Properties

Label 414.3.k.b.71.1
Level $414$
Weight $3$
Character 414.71
Analytic conductor $11.281$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 414.k (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.2806829445\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(8\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 71.1
Character \(\chi\) \(=\) 414.71
Dual form 414.3.k.b.35.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-2.17725 + 7.41503i) q^{5} +(6.85488 - 7.91095i) q^{7} +(2.79964 + 0.402527i) q^{8} +O(q^{10})\) \(q+(-0.764582 + 1.18971i) q^{2} +(-0.830830 - 1.81926i) q^{4} +(-2.17725 + 7.41503i) q^{5} +(6.85488 - 7.91095i) q^{7} +(2.79964 + 0.402527i) q^{8} +(-7.15707 - 8.25969i) q^{10} +(-0.214579 - 0.333892i) q^{11} +(7.09545 + 8.18859i) q^{13} +(4.17064 + 14.2039i) q^{14} +(-2.61944 + 3.02300i) q^{16} +(9.43996 + 4.31109i) q^{17} +(6.43909 + 14.0996i) q^{19} +(15.2988 - 2.19964i) q^{20} +0.561299 q^{22} +(21.1528 + 9.03111i) q^{23} +(-29.2109 - 18.7727i) q^{25} +(-15.1671 + 2.18070i) q^{26} +(-20.0873 - 5.89818i) q^{28} +(-38.3477 - 17.5128i) q^{29} +(-1.84235 + 12.8139i) q^{31} +(-1.59372 - 5.42771i) q^{32} +(-12.3466 + 7.93466i) q^{34} +(43.7352 + 68.0532i) q^{35} +(-25.4655 + 7.47734i) q^{37} +(-21.6977 - 3.11966i) q^{38} +(-9.08026 + 19.8830i) q^{40} +(-14.1920 + 48.3334i) q^{41} +(2.60054 + 18.0871i) q^{43} +(-0.429159 + 0.667784i) q^{44} +(-26.9174 + 18.2607i) q^{46} +47.1029i q^{47} +(-8.62036 - 59.9559i) q^{49} +(44.6682 - 20.3993i) q^{50} +(9.00209 - 19.7118i) q^{52} +(40.3577 + 34.9701i) q^{53} +(2.94301 - 0.864146i) q^{55} +(22.3755 - 19.3885i) q^{56} +(50.1552 - 32.2328i) q^{58} +(-36.5799 + 31.6966i) q^{59} +(-9.80873 + 68.2212i) q^{61} +(-13.8362 - 11.9891i) q^{62} +(7.67594 + 2.25386i) q^{64} +(-76.1672 + 34.7844i) q^{65} +(79.4192 + 51.0396i) q^{67} -20.7556i q^{68} -114.403 q^{70} +(59.1643 - 92.0615i) q^{71} +(-6.28038 - 13.7521i) q^{73} +(10.5745 - 36.0136i) q^{74} +(20.3012 - 23.4288i) q^{76} +(-4.11232 - 0.591262i) q^{77} +(-2.59730 - 2.99744i) q^{79} +(-16.7124 - 26.0051i) q^{80} +(-46.6520 - 53.8392i) q^{82} +(-29.9013 - 101.835i) q^{83} +(-52.5200 + 60.6113i) q^{85} +(-23.5068 - 10.7352i) q^{86} +(-0.466344 - 1.02115i) q^{88} +(-96.4907 + 13.8733i) q^{89} +113.418 q^{91} +(-1.14437 - 45.9858i) q^{92} +(-56.0389 - 36.0140i) q^{94} +(-118.569 + 17.0476i) q^{95} +(136.320 + 40.0270i) q^{97} +(77.9213 + 35.5854i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 16 q^{4} + 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 16 q^{4} + 16 q^{7} - 8 q^{10} - 24 q^{13} - 32 q^{16} + 208 q^{19} + 64 q^{22} + 256 q^{25} - 32 q^{28} + 268 q^{34} - 256 q^{37} + 16 q^{40} - 524 q^{43} - 48 q^{46} + 144 q^{49} + 48 q^{52} + 396 q^{55} + 456 q^{58} + 376 q^{61} + 64 q^{64} + 44 q^{67} - 520 q^{70} - 188 q^{73} - 64 q^{76} + 164 q^{79} - 924 q^{82} - 1524 q^{85} + 48 q^{88} + 128 q^{91} - 176 q^{94} - 1144 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(235\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.764582 + 1.18971i −0.382291 + 0.594856i
\(3\) 0 0
\(4\) −0.830830 1.81926i −0.207708 0.454816i
\(5\) −2.17725 + 7.41503i −0.435450 + 1.48301i 0.391209 + 0.920302i \(0.372057\pi\)
−0.826659 + 0.562704i \(0.809761\pi\)
\(6\) 0 0
\(7\) 6.85488 7.91095i 0.979268 1.13014i −0.0122182 0.999925i \(-0.503889\pi\)
0.991486 0.130210i \(-0.0415653\pi\)
\(8\) 2.79964 + 0.402527i 0.349955 + 0.0503159i
\(9\) 0 0
\(10\) −7.15707 8.25969i −0.715707 0.825969i
\(11\) −0.214579 0.333892i −0.0195072 0.0303538i 0.831363 0.555730i \(-0.187561\pi\)
−0.850870 + 0.525376i \(0.823925\pi\)
\(12\) 0 0
\(13\) 7.09545 + 8.18859i 0.545804 + 0.629891i 0.959900 0.280342i \(-0.0904478\pi\)
−0.414096 + 0.910233i \(0.635902\pi\)
\(14\) 4.17064 + 14.2039i 0.297903 + 1.01456i
\(15\) 0 0
\(16\) −2.61944 + 3.02300i −0.163715 + 0.188937i
\(17\) 9.43996 + 4.31109i 0.555292 + 0.253593i 0.673237 0.739427i \(-0.264903\pi\)
−0.117945 + 0.993020i \(0.537631\pi\)
\(18\) 0 0
\(19\) 6.43909 + 14.0996i 0.338899 + 0.742086i 0.999966 0.00824092i \(-0.00262319\pi\)
−0.661067 + 0.750327i \(0.729896\pi\)
\(20\) 15.2988 2.19964i 0.764941 0.109982i
\(21\) 0 0
\(22\) 0.561299 0.0255136
\(23\) 21.1528 + 9.03111i 0.919685 + 0.392657i
\(24\) 0 0
\(25\) −29.2109 18.7727i −1.16844 0.750908i
\(26\) −15.1671 + 2.18070i −0.583351 + 0.0838731i
\(27\) 0 0
\(28\) −20.0873 5.89818i −0.717405 0.210649i
\(29\) −38.3477 17.5128i −1.32234 0.603890i −0.375863 0.926675i \(-0.622654\pi\)
−0.946472 + 0.322785i \(0.895381\pi\)
\(30\) 0 0
\(31\) −1.84235 + 12.8139i −0.0594308 + 0.413350i 0.938289 + 0.345853i \(0.112410\pi\)
−0.997719 + 0.0674970i \(0.978499\pi\)
\(32\) −1.59372 5.42771i −0.0498038 0.169616i
\(33\) 0 0
\(34\) −12.3466 + 7.93466i −0.363135 + 0.233372i
\(35\) 43.7352 + 68.0532i 1.24958 + 1.94438i
\(36\) 0 0
\(37\) −25.4655 + 7.47734i −0.688256 + 0.202090i −0.607117 0.794613i \(-0.707674\pi\)
−0.0811391 + 0.996703i \(0.525856\pi\)
\(38\) −21.6977 3.11966i −0.570993 0.0820964i
\(39\) 0 0
\(40\) −9.08026 + 19.8830i −0.227006 + 0.497075i
\(41\) −14.1920 + 48.3334i −0.346146 + 1.17886i 0.584025 + 0.811736i \(0.301477\pi\)
−0.930170 + 0.367128i \(0.880341\pi\)
\(42\) 0 0
\(43\) 2.60054 + 18.0871i 0.0604777 + 0.420631i 0.997458 + 0.0712505i \(0.0226990\pi\)
−0.936981 + 0.349381i \(0.886392\pi\)
\(44\) −0.429159 + 0.667784i −0.00975360 + 0.0151769i
\(45\) 0 0
\(46\) −26.9174 + 18.2607i −0.585161 + 0.396971i
\(47\) 47.1029i 1.00219i 0.865392 + 0.501095i \(0.167069\pi\)
−0.865392 + 0.501095i \(0.832931\pi\)
\(48\) 0 0
\(49\) −8.62036 59.9559i −0.175926 1.22359i
\(50\) 44.6682 20.3993i 0.893365 0.407986i
\(51\) 0 0
\(52\) 9.00209 19.7118i 0.173117 0.379074i
\(53\) 40.3577 + 34.9701i 0.761466 + 0.659814i 0.946422 0.322933i \(-0.104669\pi\)
−0.184956 + 0.982747i \(0.559214\pi\)
\(54\) 0 0
\(55\) 2.94301 0.864146i 0.0535093 0.0157117i
\(56\) 22.3755 19.3885i 0.399563 0.346224i
\(57\) 0 0
\(58\) 50.1552 32.2328i 0.864745 0.555738i
\(59\) −36.5799 + 31.6966i −0.619998 + 0.537231i −0.907233 0.420629i \(-0.861809\pi\)
0.287235 + 0.957860i \(0.407264\pi\)
\(60\) 0 0
\(61\) −9.80873 + 68.2212i −0.160799 + 1.11838i 0.736334 + 0.676619i \(0.236555\pi\)
−0.897132 + 0.441762i \(0.854354\pi\)
\(62\) −13.8362 11.9891i −0.223164 0.193373i
\(63\) 0 0
\(64\) 7.67594 + 2.25386i 0.119937 + 0.0352166i
\(65\) −76.1672 + 34.7844i −1.17180 + 0.535144i
\(66\) 0 0
\(67\) 79.4192 + 51.0396i 1.18536 + 0.761785i 0.976364 0.216131i \(-0.0693438\pi\)
0.208997 + 0.977916i \(0.432980\pi\)
\(68\) 20.7556i 0.305229i
\(69\) 0 0
\(70\) −114.403 −1.63433
\(71\) 59.1643 92.0615i 0.833300 1.29664i −0.119436 0.992842i \(-0.538109\pi\)
0.952736 0.303799i \(-0.0982550\pi\)
\(72\) 0 0
\(73\) −6.28038 13.7521i −0.0860325 0.188385i 0.861726 0.507374i \(-0.169384\pi\)
−0.947758 + 0.318989i \(0.896657\pi\)
\(74\) 10.5745 36.0136i 0.142899 0.486670i
\(75\) 0 0
\(76\) 20.3012 23.4288i 0.267121 0.308274i
\(77\) −4.11232 0.591262i −0.0534067 0.00767873i
\(78\) 0 0
\(79\) −2.59730 2.99744i −0.0328772 0.0379423i 0.739073 0.673626i \(-0.235264\pi\)
−0.771950 + 0.635683i \(0.780718\pi\)
\(80\) −16.7124 26.0051i −0.208906 0.325063i
\(81\) 0 0
\(82\) −46.6520 53.8392i −0.568926 0.656576i
\(83\) −29.9013 101.835i −0.360257 1.22692i −0.917890 0.396835i \(-0.870108\pi\)
0.557633 0.830088i \(-0.311710\pi\)
\(84\) 0 0
\(85\) −52.5200 + 60.6113i −0.617882 + 0.713074i
\(86\) −23.5068 10.7352i −0.273335 0.124828i
\(87\) 0 0
\(88\) −0.466344 1.02115i −0.00529936 0.0116040i
\(89\) −96.4907 + 13.8733i −1.08417 + 0.155879i −0.661158 0.750247i \(-0.729935\pi\)
−0.423007 + 0.906126i \(0.639026\pi\)
\(90\) 0 0
\(91\) 113.418 1.24635
\(92\) −1.14437 45.9858i −0.0124388 0.499845i
\(93\) 0 0
\(94\) −56.0389 36.0140i −0.596159 0.383128i
\(95\) −118.569 + 17.0476i −1.24809 + 0.179449i
\(96\) 0 0
\(97\) 136.320 + 40.0270i 1.40536 + 0.412650i 0.894520 0.447028i \(-0.147518\pi\)
0.510836 + 0.859678i \(0.329336\pi\)
\(98\) 77.9213 + 35.5854i 0.795115 + 0.363117i
\(99\) 0 0
\(100\) −9.88322 + 68.7393i −0.0988322 + 0.687393i
\(101\) 17.9643 + 61.1809i 0.177865 + 0.605751i 0.999368 + 0.0355476i \(0.0113175\pi\)
−0.821503 + 0.570204i \(0.806864\pi\)
\(102\) 0 0
\(103\) −159.755 + 102.668i −1.55102 + 0.996779i −0.565986 + 0.824415i \(0.691504\pi\)
−0.985033 + 0.172364i \(0.944859\pi\)
\(104\) 16.5686 + 25.7812i 0.159313 + 0.247896i
\(105\) 0 0
\(106\) −72.4611 + 21.2765i −0.683596 + 0.200722i
\(107\) 8.05726 + 1.15846i 0.0753015 + 0.0108267i 0.179863 0.983692i \(-0.442435\pi\)
−0.104561 + 0.994518i \(0.533344\pi\)
\(108\) 0 0
\(109\) 80.0266 175.234i 0.734189 1.60765i −0.0586952 0.998276i \(-0.518694\pi\)
0.792884 0.609373i \(-0.208579\pi\)
\(110\) −1.22209 + 4.16205i −0.0111099 + 0.0378368i
\(111\) 0 0
\(112\) 5.95883 + 41.4446i 0.0532038 + 0.370041i
\(113\) 94.9377 147.726i 0.840157 1.30731i −0.109490 0.993988i \(-0.534922\pi\)
0.949647 0.313322i \(-0.101442\pi\)
\(114\) 0 0
\(115\) −113.021 + 137.185i −0.982789 + 1.19292i
\(116\) 84.3148i 0.726852i
\(117\) 0 0
\(118\) −9.74158 67.7542i −0.0825558 0.574188i
\(119\) 98.8146 45.1271i 0.830375 0.379219i
\(120\) 0 0
\(121\) 50.1998 109.922i 0.414874 0.908448i
\(122\) −73.6640 63.8302i −0.603803 0.523199i
\(123\) 0 0
\(124\) 24.8425 7.29440i 0.200342 0.0588258i
\(125\) 56.7875 49.2066i 0.454300 0.393653i
\(126\) 0 0
\(127\) 188.425 121.094i 1.48366 0.953493i 0.486871 0.873474i \(-0.338138\pi\)
0.996793 0.0800193i \(-0.0254982\pi\)
\(128\) −8.55033 + 7.40890i −0.0667995 + 0.0578821i
\(129\) 0 0
\(130\) 16.8526 117.213i 0.129636 0.901635i
\(131\) −32.8193 28.4381i −0.250529 0.217085i 0.520538 0.853838i \(-0.325731\pi\)
−0.771067 + 0.636754i \(0.780277\pi\)
\(132\) 0 0
\(133\) 155.681 + 45.7120i 1.17053 + 0.343699i
\(134\) −121.445 + 55.4620i −0.906305 + 0.413896i
\(135\) 0 0
\(136\) 24.6931 + 15.8693i 0.181567 + 0.116686i
\(137\) 144.020i 1.05124i −0.850720 0.525620i \(-0.823834\pi\)
0.850720 0.525620i \(-0.176166\pi\)
\(138\) 0 0
\(139\) 152.496 1.09710 0.548548 0.836119i \(-0.315181\pi\)
0.548548 + 0.836119i \(0.315181\pi\)
\(140\) 87.4703 136.106i 0.624788 0.972189i
\(141\) 0 0
\(142\) 64.2907 + 140.777i 0.452751 + 0.991387i
\(143\) 1.21157 4.12622i 0.00847249 0.0288547i
\(144\) 0 0
\(145\) 213.351 246.220i 1.47138 1.69807i
\(146\) 21.1629 + 3.04277i 0.144951 + 0.0208409i
\(147\) 0 0
\(148\) 34.7607 + 40.1160i 0.234870 + 0.271054i
\(149\) 72.5921 + 112.955i 0.487195 + 0.758090i 0.994618 0.103607i \(-0.0330383\pi\)
−0.507423 + 0.861697i \(0.669402\pi\)
\(150\) 0 0
\(151\) −38.5745 44.5173i −0.255460 0.294817i 0.613504 0.789692i \(-0.289759\pi\)
−0.868964 + 0.494875i \(0.835214\pi\)
\(152\) 12.3516 + 42.0658i 0.0812607 + 0.276749i
\(153\) 0 0
\(154\) 3.84763 4.44041i 0.0249846 0.0288338i
\(155\) −91.0038 41.5601i −0.587121 0.268129i
\(156\) 0 0
\(157\) −91.0843 199.447i −0.580155 1.27036i −0.941211 0.337818i \(-0.890311\pi\)
0.361056 0.932544i \(-0.382416\pi\)
\(158\) 5.55193 0.798248i 0.0351388 0.00505220i
\(159\) 0 0
\(160\) 43.7166 0.273229
\(161\) 216.444 105.431i 1.34437 0.654852i
\(162\) 0 0
\(163\) 233.616 + 150.136i 1.43323 + 0.921080i 0.999802 + 0.0198904i \(0.00633172\pi\)
0.433426 + 0.901189i \(0.357305\pi\)
\(164\) 99.7224 14.3379i 0.608063 0.0874263i
\(165\) 0 0
\(166\) 144.016 + 42.2869i 0.867565 + 0.254740i
\(167\) −198.914 90.8409i −1.19110 0.543958i −0.281549 0.959547i \(-0.590848\pi\)
−0.909552 + 0.415589i \(0.863575\pi\)
\(168\) 0 0
\(169\) 7.34367 51.0764i 0.0434537 0.302227i
\(170\) −31.9542 108.826i −0.187966 0.640153i
\(171\) 0 0
\(172\) 30.7447 19.7584i 0.178748 0.114874i
\(173\) 148.356 + 230.846i 0.857549 + 1.33437i 0.941191 + 0.337876i \(0.109708\pi\)
−0.0836422 + 0.996496i \(0.526655\pi\)
\(174\) 0 0
\(175\) −348.747 + 102.401i −1.99284 + 0.585151i
\(176\) 1.57143 + 0.225938i 0.00892860 + 0.00128374i
\(177\) 0 0
\(178\) 57.2698 125.403i 0.321741 0.704514i
\(179\) −68.5892 + 233.593i −0.383180 + 1.30499i 0.511885 + 0.859054i \(0.328948\pi\)
−0.895065 + 0.445937i \(0.852871\pi\)
\(180\) 0 0
\(181\) 26.2047 + 182.258i 0.144778 + 1.00695i 0.924597 + 0.380946i \(0.124402\pi\)
−0.779820 + 0.626004i \(0.784689\pi\)
\(182\) −86.7173 + 134.935i −0.476469 + 0.741400i
\(183\) 0 0
\(184\) 55.5848 + 33.7984i 0.302091 + 0.183687i
\(185\) 205.107i 1.10869i
\(186\) 0 0
\(187\) −0.586184 4.07700i −0.00313467 0.0218021i
\(188\) 85.6926 39.1345i 0.455812 0.208162i
\(189\) 0 0
\(190\) 70.3737 154.097i 0.370388 0.811037i
\(191\) −106.359 92.1603i −0.556852 0.482515i 0.330374 0.943850i \(-0.392825\pi\)
−0.887226 + 0.461335i \(0.847371\pi\)
\(192\) 0 0
\(193\) −364.220 + 106.945i −1.88715 + 0.554117i −0.892470 + 0.451107i \(0.851029\pi\)
−0.994680 + 0.103010i \(0.967153\pi\)
\(194\) −151.848 + 131.577i −0.782722 + 0.678232i
\(195\) 0 0
\(196\) −101.914 + 65.4959i −0.519967 + 0.334163i
\(197\) 139.830 121.163i 0.709796 0.615042i −0.223266 0.974758i \(-0.571672\pi\)
0.933062 + 0.359716i \(0.117126\pi\)
\(198\) 0 0
\(199\) −19.0391 + 132.420i −0.0956739 + 0.665427i 0.884391 + 0.466748i \(0.154574\pi\)
−0.980065 + 0.198679i \(0.936335\pi\)
\(200\) −74.2234 64.3150i −0.371117 0.321575i
\(201\) 0 0
\(202\) −86.5228 25.4054i −0.428331 0.125769i
\(203\) −401.412 + 183.319i −1.97740 + 0.903048i
\(204\) 0 0
\(205\) −327.494 210.468i −1.59753 1.02667i
\(206\) 268.561i 1.30369i
\(207\) 0 0
\(208\) −43.3402 −0.208366
\(209\) 3.32606 5.17545i 0.0159142 0.0247629i
\(210\) 0 0
\(211\) −73.6327 161.233i −0.348970 0.764138i −0.999987 0.00507499i \(-0.998385\pi\)
0.651017 0.759063i \(-0.274343\pi\)
\(212\) 30.0895 102.476i 0.141932 0.483375i
\(213\) 0 0
\(214\) −7.53867 + 8.70009i −0.0352274 + 0.0406546i
\(215\) −139.779 20.0971i −0.650134 0.0934751i
\(216\) 0 0
\(217\) 88.7406 + 102.412i 0.408943 + 0.471945i
\(218\) 147.291 + 229.189i 0.675646 + 1.05133i
\(219\) 0 0
\(220\) −4.01725 4.63616i −0.0182602 0.0210734i
\(221\) 31.6791 + 107.889i 0.143344 + 0.488186i
\(222\) 0 0
\(223\) −98.4729 + 113.644i −0.441582 + 0.509613i −0.932290 0.361711i \(-0.882193\pi\)
0.490708 + 0.871324i \(0.336738\pi\)
\(224\) −53.8631 24.5985i −0.240460 0.109815i
\(225\) 0 0
\(226\) 103.164 + 225.897i 0.456477 + 0.999545i
\(227\) 28.9087 4.15644i 0.127351 0.0183103i −0.0783445 0.996926i \(-0.524963\pi\)
0.205696 + 0.978616i \(0.434054\pi\)
\(228\) 0 0
\(229\) 112.703 0.492155 0.246077 0.969250i \(-0.420858\pi\)
0.246077 + 0.969250i \(0.420858\pi\)
\(230\) −76.7975 239.352i −0.333902 1.04066i
\(231\) 0 0
\(232\) −100.310 64.4656i −0.432372 0.277869i
\(233\) −327.182 + 47.0417i −1.40421 + 0.201896i −0.802422 0.596757i \(-0.796456\pi\)
−0.601792 + 0.798653i \(0.705547\pi\)
\(234\) 0 0
\(235\) −349.269 102.555i −1.48625 0.436403i
\(236\) 88.0562 + 40.2139i 0.373119 + 0.170398i
\(237\) 0 0
\(238\) −21.8635 + 152.064i −0.0918636 + 0.638925i
\(239\) −25.3309 86.2691i −0.105987 0.360959i 0.889373 0.457183i \(-0.151142\pi\)
−0.995360 + 0.0962243i \(0.969323\pi\)
\(240\) 0 0
\(241\) 119.043 76.5040i 0.493953 0.317444i −0.269841 0.962905i \(-0.586971\pi\)
0.763793 + 0.645461i \(0.223335\pi\)
\(242\) 92.3939 + 143.768i 0.381793 + 0.594082i
\(243\) 0 0
\(244\) 132.262 38.8356i 0.542056 0.159162i
\(245\) 463.344 + 66.6188i 1.89120 + 0.271913i
\(246\) 0 0
\(247\) −69.7679 + 152.770i −0.282461 + 0.618504i
\(248\) −10.3158 + 35.1325i −0.0415962 + 0.141663i
\(249\) 0 0
\(250\) 15.1231 + 105.183i 0.0604923 + 0.420733i
\(251\) 23.0848 35.9207i 0.0919714 0.143110i −0.792219 0.610237i \(-0.791074\pi\)
0.884191 + 0.467126i \(0.154711\pi\)
\(252\) 0 0
\(253\) −1.52353 9.00062i −0.00602185 0.0355756i
\(254\) 316.758i 1.24708i
\(255\) 0 0
\(256\) −2.27704 15.8371i −0.00889468 0.0618638i
\(257\) 180.478 82.4214i 0.702247 0.320706i −0.0320950 0.999485i \(-0.510218\pi\)
0.734342 + 0.678779i \(0.237491\pi\)
\(258\) 0 0
\(259\) −115.410 + 252.712i −0.445598 + 0.975723i
\(260\) 126.564 + 109.668i 0.486785 + 0.421801i
\(261\) 0 0
\(262\) 58.9261 17.3023i 0.224909 0.0660392i
\(263\) 270.739 234.597i 1.02943 0.892002i 0.0352069 0.999380i \(-0.488791\pi\)
0.994218 + 0.107378i \(0.0342455\pi\)
\(264\) 0 0
\(265\) −347.173 + 223.115i −1.31009 + 0.841942i
\(266\) −173.415 + 150.265i −0.651935 + 0.564905i
\(267\) 0 0
\(268\) 26.8707 186.890i 0.100264 0.697350i
\(269\) 222.628 + 192.908i 0.827612 + 0.717130i 0.961778 0.273829i \(-0.0882902\pi\)
−0.134166 + 0.990959i \(0.542836\pi\)
\(270\) 0 0
\(271\) 340.168 + 99.8824i 1.25523 + 0.368570i 0.840718 0.541473i \(-0.182133\pi\)
0.414515 + 0.910043i \(0.363951\pi\)
\(272\) −37.7599 + 17.2443i −0.138823 + 0.0633983i
\(273\) 0 0
\(274\) 171.342 + 110.115i 0.625336 + 0.401879i
\(275\) 13.7815i 0.0501146i
\(276\) 0 0
\(277\) −185.653 −0.670227 −0.335114 0.942178i \(-0.608775\pi\)
−0.335114 + 0.942178i \(0.608775\pi\)
\(278\) −116.596 + 181.427i −0.419410 + 0.652614i
\(279\) 0 0
\(280\) 95.0493 + 208.129i 0.339462 + 0.743318i
\(281\) 57.0523 194.302i 0.203033 0.691467i −0.793523 0.608541i \(-0.791755\pi\)
0.996556 0.0829263i \(-0.0264266\pi\)
\(282\) 0 0
\(283\) 5.73619 6.61992i 0.0202692 0.0233919i −0.745524 0.666478i \(-0.767801\pi\)
0.765794 + 0.643086i \(0.222346\pi\)
\(284\) −216.640 31.1481i −0.762816 0.109676i
\(285\) 0 0
\(286\) 3.98267 + 4.59624i 0.0139254 + 0.0160708i
\(287\) 285.079 + 443.592i 0.993307 + 1.54562i
\(288\) 0 0
\(289\) −118.727 137.019i −0.410821 0.474113i
\(290\) 129.807 + 442.081i 0.447609 + 1.52442i
\(291\) 0 0
\(292\) −19.8008 + 22.8513i −0.0678109 + 0.0782580i
\(293\) 50.5346 + 23.0784i 0.172473 + 0.0787659i 0.499781 0.866152i \(-0.333414\pi\)
−0.327307 + 0.944918i \(0.606141\pi\)
\(294\) 0 0
\(295\) −155.388 340.252i −0.526739 1.15340i
\(296\) −74.3039 + 10.6833i −0.251027 + 0.0360922i
\(297\) 0 0
\(298\) −189.887 −0.637205
\(299\) 76.1363 + 237.291i 0.254637 + 0.793615i
\(300\) 0 0
\(301\) 160.913 + 103.412i 0.534594 + 0.343563i
\(302\) 82.4562 11.8554i 0.273034 0.0392563i
\(303\) 0 0
\(304\) −59.4900 17.4678i −0.195691 0.0574600i
\(305\) −484.506 221.267i −1.58854 0.725464i
\(306\) 0 0
\(307\) 59.4323 413.361i 0.193590 1.34645i −0.628817 0.777553i \(-0.716461\pi\)
0.822408 0.568898i \(-0.192630\pi\)
\(308\) 2.34097 + 7.97263i 0.00760057 + 0.0258852i
\(309\) 0 0
\(310\) 119.024 76.4923i 0.383949 0.246749i
\(311\) −206.787 321.768i −0.664912 1.03462i −0.995854 0.0909714i \(-0.971003\pi\)
0.330942 0.943651i \(-0.392634\pi\)
\(312\) 0 0
\(313\) −290.730 + 85.3659i −0.928848 + 0.272735i −0.710955 0.703238i \(-0.751737\pi\)
−0.217894 + 0.975972i \(0.569919\pi\)
\(314\) 306.926 + 44.1293i 0.977470 + 0.140539i
\(315\) 0 0
\(316\) −3.29522 + 7.21553i −0.0104279 + 0.0228340i
\(317\) 31.8532 108.482i 0.100483 0.342215i −0.893871 0.448324i \(-0.852021\pi\)
0.994355 + 0.106109i \(0.0338393\pi\)
\(318\) 0 0
\(319\) 2.38124 + 16.5619i 0.00746470 + 0.0519181i
\(320\) −33.4249 + 52.0101i −0.104453 + 0.162532i
\(321\) 0 0
\(322\) −40.0564 + 338.117i −0.124399 + 1.05005i
\(323\) 160.860i 0.498017i
\(324\) 0 0
\(325\) −53.5426 372.397i −0.164746 1.14584i
\(326\) −357.237 + 163.145i −1.09582 + 0.500444i
\(327\) 0 0
\(328\) −59.1879 + 129.603i −0.180451 + 0.395133i
\(329\) 372.629 + 322.885i 1.13261 + 0.981412i
\(330\) 0 0
\(331\) −237.912 + 69.8572i −0.718767 + 0.211049i −0.620607 0.784122i \(-0.713114\pi\)
−0.0981597 + 0.995171i \(0.531296\pi\)
\(332\) −160.421 + 139.006i −0.483196 + 0.418692i
\(333\) 0 0
\(334\) 260.160 167.195i 0.778924 0.500584i
\(335\) −551.376 + 477.770i −1.64590 + 1.42618i
\(336\) 0 0
\(337\) 83.4853 580.653i 0.247731 1.72301i −0.363535 0.931581i \(-0.618430\pi\)
0.611266 0.791426i \(-0.290661\pi\)
\(338\) 55.1513 + 47.7889i 0.163170 + 0.141387i
\(339\) 0 0
\(340\) 153.903 + 45.1900i 0.452656 + 0.132912i
\(341\) 4.67377 2.13444i 0.0137061 0.00625936i
\(342\) 0 0
\(343\) −101.907 65.4916i −0.297105 0.190938i
\(344\) 51.6842i 0.150245i
\(345\) 0 0
\(346\) −388.071 −1.12159
\(347\) 8.34115 12.9791i 0.0240379 0.0374037i −0.829027 0.559209i \(-0.811105\pi\)
0.853065 + 0.521805i \(0.174741\pi\)
\(348\) 0 0
\(349\) 53.7344 + 117.662i 0.153967 + 0.337140i 0.970859 0.239649i \(-0.0770325\pi\)
−0.816893 + 0.576790i \(0.804305\pi\)
\(350\) 144.817 493.203i 0.413764 1.40915i
\(351\) 0 0
\(352\) −1.47029 + 1.69680i −0.00417696 + 0.00482047i
\(353\) −29.1790 4.19531i −0.0826601 0.0118847i 0.100861 0.994901i \(-0.467840\pi\)
−0.183521 + 0.983016i \(0.558749\pi\)
\(354\) 0 0
\(355\) 553.823 + 639.146i 1.56007 + 1.80041i
\(356\) 105.407 + 164.016i 0.296086 + 0.460718i
\(357\) 0 0
\(358\) −225.467 260.203i −0.629796 0.726823i
\(359\) −88.9595 302.968i −0.247798 0.843922i −0.985627 0.168935i \(-0.945967\pi\)
0.737829 0.674987i \(-0.235851\pi\)
\(360\) 0 0
\(361\) 79.0667 91.2479i 0.219021 0.252764i
\(362\) −236.870 108.175i −0.654337 0.298826i
\(363\) 0 0
\(364\) −94.2310 206.337i −0.258877 0.566860i
\(365\) 115.646 16.6274i 0.316839 0.0455546i
\(366\) 0 0
\(367\) −471.775 −1.28549 −0.642745 0.766080i \(-0.722205\pi\)
−0.642745 + 0.766080i \(0.722205\pi\)
\(368\) −82.7095 + 40.2883i −0.224754 + 0.109479i
\(369\) 0 0
\(370\) 244.019 + 156.821i 0.659510 + 0.423841i
\(371\) 553.294 79.5517i 1.49136 0.214425i
\(372\) 0 0
\(373\) −326.699 95.9274i −0.875868 0.257178i −0.187259 0.982311i \(-0.559960\pi\)
−0.688609 + 0.725133i \(0.741778\pi\)
\(374\) 5.29864 + 2.41981i 0.0141675 + 0.00647007i
\(375\) 0 0
\(376\) −18.9602 + 131.871i −0.0504261 + 0.350721i
\(377\) −128.689 438.275i −0.341351 1.16253i
\(378\) 0 0
\(379\) −151.044 + 97.0703i −0.398534 + 0.256122i −0.724522 0.689252i \(-0.757939\pi\)
0.325988 + 0.945374i \(0.394303\pi\)
\(380\) 129.525 + 201.544i 0.340854 + 0.530379i
\(381\) 0 0
\(382\) 190.964 56.0721i 0.499906 0.146786i
\(383\) −0.639392 0.0919307i −0.00166943 0.000240028i 0.141480 0.989941i \(-0.454814\pi\)
−0.143150 + 0.989701i \(0.545723\pi\)
\(384\) 0 0
\(385\) 13.3378 29.2056i 0.0346435 0.0758588i
\(386\) 151.243 515.085i 0.391820 1.33442i
\(387\) 0 0
\(388\) −40.4386 281.257i −0.104223 0.724889i
\(389\) 56.5933 88.0609i 0.145484 0.226378i −0.760862 0.648914i \(-0.775224\pi\)
0.906346 + 0.422536i \(0.138860\pi\)
\(390\) 0 0
\(391\) 160.747 + 176.445i 0.411119 + 0.451265i
\(392\) 171.325i 0.437053i
\(393\) 0 0
\(394\) 37.2381 + 258.997i 0.0945129 + 0.657352i
\(395\) 27.8811 12.7329i 0.0705850 0.0322351i
\(396\) 0 0
\(397\) −84.9125 + 185.933i −0.213885 + 0.468344i −0.985916 0.167242i \(-0.946514\pi\)
0.772030 + 0.635586i \(0.219241\pi\)
\(398\) −142.985 123.897i −0.359258 0.311299i
\(399\) 0 0
\(400\) 133.266 39.1305i 0.333165 0.0978262i
\(401\) −372.390 + 322.678i −0.928654 + 0.804684i −0.981012 0.193945i \(-0.937872\pi\)
0.0523581 + 0.998628i \(0.483326\pi\)
\(402\) 0 0
\(403\) −118.000 + 75.8338i −0.292803 + 0.188173i
\(404\) 96.3789 83.5128i 0.238562 0.206715i
\(405\) 0 0
\(406\) 88.8157 617.727i 0.218758 1.52149i
\(407\) 7.96098 + 6.89823i 0.0195602 + 0.0169490i
\(408\) 0 0
\(409\) 482.202 + 141.587i 1.17898 + 0.346179i 0.811780 0.583964i \(-0.198499\pi\)
0.367198 + 0.930143i \(0.380317\pi\)
\(410\) 500.792 228.704i 1.22144 0.557815i
\(411\) 0 0
\(412\) 319.510 + 205.337i 0.775509 + 0.498390i
\(413\) 506.658i 1.22677i
\(414\) 0 0
\(415\) 820.209 1.97641
\(416\) 33.1371 51.5624i 0.0796566 0.123948i
\(417\) 0 0
\(418\) 3.61425 + 7.91411i 0.00864654 + 0.0189333i
\(419\) 128.899 438.990i 0.307635 1.04771i −0.650051 0.759891i \(-0.725252\pi\)
0.957685 0.287817i \(-0.0929295\pi\)
\(420\) 0 0
\(421\) −135.667 + 156.568i −0.322250 + 0.371897i −0.893642 0.448781i \(-0.851858\pi\)
0.571392 + 0.820678i \(0.306404\pi\)
\(422\) 248.119 + 35.6742i 0.587960 + 0.0845359i
\(423\) 0 0
\(424\) 98.9105 + 114.149i 0.233279 + 0.269219i
\(425\) −194.819 303.144i −0.458398 0.713281i
\(426\) 0 0
\(427\) 472.457 + 545.244i 1.10646 + 1.27692i
\(428\) −4.58667 15.6208i −0.0107165 0.0364971i
\(429\) 0 0
\(430\) 130.782 150.931i 0.304144 0.351001i
\(431\) 622.110 + 284.108i 1.44341 + 0.659183i 0.974567 0.224098i \(-0.0719436\pi\)
0.468843 + 0.883281i \(0.344671\pi\)
\(432\) 0 0
\(433\) −323.484 708.331i −0.747076 1.63587i −0.771551 0.636167i \(-0.780519\pi\)
0.0244753 0.999700i \(-0.492208\pi\)
\(434\) −189.690 + 27.2734i −0.437075 + 0.0628419i
\(435\) 0 0
\(436\) −385.285 −0.883681
\(437\) 8.86909 + 356.398i 0.0202954 + 0.815557i
\(438\) 0 0
\(439\) 124.273 + 79.8656i 0.283083 + 0.181926i 0.674475 0.738298i \(-0.264370\pi\)
−0.391392 + 0.920224i \(0.628006\pi\)
\(440\) 8.58721 1.23465i 0.0195164 0.00280603i
\(441\) 0 0
\(442\) −152.578 44.8010i −0.345200 0.101360i
\(443\) −520.016 237.483i −1.17385 0.536079i −0.269554 0.962985i \(-0.586876\pi\)
−0.904296 + 0.426906i \(0.859604\pi\)
\(444\) 0 0
\(445\) 107.214 745.687i 0.240929 1.67570i
\(446\) −59.9128 204.044i −0.134334 0.457498i
\(447\) 0 0
\(448\) 70.4478 45.2741i 0.157250 0.101058i
\(449\) 41.2854 + 64.2414i 0.0919497 + 0.143077i 0.884181 0.467144i \(-0.154717\pi\)
−0.792231 + 0.610221i \(0.791081\pi\)
\(450\) 0 0
\(451\) 19.1834 5.63277i 0.0425354 0.0124895i
\(452\) −347.630 49.9816i −0.769092 0.110579i
\(453\) 0 0
\(454\) −17.1581 + 37.5710i −0.0377932 + 0.0827555i
\(455\) −246.939 + 840.998i −0.542723 + 1.84835i
\(456\) 0 0
\(457\) 56.5161 + 393.078i 0.123668 + 0.860127i 0.953345 + 0.301884i \(0.0976154\pi\)
−0.829677 + 0.558244i \(0.811475\pi\)
\(458\) −86.1710 + 134.085i −0.188146 + 0.292761i
\(459\) 0 0
\(460\) 343.477 + 91.6369i 0.746690 + 0.199211i
\(461\) 682.564i 1.48062i −0.672268 0.740308i \(-0.734680\pi\)
0.672268 0.740308i \(-0.265320\pi\)
\(462\) 0 0
\(463\) 42.7124 + 297.071i 0.0922513 + 0.641622i 0.982516 + 0.186178i \(0.0596103\pi\)
−0.890265 + 0.455444i \(0.849481\pi\)
\(464\) 153.391 70.0513i 0.330584 0.150973i
\(465\) 0 0
\(466\) 194.191 425.220i 0.416719 0.912488i
\(467\) −312.270 270.583i −0.668671 0.579407i 0.252958 0.967477i \(-0.418596\pi\)
−0.921630 + 0.388070i \(0.873142\pi\)
\(468\) 0 0
\(469\) 948.181 278.411i 2.02171 0.593627i
\(470\) 389.056 337.119i 0.827778 0.717274i
\(471\) 0 0
\(472\) −115.169 + 74.0147i −0.244002 + 0.156811i
\(473\) 5.48113 4.74943i 0.0115880 0.0100411i
\(474\) 0 0
\(475\) 76.5968 532.742i 0.161256 1.12156i
\(476\) −164.196 142.277i −0.344950 0.298901i
\(477\) 0 0
\(478\) 122.003 + 35.8233i 0.255236 + 0.0749442i
\(479\) 382.352 174.614i 0.798230 0.364539i 0.0258223 0.999667i \(-0.491780\pi\)
0.772408 + 0.635127i \(0.219052\pi\)
\(480\) 0 0
\(481\) −241.918 155.471i −0.502948 0.323225i
\(482\) 200.120i 0.415187i
\(483\) 0 0
\(484\) −241.685 −0.499349
\(485\) −593.603 + 923.665i −1.22392 + 1.90446i
\(486\) 0 0
\(487\) 222.909 + 488.103i 0.457719 + 1.00226i 0.988002 + 0.154444i \(0.0493585\pi\)
−0.530283 + 0.847821i \(0.677914\pi\)
\(488\) −54.9218 + 187.046i −0.112545 + 0.383292i
\(489\) 0 0
\(490\) −433.521 + 500.310i −0.884737 + 1.02104i
\(491\) 347.574 + 49.9736i 0.707891 + 0.101779i 0.486850 0.873485i \(-0.338146\pi\)
0.221040 + 0.975265i \(0.429055\pi\)
\(492\) 0 0
\(493\) −286.502 330.641i −0.581140 0.670671i
\(494\) −128.410 199.809i −0.259938 0.404472i
\(495\) 0 0
\(496\) −33.9103 39.1346i −0.0683676 0.0789004i
\(497\) −322.730 1099.12i −0.649355 2.21150i
\(498\) 0 0
\(499\) 123.886 142.972i 0.248268 0.286517i −0.617913 0.786246i \(-0.712022\pi\)
0.866182 + 0.499729i \(0.166567\pi\)
\(500\) −136.701 62.4291i −0.273401 0.124858i
\(501\) 0 0
\(502\) 25.0851 + 54.9286i 0.0499702 + 0.109420i
\(503\) −291.381 + 41.8942i −0.579285 + 0.0832887i −0.425728 0.904851i \(-0.639982\pi\)
−0.153557 + 0.988140i \(0.549073\pi\)
\(504\) 0 0
\(505\) −492.771 −0.975784
\(506\) 11.8730 + 5.06915i 0.0234645 + 0.0100181i
\(507\) 0 0
\(508\) −376.851 242.187i −0.741832 0.476747i
\(509\) 800.318 115.068i 1.57233 0.226067i 0.699698 0.714439i \(-0.253318\pi\)
0.872636 + 0.488372i \(0.162409\pi\)
\(510\) 0 0
\(511\) −151.843 44.5853i −0.297150 0.0872510i
\(512\) 20.5826 + 9.39977i 0.0402004 + 0.0183589i
\(513\) 0 0
\(514\) −39.9322 + 277.734i −0.0776890 + 0.540339i
\(515\) −413.462 1408.12i −0.802839 2.73422i
\(516\) 0 0
\(517\) 15.7273 10.1073i 0.0304203 0.0195499i
\(518\) −212.415 330.524i −0.410067 0.638076i
\(519\) 0 0
\(520\) −227.242 + 66.7243i −0.437004 + 0.128316i
\(521\) 177.353 + 25.4995i 0.340409 + 0.0489434i 0.310400 0.950606i \(-0.399537\pi\)
0.0300095 + 0.999550i \(0.490446\pi\)
\(522\) 0 0
\(523\) −289.038 + 632.906i −0.552655 + 1.21014i 0.402877 + 0.915254i \(0.368010\pi\)
−0.955531 + 0.294890i \(0.904717\pi\)
\(524\) −24.4691 + 83.3342i −0.0466968 + 0.159035i
\(525\) 0 0
\(526\) 72.1004 + 501.469i 0.137073 + 0.953364i
\(527\) −72.6334 + 113.020i −0.137824 + 0.214459i
\(528\) 0 0
\(529\) 365.878 + 382.066i 0.691641 + 0.722241i
\(530\) 583.626i 1.10118i
\(531\) 0 0
\(532\) −46.1821 321.203i −0.0868084 0.603765i
\(533\) −496.481 + 226.735i −0.931484 + 0.425395i
\(534\) 0 0
\(535\) −26.1327 + 57.2226i −0.0488461 + 0.106958i
\(536\) 201.800 + 174.861i 0.376493 + 0.326233i
\(537\) 0 0
\(538\) −399.722 + 117.369i −0.742977 + 0.218158i
\(539\) −18.1690 + 15.7436i −0.0337088 + 0.0292088i
\(540\) 0 0
\(541\) 884.439 568.394i 1.63482 1.05064i 0.689609 0.724182i \(-0.257782\pi\)
0.945213 0.326454i \(-0.105854\pi\)
\(542\) −378.918 + 328.334i −0.699110 + 0.605782i
\(543\) 0 0
\(544\) 8.35468 58.1081i 0.0153579 0.106816i
\(545\) 1125.13 + 974.927i 2.06445 + 1.78886i
\(546\) 0 0
\(547\) 325.715 + 95.6385i 0.595457 + 0.174842i 0.565554 0.824711i \(-0.308662\pi\)
0.0299023 + 0.999553i \(0.490480\pi\)
\(548\) −262.010 + 119.656i −0.478120 + 0.218350i
\(549\) 0 0
\(550\) −16.3960 10.5371i −0.0298110 0.0191584i
\(551\) 653.456i 1.18595i
\(552\) 0 0
\(553\) −41.5167 −0.0750755
\(554\) 141.947 220.874i 0.256222 0.398689i
\(555\) 0 0
\(556\) −126.699 277.431i −0.227875 0.498977i
\(557\) 206.082 701.853i 0.369987 1.26006i −0.538671 0.842516i \(-0.681073\pi\)
0.908658 0.417542i \(-0.137108\pi\)
\(558\) 0 0
\(559\) −129.656 + 149.631i −0.231943 + 0.267677i
\(560\) −320.287 46.0502i −0.571940 0.0822326i
\(561\) 0 0
\(562\) 187.543 + 216.436i 0.333706 + 0.385117i
\(563\) −300.394 467.422i −0.533560 0.830235i 0.464920 0.885353i \(-0.346083\pi\)
−0.998480 + 0.0551177i \(0.982447\pi\)
\(564\) 0 0
\(565\) 888.690 + 1025.60i 1.57290 + 1.81523i
\(566\) 3.49001 + 11.8859i 0.00616610 + 0.0209998i
\(567\) 0 0
\(568\) 202.696 233.924i 0.356859 0.411837i
\(569\) −666.120 304.207i −1.17069 0.534634i −0.267363 0.963596i \(-0.586152\pi\)
−0.903323 + 0.428962i \(0.858879\pi\)
\(570\) 0 0
\(571\) −107.957 236.393i −0.189067 0.413998i 0.791233 0.611515i \(-0.209440\pi\)
−0.980300 + 0.197517i \(0.936712\pi\)
\(572\) −8.51328 + 1.22402i −0.0148834 + 0.00213990i
\(573\) 0 0
\(574\) −745.713 −1.29915
\(575\) −448.353 660.901i −0.779744 1.14939i
\(576\) 0 0
\(577\) −214.902 138.109i −0.372447 0.239357i 0.341004 0.940062i \(-0.389233\pi\)
−0.713452 + 0.700704i \(0.752869\pi\)
\(578\) 253.789 36.4894i 0.439082 0.0631305i
\(579\) 0 0
\(580\) −625.197 183.574i −1.07793 0.316508i
\(581\) −1010.58 461.516i −1.73938 0.794347i
\(582\) 0 0
\(583\) 3.01632 20.9790i 0.00517379 0.0359845i
\(584\) −12.0472 41.0289i −0.0206287 0.0702550i
\(585\) 0 0
\(586\) −66.0945 + 42.4764i −0.112789 + 0.0724853i
\(587\) 192.947 + 300.231i 0.328699 + 0.511466i 0.965791 0.259322i \(-0.0834990\pi\)
−0.637091 + 0.770788i \(0.719863\pi\)
\(588\) 0 0
\(589\) −192.534 + 56.5330i −0.326882 + 0.0959814i
\(590\) 523.609 + 75.2836i 0.887473 + 0.127599i
\(591\) 0 0
\(592\) 44.1014 96.5685i 0.0744955 0.163122i
\(593\) 8.41659 28.6643i 0.0141932 0.0483377i −0.952092 0.305812i \(-0.901072\pi\)
0.966285 + 0.257474i \(0.0828903\pi\)
\(594\) 0 0
\(595\) 119.475 + 830.966i 0.200798 + 1.39658i
\(596\) 145.184 225.911i 0.243598 0.379045i
\(597\) 0 0
\(598\) −340.520 90.8480i −0.569432 0.151920i
\(599\) 408.464i 0.681910i −0.940080 0.340955i \(-0.889250\pi\)
0.940080 0.340955i \(-0.110750\pi\)
\(600\) 0 0
\(601\) 105.635 + 734.708i 0.175765 + 1.22248i 0.866429 + 0.499300i \(0.166409\pi\)
−0.690664 + 0.723176i \(0.742682\pi\)
\(602\) −246.062 + 112.373i −0.408741 + 0.186666i
\(603\) 0 0
\(604\) −48.9400 + 107.164i −0.0810264 + 0.177423i
\(605\) 705.779 + 611.561i 1.16658 + 1.01084i
\(606\) 0 0
\(607\) 89.8448 26.3808i 0.148014 0.0434610i −0.206886 0.978365i \(-0.566333\pi\)
0.354900 + 0.934904i \(0.384515\pi\)
\(608\) 66.2667 57.4204i 0.108991 0.0944415i
\(609\) 0 0
\(610\) 633.688 407.247i 1.03883 0.667617i
\(611\) −385.706 + 334.216i −0.631271 + 0.546999i
\(612\) 0 0
\(613\) 129.544 901.001i 0.211329 1.46982i −0.557398 0.830245i \(-0.688200\pi\)
0.768727 0.639577i \(-0.220891\pi\)
\(614\) 446.339 + 386.755i 0.726937 + 0.629894i
\(615\) 0 0
\(616\) −11.2750 3.31064i −0.0183036 0.00537441i
\(617\) 190.549 87.0207i 0.308831 0.141038i −0.254970 0.966949i \(-0.582066\pi\)
0.563801 + 0.825910i \(0.309338\pi\)
\(618\) 0 0
\(619\) −442.527 284.395i −0.714906 0.459442i 0.131955 0.991256i \(-0.457874\pi\)
−0.846862 + 0.531813i \(0.821511\pi\)
\(620\) 200.089i 0.322725i
\(621\) 0 0
\(622\) 540.917 0.869641
\(623\) −551.681 + 858.433i −0.885524 + 1.37790i
\(624\) 0 0
\(625\) −119.384 261.415i −0.191014 0.418263i
\(626\) 120.726 411.154i 0.192852 0.656795i
\(627\) 0 0
\(628\) −287.171 + 331.413i −0.457278 + 0.527727i
\(629\) −272.629 39.1981i −0.433432 0.0623181i
\(630\) 0 0
\(631\) 589.269 + 680.052i 0.933865 + 1.07774i 0.996817 + 0.0797211i \(0.0254030\pi\)
−0.0629522 + 0.998017i \(0.520052\pi\)
\(632\) −6.06494 9.43723i −0.00959642 0.0149323i
\(633\) 0 0
\(634\) 104.708 + 120.840i 0.165155 + 0.190599i
\(635\) 487.664 + 1660.83i 0.767975 + 2.61548i
\(636\) 0 0
\(637\) 429.789 496.003i 0.674708 0.778655i
\(638\) −21.5245 9.82992i −0.0337375 0.0154074i
\(639\) 0 0
\(640\) −36.3210 79.5320i −0.0567516 0.124269i
\(641\) 36.0611 5.18480i 0.0562575 0.00808861i −0.114129 0.993466i \(-0.536408\pi\)
0.170386 + 0.985377i \(0.445499\pi\)
\(642\) 0 0
\(643\) −1071.17 −1.66589 −0.832945 0.553356i \(-0.813347\pi\)
−0.832945 + 0.553356i \(0.813347\pi\)
\(644\) −371.636 306.174i −0.577074 0.475425i
\(645\) 0 0
\(646\) −191.377 122.990i −0.296249 0.190387i
\(647\) 832.802 119.739i 1.28718 0.185068i 0.535463 0.844559i \(-0.320137\pi\)
0.751713 + 0.659491i \(0.229228\pi\)
\(648\) 0 0
\(649\) 18.4325 + 5.41228i 0.0284014 + 0.00833941i
\(650\) 483.983 + 221.028i 0.744589 + 0.340042i
\(651\) 0 0
\(652\) 79.0417 549.747i 0.121230 0.843170i
\(653\) 147.684 + 502.964i 0.226162 + 0.770237i 0.991893 + 0.127076i \(0.0405591\pi\)
−0.765731 + 0.643161i \(0.777623\pi\)
\(654\) 0 0
\(655\) 282.325 181.439i 0.431030 0.277006i
\(656\) −108.937 169.509i −0.166062 0.258398i
\(657\) 0 0
\(658\) −669.045 + 196.449i −1.01679 + 0.298555i
\(659\) −249.250 35.8367i −0.378224 0.0543804i −0.0494187 0.998778i \(-0.515737\pi\)
−0.328805 + 0.944398i \(0.606646\pi\)
\(660\) 0 0
\(661\) 314.017 687.602i 0.475064 1.04024i −0.508728 0.860927i \(-0.669884\pi\)
0.983791 0.179317i \(-0.0573887\pi\)
\(662\) 98.7930 336.458i 0.149234 0.508245i
\(663\) 0 0
\(664\) −42.7217 297.136i −0.0643399 0.447494i
\(665\) −677.911 + 1054.85i −1.01942 + 1.58624i
\(666\) 0 0
\(667\) −653.000 716.767i −0.979010 1.07461i
\(668\) 437.350i 0.654716i
\(669\) 0 0
\(670\) −146.837 1021.27i −0.219159 1.52429i
\(671\) 24.8833 11.3638i 0.0370838 0.0169356i
\(672\) 0 0
\(673\) −203.597 + 445.815i −0.302522 + 0.662430i −0.998449 0.0556828i \(-0.982266\pi\)
0.695927 + 0.718113i \(0.254994\pi\)
\(674\) 626.979 + 543.280i 0.930235 + 0.806054i
\(675\) 0 0
\(676\) −99.0227 + 29.0757i −0.146483 + 0.0430114i
\(677\) 177.566 153.861i 0.262283 0.227269i −0.513785 0.857919i \(-0.671757\pi\)
0.776068 + 0.630650i \(0.217212\pi\)
\(678\) 0 0
\(679\) 1251.11 804.037i 1.84257 1.18415i
\(680\) −171.435 + 148.549i −0.252110 + 0.218454i
\(681\) 0 0
\(682\) −1.03411 + 7.19240i −0.00151629 + 0.0105460i
\(683\) 548.881 + 475.608i 0.803632 + 0.696352i 0.956448 0.291903i \(-0.0942885\pi\)
−0.152815 + 0.988255i \(0.548834\pi\)
\(684\) 0 0
\(685\) 1067.91 + 313.567i 1.55899 + 0.457762i
\(686\) 155.832 71.1662i 0.227161 0.103741i
\(687\) 0 0
\(688\) −61.4894 39.5168i −0.0893741 0.0574372i
\(689\) 578.601i 0.839770i
\(690\) 0 0
\(691\) −508.308 −0.735612 −0.367806 0.929903i \(-0.619891\pi\)
−0.367806 + 0.929903i \(0.619891\pi\)
\(692\) 296.712 461.693i 0.428774 0.667186i
\(693\) 0 0
\(694\) 9.06388 + 19.8471i 0.0130604 + 0.0285982i
\(695\) −332.023 + 1130.77i −0.477730 + 1.62700i
\(696\) 0 0
\(697\) −342.341 + 395.083i −0.491164 + 0.566834i
\(698\) −181.068 26.0337i −0.259410 0.0372975i
\(699\) 0 0
\(700\) 476.045 + 549.385i 0.680064 + 0.784836i
\(701\) 133.697 + 208.037i 0.190724 + 0.296772i 0.923425 0.383778i \(-0.125377\pi\)
−0.732702 + 0.680550i \(0.761741\pi\)
\(702\) 0 0
\(703\) −269.402 310.907i −0.383218 0.442257i
\(704\) −0.894553 3.04657i −0.00127067 0.00432751i
\(705\) 0 0
\(706\) 27.3010 31.5070i 0.0386699 0.0446274i
\(707\) 607.142 + 277.272i 0.858758 + 0.392182i
\(708\) 0 0
\(709\) 309.539 + 677.795i 0.436585 + 0.955987i 0.992213 + 0.124556i \(0.0397506\pi\)
−0.555628 + 0.831431i \(0.687522\pi\)
\(710\) −1183.84 + 170.211i −1.66738 + 0.239734i
\(711\) 0 0
\(712\) −275.723 −0.387252
\(713\) −154.694 + 254.410i −0.216962 + 0.356816i
\(714\) 0 0
\(715\) 27.9581 + 17.9676i 0.0391023 + 0.0251295i
\(716\) 481.954 69.2945i 0.673120 0.0967800i
\(717\) 0 0
\(718\) 428.462 + 125.808i 0.596743 + 0.175220i
\(719\) 737.674 + 336.884i 1.02597 + 0.468546i 0.856040 0.516910i \(-0.172918\pi\)
0.169932 + 0.985456i \(0.445645\pi\)
\(720\) 0 0
\(721\) −282.897 + 1967.59i −0.392368 + 2.72898i
\(722\) 48.1057 + 163.833i 0.0666285 + 0.226916i
\(723\) 0 0
\(724\) 309.804 199.099i 0.427906 0.274998i
\(725\) 791.409 + 1231.46i 1.09160 + 1.69856i
\(726\) 0 0
\(727\) 175.447 51.5160i 0.241331 0.0708610i −0.158831 0.987306i \(-0.550772\pi\)
0.400161 + 0.916445i \(0.368954\pi\)
\(728\) 317.529 + 45.6538i 0.436167 + 0.0627113i
\(729\) 0 0
\(730\) −68.6391 + 150.299i −0.0940262 + 0.205889i
\(731\) −53.4263 + 181.953i −0.0730866 + 0.248910i
\(732\) 0 0
\(733\) 31.3162 + 217.809i 0.0427233 + 0.297147i 0.999969 + 0.00787097i \(0.00250543\pi\)
−0.957246 + 0.289276i \(0.906585\pi\)
\(734\) 360.711 561.277i 0.491431 0.764682i
\(735\) 0 0
\(736\) 15.3067 129.204i 0.0207971 0.175549i
\(737\) 37.4695i 0.0508405i
\(738\) 0 0
\(739\) −45.4556 316.150i −0.0615095 0.427808i −0.997187 0.0749522i \(-0.976120\pi\)
0.935678 0.352856i \(-0.114790\pi\)
\(740\) −373.144 + 170.409i −0.504249 + 0.230283i
\(741\) 0 0
\(742\) −328.395 + 719.084i −0.442581 + 0.969116i
\(743\) 237.966 + 206.199i 0.320277 + 0.277522i 0.800129 0.599828i \(-0.204764\pi\)
−0.479852 + 0.877350i \(0.659310\pi\)
\(744\) 0 0
\(745\) −995.619 + 292.340i −1.33640 + 0.392403i
\(746\) 363.914 315.333i 0.487820 0.422698i
\(747\) 0 0
\(748\) −6.93012 + 4.45371i −0.00926486 + 0.00595416i
\(749\) 64.3961 55.7995i 0.0859761 0.0744987i
\(750\) 0 0
\(751\) −36.9006 + 256.650i −0.0491353 + 0.341744i 0.950393 + 0.311050i \(0.100681\pi\)
−0.999529 + 0.0306937i \(0.990228\pi\)
\(752\) −142.392 123.383i −0.189351 0.164074i
\(753\) 0 0
\(754\) 619.815 + 181.994i 0.822035 + 0.241371i
\(755\) 414.084 189.106i 0.548455 0.250471i
\(756\) 0 0
\(757\) −804.231 516.848i −1.06239 0.682758i −0.111967 0.993712i \(-0.535715\pi\)
−0.950425 + 0.310954i \(0.899351\pi\)
\(758\) 253.917i 0.334983i
\(759\) 0 0
\(760\) −338.812 −0.445805
\(761\) 571.286 888.939i 0.750705 1.16812i −0.230108 0.973165i \(-0.573908\pi\)
0.980812 0.194954i \(-0.0624558\pi\)
\(762\) 0 0
\(763\) −837.693 1834.29i −1.09789 2.40405i
\(764\) −79.2980 + 270.064i −0.103793 + 0.353487i
\(765\) 0 0
\(766\) 0.598239 0.690404i 0.000780990 0.000901311i
\(767\) −519.101 74.6355i −0.676794 0.0973083i
\(768\) 0 0
\(769\) −790.021 911.733i −1.02734 1.18561i −0.982433 0.186617i \(-0.940248\pi\)
−0.0449032 0.998991i \(-0.514298\pi\)
\(770\) 24.5485 + 38.1982i 0.0318811 + 0.0496080i
\(771\) 0 0
\(772\) 497.165 + 573.759i 0.643997 + 0.743212i
\(773\) −274.649 935.369i −0.355303 1.21005i −0.922347 0.386363i \(-0.873731\pi\)
0.567044 0.823687i \(-0.308087\pi\)
\(774\) 0 0
\(775\) 294.368 339.718i 0.379829 0.438346i
\(776\) 365.533 + 166.933i 0.471048 + 0.215120i
\(777\) 0 0
\(778\) 61.4969 + 134.659i 0.0790449 + 0.173084i
\(779\) −772.868 + 111.122i −0.992128 + 0.142646i
\(780\) 0 0
\(781\) −43.4340 −0.0556133
\(782\) −332.823 + 56.3367i −0.425605 + 0.0720418i
\(783\) 0 0
\(784\) 203.827 + 130.992i 0.259984 + 0.167081i
\(785\) 1677.22 241.147i 2.13658 0.307194i
\(786\) 0 0
\(787\) −894.448