Properties

Label 546.2.o.d.307.2
Level $546$
Weight $2$
Character 546.307
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.7442857984.4
Defining polynomial: \(x^{8} + 26 x^{6} + 205 x^{4} + 540 x^{2} + 324\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.2
Root \(-2.73923i\) of defining polynomial
Character \(\chi\) \(=\) 546.307
Dual form 546.2.o.d.265.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{3} +1.00000i q^{4} +(1.80230 - 1.80230i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.80230 - 1.93693i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{3} +1.00000i q^{4} +(1.80230 - 1.80230i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.80230 - 1.93693i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} -2.54884 q^{10} +(0.936931 - 0.936931i) q^{11} -1.00000 q^{12} +(-2.00000 - 3.00000i) q^{13} +(-2.64404 + 0.0951965i) q^{14} +(1.80230 + 1.80230i) q^{15} -1.00000 q^{16} +0.496594 q^{17} +(0.707107 + 0.707107i) q^{18} +(-3.07156 + 3.07156i) q^{19} +(1.80230 + 1.80230i) q^{20} +(1.93693 + 1.80230i) q^{21} -1.32502 q^{22} -7.37727i q^{23} +(0.707107 + 0.707107i) q^{24} -1.49659i q^{25} +(-0.707107 + 3.53553i) q^{26} -1.00000i q^{27} +(1.93693 + 1.80230i) q^{28} +7.25113 q^{29} -2.54884i q^{30} +(-5.73923 + 5.73923i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.936931 + 0.936931i) q^{33} +(-0.351145 - 0.351145i) q^{34} +(-0.242641 - 6.73923i) q^{35} -1.00000i q^{36} +(3.54154 - 3.54154i) q^{37} +4.34384 q^{38} +(3.00000 - 2.00000i) q^{39} -2.54884i q^{40} +(6.11650 - 6.11650i) q^{41} +(-0.0951965 - 2.64404i) q^{42} -6.85574i q^{43} +(0.936931 + 0.936931i) q^{44} +(-1.80230 + 1.80230i) q^{45} +(-5.21652 + 5.21652i) q^{46} +(5.87386 + 5.87386i) q^{47} -1.00000i q^{48} +(-0.503406 - 6.98188i) q^{49} +(-1.05825 + 1.05825i) q^{50} +0.496594i q^{51} +(3.00000 - 2.00000i) q^{52} -4.26926 q^{53} +(-0.707107 + 0.707107i) q^{54} -3.37727i q^{55} +(-0.0951965 - 2.64404i) q^{56} +(-3.07156 - 3.07156i) q^{57} +(-5.12732 - 5.12732i) q^{58} +(1.37727 + 1.37727i) q^{59} +(-1.80230 + 1.80230i) q^{60} -0.496594i q^{61} +8.11650 q^{62} +(-1.80230 + 1.93693i) q^{63} -1.00000i q^{64} +(-9.01152 - 1.80230i) q^{65} -1.32502i q^{66} +(9.11650 + 9.11650i) q^{67} +0.496594i q^{68} +7.37727 q^{69} +(-4.59379 + 4.93693i) q^{70} +(11.3773 + 11.3773i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(-3.54154 - 3.54154i) q^{73} -5.00849 q^{74} +1.49659 q^{75} +(-3.07156 - 3.07156i) q^{76} +(-0.126137 - 3.50341i) q^{77} +(-3.53553 - 0.707107i) q^{78} -13.1499 q^{79} +(-1.80230 + 1.80230i) q^{80} +1.00000 q^{81} -8.65004 q^{82} +(-7.87386 + 7.87386i) q^{83} +(-1.80230 + 1.93693i) q^{84} +(0.895013 - 0.895013i) q^{85} +(-4.84774 + 4.84774i) q^{86} +7.25113i q^{87} -1.32502i q^{88} +(-10.2177 - 10.2177i) q^{89} +2.54884 q^{90} +(-9.41540 - 1.53305i) q^{91} +7.37727 q^{92} +(-5.73923 - 5.73923i) q^{93} -8.30690i q^{94} +11.0718i q^{95} +(-0.707107 + 0.707107i) q^{96} +(-9.46034 + 9.46034i) q^{97} +(-4.58097 + 5.29289i) q^{98} +(-0.936931 + 0.936931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{5} + 4q^{7} - 8q^{9} + O(q^{10}) \) \( 8q + 4q^{5} + 4q^{7} - 8q^{9} - 4q^{10} - 8q^{11} - 8q^{12} - 16q^{13} + 4q^{15} - 8q^{16} + 12q^{17} - 4q^{19} + 4q^{20} + 4q^{22} - 12q^{29} - 20q^{31} - 8q^{33} + 24q^{34} + 32q^{35} - 8q^{37} - 12q^{38} + 24q^{39} - 16q^{41} + 4q^{42} - 8q^{44} - 4q^{45} - 20q^{46} + 16q^{47} + 4q^{49} + 24q^{50} + 24q^{52} - 24q^{53} + 4q^{56} - 4q^{57} - 16q^{58} - 28q^{59} - 4q^{60} - 4q^{63} - 20q^{65} + 8q^{67} + 20q^{69} + 24q^{70} + 52q^{71} + 8q^{73} - 4q^{74} + 20q^{75} - 4q^{76} - 32q^{77} - 48q^{79} - 4q^{80} + 8q^{81} - 40q^{82} - 32q^{83} - 4q^{84} + 20q^{85} - 20q^{86} - 4q^{89} + 4q^{90} - 8q^{91} + 20q^{92} - 20q^{93} + 36q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 1.00000i 0.577350i
\(4\) 1.00000i 0.500000i
\(5\) 1.80230 1.80230i 0.806015 0.806015i −0.178014 0.984028i \(-0.556967\pi\)
0.984028 + 0.178014i \(0.0569671\pi\)
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) 1.80230 1.93693i 0.681207 0.732091i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −1.00000 −0.333333
\(10\) −2.54884 −0.806015
\(11\) 0.936931 0.936931i 0.282495 0.282495i −0.551608 0.834103i \(-0.685986\pi\)
0.834103 + 0.551608i \(0.185986\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.00000 3.00000i −0.554700 0.832050i
\(14\) −2.64404 + 0.0951965i −0.706649 + 0.0254423i
\(15\) 1.80230 + 1.80230i 0.465353 + 0.465353i
\(16\) −1.00000 −0.250000
\(17\) 0.496594 0.120442 0.0602209 0.998185i \(-0.480820\pi\)
0.0602209 + 0.998185i \(0.480820\pi\)
\(18\) 0.707107 + 0.707107i 0.166667 + 0.166667i
\(19\) −3.07156 + 3.07156i −0.704664 + 0.704664i −0.965408 0.260744i \(-0.916032\pi\)
0.260744 + 0.965408i \(0.416032\pi\)
\(20\) 1.80230 + 1.80230i 0.403007 + 0.403007i
\(21\) 1.93693 + 1.80230i 0.422673 + 0.393295i
\(22\) −1.32502 −0.282495
\(23\) 7.37727i 1.53827i −0.639088 0.769133i \(-0.720688\pi\)
0.639088 0.769133i \(-0.279312\pi\)
\(24\) 0.707107 + 0.707107i 0.144338 + 0.144338i
\(25\) 1.49659i 0.299319i
\(26\) −0.707107 + 3.53553i −0.138675 + 0.693375i
\(27\) 1.00000i 0.192450i
\(28\) 1.93693 + 1.80230i 0.366046 + 0.340603i
\(29\) 7.25113 1.34650 0.673251 0.739414i \(-0.264897\pi\)
0.673251 + 0.739414i \(0.264897\pi\)
\(30\) 2.54884i 0.465353i
\(31\) −5.73923 + 5.73923i −1.03080 + 1.03080i −0.0312865 + 0.999510i \(0.509960\pi\)
−0.999510 + 0.0312865i \(0.990040\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) 0.936931 + 0.936931i 0.163099 + 0.163099i
\(34\) −0.351145 0.351145i −0.0602209 0.0602209i
\(35\) −0.242641 6.73923i −0.0410138 1.13914i
\(36\) 1.00000i 0.166667i
\(37\) 3.54154 3.54154i 0.582225 0.582225i −0.353289 0.935514i \(-0.614937\pi\)
0.935514 + 0.353289i \(0.114937\pi\)
\(38\) 4.34384 0.704664
\(39\) 3.00000 2.00000i 0.480384 0.320256i
\(40\) 2.54884i 0.403007i
\(41\) 6.11650 6.11650i 0.955237 0.955237i −0.0438029 0.999040i \(-0.513947\pi\)
0.999040 + 0.0438029i \(0.0139473\pi\)
\(42\) −0.0951965 2.64404i −0.0146891 0.407984i
\(43\) 6.85574i 1.04549i −0.852489 0.522745i \(-0.824908\pi\)
0.852489 0.522745i \(-0.175092\pi\)
\(44\) 0.936931 + 0.936931i 0.141248 + 0.141248i
\(45\) −1.80230 + 1.80230i −0.268672 + 0.268672i
\(46\) −5.21652 + 5.21652i −0.769133 + 0.769133i
\(47\) 5.87386 + 5.87386i 0.856791 + 0.856791i 0.990959 0.134168i \(-0.0428361\pi\)
−0.134168 + 0.990959i \(0.542836\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −0.503406 6.98188i −0.0719152 0.997411i
\(50\) −1.05825 + 1.05825i −0.149659 + 0.149659i
\(51\) 0.496594i 0.0695371i
\(52\) 3.00000 2.00000i 0.416025 0.277350i
\(53\) −4.26926 −0.586427 −0.293214 0.956047i \(-0.594725\pi\)
−0.293214 + 0.956047i \(0.594725\pi\)
\(54\) −0.707107 + 0.707107i −0.0962250 + 0.0962250i
\(55\) 3.37727i 0.455391i
\(56\) −0.0951965 2.64404i −0.0127212 0.353324i
\(57\) −3.07156 3.07156i −0.406838 0.406838i
\(58\) −5.12732 5.12732i −0.673251 0.673251i
\(59\) 1.37727 + 1.37727i 0.179305 + 0.179305i 0.791053 0.611748i \(-0.209533\pi\)
−0.611748 + 0.791053i \(0.709533\pi\)
\(60\) −1.80230 + 1.80230i −0.232676 + 0.232676i
\(61\) 0.496594i 0.0635823i −0.999495 0.0317912i \(-0.989879\pi\)
0.999495 0.0317912i \(-0.0101211\pi\)
\(62\) 8.11650 1.03080
\(63\) −1.80230 + 1.93693i −0.227069 + 0.244030i
\(64\) 1.00000i 0.125000i
\(65\) −9.01152 1.80230i −1.11774 0.223548i
\(66\) 1.32502i 0.163099i
\(67\) 9.11650 + 9.11650i 1.11376 + 1.11376i 0.992638 + 0.121120i \(0.0386487\pi\)
0.121120 + 0.992638i \(0.461351\pi\)
\(68\) 0.496594i 0.0602209i
\(69\) 7.37727 0.888119
\(70\) −4.59379 + 4.93693i −0.549062 + 0.590076i
\(71\) 11.3773 + 11.3773i 1.35023 + 1.35023i 0.885396 + 0.464837i \(0.153887\pi\)
0.464837 + 0.885396i \(0.346113\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) −3.54154 3.54154i −0.414506 0.414506i 0.468799 0.883305i \(-0.344687\pi\)
−0.883305 + 0.468799i \(0.844687\pi\)
\(74\) −5.00849 −0.582225
\(75\) 1.49659 0.172812
\(76\) −3.07156 3.07156i −0.352332 0.352332i
\(77\) −0.126137 3.50341i −0.0143747 0.399250i
\(78\) −3.53553 0.707107i −0.400320 0.0800641i
\(79\) −13.1499 −1.47948 −0.739741 0.672891i \(-0.765052\pi\)
−0.739741 + 0.672891i \(0.765052\pi\)
\(80\) −1.80230 + 1.80230i −0.201504 + 0.201504i
\(81\) 1.00000 0.111111
\(82\) −8.65004 −0.955237
\(83\) −7.87386 + 7.87386i −0.864269 + 0.864269i −0.991831 0.127562i \(-0.959285\pi\)
0.127562 + 0.991831i \(0.459285\pi\)
\(84\) −1.80230 + 1.93693i −0.196647 + 0.211337i
\(85\) 0.895013 0.895013i 0.0970778 0.0970778i
\(86\) −4.84774 + 4.84774i −0.522745 + 0.522745i
\(87\) 7.25113i 0.777403i
\(88\) 1.32502i 0.141248i
\(89\) −10.2177 10.2177i −1.08307 1.08307i −0.996221 0.0868533i \(-0.972319\pi\)
−0.0868533 0.996221i \(-0.527681\pi\)
\(90\) 2.54884 0.268672
\(91\) −9.41540 1.53305i −0.987002 0.160707i
\(92\) 7.37727 0.769133
\(93\) −5.73923 5.73923i −0.595131 0.595131i
\(94\) 8.30690i 0.856791i
\(95\) 11.0718i 1.13594i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) −9.46034 + 9.46034i −0.960552 + 0.960552i −0.999251 0.0386985i \(-0.987679\pi\)
0.0386985 + 0.999251i \(0.487679\pi\)
\(98\) −4.58097 + 5.29289i −0.462748 + 0.534663i
\(99\) −0.936931 + 0.936931i −0.0941651 + 0.0941651i
\(100\) 1.49659 0.149659
\(101\) 4.66465 0.464150 0.232075 0.972698i \(-0.425449\pi\)
0.232075 + 0.972698i \(0.425449\pi\)
\(102\) 0.351145 0.351145i 0.0347685 0.0347685i
\(103\) 18.5865 1.83138 0.915690 0.401885i \(-0.131645\pi\)
0.915690 + 0.401885i \(0.131645\pi\)
\(104\) −3.53553 0.707107i −0.346688 0.0693375i
\(105\) 6.73923 0.242641i 0.657682 0.0236793i
\(106\) 3.01882 + 3.01882i 0.293214 + 0.293214i
\(107\) 6.95694 0.672553 0.336276 0.941763i \(-0.390832\pi\)
0.336276 + 0.941763i \(0.390832\pi\)
\(108\) 1.00000 0.0962250
\(109\) 2.94374 + 2.94374i 0.281959 + 0.281959i 0.833890 0.551931i \(-0.186109\pi\)
−0.551931 + 0.833890i \(0.686109\pi\)
\(110\) −2.38809 + 2.38809i −0.227695 + 0.227695i
\(111\) 3.54154 + 3.54154i 0.336148 + 0.336148i
\(112\) −1.80230 + 1.93693i −0.170302 + 0.183023i
\(113\) −2.93996 −0.276568 −0.138284 0.990393i \(-0.544159\pi\)
−0.138284 + 0.990393i \(0.544159\pi\)
\(114\) 4.34384i 0.406838i
\(115\) −13.2961 13.2961i −1.23987 1.23987i
\(116\) 7.25113i 0.673251i
\(117\) 2.00000 + 3.00000i 0.184900 + 0.277350i
\(118\) 1.94775i 0.179305i
\(119\) 0.895013 0.961868i 0.0820457 0.0881743i
\(120\) 2.54884 0.232676
\(121\) 9.24432i 0.840393i
\(122\) −0.351145 + 0.351145i −0.0317912 + 0.0317912i
\(123\) 6.11650 + 6.11650i 0.551507 + 0.551507i
\(124\) −5.73923 5.73923i −0.515398 0.515398i
\(125\) 6.31420 + 6.31420i 0.564759 + 0.564759i
\(126\) 2.64404 0.0951965i 0.235550 0.00848077i
\(127\) 19.8376i 1.76030i 0.474692 + 0.880152i \(0.342559\pi\)
−0.474692 + 0.880152i \(0.657441\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 6.85574 0.603614
\(130\) 5.09768 + 7.64653i 0.447096 + 0.670645i
\(131\) 5.10801i 0.446289i 0.974785 + 0.223145i \(0.0716322\pi\)
−0.974785 + 0.223145i \(0.928368\pi\)
\(132\) −0.936931 + 0.936931i −0.0815494 + 0.0815494i
\(133\) 0.413518 + 11.4853i 0.0358566 + 0.995900i
\(134\) 12.8927i 1.11376i
\(135\) −1.80230 1.80230i −0.155118 0.155118i
\(136\) 0.351145 0.351145i 0.0301104 0.0301104i
\(137\) 3.80230 3.80230i 0.324853 0.324853i −0.525773 0.850625i \(-0.676224\pi\)
0.850625 + 0.525773i \(0.176224\pi\)
\(138\) −5.21652 5.21652i −0.444059 0.444059i
\(139\) 2.93996i 0.249364i −0.992197 0.124682i \(-0.960209\pi\)
0.992197 0.124682i \(-0.0397910\pi\)
\(140\) 6.73923 0.242641i 0.569569 0.0205069i
\(141\) −5.87386 + 5.87386i −0.494668 + 0.494668i
\(142\) 16.0899i 1.35023i
\(143\) −4.68466 0.936931i −0.391751 0.0783501i
\(144\) 1.00000 0.0833333
\(145\) 13.0687 13.0687i 1.08530 1.08530i
\(146\) 5.00849i 0.414506i
\(147\) 6.98188 0.503406i 0.575855 0.0415202i
\(148\) 3.54154 + 3.54154i 0.291113 + 0.291113i
\(149\) −1.74605 1.74605i −0.143042 0.143042i 0.631960 0.775001i \(-0.282251\pi\)
−0.775001 + 0.631960i \(0.782251\pi\)
\(150\) −1.05825 1.05825i −0.0864059 0.0864059i
\(151\) −6.55003 + 6.55003i −0.533034 + 0.533034i −0.921474 0.388440i \(-0.873014\pi\)
0.388440 + 0.921474i \(0.373014\pi\)
\(152\) 4.34384i 0.352332i
\(153\) −0.496594 −0.0401472
\(154\) −2.38809 + 2.56647i −0.192438 + 0.206812i
\(155\) 20.6877i 1.66167i
\(156\) 2.00000 + 3.00000i 0.160128 + 0.240192i
\(157\) 1.70581i 0.136138i 0.997681 + 0.0680691i \(0.0216838\pi\)
−0.997681 + 0.0680691i \(0.978316\pi\)
\(158\) 9.29841 + 9.29841i 0.739741 + 0.739741i
\(159\) 4.26926i 0.338574i
\(160\) 2.54884 0.201504
\(161\) −14.2893 13.2961i −1.12615 1.04788i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) −4.23583 + 4.23583i −0.331776 + 0.331776i −0.853261 0.521485i \(-0.825378\pi\)
0.521485 + 0.853261i \(0.325378\pi\)
\(164\) 6.11650 + 6.11650i 0.477619 + 0.477619i
\(165\) 3.37727 0.262920
\(166\) 11.1353 0.864269
\(167\) −8.02001 8.02001i −0.620607 0.620607i 0.325080 0.945687i \(-0.394609\pi\)
−0.945687 + 0.325080i \(0.894609\pi\)
\(168\) 2.64404 0.0951965i 0.203992 0.00734457i
\(169\) −5.00000 + 12.0000i −0.384615 + 0.923077i
\(170\) −1.26574 −0.0970778
\(171\) 3.07156 3.07156i 0.234888 0.234888i
\(172\) 6.85574 0.522745
\(173\) −4.21603 −0.320538 −0.160269 0.987073i \(-0.551236\pi\)
−0.160269 + 0.987073i \(0.551236\pi\)
\(174\) 5.12732 5.12732i 0.388701 0.388701i
\(175\) −2.89880 2.69732i −0.219129 0.203898i
\(176\) −0.936931 + 0.936931i −0.0706239 + 0.0706239i
\(177\) −1.37727 + 1.37727i −0.103522 + 0.103522i
\(178\) 14.4500i 1.08307i
\(179\) 5.33535i 0.398783i 0.979920 + 0.199391i \(0.0638965\pi\)
−0.979920 + 0.199391i \(0.936103\pi\)
\(180\) −1.80230 1.80230i −0.134336 0.134336i
\(181\) −1.79760 −0.133615 −0.0668073 0.997766i \(-0.521281\pi\)
−0.0668073 + 0.997766i \(0.521281\pi\)
\(182\) 5.57367 + 7.74172i 0.413148 + 0.573855i
\(183\) 0.496594 0.0367093
\(184\) −5.21652 5.21652i −0.384567 0.384567i
\(185\) 12.7659i 0.938564i
\(186\) 8.11650i 0.595131i
\(187\) 0.465274 0.465274i 0.0340242 0.0340242i
\(188\) −5.87386 + 5.87386i −0.428395 + 0.428395i
\(189\) −1.93693 1.80230i −0.140891 0.131098i
\(190\) 7.82892 7.82892i 0.567969 0.567969i
\(191\) −18.7889 −1.35952 −0.679758 0.733437i \(-0.737915\pi\)
−0.679758 + 0.733437i \(0.737915\pi\)
\(192\) 1.00000 0.0721688
\(193\) 1.37046 1.37046i 0.0986476 0.0986476i −0.656061 0.754708i \(-0.727778\pi\)
0.754708 + 0.656061i \(0.227778\pi\)
\(194\) 13.3789 0.960552
\(195\) 1.80230 9.01152i 0.129066 0.645328i
\(196\) 6.98188 0.503406i 0.498705 0.0359576i
\(197\) −2.86537 2.86537i −0.204149 0.204149i 0.597626 0.801775i \(-0.296111\pi\)
−0.801775 + 0.597626i \(0.796111\pi\)
\(198\) 1.32502 0.0941651
\(199\) 14.0650 0.997038 0.498519 0.866879i \(-0.333877\pi\)
0.498519 + 0.866879i \(0.333877\pi\)
\(200\) −1.05825 1.05825i −0.0748297 0.0748297i
\(201\) −9.11650 + 9.11650i −0.643029 + 0.643029i
\(202\) −3.29841 3.29841i −0.232075 0.232075i
\(203\) 13.0687 14.0449i 0.917246 0.985762i
\(204\) −0.496594 −0.0347685
\(205\) 22.0476i 1.53987i
\(206\) −13.1426 13.1426i −0.915690 0.915690i
\(207\) 7.37727i 0.512756i
\(208\) 2.00000 + 3.00000i 0.138675 + 0.208013i
\(209\) 5.75568i 0.398129i
\(210\) −4.93693 4.59379i −0.340681 0.317001i
\(211\) −14.8557 −1.02271 −0.511356 0.859369i \(-0.670856\pi\)
−0.511356 + 0.859369i \(0.670856\pi\)
\(212\) 4.26926i 0.293214i
\(213\) −11.3773 + 11.3773i −0.779558 + 0.779558i
\(214\) −4.91930 4.91930i −0.336276 0.336276i
\(215\) −12.3561 12.3561i −0.842680 0.842680i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 0.772662 + 21.4603i 0.0524517 + 1.45682i
\(218\) 4.16308i 0.281959i
\(219\) 3.54154 3.54154i 0.239315 0.239315i
\(220\) 3.37727 0.227695
\(221\) −0.993188 1.48978i −0.0668090 0.100214i
\(222\) 5.00849i 0.336148i
\(223\) −6.24945 + 6.24945i −0.418494 + 0.418494i −0.884685 0.466190i \(-0.845626\pi\)
0.466190 + 0.884685i \(0.345626\pi\)
\(224\) 2.64404 0.0951965i 0.176662 0.00636058i
\(225\) 1.49659i 0.0997729i
\(226\) 2.07886 + 2.07886i 0.138284 + 0.138284i
\(227\) 5.50341 5.50341i 0.365274 0.365274i −0.500476 0.865750i \(-0.666842\pi\)
0.865750 + 0.500476i \(0.166842\pi\)
\(228\) 3.07156 3.07156i 0.203419 0.203419i
\(229\) 2.50341 + 2.50341i 0.165430 + 0.165430i 0.784967 0.619537i \(-0.212680\pi\)
−0.619537 + 0.784967i \(0.712680\pi\)
\(230\) 18.8035i 1.23987i
\(231\) 3.50341 0.126137i 0.230507 0.00829923i
\(232\) 5.12732 5.12732i 0.336625 0.336625i
\(233\) 16.5615i 1.08498i −0.840061 0.542491i \(-0.817481\pi\)
0.840061 0.542491i \(-0.182519\pi\)
\(234\) 0.707107 3.53553i 0.0462250 0.231125i
\(235\) 21.1730 1.38117
\(236\) −1.37727 + 1.37727i −0.0896526 + 0.0896526i
\(237\) 13.1499i 0.854180i
\(238\) −1.31301 + 0.0472740i −0.0851100 + 0.00306432i
\(239\) −2.41238 2.41238i −0.156044 0.156044i 0.624767 0.780811i \(-0.285194\pi\)
−0.780811 + 0.624767i \(0.785194\pi\)
\(240\) −1.80230 1.80230i −0.116338 0.116338i
\(241\) 8.37727 + 8.37727i 0.539627 + 0.539627i 0.923419 0.383792i \(-0.125382\pi\)
−0.383792 + 0.923419i \(0.625382\pi\)
\(242\) 6.53672 6.53672i 0.420196 0.420196i
\(243\) 1.00000i 0.0641500i
\(244\) 0.496594 0.0317912
\(245\) −13.4907 11.6762i −0.861892 0.745963i
\(246\) 8.65004i 0.551507i
\(247\) 15.3578 + 3.07156i 0.977193 + 0.195439i
\(248\) 8.11650i 0.515398i
\(249\) −7.87386 7.87386i −0.498986 0.498986i
\(250\) 8.92963i 0.564759i
\(251\) −26.8727 −1.69619 −0.848096 0.529843i \(-0.822251\pi\)
−0.848096 + 0.529843i \(0.822251\pi\)
\(252\) −1.93693 1.80230i −0.122015 0.113534i
\(253\) −6.91199 6.91199i −0.434553 0.434553i
\(254\) 14.0273 14.0273i 0.880152 0.880152i
\(255\) 0.895013 + 0.895013i 0.0560479 + 0.0560479i
\(256\) 1.00000 0.0625000
\(257\) −7.98302 −0.497967 −0.248984 0.968508i \(-0.580096\pi\)
−0.248984 + 0.968508i \(0.580096\pi\)
\(258\) −4.84774 4.84774i −0.301807 0.301807i
\(259\) −0.476791 13.2426i −0.0296263 0.822858i
\(260\) 1.80230 9.01152i 0.111774 0.558871i
\(261\) −7.25113 −0.448834
\(262\) 3.61191 3.61191i 0.223145 0.223145i
\(263\) −2.47166 −0.152409 −0.0762044 0.997092i \(-0.524280\pi\)
−0.0762044 + 0.997092i \(0.524280\pi\)
\(264\) 1.32502 0.0815494
\(265\) −7.69449 + 7.69449i −0.472669 + 0.472669i
\(266\) 7.82892 8.41372i 0.480022 0.515878i
\(267\) 10.2177 10.2177i 0.625313 0.625313i
\(268\) −9.11650 + 9.11650i −0.556879 + 0.556879i
\(269\) 5.83761i 0.355926i −0.984037 0.177963i \(-0.943049\pi\)
0.984037 0.177963i \(-0.0569507\pi\)
\(270\) 2.54884i 0.155118i
\(271\) 8.57799 + 8.57799i 0.521076 + 0.521076i 0.917896 0.396820i \(-0.129886\pi\)
−0.396820 + 0.917896i \(0.629886\pi\)
\(272\) −0.496594 −0.0301104
\(273\) 1.53305 9.41540i 0.0927842 0.569846i
\(274\) −5.37727 −0.324853
\(275\) −1.40221 1.40221i −0.0845562 0.0845562i
\(276\) 7.37727i 0.444059i
\(277\) 2.66465i 0.160103i −0.996791 0.0800516i \(-0.974491\pi\)
0.996791 0.0800516i \(-0.0255085\pi\)
\(278\) −2.07886 + 2.07886i −0.124682 + 0.124682i
\(279\) 5.73923 5.73923i 0.343599 0.343599i
\(280\) −4.93693 4.59379i −0.295038 0.274531i
\(281\) −8.09952 + 8.09952i −0.483177 + 0.483177i −0.906145 0.422968i \(-0.860988\pi\)
0.422968 + 0.906145i \(0.360988\pi\)
\(282\) 8.30690 0.494668
\(283\) 30.2730 1.79954 0.899772 0.436360i \(-0.143733\pi\)
0.899772 + 0.436360i \(0.143733\pi\)
\(284\) −11.3773 + 11.3773i −0.675117 + 0.675117i
\(285\) −11.0718 −0.655835
\(286\) 2.65004 + 3.97506i 0.156700 + 0.235050i
\(287\) −0.823453 22.8710i −0.0486069 1.35003i
\(288\) −0.707107 0.707107i −0.0416667 0.0416667i
\(289\) −16.7534 −0.985494
\(290\) −18.4820 −1.08530
\(291\) −9.46034 9.46034i −0.554575 0.554575i
\(292\) 3.54154 3.54154i 0.207253 0.207253i
\(293\) 17.9235 + 17.9235i 1.04710 + 1.04710i 0.998834 + 0.0482683i \(0.0153702\pi\)
0.0482683 + 0.998834i \(0.484630\pi\)
\(294\) −5.29289 4.58097i −0.308688 0.267168i
\(295\) 4.96451 0.289045
\(296\) 5.00849i 0.291113i
\(297\) −0.936931 0.936931i −0.0543663 0.0543663i
\(298\) 2.46928i 0.143042i
\(299\) −22.1318 + 14.7545i −1.27992 + 0.853277i
\(300\) 1.49659i 0.0864059i
\(301\) −13.2791 12.3561i −0.765394 0.712195i
\(302\) 9.26314 0.533034
\(303\) 4.66465i 0.267977i
\(304\) 3.07156 3.07156i 0.176166 0.176166i
\(305\) −0.895013 0.895013i −0.0512483 0.0512483i
\(306\) 0.351145 + 0.351145i 0.0200736 + 0.0200736i
\(307\) 5.09157 + 5.09157i 0.290591 + 0.290591i 0.837314 0.546723i \(-0.184125\pi\)
−0.546723 + 0.837314i \(0.684125\pi\)
\(308\) 3.50341 0.126137i 0.199625 0.00718734i
\(309\) 18.5865i 1.05735i
\(310\) 14.6284 14.6284i 0.830837 0.830837i
\(311\) 14.0729 0.798001 0.399001 0.916951i \(-0.369357\pi\)
0.399001 + 0.916951i \(0.369357\pi\)
\(312\) 0.707107 3.53553i 0.0400320 0.200160i
\(313\) 28.3059i 1.59994i −0.600037 0.799972i \(-0.704847\pi\)
0.600037 0.799972i \(-0.295153\pi\)
\(314\) 1.20619 1.20619i 0.0680691 0.0680691i
\(315\) 0.242641 + 6.73923i 0.0136713 + 0.379713i
\(316\) 13.1499i 0.739741i
\(317\) 20.5119 + 20.5119i 1.15206 + 1.15206i 0.986138 + 0.165924i \(0.0530608\pi\)
0.165924 + 0.986138i \(0.446939\pi\)
\(318\) −3.01882 + 3.01882i −0.169287 + 0.169287i
\(319\) 6.79381 6.79381i 0.380380 0.380380i
\(320\) −1.80230 1.80230i −0.100752 0.100752i
\(321\) 6.95694i 0.388298i
\(322\) 0.702290 + 19.5058i 0.0391371 + 1.08701i
\(323\) −1.52532 + 1.52532i −0.0848709 + 0.0848709i
\(324\) 1.00000i 0.0555556i
\(325\) −4.48978 + 2.99319i −0.249048 + 0.166032i
\(326\) 5.99037 0.331776
\(327\) −2.94374 + 2.94374i −0.162789 + 0.162789i
\(328\) 8.65004i 0.477619i
\(329\) 21.9638 0.790787i 1.21090 0.0435975i
\(330\) −2.38809 2.38809i −0.131460 0.131460i
\(331\) −9.65502 9.65502i −0.530688 0.530688i 0.390089 0.920777i \(-0.372444\pi\)
−0.920777 + 0.390089i \(0.872444\pi\)
\(332\) −7.87386 7.87386i −0.432134 0.432134i
\(333\) −3.54154 + 3.54154i −0.194075 + 0.194075i
\(334\) 11.3420i 0.620607i
\(335\) 32.8614 1.79541
\(336\) −1.93693 1.80230i −0.105668 0.0983237i
\(337\) 7.25113i 0.394994i −0.980303 0.197497i \(-0.936719\pi\)
0.980303 0.197497i \(-0.0632813\pi\)
\(338\) 12.0208 4.94975i 0.653846 0.269231i
\(339\) 2.93996i 0.159677i
\(340\) 0.895013 + 0.895013i 0.0485389 + 0.0485389i
\(341\) 10.7545i 0.582391i
\(342\) −4.34384 −0.234888
\(343\) −14.4307 11.6084i −0.779185 0.626794i
\(344\) −4.84774 4.84774i −0.261373 0.261373i
\(345\) 13.2961 13.2961i 0.715837 0.715837i
\(346\) 2.98118 + 2.98118i 0.160269 + 0.160269i
\(347\) 29.7647 1.59785 0.798927 0.601429i \(-0.205402\pi\)
0.798927 + 0.601429i \(0.205402\pi\)
\(348\) −7.25113 −0.388701
\(349\) −13.1431 13.1431i −0.703535 0.703535i 0.261633 0.965168i \(-0.415739\pi\)
−0.965168 + 0.261633i \(0.915739\pi\)
\(350\) 0.142470 + 3.95705i 0.00761536 + 0.211513i
\(351\) −3.00000 + 2.00000i −0.160128 + 0.106752i
\(352\) 1.32502 0.0706239
\(353\) 13.5531 13.5531i 0.721356 0.721356i −0.247525 0.968881i \(-0.579617\pi\)
0.968881 + 0.247525i \(0.0796173\pi\)
\(354\) 1.94775 0.103522
\(355\) 41.0106 2.17662
\(356\) 10.2177 10.2177i 0.541537 0.541537i
\(357\) 0.961868 + 0.895013i 0.0509075 + 0.0473691i
\(358\) 3.77266 3.77266i 0.199391 0.199391i
\(359\) −4.04192 + 4.04192i −0.213324 + 0.213324i −0.805678 0.592354i \(-0.798199\pi\)
0.592354 + 0.805678i \(0.298199\pi\)
\(360\) 2.54884i 0.134336i
\(361\) 0.131045i 0.00689710i
\(362\) 1.27109 + 1.27109i 0.0668073 + 0.0668073i
\(363\) −9.24432 −0.485201
\(364\) 1.53305 9.41540i 0.0803535 0.493501i
\(365\) −12.7659 −0.668195
\(366\) −0.351145 0.351145i −0.0183546 0.0183546i
\(367\) 4.26926i 0.222853i 0.993773 + 0.111427i \(0.0355420\pi\)
−0.993773 + 0.111427i \(0.964458\pi\)
\(368\) 7.37727i 0.384567i
\(369\) −6.11650 + 6.11650i −0.318412 + 0.318412i
\(370\) −9.02682 + 9.02682i −0.469282 + 0.469282i
\(371\) −7.69449 + 8.26926i −0.399478 + 0.429318i
\(372\) 5.73923 5.73923i 0.297565 0.297565i
\(373\) 9.67146 0.500769 0.250385 0.968146i \(-0.419443\pi\)
0.250385 + 0.968146i \(0.419443\pi\)
\(374\) −0.657997 −0.0340242
\(375\) −6.31420 + 6.31420i −0.326064 + 0.326064i
\(376\) 8.30690 0.428395
\(377\) −14.5023 21.7534i −0.746905 1.12036i
\(378\) 0.0951965 + 2.64404i 0.00489638 + 0.135995i
\(379\) −0.746047 0.746047i −0.0383218 0.0383218i 0.687686 0.726008i \(-0.258627\pi\)
−0.726008 + 0.687686i \(0.758627\pi\)
\(380\) −11.0718 −0.567969
\(381\) −19.8376 −1.01631
\(382\) 13.2857 + 13.2857i 0.679758 + 0.679758i
\(383\) −18.1461 + 18.1461i −0.927225 + 0.927225i −0.997526 0.0703012i \(-0.977604\pi\)
0.0703012 + 0.997526i \(0.477604\pi\)
\(384\) −0.707107 0.707107i −0.0360844 0.0360844i
\(385\) −6.54154 6.08686i −0.333388 0.310215i
\(386\) −1.93812 −0.0986476
\(387\) 6.85574i 0.348497i
\(388\) −9.46034 9.46034i −0.480276 0.480276i
\(389\) 6.73756i 0.341608i −0.985305 0.170804i \(-0.945364\pi\)
0.985305 0.170804i \(-0.0546364\pi\)
\(390\) −7.64653 + 5.09768i −0.387197 + 0.258131i
\(391\) 3.66351i 0.185271i
\(392\) −5.29289 4.58097i −0.267331 0.231374i
\(393\) −5.10801 −0.257665
\(394\) 4.05225i 0.204149i
\(395\) −23.7002 + 23.7002i −1.19248 + 1.19248i
\(396\) −0.936931 0.936931i −0.0470826 0.0470826i
\(397\) 21.7715 + 21.7715i 1.09268 + 1.09268i 0.995241 + 0.0974398i \(0.0310653\pi\)
0.0974398 + 0.995241i \(0.468935\pi\)
\(398\) −9.94542 9.94542i −0.498519 0.498519i
\(399\) −11.4853 + 0.413518i −0.574983 + 0.0207018i
\(400\) 1.49659i 0.0748297i
\(401\) 16.5119 16.5119i 0.824565 0.824565i −0.162194 0.986759i \(-0.551857\pi\)
0.986759 + 0.162194i \(0.0518571\pi\)
\(402\) 12.8927 0.643029
\(403\) 28.6962 + 5.73923i 1.42946 + 0.285892i
\(404\) 4.66465i 0.232075i
\(405\) 1.80230 1.80230i 0.0895572 0.0895572i
\(406\) −19.1723 + 0.690282i −0.951504 + 0.0342581i
\(407\) 6.63636i 0.328952i
\(408\) 0.351145 + 0.351145i 0.0173843 + 0.0173843i
\(409\) −4.00379 + 4.00379i −0.197975 + 0.197975i −0.799131 0.601157i \(-0.794707\pi\)
0.601157 + 0.799131i \(0.294707\pi\)
\(410\) −15.5900 + 15.5900i −0.769935 + 0.769935i
\(411\) 3.80230 + 3.80230i 0.187554 + 0.187554i
\(412\) 18.5865i 0.915690i
\(413\) 5.14993 0.185419i 0.253412 0.00912388i
\(414\) 5.21652 5.21652i 0.256378 0.256378i
\(415\) 28.3822i 1.39323i
\(416\) 0.707107 3.53553i 0.0346688 0.173344i
\(417\) 2.93996 0.143970
\(418\) 4.06988 4.06988i 0.199064 0.199064i
\(419\) 15.1782i 0.741505i 0.928732 + 0.370752i \(0.120900\pi\)
−0.928732 + 0.370752i \(0.879100\pi\)
\(420\) 0.242641 + 6.73923i 0.0118397 + 0.328841i
\(421\) 11.0650 + 11.0650i 0.539273 + 0.539273i 0.923315 0.384043i \(-0.125468\pi\)
−0.384043 + 0.923315i \(0.625468\pi\)
\(422\) 10.5046 + 10.5046i 0.511356 + 0.511356i
\(423\) −5.87386 5.87386i −0.285597 0.285597i
\(424\) −3.01882 + 3.01882i −0.146607 + 0.146607i
\(425\) 0.743199i 0.0360505i
\(426\) 16.0899 0.779558
\(427\) −0.961868 0.895013i −0.0465481 0.0433127i
\(428\) 6.95694i 0.336276i
\(429\) 0.936931 4.68466i 0.0452355 0.226177i
\(430\) 17.4742i 0.842680i
\(431\) 9.60461 + 9.60461i 0.462638 + 0.462638i 0.899519 0.436881i \(-0.143917\pi\)
−0.436881 + 0.899519i \(0.643917\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 6.52489 0.313566 0.156783 0.987633i \(-0.449888\pi\)
0.156783 + 0.987633i \(0.449888\pi\)
\(434\) 14.6284 15.7211i 0.702186 0.754637i
\(435\) 13.0687 + 13.0687i 0.626598 + 0.626598i
\(436\) −2.94374 + 2.94374i −0.140980 + 0.140980i
\(437\) 22.6597 + 22.6597i 1.08396 + 1.08396i
\(438\) −5.00849 −0.239315
\(439\) −1.61592 −0.0771236 −0.0385618 0.999256i \(-0.512278\pi\)
−0.0385618 + 0.999256i \(0.512278\pi\)
\(440\) −2.38809 2.38809i −0.113848 0.113848i
\(441\) 0.503406 + 6.98188i 0.0239717 + 0.332470i
\(442\) −0.351145 + 1.75572i −0.0167023 + 0.0835113i
\(443\) −19.0408 −0.904655 −0.452327 0.891852i \(-0.649406\pi\)
−0.452327 + 0.891852i \(0.649406\pi\)
\(444\) −3.54154 + 3.54154i −0.168074 + 0.168074i
\(445\) −36.8308 −1.74595
\(446\) 8.83806 0.418494
\(447\) 1.74605 1.74605i 0.0825852 0.0825852i
\(448\) −1.93693 1.80230i −0.0915114 0.0851508i
\(449\) −10.3408 + 10.3408i −0.488013 + 0.488013i −0.907679 0.419666i \(-0.862147\pi\)
0.419666 + 0.907679i \(0.362147\pi\)
\(450\) 1.05825 1.05825i 0.0498865 0.0498865i
\(451\) 11.4615i 0.539700i
\(452\) 2.93996i 0.138284i
\(453\) −6.55003 6.55003i −0.307747 0.307747i
\(454\) −7.78299 −0.365274
\(455\) −19.7324 + 14.2064i −0.925070 + 0.666006i
\(456\) −4.34384 −0.203419
\(457\) 20.0718 + 20.0718i 0.938917 + 0.938917i 0.998239 0.0593215i \(-0.0188937\pi\)
−0.0593215 + 0.998239i \(0.518894\pi\)
\(458\) 3.54035i 0.165430i
\(459\) 0.496594i 0.0231790i
\(460\) 13.2961 13.2961i 0.619933 0.619933i
\(461\) 13.4069 13.4069i 0.624422 0.624422i −0.322237 0.946659i \(-0.604435\pi\)
0.946659 + 0.322237i \(0.104435\pi\)
\(462\) −2.56647 2.38809i −0.119403 0.111104i
\(463\) −17.7592 + 17.7592i −0.825342 + 0.825342i −0.986868 0.161526i \(-0.948358\pi\)
0.161526 + 0.986868i \(0.448358\pi\)
\(464\) −7.25113 −0.336625
\(465\) −20.6877 −0.959368
\(466\) −11.7108 + 11.7108i −0.542491 + 0.542491i
\(467\) −39.5072 −1.82817 −0.914087 0.405518i \(-0.867091\pi\)
−0.914087 + 0.405518i \(0.867091\pi\)
\(468\) −3.00000 + 2.00000i −0.138675 + 0.0924500i
\(469\) 34.0887 1.22734i 1.57407 0.0566732i
\(470\) −14.9715 14.9715i −0.690586 0.690586i
\(471\) −1.70581 −0.0785994
\(472\) 1.94775 0.0896526
\(473\) −6.42336 6.42336i −0.295346 0.295346i
\(474\) −9.29841 + 9.29841i −0.427090 + 0.427090i
\(475\) 4.59688 + 4.59688i 0.210919 + 0.210919i
\(476\) 0.961868 + 0.895013i 0.0440872 + 0.0410228i
\(477\) 4.26926 0.195476
\(478\) 3.41161i 0.156044i
\(479\) −20.1768 20.1768i −0.921899 0.921899i 0.0752644 0.997164i \(-0.476020\pi\)
−0.997164 + 0.0752644i \(0.976020\pi\)
\(480\) 2.54884i 0.116338i
\(481\) −17.7077 3.54154i −0.807401 0.161480i
\(482\) 11.8472i 0.539627i
\(483\) 13.2961 14.2893i 0.604992 0.650184i
\(484\) −9.24432 −0.420196
\(485\) 34.1008i 1.54844i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) −14.5837 14.5837i −0.660849 0.660849i 0.294731 0.955580i \(-0.404770\pi\)
−0.955580 + 0.294731i \(0.904770\pi\)
\(488\) −0.351145 0.351145i −0.0158956 0.0158956i
\(489\) −4.23583 4.23583i −0.191551 0.191551i
\(490\) 1.28310 + 17.7957i 0.0579647 + 0.803928i
\(491\) 10.3591i 0.467502i −0.972297 0.233751i \(-0.924900\pi\)
0.972297 0.233751i \(-0.0751000\pi\)
\(492\) −6.11650 + 6.11650i −0.275753 + 0.275753i
\(493\) 3.60087 0.162175
\(494\) −8.68768 13.0315i −0.390877 0.586316i
\(495\) 3.37727i 0.151797i
\(496\) 5.73923 5.73923i 0.257699 0.257699i
\(497\) 42.5423 1.53170i 1.90828 0.0687061i
\(498\) 11.1353i 0.498986i
\(499\) 30.2834 + 30.2834i 1.35567 + 1.35567i 0.879178 + 0.476494i \(0.158093\pi\)
0.476494 + 0.879178i \(0.341907\pi\)
\(500\) −6.31420 + 6.31420i −0.282380 + 0.282380i
\(501\) 8.02001 8.02001i 0.358307 0.358307i
\(502\) 19.0019 + 19.0019i 0.848096 + 0.848096i
\(503\) 12.0000i 0.535054i 0.963550 + 0.267527i \(0.0862064\pi\)
−0.963550 + 0.267527i \(0.913794\pi\)
\(504\) 0.0951965 + 2.64404i 0.00424039 + 0.117775i
\(505\) 8.40711 8.40711i 0.374112 0.374112i
\(506\) 9.77504i 0.434553i
\(507\) −12.0000 5.00000i −0.532939 0.222058i
\(508\) −19.8376 −0.880152
\(509\) 27.9685 27.9685i 1.23968 1.23968i 0.279548 0.960132i \(-0.409815\pi\)
0.960132 0.279548i \(-0.0901847\pi\)
\(510\) 1.26574i 0.0560479i
\(511\) −13.2426 + 0.476791i −0.585820 + 0.0210920i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 3.07156 + 3.07156i 0.135613 + 0.135613i
\(514\) 5.64485 + 5.64485i 0.248984 + 0.248984i
\(515\) 33.4985 33.4985i 1.47612 1.47612i
\(516\) 6.85574i 0.301807i
\(517\) 11.0068 0.484079
\(518\) −9.02682 + 9.70110i −0.396616 + 0.426242i
\(519\) 4.21603i 0.185063i
\(520\) −7.64653 + 5.09768i −0.335322 + 0.223548i
\(521\) 18.7160i 0.819962i −0.912094 0.409981i \(-0.865535\pi\)
0.912094 0.409981i \(-0.134465\pi\)
\(522\) 5.12732 + 5.12732i 0.224417 + 0.224417i
\(523\) 5.69449i 0.249003i −0.992219 0.124501i \(-0.960267\pi\)
0.992219 0.124501i \(-0.0397331\pi\)
\(524\) −5.10801 −0.223145
\(525\) 2.69732 2.89880i 0.117721 0.126514i
\(526\) 1.74773 + 1.74773i 0.0762044 + 0.0762044i
\(527\) −2.85007 + 2.85007i −0.124151 + 0.124151i
\(528\) −0.936931 0.936931i −0.0407747 0.0407747i
\(529\) −31.4241 −1.36626
\(530\) 10.8817 0.472669
\(531\) −1.37727 1.37727i −0.0597684 0.0597684i
\(532\) −11.4853 + 0.413518i −0.497950 + 0.0179283i
\(533\) −30.5825 6.11650i −1.32468 0.264935i
\(534\) −14.4500 −0.625313
\(535\) 12.5385 12.5385i 0.542087 0.542087i
\(536\) 12.8927 0.556879
\(537\) −5.33535 −0.230237
\(538\) −4.12782 + 4.12782i −0.177963 + 0.177963i
\(539\) −7.01319 6.06988i −0.302080 0.261448i
\(540\) 1.80230 1.80230i 0.0775588 0.0775588i
\(541\) 6.48149 6.48149i 0.278661 0.278661i −0.553913 0.832574i \(-0.686866\pi\)
0.832574 + 0.553913i \(0.186866\pi\)
\(542\) 12.1311i 0.521076i
\(543\) 1.79760i 0.0771424i
\(544\) 0.351145 + 0.351145i 0.0150552 + 0.0150552i
\(545\) 10.6110 0.454527
\(546\) −7.74172 + 5.57367i −0.331315 + 0.238531i
\(547\) 39.5294 1.69016 0.845078 0.534643i \(-0.179554\pi\)
0.845078 + 0.534643i \(0.179554\pi\)
\(548\) 3.80230 + 3.80230i 0.162426 + 0.162426i
\(549\) 0.496594i 0.0211941i
\(550\) 1.98302i 0.0845562i
\(551\) −22.2723 + 22.2723i −0.948831 + 0.948831i
\(552\) 5.21652 5.21652i 0.222030 0.222030i
\(553\) −23.7002 + 25.4705i −1.00783 + 1.08312i
\(554\) −1.88419 + 1.88419i −0.0800516 + 0.0800516i
\(555\) 12.7659 0.541880
\(556\) 2.93996 0.124682
\(557\) −0.806090 + 0.806090i −0.0341551 + 0.0341551i −0.723978 0.689823i \(-0.757688\pi\)
0.689823 + 0.723978i \(0.257688\pi\)
\(558\) −8.11650 −0.343599
\(559\) −20.5672 + 13.7115i −0.869900 + 0.579934i
\(560\) 0.242641 + 6.73923i 0.0102534 + 0.284785i
\(561\) 0.465274 + 0.465274i 0.0196439 + 0.0196439i
\(562\) 11.4545 0.483177
\(563\) 44.4350 1.87271 0.936357 0.351050i \(-0.114175\pi\)
0.936357 + 0.351050i \(0.114175\pi\)
\(564\) −5.87386 5.87386i −0.247334 0.247334i
\(565\) −5.29869 + 5.29869i −0.222918 + 0.222918i
\(566\) −21.4063 21.4063i −0.899772 0.899772i
\(567\) 1.80230 1.93693i 0.0756896 0.0813435i
\(568\) 16.0899 0.675117
\(569\) 5.40826i 0.226726i 0.993554 + 0.113363i \(0.0361623\pi\)
−0.993554 + 0.113363i \(0.963838\pi\)
\(570\) 7.82892 + 7.82892i 0.327917 + 0.327917i
\(571\) 2.46830i 0.103295i 0.998665 + 0.0516476i \(0.0164472\pi\)
−0.998665 + 0.0516476i \(0.983553\pi\)
\(572\) 0.936931 4.68466i 0.0391751 0.195875i
\(573\) 18.7889i 0.784917i
\(574\) −15.5900 + 16.7545i −0.650714 + 0.699321i
\(575\) −11.0408 −0.460432
\(576\) 1.00000i 0.0416667i
\(577\) −27.0650 + 27.0650i −1.12673 + 1.12673i −0.136023 + 0.990706i \(0.543432\pi\)
−0.990706 + 0.136023i \(0.956568\pi\)
\(578\) 11.8464 + 11.8464i 0.492747 + 0.492747i
\(579\) 1.37046 + 1.37046i 0.0569542 + 0.0569542i
\(580\) 13.0687 + 13.0687i 0.542650 + 0.542650i
\(581\) 1.06004 + 29.4422i 0.0439780 + 1.22147i
\(582\) 13.3789i 0.554575i
\(583\) −4.00000 + 4.00000i −0.165663 + 0.165663i
\(584\) −5.00849 −0.207253
\(585\) 9.01152 + 1.80230i 0.372580 + 0.0745161i
\(586\) 25.3477i 1.04710i
\(587\) 10.6533 10.6533i 0.439710 0.439710i −0.452204 0.891914i \(-0.649362\pi\)
0.891914 + 0.452204i \(0.149362\pi\)
\(588\) 0.503406 + 6.98188i 0.0207601 + 0.287928i
\(589\) 35.2568i 1.45273i
\(590\) −3.51044 3.51044i −0.144523 0.144523i
\(591\) 2.86537 2.86537i 0.117866 0.117866i
\(592\) −3.54154 + 3.54154i −0.145556 + 0.145556i
\(593\) −11.4938 11.4938i −0.471993 0.471993i 0.430566 0.902559i \(-0.358314\pi\)
−0.902559 + 0.430566i \(0.858314\pi\)
\(594\) 1.32502i 0.0543663i
\(595\) −0.120494 3.34666i −0.00493977 0.137200i
\(596\) 1.74605 1.74605i 0.0715209 0.0715209i
\(597\) 14.0650i 0.575640i
\(598\) 26.0826 + 5.21652i 1.06660 + 0.213319i
\(599\) −30.3149 −1.23863 −0.619317 0.785141i \(-0.712591\pi\)
−0.619317 + 0.785141i \(0.712591\pi\)
\(600\) 1.05825 1.05825i 0.0432029 0.0432029i
\(601\) 11.9638i 0.488012i −0.969774 0.244006i \(-0.921538\pi\)
0.969774 0.244006i \(-0.0784616\pi\)
\(602\) 0.652642 + 18.1268i 0.0265997 + 0.738795i
\(603\) −9.11650 9.11650i −0.371253 0.371253i
\(604\) −6.55003 6.55003i −0.266517 0.266517i
\(605\) 16.6611 + 16.6611i 0.677369 + 0.677369i
\(606\) 3.29841 3.29841i 0.133989 0.133989i
\(607\) 41.6103i 1.68891i −0.535627 0.844454i \(-0.679925\pi\)
0.535627 0.844454i \(-0.320075\pi\)
\(608\) −4.34384 −0.176166
\(609\) 14.0449 + 13.0687i 0.569130 + 0.529572i
\(610\) 1.26574i 0.0512483i
\(611\) 5.87386 29.3693i 0.237631 1.18816i
\(612\) 0.496594i 0.0200736i
\(613\) −27.9736 27.9736i −1.12984 1.12984i −0.990202 0.139640i \(-0.955405\pi\)
−0.139640 0.990202i \(-0.544595\pi\)
\(614\) 7.20056i 0.290591i
\(615\) 22.0476 0.889045
\(616\) −2.56647 2.38809i −0.103406 0.0962189i
\(617\) 15.7830 + 15.7830i 0.635401 + 0.635401i 0.949418 0.314016i \(-0.101675\pi\)
−0.314016 + 0.949418i \(0.601675\pi\)
\(618\) 13.1426 13.1426i 0.528674 0.528674i
\(619\) 0.473765 + 0.473765i 0.0190422 + 0.0190422i 0.716564 0.697522i \(-0.245714\pi\)
−0.697522 + 0.716564i \(0.745714\pi\)
\(620\) −20.6877 −0.830837
\(621\) −7.37727 −0.296040
\(622\) −9.95105 9.95105i −0.399001 0.399001i
\(623\) −38.2064 + 1.37559i −1.53071 + 0.0551119i
\(624\) −3.00000 + 2.00000i −0.120096 + 0.0800641i
\(625\) 30.2432 1.20973
\(626\) −20.0153 + 20.0153i −0.799972 + 0.799972i
\(627\) −5.75568 −0.229860
\(628\) −1.70581 −0.0680691
\(629\) 1.75871 1.75871i 0.0701242 0.0701242i
\(630\) 4.59379 4.93693i 0.183021 0.196692i
\(631\) −30.2978 + 30.2978i −1.20613 + 1.20613i −0.233866 + 0.972269i \(0.575138\pi\)
−0.972269 + 0.233866i \(0.924862\pi\)
\(632\) −9.29841 + 9.29841i −0.369871 + 0.369871i
\(633\) 14.8557i 0.590463i
\(634\) 29.0082i 1.15206i
\(635\) 35.7534 + 35.7534i 1.41883 + 1.41883i
\(636\) 4.26926 0.169287
\(637\) −19.9388 + 15.4740i −0.790005 + 0.613101i
\(638\) −9.60790 −0.380380
\(639\) −11.3773 11.3773i −0.450078 0.450078i
\(640\) 2.54884i 0.100752i
\(641\) 5.40556i 0.213507i 0.994286 + 0.106753i \(0.0340456\pi\)
−0.994286 + 0.106753i \(0.965954\pi\)
\(642\) 4.91930 4.91930i 0.194149 0.194149i
\(643\) −9.08518 + 9.08518i −0.358285 + 0.358285i −0.863180 0.504896i \(-0.831531\pi\)
0.504896 + 0.863180i \(0.331531\pi\)
\(644\) 13.2961 14.2893i 0.523939 0.563076i
\(645\) 12.3561 12.3561i 0.486522 0.486522i
\(646\) 2.15712 0.0848709
\(647\) −15.0468 −0.591552 −0.295776 0.955257i \(-0.595578\pi\)
−0.295776 + 0.955257i \(0.595578\pi\)
\(648\) 0.707107 0.707107i 0.0277778 0.0277778i
\(649\) 2.58081 0.101306
\(650\) 5.29126 + 1.05825i 0.207540 + 0.0415080i
\(651\) −21.4603 + 0.772662i −0.841097 + 0.0302830i
\(652\) −4.23583 4.23583i −0.165888 0.165888i
\(653\) 6.17411 0.241611 0.120806 0.992676i \(-0.461452\pi\)
0.120806 + 0.992676i \(0.461452\pi\)
\(654\) 4.16308 0.162789
\(655\) 9.20619 + 9.20619i 0.359716 + 0.359716i
\(656\) −6.11650 + 6.11650i −0.238809 + 0.238809i
\(657\) 3.54154 + 3.54154i 0.138169 + 0.138169i
\(658\) −16.0899 14.9715i −0.627249 0.583652i
\(659\) 2.70131 0.105228 0.0526140 0.998615i \(-0.483245\pi\)
0.0526140 + 0.998615i \(0.483245\pi\)
\(660\) 3.37727i 0.131460i
\(661\) −15.1148 15.1148i −0.587899 0.587899i 0.349163 0.937062i \(-0.386466\pi\)
−0.937062 + 0.349163i \(0.886466\pi\)
\(662\) 13.6543i 0.530688i
\(663\) 1.48978 0.993188i 0.0578583 0.0385722i
\(664\) 11.1353i 0.432134i
\(665\) 21.4452 + 19.9547i 0.831611 + 0.773809i
\(666\) 5.00849 0.194075
\(667\) 53.4935i 2.07128i
\(668\) 8.02001 8.02001i 0.310303 0.310303i
\(669\) −6.24945 6.24945i −0.241618 0.241618i
\(670\) −23.2365 23.2365i −0.897705 0.897705i
\(671\) −0.465274 0.465274i −0.0179617 0.0179617i
\(672\) 0.0951965 + 2.64404i 0.00367228 + 0.101996i
\(673\) 18.7262i 0.721844i 0.932596 + 0.360922i \(0.117538\pi\)
−0.932596 + 0.360922i \(0.882462\pi\)
\(674\) −5.12732 + 5.12732i −0.197497 + 0.197497i
\(675\) −1.49659 −0.0576039
\(676\) −12.0000 5.00000i −0.461538 0.192308i
\(677\) 25.6884i 0.987287i −0.869664 0.493644i \(-0.835665\pi\)
0.869664 0.493644i \(-0.164335\pi\)
\(678\) −2.07886 + 2.07886i −0.0798383 + 0.0798383i
\(679\) 1.27363 + 35.3744i 0.0488774 + 1.35755i
\(680\) 1.26574i 0.0485389i
\(681\) 5.50341 + 5.50341i 0.210891 + 0.210891i
\(682\) 7.60461 7.60461i 0.291195 0.291195i
\(683\) 10.6677 10.6677i 0.408187 0.408187i −0.472919 0.881106i \(-0.656800\pi\)
0.881106 + 0.472919i \(0.156800\pi\)
\(684\) 3.07156 + 3.07156i 0.117444 + 0.117444i
\(685\) 13.7058i 0.523672i
\(686\) 1.99567 + 18.4124i 0.0761952 + 0.702990i
\(687\) −2.50341 + 2.50341i −0.0955109 + 0.0955109i
\(688\) 6.85574i 0.261373i
\(689\) 8.53851 + 12.8078i 0.325291 + 0.487937i
\(690\) −18.8035 −0.715837
\(691\) 18.7630 18.7630i 0.713779 0.713779i −0.253544 0.967324i \(-0.581596\pi\)
0.967324 + 0.253544i \(0.0815964\pi\)
\(692\) 4.21603i 0.160269i
\(693\) 0.126137 + 3.50341i 0.00479156 + 0.133083i
\(694\) −21.0468 21.0468i −0.798927 0.798927i
\(695\) −5.29869 5.29869i −0.200991 0.200991i
\(696\) 5.12732 + 5.12732i 0.194351 + 0.194351i
\(697\) 3.03742 3.03742i 0.115050 0.115050i
\(698\) 18.5872i 0.703535i
\(699\) 16.5615 0.626415
\(700\) 2.69732 2.89880i 0.101949 0.109564i
\(701\) 30.4354i 1.14953i −0.818319 0.574765i \(-0.805094\pi\)
0.818319 0.574765i \(-0.194906\pi\)
\(702\) 3.53553 + 0.707107i 0.133440 + 0.0266880i
\(703\) 21.7561i 0.820546i
\(704\) −0.936931 0.936931i −0.0353119 0.0353119i
\(705\) 21.1730i 0.797420i
\(706\) −19.1669 −0.721356
\(707\) 8.40711 9.03511i 0.316182 0.339800i
\(708\) −1.37727 1.37727i −0.0517609 0.0517609i
\(709\) −31.7070 + 31.7070i −1.19078 + 1.19078i −0.213932 + 0.976849i \(0.568627\pi\)
−0.976849 + 0.213932i \(0.931373\pi\)
\(710\) −28.9989 28.9989i −1.08831 1.08831i
\(711\) 13.1499 0.493161
\(712\) −14.4500 −0.541537
\(713\) 42.3399 + 42.3399i 1.58564 + 1.58564i
\(714\) −0.0472740 1.31301i −0.00176918 0.0491383i
\(715\) −10.1318 + 6.75454i −0.378908 + 0.252605i
\(716\) −5.33535 −0.199391
\(717\) 2.41238 2.41238i 0.0900918 0.0900918i
\(718\) 5.71614 0.213324
\(719\) 0.575169 0.0214502 0.0107251 0.999942i \(-0.496586\pi\)
0.0107251 + 0.999942i \(0.496586\pi\)
\(720\) 1.80230 1.80230i 0.0671679 0.0671679i
\(721\) 33.4985 36.0007i 1.24755 1.34074i
\(722\) 0.0926627 0.0926627i 0.00344855 0.00344855i
\(723\) −8.37727 + 8.37727i −0.311554 + 0.311554i
\(724\) 1.79760i 0.0668073i
\(725\) 10.8520i 0.403033i
\(726\) 6.53672 + 6.53672i 0.242600 + 0.242600i
\(727\) −32.1850 −1.19368 −0.596838 0.802361i \(-0.703577\pi\)
−0.596838 + 0.802361i \(0.703577\pi\)
\(728\) −7.74172 + 5.57367i −0.286927 + 0.206574i
\(729\) −1.00000 −0.0370370
\(730\) 9.02682 + 9.02682i 0.334098 + 0.334098i
\(731\) 3.40452i 0.125921i
\(732\) 0.496594i 0.0183546i
\(733\) 31.3478 31.3478i 1.15786 1.15786i 0.172923 0.984935i \(-0.444679\pi\)
0.984935 0.172923i \(-0.0553213\pi\)
\(734\) 3.01882 3.01882i 0.111427 0.111427i
\(735\) 11.6762 13.4907i 0.430682 0.497614i
\(736\) 5.21652 5.21652i 0.192283 0.192283i
\(737\) 17.0831 0.629263
\(738\) 8.65004 0.318412
\(739\) 18.7211 18.7211i 0.688667 0.688667i −0.273270 0.961937i \(-0.588105\pi\)
0.961937 + 0.273270i \(0.0881053\pi\)
\(740\) 12.7659 0.469282
\(741\) −3.07156 + 15.3578i −0.112837 + 0.564183i
\(742\) 11.2881 0.406418i 0.414398 0.0149201i
\(743\) 20.3172 + 20.3172i 0.745367 + 0.745367i 0.973605 0.228239i \(-0.0732966\pi\)
−0.228239 + 0.973605i \(0.573297\pi\)
\(744\) −8.11650 −0.297565
\(745\) −6.29381 −0.230587
\(746\) −6.83876 6.83876i −0.250385 0.250385i
\(747\) 7.87386 7.87386i 0.288090 0.288090i
\(748\) 0.465274 + 0.465274i 0.0170121 + 0.0170121i
\(749\) 12.5385 13.4751i 0.458147 0.492370i
\(750\) 8.92963 0.326064
\(751\) 37.6220i 1.37285i −0.727202 0.686423i \(-0.759180\pi\)
0.727202 0.686423i \(-0.240820\pi\)
\(752\) −5.87386 5.87386i −0.214198 0.214198i
\(753\) 26.8727i 0.979296i
\(754\) −5.12732 + 25.6366i −0.186726 + 0.933631i
\(755\) 23.6103i 0.859266i
\(756\) 1.80230 1.93693i 0.0655491 0.0704455i
\(757\) 18.5249 0.673299 0.336649 0.941630i \(-0.390706\pi\)
0.336649 + 0.941630i \(0.390706\pi\)
\(758\) 1.05507i 0.0383218i
\(759\) 6.91199 6.91199i 0.250890 0.250890i
\(760\) 7.82892 + 7.82892i 0.283985 + 0.283985i
\(761\) −20.0153 20.0153i −0.725554 0.725554i 0.244177 0.969731i \(-0.421482\pi\)
−0.969731 + 0.244177i \(0.921482\pi\)
\(762\) 14.0273 + 14.0273i 0.508156 + 0.508156i
\(763\) 11.0073 0.396311i 0.398493 0.0143474i
\(764\) 18.7889i 0.679758i
\(765\) −0.895013 + 0.895013i −0.0323593 + 0.0323593i
\(766\) 25.6625 0.927225
\(767\) 1.37727 6.88634i 0.0497303 0.248651i
\(768\) 1.00000i 0.0360844i
\(769\) −22.3493 + 22.3493i −0.805937 + 0.805937i −0.984016 0.178079i \(-0.943012\pi\)
0.178079 + 0.984016i \(0.443012\pi\)
\(770\) 0.321504 + 8.92963i 0.0115862 + 0.321801i
\(771\) 7.98302i 0.287501i
\(772\) 1.37046 + 1.37046i 0.0493238 + 0.0493238i
\(773\) −27.6399 + 27.6399i −0.994139 + 0.994139i −0.999983 0.00584422i \(-0.998140\pi\)
0.00584422 + 0.999983i \(0.498140\pi\)
\(774\) 4.84774 4.84774i 0.174248 0.174248i
\(775\) 8.58930 + 8.58930i 0.308537 + 0.308537i
\(776\) 13.3789i 0.480276i
\(777\) 13.2426 0.476791i 0.475077 0.0171048i
\(778\) −4.76417 + 4.76417i −0.170804 +