Properties

Label 637.2.u.h.30.5
Level $637$
Weight $2$
Character 637.30
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.u (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: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
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 30.5
Root \(0.759479 - 1.19298i\) of defining polynomial
Character \(\chi\) \(=\) 637.30
Dual form 637.2.u.h.361.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.20027 - 0.692976i) q^{2} -2.82577 q^{3} +(-0.0395678 + 0.0685334i) q^{4} +(-0.449430 - 0.259479i) q^{5} +(-3.39169 + 1.95819i) q^{6} +2.88158i q^{8} +4.98500 q^{9} +O(q^{10})\) \(q+(1.20027 - 0.692976i) q^{2} -2.82577 q^{3} +(-0.0395678 + 0.0685334i) q^{4} +(-0.449430 - 0.259479i) q^{5} +(-3.39169 + 1.95819i) q^{6} +2.88158i q^{8} +4.98500 q^{9} -0.719250 q^{10} -1.62416i q^{11} +(0.111810 - 0.193660i) q^{12} +(1.42641 - 3.31140i) q^{13} +(1.26999 + 0.733228i) q^{15} +(1.91773 + 3.32161i) q^{16} +(0.974127 - 1.68724i) q^{17} +(5.98335 - 3.45449i) q^{18} +2.49115i q^{19} +(0.0355659 - 0.0205340i) q^{20} +(-1.12550 - 1.94943i) q^{22} +(-4.57029 - 7.91598i) q^{23} -8.14270i q^{24} +(-2.36534 - 4.09689i) q^{25} +(-0.582637 - 4.96304i) q^{26} -5.60916 q^{27} +(2.61498 - 4.52928i) q^{29} +2.03244 q^{30} +(5.01767 - 2.89695i) q^{31} +(-0.387453 - 0.223696i) q^{32} +4.58951i q^{33} -2.70019i q^{34} +(-0.197245 + 0.341639i) q^{36} +(8.85879 - 5.11463i) q^{37} +(1.72631 + 2.99006i) q^{38} +(-4.03072 + 9.35726i) 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} +(-2.24041 - 1.29350i) q^{45} +(-10.9712 - 6.33421i) 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} +(0.170501 + 0.228782i) q^{52} +(4.44825 + 7.70460i) q^{53} +(-6.73251 + 3.88701i) q^{54} +(-0.421434 + 0.729946i) q^{55} -7.03944i q^{57} -7.24847i q^{58} +(5.37392 + 3.10263i) q^{59} +(-0.100501 + 0.0580244i) q^{60} -13.4707 q^{61} +(4.01504 - 6.95426i) q^{62} -8.29100 q^{64} +(-1.50031 + 1.11812i) q^{65} +(3.18042 + 5.50865i) q^{66} +8.37266i q^{67} +(0.0770880 + 0.133520i) q^{68} +(12.9146 + 22.3688i) q^{69} +(-4.50168 + 2.59905i) q^{71} +14.3647i q^{72} +(10.2533 - 5.91976i) q^{73} +(7.08863 - 12.2779i) q^{74} +(6.68392 + 11.5769i) q^{75} +(-0.170727 - 0.0985694i) q^{76} +(1.64640 + 14.0244i) q^{78} +(-0.491155 + 0.850705i) q^{79} -1.99044i q^{80} +0.895217 q^{81} +5.83352 q^{82} -8.91851i q^{83} +(-0.875603 + 0.505530i) q^{85} +(-1.19704 - 0.691113i) q^{86} +(-7.38934 + 12.7987i) q^{87} +4.68015 q^{88} +(10.4087 - 6.00949i) q^{89} -3.58546 q^{90} +0.723345 q^{92} +(-14.1788 + 8.18614i) q^{93} -6.26070 q^{94} +(0.646401 - 1.11960i) q^{95} +(1.09485 + 0.632114i) q^{96} +(3.82981 - 2.21114i) q^{97} -8.09643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29} - 16 q^{30} + 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} - 2 q^{38} - 10 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} + 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} + 26 q^{52} + 22 q^{53} - 12 q^{54} - 6 q^{55} - 18 q^{59} + 66 q^{60} - 28 q^{61} - 4 q^{62} - 52 q^{64} - 42 q^{65} + 26 q^{66} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 30 q^{73} + 6 q^{74} + 46 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} - 28 q^{82} - 48 q^{85} - 60 q^{86} - 2 q^{87} + 28 q^{88} + 12 q^{89} + 24 q^{90} + 24 q^{92} + 18 q^{93} - 8 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{97} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20027 0.692976i 0.848719 0.490008i −0.0114993 0.999934i \(-0.503660\pi\)
0.860218 + 0.509926i \(0.170327\pi\)
\(3\) −2.82577 −1.63146 −0.815731 0.578432i \(-0.803665\pi\)
−0.815731 + 0.578432i \(0.803665\pi\)
\(4\) −0.0395678 + 0.0685334i −0.0197839 + 0.0342667i
\(5\) −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
\(9\) 4.98500 1.66167
\(10\) −0.719250 −0.227447
\(11\) 1.62416i 0.489702i −0.969561 0.244851i \(-0.921261\pi\)
0.969561 0.244851i \(-0.0787391\pi\)
\(12\) 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
\(16\) 1.91773 + 3.32161i 0.479433 + 0.830403i
\(17\) 0.974127 1.68724i 0.236260 0.409215i −0.723378 0.690452i \(-0.757411\pi\)
0.959638 + 0.281237i \(0.0907448\pi\)
\(18\) 5.98335 3.45449i 1.41029 0.814230i
\(19\) 2.49115i 0.571510i 0.958303 + 0.285755i \(0.0922444\pi\)
−0.958303 + 0.285755i \(0.907756\pi\)
\(20\) 0.0355659 0.0205340i 0.00795277 0.00459154i
\(21\) 0 0
\(22\) −1.12550 1.94943i −0.239958 0.415620i
\(23\) −4.57029 7.91598i −0.952971 1.65059i −0.738943 0.673767i \(-0.764675\pi\)
−0.214028 0.976828i \(-0.568658\pi\)
\(24\) 8.14270i 1.66212i
\(25\) −2.36534 4.09689i −0.473068 0.819378i
\(26\) −0.582637 4.96304i −0.114265 0.973332i
\(27\) −5.60916 −1.07948
\(28\) 0 0
\(29\) 2.61498 4.52928i 0.485589 0.841065i −0.514274 0.857626i \(-0.671938\pi\)
0.999863 + 0.0165608i \(0.00527172\pi\)
\(30\) 2.03244 0.371071
\(31\) 5.01767 2.89695i 0.901201 0.520308i 0.0236111 0.999721i \(-0.492484\pi\)
0.877590 + 0.479413i \(0.159150\pi\)
\(32\) −0.387453 0.223696i −0.0684926 0.0395442i
\(33\) 4.58951i 0.798931i
\(34\) 2.70019i 0.463078i
\(35\) 0 0
\(36\) −0.197245 + 0.341639i −0.0328742 + 0.0569398i
\(37\) 8.85879 5.11463i 1.45638 0.840840i 0.457546 0.889186i \(-0.348728\pi\)
0.998831 + 0.0483462i \(0.0153951\pi\)
\(38\) 1.72631 + 2.99006i 0.280045 + 0.485052i
\(39\) −4.03072 + 9.35726i −0.645432 + 1.49836i
\(40\) 0.747709 1.29507i 0.118223 0.204769i
\(41\) 3.64513 + 2.10452i 0.569273 + 0.328670i 0.756859 0.653578i \(-0.226733\pi\)
−0.187586 + 0.982248i \(0.560066\pi\)
\(42\) 0 0
\(43\) −0.498655 0.863697i −0.0760442 0.131712i 0.825496 0.564408i \(-0.190896\pi\)
−0.901540 + 0.432696i \(0.857562\pi\)
\(44\) 0.111309 + 0.0642644i 0.0167805 + 0.00968822i
\(45\) −2.24041 1.29350i −0.333980 0.192824i
\(46\) −10.9712 6.33421i −1.61761 0.933928i
\(47\) −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
\(52\) 0.170501 + 0.228782i 0.0236443 + 0.0317263i
\(53\) 4.44825 + 7.70460i 0.611015 + 1.05831i 0.991070 + 0.133344i \(0.0425717\pi\)
−0.380055 + 0.924964i \(0.624095\pi\)
\(54\) −6.73251 + 3.88701i −0.916178 + 0.528956i
\(55\) −0.421434 + 0.729946i −0.0568262 + 0.0984259i
\(56\) 0 0
\(57\) 7.03944i 0.932397i
\(58\) 7.24847i 0.951771i
\(59\) 5.37392 + 3.10263i 0.699624 + 0.403928i 0.807207 0.590268i \(-0.200978\pi\)
−0.107583 + 0.994196i \(0.534311\pi\)
\(60\) −0.100501 + 0.0580244i −0.0129746 + 0.00749091i
\(61\) −13.4707 −1.72475 −0.862375 0.506270i \(-0.831024\pi\)
−0.862375 + 0.506270i \(0.831024\pi\)
\(62\) 4.01504 6.95426i 0.509911 0.883191i
\(63\) 0 0
\(64\) −8.29100 −1.03637
\(65\) −1.50031 + 1.11812i −0.186090 + 0.138685i
\(66\) 3.18042 + 5.50865i 0.391483 + 0.678068i
\(67\) 8.37266i 1.02288i 0.859318 + 0.511442i \(0.170888\pi\)
−0.859318 + 0.511442i \(0.829112\pi\)
\(68\) 0.0770880 + 0.133520i 0.00934830 + 0.0161917i
\(69\) 12.9146 + 22.3688i 1.55474 + 2.69288i
\(70\) 0 0
\(71\) −4.50168 + 2.59905i −0.534251 + 0.308450i −0.742746 0.669573i \(-0.766477\pi\)
0.208495 + 0.978023i \(0.433144\pi\)
\(72\) 14.3647i 1.69289i
\(73\) 10.2533 5.91976i 1.20006 0.692856i 0.239493 0.970898i \(-0.423019\pi\)
0.960569 + 0.278042i \(0.0896855\pi\)
\(74\) 7.08863 12.2779i 0.824037 1.42727i
\(75\) 6.68392 + 11.5769i 0.771793 + 1.33678i
\(76\) −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 \(0.184265\pi\)
\(80\) 1.99044i 0.222538i
\(81\) 0.895217 0.0994686
\(82\) 5.83352 0.644204
\(83\) 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
\(87\) −7.38934 + 12.7987i −0.792220 + 1.37217i
\(88\) 4.68015 0.498906
\(89\) 10.4087 6.00949i 1.10332 0.637005i 0.166233 0.986087i \(-0.446840\pi\)
0.937092 + 0.349082i \(0.113506\pi\)
\(90\) −3.58546 −0.377941
\(91\) 0 0
\(92\) 0.723345 0.0754139
\(93\) −14.1788 + 8.18614i −1.47027 + 0.848863i
\(94\) −6.26070 −0.645742
\(95\) 0.646401 1.11960i 0.0663194 0.114869i
\(96\) 1.09485 + 0.632114i 0.111743 + 0.0645149i
\(97\) 3.82981 2.21114i 0.388858 0.224507i −0.292807 0.956172i \(-0.594589\pi\)
0.681665 + 0.731664i \(0.261256\pi\)
\(98\) 0 0
\(99\) 8.09643i 0.813722i
\(100\) 0.374365 0.0374365
\(101\) −18.3026 −1.82118 −0.910591 0.413309i \(-0.864373\pi\)
−0.910591 + 0.413309i \(0.864373\pi\)
\(102\) 7.63012i 0.755494i
\(103\) 2.51023 4.34784i 0.247340 0.428406i −0.715447 0.698667i \(-0.753777\pi\)
0.962787 + 0.270262i \(0.0871102\pi\)
\(104\) 9.54206 + 4.11033i 0.935676 + 0.403051i
\(105\) 0 0
\(106\) 10.6782 + 6.16507i 1.03716 + 0.598804i
\(107\) −3.07228 5.32134i −0.297008 0.514434i 0.678442 0.734654i \(-0.262656\pi\)
−0.975450 + 0.220221i \(0.929322\pi\)
\(108\) 0.221942 0.384415i 0.0213564 0.0369903i
\(109\) 10.3025 5.94812i 0.986796 0.569727i 0.0824809 0.996593i \(-0.473716\pi\)
0.904315 + 0.426866i \(0.140382\pi\)
\(110\) 1.16818i 0.111381i
\(111\) −25.0330 + 14.4528i −2.37602 + 1.37180i
\(112\) 0 0
\(113\) −1.77806 3.07969i −0.167266 0.289713i 0.770192 0.637812i \(-0.220161\pi\)
−0.937458 + 0.348099i \(0.886827\pi\)
\(114\) −4.87817 8.44923i −0.456882 0.791343i
\(115\) 4.74357i 0.442340i
\(116\) 0.206938 + 0.358427i 0.0192137 + 0.0332791i
\(117\) 7.11067 16.5073i 0.657382 1.52610i
\(118\) 8.60020 0.791713
\(119\) 0 0
\(120\) −2.11286 + 3.65957i −0.192877 + 0.334072i
\(121\) 8.36211 0.760191
\(122\) −16.1685 + 9.33489i −1.46383 + 0.845141i
\(123\) −10.3003 5.94689i −0.928748 0.536213i
\(124\) 0.458504i 0.0411749i
\(125\) 5.04981i 0.451668i
\(126\) 0 0
\(127\) −0.711749 + 1.23279i −0.0631575 + 0.109392i −0.895875 0.444306i \(-0.853450\pi\)
0.832718 + 0.553698i \(0.186784\pi\)
\(128\) −9.17653 + 5.29807i −0.811098 + 0.468288i
\(129\) 1.40909 + 2.44061i 0.124063 + 0.214884i
\(130\) −1.02595 + 2.38172i −0.0899816 + 0.208891i
\(131\) −4.33687 + 7.51168i −0.378914 + 0.656298i −0.990905 0.134567i \(-0.957036\pi\)
0.611990 + 0.790865i \(0.290369\pi\)
\(132\) −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
\(136\) 4.86191 + 2.80703i 0.416906 + 0.240701i
\(137\) −7.37667 4.25892i −0.630231 0.363864i 0.150611 0.988593i \(-0.451876\pi\)
−0.780842 + 0.624729i \(0.785209\pi\)
\(138\) 31.0020 + 17.8990i 2.63907 + 1.52367i
\(139\) 2.51922 + 4.36342i 0.213677 + 0.370100i 0.952863 0.303402i \(-0.0981225\pi\)
−0.739185 + 0.673502i \(0.764789\pi\)
\(140\) 0 0
\(141\) 11.0546 + 6.38237i 0.930964 + 0.537493i
\(142\) −3.60215 + 6.23912i −0.302286 + 0.523575i
\(143\) −5.37824 2.31672i −0.449751 0.193734i
\(144\) 9.55990 + 16.5582i 0.796658 + 1.37985i
\(145\) −2.35050 + 1.35706i −0.195198 + 0.112698i
\(146\) 8.20451 14.2106i 0.679010 1.17608i
\(147\) 0 0
\(148\) 0.809498i 0.0665403i
\(149\) 3.36490i 0.275663i 0.990456 + 0.137832i \(0.0440133\pi\)
−0.990456 + 0.137832i \(0.955987\pi\)
\(150\) 16.0450 + 9.26360i 1.31007 + 0.756370i
\(151\) −10.9610 + 6.32831i −0.891990 + 0.514991i −0.874593 0.484858i \(-0.838871\pi\)
−0.0173971 + 0.999849i \(0.505538\pi\)
\(152\) −7.17847 −0.582251
\(153\) 4.85602 8.41087i 0.392586 0.679979i
\(154\) 0 0
\(155\) −3.00679 −0.241511
\(156\) −0.481798 0.646485i −0.0385747 0.0517602i
\(157\) −5.18457 8.97993i −0.413773 0.716677i 0.581525 0.813528i \(-0.302456\pi\)
−0.995299 + 0.0968517i \(0.969123\pi\)
\(158\) 1.36143i 0.108310i
\(159\) −12.5698 21.7715i −0.996847 1.72659i
\(160\) 0.116089 + 0.201071i 0.00917761 + 0.0158961i
\(161\) 0 0
\(162\) 1.07450 0.620364i 0.0844209 0.0487404i
\(163\) 15.7534i 1.23390i 0.787002 + 0.616950i \(0.211632\pi\)
−0.787002 + 0.616950i \(0.788368\pi\)
\(164\) −0.288459 + 0.166542i −0.0225249 + 0.0130047i
\(165\) 1.19088 2.06266i 0.0927098 0.160578i
\(166\) −6.18032 10.7046i −0.479686 0.830840i
\(167\) −14.2016 8.19930i −1.09895 0.634481i −0.163007 0.986625i \(-0.552119\pi\)
−0.935946 + 0.352144i \(0.885453\pi\)
\(168\) 0 0
\(169\) −8.93069 9.44684i −0.686976 0.726680i
\(170\) −0.700640 + 1.21354i −0.0537367 + 0.0930746i
\(171\) 12.4184i 0.949659i
\(172\) 0.0789227 0.00601780
\(173\) 0.301355 0.0229116 0.0114558 0.999934i \(-0.496353\pi\)
0.0114558 + 0.999934i \(0.496353\pi\)
\(174\) 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
\(178\) 8.32887 14.4260i 0.624275 1.08128i
\(179\) 9.81582 0.733669 0.366834 0.930286i \(-0.380442\pi\)
0.366834 + 0.930286i \(0.380442\pi\)
\(180\) 0.177296 0.102362i 0.0132149 0.00762960i
\(181\) 12.4320 0.924062 0.462031 0.886864i \(-0.347121\pi\)
0.462031 + 0.886864i \(0.347121\pi\)
\(182\) 0 0
\(183\) 38.0652 2.81386
\(184\) 22.8105 13.1697i 1.68162 0.970881i
\(185\) −5.30854 −0.390292
\(186\) −11.3456 + 19.6512i −0.831900 + 1.44089i
\(187\) −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
\(191\) −12.2469 −0.886156 −0.443078 0.896483i \(-0.646114\pi\)
−0.443078 + 0.896483i \(0.646114\pi\)
\(192\) 23.4285 1.69081
\(193\) 11.6338i 0.837422i 0.908119 + 0.418711i \(0.137518\pi\)
−0.908119 + 0.418711i \(0.862482\pi\)
\(194\) 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 0.443403 0.896322i \(-0.353771\pi\)
−0.554537 + 0.832159i \(0.687104\pi\)
\(198\) −5.61064 9.71791i −0.398731 0.690622i
\(199\) 3.29657 5.70982i 0.233687 0.404759i −0.725203 0.688535i \(-0.758254\pi\)
0.958890 + 0.283777i \(0.0915874\pi\)
\(200\) 11.8055 6.81593i 0.834777 0.481959i
\(201\) 23.6592i 1.66879i
\(202\) −21.9681 + 12.6833i −1.54567 + 0.892394i
\(203\) 0 0
\(204\) −0.217833 0.377298i −0.0152514 0.0264162i
\(205\) −1.09215 1.89166i −0.0762793 0.132120i
\(206\) 6.95811i 0.484795i
\(207\) −22.7829 39.4611i −1.58352 2.74274i
\(208\) 13.7347 1.61238i 0.952327 0.111799i
\(209\) 4.04603 0.279870
\(210\) 0 0
\(211\) −5.35996 + 9.28373i −0.368995 + 0.639118i −0.989409 0.145157i \(-0.953631\pi\)
0.620414 + 0.784275i \(0.286965\pi\)
\(212\) −0.704030 −0.0483530
\(213\) 12.7207 7.34432i 0.871610 0.503224i
\(214\) −7.37513 4.25803i −0.504154 0.291073i
\(215\) 0.517562i 0.0352974i
\(216\) 16.1633i 1.09977i
\(217\) 0 0
\(218\) 8.24382 14.2787i 0.558342 0.967076i
\(219\) −28.9736 + 16.7279i −1.95785 + 1.13037i
\(220\) −0.0333504 0.0577647i −0.00224849 0.00389449i
\(221\) −4.19760 5.63242i −0.282361 0.378877i
\(222\) −20.0309 + 34.6945i −1.34438 + 2.32854i
\(223\) −11.1612 6.44392i −0.747409 0.431517i 0.0773480 0.997004i \(-0.475355\pi\)
−0.824757 + 0.565487i \(0.808688\pi\)
\(224\) 0 0
\(225\) −11.7912 20.4230i −0.786082 1.36153i
\(226\) −4.26831 2.46431i −0.283924 0.163923i
\(227\) 0.605486 + 0.349577i 0.0401875 + 0.0232023i 0.519959 0.854191i \(-0.325947\pi\)
−0.479772 + 0.877393i \(0.659280\pi\)
\(228\) 0.482437 + 0.278535i 0.0319502 + 0.0184464i
\(229\) 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 \(-0.173920\pi\)
\(234\) −2.90445 24.7408i −0.189870 1.61735i
\(235\) 1.17213 + 2.03019i 0.0764614 + 0.132435i
\(236\) −0.425268 + 0.245528i −0.0276826 + 0.0159825i
\(237\) 1.38789 2.40390i 0.0901533 0.156150i
\(238\) 0 0
\(239\) 16.6177i 1.07491i −0.843293 0.537454i \(-0.819386\pi\)
0.843293 0.537454i \(-0.180614\pi\)
\(240\) 5.62454i 0.363063i
\(241\) −15.0800 8.70643i −0.971387 0.560830i −0.0717279 0.997424i \(-0.522851\pi\)
−0.899659 + 0.436594i \(0.856185\pi\)
\(242\) 10.0368 5.79474i 0.645189 0.372500i
\(243\) 14.2978 0.917204
\(244\) 0.533007 0.923194i 0.0341222 0.0591015i
\(245\) 0 0
\(246\) −16.4842 −1.05099
\(247\) 8.24920 + 3.55342i 0.524884 + 0.226099i
\(248\) 8.34782 + 14.4588i 0.530087 + 0.918137i
\(249\) 25.2017i 1.59709i
\(250\) 3.49940 + 6.06113i 0.221321 + 0.383340i
\(251\) −3.22491 5.58571i −0.203554 0.352567i 0.746117 0.665815i \(-0.231916\pi\)
−0.949671 + 0.313249i \(0.898583\pi\)
\(252\) 0 0
\(253\) −12.8568 + 7.42288i −0.808300 + 0.466672i
\(254\) 1.97290i 0.123791i
\(255\) 2.47426 1.42851i 0.154944 0.0894570i
\(256\) 0.948120 1.64219i 0.0592575 0.102637i
\(257\) −1.83578 3.17966i −0.114513 0.198342i 0.803072 0.595882i \(-0.203197\pi\)
−0.917585 + 0.397540i \(0.869864\pi\)
\(258\) 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
\(262\) 12.0214i 0.742684i
\(263\) 18.3193 1.12961 0.564807 0.825223i \(-0.308950\pi\)
0.564807 + 0.825223i \(0.308950\pi\)
\(264\) −13.2250 −0.813945
\(265\) 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
\(269\) −13.7715 + 23.8529i −0.839661 + 1.45434i 0.0505171 + 0.998723i \(0.483913\pi\)
−0.890178 + 0.455613i \(0.849420\pi\)
\(270\) 4.03439 0.245525
\(271\) −5.64582 + 3.25961i −0.342959 + 0.198007i −0.661580 0.749875i \(-0.730114\pi\)
0.318621 + 0.947882i \(0.396780\pi\)
\(272\) 7.47246 0.453084
\(273\) 0 0
\(274\) −11.8053 −0.713186
\(275\) −6.65401 + 3.84169i −0.401252 + 0.231663i
\(276\) −2.04401 −0.123035
\(277\) 2.72093 4.71279i 0.163485 0.283164i −0.772631 0.634855i \(-0.781060\pi\)
0.936116 + 0.351691i \(0.114393\pi\)
\(278\) 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 \(-0.966304\pi\)
0.994402 0.105660i \(-0.0336955\pi\)
\(282\) 17.6913 1.05350
\(283\) 14.1391 0.840484 0.420242 0.907412i \(-0.361945\pi\)
0.420242 + 0.907412i \(0.361945\pi\)
\(284\) 0.411354i 0.0244094i
\(285\) −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
\(289\) 6.60215 + 11.4353i 0.388362 + 0.672663i
\(290\) −1.88082 + 3.25768i −0.110446 + 0.191298i
\(291\) −10.8222 + 6.24819i −0.634407 + 0.366275i
\(292\) 0.936928i 0.0548295i
\(293\) −7.23071 + 4.17465i −0.422423 + 0.243886i −0.696113 0.717932i \(-0.745089\pi\)
0.273691 + 0.961818i \(0.411756\pi\)
\(294\) 0 0
\(295\) −1.61013 2.78883i −0.0937455 0.162372i
\(296\) 14.7382 + 25.5274i 0.856642 + 1.48375i
\(297\) 9.11017i 0.528626i
\(298\) 2.33180 + 4.03879i 0.135077 + 0.233961i
\(299\) −32.7321 + 3.84259i −1.89294 + 0.222223i
\(300\) −1.05787 −0.0610762
\(301\) 0 0
\(302\) −8.77074 + 15.1914i −0.504699 + 0.874165i
\(303\) 51.7192 2.97119
\(304\) −8.27465 + 4.77737i −0.474584 + 0.274001i
\(305\) 6.05415 + 3.49536i 0.346659 + 0.200144i
\(306\) 13.4604i 0.769481i
\(307\) 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
\(310\) −3.60896 + 2.08363i −0.204975 + 0.118342i
\(311\) −7.31134 12.6636i −0.414588 0.718088i 0.580797 0.814048i \(-0.302741\pi\)
−0.995385 + 0.0959606i \(0.969408\pi\)
\(312\) −26.9637 11.6149i −1.52652 0.657562i
\(313\) −8.56641 + 14.8375i −0.484202 + 0.838663i −0.999835 0.0181467i \(-0.994223\pi\)
0.515633 + 0.856809i \(0.327557\pi\)
\(314\) −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 0.800222 0.599704i \(-0.204715\pi\)
−0.119248 + 0.992864i \(0.538048\pi\)
\(318\) −30.1742 17.4211i −1.69209 0.976926i
\(319\) −7.35627 4.24714i −0.411872 0.237794i
\(320\) 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
\(325\) −16.9404 + 1.98872i −0.939684 + 0.110314i
\(326\) 10.9167 + 18.9083i 0.604621 + 1.04724i
\(327\) −29.1124 + 16.8081i −1.60992 + 0.929487i
\(328\) −6.06434 + 10.5037i −0.334847 + 0.579972i
\(329\) 0 0
\(330\) 3.30100i 0.181714i
\(331\) 6.91996i 0.380355i 0.981750 + 0.190178i \(0.0609064\pi\)
−0.981750 + 0.190178i \(0.939094\pi\)
\(332\) 0.611216 + 0.352886i 0.0335448 + 0.0193671i
\(333\) 44.1611 25.4964i 2.42001 1.39719i
\(334\) −22.7277 −1.24360
\(335\) 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 \(0.401727\pi\)
\(338\) −17.2657 5.15001i −0.939129 0.280123i
\(339\) 5.02440 + 8.70251i 0.272888 + 0.472656i
\(340\) 0.0800108i 0.00433919i
\(341\) −4.70512 8.14950i −0.254796 0.441320i
\(342\) 8.60566 + 14.9054i 0.465341 + 0.805994i
\(343\) 0 0
\(344\) 2.48881 1.43692i 0.134188 0.0774734i
\(345\) 13.4043i 0.721661i
\(346\) 0.361707 0.208832i 0.0194455 0.0112269i
\(347\) 2.46255 4.26527i 0.132197 0.228971i −0.792326 0.610097i \(-0.791130\pi\)
0.924523 + 0.381126i \(0.124464\pi\)
\(348\) −0.584759 1.01283i −0.0313464 0.0542935i
\(349\) 1.31926 + 0.761675i 0.0706183 + 0.0407715i 0.534893 0.844920i \(-0.320352\pi\)
−0.464275 + 0.885691i \(0.653685\pi\)
\(350\) 0 0
\(351\) −8.00098 + 18.5741i −0.427061 + 0.991415i
\(352\) −0.363318 + 0.629285i −0.0193649 + 0.0335410i
\(353\) 17.9280i 0.954212i −0.878846 0.477106i \(-0.841686\pi\)
0.878846 0.477106i \(-0.158314\pi\)
\(354\) −24.3022 −1.29165
\(355\) 2.69759 0.143173
\(356\) 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 −0.0324227 0.999474i \(-0.510322\pi\)
−0.881781 + 0.471658i \(0.843656\pi\)
\(360\) 3.72733 6.45592i 0.196447 0.340257i
\(361\) 12.7941 0.673376
\(362\) 14.9217 8.61507i 0.784269 0.452798i
\(363\) −23.6294 −1.24022
\(364\) 0 0
\(365\) −6.14421 −0.321602
\(366\) 45.6885 26.3783i 2.38818 1.37882i
\(367\) 27.4157 1.43109 0.715544 0.698568i \(-0.246179\pi\)
0.715544 + 0.698568i \(0.246179\pi\)
\(368\) 17.5292 30.3615i 0.913772 1.58270i
\(369\) 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
\(373\) −15.8929 −0.822901 −0.411451 0.911432i \(-0.634978\pi\)
−0.411451 + 0.911432i \(0.634978\pi\)
\(374\) −4.38553 −0.226771
\(375\) 14.2696i 0.736880i
\(376\) 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 0.682390 0.730988i \(-0.260940\pi\)
−0.291859 + 0.956461i \(0.594274\pi\)
\(380\) 0.0511533 + 0.0886001i 0.00262411 + 0.00454509i
\(381\) 2.01124 3.48357i 0.103039 0.178469i
\(382\) −14.6996 + 8.48682i −0.752098 + 0.434224i
\(383\) 7.96237i 0.406858i 0.979090 + 0.203429i \(0.0652086\pi\)
−0.979090 + 0.203429i \(0.934791\pi\)
\(384\) 25.9308 14.9712i 1.32328 0.763994i
\(385\) 0 0
\(386\) 8.06198 + 13.9638i 0.410344 + 0.710736i
\(387\) −2.48580 4.30553i −0.126360 0.218862i
\(388\) 0.349960i 0.0177665i
\(389\) 16.0217 + 27.7504i 0.812333 + 1.40700i 0.911227 + 0.411904i \(0.135136\pi\)
−0.0988938 + 0.995098i \(0.531530\pi\)
\(390\) 2.89910 6.73021i 0.146801 0.340797i
\(391\) −17.8082 −0.900598
\(392\) 0 0
\(393\) 12.2550 21.2263i 0.618184 1.07073i
\(394\) −2.49630 −0.125762
\(395\) 0.441479 0.254888i 0.0222132 0.0128248i
\(396\) 0.554876 + 0.320358i 0.0278836 + 0.0160986i
\(397\) 6.43457i 0.322942i 0.986877 + 0.161471i \(0.0516238\pi\)
−0.986877 + 0.161471i \(0.948376\pi\)
\(398\) 9.13777i 0.458035i
\(399\) 0 0
\(400\) 9.07219 15.7135i 0.453609 0.785675i
\(401\) 0.462092 0.266789i 0.0230758 0.0133228i −0.488418 0.872610i \(-0.662426\pi\)
0.511494 + 0.859287i \(0.329092\pi\)
\(402\) −16.3953 28.3975i −0.817723 1.41634i
\(403\) −2.43569 20.7478i −0.121330 1.03352i
\(404\) 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
\(409\) 34.4269 + 19.8764i 1.70230 + 0.982824i 0.943424 + 0.331590i \(0.107585\pi\)
0.758877 + 0.651234i \(0.225748\pi\)
\(410\) −2.62176 1.51367i −0.129479 0.0747550i
\(411\) 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
\(416\) −1.29341 + 0.963926i −0.0634148 + 0.0472604i
\(417\) −7.11875 12.3300i −0.348607 0.603804i
\(418\) 4.85633 2.80380i 0.237531 0.137139i
\(419\) −11.9088 + 20.6266i −0.581783 + 1.00768i 0.413485 + 0.910511i \(0.364311\pi\)
−0.995268 + 0.0971665i \(0.969022\pi\)
\(420\) 0 0
\(421\) 23.2419i 1.13274i 0.824151 + 0.566370i \(0.191653\pi\)
−0.824151 + 0.566370i \(0.808347\pi\)
\(422\) 14.8573i 0.723243i
\(423\) −19.5016 11.2593i −0.948200 0.547444i
\(424\) −22.2014 + 12.8180i −1.07820 + 0.622498i
\(425\) −9.21657 −0.447069
\(426\) 10.1789 17.6303i 0.493168 0.854192i
\(427\) 0 0
\(428\) 0.486253 0.0235039
\(429\) 15.1977 + 6.54654i 0.733751 + 0.316070i
\(430\) 0.358658 + 0.621214i 0.0172960 + 0.0299576i
\(431\) 2.70689i 0.130386i 0.997873 + 0.0651932i \(0.0207664\pi\)
−0.997873 + 0.0651932i \(0.979234\pi\)
\(432\) −10.7569 18.6314i −0.517540 0.896406i
\(433\) −2.90945 5.03932i −0.139819 0.242174i 0.787609 0.616176i \(-0.211319\pi\)
−0.927428 + 0.374002i \(0.877985\pi\)
\(434\) 0 0
\(435\) 6.64198 3.83475i 0.318459 0.183862i
\(436\) 0.941416i 0.0450856i
\(437\) 19.7199 11.3853i 0.943332 0.544633i
\(438\) −23.1841 + 40.1560i −1.10778 + 1.91873i
\(439\) 19.0851 + 33.0563i 0.910882 + 1.57769i 0.812822 + 0.582513i \(0.197930\pi\)
0.0980599 + 0.995181i \(0.468736\pi\)
\(440\) −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 \(-0.104456\pi\)
\(444\) 2.28746i 0.108558i
\(445\) −6.23734 −0.295678
\(446\) −17.8619 −0.845787
\(447\) 9.50845i 0.449734i
\(448\) 0 0
\(449\) 27.1975 15.7025i 1.28353 0.741045i 0.306036 0.952020i \(-0.400997\pi\)
0.977491 + 0.210975i \(0.0676638\pi\)
\(450\) −28.3053 16.3421i −1.33433 0.770373i
\(451\) 3.41807 5.92027i 0.160951 0.278775i
\(452\) 0.281416 0.0132367
\(453\) 30.9732 17.8824i 1.45525 0.840187i
\(454\) 0.968995 0.0454772
\(455\) 0 0
\(456\) 20.2847 0.949920
\(457\) −27.5640 + 15.9141i −1.28939 + 0.744429i −0.978545 0.206032i \(-0.933945\pi\)
−0.310844 + 0.950461i \(0.600612\pi\)
\(458\) 25.3447 1.18428
\(459\) −5.46403 + 9.46398i −0.255039 + 0.441741i
\(460\) −0.325093 0.187692i −0.0151575 0.00875121i
\(461\) 1.01005 0.583153i 0.0470427 0.0271601i −0.476294 0.879286i \(-0.658020\pi\)
0.523337 + 0.852126i \(0.324687\pi\)
\(462\) 0 0
\(463\) 20.3441i 0.945469i −0.881205 0.472734i \(-0.843267\pi\)
0.881205 0.472734i \(-0.156733\pi\)
\(464\) 20.0593 0.931231
\(465\) 8.49651 0.394016
\(466\) 37.1152i 1.71933i
\(467\) −0.784697 + 1.35913i −0.0363114 + 0.0628932i −0.883610 0.468224i \(-0.844894\pi\)
0.847299 + 0.531117i \(0.178227\pi\)
\(468\) 0.849948 + 1.14048i 0.0392889 + 0.0527185i
\(469\) 0 0
\(470\) 2.81375 + 1.62452i 0.129788 + 0.0749334i
\(471\) 14.6504 + 25.3753i 0.675055 + 1.16923i
\(472\) −8.94049 + 15.4854i −0.411519 + 0.712773i
\(473\) −1.40278 + 0.809896i −0.0644999 + 0.0372391i
\(474\) 3.84711i 0.176703i
\(475\) 10.2060 5.89243i 0.468283 0.270363i
\(476\) 0 0
\(477\) 22.1745 + 38.4074i 1.01530 + 1.75856i
\(478\) −11.5157 19.9457i −0.526714 0.912295i
\(479\) 7.71918i 0.352699i −0.984328 0.176349i \(-0.943571\pi\)
0.984328 0.176349i \(-0.0564288\pi\)
\(480\) −0.328040 0.568182i −0.0149729 0.0259338i
\(481\) −4.30025 36.6306i −0.196075 1.67021i
\(482\) −24.1334 −1.09925
\(483\) 0 0
\(484\) −0.330870 + 0.573083i −0.0150395 + 0.0260492i
\(485\) −2.29498 −0.104209
\(486\) 17.1612 9.90803i 0.778448 0.449437i
\(487\) 0.0659739 + 0.0380900i 0.00298956 + 0.00172602i 0.501494 0.865161i \(-0.332784\pi\)
−0.498504 + 0.866887i \(0.666117\pi\)
\(488\) 38.8170i 1.75716i
\(489\) 44.5155i 2.01306i
\(490\) 0 0
\(491\) 0.893574 1.54772i 0.0403264 0.0698474i −0.845158 0.534517i \(-0.820494\pi\)
0.885484 + 0.464670i \(0.153827\pi\)
\(492\) 0.815121 0.470610i 0.0367485 0.0212167i
\(493\) −5.09464 8.82418i −0.229451 0.397421i
\(494\) 12.3637 1.45144i 0.556269 0.0653034i
\(495\) −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 0.329655 0.944102i \(-0.393068\pi\)
−0.652789 + 0.757540i \(0.726401\pi\)
\(500\) −0.346080 0.199810i −0.0154772 0.00893576i
\(501\) 40.1305 + 23.1694i 1.79290 + 1.03513i
\(502\) −7.74152 4.46957i −0.345521 0.199487i
\(503\) −0.720238 1.24749i −0.0321138 0.0556228i 0.849522 0.527554i \(-0.176891\pi\)
−0.881636 + 0.471931i \(0.843557\pi\)
\(504\) 0 0
\(505\) 8.22576 + 4.74914i 0.366041 + 0.211334i
\(506\) −10.2878 + 17.8189i −0.457347 + 0.792148i
\(507\) 25.2361 + 26.6946i 1.12077 + 1.18555i
\(508\) −0.0563247 0.0975572i −0.00249900 0.00432840i
\(509\) −12.8394 + 7.41282i −0.569096 + 0.328568i −0.756788 0.653660i \(-0.773233\pi\)
0.187692 + 0.982228i \(0.439899\pi\)
\(510\) 1.97985 3.42920i 0.0876693 0.151848i
\(511\) 0 0
\(512\) 23.8204i 1.05272i
\(513\) 13.9733i 0.616935i
\(514\) −4.40686 2.54430i −0.194378 0.112224i
\(515\) −2.25634 + 1.30270i −0.0994264 + 0.0574038i
\(516\) −0.223018 −0.00981781
\(517\) −3.66837 + 6.35380i −0.161335 + 0.279440i
\(518\) 0 0
\(519\) −0.851561 −0.0373794
\(520\) −3.22195 4.32327i −0.141292 0.189588i
\(521\) 0.167194 + 0.289588i 0.00732489 + 0.0126871i 0.869665 0.493643i \(-0.164335\pi\)
−0.862340 + 0.506330i \(0.831002\pi\)
\(522\) 36.1336i 1.58153i
\(523\) 16.2533 + 28.1515i 0.710705 + 1.23098i 0.964593 + 0.263744i \(0.0849574\pi\)
−0.253887 + 0.967234i \(0.581709\pi\)
\(524\) −0.343201 0.594441i −0.0149928 0.0259683i
\(525\) 0 0
\(526\) 21.9881 12.6948i 0.958726 0.553521i
\(527\) 11.2880i 0.491713i
\(528\) −15.2446 + 8.80145i −0.663434 + 0.383034i
\(529\) −30.2751 + 52.4380i −1.31631 + 2.27991i
\(530\) −3.19941 5.54153i −0.138973 0.240709i
\(531\) 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
\(535\) 3.18876i 0.137862i
\(536\) −24.1265 −1.04211
\(537\) −27.7373 −1.19695
\(538\) 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 0.684208 0.729287i \(-0.260148\pi\)
−0.289477 + 0.957185i \(0.593481\pi\)
\(542\) −4.51767 + 7.82483i −0.194051 + 0.336105i
\(543\) −35.1300 −1.50757
\(544\) −0.754856 + 0.435816i −0.0323642 + 0.0186855i
\(545\) −6.17364 −0.264450
\(546\) 0 0
\(547\) 10.2327 0.437519 0.218760 0.975779i \(-0.429799\pi\)
0.218760 + 0.975779i \(0.429799\pi\)
\(548\) 0.583756 0.337032i 0.0249368 0.0143973i
\(549\) −67.1515 −2.86596
\(550\) −5.32440 + 9.22214i −0.227033 + 0.393233i
\(551\) 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
\(555\) 15.0007 0.636746
\(556\) −0.398720 −0.0169095
\(557\) 31.9930i 1.35559i −0.735253 0.677793i \(-0.762937\pi\)
0.735253 0.677793i \(-0.237063\pi\)
\(558\) 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
\(562\) −2.45478 4.25180i −0.103549 0.179351i
\(563\) 5.39566 9.34556i 0.227400 0.393868i −0.729637 0.683835i \(-0.760311\pi\)
0.957037 + 0.289967i \(0.0936442\pi\)
\(564\) −0.874811 + 0.505072i −0.0368362 + 0.0212674i
\(565\) 1.84547i 0.0776397i
\(566\) 16.9708 9.79808i 0.713335 0.411844i
\(567\) 0 0
\(568\) −7.48937 12.9720i −0.314247 0.544292i
\(569\) −12.3007 21.3054i −0.515672 0.893170i −0.999835 0.0181917i \(-0.994209\pi\)
0.484163 0.874978i \(-0.339124\pi\)
\(570\) 5.06312i 0.212071i
\(571\) 8.28621 + 14.3521i 0.346767 + 0.600618i 0.985673 0.168667i \(-0.0539461\pi\)
−0.638906 + 0.769285i \(0.720613\pi\)
\(572\) 0.371578 0.276921i 0.0155364 0.0115787i
\(573\) 34.6070 1.44573
\(574\) 0 0
\(575\) −21.6206 + 37.4480i −0.901641 + 1.56169i
\(576\) −41.3306 −1.72211
\(577\) 12.6969 7.33053i 0.528577 0.305174i −0.211860 0.977300i \(-0.567952\pi\)
0.740437 + 0.672126i \(0.234619\pi\)
\(578\) 15.8487 + 9.15027i 0.659221 + 0.380601i
\(579\) 32.8746i 1.36622i
\(580\) 0.214784i 0.00891840i
\(581\) 0 0
\(582\) −8.65969 + 14.9990i −0.358956 + 0.621730i
\(583\) 12.5135 7.22467i 0.518256 0.299215i
\(584\) 17.0583 + 29.5458i 0.705877 + 1.22262i
\(585\) −7.47904 + 5.57381i −0.309220 + 0.230449i
\(586\) −5.78587 + 10.0214i −0.239012 + 0.413981i
\(587\) 30.5998 + 17.6668i 1.26299 + 0.729186i 0.973652 0.228041i \(-0.0732320\pi\)
0.289336 + 0.957227i \(0.406565\pi\)
\(588\) 0 0
\(589\) 7.21676 + 12.4998i 0.297362 + 0.515045i
\(590\) −3.86519 2.23157i −0.159127 0.0918722i
\(591\) 4.40775 + 2.54481i 0.181310 + 0.104680i
\(592\) 33.9776 + 19.6170i 1.39647 + 0.806253i
\(593\) 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
\(598\) −36.6245 + 27.2947i −1.49769 + 1.11616i
\(599\) −6.04094 10.4632i −0.246826 0.427516i 0.715817 0.698288i \(-0.246054\pi\)
−0.962644 + 0.270772i \(0.912721\pi\)
\(600\) −33.3598 + 19.2603i −1.36191 + 0.786297i
\(601\) −3.90743 + 6.76787i −0.159387 + 0.276067i −0.934648 0.355574i \(-0.884285\pi\)
0.775261 + 0.631642i \(0.217619\pi\)
\(602\) 0 0
\(603\) 41.7377i 1.69969i
\(604\) 1.00159i 0.0407541i
\(605\) −3.75818 2.16979i −0.152792 0.0882144i
\(606\) 62.0770 35.8401i 2.52170 1.45591i
\(607\) 35.5649 1.44354 0.721768 0.692135i \(-0.243330\pi\)
0.721768 + 0.692135i \(0.243330\pi\)
\(608\) 0.557261 0.965205i 0.0225999 0.0391442i
\(609\) 0 0
\(610\) 9.68882 0.392289
\(611\) −13.0594 + 9.73263i −0.528328 + 0.393740i
\(612\) 0.384284 + 0.665599i 0.0155338 + 0.0269052i
\(613\) 11.9368i 0.482122i 0.970510 + 0.241061i \(0.0774954\pi\)
−0.970510 + 0.241061i \(0.922505\pi\)
\(614\) 5.77500 + 10.0026i 0.233060 + 0.403672i
\(615\) 3.08618 + 5.34542i 0.124447 + 0.215548i
\(616\) 0 0
\(617\) −20.4124 + 11.7851i −0.821772 + 0.474450i −0.851027 0.525122i \(-0.824020\pi\)
0.0292550 + 0.999572i \(0.490687\pi\)
\(618\) 19.6621i 0.790924i
\(619\) −24.7312 + 14.2786i −0.994031 + 0.573904i −0.906477 0.422256i \(-0.861238\pi\)
−0.0875541 + 0.996160i \(0.527905\pi\)
\(620\) 0.118972 0.206066i 0.00477803 0.00827579i
\(621\) 25.6355 + 44.4020i 1.02872 + 1.78179i
\(622\) −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
\(626\) 23.7453i 0.949052i
\(627\) −11.4332 −0.456597
\(628\) 0.820567 0.0327442
\(629\) 19.9292i 0.794628i
\(630\) 0 0
\(631\) −38.9646 + 22.4962i −1.55116 + 0.895561i −0.553109 + 0.833109i \(0.686559\pi\)
−0.998048 + 0.0624526i \(0.980108\pi\)
\(632\) −2.45138 1.41530i −0.0975106 0.0562978i
\(633\) 15.1460 26.2337i 0.602001 1.04270i
\(634\) 19.4034 0.770607
\(635\) 0.639763 0.369367i 0.0253882 0.0146579i
\(636\) 1.98943 0.0788860
\(637\) 0 0
\(638\) −11.7727 −0.466085
\(639\) −22.4409 + 12.9562i −0.887747 + 0.512541i
\(640\) 5.49894 0.217365
\(641\) −1.26650 + 2.19364i −0.0500238 + 0.0866437i −0.889953 0.456052i \(-0.849263\pi\)
0.839929 + 0.542696i \(0.182596\pi\)
\(642\) 20.8405 + 12.0322i 0.822507 + 0.474875i
\(643\) 15.9150 9.18853i 0.627627 0.362360i −0.152206 0.988349i \(-0.548638\pi\)
0.779832 + 0.625988i \(0.215304\pi\)
\(644\) 0 0
\(645\) 1.46251i 0.0575863i
\(646\) 6.72658 0.264654
\(647\) −20.9287 −0.822791 −0.411396 0.911457i \(-0.634959\pi\)
−0.411396 + 0.911457i \(0.634959\pi\)
\(648\) 2.57964i 0.101338i
\(649\) 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
\(653\) 24.0580 + 41.6696i 0.941461 + 1.63066i 0.762686 + 0.646769i \(0.223880\pi\)
0.178775 + 0.983890i \(0.442786\pi\)
\(654\) −23.2952 + 40.3484i −0.910913 + 1.57775i
\(655\) 3.89824 2.25065i 0.152317 0.0879401i
\(656\) 16.1436i 0.630302i
\(657\) 51.1129 29.5100i 1.99410 1.15130i
\(658\) 0 0
\(659\) 1.10819 + 1.91944i 0.0431690 + 0.0747708i 0.886803 0.462148i \(-0.152921\pi\)
−0.843634 + 0.536919i \(0.819588\pi\)
\(660\) 0.0942408 + 0.163230i 0.00366832 + 0.00635371i
\(661\) 0.637434i 0.0247933i 0.999923 + 0.0123966i \(0.00394608\pi\)
−0.999923 + 0.0123966i \(0.996054\pi\)
\(662\) 4.79537 + 8.30582i 0.186377 + 0.322815i
\(663\) 11.8615 + 15.9159i 0.460661 + 0.618124i
\(664\) 25.6994 0.997331
\(665\) 0 0
\(666\) 35.3368 61.2052i 1.36927 2.37165i
\(667\) −47.8048 −1.85101
\(668\) 1.12385 0.648856i 0.0434831 0.0251050i
\(669\) 31.5390 + 18.2091i 1.21937 + 0.704003i
\(670\) 6.02203i 0.232651i
\(671\) 21.8786i 0.844614i
\(672\) 0 0
\(673\) 7.70343 13.3427i 0.296945 0.514324i −0.678490 0.734609i \(-0.737365\pi\)
0.975436 + 0.220285i \(0.0706988\pi\)
\(674\) 13.3901 7.73081i 0.515769 0.297780i
\(675\) 13.2676 + 22.9801i 0.510669 + 0.884505i
\(676\) 1.00079 0.238260i 0.0384920 0.00916384i
\(677\) 5.84060 10.1162i 0.224473 0.388798i −0.731689 0.681639i \(-0.761267\pi\)
0.956161 + 0.292841i \(0.0946008\pi\)
\(678\) 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
\(682\) −11.2948 6.52107i −0.432501 0.249705i
\(683\) −19.8419 11.4557i −0.759227 0.438340i 0.0697909 0.997562i \(-0.477767\pi\)
−0.829018 + 0.559221i \(0.811100\pi\)
\(684\) −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
\(689\) 31.8580 3.73998i 1.21369 0.142482i
\(690\) −9.28883 16.0887i −0.353620 0.612487i
\(691\) 40.9046 23.6163i 1.55608 0.898405i 0.558458 0.829533i \(-0.311393\pi\)
0.997625 0.0688729i \(-0.0219403\pi\)
\(692\) −0.0119239 + 0.0206529i −0.000453280 + 0.000785104i
\(693\) 0 0
\(694\) 6.82596i 0.259110i
\(695\) 2.61473i 0.0991825i
\(696\) −36.8805 21.2930i −1.39795 0.807109i
\(697\) 7.10163 4.10013i 0.268994 0.155303i
\(698\) 2.11129 0.0799135
\(699\) −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 \(0.425938\pi\)
\(702\) 3.26810 + 27.8385i 0.123347 + 1.05070i
\(703\) 12.7413 + 22.0686i 0.480548 + 0.832334i
\(704\) 13.4659i 0.507515i
\(705\) −3.31218 5.73686i −0.124744 0.216063i
\(706\) −12.4237 21.5185i −0.467572 0.809858i
\(707\) 0 0
\(708\) 1.20171 0.693808i 0.0451630 0.0260749i
\(709\) 17.8875i 0.671778i −0.941902 0.335889i \(-0.890963\pi\)
0.941902 0.335889i \(-0.109037\pi\)
\(710\) 3.23783 1.86936i 0.121514 0.0701560i
\(711\) −2.44841 + 4.24076i −0.0918224 + 0.159041i
\(712\) 17.3169 + 29.9937i 0.648977 + 1.12406i
\(713\) −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
\(717\) 46.9578i 1.75367i
\(718\) −27.7210 −1.03454
\(719\) −9.12634 −0.340355 −0.170178 0.985413i \(-0.554434\pi\)
−0.170178 + 0.985413i \(0.554434\pi\)
\(720\) 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
\(724\) −0.491906 + 0.852006i −0.0182815 + 0.0316646i
\(725\) −24.7413 −0.918868
\(726\) −28.3617 + 16.3746i −1.05260 + 0.607719i
\(727\) 33.6859 1.24934 0.624670 0.780889i \(-0.285233\pi\)
0.624670 + 0.780889i \(0.285233\pi\)
\(728\) 0 0
\(729\) −43.0880 −1.59585
\(730\) −7.37471 + 4.25779i −0.272950 + 0.157588i
\(731\) −1.94301 −0.0718650
\(732\) −1.50616 + 2.60874i −0.0556691 + 0.0964218i
\(733\) −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
\(737\) 13.5985 0.500908
\(738\) 29.0801 1.07045
\(739\) 1.85025i 0.0680627i 0.999421 + 0.0340314i \(0.0108346\pi\)
−0.999421 + 0.0340314i \(0.989165\pi\)
\(740\) 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 0.923558 0.383460i \(-0.125268\pi\)
0.129693 + 0.991554i \(0.458601\pi\)
\(744\) −23.5890 40.8574i −0.864816 1.49791i
\(745\) 0.873120 1.51229i 0.0319886 0.0554059i
\(746\) −19.0757 + 11.0134i −0.698412 + 0.403228i
\(747\) 44.4588i 1.62666i
\(748\) 0.216858 0.125203i 0.00792913 0.00457788i
\(749\) 0 0
\(750\) −9.88850 17.1274i −0.361077 0.625404i
\(751\) −10.3871 17.9910i −0.379032 0.656503i 0.611890 0.790943i \(-0.290410\pi\)
−0.990922 + 0.134441i \(0.957076\pi\)
\(752\) 17.3258i 0.631806i
\(753\) 9.11286 + 15.7839i 0.332091 + 0.575199i
\(754\) −24.0026 10.3393i −0.874122 0.376536i
\(755\) 6.56824 0.239043
\(756\) 0 0
\(757\) −21.8075 + 37.7717i −0.792607 + 1.37283i 0.131741 + 0.991284i \(0.457943\pi\)
−0.924348 + 0.381551i \(0.875390\pi\)
\(758\) 12.1673 0.441936
\(759\) 36.3304 20.9754i 1.31871 0.761358i
\(760\) 3.22622 + 1.86266i 0.117027 + 0.0675657i
\(761\) 12.3902i 0.449145i 0.974457 + 0.224573i \(0.0720986\pi\)
−0.974457 + 0.224573i \(0.927901\pi\)
\(762\) 5.57497i 0.201960i
\(763\) 0 0
\(764\) 0.484583 0.839323i 0.0175316 0.0303656i
\(765\) −4.36488 + 2.52007i −0.157813 + 0.0911132i
\(766\) 5.51773 + 9.55700i 0.199364 + 0.345308i
\(767\) 17.9395 13.3695i 0.647757 0.482746i
\(768\) −2.67917 + 4.64046i −0.0966763 + 0.167448i
\(769\) −4.80955 2.77680i −0.173437 0.100134i 0.410769 0.911740i \(-0.365260\pi\)
−0.584205 + 0.811606i \(0.698594\pi\)
\(770\) 0 0
\(771\) 5.18750 + 8.98501i 0.186823 + 0.323587i
\(772\) −0.797307 0.460325i −0.0286957 0.0165675i
\(773\) −37.9355 21.9021i −1.36445 0.787764i −0.374235 0.927334i \(-0.622095\pi\)
−0.990212 + 0.139570i \(0.955428\pi\)
\(774\) −5.96726 3.44520i −0.214489 0.123835i
\(775\) −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
\(779\) −5.24267 + 9.08058i −0.187838 + 0.325346i
\(780\) 0.0487854 + 0.415566i 0.00174680 + 0.0148796i