Properties

Label 525.3.l.e.43.12
Level $525$
Weight $3$
Character 525.43
Analytic conductor $14.305$
Analytic rank $0$
Dimension $24$
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] = [525,3,Mod(43,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.43");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.l (of order \(4\), degree \(2\), 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: \(14.3052138789\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.12
Character \(\chi\) \(=\) 525.43
Dual form 525.3.l.e.232.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.72310 - 2.72310i) q^{2} +(1.22474 + 1.22474i) q^{3} -10.8306i q^{4} +6.67022 q^{6} +(1.87083 - 1.87083i) q^{7} +(-18.6004 - 18.6004i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(2.72310 - 2.72310i) q^{2} +(1.22474 + 1.22474i) q^{3} -10.8306i q^{4} +6.67022 q^{6} +(1.87083 - 1.87083i) q^{7} +(-18.6004 - 18.6004i) q^{8} +3.00000i q^{9} +3.42164 q^{11} +(13.2647 - 13.2647i) q^{12} +(-7.98120 - 7.98120i) q^{13} -10.1889i q^{14} -57.9794 q^{16} +(16.5713 - 16.5713i) q^{17} +(8.16931 + 8.16931i) q^{18} -1.38069i q^{19} +4.58258 q^{21} +(9.31750 - 9.31750i) q^{22} +(-18.8473 - 18.8473i) q^{23} -45.5616i q^{24} -43.4673 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-20.2622 - 20.2622i) q^{28} +45.7370i q^{29} +43.2632 q^{31} +(-83.4823 + 83.4823i) q^{32} +(4.19064 + 4.19064i) q^{33} -90.2505i q^{34} +32.4918 q^{36} +(-2.18941 + 2.18941i) q^{37} +(-3.75977 - 3.75977i) q^{38} -19.5499i q^{39} +6.61005 q^{41} +(12.4788 - 12.4788i) q^{42} +(44.1187 + 44.1187i) q^{43} -37.0585i q^{44} -102.646 q^{46} +(-14.2193 + 14.2193i) q^{47} +(-71.0100 - 71.0100i) q^{48} -7.00000i q^{49} +40.5911 q^{51} +(-86.4412 + 86.4412i) q^{52} +(44.4359 + 44.4359i) q^{53} +20.0106i q^{54} -69.5964 q^{56} +(1.69100 - 1.69100i) q^{57} +(124.547 + 124.547i) q^{58} -17.2928i q^{59} +48.0848 q^{61} +(117.810 - 117.810i) q^{62} +(5.61249 + 5.61249i) q^{63} +222.745i q^{64} +22.8231 q^{66} +(-40.9435 + 40.9435i) q^{67} +(-179.477 - 179.477i) q^{68} -46.1662i q^{69} -38.7743 q^{71} +(55.8013 - 55.8013i) q^{72} +(-66.4788 - 66.4788i) q^{73} +11.9240i q^{74} -14.9537 q^{76} +(6.40131 - 6.40131i) q^{77} +(-53.2363 - 53.2363i) q^{78} +5.30864i q^{79} -9.00000 q^{81} +(17.9999 - 17.9999i) q^{82} +(62.5835 + 62.5835i) q^{83} -49.6320i q^{84} +240.280 q^{86} +(-56.0161 + 56.0161i) q^{87} +(-63.6441 - 63.6441i) q^{88} -44.8163i q^{89} -29.8629 q^{91} +(-204.127 + 204.127i) q^{92} +(52.9864 + 52.9864i) q^{93} +77.4411i q^{94} -204.489 q^{96} +(30.5196 - 30.5196i) q^{97} +(-19.0617 - 19.0617i) q^{98} +10.2649i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 8 q^{2} + 24 q^{6} + 48 q^{8} + 48 q^{12} - 64 q^{13} - 184 q^{16} - 24 q^{17} - 24 q^{18} - 8 q^{22} - 8 q^{23} - 80 q^{26} + 96 q^{31} - 56 q^{32} + 72 q^{33} + 168 q^{36} - 8 q^{37} - 56 q^{38} + 320 q^{41} + 112 q^{43} + 320 q^{46} - 64 q^{47} - 192 q^{48} - 192 q^{51} - 96 q^{52} + 72 q^{53} - 336 q^{56} - 48 q^{57} + 512 q^{58} - 496 q^{61} + 776 q^{62} - 192 q^{66} + 192 q^{67} - 568 q^{68} - 144 q^{71} - 144 q^{72} - 224 q^{73} + 416 q^{76} - 112 q^{77} + 216 q^{78} - 216 q^{81} - 352 q^{82} + 32 q^{83} + 240 q^{86} - 384 q^{87} - 216 q^{88} - 1304 q^{92} + 168 q^{96} + 816 q^{97} + 56 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.72310 2.72310i 1.36155 1.36155i 0.489612 0.871941i \(-0.337139\pi\)
0.871941 0.489612i \(-0.162861\pi\)
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) 10.8306i 2.70765i
\(5\) 0 0
\(6\) 6.67022 1.11170
\(7\) 1.87083 1.87083i 0.267261 0.267261i
\(8\) −18.6004 18.6004i −2.32505 2.32505i
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) 3.42164 0.311059 0.155529 0.987831i \(-0.450292\pi\)
0.155529 + 0.987831i \(0.450292\pi\)
\(12\) 13.2647 13.2647i 1.10539 1.10539i
\(13\) −7.98120 7.98120i −0.613939 0.613939i 0.330031 0.943970i \(-0.392941\pi\)
−0.943970 + 0.330031i \(0.892941\pi\)
\(14\) 10.1889i 0.727780i
\(15\) 0 0
\(16\) −57.9794 −3.62371
\(17\) 16.5713 16.5713i 0.974780 0.974780i −0.0249097 0.999690i \(-0.507930\pi\)
0.999690 + 0.0249097i \(0.00792981\pi\)
\(18\) 8.16931 + 8.16931i 0.453851 + 0.453851i
\(19\) 1.38069i 0.0726681i −0.999340 0.0363341i \(-0.988432\pi\)
0.999340 0.0363341i \(-0.0115680\pi\)
\(20\) 0 0
\(21\) 4.58258 0.218218
\(22\) 9.31750 9.31750i 0.423523 0.423523i
\(23\) −18.8473 18.8473i −0.819447 0.819447i 0.166581 0.986028i \(-0.446727\pi\)
−0.986028 + 0.166581i \(0.946727\pi\)
\(24\) 45.5616i 1.89840i
\(25\) 0 0
\(26\) −43.4673 −1.67182
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) −20.2622 20.2622i −0.723650 0.723650i
\(29\) 45.7370i 1.57714i 0.614947 + 0.788568i \(0.289177\pi\)
−0.614947 + 0.788568i \(0.710823\pi\)
\(30\) 0 0
\(31\) 43.2632 1.39559 0.697793 0.716299i \(-0.254165\pi\)
0.697793 + 0.716299i \(0.254165\pi\)
\(32\) −83.4823 + 83.4823i −2.60882 + 2.60882i
\(33\) 4.19064 + 4.19064i 0.126989 + 0.126989i
\(34\) 90.2505i 2.65443i
\(35\) 0 0
\(36\) 32.4918 0.902550
\(37\) −2.18941 + 2.18941i −0.0591732 + 0.0591732i −0.736074 0.676901i \(-0.763323\pi\)
0.676901 + 0.736074i \(0.263323\pi\)
\(38\) −3.75977 3.75977i −0.0989414 0.0989414i
\(39\) 19.5499i 0.501279i
\(40\) 0 0
\(41\) 6.61005 0.161221 0.0806104 0.996746i \(-0.474313\pi\)
0.0806104 + 0.996746i \(0.474313\pi\)
\(42\) 12.4788 12.4788i 0.297115 0.297115i
\(43\) 44.1187 + 44.1187i 1.02602 + 1.02602i 0.999652 + 0.0263634i \(0.00839271\pi\)
0.0263634 + 0.999652i \(0.491607\pi\)
\(44\) 37.0585i 0.842238i
\(45\) 0 0
\(46\) −102.646 −2.23144
\(47\) −14.2193 + 14.2193i −0.302538 + 0.302538i −0.842006 0.539468i \(-0.818625\pi\)
0.539468 + 0.842006i \(0.318625\pi\)
\(48\) −71.0100 71.0100i −1.47938 1.47938i
\(49\) 7.00000i 0.142857i
\(50\) 0 0
\(51\) 40.5911 0.795905
\(52\) −86.4412 + 86.4412i −1.66233 + 1.66233i
\(53\) 44.4359 + 44.4359i 0.838413 + 0.838413i 0.988650 0.150237i \(-0.0480037\pi\)
−0.150237 + 0.988650i \(0.548004\pi\)
\(54\) 20.0106i 0.370568i
\(55\) 0 0
\(56\) −69.5964 −1.24279
\(57\) 1.69100 1.69100i 0.0296666 0.0296666i
\(58\) 124.547 + 124.547i 2.14735 + 2.14735i
\(59\) 17.2928i 0.293099i −0.989203 0.146549i \(-0.953183\pi\)
0.989203 0.146549i \(-0.0468167\pi\)
\(60\) 0 0
\(61\) 48.0848 0.788276 0.394138 0.919051i \(-0.371043\pi\)
0.394138 + 0.919051i \(0.371043\pi\)
\(62\) 117.810 117.810i 1.90016 1.90016i
\(63\) 5.61249 + 5.61249i 0.0890871 + 0.0890871i
\(64\) 222.745i 3.48038i
\(65\) 0 0
\(66\) 22.8231 0.345805
\(67\) −40.9435 + 40.9435i −0.611097 + 0.611097i −0.943232 0.332135i \(-0.892231\pi\)
0.332135 + 0.943232i \(0.392231\pi\)
\(68\) −179.477 179.477i −2.63936 2.63936i
\(69\) 46.1662i 0.669075i
\(70\) 0 0
\(71\) −38.7743 −0.546118 −0.273059 0.961997i \(-0.588035\pi\)
−0.273059 + 0.961997i \(0.588035\pi\)
\(72\) 55.8013 55.8013i 0.775018 0.775018i
\(73\) −66.4788 66.4788i −0.910668 0.910668i 0.0856565 0.996325i \(-0.472701\pi\)
−0.996325 + 0.0856565i \(0.972701\pi\)
\(74\) 11.9240i 0.161135i
\(75\) 0 0
\(76\) −14.9537 −0.196760
\(77\) 6.40131 6.40131i 0.0831339 0.0831339i
\(78\) −53.2363 53.2363i −0.682517 0.682517i
\(79\) 5.30864i 0.0671980i 0.999435 + 0.0335990i \(0.0106969\pi\)
−0.999435 + 0.0335990i \(0.989303\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 17.9999 17.9999i 0.219511 0.219511i
\(83\) 62.5835 + 62.5835i 0.754017 + 0.754017i 0.975226 0.221209i \(-0.0710003\pi\)
−0.221209 + 0.975226i \(0.571000\pi\)
\(84\) 49.6320i 0.590857i
\(85\) 0 0
\(86\) 240.280 2.79395
\(87\) −56.0161 + 56.0161i −0.643863 + 0.643863i
\(88\) −63.6441 63.6441i −0.723228 0.723228i
\(89\) 44.8163i 0.503554i −0.967785 0.251777i \(-0.918985\pi\)
0.967785 0.251777i \(-0.0810149\pi\)
\(90\) 0 0
\(91\) −29.8629 −0.328164
\(92\) −204.127 + 204.127i −2.21877 + 2.21877i
\(93\) 52.9864 + 52.9864i 0.569746 + 0.569746i
\(94\) 77.4411i 0.823842i
\(95\) 0 0
\(96\) −204.489 −2.13010
\(97\) 30.5196 30.5196i 0.314635 0.314635i −0.532067 0.846702i \(-0.678585\pi\)
0.846702 + 0.532067i \(0.178585\pi\)
\(98\) −19.0617 19.0617i −0.194507 0.194507i
\(99\) 10.2649i 0.103686i
\(100\) 0 0
\(101\) 115.859 1.14712 0.573561 0.819163i \(-0.305561\pi\)
0.573561 + 0.819163i \(0.305561\pi\)
\(102\) 110.534 110.534i 1.08367 1.08367i
\(103\) 36.9871 + 36.9871i 0.359098 + 0.359098i 0.863480 0.504382i \(-0.168280\pi\)
−0.504382 + 0.863480i \(0.668280\pi\)
\(104\) 296.908i 2.85488i
\(105\) 0 0
\(106\) 242.007 2.28309
\(107\) 105.863 105.863i 0.989371 0.989371i −0.0105734 0.999944i \(-0.503366\pi\)
0.999944 + 0.0105734i \(0.00336567\pi\)
\(108\) 39.7942 + 39.7942i 0.368464 + 0.368464i
\(109\) 41.7489i 0.383017i 0.981491 + 0.191509i \(0.0613380\pi\)
−0.981491 + 0.191509i \(0.938662\pi\)
\(110\) 0 0
\(111\) −5.36293 −0.0483147
\(112\) −108.470 + 108.470i −0.968478 + 0.968478i
\(113\) 154.947 + 154.947i 1.37121 + 1.37121i 0.858655 + 0.512554i \(0.171300\pi\)
0.512554 + 0.858655i \(0.328700\pi\)
\(114\) 9.20953i 0.0807853i
\(115\) 0 0
\(116\) 495.358 4.27033
\(117\) 23.9436 23.9436i 0.204646 0.204646i
\(118\) −47.0902 47.0902i −0.399069 0.399069i
\(119\) 62.0040i 0.521042i
\(120\) 0 0
\(121\) −109.292 −0.903243
\(122\) 130.940 130.940i 1.07328 1.07328i
\(123\) 8.09563 + 8.09563i 0.0658181 + 0.0658181i
\(124\) 468.566i 3.77876i
\(125\) 0 0
\(126\) 30.5668 0.242593
\(127\) −84.5679 + 84.5679i −0.665889 + 0.665889i −0.956762 0.290873i \(-0.906054\pi\)
0.290873 + 0.956762i \(0.406054\pi\)
\(128\) 272.627 + 272.627i 2.12990 + 2.12990i
\(129\) 108.068i 0.837738i
\(130\) 0 0
\(131\) 75.1775 0.573874 0.286937 0.957949i \(-0.407363\pi\)
0.286937 + 0.957949i \(0.407363\pi\)
\(132\) 45.3872 45.3872i 0.343842 0.343842i
\(133\) −2.58304 2.58304i −0.0194214 0.0194214i
\(134\) 222.987i 1.66408i
\(135\) 0 0
\(136\) −616.465 −4.53283
\(137\) 1.34004 1.34004i 0.00978134 0.00978134i −0.702199 0.711981i \(-0.747798\pi\)
0.711981 + 0.702199i \(0.247798\pi\)
\(138\) −125.715 125.715i −0.910981 0.910981i
\(139\) 14.7459i 0.106086i −0.998592 0.0530429i \(-0.983108\pi\)
0.998592 0.0530429i \(-0.0168920\pi\)
\(140\) 0 0
\(141\) −34.8300 −0.247021
\(142\) −105.587 + 105.587i −0.743568 + 0.743568i
\(143\) −27.3088 27.3088i −0.190971 0.190971i
\(144\) 173.938i 1.20790i
\(145\) 0 0
\(146\) −362.057 −2.47984
\(147\) 8.57321 8.57321i 0.0583212 0.0583212i
\(148\) 23.7126 + 23.7126i 0.160220 + 0.160220i
\(149\) 13.4239i 0.0900930i 0.998985 + 0.0450465i \(0.0143436\pi\)
−0.998985 + 0.0450465i \(0.985656\pi\)
\(150\) 0 0
\(151\) −133.609 −0.884826 −0.442413 0.896811i \(-0.645877\pi\)
−0.442413 + 0.896811i \(0.645877\pi\)
\(152\) −25.6815 + 25.6815i −0.168957 + 0.168957i
\(153\) 49.7138 + 49.7138i 0.324927 + 0.324927i
\(154\) 34.8629i 0.226382i
\(155\) 0 0
\(156\) −211.737 −1.35729
\(157\) −144.591 + 144.591i −0.920959 + 0.920959i −0.997097 0.0761383i \(-0.975741\pi\)
0.0761383 + 0.997097i \(0.475741\pi\)
\(158\) 14.4560 + 14.4560i 0.0914936 + 0.0914936i
\(159\) 108.845i 0.684561i
\(160\) 0 0
\(161\) −70.5200 −0.438013
\(162\) −24.5079 + 24.5079i −0.151284 + 0.151284i
\(163\) −141.760 141.760i −0.869693 0.869693i 0.122746 0.992438i \(-0.460830\pi\)
−0.992438 + 0.122746i \(0.960830\pi\)
\(164\) 71.5908i 0.436529i
\(165\) 0 0
\(166\) 340.843 2.05327
\(167\) −119.348 + 119.348i −0.714660 + 0.714660i −0.967506 0.252847i \(-0.918633\pi\)
0.252847 + 0.967506i \(0.418633\pi\)
\(168\) −85.2379 85.2379i −0.507368 0.507368i
\(169\) 41.6008i 0.246159i
\(170\) 0 0
\(171\) 4.14208 0.0242227
\(172\) 477.832 477.832i 2.77809 2.77809i
\(173\) −6.11726 6.11726i −0.0353599 0.0353599i 0.689206 0.724566i \(-0.257960\pi\)
−0.724566 + 0.689206i \(0.757960\pi\)
\(174\) 305.075i 1.75331i
\(175\) 0 0
\(176\) −198.385 −1.12719
\(177\) 21.1793 21.1793i 0.119657 0.119657i
\(178\) −122.039 122.039i −0.685615 0.685615i
\(179\) 234.919i 1.31240i −0.754588 0.656199i \(-0.772163\pi\)
0.754588 0.656199i \(-0.227837\pi\)
\(180\) 0 0
\(181\) 128.874 0.712013 0.356007 0.934483i \(-0.384138\pi\)
0.356007 + 0.934483i \(0.384138\pi\)
\(182\) −81.3199 + 81.3199i −0.446812 + 0.446812i
\(183\) 58.8917 + 58.8917i 0.321812 + 0.321812i
\(184\) 701.135i 3.81051i
\(185\) 0 0
\(186\) 288.575 1.55148
\(187\) 56.7010 56.7010i 0.303214 0.303214i
\(188\) 154.003 + 154.003i 0.819166 + 0.819166i
\(189\) 13.7477i 0.0727393i
\(190\) 0 0
\(191\) 73.4776 0.384699 0.192350 0.981326i \(-0.438389\pi\)
0.192350 + 0.981326i \(0.438389\pi\)
\(192\) −272.805 + 272.805i −1.42086 + 1.42086i
\(193\) −120.661 120.661i −0.625187 0.625187i 0.321666 0.946853i \(-0.395757\pi\)
−0.946853 + 0.321666i \(0.895757\pi\)
\(194\) 166.216i 0.856783i
\(195\) 0 0
\(196\) −75.8142 −0.386807
\(197\) 34.8422 34.8422i 0.176864 0.176864i −0.613123 0.789987i \(-0.710087\pi\)
0.789987 + 0.613123i \(0.210087\pi\)
\(198\) 27.9525 + 27.9525i 0.141174 + 0.141174i
\(199\) 22.8910i 0.115030i −0.998345 0.0575151i \(-0.981682\pi\)
0.998345 0.0575151i \(-0.0183177\pi\)
\(200\) 0 0
\(201\) −100.291 −0.498959
\(202\) 315.497 315.497i 1.56187 1.56187i
\(203\) 85.5660 + 85.5660i 0.421507 + 0.421507i
\(204\) 439.626i 2.15503i
\(205\) 0 0
\(206\) 201.439 0.977861
\(207\) 56.5418 56.5418i 0.273149 0.273149i
\(208\) 462.746 + 462.746i 2.22474 + 2.22474i
\(209\) 4.72425i 0.0226040i
\(210\) 0 0
\(211\) −216.288 −1.02506 −0.512531 0.858668i \(-0.671292\pi\)
−0.512531 + 0.858668i \(0.671292\pi\)
\(212\) 481.267 481.267i 2.27013 2.27013i
\(213\) −47.4887 47.4887i −0.222952 0.222952i
\(214\) 576.550i 2.69416i
\(215\) 0 0
\(216\) 136.685 0.632799
\(217\) 80.9380 80.9380i 0.372986 0.372986i
\(218\) 113.687 + 113.687i 0.521498 + 0.521498i
\(219\) 162.839i 0.743557i
\(220\) 0 0
\(221\) −264.517 −1.19691
\(222\) −14.6038 + 14.6038i −0.0657830 + 0.0657830i
\(223\) 55.1194 + 55.1194i 0.247172 + 0.247172i 0.819809 0.572637i \(-0.194079\pi\)
−0.572637 + 0.819809i \(0.694079\pi\)
\(224\) 312.362i 1.39447i
\(225\) 0 0
\(226\) 843.872 3.73395
\(227\) −163.968 + 163.968i −0.722327 + 0.722327i −0.969079 0.246752i \(-0.920637\pi\)
0.246752 + 0.969079i \(0.420637\pi\)
\(228\) −18.3145 18.3145i −0.0803268 0.0803268i
\(229\) 161.221i 0.704022i 0.935996 + 0.352011i \(0.114502\pi\)
−0.935996 + 0.352011i \(0.885498\pi\)
\(230\) 0 0
\(231\) 15.6799 0.0678786
\(232\) 850.727 850.727i 3.66693 3.66693i
\(233\) −8.28891 8.28891i −0.0355747 0.0355747i 0.689096 0.724670i \(-0.258008\pi\)
−0.724670 + 0.689096i \(0.758008\pi\)
\(234\) 130.402i 0.557273i
\(235\) 0 0
\(236\) −187.292 −0.793608
\(237\) −6.50173 + 6.50173i −0.0274335 + 0.0274335i
\(238\) −168.843 168.843i −0.709426 0.709426i
\(239\) 66.4975i 0.278232i 0.990276 + 0.139116i \(0.0444261\pi\)
−0.990276 + 0.139116i \(0.955574\pi\)
\(240\) 0 0
\(241\) −152.923 −0.634535 −0.317267 0.948336i \(-0.602765\pi\)
−0.317267 + 0.948336i \(0.602765\pi\)
\(242\) −297.614 + 297.614i −1.22981 + 1.22981i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 520.788i 2.13438i
\(245\) 0 0
\(246\) 44.0905 0.179230
\(247\) −11.0196 + 11.0196i −0.0446138 + 0.0446138i
\(248\) −804.714 804.714i −3.24481 3.24481i
\(249\) 153.298i 0.615653i
\(250\) 0 0
\(251\) 462.911 1.84427 0.922134 0.386871i \(-0.126444\pi\)
0.922134 + 0.386871i \(0.126444\pi\)
\(252\) 60.7866 60.7866i 0.241217 0.241217i
\(253\) −64.4887 64.4887i −0.254896 0.254896i
\(254\) 460.575i 1.81329i
\(255\) 0 0
\(256\) 593.807 2.31956
\(257\) −54.4719 + 54.4719i −0.211953 + 0.211953i −0.805097 0.593144i \(-0.797887\pi\)
0.593144 + 0.805097i \(0.297887\pi\)
\(258\) 294.281 + 294.281i 1.14062 + 1.14062i
\(259\) 8.19201i 0.0316294i
\(260\) 0 0
\(261\) −137.211 −0.525712
\(262\) 204.716 204.716i 0.781360 0.781360i
\(263\) 132.088 + 132.088i 0.502236 + 0.502236i 0.912132 0.409896i \(-0.134435\pi\)
−0.409896 + 0.912132i \(0.634435\pi\)
\(264\) 155.895i 0.590513i
\(265\) 0 0
\(266\) −14.0678 −0.0528864
\(267\) 54.8885 54.8885i 0.205575 0.205575i
\(268\) 443.443 + 443.443i 1.65464 + 1.65464i
\(269\) 200.132i 0.743985i −0.928236 0.371993i \(-0.878675\pi\)
0.928236 0.371993i \(-0.121325\pi\)
\(270\) 0 0
\(271\) −119.987 −0.442758 −0.221379 0.975188i \(-0.571056\pi\)
−0.221379 + 0.975188i \(0.571056\pi\)
\(272\) −960.792 + 960.792i −3.53232 + 3.53232i
\(273\) −36.5745 36.5745i −0.133972 0.133972i
\(274\) 7.29816i 0.0266356i
\(275\) 0 0
\(276\) −500.007 −1.81162
\(277\) −202.673 + 202.673i −0.731672 + 0.731672i −0.970951 0.239279i \(-0.923089\pi\)
0.239279 + 0.970951i \(0.423089\pi\)
\(278\) −40.1547 40.1547i −0.144441 0.144441i
\(279\) 129.790i 0.465196i
\(280\) 0 0
\(281\) −283.806 −1.00999 −0.504994 0.863123i \(-0.668505\pi\)
−0.504994 + 0.863123i \(0.668505\pi\)
\(282\) −94.8456 + 94.8456i −0.336332 + 0.336332i
\(283\) −19.2062 19.2062i −0.0678664 0.0678664i 0.672359 0.740225i \(-0.265281\pi\)
−0.740225 + 0.672359i \(0.765281\pi\)
\(284\) 419.949i 1.47869i
\(285\) 0 0
\(286\) −148.730 −0.520034
\(287\) 12.3663 12.3663i 0.0430881 0.0430881i
\(288\) −250.447 250.447i −0.869608 0.869608i
\(289\) 260.213i 0.900392i
\(290\) 0 0
\(291\) 74.7573 0.256898
\(292\) −720.005 + 720.005i −2.46577 + 2.46577i
\(293\) −276.326 276.326i −0.943093 0.943093i 0.0553728 0.998466i \(-0.482365\pi\)
−0.998466 + 0.0553728i \(0.982365\pi\)
\(294\) 46.6915i 0.158815i
\(295\) 0 0
\(296\) 81.4478 0.275162
\(297\) −12.5719 + 12.5719i −0.0423297 + 0.0423297i
\(298\) 36.5546 + 36.5546i 0.122666 + 0.122666i
\(299\) 300.848i 1.00618i
\(300\) 0 0
\(301\) 165.077 0.548429
\(302\) −363.830 + 363.830i −1.20474 + 1.20474i
\(303\) 141.898 + 141.898i 0.468311 + 0.468311i
\(304\) 80.0519i 0.263328i
\(305\) 0 0
\(306\) 270.752 0.884809
\(307\) −84.0526 + 84.0526i −0.273787 + 0.273787i −0.830623 0.556836i \(-0.812015\pi\)
0.556836 + 0.830623i \(0.312015\pi\)
\(308\) −69.3300 69.3300i −0.225097 0.225097i
\(309\) 90.5995i 0.293202i
\(310\) 0 0
\(311\) −228.140 −0.733569 −0.366785 0.930306i \(-0.619541\pi\)
−0.366785 + 0.930306i \(0.619541\pi\)
\(312\) −363.636 + 363.636i −1.16550 + 1.16550i
\(313\) −415.710 415.710i −1.32815 1.32815i −0.906985 0.421163i \(-0.861622\pi\)
−0.421163 0.906985i \(-0.638378\pi\)
\(314\) 787.470i 2.50787i
\(315\) 0 0
\(316\) 57.4958 0.181949
\(317\) 167.997 167.997i 0.529960 0.529960i −0.390600 0.920560i \(-0.627733\pi\)
0.920560 + 0.390600i \(0.127733\pi\)
\(318\) 296.397 + 296.397i 0.932066 + 0.932066i
\(319\) 156.496i 0.490582i
\(320\) 0 0
\(321\) 259.310 0.807818
\(322\) −192.033 + 192.033i −0.596377 + 0.596377i
\(323\) −22.8798 22.8798i −0.0708354 0.0708354i
\(324\) 97.4754i 0.300850i
\(325\) 0 0
\(326\) −772.054 −2.36826
\(327\) −51.1317 + 51.1317i −0.156366 + 0.156366i
\(328\) −122.950 122.950i −0.374847 0.374847i
\(329\) 53.2036i 0.161713i
\(330\) 0 0
\(331\) −379.871 −1.14765 −0.573823 0.818979i \(-0.694540\pi\)
−0.573823 + 0.818979i \(0.694540\pi\)
\(332\) 677.816 677.816i 2.04161 2.04161i
\(333\) −6.56822 6.56822i −0.0197244 0.0197244i
\(334\) 649.995i 1.94609i
\(335\) 0 0
\(336\) −265.695 −0.790759
\(337\) −251.400 + 251.400i −0.745994 + 0.745994i −0.973724 0.227730i \(-0.926870\pi\)
0.227730 + 0.973724i \(0.426870\pi\)
\(338\) −113.283 113.283i −0.335158 0.335158i
\(339\) 379.540i 1.11959i
\(340\) 0 0
\(341\) 148.031 0.434109
\(342\) 11.2793 11.2793i 0.0329805 0.0329805i
\(343\) −13.0958 13.0958i −0.0381802 0.0381802i
\(344\) 1641.25i 4.77108i
\(345\) 0 0
\(346\) −33.3159 −0.0962886
\(347\) −234.925 + 234.925i −0.677016 + 0.677016i −0.959324 0.282308i \(-0.908900\pi\)
0.282308 + 0.959324i \(0.408900\pi\)
\(348\) 606.688 + 606.688i 1.74336 + 1.74336i
\(349\) 497.584i 1.42574i −0.701295 0.712871i \(-0.747395\pi\)
0.701295 0.712871i \(-0.252605\pi\)
\(350\) 0 0
\(351\) 58.6496 0.167093
\(352\) −285.647 + 285.647i −0.811497 + 0.811497i
\(353\) 217.500 + 217.500i 0.616146 + 0.616146i 0.944541 0.328394i \(-0.106508\pi\)
−0.328394 + 0.944541i \(0.606508\pi\)
\(354\) 115.347i 0.325839i
\(355\) 0 0
\(356\) −485.387 −1.36345
\(357\) 75.9391 75.9391i 0.212714 0.212714i
\(358\) −639.709 639.709i −1.78690 1.78690i
\(359\) 531.115i 1.47943i 0.672921 + 0.739714i \(0.265039\pi\)
−0.672921 + 0.739714i \(0.734961\pi\)
\(360\) 0 0
\(361\) 359.094 0.994719
\(362\) 350.938 350.938i 0.969443 0.969443i
\(363\) −133.855 133.855i −0.368747 0.368747i
\(364\) 323.433i 0.888553i
\(365\) 0 0
\(366\) 320.736 0.876329
\(367\) 190.791 190.791i 0.519867 0.519867i −0.397664 0.917531i \(-0.630179\pi\)
0.917531 + 0.397664i \(0.130179\pi\)
\(368\) 1092.75 + 1092.75i 2.96944 + 2.96944i
\(369\) 19.8302i 0.0537403i
\(370\) 0 0
\(371\) 166.264 0.448151
\(372\) 573.874 573.874i 1.54267 1.54267i
\(373\) 178.025 + 178.025i 0.477279 + 0.477279i 0.904260 0.426981i \(-0.140423\pi\)
−0.426981 + 0.904260i \(0.640423\pi\)
\(374\) 308.805i 0.825683i
\(375\) 0 0
\(376\) 528.969 1.40683
\(377\) 365.036 365.036i 0.968265 0.968265i
\(378\) 37.4365 + 37.4365i 0.0990384 + 0.0990384i
\(379\) 427.303i 1.12745i 0.825963 + 0.563725i \(0.190632\pi\)
−0.825963 + 0.563725i \(0.809368\pi\)
\(380\) 0 0
\(381\) −207.148 −0.543696
\(382\) 200.087 200.087i 0.523788 0.523788i
\(383\) 408.586 + 408.586i 1.06680 + 1.06680i 0.997603 + 0.0692020i \(0.0220453\pi\)
0.0692020 + 0.997603i \(0.477955\pi\)
\(384\) 667.798i 1.73906i
\(385\) 0 0
\(386\) −657.146 −1.70245
\(387\) −132.356 + 132.356i −0.342005 + 0.342005i
\(388\) −330.545 330.545i −0.851920 0.851920i
\(389\) 380.438i 0.977990i 0.872286 + 0.488995i \(0.162636\pi\)
−0.872286 + 0.488995i \(0.837364\pi\)
\(390\) 0 0
\(391\) −624.646 −1.59756
\(392\) −130.203 + 130.203i −0.332150 + 0.332150i
\(393\) 92.0733 + 92.0733i 0.234283 + 0.234283i
\(394\) 189.758i 0.481619i
\(395\) 0 0
\(396\) 111.175 0.280746
\(397\) −419.765 + 419.765i −1.05734 + 1.05734i −0.0590903 + 0.998253i \(0.518820\pi\)
−0.998253 + 0.0590903i \(0.981180\pi\)
\(398\) −62.3346 62.3346i −0.156620 0.156620i
\(399\) 6.32714i 0.0158575i
\(400\) 0 0
\(401\) −116.260 −0.289926 −0.144963 0.989437i \(-0.546306\pi\)
−0.144963 + 0.989437i \(0.546306\pi\)
\(402\) −273.102 + 273.102i −0.679359 + 0.679359i
\(403\) −345.292 345.292i −0.856805 0.856805i
\(404\) 1254.83i 3.10600i
\(405\) 0 0
\(406\) 466.010 1.14781
\(407\) −7.49137 + 7.49137i −0.0184063 + 0.0184063i
\(408\) −755.012 755.012i −1.85052 1.85052i
\(409\) 510.537i 1.24826i −0.781322 0.624129i \(-0.785454\pi\)
0.781322 0.624129i \(-0.214546\pi\)
\(410\) 0 0
\(411\) 3.28242 0.00798643
\(412\) 400.592 400.592i 0.972311 0.972311i
\(413\) −32.3519 32.3519i −0.0783339 0.0783339i
\(414\) 307.939i 0.743813i
\(415\) 0 0
\(416\) 1332.58 3.20331
\(417\) 18.0600 18.0600i 0.0433093 0.0433093i
\(418\) −12.8646 12.8646i −0.0307766 0.0307766i
\(419\) 421.546i 1.00608i 0.864265 + 0.503038i \(0.167784\pi\)
−0.864265 + 0.503038i \(0.832216\pi\)
\(420\) 0 0
\(421\) −617.382 −1.46646 −0.733232 0.679978i \(-0.761989\pi\)
−0.733232 + 0.679978i \(0.761989\pi\)
\(422\) −588.976 + 588.976i −1.39568 + 1.39568i
\(423\) −42.6578 42.6578i −0.100846 0.100846i
\(424\) 1653.05i 3.89871i
\(425\) 0 0
\(426\) −258.633 −0.607120
\(427\) 89.9585 89.9585i 0.210676 0.210676i
\(428\) −1146.56 1146.56i −2.67887 2.67887i
\(429\) 66.8927i 0.155927i
\(430\) 0 0
\(431\) −13.8516 −0.0321382 −0.0160691 0.999871i \(-0.505115\pi\)
−0.0160691 + 0.999871i \(0.505115\pi\)
\(432\) 213.030 213.030i 0.493125 0.493125i
\(433\) −539.624 539.624i −1.24624 1.24624i −0.957366 0.288879i \(-0.906718\pi\)
−0.288879 0.957366i \(-0.593282\pi\)
\(434\) 440.805i 1.01568i
\(435\) 0 0
\(436\) 452.165 1.03708
\(437\) −26.0223 + 26.0223i −0.0595476 + 0.0595476i
\(438\) −443.428 443.428i −1.01239 1.01239i
\(439\) 41.4994i 0.0945318i 0.998882 + 0.0472659i \(0.0150508\pi\)
−0.998882 + 0.0472659i \(0.984949\pi\)
\(440\) 0 0
\(441\) 21.0000 0.0476190
\(442\) −720.308 + 720.308i −1.62966 + 1.62966i
\(443\) −577.471 577.471i −1.30355 1.30355i −0.925984 0.377563i \(-0.876762\pi\)
−0.377563 0.925984i \(-0.623238\pi\)
\(444\) 58.0837i 0.130819i
\(445\) 0 0
\(446\) 300.192 0.673076
\(447\) −16.4408 + 16.4408i −0.0367803 + 0.0367803i
\(448\) 416.717 + 416.717i 0.930172 + 0.930172i
\(449\) 234.581i 0.522451i 0.965278 + 0.261226i \(0.0841266\pi\)
−0.965278 + 0.261226i \(0.915873\pi\)
\(450\) 0 0
\(451\) 22.6173 0.0501491
\(452\) 1678.16 1678.16i 3.71275 3.71275i
\(453\) −163.637 163.637i −0.361229 0.361229i
\(454\) 893.005i 1.96697i
\(455\) 0 0
\(456\) −62.9066 −0.137953
\(457\) −153.225 + 153.225i −0.335284 + 0.335284i −0.854589 0.519305i \(-0.826191\pi\)
0.519305 + 0.854589i \(0.326191\pi\)
\(458\) 439.022 + 439.022i 0.958562 + 0.958562i
\(459\) 121.773i 0.265302i
\(460\) 0 0
\(461\) 623.452 1.35239 0.676195 0.736723i \(-0.263628\pi\)
0.676195 + 0.736723i \(0.263628\pi\)
\(462\) 42.6981 42.6981i 0.0924202 0.0924202i
\(463\) 613.771 + 613.771i 1.32564 + 1.32564i 0.909133 + 0.416506i \(0.136745\pi\)
0.416506 + 0.909133i \(0.363255\pi\)
\(464\) 2651.80i 5.71509i
\(465\) 0 0
\(466\) −45.1431 −0.0968737
\(467\) 439.249 439.249i 0.940575 0.940575i −0.0577556 0.998331i \(-0.518394\pi\)
0.998331 + 0.0577556i \(0.0183944\pi\)
\(468\) −259.324 259.324i −0.554110 0.554110i
\(469\) 153.197i 0.326645i
\(470\) 0 0
\(471\) −354.173 −0.751960
\(472\) −321.654 + 321.654i −0.681470 + 0.681470i
\(473\) 150.958 + 150.958i 0.319151 + 0.319151i
\(474\) 35.4098i 0.0747042i
\(475\) 0 0
\(476\) −671.540 −1.41080
\(477\) −133.308 + 133.308i −0.279471 + 0.279471i
\(478\) 181.080 + 181.080i 0.378828 + 0.378828i
\(479\) 15.2748i 0.0318889i 0.999873 + 0.0159445i \(0.00507549\pi\)
−0.999873 + 0.0159445i \(0.994925\pi\)
\(480\) 0 0
\(481\) 34.9482 0.0726574
\(482\) −416.425 + 416.425i −0.863952 + 0.863952i
\(483\) −86.3690 86.3690i −0.178818 0.178818i
\(484\) 1183.70i 2.44566i
\(485\) 0 0
\(486\) −60.0319 −0.123523
\(487\) 170.456 170.456i 0.350013 0.350013i −0.510101 0.860114i \(-0.670392\pi\)
0.860114 + 0.510101i \(0.170392\pi\)
\(488\) −894.399 894.399i −1.83278 1.83278i
\(489\) 347.239i 0.710101i
\(490\) 0 0
\(491\) 539.988 1.09977 0.549886 0.835239i \(-0.314671\pi\)
0.549886 + 0.835239i \(0.314671\pi\)
\(492\) 87.6805 87.6805i 0.178212 0.178212i
\(493\) 757.919 + 757.919i 1.53736 + 1.53736i
\(494\) 60.0150i 0.121488i
\(495\) 0 0
\(496\) −2508.38 −5.05721
\(497\) −72.5402 + 72.5402i −0.145956 + 0.145956i
\(498\) 417.445 + 417.445i 0.838243 + 0.838243i
\(499\) 594.406i 1.19119i −0.803284 0.595597i \(-0.796916\pi\)
0.803284 0.595597i \(-0.203084\pi\)
\(500\) 0 0
\(501\) −292.342 −0.583517
\(502\) 1260.56 1260.56i 2.51107 2.51107i
\(503\) 416.709 + 416.709i 0.828447 + 0.828447i 0.987302 0.158855i \(-0.0507803\pi\)
−0.158855 + 0.987302i \(0.550780\pi\)
\(504\) 208.789i 0.414264i
\(505\) 0 0
\(506\) −351.219 −0.694108
\(507\) 50.9504 50.9504i 0.100494 0.100494i
\(508\) 915.921 + 915.921i 1.80299 + 1.80299i
\(509\) 932.017i 1.83107i −0.402234 0.915537i \(-0.631766\pi\)
0.402234 0.915537i \(-0.368234\pi\)
\(510\) 0 0
\(511\) −248.741 −0.486773
\(512\) 526.490 526.490i 1.02830 1.02830i
\(513\) 5.07299 + 5.07299i 0.00988888 + 0.00988888i
\(514\) 296.665i 0.577170i
\(515\) 0 0
\(516\) 1170.44 2.26830
\(517\) −48.6533 + 48.6533i −0.0941069 + 0.0941069i
\(518\) 22.3077 + 22.3077i 0.0430651 + 0.0430651i
\(519\) 14.9842i 0.0288712i
\(520\) 0 0
\(521\) −536.572 −1.02989 −0.514945 0.857223i \(-0.672188\pi\)
−0.514945 + 0.857223i \(0.672188\pi\)
\(522\) −373.640 + 373.640i −0.715785 + 0.715785i
\(523\) −151.430 151.430i −0.289542 0.289542i 0.547357 0.836899i \(-0.315634\pi\)
−0.836899 + 0.547357i \(0.815634\pi\)
\(524\) 814.217i 1.55385i
\(525\) 0 0
\(526\) 719.379 1.36764
\(527\) 716.926 716.926i 1.36039 1.36039i
\(528\) −242.971 242.971i −0.460172 0.460172i
\(529\) 181.439i 0.342985i
\(530\) 0 0
\(531\) 51.8785 0.0976995
\(532\) −27.9759 + 27.9759i −0.0525863 + 0.0525863i
\(533\) −52.7562 52.7562i −0.0989797 0.0989797i
\(534\) 298.934i 0.559802i
\(535\) 0 0
\(536\) 1523.13 2.84167
\(537\) 287.716 287.716i 0.535784 0.535784i
\(538\) −544.981 544.981i −1.01298 1.01298i
\(539\) 23.9515i 0.0444369i
\(540\) 0 0
\(541\) 363.668 0.672215 0.336107 0.941824i \(-0.390890\pi\)
0.336107 + 0.941824i \(0.390890\pi\)
\(542\) −326.738 + 326.738i −0.602838 + 0.602838i
\(543\) 157.838 + 157.838i 0.290678 + 0.290678i
\(544\) 2766.82i 5.08606i
\(545\) 0 0
\(546\) −199.192 −0.364821
\(547\) −426.746 + 426.746i −0.780158 + 0.780158i −0.979857 0.199699i \(-0.936003\pi\)
0.199699 + 0.979857i \(0.436003\pi\)
\(548\) −14.5135 14.5135i −0.0264844 0.0264844i
\(549\) 144.255i 0.262759i
\(550\) 0 0
\(551\) 63.1487 0.114608
\(552\) −858.711 + 858.711i −1.55564 + 1.55564i
\(553\) 9.93156 + 9.93156i 0.0179594 + 0.0179594i
\(554\) 1103.80i 1.99242i
\(555\) 0 0
\(556\) −159.707 −0.287243
\(557\) −199.988 + 199.988i −0.359045 + 0.359045i −0.863461 0.504416i \(-0.831708\pi\)
0.504416 + 0.863461i \(0.331708\pi\)
\(558\) 353.431 + 353.431i 0.633388 + 0.633388i
\(559\) 704.240i 1.25982i
\(560\) 0 0
\(561\) 138.888 0.247573
\(562\) −772.835 + 772.835i −1.37515 + 1.37515i
\(563\) 85.4562 + 85.4562i 0.151787 + 0.151787i 0.778916 0.627129i \(-0.215770\pi\)
−0.627129 + 0.778916i \(0.715770\pi\)
\(564\) 377.229i 0.668846i
\(565\) 0 0
\(566\) −104.601 −0.184807
\(567\) −16.8375 + 16.8375i −0.0296957 + 0.0296957i
\(568\) 721.219 + 721.219i 1.26975 + 1.26975i
\(569\) 991.963i 1.74334i −0.490090 0.871672i \(-0.663036\pi\)
0.490090 0.871672i \(-0.336964\pi\)
\(570\) 0 0
\(571\) 273.348 0.478719 0.239359 0.970931i \(-0.423063\pi\)
0.239359 + 0.970931i \(0.423063\pi\)
\(572\) −295.771 + 295.771i −0.517082 + 0.517082i
\(573\) 89.9913 + 89.9913i 0.157053 + 0.157053i
\(574\) 67.3493i 0.117333i
\(575\) 0 0
\(576\) −668.234 −1.16013
\(577\) −639.002 + 639.002i −1.10746 + 1.10746i −0.113972 + 0.993484i \(0.536357\pi\)
−0.993484 + 0.113972i \(0.963643\pi\)
\(578\) −708.588 708.588i −1.22593 1.22593i
\(579\) 295.558i 0.510463i
\(580\) 0 0
\(581\) 234.166 0.403039
\(582\) 203.572 203.572i 0.349780 0.349780i
\(583\) 152.044 + 152.044i 0.260796 + 0.260796i
\(584\) 2473.07i 4.23470i
\(585\) 0 0
\(586\) −1504.93 −2.56814
\(587\) 367.435 367.435i 0.625953 0.625953i −0.321094 0.947047i \(-0.604051\pi\)
0.947047 + 0.321094i \(0.104051\pi\)
\(588\) −92.8530 92.8530i −0.157913 0.157913i
\(589\) 59.7332i 0.101415i
\(590\) 0 0
\(591\) 85.3456 0.144409
\(592\) 126.941 126.941i 0.214427 0.214427i
\(593\) 319.591 + 319.591i 0.538939 + 0.538939i 0.923217 0.384278i \(-0.125550\pi\)
−0.384278 + 0.923217i \(0.625550\pi\)
\(594\) 68.4693i 0.115268i
\(595\) 0 0
\(596\) 145.388 0.243940
\(597\) 28.0356 28.0356i 0.0469608 0.0469608i
\(598\) 819.240 + 819.240i 1.36997 + 1.36997i
\(599\) 119.408i 0.199346i 0.995020 + 0.0996730i \(0.0317797\pi\)
−0.995020 + 0.0996730i \(0.968220\pi\)
\(600\) 0 0
\(601\) 183.966 0.306100 0.153050 0.988218i \(-0.451090\pi\)
0.153050 + 0.988218i \(0.451090\pi\)
\(602\) 449.522 449.522i 0.746714 0.746714i
\(603\) −122.831 122.831i −0.203699 0.203699i
\(604\) 1447.06i 2.39580i
\(605\) 0 0
\(606\) 772.807 1.27526
\(607\) 757.520 757.520i 1.24797 1.24797i 0.291360 0.956614i \(-0.405892\pi\)
0.956614 0.291360i \(-0.0941076\pi\)
\(608\) 115.264 + 115.264i 0.189578 + 0.189578i
\(609\) 209.593i 0.344159i
\(610\) 0 0
\(611\) 226.974 0.371479
\(612\) 538.430 538.430i 0.879787 0.879787i
\(613\) −584.336 584.336i −0.953239 0.953239i 0.0457151 0.998955i \(-0.485443\pi\)
−0.998955 + 0.0457151i \(0.985443\pi\)
\(614\) 457.768i 0.745550i
\(615\) 0 0
\(616\) −238.134 −0.386582
\(617\) −483.308 + 483.308i −0.783319 + 0.783319i −0.980389 0.197070i \(-0.936857\pi\)
0.197070 + 0.980389i \(0.436857\pi\)
\(618\) 246.712 + 246.712i 0.399210 + 0.399210i
\(619\) 1053.61i 1.70211i 0.525074 + 0.851056i \(0.324038\pi\)
−0.525074 + 0.851056i \(0.675962\pi\)
\(620\) 0 0
\(621\) 138.499 0.223025
\(622\) −621.249 + 621.249i −0.998793 + 0.998793i
\(623\) −83.8436 83.8436i −0.134580 0.134580i
\(624\) 1133.49i 1.81649i
\(625\) 0 0
\(626\) −2264.05 −3.61669
\(627\) 5.78599 5.78599i 0.00922806 0.00922806i
\(628\) 1566.00 + 1566.00i 2.49363 + 2.49363i
\(629\) 72.5625i 0.115362i
\(630\) 0 0
\(631\) −127.766 −0.202481 −0.101241 0.994862i \(-0.532281\pi\)
−0.101241 + 0.994862i \(0.532281\pi\)
\(632\) 98.7430 98.7430i 0.156239 0.156239i
\(633\) −264.898 264.898i −0.418480 0.418480i
\(634\) 914.949i 1.44314i
\(635\) 0 0
\(636\) 1178.86 1.85355
\(637\) −55.8684 + 55.8684i −0.0877055 + 0.0877055i
\(638\) 426.154 + 426.154i 0.667953 + 0.667953i
\(639\) 116.323i 0.182039i
\(640\) 0 0
\(641\) 745.868 1.16360 0.581801 0.813331i \(-0.302348\pi\)
0.581801 + 0.813331i \(0.302348\pi\)
\(642\) 706.127 706.127i 1.09989 1.09989i
\(643\) −43.5132 43.5132i −0.0676721 0.0676721i 0.672461 0.740133i \(-0.265237\pi\)
−0.740133 + 0.672461i \(0.765237\pi\)
\(644\) 763.774i 1.18598i
\(645\) 0 0
\(646\) −124.608 −0.192892
\(647\) −434.895 + 434.895i −0.672171 + 0.672171i −0.958216 0.286045i \(-0.907659\pi\)
0.286045 + 0.958216i \(0.407659\pi\)
\(648\) 167.404 + 167.404i 0.258339 + 0.258339i
\(649\) 59.1699i 0.0911708i
\(650\) 0 0
\(651\) 198.257 0.304542
\(652\) −1535.34 + 1535.34i −2.35482 + 2.35482i
\(653\) −495.522 495.522i −0.758839 0.758839i 0.217272 0.976111i \(-0.430284\pi\)
−0.976111 + 0.217272i \(0.930284\pi\)
\(654\) 278.474i 0.425801i
\(655\) 0 0
\(656\) −383.247 −0.584218
\(657\) 199.436 199.436i 0.303556 0.303556i
\(658\) 144.879 + 144.879i 0.220181 + 0.220181i
\(659\) 250.489i 0.380104i −0.981774 0.190052i \(-0.939134\pi\)
0.981774 0.190052i \(-0.0608657\pi\)
\(660\) 0 0
\(661\) 48.3637 0.0731674 0.0365837 0.999331i \(-0.488352\pi\)
0.0365837 + 0.999331i \(0.488352\pi\)
\(662\) −1034.43 + 1034.43i −1.56258 + 1.56258i
\(663\) −323.966 323.966i −0.488637 0.488637i
\(664\) 2328.16i 3.50626i
\(665\) 0 0
\(666\) −35.7719 −0.0537116
\(667\) 862.017 862.017i 1.29238 1.29238i
\(668\) 1292.61 + 1292.61i 1.93505 + 1.93505i
\(669\) 135.014i 0.201815i
\(670\) 0 0
\(671\) 164.529 0.245200
\(672\) −382.564 + 382.564i −0.569292 + 0.569292i
\(673\) −621.928 621.928i −0.924113 0.924113i 0.0732040 0.997317i \(-0.476678\pi\)
−0.997317 + 0.0732040i \(0.976678\pi\)
\(674\) 1369.18i 2.03142i
\(675\) 0 0
\(676\) −450.562 −0.666511
\(677\) 446.844 446.844i 0.660035 0.660035i −0.295353 0.955388i \(-0.595437\pi\)
0.955388 + 0.295353i \(0.0954372\pi\)
\(678\) 1033.53 + 1033.53i 1.52438 + 1.52438i
\(679\) 114.194i 0.168179i
\(680\) 0 0
\(681\) −401.638 −0.589777
\(682\) 403.105 403.105i 0.591062 0.591062i
\(683\) 571.060 + 571.060i 0.836106 + 0.836106i 0.988344 0.152238i \(-0.0486481\pi\)
−0.152238 + 0.988344i \(0.548648\pi\)
\(684\) 44.8612i 0.0655866i
\(685\) 0 0
\(686\) −71.3225 −0.103969
\(687\) −197.455 + 197.455i −0.287416 + 0.287416i
\(688\) −2557.98 2557.98i −3.71799 3.71799i
\(689\) 709.304i 1.02947i
\(690\) 0 0
\(691\) 988.525 1.43057 0.715286 0.698832i \(-0.246296\pi\)
0.715286 + 0.698832i \(0.246296\pi\)
\(692\) −66.2535 + 66.2535i −0.0957421 + 0.0957421i
\(693\) 19.2039 + 19.2039i 0.0277113 + 0.0277113i
\(694\) 1279.45i 1.84359i
\(695\) 0 0
\(696\) 2083.85 2.99403
\(697\) 109.537 109.537i 0.157155 0.157155i
\(698\) −1354.97 1354.97i −1.94122 1.94122i
\(699\) 20.3036i 0.0290466i
\(700\) 0 0
\(701\) 271.597 0.387443 0.193721 0.981057i \(-0.437944\pi\)
0.193721 + 0.981057i \(0.437944\pi\)
\(702\) 159.709 159.709i 0.227506 0.227506i
\(703\) 3.02290 + 3.02290i 0.00430000 + 0.00430000i
\(704\) 762.153i 1.08260i
\(705\) 0 0
\(706\) 1184.55 1.67783
\(707\) 216.753 216.753i 0.306581 0.306581i
\(708\) −229.384 229.384i −0.323989 0.323989i
\(709\) 181.787i 0.256400i −0.991748 0.128200i \(-0.959080\pi\)
0.991748 0.128200i \(-0.0409199\pi\)
\(710\) 0 0
\(711\) −15.9259 −0.0223993
\(712\) −833.602 + 833.602i −1.17079 + 1.17079i
\(713\) −815.393 815.393i −1.14361 1.14361i
\(714\) 413.580i 0.579244i
\(715\) 0 0
\(716\) −2544.31 −3.55351
\(717\) −81.4424 + 81.4424i −0.113588 + 0.113588i
\(718\) 1446.28 + 1446.28i 2.01432 + 2.01432i
\(719\) 286.878i 0.398995i 0.979898 + 0.199498i \(0.0639310\pi\)
−0.979898 + 0.199498i \(0.936069\pi\)
\(720\) 0 0
\(721\) 138.393 0.191946
\(722\) 977.850 977.850i 1.35436 1.35436i
\(723\) −187.291 187.291i −0.259048 0.259048i
\(724\) 1395.79i 1.92788i
\(725\) 0 0
\(726\) −729.004 −1.00414
\(727\) 857.435 857.435i 1.17941 1.17941i 0.199521 0.979893i \(-0.436061\pi\)
0.979893 0.199521i \(-0.0639387\pi\)
\(728\) 555.463 + 555.463i 0.762999 + 0.762999i
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) 1462.20 2.00028
\(732\) 637.832 637.832i 0.871355 0.871355i
\(733\) −291.875 291.875i −0.398193 0.398193i 0.479402 0.877595i \(-0.340853\pi\)
−0.877595 + 0.479402i \(0.840853\pi\)
\(734\) 1039.09i 1.41565i
\(735\) 0 0
\(736\) 3146.83 4.27558
\(737\) −140.094 + 140.094i −0.190087 + 0.190087i
\(738\) 53.9996 + 53.9996i 0.0731702 + 0.0731702i
\(739\) 1080.02i 1.46147i 0.682662 + 0.730734i \(0.260822\pi\)
−0.682662 + 0.730734i \(0.739178\pi\)
\(740\) 0 0
\(741\) −26.9924 −0.0364270
\(742\) 452.754 452.754i 0.610181 0.610181i
\(743\) 821.950 + 821.950i 1.10626 + 1.10626i 0.993638 + 0.112621i \(0.0359246\pi\)
0.112621 + 0.993638i \(0.464075\pi\)
\(744\) 1971.14i 2.64938i
\(745\) 0 0
\(746\) 969.562 1.29968
\(747\) −187.750 + 187.750i −0.251339 + 0.251339i
\(748\) −614.105 614.105i −0.820996 0.820996i
\(749\) 396.102i 0.528841i
\(750\) 0 0
\(751\) 834.946 1.11178 0.555889 0.831256i \(-0.312378\pi\)
0.555889 + 0.831256i \(0.312378\pi\)
\(752\) 824.425 824.425i 1.09631 1.09631i
\(753\) 566.948 + 566.948i 0.752919 + 0.752919i
\(754\) 1988.06i 2.63669i
\(755\) 0 0
\(756\) 148.896 0.196952
\(757\) 192.396 192.396i 0.254156 0.254156i −0.568516 0.822672i \(-0.692482\pi\)
0.822672 + 0.568516i \(0.192482\pi\)
\(758\) 1163.59 + 1163.59i 1.53508 + 1.53508i
\(759\) 157.964i 0.208122i
\(760\) 0 0
\(761\) 95.1019 0.124970 0.0624848 0.998046i \(-0.480097\pi\)
0.0624848 + 0.998046i \(0.480097\pi\)
\(762\) −564.086 + 564.086i −0.740271 + 0.740271i
\(763\) 78.1050 + 78.1050i 0.102366 + 0.102366i
\(764\) 795.806i 1.04163i
\(765\) 0 0
\(766\) 2225.25 2.90502
\(767\) −138.017 + 138.017i −0.179945 + 0.179945i
\(768\) 727.262 + 727.262i 0.946956 + 0.946956i
\(769\) 368.887i 0.479697i 0.970810 + 0.239848i \(0.0770977\pi\)
−0.970810 + 0.239848i \(0.922902\pi\)
\(770\) 0 0
\(771\) −133.428 −0.173059
\(772\) −1306.83 + 1306.83i −1.69279 + 1.69279i
\(773\) 87.2860 + 87.2860i 0.112918 + 0.112918i 0.761308 0.648390i \(-0.224557\pi\)
−0.648390 + 0.761308i \(0.724557\pi\)
\(774\) 720.839i 0.931316i
\(775\) 0 0
\(776\) −1135.35 −1.46308
\(777\) −10.0331 + 10.0331i −0.0129126 + 0.0129126i
\(778\) 1035.97 + 1035.97i 1.33158 + 1.33158i
\(779\) 9.12646i 0.0117156i
\(780\) 0 0
\(781\) −132.672 −0.169875
\(782\) −1700.98 + 1700.98i −2.17516 + 2.17516i
\(783\) −168.048 168.048i −0.214621 0.214621i
\(784\) 405.856i 0.517673i
\(785\) 0 0
\(786\) 501.450 0.637977
\(787\) 984.039 984.039i 1.25037 1.25037i 0.294811 0.955556i \(-0.404743\pi\)
0.955556 0.294811i \(-0.0952567\pi\)
\(788\) −377.362 377.362i −0.478886 0.478886i
\(789\) 323.548i 0.410074i
\(790\) 0 0
\(791\) 579.757 0.732942
\(792\) 190.932 190.932i 0.241076 0.241076i
\(793\) −383.775 383.775i −0.483953 0.483953i
\(794\) 2286.13i 2.87926i
\(795\) 0 0
\(796\) −247.923 −0.311461
\(797\) 130.781 130.781i 0.164092 0.164092i −0.620285 0.784377i \(-0.712983\pi\)
0.784377 + 0.620285i \(0.212983\pi\)
\(798\) −17.2295 17.2295i −0.0215908 0.0215908i
\(799\) 471.262i 0.589815i
\(800\) 0 0
\(801\) 134.449 0.167851
\(802\) −316.589 + 316.589i −0.394749 + 0.394749i
\(803\) −227.467 227.467i −0.283271 0.283271i
\(804\) 1086.21i 1.35101i
\(805\) 0 0
\(806\) −1880.53 −2.33317
\(807\) 245.111 245.111i 0.303731 0.303731i
\(808\) −2155.03 2155.03i −2.66712 2.66712i
\(809\) 918.729i 1.13564i −0.823154 0.567818i \(-0.807788\pi\)
0.823154 0.567818i \(-0.192212\pi\)
\(810\) 0 0
\(811\) −70.2534 −0.0866256 −0.0433128 0.999062i \(-0.513791\pi\)
−0.0433128 + 0.999062i \(0.513791\pi\)
\(812\) 926.731 926.731i 1.14129 1.14129i
\(813\) −146.954 146.954i −0.180755 0.180755i
\(814\) 40.7996i 0.0501223i
\(815\) 0 0
\(816\) −2353.45 −2.88413
\(817\) 60.9144 60.9144i 0.0745586 0.0745586i
\(818\) −1390.25 1390.25i −1.69957 1.69957i
\(819\) 89.5888i 0.109388i
\(820\) 0 0
\(821\) 346.864 0.422489 0.211245 0.977433i \(-0.432248\pi\)
0.211245 + 0.977433i \(0.432248\pi\)
\(822\) 8.93838 8.93838i 0.0108739 0.0108739i
\(823\) 717.973 + 717.973i 0.872385 + 0.872385i 0.992732 0.120347i \(-0.0384006\pi\)
−0.120347 + 0.992732i \(0.538401\pi\)
\(824\) 1375.95i 1.66984i
\(825\) 0 0
\(826\) −176.195 −0.213311
\(827\) 480.121 480.121i 0.580557 0.580557i −0.354499 0.935056i \(-0.615349\pi\)
0.935056 + 0.354499i \(0.115349\pi\)
\(828\) −612.382 612.382i −0.739591 0.739591i
\(829\) 801.779i 0.967164i −0.875299 0.483582i \(-0.839335\pi\)
0.875299 0.483582i \(-0.160665\pi\)
\(830\) 0 0
\(831\) −496.446 −0.597408
\(832\) 1777.77 1777.77i 2.13674 2.13674i
\(833\) −115.999 115.999i −0.139254 0.139254i
\(834\) 98.3585i 0.117936i
\(835\) 0 0
\(836\) −51.1664 −0.0612038
\(837\) −158.959 + 158.959i −0.189915 + 0.189915i
\(838\) 1147.91 + 1147.91i 1.36982 + 1.36982i
\(839\) 1436.37i 1.71200i −0.516974 0.856001i \(-0.672941\pi\)
0.516974 0.856001i \(-0.327059\pi\)
\(840\) 0 0
\(841\) −1250.87 −1.48736
\(842\) −1681.19 + 1681.19i −1.99667 + 1.99667i
\(843\) −347.590 347.590i −0.412326 0.412326i
\(844\) 2342.53i 2.77551i
\(845\) 0 0
\(846\) −232.323 −0.274614
\(847\) −204.467 + 204.467i −0.241402 + 0.241402i
\(848\) −2576.37 2576.37i −3.03817 3.03817i
\(849\) 47.0454i 0.0554127i
\(850\) 0 0
\(851\) 82.5287 0.0969785
\(852\) −514.331 + 514.331i −0.603675 + 0.603675i
\(853\) 882.412 + 882.412i 1.03448 + 1.03448i 0.999384 + 0.0350966i \(0.0111739\pi\)
0.0350966 + 0.999384i \(0.488826\pi\)
\(854\) 489.933i 0.573692i
\(855\) 0 0
\(856\) −3938.18 −4.60068
\(857\) −1086.13 + 1086.13i −1.26736 + 1.26736i −0.319917 + 0.947445i \(0.603655\pi\)
−0.947445 + 0.319917i \(0.896345\pi\)
\(858\) −182.156 182.156i −0.212303 0.212303i
\(859\) 330.016i 0.384186i −0.981377 0.192093i \(-0.938472\pi\)
0.981377 0.192093i \(-0.0615276\pi\)
\(860\) 0 0
\(861\) 30.2911 0.0351813
\(862\) −37.7193 + 37.7193i −0.0437578 + 0.0437578i
\(863\) 31.2182 + 31.2182i 0.0361741 + 0.0361741i 0.724962 0.688788i \(-0.241857\pi\)
−0.688788 + 0.724962i \(0.741857\pi\)
\(864\) 613.467i 0.710032i
\(865\) 0 0
\(866\) −2938.90 −3.39365
\(867\) 318.695 318.695i 0.367584 0.367584i
\(868\) −876.607 876.607i −1.00992 1.00992i
\(869\) 18.1643i 0.0209025i
\(870\) 0 0
\(871\) 653.557 0.750353
\(872\) 776.547 776.547i 0.890535 0.890535i
\(873\) 91.5587 + 91.5587i 0.104878 + 0.104878i
\(874\) 141.723i 0.162154i
\(875\) 0 0
\(876\) −1763.64 −2.01329
\(877\) 123.525 123.525i 0.140849 0.140849i −0.633167 0.774016i \(-0.718245\pi\)
0.774016 + 0.633167i \(0.218245\pi\)
\(878\) 113.007 + 113.007i 0.128710 + 0.128710i
\(879\) 676.858i 0.770032i
\(880\) 0 0
\(881\) −1251.95 −1.42106 −0.710530 0.703667i \(-0.751545\pi\)
−0.710530 + 0.703667i \(0.751545\pi\)
\(882\) 57.1852 57.1852i 0.0648358 0.0648358i
\(883\) 789.617 + 789.617i 0.894244 + 0.894244i 0.994919 0.100676i \(-0.0321005\pi\)
−0.100676 + 0.994919i \(0.532100\pi\)
\(884\) 2864.88i 3.24081i
\(885\) 0 0
\(886\) −3145.03 −3.54969
\(887\) −543.479 + 543.479i −0.612716 + 0.612716i −0.943653 0.330937i \(-0.892635\pi\)
0.330937 + 0.943653i \(0.392635\pi\)
\(888\) 99.7528 + 99.7528i 0.112334 + 0.112334i
\(889\) 316.424i 0.355933i
\(890\) 0 0
\(891\) −30.7948 −0.0345621
\(892\) 596.976 596.976i 0.669256 0.669256i
\(893\) 19.6325 + 19.6325i 0.0219848 + 0.0219848i
\(894\) 89.5401i 0.100157i
\(895\) 0 0
\(896\) 1020.08 1.13848
\(897\) −368.462 + 368.462i −0.410771 + 0.410771i
\(898\) 638.787 + 638.787i 0.711344 + 0.711344i
\(899\) 1978.73i 2.20103i
\(900\) 0 0
\(901\) 1472.72 1.63454
\(902\) 61.5891 61.5891i 0.0682806 0.0682806i
\(903\) 202.177 + 202.177i 0.223895 + 0.223895i
\(904\) 5764.15i 6.37627i
\(905\) 0 0
\(906\) −891.199 −0.983663
\(907\) −650.529 + 650.529i −0.717232 + 0.717232i −0.968037 0.250806i \(-0.919305\pi\)
0.250806 + 0.968037i \(0.419305\pi\)
\(908\) 1775.87 + 1775.87i 1.95581 + 1.95581i
\(909\) 347.578i 0.382374i
\(910\) 0 0
\(911\) −64.0563 −0.0703143 −0.0351572 0.999382i \(-0.511193\pi\)
−0.0351572 + 0.999382i \(0.511193\pi\)
\(912\) −98.0431 + 98.0431i −0.107503 + 0.107503i
\(913\) 214.138 + 214.138i 0.234544 + 0.234544i
\(914\) 834.494i 0.913013i
\(915\) 0 0
\(916\) 1746.12 1.90624
\(917\) 140.644 140.644i 0.153374 0.153374i
\(918\) 331.602 + 331.602i 0.361222 + 0.361222i
\(919\) 550.055i 0.598536i −0.954169 0.299268i \(-0.903257\pi\)
0.954169 0.299268i \(-0.0967425\pi\)
\(920\) 0 0
\(921\) −205.886 −0.223546
\(922\) 1697.72 1697.72i 1.84135 1.84135i
\(923\) 309.466 + 309.466i 0.335283 + 0.335283i
\(924\) 169.823i 0.183791i
\(925\) 0 0
\(926\) 3342.72 3.60985
\(927\) −110.961 + 110.961i −0.119699 + 0.119699i
\(928\) −3818.23 3818.23i −4.11447 4.11447i
\(929\) 509.593i 0.548540i −0.961653 0.274270i \(-0.911564\pi\)
0.961653 0.274270i \(-0.0884361\pi\)
\(930\) 0 0
\(931\) −9.66486 −0.0103812
\(932\) −89.7738 + 89.7738i −0.0963239 + 0.0963239i
\(933\) −279.413 279.413i −0.299478 0.299478i
\(934\) 2392.24i 2.56128i
\(935\) 0 0
\(936\) −890.723 −0.951627
\(937\) 1254.00 1254.00i 1.33831 1.33831i 0.440612 0.897698i \(-0.354761\pi\)
0.897698 0.440612i \(-0.145239\pi\)
\(938\) 417.170 + 417.170i 0.444745 + 0.444745i
\(939\) 1018.28i 1.08443i
\(940\) 0 0
\(941\) −1596.36 −1.69645 −0.848223 0.529639i \(-0.822327\pi\)
−0.848223 + 0.529639i \(0.822327\pi\)
\(942\) −964.450 + 964.450i −1.02383 + 1.02383i
\(943\) −124.581 124.581i −0.132112 0.132112i
\(944\) 1002.63i 1.06211i
\(945\) 0 0
\(946\) 822.151 0.869082
\(947\) −484.352 + 484.352i −0.511459 + 0.511459i −0.914973 0.403514i \(-0.867789\pi\)
0.403514 + 0.914973i \(0.367789\pi\)
\(948\) 70.4176 + 70.4176i 0.0742802 + 0.0742802i
\(949\) 1061.16i 1.11819i
\(950\) 0 0
\(951\) 411.508 0.432711
\(952\) −1153.30 + 1153.30i −1.21145 + 1.21145i
\(953\) 79.3357 + 79.3357i 0.0832483 + 0.0832483i 0.747505 0.664256i \(-0.231252\pi\)
−0.664256 + 0.747505i \(0.731252\pi\)
\(954\) 726.021i 0.761029i
\(955\) 0 0
\(956\) 720.207 0.753355
\(957\) −191.667 + 191.667i −0.200279 + 0.200279i
\(958\) 41.5948 + 41.5948i 0.0434184 + 0.0434184i
\(959\) 5.01398i 0.00522835i
\(960\) 0 0
\(961\) 910.704 0.947663
\(962\) 95.1676 95.1676i 0.0989268 0.0989268i
\(963\) 317.588 + 317.588i 0.329790 + 0.329790i
\(964\) 1656.25i 1.71810i
\(965\) 0 0
\(966\) −470.384 −0.486940
\(967\) −733.793 + 733.793i −0.758835 + 0.758835i −0.976110 0.217276i \(-0.930283\pi\)
0.217276 + 0.976110i \(0.430283\pi\)
\(968\) 2032.88 + 2032.88i 2.10009 + 2.10009i
\(969\) 56.0439i 0.0578369i
\(970\) 0 0
\(971\) 907.453 0.934556 0.467278 0.884111i \(-0.345235\pi\)
0.467278 + 0.884111i \(0.345235\pi\)
\(972\) −119.382 + 119.382i −0.122821 + 0.122821i
\(973\) −27.5871 27.5871i −0.0283526 0.0283526i
\(974\) 928.341i 0.953123i
\(975\) 0 0
\(976\) −2787.93 −2.85649
\(977\) 643.316 643.316i 0.658460 0.658460i −0.296555 0.955016i \(-0.595838\pi\)
0.955016 + 0.296555i \(0.0958379\pi\)
\(978\) −945.569 945.569i −0.966840 0.966840i
\(979\) 153.345i 0.156635i
\(980\) 0 0
\(981\) −125.247 −0.127672
\(982\) 1470.44 1470.44i 1.49740 1.49740i
\(983\) 106.552 + 106.552i 0.108395 + 0.108395i 0.759224 0.650829i \(-0.225579\pi\)
−0.650829 + 0.759224i \(0.725579\pi\)
\(984\) 301.164i 0.306061i
\(985\) 0 0
\(986\) 4127.79 4.18639
\(987\) −65.1609 + 65.1609i −0.0660191 + 0.0660191i
\(988\) 119.349 + 119.349i 0.120798 + 0.120798i
\(989\) 1663.03i 1.68153i
\(990\) 0 0
\(991\) −1218.66 −1.22972 −0.614862 0.788634i \(-0.710788\pi\)
−0.614862 + 0.788634i \(0.710788\pi\)
\(992\) −3611.71 + 3611.71i −3.64084 + 3.64084i
\(993\) −465.245 465.245i −0.468525 0.468525i
\(994\) 395.069i 0.397454i
\(995\) 0 0
\(996\) 1660.30 1.66697
\(997\) −7.41944 + 7.41944i −0.00744176 + 0.00744176i −0.710818 0.703376i \(-0.751675\pi\)
0.703376 + 0.710818i \(0.251675\pi\)
\(998\) −1618.63 1618.63i −1.62187 1.62187i
\(999\) 16.0888i 0.0161049i
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 525.3.l.e.43.12 24
5.2 odd 4 inner 525.3.l.e.232.12 24
5.3 odd 4 105.3.l.a.22.1 24
5.4 even 2 105.3.l.a.43.1 yes 24
15.8 even 4 315.3.o.b.127.12 24
15.14 odd 2 315.3.o.b.253.12 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.3.l.a.22.1 24 5.3 odd 4
105.3.l.a.43.1 yes 24 5.4 even 2
315.3.o.b.127.12 24 15.8 even 4
315.3.o.b.253.12 24 15.14 odd 2
525.3.l.e.43.12 24 1.1 even 1 trivial
525.3.l.e.232.12 24 5.2 odd 4 inner