Properties

Label 76.3.b.b.39.8
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 39.8
Root \(0.645572 - 1.89294i\) of defining polynomial
Character \(\chi\) \(=\) 76.39
Dual form 76.3.b.b.39.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.645572 + 1.89294i) q^{2} +0.820457i q^{3} +(-3.16647 + 2.44406i) q^{4} -2.38184 q^{5} +(-1.55308 + 0.529664i) q^{6} +12.3764i q^{7} +(-6.67066 - 4.41614i) q^{8} +8.32685 q^{9} +O(q^{10})\) \(q+(0.645572 + 1.89294i) q^{2} +0.820457i q^{3} +(-3.16647 + 2.44406i) q^{4} -2.38184 q^{5} +(-1.55308 + 0.529664i) q^{6} +12.3764i q^{7} +(-6.67066 - 4.41614i) q^{8} +8.32685 q^{9} +(-1.53765 - 4.50868i) q^{10} -9.15034i q^{11} +(-2.00525 - 2.59795i) q^{12} +0.940214 q^{13} +(-23.4279 + 7.98989i) q^{14} -1.95419i q^{15} +(4.05310 - 15.4781i) q^{16} +27.1792 q^{17} +(5.37558 + 15.7623i) q^{18} -4.35890i q^{19} +(7.54202 - 5.82136i) q^{20} -10.1543 q^{21} +(17.3211 - 5.90721i) q^{22} +13.8004i q^{23} +(3.62325 - 5.47299i) q^{24} -19.3269 q^{25} +(0.606976 + 1.77977i) q^{26} +14.2159i q^{27} +(-30.2488 - 39.1897i) q^{28} +49.8488 q^{29} +(3.69918 - 1.26157i) q^{30} -24.6752i q^{31} +(31.9158 - 2.31995i) q^{32} +7.50746 q^{33} +(17.5461 + 51.4487i) q^{34} -29.4787i q^{35} +(-26.3667 + 20.3514i) q^{36} -27.3757 q^{37} +(8.25115 - 2.81398i) q^{38} +0.771405i q^{39} +(15.8884 + 10.5185i) q^{40} -38.4024 q^{41} +(-6.55536 - 19.2216i) q^{42} -41.2108i q^{43} +(22.3640 + 28.9743i) q^{44} -19.8332 q^{45} +(-26.1234 + 8.90917i) q^{46} +45.1842i q^{47} +(12.6991 + 3.32539i) q^{48} -104.176 q^{49} +(-12.4769 - 36.5846i) q^{50} +22.2994i q^{51} +(-2.97716 + 2.29794i) q^{52} -19.9964 q^{53} +(-26.9100 + 9.17741i) q^{54} +21.7946i q^{55} +(54.6561 - 82.5591i) q^{56} +3.57629 q^{57} +(32.1810 + 94.3610i) q^{58} -34.7054i q^{59} +(4.77618 + 6.18790i) q^{60} +33.2008 q^{61} +(46.7088 - 15.9296i) q^{62} +103.057i q^{63} +(24.9955 + 58.9171i) q^{64} -2.23944 q^{65} +(4.84661 + 14.2112i) q^{66} +3.48192i q^{67} +(-86.0622 + 66.4277i) q^{68} -11.3226 q^{69} +(55.8015 - 19.0306i) q^{70} -88.8887i q^{71} +(-55.5456 - 36.7725i) q^{72} -19.8573 q^{73} +(-17.6730 - 51.8206i) q^{74} -15.8568i q^{75} +(10.6534 + 13.8023i) q^{76} +113.249 q^{77} +(-1.46023 + 0.497998i) q^{78} -51.7431i q^{79} +(-9.65383 + 36.8664i) q^{80} +63.2781 q^{81} +(-24.7915 - 72.6936i) q^{82} -6.62943i q^{83} +(32.1534 - 24.8178i) q^{84} -64.7365 q^{85} +(78.0097 - 26.6046i) q^{86} +40.8988i q^{87} +(-40.4091 + 61.0388i) q^{88} +31.5105 q^{89} +(-12.8038 - 37.5431i) q^{90} +11.6365i q^{91} +(-33.7291 - 43.6987i) q^{92} +20.2449 q^{93} +(-85.5312 + 29.1697i) q^{94} +10.3822i q^{95} +(1.90342 + 26.1855i) q^{96} +159.282 q^{97} +(-67.2534 - 197.200i) q^{98} -76.1935i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.645572 + 1.89294i 0.322786 + 0.946472i
\(3\) 0.820457i 0.273486i 0.990607 + 0.136743i \(0.0436634\pi\)
−0.990607 + 0.136743i \(0.956337\pi\)
\(4\) −3.16647 + 2.44406i −0.791618 + 0.611016i
\(5\) −2.38184 −0.476367 −0.238184 0.971220i \(-0.576552\pi\)
−0.238184 + 0.971220i \(0.576552\pi\)
\(6\) −1.55308 + 0.529664i −0.258846 + 0.0882773i
\(7\) 12.3764i 1.76806i 0.467427 + 0.884032i \(0.345181\pi\)
−0.467427 + 0.884032i \(0.654819\pi\)
\(8\) −6.67066 4.41614i −0.833833 0.552017i
\(9\) 8.32685 0.925206
\(10\) −1.53765 4.50868i −0.153765 0.450868i
\(11\) 9.15034i 0.831849i −0.909399 0.415925i \(-0.863458\pi\)
0.909399 0.415925i \(-0.136542\pi\)
\(12\) −2.00525 2.59795i −0.167104 0.216496i
\(13\) 0.940214 0.0723242 0.0361621 0.999346i \(-0.488487\pi\)
0.0361621 + 0.999346i \(0.488487\pi\)
\(14\) −23.4279 + 7.98989i −1.67342 + 0.570706i
\(15\) 1.95419i 0.130280i
\(16\) 4.05310 15.4781i 0.253319 0.967383i
\(17\) 27.1792 1.59878 0.799388 0.600814i \(-0.205157\pi\)
0.799388 + 0.600814i \(0.205157\pi\)
\(18\) 5.37558 + 15.7623i 0.298644 + 0.875681i
\(19\) 4.35890i 0.229416i
\(20\) 7.54202 5.82136i 0.377101 0.291068i
\(21\) −10.1543 −0.483540
\(22\) 17.3211 5.90721i 0.787322 0.268509i
\(23\) 13.8004i 0.600018i 0.953936 + 0.300009i \(0.0969898\pi\)
−0.953936 + 0.300009i \(0.903010\pi\)
\(24\) 3.62325 5.47299i 0.150969 0.228041i
\(25\) −19.3269 −0.773074
\(26\) 0.606976 + 1.77977i 0.0233452 + 0.0684528i
\(27\) 14.2159i 0.526516i
\(28\) −30.2488 39.1897i −1.08032 1.39963i
\(29\) 49.8488 1.71892 0.859462 0.511200i \(-0.170799\pi\)
0.859462 + 0.511200i \(0.170799\pi\)
\(30\) 3.69918 1.26157i 0.123306 0.0420525i
\(31\) 24.6752i 0.795974i −0.917391 0.397987i \(-0.869709\pi\)
0.917391 0.397987i \(-0.130291\pi\)
\(32\) 31.9158 2.31995i 0.997369 0.0724986i
\(33\) 7.50746 0.227499
\(34\) 17.5461 + 51.4487i 0.516063 + 1.51320i
\(35\) 29.4787i 0.842248i
\(36\) −26.3667 + 20.3514i −0.732410 + 0.565315i
\(37\) −27.3757 −0.739883 −0.369942 0.929055i \(-0.620622\pi\)
−0.369942 + 0.929055i \(0.620622\pi\)
\(38\) 8.25115 2.81398i 0.217136 0.0740522i
\(39\) 0.771405i 0.0197796i
\(40\) 15.8884 + 10.5185i 0.397211 + 0.262963i
\(41\) −38.4024 −0.936644 −0.468322 0.883558i \(-0.655141\pi\)
−0.468322 + 0.883558i \(0.655141\pi\)
\(42\) −6.55536 19.2216i −0.156080 0.457657i
\(43\) 41.2108i 0.958391i −0.877708 0.479195i \(-0.840929\pi\)
0.877708 0.479195i \(-0.159071\pi\)
\(44\) 22.3640 + 28.9743i 0.508273 + 0.658507i
\(45\) −19.8332 −0.440738
\(46\) −26.1234 + 8.90917i −0.567901 + 0.193678i
\(47\) 45.1842i 0.961367i 0.876894 + 0.480683i \(0.159611\pi\)
−0.876894 + 0.480683i \(0.840389\pi\)
\(48\) 12.6991 + 3.32539i 0.264565 + 0.0692790i
\(49\) −104.176 −2.12605
\(50\) −12.4769 36.5846i −0.249538 0.731693i
\(51\) 22.2994i 0.437242i
\(52\) −2.97716 + 2.29794i −0.0572531 + 0.0441912i
\(53\) −19.9964 −0.377291 −0.188646 0.982045i \(-0.560410\pi\)
−0.188646 + 0.982045i \(0.560410\pi\)
\(54\) −26.9100 + 9.17741i −0.498333 + 0.169952i
\(55\) 21.7946i 0.396266i
\(56\) 54.6561 82.5591i 0.976001 1.47427i
\(57\) 3.57629 0.0627419
\(58\) 32.1810 + 94.3610i 0.554845 + 1.62691i
\(59\) 34.7054i 0.588228i −0.955770 0.294114i \(-0.904976\pi\)
0.955770 0.294114i \(-0.0950245\pi\)
\(60\) 4.77618 + 6.18790i 0.0796029 + 0.103132i
\(61\) 33.2008 0.544276 0.272138 0.962258i \(-0.412269\pi\)
0.272138 + 0.962258i \(0.412269\pi\)
\(62\) 46.7088 15.9296i 0.753367 0.256929i
\(63\) 103.057i 1.63582i
\(64\) 24.9955 + 58.9171i 0.390555 + 0.920580i
\(65\) −2.23944 −0.0344529
\(66\) 4.84661 + 14.2112i 0.0734334 + 0.215321i
\(67\) 3.48192i 0.0519690i 0.999662 + 0.0259845i \(0.00827205\pi\)
−0.999662 + 0.0259845i \(0.991728\pi\)
\(68\) −86.0622 + 66.4277i −1.26562 + 0.976878i
\(69\) −11.3226 −0.164096
\(70\) 55.8015 19.0306i 0.797164 0.271866i
\(71\) 88.8887i 1.25195i −0.779842 0.625977i \(-0.784700\pi\)
0.779842 0.625977i \(-0.215300\pi\)
\(72\) −55.5456 36.7725i −0.771467 0.510729i
\(73\) −19.8573 −0.272018 −0.136009 0.990708i \(-0.543428\pi\)
−0.136009 + 0.990708i \(0.543428\pi\)
\(74\) −17.6730 51.8206i −0.238824 0.700279i
\(75\) 15.8568i 0.211425i
\(76\) 10.6534 + 13.8023i 0.140177 + 0.181610i
\(77\) 113.249 1.47076
\(78\) −1.46023 + 0.497998i −0.0187208 + 0.00638458i
\(79\) 51.7431i 0.654976i −0.944855 0.327488i \(-0.893798\pi\)
0.944855 0.327488i \(-0.106202\pi\)
\(80\) −9.65383 + 36.8664i −0.120673 + 0.460830i
\(81\) 63.2781 0.781211
\(82\) −24.7915 72.6936i −0.302336 0.886507i
\(83\) 6.62943i 0.0798727i −0.999202 0.0399363i \(-0.987284\pi\)
0.999202 0.0399363i \(-0.0127155\pi\)
\(84\) 32.1534 24.8178i 0.382779 0.295451i
\(85\) −64.7365 −0.761605
\(86\) 78.0097 26.6046i 0.907090 0.309355i
\(87\) 40.8988i 0.470101i
\(88\) −40.4091 + 61.0388i −0.459195 + 0.693623i
\(89\) 31.5105 0.354051 0.177025 0.984206i \(-0.443353\pi\)
0.177025 + 0.984206i \(0.443353\pi\)
\(90\) −12.8038 37.5431i −0.142264 0.417146i
\(91\) 11.6365i 0.127874i
\(92\) −33.7291 43.6987i −0.366621 0.474986i
\(93\) 20.2449 0.217687
\(94\) −85.5312 + 29.1697i −0.909907 + 0.310316i
\(95\) 10.3822i 0.109286i
\(96\) 1.90342 + 26.1855i 0.0198273 + 0.272766i
\(97\) 159.282 1.64208 0.821039 0.570873i \(-0.193395\pi\)
0.821039 + 0.570873i \(0.193395\pi\)
\(98\) −67.2534 197.200i −0.686259 2.01225i
\(99\) 76.1935i 0.769632i
\(100\) 61.1980 47.2361i 0.611980 0.472361i
\(101\) 35.1573 0.348092 0.174046 0.984738i \(-0.444316\pi\)
0.174046 + 0.984738i \(0.444316\pi\)
\(102\) −42.2114 + 14.3958i −0.413838 + 0.141136i
\(103\) 117.214i 1.13800i 0.822339 + 0.568998i \(0.192669\pi\)
−0.822339 + 0.568998i \(0.807331\pi\)
\(104\) −6.27185 4.15211i −0.0603063 0.0399242i
\(105\) 24.1860 0.230343
\(106\) −12.9092 37.8522i −0.121784 0.357096i
\(107\) 191.832i 1.79282i −0.443228 0.896409i \(-0.646167\pi\)
0.443228 0.896409i \(-0.353833\pi\)
\(108\) −34.7446 45.0144i −0.321710 0.416800i
\(109\) −183.807 −1.68630 −0.843152 0.537675i \(-0.819303\pi\)
−0.843152 + 0.537675i \(0.819303\pi\)
\(110\) −41.2560 + 14.0700i −0.375055 + 0.127909i
\(111\) 22.4606i 0.202347i
\(112\) 191.564 + 50.1630i 1.71039 + 0.447884i
\(113\) 72.9718 0.645768 0.322884 0.946439i \(-0.395348\pi\)
0.322884 + 0.946439i \(0.395348\pi\)
\(114\) 2.30875 + 6.76971i 0.0202522 + 0.0593834i
\(115\) 32.8704i 0.285829i
\(116\) −157.845 + 121.834i −1.36073 + 1.05029i
\(117\) 7.82902 0.0669147
\(118\) 65.6954 22.4049i 0.556741 0.189872i
\(119\) 336.382i 2.82674i
\(120\) −8.62999 + 13.0358i −0.0719166 + 0.108631i
\(121\) 37.2713 0.308027
\(122\) 21.4335 + 62.8473i 0.175685 + 0.515142i
\(123\) 31.5075i 0.256159i
\(124\) 60.3078 + 78.1334i 0.486353 + 0.630108i
\(125\) 105.579 0.844635
\(126\) −195.081 + 66.5306i −1.54826 + 0.528021i
\(127\) 11.4215i 0.0899331i 0.998988 + 0.0449665i \(0.0143181\pi\)
−0.998988 + 0.0449665i \(0.985682\pi\)
\(128\) −95.3904 + 85.3503i −0.745237 + 0.666799i
\(129\) 33.8117 0.262106
\(130\) −1.44572 4.23913i −0.0111209 0.0326087i
\(131\) 36.9512i 0.282070i 0.990005 + 0.141035i \(0.0450430\pi\)
−0.990005 + 0.141035i \(0.954957\pi\)
\(132\) −23.7722 + 18.3487i −0.180092 + 0.139005i
\(133\) 53.9477 0.405622
\(134\) −6.59108 + 2.24783i −0.0491872 + 0.0167749i
\(135\) 33.8600i 0.250815i
\(136\) −181.303 120.027i −1.33311 0.882552i
\(137\) −162.786 −1.18822 −0.594109 0.804385i \(-0.702495\pi\)
−0.594109 + 0.804385i \(0.702495\pi\)
\(138\) −7.30959 21.4331i −0.0529680 0.155313i
\(139\) 229.233i 1.64916i 0.565744 + 0.824581i \(0.308589\pi\)
−0.565744 + 0.824581i \(0.691411\pi\)
\(140\) 72.0478 + 93.3434i 0.514627 + 0.666739i
\(141\) −37.0717 −0.262920
\(142\) 168.261 57.3841i 1.18494 0.404113i
\(143\) 8.60328i 0.0601628i
\(144\) 33.7496 128.884i 0.234372 0.895028i
\(145\) −118.732 −0.818839
\(146\) −12.8193 37.5887i −0.0878035 0.257457i
\(147\) 85.4722i 0.581444i
\(148\) 86.6844 66.9079i 0.585705 0.452081i
\(149\) −110.328 −0.740459 −0.370229 0.928940i \(-0.620721\pi\)
−0.370229 + 0.928940i \(0.620721\pi\)
\(150\) 30.0161 10.2367i 0.200107 0.0682449i
\(151\) 104.737i 0.693621i 0.937935 + 0.346810i \(0.112735\pi\)
−0.937935 + 0.346810i \(0.887265\pi\)
\(152\) −19.2495 + 29.0767i −0.126641 + 0.191294i
\(153\) 226.317 1.47920
\(154\) 73.1102 + 214.373i 0.474742 + 1.39204i
\(155\) 58.7723i 0.379176i
\(156\) −1.88536 2.44263i −0.0120857 0.0156579i
\(157\) −147.695 −0.940732 −0.470366 0.882471i \(-0.655878\pi\)
−0.470366 + 0.882471i \(0.655878\pi\)
\(158\) 97.9468 33.4039i 0.619917 0.211417i
\(159\) 16.4062i 0.103184i
\(160\) −76.0182 + 5.52575i −0.475114 + 0.0345360i
\(161\) −170.800 −1.06087
\(162\) 40.8506 + 119.782i 0.252164 + 0.739394i
\(163\) 183.104i 1.12334i −0.827363 0.561668i \(-0.810160\pi\)
0.827363 0.561668i \(-0.189840\pi\)
\(164\) 121.600 93.8580i 0.741465 0.572305i
\(165\) −17.8815 −0.108373
\(166\) 12.5491 4.27978i 0.0755973 0.0257818i
\(167\) 214.501i 1.28444i −0.766522 0.642218i \(-0.778014\pi\)
0.766522 0.642218i \(-0.221986\pi\)
\(168\) 67.7362 + 44.8429i 0.403191 + 0.266922i
\(169\) −168.116 −0.994769
\(170\) −41.7921 122.542i −0.245836 0.720838i
\(171\) 36.2959i 0.212257i
\(172\) 100.722 + 130.493i 0.585592 + 0.758680i
\(173\) 27.1849 0.157138 0.0785692 0.996909i \(-0.474965\pi\)
0.0785692 + 0.996909i \(0.474965\pi\)
\(174\) −77.4191 + 26.4031i −0.444937 + 0.151742i
\(175\) 239.198i 1.36684i
\(176\) −141.630 37.0873i −0.804717 0.210723i
\(177\) 28.4743 0.160872
\(178\) 20.3423 + 59.6476i 0.114283 + 0.335099i
\(179\) 185.284i 1.03511i −0.855651 0.517553i \(-0.826843\pi\)
0.855651 0.517553i \(-0.173157\pi\)
\(180\) 62.8013 48.4736i 0.348896 0.269298i
\(181\) 17.0150 0.0940053 0.0470026 0.998895i \(-0.485033\pi\)
0.0470026 + 0.998895i \(0.485033\pi\)
\(182\) −22.0273 + 7.51221i −0.121029 + 0.0412759i
\(183\) 27.2398i 0.148852i
\(184\) 60.9445 92.0580i 0.331220 0.500315i
\(185\) 65.2044 0.352456
\(186\) 13.0696 + 38.3225i 0.0702665 + 0.206035i
\(187\) 248.699i 1.32994i
\(188\) −110.433 143.075i −0.587411 0.761036i
\(189\) −175.943 −0.930914
\(190\) −19.6529 + 6.70245i −0.103436 + 0.0352761i
\(191\) 2.41797i 0.0126595i 0.999980 + 0.00632976i \(0.00201484\pi\)
−0.999980 + 0.00632976i \(0.997985\pi\)
\(192\) −48.3389 + 20.5077i −0.251765 + 0.106811i
\(193\) −150.712 −0.780892 −0.390446 0.920626i \(-0.627679\pi\)
−0.390446 + 0.920626i \(0.627679\pi\)
\(194\) 102.828 + 301.511i 0.530040 + 1.55418i
\(195\) 1.83736i 0.00942236i
\(196\) 329.872 254.614i 1.68302 1.29905i
\(197\) 268.203 1.36144 0.680718 0.732545i \(-0.261668\pi\)
0.680718 + 0.732545i \(0.261668\pi\)
\(198\) 144.230 49.1884i 0.728435 0.248426i
\(199\) 308.615i 1.55083i 0.631452 + 0.775415i \(0.282459\pi\)
−0.631452 + 0.775415i \(0.717541\pi\)
\(200\) 128.923 + 85.3500i 0.644615 + 0.426750i
\(201\) −2.85676 −0.0142128
\(202\) 22.6966 + 66.5507i 0.112359 + 0.329459i
\(203\) 616.951i 3.03917i
\(204\) −54.5011 70.6103i −0.267162 0.346129i
\(205\) 91.4683 0.446187
\(206\) −221.879 + 75.6698i −1.07708 + 0.367329i
\(207\) 114.914i 0.555140i
\(208\) 3.81078 14.5528i 0.0183211 0.0699652i
\(209\) −39.8854 −0.190839
\(210\) 15.6138 + 45.7827i 0.0743514 + 0.218013i
\(211\) 334.011i 1.58299i −0.611176 0.791495i \(-0.709303\pi\)
0.611176 0.791495i \(-0.290697\pi\)
\(212\) 63.3182 48.8726i 0.298671 0.230531i
\(213\) 72.9293 0.342391
\(214\) 363.126 123.841i 1.69685 0.578697i
\(215\) 98.1574i 0.456546i
\(216\) 62.7795 94.8297i 0.290646 0.439026i
\(217\) 305.391 1.40733
\(218\) −118.661 347.937i −0.544316 1.59604i
\(219\) 16.2920i 0.0743929i
\(220\) −53.2675 69.0121i −0.242125 0.313691i
\(221\) 25.5543 0.115630
\(222\) 42.5166 14.4999i 0.191516 0.0653149i
\(223\) 290.142i 1.30108i −0.759470 0.650542i \(-0.774542\pi\)
0.759470 0.650542i \(-0.225458\pi\)
\(224\) 28.7128 + 395.004i 0.128182 + 1.76341i
\(225\) −160.932 −0.715252
\(226\) 47.1086 + 138.132i 0.208445 + 0.611202i
\(227\) 76.2561i 0.335930i −0.985793 0.167965i \(-0.946280\pi\)
0.985793 0.167965i \(-0.0537195\pi\)
\(228\) −11.3242 + 8.74068i −0.0496676 + 0.0383363i
\(229\) −212.780 −0.929169 −0.464585 0.885529i \(-0.653796\pi\)
−0.464585 + 0.885529i \(0.653796\pi\)
\(230\) 62.2218 21.2202i 0.270529 0.0922617i
\(231\) 92.9156i 0.402232i
\(232\) −332.525 220.139i −1.43330 0.948875i
\(233\) −108.504 −0.465680 −0.232840 0.972515i \(-0.574802\pi\)
−0.232840 + 0.972515i \(0.574802\pi\)
\(234\) 5.05420 + 14.8199i 0.0215991 + 0.0633329i
\(235\) 107.622i 0.457964i
\(236\) 84.8223 + 109.894i 0.359416 + 0.465652i
\(237\) 42.4530 0.179127
\(238\) −636.752 + 217.159i −2.67543 + 0.912432i
\(239\) 14.5126i 0.0607222i −0.999539 0.0303611i \(-0.990334\pi\)
0.999539 0.0303611i \(-0.00966573\pi\)
\(240\) −30.2473 7.92055i −0.126030 0.0330023i
\(241\) −278.238 −1.15451 −0.577257 0.816563i \(-0.695877\pi\)
−0.577257 + 0.816563i \(0.695877\pi\)
\(242\) 24.0613 + 70.5524i 0.0994268 + 0.291539i
\(243\) 179.860i 0.740166i
\(244\) −105.130 + 81.1449i −0.430859 + 0.332561i
\(245\) 248.131 1.01278
\(246\) 59.6419 20.3404i 0.242447 0.0826845i
\(247\) 4.09830i 0.0165923i
\(248\) −108.969 + 164.600i −0.439391 + 0.663710i
\(249\) 5.43916 0.0218440
\(250\) 68.1591 + 199.856i 0.272636 + 0.799423i
\(251\) 344.252i 1.37152i 0.727828 + 0.685760i \(0.240530\pi\)
−0.727828 + 0.685760i \(0.759470\pi\)
\(252\) −251.877 326.327i −0.999514 1.29495i
\(253\) 126.279 0.499125
\(254\) −21.6203 + 7.37340i −0.0851191 + 0.0290291i
\(255\) 53.1134i 0.208288i
\(256\) −223.145 125.469i −0.871659 0.490113i
\(257\) 50.0048 0.194571 0.0972856 0.995257i \(-0.468984\pi\)
0.0972856 + 0.995257i \(0.468984\pi\)
\(258\) 21.8279 + 64.0036i 0.0846042 + 0.248076i
\(259\) 338.814i 1.30816i
\(260\) 7.09112 5.47333i 0.0272735 0.0210513i
\(261\) 415.084 1.59036
\(262\) −69.9465 + 23.8546i −0.266971 + 0.0910483i
\(263\) 155.273i 0.590391i 0.955437 + 0.295195i \(0.0953848\pi\)
−0.955437 + 0.295195i \(0.904615\pi\)
\(264\) −50.0797 33.1539i −0.189696 0.125583i
\(265\) 47.6283 0.179729
\(266\) 34.8271 + 102.120i 0.130929 + 0.383909i
\(267\) 25.8530i 0.0968277i
\(268\) −8.51004 11.0254i −0.0317539 0.0411396i
\(269\) −457.281 −1.69993 −0.849964 0.526840i \(-0.823377\pi\)
−0.849964 + 0.526840i \(0.823377\pi\)
\(270\) 64.0951 21.8591i 0.237389 0.0809596i
\(271\) 349.279i 1.28885i 0.764666 + 0.644427i \(0.222904\pi\)
−0.764666 + 0.644427i \(0.777096\pi\)
\(272\) 110.160 420.683i 0.405000 1.54663i
\(273\) −9.54725 −0.0349716
\(274\) −105.090 308.144i −0.383540 1.12461i
\(275\) 176.847i 0.643081i
\(276\) 35.8529 27.6733i 0.129902 0.100266i
\(277\) −108.548 −0.391870 −0.195935 0.980617i \(-0.562774\pi\)
−0.195935 + 0.980617i \(0.562774\pi\)
\(278\) −433.926 + 147.987i −1.56089 + 0.532326i
\(279\) 205.467i 0.736440i
\(280\) −130.182 + 196.642i −0.464935 + 0.702294i
\(281\) 190.452 0.677767 0.338883 0.940828i \(-0.389951\pi\)
0.338883 + 0.940828i \(0.389951\pi\)
\(282\) −23.9325 70.1747i −0.0848669 0.248846i
\(283\) 289.950i 1.02456i 0.858819 + 0.512279i \(0.171198\pi\)
−0.858819 + 0.512279i \(0.828802\pi\)
\(284\) 217.250 + 281.464i 0.764964 + 0.991069i
\(285\) −8.51813 −0.0298882
\(286\) 16.2855 5.55404i 0.0569424 0.0194197i
\(287\) 475.285i 1.65605i
\(288\) 265.758 19.3179i 0.922771 0.0670761i
\(289\) 449.709 1.55609
\(290\) −76.6499 224.752i −0.264310 0.775009i
\(291\) 130.684i 0.449084i
\(292\) 62.8776 48.5325i 0.215334 0.166207i
\(293\) −177.881 −0.607102 −0.303551 0.952815i \(-0.598172\pi\)
−0.303551 + 0.952815i \(0.598172\pi\)
\(294\) 161.794 55.1785i 0.550320 0.187682i
\(295\) 82.6627i 0.280212i
\(296\) 182.614 + 120.895i 0.616939 + 0.408428i
\(297\) 130.081 0.437982
\(298\) −71.2249 208.845i −0.239010 0.700823i
\(299\) 12.9754i 0.0433958i
\(300\) 38.7551 + 50.2103i 0.129184 + 0.167368i
\(301\) 510.043 1.69450
\(302\) −198.261 + 67.6151i −0.656492 + 0.223891i
\(303\) 28.8450i 0.0951981i
\(304\) −67.4676 17.6671i −0.221933 0.0581153i
\(305\) −79.0790 −0.259275
\(306\) 146.104 + 428.406i 0.477464 + 1.40002i
\(307\) 554.295i 1.80552i 0.430143 + 0.902761i \(0.358463\pi\)
−0.430143 + 0.902761i \(0.641537\pi\)
\(308\) −358.599 + 276.787i −1.16428 + 0.898659i
\(309\) −96.1686 −0.311225
\(310\) −111.253 + 37.9418i −0.358880 + 0.122393i
\(311\) 67.7563i 0.217866i −0.994049 0.108933i \(-0.965257\pi\)
0.994049 0.108933i \(-0.0347434\pi\)
\(312\) 3.40663 5.14578i 0.0109187 0.0164929i
\(313\) 447.248 1.42891 0.714454 0.699683i \(-0.246675\pi\)
0.714454 + 0.699683i \(0.246675\pi\)
\(314\) −95.3477 279.578i −0.303655 0.890376i
\(315\) 245.465i 0.779253i
\(316\) 126.463 + 163.843i 0.400201 + 0.518491i
\(317\) 67.2154 0.212036 0.106018 0.994364i \(-0.466190\pi\)
0.106018 + 0.994364i \(0.466190\pi\)
\(318\) 31.0560 10.5914i 0.0976605 0.0333063i
\(319\) 456.133i 1.42989i
\(320\) −59.5352 140.331i −0.186048 0.438534i
\(321\) 157.389 0.490310
\(322\) −110.264 323.315i −0.342434 1.00408i
\(323\) 118.471i 0.366785i
\(324\) −200.368 + 154.656i −0.618421 + 0.477333i
\(325\) −18.1714 −0.0559119
\(326\) 346.605 118.207i 1.06321 0.362597i
\(327\) 150.806i 0.461180i
\(328\) 256.170 + 169.590i 0.781005 + 0.517043i
\(329\) −559.220 −1.69976
\(330\) −11.5438 33.8488i −0.0349813 0.102572i
\(331\) 178.449i 0.539122i 0.962983 + 0.269561i \(0.0868785\pi\)
−0.962983 + 0.269561i \(0.913121\pi\)
\(332\) 16.2028 + 20.9919i 0.0488035 + 0.0632287i
\(333\) −227.953 −0.684544
\(334\) 406.038 138.476i 1.21568 0.414598i
\(335\) 8.29337i 0.0247563i
\(336\) −41.1566 + 157.170i −0.122490 + 0.467768i
\(337\) −280.146 −0.831292 −0.415646 0.909526i \(-0.636445\pi\)
−0.415646 + 0.909526i \(0.636445\pi\)
\(338\) −108.531 318.234i −0.321098 0.941521i
\(339\) 59.8702i 0.176608i
\(340\) 204.986 158.220i 0.602901 0.465353i
\(341\) −225.787 −0.662131
\(342\) 68.7061 23.4316i 0.200895 0.0685135i
\(343\) 682.888i 1.99093i
\(344\) −181.992 + 274.903i −0.529048 + 0.799138i
\(345\) 26.9687 0.0781702
\(346\) 17.5498 + 51.4596i 0.0507221 + 0.148727i
\(347\) 89.6003i 0.258214i 0.991631 + 0.129107i \(0.0412111\pi\)
−0.991631 + 0.129107i \(0.958789\pi\)
\(348\) −99.9592 129.505i −0.287239 0.372140i
\(349\) 5.38420 0.0154275 0.00771376 0.999970i \(-0.497545\pi\)
0.00771376 + 0.999970i \(0.497545\pi\)
\(350\) 452.788 154.419i 1.29368 0.441198i
\(351\) 13.3660i 0.0380798i
\(352\) −21.2284 292.040i −0.0603079 0.829660i
\(353\) 357.844 1.01372 0.506861 0.862028i \(-0.330806\pi\)
0.506861 + 0.862028i \(0.330806\pi\)
\(354\) 18.3822 + 53.9002i 0.0519272 + 0.152261i
\(355\) 211.718i 0.596390i
\(356\) −99.7772 + 77.0137i −0.280273 + 0.216331i
\(357\) −275.987 −0.773072
\(358\) 350.732 119.614i 0.979699 0.334118i
\(359\) 415.792i 1.15820i −0.815258 0.579098i \(-0.803405\pi\)
0.815258 0.579098i \(-0.196595\pi\)
\(360\) 132.301 + 87.5861i 0.367502 + 0.243295i
\(361\) −19.0000 −0.0526316
\(362\) 10.9844 + 32.2084i 0.0303436 + 0.0889734i
\(363\) 30.5795i 0.0842409i
\(364\) −28.4404 36.8467i −0.0781329 0.101227i
\(365\) 47.2968 0.129580
\(366\) −51.5635 + 17.5853i −0.140884 + 0.0480472i
\(367\) 262.695i 0.715789i 0.933762 + 0.357894i \(0.116505\pi\)
−0.933762 + 0.357894i \(0.883495\pi\)
\(368\) 213.605 + 55.9345i 0.580448 + 0.151996i
\(369\) −319.771 −0.866588
\(370\) 42.0942 + 123.428i 0.113768 + 0.333590i
\(371\) 247.485i 0.667075i
\(372\) −64.1050 + 49.4799i −0.172325 + 0.133011i
\(373\) 158.344 0.424516 0.212258 0.977214i \(-0.431918\pi\)
0.212258 + 0.977214i \(0.431918\pi\)
\(374\) 470.773 160.553i 1.25875 0.429287i
\(375\) 86.6233i 0.230995i
\(376\) 199.540 301.409i 0.530691 0.801619i
\(377\) 46.8685 0.124320
\(378\) −113.584 333.050i −0.300486 0.881084i
\(379\) 539.136i 1.42252i 0.702928 + 0.711261i \(0.251876\pi\)
−0.702928 + 0.711261i \(0.748124\pi\)
\(380\) −25.3747 32.8749i −0.0667756 0.0865129i
\(381\) −9.37084 −0.0245954
\(382\) −4.57708 + 1.56097i −0.0119819 + 0.00408631i
\(383\) 422.810i 1.10394i −0.833863 0.551971i \(-0.813876\pi\)
0.833863 0.551971i \(-0.186124\pi\)
\(384\) −70.0262 78.2637i −0.182360 0.203812i
\(385\) −269.740 −0.700623
\(386\) −97.2956 285.290i −0.252061 0.739092i
\(387\) 343.156i 0.886709i
\(388\) −504.361 + 389.294i −1.29990 + 1.00334i
\(389\) −487.091 −1.25216 −0.626081 0.779758i \(-0.715342\pi\)
−0.626081 + 0.779758i \(0.715342\pi\)
\(390\) 3.47802 1.18615i 0.00891800 0.00304141i
\(391\) 375.085i 0.959296i
\(392\) 694.926 + 460.057i 1.77277 + 1.17362i
\(393\) −30.3168 −0.0771420
\(394\) 173.144 + 507.693i 0.439453 + 1.28856i
\(395\) 123.244i 0.312009i
\(396\) 186.222 + 241.265i 0.470257 + 0.609254i
\(397\) −646.684 −1.62893 −0.814464 0.580215i \(-0.802969\pi\)
−0.814464 + 0.580215i \(0.802969\pi\)
\(398\) −584.191 + 199.233i −1.46782 + 0.500586i
\(399\) 44.2617i 0.110932i
\(400\) −78.3337 + 299.143i −0.195834 + 0.747859i
\(401\) −14.0555 −0.0350512 −0.0175256 0.999846i \(-0.505579\pi\)
−0.0175256 + 0.999846i \(0.505579\pi\)
\(402\) −1.84425 5.40770i −0.00458768 0.0134520i
\(403\) 23.2000i 0.0575682i
\(404\) −111.325 + 85.9266i −0.275556 + 0.212690i
\(405\) −150.718 −0.372144
\(406\) −1167.85 + 398.286i −2.87649 + 0.981001i
\(407\) 250.497i 0.615471i
\(408\) 98.4770 148.752i 0.241365 0.364587i
\(409\) 143.668 0.351266 0.175633 0.984456i \(-0.443803\pi\)
0.175633 + 0.984456i \(0.443803\pi\)
\(410\) 59.0494 + 173.144i 0.144023 + 0.422303i
\(411\) 133.559i 0.324960i
\(412\) −286.477 371.153i −0.695333 0.900858i
\(413\) 429.530 1.04002
\(414\) −217.526 + 74.1853i −0.525425 + 0.179192i
\(415\) 15.7902i 0.0380488i
\(416\) 30.0077 2.18125i 0.0721338 0.00524340i
\(417\) −188.076 −0.451022
\(418\) −25.7489 75.5008i −0.0616003 0.180624i
\(419\) 572.449i 1.36623i −0.730312 0.683114i \(-0.760625\pi\)
0.730312 0.683114i \(-0.239375\pi\)
\(420\) −76.5842 + 59.1121i −0.182343 + 0.140743i
\(421\) 718.562 1.70680 0.853399 0.521258i \(-0.174537\pi\)
0.853399 + 0.521258i \(0.174537\pi\)
\(422\) 632.264 215.628i 1.49825 0.510967i
\(423\) 376.242i 0.889462i
\(424\) 133.390 + 88.3070i 0.314598 + 0.208271i
\(425\) −525.289 −1.23597
\(426\) 47.0811 + 138.051i 0.110519 + 0.324064i
\(427\) 410.908i 0.962314i
\(428\) 468.849 + 607.429i 1.09544 + 1.41923i
\(429\) 7.05862 0.0164537
\(430\) −185.807 + 63.3677i −0.432108 + 0.147367i
\(431\) 252.198i 0.585147i −0.956243 0.292573i \(-0.905488\pi\)
0.956243 0.292573i \(-0.0945116\pi\)
\(432\) 220.036 + 57.6186i 0.509342 + 0.133376i
\(433\) 239.008 0.551982 0.275991 0.961160i \(-0.410994\pi\)
0.275991 + 0.961160i \(0.410994\pi\)
\(434\) 197.152 + 578.089i 0.454268 + 1.33200i
\(435\) 97.4142i 0.223941i
\(436\) 582.021 449.237i 1.33491 1.03036i
\(437\) 60.1547 0.137654
\(438\) 30.8399 10.5177i 0.0704108 0.0240130i
\(439\) 17.2750i 0.0393508i 0.999806 + 0.0196754i \(0.00626327\pi\)
−0.999806 + 0.0196754i \(0.993737\pi\)
\(440\) 96.2480 145.385i 0.218745 0.330420i
\(441\) −867.461 −1.96703
\(442\) 16.4971 + 48.3728i 0.0373238 + 0.109441i
\(443\) 161.249i 0.363993i 0.983299 + 0.181997i \(0.0582560\pi\)
−0.983299 + 0.181997i \(0.941744\pi\)
\(444\) 54.8950 + 71.1208i 0.123637 + 0.160182i
\(445\) −75.0529 −0.168658
\(446\) 549.222 187.307i 1.23144 0.419972i
\(447\) 90.5196i 0.202505i
\(448\) −729.184 + 309.355i −1.62764 + 0.690525i
\(449\) 561.952 1.25156 0.625782 0.779998i \(-0.284780\pi\)
0.625782 + 0.779998i \(0.284780\pi\)
\(450\) −103.893 304.635i −0.230874 0.676966i
\(451\) 351.395i 0.779147i
\(452\) −231.063 + 178.348i −0.511202 + 0.394575i
\(453\) −85.9319 −0.189695
\(454\) 144.349 49.2288i 0.317948 0.108434i
\(455\) 27.7163i 0.0609149i
\(456\) −23.8562 15.7934i −0.0523162 0.0346346i
\(457\) −107.375 −0.234957 −0.117479 0.993075i \(-0.537481\pi\)
−0.117479 + 0.993075i \(0.537481\pi\)
\(458\) −137.365 402.780i −0.299923 0.879433i
\(459\) 386.378i 0.841781i
\(460\) 80.3373 + 104.083i 0.174646 + 0.226268i
\(461\) 666.303 1.44534 0.722672 0.691191i \(-0.242914\pi\)
0.722672 + 0.691191i \(0.242914\pi\)
\(462\) −175.884 + 59.9838i −0.380701 + 0.129835i
\(463\) 272.358i 0.588246i −0.955768 0.294123i \(-0.904972\pi\)
0.955768 0.294123i \(-0.0950276\pi\)
\(464\) 202.042 771.566i 0.435436 1.66286i
\(465\) −48.2201 −0.103699
\(466\) −70.0469 205.391i −0.150315 0.440753i
\(467\) 703.386i 1.50618i 0.657917 + 0.753090i \(0.271438\pi\)
−0.657917 + 0.753090i \(0.728562\pi\)
\(468\) −24.7904 + 19.1346i −0.0529709 + 0.0408860i
\(469\) −43.0938 −0.0918844
\(470\) 203.721 69.4775i 0.433450 0.147824i
\(471\) 121.177i 0.257277i
\(472\) −153.264 + 231.508i −0.324712 + 0.490484i
\(473\) −377.093 −0.797237
\(474\) 27.4065 + 80.3611i 0.0578196 + 0.169538i
\(475\) 84.2438i 0.177355i
\(476\) −822.139 1065.14i −1.72718 2.23770i
\(477\) −166.507 −0.349072
\(478\) 27.4716 9.36894i 0.0574719 0.0196003i
\(479\) 451.971i 0.943572i −0.881713 0.471786i \(-0.843609\pi\)
0.881713 0.471786i \(-0.156391\pi\)
\(480\) −4.53364 62.3697i −0.00944509 0.129937i
\(481\) −25.7390 −0.0535114
\(482\) −179.623 526.689i −0.372661 1.09272i
\(483\) 140.134i 0.290133i
\(484\) −118.018 + 91.0934i −0.243840 + 0.188209i
\(485\) −379.383 −0.782232
\(486\) −340.465 + 116.113i −0.700546 + 0.238915i
\(487\) 293.894i 0.603478i 0.953391 + 0.301739i \(0.0975671\pi\)
−0.953391 + 0.301739i \(0.902433\pi\)
\(488\) −221.472 146.619i −0.453835 0.300449i
\(489\) 150.229 0.307216
\(490\) 160.187 + 469.699i 0.326912 + 0.958568i
\(491\) 91.3499i 0.186049i −0.995664 0.0930243i \(-0.970347\pi\)
0.995664 0.0930243i \(-0.0296534\pi\)
\(492\) 77.0064 + 99.7677i 0.156517 + 0.202780i
\(493\) 1354.85 2.74818
\(494\) 7.75785 2.64575i 0.0157041 0.00535576i
\(495\) 181.481i 0.366627i
\(496\) −381.926 100.011i −0.770012 0.201635i
\(497\) 1100.13 2.21353
\(498\) 3.51137 + 10.2960i 0.00705095 + 0.0206748i
\(499\) 758.796i 1.52063i −0.649553 0.760316i \(-0.725044\pi\)
0.649553 0.760316i \(-0.274956\pi\)
\(500\) −334.314 + 258.043i −0.668628 + 0.516085i
\(501\) 175.989 0.351275
\(502\) −651.649 + 222.239i −1.29811 + 0.442708i
\(503\) 55.4556i 0.110250i −0.998479 0.0551248i \(-0.982444\pi\)
0.998479 0.0551248i \(-0.0175557\pi\)
\(504\) 455.113 687.457i 0.903002 1.36400i
\(505\) −83.7389 −0.165820
\(506\) 81.5220 + 239.038i 0.161111 + 0.472408i
\(507\) 137.932i 0.272055i
\(508\) −27.9149 36.1659i −0.0549505 0.0711927i
\(509\) −479.828 −0.942688 −0.471344 0.881949i \(-0.656231\pi\)
−0.471344 + 0.881949i \(0.656231\pi\)
\(510\) 100.541 34.2886i 0.197139 0.0672325i
\(511\) 245.763i 0.480945i
\(512\) 93.4494 503.400i 0.182518 0.983202i
\(513\) 61.9658 0.120791
\(514\) 32.2817 + 94.6563i 0.0628049 + 0.184156i
\(515\) 279.184i 0.542104i
\(516\) −107.064 + 82.6379i −0.207488 + 0.160151i
\(517\) 413.451 0.799712
\(518\) 641.355 218.729i 1.23814 0.422256i
\(519\) 22.3041i 0.0429751i
\(520\) 14.9385 + 9.88966i 0.0287279 + 0.0190186i
\(521\) 29.8875 0.0573656 0.0286828 0.999589i \(-0.490869\pi\)
0.0286828 + 0.999589i \(0.490869\pi\)
\(522\) 267.966 + 785.730i 0.513346 + 1.50523i
\(523\) 324.051i 0.619600i −0.950802 0.309800i \(-0.899738\pi\)
0.950802 0.309800i \(-0.100262\pi\)
\(524\) −90.3110 117.005i −0.172349 0.223292i
\(525\) 196.251 0.373812
\(526\) −293.923 + 100.240i −0.558788 + 0.190570i
\(527\) 670.652i 1.27259i
\(528\) 30.4285 116.201i 0.0576297 0.220078i
\(529\) 338.548 0.639978
\(530\) 30.7475 + 90.1577i 0.0580141 + 0.170109i
\(531\) 288.987i 0.544232i
\(532\) −170.824 + 131.852i −0.321097 + 0.247841i
\(533\) −36.1065 −0.0677420
\(534\) −48.9383 + 16.6900i −0.0916447 + 0.0312546i
\(535\) 456.912i 0.854040i
\(536\) 15.3766 23.2267i 0.0286878 0.0433334i
\(537\) 152.018 0.283087
\(538\) −295.208 865.607i −0.548713 1.60893i
\(539\) 953.250i 1.76855i
\(540\) 82.7561 + 107.217i 0.153252 + 0.198550i
\(541\) −584.274 −1.07999 −0.539994 0.841669i \(-0.681574\pi\)
−0.539994 + 0.841669i \(0.681574\pi\)
\(542\) −661.166 + 225.485i −1.21986 + 0.416024i
\(543\) 13.9600i 0.0257091i
\(544\) 867.446 63.0545i 1.59457 0.115909i
\(545\) 437.799 0.803301
\(546\) −6.16344 18.0724i −0.0112884 0.0330996i
\(547\) 173.706i 0.317562i 0.987314 + 0.158781i \(0.0507564\pi\)
−0.987314 + 0.158781i \(0.949244\pi\)
\(548\) 515.457 397.859i 0.940614 0.726020i
\(549\) 276.458 0.503567
\(550\) −334.762 + 114.168i −0.608658 + 0.207578i
\(551\) 217.286i 0.394348i
\(552\) 75.5296 + 50.0024i 0.136829 + 0.0905840i
\(553\) 640.396 1.15804
\(554\) −70.0755 205.475i −0.126490 0.370894i
\(555\) 53.4974i 0.0963917i
\(556\) −560.261 725.862i −1.00766 1.30551i
\(557\) −590.355 −1.05988 −0.529942 0.848034i \(-0.677786\pi\)
−0.529942 + 0.848034i \(0.677786\pi\)
\(558\) 388.937 132.644i 0.697020 0.237713i
\(559\) 38.7470i 0.0693148i
\(560\) −456.275 119.480i −0.814776 0.213357i
\(561\) 204.047 0.363720
\(562\) 122.951 + 360.516i 0.218774 + 0.641487i
\(563\) 1015.03i 1.80290i 0.432882 + 0.901450i \(0.357497\pi\)
−0.432882 + 0.901450i \(0.642503\pi\)
\(564\) 117.387 90.6056i 0.208132 0.160648i
\(565\) −173.807 −0.307623
\(566\) −548.859 + 187.183i −0.969715 + 0.330713i
\(567\) 783.158i 1.38123i
\(568\) −392.545 + 592.947i −0.691100 + 1.04392i
\(569\) −98.2869 −0.172736 −0.0863681 0.996263i \(-0.527526\pi\)
−0.0863681 + 0.996263i \(0.527526\pi\)
\(570\) −5.49907 16.1244i −0.00964749 0.0282883i
\(571\) 366.213i 0.641354i 0.947189 + 0.320677i \(0.103910\pi\)
−0.947189 + 0.320677i \(0.896090\pi\)
\(572\) 21.0270 + 27.2421i 0.0367604 + 0.0476260i
\(573\) −1.98384 −0.00346219
\(574\) 899.689 306.831i 1.56740 0.534549i
\(575\) 266.719i 0.463859i
\(576\) 208.134 + 490.594i 0.361343 + 0.851726i
\(577\) −267.138 −0.462977 −0.231489 0.972838i \(-0.574360\pi\)
−0.231489 + 0.972838i \(0.574360\pi\)
\(578\) 290.320 + 851.275i 0.502284 + 1.47279i
\(579\) 123.653i 0.213563i
\(580\) 375.961 290.188i 0.648208 0.500324i
\(581\) 82.0488 0.141220
\(582\) −247.377 + 84.3657i −0.425046 + 0.144958i
\(583\) 182.974i 0.313850i
\(584\) 132.461 + 87.6925i 0.226817 + 0.150158i
\(585\) −18.6475 −0.0318760
\(586\) −114.835 336.719i −0.195964 0.574605i
\(587\) 245.452i 0.418147i 0.977900 + 0.209074i \(0.0670448\pi\)
−0.977900 + 0.209074i \(0.932955\pi\)
\(588\) 208.900 + 270.645i 0.355271 + 0.460281i
\(589\) −107.557 −0.182609
\(590\) −156.476 + 53.3647i −0.265213 + 0.0904487i
\(591\) 220.049i 0.372333i
\(592\) −110.956 + 423.724i −0.187426 + 0.715750i
\(593\) 33.3697 0.0562726 0.0281363 0.999604i \(-0.491043\pi\)
0.0281363 + 0.999604i \(0.491043\pi\)
\(594\) 83.9764 + 246.235i 0.141374 + 0.414537i
\(595\) 801.207i 1.34657i
\(596\) 349.352 269.649i 0.586160 0.452432i
\(597\) −253.205 −0.424129
\(598\) −24.5616 + 8.37653i −0.0410729 + 0.0140076i
\(599\) 427.260i 0.713288i −0.934240 0.356644i \(-0.883921\pi\)
0.934240 0.356644i \(-0.116079\pi\)
\(600\) −70.0260 + 105.776i −0.116710 + 0.176293i
\(601\) −316.625 −0.526831 −0.263415 0.964683i \(-0.584849\pi\)
−0.263415 + 0.964683i \(0.584849\pi\)
\(602\) 329.270 + 965.483i 0.546960 + 1.60379i
\(603\) 28.9934i 0.0480820i
\(604\) −255.983 331.646i −0.423813 0.549083i
\(605\) −88.7741 −0.146734
\(606\) −54.6020 + 18.6215i −0.0901023 + 0.0307286i
\(607\) 467.840i 0.770741i −0.922762 0.385370i \(-0.874074\pi\)
0.922762 0.385370i \(-0.125926\pi\)
\(608\) −10.1124 139.118i −0.0166323 0.228812i
\(609\) −506.181 −0.831168
\(610\) −51.0512 149.692i −0.0836905 0.245397i
\(611\) 42.4829i 0.0695300i
\(612\) −716.627 + 553.134i −1.17096 + 0.903813i
\(613\) −636.118 −1.03771 −0.518856 0.854861i \(-0.673642\pi\)
−0.518856 + 0.854861i \(0.673642\pi\)
\(614\) −1049.25 + 357.838i −1.70888 + 0.582797i
\(615\) 75.0458i 0.122026i
\(616\) −755.444 500.122i −1.22637 0.811886i
\(617\) 331.487 0.537256 0.268628 0.963244i \(-0.413430\pi\)
0.268628 + 0.963244i \(0.413430\pi\)
\(618\) −62.0838 182.042i −0.100459 0.294566i
\(619\) 479.724i 0.774999i −0.921870 0.387500i \(-0.873339\pi\)
0.921870 0.387500i \(-0.126661\pi\)
\(620\) −143.643 186.101i −0.231683 0.300163i
\(621\) −196.186 −0.315919
\(622\) 128.259 43.7416i 0.206204 0.0703241i
\(623\) 389.988i 0.625984i
\(624\) 11.9399 + 3.12658i 0.0191345 + 0.00501055i
\(625\) 231.698 0.370718
\(626\) 288.731 + 846.615i 0.461231 + 1.35242i
\(627\) 32.7242i 0.0521918i
\(628\) 467.672 360.976i 0.744700 0.574802i
\(629\) −744.049 −1.18291
\(630\) 464.651 158.465i 0.737541 0.251532i
\(631\) 389.892i 0.617896i 0.951079 + 0.308948i \(0.0999768\pi\)
−0.951079 + 0.308948i \(0.900023\pi\)
\(632\) −228.505 + 345.161i −0.361558 + 0.546141i
\(633\) 274.041 0.432925
\(634\) 43.3924 + 127.235i 0.0684423 + 0.200686i
\(635\) 27.2042i 0.0428412i
\(636\) 40.0978 + 51.9498i 0.0630469 + 0.0816821i
\(637\) −97.9481 −0.153765
\(638\) 863.435 294.467i 1.35335 0.461547i
\(639\) 740.163i 1.15831i
\(640\) 227.204 203.291i 0.355007 0.317642i
\(641\) −170.264 −0.265623 −0.132811 0.991141i \(-0.542400\pi\)
−0.132811 + 0.991141i \(0.542400\pi\)
\(642\) 101.606 + 297.929i 0.158265 + 0.464064i
\(643\) 420.651i 0.654200i −0.944990 0.327100i \(-0.893929\pi\)
0.944990 0.327100i \(-0.106071\pi\)
\(644\) 540.834 417.447i 0.839805 0.648209i
\(645\) −80.5339 −0.124859
\(646\) 224.260 76.4819i 0.347151 0.118393i
\(647\) 178.658i 0.276133i 0.990423 + 0.138067i \(0.0440888\pi\)
−0.990423 + 0.138067i \(0.955911\pi\)
\(648\) −422.107 279.445i −0.651400 0.431242i
\(649\) −317.566 −0.489317
\(650\) −11.7309 34.3974i −0.0180476 0.0529191i
\(651\) 250.560i 0.384885i
\(652\) 447.517 + 579.793i 0.686376 + 0.889253i
\(653\) −950.370 −1.45539 −0.727696 0.685900i \(-0.759409\pi\)
−0.727696 + 0.685900i \(0.759409\pi\)
\(654\) 285.467 97.3561i 0.436494 0.148862i
\(655\) 88.0117i 0.134369i
\(656\) −155.649 + 594.397i −0.237270 + 0.906094i
\(657\) −165.349 −0.251672
\(658\) −361.017 1058.57i −0.548658 1.60877i
\(659\) 327.948i 0.497645i −0.968549 0.248823i \(-0.919956\pi\)
0.968549 0.248823i \(-0.0800436\pi\)
\(660\) 56.6214 43.7036i 0.0857900 0.0662176i
\(661\) 256.403 0.387902 0.193951 0.981011i \(-0.437870\pi\)
0.193951 + 0.981011i \(0.437870\pi\)
\(662\) −337.794 + 115.202i −0.510264 + 0.174021i
\(663\) 20.9662i 0.0316232i
\(664\) −29.2765 + 44.2227i −0.0440911 + 0.0666005i
\(665\) −128.495 −0.193225
\(666\) −147.160 431.503i −0.220961 0.647902i
\(667\) 687.935i 1.03139i
\(668\) 524.254 + 679.211i 0.784811 + 1.01678i
\(669\) 238.049 0.355828
\(670\) 15.6989 5.35397i 0.0234312 0.00799100i
\(671\) 303.799i 0.452755i
\(672\) −324.084 + 23.5576i −0.482267 + 0.0350560i
\(673\) −624.347 −0.927707 −0.463853 0.885912i \(-0.653534\pi\)
−0.463853 + 0.885912i \(0.653534\pi\)
\(674\) −180.854 530.300i −0.268330 0.786795i
\(675\) 274.749i 0.407036i
\(676\) 532.335 410.886i 0.787477 0.607820i
\(677\) −135.259 −0.199791 −0.0998955 0.994998i \(-0.531851\pi\)
−0.0998955 + 0.994998i \(0.531851\pi\)
\(678\) −113.331 + 38.6505i −0.167155 + 0.0570067i
\(679\) 1971.34i 2.90330i
\(680\) 431.835 + 285.885i 0.635052 + 0.420419i
\(681\) 62.5648 0.0918720
\(682\) −145.762 427.401i −0.213727 0.626688i
\(683\) 84.9635i 0.124398i 0.998064 + 0.0621988i \(0.0198113\pi\)
−0.998064 + 0.0621988i \(0.980189\pi\)
\(684\) 88.7095 + 114.930i 0.129692 + 0.168026i
\(685\) 387.729 0.566028
\(686\) 1292.67 440.853i 1.88436 0.642644i
\(687\) 174.577i 0.254114i
\(688\) −637.866 167.032i −0.927131 0.242778i
\(689\) −18.8009 −0.0272873
\(690\) 17.4103 + 51.0503i 0.0252322 + 0.0739859i
\(691\) 673.647i 0.974887i −0.873155 0.487443i \(-0.837930\pi\)
0.873155 0.487443i \(-0.162070\pi\)
\(692\) −86.0804 + 66.4418i −0.124394 + 0.0960141i
\(693\) 943.005 1.36076
\(694\) −169.608 + 57.8435i −0.244392 + 0.0833479i
\(695\) 545.997i 0.785607i
\(696\) 180.615 272.822i 0.259504 0.391986i
\(697\) −1043.75 −1.49749
\(698\) 3.47589 + 10.1920i 0.00497979 + 0.0146017i
\(699\) 89.0225i 0.127357i
\(700\) 584.615 + 757.413i 0.835164 + 1.08202i
\(701\) 406.227 0.579496 0.289748 0.957103i \(-0.406429\pi\)
0.289748 + 0.957103i \(0.406429\pi\)
\(702\) −25.3011 + 8.62873i −0.0360415 + 0.0122916i
\(703\) 119.328i 0.169741i
\(704\) 539.112 228.717i 0.765784 0.324883i
\(705\) 88.2988 0.125246
\(706\) 231.014 + 677.378i 0.327215 + 0.959459i
\(707\) 435.122i 0.615448i
\(708\) −90.1631 + 69.5930i −0.127349 + 0.0982952i
\(709\) 668.985 0.943561 0.471780 0.881716i \(-0.343611\pi\)
0.471780 + 0.881716i \(0.343611\pi\)
\(710\) −400.771 + 136.680i −0.564466 + 0.192506i
\(711\) 430.857i 0.605988i
\(712\) −210.196 139.155i −0.295219 0.195442i
\(713\) 340.528 0.477599
\(714\) −178.169 522.428i −0.249537 0.731691i
\(715\) 20.4916i 0.0286596i
\(716\) 452.846 + 586.697i 0.632467 + 0.819409i
\(717\) 11.9070 0.0166066
\(718\) 787.072 268.424i 1.09620 0.373850i
\(719\) 357.444i 0.497140i −0.968614 0.248570i \(-0.920039\pi\)
0.968614 0.248570i \(-0.0799606\pi\)
\(720\) −80.3860 + 306.981i −0.111647 + 0.426362i
\(721\) −1450.69 −2.01205
\(722\) −12.2659 35.9659i −0.0169887 0.0498143i
\(723\) 228.282i 0.315743i
\(724\) −53.8774 + 41.5857i −0.0744163 + 0.0574387i
\(725\) −963.420 −1.32886
\(726\) −57.8852 + 19.7412i −0.0797317 + 0.0271918i
\(727\) 931.519i 1.28132i −0.767825 0.640659i \(-0.778661\pi\)
0.767825 0.640659i \(-0.221339\pi\)
\(728\) 51.3884 77.6232i 0.0705885 0.106625i
\(729\) 421.935 0.578787
\(730\) 30.5335 + 89.5303i 0.0418267 + 0.122644i
\(731\) 1120.08i 1.53225i
\(732\) −66.5759 86.2542i −0.0909507 0.117834i
\(733\) −342.315 −0.467006 −0.233503 0.972356i \(-0.575019\pi\)
−0.233503 + 0.972356i \(0.575019\pi\)
\(734\) −497.266 + 169.588i −0.677474 + 0.231047i
\(735\) 203.581i 0.276981i
\(736\) 32.0164 + 440.451i 0.0435005 + 0.598440i
\(737\) 31.8608 0.0432303
\(738\) −206.435 605.309i −0.279723 0.820202i
\(739\) 233.486i 0.315949i 0.987443 + 0.157975i \(0.0504964\pi\)
−0.987443 + 0.157975i \(0.949504\pi\)
\(740\) −206.468 + 159.364i −0.279011 + 0.215356i
\(741\) 3.36248 0.00453775
\(742\) 468.475 159.769i 0.631368 0.215323i
\(743\) 684.601i 0.921401i 0.887556 + 0.460701i \(0.152402\pi\)
−0.887556 + 0.460701i \(0.847598\pi\)
\(744\) −135.047 89.4044i −0.181515 0.120167i
\(745\) 262.784 0.352730
\(746\) 102.223 + 299.737i 0.137028 + 0.401792i
\(747\) 55.2023i 0.0738987i
\(748\) 607.836 + 787.499i 0.812615 + 1.05281i
\(749\) 2374.19 3.16982
\(750\) −163.973 + 55.9216i −0.218631 + 0.0745621i
\(751\) 985.017i 1.31161i 0.754931 + 0.655804i \(0.227670\pi\)
−0.754931 + 0.655804i \(0.772330\pi\)
\(752\) 699.367 + 183.136i 0.930010 + 0.243532i
\(753\) −282.444 −0.375091
\(754\) 30.2570 + 88.7195i 0.0401287 + 0.117665i
\(755\) 249.466i 0.330418i
\(756\) 557.118 430.015i 0.736928 0.568803i
\(757\) 1162.89 1.53619 0.768094 0.640338i \(-0.221206\pi\)
0.768094 + 0.640338i \(0.221206\pi\)
\(758\) −1020.55 + 348.051i −1.34638 + 0.459171i
\(759\) 103.606i 0.136503i
\(760\) 45.8491 69.2561i 0.0603278 0.0911264i
\(761\) −460.254 −0.604802 −0.302401 0.953181i \(-0.597788\pi\)
−0.302401 + 0.953181i \(0.597788\pi\)
\(762\) −6.04956 17.7385i −0.00793905 0.0232788i
\(763\) 2274.88i 2.98149i
\(764\) −5.90967 7.65643i −0.00773516 0.0100215i
\(765\) −539.051 −0.704642
\(766\) 800.356 272.954i 1.04485 0.356337i
\(767\) 32.6305i 0.0425431i
\(768\) 102.942 183.081i 0.134039 0.238386i
\(769\) 757.145 0.984584 0.492292 0.870430i \(-0.336159\pi\)
0.492292 + 0.870430i \(0.336159\pi\)
\(770\) −174.137 510.603i −0.226151 0.663120i
\(771\) 41.0268i 0.0532124i
\(772\) 477.226 368.350i 0.618168 0.477138i
\(773\) 1071.48 1.38614 0.693068 0.720872i \(-0.256258\pi\)
0.693068 + 0.720872i \(0.256258\pi\)
\(774\) 649.575 221.532i 0.839245 0.286217i
\(775\) 476.894i 0.615347i
\(776\) −1062.51 703.409i −1.36922 0.906455i
\(777\) 277.982 0.357763
\(778\) −314.452 922.036i −0.404180 1.18514i
\(779\) 167.392i 0.214881i