Properties

Label 300.5.c.c.151.13
Level $300$
Weight $5$
Character 300.151
Analytic conductor $31.011$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(31.0109889252\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + 234752 x^{8} - 632832 x^{7} + 1884160 x^{6} - 8847360 x^{5} + 32243712 x^{4} - 113246208 x^{3} + 335544320 x^{2} - 1610612736 x + 4294967296\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.13
Root \(3.79586 - 1.26152i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.5.c.c.151.14

$q$-expansion

\(f(q)\) \(=\) \(q+(2.99044 - 2.65655i) q^{2} +5.19615i q^{3} +(1.88545 - 15.8885i) q^{4} +(13.8039 + 15.5388i) q^{6} -74.3539i q^{7} +(-36.5704 - 52.5224i) q^{8} -27.0000 q^{9} +O(q^{10})\) \(q+(2.99044 - 2.65655i) q^{2} +5.19615i q^{3} +(1.88545 - 15.8885i) q^{4} +(13.8039 + 15.5388i) q^{6} -74.3539i q^{7} +(-36.5704 - 52.5224i) q^{8} -27.0000 q^{9} +107.360i q^{11} +(82.5592 + 9.79706i) q^{12} -30.7085 q^{13} +(-197.525 - 222.351i) q^{14} +(-248.890 - 59.9139i) q^{16} -292.805 q^{17} +(-80.7418 + 71.7269i) q^{18} -357.767i q^{19} +386.354 q^{21} +(285.207 + 321.053i) q^{22} +488.885i q^{23} +(272.915 - 190.025i) q^{24} +(-91.8318 + 81.5787i) q^{26} -140.296i q^{27} +(-1181.37 - 140.190i) q^{28} -1035.75 q^{29} +411.471i q^{31} +(-903.455 + 482.021i) q^{32} -557.858 q^{33} +(-875.616 + 777.852i) q^{34} +(-50.9070 + 428.990i) q^{36} +1506.64 q^{37} +(-950.428 - 1069.88i) q^{38} -159.566i q^{39} -2003.19 q^{41} +(1155.37 - 1026.37i) q^{42} -3279.91i q^{43} +(1705.79 + 202.421i) q^{44} +(1298.75 + 1461.98i) q^{46} -1602.96i q^{47} +(311.322 - 1293.27i) q^{48} -3127.50 q^{49} -1521.46i q^{51} +(-57.8991 + 487.912i) q^{52} -4381.56 q^{53} +(-372.704 - 419.547i) q^{54} +(-3905.25 + 2719.15i) q^{56} +1859.01 q^{57} +(-3097.35 + 2751.53i) q^{58} +851.518i q^{59} -5539.08 q^{61} +(1093.09 + 1230.48i) q^{62} +2007.55i q^{63} +(-1421.21 + 3841.53i) q^{64} +(-1668.24 + 1481.98i) q^{66} -4189.05i q^{67} +(-552.068 + 4652.24i) q^{68} -2540.32 q^{69} -6302.56i q^{71} +(987.401 + 1418.11i) q^{72} +7030.68 q^{73} +(4505.52 - 4002.48i) q^{74} +(-5684.40 - 674.551i) q^{76} +7982.62 q^{77} +(-423.895 - 477.172i) q^{78} +7014.54i q^{79} +729.000 q^{81} +(-5990.42 + 5321.58i) q^{82} +9127.59i q^{83} +(728.449 - 6138.59i) q^{84} +(-8713.26 - 9808.37i) q^{86} -5381.92i q^{87} +(5638.80 - 3926.19i) q^{88} +3180.88 q^{89} +2283.29i q^{91} +(7767.67 + 921.767i) q^{92} -2138.07 q^{93} +(-4258.35 - 4793.55i) q^{94} +(-2504.66 - 4694.49i) q^{96} +12299.4 q^{97} +(-9352.59 + 8308.37i) q^{98} -2898.72i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + O(q^{10}) \) \( 16q + 6q^{2} + 8q^{4} + 18q^{6} - 180q^{8} - 432q^{9} + 176q^{13} + 78q^{14} - 376q^{16} - 162q^{18} - 144q^{21} - 788q^{22} + 108q^{24} + 678q^{26} + 3368q^{28} + 1728q^{29} + 2016q^{32} - 2932q^{34} - 216q^{36} - 1568q^{37} - 6990q^{38} + 1248q^{41} + 162q^{42} + 8088q^{44} + 5956q^{46} + 2088q^{48} - 10720q^{49} + 3128q^{52} - 288q^{53} - 486q^{54} - 10236q^{56} + 5616q^{57} - 16164q^{58} - 3760q^{61} - 12714q^{62} + 10544q^{64} + 8100q^{66} + 26136q^{68} + 9792q^{69} + 4860q^{72} + 11040q^{73} - 17004q^{74} - 28344q^{76} + 768q^{77} - 16830q^{78} + 11664q^{81} - 21280q^{82} + 15120q^{84} + 24414q^{86} + 52840q^{88} - 768q^{89} + 23736q^{92} - 9936q^{93} - 45156q^{94} - 11088q^{96} + 7248q^{97} - 58140q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.99044 2.65655i 0.747610 0.664138i
\(3\) 5.19615i 0.577350i
\(4\) 1.88545 15.8885i 0.117840 0.993033i
\(5\) 0 0
\(6\) 13.8039 + 15.5388i 0.383440 + 0.431633i
\(7\) 74.3539i 1.51743i −0.651425 0.758713i \(-0.725829\pi\)
0.651425 0.758713i \(-0.274171\pi\)
\(8\) −36.5704 52.5224i −0.571413 0.820663i
\(9\) −27.0000 −0.333333
\(10\) 0 0
\(11\) 107.360i 0.887271i 0.896207 + 0.443636i \(0.146312\pi\)
−0.896207 + 0.443636i \(0.853688\pi\)
\(12\) 82.5592 + 9.79706i 0.573328 + 0.0680351i
\(13\) −30.7085 −0.181707 −0.0908535 0.995864i \(-0.528959\pi\)
−0.0908535 + 0.995864i \(0.528959\pi\)
\(14\) −197.525 222.351i −1.00778 1.13444i
\(15\) 0 0
\(16\) −248.890 59.9139i −0.972227 0.234039i
\(17\) −292.805 −1.01317 −0.506583 0.862191i \(-0.669092\pi\)
−0.506583 + 0.862191i \(0.669092\pi\)
\(18\) −80.7418 + 71.7269i −0.249203 + 0.221379i
\(19\) 357.767i 0.991046i −0.868595 0.495523i \(-0.834977\pi\)
0.868595 0.495523i \(-0.165023\pi\)
\(20\) 0 0
\(21\) 386.354 0.876086
\(22\) 285.207 + 321.053i 0.589271 + 0.663333i
\(23\) 488.885i 0.924169i 0.886836 + 0.462084i \(0.152898\pi\)
−0.886836 + 0.462084i \(0.847102\pi\)
\(24\) 272.915 190.025i 0.473810 0.329905i
\(25\) 0 0
\(26\) −91.8318 + 81.5787i −0.135846 + 0.120679i
\(27\) 140.296i 0.192450i
\(28\) −1181.37 140.190i −1.50685 0.178814i
\(29\) −1035.75 −1.23157 −0.615785 0.787914i \(-0.711161\pi\)
−0.615785 + 0.787914i \(0.711161\pi\)
\(30\) 0 0
\(31\) 411.471i 0.428169i 0.976815 + 0.214085i \(0.0686769\pi\)
−0.976815 + 0.214085i \(0.931323\pi\)
\(32\) −903.455 + 482.021i −0.882280 + 0.470724i
\(33\) −557.858 −0.512266
\(34\) −875.616 + 777.852i −0.757453 + 0.672883i
\(35\) 0 0
\(36\) −50.9070 + 428.990i −0.0392801 + 0.331011i
\(37\) 1506.64 1.10054 0.550272 0.834986i \(-0.314524\pi\)
0.550272 + 0.834986i \(0.314524\pi\)
\(38\) −950.428 1069.88i −0.658191 0.740915i
\(39\) 159.566i 0.104909i
\(40\) 0 0
\(41\) −2003.19 −1.19167 −0.595833 0.803108i \(-0.703178\pi\)
−0.595833 + 0.803108i \(0.703178\pi\)
\(42\) 1155.37 1026.37i 0.654971 0.581843i
\(43\) 3279.91i 1.77388i −0.461882 0.886942i \(-0.652825\pi\)
0.461882 0.886942i \(-0.347175\pi\)
\(44\) 1705.79 + 202.421i 0.881089 + 0.104556i
\(45\) 0 0
\(46\) 1298.75 + 1461.98i 0.613776 + 0.690918i
\(47\) 1602.96i 0.725650i −0.931857 0.362825i \(-0.881812\pi\)
0.931857 0.362825i \(-0.118188\pi\)
\(48\) 311.322 1293.27i 0.135122 0.561316i
\(49\) −3127.50 −1.30258
\(50\) 0 0
\(51\) 1521.46i 0.584952i
\(52\) −57.8991 + 487.912i −0.0214124 + 0.180441i
\(53\) −4381.56 −1.55983 −0.779915 0.625885i \(-0.784738\pi\)
−0.779915 + 0.625885i \(0.784738\pi\)
\(54\) −372.704 419.547i −0.127813 0.143878i
\(55\) 0 0
\(56\) −3905.25 + 2719.15i −1.24530 + 0.867076i
\(57\) 1859.01 0.572180
\(58\) −3097.35 + 2751.53i −0.920734 + 0.817933i
\(59\) 851.518i 0.244619i 0.992492 + 0.122309i \(0.0390300\pi\)
−0.992492 + 0.122309i \(0.960970\pi\)
\(60\) 0 0
\(61\) −5539.08 −1.48860 −0.744300 0.667845i \(-0.767217\pi\)
−0.744300 + 0.667845i \(0.767217\pi\)
\(62\) 1093.09 + 1230.48i 0.284364 + 0.320104i
\(63\) 2007.55i 0.505809i
\(64\) −1421.21 + 3841.53i −0.346975 + 0.937874i
\(65\) 0 0
\(66\) −1668.24 + 1481.98i −0.382975 + 0.340216i
\(67\) 4189.05i 0.933181i −0.884473 0.466590i \(-0.845482\pi\)
0.884473 0.466590i \(-0.154518\pi\)
\(68\) −552.068 + 4652.24i −0.119392 + 1.00611i
\(69\) −2540.32 −0.533569
\(70\) 0 0
\(71\) 6302.56i 1.25026i −0.780521 0.625130i \(-0.785046\pi\)
0.780521 0.625130i \(-0.214954\pi\)
\(72\) 987.401 + 1418.11i 0.190471 + 0.273554i
\(73\) 7030.68 1.31933 0.659663 0.751562i \(-0.270699\pi\)
0.659663 + 0.751562i \(0.270699\pi\)
\(74\) 4505.52 4002.48i 0.822777 0.730913i
\(75\) 0 0
\(76\) −5684.40 674.551i −0.984140 0.116785i
\(77\) 7982.62 1.34637
\(78\) −423.895 477.172i −0.0696738 0.0784306i
\(79\) 7014.54i 1.12395i 0.827156 + 0.561973i \(0.189957\pi\)
−0.827156 + 0.561973i \(0.810043\pi\)
\(80\) 0 0
\(81\) 729.000 0.111111
\(82\) −5990.42 + 5321.58i −0.890901 + 0.791431i
\(83\) 9127.59i 1.32495i 0.749083 + 0.662476i \(0.230494\pi\)
−0.749083 + 0.662476i \(0.769506\pi\)
\(84\) 728.449 6138.59i 0.103238 0.869982i
\(85\) 0 0
\(86\) −8713.26 9808.37i −1.17810 1.32617i
\(87\) 5381.92i 0.711048i
\(88\) 5638.80 3926.19i 0.728151 0.506998i
\(89\) 3180.88 0.401575 0.200788 0.979635i \(-0.435650\pi\)
0.200788 + 0.979635i \(0.435650\pi\)
\(90\) 0 0
\(91\) 2283.29i 0.275727i
\(92\) 7767.67 + 921.767i 0.917730 + 0.108904i
\(93\) −2138.07 −0.247204
\(94\) −4258.35 4793.55i −0.481932 0.542503i
\(95\) 0 0
\(96\) −2504.66 4694.49i −0.271773 0.509385i
\(97\) 12299.4 1.30720 0.653600 0.756840i \(-0.273258\pi\)
0.653600 + 0.756840i \(0.273258\pi\)
\(98\) −9352.59 + 8308.37i −0.973822 + 0.865094i
\(99\) 2898.72i 0.295757i
\(100\) 0 0
\(101\) 8454.27 0.828769 0.414385 0.910102i \(-0.363997\pi\)
0.414385 + 0.910102i \(0.363997\pi\)
\(102\) −4041.84 4549.83i −0.388489 0.437316i
\(103\) 12655.1i 1.19287i −0.802662 0.596435i \(-0.796584\pi\)
0.802662 0.596435i \(-0.203416\pi\)
\(104\) 1123.02 + 1612.88i 0.103830 + 0.149120i
\(105\) 0 0
\(106\) −13102.8 + 11639.9i −1.16614 + 1.03594i
\(107\) 6961.91i 0.608080i −0.952659 0.304040i \(-0.901664\pi\)
0.952659 0.304040i \(-0.0983357\pi\)
\(108\) −2229.10 264.521i −0.191109 0.0226784i
\(109\) −10686.8 −0.899489 −0.449744 0.893157i \(-0.648485\pi\)
−0.449744 + 0.893157i \(0.648485\pi\)
\(110\) 0 0
\(111\) 7828.75i 0.635399i
\(112\) −4454.83 + 18505.9i −0.355136 + 1.47528i
\(113\) 18780.7 1.47080 0.735402 0.677632i \(-0.236994\pi\)
0.735402 + 0.677632i \(0.236994\pi\)
\(114\) 5559.27 4938.57i 0.427768 0.380007i
\(115\) 0 0
\(116\) −1952.85 + 16456.5i −0.145129 + 1.22299i
\(117\) 829.129 0.0605690
\(118\) 2262.10 + 2546.41i 0.162461 + 0.182879i
\(119\) 21771.2i 1.53740i
\(120\) 0 0
\(121\) 3114.87 0.212750
\(122\) −16564.3 + 14714.9i −1.11289 + 0.988637i
\(123\) 10408.9i 0.688009i
\(124\) 6537.66 + 775.806i 0.425186 + 0.0504556i
\(125\) 0 0
\(126\) 5333.18 + 6003.47i 0.335927 + 0.378147i
\(127\) 4370.53i 0.270974i 0.990779 + 0.135487i \(0.0432598\pi\)
−0.990779 + 0.135487i \(0.956740\pi\)
\(128\) 5955.19 + 15263.4i 0.363476 + 0.931604i
\(129\) 17042.9 1.02415
\(130\) 0 0
\(131\) 20280.0i 1.18175i −0.806763 0.590875i \(-0.798783\pi\)
0.806763 0.590875i \(-0.201217\pi\)
\(132\) −1051.81 + 8863.54i −0.0603656 + 0.508697i
\(133\) −26601.4 −1.50384
\(134\) −11128.4 12527.1i −0.619761 0.697655i
\(135\) 0 0
\(136\) 10708.0 + 15378.8i 0.578936 + 0.831468i
\(137\) 25989.4 1.38470 0.692349 0.721563i \(-0.256576\pi\)
0.692349 + 0.721563i \(0.256576\pi\)
\(138\) −7596.68 + 6748.50i −0.398901 + 0.354364i
\(139\) 21049.3i 1.08945i 0.838614 + 0.544726i \(0.183366\pi\)
−0.838614 + 0.544726i \(0.816634\pi\)
\(140\) 0 0
\(141\) 8329.22 0.418954
\(142\) −16743.1 18847.4i −0.830346 0.934707i
\(143\) 3296.86i 0.161223i
\(144\) 6720.04 + 1617.67i 0.324076 + 0.0780128i
\(145\) 0 0
\(146\) 21024.8 18677.4i 0.986340 0.876214i
\(147\) 16251.0i 0.752046i
\(148\) 2840.69 23938.3i 0.129688 1.09288i
\(149\) −19502.4 −0.878447 −0.439223 0.898378i \(-0.644746\pi\)
−0.439223 + 0.898378i \(0.644746\pi\)
\(150\) 0 0
\(151\) 33284.1i 1.45977i −0.683572 0.729883i \(-0.739574\pi\)
0.683572 0.729883i \(-0.260426\pi\)
\(152\) −18790.8 + 13083.7i −0.813314 + 0.566296i
\(153\) 7905.74 0.337722
\(154\) 23871.5 21206.3i 1.00656 0.894175i
\(155\) 0 0
\(156\) −2535.27 300.853i −0.104178 0.0123625i
\(157\) −10857.6 −0.440487 −0.220243 0.975445i \(-0.570685\pi\)
−0.220243 + 0.975445i \(0.570685\pi\)
\(158\) 18634.5 + 20976.6i 0.746455 + 0.840272i
\(159\) 22767.3i 0.900568i
\(160\) 0 0
\(161\) 36350.5 1.40236
\(162\) 2180.03 1936.63i 0.0830677 0.0737932i
\(163\) 28923.6i 1.08862i −0.838883 0.544311i \(-0.816791\pi\)
0.838883 0.544311i \(-0.183209\pi\)
\(164\) −3776.91 + 31827.7i −0.140426 + 1.18336i
\(165\) 0 0
\(166\) 24247.9 + 27295.5i 0.879951 + 0.990546i
\(167\) 31156.8i 1.11717i −0.829447 0.558585i \(-0.811344\pi\)
0.829447 0.558585i \(-0.188656\pi\)
\(168\) −14129.1 20292.3i −0.500607 0.718972i
\(169\) −27618.0 −0.966983
\(170\) 0 0
\(171\) 9659.72i 0.330349i
\(172\) −52112.9 6184.09i −1.76152 0.209035i
\(173\) 11118.3 0.371489 0.185744 0.982598i \(-0.440530\pi\)
0.185744 + 0.982598i \(0.440530\pi\)
\(174\) −14297.4 16094.3i −0.472234 0.531586i
\(175\) 0 0
\(176\) 6432.34 26720.8i 0.207656 0.862629i
\(177\) −4424.62 −0.141231
\(178\) 9512.22 8450.18i 0.300222 0.266702i
\(179\) 8347.18i 0.260515i 0.991480 + 0.130258i \(0.0415805\pi\)
−0.991480 + 0.130258i \(0.958420\pi\)
\(180\) 0 0
\(181\) 54703.3 1.66977 0.834885 0.550425i \(-0.185534\pi\)
0.834885 + 0.550425i \(0.185534\pi\)
\(182\) 6065.69 + 6828.05i 0.183121 + 0.206136i
\(183\) 28781.9i 0.859444i
\(184\) 25677.4 17878.7i 0.758431 0.528082i
\(185\) 0 0
\(186\) −6393.75 + 5679.88i −0.184812 + 0.164178i
\(187\) 31435.5i 0.898953i
\(188\) −25468.7 3022.29i −0.720594 0.0855108i
\(189\) −10431.6 −0.292029
\(190\) 0 0
\(191\) 170.614i 0.00467678i 0.999997 + 0.00233839i \(0.000744333\pi\)
−0.999997 + 0.00233839i \(0.999256\pi\)
\(192\) −19961.2 7384.83i −0.541482 0.200326i
\(193\) 38429.3 1.03169 0.515843 0.856683i \(-0.327479\pi\)
0.515843 + 0.856683i \(0.327479\pi\)
\(194\) 36780.7 32674.1i 0.977276 0.868162i
\(195\) 0 0
\(196\) −5896.73 + 49691.3i −0.153497 + 1.29351i
\(197\) −47014.6 −1.21143 −0.605717 0.795680i \(-0.707114\pi\)
−0.605717 + 0.795680i \(0.707114\pi\)
\(198\) −7700.59 8668.43i −0.196424 0.221111i
\(199\) 49175.8i 1.24178i −0.783897 0.620891i \(-0.786771\pi\)
0.783897 0.620891i \(-0.213229\pi\)
\(200\) 0 0
\(201\) 21766.9 0.538772
\(202\) 25282.0 22459.2i 0.619596 0.550417i
\(203\) 77012.1i 1.86882i
\(204\) −24173.7 2868.63i −0.580876 0.0689309i
\(205\) 0 0
\(206\) −33619.1 37844.4i −0.792230 0.891800i
\(207\) 13199.9i 0.308056i
\(208\) 7643.04 + 1839.86i 0.176660 + 0.0425264i
\(209\) 38409.8 0.879326
\(210\) 0 0
\(211\) 4500.34i 0.101084i −0.998722 0.0505418i \(-0.983905\pi\)
0.998722 0.0505418i \(-0.0160948\pi\)
\(212\) −8261.20 + 69616.6i −0.183811 + 1.54896i
\(213\) 32749.1 0.721838
\(214\) −18494.7 20819.2i −0.403849 0.454607i
\(215\) 0 0
\(216\) −7368.69 + 5130.69i −0.157937 + 0.109968i
\(217\) 30594.4 0.649715
\(218\) −31958.3 + 28390.1i −0.672466 + 0.597385i
\(219\) 36532.5i 0.761713i
\(220\) 0 0
\(221\) 8991.60 0.184099
\(222\) 20797.5 + 23411.4i 0.421993 + 0.475030i
\(223\) 480.278i 0.00965790i 0.999988 + 0.00482895i \(0.00153711\pi\)
−0.999988 + 0.00482895i \(0.998463\pi\)
\(224\) 35840.2 + 67175.4i 0.714289 + 1.33880i
\(225\) 0 0
\(226\) 56162.5 49891.9i 1.09959 0.976817i
\(227\) 38994.8i 0.756754i 0.925652 + 0.378377i \(0.123518\pi\)
−0.925652 + 0.378377i \(0.876482\pi\)
\(228\) 3505.07 29537.0i 0.0674259 0.568194i
\(229\) 27569.4 0.525723 0.262861 0.964834i \(-0.415334\pi\)
0.262861 + 0.964834i \(0.415334\pi\)
\(230\) 0 0
\(231\) 41478.9i 0.777326i
\(232\) 37877.8 + 54400.1i 0.703735 + 1.01070i
\(233\) 42015.1 0.773915 0.386957 0.922098i \(-0.373526\pi\)
0.386957 + 0.922098i \(0.373526\pi\)
\(234\) 2479.46 2202.63i 0.0452820 0.0402262i
\(235\) 0 0
\(236\) 13529.4 + 1605.49i 0.242914 + 0.0288260i
\(237\) −36448.6 −0.648910
\(238\) 57836.3 + 65105.4i 1.02105 + 1.14938i
\(239\) 93158.6i 1.63090i 0.578828 + 0.815450i \(0.303510\pi\)
−0.578828 + 0.815450i \(0.696490\pi\)
\(240\) 0 0
\(241\) −108882. −1.87466 −0.937328 0.348447i \(-0.886709\pi\)
−0.937328 + 0.348447i \(0.886709\pi\)
\(242\) 9314.82 8274.81i 0.159054 0.141295i
\(243\) 3788.00i 0.0641500i
\(244\) −10443.6 + 88007.8i −0.175417 + 1.47823i
\(245\) 0 0
\(246\) −27651.8 31127.1i −0.456933 0.514362i
\(247\) 10986.5i 0.180080i
\(248\) 21611.4 15047.7i 0.351383 0.244661i
\(249\) −47428.3 −0.764961
\(250\) 0 0
\(251\) 31606.9i 0.501689i −0.968027 0.250845i \(-0.919292\pi\)
0.968027 0.250845i \(-0.0807083\pi\)
\(252\) 31897.1 + 3785.13i 0.502284 + 0.0596047i
\(253\) −52486.6 −0.819989
\(254\) 11610.6 + 13069.8i 0.179964 + 0.202582i
\(255\) 0 0
\(256\) 58356.7 + 29823.9i 0.890452 + 0.455077i
\(257\) −20019.5 −0.303101 −0.151550 0.988450i \(-0.548427\pi\)
−0.151550 + 0.988450i \(0.548427\pi\)
\(258\) 50965.8 45275.4i 0.765666 0.680179i
\(259\) 112025.i 1.66999i
\(260\) 0 0
\(261\) 27965.3 0.410523
\(262\) −53875.0 60646.2i −0.784846 0.883488i
\(263\) 62700.2i 0.906478i 0.891389 + 0.453239i \(0.149732\pi\)
−0.891389 + 0.453239i \(0.850268\pi\)
\(264\) 20401.1 + 29300.1i 0.292715 + 0.420398i
\(265\) 0 0
\(266\) −79549.8 + 70668.0i −1.12428 + 0.998757i
\(267\) 16528.3i 0.231850i
\(268\) −66557.8 7898.22i −0.926679 0.109966i
\(269\) 33804.6 0.467166 0.233583 0.972337i \(-0.424955\pi\)
0.233583 + 0.972337i \(0.424955\pi\)
\(270\) 0 0
\(271\) 56181.7i 0.764991i −0.923957 0.382496i \(-0.875065\pi\)
0.923957 0.382496i \(-0.124935\pi\)
\(272\) 72876.3 + 17543.1i 0.985028 + 0.237120i
\(273\) −11864.3 −0.159191
\(274\) 77719.7 69042.2i 1.03521 0.919631i
\(275\) 0 0
\(276\) −4789.64 + 40362.0i −0.0628760 + 0.529852i
\(277\) 121560. 1.58428 0.792141 0.610338i \(-0.208966\pi\)
0.792141 + 0.610338i \(0.208966\pi\)
\(278\) 55918.6 + 62946.7i 0.723547 + 0.814485i
\(279\) 11109.7i 0.142723i
\(280\) 0 0
\(281\) −51790.9 −0.655905 −0.327952 0.944694i \(-0.606359\pi\)
−0.327952 + 0.944694i \(0.606359\pi\)
\(282\) 24908.0 22127.0i 0.313214 0.278243i
\(283\) 126660.i 1.58149i −0.612149 0.790743i \(-0.709695\pi\)
0.612149 0.790743i \(-0.290305\pi\)
\(284\) −100138. 11883.1i −1.24155 0.147331i
\(285\) 0 0
\(286\) −8758.28 9859.05i −0.107075 0.120532i
\(287\) 148945.i 1.80826i
\(288\) 24393.3 13014.6i 0.294093 0.156908i
\(289\) 2213.80 0.0265059
\(290\) 0 0
\(291\) 63909.8i 0.754712i
\(292\) 13256.0 111707.i 0.155470 1.31013i
\(293\) −5958.17 −0.0694029 −0.0347014 0.999398i \(-0.511048\pi\)
−0.0347014 + 0.999398i \(0.511048\pi\)
\(294\) −43171.5 48597.5i −0.499462 0.562237i
\(295\) 0 0
\(296\) −55098.6 79132.6i −0.628864 0.903175i
\(297\) 15062.2 0.170755
\(298\) −58320.7 + 51809.2i −0.656735 + 0.583410i
\(299\) 15012.9i 0.167928i
\(300\) 0 0
\(301\) −243874. −2.69174
\(302\) −88421.1 99534.1i −0.969487 1.09134i
\(303\) 43929.7i 0.478490i
\(304\) −21435.2 + 89044.8i −0.231943 + 0.963522i
\(305\) 0 0
\(306\) 23641.6 21002.0i 0.252484 0.224294i
\(307\) 78071.0i 0.828348i 0.910198 + 0.414174i \(0.135930\pi\)
−0.910198 + 0.414174i \(0.864070\pi\)
\(308\) 15050.8 126832.i 0.158656 1.33699i
\(309\) 65758.1 0.688703
\(310\) 0 0
\(311\) 36755.5i 0.380016i 0.981783 + 0.190008i \(0.0608514\pi\)
−0.981783 + 0.190008i \(0.939149\pi\)
\(312\) −8380.79 + 5835.39i −0.0860946 + 0.0599461i
\(313\) −169020. −1.72524 −0.862619 0.505854i \(-0.831177\pi\)
−0.862619 + 0.505854i \(0.831177\pi\)
\(314\) −32468.8 + 28843.7i −0.329312 + 0.292544i
\(315\) 0 0
\(316\) 111451. + 13225.5i 1.11611 + 0.132446i
\(317\) −129820. −1.29188 −0.645939 0.763389i \(-0.723534\pi\)
−0.645939 + 0.763389i \(0.723534\pi\)
\(318\) −60482.5 68084.1i −0.598102 0.673274i
\(319\) 111198.i 1.09274i
\(320\) 0 0
\(321\) 36175.1 0.351075
\(322\) 108704. 96567.1i 1.04842 0.931360i
\(323\) 104756.i 1.00409i
\(324\) 1374.49 11582.7i 0.0130934 0.110337i
\(325\) 0 0
\(326\) −76837.1 86494.3i −0.722996 0.813865i
\(327\) 55530.4i 0.519320i
\(328\) 73257.5 + 105212.i 0.680933 + 0.977956i
\(329\) −119186. −1.10112
\(330\) 0 0
\(331\) 58912.8i 0.537717i 0.963180 + 0.268858i \(0.0866463\pi\)
−0.963180 + 0.268858i \(0.913354\pi\)
\(332\) 145024. + 17209.6i 1.31572 + 0.156133i
\(333\) −40679.4 −0.366848
\(334\) −82769.6 93172.4i −0.741956 0.835208i
\(335\) 0 0
\(336\) −96159.7 23148.0i −0.851755 0.205038i
\(337\) 46849.1 0.412517 0.206258 0.978498i \(-0.433871\pi\)
0.206258 + 0.978498i \(0.433871\pi\)
\(338\) −82589.9 + 73368.7i −0.722925 + 0.642210i
\(339\) 97587.3i 0.849169i
\(340\) 0 0
\(341\) −44175.4 −0.379902
\(342\) 25661.6 + 28886.8i 0.219397 + 0.246972i
\(343\) 54017.9i 0.459145i
\(344\) −172269. + 119948.i −1.45576 + 1.01362i
\(345\) 0 0
\(346\) 33248.6 29536.3i 0.277729 0.246720i
\(347\) 170481.i 1.41585i −0.706290 0.707923i \(-0.749632\pi\)
0.706290 0.707923i \(-0.250368\pi\)
\(348\) −85510.7 10147.3i −0.706093 0.0837901i
\(349\) 93820.0 0.770273 0.385136 0.922860i \(-0.374154\pi\)
0.385136 + 0.922860i \(0.374154\pi\)
\(350\) 0 0
\(351\) 4308.28i 0.0349695i
\(352\) −51749.7 96994.8i −0.417660 0.782822i
\(353\) −150254. −1.20581 −0.602903 0.797814i \(-0.705989\pi\)
−0.602903 + 0.797814i \(0.705989\pi\)
\(354\) −13231.5 + 11754.2i −0.105585 + 0.0937968i
\(355\) 0 0
\(356\) 5997.37 50539.5i 0.0473218 0.398778i
\(357\) −113126. −0.887621
\(358\) 22174.7 + 24961.7i 0.173018 + 0.194764i
\(359\) 6723.72i 0.0521700i −0.999660 0.0260850i \(-0.991696\pi\)
0.999660 0.0260850i \(-0.00830406\pi\)
\(360\) 0 0
\(361\) 2323.47 0.0178288
\(362\) 163587. 145322.i 1.24834 1.10896i
\(363\) 16185.3i 0.122831i
\(364\) 36278.2 + 4305.03i 0.273806 + 0.0324917i
\(365\) 0 0
\(366\) −76460.7 86070.6i −0.570790 0.642529i
\(367\) 119927.i 0.890401i 0.895431 + 0.445200i \(0.146868\pi\)
−0.895431 + 0.445200i \(0.853132\pi\)
\(368\) 29291.0 121679.i 0.216291 0.898502i
\(369\) 54086.1 0.397222
\(370\) 0 0
\(371\) 325786.i 2.36693i
\(372\) −4031.20 + 33970.7i −0.0291306 + 0.245481i
\(373\) −49886.2 −0.358561 −0.179280 0.983798i \(-0.557377\pi\)
−0.179280 + 0.983798i \(0.557377\pi\)
\(374\) −83510.1 94005.9i −0.597029 0.672066i
\(375\) 0 0
\(376\) −84191.4 + 58620.9i −0.595514 + 0.414645i
\(377\) 31806.3 0.223785
\(378\) −31194.9 + 27712.0i −0.218324 + 0.193948i
\(379\) 42377.4i 0.295023i 0.989060 + 0.147512i \(0.0471264\pi\)
−0.989060 + 0.147512i \(0.952874\pi\)
\(380\) 0 0
\(381\) −22710.0 −0.156447
\(382\) 453.244 + 510.209i 0.00310603 + 0.00349641i
\(383\) 249132.i 1.69837i −0.528098 0.849184i \(-0.677095\pi\)
0.528098 0.849184i \(-0.322905\pi\)
\(384\) −79310.9 + 30944.1i −0.537862 + 0.209853i
\(385\) 0 0
\(386\) 114920. 102089.i 0.771299 0.685183i
\(387\) 88557.6i 0.591294i
\(388\) 23189.9 195420.i 0.154041 1.29809i
\(389\) 187712. 1.24049 0.620244 0.784409i \(-0.287034\pi\)
0.620244 + 0.784409i \(0.287034\pi\)
\(390\) 0 0
\(391\) 143148.i 0.936337i
\(392\) 114374. + 164264.i 0.744311 + 1.06898i
\(393\) 105378. 0.682284
\(394\) −140594. + 124897.i −0.905680 + 0.804560i
\(395\) 0 0
\(396\) −46056.3 5465.37i −0.293696 0.0348521i
\(397\) −239081. −1.51693 −0.758463 0.651716i \(-0.774049\pi\)
−0.758463 + 0.651716i \(0.774049\pi\)
\(398\) −130638. 147057.i −0.824715 0.928368i
\(399\) 138225.i 0.868241i
\(400\) 0 0
\(401\) 226859. 1.41080 0.705402 0.708807i \(-0.250766\pi\)
0.705402 + 0.708807i \(0.250766\pi\)
\(402\) 65092.7 57825.0i 0.402791 0.357819i
\(403\) 12635.6i 0.0778014i
\(404\) 15940.1 134326.i 0.0976624 0.822995i
\(405\) 0 0
\(406\) 204587. + 230300.i 1.24115 + 1.39715i
\(407\) 161753.i 0.976480i
\(408\) −79910.8 + 55640.4i −0.480048 + 0.334249i
\(409\) −165859. −0.991497 −0.495748 0.868466i \(-0.665106\pi\)
−0.495748 + 0.868466i \(0.665106\pi\)
\(410\) 0 0
\(411\) 135045.i 0.799456i
\(412\) −201072. 23860.6i −1.18456 0.140568i
\(413\) 63313.7 0.371191
\(414\) −35066.3 39473.5i −0.204592 0.230306i
\(415\) 0 0
\(416\) 27743.7 14802.1i 0.160317 0.0855338i
\(417\) −109375. −0.628996
\(418\) 114862. 102038.i 0.657393 0.583994i
\(419\) 154230.i 0.878498i −0.898365 0.439249i \(-0.855245\pi\)
0.898365 0.439249i \(-0.144755\pi\)
\(420\) 0 0
\(421\) −247852. −1.39839 −0.699196 0.714930i \(-0.746459\pi\)
−0.699196 + 0.714930i \(0.746459\pi\)
\(422\) −11955.4 13458.0i −0.0671335 0.0755711i
\(423\) 43279.9i 0.241883i
\(424\) 160236. + 230130.i 0.891306 + 1.28009i
\(425\) 0 0
\(426\) 97934.1 86999.7i 0.539653 0.479400i
\(427\) 411852.i 2.25884i
\(428\) −110614. 13126.3i −0.603843 0.0716564i
\(429\) 17131.0 0.0930824
\(430\) 0 0
\(431\) 132150.i 0.711396i 0.934601 + 0.355698i \(0.115757\pi\)
−0.934601 + 0.355698i \(0.884243\pi\)
\(432\) −8405.68 + 34918.3i −0.0450407 + 0.187105i
\(433\) −341105. −1.81933 −0.909666 0.415341i \(-0.863662\pi\)
−0.909666 + 0.415341i \(0.863662\pi\)
\(434\) 91490.8 81275.8i 0.485733 0.431501i
\(435\) 0 0
\(436\) −20149.4 + 169798.i −0.105996 + 0.893222i
\(437\) 174907. 0.915893
\(438\) 97050.6 + 109248.i 0.505883 + 0.569464i
\(439\) 1536.95i 0.00797498i 0.999992 + 0.00398749i \(0.00126926\pi\)
−0.999992 + 0.00398749i \(0.998731\pi\)
\(440\) 0 0
\(441\) 84442.4 0.434194
\(442\) 26888.8 23886.7i 0.137634 0.122267i
\(443\) 259829.i 1.32398i 0.749513 + 0.661989i \(0.230288\pi\)
−0.749513 + 0.661989i \(0.769712\pi\)
\(444\) 124387. + 14760.7i 0.630972 + 0.0748756i
\(445\) 0 0
\(446\) 1275.88 + 1436.24i 0.00641418 + 0.00722034i
\(447\) 101337.i 0.507171i
\(448\) 285633. + 105673.i 1.42315 + 0.526510i
\(449\) 123490. 0.612547 0.306274 0.951944i \(-0.400918\pi\)
0.306274 + 0.951944i \(0.400918\pi\)
\(450\) 0 0
\(451\) 215062.i 1.05733i
\(452\) 35409.9 298397.i 0.173320 1.46056i
\(453\) 172949. 0.842796
\(454\) 103592. + 116611.i 0.502589 + 0.565756i
\(455\) 0 0
\(456\) −67984.9 97639.9i −0.326951 0.469567i
\(457\) 24937.6 0.119405 0.0597024 0.998216i \(-0.480985\pi\)
0.0597024 + 0.998216i \(0.480985\pi\)
\(458\) 82444.7 73239.7i 0.393036 0.349153i
\(459\) 41079.4i 0.194984i
\(460\) 0 0
\(461\) −142842. −0.672130 −0.336065 0.941839i \(-0.609096\pi\)
−0.336065 + 0.941839i \(0.609096\pi\)
\(462\) 110191. + 124040.i 0.516252 + 0.581137i
\(463\) 58133.2i 0.271183i 0.990765 + 0.135591i \(0.0432935\pi\)
−0.990765 + 0.135591i \(0.956707\pi\)
\(464\) 257788. + 62055.8i 1.19737 + 0.288235i
\(465\) 0 0
\(466\) 125643. 111615.i 0.578586 0.513986i
\(467\) 305454.i 1.40059i −0.713852 0.700296i \(-0.753051\pi\)
0.713852 0.700296i \(-0.246949\pi\)
\(468\) 1563.28 13173.6i 0.00713747 0.0601470i
\(469\) −311472. −1.41603
\(470\) 0 0
\(471\) 56417.5i 0.254315i
\(472\) 44723.8 31140.4i 0.200750 0.139778i
\(473\) 352131. 1.57392
\(474\) −108997. + 96827.7i −0.485131 + 0.430966i
\(475\) 0 0
\(476\) 345912. + 41048.4i 1.52669 + 0.181168i
\(477\) 118302. 0.519943
\(478\) 247481. + 278585.i 1.08314 + 1.21928i
\(479\) 214385.i 0.934378i −0.884157 0.467189i \(-0.845267\pi\)
0.884157 0.467189i \(-0.154733\pi\)
\(480\) 0 0
\(481\) −46266.7 −0.199976
\(482\) −325605. + 289251.i −1.40151 + 1.24503i
\(483\) 188883.i 0.809652i
\(484\) 5872.91 49490.6i 0.0250705 0.211267i
\(485\) 0 0
\(486\) 10063.0 + 11327.8i 0.0426045 + 0.0479592i
\(487\) 132928.i 0.560480i 0.959930 + 0.280240i \(0.0904140\pi\)
−0.959930 + 0.280240i \(0.909586\pi\)
\(488\) 202566. + 290926.i 0.850605 + 1.22164i
\(489\) 150292. 0.628517
\(490\) 0 0
\(491\) 203534.i 0.844256i −0.906536 0.422128i \(-0.861283\pi\)
0.906536 0.422128i \(-0.138717\pi\)
\(492\) −165382. 19625.4i −0.683215 0.0810752i
\(493\) 303273. 1.24779
\(494\) 29186.2 + 32854.4i 0.119598 + 0.134629i
\(495\) 0 0
\(496\) 24652.8 102411.i 0.100208 0.416278i
\(497\) −468620. −1.89718
\(498\) −141832. + 125996.i −0.571892 + 0.508040i
\(499\) 282205.i 1.13335i 0.823942 + 0.566674i \(0.191770\pi\)
−0.823942 + 0.566674i \(0.808230\pi\)
\(500\) 0 0
\(501\) 161895. 0.644999
\(502\) −83965.5 94518.6i −0.333191 0.375068i
\(503\) 307654.i 1.21598i −0.793944 0.607991i \(-0.791976\pi\)
0.793944 0.607991i \(-0.208024\pi\)
\(504\) 105442. 73417.1i 0.415098 0.289025i
\(505\) 0 0
\(506\) −156958. + 139434.i −0.613031 + 0.544586i
\(507\) 143507.i 0.558288i
\(508\) 69441.3 + 8240.40i 0.269086 + 0.0319316i
\(509\) 164324. 0.634256 0.317128 0.948383i \(-0.397282\pi\)
0.317128 + 0.948383i \(0.397282\pi\)
\(510\) 0 0
\(511\) 522759.i 2.00198i
\(512\) 253741. 65840.9i 0.967945 0.251163i
\(513\) −50193.4 −0.190727
\(514\) −59867.1 + 53182.9i −0.226601 + 0.201301i
\(515\) 0 0
\(516\) 32133.5 270787.i 0.120686 1.01702i
\(517\) 172094. 0.643848
\(518\) −297600. 335003.i −1.10911 1.24850i
\(519\) 57772.3i 0.214479i
\(520\) 0 0
\(521\) 317062. 1.16807 0.584034 0.811729i \(-0.301473\pi\)
0.584034 + 0.811729i \(0.301473\pi\)
\(522\) 83628.4 74291.2i 0.306911 0.272644i
\(523\) 55332.3i 0.202290i 0.994872 + 0.101145i \(0.0322507\pi\)
−0.994872 + 0.101145i \(0.967749\pi\)
\(524\) −322220. 38236.9i −1.17352 0.139258i
\(525\) 0 0
\(526\) 166566. + 187501.i 0.602027 + 0.677692i
\(527\) 120481.i 0.433807i
\(528\) 138845. + 33423.4i 0.498039 + 0.119890i
\(529\) 40832.1 0.145912
\(530\) 0 0
\(531\) 22991.0i 0.0815396i
\(532\) −50155.5 + 422657.i −0.177213 + 1.49336i
\(533\) 61514.9 0.216534
\(534\) 43908.4 + 49427.0i 0.153980 + 0.173333i
\(535\) 0 0
\(536\) −220019. + 153195.i −0.765827 + 0.533231i
\(537\) −43373.2 −0.150409
\(538\) 101091. 89803.7i 0.349258 0.310263i
\(539\) 335768.i 1.15574i
\(540\) 0 0
\(541\) −86217.1 −0.294577 −0.147289 0.989094i \(-0.547055\pi\)
−0.147289 + 0.989094i \(0.547055\pi\)
\(542\) −149250. 168008.i −0.508060 0.571915i
\(543\) 284247.i 0.964042i
\(544\) 264536. 141138.i 0.893897 0.476922i
\(545\) 0 0
\(546\) −35479.6 + 31518.3i −0.119013 + 0.105725i
\(547\) 288324.i 0.963620i −0.876276 0.481810i \(-0.839980\pi\)
0.876276 0.481810i \(-0.160020\pi\)
\(548\) 49001.6 412933.i 0.163173 1.37505i
\(549\) 149555. 0.496200
\(550\) 0 0
\(551\) 370558.i 1.22054i
\(552\) 92900.6 + 133424.i 0.304888 + 0.437880i
\(553\) 521558. 1.70550
\(554\) 363519. 322932.i 1.18442 1.05218i
\(555\) 0 0
\(556\) 334442. + 39687.3i 1.08186 + 0.128381i
\(557\) −465454. −1.50026 −0.750129 0.661291i \(-0.770009\pi\)
−0.750129 + 0.661291i \(0.770009\pi\)
\(558\) −29513.5 33222.9i −0.0947879 0.106701i
\(559\) 100721.i 0.322327i
\(560\) 0 0
\(561\) 163344. 0.519011
\(562\) −154877. + 137585.i −0.490361 + 0.435611i
\(563\) 276410.i 0.872040i −0.899937 0.436020i \(-0.856388\pi\)
0.899937 0.436020i \(-0.143612\pi\)
\(564\) 15704.3 132339.i 0.0493697 0.416035i
\(565\) 0 0
\(566\) −336478. 378768.i −1.05033 1.18233i
\(567\) 54204.0i 0.168603i
\(568\) −331026. + 230487.i −1.02604 + 0.714414i
\(569\) −178268. −0.550615 −0.275307 0.961356i \(-0.588780\pi\)
−0.275307 + 0.961356i \(0.588780\pi\)
\(570\) 0 0
\(571\) 430413.i 1.32012i 0.751213 + 0.660060i \(0.229469\pi\)
−0.751213 + 0.660060i \(0.770531\pi\)
\(572\) −52382.2 6216.04i −0.160100 0.0189986i
\(573\) −886.534 −0.00270014
\(574\) 395680. + 445411.i 1.20094 + 1.35188i
\(575\) 0 0
\(576\) 38372.7 103721.i 0.115658 0.312625i
\(577\) 349598. 1.05007 0.525034 0.851081i \(-0.324053\pi\)
0.525034 + 0.851081i \(0.324053\pi\)
\(578\) 6620.22 5881.07i 0.0198160 0.0176036i
\(579\) 199684.i 0.595645i
\(580\) 0 0
\(581\) 678672. 2.01052
\(582\) 169780. + 191118.i 0.501234 + 0.564230i
\(583\) 470404.i 1.38399i
\(584\) −257115. 369269.i −0.753879 1.08272i
\(585\) 0 0
\(586\) −17817.5 + 15828.2i −0.0518862 + 0.0460931i
\(587\) 401716.i 1.16585i −0.812525 0.582926i \(-0.801908\pi\)
0.812525 0.582926i \(-0.198092\pi\)
\(588\) −258204. 30640.3i −0.746806 0.0886213i
\(589\) 147211. 0.424335
\(590\) 0 0
\(591\) 244295.i 0.699422i
\(592\) −374989. 90268.8i −1.06998 0.257569i
\(593\) −83500.7 −0.237455 −0.118727 0.992927i \(-0.537881\pi\)
−0.118727 + 0.992927i \(0.537881\pi\)
\(594\) 45042.5 40013.5i 0.127658 0.113405i
\(595\) 0 0
\(596\) −36770.7 + 309864.i −0.103516 + 0.872326i
\(597\) 255525. 0.716943
\(598\) −39882.6 44895.2i −0.111527 0.125545i
\(599\) 655204.i 1.82609i 0.407855 + 0.913047i \(0.366277\pi\)
−0.407855 + 0.913047i \(0.633723\pi\)
\(600\) 0 0
\(601\) 350508. 0.970396 0.485198 0.874404i \(-0.338747\pi\)
0.485198 + 0.874404i \(0.338747\pi\)
\(602\) −729290. + 647864.i −2.01237 + 1.78769i
\(603\) 113104.i 0.311060i
\(604\) −528836. 62755.4i −1.44960 0.172019i
\(605\) 0 0
\(606\) 116702. + 131369.i 0.317784 + 0.357724i
\(607\) 14709.5i 0.0399228i 0.999801 + 0.0199614i \(0.00635434\pi\)
−0.999801 + 0.0199614i \(0.993646\pi\)
\(608\) 172452. + 323227.i 0.466509 + 0.874380i
\(609\) −400166. −1.07896
\(610\) 0 0
\(611\) 49224.5i 0.131856i
\(612\) 14905.8 125610.i 0.0397973 0.335369i
\(613\) −440819. −1.17311 −0.586556 0.809909i \(-0.699517\pi\)
−0.586556 + 0.809909i \(0.699517\pi\)
\(614\) 207400. + 233467.i 0.550138 + 0.619281i
\(615\) 0 0
\(616\) −291928. 419267.i −0.769332 1.10491i
\(617\) 670222. 1.76055 0.880275 0.474465i \(-0.157358\pi\)
0.880275 + 0.474465i \(0.157358\pi\)
\(618\) 196646. 174690.i 0.514881 0.457394i
\(619\) 273459.i 0.713692i 0.934163 + 0.356846i \(0.116148\pi\)
−0.934163 + 0.356846i \(0.883852\pi\)
\(620\) 0 0
\(621\) 68588.7 0.177856
\(622\) 97643.1 + 109915.i 0.252383 + 0.284104i
\(623\) 236511.i 0.609361i
\(624\) −9560.21 + 39714.4i −0.0245526 + 0.101995i
\(625\) 0 0
\(626\) −505443. + 449010.i −1.28980 + 1.14580i
\(627\) 199583.i 0.507679i
\(628\) −20471.3 + 172510.i −0.0519071 + 0.437417i
\(629\) −441153. −1.11503
\(630\) 0 0
\(631\) 322420.i 0.809774i −0.914367 0.404887i \(-0.867311\pi\)
0.914367 0.404887i \(-0.132689\pi\)
\(632\) 368421. 256525.i 0.922380 0.642236i
\(633\) 23384.5 0.0583606
\(634\) −388218. + 344873.i −0.965821 + 0.857986i
\(635\) 0 0
\(636\) −361738. 42926.4i −0.894294 0.106123i
\(637\) 96040.7 0.236688
\(638\) −295404. 332531.i −0.725729 0.816941i
\(639\) 170169.i 0.416753i
\(640\) 0 0
\(641\) −534654. −1.30124 −0.650619 0.759404i \(-0.725490\pi\)
−0.650619 + 0.759404i \(0.725490\pi\)
\(642\) 108180. 96101.2i 0.262467 0.233163i
\(643\) 83676.6i 0.202387i 0.994867 + 0.101193i \(0.0322661\pi\)
−0.994867 + 0.101193i \(0.967734\pi\)
\(644\) 68536.9 577556.i 0.165254 1.39259i
\(645\) 0 0
\(646\) 278290. + 313267.i 0.666857 + 0.750670i
\(647\) 226640.i 0.541411i 0.962662 + 0.270706i \(0.0872570\pi\)
−0.962662 + 0.270706i \(0.912743\pi\)
\(648\) −26659.8 38288.9i −0.0634903 0.0911848i
\(649\) −91418.8 −0.217043
\(650\) 0 0
\(651\) 158973.i 0.375113i
\(652\) −459554. 54533.9i −1.08104 0.128284i
\(653\) −499953. −1.17247 −0.586236 0.810140i \(-0.699391\pi\)
−0.586236 + 0.810140i \(0.699391\pi\)
\(654\) −147519. 166060.i −0.344900 0.388249i
\(655\) 0 0
\(656\) 498574. + 120019.i 1.15857 + 0.278896i
\(657\) −189828. −0.439775
\(658\) −356419. + 316625.i −0.823208 + 0.731296i
\(659\) 15572.3i 0.0358576i −0.999839 0.0179288i \(-0.994293\pi\)
0.999839 0.0179288i \(-0.00570722\pi\)
\(660\) 0 0
\(661\) 17974.5 0.0411390 0.0205695 0.999788i \(-0.493452\pi\)
0.0205695 + 0.999788i \(0.493452\pi\)
\(662\) 156505. + 176175.i 0.357118 + 0.402002i
\(663\) 46721.7i 0.106290i
\(664\) 479403. 333800.i 1.08734 0.757094i
\(665\) 0 0
\(666\) −121649. + 108067.i −0.274259 + 0.243638i
\(667\) 506363.i 1.13818i
\(668\) −495035. 58744.4i −1.10939 0.131648i
\(669\) −2495.60 −0.00557599
\(670\) 0 0
\(671\) 594675.i 1.32079i
\(672\) −349054. + 186231.i −0.772954 + 0.412395i
\(673\) −53880.1 −0.118959 −0.0594796 0.998230i \(-0.518944\pi\)
−0.0594796 + 0.998230i \(0.518944\pi\)
\(674\) 140099. 124457.i 0.308401 0.273968i
\(675\) 0 0
\(676\) −52072.2 + 438809.i −0.113950 + 0.960245i
\(677\) 694984. 1.51634 0.758172 0.652055i \(-0.226093\pi\)
0.758172 + 0.652055i \(0.226093\pi\)
\(678\) 259246. + 291829.i 0.563965 + 0.634847i
\(679\) 914512.i 1.98358i
\(680\) 0 0
\(681\) −202623. −0.436912
\(682\) −132104. + 117354.i −0.284019 + 0.252308i
\(683\) 54187.4i 0.116160i −0.998312 0.0580800i \(-0.981502\pi\)
0.998312 0.0580800i \(-0.0184979\pi\)
\(684\) 153479. + 18212.9i 0.328047 + 0.0389284i
\(685\) 0 0
\(686\) 143502. + 161537.i 0.304936 + 0.343261i
\(687\) 143255.i 0.303526i
\(688\) −196512. + 816337.i −0.415157 + 1.72462i
\(689\) 134551. 0.283432
\(690\) 0 0
\(691\) 138548.i 0.290165i −0.989420 0.145083i \(-0.953655\pi\)
0.989420 0.145083i \(-0.0463448\pi\)
\(692\) 20962.9 176653.i 0.0437764 0.368900i
\(693\) −215531. −0.448789
\(694\) −452891. 509812.i −0.940317 1.05850i
\(695\) 0 0
\(696\) −282671. + 196819.i −0.583530 + 0.406301i
\(697\) 586544. 1.20736
\(698\) 280563. 249238.i 0.575863 0.511568i
\(699\) 218317.i 0.446820i
\(700\) 0 0
\(701\) 140668. 0.286259 0.143130 0.989704i \(-0.454283\pi\)
0.143130 + 0.989704i \(0.454283\pi\)
\(702\) 11445.2 + 12883.6i 0.0232246 + 0.0261435i
\(703\) 539028.i 1.09069i
\(704\) −412426. 152581.i −0.832149 0.307861i
\(705\) 0 0
\(706\) −449326. + 399159.i −0.901472 + 0.800822i
\(707\) 628608.i 1.25760i
\(708\) −8342.37 + 70300.6i −0.0166427 + 0.140247i
\(709\) −381395. −0.758723 −0.379361 0.925249i \(-0.623856\pi\)
−0.379361 + 0.925249i \(0.623856\pi\)
\(710\) 0 0
\(711\) 189393.i 0.374648i
\(712\) −116326. 167068.i −0.229465 0.329558i
\(713\) −201162. −0.395701
\(714\) −338298. + 300526.i −0.663594 + 0.589503i
\(715\) 0 0
\(716\) 132624. + 15738.1i 0.258700 + 0.0306992i
\(717\) −484066. −0.941600
\(718\) −17861.9 20106.9i −0.0346481 0.0390028i
\(719\) 66799.3i 0.129215i −0.997911 0.0646076i \(-0.979420\pi\)
0.997911 0.0646076i \(-0.0205796\pi\)
\(720\) 0 0
\(721\) −940959. −1.81009
\(722\) 6948.19 6172.42i 0.0133290 0.0118408i
\(723\) 565767.i 1.08233i
\(724\) 103140. 869155.i 0.196766 1.65814i
\(725\) 0 0
\(726\) 42997.2 + 48401.2i 0.0815768 + 0.0918297i
\(727\) 53183.1i 0.100625i −0.998734 0.0503124i \(-0.983978\pi\)
0.998734 0.0503124i \(-0.0160217\pi\)
\(728\) 119924. 83501.0i 0.226279 0.157554i
\(729\) −19683.0 −0.0370370
\(730\) 0 0
\(731\) 960374.i 1.79724i
\(732\) −457302. 54266.7i −0.853456 0.101277i
\(733\) −251943. −0.468915 −0.234457 0.972126i \(-0.575331\pi\)
−0.234457 + 0.972126i \(0.575331\pi\)
\(734\) 318593. + 358635.i 0.591349 + 0.665672i
\(735\) 0 0
\(736\) −235653. 441686.i −0.435029 0.815376i
\(737\) 449736. 0.827985
\(738\) 161741. 143683.i 0.296967 0.263810i
\(739\) 417899.i 0.765213i 0.923911 + 0.382607i \(0.124974\pi\)
−0.923911 + 0.382607i \(0.875026\pi\)
\(740\) 0 0
\(741\) −57087.5 −0.103969
\(742\) 865468. + 974243.i 1.57197 + 1.76954i
\(743\) 95941.3i 0.173791i −0.996217 0.0868956i \(-0.972305\pi\)
0.996217 0.0868956i \(-0.0276947\pi\)
\(744\) 78189.9 + 112296.i 0.141255 + 0.202871i
\(745\) 0 0
\(746\) −149182. + 132525.i −0.268063 + 0.238134i
\(747\) 246445.i 0.441650i
\(748\) −499464. 59269.9i −0.892690 0.105933i
\(749\) −517645. −0.922717
\(750\) 0 0
\(751\) 313222.i 0.555358i −0.960674 0.277679i \(-0.910435\pi\)
0.960674 0.277679i \(-0.0895651\pi\)
\(752\) −96039.5 + 398961.i −0.169830 + 0.705496i
\(753\) 164234. 0.289650
\(754\) 95114.9 84495.2i 0.167304 0.148624i
\(755\) 0 0
\(756\) −19668.1 + 165742.i −0.0344128 + 0.289994i
\(757\) 386817. 0.675016 0.337508 0.941323i \(-0.390416\pi\)
0.337508 + 0.941323i \(0.390416\pi\)
\(758\) 112578. + 126727.i 0.195936 + 0.220562i
\(759\) 272729.i 0.473421i
\(760\) 0 0
\(761\) −447721. −0.773105 −0.386552 0.922267i \(-0.626334\pi\)
−0.386552 + 0.922267i \(0.626334\pi\)
\(762\) −67912.7 + 60330.2i −0.116961 + 0.103902i
\(763\) 794607.i 1.36491i
\(764\) 2710.80 + 321.683i 0.00464419 + 0.000551113i
\(765\) 0 0
\(766\) −661832. 745013.i −1.12795 1.26972i
\(767\) 26148.8i 0.0444489i
\(768\) −154970. + 303230.i −0.262739 + 0.514103i
\(769\) 351782. 0.594869 0.297434 0.954742i \(-0.403869\pi\)
0.297434 + 0.954742i \(0.403869\pi\)
\(770\) 0 0
\(771\) 104024.i 0.174995i
\(772\) 72456.3 610585.i 0.121574 1.02450i
\(773\) 550849. 0.921878 0.460939 0.887432i \(-0.347513\pi\)
0.460939 + 0.887432i \(0.347513\pi\)
\(774\) 235258. + 264826.i 0.392701 + 0.442057i
\(775\) 0 0
\(776\) −449796. 645997.i −0.746951 1.07277i
\(777\) 582098. 0.964171
\(778\) 561341. 498667.i 0.927401 0.823856i
\(779\) 716676.i 1.18100i
\(780\) 0 0
\(781\) 676642. 1.10932
\(782\) −380281. 428076.i −0.621857 0.700014i
\(783\) 145312.i 0.237016i