Properties

Label 287.3.b.a.83.6
Level $287$
Weight $3$
Character 287.83
Analytic conductor $7.820$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [287,3,Mod(83,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.83");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 287.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 83.6
Character \(\chi\) \(=\) 287.83
Dual form 287.3.b.a.83.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.35920 q^{2} +4.56039i q^{3} +7.28419 q^{4} -3.56634i q^{5} -15.3193i q^{6} +(1.27295 - 6.88328i) q^{7} -11.0323 q^{8} -11.7972 q^{9} +O(q^{10})\) \(q-3.35920 q^{2} +4.56039i q^{3} +7.28419 q^{4} -3.56634i q^{5} -15.3193i q^{6} +(1.27295 - 6.88328i) q^{7} -11.0323 q^{8} -11.7972 q^{9} +11.9800i q^{10} +0.313836 q^{11} +33.2188i q^{12} +10.3956i q^{13} +(-4.27608 + 23.1223i) q^{14} +16.2639 q^{15} +7.92271 q^{16} +26.5564i q^{17} +39.6291 q^{18} -4.84799i q^{19} -25.9779i q^{20} +(31.3905 + 5.80514i) q^{21} -1.05424 q^{22} -34.6765 q^{23} -50.3114i q^{24} +12.2812 q^{25} -34.9207i q^{26} -12.7563i q^{27} +(9.27239 - 50.1392i) q^{28} -45.2334 q^{29} -54.6337 q^{30} +35.3890i q^{31} +17.5151 q^{32} +1.43122i q^{33} -89.2080i q^{34} +(-24.5482 - 4.53977i) q^{35} -85.9331 q^{36} +17.8108 q^{37} +16.2853i q^{38} -47.4078 q^{39} +39.3448i q^{40} +6.40312i q^{41} +(-105.447 - 19.5006i) q^{42} -0.974054 q^{43} +2.28604 q^{44} +42.0729i q^{45} +116.485 q^{46} +56.7092i q^{47} +36.1307i q^{48} +(-45.7592 - 17.5241i) q^{49} -41.2549 q^{50} -121.108 q^{51} +75.7233i q^{52} -87.2889 q^{53} +42.8511i q^{54} -1.11925i q^{55} +(-14.0435 + 75.9381i) q^{56} +22.1087 q^{57} +151.948 q^{58} -15.1393i q^{59} +118.470 q^{60} -6.27574i q^{61} -118.879i q^{62} +(-15.0172 + 81.2035i) q^{63} -90.5274 q^{64} +37.0741 q^{65} -4.80774i q^{66} +39.9510 q^{67} +193.442i q^{68} -158.138i q^{69} +(82.4621 + 15.2500i) q^{70} -48.0225 q^{71} +130.150 q^{72} -28.6886i q^{73} -59.8300 q^{74} +56.0071i q^{75} -35.3137i q^{76} +(0.399497 - 2.16022i) q^{77} +159.252 q^{78} +38.1014 q^{79} -28.2551i q^{80} -48.0008 q^{81} -21.5093i q^{82} +73.4375i q^{83} +(228.654 + 42.2858i) q^{84} +94.7091 q^{85} +3.27204 q^{86} -206.282i q^{87} -3.46232 q^{88} -104.582i q^{89} -141.331i q^{90} +(71.5556 + 13.2330i) q^{91} -252.590 q^{92} -161.388 q^{93} -190.497i q^{94} -17.2896 q^{95} +79.8757i q^{96} +65.6700i q^{97} +(153.714 + 58.8669i) q^{98} -3.70239 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9} + 24 q^{11} - 14 q^{14} + 44 q^{15} + 194 q^{16} + 70 q^{18} - 16 q^{21} - 48 q^{22} - 80 q^{23} - 304 q^{25} + 64 q^{28} - 12 q^{29} + 64 q^{30} - 166 q^{32} + 30 q^{35} - 70 q^{36} + 36 q^{37} - 68 q^{39} + 164 q^{42} - 172 q^{43} + 72 q^{44} + 68 q^{46} - 172 q^{49} - 234 q^{50} + 156 q^{51} + 64 q^{53} - 234 q^{56} + 140 q^{57} - 556 q^{58} + 152 q^{60} - 130 q^{63} + 334 q^{64} - 76 q^{65} + 160 q^{67} + 202 q^{70} - 408 q^{71} - 40 q^{72} + 398 q^{74} - 248 q^{77} + 390 q^{78} + 264 q^{79} - 116 q^{81} - 418 q^{84} + 232 q^{85} + 368 q^{86} - 220 q^{88} + 32 q^{91} - 74 q^{92} + 240 q^{93} - 44 q^{95} + 838 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.35920 −1.67960 −0.839799 0.542898i \(-0.817327\pi\)
−0.839799 + 0.542898i \(0.817327\pi\)
\(3\) 4.56039i 1.52013i 0.649846 + 0.760066i \(0.274833\pi\)
−0.649846 + 0.760066i \(0.725167\pi\)
\(4\) 7.28419 1.82105
\(5\) 3.56634i 0.713269i −0.934244 0.356634i \(-0.883924\pi\)
0.934244 0.356634i \(-0.116076\pi\)
\(6\) 15.3193i 2.55321i
\(7\) 1.27295 6.88328i 0.181850 0.983326i
\(8\) −11.0323 −1.37903
\(9\) −11.7972 −1.31080
\(10\) 11.9800i 1.19800i
\(11\) 0.313836 0.0285306 0.0142653 0.999898i \(-0.495459\pi\)
0.0142653 + 0.999898i \(0.495459\pi\)
\(12\) 33.2188i 2.76823i
\(13\) 10.3956i 0.799658i 0.916590 + 0.399829i \(0.130931\pi\)
−0.916590 + 0.399829i \(0.869069\pi\)
\(14\) −4.27608 + 23.1223i −0.305434 + 1.65159i
\(15\) 16.2639 1.08426
\(16\) 7.92271 0.495169
\(17\) 26.5564i 1.56214i 0.624444 + 0.781070i \(0.285326\pi\)
−0.624444 + 0.781070i \(0.714674\pi\)
\(18\) 39.6291 2.20162
\(19\) 4.84799i 0.255157i −0.991828 0.127579i \(-0.959280\pi\)
0.991828 0.127579i \(-0.0407205\pi\)
\(20\) 25.9779i 1.29890i
\(21\) 31.3905 + 5.80514i 1.49479 + 0.276435i
\(22\) −1.05424 −0.0479199
\(23\) −34.6765 −1.50767 −0.753836 0.657063i \(-0.771799\pi\)
−0.753836 + 0.657063i \(0.771799\pi\)
\(24\) 50.3114i 2.09631i
\(25\) 12.2812 0.491248
\(26\) 34.9207i 1.34310i
\(27\) 12.7563i 0.472457i
\(28\) 9.27239 50.1392i 0.331157 1.79069i
\(29\) −45.2334 −1.55977 −0.779886 0.625922i \(-0.784723\pi\)
−0.779886 + 0.625922i \(0.784723\pi\)
\(30\) −54.6337 −1.82112
\(31\) 35.3890i 1.14158i 0.821096 + 0.570790i \(0.193363\pi\)
−0.821096 + 0.570790i \(0.806637\pi\)
\(32\) 17.5151 0.547346
\(33\) 1.43122i 0.0433702i
\(34\) 89.2080i 2.62377i
\(35\) −24.5482 4.53977i −0.701376 0.129708i
\(36\) −85.9331 −2.38703
\(37\) 17.8108 0.481373 0.240687 0.970603i \(-0.422627\pi\)
0.240687 + 0.970603i \(0.422627\pi\)
\(38\) 16.2853i 0.428561i
\(39\) −47.4078 −1.21559
\(40\) 39.3448i 0.983620i
\(41\) 6.40312i 0.156174i
\(42\) −105.447 19.5006i −2.51064 0.464300i
\(43\) −0.974054 −0.0226524 −0.0113262 0.999936i \(-0.503605\pi\)
−0.0113262 + 0.999936i \(0.503605\pi\)
\(44\) 2.28604 0.0519556
\(45\) 42.0729i 0.934953i
\(46\) 116.485 2.53228
\(47\) 56.7092i 1.20658i 0.797522 + 0.603290i \(0.206144\pi\)
−0.797522 + 0.603290i \(0.793856\pi\)
\(48\) 36.1307i 0.752723i
\(49\) −45.7592 17.5241i −0.933861 0.357635i
\(50\) −41.2549 −0.825099
\(51\) −121.108 −2.37466
\(52\) 75.7233i 1.45622i
\(53\) −87.2889 −1.64696 −0.823480 0.567345i \(-0.807971\pi\)
−0.823480 + 0.567345i \(0.807971\pi\)
\(54\) 42.8511i 0.793538i
\(55\) 1.11925i 0.0203500i
\(56\) −14.0435 + 75.9381i −0.250776 + 1.35604i
\(57\) 22.1087 0.387872
\(58\) 151.948 2.61979
\(59\) 15.1393i 0.256599i −0.991735 0.128299i \(-0.959048\pi\)
0.991735 0.128299i \(-0.0409518\pi\)
\(60\) 118.470 1.97449
\(61\) 6.27574i 0.102881i −0.998676 0.0514405i \(-0.983619\pi\)
0.998676 0.0514405i \(-0.0163812\pi\)
\(62\) 118.879i 1.91740i
\(63\) −15.0172 + 81.2035i −0.238368 + 1.28894i
\(64\) −90.5274 −1.41449
\(65\) 37.0741 0.570371
\(66\) 4.80774i 0.0728445i
\(67\) 39.9510 0.596283 0.298141 0.954522i \(-0.403633\pi\)
0.298141 + 0.954522i \(0.403633\pi\)
\(68\) 193.442i 2.84473i
\(69\) 158.138i 2.29186i
\(70\) 82.4621 + 15.2500i 1.17803 + 0.217857i
\(71\) −48.0225 −0.676374 −0.338187 0.941079i \(-0.609814\pi\)
−0.338187 + 0.941079i \(0.609814\pi\)
\(72\) 130.150 1.80763
\(73\) 28.6886i 0.392994i −0.980504 0.196497i \(-0.937043\pi\)
0.980504 0.196497i \(-0.0629566\pi\)
\(74\) −59.8300 −0.808513
\(75\) 56.0071i 0.746761i
\(76\) 35.3137i 0.464654i
\(77\) 0.399497 2.16022i 0.00518827 0.0280549i
\(78\) 159.252 2.04170
\(79\) 38.1014 0.482296 0.241148 0.970488i \(-0.422476\pi\)
0.241148 + 0.970488i \(0.422476\pi\)
\(80\) 28.2551i 0.353189i
\(81\) −48.0008 −0.592603
\(82\) 21.5093i 0.262309i
\(83\) 73.4375i 0.884790i 0.896820 + 0.442395i \(0.145871\pi\)
−0.896820 + 0.442395i \(0.854129\pi\)
\(84\) 228.654 + 42.2858i 2.72208 + 0.503402i
\(85\) 94.7091 1.11423
\(86\) 3.27204 0.0380469
\(87\) 206.282i 2.37106i
\(88\) −3.46232 −0.0393445
\(89\) 104.582i 1.17508i −0.809196 0.587539i \(-0.800097\pi\)
0.809196 0.587539i \(-0.199903\pi\)
\(90\) 141.331i 1.57034i
\(91\) 71.5556 + 13.2330i 0.786325 + 0.145417i
\(92\) −252.590 −2.74554
\(93\) −161.388 −1.73535
\(94\) 190.497i 2.02657i
\(95\) −17.2896 −0.181996
\(96\) 79.8757i 0.832038i
\(97\) 65.6700i 0.677010i 0.940965 + 0.338505i \(0.109921\pi\)
−0.940965 + 0.338505i \(0.890079\pi\)
\(98\) 153.714 + 58.8669i 1.56851 + 0.600683i
\(99\) −3.70239 −0.0373979
\(100\) 89.4586 0.894586
\(101\) 21.6084i 0.213944i 0.994262 + 0.106972i \(0.0341155\pi\)
−0.994262 + 0.106972i \(0.965884\pi\)
\(102\) 406.824 3.98847
\(103\) 73.2761i 0.711418i 0.934597 + 0.355709i \(0.115761\pi\)
−0.934597 + 0.355709i \(0.884239\pi\)
\(104\) 114.686i 1.10275i
\(105\) 20.7031 111.949i 0.197173 1.06618i
\(106\) 293.220 2.76623
\(107\) 74.1395 0.692892 0.346446 0.938070i \(-0.387388\pi\)
0.346446 + 0.938070i \(0.387388\pi\)
\(108\) 92.9197i 0.860367i
\(109\) −109.258 −1.00237 −0.501184 0.865341i \(-0.667102\pi\)
−0.501184 + 0.865341i \(0.667102\pi\)
\(110\) 3.75977i 0.0341797i
\(111\) 81.2243i 0.731751i
\(112\) 10.0852 54.5343i 0.0900463 0.486913i
\(113\) 126.959 1.12353 0.561764 0.827297i \(-0.310123\pi\)
0.561764 + 0.827297i \(0.310123\pi\)
\(114\) −74.2675 −0.651470
\(115\) 123.668i 1.07538i
\(116\) −329.489 −2.84042
\(117\) 122.638i 1.04819i
\(118\) 50.8560i 0.430983i
\(119\) 182.795 + 33.8048i 1.53609 + 0.284074i
\(120\) −179.428 −1.49523
\(121\) −120.902 −0.999186
\(122\) 21.0814i 0.172799i
\(123\) −29.2008 −0.237405
\(124\) 257.780i 2.07887i
\(125\) 132.958i 1.06366i
\(126\) 50.4457 272.778i 0.400363 2.16491i
\(127\) 120.508 0.948880 0.474440 0.880288i \(-0.342651\pi\)
0.474440 + 0.880288i \(0.342651\pi\)
\(128\) 234.039 1.82843
\(129\) 4.44207i 0.0344346i
\(130\) −124.539 −0.957994
\(131\) 214.162i 1.63482i 0.576054 + 0.817412i \(0.304592\pi\)
−0.576054 + 0.817412i \(0.695408\pi\)
\(132\) 10.4253i 0.0789793i
\(133\) −33.3701 6.17123i −0.250903 0.0464002i
\(134\) −134.203 −1.00152
\(135\) −45.4935 −0.336989
\(136\) 292.977i 2.15424i
\(137\) −146.468 −1.06911 −0.534556 0.845133i \(-0.679521\pi\)
−0.534556 + 0.845133i \(0.679521\pi\)
\(138\) 531.217i 3.84940i
\(139\) 226.849i 1.63200i 0.578049 + 0.816002i \(0.303814\pi\)
−0.578049 + 0.816002i \(0.696186\pi\)
\(140\) −178.814 33.0685i −1.27724 0.236204i
\(141\) −258.617 −1.83416
\(142\) 161.317 1.13604
\(143\) 3.26250i 0.0228147i
\(144\) −93.4658 −0.649068
\(145\) 161.318i 1.11254i
\(146\) 96.3705i 0.660072i
\(147\) 79.9169 208.680i 0.543652 1.41959i
\(148\) 129.737 0.876604
\(149\) −151.441 −1.01638 −0.508192 0.861244i \(-0.669686\pi\)
−0.508192 + 0.861244i \(0.669686\pi\)
\(150\) 188.139i 1.25426i
\(151\) −264.889 −1.75423 −0.877117 0.480277i \(-0.840536\pi\)
−0.877117 + 0.480277i \(0.840536\pi\)
\(152\) 53.4842i 0.351870i
\(153\) 313.291i 2.04765i
\(154\) −1.34199 + 7.25662i −0.00871421 + 0.0471209i
\(155\) 126.209 0.814254
\(156\) −345.328 −2.21364
\(157\) 120.013i 0.764417i 0.924076 + 0.382209i \(0.124836\pi\)
−0.924076 + 0.382209i \(0.875164\pi\)
\(158\) −127.990 −0.810063
\(159\) 398.072i 2.50360i
\(160\) 62.4648i 0.390405i
\(161\) −44.1413 + 238.688i −0.274169 + 1.48253i
\(162\) 161.244 0.995335
\(163\) 57.9974 0.355812 0.177906 0.984047i \(-0.443068\pi\)
0.177906 + 0.984047i \(0.443068\pi\)
\(164\) 46.6416i 0.284400i
\(165\) 5.10421 0.0309346
\(166\) 246.691i 1.48609i
\(167\) 109.476i 0.655547i −0.944756 0.327773i \(-0.893702\pi\)
0.944756 0.327773i \(-0.106298\pi\)
\(168\) −346.308 64.0438i −2.06136 0.381213i
\(169\) 60.9324 0.360547
\(170\) −318.147 −1.87145
\(171\) 57.1927i 0.334460i
\(172\) −7.09519 −0.0412511
\(173\) 172.305i 0.995981i 0.867182 + 0.497991i \(0.165929\pi\)
−0.867182 + 0.497991i \(0.834071\pi\)
\(174\) 692.942i 3.98242i
\(175\) 15.6333 84.5350i 0.0893332 0.483057i
\(176\) 2.48643 0.0141275
\(177\) 69.0413 0.390064
\(178\) 351.311i 1.97366i
\(179\) 308.450 1.72319 0.861593 0.507599i \(-0.169467\pi\)
0.861593 + 0.507599i \(0.169467\pi\)
\(180\) 306.467i 1.70259i
\(181\) 310.847i 1.71739i −0.512490 0.858693i \(-0.671277\pi\)
0.512490 0.858693i \(-0.328723\pi\)
\(182\) −240.369 44.4522i −1.32071 0.244243i
\(183\) 28.6198 0.156393
\(184\) 382.559 2.07913
\(185\) 63.5195i 0.343348i
\(186\) 542.133 2.91469
\(187\) 8.33435i 0.0445687i
\(188\) 413.081i 2.19724i
\(189\) −87.8055 16.2381i −0.464580 0.0859161i
\(190\) 58.0791 0.305679
\(191\) 100.425 0.525787 0.262894 0.964825i \(-0.415323\pi\)
0.262894 + 0.964825i \(0.415323\pi\)
\(192\) 412.841i 2.15021i
\(193\) −35.3561 −0.183192 −0.0915960 0.995796i \(-0.529197\pi\)
−0.0915960 + 0.995796i \(0.529197\pi\)
\(194\) 220.598i 1.13710i
\(195\) 169.073i 0.867039i
\(196\) −333.319 127.649i −1.70061 0.651271i
\(197\) 169.453 0.860170 0.430085 0.902788i \(-0.358484\pi\)
0.430085 + 0.902788i \(0.358484\pi\)
\(198\) 12.4371 0.0628134
\(199\) 26.0523i 0.130916i 0.997855 + 0.0654581i \(0.0208509\pi\)
−0.997855 + 0.0654581i \(0.979149\pi\)
\(200\) −135.489 −0.677446
\(201\) 182.192i 0.906429i
\(202\) 72.5867i 0.359340i
\(203\) −57.5797 + 311.354i −0.283644 + 1.53376i
\(204\) −882.171 −4.32437
\(205\) 22.8357 0.111394
\(206\) 246.149i 1.19490i
\(207\) 409.085 1.97626
\(208\) 82.3610i 0.395966i
\(209\) 1.52147i 0.00727978i
\(210\) −69.5458 + 376.060i −0.331171 + 1.79076i
\(211\) −42.6517 −0.202141 −0.101070 0.994879i \(-0.532227\pi\)
−0.101070 + 0.994879i \(0.532227\pi\)
\(212\) −635.829 −2.99919
\(213\) 219.002i 1.02818i
\(214\) −249.049 −1.16378
\(215\) 3.47381i 0.0161573i
\(216\) 140.731i 0.651533i
\(217\) 243.593 + 45.0483i 1.12255 + 0.207596i
\(218\) 367.019 1.68357
\(219\) 130.831 0.597403
\(220\) 8.15282i 0.0370583i
\(221\) −276.068 −1.24918
\(222\) 272.848i 1.22905i
\(223\) 292.007i 1.30945i −0.755868 0.654724i \(-0.772785\pi\)
0.755868 0.654724i \(-0.227215\pi\)
\(224\) 22.2958 120.561i 0.0995346 0.538220i
\(225\) −144.884 −0.643928
\(226\) −426.479 −1.88708
\(227\) 55.3238i 0.243717i 0.992547 + 0.121859i \(0.0388854\pi\)
−0.992547 + 0.121859i \(0.961115\pi\)
\(228\) 161.044 0.706335
\(229\) 78.9671i 0.344835i −0.985024 0.172417i \(-0.944842\pi\)
0.985024 0.172417i \(-0.0551577\pi\)
\(230\) 415.425i 1.80620i
\(231\) 9.85148 + 1.82186i 0.0426471 + 0.00788685i
\(232\) 499.026 2.15097
\(233\) 357.687 1.53514 0.767569 0.640967i \(-0.221466\pi\)
0.767569 + 0.640967i \(0.221466\pi\)
\(234\) 411.967i 1.76054i
\(235\) 202.245 0.860616
\(236\) 110.278i 0.467279i
\(237\) 173.757i 0.733153i
\(238\) −614.044 113.557i −2.58002 0.477131i
\(239\) −342.471 −1.43293 −0.716466 0.697622i \(-0.754241\pi\)
−0.716466 + 0.697622i \(0.754241\pi\)
\(240\) 128.854 0.536893
\(241\) 316.926i 1.31505i −0.753435 0.657523i \(-0.771604\pi\)
0.753435 0.657523i \(-0.228396\pi\)
\(242\) 406.132 1.67823
\(243\) 333.710i 1.37329i
\(244\) 45.7137i 0.187351i
\(245\) −62.4970 + 163.193i −0.255090 + 0.666094i
\(246\) 98.0911 0.398744
\(247\) 50.3975 0.204039
\(248\) 390.420i 1.57428i
\(249\) −334.904 −1.34500
\(250\) 446.630i 1.78652i
\(251\) 55.4944i 0.221093i 0.993871 + 0.110547i \(0.0352601\pi\)
−0.993871 + 0.110547i \(0.964740\pi\)
\(252\) −109.388 + 591.502i −0.434080 + 2.34723i
\(253\) −10.8827 −0.0430147
\(254\) −404.809 −1.59374
\(255\) 431.911i 1.69377i
\(256\) −424.073 −1.65653
\(257\) 470.721i 1.83160i −0.401636 0.915799i \(-0.631558\pi\)
0.401636 0.915799i \(-0.368442\pi\)
\(258\) 14.9218i 0.0578363i
\(259\) 22.6722 122.597i 0.0875375 0.473347i
\(260\) 270.055 1.03867
\(261\) 533.627 2.04455
\(262\) 719.412i 2.74585i
\(263\) −461.940 −1.75643 −0.878213 0.478271i \(-0.841264\pi\)
−0.878213 + 0.478271i \(0.841264\pi\)
\(264\) 15.7895i 0.0598089i
\(265\) 311.302i 1.17473i
\(266\) 112.097 + 20.7304i 0.421416 + 0.0779337i
\(267\) 476.935 1.78627
\(268\) 291.011 1.08586
\(269\) 96.5332i 0.358859i −0.983771 0.179430i \(-0.942575\pi\)
0.983771 0.179430i \(-0.0574252\pi\)
\(270\) 152.822 0.566006
\(271\) 281.587i 1.03907i 0.854450 + 0.519533i \(0.173894\pi\)
−0.854450 + 0.519533i \(0.826106\pi\)
\(272\) 210.398i 0.773524i
\(273\) −60.3477 + 326.322i −0.221054 + 1.19532i
\(274\) 492.016 1.79568
\(275\) 3.85428 0.0140156
\(276\) 1151.91i 4.17359i
\(277\) 295.004 1.06500 0.532498 0.846431i \(-0.321253\pi\)
0.532498 + 0.846431i \(0.321253\pi\)
\(278\) 762.029i 2.74111i
\(279\) 417.491i 1.49638i
\(280\) 270.821 + 50.0838i 0.967219 + 0.178871i
\(281\) 433.500 1.54270 0.771352 0.636409i \(-0.219581\pi\)
0.771352 + 0.636409i \(0.219581\pi\)
\(282\) 868.744 3.08065
\(283\) 453.321i 1.60184i 0.598770 + 0.800921i \(0.295656\pi\)
−0.598770 + 0.800921i \(0.704344\pi\)
\(284\) −349.805 −1.23171
\(285\) 78.8473i 0.276657i
\(286\) 10.9594i 0.0383195i
\(287\) 44.0745 + 8.15084i 0.153570 + 0.0284001i
\(288\) −206.629 −0.717461
\(289\) −416.241 −1.44028
\(290\) 541.898i 1.86861i
\(291\) −299.481 −1.02914
\(292\) 208.973i 0.715661i
\(293\) 287.106i 0.979882i 0.871756 + 0.489941i \(0.162982\pi\)
−0.871756 + 0.489941i \(0.837018\pi\)
\(294\) −268.456 + 700.997i −0.913117 + 2.38434i
\(295\) −53.9920 −0.183024
\(296\) −196.493 −0.663829
\(297\) 4.00340i 0.0134795i
\(298\) 508.720 1.70711
\(299\) 360.481i 1.20562i
\(300\) 407.967i 1.35989i
\(301\) −1.23992 + 6.70469i −0.00411933 + 0.0222747i
\(302\) 889.815 2.94641
\(303\) −98.5427 −0.325223
\(304\) 38.4092i 0.126346i
\(305\) −22.3814 −0.0733818
\(306\) 1052.41i 3.43923i
\(307\) 455.564i 1.48392i 0.670443 + 0.741961i \(0.266104\pi\)
−0.670443 + 0.741961i \(0.733896\pi\)
\(308\) 2.91001 15.7355i 0.00944809 0.0510893i
\(309\) −334.168 −1.08145
\(310\) −423.962 −1.36762
\(311\) 164.684i 0.529531i −0.964313 0.264766i \(-0.914705\pi\)
0.964313 0.264766i \(-0.0852946\pi\)
\(312\) 523.015 1.67633
\(313\) 79.6054i 0.254330i −0.991882 0.127165i \(-0.959412\pi\)
0.991882 0.127165i \(-0.0405878\pi\)
\(314\) 403.149i 1.28391i
\(315\) 289.600 + 53.5565i 0.919364 + 0.170021i
\(316\) 277.538 0.878284
\(317\) 309.299 0.975705 0.487853 0.872926i \(-0.337780\pi\)
0.487853 + 0.872926i \(0.337780\pi\)
\(318\) 1337.20i 4.20504i
\(319\) −14.1959 −0.0445012
\(320\) 322.852i 1.00891i
\(321\) 338.105i 1.05329i
\(322\) 148.279 801.799i 0.460494 2.49006i
\(323\) 128.745 0.398591
\(324\) −349.648 −1.07916
\(325\) 127.670i 0.392830i
\(326\) −194.825 −0.597622
\(327\) 498.260i 1.52373i
\(328\) 70.6409i 0.215369i
\(329\) 390.346 + 72.1879i 1.18646 + 0.219416i
\(330\) −17.1460 −0.0519577
\(331\) 382.963 1.15699 0.578495 0.815686i \(-0.303640\pi\)
0.578495 + 0.815686i \(0.303640\pi\)
\(332\) 534.933i 1.61124i
\(333\) −210.118 −0.630984
\(334\) 367.752i 1.10106i
\(335\) 142.479i 0.425310i
\(336\) 248.698 + 45.9924i 0.740172 + 0.136882i
\(337\) −524.806 −1.55729 −0.778644 0.627466i \(-0.784092\pi\)
−0.778644 + 0.627466i \(0.784092\pi\)
\(338\) −204.684 −0.605573
\(339\) 578.982i 1.70791i
\(340\) 689.880 2.02906
\(341\) 11.1064i 0.0325699i
\(342\) 192.121i 0.561758i
\(343\) −178.872 + 292.666i −0.521494 + 0.853255i
\(344\) 10.7460 0.0312384
\(345\) −563.976 −1.63471
\(346\) 578.805i 1.67285i
\(347\) −198.980 −0.573430 −0.286715 0.958016i \(-0.592563\pi\)
−0.286715 + 0.958016i \(0.592563\pi\)
\(348\) 1502.60i 4.31781i
\(349\) 520.274i 1.49076i −0.666642 0.745378i \(-0.732269\pi\)
0.666642 0.745378i \(-0.267731\pi\)
\(350\) −52.5153 + 283.969i −0.150044 + 0.811341i
\(351\) 132.609 0.377804
\(352\) 5.49687 0.0156161
\(353\) 357.173i 1.01182i 0.862586 + 0.505911i \(0.168844\pi\)
−0.862586 + 0.505911i \(0.831156\pi\)
\(354\) −231.923 −0.655150
\(355\) 171.265i 0.482436i
\(356\) 761.796i 2.13988i
\(357\) −154.163 + 833.618i −0.431830 + 2.33506i
\(358\) −1036.15 −2.89426
\(359\) 706.755 1.96868 0.984338 0.176293i \(-0.0564105\pi\)
0.984338 + 0.176293i \(0.0564105\pi\)
\(360\) 464.158i 1.28933i
\(361\) 337.497 0.934895
\(362\) 1044.20i 2.88452i
\(363\) 551.359i 1.51889i
\(364\) 521.225 + 96.3917i 1.43194 + 0.264812i
\(365\) −102.313 −0.280310
\(366\) −96.1396 −0.262677
\(367\) 197.305i 0.537616i 0.963194 + 0.268808i \(0.0866296\pi\)
−0.963194 + 0.268808i \(0.913370\pi\)
\(368\) −274.731 −0.746553
\(369\) 75.5389i 0.204713i
\(370\) 213.374i 0.576687i
\(371\) −111.114 + 600.834i −0.299499 + 1.61950i
\(372\) −1175.58 −3.16016
\(373\) −4.03029 −0.0108051 −0.00540253 0.999985i \(-0.501720\pi\)
−0.00540253 + 0.999985i \(0.501720\pi\)
\(374\) 27.9967i 0.0748575i
\(375\) 606.339 1.61690
\(376\) 625.631i 1.66391i
\(377\) 470.226i 1.24728i
\(378\) 294.956 + 54.5471i 0.780307 + 0.144305i
\(379\) −322.599 −0.851183 −0.425592 0.904915i \(-0.639934\pi\)
−0.425592 + 0.904915i \(0.639934\pi\)
\(380\) −125.941 −0.331423
\(381\) 549.563i 1.44242i
\(382\) −337.349 −0.883111
\(383\) 623.478i 1.62788i −0.580948 0.813941i \(-0.697318\pi\)
0.580948 0.813941i \(-0.302682\pi\)
\(384\) 1067.31i 2.77945i
\(385\) −7.70410 1.42474i −0.0200107 0.00370063i
\(386\) 118.768 0.307689
\(387\) 11.4911 0.0296928
\(388\) 478.353i 1.23287i
\(389\) −346.644 −0.891115 −0.445557 0.895253i \(-0.646994\pi\)
−0.445557 + 0.895253i \(0.646994\pi\)
\(390\) 567.948i 1.45628i
\(391\) 920.881i 2.35519i
\(392\) 504.827 + 193.330i 1.28782 + 0.493190i
\(393\) −976.663 −2.48515
\(394\) −569.227 −1.44474
\(395\) 135.883i 0.344007i
\(396\) −26.9689 −0.0681033
\(397\) 97.5499i 0.245718i −0.992424 0.122859i \(-0.960794\pi\)
0.992424 0.122859i \(-0.0392062\pi\)
\(398\) 87.5148i 0.219887i
\(399\) 28.1432 152.181i 0.0705344 0.381405i
\(400\) 97.3003 0.243251
\(401\) 375.671 0.936836 0.468418 0.883507i \(-0.344824\pi\)
0.468418 + 0.883507i \(0.344824\pi\)
\(402\) 612.019i 1.52244i
\(403\) −367.888 −0.912874
\(404\) 157.400i 0.389603i
\(405\) 171.188i 0.422685i
\(406\) 193.421 1045.90i 0.476407 2.57611i
\(407\) 5.58968 0.0137339
\(408\) 1336.09 3.27473
\(409\) 13.2401i 0.0323719i 0.999869 + 0.0161859i \(0.00515237\pi\)
−0.999869 + 0.0161859i \(0.994848\pi\)
\(410\) −76.7097 −0.187097
\(411\) 667.953i 1.62519i
\(412\) 533.757i 1.29553i
\(413\) −104.208 19.2716i −0.252320 0.0466624i
\(414\) −1374.20 −3.31932
\(415\) 261.903 0.631093
\(416\) 182.079i 0.437690i
\(417\) −1034.52 −2.48086
\(418\) 5.11093i 0.0122271i
\(419\) 275.854i 0.658363i 0.944267 + 0.329182i \(0.106773\pi\)
−0.944267 + 0.329182i \(0.893227\pi\)
\(420\) 150.806 815.460i 0.359061 1.94157i
\(421\) 284.626 0.676072 0.338036 0.941133i \(-0.390237\pi\)
0.338036 + 0.941133i \(0.390237\pi\)
\(422\) 143.276 0.339516
\(423\) 669.010i 1.58158i
\(424\) 962.993 2.27121
\(425\) 326.144i 0.767398i
\(426\) 735.669i 1.72692i
\(427\) −43.1977 7.98868i −0.101166 0.0187089i
\(428\) 540.046 1.26179
\(429\) −14.8783 −0.0346814
\(430\) 11.6692i 0.0271377i
\(431\) 312.665 0.725441 0.362721 0.931898i \(-0.381848\pi\)
0.362721 + 0.931898i \(0.381848\pi\)
\(432\) 101.065i 0.233946i
\(433\) 345.940i 0.798937i 0.916747 + 0.399468i \(0.130805\pi\)
−0.916747 + 0.399468i \(0.869195\pi\)
\(434\) −818.275 151.326i −1.88543 0.348678i
\(435\) −735.673 −1.69120
\(436\) −795.857 −1.82536
\(437\) 168.111i 0.384693i
\(438\) −439.488 −1.00340
\(439\) 52.2923i 0.119117i −0.998225 0.0595585i \(-0.981031\pi\)
0.998225 0.0595585i \(-0.0189693\pi\)
\(440\) 12.3478i 0.0280632i
\(441\) 539.831 + 206.735i 1.22411 + 0.468788i
\(442\) 927.367 2.09812
\(443\) 552.013 1.24608 0.623039 0.782191i \(-0.285898\pi\)
0.623039 + 0.782191i \(0.285898\pi\)
\(444\) 591.654i 1.33255i
\(445\) −372.975 −0.838147
\(446\) 980.909i 2.19935i
\(447\) 690.631i 1.54504i
\(448\) −115.237 + 623.126i −0.257224 + 1.39091i
\(449\) 226.412 0.504259 0.252129 0.967694i \(-0.418869\pi\)
0.252129 + 0.967694i \(0.418869\pi\)
\(450\) 486.693 1.08154
\(451\) 2.00953i 0.00445573i
\(452\) 924.792 2.04600
\(453\) 1208.00i 2.66667i
\(454\) 185.843i 0.409347i
\(455\) 47.1934 255.192i 0.103722 0.560861i
\(456\) −243.909 −0.534888
\(457\) −434.321 −0.950375 −0.475188 0.879884i \(-0.657620\pi\)
−0.475188 + 0.879884i \(0.657620\pi\)
\(458\) 265.266i 0.579183i
\(459\) 338.762 0.738044
\(460\) 900.823i 1.95831i
\(461\) 254.309i 0.551646i 0.961208 + 0.275823i \(0.0889504\pi\)
−0.961208 + 0.275823i \(0.911050\pi\)
\(462\) −33.0930 6.12000i −0.0716299 0.0132467i
\(463\) 152.748 0.329908 0.164954 0.986301i \(-0.447252\pi\)
0.164954 + 0.986301i \(0.447252\pi\)
\(464\) −358.371 −0.772351
\(465\) 575.564i 1.23777i
\(466\) −1201.54 −2.57841
\(467\) 224.444i 0.480608i −0.970698 0.240304i \(-0.922753\pi\)
0.970698 0.240304i \(-0.0772472\pi\)
\(468\) 893.323i 1.90881i
\(469\) 50.8554 274.994i 0.108434 0.586341i
\(470\) −679.379 −1.44549
\(471\) −547.309 −1.16201
\(472\) 167.021i 0.353858i
\(473\) −0.305693 −0.000646286
\(474\) 583.685i 1.23140i
\(475\) 59.5391i 0.125345i
\(476\) 1331.51 + 246.241i 2.79730 + 0.517313i
\(477\) 1029.76 2.15884
\(478\) 1150.43 2.40675
\(479\) 198.911i 0.415263i −0.978207 0.207632i \(-0.933424\pi\)
0.978207 0.207632i \(-0.0665755\pi\)
\(480\) 284.864 0.593467
\(481\) 185.153i 0.384934i
\(482\) 1064.62i 2.20875i
\(483\) −1088.51 201.302i −2.25365 0.416774i
\(484\) −880.670 −1.81957
\(485\) 234.202 0.482890
\(486\) 1121.00i 2.30658i
\(487\) 431.443 0.885919 0.442960 0.896542i \(-0.353928\pi\)
0.442960 + 0.896542i \(0.353928\pi\)
\(488\) 69.2355i 0.141876i
\(489\) 264.491i 0.540882i
\(490\) 209.940 548.197i 0.428448 1.11877i
\(491\) 746.425 1.52021 0.760107 0.649798i \(-0.225147\pi\)
0.760107 + 0.649798i \(0.225147\pi\)
\(492\) −212.704 −0.432325
\(493\) 1201.23i 2.43658i
\(494\) −169.295 −0.342703
\(495\) 13.2040i 0.0266747i
\(496\) 280.377i 0.565276i
\(497\) −61.1301 + 330.553i −0.122998 + 0.665096i
\(498\) 1125.01 2.25905
\(499\) 726.174 1.45526 0.727629 0.685971i \(-0.240622\pi\)
0.727629 + 0.685971i \(0.240622\pi\)
\(500\) 968.489i 1.93698i
\(501\) 499.255 0.996518
\(502\) 186.416i 0.371348i
\(503\) 84.2302i 0.167456i 0.996489 + 0.0837278i \(0.0266826\pi\)
−0.996489 + 0.0837278i \(0.973317\pi\)
\(504\) 165.674 895.857i 0.328717 1.77749i
\(505\) 77.0628 0.152600
\(506\) 36.5572 0.0722474
\(507\) 277.876i 0.548078i
\(508\) 877.802 1.72796
\(509\) 183.067i 0.359659i 0.983698 + 0.179830i \(0.0575546\pi\)
−0.983698 + 0.179830i \(0.942445\pi\)
\(510\) 1450.87i 2.84485i
\(511\) −197.472 36.5190i −0.386442 0.0714658i
\(512\) 488.388 0.953883
\(513\) −61.8426 −0.120551
\(514\) 1581.24i 3.07635i
\(515\) 261.328 0.507432
\(516\) 32.3569i 0.0627072i
\(517\) 17.7974i 0.0344244i
\(518\) −76.1604 + 411.827i −0.147028 + 0.795032i
\(519\) −785.778 −1.51402
\(520\) −409.011 −0.786560
\(521\) 1012.94i 1.94421i −0.234539 0.972107i \(-0.575358\pi\)
0.234539 0.972107i \(-0.424642\pi\)
\(522\) −1792.56 −3.43402
\(523\) 183.566i 0.350987i −0.984481 0.175493i \(-0.943848\pi\)
0.984481 0.175493i \(-0.0561521\pi\)
\(524\) 1560.00i 2.97709i
\(525\) 385.513 + 71.2941i 0.734310 + 0.135798i
\(526\) 1551.75 2.95009
\(527\) −939.803 −1.78331
\(528\) 11.3391i 0.0214756i
\(529\) 673.456 1.27307
\(530\) 1045.72i 1.97307i
\(531\) 178.602i 0.336350i
\(532\) −243.074 44.9524i −0.456906 0.0844970i
\(533\) −66.5640 −0.124886
\(534\) −1602.12 −3.00022
\(535\) 264.407i 0.494218i
\(536\) −440.749 −0.822293
\(537\) 1406.66i 2.61947i
\(538\) 324.274i 0.602739i
\(539\) −14.3609 5.49970i −0.0266436 0.0102035i
\(540\) −331.383 −0.613673
\(541\) −361.613 −0.668417 −0.334208 0.942499i \(-0.608469\pi\)
−0.334208 + 0.942499i \(0.608469\pi\)
\(542\) 945.906i 1.74521i
\(543\) 1417.58 2.61065
\(544\) 465.137i 0.855031i
\(545\) 389.652i 0.714957i
\(546\) 202.720 1096.18i 0.371281 2.00765i
\(547\) −811.077 −1.48277 −0.741386 0.671079i \(-0.765831\pi\)
−0.741386 + 0.671079i \(0.765831\pi\)
\(548\) −1066.90 −1.94690
\(549\) 74.0361i 0.134856i
\(550\) −12.9473 −0.0235405
\(551\) 219.291i 0.397987i
\(552\) 1744.62i 3.16055i
\(553\) 48.5010 262.263i 0.0877053 0.474254i
\(554\) −990.976 −1.78877
\(555\) 289.674 0.521935
\(556\) 1652.41i 2.97196i
\(557\) 144.121 0.258745 0.129373 0.991596i \(-0.458704\pi\)
0.129373 + 0.991596i \(0.458704\pi\)
\(558\) 1402.43i 2.51332i
\(559\) 10.1258i 0.0181142i
\(560\) −194.488 35.9672i −0.347300 0.0642272i
\(561\) −38.0079 −0.0677503
\(562\) −1456.21 −2.59112
\(563\) 310.122i 0.550838i −0.961324 0.275419i \(-0.911183\pi\)
0.961324 0.275419i \(-0.0888166\pi\)
\(564\) −1883.81 −3.34009
\(565\) 452.778i 0.801378i
\(566\) 1522.79i 2.69045i
\(567\) −61.1025 + 330.404i −0.107765 + 0.582722i
\(568\) 529.796 0.932740
\(569\) −411.027 −0.722367 −0.361183 0.932495i \(-0.617627\pi\)
−0.361183 + 0.932495i \(0.617627\pi\)
\(570\) 264.864i 0.464673i
\(571\) −356.814 −0.624893 −0.312447 0.949935i \(-0.601149\pi\)
−0.312447 + 0.949935i \(0.601149\pi\)
\(572\) 23.7647i 0.0415467i
\(573\) 457.979i 0.799266i
\(574\) −148.055 27.3803i −0.257935 0.0477008i
\(575\) −425.868 −0.740640
\(576\) 1067.97 1.85411
\(577\) 391.139i 0.677884i −0.940807 0.338942i \(-0.889931\pi\)
0.940807 0.338942i \(-0.110069\pi\)
\(578\) 1398.23 2.41909
\(579\) 161.238i 0.278476i
\(580\) 1175.07i 2.02598i
\(581\) 505.491 + 93.4821i 0.870037 + 0.160899i
\(582\) 1006.02 1.72855
\(583\) −27.3944 −0.0469887
\(584\) 316.500i 0.541951i
\(585\) −437.371 −0.747643
\(586\) 964.443i 1.64581i
\(587\) 513.174i 0.874231i −0.899405 0.437116i \(-0.856000\pi\)
0.899405 0.437116i \(-0.144000\pi\)
\(588\) 582.130 1520.07i 0.990017 2.58515i
\(589\) 171.565 0.291282
\(590\) 181.370 0.307406
\(591\) 772.775i 1.30757i
\(592\) 141.110 0.238361
\(593\) 1140.99i 1.92410i 0.272874 + 0.962050i \(0.412026\pi\)
−0.272874 + 0.962050i \(0.587974\pi\)
\(594\) 13.4482i 0.0226401i
\(595\) 120.560 651.910i 0.202621 1.09565i
\(596\) −1103.13 −1.85088
\(597\) −118.809 −0.199010
\(598\) 1210.93i 2.02496i
\(599\) 863.757 1.44200 0.720999 0.692936i \(-0.243683\pi\)
0.720999 + 0.692936i \(0.243683\pi\)
\(600\) 617.884i 1.02981i
\(601\) 263.404i 0.438276i −0.975694 0.219138i \(-0.929676\pi\)
0.975694 0.219138i \(-0.0703245\pi\)
\(602\) 4.16513 22.5224i 0.00691882 0.0374126i
\(603\) −471.310 −0.781608
\(604\) −1929.50 −3.19454
\(605\) 431.176i 0.712688i
\(606\) 331.024 0.546244
\(607\) 468.563i 0.771932i 0.922513 + 0.385966i \(0.126132\pi\)
−0.922513 + 0.385966i \(0.873868\pi\)
\(608\) 84.9128i 0.139659i
\(609\) −1419.90 262.586i −2.33152 0.431176i
\(610\) 75.1836 0.123252
\(611\) −589.524 −0.964851
\(612\) 2282.07i 3.72888i
\(613\) −285.996 −0.466551 −0.233275 0.972411i \(-0.574944\pi\)
−0.233275 + 0.972411i \(0.574944\pi\)
\(614\) 1530.33i 2.49239i
\(615\) 104.140i 0.169333i
\(616\) −4.40735 + 23.8321i −0.00715479 + 0.0386885i
\(617\) −793.126 −1.28546 −0.642728 0.766095i \(-0.722197\pi\)
−0.642728 + 0.766095i \(0.722197\pi\)
\(618\) 1122.54 1.81640
\(619\) 1010.76i 1.63290i 0.577419 + 0.816448i \(0.304060\pi\)
−0.577419 + 0.816448i \(0.695940\pi\)
\(620\) 919.333 1.48280
\(621\) 442.345i 0.712310i
\(622\) 553.206i 0.889399i
\(623\) −719.868 133.127i −1.15549 0.213688i
\(624\) −375.599 −0.601921
\(625\) −167.142 −0.267428
\(626\) 267.410i 0.427173i
\(627\) 6.93852 0.0110662
\(628\) 874.202i 1.39204i
\(629\) 472.990i 0.751972i
\(630\) −972.821 179.907i −1.54416 0.285566i
\(631\) 322.792 0.511556 0.255778 0.966736i \(-0.417668\pi\)
0.255778 + 0.966736i \(0.417668\pi\)
\(632\) −420.344 −0.665101
\(633\) 194.509i 0.307281i
\(634\) −1038.99 −1.63879
\(635\) 429.772i 0.676807i
\(636\) 2899.63i 4.55917i
\(637\) 182.173 475.693i 0.285986 0.746770i
\(638\) 47.6867 0.0747441
\(639\) 566.531 0.886591
\(640\) 834.663i 1.30416i
\(641\) −322.875 −0.503706 −0.251853 0.967766i \(-0.581040\pi\)
−0.251853 + 0.967766i \(0.581040\pi\)
\(642\) 1135.76i 1.76910i
\(643\) 576.809i 0.897059i 0.893768 + 0.448530i \(0.148052\pi\)
−0.893768 + 0.448530i \(0.851948\pi\)
\(644\) −321.534 + 1738.65i −0.499276 + 2.69977i
\(645\) −15.8419 −0.0245612
\(646\) −432.479 −0.669473
\(647\) 1110.71i 1.71670i −0.513061 0.858352i \(-0.671489\pi\)
0.513061 0.858352i \(-0.328511\pi\)
\(648\) 529.557 0.817218
\(649\) 4.75127i 0.00732091i
\(650\) 428.868i 0.659797i
\(651\) −205.438 + 1110.88i −0.315573 + 1.70642i
\(652\) 422.464 0.647952
\(653\) −1043.70 −1.59831 −0.799157 0.601123i \(-0.794720\pi\)
−0.799157 + 0.601123i \(0.794720\pi\)
\(654\) 1673.75i 2.55925i
\(655\) 763.775 1.16607
\(656\) 50.7301i 0.0773325i
\(657\) 338.445i 0.515137i
\(658\) −1311.25 242.493i −1.99278 0.368531i
\(659\) 644.973 0.978715 0.489358 0.872083i \(-0.337231\pi\)
0.489358 + 0.872083i \(0.337231\pi\)
\(660\) 37.1801 0.0563334
\(661\) 985.098i 1.49031i 0.666889 + 0.745157i \(0.267626\pi\)
−0.666889 + 0.745157i \(0.732374\pi\)
\(662\) −1286.45 −1.94328
\(663\) 1258.98i 1.89891i
\(664\) 810.181i 1.22015i
\(665\) −22.0087 + 119.009i −0.0330958 + 0.178961i
\(666\) 705.826 1.05980
\(667\) 1568.53 2.35162
\(668\) 797.447i 1.19378i
\(669\) 1331.67 1.99053
\(670\) 478.614i 0.714350i
\(671\) 1.96955i 0.00293525i
\(672\) 549.807 + 101.677i 0.818165 + 0.151306i
\(673\) −505.650 −0.751337 −0.375668 0.926754i \(-0.622587\pi\)
−0.375668 + 0.926754i \(0.622587\pi\)
\(674\) 1762.93 2.61562
\(675\) 156.663i 0.232094i
\(676\) 443.843 0.656573
\(677\) 330.539i 0.488241i 0.969745 + 0.244120i \(0.0784992\pi\)
−0.969745 + 0.244120i \(0.921501\pi\)
\(678\) 1944.91i 2.86860i
\(679\) 452.025 + 83.5944i 0.665722 + 0.123114i
\(680\) −1044.85 −1.53655
\(681\) −252.298 −0.370482
\(682\) 37.3084i 0.0547044i
\(683\) 1198.70 1.75506 0.877529 0.479523i \(-0.159190\pi\)
0.877529 + 0.479523i \(0.159190\pi\)
\(684\) 416.602i 0.609068i
\(685\) 522.356i 0.762564i
\(686\) 600.868 983.124i 0.875900 1.43312i
\(687\) 360.121 0.524194
\(688\) −7.71714 −0.0112168
\(689\) 907.417i 1.31701i
\(690\) 1894.50 2.74566
\(691\) 41.6454i 0.0602683i 0.999546 + 0.0301342i \(0.00959345\pi\)
−0.999546 + 0.0301342i \(0.990407\pi\)
\(692\) 1255.10i 1.81373i
\(693\) −4.71294 + 25.4846i −0.00680079 + 0.0367743i
\(694\) 668.414 0.963132
\(695\) 809.020 1.16406
\(696\) 2275.76i 3.26976i
\(697\) −170.044 −0.243965
\(698\) 1747.70i 2.50387i
\(699\) 1631.19i 2.33361i
\(700\) 113.876 615.769i 0.162680 0.879670i
\(701\) 1216.91 1.73597 0.867984 0.496592i \(-0.165415\pi\)
0.867984 + 0.496592i \(0.165415\pi\)
\(702\) −445.461 −0.634559
\(703\) 86.3465i 0.122826i
\(704\) −28.4108 −0.0403562
\(705\) 922.315i 1.30825i
\(706\) 1199.81i 1.69945i
\(707\) 148.736 + 27.5063i 0.210377 + 0.0389056i
\(708\) 502.910 0.710325
\(709\) −1040.79 −1.46797 −0.733985 0.679166i \(-0.762342\pi\)
−0.733985 + 0.679166i \(0.762342\pi\)
\(710\) 575.312i 0.810298i
\(711\) −449.490 −0.632194
\(712\) 1153.78i 1.62047i
\(713\) 1227.16i 1.72113i
\(714\) 517.865 2800.28i 0.725301 3.92197i
\(715\) 11.6352 0.0162730
\(716\) 2246.81 3.13801
\(717\) 1561.80i 2.17824i
\(718\) −2374.13 −3.30658
\(719\) 1297.76i 1.80496i 0.430735 + 0.902479i \(0.358254\pi\)
−0.430735 + 0.902479i \(0.641746\pi\)
\(720\) 333.331i 0.462960i
\(721\) 504.380 + 93.2766i 0.699556 + 0.129371i
\(722\) −1133.72 −1.57025
\(723\) 1445.31 1.99904
\(724\) 2264.27i 3.12744i
\(725\) −555.520 −0.766234
\(726\) 1852.12i 2.55113i
\(727\) 193.812i 0.266592i −0.991076 0.133296i \(-0.957444\pi\)
0.991076 0.133296i \(-0.0425561\pi\)
\(728\) −789.419 145.990i −1.08437 0.200535i
\(729\) 1089.84 1.49498
\(730\) 343.690 0.470809
\(731\) 25.8673i 0.0353862i
\(732\) 208.472 0.284798
\(733\) 206.817i 0.282152i −0.989999 0.141076i \(-0.954944\pi\)
0.989999 0.141076i \(-0.0450562\pi\)
\(734\) 662.786i 0.902978i
\(735\) −744.225 285.011i −1.01255 0.387770i
\(736\) −607.361 −0.825218
\(737\) 12.5381 0.0170123
\(738\) 253.750i 0.343835i
\(739\) 226.483 0.306473 0.153236 0.988190i \(-0.451030\pi\)
0.153236 + 0.988190i \(0.451030\pi\)
\(740\) 462.688i 0.625254i
\(741\) 229.833i 0.310165i
\(742\) 373.254 2018.32i 0.503038 2.72011i
\(743\) 485.772 0.653798 0.326899 0.945059i \(-0.393996\pi\)
0.326899 + 0.945059i \(0.393996\pi\)
\(744\) 1780.47 2.39311
\(745\) 540.091i 0.724954i
\(746\) 13.5385 0.0181482
\(747\) 866.357i 1.15978i
\(748\) 60.7090i 0.0811618i
\(749\) 94.3756 510.323i 0.126002 0.681339i
\(750\) −2036.81 −2.71575
\(751\) −1070.91 −1.42598 −0.712990 0.701175i \(-0.752659\pi\)
−0.712990 + 0.701175i \(0.752659\pi\)
\(752\) 449.291i 0.597461i
\(753\) −253.076 −0.336091
\(754\) 1579.58i 2.09494i
\(755\) 944.686i 1.25124i
\(756\) −639.593 118.282i −0.846022 0.156457i
\(757\) −685.121 −0.905047 −0.452524 0.891752i \(-0.649476\pi\)
−0.452524 + 0.891752i \(0.649476\pi\)
\(758\) 1083.67 1.42965
\(759\) 49.6295i 0.0653881i
\(760\) 190.743 0.250978
\(761\) 630.601i 0.828648i −0.910129 0.414324i \(-0.864018\pi\)
0.910129 0.414324i \(-0.135982\pi\)
\(762\) 1846.09i 2.42269i
\(763\) −139.080 + 752.054i −0.182280 + 0.985654i
\(764\) 731.518 0.957484
\(765\) −1117.30 −1.46053
\(766\) 2094.39i 2.73419i
\(767\) 157.382 0.205191
\(768\) 1933.94i 2.51815i
\(769\) 253.107i 0.329138i −0.986366 0.164569i \(-0.947377\pi\)
0.986366 0.164569i \(-0.0526233\pi\)
\(770\) 25.8796 + 4.78599i 0.0336098 + 0.00621557i
\(771\) 2146.67 2.78427
\(772\) −257.540 −0.333602
\(773\) 719.710i 0.931060i 0.885032 + 0.465530i \(0.154136\pi\)
−0.885032 + 0.465530i \(0.845864\pi\)
\(774\) −38.6009 −0.0498719
\(775\) 434.619i 0.560799i
\(776\) 724.488i 0.933618i
\(777\) 559.090 + 103.394i 0.719550 + 0.133069i
\(778\) 1164.44 1.49671
\(779\) 31.0423 0.0398489
\(780\) 1231.56i 1.57892i
\(781\) −15.0712 −0.0192973
\(782\) 3093.42i 3.95578i
\(783\) 577.012i 0.736925i
\(784\) −362.537 138.838i −0.462420 0.177090i
\(785\) 428.009 0.545235
\(786\) 3280.80 4.17405
\(787\) 1179.98i 1.49934i 0.661812 + 0.749670i \(0.269788\pi\)
−0.661812 + 0.749670i \(0.730212\pi\)
\(788\) 1234.33 1.56641
\(789\) 2106.63i 2.67000i
\(790\) 456.456i 0.577793i
\(791\) 161.612 873.893i 0.204313 1.10479i
\(792\) 40.8457 0.0515728
\(793\) 65.2398 0.0822696
\(794\) 327.689i 0.412707i
\(795\) −1419.66 −1.78574
\(796\) 189.770i 0.238405i
\(797\) 667.758i 0.837840i 0.908023 + 0.418920i \(0.137591\pi\)
−0.908023 + 0.418920i \(0.862409\pi\)
\(798\) −94.5386 + 511.205i −0.118469 + 0.640607i
\(799\) −1505.99 −1.88485
\(800\) 215.106 0.268883
\(801\) 1233.78i 1.54029i
\(802\) −1261.95 −1.57351
\(803\) 9.00351i 0.0112123i
\(804\) 1327.12i 1.65065i
\(805\) 851.243 + 157.423i 1.05744 + 0.195556i
\(806\) 1235.81 1.53326
\(807\) 440.229 0.545513
\(808\) 238.389i 0.295036i
\(809\) −1168.53 −1.44441 −0.722204 0.691681i \(-0.756871\pi\)
−0.722204 + 0.691681i \(0.756871\pi\)
\(810\) 575.052i 0.709941i
\(811\) 59.9705i 0.0739464i −0.999316 0.0369732i \(-0.988228\pi\)
0.999316 0.0369732i \(-0.0117716\pi\)
\(812\) −419.422 + 2267.96i −0.516529 + 2.79306i
\(813\) −1284.15 −1.57952
\(814\) −18.7768 −0.0230673
\(815\) 206.839i 0.253790i
\(816\) −959.500 −1.17586
\(817\) 4.72220i 0.00577992i
\(818\) 44.4761i 0.0543717i
\(819\) −844.156 156.112i −1.03072 0.190613i
\(820\) 166.340 0.202854
\(821\) −286.648 −0.349145 −0.174573 0.984644i \(-0.555854\pi\)
−0.174573 + 0.984644i \(0.555854\pi\)
\(822\) 2243.79i 2.72967i
\(823\) −114.212 −0.138776 −0.0693879 0.997590i \(-0.522105\pi\)
−0.0693879 + 0.997590i \(0.522105\pi\)
\(824\) 808.400i 0.981068i
\(825\) 17.5771i 0.0213055i
\(826\) 350.056 + 64.7369i 0.423797 + 0.0783740i
\(827\) −911.840 −1.10259 −0.551294 0.834311i \(-0.685866\pi\)
−0.551294 + 0.834311i \(0.685866\pi\)
\(828\) 2979.86 3.59886
\(829\) 371.561i 0.448204i −0.974566 0.224102i \(-0.928055\pi\)
0.974566 0.224102i \(-0.0719449\pi\)
\(830\) −879.785 −1.05998
\(831\) 1345.33i 1.61893i
\(832\) 941.083i 1.13111i
\(833\) 465.377 1215.20i 0.558676 1.45882i
\(834\) 3475.15 4.16685
\(835\) −390.430 −0.467581
\(836\) 11.0827i 0.0132568i
\(837\) 451.434 0.539348
\(838\) 926.648i 1.10579i
\(839\) 1373.24i 1.63676i −0.574676 0.818381i \(-0.694872\pi\)
0.574676 0.818381i \(-0.305128\pi\)
\(840\) −228.402 + 1235.05i −0.271907 + 1.47030i
\(841\) 1205.06 1.43289
\(842\) −956.115 −1.13553
\(843\) 1976.93i 2.34511i
\(844\) −310.684 −0.368109
\(845\) 217.306i 0.257167i
\(846\) 2247.34i 2.65643i
\(847\) −153.901 + 832.199i −0.181702 + 0.982526i
\(848\) −691.565 −0.815524
\(849\) −2067.32 −2.43501
\(850\) 1095.58i 1.28892i
\(851\) −617.616 −0.725753
\(852\) 1595.25i 1.87236i
\(853\) 207.974i 0.243814i −0.992542 0.121907i \(-0.961099\pi\)
0.992542 0.121907i \(-0.0389010\pi\)
\(854\) 145.109 + 26.8355i 0.169917 + 0.0314233i
\(855\) 203.969 0.238560
\(856\) −817.925 −0.955520
\(857\) 348.844i 0.407053i 0.979069 + 0.203526i \(0.0652403\pi\)
−0.979069 + 0.203526i \(0.934760\pi\)
\(858\) 49.9791 0.0582507
\(859\) 1250.96i 1.45630i −0.685417 0.728150i \(-0.740380\pi\)
0.685417 0.728150i \(-0.259620\pi\)
\(860\) 25.3039i 0.0294231i
\(861\) −37.1710 + 200.997i −0.0431719 + 0.233446i
\(862\) −1050.30 −1.21845
\(863\) −816.828 −0.946498 −0.473249 0.880929i \(-0.656919\pi\)
−0.473249 + 0.880929i \(0.656919\pi\)
\(864\) 223.428i 0.258598i
\(865\) 614.498 0.710402
\(866\) 1162.08i 1.34189i
\(867\) 1898.22i 2.18942i
\(868\) 1774.38 + 328.141i 2.04421 + 0.378042i
\(869\) 11.9576 0.0137602
\(870\) 2471.27 2.84054
\(871\) 415.313i 0.476823i
\(872\) 1205.36 1.38230
\(873\) 774.722i 0.887425i
\(874\) 564.718i 0.646130i
\(875\) −915.185 169.248i −1.04593 0.193426i
\(876\) 953.000 1.08790
\(877\) 961.635 1.09650 0.548252 0.836313i \(-0.315293\pi\)
0.548252 + 0.836313i \(0.315293\pi\)
\(878\) 175.660i 0.200069i
\(879\) −1309.31 −1.48955
\(880\) 8.86747i 0.0100767i
\(881\) 1434.50i 1.62826i −0.580684 0.814129i \(-0.697215\pi\)
0.580684 0.814129i \(-0.302785\pi\)
\(882\) −1813.40 694.465i −2.05601 0.787375i
\(883\) −455.276 −0.515602 −0.257801 0.966198i \(-0.582998\pi\)
−0.257801 + 0.966198i \(0.582998\pi\)
\(884\) −2010.94 −2.27481
\(885\) 246.225i 0.278220i
\(886\) −1854.32 −2.09291
\(887\) 644.091i 0.726146i −0.931761 0.363073i \(-0.881728\pi\)
0.931761 0.363073i \(-0.118272\pi\)
\(888\) 896.087i 1.00911i
\(889\) 153.400 829.490i 0.172553 0.933059i
\(890\) 1252.90 1.40775
\(891\) −15.0644 −0.0169073
\(892\) 2127.04i 2.38457i
\(893\) 274.926 0.307867
\(894\) 2319.97i 2.59504i
\(895\) 1100.04i 1.22910i
\(896\) 297.919 1610.96i 0.332499 1.79794i
\(897\) 1643.94 1.83270
\(898\) −760.563 −0.846952
\(899\) 1600.76i 1.78060i
\(900\) −1055.36 −1.17262
\(901\) 2318.08i 2.57278i
\(902\) 6.75041i 0.00748383i
\(903\) −30.5760 5.65452i −0.0338605 0.00626192i
\(904\) −1400.64 −1.54938
\(905\) −1108.59 −1.22496
\(906\) 4057.91i 4.47893i
\(907\) −925.902 −1.02084 −0.510420 0.859925i \(-0.670510\pi\)
−0.510420 + 0.859925i \(0.670510\pi\)
\(908\) 402.989i 0.443821i
\(909\) 254.918i 0.280438i
\(910\) −158.532 + 857.239i −0.174211 + 0.942021i
\(911\) −1443.40 −1.58441 −0.792205 0.610254i \(-0.791067\pi\)
−0.792205 + 0.610254i \(0.791067\pi\)
\(912\) 175.161 0.192063
\(913\) 23.0474i 0.0252435i
\(914\) 1458.97 1.59625
\(915\) 102.068i 0.111550i
\(916\) 575.212i 0.627960i
\(917\) 1474.14 + 272.617i 1.60757 + 0.297292i
\(918\) −1137.97 −1.23962
\(919\) 306.624 0.333650 0.166825 0.985987i \(-0.446649\pi\)
0.166825 + 0.985987i \(0.446649\pi\)
\(920\) 1364.34i 1.48298i
\(921\) −2077.55 −2.25576
\(922\) 854.273i 0.926544i
\(923\) 499.221i 0.540868i
\(924\) 71.7601 + 13.2708i 0.0776624 + 0.0143623i
\(925\) 218.738 0.236474
\(926\) −513.109 −0.554113
\(927\) 864.453i 0.932527i
\(928\) −792.266 −0.853735
\(929\) 253.479i 0.272852i 0.990650 + 0.136426i \(0.0435616\pi\)
−0.990650 + 0.136426i \(0.956438\pi\)
\(930\) 1933.43i 2.07896i
\(931\) −84.9566 + 221.840i −0.0912531 + 0.238281i
\(932\) 2605.46 2.79556
\(933\) 751.025 0.804957
\(934\) 753.951i 0.807229i
\(935\) 29.7232 0.0317895
\(936\) 1352.98i 1.44549i
\(937\) 604.636i 0.645289i 0.946520 + 0.322645i \(0.104572\pi\)
−0.946520 + 0.322645i \(0.895428\pi\)
\(938\) −170.833 + 923.758i −0.182125 + 0.984817i
\(939\) 363.032 0.386616
\(940\) 1473.19 1.56722
\(941\) 114.537i 0.121719i 0.998146 + 0.0608593i \(0.0193841\pi\)
−0.998146 + 0.0608593i \(0.980616\pi\)
\(942\) 1838.52 1.95172
\(943\) 222.038i 0.235459i
\(944\) 119.944i 0.127060i
\(945\) −57.9108 + 313.145i −0.0612813 + 0.331370i
\(946\) 1.02688 0.00108550
\(947\) 110.502 0.116686 0.0583431 0.998297i \(-0.481418\pi\)
0.0583431 + 0.998297i \(0.481418\pi\)
\(948\) 1265.68i 1.33511i
\(949\) 298.234 0.314261
\(950\) 200.003i 0.210530i
\(951\) 1410.52i 1.48320i
\(952\) −2016.64 372.944i −2.11832 0.391747i
\(953\) −954.457 −1.00153 −0.500764 0.865584i \(-0.666948\pi\)
−0.500764 + 0.865584i \(0.666948\pi\)
\(954\) −3459.18 −3.62598
\(955\) 358.151i 0.375028i
\(956\) −2494.62 −2.60944
\(957\) 64.7388i 0.0676476i
\(958\) 668.181i 0.697475i
\(959\) −186.446 + 1008.18i −0.194417 + 1.05129i
\(960\) −1472.33 −1.53368
\(961\) −291.381 −0.303206
\(962\) 621.966i 0.646534i
\(963\) −874.638 −0.908243
\(964\) 2308.55i 2.39476i
\(965\) 126.092i 0.130665i
\(966\) 3656.52 + 676.212i 3.78522 + 0.700012i
\(967\) −175.233 −0.181213 −0.0906063 0.995887i \(-0.528880\pi\)
−0.0906063 + 0.995887i \(0.528880\pi\)
\(968\) 1333.82 1.37791
\(969\) 587.128i 0.605911i
\(970\) −786.729 −0.811061
\(971\) 1515.13i 1.56039i 0.625539 + 0.780193i \(0.284879\pi\)
−0.625539 + 0.780193i \(0.715121\pi\)
\(972\) 2430.81i 2.50083i
\(973\) 1561.46 + 288.766i 1.60479 + 0.296779i
\(974\) −1449.30 −1.48799
\(975\) −582.225 −0.597154
\(976\) 49.7208i 0.0509435i
\(977\) −1089.12 −1.11476 −0.557381 0.830257i \(-0.688194\pi\)
−0.557381 + 0.830257i \(0.688194\pi\)
\(978\) 888.477i 0.908464i
\(979\) 32.8216i 0.0335257i
\(980\) −455.240 + 1188.73i −0.464531 + 1.21299i
\(981\) 1288.94 1.31390
\(982\) −2507.39 −2.55335
\(983\) 1353.41i 1.37682i 0.725323 + 0.688409i \(0.241691\pi\)
−0.725323 + 0.688409i \(0.758309\pi\)
\(984\) 322.150 0.327388
\(985\) 604.329i 0.613532i
\(986\) 4035.18i 4.09248i
\(987\) −329.205 + 1780.13i −0.333541 + 1.80358i
\(988\) 367.105 0.371564
\(989\) 33.7767 0.0341524
\(990\) 44.3548i 0.0448028i
\(991\) 529.599 0.534409 0.267204 0.963640i \(-0.413900\pi\)
0.267204 + 0.963640i \(0.413900\pi\)
\(992\) 619.841i 0.624840i
\(993\) 1746.46i 1.75878i
\(994\) 205.348 1110.39i 0.206588 1.11709i
\(995\) 92.9115 0.0933784
\(996\) −2439.51 −2.44930
\(997\) 113.108i 0.113448i 0.998390 + 0.0567241i \(0.0180656\pi\)
−0.998390 + 0.0567241i \(0.981934\pi\)
\(998\) −2439.36 −2.44425
\(999\) 227.201i 0.227428i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 287.3.b.a.83.6 yes 52
7.6 odd 2 inner 287.3.b.a.83.5 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.3.b.a.83.5 52 7.6 odd 2 inner
287.3.b.a.83.6 yes 52 1.1 even 1 trivial