Properties

Label 637.2.x.b.570.1
Level $637$
Weight $2$
Character 637.570
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 570.1
Character \(\chi\) \(=\) 637.570
Dual form 637.2.x.b.19.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.28713 + 0.612835i) q^{2} -1.20226i q^{3} +(3.12335 - 1.80327i) q^{4} +(-3.08075 - 0.825486i) q^{5} +(0.736784 + 2.74971i) q^{6} +(-2.68981 + 2.68981i) q^{8} +1.55458 q^{9} +O(q^{10})\) \(q+(-2.28713 + 0.612835i) q^{2} -1.20226i q^{3} +(3.12335 - 1.80327i) q^{4} +(-3.08075 - 0.825486i) q^{5} +(0.736784 + 2.74971i) q^{6} +(-2.68981 + 2.68981i) q^{8} +1.55458 q^{9} +7.55197 q^{10} +(-3.00989 + 3.00989i) q^{11} +(-2.16799 - 3.75506i) q^{12} +(3.48609 + 0.920440i) q^{13} +(-0.992444 + 3.70385i) q^{15} +(0.897005 - 1.55366i) q^{16} +(0.721872 + 1.25032i) q^{17} +(-3.55553 + 0.952702i) q^{18} +(1.77447 - 1.77447i) q^{19} +(-11.1108 + 2.97714i) q^{20} +(5.03945 - 8.72858i) q^{22} +(4.52952 + 2.61512i) q^{23} +(3.23384 + 3.23384i) q^{24} +(4.47949 + 2.58624i) q^{25} +(-8.53721 + 0.0312285i) q^{26} -5.47577i q^{27} +(1.34350 + 2.32701i) q^{29} -9.07940i q^{30} +(-1.37793 - 5.14250i) q^{31} +(0.869646 - 3.24556i) q^{32} +(3.61866 + 3.61866i) q^{33} +(-2.41725 - 2.41725i) q^{34} +(4.85550 - 2.80333i) q^{36} +(0.160626 + 0.599466i) q^{37} +(-2.97099 + 5.14591i) q^{38} +(1.10660 - 4.19116i) q^{39} +(10.5070 - 6.06624i) q^{40} +(-5.04879 - 1.35282i) q^{41} +(-5.46143 - 3.15316i) q^{43} +(-3.97331 + 14.8286i) q^{44} +(-4.78929 - 1.28329i) q^{45} +(-11.9622 - 3.20527i) q^{46} +(1.71303 - 6.39313i) q^{47} +(-1.86789 - 1.07843i) q^{48} +(-11.8301 - 3.16987i) q^{50} +(1.50320 - 0.867874i) q^{51} +(12.5481 - 3.41149i) q^{52} +(3.79264 - 6.56904i) q^{53} +(3.35574 + 12.5238i) q^{54} +(11.7574 - 6.78811i) q^{55} +(-2.13337 - 2.13337i) q^{57} +(-4.49884 - 4.49884i) q^{58} +(0.525675 - 1.96185i) q^{59} +(3.57928 + 13.3581i) q^{60} -5.24062i q^{61} +(6.30300 + 10.9171i) q^{62} +11.5440i q^{64} +(-9.97996 - 5.71336i) q^{65} +(-10.4940 - 6.05870i) q^{66} +(6.19777 + 6.19777i) q^{67} +(4.50931 + 2.60345i) q^{68} +(3.14404 - 5.44564i) q^{69} +(8.31929 - 2.22915i) q^{71} +(-4.18153 + 4.18153i) q^{72} +(15.2724 - 4.09222i) q^{73} +(-0.734747 - 1.27262i) q^{74} +(3.10932 - 5.38549i) q^{75} +(2.34245 - 8.74214i) q^{76} +(0.0375447 + 10.2639i) q^{78} +(-1.00643 - 1.74319i) q^{79} +(-4.04597 + 4.04597i) q^{80} -1.91953 q^{81} +12.3763 q^{82} +(5.11623 - 5.11623i) q^{83} +(-1.19179 - 4.44782i) q^{85} +(14.4234 + 3.86473i) q^{86} +(2.79766 - 1.61523i) q^{87} -16.1921i q^{88} +(6.76189 - 1.81184i) q^{89} +11.7402 q^{90} +18.8630 q^{92} +(-6.18260 + 1.65662i) q^{93} +15.6717i q^{94} +(-6.93151 + 4.00191i) q^{95} +(-3.90200 - 1.04554i) q^{96} +(1.62618 + 6.06897i) q^{97} +(-4.67912 + 4.67912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + O(q^{10}) \) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + 20q^{11} - 8q^{15} + 12q^{16} - 64q^{18} + 4q^{22} + 12q^{23} + 4q^{29} + 64q^{32} + 4q^{37} + 36q^{39} - 48q^{43} - 84q^{44} - 108q^{46} - 44q^{50} + 12q^{51} - 36q^{53} - 92q^{57} + 44q^{58} + 28q^{60} + 28q^{65} + 64q^{67} + 84q^{71} + 4q^{72} - 24q^{74} + 148q^{78} + 40q^{79} - 56q^{81} + 36q^{85} + 108q^{86} + 24q^{92} - 24q^{93} + 84q^{95} - 60q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28713 + 0.612835i −1.61725 + 0.433340i −0.950191 0.311669i \(-0.899112\pi\)
−0.667055 + 0.745009i \(0.732445\pi\)
\(3\) 1.20226i 0.694122i −0.937842 0.347061i \(-0.887180\pi\)
0.937842 0.347061i \(-0.112820\pi\)
\(4\) 3.12335 1.80327i 1.56167 0.901633i
\(5\) −3.08075 0.825486i −1.37776 0.369168i −0.507450 0.861681i \(-0.669412\pi\)
−0.870305 + 0.492513i \(0.836078\pi\)
\(6\) 0.736784 + 2.74971i 0.300791 + 1.12257i
\(7\) 0 0
\(8\) −2.68981 + 2.68981i −0.950991 + 0.950991i
\(9\) 1.55458 0.518194
\(10\) 7.55197 2.38814
\(11\) −3.00989 + 3.00989i −0.907517 + 0.907517i −0.996071 0.0885547i \(-0.971775\pi\)
0.0885547 + 0.996071i \(0.471775\pi\)
\(12\) −2.16799 3.75506i −0.625844 1.08399i
\(13\) 3.48609 + 0.920440i 0.966866 + 0.255284i
\(14\) 0 0
\(15\) −0.992444 + 3.70385i −0.256248 + 0.956331i
\(16\) 0.897005 1.55366i 0.224251 0.388414i
\(17\) 0.721872 + 1.25032i 0.175080 + 0.303247i 0.940189 0.340654i \(-0.110648\pi\)
−0.765109 + 0.643901i \(0.777315\pi\)
\(18\) −3.55553 + 0.952702i −0.838047 + 0.224554i
\(19\) 1.77447 1.77447i 0.407092 0.407092i −0.473631 0.880723i \(-0.657057\pi\)
0.880723 + 0.473631i \(0.157057\pi\)
\(20\) −11.1108 + 2.97714i −2.48446 + 0.665709i
\(21\) 0 0
\(22\) 5.03945 8.72858i 1.07441 1.86094i
\(23\) 4.52952 + 2.61512i 0.944470 + 0.545290i 0.891359 0.453299i \(-0.149753\pi\)
0.0531111 + 0.998589i \(0.483086\pi\)
\(24\) 3.23384 + 3.23384i 0.660104 + 0.660104i
\(25\) 4.47949 + 2.58624i 0.895898 + 0.517247i
\(26\) −8.53721 + 0.0312285i −1.67428 + 0.00612442i
\(27\) 5.47577i 1.05381i
\(28\) 0 0
\(29\) 1.34350 + 2.32701i 0.249482 + 0.432116i 0.963382 0.268132i \(-0.0864063\pi\)
−0.713900 + 0.700248i \(0.753073\pi\)
\(30\) 9.07940i 1.65766i
\(31\) −1.37793 5.14250i −0.247483 0.923620i −0.972119 0.234488i \(-0.924659\pi\)
0.724636 0.689132i \(-0.242008\pi\)
\(32\) 0.869646 3.24556i 0.153733 0.573740i
\(33\) 3.61866 + 3.61866i 0.629928 + 0.629928i
\(34\) −2.41725 2.41725i −0.414555 0.414555i
\(35\) 0 0
\(36\) 4.85550 2.80333i 0.809250 0.467221i
\(37\) 0.160626 + 0.599466i 0.0264068 + 0.0985516i 0.977872 0.209206i \(-0.0670880\pi\)
−0.951465 + 0.307758i \(0.900421\pi\)
\(38\) −2.97099 + 5.14591i −0.481958 + 0.834776i
\(39\) 1.10660 4.19116i 0.177198 0.671123i
\(40\) 10.5070 6.06624i 1.66131 0.959157i
\(41\) −5.04879 1.35282i −0.788488 0.211275i −0.157965 0.987445i \(-0.550493\pi\)
−0.630524 + 0.776170i \(0.717160\pi\)
\(42\) 0 0
\(43\) −5.46143 3.15316i −0.832860 0.480852i 0.0219711 0.999759i \(-0.493006\pi\)
−0.854831 + 0.518907i \(0.826339\pi\)
\(44\) −3.97331 + 14.8286i −0.598998 + 2.23549i
\(45\) −4.78929 1.28329i −0.713944 0.191301i
\(46\) −11.9622 3.20527i −1.76374 0.472591i
\(47\) 1.71303 6.39313i 0.249872 0.932533i −0.721000 0.692935i \(-0.756317\pi\)
0.970872 0.239599i \(-0.0770159\pi\)
\(48\) −1.86789 1.07843i −0.269607 0.155658i
\(49\) 0 0
\(50\) −11.8301 3.16987i −1.67303 0.448287i
\(51\) 1.50320 0.867874i 0.210490 0.121527i
\(52\) 12.5481 3.41149i 1.74010 0.473088i
\(53\) 3.79264 6.56904i 0.520959 0.902328i −0.478744 0.877955i \(-0.658908\pi\)
0.999703 0.0243730i \(-0.00775895\pi\)
\(54\) 3.35574 + 12.5238i 0.456659 + 1.70427i
\(55\) 11.7574 6.78811i 1.58536 0.915309i
\(56\) 0 0
\(57\) −2.13337 2.13337i −0.282571 0.282571i
\(58\) −4.49884 4.49884i −0.590727 0.590727i
\(59\) 0.525675 1.96185i 0.0684370 0.255410i −0.923228 0.384252i \(-0.874459\pi\)
0.991665 + 0.128842i \(0.0411259\pi\)
\(60\) 3.57928 + 13.3581i 0.462083 + 1.72452i
\(61\) 5.24062i 0.670993i −0.942041 0.335496i \(-0.891096\pi\)
0.942041 0.335496i \(-0.108904\pi\)
\(62\) 6.30300 + 10.9171i 0.800482 + 1.38648i
\(63\) 0 0
\(64\) 11.5440i 1.44300i
\(65\) −9.97996 5.71336i −1.23786 0.708655i
\(66\) −10.4940 6.05870i −1.29172 0.745775i
\(67\) 6.19777 + 6.19777i 0.757178 + 0.757178i 0.975808 0.218630i \(-0.0701586\pi\)
−0.218630 + 0.975808i \(0.570159\pi\)
\(68\) 4.50931 + 2.60345i 0.546835 + 0.315715i
\(69\) 3.14404 5.44564i 0.378498 0.655578i
\(70\) 0 0
\(71\) 8.31929 2.22915i 0.987318 0.264551i 0.271194 0.962525i \(-0.412581\pi\)
0.716124 + 0.697974i \(0.245915\pi\)
\(72\) −4.18153 + 4.18153i −0.492798 + 0.492798i
\(73\) 15.2724 4.09222i 1.78749 0.478958i 0.795578 0.605852i \(-0.207167\pi\)
0.991916 + 0.126894i \(0.0405008\pi\)
\(74\) −0.734747 1.27262i −0.0854126 0.147939i
\(75\) 3.10932 5.38549i 0.359033 0.621863i
\(76\) 2.34245 8.74214i 0.268697 1.00279i
\(77\) 0 0
\(78\) 0.0375447 + 10.2639i 0.00425110 + 1.16216i
\(79\) −1.00643 1.74319i −0.113233 0.196125i 0.803839 0.594847i \(-0.202787\pi\)
−0.917072 + 0.398722i \(0.869454\pi\)
\(80\) −4.04597 + 4.04597i −0.452353 + 0.452353i
\(81\) −1.91953 −0.213281
\(82\) 12.3763 1.36673
\(83\) 5.11623 5.11623i 0.561579 0.561579i −0.368177 0.929756i \(-0.620018\pi\)
0.929756 + 0.368177i \(0.120018\pi\)
\(84\) 0 0
\(85\) −1.19179 4.44782i −0.129268 0.482434i
\(86\) 14.4234 + 3.86473i 1.55531 + 0.416744i
\(87\) 2.79766 1.61523i 0.299941 0.173171i
\(88\) 16.1921i 1.72608i
\(89\) 6.76189 1.81184i 0.716759 0.192055i 0.118034 0.993010i \(-0.462341\pi\)
0.598725 + 0.800955i \(0.295674\pi\)
\(90\) 11.7402 1.23752
\(91\) 0 0
\(92\) 18.8630 1.96661
\(93\) −6.18260 + 1.65662i −0.641105 + 0.171784i
\(94\) 15.6717i 1.61641i
\(95\) −6.93151 + 4.00191i −0.711158 + 0.410587i
\(96\) −3.90200 1.04554i −0.398246 0.106710i
\(97\) 1.62618 + 6.06897i 0.165113 + 0.616211i 0.998026 + 0.0628062i \(0.0200050\pi\)
−0.832913 + 0.553405i \(0.813328\pi\)
\(98\) 0 0
\(99\) −4.67912 + 4.67912i −0.470270 + 0.470270i
\(100\) 18.6547 1.86547
\(101\) −13.3392 −1.32730 −0.663649 0.748044i \(-0.730993\pi\)
−0.663649 + 0.748044i \(0.730993\pi\)
\(102\) −2.90616 + 2.90616i −0.287752 + 0.287752i
\(103\) 3.08727 + 5.34730i 0.304197 + 0.526885i 0.977082 0.212862i \(-0.0682785\pi\)
−0.672885 + 0.739747i \(0.734945\pi\)
\(104\) −11.8527 + 6.90110i −1.16225 + 0.676708i
\(105\) 0 0
\(106\) −4.64852 + 17.3485i −0.451504 + 1.68504i
\(107\) 4.27353 7.40196i 0.413137 0.715575i −0.582094 0.813122i \(-0.697766\pi\)
0.995231 + 0.0975469i \(0.0310996\pi\)
\(108\) −9.87427 17.1027i −0.950152 1.64571i
\(109\) −4.50957 + 1.20834i −0.431939 + 0.115738i −0.468236 0.883603i \(-0.655110\pi\)
0.0362973 + 0.999341i \(0.488444\pi\)
\(110\) −22.7306 + 22.7306i −2.16728 + 2.16728i
\(111\) 0.720711 0.193114i 0.0684069 0.0183296i
\(112\) 0 0
\(113\) 9.80118 16.9761i 0.922018 1.59698i 0.125729 0.992065i \(-0.459873\pi\)
0.796289 0.604917i \(-0.206794\pi\)
\(114\) 6.18669 + 3.57189i 0.579437 + 0.334538i
\(115\) −11.7956 11.7956i −1.09994 1.09994i
\(116\) 8.39245 + 4.84538i 0.779219 + 0.449883i
\(117\) 5.41941 + 1.43090i 0.501024 + 0.132287i
\(118\) 4.80915i 0.442718i
\(119\) 0 0
\(120\) −7.29317 12.6321i −0.665773 1.15315i
\(121\) 7.11890i 0.647173i
\(122\) 3.21164 + 11.9860i 0.290768 + 1.08516i
\(123\) −1.62643 + 6.06993i −0.146651 + 0.547308i
\(124\) −13.5770 13.5770i −1.21925 1.21925i
\(125\) −0.388969 0.388969i −0.0347904 0.0347904i
\(126\) 0 0
\(127\) 1.02476 0.591646i 0.0909329 0.0525001i −0.453844 0.891081i \(-0.649948\pi\)
0.544777 + 0.838581i \(0.316614\pi\)
\(128\) −5.33527 19.9115i −0.471576 1.75994i
\(129\) −3.79090 + 6.56603i −0.333770 + 0.578107i
\(130\) 26.3268 + 6.95114i 2.30901 + 0.609655i
\(131\) −8.37536 + 4.83552i −0.731758 + 0.422481i −0.819065 0.573701i \(-0.805507\pi\)
0.0873067 + 0.996181i \(0.472174\pi\)
\(132\) 17.8277 + 4.77693i 1.55171 + 0.415778i
\(133\) 0 0
\(134\) −17.9733 10.3769i −1.55266 0.896428i
\(135\) −4.52017 + 16.8695i −0.389034 + 1.45190i
\(136\) −5.30482 1.42142i −0.454884 0.121886i
\(137\) −6.37069 1.70702i −0.544285 0.145841i −0.0238082 0.999717i \(-0.507579\pi\)
−0.520477 + 0.853876i \(0.674246\pi\)
\(138\) −3.85355 + 14.3817i −0.328036 + 1.22425i
\(139\) −19.6752 11.3595i −1.66883 0.963500i −0.968269 0.249909i \(-0.919599\pi\)
−0.700562 0.713591i \(-0.747067\pi\)
\(140\) 0 0
\(141\) −7.68617 2.05950i −0.647292 0.173441i
\(142\) −17.6612 + 10.1967i −1.48210 + 0.855688i
\(143\) −13.2632 + 7.72232i −1.10912 + 0.645773i
\(144\) 1.39447 2.41529i 0.116206 0.201274i
\(145\) −2.21808 8.27800i −0.184202 0.687450i
\(146\) −32.4220 + 18.7189i −2.68327 + 1.54918i
\(147\) 0 0
\(148\) 1.58269 + 1.58269i 0.130096 + 0.130096i
\(149\) 10.7410 + 10.7410i 0.879936 + 0.879936i 0.993528 0.113591i \(-0.0362354\pi\)
−0.113591 + 0.993528i \(0.536235\pi\)
\(150\) −3.81099 + 14.2228i −0.311166 + 1.16129i
\(151\) −1.86148 6.94712i −0.151485 0.565349i −0.999381 0.0351862i \(-0.988798\pi\)
0.847896 0.530163i \(-0.177869\pi\)
\(152\) 9.54598i 0.774281i
\(153\) 1.12221 + 1.94372i 0.0907252 + 0.157141i
\(154\) 0 0
\(155\) 16.9802i 1.36389i
\(156\) −4.10148 15.0860i −0.328381 1.20784i
\(157\) 16.4569 + 9.50142i 1.31341 + 0.758296i 0.982659 0.185423i \(-0.0593656\pi\)
0.330748 + 0.943719i \(0.392699\pi\)
\(158\) 3.37014 + 3.37014i 0.268114 + 0.268114i
\(159\) −7.89767 4.55972i −0.626326 0.361609i
\(160\) −5.35833 + 9.28090i −0.423613 + 0.733720i
\(161\) 0 0
\(162\) 4.39021 1.17635i 0.344928 0.0924231i
\(163\) −0.717062 + 0.717062i −0.0561646 + 0.0561646i −0.734631 0.678467i \(-0.762645\pi\)
0.678467 + 0.734631i \(0.262645\pi\)
\(164\) −18.2086 + 4.87899i −1.42185 + 0.380985i
\(165\) −8.16105 14.1353i −0.635337 1.10044i
\(166\) −8.56608 + 14.8369i −0.664857 + 1.15157i
\(167\) 0.522634 1.95050i 0.0404426 0.150934i −0.942752 0.333495i \(-0.891772\pi\)
0.983195 + 0.182561i \(0.0584387\pi\)
\(168\) 0 0
\(169\) 11.3056 + 6.41746i 0.869660 + 0.493651i
\(170\) 5.45155 + 9.44237i 0.418115 + 0.724197i
\(171\) 2.75856 2.75856i 0.210952 0.210952i
\(172\) −22.7439 −1.73421
\(173\) 2.45048 0.186307 0.0931533 0.995652i \(-0.470305\pi\)
0.0931533 + 0.995652i \(0.470305\pi\)
\(174\) −5.40875 + 5.40875i −0.410037 + 0.410037i
\(175\) 0 0
\(176\) 1.97645 + 7.37623i 0.148981 + 0.556004i
\(177\) −2.35864 0.631995i −0.177286 0.0475037i
\(178\) −14.3550 + 8.28784i −1.07595 + 0.621200i
\(179\) 7.50965i 0.561298i −0.959811 0.280649i \(-0.909450\pi\)
0.959811 0.280649i \(-0.0905496\pi\)
\(180\) −17.2727 + 4.62821i −1.28743 + 0.344966i
\(181\) −4.93320 −0.366682 −0.183341 0.983049i \(-0.558691\pi\)
−0.183341 + 0.983049i \(0.558691\pi\)
\(182\) 0 0
\(183\) −6.30057 −0.465751
\(184\) −19.2177 + 5.14937i −1.41675 + 0.379617i
\(185\) 1.97940i 0.145528i
\(186\) 13.1252 7.57782i 0.962384 0.555633i
\(187\) −5.93608 1.59057i −0.434089 0.116314i
\(188\) −6.17811 23.0570i −0.450585 1.68161i
\(189\) 0 0
\(190\) 13.4008 13.4008i 0.972193 0.972193i
\(191\) −6.08863 −0.440558 −0.220279 0.975437i \(-0.570697\pi\)
−0.220279 + 0.975437i \(0.570697\pi\)
\(192\) 13.8788 1.00162
\(193\) 10.2443 10.2443i 0.737402 0.737402i −0.234672 0.972074i \(-0.575402\pi\)
0.972074 + 0.234672i \(0.0754018\pi\)
\(194\) −7.43855 12.8840i −0.534057 0.925014i
\(195\) −6.86892 + 11.9985i −0.491894 + 0.859228i
\(196\) 0 0
\(197\) −4.33340 + 16.1725i −0.308742 + 1.15224i 0.620934 + 0.783863i \(0.286754\pi\)
−0.929676 + 0.368379i \(0.879913\pi\)
\(198\) 7.83424 13.5693i 0.556755 0.964328i
\(199\) 9.90747 + 17.1602i 0.702322 + 1.21646i 0.967649 + 0.252298i \(0.0811865\pi\)
−0.265328 + 0.964158i \(0.585480\pi\)
\(200\) −19.0055 + 5.09250i −1.34389 + 0.360094i
\(201\) 7.45130 7.45130i 0.525574 0.525574i
\(202\) 30.5084 8.17471i 2.14657 0.575171i
\(203\) 0 0
\(204\) 3.13002 5.42135i 0.219145 0.379570i
\(205\) 14.4373 + 8.33541i 1.00835 + 0.582170i
\(206\) −10.3380 10.3380i −0.720282 0.720282i
\(207\) 7.04151 + 4.06542i 0.489419 + 0.282566i
\(208\) 4.55708 4.59054i 0.315977 0.318297i
\(209\) 10.6819i 0.738885i
\(210\) 0 0
\(211\) −9.56393 16.5652i −0.658408 1.14040i −0.981028 0.193868i \(-0.937897\pi\)
0.322619 0.946529i \(-0.395437\pi\)
\(212\) 27.3566i 1.87886i
\(213\) −2.68000 10.0019i −0.183631 0.685320i
\(214\) −5.23793 + 19.5482i −0.358058 + 1.33629i
\(215\) 14.2224 + 14.2224i 0.969961 + 0.969961i
\(216\) 14.7288 + 14.7288i 1.00217 + 1.00217i
\(217\) 0 0
\(218\) 9.57347 5.52725i 0.648397 0.374352i
\(219\) −4.91989 18.3613i −0.332455 1.24074i
\(220\) 24.4816 42.4033i 1.65055 2.85883i
\(221\) 1.36566 + 5.02316i 0.0918645 + 0.337894i
\(222\) −1.53001 + 0.883353i −0.102688 + 0.0592868i
\(223\) −0.670621 0.179692i −0.0449081 0.0120331i 0.236295 0.971681i \(-0.424067\pi\)
−0.281203 + 0.959648i \(0.590733\pi\)
\(224\) 0 0
\(225\) 6.96374 + 4.02052i 0.464249 + 0.268034i
\(226\) −12.0130 + 44.8332i −0.799094 + 2.98226i
\(227\) 5.03400 + 1.34886i 0.334118 + 0.0895267i 0.421978 0.906606i \(-0.361336\pi\)
−0.0878596 + 0.996133i \(0.528003\pi\)
\(228\) −10.5103 2.81622i −0.696060 0.186509i
\(229\) 0.274163 1.02319i 0.0181172 0.0676142i −0.956275 0.292468i \(-0.905524\pi\)
0.974393 + 0.224853i \(0.0721903\pi\)
\(230\) 34.2068 + 19.7493i 2.25553 + 1.30223i
\(231\) 0 0
\(232\) −9.87299 2.64546i −0.648193 0.173683i
\(233\) 1.14405 0.660517i 0.0749492 0.0432719i −0.462057 0.886850i \(-0.652888\pi\)
0.537006 + 0.843578i \(0.319555\pi\)
\(234\) −13.2718 + 0.0485473i −0.867604 + 0.00317364i
\(235\) −10.5549 + 18.2816i −0.688524 + 1.19256i
\(236\) −1.89586 7.07546i −0.123410 0.460573i
\(237\) −2.09577 + 1.20999i −0.136135 + 0.0785973i
\(238\) 0 0
\(239\) 15.2273 + 15.2273i 0.984972 + 0.984972i 0.999889 0.0149168i \(-0.00474835\pi\)
−0.0149168 + 0.999889i \(0.504748\pi\)
\(240\) 4.86429 + 4.86429i 0.313989 + 0.313989i
\(241\) −0.908152 + 3.38927i −0.0584992 + 0.218322i −0.988987 0.148000i \(-0.952716\pi\)
0.930488 + 0.366322i \(0.119383\pi\)
\(242\) 4.36271 + 16.2819i 0.280446 + 1.04664i
\(243\) 14.1195i 0.905769i
\(244\) −9.45024 16.3683i −0.604989 1.04787i
\(245\) 0 0
\(246\) 14.8795i 0.948680i
\(247\) 7.81925 4.55266i 0.497527 0.289679i
\(248\) 17.5387 + 10.1260i 1.11371 + 0.643000i
\(249\) −6.15101 6.15101i −0.389805 0.389805i
\(250\) 1.12800 + 0.651249i 0.0713407 + 0.0411886i
\(251\) 8.75834 15.1699i 0.552822 0.957515i −0.445248 0.895407i \(-0.646884\pi\)
0.998069 0.0621079i \(-0.0197823\pi\)
\(252\) 0 0
\(253\) −21.5046 + 5.76214i −1.35198 + 0.362262i
\(254\) −1.98118 + 1.98118i −0.124310 + 0.124310i
\(255\) −5.34741 + 1.43283i −0.334868 + 0.0897276i
\(256\) 12.8609 + 22.2758i 0.803807 + 1.39224i
\(257\) 3.42559 5.93330i 0.213683 0.370109i −0.739182 0.673506i \(-0.764788\pi\)
0.952864 + 0.303397i \(0.0981208\pi\)
\(258\) 4.64639 17.3406i 0.289272 1.07958i
\(259\) 0 0
\(260\) −41.4736 + 0.151708i −2.57208 + 0.00940850i
\(261\) 2.08858 + 3.61753i 0.129280 + 0.223920i
\(262\) 16.1922 16.1922i 1.00036 1.00036i
\(263\) 17.4170 1.07398 0.536989 0.843589i \(-0.319562\pi\)
0.536989 + 0.843589i \(0.319562\pi\)
\(264\) −19.4670 −1.19811
\(265\) −17.1068 + 17.1068i −1.05086 + 1.05086i
\(266\) 0 0
\(267\) −2.17830 8.12952i −0.133310 0.497518i
\(268\) 30.5340 + 8.18157i 1.86516 + 0.499769i
\(269\) 0.145276 0.0838752i 0.00885764 0.00511396i −0.495565 0.868571i \(-0.665039\pi\)
0.504422 + 0.863457i \(0.331706\pi\)
\(270\) 41.3529i 2.51666i
\(271\) 2.40913 0.645525i 0.146344 0.0392128i −0.184903 0.982757i \(-0.559197\pi\)
0.331248 + 0.943544i \(0.392530\pi\)
\(272\) 2.59009 0.157047
\(273\) 0 0
\(274\) 15.6167 0.943441
\(275\) −21.2671 + 5.69850i −1.28245 + 0.343632i
\(276\) 22.6782i 1.36506i
\(277\) 7.38731 4.26506i 0.443860 0.256263i −0.261373 0.965238i \(-0.584175\pi\)
0.705234 + 0.708975i \(0.250842\pi\)
\(278\) 51.9613 + 13.9230i 3.11643 + 0.835046i
\(279\) −2.14210 7.99444i −0.128244 0.478614i
\(280\) 0 0
\(281\) 15.7936 15.7936i 0.942166 0.942166i −0.0562508 0.998417i \(-0.517915\pi\)
0.998417 + 0.0562508i \(0.0179146\pi\)
\(282\) 18.8414 1.12199
\(283\) −9.58097 −0.569530 −0.284765 0.958597i \(-0.591915\pi\)
−0.284765 + 0.958597i \(0.591915\pi\)
\(284\) 21.9643 21.9643i 1.30334 1.30334i
\(285\) 4.81132 + 8.33345i 0.284998 + 0.493631i
\(286\) 25.6021 25.7901i 1.51388 1.52500i
\(287\) 0 0
\(288\) 1.35194 5.04550i 0.0796636 0.297309i
\(289\) 7.45780 12.9173i 0.438694 0.759841i
\(290\) 10.1461 + 17.5735i 0.595799 + 1.03195i
\(291\) 7.29645 1.95508i 0.427726 0.114609i
\(292\) 40.3215 40.3215i 2.35964 2.35964i
\(293\) −14.5286 + 3.89292i −0.848769 + 0.227427i −0.656885 0.753991i \(-0.728126\pi\)
−0.191884 + 0.981418i \(0.561460\pi\)
\(294\) 0 0
\(295\) −3.23895 + 5.61003i −0.188579 + 0.326628i
\(296\) −2.04450 1.18039i −0.118834 0.0686090i
\(297\) 16.4815 + 16.4815i 0.956352 + 0.956352i
\(298\) −31.1485 17.9836i −1.80438 1.04176i
\(299\) 13.3832 + 13.2857i 0.773972 + 0.768330i
\(300\) 22.4277i 1.29486i
\(301\) 0 0
\(302\) 8.51488 + 14.7482i 0.489976 + 0.848663i
\(303\) 16.0371i 0.921307i
\(304\) −1.16521 4.34863i −0.0668295 0.249411i
\(305\) −4.32606 + 16.1451i −0.247709 + 0.924464i
\(306\) −3.75782 3.75782i −0.214820 0.214820i
\(307\) 15.7439 + 15.7439i 0.898552 + 0.898552i 0.995308 0.0967560i \(-0.0308467\pi\)
−0.0967560 + 0.995308i \(0.530847\pi\)
\(308\) 0 0
\(309\) 6.42882 3.71168i 0.365723 0.211150i
\(310\) −10.4061 38.8360i −0.591025 2.20574i
\(311\) 1.94686 3.37206i 0.110396 0.191212i −0.805534 0.592550i \(-0.798121\pi\)
0.915930 + 0.401338i \(0.131455\pi\)
\(312\) 8.29688 + 14.2500i 0.469718 + 0.806747i
\(313\) −8.63858 + 4.98749i −0.488282 + 0.281910i −0.723861 0.689946i \(-0.757634\pi\)
0.235580 + 0.971855i \(0.424301\pi\)
\(314\) −43.4620 11.6456i −2.45270 0.657199i
\(315\) 0 0
\(316\) −6.28689 3.62974i −0.353665 0.204189i
\(317\) 4.01848 14.9972i 0.225701 0.842326i −0.756422 0.654084i \(-0.773054\pi\)
0.982123 0.188242i \(-0.0602790\pi\)
\(318\) 20.8574 + 5.58871i 1.16962 + 0.313399i
\(319\) −11.0479 2.96026i −0.618561 0.165743i
\(320\) 9.52940 35.5642i 0.532710 1.98810i
\(321\) −8.89905 5.13787i −0.496697 0.286768i
\(322\) 0 0
\(323\) 3.49959 + 0.937714i 0.194723 + 0.0521758i
\(324\) −5.99535 + 3.46142i −0.333075 + 0.192301i
\(325\) 13.2354 + 13.1389i 0.734169 + 0.728817i
\(326\) 1.20057 2.07946i 0.0664936 0.115170i
\(327\) 1.45273 + 5.42166i 0.0803361 + 0.299818i
\(328\) 17.2191 9.94146i 0.950766 0.548925i
\(329\) 0 0
\(330\) 27.3280 + 27.3280i 1.50436 + 1.50436i
\(331\) −10.3551 10.3551i −0.569166 0.569166i 0.362729 0.931895i \(-0.381845\pi\)
−0.931895 + 0.362729i \(0.881845\pi\)
\(332\) 6.75384 25.2057i 0.370665 1.38334i
\(333\) 0.249707 + 0.931919i 0.0136839 + 0.0510688i
\(334\) 4.78133i 0.261622i
\(335\) −13.9776 24.2100i −0.763680 1.32273i
\(336\) 0 0
\(337\) 11.8235i 0.644066i 0.946728 + 0.322033i \(0.104366\pi\)
−0.946728 + 0.322033i \(0.895634\pi\)
\(338\) −29.7902 7.74912i −1.62037 0.421497i
\(339\) −20.4097 11.7835i −1.10850 0.639993i
\(340\) −11.7430 11.7430i −0.636852 0.636852i
\(341\) 19.6258 + 11.3309i 1.06280 + 0.613605i
\(342\) −4.61865 + 7.99973i −0.249748 + 0.432576i
\(343\) 0 0
\(344\) 23.1716 6.20881i 1.24933 0.334756i
\(345\) −14.1813 + 14.1813i −0.763496 + 0.763496i
\(346\) −5.60457 + 1.50174i −0.301303 + 0.0807340i
\(347\) 5.00685 + 8.67212i 0.268782 + 0.465544i 0.968548 0.248829i \(-0.0800456\pi\)
−0.699766 + 0.714372i \(0.746712\pi\)
\(348\) 5.82539 10.0899i 0.312274 0.540874i
\(349\) −4.39634 + 16.4073i −0.235330 + 0.878265i 0.742669 + 0.669658i \(0.233559\pi\)
−0.978000 + 0.208607i \(0.933107\pi\)
\(350\) 0 0
\(351\) 5.04012 19.0890i 0.269022 1.01890i
\(352\) 7.15125 + 12.3863i 0.381163 + 0.660194i
\(353\) −25.5124 + 25.5124i −1.35789 + 1.35789i −0.481366 + 0.876520i \(0.659859\pi\)
−0.876520 + 0.481366i \(0.840141\pi\)
\(354\) 5.78182 0.307300
\(355\) −27.4698 −1.45795
\(356\) 17.8525 17.8525i 0.946181 0.946181i
\(357\) 0 0
\(358\) 4.60217 + 17.1755i 0.243232 + 0.907756i
\(359\) 3.34645 + 0.896679i 0.176619 + 0.0473249i 0.346045 0.938218i \(-0.387525\pi\)
−0.169426 + 0.985543i \(0.554191\pi\)
\(360\) 16.3341 9.43047i 0.860880 0.497030i
\(361\) 12.7025i 0.668553i
\(362\) 11.2829 3.02324i 0.593014 0.158898i
\(363\) −8.55873 −0.449217
\(364\) 0 0
\(365\) −50.4284 −2.63954
\(366\) 14.4102 3.86121i 0.753234 0.201828i
\(367\) 12.6820i 0.661994i −0.943632 0.330997i \(-0.892615\pi\)
0.943632 0.330997i \(-0.107385\pi\)
\(368\) 8.12600 4.69155i 0.423597 0.244564i
\(369\) −7.84876 2.10307i −0.408590 0.109481i
\(370\) 1.21305 + 4.52715i 0.0630633 + 0.235355i
\(371\) 0 0
\(372\) −16.3231 + 16.3231i −0.846312 + 0.846312i
\(373\) 30.0385 1.55533 0.777667 0.628677i \(-0.216403\pi\)
0.777667 + 0.628677i \(0.216403\pi\)
\(374\) 14.5513 0.752432
\(375\) −0.467640 + 0.467640i −0.0241488 + 0.0241488i
\(376\) 12.5886 + 21.8040i 0.649206 + 1.12446i
\(377\) 2.54169 + 9.34878i 0.130904 + 0.481487i
\(378\) 0 0
\(379\) 3.10882 11.6023i 0.159689 0.595969i −0.838969 0.544180i \(-0.816841\pi\)
0.998658 0.0517891i \(-0.0164924\pi\)
\(380\) −14.4330 + 24.9987i −0.740398 + 1.28241i
\(381\) −0.711310 1.23202i −0.0364415 0.0631185i
\(382\) 13.9255 3.73133i 0.712490 0.190911i
\(383\) 4.04719 4.04719i 0.206802 0.206802i −0.596105 0.802907i \(-0.703286\pi\)
0.802907 + 0.596105i \(0.203286\pi\)
\(384\) −23.9387 + 6.41436i −1.22162 + 0.327331i
\(385\) 0 0
\(386\) −17.1520 + 29.7082i −0.873015 + 1.51211i
\(387\) −8.49024 4.90184i −0.431583 0.249175i
\(388\) 16.0231 + 16.0231i 0.813449 + 0.813449i
\(389\) 14.2446 + 8.22413i 0.722231 + 0.416980i 0.815573 0.578654i \(-0.196422\pi\)
−0.0933424 + 0.995634i \(0.529755\pi\)
\(390\) 8.35704 31.6516i 0.423175 1.60274i
\(391\) 7.55112i 0.381877i
\(392\) 0 0
\(393\) 5.81352 + 10.0693i 0.293253 + 0.507930i
\(394\) 39.6442i 1.99725i
\(395\) 1.66159 + 6.20115i 0.0836038 + 0.312014i
\(396\) −6.17683 + 23.0522i −0.310397 + 1.15842i
\(397\) −7.98783 7.98783i −0.400898 0.400898i 0.477652 0.878549i \(-0.341488\pi\)
−0.878549 + 0.477652i \(0.841488\pi\)
\(398\) −33.1761 33.1761i −1.66297 1.66297i
\(399\) 0 0
\(400\) 8.03625 4.63973i 0.401812 0.231987i
\(401\) 6.26544 + 23.3830i 0.312881 + 1.16769i 0.925946 + 0.377656i \(0.123270\pi\)
−0.613064 + 0.790033i \(0.710063\pi\)
\(402\) −12.4757 + 21.6085i −0.622231 + 1.07774i
\(403\) −0.0702158 19.1955i −0.00349770 0.956195i
\(404\) −41.6629 + 24.0541i −2.07281 + 1.19674i
\(405\) 5.91359 + 1.58454i 0.293849 + 0.0787366i
\(406\) 0 0
\(407\) −2.28780 1.32086i −0.113402 0.0654726i
\(408\) −1.70891 + 6.37774i −0.0846037 + 0.315745i
\(409\) −0.348508 0.0933824i −0.0172326 0.00461746i 0.250192 0.968196i \(-0.419506\pi\)
−0.267425 + 0.963579i \(0.586173\pi\)
\(410\) −38.1283 10.2165i −1.88302 0.504555i
\(411\) −2.05228 + 7.65920i −0.101231 + 0.377800i
\(412\) 19.2852 + 11.1343i 0.950114 + 0.548549i
\(413\) 0 0
\(414\) −18.5963 4.98286i −0.913957 0.244894i
\(415\) −19.9852 + 11.5385i −0.981036 + 0.566401i
\(416\) 6.01901 10.5139i 0.295106 0.515484i
\(417\) −13.6570 + 23.6547i −0.668787 + 1.15837i
\(418\) −6.54626 24.4310i −0.320188 1.19496i
\(419\) 15.9181 9.19033i 0.777651 0.448977i −0.0579460 0.998320i \(-0.518455\pi\)
0.835597 + 0.549343i \(0.185122\pi\)
\(420\) 0 0
\(421\) 20.7439 + 20.7439i 1.01099 + 1.01099i 0.999939 + 0.0110561i \(0.00351933\pi\)
0.0110561 + 0.999939i \(0.496481\pi\)
\(422\) 32.0257 + 32.0257i 1.55899 + 1.55899i
\(423\) 2.66305 9.93864i 0.129482 0.483233i
\(424\) 7.46800 + 27.8710i 0.362678 + 1.35353i
\(425\) 7.46772i 0.362238i
\(426\) 12.2590 + 21.2333i 0.593952 + 1.02876i
\(427\) 0 0
\(428\) 30.8252i 1.48999i
\(429\) 9.28420 + 15.9457i 0.448245 + 0.769866i
\(430\) −41.2445 23.8125i −1.98899 1.14834i
\(431\) −6.82413 6.82413i −0.328707 0.328707i 0.523388 0.852095i \(-0.324668\pi\)
−0.852095 + 0.523388i \(0.824668\pi\)
\(432\) −8.50747 4.91179i −0.409316 0.236319i
\(433\) −13.6960 + 23.7221i −0.658186 + 1.14001i 0.322899 + 0.946433i \(0.395343\pi\)
−0.981085 + 0.193578i \(0.937991\pi\)
\(434\) 0 0
\(435\) −9.95227 + 2.66670i −0.477175 + 0.127859i
\(436\) −11.9060 + 11.9060i −0.570195 + 0.570195i
\(437\) 12.6780 3.39705i 0.606469 0.162503i
\(438\) 22.5048 + 38.9795i 1.07532 + 1.86251i
\(439\) −17.2958 + 29.9571i −0.825481 + 1.42978i 0.0760695 + 0.997103i \(0.475763\pi\)
−0.901551 + 0.432673i \(0.857570\pi\)
\(440\) −13.3663 + 49.8838i −0.637214 + 2.37812i
\(441\) 0 0
\(442\) −6.20181 10.6517i −0.294990 0.506649i
\(443\) −3.98607 6.90408i −0.189384 0.328023i 0.755661 0.654963i \(-0.227316\pi\)
−0.945045 + 0.326940i \(0.893982\pi\)
\(444\) 1.90280 1.90280i 0.0903027 0.0903027i
\(445\) −22.3274 −1.05842
\(446\) 1.64392 0.0778418
\(447\) 12.9134 12.9134i 0.610784 0.610784i
\(448\) 0 0
\(449\) −5.25579 19.6149i −0.248036 0.925683i −0.971833 0.235670i \(-0.924271\pi\)
0.723797 0.690013i \(-0.242395\pi\)
\(450\) −18.3909 4.92782i −0.866955 0.232300i
\(451\) 19.2682 11.1245i 0.907302 0.523831i
\(452\) 70.6966i 3.32529i
\(453\) −8.35221 + 2.23797i −0.392421 + 0.105149i
\(454\) −12.3400 −0.579146
\(455\) 0 0
\(456\) 11.4767 0.537446
\(457\) −1.35752 + 0.363747i −0.0635022 + 0.0170154i −0.290430 0.956896i \(-0.593798\pi\)
0.226928 + 0.973912i \(0.427132\pi\)
\(458\) 2.50818i 0.117200i
\(459\) 6.84646 3.95280i 0.319565 0.184501i
\(460\) −58.1123 15.5711i −2.70950 0.726009i
\(461\) 4.89285 + 18.2604i 0.227883 + 0.850469i 0.981229 + 0.192846i \(0.0617717\pi\)
−0.753347 + 0.657624i \(0.771562\pi\)
\(462\) 0 0
\(463\) 22.4573 22.4573i 1.04368 1.04368i 0.0446754 0.999002i \(-0.485775\pi\)
0.999002 0.0446754i \(-0.0142253\pi\)
\(464\) 4.82051 0.223787
\(465\) 20.4146 0.946703
\(466\) −2.21180 + 2.21180i −0.102460 + 0.102460i
\(467\) −14.1945 24.5855i −0.656841 1.13768i −0.981429 0.191826i \(-0.938559\pi\)
0.324588 0.945855i \(-0.394774\pi\)
\(468\) 19.5070 5.30343i 0.901711 0.245151i
\(469\) 0 0
\(470\) 12.9368 48.2807i 0.596729 2.22702i
\(471\) 11.4231 19.7854i 0.526350 0.911665i
\(472\) 3.86302 + 6.69096i 0.177810 + 0.307976i
\(473\) 25.9290 6.94764i 1.19221 0.319453i
\(474\) 4.05176 4.05176i 0.186104 0.186104i
\(475\) 12.5379 3.35953i 0.575280 0.154146i
\(476\) 0 0
\(477\) 5.89597 10.2121i 0.269958 0.467581i
\(478\) −44.1586 25.4950i −2.01977 1.16611i
\(479\) −2.47311 2.47311i −0.112999 0.112999i 0.648346 0.761346i \(-0.275461\pi\)
−0.761346 + 0.648346i \(0.775461\pi\)
\(480\) 11.1580 + 6.44208i 0.509291 + 0.294039i
\(481\) 0.00818512 + 2.23764i 0.000373209 + 0.102027i
\(482\) 8.30825i 0.378430i
\(483\) 0 0
\(484\) −12.8373 22.2348i −0.583512 1.01067i
\(485\) 20.0394i 0.909942i
\(486\) 8.65295 + 32.2933i 0.392506 + 1.46485i
\(487\) 6.29214 23.4826i 0.285124 1.06410i −0.663625 0.748066i \(-0.730983\pi\)
0.948749 0.316032i \(-0.102351\pi\)
\(488\) 14.0963 + 14.0963i 0.638108 + 0.638108i
\(489\) 0.862092 + 0.862092i 0.0389851 + 0.0389851i
\(490\) 0 0
\(491\) −5.24444 + 3.02788i −0.236678 + 0.136646i −0.613649 0.789579i \(-0.710299\pi\)
0.376971 + 0.926225i \(0.376966\pi\)
\(492\) 5.86579 + 21.8914i 0.264450 + 0.986941i
\(493\) −1.93967 + 3.35961i −0.0873584 + 0.151309i
\(494\) −15.0936 + 15.2044i −0.679094 + 0.684080i
\(495\) 18.2778 10.5527i 0.821525 0.474308i
\(496\) −9.22569 2.47202i −0.414246 0.110997i
\(497\) 0 0
\(498\) 17.8377 + 10.2986i 0.799328 + 0.461492i
\(499\) 4.73497 17.6712i 0.211967 0.791070i −0.775246 0.631660i \(-0.782374\pi\)
0.987212 0.159410i \(-0.0509593\pi\)
\(500\) −1.91630 0.513471i −0.0856995 0.0229631i
\(501\) −2.34499 0.628339i −0.104767 0.0280721i
\(502\) −10.7348 + 40.0629i −0.479119 + 1.78810i
\(503\) 7.01237 + 4.04859i 0.312666 + 0.180518i 0.648119 0.761539i \(-0.275556\pi\)
−0.335453 + 0.942057i \(0.608889\pi\)
\(504\) 0 0
\(505\) 41.0947 + 11.0113i 1.82869 + 0.489996i
\(506\) 45.6526 26.3575i 2.02950 1.17173i
\(507\) 7.71543 13.5922i 0.342654 0.603651i
\(508\) 2.13379 3.69583i 0.0946717 0.163976i
\(509\) −4.18077 15.6029i −0.185309 0.691584i −0.994564 0.104126i \(-0.966795\pi\)
0.809255 0.587458i \(-0.199871\pi\)
\(510\) 11.3521 6.55416i 0.502681 0.290223i
\(511\) 0 0
\(512\) −13.9135 13.9135i −0.614896 0.614896i
\(513\) −9.71660 9.71660i −0.428998 0.428998i
\(514\) −4.19864 + 15.6696i −0.185194 + 0.691154i
\(515\) −5.09699 19.0222i −0.224600 0.838219i
\(516\) 27.3440i 1.20375i
\(517\) 14.0866 + 24.3987i 0.619527 + 1.07305i
\(518\) 0 0
\(519\) 2.94610i 0.129320i
\(520\) 42.2121 11.4763i 1.85112 0.503271i
\(521\) 28.0133 + 16.1735i 1.22729 + 0.708574i 0.966461 0.256812i \(-0.0826721\pi\)
0.260825 + 0.965386i \(0.416005\pi\)
\(522\) −6.99382 6.99382i −0.306111 0.306111i
\(523\) −18.4602 10.6580i −0.807210 0.466043i 0.0387760 0.999248i \(-0.487654\pi\)
−0.845986 + 0.533205i \(0.820987\pi\)
\(524\) −17.4394 + 30.2060i −0.761845 + 1.31956i
\(525\) 0 0
\(526\) −39.8349 + 10.6737i −1.73688 + 0.465397i
\(527\) 5.43507 5.43507i 0.236755 0.236755i
\(528\) 8.86811 2.37620i 0.385935 0.103411i
\(529\) 2.17769 + 3.77187i 0.0946821 + 0.163994i
\(530\) 28.6419 49.6092i 1.24413 2.15489i
\(531\) 0.817205 3.04985i 0.0354637 0.132352i
\(532\) 0 0
\(533\) −16.3553 9.36315i −0.708428 0.405563i
\(534\) 9.96410 + 17.2583i 0.431189 + 0.746841i
\(535\) −19.2759 + 19.2759i −0.833370 + 0.833370i
\(536\) −33.3417 −1.44014
\(537\) −9.02852 −0.389609
\(538\) −0.280864 + 0.280864i −0.0121089 + 0.0121089i
\(539\) 0 0
\(540\) 16.3021 + 60.8404i 0.701532 + 2.61815i
\(541\) −17.8879 4.79305i −0.769061 0.206069i −0.147104 0.989121i \(-0.546995\pi\)
−0.621957 + 0.783052i \(0.713662\pi\)
\(542\) −5.11440 + 2.95280i −0.219682 + 0.126834i
\(543\) 5.93096i 0.254522i
\(544\) 4.68576 1.25555i 0.200900 0.0538311i
\(545\) 14.8904 0.637833
\(546\) 0 0
\(547\) −35.0943 −1.50053 −0.750263 0.661140i \(-0.770073\pi\)
−0.750263 + 0.661140i \(0.770073\pi\)
\(548\) −22.9761 + 6.15643i −0.981490 + 0.262990i
\(549\) 8.14698i 0.347705i
\(550\) 45.1483 26.0664i 1.92513 1.11148i
\(551\) 6.51323 + 1.74521i 0.277473 + 0.0743486i
\(552\) 6.19086 + 23.1046i 0.263500 + 0.983397i
\(553\) 0 0
\(554\) −14.2820 + 14.2820i −0.606782 + 0.606782i
\(555\) −2.37975 −0.101015
\(556\) −81.9368 −3.47490
\(557\) −6.70621 + 6.70621i −0.284151 + 0.284151i −0.834762 0.550611i \(-0.814395\pi\)
0.550611 + 0.834762i \(0.314395\pi\)
\(558\) 9.79854 + 16.9716i 0.414805 + 0.718464i
\(559\) −16.1367 16.0191i −0.682510 0.677535i
\(560\) 0 0
\(561\) −1.91227 + 7.13668i −0.0807360 + 0.301311i
\(562\) −26.4431 + 45.8008i −1.11544 + 1.93199i
\(563\) −15.8351 27.4272i −0.667369 1.15592i −0.978637 0.205595i \(-0.934087\pi\)
0.311268 0.950322i \(-0.399246\pi\)
\(564\) −27.7204 + 7.42767i −1.16724 + 0.312761i
\(565\) −44.2086 + 44.2086i −1.85987 + 1.85987i
\(566\) 21.9129 5.87155i 0.921069 0.246800i
\(567\) 0 0
\(568\) −16.3813 + 28.3733i −0.687345 + 1.19052i
\(569\) 6.05848 + 3.49787i 0.253985 + 0.146638i 0.621587 0.783345i \(-0.286488\pi\)
−0.367603 + 0.929983i \(0.619821\pi\)
\(570\) −16.1111 16.1111i −0.674821 0.674821i
\(571\) −13.2500 7.64990i −0.554496 0.320139i 0.196437 0.980516i \(-0.437063\pi\)
−0.750933 + 0.660378i \(0.770396\pi\)
\(572\) −27.5001 + 48.0365i −1.14984 + 2.00851i
\(573\) 7.32009i 0.305801i
\(574\) 0 0
\(575\) 13.5266 + 23.4288i 0.564099 + 0.977049i
\(576\) 17.9461i 0.747754i
\(577\) −10.8175 40.3714i −0.450338 1.68068i −0.701444 0.712725i \(-0.747461\pi\)
0.251106 0.967960i \(-0.419206\pi\)
\(578\) −9.14080 + 34.1139i −0.380207 + 1.41895i
\(579\) −12.3163 12.3163i −0.511847 0.511847i
\(580\) −21.8553 21.8553i −0.907491 0.907491i
\(581\) 0 0
\(582\) −15.4898 + 8.94304i −0.642073 + 0.370701i
\(583\) 8.35668 + 31.1876i 0.346098 + 1.29166i
\(584\) −30.0724 + 52.0870i −1.24441 + 2.15538i
\(585\) −15.5147 8.88189i −0.641453 0.367221i
\(586\) 30.8431 17.8073i 1.27412 0.735611i
\(587\) 0.941084 + 0.252163i 0.0388427 + 0.0104079i 0.278188 0.960527i \(-0.410266\pi\)
−0.239345 + 0.970934i \(0.576933\pi\)
\(588\) 0 0
\(589\) −11.5703 6.68012i −0.476746 0.275250i
\(590\) 3.96988 14.8158i 0.163437 0.609957i
\(591\) 19.4435 + 5.20986i 0.799797 + 0.214305i
\(592\) 1.07545 + 0.288165i 0.0442006 + 0.0118435i
\(593\) −10.2197 + 38.1404i −0.419673 + 1.56624i 0.355616 + 0.934632i \(0.384271\pi\)
−0.775288 + 0.631608i \(0.782395\pi\)
\(594\) −47.7957 27.5949i −1.96108 1.13223i
\(595\) 0 0
\(596\) 52.9167 + 14.1790i 2.16755 + 0.580794i
\(597\) 20.6310 11.9113i 0.844370 0.487497i
\(598\) −38.7511 22.1844i −1.58465 0.907186i
\(599\) −8.27438 + 14.3316i −0.338082 + 0.585575i −0.984072 0.177771i \(-0.943111\pi\)
0.645990 + 0.763346i \(0.276445\pi\)
\(600\) 6.12248 + 22.8494i 0.249949 + 0.932824i
\(601\) −9.99562 + 5.77097i −0.407730 + 0.235403i −0.689814 0.723987i \(-0.742308\pi\)
0.282084 + 0.959390i \(0.408974\pi\)
\(602\) 0 0
\(603\) 9.63495 + 9.63495i 0.392365 + 0.392365i
\(604\) −18.3415 18.3415i −0.746307 0.746307i
\(605\) −5.87655 + 21.9316i −0.238916 + 0.891645i
\(606\) −9.82809 36.6789i −0.399239 1.48998i
\(607\) 21.3778i 0.867696i 0.900986 + 0.433848i \(0.142845\pi\)
−0.900986 + 0.433848i \(0.857155\pi\)
\(608\) −4.21600 7.30232i −0.170981 0.296148i
\(609\) 0 0
\(610\) 39.5770i 1.60243i
\(611\) 11.8563 20.7102i 0.479653 0.837847i
\(612\) 7.01010 + 4.04728i 0.283366 + 0.163602i
\(613\) 22.0693 + 22.0693i 0.891372 + 0.891372i 0.994652 0.103281i \(-0.0329340\pi\)
−0.103281 + 0.994652i \(0.532934\pi\)
\(614\) −45.6568 26.3600i −1.84256 1.06380i
\(615\) 10.0213 17.3574i 0.404097 0.699917i
\(616\) 0 0
\(617\) 26.9421 7.21911i 1.08465 0.290630i 0.328149 0.944626i \(-0.393575\pi\)
0.756498 + 0.653996i \(0.226909\pi\)
\(618\) −12.4289 + 12.4289i −0.499964 + 0.499964i
\(619\) −46.5004 + 12.4597i −1.86901 + 0.500799i −0.869025 + 0.494768i \(0.835253\pi\)
−0.999982 + 0.00603119i \(0.998080\pi\)
\(620\) 30.6199 + 53.0352i 1.22972 + 2.12994i
\(621\) 14.3198 24.8026i 0.574633 0.995294i
\(622\) −2.38621 + 8.90546i −0.0956783 + 0.357076i
\(623\) 0 0
\(624\) −5.51901 5.47878i −0.220937 0.219327i
\(625\) −12.0539 20.8781i −0.482158 0.835122i
\(626\) 16.7011 16.7011i 0.667509 0.667509i
\(627\) 12.8424 0.512877
\(628\) 68.5343 2.73482
\(629\) −0.633571 + 0.633571i −0.0252621 + 0.0252621i
\(630\) 0 0
\(631\) −2.94853 11.0041i −0.117379 0.438064i 0.882075 0.471109i \(-0.156146\pi\)
−0.999454 + 0.0330448i \(0.989480\pi\)
\(632\) 7.39598 + 1.98175i 0.294196 + 0.0788296i
\(633\) −19.9156 + 11.4983i −0.791575 + 0.457016i
\(634\) 36.7632i 1.46005i
\(635\) −3.64543 + 0.976791i −0.144665 + 0.0387628i
\(636\) −32.8896 −1.30416
\(637\) 0 0
\(638\) 27.0820 1.07219
\(639\) 12.9330 3.46539i 0.511622 0.137089i
\(640\) 65.7466i 2.59886i
\(641\) 16.9100 9.76301i 0.667906 0.385616i −0.127377 0.991854i \(-0.540656\pi\)
0.795283 + 0.606239i \(0.207322\pi\)
\(642\) 23.5020 + 6.29733i 0.927548 + 0.248536i
\(643\) −9.35047 34.8964i −0.368747 1.37618i −0.862270 0.506449i \(-0.830958\pi\)
0.493524 0.869732i \(-0.335709\pi\)
\(644\) 0 0
\(645\) 17.0990 17.0990i 0.673272 0.673272i
\(646\) −8.57869 −0.337524
\(647\) −5.79390 −0.227782 −0.113891 0.993493i \(-0.536331\pi\)
−0.113891 + 0.993493i \(0.536331\pi\)
\(648\) 5.16316 5.16316i 0.202828 0.202828i
\(649\) 4.32272 + 7.48717i 0.169682 + 0.293897i
\(650\) −38.3231 21.9393i −1.50316 0.860532i
\(651\) 0 0
\(652\) −0.946581 + 3.53269i −0.0370710 + 0.138351i
\(653\) −18.1035 + 31.3562i −0.708445 + 1.22706i 0.256989 + 0.966414i \(0.417270\pi\)
−0.965434 + 0.260648i \(0.916064\pi\)
\(654\) −6.64516 11.5098i −0.259846 0.450067i
\(655\) 29.7941 7.98330i 1.16415 0.311933i
\(656\) −6.63060 + 6.63060i −0.258882 + 0.258882i
\(657\) 23.7421 6.36168i 0.926269 0.248193i
\(658\) 0 0
\(659\) −10.3685 + 17.9588i −0.403901 + 0.699576i −0.994193 0.107613i \(-0.965679\pi\)
0.590292 + 0.807190i \(0.299013\pi\)
\(660\) −50.9796 29.4331i −1.98438 1.14568i
\(661\) 23.9986 + 23.9986i 0.933438 + 0.933438i 0.997919 0.0644808i \(-0.0205391\pi\)
−0.0644808 + 0.997919i \(0.520539\pi\)
\(662\) 30.0293 + 17.3374i 1.16712 + 0.673838i
\(663\) 6.03912 1.64188i 0.234540 0.0637652i
\(664\) 27.5234i 1.06811i
\(665\) 0 0
\(666\) −1.14222 1.97839i −0.0442603 0.0766611i
\(667\) 14.0537i 0.544160i
\(668\) −1.88490 7.03452i −0.0729288 0.272174i
\(669\) −0.216036 + 0.806257i −0.00835243 + 0.0311717i
\(670\) 46.8054 + 46.8054i 1.80825 + 1.80825i
\(671\) 15.7737 + 15.7737i 0.608937 + 0.608937i
\(672\) 0 0
\(673\) −35.7571 + 20.6444i −1.37834 + 0.795783i −0.991959 0.126558i \(-0.959607\pi\)
−0.386377 + 0.922341i \(0.626274\pi\)
\(674\) −7.24584 27.0419i −0.279099 1.04161i
\(675\) 14.1616 24.5287i 0.545082 0.944109i
\(676\) 46.8837 0.342999i 1.80322 0.0131923i
\(677\) 39.1750 22.6177i 1.50562 0.869268i 0.505638 0.862746i \(-0.331257\pi\)
0.999979 0.00652270i \(-0.00207626\pi\)
\(678\) 53.9009 + 14.4427i 2.07005 + 0.554669i
\(679\) 0 0
\(680\) 15.1695 + 8.75810i 0.581723 + 0.335858i
\(681\) 1.62167 6.05215i 0.0621425 0.231919i
\(682\) −51.8307 13.8880i −1.98470 0.531799i
\(683\) −42.0091 11.2563i −1.60743 0.430710i −0.660156 0.751129i \(-0.729510\pi\)
−0.947276 + 0.320419i \(0.896176\pi\)
\(684\) 3.64153 13.5904i 0.139237 0.519641i
\(685\) 18.2174 + 10.5178i 0.696051 + 0.401866i
\(686\) 0 0
\(687\) −1.23013 0.329613i −0.0469325 0.0125755i
\(688\) −9.79785 + 5.65679i −0.373539 + 0.215663i
\(689\) 19.2679 19.4094i 0.734048 0.739438i
\(690\) 23.7437 41.1253i 0.903907 1.56561i
\(691\) 5.57267 + 20.7975i 0.211994 + 0.791174i 0.987203 + 0.159468i \(0.0509780\pi\)
−0.775209 + 0.631705i \(0.782355\pi\)
\(692\) 7.65370 4.41887i 0.290950 0.167980i
\(693\) 0 0
\(694\) −16.7659 16.7659i −0.636425 0.636425i
\(695\) 51.2375 + 51.2375i 1.94355 + 1.94355i
\(696\) −3.18052 + 11.8699i −0.120557 + 0.449926i
\(697\) −1.95312 7.28916i −0.0739798 0.276096i
\(698\) 40.2200i 1.52235i
\(699\) −0.794111 1.37544i −0.0300360 0.0520239i
\(700\) 0 0
\(701\) 8.77295i 0.331350i 0.986180 + 0.165675i \(0.0529803\pi\)
−0.986180 + 0.165675i \(0.947020\pi\)
\(702\) 0.171000 + 46.7478i 0.00645399 + 1.76438i
\(703\) 1.34876 + 0.778708i 0.0508695 + 0.0293695i
\(704\) −34.7462 34.7462i −1.30955 1.30955i
\(705\) 21.9791 + 12.6896i 0.827781 + 0.477920i
\(706\) 42.7152 73.9850i 1.60761 2.78446i
\(707\) 0 0
\(708\) −8.50651 + 2.27931i −0.319694 + 0.0856618i
\(709\) −29.9934 + 29.9934i −1.12643 + 1.12643i −0.135672 + 0.990754i \(0.543319\pi\)
−0.990754 + 0.135672i \(0.956681\pi\)
\(710\) 62.8270 16.8345i 2.35786 0.631786i
\(711\) −1.56458 2.70994i −0.0586765 0.101631i
\(712\) −13.3147 + 23.0617i −0.498989 + 0.864274i
\(713\) 7.20689 26.8965i 0.269900 1.00728i
\(714\) 0 0
\(715\) 47.2352 12.8420i 1.76650 0.480264i
\(716\) −13.5419 23.4553i −0.506084 0.876564i
\(717\) 18.3071 18.3071i 0.683691 0.683691i
\(718\) −8.20329 −0.306144
\(719\) −5.60019 −0.208852 −0.104426 0.994533i \(-0.533301\pi\)
−0.104426 + 0.994533i \(0.533301\pi\)
\(720\) −6.28980 + 6.28980i −0.234407 + 0.234407i
\(721\) 0 0
\(722\) −7.78453 29.0523i −0.289710 1.08121i
\(723\) 4.07477 + 1.09183i 0.151542 + 0.0406056i
\(724\) −15.4081 + 8.89587i −0.572637 + 0.330612i
\(725\) 13.8985i 0.516176i
\(726\) 19.5749 5.24509i 0.726494 0.194664i
\(727\) 32.0200 1.18756 0.593778 0.804629i \(-0.297636\pi\)
0.593778 + 0.804629i \(0.297636\pi\)
\(728\) 0 0
\(729\) −22.7339 −0.841996
\(730\) 115.336 30.9043i 4.26879 1.14382i
\(731\) 9.10469i 0.336749i
\(732\) −19.6789 + 11.3616i −0.727352 + 0.419937i
\(733\) −0.884660 0.237044i −0.0326757 0.00875542i 0.242444 0.970165i \(-0.422051\pi\)
−0.275120 + 0.961410i \(0.588718\pi\)
\(734\) 7.77195 + 29.0053i 0.286868 + 1.07061i
\(735\) 0 0
\(736\) 12.4266 12.4266i 0.458051 0.458051i
\(737\) −37.3092 −1.37430
\(738\) 19.2400 0.708233
\(739\) 6.20218 6.20218i 0.228151 0.228151i −0.583769 0.811920i \(-0.698423\pi\)
0.811920 + 0.583769i \(0.198423\pi\)
\(740\) −3.56939 6.18236i −0.131213 0.227268i
\(741\) −5.47347 9.40074i −0.201073 0.345345i
\(742\) 0 0
\(743\) −9.56609 + 35.7011i −0.350946 + 1.30975i 0.534564 + 0.845128i \(0.320476\pi\)
−0.885510 + 0.464620i \(0.846191\pi\)
\(744\) 12.1740 21.0860i 0.446321 0.773050i
\(745\) −24.2238 41.9569i −0.887492 1.53718i
\(746\) −68.7019 + 18.4086i −2.51536 + 0.673988i
\(747\) 7.95360 7.95360i 0.291007 0.291007i
\(748\) −21.4087 + 5.73643i −0.782778 + 0.209745i
\(749\) 0 0
\(750\) 0.782967 1.35614i 0.0285899 0.0495192i
\(751\) 10.7508 + 6.20698i 0.392303 + 0.226496i 0.683157 0.730271i \(-0.260606\pi\)
−0.290855 + 0.956767i \(0.593940\pi\)
\(752\) −8.39613 8.39613i −0.306175 0.306175i
\(753\) −18.2381 10.5298i −0.664633 0.383726i
\(754\) −11.5424 19.8242i −0.420350 0.721957i
\(755\) 22.9390i 0.834835i
\(756\) 0 0
\(757\) 11.7793 + 20.4023i 0.428124 + 0.741533i 0.996707 0.0810934i \(-0.0258412\pi\)
−0.568582 + 0.822626i \(0.692508\pi\)
\(758\) 28.4411i 1.03303i
\(759\) 6.92756 + 25.8540i 0.251454 + 0.938441i
\(760\) 7.88007 29.4088i 0.285840 1.06677i
\(761\) −9.57799 9.57799i −0.347202 0.347202i 0.511864 0.859066i \(-0.328955\pi\)
−0.859066 + 0.511864i \(0.828955\pi\)
\(762\) 2.38189 + 2.38189i 0.0862866 + 0.0862866i
\(763\) 0 0
\(764\) −19.0169 + 10.9794i −0.688008 + 0.397222i
\(765\) −1.85273 6.91450i −0.0669857 0.249994i
\(766\) −6.77619 + 11.7367i −0.244834 + 0.424064i
\(767\) 3.63831 6.35531i 0.131372 0.229477i
\(768\) 26.7812 15.4621i 0.966382 0.557941i
\(769\) 29.8604 + 8.00107i 1.07679 + 0.288526i 0.753282 0.657698i \(-0.228470\pi\)
0.323512 + 0.946224i \(0.395136\pi\)
\(770\) 0 0
\(771\) −7.13334 4.11844i −0.256901 0.148322i
\(772\) 13.5233 50.4698i 0.486716 1.81645i
\(773\) −19.2999 5.17138i −0.694167 0.186002i −0.105551 0.994414i \(-0.533661\pi\)
−0.588617 + 0.808412i \(0.700327\pi\)
\(774\) 22.4223 + 6.00804i 0.805953 + 0.215954i
\(775\) 7.12729 26.5994i 0.256020 0.955480i
\(776\) −20.6985 11.9503i −0.743032 0.428990i
\(777\) 0 0
\(778\) −37.6193 10.0801i −1.34872 0.361388i
\(779\) −11.3595 + 6.55839i −0.406995 + 0.234979i
\(780\) 0.182391 + 49.8619i 0.00653065 + 1.78534i