Properties

Label 210.3.o.b.31.2
Level 210
Weight 3
Character 210.31
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.2
Root \(2.96377 + 5.13339i\) of \(x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + 4836403 x^{8} - 6808704 x^{7} + 64376800 x^{6} - 91953512 x^{5} + 595763862 x^{4} - 630430976 x^{3} + 1087013404 x^{2} + 294123256 x + 101626561\)
Character \(\chi\) \(=\) 210.31
Dual form 210.3.o.b.61.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(5.73733 + 4.01037i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(5.73733 + 4.01037i) q^{7} +2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.73861 + 1.58114i) q^{10} +(8.69259 - 15.0560i) q^{11} +(3.00000 - 1.73205i) q^{12} -7.22559i q^{13} +(0.854777 - 9.86252i) q^{14} +3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-2.29669 - 1.32600i) q^{17} +(2.12132 - 3.67423i) q^{18} +(2.20128 - 1.27091i) q^{19} -4.47214i q^{20} +(-5.13291 - 10.9842i) q^{21} -24.5864 q^{22} +(-20.0507 - 34.7289i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-8.84951 + 5.10926i) q^{26} -5.19615i q^{27} +(-12.6835 + 5.92697i) q^{28} +47.0080 q^{29} +(-2.73861 - 4.74342i) q^{30} +(34.9025 + 20.1510i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(-26.0778 + 15.0560i) q^{33} +3.75049i q^{34} +(-15.5940 - 1.35152i) q^{35} -6.00000 q^{36} +(-16.2514 - 28.1482i) q^{37} +(-3.11308 - 1.79734i) q^{38} +(-6.25755 + 10.8384i) q^{39} +(-5.47723 + 3.16228i) q^{40} -70.6679i q^{41} +(-9.82336 + 14.0535i) q^{42} +37.3732 q^{43} +(17.3852 + 30.1120i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-28.3560 + 49.1141i) q^{46} +(-28.9672 + 16.7242i) q^{47} +6.92820i q^{48} +(16.8339 + 46.0176i) q^{49} -7.07107 q^{50} +(2.29669 + 3.97799i) q^{51} +(12.5151 + 7.22559i) q^{52} +(35.4442 - 61.3911i) q^{53} +(-6.36396 + 3.67423i) q^{54} +38.8745i q^{55} +(16.2276 + 11.3430i) q^{56} -4.40256 q^{57} +(-33.2397 - 57.5728i) q^{58} +(87.0863 + 50.2793i) q^{59} +(-3.87298 + 6.70820i) q^{60} +(-11.1621 + 6.44446i) q^{61} -56.9955i q^{62} +(-1.81326 + 20.9216i) q^{63} +8.00000 q^{64} +(8.07846 + 13.9923i) q^{65} +(36.8795 + 21.2924i) q^{66} +(-47.0361 + 81.4689i) q^{67} +(4.59339 - 2.65199i) q^{68} +69.4578i q^{69} +(9.37137 + 20.0544i) q^{70} -11.5793 q^{71} +(4.24264 + 7.34847i) q^{72} +(-19.6320 - 11.3345i) q^{73} +(-22.9829 + 39.8076i) q^{74} +(-7.50000 + 4.33013i) q^{75} +5.08364i q^{76} +(110.252 - 51.5208i) q^{77} +17.6990 q^{78} +(12.0542 + 20.8785i) q^{79} +(7.74597 + 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-86.5502 + 49.9698i) q^{82} +111.664i q^{83} +(24.1581 + 2.09377i) q^{84} +5.93004 q^{85} +(-26.4268 - 45.7726i) q^{86} +(-70.5120 - 40.7101i) q^{87} +(24.5864 - 42.5848i) q^{88} +(-110.770 + 63.9533i) q^{89} +9.48683i q^{90} +(28.9773 - 41.4556i) q^{91} +80.2029 q^{92} +(-34.9025 - 60.4529i) q^{93} +(40.9658 + 23.6516i) q^{94} +(-2.84184 + 4.92221i) q^{95} +(8.48528 - 4.89898i) q^{96} -7.48256i q^{97} +(44.4565 - 53.1566i) q^{98} +52.1556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} + O(q^{10}) \) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} - 4q^{11} + 48q^{12} + 8q^{14} - 32q^{16} + 12q^{17} - 72q^{19} - 24q^{21} - 48q^{22} - 12q^{23} + 40q^{25} + 32q^{28} + 72q^{29} + 120q^{31} + 12q^{33} - 20q^{35} - 96q^{36} + 44q^{37} - 72q^{38} + 36q^{39} - 24q^{42} - 56q^{43} - 8q^{44} + 8q^{46} - 24q^{47} - 40q^{49} - 12q^{51} - 72q^{52} + 32q^{53} + 16q^{56} + 144q^{57} - 88q^{58} + 132q^{59} + 96q^{61} + 60q^{63} + 128q^{64} + 20q^{65} + 72q^{66} - 164q^{67} - 24q^{68} - 136q^{71} - 348q^{73} - 112q^{74} - 120q^{75} + 96q^{77} + 280q^{79} - 72q^{81} + 264q^{82} - 24q^{84} + 120q^{85} - 88q^{86} - 108q^{87} + 48q^{88} - 300q^{89} - 272q^{91} + 48q^{92} - 120q^{93} + 200q^{95} + 384q^{98} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.22474i −0.353553 0.612372i
\(3\) −1.50000 0.866025i −0.500000 0.288675i
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) −1.93649 + 1.11803i −0.387298 + 0.223607i
\(6\) 2.44949i 0.408248i
\(7\) 5.73733 + 4.01037i 0.819618 + 0.572910i
\(8\) 2.82843 0.353553
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) 2.73861 + 1.58114i 0.273861 + 0.158114i
\(11\) 8.69259 15.0560i 0.790236 1.36873i −0.135585 0.990766i \(-0.543291\pi\)
0.925821 0.377963i \(-0.123375\pi\)
\(12\) 3.00000 1.73205i 0.250000 0.144338i
\(13\) 7.22559i 0.555815i −0.960608 0.277907i \(-0.910359\pi\)
0.960608 0.277907i \(-0.0896408\pi\)
\(14\) 0.854777 9.86252i 0.0610555 0.704466i
\(15\) 3.87298 0.258199
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −2.29669 1.32600i −0.135100 0.0779998i 0.430927 0.902387i \(-0.358187\pi\)
−0.566027 + 0.824387i \(0.691520\pi\)
\(18\) 2.12132 3.67423i 0.117851 0.204124i
\(19\) 2.20128 1.27091i 0.115857 0.0668900i −0.440952 0.897531i \(-0.645359\pi\)
0.556809 + 0.830641i \(0.312026\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −5.13291 10.9842i −0.244424 0.523058i
\(22\) −24.5864 −1.11756
\(23\) −20.0507 34.7289i −0.871771 1.50995i −0.860163 0.510019i \(-0.829639\pi\)
−0.0116074 0.999933i \(-0.503695\pi\)
\(24\) −4.24264 2.44949i −0.176777 0.102062i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) −8.84951 + 5.10926i −0.340366 + 0.196510i
\(27\) 5.19615i 0.192450i
\(28\) −12.6835 + 5.92697i −0.452982 + 0.211678i
\(29\) 47.0080 1.62096 0.810482 0.585763i \(-0.199205\pi\)
0.810482 + 0.585763i \(0.199205\pi\)
\(30\) −2.73861 4.74342i −0.0912871 0.158114i
\(31\) 34.9025 + 20.1510i 1.12589 + 0.650031i 0.942897 0.333084i \(-0.108089\pi\)
0.182990 + 0.983115i \(0.441422\pi\)
\(32\) −2.82843 + 4.89898i −0.0883883 + 0.153093i
\(33\) −26.0778 + 15.0560i −0.790236 + 0.456243i
\(34\) 3.75049i 0.110308i
\(35\) −15.5940 1.35152i −0.445543 0.0386149i
\(36\) −6.00000 −0.166667
\(37\) −16.2514 28.1482i −0.439226 0.760762i 0.558404 0.829569i \(-0.311414\pi\)
−0.997630 + 0.0688071i \(0.978081\pi\)
\(38\) −3.11308 1.79734i −0.0819232 0.0472984i
\(39\) −6.25755 + 10.8384i −0.160450 + 0.277907i
\(40\) −5.47723 + 3.16228i −0.136931 + 0.0790569i
\(41\) 70.6679i 1.72361i −0.507241 0.861804i \(-0.669335\pi\)
0.507241 0.861804i \(-0.330665\pi\)
\(42\) −9.82336 + 14.0535i −0.233890 + 0.334608i
\(43\) 37.3732 0.869144 0.434572 0.900637i \(-0.356900\pi\)
0.434572 + 0.900637i \(0.356900\pi\)
\(44\) 17.3852 + 30.1120i 0.395118 + 0.684364i
\(45\) −5.80948 3.35410i −0.129099 0.0745356i
\(46\) −28.3560 + 49.1141i −0.616435 + 1.06770i
\(47\) −28.9672 + 16.7242i −0.616324 + 0.355835i −0.775436 0.631426i \(-0.782470\pi\)
0.159113 + 0.987260i \(0.449137\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 16.8339 + 46.0176i 0.343548 + 0.939135i
\(50\) −7.07107 −0.141421
\(51\) 2.29669 + 3.97799i 0.0450332 + 0.0779998i
\(52\) 12.5151 + 7.22559i 0.240675 + 0.138954i
\(53\) 35.4442 61.3911i 0.668758 1.15832i −0.309493 0.950902i \(-0.600159\pi\)
0.978252 0.207422i \(-0.0665073\pi\)
\(54\) −6.36396 + 3.67423i −0.117851 + 0.0680414i
\(55\) 38.8745i 0.706808i
\(56\) 16.2276 + 11.3430i 0.289779 + 0.202554i
\(57\) −4.40256 −0.0772379
\(58\) −33.2397 57.5728i −0.573098 0.992634i
\(59\) 87.0863 + 50.2793i 1.47604 + 0.852192i 0.999635 0.0270340i \(-0.00860625\pi\)
0.476405 + 0.879226i \(0.341940\pi\)
\(60\) −3.87298 + 6.70820i −0.0645497 + 0.111803i
\(61\) −11.1621 + 6.44446i −0.182986 + 0.105647i −0.588695 0.808355i \(-0.700358\pi\)
0.405709 + 0.914002i \(0.367025\pi\)
\(62\) 56.9955i 0.919283i
\(63\) −1.81326 + 20.9216i −0.0287819 + 0.332088i
\(64\) 8.00000 0.125000
\(65\) 8.07846 + 13.9923i 0.124284 + 0.215266i
\(66\) 36.8795 + 21.2924i 0.558781 + 0.322612i
\(67\) −47.0361 + 81.4689i −0.702031 + 1.21595i 0.265721 + 0.964050i \(0.414390\pi\)
−0.967752 + 0.251904i \(0.918943\pi\)
\(68\) 4.59339 2.65199i 0.0675498 0.0389999i
\(69\) 69.4578i 1.00663i
\(70\) 9.37137 + 20.0544i 0.133877 + 0.286491i
\(71\) −11.5793 −0.163088 −0.0815440 0.996670i \(-0.525985\pi\)
−0.0815440 + 0.996670i \(0.525985\pi\)
\(72\) 4.24264 + 7.34847i 0.0589256 + 0.102062i
\(73\) −19.6320 11.3345i −0.268931 0.155267i 0.359471 0.933156i \(-0.382957\pi\)
−0.628402 + 0.777889i \(0.716291\pi\)
\(74\) −22.9829 + 39.8076i −0.310580 + 0.537940i
\(75\) −7.50000 + 4.33013i −0.100000 + 0.0577350i
\(76\) 5.08364i 0.0668900i
\(77\) 110.252 51.5208i 1.43185 0.669101i
\(78\) 17.6990 0.226910
\(79\) 12.0542 + 20.8785i 0.152585 + 0.264285i 0.932177 0.362003i \(-0.117907\pi\)
−0.779592 + 0.626287i \(0.784574\pi\)
\(80\) 7.74597 + 4.47214i 0.0968246 + 0.0559017i
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −86.5502 + 49.9698i −1.05549 + 0.609388i
\(83\) 111.664i 1.34535i 0.739937 + 0.672676i \(0.234855\pi\)
−0.739937 + 0.672676i \(0.765145\pi\)
\(84\) 24.1581 + 2.09377i 0.287597 + 0.0249258i
\(85\) 5.93004 0.0697652
\(86\) −26.4268 45.7726i −0.307289 0.532240i
\(87\) −70.5120 40.7101i −0.810482 0.467932i
\(88\) 24.5864 42.5848i 0.279390 0.483919i
\(89\) −110.770 + 63.9533i −1.24461 + 0.718577i −0.970030 0.242987i \(-0.921873\pi\)
−0.274582 + 0.961564i \(0.588540\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 28.9773 41.4556i 0.318432 0.455556i
\(92\) 80.2029 0.871771
\(93\) −34.9025 60.4529i −0.375296 0.650031i
\(94\) 40.9658 + 23.6516i 0.435807 + 0.251613i
\(95\) −2.84184 + 4.92221i −0.0299141 + 0.0518128i
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) 7.48256i 0.0771398i −0.999256 0.0385699i \(-0.987720\pi\)
0.999256 0.0385699i \(-0.0122802\pi\)
\(98\) 44.4565 53.1566i 0.453638 0.542414i
\(99\) 52.1556 0.526824
\(100\) 5.00000 + 8.66025i 0.0500000 + 0.0866025i
\(101\) −81.9228 47.2982i −0.811117 0.468299i 0.0362267 0.999344i \(-0.488466\pi\)
−0.847344 + 0.531045i \(0.821799\pi\)
\(102\) 3.24802 5.62573i 0.0318433 0.0551542i
\(103\) −51.8072 + 29.9109i −0.502982 + 0.290397i −0.729944 0.683507i \(-0.760454\pi\)
0.226962 + 0.973904i \(0.427121\pi\)
\(104\) 20.4371i 0.196510i
\(105\) 22.2206 + 15.5321i 0.211625 + 0.147925i
\(106\) −100.251 −0.945767
\(107\) −3.23081 5.59592i −0.0301945 0.0522983i 0.850533 0.525921i \(-0.176279\pi\)
−0.880728 + 0.473623i \(0.842946\pi\)
\(108\) 9.00000 + 5.19615i 0.0833333 + 0.0481125i
\(109\) 81.9201 141.890i 0.751560 1.30174i −0.195506 0.980703i \(-0.562635\pi\)
0.947066 0.321038i \(-0.104032\pi\)
\(110\) 47.6113 27.4884i 0.432830 0.249894i
\(111\) 56.2964i 0.507175i
\(112\) 2.41768 27.8954i 0.0215864 0.249066i
\(113\) −105.434 −0.933040 −0.466520 0.884511i \(-0.654492\pi\)
−0.466520 + 0.884511i \(0.654492\pi\)
\(114\) 3.11308 + 5.39202i 0.0273077 + 0.0472984i
\(115\) 77.6561 + 44.8348i 0.675271 + 0.389868i
\(116\) −47.0080 + 81.4202i −0.405241 + 0.701898i
\(117\) 18.7726 10.8384i 0.160450 0.0926358i
\(118\) 142.211i 1.20518i
\(119\) −7.85915 16.8183i −0.0660433 0.141330i
\(120\) 10.9545 0.0912871
\(121\) −90.6223 156.962i −0.748945 1.29721i
\(122\) 15.7856 + 9.11384i 0.129391 + 0.0747036i
\(123\) −61.2002 + 106.002i −0.497563 + 0.861804i
\(124\) −69.8050 + 40.3019i −0.562944 + 0.325016i
\(125\) 11.1803i 0.0894427i
\(126\) 26.9058 12.5730i 0.213538 0.0997858i
\(127\) 53.7033 0.422860 0.211430 0.977393i \(-0.432188\pi\)
0.211430 + 0.977393i \(0.432188\pi\)
\(128\) −5.65685 9.79796i −0.0441942 0.0765466i
\(129\) −56.0598 32.3661i −0.434572 0.250900i
\(130\) 11.4247 19.7881i 0.0878820 0.152216i
\(131\) −50.6489 + 29.2421i −0.386632 + 0.223222i −0.680700 0.732562i \(-0.738324\pi\)
0.294068 + 0.955785i \(0.404991\pi\)
\(132\) 60.2240i 0.456243i
\(133\) 17.7263 + 1.53632i 0.133280 + 0.0115513i
\(134\) 133.038 0.992822
\(135\) 5.80948 + 10.0623i 0.0430331 + 0.0745356i
\(136\) −6.49603 3.75049i −0.0477650 0.0275771i
\(137\) 6.05848 10.4936i 0.0442225 0.0765956i −0.843067 0.537809i \(-0.819252\pi\)
0.887289 + 0.461213i \(0.152586\pi\)
\(138\) 85.0680 49.1141i 0.616435 0.355899i
\(139\) 45.2562i 0.325584i 0.986660 + 0.162792i \(0.0520500\pi\)
−0.986660 + 0.162792i \(0.947950\pi\)
\(140\) 17.9349 25.6581i 0.128107 0.183272i
\(141\) 57.9344 0.410882
\(142\) 8.18777 + 14.1816i 0.0576603 + 0.0998706i
\(143\) −108.789 62.8091i −0.760759 0.439225i
\(144\) 6.00000 10.3923i 0.0416667 0.0721688i
\(145\) −91.0306 + 52.5565i −0.627797 + 0.362459i
\(146\) 32.0589i 0.219581i
\(147\) 14.6016 83.6050i 0.0993309 0.568741i
\(148\) 65.0055 0.439226
\(149\) 25.4474 + 44.0762i 0.170788 + 0.295814i 0.938696 0.344747i \(-0.112035\pi\)
−0.767908 + 0.640561i \(0.778702\pi\)
\(150\) 10.6066 + 6.12372i 0.0707107 + 0.0408248i
\(151\) 78.8476 136.568i 0.522169 0.904424i −0.477498 0.878633i \(-0.658456\pi\)
0.999667 0.0257911i \(-0.00821047\pi\)
\(152\) 6.22616 3.59468i 0.0409616 0.0236492i
\(153\) 7.95598i 0.0519999i
\(154\) −141.060 98.6004i −0.915974 0.640263i
\(155\) −90.1179 −0.581406
\(156\) −12.5151 21.6768i −0.0802249 0.138954i
\(157\) 145.359 + 83.9231i 0.925854 + 0.534542i 0.885498 0.464643i \(-0.153817\pi\)
0.0403562 + 0.999185i \(0.487151\pi\)
\(158\) 17.0472 29.5266i 0.107894 0.186877i
\(159\) −106.333 + 61.3911i −0.668758 + 0.386108i
\(160\) 12.6491i 0.0790569i
\(161\) 24.2381 279.662i 0.150547 1.73703i
\(162\) 12.7279 0.0785674
\(163\) −138.285 239.517i −0.848374 1.46943i −0.882658 0.470015i \(-0.844248\pi\)
0.0342839 0.999412i \(-0.489085\pi\)
\(164\) 122.400 + 70.6679i 0.746344 + 0.430902i
\(165\) 33.6663 58.3117i 0.204038 0.353404i
\(166\) 136.760 78.9586i 0.823857 0.475654i
\(167\) 48.4258i 0.289975i −0.989433 0.144987i \(-0.953686\pi\)
0.989433 0.144987i \(-0.0463142\pi\)
\(168\) −14.5181 31.0681i −0.0864170 0.184929i
\(169\) 116.791 0.691070
\(170\) −4.19317 7.26279i −0.0246657 0.0427223i
\(171\) 6.60384 + 3.81273i 0.0386190 + 0.0222967i
\(172\) −37.3732 + 64.7323i −0.217286 + 0.376351i
\(173\) −97.8337 + 56.4843i −0.565513 + 0.326499i −0.755355 0.655316i \(-0.772536\pi\)
0.189842 + 0.981815i \(0.439202\pi\)
\(174\) 115.146i 0.661756i
\(175\) 31.7087 14.8174i 0.181193 0.0846710i
\(176\) −69.5407 −0.395118
\(177\) −87.0863 150.838i −0.492013 0.852192i
\(178\) 156.653 + 90.4437i 0.880073 + 0.508111i
\(179\) −165.708 + 287.015i −0.925744 + 1.60344i −0.135384 + 0.990793i \(0.543227\pi\)
−0.790360 + 0.612642i \(0.790107\pi\)
\(180\) 11.6190 6.70820i 0.0645497 0.0372678i
\(181\) 213.328i 1.17861i 0.807912 + 0.589303i \(0.200598\pi\)
−0.807912 + 0.589303i \(0.799402\pi\)
\(182\) −71.2626 6.17627i −0.391553 0.0339356i
\(183\) 22.3243 0.121991
\(184\) −56.7120 98.2281i −0.308218 0.533848i
\(185\) 62.9413 + 36.3392i 0.340223 + 0.196428i
\(186\) −49.3596 + 85.4933i −0.265374 + 0.459642i
\(187\) −39.9285 + 23.0527i −0.213521 + 0.123277i
\(188\) 66.8969i 0.355835i
\(189\) 20.8385 29.8120i 0.110257 0.157736i
\(190\) 8.03794 0.0423050
\(191\) 33.4517 + 57.9400i 0.175140 + 0.303351i 0.940210 0.340596i \(-0.110629\pi\)
−0.765070 + 0.643947i \(0.777296\pi\)
\(192\) −12.0000 6.92820i −0.0625000 0.0360844i
\(193\) 56.3020 97.5179i 0.291720 0.505274i −0.682497 0.730889i \(-0.739106\pi\)
0.974217 + 0.225615i \(0.0724391\pi\)
\(194\) −9.16422 + 5.29097i −0.0472383 + 0.0272730i
\(195\) 27.9846i 0.143511i
\(196\) −96.5387 16.8605i −0.492544 0.0860231i
\(197\) −61.0211 −0.309752 −0.154876 0.987934i \(-0.549498\pi\)
−0.154876 + 0.987934i \(0.549498\pi\)
\(198\) −36.8795 63.8772i −0.186260 0.322612i
\(199\) −165.554 95.5826i −0.831929 0.480314i 0.0225837 0.999745i \(-0.492811\pi\)
−0.854513 + 0.519431i \(0.826144\pi\)
\(200\) 7.07107 12.2474i 0.0353553 0.0612372i
\(201\) 141.108 81.4689i 0.702031 0.405318i
\(202\) 133.779i 0.662274i
\(203\) 269.700 + 188.519i 1.32857 + 0.928667i
\(204\) −9.18678 −0.0450332
\(205\) 79.0092 + 136.848i 0.385410 + 0.667551i
\(206\) 73.2664 + 42.3004i 0.355662 + 0.205342i
\(207\) 60.1522 104.187i 0.290590 0.503317i
\(208\) −25.0302 + 14.4512i −0.120337 + 0.0694768i
\(209\) 44.1900i 0.211435i
\(210\) 3.31054 38.1974i 0.0157645 0.181892i
\(211\) 280.115 1.32756 0.663781 0.747927i \(-0.268951\pi\)
0.663781 + 0.747927i \(0.268951\pi\)
\(212\) 70.8884 + 122.782i 0.334379 + 0.579162i
\(213\) 17.3689 + 10.0279i 0.0815440 + 0.0470795i
\(214\) −4.56905 + 7.91383i −0.0213507 + 0.0369805i
\(215\) −72.3729 + 41.7845i −0.336618 + 0.194347i
\(216\) 14.6969i 0.0680414i
\(217\) 119.434 + 255.585i 0.550388 + 1.17781i
\(218\) −231.705 −1.06287
\(219\) 19.6320 + 34.0036i 0.0896437 + 0.155267i
\(220\) −67.3325 38.8745i −0.306057 0.176702i
\(221\) −9.58111 + 16.5950i −0.0433535 + 0.0750904i
\(222\) 68.9487 39.8076i 0.310580 0.179313i
\(223\) 272.759i 1.22313i 0.791192 + 0.611567i \(0.209461\pi\)
−0.791192 + 0.611567i \(0.790539\pi\)
\(224\) −35.8743 + 16.7640i −0.160153 + 0.0748393i
\(225\) 15.0000 0.0666667
\(226\) 74.5528 + 129.129i 0.329879 + 0.571368i
\(227\) 13.9191 + 8.03620i 0.0613176 + 0.0354018i 0.530345 0.847782i \(-0.322062\pi\)
−0.469028 + 0.883183i \(0.655396\pi\)
\(228\) 4.40256 7.62546i 0.0193095 0.0334450i
\(229\) 128.261 74.0517i 0.560093 0.323370i −0.193090 0.981181i \(-0.561851\pi\)
0.753183 + 0.657811i \(0.228518\pi\)
\(230\) 126.812i 0.551356i
\(231\) −209.997 18.2003i −0.909078 0.0787891i
\(232\) 132.959 0.573098
\(233\) 149.559 + 259.044i 0.641885 + 1.11178i 0.985012 + 0.172488i \(0.0551806\pi\)
−0.343127 + 0.939289i \(0.611486\pi\)
\(234\) −26.5485 15.3278i −0.113455 0.0655034i
\(235\) 37.3965 64.7727i 0.159134 0.275628i
\(236\) −174.173 + 100.559i −0.738020 + 0.426096i
\(237\) 41.7570i 0.176190i
\(238\) −15.0408 + 21.5178i −0.0631968 + 0.0904108i
\(239\) −114.253 −0.478046 −0.239023 0.971014i \(-0.576827\pi\)
−0.239023 + 0.971014i \(0.576827\pi\)
\(240\) −7.74597 13.4164i −0.0322749 0.0559017i
\(241\) −118.162 68.2209i −0.490299 0.283074i 0.234399 0.972140i \(-0.424688\pi\)
−0.724699 + 0.689066i \(0.758021\pi\)
\(242\) −128.159 + 221.978i −0.529584 + 0.917266i
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 25.7778i 0.105647i
\(245\) −84.0479 70.2919i −0.343053 0.286906i
\(246\) 173.100 0.703660
\(247\) −9.18308 15.9056i −0.0371785 0.0643950i
\(248\) 98.7192 + 56.9955i 0.398061 + 0.229821i
\(249\) 96.7041 167.496i 0.388370 0.672676i
\(250\) 13.6931 7.90569i 0.0547723 0.0316228i
\(251\) 457.024i 1.82081i 0.413717 + 0.910406i \(0.364230\pi\)
−0.413717 + 0.910406i \(0.635770\pi\)
\(252\) −34.4240 24.0622i −0.136603 0.0954850i
\(253\) −697.171 −2.75562
\(254\) −37.9739 65.7728i −0.149504 0.258948i
\(255\) −8.89506 5.13557i −0.0348826 0.0201395i
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 43.2997 24.9991i 0.168481 0.0972726i −0.413388 0.910555i \(-0.635655\pi\)
0.581869 + 0.813282i \(0.302321\pi\)
\(258\) 91.5453i 0.354827i
\(259\) 19.6453 226.669i 0.0758505 0.875172i
\(260\) −32.3138 −0.124284
\(261\) 70.5120 + 122.130i 0.270161 + 0.467932i
\(262\) 71.6283 + 41.3546i 0.273390 + 0.157842i
\(263\) −91.1388 + 157.857i −0.346535 + 0.600217i −0.985631 0.168910i \(-0.945975\pi\)
0.639096 + 0.769127i \(0.279309\pi\)
\(264\) −73.7591 + 42.5848i −0.279390 + 0.161306i
\(265\) 158.511i 0.598156i
\(266\) −10.6528 22.7965i −0.0400480 0.0857012i
\(267\) 221.541 0.829741
\(268\) −94.0722 162.938i −0.351016 0.607977i
\(269\) −32.5814 18.8109i −0.121120 0.0699289i 0.438216 0.898870i \(-0.355611\pi\)
−0.559336 + 0.828941i \(0.688944\pi\)
\(270\) 8.21584 14.2302i 0.0304290 0.0527046i
\(271\) 175.576 101.369i 0.647880 0.374054i −0.139763 0.990185i \(-0.544634\pi\)
0.787644 + 0.616131i \(0.211301\pi\)
\(272\) 10.6080i 0.0389999i
\(273\) −79.3675 + 37.0883i −0.290724 + 0.135855i
\(274\) −17.1360 −0.0625401
\(275\) −43.4630 75.2801i −0.158047 0.273746i
\(276\) −120.304 69.4578i −0.435885 0.251659i
\(277\) −128.121 + 221.912i −0.462530 + 0.801126i −0.999086 0.0427390i \(-0.986392\pi\)
0.536556 + 0.843865i \(0.319725\pi\)
\(278\) 55.4273 32.0010i 0.199379 0.115111i
\(279\) 120.906i 0.433354i
\(280\) −44.1065 3.82268i −0.157523 0.0136524i
\(281\) −141.462 −0.503423 −0.251711 0.967802i \(-0.580993\pi\)
−0.251711 + 0.967802i \(0.580993\pi\)
\(282\) −40.9658 70.9549i −0.145269 0.251613i
\(283\) 470.571 + 271.684i 1.66279 + 0.960014i 0.971372 + 0.237562i \(0.0763483\pi\)
0.691421 + 0.722452i \(0.256985\pi\)
\(284\) 11.5793 20.0559i 0.0407720 0.0706192i
\(285\) 8.52553 4.92221i 0.0299141 0.0172709i
\(286\) 177.651i 0.621157i
\(287\) 283.405 405.445i 0.987472 1.41270i
\(288\) −16.9706 −0.0589256
\(289\) −140.983 244.191i −0.487832 0.844950i
\(290\) 128.737 + 74.3261i 0.443920 + 0.256297i
\(291\) −6.48008 + 11.2238i −0.0222683 + 0.0385699i
\(292\) 39.2639 22.6690i 0.134466 0.0776337i
\(293\) 375.289i 1.28085i −0.768021 0.640424i \(-0.778759\pi\)
0.768021 0.640424i \(-0.221241\pi\)
\(294\) −112.720 + 41.2344i −0.383400 + 0.140253i
\(295\) −224.856 −0.762224
\(296\) −45.9658 79.6151i −0.155290 0.268970i
\(297\) −78.2333 45.1680i −0.263412 0.152081i
\(298\) 35.9881 62.3332i 0.120765 0.209172i
\(299\) −250.937 + 144.878i −0.839253 + 0.484543i
\(300\) 17.3205i 0.0577350i
\(301\) 214.422 + 149.880i 0.712367 + 0.497942i
\(302\) −223.015 −0.738459
\(303\) 81.9228 + 141.894i 0.270372 + 0.468299i
\(304\) −8.80512 5.08364i −0.0289642 0.0167225i
\(305\) 14.4103 24.9593i 0.0472467 0.0818337i
\(306\) −9.74405 + 5.62573i −0.0318433 + 0.0183847i
\(307\) 41.3436i 0.134670i 0.997730 + 0.0673349i \(0.0214496\pi\)
−0.997730 + 0.0673349i \(0.978550\pi\)
\(308\) −21.0159 + 242.484i −0.0682333 + 0.787284i
\(309\) 103.614 0.335321
\(310\) 63.7230 + 110.371i 0.205558 + 0.356037i
\(311\) −126.924 73.2794i −0.408115 0.235625i 0.281865 0.959454i \(-0.409047\pi\)
−0.689979 + 0.723829i \(0.742380\pi\)
\(312\) −17.6990 + 30.6556i −0.0567276 + 0.0982551i
\(313\) 194.744 112.435i 0.622184 0.359218i −0.155535 0.987830i \(-0.549710\pi\)
0.777719 + 0.628612i \(0.216377\pi\)
\(314\) 237.370i 0.755957i
\(315\) −19.8797 42.5417i −0.0631101 0.135053i
\(316\) −48.2168 −0.152585
\(317\) 113.113 + 195.918i 0.356825 + 0.618038i 0.987428 0.158067i \(-0.0505261\pi\)
−0.630604 + 0.776105i \(0.717193\pi\)
\(318\) 150.377 + 86.8202i 0.472884 + 0.273019i
\(319\) 408.621 707.753i 1.28094 2.21866i
\(320\) −15.4919 + 8.94427i −0.0484123 + 0.0279508i
\(321\) 11.1918i 0.0348656i
\(322\) −359.653 + 168.065i −1.11694 + 0.521942i
\(323\) −6.74089 −0.0208696
\(324\) −9.00000 15.5885i −0.0277778 0.0481125i
\(325\) −31.2877 18.0640i −0.0962699 0.0555815i
\(326\) −195.565 + 338.728i −0.599891 + 1.03904i
\(327\) −245.760 + 141.890i −0.751560 + 0.433914i
\(328\) 199.879i 0.609388i
\(329\) −233.265 20.2169i −0.709011 0.0614495i
\(330\) −95.2226 −0.288553
\(331\) −69.9082 121.085i −0.211203 0.365814i 0.740888 0.671628i \(-0.234405\pi\)
−0.952091 + 0.305814i \(0.901071\pi\)
\(332\) −193.408 111.664i −0.582555 0.336338i
\(333\) 48.7541 84.4446i 0.146409 0.253587i
\(334\) −59.3093 + 34.2422i −0.177573 + 0.102522i
\(335\) 210.352i 0.627916i
\(336\) −27.7847 + 39.7494i −0.0826924 + 0.118302i
\(337\) 30.1128 0.0893556 0.0446778 0.999001i \(-0.485774\pi\)
0.0446778 + 0.999001i \(0.485774\pi\)
\(338\) −82.5836 143.039i −0.244330 0.423192i
\(339\) 158.150 + 91.3081i 0.466520 + 0.269345i
\(340\) −5.93004 + 10.2711i −0.0174413 + 0.0302092i
\(341\) 606.786 350.328i 1.77943 1.02736i
\(342\) 10.7840i 0.0315323i
\(343\) −87.9664 + 331.528i −0.256462 + 0.966554i
\(344\) 105.707 0.307289
\(345\) −77.6561 134.504i −0.225090 0.389868i
\(346\) 138.358 + 79.8809i 0.399878 + 0.230870i
\(347\) 207.954 360.186i 0.599290 1.03800i −0.393636 0.919266i \(-0.628783\pi\)
0.992926 0.118734i \(-0.0378836\pi\)
\(348\) 141.024 81.4202i 0.405241 0.233966i
\(349\) 594.950i 1.70473i −0.522950 0.852363i \(-0.675169\pi\)
0.522950 0.852363i \(-0.324831\pi\)
\(350\) −40.5690 28.3576i −0.115912 0.0810217i
\(351\) −37.5453 −0.106967
\(352\) 49.1727 + 85.1697i 0.139695 + 0.241959i
\(353\) 315.509 + 182.159i 0.893793 + 0.516031i 0.875181 0.483795i \(-0.160742\pi\)
0.0186116 + 0.999827i \(0.494075\pi\)
\(354\) −123.159 + 213.317i −0.347906 + 0.602591i
\(355\) 22.4231 12.9460i 0.0631637 0.0364676i
\(356\) 255.813i 0.718577i
\(357\) −2.77633 + 32.0336i −0.00777684 + 0.0897301i
\(358\) 468.693 1.30920
\(359\) 306.381 + 530.668i 0.853430 + 1.47818i 0.878094 + 0.478488i \(0.158815\pi\)
−0.0246647 + 0.999696i \(0.507852\pi\)
\(360\) −16.4317 9.48683i −0.0456435 0.0263523i
\(361\) −177.270 + 307.040i −0.491051 + 0.850526i
\(362\) 261.272 150.846i 0.721746 0.416700i
\(363\) 313.925i 0.864807i
\(364\) 42.8259 + 91.6457i 0.117654 + 0.251774i
\(365\) 50.6895 0.138875
\(366\) −15.7856 27.3415i −0.0431302 0.0747036i
\(367\) −426.967 246.509i −1.16340 0.671687i −0.211281 0.977425i \(-0.567764\pi\)
−0.952116 + 0.305738i \(0.901097\pi\)
\(368\) −80.2029 + 138.916i −0.217943 + 0.377488i
\(369\) 183.601 106.002i 0.497563 0.287268i
\(370\) 102.783i 0.277791i
\(371\) 449.556 210.077i 1.21174 0.566245i
\(372\) 139.610 0.375296
\(373\) −82.7013 143.243i −0.221719 0.384029i 0.733611 0.679570i \(-0.237834\pi\)
−0.955330 + 0.295541i \(0.904500\pi\)
\(374\) 56.4674 + 32.6015i 0.150982 + 0.0871697i
\(375\) 9.68246 16.7705i 0.0258199 0.0447214i
\(376\) −81.9317 + 47.3033i −0.217903 + 0.125807i
\(377\) 339.660i 0.900956i
\(378\) −51.2472 4.44155i −0.135575 0.0117501i
\(379\) −179.349 −0.473215 −0.236608 0.971605i \(-0.576036\pi\)
−0.236608 + 0.971605i \(0.576036\pi\)
\(380\) −5.68368 9.84443i −0.0149571 0.0259064i
\(381\) −80.5549 46.5084i −0.211430 0.122069i
\(382\) 47.3078 81.9395i 0.123842 0.214501i
\(383\) 233.108 134.585i 0.608636 0.351396i −0.163795 0.986494i \(-0.552374\pi\)
0.772432 + 0.635098i \(0.219040\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −155.901 + 223.035i −0.404938 + 0.579313i
\(386\) −159.246 −0.412554
\(387\) 56.0598 + 97.0984i 0.144857 + 0.250900i
\(388\) 12.9602 + 7.48256i 0.0334025 + 0.0192849i
\(389\) 236.874 410.277i 0.608930 1.05470i −0.382487 0.923961i \(-0.624932\pi\)
0.991417 0.130737i \(-0.0417344\pi\)
\(390\) −34.2740 + 19.7881i −0.0878820 + 0.0507387i
\(391\) 106.349i 0.271992i
\(392\) 47.6133 + 130.157i 0.121463 + 0.332034i
\(393\) 101.298 0.257755
\(394\) 43.1484 + 74.7353i 0.109514 + 0.189683i
\(395\) −46.6857 26.9540i −0.118192 0.0682380i
\(396\) −52.1556 + 90.3361i −0.131706 + 0.228121i
\(397\) −445.080 + 256.967i −1.12111 + 0.647271i −0.941683 0.336500i \(-0.890757\pi\)
−0.179424 + 0.983772i \(0.557423\pi\)
\(398\) 270.348i 0.679267i
\(399\) −25.2589 17.6559i −0.0633056 0.0442504i
\(400\) −20.0000 −0.0500000
\(401\) 203.367 + 352.242i 0.507150 + 0.878410i 0.999966 + 0.00827591i \(0.00263433\pi\)
−0.492816 + 0.870134i \(0.664032\pi\)
\(402\) −199.557 115.214i −0.496411 0.286603i
\(403\) 145.603 252.191i 0.361297 0.625785i
\(404\) 163.846 94.5963i 0.405558 0.234149i
\(405\) 20.1246i 0.0496904i
\(406\) 40.1814 463.617i 0.0989689 1.14191i
\(407\) −565.066 −1.38837
\(408\) 6.49603 + 11.2515i 0.0159217 + 0.0275771i
\(409\) −422.173 243.742i −1.03221 0.595946i −0.114592 0.993413i \(-0.536556\pi\)
−0.917617 + 0.397467i \(0.869889\pi\)
\(410\) 111.736 193.532i 0.272526 0.472030i
\(411\) −18.1755 + 10.4936i −0.0442225 + 0.0255319i
\(412\) 119.643i 0.290397i
\(413\) 298.004 + 637.717i 0.721560 + 1.54411i
\(414\) −170.136 −0.410957
\(415\) −124.844 216.237i −0.300830 0.521053i
\(416\) 35.3980 + 20.4371i 0.0850914 + 0.0491275i
\(417\) 39.1930 67.8843i 0.0939881 0.162792i
\(418\) −54.1215 + 31.2471i −0.129477 + 0.0747537i
\(419\) 552.257i 1.31804i −0.752127 0.659018i \(-0.770972\pi\)
0.752127 0.659018i \(-0.229028\pi\)
\(420\) −49.1230 + 22.9551i −0.116959 + 0.0546549i
\(421\) −74.6870 −0.177404 −0.0887019 0.996058i \(-0.528272\pi\)
−0.0887019 + 0.996058i \(0.528272\pi\)
\(422\) −198.072 343.070i −0.469364 0.812962i
\(423\) −86.9016 50.1727i −0.205441 0.118612i
\(424\) 100.251 173.640i 0.236442 0.409529i
\(425\) −11.4835 + 6.62999i −0.0270199 + 0.0156000i
\(426\) 28.3633i 0.0665804i
\(427\) −89.8855 7.79031i −0.210505 0.0182443i
\(428\) 12.9232 0.0301945
\(429\) 108.789 + 188.427i 0.253586 + 0.439225i
\(430\) 102.351 + 59.0922i 0.238025 + 0.137424i
\(431\) −242.339 + 419.743i −0.562271 + 0.973881i 0.435027 + 0.900417i \(0.356739\pi\)
−0.997298 + 0.0734641i \(0.976595\pi\)
\(432\) −18.0000 + 10.3923i −0.0416667 + 0.0240563i
\(433\) 458.196i 1.05819i 0.848563 + 0.529094i \(0.177468\pi\)
−0.848563 + 0.529094i \(0.822532\pi\)
\(434\) 228.573 327.002i 0.526667 0.753461i
\(435\) 182.061 0.418531
\(436\) 163.840 + 283.779i 0.375780 + 0.650870i
\(437\) −88.2746 50.9653i −0.202001 0.116626i
\(438\) 27.7638 48.0883i 0.0633877 0.109791i
\(439\) 121.167 69.9559i 0.276007 0.159353i −0.355607 0.934635i \(-0.615726\pi\)
0.631614 + 0.775283i \(0.282393\pi\)
\(440\) 109.954i 0.249894i
\(441\) −94.3065 + 112.762i −0.213847 + 0.255696i
\(442\) 27.0995 0.0613110
\(443\) 8.04616 + 13.9364i 0.0181629 + 0.0314591i 0.874964 0.484188i \(-0.160885\pi\)
−0.856801 + 0.515647i \(0.827552\pi\)
\(444\) −97.5082 56.2964i −0.219613 0.126794i
\(445\) 143.004 247.690i 0.321357 0.556607i
\(446\) 334.060 192.870i 0.749014 0.432444i
\(447\) 88.1524i 0.197209i
\(448\) 45.8986 + 32.0830i 0.102452 + 0.0716138i
\(449\) −329.314 −0.733439 −0.366720 0.930332i \(-0.619519\pi\)
−0.366720 + 0.930332i \(0.619519\pi\)
\(450\) −10.6066 18.3712i −0.0235702 0.0408248i
\(451\) −1063.98 614.288i −2.35915 1.36206i
\(452\) 105.434 182.616i 0.233260 0.404018i
\(453\) −236.543 + 136.568i −0.522169 + 0.301475i
\(454\) 22.7298i 0.0500657i
\(455\) −9.76554 + 112.676i −0.0214627 + 0.247640i
\(456\) −12.4523 −0.0273077
\(457\) 445.459 + 771.557i 0.974745 + 1.68831i 0.680773 + 0.732494i \(0.261644\pi\)
0.293972 + 0.955814i \(0.405023\pi\)
\(458\) −181.389 104.725i −0.396046 0.228657i
\(459\) −6.89008 + 11.9340i −0.0150111 + 0.0259999i
\(460\) −155.312 + 89.6696i −0.337635 + 0.194934i
\(461\) 534.019i 1.15839i −0.815188 0.579196i \(-0.803367\pi\)
0.815188 0.579196i \(-0.196633\pi\)
\(462\) 126.200 + 270.062i 0.273159 + 0.584550i
\(463\) 158.679 0.342719 0.171359 0.985209i \(-0.445184\pi\)
0.171359 + 0.985209i \(0.445184\pi\)
\(464\) −94.0160 162.840i −0.202621 0.350949i
\(465\) 135.177 + 78.0444i 0.290703 + 0.167837i
\(466\) 211.509 366.344i 0.453881 0.786145i
\(467\) −97.1671 + 56.0995i −0.208067 + 0.120127i −0.600413 0.799690i \(-0.704997\pi\)
0.392346 + 0.919818i \(0.371664\pi\)
\(468\) 43.3535i 0.0926358i
\(469\) −596.582 + 278.782i −1.27203 + 0.594417i
\(470\) −105.773 −0.225050
\(471\) −145.359 251.769i −0.308618 0.534542i
\(472\) 246.317 + 142.211i 0.521859 + 0.301295i
\(473\) 324.870 562.691i 0.686829 1.18962i
\(474\) −51.1416 + 29.5266i −0.107894 + 0.0622925i
\(475\) 12.7091i 0.0267560i
\(476\) 36.9893 + 3.20583i 0.0777085 + 0.00673494i
\(477\) 212.665 0.445839
\(478\) 80.7891 + 139.931i 0.169015 + 0.292742i
\(479\) −598.669 345.642i −1.24983 0.721590i −0.278755 0.960362i \(-0.589922\pi\)
−0.971076 + 0.238772i \(0.923255\pi\)
\(480\) −10.9545 + 18.9737i −0.0228218 + 0.0395285i
\(481\) −203.387 + 117.426i −0.422843 + 0.244128i
\(482\) 192.958i 0.400328i
\(483\) −278.551 + 398.502i −0.576711 + 0.825056i
\(484\) 362.489 0.748945
\(485\) 8.36575 + 14.4899i 0.0172490 + 0.0298761i
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) −360.410 + 624.248i −0.740062 + 1.28182i 0.212405 + 0.977182i \(0.431870\pi\)
−0.952467 + 0.304643i \(0.901463\pi\)
\(488\) −31.5713 + 18.2277i −0.0646953 + 0.0373518i
\(489\) 479.033i 0.979618i
\(490\) −26.6588 + 152.641i −0.0544058 + 0.311512i
\(491\) 589.995 1.20162 0.600809 0.799392i \(-0.294845\pi\)
0.600809 + 0.799392i \(0.294845\pi\)
\(492\) −122.400 212.004i −0.248781 0.430902i
\(493\) −107.963 62.3325i −0.218992 0.126435i
\(494\) −12.9868 + 22.4939i −0.0262891 + 0.0455341i
\(495\) −100.999 + 58.3117i −0.204038 + 0.117801i
\(496\) 161.208i 0.325016i
\(497\) −66.4340 46.4371i −0.133670 0.0934348i
\(498\) −273.521 −0.549238
\(499\) 437.845 + 758.370i 0.877445 + 1.51978i 0.854135 + 0.520052i \(0.174087\pi\)
0.0233104 + 0.999728i \(0.492579\pi\)
\(500\) −19.3649 11.1803i −0.0387298 0.0223607i
\(501\) −41.9380 + 72.6387i −0.0837085 + 0.144987i
\(502\) 559.737 323.165i 1.11501 0.643754i
\(503\) 817.809i 1.62586i −0.582360 0.812931i \(-0.697871\pi\)
0.582360 0.812931i \(-0.302129\pi\)
\(504\) −5.12866 + 59.1751i −0.0101759 + 0.117411i
\(505\) 211.524 0.418859
\(506\) 492.974 + 853.857i 0.974258 + 1.68746i
\(507\) −175.186 101.144i −0.345535 0.199495i
\(508\) −53.7033 + 93.0168i −0.105715 + 0.183104i
\(509\) −657.585 + 379.657i −1.29191 + 0.745887i −0.978993 0.203892i \(-0.934641\pi\)
−0.312921 + 0.949779i \(0.601308\pi\)
\(510\) 14.5256i 0.0284815i
\(511\) −67.1794 143.761i −0.131467 0.281333i
\(512\) 22.6274 0.0441942
\(513\) −6.60384 11.4382i −0.0128730 0.0222967i
\(514\) −61.2350 35.3540i −0.119134 0.0687821i
\(515\) 66.8827 115.844i 0.129869 0.224940i
\(516\) 112.120 64.7323i 0.217286 0.125450i
\(517\) 581.508i 1.12477i
\(518\) −291.504 + 136.219i −0.562748 + 0.262971i
\(519\) 195.667 0.377009
\(520\) 22.8493 + 39.5762i 0.0439410 + 0.0761081i
\(521\) −153.671 88.7220i −0.294954 0.170292i 0.345220 0.938522i \(-0.387804\pi\)
−0.640174 + 0.768230i \(0.721138\pi\)
\(522\) 99.7190 172.718i 0.191033 0.330878i
\(523\) 91.1221 52.6094i 0.174230 0.100592i −0.410349 0.911929i \(-0.634593\pi\)
0.584579 + 0.811337i \(0.301260\pi\)
\(524\) 116.969i 0.223222i
\(525\) −60.3954 5.23442i −0.115039 0.00997033i
\(526\) 257.780 0.490075
\(527\) −53.4403 92.5612i −0.101405 0.175638i
\(528\) 104.311 + 60.2240i 0.197559 + 0.114061i
\(529\) −539.563 + 934.551i −1.01997 + 1.76664i
\(530\) 194.136 112.084i 0.366294 0.211480i
\(531\) 301.676i 0.568128i
\(532\) −20.3873 + 29.1665i −0.0383220 + 0.0548243i
\(533\) −510.618 −0.958007
\(534\) −156.653 271.331i −0.293358 0.508111i
\(535\) 12.5129 + 7.22430i 0.0233885 + 0.0135034i
\(536\) −133.038 + 230.429i −0.248206 + 0.429905i
\(537\) 497.125 287.015i 0.925744 0.534479i
\(538\) 53.2051i 0.0988943i
\(539\) 839.172 + 146.562i 1.55690 + 0.271914i
\(540\) −23.2379 −0.0430331
\(541\) 138.181 + 239.337i 0.255419 + 0.442398i 0.965009 0.262216i \(-0.0844534\pi\)
−0.709591 + 0.704614i \(0.751120\pi\)
\(542\) −248.301 143.357i −0.458121 0.264496i
\(543\) 184.747 319.992i 0.340234 0.589303i
\(544\) 12.9921 7.50097i 0.0238825 0.0137886i
\(545\) 366.358i 0.672216i
\(546\) 101.545 + 70.9796i 0.185980 + 0.129999i
\(547\) 918.409 1.67899 0.839496 0.543366i \(-0.182850\pi\)
0.839496 + 0.543366i \(0.182850\pi\)
\(548\) 12.1170 + 20.9872i 0.0221113 + 0.0382978i
\(549\) −33.4864 19.3334i −0.0609953 0.0352156i
\(550\) −61.4659 + 106.462i −0.111756 + 0.193567i
\(551\) 103.478 59.7429i 0.187800 0.108426i
\(552\) 196.456i 0.355899i
\(553\) −14.5716 + 168.128i −0.0263500 + 0.304030i
\(554\) 362.380 0.654116
\(555\) −62.9413 109.018i −0.113408 0.196428i
\(556\) −78.3861 45.2562i −0.140982 0.0813961i
\(557\) −367.505 + 636.538i −0.659794 + 1.14280i 0.320875 + 0.947122i \(0.396023\pi\)
−0.980669 + 0.195675i \(0.937310\pi\)
\(558\) 148.079 85.4933i 0.265374 0.153214i
\(559\) 270.044i 0.483083i
\(560\) 26.5062 + 56.7223i 0.0473325 + 0.101290i
\(561\) 79.8569 0.142347
\(562\) 100.029 + 173.255i 0.177987 + 0.308282i
\(563\) 715.827 + 413.283i 1.27145 + 0.734073i 0.975261 0.221056i \(-0.0709502\pi\)
0.296191 + 0.955129i \(0.404284\pi\)
\(564\) −57.9344 + 100.345i −0.102721 + 0.177917i
\(565\) 204.171 117.878i 0.361365 0.208634i
\(566\) 768.438i 1.35767i
\(567\) −57.0757 + 26.6714i −0.100663 + 0.0470395i
\(568\) −32.7511 −0.0576603
\(569\) 216.546 + 375.069i 0.380573 + 0.659172i 0.991144 0.132790i \(-0.0423935\pi\)
−0.610571 + 0.791961i \(0.709060\pi\)
\(570\) −12.0569 6.96106i −0.0211525 0.0122124i
\(571\) −240.036 + 415.754i −0.420378 + 0.728116i −0.995976 0.0896166i \(-0.971436\pi\)
0.575598 + 0.817733i \(0.304769\pi\)
\(572\) 217.577 125.618i 0.380380 0.219612i
\(573\) 115.880i 0.202234i
\(574\) −696.964 60.4054i −1.21422 0.105236i
\(575\) −200.507 −0.348708
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) −75.4646 43.5695i −0.130788 0.0755104i 0.433179 0.901308i \(-0.357392\pi\)
−0.563966 + 0.825798i \(0.690725\pi\)
\(578\) −199.381 + 345.338i −0.344949 + 0.597470i
\(579\) −168.906 + 97.5179i −0.291720 + 0.168425i
\(580\) 210.226i 0.362459i
\(581\) −447.815 + 640.655i −0.770766 + 1.10268i
\(582\) 18.3284 0.0314922
\(583\) −616.204 1067.30i −1.05695 1.83070i
\(584\) −55.5276 32.0589i −0.0950815 0.0548953i
\(585\) −24.2354 + 41.9769i −0.0414280 + 0.0717554i
\(586\) −459.633 + 265.369i −0.784356 + 0.452848i
\(587\) 104.332i 0.177737i 0.996043 + 0.0888687i \(0.0283252\pi\)
−0.996043 + 0.0888687i \(0.971675\pi\)
\(588\) 130.206 + 108.896i 0.221439 + 0.185197i
\(589\) 102.440 0.173922
\(590\) 158.997 + 275.391i 0.269487 + 0.466765i
\(591\) 91.5316 + 52.8458i 0.154876 + 0.0894176i
\(592\) −65.0055 + 112.593i −0.109807 + 0.190191i
\(593\) 252.421 145.735i 0.425668 0.245760i −0.271831 0.962345i \(-0.587629\pi\)
0.697499 + 0.716585i \(0.254296\pi\)
\(594\) 127.754i 0.215075i
\(595\) 34.0226 + 23.7817i 0.0571808 + 0.0399692i
\(596\) −101.790 −0.170788
\(597\) 165.554 + 286.748i 0.277310 + 0.480314i
\(598\) 354.878 + 204.889i 0.593442 + 0.342624i
\(599\) −298.839 + 517.604i −0.498896 + 0.864114i −0.999999 0.00127378i \(-0.999595\pi\)
0.501103 + 0.865388i \(0.332928\pi\)
\(600\) −21.2132 + 12.2474i −0.0353553 + 0.0204124i
\(601\) 447.444i 0.744499i 0.928133 + 0.372250i \(0.121413\pi\)
−0.928133 + 0.372250i \(0.878587\pi\)
\(602\) 31.9458 368.594i 0.0530661 0.612283i
\(603\) −282.217 −0.468021
\(604\) 157.695 + 273.136i 0.261085 + 0.452212i
\(605\) 350.979 + 202.638i 0.580130 + 0.334938i
\(606\) 115.856 200.669i 0.191182 0.331137i
\(607\) 533.739 308.155i 0.879307 0.507668i 0.00887709 0.999961i \(-0.497174\pi\)
0.870430 + 0.492293i \(0.163841\pi\)
\(608\) 14.3787i 0.0236492i
\(609\) −241.288 516.346i −0.396203 0.847859i
\(610\) −40.7584 −0.0668170
\(611\) 120.842 + 209.305i 0.197778 + 0.342562i
\(612\) 13.7802 + 7.95598i 0.0225166 + 0.0130000i
\(613\) 63.5384 110.052i 0.103651 0.179530i −0.809535 0.587072i \(-0.800281\pi\)
0.913186 + 0.407542i \(0.133614\pi\)
\(614\) 50.6354 29.2344i 0.0824681 0.0476130i
\(615\) 273.696i 0.445034i
\(616\) 311.841 145.723i 0.506235 0.236563i
\(617\) 68.5630 0.111123 0.0555616 0.998455i \(-0.482305\pi\)
0.0555616 + 0.998455i \(0.482305\pi\)
\(618\) −73.2664 126.901i −0.118554 0.205342i
\(619\) 833.529 + 481.238i 1.34657 + 0.777445i 0.987763 0.155965i \(-0.0498487\pi\)
0.358812 + 0.933410i \(0.383182\pi\)
\(620\) 90.1179 156.089i 0.145351 0.251756i
\(621\) −180.457 + 104.187i −0.290590 + 0.167772i
\(622\) 207.265i 0.333224i
\(623\) −892.003 77.3092i −1.43179 0.124092i
\(624\) 50.0604 0.0802249
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) −275.409 159.008i −0.439951 0.254006i
\(627\) −38.2697 + 66.2850i −0.0610362 + 0.105718i
\(628\) −290.718 + 167.846i −0.462927 + 0.267271i
\(629\) 86.1971i 0.137038i
\(630\) −38.0457 + 54.4291i −0.0603900 + 0.0863953i
\(631\) 412.586 0.653860 0.326930 0.945048i \(-0.393986\pi\)
0.326930 + 0.945048i \(0.393986\pi\)
\(632\) 34.0944 + 59.0533i 0.0539469 + 0.0934387i
\(633\) −420.173 242.587i −0.663781 0.383234i
\(634\) 159.966 277.070i 0.252313 0.437019i
\(635\) −103.996 + 60.0421i −0.163773 + 0.0945545i
\(636\) 245.565i 0.386108i
\(637\) 332.504 121.635i 0.521985 0.190949i
\(638\) −1155.76 −1.81153
\(639\) −17.3689 30.0838i −0.0271813 0.0470795i
\(640\) 21.9089 + 12.6491i 0.0342327 + 0.0197642i
\(641\) 71.3374 123.560i 0.111291 0.192761i −0.805000 0.593275i \(-0.797835\pi\)
0.916291 + 0.400513i \(0.131168\pi\)
\(642\) 13.7072 7.91383i 0.0213507 0.0123268i
\(643\) 239.942i 0.373160i −0.982440 0.186580i \(-0.940260\pi\)
0.982440 0.186580i \(-0.0597403\pi\)
\(644\) 460.150 + 321.643i 0.714519 + 0.499446i
\(645\) 144.746 0.224412
\(646\) 4.76653 + 8.25588i 0.00737853 + 0.0127800i
\(647\) −128.817 74.3724i −0.199098 0.114950i 0.397136 0.917760i \(-0.370004\pi\)
−0.596235 + 0.802810i \(0.703337\pi\)
\(648\) −12.7279 + 22.0454i −0.0196419 + 0.0340207i
\(649\) 1514.01 874.115i 2.33284 1.34686i
\(650\) 51.0926i 0.0786041i
\(651\) 42.1915 486.810i 0.0648102 0.747788i
\(652\) 553.140 0.848374
\(653\) −144.011 249.434i −0.220537 0.381982i 0.734434 0.678680i \(-0.237448\pi\)
−0.954971 + 0.296698i \(0.904114\pi\)
\(654\) 347.557 + 200.662i 0.531433 + 0.306823i
\(655\) 65.3874 113.254i 0.0998281 0.172907i
\(656\) −244.801 + 141.336i −0.373172 + 0.215451i
\(657\) 68.0071i 0.103512i
\(658\) 140.183 + 299.985i 0.213043 + 0.455905i
\(659\) −175.647 −0.266536 −0.133268 0.991080i \(-0.542547\pi\)
−0.133268 + 0.991080i \(0.542547\pi\)
\(660\) 67.3325 + 116.623i 0.102019 + 0.176702i
\(661\) −615.015 355.079i −0.930432 0.537185i −0.0434835 0.999054i \(-0.513846\pi\)
−0.886948 + 0.461869i \(0.847179\pi\)
\(662\) −98.8651 + 171.239i −0.149343 + 0.258670i
\(663\) 28.7433 16.5950i 0.0433535 0.0250301i
\(664\) 315.834i 0.475654i
\(665\) −36.0445 + 16.8435i −0.0542022 + 0.0253286i
\(666\) −137.897 −0.207053
\(667\) −942.544 1632.53i −1.41311 2.44758i
\(668\) 83.8760 + 48.4258i 0.125563 + 0.0724937i
\(669\) 236.216 409.139i 0.353089 0.611567i
\(670\) −257.627 + 148.741i −0.384518 + 0.222002i
\(671\) 224.076i 0.333944i
\(672\) 68.3296 + 5.92207i 0.101681 + 0.00881261i
\(673\) −1173.04 −1.74301 −0.871504 0.490389i \(-0.836855\pi\)
−0.871504 + 0.490389i \(0.836855\pi\)
\(674\) −21.2930 36.8806i −0.0315920 0.0547189i
\(675\) −22.5000 12.9904i −0.0333333 0.0192450i
\(676\) −116.791 + 202.288i −0.172768 + 0.299242i
\(677\) 586.699 338.731i 0.866616 0.500341i 0.000393478 1.00000i \(-0.499875\pi\)
0.866222 + 0.499659i \(0.166541\pi\)
\(678\) 258.258i 0.380912i
\(679\) 30.0078 42.9299i 0.0441941 0.0632252i
\(680\) 16.7727 0.0246657
\(681\) −13.9191 24.1086i −0.0204392 0.0354018i
\(682\) −858.126 495.439i −1.25825 0.726450i
\(683\) 415.514 719.691i 0.608366 1.05372i −0.383144 0.923689i \(-0.625159\pi\)
0.991510 0.130032i \(-0.0415079\pi\)
\(684\) −13.2077 + 7.62546i −0.0193095 + 0.0111483i
\(685\) 27.0944i 0.0395538i
\(686\) 468.239 126.689i 0.682564 0.184679i
\(687\) −256.523 −0.373395
\(688\) −74.7464 129.465i −0.108643 0.188175i
\(689\) −443.587 256.105i −0.643813 0.371706i
\(690\) −109.822 + 190.218i −0.159163 + 0.275678i
\(691\) 541.436 312.598i 0.783554 0.452385i −0.0541345 0.998534i \(-0.517240\pi\)
0.837688 + 0.546149i \(0.183907\pi\)
\(692\) 225.937i 0.326499i
\(693\) 299.233 + 209.163i 0.431794 + 0.301823i
\(694\) −588.181 −0.847524
\(695\) −50.5980 87.6383i −0.0728029 0.126098i
\(696\) −199.438 115.146i −0.286549 0.165439i
\(697\) −93.7055 + 162.303i −0.134441 + 0.232859i
\(698\) −728.661 + 420.693i −1.04393 + 0.602712i
\(699\) 518.088i 0.741185i
\(700\) −6.04419 + 69.7386i −0.00863456 + 0.0996265i
\(701\) 1030.02 1.46936 0.734678 0.678416i \(-0.237333\pi\)
0.734678 + 0.678416i \(0.237333\pi\)
\(702\) 26.5485 + 45.9834i 0.0378184 + 0.0655034i
\(703\) −71.5477 41.3081i −0.101775 0.0587597i
\(704\) 69.5407 120.448i 0.0987795 0.171091i
\(705\) −112.190 + 64.7727i −0.159134 + 0.0918761i
\(706\) 515.224i 0.729779i
\(707\) −280.335 599.906i −0.396513 0.848523i
\(708\) 348.345 0.492013
\(709\) 329.126 + 570.062i 0.464211 + 0.804037i 0.999166 0.0408438i \(-0.0130046\pi\)
−0.534955 + 0.844881i \(0.679671\pi\)
\(710\) −31.7111 18.3084i −0.0446635 0.0257865i
\(711\) −36.1626 + 62.6354i −0.0508616 + 0.0880949i
\(712\) −313.306 + 180.887i −0.440037 + 0.254055i
\(713\) 1616.17i 2.26671i
\(714\) 41.1962 19.2509i 0.0576978 0.0269621i
\(715\) 280.891 0.392854
\(716\) −331.416 574.030i −0.462872 0.801718i
\(717\) 171.380 + 98.9461i 0.239023 + 0.138000i
\(718\) 433.288 750.478i 0.603466 1.04523i
\(719\) −1166.99 + 673.760i −1.62307 + 0.937079i −0.636975 + 0.770884i \(0.719815\pi\)
−0.986093 + 0.166195i \(0.946852\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −417.188 36.1574i −0.578625 0.0501490i
\(722\) 501.394 0.694452
\(723\) 118.162 + 204.663i 0.163433 + 0.283074i
\(724\) −369.495 213.328i −0.510352 0.294652i
\(725\) 117.520 203.551i 0.162096 0.280759i
\(726\) 384.478 221.978i 0.529584 0.305755i
\(727\) 1126.18i 1.54907i −0.632530 0.774536i \(-0.717983\pi\)
0.632530 0.774536i \(-0.282017\pi\)
\(728\) 81.9602 117.254i 0.112583 0.161063i
\(729\) −27.0000 −0.0370370
\(730\) −35.8429 62.0817i −0.0490999 0.0850435i
\(731\) −85.8348 49.5568i −0.117421 0.0677931i
\(732\) −22.3243 + 38.6668i −0.0304976 + 0.0528235i
\(733\) 525.395 303.337i 0.716773 0.413829i −0.0967907 0.995305i \(-0.530858\pi\)
0.813564 + 0.581476i \(0.197524\pi\)
\(734\) 697.233i 0.949909i
\(735\) 65.1972 + 178.225i 0.0887037 + 0.242484i
\(736\) 226.848 0.308218
\(737\) 817.731 + 1416.35i 1.10954 + 1.92178i
\(738\) −259.651 149.909i −0.351830 0.203129i
\(739\) −461.084 + 798.622i −0.623930 + 1.08068i 0.364817 + 0.931079i \(0.381132\pi\)
−0.988747 + 0.149599i \(0.952202\pi\)
\(740\) −125.883 + 72.6783i −0.170112 + 0.0982140i
\(741\) 31.8111i 0.0429300i
\(742\) −575.175 402.045i −0.775168 0.541840i
\(743\) 13.3994 0.0180342 0.00901712 0.999959i \(-0.497130\pi\)
0.00901712 + 0.999959i \(0.497130\pi\)
\(744\) −98.7192 170.987i −0.132687 0.229821i
\(745\) −98.5574 56.9022i −0.132292 0.0763787i
\(746\) −116.957 + 202.576i −0.156779 + 0.271550i
\(747\) −290.112 + 167.496i −0.388370 + 0.224225i
\(748\) 92.2108i 0.123277i
\(749\) 3.90552 45.0624i 0.00521431 0.0601634i
\(750\) −27.3861 −0.0365148
\(751\) −538.071 931.967i −0.716473 1.24097i −0.962389 0.271676i \(-0.912422\pi\)
0.245916 0.969291i \(-0.420911\pi\)
\(752\) 115.869 + 66.8969i 0.154081 + 0.0889587i
\(753\) 395.794 685.536i 0.525623 0.910406i
\(754\) −415.997 + 240.176i −0.551721 + 0.318536i
\(755\) 352.617i 0.467043i
\(756\) 30.7975 + 65.9054i 0.0407374 + 0.0871764i
\(757\) −254.117 −0.335690 −0.167845 0.985813i \(-0.553681\pi\)
−0.167845 + 0.985813i \(0.553681\pi\)
\(758\) 126.819 + 219.656i 0.167307 + 0.289784i
\(759\) 1045.76 + 603.768i 1.37781 + 0.795478i
\(760\) −8.03794 + 13.9221i −0.0105762 + 0.0183186i
\(761\) −685.095 + 395.540i −0.900256 + 0.519763i −0.877283 0.479973i \(-0.840646\pi\)
−0.0229729 + 0.999736i \(0.507313\pi\)
\(762\) 131.546i 0.172632i
\(763\) 1039.03 485.538i 1.36177 0.636354i
\(764\) −133.807 −0.175140
\(765\) 8.89506 + 15.4067i 0.0116275 + 0.0201395i
\(766\) −329.664 190.332i −0.430371 0.248475i
\(767\) 363.298 629.250i 0.473661 0.820405i
\(768\) 24.0000 13.8564i 0.0312500 0.0180422i
\(769\) 464.403i 0.603905i 0.953323 + 0.301952i \(0.0976384\pi\)
−0.953323 + 0.301952i \(0.902362\pi\)
\(770\) 383.400 + 33.2290i 0.497922