 0.848961 0.528455i \(-0.177228\pi\)
−0.528455 + 0.848961i \(0.677228\pi\)
\(164\) −73.2607 191.731i −0.446712 1.16909i
\(165\) 23.2913 + 23.2913i 0.141159 + 0.141159i
\(166\) 89.5620 + 61.6556i 0.539530 + 0.371419i
\(167\) 96.5201 0.577965 0.288982 0.957334i \(-0.406683\pi\)
0.288982 + 0.957334i \(0.406683\pi\)
\(168\) 77.3329 + 18.7546i 0.460315 + 0.111635i
\(169\) 199.734i 1.18186i
\(170\) 78.0006 + 53.6966i 0.458827 + 0.315863i
\(171\) 65.0830 65.0830i 0.380602 0.380602i
\(172\) 49.5005 110.722i 0.287794 0.643731i
\(173\) −46.3076 + 46.3076i −0.267674 + 0.267674i −0.828162 0.560488i \(-0.810614\pi\)
0.560488 + 0.828162i \(0.310614\pi\)
\(174\) −7.25443 + 1.33877i −0.0416921 + 0.00769405i
\(175\) 110.404i 0.630879i
\(176\) −7.01501 + 126.419i −0.0398580 + 0.718293i
\(177\) 117.585 0.664325
\(178\) 19.2310 + 104.208i 0.108040 + 0.585439i
\(179\) −93.5440 93.5440i −0.522592 0.522592i 0.395761 0.918353i \(-0.370481\pi\)
−0.918353 + 0.395761i \(0.870481\pi\)
\(180\) −11.7700 + 26.3269i −0.0653889 + 0.146261i
\(181\) −115.810 115.810i −0.639836 0.639836i 0.310679 0.950515i \(-0.399444\pi\)
−0.950515 + 0.310679i \(0.899444\pi\)
\(182\) 125.061 181.666i 0.687150 0.998166i
\(183\) 126.292 0.690123
\(184\) 170.261 103.797i 0.925331 0.564114i
\(185\) 94.1266i 0.508792i
\(186\) 4.32214 6.27842i 0.0232373 0.0337549i
\(187\) −110.246 + 110.246i −0.589553 + 0.589553i
\(188\) 109.252 + 285.925i 0.581130 + 1.52088i
\(189\) −21.1004 + 21.1004i −0.111642 + 0.111642i
\(190\) −26.7612 145.012i −0.140849 0.763223i
\(191\) 35.2964i 0.184798i −0.995722 0.0923991i \(-0.970546\pi\)
0.995722 0.0923991i \(-0.0294535\pi\)
\(192\) −105.583 + 33.7686i −0.549909 + 0.175878i
\(193\) −364.339 −1.88777 −0.943884 0.330277i \(-0.892858\pi\)
−0.943884 + 0.330277i \(0.892858\pi\)
\(194\) 45.4345 8.38468i 0.234198 0.0432200i
\(195\) 56.5182 + 56.5182i 0.289837 + 0.289837i
\(196\) −59.8599 + 22.8726i −0.305408 + 0.116697i
\(197\) 130.582 + 130.582i 0.662851 + 0.662851i 0.956051 0.293200i \(-0.0947203\pi\)
−0.293200 + 0.956051i \(0.594720\pi\)
\(198\) −39.1090 26.9232i −0.197520 0.135976i
\(199\) −12.7493 −0.0640670 −0.0320335 0.999487i \(-0.510198\pi\)
−0.0320335 + 0.999487i \(0.510198\pi\)
\(200\) −80.0567 131.319i −0.400283 0.656595i
\(201\) 155.407i 0.773168i
\(202\) 37.5592 + 25.8562i 0.185937 + 0.128001i
\(203\) −8.64756 + 8.64756i −0.0425988 + 0.0425988i
\(204\) −124.615 55.7119i −0.610859 0.273097i
\(205\) 87.1958 87.1958i 0.425346 0.425346i
\(206\) −194.394 + 35.8743i −0.943658 + 0.174147i
\(207\) 74.7771i 0.361242i
\(208\) −17.0225 + 306.767i −0.0818388 + 1.47484i
\(209\) 242.786 1.16165
\(210\) 8.67620 + 47.0141i 0.0413152 + 0.223877i
\(211\) 8.59499 + 8.59499i 0.0407345 + 0.0407345i 0.727181 0.686446i \(-0.240830\pi\)
−0.686446 + 0.727181i \(0.740830\pi\)
\(212\) −291.855 130.480i −1.37667 0.615471i
\(213\) −53.2588 53.2588i −0.250041 0.250041i
\(214\) 25.1247 36.4966i 0.117405 0.170545i
\(215\) 72.8663 0.338913
\(216\) 9.79728 40.3982i 0.0453578 0.187029i
\(217\) 12.6363i 0.0582317i
\(218\) 135.834 197.315i 0.623094 0.905117i
\(219\) −90.6302 + 90.6302i −0.413837 + 0.413837i
\(220\) −71.0583 + 27.1515i −0.322992 + 0.123416i
\(221\) −267.522 + 267.522i −1.21051 + 1.21051i
\(222\) −24.6233 133.427i −0.110916 0.601024i
\(223\) 50.5909i 0.226865i 0.993546 + 0.113433i \(0.0361846\pi\)
−0.993546 + 0.113433i \(0.963815\pi\)
\(224\) −112.431 + 145.363i −0.501925 + 0.648944i
\(225\) 57.6742 0.256330
\(226\) 125.587 23.1763i 0.555693 0.102550i
\(227\) 31.7175 + 31.7175i 0.139725 + 0.139725i 0.773509 0.633785i \(-0.218499\pi\)
−0.633785 + 0.773509i \(0.718499\pi\)
\(228\) 75.8697 + 198.559i 0.332762 + 0.870872i
\(229\) −169.826 169.826i −0.741599 0.741599i 0.231287 0.972886i \(-0.425706\pi\)
−0.972886 + 0.231287i \(0.925706\pi\)
\(230\) 98.6796 + 67.9323i 0.429042 + 0.295358i
\(231\) −78.7129 −0.340749
\(232\) 4.01521 16.5564i 0.0173070 0.0713636i
\(233\) 363.082i 1.55829i −0.626844 0.779145i \(-0.715654\pi\)
0.626844 0.779145i \(-0.284346\pi\)
\(234\) −94.9012 65.3312i −0.405561 0.279193i
\(235\) −130.033 + 130.033i −0.553334 + 0.553334i
\(236\) −110.831 + 247.905i −0.469624 + 1.05045i
\(237\) 5.05402 5.05402i 0.0213250 0.0213250i
\(238\) −222.536 + 41.0677i −0.935024 + 0.172553i
\(239\) 27.6282i 0.115599i 0.998328 + 0.0577996i \(0.0184084\pi\)
−0.998328 + 0.0577996i \(0.981592\pi\)
\(240\) −44.4110 49.6293i −0.185046 0.206789i
\(241\) 368.121 1.52747 0.763737 0.645527i \(-0.223362\pi\)
0.763737 + 0.645527i \(0.223362\pi\)
\(242\) 21.1891 + 114.818i 0.0875581 + 0.474456i
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) −119.038 + 266.262i −0.487861 + 1.09124i
\(245\) −27.2233 27.2233i −0.111115 0.111115i
\(246\) −100.793 + 146.413i −0.409726 + 0.595175i
\(247\) 589.139 2.38518
\(248\) 9.16290 + 15.0301i 0.0369472 + 0.0606054i
\(249\) 94.1651i 0.378173i
\(250\) 120.530 175.084i 0.482119 0.700334i
\(251\) 329.839 329.839i 1.31410 1.31410i 0.395734 0.918365i \(-0.370490\pi\)
0.918365 0.395734i \(-0.129510\pi\)
\(252\) −24.5975 64.3743i −0.0976093 0.255453i
\(253\) −139.474 + 139.474i −0.551281 + 0.551281i
\(254\) −13.3896 72.5551i −0.0527151 0.285650i
\(255\) 82.0096i 0.321606i
\(256\) 28.3236 254.428i 0.110639 0.993861i
\(257\) 23.6762 0.0921252 0.0460626 0.998939i \(-0.485333\pi\)
0.0460626 + 0.998939i \(0.485333\pi\)
\(258\) −103.290 + 19.0616i −0.400350 + 0.0738823i
\(259\) −159.050 159.050i −0.614094 0.614094i
\(260\) −172.429 + 65.8854i −0.663188 + 0.253405i
\(261\) 4.51743 + 4.51743i 0.0173082 + 0.0173082i
\(262\) −94.1535 64.8164i −0.359364 0.247391i
\(263\) 243.854 0.927202 0.463601 0.886044i \(-0.346557\pi\)
0.463601 + 0.886044i \(0.346557\pi\)
\(264\) 93.6246 57.0768i 0.354639 0.216200i
\(265\) 192.071i 0.724794i
\(266\) 290.255 + 199.815i 1.09118 + 0.751184i
\(267\) 64.8918 64.8918i 0.243040 0.243040i
\(268\) 327.644 + 146.480i 1.22255 + 0.546567i
\(269\) 234.293 234.293i 0.870976 0.870976i −0.121603 0.992579i \(-0.538803\pi\)
0.992579 + 0.121603i \(0.0388035\pi\)
\(270\) 24.5599 4.53239i 0.0909624 0.0167866i
\(271\) 30.9533i 0.114219i 0.998368 + 0.0571094i \(0.0181884\pi\)
−0.998368 + 0.0571094i \(0.981812\pi\)
\(272\) 234.914 210.214i 0.863655 0.772846i
\(273\) −191.003 −0.699646
\(274\) 92.0100 + 498.579i 0.335803 + 1.81963i
\(275\) 107.574 + 107.574i 0.391178 + 0.391178i
\(276\) −157.652 70.4818i −0.571204 0.255369i
\(277\) −41.4479 41.4479i −0.149631 0.149631i 0.628322 0.777953i \(-0.283742\pi\)
−0.777953 + 0.628322i \(0.783742\pi\)
\(278\) 108.750 157.972i 0.391187 0.568245i
\(279\) −6.60110 −0.0236599
\(280\) −107.298 26.0216i −0.383206 0.0929342i
\(281\) 93.3971i 0.332374i 0.986094 + 0.166187i \(0.0531455\pi\)
−0.986094 + 0.166187i \(0.946854\pi\)
\(282\) 150.310 218.343i 0.533014 0.774265i
\(283\) 40.0982 40.0982i 0.141690 0.141690i −0.632704 0.774394i \(-0.718055\pi\)
0.774394 + 0.632704i \(0.218055\pi\)
\(284\) 162.485 62.0858i 0.572130 0.218612i
\(285\) −90.3011 + 90.3011i −0.316846 + 0.316846i
\(286\) −55.1540 298.866i −0.192846 1.04498i
\(287\) 294.678i 1.02675i
\(288\) 75.9369 + 58.7332i 0.263670 + 0.203935i
\(289\) 99.1824 0.343192
\(290\) 10.0654 1.85750i 0.0347081 0.00640519i
\(291\) −28.2926 28.2926i −0.0972256 0.0972256i
\(292\) −105.651 276.500i −0.361819 0.946917i
\(293\) 141.326 + 141.326i 0.482340 + 0.482340i 0.905878 0.423538i \(-0.139212\pi\)
−0.423538 + 0.905878i \(0.639212\pi\)
\(294\) 45.7113 + 31.4683i 0.155481 + 0.107035i
\(295\) −163.147 −0.553041
\(296\) 304.513 + 73.8499i 1.02876 + 0.249493i
\(297\) 41.1191i 0.138448i
\(298\) −102.355 70.4622i −0.343472 0.236450i
\(299\) −338.445 + 338.445i −1.13192 + 1.13192i
\(300\) −54.3613 + 121.594i −0.181204 + 0.405314i
\(301\) −123.126 + 123.126i −0.409056 + 0.409056i
\(302\) −438.759 + 80.9705i −1.45284 + 0.268114i
\(303\) 39.4896i 0.130329i
\(304\) −490.133 27.1974i −1.61228 0.0894652i
\(305\) −175.228 −0.574517
\(306\) 21.4535 + 116.251i 0.0701095 + 0.379905i
\(307\) −285.548 285.548i −0.930125 0.930125i 0.0675885 0.997713i \(-0.478470\pi\)
−0.997713 + 0.0675885i \(0.978470\pi\)
\(308\) 74.1916 165.950i 0.240882 0.538799i
\(309\) 121.051 + 121.051i 0.391752 + 0.391752i
\(310\) −5.99687 + 8.71115i −0.0193447 + 0.0281005i
\(311\) −365.454 −1.17509 −0.587547 0.809190i \(-0.699906\pi\)
−0.587547 + 0.809190i \(0.699906\pi\)
\(312\) 227.188 138.501i 0.728165 0.443915i
\(313\) 461.508i 1.47447i 0.675638 + 0.737234i \(0.263868\pi\)
−0.675638 + 0.737234i \(0.736132\pi\)
\(314\) −126.466 + 183.707i −0.402758 + 0.585054i
\(315\) 29.2763 29.2763i 0.0929406 0.0929406i
\(316\) 5.89167 + 15.4191i 0.0186445 + 0.0487946i
\(317\) −319.216 + 319.216i −1.00699 + 1.00699i −0.00701388 + 0.999975i \(0.502233\pi\)
−0.999975 + 0.00701388i \(0.997767\pi\)
\(318\) 50.2451 + 272.266i 0.158004 + 0.856182i
\(319\) 16.8518i 0.0528270i
\(320\) 146.493 46.8531i 0.457792 0.146416i
\(321\) −38.3724 −0.119540
\(322\) −281.533 + 51.9553i −0.874325 + 0.161352i
\(323\) −427.429 427.429i −1.32331 1.32331i
\(324\) −33.6287 + 12.8496i −0.103792 + 0.0396592i
\(325\) 261.037 + 261.037i 0.803190 + 0.803190i
\(326\) 121.712 + 83.7881i 0.373350 + 0.257019i
\(327\) −207.457 −0.634424
\(328\) −213.679 350.503i −0.651461 1.06861i
\(329\) 439.448i 1.33571i
\(330\) 54.2629 + 37.3552i 0.164433 + 0.113198i
\(331\) −85.7864 + 85.7864i −0.259173 + 0.259173i −0.824718 0.565544i \(-0.808666\pi\)
0.565544 + 0.824718i \(0.308666\pi\)
\(332\) 198.528 + 88.7562i 0.597976 + 0.267338i
\(333\) −83.0869 + 83.0869i −0.249510 + 0.249510i
\(334\) 189.835 35.0329i 0.568367 0.104889i
\(335\) 215.623i 0.643651i
\(336\) 158.905 + 8.81761i 0.472931 + 0.0262429i
\(337\) 258.256 0.766339 0.383170 0.923678i \(-0.374832\pi\)
0.383170 + 0.923678i \(0.374832\pi\)
\(338\) −72.4953 392.834i −0.214483 1.16223i
\(339\) −78.2045 78.2045i −0.230692 0.230692i
\(340\) 172.901 + 77.2989i 0.508531 + 0.227350i
\(341\) −12.3124 12.3124i −0.0361067 0.0361067i
\(342\) 104.382 151.627i 0.305210 0.443354i
\(343\) 373.398 1.08862
\(344\) 57.1695 235.733i 0.166190 0.685271i
\(345\) 103.751i 0.300729i
\(346\) −74.2695 + 107.885i −0.214652 + 0.311807i
\(347\) 27.7237 27.7237i 0.0798953 0.0798953i −0.666030 0.745925i \(-0.732008\pi\)
0.745925 + 0.666030i \(0.232008\pi\)
\(348\) −13.7820 + 5.26614i −0.0396035 + 0.0151326i
\(349\) 321.089 321.089i 0.920027 0.920027i −0.0770037 0.997031i \(-0.524535\pi\)
0.997031 + 0.0770037i \(0.0245353\pi\)
\(350\) 40.0722 + 217.141i 0.114492 + 0.620403i
\(351\) 99.7788i 0.284270i
\(352\) 32.0882 + 251.187i 0.0911596 + 0.713599i
\(353\) −241.363 −0.683748 −0.341874 0.939746i \(-0.611062\pi\)
−0.341874 + 0.939746i \(0.611062\pi\)
\(354\) 231.266 42.6788i 0.653293 0.120562i
\(355\) 73.8953 + 73.8953i 0.208156 + 0.208156i
\(356\) 75.6468 + 197.975i 0.212491 + 0.556111i
\(357\) 138.576 + 138.576i 0.388167 + 0.388167i
\(358\) −217.934 150.029i −0.608754 0.419074i
\(359\) −363.821 −1.01343 −0.506714 0.862114i \(-0.669140\pi\)
−0.506714 + 0.862114i \(0.669140\pi\)
\(360\) −13.5935 + 56.0515i −0.0377597 + 0.155699i
\(361\) 580.287i 1.60744i
\(362\) −269.809 185.740i −0.745329 0.513094i
\(363\) 71.4988 71.4988i 0.196966 0.196966i
\(364\) 180.032 402.692i 0.494593 1.10630i
\(365\) 125.747 125.747i 0.344513 0.344513i
\(366\) 248.391 45.8391i 0.678663 0.125244i
\(367\) 411.402i 1.12099i −0.828159 0.560493i \(-0.810612\pi\)
0.828159 0.560493i \(-0.189388\pi\)
\(368\) 297.193 265.945i 0.807590 0.722676i
\(369\) 153.938 0.417176
\(370\) 34.1642 + 185.127i 0.0923356 + 0.500344i
\(371\) 324.551 + 324.551i 0.874801 + 0.874801i
\(372\) 6.22193 13.9171i 0.0167256 0.0374115i
\(373\) −225.677 225.677i −0.605033 0.605033i 0.336611 0.941644i \(-0.390719\pi\)
−0.941644 + 0.336611i \(0.890719\pi\)
\(374\) −176.816 + 256.847i −0.472771 + 0.686756i
\(375\) −184.082 −0.490886
\(376\) 318.656 + 522.699i 0.847488 + 1.39016i
\(377\) 40.8923i 0.108468i
\(378\) −33.8414 + 49.1586i −0.0895276 + 0.130049i
\(379\) −157.180 + 157.180i −0.414724 + 0.414724i −0.883381 0.468656i \(-0.844738\pi\)
0.468656 + 0.883381i \(0.344738\pi\)
\(380\) −105.267 275.496i −0.277019 0.724988i
\(381\) −45.1810 + 45.1810i −0.118585 + 0.118585i
\(382\) −12.8112 69.4207i −0.0335372 0.181729i
\(383\) 703.356i 1.83644i −0.396072 0.918219i \(-0.629627\pi\)
0.396072 0.918219i \(-0.370373\pi\)
\(384\) −195.402 + 104.738i −0.508860 + 0.272755i
\(385\) 109.212 0.283668
\(386\) −716.578 + 132.241i −1.85642 + 0.342592i
\(387\) 64.3201 + 64.3201i 0.166202 + 0.166202i
\(388\) 86.3168 32.9818i 0.222466 0.0850047i
\(389\) 10.7401 + 10.7401i 0.0276095 + 0.0276095i 0.720777 0.693167i \(-0.243785\pi\)
−0.693167 + 0.720777i \(0.743785\pi\)
\(390\) 131.673 + 90.6455i 0.337623 + 0.232424i
\(391\) 491.095 1.25600
\(392\) −109.430 + 66.7124i −0.279158 + 0.170185i
\(393\) 98.9926i 0.251890i
\(394\) 304.222 + 209.431i 0.772138 + 0.531550i
\(395\) −7.01234 + 7.01234i −0.0177528 + 0.0177528i
\(396\) −86.6913 38.7572i −0.218917 0.0978716i
\(397\) 365.020 365.020i 0.919446 0.919446i −0.0775433 0.996989i \(-0.524708\pi\)
0.996989 + 0.0775433i \(0.0247076\pi\)
\(398\) −25.0753 + 4.62750i −0.0630032 + 0.0116269i
\(399\) 305.173i 0.764844i
\(400\) −205.118 229.220i −0.512796 0.573049i
\(401\) 341.735 0.852207 0.426104 0.904674i \(-0.359886\pi\)
0.426104 + 0.904674i \(0.359886\pi\)
\(402\) −56.4065 305.652i −0.140315 0.760329i
\(403\) −29.8770 29.8770i −0.0741364 0.0741364i
\(404\) 83.2558 + 37.2213i 0.206079 + 0.0921318i
\(405\) −15.2937 15.2937i −0.0377623 0.0377623i
\(406\) −13.8692 + 20.1467i −0.0341606 + 0.0496223i
\(407\) −309.947 −0.761541
\(408\) −265.313 64.3431i −0.650277 0.157704i
\(409\) 368.259i 0.900389i 0.892931 + 0.450194i \(0.148645\pi\)
−0.892931 + 0.450194i \(0.851355\pi\)
\(410\) 139.847 203.144i 0.341091 0.495474i
\(411\) 310.472 310.472i 0.755405 0.755405i
\(412\) −369.310 + 141.114i −0.896384 + 0.342510i
\(413\) 275.678 275.678i 0.667501 0.667501i
\(414\) 27.1411 + 147.071i 0.0655582 + 0.355243i
\(415\) 130.652i 0.314824i
\(416\) 77.8646 + 609.525i 0.187174 + 1.46520i
\(417\) −166.091 −0.398300
\(418\) 477.508 88.1215i 1.14236 0.210817i
\(419\) 407.140 + 407.140i 0.971694 + 0.971694i 0.999610 0.0279165i \(-0.00888725\pi\)
−0.0279165 + 0.999610i \(0.508887\pi\)
\(420\) 34.1285 + 89.3178i 0.0812583 + 0.212661i
\(421\) 57.5576 + 57.5576i 0.136716 + 0.136716i 0.772153 0.635437i \(-0.219180\pi\)
−0.635437 + 0.772153i \(0.719180\pi\)
\(422\) 20.0242 + 13.7849i 0.0474506 + 0.0326656i
\(423\) −229.565 −0.542706
\(424\) −621.376 150.695i −1.46551 0.355412i
\(425\) 378.772i 0.891229i
\(426\) −124.080 85.4180i −0.291267 0.200512i
\(427\) 296.091 296.091i 0.693422 0.693422i
\(428\) 36.1683 80.9005i 0.0845053 0.189020i
\(429\) −186.107 + 186.107i −0.433817 + 0.433817i
\(430\) 143.313 26.4476i 0.333285 0.0615060i
\(431\) 796.565i 1.84818i 0.382177 + 0.924089i \(0.375174\pi\)
−0.382177 + 0.924089i \(0.624826\pi\)
\(432\) 4.60626 83.0107i 0.0106626 0.192154i
\(433\) −335.804 −0.775529 −0.387764 0.921758i \(-0.626753\pi\)
−0.387764 + 0.921758i \(0.626753\pi\)
\(434\) −4.58646 24.8529i −0.0105679 0.0572647i
\(435\) −6.26782 6.26782i −0.0144088 0.0144088i
\(436\) 195.540 437.380i 0.448487 1.00317i
\(437\) −540.746 540.746i −1.23741 1.23741i
\(438\) −145.355 + 211.146i −0.331862 + 0.482068i
\(439\) −285.630 −0.650638 −0.325319 0.945604i \(-0.605472\pi\)
−0.325319 + 0.945604i \(0.605472\pi\)
\(440\) −129.902 + 79.1927i −0.295232 + 0.179983i
\(441\) 48.0607i 0.108981i
\(442\) −429.059 + 623.259i −0.970722 + 1.41009i
\(443\) 111.596 111.596i 0.251909 0.251909i −0.569844 0.821753i \(-0.692996\pi\)
0.821753 + 0.569844i \(0.192996\pi\)
\(444\) −96.8575 253.486i −0.218148 0.570914i
\(445\) −90.0358 + 90.0358i −0.202328 + 0.202328i
\(446\) 18.3625 + 99.5017i 0.0411715 + 0.223098i
\(447\) 107.615i 0.240750i
\(448\) −168.367 + 326.707i −0.375820 + 0.729257i
\(449\) −99.6741 −0.221991 −0.110996 0.993821i \(-0.535404\pi\)
−0.110996 + 0.993821i \(0.535404\pi\)
\(450\) 113.433 20.9334i 0.252073 0.0465187i
\(451\) 287.125 + 287.125i 0.636641 + 0.636641i
\(452\) 238.591 91.1659i 0.527855 0.201695i
\(453\) 273.221 + 273.221i 0.603137 + 0.603137i
\(454\) 73.8939 + 50.8695i 0.162762 + 0.112047i
\(455\) 265.012 0.582445
\(456\) 221.289 + 362.986i 0.485282 + 0.796021i
\(457\) 32.1643i 0.0703813i −0.999381 0.0351907i \(-0.988796\pi\)
0.999381 0.0351907i \(-0.0112039\pi\)
\(458\) −395.652 272.372i −0.863870 0.594699i
\(459\) 72.3910 72.3910i 0.157715 0.157715i
\(460\) 218.739 + 97.7918i 0.475519 + 0.212591i
\(461\) 165.361 165.361i 0.358701 0.358701i −0.504633 0.863334i \(-0.668372\pi\)
0.863334 + 0.504633i \(0.168372\pi\)
\(462\) −154.812 + 28.5697i −0.335090 + 0.0618391i
\(463\) 923.215i 1.99398i −0.0774991 0.996992i \(-0.524693\pi\)
0.0774991 0.996992i \(-0.475307\pi\)
\(464\) 1.88778 34.0202i 0.00406849 0.0733195i
\(465\) 9.15887 0.0196965
\(466\) −131.784 714.105i −0.282798 1.53241i
\(467\) 507.842 + 507.842i 1.08746 + 1.08746i 0.995790 + 0.0916660i \(0.0292192\pi\)
0.0916660 + 0.995790i \(0.470781\pi\)
\(468\) −210.363 94.0474i −0.449494 0.200956i
\(469\) −364.349 364.349i −0.776864 0.776864i
\(470\) −208.551 + 302.945i −0.443727 + 0.644565i
\(471\) 193.149 0.410082
\(472\) −128.002 + 527.805i −0.271191 + 1.11823i
\(473\) 239.940i 0.507272i
\(474\) 8.10579 11.7746i 0.0171008 0.0248409i
\(475\) −417.068 + 417.068i −0.878037 + 0.878037i
\(476\) −422.775 + 161.543i −0.888182 + 0.339376i
\(477\) 169.543 169.543i 0.355437 0.355437i
\(478\) 10.0279 + 54.3389i 0.0209789 + 0.113680i
\(479\) 52.3866i 0.109367i 0.998504 + 0.0546833i \(0.0174149\pi\)
−0.998504 + 0.0546833i \(0.982585\pi\)
\(480\) −105.361 81.4910i −0.219501 0.169773i
\(481\) −752.112 −1.56364
\(482\) 724.017 133.613i 1.50211 0.277206i
\(483\) 175.314 + 175.314i 0.362969 + 0.362969i
\(484\) 83.3489 + 218.132i 0.172208 + 0.450687i
\(485\) 39.2554 + 39.2554i 0.0809389 + 0.0809389i
\(486\) 25.6801 + 17.6785i 0.0528398 + 0.0363756i
\(487\) −715.733 −1.46968 −0.734839 0.678241i \(-0.762742\pi\)
−0.734839 + 0.678241i \(0.762742\pi\)
\(488\) −137.480 + 566.887i −0.281722 + 1.16165i
\(489\) 127.968i 0.261692i
\(490\) −63.4234 43.6614i −0.129435 0.0891050i
\(491\) −22.3258 + 22.3258i −0.0454701 + 0.0454701i −0.729476 0.684006i \(-0.760236\pi\)
0.684006 + 0.729476i \(0.260236\pi\)
\(492\) −145.096 + 324.547i −0.294910 + 0.659649i
\(493\) 29.6680 29.6680i 0.0601784 0.0601784i
\(494\) 1158.71 213.834i 2.34557 0.432862i
\(495\) 57.0518i 0.115256i
\(496\) 23.4768 + 26.2353i 0.0473323 + 0.0528938i
\(497\) −249.729 −0.502473
\(498\) −34.1782 185.203i −0.0686309 0.371894i
\(499\) 84.0984 + 84.0984i 0.168534 + 0.168534i 0.786335 0.617801i \(-0.211976\pi\)
−0.617801 + 0.786335i \(0.711976\pi\)
\(500\) 173.508 388.100i 0.347017 0.776200i
\(501\) −118.213 118.213i −0.235953 0.235953i
\(502\) 529.005 768.442i 1.05380 1.53076i
\(503\) 327.870 0.651829 0.325914 0.945399i \(-0.394328\pi\)
0.325914 + 0.945399i \(0.394328\pi\)
\(504\) −71.7435 117.683i −0.142348 0.233497i
\(505\) 54.7909i 0.108497i
\(506\) −223.693 + 324.940i −0.442081 + 0.642174i
\(507\) −244.623 + 244.623i −0.482490 + 0.482490i
\(508\) −52.6692 137.841i −0.103680 0.271340i
\(509\) 34.6224 34.6224i 0.0680205 0.0680205i −0.672278 0.740299i \(-0.734684\pi\)
0.740299 + 0.672278i \(0.234684\pi\)
\(510\) −29.7662 161.296i −0.0583651 0.316266i
\(511\) 424.963i 0.831630i
\(512\) −36.6407 510.687i −0.0715639 0.997436i
\(513\) −159.420 −0.310760
\(514\) 46.5661 8.59351i 0.0905954 0.0167189i
\(515\) −167.956 167.956i −0.326128 0.326128i
\(516\) −196.231 + 74.9804i −0.380294 + 0.145311i
\(517\) −428.184 428.184i −0.828210 0.828210i
\(518\) −370.548 255.090i −0.715343 0.492451i
\(519\) 113.430 0.218555
\(520\) −315.217 + 192.167i −0.606187 + 0.369553i
\(521\) 235.719i 0.452436i 0.974077 + 0.226218i \(0.0726362\pi\)
−0.974077 + 0.226218i \(0.927364\pi\)
\(522\) 10.5245 + 7.24518i 0.0201618 + 0.0138797i
\(523\) −185.851 + 185.851i −0.355356 + 0.355356i −0.862098 0.506742i \(-0.830850\pi\)
0.506742 + 0.862098i \(0.330850\pi\)
\(524\) −208.706 93.3063i −0.398294 0.178066i
\(525\) 135.216 135.216i 0.257555 0.257555i
\(526\) 479.610 88.5093i 0.911805 0.168269i
\(527\) 43.3524i 0.0822626i
\(528\) 163.423 146.240i 0.309514 0.276970i
\(529\) 92.2900 0.174461
\(530\) −69.7139 377.762i −0.131536 0.712759i
\(531\) −144.012 144.012i −0.271209 0.271209i
\(532\) 643.394 + 287.643i 1.20939 + 0.540683i
\(533\) 696.732 + 696.732i 1.30719 + 1.30719i
\(534\) 104.075 151.182i 0.194898 0.283111i
\(535\) 53.2408 0.0995155
\(536\) 697.572 + 169.174i 1.30144 + 0.315623i
\(537\) 229.135i 0.426695i
\(538\) 375.765 545.843i 0.698448 1.01458i
\(539\) 89.6428 89.6428i 0.166313 0.166313i
\(540\) 46.6590 17.8285i 0.0864055 0.0330157i
\(541\) −315.952 + 315.952i −0.584015 + 0.584015i −0.936004 0.351989i \(-0.885506\pi\)
0.351989 + 0.936004i \(0.385506\pi\)
\(542\) 11.2348 + 60.8786i 0.0207284 + 0.112322i
\(543\) 283.676i 0.522424i
\(544\) 385.728 498.711i 0.709058 0.916749i
\(545\) 287.841 0.528149
\(546\) −375.663 + 69.3266i −0.688028 + 0.126972i
\(547\) −550.957 550.957i −1.00723 1.00723i −0.999974 0.00725954i \(-0.997689\pi\)
−0.00725954 0.999974i \(-0.502311\pi\)
\(548\) 361.929 + 947.204i 0.660454 + 1.72847i
\(549\) −154.676 154.676i −0.281741 0.281741i
\(550\) 250.620 + 172.530i 0.455673 + 0.313691i
\(551\) −65.3350 −0.118575
\(552\) −335.651 81.4013i −0.608063 0.147466i
\(553\) 23.6982i 0.0428539i
\(554\) −96.5631 66.4753i −0.174302 0.119992i
\(555\) 115.281 115.281i 0.207714 0.207714i
\(556\) 156.551 350.170i 0.281566 0.629802i
\(557\) 2.35545 2.35545i 0.00422882 0.00422882i −0.704989 0.709218i \(-0.749048\pi\)
0.709218 + 0.704989i \(0.249048\pi\)
\(558\) −12.9830 + 2.39594i −0.0232670 + 0.00429379i
\(559\) 582.233i 1.04156i
\(560\) −220.476 12.2342i −0.393708 0.0218468i
\(561\) 270.048 0.481368
\(562\) 33.8994 + 183.692i 0.0603192 + 0.326855i
\(563\) 269.210 + 269.210i 0.478170 + 0.478170i 0.904546 0.426376i \(-0.140210\pi\)
−0.426376 + 0.904546i \(0.640210\pi\)
\(564\) 216.378 483.991i 0.383650 0.858140i
\(565\) 108.507 + 108.507i 0.192047 + 0.192047i
\(566\) 64.3106 93.4187i 0.113623 0.165051i
\(567\) 51.6852 0.0911556
\(568\) 297.039 181.085i 0.522956 0.318812i
\(569\) 342.558i 0.602035i −0.953619 0.301018i \(-0.902674\pi\)
0.953619 0.301018i \(-0.0973263\pi\)
\(570\) −144.827 + 210.379i −0.254083 + 0.369086i
\(571\) 153.948 153.948i 0.269610 0.269610i −0.559333 0.828943i \(-0.688943\pi\)
0.828943 + 0.559333i \(0.188943\pi\)
\(572\) −216.953 567.787i −0.379288 0.992634i
\(573\) −43.2291 + 43.2291i −0.0754435 + 0.0754435i
\(574\) 106.957 + 579.570i 0.186335 + 1.00970i
\(575\) 479.190i 0.833373i
\(576\) 170.670 + 87.9539i 0.296301 + 0.152698i
\(577\) 563.693 0.976938 0.488469 0.872581i \(-0.337556\pi\)
0.488469 + 0.872581i \(0.337556\pi\)
\(578\) 195.071 35.9992i 0.337493 0.0622824i
\(579\) 446.223 + 446.223i 0.770678 + 0.770678i
\(580\) 19.1222 7.30664i 0.0329693 0.0125977i
\(581\) −220.769 220.769i −0.379981 0.379981i
\(582\) −65.9148 45.3766i −0.113256 0.0779666i
\(583\) 632.465 1.08484
\(584\) −308.152 505.469i −0.527657 0.865530i
\(585\) 138.441i 0.236651i
\(586\) 329.253 + 226.662i 0.561866 + 0.386796i
\(587\) 176.603 176.603i 0.300857 0.300857i −0.540492 0.841349i \(-0.681762\pi\)
0.841349 + 0.540492i \(0.181762\pi\)
\(588\) 101.326 + 45.3000i 0.172324 + 0.0770409i
\(589\) 47.7355 47.7355i 0.0810450 0.0810450i
\(590\) −320.876 + 59.2159i −0.543857 + 0.100366i
\(591\) 319.858i 0.541215i
\(592\) 625.718 + 34.7210i 1.05696 + 0.0586504i
\(593\) −996.597 −1.68060 −0.840301 0.542120i \(-0.817622\pi\)
−0.840301 + 0.542120i \(0.817622\pi\)
\(594\) 14.9246 + 80.8726i 0.0251256 + 0.136149i
\(595\) −192.271 192.271i −0.323144 0.323144i
\(596\) −226.885 101.434i −0.380679 0.170191i
\(597\) 15.6147 + 15.6147i 0.0261553 + 0.0261553i
\(598\) −542.808 + 788.493i −0.907707 + 1.31855i
\(599\) −854.031 −1.42576 −0.712880 0.701286i \(-0.752610\pi\)
−0.712880 + 0.701286i \(0.752610\pi\)
\(600\) −62.7834 + 258.881i −0.104639 + 0.431469i
\(601\) 345.733i 0.575263i −0.957741 0.287631i \(-0.907132\pi\)
0.957741 0.287631i \(-0.0928678\pi\)
\(602\) −197.473 + 286.853i −0.328028 + 0.476499i
\(603\) −190.334 + 190.334i −0.315645 + 0.315645i
\(604\) −833.557 + 318.504i −1.38006 + 0.527325i
\(605\) −99.2029 + 99.2029i −0.163972 + 0.163972i
\(606\) −14.3331 77.6677i −0.0236521 0.128165i
\(607\) 526.354i 0.867141i 0.901120 + 0.433570i \(0.142746\pi\)
−0.901120 + 0.433570i \(0.857254\pi\)
\(608\) −973.859 + 124.407i −1.60174 + 0.204617i
\(609\) 21.1821 0.0347818
\(610\) −344.636 + 63.6007i −0.564977 + 0.104263i
\(611\) −1039.02 1039.02i −1.70053 1.70053i
\(612\) 84.3890 + 220.855i 0.137891 + 0.360874i
\(613\) 410.567 + 410.567i 0.669767 + 0.669767i 0.957662 0.287895i \(-0.0929554\pi\)
−0.287895 + 0.957662i \(0.592955\pi\)
\(614\) −665.256 457.971i −1.08348 0.745881i
\(615\) −213.585 −0.347293
\(616\) 85.6859 353.318i 0.139100 0.573568i
\(617\) 514.755i 0.834287i 0.908841 + 0.417144i \(0.136969\pi\)
−0.908841 + 0.417144i \(0.863031\pi\)
\(618\) 282.019 + 194.146i 0.456342 + 0.314152i
\(619\) 314.214 314.214i 0.507615 0.507615i −0.406179 0.913794i \(-0.633139\pi\)
0.913794 + 0.406179i \(0.133139\pi\)
\(620\) −8.63278 + 19.3096i −0.0139238 + 0.0311446i
\(621\) 91.5828 91.5828i 0.147476 0.147476i
\(622\) −718.772 + 132.645i −1.15558 + 0.213256i
\(623\) 304.276i 0.488404i
\(624\) 396.560 354.863i 0.635512 0.568691i
\(625\) −225.209 −0.360334
\(626\) 167.509 + 907.690i 0.267586 + 1.44998i
\(627\) −297.350 297.350i −0.474243 0.474243i
\(628\) −182.054 + 407.215i −0.289895 + 0.648431i
\(629\) 545.669 + 545.669i 0.867518 + 0.867518i
\(630\) 46.9542 68.2064i 0.0745304 0.108264i
\(631\) −230.081 −0.364629 −0.182315 0.983240i \(-0.558359\pi\)
−0.182315 + 0.983240i \(0.558359\pi\)
\(632\) 17.1842 + 28.1877i 0.0271902 + 0.0446008i
\(633\) 21.0533i 0.0332596i
\(634\) −511.967 + 743.692i −0.807519 + 1.17302i
\(635\) 62.6875 62.6875i 0.0987205 0.0987205i
\(636\) 197.643 + 517.252i 0.310760 + 0.813290i
\(637\) 217.526 217.526i 0.341484 0.341484i
\(638\) 6.11654 + 33.1440i 0.00958705 + 0.0519498i
\(639\) 130.457i 0.204158i
\(640\) 271.116 145.321i 0.423618 0.227065i
\(641\) 746.825 1.16509 0.582547 0.812797i \(-0.302056\pi\)
0.582547 + 0.812797i \(0.302056\pi\)
\(642\) −75.4705 + 13.9277i −0.117555 + 0.0216942i
\(643\) 548.092 + 548.092i 0.852398 + 0.852398i 0.990428 0.138030i \(-0.0440772\pi\)
−0.138030 + 0.990428i \(0.544077\pi\)
\(644\) −534.858 + 204.370i −0.830524 + 0.317345i
\(645\) −89.2426 89.2426i −0.138361 0.138361i
\(646\) −995.803 685.523i −1.54149 1.06118i
\(647\) 1055.00 1.63060 0.815302 0.579036i \(-0.196571\pi\)
0.815302 + 0.579036i \(0.196571\pi\)
\(648\) −61.4766 + 37.4783i −0.0948714 + 0.0578369i
\(649\) 537.223i 0.827771i
\(650\) 608.150 + 418.658i 0.935616 + 0.644090i
\(651\) −15.4762 + 15.4762i −0.0237730 + 0.0237730i
\(652\) 269.794 + 120.617i 0.413794 + 0.184995i
\(653\) −854.888 + 854.888i −1.30917 + 1.30917i −0.387155 + 0.922015i \(0.626542\pi\)
−0.922015 + 0.387155i \(0.873458\pi\)
\(654\) −408.024 + 75.2985i −0.623889 + 0.115135i
\(655\) 137.350i 0.209694i
\(656\) −547.480 611.809i −0.834574 0.932636i
\(657\) 221.998 0.337896
\(658\) −159.502 864.302i −0.242405 1.31353i
\(659\) −768.766 768.766i −1.16656 1.16656i −0.983009 0.183556i \(-0.941239\pi\)
−0.183556 0.983009i \(-0.558761\pi\)
\(660\) 120.282 + 53.7746i 0.182246 + 0.0814767i
\(661\) 312.323 + 312.323i 0.472500 + 0.472500i 0.902723 0.430223i \(-0.141565\pi\)
−0.430223 + 0.902723i \(0.641565\pi\)
\(662\) −137.587 + 199.861i −0.207835 + 0.301904i
\(663\) 655.292 0.988374
\(664\) 422.678 + 102.507i 0.636563 + 0.154378i
\(665\) 423.420i 0.636721i
\(666\) −133.257 + 193.572i −0.200086 + 0.290648i
\(667\) 37.5333 37.5333i 0.0562719 0.0562719i
\(668\) 360.649 137.805i 0.539894 0.206295i
\(669\) 61.9610 61.9610i 0.0926173 0.0926173i
\(670\) 78.2626 + 424.085i 0.116810 + 0.632963i
\(671\) 577.004i 0.859916i
\(672\) 315.733 40.3337i 0.469840 0.0600204i
\(673\) 740.565 1.10039 0.550197 0.835035i \(-0.314553\pi\)
0.550197 + 0.835035i \(0.314553\pi\)
\(674\) 507.936 93.7367i 0.753614 0.139075i
\(675\) −70.6362 70.6362i −0.104646 0.104646i
\(676\) −285.166 746.308i −0.421843 1.10401i
\(677\) −547.118 547.118i −0.808151 0.808151i 0.176203 0.984354i \(-0.443619\pi\)
−0.984354 + 0.176203i \(0.943619\pi\)
\(678\) −182.197 125.427i −0.268727 0.184995i
\(679\) −132.664 −0.195381
\(680\) 368.115 + 89.2746i 0.541346 + 0.131286i
\(681\) 77.6918i 0.114085i
\(682\) −28.6848 19.7470i −0.0420598 0.0289545i
\(683\) −407.623 + 407.623i −0.596813 + 0.596813i −0.939463 0.342650i \(-0.888676\pi\)
0.342650 + 0.939463i \(0.388676\pi\)
\(684\) 150.263 336.105i 0.219682 0.491381i
\(685\) −430.772 + 430.772i −0.628864 + 0.628864i
\(686\) 734.396 135.529i 1.07055 0.197564i
\(687\) 415.987i 0.605513i
\(688\) 26.8786 484.388i 0.0390678 0.704052i
\(689\) 1534.73 2.22747
\(690\) −37.6576 204.057i −0.0545763 0.295735i
\(691\) 17.6037 + 17.6037i 0.0254757 + 0.0254757i 0.719730 0.694254i \(-0.244266\pi\)
−0.694254 + 0.719730i \(0.744266\pi\)
\(692\) −106.915 + 239.144i −0.154501 + 0.345584i
\(693\) 96.4033 + 96.4033i 0.139110 + 0.139110i
\(694\) 44.4640 64.5892i 0.0640692 0.0930680i
\(695\) 230.448 0.331579
\(696\) −25.1949 + 15.3597i −0.0361996 + 0.0220685i
\(697\) 1010.98i 1.45047i
\(698\) 514.973 748.058i 0.737783 1.07172i
\(699\) −444.682 + 444.682i −0.636169 + 0.636169i
\(700\) 157.627 + 412.526i 0.225181 + 0.589323i
\(701\) 164.273 164.273i 0.234341 0.234341i −0.580161 0.814502i \(-0.697010\pi\)
0.814502 + 0.580161i \(0.197010\pi\)
\(702\) 36.2157 + 196.244i 0.0515893 + 0.279550i
\(703\) 1201.68i 1.70935i
\(704\) 154.281 + 482.385i 0.219150 + 0.685205i
\(705\) 318.516 0.451795
\(706\) −474.710 + 87.6051i −0.672394 + 0.124087i
\(707\) −92.5829 92.5829i −0.130952 0.130952i
\(708\) 439.361 167.881i 0.620566 0.237119i
\(709\) 422.796 + 422.796i 0.596327 + 0.596327i 0.939333 0.343006i \(-0.111445\pi\)
−0.343006 + 0.939333i \(0.611445\pi\)
\(710\) 172.157 + 118.515i 0.242475 + 0.166923i
\(711\) −12.3798 −0.0174118
\(712\) 220.638 + 361.919i 0.309886 + 0.508313i
\(713\) 54.8457i 0.0769224i
\(714\) 322.847 + 222.252i 0.452166 + 0.311277i
\(715\) 258.220 258.220i 0.361146 0.361146i
\(716\) −483.085 215.973i −0.674699 0.301639i
\(717\) 33.8375 33.8375i 0.0471932 0.0471932i
\(718\) −715.559 + 132.052i −0.996601 + 0.183917i
\(719\) 1029.00i 1.43115i 0.698534 + 0.715577i \(0.253836\pi\)
−0.698534 + 0.715577i \(0.746164\pi\)
\(720\) −6.39107 + 115.175i −0.00887649 + 0.159966i
\(721\) 567.607 0.787250
\(722\) 210.621 + 1141.30i 0.291719 + 1.58075i
\(723\) −450.855 450.855i −0.623589 0.623589i
\(724\) −598.074 267.381i −0.826068 0.369311i
\(725\) −28.9488 28.9488i −0.0399293 0.0399293i
\(726\) 114.672 166.574i 0.157950 0.229441i
\(727\) −475.001 −0.653372 −0.326686 0.945133i \(-0.605932\pi\)
−0.326686 + 0.945133i \(0.605932\pi\)
\(728\) 207.924 857.354i 0.285609 1.17768i
\(729\) 27.0000i 0.0370370i
\(730\) 201.677 292.960i 0.276270 0.401314i
\(731\) 422.419 422.419i 0.577865 0.577865i
\(732\) 471.894 180.312i 0.644664 0.246328i
\(733\) −344.939 + 344.939i −0.470586 + 0.470586i −0.902104 0.431519i \(-0.857978\pi\)
0.431519 + 0.902104i \(0.357978\pi\)
\(734\) −149.322 809.141i −0.203437 1.10237i
\(735\) 66.6831i 0.0907253i
\(736\) 487.989 630.926i 0.663028 0.857237i
\(737\) −710.021 −0.963393
\(738\) 302.764 55.8734i 0.410249 0.0757092i
\(739\) 363.340 + 363.340i 0.491665 + 0.491665i 0.908831 0.417166i \(-0.136976\pi\)
−0.417166 + 0.908831i \(0.636976\pi\)
\(740\) 134.388 + 351.706i 0.181605 + 0.475278i
\(741\) −721.544 721.544i −0.973744 0.973744i
\(742\) 756.123 + 520.525i 1.01903 + 0.701516i
\(743\) 271.667 0.365636 0.182818 0.983147i \(-0.441478\pi\)
0.182818 + 0.983147i \(0.441478\pi\)
\(744\) 7.18588 29.6303i 0.00965843 0.0398257i
\(745\) 149.314i 0.200421i
\(746\) −525.771 361.948i −0.704787 0.485185i
\(747\) −115.328 + 115.328i −0.154389 + 0.154389i
\(748\) −254.536 + 569.340i −0.340288 + 0.761150i
\(749\) −89.9637 + 89.9637i −0.120112 + 0.120112i
\(750\) −362.051 + 66.8145i −0.482735 + 0.0890860i
\(751\) 1105.27i 1.47173i 0.677128 + 0.735866i \(0.263224\pi\)
−0.677128 + 0.735866i \(0.736776\pi\)
\(752\) 816.447 + 912.380i 1.08570 + 1.21327i
\(753\) −807.937 −1.07296
\(754\) 14.8423 + 80.4265i 0.0196847 + 0.106666i
\(755\) −379.087 379.087i −0.502102 0.502102i
\(756\) −48.7163 + 108.968i −0.0644396 + 0.144137i
\(757\) 554.565 + 554.565i 0.732583 + 0.732583i 0.971131 0.238548i \(-0.0766713\pi\)
−0.238548 + 0.971131i \(0.576671\pi\)
\(758\) −252.091 + 366.191i −0.332573 + 0.483102i
\(759\) 341.641 0.450119
\(760\) −307.033 503.634i −0.403990 0.662676i
\(761\) 188.496i 0.247695i −0.992301 0.123847i \(-0.960477\pi\)
0.992301 0.123847i \(-0.0395234\pi\)
\(762\) −72.4626 + 105.260i −0.0950952 + 0.138137i
\(763\) −486.380 + 486.380i −0.637457 + 0.637457i
\(764\) −50.3939 131.886i −0.0659605 0.172625i
\(765\) −100.441 + 100.441i −0.131295 + 0.131295i
\(766\) −255.290 1383.35i −0.333277 1.80594i
\(767\) 1303.62i 1.69963i
\(768\) −346.299 + 276.921i −0.450910 + 0.360574i
\(769\) −593.354 −0.771592 −0.385796 0.922584i \(-0.626073\pi\)
−0.385796 + 0.922584i \(0.626073\pi\)
\(770\) 214.798 39.6397i 0.278958 0.0514801i
\(771\) −28.9973 28.9973i −0.0376100 0.0376100i