Properties

Label 280.2.h.b.251.9
Level $280$
Weight $2$
Character 280.251
Analytic conductor $2.236$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - x^{15} - 2 x^{12} + 6 x^{11} - 12 x^{9} + 8 x^{8} - 24 x^{7} + 48 x^{5} - 32 x^{4} - 128 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.9
Root \(0.244064 + 1.39299i\) of defining polynomial
Character \(\chi\) \(=\) 280.251
Dual form 280.2.h.b.251.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.244064 - 1.39299i) q^{2} +1.68420i q^{3} +(-1.88087 - 0.679959i) q^{4} +1.00000 q^{5} +(2.34608 + 0.411052i) q^{6} +(0.695780 - 2.55262i) q^{7} +(-1.40623 + 2.45408i) q^{8} +0.163484 q^{9} +O(q^{10})\) \(q+(0.244064 - 1.39299i) q^{2} +1.68420i q^{3} +(-1.88087 - 0.679959i) q^{4} +1.00000 q^{5} +(2.34608 + 0.411052i) q^{6} +(0.695780 - 2.55262i) q^{7} +(-1.40623 + 2.45408i) q^{8} +0.163484 q^{9} +(0.244064 - 1.39299i) q^{10} +1.45385 q^{11} +(1.14518 - 3.16775i) q^{12} +5.12034 q^{13} +(-3.38598 - 1.59222i) q^{14} +1.68420i q^{15} +(3.07531 + 2.55782i) q^{16} -0.313877i q^{17} +(0.0399006 - 0.227732i) q^{18} -0.250100i q^{19} +(-1.88087 - 0.679959i) q^{20} +(4.29912 + 1.17183i) q^{21} +(0.354833 - 2.02521i) q^{22} -4.27001i q^{23} +(-4.13315 - 2.36837i) q^{24} +1.00000 q^{25} +(1.24969 - 7.13260i) q^{26} +5.32793i q^{27} +(-3.04435 + 4.32804i) q^{28} +1.63961i q^{29} +(2.34608 + 0.411052i) q^{30} -8.96308 q^{31} +(4.31361 - 3.65962i) q^{32} +2.44857i q^{33} +(-0.437228 - 0.0766060i) q^{34} +(0.695780 - 2.55262i) q^{35} +(-0.307492 - 0.111163i) q^{36} -3.47842i q^{37} +(-0.348388 - 0.0610404i) q^{38} +8.62365i q^{39} +(-1.40623 + 2.45408i) q^{40} +9.88374i q^{41} +(2.68161 - 5.70265i) q^{42} -8.65164 q^{43} +(-2.73450 - 0.988561i) q^{44} +0.163484 q^{45} +(-5.94810 - 1.04216i) q^{46} -7.77853 q^{47} +(-4.30788 + 5.17943i) q^{48} +(-6.03178 - 3.55213i) q^{49} +(0.244064 - 1.39299i) q^{50} +0.528630 q^{51} +(-9.63067 - 3.48162i) q^{52} -1.90687i q^{53} +(7.42177 + 1.30036i) q^{54} +1.45385 q^{55} +(5.28592 + 5.29708i) q^{56} +0.421218 q^{57} +(2.28396 + 0.400169i) q^{58} +7.73295i q^{59} +(1.14518 - 3.16775i) q^{60} +0.415877 q^{61} +(-2.18757 + 12.4855i) q^{62} +(0.113749 - 0.417313i) q^{63} +(-4.04503 - 6.90201i) q^{64} +5.12034 q^{65} +(3.41085 + 0.597609i) q^{66} +15.2878 q^{67} +(-0.213423 + 0.590360i) q^{68} +7.19153 q^{69} +(-3.38598 - 1.59222i) q^{70} +1.50413i q^{71} +(-0.229896 + 0.401203i) q^{72} -10.7072i q^{73} +(-4.84541 - 0.848956i) q^{74} +1.68420i q^{75} +(-0.170058 + 0.470405i) q^{76} +(1.01156 - 3.71114i) q^{77} +(12.0127 + 2.10472i) q^{78} +9.36521i q^{79} +(3.07531 + 2.55782i) q^{80} -8.48282 q^{81} +(13.7680 + 2.41226i) q^{82} +3.45276i q^{83} +(-7.28927 - 5.12728i) q^{84} -0.313877i q^{85} +(-2.11155 + 12.0517i) q^{86} -2.76142 q^{87} +(-2.04445 + 3.56788i) q^{88} +9.12705i q^{89} +(0.0399006 - 0.227732i) q^{90} +(3.56263 - 13.0703i) q^{91} +(-2.90343 + 8.03131i) q^{92} -15.0956i q^{93} +(-1.89846 + 10.8354i) q^{94} -0.250100i q^{95} +(6.16351 + 7.26496i) q^{96} -16.5442i q^{97} +(-6.42024 + 7.53529i) q^{98} +0.237682 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + O(q^{10}) \) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + q^{10} - 4q^{11} + 14q^{12} - q^{14} + 9q^{16} - 15q^{18} + q^{20} - 4q^{21} + 6q^{22} + 22q^{24} + 16q^{25} - 20q^{26} + q^{28} - 16q^{31} - 19q^{32} - 14q^{34} + 15q^{36} - 30q^{38} + q^{40} + 44q^{42} - 4q^{43} - 20q^{44} - 16q^{45} + 6q^{46} - 34q^{48} - 8q^{49} + q^{50} - 40q^{51} - 38q^{52} + 26q^{54} - 4q^{55} + 33q^{56} - 16q^{57} + 18q^{58} + 14q^{60} - 8q^{61} + 28q^{62} + 28q^{63} - 23q^{64} + 46q^{66} + 20q^{67} + 12q^{68} - 40q^{69} - q^{70} - 13q^{72} - 28q^{74} + 34q^{76} - 4q^{77} - 6q^{78} + 9q^{80} + 24q^{81} - 16q^{82} - 42q^{84} - 24q^{86} + 72q^{87} - 44q^{88} - 15q^{90} - 32q^{91} - 30q^{92} - 58q^{94} - 30q^{96} + 5q^{98} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.244064 1.39299i 0.172579 0.984996i
\(3\) 1.68420i 0.972371i 0.873856 + 0.486185i \(0.161612\pi\)
−0.873856 + 0.486185i \(0.838388\pi\)
\(4\) −1.88087 0.679959i −0.940433 0.339980i
\(5\) 1.00000 0.447214
\(6\) 2.34608 + 0.411052i 0.957781 + 0.167811i
\(7\) 0.695780 2.55262i 0.262980 0.964801i
\(8\) −1.40623 + 2.45408i −0.497178 + 0.867649i
\(9\) 0.163484 0.0544947
\(10\) 0.244064 1.39299i 0.0771798 0.440503i
\(11\) 1.45385 0.438353 0.219177 0.975685i \(-0.429663\pi\)
0.219177 + 0.975685i \(0.429663\pi\)
\(12\) 1.14518 3.16775i 0.330586 0.914450i
\(13\) 5.12034 1.42013 0.710063 0.704138i \(-0.248666\pi\)
0.710063 + 0.704138i \(0.248666\pi\)
\(14\) −3.38598 1.59222i −0.904940 0.425539i
\(15\) 1.68420i 0.434858i
\(16\) 3.07531 + 2.55782i 0.768828 + 0.639456i
\(17\) 0.313877i 0.0761263i −0.999275 0.0380631i \(-0.987881\pi\)
0.999275 0.0380631i \(-0.0121188\pi\)
\(18\) 0.0399006 0.227732i 0.00940466 0.0536770i
\(19\) 0.250100i 0.0573769i −0.999588 0.0286884i \(-0.990867\pi\)
0.999588 0.0286884i \(-0.00913307\pi\)
\(20\) −1.88087 0.679959i −0.420574 0.152044i
\(21\) 4.29912 + 1.17183i 0.938145 + 0.255714i
\(22\) 0.354833 2.02521i 0.0756507 0.431776i
\(23\) 4.27001i 0.890358i −0.895442 0.445179i \(-0.853140\pi\)
0.895442 0.445179i \(-0.146860\pi\)
\(24\) −4.13315 2.36837i −0.843676 0.483441i
\(25\) 1.00000 0.200000
\(26\) 1.24969 7.13260i 0.245084 1.39882i
\(27\) 5.32793i 1.02536i
\(28\) −3.04435 + 4.32804i −0.575328 + 0.817923i
\(29\) 1.63961i 0.304468i 0.988345 + 0.152234i \(0.0486467\pi\)
−0.988345 + 0.152234i \(0.951353\pi\)
\(30\) 2.34608 + 0.411052i 0.428333 + 0.0750474i
\(31\) −8.96308 −1.60982 −0.804909 0.593399i \(-0.797786\pi\)
−0.804909 + 0.593399i \(0.797786\pi\)
\(32\) 4.31361 3.65962i 0.762545 0.646935i
\(33\) 2.44857i 0.426242i
\(34\) −0.437228 0.0766060i −0.0749841 0.0131378i
\(35\) 0.695780 2.55262i 0.117608 0.431472i
\(36\) −0.307492 0.111163i −0.0512486 0.0185271i
\(37\) 3.47842i 0.571848i −0.958252 0.285924i \(-0.907699\pi\)
0.958252 0.285924i \(-0.0923005\pi\)
\(38\) −0.348388 0.0610404i −0.0565160 0.00990206i
\(39\) 8.62365i 1.38089i
\(40\) −1.40623 + 2.45408i −0.222345 + 0.388024i
\(41\) 9.88374i 1.54358i 0.635877 + 0.771790i \(0.280638\pi\)
−0.635877 + 0.771790i \(0.719362\pi\)
\(42\) 2.68161 5.70265i 0.413782 0.879937i
\(43\) −8.65164 −1.31936 −0.659681 0.751545i \(-0.729309\pi\)
−0.659681 + 0.751545i \(0.729309\pi\)
\(44\) −2.73450 0.988561i −0.412242 0.149031i
\(45\) 0.163484 0.0243708
\(46\) −5.94810 1.04216i −0.876999 0.153657i
\(47\) −7.77853 −1.13461 −0.567307 0.823506i \(-0.692015\pi\)
−0.567307 + 0.823506i \(0.692015\pi\)
\(48\) −4.30788 + 5.17943i −0.621789 + 0.747586i
\(49\) −6.03178 3.55213i −0.861683 0.507447i
\(50\) 0.244064 1.39299i 0.0345159 0.196999i
\(51\) 0.528630 0.0740230
\(52\) −9.63067 3.48162i −1.33553 0.482814i
\(53\) 1.90687i 0.261929i −0.991387 0.130965i \(-0.958193\pi\)
0.991387 0.130965i \(-0.0418075\pi\)
\(54\) 7.42177 + 1.30036i 1.00998 + 0.176956i
\(55\) 1.45385 0.196038
\(56\) 5.28592 + 5.29708i 0.706361 + 0.707852i
\(57\) 0.421218 0.0557916
\(58\) 2.28396 + 0.400169i 0.299899 + 0.0525448i
\(59\) 7.73295i 1.00674i 0.864070 + 0.503372i \(0.167907\pi\)
−0.864070 + 0.503372i \(0.832093\pi\)
\(60\) 1.14518 3.16775i 0.147843 0.408954i
\(61\) 0.415877 0.0532475 0.0266238 0.999646i \(-0.491524\pi\)
0.0266238 + 0.999646i \(0.491524\pi\)
\(62\) −2.18757 + 12.4855i −0.277821 + 1.58566i
\(63\) 0.113749 0.417313i 0.0143310 0.0525766i
\(64\) −4.04503 6.90201i −0.505629 0.862751i
\(65\) 5.12034 0.635100
\(66\) 3.41085 + 0.597609i 0.419847 + 0.0735606i
\(67\) 15.2878 1.86770 0.933848 0.357670i \(-0.116429\pi\)
0.933848 + 0.357670i \(0.116429\pi\)
\(68\) −0.213423 + 0.590360i −0.0258814 + 0.0715916i
\(69\) 7.19153 0.865759
\(70\) −3.38598 1.59222i −0.404702 0.190307i
\(71\) 1.50413i 0.178507i 0.996009 + 0.0892537i \(0.0284482\pi\)
−0.996009 + 0.0892537i \(0.971552\pi\)
\(72\) −0.229896 + 0.401203i −0.0270936 + 0.0472823i
\(73\) 10.7072i 1.25318i −0.779349 0.626590i \(-0.784450\pi\)
0.779349 0.626590i \(-0.215550\pi\)
\(74\) −4.84541 0.848956i −0.563268 0.0986892i
\(75\) 1.68420i 0.194474i
\(76\) −0.170058 + 0.470405i −0.0195070 + 0.0539591i
\(77\) 1.01156 3.71114i 0.115278 0.422924i
\(78\) 12.0127 + 2.10472i 1.36017 + 0.238313i
\(79\) 9.36521i 1.05367i 0.849968 + 0.526834i \(0.176621\pi\)
−0.849968 + 0.526834i \(0.823379\pi\)
\(80\) 3.07531 + 2.55782i 0.343830 + 0.285973i
\(81\) −8.48282 −0.942536
\(82\) 13.7680 + 2.41226i 1.52042 + 0.266390i
\(83\) 3.45276i 0.378989i 0.981882 + 0.189495i \(0.0606850\pi\)
−0.981882 + 0.189495i \(0.939315\pi\)
\(84\) −7.28927 5.12728i −0.795324 0.559432i
\(85\) 0.313877i 0.0340447i
\(86\) −2.11155 + 12.0517i −0.227695 + 1.29957i
\(87\) −2.76142 −0.296055
\(88\) −2.04445 + 3.56788i −0.217940 + 0.380337i
\(89\) 9.12705i 0.967466i 0.875216 + 0.483733i \(0.160719\pi\)
−0.875216 + 0.483733i \(0.839281\pi\)
\(90\) 0.0399006 0.227732i 0.00420589 0.0240051i
\(91\) 3.56263 13.0703i 0.373465 1.37014i
\(92\) −2.90343 + 8.03131i −0.302704 + 0.837322i
\(93\) 15.0956i 1.56534i
\(94\) −1.89846 + 10.8354i −0.195811 + 1.11759i
\(95\) 0.250100i 0.0256597i
\(96\) 6.16351 + 7.26496i 0.629061 + 0.741477i
\(97\) 16.5442i 1.67981i −0.542732 0.839906i \(-0.682610\pi\)
0.542732 0.839906i \(-0.317390\pi\)
\(98\) −6.42024 + 7.53529i −0.648542 + 0.761179i
\(99\) 0.237682 0.0238879
\(100\) −1.88087 0.679959i −0.188087 0.0679959i
\(101\) −11.1440 −1.10887 −0.554437 0.832226i \(-0.687066\pi\)
−0.554437 + 0.832226i \(0.687066\pi\)
\(102\) 0.129019 0.736378i 0.0127748 0.0729123i
\(103\) −11.5479 −1.13785 −0.568923 0.822391i \(-0.692640\pi\)
−0.568923 + 0.822391i \(0.692640\pi\)
\(104\) −7.20038 + 12.5657i −0.706055 + 1.23217i
\(105\) 4.29912 + 1.17183i 0.419551 + 0.114359i
\(106\) −2.65627 0.465399i −0.257999 0.0452036i
\(107\) −3.37404 −0.326181 −0.163091 0.986611i \(-0.552146\pi\)
−0.163091 + 0.986611i \(0.552146\pi\)
\(108\) 3.62277 10.0211i 0.348602 0.964282i
\(109\) 12.6125i 1.20805i 0.796964 + 0.604027i \(0.206438\pi\)
−0.796964 + 0.604027i \(0.793562\pi\)
\(110\) 0.354833 2.02521i 0.0338320 0.193096i
\(111\) 5.85834 0.556049
\(112\) 8.66890 6.07043i 0.819134 0.573602i
\(113\) 13.5643 1.27602 0.638009 0.770029i \(-0.279758\pi\)
0.638009 + 0.770029i \(0.279758\pi\)
\(114\) 0.102804 0.586754i 0.00962848 0.0549545i
\(115\) 4.27001i 0.398180i
\(116\) 1.11487 3.08388i 0.103513 0.286331i
\(117\) 0.837094 0.0773894
\(118\) 10.7720 + 1.88733i 0.991639 + 0.173743i
\(119\) −0.801209 0.218389i −0.0734467 0.0200197i
\(120\) −4.13315 2.36837i −0.377304 0.216201i
\(121\) −8.88631 −0.807846
\(122\) 0.101500 0.579314i 0.00918942 0.0524486i
\(123\) −16.6461 −1.50093
\(124\) 16.8584 + 6.09453i 1.51392 + 0.547305i
\(125\) 1.00000 0.0894427
\(126\) −0.553553 0.260303i −0.0493144 0.0231896i
\(127\) 2.17011i 0.192566i −0.995354 0.0962832i \(-0.969305\pi\)
0.995354 0.0962832i \(-0.0306954\pi\)
\(128\) −10.6017 + 3.95017i −0.937067 + 0.349149i
\(129\) 14.5711i 1.28291i
\(130\) 1.24969 7.13260i 0.109605 0.625571i
\(131\) 8.82257i 0.770832i −0.922743 0.385416i \(-0.874058\pi\)
0.922743 0.385416i \(-0.125942\pi\)
\(132\) 1.66493 4.60544i 0.144914 0.400852i
\(133\) −0.638411 0.174015i −0.0553573 0.0150890i
\(134\) 3.73119 21.2958i 0.322326 1.83967i
\(135\) 5.32793i 0.458555i
\(136\) 0.770279 + 0.441383i 0.0660509 + 0.0378483i
\(137\) 0.361903 0.0309195 0.0154597 0.999880i \(-0.495079\pi\)
0.0154597 + 0.999880i \(0.495079\pi\)
\(138\) 1.75519 10.0178i 0.149412 0.852768i
\(139\) 8.49740i 0.720740i −0.932809 0.360370i \(-0.882650\pi\)
0.932809 0.360370i \(-0.117350\pi\)
\(140\) −3.04435 + 4.32804i −0.257295 + 0.365786i
\(141\) 13.1006i 1.10327i
\(142\) 2.09525 + 0.367104i 0.175829 + 0.0308067i
\(143\) 7.44422 0.622517
\(144\) 0.502764 + 0.418164i 0.0418970 + 0.0348470i
\(145\) 1.63961i 0.136162i
\(146\) −14.9150 2.61323i −1.23438 0.216273i
\(147\) 5.98248 10.1587i 0.493427 0.837875i
\(148\) −2.36518 + 6.54243i −0.194417 + 0.537785i
\(149\) 14.7688i 1.20991i 0.796260 + 0.604955i \(0.206809\pi\)
−0.796260 + 0.604955i \(0.793191\pi\)
\(150\) 2.34608 + 0.411052i 0.191556 + 0.0335622i
\(151\) 17.6833i 1.43905i −0.694468 0.719523i \(-0.744360\pi\)
0.694468 0.719523i \(-0.255640\pi\)
\(152\) 0.613766 + 0.351698i 0.0497830 + 0.0285265i
\(153\) 0.0513138i 0.00414848i
\(154\) −4.92271 2.31486i −0.396684 0.186536i
\(155\) −8.96308 −0.719932
\(156\) 5.86373 16.2199i 0.469475 1.29863i
\(157\) 0.628228 0.0501380 0.0250690 0.999686i \(-0.492019\pi\)
0.0250690 + 0.999686i \(0.492019\pi\)
\(158\) 13.0457 + 2.28571i 1.03786 + 0.181841i
\(159\) 3.21155 0.254693
\(160\) 4.31361 3.65962i 0.341021 0.289318i
\(161\) −10.8997 2.97099i −0.859019 0.234147i
\(162\) −2.07035 + 11.8165i −0.162662 + 0.928393i
\(163\) −15.7162 −1.23099 −0.615493 0.788142i \(-0.711043\pi\)
−0.615493 + 0.788142i \(0.711043\pi\)
\(164\) 6.72054 18.5900i 0.524786 1.45163i
\(165\) 2.44857i 0.190621i
\(166\) 4.80967 + 0.842693i 0.373303 + 0.0654057i
\(167\) 18.6731 1.44497 0.722485 0.691386i \(-0.243000\pi\)
0.722485 + 0.691386i \(0.243000\pi\)
\(168\) −8.92132 + 8.90252i −0.688295 + 0.686845i
\(169\) 13.2179 1.01676
\(170\) −0.437228 0.0766060i −0.0335339 0.00587541i
\(171\) 0.0408874i 0.00312674i
\(172\) 16.2726 + 5.88276i 1.24077 + 0.448557i
\(173\) −24.7373 −1.88074 −0.940372 0.340147i \(-0.889523\pi\)
−0.940372 + 0.340147i \(0.889523\pi\)
\(174\) −0.673963 + 3.84664i −0.0510930 + 0.291613i
\(175\) 0.695780 2.55262i 0.0525960 0.192960i
\(176\) 4.47105 + 3.71870i 0.337018 + 0.280308i
\(177\) −13.0238 −0.978929
\(178\) 12.7139 + 2.22759i 0.952950 + 0.166965i
\(179\) 6.86464 0.513088 0.256544 0.966533i \(-0.417416\pi\)
0.256544 + 0.966533i \(0.417416\pi\)
\(180\) −0.307492 0.111163i −0.0229191 0.00828557i
\(181\) 13.8072 1.02628 0.513141 0.858304i \(-0.328482\pi\)
0.513141 + 0.858304i \(0.328482\pi\)
\(182\) −17.3373 8.15271i −1.28513 0.604319i
\(183\) 0.700418i 0.0517764i
\(184\) 10.4789 + 6.00462i 0.772518 + 0.442666i
\(185\) 3.47842i 0.255738i
\(186\) −21.0281 3.68429i −1.54185 0.270145i
\(187\) 0.456331i 0.0333702i
\(188\) 14.6304 + 5.28908i 1.06703 + 0.385746i
\(189\) 13.6002 + 3.70707i 0.989269 + 0.269649i
\(190\) −0.348388 0.0610404i −0.0252747 0.00442834i
\(191\) 6.79373i 0.491577i −0.969324 0.245788i \(-0.920953\pi\)
0.969324 0.245788i \(-0.0790468\pi\)
\(192\) 11.6243 6.81262i 0.838914 0.491659i
\(193\) −6.94798 −0.500127 −0.250063 0.968229i \(-0.580451\pi\)
−0.250063 + 0.968229i \(0.580451\pi\)
\(194\) −23.0460 4.03785i −1.65461 0.289901i
\(195\) 8.62365i 0.617553i
\(196\) 8.92966 + 10.7824i 0.637833 + 0.770175i
\(197\) 25.0020i 1.78132i 0.454670 + 0.890660i \(0.349757\pi\)
−0.454670 + 0.890660i \(0.650243\pi\)
\(198\) 0.0580096 0.331090i 0.00412256 0.0235295i
\(199\) 8.86022 0.628084 0.314042 0.949409i \(-0.398317\pi\)
0.314042 + 0.949409i \(0.398317\pi\)
\(200\) −1.40623 + 2.45408i −0.0994355 + 0.173530i
\(201\) 25.7476i 1.81609i
\(202\) −2.71986 + 15.5236i −0.191369 + 1.09224i
\(203\) 4.18530 + 1.14081i 0.293751 + 0.0800689i
\(204\) −0.994282 0.359447i −0.0696136 0.0251663i
\(205\) 9.88374i 0.690310i
\(206\) −2.81842 + 16.0861i −0.196369 + 1.12077i
\(207\) 0.698079i 0.0485198i
\(208\) 15.7466 + 13.0969i 1.09183 + 0.908109i
\(209\) 0.363609i 0.0251514i
\(210\) 2.68161 5.70265i 0.185049 0.393520i
\(211\) 13.6470 0.939501 0.469751 0.882799i \(-0.344344\pi\)
0.469751 + 0.882799i \(0.344344\pi\)
\(212\) −1.29660 + 3.58657i −0.0890507 + 0.246327i
\(213\) −2.53325 −0.173576
\(214\) −0.823483 + 4.70002i −0.0562921 + 0.321287i
\(215\) −8.65164 −0.590037
\(216\) −13.0752 7.49230i −0.889652 0.509786i
\(217\) −6.23634 + 22.8794i −0.423350 + 1.55315i
\(218\) 17.5691 + 3.07825i 1.18993 + 0.208485i
\(219\) 18.0330 1.21856
\(220\) −2.73450 0.988561i −0.184360 0.0666488i
\(221\) 1.60716i 0.108109i
\(222\) 1.42981 8.16063i 0.0959625 0.547705i
\(223\) 7.67172 0.513737 0.256868 0.966446i \(-0.417309\pi\)
0.256868 + 0.966446i \(0.417309\pi\)
\(224\) −6.34030 13.5573i −0.423629 0.905836i
\(225\) 0.163484 0.0108989
\(226\) 3.31055 18.8949i 0.220214 1.25687i
\(227\) 18.4879i 1.22708i 0.789662 + 0.613542i \(0.210256\pi\)
−0.789662 + 0.613542i \(0.789744\pi\)
\(228\) −0.792254 0.286411i −0.0524683 0.0189680i
\(229\) −22.6715 −1.49817 −0.749087 0.662472i \(-0.769507\pi\)
−0.749087 + 0.662472i \(0.769507\pi\)
\(230\) −5.94810 1.04216i −0.392206 0.0687177i
\(231\) 6.25029 + 1.70367i 0.411239 + 0.112093i
\(232\) −4.02373 2.30567i −0.264171 0.151375i
\(233\) 25.4680 1.66847 0.834234 0.551411i \(-0.185910\pi\)
0.834234 + 0.551411i \(0.185910\pi\)
\(234\) 0.204305 1.16607i 0.0133558 0.0762282i
\(235\) −7.77853 −0.507415
\(236\) 5.25809 14.5446i 0.342273 0.946775i
\(237\) −15.7728 −1.02456
\(238\) −0.499761 + 1.06278i −0.0323947 + 0.0688897i
\(239\) 17.5044i 1.13227i −0.824314 0.566134i \(-0.808439\pi\)
0.824314 0.566134i \(-0.191561\pi\)
\(240\) −4.30788 + 5.17943i −0.278072 + 0.334330i
\(241\) 20.7733i 1.33813i −0.743206 0.669063i \(-0.766696\pi\)
0.743206 0.669063i \(-0.233304\pi\)
\(242\) −2.16883 + 12.3786i −0.139418 + 0.795725i
\(243\) 1.69705i 0.108866i
\(244\) −0.782208 0.282779i −0.0500757 0.0181031i
\(245\) −6.03178 3.55213i −0.385356 0.226937i
\(246\) −4.06272 + 23.1880i −0.259030 + 1.47841i
\(247\) 1.28060i 0.0814825i
\(248\) 12.6042 21.9961i 0.800365 1.39676i
\(249\) −5.81512 −0.368518
\(250\) 0.244064 1.39299i 0.0154360 0.0881007i
\(251\) 18.9279i 1.19472i 0.801973 + 0.597361i \(0.203784\pi\)
−0.801973 + 0.597361i \(0.796216\pi\)
\(252\) −0.497703 + 0.707566i −0.0313523 + 0.0445725i
\(253\) 6.20797i 0.390292i
\(254\) −3.02295 0.529646i −0.189677 0.0332330i
\(255\) 0.528630 0.0331041
\(256\) 2.91507 + 15.7322i 0.182192 + 0.983263i
\(257\) 4.31841i 0.269375i 0.990888 + 0.134688i \(0.0430031\pi\)
−0.990888 + 0.134688i \(0.956997\pi\)
\(258\) −20.2974 3.55627i −1.26366 0.221404i
\(259\) −8.87909 2.42021i −0.551720 0.150385i
\(260\) −9.63067 3.48162i −0.597269 0.215921i
\(261\) 0.268050i 0.0165919i
\(262\) −12.2898 2.15327i −0.759266 0.133030i
\(263\) 1.43331i 0.0883814i 0.999023 + 0.0441907i \(0.0140709\pi\)
−0.999023 + 0.0441907i \(0.985929\pi\)
\(264\) −6.00900 3.44326i −0.369828 0.211918i
\(265\) 1.90687i 0.117138i
\(266\) −0.398215 + 0.846833i −0.0244161 + 0.0519226i
\(267\) −15.3717 −0.940736
\(268\) −28.7542 10.3951i −1.75644 0.634979i
\(269\) −12.1457 −0.740537 −0.370268 0.928925i \(-0.620734\pi\)
−0.370268 + 0.928925i \(0.620734\pi\)
\(270\) 7.42177 + 1.30036i 0.451675 + 0.0791371i
\(271\) −6.48716 −0.394067 −0.197034 0.980397i \(-0.563131\pi\)
−0.197034 + 0.980397i \(0.563131\pi\)
\(272\) 0.802841 0.965268i 0.0486794 0.0585280i
\(273\) 22.0129 + 6.00017i 1.33228 + 0.363147i
\(274\) 0.0883275 0.504129i 0.00533606 0.0304555i
\(275\) 1.45385 0.0876707
\(276\) −13.5263 4.88995i −0.814188 0.294340i
\(277\) 23.8861i 1.43518i −0.696467 0.717589i \(-0.745246\pi\)
0.696467 0.717589i \(-0.254754\pi\)
\(278\) −11.8368 2.07391i −0.709926 0.124385i
\(279\) −1.46532 −0.0877265
\(280\) 5.28592 + 5.29708i 0.315894 + 0.316561i
\(281\) −14.4015 −0.859120 −0.429560 0.903038i \(-0.641331\pi\)
−0.429560 + 0.903038i \(0.641331\pi\)
\(282\) −18.2490 3.19737i −1.08671 0.190401i
\(283\) 24.0556i 1.42996i 0.699146 + 0.714979i \(0.253564\pi\)
−0.699146 + 0.714979i \(0.746436\pi\)
\(284\) 1.02275 2.82907i 0.0606889 0.167874i
\(285\) 0.421218 0.0249508
\(286\) 1.81687 10.3698i 0.107434 0.613177i
\(287\) 25.2295 + 6.87691i 1.48925 + 0.405931i
\(288\) 0.705206 0.598289i 0.0415547 0.0352545i
\(289\) 16.9015 0.994205
\(290\) 2.28396 + 0.400169i 0.134119 + 0.0234987i
\(291\) 27.8637 1.63340
\(292\) −7.28044 + 20.1387i −0.426055 + 1.17853i
\(293\) −4.78803 −0.279720 −0.139860 0.990171i \(-0.544665\pi\)
−0.139860 + 0.990171i \(0.544665\pi\)
\(294\) −12.6909 10.8129i −0.740148 0.630623i
\(295\) 7.73295i 0.450230i
\(296\) 8.53632 + 4.89146i 0.496163 + 0.284310i
\(297\) 7.74603i 0.449470i
\(298\) 20.5729 + 3.60454i 1.19176 + 0.208805i
\(299\) 21.8639i 1.26442i
\(300\) 1.14518 3.16775i 0.0661173 0.182890i
\(301\) −6.01964 + 22.0844i −0.346966 + 1.27292i
\(302\) −24.6327 4.31586i −1.41745 0.248350i
\(303\) 18.7688i 1.07824i
\(304\) 0.639712 0.769135i 0.0366900 0.0441129i
\(305\) 0.415877 0.0238130
\(306\) −0.0714799 0.0125239i −0.00408623 0.000715942i
\(307\) 23.6121i 1.34762i −0.738907 0.673808i \(-0.764658\pi\)
0.738907 0.673808i \(-0.235342\pi\)
\(308\) −4.42604 + 6.29234i −0.252197 + 0.358539i
\(309\) 19.4489i 1.10641i
\(310\) −2.18757 + 12.4855i −0.124245 + 0.709130i
\(311\) 23.6203 1.33939 0.669693 0.742638i \(-0.266426\pi\)
0.669693 + 0.742638i \(0.266426\pi\)
\(312\) −21.1631 12.1269i −1.19813 0.686548i
\(313\) 20.6514i 1.16728i 0.812011 + 0.583642i \(0.198373\pi\)
−0.812011 + 0.583642i \(0.801627\pi\)
\(314\) 0.153328 0.875117i 0.00865278 0.0493857i
\(315\) 0.113749 0.417313i 0.00640903 0.0235130i
\(316\) 6.36796 17.6147i 0.358226 0.990904i
\(317\) 13.1857i 0.740580i 0.928916 + 0.370290i \(0.120742\pi\)
−0.928916 + 0.370290i \(0.879258\pi\)
\(318\) 0.783824 4.47367i 0.0439547 0.250871i
\(319\) 2.38375i 0.133464i
\(320\) −4.04503 6.90201i −0.226124 0.385834i
\(321\) 5.68255i 0.317169i
\(322\) −6.79880 + 14.4581i −0.378882 + 0.805721i
\(323\) −0.0785006 −0.00436789
\(324\) 15.9550 + 5.76797i 0.886391 + 0.320443i
\(325\) 5.12034 0.284025
\(326\) −3.83575 + 21.8926i −0.212443 + 1.21252i
\(327\) −21.2419 −1.17468
\(328\) −24.2555 13.8988i −1.33929 0.767434i
\(329\) −5.41214 + 19.8557i −0.298381 + 1.09468i
\(330\) 3.41085 + 0.597609i 0.187761 + 0.0328973i
\(331\) 4.29166 0.235891 0.117945 0.993020i \(-0.462369\pi\)
0.117945 + 0.993020i \(0.462369\pi\)
\(332\) 2.34773 6.49417i 0.128849 0.356414i
\(333\) 0.568666i 0.0311627i
\(334\) 4.55744 26.0116i 0.249372 1.42329i
\(335\) 15.2878 0.835259
\(336\) 10.2238 + 14.6001i 0.557754 + 0.796503i
\(337\) −23.8194 −1.29752 −0.648762 0.760991i \(-0.724713\pi\)
−0.648762 + 0.760991i \(0.724713\pi\)
\(338\) 3.22601 18.4124i 0.175472 1.00150i
\(339\) 22.8449i 1.24076i
\(340\) −0.213423 + 0.590360i −0.0115745 + 0.0320168i
\(341\) −13.0310 −0.705669
\(342\) −0.0569559 0.00997914i −0.00307982 0.000539610i
\(343\) −13.2640 + 12.9254i −0.716191 + 0.697904i
\(344\) 12.1662 21.2318i 0.655958 1.14474i
\(345\) 7.19153 0.387179
\(346\) −6.03749 + 34.4590i −0.324578 + 1.85253i
\(347\) −1.81968 −0.0976858 −0.0488429 0.998806i \(-0.515553\pi\)
−0.0488429 + 0.998806i \(0.515553\pi\)
\(348\) 5.19386 + 1.87765i 0.278420 + 0.100653i
\(349\) 8.94236 0.478673 0.239337 0.970937i \(-0.423070\pi\)
0.239337 + 0.970937i \(0.423070\pi\)
\(350\) −3.38598 1.59222i −0.180988 0.0851078i
\(351\) 27.2808i 1.45614i
\(352\) 6.27135 5.32055i 0.334264 0.283586i
\(353\) 16.0890i 0.856331i −0.903700 0.428165i \(-0.859160\pi\)
0.903700 0.428165i \(-0.140840\pi\)
\(354\) −3.17864 + 18.1421i −0.168943 + 0.964240i
\(355\) 1.50413i 0.0798310i
\(356\) 6.20603 17.1668i 0.328919 0.909837i
\(357\) 0.367810 1.34939i 0.0194666 0.0714175i
\(358\) 1.67541 9.56241i 0.0885483 0.505389i
\(359\) 10.1838i 0.537481i 0.963213 + 0.268740i \(0.0866073\pi\)
−0.963213 + 0.268740i \(0.913393\pi\)
\(360\) −0.229896 + 0.401203i −0.0121166 + 0.0211453i
\(361\) 18.9374 0.996708
\(362\) 3.36984 19.2334i 0.177115 1.01088i
\(363\) 14.9663i 0.785526i
\(364\) −15.5881 + 22.1610i −0.817039 + 1.16155i
\(365\) 10.7072i 0.560439i
\(366\) 0.975678 + 0.170947i 0.0509995 + 0.00893553i
\(367\) −3.78238 −0.197438 −0.0987192 0.995115i \(-0.531475\pi\)
−0.0987192 + 0.995115i \(0.531475\pi\)
\(368\) 10.9219 13.1316i 0.569345 0.684532i
\(369\) 1.61583i 0.0841169i
\(370\) −4.84541 0.848956i −0.251901 0.0441351i
\(371\) −4.86753 1.32677i −0.252710 0.0688822i
\(372\) −10.2644 + 28.3928i −0.532184 + 1.47210i
\(373\) 2.84339i 0.147225i −0.997287 0.0736127i \(-0.976547\pi\)
0.997287 0.0736127i \(-0.0234529\pi\)
\(374\) −0.635666 0.111374i −0.0328695 0.00575901i
\(375\) 1.68420i 0.0869715i
\(376\) 10.9384 19.0891i 0.564105 0.984447i
\(377\) 8.39535i 0.432383i
\(378\) 8.48324 18.0402i 0.436331 0.927889i
\(379\) 5.22176 0.268224 0.134112 0.990966i \(-0.457182\pi\)
0.134112 + 0.990966i \(0.457182\pi\)
\(380\) −0.170058 + 0.470405i −0.00872379 + 0.0241312i
\(381\) 3.65490 0.187246
\(382\) −9.46362 1.65810i −0.484201 0.0848360i
\(383\) 25.8702 1.32191 0.660953 0.750428i \(-0.270152\pi\)
0.660953 + 0.750428i \(0.270152\pi\)
\(384\) −6.65286 17.8553i −0.339502 0.911177i
\(385\) 1.01156 3.71114i 0.0515540 0.189137i
\(386\) −1.69575 + 9.67850i −0.0863115 + 0.492623i
\(387\) −1.41441 −0.0718983
\(388\) −11.2494 + 31.1175i −0.571102 + 1.57975i
\(389\) 26.1792i 1.32734i −0.748025 0.663670i \(-0.768998\pi\)
0.748025 0.663670i \(-0.231002\pi\)
\(390\) 12.0127 + 2.10472i 0.608287 + 0.106577i
\(391\) −1.34026 −0.0677797
\(392\) 17.1993 9.80736i 0.868695 0.495347i
\(393\) 14.8589 0.749534
\(394\) 34.8277 + 6.10209i 1.75459 + 0.307419i
\(395\) 9.36521i 0.471215i
\(396\) −0.447048 0.161614i −0.0224650 0.00812141i
\(397\) 30.6192 1.53674 0.768368 0.640009i \(-0.221069\pi\)
0.768368 + 0.640009i \(0.221069\pi\)
\(398\) 2.16246 12.3422i 0.108394 0.618660i
\(399\) 0.293075 1.07521i 0.0146721 0.0538278i
\(400\) 3.07531 + 2.55782i 0.153766 + 0.127891i
\(401\) −32.6992 −1.63292 −0.816461 0.577401i \(-0.804067\pi\)
−0.816461 + 0.577401i \(0.804067\pi\)
\(402\) 35.8662 + 6.28406i 1.78884 + 0.313420i
\(403\) −45.8940 −2.28614
\(404\) 20.9604 + 7.57750i 1.04282 + 0.376995i
\(405\) −8.48282 −0.421515
\(406\) 2.61062 5.55167i 0.129563 0.275525i
\(407\) 5.05711i 0.250672i
\(408\) −0.743376 + 1.29730i −0.0368026 + 0.0642259i
\(409\) 15.2212i 0.752642i 0.926489 + 0.376321i \(0.122811\pi\)
−0.926489 + 0.376321i \(0.877189\pi\)
\(410\) 13.7680 + 2.41226i 0.679952 + 0.119133i
\(411\) 0.609516i 0.0300652i
\(412\) 21.7200 + 7.85209i 1.07007 + 0.386845i
\(413\) 19.7393 + 5.38043i 0.971308 + 0.264754i
\(414\) −0.972419 0.170376i −0.0477918 0.00837351i
\(415\) 3.45276i 0.169489i
\(416\) 22.0871 18.7385i 1.08291 0.918730i
\(417\) 14.3113 0.700827
\(418\) −0.506505 0.0887438i −0.0247740 0.00434060i
\(419\) 1.51292i 0.0739111i −0.999317 0.0369555i \(-0.988234\pi\)
0.999317 0.0369555i \(-0.0117660\pi\)
\(420\) −7.28927 5.12728i −0.355680 0.250186i
\(421\) 4.42587i 0.215704i 0.994167 + 0.107852i \(0.0343973\pi\)
−0.994167 + 0.107852i \(0.965603\pi\)
\(422\) 3.33075 19.0103i 0.162138 0.925405i
\(423\) −1.27167 −0.0618305
\(424\) 4.67963 + 2.68151i 0.227263 + 0.130225i
\(425\) 0.313877i 0.0152253i
\(426\) −0.618275 + 3.52880i −0.0299555 + 0.170971i
\(427\) 0.289359 1.06158i 0.0140030 0.0513733i
\(428\) 6.34612 + 2.29421i 0.306751 + 0.110895i
\(429\) 12.5375i 0.605318i
\(430\) −2.11155 + 12.0517i −0.101828 + 0.581184i
\(431\) 15.7807i 0.760128i −0.924960 0.380064i \(-0.875902\pi\)
0.924960 0.380064i \(-0.124098\pi\)
\(432\) −13.6279 + 16.3850i −0.655673 + 0.788325i
\(433\) 38.5048i 1.85042i −0.379452 0.925211i \(-0.623888\pi\)
0.379452 0.925211i \(-0.376112\pi\)
\(434\) 30.3488 + 14.2712i 1.45679 + 0.685040i
\(435\) −2.76142 −0.132400
\(436\) 8.57596 23.7223i 0.410714 1.13609i
\(437\) −1.06793 −0.0510860
\(438\) 4.40120 25.1198i 0.210297 1.20027i
\(439\) 8.16215 0.389558 0.194779 0.980847i \(-0.437601\pi\)
0.194779 + 0.980847i \(0.437601\pi\)
\(440\) −2.04445 + 3.56788i −0.0974655 + 0.170092i
\(441\) −0.986100 0.580717i −0.0469572 0.0276532i
\(442\) −2.23876 0.392249i −0.106487 0.0186574i
\(443\) 14.4962 0.688735 0.344368 0.938835i \(-0.388093\pi\)
0.344368 + 0.938835i \(0.388093\pi\)
\(444\) −11.0187 3.98343i −0.522926 0.189045i
\(445\) 9.12705i 0.432664i
\(446\) 1.87239 10.6867i 0.0886603 0.506028i
\(447\) −24.8736 −1.17648
\(448\) −20.4327 + 5.52316i −0.965354 + 0.260945i
\(449\) −26.2203 −1.23741 −0.618705 0.785623i \(-0.712342\pi\)
−0.618705 + 0.785623i \(0.712342\pi\)
\(450\) 0.0399006 0.227732i 0.00188093 0.0107354i
\(451\) 14.3695i 0.676634i
\(452\) −25.5126 9.22315i −1.20001 0.433820i
\(453\) 29.7821 1.39929
\(454\) 25.7535 + 4.51222i 1.20867 + 0.211769i
\(455\) 3.56263 13.0703i 0.167019 0.612745i
\(456\) −0.592329 + 1.03370i −0.0277384 + 0.0484075i
\(457\) −10.8518 −0.507624 −0.253812 0.967254i \(-0.581684\pi\)
−0.253812 + 0.967254i \(0.581684\pi\)
\(458\) −5.53329 + 31.5812i −0.258554 + 1.47569i
\(459\) 1.67231 0.0780568
\(460\) −2.90343 + 8.03131i −0.135373 + 0.374462i
\(461\) −10.9727 −0.511049 −0.255525 0.966803i \(-0.582248\pi\)
−0.255525 + 0.966803i \(0.582248\pi\)
\(462\) 3.89867 8.29081i 0.181383 0.385724i
\(463\) 12.8266i 0.596102i 0.954550 + 0.298051i \(0.0963365\pi\)
−0.954550 + 0.298051i \(0.903663\pi\)
\(464\) −4.19383 + 5.04230i −0.194694 + 0.234083i
\(465\) 15.0956i 0.700041i
\(466\) 6.21583 35.4768i 0.287943 1.64343i
\(467\) 27.2475i 1.26087i −0.776244 0.630433i \(-0.782878\pi\)
0.776244 0.630433i \(-0.217122\pi\)
\(468\) −1.57446 0.569190i −0.0727795 0.0263108i
\(469\) 10.6369 39.0239i 0.491167 1.80196i
\(470\) −1.89846 + 10.8354i −0.0875693 + 0.499802i
\(471\) 1.05806i 0.0487527i
\(472\) −18.9773 10.8743i −0.873500 0.500531i
\(473\) −12.5782 −0.578347
\(474\) −3.84958 + 21.9715i −0.176817 + 1.00918i
\(475\) 0.250100i 0.0114754i
\(476\) 1.35847 + 0.955550i 0.0622654 + 0.0437976i
\(477\) 0.311744i 0.0142738i
\(478\) −24.3836 4.27220i −1.11528 0.195406i
\(479\) −5.93280 −0.271076 −0.135538 0.990772i \(-0.543276\pi\)
−0.135538 + 0.990772i \(0.543276\pi\)
\(480\) 6.16351 + 7.26496i 0.281325 + 0.331599i
\(481\) 17.8107i 0.812097i
\(482\) −28.9371 5.07002i −1.31805 0.230933i
\(483\) 5.00372 18.3573i 0.227677 0.835285i
\(484\) 16.7140 + 6.04233i 0.759725 + 0.274651i
\(485\) 16.5442i 0.751235i
\(486\) 2.36398 + 0.414189i 0.107232 + 0.0187880i
\(487\) 0.799878i 0.0362459i −0.999836 0.0181230i \(-0.994231\pi\)
0.999836 0.0181230i \(-0.00576903\pi\)
\(488\) −0.584819 + 1.02059i −0.0264735 + 0.0462002i
\(489\) 26.4691i 1.19698i
\(490\) −6.42024 + 7.53529i −0.290037 + 0.340410i
\(491\) 35.4782 1.60111 0.800555 0.599259i \(-0.204538\pi\)
0.800555 + 0.599259i \(0.204538\pi\)
\(492\) 31.3092 + 11.3187i 1.41153 + 0.510287i
\(493\) 0.514635 0.0231780
\(494\) −1.78386 0.312548i −0.0802599 0.0140622i
\(495\) 0.237682 0.0106830
\(496\) −27.5643 22.9260i −1.23767 1.02941i
\(497\) 3.83948 + 1.04654i 0.172224 + 0.0469439i
\(498\) −1.41926 + 8.10043i −0.0635986 + 0.362989i
\(499\) −13.8343 −0.619306 −0.309653 0.950850i \(-0.600213\pi\)
−0.309653 + 0.950850i \(0.600213\pi\)
\(500\) −1.88087 0.679959i −0.0841149 0.0304087i
\(501\) 31.4492i 1.40505i
\(502\) 26.3665 + 4.61963i 1.17680 + 0.206184i
\(503\) −24.9750 −1.11358 −0.556790 0.830653i \(-0.687967\pi\)
−0.556790 + 0.830653i \(0.687967\pi\)
\(504\) 0.864164 + 0.865988i 0.0384929 + 0.0385742i
\(505\) −11.1440 −0.495903
\(506\) −8.64766 1.51514i −0.384436 0.0673562i
\(507\) 22.2615i 0.988668i
\(508\) −1.47559 + 4.08169i −0.0654687 + 0.181096i
\(509\) −6.97858 −0.309320 −0.154660 0.987968i \(-0.549428\pi\)
−0.154660 + 0.987968i \(0.549428\pi\)
\(510\) 0.129019 0.736378i 0.00571308 0.0326074i
\(511\) −27.3314 7.44983i −1.20907 0.329561i
\(512\) 22.6263 0.221009i 0.999952 0.00976731i
\(513\) 1.33251 0.0588320
\(514\) 6.01552 + 1.05397i 0.265333 + 0.0464886i
\(515\) −11.5479 −0.508860
\(516\) −9.90773 + 27.4062i −0.436163 + 1.20649i
\(517\) −11.3088 −0.497362
\(518\) −5.53841 + 11.7778i −0.243344 + 0.517488i
\(519\) 41.6625i 1.82878i
\(520\) −7.20038 + 12.5657i −0.315758 + 0.551044i
\(521\) 16.4401i 0.720253i −0.932904 0.360126i \(-0.882734\pi\)
0.932904 0.360126i \(-0.117266\pi\)
\(522\) 0.373392 + 0.0654213i 0.0163429 + 0.00286341i
\(523\) 23.0349i 1.00725i −0.863923 0.503624i \(-0.832000\pi\)
0.863923 0.503624i \(-0.168000\pi\)
\(524\) −5.99899 + 16.5941i −0.262067 + 0.724915i
\(525\) 4.29912 + 1.17183i 0.187629 + 0.0511429i
\(526\) 1.99659 + 0.349818i 0.0870553 + 0.0152528i
\(527\) 2.81330i 0.122549i
\(528\) −6.26302 + 7.53013i −0.272563 + 0.327707i
\(529\) 4.76703 0.207262
\(530\) −2.65627 0.465399i −0.115381 0.0202157i
\(531\) 1.26421i 0.0548622i
\(532\) 1.08244 + 0.761392i 0.0469299 + 0.0330105i
\(533\) 50.6081i 2.19208i
\(534\) −3.75169 + 21.4128i −0.162351 + 0.926620i
\(535\) −3.37404 −0.145873
\(536\) −21.4981 + 37.5174i −0.928577 + 1.62050i
\(537\) 11.5614i 0.498911i
\(538\) −2.96433 + 16.9189i −0.127801 + 0.729425i
\(539\) −8.76933 5.16428i −0.377722 0.222441i
\(540\) 3.62277 10.0211i 0.155899 0.431240i
\(541\) 12.6920i 0.545671i −0.962061 0.272835i \(-0.912039\pi\)
0.962061 0.272835i \(-0.0879615\pi\)
\(542\) −1.58328 + 9.03658i −0.0680078 + 0.388154i
\(543\) 23.2540i 0.997926i
\(544\) −1.14867 1.35394i −0.0492488 0.0580497i
\(545\) 12.6125i 0.540258i
\(546\) 13.7308 29.1995i 0.587623 1.24962i
\(547\) 21.0334 0.899321 0.449661 0.893199i \(-0.351545\pi\)
0.449661 + 0.893199i \(0.351545\pi\)
\(548\) −0.680691 0.246079i −0.0290777 0.0105120i
\(549\) 0.0679892 0.00290171
\(550\) 0.354833 2.02521i 0.0151301 0.0863552i
\(551\) 0.410066 0.0174694
\(552\) −10.1130 + 17.6486i −0.430436 + 0.751174i
\(553\) 23.9059 + 6.51613i 1.01658 + 0.277094i
\(554\) −33.2732 5.82974i −1.41364 0.247682i
\(555\) 5.85834 0.248672
\(556\) −5.77789 + 15.9825i −0.245037 + 0.677808i
\(557\) 0.724648i 0.0307043i 0.999882 + 0.0153522i \(0.00488694\pi\)
−0.999882 + 0.0153522i \(0.995113\pi\)
\(558\) −0.357632 + 2.04118i −0.0151398 + 0.0864102i
\(559\) −44.2993 −1.87366
\(560\) 8.66890 6.07043i 0.366328 0.256522i
\(561\) 0.768550 0.0324482
\(562\) −3.51488 + 20.0612i −0.148266 + 0.846230i
\(563\) 8.62465i 0.363486i 0.983346 + 0.181743i \(0.0581739\pi\)
−0.983346 + 0.181743i \(0.941826\pi\)
\(564\) −8.90785 + 24.6404i −0.375088 + 1.03755i
\(565\) 13.5643 0.570653
\(566\) 33.5093 + 5.87111i 1.40850 + 0.246781i
\(567\) −5.90218 + 21.6535i −0.247868 + 0.909360i
\(568\) −3.69126 2.11516i −0.154882 0.0887499i
\(569\) 2.20005 0.0922311 0.0461155 0.998936i \(-0.485316\pi\)
0.0461155 + 0.998936i \(0.485316\pi\)
\(570\) 0.102804 0.586754i 0.00430599 0.0245764i
\(571\) 22.8120 0.954654 0.477327 0.878726i \(-0.341606\pi\)
0.477327 + 0.878726i \(0.341606\pi\)
\(572\) −14.0016 5.06177i −0.585436 0.211643i
\(573\) 11.4420 0.477995
\(574\) 15.7371 33.4661i 0.656854 1.39685i
\(575\) 4.27001i 0.178072i
\(576\) −0.661298 1.12837i −0.0275541 0.0470154i
\(577\) 19.6510i 0.818081i −0.912516 0.409040i \(-0.865864\pi\)
0.912516 0.409040i \(-0.134136\pi\)
\(578\) 4.12504 23.5437i 0.171579 0.979287i
\(579\) 11.7018i 0.486309i
\(580\) 1.11487 3.08388i 0.0462923 0.128051i
\(581\) 8.81359 + 2.40236i 0.365649 + 0.0996667i
\(582\) 6.80053 38.8140i 0.281891 1.60889i
\(583\) 2.77232i 0.114818i
\(584\) 26.2763 + 15.0568i 1.08732 + 0.623053i
\(585\) 0.837094 0.0346096
\(586\) −1.16859 + 6.66970i −0.0482738 + 0.275523i
\(587\) 24.2904i 1.00257i −0.865281 0.501287i \(-0.832860\pi\)
0.865281 0.501287i \(-0.167140\pi\)
\(588\) −18.1598 + 15.0393i −0.748895 + 0.620210i
\(589\) 2.24167i 0.0923663i
\(590\) 10.7720 + 1.88733i 0.443474 + 0.0777003i
\(591\) −42.1083 −1.73210
\(592\) 8.89718 10.6972i 0.365672 0.439653i
\(593\) 25.4337i 1.04444i −0.852811 0.522219i \(-0.825104\pi\)
0.852811 0.522219i \(-0.174896\pi\)
\(594\) 10.7902 + 1.89053i 0.442726 + 0.0775692i
\(595\) −0.801209 0.218389i −0.0328464 0.00895308i
\(596\) 10.0422 27.7782i 0.411345 1.13784i
\(597\) 14.9223i 0.610731i
\(598\) −30.4563 5.33619i −1.24545 0.218213i
\(599\) 4.24448i 0.173425i 0.996233 + 0.0867124i \(0.0276361\pi\)
−0.996233 + 0.0867124i \(0.972364\pi\)
\(600\) −4.13315 2.36837i −0.168735 0.0966882i
\(601\) 1.00464i 0.0409800i −0.999790 0.0204900i \(-0.993477\pi\)
0.999790 0.0204900i \(-0.00652263\pi\)
\(602\) 29.2942 + 13.7753i 1.19394 + 0.561440i
\(603\) 2.49930 0.101780
\(604\) −12.0239 + 33.2599i −0.489247 + 1.35333i
\(605\) −8.88631 −0.361280
\(606\) −26.1448 4.58078i −1.06206 0.186081i
\(607\) −31.5181 −1.27928 −0.639640 0.768675i \(-0.720917\pi\)
−0.639640 + 0.768675i \(0.720917\pi\)
\(608\) −0.915270 1.07883i −0.0371191 0.0437525i
\(609\) −1.92134 + 7.04887i −0.0778567 + 0.285635i
\(610\) 0.101500 0.579314i 0.00410963 0.0234557i
\(611\) −39.8287 −1.61130
\(612\) −0.0348913 + 0.0965145i −0.00141040 + 0.00390137i
\(613\) 22.3851i 0.904126i 0.891986 + 0.452063i \(0.149312\pi\)
−0.891986 + 0.452063i \(0.850688\pi\)
\(614\) −32.8916 5.76287i −1.32740 0.232570i
\(615\) −16.6461 −0.671237
\(616\) 7.68495 + 7.70118i 0.309636 + 0.310289i
\(617\) 27.1721 1.09391 0.546954 0.837163i \(-0.315787\pi\)
0.546954 + 0.837163i \(0.315787\pi\)
\(618\) −27.0922 4.74677i −1.08981 0.190943i
\(619\) 16.7190i 0.671993i −0.941863 0.335997i \(-0.890927\pi\)
0.941863 0.335997i \(-0.109073\pi\)
\(620\) 16.8584 + 6.09453i 0.677048 + 0.244762i
\(621\) 22.7503 0.912938
\(622\) 5.76487 32.9030i 0.231150 1.31929i
\(623\) 23.2979 + 6.35042i 0.933412 + 0.254424i
\(624\) −22.0578 + 26.5204i −0.883018 + 1.06167i
\(625\) 1.00000 0.0400000
\(626\) 28.7672 + 5.04026i 1.14977 + 0.201449i
\(627\) 0.612389 0.0244564
\(628\) −1.18161 0.427169i −0.0471514 0.0170459i
\(629\) −1.09179 −0.0435327
\(630\) −0.553553 0.260303i −0.0220541 0.0103707i
\(631\) 25.9280i 1.03218i 0.856535 + 0.516090i \(0.172613\pi\)
−0.856535 + 0.516090i \(0.827387\pi\)
\(632\) −22.9830 13.1696i −0.914214 0.523860i
\(633\) 22.9843i 0.913544i
\(634\) 18.3675 + 3.21814i 0.729468 + 0.127809i
\(635\) 2.17011i 0.0861183i
\(636\) −6.04049 2.18372i −0.239521 0.0865903i
\(637\) −30.8848 18.1881i −1.22370 0.720639i
\(638\) 3.32055 + 0.581788i 0.131462 + 0.0230332i
\(639\) 0.245901i 0.00972771i
\(640\) −10.6017 + 3.95017i −0.419069 + 0.156144i
\(641\) 40.1639 1.58638 0.793189 0.608975i \(-0.208419\pi\)
0.793189 + 0.608975i \(0.208419\pi\)
\(642\) −7.91576 1.38691i −0.312410 0.0547368i
\(643\) 40.5245i 1.59813i 0.601244 + 0.799065i \(0.294672\pi\)
−0.601244 + 0.799065i \(0.705328\pi\)
\(644\) 18.4808 + 12.9994i 0.728244 + 0.512248i
\(645\) 14.5711i 0.573735i
\(646\) −0.0191592 + 0.109351i −0.000753807 + 0.00430235i
\(647\) 14.3559 0.564387 0.282193 0.959358i \(-0.408938\pi\)
0.282193 + 0.959358i \(0.408938\pi\)
\(648\) 11.9288 20.8175i 0.468608 0.817790i
\(649\) 11.2426i 0.441310i
\(650\) 1.24969 7.13260i 0.0490169 0.279764i
\(651\) −38.5334 10.5032i −1.51024 0.411653i
\(652\) 29.5600 + 10.6864i 1.15766 + 0.418510i
\(653\) 34.5999i 1.35400i −0.735984 0.676999i \(-0.763280\pi\)
0.735984 0.676999i \(-0.236720\pi\)
\(654\) −5.18437 + 29.5898i −0.202725 + 1.15705i
\(655\) 8.82257i 0.344726i
\(656\) −25.2809 + 30.3956i −0.987052 + 1.18675i
\(657\) 1.75045i 0.0682916i
\(658\) 26.3379 + 12.3851i 1.02676 + 0.482823i
\(659\) −10.6325 −0.414185 −0.207092 0.978321i \(-0.566400\pi\)
−0.207092 + 0.978321i \(0.566400\pi\)
\(660\) 1.66493 4.60544i 0.0648074 0.179266i
\(661\) 16.0278 0.623410 0.311705 0.950179i \(-0.399100\pi\)
0.311705 + 0.950179i \(0.399100\pi\)
\(662\) 1.04744 5.97825i 0.0407099 0.232351i
\(663\) 2.70676 0.105122
\(664\) −8.47334 4.85537i −0.328830 0.188425i
\(665\) −0.638411 0.174015i −0.0247565 0.00674800i
\(666\) −0.792148 0.138791i −0.0306951 0.00537804i
\(667\) 7.00114 0.271085
\(668\) −35.1217 12.6970i −1.35890 0.491261i
\(669\) 12.9207i 0.499542i
\(670\) 3.73119 21.2958i 0.144148 0.822727i
\(671\) 0.604624 0.0233412
\(672\) 22.8332 10.6783i 0.880808 0.411925i
\(673\) −24.0119 −0.925591 −0.462796 0.886465i \(-0.653154\pi\)
−0.462796 + 0.886465i \(0.653154\pi\)
\(674\) −5.81345 + 33.1803i −0.223926 + 1.27806i
\(675\) 5.32793i 0.205072i
\(676\) −24.8610 8.98762i −0.956194 0.345678i
\(677\) 32.1429 1.23535 0.617676 0.786432i \(-0.288074\pi\)
0.617676 + 0.786432i \(0.288074\pi\)
\(678\) 31.8228 + 5.57561i 1.22215 + 0.214130i
\(679\) −42.2312 11.5111i −1.62068 0.441757i
\(680\) 0.770279 + 0.441383i 0.0295388 + 0.0169263i
\(681\) −31.1372 −1.19318
\(682\) −3.18040 + 18.1521i −0.121784 + 0.695081i
\(683\) −2.97604 −0.113875 −0.0569374 0.998378i \(-0.518134\pi\)
−0.0569374 + 0.998378i \(0.518134\pi\)
\(684\) −0.0278018 + 0.0769037i −0.00106303 + 0.00294049i
\(685\) 0.361903 0.0138276
\(686\) 14.7677 + 21.6314i 0.563833 + 0.825889i
\(687\) 38.1832i 1.45678i
\(688\) −26.6065 22.1294i −1.01436 0.843675i
\(689\) 9.76385i 0.371973i
\(690\) 1.75519 10.0178i 0.0668191 0.381370i
\(691\) 13.7448i 0.522877i 0.965220 + 0.261439i \(0.0841969\pi\)
−0.965220 + 0.261439i \(0.915803\pi\)
\(692\) 46.5276 + 16.8204i 1.76871 + 0.639415i
\(693\) 0.165374 0.606713i 0.00628205 0.0230471i
\(694\) −0.444120 + 2.53481i −0.0168585 + 0.0962201i
\(695\) 8.49740i 0.322325i
\(696\) 3.88320 6.77675i 0.147192 0.256872i
\(697\) 3.10227 0.117507
\(698\) 2.18251 12.4567i 0.0826091 0.471491i
\(699\) 42.8932i 1.62237i
\(700\) −3.04435 + 4.32804i −0.115066 + 0.163585i
\(701\) 49.8152i 1.88149i −0.339111 0.940746i \(-0.610126\pi\)
0.339111 0.940746i \(-0.389874\pi\)
\(702\) 38.0020 + 6.65826i 1.43429 + 0.251300i
\(703\) −0.869952 −0.0328109
\(704\) −5.88088 10.0345i −0.221644 0.378190i
\(705\) 13.1006i 0.493396i
\(706\) −22.4119 3.92674i −0.843482 0.147785i
\(707\) −7.75380 + 28.4466i −0.291612 + 1.06984i
\(708\) 24.4960 + 8.85565i 0.920617 + 0.332816i
\(709\) 5.24482i 0.196973i −0.995138 0.0984867i \(-0.968600\pi\)
0.995138 0.0984867i \(-0.0314002\pi\)
\(710\) 2.09525 + 0.367104i 0.0786332 + 0.0137772i
\(711\) 1.53106i 0.0574193i
\(712\) −22.3985 12.8347i −0.839420 0.481002i
\(713\) 38.2724i 1.43331i
\(714\) −1.78993 0.841696i −0.0669864 0.0314997i
\(715\) 7.44422 0.278398
\(716\) −12.9115 4.66768i −0.482524 0.174439i
\(717\) 29.4809 1.10098
\(718\) 14.1860 + 2.48550i 0.529416 + 0.0927580i
\(719\) 35.6884 1.33095 0.665476 0.746419i \(-0.268229\pi\)
0.665476 + 0.746419i \(0.268229\pi\)
\(720\) 0.502764 + 0.418164i 0.0187369 + 0.0155840i
\(721\) −8.03479 + 29.4774i −0.299231 + 1.09780i
\(722\) 4.62195 26.3798i 0.172011 0.981753i
\(723\) 34.9863 1.30116
\(724\) −25.9695 9.38834i −0.965149 0.348915i
\(725\) 1.63961i 0.0608935i
\(726\) −20.8479 3.65273i −0.773740 0.135566i
\(727\) 49.5564 1.83794 0.918972 0.394322i \(-0.129020\pi\)
0.918972 + 0.394322i \(0.129020\pi\)
\(728\) 27.0657 + 27.1228i 1.00312 + 1.00524i
\(729\) −28.3066 −1.04839
\(730\) −14.9150 2.61323i −0.552030 0.0967201i
\(731\) 2.71555i 0.100438i
\(732\) 0.476256 1.31739i 0.0176029 0.0486922i
\(733\) −9.76884 −0.360820 −0.180410 0.983591i \(-0.557743\pi\)
−0.180410 + 0.983591i \(0.557743\pi\)
\(734\) −0.923141 + 5.26883i −0.0340738 + 0.194476i
\(735\) 5.98248 10.1587i 0.220667 0.374709i
\(736\) −15.6266 18.4191i −0.576004 0.678938i
\(737\) 22.2262 0.818711
\(738\) 2.25085 + 0.394367i 0.0828548 + 0.0145168i
\(739\) −28.7691 −1.05829 −0.529145 0.848531i \(-0.677487\pi\)
−0.529145 + 0.848531i \(0.677487\pi\)
\(740\) −2.36518 + 6.54243i −0.0869458 + 0.240505i
\(741\) 2.15678 0.0792312
\(742\) −3.03617 + 6.45663i −0.111461 + 0.237030i
\(743\) 34.3244i 1.25924i 0.776903 + 0.629620i \(0.216789\pi\)
−0.776903 + 0.629620i \(0.783211\pi\)
\(744\) 37.0458 + 21.2279i 1.35816 + 0.778252i
\(745\) 14.7688i 0.541088i
\(746\) −3.96083 0.693970i −0.145016 0.0254081i
\(747\) 0.564471i 0.0206529i
\(748\) −0.310286 + 0.858297i −0.0113452 + 0.0313824i
\(749\) −2.34759 + 8.61267i −0.0857792 + 0.314700i
\(750\) 2.34608 + 0.411052i 0.0856666 + 0.0150095i
\(751\) 40.8689i 1.49133i 0.666323 + 0.745663i \(0.267867\pi\)
−0.666323 + 0.745663i \(0.732133\pi\)
\(752\) −23.9214 19.8961i −0.872323 0.725536i
\(753\) −31.8784 −1.16171
\(754\) 11.6947 + 2.04900i 0.425895 + 0.0746203i
\(755\) 17.6833i 0.643561i
\(756\) −23.0595 16.2201i −0.838665 0.589918i
\(757\) 35.1958i 1.27921i 0.768703 + 0.639606i \(0.220902\pi\)
−0.768703 + 0.639606i \(0.779098\pi\)
\(758\) 1.27444 7.27388i 0.0462898 0.264199i
\(759\) 10.4554 0.379508
\(760\) 0.613766 + 0.351698i 0.0222636 + 0.0127574i
\(761\) 9.03383i 0.327476i 0.986504 + 0.163738i \(0.0523552\pi\)
−0.986504 + 0.163738i \(0.947645\pi\)
\(762\) 0.892028 5.09125i 0.0323148 0.184436i
\(763\) 32.1949 + 8.77550i 1.16553 + 0.317694i
\(764\) −4.61946 + 12.7781i −0.167126 + 0.462295i
\(765\) 0.0513138i 0.00185526i
\(766\) 6.31398 36.0370i 0.228134 1.30207i
\(767\) 39.5953i 1.42970i
\(768\) −26.4961 + 4.90955i −0.956096 + 0.177158i
\(769\) 16.4068i 0.591645i −0.955243 0.295823i \(-0.904406\pi\)
0.955243 0.295823i \(-0.0955937\pi\)
\(770\) −4.92271 2.31486i −0.177402 0.0834217i
\(771\) −7.27305 −0.261933
\(772\) 13.0682 + 4.72435i 0.470336 + 0.170033i
\(773\) −9.49352 −0.341458 −0.170729 0.985318i \(-0.554612\pi\)
−0.170729 + 0.985318i \(0.554612\pi\)
\(774\) −0.345205 + 1.97026i −0.0124082 + 0.0708195i
\(775\) −8.96308 −0.321963
\(776\) 40.6009 + 23.2650i 1.45749 + 0.835165i
\(777\) 4.07611 14.9541i 0.146230 0.536476i
\(778\) −36.4675 6.38941i −1.30742 0.229071i
\(779\) 2.47192