Properties

Label 1045.2.a.h.1.7
Level $1045$
Weight $2$
Character 1045.1
Self dual yes
Analytic conductor $8.344$
Analytic rank $0$
Dimension $7$
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] = [1045,2,Mod(1,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1045.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.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: \(8.34436701122\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 10x^{5} + 8x^{4} + 27x^{3} - 16x^{2} - 18x + 11 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(2.58611\) of defining polynomial
Character \(\chi\) \(=\) 1045.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.58611 q^{2} +1.69436 q^{3} +4.68797 q^{4} -1.00000 q^{5} +4.38180 q^{6} +2.28823 q^{7} +6.95140 q^{8} -0.129144 q^{9} +O(q^{10})\) \(q+2.58611 q^{2} +1.69436 q^{3} +4.68797 q^{4} -1.00000 q^{5} +4.38180 q^{6} +2.28823 q^{7} +6.95140 q^{8} -0.129144 q^{9} -2.58611 q^{10} +1.00000 q^{11} +7.94312 q^{12} -1.76398 q^{13} +5.91761 q^{14} -1.69436 q^{15} +8.60115 q^{16} -7.54854 q^{17} -0.333980 q^{18} -1.00000 q^{19} -4.68797 q^{20} +3.87708 q^{21} +2.58611 q^{22} -6.89418 q^{23} +11.7782 q^{24} +1.00000 q^{25} -4.56184 q^{26} -5.30190 q^{27} +10.7271 q^{28} +6.12329 q^{29} -4.38180 q^{30} +8.39796 q^{31} +8.34073 q^{32} +1.69436 q^{33} -19.5214 q^{34} -2.28823 q^{35} -0.605423 q^{36} -10.1774 q^{37} -2.58611 q^{38} -2.98881 q^{39} -6.95140 q^{40} +4.07706 q^{41} +10.0266 q^{42} -5.51693 q^{43} +4.68797 q^{44} +0.129144 q^{45} -17.8291 q^{46} +11.6612 q^{47} +14.5734 q^{48} -1.76402 q^{49} +2.58611 q^{50} -12.7899 q^{51} -8.26948 q^{52} +12.7919 q^{53} -13.7113 q^{54} -1.00000 q^{55} +15.9064 q^{56} -1.69436 q^{57} +15.8355 q^{58} +13.5651 q^{59} -7.94312 q^{60} +5.89246 q^{61} +21.7180 q^{62} -0.295510 q^{63} +4.36777 q^{64} +1.76398 q^{65} +4.38180 q^{66} -8.79079 q^{67} -35.3873 q^{68} -11.6812 q^{69} -5.91761 q^{70} -9.61429 q^{71} -0.897730 q^{72} +8.70551 q^{73} -26.3199 q^{74} +1.69436 q^{75} -4.68797 q^{76} +2.28823 q^{77} -7.72940 q^{78} +4.40940 q^{79} -8.60115 q^{80} -8.59589 q^{81} +10.5437 q^{82} +0.146311 q^{83} +18.1757 q^{84} +7.54854 q^{85} -14.2674 q^{86} +10.3751 q^{87} +6.95140 q^{88} -1.54279 q^{89} +0.333980 q^{90} -4.03638 q^{91} -32.3197 q^{92} +14.2292 q^{93} +30.1572 q^{94} +1.00000 q^{95} +14.1322 q^{96} -7.32786 q^{97} -4.56195 q^{98} -0.129144 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} + 8 q^{6} - q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} + 8 q^{6} - q^{7} + 3 q^{8} + 2 q^{9} - q^{10} + 7 q^{11} + 13 q^{12} + q^{13} + 12 q^{14} - 3 q^{15} + 3 q^{16} + q^{17} + 7 q^{18} - 7 q^{19} - 7 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 25 q^{24} + 7 q^{25} + 12 q^{27} + 4 q^{28} + 11 q^{29} - 8 q^{30} + 7 q^{31} + 12 q^{32} + 3 q^{33} - 14 q^{34} + q^{35} + 7 q^{36} - 17 q^{37} - q^{38} + 30 q^{39} - 3 q^{40} + 17 q^{41} + 33 q^{42} - 3 q^{43} + 7 q^{44} - 2 q^{45} + 18 q^{46} + 14 q^{47} - 12 q^{48} + 6 q^{49} + q^{50} + 8 q^{51} - 17 q^{52} + 7 q^{53} - 27 q^{54} - 7 q^{55} + 36 q^{56} - 3 q^{57} - 15 q^{58} + 35 q^{59} - 13 q^{60} + 17 q^{61} + 46 q^{62} - 22 q^{63} + 5 q^{64} - q^{65} + 8 q^{66} + 4 q^{67} - 35 q^{68} - 4 q^{69} - 12 q^{70} + 10 q^{71} + 12 q^{72} + 22 q^{73} - 11 q^{74} + 3 q^{75} - 7 q^{76} - q^{77} - 41 q^{78} + 11 q^{79} - 3 q^{80} - 21 q^{81} - 14 q^{82} + 39 q^{83} + 21 q^{84} - q^{85} - 24 q^{86} - 2 q^{87} + 3 q^{88} + 18 q^{89} - 7 q^{90} - 22 q^{91} - 51 q^{92} + 10 q^{93} + 14 q^{94} + 7 q^{95} - 11 q^{96} - 4 q^{97} - 26 q^{98} + 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58611 1.82866 0.914329 0.404973i \(-0.132719\pi\)
0.914329 + 0.404973i \(0.132719\pi\)
\(3\) 1.69436 0.978239 0.489120 0.872217i \(-0.337318\pi\)
0.489120 + 0.872217i \(0.337318\pi\)
\(4\) 4.68797 2.34399
\(5\) −1.00000 −0.447214
\(6\) 4.38180 1.78886
\(7\) 2.28823 0.864869 0.432434 0.901665i \(-0.357655\pi\)
0.432434 + 0.901665i \(0.357655\pi\)
\(8\) 6.95140 2.45769
\(9\) −0.129144 −0.0430479
\(10\) −2.58611 −0.817800
\(11\) 1.00000 0.301511
\(12\) 7.94312 2.29298
\(13\) −1.76398 −0.489239 −0.244620 0.969619i \(-0.578663\pi\)
−0.244620 + 0.969619i \(0.578663\pi\)
\(14\) 5.91761 1.58155
\(15\) −1.69436 −0.437482
\(16\) 8.60115 2.15029
\(17\) −7.54854 −1.83079 −0.915395 0.402557i \(-0.868121\pi\)
−0.915395 + 0.402557i \(0.868121\pi\)
\(18\) −0.333980 −0.0787199
\(19\) −1.00000 −0.229416
\(20\) −4.68797 −1.04826
\(21\) 3.87708 0.846048
\(22\) 2.58611 0.551361
\(23\) −6.89418 −1.43754 −0.718768 0.695250i \(-0.755294\pi\)
−0.718768 + 0.695250i \(0.755294\pi\)
\(24\) 11.7782 2.40421
\(25\) 1.00000 0.200000
\(26\) −4.56184 −0.894651
\(27\) −5.30190 −1.02035
\(28\) 10.7271 2.02724
\(29\) 6.12329 1.13707 0.568533 0.822661i \(-0.307511\pi\)
0.568533 + 0.822661i \(0.307511\pi\)
\(30\) −4.38180 −0.800004
\(31\) 8.39796 1.50832 0.754159 0.656692i \(-0.228045\pi\)
0.754159 + 0.656692i \(0.228045\pi\)
\(32\) 8.34073 1.47445
\(33\) 1.69436 0.294950
\(34\) −19.5214 −3.34789
\(35\) −2.28823 −0.386781
\(36\) −0.605423 −0.100904
\(37\) −10.1774 −1.67315 −0.836577 0.547850i \(-0.815446\pi\)
−0.836577 + 0.547850i \(0.815446\pi\)
\(38\) −2.58611 −0.419523
\(39\) −2.98881 −0.478593
\(40\) −6.95140 −1.09911
\(41\) 4.07706 0.636730 0.318365 0.947968i \(-0.396866\pi\)
0.318365 + 0.947968i \(0.396866\pi\)
\(42\) 10.0266 1.54713
\(43\) −5.51693 −0.841323 −0.420662 0.907218i \(-0.638202\pi\)
−0.420662 + 0.907218i \(0.638202\pi\)
\(44\) 4.68797 0.706739
\(45\) 0.129144 0.0192516
\(46\) −17.8291 −2.62876
\(47\) 11.6612 1.70096 0.850481 0.526006i \(-0.176311\pi\)
0.850481 + 0.526006i \(0.176311\pi\)
\(48\) 14.5734 2.10350
\(49\) −1.76402 −0.252002
\(50\) 2.58611 0.365731
\(51\) −12.7899 −1.79095
\(52\) −8.26948 −1.14677
\(53\) 12.7919 1.75710 0.878551 0.477649i \(-0.158511\pi\)
0.878551 + 0.477649i \(0.158511\pi\)
\(54\) −13.7113 −1.86587
\(55\) −1.00000 −0.134840
\(56\) 15.9064 2.12558
\(57\) −1.69436 −0.224423
\(58\) 15.8355 2.07930
\(59\) 13.5651 1.76603 0.883013 0.469348i \(-0.155511\pi\)
0.883013 + 0.469348i \(0.155511\pi\)
\(60\) −7.94312 −1.02545
\(61\) 5.89246 0.754452 0.377226 0.926121i \(-0.376878\pi\)
0.377226 + 0.926121i \(0.376878\pi\)
\(62\) 21.7180 2.75820
\(63\) −0.295510 −0.0372308
\(64\) 4.36777 0.545971
\(65\) 1.76398 0.218794
\(66\) 4.38180 0.539363
\(67\) −8.79079 −1.07397 −0.536983 0.843593i \(-0.680436\pi\)
−0.536983 + 0.843593i \(0.680436\pi\)
\(68\) −35.3873 −4.29135
\(69\) −11.6812 −1.40625
\(70\) −5.91761 −0.707290
\(71\) −9.61429 −1.14101 −0.570503 0.821295i \(-0.693252\pi\)
−0.570503 + 0.821295i \(0.693252\pi\)
\(72\) −0.897730 −0.105798
\(73\) 8.70551 1.01890 0.509451 0.860499i \(-0.329848\pi\)
0.509451 + 0.860499i \(0.329848\pi\)
\(74\) −26.3199 −3.05962
\(75\) 1.69436 0.195648
\(76\) −4.68797 −0.537747
\(77\) 2.28823 0.260768
\(78\) −7.72940 −0.875182
\(79\) 4.40940 0.496096 0.248048 0.968748i \(-0.420211\pi\)
0.248048 + 0.968748i \(0.420211\pi\)
\(80\) −8.60115 −0.961638
\(81\) −8.59589 −0.955099
\(82\) 10.5437 1.16436
\(83\) 0.146311 0.0160597 0.00802984 0.999968i \(-0.497444\pi\)
0.00802984 + 0.999968i \(0.497444\pi\)
\(84\) 18.1757 1.98313
\(85\) 7.54854 0.818754
\(86\) −14.2674 −1.53849
\(87\) 10.3751 1.11232
\(88\) 6.95140 0.741022
\(89\) −1.54279 −0.163535 −0.0817677 0.996651i \(-0.526057\pi\)
−0.0817677 + 0.996651i \(0.526057\pi\)
\(90\) 0.333980 0.0352046
\(91\) −4.03638 −0.423127
\(92\) −32.3197 −3.36956
\(93\) 14.2292 1.47550
\(94\) 30.1572 3.11048
\(95\) 1.00000 0.102598
\(96\) 14.1322 1.44236
\(97\) −7.32786 −0.744032 −0.372016 0.928226i \(-0.621333\pi\)
−0.372016 + 0.928226i \(0.621333\pi\)
\(98\) −4.56195 −0.460826
\(99\) −0.129144 −0.0129794
\(100\) 4.68797 0.468797
\(101\) 10.5365 1.04843 0.524213 0.851587i \(-0.324360\pi\)
0.524213 + 0.851587i \(0.324360\pi\)
\(102\) −33.0762 −3.27503
\(103\) −11.4973 −1.13286 −0.566430 0.824110i \(-0.691676\pi\)
−0.566430 + 0.824110i \(0.691676\pi\)
\(104\) −12.2621 −1.20240
\(105\) −3.87708 −0.378364
\(106\) 33.0813 3.21314
\(107\) −9.18318 −0.887772 −0.443886 0.896083i \(-0.646400\pi\)
−0.443886 + 0.896083i \(0.646400\pi\)
\(108\) −24.8552 −2.39169
\(109\) −18.0299 −1.72696 −0.863478 0.504387i \(-0.831718\pi\)
−0.863478 + 0.504387i \(0.831718\pi\)
\(110\) −2.58611 −0.246576
\(111\) −17.2442 −1.63674
\(112\) 19.6814 1.85972
\(113\) 10.1400 0.953888 0.476944 0.878934i \(-0.341745\pi\)
0.476944 + 0.878934i \(0.341745\pi\)
\(114\) −4.38180 −0.410394
\(115\) 6.89418 0.642885
\(116\) 28.7058 2.66527
\(117\) 0.227807 0.0210607
\(118\) 35.0809 3.22946
\(119\) −17.2728 −1.58339
\(120\) −11.7782 −1.07520
\(121\) 1.00000 0.0909091
\(122\) 15.2385 1.37963
\(123\) 6.90801 0.622874
\(124\) 39.3694 3.53548
\(125\) −1.00000 −0.0894427
\(126\) −0.764223 −0.0680824
\(127\) −14.3078 −1.26961 −0.634806 0.772672i \(-0.718920\pi\)
−0.634806 + 0.772672i \(0.718920\pi\)
\(128\) −5.38593 −0.476053
\(129\) −9.34766 −0.823016
\(130\) 4.56184 0.400100
\(131\) 9.36028 0.817811 0.408906 0.912577i \(-0.365911\pi\)
0.408906 + 0.912577i \(0.365911\pi\)
\(132\) 7.94312 0.691359
\(133\) −2.28823 −0.198414
\(134\) −22.7340 −1.96391
\(135\) 5.30190 0.456315
\(136\) −52.4729 −4.49951
\(137\) 20.7172 1.76999 0.884995 0.465601i \(-0.154162\pi\)
0.884995 + 0.465601i \(0.154162\pi\)
\(138\) −30.2089 −2.57156
\(139\) 4.10420 0.348113 0.174057 0.984736i \(-0.444312\pi\)
0.174057 + 0.984736i \(0.444312\pi\)
\(140\) −10.7271 −0.906609
\(141\) 19.7583 1.66395
\(142\) −24.8636 −2.08651
\(143\) −1.76398 −0.147511
\(144\) −1.11078 −0.0925654
\(145\) −6.12329 −0.508511
\(146\) 22.5134 1.86322
\(147\) −2.98888 −0.246519
\(148\) −47.7113 −3.92185
\(149\) −4.70130 −0.385146 −0.192573 0.981283i \(-0.561683\pi\)
−0.192573 + 0.981283i \(0.561683\pi\)
\(150\) 4.38180 0.357773
\(151\) 0.894112 0.0727618 0.0363809 0.999338i \(-0.488417\pi\)
0.0363809 + 0.999338i \(0.488417\pi\)
\(152\) −6.95140 −0.563833
\(153\) 0.974847 0.0788117
\(154\) 5.91761 0.476855
\(155\) −8.39796 −0.674540
\(156\) −14.0115 −1.12182
\(157\) 4.74289 0.378524 0.189262 0.981927i \(-0.439390\pi\)
0.189262 + 0.981927i \(0.439390\pi\)
\(158\) 11.4032 0.907190
\(159\) 21.6741 1.71887
\(160\) −8.34073 −0.659393
\(161\) −15.7754 −1.24328
\(162\) −22.2299 −1.74655
\(163\) −14.8395 −1.16232 −0.581159 0.813790i \(-0.697401\pi\)
−0.581159 + 0.813790i \(0.697401\pi\)
\(164\) 19.1132 1.49249
\(165\) −1.69436 −0.131906
\(166\) 0.378376 0.0293676
\(167\) −7.69641 −0.595566 −0.297783 0.954634i \(-0.596247\pi\)
−0.297783 + 0.954634i \(0.596247\pi\)
\(168\) 26.9511 2.07933
\(169\) −9.88839 −0.760645
\(170\) 19.5214 1.49722
\(171\) 0.129144 0.00987587
\(172\) −25.8632 −1.97205
\(173\) 4.96012 0.377111 0.188555 0.982063i \(-0.439619\pi\)
0.188555 + 0.982063i \(0.439619\pi\)
\(174\) 26.8310 2.03406
\(175\) 2.28823 0.172974
\(176\) 8.60115 0.648336
\(177\) 22.9842 1.72760
\(178\) −3.98983 −0.299050
\(179\) −15.6163 −1.16722 −0.583610 0.812034i \(-0.698360\pi\)
−0.583610 + 0.812034i \(0.698360\pi\)
\(180\) 0.605423 0.0451255
\(181\) 11.4001 0.847364 0.423682 0.905811i \(-0.360737\pi\)
0.423682 + 0.905811i \(0.360737\pi\)
\(182\) −10.4385 −0.773755
\(183\) 9.98394 0.738034
\(184\) −47.9242 −3.53302
\(185\) 10.1774 0.748257
\(186\) 36.7982 2.69817
\(187\) −7.54854 −0.552004
\(188\) 54.6674 3.98703
\(189\) −12.1319 −0.882469
\(190\) 2.58611 0.187616
\(191\) 19.0989 1.38195 0.690974 0.722880i \(-0.257182\pi\)
0.690974 + 0.722880i \(0.257182\pi\)
\(192\) 7.40057 0.534090
\(193\) −3.00325 −0.216179 −0.108089 0.994141i \(-0.534473\pi\)
−0.108089 + 0.994141i \(0.534473\pi\)
\(194\) −18.9507 −1.36058
\(195\) 2.98881 0.214033
\(196\) −8.26967 −0.590690
\(197\) 7.23568 0.515521 0.257761 0.966209i \(-0.417015\pi\)
0.257761 + 0.966209i \(0.417015\pi\)
\(198\) −0.333980 −0.0237349
\(199\) −7.80636 −0.553378 −0.276689 0.960960i \(-0.589237\pi\)
−0.276689 + 0.960960i \(0.589237\pi\)
\(200\) 6.95140 0.491538
\(201\) −14.8948 −1.05060
\(202\) 27.2487 1.91721
\(203\) 14.0115 0.983412
\(204\) −59.9589 −4.19796
\(205\) −4.07706 −0.284754
\(206\) −29.7332 −2.07161
\(207\) 0.890340 0.0618829
\(208\) −15.1722 −1.05200
\(209\) −1.00000 −0.0691714
\(210\) −10.0266 −0.691899
\(211\) 26.6833 1.83696 0.918478 0.395472i \(-0.129419\pi\)
0.918478 + 0.395472i \(0.129419\pi\)
\(212\) 59.9681 4.11862
\(213\) −16.2901 −1.11618
\(214\) −23.7487 −1.62343
\(215\) 5.51693 0.376251
\(216\) −36.8556 −2.50771
\(217\) 19.2164 1.30450
\(218\) −46.6274 −3.15801
\(219\) 14.7503 0.996731
\(220\) −4.68797 −0.316063
\(221\) 13.3154 0.895694
\(222\) −44.5953 −2.99304
\(223\) 5.24587 0.351289 0.175645 0.984454i \(-0.443799\pi\)
0.175645 + 0.984454i \(0.443799\pi\)
\(224\) 19.0855 1.27520
\(225\) −0.129144 −0.00860958
\(226\) 26.2231 1.74433
\(227\) 6.00645 0.398662 0.199331 0.979932i \(-0.436123\pi\)
0.199331 + 0.979932i \(0.436123\pi\)
\(228\) −7.94312 −0.526046
\(229\) 10.4545 0.690853 0.345427 0.938446i \(-0.387734\pi\)
0.345427 + 0.938446i \(0.387734\pi\)
\(230\) 17.8291 1.17562
\(231\) 3.87708 0.255093
\(232\) 42.5654 2.79456
\(233\) 23.3656 1.53073 0.765365 0.643597i \(-0.222559\pi\)
0.765365 + 0.643597i \(0.222559\pi\)
\(234\) 0.589133 0.0385128
\(235\) −11.6612 −0.760693
\(236\) 63.5929 4.13954
\(237\) 7.47111 0.485301
\(238\) −44.6693 −2.89548
\(239\) −10.1351 −0.655583 −0.327791 0.944750i \(-0.606304\pi\)
−0.327791 + 0.944750i \(0.606304\pi\)
\(240\) −14.5734 −0.940712
\(241\) 10.6219 0.684218 0.342109 0.939660i \(-0.388859\pi\)
0.342109 + 0.939660i \(0.388859\pi\)
\(242\) 2.58611 0.166242
\(243\) 1.34116 0.0860351
\(244\) 27.6237 1.76842
\(245\) 1.76402 0.112699
\(246\) 17.8649 1.13902
\(247\) 1.76398 0.112239
\(248\) 58.3775 3.70698
\(249\) 0.247903 0.0157102
\(250\) −2.58611 −0.163560
\(251\) 4.01095 0.253169 0.126584 0.991956i \(-0.459599\pi\)
0.126584 + 0.991956i \(0.459599\pi\)
\(252\) −1.38534 −0.0872685
\(253\) −6.89418 −0.433433
\(254\) −37.0015 −2.32168
\(255\) 12.7899 0.800937
\(256\) −22.6641 −1.41651
\(257\) −0.550435 −0.0343352 −0.0171676 0.999853i \(-0.505465\pi\)
−0.0171676 + 0.999853i \(0.505465\pi\)
\(258\) −24.1741 −1.50501
\(259\) −23.2882 −1.44706
\(260\) 8.26948 0.512851
\(261\) −0.790784 −0.0489483
\(262\) 24.2067 1.49550
\(263\) 9.07131 0.559361 0.279681 0.960093i \(-0.409771\pi\)
0.279681 + 0.960093i \(0.409771\pi\)
\(264\) 11.7782 0.724897
\(265\) −12.7919 −0.785800
\(266\) −5.91761 −0.362832
\(267\) −2.61404 −0.159977
\(268\) −41.2110 −2.51736
\(269\) −25.8765 −1.57772 −0.788858 0.614576i \(-0.789327\pi\)
−0.788858 + 0.614576i \(0.789327\pi\)
\(270\) 13.7113 0.834443
\(271\) −6.26185 −0.380380 −0.190190 0.981747i \(-0.560910\pi\)
−0.190190 + 0.981747i \(0.560910\pi\)
\(272\) −64.9261 −3.93672
\(273\) −6.83908 −0.413920
\(274\) 53.5770 3.23670
\(275\) 1.00000 0.0603023
\(276\) −54.7613 −3.29624
\(277\) −16.5892 −0.996749 −0.498374 0.866962i \(-0.666070\pi\)
−0.498374 + 0.866962i \(0.666070\pi\)
\(278\) 10.6139 0.636580
\(279\) −1.08454 −0.0649299
\(280\) −15.9064 −0.950588
\(281\) −1.60057 −0.0954817 −0.0477409 0.998860i \(-0.515202\pi\)
−0.0477409 + 0.998860i \(0.515202\pi\)
\(282\) 51.0971 3.04279
\(283\) 15.1474 0.900420 0.450210 0.892923i \(-0.351349\pi\)
0.450210 + 0.892923i \(0.351349\pi\)
\(284\) −45.0715 −2.67450
\(285\) 1.69436 0.100365
\(286\) −4.56184 −0.269747
\(287\) 9.32924 0.550688
\(288\) −1.07715 −0.0634719
\(289\) 39.9804 2.35179
\(290\) −15.8355 −0.929893
\(291\) −12.4160 −0.727841
\(292\) 40.8112 2.38829
\(293\) −24.1930 −1.41337 −0.706686 0.707528i \(-0.749810\pi\)
−0.706686 + 0.707528i \(0.749810\pi\)
\(294\) −7.72958 −0.450798
\(295\) −13.5651 −0.789791
\(296\) −70.7471 −4.11209
\(297\) −5.30190 −0.307647
\(298\) −12.1581 −0.704300
\(299\) 12.1612 0.703299
\(300\) 7.94312 0.458596
\(301\) −12.6240 −0.727634
\(302\) 2.31227 0.133056
\(303\) 17.8527 1.02561
\(304\) −8.60115 −0.493310
\(305\) −5.89246 −0.337401
\(306\) 2.52106 0.144120
\(307\) 10.5674 0.603115 0.301557 0.953448i \(-0.402494\pi\)
0.301557 + 0.953448i \(0.402494\pi\)
\(308\) 10.7271 0.611236
\(309\) −19.4805 −1.10821
\(310\) −21.7180 −1.23350
\(311\) −10.0555 −0.570194 −0.285097 0.958499i \(-0.592026\pi\)
−0.285097 + 0.958499i \(0.592026\pi\)
\(312\) −20.7764 −1.17623
\(313\) 7.08386 0.400403 0.200202 0.979755i \(-0.435840\pi\)
0.200202 + 0.979755i \(0.435840\pi\)
\(314\) 12.2656 0.692190
\(315\) 0.295510 0.0166501
\(316\) 20.6712 1.16284
\(317\) 22.1335 1.24314 0.621572 0.783357i \(-0.286494\pi\)
0.621572 + 0.783357i \(0.286494\pi\)
\(318\) 56.0516 3.14322
\(319\) 6.12329 0.342838
\(320\) −4.36777 −0.244166
\(321\) −15.5596 −0.868453
\(322\) −40.7971 −2.27353
\(323\) 7.54854 0.420012
\(324\) −40.2973 −2.23874
\(325\) −1.76398 −0.0978478
\(326\) −38.3766 −2.12548
\(327\) −30.5492 −1.68938
\(328\) 28.3413 1.56489
\(329\) 26.6835 1.47111
\(330\) −4.38180 −0.241210
\(331\) −16.1808 −0.889377 −0.444689 0.895685i \(-0.646686\pi\)
−0.444689 + 0.895685i \(0.646686\pi\)
\(332\) 0.685900 0.0376437
\(333\) 1.31435 0.0720258
\(334\) −19.9038 −1.08909
\(335\) 8.79079 0.480292
\(336\) 33.3474 1.81925
\(337\) 3.94070 0.214664 0.107332 0.994223i \(-0.465769\pi\)
0.107332 + 0.994223i \(0.465769\pi\)
\(338\) −25.5725 −1.39096
\(339\) 17.1808 0.933130
\(340\) 35.3873 1.91915
\(341\) 8.39796 0.454775
\(342\) 0.333980 0.0180596
\(343\) −20.0541 −1.08282
\(344\) −38.3504 −2.06771
\(345\) 11.6812 0.628896
\(346\) 12.8274 0.689606
\(347\) 10.5072 0.564056 0.282028 0.959406i \(-0.408993\pi\)
0.282028 + 0.959406i \(0.408993\pi\)
\(348\) 48.6380 2.60727
\(349\) −28.5144 −1.52634 −0.763170 0.646198i \(-0.776358\pi\)
−0.763170 + 0.646198i \(0.776358\pi\)
\(350\) 5.91761 0.316310
\(351\) 9.35242 0.499195
\(352\) 8.34073 0.444563
\(353\) −1.73131 −0.0921485 −0.0460742 0.998938i \(-0.514671\pi\)
−0.0460742 + 0.998938i \(0.514671\pi\)
\(354\) 59.4396 3.15918
\(355\) 9.61429 0.510274
\(356\) −7.23256 −0.383325
\(357\) −29.2663 −1.54894
\(358\) −40.3856 −2.13444
\(359\) 9.07665 0.479047 0.239524 0.970891i \(-0.423009\pi\)
0.239524 + 0.970891i \(0.423009\pi\)
\(360\) 0.897730 0.0473145
\(361\) 1.00000 0.0526316
\(362\) 29.4820 1.54954
\(363\) 1.69436 0.0889308
\(364\) −18.9224 −0.991805
\(365\) −8.70551 −0.455667
\(366\) 25.8196 1.34961
\(367\) 2.85316 0.148934 0.0744668 0.997223i \(-0.476275\pi\)
0.0744668 + 0.997223i \(0.476275\pi\)
\(368\) −59.2979 −3.09111
\(369\) −0.526527 −0.0274099
\(370\) 26.3199 1.36831
\(371\) 29.2708 1.51966
\(372\) 66.7059 3.45854
\(373\) −8.36241 −0.432989 −0.216494 0.976284i \(-0.569462\pi\)
−0.216494 + 0.976284i \(0.569462\pi\)
\(374\) −19.5214 −1.00943
\(375\) −1.69436 −0.0874964
\(376\) 81.0617 4.18044
\(377\) −10.8013 −0.556297
\(378\) −31.3746 −1.61373
\(379\) −4.08929 −0.210052 −0.105026 0.994469i \(-0.533493\pi\)
−0.105026 + 0.994469i \(0.533493\pi\)
\(380\) 4.68797 0.240488
\(381\) −24.2425 −1.24198
\(382\) 49.3919 2.52711
\(383\) −4.95123 −0.252996 −0.126498 0.991967i \(-0.540374\pi\)
−0.126498 + 0.991967i \(0.540374\pi\)
\(384\) −9.12570 −0.465694
\(385\) −2.28823 −0.116619
\(386\) −7.76675 −0.395317
\(387\) 0.712477 0.0362172
\(388\) −34.3528 −1.74400
\(389\) −3.51207 −0.178069 −0.0890344 0.996029i \(-0.528378\pi\)
−0.0890344 + 0.996029i \(0.528378\pi\)
\(390\) 7.72940 0.391393
\(391\) 52.0410 2.63183
\(392\) −12.2624 −0.619344
\(393\) 15.8597 0.800015
\(394\) 18.7123 0.942711
\(395\) −4.40940 −0.221861
\(396\) −0.605423 −0.0304236
\(397\) −14.2944 −0.717414 −0.358707 0.933450i \(-0.616782\pi\)
−0.358707 + 0.933450i \(0.616782\pi\)
\(398\) −20.1881 −1.01194
\(399\) −3.87708 −0.194097
\(400\) 8.60115 0.430057
\(401\) 2.09312 0.104526 0.0522628 0.998633i \(-0.483357\pi\)
0.0522628 + 0.998633i \(0.483357\pi\)
\(402\) −38.5195 −1.92118
\(403\) −14.8138 −0.737928
\(404\) 49.3951 2.45750
\(405\) 8.59589 0.427133
\(406\) 36.2352 1.79832
\(407\) −10.1774 −0.504475
\(408\) −88.9080 −4.40160
\(409\) 30.9423 1.53000 0.764998 0.644032i \(-0.222740\pi\)
0.764998 + 0.644032i \(0.222740\pi\)
\(410\) −10.5437 −0.520718
\(411\) 35.1024 1.73147
\(412\) −53.8989 −2.65541
\(413\) 31.0400 1.52738
\(414\) 2.30252 0.113163
\(415\) −0.146311 −0.00718211
\(416\) −14.7129 −0.721357
\(417\) 6.95399 0.340538
\(418\) −2.58611 −0.126491
\(419\) −14.5113 −0.708923 −0.354461 0.935071i \(-0.615336\pi\)
−0.354461 + 0.935071i \(0.615336\pi\)
\(420\) −18.1757 −0.886881
\(421\) 18.1495 0.884553 0.442276 0.896879i \(-0.354171\pi\)
0.442276 + 0.896879i \(0.354171\pi\)
\(422\) 69.0061 3.35916
\(423\) −1.50597 −0.0732229
\(424\) 88.9216 4.31841
\(425\) −7.54854 −0.366158
\(426\) −42.1279 −2.04111
\(427\) 13.4833 0.652502
\(428\) −43.0505 −2.08093
\(429\) −2.98881 −0.144301
\(430\) 14.2674 0.688035
\(431\) 17.5233 0.844068 0.422034 0.906580i \(-0.361316\pi\)
0.422034 + 0.906580i \(0.361316\pi\)
\(432\) −45.6024 −2.19405
\(433\) −25.5188 −1.22636 −0.613178 0.789944i \(-0.710109\pi\)
−0.613178 + 0.789944i \(0.710109\pi\)
\(434\) 49.6958 2.38548
\(435\) −10.3751 −0.497446
\(436\) −84.5239 −4.04796
\(437\) 6.89418 0.329793
\(438\) 38.1458 1.82268
\(439\) 23.5383 1.12342 0.561711 0.827334i \(-0.310143\pi\)
0.561711 + 0.827334i \(0.310143\pi\)
\(440\) −6.95140 −0.331395
\(441\) 0.227812 0.0108482
\(442\) 34.4352 1.63792
\(443\) −26.3065 −1.24986 −0.624929 0.780682i \(-0.714872\pi\)
−0.624929 + 0.780682i \(0.714872\pi\)
\(444\) −80.8402 −3.83651
\(445\) 1.54279 0.0731353
\(446\) 13.5664 0.642387
\(447\) −7.96570 −0.376765
\(448\) 9.99445 0.472193
\(449\) −28.8800 −1.36293 −0.681465 0.731851i \(-0.738657\pi\)
−0.681465 + 0.731851i \(0.738657\pi\)
\(450\) −0.333980 −0.0157440
\(451\) 4.07706 0.191981
\(452\) 47.5359 2.23590
\(453\) 1.51495 0.0711785
\(454\) 15.5334 0.729017
\(455\) 4.03638 0.189228
\(456\) −11.7782 −0.551564
\(457\) −14.8718 −0.695675 −0.347838 0.937555i \(-0.613084\pi\)
−0.347838 + 0.937555i \(0.613084\pi\)
\(458\) 27.0365 1.26333
\(459\) 40.0216 1.86805
\(460\) 32.3197 1.50692
\(461\) −8.11094 −0.377764 −0.188882 0.982000i \(-0.560486\pi\)
−0.188882 + 0.982000i \(0.560486\pi\)
\(462\) 10.0266 0.466478
\(463\) −2.42168 −0.112545 −0.0562725 0.998415i \(-0.517922\pi\)
−0.0562725 + 0.998415i \(0.517922\pi\)
\(464\) 52.6673 2.44502
\(465\) −14.2292 −0.659862
\(466\) 60.4260 2.79918
\(467\) 1.70942 0.0791026 0.0395513 0.999218i \(-0.487407\pi\)
0.0395513 + 0.999218i \(0.487407\pi\)
\(468\) 1.06795 0.0493661
\(469\) −20.1153 −0.928839
\(470\) −30.1572 −1.39105
\(471\) 8.03616 0.370287
\(472\) 94.2965 4.34035
\(473\) −5.51693 −0.253669
\(474\) 19.3211 0.887449
\(475\) −1.00000 −0.0458831
\(476\) −80.9743 −3.71145
\(477\) −1.65199 −0.0756396
\(478\) −26.2104 −1.19884
\(479\) −4.20304 −0.192042 −0.0960208 0.995379i \(-0.530612\pi\)
−0.0960208 + 0.995379i \(0.530612\pi\)
\(480\) −14.1322 −0.645044
\(481\) 17.9527 0.818572
\(482\) 27.4695 1.25120
\(483\) −26.7293 −1.21622
\(484\) 4.68797 0.213090
\(485\) 7.32786 0.332741
\(486\) 3.46838 0.157329
\(487\) −4.04855 −0.183458 −0.0917288 0.995784i \(-0.529239\pi\)
−0.0917288 + 0.995784i \(0.529239\pi\)
\(488\) 40.9608 1.85421
\(489\) −25.1434 −1.13703
\(490\) 4.56195 0.206088
\(491\) 18.3438 0.827844 0.413922 0.910312i \(-0.364159\pi\)
0.413922 + 0.910312i \(0.364159\pi\)
\(492\) 32.3846 1.46001
\(493\) −46.2219 −2.08173
\(494\) 4.56184 0.205247
\(495\) 0.129144 0.00580458
\(496\) 72.2321 3.24332
\(497\) −21.9997 −0.986820
\(498\) 0.641105 0.0287286
\(499\) −28.2235 −1.26346 −0.631728 0.775190i \(-0.717654\pi\)
−0.631728 + 0.775190i \(0.717654\pi\)
\(500\) −4.68797 −0.209653
\(501\) −13.0405 −0.582606
\(502\) 10.3728 0.462959
\(503\) −44.2412 −1.97262 −0.986309 0.164910i \(-0.947267\pi\)
−0.986309 + 0.164910i \(0.947267\pi\)
\(504\) −2.05421 −0.0915018
\(505\) −10.5365 −0.468870
\(506\) −17.8291 −0.792601
\(507\) −16.7545 −0.744093
\(508\) −67.0745 −2.97595
\(509\) 12.9450 0.573776 0.286888 0.957964i \(-0.407379\pi\)
0.286888 + 0.957964i \(0.407379\pi\)
\(510\) 33.0762 1.46464
\(511\) 19.9202 0.881217
\(512\) −47.8402 −2.11426
\(513\) 5.30190 0.234084
\(514\) −1.42349 −0.0627873
\(515\) 11.4973 0.506630
\(516\) −43.8216 −1.92914
\(517\) 11.6612 0.512859
\(518\) −60.2258 −2.64617
\(519\) 8.40423 0.368905
\(520\) 12.2621 0.537729
\(521\) −33.8184 −1.48161 −0.740806 0.671719i \(-0.765556\pi\)
−0.740806 + 0.671719i \(0.765556\pi\)
\(522\) −2.04506 −0.0895097
\(523\) 17.1148 0.748380 0.374190 0.927352i \(-0.377921\pi\)
0.374190 + 0.927352i \(0.377921\pi\)
\(524\) 43.8807 1.91694
\(525\) 3.87708 0.169210
\(526\) 23.4594 1.02288
\(527\) −63.3923 −2.76141
\(528\) 14.5734 0.634228
\(529\) 24.5297 1.06651
\(530\) −33.0813 −1.43696
\(531\) −1.75185 −0.0760238
\(532\) −10.7271 −0.465081
\(533\) −7.19184 −0.311513
\(534\) −6.76021 −0.292543
\(535\) 9.18318 0.397024
\(536\) −61.1083 −2.63948
\(537\) −26.4597 −1.14182
\(538\) −66.9194 −2.88510
\(539\) −1.76402 −0.0759816
\(540\) 24.8552 1.06960
\(541\) 38.6274 1.66072 0.830361 0.557225i \(-0.188134\pi\)
0.830361 + 0.557225i \(0.188134\pi\)
\(542\) −16.1938 −0.695585
\(543\) 19.3159 0.828925
\(544\) −62.9603 −2.69940
\(545\) 18.0299 0.772318
\(546\) −17.6866 −0.756918
\(547\) 21.0804 0.901333 0.450667 0.892692i \(-0.351186\pi\)
0.450667 + 0.892692i \(0.351186\pi\)
\(548\) 97.1217 4.14883
\(549\) −0.760974 −0.0324776
\(550\) 2.58611 0.110272
\(551\) −6.12329 −0.260861
\(552\) −81.2008 −3.45614
\(553\) 10.0897 0.429058
\(554\) −42.9015 −1.82271
\(555\) 17.2442 0.731974
\(556\) 19.2404 0.815973
\(557\) −41.4863 −1.75783 −0.878915 0.476978i \(-0.841732\pi\)
−0.878915 + 0.476978i \(0.841732\pi\)
\(558\) −2.80475 −0.118735
\(559\) 9.73173 0.411608
\(560\) −19.6814 −0.831690
\(561\) −12.7899 −0.539992
\(562\) −4.13924 −0.174603
\(563\) 22.1691 0.934317 0.467159 0.884174i \(-0.345278\pi\)
0.467159 + 0.884174i \(0.345278\pi\)
\(564\) 92.6263 3.90027
\(565\) −10.1400 −0.426592
\(566\) 39.1729 1.64656
\(567\) −19.6693 −0.826035
\(568\) −66.8328 −2.80424
\(569\) 26.7108 1.11977 0.559887 0.828569i \(-0.310844\pi\)
0.559887 + 0.828569i \(0.310844\pi\)
\(570\) 4.38180 0.183534
\(571\) −5.12388 −0.214428 −0.107214 0.994236i \(-0.534193\pi\)
−0.107214 + 0.994236i \(0.534193\pi\)
\(572\) −8.26948 −0.345764
\(573\) 32.3604 1.35188
\(574\) 24.1265 1.00702
\(575\) −6.89418 −0.287507
\(576\) −0.564070 −0.0235029
\(577\) −31.2035 −1.29902 −0.649510 0.760353i \(-0.725026\pi\)
−0.649510 + 0.760353i \(0.725026\pi\)
\(578\) 103.394 4.30062
\(579\) −5.08859 −0.211475
\(580\) −28.7058 −1.19194
\(581\) 0.334792 0.0138895
\(582\) −32.1093 −1.33097
\(583\) 12.7919 0.529786
\(584\) 60.5155 2.50415
\(585\) −0.227807 −0.00941864
\(586\) −62.5659 −2.58457
\(587\) 18.0911 0.746698 0.373349 0.927691i \(-0.378209\pi\)
0.373349 + 0.927691i \(0.378209\pi\)
\(588\) −14.0118 −0.577837
\(589\) −8.39796 −0.346032
\(590\) −35.0809 −1.44426
\(591\) 12.2599 0.504303
\(592\) −87.5373 −3.59776
\(593\) 17.3157 0.711072 0.355536 0.934663i \(-0.384298\pi\)
0.355536 + 0.934663i \(0.384298\pi\)
\(594\) −13.7113 −0.562581
\(595\) 17.2728 0.708115
\(596\) −22.0396 −0.902777
\(597\) −13.2268 −0.541336
\(598\) 31.4501 1.28609
\(599\) −10.4764 −0.428054 −0.214027 0.976828i \(-0.568658\pi\)
−0.214027 + 0.976828i \(0.568658\pi\)
\(600\) 11.7782 0.480842
\(601\) 6.37465 0.260027 0.130014 0.991512i \(-0.458498\pi\)
0.130014 + 0.991512i \(0.458498\pi\)
\(602\) −32.6470 −1.33059
\(603\) 1.13528 0.0462320
\(604\) 4.19158 0.170553
\(605\) −1.00000 −0.0406558
\(606\) 46.1691 1.87549
\(607\) −22.0826 −0.896306 −0.448153 0.893957i \(-0.647918\pi\)
−0.448153 + 0.893957i \(0.647918\pi\)
\(608\) −8.34073 −0.338261
\(609\) 23.7405 0.962013
\(610\) −15.2385 −0.616991
\(611\) −20.5701 −0.832177
\(612\) 4.57006 0.184734
\(613\) 33.9519 1.37130 0.685651 0.727930i \(-0.259517\pi\)
0.685651 + 0.727930i \(0.259517\pi\)
\(614\) 27.3285 1.10289
\(615\) −6.90801 −0.278558
\(616\) 15.9064 0.640886
\(617\) 8.00878 0.322422 0.161211 0.986920i \(-0.448460\pi\)
0.161211 + 0.986920i \(0.448460\pi\)
\(618\) −50.3788 −2.02653
\(619\) 2.72497 0.109526 0.0547628 0.998499i \(-0.482560\pi\)
0.0547628 + 0.998499i \(0.482560\pi\)
\(620\) −39.3694 −1.58111
\(621\) 36.5522 1.46679
\(622\) −26.0046 −1.04269
\(623\) −3.53025 −0.141437
\(624\) −25.7072 −1.02911
\(625\) 1.00000 0.0400000
\(626\) 18.3196 0.732200
\(627\) −1.69436 −0.0676662
\(628\) 22.2345 0.887255
\(629\) 76.8244 3.06319
\(630\) 0.764223 0.0304474
\(631\) −28.2517 −1.12468 −0.562342 0.826905i \(-0.690100\pi\)
−0.562342 + 0.826905i \(0.690100\pi\)
\(632\) 30.6515 1.21925
\(633\) 45.2112 1.79698
\(634\) 57.2398 2.27328
\(635\) 14.3078 0.567787
\(636\) 101.607 4.02900
\(637\) 3.11168 0.123289
\(638\) 15.8355 0.626934
\(639\) 1.24163 0.0491180
\(640\) 5.38593 0.212897
\(641\) −12.7920 −0.505255 −0.252627 0.967564i \(-0.581295\pi\)
−0.252627 + 0.967564i \(0.581295\pi\)
\(642\) −40.2389 −1.58810
\(643\) 10.3456 0.407991 0.203996 0.978972i \(-0.434607\pi\)
0.203996 + 0.978972i \(0.434607\pi\)
\(644\) −73.9549 −2.91423
\(645\) 9.34766 0.368064
\(646\) 19.5214 0.768058
\(647\) 13.6757 0.537647 0.268824 0.963189i \(-0.413365\pi\)
0.268824 + 0.963189i \(0.413365\pi\)
\(648\) −59.7535 −2.34734
\(649\) 13.5651 0.532477
\(650\) −4.56184 −0.178930
\(651\) 32.5595 1.27611
\(652\) −69.5672 −2.72446
\(653\) 4.65063 0.181993 0.0909966 0.995851i \(-0.470995\pi\)
0.0909966 + 0.995851i \(0.470995\pi\)
\(654\) −79.0037 −3.08929
\(655\) −9.36028 −0.365736
\(656\) 35.0674 1.36915
\(657\) −1.12426 −0.0438616
\(658\) 69.0065 2.69015
\(659\) 14.0335 0.546667 0.273333 0.961919i \(-0.411874\pi\)
0.273333 + 0.961919i \(0.411874\pi\)
\(660\) −7.94312 −0.309185
\(661\) −19.7867 −0.769615 −0.384807 0.922997i \(-0.625732\pi\)
−0.384807 + 0.922997i \(0.625732\pi\)
\(662\) −41.8454 −1.62637
\(663\) 22.5612 0.876203
\(664\) 1.01706 0.0394697
\(665\) 2.28823 0.0887336
\(666\) 3.39905 0.131710
\(667\) −42.2150 −1.63457
\(668\) −36.0805 −1.39600
\(669\) 8.88839 0.343645
\(670\) 22.7340 0.878289
\(671\) 5.89246 0.227476
\(672\) 32.3377 1.24745
\(673\) 34.9325 1.34655 0.673274 0.739393i \(-0.264887\pi\)
0.673274 + 0.739393i \(0.264887\pi\)
\(674\) 10.1911 0.392546
\(675\) −5.30190 −0.204070
\(676\) −46.3565 −1.78294
\(677\) 9.72087 0.373603 0.186802 0.982398i \(-0.440188\pi\)
0.186802 + 0.982398i \(0.440188\pi\)
\(678\) 44.4313 1.70638
\(679\) −16.7678 −0.643490
\(680\) 52.4729 2.01224
\(681\) 10.1771 0.389987
\(682\) 21.7180 0.831627
\(683\) 25.5204 0.976511 0.488255 0.872701i \(-0.337633\pi\)
0.488255 + 0.872701i \(0.337633\pi\)
\(684\) 0.605423 0.0231489
\(685\) −20.7172 −0.791563
\(686\) −51.8620 −1.98010
\(687\) 17.7137 0.675820
\(688\) −47.4519 −1.80909
\(689\) −22.5646 −0.859643
\(690\) 30.2089 1.15003
\(691\) 2.08781 0.0794241 0.0397120 0.999211i \(-0.487356\pi\)
0.0397120 + 0.999211i \(0.487356\pi\)
\(692\) 23.2529 0.883943
\(693\) −0.295510 −0.0112255
\(694\) 27.1728 1.03146
\(695\) −4.10420 −0.155681
\(696\) 72.1211 2.73374
\(697\) −30.7759 −1.16572
\(698\) −73.7414 −2.79115
\(699\) 39.5897 1.49742
\(700\) 10.7271 0.405448
\(701\) 20.5119 0.774724 0.387362 0.921928i \(-0.373386\pi\)
0.387362 + 0.921928i \(0.373386\pi\)
\(702\) 24.1864 0.912857
\(703\) 10.1774 0.383848
\(704\) 4.36777 0.164617
\(705\) −19.7583 −0.744140
\(706\) −4.47737 −0.168508
\(707\) 24.1100 0.906750
\(708\) 107.749 4.04946
\(709\) −51.7570 −1.94377 −0.971887 0.235447i \(-0.924345\pi\)
−0.971887 + 0.235447i \(0.924345\pi\)
\(710\) 24.8636 0.933115
\(711\) −0.569447 −0.0213559
\(712\) −10.7246 −0.401920
\(713\) −57.8970 −2.16826
\(714\) −75.6859 −2.83247
\(715\) 1.76398 0.0659690
\(716\) −73.2090 −2.73595
\(717\) −17.1725 −0.641317
\(718\) 23.4732 0.876013
\(719\) 8.16836 0.304629 0.152314 0.988332i \(-0.451327\pi\)
0.152314 + 0.988332i \(0.451327\pi\)
\(720\) 1.11078 0.0413965
\(721\) −26.3084 −0.979774
\(722\) 2.58611 0.0962451
\(723\) 17.9974 0.669329
\(724\) 53.4435 1.98621
\(725\) 6.12329 0.227413
\(726\) 4.38180 0.162624
\(727\) −0.887737 −0.0329244 −0.0164622 0.999864i \(-0.505240\pi\)
−0.0164622 + 0.999864i \(0.505240\pi\)
\(728\) −28.0585 −1.03992
\(729\) 28.0601 1.03926
\(730\) −22.5134 −0.833259
\(731\) 41.6447 1.54029
\(732\) 46.8045 1.72994
\(733\) 30.3814 1.12216 0.561082 0.827761i \(-0.310385\pi\)
0.561082 + 0.827761i \(0.310385\pi\)
\(734\) 7.37858 0.272349
\(735\) 2.98888 0.110247
\(736\) −57.5025 −2.11957
\(737\) −8.79079 −0.323813
\(738\) −1.36166 −0.0501233
\(739\) 26.0766 0.959242 0.479621 0.877476i \(-0.340774\pi\)
0.479621 + 0.877476i \(0.340774\pi\)
\(740\) 47.7113 1.75390
\(741\) 2.98881 0.109797
\(742\) 75.6974 2.77894
\(743\) 7.70703 0.282744 0.141372 0.989957i \(-0.454849\pi\)
0.141372 + 0.989957i \(0.454849\pi\)
\(744\) 98.9126 3.62631
\(745\) 4.70130 0.172242
\(746\) −21.6261 −0.791788
\(747\) −0.0188951 −0.000691336 0
\(748\) −35.3873 −1.29389
\(749\) −21.0132 −0.767806
\(750\) −4.38180 −0.160001
\(751\) 22.8187 0.832666 0.416333 0.909212i \(-0.363315\pi\)
0.416333 + 0.909212i \(0.363315\pi\)
\(752\) 100.300 3.65756
\(753\) 6.79599 0.247660
\(754\) −27.9335 −1.01728
\(755\) −0.894112 −0.0325401
\(756\) −56.8742 −2.06850
\(757\) −23.9190 −0.869350 −0.434675 0.900587i \(-0.643137\pi\)
−0.434675 + 0.900587i \(0.643137\pi\)
\(758\) −10.5753 −0.384114
\(759\) −11.6812 −0.424001
\(760\) 6.95140 0.252154
\(761\) −16.5720 −0.600734 −0.300367 0.953824i \(-0.597109\pi\)
−0.300367 + 0.953824i \(0.597109\pi\)
\(762\) −62.6939 −2.27116
\(763\) −41.2566 −1.49359
\(764\) 89.5352 3.23927
\(765\) −0.974847 −0.0352457
\(766\) −12.8044 −0.462643
\(767\) −23.9285 −0.864009
\(768\) −38.4012 −1.38569
\(769\) 14.7713 0.532668 0.266334 0.963881i \(-0.414188\pi\)
0.266334 + 0.963881i \(0.414188\pi\)
\(770\) −5.91761 −0.213256
\(771\) −0.932636 −0.0335881
\(772\) −14.0792 −0.506721
\(773\) 24.5744 0.883879 0.441939 0.897045i \(-0.354291\pi\)
0.441939 + 0.897045i \(0.354291\pi\)
\(774\) 1.84254 0.0662289
\(775\) 8.39796 0.301663
\(776\) −50.9389 −1.82860
\(777\) −39.4586 −1.41557
\(778\) −9.08259 −0.325627
\(779\) −4.07706 −0.146076
\(780\) 14.0115 0.501691
\(781\) −9.61429 −0.344026
\(782\) 134.584 4.81271
\(783\) −32.4650 −1.16021
\(784\) −15.1726 −0.541878
\(785\) −4.74289 −0.169281
\(786\) 41.0149 1.46295
\(787\) −42.8976 −1.52913 −0.764566 0.644545i \(-0.777047\pi\)
−0.764566 + 0.644545i \(0.777047\pi\)
\(788\) 33.9207 1.20837
\(789\) 15.3701 0.547189
\(790\) −11.4032 −0.405708
\(791\) 23.2025 0.824987
\(792\) −0.897730 −0.0318994
\(793\) −10.3942 −0.369107
\(794\) −36.9668 −1.31190
\(795\) −21.6741 −0.768700
\(796\) −36.5960 −1.29711
\(797\) −3.74141 −0.132528 −0.0662638 0.997802i \(-0.521108\pi\)
−0.0662638 + 0.997802i \(0.521108\pi\)
\(798\) −10.0266 −0.354937
\(799\) −88.0251 −3.11410
\(800\) 8.34073 0.294889
\(801\) 0.199242 0.00703986
\(802\) 5.41305 0.191141
\(803\) 8.70551 0.307211
\(804\) −69.8262 −2.46258
\(805\) 15.7754 0.556011
\(806\) −38.3101 −1.34942
\(807\) −43.8440 −1.54338
\(808\) 73.2438 2.57671
\(809\) 35.5668 1.25046 0.625232 0.780439i \(-0.285005\pi\)
0.625232 + 0.780439i \(0.285005\pi\)
\(810\) 22.2299 0.781080
\(811\) 16.5102 0.579753 0.289877 0.957064i \(-0.406386\pi\)
0.289877 + 0.957064i \(0.406386\pi\)
\(812\) 65.6854 2.30511
\(813\) −10.6098 −0.372103
\(814\) −26.3199 −0.922511
\(815\) 14.8395 0.519805
\(816\) −110.008 −3.85106
\(817\) 5.51693 0.193013
\(818\) 80.0202 2.79784
\(819\) 0.521273 0.0182148
\(820\) −19.1132 −0.667460
\(821\) −38.9813 −1.36046 −0.680228 0.733001i \(-0.738119\pi\)
−0.680228 + 0.733001i \(0.738119\pi\)
\(822\) 90.7787 3.16627
\(823\) 51.7892 1.80526 0.902630 0.430418i \(-0.141634\pi\)
0.902630 + 0.430418i \(0.141634\pi\)
\(824\) −79.9221 −2.78422
\(825\) 1.69436 0.0589900
\(826\) 80.2730 2.79306
\(827\) 1.01711 0.0353684 0.0176842 0.999844i \(-0.494371\pi\)
0.0176842 + 0.999844i \(0.494371\pi\)
\(828\) 4.17389 0.145053
\(829\) −19.8623 −0.689848 −0.344924 0.938631i \(-0.612095\pi\)
−0.344924 + 0.938631i \(0.612095\pi\)
\(830\) −0.378376 −0.0131336
\(831\) −28.1081 −0.975059
\(832\) −7.70464 −0.267110
\(833\) 13.3158 0.461363
\(834\) 17.9838 0.622728
\(835\) 7.69641 0.266345
\(836\) −4.68797 −0.162137
\(837\) −44.5251 −1.53901
\(838\) −37.5278 −1.29638
\(839\) −9.36663 −0.323372 −0.161686 0.986842i \(-0.551693\pi\)
−0.161686 + 0.986842i \(0.551693\pi\)
\(840\) −26.9511 −0.929903
\(841\) 8.49464 0.292919
\(842\) 46.9366 1.61754
\(843\) −2.71193 −0.0934040
\(844\) 125.091 4.30580
\(845\) 9.88839 0.340171
\(846\) −3.89461 −0.133900
\(847\) 2.28823 0.0786244
\(848\) 110.025 3.77827
\(849\) 25.6652 0.880826
\(850\) −19.5214 −0.669577
\(851\) 70.1648 2.40522
\(852\) −76.3674 −2.61630
\(853\) 34.7410 1.18951 0.594755 0.803907i \(-0.297249\pi\)
0.594755 + 0.803907i \(0.297249\pi\)
\(854\) 34.8693 1.19320
\(855\) −0.129144 −0.00441662
\(856\) −63.8360 −2.18187
\(857\) −7.19129 −0.245650 −0.122825 0.992428i \(-0.539195\pi\)
−0.122825 + 0.992428i \(0.539195\pi\)
\(858\) −7.72940 −0.263877
\(859\) 13.9328 0.475383 0.237691 0.971341i \(-0.423609\pi\)
0.237691 + 0.971341i \(0.423609\pi\)
\(860\) 25.8632 0.881928
\(861\) 15.8071 0.538704
\(862\) 45.3172 1.54351
\(863\) −38.8902 −1.32384 −0.661918 0.749576i \(-0.730257\pi\)
−0.661918 + 0.749576i \(0.730257\pi\)
\(864\) −44.2217 −1.50445
\(865\) −4.96012 −0.168649
\(866\) −65.9945 −2.24259
\(867\) 67.7412 2.30061
\(868\) 90.0861 3.05772
\(869\) 4.40940 0.149579
\(870\) −26.8310 −0.909658
\(871\) 15.5067 0.525426
\(872\) −125.333 −4.24432
\(873\) 0.946348 0.0320290
\(874\) 17.8291 0.603079
\(875\) −2.28823 −0.0773562
\(876\) 69.1489 2.33632
\(877\) −40.2540 −1.35928 −0.679640 0.733546i \(-0.737864\pi\)
−0.679640 + 0.733546i \(0.737864\pi\)
\(878\) 60.8726 2.05435
\(879\) −40.9917 −1.38262
\(880\) −8.60115 −0.289945
\(881\) −38.5849 −1.29996 −0.649978 0.759953i \(-0.725222\pi\)
−0.649978 + 0.759953i \(0.725222\pi\)
\(882\) 0.589147 0.0198376
\(883\) −41.6274 −1.40087 −0.700437 0.713714i \(-0.747011\pi\)
−0.700437 + 0.713714i \(0.747011\pi\)
\(884\) 62.4225 2.09949
\(885\) −22.9842 −0.772605
\(886\) −68.0314 −2.28556
\(887\) −12.8070 −0.430018 −0.215009 0.976612i \(-0.568978\pi\)
−0.215009 + 0.976612i \(0.568978\pi\)
\(888\) −119.871 −4.02261
\(889\) −32.7395 −1.09805
\(890\) 3.98983 0.133739
\(891\) −8.59589 −0.287973
\(892\) 24.5925 0.823417
\(893\) −11.6612 −0.390227
\(894\) −20.6002 −0.688974
\(895\) 15.6163 0.521997
\(896\) −12.3242 −0.411723
\(897\) 20.6054 0.687994
\(898\) −74.6868 −2.49233
\(899\) 51.4231 1.71506
\(900\) −0.605423 −0.0201808
\(901\) −96.5601 −3.21688
\(902\) 10.5437 0.351068
\(903\) −21.3896 −0.711800
\(904\) 70.4870 2.34436
\(905\) −11.4001 −0.378953
\(906\) 3.91783 0.130161
\(907\) 28.3828 0.942436 0.471218 0.882017i \(-0.343815\pi\)
0.471218 + 0.882017i \(0.343815\pi\)
\(908\) 28.1581 0.934459
\(909\) −1.36073 −0.0451325
\(910\) 10.4385 0.346034
\(911\) −11.6094 −0.384637 −0.192319 0.981333i \(-0.561601\pi\)
−0.192319 + 0.981333i \(0.561601\pi\)
\(912\) −14.5734 −0.482575
\(913\) 0.146311 0.00484218
\(914\) −38.4602 −1.27215
\(915\) −9.98394 −0.330059
\(916\) 49.0104 1.61935
\(917\) 21.4184 0.707299
\(918\) 103.500 3.41602
\(919\) 12.1480 0.400726 0.200363 0.979722i \(-0.435788\pi\)
0.200363 + 0.979722i \(0.435788\pi\)
\(920\) 47.9242 1.58001
\(921\) 17.9050 0.589991
\(922\) −20.9758 −0.690801
\(923\) 16.9594 0.558225
\(924\) 18.1757 0.597935
\(925\) −10.1774 −0.334631
\(926\) −6.26274 −0.205806
\(927\) 1.48480 0.0487672
\(928\) 51.0727 1.67654
\(929\) −30.4949 −1.00051 −0.500253 0.865879i \(-0.666760\pi\)
−0.500253 + 0.865879i \(0.666760\pi\)
\(930\) −36.7982 −1.20666
\(931\) 1.76402 0.0578133
\(932\) 109.537 3.58801
\(933\) −17.0376 −0.557786
\(934\) 4.42076 0.144652
\(935\) 7.54854 0.246864
\(936\) 1.58357 0.0517608
\(937\) 10.8722 0.355179 0.177589 0.984105i \(-0.443170\pi\)
0.177589 + 0.984105i \(0.443170\pi\)
\(938\) −52.0204 −1.69853
\(939\) 12.0026 0.391690
\(940\) −54.6674 −1.78305
\(941\) −33.5654 −1.09420 −0.547100 0.837067i \(-0.684268\pi\)
−0.547100 + 0.837067i \(0.684268\pi\)
\(942\) 20.7824 0.677128
\(943\) −28.1080 −0.915322
\(944\) 116.676 3.79746
\(945\) 12.1319 0.394652
\(946\) −14.2674 −0.463873
\(947\) −19.9608 −0.648639 −0.324319 0.945948i \(-0.605135\pi\)
−0.324319 + 0.945948i \(0.605135\pi\)
\(948\) 35.0244 1.13754
\(949\) −15.3563 −0.498487
\(950\) −2.58611 −0.0839045
\(951\) 37.5022 1.21609
\(952\) −120.070 −3.89149
\(953\) −51.9269 −1.68208 −0.841039 0.540975i \(-0.818055\pi\)
−0.841039 + 0.540975i \(0.818055\pi\)
\(954\) −4.27224 −0.138319
\(955\) −19.0989 −0.618026
\(956\) −47.5129 −1.53668
\(957\) 10.3751 0.335378
\(958\) −10.8695 −0.351178
\(959\) 47.4056 1.53081
\(960\) −7.40057 −0.238853
\(961\) 39.5257 1.27502
\(962\) 46.4276 1.49689
\(963\) 1.18595 0.0382167
\(964\) 49.7953 1.60380
\(965\) 3.00325 0.0966781
\(966\) −69.1249 −2.22406
\(967\) 32.5944 1.04817 0.524083 0.851667i \(-0.324408\pi\)
0.524083 + 0.851667i \(0.324408\pi\)
\(968\) 6.95140 0.223426
\(969\) 12.7899 0.410872
\(970\) 18.9507 0.608469
\(971\) 45.4145 1.45742 0.728710 0.684823i \(-0.240120\pi\)
0.728710 + 0.684823i \(0.240120\pi\)
\(972\) 6.28730 0.201665
\(973\) 9.39133 0.301072
\(974\) −10.4700 −0.335481
\(975\) −2.98881 −0.0957186
\(976\) 50.6819 1.62229
\(977\) −29.4277 −0.941475 −0.470737 0.882273i \(-0.656012\pi\)
−0.470737 + 0.882273i \(0.656012\pi\)
\(978\) −65.0238 −2.07923
\(979\) −1.54279 −0.0493078
\(980\) 8.26967 0.264165
\(981\) 2.32845 0.0743418
\(982\) 47.4391 1.51384
\(983\) 37.4646 1.19494 0.597468 0.801893i \(-0.296174\pi\)
0.597468 + 0.801893i \(0.296174\pi\)
\(984\) 48.0203 1.53083
\(985\) −7.23568 −0.230548
\(986\) −119.535 −3.80677
\(987\) 45.2114 1.43910
\(988\) 8.26948 0.263087
\(989\) 38.0347 1.20943
\(990\) 0.333980 0.0106146
\(991\) −49.2749 −1.56527 −0.782634 0.622482i \(-0.786124\pi\)
−0.782634 + 0.622482i \(0.786124\pi\)
\(992\) 70.0451 2.22393
\(993\) −27.4161 −0.870024
\(994\) −56.8936 −1.80456
\(995\) 7.80636 0.247478
\(996\) 1.16216 0.0368245
\(997\) 25.3145 0.801719 0.400859 0.916140i \(-0.368712\pi\)
0.400859 + 0.916140i \(0.368712\pi\)
\(998\) −72.9890 −2.31043
\(999\) 53.9595 1.70720
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 1045.2.a.h.1.7 7
3.2 odd 2 9405.2.a.bd.1.1 7
5.4 even 2 5225.2.a.m.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.a.h.1.7 7 1.1 even 1 trivial
5225.2.a.m.1.1 7 5.4 even 2
9405.2.a.bd.1.1 7 3.2 odd 2