Properties

Label 804.2.c.b.671.4
Level 804
Weight 2
Character 804.671
Analytic conductor 6.420
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(128\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 671.4
Character \(\chi\) = 804.671
Dual form 804.2.c.b.671.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.40995 + 0.109793i) q^{2} +(-0.420694 + 1.68018i) q^{3} +(1.97589 - 0.309604i) q^{4} +0.933302i q^{5} +(0.408683 - 2.41516i) q^{6} -1.91511i q^{7} +(-2.75191 + 0.653464i) q^{8} +(-2.64603 - 1.41369i) q^{9} +O(q^{10})\) \(q+(-1.40995 + 0.109793i) q^{2} +(-0.420694 + 1.68018i) q^{3} +(1.97589 - 0.309604i) q^{4} +0.933302i q^{5} +(0.408683 - 2.41516i) q^{6} -1.91511i q^{7} +(-2.75191 + 0.653464i) q^{8} +(-2.64603 - 1.41369i) q^{9} +(-0.102470 - 1.31591i) q^{10} -1.29586 q^{11} +(-0.311053 + 3.45011i) q^{12} +3.83589 q^{13} +(0.210266 + 2.70021i) q^{14} +(-1.56812 - 0.392634i) q^{15} +(3.80829 - 1.22349i) q^{16} -7.71164i q^{17} +(3.88597 + 1.70270i) q^{18} -0.375504i q^{19} +(0.288954 + 1.84410i) q^{20} +(3.21774 + 0.805677i) q^{21} +(1.82709 - 0.142276i) q^{22} +1.08412 q^{23} +(0.0597709 - 4.89861i) q^{24} +4.12895 q^{25} +(-5.40840 + 0.421154i) q^{26} +(3.48842 - 3.85109i) q^{27} +(-0.592927 - 3.78406i) q^{28} +3.74170i q^{29} +(2.25407 + 0.381425i) q^{30} -8.96952i q^{31} +(-5.23515 + 2.14317i) q^{32} +(0.545160 - 2.17728i) q^{33} +(0.846683 + 10.8730i) q^{34} +1.78738 q^{35} +(-5.66596 - 1.97407i) q^{36} -7.86919 q^{37} +(0.0412277 + 0.529440i) q^{38} +(-1.61374 + 6.44500i) q^{39} +(-0.609879 - 2.56836i) q^{40} -7.73078i q^{41} +(-4.62530 - 0.782674i) q^{42} +7.24655i q^{43} +(-2.56048 + 0.401203i) q^{44} +(1.31940 - 2.46955i) q^{45} +(-1.52855 + 0.119029i) q^{46} +11.3216 q^{47} +(0.453560 + 6.91334i) q^{48} +3.33234 q^{49} +(-5.82159 + 0.453329i) q^{50} +(12.9570 + 3.24424i) q^{51} +(7.57930 - 1.18761i) q^{52} +5.24766i q^{53} +(-4.49566 + 5.81283i) q^{54} -1.20943i q^{55} +(1.25146 + 5.27021i) q^{56} +(0.630915 + 0.157972i) q^{57} +(-0.410812 - 5.27559i) q^{58} -0.895292 q^{59} +(-3.21999 - 0.290307i) q^{60} -12.6762 q^{61} +(0.984790 + 12.6465i) q^{62} +(-2.70737 + 5.06746i) q^{63} +(7.14597 - 3.59654i) q^{64} +3.58005i q^{65} +(-0.529596 + 3.12970i) q^{66} +1.00000i q^{67} +(-2.38755 - 15.2374i) q^{68} +(-0.456083 + 1.82152i) q^{69} +(-2.52011 + 0.196242i) q^{70} +12.8894 q^{71} +(8.20543 + 2.16124i) q^{72} +8.12415 q^{73} +(11.0951 - 0.863981i) q^{74} +(-1.73702 + 6.93739i) q^{75} +(-0.116258 - 0.741955i) q^{76} +2.48172i q^{77} +(1.56766 - 9.26427i) q^{78} -10.3413i q^{79} +(1.14188 + 3.55429i) q^{80} +(5.00299 + 7.48132i) q^{81} +(0.848785 + 10.9000i) q^{82} +12.4637 q^{83} +(6.60735 + 0.595703i) q^{84} +7.19729 q^{85} +(-0.795620 - 10.2172i) q^{86} +(-6.28674 - 1.57411i) q^{87} +(3.56608 - 0.846797i) q^{88} +2.29328i q^{89} +(-1.58914 + 3.62679i) q^{90} -7.34617i q^{91} +(2.14211 - 0.335649i) q^{92} +(15.0704 + 3.77342i) q^{93} +(-15.9628 + 1.24303i) q^{94} +0.350459 q^{95} +(-1.39853 - 9.69763i) q^{96} -2.62800 q^{97} +(-4.69841 + 0.365867i) q^{98} +(3.42889 + 1.83194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} - 4q^{10} + 4q^{12} - 8q^{13} - 4q^{16} + 18q^{18} - 8q^{21} - 8q^{22} - 24q^{24} - 136q^{25} + 14q^{30} - 32q^{33} + 34q^{36} - 48q^{37} + 16q^{40} - 28q^{42} - 16q^{45} - 28q^{46} - 22q^{48} - 152q^{49} + 8q^{52} - 16q^{54} - 32q^{57} - 20q^{58} - 14q^{60} + 8q^{61} + 16q^{64} + 14q^{66} + 56q^{69} - 4q^{70} - 8q^{72} - 48q^{73} - 36q^{76} + 40q^{78} + 44q^{81} + 60q^{82} + 46q^{84} + 64q^{85} - 28q^{88} - 14q^{90} + 32q^{93} - 8q^{96} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.40995 + 0.109793i −0.996982 + 0.0776353i
\(3\) −0.420694 + 1.68018i −0.242888 + 0.970054i
\(4\) 1.97589 0.309604i 0.987946 0.154802i
\(5\) 0.933302i 0.417385i 0.977981 + 0.208693i \(0.0669209\pi\)
−0.977981 + 0.208693i \(0.933079\pi\)
\(6\) 0.408683 2.41516i 0.166844 0.985983i
\(7\) 1.91511i 0.723845i −0.932208 0.361923i \(-0.882120\pi\)
0.932208 0.361923i \(-0.117880\pi\)
\(8\) −2.75191 + 0.653464i −0.972946 + 0.231034i
\(9\) −2.64603 1.41369i −0.882011 0.471229i
\(10\) −0.102470 1.31591i −0.0324039 0.416126i
\(11\) −1.29586 −0.390716 −0.195358 0.980732i \(-0.562587\pi\)
−0.195358 + 0.980732i \(0.562587\pi\)
\(12\) −0.311053 + 3.45011i −0.0897934 + 0.995960i
\(13\) 3.83589 1.06388 0.531942 0.846781i \(-0.321462\pi\)
0.531942 + 0.846781i \(0.321462\pi\)
\(14\) 0.210266 + 2.70021i 0.0561959 + 0.721660i
\(15\) −1.56812 0.392634i −0.404887 0.101378i
\(16\) 3.80829 1.22349i 0.952073 0.305872i
\(17\) 7.71164i 1.87035i −0.354190 0.935173i \(-0.615244\pi\)
0.354190 0.935173i \(-0.384756\pi\)
\(18\) 3.88597 + 1.70270i 0.915933 + 0.401331i
\(19\) 0.375504i 0.0861465i −0.999072 0.0430732i \(-0.986285\pi\)
0.999072 0.0430732i \(-0.0137149\pi\)
\(20\) 0.288954 + 1.84410i 0.0646121 + 0.412354i
\(21\) 3.21774 + 0.805677i 0.702169 + 0.175813i
\(22\) 1.82709 0.142276i 0.389537 0.0303334i
\(23\) 1.08412 0.226055 0.113028 0.993592i \(-0.463945\pi\)
0.113028 + 0.993592i \(0.463945\pi\)
\(24\) 0.0597709 4.89861i 0.0122007 0.999926i
\(25\) 4.12895 0.825789
\(26\) −5.40840 + 0.421154i −1.06067 + 0.0825950i
\(27\) 3.48842 3.85109i 0.671347 0.741143i
\(28\) −0.592927 3.78406i −0.112053 0.715120i
\(29\) 3.74170i 0.694816i 0.937714 + 0.347408i \(0.112938\pi\)
−0.937714 + 0.347408i \(0.887062\pi\)
\(30\) 2.25407 + 0.381425i 0.411535 + 0.0696383i
\(31\) 8.96952i 1.61097i −0.592613 0.805487i \(-0.701904\pi\)
0.592613 0.805487i \(-0.298096\pi\)
\(32\) −5.23515 + 2.14317i −0.925453 + 0.378863i
\(33\) 0.545160 2.17728i 0.0949002 0.379016i
\(34\) 0.846683 + 10.8730i 0.145205 + 1.86470i
\(35\) 1.78738 0.302122
\(36\) −5.66596 1.97407i −0.944326 0.329011i
\(37\) −7.86919 −1.29369 −0.646843 0.762623i \(-0.723911\pi\)
−0.646843 + 0.762623i \(0.723911\pi\)
\(38\) 0.0412277 + 0.529440i 0.00668801 + 0.0858865i
\(39\) −1.61374 + 6.44500i −0.258404 + 1.03203i
\(40\) −0.609879 2.56836i −0.0964303 0.406093i
\(41\) 7.73078i 1.20735i −0.797232 0.603673i \(-0.793703\pi\)
0.797232 0.603673i \(-0.206297\pi\)
\(42\) −4.62530 0.782674i −0.713699 0.120769i
\(43\) 7.24655i 1.10509i 0.833483 + 0.552545i \(0.186343\pi\)
−0.833483 + 0.552545i \(0.813657\pi\)
\(44\) −2.56048 + 0.401203i −0.386007 + 0.0604837i
\(45\) 1.31940 2.46955i 0.196684 0.368139i
\(46\) −1.52855 + 0.119029i −0.225373 + 0.0175499i
\(47\) 11.3216 1.65142 0.825712 0.564092i \(-0.190774\pi\)
0.825712 + 0.564092i \(0.190774\pi\)
\(48\) 0.453560 + 6.91334i 0.0654657 + 0.997855i
\(49\) 3.33234 0.476048
\(50\) −5.82159 + 0.453329i −0.823297 + 0.0641104i
\(51\) 12.9570 + 3.24424i 1.81434 + 0.454284i
\(52\) 7.57930 1.18761i 1.05106 0.164691i
\(53\) 5.24766i 0.720822i 0.932794 + 0.360411i \(0.117363\pi\)
−0.932794 + 0.360411i \(0.882637\pi\)
\(54\) −4.49566 + 5.81283i −0.611782 + 0.791027i
\(55\) 1.20943i 0.163079i
\(56\) 1.25146 + 5.27021i 0.167233 + 0.704262i
\(57\) 0.630915 + 0.157972i 0.0835668 + 0.0209239i
\(58\) −0.410812 5.27559i −0.0539423 0.692719i
\(59\) −0.895292 −0.116557 −0.0582786 0.998300i \(-0.518561\pi\)
−0.0582786 + 0.998300i \(0.518561\pi\)
\(60\) −3.21999 0.290307i −0.415699 0.0374785i
\(61\) −12.6762 −1.62302 −0.811508 0.584341i \(-0.801353\pi\)
−0.811508 + 0.584341i \(0.801353\pi\)
\(62\) 0.984790 + 12.6465i 0.125068 + 1.60611i
\(63\) −2.70737 + 5.06746i −0.341096 + 0.638439i
\(64\) 7.14597 3.59654i 0.893246 0.449568i
\(65\) 3.58005i 0.444050i
\(66\) −0.529596 + 3.12970i −0.0651887 + 0.385240i
\(67\) 1.00000i 0.122169i
\(68\) −2.38755 15.2374i −0.289533 1.84780i
\(69\) −0.456083 + 1.82152i −0.0549060 + 0.219286i
\(70\) −2.52011 + 0.196242i −0.301211 + 0.0234554i
\(71\) 12.8894 1.52969 0.764844 0.644216i \(-0.222816\pi\)
0.764844 + 0.644216i \(0.222816\pi\)
\(72\) 8.20543 + 2.16124i 0.967019 + 0.254705i
\(73\) 8.12415 0.950860 0.475430 0.879754i \(-0.342292\pi\)
0.475430 + 0.879754i \(0.342292\pi\)
\(74\) 11.0951 0.863981i 1.28978 0.100436i
\(75\) −1.73702 + 6.93739i −0.200574 + 0.801061i
\(76\) −0.116258 0.741955i −0.0133357 0.0851080i
\(77\) 2.48172i 0.282818i
\(78\) 1.56766 9.26427i 0.177503 1.04897i
\(79\) 10.3413i 1.16349i −0.813371 0.581746i \(-0.802370\pi\)
0.813371 0.581746i \(-0.197630\pi\)
\(80\) 1.14188 + 3.55429i 0.127666 + 0.397381i
\(81\) 5.00299 + 7.48132i 0.555887 + 0.831258i
\(82\) 0.848785 + 10.9000i 0.0937326 + 1.20370i
\(83\) 12.4637 1.36807 0.684035 0.729450i \(-0.260224\pi\)
0.684035 + 0.729450i \(0.260224\pi\)
\(84\) 6.60735 + 0.595703i 0.720921 + 0.0649965i
\(85\) 7.19729 0.780656
\(86\) −0.795620 10.2172i −0.0857939 1.10175i
\(87\) −6.28674 1.57411i −0.674009 0.168762i
\(88\) 3.56608 0.846797i 0.380146 0.0902689i
\(89\) 2.29328i 0.243087i 0.992586 + 0.121543i \(0.0387844\pi\)
−0.992586 + 0.121543i \(0.961216\pi\)
\(90\) −1.58914 + 3.62679i −0.167510 + 0.382297i
\(91\) 7.34617i 0.770088i
\(92\) 2.14211 0.335649i 0.223330 0.0349938i
\(93\) 15.0704 + 3.77342i 1.56273 + 0.391286i
\(94\) −15.9628 + 1.24303i −1.64644 + 0.128209i
\(95\) 0.350459 0.0359563
\(96\) −1.39853 9.69763i −0.142737 0.989761i
\(97\) −2.62800 −0.266833 −0.133417 0.991060i \(-0.542595\pi\)
−0.133417 + 0.991060i \(0.542595\pi\)
\(98\) −4.69841 + 0.365867i −0.474611 + 0.0369582i
\(99\) 3.42889 + 1.83194i 0.344616 + 0.184117i
\(100\) 8.15835 1.27834i 0.815835 0.127834i
\(101\) 10.6137i 1.05610i −0.849212 0.528052i \(-0.822923\pi\)
0.849212 0.528052i \(-0.177077\pi\)
\(102\) −18.6248 3.15161i −1.84413 0.312056i
\(103\) 3.79342i 0.373776i −0.982381 0.186888i \(-0.940160\pi\)
0.982381 0.186888i \(-0.0598402\pi\)
\(104\) −10.5560 + 2.50661i −1.03510 + 0.245794i
\(105\) −0.751940 + 3.00313i −0.0733818 + 0.293075i
\(106\) −0.576156 7.39891i −0.0559612 0.718646i
\(107\) 8.96867 0.867035 0.433517 0.901145i \(-0.357272\pi\)
0.433517 + 0.901145i \(0.357272\pi\)
\(108\) 5.70043 8.68937i 0.548524 0.836135i
\(109\) 9.06897 0.868649 0.434325 0.900756i \(-0.356987\pi\)
0.434325 + 0.900756i \(0.356987\pi\)
\(110\) 0.132787 + 1.70523i 0.0126607 + 0.162587i
\(111\) 3.31052 13.2217i 0.314221 1.25495i
\(112\) −2.34312 7.29331i −0.221404 0.689153i
\(113\) 3.41933i 0.321664i 0.986982 + 0.160832i \(0.0514177\pi\)
−0.986982 + 0.160832i \(0.948582\pi\)
\(114\) −0.906900 0.153462i −0.0849390 0.0143730i
\(115\) 1.01181i 0.0943521i
\(116\) 1.15845 + 7.39319i 0.107559 + 0.686440i
\(117\) −10.1499 5.42274i −0.938358 0.501333i
\(118\) 1.26231 0.0982967i 0.116205 0.00904895i
\(119\) −14.7687 −1.35384
\(120\) 4.57189 + 0.0557844i 0.417354 + 0.00509239i
\(121\) −9.32075 −0.847341
\(122\) 17.8727 1.39175i 1.61812 0.126003i
\(123\) 12.9891 + 3.25229i 1.17119 + 0.293249i
\(124\) −2.77700 17.7228i −0.249382 1.59155i
\(125\) 8.52007i 0.762058i
\(126\) 3.26087 7.44209i 0.290502 0.662994i
\(127\) 8.07104i 0.716189i 0.933685 + 0.358095i \(0.116573\pi\)
−0.933685 + 0.358095i \(0.883427\pi\)
\(128\) −9.68055 + 5.85550i −0.855648 + 0.517558i
\(129\) −12.1755 3.04858i −1.07200 0.268413i
\(130\) −0.393064 5.04767i −0.0344740 0.442710i
\(131\) −19.5624 −1.70918 −0.854588 0.519306i \(-0.826190\pi\)
−0.854588 + 0.519306i \(0.826190\pi\)
\(132\) 0.403082 4.47086i 0.0350838 0.389138i
\(133\) −0.719133 −0.0623567
\(134\) −0.109793 1.40995i −0.00948466 0.121801i
\(135\) 3.59423 + 3.25575i 0.309342 + 0.280210i
\(136\) 5.03927 + 21.2217i 0.432114 + 1.81975i
\(137\) 5.50987i 0.470740i 0.971906 + 0.235370i \(0.0756302\pi\)
−0.971906 + 0.235370i \(0.924370\pi\)
\(138\) 0.443062 2.61832i 0.0377160 0.222887i
\(139\) 0.159637i 0.0135402i 0.999977 + 0.00677012i \(0.00215501\pi\)
−0.999977 + 0.00677012i \(0.997845\pi\)
\(140\) 3.53167 0.553380i 0.298481 0.0467692i
\(141\) −4.76292 + 19.0224i −0.401111 + 1.60197i
\(142\) −18.1733 + 1.41516i −1.52507 + 0.118758i
\(143\) −4.97078 −0.415677
\(144\) −11.8065 2.14634i −0.983874 0.178861i
\(145\) −3.49214 −0.290006
\(146\) −11.4546 + 0.891974i −0.947990 + 0.0738203i
\(147\) −1.40189 + 5.59894i −0.115626 + 0.461793i
\(148\) −15.5487 + 2.43633i −1.27809 + 0.200265i
\(149\) 2.11710i 0.173440i −0.996233 0.0867199i \(-0.972361\pi\)
0.996233 0.0867199i \(-0.0276385\pi\)
\(150\) 1.68743 9.97205i 0.137778 0.814214i
\(151\) 11.9780i 0.974759i −0.873190 0.487380i \(-0.837953\pi\)
0.873190 0.487380i \(-0.162047\pi\)
\(152\) 0.245378 + 1.03335i 0.0199028 + 0.0838159i
\(153\) −10.9018 + 20.4052i −0.881361 + 1.64967i
\(154\) −0.272475 3.49909i −0.0219567 0.281965i
\(155\) 8.37128 0.672397
\(156\) −1.19317 + 13.2342i −0.0955298 + 1.05959i
\(157\) 23.1950 1.85117 0.925583 0.378546i \(-0.123576\pi\)
0.925583 + 0.378546i \(0.123576\pi\)
\(158\) 1.13541 + 14.5807i 0.0903280 + 1.15998i
\(159\) −8.81703 2.20766i −0.699236 0.175079i
\(160\) −2.00023 4.88598i −0.158132 0.386271i
\(161\) 2.07622i 0.163629i
\(162\) −7.87533 9.99896i −0.618745 0.785592i
\(163\) 5.61801i 0.440037i −0.975496 0.220018i \(-0.929388\pi\)
0.975496 0.220018i \(-0.0706117\pi\)
\(164\) −2.39348 15.2752i −0.186899 1.19279i
\(165\) 2.03206 + 0.508799i 0.158196 + 0.0396100i
\(166\) −17.5731 + 1.36843i −1.36394 + 0.106210i
\(167\) 12.7935 0.989992 0.494996 0.868895i \(-0.335169\pi\)
0.494996 + 0.868895i \(0.335169\pi\)
\(168\) −9.38141 0.114468i −0.723791 0.00883141i
\(169\) 1.71406 0.131850
\(170\) −10.1478 + 0.790211i −0.778299 + 0.0606064i
\(171\) −0.530844 + 0.993596i −0.0405947 + 0.0759822i
\(172\) 2.24356 + 14.3184i 0.171070 + 1.09177i
\(173\) 14.1345i 1.07463i −0.843383 0.537313i \(-0.819439\pi\)
0.843383 0.537313i \(-0.180561\pi\)
\(174\) 9.03679 + 1.52917i 0.685077 + 0.115926i
\(175\) 7.90740i 0.597744i
\(176\) −4.93501 + 1.58547i −0.371990 + 0.119509i
\(177\) 0.376644 1.50426i 0.0283103 0.113067i
\(178\) −0.251786 3.23340i −0.0188721 0.242353i
\(179\) −13.8602 −1.03596 −0.517979 0.855393i \(-0.673315\pi\)
−0.517979 + 0.855393i \(0.673315\pi\)
\(180\) 1.84240 5.28805i 0.137324 0.394148i
\(181\) −13.7462 −1.02175 −0.510873 0.859656i \(-0.670678\pi\)
−0.510873 + 0.859656i \(0.670678\pi\)
\(182\) 0.806557 + 10.3577i 0.0597860 + 0.767763i
\(183\) 5.33278 21.2983i 0.394211 1.57441i
\(184\) −2.98340 + 0.708434i −0.219939 + 0.0522265i
\(185\) 7.34433i 0.539966i
\(186\) −21.6628 3.66569i −1.58839 0.268782i
\(187\) 9.99320i 0.730775i
\(188\) 22.3702 3.50521i 1.63152 0.255644i
\(189\) −7.37528 6.68072i −0.536473 0.485951i
\(190\) −0.494127 + 0.0384779i −0.0358478 + 0.00279148i
\(191\) −6.72702 −0.486750 −0.243375 0.969932i \(-0.578255\pi\)
−0.243375 + 0.969932i \(0.578255\pi\)
\(192\) 3.03658 + 13.5196i 0.219146 + 0.975692i
\(193\) −19.3056 −1.38965 −0.694824 0.719180i \(-0.744518\pi\)
−0.694824 + 0.719180i \(0.744518\pi\)
\(194\) 3.70534 0.288536i 0.266028 0.0207157i
\(195\) −6.01513 1.50610i −0.430753 0.107854i
\(196\) 6.58434 1.03171i 0.470310 0.0736932i
\(197\) 13.6055i 0.969354i −0.874693 0.484677i \(-0.838937\pi\)
0.874693 0.484677i \(-0.161063\pi\)
\(198\) −5.03568 2.20646i −0.357870 0.156807i
\(199\) 14.8497i 1.05267i 0.850278 + 0.526334i \(0.176434\pi\)
−0.850278 + 0.526334i \(0.823566\pi\)
\(200\) −11.3625 + 2.69812i −0.803448 + 0.190786i
\(201\) −1.68018 0.420694i −0.118511 0.0296735i
\(202\) 1.16531 + 14.9647i 0.0819909 + 1.05292i
\(203\) 7.16578 0.502939
\(204\) 26.6060 + 2.39873i 1.86279 + 0.167945i
\(205\) 7.21516 0.503928
\(206\) 0.416490 + 5.34851i 0.0290183 + 0.372648i
\(207\) −2.86862 1.53261i −0.199383 0.106524i
\(208\) 14.6082 4.69316i 1.01290 0.325412i
\(209\) 0.486600i 0.0336589i
\(210\) 0.730472 4.31680i 0.0504074 0.297888i
\(211\) 19.1746i 1.32003i −0.751252 0.660015i \(-0.770550\pi\)
0.751252 0.660015i \(-0.229450\pi\)
\(212\) 1.62470 + 10.3688i 0.111585 + 0.712133i
\(213\) −5.42248 + 21.6565i −0.371542 + 1.48388i
\(214\) −12.6453 + 0.984697i −0.864418 + 0.0673125i
\(215\) −6.76323 −0.461248
\(216\) −7.08326 + 12.8774i −0.481955 + 0.876196i
\(217\) −17.1777 −1.16610
\(218\) −12.7867 + 0.995708i −0.866028 + 0.0674379i
\(219\) −3.41778 + 13.6501i −0.230952 + 0.922386i
\(220\) −0.374444 2.38970i −0.0252450 0.161114i
\(221\) 29.5810i 1.98983i
\(222\) −3.21600 + 19.0053i −0.215844 + 1.27555i
\(223\) 9.23297i 0.618285i −0.951016 0.309143i \(-0.899958\pi\)
0.951016 0.309143i \(-0.100042\pi\)
\(224\) 4.10442 + 10.0259i 0.274238 + 0.669884i
\(225\) −10.9253 5.83703i −0.728355 0.389135i
\(226\) −0.375418 4.82107i −0.0249725 0.320693i
\(227\) 4.98229 0.330686 0.165343 0.986236i \(-0.447127\pi\)
0.165343 + 0.986236i \(0.447127\pi\)
\(228\) 1.29553 + 0.116802i 0.0857985 + 0.00773539i
\(229\) 6.25758 0.413513 0.206756 0.978392i \(-0.433709\pi\)
0.206756 + 0.978392i \(0.433709\pi\)
\(230\) −0.111090 1.42660i −0.00732506 0.0940673i
\(231\) −4.16974 1.04404i −0.274349 0.0686931i
\(232\) −2.44506 10.2968i −0.160526 0.676018i
\(233\) 12.2211i 0.800632i 0.916377 + 0.400316i \(0.131100\pi\)
−0.916377 + 0.400316i \(0.868900\pi\)
\(234\) 14.9062 + 6.53138i 0.974447 + 0.426970i
\(235\) 10.5665i 0.689280i
\(236\) −1.76900 + 0.277186i −0.115152 + 0.0180433i
\(237\) 17.3753 + 4.35054i 1.12865 + 0.282598i
\(238\) 20.8230 1.62149i 1.34976 0.105106i
\(239\) −8.13591 −0.526268 −0.263134 0.964759i \(-0.584756\pi\)
−0.263134 + 0.964759i \(0.584756\pi\)
\(240\) −6.45224 + 0.423308i −0.416490 + 0.0273244i
\(241\) −6.85630 −0.441653 −0.220826 0.975313i \(-0.570875\pi\)
−0.220826 + 0.975313i \(0.570875\pi\)
\(242\) 13.1417 1.02335i 0.844783 0.0657836i
\(243\) −14.6747 + 5.25859i −0.941383 + 0.337339i
\(244\) −25.0467 + 3.92459i −1.60345 + 0.251246i
\(245\) 3.11008i 0.198696i
\(246\) −18.6710 3.15944i −1.19042 0.201438i
\(247\) 1.44039i 0.0916499i
\(248\) 5.86126 + 24.6833i 0.372190 + 1.56739i
\(249\) −5.24340 + 20.9413i −0.332287 + 1.32710i
\(250\) −0.935443 12.0128i −0.0591626 0.759758i
\(251\) −6.28732 −0.396852 −0.198426 0.980116i \(-0.563583\pi\)
−0.198426 + 0.980116i \(0.563583\pi\)
\(252\) −3.78056 + 10.8510i −0.238153 + 0.683546i
\(253\) −1.40487 −0.0883234
\(254\) −0.886143 11.3797i −0.0556016 0.714028i
\(255\) −3.02785 + 12.0928i −0.189612 + 0.757278i
\(256\) 13.0062 9.31879i 0.812885 0.582425i
\(257\) 16.1674i 1.00849i −0.863560 0.504246i \(-0.831771\pi\)
0.863560 0.504246i \(-0.168229\pi\)
\(258\) 17.5016 + 2.96154i 1.08960 + 0.184378i
\(259\) 15.0704i 0.936429i
\(260\) 1.10840 + 7.07378i 0.0687398 + 0.438697i
\(261\) 5.28959 9.90066i 0.327417 0.612836i
\(262\) 27.5819 2.14782i 1.70402 0.132692i
\(263\) −4.46023 −0.275030 −0.137515 0.990500i \(-0.543911\pi\)
−0.137515 + 0.990500i \(0.543911\pi\)
\(264\) −0.0774548 + 6.34792i −0.00476701 + 0.390687i
\(265\) −4.89765 −0.300861
\(266\) 1.01394 0.0789557i 0.0621685 0.00484108i
\(267\) −3.85313 0.964768i −0.235808 0.0590428i
\(268\) 0.309604 + 1.97589i 0.0189121 + 0.120697i
\(269\) 10.2424i 0.624488i −0.950002 0.312244i \(-0.898919\pi\)
0.950002 0.312244i \(-0.101081\pi\)
\(270\) −5.42513 4.19581i −0.330163 0.255349i
\(271\) 16.8258i 1.02209i 0.859553 + 0.511046i \(0.170742\pi\)
−0.859553 + 0.511046i \(0.829258\pi\)
\(272\) −9.43509 29.3682i −0.572086 1.78071i
\(273\) 12.3429 + 3.09049i 0.747027 + 0.187045i
\(274\) −0.604945 7.76862i −0.0365461 0.469320i
\(275\) −5.35054 −0.322649
\(276\) −0.337220 + 3.74034i −0.0202983 + 0.225142i
\(277\) −1.07933 −0.0648507 −0.0324253 0.999474i \(-0.510323\pi\)
−0.0324253 + 0.999474i \(0.510323\pi\)
\(278\) −0.0175270 0.225080i −0.00105120 0.0134994i
\(279\) −12.6801 + 23.7337i −0.759137 + 1.42090i
\(280\) −4.91870 + 1.16799i −0.293949 + 0.0698006i
\(281\) 33.0090i 1.96915i −0.174957 0.984576i \(-0.555979\pi\)
0.174957 0.984576i \(-0.444021\pi\)
\(282\) 4.62694 27.3434i 0.275530 1.62828i
\(283\) 31.1037i 1.84892i 0.381278 + 0.924460i \(0.375484\pi\)
−0.381278 + 0.924460i \(0.624516\pi\)
\(284\) 25.4680 3.99060i 1.51125 0.236799i
\(285\) −0.147436 + 0.588835i −0.00873334 + 0.0348796i
\(286\) 7.00852 0.545756i 0.414423 0.0322712i
\(287\) −14.8053 −0.873931
\(288\) 16.8822 + 1.72995i 0.994791 + 0.101938i
\(289\) −42.4693 −2.49820
\(290\) 4.92372 0.383412i 0.289131 0.0225147i
\(291\) 1.10558 4.41552i 0.0648105 0.258843i
\(292\) 16.0524 2.51527i 0.939398 0.147195i
\(293\) 22.9596i 1.34131i −0.741768 0.670656i \(-0.766013\pi\)
0.741768 0.670656i \(-0.233987\pi\)
\(294\) 1.36187 8.04812i 0.0794258 0.469376i
\(295\) 0.835578i 0.0486492i
\(296\) 21.6553 5.14223i 1.25869 0.298886i
\(297\) −4.52050 + 4.99048i −0.262306 + 0.289577i
\(298\) 0.232443 + 2.98500i 0.0134651 + 0.172916i
\(299\) 4.15857 0.240497
\(300\) −1.28432 + 14.2453i −0.0741504 + 0.822454i
\(301\) 13.8780 0.799913
\(302\) 1.31510 + 16.8884i 0.0756757 + 0.971817i
\(303\) 17.8330 + 4.46512i 1.02448 + 0.256515i
\(304\) −0.459424 1.43003i −0.0263498 0.0820177i
\(305\) 11.8307i 0.677423i
\(306\) 13.1306 29.9672i 0.750628 1.71311i
\(307\) 24.2941i 1.38654i −0.720680 0.693268i \(-0.756170\pi\)
0.720680 0.693268i \(-0.243830\pi\)
\(308\) 0.768350 + 4.90361i 0.0437808 + 0.279409i
\(309\) 6.37364 + 1.59587i 0.362584 + 0.0907857i
\(310\) −11.8030 + 0.919107i −0.670368 + 0.0522018i
\(311\) −1.10845 −0.0628545 −0.0314272 0.999506i \(-0.510005\pi\)
−0.0314272 + 0.999506i \(0.510005\pi\)
\(312\) 0.229275 18.7906i 0.0129801 1.06381i
\(313\) 14.0924 0.796549 0.398275 0.917266i \(-0.369609\pi\)
0.398275 + 0.917266i \(0.369609\pi\)
\(314\) −32.7037 + 2.54665i −1.84558 + 0.143716i
\(315\) −4.72947 2.52679i −0.266475 0.142369i
\(316\) −3.20172 20.4334i −0.180111 1.14947i
\(317\) 3.02987i 0.170175i 0.996373 + 0.0850874i \(0.0271169\pi\)
−0.996373 + 0.0850874i \(0.972883\pi\)
\(318\) 12.6739 + 2.14463i 0.710718 + 0.120265i
\(319\) 4.84872i 0.271476i
\(320\) 3.35666 + 6.66935i 0.187643 + 0.372828i
\(321\) −3.77307 + 15.0690i −0.210592 + 0.841071i
\(322\) 0.227954 + 2.92735i 0.0127034 + 0.163135i
\(323\) −2.89575 −0.161124
\(324\) 12.2016 + 13.2333i 0.677867 + 0.735185i
\(325\) 15.8382 0.878545
\(326\) 0.616818 + 7.92109i 0.0341624 + 0.438709i
\(327\) −3.81526 + 15.2375i −0.210984 + 0.842637i
\(328\) 5.05178 + 21.2744i 0.278938 + 1.17468i
\(329\) 21.6821i 1.19538i
\(330\) −2.92096 0.494273i −0.160794 0.0272088i
\(331\) 8.71346i 0.478935i −0.970904 0.239467i \(-0.923027\pi\)
0.970904 0.239467i \(-0.0769728\pi\)
\(332\) 24.6269 3.85881i 1.35158 0.211780i
\(333\) 20.8221 + 11.1246i 1.14105 + 0.609622i
\(334\) −18.0382 + 1.40464i −0.987004 + 0.0768584i
\(335\) −0.933302 −0.0509918
\(336\) 13.2398 0.868618i 0.722292 0.0473870i
\(337\) 10.7456 0.585352 0.292676 0.956212i \(-0.405454\pi\)
0.292676 + 0.956212i \(0.405454\pi\)
\(338\) −2.41673 + 0.188191i −0.131453 + 0.0102363i
\(339\) −5.74510 1.43849i −0.312031 0.0781281i
\(340\) 14.2211 2.22831i 0.771245 0.120847i
\(341\) 11.6232i 0.629434i
\(342\) 0.639372 1.45920i 0.0345733 0.0789044i
\(343\) 19.7876i 1.06843i
\(344\) −4.73536 19.9418i −0.255313 1.07519i
\(345\) −1.70003 0.425664i −0.0915267 0.0229170i
\(346\) 1.55187 + 19.9289i 0.0834290 + 1.07138i
\(347\) −13.0393 −0.699985 −0.349992 0.936753i \(-0.613816\pi\)
−0.349992 + 0.936753i \(0.613816\pi\)
\(348\) −12.9093 1.16387i −0.692009 0.0623899i
\(349\) 30.6809 1.64231 0.821155 0.570705i \(-0.193330\pi\)
0.821155 + 0.570705i \(0.193330\pi\)
\(350\) 0.868177 + 11.1490i 0.0464060 + 0.595940i
\(351\) 13.3812 14.7724i 0.714236 0.788491i
\(352\) 6.78402 2.77725i 0.361590 0.148028i
\(353\) 33.6065i 1.78869i 0.447377 + 0.894345i \(0.352358\pi\)
−0.447377 + 0.894345i \(0.647642\pi\)
\(354\) −0.365891 + 2.16227i −0.0194469 + 0.114923i
\(355\) 12.0297i 0.638469i
\(356\) 0.710008 + 4.53127i 0.0376303 + 0.240157i
\(357\) 6.21309 24.8141i 0.328831 1.31330i
\(358\) 19.5421 1.52175i 1.03283 0.0804269i
\(359\) −6.51712 −0.343960 −0.171980 0.985100i \(-0.555017\pi\)
−0.171980 + 0.985100i \(0.555017\pi\)
\(360\) −2.01709 + 7.65814i −0.106310 + 0.403620i
\(361\) 18.8590 0.992579
\(362\) 19.3814 1.50923i 1.01866 0.0793236i
\(363\) 3.92118 15.6606i 0.205809 0.821967i
\(364\) −2.27440 14.5152i −0.119211 0.760805i
\(365\) 7.58229i 0.396875i
\(366\) −5.18053 + 30.6149i −0.270791 + 1.60027i
\(367\) 11.9080i 0.621592i 0.950477 + 0.310796i \(0.100596\pi\)
−0.950477 + 0.310796i \(0.899404\pi\)
\(368\) 4.12865 1.32641i 0.215221 0.0691439i
\(369\) −10.9289 + 20.4559i −0.568936 + 1.06489i
\(370\) 0.806356 + 10.3551i 0.0419204 + 0.538336i
\(371\) 10.0499 0.521763
\(372\) 30.9458 + 2.79000i 1.60447 + 0.144655i
\(373\) −9.90047 −0.512627 −0.256313 0.966594i \(-0.582508\pi\)
−0.256313 + 0.966594i \(0.582508\pi\)
\(374\) −1.09718 14.0899i −0.0567340 0.728570i
\(375\) −14.3153 3.58434i −0.739238 0.185094i
\(376\) −31.1560 + 7.39825i −1.60675 + 0.381536i
\(377\) 14.3527i 0.739204i
\(378\) 11.1322 + 8.60970i 0.572581 + 0.442835i
\(379\) 24.3681i 1.25171i 0.779941 + 0.625854i \(0.215249\pi\)
−0.779941 + 0.625854i \(0.784751\pi\)
\(380\) 0.692468 0.108503i 0.0355229 0.00556611i
\(381\) −13.5608 3.39544i −0.694742 0.173954i
\(382\) 9.48472 0.738579i 0.485281 0.0377890i
\(383\) 27.6538 1.41304 0.706521 0.707692i \(-0.250263\pi\)
0.706521 + 0.707692i \(0.250263\pi\)
\(384\) −5.76577 18.7285i −0.294233 0.955734i
\(385\) −2.31619 −0.118044
\(386\) 27.2199 2.11962i 1.38545 0.107886i
\(387\) 10.2443 19.1746i 0.520749 0.974701i
\(388\) −5.19264 + 0.813640i −0.263617 + 0.0413063i
\(389\) 22.3928i 1.13536i 0.823250 + 0.567680i \(0.192159\pi\)
−0.823250 + 0.567680i \(0.807841\pi\)
\(390\) 8.64637 + 1.46310i 0.437826 + 0.0740871i
\(391\) 8.36036i 0.422801i
\(392\) −9.17028 + 2.17756i −0.463169 + 0.109983i
\(393\) 8.22979 32.8685i 0.415138 1.65799i
\(394\) 1.49379 + 19.1831i 0.0752561 + 0.966428i
\(395\) 9.65160 0.485624
\(396\) 7.34229 + 2.55811i 0.368964 + 0.128550i
\(397\) −12.6710 −0.635937 −0.317969 0.948101i \(-0.603001\pi\)
−0.317969 + 0.948101i \(0.603001\pi\)
\(398\) −1.63039 20.9373i −0.0817242 1.04949i
\(399\) 0.302535 1.20828i 0.0151457 0.0604894i
\(400\) 15.7242 5.05172i 0.786211 0.252586i
\(401\) 18.8895i 0.943298i 0.881786 + 0.471649i \(0.156341\pi\)
−0.881786 + 0.471649i \(0.843659\pi\)
\(402\) 2.41516 + 0.408683i 0.120457 + 0.0203833i
\(403\) 34.4061i 1.71389i
\(404\) −3.28605 20.9715i −0.163487 1.04337i
\(405\) −6.98233 + 4.66930i −0.346955 + 0.232019i
\(406\) −10.1034 + 0.786752i −0.501421 + 0.0390459i
\(407\) 10.1974 0.505465
\(408\) −37.7763 0.460932i −1.87021 0.0228195i
\(409\) 12.0394 0.595311 0.297655 0.954673i \(-0.403795\pi\)
0.297655 + 0.954673i \(0.403795\pi\)
\(410\) −10.1730 + 0.792173i −0.502408 + 0.0391226i
\(411\) −9.25760 2.31797i −0.456644 0.114337i
\(412\) −1.17446 7.49538i −0.0578614 0.369271i
\(413\) 1.71459i 0.0843693i
\(414\) 4.21287 + 1.84594i 0.207051 + 0.0907229i
\(415\) 11.6324i 0.571012i
\(416\) −20.0815 + 8.22098i −0.984575 + 0.403067i
\(417\) −0.268220 0.0671584i −0.0131348 0.00328876i
\(418\) −0.0534253 0.686080i −0.00261312 0.0335573i
\(419\) −9.40533 −0.459480 −0.229740 0.973252i \(-0.573788\pi\)
−0.229740 + 0.973252i \(0.573788\pi\)
\(420\) −0.555971 + 6.16666i −0.0271286 + 0.300902i
\(421\) 1.84317 0.0898308 0.0449154 0.998991i \(-0.485698\pi\)
0.0449154 + 0.998991i \(0.485698\pi\)
\(422\) 2.10523 + 27.0351i 0.102481 + 1.31605i
\(423\) −29.9573 16.0052i −1.45657 0.778198i
\(424\) −3.42916 14.4411i −0.166535 0.701320i
\(425\) 31.8409i 1.54451i
\(426\) 5.26767 31.1299i 0.255219 1.50825i
\(427\) 24.2763i 1.17481i
\(428\) 17.7211 2.77674i 0.856583 0.134219i
\(429\) 2.09117 8.35182i 0.100963 0.403230i
\(430\) 9.53578 0.742554i 0.459856 0.0358091i
\(431\) −1.16679 −0.0562024 −0.0281012 0.999605i \(-0.508946\pi\)
−0.0281012 + 0.999605i \(0.508946\pi\)
\(432\) 8.57316 18.9341i 0.412476 0.910968i
\(433\) 29.4866 1.41703 0.708517 0.705693i \(-0.249364\pi\)
0.708517 + 0.705693i \(0.249364\pi\)
\(434\) 24.2196 1.88599i 1.16258 0.0905302i
\(435\) 1.46912 5.86743i 0.0704389 0.281322i
\(436\) 17.9193 2.80779i 0.858178 0.134469i
\(437\) 0.407092i 0.0194739i
\(438\) 3.32020 19.6211i 0.158645 0.937532i
\(439\) 18.6446i 0.889858i −0.895566 0.444929i \(-0.853229\pi\)
0.895566 0.444929i \(-0.146771\pi\)
\(440\) 0.790318 + 3.32823i 0.0376769 + 0.158667i
\(441\) −8.81748 4.71088i −0.419880 0.224328i
\(442\) 3.24778 + 41.7076i 0.154481 + 1.98383i
\(443\) −6.97748 −0.331510 −0.165755 0.986167i \(-0.553006\pi\)
−0.165755 + 0.986167i \(0.553006\pi\)
\(444\) 2.44774 27.1495i 0.116165 1.28846i
\(445\) −2.14032 −0.101461
\(446\) 1.01371 + 13.0180i 0.0480008 + 0.616419i
\(447\) 3.55712 + 0.890652i 0.168246 + 0.0421264i
\(448\) −6.88779 13.6854i −0.325417 0.646572i
\(449\) 10.5665i 0.498664i 0.968418 + 0.249332i \(0.0802111\pi\)
−0.968418 + 0.249332i \(0.919789\pi\)
\(450\) 16.0450 + 7.03037i 0.756368 + 0.331415i
\(451\) 10.0180i 0.471730i
\(452\) 1.05864 + 6.75623i 0.0497942 + 0.317786i
\(453\) 20.1253 + 5.03909i 0.945569 + 0.236757i
\(454\) −7.02475 + 0.547020i −0.329688 + 0.0256729i
\(455\) 6.85620 0.321423
\(456\) −1.83945 0.0224442i −0.0861401 0.00105105i
\(457\) −8.54480 −0.399709 −0.199854 0.979826i \(-0.564047\pi\)
−0.199854 + 0.979826i \(0.564047\pi\)
\(458\) −8.82285 + 0.687038i −0.412265 + 0.0321032i
\(459\) −29.6982 26.9014i −1.38619 1.25565i
\(460\) 0.313262 + 1.99923i 0.0146059 + 0.0932147i
\(461\) 25.7095i 1.19741i 0.800969 + 0.598705i \(0.204318\pi\)
−0.800969 + 0.598705i \(0.795682\pi\)
\(462\) 5.99374 + 1.01424i 0.278854 + 0.0471865i
\(463\) 13.2973i 0.617976i 0.951066 + 0.308988i \(0.0999903\pi\)
−0.951066 + 0.308988i \(0.900010\pi\)
\(464\) 4.57792 + 14.2495i 0.212525 + 0.661515i
\(465\) −3.52174 + 14.0653i −0.163317 + 0.652262i
\(466\) −1.34179 17.2311i −0.0621573 0.798216i
\(467\) −28.3214 −1.31056 −0.655279 0.755387i \(-0.727449\pi\)
−0.655279 + 0.755387i \(0.727449\pi\)
\(468\) −21.7340 7.57230i −1.00465 0.350030i
\(469\) 1.91511 0.0884318
\(470\) −1.16012 14.8981i −0.0535125 0.687200i
\(471\) −9.75801 + 38.9719i −0.449625 + 1.79573i
\(472\) 2.46376 0.585041i 0.113404 0.0269287i
\(473\) 9.39052i 0.431776i
\(474\) −24.9759 4.22633i −1.14718 0.194122i
\(475\) 1.55044i 0.0711389i
\(476\) −29.1813 + 4.57244i −1.33752 + 0.209577i
\(477\) 7.41854 13.8855i 0.339672 0.635773i
\(478\) 11.4712 0.893265i 0.524680 0.0408570i
\(479\) −0.850005 −0.0388377 −0.0194189 0.999811i \(-0.506182\pi\)
−0.0194189 + 0.999811i \(0.506182\pi\)
\(480\) 9.05082 1.30525i 0.413112 0.0595763i
\(481\) −30.1853 −1.37633
\(482\) 9.66700 0.752773i 0.440320 0.0342879i
\(483\) 3.48843 + 0.873452i 0.158729 + 0.0397434i
\(484\) −18.4168 + 2.88574i −0.837126 + 0.131170i
\(485\) 2.45272i 0.111372i
\(486\) 20.1132 9.02551i 0.912353 0.409405i
\(487\) 6.13442i 0.277977i 0.990294 + 0.138989i \(0.0443851\pi\)
−0.990294 + 0.138989i \(0.955615\pi\)
\(488\) 34.8836 8.28341i 1.57911 0.374972i
\(489\) 9.43929 + 2.36346i 0.426859 + 0.106879i
\(490\) −0.341465 4.38504i −0.0154258 0.198096i
\(491\) 39.3299 1.77493 0.887467 0.460871i \(-0.152463\pi\)
0.887467 + 0.460871i \(0.152463\pi\)
\(492\) 26.6720 + 2.40469i 1.20247 + 0.108412i
\(493\) 28.8546 1.29955
\(494\) 0.158145 + 2.03087i 0.00711527 + 0.0913733i
\(495\) −1.70975 + 3.20019i −0.0768477 + 0.143838i
\(496\) −10.9741 34.1586i −0.492752 1.53376i
\(497\) 24.6846i 1.10726i
\(498\) 5.09370 30.1018i 0.228254 1.34889i
\(499\) 5.67525i 0.254059i −0.991899 0.127030i \(-0.959456\pi\)
0.991899 0.127030i \(-0.0405443\pi\)
\(500\) 2.63785 + 16.8347i 0.117968 + 0.752872i
\(501\) −5.38215 + 21.4955i −0.240457 + 0.960346i
\(502\) 8.86478 0.690304i 0.395655 0.0308098i
\(503\) −24.8415 −1.10763 −0.553815 0.832640i \(-0.686828\pi\)
−0.553815 + 0.832640i \(0.686828\pi\)
\(504\) 4.13903 15.7143i 0.184367 0.699972i
\(505\) 9.90580 0.440802
\(506\) 1.98079 0.154245i 0.0880569 0.00685702i
\(507\) −0.721093 + 2.87993i −0.0320249 + 0.127902i
\(508\) 2.49883 + 15.9475i 0.110868 + 0.707556i
\(509\) 27.6094i 1.22376i −0.790949 0.611882i \(-0.790413\pi\)
0.790949 0.611882i \(-0.209587\pi\)
\(510\) 2.94141 17.3826i 0.130248 0.769713i
\(511\) 15.5587i 0.688275i
\(512\) −17.3148 + 14.5670i −0.765215 + 0.643775i
\(513\) −1.44610 1.30992i −0.0638469 0.0578342i
\(514\) 1.77506 + 22.7951i 0.0782946 + 1.00545i
\(515\) 3.54041 0.156009
\(516\) −25.0014 2.25407i −1.10062 0.0992297i
\(517\) −14.6712 −0.645239
\(518\) −1.65462 21.2484i −0.0726999 0.933602i
\(519\) 23.7486 + 5.94630i 1.04245 + 0.261014i
\(520\) −2.33943 9.85195i −0.102591 0.432037i
\(521\) 42.9867i 1.88328i 0.336621 + 0.941640i \(0.390716\pi\)
−0.336621 + 0.941640i \(0.609284\pi\)
\(522\) −6.37100 + 14.5401i −0.278851 + 0.636405i
\(523\) 32.0916i 1.40327i 0.712538 + 0.701634i \(0.247546\pi\)
−0.712538 + 0.701634i \(0.752454\pi\)
\(524\) −38.6532 + 6.05660i −1.68857 + 0.264584i
\(525\) 13.2859 + 3.32660i 0.579844 + 0.145185i
\(526\) 6.28868 0.489702i 0.274199 0.0213520i
\(527\) −69.1697 −3.01308
\(528\) −0.587750 8.95872i −0.0255785 0.389878i
\(529\) −21.8247 −0.948899
\(530\) 6.90542 0.537728i 0.299952 0.0233574i
\(531\) 2.36897 + 1.26566i 0.102805 + 0.0549250i
\(532\) −1.42093 + 0.222646i −0.0616050 + 0.00965295i
\(533\) 29.6544i 1.28448i
\(534\) 5.53862 + 0.937223i 0.239680 + 0.0405576i
\(535\) 8.37049i 0.361888i
\(536\) −0.653464 2.75191i −0.0282253 0.118864i
\(537\) 5.83089 23.2876i 0.251621 1.00494i
\(538\) 1.12454 + 14.4412i 0.0484823 + 0.622603i
\(539\) −4.31824 −0.186000
\(540\) 8.10981 + 5.32022i 0.348991 + 0.228946i
\(541\) 14.6267 0.628852 0.314426 0.949282i \(-0.398188\pi\)
0.314426 + 0.949282i \(0.398188\pi\)
\(542\) −1.84735 23.7234i −0.0793504 1.01901i
\(543\) 5.78294 23.0961i 0.248170 0.991150i
\(544\) 16.5274 + 40.3716i 0.708605 + 1.73092i
\(545\) 8.46409i 0.362562i
\(546\) −17.7421 3.00225i −0.759294 0.128485i
\(547\) 16.9243i 0.723631i 0.932250 + 0.361816i \(0.117843\pi\)
−0.932250 + 0.361816i \(0.882157\pi\)
\(548\) 1.70588 + 10.8869i 0.0728716 + 0.465066i
\(549\) 33.5415 + 17.9201i 1.43152 + 0.764811i
\(550\) 7.54396 0.587451i 0.321676 0.0250490i
\(551\) 1.40502 0.0598560
\(552\) 0.0647990 5.31070i 0.00275803 0.226038i
\(553\) −19.8048 −0.842188
\(554\) 1.52180 0.118503i 0.0646549 0.00503470i
\(555\) 12.3398 + 3.08971i 0.523796 + 0.131151i
\(556\) 0.0494243 + 0.315426i 0.00209606 + 0.0133770i
\(557\) 3.01253i 0.127645i −0.997961 0.0638225i \(-0.979671\pi\)
0.997961 0.0638225i \(-0.0203291\pi\)
\(558\) 15.2724 34.8553i 0.646534 1.47554i
\(559\) 27.7970i 1.17569i
\(560\) 6.80686 2.18684i 0.287643 0.0924108i
\(561\) −16.7904 4.20408i −0.708892 0.177496i
\(562\) 3.62415 + 46.5409i 0.152876 + 1.96321i
\(563\) −20.2851 −0.854914 −0.427457 0.904036i \(-0.640590\pi\)
−0.427457 + 0.904036i \(0.640590\pi\)
\(564\) −3.52162 + 39.0607i −0.148287 + 1.64475i
\(565\) −3.19127 −0.134258
\(566\) −3.41496 43.8545i −0.143542 1.84334i
\(567\) 14.3276 9.58129i 0.601702 0.402376i
\(568\) −35.4704 + 8.42274i −1.48830 + 0.353410i
\(569\) 11.9558i 0.501214i −0.968089 0.250607i \(-0.919370\pi\)
0.968089 0.250607i \(-0.0806302\pi\)
\(570\) 0.143226 0.846412i 0.00599910 0.0354523i
\(571\) 16.9893i 0.710979i 0.934680 + 0.355489i \(0.115686\pi\)
−0.934680 + 0.355489i \(0.884314\pi\)
\(572\) −9.82171 + 1.53897i −0.410666 + 0.0643477i
\(573\) 2.83001 11.3026i 0.118226 0.472174i
\(574\) 20.8747 1.62552i 0.871293 0.0678479i
\(575\) 4.47628 0.186674
\(576\) −23.9929 0.585590i −0.999702 0.0243996i
\(577\) 10.7907 0.449221 0.224611 0.974449i \(-0.427889\pi\)
0.224611 + 0.974449i \(0.427889\pi\)
\(578\) 59.8794 4.66283i 2.49066 0.193948i
\(579\) 8.12175 32.4370i 0.337528 1.34803i
\(580\) −6.90008 + 1.08118i −0.286510 + 0.0448935i
\(581\) 23.8694i 0.990270i
\(582\) −1.07402 + 6.34703i −0.0445195 + 0.263093i
\(583\) 6.80023i 0.281637i
\(584\) −22.3569 + 5.30884i −0.925135 + 0.219681i
\(585\) 5.06106 9.47292i 0.209249 0.391657i
\(586\) 2.52080 + 32.3717i 0.104133 + 1.33726i
\(587\) −34.3462 −1.41762 −0.708809 0.705401i \(-0.750767\pi\)
−0.708809 + 0.705401i \(0.750767\pi\)
\(588\) −1.03654 + 11.4969i −0.0427460 + 0.474125i
\(589\) −3.36809 −0.138780
\(590\) 0.0917406 + 1.17812i 0.00377690 + 0.0485024i
\(591\) 22.8598 + 5.72376i 0.940326 + 0.235444i
\(592\) −29.9682 + 9.62785i −1.23168 + 0.395702i
\(593\) 38.4716i 1.57984i 0.613211 + 0.789919i \(0.289878\pi\)
−0.613211 + 0.789919i \(0.710122\pi\)
\(594\) 5.82574 7.53262i 0.239033 0.309067i
\(595\) 13.7836i 0.565074i
\(596\) −0.655464 4.18316i −0.0268488 0.171349i
\(597\) −24.9502 6.24718i −1.02114 0.255680i
\(598\) −5.86336 + 0.456582i −0.239771 + 0.0186710i
\(599\) 17.0584 0.696987 0.348493 0.937311i \(-0.386693\pi\)
0.348493 + 0.937311i \(0.386693\pi\)
\(600\) 0.246791 20.2261i 0.0100752 0.825728i
\(601\) 2.00283 0.0816970 0.0408485 0.999165i \(-0.486994\pi\)
0.0408485 + 0.999165i \(0.486994\pi\)
\(602\) −19.5672 + 1.52370i −0.797499 + 0.0621015i
\(603\) 1.41369 2.64603i 0.0575697 0.107755i
\(604\) −3.70845 23.6673i −0.150895 0.963009i
\(605\) 8.69908i 0.353668i
\(606\) −25.6338 4.33764i −1.04130 0.176205i
\(607\) 37.4559i 1.52029i 0.649754 + 0.760145i \(0.274872\pi\)
−0.649754 + 0.760145i \(0.725128\pi\)
\(608\) 0.804770 + 1.96582i 0.0326377 + 0.0797245i
\(609\) −3.01460 + 12.0398i −0.122158 + 0.487878i
\(610\) 1.29893 + 16.6806i 0.0525920 + 0.675379i
\(611\) 43.4284 1.75692
\(612\) −15.2233 + 43.6938i −0.615365 + 1.76622i
\(613\) −1.00833 −0.0407259 −0.0203629 0.999793i \(-0.506482\pi\)
−0.0203629 + 0.999793i \(0.506482\pi\)
\(614\) 2.66732 + 34.2533i 0.107644 + 1.38235i
\(615\) −3.03537 + 12.1228i −0.122398 + 0.488838i
\(616\) −1.62171 6.82946i −0.0653407 0.275167i
\(617\) 24.7964i 0.998265i 0.866526 + 0.499133i \(0.166348\pi\)
−0.866526 + 0.499133i \(0.833652\pi\)
\(618\) −9.16169 1.55030i −0.368537 0.0623624i
\(619\) 8.24346i 0.331333i 0.986182 + 0.165666i \(0.0529775\pi\)
−0.986182 + 0.165666i \(0.947023\pi\)
\(620\) 16.5407 2.59178i 0.664292 0.104088i
\(621\) 3.78187 4.17505i 0.151761 0.167539i
\(622\) 1.56285 0.121700i 0.0626648 0.00487973i
\(623\) 4.39189 0.175957
\(624\) 1.73980 + 26.5188i 0.0696479 + 1.06160i
\(625\) 12.6929 0.507717
\(626\) −19.8695 + 1.54725i −0.794145 + 0.0618404i
\(627\) −0.817578 0.204710i −0.0326509 0.00817532i
\(628\) 45.8309 7.18128i 1.82885 0.286564i
\(629\) 60.6843i 2.41964i
\(630\) 6.94572 + 3.04338i 0.276724 + 0.121251i
\(631\) 16.5330i 0.658169i −0.944300 0.329084i \(-0.893260\pi\)
0.944300 0.329084i \(-0.106740\pi\)
\(632\) 6.75769 + 28.4584i 0.268806 + 1.13201i
\(633\) 32.2168 + 8.06662i 1.28050 + 0.320619i
\(634\) −0.332659 4.27196i −0.0132116 0.169661i
\(635\) −7.53272 −0.298927
\(636\) −18.1050 1.63230i −0.717910 0.0647250i
\(637\) 12.7825 0.506460
\(638\) 0.532355 + 6.83643i 0.0210761 + 0.270657i
\(639\) −34.1057 18.2215i −1.34920 0.720832i
\(640\) −5.46495 9.03488i −0.216021 0.357135i
\(641\) 20.6339i 0.814990i 0.913207 + 0.407495i \(0.133598\pi\)
−0.913207 + 0.407495i \(0.866402\pi\)
\(642\) 3.66534 21.6607i 0.144660 0.854882i
\(643\) 13.7213i 0.541116i 0.962704 + 0.270558i \(0.0872082\pi\)
−0.962704 + 0.270558i \(0.912792\pi\)
\(644\) −0.642805 4.10238i −0.0253301 0.161656i
\(645\) 2.84525 11.3635i 0.112031 0.447436i
\(646\) 4.08285 0.317933i 0.160638 0.0125089i
\(647\) 50.4334 1.98274 0.991370 0.131093i \(-0.0418486\pi\)
0.991370 + 0.131093i \(0.0418486\pi\)
\(648\) −18.6565 17.3186i −0.732897 0.680339i
\(649\) 1.16017 0.0455408
\(650\) −22.3310 + 1.73892i −0.875893 + 0.0682061i
\(651\) 7.22654 28.8616i 0.283230 1.13118i
\(652\) −1.73936 11.1006i −0.0681186 0.434732i
\(653\) 0.551597i 0.0215857i 0.999942 + 0.0107928i \(0.00343553\pi\)
−0.999942 + 0.0107928i \(0.996564\pi\)
\(654\) 3.70633 21.9030i 0.144929 0.856474i
\(655\) 18.2577i 0.713386i
\(656\) −9.45852 29.4411i −0.369293 1.14948i
\(657\) −21.4968 11.4850i −0.838669 0.448072i
\(658\) 2.38055 + 30.5706i 0.0928033 + 1.19177i
\(659\) 4.27611 0.166574 0.0832868 0.996526i \(-0.473458\pi\)
0.0832868 + 0.996526i \(0.473458\pi\)
\(660\) 4.17266 + 0.376197i 0.162421 + 0.0146435i
\(661\) −22.5131 −0.875656 −0.437828 0.899059i \(-0.644252\pi\)
−0.437828 + 0.899059i \(0.644252\pi\)
\(662\) 0.956676 + 12.2855i 0.0371823 + 0.477489i
\(663\) 49.7015 + 12.4445i 1.93025 + 0.483306i
\(664\) −34.2989 + 8.14458i −1.33106 + 0.316071i
\(665\) 0.671168i 0.0260268i
\(666\) −30.5795 13.3989i −1.18493 0.519197i
\(667\) 4.05646i 0.157067i
\(668\) 25.2786 3.96092i 0.978058 0.153253i
\(669\) 15.5131 + 3.88425i 0.599770 + 0.150174i
\(670\) 1.31591 0.102470i 0.0508379 0.00395876i
\(671\) 16.4265 0.634139
\(672\) −18.5721 + 2.67834i −0.716433 + 0.103319i
\(673\) 8.71009 0.335749 0.167875 0.985808i \(-0.446310\pi\)
0.167875 + 0.985808i \(0.446310\pi\)
\(674\) −15.1507 + 1.17979i −0.583585 + 0.0454440i
\(675\) 14.4035 15.9010i 0.554391 0.612028i
\(676\) 3.38679 0.530679i 0.130261 0.0204107i
\(677\) 3.87652i 0.148987i 0.997222 + 0.0744935i \(0.0237340\pi\)
−0.997222 + 0.0744935i \(0.976266\pi\)
\(678\) 8.25822 + 1.39742i 0.317155 + 0.0536677i
\(679\) 5.03292i 0.193146i
\(680\) −19.8063 + 4.70317i −0.759535 + 0.180358i
\(681\) −2.09602 + 8.37116i −0.0803196 + 0.320783i
\(682\) −1.27615 16.3881i −0.0488663 0.627534i
\(683\) −16.0945 −0.615839 −0.307919 0.951412i \(-0.599633\pi\)
−0.307919 + 0.951412i \(0.599633\pi\)
\(684\) −0.741269 + 2.12759i −0.0283431 + 0.0813504i
\(685\) −5.14238 −0.196480
\(686\) 2.17254 + 27.8994i 0.0829479 + 1.06521i
\(687\) −2.63253 + 10.5139i −0.100437 + 0.401130i
\(688\) 8.86607 + 27.5970i 0.338016 + 1.05213i
\(689\) 20.1295i 0.766871i
\(690\) 2.44369 + 0.413511i 0.0930296 + 0.0157421i
\(691\) 19.7417i 0.751011i 0.926820 + 0.375505i \(0.122531\pi\)
−0.926820 + 0.375505i \(0.877469\pi\)
\(692\) −4.37610 27.9282i −0.166354 1.06167i
\(693\) 3.50837 6.56671i 0.133272 0.249449i
\(694\) 18.3847 1.43162i 0.697872 0.0543435i
\(695\) −0.148990 −0.00565150
\(696\) 18.3291 + 0.223645i 0.694764 + 0.00847724i
\(697\) −59.6170 −2.25815
\(698\) −43.2584 + 3.36854i −1.63735 + 0.127501i
\(699\) −20.5337 5.14135i −0.776657 0.194464i
\(700\) −2.44816 15.6242i −0.0925319 0.590538i
\(701\) 0.697335i 0.0263380i −0.999913 0.0131690i \(-0.995808\pi\)
0.999913 0.0131690i \(-0.00419194\pi\)
\(702\) −17.2449 + 22.2974i −0.650865 + 0.841561i
\(703\) 2.95491i 0.111447i
\(704\) −9.26018 + 4.66061i −0.349006 + 0.175653i
\(705\) −17.7536 4.44525i −0.668640 0.167418i
\(706\) −3.68975 47.3833i −0.138866 1.78329i
\(707\) −20.3265 −0.764455
\(708\) 0.278484 3.08885i 0.0104661 0.116086i
\(709\) −33.9166 −1.27376 −0.636882 0.770962i \(-0.719776\pi\)
−0.636882 + 0.770962i \(0.719776\pi\)
\(710\) −1.32077 16.9612i −0.0495678 0.636542i
\(711\) −14.6194 + 27.3635i −0.548270 + 1.02621i
\(712\) −1.49857 6.31088i −0.0561614 0.236510i
\(713\) 9.72406i 0.364169i
\(714\) −6.03570 + 35.6686i −0.225880 + 1.33486i
\(715\) 4.63924i 0.173498i
\(716\) −27.3862 + 4.29116i −1.02347 + 0.160368i
\(717\) 3.42273 13.6698i 0.127824 0.510509i
\(718\) 9.18878 0.715534i 0.342922 0.0267035i
\(719\) −42.9177 −1.60056 −0.800281 0.599625i \(-0.795316\pi\)
−0.800281 + 0.599625i \(0.795316\pi\)
\(720\) 2.00318 11.0190i 0.0746541 0.410655i
\(721\) −7.26483 −0.270556
\(722\) −26.5902 + 2.07058i −0.989583 + 0.0770592i
\(723\) 2.88440 11.5198i 0.107272 0.428427i
\(724\) −27.1610 + 4.25588i −1.00943 + 0.158168i
\(725\) 15.4493i 0.573772i
\(726\) −3.80923 + 22.5111i −0.141374 + 0.835464i
\(727\) 29.4179i 1.09105i 0.838095 + 0.545524i \(0.183670\pi\)
−0.838095 + 0.545524i \(0.816330\pi\)
\(728\) 4.80045 + 20.2160i 0.177917 + 0.749253i
\(729\) −2.66184 26.8685i −0.0985866 0.995128i
\(730\) −0.832482 10.6906i −0.0308115 0.395677i
\(731\) 55.8828 2.06690
\(732\) 3.94296 43.7341i 0.145736 1.61646i
\(733\) 8.78246 0.324388 0.162194 0.986759i \(-0.448143\pi\)
0.162194 + 0.986759i \(0.448143\pi\)
\(734\) −1.30741 16.7896i −0.0482575 0.619716i
\(735\) −5.22550 1.30839i −0.192746 0.0482607i
\(736\) −5.67554 + 2.32346i −0.209203 + 0.0856439i
\(737\) 1.29586i 0.0477336i
\(738\) 13.1632 30.0416i 0.484545 1.10585i
\(739\) 14.6462i 0.538768i −0.963033 0.269384i \(-0.913180\pi\)
0.963033 0.269384i \(-0.0868201\pi\)
\(740\) −2.27383 14.5116i −0.0835878 0.533457i
\(741\) 2.42012 + 0.605964i 0.0889054 + 0.0222606i
\(742\) −14.1698 + 1.10340i −0.520188 + 0.0405073i
\(743\) 29.6336 1.08715 0.543575 0.839360i \(-0.317070\pi\)
0.543575 + 0.839360i \(0.317070\pi\)
\(744\) −43.9382 0.536117i −1.61085 0.0196550i
\(745\) 1.97590 0.0723913
\(746\) 13.9591 1.08700i 0.511080 0.0397980i
\(747\) −32.9794 17.6198i −1.20665 0.644673i
\(748\) 3.09393 + 19.7455i 0.113125 + 0.721966i
\(749\) 17.1760i 0.627599i
\(750\) 20.5773 + 3.48201i 0.751376 + 0.127145i
\(751\) 54.3361i 1.98275i −0.131040 0.991377i \(-0.541832\pi\)
0.131040 0.991377i \(-0.458168\pi\)
\(752\) 43.1159 13.8518i 1.57228 0.505124i
\(753\) 2.64504 10.5639i 0.0963905 0.384968i
\(754\) −1.57583 20.2366i −0.0573884 0.736973i
\(755\) 11.1791 0.406850
\(756\) −16.6411 10.9170i −0.605232 0.397046i
\(757\) −30.0177 −1.09101 −0.545506 0.838107i \(-0.683662\pi\)
−0.545506 + 0.838107i \(0.683662\pi\)
\(758\) −2.67545 34.3577i −0.0971767 1.24793i
\(759\) 0.591020 2.36044i 0.0214527 0.0856785i
\(760\) −0.964429 + 0.229012i −0.0349835 + 0.00830714i
\(761\) 6.06585i 0.219887i 0.993938 + 0.109943i \(0.0350670\pi\)
−0.993938 + 0.109943i \(0.964933\pi\)
\(762\) 19.4928 + 3.29850i 0.706150 + 0.119492i
\(763\) 17.3681i &mi