Properties

Label 637.2.e.l.79.1
Level $637$
Weight $2$
Character 637.79
Analytic conductor $5.086$
Analytic rank $0$
Dimension $6$
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.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.4406832.1
Defining polynomial: \(x^{6} - x^{5} + 6 x^{4} + 7 x^{3} + 24 x^{2} + 5 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(1.43310 + 2.48220i\) of defining polynomial
Character \(\chi\) \(=\) 637.79
Dual form 637.2.e.l.508.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.933099 + 1.61618i) q^{2} +(1.67445 + 2.90023i) q^{3} +(-0.741348 - 1.28405i) q^{4} +(-0.433099 + 0.750150i) q^{5} -6.24970 q^{6} -0.965392 q^{8} +(-4.10755 + 7.11448i) q^{9} +O(q^{10})\) \(q+(-0.933099 + 1.61618i) q^{2} +(1.67445 + 2.90023i) q^{3} +(-0.741348 - 1.28405i) q^{4} +(-0.433099 + 0.750150i) q^{5} -6.24970 q^{6} -0.965392 q^{8} +(-4.10755 + 7.11448i) q^{9} +(-0.808249 - 1.39993i) q^{10} +(1.93310 + 3.34823i) q^{11} +(2.48270 - 4.30016i) q^{12} +1.00000 q^{13} -2.90081 q^{15} +(2.38350 - 4.12835i) q^{16} +(1.67445 + 2.90023i) q^{17} +(-7.66550 - 13.2770i) q^{18} +(2.69175 - 4.66225i) q^{19} +1.28431 q^{20} -7.21509 q^{22} +(2.62485 - 4.54637i) q^{23} +(-1.61650 - 2.79986i) q^{24} +(2.12485 + 3.68035i) q^{25} +(-0.933099 + 1.61618i) q^{26} -17.4648 q^{27} +1.69779 q^{29} +(2.70674 - 4.68821i) q^{30} +(-3.78199 - 6.55060i) q^{31} +(3.48270 + 6.03221i) q^{32} +(-6.47374 + 11.2129i) q^{33} -6.24970 q^{34} +12.1805 q^{36} +(2.41580 - 4.18428i) q^{37} +(5.02334 + 8.70068i) q^{38} +(1.67445 + 2.90023i) q^{39} +(0.418110 - 0.724188i) q^{40} -4.06922 q^{41} +4.03461 q^{43} +(2.86620 - 4.96440i) q^{44} +(-3.55795 - 6.16255i) q^{45} +(4.89849 + 8.48444i) q^{46} +(1.82555 - 3.16195i) q^{47} +15.9642 q^{48} -7.93078 q^{50} +(-5.60755 + 9.71255i) q^{51} +(-0.741348 - 1.28405i) q^{52} +(0.107546 + 0.186276i) q^{53} +(16.2964 - 28.2262i) q^{54} -3.34889 q^{55} +18.0288 q^{57} +(-1.58420 + 2.74392i) q^{58} +(1.39245 + 2.41180i) q^{59} +(2.15051 + 3.72479i) q^{60} +(-4.51730 + 7.82420i) q^{61} +14.1159 q^{62} -3.46479 q^{64} +(-0.433099 + 0.750150i) q^{65} +(-12.0813 - 20.9254i) q^{66} +(3.83159 + 6.63651i) q^{67} +(2.48270 - 4.30016i) q^{68} +17.5807 q^{69} +4.90081 q^{71} +(3.96539 - 6.86826i) q^{72} +(-7.77304 - 13.4633i) q^{73} +(4.50835 + 7.80870i) q^{74} +(-7.11590 + 12.3251i) q^{75} -7.98210 q^{76} -6.24970 q^{78} +(-4.71509 + 8.16678i) q^{79} +(2.06459 + 3.57597i) q^{80} +(-16.9212 - 29.3084i) q^{81} +(3.79698 - 6.57657i) q^{82} -4.09919 q^{83} -2.90081 q^{85} +(-3.76469 + 6.52063i) q^{86} +(2.84286 + 4.92397i) q^{87} +(-1.86620 - 3.23235i) q^{88} +(0.209055 - 0.362094i) q^{89} +13.2797 q^{90} -7.78371 q^{92} +(12.6655 - 21.9373i) q^{93} +(3.40684 + 5.90083i) q^{94} +(2.33159 + 4.03843i) q^{95} +(-11.6632 + 20.2012i) q^{96} -7.11590 q^{97} -31.7612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{2} + 4q^{3} - 6q^{4} + 5q^{5} - 4q^{6} - 12q^{8} - 11q^{9} + O(q^{10}) \) \( 6q + 2q^{2} + 4q^{3} - 6q^{4} + 5q^{5} - 4q^{6} - 12q^{8} - 11q^{9} - 14q^{10} + 4q^{11} + 18q^{12} + 6q^{13} + 4q^{15} - 4q^{16} + 4q^{17} - 8q^{18} + 7q^{19} - 32q^{20} - 16q^{22} - q^{23} - 28q^{24} - 4q^{25} + 2q^{26} - 44q^{27} - 14q^{29} + 24q^{30} - 3q^{31} + 24q^{32} - 10q^{33} - 4q^{34} + 52q^{36} + 10q^{37} + 12q^{38} + 4q^{39} - 22q^{40} - 12q^{41} + 18q^{43} + 2q^{44} + 3q^{45} + 28q^{46} + 17q^{47} - 32q^{48} - 60q^{50} - 20q^{51} - 6q^{52} - 13q^{53} + 28q^{54} - 8q^{55} + 8q^{57} - 14q^{58} + 22q^{59} - 42q^{60} - 24q^{61} + 36q^{62} + 40q^{64} + 5q^{65} - 30q^{66} + 14q^{67} + 18q^{68} - 4q^{69} + 8q^{71} + 30q^{72} + 5q^{73} - 8q^{74} + 6q^{75} + 16q^{76} - 4q^{78} - q^{79} + 40q^{80} - 15q^{81} + 20q^{82} - 46q^{83} + 4q^{85} - 6q^{86} + 20q^{87} + 4q^{88} - 11q^{89} + 80q^{90} + 60q^{92} + 38q^{93} - 16q^{94} + 5q^{95} - 52q^{96} + 6q^{97} - 60q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.933099 + 1.61618i −0.659801 + 1.14281i 0.320866 + 0.947124i \(0.396026\pi\)
−0.980667 + 0.195684i \(0.937307\pi\)
\(3\) 1.67445 + 2.90023i 0.966742 + 1.67445i 0.704859 + 0.709348i \(0.251010\pi\)
0.261884 + 0.965099i \(0.415656\pi\)
\(4\) −0.741348 1.28405i −0.370674 0.642026i
\(5\) −0.433099 + 0.750150i −0.193688 + 0.335477i −0.946470 0.322793i \(-0.895378\pi\)
0.752782 + 0.658270i \(0.228712\pi\)
\(6\) −6.24970 −2.55143
\(7\) 0 0
\(8\) −0.965392 −0.341318
\(9\) −4.10755 + 7.11448i −1.36918 + 2.37149i
\(10\) −0.808249 1.39993i −0.255591 0.442696i
\(11\) 1.93310 + 3.34823i 0.582851 + 1.00953i 0.995140 + 0.0984746i \(0.0313963\pi\)
−0.412288 + 0.911053i \(0.635270\pi\)
\(12\) 2.48270 4.30016i 0.716693 1.24135i
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −2.90081 −0.748985
\(16\) 2.38350 4.12835i 0.595876 1.03209i
\(17\) 1.67445 + 2.90023i 0.406113 + 0.703408i 0.994450 0.105207i \(-0.0335506\pi\)
−0.588337 + 0.808616i \(0.700217\pi\)
\(18\) −7.66550 13.2770i −1.80677 3.12943i
\(19\) 2.69175 4.66225i 0.617530 1.06959i −0.372405 0.928070i \(-0.621467\pi\)
0.989935 0.141523i \(-0.0451999\pi\)
\(20\) 1.28431 0.287180
\(21\) 0 0
\(22\) −7.21509 −1.53826
\(23\) 2.62485 4.54637i 0.547319 0.947985i −0.451138 0.892454i \(-0.648982\pi\)
0.998457 0.0555303i \(-0.0176849\pi\)
\(24\) −1.61650 2.79986i −0.329966 0.571518i
\(25\) 2.12485 + 3.68035i 0.424970 + 0.736070i
\(26\) −0.933099 + 1.61618i −0.182996 + 0.316958i
\(27\) −17.4648 −3.36110
\(28\) 0 0
\(29\) 1.69779 0.315271 0.157636 0.987497i \(-0.449613\pi\)
0.157636 + 0.987497i \(0.449613\pi\)
\(30\) 2.70674 4.68821i 0.494181 0.855946i
\(31\) −3.78199 6.55060i −0.679266 1.17652i −0.975202 0.221316i \(-0.928965\pi\)
0.295936 0.955208i \(-0.404368\pi\)
\(32\) 3.48270 + 6.03221i 0.615659 + 1.06635i
\(33\) −6.47374 + 11.2129i −1.12693 + 1.95191i
\(34\) −6.24970 −1.07181
\(35\) 0 0
\(36\) 12.1805 2.03008
\(37\) 2.41580 4.18428i 0.397154 0.687891i −0.596219 0.802822i \(-0.703331\pi\)
0.993374 + 0.114930i \(0.0366645\pi\)
\(38\) 5.02334 + 8.70068i 0.814894 + 1.41144i
\(39\) 1.67445 + 2.90023i 0.268126 + 0.464408i
\(40\) 0.418110 0.724188i 0.0661091 0.114504i
\(41\) −4.06922 −0.635505 −0.317752 0.948174i \(-0.602928\pi\)
−0.317752 + 0.948174i \(0.602928\pi\)
\(42\) 0 0
\(43\) 4.03461 0.615272 0.307636 0.951504i \(-0.400462\pi\)
0.307636 + 0.951504i \(0.400462\pi\)
\(44\) 2.86620 4.96440i 0.432096 0.748412i
\(45\) −3.55795 6.16255i −0.530388 0.918659i
\(46\) 4.89849 + 8.48444i 0.722243 + 1.25096i
\(47\) 1.82555 3.16195i 0.266284 0.461218i −0.701615 0.712556i \(-0.747537\pi\)
0.967899 + 0.251338i \(0.0808707\pi\)
\(48\) 15.9642 2.30423
\(49\) 0 0
\(50\) −7.93078 −1.12158
\(51\) −5.60755 + 9.71255i −0.785214 + 1.36003i
\(52\) −0.741348 1.28405i −0.102806 0.178066i
\(53\) 0.107546 + 0.186276i 0.0147726 + 0.0255869i 0.873317 0.487152i \(-0.161964\pi\)
−0.858545 + 0.512739i \(0.828631\pi\)
\(54\) 16.2964 28.2262i 2.21766 3.84109i
\(55\) −3.34889 −0.451565
\(56\) 0 0
\(57\) 18.0288 2.38797
\(58\) −1.58420 + 2.74392i −0.208016 + 0.360295i
\(59\) 1.39245 + 2.41180i 0.181282 + 0.313990i 0.942317 0.334721i \(-0.108642\pi\)
−0.761035 + 0.648710i \(0.775309\pi\)
\(60\) 2.15051 + 3.72479i 0.277629 + 0.480868i
\(61\) −4.51730 + 7.82420i −0.578382 + 1.00179i 0.417284 + 0.908776i \(0.362982\pi\)
−0.995665 + 0.0930099i \(0.970351\pi\)
\(62\) 14.1159 1.79272
\(63\) 0 0
\(64\) −3.46479 −0.433099
\(65\) −0.433099 + 0.750150i −0.0537193 + 0.0930446i
\(66\) −12.0813 20.9254i −1.48710 2.57574i
\(67\) 3.83159 + 6.63651i 0.468103 + 0.810779i 0.999336 0.0364476i \(-0.0116042\pi\)
−0.531232 + 0.847226i \(0.678271\pi\)
\(68\) 2.48270 4.30016i 0.301071 0.521470i
\(69\) 17.5807 2.11647
\(70\) 0 0
\(71\) 4.90081 0.581619 0.290809 0.956781i \(-0.406075\pi\)
0.290809 + 0.956781i \(0.406075\pi\)
\(72\) 3.96539 6.86826i 0.467326 0.809432i
\(73\) −7.77304 13.4633i −0.909766 1.57576i −0.814389 0.580319i \(-0.802928\pi\)
−0.0953766 0.995441i \(-0.530406\pi\)
\(74\) 4.50835 + 7.80870i 0.524085 + 0.907742i
\(75\) −7.11590 + 12.3251i −0.821673 + 1.42318i
\(76\) −7.98210 −0.915609
\(77\) 0 0
\(78\) −6.24970 −0.707639
\(79\) −4.71509 + 8.16678i −0.530489 + 0.918835i 0.468878 + 0.883263i \(0.344658\pi\)
−0.999367 + 0.0355715i \(0.988675\pi\)
\(80\) 2.06459 + 3.57597i 0.230828 + 0.399805i
\(81\) −16.9212 29.3084i −1.88014 3.25649i
\(82\) 3.79698 6.57657i 0.419307 0.726260i
\(83\) −4.09919 −0.449945 −0.224972 0.974365i \(-0.572229\pi\)
−0.224972 + 0.974365i \(0.572229\pi\)
\(84\) 0 0
\(85\) −2.90081 −0.314637
\(86\) −3.76469 + 6.52063i −0.405957 + 0.703138i
\(87\) 2.84286 + 4.92397i 0.304786 + 0.527905i
\(88\) −1.86620 3.23235i −0.198937 0.344570i
\(89\) 0.209055 0.362094i 0.0221598 0.0383819i −0.854733 0.519068i \(-0.826279\pi\)
0.876893 + 0.480686i \(0.159612\pi\)
\(90\) 13.2797 1.39980
\(91\) 0 0
\(92\) −7.78371 −0.811508
\(93\) 12.6655 21.9373i 1.31335 2.27479i
\(94\) 3.40684 + 5.90083i 0.351389 + 0.608624i
\(95\) 2.33159 + 4.03843i 0.239216 + 0.414334i
\(96\) −11.6632 + 20.2012i −1.19037 + 2.06178i
\(97\) −7.11590 −0.722510 −0.361255 0.932467i \(-0.617652\pi\)
−0.361255 + 0.932467i \(0.617652\pi\)
\(98\) 0 0
\(99\) −31.7612 −3.19212
\(100\) 3.15051 5.45684i 0.315051 0.545684i
\(101\) 7.05795 + 12.2247i 0.702292 + 1.21641i 0.967660 + 0.252259i \(0.0811733\pi\)
−0.265368 + 0.964147i \(0.585493\pi\)
\(102\) −10.4648 18.1256i −1.03617 1.79470i
\(103\) 8.43018 14.6015i 0.830651 1.43873i −0.0668721 0.997762i \(-0.521302\pi\)
0.897523 0.440968i \(-0.145365\pi\)
\(104\) −0.965392 −0.0946645
\(105\) 0 0
\(106\) −0.401405 −0.0389879
\(107\) −5.09024 + 8.81656i −0.492092 + 0.852329i −0.999959 0.00910710i \(-0.997101\pi\)
0.507866 + 0.861436i \(0.330434\pi\)
\(108\) 12.9475 + 22.4257i 1.24587 + 2.15791i
\(109\) 3.10151 + 5.37197i 0.297071 + 0.514542i 0.975464 0.220157i \(-0.0706570\pi\)
−0.678394 + 0.734699i \(0.737324\pi\)
\(110\) 3.12485 5.41240i 0.297943 0.516052i
\(111\) 16.1805 1.53578
\(112\) 0 0
\(113\) 10.2843 0.967466 0.483733 0.875216i \(-0.339281\pi\)
0.483733 + 0.875216i \(0.339281\pi\)
\(114\) −16.8226 + 29.1377i −1.57558 + 2.72899i
\(115\) 2.27364 + 3.93806i 0.212018 + 0.367226i
\(116\) −1.25865 2.18005i −0.116863 0.202412i
\(117\) −4.10755 + 7.11448i −0.379743 + 0.657734i
\(118\) −5.19719 −0.478440
\(119\) 0 0
\(120\) 2.80041 0.255642
\(121\) −1.97374 + 3.41863i −0.179431 + 0.310784i
\(122\) −8.43018 14.6015i −0.763233 1.32196i
\(123\) −6.81369 11.8017i −0.614369 1.06412i
\(124\) −5.60755 + 9.71255i −0.503573 + 0.872213i
\(125\) −8.01207 −0.716622
\(126\) 0 0
\(127\) −1.91288 −0.169741 −0.0848704 0.996392i \(-0.527048\pi\)
−0.0848704 + 0.996392i \(0.527048\pi\)
\(128\) −3.73240 + 6.46470i −0.329900 + 0.571404i
\(129\) 6.75574 + 11.7013i 0.594810 + 1.03024i
\(130\) −0.808249 1.39993i −0.0708881 0.122782i
\(131\) −5.08129 + 8.80105i −0.443954 + 0.768952i −0.997979 0.0635489i \(-0.979758\pi\)
0.554024 + 0.832500i \(0.313091\pi\)
\(132\) 19.1972 1.67090
\(133\) 0 0
\(134\) −14.3010 −1.23542
\(135\) 7.56399 13.1012i 0.651004 1.12757i
\(136\) −1.61650 2.79986i −0.138614 0.240086i
\(137\) −3.89849 6.75238i −0.333071 0.576895i 0.650042 0.759899i \(-0.274751\pi\)
−0.983112 + 0.183003i \(0.941418\pi\)
\(138\) −16.4045 + 28.4135i −1.39645 + 2.41872i
\(139\) −5.08129 −0.430989 −0.215495 0.976505i \(-0.569136\pi\)
−0.215495 + 0.976505i \(0.569136\pi\)
\(140\) 0 0
\(141\) 12.2272 1.02971
\(142\) −4.57294 + 7.92056i −0.383752 + 0.664679i
\(143\) 1.93310 + 3.34823i 0.161654 + 0.279993i
\(144\) 19.5807 + 33.9148i 1.63172 + 2.82623i
\(145\) −0.735311 + 1.27360i −0.0610642 + 0.105766i
\(146\) 29.0121 2.40106
\(147\) 0 0
\(148\) −7.16378 −0.588859
\(149\) 1.24739 2.16053i 0.102190 0.176998i −0.810397 0.585881i \(-0.800748\pi\)
0.912587 + 0.408884i \(0.134082\pi\)
\(150\) −13.2797 23.0011i −1.08428 1.87803i
\(151\) 1.63089 + 2.82478i 0.132720 + 0.229877i 0.924724 0.380638i \(-0.124296\pi\)
−0.792004 + 0.610515i \(0.790962\pi\)
\(152\) −2.59859 + 4.50090i −0.210774 + 0.365071i
\(153\) −27.5115 −2.22417
\(154\) 0 0
\(155\) 6.55191 0.526262
\(156\) 2.48270 4.30016i 0.198775 0.344288i
\(157\) 0.360161 + 0.623817i 0.0287440 + 0.0497860i 0.880040 0.474900i \(-0.157516\pi\)
−0.851296 + 0.524686i \(0.824183\pi\)
\(158\) −8.79930 15.2408i −0.700035 1.21250i
\(159\) −0.360161 + 0.623817i −0.0285626 + 0.0494719i
\(160\) −6.03341 −0.476983
\(161\) 0 0
\(162\) 63.1568 4.96206
\(163\) −0.651106 + 1.12775i −0.0509985 + 0.0883321i −0.890398 0.455183i \(-0.849574\pi\)
0.839399 + 0.543515i \(0.182907\pi\)
\(164\) 3.01671 + 5.22509i 0.235565 + 0.408011i
\(165\) −5.60755 9.71255i −0.436547 0.756121i
\(166\) 3.82495 6.62501i 0.296874 0.514201i
\(167\) 16.1505 1.24976 0.624882 0.780719i \(-0.285147\pi\)
0.624882 + 0.780719i \(0.285147\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 2.70674 4.68821i 0.207597 0.359569i
\(171\) 22.1130 + 38.3008i 1.69102 + 2.92894i
\(172\) −2.99105 5.18065i −0.228065 0.395021i
\(173\) 7.92415 13.7250i 0.602462 1.04349i −0.389985 0.920821i \(-0.627520\pi\)
0.992447 0.122673i \(-0.0391467\pi\)
\(174\) −10.6107 −0.804393
\(175\) 0 0
\(176\) 18.4302 1.38923
\(177\) −4.66318 + 8.07687i −0.350506 + 0.607094i
\(178\) 0.390138 + 0.675740i 0.0292421 + 0.0506488i
\(179\) 10.2324 + 17.7230i 0.764805 + 1.32468i 0.940349 + 0.340210i \(0.110498\pi\)
−0.175544 + 0.984472i \(0.556169\pi\)
\(180\) −5.27536 + 9.13719i −0.393202 + 0.681046i
\(181\) −6.58189 −0.489228 −0.244614 0.969621i \(-0.578661\pi\)
−0.244614 + 0.969621i \(0.578661\pi\)
\(182\) 0 0
\(183\) −30.2559 −2.23658
\(184\) −2.53401 + 4.38903i −0.186810 + 0.323564i
\(185\) 2.09256 + 3.62442i 0.153848 + 0.266472i
\(186\) 23.6363 + 40.9393i 1.73310 + 3.00182i
\(187\) −6.47374 + 11.2129i −0.473407 + 0.819965i
\(188\) −5.41348 −0.394819
\(189\) 0 0
\(190\) −8.70242 −0.631340
\(191\) −6.37455 + 11.0410i −0.461246 + 0.798902i −0.999023 0.0441850i \(-0.985931\pi\)
0.537777 + 0.843087i \(0.319264\pi\)
\(192\) −5.80161 10.0487i −0.418695 0.725202i
\(193\) −1.13380 1.96380i −0.0816128 0.141358i 0.822330 0.569011i \(-0.192674\pi\)
−0.903943 + 0.427653i \(0.859340\pi\)
\(194\) 6.63984 11.5005i 0.476713 0.825691i
\(195\) −2.90081 −0.207731
\(196\) 0 0
\(197\) −18.6978 −1.33216 −0.666081 0.745879i \(-0.732030\pi\)
−0.666081 + 0.745879i \(0.732030\pi\)
\(198\) 29.6363 51.3316i 2.10616 3.64798i
\(199\) −9.95876 17.2491i −0.705957 1.22275i −0.966345 0.257250i \(-0.917184\pi\)
0.260387 0.965504i \(-0.416150\pi\)
\(200\) −2.05131 3.55298i −0.145050 0.251234i
\(201\) −12.8316 + 22.2250i −0.905071 + 1.56763i
\(202\) −26.3431 −1.85349
\(203\) 0 0
\(204\) 16.6286 1.16423
\(205\) 1.76237 3.05252i 0.123090 0.213197i
\(206\) 15.7324 + 27.2493i 1.09613 + 1.89855i
\(207\) 21.5634 + 37.3489i 1.49876 + 2.59593i
\(208\) 2.38350 4.12835i 0.165266 0.286249i
\(209\) 20.8137 1.43971
\(210\) 0 0
\(211\) 0.645277 0.0444227 0.0222114 0.999753i \(-0.492929\pi\)
0.0222114 + 0.999753i \(0.492929\pi\)
\(212\) 0.159458 0.276190i 0.0109516 0.0189688i
\(213\) 8.20614 + 14.2135i 0.562276 + 0.973890i
\(214\) −9.49940 16.4534i −0.649366 1.12473i
\(215\) −1.74739 + 3.02656i −0.119171 + 0.206410i
\(216\) 16.8604 1.14720
\(217\) 0 0
\(218\) −11.5761 −0.784030
\(219\) 26.0311 45.0872i 1.75902 3.04671i
\(220\) 2.48270 + 4.30016i 0.167383 + 0.289916i
\(221\) 1.67445 + 2.90023i 0.112636 + 0.195090i
\(222\) −15.0980 + 26.1505i −1.01331 + 1.75511i
\(223\) 5.83159 0.390512 0.195256 0.980752i \(-0.437446\pi\)
0.195256 + 0.980752i \(0.437446\pi\)
\(224\) 0 0
\(225\) −34.9117 −2.32745
\(226\) −9.59628 + 16.6212i −0.638335 + 1.10563i
\(227\) 7.86620 + 13.6247i 0.522098 + 0.904300i 0.999670 + 0.0257073i \(0.00818378\pi\)
−0.477572 + 0.878593i \(0.658483\pi\)
\(228\) −13.3656 23.1499i −0.885158 1.53314i
\(229\) 4.43914 7.68881i 0.293346 0.508091i −0.681252 0.732049i \(-0.738564\pi\)
0.974599 + 0.223958i \(0.0718977\pi\)
\(230\) −8.48613 −0.559559
\(231\) 0 0
\(232\) −1.63903 −0.107608
\(233\) 5.89558 10.2114i 0.386232 0.668974i −0.605707 0.795688i \(-0.707110\pi\)
0.991939 + 0.126714i \(0.0404431\pi\)
\(234\) −7.66550 13.2770i −0.501109 0.867946i
\(235\) 1.58129 + 2.73888i 0.103152 + 0.178665i
\(236\) 2.06459 3.57597i 0.134393 0.232776i
\(237\) −31.5807 −2.05139
\(238\) 0 0
\(239\) −16.0692 −1.03943 −0.519716 0.854339i \(-0.673962\pi\)
−0.519716 + 0.854339i \(0.673962\pi\)
\(240\) −6.91408 + 11.9755i −0.446302 + 0.773017i
\(241\) −2.46771 4.27419i −0.158959 0.275325i 0.775535 0.631305i \(-0.217480\pi\)
−0.934494 + 0.355980i \(0.884147\pi\)
\(242\) −3.68340 6.37983i −0.236778 0.410111i
\(243\) 30.4702 52.7760i 1.95467 3.38558i
\(244\) 13.3956 0.857564
\(245\) 0 0
\(246\) 25.4314 1.62145
\(247\) 2.69175 4.66225i 0.171272 0.296652i
\(248\) 3.65111 + 6.32390i 0.231845 + 0.401568i
\(249\) −6.86388 11.8886i −0.434981 0.753409i
\(250\) 7.47606 12.9489i 0.472828 0.818961i
\(251\) 15.2439 0.962185 0.481092 0.876670i \(-0.340240\pi\)
0.481092 + 0.876670i \(0.340240\pi\)
\(252\) 0 0
\(253\) 20.2964 1.27602
\(254\) 1.78491 3.09155i 0.111995 0.193981i
\(255\) −4.85725 8.41300i −0.304173 0.526842i
\(256\) −10.4302 18.0656i −0.651887 1.12910i
\(257\) 7.80825 13.5243i 0.487065 0.843622i −0.512824 0.858494i \(-0.671401\pi\)
0.999889 + 0.0148720i \(0.00473408\pi\)
\(258\) −25.2151 −1.56982
\(259\) 0 0
\(260\) 1.28431 0.0796494
\(261\) −6.97374 + 12.0789i −0.431664 + 0.747664i
\(262\) −9.48270 16.4245i −0.585843 1.01471i
\(263\) −8.54668 14.8033i −0.527011 0.912810i −0.999505 0.0314757i \(-0.989979\pi\)
0.472493 0.881334i \(-0.343354\pi\)
\(264\) 6.24970 10.8248i 0.384642 0.666220i
\(265\) −0.186313 −0.0114451
\(266\) 0 0
\(267\) 1.40021 0.0856913
\(268\) 5.68108 9.83992i 0.347027 0.601069i
\(269\) −8.16841 14.1481i −0.498037 0.862625i 0.501961 0.864890i \(-0.332612\pi\)
−0.999997 + 0.00226550i \(0.999279\pi\)
\(270\) 14.1159 + 24.4495i 0.859066 + 1.48795i
\(271\) 6.24970 10.8248i 0.379642 0.657560i −0.611368 0.791347i \(-0.709380\pi\)
0.991010 + 0.133787i \(0.0427137\pi\)
\(272\) 15.9642 0.967971
\(273\) 0 0
\(274\) 14.5507 0.879041
\(275\) −8.21509 + 14.2290i −0.495389 + 0.858038i
\(276\) −13.0334 22.5745i −0.784519 1.35883i
\(277\) 1.50000 + 2.59808i 0.0901263 + 0.156103i 0.907564 0.419914i \(-0.137940\pi\)
−0.817438 + 0.576017i \(0.804606\pi\)
\(278\) 4.74135 8.21226i 0.284367 0.492538i
\(279\) 62.1389 3.72016
\(280\) 0 0
\(281\) 0.831590 0.0496085 0.0248043 0.999692i \(-0.492104\pi\)
0.0248043 + 0.999692i \(0.492104\pi\)
\(282\) −11.4092 + 19.7612i −0.679406 + 1.17676i
\(283\) −5.52938 9.57716i −0.328687 0.569303i 0.653564 0.756871i \(-0.273273\pi\)
−0.982252 + 0.187568i \(0.939940\pi\)
\(284\) −3.63320 6.29289i −0.215591 0.373414i
\(285\) −7.80825 + 13.5243i −0.462521 + 0.801109i
\(286\) −7.21509 −0.426637
\(287\) 0 0
\(288\) −57.2213 −3.37180
\(289\) 2.89245 5.00988i 0.170144 0.294699i
\(290\) −1.37224 2.37678i −0.0805804 0.139569i
\(291\) −11.9152 20.6377i −0.698481 1.20980i
\(292\) −11.5251 + 19.9620i −0.674453 + 1.16819i
\(293\) −26.9175 −1.57254 −0.786269 0.617884i \(-0.787990\pi\)
−0.786269 + 0.617884i \(0.787990\pi\)
\(294\) 0 0
\(295\) −2.41228 −0.140448
\(296\) −2.33219 + 4.03947i −0.135556 + 0.234789i
\(297\) −33.7612 58.4761i −1.95902 3.39313i
\(298\) 2.32787 + 4.03199i 0.134850 + 0.233567i
\(299\) 2.62485 4.54637i 0.151799 0.262924i
\(300\) 21.1014 1.21829
\(301\) 0 0
\(302\) −6.08712 −0.350274
\(303\) −23.6363 + 40.9393i −1.35787 + 2.35190i
\(304\) −12.8316 22.2250i −0.735942 1.27469i
\(305\) −3.91288 6.77731i −0.224051 0.388068i
\(306\) 25.6709 44.4634i 1.46751 2.54180i
\(307\) −15.1580 −0.865110 −0.432555 0.901608i \(-0.642388\pi\)
−0.432555 + 0.901608i \(0.642388\pi\)
\(308\) 0 0
\(309\) 56.4636 3.21210
\(310\) −6.11358 + 10.5890i −0.347228 + 0.601417i
\(311\) −2.12253 3.67634i −0.120358 0.208466i 0.799551 0.600598i \(-0.205071\pi\)
−0.919909 + 0.392132i \(0.871738\pi\)
\(312\) −1.61650 2.79986i −0.0915162 0.158511i
\(313\) −8.97666 + 15.5480i −0.507391 + 0.878827i 0.492573 + 0.870271i \(0.336057\pi\)
−0.999963 + 0.00855523i \(0.997277\pi\)
\(314\) −1.34426 −0.0758612
\(315\) 0 0
\(316\) 13.9821 0.786554
\(317\) 7.63320 13.2211i 0.428723 0.742571i −0.568037 0.823003i \(-0.692297\pi\)
0.996760 + 0.0804326i \(0.0256302\pi\)
\(318\) −0.672132 1.16417i −0.0376913 0.0652832i
\(319\) 3.28199 + 5.68458i 0.183756 + 0.318275i
\(320\) 1.50060 2.59911i 0.0838860 0.145295i
\(321\) −34.0934 −1.90291
\(322\) 0 0
\(323\) 18.0288 1.00315
\(324\) −25.0890 + 43.4555i −1.39384 + 2.41419i
\(325\) 2.12485 + 3.68035i 0.117865 + 0.204149i
\(326\) −1.21509 2.10460i −0.0672977 0.116563i
\(327\) −10.3866 + 17.9902i −0.574382 + 0.994858i
\(328\) 3.92839 0.216909
\(329\) 0 0
\(330\) 20.9296 1.15214
\(331\) −8.63320 + 14.9531i −0.474524 + 0.821899i −0.999574 0.0291717i \(-0.990713\pi\)
0.525051 + 0.851071i \(0.324046\pi\)
\(332\) 3.03893 + 5.26358i 0.166783 + 0.288876i
\(333\) 19.8460 + 34.3742i 1.08755 + 1.88370i
\(334\) −15.0700 + 26.1020i −0.824595 + 1.42824i
\(335\) −6.63783 −0.362664
\(336\) 0 0
\(337\) −25.5415 −1.39133 −0.695666 0.718366i \(-0.744891\pi\)
−0.695666 + 0.718366i \(0.744891\pi\)
\(338\) −0.933099 + 1.61618i −0.0507539 + 0.0879083i
\(339\) 17.2205 + 29.8268i 0.935291 + 1.61997i
\(340\) 2.15051 + 3.72479i 0.116628 + 0.202005i
\(341\) 14.6219 25.3259i 0.791822 1.37148i
\(342\) −82.5344 −4.46295
\(343\) 0 0
\(344\) −3.89498 −0.210003
\(345\) −7.61418 + 13.1882i −0.409934 + 0.710026i
\(346\) 14.7880 + 25.6136i 0.795009 + 1.37700i
\(347\) 6.31429 + 10.9367i 0.338969 + 0.587111i 0.984239 0.176843i \(-0.0565886\pi\)
−0.645270 + 0.763954i \(0.723255\pi\)
\(348\) 4.21509 7.30075i 0.225953 0.391362i
\(349\) 35.6394 1.90774 0.953868 0.300226i \(-0.0970622\pi\)
0.953868 + 0.300226i \(0.0970622\pi\)
\(350\) 0 0
\(351\) −17.4648 −0.932202
\(352\) −13.4648 + 23.3217i −0.717676 + 1.24305i
\(353\) −2.70674 4.68821i −0.144065 0.249528i 0.784959 0.619548i \(-0.212684\pi\)
−0.929024 + 0.370020i \(0.879351\pi\)
\(354\) −8.70242 15.0730i −0.462528 0.801123i
\(355\) −2.12253 + 3.67634i −0.112652 + 0.195120i
\(356\) −0.619931 −0.0328563
\(357\) 0 0
\(358\) −38.1914 −2.01848
\(359\) 9.41580 16.3086i 0.496947 0.860737i −0.503047 0.864259i \(-0.667788\pi\)
0.999994 + 0.00352211i \(0.00112113\pi\)
\(360\) 3.43482 + 5.94928i 0.181031 + 0.313554i
\(361\) −4.99105 8.64475i −0.262687 0.454987i
\(362\) 6.14156 10.6375i 0.322793 0.559094i
\(363\) −13.2197 −0.693856
\(364\) 0 0
\(365\) 13.4660 0.704842
\(366\) 28.2318 48.8989i 1.47570 2.55599i
\(367\) 11.5753 + 20.0489i 0.604223 + 1.04655i 0.992174 + 0.124865i \(0.0398498\pi\)
−0.387950 + 0.921680i \(0.626817\pi\)
\(368\) −12.5127 21.6726i −0.652268 1.12976i
\(369\) 16.7145 28.9504i 0.870122 1.50710i
\(370\) −7.81025 −0.406036
\(371\) 0 0
\(372\) −37.5582 −1.94730
\(373\) 16.5896 28.7341i 0.858979 1.48780i −0.0139245 0.999903i \(-0.504432\pi\)
0.872904 0.487893i \(-0.162234\pi\)
\(374\) −12.0813 20.9254i −0.624709 1.08203i
\(375\) −13.4158 23.2368i −0.692789 1.19995i
\(376\) −1.76237 + 3.05252i −0.0908875 + 0.157422i
\(377\) 1.69779 0.0874406
\(378\) 0 0
\(379\) 37.7853 1.94090 0.970451 0.241299i \(-0.0775733\pi\)
0.970451 + 0.241299i \(0.0775733\pi\)
\(380\) 3.45704 5.98777i 0.177342 0.307166i
\(381\) −3.20302 5.54779i −0.164096 0.284222i
\(382\) −11.8962 20.6048i −0.608661 1.05423i
\(383\) −0.115899 + 0.200743i −0.00592215 + 0.0102575i −0.868971 0.494862i \(-0.835218\pi\)
0.863049 + 0.505120i \(0.168552\pi\)
\(384\) −24.9988 −1.27571
\(385\) 0 0
\(386\) 4.23180 0.215393
\(387\) −16.5723 + 28.7041i −0.842419 + 1.45911i
\(388\) 5.27536 + 9.13719i 0.267816 + 0.463870i
\(389\) −4.67676 8.10039i −0.237121 0.410706i 0.722766 0.691093i \(-0.242871\pi\)
−0.959887 + 0.280387i \(0.909537\pi\)
\(390\) 2.70674 4.68821i 0.137061 0.237397i
\(391\) 17.5807 0.889094
\(392\) 0 0
\(393\) −34.0334 −1.71676
\(394\) 17.4469 30.2189i 0.878962 1.52241i
\(395\) −4.08420 7.07405i −0.205499 0.355934i
\(396\) 23.5461 + 40.7830i 1.18324 + 2.04942i
\(397\) −4.87224 + 8.43896i −0.244530 + 0.423539i −0.962000 0.273051i \(-0.911967\pi\)
0.717469 + 0.696590i \(0.245300\pi\)
\(398\) 37.1700 1.86317
\(399\) 0 0
\(400\) 20.2583 1.01292
\(401\) −4.86620 + 8.42850i −0.243006 + 0.420899i −0.961569 0.274563i \(-0.911467\pi\)
0.718563 + 0.695462i \(0.244800\pi\)
\(402\) −23.9463 41.4762i −1.19433 2.06864i
\(403\) −3.78199 6.55060i −0.188395 0.326309i
\(404\) 10.4648 18.1256i 0.520643 0.901780i
\(405\) 29.3143 1.45664
\(406\) 0 0
\(407\) 18.6799 0.925928
\(408\) 5.41348 9.37642i 0.268007 0.464202i
\(409\) 6.18652 + 10.7154i 0.305904 + 0.529841i 0.977462 0.211111i \(-0.0677081\pi\)
−0.671558 + 0.740952i \(0.734375\pi\)
\(410\) 3.28894 + 5.69661i 0.162429 + 0.281336i
\(411\) 13.0556 22.6130i 0.643987 1.11542i
\(412\) −24.9988 −1.23160
\(413\) 0 0
\(414\) −80.4831 −3.95553
\(415\) 1.77536 3.07501i 0.0871489 0.150946i
\(416\) 3.48270 + 6.03221i 0.170753 + 0.295753i
\(417\) −8.50835 14.7369i −0.416656 0.721669i
\(418\) −19.4212 + 33.6386i −0.949924 + 1.64532i
\(419\) −21.1054 −1.03107 −0.515534 0.856869i \(-0.672406\pi\)
−0.515534 + 0.856869i \(0.672406\pi\)
\(420\) 0 0
\(421\) 23.2618 1.13371 0.566855 0.823818i \(-0.308160\pi\)
0.566855 + 0.823818i \(0.308160\pi\)
\(422\) −0.602108 + 1.04288i −0.0293102 + 0.0507667i
\(423\) 14.9971 + 25.9757i 0.729183 + 1.26298i
\(424\) −0.103824 0.179829i −0.00504215 0.00873326i
\(425\) −7.11590 + 12.3251i −0.345172 + 0.597855i
\(426\) −30.6286 −1.48396
\(427\) 0 0
\(428\) 15.0946 0.729623
\(429\) −6.47374 + 11.2129i −0.312555 + 0.541362i
\(430\) −3.26097 5.64816i −0.157258 0.272379i
\(431\) 8.49477 + 14.7134i 0.409179 + 0.708718i 0.994798 0.101868i \(-0.0324819\pi\)
−0.585619 + 0.810586i \(0.699149\pi\)
\(432\) −41.6274 + 72.1007i −2.00280 + 3.46895i
\(433\) 30.8604 1.48305 0.741527 0.670923i \(-0.234102\pi\)
0.741527 + 0.670923i \(0.234102\pi\)
\(434\) 0 0
\(435\) −4.92496 −0.236134
\(436\) 4.59859 7.96500i 0.220233 0.381454i
\(437\) −14.1309 24.4754i −0.675972 1.17082i
\(438\) 48.5792 + 84.1416i 2.32120 + 4.02044i
\(439\) 9.59859 16.6253i 0.458116 0.793480i −0.540745 0.841186i \(-0.681858\pi\)
0.998861 + 0.0477062i \(0.0151911\pi\)
\(440\) 3.23300 0.154127
\(441\) 0 0
\(442\) −6.24970 −0.297268
\(443\) 17.1888 29.7719i 0.816666 1.41451i −0.0914589 0.995809i \(-0.529153\pi\)
0.908125 0.418699i \(-0.137514\pi\)
\(444\) −11.9954 20.7766i −0.569275 0.986013i
\(445\) 0.181083 + 0.313645i 0.00858417 + 0.0148682i
\(446\) −5.44145 + 9.42487i −0.257660 + 0.446281i
\(447\) 8.35472 0.395165
\(448\) 0 0
\(449\) 29.6274 1.39820 0.699101 0.715023i \(-0.253584\pi\)
0.699101 + 0.715023i \(0.253584\pi\)
\(450\) 32.5761 56.4234i 1.53565 2.65982i
\(451\) −7.86620 13.6247i −0.370405 0.641560i
\(452\) −7.62425 13.2056i −0.358615 0.621139i
\(453\) −5.46167 + 9.45989i −0.256612 + 0.444464i
\(454\) −29.3598 −1.37792
\(455\) 0 0
\(456\) −17.4048 −0.815056
\(457\) 8.51962 14.7564i 0.398531 0.690276i −0.595014 0.803715i \(-0.702853\pi\)
0.993545 + 0.113439i \(0.0361868\pi\)
\(458\) 8.28431 + 14.3488i 0.387100 + 0.670477i
\(459\) −29.2439 50.6519i −1.36499 2.36423i
\(460\) 3.37112 5.83895i 0.157179 0.272242i
\(461\) −15.1280 −0.704580 −0.352290 0.935891i \(-0.614597\pi\)
−0.352290 + 0.935891i \(0.614597\pi\)
\(462\) 0 0
\(463\) 26.1221 1.21400 0.607000 0.794702i \(-0.292373\pi\)
0.607000 + 0.794702i \(0.292373\pi\)
\(464\) 4.04668 7.00906i 0.187863 0.325387i
\(465\) 10.9708 + 19.0020i 0.508760 + 0.881198i
\(466\) 11.0023 + 19.0566i 0.509672 + 0.882779i
\(467\) 11.4594 19.8482i 0.530276 0.918464i −0.469100 0.883145i \(-0.655422\pi\)
0.999376 0.0353196i \(-0.0112449\pi\)
\(468\) 12.1805 0.563043
\(469\) 0 0
\(470\) −5.90200 −0.272239
\(471\) −1.20614 + 2.08910i −0.0555760 + 0.0962605i
\(472\) −1.34426 2.32833i −0.0618747 0.107170i
\(473\) 7.79930 + 13.5088i 0.358612 + 0.621134i
\(474\) 29.4679 51.0399i 1.35351 2.34434i
\(475\) 22.8783 1.04973
\(476\) 0 0
\(477\) −1.76700 −0.0809056
\(478\) 14.9942 25.9707i 0.685817 1.18787i
\(479\) 17.5957 + 30.4766i 0.803967 + 1.39251i 0.916986 + 0.398919i \(0.130615\pi\)
−0.113019 + 0.993593i \(0.536052\pi\)
\(480\) −10.1026 17.4983i −0.461120 0.798683i
\(481\) 2.41580 4.18428i 0.110151 0.190787i
\(482\) 9.21046 0.419525
\(483\) 0 0
\(484\) 5.85293 0.266042
\(485\) 3.08189 5.33799i 0.139941 0.242386i
\(486\) 56.8635 + 98.4905i 2.57938 + 4.46762i
\(487\) 14.1505 + 24.5094i 0.641221 + 1.11063i 0.985161 + 0.171635i \(0.0549050\pi\)
−0.343940 + 0.938992i \(0.611762\pi\)
\(488\) 4.36097 7.55342i 0.197412 0.341927i
\(489\) −4.36097 −0.197210
\(490\) 0 0
\(491\) 8.24970 0.372304 0.186152 0.982521i \(-0.440398\pi\)
0.186152 + 0.982521i \(0.440398\pi\)
\(492\) −10.1026 + 17.4983i −0.455462 + 0.788883i
\(493\) 2.84286 + 4.92397i 0.128036 + 0.221765i
\(494\) 5.02334 + 8.70068i 0.226011 + 0.391462i
\(495\) 13.7557 23.8256i 0.618274 1.07088i
\(496\) −36.0576 −1.61903
\(497\) 0 0
\(498\) 25.6187 1.14800
\(499\) 8.36328 14.4856i 0.374392 0.648466i −0.615844 0.787868i \(-0.711185\pi\)
0.990236 + 0.139402i \(0.0445181\pi\)
\(500\) 5.93974 + 10.2879i 0.265633 + 0.460090i
\(501\) 27.0432 + 46.8401i 1.20820 + 2.09266i
\(502\) −14.2240 + 24.6368i −0.634850 + 1.09959i
\(503\) −21.2213 −0.946213 −0.473106 0.881005i \(-0.656867\pi\)
−0.473106 + 0.881005i \(0.656867\pi\)
\(504\) 0 0
\(505\) −12.2272 −0.544102
\(506\) −18.9385 + 32.8025i −0.841921 + 1.45825i
\(507\) 1.67445 + 2.90023i 0.0743648 + 0.128804i
\(508\) 1.41811 + 2.45624i 0.0629185 + 0.108978i
\(509\) −20.3024 + 35.1648i −0.899889 + 1.55865i −0.0722543 + 0.997386i \(0.523019\pi\)
−0.827635 + 0.561267i \(0.810314\pi\)
\(510\) 18.1292 0.802773
\(511\) 0 0
\(512\) 24.0000 1.06066
\(513\) −47.0109 + 81.4252i −2.07558 + 3.59501i
\(514\) 14.5717 + 25.2390i 0.642732 + 1.11324i
\(515\) 7.30221 + 12.6478i 0.321774 + 0.557329i
\(516\) 10.0167 17.3494i 0.440961 0.763767i
\(517\) 14.1159 0.620817
\(518\) 0 0
\(519\) 53.0743 2.32970
\(520\) 0.418110 0.724188i 0.0183354 0.0317578i
\(521\) 1.73240 + 3.00060i 0.0758977 + 0.131459i 0.901476 0.432828i \(-0.142484\pi\)
−0.825579 + 0.564287i \(0.809151\pi\)
\(522\) −13.0144 22.5416i −0.569624 0.986618i
\(523\) 2.78491 4.82360i 0.121776 0.210921i −0.798692 0.601740i \(-0.794475\pi\)
0.920468 + 0.390818i \(0.127808\pi\)
\(524\) 15.0680 0.658249
\(525\) 0 0
\(526\) 31.8996 1.39089
\(527\) 12.6655 21.9373i 0.551718 0.955603i
\(528\) 30.8604 + 53.4517i 1.34303 + 2.32619i
\(529\) −2.27968 3.94852i −0.0991164 0.171675i
\(530\) 0.173848 0.301114i 0.00755149 0.0130796i
\(531\) −22.8783 −0.992832
\(532\) 0 0
\(533\) −4.06922 −0.176257
\(534\) −1.30653 + 2.26298i −0.0565392 + 0.0979287i
\(535\) −4.40916 7.63689i −0.190625 0.330171i
\(536\) −3.69899 6.40683i −0.159772 0.276733i
\(537\) −34.2672 + 59.3526i −1.47874 + 2.56125i
\(538\) 30.4877 1.31442
\(539\) 0 0
\(540\) −22.4302 −0.965241
\(541\) −12.1182 + 20.9894i −0.521003 + 0.902403i 0.478699 + 0.877979i \(0.341109\pi\)
−0.999702 + 0.0244241i \(0.992225\pi\)
\(542\) 11.6632 + 20.2012i 0.500976 + 0.867717i
\(543\) −11.0210 19.0890i −0.472957 0.819186i
\(544\) −11.6632 + 20.2012i −0.500055 + 0.866120i
\(545\) −5.37304 −0.230156
\(546\) 0 0
\(547\) 15.7733 0.674416 0.337208 0.941430i \(-0.390518\pi\)
0.337208 + 0.941430i \(0.390518\pi\)
\(548\) −5.78028 + 10.0117i −0.246921 + 0.427680i
\(549\) −37.1101 64.2765i −1.58382 2.74326i
\(550\) −15.3310 26.5541i −0.653716 1.13227i
\(551\) 4.57002 7.91551i 0.194690 0.337212i
\(552\) −16.9723 −0.722387
\(553\) 0 0
\(554\) −5.59859 −0.237861
\(555\) −7.00775 + 12.1378i −0.297463 + 0.515220i
\(556\) 3.76700 + 6.52464i 0.159757 + 0.276707i
\(557\) 8.61067 + 14.9141i 0.364846 + 0.631931i 0.988751 0.149568i \(-0.0477884\pi\)
−0.623906 + 0.781500i \(0.714455\pi\)
\(558\) −57.9817 + 100.427i −2.45456 + 4.25143i
\(559\) 4.03461 0.170646
\(560\) 0 0
\(561\) −43.3598 −1.83065
\(562\) −0.775956 + 1.34400i −0.0327317 + 0.0566930i
\(563\) −7.67989 13.3020i −0.323669 0.560610i 0.657573 0.753390i \(-0.271583\pi\)
−0.981242 + 0.192780i \(0.938250\pi\)
\(564\) −9.06459 15.7003i −0.381688 0.661103i
\(565\) −4.45413 + 7.71477i −0.187386 + 0.324563i
\(566\) 20.6378 0.867473
\(567\) 0 0
\(568\) −4.73120 −0.198517
\(569\) −11.8610 + 20.5438i −0.497238 + 0.861241i −0.999995 0.00318672i \(-0.998986\pi\)
0.502757 + 0.864428i \(0.332319\pi\)
\(570\) −14.5717 25.2390i −0.610343 1.05715i
\(571\) 13.6595 + 23.6589i 0.571631 + 0.990093i 0.996399 + 0.0847910i \(0.0270223\pi\)
−0.424768 + 0.905302i \(0.639644\pi\)
\(572\) 2.86620 4.96440i 0.119842 0.207572i
\(573\) −42.6954 −1.78363
\(574\) 0 0
\(575\) 22.3097 0.930377
\(576\) 14.2318 24.6502i 0.592992 1.02709i
\(577\) −11.6332 20.1493i −0.484297 0.838826i 0.515541 0.856865i \(-0.327591\pi\)
−0.999837 + 0.0180388i \(0.994258\pi\)
\(578\) 5.39789 + 9.34942i 0.224523 + 0.388885i
\(579\) 3.79698 6.57657i 0.157797 0.273313i
\(580\) 2.18048 0.0905397
\(581\) 0 0
\(582\) 44.4722 1.84343
\(583\) −0.415795 + 0.720178i −0.0172205 + 0.0298267i
\(584\) 7.50403 + 12.9974i 0.310519 + 0.537835i
\(585\) −3.55795 6.16255i −0.147103 0.254790i
\(586\) 25.1167 43.5034i 1.03756 1.79711i
\(587\) −45.7266 −1.88734 −0.943669 0.330892i \(-0.892651\pi\)
−0.943669 + 0.330892i \(0.892651\pi\)
\(588\) 0 0
\(589\) −40.7207 −1.67787
\(590\) 2.25090 3.89867i 0.0926680 0.160506i
\(591\) −31.3085 54.2278i −1.28786 2.23064i
\(592\) −11.5161 19.9465i −0.473309 0.819795i
\(593\) 14.6949 25.4523i 0.603446 1.04520i −0.388849 0.921302i \(-0.627127\pi\)
0.992295 0.123898i \(-0.0395395\pi\)
\(594\) 126.010 5.17026
\(595\) 0 0
\(596\) −3.69899 −0.151516
\(597\) 33.3508 57.7653i 1.36496 2.36418i
\(598\) 4.89849 + 8.48444i 0.200314 + 0.346954i
\(599\) −11.0294 19.1034i −0.450648 0.780546i 0.547778 0.836624i \(-0.315474\pi\)
−0.998426 + 0.0560780i \(0.982140\pi\)
\(600\) 6.86963 11.8986i 0.280452 0.485756i
\(601\) 30.8604 1.25882 0.629410 0.777073i \(-0.283296\pi\)
0.629410 + 0.777073i \(0.283296\pi\)
\(602\) 0 0
\(603\) −62.9537 −2.56367
\(604\) 2.41811 4.18829i 0.0983915 0.170419i
\(605\) −1.70965 2.96121i −0.0695073 0.120390i
\(606\) −44.1101 76.4009i −1.79185 3.10357i
\(607\) −18.2431 + 31.5979i −0.740463 + 1.28252i 0.211821 + 0.977308i \(0.432060\pi\)
−0.952285 + 0.305211i \(0.901273\pi\)
\(608\) 37.4982 1.52075
\(609\) 0 0
\(610\) 14.6044 0.591316
\(611\) 1.82555 3.16195i 0.0738540 0.127919i
\(612\) 20.3956 + 35.3262i 0.824442 + 1.42798i
\(613\) −14.4994 25.1137i −0.585625 1.01433i −0.994797 0.101875i \(-0.967516\pi\)
0.409172 0.912457i \(-0.365818\pi\)
\(614\) 14.1439 24.4979i 0.570800 0.988655i
\(615\) 11.8040 0.475984
\(616\) 0 0
\(617\) −41.6515 −1.67683 −0.838414 0.545035i \(-0.816517\pi\)
−0.838414 + 0.545035i \(0.816517\pi\)
\(618\) −52.6861 + 91.2551i −2.11935 + 3.67082i
\(619\) −6.24970 10.8248i −0.251197 0.435085i 0.712659 0.701511i \(-0.247491\pi\)
−0.963856 + 0.266425i \(0.914157\pi\)
\(620\) −4.85725 8.41300i −0.195072 0.337874i
\(621\) −45.8425 + 79.4015i −1.83959 + 3.18627i
\(622\) 7.92214 0.317649
\(623\) 0 0
\(624\) 15.9642 0.639079
\(625\) −7.15423 + 12.3915i −0.286169 + 0.495660i
\(626\) −16.7522 29.0157i −0.669554 1.15970i
\(627\) 34.8514 + 60.3644i 1.39183 + 2.41072i
\(628\) 0.534009 0.924931i 0.0213093 0.0369088i
\(629\) 16.1805 0.645158
\(630\) 0 0
\(631\) −35.5582 −1.41555 −0.707774 0.706439i \(-0.750300\pi\)
−0.707774 + 0.706439i \(0.750300\pi\)
\(632\) 4.55191 7.88414i 0.181065 0.313614i
\(633\) 1.08048 + 1.87145i 0.0429453 + 0.0743835i
\(634\) 14.2451 + 24.6732i 0.565744 + 0.979897i
\(635\) 0.828467 1.43495i 0.0328767 0.0569441i
\(636\) 1.06802 0.0423497
\(637\) 0 0
\(638\) −12.2497 −0.484970
\(639\) −20.1303 + 34.8667i −0.796342 + 1.37930i
\(640\) −3.23300 5.59971i −0.127795 0.221348i
\(641\) −0.680484 1.17863i −0.0268775 0.0465532i 0.852274 0.523096i \(-0.175223\pi\)
−0.879151 + 0.476543i \(0.841890\pi\)
\(642\) 31.8125 55.1008i 1.25554 2.17466i
\(643\) 12.1867 0.480598 0.240299 0.970699i \(-0.422755\pi\)
0.240299 + 0.970699i \(0.422755\pi\)
\(644\) 0 0
\(645\) −11.7036 −0.460829
\(646\) −16.8226 + 29.1377i −0.661878 + 1.14641i
\(647\) 1.86076 + 3.22293i 0.0731540 + 0.126706i 0.900282 0.435307i \(-0.143360\pi\)
−0.827128 + 0.562014i \(0.810027\pi\)
\(648\) 16.3356 + 28.2941i 0.641724 + 1.11150i
\(649\) −5.38350 + 9.32450i −0.211321 + 0.366019i
\(650\) −7.93078 −0.311071
\(651\) 0 0
\(652\) 1.93078 0.0756153
\(653\) 22.5294 39.0220i 0.881643 1.52705i 0.0321288 0.999484i \(-0.489771\pi\)
0.849514 0.527566i \(-0.176895\pi\)
\(654\) −19.3835 33.5732i −0.757955 1.31282i
\(655\) −4.40141 7.62346i −0.171977 0.297873i
\(656\) −9.69899 + 16.7991i −0.378682 + 0.655896i
\(657\) 127.713 4.98254
\(658\) 0 0
\(659\) 5.37887 0.209531 0.104766 0.994497i \(-0.466591\pi\)
0.104766 + 0.994497i \(0.466591\pi\)
\(660\) −8.31429 + 14.4008i −0.323633 + 0.560549i
\(661\) 21.2468 + 36.8005i 0.826404 + 1.43137i 0.900841 + 0.434148i \(0.142951\pi\)
−0.0744372 + 0.997226i \(0.523716\pi\)
\(662\) −16.1113 27.9055i −0.626182 1.08458i
\(663\) −5.60755 + 9.71255i −0.217779 + 0.377204i
\(664\) 3.95733 0.153574
\(665\) 0 0
\(666\) −74.0731 −2.87027
\(667\) 4.45644 7.71878i 0.172554 0.298872i
\(668\) −11.9731 20.7381i −0.463255 0.802381i
\(669\) 9.76469 + 16.9129i 0.377525 + 0.653892i
\(670\) 6.19376 10.7279i 0.239286 0.414455i
\(671\) −34.9296 −1.34844
\(672\) 0 0
\(673\) −37.3765 −1.44076 −0.720379 0.693581i \(-0.756032\pi\)
−0.720379 + 0.693581i \(0.756032\pi\)
\(674\) 23.8327 41.2795i 0.918002 1.59003i
\(675\) −37.1101 64.2765i −1.42837 2.47400i
\(676\) −0.741348 1.28405i −0.0285134 0.0493866i
\(677\) 21.7378 37.6510i 0.835453 1.44705i −0.0582083 0.998304i \(-0.518539\pi\)
0.893661 0.448742i \(-0.148128\pi\)
\(678\) −64.2738 −2.46842
\(679\) 0 0
\(680\) 2.80041 0.107391
\(681\) −26.3431 + 45.6275i −1.00947 + 1.74845i
\(682\) 27.2874 + 47.2632i 1.04489 + 1.80980i
\(683\) −15.6978 27.1894i −0.600659 1.04037i −0.992721 0.120434i \(-0.961572\pi\)
0.392062 0.919939i \(-0.371762\pi\)
\(684\) 32.7868 56.7885i 1.25364 2.17136i
\(685\) 6.75373 0.258047
\(686\) 0 0
\(687\) 29.7324 1.13436
\(688\) 9.61650 16.6563i 0.366626 0.635014i
\(689\) 0.107546 + 0.186276i 0.00409719 + 0.00709653i
\(690\) −14.2096 24.6117i −0.540949 0.936952i
\(691\) −6.72053 + 11.6403i −0.255661 + 0.442818i −0.965075 0.261974i \(-0.915626\pi\)
0.709414 + 0.704792i \(0.248960\pi\)
\(692\) −23.4982 −0.893268
\(693\) 0 0
\(694\) −23.5674 −0.894607
\(695\) 2.20070 3.81173i 0.0834774 0.144587i
\(696\) −2.74447 4.75356i −0.104029 0.180183i
\(697\) −6.81369 11.8017i −0.258087 0.447019i
\(698\) −33.2551 + 57.5996i −1.25873 + 2.18018i
\(699\) 39.4873 1.49355
\(700\) 0 0
\(701\) −28.0346 −1.05885 −0.529426 0.848356i \(-0.677593\pi\)
−0.529426 + 0.848356i \(0.677593\pi\)
\(702\) 16.2964 28.2262i 0.615067 1.06533i
\(703\) −13.0054 22.5261i −0.490509 0.849587i
\(704\) −6.69779 11.6009i −0.252432 0.437226i
\(705\) −5.29558 + 9.17221i −0.199443 + 0.345445i
\(706\) 10.1026 0.380217
\(707\) 0 0
\(708\) 13.8282 0.519694
\(709\) 20.1424 34.8876i 0.756462 1.31023i −0.188182 0.982134i \(-0.560259\pi\)
0.944644 0.328097i \(-0.106407\pi\)
\(710\) −3.96107 6.86078i −0.148656 0.257480i
\(711\) −38.7349 67.0909i −1.45267 2.51610i
\(712\) −0.201820 + 0.349563i −0.00756353 + 0.0131004i
\(713\) −39.7087 −1.48710
\(714\) 0 0
\(715\) −3.34889 −0.125242
\(716\) 15.1715 26.2779i 0.566987 0.982050i
\(717\) −26.9071 46.6044i −1.00486 1.74047i
\(718\) 17.5717 + 30.4351i 0.655772 + 1.13583i
\(719\) −8.37224 + 14.5011i −0.312232 + 0.540801i −0.978845 0.204602i \(-0.934410\pi\)
0.666613 + 0.745404i \(0.267743\pi\)
\(720\) −33.9215 −1.26418
\(721\) 0 0
\(722\) 18.6286 0.693284
\(723\) 8.26409 14.3138i 0.307345 0.532337i
\(724\) 4.87947 + 8.45149i 0.181344 + 0.314097i
\(725\) 3.60755 + 6.24845i 0.133981 + 0.232062i
\(726\) 12.3353 21.3654i 0.457806 0.792944i
\(727\) 51.4982 1.90996 0.954981 0.296666i \(-0.0958748\pi\)
0.954981 + 0.296666i \(0.0958748\pi\)
\(728\) 0 0
\(729\) 102.556 3.79836
\(730\) −12.5651 + 21.7634i −0.465055 + 0.805500i
\(731\) 6.75574 + 11.7013i 0.249870 + 0.432788i
\(732\) 22.4302 + 38.8502i 0.829043 + 1.43595i
\(733\) −16.9158 + 29.2990i −0.624799 + 1.08218i 0.363781 + 0.931485i \(0.381486\pi\)
−0.988580 + 0.150699i \(0.951848\pi\)
\(734\) −43.2034 −1.59467
\(735\) 0 0
\(736\) 36.5662 1.34785
\(737\) −14.8137 + 25.6581i −0.545669 + 0.945127i
\(738\) 31.1926 + 54.0271i 1.14821 + 1.98876i
\(739\) −10.3345 17.8999i −0.380161 0.658458i 0.610924 0.791689i \(-0.290798\pi\)
−0.991085 + 0.133231i \(0.957465\pi\)
\(740\) 3.10263 5.37391i 0.114055 0.197549i
\(741\) 18.0288 0.662304
\(742\) 0 0
\(743\) −29.6966 −1.08946 −0.544731 0.838611i \(-0.683368\pi\)
−0.544731 + 0.838611i \(0.683368\pi\)
\(744\) −12.2272 + 21.1781i −0.448270 + 0.776426i
\(745\) 1.08048 + 1.87145i 0.0395858 + 0.0685647i
\(746\) 30.9596 + 53.6235i 1.13351 + 1.96330i
\(747\) 16.8376 29.1636i 0.616057 1.06704i
\(748\) 19.1972 0.701919
\(749\) 0 0
\(750\) 50.0731 1.82841
\(751\) 6.01148 10.4122i 0.219362 0.379946i −0.735251 0.677795i \(-0.762936\pi\)
0.954613 + 0.297849i \(0.0962691\pi\)
\(752\) −8.70242 15.0730i −0.317345 0.549657i
\(753\) 25.5251 + 44.2107i 0.930185 + 1.61113i
\(754\) −1.58420 + 2.74392i −0.0576933 + 0.0999278i
\(755\) −2.82534 −0.102825
\(756\) 0 0
\(757\) −30.2906 −1.10093 −0.550464 0.834859i \(-0.685549\pi\)
−0.550464 + 0.834859i \(0.685549\pi\)
\(758\) −35.2575 + 61.0677i −1.28061 + 2.21808i
\(759\) 33.9852 + 58.8641i 1.23359 + 2.13663i
\(760\) −2.25090 3.89867i −0.0816487 0.141420i
\(761\) −22.9792 + 39.8011i −0.832995 + 1.44279i 0.0626580 + 0.998035i \(0.480042\pi\)
−0.895653 + 0.444754i \(0.853291\pi\)
\(762\) 11.9549 0.433082
\(763\) 0 0
\(764\) 18.9030 0.683888
\(765\) 11.9152 20.6377i 0.430795 0.746159i
\(766\) −0.216290 0.374626i −0.00781488 0.0135358i
\(767\) 1.39245 + 2.41180i 0.0502786 + 0.0870851i
\(768\) 34.9296 60.4998i 1.26041 2.18310i
\(769\) −4.03924 −0.145659 −0.0728293 0.997344i \(-0.523203\pi\)
−0.0728293 + 0.997344i \(0.523203\pi\)
\(770\) 0 0
\(771\) 52.2980 1.88347
\(772\) −1.68108 + 2.91172i −0.0605035 + 0.104795i
\(773\) 18.0588 + 31.2787i 0.649528 + 1.12502i 0.983236 + 0.182339i \(0.0583670\pi\)
−0.333707 + 0.942677i \(0.608300\pi\)
\(774\) −30.9273 53.5676i −1.11166 1.92545i
\(775\) 16.0723 27.8381i 0.577335 0.999974i
\(776\) 6.86963 0.246605
\(777\) 0 0
\(778\) 17.4555 0.625811
\(779\) −10.9533 + 18.9717i −0.392443 + 0.679732i
\(780\) 2.15051 + 3.72479i 0.0770005 + 0.133369i
\(781\) 9.47374 + 16.4090i 0.338997 + 0.587160i
\(782\) −16.4045 + 28.4135i −0.586625 + 1.01606i
\(783\) −29.6515