Properties

Label 9025.2.a.x.1.2
Level $9025$
Weight $2$
Character 9025.1
Self dual yes
Analytic conductor $72.065$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9025,2,Mod(1,9025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9025, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9025 = 5^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9025.a (trivial)

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: yes
Analytic conductor: \(72.0649878242\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{18})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - 3x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 19)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.347296\) of defining polynomial
Character \(\chi\) \(=\) 9025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.34730 q^{2} -2.87939 q^{3} -0.184793 q^{4} +3.87939 q^{6} -0.347296 q^{7} +2.94356 q^{8} +5.29086 q^{9} +O(q^{10})\) \(q-1.34730 q^{2} -2.87939 q^{3} -0.184793 q^{4} +3.87939 q^{6} -0.347296 q^{7} +2.94356 q^{8} +5.29086 q^{9} -2.22668 q^{11} +0.532089 q^{12} +2.57398 q^{13} +0.467911 q^{14} -3.59627 q^{16} -0.467911 q^{17} -7.12836 q^{18} +1.00000 q^{21} +3.00000 q^{22} +2.69459 q^{23} -8.47565 q^{24} -3.46791 q^{26} -6.59627 q^{27} +0.0641778 q^{28} +6.87939 q^{29} +7.10607 q^{31} -1.04189 q^{32} +6.41147 q^{33} +0.630415 q^{34} -0.977711 q^{36} +4.94356 q^{37} -7.41147 q^{39} -2.47565 q^{41} -1.34730 q^{42} -3.90167 q^{43} +0.411474 q^{44} -3.63041 q^{46} +7.29086 q^{47} +10.3550 q^{48} -6.87939 q^{49} +1.34730 q^{51} -0.475652 q^{52} -2.83750 q^{53} +8.88713 q^{54} -1.02229 q^{56} -9.26857 q^{58} +6.30541 q^{59} +9.12836 q^{61} -9.57398 q^{62} -1.83750 q^{63} +8.59627 q^{64} -8.63816 q^{66} +7.67499 q^{67} +0.0864665 q^{68} -7.75877 q^{69} +9.30541 q^{71} +15.5740 q^{72} -1.38919 q^{73} -6.66044 q^{74} +0.773318 q^{77} +9.98545 q^{78} +11.8452 q^{79} +3.12061 q^{81} +3.33544 q^{82} +14.8307 q^{83} -0.184793 q^{84} +5.25671 q^{86} -19.8084 q^{87} -6.55438 q^{88} +10.2909 q^{89} -0.893933 q^{91} -0.497941 q^{92} -20.4611 q^{93} -9.82295 q^{94} +3.00000 q^{96} +9.45336 q^{97} +9.26857 q^{98} -11.7811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 6 q^{6} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 6 q^{6} - 6 q^{8} - 3 q^{12} + 6 q^{14} + 3 q^{16} - 6 q^{17} - 3 q^{18} + 3 q^{21} + 9 q^{22} + 6 q^{23} - 6 q^{24} - 15 q^{26} - 6 q^{27} - 9 q^{28} + 15 q^{29} + 9 q^{31} + 9 q^{33} + 9 q^{34} - 9 q^{36} - 12 q^{39} + 12 q^{41} - 3 q^{42} - 9 q^{44} - 18 q^{46} + 6 q^{47} + 6 q^{48} - 15 q^{49} + 3 q^{51} + 18 q^{52} - 6 q^{53} - 3 q^{54} + 3 q^{56} - 18 q^{58} + 21 q^{59} + 9 q^{61} - 21 q^{62} - 3 q^{63} + 12 q^{64} - 9 q^{66} + 18 q^{67} - 15 q^{68} - 12 q^{69} + 30 q^{71} + 39 q^{72} + 3 q^{74} + 9 q^{77} + 12 q^{78} + 9 q^{79} + 15 q^{81} - 18 q^{82} + 3 q^{84} - 21 q^{86} - 21 q^{87} - 9 q^{88} + 15 q^{89} - 15 q^{91} + 24 q^{92} - 24 q^{93} - 9 q^{94} + 9 q^{96} + 15 q^{97} + 18 q^{98} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34730 −0.952682 −0.476341 0.879261i \(-0.658037\pi\)
−0.476341 + 0.879261i \(0.658037\pi\)
\(3\) −2.87939 −1.66241 −0.831207 0.555963i \(-0.812350\pi\)
−0.831207 + 0.555963i \(0.812350\pi\)
\(4\) −0.184793 −0.0923963
\(5\) 0 0
\(6\) 3.87939 1.58375
\(7\) −0.347296 −0.131266 −0.0656328 0.997844i \(-0.520907\pi\)
−0.0656328 + 0.997844i \(0.520907\pi\)
\(8\) 2.94356 1.04071
\(9\) 5.29086 1.76362
\(10\) 0 0
\(11\) −2.22668 −0.671370 −0.335685 0.941974i \(-0.608968\pi\)
−0.335685 + 0.941974i \(0.608968\pi\)
\(12\) 0.532089 0.153601
\(13\) 2.57398 0.713893 0.356947 0.934125i \(-0.383818\pi\)
0.356947 + 0.934125i \(0.383818\pi\)
\(14\) 0.467911 0.125055
\(15\) 0 0
\(16\) −3.59627 −0.899067
\(17\) −0.467911 −0.113485 −0.0567426 0.998389i \(-0.518071\pi\)
−0.0567426 + 0.998389i \(0.518071\pi\)
\(18\) −7.12836 −1.68017
\(19\) 0 0
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 3.00000 0.639602
\(23\) 2.69459 0.561861 0.280931 0.959728i \(-0.409357\pi\)
0.280931 + 0.959728i \(0.409357\pi\)
\(24\) −8.47565 −1.73009
\(25\) 0 0
\(26\) −3.46791 −0.680113
\(27\) −6.59627 −1.26945
\(28\) 0.0641778 0.0121285
\(29\) 6.87939 1.27747 0.638735 0.769427i \(-0.279458\pi\)
0.638735 + 0.769427i \(0.279458\pi\)
\(30\) 0 0
\(31\) 7.10607 1.27629 0.638144 0.769917i \(-0.279703\pi\)
0.638144 + 0.769917i \(0.279703\pi\)
\(32\) −1.04189 −0.184182
\(33\) 6.41147 1.11609
\(34\) 0.630415 0.108115
\(35\) 0 0
\(36\) −0.977711 −0.162952
\(37\) 4.94356 0.812717 0.406358 0.913714i \(-0.366798\pi\)
0.406358 + 0.913714i \(0.366798\pi\)
\(38\) 0 0
\(39\) −7.41147 −1.18679
\(40\) 0 0
\(41\) −2.47565 −0.386632 −0.193316 0.981137i \(-0.561924\pi\)
−0.193316 + 0.981137i \(0.561924\pi\)
\(42\) −1.34730 −0.207892
\(43\) −3.90167 −0.595000 −0.297500 0.954722i \(-0.596153\pi\)
−0.297500 + 0.954722i \(0.596153\pi\)
\(44\) 0.411474 0.0620321
\(45\) 0 0
\(46\) −3.63041 −0.535275
\(47\) 7.29086 1.06348 0.531741 0.846907i \(-0.321538\pi\)
0.531741 + 0.846907i \(0.321538\pi\)
\(48\) 10.3550 1.49462
\(49\) −6.87939 −0.982769
\(50\) 0 0
\(51\) 1.34730 0.188659
\(52\) −0.475652 −0.0659611
\(53\) −2.83750 −0.389760 −0.194880 0.980827i \(-0.562432\pi\)
−0.194880 + 0.980827i \(0.562432\pi\)
\(54\) 8.88713 1.20938
\(55\) 0 0
\(56\) −1.02229 −0.136609
\(57\) 0 0
\(58\) −9.26857 −1.21702
\(59\) 6.30541 0.820894 0.410447 0.911884i \(-0.365373\pi\)
0.410447 + 0.911884i \(0.365373\pi\)
\(60\) 0 0
\(61\) 9.12836 1.16877 0.584383 0.811478i \(-0.301337\pi\)
0.584383 + 0.811478i \(0.301337\pi\)
\(62\) −9.57398 −1.21590
\(63\) −1.83750 −0.231503
\(64\) 8.59627 1.07453
\(65\) 0 0
\(66\) −8.63816 −1.06328
\(67\) 7.67499 0.937650 0.468825 0.883291i \(-0.344678\pi\)
0.468825 + 0.883291i \(0.344678\pi\)
\(68\) 0.0864665 0.0104856
\(69\) −7.75877 −0.934046
\(70\) 0 0
\(71\) 9.30541 1.10435 0.552174 0.833729i \(-0.313798\pi\)
0.552174 + 0.833729i \(0.313798\pi\)
\(72\) 15.5740 1.83541
\(73\) −1.38919 −0.162592 −0.0812959 0.996690i \(-0.525906\pi\)
−0.0812959 + 0.996690i \(0.525906\pi\)
\(74\) −6.66044 −0.774261
\(75\) 0 0
\(76\) 0 0
\(77\) 0.773318 0.0881278
\(78\) 9.98545 1.13063
\(79\) 11.8452 1.33269 0.666347 0.745642i \(-0.267857\pi\)
0.666347 + 0.745642i \(0.267857\pi\)
\(80\) 0 0
\(81\) 3.12061 0.346735
\(82\) 3.33544 0.368337
\(83\) 14.8307 1.62788 0.813940 0.580949i \(-0.197319\pi\)
0.813940 + 0.580949i \(0.197319\pi\)
\(84\) −0.184793 −0.0201625
\(85\) 0 0
\(86\) 5.25671 0.566846
\(87\) −19.8084 −2.12368
\(88\) −6.55438 −0.698699
\(89\) 10.2909 1.09083 0.545414 0.838166i \(-0.316372\pi\)
0.545414 + 0.838166i \(0.316372\pi\)
\(90\) 0 0
\(91\) −0.893933 −0.0937097
\(92\) −0.497941 −0.0519139
\(93\) −20.4611 −2.12172
\(94\) −9.82295 −1.01316
\(95\) 0 0
\(96\) 3.00000 0.306186
\(97\) 9.45336 0.959844 0.479922 0.877311i \(-0.340665\pi\)
0.479922 + 0.877311i \(0.340665\pi\)
\(98\) 9.26857 0.936267
\(99\) −11.7811 −1.18404
\(100\) 0 0
\(101\) −9.24897 −0.920307 −0.460153 0.887839i \(-0.652206\pi\)
−0.460153 + 0.887839i \(0.652206\pi\)
\(102\) −1.81521 −0.179732
\(103\) −5.50980 −0.542897 −0.271448 0.962453i \(-0.587503\pi\)
−0.271448 + 0.962453i \(0.587503\pi\)
\(104\) 7.57667 0.742953
\(105\) 0 0
\(106\) 3.82295 0.371318
\(107\) 10.2344 0.989399 0.494699 0.869064i \(-0.335278\pi\)
0.494699 + 0.869064i \(0.335278\pi\)
\(108\) 1.21894 0.117293
\(109\) 1.82295 0.174607 0.0873034 0.996182i \(-0.472175\pi\)
0.0873034 + 0.996182i \(0.472175\pi\)
\(110\) 0 0
\(111\) −14.2344 −1.35107
\(112\) 1.24897 0.118017
\(113\) −17.6878 −1.66393 −0.831963 0.554830i \(-0.812783\pi\)
−0.831963 + 0.554830i \(0.812783\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.27126 −0.118033
\(117\) 13.6186 1.25904
\(118\) −8.49525 −0.782051
\(119\) 0.162504 0.0148967
\(120\) 0 0
\(121\) −6.04189 −0.549263
\(122\) −12.2986 −1.11346
\(123\) 7.12836 0.642742
\(124\) −1.31315 −0.117924
\(125\) 0 0
\(126\) 2.47565 0.220549
\(127\) 11.6040 1.02969 0.514845 0.857284i \(-0.327850\pi\)
0.514845 + 0.857284i \(0.327850\pi\)
\(128\) −9.49794 −0.839507
\(129\) 11.2344 0.989136
\(130\) 0 0
\(131\) 1.84524 0.161219 0.0806096 0.996746i \(-0.474313\pi\)
0.0806096 + 0.996746i \(0.474313\pi\)
\(132\) −1.18479 −0.103123
\(133\) 0 0
\(134\) −10.3405 −0.893282
\(135\) 0 0
\(136\) −1.37733 −0.118105
\(137\) −0.255777 −0.0218525 −0.0109263 0.999940i \(-0.503478\pi\)
−0.0109263 + 0.999940i \(0.503478\pi\)
\(138\) 10.4534 0.889849
\(139\) 4.26352 0.361627 0.180813 0.983517i \(-0.442127\pi\)
0.180813 + 0.983517i \(0.442127\pi\)
\(140\) 0 0
\(141\) −20.9932 −1.76795
\(142\) −12.5371 −1.05209
\(143\) −5.73143 −0.479286
\(144\) −19.0273 −1.58561
\(145\) 0 0
\(146\) 1.87164 0.154898
\(147\) 19.8084 1.63377
\(148\) −0.913534 −0.0750920
\(149\) 16.5594 1.35660 0.678301 0.734784i \(-0.262717\pi\)
0.678301 + 0.734784i \(0.262717\pi\)
\(150\) 0 0
\(151\) 4.36184 0.354962 0.177481 0.984124i \(-0.443205\pi\)
0.177481 + 0.984124i \(0.443205\pi\)
\(152\) 0 0
\(153\) −2.47565 −0.200145
\(154\) −1.04189 −0.0839578
\(155\) 0 0
\(156\) 1.36959 0.109655
\(157\) 9.61856 0.767644 0.383822 0.923407i \(-0.374608\pi\)
0.383822 + 0.923407i \(0.374608\pi\)
\(158\) −15.9590 −1.26963
\(159\) 8.17024 0.647943
\(160\) 0 0
\(161\) −0.935822 −0.0737531
\(162\) −4.20439 −0.330328
\(163\) −8.35504 −0.654417 −0.327209 0.944952i \(-0.606108\pi\)
−0.327209 + 0.944952i \(0.606108\pi\)
\(164\) 0.457482 0.0357233
\(165\) 0 0
\(166\) −19.9813 −1.55085
\(167\) 4.03508 0.312244 0.156122 0.987738i \(-0.450101\pi\)
0.156122 + 0.987738i \(0.450101\pi\)
\(168\) 2.94356 0.227101
\(169\) −6.37464 −0.490357
\(170\) 0 0
\(171\) 0 0
\(172\) 0.721000 0.0549758
\(173\) −20.1438 −1.53151 −0.765754 0.643134i \(-0.777634\pi\)
−0.765754 + 0.643134i \(0.777634\pi\)
\(174\) 26.6878 2.02320
\(175\) 0 0
\(176\) 8.00774 0.603606
\(177\) −18.1557 −1.36467
\(178\) −13.8648 −1.03921
\(179\) 11.5125 0.860484 0.430242 0.902714i \(-0.358428\pi\)
0.430242 + 0.902714i \(0.358428\pi\)
\(180\) 0 0
\(181\) −8.53714 −0.634561 −0.317280 0.948332i \(-0.602770\pi\)
−0.317280 + 0.948332i \(0.602770\pi\)
\(182\) 1.20439 0.0892755
\(183\) −26.2841 −1.94297
\(184\) 7.93170 0.584733
\(185\) 0 0
\(186\) 27.5672 2.02132
\(187\) 1.04189 0.0761905
\(188\) −1.34730 −0.0982617
\(189\) 2.29086 0.166635
\(190\) 0 0
\(191\) 18.3354 1.32671 0.663353 0.748307i \(-0.269133\pi\)
0.663353 + 0.748307i \(0.269133\pi\)
\(192\) −24.7520 −1.78632
\(193\) 0.297667 0.0214265 0.0107133 0.999943i \(-0.496590\pi\)
0.0107133 + 0.999943i \(0.496590\pi\)
\(194\) −12.7365 −0.914426
\(195\) 0 0
\(196\) 1.27126 0.0908042
\(197\) −13.1411 −0.936268 −0.468134 0.883657i \(-0.655074\pi\)
−0.468134 + 0.883657i \(0.655074\pi\)
\(198\) 15.8726 1.12802
\(199\) −0.256711 −0.0181978 −0.00909888 0.999959i \(-0.502896\pi\)
−0.00909888 + 0.999959i \(0.502896\pi\)
\(200\) 0 0
\(201\) −22.0993 −1.55876
\(202\) 12.4611 0.876760
\(203\) −2.38919 −0.167688
\(204\) −0.248970 −0.0174314
\(205\) 0 0
\(206\) 7.42333 0.517208
\(207\) 14.2567 0.990910
\(208\) −9.25671 −0.641837
\(209\) 0 0
\(210\) 0 0
\(211\) −2.44831 −0.168549 −0.0842743 0.996443i \(-0.526857\pi\)
−0.0842743 + 0.996443i \(0.526857\pi\)
\(212\) 0.524348 0.0360124
\(213\) −26.7939 −1.83588
\(214\) −13.7888 −0.942583
\(215\) 0 0
\(216\) −19.4165 −1.32113
\(217\) −2.46791 −0.167533
\(218\) −2.45605 −0.166345
\(219\) 4.00000 0.270295
\(220\) 0 0
\(221\) −1.20439 −0.0810162
\(222\) 19.1780 1.28714
\(223\) −8.50980 −0.569858 −0.284929 0.958549i \(-0.591970\pi\)
−0.284929 + 0.958549i \(0.591970\pi\)
\(224\) 0.361844 0.0241767
\(225\) 0 0
\(226\) 23.8307 1.58519
\(227\) −14.1506 −0.939211 −0.469606 0.882876i \(-0.655604\pi\)
−0.469606 + 0.882876i \(0.655604\pi\)
\(228\) 0 0
\(229\) −20.5330 −1.35686 −0.678430 0.734665i \(-0.737339\pi\)
−0.678430 + 0.734665i \(0.737339\pi\)
\(230\) 0 0
\(231\) −2.22668 −0.146505
\(232\) 20.2499 1.32947
\(233\) −17.6509 −1.15635 −0.578176 0.815912i \(-0.696235\pi\)
−0.578176 + 0.815912i \(0.696235\pi\)
\(234\) −18.3482 −1.19946
\(235\) 0 0
\(236\) −1.16519 −0.0758475
\(237\) −34.1070 −2.21549
\(238\) −0.218941 −0.0141918
\(239\) 2.35235 0.152161 0.0760804 0.997102i \(-0.475759\pi\)
0.0760804 + 0.997102i \(0.475759\pi\)
\(240\) 0 0
\(241\) −13.8007 −0.888979 −0.444489 0.895784i \(-0.646615\pi\)
−0.444489 + 0.895784i \(0.646615\pi\)
\(242\) 8.14022 0.523273
\(243\) 10.8033 0.693035
\(244\) −1.68685 −0.107990
\(245\) 0 0
\(246\) −9.60401 −0.612329
\(247\) 0 0
\(248\) 20.9172 1.32824
\(249\) −42.7033 −2.70621
\(250\) 0 0
\(251\) −4.16519 −0.262905 −0.131452 0.991322i \(-0.541964\pi\)
−0.131452 + 0.991322i \(0.541964\pi\)
\(252\) 0.339556 0.0213900
\(253\) −6.00000 −0.377217
\(254\) −15.6340 −0.980967
\(255\) 0 0
\(256\) −4.39599 −0.274750
\(257\) 0.667252 0.0416220 0.0208110 0.999783i \(-0.493375\pi\)
0.0208110 + 0.999783i \(0.493375\pi\)
\(258\) −15.1361 −0.942332
\(259\) −1.71688 −0.106682
\(260\) 0 0
\(261\) 36.3979 2.25297
\(262\) −2.48608 −0.153591
\(263\) −11.3996 −0.702930 −0.351465 0.936201i \(-0.614316\pi\)
−0.351465 + 0.936201i \(0.614316\pi\)
\(264\) 18.8726 1.16153
\(265\) 0 0
\(266\) 0 0
\(267\) −29.6313 −1.81341
\(268\) −1.41828 −0.0866353
\(269\) −19.3901 −1.18224 −0.591118 0.806585i \(-0.701313\pi\)
−0.591118 + 0.806585i \(0.701313\pi\)
\(270\) 0 0
\(271\) −13.3942 −0.813642 −0.406821 0.913508i \(-0.633363\pi\)
−0.406821 + 0.913508i \(0.633363\pi\)
\(272\) 1.68273 0.102031
\(273\) 2.57398 0.155784
\(274\) 0.344608 0.0208185
\(275\) 0 0
\(276\) 1.43376 0.0863024
\(277\) −17.7469 −1.06631 −0.533154 0.846018i \(-0.678993\pi\)
−0.533154 + 0.846018i \(0.678993\pi\)
\(278\) −5.74422 −0.344516
\(279\) 37.5972 2.25089
\(280\) 0 0
\(281\) −18.2790 −1.09043 −0.545217 0.838295i \(-0.683553\pi\)
−0.545217 + 0.838295i \(0.683553\pi\)
\(282\) 28.2841 1.68429
\(283\) −7.68779 −0.456991 −0.228496 0.973545i \(-0.573381\pi\)
−0.228496 + 0.973545i \(0.573381\pi\)
\(284\) −1.71957 −0.102038
\(285\) 0 0
\(286\) 7.72193 0.456608
\(287\) 0.859785 0.0507515
\(288\) −5.51249 −0.324827
\(289\) −16.7811 −0.987121
\(290\) 0 0
\(291\) −27.2199 −1.59566
\(292\) 0.256711 0.0150229
\(293\) −10.5030 −0.613591 −0.306796 0.951775i \(-0.599257\pi\)
−0.306796 + 0.951775i \(0.599257\pi\)
\(294\) −26.6878 −1.55646
\(295\) 0 0
\(296\) 14.5517 0.845800
\(297\) 14.6878 0.852272
\(298\) −22.3105 −1.29241
\(299\) 6.93582 0.401109
\(300\) 0 0
\(301\) 1.35504 0.0781030
\(302\) −5.87670 −0.338166
\(303\) 26.6313 1.52993
\(304\) 0 0
\(305\) 0 0
\(306\) 3.33544 0.190674
\(307\) −11.6955 −0.667499 −0.333749 0.942662i \(-0.608314\pi\)
−0.333749 + 0.942662i \(0.608314\pi\)
\(308\) −0.142903 −0.00814268
\(309\) 15.8648 0.902519
\(310\) 0 0
\(311\) 15.9659 0.905340 0.452670 0.891678i \(-0.350471\pi\)
0.452670 + 0.891678i \(0.350471\pi\)
\(312\) −21.8161 −1.23510
\(313\) 26.6287 1.50514 0.752570 0.658512i \(-0.228814\pi\)
0.752570 + 0.658512i \(0.228814\pi\)
\(314\) −12.9590 −0.731321
\(315\) 0 0
\(316\) −2.18891 −0.123136
\(317\) 29.5321 1.65869 0.829344 0.558739i \(-0.188715\pi\)
0.829344 + 0.558739i \(0.188715\pi\)
\(318\) −11.0077 −0.617283
\(319\) −15.3182 −0.857655
\(320\) 0 0
\(321\) −29.4688 −1.64479
\(322\) 1.26083 0.0702633
\(323\) 0 0
\(324\) −0.576666 −0.0320370
\(325\) 0 0
\(326\) 11.2567 0.623452
\(327\) −5.24897 −0.290269
\(328\) −7.28724 −0.402370
\(329\) −2.53209 −0.139599
\(330\) 0 0
\(331\) −27.6655 −1.52063 −0.760317 0.649553i \(-0.774956\pi\)
−0.760317 + 0.649553i \(0.774956\pi\)
\(332\) −2.74060 −0.150410
\(333\) 26.1557 1.43332
\(334\) −5.43645 −0.297469
\(335\) 0 0
\(336\) −3.59627 −0.196192
\(337\) 17.8598 0.972884 0.486442 0.873713i \(-0.338294\pi\)
0.486442 + 0.873713i \(0.338294\pi\)
\(338\) 8.58853 0.467154
\(339\) 50.9299 2.76614
\(340\) 0 0
\(341\) −15.8229 −0.856861
\(342\) 0 0
\(343\) 4.82026 0.260270
\(344\) −11.4848 −0.619220
\(345\) 0 0
\(346\) 27.1397 1.45904
\(347\) 5.80066 0.311396 0.155698 0.987805i \(-0.450237\pi\)
0.155698 + 0.987805i \(0.450237\pi\)
\(348\) 3.66044 0.196220
\(349\) 5.37227 0.287571 0.143786 0.989609i \(-0.454072\pi\)
0.143786 + 0.989609i \(0.454072\pi\)
\(350\) 0 0
\(351\) −16.9786 −0.906253
\(352\) 2.31996 0.123654
\(353\) 25.2344 1.34309 0.671546 0.740963i \(-0.265630\pi\)
0.671546 + 0.740963i \(0.265630\pi\)
\(354\) 24.4611 1.30009
\(355\) 0 0
\(356\) −1.90167 −0.100789
\(357\) −0.467911 −0.0247645
\(358\) −15.5107 −0.819768
\(359\) 6.68685 0.352919 0.176459 0.984308i \(-0.443536\pi\)
0.176459 + 0.984308i \(0.443536\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 11.5021 0.604535
\(363\) 17.3969 0.913102
\(364\) 0.165192 0.00865842
\(365\) 0 0
\(366\) 35.4124 1.85104
\(367\) −8.11886 −0.423801 −0.211901 0.977291i \(-0.567965\pi\)
−0.211901 + 0.977291i \(0.567965\pi\)
\(368\) −9.69047 −0.505151
\(369\) −13.0983 −0.681872
\(370\) 0 0
\(371\) 0.985452 0.0511621
\(372\) 3.78106 0.196039
\(373\) 34.8976 1.80693 0.903463 0.428665i \(-0.141016\pi\)
0.903463 + 0.428665i \(0.141016\pi\)
\(374\) −1.40373 −0.0725853
\(375\) 0 0
\(376\) 21.4611 1.10677
\(377\) 17.7074 0.911977
\(378\) −3.08647 −0.158751
\(379\) −1.70140 −0.0873950 −0.0436975 0.999045i \(-0.513914\pi\)
−0.0436975 + 0.999045i \(0.513914\pi\)
\(380\) 0 0
\(381\) −33.4124 −1.71177
\(382\) −24.7033 −1.26393
\(383\) 2.93676 0.150061 0.0750306 0.997181i \(-0.476095\pi\)
0.0750306 + 0.997181i \(0.476095\pi\)
\(384\) 27.3482 1.39561
\(385\) 0 0
\(386\) −0.401045 −0.0204127
\(387\) −20.6432 −1.04935
\(388\) −1.74691 −0.0886860
\(389\) −24.5672 −1.24561 −0.622803 0.782379i \(-0.714006\pi\)
−0.622803 + 0.782379i \(0.714006\pi\)
\(390\) 0 0
\(391\) −1.26083 −0.0637629
\(392\) −20.2499 −1.02277
\(393\) −5.31315 −0.268013
\(394\) 17.7050 0.891966
\(395\) 0 0
\(396\) 2.17705 0.109401
\(397\) 31.8357 1.59779 0.798895 0.601470i \(-0.205418\pi\)
0.798895 + 0.601470i \(0.205418\pi\)
\(398\) 0.345866 0.0173367
\(399\) 0 0
\(400\) 0 0
\(401\) 0.0864665 0.00431793 0.00215896 0.999998i \(-0.499313\pi\)
0.00215896 + 0.999998i \(0.499313\pi\)
\(402\) 29.7743 1.48500
\(403\) 18.2909 0.911133
\(404\) 1.70914 0.0850329
\(405\) 0 0
\(406\) 3.21894 0.159753
\(407\) −11.0077 −0.545633
\(408\) 3.96585 0.196339
\(409\) −20.0060 −0.989232 −0.494616 0.869112i \(-0.664691\pi\)
−0.494616 + 0.869112i \(0.664691\pi\)
\(410\) 0 0
\(411\) 0.736482 0.0363280
\(412\) 1.01817 0.0501616
\(413\) −2.18984 −0.107755
\(414\) −19.2080 −0.944022
\(415\) 0 0
\(416\) −2.68180 −0.131486
\(417\) −12.2763 −0.601174
\(418\) 0 0
\(419\) 25.4097 1.24135 0.620673 0.784070i \(-0.286859\pi\)
0.620673 + 0.784070i \(0.286859\pi\)
\(420\) 0 0
\(421\) −4.36959 −0.212961 −0.106480 0.994315i \(-0.533958\pi\)
−0.106480 + 0.994315i \(0.533958\pi\)
\(422\) 3.29860 0.160573
\(423\) 38.5749 1.87558
\(424\) −8.35235 −0.405626
\(425\) 0 0
\(426\) 36.0993 1.74901
\(427\) −3.17024 −0.153419
\(428\) −1.89124 −0.0914168
\(429\) 16.5030 0.796772
\(430\) 0 0
\(431\) 38.3063 1.84515 0.922576 0.385816i \(-0.126080\pi\)
0.922576 + 0.385816i \(0.126080\pi\)
\(432\) 23.7219 1.14132
\(433\) −18.1310 −0.871322 −0.435661 0.900111i \(-0.643485\pi\)
−0.435661 + 0.900111i \(0.643485\pi\)
\(434\) 3.32501 0.159605
\(435\) 0 0
\(436\) −0.336867 −0.0161330
\(437\) 0 0
\(438\) −5.38919 −0.257505
\(439\) 6.09059 0.290688 0.145344 0.989381i \(-0.453571\pi\)
0.145344 + 0.989381i \(0.453571\pi\)
\(440\) 0 0
\(441\) −36.3979 −1.73323
\(442\) 1.62267 0.0771827
\(443\) 29.8931 1.42026 0.710132 0.704068i \(-0.248635\pi\)
0.710132 + 0.704068i \(0.248635\pi\)
\(444\) 2.63041 0.124834
\(445\) 0 0
\(446\) 11.4652 0.542894
\(447\) −47.6810 −2.25523
\(448\) −2.98545 −0.141049
\(449\) 11.2499 0.530916 0.265458 0.964122i \(-0.414477\pi\)
0.265458 + 0.964122i \(0.414477\pi\)
\(450\) 0 0
\(451\) 5.51249 0.259573
\(452\) 3.26857 0.153741
\(453\) −12.5594 −0.590093
\(454\) 19.0651 0.894770
\(455\) 0 0
\(456\) 0 0
\(457\) 23.3901 1.09414 0.547072 0.837086i \(-0.315742\pi\)
0.547072 + 0.837086i \(0.315742\pi\)
\(458\) 27.6641 1.29266
\(459\) 3.08647 0.144064
\(460\) 0 0
\(461\) −36.6236 −1.70573 −0.852866 0.522130i \(-0.825137\pi\)
−0.852866 + 0.522130i \(0.825137\pi\)
\(462\) 3.00000 0.139573
\(463\) 42.9864 1.99775 0.998873 0.0474549i \(-0.0151110\pi\)
0.998873 + 0.0474549i \(0.0151110\pi\)
\(464\) −24.7401 −1.14853
\(465\) 0 0
\(466\) 23.7811 1.10164
\(467\) −25.5963 −1.18445 −0.592227 0.805771i \(-0.701751\pi\)
−0.592227 + 0.805771i \(0.701751\pi\)
\(468\) −2.51661 −0.116330
\(469\) −2.66550 −0.123081
\(470\) 0 0
\(471\) −27.6955 −1.27614
\(472\) 18.5604 0.854310
\(473\) 8.68779 0.399465
\(474\) 45.9522 2.11066
\(475\) 0 0
\(476\) −0.0300295 −0.00137640
\(477\) −15.0128 −0.687389
\(478\) −3.16931 −0.144961
\(479\) 38.1762 1.74432 0.872158 0.489224i \(-0.162720\pi\)
0.872158 + 0.489224i \(0.162720\pi\)
\(480\) 0 0
\(481\) 12.7246 0.580193
\(482\) 18.5936 0.846914
\(483\) 2.69459 0.122608
\(484\) 1.11650 0.0507498
\(485\) 0 0
\(486\) −14.5553 −0.660242
\(487\) 7.76382 0.351812 0.175906 0.984407i \(-0.443714\pi\)
0.175906 + 0.984407i \(0.443714\pi\)
\(488\) 26.8699 1.21634
\(489\) 24.0574 1.08791
\(490\) 0 0
\(491\) −36.7229 −1.65728 −0.828640 0.559782i \(-0.810885\pi\)
−0.828640 + 0.559782i \(0.810885\pi\)
\(492\) −1.31727 −0.0593870
\(493\) −3.21894 −0.144974
\(494\) 0 0
\(495\) 0 0
\(496\) −25.5553 −1.14747
\(497\) −3.23173 −0.144963
\(498\) 57.5340 2.57816
\(499\) 4.92633 0.220533 0.110266 0.993902i \(-0.464830\pi\)
0.110266 + 0.993902i \(0.464830\pi\)
\(500\) 0 0
\(501\) −11.6186 −0.519079
\(502\) 5.61175 0.250465
\(503\) −32.9495 −1.46915 −0.734574 0.678529i \(-0.762618\pi\)
−0.734574 + 0.678529i \(0.762618\pi\)
\(504\) −5.40879 −0.240926
\(505\) 0 0
\(506\) 8.08378 0.359368
\(507\) 18.3550 0.815176
\(508\) −2.14433 −0.0951394
\(509\) 36.9350 1.63712 0.818558 0.574424i \(-0.194774\pi\)
0.818558 + 0.574424i \(0.194774\pi\)
\(510\) 0 0
\(511\) 0.482459 0.0213427
\(512\) 24.9186 1.10126
\(513\) 0 0
\(514\) −0.898986 −0.0396526
\(515\) 0 0
\(516\) −2.07604 −0.0913924
\(517\) −16.2344 −0.713989
\(518\) 2.31315 0.101634
\(519\) 58.0019 2.54600
\(520\) 0 0
\(521\) −9.29179 −0.407081 −0.203540 0.979067i \(-0.565245\pi\)
−0.203540 + 0.979067i \(0.565245\pi\)
\(522\) −49.0387 −2.14637
\(523\) −28.4151 −1.24251 −0.621253 0.783610i \(-0.713376\pi\)
−0.621253 + 0.783610i \(0.713376\pi\)
\(524\) −0.340986 −0.0148960
\(525\) 0 0
\(526\) 15.3587 0.669669
\(527\) −3.32501 −0.144840
\(528\) −23.0574 −1.00344
\(529\) −15.7392 −0.684312
\(530\) 0 0
\(531\) 33.3610 1.44775
\(532\) 0 0
\(533\) −6.37227 −0.276014
\(534\) 39.9222 1.72760
\(535\) 0 0
\(536\) 22.5918 0.975818
\(537\) −33.1489 −1.43048
\(538\) 26.1242 1.12630
\(539\) 15.3182 0.659802
\(540\) 0 0
\(541\) 14.9855 0.644275 0.322137 0.946693i \(-0.395599\pi\)
0.322137 + 0.946693i \(0.395599\pi\)
\(542\) 18.0460 0.775142
\(543\) 24.5817 1.05490
\(544\) 0.487511 0.0209019
\(545\) 0 0
\(546\) −3.46791 −0.148413
\(547\) −3.88713 −0.166202 −0.0831008 0.996541i \(-0.526482\pi\)
−0.0831008 + 0.996541i \(0.526482\pi\)
\(548\) 0.0472658 0.00201909
\(549\) 48.2968 2.06126
\(550\) 0 0
\(551\) 0 0
\(552\) −22.8384 −0.972068
\(553\) −4.11381 −0.174937
\(554\) 23.9103 1.01585
\(555\) 0 0
\(556\) −0.787866 −0.0334130
\(557\) −13.2044 −0.559488 −0.279744 0.960075i \(-0.590250\pi\)
−0.279744 + 0.960075i \(0.590250\pi\)
\(558\) −50.6546 −2.14438
\(559\) −10.0428 −0.424766
\(560\) 0 0
\(561\) −3.00000 −0.126660
\(562\) 24.6272 1.03884
\(563\) 10.7128 0.451489 0.225745 0.974187i \(-0.427519\pi\)
0.225745 + 0.974187i \(0.427519\pi\)
\(564\) 3.87939 0.163352
\(565\) 0 0
\(566\) 10.3577 0.435368
\(567\) −1.08378 −0.0455144
\(568\) 27.3911 1.14930
\(569\) 13.4706 0.564717 0.282358 0.959309i \(-0.408883\pi\)
0.282358 + 0.959309i \(0.408883\pi\)
\(570\) 0 0
\(571\) 12.6655 0.530035 0.265017 0.964244i \(-0.414622\pi\)
0.265017 + 0.964244i \(0.414622\pi\)
\(572\) 1.05913 0.0442843
\(573\) −52.7948 −2.20553
\(574\) −1.15839 −0.0483501
\(575\) 0 0
\(576\) 45.4816 1.89507
\(577\) 10.5544 0.439384 0.219692 0.975569i \(-0.429495\pi\)
0.219692 + 0.975569i \(0.429495\pi\)
\(578\) 22.6091 0.940413
\(579\) −0.857097 −0.0356197
\(580\) 0 0
\(581\) −5.15064 −0.213685
\(582\) 36.6732 1.52015
\(583\) 6.31820 0.261673
\(584\) −4.08915 −0.169210
\(585\) 0 0
\(586\) 14.1506 0.584558
\(587\) 19.1548 0.790602 0.395301 0.918552i \(-0.370640\pi\)
0.395301 + 0.918552i \(0.370640\pi\)
\(588\) −3.66044 −0.150954
\(589\) 0 0
\(590\) 0 0
\(591\) 37.8384 1.55647
\(592\) −17.7784 −0.730687
\(593\) 8.69459 0.357044 0.178522 0.983936i \(-0.442868\pi\)
0.178522 + 0.983936i \(0.442868\pi\)
\(594\) −19.7888 −0.811944
\(595\) 0 0
\(596\) −3.06006 −0.125345
\(597\) 0.739170 0.0302522
\(598\) −9.34461 −0.382129
\(599\) −19.8316 −0.810298 −0.405149 0.914251i \(-0.632780\pi\)
−0.405149 + 0.914251i \(0.632780\pi\)
\(600\) 0 0
\(601\) 33.7615 1.37716 0.688579 0.725161i \(-0.258235\pi\)
0.688579 + 0.725161i \(0.258235\pi\)
\(602\) −1.82564 −0.0744074
\(603\) 40.6073 1.65366
\(604\) −0.806036 −0.0327971
\(605\) 0 0
\(606\) −35.8803 −1.45754
\(607\) 35.2850 1.43217 0.716087 0.698011i \(-0.245932\pi\)
0.716087 + 0.698011i \(0.245932\pi\)
\(608\) 0 0
\(609\) 6.87939 0.278767
\(610\) 0 0
\(611\) 18.7665 0.759212
\(612\) 0.457482 0.0184926
\(613\) −18.4534 −0.745324 −0.372662 0.927967i \(-0.621555\pi\)
−0.372662 + 0.927967i \(0.621555\pi\)
\(614\) 15.7573 0.635914
\(615\) 0 0
\(616\) 2.27631 0.0917152
\(617\) 35.6854 1.43664 0.718320 0.695712i \(-0.244911\pi\)
0.718320 + 0.695712i \(0.244911\pi\)
\(618\) −21.3746 −0.859814
\(619\) 3.65951 0.147088 0.0735441 0.997292i \(-0.476569\pi\)
0.0735441 + 0.997292i \(0.476569\pi\)
\(620\) 0 0
\(621\) −17.7743 −0.713256
\(622\) −21.5107 −0.862502
\(623\) −3.57398 −0.143188
\(624\) 26.6536 1.06700
\(625\) 0 0
\(626\) −35.8767 −1.43392
\(627\) 0 0
\(628\) −1.77744 −0.0709275
\(629\) −2.31315 −0.0922313
\(630\) 0 0
\(631\) −0.793852 −0.0316028 −0.0158014 0.999875i \(-0.505030\pi\)
−0.0158014 + 0.999875i \(0.505030\pi\)
\(632\) 34.8672 1.38694
\(633\) 7.04963 0.280198
\(634\) −39.7885 −1.58020
\(635\) 0 0
\(636\) −1.50980 −0.0598675
\(637\) −17.7074 −0.701592
\(638\) 20.6382 0.817072
\(639\) 49.2336 1.94765
\(640\) 0 0
\(641\) −29.3824 −1.16053 −0.580267 0.814426i \(-0.697052\pi\)
−0.580267 + 0.814426i \(0.697052\pi\)
\(642\) 39.7033 1.56696
\(643\) −22.2139 −0.876030 −0.438015 0.898968i \(-0.644318\pi\)
−0.438015 + 0.898968i \(0.644318\pi\)
\(644\) 0.172933 0.00681451
\(645\) 0 0
\(646\) 0 0
\(647\) −11.2591 −0.442640 −0.221320 0.975201i \(-0.571037\pi\)
−0.221320 + 0.975201i \(0.571037\pi\)
\(648\) 9.18573 0.360849
\(649\) −14.0401 −0.551123
\(650\) 0 0
\(651\) 7.10607 0.278509
\(652\) 1.54395 0.0604657
\(653\) −27.0000 −1.05659 −0.528296 0.849060i \(-0.677169\pi\)
−0.528296 + 0.849060i \(0.677169\pi\)
\(654\) 7.07192 0.276534
\(655\) 0 0
\(656\) 8.90310 0.347608
\(657\) −7.34998 −0.286750
\(658\) 3.41147 0.132993
\(659\) −28.0259 −1.09173 −0.545867 0.837872i \(-0.683800\pi\)
−0.545867 + 0.837872i \(0.683800\pi\)
\(660\) 0 0
\(661\) −11.3678 −0.442157 −0.221079 0.975256i \(-0.570958\pi\)
−0.221079 + 0.975256i \(0.570958\pi\)
\(662\) 37.2736 1.44868
\(663\) 3.46791 0.134683
\(664\) 43.6551 1.69415
\(665\) 0 0
\(666\) −35.2395 −1.36550
\(667\) 18.5371 0.717761
\(668\) −0.745653 −0.0288502
\(669\) 24.5030 0.947340
\(670\) 0 0
\(671\) −20.3259 −0.784674
\(672\) −1.04189 −0.0401917
\(673\) −16.5672 −0.638618 −0.319309 0.947651i \(-0.603451\pi\)
−0.319309 + 0.947651i \(0.603451\pi\)
\(674\) −24.0624 −0.926850
\(675\) 0 0
\(676\) 1.17799 0.0453071
\(677\) −9.04963 −0.347806 −0.173903 0.984763i \(-0.555638\pi\)
−0.173903 + 0.984763i \(0.555638\pi\)
\(678\) −68.6177 −2.63525
\(679\) −3.28312 −0.125995
\(680\) 0 0
\(681\) 40.7452 1.56136
\(682\) 21.3182 0.816316
\(683\) 8.73143 0.334099 0.167049 0.985949i \(-0.446576\pi\)
0.167049 + 0.985949i \(0.446576\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −6.49432 −0.247954
\(687\) 59.1225 2.25566
\(688\) 14.0315 0.534944
\(689\) −7.30365 −0.278247
\(690\) 0 0
\(691\) 34.7202 1.32082 0.660409 0.750906i \(-0.270383\pi\)
0.660409 + 0.750906i \(0.270383\pi\)
\(692\) 3.72243 0.141506
\(693\) 4.09152 0.155424
\(694\) −7.81521 −0.296661
\(695\) 0 0
\(696\) −58.3073 −2.21013
\(697\) 1.15839 0.0438770
\(698\) −7.23804 −0.273964
\(699\) 50.8239 1.92234
\(700\) 0 0
\(701\) 39.4151 1.48869 0.744344 0.667797i \(-0.232762\pi\)
0.744344 + 0.667797i \(0.232762\pi\)
\(702\) 22.8753 0.863371
\(703\) 0 0
\(704\) −19.1411 −0.721409
\(705\) 0 0
\(706\) −33.9982 −1.27954
\(707\) 3.21213 0.120805
\(708\) 3.35504 0.126090
\(709\) −41.1215 −1.54435 −0.772176 0.635409i \(-0.780832\pi\)
−0.772176 + 0.635409i \(0.780832\pi\)
\(710\) 0 0
\(711\) 62.6715 2.35036
\(712\) 30.2918 1.13523
\(713\) 19.1480 0.717097
\(714\) 0.630415 0.0235927
\(715\) 0 0
\(716\) −2.12742 −0.0795055
\(717\) −6.77332 −0.252954
\(718\) −9.00917 −0.336219
\(719\) −42.3955 −1.58109 −0.790543 0.612407i \(-0.790201\pi\)
−0.790543 + 0.612407i \(0.790201\pi\)
\(720\) 0 0
\(721\) 1.91353 0.0712637
\(722\) 0 0
\(723\) 39.7374 1.47785
\(724\) 1.57760 0.0586310
\(725\) 0 0
\(726\) −23.4388 −0.869896
\(727\) −51.6563 −1.91583 −0.957914 0.287057i \(-0.907323\pi\)
−0.957914 + 0.287057i \(0.907323\pi\)
\(728\) −2.63135 −0.0975243
\(729\) −40.4688 −1.49885
\(730\) 0 0
\(731\) 1.82564 0.0675236
\(732\) 4.85710 0.179523
\(733\) 22.9162 0.846430 0.423215 0.906029i \(-0.360902\pi\)
0.423215 + 0.906029i \(0.360902\pi\)
\(734\) 10.9385 0.403748
\(735\) 0 0
\(736\) −2.80747 −0.103485
\(737\) −17.0898 −0.629510
\(738\) 17.6473 0.649607
\(739\) 28.1266 1.03465 0.517327 0.855788i \(-0.326927\pi\)
0.517327 + 0.855788i \(0.326927\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.32770 −0.0487413
\(743\) 6.13247 0.224979 0.112489 0.993653i \(-0.464118\pi\)
0.112489 + 0.993653i \(0.464118\pi\)
\(744\) −60.2285 −2.20809
\(745\) 0 0
\(746\) −47.0173 −1.72143
\(747\) 78.4671 2.87096
\(748\) −0.192533 −0.00703972
\(749\) −3.55438 −0.129874
\(750\) 0 0
\(751\) −5.64084 −0.205837 −0.102919 0.994690i \(-0.532818\pi\)
−0.102919 + 0.994690i \(0.532818\pi\)
\(752\) −26.2199 −0.956140
\(753\) 11.9932 0.437056
\(754\) −23.8571 −0.868824
\(755\) 0 0
\(756\) −0.423334 −0.0153965
\(757\) −15.6919 −0.570332 −0.285166 0.958478i \(-0.592049\pi\)
−0.285166 + 0.958478i \(0.592049\pi\)
\(758\) 2.29229 0.0832597
\(759\) 17.2763 0.627090
\(760\) 0 0
\(761\) 4.86484 0.176350 0.0881751 0.996105i \(-0.471896\pi\)
0.0881751 + 0.996105i \(0.471896\pi\)
\(762\) 45.0164 1.63077
\(763\) −0.633103 −0.0229199
\(764\) −3.38825 −0.122583
\(765\) 0 0
\(766\) −3.95668 −0.142961
\(767\) 16.2300 0.586031
\(768\) 12.6578 0.456747
\(769\) 22.5321 0.812528 0.406264 0.913756i \(-0.366831\pi\)
0.406264 + 0.913756i \(0.366831\pi\)
\(770\) 0 0
\(771\) −1.92127 −0.0691930
\(772\) −0.0550065 −0.00197973
\(773\) −26.4320 −0.950693 −0.475347 0.879799i \(-0.657677\pi\)
−0.475347 + 0.879799i \(0.657677\pi\)
\(774\) 27.8125 0.999700
\(775\) 0 0
\(776\) 27.8266 0.998916
\(777\) 4.94356 0.177349
\(778\) 33.0993 1.18667
\(779\) 0 0
\(780\) 0 0
\(781\) −20.7202 −0.741426
\(782\) 1.69871 0.0607458
\(783\) −45.3783 −1.62169
\(784\) 24.7401 0.883575
\(785\) 0 0
\(786\) 7.15839 0.255331
\(787\) −15.5577 −0.554571 −0.277286 0.960788i \(-0.589435\pi\)
−0.277286 + 0.960788i \(0.589435\pi\)
\(788\) 2.42839 0.0865077
\(789\) 32.8239 1.16856
\(790\) 0 0
\(791\) 6.14290 0.218417
\(792\) −34.6783 −1.23224
\(793\) 23.4962 0.834374
\(794\) −42.8922 −1.52219
\(795\) 0 0
\(796\) 0.0474383 0.00168141
\(797\) 33.4935 1.18640 0.593200 0.805055i \(-0.297864\pi\)
0.593200 + 0.805055i \(0.297864\pi\)
\(798\) 0 0
\(799\) −3.41147 −0.120689
\(800\) 0 0
\(801\) 54.4475 1.92381
\(802\) −0.116496 −0.00411362
\(803\) 3.09327 0.109159
\(804\) 4.08378 0.144024
\(805\) 0 0
\(806\) −24.6432 −0.868020
\(807\) 55.8316 1.96537
\(808\) −27.2249 −0.957770
\(809\) 41.1162 1.44557 0.722784 0.691074i \(-0.242862\pi\)
0.722784 + 0.691074i \(0.242862\pi\)
\(810\) 0 0
\(811\) −16.6878 −0.585987 −0.292994 0.956114i \(-0.594651\pi\)
−0.292994 + 0.956114i \(0.594651\pi\)
\(812\) 0.441504 0.0154937
\(813\) 38.5672 1.35261
\(814\) 14.8307 0.519815
\(815\) 0 0
\(816\) −4.84524 −0.169617
\(817\) 0 0
\(818\) 26.9540 0.942424
\(819\) −4.72967 −0.165268
\(820\) 0 0
\(821\) −31.3901 −1.09552 −0.547761 0.836635i \(-0.684520\pi\)
−0.547761 + 0.836635i \(0.684520\pi\)
\(822\) −0.992259 −0.0346090
\(823\) −46.3259 −1.61482 −0.807410 0.589990i \(-0.799132\pi\)
−0.807410 + 0.589990i \(0.799132\pi\)
\(824\) −16.2184 −0.564996
\(825\) 0 0
\(826\) 2.95037 0.102657
\(827\) 40.7588 1.41732 0.708661 0.705549i \(-0.249300\pi\)
0.708661 + 0.705549i \(0.249300\pi\)
\(828\) −2.63453 −0.0915564
\(829\) 35.4834 1.23239 0.616195 0.787594i \(-0.288673\pi\)
0.616195 + 0.787594i \(0.288673\pi\)
\(830\) 0 0
\(831\) 51.1002 1.77265
\(832\) 22.1266 0.767102
\(833\) 3.21894 0.111530
\(834\) 16.5398 0.572727
\(835\) 0 0
\(836\) 0 0
\(837\) −46.8735 −1.62019
\(838\) −34.2344 −1.18261
\(839\) 38.2026 1.31890 0.659451 0.751748i \(-0.270789\pi\)
0.659451 + 0.751748i \(0.270789\pi\)
\(840\) 0 0
\(841\) 18.3259 0.631929
\(842\) 5.88713 0.202884
\(843\) 52.6323 1.81275
\(844\) 0.452430 0.0155733
\(845\) 0 0
\(846\) −51.9718 −1.78683
\(847\) 2.09833 0.0720993
\(848\) 10.2044 0.350420
\(849\) 22.1361 0.759709
\(850\) 0 0
\(851\) 13.3209 0.456634
\(852\) 4.95130 0.169629
\(853\) 25.6016 0.876584 0.438292 0.898833i \(-0.355584\pi\)
0.438292 + 0.898833i \(0.355584\pi\)
\(854\) 4.27126 0.146159
\(855\) 0 0
\(856\) 30.1257 1.02967
\(857\) −21.0865 −0.720300 −0.360150 0.932894i \(-0.617274\pi\)
−0.360150 + 0.932894i \(0.617274\pi\)
\(858\) −22.2344 −0.759071
\(859\) −19.5672 −0.667623 −0.333812 0.942640i \(-0.608335\pi\)
−0.333812 + 0.942640i \(0.608335\pi\)
\(860\) 0 0
\(861\) −2.47565 −0.0843700
\(862\) −51.6100 −1.75784
\(863\) 4.94894 0.168464 0.0842319 0.996446i \(-0.473156\pi\)
0.0842319 + 0.996446i \(0.473156\pi\)
\(864\) 6.87258 0.233810
\(865\) 0 0
\(866\) 24.4279 0.830093
\(867\) 48.3191 1.64100
\(868\) 0.456052 0.0154794
\(869\) −26.3756 −0.894730
\(870\) 0 0
\(871\) 19.7553 0.669381
\(872\) 5.36596 0.181714
\(873\) 50.0164 1.69280
\(874\) 0 0
\(875\) 0 0
\(876\) −0.739170 −0.0249742
\(877\) 1.21987 0.0411922 0.0205961 0.999788i \(-0.493444\pi\)
0.0205961 + 0.999788i \(0.493444\pi\)
\(878\) −8.20582 −0.276933
\(879\) 30.2422 1.02004
\(880\) 0 0
\(881\) 46.5030 1.56673 0.783363 0.621565i \(-0.213503\pi\)
0.783363 + 0.621565i \(0.213503\pi\)
\(882\) 49.0387 1.65122
\(883\) −12.9249 −0.434957 −0.217479 0.976065i \(-0.569783\pi\)
−0.217479 + 0.976065i \(0.569783\pi\)
\(884\) 0.222563 0.00748560
\(885\) 0 0
\(886\) −40.2749 −1.35306
\(887\) −23.2243 −0.779796 −0.389898 0.920858i \(-0.627490\pi\)
−0.389898 + 0.920858i \(0.627490\pi\)
\(888\) −41.8999 −1.40607
\(889\) −4.03003 −0.135163
\(890\) 0 0
\(891\) −6.94862 −0.232787
\(892\) 1.57255 0.0526528
\(893\) 0 0
\(894\) 64.2404 2.14852
\(895\) 0 0
\(896\) 3.29860 0.110198
\(897\) −19.9709 −0.666809
\(898\) −15.1570 −0.505794
\(899\) 48.8854 1.63042
\(900\) 0 0
\(901\) 1.32770 0.0442320
\(902\) −7.42696 −0.247291
\(903\) −3.90167 −0.129840
\(904\) −52.0651 −1.73166
\(905\) 0 0
\(906\) 16.9213 0.562172
\(907\) −39.9968 −1.32807 −0.664036 0.747700i \(-0.731158\pi\)
−0.664036 + 0.747700i \(0.731158\pi\)
\(908\) 2.61493 0.0867796
\(909\) −48.9350 −1.62307
\(910\) 0 0
\(911\) 18.7997 0.622863 0.311431 0.950269i \(-0.399192\pi\)
0.311431 + 0.950269i \(0.399192\pi\)
\(912\) 0 0
\(913\) −33.0232 −1.09291
\(914\) −31.5134 −1.04237
\(915\) 0 0
\(916\) 3.79435 0.125369
\(917\) −0.640844 −0.0211625
\(918\) −4.15839 −0.137247
\(919\) 39.8316 1.31392 0.656962 0.753924i \(-0.271841\pi\)
0.656962 + 0.753924i \(0.271841\pi\)
\(920\) 0 0
\(921\) 33.6759 1.10966
\(922\) 49.3429 1.62502
\(923\) 23.9519 0.788387
\(924\) 0.411474 0.0135365
\(925\) 0 0
\(926\) −57.9154 −1.90322
\(927\) −29.1516 −0.957463
\(928\) −7.16756 −0.235287
\(929\) 26.9540 0.884332 0.442166 0.896933i \(-0.354210\pi\)
0.442166 + 0.896933i \(0.354210\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 3.26176 0.106843
\(933\) −45.9718 −1.50505
\(934\) 34.4858 1.12841
\(935\) 0 0
\(936\) 40.0871 1.31029
\(937\) −2.62361 −0.0857095 −0.0428548 0.999081i \(-0.513645\pi\)
−0.0428548 + 0.999081i \(0.513645\pi\)
\(938\) 3.59121 0.117257
\(939\) −76.6742 −2.50217
\(940\) 0 0
\(941\) 18.6696 0.608612 0.304306 0.952574i \(-0.401575\pi\)
0.304306 + 0.952574i \(0.401575\pi\)
\(942\) 37.3141 1.21576
\(943\) −6.67087 −0.217234
\(944\) −22.6759 −0.738039
\(945\) 0 0
\(946\) −11.7050 −0.380563
\(947\) −8.39961 −0.272951 −0.136475 0.990643i \(-0.543577\pi\)
−0.136475 + 0.990643i \(0.543577\pi\)
\(948\) 6.30272 0.204703
\(949\) −3.57573 −0.116073
\(950\) 0 0
\(951\) −85.0343 −2.75742
\(952\) 0.478340 0.0155031
\(953\) 33.6928 1.09142 0.545709 0.837975i \(-0.316260\pi\)
0.545709 + 0.837975i \(0.316260\pi\)
\(954\) 20.2267 0.654863
\(955\) 0 0
\(956\) −0.434696 −0.0140591
\(957\) 44.1070 1.42578
\(958\) −51.4347 −1.66178
\(959\) 0.0888306 0.00286849
\(960\) 0 0
\(961\) 19.4962 0.628909
\(962\) −17.1438 −0.552739
\(963\) 54.1489 1.74492
\(964\) 2.55026 0.0821383
\(965\) 0 0
\(966\) −3.63041 −0.116807
\(967\) −11.7433 −0.377639 −0.188819 0.982012i \(-0.560466\pi\)
−0.188819 + 0.982012i \(0.560466\pi\)
\(968\) −17.7847 −0.571621
\(969\) 0 0
\(970\) 0 0
\(971\) −12.8093 −0.411071 −0.205536 0.978650i \(-0.565894\pi\)
−0.205536 + 0.978650i \(0.565894\pi\)
\(972\) −1.99638 −0.0640339
\(973\) −1.48070 −0.0474692
\(974\) −10.4602 −0.335165
\(975\) 0 0
\(976\) −32.8280 −1.05080
\(977\) 14.5276 0.464781 0.232390 0.972623i \(-0.425345\pi\)
0.232390 + 0.972623i \(0.425345\pi\)
\(978\) −32.4124 −1.03643
\(979\) −22.9145 −0.732350
\(980\) 0 0
\(981\) 9.64496 0.307940
\(982\) 49.4766 1.57886
\(983\) −37.0502 −1.18172 −0.590860 0.806774i \(-0.701211\pi\)
−0.590860 + 0.806774i \(0.701211\pi\)
\(984\) 20.9828 0.668906
\(985\) 0 0
\(986\) 4.33687 0.138114
\(987\) 7.29086 0.232071
\(988\) 0 0
\(989\) −10.5134 −0.334307
\(990\) 0 0
\(991\) −3.43140 −0.109002 −0.0545010 0.998514i \(-0.517357\pi\)
−0.0545010 + 0.998514i \(0.517357\pi\)
\(992\) −7.40373 −0.235069
\(993\) 79.6596 2.52792
\(994\) 4.35410 0.138104
\(995\) 0 0
\(996\) 7.89124 0.250044
\(997\) −12.7760 −0.404620 −0.202310 0.979322i \(-0.564845\pi\)
−0.202310 + 0.979322i \(0.564845\pi\)
\(998\) −6.63722 −0.210098
\(999\) −32.6091 −1.03170
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 9025.2.a.x.1.2 3
5.4 even 2 361.2.a.h.1.2 3
15.14 odd 2 3249.2.a.s.1.2 3
19.3 odd 18 475.2.l.a.351.1 6
19.13 odd 18 475.2.l.a.226.1 6
19.18 odd 2 9025.2.a.bd.1.2 3
20.19 odd 2 5776.2.a.bi.1.1 3
95.3 even 36 475.2.u.a.199.2 12
95.4 even 18 361.2.e.a.54.1 6
95.9 even 18 361.2.e.b.62.1 6
95.13 even 36 475.2.u.a.74.1 12
95.14 odd 18 361.2.e.g.234.1 6
95.22 even 36 475.2.u.a.199.1 12
95.24 even 18 361.2.e.a.234.1 6
95.29 odd 18 361.2.e.f.62.1 6
95.32 even 36 475.2.u.a.74.2 12
95.34 odd 18 361.2.e.g.54.1 6
95.44 even 18 361.2.e.h.245.1 6
95.49 even 6 361.2.c.h.292.2 6
95.54 even 18 361.2.e.h.28.1 6
95.59 odd 18 361.2.e.f.99.1 6
95.64 even 6 361.2.c.h.68.2 6
95.69 odd 6 361.2.c.i.68.2 6
95.74 even 18 361.2.e.b.99.1 6
95.79 odd 18 19.2.e.a.9.1 6
95.84 odd 6 361.2.c.i.292.2 6
95.89 odd 18 19.2.e.a.17.1 yes 6
95.94 odd 2 361.2.a.g.1.2 3
285.89 even 18 171.2.u.c.55.1 6
285.269 even 18 171.2.u.c.28.1 6
285.284 even 2 3249.2.a.z.1.2 3
380.79 even 18 304.2.u.b.161.1 6
380.279 even 18 304.2.u.b.17.1 6
380.379 even 2 5776.2.a.br.1.3 3
665.79 odd 18 931.2.x.a.655.1 6
665.89 even 18 931.2.v.a.606.1 6
665.174 even 18 931.2.w.a.883.1 6
665.184 odd 18 931.2.v.b.606.1 6
665.269 even 18 931.2.v.a.275.1 6
665.279 even 18 931.2.w.a.834.1 6
665.374 even 18 931.2.x.b.226.1 6
665.459 odd 18 931.2.v.b.275.1 6
665.564 odd 18 931.2.x.a.226.1 6
665.649 even 18 931.2.x.b.655.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
19.2.e.a.9.1 6 95.79 odd 18
19.2.e.a.17.1 yes 6 95.89 odd 18
171.2.u.c.28.1 6 285.269 even 18
171.2.u.c.55.1 6 285.89 even 18
304.2.u.b.17.1 6 380.279 even 18
304.2.u.b.161.1 6 380.79 even 18
361.2.a.g.1.2 3 95.94 odd 2
361.2.a.h.1.2 3 5.4 even 2
361.2.c.h.68.2 6 95.64 even 6
361.2.c.h.292.2 6 95.49 even 6
361.2.c.i.68.2 6 95.69 odd 6
361.2.c.i.292.2 6 95.84 odd 6
361.2.e.a.54.1 6 95.4 even 18
361.2.e.a.234.1 6 95.24 even 18
361.2.e.b.62.1 6 95.9 even 18
361.2.e.b.99.1 6 95.74 even 18
361.2.e.f.62.1 6 95.29 odd 18
361.2.e.f.99.1 6 95.59 odd 18
361.2.e.g.54.1 6 95.34 odd 18
361.2.e.g.234.1 6 95.14 odd 18
361.2.e.h.28.1 6 95.54 even 18
361.2.e.h.245.1 6 95.44 even 18
475.2.l.a.226.1 6 19.13 odd 18
475.2.l.a.351.1 6 19.3 odd 18
475.2.u.a.74.1 12 95.13 even 36
475.2.u.a.74.2 12 95.32 even 36
475.2.u.a.199.1 12 95.22 even 36
475.2.u.a.199.2 12 95.3 even 36
931.2.v.a.275.1 6 665.269 even 18
931.2.v.a.606.1 6 665.89 even 18
931.2.v.b.275.1 6 665.459 odd 18
931.2.v.b.606.1 6 665.184 odd 18
931.2.w.a.834.1 6 665.279 even 18
931.2.w.a.883.1 6 665.174 even 18
931.2.x.a.226.1 6 665.564 odd 18
931.2.x.a.655.1 6 665.79 odd 18
931.2.x.b.226.1 6 665.374 even 18
931.2.x.b.655.1 6 665.649 even 18
3249.2.a.s.1.2 3 15.14 odd 2
3249.2.a.z.1.2 3 285.284 even 2
5776.2.a.bi.1.1 3 20.19 odd 2
5776.2.a.br.1.3 3 380.379 even 2
9025.2.a.x.1.2 3 1.1 even 1 trivial
9025.2.a.bd.1.2 3 19.18 odd 2