Properties

Label 637.2.k.g.569.2
Level $637$
Weight $2$
Character 637.569
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 569.2
Root \(0.759479 - 1.19298i\) of defining polynomial
Character \(\chi\) \(=\) 637.569
Dual form 637.2.k.g.459.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.38595i q^{2} +(-1.41289 + 2.44719i) q^{3} +0.0791355 q^{4} +(-0.449430 - 0.259479i) q^{5} +(3.39169 + 1.95819i) q^{6} -2.88158i q^{8} +(-2.49250 - 4.31714i) q^{9} +O(q^{10})\) \(q-1.38595i q^{2} +(-1.41289 + 2.44719i) q^{3} +0.0791355 q^{4} +(-0.449430 - 0.259479i) q^{5} +(3.39169 + 1.95819i) q^{6} -2.88158i q^{8} +(-2.49250 - 4.31714i) q^{9} +(-0.359625 + 0.622889i) q^{10} +(-1.40656 - 0.812080i) q^{11} +(-0.111810 + 0.193660i) q^{12} +(-1.42641 - 3.31140i) q^{13} +(1.26999 - 0.733228i) q^{15} -3.83547 q^{16} +1.94825 q^{17} +(-5.98335 + 3.45449i) q^{18} +(2.15740 - 1.24558i) q^{19} +(-0.0355659 - 0.0205340i) q^{20} +(-1.12550 + 1.94943i) q^{22} +9.14058 q^{23} +(7.05179 + 4.07135i) q^{24} +(-2.36534 - 4.09689i) q^{25} +(-4.58944 + 1.97694i) q^{26} +5.60916 q^{27} +(2.61498 + 4.52928i) q^{29} +(-1.01622 - 1.76014i) q^{30} +(5.01767 - 2.89695i) q^{31} -0.447392i q^{32} +(3.97463 - 2.29475i) q^{33} -2.70019i q^{34} +(-0.197245 - 0.341639i) q^{36} -10.2293i q^{37} +(-1.72631 - 2.99006i) q^{38} +(10.1190 + 1.18792i) q^{39} +(-0.747709 + 1.29507i) q^{40} +(-3.64513 + 2.10452i) q^{41} +(-0.498655 + 0.863697i) q^{43} +(-0.111309 - 0.0642644i) q^{44} +2.58700i q^{45} -12.6684i q^{46} +(-3.91206 - 2.25863i) q^{47} +(5.41908 - 9.38612i) q^{48} +(-5.67810 + 3.27825i) q^{50} +(-2.75266 + 4.76775i) q^{51} +(-0.112880 - 0.262049i) q^{52} +(4.44825 + 7.70460i) q^{53} -7.77403i q^{54} +(0.421434 + 0.729946i) q^{55} +7.03944i q^{57} +(6.27736 - 3.62424i) q^{58} -6.20526i q^{59} +(0.100501 - 0.0580244i) q^{60} +(-6.73536 - 11.6660i) q^{61} +(-4.01504 - 6.95426i) q^{62} -8.29100 q^{64} +(-0.218163 + 1.85836i) q^{65} +(-3.18042 - 5.50865i) q^{66} +(7.25094 + 4.18633i) q^{67} +0.154176 q^{68} +(-12.9146 + 22.3688i) q^{69} +(-4.50168 - 2.59905i) q^{71} +(-12.4402 + 7.18234i) q^{72} +(10.2533 - 5.91976i) q^{73} -14.1773 q^{74} +13.3678 q^{75} +(0.170727 - 0.0985694i) q^{76} +(1.64640 - 14.0244i) q^{78} +(-0.491155 + 0.850705i) q^{79} +(1.72377 + 0.995221i) q^{80} +(-0.447609 + 0.775281i) q^{81} +(2.91676 + 5.05197i) q^{82} -8.91851i q^{83} +(-0.875603 - 0.505530i) q^{85} +(1.19704 + 0.691113i) q^{86} -14.7787 q^{87} +(-2.34008 + 4.05313i) q^{88} +12.0190i q^{89} +3.58546 q^{90} +0.723345 q^{92} +16.3723i q^{93} +(-3.13035 + 5.42193i) q^{94} -1.29280 q^{95} +(1.09485 + 0.632114i) q^{96} +(-3.82981 - 2.21114i) q^{97} +8.09643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 8 q^{4} - 6 q^{5} + 18 q^{6} - 4 q^{9} - 12 q^{10} - 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{15} + 16 q^{16} - 8 q^{17} + 12 q^{18} + 12 q^{20} + 6 q^{22} + 24 q^{23} + 12 q^{24} + 10 q^{25} - 18 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 18 q^{31} - 30 q^{33} - 10 q^{36} + 2 q^{38} + 14 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} - 24 q^{44} + 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} + 28 q^{52} + 22 q^{53} + 6 q^{55} + 12 q^{58} - 66 q^{60} - 14 q^{61} + 4 q^{62} - 52 q^{64} - 18 q^{65} - 26 q^{66} + 24 q^{67} - 16 q^{68} - 4 q^{69} - 24 q^{71} - 60 q^{72} + 30 q^{73} - 12 q^{74} + 92 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 60 q^{86} - 4 q^{87} - 14 q^{88} - 24 q^{90} + 24 q^{92} - 4 q^{94} + 44 q^{95} + 6 q^{96} - 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38595i 0.980016i −0.871718 0.490008i \(-0.836994\pi\)
0.871718 0.490008i \(-0.163006\pi\)
\(3\) −1.41289 + 2.44719i −0.815731 + 1.41289i 0.0930713 + 0.995659i \(0.470332\pi\)
−0.908802 + 0.417228i \(0.863002\pi\)
\(4\) 0.0791355 0.0395678
\(5\) −0.449430 0.259479i −0.200991 0.116042i 0.396127 0.918196i \(-0.370354\pi\)
−0.597118 + 0.802154i \(0.703687\pi\)
\(6\) 3.39169 + 1.95819i 1.38465 + 0.799429i
\(7\) 0 0
\(8\) 2.88158i 1.01879i
\(9\) −2.49250 4.31714i −0.830833 1.43905i
\(10\) −0.359625 + 0.622889i −0.113723 + 0.196975i
\(11\) −1.40656 0.812080i −0.424095 0.244851i 0.272733 0.962090i \(-0.412072\pi\)
−0.696828 + 0.717239i \(0.745406\pi\)
\(12\) −0.111810 + 0.193660i −0.0322766 + 0.0559048i
\(13\) −1.42641 3.31140i −0.395616 0.918416i
\(14\) 0 0
\(15\) 1.26999 0.733228i 0.327909 0.189319i
\(16\) −3.83547 −0.958867
\(17\) 1.94825 0.472521 0.236260 0.971690i \(-0.424078\pi\)
0.236260 + 0.971690i \(0.424078\pi\)
\(18\) −5.98335 + 3.45449i −1.41029 + 0.814230i
\(19\) 2.15740 1.24558i 0.494942 0.285755i −0.231680 0.972792i \(-0.574422\pi\)
0.726622 + 0.687037i \(0.241089\pi\)
\(20\) −0.0355659 0.0205340i −0.00795277 0.00459154i
\(21\) 0 0
\(22\) −1.12550 + 1.94943i −0.239958 + 0.415620i
\(23\) 9.14058 1.90594 0.952971 0.303060i \(-0.0980083\pi\)
0.952971 + 0.303060i \(0.0980083\pi\)
\(24\) 7.05179 + 4.07135i 1.43944 + 0.831061i
\(25\) −2.36534 4.09689i −0.473068 0.819378i
\(26\) −4.58944 + 1.97694i −0.900063 + 0.387710i
\(27\) 5.60916 1.07948
\(28\) 0 0
\(29\) 2.61498 + 4.52928i 0.485589 + 0.841065i 0.999863 0.0165608i \(-0.00527172\pi\)
−0.514274 + 0.857626i \(0.671938\pi\)
\(30\) −1.01622 1.76014i −0.185535 0.321357i
\(31\) 5.01767 2.89695i 0.901201 0.520308i 0.0236111 0.999721i \(-0.492484\pi\)
0.877590 + 0.479413i \(0.159150\pi\)
\(32\) 0.447392i 0.0790885i
\(33\) 3.97463 2.29475i 0.691894 0.399465i
\(34\) 2.70019i 0.463078i
\(35\) 0 0
\(36\) −0.197245 0.341639i −0.0328742 0.0569398i
\(37\) 10.2293i 1.68168i −0.541284 0.840840i \(-0.682062\pi\)
0.541284 0.840840i \(-0.317938\pi\)
\(38\) −1.72631 2.99006i −0.280045 0.485052i
\(39\) 10.1190 + 1.18792i 1.62033 + 0.190219i
\(40\) −0.747709 + 1.29507i −0.118223 + 0.204769i
\(41\) −3.64513 + 2.10452i −0.569273 + 0.328670i −0.756859 0.653578i \(-0.773267\pi\)
0.187586 + 0.982248i \(0.439934\pi\)
\(42\) 0 0
\(43\) −0.498655 + 0.863697i −0.0760442 + 0.131712i −0.901540 0.432696i \(-0.857562\pi\)
0.825496 + 0.564408i \(0.190896\pi\)
\(44\) −0.111309 0.0642644i −0.0167805 0.00968822i
\(45\) 2.58700i 0.385647i
\(46\) 12.6684i 1.86786i
\(47\) −3.91206 2.25863i −0.570632 0.329455i 0.186770 0.982404i \(-0.440198\pi\)
−0.757402 + 0.652949i \(0.773532\pi\)
\(48\) 5.41908 9.38612i 0.782177 1.35477i
\(49\) 0 0
\(50\) −5.67810 + 3.27825i −0.803004 + 0.463615i
\(51\) −2.75266 + 4.76775i −0.385450 + 0.667618i
\(52\) −0.112880 0.262049i −0.0156536 0.0363397i
\(53\) 4.44825 + 7.70460i 0.611015 + 1.05831i 0.991070 + 0.133344i \(0.0425717\pi\)
−0.380055 + 0.924964i \(0.624095\pi\)
\(54\) 7.77403i 1.05791i
\(55\) 0.421434 + 0.729946i 0.0568262 + 0.0984259i
\(56\) 0 0
\(57\) 7.03944i 0.932397i
\(58\) 6.27736 3.62424i 0.824258 0.475886i
\(59\) 6.20526i 0.807856i −0.914791 0.403928i \(-0.867645\pi\)
0.914791 0.403928i \(-0.132355\pi\)
\(60\) 0.100501 0.0580244i 0.0129746 0.00749091i
\(61\) −6.73536 11.6660i −0.862375 1.49368i −0.869630 0.493703i \(-0.835643\pi\)
0.00725571 0.999974i \(-0.497690\pi\)
\(62\) −4.01504 6.95426i −0.509911 0.883191i
\(63\) 0 0
\(64\) −8.29100 −1.03637
\(65\) −0.218163 + 1.85836i −0.0270598 + 0.230502i
\(66\) −3.18042 5.50865i −0.391483 0.678068i
\(67\) 7.25094 + 4.18633i 0.885843 + 0.511442i 0.872580 0.488470i \(-0.162445\pi\)
0.0132624 + 0.999912i \(0.495778\pi\)
\(68\) 0.154176 0.0186966
\(69\) −12.9146 + 22.3688i −1.55474 + 2.69288i
\(70\) 0 0
\(71\) −4.50168 2.59905i −0.534251 0.308450i 0.208495 0.978023i \(-0.433144\pi\)
−0.742746 + 0.669573i \(0.766477\pi\)
\(72\) −12.4402 + 7.18234i −1.46609 + 0.846447i
\(73\) 10.2533 5.91976i 1.20006 0.692856i 0.239493 0.970898i \(-0.423019\pi\)
0.960569 + 0.278042i \(0.0896855\pi\)
\(74\) −14.1773 −1.64807
\(75\) 13.3678 1.54359
\(76\) 0.170727 0.0985694i 0.0195838 0.0113067i
\(77\) 0 0
\(78\) 1.64640 14.0244i 0.186418 1.58795i
\(79\) −0.491155 + 0.850705i −0.0552592 + 0.0957118i −0.892332 0.451380i \(-0.850932\pi\)
0.837073 + 0.547092i \(0.184265\pi\)
\(80\) 1.72377 + 0.995221i 0.192724 + 0.111269i
\(81\) −0.447609 + 0.775281i −0.0497343 + 0.0861423i
\(82\) 2.91676 + 5.05197i 0.322102 + 0.557897i
\(83\) 8.91851i 0.978934i −0.872022 0.489467i \(-0.837191\pi\)
0.872022 0.489467i \(-0.162809\pi\)
\(84\) 0 0
\(85\) −0.875603 0.505530i −0.0949725 0.0548324i
\(86\) 1.19704 + 0.691113i 0.129080 + 0.0745246i
\(87\) −14.7787 −1.58444
\(88\) −2.34008 + 4.05313i −0.249453 + 0.432065i
\(89\) 12.0190i 1.27401i 0.770860 + 0.637005i \(0.219827\pi\)
−0.770860 + 0.637005i \(0.780173\pi\)
\(90\) 3.58546 0.377941
\(91\) 0 0
\(92\) 0.723345 0.0754139
\(93\) 16.3723i 1.69773i
\(94\) −3.13035 + 5.42193i −0.322871 + 0.559229i
\(95\) −1.29280 −0.132639
\(96\) 1.09485 + 0.632114i 0.111743 + 0.0645149i
\(97\) −3.82981 2.21114i −0.388858 0.224507i 0.292807 0.956172i \(-0.405411\pi\)
−0.681665 + 0.731664i \(0.738744\pi\)
\(98\) 0 0
\(99\) 8.09643i 0.813722i
\(100\) −0.187183 0.324210i −0.0187183 0.0324210i
\(101\) −9.15132 + 15.8506i −0.910591 + 1.57719i −0.0973594 + 0.995249i \(0.531040\pi\)
−0.813231 + 0.581940i \(0.802294\pi\)
\(102\) 6.60787 + 3.81506i 0.654277 + 0.377747i
\(103\) −2.51023 + 4.34784i −0.247340 + 0.428406i −0.962787 0.270262i \(-0.912890\pi\)
0.715447 + 0.698667i \(0.246223\pi\)
\(104\) −9.54206 + 4.11033i −0.935676 + 0.403051i
\(105\) 0 0
\(106\) 10.6782 6.16507i 1.03716 0.598804i
\(107\) 6.14456 0.594017 0.297008 0.954875i \(-0.404011\pi\)
0.297008 + 0.954875i \(0.404011\pi\)
\(108\) 0.443884 0.0427127
\(109\) −10.3025 + 5.94812i −0.986796 + 0.569727i −0.904315 0.426866i \(-0.859618\pi\)
−0.0824809 + 0.996593i \(0.526284\pi\)
\(110\) 1.01167 0.584088i 0.0964590 0.0556906i
\(111\) 25.0330 + 14.4528i 2.37602 + 1.37180i
\(112\) 0 0
\(113\) −1.77806 + 3.07969i −0.167266 + 0.289713i −0.937458 0.348099i \(-0.886827\pi\)
0.770192 + 0.637812i \(0.220161\pi\)
\(114\) 9.75633 0.913764
\(115\) −4.10805 2.37178i −0.383078 0.221170i
\(116\) 0.206938 + 0.358427i 0.0192137 + 0.0332791i
\(117\) −10.7404 + 14.4117i −0.992951 + 1.33236i
\(118\) −8.60020 −0.791713
\(119\) 0 0
\(120\) −2.11286 3.65957i −0.192877 0.334072i
\(121\) −4.18105 7.24180i −0.380096 0.658345i
\(122\) −16.1685 + 9.33489i −1.46383 + 0.845141i
\(123\) 11.8938i 1.07243i
\(124\) 0.397076 0.229252i 0.0356585 0.0205874i
\(125\) 5.04981i 0.451668i
\(126\) 0 0
\(127\) −0.711749 1.23279i −0.0631575 0.109392i 0.832718 0.553698i \(-0.186784\pi\)
−0.895875 + 0.444306i \(0.853450\pi\)
\(128\) 10.5961i 0.936576i
\(129\) −1.40909 2.44061i −0.124063 0.214884i
\(130\) 2.57560 + 0.302364i 0.225895 + 0.0265190i
\(131\) 4.33687 7.51168i 0.378914 0.656298i −0.611990 0.790865i \(-0.709631\pi\)
0.990905 + 0.134567i \(0.0429643\pi\)
\(132\) 0.314535 0.181597i 0.0273767 0.0158060i
\(133\) 0 0
\(134\) 5.80205 10.0495i 0.501221 0.868141i
\(135\) −2.52092 1.45546i −0.216967 0.125266i
\(136\) 5.61405i 0.481401i
\(137\) 8.51784i 0.727728i −0.931452 0.363864i \(-0.881457\pi\)
0.931452 0.363864i \(-0.118543\pi\)
\(138\) 31.0020 + 17.8990i 2.63907 + 1.52367i
\(139\) −2.51922 + 4.36342i −0.213677 + 0.370100i −0.952863 0.303402i \(-0.901877\pi\)
0.739185 + 0.673502i \(0.235211\pi\)
\(140\) 0 0
\(141\) 11.0546 6.38237i 0.930964 0.537493i
\(142\) −3.60215 + 6.23912i −0.302286 + 0.523575i
\(143\) −0.682776 + 5.81605i −0.0570966 + 0.486363i
\(144\) 9.55990 + 16.5582i 0.796658 + 1.37985i
\(145\) 2.71412i 0.225396i
\(146\) −8.20451 14.2106i −0.679010 1.17608i
\(147\) 0 0
\(148\) 0.809498i 0.0665403i
\(149\) −2.91409 + 1.68245i −0.238732 + 0.137832i −0.614594 0.788844i \(-0.710680\pi\)
0.375862 + 0.926676i \(0.377347\pi\)
\(150\) 18.5272i 1.51274i
\(151\) 10.9610 6.32831i 0.891990 0.514991i 0.0173971 0.999849i \(-0.494462\pi\)
0.874593 + 0.484858i \(0.161129\pi\)
\(152\) −3.58924 6.21674i −0.291125 0.504244i
\(153\) −4.85602 8.41087i −0.392586 0.679979i
\(154\) 0 0
\(155\) −3.00679 −0.241511
\(156\) 0.800771 + 0.0940067i 0.0641130 + 0.00752656i
\(157\) 5.18457 + 8.97993i 0.413773 + 0.716677i 0.995299 0.0968517i \(-0.0308772\pi\)
−0.581525 + 0.813528i \(0.697544\pi\)
\(158\) 1.17904 + 0.680717i 0.0937992 + 0.0541550i
\(159\) −25.1395 −1.99369
\(160\) −0.116089 + 0.201071i −0.00917761 + 0.0158961i
\(161\) 0 0
\(162\) 1.07450 + 0.620364i 0.0844209 + 0.0487404i
\(163\) −13.6428 + 7.87669i −1.06859 + 0.616950i −0.927796 0.373089i \(-0.878299\pi\)
−0.140794 + 0.990039i \(0.544965\pi\)
\(164\) −0.288459 + 0.166542i −0.0225249 + 0.0130047i
\(165\) −2.38176 −0.185420
\(166\) −12.3606 −0.959371
\(167\) 14.2016 8.19930i 1.09895 0.634481i 0.163007 0.986625i \(-0.447881\pi\)
0.935946 + 0.352144i \(0.114547\pi\)
\(168\) 0 0
\(169\) −8.93069 + 9.44684i −0.686976 + 0.726680i
\(170\) −0.700640 + 1.21354i −0.0537367 + 0.0930746i
\(171\) −10.7547 6.20920i −0.822429 0.474830i
\(172\) −0.0394614 + 0.0683491i −0.00300890 + 0.00521157i
\(173\) 0.150677 + 0.260981i 0.0114558 + 0.0198420i 0.871696 0.490046i \(-0.163020\pi\)
−0.860241 + 0.509888i \(0.829687\pi\)
\(174\) 20.4825i 1.55278i
\(175\) 0 0
\(176\) 5.39483 + 3.11470i 0.406650 + 0.234780i
\(177\) 15.1855 + 8.76734i 1.14141 + 0.658993i
\(178\) 16.6577 1.24855
\(179\) −4.90791 + 8.50075i −0.366834 + 0.635376i −0.989069 0.147455i \(-0.952892\pi\)
0.622234 + 0.782831i \(0.286225\pi\)
\(180\) 0.204724i 0.0152592i
\(181\) −12.4320 −0.924062 −0.462031 0.886864i \(-0.652879\pi\)
−0.462031 + 0.886864i \(0.652879\pi\)
\(182\) 0 0
\(183\) 38.0652 2.81386
\(184\) 26.3393i 1.94176i
\(185\) −2.65427 + 4.59733i −0.195146 + 0.338003i
\(186\) 22.6912 1.66380
\(187\) −2.74034 1.58214i −0.200394 0.115697i
\(188\) −0.309583 0.178738i −0.0225786 0.0130358i
\(189\) 0 0
\(190\) 1.79176i 0.129988i
\(191\) 6.12346 + 10.6061i 0.443078 + 0.767434i 0.997916 0.0645248i \(-0.0205531\pi\)
−0.554838 + 0.831958i \(0.687220\pi\)
\(192\) 11.7142 20.2897i 0.845403 1.46428i
\(193\) 10.0752 + 5.81692i 0.725229 + 0.418711i 0.816674 0.577099i \(-0.195815\pi\)
−0.0914452 + 0.995810i \(0.529149\pi\)
\(194\) −3.06454 + 5.30794i −0.220021 + 0.381088i
\(195\) −4.23953 3.15955i −0.303599 0.226260i
\(196\) 0 0
\(197\) −1.55984 + 0.900572i −0.111134 + 0.0641631i −0.554537 0.832159i \(-0.687104\pi\)
0.443403 + 0.896322i \(0.353771\pi\)
\(198\) 11.2213 0.797461
\(199\) 6.59313 0.467375 0.233687 0.972312i \(-0.424921\pi\)
0.233687 + 0.972312i \(0.424921\pi\)
\(200\) −11.8055 + 6.81593i −0.834777 + 0.481959i
\(201\) −20.4895 + 11.8296i −1.44522 + 0.834397i
\(202\) 21.9681 + 12.6833i 1.54567 + 0.892394i
\(203\) 0 0
\(204\) −0.217833 + 0.377298i −0.0152514 + 0.0264162i
\(205\) 2.18431 0.152559
\(206\) 6.02590 + 3.47906i 0.419845 + 0.242397i
\(207\) −22.7829 39.4611i −1.58352 2.74274i
\(208\) 5.47096 + 12.7007i 0.379343 + 0.880638i
\(209\) −4.04603 −0.279870
\(210\) 0 0
\(211\) −5.35996 9.28373i −0.368995 0.639118i 0.620414 0.784275i \(-0.286965\pi\)
−0.989409 + 0.145157i \(0.953631\pi\)
\(212\) 0.352015 + 0.609708i 0.0241765 + 0.0418749i
\(213\) 12.7207 7.34432i 0.871610 0.503224i
\(214\) 8.51607i 0.582146i
\(215\) 0.448221 0.258781i 0.0305684 0.0176487i
\(216\) 16.1633i 1.09977i
\(217\) 0 0
\(218\) 8.24382 + 14.2787i 0.558342 + 0.967076i
\(219\) 33.4558i 2.26074i
\(220\) 0.0333504 + 0.0577647i 0.00224849 + 0.00389449i
\(221\) −2.77901 6.45144i −0.186937 0.433971i
\(222\) 20.0309 34.6945i 1.34438 2.32854i
\(223\) 11.1612 6.44392i 0.747409 0.431517i −0.0773480 0.997004i \(-0.524645\pi\)
0.824757 + 0.565487i \(0.191312\pi\)
\(224\) 0 0
\(225\) −11.7912 + 20.4230i −0.786082 + 1.36153i
\(226\) 4.26831 + 2.46431i 0.283924 + 0.163923i
\(227\) 0.699155i 0.0464045i −0.999731 0.0232023i \(-0.992614\pi\)
0.999731 0.0232023i \(-0.00738617\pi\)
\(228\) 0.557070i 0.0368929i
\(229\) 15.8369 + 9.14342i 1.04653 + 0.604214i 0.921676 0.387961i \(-0.126820\pi\)
0.124854 + 0.992175i \(0.460154\pi\)
\(230\) −3.28718 + 5.69356i −0.216750 + 0.375422i
\(231\) 0 0
\(232\) 13.0515 7.53528i 0.856872 0.494715i
\(233\) 13.3898 23.1918i 0.877194 1.51934i 0.0227864 0.999740i \(-0.492746\pi\)
0.854407 0.519604i \(-0.173920\pi\)
\(234\) 19.9739 + 14.8857i 1.30573 + 0.973109i
\(235\) 1.17213 + 2.03019i 0.0764614 + 0.132435i
\(236\) 0.491057i 0.0319651i
\(237\) −1.38789 2.40390i −0.0901533 0.156150i
\(238\) 0 0
\(239\) 16.6177i 1.07491i 0.843293 + 0.537454i \(0.180614\pi\)
−0.843293 + 0.537454i \(0.819386\pi\)
\(240\) −4.87099 + 2.81227i −0.314421 + 0.181531i
\(241\) 17.4129i 1.12166i 0.827931 + 0.560830i \(0.189518\pi\)
−0.827931 + 0.560830i \(0.810482\pi\)
\(242\) −10.0368 + 5.79474i −0.645189 + 0.372500i
\(243\) 7.14890 + 12.3823i 0.458602 + 0.794322i
\(244\) −0.533007 0.923194i −0.0341222 0.0591015i
\(245\) 0 0
\(246\) −16.4842 −1.05099
\(247\) −7.20195 5.36731i −0.458249 0.341514i
\(248\) −8.34782 14.4588i −0.530087 0.918137i
\(249\) 21.8253 + 12.6008i 1.38312 + 0.798546i
\(250\) 6.99879 0.442642
\(251\) 3.22491 5.58571i 0.203554 0.352567i −0.746117 0.665815i \(-0.768084\pi\)
0.949671 + 0.313249i \(0.101417\pi\)
\(252\) 0 0
\(253\) −12.8568 7.42288i −0.808300 0.466672i
\(254\) −1.70858 + 0.986451i −0.107206 + 0.0618954i
\(255\) 2.47426 1.42851i 0.154944 0.0894570i
\(256\) −1.89624 −0.118515
\(257\) −3.67156 −0.229025 −0.114513 0.993422i \(-0.536531\pi\)
−0.114513 + 0.993422i \(0.536531\pi\)
\(258\) −3.38257 + 1.95293i −0.210590 + 0.121584i
\(259\) 0 0
\(260\) −0.0172645 + 0.147063i −0.00107070 + 0.00912044i
\(261\) 13.0357 22.5784i 0.806887 1.39757i
\(262\) −10.4108 6.01070i −0.643183 0.371342i
\(263\) −9.15964 + 15.8650i −0.564807 + 0.978275i 0.432260 + 0.901749i \(0.357716\pi\)
−0.997068 + 0.0765263i \(0.975617\pi\)
\(264\) −6.61252 11.4532i −0.406973 0.704897i
\(265\) 4.61690i 0.283614i
\(266\) 0 0
\(267\) −29.4128 16.9815i −1.80003 1.03925i
\(268\) 0.573807 + 0.331287i 0.0350508 + 0.0202366i
\(269\) −27.5429 −1.67932 −0.839661 0.543111i \(-0.817246\pi\)
−0.839661 + 0.543111i \(0.817246\pi\)
\(270\) −2.01719 + 3.49388i −0.122762 + 0.212631i
\(271\) 6.51923i 0.396015i −0.980201 0.198007i \(-0.936553\pi\)
0.980201 0.198007i \(-0.0634470\pi\)
\(272\) −7.47246 −0.453084
\(273\) 0 0
\(274\) −11.8053 −0.713186
\(275\) 7.68338i 0.463325i
\(276\) −1.02200 + 1.77016i −0.0615174 + 0.106551i
\(277\) −5.44186 −0.326970 −0.163485 0.986546i \(-0.552273\pi\)
−0.163485 + 0.986546i \(0.552273\pi\)
\(278\) 6.04749 + 3.49152i 0.362704 + 0.209407i
\(279\) −25.0131 14.4413i −1.49749 0.864579i
\(280\) 0 0
\(281\) 3.54237i 0.211320i 0.994402 + 0.105660i \(0.0336955\pi\)
−0.994402 + 0.105660i \(0.966304\pi\)
\(282\) −8.84566 15.3211i −0.526752 0.912360i
\(283\) 7.06956 12.2448i 0.420242 0.727880i −0.575721 0.817646i \(-0.695279\pi\)
0.995963 + 0.0897658i \(0.0286119\pi\)
\(284\) −0.356243 0.205677i −0.0211391 0.0122047i
\(285\) 1.82658 3.16374i 0.108197 0.187404i
\(286\) 8.06077 + 0.946296i 0.476643 + 0.0559556i
\(287\) 0 0
\(288\) −1.93145 + 1.11512i −0.113812 + 0.0657093i
\(289\) −13.2043 −0.776724
\(290\) −3.76165 −0.220891
\(291\) 10.8222 6.24819i 0.634407 0.366275i
\(292\) 0.811403 0.468464i 0.0474838 0.0274148i
\(293\) 7.23071 + 4.17465i 0.422423 + 0.243886i 0.696113 0.717932i \(-0.254911\pi\)
−0.273691 + 0.961818i \(0.588244\pi\)
\(294\) 0 0
\(295\) −1.61013 + 2.78883i −0.0937455 + 0.162372i
\(296\) −29.4765 −1.71328
\(297\) −7.88964 4.55508i −0.457803 0.264313i
\(298\) 2.33180 + 4.03879i 0.135077 + 0.233961i
\(299\) −13.0382 30.2681i −0.754021 1.75045i
\(300\) 1.05787 0.0610762
\(301\) 0 0
\(302\) −8.77074 15.1914i −0.504699 0.874165i
\(303\) −25.8596 44.7901i −1.48559 2.57312i
\(304\) −8.27465 + 4.77737i −0.474584 + 0.274001i
\(305\) 6.99073i 0.400288i
\(306\) −11.6571 + 6.73021i −0.666390 + 0.384741i
\(307\) 8.33362i 0.475625i 0.971311 + 0.237813i \(0.0764304\pi\)
−0.971311 + 0.237813i \(0.923570\pi\)
\(308\) 0 0
\(309\) −7.09334 12.2860i −0.403526 0.698927i
\(310\) 4.16727i 0.236685i
\(311\) 7.31134 + 12.6636i 0.414588 + 0.718088i 0.995385 0.0959606i \(-0.0305923\pi\)
−0.580797 + 0.814048i \(0.697259\pi\)
\(312\) 3.42309 29.1587i 0.193794 1.65079i
\(313\) 8.56641 14.8375i 0.484202 0.838663i −0.515633 0.856809i \(-0.672443\pi\)
0.999835 + 0.0181467i \(0.00577661\pi\)
\(314\) 12.4458 7.18556i 0.702355 0.405505i
\(315\) 0 0
\(316\) −0.0388678 + 0.0673210i −0.00218649 + 0.00378710i
\(317\) −12.1244 7.00002i −0.680973 0.393160i 0.119248 0.992864i \(-0.461952\pi\)
−0.800222 + 0.599704i \(0.795285\pi\)
\(318\) 34.8422i 1.95385i
\(319\) 8.49428i 0.475589i
\(320\) 3.72622 + 2.15134i 0.208302 + 0.120263i
\(321\) −8.68157 + 15.0369i −0.484558 + 0.839279i
\(322\) 0 0
\(323\) 4.20317 2.42670i 0.233871 0.135025i
\(324\) −0.0354217 + 0.0613523i −0.00196787 + 0.00340846i
\(325\) −10.1925 + 13.6764i −0.565377 + 0.758633i
\(326\) 10.9167 + 18.9083i 0.604621 + 1.04724i
\(327\) 33.6161i 1.85897i
\(328\) 6.06434 + 10.5037i 0.334847 + 0.579972i
\(329\) 0 0
\(330\) 3.30100i 0.181714i
\(331\) −5.99286 + 3.45998i −0.329397 + 0.190178i −0.655574 0.755131i \(-0.727573\pi\)
0.326176 + 0.945309i \(0.394240\pi\)
\(332\) 0.705771i 0.0387342i
\(333\) −44.1611 + 25.4964i −2.42001 + 1.39719i
\(334\) −11.3638 19.6827i −0.621801 1.07699i
\(335\) −2.17253 3.76292i −0.118698 0.205591i
\(336\) 0 0
\(337\) 11.1559 0.607703 0.303852 0.952719i \(-0.401727\pi\)
0.303852 + 0.952719i \(0.401727\pi\)
\(338\) 13.0929 + 12.3775i 0.712158 + 0.673248i
\(339\) −5.02440 8.70251i −0.272888 0.472656i
\(340\) −0.0692913 0.0400054i −0.00375785 0.00216960i
\(341\) −9.41023 −0.509593
\(342\) −8.60566 + 14.9054i −0.465341 + 0.805994i
\(343\) 0 0
\(344\) 2.48881 + 1.43692i 0.134188 + 0.0774734i
\(345\) 11.6084 6.70213i 0.624977 0.360830i
\(346\) 0.361707 0.208832i 0.0194455 0.0112269i
\(347\) −4.92511 −0.264393 −0.132197 0.991223i \(-0.542203\pi\)
−0.132197 + 0.991223i \(0.542203\pi\)
\(348\) −1.16952 −0.0626928
\(349\) −1.31926 + 0.761675i −0.0706183 + 0.0407715i −0.534893 0.844920i \(-0.679648\pi\)
0.464275 + 0.885691i \(0.346315\pi\)
\(350\) 0 0
\(351\) −8.00098 18.5741i −0.427061 0.991415i
\(352\) −0.363318 + 0.629285i −0.0193649 + 0.0335410i
\(353\) 15.5261 + 8.96401i 0.826372 + 0.477106i 0.852609 0.522550i \(-0.175019\pi\)
−0.0262367 + 0.999656i \(0.508352\pi\)
\(354\) 12.1511 21.0463i 0.645824 1.11860i
\(355\) 1.34879 + 2.33618i 0.0715865 + 0.123991i
\(356\) 0.951129i 0.0504097i
\(357\) 0 0
\(358\) 11.7816 + 6.80213i 0.622679 + 0.359504i
\(359\) 17.3217 + 10.0007i 0.914204 + 0.527816i 0.881781 0.471658i \(-0.156344\pi\)
0.0324227 + 0.999474i \(0.489678\pi\)
\(360\) 7.45466 0.392895
\(361\) −6.39707 + 11.0801i −0.336688 + 0.583161i
\(362\) 17.2301i 0.905596i
\(363\) 23.6294 1.24022
\(364\) 0 0
\(365\) −6.14421 −0.321602
\(366\) 52.7566i 2.75763i
\(367\) 13.7078 23.7427i 0.715544 1.23936i −0.247206 0.968963i \(-0.579512\pi\)
0.962749 0.270395i \(-0.0871543\pi\)
\(368\) −35.0584 −1.82754
\(369\) 18.1710 + 10.4910i 0.945942 + 0.546140i
\(370\) 6.37169 + 3.67870i 0.331248 + 0.191246i
\(371\) 0 0
\(372\) 1.29563i 0.0671752i
\(373\) 7.94643 + 13.7636i 0.411451 + 0.712653i 0.995049 0.0993893i \(-0.0316889\pi\)
−0.583598 + 0.812043i \(0.698356\pi\)
\(374\) −2.19277 + 3.79798i −0.113385 + 0.196389i
\(375\) −12.3578 7.13481i −0.638156 0.368440i
\(376\) −6.50842 + 11.2729i −0.335646 + 0.581356i
\(377\) 11.2682 15.1199i 0.580341 0.778712i
\(378\) 0 0
\(379\) 7.60284 4.38950i 0.390532 0.225474i −0.291859 0.956461i \(-0.594274\pi\)
0.682390 + 0.730988i \(0.260940\pi\)
\(380\) −0.102307 −0.00524822
\(381\) 4.02249 0.206078
\(382\) 14.6996 8.48682i 0.752098 0.434224i
\(383\) 6.89562 3.98119i 0.352349 0.203429i −0.313370 0.949631i \(-0.601458\pi\)
0.665720 + 0.746202i \(0.268125\pi\)
\(384\) −25.9308 14.9712i −1.32328 0.763994i
\(385\) 0 0
\(386\) 8.06198 13.9638i 0.410344 0.710736i
\(387\) 4.97159 0.252720
\(388\) −0.303074 0.174980i −0.0153863 0.00888326i
\(389\) 16.0217 + 27.7504i 0.812333 + 1.40700i 0.911227 + 0.411904i \(0.135136\pi\)
−0.0988938 + 0.995098i \(0.531530\pi\)
\(390\) −4.37898 + 5.87579i −0.221738 + 0.297532i
\(391\) 17.8082 0.900598
\(392\) 0 0
\(393\) 12.2550 + 21.2263i 0.618184 + 1.07073i
\(394\) 1.24815 + 2.16186i 0.0628809 + 0.108913i
\(395\) 0.441479 0.254888i 0.0222132 0.0128248i
\(396\) 0.640716i 0.0321972i
\(397\) 5.57251 3.21729i 0.279676 0.161471i −0.353601 0.935396i \(-0.615043\pi\)
0.633277 + 0.773925i \(0.281710\pi\)
\(398\) 9.13777i 0.458035i
\(399\) 0 0
\(400\) 9.07219 + 15.7135i 0.453609 + 0.785675i
\(401\) 0.533577i 0.0266456i −0.999911 0.0133228i \(-0.995759\pi\)
0.999911 0.0133228i \(-0.00424090\pi\)
\(402\) 16.3953 + 28.3975i 0.817723 + 1.41634i
\(403\) −16.7502 12.4832i −0.834389 0.621835i
\(404\) −0.724195 + 1.25434i −0.0360301 + 0.0624059i
\(405\) 0.402337 0.232290i 0.0199923 0.0115426i
\(406\) 0 0
\(407\) −8.30697 + 14.3881i −0.411761 + 0.713191i
\(408\) 13.7387 + 7.93202i 0.680165 + 0.392694i
\(409\) 39.7528i 1.96565i −0.184547 0.982824i \(-0.559082\pi\)
0.184547 0.982824i \(-0.440918\pi\)
\(410\) 3.02735i 0.149510i
\(411\) 20.8448 + 12.0347i 1.02820 + 0.593630i
\(412\) −0.198648 + 0.344069i −0.00978670 + 0.0169511i
\(413\) 0 0
\(414\) −54.6913 + 31.5760i −2.68793 + 1.55188i
\(415\) −2.31416 + 4.00825i −0.113598 + 0.196757i
\(416\) −1.48149 + 0.638166i −0.0726361 + 0.0312887i
\(417\) −7.11875 12.3300i −0.348607 0.603804i
\(418\) 5.60761i 0.274277i
\(419\) 11.9088 + 20.6266i 0.581783 + 1.00768i 0.995268 + 0.0971665i \(0.0309779\pi\)
−0.413485 + 0.910511i \(0.635689\pi\)
\(420\) 0 0
\(421\) 23.2419i 1.13274i −0.824151 0.566370i \(-0.808347\pi\)
0.824151 0.566370i \(-0.191653\pi\)
\(422\) −12.8668 + 7.42865i −0.626346 + 0.361621i
\(423\) 22.5185i 1.09489i
\(424\) 22.2014 12.8180i 1.07820 0.622498i
\(425\) −4.60828 7.98178i −0.223535 0.387173i
\(426\) −10.1789 17.6303i −0.493168 0.854192i
\(427\) 0 0
\(428\) 0.486253 0.0235039
\(429\) −13.2683 9.88831i −0.640600 0.477412i
\(430\) −0.358658 0.621214i −0.0172960 0.0299576i
\(431\) 2.34424 + 1.35345i 0.112918 + 0.0651932i 0.555395 0.831586i \(-0.312567\pi\)
−0.442477 + 0.896780i \(0.645900\pi\)
\(432\) −21.5137 −1.03508
\(433\) 2.90945 5.03932i 0.139819 0.242174i −0.787609 0.616176i \(-0.788681\pi\)
0.927428 + 0.374002i \(0.122015\pi\)
\(434\) 0 0
\(435\) 6.64198 + 3.83475i 0.318459 + 0.183862i
\(436\) −0.815290 + 0.470708i −0.0390453 + 0.0225428i
\(437\) 19.7199 11.3853i 0.943332 0.544633i
\(438\) 46.3682 2.21556
\(439\) 38.1702 1.82176 0.910882 0.412668i \(-0.135403\pi\)
0.910882 + 0.412668i \(0.135403\pi\)
\(440\) 2.10340 1.21440i 0.100276 0.0578942i
\(441\) 0 0
\(442\) −8.94139 + 3.85158i −0.425298 + 0.183201i
\(443\) 15.8370 27.4305i 0.752440 1.30326i −0.194198 0.980962i \(-0.562210\pi\)
0.946637 0.322301i \(-0.104456\pi\)
\(444\) 1.98100 + 1.14373i 0.0940139 + 0.0542790i
\(445\) 3.11867 5.40169i 0.147839 0.256065i
\(446\) −8.93097 15.4689i −0.422894 0.732473i
\(447\) 9.50845i 0.449734i
\(448\) 0 0
\(449\) 27.1975 + 15.7025i 1.28353 + 0.741045i 0.977491 0.210975i \(-0.0676638\pi\)
0.306036 + 0.952020i \(0.400997\pi\)
\(450\) 28.3053 + 16.3421i 1.33433 + 0.770373i
\(451\) 6.83614 0.321901
\(452\) −0.140708 + 0.243713i −0.00661834 + 0.0114633i
\(453\) 35.7648i 1.68037i
\(454\) −0.968995 −0.0454772
\(455\) 0 0
\(456\) 20.2847 0.949920
\(457\) 31.8281i 1.48886i 0.667702 + 0.744429i \(0.267278\pi\)
−0.667702 + 0.744429i \(0.732722\pi\)
\(458\) 12.6723 21.9491i 0.592140 1.02562i
\(459\) 10.9281 0.510078
\(460\) −0.325093 0.187692i −0.0151575 0.00875121i
\(461\) −1.01005 0.583153i −0.0470427 0.0271601i 0.476294 0.879286i \(-0.341980\pi\)
−0.523337 + 0.852126i \(0.675313\pi\)
\(462\) 0 0
\(463\) 20.3441i 0.945469i 0.881205 + 0.472734i \(0.156733\pi\)
−0.881205 + 0.472734i \(0.843267\pi\)
\(464\) −10.0297 17.3719i −0.465615 0.806470i
\(465\) 4.24825 7.35819i 0.197008 0.341228i
\(466\) −32.1427 18.5576i −1.48898 0.859664i
\(467\) 0.784697 1.35913i 0.0363114 0.0628932i −0.847299 0.531117i \(-0.821773\pi\)
0.883610 + 0.468224i \(0.155106\pi\)
\(468\) −0.849948 + 1.14048i −0.0392889 + 0.0527185i
\(469\) 0 0
\(470\) 2.81375 1.62452i 0.129788 0.0749334i
\(471\) −29.3008 −1.35011
\(472\) −17.8810 −0.823039
\(473\) 1.40278 0.809896i 0.0644999 0.0372391i
\(474\) −3.33169 + 1.92355i −0.153030 + 0.0883517i
\(475\) −10.2060 5.89243i −0.468283 0.270363i
\(476\) 0 0
\(477\) 22.1745 38.4074i 1.01530 1.75856i
\(478\) 23.0313 1.05343
\(479\) 6.68501 + 3.85959i 0.305446 + 0.176349i 0.644887 0.764278i \(-0.276905\pi\)
−0.339441 + 0.940627i \(0.610238\pi\)
\(480\) −0.328040 0.568182i −0.0149729 0.0259338i
\(481\) −33.8731 + 14.5911i −1.54448 + 0.665299i
\(482\) 24.1334 1.09925
\(483\) 0 0
\(484\) −0.330870 0.573083i −0.0150395 0.0260492i
\(485\) 1.14749 + 1.98751i 0.0521047 + 0.0902481i
\(486\) 17.1612 9.90803i 0.778448 0.449437i
\(487\) 0.0761801i 0.00345205i 0.999999 + 0.00172602i \(0.000549411\pi\)
−0.999999 + 0.00172602i \(0.999451\pi\)
\(488\) −33.6165 + 19.4085i −1.52175 + 0.878582i
\(489\) 44.5155i 2.01306i
\(490\) 0 0
\(491\) 0.893574 + 1.54772i 0.0403264 + 0.0698474i 0.885484 0.464670i \(-0.153827\pi\)
−0.845158 + 0.534517i \(0.820494\pi\)
\(492\) 0.941220i 0.0424335i
\(493\) 5.09464 + 8.82418i 0.229451 + 0.397421i
\(494\) −7.43884 + 9.98156i −0.334689 + 0.449092i
\(495\) 2.10085 3.63878i 0.0944262 0.163551i
\(496\) −19.2451 + 11.1112i −0.864131 + 0.498906i
\(497\) 0 0
\(498\) 17.4642 30.2488i 0.782589 1.35548i
\(499\) 7.21826 + 4.16747i 0.323134 + 0.186561i 0.652789 0.757540i \(-0.273599\pi\)
−0.329655 + 0.944102i \(0.606932\pi\)
\(500\) 0.399619i 0.0178715i
\(501\) 46.3387i 2.07026i
\(502\) −7.74152 4.46957i −0.345521 0.199487i
\(503\) 0.720238 1.24749i 0.0321138 0.0556228i −0.849522 0.527554i \(-0.823109\pi\)
0.881636 + 0.471931i \(0.156443\pi\)
\(504\) 0 0
\(505\) 8.22576 4.74914i 0.366041 0.211334i
\(506\) −10.2878 + 17.8189i −0.457347 + 0.792148i
\(507\) −10.5002 35.2024i −0.466329 1.56339i
\(508\) −0.0563247 0.0975572i −0.00249900 0.00432840i
\(509\) 14.8256i 0.657135i −0.944480 0.328568i \(-0.893434\pi\)
0.944480 0.328568i \(-0.106566\pi\)
\(510\) −1.97985 3.42920i −0.0876693 0.151848i
\(511\) 0 0
\(512\) 23.8204i 1.05272i
\(513\) 12.1012 6.98664i 0.534282 0.308468i
\(514\) 5.08860i 0.224449i
\(515\) 2.25634 1.30270i 0.0994264 0.0574038i
\(516\) −0.111509 0.193139i −0.00490891 0.00850248i
\(517\) 3.66837 + 6.35380i 0.161335 + 0.279440i
\(518\) 0 0
\(519\) −0.851561 −0.0373794
\(520\) 5.35503 + 0.628655i 0.234834 + 0.0275683i
\(521\) −0.167194 0.289588i −0.00732489 0.0126871i 0.862340 0.506330i \(-0.168998\pi\)
−0.869665 + 0.493643i \(0.835665\pi\)
\(522\) −31.2926 18.0668i −1.36964 0.790763i
\(523\) 32.5065 1.42141 0.710705 0.703490i \(-0.248376\pi\)
0.710705 + 0.703490i \(0.248376\pi\)
\(524\) 0.343201 0.594441i 0.0149928 0.0259683i
\(525\) 0 0
\(526\) 21.9881 + 12.6948i 0.958726 + 0.553521i
\(527\) 9.77570 5.64400i 0.425836 0.245857i
\(528\) −15.2446 + 8.80145i −0.663434 + 0.383034i
\(529\) 60.5502 2.63262
\(530\) −6.39881 −0.277947
\(531\) −26.7890 + 15.4666i −1.16254 + 0.671194i
\(532\) 0 0
\(533\) 12.1683 + 9.06855i 0.527070 + 0.392803i
\(534\) −23.5355 + 40.7647i −1.01848 + 1.76406i
\(535\) −2.76155 1.59438i −0.119392 0.0689311i
\(536\) 12.0633 20.8942i 0.521053 0.902491i
\(537\) −13.8686 24.0212i −0.598476 1.03659i
\(538\) 38.1732i 1.64576i
\(539\) 0 0
\(540\) −0.199495 0.115178i −0.00858488 0.00495649i
\(541\) −9.18120 5.30077i −0.394731 0.227898i 0.289477 0.957185i \(-0.406519\pi\)
−0.684208 + 0.729287i \(0.739852\pi\)
\(542\) −9.03534 −0.388101
\(543\) 17.5650 30.4235i 0.753786 1.30560i
\(544\) 0.871633i 0.0373709i
\(545\) 6.17364 0.264450
\(546\) 0 0
\(547\) 10.2327 0.437519 0.218760 0.975779i \(-0.429799\pi\)
0.218760 + 0.975779i \(0.429799\pi\)
\(548\) 0.674064i 0.0287946i
\(549\) −33.5758 + 58.1549i −1.43298 + 2.48199i
\(550\) 10.6488 0.454067
\(551\) 11.2831 + 6.51432i 0.480677 + 0.277519i
\(552\) 64.4574 + 37.2145i 2.74349 + 1.58396i
\(553\) 0 0
\(554\) 7.54216i 0.320436i
\(555\) −7.50037 12.9910i −0.318373 0.551438i
\(556\) −0.199360 + 0.345301i −0.00845474 + 0.0146440i
\(557\) −27.7067 15.9965i −1.17397 0.677793i −0.219359 0.975644i \(-0.570397\pi\)
−0.954612 + 0.297851i \(0.903730\pi\)
\(558\) −20.0150 + 34.6670i −0.847302 + 1.46757i
\(559\) 3.57133 + 0.419257i 0.151051 + 0.0177327i
\(560\) 0 0
\(561\) 7.74359 4.47076i 0.326934 0.188756i
\(562\) 4.90956 0.207097
\(563\) 10.7913 0.454800 0.227400 0.973801i \(-0.426978\pi\)
0.227400 + 0.973801i \(0.426978\pi\)
\(564\) 0.874811 0.505072i 0.0368362 0.0212674i
\(565\) 1.59823 0.922737i 0.0672380 0.0388199i
\(566\) −16.9708 9.79808i −0.713335 0.411844i
\(567\) 0 0
\(568\) −7.48937 + 12.9720i −0.314247 + 0.544292i
\(569\) 24.6014 1.03134 0.515672 0.856786i \(-0.327542\pi\)
0.515672 + 0.856786i \(0.327542\pi\)
\(570\) −4.38479 2.53156i −0.183659 0.106035i
\(571\) 8.28621 + 14.3521i 0.346767 + 0.600618i 0.985673 0.168667i \(-0.0539461\pi\)
−0.638906 + 0.769285i \(0.720613\pi\)
\(572\) −0.0540319 + 0.460256i −0.00225919 + 0.0192443i
\(573\) −34.6070 −1.44573
\(574\) 0 0
\(575\) −21.6206 37.4480i −0.901641 1.56169i
\(576\) 20.6653 + 35.7934i 0.861054 + 1.49139i
\(577\) 12.6969 7.33053i 0.528577 0.305174i −0.211860 0.977300i \(-0.567952\pi\)
0.740437 + 0.672126i \(0.234619\pi\)
\(578\) 18.3005i 0.761202i
\(579\) −28.4702 + 16.4373i −1.18318 + 0.683111i
\(580\) 0.214784i 0.00891840i
\(581\) 0 0
\(582\) −8.65969 14.9990i −0.358956 0.621730i
\(583\) 14.4493i 0.598431i
\(584\) −17.0583 29.5458i −0.705877 1.22262i
\(585\) 8.56658 3.69013i 0.354185 0.152568i
\(586\) 5.78587 10.0214i 0.239012 0.413981i
\(587\) −30.5998 + 17.6668i −1.26299 + 0.729186i −0.973652 0.228041i \(-0.926768\pi\)
−0.289336 + 0.957227i \(0.593435\pi\)
\(588\) 0 0
\(589\) 7.21676 12.4998i 0.297362 0.515045i
\(590\) 3.86519 + 2.23157i 0.159127 + 0.0918722i
\(591\) 5.08963i 0.209359i
\(592\) 39.2340i 1.61251i
\(593\) 14.2283 + 8.21471i 0.584286 + 0.337338i 0.762835 0.646593i \(-0.223807\pi\)
−0.178549 + 0.983931i \(0.557140\pi\)
\(594\) −6.31313 + 10.9347i −0.259031 + 0.448655i
\(595\) 0 0
\(596\) −0.230608 + 0.133142i −0.00944608 + 0.00545370i
\(597\) −9.31535 + 16.1347i −0.381252 + 0.660348i
\(598\) −41.9501 + 18.0704i −1.71547 + 0.738953i
\(599\) −6.04094 10.4632i −0.246826 0.427516i 0.715817 0.698288i \(-0.246054\pi\)
−0.962644 + 0.270772i \(0.912721\pi\)
\(600\) 38.5206i 1.57259i
\(601\) 3.90743 + 6.76787i 0.159387 + 0.276067i 0.934648 0.355574i \(-0.115715\pi\)
−0.775261 + 0.631642i \(0.782381\pi\)
\(602\) 0 0
\(603\) 41.7377i 1.69969i
\(604\) 0.867401 0.500794i 0.0352941 0.0203770i
\(605\) 4.33957i 0.176429i
\(606\) −62.0770 + 35.8401i −2.52170 + 1.45591i
\(607\) 17.7825 + 30.8001i 0.721768 + 1.25014i 0.960291 + 0.279002i \(0.0900035\pi\)
−0.238523 + 0.971137i \(0.576663\pi\)
\(608\) −0.557261 0.965205i −0.0225999 0.0391442i
\(609\) 0 0
\(610\) 9.68882 0.392289
\(611\) −1.89900 + 16.1761i −0.0768252 + 0.654415i
\(612\) −0.384284 0.665599i −0.0155338 0.0269052i
\(613\) 10.3376 + 5.96839i 0.417530 + 0.241061i 0.694020 0.719956i \(-0.255838\pi\)
−0.276490 + 0.961017i \(0.589171\pi\)
\(614\) 11.5500 0.466120
\(615\) −3.08618 + 5.34542i −0.124447 + 0.215548i
\(616\) 0 0
\(617\) −20.4124 11.7851i −0.821772 0.474450i 0.0292550 0.999572i \(-0.490687\pi\)
−0.851027 + 0.525122i \(0.824020\pi\)
\(618\) −17.0278 + 9.83103i −0.684960 + 0.395462i
\(619\) −24.7312 + 14.2786i −0.994031 + 0.573904i −0.906477 0.422256i \(-0.861238\pi\)
−0.0875541 + 0.996160i \(0.527905\pi\)
\(620\) −0.237944 −0.00955606
\(621\) 51.2710 2.05743
\(622\) 17.5512 10.1332i 0.703738 0.406303i
\(623\) 0 0
\(624\) −38.8110 4.55623i −1.55368 0.182395i
\(625\) −10.5164 + 18.2149i −0.420656 + 0.728597i
\(626\) −20.5640 11.8726i −0.821903 0.474526i
\(627\) 5.71659 9.90142i 0.228298 0.395425i
\(628\) 0.410283 + 0.710632i 0.0163721 + 0.0283573i
\(629\) 19.9292i 0.794628i
\(630\) 0 0
\(631\) −38.9646 22.4962i −1.55116 0.895561i −0.998048 0.0624526i \(-0.980108\pi\)
−0.553109 0.833109i \(-0.686559\pi\)
\(632\) 2.45138 + 1.41530i 0.0975106 + 0.0562978i
\(633\) 30.2921 1.20400
\(634\) −9.70169 + 16.8038i −0.385303 + 0.667365i
\(635\) 0.738735i 0.0293158i
\(636\) −1.98943 −0.0788860
\(637\) 0 0
\(638\) −11.7727 −0.466085
\(639\) 25.9125i 1.02508i
\(640\) 2.74947 4.76222i 0.108682 0.188243i
\(641\) 2.53300 0.100048 0.0500238 0.998748i \(-0.484070\pi\)
0.0500238 + 0.998748i \(0.484070\pi\)
\(642\) 20.8405 + 12.0322i 0.822507 + 0.474875i
\(643\) −15.9150 9.18853i −0.627627 0.362360i 0.152206 0.988349i \(-0.451362\pi\)
−0.779832 + 0.625988i \(0.784696\pi\)
\(644\) 0 0
\(645\) 1.46251i 0.0575863i
\(646\) −3.36329 5.82539i −0.132327 0.229197i
\(647\) −10.4643 + 18.1248i −0.411396 + 0.712558i −0.995043 0.0994494i \(-0.968292\pi\)
0.583647 + 0.812008i \(0.301625\pi\)
\(648\) 2.23404 + 1.28982i 0.0877612 + 0.0506690i
\(649\) −5.03917 + 8.72810i −0.197805 + 0.342608i
\(650\) 18.9549 + 14.1263i 0.743473 + 0.554079i
\(651\) 0 0
\(652\) −1.07963 + 0.623326i −0.0422817 + 0.0244113i
\(653\) −48.1160 −1.88292 −0.941461 0.337121i \(-0.890547\pi\)
−0.941461 + 0.337121i \(0.890547\pi\)
\(654\) −46.5903 −1.82183
\(655\) −3.89824 + 2.25065i −0.152317 + 0.0879401i
\(656\) 13.9808 8.07180i 0.545857 0.315151i
\(657\) −51.1129 29.5100i −1.99410 1.15130i
\(658\) 0 0
\(659\) 1.10819 1.91944i 0.0431690 0.0747708i −0.843634 0.536919i \(-0.819588\pi\)
0.886803 + 0.462148i \(0.152921\pi\)
\(660\) −0.188482 −0.00733664
\(661\) −0.552034 0.318717i −0.0214716 0.0123966i 0.489226 0.872157i \(-0.337279\pi\)
−0.510697 + 0.859761i \(0.670613\pi\)
\(662\) 4.79537 + 8.30582i 0.186377 + 0.322815i
\(663\) 19.7143 + 2.31437i 0.765642 + 0.0898827i
\(664\) −25.6994 −0.997331
\(665\) 0 0
\(666\) 35.3368 + 61.2052i 1.36927 + 2.37165i
\(667\) 23.9024 + 41.4002i 0.925506 + 1.60302i
\(668\) 1.12385 0.648856i 0.0434831 0.0251050i
\(669\) 36.4181i 1.40801i
\(670\) −5.21523 + 3.01102i −0.201482 + 0.116326i
\(671\) 21.8786i 0.844614i
\(672\) 0 0
\(673\) 7.70343 + 13.3427i 0.296945 + 0.514324i 0.975436 0.220285i \(-0.0706988\pi\)
−0.678490 + 0.734609i \(0.737365\pi\)
\(674\) 15.4616i 0.595559i
\(675\) −13.2676 22.9801i −0.510669 0.884505i
\(676\) −0.706735 + 0.747581i −0.0271821 + 0.0287531i
\(677\) −5.84060 + 10.1162i −0.224473 + 0.388798i −0.956161 0.292841i \(-0.905399\pi\)
0.731689 + 0.681639i \(0.238733\pi\)
\(678\) −12.0613 + 6.96358i −0.463210 + 0.267435i
\(679\) 0 0
\(680\) −1.45673 + 2.52312i −0.0558629 + 0.0967574i
\(681\) 1.71097 + 0.987826i 0.0655643 + 0.0378536i
\(682\) 13.0421i 0.499409i
\(683\) 22.9114i 0.876680i −0.898809 0.438340i \(-0.855567\pi\)
0.898809 0.438340i \(-0.144433\pi\)
\(684\) −0.851075 0.491369i −0.0325417 0.0187879i
\(685\) −2.21020 + 3.82817i −0.0844473 + 0.146267i
\(686\) 0 0
\(687\) −44.7514 + 25.8372i −1.70737 + 0.985752i
\(688\) 1.91258 3.31268i 0.0729163 0.126295i
\(689\) 19.1679 25.7199i 0.730240 0.979849i
\(690\) −9.28883 16.0887i −0.353620 0.612487i
\(691\) 47.2325i 1.79681i 0.439167 + 0.898405i \(0.355274\pi\)
−0.439167 + 0.898405i \(0.644726\pi\)
\(692\) 0.0119239 + 0.0206529i 0.000453280 + 0.000785104i
\(693\) 0 0
\(694\) 6.82596i 0.259110i
\(695\) 2.26443 1.30737i 0.0858946 0.0495913i
\(696\) 42.5860i 1.61422i
\(697\) −7.10163 + 4.10013i −0.268994 + 0.155303i
\(698\) 1.05565 + 1.82843i 0.0399568 + 0.0692071i
\(699\) 37.8365 + 65.5347i 1.43111 + 2.47875i
\(700\) 0 0
\(701\) 12.2098 0.461158 0.230579 0.973054i \(-0.425938\pi\)
0.230579 + 0.973054i \(0.425938\pi\)
\(702\) −25.7429 + 11.0890i −0.971603 + 0.418527i
\(703\) −12.7413 22.0686i −0.480548 0.832334i
\(704\) 11.6618 + 6.73295i 0.439521 + 0.253758i
\(705\) −6.62435 −0.249488
\(706\) 12.4237 21.5185i 0.467572 0.809858i
\(707\) 0 0
\(708\) 1.20171 + 0.693808i 0.0451630 + 0.0260749i
\(709\) 15.4910 8.94374i 0.581777 0.335889i −0.180062 0.983655i \(-0.557630\pi\)
0.761839 + 0.647766i \(0.224297\pi\)
\(710\) 3.23783 1.86936i 0.121514 0.0701560i
\(711\) 4.89681 0.183645
\(712\) 34.6337 1.29795
\(713\) 45.8644 26.4798i 1.71764 0.991678i
\(714\) 0 0
\(715\) 1.81600 2.43674i 0.0679146 0.0911290i
\(716\) −0.388390 + 0.672711i −0.0145148 + 0.0251404i
\(717\) −40.6667 23.4789i −1.51872 0.876836i
\(718\) 13.8605 24.0070i 0.517268 0.895935i
\(719\) −4.56317 7.90364i −0.170178 0.294756i 0.768304 0.640085i \(-0.221101\pi\)
−0.938482 + 0.345329i \(0.887767\pi\)
\(720\) 9.92235i 0.369784i
\(721\) 0 0
\(722\) 15.3564 + 8.86604i 0.571507 + 0.329960i
\(723\) −42.6126 24.6024i −1.58478 0.914973i
\(724\) −0.983812 −0.0365631
\(725\) 12.3706 21.4266i 0.459434 0.795763i
\(726\) 32.7493i 1.21544i
\(727\) −33.6859 −1.24934 −0.624670 0.780889i \(-0.714767\pi\)
−0.624670 + 0.780889i \(0.714767\pi\)
\(728\) 0 0
\(729\) −43.0880 −1.59585
\(730\) 8.51558i 0.315176i
\(731\) −0.971507 + 1.68270i −0.0359325 + 0.0622369i
\(732\) 3.01231 0.111338
\(733\) −40.2134 23.2172i −1.48532 0.857547i −0.485455 0.874262i \(-0.661346\pi\)
−0.999860 + 0.0167147i \(0.994679\pi\)
\(734\) −32.9062 18.9984i −1.21459 0.701245i
\(735\) 0 0
\(736\) 4.08942i 0.150738i
\(737\) −6.79927 11.7767i −0.250454 0.433799i
\(738\) 14.5400 25.1841i 0.535226 0.927039i
\(739\) 1.60237 + 0.925127i 0.0589440 + 0.0340314i 0.529182 0.848508i \(-0.322499\pi\)
−0.470238 + 0.882539i \(0.655832\pi\)
\(740\) −0.210047 + 0.363813i −0.00772149 + 0.0133740i
\(741\) 23.3104 10.0412i 0.856328 0.368871i
\(742\) 0 0
\(743\) 28.7095 16.5755i 1.05325 0.608094i 0.129693 0.991554i \(-0.458601\pi\)
0.923558 + 0.383460i \(0.125268\pi\)
\(744\) 47.1781 1.72963
\(745\) 1.74624 0.0639773
\(746\) 19.0757 11.0134i 0.698412 0.403228i
\(747\) −38.5024 + 22.2294i −1.40873 + 0.813331i
\(748\) −0.216858 0.125203i −0.00792913 0.00457788i
\(749\) 0 0
\(750\) −9.88850 + 17.1274i −0.361077 + 0.625404i
\(751\) 20.7743 0.758064 0.379032 0.925384i \(-0.376257\pi\)
0.379032 + 0.925384i \(0.376257\pi\)
\(752\) 15.0046 + 8.66289i 0.547160 + 0.315903i
\(753\) 9.11286 + 15.7839i 0.332091 + 0.575199i
\(754\) −20.9554 15.6172i −0.763150 0.568744i
\(755\) −6.56824 −0.239043
\(756\) 0 0
\(757\) −21.8075 37.7717i −0.792607 1.37283i −0.924348 0.381551i \(-0.875390\pi\)
0.131741 0.991284i \(-0.457943\pi\)
\(758\) −6.08364 10.5372i −0.220968 0.382727i
\(759\) 36.3304 20.9754i 1.31871 0.761358i
\(760\) 3.72532i 0.135131i
\(761\) 10.7302 6.19511i 0.388971 0.224573i −0.292743 0.956191i \(-0.594568\pi\)
0.681714 + 0.731619i \(0.261235\pi\)
\(762\) 5.57497i 0.201960i
\(763\) 0 0
\(764\) 0.484583 + 0.839323i 0.0175316 + 0.0303656i
\(765\) 5.04013i 0.182226i
\(766\) −5.51773 9.55700i −0.199364 0.345308i
\(767\) −20.5481 + 8.85127i −0.741948 + 0.319601i
\(768\) 2.67917 4.64046i 0.0966763 0.167448i
\(769\) 4.80955 2.77680i 0.173437 0.100134i −0.410769 0.911740i \(-0.634740\pi\)
0.584205 + 0.811606i \(0.301406\pi\)
\(770\) 0 0
\(771\) 5.18750 8.98501i 0.186823 0.323587i
\(772\) 0.797307 + 0.460325i 0.0286957 + 0.0165675i
\(773\) 43.8042i 1.57553i 0.615977 + 0.787764i \(0.288761\pi\)
−0.615977 + 0.787764i \(0.711239\pi\)
\(774\) 6.89039i 0.247670i
\(775\) −23.7370 13.7046i −0.852659 0.492283i
\(776\) −6.37159 + 11.0359i −0.228727 + 0.396166i
\(777\) 0 0
\(778\) 38.4608 22.2053i 1.37889 0.796100i