Properties

Label 48.3.l.a.19.5
Level 48
Weight 3
Character 48.19
Analytic conductor 1.308
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 19.5
Root \(-0.455024 + 1.94755i\) of defining polynomial
Character \(\chi\) \(=\) 48.19
Dual form 48.3.l.a.43.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.455024 + 1.94755i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(-3.58591 + 1.77236i) q^{4} +(-3.40572 + 3.40572i) q^{5} +(-2.94254 - 1.82796i) q^{6} +12.1303 q^{7} +(-5.08344 - 6.17727i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(0.455024 + 1.94755i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(-3.58591 + 1.77236i) q^{4} +(-3.40572 + 3.40572i) q^{5} +(-2.94254 - 1.82796i) q^{6} +12.1303 q^{7} +(-5.08344 - 6.17727i) q^{8} -3.00000i q^{9} +(-8.18251 - 5.08314i) q^{10} +(9.81086 + 9.81086i) q^{11} +(2.22113 - 6.56251i) q^{12} +(-7.76859 - 7.76859i) q^{13} +(5.51959 + 23.6244i) q^{14} -8.34229i q^{15} +(9.71745 - 12.7111i) q^{16} +9.73087 q^{17} +(5.84265 - 1.36507i) q^{18} +(11.2823 - 11.2823i) q^{19} +(6.17643 - 18.2488i) q^{20} +(-14.8566 + 14.8566i) q^{21} +(-14.6430 + 23.5713i) q^{22} -20.2635 q^{23} +(13.7915 + 1.33965i) q^{24} +1.80207i q^{25} +(11.5948 - 18.6646i) q^{26} +(3.67423 + 3.67423i) q^{27} +(-43.4982 + 21.4994i) q^{28} +(-16.4069 - 16.4069i) q^{29} +(16.2470 - 3.79594i) q^{30} -26.3542i q^{31} +(29.1771 + 13.1414i) q^{32} -24.0316 q^{33} +(4.42778 + 18.9514i) q^{34} +(-41.3125 + 41.3125i) q^{35} +(5.31709 + 10.7577i) q^{36} +(-23.7263 + 23.7263i) q^{37} +(27.1066 + 16.8392i) q^{38} +19.0291 q^{39} +(38.3509 + 3.72526i) q^{40} -24.7452i q^{41} +(-35.6940 - 22.1738i) q^{42} +(29.8844 + 29.8844i) q^{43} +(-52.5692 - 17.7924i) q^{44} +(10.2172 + 10.2172i) q^{45} +(-9.22036 - 39.4641i) q^{46} -31.3325i q^{47} +(3.66642 + 27.4692i) q^{48} +98.1448 q^{49} +(-3.50963 + 0.819987i) q^{50} +(-11.9178 + 11.9178i) q^{51} +(41.6262 + 14.0887i) q^{52} +(36.8742 - 36.8742i) q^{53} +(-5.48389 + 8.82762i) q^{54} -66.8262 q^{55} +(-61.6638 - 74.9322i) q^{56} +27.6359i q^{57} +(24.4877 - 39.4188i) q^{58} +(-14.1325 - 14.1325i) q^{59} +(14.7856 + 29.9147i) q^{60} +(-42.5199 - 42.5199i) q^{61} +(51.3260 - 11.9918i) q^{62} -36.3910i q^{63} +(-12.3172 + 62.8036i) q^{64} +52.9153 q^{65} +(-10.9350 - 46.8028i) q^{66} +(48.7789 - 48.7789i) q^{67} +(-34.8940 + 17.2467i) q^{68} +(24.8176 - 24.8176i) q^{69} +(-99.2565 - 61.6601i) q^{70} +7.73935 q^{71} +(-18.5318 + 15.2503i) q^{72} +85.4163i q^{73} +(-57.0041 - 35.4121i) q^{74} +(-2.20708 - 2.20708i) q^{75} +(-20.4610 + 60.4537i) q^{76} +(119.009 + 119.009i) q^{77} +(8.65869 + 37.0601i) q^{78} +105.294i q^{79} +(10.1954 + 76.3854i) q^{80} -9.00000 q^{81} +(48.1926 - 11.2597i) q^{82} +(-62.1229 + 62.1229i) q^{83} +(26.9430 - 79.6054i) q^{84} +(-33.1407 + 33.1407i) q^{85} +(-44.6033 + 71.7996i) q^{86} +40.1885 q^{87} +(10.7313 - 110.477i) q^{88} -127.172i q^{89} +(-15.2494 + 24.5475i) q^{90} +(-94.2355 - 94.2355i) q^{91} +(72.6629 - 35.9142i) q^{92} +(32.2771 + 32.2771i) q^{93} +(61.0215 - 14.2570i) q^{94} +76.8489i q^{95} +(-51.8294 + 19.6397i) q^{96} -147.348 q^{97} +(44.6582 + 191.142i) q^{98} +(29.4326 - 29.4326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} - 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} - 12q^{8} - 56q^{10} + 32q^{11} - 24q^{12} - 44q^{14} + 32q^{16} + 12q^{18} - 32q^{19} + 80q^{20} + 32q^{22} - 128q^{23} + 36q^{24} - 100q^{26} - 120q^{28} + 32q^{29} + 72q^{30} + 160q^{32} + 96q^{34} + 96q^{35} + 12q^{36} - 96q^{37} + 168q^{38} + 48q^{40} - 60q^{42} + 160q^{43} + 88q^{44} + 136q^{46} - 144q^{48} + 112q^{49} - 236q^{50} - 96q^{51} - 48q^{52} - 160q^{53} - 36q^{54} - 256q^{55} - 224q^{56} + 144q^{58} - 128q^{59} - 72q^{60} - 32q^{61} - 276q^{62} - 408q^{64} - 32q^{65} + 72q^{66} + 320q^{67} - 448q^{68} + 96q^{69} - 384q^{70} + 512q^{71} + 60q^{72} + 348q^{74} + 192q^{75} + 72q^{76} + 224q^{77} + 396q^{78} + 552q^{80} - 144q^{81} - 40q^{82} - 160q^{83} + 72q^{84} + 160q^{85} + 528q^{86} + 480q^{88} - 24q^{90} - 480q^{91} + 496q^{92} + 312q^{94} - 480q^{96} - 440q^{98} + 96q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.455024 + 1.94755i 0.227512 + 0.973775i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) −3.58591 + 1.77236i −0.896477 + 0.443091i
\(5\) −3.40572 + 3.40572i −0.681145 + 0.681145i −0.960258 0.279113i \(-0.909960\pi\)
0.279113 + 0.960258i \(0.409960\pi\)
\(6\) −2.94254 1.82796i −0.490423 0.304661i
\(7\) 12.1303 1.73290 0.866452 0.499261i \(-0.166395\pi\)
0.866452 + 0.499261i \(0.166395\pi\)
\(8\) −5.08344 6.17727i −0.635430 0.772158i
\(9\) 3.00000i 0.333333i
\(10\) −8.18251 5.08314i −0.818251 0.508314i
\(11\) 9.81086 + 9.81086i 0.891896 + 0.891896i 0.994702 0.102805i \(-0.0327818\pi\)
−0.102805 + 0.994702i \(0.532782\pi\)
\(12\) 2.22113 6.56251i 0.185094 0.546876i
\(13\) −7.76859 7.76859i −0.597584 0.597584i 0.342085 0.939669i \(-0.388867\pi\)
−0.939669 + 0.342085i \(0.888867\pi\)
\(14\) 5.51959 + 23.6244i 0.394256 + 1.68746i
\(15\) 8.34229i 0.556153i
\(16\) 9.71745 12.7111i 0.607341 0.794442i
\(17\) 9.73087 0.572404 0.286202 0.958169i \(-0.407607\pi\)
0.286202 + 0.958169i \(0.407607\pi\)
\(18\) 5.84265 1.36507i 0.324592 0.0758373i
\(19\) 11.2823 11.2823i 0.593806 0.593806i −0.344851 0.938657i \(-0.612071\pi\)
0.938657 + 0.344851i \(0.112071\pi\)
\(20\) 6.17643 18.2488i 0.308821 0.912440i
\(21\) −14.8566 + 14.8566i −0.707455 + 0.707455i
\(22\) −14.6430 + 23.5713i −0.665589 + 1.07142i
\(23\) −20.2635 −0.881020 −0.440510 0.897748i \(-0.645202\pi\)
−0.440510 + 0.897748i \(0.645202\pi\)
\(24\) 13.7915 + 1.33965i 0.574646 + 0.0558189i
\(25\) 1.80207i 0.0720830i
\(26\) 11.5948 18.6646i 0.445955 0.717870i
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −43.4982 + 21.4994i −1.55351 + 0.767834i
\(29\) −16.4069 16.4069i −0.565754 0.565754i 0.365182 0.930936i \(-0.381007\pi\)
−0.930936 + 0.365182i \(0.881007\pi\)
\(30\) 16.2470 3.79594i 0.541568 0.126531i
\(31\) 26.3542i 0.850134i −0.905162 0.425067i \(-0.860251\pi\)
0.905162 0.425067i \(-0.139749\pi\)
\(32\) 29.1771 + 13.1414i 0.911785 + 0.410668i
\(33\) −24.0316 −0.728230
\(34\) 4.42778 + 18.9514i 0.130229 + 0.557393i
\(35\) −41.3125 + 41.3125i −1.18036 + 1.18036i
\(36\) 5.31709 + 10.7577i 0.147697 + 0.298826i
\(37\) −23.7263 + 23.7263i −0.641250 + 0.641250i −0.950863 0.309613i \(-0.899801\pi\)
0.309613 + 0.950863i \(0.399801\pi\)
\(38\) 27.1066 + 16.8392i 0.713332 + 0.443136i
\(39\) 19.0291 0.487925
\(40\) 38.3509 + 3.72526i 0.958772 + 0.0931315i
\(41\) 24.7452i 0.603542i −0.953380 0.301771i \(-0.902422\pi\)
0.953380 0.301771i \(-0.0975779\pi\)
\(42\) −35.6940 22.1738i −0.849856 0.527948i
\(43\) 29.8844 + 29.8844i 0.694987 + 0.694987i 0.963325 0.268338i \(-0.0864744\pi\)
−0.268338 + 0.963325i \(0.586474\pi\)
\(44\) −52.5692 17.7924i −1.19476 0.404373i
\(45\) 10.2172 + 10.2172i 0.227048 + 0.227048i
\(46\) −9.22036 39.4641i −0.200443 0.857915i
\(47\) 31.3325i 0.666648i −0.942812 0.333324i \(-0.891830\pi\)
0.942812 0.333324i \(-0.108170\pi\)
\(48\) 3.66642 + 27.4692i 0.0763837 + 0.572275i
\(49\) 98.1448 2.00295
\(50\) −3.50963 + 0.819987i −0.0701926 + 0.0163997i
\(51\) −11.9178 + 11.9178i −0.233683 + 0.233683i
\(52\) 41.6262 + 14.0887i 0.800504 + 0.270936i
\(53\) 36.8742 36.8742i 0.695739 0.695739i −0.267750 0.963489i \(-0.586280\pi\)
0.963489 + 0.267750i \(0.0862800\pi\)
\(54\) −5.48389 + 8.82762i −0.101554 + 0.163474i
\(55\) −66.8262 −1.21502
\(56\) −61.6638 74.9322i −1.10114 1.33808i
\(57\) 27.6359i 0.484841i
\(58\) 24.4877 39.4188i 0.422202 0.679634i
\(59\) −14.1325 14.1325i −0.239534 0.239534i 0.577123 0.816657i \(-0.304175\pi\)
−0.816657 + 0.577123i \(0.804175\pi\)
\(60\) 14.7856 + 29.9147i 0.246426 + 0.498578i
\(61\) −42.5199 42.5199i −0.697048 0.697048i 0.266725 0.963773i \(-0.414059\pi\)
−0.963773 + 0.266725i \(0.914059\pi\)
\(62\) 51.3260 11.9918i 0.827839 0.193416i
\(63\) 36.3910i 0.577634i
\(64\) −12.3172 + 62.8036i −0.192457 + 0.981305i
\(65\) 52.9153 0.814082
\(66\) −10.9350 46.8028i −0.165681 0.709133i
\(67\) 48.7789 48.7789i 0.728044 0.728044i −0.242186 0.970230i \(-0.577864\pi\)
0.970230 + 0.242186i \(0.0778644\pi\)
\(68\) −34.8940 + 17.2467i −0.513147 + 0.253627i
\(69\) 24.8176 24.8176i 0.359675 0.359675i
\(70\) −99.2565 61.6601i −1.41795 0.880858i
\(71\) 7.73935 0.109005 0.0545025 0.998514i \(-0.482643\pi\)
0.0545025 + 0.998514i \(0.482643\pi\)
\(72\) −18.5318 + 15.2503i −0.257386 + 0.211810i
\(73\) 85.4163i 1.17009i 0.811002 + 0.585043i \(0.198923\pi\)
−0.811002 + 0.585043i \(0.801077\pi\)
\(74\) −57.0041 35.4121i −0.770326 0.478541i
\(75\) −2.20708 2.20708i −0.0294278 0.0294278i
\(76\) −20.4610 + 60.4537i −0.269223 + 0.795443i
\(77\) 119.009 + 119.009i 1.54557 + 1.54557i
\(78\) 8.65869 + 37.0601i 0.111009 + 0.475129i
\(79\) 105.294i 1.33283i 0.745581 + 0.666416i \(0.232172\pi\)
−0.745581 + 0.666416i \(0.767828\pi\)
\(80\) 10.1954 + 76.3854i 0.127443 + 0.954817i
\(81\) −9.00000 −0.111111
\(82\) 48.1926 11.2597i 0.587715 0.137313i
\(83\) −62.1229 + 62.1229i −0.748469 + 0.748469i −0.974192 0.225723i \(-0.927526\pi\)
0.225723 + 0.974192i \(0.427526\pi\)
\(84\) 26.9430 79.6054i 0.320750 0.947684i
\(85\) −33.1407 + 33.1407i −0.389890 + 0.389890i
\(86\) −44.6033 + 71.7996i −0.518643 + 0.834879i
\(87\) 40.1885 0.461937
\(88\) 10.7313 110.477i 0.121947 1.25542i
\(89\) 127.172i 1.42890i −0.699685 0.714451i \(-0.746676\pi\)
0.699685 0.714451i \(-0.253324\pi\)
\(90\) −15.2494 + 24.5475i −0.169438 + 0.272750i
\(91\) −94.2355 94.2355i −1.03555 1.03555i
\(92\) 72.6629 35.9142i 0.789814 0.390372i
\(93\) 32.2771 + 32.2771i 0.347066 + 0.347066i
\(94\) 61.0215 14.2570i 0.649165 0.151670i
\(95\) 76.8489i 0.808936i
\(96\) −51.8294 + 19.6397i −0.539889 + 0.204580i
\(97\) −147.348 −1.51905 −0.759525 0.650478i \(-0.774569\pi\)
−0.759525 + 0.650478i \(0.774569\pi\)
\(98\) 44.6582 + 191.142i 0.455696 + 1.95043i
\(99\) 29.4326 29.4326i 0.297299 0.297299i
\(100\) −3.19393 6.46207i −0.0319393 0.0646207i
\(101\) 12.7690 12.7690i 0.126426 0.126426i −0.641063 0.767489i \(-0.721506\pi\)
0.767489 + 0.641063i \(0.221506\pi\)
\(102\) −28.6335 17.7877i −0.280721 0.174389i
\(103\) −17.7621 −0.172448 −0.0862240 0.996276i \(-0.527480\pi\)
−0.0862240 + 0.996276i \(0.527480\pi\)
\(104\) −8.49746 + 87.4798i −0.0817063 + 0.841152i
\(105\) 101.195i 0.963759i
\(106\) 88.5929 + 55.0357i 0.835782 + 0.519204i
\(107\) −15.8889 15.8889i −0.148494 0.148494i 0.628951 0.777445i \(-0.283485\pi\)
−0.777445 + 0.628951i \(0.783485\pi\)
\(108\) −19.6875 6.66338i −0.182292 0.0616980i
\(109\) −79.3257 79.3257i −0.727758 0.727758i 0.242414 0.970173i \(-0.422061\pi\)
−0.970173 + 0.242414i \(0.922061\pi\)
\(110\) −30.4075 130.147i −0.276432 1.18316i
\(111\) 58.1172i 0.523579i
\(112\) 117.876 154.189i 1.05246 1.37669i
\(113\) −167.538 −1.48263 −0.741317 0.671155i \(-0.765799\pi\)
−0.741317 + 0.671155i \(0.765799\pi\)
\(114\) −53.8223 + 12.5750i −0.472126 + 0.110307i
\(115\) 69.0118 69.0118i 0.600102 0.600102i
\(116\) 87.9125 + 29.7546i 0.757866 + 0.256505i
\(117\) −23.3058 + 23.3058i −0.199195 + 0.199195i
\(118\) 21.0932 33.9545i 0.178756 0.287750i
\(119\) 118.039 0.991921
\(120\) −51.5325 + 42.4075i −0.429438 + 0.353396i
\(121\) 71.5059i 0.590958i
\(122\) 63.4621 102.157i 0.520181 0.837355i
\(123\) 30.3066 + 30.3066i 0.246395 + 0.246395i
\(124\) 46.7092 + 94.5035i 0.376687 + 0.762125i
\(125\) −91.2805 91.2805i −0.730244 0.730244i
\(126\) 70.8733 16.5588i 0.562486 0.131419i
\(127\) 198.247i 1.56100i 0.625156 + 0.780500i \(0.285035\pi\)
−0.625156 + 0.780500i \(0.714965\pi\)
\(128\) −127.918 + 4.58871i −0.999357 + 0.0358493i
\(129\) −73.2016 −0.567454
\(130\) 24.0778 + 103.055i 0.185213 + 0.792733i
\(131\) 134.339 134.339i 1.02549 1.02549i 0.0258197 0.999667i \(-0.491780\pi\)
0.999667 0.0258197i \(-0.00821957\pi\)
\(132\) 86.1751 42.5927i 0.652841 0.322672i
\(133\) 136.858 136.858i 1.02901 1.02901i
\(134\) 117.195 + 72.8039i 0.874590 + 0.543313i
\(135\) −25.0269 −0.185384
\(136\) −49.4663 60.1102i −0.363723 0.441987i
\(137\) 255.937i 1.86816i 0.357069 + 0.934078i \(0.383776\pi\)
−0.357069 + 0.934078i \(0.616224\pi\)
\(138\) 59.6261 + 37.0409i 0.432073 + 0.268412i
\(139\) −21.7231 21.7231i −0.156281 0.156281i 0.624635 0.780917i \(-0.285248\pi\)
−0.780917 + 0.624635i \(0.785248\pi\)
\(140\) 74.9220 221.364i 0.535157 1.58117i
\(141\) 38.3743 + 38.3743i 0.272158 + 0.272158i
\(142\) 3.52159 + 15.0728i 0.0247999 + 0.106146i
\(143\) 152.433i 1.06597i
\(144\) −38.1332 29.1523i −0.264814 0.202447i
\(145\) 111.755 0.770722
\(146\) −166.353 + 38.8665i −1.13940 + 0.266209i
\(147\) −120.202 + 120.202i −0.817703 + 0.817703i
\(148\) 43.0286 127.132i 0.290734 0.858998i
\(149\) −34.2444 + 34.2444i −0.229828 + 0.229828i −0.812621 0.582793i \(-0.801960\pi\)
0.582793 + 0.812621i \(0.301960\pi\)
\(150\) 3.29413 5.30268i 0.0219609 0.0353512i
\(151\) −14.4645 −0.0957913 −0.0478956 0.998852i \(-0.515251\pi\)
−0.0478956 + 0.998852i \(0.515251\pi\)
\(152\) −127.047 12.3409i −0.835835 0.0811898i
\(153\) 29.1926i 0.190801i
\(154\) −177.624 + 285.928i −1.15340 + 1.85667i
\(155\) 89.7550 + 89.7550i 0.579064 + 0.579064i
\(156\) −68.2365 + 33.7265i −0.437413 + 0.216195i
\(157\) 31.4652 + 31.4652i 0.200415 + 0.200415i 0.800178 0.599763i \(-0.204738\pi\)
−0.599763 + 0.800178i \(0.704738\pi\)
\(158\) −205.065 + 47.9111i −1.29788 + 0.303235i
\(159\) 90.3229i 0.568068i
\(160\) −144.125 + 54.6133i −0.900782 + 0.341333i
\(161\) −245.802 −1.52672
\(162\) −4.09522 17.5280i −0.0252791 0.108197i
\(163\) 31.4002 31.4002i 0.192640 0.192640i −0.604196 0.796836i \(-0.706506\pi\)
0.796836 + 0.604196i \(0.206506\pi\)
\(164\) 43.8576 + 88.7341i 0.267424 + 0.541062i
\(165\) 81.8450 81.8450i 0.496030 0.496030i
\(166\) −149.255 92.7201i −0.899126 0.558555i
\(167\) 36.4796 0.218441 0.109220 0.994018i \(-0.465165\pi\)
0.109220 + 0.994018i \(0.465165\pi\)
\(168\) 167.295 + 16.2504i 0.995805 + 0.0967288i
\(169\) 48.2981i 0.285788i
\(170\) −79.6229 49.4633i −0.468370 0.290961i
\(171\) −33.8469 33.8469i −0.197935 0.197935i
\(172\) −160.129 54.1967i −0.930982 0.315097i
\(173\) 97.6419 + 97.6419i 0.564404 + 0.564404i 0.930555 0.366151i \(-0.119325\pi\)
−0.366151 + 0.930555i \(0.619325\pi\)
\(174\) 18.2867 + 78.2691i 0.105096 + 0.449822i
\(175\) 21.8598i 0.124913i
\(176\) 220.043 29.3700i 1.25024 0.166875i
\(177\) 34.6175 0.195579
\(178\) 247.674 57.8664i 1.39143 0.325092i
\(179\) 89.7427 89.7427i 0.501356 0.501356i −0.410503 0.911859i \(-0.634647\pi\)
0.911859 + 0.410503i \(0.134647\pi\)
\(180\) −54.7464 18.5293i −0.304147 0.102940i
\(181\) −115.497 + 115.497i −0.638108 + 0.638108i −0.950088 0.311981i \(-0.899008\pi\)
0.311981 + 0.950088i \(0.399008\pi\)
\(182\) 140.649 226.408i 0.772796 1.24400i
\(183\) 104.152 0.569137
\(184\) 103.008 + 125.173i 0.559827 + 0.680287i
\(185\) 161.610i 0.873569i
\(186\) −48.1744 + 77.5482i −0.259002 + 0.416926i
\(187\) 95.4682 + 95.4682i 0.510525 + 0.510525i
\(188\) 55.5325 + 112.355i 0.295386 + 0.597634i
\(189\) 44.5697 + 44.5697i 0.235818 + 0.235818i
\(190\) −149.667 + 34.9681i −0.787722 + 0.184043i
\(191\) 62.6278i 0.327894i 0.986469 + 0.163947i \(0.0524227\pi\)
−0.986469 + 0.163947i \(0.947577\pi\)
\(192\) −61.8329 92.0038i −0.322046 0.479186i
\(193\) 223.342 1.15721 0.578607 0.815607i \(-0.303597\pi\)
0.578607 + 0.815607i \(0.303597\pi\)
\(194\) −67.0468 286.967i −0.345602 1.47921i
\(195\) −64.8078 + 64.8078i −0.332348 + 0.332348i
\(196\) −351.938 + 173.948i −1.79560 + 0.887491i
\(197\) 29.0959 29.0959i 0.147695 0.147695i −0.629393 0.777087i \(-0.716696\pi\)
0.777087 + 0.629393i \(0.216696\pi\)
\(198\) 70.7140 + 43.9289i 0.357141 + 0.221863i
\(199\) 11.6967 0.0587776 0.0293888 0.999568i \(-0.490644\pi\)
0.0293888 + 0.999568i \(0.490644\pi\)
\(200\) 11.1319 9.16074i 0.0556595 0.0458037i
\(201\) 119.484i 0.594445i
\(202\) 30.6786 + 19.0581i 0.151874 + 0.0943472i
\(203\) −199.021 199.021i −0.980398 0.980398i
\(204\) 21.6135 63.8590i 0.105949 0.313034i
\(205\) 84.2755 + 84.2755i 0.411100 + 0.411100i
\(206\) −8.08220 34.5927i −0.0392340 0.167926i
\(207\) 60.7904i 0.293673i
\(208\) −174.238 + 23.2562i −0.837682 + 0.111809i
\(209\) 221.378 1.05923
\(210\) 197.082 46.0460i 0.938484 0.219267i
\(211\) −0.215765 + 0.215765i −0.00102258 + 0.00102258i −0.707618 0.706595i \(-0.750230\pi\)
0.706595 + 0.707618i \(0.250230\pi\)
\(212\) −66.8728 + 197.582i −0.315438 + 0.931989i
\(213\) −9.47873 + 9.47873i −0.0445011 + 0.0445011i
\(214\) 23.7146 38.1742i 0.110816 0.178384i
\(215\) −203.556 −0.946773
\(216\) 4.01896 41.3745i 0.0186063 0.191549i
\(217\) 319.684i 1.47320i
\(218\) 118.396 190.586i 0.543099 0.874247i
\(219\) −104.613 104.613i −0.477686 0.477686i
\(220\) 239.632 118.440i 1.08924 0.538365i
\(221\) −75.5951 75.5951i −0.342059 0.342059i
\(222\) 113.186 26.4447i 0.509848 0.119120i
\(223\) 371.347i 1.66523i −0.553850 0.832617i \(-0.686842\pi\)
0.553850 0.832617i \(-0.313158\pi\)
\(224\) 353.928 + 159.409i 1.58004 + 0.711648i
\(225\) 5.40622 0.0240277
\(226\) −76.2337 326.288i −0.337317 1.44375i
\(227\) −209.823 + 209.823i −0.924330 + 0.924330i −0.997332 0.0730018i \(-0.976742\pi\)
0.0730018 + 0.997332i \(0.476742\pi\)
\(228\) −48.9809 99.0998i −0.214829 0.434648i
\(229\) 152.751 152.751i 0.667037 0.667037i −0.289992 0.957029i \(-0.593653\pi\)
0.957029 + 0.289992i \(0.0936527\pi\)
\(230\) 165.806 + 103.002i 0.720895 + 0.447834i
\(231\) −291.511 −1.26195
\(232\) −17.9462 + 184.753i −0.0773544 + 0.796350i
\(233\) 272.899i 1.17124i 0.810586 + 0.585619i \(0.199149\pi\)
−0.810586 + 0.585619i \(0.800851\pi\)
\(234\) −55.9938 34.7845i −0.239290 0.148652i
\(235\) 106.710 + 106.710i 0.454084 + 0.454084i
\(236\) 75.7259 + 25.6299i 0.320873 + 0.108601i
\(237\) −128.958 128.958i −0.544126 0.544126i
\(238\) 53.7104 + 229.886i 0.225674 + 0.965908i
\(239\) 104.650i 0.437866i −0.975740 0.218933i \(-0.929742\pi\)
0.975740 0.218933i \(-0.0702576\pi\)
\(240\) −106.039 81.0658i −0.441831 0.337774i
\(241\) 148.875 0.617737 0.308869 0.951105i \(-0.400050\pi\)
0.308869 + 0.951105i \(0.400050\pi\)
\(242\) −139.261 + 32.5369i −0.575460 + 0.134450i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 227.833 + 77.1117i 0.933743 + 0.316031i
\(245\) −334.254 + 334.254i −1.36430 + 1.36430i
\(246\) −45.2334 + 72.8139i −0.183876 + 0.295991i
\(247\) −175.295 −0.709698
\(248\) −162.797 + 133.970i −0.656438 + 0.540201i
\(249\) 152.169i 0.611122i
\(250\) 136.239 219.308i 0.544954 0.877233i
\(251\) 143.712 + 143.712i 0.572558 + 0.572558i 0.932843 0.360284i \(-0.117320\pi\)
−0.360284 + 0.932843i \(0.617320\pi\)
\(252\) 64.4981 + 130.495i 0.255945 + 0.517836i
\(253\) −198.802 198.802i −0.785778 0.785778i
\(254\) −386.096 + 90.2071i −1.52006 + 0.355146i
\(255\) 81.1777i 0.318344i
\(256\) −67.1424 247.038i −0.262275 0.964993i
\(257\) 134.023 0.521489 0.260745 0.965408i \(-0.416032\pi\)
0.260745 + 0.965408i \(0.416032\pi\)
\(258\) −33.3085 142.564i −0.129103 0.552573i
\(259\) −287.807 + 287.807i −1.11122 + 1.11122i
\(260\) −189.749 + 93.7853i −0.729806 + 0.360713i
\(261\) −49.2206 + 49.2206i −0.188585 + 0.188585i
\(262\) 322.759 + 200.504i 1.23190 + 0.765283i
\(263\) 290.386 1.10413 0.552066 0.833801i \(-0.313840\pi\)
0.552066 + 0.833801i \(0.313840\pi\)
\(264\) 122.163 + 148.450i 0.462740 + 0.562309i
\(265\) 251.166i 0.947798i
\(266\) 328.812 + 204.264i 1.23613 + 0.767911i
\(267\) 155.754 + 155.754i 0.583347 + 0.583347i
\(268\) −88.4627 + 261.371i −0.330085 + 0.975264i
\(269\) −74.2628 74.2628i −0.276070 0.276070i 0.555468 0.831538i \(-0.312539\pi\)
−0.831538 + 0.555468i \(0.812539\pi\)
\(270\) −11.3878 48.7411i −0.0421771 0.180523i
\(271\) 70.8329i 0.261376i 0.991424 + 0.130688i \(0.0417186\pi\)
−0.991424 + 0.130688i \(0.958281\pi\)
\(272\) 94.5593 123.690i 0.347644 0.454742i
\(273\) 230.829 0.845527
\(274\) −498.451 + 116.458i −1.81916 + 0.425028i
\(275\) −17.6799 + 17.6799i −0.0642906 + 0.0642906i
\(276\) −45.0077 + 132.979i −0.163071 + 0.481809i
\(277\) −96.6953 + 96.6953i −0.349081 + 0.349081i −0.859767 0.510686i \(-0.829391\pi\)
0.510686 + 0.859767i \(0.329391\pi\)
\(278\) 32.4223 52.1914i 0.116627 0.187739i
\(279\) −79.0625 −0.283378
\(280\) 465.209 + 45.1886i 1.66146 + 0.161388i
\(281\) 138.151i 0.491640i −0.969316 0.245820i \(-0.920943\pi\)
0.969316 0.245820i \(-0.0790572\pi\)
\(282\) −57.2746 + 92.1970i −0.203101 + 0.326940i
\(283\) −295.011 295.011i −1.04244 1.04244i −0.999059 0.0433821i \(-0.986187\pi\)
−0.0433821 0.999059i \(-0.513813\pi\)
\(284\) −27.7526 + 13.7170i −0.0977204 + 0.0482991i
\(285\) −94.1203 94.1203i −0.330247 0.330247i
\(286\) 296.871 69.3607i 1.03801 0.242520i
\(287\) 300.168i 1.04588i
\(288\) 39.4241 87.5313i 0.136889 0.303928i
\(289\) −194.310 −0.672353
\(290\) 50.8510 + 217.648i 0.175348 + 0.750510i
\(291\) 180.464 180.464i 0.620150 0.620150i
\(292\) −151.389 306.295i −0.518455 1.04896i
\(293\) −33.4759 + 33.4759i −0.114252 + 0.114252i −0.761922 0.647669i \(-0.775744\pi\)
0.647669 + 0.761922i \(0.275744\pi\)
\(294\) −288.795 179.405i −0.982296 0.610221i
\(295\) 96.2630 0.326315
\(296\) 267.174 + 25.9523i 0.902616 + 0.0876768i
\(297\) 72.0948i 0.242743i
\(298\) −82.2748 51.1107i −0.276090 0.171513i
\(299\) 157.418 + 157.418i 0.526483 + 0.526483i
\(300\) 11.8261 + 4.00264i 0.0394205 + 0.0133421i
\(301\) 362.508 + 362.508i 1.20434 + 1.20434i
\(302\) −6.58169 28.1703i −0.0217937 0.0932792i
\(303\) 31.2776i 0.103226i
\(304\) −33.7749 253.046i −0.111102 0.832387i
\(305\) 289.622 0.949582
\(306\) 56.8541 13.2833i 0.185798 0.0434096i
\(307\) −92.6638 + 92.6638i −0.301836 + 0.301836i −0.841732 0.539896i \(-0.818464\pi\)
0.539896 + 0.841732i \(0.318464\pi\)
\(308\) −637.682 215.828i −2.07040 0.700739i
\(309\) 21.7541 21.7541i 0.0704016 0.0704016i
\(310\) −133.962 + 215.643i −0.432135 + 0.695623i
\(311\) −18.5610 −0.0596817 −0.0298408 0.999555i \(-0.509500\pi\)
−0.0298408 + 0.999555i \(0.509500\pi\)
\(312\) −96.7332 117.548i −0.310042 0.376755i
\(313\) 55.1534i 0.176209i −0.996111 0.0881045i \(-0.971919\pi\)
0.996111 0.0881045i \(-0.0280809\pi\)
\(314\) −46.9626 + 75.5975i −0.149563 + 0.240756i
\(315\) 123.938 + 123.938i 0.393453 + 0.393453i
\(316\) −186.619 377.573i −0.590566 1.19485i
\(317\) 62.2977 + 62.2977i 0.196523 + 0.196523i 0.798507 0.601985i \(-0.205623\pi\)
−0.601985 + 0.798507i \(0.705623\pi\)
\(318\) −175.908 + 41.0991i −0.553171 + 0.129242i
\(319\) 321.931i 1.00919i
\(320\) −171.943 255.841i −0.537320 0.799502i
\(321\) 38.9197 0.121245
\(322\) −111.846 478.712i −0.347348 1.48668i
\(323\) 109.787 109.787i 0.339897 0.339897i
\(324\) 32.2732 15.9513i 0.0996085 0.0492323i
\(325\) 13.9996 13.9996i 0.0430756 0.0430756i
\(326\) 75.4414 + 46.8657i 0.231415 + 0.143760i
\(327\) 194.307 0.594212
\(328\) −152.858 + 125.791i −0.466030 + 0.383509i
\(329\) 380.073i 1.15524i
\(330\) 196.639 + 122.156i 0.595875 + 0.370169i
\(331\) 373.767 + 373.767i 1.12921 + 1.12921i 0.990307 + 0.138899i \(0.0443564\pi\)
0.138899 + 0.990307i \(0.455644\pi\)
\(332\) 112.663 332.871i 0.339345 1.00262i
\(333\) 71.1788 + 71.1788i 0.213750 + 0.213750i
\(334\) 16.5991 + 71.0459i 0.0496979 + 0.212712i
\(335\) 332.255i 0.991807i
\(336\) 44.4748 + 333.210i 0.132366 + 0.991698i
\(337\) −519.936 −1.54284 −0.771419 0.636328i \(-0.780453\pi\)
−0.771419 + 0.636328i \(0.780453\pi\)
\(338\) 94.0630 21.9768i 0.278293 0.0650201i
\(339\) 205.191 205.191i 0.605283 0.605283i
\(340\) 60.1020 177.577i 0.176771 0.522284i
\(341\) 258.557 258.557i 0.758231 0.758231i
\(342\) 50.5175 81.3198i 0.147712 0.237777i
\(343\) 596.142 1.73802
\(344\) 32.6883 336.520i 0.0950240 0.978255i
\(345\) 169.044i 0.489981i
\(346\) −145.733 + 234.592i −0.421194 + 0.678011i
\(347\) 122.160 + 122.160i 0.352045 + 0.352045i 0.860870 0.508825i \(-0.169920\pi\)
−0.508825 + 0.860870i \(0.669920\pi\)
\(348\) −144.112 + 71.2286i −0.414115 + 0.204680i
\(349\) −279.483 279.483i −0.800810 0.800810i 0.182412 0.983222i \(-0.441609\pi\)
−0.983222 + 0.182412i \(0.941609\pi\)
\(350\) −42.5730 + 9.94671i −0.121637 + 0.0284192i
\(351\) 57.0872i 0.162642i
\(352\) 157.324 + 415.181i 0.446944 + 1.17949i
\(353\) −212.266 −0.601320 −0.300660 0.953731i \(-0.597207\pi\)
−0.300660 + 0.953731i \(0.597207\pi\)
\(354\) 15.7518 + 67.4193i 0.0444966 + 0.190450i
\(355\) −26.3581 + 26.3581i −0.0742482 + 0.0742482i
\(356\) 225.396 + 456.028i 0.633134 + 1.28098i
\(357\) −144.567 + 144.567i −0.404950 + 0.404950i
\(358\) 215.614 + 133.943i 0.602272 + 0.374144i
\(359\) −435.033 −1.21179 −0.605895 0.795545i \(-0.707185\pi\)
−0.605895 + 0.795545i \(0.707185\pi\)
\(360\) 11.1758 115.053i 0.0310438 0.319591i
\(361\) 106.419i 0.294789i
\(362\) −277.491 172.383i −0.766551 0.476196i
\(363\) −87.5765 87.5765i −0.241258 0.241258i
\(364\) 504.939 + 170.900i 1.38720 + 0.469505i
\(365\) −290.905 290.905i −0.796999 0.796999i
\(366\) 47.3917 + 202.842i 0.129486 + 0.554212i
\(367\) 125.535i 0.342058i 0.985266 + 0.171029i \(0.0547091\pi\)
−0.985266 + 0.171029i \(0.945291\pi\)
\(368\) −196.909 + 257.570i −0.535079 + 0.699919i
\(369\) −74.2357 −0.201181
\(370\) 314.744 73.5365i 0.850660 0.198747i
\(371\) 447.295 447.295i 1.20565 1.20565i
\(372\) −172.950 58.5359i −0.464918 0.157355i
\(373\) −302.389 + 302.389i −0.810694 + 0.810694i −0.984738 0.174044i \(-0.944317\pi\)
0.174044 + 0.984738i \(0.444317\pi\)
\(374\) −142.489 + 229.370i −0.380986 + 0.613287i
\(375\) 223.591 0.596242
\(376\) −193.549 + 159.277i −0.514758 + 0.423608i
\(377\) 254.917i 0.676171i
\(378\) −66.5214 + 107.082i −0.175983 + 0.283285i
\(379\) 189.784 + 189.784i 0.500751 + 0.500751i 0.911671 0.410921i \(-0.134793\pi\)
−0.410921 + 0.911671i \(0.634793\pi\)
\(380\) −136.204 275.573i −0.358432 0.725192i
\(381\) −242.802 242.802i −0.637275 0.637275i
\(382\) −121.971 + 28.4972i −0.319296 + 0.0745999i
\(383\) 639.916i 1.67080i 0.549644 + 0.835399i \(0.314763\pi\)
−0.549644 + 0.835399i \(0.685237\pi\)
\(384\) 151.047 162.287i 0.393350 0.422621i
\(385\) −810.623 −2.10551
\(386\) 101.626 + 434.970i 0.263280 + 1.12687i
\(387\) 89.6533 89.6533i 0.231662 0.231662i
\(388\) 528.376 261.154i 1.36179 0.673078i
\(389\) 499.333 499.333i 1.28363 1.28363i 0.345046 0.938586i \(-0.387863\pi\)
0.938586 0.345046i \(-0.112137\pi\)
\(390\) −155.706 96.7274i −0.399245 0.248019i
\(391\) −197.181 −0.504300
\(392\) −498.913 606.266i −1.27274 1.54660i
\(393\) 329.061i 0.837306i
\(394\) 69.9050 + 43.4264i 0.177424 + 0.110219i
\(395\) −358.601 358.601i −0.907851 0.907851i
\(396\) −53.3772 + 157.708i −0.134791 + 0.398252i
\(397\) 492.518 + 492.518i 1.24060 + 1.24060i 0.959753 + 0.280846i \(0.0906151\pi\)
0.280846 + 0.959753i \(0.409385\pi\)
\(398\) 5.32230 + 22.7800i 0.0133726 + 0.0572361i
\(399\) 335.233i 0.840182i
\(400\) 22.9063 + 17.5116i 0.0572657 + 0.0437789i
\(401\) 705.045 1.75822 0.879109 0.476621i \(-0.158138\pi\)
0.879109 + 0.476621i \(0.158138\pi\)
\(402\) −232.700 + 54.3679i −0.578856 + 0.135243i
\(403\) −204.735 + 204.735i −0.508026 + 0.508026i
\(404\) −23.1572 + 68.4200i −0.0573198 + 0.169356i
\(405\) 30.6515 30.6515i 0.0756828 0.0756828i
\(406\) 297.044 478.162i 0.731635 1.17774i
\(407\) −465.550 −1.14386
\(408\) 134.203 + 13.0360i 0.328930 + 0.0319510i
\(409\) 279.815i 0.684144i −0.939674 0.342072i \(-0.888871\pi\)
0.939674 0.342072i \(-0.111129\pi\)
\(410\) −125.783 + 202.478i −0.306789 + 0.493849i
\(411\) −313.458 313.458i −0.762671 0.762671i
\(412\) 63.6934 31.4810i 0.154596 0.0764102i
\(413\) −171.432 171.432i −0.415090 0.415090i
\(414\) −118.392 + 27.6611i −0.285972 + 0.0668142i
\(415\) 423.147i 1.01963i
\(416\) −124.575 328.755i −0.299459 0.790276i
\(417\) 53.2106 0.127603
\(418\) 100.732 + 431.146i 0.240987 + 1.03145i
\(419\) −573.583 + 573.583i −1.36893 + 1.36893i −0.506968 + 0.861965i \(0.669234\pi\)
−0.861965 + 0.506968i \(0.830766\pi\)
\(420\) 179.354 + 362.875i 0.427033 + 0.863987i
\(421\) −213.341 + 213.341i −0.506749 + 0.506749i −0.913527 0.406778i \(-0.866652\pi\)
0.406778 + 0.913527i \(0.366652\pi\)
\(422\) −0.518392 0.322035i −0.00122842 0.000763117i
\(423\) −93.9974 −0.222216
\(424\) −415.229 40.3338i −0.979314 0.0951269i
\(425\) 17.5358i 0.0412606i
\(426\) −22.7734 14.1473i −0.0534586 0.0332095i
\(427\) −515.781 515.781i −1.20792 1.20792i
\(428\) 85.1369 + 28.8152i 0.198918 + 0.0673251i
\(429\) 186.692 + 186.692i 0.435178 + 0.435178i
\(430\) −92.6230 396.436i −0.215402 0.921944i
\(431\) 166.900i 0.387239i −0.981077 0.193619i \(-0.937977\pi\)
0.981077 0.193619i \(-0.0620227\pi\)
\(432\) 82.4076 10.9993i 0.190758 0.0254612i
\(433\) 233.153 0.538459 0.269230 0.963076i \(-0.413231\pi\)
0.269230 + 0.963076i \(0.413231\pi\)
\(434\) 622.602 145.464i 1.43457 0.335171i
\(435\) −136.871 + 136.871i −0.314646 + 0.314646i
\(436\) 425.048 + 143.860i 0.974882 + 0.329955i
\(437\) −228.619 + 228.619i −0.523155 + 0.523155i
\(438\) 156.138 251.341i 0.356479 0.573838i
\(439\) 440.480 1.00337 0.501686 0.865050i \(-0.332713\pi\)
0.501686 + 0.865050i \(0.332713\pi\)
\(440\) 339.707 + 412.803i 0.772061 + 0.938189i
\(441\) 294.434i 0.667651i
\(442\) 112.828 181.623i 0.255266 0.410912i
\(443\) −312.524 312.524i −0.705473 0.705473i 0.260107 0.965580i \(-0.416242\pi\)
−0.965580 + 0.260107i \(0.916242\pi\)
\(444\) 103.005 + 208.403i 0.231993 + 0.469376i
\(445\) 433.114 + 433.114i 0.973290 + 0.973290i
\(446\) 723.217 168.972i 1.62156 0.378861i
\(447\) 83.8814i 0.187654i
\(448\) −149.412 + 761.827i −0.333509 + 1.70051i
\(449\) −734.338 −1.63550 −0.817748 0.575576i \(-0.804778\pi\)
−0.817748 + 0.575576i \(0.804778\pi\)
\(450\) 2.45996 + 10.5289i 0.00546658 + 0.0233975i
\(451\) 242.772 242.772i 0.538297 0.538297i
\(452\) 600.774 296.938i 1.32915 0.656942i
\(453\) 17.7153 17.7153i 0.0391066 0.0391066i
\(454\) −504.115 313.166i −1.11039 0.689794i
\(455\) 641.880 1.41073
\(456\) 170.714 140.486i 0.374374 0.308082i
\(457\) 692.749i 1.51586i −0.652335 0.757931i \(-0.726211\pi\)
0.652335 0.757931i \(-0.273789\pi\)
\(458\) 366.997 + 227.986i 0.801303 + 0.497785i
\(459\) 35.7535 + 35.7535i 0.0778944 + 0.0778944i
\(460\) −125.156 + 369.784i −0.272078 + 0.803878i
\(461\) 298.447 + 298.447i 0.647391 + 0.647391i 0.952362 0.304971i \(-0.0986467\pi\)
−0.304971 + 0.952362i \(0.598647\pi\)
\(462\) −132.645 567.733i −0.287109 1.22886i
\(463\) 281.830i 0.608705i −0.952560 0.304352i \(-0.901560\pi\)
0.952560 0.304352i \(-0.0984400\pi\)
\(464\) −367.982 + 49.1159i −0.793065 + 0.105853i
\(465\) −219.854 −0.472804
\(466\) −531.484 + 124.175i −1.14052 + 0.266471i
\(467\) 198.116 198.116i 0.424232 0.424232i −0.462426 0.886658i \(-0.653021\pi\)
0.886658 + 0.462426i \(0.153021\pi\)
\(468\) 42.2660 124.879i 0.0903119 0.266835i
\(469\) 591.704 591.704i 1.26163 1.26163i
\(470\) −159.267 + 256.378i −0.338866 + 0.545485i
\(471\) −77.0737 −0.163638
\(472\) −15.4585 + 159.142i −0.0327510 + 0.337166i
\(473\) 586.384i 1.23971i
\(474\) 192.473 309.831i 0.406061 0.653652i
\(475\) 20.3316 + 20.3316i 0.0428033 + 0.0428033i
\(476\) −423.276 + 209.207i −0.889234 + 0.439512i
\(477\) −110.622 110.622i −0.231913 0.231913i
\(478\) 203.811 47.6182i 0.426383 0.0996197i
\(479\) 917.713i 1.91589i 0.286945 + 0.957947i \(0.407360\pi\)
−0.286945 + 0.957947i \(0.592640\pi\)
\(480\) 109.629 243.404i 0.228394 0.507091i
\(481\) 368.639 0.766401
\(482\) 67.7416 + 289.941i 0.140543 + 0.601537i
\(483\) 301.045 301.045i 0.623282 0.623282i
\(484\) −126.735 256.413i −0.261848 0.529780i
\(485\) 501.826 501.826i 1.03469 1.03469i
\(486\) 26.4829 + 16.4517i 0.0544915 + 0.0338512i
\(487\) −426.183 −0.875119 −0.437559 0.899190i \(-0.644157\pi\)
−0.437559 + 0.899190i \(0.644157\pi\)
\(488\) −46.5093 + 478.805i −0.0953059 + 0.981157i
\(489\) 76.9146i 0.157290i
\(490\) −803.070 498.883i −1.63892 1.01813i
\(491\) −266.299 266.299i −0.542361 0.542361i 0.381859 0.924220i \(-0.375284\pi\)
−0.924220 + 0.381859i \(0.875284\pi\)
\(492\) −162.391 54.9623i −0.330063 0.111712i
\(493\) −159.653 159.653i −0.323840 0.323840i
\(494\) −79.7636 341.396i −0.161465 0.691086i
\(495\) 200.479i 0.405007i
\(496\) −334.989 256.095i −0.675382 0.516321i
\(497\) 93.8809 0.188895
\(498\) 296.358 69.2408i 0.595096 0.139038i
\(499\) −264.104 + 264.104i −0.529266 + 0.529266i −0.920353 0.391088i \(-0.872099\pi\)
0.391088 + 0.920353i \(0.372099\pi\)
\(500\) 489.106 + 165.541i 0.978211 + 0.331082i
\(501\) −44.6782 + 44.6782i −0.0891781 + 0.0891781i
\(502\) −214.494 + 345.279i −0.427279 + 0.687807i
\(503\) −574.766 −1.14268 −0.571338 0.820715i \(-0.693575\pi\)
−0.571338 + 0.820715i \(0.693575\pi\)
\(504\) −224.797 + 184.991i −0.446025 + 0.367046i
\(505\) 86.9756i 0.172229i
\(506\) 296.717 477.636i 0.586398 0.943946i
\(507\) 59.1528 + 59.1528i 0.116672 + 0.116672i
\(508\) −351.366 710.895i −0.691665 1.39940i
\(509\) 170.592 + 170.592i 0.335152 + 0.335152i 0.854539 0.519387i \(-0.173840\pi\)
−0.519387 + 0.854539i \(0.673840\pi\)
\(510\) 158.098 36.9378i 0.309996 0.0724271i
\(511\) 1036.13i 2.02765i
\(512\) 450.568 243.172i 0.880016 0.474944i
\(513\) 82.9077 0.161614
\(514\) 60.9835 + 261.016i 0.118645 + 0.507813i
\(515\) 60.4930 60.4930i 0.117462 0.117462i
\(516\) 262.494 129.740i 0.508709 0.251434i
\(517\) 307.398 307.398i 0.594581 0.594581i
\(518\) −691.478 429.560i −1.33490 0.829266i
\(519\) −239.173 −0.460834
\(520\) −268.992 326.872i −0.517293 0.628600i
\(521\) 37.1210i 0.0712496i −0.999365 0.0356248i \(-0.988658\pi\)
0.999365 0.0356248i \(-0.0113421\pi\)
\(522\) −118.256 73.4631i −0.226545 0.140734i
\(523\) −199.555 199.555i −0.381558 0.381558i 0.490105 0.871663i \(-0.336958\pi\)
−0.871663 + 0.490105i \(0.836958\pi\)
\(524\) −243.629 + 719.823i −0.464941 + 1.37371i
\(525\) −26.7726 26.7726i −0.0509955 0.0509955i
\(526\) 132.133 + 565.542i 0.251203 + 1.07518i
\(527\) 256.449i 0.486620i
\(528\) −233.526 + 305.467i −0.442284 + 0.578536i
\(529\) −118.392 −0.223804
\(530\) −489.159 + 114.287i −0.922942 + 0.215635i
\(531\) −42.3976 + 42.3976i −0.0798448 + 0.0798448i
\(532\) −248.198 + 733.323i −0.466538 + 1.37843i
\(533\) −192.236 + 192.236i −0.360667 + 0.360667i
\(534\) −232.466 + 374.210i −0.435330 + 0.700767i
\(535\) 108.226 0.202292
\(536\) −549.286 53.3555i −1.02479 0.0995439i
\(537\) 219.824i 0.409355i
\(538\) 110.839 178.422i 0.206021 0.331639i
\(539\) 962.884 + 962.884i 1.78643 + 1.78643i
\(540\) 89.7440 44.3567i 0.166193 0.0821421i
\(541\) 278.121 + 278.121i 0.514086 + 0.514086i 0.915776 0.401690i \(-0.131577\pi\)
−0.401690 + 0.915776i \(0.631577\pi\)
\(542\) −137.951 + 32.2307i −0.254521 + 0.0594661i
\(543\) 282.910i 0.521013i
\(544\) 283.919 + 127.877i 0.521910 + 0.235068i
\(545\) 540.323 0.991418
\(546\) 105.033 + 449.551i 0.192368 + 0.823353i
\(547\) 724.938 724.938i 1.32530 1.32530i 0.415876 0.909421i \(-0.363475\pi\)
0.909421 0.415876i \(-0.136525\pi\)
\(548\) −453.614 917.767i −0.827763 1.67476i
\(549\) −127.560 + 127.560i −0.232349 + 0.232349i
\(550\) −42.4773 26.3877i −0.0772314 0.0479777i
\(551\) −370.215 −0.671897
\(552\) −279.463 27.1460i −0.506274 0.0491776i
\(553\) 1277.25i 2.30967i
\(554\) −232.318 144.320i −0.419346 0.260506i
\(555\) 197.931 + 197.931i 0.356633 + 0.356633i
\(556\) 116.398 + 39.3958i 0.209350 + 0.0708558i
\(557\) 268.298 + 268.298i 0.481685 + 0.481685i 0.905669 0.423985i \(-0.139369\pi\)
−0.423985 + 0.905669i \(0.639369\pi\)
\(558\) −35.9753 153.978i −0.0644719 0.275946i
\(559\) 464.320i 0.830625i
\(560\) 123.674 + 926.579i 0.220846 + 1.65461i
\(561\) −233.848 −0.416842
\(562\) 269.056 62.8619i 0.478747 0.111854i
\(563\) −78.4662 + 78.4662i −0.139372 + 0.139372i −0.773350 0.633979i \(-0.781421\pi\)
0.633979 + 0.773350i \(0.281421\pi\)
\(564\) −205.620 69.5933i −0.364574 0.123392i
\(565\) 570.587 570.587i 1.00989 1.00989i
\(566\) 440.311 708.785i 0.777935 1.25227i
\(567\) −109.173 −0.192545
\(568\) −39.3426 47.8080i −0.0692651 0.0841691i
\(569\) 801.999i 1.40949i −0.709461 0.704744i \(-0.751062\pi\)
0.709461 0.704744i \(-0.248938\pi\)
\(570\) 140.477 226.131i 0.246451 0.396721i
\(571\) 79.9964 + 79.9964i 0.140099 + 0.140099i 0.773678 0.633579i \(-0.218415\pi\)
−0.633579 + 0.773678i \(0.718415\pi\)
\(572\) 270.167 + 546.611i 0.472320 + 0.955613i
\(573\) −76.7031 76.7031i −0.133862 0.133862i
\(574\) 584.592 136.583i 1.01845 0.237950i
\(575\) 36.5163i 0.0635066i
\(576\) 188.411 + 36.9517i 0.327102 + 0.0641522i
\(577\) −237.186 −0.411068 −0.205534 0.978650i \(-0.565893\pi\)
−0.205534 + 0.978650i \(0.565893\pi\)
\(578\) −88.4158 378.429i −0.152968 0.654721i
\(579\) −273.537 + 273.537i −0.472430 + 0.472430i
\(580\) −400.742 + 198.070i −0.690934 + 0.341500i
\(581\) −753.571 + 753.571i −1.29702 + 1.29702i
\(582\) 433.577 + 269.347i 0.744978 + 0.462795i
\(583\) 723.534 1.24105
\(584\) 527.639 434.209i 0.903492 0.743509i
\(585\) 158.746i 0.271361i
\(586\) −80.4283 49.9637i −0.137250 0.0852622i
\(587\) −267.958 267.958i −0.456487 0.456487i 0.441014 0.897500i \(-0.354619\pi\)
−0.897500 + 0.441014i \(0.854619\pi\)
\(588\) 217.992 644.076i 0.370734 1.09537i
\(589\) −297.336 297.336i −0.504815 0.504815i
\(590\) 43.8020 + 187.477i 0.0742407 + 0.317758i
\(591\) 71.2701i 0.120592i
\(592\) 71.0273 + 532.145i 0.119979 + 0.898893i
\(593\) −607.086 −1.02375 −0.511877 0.859059i \(-0.671050\pi\)
−0.511877 + 0.859059i \(0.671050\pi\)
\(594\) −140.408 + 32.8049i −0.236378 + 0.0552270i
\(595\) −402.007 + 402.007i −0.675642 + 0.675642i
\(596\) 62.1037 183.491i 0.104201 0.307871i
\(597\) −14.3255 + 14.3255i −0.0239958 + 0.0239958i
\(598\) −234.951 + 378.210i −0.392895 + 0.632457i
\(599\) 575.392 0.960587 0.480294 0.877108i \(-0.340530\pi\)
0.480294 + 0.877108i \(0.340530\pi\)
\(600\) −2.41416 + 24.8533i −0.00402359 + 0.0414222i
\(601\) 310.094i 0.515963i −0.966150 0.257981i \(-0.916943\pi\)
0.966150 0.257981i \(-0.0830573\pi\)
\(602\) −541.052 + 870.952i −0.898758 + 1.44676i
\(603\) −146.337 146.337i −0.242681 0.242681i
\(604\) 51.8683 25.6363i 0.0858746 0.0424443i
\(605\) −243.529 243.529i −0.402528 0.402528i
\(606\) −60.9148 + 14.2321i −0.100519 + 0.0234853i
\(607\) 556.510i 0.916820i −0.888741 0.458410i \(-0.848419\pi\)
0.888741 0.458410i \(-0.151581\pi\)
\(608\) 477.451 180.920i 0.785281 0.297566i
\(609\) 487.499 0.800492
\(610\) 131.785 + 564.054i 0.216041 + 0.924679i
\(611\) −243.409 + 243.409i −0.398378 + 0.398378i
\(612\) 51.7400 + 104.682i 0.0845424 + 0.171049i
\(613\) −326.241 + 326.241i −0.532204 + 0.532204i −0.921228 0.389024i \(-0.872812\pi\)
0.389024 + 0.921228i \(0.372812\pi\)
\(614\) −222.632 138.303i −0.362592 0.225249i
\(615\) −206.432 −0.335662
\(616\) 130.175 1340.12i 0.211323 2.17553i
\(617\) 502.068i 0.813725i −0.913490 0.406862i \(-0.866623\pi\)
0.913490 0.406862i \(-0.133377\pi\)
\(618\) 52.2659 + 32.4686i 0.0845726 + 0.0525381i
\(619\) 304.429 + 304.429i 0.491808 + 0.491808i 0.908876 0.417067i \(-0.136942\pi\)
−0.417067 + 0.908876i \(0.636942\pi\)
\(620\) −480.932 162.774i −0.775696 0.262539i
\(621\) −74.4527 74.4527i −0.119892 0.119892i
\(622\) −8.44570 36.1485i −0.0135783 0.0581166i
\(623\) 1542.64i 2.47615i
\(624\) 184.914 241.880i 0.296337 0.387628i
\(625\) 576.701 0.922721
\(626\) 107.414 25.0961i 0.171588 0.0400896i
\(627\) −271.132 + 271.132i −0.432428 + 0.432428i
\(628\) −168.599 57.0635i −0.268470 0.0908654i
\(629\) −230.877 + 230.877i −0.367054 + 0.367054i
\(630\) −184.980 + 297.769i −0.293619 + 0.472650i
\(631\) 8.60592 0.0136385 0.00681927 0.999977i \(-0.497829\pi\)
0.00681927 + 0.999977i \(0.497829\pi\)
\(632\) 650.427 535.254i 1.02916 0.846921i
\(633\) 0.528515i 0.000834936i
\(634\) −92.9809 + 149.675i −0.146658 + 0.236080i
\(635\) −675.174 675.174i −1.06327 1.06327i
\(636\) −160.085 323.889i −0.251706 0.509260i
\(637\) −762.446 762.446i −1.19693 1.19693i
\(638\) 626.977 146.486i 0.982723 0.229603i
\(639\) 23.2181i 0.0363350i
\(640\) 420.025 451.280i 0.656289 0.705126i
\(641\) −445.780 −0.695445 −0.347722 0.937598i \(-0.613045\pi\)
−0.347722 + 0.937598i \(0.613045\pi\)
\(642\) 17.7094 + 75.7980i 0.0275847 + 0.118065i
\(643\) −118.001 + 118.001i −0.183517 + 0.183517i −0.792886 0.609369i \(-0.791423\pi\)
0.609369 + 0.792886i \(0.291423\pi\)
\(644\) 881.424 435.651i 1.36867 0.676477i
\(645\) 249.304 249.304i 0.386519 0.386519i
\(646\) 263.771 + 163.860i 0.408314 + 0.253653i
\(647\) 1081.35 1.67132 0.835662 0.549243i \(-0.185084\pi\)
0.835662 + 0.549243i \(0.185084\pi\)
\(648\) 45.7510 + 55.5954i 0.0706034 + 0.0857954i
\(649\) 277.305i 0.427280i
\(650\) 33.6350 + 20.8947i 0.0517462 + 0.0321458i
\(651\) 391.532 + 391.532i 0.601431 + 0.601431i
\(652\) −56.9457 + 168.251i −0.0873400 + 0.258054i
\(653\) −586.227 586.227i −0.897744 0.897744i 0.0974927 0.995236i \(-0.468918\pi\)
−0.995236 + 0.0974927i \(0.968918\pi\)
\(654\) 88.4145 + 378.423i 0.135190 + 0.578629i
\(655\) 915.041i 1.39701i
\(656\) −314.538 240.461i −0.479479 0.366556i
\(657\) 256.249 0.390029
\(658\) 740.211 172.942i 1.12494 0.262830i
\(659\) 469.999 469.999i 0.713201 0.713201i −0.254003 0.967204i \(-0.581747\pi\)
0.967204 + 0.254003i \(0.0817472\pi\)
\(660\) −148.429 + 438.548i −0.224893 + 0.664466i
\(661\) −884.745 + 884.745i −1.33849 + 1.33849i −0.440976 + 0.897519i \(0.645368\pi\)
−0.897519 + 0.440976i \(0.854632\pi\)
\(662\) −557.857 + 898.003i −0.842685 + 1.35650i
\(663\) 185.170 0.279290
\(664\) 699.548 + 67.9515i 1.05354 + 0.102337i
\(665\) 932.202i 1.40181i
\(666\) −106.236 + 171.012i −0.159514 + 0.256775i
\(667\) 332.460 + 332.460i 0.498441 + 0.498441i
\(668\) −130.813 + 64.6552i −0.195827 + 0.0967892i
\(669\) 454.805 + 454.805i 0.679829 + 0.679829i
\(670\) −647.084 + 151.184i −0.965797 + 0.225648i
\(671\) 834.314i 1.24339i
\(672\) −628.707 + 238.236i −0.935576 + 0.354517i
\(673\) 684.329 1.01683 0.508417 0.861111i \(-0.330231\pi\)
0.508417 + 0.861111i \(0.330231\pi\)
\(674\) −236.584 1012.60i −0.351014 1.50238i
\(675\) −6.62125 + 6.62125i −0.00980925 + 0.00980925i
\(676\) 85.6018 + 173.192i 0.126630 + 0.256202i
\(677\) −383.762 + 383.762i −0.566857 + 0.566857i −0.931246 0.364390i \(-0.881278\pi\)
0.364390 + 0.931246i \(0.381278\pi\)
\(678\) 492.987 + 306.253i 0.727119 + 0.451700i
\(679\) −1787.38 −2.63237
\(680\) 373.188 + 36.2500i 0.548805 + 0.0533089i
\(681\) 513.959i 0.754712i
\(682\) 621.202 + 385.903i 0.910854 + 0.565840i
\(683\) 903.626 + 903.626i 1.32302 + 1.32302i 0.911315 + 0.411709i \(0.135068\pi\)
0.411709 + 0.911315i \(0.364932\pi\)
\(684\) 181.361 + 61.3829i 0.265148 + 0.0897410i
\(685\) −871.652 871.652i −1.27248 1.27248i
\(686\) 271.259 + 1161.02i 0.395421 + 1.69244i
\(687\) 374.163i 0.544633i
\(688\) 670.263 89.4625i 0.974220 0.130033i
\(689\) −572.920 −0.831524
\(690\) −329.221 + 76.9189i −0.477132 + 0.111477i
\(691\) −63.6870 + 63.6870i −0.0921665 + 0.0921665i −0.751687 0.659520i \(-0.770759\pi\)
0.659520 + 0.751687i \(0.270759\pi\)
\(692\) −523.192 177.078i −0.756057 0.255893i
\(693\) 357.027 357.027i 0.515190 0.515190i
\(694\) −182.326 + 293.497i −0.262718 + 0.422907i
\(695\) 147.966 0.212901
\(696\) −204.296 248.255i −0.293529 0.356688i
\(697\) 240.793i 0.345470i
\(698\) 417.135 671.478i 0.597615 0.962003i
\(699\) −334.231 334.231i −0.478156 0.478156i
\(700\) −38.7434 78.3870i −0.0553478 0.111981i
\(701\) 218.312 + 218.312i 0.311430 + 0.311430i 0.845463 0.534033i \(-0.179324\pi\)
−0.534033 + 0.845463i \(0.679324\pi\)
\(702\) 111.180 25.9761i 0.158376 0.0370029i
\(703\) 535.374i 0.761557i
\(704\) −736.999 + 495.314i −1.04687 + 0.703571i
\(705\) −261.384 −0.370758
\(706\) −96.5861 413.399i −0.136808 0.585551i
\(707\) 154.893 154.893i 0.219084 0.219084i
\(708\) −124.135 + 61.3548i −0.175332 + 0.0866593i
\(709\) −822.199 + 822.199i −1.15966 + 1.15966i −0.175112 + 0.984548i \(0.556029\pi\)
−0.984548 + 0.175112i \(0.943971\pi\)
\(710\) −63.3273 39.3402i −0.0891934 0.0554087i
\(711\) 315.881 0.444277
\(712\) −785.577 + 646.473i −1.10334 + 0.907968i
\(713\) 534.026i 0.748985i
\(714\) −347.334 215.770i −0.486462 0.302199i
\(715\) 519.145 + 519.145i 0.726077 + 0.726077i
\(716\) −162.752 + 480.866i −0.227307 + 0.671600i
\(717\) 128.169 + 128.169i 0.178758 + 0.178758i
\(718\) −197.950 847.248i −0.275697 1.18001i
\(719\) 340.913i 0.474149i 0.971491 + 0.237074i \(0.0761885\pi\)
−0.971491 + 0.237074i \(0.923811\pi\)
\(720\) 229.156 30.5863i 0.318272 0.0424810i
\(721\) −215.461 −0.298836
\(722\) −207.256 + 48.4231i −0.287058 + 0.0670680i
\(723\) −182.334 + 182.334i −0.252190 + 0.252190i
\(724\) 209.460 618.867i 0.289309 0.854788i
\(725\) 29.5664 29.5664i 0.0407813 0.0407813i
\(726\) 130.710 210.409i 0.180042 0.289820i
\(727\) −803.090 −1.10466 −0.552331 0.833625i \(-0.686262\pi\)
−0.552331 + 0.833625i \(0.686262\pi\)
\(728\) −103.077 + 1061.16i −0.141589 + 1.45763i
\(729\) 27.0000i 0.0370370i
\(730\) 434.183 698.920i 0.594771 0.957424i
\(731\) 290.802 + 290.802i 0.397813 + 0.397813i
\(732\) −373.480 + 184.596i −0.510218 + 0.252180i
\(733\) 481.592 + 481.592i 0.657015 + 0.657015i 0.954673 0.297658i \(-0.0962054\pi\)
−0.297658 + 0.954673i \(0.596205\pi\)
\(734\) −244.486 + 57.1215i −0.333087 + 0.0778222i
\(735\) 818.752i 1.11395i
\(736\) −591.229 266.290i −0.803301 0.361807i
\(737\) 957.127 1.29868
\(738\) −33.7790 144.578i −0.0457710 0.195905i
\(739\) 173.622 173.622i 0.234941 0.234941i −0.579810 0.814752i \(-0.696873\pi\)
0.814752 + 0.579810i \(0.196873\pi\)
\(740\) 286.432 + 579.519i 0.387071 + 0.783134i
\(741\) 214.692 214.692i 0.289733 0.289733i
\(742\) 1074.66 + 667.600i 1.44833 + 0.899731i
\(743\) 1316.22 1.77149 0.885744 0.464173i \(-0.153649\pi\)
0.885744 + 0.464173i \(0.153649\pi\)
\(744\) 35.3054 363.463i 0.0474536 0.488526i
\(745\) 233.254i 0.313093i
\(746\) −726.512 451.323i −0.973876 0.604991i
\(747\) 186.369 + 186.369i 0.249490 + 0.249490i
\(748\) −511.545 173.136i −0.683883 0.231465i
\(749\) −192.737 192.737i −0.257326 0.257326i
\(750\) 101.739 + 435.454i 0.135652 + 0.580605i
\(751\) 322.977i 0.430062i −0.976607 0.215031i \(-0.931015\pi\)
0.976607 0.215031i \(-0.0689853\pi\)
\(752\) −398.269 304.472i −0.529613 0.404882i
\(753\) −352.021 −0.467492
\(754\) −496.463 + 115.993i −0.658439 + 0.153837i
\(755\) 49.2621 49.2621i 0.0652478 0.0652478i
\(756\) −238.816 80.8289i −0.315895 0.106917i
\(757\) −80.2744 + 80.2744i −0.106043 + 0.106043i −0.758138 0.652095i \(-0.773890\pi\)
0.652095 + 0.758138i \(0.273890\pi\)
\(758\) −283.258 + 455.971i −0.373692 + 0.601545i
\(759\) 486.963 0.641585
\(760\) 474.716 390.657i 0.624627 0.514023i
\(761\) 596.664i 0.784053i −0.919954 0.392027i \(-0.871774\pi\)
0.919954 0.392027i \(-0.128226\pi\)
\(762\) 362.388 583.350i 0.475575 0.765551i
\(763\) −962.246 962.246i −1.26113 1.26113i
\(764\) −110.999 224.578i −0.145287 0.293950i
\(765\) 99.4220 + 99.4220i 0.129963 + 0.129963i
\(766\) −1246.27 + 291.177i −1.62698 + 0.380127i
\(767\) 219.580i 0.286284i
\(768\) 384.791 + 220.327i 0.501030 + 0.286884i
\(769\) 1515.31 1.97050 0.985249 0.171129i \(-0.0547416\pi\)
0.985249 + 0.171129i \(0.0547416\pi\)
\(770\) −368.853 1578.73i −0.479030 2.05030i
\(771\) −164.144 + 164.144i −0.212897 + 0.212897i