Properties

Label 4334.2.a.e.1.15
Level $4334$
Weight $2$
Character 4334.1
Self dual yes
Analytic conductor $34.607$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4334,2,Mod(1,4334)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4334, 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("4334.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4334 = 2 \cdot 11 \cdot 197 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4334.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: \(34.6071642360\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 4334.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.626459 q^{3} +1.00000 q^{4} -4.16763 q^{5} -0.626459 q^{6} +4.47360 q^{7} -1.00000 q^{8} -2.60755 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.626459 q^{3} +1.00000 q^{4} -4.16763 q^{5} -0.626459 q^{6} +4.47360 q^{7} -1.00000 q^{8} -2.60755 q^{9} +4.16763 q^{10} -1.00000 q^{11} +0.626459 q^{12} -4.07211 q^{13} -4.47360 q^{14} -2.61085 q^{15} +1.00000 q^{16} +0.444921 q^{17} +2.60755 q^{18} -4.25443 q^{19} -4.16763 q^{20} +2.80253 q^{21} +1.00000 q^{22} -7.47445 q^{23} -0.626459 q^{24} +12.3691 q^{25} +4.07211 q^{26} -3.51290 q^{27} +4.47360 q^{28} +4.69923 q^{29} +2.61085 q^{30} +4.49682 q^{31} -1.00000 q^{32} -0.626459 q^{33} -0.444921 q^{34} -18.6443 q^{35} -2.60755 q^{36} -2.54821 q^{37} +4.25443 q^{38} -2.55101 q^{39} +4.16763 q^{40} +4.86454 q^{41} -2.80253 q^{42} -3.43878 q^{43} -1.00000 q^{44} +10.8673 q^{45} +7.47445 q^{46} -10.9174 q^{47} +0.626459 q^{48} +13.0131 q^{49} -12.3691 q^{50} +0.278725 q^{51} -4.07211 q^{52} -9.00211 q^{53} +3.51290 q^{54} +4.16763 q^{55} -4.47360 q^{56} -2.66523 q^{57} -4.69923 q^{58} +5.40428 q^{59} -2.61085 q^{60} +10.0903 q^{61} -4.49682 q^{62} -11.6651 q^{63} +1.00000 q^{64} +16.9710 q^{65} +0.626459 q^{66} +11.9951 q^{67} +0.444921 q^{68} -4.68244 q^{69} +18.6443 q^{70} +6.77175 q^{71} +2.60755 q^{72} -7.28899 q^{73} +2.54821 q^{74} +7.74875 q^{75} -4.25443 q^{76} -4.47360 q^{77} +2.55101 q^{78} +6.11012 q^{79} -4.16763 q^{80} +5.62196 q^{81} -4.86454 q^{82} -2.21493 q^{83} +2.80253 q^{84} -1.85426 q^{85} +3.43878 q^{86} +2.94388 q^{87} +1.00000 q^{88} -5.18723 q^{89} -10.8673 q^{90} -18.2170 q^{91} -7.47445 q^{92} +2.81708 q^{93} +10.9174 q^{94} +17.7309 q^{95} -0.626459 q^{96} +7.86006 q^{97} -13.0131 q^{98} +2.60755 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9} + 4 q^{10} - 24 q^{11} - 4 q^{12} + 21 q^{13} - 7 q^{14} - 2 q^{15} + 24 q^{16} + 15 q^{17} - 28 q^{18} + 21 q^{19} - 4 q^{20} + 15 q^{21} + 24 q^{22} - 17 q^{23} + 4 q^{24} + 46 q^{25} - 21 q^{26} - 19 q^{27} + 7 q^{28} + 9 q^{29} + 2 q^{30} + 27 q^{31} - 24 q^{32} + 4 q^{33} - 15 q^{34} - 2 q^{35} + 28 q^{36} + 5 q^{37} - 21 q^{38} + 17 q^{39} + 4 q^{40} + 16 q^{41} - 15 q^{42} + 3 q^{43} - 24 q^{44} - 21 q^{45} + 17 q^{46} - 24 q^{47} - 4 q^{48} + 55 q^{49} - 46 q^{50} - 12 q^{51} + 21 q^{52} - 26 q^{53} + 19 q^{54} + 4 q^{55} - 7 q^{56} + 30 q^{57} - 9 q^{58} - 17 q^{59} - 2 q^{60} + 44 q^{61} - 27 q^{62} + 4 q^{63} + 24 q^{64} + 35 q^{65} - 4 q^{66} + 10 q^{67} + 15 q^{68} + 3 q^{69} + 2 q^{70} - 6 q^{71} - 28 q^{72} + 77 q^{73} - 5 q^{74} - 32 q^{75} + 21 q^{76} - 7 q^{77} - 17 q^{78} + 43 q^{79} - 4 q^{80} + 48 q^{81} - 16 q^{82} - 20 q^{83} + 15 q^{84} + 35 q^{85} - 3 q^{86} + 36 q^{87} + 24 q^{88} + 3 q^{89} + 21 q^{90} + 63 q^{91} - 17 q^{92} + 36 q^{93} + 24 q^{94} - 3 q^{95} + 4 q^{96} + 16 q^{97} - 55 q^{98} - 28 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.626459 0.361687 0.180843 0.983512i \(-0.442117\pi\)
0.180843 + 0.983512i \(0.442117\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.16763 −1.86382 −0.931910 0.362690i \(-0.881858\pi\)
−0.931910 + 0.362690i \(0.881858\pi\)
\(6\) −0.626459 −0.255751
\(7\) 4.47360 1.69086 0.845430 0.534086i \(-0.179344\pi\)
0.845430 + 0.534086i \(0.179344\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.60755 −0.869183
\(10\) 4.16763 1.31792
\(11\) −1.00000 −0.301511
\(12\) 0.626459 0.180843
\(13\) −4.07211 −1.12940 −0.564700 0.825296i \(-0.691008\pi\)
−0.564700 + 0.825296i \(0.691008\pi\)
\(14\) −4.47360 −1.19562
\(15\) −2.61085 −0.674118
\(16\) 1.00000 0.250000
\(17\) 0.444921 0.107909 0.0539546 0.998543i \(-0.482817\pi\)
0.0539546 + 0.998543i \(0.482817\pi\)
\(18\) 2.60755 0.614605
\(19\) −4.25443 −0.976034 −0.488017 0.872834i \(-0.662280\pi\)
−0.488017 + 0.872834i \(0.662280\pi\)
\(20\) −4.16763 −0.931910
\(21\) 2.80253 0.611561
\(22\) 1.00000 0.213201
\(23\) −7.47445 −1.55853 −0.779266 0.626694i \(-0.784408\pi\)
−0.779266 + 0.626694i \(0.784408\pi\)
\(24\) −0.626459 −0.127875
\(25\) 12.3691 2.47382
\(26\) 4.07211 0.798606
\(27\) −3.51290 −0.676058
\(28\) 4.47360 0.845430
\(29\) 4.69923 0.872625 0.436313 0.899795i \(-0.356284\pi\)
0.436313 + 0.899795i \(0.356284\pi\)
\(30\) 2.61085 0.476674
\(31\) 4.49682 0.807653 0.403826 0.914836i \(-0.367680\pi\)
0.403826 + 0.914836i \(0.367680\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.626459 −0.109053
\(34\) −0.444921 −0.0763033
\(35\) −18.6443 −3.15146
\(36\) −2.60755 −0.434591
\(37\) −2.54821 −0.418923 −0.209461 0.977817i \(-0.567171\pi\)
−0.209461 + 0.977817i \(0.567171\pi\)
\(38\) 4.25443 0.690160
\(39\) −2.55101 −0.408489
\(40\) 4.16763 0.658960
\(41\) 4.86454 0.759714 0.379857 0.925045i \(-0.375973\pi\)
0.379857 + 0.925045i \(0.375973\pi\)
\(42\) −2.80253 −0.432439
\(43\) −3.43878 −0.524409 −0.262204 0.965012i \(-0.584449\pi\)
−0.262204 + 0.965012i \(0.584449\pi\)
\(44\) −1.00000 −0.150756
\(45\) 10.8673 1.62000
\(46\) 7.47445 1.10205
\(47\) −10.9174 −1.59247 −0.796234 0.604989i \(-0.793177\pi\)
−0.796234 + 0.604989i \(0.793177\pi\)
\(48\) 0.626459 0.0904216
\(49\) 13.0131 1.85901
\(50\) −12.3691 −1.74926
\(51\) 0.278725 0.0390293
\(52\) −4.07211 −0.564700
\(53\) −9.00211 −1.23653 −0.618267 0.785968i \(-0.712165\pi\)
−0.618267 + 0.785968i \(0.712165\pi\)
\(54\) 3.51290 0.478045
\(55\) 4.16763 0.561963
\(56\) −4.47360 −0.597809
\(57\) −2.66523 −0.353018
\(58\) −4.69923 −0.617039
\(59\) 5.40428 0.703577 0.351789 0.936079i \(-0.385574\pi\)
0.351789 + 0.936079i \(0.385574\pi\)
\(60\) −2.61085 −0.337059
\(61\) 10.0903 1.29193 0.645965 0.763367i \(-0.276455\pi\)
0.645965 + 0.763367i \(0.276455\pi\)
\(62\) −4.49682 −0.571097
\(63\) −11.6651 −1.46967
\(64\) 1.00000 0.125000
\(65\) 16.9710 2.10500
\(66\) 0.626459 0.0771118
\(67\) 11.9951 1.46543 0.732717 0.680533i \(-0.238252\pi\)
0.732717 + 0.680533i \(0.238252\pi\)
\(68\) 0.444921 0.0539546
\(69\) −4.68244 −0.563700
\(70\) 18.6443 2.22842
\(71\) 6.77175 0.803659 0.401829 0.915715i \(-0.368374\pi\)
0.401829 + 0.915715i \(0.368374\pi\)
\(72\) 2.60755 0.307303
\(73\) −7.28899 −0.853112 −0.426556 0.904461i \(-0.640273\pi\)
−0.426556 + 0.904461i \(0.640273\pi\)
\(74\) 2.54821 0.296223
\(75\) 7.74875 0.894749
\(76\) −4.25443 −0.488017
\(77\) −4.47360 −0.509813
\(78\) 2.55101 0.288845
\(79\) 6.11012 0.687443 0.343721 0.939072i \(-0.388312\pi\)
0.343721 + 0.939072i \(0.388312\pi\)
\(80\) −4.16763 −0.465955
\(81\) 5.62196 0.624662
\(82\) −4.86454 −0.537199
\(83\) −2.21493 −0.243120 −0.121560 0.992584i \(-0.538790\pi\)
−0.121560 + 0.992584i \(0.538790\pi\)
\(84\) 2.80253 0.305781
\(85\) −1.85426 −0.201123
\(86\) 3.43878 0.370813
\(87\) 2.94388 0.315617
\(88\) 1.00000 0.106600
\(89\) −5.18723 −0.549845 −0.274923 0.961466i \(-0.588652\pi\)
−0.274923 + 0.961466i \(0.588652\pi\)
\(90\) −10.8673 −1.14551
\(91\) −18.2170 −1.90966
\(92\) −7.47445 −0.779266
\(93\) 2.81708 0.292117
\(94\) 10.9174 1.12604
\(95\) 17.7309 1.81915
\(96\) −0.626459 −0.0639377
\(97\) 7.86006 0.798068 0.399034 0.916936i \(-0.369346\pi\)
0.399034 + 0.916936i \(0.369346\pi\)
\(98\) −13.0131 −1.31452
\(99\) 2.60755 0.262068
\(100\) 12.3691 1.23691
\(101\) −3.88590 −0.386661 −0.193331 0.981134i \(-0.561929\pi\)
−0.193331 + 0.981134i \(0.561929\pi\)
\(102\) −0.278725 −0.0275979
\(103\) 5.67975 0.559642 0.279821 0.960052i \(-0.409725\pi\)
0.279821 + 0.960052i \(0.409725\pi\)
\(104\) 4.07211 0.399303
\(105\) −11.6799 −1.13984
\(106\) 9.00211 0.874362
\(107\) −11.7007 −1.13115 −0.565574 0.824697i \(-0.691345\pi\)
−0.565574 + 0.824697i \(0.691345\pi\)
\(108\) −3.51290 −0.338029
\(109\) −1.34647 −0.128969 −0.0644844 0.997919i \(-0.520540\pi\)
−0.0644844 + 0.997919i \(0.520540\pi\)
\(110\) −4.16763 −0.397368
\(111\) −1.59635 −0.151519
\(112\) 4.47360 0.422715
\(113\) 17.7627 1.67098 0.835489 0.549507i \(-0.185185\pi\)
0.835489 + 0.549507i \(0.185185\pi\)
\(114\) 2.66523 0.249622
\(115\) 31.1507 2.90482
\(116\) 4.69923 0.436313
\(117\) 10.6182 0.981655
\(118\) −5.40428 −0.497504
\(119\) 1.99040 0.182459
\(120\) 2.61085 0.238337
\(121\) 1.00000 0.0909091
\(122\) −10.0903 −0.913532
\(123\) 3.04744 0.274778
\(124\) 4.49682 0.403826
\(125\) −30.7117 −2.74694
\(126\) 11.6651 1.03921
\(127\) −8.80634 −0.781437 −0.390718 0.920510i \(-0.627773\pi\)
−0.390718 + 0.920510i \(0.627773\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.15426 −0.189672
\(130\) −16.9710 −1.48846
\(131\) 12.2052 1.06637 0.533186 0.845998i \(-0.320995\pi\)
0.533186 + 0.845998i \(0.320995\pi\)
\(132\) −0.626459 −0.0545263
\(133\) −19.0326 −1.65034
\(134\) −11.9951 −1.03622
\(135\) 14.6405 1.26005
\(136\) −0.444921 −0.0381516
\(137\) 8.96291 0.765753 0.382877 0.923799i \(-0.374933\pi\)
0.382877 + 0.923799i \(0.374933\pi\)
\(138\) 4.68244 0.398596
\(139\) −8.13266 −0.689803 −0.344902 0.938639i \(-0.612088\pi\)
−0.344902 + 0.938639i \(0.612088\pi\)
\(140\) −18.6443 −1.57573
\(141\) −6.83931 −0.575974
\(142\) −6.77175 −0.568273
\(143\) 4.07211 0.340527
\(144\) −2.60755 −0.217296
\(145\) −19.5846 −1.62642
\(146\) 7.28899 0.603241
\(147\) 8.15215 0.672378
\(148\) −2.54821 −0.209461
\(149\) −8.96440 −0.734393 −0.367196 0.930143i \(-0.619682\pi\)
−0.367196 + 0.930143i \(0.619682\pi\)
\(150\) −7.74875 −0.632683
\(151\) 1.89519 0.154228 0.0771140 0.997022i \(-0.475429\pi\)
0.0771140 + 0.997022i \(0.475429\pi\)
\(152\) 4.25443 0.345080
\(153\) −1.16015 −0.0937928
\(154\) 4.47360 0.360493
\(155\) −18.7411 −1.50532
\(156\) −2.55101 −0.204244
\(157\) −2.60712 −0.208070 −0.104035 0.994574i \(-0.533175\pi\)
−0.104035 + 0.994574i \(0.533175\pi\)
\(158\) −6.11012 −0.486095
\(159\) −5.63945 −0.447238
\(160\) 4.16763 0.329480
\(161\) −33.4377 −2.63526
\(162\) −5.62196 −0.441703
\(163\) 1.01058 0.0791544 0.0395772 0.999217i \(-0.487399\pi\)
0.0395772 + 0.999217i \(0.487399\pi\)
\(164\) 4.86454 0.379857
\(165\) 2.61085 0.203254
\(166\) 2.21493 0.171912
\(167\) 8.19178 0.633899 0.316950 0.948442i \(-0.397341\pi\)
0.316950 + 0.948442i \(0.397341\pi\)
\(168\) −2.80253 −0.216220
\(169\) 3.58208 0.275545
\(170\) 1.85426 0.142216
\(171\) 11.0936 0.848352
\(172\) −3.43878 −0.262204
\(173\) 4.55859 0.346584 0.173292 0.984871i \(-0.444560\pi\)
0.173292 + 0.984871i \(0.444560\pi\)
\(174\) −2.94388 −0.223175
\(175\) 55.3344 4.18289
\(176\) −1.00000 −0.0753778
\(177\) 3.38556 0.254474
\(178\) 5.18723 0.388799
\(179\) 1.88182 0.140654 0.0703270 0.997524i \(-0.477596\pi\)
0.0703270 + 0.997524i \(0.477596\pi\)
\(180\) 10.8673 0.810000
\(181\) 16.3687 1.21668 0.608339 0.793677i \(-0.291836\pi\)
0.608339 + 0.793677i \(0.291836\pi\)
\(182\) 18.2170 1.35033
\(183\) 6.32116 0.467274
\(184\) 7.47445 0.551024
\(185\) 10.6200 0.780797
\(186\) −2.81708 −0.206558
\(187\) −0.444921 −0.0325358
\(188\) −10.9174 −0.796234
\(189\) −15.7153 −1.14312
\(190\) −17.7309 −1.28633
\(191\) 23.1874 1.67778 0.838889 0.544302i \(-0.183206\pi\)
0.838889 + 0.544302i \(0.183206\pi\)
\(192\) 0.626459 0.0452108
\(193\) −14.0347 −1.01024 −0.505119 0.863050i \(-0.668551\pi\)
−0.505119 + 0.863050i \(0.668551\pi\)
\(194\) −7.86006 −0.564319
\(195\) 10.6317 0.761349
\(196\) 13.0131 0.929504
\(197\) 1.00000 0.0712470
\(198\) −2.60755 −0.185310
\(199\) −10.8008 −0.765649 −0.382825 0.923821i \(-0.625049\pi\)
−0.382825 + 0.923821i \(0.625049\pi\)
\(200\) −12.3691 −0.874629
\(201\) 7.51444 0.530028
\(202\) 3.88590 0.273411
\(203\) 21.0225 1.47549
\(204\) 0.278725 0.0195146
\(205\) −20.2736 −1.41597
\(206\) −5.67975 −0.395727
\(207\) 19.4900 1.35465
\(208\) −4.07211 −0.282350
\(209\) 4.25443 0.294285
\(210\) 11.6799 0.805989
\(211\) −22.0923 −1.52090 −0.760450 0.649397i \(-0.775021\pi\)
−0.760450 + 0.649397i \(0.775021\pi\)
\(212\) −9.00211 −0.618267
\(213\) 4.24223 0.290673
\(214\) 11.7007 0.799843
\(215\) 14.3316 0.977404
\(216\) 3.51290 0.239023
\(217\) 20.1170 1.36563
\(218\) 1.34647 0.0911947
\(219\) −4.56626 −0.308559
\(220\) 4.16763 0.280981
\(221\) −1.81177 −0.121873
\(222\) 1.59635 0.107140
\(223\) −18.1199 −1.21340 −0.606701 0.794930i \(-0.707507\pi\)
−0.606701 + 0.794930i \(0.707507\pi\)
\(224\) −4.47360 −0.298905
\(225\) −32.2531 −2.15021
\(226\) −17.7627 −1.18156
\(227\) 24.5850 1.63176 0.815882 0.578219i \(-0.196252\pi\)
0.815882 + 0.578219i \(0.196252\pi\)
\(228\) −2.66523 −0.176509
\(229\) 27.5729 1.82207 0.911035 0.412330i \(-0.135285\pi\)
0.911035 + 0.412330i \(0.135285\pi\)
\(230\) −31.1507 −2.05402
\(231\) −2.80253 −0.184393
\(232\) −4.69923 −0.308520
\(233\) −14.7600 −0.966962 −0.483481 0.875355i \(-0.660628\pi\)
−0.483481 + 0.875355i \(0.660628\pi\)
\(234\) −10.6182 −0.694135
\(235\) 45.4997 2.96807
\(236\) 5.40428 0.351789
\(237\) 3.82774 0.248639
\(238\) −1.99040 −0.129018
\(239\) −1.55374 −0.100503 −0.0502514 0.998737i \(-0.516002\pi\)
−0.0502514 + 0.998737i \(0.516002\pi\)
\(240\) −2.61085 −0.168530
\(241\) 27.7317 1.78635 0.893177 0.449706i \(-0.148471\pi\)
0.893177 + 0.449706i \(0.148471\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 14.0606 0.901990
\(244\) 10.0903 0.645965
\(245\) −54.2336 −3.46485
\(246\) −3.04744 −0.194298
\(247\) 17.3245 1.10233
\(248\) −4.49682 −0.285548
\(249\) −1.38756 −0.0879333
\(250\) 30.7117 1.94238
\(251\) 30.1022 1.90003 0.950017 0.312198i \(-0.101065\pi\)
0.950017 + 0.312198i \(0.101065\pi\)
\(252\) −11.6651 −0.734833
\(253\) 7.47445 0.469915
\(254\) 8.80634 0.552559
\(255\) −1.16162 −0.0727436
\(256\) 1.00000 0.0625000
\(257\) 2.71774 0.169528 0.0847641 0.996401i \(-0.472986\pi\)
0.0847641 + 0.996401i \(0.472986\pi\)
\(258\) 2.15426 0.134118
\(259\) −11.3997 −0.708340
\(260\) 16.9710 1.05250
\(261\) −12.2535 −0.758471
\(262\) −12.2052 −0.754038
\(263\) 22.7444 1.40248 0.701239 0.712926i \(-0.252630\pi\)
0.701239 + 0.712926i \(0.252630\pi\)
\(264\) 0.626459 0.0385559
\(265\) 37.5174 2.30468
\(266\) 19.0326 1.16696
\(267\) −3.24959 −0.198872
\(268\) 11.9951 0.732717
\(269\) 1.22328 0.0745847 0.0372923 0.999304i \(-0.488127\pi\)
0.0372923 + 0.999304i \(0.488127\pi\)
\(270\) −14.6405 −0.890990
\(271\) 7.27048 0.441650 0.220825 0.975313i \(-0.429125\pi\)
0.220825 + 0.975313i \(0.429125\pi\)
\(272\) 0.444921 0.0269773
\(273\) −11.4122 −0.690697
\(274\) −8.96291 −0.541469
\(275\) −12.3691 −0.745886
\(276\) −4.68244 −0.281850
\(277\) 14.9228 0.896625 0.448312 0.893877i \(-0.352025\pi\)
0.448312 + 0.893877i \(0.352025\pi\)
\(278\) 8.13266 0.487764
\(279\) −11.7257 −0.701998
\(280\) 18.6443 1.11421
\(281\) 12.5957 0.751397 0.375699 0.926742i \(-0.377403\pi\)
0.375699 + 0.926742i \(0.377403\pi\)
\(282\) 6.83931 0.407275
\(283\) −17.7153 −1.05307 −0.526533 0.850154i \(-0.676508\pi\)
−0.526533 + 0.850154i \(0.676508\pi\)
\(284\) 6.77175 0.401829
\(285\) 11.1077 0.657962
\(286\) −4.07211 −0.240789
\(287\) 21.7620 1.28457
\(288\) 2.60755 0.153651
\(289\) −16.8020 −0.988356
\(290\) 19.5846 1.15005
\(291\) 4.92401 0.288650
\(292\) −7.28899 −0.426556
\(293\) 6.37338 0.372337 0.186168 0.982518i \(-0.440393\pi\)
0.186168 + 0.982518i \(0.440393\pi\)
\(294\) −8.15215 −0.475443
\(295\) −22.5230 −1.31134
\(296\) 2.54821 0.148112
\(297\) 3.51290 0.203839
\(298\) 8.96440 0.519294
\(299\) 30.4368 1.76021
\(300\) 7.74875 0.447374
\(301\) −15.3837 −0.886702
\(302\) −1.89519 −0.109056
\(303\) −2.43436 −0.139850
\(304\) −4.25443 −0.244008
\(305\) −42.0526 −2.40792
\(306\) 1.16015 0.0663215
\(307\) 19.2388 1.09802 0.549008 0.835817i \(-0.315006\pi\)
0.549008 + 0.835817i \(0.315006\pi\)
\(308\) −4.47360 −0.254907
\(309\) 3.55813 0.202415
\(310\) 18.7411 1.06442
\(311\) 16.1876 0.917915 0.458958 0.888458i \(-0.348223\pi\)
0.458958 + 0.888458i \(0.348223\pi\)
\(312\) 2.55101 0.144423
\(313\) 18.1215 1.02429 0.512143 0.858900i \(-0.328852\pi\)
0.512143 + 0.858900i \(0.328852\pi\)
\(314\) 2.60712 0.147128
\(315\) 48.6159 2.73919
\(316\) 6.11012 0.343721
\(317\) −14.8092 −0.831769 −0.415884 0.909418i \(-0.636528\pi\)
−0.415884 + 0.909418i \(0.636528\pi\)
\(318\) 5.63945 0.316245
\(319\) −4.69923 −0.263106
\(320\) −4.16763 −0.232977
\(321\) −7.33001 −0.409121
\(322\) 33.4377 1.86341
\(323\) −1.89289 −0.105323
\(324\) 5.62196 0.312331
\(325\) −50.3684 −2.79394
\(326\) −1.01058 −0.0559706
\(327\) −0.843511 −0.0466463
\(328\) −4.86454 −0.268599
\(329\) −48.8400 −2.69264
\(330\) −2.61085 −0.143723
\(331\) 18.7996 1.03332 0.516658 0.856192i \(-0.327176\pi\)
0.516658 + 0.856192i \(0.327176\pi\)
\(332\) −2.21493 −0.121560
\(333\) 6.64458 0.364121
\(334\) −8.19178 −0.448234
\(335\) −49.9911 −2.73131
\(336\) 2.80253 0.152890
\(337\) 21.2196 1.15590 0.577951 0.816071i \(-0.303852\pi\)
0.577951 + 0.816071i \(0.303852\pi\)
\(338\) −3.58208 −0.194839
\(339\) 11.1276 0.604370
\(340\) −1.85426 −0.100562
\(341\) −4.49682 −0.243517
\(342\) −11.0936 −0.599875
\(343\) 26.9000 1.45246
\(344\) 3.43878 0.185407
\(345\) 19.5147 1.05063
\(346\) −4.55859 −0.245072
\(347\) −13.5398 −0.726856 −0.363428 0.931622i \(-0.618394\pi\)
−0.363428 + 0.931622i \(0.618394\pi\)
\(348\) 2.94388 0.157808
\(349\) −22.8194 −1.22149 −0.610746 0.791827i \(-0.709130\pi\)
−0.610746 + 0.791827i \(0.709130\pi\)
\(350\) −55.3344 −2.95775
\(351\) 14.3049 0.763540
\(352\) 1.00000 0.0533002
\(353\) 21.6564 1.15265 0.576326 0.817220i \(-0.304486\pi\)
0.576326 + 0.817220i \(0.304486\pi\)
\(354\) −3.38556 −0.179941
\(355\) −28.2221 −1.49788
\(356\) −5.18723 −0.274923
\(357\) 1.24690 0.0659931
\(358\) −1.88182 −0.0994574
\(359\) 28.1899 1.48781 0.743904 0.668286i \(-0.232972\pi\)
0.743904 + 0.668286i \(0.232972\pi\)
\(360\) −10.8673 −0.572757
\(361\) −0.899802 −0.0473580
\(362\) −16.3687 −0.860322
\(363\) 0.626459 0.0328806
\(364\) −18.2170 −0.954829
\(365\) 30.3778 1.59005
\(366\) −6.32116 −0.330412
\(367\) 19.0747 0.995692 0.497846 0.867265i \(-0.334124\pi\)
0.497846 + 0.867265i \(0.334124\pi\)
\(368\) −7.47445 −0.389633
\(369\) −12.6845 −0.660330
\(370\) −10.6200 −0.552107
\(371\) −40.2718 −2.09081
\(372\) 2.81708 0.146059
\(373\) −5.12196 −0.265205 −0.132603 0.991169i \(-0.542333\pi\)
−0.132603 + 0.991169i \(0.542333\pi\)
\(374\) 0.444921 0.0230063
\(375\) −19.2397 −0.993532
\(376\) 10.9174 0.563022
\(377\) −19.1358 −0.985543
\(378\) 15.7153 0.808308
\(379\) −18.5956 −0.955191 −0.477595 0.878580i \(-0.658491\pi\)
−0.477595 + 0.878580i \(0.658491\pi\)
\(380\) 17.7309 0.909576
\(381\) −5.51682 −0.282635
\(382\) −23.1874 −1.18637
\(383\) −24.9294 −1.27383 −0.636917 0.770932i \(-0.719791\pi\)
−0.636917 + 0.770932i \(0.719791\pi\)
\(384\) −0.626459 −0.0319689
\(385\) 18.6443 0.950200
\(386\) 14.0347 0.714345
\(387\) 8.96678 0.455807
\(388\) 7.86006 0.399034
\(389\) −32.5822 −1.65198 −0.825991 0.563684i \(-0.809384\pi\)
−0.825991 + 0.563684i \(0.809384\pi\)
\(390\) −10.6317 −0.538355
\(391\) −3.32554 −0.168180
\(392\) −13.0131 −0.657258
\(393\) 7.64605 0.385692
\(394\) −1.00000 −0.0503793
\(395\) −25.4647 −1.28127
\(396\) 2.60755 0.131034
\(397\) 18.4904 0.928007 0.464003 0.885833i \(-0.346413\pi\)
0.464003 + 0.885833i \(0.346413\pi\)
\(398\) 10.8008 0.541396
\(399\) −11.9232 −0.596904
\(400\) 12.3691 0.618456
\(401\) 9.77410 0.488095 0.244048 0.969763i \(-0.421525\pi\)
0.244048 + 0.969763i \(0.421525\pi\)
\(402\) −7.51444 −0.374786
\(403\) −18.3116 −0.912163
\(404\) −3.88590 −0.193331
\(405\) −23.4302 −1.16426
\(406\) −21.0225 −1.04333
\(407\) 2.54821 0.126310
\(408\) −0.278725 −0.0137989
\(409\) 0.0983273 0.00486197 0.00243099 0.999997i \(-0.499226\pi\)
0.00243099 + 0.999997i \(0.499226\pi\)
\(410\) 20.2736 1.00124
\(411\) 5.61490 0.276963
\(412\) 5.67975 0.279821
\(413\) 24.1766 1.18965
\(414\) −19.4900 −0.957881
\(415\) 9.23100 0.453132
\(416\) 4.07211 0.199652
\(417\) −5.09478 −0.249492
\(418\) −4.25443 −0.208091
\(419\) −39.0863 −1.90949 −0.954746 0.297424i \(-0.903873\pi\)
−0.954746 + 0.297424i \(0.903873\pi\)
\(420\) −11.6799 −0.569920
\(421\) −6.01618 −0.293211 −0.146605 0.989195i \(-0.546835\pi\)
−0.146605 + 0.989195i \(0.546835\pi\)
\(422\) 22.0923 1.07544
\(423\) 28.4677 1.38415
\(424\) 9.00211 0.437181
\(425\) 5.50328 0.266948
\(426\) −4.24223 −0.205537
\(427\) 45.1399 2.18447
\(428\) −11.7007 −0.565574
\(429\) 2.55101 0.123164
\(430\) −14.3316 −0.691129
\(431\) 8.12680 0.391454 0.195727 0.980658i \(-0.437293\pi\)
0.195727 + 0.980658i \(0.437293\pi\)
\(432\) −3.51290 −0.169015
\(433\) 5.74742 0.276203 0.138102 0.990418i \(-0.455900\pi\)
0.138102 + 0.990418i \(0.455900\pi\)
\(434\) −20.1170 −0.965645
\(435\) −12.2690 −0.588253
\(436\) −1.34647 −0.0644844
\(437\) 31.7996 1.52118
\(438\) 4.56626 0.218184
\(439\) 26.9288 1.28524 0.642621 0.766185i \(-0.277847\pi\)
0.642621 + 0.766185i \(0.277847\pi\)
\(440\) −4.16763 −0.198684
\(441\) −33.9322 −1.61582
\(442\) 1.81177 0.0861769
\(443\) −37.2622 −1.77038 −0.885191 0.465229i \(-0.845972\pi\)
−0.885191 + 0.465229i \(0.845972\pi\)
\(444\) −1.59635 −0.0757594
\(445\) 21.6184 1.02481
\(446\) 18.1199 0.858004
\(447\) −5.61583 −0.265620
\(448\) 4.47360 0.211357
\(449\) 4.55500 0.214964 0.107482 0.994207i \(-0.465721\pi\)
0.107482 + 0.994207i \(0.465721\pi\)
\(450\) 32.2531 1.52042
\(451\) −4.86454 −0.229062
\(452\) 17.7627 0.835489
\(453\) 1.18726 0.0557822
\(454\) −24.5850 −1.15383
\(455\) 75.9215 3.55926
\(456\) 2.66523 0.124811
\(457\) 7.01789 0.328283 0.164142 0.986437i \(-0.447515\pi\)
0.164142 + 0.986437i \(0.447515\pi\)
\(458\) −27.5729 −1.28840
\(459\) −1.56296 −0.0729529
\(460\) 31.1507 1.45241
\(461\) −18.7876 −0.875027 −0.437513 0.899212i \(-0.644141\pi\)
−0.437513 + 0.899212i \(0.644141\pi\)
\(462\) 2.80253 0.130385
\(463\) 7.49611 0.348374 0.174187 0.984713i \(-0.444270\pi\)
0.174187 + 0.984713i \(0.444270\pi\)
\(464\) 4.69923 0.218156
\(465\) −11.7405 −0.544454
\(466\) 14.7600 0.683745
\(467\) 26.8727 1.24352 0.621760 0.783208i \(-0.286418\pi\)
0.621760 + 0.783208i \(0.286418\pi\)
\(468\) 10.6182 0.490828
\(469\) 53.6612 2.47784
\(470\) −45.4997 −2.09874
\(471\) −1.63325 −0.0752563
\(472\) −5.40428 −0.248752
\(473\) 3.43878 0.158115
\(474\) −3.82774 −0.175814
\(475\) −52.6236 −2.41454
\(476\) 1.99040 0.0912296
\(477\) 23.4734 1.07477
\(478\) 1.55374 0.0710662
\(479\) −0.205380 −0.00938406 −0.00469203 0.999989i \(-0.501494\pi\)
−0.00469203 + 0.999989i \(0.501494\pi\)
\(480\) 2.61085 0.119168
\(481\) 10.3766 0.473132
\(482\) −27.7317 −1.26314
\(483\) −20.9474 −0.953138
\(484\) 1.00000 0.0454545
\(485\) −32.7578 −1.48745
\(486\) −14.0606 −0.637803
\(487\) 22.5602 1.02230 0.511150 0.859491i \(-0.329219\pi\)
0.511150 + 0.859491i \(0.329219\pi\)
\(488\) −10.0903 −0.456766
\(489\) 0.633085 0.0286291
\(490\) 54.2336 2.45002
\(491\) 5.88987 0.265806 0.132903 0.991129i \(-0.457570\pi\)
0.132903 + 0.991129i \(0.457570\pi\)
\(492\) 3.04744 0.137389
\(493\) 2.09079 0.0941642
\(494\) −17.3245 −0.779467
\(495\) −10.8673 −0.488448
\(496\) 4.49682 0.201913
\(497\) 30.2941 1.35887
\(498\) 1.38756 0.0621782
\(499\) 4.04749 0.181190 0.0905952 0.995888i \(-0.471123\pi\)
0.0905952 + 0.995888i \(0.471123\pi\)
\(500\) −30.7117 −1.37347
\(501\) 5.13182 0.229273
\(502\) −30.1022 −1.34353
\(503\) 6.35173 0.283209 0.141605 0.989923i \(-0.454774\pi\)
0.141605 + 0.989923i \(0.454774\pi\)
\(504\) 11.6651 0.519606
\(505\) 16.1950 0.720667
\(506\) −7.47445 −0.332280
\(507\) 2.24403 0.0996607
\(508\) −8.80634 −0.390718
\(509\) 21.3356 0.945684 0.472842 0.881147i \(-0.343228\pi\)
0.472842 + 0.881147i \(0.343228\pi\)
\(510\) 1.16162 0.0514375
\(511\) −32.6080 −1.44249
\(512\) −1.00000 −0.0441942
\(513\) 14.9454 0.659856
\(514\) −2.71774 −0.119874
\(515\) −23.6711 −1.04307
\(516\) −2.15426 −0.0948358
\(517\) 10.9174 0.480147
\(518\) 11.3997 0.500872
\(519\) 2.85577 0.125355
\(520\) −16.9710 −0.744229
\(521\) −14.7531 −0.646347 −0.323173 0.946340i \(-0.604750\pi\)
−0.323173 + 0.946340i \(0.604750\pi\)
\(522\) 12.2535 0.536320
\(523\) −30.1474 −1.31826 −0.659128 0.752031i \(-0.729074\pi\)
−0.659128 + 0.752031i \(0.729074\pi\)
\(524\) 12.2052 0.533186
\(525\) 34.6648 1.51289
\(526\) −22.7444 −0.991702
\(527\) 2.00073 0.0871531
\(528\) −0.626459 −0.0272631
\(529\) 32.8675 1.42902
\(530\) −37.5174 −1.62965
\(531\) −14.0919 −0.611537
\(532\) −19.0326 −0.825168
\(533\) −19.8090 −0.858021
\(534\) 3.24959 0.140623
\(535\) 48.7641 2.10826
\(536\) −11.9951 −0.518109
\(537\) 1.17889 0.0508727
\(538\) −1.22328 −0.0527393
\(539\) −13.0131 −0.560512
\(540\) 14.6405 0.630025
\(541\) 44.2864 1.90402 0.952010 0.306066i \(-0.0990128\pi\)
0.952010 + 0.306066i \(0.0990128\pi\)
\(542\) −7.27048 −0.312294
\(543\) 10.2544 0.440056
\(544\) −0.444921 −0.0190758
\(545\) 5.61160 0.240375
\(546\) 11.4122 0.488397
\(547\) 12.2836 0.525211 0.262605 0.964903i \(-0.415418\pi\)
0.262605 + 0.964903i \(0.415418\pi\)
\(548\) 8.96291 0.382877
\(549\) −26.3109 −1.12292
\(550\) 12.3691 0.527421
\(551\) −19.9926 −0.851712
\(552\) 4.68244 0.199298
\(553\) 27.3342 1.16237
\(554\) −14.9228 −0.634010
\(555\) 6.65299 0.282404
\(556\) −8.13266 −0.344902
\(557\) −22.2440 −0.942507 −0.471253 0.881998i \(-0.656198\pi\)
−0.471253 + 0.881998i \(0.656198\pi\)
\(558\) 11.7257 0.496388
\(559\) 14.0031 0.592267
\(560\) −18.6443 −0.787865
\(561\) −0.278725 −0.0117678
\(562\) −12.5957 −0.531318
\(563\) 36.1852 1.52503 0.762513 0.646973i \(-0.223965\pi\)
0.762513 + 0.646973i \(0.223965\pi\)
\(564\) −6.83931 −0.287987
\(565\) −74.0285 −3.11440
\(566\) 17.7153 0.744631
\(567\) 25.1504 1.05622
\(568\) −6.77175 −0.284136
\(569\) 9.53062 0.399544 0.199772 0.979842i \(-0.435980\pi\)
0.199772 + 0.979842i \(0.435980\pi\)
\(570\) −11.1077 −0.465250
\(571\) 33.5689 1.40481 0.702407 0.711775i \(-0.252109\pi\)
0.702407 + 0.711775i \(0.252109\pi\)
\(572\) 4.07211 0.170263
\(573\) 14.5259 0.606830
\(574\) −21.7620 −0.908328
\(575\) −92.4524 −3.85553
\(576\) −2.60755 −0.108648
\(577\) −14.5063 −0.603907 −0.301953 0.953323i \(-0.597639\pi\)
−0.301953 + 0.953323i \(0.597639\pi\)
\(578\) 16.8020 0.698873
\(579\) −8.79215 −0.365389
\(580\) −19.5846 −0.813208
\(581\) −9.90870 −0.411082
\(582\) −4.92401 −0.204107
\(583\) 9.00211 0.372829
\(584\) 7.28899 0.301621
\(585\) −44.2528 −1.82963
\(586\) −6.37338 −0.263282
\(587\) −48.2441 −1.99125 −0.995624 0.0934507i \(-0.970210\pi\)
−0.995624 + 0.0934507i \(0.970210\pi\)
\(588\) 8.15215 0.336189
\(589\) −19.1314 −0.788297
\(590\) 22.5230 0.927258
\(591\) 0.626459 0.0257691
\(592\) −2.54821 −0.104731
\(593\) −4.42315 −0.181637 −0.0908184 0.995867i \(-0.528948\pi\)
−0.0908184 + 0.995867i \(0.528948\pi\)
\(594\) −3.51290 −0.144136
\(595\) −8.29523 −0.340071
\(596\) −8.96440 −0.367196
\(597\) −6.76627 −0.276925
\(598\) −30.4368 −1.24465
\(599\) −38.2203 −1.56164 −0.780820 0.624756i \(-0.785198\pi\)
−0.780820 + 0.624756i \(0.785198\pi\)
\(600\) −7.74875 −0.316341
\(601\) −18.5598 −0.757071 −0.378535 0.925587i \(-0.623572\pi\)
−0.378535 + 0.925587i \(0.623572\pi\)
\(602\) 15.3837 0.626993
\(603\) −31.2778 −1.27373
\(604\) 1.89519 0.0771140
\(605\) −4.16763 −0.169438
\(606\) 2.43436 0.0988890
\(607\) −4.02069 −0.163195 −0.0815974 0.996665i \(-0.526002\pi\)
−0.0815974 + 0.996665i \(0.526002\pi\)
\(608\) 4.25443 0.172540
\(609\) 13.1697 0.533664
\(610\) 42.0526 1.70266
\(611\) 44.4569 1.79853
\(612\) −1.16015 −0.0468964
\(613\) −3.69453 −0.149221 −0.0746103 0.997213i \(-0.523771\pi\)
−0.0746103 + 0.997213i \(0.523771\pi\)
\(614\) −19.2388 −0.776415
\(615\) −12.7006 −0.512137
\(616\) 4.47360 0.180246
\(617\) −25.0018 −1.00653 −0.503267 0.864131i \(-0.667869\pi\)
−0.503267 + 0.864131i \(0.667869\pi\)
\(618\) −3.55813 −0.143129
\(619\) −15.5984 −0.626952 −0.313476 0.949596i \(-0.601494\pi\)
−0.313476 + 0.949596i \(0.601494\pi\)
\(620\) −18.7411 −0.752660
\(621\) 26.2570 1.05366
\(622\) −16.1876 −0.649064
\(623\) −23.2056 −0.929711
\(624\) −2.55101 −0.102122
\(625\) 66.1495 2.64598
\(626\) −18.1215 −0.724280
\(627\) 2.66523 0.106439
\(628\) −2.60712 −0.104035
\(629\) −1.13375 −0.0452056
\(630\) −48.6159 −1.93690
\(631\) −13.7411 −0.547025 −0.273512 0.961868i \(-0.588185\pi\)
−0.273512 + 0.961868i \(0.588185\pi\)
\(632\) −6.11012 −0.243048
\(633\) −13.8400 −0.550089
\(634\) 14.8092 0.588149
\(635\) 36.7016 1.45646
\(636\) −5.63945 −0.223619
\(637\) −52.9906 −2.09956
\(638\) 4.69923 0.186044
\(639\) −17.6577 −0.698527
\(640\) 4.16763 0.164740
\(641\) 36.2459 1.43163 0.715813 0.698292i \(-0.246056\pi\)
0.715813 + 0.698292i \(0.246056\pi\)
\(642\) 7.33001 0.289292
\(643\) 40.5624 1.59962 0.799812 0.600250i \(-0.204932\pi\)
0.799812 + 0.600250i \(0.204932\pi\)
\(644\) −33.4377 −1.31763
\(645\) 8.97814 0.353514
\(646\) 1.89289 0.0744746
\(647\) −10.7150 −0.421249 −0.210624 0.977567i \(-0.567550\pi\)
−0.210624 + 0.977567i \(0.567550\pi\)
\(648\) −5.62196 −0.220851
\(649\) −5.40428 −0.212137
\(650\) 50.3684 1.97561
\(651\) 12.6025 0.493929
\(652\) 1.01058 0.0395772
\(653\) 34.9546 1.36788 0.683939 0.729539i \(-0.260265\pi\)
0.683939 + 0.729539i \(0.260265\pi\)
\(654\) 0.843511 0.0329839
\(655\) −50.8666 −1.98752
\(656\) 4.86454 0.189929
\(657\) 19.0064 0.741510
\(658\) 48.8400 1.90398
\(659\) 27.0845 1.05506 0.527532 0.849535i \(-0.323118\pi\)
0.527532 + 0.849535i \(0.323118\pi\)
\(660\) 2.61085 0.101627
\(661\) 42.9914 1.67217 0.836086 0.548598i \(-0.184838\pi\)
0.836086 + 0.548598i \(0.184838\pi\)
\(662\) −18.7996 −0.730665
\(663\) −1.13500 −0.0440797
\(664\) 2.21493 0.0859560
\(665\) 79.3208 3.07593
\(666\) −6.64458 −0.257472
\(667\) −35.1242 −1.36001
\(668\) 8.19178 0.316950
\(669\) −11.3514 −0.438871
\(670\) 49.9911 1.93132
\(671\) −10.0903 −0.389531
\(672\) −2.80253 −0.108110
\(673\) −7.33126 −0.282599 −0.141300 0.989967i \(-0.545128\pi\)
−0.141300 + 0.989967i \(0.545128\pi\)
\(674\) −21.2196 −0.817347
\(675\) −43.4515 −1.67245
\(676\) 3.58208 0.137772
\(677\) 45.1797 1.73640 0.868198 0.496218i \(-0.165278\pi\)
0.868198 + 0.496218i \(0.165278\pi\)
\(678\) −11.1276 −0.427354
\(679\) 35.1627 1.34942
\(680\) 1.85426 0.0711078
\(681\) 15.4015 0.590187
\(682\) 4.49682 0.172192
\(683\) 29.6601 1.13491 0.567456 0.823404i \(-0.307928\pi\)
0.567456 + 0.823404i \(0.307928\pi\)
\(684\) 11.0936 0.424176
\(685\) −37.3541 −1.42723
\(686\) −26.9000 −1.02705
\(687\) 17.2733 0.659018
\(688\) −3.43878 −0.131102
\(689\) 36.6576 1.39654
\(690\) −19.5147 −0.742911
\(691\) 8.83205 0.335987 0.167993 0.985788i \(-0.446271\pi\)
0.167993 + 0.985788i \(0.446271\pi\)
\(692\) 4.55859 0.173292
\(693\) 11.6651 0.443121
\(694\) 13.5398 0.513965
\(695\) 33.8939 1.28567
\(696\) −2.94388 −0.111587
\(697\) 2.16434 0.0819801
\(698\) 22.8194 0.863725
\(699\) −9.24656 −0.349737
\(700\) 55.3344 2.09144
\(701\) −45.5992 −1.72226 −0.861128 0.508388i \(-0.830242\pi\)
−0.861128 + 0.508388i \(0.830242\pi\)
\(702\) −14.3049 −0.539904
\(703\) 10.8412 0.408883
\(704\) −1.00000 −0.0376889
\(705\) 28.5037 1.07351
\(706\) −21.6564 −0.815048
\(707\) −17.3839 −0.653790
\(708\) 3.38556 0.127237
\(709\) −45.1937 −1.69729 −0.848643 0.528966i \(-0.822580\pi\)
−0.848643 + 0.528966i \(0.822580\pi\)
\(710\) 28.2221 1.05916
\(711\) −15.9324 −0.597513
\(712\) 5.18723 0.194400
\(713\) −33.6113 −1.25875
\(714\) −1.24690 −0.0466641
\(715\) −16.9710 −0.634681
\(716\) 1.88182 0.0703270
\(717\) −0.973353 −0.0363505
\(718\) −28.1899 −1.05204
\(719\) −15.6177 −0.582441 −0.291220 0.956656i \(-0.594061\pi\)
−0.291220 + 0.956656i \(0.594061\pi\)
\(720\) 10.8673 0.405000
\(721\) 25.4089 0.946277
\(722\) 0.899802 0.0334872
\(723\) 17.3728 0.646100
\(724\) 16.3687 0.608339
\(725\) 58.1253 2.15872
\(726\) −0.626459 −0.0232501
\(727\) −17.1544 −0.636220 −0.318110 0.948054i \(-0.603048\pi\)
−0.318110 + 0.948054i \(0.603048\pi\)
\(728\) 18.2170 0.675166
\(729\) −8.05745 −0.298424
\(730\) −30.3778 −1.12433
\(731\) −1.52998 −0.0565885
\(732\) 6.32116 0.233637
\(733\) 7.68895 0.283998 0.141999 0.989867i \(-0.454647\pi\)
0.141999 + 0.989867i \(0.454647\pi\)
\(734\) −19.0747 −0.704061
\(735\) −33.9751 −1.25319
\(736\) 7.47445 0.275512
\(737\) −11.9951 −0.441845
\(738\) 12.6845 0.466924
\(739\) 22.5548 0.829694 0.414847 0.909891i \(-0.363835\pi\)
0.414847 + 0.909891i \(0.363835\pi\)
\(740\) 10.6200 0.390398
\(741\) 10.8531 0.398699
\(742\) 40.2718 1.47842
\(743\) −7.22267 −0.264974 −0.132487 0.991185i \(-0.542296\pi\)
−0.132487 + 0.991185i \(0.542296\pi\)
\(744\) −2.81708 −0.103279
\(745\) 37.3603 1.36878
\(746\) 5.12196 0.187528
\(747\) 5.77554 0.211316
\(748\) −0.444921 −0.0162679
\(749\) −52.3441 −1.91261
\(750\) 19.2397 0.702533
\(751\) −22.0384 −0.804194 −0.402097 0.915597i \(-0.631719\pi\)
−0.402097 + 0.915597i \(0.631719\pi\)
\(752\) −10.9174 −0.398117
\(753\) 18.8578 0.687217
\(754\) 19.1358 0.696884
\(755\) −7.89843 −0.287453
\(756\) −15.7153 −0.571560
\(757\) −22.0851 −0.802697 −0.401349 0.915925i \(-0.631458\pi\)
−0.401349 + 0.915925i \(0.631458\pi\)
\(758\) 18.5956 0.675422
\(759\) 4.68244 0.169962
\(760\) −17.7309 −0.643167
\(761\) 4.63588 0.168051 0.0840253 0.996464i \(-0.473222\pi\)
0.0840253 + 0.996464i \(0.473222\pi\)
\(762\) 5.51682 0.199853
\(763\) −6.02358 −0.218068
\(764\) 23.1874 0.838889
\(765\) 4.83508 0.174813
\(766\) 24.9294 0.900736
\(767\) −22.0068 −0.794620
\(768\) 0.626459 0.0226054
\(769\) −44.9088 −1.61945 −0.809727 0.586807i \(-0.800385\pi\)
−0.809727 + 0.586807i \(0.800385\pi\)
\(770\) −18.6443 −0.671893
\(771\) 1.70256 0.0613160
\(772\) −14.0347 −0.505119
\(773\) −9.84211 −0.353996 −0.176998 0.984211i \(-0.556639\pi\)
−0.176998 + 0.984211i \(0.556639\pi\)
\(774\) −8.96678 −0.322304
\(775\) 55.6217 1.99799
\(776\) −7.86006 −0.282160
\(777\) −7.14142 −0.256197
\(778\) 32.5822 1.16813
\(779\) −20.6959 −0.741507
\(780\) 10.6317 0.380675
\(781\) −6.77175 −0.242312
\(782\) 3.32554 0.118921
\(783\) −16.5079 −0.589945
\(784\) 13.0131 0.464752
\(785\) 10.8655 0.387806
\(786\) −7.64605 −0.272725
\(787\) −34.1292 −1.21658 −0.608288 0.793716i \(-0.708143\pi\)
−0.608288 + 0.793716i \(0.708143\pi\)
\(788\) 1.00000 0.0356235
\(789\) 14.2484 0.507258
\(790\) 25.4647 0.905994
\(791\) 79.4633 2.82539
\(792\) −2.60755 −0.0926552
\(793\) −41.0888 −1.45911
\(794\) −18.4904 −0.656200
\(795\) 23.5031 0.833571
\(796\) −10.8008 −0.382825
\(797\) −13.3246 −0.471980 −0.235990 0.971755i \(-0.575833\pi\)
−0.235990 + 0.971755i \(0.575833\pi\)
\(798\) 11.9232 0.422075
\(799\) −4.85738 −0.171842
\(800\) −12.3691 −0.437314
\(801\) 13.5260 0.477916
\(802\) −9.77410 −0.345135
\(803\) 7.28899 0.257223
\(804\) 7.51444 0.265014
\(805\) 139.356 4.91165
\(806\) 18.3116 0.644997
\(807\) 0.766335 0.0269763
\(808\) 3.88590 0.136705
\(809\) 37.0355 1.30210 0.651050 0.759035i \(-0.274329\pi\)
0.651050 + 0.759035i \(0.274329\pi\)
\(810\) 23.4302 0.823254
\(811\) 33.3196 1.17001 0.585005 0.811030i \(-0.301093\pi\)
0.585005 + 0.811030i \(0.301093\pi\)
\(812\) 21.0225 0.737743
\(813\) 4.55466 0.159739
\(814\) −2.54821 −0.0893147
\(815\) −4.21170 −0.147530
\(816\) 0.278725 0.00975732
\(817\) 14.6301 0.511841
\(818\) −0.0983273 −0.00343793
\(819\) 47.5016 1.65984
\(820\) −20.2736 −0.707985
\(821\) −11.4714 −0.400356 −0.200178 0.979760i \(-0.564152\pi\)
−0.200178 + 0.979760i \(0.564152\pi\)
\(822\) −5.61490 −0.195842
\(823\) −36.2024 −1.26193 −0.630967 0.775809i \(-0.717342\pi\)
−0.630967 + 0.775809i \(0.717342\pi\)
\(824\) −5.67975 −0.197863
\(825\) −7.74875 −0.269777
\(826\) −24.1766 −0.841210
\(827\) −3.80820 −0.132424 −0.0662120 0.997806i \(-0.521091\pi\)
−0.0662120 + 0.997806i \(0.521091\pi\)
\(828\) 19.4900 0.677324
\(829\) −32.3942 −1.12510 −0.562549 0.826764i \(-0.690179\pi\)
−0.562549 + 0.826764i \(0.690179\pi\)
\(830\) −9.23100 −0.320413
\(831\) 9.34854 0.324297
\(832\) −4.07211 −0.141175
\(833\) 5.78978 0.200604
\(834\) 5.09478 0.176418
\(835\) −34.1403 −1.18147
\(836\) 4.25443 0.147143
\(837\) −15.7969 −0.546020
\(838\) 39.0863 1.35021
\(839\) 43.9926 1.51879 0.759396 0.650629i \(-0.225495\pi\)
0.759396 + 0.650629i \(0.225495\pi\)
\(840\) 11.6799 0.402994
\(841\) −6.91724 −0.238526
\(842\) 6.01618 0.207331
\(843\) 7.89070 0.271770
\(844\) −22.0923 −0.760450
\(845\) −14.9288 −0.513565
\(846\) −28.4677 −0.978738
\(847\) 4.47360 0.153715
\(848\) −9.00211 −0.309134
\(849\) −11.0979 −0.380880
\(850\) −5.50328 −0.188761
\(851\) 19.0465 0.652905
\(852\) 4.24223 0.145336
\(853\) −19.5873 −0.670656 −0.335328 0.942102i \(-0.608847\pi\)
−0.335328 + 0.942102i \(0.608847\pi\)
\(854\) −45.1399 −1.54466
\(855\) −46.2342 −1.58117
\(856\) 11.7007 0.399921
\(857\) 9.81358 0.335226 0.167613 0.985853i \(-0.446394\pi\)
0.167613 + 0.985853i \(0.446394\pi\)
\(858\) −2.55101 −0.0870901
\(859\) 20.3992 0.696013 0.348006 0.937492i \(-0.386859\pi\)
0.348006 + 0.937492i \(0.386859\pi\)
\(860\) 14.3316 0.488702
\(861\) 13.6330 0.464612
\(862\) −8.12680 −0.276800
\(863\) −32.9560 −1.12184 −0.560918 0.827871i \(-0.689552\pi\)
−0.560918 + 0.827871i \(0.689552\pi\)
\(864\) 3.51290 0.119511
\(865\) −18.9985 −0.645969
\(866\) −5.74742 −0.195305
\(867\) −10.5258 −0.357475
\(868\) 20.1170 0.682814
\(869\) −6.11012 −0.207272
\(870\) 12.2690 0.415957
\(871\) −48.8454 −1.65506
\(872\) 1.34647 0.0455974
\(873\) −20.4955 −0.693667
\(874\) −31.7996 −1.07564
\(875\) −137.392 −4.64469
\(876\) −4.56626 −0.154280
\(877\) 6.04920 0.204267 0.102134 0.994771i \(-0.467433\pi\)
0.102134 + 0.994771i \(0.467433\pi\)
\(878\) −26.9288 −0.908803
\(879\) 3.99266 0.134669
\(880\) 4.16763 0.140491
\(881\) 6.53949 0.220321 0.110161 0.993914i \(-0.464863\pi\)
0.110161 + 0.993914i \(0.464863\pi\)
\(882\) 33.9322 1.14256
\(883\) 9.44762 0.317938 0.158969 0.987284i \(-0.449183\pi\)
0.158969 + 0.987284i \(0.449183\pi\)
\(884\) −1.81177 −0.0609363
\(885\) −14.1098 −0.474294
\(886\) 37.2622 1.25185
\(887\) −12.4433 −0.417805 −0.208903 0.977936i \(-0.566989\pi\)
−0.208903 + 0.977936i \(0.566989\pi\)
\(888\) 1.59635 0.0535700
\(889\) −39.3960 −1.32130
\(890\) −21.6184 −0.724652
\(891\) −5.62196 −0.188343
\(892\) −18.1199 −0.606701
\(893\) 46.4474 1.55430
\(894\) 5.61583 0.187822
\(895\) −7.84274 −0.262154
\(896\) −4.47360 −0.149452
\(897\) 19.0674 0.636643
\(898\) −4.55500 −0.152002
\(899\) 21.1316 0.704778
\(900\) −32.2531 −1.07510
\(901\) −4.00522 −0.133433
\(902\) 4.86454 0.161972
\(903\) −9.63727 −0.320708
\(904\) −17.7627 −0.590780
\(905\) −68.2188 −2.26767
\(906\) −1.18726 −0.0394440
\(907\) 38.1348 1.26624 0.633122 0.774052i \(-0.281773\pi\)
0.633122 + 0.774052i \(0.281773\pi\)
\(908\) 24.5850 0.815882
\(909\) 10.1327 0.336079
\(910\) −75.9215 −2.51677
\(911\) 2.52811 0.0837601 0.0418801 0.999123i \(-0.486665\pi\)
0.0418801 + 0.999123i \(0.486665\pi\)
\(912\) −2.66523 −0.0882546
\(913\) 2.21493 0.0733035
\(914\) −7.01789 −0.232131
\(915\) −26.3442 −0.870914
\(916\) 27.5729 0.911035
\(917\) 54.6010 1.80308
\(918\) 1.56296 0.0515855
\(919\) −41.9851 −1.38496 −0.692481 0.721436i \(-0.743482\pi\)
−0.692481 + 0.721436i \(0.743482\pi\)
\(920\) −31.1507 −1.02701
\(921\) 12.0523 0.397138
\(922\) 18.7876 0.618737
\(923\) −27.5753 −0.907652
\(924\) −2.80253 −0.0921963
\(925\) −31.5191 −1.03634
\(926\) −7.49611 −0.246337
\(927\) −14.8102 −0.486431
\(928\) −4.69923 −0.154260
\(929\) 58.8996 1.93243 0.966217 0.257731i \(-0.0829747\pi\)
0.966217 + 0.257731i \(0.0829747\pi\)
\(930\) 11.7405 0.384987
\(931\) −55.3632 −1.81445
\(932\) −14.7600 −0.483481
\(933\) 10.1409 0.331998
\(934\) −26.8727 −0.879301
\(935\) 1.85426 0.0606409
\(936\) −10.6182 −0.347068
\(937\) 41.8501 1.36718 0.683591 0.729865i \(-0.260417\pi\)
0.683591 + 0.729865i \(0.260417\pi\)
\(938\) −53.6612 −1.75210
\(939\) 11.3524 0.370471
\(940\) 45.4997 1.48404
\(941\) −23.9002 −0.779126 −0.389563 0.921000i \(-0.627374\pi\)
−0.389563 + 0.921000i \(0.627374\pi\)
\(942\) 1.63325 0.0532142
\(943\) −36.3598 −1.18404
\(944\) 5.40428 0.175894
\(945\) 65.4955 2.13057
\(946\) −3.43878 −0.111804
\(947\) −59.0902 −1.92017 −0.960086 0.279704i \(-0.909764\pi\)
−0.960086 + 0.279704i \(0.909764\pi\)
\(948\) 3.82774 0.124319
\(949\) 29.6816 0.963504
\(950\) 52.6236 1.70733
\(951\) −9.27737 −0.300839
\(952\) −1.99040 −0.0645091
\(953\) 14.5996 0.472928 0.236464 0.971640i \(-0.424011\pi\)
0.236464 + 0.971640i \(0.424011\pi\)
\(954\) −23.4734 −0.759980
\(955\) −96.6363 −3.12708
\(956\) −1.55374 −0.0502514
\(957\) −2.94388 −0.0951620
\(958\) 0.205380 0.00663553
\(959\) 40.0964 1.29478
\(960\) −2.61085 −0.0842648
\(961\) −10.7786 −0.347697
\(962\) −10.3766 −0.334555
\(963\) 30.5101 0.983175
\(964\) 27.7317 0.893177
\(965\) 58.4912 1.88290
\(966\) 20.9474 0.673970
\(967\) −60.7609 −1.95394 −0.976970 0.213377i \(-0.931554\pi\)
−0.976970 + 0.213377i \(0.931554\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −1.18582 −0.0380939
\(970\) 32.7578 1.05179
\(971\) −31.1634 −1.00008 −0.500040 0.866002i \(-0.666681\pi\)
−0.500040 + 0.866002i \(0.666681\pi\)
\(972\) 14.0606 0.450995
\(973\) −36.3822 −1.16636
\(974\) −22.5602 −0.722876
\(975\) −31.5538 −1.01053
\(976\) 10.0903 0.322982
\(977\) −34.2463 −1.09564 −0.547819 0.836597i \(-0.684542\pi\)
−0.547819 + 0.836597i \(0.684542\pi\)
\(978\) −0.633085 −0.0202438
\(979\) 5.18723 0.165785
\(980\) −54.2336 −1.73243
\(981\) 3.51100 0.112097
\(982\) −5.88987 −0.187953
\(983\) −16.7546 −0.534389 −0.267194 0.963643i \(-0.586097\pi\)
−0.267194 + 0.963643i \(0.586097\pi\)
\(984\) −3.04744 −0.0971488
\(985\) −4.16763 −0.132792
\(986\) −2.09079 −0.0665842
\(987\) −30.5963 −0.973891
\(988\) 17.3245 0.551166
\(989\) 25.7030 0.817308
\(990\) 10.8673 0.345385
\(991\) 14.4907 0.460312 0.230156 0.973154i \(-0.426076\pi\)
0.230156 + 0.973154i \(0.426076\pi\)
\(992\) −4.49682 −0.142774
\(993\) 11.7772 0.373737
\(994\) −30.2941 −0.960870
\(995\) 45.0138 1.42703
\(996\) −1.38756 −0.0439666
\(997\) −45.3743 −1.43702 −0.718510 0.695517i \(-0.755175\pi\)
−0.718510 + 0.695517i \(0.755175\pi\)
\(998\) −4.04749 −0.128121
\(999\) 8.95161 0.283216
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 4334.2.a.e.1.15 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4334.2.a.e.1.15 24 1.1 even 1 trivial