Properties

Label 35.4.e.a.11.1
Level $35$
Weight $4$
Character 35.11
Analytic conductor $2.065$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 35.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.06506685020\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 35.11
Dual form 35.4.e.a.16.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.50000 - 4.33013i) q^{5} -6.00000 q^{6} +(-14.0000 - 12.1244i) q^{7} -21.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.50000 - 4.33013i) q^{5} -6.00000 q^{6} +(-14.0000 - 12.1244i) q^{7} -21.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +(-7.50000 + 12.9904i) q^{10} +(22.5000 - 38.9711i) q^{11} +(1.00000 + 1.73205i) q^{12} +59.0000 q^{13} +(-10.5000 + 54.5596i) q^{14} -10.0000 q^{15} +(35.5000 + 61.4878i) q^{16} +(27.0000 - 46.7654i) q^{17} +(34.5000 - 59.7558i) q^{18} +(60.5000 + 104.789i) q^{19} +5.00000 q^{20} +(-35.0000 + 12.1244i) q^{21} -135.000 q^{22} +(-34.5000 - 59.7558i) q^{23} +(-21.0000 + 36.3731i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-88.5000 - 153.286i) q^{26} +100.000 q^{27} +(17.5000 - 6.06218i) q^{28} -162.000 q^{29} +(15.0000 + 25.9808i) q^{30} +(44.0000 - 76.2102i) q^{31} +(22.5000 - 38.9711i) q^{32} +(-45.0000 - 77.9423i) q^{33} -162.000 q^{34} +(-17.5000 + 90.9327i) q^{35} -23.0000 q^{36} +(129.500 + 224.301i) q^{37} +(181.500 - 314.367i) q^{38} +(59.0000 - 102.191i) q^{39} +(52.5000 + 90.9327i) q^{40} +195.000 q^{41} +(84.0000 + 72.7461i) q^{42} -286.000 q^{43} +(22.5000 + 38.9711i) q^{44} +(57.5000 - 99.5929i) q^{45} +(-103.500 + 179.267i) q^{46} +(-22.5000 - 38.9711i) q^{47} +142.000 q^{48} +(49.0000 + 339.482i) q^{49} +75.0000 q^{50} +(-54.0000 - 93.5307i) q^{51} +(-29.5000 + 51.0955i) q^{52} +(-298.500 + 517.017i) q^{53} +(-150.000 - 259.808i) q^{54} -225.000 q^{55} +(294.000 + 254.611i) q^{56} +242.000 q^{57} +(243.000 + 420.888i) q^{58} +(180.000 - 311.769i) q^{59} +(5.00000 - 8.66025i) q^{60} +(-196.000 - 339.482i) q^{61} -264.000 q^{62} +(80.5000 - 418.290i) q^{63} +433.000 q^{64} +(-147.500 - 255.477i) q^{65} +(-135.000 + 233.827i) q^{66} +(140.000 - 242.487i) q^{67} +(27.0000 + 46.7654i) q^{68} -138.000 q^{69} +(262.500 - 90.9327i) q^{70} +48.0000 q^{71} +(-241.500 - 418.290i) q^{72} +(-334.000 + 578.505i) q^{73} +(388.500 - 672.902i) q^{74} +(25.0000 + 43.3013i) q^{75} -121.000 q^{76} +(-787.500 + 272.798i) q^{77} -354.000 q^{78} +(-391.000 - 677.232i) q^{79} +(177.500 - 307.439i) q^{80} +(-210.500 + 364.597i) q^{81} +(-292.500 - 506.625i) q^{82} +768.000 q^{83} +(7.00000 - 36.3731i) q^{84} -270.000 q^{85} +(429.000 + 743.050i) q^{86} +(-162.000 + 280.592i) q^{87} +(-472.500 + 818.394i) q^{88} +(597.000 + 1034.03i) q^{89} -345.000 q^{90} +(-826.000 - 715.337i) q^{91} +69.0000 q^{92} +(-88.0000 - 152.420i) q^{93} +(-67.5000 + 116.913i) q^{94} +(302.500 - 523.945i) q^{95} +(-45.0000 - 77.9423i) q^{96} +902.000 q^{97} +(808.500 - 636.529i) q^{98} +1035.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{2} + 2 q^{3} - q^{4} - 5 q^{5} - 12 q^{6} - 28 q^{7} - 42 q^{8} + 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{2} + 2 q^{3} - q^{4} - 5 q^{5} - 12 q^{6} - 28 q^{7} - 42 q^{8} + 23 q^{9} - 15 q^{10} + 45 q^{11} + 2 q^{12} + 118 q^{13} - 21 q^{14} - 20 q^{15} + 71 q^{16} + 54 q^{17} + 69 q^{18} + 121 q^{19} + 10 q^{20} - 70 q^{21} - 270 q^{22} - 69 q^{23} - 42 q^{24} - 25 q^{25} - 177 q^{26} + 200 q^{27} + 35 q^{28} - 324 q^{29} + 30 q^{30} + 88 q^{31} + 45 q^{32} - 90 q^{33} - 324 q^{34} - 35 q^{35} - 46 q^{36} + 259 q^{37} + 363 q^{38} + 118 q^{39} + 105 q^{40} + 390 q^{41} + 168 q^{42} - 572 q^{43} + 45 q^{44} + 115 q^{45} - 207 q^{46} - 45 q^{47} + 284 q^{48} + 98 q^{49} + 150 q^{50} - 108 q^{51} - 59 q^{52} - 597 q^{53} - 300 q^{54} - 450 q^{55} + 588 q^{56} + 484 q^{57} + 486 q^{58} + 360 q^{59} + 10 q^{60} - 392 q^{61} - 528 q^{62} + 161 q^{63} + 866 q^{64} - 295 q^{65} - 270 q^{66} + 280 q^{67} + 54 q^{68} - 276 q^{69} + 525 q^{70} + 96 q^{71} - 483 q^{72} - 668 q^{73} + 777 q^{74} + 50 q^{75} - 242 q^{76} - 1575 q^{77} - 708 q^{78} - 782 q^{79} + 355 q^{80} - 421 q^{81} - 585 q^{82} + 1536 q^{83} + 14 q^{84} - 540 q^{85} + 858 q^{86} - 324 q^{87} - 945 q^{88} + 1194 q^{89} - 690 q^{90} - 1652 q^{91} + 138 q^{92} - 176 q^{93} - 135 q^{94} + 605 q^{95} - 90 q^{96} + 1804 q^{97} + 1617 q^{98} + 2070 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 2.59808i −0.530330 0.918559i −0.999374 0.0353837i \(-0.988735\pi\)
0.469044 0.883175i \(-0.344599\pi\)
\(3\) 1.00000 1.73205i 0.192450 0.333333i −0.753612 0.657320i \(-0.771690\pi\)
0.946062 + 0.323987i \(0.105023\pi\)
\(4\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(5\) −2.50000 4.33013i −0.223607 0.387298i
\(6\) −6.00000 −0.408248
\(7\) −14.0000 12.1244i −0.755929 0.654654i
\(8\) −21.0000 −0.928078
\(9\) 11.5000 + 19.9186i 0.425926 + 0.737725i
\(10\) −7.50000 + 12.9904i −0.237171 + 0.410792i
\(11\) 22.5000 38.9711i 0.616728 1.06820i −0.373351 0.927690i \(-0.621791\pi\)
0.990079 0.140514i \(-0.0448754\pi\)
\(12\) 1.00000 + 1.73205i 0.0240563 + 0.0416667i
\(13\) 59.0000 1.25874 0.629371 0.777105i \(-0.283312\pi\)
0.629371 + 0.777105i \(0.283312\pi\)
\(14\) −10.5000 + 54.5596i −0.200446 + 1.04155i
\(15\) −10.0000 −0.172133
\(16\) 35.5000 + 61.4878i 0.554688 + 0.960747i
\(17\) 27.0000 46.7654i 0.385204 0.667192i −0.606594 0.795012i \(-0.707465\pi\)
0.991797 + 0.127820i \(0.0407979\pi\)
\(18\) 34.5000 59.7558i 0.451763 0.782476i
\(19\) 60.5000 + 104.789i 0.730508 + 1.26528i 0.956666 + 0.291186i \(0.0940500\pi\)
−0.226158 + 0.974091i \(0.572617\pi\)
\(20\) 5.00000 0.0559017
\(21\) −35.0000 + 12.1244i −0.363696 + 0.125988i
\(22\) −135.000 −1.30828
\(23\) −34.5000 59.7558i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) −21.0000 + 36.3731i −0.178609 + 0.309359i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −88.5000 153.286i −0.667549 1.15623i
\(27\) 100.000 0.712778
\(28\) 17.5000 6.06218i 0.118114 0.0409159i
\(29\) −162.000 −1.03733 −0.518666 0.854977i \(-0.673571\pi\)
−0.518666 + 0.854977i \(0.673571\pi\)
\(30\) 15.0000 + 25.9808i 0.0912871 + 0.158114i
\(31\) 44.0000 76.2102i 0.254924 0.441541i −0.709951 0.704251i \(-0.751283\pi\)
0.964875 + 0.262710i \(0.0846163\pi\)
\(32\) 22.5000 38.9711i 0.124296 0.215287i
\(33\) −45.0000 77.9423i −0.237379 0.411152i
\(34\) −162.000 −0.817140
\(35\) −17.5000 + 90.9327i −0.0845154 + 0.439155i
\(36\) −23.0000 −0.106481
\(37\) 129.500 + 224.301i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) 181.500 314.367i 0.774821 1.34203i
\(39\) 59.0000 102.191i 0.242245 0.419581i
\(40\) 52.5000 + 90.9327i 0.207524 + 0.359443i
\(41\) 195.000 0.742778 0.371389 0.928477i \(-0.378882\pi\)
0.371389 + 0.928477i \(0.378882\pi\)
\(42\) 84.0000 + 72.7461i 0.308607 + 0.267261i
\(43\) −286.000 −1.01429 −0.507146 0.861860i \(-0.669300\pi\)
−0.507146 + 0.861860i \(0.669300\pi\)
\(44\) 22.5000 + 38.9711i 0.0770910 + 0.133525i
\(45\) 57.5000 99.5929i 0.190480 0.329921i
\(46\) −103.500 + 179.267i −0.331744 + 0.574598i
\(47\) −22.5000 38.9711i −0.0698290 0.120947i 0.828997 0.559253i \(-0.188912\pi\)
−0.898826 + 0.438306i \(0.855579\pi\)
\(48\) 142.000 0.426999
\(49\) 49.0000 + 339.482i 0.142857 + 0.989743i
\(50\) 75.0000 0.212132
\(51\) −54.0000 93.5307i −0.148265 0.256802i
\(52\) −29.5000 + 51.0955i −0.0786714 + 0.136263i
\(53\) −298.500 + 517.017i −0.773625 + 1.33996i 0.161939 + 0.986801i \(0.448225\pi\)
−0.935564 + 0.353157i \(0.885108\pi\)
\(54\) −150.000 259.808i −0.378008 0.654729i
\(55\) −225.000 −0.551618
\(56\) 294.000 + 254.611i 0.701561 + 0.607569i
\(57\) 242.000 0.562345
\(58\) 243.000 + 420.888i 0.550129 + 0.952851i
\(59\) 180.000 311.769i 0.397187 0.687947i −0.596191 0.802843i \(-0.703320\pi\)
0.993378 + 0.114895i \(0.0366533\pi\)
\(60\) 5.00000 8.66025i 0.0107583 0.0186339i
\(61\) −196.000 339.482i −0.411397 0.712561i 0.583646 0.812009i \(-0.301626\pi\)
−0.995043 + 0.0994477i \(0.968292\pi\)
\(62\) −264.000 −0.540775
\(63\) 80.5000 418.290i 0.160985 0.836502i
\(64\) 433.000 0.845703
\(65\) −147.500 255.477i −0.281463 0.487509i
\(66\) −135.000 + 233.827i −0.251778 + 0.436092i
\(67\) 140.000 242.487i 0.255279 0.442157i −0.709692 0.704512i \(-0.751166\pi\)
0.964971 + 0.262355i \(0.0844992\pi\)
\(68\) 27.0000 + 46.7654i 0.0481505 + 0.0833990i
\(69\) −138.000 −0.240772
\(70\) 262.500 90.9327i 0.448211 0.155265i
\(71\) 48.0000 0.0802331 0.0401166 0.999195i \(-0.487227\pi\)
0.0401166 + 0.999195i \(0.487227\pi\)
\(72\) −241.500 418.290i −0.395292 0.684666i
\(73\) −334.000 + 578.505i −0.535503 + 0.927519i 0.463635 + 0.886026i \(0.346545\pi\)
−0.999139 + 0.0414929i \(0.986789\pi\)
\(74\) 388.500 672.902i 0.610300 1.05707i
\(75\) 25.0000 + 43.3013i 0.0384900 + 0.0666667i
\(76\) −121.000 −0.182627
\(77\) −787.500 + 272.798i −1.16551 + 0.403743i
\(78\) −354.000 −0.513880
\(79\) −391.000 677.232i −0.556847 0.964488i −0.997757 0.0669365i \(-0.978678\pi\)
0.440910 0.897551i \(-0.354656\pi\)
\(80\) 177.500 307.439i 0.248064 0.429659i
\(81\) −210.500 + 364.597i −0.288752 + 0.500133i
\(82\) −292.500 506.625i −0.393917 0.682285i
\(83\) 768.000 1.01565 0.507825 0.861460i \(-0.330450\pi\)
0.507825 + 0.861460i \(0.330450\pi\)
\(84\) 7.00000 36.3731i 0.00909241 0.0472456i
\(85\) −270.000 −0.344537
\(86\) 429.000 + 743.050i 0.537910 + 0.931687i
\(87\) −162.000 + 280.592i −0.199635 + 0.345778i
\(88\) −472.500 + 818.394i −0.572371 + 0.991376i
\(89\) 597.000 + 1034.03i 0.711032 + 1.23154i 0.964470 + 0.264192i \(0.0851054\pi\)
−0.253438 + 0.967352i \(0.581561\pi\)
\(90\) −345.000 −0.404069
\(91\) −826.000 715.337i −0.951520 0.824041i
\(92\) 69.0000 0.0781929
\(93\) −88.0000 152.420i −0.0981202 0.169949i
\(94\) −67.5000 + 116.913i −0.0740648 + 0.128284i
\(95\) 302.500 523.945i 0.326693 0.565849i
\(96\) −45.0000 77.9423i −0.0478416 0.0828641i
\(97\) 902.000 0.944167 0.472084 0.881554i \(-0.343502\pi\)
0.472084 + 0.881554i \(0.343502\pi\)
\(98\) 808.500 636.529i 0.833376 0.656113i
\(99\) 1035.00 1.05072
\(100\) −12.5000 21.6506i −0.0125000 0.0216506i
\(101\) −342.000 + 592.361i −0.336933 + 0.583586i −0.983854 0.178971i \(-0.942723\pi\)
0.646921 + 0.762557i \(0.276056\pi\)
\(102\) −162.000 + 280.592i −0.157259 + 0.272380i
\(103\) 758.000 + 1312.89i 0.725126 + 1.25595i 0.958922 + 0.283669i \(0.0915518\pi\)
−0.233796 + 0.972286i \(0.575115\pi\)
\(104\) −1239.00 −1.16821
\(105\) 140.000 + 121.244i 0.130120 + 0.112687i
\(106\) 1791.00 1.64111
\(107\) 366.000 + 633.931i 0.330678 + 0.572751i 0.982645 0.185496i \(-0.0593892\pi\)
−0.651967 + 0.758247i \(0.726056\pi\)
\(108\) −50.0000 + 86.6025i −0.0445486 + 0.0771605i
\(109\) 800.000 1385.64i 0.702992 1.21762i −0.264420 0.964408i \(-0.585180\pi\)
0.967411 0.253210i \(-0.0814863\pi\)
\(110\) 337.500 + 584.567i 0.292540 + 0.506694i
\(111\) 518.000 0.442940
\(112\) 248.500 1291.24i 0.209652 1.08938i
\(113\) −1392.00 −1.15883 −0.579417 0.815031i \(-0.696720\pi\)
−0.579417 + 0.815031i \(0.696720\pi\)
\(114\) −363.000 628.734i −0.298229 0.516547i
\(115\) −172.500 + 298.779i −0.139876 + 0.242272i
\(116\) 81.0000 140.296i 0.0648333 0.112295i
\(117\) 678.500 + 1175.20i 0.536131 + 0.928606i
\(118\) −1080.00 −0.842560
\(119\) −945.000 + 327.358i −0.727966 + 0.252175i
\(120\) 210.000 0.159752
\(121\) −347.000 601.022i −0.260706 0.451556i
\(122\) −588.000 + 1018.45i −0.436353 + 0.755785i
\(123\) 195.000 337.750i 0.142948 0.247593i
\(124\) 44.0000 + 76.2102i 0.0318655 + 0.0551926i
\(125\) 125.000 0.0894427
\(126\) −1207.50 + 418.290i −0.853751 + 0.295748i
\(127\) 803.000 0.561061 0.280530 0.959845i \(-0.409490\pi\)
0.280530 + 0.959845i \(0.409490\pi\)
\(128\) −829.500 1436.74i −0.572798 0.992115i
\(129\) −286.000 + 495.367i −0.195201 + 0.338098i
\(130\) −442.500 + 766.432i −0.298537 + 0.517081i
\(131\) −1009.50 1748.51i −0.673286 1.16617i −0.976967 0.213391i \(-0.931549\pi\)
0.303681 0.952774i \(-0.401784\pi\)
\(132\) 90.0000 0.0593447
\(133\) 423.500 2200.57i 0.276106 1.43469i
\(134\) −840.000 −0.541529
\(135\) −250.000 433.013i −0.159382 0.276058i
\(136\) −567.000 + 982.073i −0.357499 + 0.619206i
\(137\) −30.0000 + 51.9615i −0.0187086 + 0.0324042i −0.875228 0.483710i \(-0.839289\pi\)
0.856520 + 0.516115i \(0.172622\pi\)
\(138\) 207.000 + 358.535i 0.127688 + 0.221163i
\(139\) −1708.00 −1.04224 −0.521118 0.853485i \(-0.674485\pi\)
−0.521118 + 0.853485i \(0.674485\pi\)
\(140\) −70.0000 60.6218i −0.0422577 0.0365963i
\(141\) −90.0000 −0.0537544
\(142\) −72.0000 124.708i −0.0425500 0.0736988i
\(143\) 1327.50 2299.30i 0.776302 1.34459i
\(144\) −816.500 + 1414.22i −0.472512 + 0.818414i
\(145\) 405.000 + 701.481i 0.231955 + 0.401757i
\(146\) 2004.00 1.13597
\(147\) 637.000 + 254.611i 0.357407 + 0.142857i
\(148\) −259.000 −0.143849
\(149\) 543.000 + 940.504i 0.298552 + 0.517108i 0.975805 0.218643i \(-0.0701629\pi\)
−0.677253 + 0.735751i \(0.736830\pi\)
\(150\) 75.0000 129.904i 0.0408248 0.0707107i
\(151\) 1433.00 2482.03i 0.772291 1.33765i −0.164014 0.986458i \(-0.552444\pi\)
0.936305 0.351189i \(-0.114222\pi\)
\(152\) −1270.50 2200.57i −0.677968 1.17428i
\(153\) 1242.00 0.656273
\(154\) 1890.00 + 1636.79i 0.988965 + 0.856468i
\(155\) −440.000 −0.228011
\(156\) 59.0000 + 102.191i 0.0302806 + 0.0524476i
\(157\) 114.500 198.320i 0.0582044 0.100813i −0.835455 0.549559i \(-0.814796\pi\)
0.893659 + 0.448746i \(0.148129\pi\)
\(158\) −1173.00 + 2031.70i −0.590626 + 1.02299i
\(159\) 597.000 + 1034.03i 0.297768 + 0.515750i
\(160\) −225.000 −0.111174
\(161\) −241.500 + 1254.87i −0.118217 + 0.614271i
\(162\) 1263.00 0.612535
\(163\) 614.000 + 1063.48i 0.295044 + 0.511031i 0.974995 0.222226i \(-0.0713323\pi\)
−0.679951 + 0.733258i \(0.737999\pi\)
\(164\) −97.5000 + 168.875i −0.0464236 + 0.0804080i
\(165\) −225.000 + 389.711i −0.106159 + 0.183873i
\(166\) −1152.00 1995.32i −0.538630 0.932934i
\(167\) −1929.00 −0.893835 −0.446918 0.894575i \(-0.647478\pi\)
−0.446918 + 0.894575i \(0.647478\pi\)
\(168\) 735.000 254.611i 0.337539 0.116927i
\(169\) 1284.00 0.584433
\(170\) 405.000 + 701.481i 0.182718 + 0.316477i
\(171\) −1391.50 + 2410.15i −0.622285 + 1.07783i
\(172\) 143.000 247.683i 0.0633933 0.109800i
\(173\) 349.500 + 605.352i 0.153595 + 0.266035i 0.932547 0.361049i \(-0.117581\pi\)
−0.778951 + 0.627084i \(0.784248\pi\)
\(174\) 972.000 0.423489
\(175\) 437.500 151.554i 0.188982 0.0654654i
\(176\) 3195.00 1.36836
\(177\) −360.000 623.538i −0.152877 0.264791i
\(178\) 1791.00 3102.10i 0.754164 1.30625i
\(179\) −1558.50 + 2699.40i −0.650770 + 1.12717i 0.332167 + 0.943221i \(0.392220\pi\)
−0.982936 + 0.183945i \(0.941113\pi\)
\(180\) 57.5000 + 99.5929i 0.0238100 + 0.0412401i
\(181\) −1798.00 −0.738366 −0.369183 0.929357i \(-0.620362\pi\)
−0.369183 + 0.929357i \(0.620362\pi\)
\(182\) −619.500 + 3219.02i −0.252310 + 1.31104i
\(183\) −784.000 −0.316694
\(184\) 724.500 + 1254.87i 0.290276 + 0.502773i
\(185\) 647.500 1121.50i 0.257325 0.445700i
\(186\) −264.000 + 457.261i −0.104072 + 0.180258i
\(187\) −1215.00 2104.44i −0.475132 0.822952i
\(188\) 45.0000 0.0174572
\(189\) −1400.00 1212.44i −0.538810 0.466623i
\(190\) −1815.00 −0.693021
\(191\) 1194.00 + 2068.07i 0.452329 + 0.783457i 0.998530 0.0541974i \(-0.0172600\pi\)
−0.546201 + 0.837654i \(0.683927\pi\)
\(192\) 433.000 749.978i 0.162756 0.281901i
\(193\) −136.000 + 235.559i −0.0507228 + 0.0878544i −0.890272 0.455429i \(-0.849486\pi\)
0.839549 + 0.543284i \(0.182819\pi\)
\(194\) −1353.00 2343.46i −0.500720 0.867273i
\(195\) −590.000 −0.216671
\(196\) −318.500 127.306i −0.116071 0.0463942i
\(197\) −2109.00 −0.762741 −0.381371 0.924422i \(-0.624548\pi\)
−0.381371 + 0.924422i \(0.624548\pi\)
\(198\) −1552.50 2689.01i −0.557229 0.965149i
\(199\) −712.000 + 1233.22i −0.253630 + 0.439300i −0.964522 0.264001i \(-0.914958\pi\)
0.710893 + 0.703301i \(0.248291\pi\)
\(200\) 262.500 454.663i 0.0928078 0.160748i
\(201\) −280.000 484.974i −0.0982571 0.170186i
\(202\) 2052.00 0.714744
\(203\) 2268.00 + 1964.15i 0.784150 + 0.679094i
\(204\) 108.000 0.0370662
\(205\) −487.500 844.375i −0.166090 0.287677i
\(206\) 2274.00 3938.68i 0.769112 1.33214i
\(207\) 793.500 1374.38i 0.266435 0.461479i
\(208\) 2094.50 + 3627.78i 0.698209 + 1.20933i
\(209\) 5445.00 1.80210
\(210\) 105.000 545.596i 0.0345033 0.179284i
\(211\) −3625.00 −1.18273 −0.591363 0.806405i \(-0.701410\pi\)
−0.591363 + 0.806405i \(0.701410\pi\)
\(212\) −298.500 517.017i −0.0967031 0.167495i
\(213\) 48.0000 83.1384i 0.0154409 0.0267444i
\(214\) 1098.00 1901.79i 0.350737 0.607494i
\(215\) 715.000 + 1238.42i 0.226803 + 0.392834i
\(216\) −2100.00 −0.661513
\(217\) −1540.00 + 533.472i −0.481760 + 0.166887i
\(218\) −4800.00 −1.49127
\(219\) 668.000 + 1157.01i 0.206115 + 0.357002i
\(220\) 112.500 194.856i 0.0344761 0.0597144i
\(221\) 1593.00 2759.16i 0.484872 0.839823i
\(222\) −777.000 1345.80i −0.234905 0.406867i
\(223\) −4960.00 −1.48944 −0.744722 0.667374i \(-0.767418\pi\)
−0.744722 + 0.667374i \(0.767418\pi\)
\(224\) −787.500 + 272.798i −0.234898 + 0.0813709i
\(225\) −575.000 −0.170370
\(226\) 2088.00 + 3616.52i 0.614565 + 1.06446i
\(227\) 750.000 1299.04i 0.219292 0.379825i −0.735300 0.677742i \(-0.762959\pi\)
0.954592 + 0.297917i \(0.0962920\pi\)
\(228\) −121.000 + 209.578i −0.0351466 + 0.0608757i
\(229\) −3046.00 5275.83i −0.878975 1.52243i −0.852467 0.522781i \(-0.824894\pi\)
−0.0265085 0.999649i \(-0.508439\pi\)
\(230\) 1035.00 0.296721
\(231\) −315.000 + 1636.79i −0.0897207 + 0.466202i
\(232\) 3402.00 0.962725
\(233\) −69.0000 119.512i −0.0194006 0.0336028i 0.856162 0.516707i \(-0.172842\pi\)
−0.875563 + 0.483104i \(0.839509\pi\)
\(234\) 2035.50 3525.59i 0.568653 0.984936i
\(235\) −112.500 + 194.856i −0.0312285 + 0.0540893i
\(236\) 180.000 + 311.769i 0.0496483 + 0.0859934i
\(237\) −1564.00 −0.428661
\(238\) 2268.00 + 1964.15i 0.617700 + 0.534944i
\(239\) −5502.00 −1.48910 −0.744550 0.667567i \(-0.767336\pi\)
−0.744550 + 0.667567i \(0.767336\pi\)
\(240\) −355.000 614.878i −0.0954798 0.165376i
\(241\) −1775.50 + 3075.26i −0.474564 + 0.821970i −0.999576 0.0291256i \(-0.990728\pi\)
0.525011 + 0.851095i \(0.324061\pi\)
\(242\) −1041.00 + 1803.06i −0.276521 + 0.478948i
\(243\) 1771.00 + 3067.46i 0.467530 + 0.809785i
\(244\) 392.000 0.102849
\(245\) 1347.50 1060.88i 0.351382 0.276642i
\(246\) −1170.00 −0.303238
\(247\) 3569.50 + 6182.56i 0.919522 + 1.59266i
\(248\) −924.000 + 1600.41i −0.236589 + 0.409784i
\(249\) 768.000 1330.22i 0.195462 0.338550i
\(250\) −187.500 324.760i −0.0474342 0.0821584i
\(251\) 7065.00 1.77665 0.888324 0.459216i \(-0.151870\pi\)
0.888324 + 0.459216i \(0.151870\pi\)
\(252\) 322.000 + 278.860i 0.0804924 + 0.0697085i
\(253\) −3105.00 −0.771580
\(254\) −1204.50 2086.26i −0.297547 0.515367i
\(255\) −270.000 + 467.654i −0.0663061 + 0.114846i
\(256\) −756.500 + 1310.30i −0.184692 + 0.319897i
\(257\) 2040.00 + 3533.38i 0.495143 + 0.857613i 0.999984 0.00559954i \(-0.00178240\pi\)
−0.504842 + 0.863212i \(0.668449\pi\)
\(258\) 1716.00 0.414083
\(259\) 906.500 4710.31i 0.217479 1.13006i
\(260\) 295.000 0.0703659
\(261\) −1863.00 3226.81i −0.441827 0.765267i
\(262\) −3028.50 + 5245.52i −0.714127 + 1.23690i
\(263\) 1644.00 2847.49i 0.385450 0.667619i −0.606381 0.795174i \(-0.707380\pi\)
0.991832 + 0.127555i \(0.0407128\pi\)
\(264\) 945.000 + 1636.79i 0.220306 + 0.381581i
\(265\) 2985.00 0.691951
\(266\) −6352.50 + 2200.57i −1.46427 + 0.507239i
\(267\) 2388.00 0.547353
\(268\) 140.000 + 242.487i 0.0319099 + 0.0552696i
\(269\) 1632.00 2826.71i 0.369906 0.640697i −0.619644 0.784883i \(-0.712723\pi\)
0.989551 + 0.144186i \(0.0460564\pi\)
\(270\) −750.000 + 1299.04i −0.169050 + 0.292803i
\(271\) 1376.00 + 2383.30i 0.308436 + 0.534226i 0.978020 0.208510i \(-0.0668612\pi\)
−0.669585 + 0.742736i \(0.733528\pi\)
\(272\) 3834.00 0.854671
\(273\) −2065.00 + 715.337i −0.457800 + 0.158587i
\(274\) 180.000 0.0396869
\(275\) 562.500 + 974.279i 0.123346 + 0.213641i
\(276\) 69.0000 119.512i 0.0150482 0.0260643i
\(277\) 2345.00 4061.66i 0.508655 0.881016i −0.491295 0.870993i \(-0.663476\pi\)
0.999950 0.0100228i \(-0.00319040\pi\)
\(278\) 2562.00 + 4437.51i 0.552729 + 0.957354i
\(279\) 2024.00 0.434314
\(280\) 367.500 1909.59i 0.0784369 0.407570i
\(281\) 7821.00 1.66036 0.830181 0.557494i \(-0.188237\pi\)
0.830181 + 0.557494i \(0.188237\pi\)
\(282\) 135.000 + 233.827i 0.0285076 + 0.0493765i
\(283\) 329.000 569.845i 0.0691061 0.119695i −0.829402 0.558652i \(-0.811319\pi\)
0.898508 + 0.438957i \(0.144652\pi\)
\(284\) −24.0000 + 41.5692i −0.00501457 + 0.00868549i
\(285\) −605.000 1047.89i −0.125744 0.217795i
\(286\) −7965.00 −1.64678
\(287\) −2730.00 2364.25i −0.561487 0.486262i
\(288\) 1035.00 0.211764
\(289\) 998.500 + 1729.45i 0.203236 + 0.352016i
\(290\) 1215.00 2104.44i 0.246025 0.426128i
\(291\) 902.000 1562.31i 0.181705 0.314722i
\(292\) −334.000 578.505i −0.0669379 0.115940i
\(293\) −5997.00 −1.19573 −0.597864 0.801597i \(-0.703984\pi\)
−0.597864 + 0.801597i \(0.703984\pi\)
\(294\) −294.000 2036.89i −0.0583212 0.404061i
\(295\) −1800.00 −0.355254
\(296\) −2719.50 4710.31i −0.534013 0.924937i
\(297\) 2250.00 3897.11i 0.439590 0.761392i
\(298\) 1629.00 2821.51i 0.316663 0.548476i
\(299\) −2035.50 3525.59i −0.393699 0.681907i
\(300\) −50.0000 −0.00962250
\(301\) 4004.00 + 3467.57i 0.766733 + 0.664011i
\(302\) −8598.00 −1.63828
\(303\) 684.000 + 1184.72i 0.129686 + 0.224622i
\(304\) −4295.50 + 7440.02i −0.810407 + 1.40367i
\(305\) −980.000 + 1697.41i −0.183982 + 0.318667i
\(306\) −1863.00 3226.81i −0.348041 0.602825i
\(307\) −6226.00 −1.15745 −0.578724 0.815523i \(-0.696449\pi\)
−0.578724 + 0.815523i \(0.696449\pi\)
\(308\) 157.500 818.394i 0.0291376 0.151404i
\(309\) 3032.00 0.558202
\(310\) 660.000 + 1143.15i 0.120921 + 0.209441i
\(311\) −2340.00 + 4053.00i −0.426653 + 0.738985i −0.996573 0.0827149i \(-0.973641\pi\)
0.569920 + 0.821700i \(0.306974\pi\)
\(312\) −1239.00 + 2146.01i −0.224822 + 0.389404i
\(313\) −514.000 890.274i −0.0928211 0.160771i 0.815876 0.578227i \(-0.196255\pi\)
−0.908697 + 0.417456i \(0.862922\pi\)
\(314\) −687.000 −0.123470
\(315\) −2012.50 + 697.150i −0.359973 + 0.124698i
\(316\) 782.000 0.139212
\(317\) −4311.00 7466.87i −0.763817 1.32297i −0.940870 0.338768i \(-0.889990\pi\)
0.177053 0.984201i \(-0.443344\pi\)
\(318\) 1791.00 3102.10i 0.315831 0.547036i
\(319\) −3645.00 + 6313.33i −0.639752 + 1.10808i
\(320\) −1082.50 1874.94i −0.189105 0.327539i
\(321\) 1464.00 0.254556
\(322\) 3622.50 1254.87i 0.626938 0.217178i
\(323\) 6534.00 1.12558
\(324\) −210.500 364.597i −0.0360940 0.0625166i
\(325\) −737.500 + 1277.39i −0.125874 + 0.218021i
\(326\) 1842.00 3190.44i 0.312942 0.542031i
\(327\) −1600.00 2771.28i −0.270582 0.468661i
\(328\) −4095.00 −0.689355
\(329\) −157.500 + 818.394i −0.0263929 + 0.137141i
\(330\) 1350.00 0.225197
\(331\) 999.500 + 1731.18i 0.165974 + 0.287476i 0.937001 0.349327i \(-0.113590\pi\)
−0.771027 + 0.636803i \(0.780256\pi\)
\(332\) −384.000 + 665.108i −0.0634781 + 0.109947i
\(333\) −2978.50 + 5158.91i −0.490153 + 0.848969i
\(334\) 2893.50 + 5011.69i 0.474028 + 0.821040i
\(335\) −1400.00 −0.228329
\(336\) −1988.00 1721.66i −0.322781 0.279536i
\(337\) 5114.00 0.826639 0.413319 0.910586i \(-0.364369\pi\)
0.413319 + 0.910586i \(0.364369\pi\)
\(338\) −1926.00 3335.93i −0.309943 0.536836i
\(339\) −1392.00 + 2411.01i −0.223018 + 0.386278i
\(340\) 135.000 233.827i 0.0215335 0.0372972i
\(341\) −1980.00 3429.46i −0.314437 0.544621i
\(342\) 8349.00 1.32006
\(343\) 3430.00 5346.84i 0.539949 0.841698i
\(344\) 6006.00 0.941342
\(345\) 345.000 + 597.558i 0.0538382 + 0.0932505i
\(346\) 1048.50 1816.06i 0.162912 0.282173i
\(347\) −2160.00 + 3741.23i −0.334164 + 0.578789i −0.983324 0.181863i \(-0.941787\pi\)
0.649160 + 0.760652i \(0.275121\pi\)
\(348\) −162.000 280.592i −0.0249543 0.0432222i
\(349\) 7922.00 1.21506 0.607529 0.794298i \(-0.292161\pi\)
0.607529 + 0.794298i \(0.292161\pi\)
\(350\) −1050.00 909.327i −0.160357 0.138873i
\(351\) 5900.00 0.897204
\(352\) −1012.50 1753.70i −0.153314 0.265547i
\(353\) −414.000 + 717.069i −0.0624221 + 0.108118i −0.895548 0.444966i \(-0.853216\pi\)
0.833125 + 0.553084i \(0.186549\pi\)
\(354\) −1080.00 + 1870.61i −0.162151 + 0.280853i
\(355\) −120.000 207.846i −0.0179407 0.0310742i
\(356\) −1194.00 −0.177758
\(357\) −378.000 + 1964.15i −0.0560389 + 0.291187i
\(358\) 9351.00 1.38049
\(359\) 675.000 + 1169.13i 0.0992344 + 0.171879i 0.911368 0.411593i \(-0.135027\pi\)
−0.812134 + 0.583472i \(0.801694\pi\)
\(360\) −1207.50 + 2091.45i −0.176780 + 0.306192i
\(361\) −3891.00 + 6739.41i −0.567284 + 0.982564i
\(362\) 2697.00 + 4671.34i 0.391578 + 0.678233i
\(363\) −1388.00 −0.200692
\(364\) 1032.50 357.668i 0.148675 0.0515025i
\(365\) 3340.00 0.478969
\(366\) 1176.00 + 2036.89i 0.167952 + 0.290902i
\(367\) −1400.50 + 2425.74i −0.199198 + 0.345020i −0.948268 0.317470i \(-0.897167\pi\)
0.749071 + 0.662490i \(0.230500\pi\)
\(368\) 2449.50 4242.66i 0.346981 0.600989i
\(369\) 2242.50 + 3884.12i 0.316368 + 0.547966i
\(370\) −3885.00 −0.545869
\(371\) 10447.5 3619.12i 1.46201 0.506456i
\(372\) 176.000 0.0245300
\(373\) −3301.00 5717.50i −0.458229 0.793675i 0.540639 0.841255i \(-0.318183\pi\)
−0.998867 + 0.0475795i \(0.984849\pi\)
\(374\) −3645.00 + 6313.33i −0.503953 + 0.872872i
\(375\) 125.000 216.506i 0.0172133 0.0298142i
\(376\) 472.500 + 818.394i 0.0648067 + 0.112249i
\(377\) −9558.00 −1.30573
\(378\) −1050.00 + 5455.96i −0.142873 + 0.742392i
\(379\) −8305.00 −1.12559 −0.562796 0.826596i \(-0.690274\pi\)
−0.562796 + 0.826596i \(0.690274\pi\)
\(380\) 302.500 + 523.945i 0.0408366 + 0.0707311i
\(381\) 803.000 1390.84i 0.107976 0.187020i
\(382\) 3582.00 6204.21i 0.479767 0.830981i
\(383\) −472.500 818.394i −0.0630382 0.109185i 0.832784 0.553598i \(-0.186746\pi\)
−0.895822 + 0.444413i \(0.853412\pi\)
\(384\) −3318.00 −0.440940
\(385\) 3150.00 + 2727.98i 0.416984 + 0.361119i
\(386\) 816.000 0.107599
\(387\) −3289.00 5696.72i −0.432014 0.748270i
\(388\) −451.000 + 781.155i −0.0590105 + 0.102209i
\(389\) −6018.00 + 10423.5i −0.784382 + 1.35859i 0.144985 + 0.989434i \(0.453687\pi\)
−0.929367 + 0.369156i \(0.879647\pi\)
\(390\) 885.000 + 1532.86i 0.114907 + 0.199025i
\(391\) −3726.00 −0.481923
\(392\) −1029.00 7129.12i −0.132583 0.918559i
\(393\) −4038.00 −0.518296
\(394\) 3163.50 + 5479.34i 0.404505 + 0.700623i
\(395\) −1955.00 + 3386.16i −0.249030 + 0.431332i
\(396\) −517.500 + 896.336i −0.0656701 + 0.113744i
\(397\) 1349.00 + 2336.54i 0.170540 + 0.295384i 0.938609 0.344983i \(-0.112115\pi\)
−0.768069 + 0.640367i \(0.778782\pi\)
\(398\) 4272.00 0.538030
\(399\) −3388.00 2934.09i −0.425093 0.368141i
\(400\) −1775.00 −0.221875
\(401\) −3526.50 6108.08i −0.439165 0.760655i 0.558461 0.829531i \(-0.311392\pi\)
−0.997625 + 0.0688756i \(0.978059\pi\)
\(402\) −840.000 + 1454.92i −0.104217 + 0.180510i
\(403\) 2596.00 4496.40i 0.320883 0.555786i
\(404\) −342.000 592.361i −0.0421167 0.0729482i
\(405\) 2105.00 0.258267
\(406\) 1701.00 8838.66i 0.207929 1.08043i
\(407\) 11655.0 1.41945
\(408\) 1134.00 + 1964.15i 0.137601 + 0.238333i
\(409\) 5435.00 9413.70i 0.657074 1.13809i −0.324295 0.945956i \(-0.605127\pi\)
0.981369 0.192130i \(-0.0615396\pi\)
\(410\) −1462.50 + 2533.12i −0.176165 + 0.305127i
\(411\) 60.0000 + 103.923i 0.00720093 + 0.0124724i
\(412\) −1516.00 −0.181281
\(413\) −6300.00 + 2182.38i −0.750612 + 0.260020i
\(414\) −4761.00 −0.565194
\(415\) −1920.00 3325.54i −0.227106 0.393360i
\(416\) 1327.50 2299.30i 0.156457 0.270991i
\(417\) −1708.00 + 2958.34i −0.200578 + 0.347412i
\(418\) −8167.50 14146.5i −0.955707 1.65533i
\(419\) −9729.00 −1.13435 −0.567175 0.823597i \(-0.691964\pi\)
−0.567175 + 0.823597i \(0.691964\pi\)
\(420\) −175.000 + 60.6218i −0.0203313 + 0.00704295i
\(421\) −12550.0 −1.45285 −0.726425 0.687246i \(-0.758819\pi\)
−0.726425 + 0.687246i \(0.758819\pi\)
\(422\) 5437.50 + 9418.03i 0.627235 + 1.08640i
\(423\) 517.500 896.336i 0.0594840 0.103029i
\(424\) 6268.50 10857.4i 0.717984 1.24358i
\(425\) 675.000 + 1169.13i 0.0770407 + 0.133438i
\(426\) −288.000 −0.0327550
\(427\) −1372.00 + 7129.12i −0.155494 + 0.807968i
\(428\) −732.000 −0.0826695
\(429\) −2655.00 4598.59i −0.298799 0.517534i
\(430\) 2145.00 3715.25i 0.240561 0.416663i
\(431\) −1494.00 + 2587.68i −0.166969 + 0.289198i −0.937353 0.348382i \(-0.886731\pi\)
0.770384 + 0.637580i \(0.220065\pi\)
\(432\) 3550.00 + 6148.78i 0.395369 + 0.684799i
\(433\) 16616.0 1.84414 0.922072 0.387019i \(-0.126495\pi\)
0.922072 + 0.387019i \(0.126495\pi\)
\(434\) 3696.00 + 3200.83i 0.408787 + 0.354020i
\(435\) 1620.00 0.178559
\(436\) 800.000 + 1385.64i 0.0878740 + 0.152202i
\(437\) 4174.50 7230.45i 0.456964 0.791485i
\(438\) 2004.00 3471.03i 0.218618 0.378658i
\(439\) −3673.00 6361.82i −0.399323 0.691647i 0.594320 0.804229i \(-0.297421\pi\)
−0.993642 + 0.112581i \(0.964088\pi\)
\(440\) 4725.00 0.511944
\(441\) −6198.50 + 4880.05i −0.669312 + 0.526947i
\(442\) −9558.00 −1.02857
\(443\) −6.00000 10.3923i −0.000643496 0.00111457i 0.865703 0.500557i \(-0.166871\pi\)
−0.866347 + 0.499443i \(0.833538\pi\)
\(444\) −259.000 + 448.601i −0.0276838 + 0.0479497i
\(445\) 2985.00 5170.17i 0.317983 0.550763i
\(446\) 7440.00 + 12886.5i 0.789897 + 1.36814i
\(447\) 2172.00 0.229826
\(448\) −6062.00 5249.85i −0.639291 0.553643i
\(449\) 9669.00 1.01628 0.508138 0.861275i \(-0.330334\pi\)
0.508138 + 0.861275i \(0.330334\pi\)
\(450\) 862.500 + 1493.89i 0.0903525 + 0.156495i
\(451\) 4387.50 7599.37i 0.458092 0.793438i
\(452\) 696.000 1205.51i 0.0724272 0.125448i
\(453\) −2866.00 4964.06i −0.297255 0.514860i
\(454\) −4500.00 −0.465188
\(455\) −1032.50 + 5365.03i −0.106383 + 0.552783i
\(456\) −5082.00 −0.521900
\(457\) 4817.00 + 8343.29i 0.493063 + 0.854010i 0.999968 0.00799181i \(-0.00254390\pi\)
−0.506905 + 0.862002i \(0.669211\pi\)
\(458\) −9138.00 + 15827.5i −0.932294 + 1.61478i
\(459\) 2700.00 4676.54i 0.274565 0.475560i
\(460\) −172.500 298.779i −0.0174845 0.0302840i
\(461\) −342.000 −0.0345521 −0.0172761 0.999851i \(-0.505499\pi\)
−0.0172761 + 0.999851i \(0.505499\pi\)
\(462\) 4725.00 1636.79i 0.475816 0.164827i
\(463\) 2411.00 0.242006 0.121003 0.992652i \(-0.461389\pi\)
0.121003 + 0.992652i \(0.461389\pi\)
\(464\) −5751.00 9961.02i −0.575395 0.996614i
\(465\) −440.000 + 762.102i −0.0438807 + 0.0760035i
\(466\) −207.000 + 358.535i −0.0205774 + 0.0356412i
\(467\) 603.000 + 1044.43i 0.0597506 + 0.103491i 0.894353 0.447361i \(-0.147636\pi\)
−0.834603 + 0.550852i \(0.814303\pi\)
\(468\) −1357.00 −0.134033
\(469\) −4900.00 + 1697.41i −0.482433 + 0.167120i
\(470\) 675.000 0.0662456
\(471\) −229.000 396.640i −0.0224029 0.0388030i
\(472\) −3780.00 + 6547.15i −0.368620 + 0.638468i
\(473\) −6435.00 + 11145.7i −0.625543 + 1.08347i
\(474\) 2346.00 + 4063.39i 0.227332 + 0.393751i
\(475\) −3025.00 −0.292203
\(476\) 189.000 982.073i 0.0181992 0.0945656i
\(477\) −13731.0 −1.31803
\(478\) 8253.00 + 14294.6i 0.789714 + 1.36783i
\(479\) 216.000 374.123i 0.0206039 0.0356871i −0.855540 0.517737i \(-0.826774\pi\)
0.876144 + 0.482050i \(0.160108\pi\)
\(480\) −225.000 + 389.711i −0.0213954 + 0.0370579i
\(481\) 7640.50 + 13233.7i 0.724276 + 1.25448i
\(482\) 10653.0 1.00670
\(483\) 1932.00 + 1673.16i 0.182006 + 0.157622i
\(484\) 694.000 0.0651766
\(485\) −2255.00 3905.77i −0.211122 0.365674i
\(486\) 5313.00 9202.39i 0.495890 0.858907i
\(487\) 5948.00 10302.2i 0.553449 0.958602i −0.444574 0.895742i \(-0.646645\pi\)
0.998022 0.0628592i \(-0.0200219\pi\)
\(488\) 4116.00 + 7129.12i 0.381809 + 0.661312i
\(489\) 2456.00 0.227125
\(490\) −4777.50 1909.59i −0.440460 0.176054i
\(491\) −12276.0 −1.12833 −0.564163 0.825663i \(-0.690801\pi\)
−0.564163 + 0.825663i \(0.690801\pi\)
\(492\) 195.000 + 337.750i 0.0178685 + 0.0309491i
\(493\) −4374.00 + 7575.99i −0.399584 + 0.692100i
\(494\) 10708.5 18547.7i 0.975300 1.68927i
\(495\) −2587.50 4481.68i −0.234948 0.406943i
\(496\) 6248.00 0.565612
\(497\) −672.000 581.969i −0.0606505 0.0525249i
\(498\) −4608.00 −0.414637
\(499\) 5438.00 + 9418.89i 0.487852 + 0.844985i 0.999902 0.0139706i \(-0.00444712\pi\)
−0.512050 + 0.858956i \(0.671114\pi\)
\(500\) −62.5000 + 108.253i −0.00559017 + 0.00968246i
\(501\) −1929.00 + 3341.13i −0.172019 + 0.297945i
\(502\) −10597.5 18355.4i −0.942210 1.63196i
\(503\) 12000.0 1.06372 0.531862 0.846831i \(-0.321492\pi\)
0.531862 + 0.846831i \(0.321492\pi\)
\(504\) −1690.50 + 8784.10i −0.149406 + 0.776339i
\(505\) 3420.00 0.301362
\(506\) 4657.50 + 8067.03i 0.409192 + 0.708741i
\(507\) 1284.00 2223.95i 0.112474 0.194811i
\(508\) −401.500 + 695.418i −0.0350663 + 0.0607366i
\(509\) 5841.00 + 10116.9i 0.508640 + 0.880990i 0.999950 + 0.0100055i \(0.00318492\pi\)
−0.491310 + 0.870985i \(0.663482\pi\)
\(510\) 1620.00 0.140656
\(511\) 11690.0 4049.53i 1.01201 0.350569i
\(512\) −8733.00 −0.753804
\(513\) 6050.00 + 10478.9i 0.520690 + 0.901862i
\(514\) 6120.00 10600.2i 0.525178 0.909635i
\(515\) 3790.00 6564.47i 0.324286 0.561680i
\(516\) −286.000 495.367i −0.0244001 0.0422622i
\(517\) −2025.00 −0.172262
\(518\) −13597.5 + 4710.31i −1.15336 + 0.399535i
\(519\) 1398.00 0.118238
\(520\) 3097.50 + 5365.03i 0.261220 + 0.452446i
\(521\) −4804.50 + 8321.64i −0.404010 + 0.699765i −0.994206 0.107495i \(-0.965717\pi\)
0.590196 + 0.807260i \(0.299050\pi\)
\(522\) −5589.00 + 9680.43i −0.468628 + 0.811688i
\(523\) −10594.0 18349.3i −0.885742 1.53415i −0.844860 0.534987i \(-0.820317\pi\)
−0.0408820 0.999164i \(-0.513017\pi\)
\(524\) 2019.00 0.168321
\(525\) 175.000 909.327i 0.0145479 0.0755929i
\(526\) −9864.00 −0.817663
\(527\) −2376.00 4115.35i −0.196395 0.340166i
\(528\) 3195.00 5533.90i 0.263342 0.456122i
\(529\) 3703.00 6413.78i 0.304348 0.527146i
\(530\) −4477.50 7755.26i −0.366963 0.635598i
\(531\) 8280.00 0.676688
\(532\) 1694.00 + 1467.05i 0.138053 + 0.119557i
\(533\) 11505.0 0.934966
\(534\) −3582.00 6204.21i −0.290278 0.502776i
\(535\) 1830.00 3169.65i 0.147884 0.256142i
\(536\) −2940.00 + 5092.23i −0.236919 + 0.410356i
\(537\) 3117.00 + 5398.80i 0.250481 + 0.433846i
\(538\) −9792.00 −0.784690
\(539\) 14332.5 + 5728.76i 1.14535 + 0.457802i
\(540\) 500.000 0.0398455
\(541\) −4036.00 6990.56i −0.320742 0.555541i 0.659900 0.751354i \(-0.270599\pi\)
−0.980641 + 0.195813i \(0.937265\pi\)
\(542\) 4128.00 7149.91i 0.327145 0.566632i
\(543\) −1798.00 + 3114.23i −0.142099 + 0.246122i
\(544\) −1215.00 2104.44i −0.0957586 0.165859i
\(545\) −8000.00 −0.628775
\(546\) 4956.00 + 4292.02i 0.388456 + 0.336413i
\(547\) 344.000 0.0268892 0.0134446 0.999910i \(-0.495720\pi\)
0.0134446 + 0.999910i \(0.495720\pi\)
\(548\) −30.0000 51.9615i −0.00233857 0.00405052i
\(549\) 4508.00 7808.09i 0.350449 0.606996i
\(550\) 1687.50 2922.84i 0.130828 0.226600i
\(551\) −9801.00 16975.8i −0.757780 1.31251i
\(552\) 2898.00 0.223455
\(553\) −2737.00 + 14221.9i −0.210468 + 1.09363i
\(554\) −14070.0 −1.07902
\(555\) −1295.00 2243.01i −0.0990445 0.171550i
\(556\) 854.000 1479.17i 0.0651397 0.112825i
\(557\) −9181.50 + 15902.8i −0.698443 + 1.20974i 0.270563 + 0.962702i \(0.412790\pi\)
−0.969006 + 0.247036i \(0.920543\pi\)
\(558\) −3036.00 5258.51i −0.230330 0.398943i
\(559\) −16874.0 −1.27673
\(560\) −6212.50 + 2152.07i −0.468797 + 0.162396i
\(561\) −4860.00 −0.365756
\(562\) −11731.5 20319.6i −0.880540 1.52514i
\(563\) 3147.00 5450.76i 0.235578 0.408033i −0.723863 0.689944i \(-0.757635\pi\)
0.959440 + 0.281912i \(0.0909685\pi\)
\(564\) 45.0000 77.9423i 0.00335965 0.00581908i
\(565\) 3480.00 + 6027.54i 0.259123 + 0.448815i
\(566\) −1974.00 −0.146596
\(567\) 7367.50 2552.18i 0.545689 0.189032i
\(568\) −1008.00 −0.0744626
\(569\) −5866.50 10161.1i −0.432226 0.748637i 0.564839 0.825201i \(-0.308938\pi\)
−0.997065 + 0.0765642i \(0.975605\pi\)
\(570\) −1815.00 + 3143.67i −0.133372 + 0.231007i
\(571\) −526.000 + 911.059i −0.0385506 + 0.0667717i −0.884657 0.466242i \(-0.845607\pi\)
0.846106 + 0.533014i \(0.178941\pi\)
\(572\) 1327.50 + 2299.30i 0.0970377 + 0.168074i
\(573\) 4776.00 0.348203
\(574\) −2047.50 + 10639.1i −0.148887 + 0.773638i
\(575\) 1725.00 0.125109
\(576\) 4979.50 + 8624.75i 0.360207 + 0.623897i
\(577\) 6578.00 11393.4i 0.474603 0.822036i −0.524974 0.851118i \(-0.675925\pi\)
0.999577 + 0.0290821i \(0.00925844\pi\)
\(578\) 2995.50 5188.36i 0.215565 0.373369i
\(579\) 272.000 + 471.118i 0.0195232 + 0.0338152i
\(580\) −810.000 −0.0579887
\(581\) −10752.0 9311.51i −0.767759 0.664899i
\(582\) −5412.00 −0.385455
\(583\) 13432.5 + 23265.8i 0.954232 + 1.65278i
\(584\) 7014.00 12148.6i 0.496989 0.860810i
\(585\) 3392.50 5875.98i 0.239765 0.415285i
\(586\) 8995.50 + 15580.7i 0.634131 + 1.09835i
\(587\) −13368.0 −0.939960 −0.469980 0.882677i \(-0.655739\pi\)
−0.469980 + 0.882677i \(0.655739\pi\)
\(588\) −539.000 + 424.352i −0.0378027 + 0.0297619i
\(589\) 10648.0 0.744895
\(590\) 2700.00 + 4676.54i 0.188402 + 0.326322i
\(591\) −2109.00 + 3652.90i −0.146790 + 0.254247i
\(592\) −9194.50 + 15925.3i −0.638330 + 1.10562i
\(593\) −13332.0 23091.7i −0.923237 1.59909i −0.794372 0.607431i \(-0.792200\pi\)
−0.128865 0.991662i \(-0.541133\pi\)
\(594\) −13500.0 −0.932511
\(595\) 3780.00 + 3273.58i 0.260445 + 0.225552i
\(596\) −1086.00 −0.0746381
\(597\) 1424.00 + 2466.44i 0.0976222 + 0.169087i
\(598\) −6106.50 + 10576.8i −0.417581 + 0.723271i
\(599\) −3807.00 + 6593.92i −0.259682 + 0.449783i −0.966157 0.257955i \(-0.916951\pi\)
0.706474 + 0.707739i \(0.250285\pi\)
\(600\) −525.000 909.327i −0.0357217 0.0618718i
\(601\) 6410.00 0.435057 0.217529 0.976054i \(-0.430200\pi\)
0.217529 + 0.976054i \(0.430200\pi\)
\(602\) 3003.00 15604.0i 0.203311 1.05643i
\(603\) 6440.00 0.434921
\(604\) 1433.00 + 2482.03i 0.0965363 + 0.167206i
\(605\) −1735.00 + 3005.11i −0.116591 + 0.201942i
\(606\) 2052.00 3554.17i 0.137552 0.238248i
\(607\) 10734.5 + 18592.7i 0.717792 + 1.24325i 0.961873 + 0.273498i \(0.0881806\pi\)
−0.244080 + 0.969755i \(0.578486\pi\)
\(608\) 5445.00 0.363197
\(609\) 5670.00 1964.15i 0.377274 0.130692i
\(610\) 5880.00 0.390286
\(611\) −1327.50 2299.30i −0.0878967 0.152242i
\(612\) −621.000 + 1075.60i −0.0410171 + 0.0710436i
\(613\) −1868.50 + 3236.34i −0.123113 + 0.213237i −0.920994 0.389578i \(-0.872621\pi\)
0.797881 + 0.602815i \(0.205954\pi\)
\(614\) 9339.00 + 16175.6i 0.613830 + 1.06318i
\(615\) −1950.00 −0.127856
\(616\) 16537.5 5728.76i 1.08168 0.374705i
\(617\) 18078.0 1.17957 0.589784 0.807561i \(-0.299213\pi\)
0.589784 + 0.807561i \(0.299213\pi\)
\(618\) −4548.00 7877.37i −0.296031 0.512741i
\(619\) −6143.50 + 10640.9i −0.398915 + 0.690940i −0.993592 0.113024i \(-0.963946\pi\)
0.594678 + 0.803964i \(0.297280\pi\)
\(620\) 220.000 381.051i 0.0142507 0.0246829i
\(621\) −3450.00 5975.58i −0.222937 0.386138i
\(622\) 14040.0 0.905069
\(623\) 4179.00 21714.7i 0.268745 1.39644i
\(624\) 8378.00 0.537481
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −1542.00 + 2670.82i −0.0984516 + 0.170523i
\(627\) 5445.00 9431.02i 0.346814 0.600699i
\(628\) 114.500 + 198.320i 0.00727555 + 0.0126016i
\(629\) 13986.0 0.886579
\(630\) 4830.00 + 4182.90i 0.305447 + 0.264525i
\(631\) −9580.00 −0.604396 −0.302198 0.953245i \(-0.597720\pi\)
−0.302198 + 0.953245i \(0.597720\pi\)
\(632\) 8211.00 + 14221.9i 0.516798 + 0.895120i
\(633\) −3625.00 + 6278.68i −0.227616 + 0.394242i
\(634\) −12933.0 + 22400.6i −0.810150 + 1.40322i
\(635\) −2007.50 3477.09i −0.125457 0.217298i
\(636\) −1194.00 −0.0744421
\(637\) 2891.00 + 20029.4i 0.179820 + 1.24583i
\(638\) 21870.0 1.35712
\(639\) 552.000 + 956.092i 0.0341734 + 0.0591900i
\(640\) −4147.50 + 7183.68i −0.256163 + 0.443687i
\(641\) −5389.50 + 9334.89i −0.332094 + 0.575204i −0.982922 0.184021i \(-0.941089\pi\)
0.650828 + 0.759225i \(0.274422\pi\)
\(642\) −2196.00 3803.58i −0.134999 0.233825i
\(643\) 8882.00 0.544746 0.272373 0.962192i \(-0.412191\pi\)
0.272373 + 0.962192i \(0.412191\pi\)
\(644\) −966.000 836.581i −0.0591083 0.0511893i
\(645\) 2860.00 0.174593
\(646\) −9801.00 16975.8i −0.596928 1.03391i
\(647\) 5509.50 9542.73i 0.334777 0.579851i −0.648665 0.761074i \(-0.724672\pi\)
0.983442 + 0.181223i \(0.0580056\pi\)
\(648\) 4420.50 7656.53i 0.267984 0.464162i
\(649\) −8100.00 14029.6i −0.489912 0.848552i
\(650\) 4425.00 0.267020
\(651\) −616.000 + 3200.83i −0.0370859 + 0.192704i
\(652\) −1228.00 −0.0737610
\(653\) −11161.5 19332.3i −0.668887 1.15855i −0.978216 0.207591i \(-0.933438\pi\)
0.309329 0.950955i \(-0.399896\pi\)
\(654\) −4800.00 + 8313.84i −0.286995 + 0.497090i
\(655\) −5047.50 + 8742.53i −0.301103 + 0.521525i
\(656\) 6922.50 + 11990.1i 0.412009 + 0.713621i
\(657\) −15364.0 −0.912339
\(658\) 2362.50 818.394i 0.139969 0.0484868i
\(659\) −11856.0 −0.700826 −0.350413 0.936595i \(-0.613959\pi\)
−0.350413 + 0.936595i \(0.613959\pi\)
\(660\) −225.000 389.711i −0.0132699 0.0229841i
\(661\) 16622.0 28790.1i 0.978095 1.69411i 0.308777 0.951134i \(-0.400080\pi\)
0.669318 0.742976i \(-0.266586\pi\)
\(662\) 2998.50 5193.55i 0.176042 0.304914i
\(663\) −3186.00 5518.31i −0.186627 0.323248i
\(664\) −16128.0 −0.942602
\(665\) −10587.5 + 3667.62i −0.617392 + 0.213871i
\(666\) 17871.0 1.03977
\(667\) 5589.00 + 9680.43i 0.324448 + 0.561961i
\(668\) 964.500 1670.56i 0.0558647 0.0967605i
\(669\) −4960.00 + 8590.97i −0.286644 + 0.496482i
\(670\) 2100.00 + 3637.31i 0.121090 + 0.209733i
\(671\) −17640.0 −1.01488
\(672\) −315.000 + 1636.79i −0.0180824 + 0.0939590i
\(673\) −12322.0 −0.705763 −0.352881 0.935668i \(-0.614798\pi\)
−0.352881 + 0.935668i \(0.614798\pi\)
\(674\) −7671.00 13286.6i −0.438392 0.759316i
\(675\) −1250.00 + 2165.06i −0.0712778 + 0.123457i
\(676\) −642.000 + 1111.98i −0.0365271 + 0.0632668i
\(677\) 6298.50 + 10909.3i 0.357564 + 0.619320i 0.987553 0.157285i \(-0.0502740\pi\)
−0.629989 + 0.776604i \(0.716941\pi\)
\(678\) 8352.00 0.473092
\(679\) −12628.0 10936.2i −0.713723 0.618103i
\(680\) 5670.00 0.319757
\(681\) −1500.00 2598.08i −0.0844055 0.146195i
\(682\) −5940.00 + 10288.4i −0.333511 + 0.577658i
\(683\) 4170.00 7222.65i 0.233617 0.404637i −0.725253 0.688483i \(-0.758277\pi\)
0.958870 + 0.283846i \(0.0916104\pi\)
\(684\) −1391.50 2410.15i −0.0777856 0.134729i
\(685\) 300.000 0.0167334
\(686\) −19036.5 891.140i −1.05950 0.0495975i
\(687\) −12184.0 −0.676636
\(688\) −10153.0 17585.5i −0.562616 0.974479i
\(689\) −17611.5 + 30504.0i −0.973795 + 1.68666i
\(690\) 1035.00 1792.67i 0.0571040 0.0989071i
\(691\) 10100.0 + 17493.7i 0.556038 + 0.963086i 0.997822 + 0.0659643i \(0.0210124\pi\)
−0.441784 + 0.897121i \(0.645654\pi\)
\(692\) −699.000 −0.0383988
\(693\) −14490.0 12548.7i −0.794271 0.687859i
\(694\) 12960.0 0.708869
\(695\) 4270.00 + 7395.86i 0.233051 + 0.403656i
\(696\) 3402.00 5892.44i 0.185277 0.320908i
\(697\) 5265.00 9119.25i 0.286121 0.495576i
\(698\) −11883.0 20582.0i −0.644381 1.11610i
\(699\) −276.000 −0.0149346
\(700\) −87.5000 + 454.663i −0.00472456 + 0.0245495i
\(701\) 474.000 0.0255388 0.0127694 0.999918i \(-0.495935\pi\)
0.0127694 + 0.999918i \(0.495935\pi\)
\(702\) −8850.00 15328.6i −0.475814 0.824135i
\(703\) −15669.5 + 27140.4i −0.840663 + 1.45607i
\(704\) 9742.50 16874.5i 0.521569 0.903383i
\(705\) 225.000 + 389.711i 0.0120198 + 0.0208190i
\(706\) 2484.00 0.132417
\(707\) 11970.0 4146.53i 0.636744 0.220575i
\(708\) 720.000 0.0382193
\(709\) 12563.0 + 21759.8i 0.665463 + 1.15262i 0.979160 + 0.203093i \(0.0650993\pi\)
−0.313696 + 0.949523i \(0.601567\pi\)
\(710\) −360.000 + 623.538i −0.0190290 + 0.0329591i
\(711\) 8993.00 15576.3i 0.474351 0.821601i
\(712\) −12537.0 21714.7i −0.659893 1.14297i
\(713\) −6072.00 −0.318932
\(714\) 5670.00 1964.15i 0.297191 0.102950i
\(715\) −13275.0 −0.694345
\(716\) −1558.50 2699.40i −0.0813462 0.140896i
\(717\) −5502.00 + 9529.74i −0.286577 + 0.496367i
\(718\) 2025.00 3507.40i 0.105254 0.182305i
\(719\) 3648.00 + 6318.52i 0.189218 + 0.327734i 0.944990 0.327100i \(-0.106072\pi\)
−0.755772 + 0.654835i \(0.772738\pi\)
\(720\) 8165.00 0.422627
\(721\) 5306.00 27570.8i 0.274072 1.42412i
\(722\) 23346.0 1.20339
\(723\) 3551.00 + 6150.51i 0.182660 + 0.316376i
\(724\) 899.000 1557.11i 0.0461479 0.0799305i
\(725\) 2025.00 3507.40i 0.103733 0.179671i
\(726\) 2082.00 + 3606.13i 0.106433 + 0.184347i
\(727\) −15421.0 −0.786703 −0.393352 0.919388i \(-0.628684\pi\)
−0.393352 + 0.919388i \(0.628684\pi\)
\(728\) 17346.0 + 15022.1i 0.883085 + 0.764774i
\(729\) −4283.00 −0.217599
\(730\) −5010.00 8677.57i −0.254012 0.439961i
\(731\) −7722.00 + 13374.9i −0.390709 + 0.676728i
\(732\) 392.000 678.964i 0.0197934 0.0342831i
\(733\) 14583.5 + 25259.4i 0.734862 + 1.27282i 0.954784 + 0.297301i \(0.0960864\pi\)
−0.219922 + 0.975517i \(0.570580\pi\)
\(734\) 8403.00 0.422562
\(735\) −490.000 3394.82i −0.0245904 0.170367i
\(736\) −3105.00 −0.155505
\(737\) −6300.00 10911.9i −0.314876 0.545381i
\(738\) 6727.50 11652.4i 0.335559 0.581206i
\(739\) 6690.50 11588.3i 0.333037 0.576836i −0.650069 0.759875i \(-0.725260\pi\)
0.983106 + 0.183039i \(0.0585934\pi\)
\(740\) 647.500 + 1121.50i 0.0321656 + 0.0557125i
\(741\) 14278.0 0.707848
\(742\) −25074.0 21714.7i −1.24056 1.07436i
\(743\) 5487.00 0.270927 0.135463 0.990782i \(-0.456748\pi\)
0.135463 + 0.990782i \(0.456748\pi\)
\(744\) 1848.00 + 3200.83i 0.0910631 + 0.157726i
\(745\) 2715.00 4702.52i 0.133517 0.231258i
\(746\) −9903.00 + 17152.5i −0.486025 + 0.841820i
\(747\) 8832.00 + 15297.5i 0.432592 + 0.749271i
\(748\) 2430.00 0.118783
\(749\) 2562.00 13312.5i 0.124985 0.649439i
\(750\) −750.000 −0.0365148
\(751\) −3319.00 5748.68i −0.161268 0.279324i 0.774056 0.633117i \(-0.218225\pi\)
−0.935324 + 0.353793i \(0.884892\pi\)
\(752\) 1597.50 2766.95i 0.0774665 0.134176i
\(753\) 7065.00 12236.9i 0.341916 0.592216i
\(754\) 14337.0 + 24832.4i 0.692470 + 1.19939i
\(755\) −14330.0 −0.690758
\(756\) 1750.00 606.218i 0.0841890 0.0291639i
\(757\) 14846.0 0.712797 0.356398 0.934334i \(-0.384005\pi\)
0.356398 + 0.934334i \(0.384005\pi\)
\(758\) 12457.5 + 21577.0i 0.596935 + 1.03392i
\(759\) −3105.00 + 5378.02i −0.148491 + 0.257193i
\(760\) −6352.50 + 11002.9i −0.303197 + 0.525152i
\(761\) 1825.50 + 3161.86i 0.0869571 + 0.150614i 0.906223 0.422799i \(-0.138952\pi\)
−0.819266 + 0.573413i \(0.805619\pi\)
\(762\) −4818.00 −0.229052
\(763\) −28000.0 + 9699.48i −1.32853 + 0.460216i
\(764\) −2388.00 −0.113082
\(765\) −3105.00 5378.02i −0.146747 0.254173i
\(766\) −1417.50 + 2455.18i −0.0668621 + 0.115809i
\(767\) 10620.0 18394.4i 0.499956 0.865949i
\(768\) 1513.00 + 2620.59i 0.0710881 + 0.123128i
\(769\) 29855.0 1.40000 0.699999 0.714144i \(-0.253184\pi\)
0.699999 + 0.714144i \(0.253184\pi\)
\(770\) 2362.50 12275.9i 0.110570 0.574536i
\(771\) 8160.00 0.381161