Properties

Label 76.3.b.b.39.6
Level $76$
Weight $3$
Character 76.39
Analytic conductor $2.071$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07085000914\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + 448 x^{5} - 2688 x^{4} + 3584 x^{3} + 1024 x^{2} - 8192 x + 16384\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.6
Root \(-0.0607713 - 1.99908i\) of defining polynomial
Character \(\chi\) \(=\) 76.39
Dual form 76.3.b.b.39.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0607713 + 1.99908i) q^{2} -5.37609i q^{3} +(-3.99261 - 0.242973i) q^{4} -5.82257 q^{5} +(10.7472 + 0.326712i) q^{6} -5.45132i q^{7} +(0.728358 - 7.96677i) q^{8} -19.9023 q^{9} +O(q^{10})\) \(q+(-0.0607713 + 1.99908i) q^{2} -5.37609i q^{3} +(-3.99261 - 0.242973i) q^{4} -5.82257 q^{5} +(10.7472 + 0.326712i) q^{6} -5.45132i q^{7} +(0.728358 - 7.96677i) q^{8} -19.9023 q^{9} +(0.353845 - 11.6398i) q^{10} -1.60915i q^{11} +(-1.30624 + 21.4646i) q^{12} +23.5274 q^{13} +(10.8976 + 0.331284i) q^{14} +31.3027i q^{15} +(15.8819 + 1.94019i) q^{16} -5.92676 q^{17} +(1.20949 - 39.7863i) q^{18} +4.35890i q^{19} +(23.2473 + 1.41473i) q^{20} -29.3068 q^{21} +(3.21681 + 0.0977900i) q^{22} -26.6121i q^{23} +(-42.8301 - 3.91572i) q^{24} +8.90234 q^{25} +(-1.42979 + 47.0331i) q^{26} +58.6120i q^{27} +(-1.32452 + 21.7650i) q^{28} -1.49241 q^{29} +(-62.5764 - 1.90230i) q^{30} -31.3933i q^{31} +(-4.84376 + 31.6313i) q^{32} -8.65093 q^{33} +(0.360177 - 11.8480i) q^{34} +31.7407i q^{35} +(79.4624 + 4.83573i) q^{36} +26.8255 q^{37} +(-8.71377 - 0.264896i) q^{38} -126.486i q^{39} +(-4.24092 + 46.3871i) q^{40} -44.0382 q^{41} +(1.78101 - 58.5865i) q^{42} -27.8586i q^{43} +(-0.390980 + 6.42471i) q^{44} +115.883 q^{45} +(53.1996 + 1.61725i) q^{46} +32.5166i q^{47} +(10.4307 - 85.3827i) q^{48} +19.2831 q^{49} +(-0.541007 + 17.7965i) q^{50} +31.8628i q^{51} +(-93.9360 - 5.71653i) q^{52} +76.7637 q^{53} +(-117.170 - 3.56193i) q^{54} +9.36938i q^{55} +(-43.4294 - 3.97051i) q^{56} +23.4338 q^{57} +(0.0906959 - 2.98345i) q^{58} +33.8895i q^{59} +(7.60570 - 124.979i) q^{60} +53.0162 q^{61} +(62.7575 + 1.90781i) q^{62} +108.494i q^{63} +(-62.9390 - 11.6053i) q^{64} -136.990 q^{65} +(0.525728 - 17.2939i) q^{66} -76.1917i q^{67} +(23.6632 + 1.44004i) q^{68} -143.069 q^{69} +(-63.4521 - 1.92892i) q^{70} -59.9326i q^{71} +(-14.4960 + 158.557i) q^{72} -49.8188 q^{73} +(-1.63022 + 53.6263i) q^{74} -47.8598i q^{75} +(1.05909 - 17.4034i) q^{76} -8.77198 q^{77} +(252.854 + 7.68670i) q^{78} +23.3990i q^{79} +(-92.4737 - 11.2969i) q^{80} +135.982 q^{81} +(2.67626 - 88.0358i) q^{82} +137.116i q^{83} +(117.011 + 7.12076i) q^{84} +34.5090 q^{85} +(55.6915 + 1.69300i) q^{86} +8.02335i q^{87} +(-12.8197 - 1.17204i) q^{88} +116.608 q^{89} +(-7.04235 + 231.659i) q^{90} -128.256i q^{91} +(-6.46602 + 106.252i) q^{92} -168.773 q^{93} +(-65.0032 - 1.97608i) q^{94} -25.3800i q^{95} +(170.053 + 26.0405i) q^{96} -65.7341 q^{97} +(-1.17186 + 38.5484i) q^{98} +32.0258i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} + O(q^{10}) \) \( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} - 12q^{10} + 4q^{12} + 54q^{13} + 30q^{14} + 58q^{16} + 34q^{17} + 36q^{18} + 32q^{20} - 38q^{21} + 36q^{22} - 98q^{24} - 86q^{25} - 16q^{26} + 18q^{28} + 54q^{29} - 204q^{30} + 72q^{32} + 20q^{33} - 82q^{34} + 96q^{36} + 100q^{37} - 148q^{40} + 224q^{41} + 224q^{42} - 96q^{44} - 168q^{45} + 46q^{46} + 296q^{48} - 220q^{49} - 58q^{50} - 288q^{52} + 14q^{53} - 128q^{54} + 12q^{56} + 38q^{57} - 72q^{58} + 188q^{60} + 28q^{61} + 396q^{62} - 118q^{64} - 472q^{65} - 32q^{66} + 30q^{68} + 122q^{69} + 156q^{70} + 80q^{72} + 70q^{73} - 224q^{74} + 228q^{77} + 274q^{78} - 348q^{80} + 334q^{81} - 400q^{82} - 216q^{84} + 48q^{85} - 124q^{86} + 472q^{88} + 416q^{90} + 126q^{92} - 176q^{93} - 88q^{94} - 106q^{96} + 308q^{97} + 68q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0607713 + 1.99908i −0.0303857 + 0.999538i
\(3\) 5.37609i 1.79203i −0.444024 0.896015i \(-0.646449\pi\)
0.444024 0.896015i \(-0.353551\pi\)
\(4\) −3.99261 0.242973i −0.998153 0.0607433i
\(5\) −5.82257 −1.16451 −0.582257 0.813005i \(-0.697830\pi\)
−0.582257 + 0.813005i \(0.697830\pi\)
\(6\) 10.7472 + 0.326712i 1.79120 + 0.0544520i
\(7\) 5.45132i 0.778760i −0.921077 0.389380i \(-0.872689\pi\)
0.921077 0.389380i \(-0.127311\pi\)
\(8\) 0.728358 7.96677i 0.0910448 0.995847i
\(9\) −19.9023 −2.21137
\(10\) 0.353845 11.6398i 0.0353845 1.16398i
\(11\) 1.60915i 0.146286i −0.997321 0.0731431i \(-0.976697\pi\)
0.997321 0.0731431i \(-0.0233030\pi\)
\(12\) −1.30624 + 21.4646i −0.108854 + 1.78872i
\(13\) 23.5274 1.80980 0.904901 0.425622i \(-0.139945\pi\)
0.904901 + 0.425622i \(0.139945\pi\)
\(14\) 10.8976 + 0.331284i 0.778401 + 0.0236631i
\(15\) 31.3027i 2.08684i
\(16\) 15.8819 + 1.94019i 0.992621 + 0.121262i
\(17\) −5.92676 −0.348633 −0.174316 0.984690i \(-0.555772\pi\)
−0.174316 + 0.984690i \(0.555772\pi\)
\(18\) 1.20949 39.7863i 0.0671940 2.21035i
\(19\) 4.35890i 0.229416i
\(20\) 23.2473 + 1.41473i 1.16236 + 0.0707364i
\(21\) −29.3068 −1.39556
\(22\) 3.21681 + 0.0977900i 0.146219 + 0.00444500i
\(23\) 26.6121i 1.15705i −0.815665 0.578524i \(-0.803629\pi\)
0.815665 0.578524i \(-0.196371\pi\)
\(24\) −42.8301 3.91572i −1.78459 0.163155i
\(25\) 8.90234 0.356094
\(26\) −1.42979 + 47.0331i −0.0549920 + 1.80897i
\(27\) 58.6120i 2.17081i
\(28\) −1.32452 + 21.7650i −0.0473044 + 0.777322i
\(29\) −1.49241 −0.0514625 −0.0257313 0.999669i \(-0.508191\pi\)
−0.0257313 + 0.999669i \(0.508191\pi\)
\(30\) −62.5764 1.90230i −2.08588 0.0634101i
\(31\) 31.3933i 1.01269i −0.862332 0.506343i \(-0.830997\pi\)
0.862332 0.506343i \(-0.169003\pi\)
\(32\) −4.84376 + 31.6313i −0.151368 + 0.988478i
\(33\) −8.65093 −0.262149
\(34\) 0.360177 11.8480i 0.0105934 0.348472i
\(35\) 31.7407i 0.906877i
\(36\) 79.4624 + 4.83573i 2.20729 + 0.134326i
\(37\) 26.8255 0.725015 0.362507 0.931981i \(-0.381921\pi\)
0.362507 + 0.931981i \(0.381921\pi\)
\(38\) −8.71377 0.264896i −0.229310 0.00697095i
\(39\) 126.486i 3.24322i
\(40\) −4.24092 + 46.3871i −0.106023 + 1.15968i
\(41\) −44.0382 −1.07410 −0.537051 0.843550i \(-0.680462\pi\)
−0.537051 + 0.843550i \(0.680462\pi\)
\(42\) 1.78101 58.5865i 0.0424051 1.39492i
\(43\) 27.8586i 0.647875i −0.946079 0.323937i \(-0.894993\pi\)
0.946079 0.323937i \(-0.105007\pi\)
\(44\) −0.390980 + 6.42471i −0.00888590 + 0.146016i
\(45\) 115.883 2.57517
\(46\) 53.1996 + 1.61725i 1.15651 + 0.0351577i
\(47\) 32.5166i 0.691843i 0.938264 + 0.345921i \(0.112434\pi\)
−0.938264 + 0.345921i \(0.887566\pi\)
\(48\) 10.4307 85.3827i 0.217305 1.77881i
\(49\) 19.2831 0.393533
\(50\) −0.541007 + 17.7965i −0.0108201 + 0.355929i
\(51\) 31.8628i 0.624760i
\(52\) −93.9360 5.71653i −1.80646 0.109933i
\(53\) 76.7637 1.44837 0.724186 0.689605i \(-0.242216\pi\)
0.724186 + 0.689605i \(0.242216\pi\)
\(54\) −117.170 3.56193i −2.16981 0.0659616i
\(55\) 9.36938i 0.170352i
\(56\) −43.4294 3.97051i −0.775526 0.0709020i
\(57\) 23.4338 0.411120
\(58\) 0.0906959 2.98345i 0.00156372 0.0514388i
\(59\) 33.8895i 0.574398i 0.957871 + 0.287199i \(0.0927241\pi\)
−0.957871 + 0.287199i \(0.907276\pi\)
\(60\) 7.60570 124.979i 0.126762 2.08299i
\(61\) 53.0162 0.869118 0.434559 0.900643i \(-0.356904\pi\)
0.434559 + 0.900643i \(0.356904\pi\)
\(62\) 62.7575 + 1.90781i 1.01222 + 0.0307711i
\(63\) 108.494i 1.72213i
\(64\) −62.9390 11.6053i −0.983422 0.181333i
\(65\) −136.990 −2.10754
\(66\) 0.525728 17.2939i 0.00796558 0.262028i
\(67\) 76.1917i 1.13719i −0.822618 0.568594i \(-0.807487\pi\)
0.822618 0.568594i \(-0.192513\pi\)
\(68\) 23.6632 + 1.44004i 0.347989 + 0.0211771i
\(69\) −143.069 −2.07346
\(70\) −63.4521 1.92892i −0.906459 0.0275561i
\(71\) 59.9326i 0.844121i −0.906568 0.422060i \(-0.861307\pi\)
0.906568 0.422060i \(-0.138693\pi\)
\(72\) −14.4960 + 158.557i −0.201334 + 2.20219i
\(73\) −49.8188 −0.682450 −0.341225 0.939982i \(-0.610842\pi\)
−0.341225 + 0.939982i \(0.610842\pi\)
\(74\) −1.63022 + 53.6263i −0.0220301 + 0.724680i
\(75\) 47.8598i 0.638131i
\(76\) 1.05909 17.4034i 0.0139355 0.228992i
\(77\) −8.77198 −0.113922
\(78\) 252.854 + 7.68670i 3.24172 + 0.0985474i
\(79\) 23.3990i 0.296190i 0.988973 + 0.148095i \(0.0473141\pi\)
−0.988973 + 0.148095i \(0.952686\pi\)
\(80\) −92.4737 11.2969i −1.15592 0.141212i
\(81\) 135.982 1.67879
\(82\) 2.67626 88.0358i 0.0326373 1.07361i
\(83\) 137.116i 1.65200i 0.563667 + 0.826002i \(0.309390\pi\)
−0.563667 + 0.826002i \(0.690610\pi\)
\(84\) 117.011 + 7.12076i 1.39298 + 0.0847709i
\(85\) 34.5090 0.405988
\(86\) 55.6915 + 1.69300i 0.647576 + 0.0196861i
\(87\) 8.02335i 0.0922224i
\(88\) −12.8197 1.17204i −0.145679 0.0133186i
\(89\) 116.608 1.31020 0.655101 0.755541i \(-0.272626\pi\)
0.655101 + 0.755541i \(0.272626\pi\)
\(90\) −7.04235 + 231.659i −0.0782483 + 2.57398i
\(91\) 128.256i 1.40940i
\(92\) −6.46602 + 106.252i −0.0702828 + 1.15491i
\(93\) −168.773 −1.81476
\(94\) −65.0032 1.97608i −0.691523 0.0210221i
\(95\) 25.3800i 0.267158i
\(96\) 170.053 + 26.0405i 1.77138 + 0.271255i
\(97\) −65.7341 −0.677671 −0.338836 0.940846i \(-0.610033\pi\)
−0.338836 + 0.940846i \(0.610033\pi\)
\(98\) −1.17186 + 38.5484i −0.0119577 + 0.393351i
\(99\) 32.0258i 0.323493i
\(100\) −35.5436 2.16303i −0.355436 0.0216303i
\(101\) 1.81406 0.0179609 0.00898047 0.999960i \(-0.497141\pi\)
0.00898047 + 0.999960i \(0.497141\pi\)
\(102\) −63.6961 1.93634i −0.624472 0.0189837i
\(103\) 0.494673i 0.00480265i 0.999997 + 0.00240133i \(0.000764367\pi\)
−0.999997 + 0.00240133i \(0.999236\pi\)
\(104\) 17.1364 187.438i 0.164773 1.80229i
\(105\) 170.641 1.62515
\(106\) −4.66503 + 153.457i −0.0440097 + 1.44770i
\(107\) 11.7361i 0.109684i 0.998495 + 0.0548418i \(0.0174654\pi\)
−0.998495 + 0.0548418i \(0.982535\pi\)
\(108\) 14.2411 234.015i 0.131862 2.16681i
\(109\) −28.9819 −0.265889 −0.132945 0.991123i \(-0.542443\pi\)
−0.132945 + 0.991123i \(0.542443\pi\)
\(110\) −18.7301 0.569390i −0.170274 0.00517627i
\(111\) 144.217i 1.29925i
\(112\) 10.5766 86.5775i 0.0944341 0.773013i
\(113\) −140.725 −1.24536 −0.622678 0.782478i \(-0.713955\pi\)
−0.622678 + 0.782478i \(0.713955\pi\)
\(114\) −1.42410 + 46.8460i −0.0124921 + 0.410930i
\(115\) 154.951i 1.34740i
\(116\) 5.95863 + 0.362616i 0.0513675 + 0.00312600i
\(117\) −468.251 −4.00215
\(118\) −67.7477 2.05951i −0.574133 0.0174535i
\(119\) 32.3086i 0.271501i
\(120\) 249.381 + 22.7996i 2.07818 + 0.189996i
\(121\) 118.411 0.978600
\(122\) −3.22186 + 105.983i −0.0264087 + 0.868716i
\(123\) 236.753i 1.92482i
\(124\) −7.62772 + 125.341i −0.0615138 + 1.01082i
\(125\) 93.7298 0.749838
\(126\) −216.888 6.59333i −1.72133 0.0523280i
\(127\) 50.4262i 0.397056i 0.980095 + 0.198528i \(0.0636161\pi\)
−0.980095 + 0.198528i \(0.936384\pi\)
\(128\) 27.0248 125.115i 0.211131 0.977458i
\(129\) −149.770 −1.16101
\(130\) 8.32507 273.854i 0.0640390 2.10657i
\(131\) 124.954i 0.953847i −0.878945 0.476924i \(-0.841752\pi\)
0.878945 0.476924i \(-0.158248\pi\)
\(132\) 34.5398 + 2.10194i 0.261665 + 0.0159238i
\(133\) 23.7618 0.178660
\(134\) 152.313 + 4.63027i 1.13666 + 0.0345542i
\(135\) 341.272i 2.52794i
\(136\) −4.31680 + 47.2171i −0.0317412 + 0.347185i
\(137\) 137.151 1.00110 0.500551 0.865707i \(-0.333131\pi\)
0.500551 + 0.865707i \(0.333131\pi\)
\(138\) 8.69449 286.006i 0.0630036 2.07251i
\(139\) 89.6885i 0.645241i 0.946528 + 0.322621i \(0.104564\pi\)
−0.946528 + 0.322621i \(0.895436\pi\)
\(140\) 7.71214 126.728i 0.0550867 0.905203i
\(141\) 174.812 1.23980
\(142\) 119.810 + 3.64218i 0.843731 + 0.0256492i
\(143\) 37.8591i 0.264749i
\(144\) −316.088 38.6144i −2.19505 0.268156i
\(145\) 8.68969 0.0599289
\(146\) 3.02756 99.5917i 0.0207367 0.682135i
\(147\) 103.668i 0.705222i
\(148\) −107.104 6.51788i −0.723676 0.0440398i
\(149\) 18.9194 0.126976 0.0634878 0.997983i \(-0.479778\pi\)
0.0634878 + 0.997983i \(0.479778\pi\)
\(150\) 95.6754 + 2.90850i 0.637836 + 0.0193900i
\(151\) 269.061i 1.78186i 0.454141 + 0.890930i \(0.349946\pi\)
−0.454141 + 0.890930i \(0.650054\pi\)
\(152\) 34.7264 + 3.17484i 0.228463 + 0.0208871i
\(153\) 117.956 0.770956
\(154\) 0.533085 17.5359i 0.00346159 0.113869i
\(155\) 182.790i 1.17929i
\(156\) −30.7326 + 505.008i −0.197004 + 3.23723i
\(157\) 11.4972 0.0732305 0.0366153 0.999329i \(-0.488342\pi\)
0.0366153 + 0.999329i \(0.488342\pi\)
\(158\) −46.7764 1.42199i −0.296053 0.00899993i
\(159\) 412.689i 2.59553i
\(160\) 28.2032 184.175i 0.176270 1.15110i
\(161\) −145.071 −0.901063
\(162\) −8.26381 + 271.839i −0.0510112 + 1.67802i
\(163\) 126.564i 0.776465i 0.921562 + 0.388232i \(0.126914\pi\)
−0.921562 + 0.388232i \(0.873086\pi\)
\(164\) 175.828 + 10.7001i 1.07212 + 0.0652445i
\(165\) 50.3706 0.305277
\(166\) −274.106 8.33274i −1.65124 0.0501972i
\(167\) 14.2424i 0.0852836i 0.999090 + 0.0426418i \(0.0135774\pi\)
−0.999090 + 0.0426418i \(0.986423\pi\)
\(168\) −21.3458 + 233.481i −0.127059 + 1.38977i
\(169\) 384.540 2.27539
\(170\) −2.09715 + 68.9860i −0.0123362 + 0.405800i
\(171\) 86.7523i 0.507323i
\(172\) −6.76889 + 111.229i −0.0393540 + 0.646678i
\(173\) −217.817 −1.25906 −0.629528 0.776978i \(-0.716752\pi\)
−0.629528 + 0.776978i \(0.716752\pi\)
\(174\) −16.0393 0.487590i −0.0921798 0.00280224i
\(175\) 48.5295i 0.277312i
\(176\) 3.12206 25.5564i 0.0177390 0.145207i
\(177\) 182.193 1.02934
\(178\) −7.08642 + 233.108i −0.0398114 + 1.30960i
\(179\) 180.223i 1.00684i −0.864043 0.503418i \(-0.832076\pi\)
0.864043 0.503418i \(-0.167924\pi\)
\(180\) −462.675 28.1564i −2.57042 0.156424i
\(181\) −95.0637 −0.525214 −0.262607 0.964903i \(-0.584582\pi\)
−0.262607 + 0.964903i \(0.584582\pi\)
\(182\) 256.393 + 7.79426i 1.40875 + 0.0428256i
\(183\) 285.020i 1.55748i
\(184\) −212.013 19.3831i −1.15224 0.105343i
\(185\) −156.194 −0.844290
\(186\) 10.2566 337.390i 0.0551428 1.81393i
\(187\) 9.53703i 0.0510001i
\(188\) 7.90066 129.826i 0.0420248 0.690565i
\(189\) 319.513 1.69054
\(190\) 50.7366 + 1.54238i 0.267035 + 0.00811777i
\(191\) 25.4789i 0.133397i 0.997773 + 0.0666987i \(0.0212466\pi\)
−0.997773 + 0.0666987i \(0.978753\pi\)
\(192\) −62.3913 + 338.366i −0.324955 + 1.76232i
\(193\) 339.566 1.75941 0.879705 0.475520i \(-0.157740\pi\)
0.879705 + 0.475520i \(0.157740\pi\)
\(194\) 3.99475 131.407i 0.0205915 0.677358i
\(195\) 736.471i 3.77678i
\(196\) −76.9900 4.68527i −0.392806 0.0239045i
\(197\) 136.859 0.694717 0.347358 0.937732i \(-0.387079\pi\)
0.347358 + 0.937732i \(0.387079\pi\)
\(198\) −64.0221 1.94625i −0.323344 0.00982955i
\(199\) 199.411i 1.00207i −0.865428 0.501034i \(-0.832953\pi\)
0.865428 0.501034i \(-0.167047\pi\)
\(200\) 6.48409 70.9230i 0.0324205 0.354615i
\(201\) −409.613 −2.03788
\(202\) −0.110243 + 3.62644i −0.000545755 + 0.0179527i
\(203\) 8.13563i 0.0400770i
\(204\) 7.74179 127.216i 0.0379500 0.623606i
\(205\) 256.416 1.25081
\(206\) −0.988890 0.0300619i −0.00480044 0.000145932i
\(207\) 529.643i 2.55866i
\(208\) 373.661 + 45.6478i 1.79645 + 0.219461i
\(209\) 7.01411 0.0335604
\(210\) −10.3701 + 341.124i −0.0493813 + 1.62440i
\(211\) 363.655i 1.72348i −0.507347 0.861742i \(-0.669374\pi\)
0.507347 0.861742i \(-0.330626\pi\)
\(212\) −306.488 18.6515i −1.44570 0.0879788i
\(213\) −322.203 −1.51269
\(214\) −23.4614 0.713221i −0.109633 0.00333281i
\(215\) 162.209i 0.754460i
\(216\) 466.948 + 42.6905i 2.16180 + 0.197641i
\(217\) −171.135 −0.788640
\(218\) 1.76127 57.9371i 0.00807922 0.265766i
\(219\) 267.831i 1.22297i
\(220\) 2.27651 37.4083i 0.0103478 0.170038i
\(221\) −139.441 −0.630956
\(222\) 288.300 + 8.76423i 1.29865 + 0.0394785i
\(223\) 268.968i 1.20614i 0.797690 + 0.603068i \(0.206055\pi\)
−0.797690 + 0.603068i \(0.793945\pi\)
\(224\) 172.432 + 26.4049i 0.769787 + 0.117879i
\(225\) −177.177 −0.787455
\(226\) 8.55206 281.320i 0.0378410 1.24478i
\(227\) 79.9913i 0.352384i −0.984356 0.176192i \(-0.943622\pi\)
0.984356 0.176192i \(-0.0563780\pi\)
\(228\) −93.5622 5.69379i −0.410361 0.0249728i
\(229\) 297.342 1.29843 0.649217 0.760603i \(-0.275097\pi\)
0.649217 + 0.760603i \(0.275097\pi\)
\(230\) −309.759 9.41657i −1.34678 0.0409416i
\(231\) 47.1590i 0.204151i
\(232\) −1.08701 + 11.8897i −0.00468539 + 0.0512488i
\(233\) −255.975 −1.09860 −0.549302 0.835624i \(-0.685106\pi\)
−0.549302 + 0.835624i \(0.685106\pi\)
\(234\) 28.4562 936.070i 0.121608 4.00030i
\(235\) 189.330i 0.805661i
\(236\) 8.23423 135.308i 0.0348908 0.573337i
\(237\) 125.795 0.530781
\(238\) −64.5875 1.96344i −0.271376 0.00824974i
\(239\) 148.674i 0.622067i −0.950399 0.311034i \(-0.899325\pi\)
0.950399 0.311034i \(-0.100675\pi\)
\(240\) −60.7333 + 497.147i −0.253055 + 2.07144i
\(241\) −330.295 −1.37052 −0.685259 0.728299i \(-0.740311\pi\)
−0.685259 + 0.728299i \(0.740311\pi\)
\(242\) −7.19597 + 236.712i −0.0297354 + 0.978148i
\(243\) 203.544i 0.837632i
\(244\) −211.673 12.8815i −0.867513 0.0527930i
\(245\) −112.277 −0.458274
\(246\) −473.288 14.3878i −1.92394 0.0584871i
\(247\) 102.554i 0.415197i
\(248\) −250.103 22.8655i −1.00848 0.0921997i
\(249\) 737.150 2.96044
\(250\) −5.69608 + 187.373i −0.0227843 + 0.749492i
\(251\) 253.493i 1.00993i −0.863139 0.504966i \(-0.831505\pi\)
0.863139 0.504966i \(-0.168495\pi\)
\(252\) 26.3611 433.175i 0.104608 1.71895i
\(253\) −42.8228 −0.169260
\(254\) −100.806 3.06446i −0.396873 0.0120648i
\(255\) 185.523i 0.727542i
\(256\) 248.471 + 61.6281i 0.970591 + 0.240735i
\(257\) 254.160 0.988950 0.494475 0.869192i \(-0.335360\pi\)
0.494475 + 0.869192i \(0.335360\pi\)
\(258\) 9.10175 299.403i 0.0352781 1.16048i
\(259\) 146.235i 0.564613i
\(260\) 546.949 + 33.2849i 2.10365 + 0.128019i
\(261\) 29.7025 0.113803
\(262\) 249.793 + 7.59362i 0.953407 + 0.0289833i
\(263\) 190.047i 0.722613i −0.932447 0.361306i \(-0.882331\pi\)
0.932447 0.361306i \(-0.117669\pi\)
\(264\) −6.30097 + 68.9200i −0.0238673 + 0.261060i
\(265\) −446.962 −1.68665
\(266\) −1.44403 + 47.5016i −0.00542870 + 0.178577i
\(267\) 626.895i 2.34792i
\(268\) −18.5125 + 304.204i −0.0690766 + 1.13509i
\(269\) 233.427 0.867758 0.433879 0.900971i \(-0.357145\pi\)
0.433879 + 0.900971i \(0.357145\pi\)
\(270\) 682.230 + 20.7396i 2.52678 + 0.0768132i
\(271\) 2.73196i 0.0100810i 0.999987 + 0.00504051i \(0.00160445\pi\)
−0.999987 + 0.00504051i \(0.998396\pi\)
\(272\) −94.1283 11.4991i −0.346060 0.0422760i
\(273\) −689.514 −2.52569
\(274\) −8.33485 + 274.175i −0.0304192 + 1.00064i
\(275\) 14.3252i 0.0520916i
\(276\) 571.219 + 34.7619i 2.06964 + 0.125949i
\(277\) −20.4896 −0.0739697 −0.0369848 0.999316i \(-0.511775\pi\)
−0.0369848 + 0.999316i \(0.511775\pi\)
\(278\) −179.294 5.45049i −0.644943 0.0196061i
\(279\) 624.800i 2.23942i
\(280\) 252.871 + 23.1186i 0.903111 + 0.0825664i
\(281\) −285.339 −1.01544 −0.507721 0.861522i \(-0.669512\pi\)
−0.507721 + 0.861522i \(0.669512\pi\)
\(282\) −10.6236 + 349.463i −0.0376722 + 1.23923i
\(283\) 4.45505i 0.0157422i 0.999969 + 0.00787112i \(0.00250548\pi\)
−0.999969 + 0.00787112i \(0.997495\pi\)
\(284\) −14.5620 + 239.288i −0.0512746 + 0.842562i
\(285\) −136.445 −0.478755
\(286\) 75.6833 + 2.30075i 0.264627 + 0.00804458i
\(287\) 240.066i 0.836468i
\(288\) 96.4022 629.537i 0.334730 2.18589i
\(289\) −253.874 −0.878455
\(290\) −0.528084 + 17.3713i −0.00182098 + 0.0599012i
\(291\) 353.392i 1.21441i
\(292\) 198.907 + 12.1046i 0.681190 + 0.0414542i
\(293\) 326.981 1.11598 0.557988 0.829849i \(-0.311574\pi\)
0.557988 + 0.829849i \(0.311574\pi\)
\(294\) 207.240 + 6.30002i 0.704897 + 0.0214286i
\(295\) 197.324i 0.668895i
\(296\) 19.5386 213.713i 0.0660088 0.722004i
\(297\) 94.3153 0.317560
\(298\) −1.14975 + 37.8213i −0.00385824 + 0.126917i
\(299\) 626.114i 2.09403i
\(300\) −11.6286 + 191.086i −0.0387621 + 0.636952i
\(301\) −151.866 −0.504539
\(302\) −537.873 16.3512i −1.78104 0.0541430i
\(303\) 9.75253i 0.0321866i
\(304\) −8.45711 + 69.2277i −0.0278195 + 0.227723i
\(305\) −308.690 −1.01210
\(306\) −7.16836 + 235.804i −0.0234260 + 0.770600i
\(307\) 352.091i 1.14688i 0.819249 + 0.573438i \(0.194391\pi\)
−0.819249 + 0.573438i \(0.805609\pi\)
\(308\) 35.0231 + 2.13136i 0.113711 + 0.00691998i
\(309\) 2.65941 0.00860650
\(310\) −365.410 11.1084i −1.17874 0.0358334i
\(311\) 75.4387i 0.242568i 0.992618 + 0.121284i \(0.0387012\pi\)
−0.992618 + 0.121284i \(0.961299\pi\)
\(312\) −1007.68 92.1268i −3.22975 0.295278i
\(313\) −13.1951 −0.0421569 −0.0210784 0.999778i \(-0.506710\pi\)
−0.0210784 + 0.999778i \(0.506710\pi\)
\(314\) −0.698699 + 22.9838i −0.00222516 + 0.0731967i
\(315\) 631.714i 2.00544i
\(316\) 5.68533 93.4232i 0.0179915 0.295643i
\(317\) 276.427 0.872011 0.436005 0.899944i \(-0.356393\pi\)
0.436005 + 0.899944i \(0.356393\pi\)
\(318\) 824.996 + 25.0796i 2.59433 + 0.0788668i
\(319\) 2.40151i 0.00752826i
\(320\) 366.467 + 67.5729i 1.14521 + 0.211165i
\(321\) 63.0946 0.196556
\(322\) 8.81616 290.008i 0.0273794 0.900647i
\(323\) 25.8341i 0.0799818i
\(324\) −542.924 33.0400i −1.67569 0.101975i
\(325\) 209.449 0.644459
\(326\) −253.011 7.69145i −0.776106 0.0235934i
\(327\) 155.809i 0.476481i
\(328\) −32.0756 + 350.843i −0.0977914 + 1.06964i
\(329\) 177.258 0.538779
\(330\) −3.06109 + 100.695i −0.00927603 + 0.305136i
\(331\) 550.110i 1.66196i 0.556301 + 0.830981i \(0.312220\pi\)
−0.556301 + 0.830981i \(0.687780\pi\)
\(332\) 33.3156 547.453i 0.100348 1.64895i
\(333\) −533.891 −1.60328
\(334\) −28.4716 0.865527i −0.0852442 0.00259140i
\(335\) 443.631i 1.32427i
\(336\) −465.448 56.8609i −1.38526 0.169229i
\(337\) −179.034 −0.531259 −0.265630 0.964075i \(-0.585580\pi\)
−0.265630 + 0.964075i \(0.585580\pi\)
\(338\) −23.3690 + 768.725i −0.0691391 + 2.27433i
\(339\) 756.551i 2.23171i
\(340\) −137.781 8.38475i −0.405238 0.0246610i
\(341\) −50.5164 −0.148142
\(342\) 173.424 + 5.27205i 0.507089 + 0.0154154i
\(343\) 372.233i 1.08523i
\(344\) −221.943 20.2910i −0.645184 0.0589856i
\(345\) 833.030 2.41458
\(346\) 13.2370 435.432i 0.0382573 1.25848i
\(347\) 161.757i 0.466157i 0.972458 + 0.233079i \(0.0748800\pi\)
−0.972458 + 0.233079i \(0.925120\pi\)
\(348\) 1.94946 32.0341i 0.00560189 0.0920521i
\(349\) −472.810 −1.35476 −0.677378 0.735635i \(-0.736884\pi\)
−0.677378 + 0.735635i \(0.736884\pi\)
\(350\) 97.0142 + 2.94920i 0.277184 + 0.00842629i
\(351\) 1378.99i 3.92874i
\(352\) 50.8994 + 7.79433i 0.144601 + 0.0221430i
\(353\) 319.200 0.904249 0.452125 0.891955i \(-0.350666\pi\)
0.452125 + 0.891955i \(0.350666\pi\)
\(354\) −11.0721 + 364.217i −0.0312771 + 1.02886i
\(355\) 348.962i 0.982991i
\(356\) −465.571 28.3326i −1.30778 0.0795860i
\(357\) 173.694 0.486538
\(358\) 360.281 + 10.9524i 1.00637 + 0.0305933i
\(359\) 545.770i 1.52025i −0.649776 0.760126i \(-0.725137\pi\)
0.649776 0.760126i \(-0.274863\pi\)
\(360\) 84.4042 923.212i 0.234456 2.56448i
\(361\) −19.0000 −0.0526316
\(362\) 5.77715 190.040i 0.0159590 0.524971i
\(363\) 636.586i 1.75368i
\(364\) −31.1626 + 512.075i −0.0856117 + 1.40680i
\(365\) 290.074 0.794723
\(366\) 569.776 + 17.3210i 1.55677 + 0.0473252i
\(367\) 90.4491i 0.246455i −0.992378 0.123228i \(-0.960675\pi\)
0.992378 0.123228i \(-0.0393246\pi\)
\(368\) 51.6327 422.651i 0.140306 1.14851i
\(369\) 876.464 2.37524
\(370\) 9.49210 312.243i 0.0256543 0.843900i
\(371\) 418.464i 1.12793i
\(372\) 673.845 + 41.0073i 1.81141 + 0.110235i
\(373\) 468.975 1.25731 0.628653 0.777686i \(-0.283606\pi\)
0.628653 + 0.777686i \(0.283606\pi\)
\(374\) −19.0652 0.579578i −0.0509766 0.00154967i
\(375\) 503.900i 1.34373i
\(376\) 259.052 + 23.6837i 0.688969 + 0.0629886i
\(377\) −35.1127 −0.0931370
\(378\) −19.4172 + 638.730i −0.0513683 + 1.68976i
\(379\) 196.529i 0.518545i −0.965804 0.259273i \(-0.916517\pi\)
0.965804 0.259273i \(-0.0834828\pi\)
\(380\) −6.16666 + 101.333i −0.0162280 + 0.266665i
\(381\) 271.096 0.711537
\(382\) −50.9342 1.54839i −0.133336 0.00405337i
\(383\) 24.8045i 0.0647637i −0.999476 0.0323819i \(-0.989691\pi\)
0.999476 0.0323819i \(-0.0103093\pi\)
\(384\) −672.627 145.288i −1.75163 0.378354i
\(385\) 51.0755 0.132664
\(386\) −20.6359 + 678.819i −0.0534608 + 1.75860i
\(387\) 554.452i 1.43269i
\(388\) 262.451 + 15.9716i 0.676420 + 0.0411639i
\(389\) −126.462 −0.325095 −0.162547 0.986701i \(-0.551971\pi\)
−0.162547 + 0.986701i \(0.551971\pi\)
\(390\) −1472.26 44.7563i −3.77503 0.114760i
\(391\) 157.723i 0.403385i
\(392\) 14.0450 153.624i 0.0358291 0.391898i
\(393\) −671.764 −1.70932
\(394\) −8.31712 + 273.592i −0.0211094 + 0.694396i
\(395\) 136.242i 0.344917i
\(396\) 7.78141 127.867i 0.0196500 0.322896i
\(397\) 403.878 1.01732 0.508662 0.860966i \(-0.330140\pi\)
0.508662 + 0.860966i \(0.330140\pi\)
\(398\) 398.639 + 12.1185i 1.00160 + 0.0304485i
\(399\) 127.745i 0.320164i
\(400\) 141.386 + 17.2723i 0.353466 + 0.0431807i
\(401\) 345.608 0.861865 0.430933 0.902384i \(-0.358185\pi\)
0.430933 + 0.902384i \(0.358185\pi\)
\(402\) 24.8927 818.848i 0.0619222 2.03694i
\(403\) 738.603i 1.83276i
\(404\) −7.24282 0.440767i −0.0179278 0.00109101i
\(405\) −791.766 −1.95498
\(406\) −16.2637 0.494413i −0.0400585 0.00121777i
\(407\) 43.1663i 0.106060i
\(408\) 253.843 + 23.2075i 0.622165 + 0.0568811i
\(409\) −429.506 −1.05014 −0.525069 0.851060i \(-0.675960\pi\)
−0.525069 + 0.851060i \(0.675960\pi\)
\(410\) −15.5827 + 512.595i −0.0380066 + 1.25023i
\(411\) 737.336i 1.79401i
\(412\) 0.120192 1.97504i 0.000291729 0.00479378i
\(413\) 184.742 0.447318
\(414\) −1058.80 32.1871i −2.55748 0.0777466i
\(415\) 798.370i 1.92378i
\(416\) −113.961 + 744.203i −0.273945 + 1.78895i
\(417\) 482.174 1.15629
\(418\) −0.426257 + 14.0218i −0.00101975 + 0.0335449i
\(419\) 345.206i 0.823881i 0.911211 + 0.411940i \(0.135149\pi\)
−0.911211 + 0.411940i \(0.864851\pi\)
\(420\) −681.303 41.4611i −1.62215 0.0987170i
\(421\) −195.468 −0.464295 −0.232148 0.972681i \(-0.574575\pi\)
−0.232148 + 0.972681i \(0.574575\pi\)
\(422\) 726.974 + 22.0998i 1.72269 + 0.0523692i
\(423\) 647.156i 1.52992i
\(424\) 55.9115 611.559i 0.131867 1.44236i
\(425\) −52.7620 −0.124146
\(426\) 19.5807 644.108i 0.0459641 1.51199i
\(427\) 289.008i 0.676834i
\(428\) 2.85157 46.8579i 0.00666254 0.109481i
\(429\) −203.534 −0.474438
\(430\) −324.268 9.85764i −0.754111 0.0229247i
\(431\) 643.698i 1.49350i 0.665106 + 0.746749i \(0.268386\pi\)
−0.665106 + 0.746749i \(0.731614\pi\)
\(432\) −113.719 + 930.871i −0.263238 + 2.15479i
\(433\) −755.385 −1.74454 −0.872269 0.489026i \(-0.837352\pi\)
−0.872269 + 0.489026i \(0.837352\pi\)
\(434\) 10.4001 342.112i 0.0239633 0.788275i
\(435\) 46.7165i 0.107394i
\(436\) 115.714 + 7.04183i 0.265398 + 0.0161510i
\(437\) 115.999 0.265445
\(438\) −535.414 16.2764i −1.22241 0.0371608i
\(439\) 522.862i 1.19103i 0.803345 + 0.595514i \(0.203052\pi\)
−0.803345 + 0.595514i \(0.796948\pi\)
\(440\) 74.6437 + 6.82426i 0.169645 + 0.0155097i
\(441\) −383.779 −0.870247
\(442\) 8.47403 278.754i 0.0191720 0.630665i
\(443\) 5.86286i 0.0132345i 0.999978 + 0.00661723i \(0.00210634\pi\)
−0.999978 + 0.00661723i \(0.997894\pi\)
\(444\) −35.0407 + 575.801i −0.0789206 + 1.29685i
\(445\) −678.959 −1.52575
\(446\) −537.688 16.3455i −1.20558 0.0366492i
\(447\) 101.712i 0.227544i
\(448\) −63.2644 + 343.101i −0.141215 + 0.765850i
\(449\) 626.982 1.39640 0.698199 0.715904i \(-0.253985\pi\)
0.698199 + 0.715904i \(0.253985\pi\)
\(450\) 10.7673 354.191i 0.0239273 0.787092i
\(451\) 70.8640i 0.157126i
\(452\) 561.861 + 34.1924i 1.24306 + 0.0756470i
\(453\) 1446.50 3.19315
\(454\) 159.909 + 4.86117i 0.352222 + 0.0107074i
\(455\) 746.777i 1.64127i
\(456\) 17.0682 186.692i 0.0374303 0.409412i
\(457\) −451.537 −0.988046 −0.494023 0.869449i \(-0.664474\pi\)
−0.494023 + 0.869449i \(0.664474\pi\)
\(458\) −18.0698 + 594.408i −0.0394538 + 1.29784i
\(459\) 347.379i 0.756817i
\(460\) 37.6489 618.659i 0.0818454 1.34491i
\(461\) 50.7723 0.110135 0.0550675 0.998483i \(-0.482463\pi\)
0.0550675 + 0.998483i \(0.482463\pi\)
\(462\) −94.2744 2.86591i −0.204057 0.00620327i
\(463\) 69.7862i 0.150726i 0.997156 + 0.0753631i \(0.0240116\pi\)
−0.997156 + 0.0753631i \(0.975988\pi\)
\(464\) −23.7024 2.89557i −0.0510828 0.00624046i
\(465\) 982.693 2.11332
\(466\) 15.5559 511.713i 0.0333818 1.09810i
\(467\) 461.829i 0.988927i 0.869198 + 0.494464i \(0.164635\pi\)
−0.869198 + 0.494464i \(0.835365\pi\)
\(468\) 1869.55 + 113.772i 3.99476 + 0.243103i
\(469\) −415.345 −0.885597
\(470\) 378.486 + 11.5058i 0.805289 + 0.0244805i
\(471\) 61.8099i 0.131231i
\(472\) 269.990 + 24.6837i 0.572012 + 0.0522959i
\(473\) −44.8286 −0.0947751
\(474\) −7.64474 + 251.474i −0.0161281 + 0.530536i
\(475\) 38.8044i 0.0816935i
\(476\) 7.85013 128.996i 0.0164919 0.271000i
\(477\) −1527.78 −3.20289
\(478\) 297.211 + 9.03512i 0.621780 + 0.0189019i
\(479\) 814.201i 1.69979i 0.526949 + 0.849897i \(0.323336\pi\)
−0.526949 + 0.849897i \(0.676664\pi\)
\(480\) −990.144 151.623i −2.06280 0.315881i
\(481\) 631.136 1.31213
\(482\) 20.0725 660.285i 0.0416441 1.36989i
\(483\) 779.915i 1.61473i
\(484\) −472.768 28.7706i −0.976793 0.0594434i
\(485\) 382.742 0.789158
\(486\) 406.901 + 12.3697i 0.837245 + 0.0254520i
\(487\) 149.015i 0.305986i −0.988227 0.152993i \(-0.951109\pi\)
0.988227 0.152993i \(-0.0488912\pi\)
\(488\) 38.6148 422.368i 0.0791286 0.865508i
\(489\) 680.418 1.39145
\(490\) 6.82323 224.451i 0.0139250 0.458063i
\(491\) 367.294i 0.748053i 0.927418 + 0.374027i \(0.122023\pi\)
−0.927418 + 0.374027i \(0.877977\pi\)
\(492\) 57.5247 945.265i 0.116920 1.92127i
\(493\) 8.84517 0.0179415
\(494\) −205.013 6.23232i −0.415005 0.0126160i
\(495\) 186.473i 0.376712i
\(496\) 60.9091 498.586i 0.122801 1.00521i
\(497\) −326.712 −0.657368
\(498\) −44.7976 + 1473.62i −0.0899549 + 2.95907i
\(499\) 138.107i 0.276767i 0.990379 + 0.138384i \(0.0441907\pi\)
−0.990379 + 0.138384i \(0.955809\pi\)
\(500\) −374.227 22.7738i −0.748454 0.0455476i
\(501\) 76.5682 0.152831
\(502\) 506.752 + 15.4051i 1.00947 + 0.0306875i
\(503\) 31.6936i 0.0630092i −0.999504 0.0315046i \(-0.989970\pi\)
0.999504 0.0315046i \(-0.0100299\pi\)
\(504\) 864.348 + 79.0225i 1.71498 + 0.156791i
\(505\) −10.5625 −0.0209158
\(506\) 2.60240 85.6061i 0.00514308 0.169182i
\(507\) 2067.32i 4.07756i
\(508\) 12.2522 201.332i 0.0241185 0.396323i
\(509\) −564.839 −1.10970 −0.554852 0.831949i \(-0.687225\pi\)
−0.554852 + 0.831949i \(0.687225\pi\)
\(510\) 370.875 + 11.2745i 0.727206 + 0.0221068i
\(511\) 271.578i 0.531465i
\(512\) −138.299 + 492.968i −0.270116 + 0.962828i
\(513\) −255.484 −0.498019
\(514\) −15.4457 + 508.086i −0.0300499 + 0.988494i
\(515\) 2.88027i 0.00559276i
\(516\) 597.975 + 36.3902i 1.15887 + 0.0705236i
\(517\) 52.3240 0.101207
\(518\) 292.334 + 8.88687i 0.564352 + 0.0171561i
\(519\) 1171.00i 2.25627i
\(520\) −99.7779 + 1091.37i −0.191881 + 2.09879i
\(521\) −304.845 −0.585114 −0.292557 0.956248i \(-0.594506\pi\)
−0.292557 + 0.956248i \(0.594506\pi\)
\(522\) −1.80506 + 59.3776i −0.00345797 + 0.113750i
\(523\) 812.948i 1.55439i 0.629257 + 0.777197i \(0.283359\pi\)
−0.629257 + 0.777197i \(0.716641\pi\)
\(524\) −30.3604 + 498.893i −0.0579398 + 0.952086i
\(525\) −260.899 −0.496951
\(526\) 379.919 + 11.5494i 0.722279 + 0.0219571i
\(527\) 186.060i 0.353055i
\(528\) −137.393 16.7845i −0.260215 0.0317888i
\(529\) −179.204 −0.338759
\(530\) 27.1625 893.512i 0.0512500 1.68587i
\(531\) 674.480i 1.27021i
\(532\) −94.8715 5.77347i −0.178330 0.0108524i
\(533\) −1036.11 −1.94391
\(534\) 1253.21 + 38.0973i 2.34684 + 0.0713432i
\(535\) 68.3345i 0.127728i
\(536\) −607.002 55.4948i −1.13247 0.103535i
\(537\) −968.898 −1.80428
\(538\) −14.1857 + 466.638i −0.0263674 + 0.867357i
\(539\) 31.0294i 0.0575684i
\(540\) −82.9200 + 1362.57i −0.153556 + 2.52328i
\(541\) −396.300 −0.732532 −0.366266 0.930510i \(-0.619364\pi\)
−0.366266 + 0.930510i \(0.619364\pi\)
\(542\) −5.46139 0.166025i −0.0100764 0.000306319i
\(543\) 511.071i 0.941199i
\(544\) 28.7078 187.471i 0.0527717 0.344616i
\(545\) 168.749 0.309632
\(546\) 41.9026 1378.39i 0.0767448 2.52452i
\(547\) 526.396i 0.962333i 0.876629 + 0.481167i \(0.159787\pi\)
−0.876629 + 0.481167i \(0.840213\pi\)
\(548\) −547.591 33.3240i −0.999254 0.0608102i
\(549\) −1055.15 −1.92194
\(550\) 28.6371 + 0.870560i 0.0520675 + 0.00158284i
\(551\) 6.50528i 0.0118063i
\(552\) −104.205 + 1139.80i −0.188778 + 2.06485i
\(553\) 127.555 0.230661
\(554\) 1.24518 40.9603i 0.00224762 0.0739355i
\(555\) 839.711i 1.51299i
\(556\) 21.7919 358.092i 0.0391940 0.644050i
\(557\) 68.8105 0.123538 0.0617688 0.998090i \(-0.480326\pi\)
0.0617688 + 0.998090i \(0.480326\pi\)
\(558\) −1249.02 37.9699i −2.23839 0.0680464i
\(559\) 655.442i 1.17253i
\(560\) −61.5832 + 504.104i −0.109970 + 0.900185i
\(561\) 51.2719 0.0913938
\(562\) 17.3404 570.415i 0.0308549 1.01497i
\(563\) 588.997i 1.04618i −0.852279 0.523088i \(-0.824780\pi\)
0.852279 0.523088i \(-0.175220\pi\)
\(564\) −697.957 42.4746i −1.23751 0.0753096i
\(565\) 819.383 1.45023
\(566\) −8.90599 0.270739i −0.0157350 0.000478338i
\(567\) 741.282i 1.30738i
\(568\) −477.469 43.6524i −0.840615 0.0768528i
\(569\) −421.857 −0.741401 −0.370700 0.928752i \(-0.620882\pi\)
−0.370700 + 0.928752i \(0.620882\pi\)
\(570\) 8.29195 272.764i 0.0145473 0.478534i
\(571\) 393.676i 0.689451i −0.938704 0.344725i \(-0.887972\pi\)
0.938704 0.344725i \(-0.112028\pi\)
\(572\) −9.19875 + 151.157i −0.0160817 + 0.264260i
\(573\) 136.977 0.239052
\(574\) −479.911 14.5892i −0.836082 0.0254166i
\(575\) 236.910i 0.412017i
\(576\) 1252.63 + 230.973i 2.17471 + 0.400995i
\(577\) 703.416 1.21909 0.609546 0.792751i \(-0.291352\pi\)
0.609546 + 0.792751i \(0.291352\pi\)
\(578\) 15.4282 507.513i 0.0266924 0.878050i
\(579\) 1825.54i 3.15292i
\(580\) −34.6946 2.11136i −0.0598182 0.00364027i
\(581\) 747.465 1.28651
\(582\) −706.458 21.4761i −1.21385 0.0369006i
\(583\) 123.524i 0.211877i
\(584\) −36.2860 + 396.895i −0.0621335 + 0.679615i
\(585\) 2726.43 4.66056
\(586\) −19.8711 + 653.660i −0.0339097 + 1.11546i
\(587\) 56.2392i 0.0958078i 0.998852 + 0.0479039i \(0.0152541\pi\)
−0.998852 + 0.0479039i \(0.984746\pi\)
\(588\) −25.1884 + 413.905i −0.0428375 + 0.703920i
\(589\) 136.840 0.232326
\(590\) 394.466 + 11.9916i 0.668586 + 0.0203248i
\(591\) 735.768i 1.24495i
\(592\) 426.041 + 52.0468i 0.719665 + 0.0879169i
\(593\) 553.916 0.934090 0.467045 0.884233i \(-0.345319\pi\)
0.467045 + 0.884233i \(0.345319\pi\)
\(594\) −5.73167 + 188.544i −0.00964927 + 0.317413i
\(595\) 188.119i 0.316167i
\(596\) −75.5377 4.59690i −0.126741 0.00771291i
\(597\) −1072.05 −1.79574
\(598\) 1251.65 + 38.0498i 2.09306 + 0.0636284i
\(599\) 724.179i 1.20898i −0.796613 0.604490i \(-0.793377\pi\)
0.796613 0.604490i \(-0.206623\pi\)
\(600\) −381.288 34.8591i −0.635480 0.0580984i
\(601\) −393.734 −0.655132 −0.327566 0.944828i \(-0.606228\pi\)
−0.327566 + 0.944828i \(0.606228\pi\)
\(602\) 9.22911 303.592i 0.0153308 0.504306i
\(603\) 1516.39i 2.51475i
\(604\) 65.3745 1074.26i 0.108236 1.77857i
\(605\) −689.454 −1.13959
\(606\) 19.4960 + 0.592674i 0.0321717 + 0.000978010i
\(607\) 860.362i 1.41740i 0.705510 + 0.708700i \(0.250718\pi\)
−0.705510 + 0.708700i \(0.749282\pi\)
\(608\) −137.878 21.1135i −0.226772 0.0347261i
\(609\) 43.7379 0.0718191
\(610\) 18.7595 617.096i 0.0307533 1.01163i
\(611\) 765.032i 1.25210i
\(612\) −470.954 28.6602i −0.769533 0.0468304i
\(613\) 563.747 0.919652 0.459826 0.888009i \(-0.347912\pi\)
0.459826 + 0.888009i \(0.347912\pi\)
\(614\) −703.856 21.3970i −1.14635 0.0348486i
\(615\) 1378.51i 2.24149i
\(616\) −6.38914 + 69.8844i −0.0103720 + 0.113449i
\(617\) −677.849 −1.09862 −0.549310 0.835619i \(-0.685109\pi\)
−0.549310 + 0.835619i \(0.685109\pi\)
\(618\) −0.161616 + 5.31636i −0.000261514 + 0.00860252i
\(619\) 997.063i 1.61076i 0.592756 + 0.805382i \(0.298040\pi\)
−0.592756 + 0.805382i \(0.701960\pi\)
\(620\) 44.4129 729.808i 0.0716338 1.17711i
\(621\) 1559.79 2.51174
\(622\) −150.808 4.58451i −0.242456 0.00737060i
\(623\) 635.668i 1.02033i
\(624\) 245.407 2008.84i 0.393280 3.21929i
\(625\) −768.307 −1.22929
\(626\) 0.801884 26.3780i 0.00128096 0.0421374i
\(627\) 37.7085i 0.0601412i
\(628\) −45.9038 2.79351i −0.0730953 0.00444826i
\(629\) −158.988 −0.252764
\(630\) 1262.85 + 38.3901i 2.00452 + 0.0609367i
\(631\) 1071.78i 1.69854i −0.527959 0.849270i \(-0.677042\pi\)
0.527959 0.849270i \(-0.322958\pi\)
\(632\) 186.415 + 17.0429i 0.294960 + 0.0269665i
\(633\) −1955.04 −3.08853
\(634\) −16.7989 + 552.599i −0.0264966 + 0.871608i
\(635\) 293.610i 0.462378i
\(636\) −100.272 + 1647.71i −0.157661 + 2.59073i
\(637\) 453.682 0.712216
\(638\) −4.80081 0.145943i −0.00752478 0.000228751i
\(639\) 1192.80i 1.86666i
\(640\) −157.354 + 728.489i −0.245866 + 1.13826i
\(641\) −627.241 −0.978536 −0.489268 0.872134i \(-0.662736\pi\)
−0.489268 + 0.872134i \(0.662736\pi\)
\(642\) −3.83434 + 126.131i −0.00597249 + 0.196466i
\(643\) 620.131i 0.964433i −0.876052 0.482217i \(-0.839832\pi\)
0.876052 0.482217i \(-0.160168\pi\)
\(644\) 579.213 + 35.2484i 0.899399 + 0.0547335i
\(645\) 872.049 1.35201
\(646\) 51.6444 + 1.56997i 0.0799449 + 0.00243030i
\(647\) 1270.23i 1.96327i 0.190778 + 0.981633i \(0.438899\pi\)
−0.190778 + 0.981633i \(0.561101\pi\)
\(648\) 99.0437 1083.34i 0.152845 1.67182i
\(649\) 54.5332 0.0840265
\(650\) −12.7285 + 418.705i −0.0195823 + 0.644162i
\(651\) 920.036i 1.41327i
\(652\) 30.7516 505.320i 0.0471650 0.775031i
\(653\) 775.383 1.18742 0.593708 0.804681i \(-0.297663\pi\)
0.593708 + 0.804681i \(0.297663\pi\)
\(654\) −311.475 9.46874i −0.476261 0.0144782i
\(655\) 727.554i 1.11077i
\(656\) −699.412 85.4427i −1.06618 0.130248i
\(657\) 991.512 1.50915
\(658\) −10.7722 + 354.353i −0.0163712 + 0.538531i
\(659\) 516.735i 0.784119i −0.919940 0.392060i \(-0.871763\pi\)
0.919940 0.392060i \(-0.128237\pi\)
\(660\) −201.110 12.2387i −0.304713 0.0185435i
\(661\) −987.675 −1.49421 −0.747107 0.664704i \(-0.768558\pi\)
−0.747107 + 0.664704i \(0.768558\pi\)
\(662\) −1099.71 33.4309i −1.66119 0.0504998i
\(663\) 749.649i 1.13069i
\(664\) 1092.37 + 99.8698i 1.64514 + 0.150406i
\(665\) −138.355 −0.208052
\(666\) 32.4453 1067.29i 0.0487166 1.60254i
\(667\) 39.7163i 0.0595446i
\(668\) 3.46051 56.8643i 0.00518041 0.0851261i
\(669\) 1446.00 2.16143
\(670\) −886.853 26.9601i −1.32366 0.0402389i
\(671\) 85.3109i 0.127140i
\(672\) 141.955 927.011i 0.211243 1.37948i
\(673\) −237.022 −0.352187 −0.176094 0.984373i \(-0.556346\pi\)
−0.176094 + 0.984373i \(0.556346\pi\)
\(674\) 10.8802 357.904i 0.0161427 0.531014i
\(675\) 521.784i 0.773013i
\(676\) −1535.32 93.4329i −2.27118 0.138214i
\(677\) 894.692 1.32155 0.660777 0.750582i \(-0.270227\pi\)
0.660777 + 0.750582i \(0.270227\pi\)
\(678\) −1512.40 45.9766i −2.23068 0.0678121i
\(679\) 358.338i 0.527743i
\(680\) 25.1349 274.925i 0.0369631 0.404302i
\(681\) −430.040 −0.631483
\(682\) 3.06995 100.986i 0.00450139 0.148074i
\(683\) 1327.94i 1.94427i −0.234421 0.972135i \(-0.575320\pi\)
0.234421 0.972135i \(-0.424680\pi\)
\(684\) −21.0785 + 346.368i −0.0308165 + 0.506387i
\(685\) −798.572 −1.16580
\(686\) 744.122 + 22.6211i 1.08473 + 0.0329754i
\(687\) 1598.53i 2.32683i
\(688\) 54.0511 442.449i 0.0785627 0.643094i
\(689\) 1806.05 2.62127
\(690\) −50.6243 + 1665.29i −0.0733686 + 2.41346i
\(691\) 552.974i 0.800252i 0.916460 + 0.400126i \(0.131034\pi\)
−0.916460 + 0.400126i \(0.868966\pi\)
\(692\) 869.658 + 52.9236i 1.25673 + 0.0764792i
\(693\) 174.583 0.251924
\(694\) −323.364 9.83016i −0.465942 0.0141645i
\(695\) 522.218i 0.751393i
\(696\) 63.9202 + 5.84387i 0.0918394 + 0.00839637i
\(697\) 261.004 0.374467
\(698\) 28.7333 945.183i 0.0411652 1.35413i
\(699\) 1376.14i 1.96873i
\(700\) −11.7914 + 193.760i −0.0168448 + 0.276799i
\(701\) 815.608 1.16349 0.581746 0.813370i \(-0.302370\pi\)
0.581746 + 0.813370i \(0.302370\pi\)
\(702\) −2756.70 83.8030i −3.92693 0.119377i
\(703\) 116.930i 0.166330i
\(704\) −18.6747 + 101.278i −0.0265266 + 0.143861i
\(705\) −1017.86 −1.44377
\(706\) −19.3982 + 638.105i −0.0274762 + 0.903832i
\(707\) 9.88900i 0.0139873i
\(708\) −727.426 44.2680i −1.02744 0.0625254i
\(709\) 764.747 1.07863 0.539314 0.842105i \(-0.318684\pi\)
0.539314 + 0.842105i \(0.318684\pi\)
\(710\) −697.601 21.2069i −0.982537 0.0298688i
\(711\) 465.695i 0.654986i
\(712\) 84.9324 928.990i 0.119287 1.30476i
\(713\) −835.441 −1.17173
\(714\) −10.5556 + 347.228i −0.0147838 + 0.486314i
\(715\) 220.437i 0.308304i
\(716\) −43.7894 + 719.563i −0.0611584 + 1.00498i
\(717\) −799.285 −1.11476
\(718\) 1091.04 + 33.1672i 1.51955 + 0.0461938i
\(719\) 713.170i 0.991892i 0.868353 + 0.495946i \(0.165179\pi\)
−0.868353 + 0.495946i \(0.834821\pi\)
\(720\) 1840.44 + 224.835i 2.55617 + 0.312271i
\(721\) 2.69662 0.00374011
\(722\) 1.15465 37.9825i 0.00159925 0.0526073i
\(723\) 1775.70i 2.45601i
\(724\) 379.553 + 23.0979i 0.524244 + 0.0319032i
\(725\) −13.2860 −0.0183255
\(726\) 1272.58 + 38.6862i 1.75287 + 0.0532868i
\(727\) 890.749i 1.22524i −0.790378 0.612619i \(-0.790116\pi\)
0.790378 0.612619i \(-0.209884\pi\)
\(728\) −1021.78 93.4160i −1.40355 0.128319i
\(729\) 129.566 0.177731
\(730\) −17.6282 + 579.880i −0.0241482 + 0.794356i
\(731\) 165.111i 0.225870i
\(732\) −69.2521 + 1137.97i −0.0946067 + 1.55461i
\(733\) −221.785 −0.302572 −0.151286 0.988490i \(-0.548341\pi\)
−0.151286 + 0.988490i \(0.548341\pi\)
\(734\) 180.815 + 5.49671i 0.246342 + 0.00748871i
\(735\) 603.612i 0.821241i
\(736\) 841.775 + 128.903i 1.14372 + 0.175140i
\(737\) −122.604 −0.166355
\(738\) −53.2638 + 1752.12i −0.0721732 + 2.37414i
\(739\) 635.372i 0.859772i −0.902883 0.429886i \(-0.858554\pi\)
0.902883 0.429886i \(-0.141446\pi\)
\(740\) 623.621 + 37.9508i 0.842731 + 0.0512849i
\(741\) 551.338 0.744046
\(742\) 836.541 + 25.4306i 1.12741 + 0.0342730i
\(743\) 795.274i 1.07036i 0.844740 + 0.535178i \(0.179755\pi\)
−0.844740 + 0.535178i \(0.820245\pi\)
\(744\) −122.927 + 1344.58i −0.165225 + 1.80723i
\(745\) −110.159 −0.147865
\(746\) −28.5002 + 937.518i −0.0382041 + 1.25673i
\(747\) 2728.94i 3.65319i
\(748\) 2.31724 38.0777i 0.00309791 0.0509060i
\(749\) 63.9775 0.0854172
\(750\) 1007.33 + 30.6226i 1.34311 + 0.0408302i
\(751\) 84.7437i 0.112841i −0.998407 0.0564206i \(-0.982031\pi\)
0.998407 0.0564206i \(-0.0179688\pi\)
\(752\) −63.0885 + 516.426i −0.0838943 + 0.686737i
\(753\) −1362.80 −1.80983
\(754\) 2.13384 70.1929i 0.00283003 0.0930940i
\(755\) 1566.63i 2.07500i
\(756\) −1275.69 77.6330i −1.68742 0.102689i
\(757\) 1207.44 1.59503 0.797514 0.603301i \(-0.206148\pi\)
0.797514 + 0.603301i \(0.206148\pi\)
\(758\) 392.876 + 11.9433i 0.518306 + 0.0157563i
\(759\) 230.219i 0.303319i
\(760\) −202.197 18.4857i −0.266048 0.0243233i
\(761\) 524.706 0.689495 0.344748 0.938695i \(-0.387965\pi\)
0.344748 + 0.938695i \(0.387965\pi\)
\(762\) −16.4748 + 541.941i −0.0216205 + 0.711208i
\(763\) 157.990i 0.207064i
\(764\) 6.19068 101.727i 0.00810299 0.133151i
\(765\) −686.809 −0.897790
\(766\) 49.5861 + 1.50740i 0.0647338 + 0.00196789i
\(767\) 797.332i 1.03955i
\(768\) 331.318 1335.80i 0.431404 1.73933i
\(769\) 531.656 0.691360 0.345680 0.938352i \(-0.387648\pi\)
0.345680 + 0.938352i \(0.387648\pi\)
\(770\) −3.10393 + 102.104i −0.00403107 + 0.132602i
\(771\) 1366.39i 1.77223i
\(772\) −1355.76 82.5054i −1.75616 0.106872i
\(773\) −249.261 −0.322459 −0.161229 0.986917i \(-0.551546\pi\)
−0.161229 + 0.986917i \(0.551546\pi\)
\(774\) −1108.39 33.6948i −1.43203 0.0435333i
\(775\) 279.474i 0.360611i
\(776\) −47.8780 + 523.689i −0.0616984 + 0.674857i
\(777\) −786.171 −1.01180
\(778\) 7.68525 252.807i 0.00987821 0.324944i
\(779\) 191.958i