Properties

Label 637.2.x.b.19.1
Level $637$
Weight $2$
Character 637.19
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 19.1
Character \(\chi\) \(=\) 637.19
Dual form 637.2.x.b.570.2

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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 −0.667055 0.745009i \(-0.732445\pi\)
−0.950191 + 0.311669i \(0.899112\pi\)
\(3\) 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 \(-0.330588\pi\)
0.870305 + 0.492513i \(0.163922\pi\)
\(6\) −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 0.0885547 0.996071i \(-0.471775\pi\)
−0.996071 + 0.0885547i \(0.971775\pi\)
\(12\) 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 \(-0.889352\pi\)
0.765109 + 0.643901i \(0.222685\pi\)
\(18\) −3.55553 0.952702i −0.838047 0.224554i
\(19\) −1.77447 1.77447i −0.407092 0.407092i 0.473631 0.880723i \(-0.342943\pi\)
−0.880723 + 0.473631i \(0.842943\pi\)
\(20\) 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 0.0531111 0.998589i \(-0.483086\pi\)
0.891359 + 0.453299i \(0.149753\pi\)
\(24\) −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 −0.713900 0.700248i \(-0.753073\pi\)
0.963382 + 0.268132i \(0.0864063\pi\)
\(30\) 9.07940i 1.65766i
\(31\) 1.37793 5.14250i 0.247483 0.923620i −0.724636 0.689132i \(-0.757992\pi\)
0.972119 0.234488i \(-0.0753413\pi\)
\(32\) 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 −0.951465 0.307758i \(-0.900421\pi\)
0.977872 + 0.209206i \(0.0670880\pi\)
\(38\) 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 \(-0.449507\pi\)
0.630524 + 0.776170i \(0.282840\pi\)
\(42\) 0 0
\(43\) −5.46143 + 3.15316i −0.832860 + 0.480852i −0.854831 0.518907i \(-0.826339\pi\)
0.0219711 + 0.999759i \(0.493006\pi\)
\(44\) −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 −0.970872 0.239599i \(-0.922984\pi\)
0.721000 0.692935i \(-0.243683\pi\)
\(48\) 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 0.999703 + 0.0243730i \(0.00775895\pi\)
−0.478744 + 0.877955i \(0.658908\pi\)
\(54\) −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 \(-0.125541\pi\)
−0.991665 + 0.128842i \(0.958874\pi\)
\(60\) 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 −0.218630 0.975808i \(-0.570159\pi\)
0.975808 + 0.218630i \(0.0701586\pi\)
\(68\) −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 0.716124 0.697974i \(-0.245915\pi\)
0.271194 + 0.962525i \(0.412581\pi\)
\(72\) −4.18153 4.18153i −0.492798 0.492798i
\(73\) −15.2724 4.09222i −1.78749 0.478958i −0.795578 0.605852i \(-0.792833\pi\)
−0.991916 + 0.126894i \(0.959499\pi\)
\(74\) −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 −0.917072 0.398722i \(-0.869454\pi\)
0.803839 + 0.594847i \(0.202787\pi\)
\(80\) 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 \(-0.379982\pi\)
−0.929756 + 0.368177i \(0.879982\pi\)
\(84\) 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 \(-0.537659\pi\)
−0.598725 + 0.800955i \(0.704326\pi\)
\(90\) −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 0.832913 + 0.553405i \(0.186672\pi\)
−0.998026 + 0.0628062i \(0.979995\pi\)
\(98\) 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 \(-0.269007\pi\)
0.663649 + 0.748044i \(0.269007\pi\)
\(102\) −2.90616 2.90616i −0.287752 0.287752i
\(103\) −3.08727 + 5.34730i −0.304197 + 0.526885i −0.977082 0.212862i \(-0.931722\pi\)
0.672885 + 0.739747i \(0.265055\pi\)
\(104\) 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 0.995231 0.0975469i \(-0.0310996\pi\)
−0.582094 + 0.813122i \(0.697766\pi\)
\(108\) 9.87427 17.1027i 0.950152 1.64571i
\(109\) −4.50957 1.20834i −0.431939 0.115738i 0.0362973 0.999341i \(-0.488444\pi\)
−0.468236 + 0.883603i \(0.655110\pi\)
\(110\) 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 0.796289 + 0.604917i \(0.206794\pi\)
0.125729 + 0.992065i \(0.459873\pi\)
\(114\) 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 0.544777 0.838581i \(-0.316614\pi\)
−0.453844 + 0.891081i \(0.649948\pi\)
\(128\) −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 \(-0.194493\pi\)
−0.0873067 + 0.996181i \(0.527826\pi\)
\(132\) −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 −0.520477 0.853876i \(-0.674246\pi\)
−0.0238082 + 0.999717i \(0.507579\pi\)
\(138\) 3.85355 + 14.3817i 0.328036 + 1.22425i
\(139\) 19.6752 11.3595i 1.66883 0.963500i 0.700562 0.713591i \(-0.252933\pi\)
0.968269 0.249909i \(-0.0804008\pi\)
\(140\) 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 −0.113591 0.993528i \(-0.536235\pi\)
0.993528 + 0.113591i \(0.0362354\pi\)
\(150\) 3.81099 + 14.2228i 0.311166 + 1.16129i
\(151\) −1.86148 + 6.94712i −0.151485 + 0.565349i 0.847896 + 0.530163i \(0.177869\pi\)
−0.999381 + 0.0351862i \(0.988798\pi\)
\(152\) 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 \(-0.940634\pi\)
−0.330748 + 0.943719i \(0.607301\pi\)
\(158\) 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 0.678467 0.734631i \(-0.262645\pi\)
−0.734631 + 0.678467i \(0.762645\pi\)
\(164\) 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 \(-0.108228\pi\)
−0.983195 + 0.182561i \(0.941561\pi\)
\(168\) 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 \(-0.529695\pi\)
−0.0931533 + 0.995652i \(0.529695\pi\)
\(174\) 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 \(0.0905496\pi\)
−0.959811 + 0.280649i \(0.909450\pi\)
\(180\) 17.2727 + 4.62821i 1.28743 + 0.344966i
\(181\) 4.93320 0.366682 0.183341 0.983049i \(-0.441309\pi\)
0.183341 + 0.983049i \(0.441309\pi\)
\(182\) 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 0.972074 0.234672i \(-0.0754018\pi\)
−0.234672 + 0.972074i \(0.575402\pi\)
\(194\) 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 −0.929676 0.368379i \(-0.879913\pi\)
0.620934 0.783863i \(-0.286754\pi\)
\(198\) 7.83424 + 13.5693i 0.556755 + 0.964328i
\(199\) −9.90747 + 17.1602i −0.702322 + 1.21646i 0.265328 + 0.964158i \(0.414520\pi\)
−0.967649 + 0.252298i \(0.918814\pi\)
\(200\) −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 0.322619 + 0.946529i \(0.395437\pi\)
−0.981028 + 0.193868i \(0.937897\pi\)
\(212\) 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 \(-0.575933\pi\)
0.281203 + 0.959648i \(0.409267\pi\)
\(224\) 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 \(-0.638664\pi\)
0.0878596 + 0.996133i \(0.471997\pi\)
\(228\) −10.5103 + 2.81622i −0.696060 + 0.186509i
\(229\) −0.274163 1.02319i −0.0181172 0.0676142i 0.956275 0.292468i \(-0.0944764\pi\)
−0.974393 + 0.224853i \(0.927810\pi\)
\(230\) −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 0.537006 0.843578i \(-0.319555\pi\)
−0.462057 + 0.886850i \(0.652888\pi\)
\(234\) 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 −0.0149168 0.999889i \(-0.504748\pi\)
0.999889 + 0.0149168i \(0.00474835\pi\)
\(240\) 4.86429 4.86429i 0.313989 0.313989i
\(241\) 0.908152 + 3.38927i 0.0584992 + 0.218322i 0.988987 0.148000i \(-0.0472835\pi\)
−0.930488 + 0.366322i \(0.880617\pi\)
\(242\) 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 −0.998069 0.0621079i \(-0.980218\pi\)
0.445248 0.895407i \(-0.353116\pi\)
\(252\) 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 \(-0.235212\pi\)
−0.952864 + 0.303397i \(0.901879\pi\)
\(258\) −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 \(-0.334961\pi\)
−0.504422 + 0.863457i \(0.668294\pi\)
\(270\) 41.3529i 2.51666i
\(271\) −2.40913 0.645525i −0.146344 0.0392128i 0.184903 0.982757i \(-0.440803\pi\)
−0.331248 + 0.943544i \(0.607470\pi\)
\(272\) −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 0.705234 0.708975i \(-0.250842\pi\)
−0.261373 + 0.965238i \(0.584175\pi\)
\(278\) −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 0.998417 0.0562508i \(-0.0179146\pi\)
−0.0562508 + 0.998417i \(0.517915\pi\)
\(282\) 18.8414 1.12199
\(283\) 9.58097 0.569530 0.284765 0.958597i \(-0.408085\pi\)
0.284765 + 0.958597i \(0.408085\pi\)
\(284\) 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 \(-0.271874\pi\)
0.191884 + 0.981418i \(0.438540\pi\)
\(294\) 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 \(-0.969153\pi\)
0.0967560 + 0.995308i \(0.469153\pi\)
\(308\) 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 \(-0.201879\pi\)
−0.915930 + 0.401338i \(0.868545\pi\)
\(312\) 8.29688 14.2500i 0.469718 0.806747i
\(313\) 8.63858 + 4.98749i 0.488282 + 0.281910i 0.723861 0.689946i \(-0.242366\pi\)
−0.235580 + 0.971855i \(0.575699\pi\)
\(314\) 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 0.982123 + 0.188242i \(0.0602790\pi\)
−0.756422 + 0.654084i \(0.773054\pi\)
\(318\) −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 −0.931895 0.362729i \(-0.881845\pi\)
0.362729 + 0.931895i \(0.381845\pi\)
\(332\) −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 \(-0.895634\pi\)
0.946728 0.322033i \(-0.104366\pi\)
\(338\) −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 −0.699766 0.714372i \(-0.746712\pi\)
0.968548 + 0.248829i \(0.0800456\pi\)
\(348\) −5.82539 10.0899i −0.312274 0.540874i
\(349\) 4.39634 + 16.4073i 0.235330 + 0.878265i 0.978000 + 0.208607i \(0.0668928\pi\)
−0.742669 + 0.669658i \(0.766441\pi\)
\(350\) 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 0.876520 + 0.481366i \(0.159859\pi\)
0.481366 + 0.876520i \(0.340141\pi\)
\(354\) 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 −0.169426 0.985543i \(-0.554191\pi\)
0.346045 + 0.938218i \(0.387525\pi\)
\(360\) −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 0.998658 + 0.0517891i \(0.0164924\pi\)
−0.838969 + 0.544180i \(0.816841\pi\)
\(380\) −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 \(-0.296714\pi\)
−0.802907 + 0.596105i \(0.796714\pi\)
\(384\) 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 −0.0933424 0.995634i \(-0.529755\pi\)
0.815573 + 0.578654i \(0.196422\pi\)
\(390\) −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 \(-0.658512\pi\)
0.878549 + 0.477652i \(0.158512\pi\)
\(398\) 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 −0.613064 0.790033i \(-0.710063\pi\)
0.925946 0.377656i \(-0.123270\pi\)
\(402\) 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 \(-0.580494\pi\)
0.267425 + 0.963579i \(0.413827\pi\)
\(410\) −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 \(-0.481545\pi\)
−0.835597 + 0.549343i \(0.814878\pi\)
\(420\) 0 0
\(421\) 20.7439 20.7439i 1.01099 1.01099i 0.0110561 0.999939i \(-0.496481\pi\)
0.999939 0.0110561i \(-0.00351933\pi\)
\(422\) 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 −0.852095 0.523388i \(-0.824668\pi\)
0.523388 + 0.852095i \(0.324668\pi\)
\(432\) 8.50747 4.91179i 0.409316 0.236319i
\(433\) 13.6960 + 23.7221i 0.658186 + 1.14001i 0.981085 + 0.193578i \(0.0620093\pi\)
−0.322899 + 0.946433i \(0.604657\pi\)
\(434\) 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 0.901551 + 0.432673i \(0.142430\pi\)
−0.0760695 + 0.997103i \(0.524237\pi\)
\(440\) 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 −0.945045 0.326940i \(-0.893982\pi\)
0.755661 + 0.654963i \(0.227316\pi\)
\(444\) −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 0.723797 + 0.690013i \(0.242395\pi\)
−0.971833 + 0.235670i \(0.924271\pi\)
\(450\) −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 0.226928 0.973912i \(-0.427132\pi\)
−0.290430 + 0.956896i \(0.593798\pi\)
\(458\) 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 0.753347 + 0.657624i \(0.228438\pi\)
−0.981229 + 0.192846i \(0.938228\pi\)
\(462\) 0 0
\(463\) 22.4573 + 22.4573i 1.04368 + 1.04368i 0.999002 + 0.0446754i \(0.0142253\pi\)
0.0446754 + 0.999002i \(0.485775\pi\)
\(464\) 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 −0.324588 0.945855i \(-0.605226\pi\)
0.981429 0.191826i \(-0.0614410\pi\)
\(468\) −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 \(-0.724539\pi\)
0.761346 + 0.648346i \(0.224539\pi\)
\(480\) 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 0.948749 + 0.316032i \(0.102351\pi\)
−0.663625 + 0.748066i \(0.730983\pi\)
\(488\) −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 0.376971 0.926225i \(-0.376966\pi\)
−0.613649 + 0.789579i \(0.710299\pi\)
\(492\) 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 0.987212 + 0.159410i \(0.0509593\pi\)
−0.775246 + 0.631660i \(0.782374\pi\)
\(500\) 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 \(-0.724444\pi\)
0.335453 + 0.942057i \(0.391111\pi\)
\(504\) 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 −0.809255 0.587458i \(-0.800129\pi\)
0.994564 0.104126i \(-0.0332046\pi\)
\(510\) −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 \(-0.917328\pi\)
−0.260825 + 0.965386i \(0.583995\pi\)
\(522\) −6.99382 + 6.99382i −0.306111 + 0.306111i
\(523\) 18.4602 10.6580i 0.807210 0.466043i −0.0387760 0.999248i \(-0.512346\pi\)
0.845986 + 0.533205i \(0.179013\pi\)
\(524\) 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 −0.621957 0.783052i \(-0.713662\pi\)
−0.147104 + 0.989121i \(0.546995\pi\)
\(542\) 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 0.550611 0.834762i \(-0.314395\pi\)
−0.834762 + 0.550611i \(0.814395\pi\)
\(558\) −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 −0.311268 0.950322i \(-0.600754\pi\)
0.978637 0.205595i \(-0.0659129\pi\)
\(564\) −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 −0.367603 0.929983i \(-0.619821\pi\)
0.621587 + 0.783345i \(0.286488\pi\)
\(570\) 16.1111 16.1111i 0.674821 0.674821i
\(571\) −13.2500 + 7.64990i −0.554496 + 0.320139i −0.750933 0.660378i \(-0.770396\pi\)
0.196437 + 0.980516i \(0.437063\pi\)
\(572\) 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 −0.251106 0.967960i \(-0.580794\pi\)
0.701444 0.712725i \(-0.252539\pi\)
\(578\) −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 \(-0.589734\pi\)
0.239345 + 0.970934i \(0.423067\pi\)
\(588\) 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 0.775288 + 0.631608i \(0.217605\pi\)
−0.355616 + 0.934632i \(0.615729\pi\)
\(594\) 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 0.645990 0.763346i \(-0.276445\pi\)
−0.984072 + 0.177771i \(0.943111\pi\)
\(600\) −6.12248 + 22.8494i −0.249949 + 0.932824i
\(601\) 9.99562 + 5.77097i 0.407730 + 0.235403i 0.689814 0.723987i \(-0.257692\pi\)
−0.282084 + 0.959390i \(0.591026\pi\)
\(602\) 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 −0.103281 0.994652i \(-0.532934\pi\)
0.994652 + 0.103281i \(0.0329340\pi\)
\(614\) 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 0.756498 0.653996i \(-0.226909\pi\)
0.328149 + 0.944626i \(0.393575\pi\)
\(618\) −12.4289 12.4289i −0.499964 0.499964i
\(619\) 46.5004 + 12.4597i 1.86901 + 0.500799i 0.999982 + 0.00603119i \(0.00191980\pi\)
0.869025 + 0.494768i \(0.164747\pi\)
\(620\) 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 −0.999454 0.0330448i \(-0.989480\pi\)
0.882075 + 0.471109i \(0.156146\pi\)
\(632\) 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 0.795283 0.606239i \(-0.207322\pi\)
−0.127377 + 0.991854i \(0.540656\pi\)
\(642\) −23.5020 + 6.29733i −0.927548 + 0.248536i
\(643\) 9.35047 34.8964i 0.368747 1.37618i −0.493524 0.869732i \(-0.664291\pi\)
0.862270 0.506449i \(-0.169042\pi\)
\(644\) 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 \(-0.463669\pi\)
0.113891 + 0.993493i \(0.463669\pi\)
\(648\) 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 −0.965434 0.260648i \(-0.916064\pi\)
0.256989 0.966414i \(-0.417270\pi\)
\(654\) 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 0.590292 0.807190i \(-0.299013\pi\)
−0.994193 + 0.107613i \(0.965679\pi\)
\(660\) −50.9796 + 29.4331i −1.98438 + 1.14568i
\(661\) −23.9986 + 23.9986i −0.933438 + 0.933438i −0.997919 0.0644808i \(-0.979461\pi\)
0.0644808 + 0.997919i \(0.479461\pi\)
\(662\) 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 −0.386377 0.922341i \(-0.626274\pi\)
−0.991959 + 0.126558i \(0.959607\pi\)
\(674\) −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 −0.999979 0.00652270i \(-0.997924\pi\)
−0.505638 0.862746i \(-0.668743\pi\)
\(678\) −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 −0.947276 0.320419i \(-0.896176\pi\)
−0.660156 + 0.751129i \(0.729510\pi\)
\(684\) −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 0.775209 + 0.631705i \(0.217645\pi\)
−0.987203 + 0.159468i \(0.949022\pi\)
\(692\) −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 \(-0.947020\pi\)
0.986180 0.165675i \(-0.0529803\pi\)
\(702\) 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 −0.990754 0.135672i \(-0.956681\pi\)
−0.135672 0.990754i \(-0.543319\pi\)
\(710\) −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 \(-0.466699\pi\)
0.104426 + 0.994533i \(0.466699\pi\)
\(720\) 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 \(-0.702364\pi\)
−0.593778 + 0.804629i \(0.702364\pi\)
\(728\) 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 \(-0.577949\pi\)
0.275120 + 0.961410i \(0.411282\pi\)
\(734\) −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 0.811920 0.583769i \(-0.198423\pi\)
−0.583769 + 0.811920i \(0.698423\pi\)
\(740\) 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 −0.885510 0.464620i \(-0.846191\pi\)
0.534564 0.845128i \(-0.320476\pi\)
\(744\) 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 −0.290855 0.956767i \(-0.593940\pi\)
0.683157 + 0.730271i \(0.260606\pi\)
\(752\) 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 −0.568582 0.822626i \(-0.692508\pi\)
0.996707 + 0.0810934i \(0.0258412\pi\)
\(758\) 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 \(-0.671045\pi\)
0.859066 + 0.511864i \(0.171045\pi\)
\(762\) −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 \(-0.771530\pi\)
−0.323512 + 0.946224i \(0.604864\pi\)
\(770\) 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 \(-0.466339\pi\)
0.588617 + 0.808412i \(0.299673\pi\)
\(774\) 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
\(781\)