Properties

Label 230.3.f.b.93.4
Level $230$
Weight $3$
Character 230.93
Analytic conductor $6.267$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 93.4
Character \(\chi\) \(=\) 230.93
Dual form 230.3.f.b.47.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(-1.36040 - 1.36040i) q^{3} -2.00000i q^{4} +(-3.17264 + 3.86450i) q^{5} -2.72079 q^{6} +(7.21891 - 7.21891i) q^{7} +(-2.00000 - 2.00000i) q^{8} -5.29864i q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(-1.36040 - 1.36040i) q^{3} -2.00000i q^{4} +(-3.17264 + 3.86450i) q^{5} -2.72079 q^{6} +(7.21891 - 7.21891i) q^{7} +(-2.00000 - 2.00000i) q^{8} -5.29864i q^{9} +(0.691863 + 7.03714i) q^{10} -14.8137 q^{11} +(-2.72079 + 2.72079i) q^{12} +(-4.91350 - 4.91350i) q^{13} -14.4378i q^{14} +(9.57330 - 0.941208i) q^{15} -4.00000 q^{16} +(-17.8271 + 17.8271i) q^{17} +(-5.29864 - 5.29864i) q^{18} -29.6011i q^{19} +(7.72900 + 6.34528i) q^{20} -19.6412 q^{21} +(-14.8137 + 14.8137i) q^{22} +(-3.39116 - 3.39116i) q^{23} +5.44159i q^{24} +(-4.86874 - 24.5213i) q^{25} -9.82700 q^{26} +(-19.4518 + 19.4518i) q^{27} +(-14.4378 - 14.4378i) q^{28} +11.0158i q^{29} +(8.63209 - 10.5145i) q^{30} +42.3661 q^{31} +(-4.00000 + 4.00000i) q^{32} +(20.1526 + 20.1526i) q^{33} +35.6542i q^{34} +(4.99449 + 50.8005i) q^{35} -10.5973 q^{36} +(14.7295 - 14.7295i) q^{37} +(-29.6011 - 29.6011i) q^{38} +13.3686i q^{39} +(14.0743 - 1.38373i) q^{40} +23.9580 q^{41} +(-19.6412 + 19.6412i) q^{42} +(0.419945 + 0.419945i) q^{43} +29.6275i q^{44} +(20.4766 + 16.8107i) q^{45} -6.78233 q^{46} +(53.0162 - 53.0162i) q^{47} +(5.44159 + 5.44159i) q^{48} -55.2252i q^{49} +(-29.3901 - 19.6526i) q^{50} +48.5039 q^{51} +(-9.82700 + 9.82700i) q^{52} +(-58.3755 - 58.3755i) q^{53} +38.9036i q^{54} +(46.9987 - 57.2477i) q^{55} -28.8756 q^{56} +(-40.2692 + 40.2692i) q^{57} +(11.0158 + 11.0158i) q^{58} -13.7747i q^{59} +(-1.88242 - 19.1466i) q^{60} +39.0198 q^{61} +(42.3661 - 42.3661i) q^{62} +(-38.2504 - 38.2504i) q^{63} +8.00000i q^{64} +(34.5770 - 3.39947i) q^{65} +40.3051 q^{66} +(-16.9106 + 16.9106i) q^{67} +(35.6542 + 35.6542i) q^{68} +9.22666i q^{69} +(55.7949 + 45.8060i) q^{70} +103.112 q^{71} +(-10.5973 + 10.5973i) q^{72} +(41.5993 + 41.5993i) q^{73} -29.4590i q^{74} +(-26.7353 + 39.9821i) q^{75} -59.2022 q^{76} +(-106.939 + 106.939i) q^{77} +(13.3686 + 13.3686i) q^{78} +155.484i q^{79} +(12.6906 - 15.4580i) q^{80} +5.23660 q^{81} +(23.9580 - 23.9580i) q^{82} +(12.7160 + 12.7160i) q^{83} +39.2823i q^{84} +(-12.3339 - 125.452i) q^{85} +0.839889 q^{86} +(14.9859 - 14.9859i) q^{87} +(29.6275 + 29.6275i) q^{88} -141.715i q^{89} +(37.2873 - 3.66593i) q^{90} -70.9402 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-57.6347 - 57.6347i) q^{93} -106.032i q^{94} +(114.393 + 93.9135i) q^{95} +10.8832 q^{96} +(-29.4379 + 29.4379i) q^{97} +(-55.2252 - 55.2252i) q^{98} +78.4927i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.500000 0.500000i
\(3\) −1.36040 1.36040i −0.453466 0.453466i 0.443038 0.896503i \(-0.353901\pi\)
−0.896503 + 0.443038i \(0.853901\pi\)
\(4\) 2.00000i 0.500000i
\(5\) −3.17264 + 3.86450i −0.634528 + 0.772900i
\(6\) −2.72079 −0.453466
\(7\) 7.21891 7.21891i 1.03127 1.03127i 0.0317775 0.999495i \(-0.489883\pi\)
0.999495 0.0317775i \(-0.0101168\pi\)
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) 5.29864i 0.588738i
\(10\) 0.691863 + 7.03714i 0.0691863 + 0.703714i
\(11\) −14.8137 −1.34670 −0.673352 0.739322i \(-0.735146\pi\)
−0.673352 + 0.739322i \(0.735146\pi\)
\(12\) −2.72079 + 2.72079i −0.226733 + 0.226733i
\(13\) −4.91350 4.91350i −0.377962 0.377962i 0.492405 0.870366i \(-0.336118\pi\)
−0.870366 + 0.492405i \(0.836118\pi\)
\(14\) 14.4378i 1.03127i
\(15\) 9.57330 0.941208i 0.638220 0.0627472i
\(16\) −4.00000 −0.250000
\(17\) −17.8271 + 17.8271i −1.04865 + 1.04865i −0.0499002 + 0.998754i \(0.515890\pi\)
−0.998754 + 0.0499002i \(0.984110\pi\)
\(18\) −5.29864 5.29864i −0.294369 0.294369i
\(19\) 29.6011i 1.55795i −0.627054 0.778976i \(-0.715739\pi\)
0.627054 0.778976i \(-0.284261\pi\)
\(20\) 7.72900 + 6.34528i 0.386450 + 0.317264i
\(21\) −19.6412 −0.935293
\(22\) −14.8137 + 14.8137i −0.673352 + 0.673352i
\(23\) −3.39116 3.39116i −0.147442 0.147442i
\(24\) 5.44159i 0.226733i
\(25\) −4.86874 24.5213i −0.194749 0.980853i
\(26\) −9.82700 −0.377962
\(27\) −19.4518 + 19.4518i −0.720438 + 0.720438i
\(28\) −14.4378 14.4378i −0.515636 0.515636i
\(29\) 11.0158i 0.379856i 0.981798 + 0.189928i \(0.0608255\pi\)
−0.981798 + 0.189928i \(0.939175\pi\)
\(30\) 8.63209 10.5145i 0.287736 0.350484i
\(31\) 42.3661 1.36665 0.683325 0.730115i \(-0.260533\pi\)
0.683325 + 0.730115i \(0.260533\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) 20.1526 + 20.1526i 0.610684 + 0.610684i
\(34\) 35.6542i 1.04865i
\(35\) 4.99449 + 50.8005i 0.142700 + 1.45144i
\(36\) −10.5973 −0.294369
\(37\) 14.7295 14.7295i 0.398095 0.398095i −0.479466 0.877561i \(-0.659169\pi\)
0.877561 + 0.479466i \(0.159169\pi\)
\(38\) −29.6011 29.6011i −0.778976 0.778976i
\(39\) 13.3686i 0.342785i
\(40\) 14.0743 1.38373i 0.351857 0.0345931i
\(41\) 23.9580 0.584341 0.292171 0.956366i \(-0.405622\pi\)
0.292171 + 0.956366i \(0.405622\pi\)
\(42\) −19.6412 + 19.6412i −0.467646 + 0.467646i
\(43\) 0.419945 + 0.419945i 0.00976615 + 0.00976615i 0.711973 0.702207i \(-0.247802\pi\)
−0.702207 + 0.711973i \(0.747802\pi\)
\(44\) 29.6275i 0.673352i
\(45\) 20.4766 + 16.8107i 0.455036 + 0.373571i
\(46\) −6.78233 −0.147442
\(47\) 53.0162 53.0162i 1.12800 1.12800i 0.137502 0.990502i \(-0.456093\pi\)
0.990502 0.137502i \(-0.0439073\pi\)
\(48\) 5.44159 + 5.44159i 0.113366 + 0.113366i
\(49\) 55.2252i 1.12705i
\(50\) −29.3901 19.6526i −0.587801 0.393052i
\(51\) 48.5039 0.951057
\(52\) −9.82700 + 9.82700i −0.188981 + 0.188981i
\(53\) −58.3755 58.3755i −1.10142 1.10142i −0.994239 0.107186i \(-0.965816\pi\)
−0.107186 0.994239i \(-0.534184\pi\)
\(54\) 38.9036i 0.720438i
\(55\) 46.9987 57.2477i 0.854521 1.04087i
\(56\) −28.8756 −0.515636
\(57\) −40.2692 + 40.2692i −0.706477 + 0.706477i
\(58\) 11.0158 + 11.0158i 0.189928 + 0.189928i
\(59\) 13.7747i 0.233469i −0.993163 0.116735i \(-0.962757\pi\)
0.993163 0.116735i \(-0.0372427\pi\)
\(60\) −1.88242 19.1466i −0.0313736 0.319110i
\(61\) 39.0198 0.639670 0.319835 0.947473i \(-0.396373\pi\)
0.319835 + 0.947473i \(0.396373\pi\)
\(62\) 42.3661 42.3661i 0.683325 0.683325i
\(63\) −38.2504 38.2504i −0.607149 0.607149i
\(64\) 8.00000i 0.125000i
\(65\) 34.5770 3.39947i 0.531954 0.0522995i
\(66\) 40.3051 0.610684
\(67\) −16.9106 + 16.9106i −0.252397 + 0.252397i −0.821953 0.569556i \(-0.807115\pi\)
0.569556 + 0.821953i \(0.307115\pi\)
\(68\) 35.6542 + 35.6542i 0.524327 + 0.524327i
\(69\) 9.22666i 0.133720i
\(70\) 55.7949 + 45.8060i 0.797071 + 0.654371i
\(71\) 103.112 1.45229 0.726143 0.687544i \(-0.241311\pi\)
0.726143 + 0.687544i \(0.241311\pi\)
\(72\) −10.5973 + 10.5973i −0.147185 + 0.147185i
\(73\) 41.5993 + 41.5993i 0.569853 + 0.569853i 0.932087 0.362234i \(-0.117986\pi\)
−0.362234 + 0.932087i \(0.617986\pi\)
\(74\) 29.4590i 0.398095i
\(75\) −26.7353 + 39.9821i −0.356471 + 0.533095i
\(76\) −59.2022 −0.778976
\(77\) −106.939 + 106.939i −1.38882 + 1.38882i
\(78\) 13.3686 + 13.3686i 0.171393 + 0.171393i
\(79\) 155.484i 1.96815i 0.177757 + 0.984074i \(0.443116\pi\)
−0.177757 + 0.984074i \(0.556884\pi\)
\(80\) 12.6906 15.4580i 0.158632 0.193225i
\(81\) 5.23660 0.0646494
\(82\) 23.9580 23.9580i 0.292171 0.292171i
\(83\) 12.7160 + 12.7160i 0.153205 + 0.153205i 0.779548 0.626343i \(-0.215449\pi\)
−0.626343 + 0.779548i \(0.715449\pi\)
\(84\) 39.2823i 0.467646i
\(85\) −12.3339 125.452i −0.145105 1.47591i
\(86\) 0.839889 0.00976615
\(87\) 14.9859 14.9859i 0.172252 0.172252i
\(88\) 29.6275 + 29.6275i 0.336676 + 0.336676i
\(89\) 141.715i 1.59230i −0.605101 0.796149i \(-0.706867\pi\)
0.605101 0.796149i \(-0.293133\pi\)
\(90\) 37.2873 3.66593i 0.414303 0.0407326i
\(91\) −70.9402 −0.779563
\(92\) −6.78233 + 6.78233i −0.0737210 + 0.0737210i
\(93\) −57.6347 57.6347i −0.619728 0.619728i
\(94\) 106.032i 1.12800i
\(95\) 114.393 + 93.9135i 1.20414 + 0.988563i
\(96\) 10.8832 0.113366
\(97\) −29.4379 + 29.4379i −0.303483 + 0.303483i −0.842375 0.538892i \(-0.818843\pi\)
0.538892 + 0.842375i \(0.318843\pi\)
\(98\) −55.2252 55.2252i −0.563523 0.563523i
\(99\) 78.4927i 0.792856i
\(100\) −49.0427 + 9.73747i −0.490427 + 0.0973747i
\(101\) 105.739 1.04692 0.523459 0.852051i \(-0.324641\pi\)
0.523459 + 0.852051i \(0.324641\pi\)
\(102\) 48.5039 48.5039i 0.475529 0.475529i
\(103\) −15.4223 15.4223i −0.149732 0.149732i 0.628267 0.777998i \(-0.283765\pi\)
−0.777998 + 0.628267i \(0.783765\pi\)
\(104\) 19.6540i 0.188981i
\(105\) 62.3143 75.9033i 0.593469 0.722888i
\(106\) −116.751 −1.10142
\(107\) −38.0079 + 38.0079i −0.355214 + 0.355214i −0.862045 0.506831i \(-0.830817\pi\)
0.506831 + 0.862045i \(0.330817\pi\)
\(108\) 38.9036 + 38.9036i 0.360219 + 0.360219i
\(109\) 146.178i 1.34108i −0.741873 0.670540i \(-0.766062\pi\)
0.741873 0.670540i \(-0.233938\pi\)
\(110\) −10.2491 104.246i −0.0931735 0.947694i
\(111\) −40.0760 −0.361045
\(112\) −28.8756 + 28.8756i −0.257818 + 0.257818i
\(113\) 2.38693 + 2.38693i 0.0211232 + 0.0211232i 0.717590 0.696466i \(-0.245245\pi\)
−0.696466 + 0.717590i \(0.745245\pi\)
\(114\) 80.5384i 0.706477i
\(115\) 23.8641 2.34622i 0.207514 0.0204019i
\(116\) 22.0317 0.189928
\(117\) −26.0349 + 26.0349i −0.222520 + 0.222520i
\(118\) −13.7747 13.7747i −0.116735 0.116735i
\(119\) 257.385i 2.16290i
\(120\) −21.0290 17.2642i −0.175242 0.143868i
\(121\) 98.4471 0.813612
\(122\) 39.0198 39.0198i 0.319835 0.319835i
\(123\) −32.5924 32.5924i −0.264979 0.264979i
\(124\) 84.7322i 0.683325i
\(125\) 110.209 + 58.9821i 0.881675 + 0.471856i
\(126\) −76.5008 −0.607149
\(127\) −134.874 + 134.874i −1.06200 + 1.06200i −0.0640551 + 0.997946i \(0.520403\pi\)
−0.997946 + 0.0640551i \(0.979597\pi\)
\(128\) 8.00000 + 8.00000i 0.0625000 + 0.0625000i
\(129\) 1.14258i 0.00885723i
\(130\) 31.1775 37.9765i 0.239827 0.292127i
\(131\) −48.2924 −0.368644 −0.184322 0.982866i \(-0.559009\pi\)
−0.184322 + 0.982866i \(0.559009\pi\)
\(132\) 40.3051 40.3051i 0.305342 0.305342i
\(133\) −213.687 213.687i −1.60667 1.60667i
\(134\) 33.8212i 0.252397i
\(135\) −13.4580 136.885i −0.0996889 1.01396i
\(136\) 71.3085 0.524327
\(137\) −3.29075 + 3.29075i −0.0240200 + 0.0240200i −0.719015 0.694995i \(-0.755407\pi\)
0.694995 + 0.719015i \(0.255407\pi\)
\(138\) 9.22666 + 9.22666i 0.0668598 + 0.0668598i
\(139\) 108.941i 0.783751i 0.920018 + 0.391876i \(0.128174\pi\)
−0.920018 + 0.391876i \(0.871826\pi\)
\(140\) 101.601 9.98899i 0.725721 0.0713499i
\(141\) −144.246 −1.02302
\(142\) 103.112 103.112i 0.726143 0.726143i
\(143\) 72.7874 + 72.7874i 0.509002 + 0.509002i
\(144\) 21.1946i 0.147185i
\(145\) −42.5707 34.9492i −0.293591 0.241029i
\(146\) 83.1985 0.569853
\(147\) −75.1282 + 75.1282i −0.511076 + 0.511076i
\(148\) −29.4590 29.4590i −0.199048 0.199048i
\(149\) 68.8768i 0.462260i −0.972923 0.231130i \(-0.925758\pi\)
0.972923 0.231130i \(-0.0742423\pi\)
\(150\) 13.2468 + 66.7175i 0.0883121 + 0.444783i
\(151\) 138.399 0.916549 0.458275 0.888811i \(-0.348468\pi\)
0.458275 + 0.888811i \(0.348468\pi\)
\(152\) −59.2022 + 59.2022i −0.389488 + 0.389488i
\(153\) 94.4596 + 94.4596i 0.617383 + 0.617383i
\(154\) 213.878i 1.38882i
\(155\) −134.412 + 163.724i −0.867177 + 1.05628i
\(156\) 26.7372 0.171393
\(157\) −135.287 + 135.287i −0.861699 + 0.861699i −0.991535 0.129836i \(-0.958555\pi\)
0.129836 + 0.991535i \(0.458555\pi\)
\(158\) 155.484 + 155.484i 0.984074 + 0.984074i
\(159\) 158.828i 0.998916i
\(160\) −2.76745 28.1486i −0.0172966 0.175928i
\(161\) −48.9610 −0.304106
\(162\) 5.23660 5.23660i 0.0323247 0.0323247i
\(163\) −84.3740 84.3740i −0.517632 0.517632i 0.399222 0.916854i \(-0.369280\pi\)
−0.916854 + 0.399222i \(0.869280\pi\)
\(164\) 47.9160i 0.292171i
\(165\) −141.816 + 13.9428i −0.859494 + 0.0845019i
\(166\) 25.4320 0.153205
\(167\) 217.730 217.730i 1.30378 1.30378i 0.377949 0.925826i \(-0.376629\pi\)
0.925826 0.377949i \(-0.123371\pi\)
\(168\) 39.2823 + 39.2823i 0.233823 + 0.233823i
\(169\) 120.715i 0.714290i
\(170\) −137.786 113.118i −0.810505 0.665400i
\(171\) −156.846 −0.917225
\(172\) 0.839889 0.839889i 0.00488308 0.00488308i
\(173\) −222.534 222.534i −1.28632 1.28632i −0.937003 0.349321i \(-0.886412\pi\)
−0.349321 0.937003i \(-0.613588\pi\)
\(174\) 29.9718i 0.172252i
\(175\) −212.164 141.870i −1.21237 0.810687i
\(176\) 59.2550 0.336676
\(177\) −18.7390 + 18.7390i −0.105870 + 0.105870i
\(178\) −141.715 141.715i −0.796149 0.796149i
\(179\) 194.058i 1.08412i −0.840339 0.542061i \(-0.817644\pi\)
0.840339 0.542061i \(-0.182356\pi\)
\(180\) 33.6214 40.9532i 0.186785 0.227518i
\(181\) −0.412795 −0.00228064 −0.00114032 0.999999i \(-0.500363\pi\)
−0.00114032 + 0.999999i \(0.500363\pi\)
\(182\) −70.9402 + 70.9402i −0.389781 + 0.389781i
\(183\) −53.0825 53.0825i −0.290068 0.290068i
\(184\) 13.5647i 0.0737210i
\(185\) 10.1908 + 103.654i 0.0550855 + 0.560290i
\(186\) −115.269 −0.619728
\(187\) 264.086 264.086i 1.41223 1.41223i
\(188\) −106.032 106.032i −0.564002 0.564002i
\(189\) 280.842i 1.48594i
\(190\) 208.307 20.4799i 1.09635 0.107789i
\(191\) −313.636 −1.64207 −0.821036 0.570877i \(-0.806603\pi\)
−0.821036 + 0.570877i \(0.806603\pi\)
\(192\) 10.8832 10.8832i 0.0566832 0.0566832i
\(193\) −11.9642 11.9642i −0.0619909 0.0619909i 0.675432 0.737423i \(-0.263957\pi\)
−0.737423 + 0.675432i \(0.763957\pi\)
\(194\) 58.8757i 0.303483i
\(195\) −51.6630 42.4138i −0.264939 0.217507i
\(196\) −110.450 −0.563523
\(197\) −57.7317 + 57.7317i −0.293054 + 0.293054i −0.838286 0.545231i \(-0.816442\pi\)
0.545231 + 0.838286i \(0.316442\pi\)
\(198\) 78.4927 + 78.4927i 0.396428 + 0.396428i
\(199\) 263.722i 1.32524i −0.748957 0.662619i \(-0.769445\pi\)
0.748957 0.662619i \(-0.230555\pi\)
\(200\) −39.3052 + 58.7801i −0.196526 + 0.293901i
\(201\) 46.0102 0.228907
\(202\) 105.739 105.739i 0.523459 0.523459i
\(203\) 79.5222 + 79.5222i 0.391735 + 0.391735i
\(204\) 97.0078i 0.475529i
\(205\) −76.0101 + 92.5857i −0.370781 + 0.451638i
\(206\) −30.8447 −0.149732
\(207\) −17.9686 + 17.9686i −0.0868047 + 0.0868047i
\(208\) 19.6540 + 19.6540i 0.0944904 + 0.0944904i
\(209\) 438.503i 2.09810i
\(210\) −13.5890 138.218i −0.0647095 0.658179i
\(211\) 321.514 1.52376 0.761881 0.647717i \(-0.224276\pi\)
0.761881 + 0.647717i \(0.224276\pi\)
\(212\) −116.751 + 116.751i −0.550712 + 0.550712i
\(213\) −140.274 140.274i −0.658561 0.658561i
\(214\) 76.0158i 0.355214i
\(215\) −2.95521 + 0.290544i −0.0137452 + 0.00135137i
\(216\) 77.8073 0.360219
\(217\) 305.837 305.837i 1.40939 1.40939i
\(218\) −146.178 146.178i −0.670540 0.670540i
\(219\) 113.183i 0.516817i
\(220\) −114.495 93.9973i −0.520434 0.427261i
\(221\) 175.187 0.792702
\(222\) −40.0760 + 40.0760i −0.180522 + 0.180522i
\(223\) −75.9702 75.9702i −0.340674 0.340674i 0.515947 0.856621i \(-0.327440\pi\)
−0.856621 + 0.515947i \(0.827440\pi\)
\(224\) 57.7513i 0.257818i
\(225\) −129.930 + 25.7977i −0.577466 + 0.114656i
\(226\) 4.77385 0.0211232
\(227\) −63.6613 + 63.6613i −0.280446 + 0.280446i −0.833287 0.552841i \(-0.813544\pi\)
0.552841 + 0.833287i \(0.313544\pi\)
\(228\) 80.5384 + 80.5384i 0.353239 + 0.353239i
\(229\) 103.156i 0.450462i 0.974305 + 0.225231i \(0.0723137\pi\)
−0.974305 + 0.225231i \(0.927686\pi\)
\(230\) 21.5179 26.2103i 0.0935560 0.113958i
\(231\) 290.959 1.25956
\(232\) 22.0317 22.0317i 0.0949640 0.0949640i
\(233\) −211.803 211.803i −0.909026 0.909026i 0.0871679 0.996194i \(-0.472218\pi\)
−0.996194 + 0.0871679i \(0.972218\pi\)
\(234\) 52.0698i 0.222520i
\(235\) 36.6799 + 373.082i 0.156085 + 1.58758i
\(236\) −27.5494 −0.116735
\(237\) 211.520 211.520i 0.892488 0.892488i
\(238\) 257.385 + 257.385i 1.08145 + 1.08145i
\(239\) 89.5138i 0.374535i 0.982309 + 0.187267i \(0.0599631\pi\)
−0.982309 + 0.187267i \(0.940037\pi\)
\(240\) −38.2932 + 3.76483i −0.159555 + 0.0156868i
\(241\) 175.324 0.727487 0.363744 0.931499i \(-0.381498\pi\)
0.363744 + 0.931499i \(0.381498\pi\)
\(242\) 98.4471 98.4471i 0.406806 0.406806i
\(243\) 167.943 + 167.943i 0.691122 + 0.691122i
\(244\) 78.0397i 0.319835i
\(245\) 213.418 + 175.210i 0.871094 + 0.715142i
\(246\) −65.1848 −0.264979
\(247\) −145.445 + 145.445i −0.588846 + 0.588846i
\(248\) −84.7322 84.7322i −0.341662 0.341662i
\(249\) 34.5976i 0.138946i
\(250\) 169.191 51.2274i 0.676766 0.204909i
\(251\) 326.776 1.30190 0.650948 0.759122i \(-0.274371\pi\)
0.650948 + 0.759122i \(0.274371\pi\)
\(252\) −76.5008 + 76.5008i −0.303575 + 0.303575i
\(253\) 50.2359 + 50.2359i 0.198561 + 0.198561i
\(254\) 269.748i 1.06200i
\(255\) −153.885 + 187.443i −0.603472 + 0.735072i
\(256\) 16.0000 0.0625000
\(257\) −44.9594 + 44.9594i −0.174939 + 0.174939i −0.789146 0.614206i \(-0.789476\pi\)
0.614206 + 0.789146i \(0.289476\pi\)
\(258\) −1.14258 1.14258i −0.00442861 0.00442861i
\(259\) 212.662i 0.821089i
\(260\) −6.79894 69.1540i −0.0261498 0.265977i
\(261\) 58.3689 0.223636
\(262\) −48.2924 + 48.2924i −0.184322 + 0.184322i
\(263\) 123.550 + 123.550i 0.469771 + 0.469771i 0.901840 0.432070i \(-0.142217\pi\)
−0.432070 + 0.901840i \(0.642217\pi\)
\(264\) 80.6103i 0.305342i
\(265\) 410.797 40.3879i 1.55018 0.152407i
\(266\) −427.375 −1.60667
\(267\) −192.788 + 192.788i −0.722052 + 0.722052i
\(268\) 33.8212 + 33.8212i 0.126198 + 0.126198i
\(269\) 237.309i 0.882189i −0.897461 0.441094i \(-0.854590\pi\)
0.897461 0.441094i \(-0.145410\pi\)
\(270\) −150.343 123.427i −0.556827 0.457138i
\(271\) 26.2193 0.0967502 0.0483751 0.998829i \(-0.484596\pi\)
0.0483751 + 0.998829i \(0.484596\pi\)
\(272\) 71.3085 71.3085i 0.262164 0.262164i
\(273\) 96.5068 + 96.5068i 0.353505 + 0.353505i
\(274\) 6.58149i 0.0240200i
\(275\) 72.1242 + 363.253i 0.262270 + 1.32092i
\(276\) 18.4533 0.0668598
\(277\) −225.480 + 225.480i −0.814007 + 0.814007i −0.985232 0.171225i \(-0.945228\pi\)
0.171225 + 0.985232i \(0.445228\pi\)
\(278\) 108.941 + 108.941i 0.391876 + 0.391876i
\(279\) 224.483i 0.804598i
\(280\) 91.6119 111.590i 0.327185 0.398535i
\(281\) −70.2491 −0.249997 −0.124998 0.992157i \(-0.539893\pi\)
−0.124998 + 0.992157i \(0.539893\pi\)
\(282\) −144.246 + 144.246i −0.511511 + 0.511511i
\(283\) 49.1215 + 49.1215i 0.173574 + 0.173574i 0.788548 0.614974i \(-0.210833\pi\)
−0.614974 + 0.788548i \(0.710833\pi\)
\(284\) 206.225i 0.726143i
\(285\) −27.8608 283.380i −0.0977571 0.994316i
\(286\) 145.575 0.509002
\(287\) 172.951 172.951i 0.602615 0.602615i
\(288\) 21.1946 + 21.1946i 0.0735923 + 0.0735923i
\(289\) 346.613i 1.19935i
\(290\) −77.5199 + 7.62144i −0.267310 + 0.0262808i
\(291\) 80.0943 0.275238
\(292\) 83.1985 83.1985i 0.284926 0.284926i
\(293\) 369.904 + 369.904i 1.26247 + 1.26247i 0.949891 + 0.312580i \(0.101193\pi\)
0.312580 + 0.949891i \(0.398807\pi\)
\(294\) 150.256i 0.511076i
\(295\) 53.2323 + 43.7021i 0.180448 + 0.148143i
\(296\) −58.9181 −0.199048
\(297\) 288.154 288.154i 0.970217 0.970217i
\(298\) −68.8768 68.8768i −0.231130 0.231130i
\(299\) 33.3250i 0.111455i
\(300\) 79.9643 + 53.4706i 0.266548 + 0.178235i
\(301\) 6.06308 0.0201431
\(302\) 138.399 138.399i 0.458275 0.458275i
\(303\) −143.847 143.847i −0.474741 0.474741i
\(304\) 118.404i 0.389488i
\(305\) −123.796 + 150.792i −0.405888 + 0.494401i
\(306\) 188.919 0.617383
\(307\) 4.17039 4.17039i 0.0135843 0.0135843i −0.700282 0.713866i \(-0.746942\pi\)
0.713866 + 0.700282i \(0.246942\pi\)
\(308\) 213.878 + 213.878i 0.694409 + 0.694409i
\(309\) 41.9610i 0.135796i
\(310\) 29.3115 + 298.136i 0.0945534 + 0.961730i
\(311\) −385.664 −1.24008 −0.620039 0.784571i \(-0.712883\pi\)
−0.620039 + 0.784571i \(0.712883\pi\)
\(312\) 26.7372 26.7372i 0.0856963 0.0856963i
\(313\) −156.465 156.465i −0.499888 0.499888i 0.411515 0.911403i \(-0.365000\pi\)
−0.911403 + 0.411515i \(0.865000\pi\)
\(314\) 270.574i 0.861699i
\(315\) 269.173 26.4640i 0.854519 0.0840128i
\(316\) 310.967 0.984074
\(317\) −172.672 + 172.672i −0.544708 + 0.544708i −0.924905 0.380198i \(-0.875856\pi\)
0.380198 + 0.924905i \(0.375856\pi\)
\(318\) 158.828 + 158.828i 0.499458 + 0.499458i
\(319\) 163.186i 0.511554i
\(320\) −30.9160 25.3811i −0.0966125 0.0793160i
\(321\) 103.412 0.322155
\(322\) −48.9610 + 48.9610i −0.152053 + 0.152053i
\(323\) 527.702 + 527.702i 1.63375 + 1.63375i
\(324\) 10.4732i 0.0323247i
\(325\) −96.5630 + 144.408i −0.297117 + 0.444333i
\(326\) −168.748 −0.517632
\(327\) −198.860 + 198.860i −0.608134 + 0.608134i
\(328\) −47.9160 47.9160i −0.146085 0.146085i
\(329\) 765.437i 2.32656i
\(330\) −127.874 + 155.759i −0.387496 + 0.471998i
\(331\) 594.585 1.79633 0.898165 0.439659i \(-0.144901\pi\)
0.898165 + 0.439659i \(0.144901\pi\)
\(332\) 25.4320 25.4320i 0.0766024 0.0766024i
\(333\) −78.0465 78.0465i −0.234374 0.234374i
\(334\) 435.461i 1.30378i
\(335\) −11.6998 119.002i −0.0349248 0.355231i
\(336\) 78.5646 0.233823
\(337\) −318.172 + 318.172i −0.944130 + 0.944130i −0.998520 0.0543895i \(-0.982679\pi\)
0.0543895 + 0.998520i \(0.482679\pi\)
\(338\) −120.715 120.715i −0.357145 0.357145i
\(339\) 6.49433i 0.0191573i
\(340\) −250.904 + 24.6679i −0.737953 + 0.0725525i
\(341\) −627.601 −1.84047
\(342\) −156.846 + 156.846i −0.458613 + 0.458613i
\(343\) −44.9394 44.9394i −0.131019 0.131019i
\(344\) 1.67978i 0.00488308i
\(345\) −35.6564 29.2728i −0.103352 0.0848488i
\(346\) −445.068 −1.28632
\(347\) 161.848 161.848i 0.466422 0.466422i −0.434331 0.900753i \(-0.643015\pi\)
0.900753 + 0.434331i \(0.143015\pi\)
\(348\) −29.9718 29.9718i −0.0861258 0.0861258i
\(349\) 66.1242i 0.189468i −0.995503 0.0947339i \(-0.969800\pi\)
0.995503 0.0947339i \(-0.0302000\pi\)
\(350\) −354.034 + 70.2939i −1.01153 + 0.200840i
\(351\) 191.153 0.544596
\(352\) 59.2550 59.2550i 0.168338 0.168338i
\(353\) 331.118 + 331.118i 0.938012 + 0.938012i 0.998188 0.0601762i \(-0.0191662\pi\)
−0.0601762 + 0.998188i \(0.519166\pi\)
\(354\) 37.4780i 0.105870i
\(355\) −327.138 + 398.478i −0.921515 + 1.12247i
\(356\) −283.429 −0.796149
\(357\) 350.145 350.145i 0.980799 0.980799i
\(358\) −194.058 194.058i −0.542061 0.542061i
\(359\) 134.587i 0.374893i −0.982275 0.187447i \(-0.939979\pi\)
0.982275 0.187447i \(-0.0600211\pi\)
\(360\) −7.33187 74.5746i −0.0203663 0.207152i
\(361\) −515.224 −1.42721
\(362\) −0.412795 + 0.412795i −0.00114032 + 0.00114032i
\(363\) −133.927 133.927i −0.368945 0.368945i
\(364\) 141.880i 0.389781i
\(365\) −292.740 + 28.7810i −0.802027 + 0.0788520i
\(366\) −106.165 −0.290068
\(367\) 451.660 451.660i 1.23068 1.23068i 0.266979 0.963702i \(-0.413975\pi\)
0.963702 0.266979i \(-0.0860254\pi\)
\(368\) 13.5647 + 13.5647i 0.0368605 + 0.0368605i
\(369\) 126.945i 0.344024i
\(370\) 113.845 + 93.4629i 0.307688 + 0.252602i
\(371\) −842.815 −2.27174
\(372\) −115.269 + 115.269i −0.309864 + 0.309864i
\(373\) 451.866 + 451.866i 1.21144 + 1.21144i 0.970554 + 0.240883i \(0.0774369\pi\)
0.240883 + 0.970554i \(0.422563\pi\)
\(374\) 528.173i 1.41223i
\(375\) −69.6895 230.168i −0.185839 0.613780i
\(376\) −212.065 −0.564002
\(377\) 54.1263 54.1263i 0.143571 0.143571i
\(378\) 280.842 + 280.842i 0.742968 + 0.742968i
\(379\) 230.954i 0.609377i −0.952452 0.304688i \(-0.901448\pi\)
0.952452 0.304688i \(-0.0985524\pi\)
\(380\) 187.827 228.787i 0.494282 0.602071i
\(381\) 366.965 0.963162
\(382\) −313.636 + 313.636i −0.821036 + 0.821036i
\(383\) 183.834 + 183.834i 0.479985 + 0.479985i 0.905127 0.425142i \(-0.139776\pi\)
−0.425142 + 0.905127i \(0.639776\pi\)
\(384\) 21.7663i 0.0566832i
\(385\) −73.9872 752.545i −0.192174 1.95466i
\(386\) −23.9285 −0.0619909
\(387\) 2.22514 2.22514i 0.00574971 0.00574971i
\(388\) 58.8757 + 58.8757i 0.151742 + 0.151742i
\(389\) 468.206i 1.20362i 0.798641 + 0.601808i \(0.205553\pi\)
−0.798641 + 0.601808i \(0.794447\pi\)
\(390\) −94.0768 + 9.24925i −0.241223 + 0.0237160i
\(391\) 120.909 0.309231
\(392\) −110.450 + 110.450i −0.281761 + 0.281761i
\(393\) 65.6968 + 65.6968i 0.167168 + 0.167168i
\(394\) 115.463i 0.293054i
\(395\) −600.867 493.294i −1.52118 1.24884i
\(396\) 156.985 0.396428
\(397\) 53.6961 53.6961i 0.135255 0.135255i −0.636238 0.771493i \(-0.719510\pi\)
0.771493 + 0.636238i \(0.219510\pi\)
\(398\) −263.722 263.722i −0.662619 0.662619i
\(399\) 581.399i 1.45714i
\(400\) 19.4749 + 98.0853i 0.0486874 + 0.245213i
\(401\) 248.645 0.620062 0.310031 0.950727i \(-0.399661\pi\)
0.310031 + 0.950727i \(0.399661\pi\)
\(402\) 46.0102 46.0102i 0.114453 0.114453i
\(403\) −208.166 208.166i −0.516541 0.516541i
\(404\) 211.477i 0.523459i
\(405\) −16.6138 + 20.2369i −0.0410218 + 0.0499675i
\(406\) 159.044 0.391735
\(407\) −218.199 + 218.199i −0.536117 + 0.536117i
\(408\) −97.0078 97.0078i −0.237764 0.237764i
\(409\) 561.926i 1.37390i −0.726703 0.686952i \(-0.758948\pi\)
0.726703 0.686952i \(-0.241052\pi\)
\(410\) 16.5756 + 168.596i 0.0404284 + 0.411209i
\(411\) 8.95344 0.0217845
\(412\) −30.8447 + 30.8447i −0.0748658 + 0.0748658i
\(413\) −99.4381 99.4381i −0.240770 0.240770i
\(414\) 35.9371i 0.0868047i
\(415\) −89.4842 + 8.79772i −0.215625 + 0.0211993i
\(416\) 39.3080 0.0944904
\(417\) 148.204 148.204i 0.355404 0.355404i
\(418\) 438.503 + 438.503i 1.04905 + 1.04905i
\(419\) 453.494i 1.08233i 0.840918 + 0.541163i \(0.182016\pi\)
−0.840918 + 0.541163i \(0.817984\pi\)
\(420\) −151.807 124.629i −0.361444 0.296735i
\(421\) −62.8563 −0.149302 −0.0746512 0.997210i \(-0.523784\pi\)
−0.0746512 + 0.997210i \(0.523784\pi\)
\(422\) 321.514 321.514i 0.761881 0.761881i
\(423\) −280.914 280.914i −0.664099 0.664099i
\(424\) 233.502i 0.550712i
\(425\) 523.940 + 350.349i 1.23280 + 0.824351i
\(426\) −280.547 −0.658561
\(427\) 281.681 281.681i 0.659674 0.659674i
\(428\) 76.0158 + 76.0158i 0.177607 + 0.177607i
\(429\) 198.039i 0.461630i
\(430\) −2.66466 + 3.24575i −0.00619689 + 0.00754826i
\(431\) −175.877 −0.408068 −0.204034 0.978964i \(-0.565405\pi\)
−0.204034 + 0.978964i \(0.565405\pi\)
\(432\) 77.8073 77.8073i 0.180109 0.180109i
\(433\) −342.932 342.932i −0.791991 0.791991i 0.189827 0.981818i \(-0.439207\pi\)
−0.981818 + 0.189827i \(0.939207\pi\)
\(434\) 611.674i 1.40939i
\(435\) 10.3682 + 105.458i 0.0238349 + 0.242432i
\(436\) −292.356 −0.670540
\(437\) −100.382 + 100.382i −0.229707 + 0.229707i
\(438\) −113.183 113.183i −0.258409 0.258409i
\(439\) 55.4496i 0.126309i −0.998004 0.0631544i \(-0.979884\pi\)
0.998004 0.0631544i \(-0.0201161\pi\)
\(440\) −208.493 + 20.4982i −0.473847 + 0.0465867i
\(441\) −292.619 −0.663535
\(442\) 175.187 175.187i 0.396351 0.396351i
\(443\) −154.793 154.793i −0.349420 0.349420i 0.510473 0.859894i \(-0.329470\pi\)
−0.859894 + 0.510473i \(0.829470\pi\)
\(444\) 80.1520i 0.180522i
\(445\) 547.656 + 449.609i 1.23069 + 1.01036i
\(446\) −151.940 −0.340674
\(447\) −93.6997 + 93.6997i −0.209619 + 0.209619i
\(448\) 57.7513 + 57.7513i 0.128909 + 0.128909i
\(449\) 658.321i 1.46619i 0.680124 + 0.733097i \(0.261926\pi\)
−0.680124 + 0.733097i \(0.738074\pi\)
\(450\) −104.132 + 155.727i −0.231405 + 0.346061i
\(451\) −354.908 −0.786935
\(452\) 4.77385 4.77385i 0.0105616 0.0105616i
\(453\) −188.277 188.277i −0.415623 0.415623i
\(454\) 127.323i 0.280446i
\(455\) 225.068 274.149i 0.494654 0.602524i
\(456\) 161.077 0.353239
\(457\) −630.005 + 630.005i −1.37857 + 1.37857i −0.531522 + 0.847045i \(0.678380\pi\)
−0.847045 + 0.531522i \(0.821620\pi\)
\(458\) 103.156 + 103.156i 0.225231 + 0.225231i
\(459\) 693.540i 1.51098i
\(460\) −4.69244 47.7282i −0.0102010 0.103757i
\(461\) −635.738 −1.37904 −0.689520 0.724266i \(-0.742179\pi\)
−0.689520 + 0.724266i \(0.742179\pi\)
\(462\) 290.959 290.959i 0.629781 0.629781i
\(463\) −30.8108 30.8108i −0.0665460 0.0665460i 0.673051 0.739597i \(-0.264984\pi\)
−0.739597 + 0.673051i \(0.764984\pi\)
\(464\) 44.0633i 0.0949640i
\(465\) 405.584 39.8753i 0.872223 0.0857534i
\(466\) −423.606 −0.909026
\(467\) 273.937 273.937i 0.586588 0.586588i −0.350118 0.936706i \(-0.613858\pi\)
0.936706 + 0.350118i \(0.113858\pi\)
\(468\) 52.0698 + 52.0698i 0.111260 + 0.111260i
\(469\) 244.152i 0.520580i
\(470\) 409.762 + 336.402i 0.871834 + 0.715749i
\(471\) 368.087 0.781502
\(472\) −27.5494 + 27.5494i −0.0583673 + 0.0583673i
\(473\) −6.22095 6.22095i −0.0131521 0.0131521i
\(474\) 423.039i 0.892488i
\(475\) −725.858 + 144.120i −1.52812 + 0.303410i
\(476\) 514.769 1.08145
\(477\) −309.311 + 309.311i −0.648451 + 0.648451i
\(478\) 89.5138 + 89.5138i 0.187267 + 0.187267i
\(479\) 617.839i 1.28985i −0.764245 0.644926i \(-0.776888\pi\)
0.764245 0.644926i \(-0.223112\pi\)
\(480\) −34.5284 + 42.0580i −0.0719341 + 0.0876209i
\(481\) −144.747 −0.300929
\(482\) 175.324 175.324i 0.363744 0.363744i
\(483\) 66.6064 + 66.6064i 0.137901 + 0.137901i
\(484\) 196.894i 0.406806i
\(485\) −20.3670 207.158i −0.0419937 0.427130i
\(486\) 335.885 0.691122
\(487\) 182.634 182.634i 0.375019 0.375019i −0.494283 0.869301i \(-0.664569\pi\)
0.869301 + 0.494283i \(0.164569\pi\)
\(488\) −78.0397 78.0397i −0.159917 0.159917i
\(489\) 229.564i 0.469456i
\(490\) 388.628 38.2083i 0.793118 0.0779761i
\(491\) −31.9547 −0.0650808 −0.0325404 0.999470i \(-0.510360\pi\)
−0.0325404 + 0.999470i \(0.510360\pi\)
\(492\) −65.1848 + 65.1848i −0.132489 + 0.132489i
\(493\) −196.381 196.381i −0.398338 0.398338i
\(494\) 290.890i 0.588846i
\(495\) −303.335 249.029i −0.612799 0.503089i
\(496\) −169.464 −0.341662
\(497\) 744.358 744.358i 1.49770 1.49770i
\(498\) −34.5976 34.5976i −0.0694731 0.0694731i
\(499\) 138.737i 0.278030i 0.990290 + 0.139015i \(0.0443936\pi\)
−0.990290 + 0.139015i \(0.955606\pi\)
\(500\) 117.964 220.419i 0.235928 0.440838i
\(501\) −592.400 −1.18243
\(502\) 326.776 326.776i 0.650948 0.650948i
\(503\) 159.071 + 159.071i 0.316245 + 0.316245i 0.847323 0.531078i \(-0.178213\pi\)
−0.531078 + 0.847323i \(0.678213\pi\)
\(504\) 153.002i 0.303575i
\(505\) −335.471 + 408.627i −0.664298 + 0.809163i
\(506\) 100.472 0.198561
\(507\) −164.220 + 164.220i −0.323906 + 0.323906i
\(508\) 269.748 + 269.748i 0.531001 + 0.531001i
\(509\) 128.670i 0.252790i 0.991980 + 0.126395i \(0.0403406\pi\)
−0.991980 + 0.126395i \(0.959659\pi\)
\(510\) 33.5581 + 341.329i 0.0658001 + 0.669272i
\(511\) 600.602 1.17535
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) 575.795 + 575.795i 1.12241 + 1.12241i
\(514\) 89.9188i 0.174939i
\(515\) 108.529 10.6701i 0.210736 0.0207187i
\(516\) −2.28516 −0.00442861
\(517\) −785.368 + 785.368i −1.51909 + 1.51909i
\(518\) −212.662 212.662i −0.410545 0.410545i
\(519\) 605.469i 1.16661i
\(520\) −75.9529 62.3550i −0.146063 0.119914i
\(521\) 452.310 0.868157 0.434078 0.900875i \(-0.357074\pi\)
0.434078 + 0.900875i \(0.357074\pi\)
\(522\) 58.3689 58.3689i 0.111818 0.111818i
\(523\) 66.3514 + 66.3514i 0.126867 + 0.126867i 0.767689 0.640822i \(-0.221406\pi\)
−0.640822 + 0.767689i \(0.721406\pi\)
\(524\) 96.5848i 0.184322i
\(525\) 95.6276 + 481.627i 0.182148 + 0.917385i
\(526\) 247.099 0.469771
\(527\) −755.266 + 755.266i −1.43314 + 1.43314i
\(528\) −80.6103 80.6103i −0.152671 0.152671i
\(529\) 23.0000i 0.0434783i
\(530\) 370.409 451.184i 0.698884 0.851291i
\(531\) −72.9871 −0.137452
\(532\) −427.375 + 427.375i −0.803336 + 0.803336i
\(533\) −117.718 117.718i −0.220859 0.220859i
\(534\) 385.576i 0.722052i
\(535\) −26.2962 267.467i −0.0491519 0.499938i
\(536\) 67.6424 0.126198
\(537\) −263.996 + 263.996i −0.491612 + 0.491612i
\(538\) −237.309 237.309i −0.441094 0.441094i
\(539\) 818.093i 1.51780i
\(540\) −273.770 + 26.9160i −0.506982 + 0.0498444i
\(541\) −598.507 −1.10630 −0.553148 0.833083i \(-0.686574\pi\)
−0.553148 + 0.833083i \(0.686574\pi\)
\(542\) 26.2193 26.2193i 0.0483751 0.0483751i
\(543\) 0.561565 + 0.561565i 0.00103419 + 0.00103419i
\(544\) 142.617i 0.262164i
\(545\) 564.904 + 463.769i 1.03652 + 0.850953i
\(546\) 193.014 0.353505
\(547\) 87.9130 87.9130i 0.160718 0.160718i −0.622166 0.782885i \(-0.713747\pi\)
0.782885 + 0.622166i \(0.213747\pi\)
\(548\) 6.58149 + 6.58149i 0.0120100 + 0.0120100i
\(549\) 206.752i 0.376598i
\(550\) 435.377 + 291.128i 0.791594 + 0.529325i
\(551\) 326.080 0.591797
\(552\) 18.4533 18.4533i 0.0334299 0.0334299i
\(553\) 1122.42 + 1122.42i 2.02970 + 2.02970i
\(554\) 450.960i 0.814007i
\(555\) 127.147 154.874i 0.229093 0.279052i
\(556\) 217.883 0.391876
\(557\) 688.697 688.697i 1.23644 1.23644i 0.274995 0.961446i \(-0.411324\pi\)
0.961446 0.274995i \(-0.0886762\pi\)
\(558\) −224.483 224.483i −0.402299 0.402299i
\(559\) 4.12680i 0.00738246i
\(560\) −19.9780 203.202i −0.0356750 0.362860i
\(561\) −718.525 −1.28079
\(562\) −70.2491 + 70.2491i −0.124998 + 0.124998i
\(563\) 51.4275 + 51.4275i 0.0913454 + 0.0913454i 0.751303 0.659958i \(-0.229426\pi\)
−0.659958 + 0.751303i \(0.729426\pi\)
\(564\) 288.492i 0.511511i
\(565\) −16.7971 + 1.65143i −0.0297294 + 0.00292288i
\(566\) 98.2430 0.173574
\(567\) 37.8025 37.8025i 0.0666712 0.0666712i
\(568\) −206.225 206.225i −0.363071 0.363071i
\(569\) 632.828i 1.11218i −0.831124 0.556088i \(-0.812302\pi\)
0.831124 0.556088i \(-0.187698\pi\)
\(570\) −311.241 255.519i −0.546036 0.448279i
\(571\) 696.211 1.21928 0.609642 0.792677i \(-0.291313\pi\)
0.609642 + 0.792677i \(0.291313\pi\)
\(572\) 145.575 145.575i 0.254501 0.254501i
\(573\) 426.669 + 426.669i 0.744623 + 0.744623i
\(574\) 345.901i 0.602615i
\(575\) −66.6452 + 99.6665i −0.115905 + 0.173333i
\(576\) 42.3891 0.0735923
\(577\) −75.3419 + 75.3419i −0.130575 + 0.130575i −0.769374 0.638799i \(-0.779432\pi\)
0.638799 + 0.769374i \(0.279432\pi\)
\(578\) −346.613 346.613i −0.599676 0.599676i
\(579\) 32.5522i 0.0562215i
\(580\) −69.8985 + 85.1413i −0.120515 + 0.146795i
\(581\) 183.591 0.315992
\(582\) 80.0943 80.0943i 0.137619 0.137619i
\(583\) 864.760 + 864.760i 1.48329 + 1.48329i
\(584\) 166.397i 0.284926i
\(585\) −18.0126 183.211i −0.0307907 0.313181i
\(586\) 739.808 1.26247
\(587\) 537.340 537.340i 0.915401 0.915401i −0.0812898 0.996691i \(-0.525904\pi\)
0.996691 + 0.0812898i \(0.0259039\pi\)
\(588\) 150.256 + 150.256i 0.255538 + 0.255538i
\(589\) 1254.08i 2.12917i
\(590\) 96.9343 9.53019i 0.164295 0.0161529i
\(591\) 157.076 0.265780
\(592\) −58.9181 + 58.9181i −0.0995238 + 0.0995238i
\(593\) −100.376 100.376i −0.169268 0.169268i 0.617390 0.786657i \(-0.288190\pi\)
−0.786657 + 0.617390i \(0.788190\pi\)
\(594\) 576.309i 0.970217i
\(595\) −994.663 816.589i −1.67170 1.37242i
\(596\) −137.754 −0.231130
\(597\) −358.767 + 358.767i −0.600949 + 0.600949i
\(598\) 33.3250 + 33.3250i 0.0557274 + 0.0557274i
\(599\) 57.7918i 0.0964805i 0.998836 + 0.0482403i \(0.0153613\pi\)
−0.998836 + 0.0482403i \(0.984639\pi\)
\(600\) 133.435 26.4936i 0.222392 0.0441561i
\(601\) 855.388 1.42327 0.711637 0.702547i \(-0.247954\pi\)
0.711637 + 0.702547i \(0.247954\pi\)
\(602\) 6.06308 6.06308i 0.0100716 0.0100716i
\(603\) 89.6032 + 89.6032i 0.148596 + 0.148596i
\(604\) 276.798i 0.458275i
\(605\) −312.337 + 380.449i −0.516259 + 0.628841i
\(606\) −287.693 −0.474741
\(607\) 171.294 171.294i 0.282198 0.282198i −0.551787 0.833985i \(-0.686054\pi\)
0.833985 + 0.551787i \(0.186054\pi\)
\(608\) 118.404 + 118.404i 0.194744 + 0.194744i
\(609\) 216.364i 0.355277i
\(610\) 26.9964 + 274.588i 0.0442564 + 0.450144i
\(611\) −520.990 −0.852684
\(612\) 188.919 188.919i 0.308691 0.308691i
\(613\) −107.859 107.859i −0.175952 0.175952i 0.613636 0.789589i \(-0.289706\pi\)
−0.789589 + 0.613636i \(0.789706\pi\)
\(614\) 8.34078i 0.0135843i
\(615\) 229.357 22.5495i 0.372938 0.0366658i
\(616\) 427.756 0.694409
\(617\) 234.765 234.765i 0.380495 0.380495i −0.490786 0.871280i \(-0.663290\pi\)
0.871280 + 0.490786i \(0.163290\pi\)
\(618\) 41.9610 + 41.9610i 0.0678981 + 0.0678981i
\(619\) 35.0950i 0.0566964i −0.999598 0.0283482i \(-0.990975\pi\)
0.999598 0.0283482i \(-0.00902472\pi\)
\(620\) 327.448 + 268.825i 0.528142 + 0.433588i
\(621\) 131.929 0.212446
\(622\) −385.664 + 385.664i −0.620039 + 0.620039i
\(623\) −1023.02 1023.02i −1.64209 1.64209i
\(624\) 53.4745i 0.0856963i
\(625\) −577.591 + 238.776i −0.924145 + 0.382041i
\(626\) −312.930 −0.499888
\(627\) 596.538 596.538i 0.951416 0.951416i
\(628\) 270.574 + 270.574i 0.430850 + 0.430850i
\(629\) 525.170i 0.834929i
\(630\) 242.709 295.637i 0.385253 0.469266i
\(631\) −826.767 −1.31025 −0.655124 0.755521i \(-0.727384\pi\)
−0.655124 + 0.755521i \(0.727384\pi\)
\(632\) 310.967 310.967i 0.492037 0.492037i
\(633\) −437.386 437.386i −0.690974 0.690974i
\(634\) 345.345i 0.544708i
\(635\) −93.3144 949.128i −0.146952 1.49469i
\(636\) 317.655 0.499458
\(637\) −271.349 + 271.349i −0.425980 + 0.425980i
\(638\) −163.186 163.186i −0.255777 0.255777i
\(639\) 546.355i 0.855016i
\(640\) −56.2971 + 5.53490i −0.0879642 + 0.00864829i
\(641\) 52.1713 0.0813904 0.0406952 0.999172i \(-0.487043\pi\)
0.0406952 + 0.999172i \(0.487043\pi\)
\(642\) 103.412 103.412i 0.161077 0.161077i
\(643\) 241.431 + 241.431i 0.375476 + 0.375476i 0.869467 0.493991i \(-0.164463\pi\)
−0.493991 + 0.869467i \(0.664463\pi\)
\(644\) 97.9220i 0.152053i
\(645\) 4.41551 + 3.62500i 0.00684575 + 0.00562016i
\(646\) 1055.40 1.63375
\(647\) −320.910 + 320.910i −0.495998 + 0.495998i −0.910190 0.414192i \(-0.864064\pi\)
0.414192 + 0.910190i \(0.364064\pi\)
\(648\) −10.4732 10.4732i −0.0161624 0.0161624i
\(649\) 204.055i 0.314414i
\(650\) 47.8451 + 240.971i 0.0736078 + 0.370725i
\(651\) −832.119 −1.27822
\(652\) −168.748 + 168.748i −0.258816 + 0.258816i
\(653\) 358.411 + 358.411i 0.548869 + 0.548869i 0.926114 0.377245i \(-0.123128\pi\)
−0.377245 + 0.926114i \(0.623128\pi\)
\(654\) 397.720i 0.608134i
\(655\) 153.214 186.626i 0.233915 0.284925i
\(656\) −95.8320 −0.146085
\(657\) 220.420 220.420i 0.335494 0.335494i
\(658\) −765.437 765.437i −1.16328 1.16328i
\(659\) 654.343i 0.992934i 0.868056 + 0.496467i \(0.165370\pi\)
−0.868056 + 0.496467i \(0.834630\pi\)
\(660\) 27.8856 + 283.633i 0.0422510 + 0.429747i
\(661\) 205.380 0.310711 0.155355 0.987859i \(-0.450348\pi\)
0.155355 + 0.987859i \(0.450348\pi\)
\(662\) 594.585 594.585i 0.898165 0.898165i
\(663\) −238.324 238.324i −0.359463 0.359463i
\(664\) 50.8640i 0.0766024i
\(665\) 1503.75 147.842i 2.26128 0.222319i
\(666\) −156.093 −0.234374
\(667\) 37.3565 37.3565i 0.0560067 0.0560067i
\(668\) −435.461 435.461i −0.651888 0.651888i
\(669\) 206.699i 0.308967i
\(670\) −130.702 107.302i −0.195078 0.160153i
\(671\) −578.030 −0.861446
\(672\) 78.5646 78.5646i 0.116912 0.116912i
\(673\) −181.364 181.364i −0.269486 0.269486i 0.559407 0.828893i \(-0.311029\pi\)
−0.828893 + 0.559407i \(0.811029\pi\)
\(674\) 636.344i 0.944130i
\(675\) 571.690 + 382.279i 0.846949 + 0.566339i
\(676\) −241.430 −0.357145
\(677\) 49.6207 49.6207i 0.0732950 0.0732950i −0.669509 0.742804i \(-0.733495\pi\)
0.742804 + 0.669509i \(0.233495\pi\)
\(678\) −6.49433 6.49433i −0.00957866 0.00957866i
\(679\) 425.018i 0.625947i
\(680\) −226.236 + 275.572i −0.332700 + 0.405253i
\(681\) 173.209 0.254345
\(682\) −627.601 + 627.601i −0.920236 + 0.920236i
\(683\) −665.906 665.906i −0.974972 0.974972i 0.0247224 0.999694i \(-0.492130\pi\)
−0.999694 + 0.0247224i \(0.992130\pi\)
\(684\) 313.691i 0.458613i
\(685\) −2.27675 23.1574i −0.00332372 0.0338065i
\(686\) −89.8789 −0.131019
\(687\) 140.333 140.333i 0.204269 0.204269i
\(688\) −1.67978 1.67978i −0.00244154 0.00244154i
\(689\) 573.656i 0.832593i
\(690\) −64.9293 + 6.38358i −0.0941004 + 0.00925157i
\(691\) 868.900 1.25745 0.628727 0.777626i \(-0.283576\pi\)
0.628727 + 0.777626i \(0.283576\pi\)
\(692\) −445.068 + 445.068i −0.643162 + 0.643162i
\(693\) 566.632 + 566.632i 0.817651 + 0.817651i
\(694\) 323.697i 0.466422i
\(695\) −421.004 345.632i −0.605761 0.497312i
\(696\) −59.9436 −0.0861258
\(697\) −427.102 + 427.102i −0.612772 + 0.612772i
\(698\) −66.1242 66.1242i −0.0947339 0.0947339i
\(699\) 576.272i 0.824424i
\(700\) −283.740 + 424.328i −0.405344 + 0.606183i
\(701\) 769.630 1.09790 0.548952 0.835854i \(-0.315027\pi\)
0.548952 + 0.835854i \(0.315027\pi\)
\(702\) 191.153 191.153i 0.272298 0.272298i
\(703\) −436.010 436.010i −0.620213 0.620213i
\(704\) 118.510i 0.168338i
\(705\) 457.640 557.439i 0.649135 0.790693i
\(706\) 662.236 0.938012
\(707\) 763.318 763.318i 1.07966 1.07966i
\(708\) 37.4780 + 37.4780i 0.0529351 + 0.0529351i
\(709\) 1193.36i 1.68316i 0.540133 + 0.841580i \(0.318374\pi\)
−0.540133 + 0.841580i \(0.681626\pi\)
\(710\) 71.3396 + 725.615i 0.100478 + 1.02199i
\(711\) 823.853 1.15872
\(712\) −283.429 + 283.429i −0.398075 + 0.398075i
\(713\) −143.671 143.671i −0.201501 0.201501i
\(714\) 700.291i 0.980799i
\(715\) −512.215 + 50.3589i −0.716384 + 0.0704320i
\(716\) −388.116 −0.542061
\(717\) 121.774 121.774i 0.169839 0.169839i
\(718\) −134.587 134.587i −0.187447 0.187447i
\(719\) 1266.00i 1.76078i 0.474252 + 0.880389i \(0.342719\pi\)
−0.474252 + 0.880389i \(0.657281\pi\)
\(720\) −81.9064 67.2427i −0.113759 0.0933926i
\(721\) −222.665 −0.308828
\(722\) −515.224 + 515.224i −0.713607 + 0.713607i
\(723\) −238.511 238.511i −0.329890 0.329890i
\(724\) 0.825590i 0.00114032i
\(725\) 270.123 53.6331i 0.372583 0.0739768i
\(726\) −267.854 −0.368945
\(727\) −712.318 + 712.318i −0.979805 + 0.979805i −0.999800 0.0199952i \(-0.993635\pi\)
0.0199952 + 0.999800i \(0.493635\pi\)
\(728\) 141.880 + 141.880i 0.194891 + 0.194891i
\(729\) 504.066i 0.691449i
\(730\) −263.959 + 321.521i −0.361587 + 0.440439i
\(731\) −14.9728 −0.0204826
\(732\) −106.165 + 106.165i −0.145034 + 0.145034i
\(733\) −785.498 785.498i −1.07162 1.07162i −0.997229 0.0743915i \(-0.976299\pi\)
−0.0743915 0.997229i \(-0.523701\pi\)
\(734\) 903.320i 1.23068i
\(735\) −51.9784 528.688i −0.0707190 0.719303i
\(736\) 27.1293 0.0368605
\(737\) 250.509 250.509i 0.339904 0.339904i
\(738\) −126.945 126.945i −0.172012 0.172012i
\(739\) 176.725i 0.239141i −0.992826 0.119570i \(-0.961848\pi\)
0.992826 0.119570i \(-0.0381517\pi\)
\(740\) 207.307 20.3816i 0.280145 0.0275427i
\(741\) 395.726 0.534043
\(742\) −842.815 + 842.815i −1.13587 + 1.13587i
\(743\) −433.606 433.606i −0.583588 0.583588i 0.352300 0.935887i \(-0.385400\pi\)
−0.935887 + 0.352300i \(0.885400\pi\)
\(744\) 230.539i 0.309864i
\(745\) 266.174 + 218.521i 0.357281 + 0.293317i
\(746\) 903.732 1.21144
\(747\) 67.3775 67.3775i 0.0901975 0.0901975i
\(748\) −528.173 528.173i −0.706114 0.706114i
\(749\) 548.751i 0.732645i
\(750\) −299.857 160.478i −0.399809 0.213971i
\(751\) 197.940 0.263569 0.131785 0.991278i \(-0.457929\pi\)
0.131785 + 0.991278i \(0.457929\pi\)
\(752\) −212.065 + 212.065i −0.282001 + 0.282001i
\(753\) −444.545 444.545i −0.590365 0.590365i
\(754\) 108.253i 0.143571i
\(755\) −439.090 + 534.843i −0.581576 + 0.708401i
\(756\) 561.684 0.742968
\(757\) −660.110 + 660.110i −0.872008 + 0.872008i −0.992691 0.120683i \(-0.961491\pi\)
0.120683 + 0.992691i \(0.461491\pi\)
\(758\) −230.954 230.954i −0.304688 0.304688i
\(759\) 136.681i 0.180081i
\(760\) −40.9598 416.614i −0.0538944 0.548176i
\(761\) 886.095 1.16438 0.582191 0.813052i \(-0.302196\pi\)
0.582191 + 0.813052i \(0.302196\pi\)
\(762\) 366.965 366.965i 0.481581 0.481581i
\(763\) −1055.24 1055.24i −1.38302 1.38302i
\(764\) 627.271i 0.821036i
\(765\) −664.725 + 65.3531i −0.868922 + 0.0854288i
\(766\) 367.668 0.479985
\(767\) −67.6819 + 67.6819i −0.0882424 + 0.0882424i
\(768\) −21.7663 21.7663i −0.0283416 0.0283416i
\(769\) 666.097i 0.866185i 0.901349 + 0.433093i \(0.142578\pi\)
−0.901349 + 0.433093i \(0.857422\pi\)
\(770\) −826.532 678.558i −1.07342 0.881244i
\(771\) 122.325 0.158658
\(772\) −23.9285 + 23.9285i −0.0309955 + 0.0309955i
\(773\) 686.942 + 686.942i 0.888670 + 0.888670i 0.994395 0.105725i \(-0.0337165\pi\)
−0.105725 + 0.994395i \(0.533716\pi\)
\(774\) 4.45027i 0.00574971i
\(775\) −206.269 1038.87i −0.266154 1.34048i
\(776\) 117.751 0.151742