Properties

Label 1183.2.e.f.508.3
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - x^{9} + 8 x^{8} + 7 x^{7} + 41 x^{6} + 18 x^{5} + 58 x^{4} + 28 x^{3} + 64 x^{2} + 16 x + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.3
Root \(-0.132804 - 0.230024i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.f.170.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.632804 + 1.09605i) q^{2} +(1.31364 - 2.27529i) q^{3} +(0.199118 - 0.344882i) q^{4} +(-1.45130 - 2.51373i) q^{5} +3.32511 q^{6} +(1.29536 - 2.30696i) q^{7} +3.03523 q^{8} +(-1.95130 - 3.37975i) q^{9} +O(q^{10})\) \(q+(0.632804 + 1.09605i) q^{2} +(1.31364 - 2.27529i) q^{3} +(0.199118 - 0.344882i) q^{4} +(-1.45130 - 2.51373i) q^{5} +3.32511 q^{6} +(1.29536 - 2.30696i) q^{7} +3.03523 q^{8} +(-1.95130 - 3.37975i) q^{9} +(1.83678 - 3.18139i) q^{10} +(1.01828 - 1.76372i) q^{11} +(-0.523138 - 0.906101i) q^{12} +(3.34825 - 0.0400756i) q^{14} -7.62594 q^{15} +(1.52247 + 2.63699i) q^{16} +(-1.99933 + 3.46294i) q^{17} +(2.46958 - 4.27744i) q^{18} +(3.48105 + 6.02935i) q^{19} -1.15592 q^{20} +(-3.54736 - 5.97783i) q^{21} +2.57749 q^{22} +(0.313640 + 0.543240i) q^{23} +(3.98720 - 6.90602i) q^{24} +(-1.71254 + 2.96621i) q^{25} -2.37138 q^{27} +(-0.537699 - 0.906101i) q^{28} +1.09606 q^{29} +(-4.82573 - 8.35841i) q^{30} +(-5.21624 + 9.03479i) q^{31} +(1.10838 - 1.91977i) q^{32} +(-2.67531 - 4.63378i) q^{33} -5.06074 q^{34} +(-7.67901 + 0.0919110i) q^{35} -1.55415 q^{36} +(-1.54268 - 2.67201i) q^{37} +(-4.40565 + 7.63080i) q^{38} +(-4.40502 - 7.62973i) q^{40} +0.521150 q^{41} +(4.30721 - 7.67088i) q^{42} +0.329024 q^{43} +(-0.405516 - 0.702374i) q^{44} +(-5.66384 + 9.81006i) q^{45} +(-0.396945 + 0.687530i) q^{46} +(5.27284 + 9.13283i) q^{47} +7.99991 q^{48} +(-3.64409 - 5.97667i) q^{49} -4.33482 q^{50} +(5.25280 + 9.09812i) q^{51} +(-3.55950 + 6.16523i) q^{53} +(-1.50062 - 2.59915i) q^{54} -5.91133 q^{55} +(3.93171 - 7.00214i) q^{56} +18.2914 q^{57} +(0.693593 + 1.20134i) q^{58} +(1.01828 - 1.76372i) q^{59} +(-1.51846 + 2.63005i) q^{60} +(-1.20041 - 2.07917i) q^{61} -13.2034 q^{62} +(-10.3246 + 0.123576i) q^{63} +8.89542 q^{64} +(3.38590 - 5.86455i) q^{66} +(7.34709 - 12.7255i) q^{67} +(0.796204 + 1.37907i) q^{68} +1.64804 q^{69} +(-4.96005 - 8.35841i) q^{70} -3.60141 q^{71} +(-5.92264 - 10.2583i) q^{72} +(1.48786 - 2.57706i) q^{73} +(1.95243 - 3.38172i) q^{74} +(4.49933 + 7.79307i) q^{75} +2.77255 q^{76} +(-2.74978 - 4.63378i) q^{77} +(4.38075 + 7.58769i) q^{79} +(4.41912 - 7.65414i) q^{80} +(2.73876 - 4.74367i) q^{81} +(0.329786 + 0.571206i) q^{82} -12.8039 q^{83} +(-2.76799 + 0.0331304i) q^{84} +11.6065 q^{85} +(0.208208 + 0.360627i) q^{86} +(1.43983 - 2.49386i) q^{87} +(3.09072 - 5.35328i) q^{88} +(-1.34049 - 2.32180i) q^{89} -14.3364 q^{90} +0.249805 q^{92} +(13.7045 + 23.7369i) q^{93} +(-6.67335 + 11.5586i) q^{94} +(10.1041 - 17.5008i) q^{95} +(-2.91202 - 5.04376i) q^{96} +2.32902 q^{97} +(4.24472 - 7.77617i) q^{98} -7.94789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 4q^{2} - 8q^{4} + 2q^{5} + 10q^{6} - q^{7} - 18q^{8} - 3q^{9} + O(q^{10}) \) \( 10q + 4q^{2} - 8q^{4} + 2q^{5} + 10q^{6} - q^{7} - 18q^{8} - 3q^{9} + 5q^{10} + 11q^{11} - 5q^{12} + 10q^{14} - 10q^{16} + 5q^{17} + 9q^{18} + 9q^{19} - 2q^{20} - 2q^{21} + 16q^{22} - 10q^{23} - 9q^{25} - 37q^{28} - 6q^{29} + 13q^{30} - 6q^{31} + 22q^{32} + 8q^{33} + 44q^{34} - 4q^{35} + 14q^{36} + 4q^{37} + 10q^{38} - 28q^{40} - 28q^{41} + 52q^{42} + 4q^{43} - 32q^{45} + 3q^{46} + q^{47} - 46q^{48} - 11q^{49} - 18q^{50} + 8q^{51} - 17q^{53} + 23q^{54} - 21q^{56} + 32q^{57} - 27q^{58} + 11q^{59} - 29q^{60} + 11q^{61} - 46q^{62} - 5q^{63} + 18q^{64} - 21q^{66} + 13q^{67} + 32q^{68} + 36q^{69} - 49q^{70} - 30q^{71} - 19q^{72} + 33q^{74} + 20q^{75} - 16q^{76} - 46q^{77} - 2q^{79} + 55q^{80} + 19q^{81} - 34q^{82} - 12q^{83} + 23q^{84} + 44q^{85} + 28q^{86} + 8q^{87} + 3q^{88} - 4q^{89} - 68q^{90} + 42q^{92} + 18q^{93} - 20q^{94} + 12q^{95} - 37q^{96} + 24q^{97} + 7q^{98} - 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.632804 + 1.09605i 0.447460 + 0.775024i 0.998220 0.0596401i \(-0.0189953\pi\)
−0.550760 + 0.834664i \(0.685662\pi\)
\(3\) 1.31364 2.27529i 0.758430 1.31364i −0.185220 0.982697i \(-0.559300\pi\)
0.943651 0.330943i \(-0.107367\pi\)
\(4\) 0.199118 0.344882i 0.0995588 0.172441i
\(5\) −1.45130 2.51373i −0.649041 1.12417i −0.983352 0.181709i \(-0.941837\pi\)
0.334311 0.942463i \(-0.391496\pi\)
\(6\) 3.32511 1.35747
\(7\) 1.29536 2.30696i 0.489599 0.871948i
\(8\) 3.03523 1.07311
\(9\) −1.95130 3.37975i −0.650433 1.12658i
\(10\) 1.83678 3.18139i 0.580840 1.00604i
\(11\) 1.01828 1.76372i 0.307024 0.531780i −0.670686 0.741741i \(-0.734000\pi\)
0.977710 + 0.209961i \(0.0673336\pi\)
\(12\) −0.523138 0.906101i −0.151017 0.261569i
\(13\) 0 0
\(14\) 3.34825 0.0400756i 0.894856 0.0107107i
\(15\) −7.62594 −1.96901
\(16\) 1.52247 + 2.63699i 0.380617 + 0.659249i
\(17\) −1.99933 + 3.46294i −0.484909 + 0.839887i −0.999850 0.0173386i \(-0.994481\pi\)
0.514941 + 0.857226i \(0.327814\pi\)
\(18\) 2.46958 4.27744i 0.582086 1.00820i
\(19\) 3.48105 + 6.02935i 0.798608 + 1.38323i 0.920523 + 0.390688i \(0.127763\pi\)
−0.121915 + 0.992540i \(0.538904\pi\)
\(20\) −1.15592 −0.258471
\(21\) −3.54736 5.97783i −0.774098 1.30447i
\(22\) 2.57749 0.549523
\(23\) 0.313640 + 0.543240i 0.0653985 + 0.113273i 0.896871 0.442293i \(-0.145835\pi\)
−0.831472 + 0.555566i \(0.812501\pi\)
\(24\) 3.98720 6.90602i 0.813883 1.40969i
\(25\) −1.71254 + 2.96621i −0.342509 + 0.593243i
\(26\) 0 0
\(27\) −2.37138 −0.456373
\(28\) −0.537699 0.906101i −0.101615 0.171237i
\(29\) 1.09606 0.203534 0.101767 0.994808i \(-0.467550\pi\)
0.101767 + 0.994808i \(0.467550\pi\)
\(30\) −4.82573 8.35841i −0.881054 1.52603i
\(31\) −5.21624 + 9.03479i −0.936864 + 1.62270i −0.165589 + 0.986195i \(0.552953\pi\)
−0.771275 + 0.636502i \(0.780381\pi\)
\(32\) 1.10838 1.91977i 0.195935 0.339370i
\(33\) −2.67531 4.63378i −0.465712 0.806637i
\(34\) −5.06074 −0.867910
\(35\) −7.67901 + 0.0919110i −1.29799 + 0.0155358i
\(36\) −1.55415 −0.259025
\(37\) −1.54268 2.67201i −0.253616 0.439275i 0.710903 0.703290i \(-0.248287\pi\)
−0.964519 + 0.264015i \(0.914953\pi\)
\(38\) −4.40565 + 7.63080i −0.714690 + 1.23788i
\(39\) 0 0
\(40\) −4.40502 7.62973i −0.696496 1.20637i
\(41\) 0.521150 0.0813900 0.0406950 0.999172i \(-0.487043\pi\)
0.0406950 + 0.999172i \(0.487043\pi\)
\(42\) 4.30721 7.67088i 0.664616 1.18364i
\(43\) 0.329024 0.0501757 0.0250879 0.999685i \(-0.492013\pi\)
0.0250879 + 0.999685i \(0.492013\pi\)
\(44\) −0.405516 0.702374i −0.0611338 0.105887i
\(45\) −5.66384 + 9.81006i −0.844316 + 1.46240i
\(46\) −0.396945 + 0.687530i −0.0585264 + 0.101371i
\(47\) 5.27284 + 9.13283i 0.769123 + 1.33216i 0.938039 + 0.346530i \(0.112640\pi\)
−0.168916 + 0.985630i \(0.554027\pi\)
\(48\) 7.99991 1.15469
\(49\) −3.64409 5.97667i −0.520585 0.853810i
\(50\) −4.33482 −0.613036
\(51\) 5.25280 + 9.09812i 0.735540 + 1.27399i
\(52\) 0 0
\(53\) −3.55950 + 6.16523i −0.488935 + 0.846860i −0.999919 0.0127302i \(-0.995948\pi\)
0.510984 + 0.859590i \(0.329281\pi\)
\(54\) −1.50062 2.59915i −0.204209 0.353700i
\(55\) −5.91133 −0.797084
\(56\) 3.93171 7.00214i 0.525396 0.935700i
\(57\) 18.2914 2.42275
\(58\) 0.693593 + 1.20134i 0.0910733 + 0.157744i
\(59\) 1.01828 1.76372i 0.132569 0.229616i −0.792097 0.610395i \(-0.791011\pi\)
0.924666 + 0.380779i \(0.124344\pi\)
\(60\) −1.51846 + 2.63005i −0.196032 + 0.339538i
\(61\) −1.20041 2.07917i −0.153696 0.266210i 0.778887 0.627164i \(-0.215784\pi\)
−0.932584 + 0.360954i \(0.882451\pi\)
\(62\) −13.2034 −1.67684
\(63\) −10.3246 + 0.123576i −1.30077 + 0.0155691i
\(64\) 8.89542 1.11193
\(65\) 0 0
\(66\) 3.38590 5.86455i 0.416775 0.721876i
\(67\) 7.34709 12.7255i 0.897589 1.55467i 0.0670226 0.997751i \(-0.478650\pi\)
0.830567 0.556919i \(-0.188017\pi\)
\(68\) 0.796204 + 1.37907i 0.0965539 + 0.167236i
\(69\) 1.64804 0.198401
\(70\) −4.96005 8.35841i −0.592839 0.999021i
\(71\) −3.60141 −0.427409 −0.213704 0.976898i \(-0.568553\pi\)
−0.213704 + 0.976898i \(0.568553\pi\)
\(72\) −5.92264 10.2583i −0.697990 1.20895i
\(73\) 1.48786 2.57706i 0.174141 0.301622i −0.765722 0.643171i \(-0.777618\pi\)
0.939864 + 0.341550i \(0.110952\pi\)
\(74\) 1.95243 3.38172i 0.226966 0.393117i
\(75\) 4.49933 + 7.79307i 0.519538 + 0.899866i
\(76\) 2.77255 0.318034
\(77\) −2.74978 4.63378i −0.313366 0.528068i
\(78\) 0 0
\(79\) 4.38075 + 7.58769i 0.492873 + 0.853681i 0.999966 0.00820995i \(-0.00261334\pi\)
−0.507093 + 0.861891i \(0.669280\pi\)
\(80\) 4.41912 7.65414i 0.494073 0.855759i
\(81\) 2.73876 4.74367i 0.304306 0.527074i
\(82\) 0.329786 + 0.571206i 0.0364188 + 0.0630792i
\(83\) −12.8039 −1.40541 −0.702703 0.711483i \(-0.748024\pi\)
−0.702703 + 0.711483i \(0.748024\pi\)
\(84\) −2.76799 + 0.0331304i −0.302012 + 0.00361482i
\(85\) 11.6065 1.25890
\(86\) 0.208208 + 0.360627i 0.0224516 + 0.0388874i
\(87\) 1.43983 2.49386i 0.154366 0.267370i
\(88\) 3.09072 5.35328i 0.329471 0.570661i
\(89\) −1.34049 2.32180i −0.142092 0.246110i 0.786192 0.617982i \(-0.212050\pi\)
−0.928284 + 0.371872i \(0.878716\pi\)
\(90\) −14.3364 −1.51119
\(91\) 0 0
\(92\) 0.249805 0.0260440
\(93\) 13.7045 + 23.7369i 1.42109 + 2.46141i
\(94\) −6.67335 + 11.5586i −0.688304 + 1.19218i
\(95\) 10.1041 17.5008i 1.03666 1.79554i
\(96\) −2.91202 5.04376i −0.297206 0.514777i
\(97\) 2.32902 0.236477 0.118238 0.992985i \(-0.462275\pi\)
0.118238 + 0.992985i \(0.462275\pi\)
\(98\) 4.24472 7.77617i 0.428782 0.785512i
\(99\) −7.94789 −0.798793
\(100\) 0.681995 + 1.18125i 0.0681995 + 0.118125i
\(101\) −0.726620 + 1.25854i −0.0723014 + 0.125230i −0.899910 0.436077i \(-0.856368\pi\)
0.827608 + 0.561306i \(0.189701\pi\)
\(102\) −6.64799 + 11.5147i −0.658249 + 1.14012i
\(103\) 5.81765 + 10.0765i 0.573230 + 0.992864i 0.996231 + 0.0867346i \(0.0276432\pi\)
−0.423001 + 0.906129i \(0.639023\pi\)
\(104\) 0 0
\(105\) −9.87833 + 17.5927i −0.964026 + 1.71687i
\(106\) −9.00987 −0.875115
\(107\) −9.81297 16.9966i −0.948656 1.64312i −0.748261 0.663405i \(-0.769111\pi\)
−0.200395 0.979715i \(-0.564223\pi\)
\(108\) −0.472184 + 0.817847i −0.0454359 + 0.0786973i
\(109\) −0.553378 + 0.958479i −0.0530040 + 0.0918057i −0.891310 0.453394i \(-0.850213\pi\)
0.838306 + 0.545200i \(0.183546\pi\)
\(110\) −3.74071 6.47911i −0.356663 0.617759i
\(111\) −8.10613 −0.769400
\(112\) 8.05557 0.0964182i 0.761180 0.00911066i
\(113\) −1.09606 −0.103109 −0.0515545 0.998670i \(-0.516418\pi\)
−0.0515545 + 0.998670i \(0.516418\pi\)
\(114\) 11.5749 + 20.0483i 1.08409 + 1.87769i
\(115\) 0.910371 1.57681i 0.0848926 0.147038i
\(116\) 0.218245 0.378012i 0.0202636 0.0350975i
\(117\) 0 0
\(118\) 2.57749 0.237277
\(119\) 5.39901 + 9.09812i 0.494926 + 0.834024i
\(120\) −23.1465 −2.11297
\(121\) 3.42620 + 5.93436i 0.311473 + 0.539487i
\(122\) 1.51925 2.63141i 0.137546 0.238237i
\(123\) 0.684604 1.18577i 0.0617286 0.106917i
\(124\) 2.07729 + 3.59797i 0.186546 + 0.323107i
\(125\) −4.57134 −0.408873
\(126\) −6.66888 11.2380i −0.594111 1.00116i
\(127\) 5.18143 0.459778 0.229889 0.973217i \(-0.426164\pi\)
0.229889 + 0.973217i \(0.426164\pi\)
\(128\) 3.41231 + 5.91029i 0.301608 + 0.522400i
\(129\) 0.432219 0.748626i 0.0380548 0.0659128i
\(130\) 0 0
\(131\) −5.28335 9.15103i −0.461609 0.799530i 0.537433 0.843307i \(-0.319394\pi\)
−0.999041 + 0.0437770i \(0.986061\pi\)
\(132\) −2.13081 −0.185463
\(133\) 18.4187 0.220455i 1.59710 0.0191159i
\(134\) 18.5971 1.60654
\(135\) 3.44159 + 5.96101i 0.296205 + 0.513042i
\(136\) −6.06842 + 10.5108i −0.520363 + 0.901295i
\(137\) −2.93589 + 5.08510i −0.250830 + 0.434450i −0.963754 0.266791i \(-0.914037\pi\)
0.712925 + 0.701241i \(0.247370\pi\)
\(138\) 1.04289 + 1.80633i 0.0887764 + 0.153765i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −1.49733 + 2.66665i −0.126547 + 0.225373i
\(141\) 27.7065 2.33331
\(142\) −2.27899 3.94732i −0.191248 0.331252i
\(143\) 0 0
\(144\) 5.94159 10.2911i 0.495132 0.857594i
\(145\) −1.59072 2.75520i −0.132102 0.228807i
\(146\) 3.76611 0.311685
\(147\) −18.3857 + 0.440185i −1.51643 + 0.0363058i
\(148\) −1.22870 −0.100999
\(149\) −5.05271 8.75155i −0.413934 0.716955i 0.581382 0.813631i \(-0.302512\pi\)
−0.995316 + 0.0966760i \(0.969179\pi\)
\(150\) −5.69439 + 9.86298i −0.464945 + 0.805309i
\(151\) −0.0938631 + 0.162576i −0.00763847 + 0.0132302i −0.869819 0.493370i \(-0.835765\pi\)
0.862181 + 0.506601i \(0.169098\pi\)
\(152\) 10.5658 + 18.3005i 0.856998 + 1.48436i
\(153\) 15.6052 1.26160
\(154\) 3.33878 5.94616i 0.269046 0.479155i
\(155\) 30.2813 2.43225
\(156\) 0 0
\(157\) 6.03590 10.4545i 0.481717 0.834358i −0.518063 0.855343i \(-0.673347\pi\)
0.999780 + 0.0209844i \(0.00668003\pi\)
\(158\) −5.54432 + 9.60304i −0.441082 + 0.763977i
\(159\) 9.35180 + 16.1978i 0.741646 + 1.28457i
\(160\) −6.43435 −0.508680
\(161\) 1.65951 0.0198629i 0.130788 0.00156541i
\(162\) 6.93239 0.544660
\(163\) 7.45678 + 12.9155i 0.584060 + 1.01162i 0.994992 + 0.0999554i \(0.0318700\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(164\) 0.103770 0.179735i 0.00810309 0.0140350i
\(165\) −7.76536 + 13.4500i −0.604532 + 1.04708i
\(166\) −8.10234 14.0337i −0.628863 1.08922i
\(167\) −5.05664 −0.391294 −0.195647 0.980674i \(-0.562681\pi\)
−0.195647 + 0.980674i \(0.562681\pi\)
\(168\) −10.7671 18.1441i −0.830696 1.39984i
\(169\) 0 0
\(170\) 7.34465 + 12.7213i 0.563309 + 0.975680i
\(171\) 13.5851 23.5302i 1.03888 1.79940i
\(172\) 0.0655145 0.113474i 0.00499543 0.00865235i
\(173\) 0.297807 + 0.515817i 0.0226419 + 0.0392169i 0.877124 0.480263i \(-0.159459\pi\)
−0.854482 + 0.519480i \(0.826126\pi\)
\(174\) 3.64453 0.276291
\(175\) 4.62457 + 7.79307i 0.349584 + 0.589101i
\(176\) 6.20121 0.467434
\(177\) −2.67531 4.63378i −0.201089 0.348296i
\(178\) 1.69654 2.93849i 0.127161 0.220249i
\(179\) −4.03832 + 6.99458i −0.301838 + 0.522799i −0.976552 0.215280i \(-0.930934\pi\)
0.674714 + 0.738079i \(0.264267\pi\)
\(180\) 2.25554 + 3.90671i 0.168118 + 0.291189i
\(181\) 1.89324 0.140724 0.0703618 0.997522i \(-0.477585\pi\)
0.0703618 + 0.997522i \(0.477585\pi\)
\(182\) 0 0
\(183\) −6.30761 −0.466272
\(184\) 0.951968 + 1.64886i 0.0701800 + 0.121555i
\(185\) −4.47780 + 7.75577i −0.329214 + 0.570216i
\(186\) −17.3446 + 30.0417i −1.27176 + 2.20276i
\(187\) 4.07177 + 7.05251i 0.297757 + 0.515730i
\(188\) 4.19966 0.306292
\(189\) −3.07179 + 5.47068i −0.223440 + 0.397933i
\(190\) 25.5757 1.85545
\(191\) −1.85087 3.20580i −0.133924 0.231964i 0.791262 0.611478i \(-0.209425\pi\)
−0.925186 + 0.379514i \(0.876091\pi\)
\(192\) 11.6854 20.2397i 0.843320 1.46067i
\(193\) 6.79373 11.7671i 0.489024 0.847014i −0.510897 0.859642i \(-0.670687\pi\)
0.999920 + 0.0126285i \(0.00401987\pi\)
\(194\) 1.47382 + 2.55272i 0.105814 + 0.183275i
\(195\) 0 0
\(196\) −2.78685 + 0.0667218i −0.199061 + 0.00476585i
\(197\) 9.70258 0.691280 0.345640 0.938367i \(-0.387662\pi\)
0.345640 + 0.938367i \(0.387662\pi\)
\(198\) −5.02946 8.71128i −0.357428 0.619084i
\(199\) −13.1360 + 22.7522i −0.931185 + 1.61286i −0.149885 + 0.988703i \(0.547891\pi\)
−0.781299 + 0.624156i \(0.785443\pi\)
\(200\) −5.19796 + 9.00313i −0.367551 + 0.636617i
\(201\) −19.3029 33.4335i −1.36152 2.35822i
\(202\) −1.83923 −0.129408
\(203\) 1.41979 2.52857i 0.0996500 0.177471i
\(204\) 4.18370 0.292918
\(205\) −0.756345 1.31003i −0.0528255 0.0914964i
\(206\) −7.36287 + 12.7529i −0.512995 + 0.888534i
\(207\) 1.22401 2.12005i 0.0850747 0.147354i
\(208\) 0 0
\(209\) 14.1788 0.980765
\(210\) −25.5335 + 0.305614i −1.76198 + 0.0210894i
\(211\) 10.0338 0.690758 0.345379 0.938463i \(-0.387750\pi\)
0.345379 + 0.938463i \(0.387750\pi\)
\(212\) 1.41752 + 2.45521i 0.0973555 + 0.168625i
\(213\) −4.73096 + 8.19426i −0.324160 + 0.561461i
\(214\) 12.4194 21.5110i 0.848971 1.47046i
\(215\) −0.477513 0.827077i −0.0325661 0.0564062i
\(216\) −7.19769 −0.489740
\(217\) 14.0860 + 23.7369i 0.956218 + 1.61137i
\(218\) −1.40072 −0.0948688
\(219\) −3.90903 6.77065i −0.264148 0.457518i
\(220\) −1.17705 + 2.03871i −0.0793567 + 0.137450i
\(221\) 0 0
\(222\) −5.12959 8.88472i −0.344276 0.596303i
\(223\) −17.4961 −1.17163 −0.585813 0.810446i \(-0.699225\pi\)
−0.585813 + 0.810446i \(0.699225\pi\)
\(224\) −2.99307 5.04376i −0.199983 0.337000i
\(225\) 13.3667 0.891116
\(226\) −0.693593 1.20134i −0.0461371 0.0799119i
\(227\) −4.75815 + 8.24136i −0.315810 + 0.546998i −0.979609 0.200912i \(-0.935609\pi\)
0.663800 + 0.747910i \(0.268943\pi\)
\(228\) 3.64214 6.30837i 0.241206 0.417782i
\(229\) 10.5585 + 18.2878i 0.697725 + 1.20849i 0.969254 + 0.246064i \(0.0791374\pi\)
−0.271529 + 0.962430i \(0.587529\pi\)
\(230\) 2.30435 0.151944
\(231\) −14.1554 + 0.169428i −0.931357 + 0.0111475i
\(232\) 3.32680 0.218415
\(233\) −7.08938 12.2792i −0.464441 0.804435i 0.534735 0.845020i \(-0.320411\pi\)
−0.999176 + 0.0405847i \(0.987078\pi\)
\(234\) 0 0
\(235\) 15.3050 26.5090i 0.998385 1.72925i
\(236\) −0.405516 0.702374i −0.0263968 0.0457206i
\(237\) 23.0189 1.49524
\(238\) −6.55547 + 11.6749i −0.424928 + 0.756772i
\(239\) 16.5275 1.06907 0.534536 0.845145i \(-0.320486\pi\)
0.534536 + 0.845145i \(0.320486\pi\)
\(240\) −11.6103 20.1096i −0.749439 1.29807i
\(241\) −6.84450 + 11.8550i −0.440893 + 0.763649i −0.997756 0.0669552i \(-0.978672\pi\)
0.556863 + 0.830604i \(0.312005\pi\)
\(242\) −4.33623 + 7.51058i −0.278744 + 0.482798i
\(243\) −10.7526 18.6240i −0.689777 1.19473i
\(244\) −0.956089 −0.0612073
\(245\) −9.73503 + 17.8342i −0.621948 + 1.13938i
\(246\) 1.73288 0.110484
\(247\) 0 0
\(248\) −15.8325 + 27.4226i −1.00536 + 1.74134i
\(249\) −16.8197 + 29.1325i −1.06590 + 1.84620i
\(250\) −2.89276 5.01042i −0.182954 0.316886i
\(251\) −14.6603 −0.925349 −0.462674 0.886528i \(-0.653110\pi\)
−0.462674 + 0.886528i \(0.653110\pi\)
\(252\) −2.01318 + 3.58536i −0.126819 + 0.225857i
\(253\) 1.27750 0.0803155
\(254\) 3.27883 + 5.67910i 0.205732 + 0.356339i
\(255\) 15.2468 26.4082i 0.954791 1.65375i
\(256\) 4.57678 7.92721i 0.286049 0.495451i
\(257\) 0.876387 + 1.51795i 0.0546675 + 0.0946869i 0.892064 0.451909i \(-0.149257\pi\)
−0.837397 + 0.546596i \(0.815923\pi\)
\(258\) 1.09404 0.0681120
\(259\) −8.16254 + 0.0976985i −0.507195 + 0.00607069i
\(260\) 0 0
\(261\) −2.13875 3.70442i −0.132385 0.229298i
\(262\) 6.68666 11.5816i 0.413103 0.715515i
\(263\) −13.4708 + 23.3321i −0.830645 + 1.43872i 0.0668823 + 0.997761i \(0.478695\pi\)
−0.897527 + 0.440959i \(0.854639\pi\)
\(264\) −8.12018 14.0646i −0.499762 0.865614i
\(265\) 20.6636 1.26936
\(266\) 11.8970 + 20.0483i 0.729454 + 1.22924i
\(267\) −7.04370 −0.431067
\(268\) −2.92587 5.06775i −0.178726 0.309562i
\(269\) 11.0346 19.1124i 0.672789 1.16530i −0.304321 0.952570i \(-0.598430\pi\)
0.977110 0.212735i \(-0.0682371\pi\)
\(270\) −4.35570 + 7.54430i −0.265080 + 0.459131i
\(271\) −4.48105 7.76141i −0.272204 0.471472i 0.697222 0.716856i \(-0.254419\pi\)
−0.969426 + 0.245384i \(0.921086\pi\)
\(272\) −12.1757 −0.738259
\(273\) 0 0
\(274\) −7.43137 −0.448945
\(275\) 3.48770 + 6.04088i 0.210316 + 0.364279i
\(276\) 0.328154 0.568379i 0.0197525 0.0342124i
\(277\) 3.76463 6.52052i 0.226194 0.391780i −0.730483 0.682931i \(-0.760705\pi\)
0.956677 + 0.291151i \(0.0940382\pi\)
\(278\) −2.53122 4.38420i −0.151812 0.262947i
\(279\) 40.7138 2.43747
\(280\) −23.3075 + 0.278971i −1.39289 + 0.0166717i
\(281\) −29.7762 −1.77630 −0.888151 0.459553i \(-0.848010\pi\)
−0.888151 + 0.459553i \(0.848010\pi\)
\(282\) 17.5328 + 30.3676i 1.04406 + 1.80837i
\(283\) −0.150726 + 0.261064i −0.00895970 + 0.0155187i −0.870470 0.492221i \(-0.836185\pi\)
0.861511 + 0.507739i \(0.169519\pi\)
\(284\) −0.717104 + 1.24206i −0.0425523 + 0.0737027i
\(285\) −26.5463 45.9795i −1.57247 2.72359i
\(286\) 0 0
\(287\) 0.675076 1.20227i 0.0398485 0.0709678i
\(288\) −8.65110 −0.509771
\(289\) 0.505347 + 0.875286i 0.0297263 + 0.0514874i
\(290\) 2.01322 3.48701i 0.118221 0.204764i
\(291\) 3.05950 5.29921i 0.179351 0.310645i
\(292\) −0.592520 1.02627i −0.0346746 0.0600582i
\(293\) 19.2471 1.12443 0.562214 0.826992i \(-0.309950\pi\)
0.562214 + 0.826992i \(0.309950\pi\)
\(294\) −12.1170 19.8731i −0.706678 1.15902i
\(295\) −5.91133 −0.344171
\(296\) −4.68240 8.11015i −0.272159 0.471393i
\(297\) −2.41474 + 4.18245i −0.140117 + 0.242690i
\(298\) 6.39475 11.0760i 0.370438 0.641618i
\(299\) 0 0
\(300\) 3.58358 0.206898
\(301\) 0.426204 0.759044i 0.0245660 0.0437506i
\(302\) −0.237588 −0.0136716
\(303\) 1.90903 + 3.30654i 0.109671 + 0.189956i
\(304\) −10.5996 + 18.3590i −0.607928 + 1.05296i
\(305\) −3.48430 + 6.03499i −0.199511 + 0.345562i
\(306\) 9.87503 + 17.1040i 0.564518 + 0.977773i
\(307\) 3.57779 0.204195 0.102098 0.994774i \(-0.467445\pi\)
0.102098 + 0.994774i \(0.467445\pi\)
\(308\) −2.14563 + 0.0256814i −0.122259 + 0.00146333i
\(309\) 30.5692 1.73902
\(310\) 19.1621 + 33.1898i 1.08834 + 1.88505i
\(311\) 11.9153 20.6379i 0.675655 1.17027i −0.300622 0.953743i \(-0.597194\pi\)
0.976277 0.216526i \(-0.0694725\pi\)
\(312\) 0 0
\(313\) 9.04068 + 15.6589i 0.511009 + 0.885094i 0.999919 + 0.0127596i \(0.00406161\pi\)
−0.488909 + 0.872335i \(0.662605\pi\)
\(314\) 15.2782 0.862196
\(315\) 15.2947 + 25.7738i 0.861758 + 1.45219i
\(316\) 3.48914 0.196279
\(317\) −13.7741 23.8574i −0.773630 1.33997i −0.935561 0.353164i \(-0.885106\pi\)
0.161931 0.986802i \(-0.448228\pi\)
\(318\) −11.8357 + 20.5001i −0.663714 + 1.14959i
\(319\) 1.11610 1.93314i 0.0624897 0.108235i
\(320\) −12.9099 22.3606i −0.721687 1.25000i
\(321\) −51.5628 −2.87796
\(322\) 1.07191 + 1.80633i 0.0597355 + 0.100663i
\(323\) −27.8391 −1.54901
\(324\) −1.09067 1.88909i −0.0605927 0.104950i
\(325\) 0 0
\(326\) −9.43736 + 16.3460i −0.522687 + 0.905321i
\(327\) 1.45388 + 2.51819i 0.0803997 + 0.139256i
\(328\) 1.58181 0.0873408
\(329\) 27.8993 0.333930i 1.53814 0.0184101i
\(330\) −19.6558 −1.08202
\(331\) −9.09069 15.7455i −0.499669 0.865453i 0.500331 0.865834i \(-0.333212\pi\)
−1.00000 0.000381757i \(0.999878\pi\)
\(332\) −2.54947 + 4.41582i −0.139921 + 0.242350i
\(333\) −6.02048 + 10.4278i −0.329920 + 0.571439i
\(334\) −3.19986 5.54232i −0.175089 0.303262i
\(335\) −42.6513 −2.33029
\(336\) 10.3627 18.4554i 0.565334 1.00683i
\(337\) −17.1381 −0.933572 −0.466786 0.884370i \(-0.654588\pi\)
−0.466786 + 0.884370i \(0.654588\pi\)
\(338\) 0 0
\(339\) −1.43983 + 2.49386i −0.0782010 + 0.135448i
\(340\) 2.31106 4.00288i 0.125335 0.217086i
\(341\) 10.6232 + 18.3999i 0.575279 + 0.996412i
\(342\) 34.3869 1.85943
\(343\) −18.5083 + 0.664840i −0.999355 + 0.0358980i
\(344\) 0.998663 0.0538443
\(345\) −2.39180 4.14272i −0.128770 0.223037i
\(346\) −0.376907 + 0.652823i −0.0202627 + 0.0350960i
\(347\) −11.1344 + 19.2853i −0.597725 + 1.03529i 0.395431 + 0.918496i \(0.370595\pi\)
−0.993156 + 0.116794i \(0.962738\pi\)
\(348\) −0.573392 0.993144i −0.0307370 0.0532381i
\(349\) −19.9368 −1.06719 −0.533595 0.845740i \(-0.679159\pi\)
−0.533595 + 0.845740i \(0.679159\pi\)
\(350\) −5.61514 + 10.0002i −0.300142 + 0.534535i
\(351\) 0 0
\(352\) −2.25728 3.90972i −0.120313 0.208389i
\(353\) 11.4576 19.8451i 0.609825 1.05625i −0.381444 0.924392i \(-0.624573\pi\)
0.991269 0.131856i \(-0.0420937\pi\)
\(354\) 3.38590 5.86455i 0.179958 0.311697i
\(355\) 5.22673 + 9.05296i 0.277406 + 0.480481i
\(356\) −1.06766 −0.0565860
\(357\) 27.7932 0.332661i 1.47097 0.0176063i
\(358\) −10.2219 −0.540242
\(359\) 13.6157 + 23.5831i 0.718610 + 1.24467i 0.961551 + 0.274628i \(0.0885547\pi\)
−0.242940 + 0.970041i \(0.578112\pi\)
\(360\) −17.1910 + 29.7758i −0.906048 + 1.56932i
\(361\) −14.7354 + 25.5225i −0.775548 + 1.34329i
\(362\) 1.19805 + 2.07509i 0.0629682 + 0.109064i
\(363\) 18.0032 0.944923
\(364\) 0 0
\(365\) −8.63735 −0.452099
\(366\) −3.99148 6.91345i −0.208638 0.361372i
\(367\) 5.42822 9.40195i 0.283351 0.490778i −0.688857 0.724897i \(-0.741887\pi\)
0.972208 + 0.234119i \(0.0752206\pi\)
\(368\) −0.955014 + 1.65413i −0.0497836 + 0.0862277i
\(369\) −1.01692 1.76136i −0.0529388 0.0916926i
\(370\) −11.3343 −0.589241
\(371\) 9.61210 + 16.1978i 0.499035 + 0.840948i
\(372\) 10.9152 0.565929
\(373\) 1.18572 + 2.05373i 0.0613943 + 0.106338i 0.895089 0.445888i \(-0.147112\pi\)
−0.833695 + 0.552226i \(0.813779\pi\)
\(374\) −5.15326 + 8.92571i −0.266469 + 0.461538i
\(375\) −6.00510 + 10.4011i −0.310102 + 0.537112i
\(376\) 16.0043 + 27.7202i 0.825357 + 1.42956i
\(377\) 0 0
\(378\) −7.93997 + 0.0950346i −0.408388 + 0.00488805i
\(379\) 29.2197 1.50092 0.750458 0.660918i \(-0.229833\pi\)
0.750458 + 0.660918i \(0.229833\pi\)
\(380\) −4.02381 6.96944i −0.206417 0.357525i
\(381\) 6.80654 11.7893i 0.348709 0.603982i
\(382\) 2.34248 4.05729i 0.119852 0.207589i
\(383\) −1.53297 2.65519i −0.0783313 0.135674i 0.824199 0.566301i \(-0.191626\pi\)
−0.902530 + 0.430627i \(0.858293\pi\)
\(384\) 17.9302 0.914995
\(385\) −7.65729 + 13.6372i −0.390252 + 0.695015i
\(386\) 17.1964 0.875274
\(387\) −0.642025 1.11202i −0.0326360 0.0565271i
\(388\) 0.463750 0.803238i 0.0235433 0.0407782i
\(389\) −13.8705 + 24.0244i −0.703261 + 1.21808i 0.264054 + 0.964508i \(0.414940\pi\)
−0.967315 + 0.253576i \(0.918393\pi\)
\(390\) 0 0
\(391\) −2.50828 −0.126849
\(392\) −11.0607 18.1405i −0.558647 0.916236i
\(393\) −27.7617 −1.40039
\(394\) 6.13984 + 10.6345i 0.309320 + 0.535759i
\(395\) 12.7156 22.0240i 0.639790 1.10815i
\(396\) −1.58257 + 2.74108i −0.0795269 + 0.137745i
\(397\) 8.61559 + 14.9226i 0.432404 + 0.748946i 0.997080 0.0763669i \(-0.0243320\pi\)
−0.564676 + 0.825313i \(0.690999\pi\)
\(398\) −33.2500 −1.66667
\(399\) 23.6939 42.1974i 1.18618 2.11251i
\(400\) −10.4292 −0.521459
\(401\) 8.32201 + 14.4142i 0.415582 + 0.719808i 0.995489 0.0948737i \(-0.0302447\pi\)
−0.579908 + 0.814682i \(0.696911\pi\)
\(402\) 24.4299 42.3137i 1.21845 2.11042i
\(403\) 0 0
\(404\) 0.289366 + 0.501196i 0.0143965 + 0.0249354i
\(405\) −15.8990 −0.790029
\(406\) 3.66989 0.0439254i 0.182133 0.00217998i
\(407\) −6.28355 −0.311464
\(408\) 15.9435 + 27.6149i 0.789318 + 1.36714i
\(409\) −6.81689 + 11.8072i −0.337073 + 0.583828i −0.983881 0.178825i \(-0.942770\pi\)
0.646807 + 0.762653i \(0.276104\pi\)
\(410\) 0.957237 1.65798i 0.0472746 0.0818820i
\(411\) 7.71340 + 13.3600i 0.380474 + 0.659000i
\(412\) 4.63359 0.228280
\(413\) −2.74978 4.63378i −0.135308 0.228013i
\(414\) 3.09824 0.152270
\(415\) 18.5822 + 32.1854i 0.912167 + 1.57992i
\(416\) 0 0
\(417\) −5.25456 + 9.10116i −0.257317 + 0.445686i
\(418\) 8.97238 + 15.5406i 0.438853 + 0.760116i
\(419\) −10.8502 −0.530066 −0.265033 0.964239i \(-0.585383\pi\)
−0.265033 + 0.964239i \(0.585383\pi\)
\(420\) 4.10046 + 6.90987i 0.200082 + 0.337167i
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 6.34946 + 10.9976i 0.309087 + 0.535354i
\(423\) 20.5778 35.6418i 1.00053 1.73296i
\(424\) −10.8039 + 18.7129i −0.524683 + 0.908778i
\(425\) −6.84788 11.8609i −0.332171 0.575337i
\(426\) −11.9751 −0.580194
\(427\) −6.35150 + 0.0760220i −0.307371 + 0.00367896i
\(428\) −7.81574 −0.377788
\(429\) 0 0
\(430\) 0.604344 1.04676i 0.0291441 0.0504790i
\(431\) 0.604764 1.04748i 0.0291304 0.0504554i −0.851093 0.525016i \(-0.824060\pi\)
0.880223 + 0.474560i \(0.157393\pi\)
\(432\) −3.61036 6.25332i −0.173703 0.300863i
\(433\) −5.56422 −0.267399 −0.133700 0.991022i \(-0.542686\pi\)
−0.133700 + 0.991022i \(0.542686\pi\)
\(434\) −17.1032 + 30.4597i −0.820979 + 1.46211i
\(435\) −8.35851 −0.400760
\(436\) 0.220375 + 0.381700i 0.0105540 + 0.0182801i
\(437\) −2.18359 + 3.78209i −0.104455 + 0.180922i
\(438\) 4.94731 8.56899i 0.236391 0.409442i
\(439\) 9.85960 + 17.0773i 0.470573 + 0.815057i 0.999434 0.0336522i \(-0.0107139\pi\)
−0.528860 + 0.848709i \(0.677381\pi\)
\(440\) −17.9422 −0.855362
\(441\) −13.0889 + 23.9784i −0.623282 + 1.14183i
\(442\) 0 0
\(443\) −11.1155 19.2526i −0.528113 0.914719i −0.999463 0.0327726i \(-0.989566\pi\)
0.471350 0.881946i \(-0.343767\pi\)
\(444\) −1.61407 + 2.79566i −0.0766005 + 0.132676i
\(445\) −3.89091 + 6.73926i −0.184447 + 0.319471i
\(446\) −11.0716 19.1766i −0.524256 0.908039i
\(447\) −26.5498 −1.25576
\(448\) 11.5228 20.5213i 0.544399 0.969542i
\(449\) −18.4579 −0.871082 −0.435541 0.900169i \(-0.643443\pi\)
−0.435541 + 0.900169i \(0.643443\pi\)
\(450\) 8.45853 + 14.6506i 0.398739 + 0.690636i
\(451\) 0.530678 0.919161i 0.0249886 0.0432816i
\(452\) −0.218245 + 0.378012i −0.0102654 + 0.0177802i
\(453\) 0.246605 + 0.427132i 0.0115865 + 0.0200684i
\(454\) −12.0439 −0.565249
\(455\) 0 0
\(456\) 55.5185 2.59989
\(457\) −14.9910 25.9651i −0.701248 1.21460i −0.968029 0.250840i \(-0.919293\pi\)
0.266781 0.963757i \(-0.414040\pi\)
\(458\) −13.3629 + 23.1452i −0.624408 + 1.08151i
\(459\) 4.74118 8.21197i 0.221299 0.383302i
\(460\) −0.362542 0.627941i −0.0169036 0.0292779i
\(461\) −29.1498 −1.35764 −0.678821 0.734304i \(-0.737509\pi\)
−0.678821 + 0.734304i \(0.737509\pi\)
\(462\) −9.14330 15.4078i −0.425385 0.716836i
\(463\) −1.55900 −0.0724530 −0.0362265 0.999344i \(-0.511534\pi\)
−0.0362265 + 0.999344i \(0.511534\pi\)
\(464\) 1.66872 + 2.89031i 0.0774685 + 0.134179i
\(465\) 39.7787 68.8988i 1.84470 3.19511i
\(466\) 8.97238 15.5406i 0.415637 0.719905i
\(467\) −6.21156 10.7587i −0.287437 0.497855i 0.685760 0.727827i \(-0.259470\pi\)
−0.973197 + 0.229972i \(0.926136\pi\)
\(468\) 0 0
\(469\) −19.8401 33.4335i −0.916132 1.54382i
\(470\) 38.7402 1.78695
\(471\) −15.8580 27.4668i −0.730697 1.26561i
\(472\) 3.09072 5.35328i 0.142262 0.246405i
\(473\) 0.335039 0.580305i 0.0154051 0.0266825i
\(474\) 14.5665 + 25.2299i 0.669060 + 1.15885i
\(475\) −23.8458 −1.09412
\(476\) 4.21281 0.0504237i 0.193094 0.00231117i
\(477\) 27.7826 1.27208
\(478\) 10.4587 + 18.1149i 0.478368 + 0.828557i
\(479\) 18.0279 31.2252i 0.823716 1.42672i −0.0791811 0.996860i \(-0.525231\pi\)
0.902897 0.429857i \(-0.141436\pi\)
\(480\) −8.45242 + 14.6400i −0.385798 + 0.668222i
\(481\) 0 0
\(482\) −17.3249 −0.789128
\(483\) 2.13480 3.80196i 0.0971369 0.172995i
\(484\) 2.72887 0.124040
\(485\) −3.38011 5.85453i −0.153483 0.265840i
\(486\) 13.6085 23.5707i 0.617295 1.06919i
\(487\) 3.65002 6.32202i 0.165398 0.286478i −0.771398 0.636352i \(-0.780442\pi\)
0.936797 + 0.349874i \(0.113776\pi\)
\(488\) −3.64351 6.31074i −0.164934 0.285674i
\(489\) 39.1821 1.77188
\(490\) −25.7075 + 0.615481i −1.16135 + 0.0278046i
\(491\) 4.49178 0.202711 0.101356 0.994850i \(-0.467682\pi\)
0.101356 + 0.994850i \(0.467682\pi\)
\(492\) −0.272633 0.472215i −0.0122913 0.0212891i
\(493\) −2.19139 + 3.79560i −0.0986954 + 0.170945i
\(494\) 0 0
\(495\) 11.5348 + 19.9788i 0.518450 + 0.897981i
\(496\) −31.7663 −1.42635
\(497\) −4.66512 + 8.30829i −0.209259 + 0.372678i
\(498\) −42.5742 −1.90780
\(499\) 5.68369 + 9.84443i 0.254437 + 0.440697i 0.964742 0.263196i \(-0.0847766\pi\)
−0.710306 + 0.703893i \(0.751443\pi\)
\(500\) −0.910235 + 1.57657i −0.0407069 + 0.0705065i
\(501\) −6.64260 + 11.5053i −0.296770 + 0.514020i
\(502\) −9.27709 16.0684i −0.414057 0.717167i
\(503\) 17.1080 0.762806 0.381403 0.924409i \(-0.375441\pi\)
0.381403 + 0.924409i \(0.375441\pi\)
\(504\) −31.3374 + 0.375082i −1.39588 + 0.0167075i
\(505\) 4.21818 0.187706
\(506\) 0.808405 + 1.40020i 0.0359380 + 0.0622464i
\(507\) 0 0
\(508\) 1.03171 1.78698i 0.0457749 0.0792845i
\(509\) 1.64142 + 2.84303i 0.0727547 + 0.126015i 0.900108 0.435667i \(-0.143488\pi\)
−0.827353 + 0.561682i \(0.810154\pi\)
\(510\) 38.5929 1.70892
\(511\) −4.01784 6.77065i −0.177739 0.299516i
\(512\) 25.2340 1.11520
\(513\) −8.25490 14.2979i −0.364463 0.631268i
\(514\) −1.10916 + 1.92113i −0.0489231 + 0.0847373i
\(515\) 16.8863 29.2479i 0.744100 1.28882i
\(516\) −0.172125 0.298129i −0.00757738 0.0131244i
\(517\) 21.4770 0.944555
\(518\) −5.27237 8.88472i −0.231655 0.390372i
\(519\) 1.56485 0.0686891
\(520\) 0 0
\(521\) 2.38530 4.13147i 0.104502 0.181003i −0.809033 0.587764i \(-0.800008\pi\)
0.913535 + 0.406761i \(0.133342\pi\)
\(522\) 2.70682 4.68835i 0.118474 0.205203i
\(523\) −12.7562 22.0944i −0.557789 0.966119i −0.997681 0.0680682i \(-0.978316\pi\)
0.439892 0.898051i \(-0.355017\pi\)
\(524\) −4.20803 −0.183829
\(525\) 23.8065 0.284943i 1.03900 0.0124359i
\(526\) −34.0975 −1.48672
\(527\) −20.8580 36.1271i −0.908588 1.57372i
\(528\) 8.14616 14.1096i 0.354516 0.614040i
\(529\) 11.3033 19.5778i 0.491446 0.851210i
\(530\) 13.0760 + 22.6483i 0.567986 + 0.983780i
\(531\) −7.94789 −0.344909
\(532\) 3.59145 6.39616i 0.155709 0.277309i
\(533\) 0 0
\(534\) −4.45728 7.72024i −0.192885 0.334087i
\(535\) −28.4831 + 49.3342i −1.23143 + 2.13290i
\(536\) 22.3001 38.6249i 0.963216 1.66834i
\(537\) 10.6098 + 18.3767i 0.457847 + 0.793013i
\(538\) 27.9309 1.20418
\(539\) −14.2519 + 0.341214i −0.613871 + 0.0146971i
\(540\) 2.74112 0.117959
\(541\) −8.25784 14.3030i −0.355032 0.614934i 0.632091 0.774894i \(-0.282197\pi\)
−0.987123 + 0.159960i \(0.948863\pi\)
\(542\) 5.67125 9.82290i 0.243601 0.421930i
\(543\) 2.48704 4.30768i 0.106729 0.184860i
\(544\) 4.43203 + 7.67649i 0.190022 + 0.329127i
\(545\) 3.21247 0.137607
\(546\) 0 0
\(547\) 23.3317 0.997591 0.498796 0.866720i \(-0.333776\pi\)
0.498796 + 0.866720i \(0.333776\pi\)
\(548\) 1.16917 + 2.02507i 0.0499446 + 0.0865066i
\(549\) −4.68471 + 8.11416i −0.199939 + 0.346304i
\(550\) −4.41407 + 7.64539i −0.188216 + 0.326001i
\(551\) 3.81545 + 6.60855i 0.162544 + 0.281534i
\(552\) 5.00218 0.212907
\(553\) 23.1791 0.277434i 0.985676 0.0117977i
\(554\) 9.52909 0.404852
\(555\) 11.7644 + 20.3766i 0.499372 + 0.864938i
\(556\) −0.796470 + 1.37953i −0.0337779 + 0.0585050i
\(557\) −10.0235 + 17.3613i −0.424711 + 0.735621i −0.996393 0.0848540i \(-0.972958\pi\)
0.571682 + 0.820475i \(0.306291\pi\)
\(558\) 25.7639 + 44.6243i 1.09067 + 1.88910i
\(559\) 0 0
\(560\) −11.9334 20.1096i −0.504279 0.849784i
\(561\) 21.3953 0.903312
\(562\) −18.8425 32.6362i −0.794824 1.37668i
\(563\) 20.2642 35.0986i 0.854034 1.47923i −0.0235047 0.999724i \(-0.507482\pi\)
0.877539 0.479506i \(-0.159184\pi\)
\(564\) 5.51684 9.55545i 0.232301 0.402357i
\(565\) 1.59072 + 2.75520i 0.0669219 + 0.115912i
\(566\) −0.381519 −0.0160364
\(567\) −7.39576 12.4629i −0.310593 0.523394i
\(568\) −10.9311 −0.458659
\(569\) 10.7252 + 18.5766i 0.449623 + 0.778770i 0.998361 0.0572245i \(-0.0182251\pi\)
−0.548739 + 0.835994i \(0.684892\pi\)
\(570\) 33.5972 58.1921i 1.40723 2.43740i
\(571\) 5.47793 9.48806i 0.229244 0.397063i −0.728340 0.685216i \(-0.759708\pi\)
0.957584 + 0.288153i \(0.0930412\pi\)
\(572\) 0 0
\(573\) −9.72552 −0.406289
\(574\) 1.74494 0.0208854i 0.0728323 0.000871740i
\(575\) −2.14849 −0.0895982
\(576\) −17.3576 30.0643i −0.723235 1.25268i
\(577\) 17.3708 30.0870i 0.723154 1.25254i −0.236575 0.971613i \(-0.576025\pi\)
0.959729 0.280927i \(-0.0906418\pi\)
\(578\) −0.639571 + 1.10777i −0.0266027 + 0.0460771i
\(579\) −17.8490 30.9154i −0.741781 1.28480i
\(580\) −1.26696 −0.0526076
\(581\) −16.5856 + 29.5380i −0.688086 + 1.22544i
\(582\) 7.74426 0.321010
\(583\) 7.24915 + 12.5559i 0.300229 + 0.520012i
\(584\) 4.51600 7.82195i 0.186874 0.323675i
\(585\) 0 0
\(586\) 12.1796 + 21.0958i 0.503136 + 0.871458i
\(587\) 22.8463 0.942967 0.471483 0.881875i \(-0.343719\pi\)
0.471483 + 0.881875i \(0.343719\pi\)
\(588\) −3.50910 + 6.42854i −0.144713 + 0.265108i
\(589\) −72.6320 −2.99275
\(590\) −3.74071 6.47911i −0.154003 0.266741i
\(591\) 12.7457 22.0762i 0.524288 0.908094i
\(592\) 4.69738 8.13610i 0.193061 0.334392i
\(593\) 8.79676 + 15.2364i 0.361240 + 0.625686i 0.988165 0.153394i \(-0.0490202\pi\)
−0.626925 + 0.779079i \(0.715687\pi\)
\(594\) −6.11222 −0.250787
\(595\) 15.0346 26.7757i 0.616359 1.09770i
\(596\) −4.02433 −0.164843
\(597\) 34.5119 + 59.7764i 1.41248 + 2.44648i
\(598\) 0 0
\(599\) −15.5036 + 26.8531i −0.633461 + 1.09719i 0.353378 + 0.935481i \(0.385033\pi\)
−0.986839 + 0.161706i \(0.948300\pi\)
\(600\) 13.6565 + 23.6537i 0.557524 + 0.965660i
\(601\) −1.43754 −0.0586385 −0.0293193 0.999570i \(-0.509334\pi\)
−0.0293193 + 0.999570i \(0.509334\pi\)
\(602\) 1.10165 0.0131858i 0.0449001 0.000537415i
\(603\) −57.3455 −2.33529
\(604\) 0.0373796 + 0.0647433i 0.00152095 + 0.00263437i
\(605\) 9.94490 17.2251i 0.404318 0.700299i
\(606\) −2.41609 + 4.18479i −0.0981470 + 0.169996i
\(607\) 16.5085 + 28.5936i 0.670061 + 1.16058i 0.977887 + 0.209136i \(0.0670652\pi\)
−0.307826 + 0.951443i \(0.599601\pi\)
\(608\) 15.4333 0.625901
\(609\) −3.88813 6.55208i −0.157555 0.265503i
\(610\) −8.81953 −0.357092
\(611\) 0 0
\(612\) 3.10727 5.38194i 0.125604 0.217552i
\(613\) −21.5829 + 37.3826i −0.871723 + 1.50987i −0.0115102 + 0.999934i \(0.503664\pi\)
−0.860213 + 0.509935i \(0.829669\pi\)
\(614\) 2.26404 + 3.92143i 0.0913692 + 0.158256i
\(615\) −3.97426 −0.160258
\(616\) −8.34619 14.0646i −0.336278 0.566677i
\(617\) −2.45772 −0.0989441 −0.0494721 0.998776i \(-0.515754\pi\)
−0.0494721 + 0.998776i \(0.515754\pi\)
\(618\) 19.3443 + 33.5053i 0.778142 + 1.34778i
\(619\) 18.8894 32.7175i 0.759231 1.31503i −0.184013 0.982924i \(-0.558909\pi\)
0.943243 0.332102i \(-0.107758\pi\)
\(620\) 6.02954 10.4435i 0.242152 0.419420i
\(621\) −0.743761 1.28823i −0.0298461 0.0516949i
\(622\) 30.1602 1.20932
\(623\) −7.09271 + 0.0848936i −0.284163 + 0.00340119i
\(624\) 0 0
\(625\) 15.1971 + 26.3222i 0.607884 + 1.05289i
\(626\) −11.4420 + 19.8181i −0.457313 + 0.792089i
\(627\) 18.6258 32.2608i 0.743842 1.28837i
\(628\) −2.40371 4.16334i −0.0959183 0.166135i
\(629\) 12.3374 0.491922
\(630\) −18.5708 + 33.0735i −0.739878 + 1.31768i
\(631\) 28.4828 1.13388 0.566942 0.823758i \(-0.308126\pi\)
0.566942 + 0.823758i \(0.308126\pi\)
\(632\) 13.2966 + 23.0303i 0.528909 + 0.916098i
\(633\) 13.1809 22.8299i 0.523892 0.907407i
\(634\) 17.4326 30.1942i 0.692337 1.19916i
\(635\) −7.51981 13.0247i −0.298415 0.516869i
\(636\) 7.44843 0.295350
\(637\) 0 0
\(638\) 2.82509 0.111847
\(639\) 7.02743 + 12.1719i 0.278001 + 0.481512i
\(640\) 9.90456 17.1552i 0.391512 0.678119i
\(641\) 13.5961 23.5492i 0.537014 0.930136i −0.462049 0.886854i \(-0.652886\pi\)
0.999063 0.0432812i \(-0.0137811\pi\)
\(642\) −32.6292 56.5154i −1.28777 2.23049i
\(643\) 37.1664 1.46570 0.732849 0.680391i \(-0.238190\pi\)
0.732849 + 0.680391i \(0.238190\pi\)
\(644\) 0.323587 0.576289i 0.0127511 0.0227090i
\(645\) −2.50912 −0.0987965
\(646\) −17.6167 30.5130i −0.693120 1.20052i
\(647\) −9.41593 + 16.3089i −0.370178 + 0.641168i −0.989593 0.143896i \(-0.954037\pi\)
0.619414 + 0.785064i \(0.287370\pi\)
\(648\) 8.31275 14.3981i 0.326556 0.565611i
\(649\) −2.07380 3.59192i −0.0814036 0.140995i
\(650\) 0 0
\(651\) 72.5123 0.867909i 2.84198 0.0340161i
\(652\) 5.93910 0.232593
\(653\) 13.0092 + 22.5326i 0.509090 + 0.881770i 0.999945 + 0.0105286i \(0.00335143\pi\)
−0.490854 + 0.871242i \(0.663315\pi\)
\(654\) −1.84004 + 3.18705i −0.0719513 + 0.124623i
\(655\) −15.3355 + 26.5618i −0.599206 + 1.03786i
\(656\) 0.793435 + 1.37427i 0.0309784 + 0.0536562i
\(657\) −11.6131 −0.453069
\(658\) 18.0208 + 30.3676i 0.702523 + 1.18385i
\(659\) −33.3339 −1.29851 −0.649253 0.760573i \(-0.724918\pi\)
−0.649253 + 0.760573i \(0.724918\pi\)
\(660\) 3.09244 + 5.35626i 0.120373 + 0.208492i
\(661\) 3.14920 5.45458i 0.122490 0.212159i −0.798259 0.602314i \(-0.794245\pi\)
0.920749 + 0.390156i \(0.127579\pi\)
\(662\) 11.5053 19.9277i 0.447164 0.774511i
\(663\) 0 0
\(664\) −38.8626 −1.50816
\(665\) −27.2852 45.9795i −1.05807 1.78301i
\(666\) −15.2391 −0.590505
\(667\) 0.343769 + 0.595426i 0.0133108 + 0.0230550i
\(668\) −1.00687 + 1.74394i −0.0389568 + 0.0674752i
\(669\) −22.9836 + 39.8088i −0.888597 + 1.53910i
\(670\) −26.9899 46.7479i −1.04271 1.80603i
\(671\) −4.88941 −0.188754
\(672\) −15.4078 + 0.184418i −0.594370 + 0.00711409i
\(673\) 18.3188 0.706137 0.353068 0.935598i \(-0.385138\pi\)
0.353068 + 0.935598i \(0.385138\pi\)
\(674\) −10.8451 18.7842i −0.417736 0.723541i
\(675\) 4.06110 7.03403i 0.156312 0.270740i
\(676\) 0 0
\(677\) −12.1696 21.0783i −0.467715 0.810106i 0.531604 0.846993i \(-0.321589\pi\)
−0.999319 + 0.0368866i \(0.988256\pi\)
\(678\) −3.64453 −0.139967
\(679\) 3.01692 5.37296i 0.115779 0.206195i
\(680\) 35.2284 1.35095
\(681\) 12.5010 + 21.6524i 0.479039 + 0.829720i
\(682\) −13.4448 + 23.2871i −0.514829 + 0.891709i
\(683\) 5.88409 10.1916i 0.225149 0.389969i −0.731215 0.682147i \(-0.761047\pi\)
0.956364 + 0.292178i \(0.0943799\pi\)
\(684\) −5.41008 9.37054i −0.206860 0.358291i
\(685\) 17.0434 0.651195
\(686\) −12.4408 19.8653i −0.474994 0.758461i
\(687\) 55.4802 2.11670
\(688\) 0.500929 + 0.867635i 0.0190977 + 0.0330783i
\(689\) 0 0
\(690\) 3.02708 5.24306i 0.115239 0.199600i
\(691\) 0.588923 + 1.02004i 0.0224037 + 0.0388043i 0.877010 0.480472i \(-0.159535\pi\)
−0.854606 + 0.519277i \(0.826201\pi\)
\(692\) 0.237195 0.00901679
\(693\) −10.2954 + 18.3354i −0.391089 + 0.696506i
\(694\) −28.1835 −1.06983
\(695\) 5.80520 + 10.0549i 0.220204 + 0.381404i
\(696\) 4.37022 7.56944i 0.165653 0.286919i
\(697\) −1.04195 + 1.80471i −0.0394668 + 0.0683584i
\(698\) −12.6161 21.8517i −0.477525 0.827097i
\(699\) −37.2516 −1.40898
\(700\) 3.60852 0.0431908i 0.136389 0.00163246i
\(701\) −31.2867 −1.18168 −0.590841 0.806788i \(-0.701204\pi\)
−0.590841 + 0.806788i \(0.701204\pi\)
\(702\) 0 0
\(703\) 10.7403 18.6028i 0.405079 0.701617i
\(704\) 9.05804 15.6890i 0.341388 0.591301i
\(705\) −40.2104 69.6464i −1.51441 2.62304i
\(706\) 29.0016 1.09149
\(707\) 1.96217 + 3.30654i 0.0737950 + 0.124355i
\(708\) −2.13081 −0.0800806
\(709\) 7.68738 + 13.3149i 0.288706 + 0.500053i 0.973501 0.228682i \(-0.0734418\pi\)
−0.684795 + 0.728735i \(0.740108\pi\)
\(710\) −6.61499 + 11.4575i −0.248256 + 0.429992i
\(711\) 17.0963 29.6117i 0.641162 1.11053i
\(712\) −4.06870 7.04719i −0.152481 0.264105i
\(713\) −6.54409 −0.245078
\(714\) 17.9523 + 30.2522i 0.671848 + 1.13216i
\(715\) 0 0
\(716\) 1.60820 + 2.78549i 0.0601013 + 0.104098i
\(717\) 21.7111 37.6048i 0.810817 1.40438i
\(718\) −17.2322 + 29.8470i −0.643099 + 1.11388i
\(719\) 5.57087 + 9.64904i 0.207759 + 0.359848i 0.951008 0.309166i \(-0.100050\pi\)
−0.743250 + 0.669014i \(0.766717\pi\)
\(720\) −34.4921 −1.28545
\(721\) 30.7819 0.368433i 1.14638 0.0137211i
\(722\) −37.2985 −1.38811
\(723\) 17.9824 + 31.1465i 0.668773 + 1.15835i
\(724\) 0.376978 0.652945i 0.0140103 0.0242665i
\(725\) −1.87706 + 3.25116i −0.0697121 + 0.120745i
\(726\) 11.3925 + 19.7324i 0.422815 + 0.732338i
\(727\) −6.24735 −0.231702 −0.115851 0.993267i \(-0.536959\pi\)
−0.115851 + 0.993267i \(0.536959\pi\)
\(728\) 0 0
\(729\) −40.0674 −1.48398
\(730\) −5.46575 9.46696i −0.202296 0.350388i
\(731\) −0.657828 + 1.13939i −0.0243307 + 0.0421419i
\(732\) −1.25596 + 2.17538i −0.0464215 + 0.0804044i
\(733\) 15.4834 + 26.8181i 0.571894 + 0.990550i 0.996371 + 0.0851111i \(0.0271245\pi\)
−0.424477 + 0.905439i \(0.639542\pi\)
\(734\) 13.7400 0.507153
\(735\) 27.7897 + 45.5777i 1.02504 + 1.68116i
\(736\) 1.39053 0.0512554
\(737\) −14.9628 25.9163i −0.551162 0.954641i
\(738\) 1.28702 2.22919i 0.0473760 0.0820576i
\(739\) 1.16872 2.02429i 0.0429921 0.0744646i −0.843729 0.536770i \(-0.819644\pi\)
0.886721 + 0.462305i \(0.152978\pi\)
\(740\) 1.78322 + 3.08862i 0.0655523 + 0.113540i
\(741\) 0 0
\(742\) −11.6710 + 20.7854i −0.428456 + 0.763055i
\(743\) −24.3612 −0.893726 −0.446863 0.894603i \(-0.647459\pi\)
−0.446863 + 0.894603i \(0.647459\pi\)
\(744\) 41.5963 + 72.0470i 1.52500 + 2.64137i
\(745\) −14.6660 + 25.4022i −0.537321 + 0.930666i
\(746\) −1.50066 + 2.59922i −0.0549430 + 0.0951641i
\(747\) 24.9842 + 43.2739i 0.914123 + 1.58331i
\(748\) 3.24304 0.118577
\(749\) −51.9216 + 0.621457i −1.89718 + 0.0227075i
\(750\) −15.2002 −0.555033
\(751\) 6.01266 + 10.4142i 0.219405 + 0.380021i 0.954626 0.297806i \(-0.0962550\pi\)
−0.735221 + 0.677827i \(0.762922\pi\)
\(752\) −16.0555 + 27.8089i −0.585483 + 1.01409i
\(753\) −19.2583 + 33.3564i −0.701813 + 1.21558i
\(754\) 0 0
\(755\) 0.544894 0.0198307
\(756\) 1.27509 + 2.14871i 0.0463746 + 0.0781479i
\(757\) 25.9905 0.944641 0.472321 0.881427i \(-0.343416\pi\)
0.472321 + 0.881427i \(0.343416\pi\)
\(758\) 18.4904 + 32.0263i 0.671600 + 1.16325i
\(759\) 1.67817 2.90667i 0.0609137 0.105506i
\(760\) 30.6682 53.1189i 1.11245 1.92683i
\(761\) 6.66350 + 11.5415i 0.241552 + 0.418380i 0.961156 0.276004i \(-0.0890103\pi\)
−0.719605 + 0.694384i \(0.755677\pi\)
\(762\) 17.2288 0.624134
\(763\) 1.49435 + 2.51819i 0.0540990 + 0.0911647i
\(764\) −1.47416 −0.0533334
\(765\) −22.6478 39.2271i −0.818833 1.41826i
\(766\) 1.94014 3.36043i 0.0701002 0.121417i
\(767\) 0 0
\(768\) −12.0245 20.8270i −0.433896 0.751530i
\(769\) −9.24486 −0.333378 −0.166689 0.986010i \(-0.553308\pi\)
−0.166689 + 0.986010i \(0.553308\pi\)
\(770\) −19.7926 + 0.236900i −0.713275 + 0.00853728i
\(771\) 4.60503 0.165846
\(772\) −2.70550 4.68607i −0.0973732 0.168655i
\(773\) −5.07097 + 8.78317i −0.182390 + 0.315909i −0.942694 0.333659i \(-0.891717\pi\)
0.760304 + 0.649568i \(0.225050\pi\)
\(774\) 0.812552 1.40738i 0.0292066 0.0505873i
\(775\) −17.8661 30.9450i −0.641768 1.11158i
\(776\) 7.06912 0.253766
\(777\) −10.5003 + 18.7005i −0.376698 + 0.670876i
\(778\) −35.1092 −1.25873
\(779\) 1.81415 + 3.14220i 0.0649987 + 0.112581i
\(780\)