Properties

Label 48.3.l.a.43.5
Level $48$
Weight $3$
Character 48.43
Analytic conductor $1.308$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 43.5
Root \(-0.455024 - 1.94755i\) of defining polynomial
Character \(\chi\) \(=\) 48.43
Dual form 48.3.l.a.19.5

$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 0.279113 0.960258i \(-0.409960\pi\)
−0.960258 + 0.279113i \(0.909960\pi\)
\(6\) −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 −0.102805 0.994702i \(-0.532782\pi\)
0.994702 + 0.102805i \(0.0327818\pi\)
\(12\) 2.22113 + 6.56251i 0.185094 + 0.546876i
\(13\) −7.76859 + 7.76859i −0.597584 + 0.597584i −0.939669 0.342085i \(-0.888867\pi\)
0.342085 + 0.939669i \(0.388867\pi\)
\(14\) 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 0.938657 0.344851i \(-0.112071\pi\)
−0.344851 + 0.938657i \(0.612071\pi\)
\(20\) 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 −0.930936 0.365182i \(-0.881007\pi\)
0.365182 + 0.930936i \(0.381007\pi\)
\(30\) 16.2470 + 3.79594i 0.541568 + 0.126531i
\(31\) 26.3542i 0.850134i 0.905162 + 0.425067i \(0.139749\pi\)
−0.905162 + 0.425067i \(0.860251\pi\)
\(32\) 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 0.309613 0.950863i \(-0.399801\pi\)
−0.950863 + 0.309613i \(0.899801\pi\)
\(38\) 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 \(0.0975779\pi\)
−0.953380 + 0.301771i \(0.902422\pi\)
\(42\) −35.6940 + 22.1738i −0.849856 + 0.527948i
\(43\) 29.8844 29.8844i 0.694987 0.694987i −0.268338 0.963325i \(-0.586474\pi\)
0.963325 + 0.268338i \(0.0864744\pi\)
\(44\) −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 \(0.108170\pi\)
−0.942812 + 0.333324i \(0.891830\pi\)
\(48\) 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 0.963489 0.267750i \(-0.0862800\pi\)
−0.267750 + 0.963489i \(0.586280\pi\)
\(54\) −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 −0.816657 0.577123i \(-0.804175\pi\)
0.577123 + 0.816657i \(0.304175\pi\)
\(60\) 14.7856 29.9147i 0.246426 0.498578i
\(61\) −42.5199 + 42.5199i −0.697048 + 0.697048i −0.963773 0.266725i \(-0.914059\pi\)
0.266725 + 0.963773i \(0.414059\pi\)
\(62\) 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 0.970230 0.242186i \(-0.0778644\pi\)
−0.242186 + 0.970230i \(0.577864\pi\)
\(68\) −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 \(-0.801077\pi\)
0.811002 0.585043i \(-0.198923\pi\)
\(74\) −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 \(-0.767828\pi\)
0.745581 0.666416i \(-0.232172\pi\)
\(80\) 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 0.225723 0.974192i \(-0.427526\pi\)
−0.974192 + 0.225723i \(0.927526\pi\)
\(84\) 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 \(0.253324\pi\)
−0.699685 + 0.714451i \(0.746676\pi\)
\(90\) −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 0.767489 0.641063i \(-0.221506\pi\)
−0.641063 + 0.767489i \(0.721506\pi\)
\(102\) −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 −0.777445 0.628951i \(-0.783485\pi\)
0.628951 + 0.777445i \(0.283485\pi\)
\(108\) −19.6875 + 6.66338i −0.182292 + 0.0616980i
\(109\) −79.3257 + 79.3257i −0.727758 + 0.727758i −0.970173 0.242414i \(-0.922061\pi\)
0.242414 + 0.970173i \(0.422061\pi\)
\(110\) −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 \(-0.714965\pi\)
0.625156 0.780500i \(-0.285035\pi\)
\(128\) −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 0.999667 + 0.0258197i \(0.00821957\pi\)
0.0258197 + 0.999667i \(0.491780\pi\)
\(132\) 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 \(-0.616224\pi\)
0.357069 0.934078i \(-0.383776\pi\)
\(138\) 59.6261 37.0409i 0.432073 0.268412i
\(139\) −21.7231 + 21.7231i −0.156281 + 0.156281i −0.780917 0.624635i \(-0.785248\pi\)
0.624635 + 0.780917i \(0.285248\pi\)
\(140\) 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 0.582793 0.812621i \(-0.301960\pi\)
−0.812621 + 0.582793i \(0.801960\pi\)
\(150\) 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 −0.599763 0.800178i \(-0.704738\pi\)
0.800178 + 0.599763i \(0.204738\pi\)
\(158\) −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 0.796836 0.604196i \(-0.206506\pi\)
−0.604196 + 0.796836i \(0.706506\pi\)
\(164\) 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 −0.366151 0.930555i \(-0.619325\pi\)
0.930555 + 0.366151i \(0.119325\pi\)
\(174\) 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 0.911859 0.410503i \(-0.134647\pi\)
−0.410503 + 0.911859i \(0.634647\pi\)
\(180\) −54.7464 + 18.5293i −0.304147 + 0.102940i
\(181\) −115.497 115.497i −0.638108 0.638108i 0.311981 0.950088i \(-0.399008\pi\)
−0.950088 + 0.311981i \(0.899008\pi\)
\(182\) 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 \(-0.947577\pi\)
0.986469 0.163947i \(-0.0524227\pi\)
\(192\) −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 0.777087 0.629393i \(-0.216696\pi\)
−0.629393 + 0.777087i \(0.716696\pi\)
\(198\) 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 0.706595 0.707618i \(-0.250230\pi\)
−0.707618 + 0.706595i \(0.750230\pi\)
\(212\) −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 \(0.313158\pi\)
−0.553850 + 0.832617i \(0.686842\pi\)
\(224\) 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 0.0730018 0.997332i \(-0.476742\pi\)
−0.997332 + 0.0730018i \(0.976742\pi\)
\(228\) −48.9809 + 99.0998i −0.214829 + 0.434648i
\(229\) 152.751 + 152.751i 0.667037 + 0.667037i 0.957029 0.289992i \(-0.0936527\pi\)
−0.289992 + 0.957029i \(0.593653\pi\)
\(230\) 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 \(-0.800851\pi\)
0.810586 0.585619i \(-0.199149\pi\)
\(234\) −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 \(0.0702576\pi\)
−0.975740 + 0.218933i \(0.929742\pi\)
\(240\) −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 −0.360284 0.932843i \(-0.617320\pi\)
0.932843 + 0.360284i \(0.117320\pi\)
\(252\) 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 −0.831538 0.555468i \(-0.812539\pi\)
0.555468 + 0.831538i \(0.312539\pi\)
\(270\) −11.3878 + 48.7411i −0.0421771 + 0.180523i
\(271\) 70.8329i 0.261376i −0.991424 0.130688i \(-0.958281\pi\)
0.991424 0.130688i \(-0.0417186\pi\)
\(272\) 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 0.510686 0.859767i \(-0.329391\pi\)
−0.859767 + 0.510686i \(0.829391\pi\)
\(278\) 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 \(0.0790572\pi\)
−0.969316 + 0.245820i \(0.920943\pi\)
\(282\) −57.2746 92.1970i −0.203101 0.326940i
\(283\) −295.011 + 295.011i −1.04244 + 1.04244i −0.0433821 + 0.999059i \(0.513813\pi\)
−0.999059 + 0.0433821i \(0.986187\pi\)
\(284\) −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 0.647669 0.761922i \(-0.275744\pi\)
−0.761922 + 0.647669i \(0.775744\pi\)
\(294\) −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 0.539896 0.841732i \(-0.318464\pi\)
−0.841732 + 0.539896i \(0.818464\pi\)
\(308\) −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 \(0.0280809\pi\)
−0.996111 + 0.0881045i \(0.971919\pi\)
\(314\) −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 −0.601985 0.798507i \(-0.705623\pi\)
0.798507 + 0.601985i \(0.205623\pi\)
\(318\) −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 0.138899 0.990307i \(-0.455644\pi\)
0.990307 0.138899i \(-0.0443564\pi\)
\(332\) 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 −0.508825 0.860870i \(-0.669920\pi\)
0.860870 + 0.508825i \(0.169920\pi\)
\(348\) −144.112 71.2286i −0.414115 0.204680i
\(349\) −279.483 + 279.483i −0.800810 + 0.800810i −0.983222 0.182412i \(-0.941609\pi\)
0.182412 + 0.983222i \(0.441609\pi\)
\(350\) −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 \(-0.945291\pi\)
0.985266 0.171029i \(-0.0547091\pi\)
\(368\) −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 0.174044 0.984738i \(-0.444317\pi\)
−0.984738 + 0.174044i \(0.944317\pi\)
\(374\) −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 −0.410921 0.911671i \(-0.634793\pi\)
0.911671 + 0.410921i \(0.134793\pi\)
\(380\) −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 \(-0.685237\pi\)
0.549644 0.835399i \(-0.314763\pi\)
\(384\) 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 0.938586 + 0.345046i \(0.112137\pi\)
0.345046 + 0.938586i \(0.387863\pi\)
\(390\) −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 0.280846 0.959753i \(-0.409385\pi\)
0.959753 0.280846i \(-0.0906151\pi\)
\(398\) 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 \(0.111129\pi\)
−0.939674 + 0.342072i \(0.888871\pi\)
\(410\) −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 −0.861965 0.506968i \(-0.830766\pi\)
−0.506968 0.861965i \(-0.669234\pi\)
\(420\) 179.354 362.875i 0.427033 0.863987i
\(421\) −213.341 213.341i −0.506749 0.506749i 0.406778 0.913527i \(-0.366652\pi\)
−0.913527 + 0.406778i \(0.866652\pi\)
\(422\) −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 \(0.0620227\pi\)
−0.981077 + 0.193619i \(0.937977\pi\)
\(432\) 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 −0.965580 0.260107i \(-0.916242\pi\)
0.260107 + 0.965580i \(0.416242\pi\)
\(444\) 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 \(0.273789\pi\)
−0.652335 + 0.757931i \(0.726211\pi\)
\(458\) 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 −0.304971 0.952362i \(-0.598647\pi\)
0.952362 + 0.304971i \(0.0986467\pi\)
\(462\) −132.645 + 567.733i −0.287109 + 1.22886i
\(463\) 281.830i 0.608705i 0.952560 + 0.304352i \(0.0984400\pi\)
−0.952560 + 0.304352i \(0.901560\pi\)
\(464\) −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 0.886658 0.462426i \(-0.153021\pi\)
−0.462426 + 0.886658i \(0.653021\pi\)
\(468\) 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 \(-0.592640\pi\)
0.286945 0.957947i \(-0.407360\pi\)
\(480\) 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 −0.924220 0.381859i \(-0.875284\pi\)
0.381859 + 0.924220i \(0.375284\pi\)
\(492\) −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 0.391088 0.920353i \(-0.372099\pi\)
−0.920353 + 0.391088i \(0.872099\pi\)
\(500\) 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 −0.519387 0.854539i \(-0.673840\pi\)
0.854539 + 0.519387i \(0.173840\pi\)
\(510\) 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 \(0.0113421\pi\)
−0.999365 + 0.0356248i \(0.988658\pi\)
\(522\) −118.256 + 73.4631i −0.226545 + 0.140734i
\(523\) −199.555 + 199.555i −0.381558 + 0.381558i −0.871663 0.490105i \(-0.836958\pi\)
0.490105 + 0.871663i \(0.336958\pi\)
\(524\) −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 −0.401690 0.915776i \(-0.631577\pi\)
0.915776 + 0.401690i \(0.131577\pi\)
\(542\) −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 0.909421 + 0.415876i \(0.136525\pi\)
0.415876 + 0.909421i \(0.363475\pi\)
\(548\) −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 −0.423985 0.905669i \(-0.639369\pi\)
0.905669 + 0.423985i \(0.139369\pi\)
\(558\) −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 0.633979 0.773350i \(-0.281421\pi\)
−0.773350 + 0.633979i \(0.781421\pi\)
\(564\) −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 \(0.248938\pi\)
−0.709461 + 0.704744i \(0.751062\pi\)
\(570\) 140.477 + 226.131i 0.246451 + 0.396721i
\(571\) 79.9964 79.9964i 0.140099 0.140099i −0.633579 0.773678i \(-0.718415\pi\)
0.773678 + 0.633579i \(0.218415\pi\)
\(572\) 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 −0.897500 0.441014i \(-0.854619\pi\)
0.441014 + 0.897500i \(0.354619\pi\)
\(588\) 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 \(0.0830573\pi\)
−0.966150 + 0.257981i \(0.916943\pi\)
\(602\) −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 \(0.151581\pi\)
−0.888741 + 0.458410i \(0.848419\pi\)
\(608\) 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 0.389024 0.921228i \(-0.372812\pi\)
−0.921228 + 0.389024i \(0.872812\pi\)
\(614\) −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 \(0.133377\pi\)
−0.913490 + 0.406862i \(0.866623\pi\)
\(618\) 52.2659 32.4686i 0.0845726 0.0525381i
\(619\) 304.429 304.429i 0.491808 0.491808i −0.417067 0.908876i \(-0.636942\pi\)
0.908876 + 0.417067i \(0.136942\pi\)
\(620\) −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 0.609369 0.792886i \(-0.291423\pi\)
−0.792886 + 0.609369i \(0.791423\pi\)
\(644\) 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 −0.995236 0.0974927i \(-0.968918\pi\)
0.0974927 + 0.995236i \(0.468918\pi\)
\(654\) 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 0.967204 0.254003i \(-0.0817472\pi\)
−0.254003 + 0.967204i \(0.581747\pi\)
\(660\) −148.429 438.548i −0.224893 0.664466i
\(661\) −884.745 884.745i −1.33849 1.33849i −0.897519 0.440976i \(-0.854632\pi\)
−0.440976 0.897519i \(-0.645368\pi\)
\(662\) −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 0.364390 0.931246i \(-0.381278\pi\)
−0.931246 + 0.364390i \(0.881278\pi\)
\(678\) 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 0.411709 0.911315i \(-0.364932\pi\)
0.911315 0.411709i \(-0.135068\pi\)
\(684\) 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 0.659520 0.751687i \(-0.270759\pi\)
−0.751687 + 0.659520i \(0.770759\pi\)
\(692\) −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 −0.534033 0.845463i \(-0.679324\pi\)
0.845463 + 0.534033i \(0.179324\pi\)
\(702\) 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 −0.984548 0.175112i \(-0.943971\pi\)
−0.175112 0.984548i \(-0.556029\pi\)
\(710\) −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 \(-0.923811\pi\)
0.971491 0.237074i \(-0.0761885\pi\)
\(720\) 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 −0.297658 0.954673i \(-0.596205\pi\)
0.954673 + 0.297658i \(0.0962054\pi\)
\(734\) −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 0.814752 0.579810i \(-0.196873\pi\)
−0.579810 + 0.814752i \(0.696873\pi\)
\(740\) 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 \(0.0689853\pi\)
−0.976607 + 0.215031i \(0.931015\pi\)
\(752\) −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 0.652095 0.758138i \(-0.273890\pi\)
−0.758138 + 0.652095i \(0.773890\pi\)
\(758\) −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 \(0.128226\pi\)
−0.919954 + 0.392027i \(0.871774\pi\)
\(762\) 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