Properties

Label 414.3.k.b.35.6
Level $414$
Weight $3$
Character 414.35
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 35.6
Character \(\chi\) \(=\) 414.35
Dual form 414.3.k.b.71.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.764582 + 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(-0.404235 - 1.37670i) q^{5} +(-1.64257 - 1.89563i) q^{7} +(-2.79964 + 0.402527i) q^{8} +O(q^{10})\) \(q+(0.764582 + 1.18971i) q^{2} +(-0.830830 + 1.81926i) q^{4} +(-0.404235 - 1.37670i) q^{5} +(-1.64257 - 1.89563i) q^{7} +(-2.79964 + 0.402527i) q^{8} +(1.32880 - 1.53352i) q^{10} +(-5.25149 + 8.17148i) q^{11} +(-7.25236 + 8.36967i) q^{13} +(0.999372 - 3.40355i) q^{14} +(-2.61944 - 3.02300i) q^{16} +(-13.6824 + 6.24852i) q^{17} +(-5.06198 + 11.0842i) q^{19} +(2.84043 + 0.408392i) q^{20} -13.7369 q^{22} +(-10.9611 + 20.2202i) q^{23} +(19.2994 - 12.4030i) q^{25} +(-15.5025 - 2.22893i) q^{26} +(4.81335 - 1.41333i) q^{28} +(-47.2529 + 21.5797i) q^{29} +(-1.03516 - 7.19967i) q^{31} +(1.59372 - 5.42771i) q^{32} +(-17.8952 - 11.5006i) q^{34} +(-1.94572 + 3.02760i) q^{35} +(-3.01096 - 0.884098i) q^{37} +(-17.0573 + 2.45247i) q^{38} +(1.68587 + 3.69154i) q^{40} +(2.24129 + 7.63313i) q^{41} +(5.87432 - 40.8568i) q^{43} +(-10.5030 - 16.3430i) q^{44} +(-32.4368 + 2.41945i) q^{46} +2.35511i q^{47} +(6.07806 - 42.2738i) q^{49} +(29.5120 + 13.4777i) q^{50} +(-9.20116 - 20.1477i) q^{52} +(-23.7885 + 20.6128i) q^{53} +(13.3725 + 3.92652i) q^{55} +(5.36165 + 4.64589i) q^{56} +(-61.8023 - 39.7179i) q^{58} +(10.3021 + 8.92680i) q^{59} +(7.14418 + 49.6889i) q^{61} +(7.77407 - 6.73627i) q^{62} +(7.67594 - 2.25386i) q^{64} +(14.4542 + 6.60100i) q^{65} +(-12.0190 + 7.72413i) q^{67} -30.0833i q^{68} -5.08964 q^{70} +(35.7687 + 55.6572i) q^{71} +(-4.40508 + 9.64578i) q^{73} +(-1.25030 - 4.25814i) q^{74} +(-15.9594 - 18.4182i) q^{76} +(24.1160 - 3.46736i) q^{77} +(69.3272 - 80.0078i) q^{79} +(-3.10289 + 4.82818i) q^{80} +(-7.36758 + 8.50264i) q^{82} +(-14.9238 + 50.8257i) q^{83} +(14.1332 + 16.3106i) q^{85} +(53.0993 - 24.2496i) q^{86} +(11.4130 - 24.9911i) q^{88} +(-43.0814 - 6.19417i) q^{89} +27.7783 q^{91} +(-27.6790 - 36.7406i) q^{92} +(-2.80191 + 1.80068i) q^{94} +(17.3058 + 2.48820i) q^{95} +(-87.4033 + 25.6639i) q^{97} +(54.9409 - 25.0907i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q + 16 q^{4} + 16 q^{7}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(235\)
\(\chi(n)\) \(-1\) \(e\left(\frac{10}{11}\right)\)

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
\(5\) −0.404235 1.37670i −0.0808470 0.275340i 0.909142 0.416487i \(-0.136739\pi\)
−0.989989 + 0.141148i \(0.954921\pi\)
\(6\) 0 0
\(7\) −1.64257 1.89563i −0.234653 0.270804i 0.626195 0.779667i \(-0.284612\pi\)
−0.860848 + 0.508863i \(0.830066\pi\)
\(8\) −2.79964 + 0.402527i −0.349955 + 0.0503159i
\(9\) 0 0
\(10\) 1.32880 1.53352i 0.132880 0.153352i
\(11\) −5.25149 + 8.17148i −0.477409 + 0.742862i −0.993520 0.113659i \(-0.963743\pi\)
0.516111 + 0.856522i \(0.327379\pi\)
\(12\) 0 0
\(13\) −7.25236 + 8.36967i −0.557874 + 0.643821i −0.962699 0.270573i \(-0.912787\pi\)
0.404826 + 0.914394i \(0.367332\pi\)
\(14\) 0.999372 3.40355i 0.0713837 0.243111i
\(15\) 0 0
\(16\) −2.61944 3.02300i −0.163715 0.188937i
\(17\) −13.6824 + 6.24852i −0.804844 + 0.367560i −0.774973 0.631994i \(-0.782237\pi\)
−0.0298707 + 0.999554i \(0.509510\pi\)
\(18\) 0 0
\(19\) −5.06198 + 11.0842i −0.266420 + 0.583378i −0.994806 0.101789i \(-0.967543\pi\)
0.728386 + 0.685167i \(0.240271\pi\)
\(20\) 2.84043 + 0.408392i 0.142021 + 0.0204196i
\(21\) 0 0
\(22\) −13.7369 −0.624405
\(23\) −10.9611 + 20.2202i −0.476568 + 0.879138i
\(24\) 0 0
\(25\) 19.2994 12.4030i 0.771978 0.496120i
\(26\) −15.5025 2.22893i −0.596251 0.0857279i
\(27\) 0 0
\(28\) 4.81335 1.41333i 0.171905 0.0504759i
\(29\) −47.2529 + 21.5797i −1.62941 + 0.744127i −0.999471 0.0325173i \(-0.989648\pi\)
−0.629939 + 0.776644i \(0.716920\pi\)
\(30\) 0 0
\(31\) −1.03516 7.19967i −0.0333921 0.232247i 0.966290 0.257456i \(-0.0828842\pi\)
−0.999682 + 0.0252084i \(0.991975\pi\)
\(32\) 1.59372 5.42771i 0.0498038 0.169616i
\(33\) 0 0
\(34\) −17.8952 11.5006i −0.526330 0.338252i
\(35\) −1.94572 + 3.02760i −0.0555921 + 0.0865030i
\(36\) 0 0
\(37\) −3.01096 0.884098i −0.0813774 0.0238946i 0.240790 0.970577i \(-0.422593\pi\)
−0.322168 + 0.946683i \(0.604412\pi\)
\(38\) −17.0573 + 2.45247i −0.448876 + 0.0645386i
\(39\) 0 0
\(40\) 1.68587 + 3.69154i 0.0421468 + 0.0922885i
\(41\) 2.24129 + 7.63313i 0.0546656 + 0.186174i 0.982300 0.187317i \(-0.0599790\pi\)
−0.927634 + 0.373491i \(0.878161\pi\)
\(42\) 0 0
\(43\) 5.87432 40.8568i 0.136612 0.950159i −0.800052 0.599930i \(-0.795195\pi\)
0.936664 0.350228i \(-0.113896\pi\)
\(44\) −10.5030 16.3430i −0.238704 0.371431i
\(45\) 0 0
\(46\) −32.4368 + 2.41945i −0.705148 + 0.0525967i
\(47\) 2.35511i 0.0501088i 0.999686 + 0.0250544i \(0.00797590\pi\)
−0.999686 + 0.0250544i \(0.992024\pi\)
\(48\) 0 0
\(49\) 6.07806 42.2738i 0.124042 0.862731i
\(50\) 29.5120 + 13.4777i 0.590240 + 0.269554i
\(51\) 0 0
\(52\) −9.20116 20.1477i −0.176945 0.387456i
\(53\) −23.7885 + 20.6128i −0.448839 + 0.388921i −0.849742 0.527199i \(-0.823242\pi\)
0.400902 + 0.916121i \(0.368697\pi\)
\(54\) 0 0
\(55\) 13.3725 + 3.92652i 0.243136 + 0.0713913i
\(56\) 5.36165 + 4.64589i 0.0957437 + 0.0829624i
\(57\) 0 0
\(58\) −61.8023 39.7179i −1.06556 0.684792i
\(59\) 10.3021 + 8.92680i 0.174612 + 0.151302i 0.737782 0.675039i \(-0.235873\pi\)
−0.563171 + 0.826341i \(0.690419\pi\)
\(60\) 0 0
\(61\) 7.14418 + 49.6889i 0.117118 + 0.814572i 0.960703 + 0.277577i \(0.0895314\pi\)
−0.843586 + 0.536995i \(0.819560\pi\)
\(62\) 7.77407 6.73627i 0.125388 0.108650i
\(63\) 0 0
\(64\) 7.67594 2.25386i 0.119937 0.0352166i
\(65\) 14.4542 + 6.60100i 0.222372 + 0.101554i
\(66\) 0 0
\(67\) −12.0190 + 7.72413i −0.179388 + 0.115286i −0.627253 0.778816i \(-0.715821\pi\)
0.447865 + 0.894101i \(0.352184\pi\)
\(68\) 30.0833i 0.442401i
\(69\) 0 0
\(70\) −5.08964 −0.0727092
\(71\) 35.7687 + 55.6572i 0.503785 + 0.783904i 0.996259 0.0864229i \(-0.0275436\pi\)
−0.492474 + 0.870327i \(0.663907\pi\)
\(72\) 0 0
\(73\) −4.40508 + 9.64578i −0.0603436 + 0.132134i −0.937401 0.348251i \(-0.886776\pi\)
0.877058 + 0.480385i \(0.159503\pi\)
\(74\) −1.25030 4.25814i −0.0168960 0.0575425i
\(75\) 0 0
\(76\) −15.9594 18.4182i −0.209992 0.242344i
\(77\) 24.1160 3.46736i 0.313195 0.0450307i
\(78\) 0 0
\(79\) 69.3272 80.0078i 0.877559 1.01276i −0.122235 0.992501i \(-0.539006\pi\)
0.999795 0.0202564i \(-0.00644826\pi\)
\(80\) −3.10289 + 4.82818i −0.0387861 + 0.0603523i
\(81\) 0 0
\(82\) −7.36758 + 8.50264i −0.0898486 + 0.103691i
\(83\) −14.9238 + 50.8257i −0.179804 + 0.612358i 0.819428 + 0.573182i \(0.194291\pi\)
−0.999232 + 0.0391755i \(0.987527\pi\)
\(84\) 0 0
\(85\) 14.1332 + 16.3106i 0.166273 + 0.191889i
\(86\) 53.0993 24.2496i 0.617433 0.281972i
\(87\) 0 0
\(88\) 11.4130 24.9911i 0.129694 0.283989i
\(89\) −43.0814 6.19417i −0.484060 0.0695974i −0.104035 0.994574i \(-0.533176\pi\)
−0.380025 + 0.924976i \(0.624085\pi\)
\(90\) 0 0
\(91\) 27.7783 0.305256
\(92\) −27.6790 36.7406i −0.300859 0.399354i
\(93\) 0 0
\(94\) −2.80191 + 1.80068i −0.0298075 + 0.0191561i
\(95\) 17.3058 + 2.48820i 0.182166 + 0.0261916i
\(96\) 0 0
\(97\) −87.4033 + 25.6639i −0.901065 + 0.264577i −0.699275 0.714852i \(-0.746494\pi\)
−0.201790 + 0.979429i \(0.564676\pi\)
\(98\) 54.9409 25.0907i 0.560621 0.256027i
\(99\) 0 0
\(100\) 6.52977 + 45.4156i 0.0652977 + 0.454156i
\(101\) 51.3919 175.025i 0.508831 1.73292i −0.157744 0.987480i \(-0.550422\pi\)
0.666574 0.745438i \(-0.267760\pi\)
\(102\) 0 0
\(103\) 104.120 + 66.9139i 1.01087 + 0.649649i 0.937619 0.347664i \(-0.113025\pi\)
0.0732546 + 0.997313i \(0.476661\pi\)
\(104\) 16.9350 26.3513i 0.162836 0.253378i
\(105\) 0 0
\(106\) −42.7116 12.5412i −0.402939 0.118314i
\(107\) −3.58386 + 0.515281i −0.0334940 + 0.00481571i −0.159041 0.987272i \(-0.550840\pi\)
0.125547 + 0.992088i \(0.459931\pi\)
\(108\) 0 0
\(109\) 45.1666 + 98.9010i 0.414372 + 0.907349i 0.995609 + 0.0936141i \(0.0298420\pi\)
−0.581236 + 0.813735i \(0.697431\pi\)
\(110\) 5.55294 + 18.9116i 0.0504813 + 0.171923i
\(111\) 0 0
\(112\) −1.42786 + 9.93098i −0.0127487 + 0.0886695i
\(113\) 58.7412 + 91.4030i 0.519833 + 0.808876i 0.997573 0.0696249i \(-0.0221802\pi\)
−0.477740 + 0.878501i \(0.658544\pi\)
\(114\) 0 0
\(115\) 32.2679 + 6.91638i 0.280591 + 0.0601425i
\(116\) 103.895i 0.895643i
\(117\) 0 0
\(118\) −2.74355 + 19.0818i −0.0232504 + 0.161710i
\(119\) 34.3191 + 15.6730i 0.288396 + 0.131706i
\(120\) 0 0
\(121\) 11.0703 + 24.2405i 0.0914897 + 0.200335i
\(122\) −53.6532 + 46.4907i −0.439780 + 0.381071i
\(123\) 0 0
\(124\) 13.9581 + 4.09848i 0.112566 + 0.0330522i
\(125\) −51.9858 45.0459i −0.415886 0.360368i
\(126\) 0 0
\(127\) 87.9935 + 56.5500i 0.692863 + 0.445276i 0.839102 0.543973i \(-0.183081\pi\)
−0.146240 + 0.989249i \(0.546717\pi\)
\(128\) 8.55033 + 7.40890i 0.0667995 + 0.0578821i
\(129\) 0 0
\(130\) 3.19810 + 22.2433i 0.0246008 + 0.171102i
\(131\) 14.5238 12.5850i 0.110869 0.0960685i −0.597662 0.801748i \(-0.703904\pi\)
0.708531 + 0.705680i \(0.249358\pi\)
\(132\) 0 0
\(133\) 29.3262 8.61094i 0.220497 0.0647439i
\(134\) −18.3790 8.39340i −0.137157 0.0626373i
\(135\) 0 0
\(136\) 35.7904 23.0011i 0.263165 0.169126i
\(137\) 88.3939i 0.645211i −0.946534 0.322605i \(-0.895441\pi\)
0.946534 0.322605i \(-0.104559\pi\)
\(138\) 0 0
\(139\) 12.2451 0.0880946 0.0440473 0.999029i \(-0.485975\pi\)
0.0440473 + 0.999029i \(0.485975\pi\)
\(140\) −3.89145 6.05521i −0.0277960 0.0432515i
\(141\) 0 0
\(142\) −38.8680 + 85.1090i −0.273718 + 0.599359i
\(143\) −30.3069 103.216i −0.211936 0.721789i
\(144\) 0 0
\(145\) 48.8100 + 56.3297i 0.336621 + 0.388481i
\(146\) −14.8437 + 2.13421i −0.101670 + 0.0146179i
\(147\) 0 0
\(148\) 4.11001 4.74320i 0.0277703 0.0320487i
\(149\) −33.9162 + 52.7746i −0.227625 + 0.354192i −0.936214 0.351430i \(-0.885696\pi\)
0.708589 + 0.705621i \(0.249332\pi\)
\(150\) 0 0
\(151\) 51.3724 59.2869i 0.340214 0.392628i −0.559700 0.828695i \(-0.689084\pi\)
0.899914 + 0.436067i \(0.143629\pi\)
\(152\) 9.71002 33.0693i 0.0638817 0.217561i
\(153\) 0 0
\(154\) 22.5638 + 26.0401i 0.146519 + 0.169091i
\(155\) −9.49332 + 4.33546i −0.0612473 + 0.0279707i
\(156\) 0 0
\(157\) −55.2251 + 120.926i −0.351752 + 0.770229i 0.648210 + 0.761462i \(0.275518\pi\)
−0.999962 + 0.00876747i \(0.997209\pi\)
\(158\) 148.193 + 21.3069i 0.937928 + 0.134854i
\(159\) 0 0
\(160\) −8.11656 −0.0507285
\(161\) 56.3342 12.4349i 0.349902 0.0772357i
\(162\) 0 0
\(163\) −96.3602 + 61.9269i −0.591167 + 0.379920i −0.801753 0.597655i \(-0.796099\pi\)
0.210586 + 0.977575i \(0.432463\pi\)
\(164\) −15.7488 2.26434i −0.0960294 0.0138069i
\(165\) 0 0
\(166\) −71.8784 + 21.1054i −0.433002 + 0.127141i
\(167\) 224.232 102.403i 1.34271 0.613193i 0.391053 0.920368i \(-0.372111\pi\)
0.951653 + 0.307175i \(0.0993838\pi\)
\(168\) 0 0
\(169\) 6.59657 + 45.8802i 0.0390330 + 0.271480i
\(170\) −8.59892 + 29.2852i −0.0505819 + 0.172266i
\(171\) 0 0
\(172\) 69.4488 + 44.6320i 0.403772 + 0.259488i
\(173\) 19.6730 30.6118i 0.113717 0.176947i −0.779730 0.626116i \(-0.784644\pi\)
0.893447 + 0.449169i \(0.148280\pi\)
\(174\) 0 0
\(175\) −55.2122 16.2118i −0.315498 0.0926386i
\(176\) 38.4584 5.52948i 0.218513 0.0314175i
\(177\) 0 0
\(178\) −25.5700 55.9904i −0.143651 0.314553i
\(179\) 9.72077 + 33.1059i 0.0543060 + 0.184949i 0.982179 0.187946i \(-0.0601831\pi\)
−0.927873 + 0.372896i \(0.878365\pi\)
\(180\) 0 0
\(181\) −15.8069 + 109.939i −0.0873307 + 0.607399i 0.898414 + 0.439150i \(0.144720\pi\)
−0.985745 + 0.168249i \(0.946189\pi\)
\(182\) 21.2388 + 33.0482i 0.116697 + 0.181583i
\(183\) 0 0
\(184\) 22.5479 61.0213i 0.122543 0.331637i
\(185\) 4.50257i 0.0243382i
\(186\) 0 0
\(187\) 20.7931 144.619i 0.111193 0.773365i
\(188\) −4.28457 1.95670i −0.0227903 0.0104080i
\(189\) 0 0
\(190\) 10.2715 + 22.4914i 0.0540603 + 0.118376i
\(191\) −76.7088 + 66.4686i −0.401617 + 0.348003i −0.832129 0.554582i \(-0.812878\pi\)
0.430512 + 0.902585i \(0.358333\pi\)
\(192\) 0 0
\(193\) −74.4912 21.8726i −0.385965 0.113329i 0.0829930 0.996550i \(-0.473552\pi\)
−0.468958 + 0.883221i \(0.655370\pi\)
\(194\) −97.3596 84.3626i −0.501854 0.434859i
\(195\) 0 0
\(196\) 71.8574 + 46.1800i 0.366620 + 0.235612i
\(197\) 59.4230 + 51.4904i 0.301640 + 0.261372i 0.792508 0.609861i \(-0.208775\pi\)
−0.490868 + 0.871234i \(0.663320\pi\)
\(198\) 0 0
\(199\) 46.7375 + 325.067i 0.234862 + 1.63350i 0.676596 + 0.736355i \(0.263454\pi\)
−0.441734 + 0.897146i \(0.645636\pi\)
\(200\) −49.0389 + 42.4925i −0.245195 + 0.212462i
\(201\) 0 0
\(202\) 247.522 72.6791i 1.22536 0.359798i
\(203\) 118.523 + 54.1278i 0.583859 + 0.266639i
\(204\) 0 0
\(205\) 9.60252 6.17116i 0.0468415 0.0301032i
\(206\) 175.034i 0.849679i
\(207\) 0 0
\(208\) 44.2986 0.212974
\(209\) −63.9913 99.5724i −0.306179 0.476423i
\(210\) 0 0
\(211\) 161.213 353.008i 0.764044 1.67302i 0.0247011 0.999695i \(-0.492137\pi\)
0.739343 0.673329i \(-0.235136\pi\)
\(212\) −17.7360 60.4033i −0.0836604 0.284921i
\(213\) 0 0
\(214\) −3.35319 3.86979i −0.0156691 0.0180831i
\(215\) −58.6221 + 8.42859i −0.272661 + 0.0392027i
\(216\) 0 0
\(217\) −11.9476 + 13.7882i −0.0550579 + 0.0635403i
\(218\) −83.1302 + 129.353i −0.381331 + 0.593363i
\(219\) 0 0
\(220\) −18.2537 + 21.0658i −0.0829712 + 0.0957538i
\(221\) 46.9313 159.833i 0.212359 0.723227i
\(222\) 0 0
\(223\) −247.681 285.840i −1.11068 1.28179i −0.955851 0.293850i \(-0.905063\pi\)
−0.154828 0.987941i \(-0.549482\pi\)
\(224\) −12.9067 + 5.89430i −0.0576193 + 0.0263138i
\(225\) 0 0
\(226\) −63.8309 + 139.770i −0.282438 + 0.618452i
\(227\) 113.873 + 16.3725i 0.501644 + 0.0721255i 0.388492 0.921452i \(-0.372996\pi\)
0.113152 + 0.993578i \(0.463905\pi\)
\(228\) 0 0
\(229\) −268.333 −1.17176 −0.585881 0.810397i \(-0.699251\pi\)
−0.585881 + 0.810397i \(0.699251\pi\)
\(230\) 16.4429 + 43.6777i 0.0714911 + 0.189903i
\(231\) 0 0
\(232\) 123.605 79.4359i 0.532779 0.342396i
\(233\) −350.806 50.4383i −1.50560 0.216473i −0.660399 0.750915i \(-0.729613\pi\)
−0.845206 + 0.534441i \(0.820522\pi\)
\(234\) 0 0
\(235\) 3.24228 0.952019i 0.0137969 0.00405115i
\(236\) −24.7995 + 11.3255i −0.105083 + 0.0479896i
\(237\) 0 0
\(238\) 7.59338 + 52.8132i 0.0319050 + 0.221904i
\(239\) 49.0286 166.976i 0.205141 0.698645i −0.791074 0.611720i \(-0.790478\pi\)
0.996215 0.0869249i \(-0.0277040\pi\)
\(240\) 0 0
\(241\) −389.353 250.222i −1.61557 1.03826i −0.958763 0.284208i \(-0.908269\pi\)
−0.656809 0.754057i \(-0.728094\pi\)
\(242\) −20.3751 + 31.7042i −0.0841945 + 0.131009i
\(243\) 0 0
\(244\) −96.3328 28.2859i −0.394807 0.115926i
\(245\) −60.6553 + 8.72091i −0.247573 + 0.0355956i
\(246\) 0 0
\(247\) −56.0597 122.754i −0.226962 0.496978i
\(248\) 5.79612 + 19.7398i 0.0233715 + 0.0795959i
\(249\) 0 0
\(250\) 13.8443 96.2894i 0.0553773 0.385158i
\(251\) 43.7765 + 68.1175i 0.174408 + 0.271385i 0.917442 0.397869i \(-0.130250\pi\)
−0.743034 + 0.669254i \(0.766614\pi\)
\(252\) 0 0
\(253\) −107.667 195.754i −0.425560 0.773732i
\(254\) 147.924i 0.582378i
\(255\) 0 0
\(256\) −2.27704 + 15.8371i −0.00889468 + 0.0618638i
\(257\) 6.40347 + 2.92436i 0.0249162 + 0.0113789i 0.427834 0.903857i \(-0.359277\pi\)
−0.402918 + 0.915236i \(0.632004\pi\)
\(258\) 0 0
\(259\) 3.26980 + 7.15986i 0.0126247 + 0.0276442i
\(260\) −24.0179 + 20.8116i −0.0923766 + 0.0800448i
\(261\) 0 0
\(262\) 26.0772 + 7.65694i 0.0995311 + 0.0292250i
\(263\) 214.095 + 185.514i 0.814050 + 0.705378i 0.958798 0.284090i \(-0.0916916\pi\)
−0.144748 + 0.989469i \(0.546237\pi\)
\(264\) 0 0
\(265\) 37.9938 + 24.4171i 0.143373 + 0.0921401i
\(266\) 32.6668 + 28.3059i 0.122807 + 0.106413i
\(267\) 0 0
\(268\) −4.06650 28.2831i −0.0151735 0.105534i
\(269\) −289.636 + 250.971i −1.07671 + 0.932977i −0.997955 0.0639169i \(-0.979641\pi\)
−0.0787575 + 0.996894i \(0.525095\pi\)
\(270\) 0 0
\(271\) 398.403 116.982i 1.47012 0.431666i 0.553982 0.832529i \(-0.313108\pi\)
0.916138 + 0.400862i \(0.131289\pi\)
\(272\) 54.7294 + 24.9941i 0.201211 + 0.0918900i
\(273\) 0 0
\(274\) 105.163 67.5843i 0.383808 0.246658i
\(275\) 222.839i 0.810325i
\(276\) 0 0
\(277\) −83.8924 −0.302860 −0.151430 0.988468i \(-0.548388\pi\)
−0.151430 + 0.988468i \(0.548388\pi\)
\(278\) 9.36241 + 14.5682i 0.0336777 + 0.0524036i
\(279\) 0 0
\(280\) 4.22863 9.25940i 0.0151022 0.0330693i
\(281\) −128.472 437.536i −0.457196 1.55707i −0.789412 0.613864i \(-0.789614\pi\)
0.332216 0.943203i \(-0.392204\pi\)
\(282\) 0 0
\(283\) −199.164 229.848i −0.703760 0.812183i 0.285495 0.958380i \(-0.407842\pi\)
−0.989255 + 0.146197i \(0.953297\pi\)
\(284\) −130.973 + 18.8311i −0.461172 + 0.0663065i
\(285\) 0 0
\(286\) 99.6250 114.973i 0.348339 0.402005i
\(287\) 10.7881 16.7866i 0.0375892 0.0584900i
\(288\) 0 0
\(289\) −41.0920 + 47.4227i −0.142187 + 0.164093i
\(290\) −29.6969 + 101.139i −0.102403 + 0.348754i
\(291\) 0 0
\(292\) −13.8884 16.0280i −0.0475628 0.0548905i
\(293\) −228.771 + 104.476i −0.780790 + 0.356575i −0.765606 0.643310i \(-0.777561\pi\)
−0.0151839 + 0.999885i \(0.504833\pi\)
\(294\) 0 0
\(295\) 8.12505 17.7914i 0.0275426 0.0603098i
\(296\) 8.78548 + 1.26316i 0.0296807 + 0.00426744i
\(297\) 0 0
\(298\) −88.7182 −0.297712
\(299\) −89.7425 238.384i −0.300142 0.797272i
\(300\) 0 0
\(301\) −87.0983 + 55.9747i −0.289363 + 0.185962i
\(302\) 109.813 + 15.7887i 0.363618 + 0.0522804i
\(303\) 0 0
\(304\) 46.7670 13.7320i 0.153839 0.0451712i
\(305\) 65.5187 29.9214i 0.214815 0.0981029i
\(306\) 0 0
\(307\) 1.74531 + 12.1389i 0.00568505 + 0.0395404i 0.992467 0.122516i \(-0.0390964\pi\)
−0.986781 + 0.162057i \(0.948187\pi\)
\(308\) −13.7283 + 46.7542i −0.0445724 + 0.151799i
\(309\) 0 0
\(310\) −12.4164 7.97951i −0.0400528 0.0257404i
\(311\) −309.179 + 481.092i −0.994146 + 1.54692i −0.166215 + 0.986089i \(0.553155\pi\)
−0.827930 + 0.560831i \(0.810482\pi\)
\(312\) 0 0
\(313\) −502.012 147.404i −1.60387 0.470939i −0.647252 0.762276i \(-0.724082\pi\)
−0.956621 + 0.291337i \(0.905900\pi\)
\(314\) −186.091 + 26.7559i −0.592647 + 0.0852098i
\(315\) 0 0
\(316\) 87.9563 + 192.597i 0.278343 + 0.609485i
\(317\) 43.9426 + 149.655i 0.138620 + 0.472097i 0.999314 0.0370254i \(-0.0117883\pi\)
−0.860694 + 0.509122i \(0.829970\pi\)
\(318\) 0 0
\(319\) 71.8103 499.452i 0.225111 1.56568i
\(320\) −6.20577 9.65637i −0.0193930 0.0301762i
\(321\) 0 0
\(322\) 57.8661 + 57.5140i 0.179708 + 0.178615i
\(323\) 183.288i 0.567454i
\(324\) 0 0
\(325\) −36.1575 + 251.481i −0.111254 + 0.773788i
\(326\) −147.350 67.2927i −0.451995 0.206419i
\(327\) 0 0
\(328\) −9.34735 20.4678i −0.0284980 0.0624019i
\(329\) 4.46442 3.86844i 0.0135697 0.0117582i
\(330\) 0 0
\(331\) 29.2276 + 8.58201i 0.0883010 + 0.0259275i 0.325585 0.945513i \(-0.394439\pi\)
−0.237284 + 0.971440i \(0.576257\pi\)
\(332\) −80.0662 69.3778i −0.241163 0.208969i
\(333\) 0 0
\(334\) 293.274 + 188.476i 0.878066 + 0.564299i
\(335\) 15.4923 + 13.4242i 0.0462457 + 0.0400721i
\(336\) 0 0
\(337\) 40.4870 + 281.593i 0.120140 + 0.835589i 0.957396 + 0.288778i \(0.0932491\pi\)
−0.837256 + 0.546810i \(0.815842\pi\)
\(338\) −49.5406 + 42.9271i −0.146570 + 0.127003i
\(339\) 0 0
\(340\) −41.4156 + 12.1607i −0.121811 + 0.0357668i
\(341\) 64.2681 + 29.3502i 0.188469 + 0.0860711i
\(342\) 0 0
\(343\) −193.514 + 124.364i −0.564180 + 0.362577i
\(344\) 116.749i 0.339386i
\(345\) 0 0
\(346\) 51.4609 0.148731
\(347\) 57.1260 + 88.8897i 0.164628 + 0.256166i 0.913760 0.406255i \(-0.133165\pi\)
−0.749132 + 0.662421i \(0.769529\pi\)
\(348\) 0 0
\(349\) −111.134 + 243.350i −0.318436 + 0.697278i −0.999385 0.0350523i \(-0.988840\pi\)
0.680949 + 0.732331i \(0.261567\pi\)
\(350\) −22.9269 78.0818i −0.0655054 0.223091i
\(351\) 0 0
\(352\) 35.9830 + 41.5267i 0.102225 + 0.117973i
\(353\) 233.071 33.5106i 0.660258 0.0949308i 0.195963 0.980611i \(-0.437217\pi\)
0.464295 + 0.885680i \(0.346308\pi\)
\(354\) 0 0
\(355\) 62.1642 71.7413i 0.175110 0.202088i
\(356\) 47.0621 73.2301i 0.132197 0.205703i
\(357\) 0 0
\(358\) −31.9542 + 36.8771i −0.0892575 + 0.103009i
\(359\) −75.0765 + 255.687i −0.209127 + 0.712220i 0.786398 + 0.617720i \(0.211943\pi\)
−0.995525 + 0.0945001i \(0.969875\pi\)
\(360\) 0 0
\(361\) 139.169 + 160.610i 0.385510 + 0.444902i
\(362\) −142.882 + 65.2518i −0.394701 + 0.180254i
\(363\) 0 0
\(364\) −23.0790 + 50.5360i −0.0634040 + 0.138835i
\(365\) 15.0600 + 2.16530i 0.0412603 + 0.00593234i
\(366\) 0 0
\(367\) −290.122 −0.790523 −0.395261 0.918569i \(-0.629346\pi\)
−0.395261 + 0.918569i \(0.629346\pi\)
\(368\) 89.8374 19.8303i 0.244123 0.0538866i
\(369\) 0 0
\(370\) −5.35676 + 3.44258i −0.0144777 + 0.00930428i
\(371\) 78.1485 + 11.2361i 0.210643 + 0.0302859i
\(372\) 0 0
\(373\) −309.875 + 90.9874i −0.830763 + 0.243934i −0.669345 0.742952i \(-0.733425\pi\)
−0.161418 + 0.986886i \(0.551607\pi\)
\(374\) 187.953 85.8354i 0.502549 0.229506i
\(375\) 0 0
\(376\) −0.947997 6.59346i −0.00252127 0.0175358i
\(377\) 162.080 551.995i 0.429921 1.46418i
\(378\) 0 0
\(379\) 384.623 + 247.182i 1.01484 + 0.652196i 0.938641 0.344896i \(-0.112086\pi\)
0.0761967 + 0.997093i \(0.475722\pi\)
\(380\) −18.9049 + 29.4166i −0.0497497 + 0.0774120i
\(381\) 0 0
\(382\) −137.729 40.4408i −0.360546 0.105866i
\(383\) −472.154 + 67.8856i −1.23278 + 0.177247i −0.727742 0.685851i \(-0.759430\pi\)
−0.505037 + 0.863098i \(0.668521\pi\)
\(384\) 0 0
\(385\) −14.5221 31.7989i −0.0377197 0.0825945i
\(386\) −30.9325 105.346i −0.0801360 0.272918i
\(387\) 0 0
\(388\) 25.9278 180.332i 0.0668243 0.464773i
\(389\) −18.9893 29.5480i −0.0488157 0.0759588i 0.815988 0.578069i \(-0.196194\pi\)
−0.864804 + 0.502110i \(0.832557\pi\)
\(390\) 0 0
\(391\) 23.6271 345.150i 0.0604273 0.882736i
\(392\) 120.798i 0.308158i
\(393\) 0 0
\(394\) −15.8249 + 110.065i −0.0401648 + 0.279352i
\(395\) −138.171 63.1007i −0.349800 0.159748i
\(396\) 0 0
\(397\) 198.254 + 434.116i 0.499380 + 1.09349i 0.976670 + 0.214745i \(0.0688919\pi\)
−0.477290 + 0.878746i \(0.658381\pi\)
\(398\) −351.001 + 304.144i −0.881912 + 0.764181i
\(399\) 0 0
\(400\) −88.0480 25.8532i −0.220120 0.0646331i
\(401\) −76.4891 66.2782i −0.190746 0.165282i 0.554252 0.832349i \(-0.313004\pi\)
−0.744998 + 0.667066i \(0.767550\pi\)
\(402\) 0 0
\(403\) 67.7661 + 43.5507i 0.168154 + 0.108066i
\(404\) 275.718 + 238.911i 0.682471 + 0.591365i
\(405\) 0 0
\(406\) 26.2243 + 182.394i 0.0645918 + 0.449246i
\(407\) 23.0364 19.9612i 0.0566006 0.0490447i
\(408\) 0 0
\(409\) 245.923 72.2094i 0.601278 0.176551i 0.0330932 0.999452i \(-0.489464\pi\)
0.568184 + 0.822901i \(0.307646\pi\)
\(410\) 14.6838 + 6.70587i 0.0358142 + 0.0163558i
\(411\) 0 0
\(412\) −208.240 + 133.828i −0.505437 + 0.324825i
\(413\) 34.1918i 0.0827889i
\(414\) 0 0
\(415\) 76.0044 0.183143
\(416\) 33.8699 + 52.7026i 0.0814181 + 0.126689i
\(417\) 0 0
\(418\) 69.5359 152.262i 0.166354 0.364264i
\(419\) −28.1458 95.8559i −0.0671739 0.228773i 0.919063 0.394110i \(-0.128947\pi\)
−0.986237 + 0.165337i \(0.947129\pi\)
\(420\) 0 0
\(421\) 434.470 + 501.405i 1.03199 + 1.19099i 0.981342 + 0.192269i \(0.0615846\pi\)
0.0506524 + 0.998716i \(0.483870\pi\)
\(422\) 543.239 78.1059i 1.28730 0.185085i
\(423\) 0 0
\(424\) 58.3019 67.2840i 0.137504 0.158689i
\(425\) −186.561 + 290.295i −0.438968 + 0.683048i
\(426\) 0 0
\(427\) 82.4568 95.1602i 0.193107 0.222858i
\(428\) 2.04015 6.94810i 0.00476670 0.0162339i
\(429\) 0 0
\(430\) −54.8490 63.2991i −0.127556 0.147207i
\(431\) 493.845 225.531i 1.14581 0.523274i 0.250236 0.968185i \(-0.419492\pi\)
0.895575 + 0.444910i \(0.146764\pi\)
\(432\) 0 0
\(433\) −103.757 + 227.196i −0.239623 + 0.524701i −0.990789 0.135412i \(-0.956764\pi\)
0.751166 + 0.660113i \(0.229492\pi\)
\(434\) −25.5389 3.67194i −0.0588455 0.00846070i
\(435\) 0 0
\(436\) −217.453 −0.498745
\(437\) −168.639 223.849i −0.385903 0.512239i
\(438\) 0 0
\(439\) 369.633 237.548i 0.841988 0.541113i −0.0470786 0.998891i \(-0.514991\pi\)
0.889066 + 0.457779i \(0.151355\pi\)
\(440\) −39.0187 5.61004i −0.0886789 0.0127501i
\(441\) 0 0
\(442\) 226.038 66.3708i 0.511399 0.150160i
\(443\) 607.498 277.435i 1.37133 0.626264i 0.412684 0.910874i \(-0.364591\pi\)
0.958643 + 0.284610i \(0.0918642\pi\)
\(444\) 0 0
\(445\) 8.88751 + 61.8140i 0.0199719 + 0.138908i
\(446\) 150.694 513.217i 0.337879 1.15071i
\(447\) 0 0
\(448\) −16.8808 10.8486i −0.0376803 0.0242156i
\(449\) −197.292 + 306.993i −0.439404 + 0.683726i −0.988361 0.152124i \(-0.951389\pi\)
0.548957 + 0.835850i \(0.315025\pi\)
\(450\) 0 0
\(451\) −74.1442 21.7707i −0.164399 0.0482720i
\(452\) −215.090 + 30.9253i −0.475863 + 0.0684188i
\(453\) 0 0
\(454\) 67.5868 + 147.994i 0.148870 + 0.325979i
\(455\) −11.2290 38.2423i −0.0246790 0.0840491i
\(456\) 0 0
\(457\) 83.4698 580.545i 0.182647 1.27034i −0.667825 0.744319i \(-0.732774\pi\)
0.850472 0.526021i \(-0.176317\pi\)
\(458\) −205.163 319.240i −0.447954 0.697029i
\(459\) 0 0
\(460\) −39.3919 + 52.9575i −0.0856345 + 0.115125i
\(461\) 610.720i 1.32477i −0.749163 0.662386i \(-0.769544\pi\)
0.749163 0.662386i \(-0.230456\pi\)
\(462\) 0 0
\(463\) −32.9509 + 229.179i −0.0711683 + 0.494986i 0.922797 + 0.385287i \(0.125898\pi\)
−0.993965 + 0.109699i \(0.965011\pi\)
\(464\) 189.012 + 86.3187i 0.407353 + 0.186032i
\(465\) 0 0
\(466\) −208.213 455.922i −0.446808 0.978374i
\(467\) 24.3225 21.0755i 0.0520824 0.0451297i −0.628431 0.777866i \(-0.716302\pi\)
0.680513 + 0.732736i \(0.261757\pi\)
\(468\) 0 0
\(469\) 34.3841 + 10.0961i 0.0733137 + 0.0215268i
\(470\) 3.61162 + 3.12948i 0.00768429 + 0.00665848i
\(471\) 0 0
\(472\) −32.4354 20.8450i −0.0687190 0.0441630i
\(473\) 303.012 + 262.561i 0.640617 + 0.555098i
\(474\) 0 0
\(475\) 39.7838 + 276.702i 0.0837554 + 0.582531i
\(476\) −57.0267 + 49.4139i −0.119804 + 0.103811i
\(477\) 0 0
\(478\) 236.140 69.3370i 0.494017 0.145056i
\(479\) 665.264 + 303.816i 1.38886 + 0.634272i 0.962748 0.270399i \(-0.0871555\pi\)
0.426113 + 0.904670i \(0.359883\pi\)
\(480\) 0 0
\(481\) 29.2362 18.7890i 0.0607821 0.0390623i
\(482\) 654.533i 1.35795i
\(483\) 0 0
\(484\) −53.2973 −0.110118
\(485\) 70.6630 + 109.954i 0.145697 + 0.226709i
\(486\) 0 0
\(487\) −211.625 + 463.394i −0.434548 + 0.951528i 0.558019 + 0.829828i \(0.311562\pi\)
−0.992567 + 0.121699i \(0.961166\pi\)
\(488\) −40.0022 136.235i −0.0819718 0.279170i
\(489\) 0 0
\(490\) −56.7513 65.4945i −0.115819 0.133662i
\(491\) 413.779 59.4924i 0.842726 0.121166i 0.292587 0.956239i \(-0.405484\pi\)
0.550139 + 0.835073i \(0.314575\pi\)
\(492\) 0 0
\(493\) 511.690 590.522i 1.03791 1.19781i
\(494\) 103.179 160.550i 0.208865 0.325000i
\(495\) 0 0
\(496\) −19.0531 + 21.9884i −0.0384134 + 0.0443314i
\(497\) 46.7527 159.225i 0.0940698 0.320372i
\(498\) 0 0
\(499\) 373.325 + 430.840i 0.748147 + 0.863407i 0.994387 0.105801i \(-0.0337408\pi\)
−0.246240 + 0.969209i \(0.579195\pi\)
\(500\) 125.142 57.1504i 0.250284 0.114301i
\(501\) 0 0
\(502\) −47.5696 + 104.163i −0.0947601 + 0.207496i
\(503\) 155.746 + 22.3929i 0.309635 + 0.0445188i 0.295381 0.955380i \(-0.404554\pi\)
0.0142541 + 0.999898i \(0.495463\pi\)
\(504\) 0 0
\(505\) −261.731 −0.518279
\(506\) 150.571 277.763i 0.297572 0.548938i
\(507\) 0 0
\(508\) −175.987 + 113.100i −0.346431 + 0.222638i
\(509\) −677.996 97.4811i −1.33202 0.191515i −0.560727 0.828001i \(-0.689478\pi\)
−0.771288 + 0.636486i \(0.780387\pi\)
\(510\) 0 0
\(511\) 25.5205 7.49349i 0.0499422 0.0146644i
\(512\) −20.5826 + 9.39977i −0.0402004 + 0.0183589i
\(513\) 0 0
\(514\) 1.41682 + 9.85420i 0.00275646 + 0.0191716i
\(515\) 50.0312 170.391i 0.0971480 0.330856i
\(516\) 0 0
\(517\) −19.2448 12.3679i −0.0372239 0.0239224i
\(518\) −6.01815 + 9.36442i −0.0116180 + 0.0180780i
\(519\) 0 0
\(520\) −43.1235 12.6622i −0.0829298 0.0243504i
\(521\) 561.406 80.7179i 1.07755 0.154929i 0.419392 0.907805i \(-0.362243\pi\)
0.658162 + 0.752876i \(0.271334\pi\)
\(522\) 0 0
\(523\) −75.0532 164.344i −0.143505 0.314232i 0.824208 0.566288i \(-0.191621\pi\)
−0.967713 + 0.252055i \(0.918894\pi\)
\(524\) 10.8286 + 36.8787i 0.0206652 + 0.0703791i
\(525\) 0 0
\(526\) −57.0156 + 396.553i −0.108395 + 0.753902i
\(527\) 59.1506 + 92.0402i 0.112240 + 0.174649i
\(528\) 0 0
\(529\) −288.710 443.269i −0.545766 0.837938i
\(530\) 63.8706i 0.120510i
\(531\) 0 0
\(532\) −8.69949 + 60.5063i −0.0163524 + 0.113734i
\(533\) −80.1414 36.5994i −0.150359 0.0686667i
\(534\) 0 0
\(535\) 2.15811 + 4.72560i 0.00403385 + 0.00883289i
\(536\) 30.5396 26.4627i 0.0569769 0.0493708i
\(537\) 0 0
\(538\) −520.033 152.696i −0.966604 0.283821i
\(539\) 313.521 + 271.668i 0.581672 + 0.504022i
\(540\) 0 0
\(541\) 618.419 + 397.434i 1.14310 + 0.734628i 0.968254 0.249968i \(-0.0804200\pi\)
0.174849 + 0.984595i \(0.444056\pi\)
\(542\) 443.786 + 384.542i 0.818793 + 0.709488i
\(543\) 0 0
\(544\) 12.1093 + 84.2223i 0.0222598 + 0.154820i
\(545\) 117.899 102.160i 0.216328 0.187450i
\(546\) 0 0
\(547\) 1016.01 298.328i 1.85742 0.545389i 0.857923 0.513779i \(-0.171755\pi\)
0.999500 0.0316100i \(-0.0100635\pi\)
\(548\) 160.812 + 73.4403i 0.293452 + 0.134015i
\(549\) 0 0
\(550\) −265.115 + 170.379i −0.482027 + 0.309780i
\(551\) 632.996i 1.14881i
\(552\) 0 0
\(553\) −265.540 −0.480181
\(554\) −64.1425 99.8077i −0.115781 0.180158i
\(555\) 0 0
\(556\) −10.1736 + 22.2771i −0.0182979 + 0.0400668i
\(557\) 26.6197 + 90.6583i 0.0477912 + 0.162762i 0.979931 0.199336i \(-0.0638787\pi\)
−0.932140 + 0.362098i \(0.882060\pi\)
\(558\) 0 0
\(559\) 299.355 + 345.474i 0.535519 + 0.618022i
\(560\) 14.2492 2.04872i 0.0254449 0.00365843i
\(561\) 0 0
\(562\) 422.314 487.377i 0.751449 0.867218i
\(563\) −575.322 + 895.219i −1.02189 + 1.59009i −0.235963 + 0.971762i \(0.575824\pi\)
−0.785923 + 0.618324i \(0.787812\pi\)
\(564\) 0 0
\(565\) 102.089 117.817i 0.180689 0.208526i
\(566\) 121.175 412.685i 0.214091 0.729126i
\(567\) 0 0
\(568\) −122.543 141.422i −0.215745 0.248983i
\(569\) −79.9703 + 36.5212i −0.140545 + 0.0641849i −0.484446 0.874821i \(-0.660979\pi\)
0.343901 + 0.939006i \(0.388252\pi\)
\(570\) 0 0
\(571\) −142.751 + 312.582i −0.250002 + 0.547429i −0.992475 0.122448i \(-0.960926\pi\)
0.742473 + 0.669876i \(0.233653\pi\)
\(572\) 212.957 + 30.6185i 0.372302 + 0.0535289i
\(573\) 0 0
\(574\) 28.2196 0.0491631
\(575\) 39.2482 + 526.188i 0.0682577 + 0.915110i
\(576\) 0 0
\(577\) 88.4919 56.8703i 0.153365 0.0985620i −0.461707 0.887032i \(-0.652763\pi\)
0.615073 + 0.788470i \(0.289127\pi\)
\(578\) −87.8376 12.6291i −0.151968 0.0218497i
\(579\) 0 0
\(580\) −143.031 + 41.9978i −0.246606 + 0.0724101i
\(581\) 120.860 55.1949i 0.208021 0.0949998i
\(582\) 0 0
\(583\) −43.5124 302.635i −0.0746353 0.519100i
\(584\) 8.44994 28.7779i 0.0144691 0.0492772i
\(585\) 0 0
\(586\) −299.211 192.291i −0.510599 0.328142i
\(587\) 70.3514 109.469i 0.119849 0.186489i −0.776145 0.630554i \(-0.782828\pi\)
0.895994 + 0.444065i \(0.146464\pi\)
\(588\) 0 0
\(589\) 85.0424 + 24.9707i 0.144384 + 0.0423951i
\(590\) 27.3789 3.93649i 0.0464049 0.00667202i
\(591\) 0 0
\(592\) 5.21442 + 11.4180i 0.00880814 + 0.0192871i
\(593\) 242.666 + 826.444i 0.409217 + 1.39367i 0.864192 + 0.503162i \(0.167830\pi\)
−0.454974 + 0.890504i \(0.650352\pi\)
\(594\) 0 0
\(595\) 7.70402 53.5826i 0.0129479 0.0900548i
\(596\) −67.8323 105.549i −0.113813 0.177096i
\(597\) 0 0
\(598\) 214.993 289.032i 0.359521 0.483331i
\(599\) 125.083i 0.208819i −0.994534 0.104410i \(-0.966705\pi\)
0.994534 0.104410i \(-0.0332953\pi\)
\(600\) 0 0
\(601\) −45.7290 + 318.052i −0.0760882 + 0.529205i 0.915755 + 0.401738i \(0.131594\pi\)
−0.991843 + 0.127467i \(0.959315\pi\)
\(602\) −133.188 60.8247i −0.221242 0.101038i
\(603\) 0 0
\(604\) 65.1768 + 142.717i 0.107909 + 0.236287i
\(605\) 28.8968 25.0393i 0.0477634 0.0413872i
\(606\) 0 0
\(607\) 133.483 + 39.1940i 0.219905 + 0.0645701i 0.389829 0.920887i \(-0.372534\pi\)
−0.169924 + 0.985457i \(0.554352\pi\)
\(608\) 52.0944 + 45.1401i 0.0856816 + 0.0742435i
\(609\) 0 0
\(610\) 85.6922 + 55.0710i 0.140479 + 0.0902804i
\(611\) −19.7115 17.0801i −0.0322611 0.0279544i
\(612\) 0 0
\(613\) 106.715 + 742.217i 0.174086 + 1.21079i 0.870140 + 0.492805i \(0.164028\pi\)
−0.696054 + 0.717989i \(0.745063\pi\)
\(614\) −13.1074 + 11.3576i −0.0213475 + 0.0184977i
\(615\) 0 0
\(616\) −66.1205 + 19.4147i −0.107338 + 0.0315174i
\(617\) −344.135 157.161i −0.557755 0.254718i 0.116533 0.993187i \(-0.462822\pi\)
−0.674288 + 0.738469i \(0.735549\pi\)
\(618\) 0 0
\(619\) −938.274 + 602.992i −1.51579 + 0.974139i −0.523255 + 0.852176i \(0.675283\pi\)
−0.992535 + 0.121963i \(0.961081\pi\)
\(620\) 20.8729i 0.0336660i
\(621\) 0 0
\(622\) −808.754 −1.30025
\(623\) 59.0224 + 91.8406i 0.0947390 + 0.147417i
\(624\) 0 0
\(625\) 197.254 431.926i 0.315606 0.691081i
\(626\) −208.461 709.952i −0.333005 1.13411i
\(627\) 0 0
\(628\) −174.114 200.938i −0.277251 0.319965i
\(629\) 46.7214 6.71752i 0.0742788 0.0106797i
\(630\) 0 0
\(631\) 274.418 316.696i 0.434894 0.501895i −0.495422 0.868652i \(-0.664987\pi\)
0.930317 + 0.366758i \(0.119532\pi\)
\(632\) −161.886 + 251.899i −0.256148 + 0.398574i
\(633\) 0 0
\(634\) −144.448 + 166.702i −0.227837 + 0.262937i
\(635\) 42.2822 144.000i 0.0665862 0.226772i
\(636\) 0 0
\(637\) 309.738 + 357.456i 0.486244 + 0.561156i
\(638\) 649.109 296.438i 1.01741 0.464637i
\(639\) 0 0
\(640\) 6.74348 14.7662i 0.0105367 0.0230721i
\(641\) 565.007 + 81.2358i 0.881447 + 0.126733i 0.568153 0.822923i \(-0.307658\pi\)
0.313294 + 0.949656i \(0.398567\pi\)
\(642\) 0 0
\(643\) −367.731 −0.571899 −0.285950 0.958245i \(-0.592309\pi\)
−0.285950 + 0.958245i \(0.592309\pi\)
\(644\) −24.1817 + 112.818i −0.0375493 + 0.175184i
\(645\) 0 0
\(646\) 218.060 140.138i 0.337553 0.216932i
\(647\) −1099.89 158.140i −1.69998 0.244420i −0.777062 0.629424i \(-0.783291\pi\)
−0.922915 + 0.385004i \(0.874200\pi\)
\(648\) 0 0
\(649\) −127.047 + 37.3042i −0.195757 + 0.0574796i
\(650\) −326.835 + 149.261i −0.502824 + 0.229632i
\(651\) 0 0
\(652\) −32.6025 226.755i −0.0500038 0.347784i
\(653\) −1.19378 + 4.06564i −0.00182815 + 0.00622610i −0.960402 0.278618i \(-0.910124\pi\)
0.958574 + 0.284844i \(0.0919418\pi\)
\(654\) 0 0
\(655\) −23.1968 14.9076i −0.0354149 0.0227598i
\(656\) 17.2040 26.7700i 0.0262256 0.0408079i
\(657\) 0 0
\(658\) 8.01574 + 2.35363i 0.0121820 + 0.00357695i
\(659\) −948.015 + 136.304i −1.43857 + 0.206835i −0.817050 0.576567i \(-0.804392\pi\)
−0.621516 + 0.783401i \(0.713483\pi\)
\(660\) 0 0
\(661\) 21.1540 + 46.3208i 0.0320030 + 0.0700769i 0.924958 0.380068i \(-0.124100\pi\)
−0.892955 + 0.450145i \(0.851372\pi\)
\(662\) 12.1368 + 41.3341i 0.0183335 + 0.0624383i
\(663\) 0 0
\(664\) 21.3224 148.301i 0.0321121 0.223345i
\(665\) −23.7093 36.8924i −0.0356531 0.0554773i
\(666\) 0 0
\(667\) 81.5977 1192.00i 0.122335 1.78710i
\(668\) 493.017i 0.738049i
\(669\) 0 0
\(670\) −4.12575 + 28.6952i −0.00615784 + 0.0428287i
\(671\) −443.549 202.562i −0.661028 0.301881i
\(672\) 0 0
\(673\) −289.728 634.416i −0.430502 0.942669i −0.993245 0.116036i \(-0.962981\pi\)
0.562743 0.826632i \(-0.309746\pi\)
\(674\) −304.059 + 263.469i −0.451127 + 0.390904i
\(675\) 0 0
\(676\) −88.9488 26.1177i −0.131581 0.0386357i
\(677\) −256.763 222.486i −0.379266 0.328636i 0.444277 0.895889i \(-0.353461\pi\)
−0.823543 + 0.567254i \(0.808006\pi\)
\(678\) 0 0
\(679\) 192.215 + 123.529i 0.283086 + 0.181928i
\(680\) −46.1333 39.9748i −0.0678431 0.0587864i
\(681\) 0 0
\(682\) 14.2198 + 98.9012i 0.0208502 + 0.145016i
\(683\) −680.355 + 589.531i −0.996127 + 0.863149i −0.990594 0.136835i \(-0.956307\pi\)
−0.00553364 + 0.999985i \(0.501761\pi\)
\(684\) 0 0
\(685\) −121.692 + 35.7319i −0.177652 + 0.0521634i
\(686\) −295.914 135.139i −0.431362 0.196996i
\(687\) 0 0
\(688\) −138.898 + 89.2640i −0.201886 + 0.129744i
\(689\) 348.593i 0.505941i
\(690\) 0 0
\(691\) 926.610 1.34097 0.670485 0.741923i \(-0.266086\pi\)
0.670485 + 0.741923i \(0.266086\pi\)
\(692\) 39.3460 + 61.2236i 0.0568584 + 0.0884734i
\(693\) 0 0
\(694\) −62.0757 + 135.927i −0.0894463 + 0.195860i
\(695\) −4.94992 16.8579i −0.00712218 0.0242559i
\(696\) 0 0
\(697\) −78.3619 90.4345i −0.112427 0.129748i
\(698\) −374.488 + 53.8432i −0.536516 + 0.0771393i
\(699\) 0 0
\(700\) 75.3654 86.9763i 0.107665 0.124252i
\(701\) −253.709 + 394.779i −0.361924 + 0.563165i −0.973691 0.227873i \(-0.926823\pi\)
0.611767 + 0.791038i \(0.290459\pi\)
\(702\) 0 0
\(703\) 25.0409 28.8988i 0.0356201 0.0411078i
\(704\) −21.8928 + 74.5600i −0.0310977 + 0.105909i
\(705\) 0 0
\(706\) 218.070 + 251.666i 0.308881 + 0.356467i
\(707\) −416.197 + 190.071i −0.588680 + 0.268841i
\(708\) 0 0
\(709\) −528.022 + 1156.21i −0.744742 + 1.63076i 0.0308519 + 0.999524i \(0.490178\pi\)
−0.775593 + 0.631233i \(0.782549\pi\)
\(710\) 132.881 + 19.1054i 0.187157 + 0.0269091i
\(711\) 0 0
\(712\) 123.106 0.172901
\(713\) 156.925 + 57.9850i 0.220091 + 0.0813254i
\(714\) 0 0
\(715\) −129.846 + 83.4469i −0.181603 + 0.116709i
\(716\) −68.3047 9.82073i −0.0953976 0.0137161i
\(717\) 0 0
\(718\) −361.596 + 106.174i −0.503616 + 0.147875i
\(719\) 466.434 213.013i 0.648726 0.296263i −0.0637434 0.997966i \(-0.520304\pi\)
0.712470 + 0.701703i \(0.247577\pi\)
\(720\) 0 0
\(721\) −44.1807 307.284i −0.0612770 0.426191i
\(722\) −84.6732 + 288.370i −0.117276 + 0.399405i
\(723\) 0 0
\(724\) −186.876 120.098i −0.258115 0.165881i
\(725\) −644.302 + 1002.55i −0.888693 + 1.38283i
\(726\) 0 0
\(727\) −733.776 215.456i −1.00932 0.296363i −0.265045 0.964236i \(-0.585387\pi\)
−0.744275 + 0.667873i \(0.767205\pi\)
\(728\) −77.7692 + 11.1815i −0.106826 + 0.0153592i
\(729\) 0 0
\(730\) 8.93853 + 19.5726i 0.0122446 + 0.0268118i
\(731\) 174.920 + 595.723i 0.239289 + 0.814943i
\(732\) 0 0
\(733\) 154.457 1074.27i 0.210719 1.46558i −0.560044 0.828463i \(-0.689216\pi\)
0.770763 0.637122i \(-0.219875\pi\)
\(734\) −221.822 345.162i −0.302210 0.470247i
\(735\) 0 0
\(736\) 92.2803 + 91.7188i 0.125381 + 0.124618i
\(737\) 138.776i 0.188299i
\(738\) 0 0
\(739\) −57.6373 + 400.876i −0.0779937 + 0.542458i 0.912939 + 0.408097i \(0.133807\pi\)
−0.990932 + 0.134361i \(0.957102\pi\)
\(740\) −8.19137 3.74087i −0.0110694 0.00505523i
\(741\) 0 0
\(742\) 46.3832 + 101.565i 0.0625111 + 0.136880i
\(743\) −92.3311 + 80.0054i −0.124268 + 0.107679i −0.714778 0.699352i \(-0.753472\pi\)
0.590510 + 0.807030i \(0.298927\pi\)
\(744\) 0 0
\(745\) 86.3648 + 25.3590i 0.115926 + 0.0340389i
\(746\) −345.173 299.094i −0.462699 0.400931i
\(747\) 0 0
\(748\) 245.825 + 157.982i 0.328643 + 0.211206i
\(749\) 6.86353 + 5.94728i 0.00916359 + 0.00794029i
\(750\) 0 0
\(751\) 172.294 + 1198.33i 0.229419 + 1.59564i 0.700565 + 0.713588i \(0.252931\pi\)
−0.471147 + 0.882055i \(0.656160\pi\)
\(752\) 7.11950 6.16908i 0.00946742 0.00820357i
\(753\) 0 0
\(754\) 780.638 229.216i 1.03533 0.304000i
\(755\) −102.387 46.7584i −0.135611 0.0619317i
\(756\) 0 0
\(757\) −28.5282 + 18.3339i −0.0376858 + 0.0242192i −0.559348 0.828933i \(-0.688948\pi\)
0.521662 + 0.853152i \(0.325312\pi\)
\(758\) 646.582i 0.853011i
\(759\) 0 0
\(760\) −49.4516 −0.0650679
\(761\) 133.040 + 207.014i 0.174822 + 0.272028i 0.917596 0.397514i \(-0.130127\pi\)
−0.742774 + 0.669542i \(0.766490\pi\)
\(762\) 0 0
\(763\) 113.290 248.071i 0.148480 0.325126i
\(764\) −57.1919 194.778i −0.0748585 0.254945i
\(765\) 0 0
\(766\) −441.765 509.824i −0.576716 0.665566i
\(767\) −149.429 + 21.4846i −0.194822 + 0.0280112i
\(768\) 0 0
\(769\) 386.110 445.595i 0.502094 0.579447i −0.446963 0.894553i \(-0.647494\pi\)
0.949057 + 0.315105i \(0.102040\pi\)
\(770\) 26.7282 41.5899i 0.0347120 0.0540129i
\(771\) 0 0
\(772\) 101.681 117.347i 0.131712 0.152003i
\(773\) −196.734 + 670.014i −0.254507 + 0.866771i 0.728786 + 0.684741i \(0.240085\pi\)
−0.983293 + 0.182029i \(0.941733\pi\)
\(774\) 0 0
\(775\) −109.275 126.111i −0.141001 0.162723i
\(776\) 234.367 107.032i 0.302020 0.137928i
\(777\) 0 0
\(778\) 20.6347 45.1836i 0.0265227 0.0580767i
\(779\) −95.9525 13.7959i −0.123174 0.0177097i
\(780\) 0 0
\(781\) −642.641 −0.822844
\(782\) 428.694 235.786i 0.548202 0.301516i
\(783\) 0 0
\(784\) −143.715 + 92.3600i −0.183310 + 0.117806i
\(785\) 188.803 + 27.1457i 0.240513 + 0.0345805i
\(786\) 0 0
\(787\) −963.580