Properties

Label 105.3.n.a.31.2
Level 105
Weight 3
Character 105.31
Analytic conductor 2.861
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.523596960000.16
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.2
Root \(-0.336732 - 0.583237i\) of \(x^{8} - 2 x^{7} + 13 x^{6} - 2 x^{5} + 91 x^{4} - 50 x^{3} + 190 x^{2} + 100 x + 100\)
Character \(\chi\) \(=\) 105.31
Dual form 105.3.n.a.61.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.336732 - 0.583237i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.77322 - 3.07131i) q^{4} +(1.93649 - 1.11803i) q^{5} +1.16647i q^{6} +(-6.82455 - 1.55742i) q^{7} -5.08226 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.336732 - 0.583237i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.77322 - 3.07131i) q^{4} +(1.93649 - 1.11803i) q^{5} +1.16647i q^{6} +(-6.82455 - 1.55742i) q^{7} -5.08226 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.30416 - 0.752955i) q^{10} +(0.0223800 - 0.0387632i) q^{11} +(-5.31967 + 3.07131i) q^{12} -23.0010i q^{13} +(1.38970 + 4.50476i) q^{14} -3.87298 q^{15} +(-5.38154 - 9.32109i) q^{16} +(-8.16292 - 4.71286i) q^{17} +(1.01020 - 1.74971i) q^{18} +(0.991050 - 0.572183i) q^{19} -7.93010i q^{20} +(8.88806 + 8.24636i) q^{21} -0.0301442 q^{22} +(22.1202 + 38.3133i) q^{23} +(7.62339 + 4.40136i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-13.4150 + 7.74518i) q^{26} -5.19615i q^{27} +(-16.8848 + 18.1987i) q^{28} +53.0004 q^{29} +(1.30416 + 2.25887i) q^{30} +(19.5690 + 11.2982i) q^{31} +(-13.7888 + 23.8829i) q^{32} +(-0.0671399 + 0.0387632i) q^{33} +6.34788i q^{34} +(-14.9569 + 4.61414i) q^{35} +10.6393 q^{36} +(-21.1418 - 36.6186i) q^{37} +(-0.667436 - 0.385344i) q^{38} +(-19.9195 + 34.5015i) q^{39} +(-9.84175 + 5.68214i) q^{40} -38.2787i q^{41} +(1.81669 - 7.96065i) q^{42} +76.5222 q^{43} +(-0.0793693 - 0.137472i) q^{44} +(5.80948 + 3.35410i) q^{45} +(14.8971 - 25.8026i) q^{46} +(-23.5070 + 13.5718i) q^{47} +18.6422i q^{48} +(44.1489 + 21.2574i) q^{49} -3.36732 q^{50} +(8.16292 + 14.1386i) q^{51} +(-70.6434 - 40.7860i) q^{52} +(-9.49388 + 16.4439i) q^{53} +(-3.03059 + 1.74971i) q^{54} -0.100086i q^{55} +(34.6841 + 7.91521i) q^{56} -1.98210 q^{57} +(-17.8469 - 30.9118i) q^{58} +(-4.21731 - 2.43486i) q^{59} +(-6.86766 + 11.8951i) q^{60} +(-33.6432 + 19.4239i) q^{61} -15.2178i q^{62} +(-6.19052 - 20.0668i) q^{63} -24.4798 q^{64} +(-25.7159 - 44.5413i) q^{65} +(0.0452163 + 0.0261056i) q^{66} +(3.50439 - 6.06978i) q^{67} +(-28.9494 + 16.7139i) q^{68} -76.6266i q^{69} +(7.72761 + 7.16970i) q^{70} -46.8735 q^{71} +(-7.62339 - 13.2041i) q^{72} +(72.3956 + 41.7976i) q^{73} +(-14.2382 + 24.6613i) q^{74} +(-7.50000 + 4.33013i) q^{75} -4.05843i q^{76} +(-0.213104 + 0.229686i) q^{77} +26.8301 q^{78} +(-10.2397 - 17.7357i) q^{79} +(-20.8426 - 12.0335i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-22.3256 + 12.8897i) q^{82} -125.683i q^{83} +(41.0877 - 12.6754i) q^{84} -21.0766 q^{85} +(-25.7674 - 44.6305i) q^{86} +(-79.5006 - 45.8997i) q^{87} +(-0.113741 + 0.197005i) q^{88} +(40.4455 - 23.3512i) q^{89} -4.51773i q^{90} +(-35.8223 + 156.972i) q^{91} +156.896 q^{92} +(-19.5690 - 33.8945i) q^{93} +(15.8311 + 9.14010i) q^{94} +(1.27944 - 2.21606i) q^{95} +(41.3663 - 23.8829i) q^{96} -3.11494i q^{97} +(-2.46826 - 32.9073i) q^{98} +0.134280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 12q^{3} - 6q^{4} - 16q^{7} - 32q^{8} + 12q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 12q^{3} - 6q^{4} - 16q^{7} - 32q^{8} + 12q^{9} + 20q^{11} + 18q^{12} - 16q^{14} - 2q^{16} - 18q^{17} - 6q^{18} + 48q^{21} - 16q^{22} + 62q^{23} + 48q^{24} + 20q^{25} + 120q^{26} - 120q^{28} - 100q^{29} - 126q^{31} + 36q^{32} - 60q^{33} - 36q^{36} - 80q^{37} + 114q^{38} - 12q^{39} + 90q^{40} + 90q^{42} + 352q^{43} - 18q^{44} - 82q^{46} - 72q^{47} + 38q^{49} + 20q^{50} + 18q^{51} - 48q^{52} - 76q^{53} + 18q^{54} + 196q^{56} - 40q^{58} - 54q^{59} - 60q^{60} - 396q^{61} - 96q^{63} - 4q^{64} - 60q^{65} + 24q^{66} + 184q^{67} - 312q^{68} + 164q^{71} - 48q^{72} + 348q^{73} - 140q^{74} - 60q^{75} + 152q^{77} - 240q^{78} - 206q^{79} - 36q^{81} + 204q^{82} + 132q^{84} - 60q^{85} + 178q^{86} + 150q^{87} + 124q^{88} + 282q^{89} - 114q^{91} - 288q^{92} + 126q^{93} + 30q^{94} - 120q^{95} - 108q^{96} - 592q^{98} + 120q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.336732 0.583237i −0.168366 0.291618i 0.769480 0.638671i \(-0.220516\pi\)
−0.937845 + 0.347053i \(0.887182\pi\)
\(3\) −1.50000 0.866025i −0.500000 0.288675i
\(4\) 1.77322 3.07131i 0.443306 0.767828i
\(5\) 1.93649 1.11803i 0.387298 0.223607i
\(6\) 1.16647i 0.194412i
\(7\) −6.82455 1.55742i −0.974935 0.222489i
\(8\) −5.08226 −0.635282
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) −1.30416 0.752955i −0.130416 0.0752955i
\(11\) 0.0223800 0.0387632i 0.00203454 0.00352393i −0.865006 0.501761i \(-0.832686\pi\)
0.867041 + 0.498237i \(0.166019\pi\)
\(12\) −5.31967 + 3.07131i −0.443306 + 0.255943i
\(13\) 23.0010i 1.76931i −0.466246 0.884655i \(-0.654394\pi\)
0.466246 0.884655i \(-0.345606\pi\)
\(14\) 1.38970 + 4.50476i 0.0992641 + 0.321768i
\(15\) −3.87298 −0.258199
\(16\) −5.38154 9.32109i −0.336346 0.582568i
\(17\) −8.16292 4.71286i −0.480172 0.277227i 0.240316 0.970695i \(-0.422749\pi\)
−0.720488 + 0.693467i \(0.756082\pi\)
\(18\) 1.01020 1.74971i 0.0561220 0.0972061i
\(19\) 0.991050 0.572183i 0.0521605 0.0301149i −0.473693 0.880690i \(-0.657079\pi\)
0.525853 + 0.850575i \(0.323746\pi\)
\(20\) 7.93010i 0.396505i
\(21\) 8.88806 + 8.24636i 0.423241 + 0.392684i
\(22\) −0.0301442 −0.00137019
\(23\) 22.1202 + 38.3133i 0.961748 + 1.66580i 0.718110 + 0.695929i \(0.245007\pi\)
0.243637 + 0.969866i \(0.421659\pi\)
\(24\) 7.62339 + 4.40136i 0.317641 + 0.183390i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) −13.4150 + 7.74518i −0.515963 + 0.297891i
\(27\) 5.19615i 0.192450i
\(28\) −16.8848 + 18.1987i −0.603028 + 0.649952i
\(29\) 53.0004 1.82760 0.913799 0.406166i \(-0.133134\pi\)
0.913799 + 0.406166i \(0.133134\pi\)
\(30\) 1.30416 + 2.25887i 0.0434719 + 0.0752955i
\(31\) 19.5690 + 11.2982i 0.631258 + 0.364457i 0.781239 0.624232i \(-0.214588\pi\)
−0.149981 + 0.988689i \(0.547921\pi\)
\(32\) −13.7888 + 23.8829i −0.430899 + 0.746340i
\(33\) −0.0671399 + 0.0387632i −0.00203454 + 0.00117464i
\(34\) 6.34788i 0.186702i
\(35\) −14.9569 + 4.61414i −0.427341 + 0.131833i
\(36\) 10.6393 0.295537
\(37\) −21.1418 36.6186i −0.571400 0.989693i −0.996423 0.0845106i \(-0.973067\pi\)
0.425023 0.905183i \(-0.360266\pi\)
\(38\) −0.667436 0.385344i −0.0175641 0.0101406i
\(39\) −19.9195 + 34.5015i −0.510756 + 0.884655i
\(40\) −9.84175 + 5.68214i −0.246044 + 0.142053i
\(41\) 38.2787i 0.933628i −0.884356 0.466814i \(-0.845402\pi\)
0.884356 0.466814i \(-0.154598\pi\)
\(42\) 1.81669 7.96065i 0.0432545 0.189539i
\(43\) 76.5222 1.77959 0.889793 0.456365i \(-0.150849\pi\)
0.889793 + 0.456365i \(0.150849\pi\)
\(44\) −0.0793693 0.137472i −0.00180385 0.00312436i
\(45\) 5.80948 + 3.35410i 0.129099 + 0.0745356i
\(46\) 14.8971 25.8026i 0.323851 0.560926i
\(47\) −23.5070 + 13.5718i −0.500149 + 0.288761i −0.728775 0.684753i \(-0.759910\pi\)
0.228626 + 0.973514i \(0.426577\pi\)
\(48\) 18.6422i 0.388379i
\(49\) 44.1489 + 21.2574i 0.900998 + 0.433824i
\(50\) −3.36732 −0.0673464
\(51\) 8.16292 + 14.1386i 0.160057 + 0.277227i
\(52\) −70.6434 40.7860i −1.35853 0.784345i
\(53\) −9.49388 + 16.4439i −0.179130 + 0.310262i −0.941583 0.336782i \(-0.890662\pi\)
0.762453 + 0.647044i \(0.223995\pi\)
\(54\) −3.03059 + 1.74971i −0.0561220 + 0.0324020i
\(55\) 0.100086i 0.00181975i
\(56\) 34.6841 + 7.91521i 0.619359 + 0.141343i
\(57\) −1.98210 −0.0347737
\(58\) −17.8469 30.9118i −0.307705 0.532961i
\(59\) −4.21731 2.43486i −0.0714798 0.0412689i 0.463834 0.885922i \(-0.346473\pi\)
−0.535314 + 0.844653i \(0.679807\pi\)
\(60\) −6.86766 + 11.8951i −0.114461 + 0.198252i
\(61\) −33.6432 + 19.4239i −0.551528 + 0.318425i −0.749738 0.661735i \(-0.769821\pi\)
0.198210 + 0.980160i \(0.436487\pi\)
\(62\) 15.2178i 0.245449i
\(63\) −6.19052 20.0668i −0.0982623 0.318521i
\(64\) −24.4798 −0.382497
\(65\) −25.7159 44.5413i −0.395630 0.685251i
\(66\) 0.0452163 + 0.0261056i 0.000685095 + 0.000395540i
\(67\) 3.50439 6.06978i 0.0523043 0.0905938i −0.838688 0.544612i \(-0.816677\pi\)
0.890992 + 0.454019i \(0.150010\pi\)
\(68\) −28.9494 + 16.7139i −0.425726 + 0.245793i
\(69\) 76.6266i 1.11053i
\(70\) 7.72761 + 7.16970i 0.110394 + 0.102424i
\(71\) −46.8735 −0.660190 −0.330095 0.943948i \(-0.607081\pi\)
−0.330095 + 0.943948i \(0.607081\pi\)
\(72\) −7.62339 13.2041i −0.105880 0.183390i
\(73\) 72.3956 + 41.7976i 0.991720 + 0.572570i 0.905788 0.423731i \(-0.139280\pi\)
0.0859319 + 0.996301i \(0.472613\pi\)
\(74\) −14.2382 + 24.6613i −0.192408 + 0.333261i
\(75\) −7.50000 + 4.33013i −0.100000 + 0.0577350i
\(76\) 4.05843i 0.0534004i
\(77\) −0.213104 + 0.229686i −0.00276758 + 0.00298294i
\(78\) 26.8301 0.343975
\(79\) −10.2397 17.7357i −0.129617 0.224502i 0.793912 0.608033i \(-0.208041\pi\)
−0.923528 + 0.383531i \(0.874708\pi\)
\(80\) −20.8426 12.0335i −0.260533 0.150419i
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −22.3256 + 12.8897i −0.272263 + 0.157191i
\(83\) 125.683i 1.51425i −0.653271 0.757124i \(-0.726604\pi\)
0.653271 0.757124i \(-0.273396\pi\)
\(84\) 41.0877 12.6754i 0.489139 0.150897i
\(85\) −21.0766 −0.247960
\(86\) −25.7674 44.6305i −0.299621 0.518960i
\(87\) −79.5006 45.8997i −0.913799 0.527582i
\(88\) −0.113741 + 0.197005i −0.00129251 + 0.00223869i
\(89\) 40.4455 23.3512i 0.454444 0.262373i −0.255261 0.966872i \(-0.582162\pi\)
0.709705 + 0.704499i \(0.248828\pi\)
\(90\) 4.51773i 0.0501970i
\(91\) −35.8223 + 156.972i −0.393651 + 1.72496i
\(92\) 156.896 1.70539
\(93\) −19.5690 33.8945i −0.210419 0.364457i
\(94\) 15.8311 + 9.14010i 0.168416 + 0.0972351i
\(95\) 1.27944 2.21606i 0.0134678 0.0233269i
\(96\) 41.3663 23.8829i 0.430899 0.248780i
\(97\) 3.11494i 0.0321128i −0.999871 0.0160564i \(-0.994889\pi\)
0.999871 0.0160564i \(-0.00511112\pi\)
\(98\) −2.46826 32.9073i −0.0251863 0.335789i
\(99\) 0.134280 0.00135636
\(100\) −8.86612 15.3566i −0.0886612 0.153566i
\(101\) −77.4555 44.7189i −0.766886 0.442762i 0.0648768 0.997893i \(-0.479335\pi\)
−0.831763 + 0.555132i \(0.812668\pi\)
\(102\) 5.49743 9.52183i 0.0538964 0.0933512i
\(103\) −79.1385 + 45.6906i −0.768335 + 0.443598i −0.832280 0.554355i \(-0.812965\pi\)
0.0639453 + 0.997953i \(0.479632\pi\)
\(104\) 116.897i 1.12401i
\(105\) 26.4314 + 6.03186i 0.251727 + 0.0574463i
\(106\) 12.7876 0.120637
\(107\) 52.5515 + 91.0219i 0.491136 + 0.850672i 0.999948 0.0102057i \(-0.00324864\pi\)
−0.508812 + 0.860877i \(0.669915\pi\)
\(108\) −15.9590 9.21394i −0.147769 0.0853143i
\(109\) −27.8507 + 48.2388i −0.255511 + 0.442558i −0.965034 0.262124i \(-0.915577\pi\)
0.709523 + 0.704682i \(0.248910\pi\)
\(110\) −0.0583739 + 0.0337022i −0.000530672 + 0.000306384i
\(111\) 73.2373i 0.659795i
\(112\) 22.2097 + 71.9936i 0.198301 + 0.642800i
\(113\) −5.25425 −0.0464978 −0.0232489 0.999730i \(-0.507401\pi\)
−0.0232489 + 0.999730i \(0.507401\pi\)
\(114\) 0.667436 + 1.15603i 0.00585470 + 0.0101406i
\(115\) 85.6711 + 49.4623i 0.744967 + 0.430107i
\(116\) 93.9815 162.781i 0.810185 1.40328i
\(117\) 59.7584 34.5015i 0.510756 0.294885i
\(118\) 3.27958i 0.0277931i
\(119\) 48.3683 + 44.8763i 0.406457 + 0.377111i
\(120\) 19.6835 0.164029
\(121\) 60.4990 + 104.787i 0.499992 + 0.866011i
\(122\) 22.6575 + 13.0813i 0.185717 + 0.107224i
\(123\) −33.1504 + 57.4181i −0.269515 + 0.466814i
\(124\) 69.4005 40.0684i 0.559681 0.323132i
\(125\) 11.1803i 0.0894427i
\(126\) −9.61916 + 10.3677i −0.0763425 + 0.0822832i
\(127\) −5.54989 −0.0436999 −0.0218500 0.999761i \(-0.506956\pi\)
−0.0218500 + 0.999761i \(0.506956\pi\)
\(128\) 63.3983 + 109.809i 0.495299 + 0.857883i
\(129\) −114.783 66.2701i −0.889793 0.513722i
\(130\) −17.3187 + 29.9969i −0.133221 + 0.230746i
\(131\) −144.212 + 83.2606i −1.10085 + 0.635577i −0.936445 0.350815i \(-0.885904\pi\)
−0.164407 + 0.986393i \(0.552571\pi\)
\(132\) 0.274943i 0.00208290i
\(133\) −7.65460 + 2.36141i −0.0575534 + 0.0177550i
\(134\) −4.72016 −0.0352251
\(135\) −5.80948 10.0623i −0.0430331 0.0745356i
\(136\) 41.4861 + 23.9520i 0.305045 + 0.176118i
\(137\) −36.4731 + 63.1733i −0.266227 + 0.461119i −0.967884 0.251395i \(-0.919111\pi\)
0.701657 + 0.712515i \(0.252444\pi\)
\(138\) −44.6914 + 25.8026i −0.323851 + 0.186975i
\(139\) 114.994i 0.827292i −0.910438 0.413646i \(-0.864255\pi\)
0.910438 0.413646i \(-0.135745\pi\)
\(140\) −12.3505 + 54.1193i −0.0882178 + 0.386567i
\(141\) 47.0140 0.333433
\(142\) 15.7838 + 27.3383i 0.111153 + 0.192523i
\(143\) −0.891594 0.514762i −0.00623492 0.00359973i
\(144\) 16.1446 27.9633i 0.112115 0.194189i
\(145\) 102.635 59.2562i 0.707826 0.408664i
\(146\) 56.2983i 0.385605i
\(147\) −47.8139 70.1201i −0.325265 0.477008i
\(148\) −149.956 −1.01322
\(149\) −36.3729 62.9997i −0.244113 0.422817i 0.717769 0.696282i \(-0.245164\pi\)
−0.961882 + 0.273465i \(0.911830\pi\)
\(150\) 5.05098 + 2.91618i 0.0336732 + 0.0194412i
\(151\) 63.5643 110.097i 0.420956 0.729117i −0.575078 0.818099i \(-0.695028\pi\)
0.996033 + 0.0889823i \(0.0283615\pi\)
\(152\) −5.03677 + 2.90798i −0.0331366 + 0.0191315i
\(153\) 28.2772i 0.184818i
\(154\) 0.205720 + 0.0469471i 0.00133585 + 0.000304851i
\(155\) 50.5270 0.325980
\(156\) 70.6434 + 122.358i 0.452842 + 0.784345i
\(157\) 130.826 + 75.5327i 0.833290 + 0.481100i 0.854978 0.518665i \(-0.173571\pi\)
−0.0216880 + 0.999765i \(0.506904\pi\)
\(158\) −6.89607 + 11.9443i −0.0436460 + 0.0755971i
\(159\) 28.4816 16.4439i 0.179130 0.103421i
\(160\) 61.6653i 0.385408i
\(161\) −91.2904 295.921i −0.567021 1.83802i
\(162\) 6.06117 0.0374146
\(163\) 29.9639 + 51.8990i 0.183828 + 0.318399i 0.943181 0.332280i \(-0.107818\pi\)
−0.759353 + 0.650679i \(0.774485\pi\)
\(164\) −117.566 67.8768i −0.716866 0.413883i
\(165\) −0.0866772 + 0.150129i −0.000525316 + 0.000909875i
\(166\) −73.3027 + 42.3213i −0.441582 + 0.254948i
\(167\) 224.089i 1.34185i 0.741526 + 0.670924i \(0.234102\pi\)
−0.741526 + 0.670924i \(0.765898\pi\)
\(168\) −45.1714 41.9101i −0.268877 0.249465i
\(169\) −360.047 −2.13046
\(170\) 7.09715 + 12.2926i 0.0417479 + 0.0723096i
\(171\) 2.97315 + 1.71655i 0.0173868 + 0.0100383i
\(172\) 135.691 235.024i 0.788901 1.36642i
\(173\) 165.080 95.3092i 0.954221 0.550920i 0.0598317 0.998208i \(-0.480944\pi\)
0.894390 + 0.447288i \(0.147610\pi\)
\(174\) 61.8235i 0.355307i
\(175\) −23.8052 + 25.6576i −0.136030 + 0.146615i
\(176\) −0.481754 −0.00273724
\(177\) 4.21731 + 7.30459i 0.0238266 + 0.0412689i
\(178\) −27.2386 15.7262i −0.153026 0.0883494i
\(179\) −108.931 + 188.674i −0.608553 + 1.05404i 0.382926 + 0.923779i \(0.374916\pi\)
−0.991479 + 0.130265i \(0.958417\pi\)
\(180\) 20.6030 11.8951i 0.114461 0.0660841i
\(181\) 39.0804i 0.215914i −0.994156 0.107957i \(-0.965569\pi\)
0.994156 0.107957i \(-0.0344309\pi\)
\(182\) 103.614 31.9645i 0.569308 0.175629i
\(183\) 67.2865 0.367686
\(184\) −112.421 194.718i −0.610981 1.05825i
\(185\) −81.8818 47.2745i −0.442604 0.255538i
\(186\) −13.1790 + 22.8267i −0.0708549 + 0.122724i
\(187\) −0.365372 + 0.210947i −0.00195386 + 0.00112806i
\(188\) 96.2632i 0.512038i
\(189\) −8.09259 + 35.4614i −0.0428179 + 0.187626i
\(190\) −1.72331 −0.00907006
\(191\) −94.7586 164.127i −0.496118 0.859302i 0.503872 0.863778i \(-0.331908\pi\)
−0.999990 + 0.00447651i \(0.998575\pi\)
\(192\) 36.7197 + 21.2001i 0.191249 + 0.110417i
\(193\) 136.570 236.547i 0.707619 1.22563i −0.258119 0.966113i \(-0.583103\pi\)
0.965738 0.259519i \(-0.0835640\pi\)
\(194\) −1.81675 + 1.04890i −0.00936467 + 0.00540669i
\(195\) 89.0826i 0.456834i
\(196\) 143.574 97.9010i 0.732520 0.499495i
\(197\) 198.898 1.00963 0.504817 0.863226i \(-0.331560\pi\)
0.504817 + 0.863226i \(0.331560\pi\)
\(198\) −0.0452163 0.0783168i −0.000228365 0.000395540i
\(199\) 33.2334 + 19.1873i 0.167002 + 0.0964185i 0.581171 0.813781i \(-0.302595\pi\)
−0.414170 + 0.910200i \(0.635928\pi\)
\(200\) −12.7056 + 22.0068i −0.0635282 + 0.110034i
\(201\) −10.5132 + 6.06978i −0.0523043 + 0.0301979i
\(202\) 60.2331i 0.298184i
\(203\) −361.704 82.5438i −1.78179 0.406620i
\(204\) 57.8987 0.283817
\(205\) −42.7969 74.1265i −0.208766 0.361593i
\(206\) 53.2969 + 30.7710i 0.258723 + 0.149374i
\(207\) −66.3606 + 114.940i −0.320583 + 0.555265i
\(208\) −214.395 + 123.781i −1.03074 + 0.595100i
\(209\) 0.0512217i 0.000245080i
\(210\) −5.38228 17.4469i −0.0256299 0.0830802i
\(211\) −127.283 −0.603238 −0.301619 0.953429i \(-0.597527\pi\)
−0.301619 + 0.953429i \(0.597527\pi\)
\(212\) 33.6695 + 58.3173i 0.158819 + 0.275082i
\(213\) 70.3102 + 40.5936i 0.330095 + 0.190580i
\(214\) 35.3915 61.2999i 0.165381 0.286448i
\(215\) 148.185 85.5544i 0.689230 0.397927i
\(216\) 26.4082i 0.122260i
\(217\) −115.954 107.582i −0.534349 0.495770i
\(218\) 37.5129 0.172077
\(219\) −72.3956 125.393i −0.330573 0.572570i
\(220\) −0.307396 0.177475i −0.00139725 0.000806705i
\(221\) −108.401 + 187.756i −0.490501 + 0.849573i
\(222\) 42.7147 24.6613i 0.192408 0.111087i
\(223\) 293.558i 1.31641i −0.752841 0.658203i \(-0.771317\pi\)
0.752841 0.658203i \(-0.228683\pi\)
\(224\) 131.298 141.515i 0.586151 0.631763i
\(225\) 15.0000 0.0666667
\(226\) 1.76927 + 3.06447i 0.00782864 + 0.0135596i
\(227\) 186.611 + 107.740i 0.822077 + 0.474626i 0.851132 0.524952i \(-0.175917\pi\)
−0.0290554 + 0.999578i \(0.509250\pi\)
\(228\) −3.51471 + 6.08765i −0.0154154 + 0.0267002i
\(229\) 124.938 72.1332i 0.545582 0.314992i −0.201756 0.979436i \(-0.564665\pi\)
0.747338 + 0.664444i \(0.231332\pi\)
\(230\) 66.6221i 0.289661i
\(231\) 0.518570 0.159976i 0.00224489 0.000692539i
\(232\) −269.361 −1.16104
\(233\) 143.216 + 248.058i 0.614662 + 1.06463i 0.990444 + 0.137918i \(0.0440410\pi\)
−0.375781 + 0.926708i \(0.622626\pi\)
\(234\) −40.2451 23.2355i −0.171988 0.0992971i
\(235\) −30.3474 + 52.5633i −0.129138 + 0.223673i
\(236\) −14.9565 + 8.63511i −0.0633748 + 0.0365895i
\(237\) 35.4714i 0.149668i
\(238\) 9.88632 43.3214i 0.0415392 0.182023i
\(239\) −413.420 −1.72979 −0.864895 0.501954i \(-0.832615\pi\)
−0.864895 + 0.501954i \(0.832615\pi\)
\(240\) 20.8426 + 36.1004i 0.0868442 + 0.150419i
\(241\) 256.252 + 147.947i 1.06329 + 0.613890i 0.926340 0.376689i \(-0.122937\pi\)
0.136948 + 0.990578i \(0.456271\pi\)
\(242\) 40.7439 70.5705i 0.168363 0.291613i
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 137.772i 0.564639i
\(245\) 109.260 8.19523i 0.445961 0.0334499i
\(246\) 44.6511 0.181509
\(247\) −13.1608 22.7952i −0.0532826 0.0922881i
\(248\) −99.4547 57.4202i −0.401027 0.231533i
\(249\) −108.844 + 188.524i −0.437126 + 0.757124i
\(250\) −6.52078 + 3.76478i −0.0260831 + 0.0150591i
\(251\) 311.712i 1.24188i 0.783858 + 0.620940i \(0.213249\pi\)
−0.783858 + 0.620940i \(0.786751\pi\)
\(252\) −72.6087 16.5699i −0.288130 0.0657537i
\(253\) 1.98020 0.00782686
\(254\) 1.86882 + 3.23690i 0.00735758 + 0.0127437i
\(255\) 31.6149 + 18.2528i 0.123980 + 0.0715798i
\(256\) −6.26320 + 10.8482i −0.0244656 + 0.0423757i
\(257\) −125.335 + 72.3619i −0.487683 + 0.281564i −0.723613 0.690206i \(-0.757520\pi\)
0.235930 + 0.971770i \(0.424186\pi\)
\(258\) 89.2610i 0.345973i
\(259\) 87.2525 + 282.832i 0.336882 + 1.09202i
\(260\) −182.400 −0.701540
\(261\) 79.5006 + 137.699i 0.304600 + 0.527582i
\(262\) 97.1213 + 56.0730i 0.370692 + 0.214019i
\(263\) 114.833 198.896i 0.436626 0.756258i −0.560801 0.827950i \(-0.689507\pi\)
0.997427 + 0.0716928i \(0.0228401\pi\)
\(264\) 0.341222 0.197005i 0.00129251 0.000746230i
\(265\) 42.4579i 0.160219i
\(266\) 3.95481 + 3.66928i 0.0148677 + 0.0137943i
\(267\) −80.8910 −0.302962
\(268\) −12.4281 21.5262i −0.0463736 0.0803215i
\(269\) 367.508 + 212.181i 1.36620 + 0.788776i 0.990440 0.137941i \(-0.0440485\pi\)
0.375760 + 0.926717i \(0.377382\pi\)
\(270\) −3.91247 + 6.77660i −0.0144906 + 0.0250985i
\(271\) 252.710 145.902i 0.932509 0.538385i 0.0449051 0.998991i \(-0.485701\pi\)
0.887604 + 0.460607i \(0.152368\pi\)
\(272\) 101.450i 0.372977i
\(273\) 189.675 204.434i 0.694779 0.748844i
\(274\) 49.1267 0.179294
\(275\) −0.111900 0.193816i −0.000406908 0.000704786i
\(276\) −235.344 135.876i −0.852697 0.492305i
\(277\) 101.450 175.717i 0.366247 0.634358i −0.622729 0.782438i \(-0.713976\pi\)
0.988975 + 0.148080i \(0.0473092\pi\)
\(278\) −67.0684 + 38.7220i −0.241253 + 0.139288i
\(279\) 67.7890i 0.242971i
\(280\) 76.0149 23.4503i 0.271482 0.0837510i
\(281\) 254.325 0.905071 0.452536 0.891746i \(-0.350520\pi\)
0.452536 + 0.891746i \(0.350520\pi\)
\(282\) −15.8311 27.4203i −0.0561387 0.0972351i
\(283\) 384.259 + 221.852i 1.35781 + 0.783930i 0.989328 0.145706i \(-0.0465455\pi\)
0.368478 + 0.929636i \(0.379879\pi\)
\(284\) −83.1172 + 143.963i −0.292666 + 0.506912i
\(285\) −3.83832 + 2.21606i −0.0134678 + 0.00777563i
\(286\) 0.693347i 0.00242429i
\(287\) −59.6161 + 261.235i −0.207722 + 0.910227i
\(288\) −82.7327 −0.287266
\(289\) −100.078 173.340i −0.346290 0.599792i
\(290\) −69.1208 39.9069i −0.238348 0.137610i
\(291\) −2.69761 + 4.67241i −0.00927015 + 0.0160564i
\(292\) 256.747 148.233i 0.879270 0.507647i
\(293\) 223.513i 0.762845i 0.924401 + 0.381422i \(0.124566\pi\)
−0.924401 + 0.381422i \(0.875434\pi\)
\(294\) −24.7962 + 51.4985i −0.0843406 + 0.175165i
\(295\) −10.8890 −0.0369120
\(296\) 107.448 + 186.105i 0.363000 + 0.628734i
\(297\) −0.201420 0.116290i −0.000678180 0.000391548i
\(298\) −24.4958 + 42.4280i −0.0822007 + 0.142376i
\(299\) 881.245 508.787i 2.94731 1.70163i
\(300\) 30.7131i 0.102377i
\(301\) −522.229 119.177i −1.73498 0.395937i
\(302\) −85.6165 −0.283498
\(303\) 77.4555 + 134.157i 0.255629 + 0.442762i
\(304\) −10.6667 6.15845i −0.0350880 0.0202580i
\(305\) −43.4332 + 75.2285i −0.142404 + 0.246651i
\(306\) −16.4923 + 9.52183i −0.0538964 + 0.0311171i
\(307\) 47.3887i 0.154361i 0.997017 + 0.0771803i \(0.0245917\pi\)
−0.997017 + 0.0771803i \(0.975408\pi\)
\(308\) 0.327559 + 1.06179i 0.00106350 + 0.00344738i
\(309\) 158.277 0.512223
\(310\) −17.0140 29.4692i −0.0548840 0.0950619i
\(311\) −313.595 181.054i −1.00834 0.582167i −0.0976367 0.995222i \(-0.531128\pi\)
−0.910706 + 0.413055i \(0.864462\pi\)
\(312\) 101.236 175.346i 0.324474 0.562005i
\(313\) −340.880 + 196.807i −1.08907 + 0.628777i −0.933330 0.359020i \(-0.883111\pi\)
−0.155744 + 0.987797i \(0.549778\pi\)
\(314\) 101.737i 0.324003i
\(315\) −34.4233 31.9380i −0.109280 0.101391i
\(316\) −72.6291 −0.229839
\(317\) −288.788 500.196i −0.911004 1.57791i −0.812648 0.582754i \(-0.801975\pi\)
−0.0983557 0.995151i \(-0.531358\pi\)
\(318\) −19.1813 11.0744i −0.0603187 0.0348250i
\(319\) 1.18615 2.05446i 0.00371833 0.00644033i
\(320\) −47.4049 + 27.3693i −0.148140 + 0.0855289i
\(321\) 182.044i 0.567114i
\(322\) −141.852 + 152.890i −0.440533 + 0.474814i
\(323\) −10.7865 −0.0333947
\(324\) 15.9590 + 27.6418i 0.0492562 + 0.0853143i
\(325\) −99.5974 57.5026i −0.306453 0.176931i
\(326\) 20.1796 34.9521i 0.0619006 0.107215i
\(327\) 83.5521 48.2388i 0.255511 0.147519i
\(328\) 194.542i 0.593117i
\(329\) 181.562 56.0109i 0.551859 0.170246i
\(330\) 0.116748 0.000353781
\(331\) 91.7974 + 158.998i 0.277333 + 0.480356i 0.970721 0.240209i \(-0.0772160\pi\)
−0.693388 + 0.720565i \(0.743883\pi\)
\(332\) −386.011 222.863i −1.16268 0.671275i
\(333\) 63.4254 109.856i 0.190467 0.329898i
\(334\) 130.697 75.4578i 0.391307 0.225921i
\(335\) 15.6721i 0.0467824i
\(336\) 29.0337 127.224i 0.0864099 0.378644i
\(337\) −205.885 −0.610934 −0.305467 0.952203i \(-0.598813\pi\)
−0.305467 + 0.952203i \(0.598813\pi\)
\(338\) 121.239 + 209.993i 0.358696 + 0.621280i
\(339\) 7.88138 + 4.55032i 0.0232489 + 0.0134228i
\(340\) −37.3735 + 64.7327i −0.109922 + 0.190390i
\(341\) 0.875907 0.505705i 0.00256864 0.00148301i
\(342\) 2.31207i 0.00676043i
\(343\) −268.190 213.830i −0.781894 0.623412i
\(344\) −388.905 −1.13054
\(345\) −85.6711 148.387i −0.248322 0.430107i
\(346\) −111.176 64.1872i −0.321317 0.185512i
\(347\) −99.7256 + 172.730i −0.287394 + 0.497780i −0.973187 0.230016i \(-0.926122\pi\)
0.685793 + 0.727796i \(0.259455\pi\)
\(348\) −281.944 + 162.781i −0.810185 + 0.467761i
\(349\) 391.231i 1.12101i 0.828152 + 0.560503i \(0.189392\pi\)
−0.828152 + 0.560503i \(0.810608\pi\)
\(350\) 22.9804 + 5.24433i 0.0656583 + 0.0149838i
\(351\) −119.517 −0.340504
\(352\) 0.617185 + 1.06900i 0.00175337 + 0.00303692i
\(353\) −81.1020 46.8243i −0.229751 0.132647i 0.380706 0.924696i \(-0.375681\pi\)
−0.610457 + 0.792049i \(0.709014\pi\)
\(354\) 2.84020 4.91937i 0.00802317 0.0138965i
\(355\) −90.7701 + 52.4061i −0.255690 + 0.147623i
\(356\) 165.628i 0.465246i
\(357\) −33.6885 109.203i −0.0943656 0.305890i
\(358\) 146.722 0.409838
\(359\) −73.8759 127.957i −0.205782 0.356426i 0.744599 0.667512i \(-0.232641\pi\)
−0.950382 + 0.311086i \(0.899307\pi\)
\(360\) −29.5252 17.0464i −0.0820146 0.0473511i
\(361\) −179.845 + 311.501i −0.498186 + 0.862884i
\(362\) −22.7931 + 13.1596i −0.0629644 + 0.0363525i
\(363\) 209.575i 0.577341i
\(364\) 418.588 + 388.367i 1.14997 + 1.06694i
\(365\) 186.925 0.512122
\(366\) −22.6575 39.2439i −0.0619057 0.107224i
\(367\) −71.5485 41.3085i −0.194955 0.112557i 0.399345 0.916801i \(-0.369238\pi\)
−0.594300 + 0.804243i \(0.702571\pi\)
\(368\) 238.081 412.369i 0.646960 1.12057i
\(369\) 99.4511 57.4181i 0.269515 0.155605i
\(370\) 63.6753i 0.172095i
\(371\) 90.4014 97.4361i 0.243670 0.262631i
\(372\) −138.801 −0.373121
\(373\) 171.325 + 296.744i 0.459318 + 0.795561i 0.998925 0.0463554i \(-0.0147607\pi\)
−0.539607 + 0.841917i \(0.681427\pi\)
\(374\) 0.246064 + 0.142065i 0.000657926 + 0.000379854i
\(375\) −9.68246 + 16.7705i −0.0258199 + 0.0447214i
\(376\) 119.469 68.9752i 0.317736 0.183445i
\(377\) 1219.06i 3.23359i
\(378\) 23.4074 7.22108i 0.0619244 0.0191034i
\(379\) 355.679 0.938467 0.469233 0.883074i \(-0.344530\pi\)
0.469233 + 0.883074i \(0.344530\pi\)
\(380\) −4.53747 7.85912i −0.0119407 0.0206819i
\(381\) 8.32483 + 4.80635i 0.0218500 + 0.0126151i
\(382\) −63.8164 + 110.533i −0.167059 + 0.289354i
\(383\) −144.616 + 83.4939i −0.377586 + 0.218000i −0.676768 0.736197i \(-0.736620\pi\)
0.299181 + 0.954196i \(0.403286\pi\)
\(384\) 219.618i 0.571922i
\(385\) −0.155876 + 0.683043i −0.000404873 + 0.00177414i
\(386\) −183.950 −0.476556
\(387\) 114.783 + 198.810i 0.296598 + 0.513722i
\(388\) −9.56695 5.52348i −0.0246571 0.0142358i
\(389\) −79.6452 + 137.950i −0.204744 + 0.354626i −0.950051 0.312095i \(-0.898969\pi\)
0.745307 + 0.666721i \(0.232303\pi\)
\(390\) 51.9562 29.9969i 0.133221 0.0769152i
\(391\) 416.998i 1.06649i
\(392\) −224.376 108.035i −0.572388 0.275601i
\(393\) 288.423 0.733901
\(394\) −66.9753 116.005i −0.169988 0.294428i
\(395\) −39.6582 22.8967i −0.100401 0.0579663i
\(396\) 0.238108 0.412415i 0.000601283 0.00104145i
\(397\) −510.352 + 294.652i −1.28552 + 0.742196i −0.977852 0.209298i \(-0.932882\pi\)
−0.307669 + 0.951494i \(0.599549\pi\)
\(398\) 25.8439i 0.0649344i
\(399\) 13.5269 + 3.08696i 0.0339021 + 0.00773675i
\(400\) −53.8154 −0.134538
\(401\) 83.1535 + 144.026i 0.207365 + 0.359167i 0.950884 0.309548i \(-0.100178\pi\)
−0.743518 + 0.668716i \(0.766844\pi\)
\(402\) 7.08024 + 4.08778i 0.0176125 + 0.0101686i
\(403\) 259.870 450.107i 0.644838 1.11689i
\(404\) −274.692 + 158.593i −0.679930 + 0.392558i
\(405\) 20.1246i 0.0496904i
\(406\) 73.6545 + 238.754i 0.181415 + 0.588064i
\(407\) −1.89261 −0.00465014
\(408\) −41.4861 71.8560i −0.101682 0.176118i
\(409\) −189.742 109.548i −0.463917 0.267843i 0.249773 0.968304i \(-0.419644\pi\)
−0.713690 + 0.700462i \(0.752977\pi\)
\(410\) −28.8222 + 49.9215i −0.0702980 + 0.121760i
\(411\) 109.419 63.1733i 0.266227 0.153706i
\(412\) 324.079i 0.786599i
\(413\) 24.9891 + 23.1850i 0.0605063 + 0.0561379i
\(414\) 89.3829 0.215901
\(415\) −140.517 243.383i −0.338596 0.586466i
\(416\) 549.331 + 317.156i 1.32051 + 0.762395i
\(417\) −99.5873 + 172.490i −0.238819 + 0.413646i
\(418\) −0.0298744 + 0.0172480i −7.14698e−5 + 4.12631e-5i
\(419\) 554.704i 1.32388i 0.749558 + 0.661938i \(0.230266\pi\)
−0.749558 + 0.661938i \(0.769734\pi\)
\(420\) 65.3944 70.4831i 0.155701 0.167817i
\(421\) 642.342 1.52575 0.762876 0.646545i \(-0.223787\pi\)
0.762876 + 0.646545i \(0.223787\pi\)
\(422\) 42.8603 + 74.2362i 0.101565 + 0.175915i
\(423\) −70.5210 40.7153i −0.166716 0.0962537i
\(424\) 48.2503 83.5720i 0.113798 0.197104i
\(425\) −40.8146 + 23.5643i −0.0960344 + 0.0554455i
\(426\) 54.6767i 0.128349i
\(427\) 259.851 80.1629i 0.608550 0.187735i
\(428\) 372.742 0.870893
\(429\) 0.891594 + 1.54429i 0.00207831 + 0.00359973i
\(430\) −99.7969 57.6178i −0.232086 0.133995i
\(431\) −37.6661 + 65.2395i −0.0873923 + 0.151368i −0.906408 0.422403i \(-0.861187\pi\)
0.819016 + 0.573771i \(0.194520\pi\)
\(432\) −48.4338 + 27.9633i −0.112115 + 0.0647298i
\(433\) 353.064i 0.815391i 0.913118 + 0.407695i \(0.133667\pi\)
−0.913118 + 0.407695i \(0.866333\pi\)
\(434\) −23.7005 + 103.855i −0.0546095 + 0.239297i
\(435\) −205.270 −0.471884
\(436\) 98.7710 + 171.076i 0.226539 + 0.392377i
\(437\) 43.8444 + 25.3136i 0.100331 + 0.0579259i
\(438\) −48.7558 + 84.4475i −0.111315 + 0.192802i
\(439\) −235.512 + 135.973i −0.536473 + 0.309733i −0.743648 0.668571i \(-0.766906\pi\)
0.207175 + 0.978304i \(0.433573\pi\)
\(440\) 0.508664i 0.00115605i
\(441\) 10.9951 + 146.588i 0.0249321 + 0.332400i
\(442\) 146.008 0.330335
\(443\) 55.1204 + 95.4714i 0.124425 + 0.215511i 0.921508 0.388359i \(-0.126958\pi\)
−0.797083 + 0.603870i \(0.793625\pi\)
\(444\) 224.935 + 129.866i 0.506610 + 0.292491i
\(445\) 52.2149 90.4389i 0.117337 0.203233i
\(446\) −171.214 + 98.8504i −0.383888 + 0.221638i
\(447\) 125.999i 0.281878i
\(448\) 167.064 + 38.1253i 0.372910 + 0.0851012i
\(449\) 59.1007 0.131627 0.0658137 0.997832i \(-0.479036\pi\)
0.0658137 + 0.997832i \(0.479036\pi\)
\(450\) −5.05098 8.74855i −0.0112244 0.0194412i
\(451\) −1.48381 0.856677i −0.00329004 0.00189950i
\(452\) −9.31696 + 16.1375i −0.0206127 + 0.0357023i
\(453\) −190.693 + 110.097i −0.420956 + 0.243039i
\(454\) 145.118i 0.319643i
\(455\) 106.130 + 344.025i 0.233253 + 0.756098i
\(456\) 10.0735 0.0220911
\(457\) 102.638 + 177.775i 0.224592 + 0.389004i 0.956197 0.292724i \(-0.0945618\pi\)
−0.731605 + 0.681729i \(0.761228\pi\)
\(458\) −84.1414 48.5791i −0.183715 0.106068i
\(459\) −24.4888 + 42.4158i −0.0533524 + 0.0924091i
\(460\) 303.828 175.415i 0.660496 0.381338i
\(461\) 466.172i 1.01122i 0.862762 + 0.505610i \(0.168732\pi\)
−0.862762 + 0.505610i \(0.831268\pi\)
\(462\) −0.267923 0.248580i −0.000579920 0.000538051i
\(463\) 191.705 0.414051 0.207025 0.978336i \(-0.433622\pi\)
0.207025 + 0.978336i \(0.433622\pi\)
\(464\) −285.223 494.021i −0.614706 1.06470i
\(465\) −75.7905 43.7576i −0.162990 0.0941024i
\(466\) 96.4510 167.058i 0.206976 0.358493i
\(467\) −730.261 + 421.617i −1.56373 + 0.902819i −0.566855 + 0.823818i \(0.691840\pi\)
−0.996874 + 0.0790015i \(0.974827\pi\)
\(468\) 244.716i 0.522897i
\(469\) −33.3691 + 35.9657i −0.0711494 + 0.0766859i
\(470\) 40.8758 0.0869697
\(471\) −130.826 226.598i −0.277763 0.481100i
\(472\) 21.4334 + 12.3746i 0.0454098 + 0.0262174i
\(473\) 1.71256 2.96625i 0.00362064 0.00627113i
\(474\) 20.6882 11.9443i 0.0436460 0.0251990i
\(475\) 5.72183i 0.0120460i
\(476\) 223.597 68.9786i 0.469741 0.144913i
\(477\) −56.9633 −0.119420
\(478\) 139.212 + 241.121i 0.291237 + 0.504438i
\(479\) −246.540 142.340i −0.514698 0.297161i 0.220065 0.975485i \(-0.429373\pi\)
−0.734763 + 0.678324i \(0.762707\pi\)
\(480\) 53.4037 92.4980i 0.111258 0.192704i
\(481\) −842.267 + 486.283i −1.75107 + 1.01098i
\(482\) 199.274i 0.413432i
\(483\) −119.340 + 522.942i −0.247080 + 1.08270i
\(484\) 429.113 0.886597
\(485\) −3.48261 6.03205i −0.00718063 0.0124372i
\(486\) −9.09176 5.24913i −0.0187073 0.0108007i
\(487\) 97.8228 169.434i 0.200868 0.347914i −0.747940 0.663766i \(-0.768957\pi\)
0.948808 + 0.315852i \(0.102290\pi\)
\(488\) 170.984 98.7174i 0.350376 0.202290i
\(489\) 103.798i 0.212266i
\(490\) −41.5712 60.9651i −0.0848392 0.124419i
\(491\) 745.464 1.51826 0.759128 0.650941i \(-0.225625\pi\)
0.759128 + 0.650941i \(0.225625\pi\)
\(492\) 117.566 + 203.630i 0.238955 + 0.413883i
\(493\) −432.638 249.784i −0.877562 0.506660i
\(494\) −8.86332 + 15.3517i −0.0179419 + 0.0310763i
\(495\) 0.260032 0.150129i 0.000525316 0.000303292i
\(496\) 243.206i 0.490335i
\(497\) 319.890 + 73.0017i 0.643642 + 0.146885i
\(498\) 146.605 0.294388
\(499\) −45.9747 79.6306i −0.0921337 0.159580i 0.816275 0.577663i \(-0.196035\pi\)
−0.908409 + 0.418083i \(0.862702\pi\)
\(500\) −34.3383 19.8252i −0.0686766 0.0396505i
\(501\) 194.066 336.133i 0.387358 0.670924i
\(502\) 181.802 104.963i 0.362155 0.209090i
\(503\) 672.220i 1.33642i −0.743972 0.668211i \(-0.767060\pi\)
0.743972 0.668211i \(-0.232940\pi\)
\(504\) 31.4618 + 101.985i 0.0624243 + 0.202351i
\(505\) −199.989 −0.396018
\(506\) −0.666795 1.15492i −0.00131778 0.00228246i
\(507\) 540.071 + 311.810i 1.06523 + 0.615010i
\(508\) −9.84119 + 17.0454i −0.0193724 + 0.0335540i
\(509\) 282.238 162.950i 0.554495 0.320138i −0.196438 0.980516i \(-0.562937\pi\)
0.750933 + 0.660378i \(0.229604\pi\)
\(510\) 24.5853i 0.0482064i
\(511\) −428.970 398.000i −0.839473 0.778865i
\(512\) 515.622 1.00707
\(513\) −2.97315 5.14965i −0.00579561 0.0100383i
\(514\) 84.4082 + 48.7331i 0.164218 + 0.0948115i
\(515\) −102.167 + 176.959i −0.198383 + 0.343610i
\(516\) −407.073 + 235.024i −0.788901 + 0.455472i
\(517\) 1.21494i 0.00234999i
\(518\) 135.577 146.127i 0.261733 0.282099i
\(519\) −330.161 −0.636148
\(520\) 130.695 + 226.370i 0.251336 + 0.435328i
\(521\) 515.449 + 297.595i 0.989346 + 0.571199i 0.905079 0.425244i \(-0.139812\pi\)
0.0842672 + 0.996443i \(0.473145\pi\)
\(522\) 53.5407 92.7353i 0.102568 0.177654i
\(523\) −43.6490 + 25.2007i −0.0834588 + 0.0481850i −0.541149 0.840927i \(-0.682010\pi\)
0.457690 + 0.889112i \(0.348677\pi\)
\(524\) 590.559i 1.12702i
\(525\) 57.9279 17.8705i 0.110339 0.0340391i
\(526\) −154.671 −0.294051
\(527\) −106.494 184.452i −0.202075 0.350004i
\(528\) 0.722631 + 0.417211i 0.00136862 + 0.000790173i
\(529\) −714.106 + 1236.87i −1.34992 + 2.33812i
\(530\) 24.7630 14.2969i 0.0467227 0.0269753i
\(531\) 14.6092i 0.0275126i
\(532\) −6.32068 + 27.6970i −0.0118810 + 0.0520620i
\(533\) −880.451 −1.65188
\(534\) 27.2386 + 47.1786i 0.0510085 + 0.0883494i
\(535\) 203.531 + 117.509i 0.380432 + 0.219642i
\(536\) −17.8102 + 30.8482i −0.0332280 + 0.0575526i
\(537\) 326.793 188.674i 0.608553 0.351348i
\(538\) 285.792i 0.531212i
\(539\) 1.81205 1.23561i 0.00336188 0.00229242i
\(540\) −41.2060 −0.0763074
\(541\) −468.381 811.260i −0.865769 1.49956i −0.866282 0.499556i \(-0.833497\pi\)
0.000512769 1.00000i \(-0.499837\pi\)
\(542\) −170.191 98.2598i −0.314006 0.181291i
\(543\) −33.8446 + 58.6206i −0.0623290 + 0.107957i
\(544\) 225.113 129.969i 0.413812 0.238914i
\(545\) 124.552i 0.228536i
\(546\) −183.103 41.7857i −0.335354 0.0765306i
\(547\) −3.89041 −0.00711227 −0.00355613 0.999994i \(-0.501132\pi\)
−0.00355613 + 0.999994i \(0.501132\pi\)
\(548\) 129.350 + 224.041i 0.236040 + 0.408834i
\(549\) −100.930 58.2718i −0.183843 0.106142i
\(550\) −0.0753604 + 0.130528i −0.000137019 + 0.000237324i
\(551\) 52.5260 30.3259i 0.0953285 0.0550379i
\(552\) 389.436i 0.705500i
\(553\) 42.2594 + 136.986i 0.0764185 + 0.247714i
\(554\) −136.646 −0.246654
\(555\) 81.8818 + 141.823i 0.147535 + 0.255538i
\(556\) −353.181 203.909i −0.635218 0.366743i
\(557\) −193.381 + 334.945i −0.347183 + 0.601338i −0.985748 0.168230i \(-0.946195\pi\)
0.638565 + 0.769568i \(0.279528\pi\)
\(558\) 39.5370 22.8267i 0.0708549 0.0409081i
\(559\) 1760.09i 3.14864i
\(560\) 123.500 + 114.584i 0.220536 + 0.204614i
\(561\) 0.730743 0.00130257
\(562\) −85.6393 148.332i −0.152383 0.263935i
\(563\) −105.001 60.6226i −0.186503 0.107678i 0.403841 0.914829i \(-0.367675\pi\)
−0.590345 + 0.807151i \(0.701008\pi\)
\(564\) 83.3663 144.395i 0.147813 0.256019i
\(565\) −10.1748 + 5.87443i −0.0180085 + 0.0103972i
\(566\) 298.819i 0.527948i
\(567\) 42.8493 46.1837i 0.0755720 0.0814527i
\(568\) 238.223 0.419407
\(569\) −204.955 354.993i −0.360202 0.623889i 0.627792 0.778381i \(-0.283959\pi\)
−0.987994 + 0.154493i \(0.950626\pi\)
\(570\) 2.58497 + 1.49243i 0.00453503 + 0.00261830i
\(571\) 287.861 498.591i 0.504136 0.873188i −0.495853 0.868406i \(-0.665145\pi\)
0.999989 0.00478199i \(-0.00152216\pi\)
\(572\) −3.16199 + 1.82558i −0.00552796 + 0.00319157i
\(573\) 328.253i 0.572868i
\(574\) 172.436 53.1959i 0.300412 0.0926758i
\(575\) 221.202 0.384699
\(576\) −36.7197 63.6004i −0.0637495 0.110417i
\(577\) −202.254 116.772i −0.350527 0.202377i 0.314390 0.949294i \(-0.398200\pi\)
−0.664917 + 0.746917i \(0.731533\pi\)
\(578\) −67.3988 + 116.738i −0.116607 + 0.201969i
\(579\) −409.711 + 236.547i −0.707619 + 0.408544i
\(580\) 420.298i 0.724652i
\(581\) −195.741 + 857.727i −0.336903 + 1.47629i
\(582\) 3.63349 0.00624311
\(583\) 0.424945 + 0.736027i 0.000728894 + 0.00126248i
\(584\) −367.933 212.426i −0.630022 0.363743i
\(585\) 77.1478 133.624i 0.131877 0.228417i
\(586\) 130.361 75.2641i 0.222459 0.128437i
\(587\) 606.882i 1.03387i −0.856024 0.516935i \(-0.827073\pi\)
0.856024 0.516935i \(-0.172927\pi\)
\(588\) −300.146 + 22.5128i −0.510452 + 0.0382872i
\(589\) 25.8585 0.0439024
\(590\) 3.66668 + 6.35088i 0.00621472 + 0.0107642i
\(591\) −298.347 172.251i −0.504817 0.291456i
\(592\) −227.551 + 394.129i −0.384376 + 0.665759i
\(593\) −701.998 + 405.299i −1.18381 + 0.683472i −0.956892 0.290443i \(-0.906197\pi\)
−0.226915 + 0.973914i \(0.572864\pi\)
\(594\) 0.156634i 0.000263693i
\(595\) 143.838 + 32.8251i 0.241745 + 0.0551682i
\(596\) −257.989 −0.432867
\(597\) −33.2334 57.5619i −0.0556673 0.0964185i
\(598\) −593.487 342.650i −0.992453 0.572993i
\(599\) 511.389 885.752i 0.853738 1.47872i −0.0240732 0.999710i \(-0.507663\pi\)
0.877811 0.479007i \(-0.159003\pi\)
\(600\) 38.1169 22.0068i 0.0635282 0.0366780i
\(601\) 147.884i 0.246063i −0.992403 0.123032i \(-0.960738\pi\)
0.992403 0.123032i \(-0.0392617\pi\)
\(602\) 106.343 + 344.714i 0.176649 + 0.572614i
\(603\) 21.0263 0.0348696
\(604\) −225.427 390.452i −0.373224 0.646443i
\(605\) 234.312 + 135.280i 0.387292 + 0.223603i
\(606\) 52.1634 90.3497i 0.0860783 0.149092i
\(607\) 815.490 470.823i 1.34348 0.775656i 0.356160 0.934425i \(-0.384086\pi\)
0.987316 + 0.158769i \(0.0507524\pi\)
\(608\) 31.5588i 0.0519060i
\(609\) 471.070 + 437.060i 0.773514 + 0.717669i
\(610\) 58.5014 0.0959039
\(611\) 312.165 + 540.685i 0.510908 + 0.884919i
\(612\) −86.8481 50.1418i −0.141909 0.0819310i
\(613\) −180.068 + 311.886i −0.293748 + 0.508786i −0.974693 0.223548i \(-0.928236\pi\)
0.680945 + 0.732335i \(0.261569\pi\)
\(614\) 27.6388 15.9573i 0.0450144 0.0259891i
\(615\) 148.253i 0.241062i
\(616\) 1.08305 1.16733i 0.00175819 0.00189501i
\(617\) 769.687 1.24747 0.623734 0.781637i \(-0.285615\pi\)
0.623734 + 0.781637i \(0.285615\pi\)
\(618\) −53.2969 92.3129i −0.0862409 0.149374i
\(619\) −853.542 492.793i −1.37890 0.796111i −0.386877 0.922131i \(-0.626446\pi\)
−0.992028 + 0.126020i \(0.959780\pi\)
\(620\) 89.5956 155.184i 0.144509 0.250297i
\(621\) 199.082 114.940i 0.320583 0.185088i
\(622\) 243.866i 0.392068i
\(623\) −312.390 + 96.3709i −0.501428 + 0.154688i
\(624\) 428.790 0.687163
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) 229.570 + 132.542i 0.366726 + 0.211729i
\(627\) −0.0443593 + 0.0768326i −7.07485e−5 + 0.000122540i
\(628\) 463.969 267.873i 0.738804 0.426549i
\(629\) 398.554i 0.633630i
\(630\) −7.03600 + 30.8315i −0.0111683 + 0.0489388i
\(631\) −89.7688 −0.142264 −0.0711322 0.997467i \(-0.522661\pi\)
−0.0711322 + 0.997467i \(0.522661\pi\)
\(632\) 52.0408 + 90.1373i 0.0823431 + 0.142622i
\(633\) 190.925 + 110.230i 0.301619 + 0.174140i
\(634\) −194.488 + 336.864i −0.306764 + 0.531331i
\(635\) −10.7473 + 6.20497i −0.0169249 + 0.00977160i
\(636\) 116.635i 0.183388i
\(637\) 488.941 1015.47i 0.767569 1.59414i
\(638\) −1.59765 −0.00250416
\(639\) −70.3102 121.781i −0.110032 0.190580i
\(640\) 245.540 + 141.763i 0.383657 + 0.221504i
\(641\) 214.166 370.947i 0.334113 0.578701i −0.649201 0.760617i \(-0.724897\pi\)
0.983314 + 0.181916i \(0.0582300\pi\)
\(642\) −106.175 + 61.2999i −0.165381 + 0.0954827i
\(643\) 111.498i 0.173403i −0.996234 0.0867015i \(-0.972367\pi\)
0.996234 0.0867015i \(-0.0276326\pi\)
\(644\) −1070.75 244.353i −1.66265 0.379431i
\(645\) −296.369 −0.459487
\(646\) 3.63215 + 6.29107i 0.00562253 + 0.00973850i
\(647\) −250.033 144.357i −0.386450 0.223117i 0.294171 0.955753i \(-0.404957\pi\)
−0.680621 + 0.732636i \(0.738290\pi\)
\(648\) 22.8702 39.6123i 0.0352934 0.0611300i
\(649\) −0.188766 + 0.108984i −0.000290857 + 0.000167926i
\(650\) 77.4518i 0.119157i
\(651\) 80.7616 + 261.792i 0.124058 + 0.402138i
\(652\) 212.531 0.325967
\(653\) −426.848 739.322i −0.653672 1.13219i −0.982225 0.187707i \(-0.939894\pi\)
0.328553 0.944485i \(-0.393439\pi\)
\(654\) −56.2693 32.4871i −0.0860387 0.0496744i
\(655\) −186.176 + 322.467i −0.284239 + 0.492316i
\(656\) −356.800 + 205.998i −0.543902 + 0.314022i
\(657\) 250.786i 0.381713i
\(658\) −93.8052 87.0327i −0.142561 0.132269i
\(659\) −288.693 −0.438077 −0.219039 0.975716i \(-0.570292\pi\)
−0.219039 + 0.975716i \(0.570292\pi\)
\(660\) 0.307396 + 0.532426i 0.000465752 + 0.000806705i
\(661\) 182.367 + 105.289i 0.275895 + 0.159288i 0.631564 0.775324i \(-0.282413\pi\)
−0.355668 + 0.934612i \(0.615747\pi\)
\(662\) 61.8222 107.079i 0.0933870 0.161751i
\(663\) 325.202 187.756i 0.490501 0.283191i
\(664\) 638.751i 0.961974i
\(665\) −12.1829 + 13.1309i −0.0183202 + 0.0197458i
\(666\) −85.4293 −0.128272
\(667\) 1172.38 + 2030.62i 1.75769 + 3.04441i
\(668\) 688.246 + 397.359i 1.03031 + 0.594849i
\(669\) −254.229 + 440.338i −0.380013 + 0.658203i
\(670\) −9.14055 + 5.27730i −0.0136426 + 0.00787656i
\(671\) 1.73883i 0.00259140i
\(672\) −319.502 + 98.5650i −0.475450 + 0.146674i
\(673\) 760.139 1.12948 0.564739 0.825269i \(-0.308977\pi\)
0.564739 + 0.825269i \(0.308977\pi\)
\(674\) 69.3279 + 120.080i 0.102860 + 0.178160i
\(675\) −22.5000 12.9904i −0.0333333 0.0192450i
\(676\) −638.444 + 1105.82i −0.944444 + 1.63583i
\(677\) 163.263 94.2600i 0.241157 0.139232i −0.374552 0.927206i \(-0.622203\pi\)
0.615708 + 0.787974i \(0.288870\pi\)
\(678\) 6.12894i 0.00903974i
\(679\) −4.85126 + 21.2580i −0.00714472 + 0.0313079i
\(680\) 107.117 0.157524
\(681\) −186.611 323.220i −0.274026 0.474626i
\(682\) −0.589892 0.340574i −0.000864944 0.000499375i
\(683\) −260.243 + 450.754i −0.381029 + 0.659962i −0.991210 0.132301i \(-0.957764\pi\)
0.610181 + 0.792262i \(0.291097\pi\)
\(684\) 10.5441 6.08765i 0.0154154 0.00890007i
\(685\) 163.113i 0.238121i
\(686\) −34.4057 + 228.421i −0.0501541 + 0.332976i
\(687\) −249.877 −0.363721
\(688\) −411.807 713.270i −0.598556 1.03673i
\(689\) 378.226 + 218.369i 0.548949 + 0.316936i
\(690\) −57.6964 + 99.9331i −0.0836180 + 0.144831i
\(691\) 590.615 340.991i 0.854724 0.493475i −0.00751772 0.999972i \(-0.502393\pi\)
0.862242 + 0.506496i \(0.169060\pi\)
\(692\) 676.018i 0.976904i
\(693\) −0.916398 0.209130i −0.00132236 0.000301775i
\(694\) 134.323 0.193549
\(695\) −128.567 222.684i −0.184988 0.320409i
\(696\) 404.042 + 233.274i 0.580520 + 0.335164i
\(697\) −180.403 + 312.466i −0.258827 + 0.448302i
\(698\) 228.180 131.740i 0.326906 0.188739i
\(699\) 496.116i 0.709751i
\(700\) 36.5906 + 118.610i 0.0522723 + 0.169443i
\(701\) −946.473 −1.35018 −0.675088 0.737737i \(-0.735894\pi\)
−0.675088 + 0.737737i \(0.735894\pi\)
\(702\) 40.2451 + 69.7066i 0.0573292 + 0.0992971i
\(703\) −41.9051 24.1939i −0.0596090 0.0344153i
\(704\) −0.547857 + 0.948916i −0.000778206 + 0.00134789i
\(705\) 91.0422 52.5633i 0.129138 0.0745578i
\(706\) 63.0689i 0.0893327i
\(707\) 458.952 + 425.817i 0.649155 + 0.602287i
\(708\) 29.9129 0.0422499
\(709\) 504.785 + 874.313i 0.711967 + 1.23316i 0.964118 + 0.265475i \(0.0855289\pi\)
−0.252150 + 0.967688i \(0.581138\pi\)
\(710\) 61.1304 + 35.2936i 0.0860991 + 0.0497093i
\(711\) 30.7191 53.2071i 0.0432055 0.0748341i
\(712\) −205.554 + 118.677i −0.288700 + 0.166681i
\(713\) 999.671i 1.40206i
\(714\) −52.3470 + 56.4204i −0.0733151 + 0.0790201i
\(715\) −2.30209 −0.00321970
\(716\) 386.318 + 669.122i 0.539550 + 0.934528i
\(717\) 620.129 + 358.032i 0.864895 + 0.499347i
\(718\) −49.7527 + 86.1742i −0.0692935 + 0.120020i
\(719\) 783.382 452.286i 1.08954 0.629049i 0.156089 0.987743i \(-0.450111\pi\)
0.933455 + 0.358694i \(0.116778\pi\)
\(720\) 72.2009i 0.100279i
\(721\) 611.244 188.566i 0.847773 0.261534i
\(722\) 242.238 0.335510
\(723\) −256.252 443.842i −0.354429 0.613890i
\(724\) −120.028 69.2983i −0.165785 0.0957159i
\(725\) 132.501 229.498i 0.182760 0.316549i
\(726\) −122.232 + 70.5705i −0.168363 + 0.0972045i
\(727\) 535.515i 0.736609i 0.929705 + 0.368304i \(0.120062\pi\)
−0.929705 + 0.368304i \(0.879938\pi\)
\(728\) 182.058 797.770i 0.250080 1.09584i
\(729\) −27.0000 −0.0370370
\(730\) −62.9434 109.021i −0.0862239 0.149344i
\(731\) −624.644 360.639i −0.854507 0.493350i
\(732\) 119.314 206.658i 0.162997 0.282319i
\(733\) −652.583 + 376.769i −0.890290 + 0.514009i −0.874037 0.485859i \(-0.838507\pi\)
−0.0162527 + 0.999868i \(0.505174\pi\)
\(734\) 55.6396i 0.0758033i
\(735\) −170.988 82.3294i −0.232637 0.112013i
\(736\) −1220.04 −1.65767
\(737\) −0.156856 0.271683i −0.000212831 0.000368634i
\(738\) −66.9767 38.6690i −0.0907543 0.0523970i
\(739\) 546.157 945.972i 0.739049 1.28007i −0.213875 0.976861i \(-0.568609\pi\)
0.952924 0.303209i \(-0.0980580\pi\)
\(740\) −290.389 + 167.656i −0.392418 + 0.226563i
\(741\) 45.5903i 0.0615254i
\(742\) −87.2693 19.9156i −0.117614 0.0268404i
\(743\) −362.303 −0.487622 −0.243811 0.969823i \(-0.578398\pi\)
−0.243811 + 0.969823i \(0.578398\pi\)
\(744\) 99.4547 + 172.261i 0.133676 + 0.231533i
\(745\) −140.872 81.3322i −0.189089 0.109171i
\(746\) 115.381 199.847i 0.154667 0.267891i
\(747\) 326.533 188.524i 0.437126 0.252375i
\(748\) 1.49623i 0.00200030i
\(749\) −216.881 703.028i −0.289561 0.938622i
\(750\) 13.0416 0.0173888
\(751\) 336.270 + 582.437i 0.447763 + 0.775548i 0.998240 0.0593020i \(-0.0188875\pi\)
−0.550477 + 0.834850i \(0.685554\pi\)
\(752\) 253.008 + 146.074i 0.336446 + 0.194247i
\(753\) 269.950 467.568i 0.358500 0.620940i
\(754\) −711.002 + 410.497i −0.942974 + 0.544426i
\(755\) 284.268i 0.376514i
\(756\) 94.5630 + 87.7358i 0.125083 + 0.116053i
\(757\) −368.166 −0.486349 −0.243174 0.969983i \(-0.578189\pi\)
−0.243174 + 0.969983i \(0.578189\pi\)
\(758\) −119.768 207.445i −0.158006 0.273674i
\(759\) −2.97029 1.71490i −0.00391343 0.00225942i
\(760\) −6.50244 + 11.2626i −0.00855585 + 0.0148192i
\(761\) 565.660 326.584i 0.743312 0.429151i −0.0799606 0.996798i \(-0.525479\pi\)
0.823272 + 0.567647i \(0.192146\pi\)
\(762\) 6.47380i 0.00849580i
\(763\) 265.197 285.833i 0.347571 0.374617i
\(764\) −672.113 −0.879728
\(765\) −31.6149 54.7585i −0.0413266 0.0715798i
\(766\) 97.3933 + 56.2301i 0.127145 + 0.0734074i
\(767\) −56.0043 + 97.0024i −0.0730174 + 0.126470i
\(768\) 18.7896 10.8482i 0.0244656 0.0141252i
\(769\) 1393.19i 1.81170i 0.423602 + 0.905848i \(0.360765\pi\)
−0.423602 + 0.905848i \(0.639235\pi\)
\(770\) 0.450864 0.139090i 0.000585538 0.000180636i
\(771\) 250.669 0.325122
\(772\) −484.340 838.901i −0.627383 1.08666i
\(773\) 1129.82 + 652.302i 1.46160 + 0.843858i 0.999086 0.0427514i \(-0.0136124\pi\)
0.462519 + 0.886609i \(0.346946\pi\)
\(774\) 77.3023 133.892i 0.0998738 0.172987i
\(775\) 97.8451 56.4909i 0.126252