Properties

Label 980.2.x.l.667.18
Level $980$
Weight $2$
Character 980.667
Analytic conductor $7.825$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 667.18
Character \(\chi\) \(=\) 980.667
Dual form 980.2.x.l.263.18

$q$-expansion

\(f(q)\) \(=\) \(q+(1.41268 + 0.0657371i) q^{2} +(0.835136 - 3.11677i) q^{3} +(1.99136 + 0.185732i) q^{4} +(-1.91459 - 1.15514i) q^{5} +(1.38467 - 4.34811i) q^{6} +(2.80095 + 0.393286i) q^{8} +(-6.41872 - 3.70585i) q^{9} +O(q^{10})\) \(q+(1.41268 + 0.0657371i) q^{2} +(0.835136 - 3.11677i) q^{3} +(1.99136 + 0.185732i) q^{4} +(-1.91459 - 1.15514i) q^{5} +(1.38467 - 4.34811i) q^{6} +(2.80095 + 0.393286i) q^{8} +(-6.41872 - 3.70585i) q^{9} +(-2.62878 - 1.75770i) q^{10} +(-1.21832 + 0.703395i) q^{11} +(2.24194 - 6.05149i) q^{12} +(0.699298 - 0.699298i) q^{13} +(-5.19924 + 5.00264i) q^{15} +(3.93101 + 0.739716i) q^{16} +(1.19641 - 4.46506i) q^{17} +(-8.82402 - 5.65715i) q^{18} +(-1.40337 + 2.43071i) q^{19} +(-3.59809 - 2.65589i) q^{20} +(-1.76734 + 0.913587i) q^{22} +(-2.03016 + 0.543980i) q^{23} +(3.56496 - 8.40147i) q^{24} +(2.33132 + 4.42323i) q^{25} +(1.03386 - 0.941917i) q^{26} +(-10.0659 + 10.0659i) q^{27} -4.85706i q^{29} +(-7.67375 + 6.72537i) q^{30} +(3.18470 - 1.83869i) q^{31} +(5.50465 + 1.30340i) q^{32} +(1.17486 + 4.38464i) q^{33} +(1.98367 - 6.22907i) q^{34} +(-12.0937 - 8.57184i) q^{36} +(7.99714 - 2.14283i) q^{37} +(-2.14231 + 3.34157i) q^{38} +(-1.59554 - 2.76356i) q^{39} +(-4.90838 - 3.98846i) q^{40} -3.53368 q^{41} +(2.49869 + 2.49869i) q^{43} +(-2.55675 + 1.17443i) q^{44} +(8.00846 + 14.5097i) q^{45} +(-2.90374 + 0.635016i) q^{46} +(0.684106 + 2.55312i) q^{47} +(5.58845 - 11.6343i) q^{48} +(3.00265 + 6.40188i) q^{50} +(-12.9174 - 7.45786i) q^{51} +(1.52243 - 1.26267i) q^{52} +(0.951495 + 0.254952i) q^{53} +(-14.8816 + 13.5582i) q^{54} +(3.14510 + 0.0606082i) q^{55} +(6.40395 + 6.40395i) q^{57} +(0.319289 - 6.86149i) q^{58} +(3.53286 + 6.11910i) q^{59} +(-11.2827 + 8.99638i) q^{60} +(1.09916 - 1.90379i) q^{61} +(4.61985 - 2.38814i) q^{62} +(7.69065 + 2.20315i) q^{64} +(-2.14665 + 0.531084i) q^{65} +(1.37148 + 6.27135i) q^{66} +(3.08671 + 0.827081i) q^{67} +(3.21178 - 8.66931i) q^{68} +6.78184i q^{69} -12.1891i q^{71} +(-16.5211 - 12.9043i) q^{72} +(6.40469 + 1.71613i) q^{73} +(11.4383 - 2.50143i) q^{74} +(15.7332 - 3.57218i) q^{75} +(-3.24607 + 4.57976i) q^{76} +(-2.07233 - 4.00892i) q^{78} +(-0.299644 + 0.518999i) q^{79} +(-6.67180 - 5.95711i) q^{80} +(11.8491 + 20.5233i) q^{81} +(-4.99198 - 0.232294i) q^{82} +(4.53764 + 4.53764i) q^{83} +(-7.44839 + 7.16674i) q^{85} +(3.36560 + 3.69412i) q^{86} +(-15.1383 - 4.05630i) q^{87} +(-3.68908 + 1.49103i) q^{88} +(-0.401553 - 0.231837i) q^{89} +(10.3596 + 21.0241i) q^{90} +(-4.14381 + 0.706194i) q^{92} +(-3.07111 - 11.4615i) q^{93} +(0.798592 + 3.65172i) q^{94} +(5.49468 - 3.03273i) q^{95} +(8.65952 - 16.0682i) q^{96} +(-8.00558 - 8.00558i) q^{97} +10.4267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 16 q^{6} + O(q^{10}) \) \( 72 q + 16 q^{6} - 16 q^{10} - 16 q^{12} + 8 q^{13} + 8 q^{16} - 20 q^{17} - 28 q^{18} - 40 q^{20} + 8 q^{22} + 20 q^{25} - 32 q^{26} + 4 q^{30} - 20 q^{37} - 36 q^{40} + 20 q^{45} - 16 q^{46} + 48 q^{48} + 80 q^{50} + 16 q^{52} + 44 q^{53} - 32 q^{57} + 4 q^{58} - 40 q^{60} - 64 q^{61} - 80 q^{62} - 4 q^{65} + 32 q^{66} + 80 q^{68} - 80 q^{72} + 52 q^{73} - 16 q^{76} - 152 q^{78} - 20 q^{80} + 36 q^{81} + 56 q^{82} - 40 q^{85} - 56 q^{86} + 40 q^{88} + 32 q^{90} - 112 q^{92} - 32 q^{93} + 120 q^{96} - 40 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41268 + 0.0657371i 0.998919 + 0.0464831i
\(3\) 0.835136 3.11677i 0.482166 1.79947i −0.110331 0.993895i \(-0.535191\pi\)
0.592497 0.805573i \(-0.298142\pi\)
\(4\) 1.99136 + 0.185732i 0.995679 + 0.0928658i
\(5\) −1.91459 1.15514i −0.856231 0.516593i
\(6\) 1.38467 4.34811i 0.565290 1.77511i
\(7\) 0 0
\(8\) 2.80095 + 0.393286i 0.990286 + 0.139048i
\(9\) −6.41872 3.70585i −2.13957 1.23528i
\(10\) −2.62878 1.75770i −0.831293 0.555835i
\(11\) −1.21832 + 0.703395i −0.367336 + 0.212082i −0.672294 0.740284i \(-0.734691\pi\)
0.304958 + 0.952366i \(0.401358\pi\)
\(12\) 2.24194 6.05149i 0.647191 1.74691i
\(13\) 0.699298 0.699298i 0.193950 0.193950i −0.603450 0.797401i \(-0.706208\pi\)
0.797401 + 0.603450i \(0.206208\pi\)
\(14\) 0 0
\(15\) −5.19924 + 5.00264i −1.34244 + 1.29168i
\(16\) 3.93101 + 0.739716i 0.982752 + 0.184929i
\(17\) 1.19641 4.46506i 0.290172 1.08294i −0.654805 0.755798i \(-0.727249\pi\)
0.944977 0.327138i \(-0.106084\pi\)
\(18\) −8.82402 5.65715i −2.07984 1.33340i
\(19\) −1.40337 + 2.43071i −0.321955 + 0.557643i −0.980891 0.194556i \(-0.937673\pi\)
0.658936 + 0.752199i \(0.271007\pi\)
\(20\) −3.59809 2.65589i −0.804557 0.593875i
\(21\) 0 0
\(22\) −1.76734 + 0.913587i −0.376797 + 0.194777i
\(23\) −2.03016 + 0.543980i −0.423318 + 0.113428i −0.464188 0.885737i \(-0.653654\pi\)
0.0408699 + 0.999164i \(0.486987\pi\)
\(24\) 3.56496 8.40147i 0.727694 1.71494i
\(25\) 2.33132 + 4.42323i 0.466263 + 0.884646i
\(26\) 1.03386 0.941917i 0.202756 0.184725i
\(27\) −10.0659 + 10.0659i −1.93718 + 1.93718i
\(28\) 0 0
\(29\) 4.85706i 0.901933i −0.892541 0.450967i \(-0.851079\pi\)
0.892541 0.450967i \(-0.148921\pi\)
\(30\) −7.67375 + 6.72537i −1.40103 + 1.22788i
\(31\) 3.18470 1.83869i 0.571990 0.330238i −0.185954 0.982558i \(-0.559538\pi\)
0.757944 + 0.652320i \(0.226204\pi\)
\(32\) 5.50465 + 1.30340i 0.973094 + 0.230410i
\(33\) 1.17486 + 4.38464i 0.204517 + 0.763268i
\(34\) 1.98367 6.22907i 0.340196 1.06828i
\(35\) 0 0
\(36\) −12.0937 8.57184i −2.01561 1.42864i
\(37\) 7.99714 2.14283i 1.31472 0.352279i 0.467724 0.883875i \(-0.345074\pi\)
0.846998 + 0.531596i \(0.178408\pi\)
\(38\) −2.14231 + 3.34157i −0.347528 + 0.542074i
\(39\) −1.59554 2.76356i −0.255491 0.442523i
\(40\) −4.90838 3.98846i −0.776082 0.630632i
\(41\) −3.53368 −0.551868 −0.275934 0.961177i \(-0.588987\pi\)
−0.275934 + 0.961177i \(0.588987\pi\)
\(42\) 0 0
\(43\) 2.49869 + 2.49869i 0.381046 + 0.381046i 0.871479 0.490433i \(-0.163161\pi\)
−0.490433 + 0.871479i \(0.663161\pi\)
\(44\) −2.55675 + 1.17443i −0.385444 + 0.177052i
\(45\) 8.00846 + 14.5097i 1.19383 + 2.16298i
\(46\) −2.90374 + 0.635016i −0.428133 + 0.0936280i
\(47\) 0.684106 + 2.55312i 0.0997872 + 0.372411i 0.997702 0.0677590i \(-0.0215849\pi\)
−0.897915 + 0.440170i \(0.854918\pi\)
\(48\) 5.58845 11.6343i 0.806623 1.67926i
\(49\) 0 0
\(50\) 3.00265 + 6.40188i 0.424638 + 0.905363i
\(51\) −12.9174 7.45786i −1.80880 1.04431i
\(52\) 1.52243 1.26267i 0.211123 0.175101i
\(53\) 0.951495 + 0.254952i 0.130698 + 0.0350204i 0.323575 0.946203i \(-0.395115\pi\)
−0.192877 + 0.981223i \(0.561782\pi\)
\(54\) −14.8816 + 13.5582i −2.02513 + 1.84504i
\(55\) 3.14510 + 0.0606082i 0.424085 + 0.00817240i
\(56\) 0 0
\(57\) 6.40395 + 6.40395i 0.848224 + 0.848224i
\(58\) 0.319289 6.86149i 0.0419247 0.900958i
\(59\) 3.53286 + 6.11910i 0.459940 + 0.796639i 0.998957 0.0456557i \(-0.0145377\pi\)
−0.539018 + 0.842294i \(0.681204\pi\)
\(60\) −11.2827 + 8.99638i −1.45659 + 1.16143i
\(61\) 1.09916 1.90379i 0.140732 0.243756i −0.787040 0.616902i \(-0.788388\pi\)
0.927773 + 0.373146i \(0.121721\pi\)
\(62\) 4.61985 2.38814i 0.586722 0.303294i
\(63\) 0 0
\(64\) 7.69065 + 2.20315i 0.961331 + 0.275394i
\(65\) −2.14665 + 0.531084i −0.266260 + 0.0658729i
\(66\) 1.37148 + 6.27135i 0.168817 + 0.771950i
\(67\) 3.08671 + 0.827081i 0.377101 + 0.101044i 0.442391 0.896822i \(-0.354130\pi\)
−0.0652895 + 0.997866i \(0.520797\pi\)
\(68\) 3.21178 8.66931i 0.389485 1.05131i
\(69\) 6.78184i 0.816438i
\(70\) 0 0
\(71\) 12.1891i 1.44658i −0.690546 0.723289i \(-0.742630\pi\)
0.690546 0.723289i \(-0.257370\pi\)
\(72\) −16.5211 12.9043i −1.94703 1.52079i
\(73\) 6.40469 + 1.71613i 0.749612 + 0.200858i 0.613346 0.789814i \(-0.289823\pi\)
0.136266 + 0.990672i \(0.456490\pi\)
\(74\) 11.4383 2.50143i 1.32968 0.290785i
\(75\) 15.7332 3.57218i 1.81671 0.412480i
\(76\) −3.24607 + 4.57976i −0.372350 + 0.525334i
\(77\) 0 0
\(78\) −2.07233 4.00892i −0.234645 0.453921i
\(79\) −0.299644 + 0.518999i −0.0337126 + 0.0583919i −0.882389 0.470520i \(-0.844066\pi\)
0.848677 + 0.528912i \(0.177400\pi\)
\(80\) −6.67180 5.95711i −0.745930 0.666025i
\(81\) 11.8491 + 20.5233i 1.31657 + 2.28036i
\(82\) −4.99198 0.232294i −0.551271 0.0256526i
\(83\) 4.53764 + 4.53764i 0.498071 + 0.498071i 0.910837 0.412766i \(-0.135437\pi\)
−0.412766 + 0.910837i \(0.635437\pi\)
\(84\) 0 0
\(85\) −7.44839 + 7.16674i −0.807891 + 0.777342i
\(86\) 3.36560 + 3.69412i 0.362922 + 0.398347i
\(87\) −15.1383 4.05630i −1.62300 0.434882i
\(88\) −3.68908 + 1.49103i −0.393257 + 0.158944i
\(89\) −0.401553 0.231837i −0.0425645 0.0245746i 0.478567 0.878051i \(-0.341156\pi\)
−0.521131 + 0.853477i \(0.674490\pi\)
\(90\) 10.3596 + 21.0241i 1.09200 + 2.21613i
\(91\) 0 0
\(92\) −4.14381 + 0.706194i −0.432022 + 0.0736258i
\(93\) −3.07111 11.4615i −0.318459 1.18851i
\(94\) 0.798592 + 3.65172i 0.0823685 + 0.376647i
\(95\) 5.49468 3.03273i 0.563742 0.311151i
\(96\) 8.65952 16.0682i 0.883809 1.63995i
\(97\) −8.00558 8.00558i −0.812843 0.812843i 0.172216 0.985059i \(-0.444907\pi\)
−0.985059 + 0.172216i \(0.944907\pi\)
\(98\) 0 0
\(99\) 10.4267 1.04792
\(100\) 3.82095 + 9.24123i 0.382095 + 0.924123i
\(101\) −3.01549 5.22299i −0.300053 0.519707i 0.676095 0.736815i \(-0.263671\pi\)
−0.976148 + 0.217108i \(0.930338\pi\)
\(102\) −17.7579 11.3848i −1.75830 1.12726i
\(103\) −13.5932 + 3.64227i −1.33937 + 0.358884i −0.856202 0.516642i \(-0.827182\pi\)
−0.483171 + 0.875526i \(0.660515\pi\)
\(104\) 2.23372 1.68367i 0.219035 0.165098i
\(105\) 0 0
\(106\) 1.32740 + 0.422716i 0.128929 + 0.0410578i
\(107\) 5.19174 + 19.3758i 0.501905 + 1.87313i 0.487290 + 0.873240i \(0.337985\pi\)
0.0146144 + 0.999893i \(0.495348\pi\)
\(108\) −21.9143 + 18.1752i −2.10871 + 1.74891i
\(109\) −0.879139 + 0.507571i −0.0842062 + 0.0486165i −0.541512 0.840693i \(-0.682148\pi\)
0.457306 + 0.889310i \(0.348815\pi\)
\(110\) 4.43904 + 0.292370i 0.423246 + 0.0278764i
\(111\) 26.7148i 2.53566i
\(112\) 0 0
\(113\) 7.39345 7.39345i 0.695518 0.695518i −0.267923 0.963440i \(-0.586337\pi\)
0.963440 + 0.267923i \(0.0863372\pi\)
\(114\) 8.62579 + 9.46774i 0.807879 + 0.886735i
\(115\) 4.51530 + 1.30362i 0.421054 + 0.121563i
\(116\) 0.902109 9.67214i 0.0837588 0.898036i
\(117\) −7.08009 + 1.89711i −0.654555 + 0.175387i
\(118\) 4.58857 + 8.87660i 0.422412 + 0.817157i
\(119\) 0 0
\(120\) −16.5303 + 11.9674i −1.50900 + 1.09247i
\(121\) −4.51047 + 7.81236i −0.410043 + 0.710215i
\(122\) 1.67791 2.61721i 0.151911 0.236951i
\(123\) −2.95110 + 11.0137i −0.266092 + 0.993069i
\(124\) 6.68339 3.06999i 0.600186 0.275693i
\(125\) 0.645919 11.1617i 0.0577727 0.998330i
\(126\) 0 0
\(127\) 8.87092 8.87092i 0.787167 0.787167i −0.193862 0.981029i \(-0.562101\pi\)
0.981029 + 0.193862i \(0.0621014\pi\)
\(128\) 10.7196 + 3.61792i 0.947491 + 0.319782i
\(129\) 9.87458 5.70109i 0.869408 0.501953i
\(130\) −3.06746 + 0.609140i −0.269034 + 0.0534251i
\(131\) −11.3871 6.57436i −0.994898 0.574404i −0.0881630 0.996106i \(-0.528100\pi\)
−0.906735 + 0.421702i \(0.861433\pi\)
\(132\) 1.52520 + 8.94960i 0.132752 + 0.778962i
\(133\) 0 0
\(134\) 4.30618 + 1.37132i 0.371997 + 0.118464i
\(135\) 30.8996 7.64458i 2.65941 0.657941i
\(136\) 5.10713 12.0359i 0.437933 1.03207i
\(137\) 1.80890 6.75090i 0.154545 0.576769i −0.844599 0.535399i \(-0.820161\pi\)
0.999144 0.0413695i \(-0.0131721\pi\)
\(138\) −0.445819 + 9.58061i −0.0379506 + 0.815556i
\(139\) 21.2377 1.80136 0.900679 0.434485i \(-0.143069\pi\)
0.900679 + 0.434485i \(0.143069\pi\)
\(140\) 0 0
\(141\) 8.52881 0.718255
\(142\) 0.801275 17.2193i 0.0672415 1.44501i
\(143\) −0.360083 + 1.34385i −0.0301117 + 0.112378i
\(144\) −22.4908 19.3158i −1.87423 1.60965i
\(145\) −5.61057 + 9.29928i −0.465932 + 0.772263i
\(146\) 8.93499 + 2.84538i 0.739465 + 0.235485i
\(147\) 0 0
\(148\) 16.3232 2.78181i 1.34176 0.228664i
\(149\) 5.75434 + 3.32227i 0.471414 + 0.272171i 0.716831 0.697247i \(-0.245592\pi\)
−0.245418 + 0.969417i \(0.578925\pi\)
\(150\) 22.4608 4.01211i 1.83392 0.327588i
\(151\) 17.6555 10.1934i 1.43679 0.829529i 0.439161 0.898408i \(-0.355276\pi\)
0.997625 + 0.0688796i \(0.0219424\pi\)
\(152\) −4.88673 + 6.25637i −0.396367 + 0.507458i
\(153\) −24.2263 + 24.2263i −1.95858 + 1.95858i
\(154\) 0 0
\(155\) −8.22134 0.158431i −0.660354 0.0127255i
\(156\) −2.66401 5.79957i −0.213292 0.464338i
\(157\) −4.59905 + 17.1639i −0.367044 + 1.36983i 0.497584 + 0.867416i \(0.334221\pi\)
−0.864628 + 0.502412i \(0.832446\pi\)
\(158\) −0.457420 + 0.713484i −0.0363904 + 0.0567617i
\(159\) 1.58925 2.75267i 0.126036 0.218301i
\(160\) −9.03355 8.85410i −0.714164 0.699978i
\(161\) 0 0
\(162\) 15.3899 + 29.7719i 1.20915 + 2.33910i
\(163\) −16.7957 + 4.50039i −1.31554 + 0.352498i −0.847305 0.531106i \(-0.821776\pi\)
−0.468235 + 0.883604i \(0.655110\pi\)
\(164\) −7.03682 0.656316i −0.549483 0.0512497i
\(165\) 2.81548 9.75192i 0.219185 0.759186i
\(166\) 6.11196 + 6.70855i 0.474380 + 0.520684i
\(167\) 6.88960 6.88960i 0.533133 0.533133i −0.388370 0.921503i \(-0.626962\pi\)
0.921503 + 0.388370i \(0.126962\pi\)
\(168\) 0 0
\(169\) 12.0220i 0.924767i
\(170\) −10.9933 + 9.63472i −0.843151 + 0.738949i
\(171\) 18.0157 10.4014i 1.37769 0.795412i
\(172\) 4.51170 + 5.43987i 0.344014 + 0.414786i
\(173\) 6.40337 + 23.8977i 0.486839 + 1.81691i 0.571632 + 0.820510i \(0.306311\pi\)
−0.0847922 + 0.996399i \(0.527023\pi\)
\(174\) −21.1190 6.72543i −1.60103 0.509854i
\(175\) 0 0
\(176\) −5.30952 + 1.86384i −0.400220 + 0.140493i
\(177\) 22.0222 5.90084i 1.65529 0.443534i
\(178\) −0.552027 0.353909i −0.0413762 0.0265266i
\(179\) −10.2777 17.8015i −0.768192 1.33055i −0.938542 0.345164i \(-0.887823\pi\)
0.170350 0.985384i \(-0.445510\pi\)
\(180\) 13.2528 + 30.3814i 0.987806 + 2.26450i
\(181\) 7.85989 0.584221 0.292110 0.956385i \(-0.405643\pi\)
0.292110 + 0.956385i \(0.405643\pi\)
\(182\) 0 0
\(183\) −5.01574 5.01574i −0.370774 0.370774i
\(184\) −5.90032 + 0.725227i −0.434978 + 0.0534645i
\(185\) −17.7865 5.13516i −1.30769 0.377544i
\(186\) −3.58506 16.3934i −0.262870 1.20203i
\(187\) 1.68310 + 6.28140i 0.123080 + 0.459342i
\(188\) 0.888105 + 5.21123i 0.0647717 + 0.380068i
\(189\) 0 0
\(190\) 7.96161 3.92308i 0.577596 0.284610i
\(191\) 7.51061 + 4.33625i 0.543449 + 0.313760i 0.746475 0.665413i \(-0.231745\pi\)
−0.203027 + 0.979173i \(0.565078\pi\)
\(192\) 13.2895 22.1301i 0.959084 1.59710i
\(193\) 5.12478 + 1.37318i 0.368890 + 0.0988437i 0.438502 0.898730i \(-0.355509\pi\)
−0.0696118 + 0.997574i \(0.522176\pi\)
\(194\) −10.7831 11.8356i −0.774181 0.849748i
\(195\) −0.137480 + 7.13415i −0.00984515 + 0.510887i
\(196\) 0 0
\(197\) −12.3437 12.3437i −0.879452 0.879452i 0.114026 0.993478i \(-0.463625\pi\)
−0.993478 + 0.114026i \(0.963625\pi\)
\(198\) 14.7297 + 0.685422i 1.04679 + 0.0487108i
\(199\) −2.14941 3.72289i −0.152368 0.263909i 0.779730 0.626116i \(-0.215356\pi\)
−0.932097 + 0.362208i \(0.882023\pi\)
\(200\) 4.79031 + 13.3061i 0.338726 + 0.940885i
\(201\) 5.15564 8.92983i 0.363651 0.629862i
\(202\) −3.91660 7.57667i −0.275571 0.533092i
\(203\) 0 0
\(204\) −24.3380 17.2504i −1.70400 1.20777i
\(205\) 6.76555 + 4.08188i 0.472527 + 0.285091i
\(206\) −19.4423 + 4.25181i −1.35461 + 0.296238i
\(207\) 15.0470 + 4.03182i 1.04584 + 0.280231i
\(208\) 3.26623 2.23166i 0.226472 0.154738i
\(209\) 3.94849i 0.273123i
\(210\) 0 0
\(211\) 19.5494i 1.34583i 0.739718 + 0.672917i \(0.234959\pi\)
−0.739718 + 0.672917i \(0.765041\pi\)
\(212\) 1.84741 + 0.684424i 0.126881 + 0.0470064i
\(213\) −37.9906 10.1795i −2.60307 0.697490i
\(214\) 6.06058 + 27.7132i 0.414293 + 1.89444i
\(215\) −1.89764 7.67029i −0.129418 0.523110i
\(216\) −32.1528 + 24.2353i −2.18772 + 1.64900i
\(217\) 0 0
\(218\) −1.27531 + 0.659246i −0.0863751 + 0.0446498i
\(219\) 10.6976 18.5287i 0.722875 1.25206i
\(220\) 6.25175 + 0.704836i 0.421493 + 0.0475200i
\(221\) −2.28576 3.95905i −0.153757 0.266315i
\(222\) 1.75615 37.7396i 0.117865 2.53292i
\(223\) −9.54503 9.54503i −0.639183 0.639183i 0.311171 0.950354i \(-0.399279\pi\)
−0.950354 + 0.311171i \(0.899279\pi\)
\(224\) 0 0
\(225\) 1.42776 37.0310i 0.0951838 2.46873i
\(226\) 10.9306 9.95860i 0.727096 0.662436i
\(227\) −17.8221 4.77541i −1.18289 0.316955i −0.386819 0.922155i \(-0.626426\pi\)
−0.796073 + 0.605200i \(0.793093\pi\)
\(228\) 11.5631 + 13.9420i 0.765788 + 0.923330i
\(229\) −13.5250 7.80865i −0.893755 0.516010i −0.0185864 0.999827i \(-0.505917\pi\)
−0.875169 + 0.483817i \(0.839250\pi\)
\(230\) 6.29300 + 2.13842i 0.414948 + 0.141003i
\(231\) 0 0
\(232\) 1.91021 13.6044i 0.125412 0.893172i
\(233\) 0.989436 + 3.69263i 0.0648201 + 0.241912i 0.990733 0.135826i \(-0.0433688\pi\)
−0.925913 + 0.377738i \(0.876702\pi\)
\(234\) −10.1266 + 2.21459i −0.662000 + 0.144772i
\(235\) 1.63942 5.67842i 0.106944 0.370419i
\(236\) 5.89868 + 12.8415i 0.383972 + 0.835909i
\(237\) 1.36736 + 1.36736i 0.0888193 + 0.0888193i
\(238\) 0 0
\(239\) −15.4752 −1.00101 −0.500505 0.865734i \(-0.666852\pi\)
−0.500505 + 0.865734i \(0.666852\pi\)
\(240\) −24.1388 + 15.8195i −1.55815 + 1.02114i
\(241\) 14.3810 + 24.9086i 0.926361 + 1.60450i 0.789357 + 0.613934i \(0.210414\pi\)
0.137004 + 0.990570i \(0.456253\pi\)
\(242\) −6.88544 + 10.7399i −0.442613 + 0.690387i
\(243\) 32.6112 8.73814i 2.09201 0.560552i
\(244\) 2.54241 3.58699i 0.162761 0.229633i
\(245\) 0 0
\(246\) −4.89298 + 15.3648i −0.311965 + 0.979626i
\(247\) 0.718415 + 2.68116i 0.0457117 + 0.170598i
\(248\) 9.64333 3.89758i 0.612352 0.247497i
\(249\) 17.9323 10.3532i 1.13641 0.656109i
\(250\) 1.64622 15.7255i 0.104116 0.994565i
\(251\) 26.0285i 1.64291i 0.570277 + 0.821453i \(0.306836\pi\)
−0.570277 + 0.821453i \(0.693164\pi\)
\(252\) 0 0
\(253\) 2.09075 2.09075i 0.131444 0.131444i
\(254\) 13.1150 11.9487i 0.822906 0.749726i
\(255\) 16.1167 + 29.2001i 1.00927 + 1.82858i
\(256\) 14.9056 + 5.81566i 0.931603 + 0.363479i
\(257\) 22.2935 5.97352i 1.39063 0.372618i 0.515659 0.856794i \(-0.327547\pi\)
0.874971 + 0.484176i \(0.160881\pi\)
\(258\) 14.3244 7.40472i 0.891801 0.460998i
\(259\) 0 0
\(260\) −4.37339 + 0.658877i −0.271226 + 0.0408618i
\(261\) −17.9995 + 31.1761i −1.11414 + 1.92975i
\(262\) −15.6542 10.0361i −0.967122 0.620029i
\(263\) −2.93759 + 10.9633i −0.181140 + 0.676023i 0.814284 + 0.580466i \(0.197130\pi\)
−0.995424 + 0.0955566i \(0.969537\pi\)
\(264\) 1.56631 + 12.7432i 0.0963997 + 0.784291i
\(265\) −1.52722 1.58724i −0.0938163 0.0975031i
\(266\) 0 0
\(267\) −1.05793 + 1.05793i −0.0647444 + 0.0647444i
\(268\) 5.99312 + 2.22031i 0.366088 + 0.135627i
\(269\) 23.5713 13.6089i 1.43717 0.829749i 0.439516 0.898235i \(-0.355150\pi\)
0.997652 + 0.0684854i \(0.0218167\pi\)
\(270\) 44.1539 8.76814i 2.68712 0.533612i
\(271\) 0.134959 + 0.0779185i 0.00819817 + 0.00473321i 0.504093 0.863649i \(-0.331827\pi\)
−0.495895 + 0.868382i \(0.665160\pi\)
\(272\) 8.00597 16.6672i 0.485433 1.01060i
\(273\) 0 0
\(274\) 2.99919 9.41799i 0.181188 0.568961i
\(275\) −5.95156 3.74906i −0.358893 0.226077i
\(276\) −1.25960 + 13.5051i −0.0758192 + 0.812910i
\(277\) −5.41783 + 20.2196i −0.325526 + 1.21488i 0.588256 + 0.808674i \(0.299815\pi\)
−0.913782 + 0.406204i \(0.866852\pi\)
\(278\) 30.0022 + 1.39610i 1.79941 + 0.0837328i
\(279\) −27.2556 −1.63175
\(280\) 0 0
\(281\) −2.56355 −0.152929 −0.0764644 0.997072i \(-0.524363\pi\)
−0.0764644 + 0.997072i \(0.524363\pi\)
\(282\) 12.0485 + 0.560659i 0.717479 + 0.0333868i
\(283\) −5.32518 + 19.8738i −0.316549 + 1.18138i 0.605990 + 0.795472i \(0.292777\pi\)
−0.922539 + 0.385904i \(0.873889\pi\)
\(284\) 2.26390 24.2728i 0.134338 1.44033i
\(285\) −4.86351 19.6584i −0.288089 1.16446i
\(286\) −0.597025 + 1.87476i −0.0353028 + 0.110857i
\(287\) 0 0
\(288\) −30.5026 28.7656i −1.79738 1.69503i
\(289\) −3.78292 2.18407i −0.222525 0.128475i
\(290\) −8.53727 + 12.7681i −0.501326 + 0.749771i
\(291\) −31.6373 + 18.2658i −1.85461 + 1.07076i
\(292\) 12.4353 + 4.60698i 0.727720 + 0.269603i
\(293\) −4.71102 + 4.71102i −0.275221 + 0.275221i −0.831198 0.555977i \(-0.812344\pi\)
0.555977 + 0.831198i \(0.312344\pi\)
\(294\) 0 0
\(295\) 0.304410 15.7965i 0.0177234 0.919708i
\(296\) 23.2423 2.85679i 1.35093 0.166047i
\(297\) 5.18314 19.3437i 0.300756 1.12244i
\(298\) 7.91067 + 5.07159i 0.458253 + 0.293790i
\(299\) −1.03928 + 1.80009i −0.0601033 + 0.104102i
\(300\) 31.9938 4.19134i 1.84716 0.241987i
\(301\) 0 0
\(302\) 25.6118 13.2395i 1.47379 0.761846i
\(303\) −18.7972 + 5.03669i −1.07987 + 0.289350i
\(304\) −7.31469 + 8.51704i −0.419526 + 0.488486i
\(305\) −4.30358 + 2.37531i −0.246422 + 0.136010i
\(306\) −35.8166 + 32.6315i −2.04750 + 1.86542i
\(307\) −16.8508 + 16.8508i −0.961723 + 0.961723i −0.999294 0.0375706i \(-0.988038\pi\)
0.0375706 + 0.999294i \(0.488038\pi\)
\(308\) 0 0
\(309\) 45.4085i 2.58320i
\(310\) −11.6038 0.764260i −0.659049 0.0434071i
\(311\) −15.7287 + 9.08099i −0.891895 + 0.514936i −0.874562 0.484914i \(-0.838851\pi\)
−0.0173329 + 0.999850i \(0.505518\pi\)
\(312\) −3.38216 8.36809i −0.191477 0.473750i
\(313\) 0.405938 + 1.51498i 0.0229450 + 0.0856319i 0.976449 0.215749i \(-0.0692192\pi\)
−0.953504 + 0.301381i \(0.902553\pi\)
\(314\) −7.62532 + 23.9449i −0.430322 + 1.35129i
\(315\) 0 0
\(316\) −0.693093 + 0.977859i −0.0389895 + 0.0550088i
\(317\) −28.5334 + 7.64549i −1.60259 + 0.429414i −0.945825 0.324678i \(-0.894744\pi\)
−0.656769 + 0.754092i \(0.728077\pi\)
\(318\) 2.42607 3.78418i 0.136047 0.212206i
\(319\) 3.41643 + 5.91743i 0.191283 + 0.331313i
\(320\) −12.1795 13.1019i −0.680855 0.732418i
\(321\) 64.7258 3.61264
\(322\) 0 0
\(323\) 9.17425 + 9.17425i 0.510469 + 0.510469i
\(324\) 19.7840 + 43.0699i 1.09911 + 2.39277i
\(325\) 4.72344 + 1.46287i 0.262009 + 0.0811454i
\(326\) −24.0229 + 5.25353i −1.33050 + 0.290966i
\(327\) 0.847782 + 3.16396i 0.0468824 + 0.174968i
\(328\) −9.89766 1.38975i −0.546507 0.0767360i
\(329\) 0 0
\(330\) 4.61845 13.5913i 0.254238 0.748177i
\(331\) −10.9400 6.31623i −0.601319 0.347172i 0.168241 0.985746i \(-0.446191\pi\)
−0.769560 + 0.638574i \(0.779525\pi\)
\(332\) 8.19328 + 9.87885i 0.449665 + 0.542172i
\(333\) −59.2724 15.8820i −3.24811 0.870328i
\(334\) 10.1857 9.27993i 0.557339 0.507775i
\(335\) −4.95439 5.14909i −0.270687 0.281325i
\(336\) 0 0
\(337\) 4.10542 + 4.10542i 0.223636 + 0.223636i 0.810028 0.586391i \(-0.199452\pi\)
−0.586391 + 0.810028i \(0.699452\pi\)
\(338\) −0.790289 + 16.9832i −0.0429861 + 0.923767i
\(339\) −16.8692 29.2182i −0.916207 1.58692i
\(340\) −16.1635 + 12.8881i −0.876588 + 0.698958i
\(341\) −2.58665 + 4.48021i −0.140075 + 0.242617i
\(342\) 26.1342 13.5095i 1.41318 0.730513i
\(343\) 0 0
\(344\) 6.01600 + 7.98140i 0.324361 + 0.430328i
\(345\) 7.83396 12.9845i 0.421766 0.699060i
\(346\) 7.47498 + 34.1809i 0.401857 + 1.83757i
\(347\) −14.2660 3.82255i −0.765837 0.205205i −0.145305 0.989387i \(-0.546416\pi\)
−0.620531 + 0.784182i \(0.713083\pi\)
\(348\) −29.3925 10.8892i −1.57560 0.583723i
\(349\) 5.05181i 0.270417i 0.990817 + 0.135209i \(0.0431705\pi\)
−0.990817 + 0.135209i \(0.956830\pi\)
\(350\) 0 0
\(351\) 14.0781i 0.751434i
\(352\) −7.62321 + 2.28399i −0.406318 + 0.121737i
\(353\) 10.5040 + 2.81454i 0.559072 + 0.149803i 0.527280 0.849692i \(-0.323212\pi\)
0.0317919 + 0.999495i \(0.489879\pi\)
\(354\) 31.4984 6.88835i 1.67412 0.366112i
\(355\) −14.0801 + 23.3371i −0.747292 + 1.23860i
\(356\) −0.756576 0.536251i −0.0400984 0.0284212i
\(357\) 0 0
\(358\) −13.3489 25.8236i −0.705514 1.36482i
\(359\) −2.49329 + 4.31850i −0.131591 + 0.227922i −0.924290 0.381691i \(-0.875342\pi\)
0.792699 + 0.609613i \(0.208675\pi\)
\(360\) 16.7248 + 43.7906i 0.881477 + 2.30797i
\(361\) 5.56111 + 9.63212i 0.292690 + 0.506954i
\(362\) 11.1035 + 0.516686i 0.583589 + 0.0271564i
\(363\) 20.5825 + 20.5825i 1.08030 + 1.08030i
\(364\) 0 0
\(365\) −10.2800 10.6840i −0.538079 0.559225i
\(366\) −6.75594 7.41538i −0.353139 0.387608i
\(367\) 15.3917 + 4.12420i 0.803442 + 0.215282i 0.637094 0.770786i \(-0.280136\pi\)
0.166347 + 0.986067i \(0.446803\pi\)
\(368\) −8.38297 + 0.636648i −0.436993 + 0.0331875i
\(369\) 22.6817 + 13.0953i 1.18076 + 0.681714i
\(370\) −24.7892 8.42359i −1.28873 0.437922i
\(371\) 0 0
\(372\) −3.98691 23.3944i −0.206712 1.21294i
\(373\) −0.152497 0.569126i −0.00789599 0.0294682i 0.961865 0.273523i \(-0.0881890\pi\)
−0.969761 + 0.244055i \(0.921522\pi\)
\(374\) 1.96476 + 8.98428i 0.101596 + 0.464566i
\(375\) −34.2489 11.3347i −1.76861 0.585321i
\(376\) 0.912041 + 7.42021i 0.0470349 + 0.382668i
\(377\) −3.39653 3.39653i −0.174930 0.174930i
\(378\) 0 0
\(379\) −23.7583 −1.22038 −0.610191 0.792254i \(-0.708907\pi\)
−0.610191 + 0.792254i \(0.708907\pi\)
\(380\) 11.5051 5.01871i 0.590201 0.257454i
\(381\) −20.2402 35.0570i −1.03694 1.79603i
\(382\) 10.3251 + 6.61948i 0.528277 + 0.338682i
\(383\) −4.14964 + 1.11189i −0.212037 + 0.0568151i −0.363274 0.931682i \(-0.618341\pi\)
0.151237 + 0.988498i \(0.451674\pi\)
\(384\) 20.2286 30.3892i 1.03229 1.55079i
\(385\) 0 0
\(386\) 7.14943 + 2.27676i 0.363896 + 0.115884i
\(387\) −6.77862 25.2982i −0.344577 1.28598i
\(388\) −14.4551 17.4289i −0.733845 0.884816i
\(389\) −21.8152 + 12.5950i −1.10608 + 0.638593i −0.937810 0.347148i \(-0.887150\pi\)
−0.168266 + 0.985742i \(0.553817\pi\)
\(390\) −0.663194 + 10.0693i −0.0335822 + 0.509877i
\(391\) 9.71561i 0.491340i
\(392\) 0 0
\(393\) −30.0006 + 30.0006i −1.51333 + 1.51333i
\(394\) −16.6263 18.2492i −0.837622 0.919381i
\(395\) 1.17321 0.647540i 0.0590306 0.0325813i
\(396\) 20.7633 + 1.93657i 1.04340 + 0.0973163i
\(397\) −3.73802 + 1.00160i −0.187606 + 0.0502689i −0.351399 0.936226i \(-0.614294\pi\)
0.163793 + 0.986495i \(0.447627\pi\)
\(398\) −2.79171 5.40057i −0.139936 0.270706i
\(399\) 0 0
\(400\) 5.89249 + 19.1123i 0.294625 + 0.955613i
\(401\) 2.74364 4.75213i 0.137011 0.237310i −0.789353 0.613940i \(-0.789584\pi\)
0.926364 + 0.376630i \(0.122917\pi\)
\(402\) 7.87032 12.2761i 0.392536 0.612277i
\(403\) 0.941265 3.51285i 0.0468877 0.174987i
\(404\) −5.03485 10.9609i −0.250493 0.545325i
\(405\) 1.02098 52.9811i 0.0507330 2.63265i
\(406\) 0 0
\(407\) −8.23579 + 8.23579i −0.408233 + 0.408233i
\(408\) −33.2479 25.9693i −1.64602 1.28567i
\(409\) −14.7164 + 8.49650i −0.727678 + 0.420125i −0.817572 0.575826i \(-0.804680\pi\)
0.0898942 + 0.995951i \(0.471347\pi\)
\(410\) 9.28926 + 6.21116i 0.458764 + 0.306747i
\(411\) −19.5303 11.2758i −0.963360 0.556196i
\(412\) −27.7453 + 4.72839i −1.36691 + 0.232951i
\(413\) 0 0
\(414\) 20.9916 + 6.68484i 1.03168 + 0.328542i
\(415\) −3.44613 13.9293i −0.169164 0.683764i
\(416\) 4.76085 2.93792i 0.233420 0.144044i
\(417\) 17.7364 66.1930i 0.868554 3.24149i
\(418\) 0.259563 5.57798i 0.0126956 0.272828i
\(419\) 3.87556 0.189334 0.0946668 0.995509i \(-0.469821\pi\)
0.0946668 + 0.995509i \(0.469821\pi\)
\(420\) 0 0
\(421\) 20.7160 1.00964 0.504818 0.863226i \(-0.331560\pi\)
0.504818 + 0.863226i \(0.331560\pi\)
\(422\) −1.28512 + 27.6171i −0.0625586 + 1.34438i
\(423\) 5.07039 18.9230i 0.246531 0.920066i
\(424\) 2.56482 + 1.08832i 0.124559 + 0.0528534i
\(425\) 22.5392 5.11747i 1.09331 0.248234i
\(426\) −52.9995 16.8779i −2.56783 0.817735i
\(427\) 0 0
\(428\) 6.73991 + 39.5485i 0.325786 + 1.91165i
\(429\) 3.88775 + 2.24459i 0.187702 + 0.108370i
\(430\) −2.17654 10.9605i −0.104962 0.528560i
\(431\) 8.46015 4.88447i 0.407511 0.235277i −0.282209 0.959353i \(-0.591067\pi\)
0.689720 + 0.724076i \(0.257734\pi\)
\(432\) −47.0150 + 32.1232i −2.26201 + 1.54553i
\(433\) −7.00877 + 7.00877i −0.336820 + 0.336820i −0.855169 0.518349i \(-0.826547\pi\)
0.518349 + 0.855169i \(0.326547\pi\)
\(434\) 0 0
\(435\) 24.2981 + 25.2530i 1.16501 + 1.21079i
\(436\) −1.84495 + 0.847472i −0.0883572 + 0.0405865i
\(437\) 1.52681 5.69814i 0.0730373 0.272579i
\(438\) 16.3303 25.4720i 0.780293 1.21710i
\(439\) 2.21290 3.83285i 0.105616 0.182932i −0.808374 0.588670i \(-0.799652\pi\)
0.913990 + 0.405737i \(0.132985\pi\)
\(440\) 8.78542 + 1.40668i 0.418828 + 0.0670610i
\(441\) 0 0
\(442\) −2.96880 5.74315i −0.141211 0.273174i
\(443\) 4.25183 1.13928i 0.202011 0.0541286i −0.156395 0.987695i \(-0.549987\pi\)
0.358405 + 0.933566i \(0.383321\pi\)
\(444\) 4.96178 53.1987i 0.235476 2.52470i
\(445\) 0.501006 + 0.907721i 0.0237500 + 0.0430301i
\(446\) −12.8567 14.1116i −0.608781 0.668203i
\(447\) 15.1604 15.1604i 0.717062 0.717062i
\(448\) 0 0
\(449\) 21.8355i 1.03048i −0.857046 0.515240i \(-0.827703\pi\)
0.857046 0.515240i \(-0.172297\pi\)
\(450\) 4.45128 52.2193i 0.209835 2.46164i
\(451\) 4.30514 2.48557i 0.202721 0.117041i
\(452\) 16.0962 13.3498i 0.757102 0.627922i
\(453\) −17.0258 63.5411i −0.799941 2.98542i
\(454\) −24.8631 7.91772i −1.16688 0.371597i
\(455\) 0 0
\(456\) 15.4186 + 20.4557i 0.722041 + 0.957928i
\(457\) 21.2792 5.70175i 0.995400 0.266717i 0.275883 0.961191i \(-0.411030\pi\)
0.719517 + 0.694475i \(0.244363\pi\)
\(458\) −18.5932 11.9203i −0.868804 0.556997i
\(459\) 32.9019 + 56.9877i 1.53573 + 2.65996i
\(460\) 8.74946 + 3.43460i 0.407945 + 0.160139i
\(461\) 19.7670 0.920641 0.460321 0.887753i \(-0.347734\pi\)
0.460321 + 0.887753i \(0.347734\pi\)
\(462\) 0 0
\(463\) −14.5239 14.5239i −0.674983 0.674983i 0.283877 0.958861i \(-0.408379\pi\)
−0.958861 + 0.283877i \(0.908379\pi\)
\(464\) 3.59284 19.0931i 0.166794 0.886377i
\(465\) −7.35973 + 25.4917i −0.341299 + 1.18215i
\(466\) 1.15502 + 5.28156i 0.0535052 + 0.244663i
\(467\) 7.29665 + 27.2315i 0.337649 + 1.26012i 0.900969 + 0.433884i \(0.142857\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(468\) −14.4513 + 2.46282i −0.668014 + 0.113844i
\(469\) 0 0
\(470\) 2.68927 7.91404i 0.124047 0.365048i
\(471\) 49.6551 + 28.6684i 2.28799 + 1.32097i
\(472\) 7.48882 + 18.5287i 0.344701 + 0.852853i
\(473\) −4.80176 1.28663i −0.220785 0.0591592i
\(474\) 1.84176 + 2.02153i 0.0845947 + 0.0928519i
\(475\) −14.0233 0.540678i −0.643432 0.0248080i
\(476\) 0 0
\(477\) −5.16257 5.16257i −0.236378 0.236378i
\(478\) −21.8616 1.01730i −0.999928 0.0465301i
\(479\) 0.709375 + 1.22867i 0.0324122 + 0.0561395i 0.881776 0.471668i \(-0.156348\pi\)
−0.849364 + 0.527807i \(0.823014\pi\)
\(480\) −35.1404 + 20.7611i −1.60393 + 0.947610i
\(481\) 4.09391 7.09086i 0.186666 0.323315i
\(482\) 18.6784 + 36.1334i 0.850777 + 1.64583i
\(483\) 0 0
\(484\) −10.4330 + 14.7195i −0.474225 + 0.669067i
\(485\) 6.07987 + 24.5749i 0.276072 + 1.11589i
\(486\) 46.6437 10.2005i 2.11580 0.462703i
\(487\) −32.5132 8.71188i −1.47331 0.394773i −0.569247 0.822166i \(-0.692765\pi\)
−0.904066 + 0.427393i \(0.859432\pi\)
\(488\) 3.82742 4.90015i 0.173259 0.221819i
\(489\) 56.1067i 2.53723i
\(490\) 0 0
\(491\) 3.16673i 0.142913i 0.997444 + 0.0714563i \(0.0227647\pi\)
−0.997444 + 0.0714563i \(0.977235\pi\)
\(492\) −7.92228 + 21.3840i −0.357164 + 0.964066i
\(493\) −21.6871 5.81103i −0.976736 0.261716i
\(494\) 0.838642 + 3.83486i 0.0377323 + 0.172539i
\(495\) −19.9629 12.0443i −0.897265 0.541350i
\(496\) 13.8792 4.87213i 0.623195 0.218765i
\(497\) 0 0
\(498\) 26.0133 13.4470i 1.16568 0.602576i
\(499\) 3.72451 6.45105i 0.166732 0.288789i −0.770537 0.637395i \(-0.780012\pi\)
0.937269 + 0.348607i \(0.113345\pi\)
\(500\) 3.35933 22.1069i 0.150234 0.988651i
\(501\) −15.7195 27.2270i −0.702297 1.21641i
\(502\) −1.71104 + 36.7701i −0.0763674 + 1.64113i
\(503\) −19.3043 19.3043i −0.860736 0.860736i 0.130687 0.991424i \(-0.458282\pi\)
−0.991424 + 0.130687i \(0.958282\pi\)
\(504\) 0 0
\(505\) −0.259830 + 13.4832i −0.0115623 + 0.599994i
\(506\) 3.09101 2.81613i 0.137412 0.125192i
\(507\) 37.4697 + 10.0400i 1.66409 + 0.445891i
\(508\) 19.3128 16.0176i 0.856866 0.710664i
\(509\) 9.85817 + 5.69161i 0.436956 + 0.252276i 0.702305 0.711876i \(-0.252154\pi\)
−0.265350 + 0.964152i \(0.585487\pi\)
\(510\) 20.8482 + 42.3100i 0.923176 + 1.87352i
\(511\) 0 0
\(512\) 20.6747 + 9.19554i 0.913700 + 0.406390i
\(513\) −10.3411 38.5934i −0.456570 1.70394i
\(514\) 31.8863 6.97319i 1.40645 0.307574i
\(515\) 30.2326 + 8.72849i 1.33221 + 0.384623i
\(516\) 20.7227 9.51889i 0.912266 0.419046i
\(517\) −2.62931 2.62931i −0.115637 0.115637i
\(518\) 0 0
\(519\) 79.8313 3.50421
\(520\) −6.22154 + 0.643292i −0.272833 + 0.0282102i
\(521\) −0.617798 1.07006i −0.0270662 0.0468801i 0.852175 0.523257i \(-0.175283\pi\)
−0.879241 + 0.476377i \(0.841950\pi\)
\(522\) −27.4771 + 42.8588i −1.20264 + 1.87588i
\(523\) −6.09797 + 1.63395i −0.266646 + 0.0714474i −0.389665 0.920957i \(-0.627409\pi\)
0.123019 + 0.992404i \(0.460742\pi\)
\(524\) −21.4548 15.2068i −0.937256 0.664314i
\(525\) 0 0
\(526\) −4.87059 + 15.2945i −0.212368 + 0.666872i
\(527\) −4.39965 16.4197i −0.191652 0.715254i
\(528\) 1.37500 + 18.1051i 0.0598392 + 0.787924i
\(529\) −16.0929 + 9.29126i −0.699693 + 0.403968i
\(530\) −2.05314 2.34266i −0.0891826 0.101759i
\(531\) 52.3691i 2.27262i
\(532\) 0 0
\(533\) −2.47109 + 2.47109i −0.107035 + 0.107035i
\(534\) −1.56407 + 1.42498i −0.0676840 + 0.0616649i
\(535\) 12.4417 43.0940i 0.537901 1.86312i
\(536\) 8.32044 + 3.53057i 0.359388 + 0.152497i
\(537\) −64.0665 + 17.1666i −2.76467 + 0.740792i
\(538\) 34.1934 17.6756i 1.47418 0.762048i
\(539\) 0 0
\(540\) 62.9519 9.48407i 2.70902 0.408129i
\(541\) 16.1355 27.9475i 0.693719 1.20156i −0.276891 0.960901i \(-0.589304\pi\)
0.970611 0.240656i \(-0.0773624\pi\)
\(542\) 0.185532 + 0.118946i 0.00796929 + 0.00510917i
\(543\) 6.56407 24.4975i 0.281691 1.05129i
\(544\) 12.4056 23.0192i 0.531884 0.986939i
\(545\) 2.26951 + 0.0437350i 0.0972150 + 0.00187340i
\(546\) 0 0
\(547\) 17.6256 17.6256i 0.753617 0.753617i −0.221536 0.975152i \(-0.571107\pi\)
0.975152 + 0.221536i \(0.0711069\pi\)
\(548\) 4.85602 13.1075i 0.207439 0.559924i
\(549\) −14.1104 + 8.14662i −0.602215 + 0.347689i
\(550\) −8.16123 5.68747i −0.347996 0.242515i
\(551\) 11.8061 + 6.81625i 0.502957 + 0.290382i
\(552\) −2.66721 + 18.9956i −0.113524 + 0.808507i
\(553\) 0 0
\(554\) −8.98286 + 28.2078i −0.381645 + 1.19843i
\(555\) −30.8593 + 51.1479i −1.30990 + 2.17111i
\(556\) 42.2919 + 3.94451i 1.79357 + 0.167285i
\(557\) 1.60273 5.98149i 0.0679101 0.253444i −0.923622 0.383304i \(-0.874786\pi\)
0.991532 + 0.129860i \(0.0414528\pi\)
\(558\) −38.5036 1.79171i −1.62999 0.0758490i
\(559\) 3.49465 0.147808
\(560\) 0 0
\(561\) 20.9833 0.885915
\(562\) −3.62149 0.168521i −0.152764 0.00710861i
\(563\) −1.32949 + 4.96172i −0.0560313 + 0.209112i −0.988266 0.152742i \(-0.951189\pi\)
0.932235 + 0.361854i \(0.117856\pi\)
\(564\) 16.9839 + 1.58407i 0.715151 + 0.0667013i
\(565\) −22.6959 + 5.61499i −0.954823 + 0.236224i
\(566\) −8.82925 + 27.7254i −0.371121 + 1.16539i
\(567\) 0 0
\(568\) 4.79380 34.1410i 0.201143 1.43253i
\(569\) −30.0136 17.3284i −1.25824 0.726442i −0.285504 0.958378i \(-0.592161\pi\)
−0.972731 + 0.231935i \(0.925494\pi\)
\(570\) −5.57832 28.0908i −0.233650 1.17660i
\(571\) 28.9237 16.6991i 1.21042 0.698836i 0.247569 0.968870i \(-0.420368\pi\)
0.962851 + 0.270034i \(0.0870350\pi\)
\(572\) −0.966649 + 2.60920i −0.0404176 + 0.109096i
\(573\) 19.7875 19.7875i 0.826634 0.826634i
\(574\) 0 0
\(575\) −7.13910 7.71168i −0.297721 0.321599i
\(576\) −41.1996 42.6418i −1.71665 1.77674i
\(577\) 8.91664 33.2773i 0.371204 1.38535i −0.487608 0.873063i \(-0.662130\pi\)
0.858812 0.512291i \(-0.171203\pi\)
\(578\) −5.20050 3.33408i −0.216312 0.138679i
\(579\) 8.55978 14.8260i 0.355732 0.616146i
\(580\) −12.8998 + 17.4761i −0.535636 + 0.725657i
\(581\) 0 0
\(582\) −45.8942 + 23.7241i −1.90238 + 0.983394i
\(583\) −1.33855 + 0.358664i −0.0554372 + 0.0148544i
\(584\) 17.2643 + 7.32567i 0.714401 + 0.303138i
\(585\) 15.7469 + 4.54630i 0.651054 + 0.187966i
\(586\) −6.96487 + 6.34549i −0.287716 + 0.262130i
\(587\) 23.3690 23.3690i 0.964544 0.964544i −0.0348489 0.999393i \(-0.511095\pi\)
0.999393 + 0.0348489i \(0.0110950\pi\)
\(588\) 0 0
\(589\) 10.3214i 0.425288i
\(590\) 1.46845 22.2955i 0.0604552 0.917890i
\(591\) −48.7811 + 28.1638i −2.00659 + 1.15850i
\(592\) 33.0219 2.50786i 1.35719 0.103072i
\(593\) 1.67934 + 6.26739i 0.0689623 + 0.257371i 0.991797 0.127826i \(-0.0408000\pi\)
−0.922834 + 0.385197i \(0.874133\pi\)
\(594\) 8.59374 26.9859i 0.352606 1.10724i
\(595\) 0 0
\(596\) 10.8419 + 7.68459i 0.444101 + 0.314773i
\(597\) −13.3984 + 3.59010i −0.548362 + 0.146933i
\(598\) −1.58651 + 2.47464i −0.0648773 + 0.101196i
\(599\) −8.75860 15.1703i −0.357867 0.619843i 0.629737 0.776808i \(-0.283162\pi\)
−0.987604 + 0.156965i \(0.949829\pi\)
\(600\) 45.4727 3.81787i 1.85641 0.155864i
\(601\) −2.55297 −0.104138 −0.0520689 0.998643i \(-0.516582\pi\)
−0.0520689 + 0.998643i \(0.516582\pi\)
\(602\) 0 0
\(603\) −16.7477 16.7477i −0.682018 0.682018i
\(604\) 37.0517 17.0196i 1.50761 0.692516i
\(605\) 17.6601 9.74727i 0.717983 0.396283i
\(606\) −26.8856 + 5.87959i −1.09215 + 0.238842i
\(607\) −5.72830 21.3783i −0.232504 0.867718i −0.979258 0.202617i \(-0.935055\pi\)
0.746754 0.665101i \(-0.231611\pi\)
\(608\) −10.8932 + 11.5510i −0.441779 + 0.468457i
\(609\) 0 0
\(610\) −6.23574 + 3.07266i −0.252478 + 0.124408i
\(611\) 2.26378 + 1.30700i 0.0915829 + 0.0528754i
\(612\) −52.7427 + 43.7436i −2.13200 + 1.76823i
\(613\) −7.79104 2.08760i −0.314677 0.0843175i 0.0980238 0.995184i \(-0.468748\pi\)
−0.412701 + 0.910867i \(0.635415\pi\)
\(614\) −24.9125 + 22.6971i −1.00539 + 0.915980i
\(615\) 18.3724 17.6777i 0.740849 0.712835i
\(616\) 0 0
\(617\) −20.7105 20.7105i −0.833772 0.833772i 0.154258 0.988031i \(-0.450701\pi\)
−0.988031 + 0.154258i \(0.950701\pi\)
\(618\) −2.98502 + 64.1479i −0.120075 + 2.58041i
\(619\) 15.2502 + 26.4141i 0.612956 + 1.06167i 0.990739 + 0.135777i \(0.0433530\pi\)
−0.377784 + 0.925894i \(0.623314\pi\)
\(620\) −16.3422 1.84246i −0.656319 0.0739948i
\(621\) 14.9597 25.9110i 0.600314 1.03977i
\(622\) −22.8167 + 11.7946i −0.914866 + 0.472921i
\(623\) 0 0
\(624\) −4.22784 12.0438i −0.169249 0.482138i
\(625\) −14.1299 + 20.6239i −0.565197 + 0.824956i
\(626\) 0.473872 + 2.16688i 0.0189398 + 0.0866059i
\(627\) −12.3065 3.29753i −0.491476 0.131691i
\(628\) −12.3462 + 33.3253i −0.492668 + 1.32982i
\(629\) 38.2714i 1.52598i
\(630\) 0 0
\(631\) 24.2931i 0.967092i −0.875319 0.483546i \(-0.839349\pi\)
0.875319 0.483546i \(-0.160651\pi\)
\(632\) −1.04340 + 1.33584i −0.0415044 + 0.0531370i
\(633\) 60.9309 + 16.3264i 2.42178 + 0.648915i
\(634\) −40.8113 + 8.92497i −1.62082 + 0.354456i
\(635\) −27.2313 + 6.73706i −1.08064 + 0.267352i
\(636\) 3.67603 5.18637i 0.145764 0.205653i
\(637\) 0 0
\(638\) 4.43735 + 8.58406i 0.175676 + 0.339846i
\(639\) −45.1709 + 78.2383i −1.78693 + 3.09506i
\(640\) −16.3445 19.3095i −0.646074 0.763274i
\(641\) −11.2086 19.4138i −0.442712 0.766800i 0.555178 0.831732i \(-0.312650\pi\)
−0.997890 + 0.0649320i \(0.979317\pi\)
\(642\) 91.4372 + 4.25489i 3.60874 + 0.167927i
\(643\) 3.56268 + 3.56268i 0.140498 + 0.140498i 0.773858 0.633359i \(-0.218325\pi\)
−0.633359 + 0.773858i \(0.718325\pi\)
\(644\) 0 0
\(645\) −25.4913 0.491236i −1.00372 0.0193424i
\(646\) 12.3572 + 13.5634i 0.486189 + 0.533645i
\(647\) −16.0227 4.29327i −0.629918 0.168786i −0.0702854 0.997527i \(-0.522391\pi\)
−0.559632 + 0.828741i \(0.689058\pi\)
\(648\) 25.1173 + 62.1448i 0.986700 + 2.44128i
\(649\) −8.60829 4.97000i −0.337905 0.195089i
\(650\) 6.57657 + 2.37708i 0.257954 + 0.0932367i
\(651\) 0 0
\(652\) −34.2821 + 5.84240i −1.34259 + 0.228806i
\(653\) −3.24782 12.1210i −0.127097 0.474332i 0.872809 0.488062i \(-0.162296\pi\)
−0.999906 + 0.0137300i \(0.995629\pi\)
\(654\) 0.989659 + 4.52542i 0.0386987 + 0.176958i
\(655\) 14.2074 + 25.7409i 0.555129 + 1.00578i
\(656\) −13.8909 2.61392i −0.542349 0.102056i
\(657\) −34.7502 34.7502i −1.35573 1.35573i
\(658\) 0 0
\(659\) −33.3787 −1.30025 −0.650126 0.759827i \(-0.725284\pi\)
−0.650126 + 0.759827i \(0.725284\pi\)
\(660\) 7.41787 18.8966i 0.288740 0.735550i
\(661\) −3.47890 6.02563i −0.135313 0.234370i 0.790404 0.612586i \(-0.209871\pi\)
−0.925717 + 0.378217i \(0.876537\pi\)
\(662\) −15.0396 9.64201i −0.584531 0.374748i
\(663\) −14.2484 + 3.81784i −0.553361 + 0.148273i
\(664\) 10.9251 + 14.4943i 0.423977 + 0.562488i
\(665\) 0 0
\(666\) −82.6892 26.3327i −3.20414 1.02037i
\(667\) 2.64214 + 9.86062i 0.102304 + 0.381805i
\(668\) 14.9993 12.4400i 0.580339 0.481320i
\(669\) −37.7211 + 21.7783i −1.45838 + 0.841997i
\(670\) −6.66051 7.59973i −0.257318 0.293603i
\(671\) 3.09256i 0.119387i
\(672\) 0 0
\(673\) −5.34897 + 5.34897i −0.206188 + 0.206188i −0.802645 0.596457i \(-0.796575\pi\)
0.596457 + 0.802645i \(0.296575\pi\)
\(674\) 5.52979 + 6.06954i 0.212999 + 0.233790i
\(675\) −67.9905 21.0570i −2.61696 0.810483i
\(676\) −2.23286 + 23.9400i −0.0858792 + 0.920770i
\(677\) 28.9931 7.76868i 1.11430 0.298575i 0.345723 0.938337i \(-0.387634\pi\)
0.768573 + 0.639762i \(0.220967\pi\)
\(678\) −21.9101 42.3851i −0.841451 1.62779i
\(679\) 0 0
\(680\) −23.6811 + 17.1443i −0.908131 + 0.657456i
\(681\) −29.7677 + 51.5592i −1.14070 + 1.97575i
\(682\) −3.94864 + 6.15909i −0.151201 + 0.235844i
\(683\) −4.92938 + 18.3967i −0.188618 + 0.703930i 0.805210 + 0.592990i \(0.202053\pi\)
−0.993827 + 0.110940i \(0.964614\pi\)
\(684\) 37.8075 17.3667i 1.44561 0.664034i
\(685\) −11.2615 + 10.8357i −0.430281 + 0.414010i
\(686\) 0 0
\(687\) −35.6329 + 35.6329i −1.35948 + 1.35948i
\(688\) 7.97404 + 11.6707i 0.304008 + 0.444941i
\(689\) 0.843665 0.487090i 0.0321411 0.0185567i
\(690\) 11.9205 17.8280i 0.453805 0.678699i
\(691\) 24.4705 + 14.1281i 0.930903 + 0.537457i 0.887097 0.461583i \(-0.152718\pi\)
0.0438058 + 0.999040i \(0.486052\pi\)
\(692\) 8.31284 + 48.7782i 0.316007 + 1.85427i
\(693\) 0 0
\(694\) −19.9020 6.33786i −0.755470 0.240582i
\(695\) −40.6615 24.5325i −1.54238 0.930569i
\(696\) −40.8064 17.3152i −1.54676 0.656331i
\(697\) −4.22772 + 15.7781i −0.160136 + 0.597638i
\(698\) −0.332091 + 7.13662i −0.0125698 + 0.270125i
\(699\) 12.3354 0.466567
\(700\) 0 0
\(701\) −26.0149 −0.982568 −0.491284 0.871000i \(-0.663472\pi\)
−0.491284 + 0.871000i \(0.663472\pi\)
\(702\) −0.925454 + 19.8879i −0.0349290 + 0.750622i
\(703\) −6.01436 + 22.4459i −0.226836 + 0.846563i
\(704\) −10.9193 + 2.72543i −0.411538 + 0.102719i
\(705\) −16.3292 9.85194i −0.614992 0.371046i
\(706\) 14.6538 + 4.66656i 0.551504 + 0.175628i
\(707\) 0 0
\(708\) 44.9501 7.66046i 1.68933 0.287898i
\(709\) −15.2471 8.80290i −0.572616 0.330600i 0.185578 0.982630i \(-0.440584\pi\)
−0.758193 + 0.652030i \(0.773918\pi\)
\(710\) −21.4248 + 32.0424i −0.804058 + 1.20253i
\(711\) 3.84667 2.22087i 0.144261 0.0832893i
\(712\) −1.03355 0.807288i −0.0387340 0.0302544i
\(713\) −5.46525 + 5.46525i −0.204675 + 0.204675i
\(714\) 0 0
\(715\) 2.24174 2.15697i 0.0838363 0.0806663i
\(716\) −17.1603 37.3581i −0.641310 1.39614i
\(717\) −12.9239 + 48.2328i −0.482653 + 1.80129i
\(718\) −3.80611 + 5.93678i −0.142043 + 0.221558i
\(719\) 11.5866 20.0685i 0.432106 0.748429i −0.564949 0.825126i \(-0.691104\pi\)
0.997054 + 0.0766969i \(0.0244374\pi\)
\(720\) 20.7483 + 62.9617i 0.773243 + 2.34644i
\(721\) 0 0
\(722\) 7.22290 + 13.9727i 0.268809 + 0.520011i
\(723\) 89.6445 24.0202i 3.33391 0.893320i
\(724\) 15.6518 + 1.45983i 0.581696 + 0.0542541i
\(725\) 21.4839 11.3233i 0.797892 0.420538i
\(726\) 27.7235 + 30.4296i 1.02892 + 1.12935i
\(727\) −15.3777 + 15.3777i −0.570326 + 0.570326i −0.932220 0.361893i \(-0.882131\pi\)
0.361893 + 0.932220i \(0.382131\pi\)
\(728\) 0 0
\(729\) 37.8443i 1.40164i
\(730\) −13.8201 15.7689i −0.511503 0.583632i
\(731\) 14.1462 8.16734i 0.523218 0.302080i
\(732\) −9.05655 10.9197i −0.334740 0.403604i
\(733\) 10.8115 + 40.3490i 0.399331 + 1.49032i 0.814276 + 0.580478i \(0.197134\pi\)
−0.414944 + 0.909847i \(0.636199\pi\)
\(734\) 21.4725 + 6.83800i 0.792566 + 0.252395i
\(735\) 0 0
\(736\) −11.8844 + 0.348310i −0.438063 + 0.0128389i
\(737\) −4.34235 + 1.16353i −0.159953 + 0.0428592i
\(738\) 31.1813 + 19.9906i 1.14780 + 0.735862i
\(739\) −14.4738 25.0693i −0.532426 0.922189i −0.999283 0.0378565i \(-0.987947\pi\)
0.466857 0.884333i \(-0.345386\pi\)
\(740\) −34.4655 13.5294i −1.26698 0.497352i
\(741\) 8.95654 0.329027
\(742\) 0 0
\(743\) 23.4115 + 23.4115i 0.858885 + 0.858885i 0.991207 0.132322i \(-0.0422432\pi\)
−0.132322 + 0.991207i \(0.542243\pi\)
\(744\) −4.09437 33.3111i −0.150107 1.22124i
\(745\) −7.17953 13.0078i −0.263038 0.476570i
\(746\) −0.178017 0.814021i −0.00651768 0.0298034i
\(747\) −12.3100 45.9417i −0.450401 1.68092i
\(748\) 2.18499 + 12.8211i 0.0798912 + 0.468786i
\(749\) 0 0
\(750\) −47.6378 18.2638i −1.73949 0.666898i
\(751\) 38.1178 + 22.0073i 1.39094 + 0.803059i 0.993419 0.114534i \(-0.0365376\pi\)
0.397520 + 0.917593i \(0.369871\pi\)
\(752\) 0.800644 + 10.5424i 0.0291965 + 0.384441i
\(753\) 81.1249 + 21.7373i 2.95636 + 0.792153i
\(754\) −4.57495 5.02151i −0.166610 0.182872i
\(755\) −45.5779 0.878318i −1.65875 0.0319653i
\(756\) 0 0
\(757\) 24.7062 + 24.7062i 0.897961 + 0.897961i 0.995256 0.0972943i \(-0.0310188\pi\)
−0.0972943 + 0.995256i \(0.531019\pi\)
\(758\) −33.5630 1.56180i −1.21906 0.0567272i
\(759\) −4.77032 8.26243i −0.173152 0.299907i
\(760\) 16.5831 6.33354i 0.601531 0.229742i
\(761\) −2.24848 + 3.89448i −0.0815073 + 0.141175i −0.903898 0.427749i \(-0.859307\pi\)
0.822390 + 0.568924i \(0.192640\pi\)
\(762\) −26.2885 50.8551i −0.952331 1.84229i
\(763\) 0 0
\(764\) 14.1509 + 10.0300i 0.511963 + 0.362872i
\(765\) 74.3680 18.3987i 2.68878 0.665207i
\(766\) −5.93523 + 1.29797i −0.214449 + 0.0468975i
\(767\) 6.74959 + 1.80855i 0.243714 + 0.0653029i
\(768\) 30.5743 41.6006i 1.10325 1.50113i
\(769\) 14.9079i 0.537593i 0.963197 + 0.268797i \(0.0866259\pi\)
−0.963197 + 0.268797i \(0.913374\pi\)
\(770\) 0 0
\(771\) 74.4723i 2.68206i
\(772\) 9.95023 + 3.68633i 0.358116 + 0.132674i
\(773\) 26.7544 + 7.16881i 0.962287 + 0.257844i 0.705568 0.708642i \(-0.250692\pi\)
0.256719 + 0.966486i \(0.417358\pi\)
\(774\) −7.91303 36.1839i −0.284428 1.30060i
\(775\) 15.5575 + 9.80011i 0.558842 + 0.352030i
\(776\) −19.2747 25.5717i −0.691923 0.917971i
\(777\) 0 0
\(778\) −31.6460 + 16.3587i −1.13456 + 0.586489i
\(779\) 4.95906 8.58934i 0.177677 0.307745i
\(780\)