Properties

Label 287.3.d.c.286.7
Level $287$
Weight $3$
Character 287.286
Analytic conductor $7.820$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [287,3,Mod(286,287)]
 
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, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.286");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 287.d (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: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 120x^{6} + 2874x^{4} + 16920x^{2} + 19881 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{41}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 286.7
Root \(-2.54461i\) of defining polynomial
Character \(\chi\) \(=\) 287.286
Dual form 287.3.d.c.286.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +4.37780 q^{3} -3.00000 q^{4} -3.17602i q^{5} -4.37780 q^{6} +(-0.818350 + 6.95200i) q^{7} +7.00000 q^{8} +10.1652 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +4.37780 q^{3} -3.00000 q^{4} -3.17602i q^{5} -4.37780 q^{6} +(-0.818350 + 6.95200i) q^{7} +7.00000 q^{8} +10.1652 q^{9} +3.17602i q^{10} +19.4050i q^{11} -13.1334 q^{12} -4.37780 q^{13} +(0.818350 - 6.95200i) q^{14} -13.9040i q^{15} +5.00000 q^{16} +25.3531 q^{17} -10.1652 q^{18} +23.3350 q^{19} +9.52807i q^{20} +(-3.58258 + 30.4345i) q^{21} -19.4050i q^{22} +0.747727 q^{23} +30.6446 q^{24} +14.9129 q^{25} +4.37780 q^{26} +5.10080 q^{27} +(2.45505 - 20.8560i) q^{28} -11.3049i q^{29} +13.9040i q^{30} -17.7304i q^{31} -33.0000 q^{32} +84.9514i q^{33} -25.3531 q^{34} +(22.0797 + 2.59910i) q^{35} -30.4955 q^{36} -37.1652 q^{37} -23.3350 q^{38} -19.1652 q^{39} -22.2322i q^{40} +(28.1896 + 29.7716i) q^{41} +(3.58258 - 30.4345i) q^{42} +35.4955 q^{43} -58.2151i q^{44} -32.2848i q^{45} -0.747727 q^{46} -52.0013 q^{47} +21.8890 q^{48} +(-47.6606 - 11.3783i) q^{49} -14.9129 q^{50} +110.991 q^{51} +13.1334 q^{52} +69.2172i q^{53} -5.10080 q^{54} +61.6308 q^{55} +(-5.72845 + 48.6640i) q^{56} +102.156 q^{57} +11.3049i q^{58} +20.9064i q^{59} +41.7120i q^{60} +75.4233i q^{61} +17.7304i q^{62} +(-8.31865 + 70.6681i) q^{63} +13.0000 q^{64} +13.9040i q^{65} -84.9514i q^{66} -61.1170i q^{67} -76.0593 q^{68} +3.27340 q^{69} +(-22.0797 - 2.59910i) q^{70} -107.724i q^{71} +71.1561 q^{72} +19.0561i q^{73} +37.1652 q^{74} +65.2856 q^{75} -70.0050 q^{76} +(-134.904 - 15.8801i) q^{77} +19.1652 q^{78} +46.9102i q^{79} -15.8801i q^{80} -69.1561 q^{81} +(-28.1896 - 29.7716i) q^{82} -165.401i q^{83} +(10.7477 - 91.3034i) q^{84} -80.5221i q^{85} -35.4955 q^{86} -49.4906i q^{87} +135.835i q^{88} -70.9187 q^{89} +32.2848i q^{90} +(3.58258 - 30.4345i) q^{91} -2.24318 q^{92} -77.6201i q^{93} +52.0013 q^{94} -74.1125i q^{95} -144.467 q^{96} +100.539 q^{97} +(47.6606 + 11.3783i) q^{98} +197.255i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} - 24 q^{4} + 56 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} - 24 q^{4} + 56 q^{8} + 8 q^{9} + 40 q^{16} - 8 q^{18} + 8 q^{21} - 104 q^{23} - 64 q^{25} - 264 q^{32} - 24 q^{36} - 224 q^{37} - 80 q^{39} - 8 q^{42} + 64 q^{43} + 104 q^{46} - 88 q^{49} + 64 q^{50} + 448 q^{51} + 304 q^{57} + 104 q^{64} + 56 q^{72} + 224 q^{74} - 456 q^{77} + 80 q^{78} - 40 q^{81} - 24 q^{84} - 64 q^{86} - 8 q^{91} + 312 q^{92} + 88 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.500000 −0.250000 0.968246i \(-0.580431\pi\)
−0.250000 + 0.968246i \(0.580431\pi\)
\(3\) 4.37780 1.45927 0.729634 0.683838i \(-0.239691\pi\)
0.729634 + 0.683838i \(0.239691\pi\)
\(4\) −3.00000 −0.750000
\(5\) 3.17602i 0.635205i −0.948224 0.317602i \(-0.897122\pi\)
0.948224 0.317602i \(-0.102878\pi\)
\(6\) −4.37780 −0.729634
\(7\) −0.818350 + 6.95200i −0.116907 + 0.993143i
\(8\) 7.00000 0.875000
\(9\) 10.1652 1.12946
\(10\) 3.17602i 0.317602i
\(11\) 19.4050i 1.76409i 0.471162 + 0.882047i \(0.343835\pi\)
−0.471162 + 0.882047i \(0.656165\pi\)
\(12\) −13.1334 −1.09445
\(13\) −4.37780 −0.336754 −0.168377 0.985723i \(-0.553853\pi\)
−0.168377 + 0.985723i \(0.553853\pi\)
\(14\) 0.818350 6.95200i 0.0584536 0.496571i
\(15\) 13.9040i 0.926933i
\(16\) 5.00000 0.312500
\(17\) 25.3531 1.49136 0.745680 0.666304i \(-0.232125\pi\)
0.745680 + 0.666304i \(0.232125\pi\)
\(18\) −10.1652 −0.564731
\(19\) 23.3350 1.22816 0.614079 0.789244i \(-0.289528\pi\)
0.614079 + 0.789244i \(0.289528\pi\)
\(20\) 9.52807i 0.476403i
\(21\) −3.58258 + 30.4345i −0.170599 + 1.44926i
\(22\) 19.4050i 0.882047i
\(23\) 0.747727 0.0325099 0.0162549 0.999868i \(-0.494826\pi\)
0.0162549 + 0.999868i \(0.494826\pi\)
\(24\) 30.6446 1.27686
\(25\) 14.9129 0.596515
\(26\) 4.37780 0.168377
\(27\) 5.10080 0.188919
\(28\) 2.45505 20.8560i 0.0876804 0.744857i
\(29\) 11.3049i 0.389824i −0.980821 0.194912i \(-0.937558\pi\)
0.980821 0.194912i \(-0.0624422\pi\)
\(30\) 13.9040i 0.463467i
\(31\) 17.7304i 0.571948i −0.958237 0.285974i \(-0.907683\pi\)
0.958237 0.285974i \(-0.0923171\pi\)
\(32\) −33.0000 −1.03125
\(33\) 84.9514i 2.57428i
\(34\) −25.3531 −0.745680
\(35\) 22.0797 + 2.59910i 0.630849 + 0.0742600i
\(36\) −30.4955 −0.847096
\(37\) −37.1652 −1.00446 −0.502232 0.864733i \(-0.667488\pi\)
−0.502232 + 0.864733i \(0.667488\pi\)
\(38\) −23.3350 −0.614079
\(39\) −19.1652 −0.491414
\(40\) 22.2322i 0.555804i
\(41\) 28.1896 + 29.7716i 0.687550 + 0.726137i
\(42\) 3.58258 30.4345i 0.0852994 0.724630i
\(43\) 35.4955 0.825476 0.412738 0.910850i \(-0.364573\pi\)
0.412738 + 0.910850i \(0.364573\pi\)
\(44\) 58.2151i 1.32307i
\(45\) 32.2848i 0.717439i
\(46\) −0.747727 −0.0162549
\(47\) −52.0013 −1.10641 −0.553206 0.833045i \(-0.686596\pi\)
−0.553206 + 0.833045i \(0.686596\pi\)
\(48\) 21.8890 0.456021
\(49\) −47.6606 11.3783i −0.972665 0.232211i
\(50\) −14.9129 −0.298258
\(51\) 110.991 2.17629
\(52\) 13.1334 0.252566
\(53\) 69.2172i 1.30598i 0.757365 + 0.652992i \(0.226487\pi\)
−0.757365 + 0.652992i \(0.773513\pi\)
\(54\) −5.10080 −0.0944593
\(55\) 61.6308 1.12056
\(56\) −5.72845 + 48.6640i −0.102294 + 0.869000i
\(57\) 102.156 1.79221
\(58\) 11.3049i 0.194912i
\(59\) 20.9064i 0.354346i 0.984180 + 0.177173i \(0.0566952\pi\)
−0.984180 + 0.177173i \(0.943305\pi\)
\(60\) 41.7120i 0.695200i
\(61\) 75.4233i 1.23645i 0.786002 + 0.618224i \(0.212148\pi\)
−0.786002 + 0.618224i \(0.787852\pi\)
\(62\) 17.7304i 0.285974i
\(63\) −8.31865 + 70.6681i −0.132042 + 1.12172i
\(64\) 13.0000 0.203125
\(65\) 13.9040i 0.213908i
\(66\) 84.9514i 1.28714i
\(67\) 61.1170i 0.912195i −0.889930 0.456097i \(-0.849247\pi\)
0.889930 0.456097i \(-0.150753\pi\)
\(68\) −76.0593 −1.11852
\(69\) 3.27340 0.0474406
\(70\) −22.0797 2.59910i −0.315424 0.0371300i
\(71\) 107.724i 1.51725i −0.651530 0.758623i \(-0.725873\pi\)
0.651530 0.758623i \(-0.274127\pi\)
\(72\) 71.1561 0.988279
\(73\) 19.0561i 0.261043i 0.991445 + 0.130521i \(0.0416652\pi\)
−0.991445 + 0.130521i \(0.958335\pi\)
\(74\) 37.1652 0.502232
\(75\) 65.2856 0.870475
\(76\) −70.0050 −0.921119
\(77\) −134.904 15.8801i −1.75200 0.206235i
\(78\) 19.1652 0.245707
\(79\) 46.9102i 0.593800i 0.954909 + 0.296900i \(0.0959528\pi\)
−0.954909 + 0.296900i \(0.904047\pi\)
\(80\) 15.8801i 0.198501i
\(81\) −69.1561 −0.853779
\(82\) −28.1896 29.7716i −0.343775 0.363068i
\(83\) 165.401i 1.99278i −0.0848743 0.996392i \(-0.527049\pi\)
0.0848743 0.996392i \(-0.472951\pi\)
\(84\) 10.7477 91.3034i 0.127949 1.08695i
\(85\) 80.5221i 0.947318i
\(86\) −35.4955 −0.412738
\(87\) 49.4906i 0.568858i
\(88\) 135.835i 1.54358i
\(89\) −70.9187 −0.796840 −0.398420 0.917203i \(-0.630441\pi\)
−0.398420 + 0.917203i \(0.630441\pi\)
\(90\) 32.2848i 0.358719i
\(91\) 3.58258 30.4345i 0.0393690 0.334445i
\(92\) −2.24318 −0.0243824
\(93\) 77.6201i 0.834625i
\(94\) 52.0013 0.553206
\(95\) 74.1125i 0.780132i
\(96\) −144.467 −1.50487
\(97\) 100.539 1.03648 0.518240 0.855235i \(-0.326587\pi\)
0.518240 + 0.855235i \(0.326587\pi\)
\(98\) 47.6606 + 11.3783i 0.486333 + 0.116106i
\(99\) 197.255i 1.99248i
\(100\) −44.7386 −0.447386
\(101\) −87.5162 −0.866497 −0.433249 0.901274i \(-0.642633\pi\)
−0.433249 + 0.901274i \(0.642633\pi\)
\(102\) −110.991 −1.08815
\(103\) 112.734i 1.09451i 0.836966 + 0.547254i \(0.184327\pi\)
−0.836966 + 0.547254i \(0.815673\pi\)
\(104\) −30.6446 −0.294660
\(105\) 96.6606 + 11.3783i 0.920577 + 0.108365i
\(106\) 69.2172i 0.652992i
\(107\) −89.6515 −0.837865 −0.418932 0.908017i \(-0.637596\pi\)
−0.418932 + 0.908017i \(0.637596\pi\)
\(108\) −15.3024 −0.141689
\(109\) 170.053i 1.56012i −0.625707 0.780059i \(-0.715189\pi\)
0.625707 0.780059i \(-0.284811\pi\)
\(110\) −61.6308 −0.560280
\(111\) −162.702 −1.46578
\(112\) −4.09175 + 34.7600i −0.0365335 + 0.310357i
\(113\) 61.4083 0.543437 0.271718 0.962377i \(-0.412408\pi\)
0.271718 + 0.962377i \(0.412408\pi\)
\(114\) −102.156 −0.896106
\(115\) 2.37480i 0.0206504i
\(116\) 33.9147i 0.292368i
\(117\) −44.5010 −0.380351
\(118\) 20.9064i 0.177173i
\(119\) −20.7477 + 176.255i −0.174351 + 1.48113i
\(120\) 97.3280i 0.811067i
\(121\) −255.555 −2.11203
\(122\) 75.4233i 0.618224i
\(123\) 123.408 + 130.334i 1.00332 + 1.05963i
\(124\) 53.1912i 0.428961i
\(125\) 126.764i 1.01411i
\(126\) 8.31865 70.6681i 0.0660211 0.560858i
\(127\) 71.5644 0.563499 0.281750 0.959488i \(-0.409085\pi\)
0.281750 + 0.959488i \(0.409085\pi\)
\(128\) 119.000 0.929688
\(129\) 155.392 1.20459
\(130\) 13.9040i 0.106954i
\(131\) 242.951i 1.85459i −0.374331 0.927295i \(-0.622128\pi\)
0.374331 0.927295i \(-0.377872\pi\)
\(132\) 254.854i 1.93071i
\(133\) −19.0962 + 162.225i −0.143581 + 1.21974i
\(134\) 61.1170i 0.456097i
\(135\) 16.2003i 0.120002i
\(136\) 177.472 1.30494
\(137\) 60.8142i 0.443899i −0.975058 0.221950i \(-0.928758\pi\)
0.975058 0.221950i \(-0.0712421\pi\)
\(138\) −3.27340 −0.0237203
\(139\) 24.8837i 0.179019i 0.995986 + 0.0895096i \(0.0285300\pi\)
−0.995986 + 0.0895096i \(0.971470\pi\)
\(140\) −66.2391 7.79730i −0.473137 0.0556950i
\(141\) −227.652 −1.61455
\(142\) 107.724i 0.758623i
\(143\) 84.9514i 0.594066i
\(144\) 50.8258 0.352957
\(145\) −35.9046 −0.247618
\(146\) 19.0561i 0.130521i
\(147\) −208.649 49.8121i −1.41938 0.338858i
\(148\) 111.495 0.753348
\(149\) 15.8974i 0.106694i 0.998576 + 0.0533471i \(0.0169890\pi\)
−0.998576 + 0.0533471i \(0.983011\pi\)
\(150\) −65.2856 −0.435238
\(151\) 100.230i 0.663774i −0.943319 0.331887i \(-0.892315\pi\)
0.943319 0.331887i \(-0.107685\pi\)
\(152\) 163.345 1.07464
\(153\) 257.718 1.68443
\(154\) 134.904 + 15.8801i 0.875999 + 0.103118i
\(155\) −56.3121 −0.363304
\(156\) 57.4955 0.368561
\(157\) 24.4792 0.155919 0.0779593 0.996957i \(-0.475160\pi\)
0.0779593 + 0.996957i \(0.475160\pi\)
\(158\) 46.9102i 0.296900i
\(159\) 303.019i 1.90578i
\(160\) 104.809i 0.655055i
\(161\) −0.611903 + 5.19820i −0.00380064 + 0.0322869i
\(162\) 69.1561 0.426889
\(163\) 199.808 1.22581 0.612907 0.790155i \(-0.290000\pi\)
0.612907 + 0.790155i \(0.290000\pi\)
\(164\) −84.5687 89.3148i −0.515663 0.544603i
\(165\) 269.808 1.63520
\(166\) 165.401i 0.996392i
\(167\) 6.13391 0.0367300 0.0183650 0.999831i \(-0.494154\pi\)
0.0183650 + 0.999831i \(0.494154\pi\)
\(168\) −25.0780 + 213.041i −0.149274 + 1.26810i
\(169\) −149.835 −0.886597
\(170\) 80.5221i 0.473659i
\(171\) 237.204 1.38716
\(172\) −106.486 −0.619107
\(173\) 117.236i 0.677666i −0.940847 0.338833i \(-0.889968\pi\)
0.940847 0.338833i \(-0.110032\pi\)
\(174\) 49.4906i 0.284429i
\(175\) −12.2040 + 103.674i −0.0697369 + 0.592425i
\(176\) 97.0252i 0.551279i
\(177\) 91.5241i 0.517085i
\(178\) 70.9187 0.398420
\(179\) 44.9168i 0.250932i −0.992098 0.125466i \(-0.959957\pi\)
0.992098 0.125466i \(-0.0400425\pi\)
\(180\) 96.8543i 0.538079i
\(181\) 143.705 0.793948 0.396974 0.917830i \(-0.370060\pi\)
0.396974 + 0.917830i \(0.370060\pi\)
\(182\) −3.58258 + 30.4345i −0.0196845 + 0.167222i
\(183\) 330.188i 1.80431i
\(184\) 5.23409 0.0284461
\(185\) 118.037i 0.638040i
\(186\) 77.6201i 0.417313i
\(187\) 491.978i 2.63090i
\(188\) 156.004 0.829808
\(189\) −4.17424 + 35.4608i −0.0220859 + 0.187623i
\(190\) 74.1125i 0.390066i
\(191\) 225.366i 1.17993i −0.807430 0.589963i \(-0.799142\pi\)
0.807430 0.589963i \(-0.200858\pi\)
\(192\) 56.9114 0.296414
\(193\) 81.7334i 0.423489i −0.977325 0.211745i \(-0.932086\pi\)
0.977325 0.211745i \(-0.0679145\pi\)
\(194\) −100.539 −0.518240
\(195\) 60.8690i 0.312149i
\(196\) 142.982 + 34.1350i 0.729499 + 0.174158i
\(197\) −49.6879 −0.252223 −0.126111 0.992016i \(-0.540250\pi\)
−0.126111 + 0.992016i \(0.540250\pi\)
\(198\) 197.255i 0.996238i
\(199\) 361.339 1.81578 0.907888 0.419213i \(-0.137694\pi\)
0.907888 + 0.419213i \(0.137694\pi\)
\(200\) 104.390 0.521951
\(201\) 267.558i 1.33114i
\(202\) 87.5162 0.433249
\(203\) 78.5917 + 9.25137i 0.387151 + 0.0455732i
\(204\) −332.973 −1.63222
\(205\) 94.5553 89.5307i 0.461245 0.436735i
\(206\) 112.734i 0.547254i
\(207\) 7.60076 0.0367186
\(208\) −21.8890 −0.105236
\(209\) 452.817i 2.16659i
\(210\) −96.6606 11.3783i −0.460289 0.0541826i
\(211\) 130.031i 0.616262i 0.951344 + 0.308131i \(0.0997036\pi\)
−0.951344 + 0.308131i \(0.900296\pi\)
\(212\) 207.651i 0.979488i
\(213\) 471.596i 2.21407i
\(214\) 89.6515 0.418932
\(215\) 112.734i 0.524346i
\(216\) 35.7056 0.165304
\(217\) 123.262 + 14.5097i 0.568026 + 0.0668648i
\(218\) 170.053i 0.780059i
\(219\) 83.4240i 0.380932i
\(220\) −184.892 −0.840420
\(221\) −110.991 −0.502221
\(222\) 162.702 0.732890
\(223\) 159.850i 0.716817i −0.933565 0.358409i \(-0.883320\pi\)
0.933565 0.358409i \(-0.116680\pi\)
\(224\) 27.0056 229.416i 0.120561 1.02418i
\(225\) 151.592 0.673741
\(226\) −61.4083 −0.271718
\(227\) −41.3072 −0.181970 −0.0909851 0.995852i \(-0.529002\pi\)
−0.0909851 + 0.995852i \(0.529002\pi\)
\(228\) −306.468 −1.34416
\(229\) 240.096 1.04845 0.524227 0.851579i \(-0.324354\pi\)
0.524227 + 0.851579i \(0.324354\pi\)
\(230\) 2.37480i 0.0103252i
\(231\) −590.582 69.5200i −2.55663 0.300952i
\(232\) 79.1343i 0.341096i
\(233\) 406.118i 1.74300i 0.490400 + 0.871498i \(0.336851\pi\)
−0.490400 + 0.871498i \(0.663149\pi\)
\(234\) 44.5010 0.190175
\(235\) 165.157i 0.702797i
\(236\) 62.7192i 0.265759i
\(237\) 205.364i 0.866513i
\(238\) 20.7477 176.255i 0.0871753 0.740567i
\(239\) 121.628i 0.508905i −0.967085 0.254453i \(-0.918105\pi\)
0.967085 0.254453i \(-0.0818953\pi\)
\(240\) 69.5200i 0.289667i
\(241\) 266.509i 1.10585i 0.833232 + 0.552924i \(0.186488\pi\)
−0.833232 + 0.552924i \(0.813512\pi\)
\(242\) 255.555 1.05601
\(243\) −348.659 −1.43481
\(244\) 226.270i 0.927336i
\(245\) −36.1379 + 151.371i −0.147502 + 0.617842i
\(246\) −123.408 130.334i −0.501660 0.529814i
\(247\) −102.156 −0.413587
\(248\) 124.113i 0.500455i
\(249\) 724.093i 2.90800i
\(250\) 126.764i 0.507057i
\(251\) 187.109i 0.745453i −0.927941 0.372726i \(-0.878423\pi\)
0.927941 0.372726i \(-0.121577\pi\)
\(252\) 24.9560 212.004i 0.0990316 0.841287i
\(253\) 14.5097i 0.0573505i
\(254\) −71.5644 −0.281750
\(255\) 352.510i 1.38239i
\(256\) −171.000 −0.667969
\(257\) −397.387 −1.54625 −0.773126 0.634253i \(-0.781308\pi\)
−0.773126 + 0.634253i \(0.781308\pi\)
\(258\) −155.392 −0.602295
\(259\) 30.4141 258.372i 0.117429 0.997576i
\(260\) 41.7120i 0.160431i
\(261\) 114.916i 0.440291i
\(262\) 242.951i 0.927295i
\(263\) 281.588i 1.07068i 0.844638 + 0.535338i \(0.179816\pi\)
−0.844638 + 0.535338i \(0.820184\pi\)
\(264\) 594.660i 2.25250i
\(265\) 219.835 0.829567
\(266\) 19.0962 162.225i 0.0717903 0.609868i
\(267\) −310.468 −1.16280
\(268\) 183.351i 0.684146i
\(269\) 207.214i 0.770312i 0.922852 + 0.385156i \(0.125852\pi\)
−0.922852 + 0.385156i \(0.874148\pi\)
\(270\) 16.2003i 0.0600010i
\(271\) 169.626i 0.625927i −0.949765 0.312963i \(-0.898678\pi\)
0.949765 0.312963i \(-0.101322\pi\)
\(272\) 126.766 0.466050
\(273\) 15.6838 133.236i 0.0574498 0.488044i
\(274\) 60.8142i 0.221950i
\(275\) 289.385i 1.05231i
\(276\) −9.82020 −0.0355804
\(277\) −85.9636 −0.310338 −0.155169 0.987888i \(-0.549592\pi\)
−0.155169 + 0.987888i \(0.549592\pi\)
\(278\) 24.8837i 0.0895096i
\(279\) 180.232i 0.645993i
\(280\) 154.558 + 18.1937i 0.551993 + 0.0649775i
\(281\) 245.074i 0.872149i −0.899911 0.436074i \(-0.856368\pi\)
0.899911 0.436074i \(-0.143632\pi\)
\(282\) 227.652 0.807275
\(283\) 203.790i 0.720106i −0.932932 0.360053i \(-0.882759\pi\)
0.932932 0.360053i \(-0.117241\pi\)
\(284\) 323.173i 1.13793i
\(285\) 324.450i 1.13842i
\(286\) 84.9514i 0.297033i
\(287\) −230.041 + 171.610i −0.801537 + 0.597945i
\(288\) −335.450 −1.16476
\(289\) 353.780 1.22415
\(290\) 35.9046 0.123809
\(291\) 440.138 1.51250
\(292\) 57.1684i 0.195782i
\(293\) −422.057 −1.44047 −0.720233 0.693732i \(-0.755965\pi\)
−0.720233 + 0.693732i \(0.755965\pi\)
\(294\) 208.649 + 49.8121i 0.709689 + 0.169429i
\(295\) 66.3992 0.225082
\(296\) −260.156 −0.878906
\(297\) 98.9812i 0.333270i
\(298\) 15.8974i 0.0533471i
\(299\) −3.27340 −0.0109478
\(300\) −195.857 −0.652856
\(301\) −29.0477 + 246.764i −0.0965040 + 0.819815i
\(302\) 100.230i 0.331887i
\(303\) −383.129 −1.26445
\(304\) 116.675 0.383800
\(305\) 239.546 0.785397
\(306\) −257.718 −0.842216
\(307\) 402.802i 1.31206i −0.754736 0.656029i \(-0.772235\pi\)
0.754736 0.656029i \(-0.227765\pi\)
\(308\) 404.711 + 47.6403i 1.31400 + 0.154676i
\(309\) 493.529i 1.59718i
\(310\) 56.3121 0.181652
\(311\) −112.670 −0.362284 −0.181142 0.983457i \(-0.557979\pi\)
−0.181142 + 0.983457i \(0.557979\pi\)
\(312\) −134.156 −0.429987
\(313\) 412.188 1.31690 0.658448 0.752626i \(-0.271213\pi\)
0.658448 + 0.752626i \(0.271213\pi\)
\(314\) −24.4792 −0.0779593
\(315\) 224.444 + 26.4202i 0.712519 + 0.0838738i
\(316\) 140.731i 0.445350i
\(317\) 322.391i 1.01701i 0.861060 + 0.508503i \(0.169801\pi\)
−0.861060 + 0.508503i \(0.830199\pi\)
\(318\) 303.019i 0.952890i
\(319\) 219.372 0.687686
\(320\) 41.2883i 0.129026i
\(321\) −392.477 −1.22267
\(322\) 0.611903 5.19820i 0.00190032 0.0161435i
\(323\) 591.615 1.83163
\(324\) 207.468 0.640334
\(325\) −65.2856 −0.200879
\(326\) −199.808 −0.612907
\(327\) 744.457i 2.27663i
\(328\) 197.327 + 208.401i 0.601607 + 0.635370i
\(329\) 42.5553 361.513i 0.129347 1.09882i
\(330\) −269.808 −0.817599
\(331\) 320.574i 0.968502i 0.874929 + 0.484251i \(0.160908\pi\)
−0.874929 + 0.484251i \(0.839092\pi\)
\(332\) 496.203i 1.49459i
\(333\) −377.789 −1.13450
\(334\) −6.13391 −0.0183650
\(335\) −194.109 −0.579430
\(336\) −17.9129 + 152.172i −0.0533121 + 0.452894i
\(337\) 264.018 0.783437 0.391718 0.920085i \(-0.371881\pi\)
0.391718 + 0.920085i \(0.371881\pi\)
\(338\) 149.835 0.443298
\(339\) 268.834 0.793019
\(340\) 241.566i 0.710489i
\(341\) 344.059 1.00897
\(342\) −237.204 −0.693579
\(343\) 118.105 322.025i 0.344330 0.938849i
\(344\) 248.468 0.722291
\(345\) 10.3964i 0.0301345i
\(346\) 117.236i 0.338833i
\(347\) 70.4285i 0.202964i 0.994837 + 0.101482i \(0.0323584\pi\)
−0.994837 + 0.101482i \(0.967642\pi\)
\(348\) 148.472i 0.426643i
\(349\) 516.862i 1.48098i 0.672068 + 0.740489i \(0.265406\pi\)
−0.672068 + 0.740489i \(0.734594\pi\)
\(350\) 12.2040 103.674i 0.0348685 0.296212i
\(351\) −22.3303 −0.0636191
\(352\) 640.366i 1.81922i
\(353\) 289.266i 0.819450i −0.912209 0.409725i \(-0.865625\pi\)
0.912209 0.409725i \(-0.134375\pi\)
\(354\) 91.5241i 0.258543i
\(355\) −342.135 −0.963761
\(356\) 212.756 0.597630
\(357\) −90.8294 + 771.609i −0.254424 + 2.16137i
\(358\) 44.9168i 0.125466i
\(359\) −606.450 −1.68928 −0.844638 0.535338i \(-0.820184\pi\)
−0.844638 + 0.535338i \(0.820184\pi\)
\(360\) 225.993i 0.627759i
\(361\) 183.523 0.508373
\(362\) −143.705 −0.396974
\(363\) −1118.77 −3.08201
\(364\) −10.7477 + 91.3034i −0.0295267 + 0.250834i
\(365\) 60.5227 0.165816
\(366\) 330.188i 0.902154i
\(367\) 443.813i 1.20930i −0.796491 0.604650i \(-0.793313\pi\)
0.796491 0.604650i \(-0.206687\pi\)
\(368\) 3.73864 0.0101593
\(369\) 286.551 + 302.633i 0.776561 + 0.820143i
\(370\) 118.037i 0.319020i
\(371\) −481.198 56.6439i −1.29703 0.152679i
\(372\) 232.860i 0.625969i
\(373\) 92.4682 0.247904 0.123952 0.992288i \(-0.460443\pi\)
0.123952 + 0.992288i \(0.460443\pi\)
\(374\) 491.978i 1.31545i
\(375\) 554.949i 1.47986i
\(376\) −364.009 −0.968110
\(377\) 49.4906i 0.131275i
\(378\) 4.17424 35.4608i 0.0110430 0.0938116i
\(379\) −325.441 −0.858683 −0.429342 0.903142i \(-0.641254\pi\)
−0.429342 + 0.903142i \(0.641254\pi\)
\(380\) 222.338i 0.585099i
\(381\) 313.295 0.822296
\(382\) 225.366i 0.589963i
\(383\) 545.025 1.42304 0.711521 0.702665i \(-0.248007\pi\)
0.711521 + 0.702665i \(0.248007\pi\)
\(384\) 520.958 1.35666
\(385\) −50.4356 + 428.458i −0.131002 + 1.11288i
\(386\) 81.7334i 0.211745i
\(387\) 360.817 0.932343
\(388\) −301.616 −0.777360
\(389\) 137.964 0.354662 0.177331 0.984151i \(-0.443254\pi\)
0.177331 + 0.984151i \(0.443254\pi\)
\(390\) 60.8690i 0.156074i
\(391\) 18.9572 0.0484839
\(392\) −333.624 79.6484i −0.851082 0.203185i
\(393\) 1063.59i 2.70634i
\(394\) 49.6879 0.126111
\(395\) 148.988 0.377184
\(396\) 591.765i 1.49436i
\(397\) −509.231 −1.28270 −0.641349 0.767249i \(-0.721625\pi\)
−0.641349 + 0.767249i \(0.721625\pi\)
\(398\) −361.339 −0.907888
\(399\) −83.5994 + 710.189i −0.209522 + 1.77992i
\(400\) 74.5644 0.186411
\(401\) 29.7568 0.0742065 0.0371033 0.999311i \(-0.488187\pi\)
0.0371033 + 0.999311i \(0.488187\pi\)
\(402\) 267.558i 0.665568i
\(403\) 77.6201i 0.192606i
\(404\) 262.549 0.649873
\(405\) 219.641i 0.542324i
\(406\) −78.5917 9.25137i −0.193576 0.0227866i
\(407\) 721.191i 1.77197i
\(408\) 776.936 1.90426
\(409\) 9.28024i 0.0226901i 0.999936 + 0.0113450i \(0.00361132\pi\)
−0.999936 + 0.0113450i \(0.996389\pi\)
\(410\) −94.5553 + 89.5307i −0.230623 + 0.218368i
\(411\) 266.233i 0.647768i
\(412\) 338.203i 0.820881i
\(413\) −145.341 17.1088i −0.351916 0.0414256i
\(414\) −7.60076 −0.0183593
\(415\) −525.317 −1.26583
\(416\) 144.467 0.347278
\(417\) 108.936i 0.261237i
\(418\) 452.817i 1.08329i
\(419\) 156.674i 0.373924i −0.982367 0.186962i \(-0.940136\pi\)
0.982367 0.186962i \(-0.0598641\pi\)
\(420\) −289.982 34.1350i −0.690433 0.0812739i
\(421\) 149.739i 0.355675i −0.984060 0.177838i \(-0.943090\pi\)
0.984060 0.177838i \(-0.0569102\pi\)
\(422\) 130.031i 0.308131i
\(423\) −528.601 −1.24965
\(424\) 484.520i 1.14274i
\(425\) 378.088 0.889619
\(426\) 471.596i 1.10703i
\(427\) −524.343 61.7227i −1.22797 0.144550i
\(428\) 268.955 0.628398
\(429\) 371.900i 0.866901i
\(430\) 112.734i 0.262173i
\(431\) −489.408 −1.13552 −0.567759 0.823195i \(-0.692189\pi\)
−0.567759 + 0.823195i \(0.692189\pi\)
\(432\) 25.5040 0.0590371
\(433\) 626.973i 1.44798i 0.689813 + 0.723988i \(0.257693\pi\)
−0.689813 + 0.723988i \(0.742307\pi\)
\(434\) −123.262 14.5097i −0.284013 0.0334324i
\(435\) −157.183 −0.361341
\(436\) 510.158i 1.17009i
\(437\) 17.4482 0.0399273
\(438\) 83.4240i 0.190466i
\(439\) 245.911 0.560163 0.280081 0.959976i \(-0.409639\pi\)
0.280081 + 0.959976i \(0.409639\pi\)
\(440\) 431.416 0.980490
\(441\) −484.477 115.663i −1.09859 0.262273i
\(442\) 110.991 0.251111
\(443\) −664.744 −1.50055 −0.750275 0.661126i \(-0.770079\pi\)
−0.750275 + 0.661126i \(0.770079\pi\)
\(444\) 488.105 1.09934
\(445\) 225.240i 0.506156i
\(446\) 159.850i 0.358409i
\(447\) 69.5958i 0.155695i
\(448\) −10.6386 + 90.3760i −0.0237468 + 0.201732i
\(449\) 2.79848 0.00623270 0.00311635 0.999995i \(-0.499008\pi\)
0.00311635 + 0.999995i \(0.499008\pi\)
\(450\) −151.592 −0.336870
\(451\) −577.719 + 547.019i −1.28097 + 1.21290i
\(452\) −184.225 −0.407577
\(453\) 438.787i 0.968624i
\(454\) 41.3072 0.0909851
\(455\) −96.6606 11.3783i −0.212441 0.0250073i
\(456\) 715.092 1.56819
\(457\) 736.912i 1.61250i −0.591576 0.806249i \(-0.701494\pi\)
0.591576 0.806249i \(-0.298506\pi\)
\(458\) −240.096 −0.524227
\(459\) 129.321 0.281746
\(460\) 7.12440i 0.0154878i
\(461\) 304.316i 0.660121i 0.943960 + 0.330061i \(0.107069\pi\)
−0.943960 + 0.330061i \(0.892931\pi\)
\(462\) 590.582 + 69.5200i 1.27832 + 0.150476i
\(463\) 438.392i 0.946851i −0.880834 0.473426i \(-0.843017\pi\)
0.880834 0.473426i \(-0.156983\pi\)
\(464\) 56.5245i 0.121820i
\(465\) −246.523 −0.530158
\(466\) 406.118i 0.871498i
\(467\) 205.116i 0.439220i 0.975588 + 0.219610i \(0.0704785\pi\)
−0.975588 + 0.219610i \(0.929522\pi\)
\(468\) 133.503 0.285263
\(469\) 424.886 + 50.0151i 0.905939 + 0.106642i
\(470\) 165.157i 0.351399i
\(471\) 107.165 0.227527
\(472\) 146.345i 0.310053i
\(473\) 688.790i 1.45622i
\(474\) 205.364i 0.433256i
\(475\) 347.992 0.732615
\(476\) 62.2432 528.765i 0.130763 1.11085i
\(477\) 703.603i 1.47506i
\(478\) 121.628i 0.254453i
\(479\) 181.269 0.378433 0.189216 0.981935i \(-0.439405\pi\)
0.189216 + 0.981935i \(0.439405\pi\)
\(480\) 458.832i 0.955900i
\(481\) 162.702 0.338257
\(482\) 266.509i 0.552924i
\(483\) −2.67879 + 22.7567i −0.00554615 + 0.0471153i
\(484\) 766.666 1.58402
\(485\) 319.313i 0.658377i
\(486\) 348.659 0.717405
\(487\) −844.083 −1.73323 −0.866615 0.498977i \(-0.833709\pi\)
−0.866615 + 0.498977i \(0.833709\pi\)
\(488\) 527.963i 1.08189i
\(489\) 874.718 1.78879
\(490\) 36.1379 151.371i 0.0737508 0.308921i
\(491\) 675.459 1.37568 0.687840 0.725862i \(-0.258559\pi\)
0.687840 + 0.725862i \(0.258559\pi\)
\(492\) −370.225 391.003i −0.752490 0.794721i
\(493\) 286.614i 0.581368i
\(494\) 102.156 0.206794
\(495\) 626.487 1.26563
\(496\) 88.6519i 0.178734i
\(497\) 748.900 + 88.1563i 1.50684 + 0.177377i
\(498\) 724.093i 1.45400i
\(499\) 676.880i 1.35647i 0.734844 + 0.678236i \(0.237255\pi\)
−0.734844 + 0.678236i \(0.762745\pi\)
\(500\) 380.293i 0.760585i
\(501\) 26.8530 0.0535989
\(502\) 187.109i 0.372726i
\(503\) 286.456 0.569495 0.284747 0.958603i \(-0.408090\pi\)
0.284747 + 0.958603i \(0.408090\pi\)
\(504\) −58.2306 + 494.677i −0.115537 + 0.981502i
\(505\) 277.954i 0.550403i
\(506\) 14.5097i 0.0286752i
\(507\) −655.947 −1.29378
\(508\) −214.693 −0.422624
\(509\) 381.854 0.750204 0.375102 0.926984i \(-0.377608\pi\)
0.375102 + 0.926984i \(0.377608\pi\)
\(510\) 352.510i 0.691195i
\(511\) −132.478 15.5946i −0.259253 0.0305178i
\(512\) −305.000 −0.595703
\(513\) 119.027 0.232022
\(514\) 397.387 0.773126
\(515\) 358.047 0.695237
\(516\) −466.176 −0.903442
\(517\) 1009.09i 1.95181i
\(518\) −30.4141 + 258.372i −0.0587145 + 0.498788i
\(519\) 513.237i 0.988895i
\(520\) 97.3280i 0.187169i
\(521\) 439.901 0.844340 0.422170 0.906517i \(-0.361269\pi\)
0.422170 + 0.906517i \(0.361269\pi\)
\(522\) 114.916i 0.220146i
\(523\) 627.498i 1.19980i 0.800073 + 0.599902i \(0.204794\pi\)
−0.800073 + 0.599902i \(0.795206\pi\)
\(524\) 728.854i 1.39094i
\(525\) −53.4265 + 453.866i −0.101765 + 0.864506i
\(526\) 281.588i 0.535338i
\(527\) 449.521i 0.852980i
\(528\) 424.757i 0.804464i
\(529\) −528.441 −0.998943
\(530\) −219.835 −0.414784
\(531\) 212.517i 0.400220i
\(532\) 57.2886 486.675i 0.107685 0.914803i
\(533\) −123.408 130.334i −0.231535 0.244529i
\(534\) 310.468 0.581401
\(535\) 284.735i 0.532215i
\(536\) 427.819i 0.798170i
\(537\) 196.637i 0.366176i
\(538\) 207.214i 0.385156i
\(539\) 220.797 924.856i 0.409642 1.71587i
\(540\) 48.6008i 0.0900015i
\(541\) 791.248 1.46257 0.731283 0.682074i \(-0.238922\pi\)
0.731283 + 0.682074i \(0.238922\pi\)
\(542\) 169.626i 0.312963i
\(543\) 629.111 1.15858
\(544\) −836.653 −1.53796
\(545\) −540.091 −0.990994
\(546\) −15.6838 + 133.236i −0.0287249 + 0.244022i
\(547\) 694.771i 1.27015i −0.772451 0.635074i \(-0.780970\pi\)
0.772451 0.635074i \(-0.219030\pi\)
\(548\) 182.443i 0.332924i
\(549\) 766.690i 1.39652i
\(550\) 289.385i 0.526154i
\(551\) 263.800i 0.478766i
\(552\) 22.9138 0.0415105
\(553\) −326.120 38.3890i −0.589728 0.0694195i
\(554\) 85.9636 0.155169
\(555\) 516.744i 0.931071i
\(556\) 74.6510i 0.134264i
\(557\) 216.837i 0.389294i 0.980873 + 0.194647i \(0.0623561\pi\)
−0.980873 + 0.194647i \(0.937644\pi\)
\(558\) 180.232i 0.322997i
\(559\) −155.392 −0.277982
\(560\) 110.399 + 12.9955i 0.197140 + 0.0232062i
\(561\) 2153.78i 3.83918i
\(562\) 245.074i 0.436074i
\(563\) −850.335 −1.51036 −0.755182 0.655515i \(-0.772452\pi\)
−0.755182 + 0.655515i \(0.772452\pi\)
\(564\) 682.955 1.21091
\(565\) 195.034i 0.345193i
\(566\) 203.790i 0.360053i
\(567\) 56.5939 480.773i 0.0998128 0.847924i
\(568\) 754.071i 1.32759i
\(569\) −21.7932 −0.0383009 −0.0191504 0.999817i \(-0.506096\pi\)
−0.0191504 + 0.999817i \(0.506096\pi\)
\(570\) 324.450i 0.569211i
\(571\) 248.152i 0.434592i −0.976106 0.217296i \(-0.930276\pi\)
0.976106 0.217296i \(-0.0697237\pi\)
\(572\) 254.854i 0.445549i
\(573\) 986.607i 1.72183i
\(574\) 230.041 171.610i 0.400769 0.298973i
\(575\) 11.1508 0.0193926
\(576\) 132.147 0.229422
\(577\) −919.649 −1.59384 −0.796922 0.604082i \(-0.793540\pi\)
−0.796922 + 0.604082i \(0.793540\pi\)
\(578\) −353.780 −0.612077
\(579\) 357.813i 0.617984i
\(580\) 107.714 0.185714
\(581\) 1149.87 + 135.356i 1.97912 + 0.232971i
\(582\) −440.138 −0.756251
\(583\) −1343.16 −2.30388
\(584\) 133.393i 0.228413i
\(585\) 141.336i 0.241600i
\(586\) 422.057 0.720233
\(587\) 284.318 0.484358 0.242179 0.970232i \(-0.422138\pi\)
0.242179 + 0.970232i \(0.422138\pi\)
\(588\) 625.946 + 149.436i 1.06453 + 0.254144i
\(589\) 413.739i 0.702443i
\(590\) −66.3992 −0.112541
\(591\) −217.524 −0.368060
\(592\) −185.826 −0.313895
\(593\) 875.768 1.47684 0.738421 0.674340i \(-0.235572\pi\)
0.738421 + 0.674340i \(0.235572\pi\)
\(594\) 98.9812i 0.166635i
\(595\) 559.789 + 65.8953i 0.940823 + 0.110748i
\(596\) 47.6923i 0.0800206i
\(597\) 1581.87 2.64970
\(598\) 3.27340 0.00547392
\(599\) −353.405 −0.589991 −0.294995 0.955499i \(-0.595318\pi\)
−0.294995 + 0.955499i \(0.595318\pi\)
\(600\) 456.999 0.761666
\(601\) 581.231 0.967107 0.483553 0.875315i \(-0.339346\pi\)
0.483553 + 0.875315i \(0.339346\pi\)
\(602\) 29.0477 246.764i 0.0482520 0.409908i
\(603\) 621.264i 1.03029i
\(604\) 300.690i 0.497831i
\(605\) 811.649i 1.34157i
\(606\) 383.129 0.632226
\(607\) 774.119i 1.27532i −0.770318 0.637660i \(-0.779902\pi\)
0.770318 0.637660i \(-0.220098\pi\)
\(608\) −770.055 −1.26654
\(609\) 344.059 + 40.5007i 0.564957 + 0.0665035i
\(610\) −239.546 −0.392699
\(611\) 227.652 0.372588
\(612\) −773.155 −1.26332
\(613\) −524.018 −0.854842 −0.427421 0.904053i \(-0.640578\pi\)
−0.427421 + 0.904053i \(0.640578\pi\)
\(614\) 402.802i 0.656029i
\(615\) 413.944 391.948i 0.673080 0.637313i
\(616\) −944.327 111.161i −1.53300 0.180456i
\(617\) −897.684 −1.45492 −0.727459 0.686151i \(-0.759299\pi\)
−0.727459 + 0.686151i \(0.759299\pi\)
\(618\) 493.529i 0.798590i
\(619\) 605.790i 0.978660i −0.872099 0.489330i \(-0.837241\pi\)
0.872099 0.489330i \(-0.162759\pi\)
\(620\) 168.936 0.272478
\(621\) 3.81401 0.00614172
\(622\) 112.670 0.181142
\(623\) 58.0364 493.027i 0.0931563 0.791376i
\(624\) −95.8258 −0.153567
\(625\) −29.7841 −0.0476545
\(626\) −412.188 −0.658448
\(627\) 1982.34i 3.16163i
\(628\) −73.4376 −0.116939
\(629\) −942.252 −1.49802
\(630\) −224.444 26.4202i −0.356260 0.0419369i
\(631\) 823.492 1.30506 0.652529 0.757764i \(-0.273708\pi\)
0.652529 + 0.757764i \(0.273708\pi\)
\(632\) 328.371i 0.519575i
\(633\) 569.252i 0.899292i
\(634\) 322.391i 0.508503i
\(635\) 227.290i 0.357937i
\(636\) 909.057i 1.42934i
\(637\) 208.649 + 49.8121i 0.327549 + 0.0781980i
\(638\) −219.372 −0.343843
\(639\) 1095.03i 1.71367i
\(640\) 377.947i 0.590542i
\(641\) 207.954i 0.324422i −0.986756 0.162211i \(-0.948138\pi\)
0.986756 0.162211i \(-0.0518625\pi\)
\(642\) 392.477 0.611334
\(643\) 1005.93 1.56444 0.782218 0.623004i \(-0.214088\pi\)
0.782218 + 0.623004i \(0.214088\pi\)
\(644\) 1.83571 15.5946i 0.00285048 0.0242152i
\(645\) 493.529i 0.765161i
\(646\) −591.615 −0.915813
\(647\) 1177.11i 1.81934i 0.415335 + 0.909669i \(0.363664\pi\)
−0.415335 + 0.909669i \(0.636336\pi\)
\(648\) −484.092 −0.747056
\(649\) −405.690 −0.625100
\(650\) 65.2856 0.100439
\(651\) 539.615 + 63.5205i 0.828902 + 0.0975737i
\(652\) −599.423 −0.919360
\(653\) 492.015i 0.753468i −0.926321 0.376734i \(-0.877047\pi\)
0.926321 0.376734i \(-0.122953\pi\)
\(654\) 744.457i 1.13831i
\(655\) −771.619 −1.17804
\(656\) 140.948 + 148.858i 0.214859 + 0.226918i
\(657\) 193.709i 0.294838i
\(658\) −42.5553 + 361.513i −0.0646737 + 0.549412i
\(659\) 490.198i 0.743851i 0.928263 + 0.371925i \(0.121302\pi\)
−0.928263 + 0.371925i \(0.878698\pi\)
\(660\) −809.423 −1.22640
\(661\) 925.986i 1.40089i 0.713708 + 0.700444i \(0.247014\pi\)
−0.713708 + 0.700444i \(0.752986\pi\)
\(662\) 320.574i 0.484251i
\(663\) −485.896 −0.732875
\(664\) 1157.81i 1.74369i
\(665\) 515.230 + 60.6500i 0.774782 + 0.0912030i
\(666\) 377.789 0.567251
\(667\) 8.45298i 0.0126731i
\(668\) −18.4017 −0.0275475
\(669\) 699.793i 1.04603i
\(670\) 194.109 0.289715
\(671\) −1463.59 −2.18121
\(672\) 118.225 1004.34i 0.175930 1.49455i
\(673\) 750.563i 1.11525i 0.830093 + 0.557625i \(0.188287\pi\)
−0.830093 + 0.557625i \(0.811713\pi\)
\(674\) −264.018 −0.391718
\(675\) 76.0676 0.112693
\(676\) 449.505 0.664948
\(677\) 208.540i 0.308035i −0.988068 0.154017i \(-0.950779\pi\)
0.988068 0.154017i \(-0.0492212\pi\)
\(678\) −268.834 −0.396510
\(679\) −82.2758 + 698.944i −0.121172 + 1.02937i
\(680\) 563.654i 0.828904i
\(681\) −180.835 −0.265543
\(682\) −344.059 −0.504485
\(683\) 693.080i 1.01476i −0.861723 0.507379i \(-0.830614\pi\)
0.861723 0.507379i \(-0.169386\pi\)
\(684\) −711.612 −1.04037
\(685\) −193.147 −0.281967
\(686\) −118.105 + 322.025i −0.172165 + 0.469424i
\(687\) 1051.09 1.52997
\(688\) 177.477 0.257961
\(689\) 303.019i 0.439795i
\(690\) 10.3964i 0.0150672i
\(691\) 345.402 0.499858 0.249929 0.968264i \(-0.419593\pi\)
0.249929 + 0.968264i \(0.419593\pi\)
\(692\) 351.708i 0.508249i
\(693\) −1371.32 161.424i −1.97881 0.232935i
\(694\) 70.4285i 0.101482i
\(695\) 79.0311 0.113714
\(696\) 346.434i 0.497750i
\(697\) 714.693 + 754.803i 1.02538 + 1.08293i
\(698\) 516.862i 0.740489i
\(699\) 1777.90i 2.54350i
\(700\) 36.6119 311.023i 0.0523027 0.444319i
\(701\) −604.359 −0.862138 −0.431069 0.902319i \(-0.641864\pi\)
−0.431069 + 0.902319i \(0.641864\pi\)
\(702\) 22.3303 0.0318095
\(703\) −867.249 −1.23364
\(704\) 252.265i 0.358332i
\(705\) 723.026i 1.02557i
\(706\) 289.266i 0.409725i
\(707\) 71.6189 608.413i 0.101300 0.860556i
\(708\) 274.572i 0.387814i
\(709\) 581.369i 0.819984i 0.912089 + 0.409992i \(0.134469\pi\)
−0.912089 + 0.409992i \(0.865531\pi\)
\(710\) 342.135 0.481880
\(711\) 476.849i 0.670674i
\(712\) −496.431 −0.697235
\(713\) 13.2575i 0.0185940i
\(714\) 90.8294 771.609i 0.127212 1.08068i
\(715\) −269.808 −0.377353
\(716\) 134.750i 0.188199i
\(717\) 532.465i 0.742629i
\(718\) 606.450 0.844638
\(719\) 320.556 0.445836 0.222918 0.974837i \(-0.428442\pi\)
0.222918 + 0.974837i \(0.428442\pi\)
\(720\) 161.424i 0.224200i
\(721\) −783.729 92.2562i −1.08700 0.127956i
\(722\) −183.523 −0.254187
\(723\) 1166.72i 1.61373i
\(724\) −431.114 −0.595461
\(725\) 168.589i 0.232536i
\(726\) 1118.77 1.54101
\(727\) 830.527 1.14240 0.571202 0.820810i \(-0.306477\pi\)
0.571202 + 0.820810i \(0.306477\pi\)
\(728\) 25.0780 213.041i 0.0344478 0.292639i
\(729\) −903.955 −1.23999
\(730\) −60.5227 −0.0829078
\(731\) 899.920 1.23108
\(732\) 990.565i 1.35323i
\(733\) 1033.69i 1.41022i −0.709096 0.705112i \(-0.750897\pi\)
0.709096 0.705112i \(-0.249103\pi\)
\(734\) 443.813i 0.604650i
\(735\) −158.204 + 662.673i −0.215244 + 0.901596i
\(736\) −24.6750 −0.0335258
\(737\) 1185.98 1.60920
\(738\) −286.551 302.633i −0.388281 0.410072i
\(739\) 224.330 0.303559 0.151780 0.988414i \(-0.451500\pi\)
0.151780 + 0.988414i \(0.451500\pi\)
\(740\) 354.112i 0.478530i
\(741\) −447.219 −0.603534
\(742\) 481.198 + 56.6439i 0.648514 + 0.0763395i
\(743\) 350.661 0.471952 0.235976 0.971759i \(-0.424171\pi\)
0.235976 + 0.971759i \(0.424171\pi\)
\(744\) 543.341i 0.730297i
\(745\) 50.4906 0.0677726
\(746\) −92.4682 −0.123952
\(747\) 1681.33i 2.25077i
\(748\) 1475.93i 1.97317i
\(749\) 73.3663 623.257i 0.0979524 0.832119i
\(750\) 554.949i 0.739932i
\(751\) 378.916i 0.504548i 0.967656 + 0.252274i \(0.0811784\pi\)
−0.967656 + 0.252274i \(0.918822\pi\)
\(752\) −260.007 −0.345753
\(753\) 819.125i 1.08781i
\(754\) 49.4906i 0.0656374i
\(755\) −318.333 −0.421633
\(756\) 12.5227 106.382i 0.0165645 0.140717i
\(757\) 1274.27i 1.68332i 0.540008 + 0.841660i \(0.318421\pi\)
−0.540008 + 0.841660i \(0.681579\pi\)
\(758\) 325.441 0.429342
\(759\) 63.5205i 0.0836897i
\(760\) 518.788i 0.682615i
\(761\) 1364.03i 1.79242i −0.443633 0.896209i \(-0.646311\pi\)
0.443633 0.896209i \(-0.353689\pi\)
\(762\) −313.295 −0.411148
\(763\) 1182.21 + 139.163i 1.54942 + 0.182389i
\(764\) 676.098i 0.884945i
\(765\) 818.519i 1.06996i
\(766\) −545.025 −0.711521
\(767\) 91.5241i 0.119327i
\(768\) −748.604 −0.974745
\(769\) 978.653i 1.27263i 0.771429 + 0.636315i \(0.219542\pi\)
−0.771429 + 0.636315i \(0.780458\pi\)
\(770\) 50.4356 428.458i 0.0655008 0.556438i
\(771\) −1739.68 −2.25639
\(772\) 245.200i 0.317617i
\(773\) −226.445 −0.292943 −0.146472 0.989215i \(-0.546792\pi\)
−0.146472 + 0.989215i \(0.546792\pi\)
\(774\) −360.817 −0.466171
\(775\) 264.411i 0.341176i
\(776\) 703.770 0.906920
\(777\) 133.147 1131.10i 0.171360 1.45573i
\(778\) −137.964 −0.177331
\(779\) 657.804 + 694.721i 0.844421 + 0.891811i
\(780\) 182.607i 0.234111i
\(781\) 2090.40 2.67656
\(782\) −18.9572 −0.0242420
\(783\) 57.6641i 0.0736450i
\(784\) −238.303 56.8917i −0.303958 0.0725660i
\(785\) 77.7465i 0.0990402i
\(786\) 1063.59i 1.35317i
\(787\) 609.986i 0.775078i 0.921853 + 0.387539i \(0.126675\pi\)
−0.921853 + 0.387539i \(0.873325\pi\)
\(788\) 149.064 0.189167
\(789\) 1232.73i 1.56240i
\(790\) −148.988 −0.188592
\(791\) −50.2535 + 426.911i −0.0635316 + 0.539710i
\(792\) 1380.79i 1.74342i
\(793\) 330.188i 0.416379i
\(794\) 509.231 0.641349
\(795\) 962.395 1.21056
\(796\) −1084.02 −1.36183
\(797\) 329.010i 0.412810i −0.978467 0.206405i \(-0.933824\pi\)
0.978467 0.206405i \(-0.0661764\pi\)
\(798\) 83.5994 710.189i 0.104761 0.889961i
\(799\) −1318.40 −1.65006
\(800\) −492.125 −0.615156
\(801\) −720.900 −0.900000
\(802\) −29.7568 −0.0371033
\(803\) −369.785 −0.460504
\(804\) 802.675i 0.998352i
\(805\) 16.5096 + 1.94342i 0.0205088 + 0.00241418i
\(806\) 77.6201i 0.0963029i
\(807\) 907.141i 1.12409i
\(808\) −612.614 −0.758185
\(809\) 1030.94i 1.27434i 0.770724 + 0.637169i \(0.219895\pi\)
−0.770724 + 0.637169i \(0.780105\pi\)
\(810\) 219.641i 0.271162i
\(811\) 1254.91i 1.54736i −0.633576 0.773680i \(-0.718414\pi\)
0.633576 0.773680i \(-0.281586\pi\)
\(812\) −235.775 27.7541i −0.290363 0.0341799i
\(813\) 742.589i 0.913394i
\(814\) 721.191i 0.885984i
\(815\) 634.593i 0.778642i
\(816\) 554.955 0.680091
\(817\) 828.287 1.01381
\(818\) 9.28024i 0.0113450i
\(819\) 36.4174 309.371i 0.0444657 0.377742i
\(820\) −283.666 + 268.592i −0.345934 + 0.327551i
\(821\) −83.4303 −0.101620 −0.0508102 0.998708i \(-0.516180\pi\)
−0.0508102 + 0.998708i \(0.516180\pi\)
\(822\) 266.233i 0.323884i
\(823\) 1216.66i 1.47833i −0.673526 0.739164i \(-0.735221\pi\)
0.673526 0.739164i \(-0.264779\pi\)
\(824\) 789.141i 0.957695i
\(825\) 1266.87i 1.53560i
\(826\) 145.341 + 17.1088i 0.175958 + 0.0207128i
\(827\) 1278.87i 1.54639i 0.634168 + 0.773195i \(0.281343\pi\)
−0.634168 + 0.773195i \(0.718657\pi\)
\(828\) −22.8023 −0.0275390
\(829\) 191.086i 0.230502i 0.993336 + 0.115251i \(0.0367672\pi\)
−0.993336 + 0.115251i \(0.963233\pi\)
\(830\) 525.317 0.632913
\(831\) −376.332 −0.452866
\(832\) −56.9114 −0.0684032
\(833\) −1208.34 288.476i −1.45059 0.346310i
\(834\) 108.936i 0.130618i
\(835\) 19.4814i 0.0233311i
\(836\) 1358.45i 1.62494i
\(837\) 90.4392i 0.108052i
\(838\) 156.674i 0.186962i
\(839\) −526.074 −0.627025 −0.313513 0.949584i \(-0.601506\pi\)
−0.313513 + 0.949584i \(0.601506\pi\)
\(840\) 676.624 + 79.6484i 0.805505 + 0.0948195i
\(841\) 713.199 0.848037
\(842\) 149.739i 0.177838i
\(843\) 1072.88i 1.27270i
\(844\) 390.094i 0.462197i
\(845\) 475.879i 0.563170i
\(846\) 528.601 0.624824
\(847\) 209.134 1776.62i 0.246911 2.09754i
\(848\) 346.086i 0.408120i
\(849\) 892.152i 1.05083i
\(850\) −378.088 −0.444809
\(851\) −27.7894 −0.0326550
\(852\) 1414.79i 1.66055i
\(853\) 336.906i 0.394966i −0.980306 0.197483i \(-0.936723\pi\)
0.980306 0.197483i \(-0.0632768\pi\)
\(854\) 524.343 + 61.7227i 0.613985 + 0.0722748i
\(855\) 753.365i 0.881129i
\(856\) −627.561 −0.733132
\(857\) 155.873i 0.181882i −0.995856 0.0909410i \(-0.971013\pi\)
0.995856 0.0909410i \(-0.0289875\pi\)
\(858\) 371.900i 0.433450i
\(859\) 694.996i 0.809075i 0.914521 + 0.404538i \(0.132568\pi\)
−0.914521 + 0.404538i \(0.867432\pi\)
\(860\) 338.203i 0.393259i
\(861\) −1007.07 + 751.276i −1.16966 + 0.872562i
\(862\) 489.408 0.567759
\(863\) −570.174 −0.660689 −0.330344 0.943861i \(-0.607165\pi\)
−0.330344 + 0.943861i \(0.607165\pi\)
\(864\) −168.326 −0.194822
\(865\) −372.345 −0.430456
\(866\) 626.973i 0.723988i
\(867\) 1548.78 1.78637
\(868\) −369.785 43.5290i −0.426020 0.0501486i
\(869\) −910.294 −1.04752
\(870\) 157.183 0.180670
\(871\) 267.558i 0.307185i
\(872\) 1190.37i 1.36510i
\(873\) 1021.99 1.17066
\(874\) −17.4482 −0.0199636
\(875\) 881.265 + 103.738i 1.00716 + 0.118557i
\(876\) 250.272i 0.285699i
\(877\) −1146.20 −1.30696 −0.653479 0.756944i \(-0.726691\pi\)
−0.653479 + 0.756944i \(0.726691\pi\)
\(878\) −245.911 −0.280081
\(879\) −1847.68 −2.10203
\(880\) 308.154 0.350175
\(881\) 749.703i 0.850968i 0.904966 + 0.425484i \(0.139896\pi\)
−0.904966 + 0.425484i \(0.860104\pi\)
\(882\) 484.477 + 115.663i 0.549294 + 0.131137i
\(883\) 1054.71i 1.19446i 0.802069 + 0.597231i \(0.203733\pi\)
−0.802069 + 0.597231i \(0.796267\pi\)
\(884\) 332.973 0.376666
\(885\) 290.683 0.328455
\(886\) 664.744 0.750275
\(887\) −27.7211 −0.0312527 −0.0156263 0.999878i \(-0.504974\pi\)
−0.0156263 + 0.999878i \(0.504974\pi\)
\(888\) −1138.91 −1.28256
\(889\) −58.5647 + 497.516i −0.0658771 + 0.559635i
\(890\) 225.240i 0.253078i
\(891\) 1341.98i 1.50615i
\(892\) 479.551i 0.537613i
\(893\) −1213.45 −1.35885
\(894\) 69.5958i 0.0778477i
\(895\) −142.657 −0.159393
\(896\) −97.3837 + 827.288i −0.108687 + 0.923312i
\(897\) −14.3303 −0.0159758
\(898\) −2.79848 −0.00311635
\(899\) −200.440 −0.222959
\(900\) −454.775 −0.505306
\(901\) 1754.87i 1.94769i
\(902\) 577.719 547.019i 0.640487 0.606452i
\(903\) −127.165 + 1080.29i −0.140825 + 1.19633i
\(904\) 429.858 0.475507
\(905\) 456.409i 0.504320i
\(906\) 438.787i 0.484312i
\(907\) −491.045 −0.541395 −0.270698 0.962664i \(-0.587254\pi\)
−0.270698 + 0.962664i \(0.587254\pi\)
\(908\) 123.922 0.136478
\(909\) −889.616 −0.978675
\(910\) 96.6606 + 11.3783i 0.106220 + 0.0125037i
\(911\) 983.070 1.07911 0.539556 0.841950i \(-0.318592\pi\)
0.539556 + 0.841950i \(0.318592\pi\)
\(912\) 510.780 0.560066
\(913\) 3209.61 3.51546
\(914\) 736.912i 0.806249i
\(915\) 1048.69 1.14610
\(916\) −720.288 −0.786340
\(917\) 1689.00 + 198.819i 1.84187 + 0.216815i
\(918\) −129.321 −0.140873
\(919\) 643.092i 0.699773i −0.936792 0.349887i \(-0.886220\pi\)
0.936792 0.349887i \(-0.113780\pi\)
\(920\) 16.6236i 0.0180691i
\(921\) 1763.39i 1.91464i
\(922\) 304.316i 0.330061i
\(923\) 471.596i 0.510938i
\(924\) 1771.75 + 208.560i 1.91747 + 0.225714i
\(925\) −554.239 −0.599178
\(926\) 438.392i 0.473426i
\(927\) 1145.96i 1.23620i
\(928\) 373.062i 0.402006i
\(929\) −210.388 −0.226467 −0.113234 0.993568i \(-0.536121\pi\)
−0.113234 + 0.993568i \(0.536121\pi\)
\(930\) 246.523 0.265079
\(931\) −1112.16 265.514i −1.19459 0.285192i
\(932\) 1218.35i 1.30725i
\(933\) −493.248 −0.528669
\(934\) 205.116i 0.219610i
\(935\) 1562.53 1.67116
\(936\) −311.507 −0.332807
\(937\) −329.915 −0.352098 −0.176049 0.984381i \(-0.556332\pi\)
−0.176049 + 0.984381i \(0.556332\pi\)
\(938\) −424.886 50.0151i −0.452970 0.0533210i
\(939\) 1804.48 1.92170
\(940\) 495.472i 0.527098i
\(941\) 947.198i 1.00659i −0.864116 0.503293i \(-0.832121\pi\)
0.864116 0.503293i \(-0.167879\pi\)
\(942\) −107.165 −0.113763
\(943\) 21.0781 + 22.2610i 0.0223522 + 0.0236066i
\(944\) 104.532i 0.110733i
\(945\) 112.624 + 13.2575i 0.119179 + 0.0140291i
\(946\) 688.790i 0.728108i
\(947\) −386.595 −0.408232 −0.204116 0.978947i \(-0.565432\pi\)
−0.204116 + 0.978947i \(0.565432\pi\)
\(948\) 616.091i 0.649885i
\(949\) 83.4240i 0.0879073i
\(950\) −347.992 −0.366308
\(951\) 1411.36i 1.48408i
\(952\) −145.234 + 1233.78i −0.152557 + 1.29599i
\(953\) −979.840 −1.02816 −0.514082 0.857741i \(-0.671867\pi\)
−0.514082 + 0.857741i \(0.671867\pi\)
\(954\) 703.603i 0.737529i
\(955\) −715.767 −0.749495
\(956\) 364.885i 0.381679i
\(957\) 960.367 1.00352
\(958\) −181.269 −0.189216
\(959\) 422.780 + 49.7673i 0.440855 + 0.0518950i
\(960\) 180.752i 0.188283i
\(961\) 646.633 0.672875
\(962\) −162.702 −0.169129
\(963\) −911.321 −0.946336
\(964\) 799.528i 0.829386i
\(965\) −259.587 −0.269002
\(966\) 2.67879 22.7567i 0.00277307 0.0235576i
\(967\) 84.0297i 0.0868973i −0.999056 0.0434486i \(-0.986166\pi\)
0.999056 0.0434486i \(-0.0138345\pi\)
\(968\) −1788.89 −1.84802
\(969\) 2589.97 2.67283
\(970\) 319.313i 0.329188i
\(971\) 147.565 0.151972 0.0759861 0.997109i \(-0.475790\pi\)
0.0759861 + 0.997109i \(0.475790\pi\)
\(972\) 1045.98 1.07611
\(973\) −172.991 20.3635i −0.177792 0.0209286i
\(974\) 844.083 0.866615
\(975\) −285.808 −0.293136
\(976\) 377.117i 0.386390i
\(977\) 116.077i 0.118810i −0.998234 0.0594050i \(-0.981080\pi\)
0.998234 0.0594050i \(-0.0189203\pi\)
\(978\) −874.718 −0.894395
\(979\) 1376.18i 1.40570i
\(980\) 108.414 454.114i 0.110626 0.463381i
\(981\) 1728.61i 1.76209i
\(982\) −675.459 −0.687840
\(983\) 1429.37i 1.45409i 0.686589 + 0.727046i \(0.259107\pi\)
−0.686589 + 0.727046i \(0.740893\pi\)
\(984\) 863.858 + 912.339i 0.877905 + 0.927174i
\(985\) 157.810i 0.160213i
\(986\) 286.614i 0.290684i
\(987\) 186.299 1582.63i 0.188752 1.60348i
\(988\) 306.468 0.310190
\(989\) 26.5409 0.0268361
\(990\) −626.487 −0.632815
\(991\) 1138.18i 1.14852i 0.818673 + 0.574261i \(0.194710\pi\)
−0.818673 + 0.574261i \(0.805290\pi\)
\(992\) 585.103i 0.589821i
\(993\) 1403.41i 1.41330i
\(994\) −748.900 88.1563i −0.753421 0.0886884i
\(995\) 1147.62i 1.15339i
\(996\) 2172.28i 2.18100i
\(997\) −456.333 −0.457706 −0.228853 0.973461i \(-0.573498\pi\)
−0.228853 + 0.973461i \(0.573498\pi\)
\(998\) 676.880i 0.678236i
\(999\) −189.572 −0.189762
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.d.c.286.7 yes 8
7.6 odd 2 inner 287.3.d.c.286.2 yes 8
41.40 even 2 inner 287.3.d.c.286.1 8
287.286 odd 2 inner 287.3.d.c.286.8 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.3.d.c.286.1 8 41.40 even 2 inner
287.3.d.c.286.2 yes 8 7.6 odd 2 inner
287.3.d.c.286.7 yes 8 1.1 even 1 trivial
287.3.d.c.286.8 yes 8 287.286 odd 2 inner