Properties

Label 78.3.l.a.67.1
Level $78$
Weight $3$
Character 78.67
Analytic conductor $2.125$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 78.l (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.12534606201\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 67.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 78.67
Dual form 78.3.l.a.7.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 - 0.366025i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-4.73205 + 4.73205i) q^{5} +(-0.633975 - 2.36603i) q^{6} +(-2.50000 + 0.669873i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.36603 - 0.366025i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-4.73205 + 4.73205i) q^{5} +(-0.633975 - 2.36603i) q^{6} +(-2.50000 + 0.669873i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(8.19615 - 4.73205i) q^{10} +(-3.92820 + 14.6603i) q^{11} +3.46410i q^{12} +(11.2583 + 6.50000i) q^{13} +3.66025 q^{14} +(-11.1962 - 3.00000i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-4.39230 - 2.53590i) q^{17} +(3.00000 - 3.00000i) q^{18} +(-0.954483 - 3.56218i) q^{19} +(-12.9282 + 3.46410i) q^{20} +(-3.16987 - 3.16987i) q^{21} +(10.7321 - 18.5885i) q^{22} +(27.5885 - 15.9282i) q^{23} +(1.26795 - 4.73205i) q^{24} -19.7846i q^{25} +(-13.0000 - 13.0000i) q^{26} -5.19615 q^{27} +(-5.00000 - 1.33975i) q^{28} +(-8.66025 - 15.0000i) q^{29} +(14.1962 + 8.19615i) q^{30} +(30.8301 - 30.8301i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-25.3923 + 6.80385i) q^{33} +(5.07180 + 5.07180i) q^{34} +(8.66025 - 15.0000i) q^{35} +(-5.19615 + 3.00000i) q^{36} +(-13.2417 + 49.4186i) q^{37} +5.21539i q^{38} +22.5167i q^{39} +18.9282 q^{40} +(-41.3205 - 11.0718i) q^{41} +(3.16987 + 5.49038i) q^{42} +(28.2846 + 16.3301i) q^{43} +(-21.4641 + 21.4641i) q^{44} +(-5.19615 - 19.3923i) q^{45} +(-43.5167 + 11.6603i) q^{46} +(58.9808 + 58.9808i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(-36.6340 + 21.1506i) q^{49} +(-7.24167 + 27.0263i) q^{50} -8.78461i q^{51} +(13.0000 + 22.5167i) q^{52} +97.6743 q^{53} +(7.09808 + 1.90192i) q^{54} +(-50.7846 - 87.9615i) q^{55} +(6.33975 + 3.66025i) q^{56} +(4.51666 - 4.51666i) q^{57} +(6.33975 + 23.6603i) q^{58} +(59.1051 - 15.8372i) q^{59} +(-16.3923 - 16.3923i) q^{60} +(-39.6506 + 68.6769i) q^{61} +(-53.3993 + 30.8301i) q^{62} +(2.00962 - 7.50000i) q^{63} +8.00000i q^{64} +(-84.0333 + 22.5167i) q^{65} +37.1769 q^{66} +(-63.8468 - 17.1077i) q^{67} +(-5.07180 - 8.78461i) q^{68} +(47.7846 + 27.5885i) q^{69} +(-17.3205 + 17.3205i) q^{70} +(-13.8897 - 51.8372i) q^{71} +(8.19615 - 2.19615i) q^{72} +(-27.5814 - 27.5814i) q^{73} +(36.1769 - 62.6603i) q^{74} +(29.6769 - 17.1340i) q^{75} +(1.90897 - 7.12436i) q^{76} -39.2820i q^{77} +(8.24167 - 30.7583i) q^{78} +36.1244 q^{79} +(-25.8564 - 6.92820i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(52.3923 + 30.2487i) q^{82} +(20.9667 - 20.9667i) q^{83} +(-2.32051 - 8.66025i) q^{84} +(32.7846 - 8.78461i) q^{85} +(-32.6603 - 32.6603i) q^{86} +(15.0000 - 25.9808i) q^{87} +(37.1769 - 21.4641i) q^{88} +(-18.0666 + 67.4256i) q^{89} +28.3923i q^{90} +(-32.5000 - 8.70835i) q^{91} +63.7128 q^{92} +(72.9449 + 19.5455i) q^{93} +(-58.9808 - 102.158i) q^{94} +(21.3731 + 12.3397i) q^{95} +(6.92820 - 6.92820i) q^{96} +(4.75387 + 17.7417i) q^{97} +(57.7846 - 15.4833i) q^{98} +(-32.1962 - 32.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 12 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 12 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9} + 12 q^{10} + 12 q^{11} - 20 q^{14} - 24 q^{15} + 8 q^{16} + 24 q^{17} + 12 q^{18} + 62 q^{19} - 24 q^{20} - 30 q^{21} + 36 q^{22} + 48 q^{23} + 12 q^{24} - 52 q^{26} - 20 q^{28} + 36 q^{30} + 106 q^{31} + 8 q^{32} - 60 q^{33} + 48 q^{34} - 98 q^{37} + 48 q^{40} - 96 q^{41} + 30 q^{42} + 30 q^{43} - 72 q^{44} - 84 q^{46} + 132 q^{47} - 150 q^{49} - 74 q^{50} + 52 q^{52} + 72 q^{53} + 18 q^{54} - 120 q^{55} + 60 q^{56} - 72 q^{57} + 60 q^{58} + 84 q^{59} - 24 q^{60} - 72 q^{61} - 30 q^{62} + 60 q^{63} - 156 q^{65} + 24 q^{66} - 148 q^{67} - 48 q^{68} + 108 q^{69} + 180 q^{71} + 12 q^{72} - 190 q^{73} + 20 q^{74} - 6 q^{75} - 124 q^{76} + 78 q^{78} + 96 q^{79} - 48 q^{80} - 18 q^{81} + 168 q^{82} + 264 q^{83} + 60 q^{84} + 48 q^{85} - 96 q^{86} + 60 q^{87} + 24 q^{88} + 288 q^{89} - 130 q^{91} + 144 q^{92} + 174 q^{93} - 132 q^{94} - 60 q^{95} + 310 q^{97} + 148 q^{98} - 108 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 0.366025i −0.683013 0.183013i
\(3\) 0.866025 + 1.50000i 0.288675 + 0.500000i
\(4\) 1.73205 + 1.00000i 0.433013 + 0.250000i
\(5\) −4.73205 + 4.73205i −0.946410 + 0.946410i −0.998635 0.0522252i \(-0.983369\pi\)
0.0522252 + 0.998635i \(0.483369\pi\)
\(6\) −0.633975 2.36603i −0.105662 0.394338i
\(7\) −2.50000 + 0.669873i −0.357143 + 0.0956961i −0.432929 0.901428i \(-0.642520\pi\)
0.0757863 + 0.997124i \(0.475853\pi\)
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) −1.50000 + 2.59808i −0.166667 + 0.288675i
\(10\) 8.19615 4.73205i 0.819615 0.473205i
\(11\) −3.92820 + 14.6603i −0.357109 + 1.33275i 0.520700 + 0.853740i \(0.325671\pi\)
−0.877809 + 0.479011i \(0.840996\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 11.2583 + 6.50000i 0.866025 + 0.500000i
\(14\) 3.66025 0.261447
\(15\) −11.1962 3.00000i −0.746410 0.200000i
\(16\) 2.00000 + 3.46410i 0.125000 + 0.216506i
\(17\) −4.39230 2.53590i −0.258371 0.149170i 0.365220 0.930921i \(-0.380994\pi\)
−0.623591 + 0.781751i \(0.714327\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) −0.954483 3.56218i −0.0502359 0.187483i 0.936248 0.351339i \(-0.114273\pi\)
−0.986484 + 0.163856i \(0.947607\pi\)
\(20\) −12.9282 + 3.46410i −0.646410 + 0.173205i
\(21\) −3.16987 3.16987i −0.150946 0.150946i
\(22\) 10.7321 18.5885i 0.487820 0.844930i
\(23\) 27.5885 15.9282i 1.19950 0.692531i 0.239055 0.971006i \(-0.423162\pi\)
0.960443 + 0.278476i \(0.0898291\pi\)
\(24\) 1.26795 4.73205i 0.0528312 0.197169i
\(25\) 19.7846i 0.791384i
\(26\) −13.0000 13.0000i −0.500000 0.500000i
\(27\) −5.19615 −0.192450
\(28\) −5.00000 1.33975i −0.178571 0.0478481i
\(29\) −8.66025 15.0000i −0.298629 0.517241i 0.677193 0.735805i \(-0.263196\pi\)
−0.975823 + 0.218564i \(0.929863\pi\)
\(30\) 14.1962 + 8.19615i 0.473205 + 0.273205i
\(31\) 30.8301 30.8301i 0.994520 0.994520i −0.00546484 0.999985i \(-0.501740\pi\)
0.999985 + 0.00546484i \(0.00173952\pi\)
\(32\) −1.46410 5.46410i −0.0457532 0.170753i
\(33\) −25.3923 + 6.80385i −0.769464 + 0.206177i
\(34\) 5.07180 + 5.07180i 0.149170 + 0.149170i
\(35\) 8.66025 15.0000i 0.247436 0.428571i
\(36\) −5.19615 + 3.00000i −0.144338 + 0.0833333i
\(37\) −13.2417 + 49.4186i −0.357883 + 1.33564i 0.518934 + 0.854814i \(0.326329\pi\)
−0.876817 + 0.480823i \(0.840338\pi\)
\(38\) 5.21539i 0.137247i
\(39\) 22.5167i 0.577350i
\(40\) 18.9282 0.473205
\(41\) −41.3205 11.0718i −1.00782 0.270044i −0.283100 0.959090i \(-0.591363\pi\)
−0.724717 + 0.689047i \(0.758030\pi\)
\(42\) 3.16987 + 5.49038i 0.0754732 + 0.130723i
\(43\) 28.2846 + 16.3301i 0.657782 + 0.379770i 0.791431 0.611258i \(-0.209336\pi\)
−0.133650 + 0.991029i \(0.542670\pi\)
\(44\) −21.4641 + 21.4641i −0.487820 + 0.487820i
\(45\) −5.19615 19.3923i −0.115470 0.430940i
\(46\) −43.5167 + 11.6603i −0.946014 + 0.253484i
\(47\) 58.9808 + 58.9808i 1.25491 + 1.25491i 0.953492 + 0.301418i \(0.0974598\pi\)
0.301418 + 0.953492i \(0.402540\pi\)
\(48\) −3.46410 + 6.00000i −0.0721688 + 0.125000i
\(49\) −36.6340 + 21.1506i −0.747632 + 0.431646i
\(50\) −7.24167 + 27.0263i −0.144833 + 0.540526i
\(51\) 8.78461i 0.172247i
\(52\) 13.0000 + 22.5167i 0.250000 + 0.433013i
\(53\) 97.6743 1.84291 0.921456 0.388483i \(-0.127001\pi\)
0.921456 + 0.388483i \(0.127001\pi\)
\(54\) 7.09808 + 1.90192i 0.131446 + 0.0352208i
\(55\) −50.7846 87.9615i −0.923357 1.59930i
\(56\) 6.33975 + 3.66025i 0.113210 + 0.0653617i
\(57\) 4.51666 4.51666i 0.0792397 0.0792397i
\(58\) 6.33975 + 23.6603i 0.109306 + 0.407935i
\(59\) 59.1051 15.8372i 1.00178 0.268427i 0.279590 0.960120i \(-0.409801\pi\)
0.722192 + 0.691693i \(0.243135\pi\)
\(60\) −16.3923 16.3923i −0.273205 0.273205i
\(61\) −39.6506 + 68.6769i −0.650010 + 1.12585i 0.333109 + 0.942888i \(0.391902\pi\)
−0.983120 + 0.182963i \(0.941431\pi\)
\(62\) −53.3993 + 30.8301i −0.861280 + 0.497260i
\(63\) 2.00962 7.50000i 0.0318987 0.119048i
\(64\) 8.00000i 0.125000i
\(65\) −84.0333 + 22.5167i −1.29282 + 0.346410i
\(66\) 37.1769 0.563287
\(67\) −63.8468 17.1077i −0.952937 0.255339i −0.251329 0.967902i \(-0.580868\pi\)
−0.701608 + 0.712563i \(0.747534\pi\)
\(68\) −5.07180 8.78461i −0.0745852 0.129185i
\(69\) 47.7846 + 27.5885i 0.692531 + 0.399833i
\(70\) −17.3205 + 17.3205i −0.247436 + 0.247436i
\(71\) −13.8897 51.8372i −0.195630 0.730101i −0.992103 0.125427i \(-0.959970\pi\)
0.796473 0.604674i \(-0.206697\pi\)
\(72\) 8.19615 2.19615i 0.113835 0.0305021i
\(73\) −27.5814 27.5814i −0.377828 0.377828i 0.492490 0.870318i \(-0.336087\pi\)
−0.870318 + 0.492490i \(0.836087\pi\)
\(74\) 36.1769 62.6603i 0.488877 0.846760i
\(75\) 29.6769 17.1340i 0.395692 0.228453i
\(76\) 1.90897 7.12436i 0.0251180 0.0937415i
\(77\) 39.2820i 0.510156i
\(78\) 8.24167 30.7583i 0.105662 0.394338i
\(79\) 36.1244 0.457270 0.228635 0.973512i \(-0.426574\pi\)
0.228635 + 0.973512i \(0.426574\pi\)
\(80\) −25.8564 6.92820i −0.323205 0.0866025i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 52.3923 + 30.2487i 0.638931 + 0.368887i
\(83\) 20.9667 20.9667i 0.252611 0.252611i −0.569430 0.822040i \(-0.692836\pi\)
0.822040 + 0.569430i \(0.192836\pi\)
\(84\) −2.32051 8.66025i −0.0276251 0.103098i
\(85\) 32.7846 8.78461i 0.385701 0.103348i
\(86\) −32.6603 32.6603i −0.379770 0.379770i
\(87\) 15.0000 25.9808i 0.172414 0.298629i
\(88\) 37.1769 21.4641i 0.422465 0.243910i
\(89\) −18.0666 + 67.4256i −0.202996 + 0.757591i 0.787055 + 0.616883i \(0.211605\pi\)
−0.990051 + 0.140709i \(0.955062\pi\)
\(90\) 28.3923i 0.315470i
\(91\) −32.5000 8.70835i −0.357143 0.0956961i
\(92\) 63.7128 0.692531
\(93\) 72.9449 + 19.5455i 0.784353 + 0.210167i
\(94\) −58.9808 102.158i −0.627455 1.08678i
\(95\) 21.3731 + 12.3397i 0.224980 + 0.129892i
\(96\) 6.92820 6.92820i 0.0721688 0.0721688i
\(97\) 4.75387 + 17.7417i 0.0490089 + 0.182904i 0.986091 0.166205i \(-0.0531512\pi\)
−0.937082 + 0.349108i \(0.886485\pi\)
\(98\) 57.7846 15.4833i 0.589639 0.157993i
\(99\) −32.1962 32.1962i −0.325214 0.325214i
\(100\) 19.7846 34.2679i 0.197846 0.342679i
\(101\) −120.215 + 69.4064i −1.19025 + 0.687192i −0.958364 0.285551i \(-0.907824\pi\)
−0.231888 + 0.972743i \(0.574490\pi\)
\(102\) −3.21539 + 12.0000i −0.0315234 + 0.117647i
\(103\) 107.263i 1.04139i 0.853744 + 0.520693i \(0.174326\pi\)
−0.853744 + 0.520693i \(0.825674\pi\)
\(104\) −9.51666 35.5167i −0.0915064 0.341506i
\(105\) 30.0000 0.285714
\(106\) −133.426 35.7513i −1.25873 0.337276i
\(107\) −2.75129 4.76537i −0.0257130 0.0445362i 0.852883 0.522103i \(-0.174852\pi\)
−0.878596 + 0.477567i \(0.841519\pi\)
\(108\) −9.00000 5.19615i −0.0833333 0.0481125i
\(109\) 108.811 108.811i 0.998265 0.998265i −0.00173346 0.999998i \(-0.500552\pi\)
0.999998 + 0.00173346i \(0.000551778\pi\)
\(110\) 37.1769 + 138.746i 0.337972 + 1.26133i
\(111\) −85.5955 + 22.9352i −0.771131 + 0.206624i
\(112\) −7.32051 7.32051i −0.0653617 0.0653617i
\(113\) 43.3923 75.1577i 0.384003 0.665112i −0.607628 0.794222i \(-0.707879\pi\)
0.991630 + 0.129110i \(0.0412120\pi\)
\(114\) −7.82309 + 4.51666i −0.0686236 + 0.0396198i
\(115\) −55.1769 + 205.923i −0.479799 + 1.79064i
\(116\) 34.6410i 0.298629i
\(117\) −33.7750 + 19.5000i −0.288675 + 0.166667i
\(118\) −86.5359 −0.733355
\(119\) 12.6795 + 3.39746i 0.106550 + 0.0285501i
\(120\) 16.3923 + 28.3923i 0.136603 + 0.236603i
\(121\) −94.7032 54.6769i −0.782671 0.451875i
\(122\) 79.3013 79.3013i 0.650010 0.650010i
\(123\) −19.1769 71.5692i −0.155910 0.581864i
\(124\) 84.2295 22.5692i 0.679270 0.182010i
\(125\) −24.6795 24.6795i −0.197436 0.197436i
\(126\) −5.49038 + 9.50962i −0.0435745 + 0.0754732i
\(127\) 154.885 89.4230i 1.21957 0.704118i 0.254743 0.967009i \(-0.418009\pi\)
0.964826 + 0.262890i \(0.0846757\pi\)
\(128\) 2.92820 10.9282i 0.0228766 0.0853766i
\(129\) 56.5692i 0.438521i
\(130\) 123.033 0.946410
\(131\) 53.6359 0.409434 0.204717 0.978821i \(-0.434373\pi\)
0.204717 + 0.978821i \(0.434373\pi\)
\(132\) −50.7846 13.6077i −0.384732 0.103089i
\(133\) 4.77241 + 8.26606i 0.0358828 + 0.0621508i
\(134\) 80.9545 + 46.7391i 0.604138 + 0.348799i
\(135\) 24.5885 24.5885i 0.182137 0.182137i
\(136\) 3.71281 + 13.8564i 0.0273001 + 0.101885i
\(137\) −119.478 + 32.0141i −0.872104 + 0.233679i −0.666997 0.745060i \(-0.732421\pi\)
−0.205106 + 0.978740i \(0.565754\pi\)
\(138\) −55.1769 55.1769i −0.399833 0.399833i
\(139\) −76.8538 + 133.115i −0.552905 + 0.957660i 0.445158 + 0.895452i \(0.353148\pi\)
−0.998063 + 0.0622079i \(0.980186\pi\)
\(140\) 30.0000 17.3205i 0.214286 0.123718i
\(141\) −37.3923 + 139.550i −0.265194 + 0.989716i
\(142\) 75.8949i 0.534471i
\(143\) −139.517 + 139.517i −0.975641 + 0.975641i
\(144\) −12.0000 −0.0833333
\(145\) 111.962 + 30.0000i 0.772148 + 0.206897i
\(146\) 27.5814 + 47.7724i 0.188914 + 0.327208i
\(147\) −63.4519 36.6340i −0.431646 0.249211i
\(148\) −72.3538 + 72.3538i −0.488877 + 0.488877i
\(149\) −41.0718 153.282i −0.275650 1.02874i −0.955405 0.295299i \(-0.904581\pi\)
0.679755 0.733439i \(-0.262086\pi\)
\(150\) −46.8109 + 12.5429i −0.312073 + 0.0836196i
\(151\) −158.962 158.962i −1.05273 1.05273i −0.998530 0.0541950i \(-0.982741\pi\)
−0.0541950 0.998530i \(-0.517259\pi\)
\(152\) −5.21539 + 9.03332i −0.0343118 + 0.0594297i
\(153\) 13.1769 7.60770i 0.0861236 0.0497235i
\(154\) −14.3782 + 53.6603i −0.0933651 + 0.348443i
\(155\) 291.779i 1.88245i
\(156\) −22.5167 + 39.0000i −0.144338 + 0.250000i
\(157\) 138.569 0.882606 0.441303 0.897358i \(-0.354516\pi\)
0.441303 + 0.897358i \(0.354516\pi\)
\(158\) −49.3468 13.2224i −0.312321 0.0836863i
\(159\) 84.5885 + 146.512i 0.532003 + 0.921456i
\(160\) 32.7846 + 18.9282i 0.204904 + 0.118301i
\(161\) −58.3013 + 58.3013i −0.362120 + 0.362120i
\(162\) 3.29423 + 12.2942i 0.0203347 + 0.0758903i
\(163\) 270.947 72.6000i 1.66225 0.445399i 0.699245 0.714882i \(-0.253520\pi\)
0.963005 + 0.269484i \(0.0868530\pi\)
\(164\) −60.4974 60.4974i −0.368887 0.368887i
\(165\) 87.9615 152.354i 0.533100 0.923357i
\(166\) −36.3154 + 20.9667i −0.218767 + 0.126305i
\(167\) 72.3154 269.885i 0.433026 1.61608i −0.312720 0.949845i \(-0.601240\pi\)
0.745746 0.666230i \(-0.232093\pi\)
\(168\) 12.6795i 0.0754732i
\(169\) 84.5000 + 146.358i 0.500000 + 0.866025i
\(170\) −48.0000 −0.282353
\(171\) 10.6865 + 2.86345i 0.0624943 + 0.0167453i
\(172\) 32.6603 + 56.5692i 0.189885 + 0.328891i
\(173\) −58.4923 33.7705i −0.338106 0.195205i 0.321328 0.946968i \(-0.395871\pi\)
−0.659434 + 0.751762i \(0.729204\pi\)
\(174\) −30.0000 + 30.0000i −0.172414 + 0.172414i
\(175\) 13.2532 + 49.4615i 0.0757324 + 0.282637i
\(176\) −58.6410 + 15.7128i −0.333188 + 0.0892773i
\(177\) 74.9423 + 74.9423i 0.423403 + 0.423403i
\(178\) 49.3590 85.4923i 0.277298 0.480294i
\(179\) 43.4923 25.1103i 0.242974 0.140281i −0.373569 0.927602i \(-0.621866\pi\)
0.616543 + 0.787322i \(0.288533\pi\)
\(180\) 10.3923 38.7846i 0.0577350 0.215470i
\(181\) 302.354i 1.67046i −0.549898 0.835232i \(-0.685334\pi\)
0.549898 0.835232i \(-0.314666\pi\)
\(182\) 41.2083 + 23.7917i 0.226419 + 0.130723i
\(183\) −137.354 −0.750567
\(184\) −87.0333 23.3205i −0.473007 0.126742i
\(185\) −171.191 296.512i −0.925357 1.60276i
\(186\) −92.4904 53.3993i −0.497260 0.287093i
\(187\) 54.4308 54.4308i 0.291074 0.291074i
\(188\) 43.1769 + 161.138i 0.229664 + 0.857119i
\(189\) 12.9904 3.48076i 0.0687322 0.0184167i
\(190\) −24.6795 24.6795i −0.129892 0.129892i
\(191\) −81.3397 + 140.885i −0.425863 + 0.737616i −0.996501 0.0835862i \(-0.973363\pi\)
0.570638 + 0.821202i \(0.306696\pi\)
\(192\) −12.0000 + 6.92820i −0.0625000 + 0.0360844i
\(193\) 21.2846 79.4352i 0.110283 0.411582i −0.888608 0.458668i \(-0.848327\pi\)
0.998891 + 0.0470861i \(0.0149935\pi\)
\(194\) 25.9756i 0.133895i
\(195\) −106.550 106.550i −0.546410 0.546410i
\(196\) −84.6025 −0.431646
\(197\) 260.851 + 69.8949i 1.32412 + 0.354796i 0.850519 0.525944i \(-0.176288\pi\)
0.473599 + 0.880741i \(0.342955\pi\)
\(198\) 32.1962 + 55.7654i 0.162607 + 0.281643i
\(199\) −55.2391 31.8923i −0.277583 0.160263i 0.354745 0.934963i \(-0.384568\pi\)
−0.632329 + 0.774700i \(0.717901\pi\)
\(200\) −39.5692 + 39.5692i −0.197846 + 0.197846i
\(201\) −29.6314 110.586i −0.147420 0.550179i
\(202\) 189.622 50.8090i 0.938722 0.251530i
\(203\) 31.6987 + 31.6987i 0.156151 + 0.156151i
\(204\) 8.78461 15.2154i 0.0430618 0.0745852i
\(205\) 247.923 143.138i 1.20938 0.698236i
\(206\) 39.2609 146.524i 0.190587 0.711280i
\(207\) 95.5692i 0.461687i
\(208\) 52.0000i 0.250000i
\(209\) 55.9718 0.267808
\(210\) −40.9808 10.9808i −0.195146 0.0522893i
\(211\) −123.899 214.600i −0.587201 1.01706i −0.994597 0.103810i \(-0.966897\pi\)
0.407396 0.913251i \(-0.366437\pi\)
\(212\) 169.177 + 97.6743i 0.798004 + 0.460728i
\(213\) 65.7269 65.7269i 0.308577 0.308577i
\(214\) 2.01408 + 7.51666i 0.00941160 + 0.0351246i
\(215\) −211.119 + 56.5692i −0.981950 + 0.263113i
\(216\) 10.3923 + 10.3923i 0.0481125 + 0.0481125i
\(217\) −56.4230 + 97.7276i −0.260014 + 0.450358i
\(218\) −188.466 + 108.811i −0.864523 + 0.499133i
\(219\) 17.4859 65.2583i 0.0798444 0.297983i
\(220\) 203.138i 0.923357i
\(221\) −32.9667 57.1000i −0.149170 0.258371i
\(222\) 125.321 0.564507
\(223\) −44.4378 11.9071i −0.199273 0.0533950i 0.157802 0.987471i \(-0.449559\pi\)
−0.357075 + 0.934076i \(0.616226\pi\)
\(224\) 7.32051 + 12.6795i 0.0326808 + 0.0566049i
\(225\) 51.4019 + 29.6769i 0.228453 + 0.131897i
\(226\) −86.7846 + 86.7846i −0.384003 + 0.384003i
\(227\) 3.55514 + 13.2679i 0.0156614 + 0.0584491i 0.973314 0.229476i \(-0.0737012\pi\)
−0.957653 + 0.287925i \(0.907035\pi\)
\(228\) 12.3397 3.30642i 0.0541217 0.0145019i
\(229\) 287.315 + 287.315i 1.25465 + 1.25465i 0.953611 + 0.301041i \(0.0973341\pi\)
0.301041 + 0.953611i \(0.402666\pi\)
\(230\) 150.746 261.100i 0.655418 1.13522i
\(231\) 58.9230 34.0192i 0.255078 0.147269i
\(232\) −12.6795 + 47.3205i −0.0546530 + 0.203968i
\(233\) 27.3308i 0.117300i −0.998279 0.0586498i \(-0.981320\pi\)
0.998279 0.0586498i \(-0.0186795\pi\)
\(234\) 53.2750 14.2750i 0.227671 0.0610042i
\(235\) −558.200 −2.37532
\(236\) 118.210 + 31.6743i 0.500891 + 0.134213i
\(237\) 31.2846 + 54.1865i 0.132003 + 0.228635i
\(238\) −16.0770 9.28203i −0.0675502 0.0390001i
\(239\) −0.861561 + 0.861561i −0.00360486 + 0.00360486i −0.708907 0.705302i \(-0.750811\pi\)
0.705302 + 0.708907i \(0.250811\pi\)
\(240\) −12.0000 44.7846i −0.0500000 0.186603i
\(241\) 82.2032 22.0263i 0.341092 0.0913954i −0.0842068 0.996448i \(-0.526836\pi\)
0.425299 + 0.905053i \(0.360169\pi\)
\(242\) 109.354 + 109.354i 0.451875 + 0.451875i
\(243\) 7.79423 13.5000i 0.0320750 0.0555556i
\(244\) −137.354 + 79.3013i −0.562926 + 0.325005i
\(245\) 73.2679 273.440i 0.299053 1.11608i
\(246\) 104.785i 0.425954i
\(247\) 12.4083 46.3083i 0.0502359 0.187483i
\(248\) −123.321 −0.497260
\(249\) 49.6077 + 13.2923i 0.199228 + 0.0533829i
\(250\) 24.6795 + 42.7461i 0.0987180 + 0.170985i
\(251\) −35.2539 20.3538i −0.140454 0.0810910i 0.428127 0.903719i \(-0.359174\pi\)
−0.568580 + 0.822628i \(0.692507\pi\)
\(252\) 10.9808 10.9808i 0.0435745 0.0435745i
\(253\) 125.138 + 467.023i 0.494618 + 1.84594i
\(254\) −244.308 + 65.4622i −0.961844 + 0.257725i
\(255\) 41.5692 + 41.5692i 0.163017 + 0.163017i
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −268.277 + 154.890i −1.04388 + 0.602684i −0.920930 0.389729i \(-0.872569\pi\)
−0.122949 + 0.992413i \(0.539235\pi\)
\(258\) 20.7058 77.2750i 0.0802549 0.299515i
\(259\) 132.417i 0.511261i
\(260\) −168.067 45.0333i −0.646410 0.173205i
\(261\) 51.9615 0.199086
\(262\) −73.2679 19.6321i −0.279649 0.0749316i
\(263\) 143.818 + 249.100i 0.546836 + 0.947148i 0.998489 + 0.0549543i \(0.0175013\pi\)
−0.451653 + 0.892194i \(0.649165\pi\)
\(264\) 64.3923 + 37.1769i 0.243910 + 0.140822i
\(265\) −462.200 + 462.200i −1.74415 + 1.74415i
\(266\) −3.49365 13.0385i −0.0131340 0.0490168i
\(267\) −116.785 + 31.2923i −0.437396 + 0.117200i
\(268\) −93.4782 93.4782i −0.348799 0.348799i
\(269\) −81.8705 + 141.804i −0.304351 + 0.527152i −0.977117 0.212704i \(-0.931773\pi\)
0.672765 + 0.739856i \(0.265106\pi\)
\(270\) −42.5885 + 24.5885i −0.157735 + 0.0910684i
\(271\) −84.1692 + 314.124i −0.310587 + 1.15913i 0.617441 + 0.786617i \(0.288170\pi\)
−0.928028 + 0.372510i \(0.878497\pi\)
\(272\) 20.2872i 0.0745852i
\(273\) −15.0833 56.2917i −0.0552502 0.206197i
\(274\) 174.928 0.638424
\(275\) 290.047 + 77.7180i 1.05472 + 0.282611i
\(276\) 55.1769 + 95.5692i 0.199916 + 0.346265i
\(277\) −116.900 67.4923i −0.422022 0.243654i 0.273920 0.961752i \(-0.411680\pi\)
−0.695942 + 0.718098i \(0.745013\pi\)
\(278\) 153.708 153.708i 0.552905 0.552905i
\(279\) 33.8538 + 126.344i 0.121340 + 0.452847i
\(280\) −47.3205 + 12.6795i −0.169002 + 0.0452839i
\(281\) 323.545 + 323.545i 1.15141 + 1.15141i 0.986271 + 0.165134i \(0.0528056\pi\)
0.165134 + 0.986271i \(0.447194\pi\)
\(282\) 102.158 176.942i 0.362261 0.627455i
\(283\) −122.416 + 70.6769i −0.432565 + 0.249742i −0.700439 0.713712i \(-0.747012\pi\)
0.267874 + 0.963454i \(0.413679\pi\)
\(284\) 27.7795 103.674i 0.0978150 0.365050i
\(285\) 42.7461i 0.149986i
\(286\) 241.650 139.517i 0.844930 0.487820i
\(287\) 110.718 0.385777
\(288\) 16.3923 + 4.39230i 0.0569177 + 0.0152511i
\(289\) −131.638 228.004i −0.455496 0.788943i
\(290\) −141.962 81.9615i −0.489522 0.282626i
\(291\) −22.4955 + 22.4955i −0.0773042 + 0.0773042i
\(292\) −20.1910 75.3538i −0.0691473 0.258061i
\(293\) 287.512 77.0385i 0.981268 0.262930i 0.267689 0.963505i \(-0.413740\pi\)
0.713578 + 0.700575i \(0.247073\pi\)
\(294\) 73.2679 + 73.2679i 0.249211 + 0.249211i
\(295\) −204.746 + 354.631i −0.694055 + 1.20214i
\(296\) 125.321 72.3538i 0.423380 0.244439i
\(297\) 20.4115 76.1769i 0.0687257 0.256488i
\(298\) 224.420i 0.753089i
\(299\) 414.133 1.38506
\(300\) 68.5359 0.228453
\(301\) −81.6506 21.8782i −0.271265 0.0726851i
\(302\) 158.962 + 275.329i 0.526363 + 0.911687i
\(303\) −208.219 120.215i −0.687192 0.396750i
\(304\) 10.4308 10.4308i 0.0343118 0.0343118i
\(305\) −137.354 512.611i −0.450340 1.68069i
\(306\) −20.7846 + 5.56922i −0.0679236 + 0.0182001i
\(307\) −70.0685 70.0685i −0.228236 0.228236i 0.583719 0.811956i \(-0.301597\pi\)
−0.811956 + 0.583719i \(0.801597\pi\)
\(308\) 39.2820 68.0385i 0.127539 0.220904i
\(309\) −160.894 + 92.8923i −0.520693 + 0.300622i
\(310\) 106.799 398.578i 0.344512 1.28574i
\(311\) 140.238i 0.450927i −0.974252 0.225464i \(-0.927610\pi\)
0.974252 0.225464i \(-0.0723897\pi\)
\(312\) 45.0333 45.0333i 0.144338 0.144338i
\(313\) −550.286 −1.75810 −0.879051 0.476728i \(-0.841823\pi\)
−0.879051 + 0.476728i \(0.841823\pi\)
\(314\) −189.289 50.7199i −0.602831 0.161528i
\(315\) 25.9808 + 45.0000i 0.0824786 + 0.142857i
\(316\) 62.5692 + 36.1244i 0.198004 + 0.114318i
\(317\) −31.2923 + 31.2923i −0.0987140 + 0.0987140i −0.754739 0.656025i \(-0.772237\pi\)
0.656025 + 0.754739i \(0.272237\pi\)
\(318\) −61.9230 231.100i −0.194727 0.726729i
\(319\) 253.923 68.0385i 0.795997 0.213287i
\(320\) −37.8564 37.8564i −0.118301 0.118301i
\(321\) 4.76537 8.25387i 0.0148454 0.0257130i
\(322\) 100.981 58.3013i 0.313605 0.181060i
\(323\) −4.84094 + 18.0666i −0.0149874 + 0.0559339i
\(324\) 18.0000i 0.0555556i
\(325\) 128.600 222.742i 0.395692 0.685359i
\(326\) −396.694 −1.21685
\(327\) 257.449 + 68.9833i 0.787307 + 0.210958i
\(328\) 60.4974 + 104.785i 0.184443 + 0.319465i
\(329\) −186.962 107.942i −0.568272 0.328092i
\(330\) −175.923 + 175.923i −0.533100 + 0.533100i
\(331\) −104.546 390.169i −0.315847 1.17876i −0.923198 0.384325i \(-0.874434\pi\)
0.607350 0.794434i \(-0.292232\pi\)
\(332\) 57.2820 15.3487i 0.172536 0.0462309i
\(333\) −108.531 108.531i −0.325918 0.325918i
\(334\) −197.569 + 342.200i −0.591525 + 1.02455i
\(335\) 383.081 221.172i 1.14352 0.660214i
\(336\) 4.64102 17.3205i 0.0138125 0.0515491i
\(337\) 638.492i 1.89464i −0.320295 0.947318i \(-0.603782\pi\)
0.320295 0.947318i \(-0.396218\pi\)
\(338\) −61.8583 230.858i −0.183013 0.683013i
\(339\) 150.315 0.443408
\(340\) 65.5692 + 17.5692i 0.192851 + 0.0516742i
\(341\) 330.870 + 573.084i 0.970295 + 1.68060i
\(342\) −13.5500 7.82309i −0.0396198 0.0228745i
\(343\) 167.093 167.093i 0.487151 0.487151i
\(344\) −23.9090 89.2295i −0.0695028 0.259388i
\(345\) −356.669 + 95.5692i −1.03382 + 0.277012i
\(346\) 67.5411 + 67.5411i 0.195205 + 0.195205i
\(347\) 2.85125 4.93851i 0.00821686 0.0142320i −0.861888 0.507099i \(-0.830718\pi\)
0.870105 + 0.492867i \(0.164051\pi\)
\(348\) 51.9615 30.0000i 0.149315 0.0862069i
\(349\) 46.8890 174.992i 0.134353 0.501411i −0.865647 0.500655i \(-0.833093\pi\)
1.00000 0.000755966i \(-0.000240632\pi\)
\(350\) 72.4167i 0.206905i
\(351\) −58.5000 33.7750i −0.166667 0.0962250i
\(352\) 85.8564 0.243910
\(353\) −280.086 75.0488i −0.793444 0.212603i −0.160741 0.986997i \(-0.551388\pi\)
−0.632704 + 0.774394i \(0.718055\pi\)
\(354\) −74.9423 129.804i −0.211701 0.366678i
\(355\) 311.023 + 179.569i 0.876121 + 0.505829i
\(356\) −98.7180 + 98.7180i −0.277298 + 0.277298i
\(357\) 5.88457 + 21.9615i 0.0164834 + 0.0615169i
\(358\) −68.6025 + 18.3820i −0.191627 + 0.0513464i
\(359\) −268.277 268.277i −0.747289 0.747289i 0.226680 0.973969i \(-0.427213\pi\)
−0.973969 + 0.226680i \(0.927213\pi\)
\(360\) −28.3923 + 49.1769i −0.0788675 + 0.136603i
\(361\) 300.857 173.700i 0.833399 0.481163i
\(362\) −110.669 + 413.023i −0.305716 + 1.14095i
\(363\) 189.406i 0.521781i
\(364\) −47.5833 47.5833i −0.130723 0.130723i
\(365\) 261.033 0.715160
\(366\) 187.629 + 50.2750i 0.512647 + 0.137363i
\(367\) 88.1077 + 152.607i 0.240075 + 0.415823i 0.960736 0.277466i \(-0.0894945\pi\)
−0.720660 + 0.693289i \(0.756161\pi\)
\(368\) 110.354 + 63.7128i 0.299875 + 0.173133i
\(369\) 90.7461 90.7461i 0.245924 0.245924i
\(370\) 125.321 + 467.703i 0.338704 + 1.26406i
\(371\) −244.186 + 65.4294i −0.658183 + 0.176360i
\(372\) 106.799 + 106.799i 0.287093 + 0.287093i
\(373\) −241.803 + 418.815i −0.648266 + 1.12283i 0.335271 + 0.942122i \(0.391172\pi\)
−0.983537 + 0.180708i \(0.942161\pi\)
\(374\) −94.2769 + 54.4308i −0.252077 + 0.145537i
\(375\) 15.6462 58.3923i 0.0417231 0.155713i
\(376\) 235.923i 0.627455i
\(377\) 225.167i 0.597259i
\(378\) −19.0192 −0.0503154
\(379\) 278.815 + 74.7083i 0.735661 + 0.197120i 0.607149 0.794588i \(-0.292313\pi\)
0.128512 + 0.991708i \(0.458980\pi\)
\(380\) 24.6795 + 42.7461i 0.0649460 + 0.112490i
\(381\) 268.269 + 154.885i 0.704118 + 0.406523i
\(382\) 162.679 162.679i 0.425863 0.425863i
\(383\) −68.1718 254.420i −0.177994 0.664283i −0.996022 0.0891049i \(-0.971599\pi\)
0.818028 0.575178i \(-0.195067\pi\)
\(384\) 18.9282 5.07180i 0.0492922 0.0132078i
\(385\) 185.885 + 185.885i 0.482817 + 0.482817i
\(386\) −58.1506 + 100.720i −0.150649 + 0.260932i
\(387\) −84.8538 + 48.9904i −0.219261 + 0.126590i
\(388\) −9.50773 + 35.4833i −0.0245045 + 0.0914519i
\(389\) 66.2487i 0.170305i 0.996368 + 0.0851526i \(0.0271378\pi\)
−0.996368 + 0.0851526i \(0.972862\pi\)
\(390\) 106.550 + 184.550i 0.273205 + 0.473205i
\(391\) −161.569 −0.413221
\(392\) 115.569 + 30.9667i 0.294819 + 0.0789966i
\(393\) 46.4500 + 80.4538i 0.118193 + 0.204717i
\(394\) −330.746 190.956i −0.839457 0.484661i
\(395\) −170.942 + 170.942i −0.432765 + 0.432765i
\(396\) −23.5692 87.9615i −0.0595182 0.222125i
\(397\) −130.651 + 35.0077i −0.329095 + 0.0881807i −0.419583 0.907717i \(-0.637824\pi\)
0.0904886 + 0.995897i \(0.471157\pi\)
\(398\) 63.7846 + 63.7846i 0.160263 + 0.160263i
\(399\) −8.26606 + 14.3172i −0.0207169 + 0.0358828i
\(400\) 68.5359 39.5692i 0.171340 0.0989230i
\(401\) −49.5654 + 184.981i −0.123605 + 0.461299i −0.999786 0.0206827i \(-0.993416\pi\)
0.876181 + 0.481981i \(0.160083\pi\)
\(402\) 161.909i 0.402759i
\(403\) 547.492 146.700i 1.35854 0.364020i
\(404\) −277.626 −0.687192
\(405\) 58.1769 + 15.5885i 0.143647 + 0.0384900i
\(406\) −31.6987 54.9038i −0.0780757 0.135231i
\(407\) −672.473 388.252i −1.65227 0.953937i
\(408\) −17.5692 + 17.5692i −0.0430618 + 0.0430618i
\(409\) 143.838 + 536.812i 0.351683 + 1.31250i 0.884608 + 0.466336i \(0.154426\pi\)
−0.532925 + 0.846163i \(0.678907\pi\)
\(410\) −391.061 + 104.785i −0.953809 + 0.255572i
\(411\) −151.492 151.492i −0.368594 0.368594i
\(412\) −107.263 + 185.785i −0.260347 + 0.450934i
\(413\) −137.154 + 79.1858i −0.332092 + 0.191733i
\(414\) 34.9808 130.550i 0.0844946 0.315338i
\(415\) 198.431i 0.478146i
\(416\) 19.0333 71.0333i 0.0457532 0.170753i
\(417\) −266.229 −0.638440
\(418\) −76.4589 20.4871i −0.182916 0.0490122i
\(419\) 328.823 + 569.538i 0.784781 + 1.35928i 0.929130 + 0.369753i \(0.120558\pi\)
−0.144349 + 0.989527i \(0.546109\pi\)
\(420\) 51.9615 + 30.0000i 0.123718 + 0.0714286i
\(421\) 328.035 328.035i 0.779181 0.779181i −0.200511 0.979692i \(-0.564260\pi\)
0.979692 + 0.200511i \(0.0642601\pi\)
\(422\) 90.7006 + 338.499i 0.214930 + 0.802131i
\(423\) −241.708 + 64.7654i −0.571413 + 0.153110i
\(424\) −195.349 195.349i −0.460728 0.460728i
\(425\) −50.1718 + 86.9000i −0.118051 + 0.204471i
\(426\) −113.842 + 65.7269i −0.267236 + 0.154288i
\(427\) 53.1218 198.253i 0.124407 0.464293i
\(428\) 11.0052i 0.0257130i
\(429\) −330.100 88.4500i −0.769464 0.206177i
\(430\) 309.100 0.718837
\(431\) −30.9948 8.30504i −0.0719138 0.0192692i 0.222683 0.974891i \(-0.428519\pi\)
−0.294597 + 0.955622i \(0.595185\pi\)
\(432\) −10.3923 18.0000i −0.0240563 0.0416667i
\(433\) 169.928 + 98.1077i 0.392442 + 0.226577i 0.683218 0.730215i \(-0.260580\pi\)
−0.290776 + 0.956791i \(0.593913\pi\)
\(434\) 112.846 112.846i 0.260014 0.260014i
\(435\) 51.9615 + 193.923i 0.119452 + 0.445800i
\(436\) 297.277 79.6551i 0.681828 0.182695i
\(437\) −83.0718 83.0718i −0.190096 0.190096i
\(438\) −47.7724 + 82.7442i −0.109069 + 0.188914i
\(439\) 35.9078 20.7314i 0.0817945 0.0472241i −0.458545 0.888671i \(-0.651629\pi\)
0.540339 + 0.841447i \(0.318296\pi\)
\(440\) −74.3538 + 277.492i −0.168986 + 0.630664i
\(441\) 126.904i 0.287764i
\(442\) 24.1333 + 90.0666i 0.0546002 + 0.203771i
\(443\) −19.9718 −0.0450831 −0.0225416 0.999746i \(-0.507176\pi\)
−0.0225416 + 0.999746i \(0.507176\pi\)
\(444\) −171.191 45.8705i −0.385565 0.103312i
\(445\) −233.569 404.554i −0.524875 0.909110i
\(446\) 56.3449 + 32.5307i 0.126334 + 0.0729389i
\(447\) 194.354 194.354i 0.434796 0.434796i
\(448\) −5.35898 20.0000i −0.0119620 0.0446429i
\(449\) 127.459 34.1525i 0.283873 0.0760635i −0.114073 0.993472i \(-0.536390\pi\)
0.397946 + 0.917409i \(0.369723\pi\)
\(450\) −59.3538 59.3538i −0.131897 0.131897i
\(451\) 324.631 562.277i 0.719802 1.24673i
\(452\) 150.315 86.7846i 0.332556 0.192001i
\(453\) 100.778 376.107i 0.222467 0.830258i
\(454\) 19.4256i 0.0427877i
\(455\) 195.000 112.583i 0.428571 0.247436i
\(456\) −18.0666 −0.0396198
\(457\) −284.842 76.3231i −0.623286 0.167009i −0.0666648 0.997775i \(-0.521236\pi\)
−0.556621 + 0.830766i \(0.687902\pi\)
\(458\) −287.315 497.645i −0.627326 1.08656i
\(459\) 22.8231 + 13.1769i 0.0497235 + 0.0287079i
\(460\) −301.492 + 301.492i −0.655418 + 0.655418i
\(461\) 121.565 + 453.688i 0.263699 + 0.984140i 0.963042 + 0.269353i \(0.0868097\pi\)
−0.699342 + 0.714787i \(0.746524\pi\)
\(462\) −92.9423 + 24.9038i −0.201174 + 0.0539044i
\(463\) 462.599 + 462.599i 0.999134 + 0.999134i 1.00000 0.000865128i \(-0.000275379\pi\)
−0.000865128 1.00000i \(0.500275\pi\)
\(464\) 34.6410 60.0000i 0.0746574 0.129310i
\(465\) −437.669 + 252.688i −0.941224 + 0.543416i
\(466\) −10.0038 + 37.3346i −0.0214673 + 0.0801171i
\(467\) 396.649i 0.849355i 0.905345 + 0.424677i \(0.139612\pi\)
−0.905345 + 0.424677i \(0.860388\pi\)
\(468\) −78.0000 −0.166667
\(469\) 171.077 0.364770
\(470\) 762.515 + 204.315i 1.62237 + 0.434714i
\(471\) 120.004 + 207.854i 0.254787 + 0.441303i
\(472\) −149.885 86.5359i −0.317552 0.183339i
\(473\) −350.512 + 350.512i −0.741039 + 0.741039i
\(474\) −22.9019 85.4711i −0.0483163 0.180319i
\(475\) −70.4763 + 18.8841i −0.148371 + 0.0397559i
\(476\) 18.5641 + 18.5641i 0.0390001 + 0.0390001i
\(477\) −146.512 + 253.765i −0.307152 + 0.532003i
\(478\) 1.49227 0.861561i 0.00312190 0.00180243i
\(479\) 93.1666 347.703i 0.194502 0.725892i −0.797893 0.602799i \(-0.794052\pi\)
0.992395 0.123093i \(-0.0392814\pi\)
\(480\) 65.5692i 0.136603i
\(481\) −470.300 + 470.300i −0.977754 + 0.977754i
\(482\) −120.354 −0.249697
\(483\) −137.942 36.9615i −0.285595 0.0765249i
\(484\) −109.354 189.406i −0.225938 0.391336i
\(485\) −106.450 61.4589i −0.219485 0.126719i
\(486\) −15.5885 + 15.5885i −0.0320750 + 0.0320750i
\(487\) −50.1455 187.145i −0.102968 0.384282i 0.895139 0.445788i \(-0.147076\pi\)
−0.998107 + 0.0615056i \(0.980410\pi\)
\(488\) 216.655 58.0526i 0.443965 0.118960i
\(489\) 343.547 + 343.547i 0.702550 + 0.702550i
\(490\) −200.172 + 346.708i −0.408514 + 0.707567i
\(491\) 19.9808 11.5359i 0.0406940 0.0234947i −0.479515 0.877534i \(-0.659187\pi\)
0.520209 + 0.854039i \(0.325854\pi\)
\(492\) 38.3538 143.138i 0.0779549 0.290932i
\(493\) 87.8461i 0.178187i
\(494\) −33.9000 + 58.7166i −0.0686236 + 0.118859i
\(495\) 304.708 0.615571
\(496\) 168.459 + 45.1384i 0.339635 + 0.0910049i
\(497\) 69.4486 + 120.289i 0.139736 + 0.242029i
\(498\) −62.9000 36.3154i −0.126305 0.0729224i
\(499\) −160.769 + 160.769i −0.322183 + 0.322183i −0.849604 0.527421i \(-0.823159\pi\)
0.527421 + 0.849604i \(0.323159\pi\)
\(500\) −18.0666 67.4256i −0.0361333 0.134851i
\(501\) 467.454 125.254i 0.933042 0.250008i
\(502\) 40.7077 + 40.7077i 0.0810910 + 0.0810910i
\(503\) 300.622 520.692i 0.597658 1.03517i −0.395508 0.918462i \(-0.629432\pi\)
0.993166 0.116711i \(-0.0372351\pi\)
\(504\) −19.0192 + 10.9808i −0.0377366 + 0.0217872i
\(505\) 240.431 897.300i 0.476101 1.77683i
\(506\) 683.769i 1.35132i
\(507\) −146.358 + 253.500i −0.288675 + 0.500000i
\(508\) 357.692 0.704118
\(509\) −475.028 127.283i −0.933258 0.250066i −0.240014 0.970769i \(-0.577152\pi\)
−0.693243 + 0.720704i \(0.743819\pi\)
\(510\) −41.5692 72.0000i −0.0815083 0.141176i
\(511\) 87.4296 + 50.4775i 0.171095 + 0.0987818i
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) 4.95964 + 18.5096i 0.00966791 + 0.0360811i
\(514\) 423.167 113.387i 0.823281 0.220598i
\(515\) −507.573 507.573i −0.985579 0.985579i
\(516\) −56.5692 + 97.9808i −0.109630 + 0.189885i
\(517\) −1096.36 + 632.985i −2.12062 + 1.22434i
\(518\) −48.4679 + 180.885i −0.0935673 + 0.349198i
\(519\) 116.985i 0.225404i
\(520\) 213.100 + 123.033i 0.409808 + 0.236603i
\(521\) 647.951 1.24367 0.621834 0.783149i \(-0.286388\pi\)
0.621834 + 0.783149i \(0.286388\pi\)
\(522\) −70.9808 19.0192i −0.135978 0.0364353i
\(523\) 82.9615 + 143.694i 0.158626 + 0.274749i 0.934374 0.356295i \(-0.115960\pi\)
−0.775747 + 0.631044i \(0.782627\pi\)
\(524\) 92.9000 + 53.6359i 0.177290 + 0.102359i
\(525\) −62.7147 + 62.7147i −0.119457 + 0.119457i
\(526\) −105.282 392.918i −0.200156 0.746992i
\(527\) −213.597 + 57.2332i −0.405308 + 0.108602i
\(528\) −74.3538 74.3538i −0.140822 0.140822i
\(529\) 242.915 420.742i 0.459197 0.795353i
\(530\) 800.554 462.200i 1.51048 0.872075i
\(531\) −47.5115 + 177.315i −0.0894755 + 0.333927i
\(532\) 19.0897i 0.0358828i
\(533\) −393.233 393.233i −0.737773 0.737773i
\(534\) 170.985 0.320196
\(535\) 35.5692 + 9.53074i 0.0664845 + 0.0178145i
\(536\) 93.4782 + 161.909i 0.174400 + 0.302069i
\(537\) 75.3308 + 43.4923i 0.140281 + 0.0809912i
\(538\) 163.741 163.741i 0.304351 0.304351i
\(539\) −166.168 620.147i −0.308289 1.15055i
\(540\) 67.1769 18.0000i 0.124402 0.0333333i
\(541\) −210.557 210.557i −0.389200 0.389200i 0.485202 0.874402i \(-0.338746\pi\)
−0.874402 + 0.485202i \(0.838746\pi\)
\(542\) 229.954 398.293i 0.424270 0.734858i
\(543\) 453.531 261.846i 0.835232 0.482221i
\(544\) −7.42563 + 27.7128i −0.0136500 + 0.0509427i
\(545\) 1029.80i 1.88954i
\(546\) 82.4167i 0.150946i
\(547\) −392.492 −0.717536 −0.358768 0.933427i \(-0.616803\pi\)
−0.358768 + 0.933427i \(0.616803\pi\)
\(548\) −238.956 64.0282i −0.436052 0.116840i
\(549\) −118.952 206.031i −0.216670 0.375284i
\(550\) −367.765 212.329i −0.668664 0.386054i
\(551\) −45.1666 + 45.1666i −0.0819721 + 0.0819721i
\(552\) −40.3923 150.746i −0.0731745 0.273091i
\(553\) −90.3109 + 24.1987i −0.163311 + 0.0437590i
\(554\) 134.985 + 134.985i 0.243654 + 0.243654i
\(555\) 296.512 513.573i 0.534255 0.925357i
\(556\) −266.229 + 153.708i −0.478830 + 0.276453i
\(557\) 18.3576 68.5115i 0.0329580 0.123001i −0.947487 0.319794i \(-0.896386\pi\)
0.980445 + 0.196793i \(0.0630528\pi\)
\(558\) 184.981i 0.331507i
\(559\) 212.292 + 367.700i 0.379770 + 0.657782i
\(560\) 69.2820 0.123718
\(561\) 128.785 + 34.5077i 0.229563 + 0.0615111i
\(562\) −323.545 560.396i −0.575703 0.997146i
\(563\) 721.161 + 416.363i 1.28093 + 0.739543i 0.977018 0.213158i \(-0.0683750\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(564\) −204.315 + 204.315i −0.362261 + 0.362261i
\(565\) 150.315 + 560.985i 0.266045 + 0.992893i
\(566\) 193.093 51.7391i 0.341154 0.0914118i
\(567\) 16.4711 + 16.4711i 0.0290496 + 0.0290496i
\(568\) −75.8949 + 131.454i −0.133618 + 0.231433i
\(569\) 301.750 174.215i 0.530316 0.306178i −0.210829 0.977523i \(-0.567616\pi\)
0.741145 + 0.671345i \(0.234283\pi\)
\(570\) 15.6462 58.3923i 0.0274494 0.102443i
\(571\) 411.892i 0.721352i −0.932691 0.360676i \(-0.882546\pi\)
0.932691 0.360676i \(-0.117454\pi\)
\(572\) −381.167 + 102.133i −0.666375 + 0.178555i
\(573\) −281.769 −0.491744
\(574\) −151.244 40.5256i −0.263491 0.0706021i
\(575\) −315.133 545.827i −0.548058 0.949264i
\(576\) −20.7846 12.0000i −0.0360844 0.0208333i
\(577\) 39.6692 39.6692i 0.0687507 0.0687507i −0.671895 0.740646i \(-0.734520\pi\)
0.740646 + 0.671895i \(0.234520\pi\)
\(578\) 96.3660 + 359.643i 0.166723 + 0.622220i
\(579\) 137.586 36.8660i 0.237627 0.0636719i
\(580\) 163.923 + 163.923i 0.282626 + 0.282626i
\(581\) −38.3717 + 66.4617i −0.0660442 + 0.114392i
\(582\) 38.9634 22.4955i 0.0669474 0.0386521i
\(583\) −383.685 + 1431.93i −0.658121 + 2.45614i
\(584\) 110.326i 0.188914i
\(585\) 67.5500 252.100i 0.115470 0.430940i
\(586\) −420.946 −0.718338
\(587\) −505.435 135.431i −0.861047 0.230717i −0.198835 0.980033i \(-0.563716\pi\)
−0.662212 + 0.749316i \(0.730382\pi\)
\(588\) −73.2679 126.904i −0.124605 0.215823i
\(589\) −139.249 80.3956i −0.236416 0.136495i
\(590\) 409.492 409.492i 0.694055 0.694055i
\(591\) 121.061 + 451.808i 0.204842 + 0.764480i
\(592\) −197.674 + 52.9667i −0.333909 + 0.0894707i
\(593\) 234.771 + 234.771i 0.395903 + 0.395903i 0.876785 0.480882i \(-0.159684\pi\)
−0.480882 + 0.876785i \(0.659684\pi\)
\(594\) −55.7654 + 96.5885i −0.0938811 + 0.162607i
\(595\) −76.0770 + 43.9230i −0.127860 + 0.0738202i
\(596\) 82.1436 306.564i 0.137825 0.514369i
\(597\) 110.478i 0.185056i
\(598\) −565.717 151.583i −0.946014 0.253484i
\(599\) −652.908 −1.09000 −0.544998 0.838437i \(-0.683470\pi\)
−0.544998 + 0.838437i \(0.683470\pi\)
\(600\) −93.6218 25.0859i −0.156036 0.0418098i
\(601\) −32.7846 56.7846i −0.0545501 0.0944835i 0.837461 0.546497i \(-0.184039\pi\)
−0.892011 + 0.452014i \(0.850706\pi\)
\(602\) 103.529 + 59.7724i 0.171975 + 0.0992897i
\(603\) 140.217 140.217i 0.232533 0.232533i
\(604\) −116.368 434.291i −0.192662 0.719025i
\(605\) 706.874 189.406i 1.16839 0.313068i
\(606\) 240.431 + 240.431i 0.396750 + 0.396750i
\(607\) 388.300 672.555i 0.639703 1.10800i −0.345795 0.938310i \(-0.612391\pi\)
0.985498 0.169688i \(-0.0542761\pi\)
\(608\) −18.0666 + 10.4308i −0.0297149 + 0.0171559i
\(609\) −20.0962 + 75.0000i −0.0329987 + 0.123153i
\(610\) 750.515i 1.23035i
\(611\) 280.650 + 1047.40i 0.459329 + 1.71424i
\(612\) 30.4308 0.0497235
\(613\) −410.842 110.085i −0.670215 0.179583i −0.0923632 0.995725i \(-0.529442\pi\)
−0.577852 + 0.816142i \(0.696109\pi\)
\(614\) 70.0685 + 121.362i 0.114118 + 0.197658i
\(615\) 429.415 + 247.923i 0.698236 + 0.403127i
\(616\) −78.5641 + 78.5641i −0.127539 + 0.127539i
\(617\) −35.0141 130.674i −0.0567489 0.211790i 0.931729 0.363154i \(-0.118300\pi\)
−0.988478 + 0.151364i \(0.951633\pi\)
\(618\) 253.786 68.0019i 0.410658 0.110035i
\(619\) −661.030 661.030i −1.06790 1.06790i −0.997520 0.0703796i \(-0.977579\pi\)
−0.0703796 0.997520i \(-0.522421\pi\)
\(620\) −291.779 + 505.377i −0.470612 + 0.815124i
\(621\) −143.354 + 82.7654i −0.230844 + 0.133278i
\(622\) −51.3308 + 191.569i −0.0825254 + 0.307989i
\(623\) 180.666i 0.289994i
\(624\) −78.0000 + 45.0333i −0.125000 + 0.0721688i
\(625\) 728.184 1.16510
\(626\) 751.704 + 201.419i 1.20081 + 0.321755i
\(627\) 48.4730 + 83.9578i 0.0773095 + 0.133904i
\(628\) 240.009 + 138.569i 0.382180 + 0.220652i
\(629\) 183.482 183.482i 0.291704 0.291704i
\(630\) −19.0192 70.9808i −0.0301893 0.112668i
\(631\) 374.899 100.454i 0.594135 0.159198i 0.0507928 0.998709i \(-0.483825\pi\)
0.543342 + 0.839511i \(0.317159\pi\)
\(632\) −72.2487 72.2487i −0.114318 0.114318i
\(633\) 214.600 371.698i 0.339020 0.587201i
\(634\) 54.1999 31.2923i 0.0854888 0.0493570i
\(635\) −309.771 + 1156.08i −0.487828 + 1.82060i
\(636\) 338.354i 0.532003i
\(637\) −549.917 −0.863291
\(638\) −371.769 −0.582710
\(639\) 155.512 + 41.6692i 0.243367 + 0.0652100i
\(640\) 37.8564 + 65.5692i 0.0591506 + 0.102452i
\(641\) 539.869 + 311.694i 0.842229 + 0.486261i 0.858021 0.513614i \(-0.171694\pi\)
−0.0157919 + 0.999875i \(0.505027\pi\)
\(642\) −9.53074 + 9.53074i −0.0148454 + 0.0148454i
\(643\) 211.661 + 789.931i 0.329178 + 1.22851i 0.910045 + 0.414510i \(0.136047\pi\)
−0.580867 + 0.813999i \(0.697286\pi\)
\(644\) −159.282 + 42.6795i −0.247332 + 0.0662725i
\(645\) −267.688 267.688i −0.415021 0.415021i
\(646\) 13.2257 22.9076i 0.0204732 0.0354607i
\(647\) −248.412 + 143.420i −0.383944 + 0.221670i −0.679533 0.733645i \(-0.737817\pi\)
0.295589 + 0.955315i \(0.404484\pi\)
\(648\) −6.58846 + 24.5885i −0.0101674 + 0.0379452i
\(649\) 928.708i 1.43098i
\(650\) −257.200 + 257.200i −0.395692 + 0.395692i
\(651\) −195.455 −0.300238
\(652\) 541.894 + 145.200i 0.831125 + 0.222699i
\(653\) −324.424 561.919i −0.496821 0.860520i 0.503172 0.864186i \(-0.332166\pi\)
−0.999993 + 0.00366668i \(0.998833\pi\)
\(654\) −326.433 188.466i −0.499133 0.288174i
\(655\) −253.808 + 253.808i −0.387493 + 0.387493i
\(656\) −44.2872 165.282i −0.0675110 0.251954i
\(657\) 113.031 30.2865i 0.172041 0.0460982i
\(658\) 215.885 + 215.885i 0.328092 + 0.328092i
\(659\) −228.158 + 395.181i −0.346218 + 0.599667i −0.985574 0.169243i \(-0.945868\pi\)
0.639356 + 0.768911i \(0.279201\pi\)
\(660\) 304.708 175.923i 0.461678 0.266550i
\(661\) −84.1814 + 314.169i −0.127355 + 0.475294i −0.999913 0.0132166i \(-0.995793\pi\)
0.872558 + 0.488510i \(0.162460\pi\)
\(662\) 571.247i 0.862911i
\(663\) 57.1000 98.9000i 0.0861236 0.149170i
\(664\) −83.8667 −0.126305
\(665\) −61.6987 16.5321i −0.0927800 0.0248603i
\(666\) 108.531 + 187.981i 0.162959 + 0.282253i
\(667\) −477.846 275.885i −0.716411 0.413620i
\(668\) 395.138 395.138i 0.591525 0.591525i
\(669\) −20.6237 76.9686i −0.0308276 0.115050i
\(670\) −604.252 + 161.909i −0.901869 + 0.241655i
\(671\) −851.065 851.065i −1.26835 1.26835i
\(672\) −12.6795 + 21.9615i −0.0188683 + 0.0326808i
\(673\) 904.138 522.004i 1.34344 0.775638i 0.356133 0.934435i \(-0.384095\pi\)
0.987311 + 0.158797i \(0.0507615\pi\)
\(674\) −233.704 + 872.197i −0.346742 + 1.29406i
\(675\) 102.804i 0.152302i
\(676\) 338.000i 0.500000i
\(677\) −193.408 −0.285684 −0.142842 0.989746i \(-0.545624\pi\)
−0.142842 + 0.989746i \(0.545624\pi\)
\(678\) −205.335 55.0192i −0.302853 0.0811493i
\(679\) −23.7693 41.1697i −0.0350064 0.0606328i
\(680\) −83.1384 48.0000i −0.122262 0.0705882i
\(681\) −16.8231 + 16.8231i −0.0247035 + 0.0247035i
\(682\) −242.214 903.955i −0.355153 1.32545i
\(683\) −802.783 + 215.105i −1.17538 + 0.314942i −0.793092 0.609102i \(-0.791530\pi\)
−0.382286 + 0.924044i \(0.624863\pi\)
\(684\) 15.6462 + 15.6462i 0.0228745 + 0.0228745i
\(685\) 413.885 716.869i 0.604211 1.04652i
\(686\) −289.413 + 167.093i −0.421885 + 0.243576i
\(687\) −182.151 + 679.795i −0.265139 + 0.989513i
\(688\) 130.641i 0.189885i
\(689\) 1099.65 + 634.883i 1.59601 + 0.921456i
\(690\) 522.200 0.756811
\(691\) 224.069 + 60.0392i 0.324268 + 0.0868874i 0.417281 0.908778i \(-0.362983\pi\)
−0.0930129 + 0.995665i \(0.529650\pi\)
\(692\) −67.5411 116.985i −0.0976027 0.169053i
\(693\) 102.058 + 58.9230i 0.147269 + 0.0850260i
\(694\) −5.70250 + 5.70250i −0.00821686 + 0.00821686i
\(695\) −266.229 993.582i −0.383064 1.42961i
\(696\) −81.9615 + 21.9615i −0.117761 + 0.0315539i
\(697\) 153.415 + 153.415i 0.220108 + 0.220108i
\(698\) −128.103 + 221.881i −0.183529 + 0.317882i
\(699\) 40.9962 23.6692i 0.0586498 0.0338615i
\(700\) −26.5064 + 98.9230i −0.0378662 + 0.141319i
\(701\) 55.6565i 0.0793958i 0.999212 + 0.0396979i \(0.0126396\pi\)
−0.999212 + 0.0396979i \(0.987360\pi\)
\(702\) 67.5500 + 67.5500i 0.0962250 + 0.0962250i
\(703\) 188.677 0.268388
\(704\) −117.282 31.4256i −0.166594 0.0446387i
\(705\) −483.415 837.300i −0.685695 1.18766i
\(706\) 355.135 + 205.037i 0.503024 + 0.290421i
\(707\) 254.045 254.045i 0.359328 0.359328i
\(708\) 54.8616 + 204.746i 0.0774881 + 0.289189i
\(709\) −299.954 + 80.3724i −0.423066 + 0.113360i −0.464069 0.885799i \(-0.653611\pi\)
0.0410035 + 0.999159i \(0.486945\pi\)
\(710\) −359.138 359.138i −0.505829 0.505829i
\(711\) −54.1865 + 93.8538i −0.0762117 + 0.132003i
\(712\) 170.985 98.7180i 0.240147 0.138649i
\(713\) 359.487 1341.62i 0.504189 1.88166i
\(714\) 32.1539i 0.0450335i
\(715\) 1320.40i 1.84671i
\(716\) 100.441 0.140281
\(717\) −2.03848 0.546208i −0.00284306 0.000761796i
\(718\) 268.277 + 464.669i 0.373645 + 0.647172i
\(719\) 269.785 + 155.760i 0.375222 + 0.216635i 0.675737 0.737142i \(-0.263825\pi\)
−0.300515 + 0.953777i \(0.597159\pi\)
\(720\) 56.7846 56.7846i 0.0788675 0.0788675i
\(721\) −71.8524 268.157i −0.0996567 0.371924i
\(722\) −474.557 + 127.157i −0.657281 + 0.176118i
\(723\) 104.229 + 104.229i 0.144162 + 0.144162i
\(724\) 302.354 523.692i 0.417616 0.723332i
\(725\) −296.769 + 171.340i −0.409337 + 0.236331i
\(726\) −69.3275 + 258.734i −0.0954925 + 0.356383i
\(727\) 379.585i 0.522125i 0.965322 + 0.261062i \(0.0840728\pi\)
−0.965322 + 0.261062i \(0.915927\pi\)
\(728\) 47.5833 + 82.4167i 0.0653617 + 0.113210i
\(729\) 27.0000 0.0370370
\(730\) −356.578 95.5448i −0.488463 0.130883i
\(731\) −82.8231 143.454i −0.113301 0.196243i
\(732\) −237.904 137.354i −0.325005 0.187642i
\(733\) 769.627 769.627i 1.04997 1.04997i 0.0512852 0.998684i \(-0.483668\pi\)
0.998684 0.0512852i \(-0.0163317\pi\)
\(734\) −64.4993 240.715i −0.0878737 0.327949i
\(735\) 473.611 126.904i 0.644369 0.172658i
\(736\) −127.426 127.426i −0.173133 0.173133i
\(737\) 501.606 868.808i 0.680606 1.17884i
\(738\) −157.177 + 90.7461i −0.212977 + 0.122962i
\(739\) 69.2379 258.399i 0.0936913 0.349661i −0.903126 0.429375i \(-0.858734\pi\)
0.996818 + 0.0797139i \(0.0254007\pi\)
\(740\) 684.764i 0.925357i
\(741\) 80.2083 21.4918i 0.108243 0.0290037i
\(742\) 357.513 0.481823
\(743\) −1070.47 286.832i −1.44074 0.386046i −0.547949 0.836512i \(-0.684591\pi\)
−0.892794 + 0.450466i \(0.851258\pi\)
\(744\) −106.799 184.981i −0.143547 0.248630i
\(745\) 919.692 + 530.985i 1.23449 + 0.712731i
\(746\) 483.606 483.606i 0.648266 0.648266i
\(747\) 23.0230 + 85.9230i 0.0308206 + 0.115024i
\(748\) 148.708 39.8461i 0.198807 0.0532702i
\(749\) 10.0704 + 10.0704i 0.0134451 + 0.0134451i
\(750\) −42.7461 + 74.0385i −0.0569948 + 0.0987180i
\(751\) 318.631 183.962i 0.424275 0.244955i −0.272630 0.962119i \(-0.587893\pi\)
0.696905 + 0.717164i \(0.254560\pi\)
\(752\) −86.3538 + 322.277i −0.114832 + 0.428560i
\(753\) 70.5077i 0.0936358i
\(754\) −82.4167 + 307.583i −0.109306 + 0.407935i
\(755\) 1504.43 1.99262
\(756\) 25.9808 + 6.96152i 0.0343661 + 0.00920837i
\(757\) −97.6922 169.208i −0.129052 0.223524i 0.794258 0.607581i \(-0.207860\pi\)
−0.923309 + 0.384057i \(0.874527\pi\)
\(758\) −353.524 204.107i −0.466390 0.269270i
\(759\) −592.161 + 592.161i −0.780186 + 0.780186i
\(760\) −18.0666 67.4256i −0.0237719 0.0887179i
\(761\) 1176.65 315.282i 1.54619 0.414300i 0.617928 0.786234i \(-0.287972\pi\)
0.928259 + 0.371935i \(0.121305\pi\)
\(762\) −309.771 309.771i −0.406523 0.406523i
\(763\) −199.138 + 344.917i −0.260993 + 0.452053i
\(764\) −281.769 + 162.679i −0.368808 + 0.212931i
\(765\) −26.3538 + 98.3538i −0.0344494 + 0.128567i
\(766\) 372.497i 0.486289i
\(767\) 768.367 + 205.883i 1.00178 + 0.268427i
\(768\) −27.7128 −0.0360844
\(769\) −1000.87