Properties

Label 1045.2.f.a.626.14
Level $1045$
Weight $2$
Character 1045.626
Analytic conductor $8.344$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1045,2,Mod(626,1045)]
 
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, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1045.626");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.f (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.34436701122\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 626.14
Character \(\chi\) \(=\) 1045.626
Dual form 1045.2.f.a.626.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.42582 q^{2} -1.05301i q^{3} +0.0329672 q^{4} -1.00000 q^{5} +1.50140i q^{6} -0.901840i q^{7} +2.80464 q^{8} +1.89118 q^{9} +O(q^{10})\) \(q-1.42582 q^{2} -1.05301i q^{3} +0.0329672 q^{4} -1.00000 q^{5} +1.50140i q^{6} -0.901840i q^{7} +2.80464 q^{8} +1.89118 q^{9} +1.42582 q^{10} +(2.88768 + 1.63135i) q^{11} -0.0347147i q^{12} -5.62988 q^{13} +1.28586i q^{14} +1.05301i q^{15} -4.06485 q^{16} +2.98133i q^{17} -2.69648 q^{18} +(-0.563246 + 4.32236i) q^{19} -0.0329672 q^{20} -0.949644 q^{21} +(-4.11732 - 2.32602i) q^{22} -5.84146 q^{23} -2.95330i q^{24} +1.00000 q^{25} +8.02721 q^{26} -5.15044i q^{27} -0.0297311i q^{28} +2.10889 q^{29} -1.50140i q^{30} -9.55444i q^{31} +0.186472 q^{32} +(1.71783 - 3.04075i) q^{33} -4.25085i q^{34} +0.901840i q^{35} +0.0623468 q^{36} +8.43084i q^{37} +(0.803089 - 6.16291i) q^{38} +5.92831i q^{39} -2.80464 q^{40} -4.89924 q^{41} +1.35402 q^{42} +10.7286i q^{43} +(0.0951988 + 0.0537811i) q^{44} -1.89118 q^{45} +8.32888 q^{46} +6.27493 q^{47} +4.28032i q^{48} +6.18669 q^{49} -1.42582 q^{50} +3.13937 q^{51} -0.185602 q^{52} +0.813546i q^{53} +7.34361i q^{54} +(-2.88768 - 1.63135i) q^{55} -2.52933i q^{56} +(4.55147 + 0.593103i) q^{57} -3.00690 q^{58} +13.9409i q^{59} +0.0347147i q^{60} +11.3812i q^{61} +13.6229i q^{62} -1.70554i q^{63} +7.86382 q^{64} +5.62988 q^{65} +(-2.44931 + 4.33556i) q^{66} +5.05376i q^{67} +0.0982862i q^{68} +6.15110i q^{69} -1.28586i q^{70} -2.36569i q^{71} +5.30406 q^{72} -4.24232i q^{73} -12.0209i q^{74} -1.05301i q^{75} +(-0.0185687 + 0.142496i) q^{76} +(1.47122 - 2.60422i) q^{77} -8.45271i q^{78} +5.64937 q^{79} +4.06485 q^{80} +0.250069 q^{81} +6.98544 q^{82} -14.6416i q^{83} -0.0313071 q^{84} -2.98133i q^{85} -15.2971i q^{86} -2.22067i q^{87} +(8.09889 + 4.57535i) q^{88} +13.7701i q^{89} +2.69648 q^{90} +5.07725i q^{91} -0.192577 q^{92} -10.0609 q^{93} -8.94693 q^{94} +(0.563246 - 4.32236i) q^{95} -0.196356i q^{96} +9.17901i q^{97} -8.82111 q^{98} +(5.46111 + 3.08517i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 40 q^{4} - 40 q^{5} - 28 q^{9} - 4 q^{11} + 32 q^{16} - 40 q^{20} - 16 q^{23} + 40 q^{25} + 8 q^{26} + 8 q^{36} + 28 q^{38} - 84 q^{42} - 48 q^{44} + 28 q^{45} + 32 q^{47} - 20 q^{49} + 4 q^{55} - 20 q^{58} + 72 q^{64} + 36 q^{66} + 16 q^{77} - 32 q^{80} + 16 q^{81} + 16 q^{82} - 20 q^{92} - 8 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).

\(n\) \(496\) \(761\) \(837\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.42582 −1.00821 −0.504104 0.863643i \(-0.668177\pi\)
−0.504104 + 0.863643i \(0.668177\pi\)
\(3\) 1.05301i 0.607954i −0.952679 0.303977i \(-0.901685\pi\)
0.952679 0.303977i \(-0.0983146\pi\)
\(4\) 0.0329672 0.0164836
\(5\) −1.00000 −0.447214
\(6\) 1.50140i 0.612944i
\(7\) 0.901840i 0.340863i −0.985369 0.170432i \(-0.945484\pi\)
0.985369 0.170432i \(-0.0545162\pi\)
\(8\) 2.80464 0.991589
\(9\) 1.89118 0.630392
\(10\) 1.42582 0.450884
\(11\) 2.88768 + 1.63135i 0.870668 + 0.491871i
\(12\) 0.0347147i 0.0100213i
\(13\) −5.62988 −1.56145 −0.780724 0.624876i \(-0.785149\pi\)
−0.780724 + 0.624876i \(0.785149\pi\)
\(14\) 1.28586i 0.343661i
\(15\) 1.05301i 0.271885i
\(16\) −4.06485 −1.01621
\(17\) 2.98133i 0.723079i 0.932357 + 0.361540i \(0.117749\pi\)
−0.932357 + 0.361540i \(0.882251\pi\)
\(18\) −2.69648 −0.635566
\(19\) −0.563246 + 4.32236i −0.129218 + 0.991616i
\(20\) −0.0329672 −0.00737169
\(21\) −0.949644 −0.207229
\(22\) −4.11732 2.32602i −0.877815 0.495908i
\(23\) −5.84146 −1.21803 −0.609014 0.793159i \(-0.708435\pi\)
−0.609014 + 0.793159i \(0.708435\pi\)
\(24\) 2.95330i 0.602841i
\(25\) 1.00000 0.200000
\(26\) 8.02721 1.57426
\(27\) 5.15044i 0.991203i
\(28\) 0.0297311i 0.00561866i
\(29\) 2.10889 0.391610 0.195805 0.980643i \(-0.437268\pi\)
0.195805 + 0.980643i \(0.437268\pi\)
\(30\) 1.50140i 0.274117i
\(31\) 9.55444i 1.71603i −0.513626 0.858014i \(-0.671698\pi\)
0.513626 0.858014i \(-0.328302\pi\)
\(32\) 0.186472 0.0329639
\(33\) 1.71783 3.04075i 0.299035 0.529326i
\(34\) 4.25085i 0.729014i
\(35\) 0.901840i 0.152439i
\(36\) 0.0623468 0.0103911
\(37\) 8.43084i 1.38602i 0.720927 + 0.693011i \(0.243716\pi\)
−0.720927 + 0.693011i \(0.756284\pi\)
\(38\) 0.803089 6.16291i 0.130278 0.999756i
\(39\) 5.92831i 0.949289i
\(40\) −2.80464 −0.443452
\(41\) −4.89924 −0.765132 −0.382566 0.923928i \(-0.624960\pi\)
−0.382566 + 0.923928i \(0.624960\pi\)
\(42\) 1.35402 0.208930
\(43\) 10.7286i 1.63610i 0.575150 + 0.818048i \(0.304944\pi\)
−0.575150 + 0.818048i \(0.695056\pi\)
\(44\) 0.0951988 + 0.0537811i 0.0143518 + 0.00810781i
\(45\) −1.89118 −0.281920
\(46\) 8.32888 1.22803
\(47\) 6.27493 0.915292 0.457646 0.889134i \(-0.348693\pi\)
0.457646 + 0.889134i \(0.348693\pi\)
\(48\) 4.28032i 0.617810i
\(49\) 6.18669 0.883812
\(50\) −1.42582 −0.201642
\(51\) 3.13937 0.439599
\(52\) −0.185602 −0.0257383
\(53\) 0.813546i 0.111749i 0.998438 + 0.0558746i \(0.0177947\pi\)
−0.998438 + 0.0558746i \(0.982205\pi\)
\(54\) 7.34361i 0.999339i
\(55\) −2.88768 1.63135i −0.389375 0.219971i
\(56\) 2.52933i 0.337996i
\(57\) 4.55147 + 0.593103i 0.602857 + 0.0785584i
\(58\) −3.00690 −0.394825
\(59\) 13.9409i 1.81494i 0.420112 + 0.907472i \(0.361991\pi\)
−0.420112 + 0.907472i \(0.638009\pi\)
\(60\) 0.0347147i 0.00448165i
\(61\) 11.3812i 1.45722i 0.684930 + 0.728609i \(0.259833\pi\)
−0.684930 + 0.728609i \(0.740167\pi\)
\(62\) 13.6229i 1.73011i
\(63\) 1.70554i 0.214877i
\(64\) 7.86382 0.982977
\(65\) 5.62988 0.698301
\(66\) −2.44931 + 4.33556i −0.301490 + 0.533671i
\(67\) 5.05376i 0.617415i 0.951157 + 0.308707i \(0.0998964\pi\)
−0.951157 + 0.308707i \(0.900104\pi\)
\(68\) 0.0982862i 0.0119190i
\(69\) 6.15110i 0.740506i
\(70\) 1.28586i 0.153690i
\(71\) 2.36569i 0.280756i −0.990098 0.140378i \(-0.955168\pi\)
0.990098 0.140378i \(-0.0448317\pi\)
\(72\) 5.30406 0.625090
\(73\) 4.24232i 0.496526i −0.968693 0.248263i \(-0.920140\pi\)
0.968693 0.248263i \(-0.0798598\pi\)
\(74\) 12.0209i 1.39740i
\(75\) 1.05301i 0.121591i
\(76\) −0.0185687 + 0.142496i −0.00212997 + 0.0163454i
\(77\) 1.47122 2.60422i 0.167661 0.296779i
\(78\) 8.45271i 0.957081i
\(79\) 5.64937 0.635604 0.317802 0.948157i \(-0.397055\pi\)
0.317802 + 0.948157i \(0.397055\pi\)
\(80\) 4.06485 0.454464
\(81\) 0.250069 0.0277855
\(82\) 6.98544 0.771413
\(83\) 14.6416i 1.60712i −0.595223 0.803561i \(-0.702936\pi\)
0.595223 0.803561i \(-0.297064\pi\)
\(84\) −0.0313071 −0.00341589
\(85\) 2.98133i 0.323371i
\(86\) 15.2971i 1.64953i
\(87\) 2.22067i 0.238081i
\(88\) 8.09889 + 4.57535i 0.863345 + 0.487734i
\(89\) 13.7701i 1.45962i 0.683648 + 0.729812i \(0.260393\pi\)
−0.683648 + 0.729812i \(0.739607\pi\)
\(90\) 2.69648 0.284234
\(91\) 5.07725i 0.532240i
\(92\) −0.192577 −0.0200775
\(93\) −10.0609 −1.04327
\(94\) −8.94693 −0.922805
\(95\) 0.563246 4.32236i 0.0577879 0.443464i
\(96\) 0.196356i 0.0200405i
\(97\) 9.17901i 0.931987i 0.884788 + 0.465994i \(0.154303\pi\)
−0.884788 + 0.465994i \(0.845697\pi\)
\(98\) −8.82111 −0.891067
\(99\) 5.46111 + 3.08517i 0.548862 + 0.310071i
\(100\) 0.0329672 0.00329672
\(101\) 4.14181i 0.412126i 0.978539 + 0.206063i \(0.0660652\pi\)
−0.978539 + 0.206063i \(0.933935\pi\)
\(102\) −4.47617 −0.443207
\(103\) 4.07026i 0.401054i 0.979688 + 0.200527i \(0.0642655\pi\)
−0.979688 + 0.200527i \(0.935735\pi\)
\(104\) −15.7898 −1.54831
\(105\) 0.949644 0.0926758
\(106\) 1.15997i 0.112666i
\(107\) −4.87597 −0.471378 −0.235689 0.971829i \(-0.575735\pi\)
−0.235689 + 0.971829i \(0.575735\pi\)
\(108\) 0.169796i 0.0163386i
\(109\) 19.4459 1.86258 0.931289 0.364281i \(-0.118685\pi\)
0.931289 + 0.364281i \(0.118685\pi\)
\(110\) 4.11732 + 2.32602i 0.392571 + 0.221777i
\(111\) 8.87774 0.842637
\(112\) 3.66584i 0.346389i
\(113\) 7.25680i 0.682662i −0.939943 0.341331i \(-0.889122\pi\)
0.939943 0.341331i \(-0.110878\pi\)
\(114\) −6.48959 0.845659i −0.607806 0.0792032i
\(115\) 5.84146 0.544719
\(116\) 0.0695241 0.00645515
\(117\) −10.6471 −0.984324
\(118\) 19.8772i 1.82984i
\(119\) 2.68868 0.246471
\(120\) 2.95330i 0.269599i
\(121\) 5.67738 + 9.42164i 0.516126 + 0.856513i
\(122\) 16.2276i 1.46918i
\(123\) 5.15893i 0.465165i
\(124\) 0.314983i 0.0282863i
\(125\) −1.00000 −0.0894427
\(126\) 2.43179i 0.216641i
\(127\) 3.03121 0.268976 0.134488 0.990915i \(-0.457061\pi\)
0.134488 + 0.990915i \(0.457061\pi\)
\(128\) −11.5853 −1.02401
\(129\) 11.2973 0.994672
\(130\) −8.02721 −0.704032
\(131\) 5.47883i 0.478687i −0.970935 0.239344i \(-0.923068\pi\)
0.970935 0.239344i \(-0.0769323\pi\)
\(132\) 0.0566319 0.100245i 0.00492918 0.00872521i
\(133\) 3.89807 + 0.507958i 0.338006 + 0.0440455i
\(134\) 7.20576i 0.622483i
\(135\) 5.15044i 0.443280i
\(136\) 8.36156i 0.716998i
\(137\) −1.26081 −0.107718 −0.0538590 0.998549i \(-0.517152\pi\)
−0.0538590 + 0.998549i \(0.517152\pi\)
\(138\) 8.77037i 0.746584i
\(139\) 16.3563i 1.38733i 0.720300 + 0.693663i \(0.244004\pi\)
−0.720300 + 0.693663i \(0.755996\pi\)
\(140\) 0.0297311i 0.00251274i
\(141\) 6.60755i 0.556456i
\(142\) 3.37305i 0.283060i
\(143\) −16.2573 9.18432i −1.35950 0.768031i
\(144\) −7.68734 −0.640612
\(145\) −2.10889 −0.175134
\(146\) 6.04880i 0.500602i
\(147\) 6.51463i 0.537317i
\(148\) 0.277941i 0.0228466i
\(149\) 18.0379i 1.47772i −0.673858 0.738860i \(-0.735364\pi\)
0.673858 0.738860i \(-0.264636\pi\)
\(150\) 1.50140i 0.122589i
\(151\) 8.10849 0.659860 0.329930 0.944005i \(-0.392975\pi\)
0.329930 + 0.944005i \(0.392975\pi\)
\(152\) −1.57970 + 12.1226i −0.128131 + 0.983276i
\(153\) 5.63822i 0.455823i
\(154\) −2.09769 + 3.71316i −0.169037 + 0.299215i
\(155\) 9.55444i 0.767431i
\(156\) 0.195440i 0.0156477i
\(157\) −12.7219 −1.01532 −0.507659 0.861558i \(-0.669489\pi\)
−0.507659 + 0.861558i \(0.669489\pi\)
\(158\) −8.05500 −0.640821
\(159\) 0.856670 0.0679383
\(160\) −0.186472 −0.0147419
\(161\) 5.26806i 0.415181i
\(162\) −0.356554 −0.0280135
\(163\) 24.4172 1.91250 0.956250 0.292550i \(-0.0945036\pi\)
0.956250 + 0.292550i \(0.0945036\pi\)
\(164\) −0.161514 −0.0126121
\(165\) −1.71783 + 3.04075i −0.133733 + 0.236722i
\(166\) 20.8763i 1.62031i
\(167\) −1.19788 −0.0926946 −0.0463473 0.998925i \(-0.514758\pi\)
−0.0463473 + 0.998925i \(0.514758\pi\)
\(168\) −2.66341 −0.205486
\(169\) 18.6956 1.43812
\(170\) 4.25085i 0.326025i
\(171\) −1.06520 + 8.17433i −0.0814577 + 0.625107i
\(172\) 0.353692i 0.0269688i
\(173\) 5.36104 0.407592 0.203796 0.979013i \(-0.434672\pi\)
0.203796 + 0.979013i \(0.434672\pi\)
\(174\) 3.16628i 0.240035i
\(175\) 0.901840i 0.0681727i
\(176\) −11.7380 6.63120i −0.884783 0.499845i
\(177\) 14.6798 1.10340
\(178\) 19.6337i 1.47161i
\(179\) 6.25624i 0.467613i 0.972283 + 0.233807i \(0.0751183\pi\)
−0.972283 + 0.233807i \(0.924882\pi\)
\(180\) −0.0623468 −0.00464706
\(181\) 6.39099i 0.475039i 0.971383 + 0.237519i \(0.0763343\pi\)
−0.971383 + 0.237519i \(0.923666\pi\)
\(182\) 7.23925i 0.536609i
\(183\) 11.9845 0.885922
\(184\) −16.3832 −1.20778
\(185\) 8.43084i 0.619848i
\(186\) 14.3450 1.05183
\(187\) −4.86360 + 8.60913i −0.355662 + 0.629562i
\(188\) 0.206867 0.0150873
\(189\) −4.64487 −0.337865
\(190\) −0.803089 + 6.16291i −0.0582622 + 0.447104i
\(191\) −11.7414 −0.849581 −0.424791 0.905292i \(-0.639652\pi\)
−0.424791 + 0.905292i \(0.639652\pi\)
\(192\) 8.28066i 0.597605i
\(193\) −19.0146 −1.36870 −0.684351 0.729152i \(-0.739915\pi\)
−0.684351 + 0.729152i \(0.739915\pi\)
\(194\) 13.0876i 0.939637i
\(195\) 5.92831i 0.424535i
\(196\) 0.203958 0.0145684
\(197\) 9.02300i 0.642862i 0.946933 + 0.321431i \(0.104164\pi\)
−0.946933 + 0.321431i \(0.895836\pi\)
\(198\) −7.78656 4.39891i −0.553367 0.312617i
\(199\) −21.1949 −1.50247 −0.751235 0.660035i \(-0.770541\pi\)
−0.751235 + 0.660035i \(0.770541\pi\)
\(200\) 2.80464 0.198318
\(201\) 5.32164 0.375360
\(202\) 5.90549i 0.415509i
\(203\) 1.90188i 0.133486i
\(204\) 0.103496 0.00724618
\(205\) 4.89924 0.342178
\(206\) 5.80346i 0.404346i
\(207\) −11.0472 −0.767835
\(208\) 22.8846 1.58676
\(209\) −8.67776 + 11.5627i −0.600253 + 0.799810i
\(210\) −1.35402 −0.0934365
\(211\) 7.76779 0.534757 0.267378 0.963592i \(-0.413843\pi\)
0.267378 + 0.963592i \(0.413843\pi\)
\(212\) 0.0268203i 0.00184203i
\(213\) −2.49109 −0.170687
\(214\) 6.95226 0.475247
\(215\) 10.7286i 0.731685i
\(216\) 14.4451i 0.982867i
\(217\) −8.61657 −0.584931
\(218\) −27.7264 −1.87787
\(219\) −4.46720 −0.301865
\(220\) −0.0951988 0.0537811i −0.00641830 0.00362592i
\(221\) 16.7845i 1.12905i
\(222\) −12.6581 −0.849554
\(223\) 11.8143i 0.791146i 0.918435 + 0.395573i \(0.129454\pi\)
−0.918435 + 0.395573i \(0.870546\pi\)
\(224\) 0.168168i 0.0112362i
\(225\) 1.89118 0.126078
\(226\) 10.3469i 0.688265i
\(227\) 9.22668 0.612396 0.306198 0.951968i \(-0.400943\pi\)
0.306198 + 0.951968i \(0.400943\pi\)
\(228\) 0.150049 + 0.0195529i 0.00993726 + 0.00129493i
\(229\) −14.4401 −0.954227 −0.477113 0.878842i \(-0.658317\pi\)
−0.477113 + 0.878842i \(0.658317\pi\)
\(230\) −8.32888 −0.549190
\(231\) −2.74227 1.54920i −0.180428 0.101930i
\(232\) 5.91466 0.388317
\(233\) 19.4161i 1.27199i −0.771693 0.635995i \(-0.780590\pi\)
0.771693 0.635995i \(-0.219410\pi\)
\(234\) 15.1809 0.992403
\(235\) −6.27493 −0.409331
\(236\) 0.459591i 0.0299168i
\(237\) 5.94883i 0.386418i
\(238\) −3.83358 −0.248494
\(239\) 14.2248i 0.920123i 0.887887 + 0.460062i \(0.152173\pi\)
−0.887887 + 0.460062i \(0.847827\pi\)
\(240\) 4.28032i 0.276293i
\(241\) −22.9488 −1.47826 −0.739132 0.673560i \(-0.764764\pi\)
−0.739132 + 0.673560i \(0.764764\pi\)
\(242\) −8.09493 13.4336i −0.520362 0.863543i
\(243\) 15.7147i 1.00810i
\(244\) 0.375208i 0.0240202i
\(245\) −6.18669 −0.395253
\(246\) 7.35572i 0.468984i
\(247\) 3.17101 24.3343i 0.201767 1.54836i
\(248\) 26.7967i 1.70159i
\(249\) −15.4177 −0.977056
\(250\) 1.42582 0.0901769
\(251\) 15.0672 0.951031 0.475516 0.879707i \(-0.342261\pi\)
0.475516 + 0.879707i \(0.342261\pi\)
\(252\) 0.0562268i 0.00354196i
\(253\) −16.8683 9.52948i −1.06050 0.599113i
\(254\) −4.32196 −0.271184
\(255\) −3.13937 −0.196595
\(256\) 0.790999 0.0494375
\(257\) 19.8073i 1.23554i 0.786358 + 0.617771i \(0.211964\pi\)
−0.786358 + 0.617771i \(0.788036\pi\)
\(258\) −16.1079 −1.00284
\(259\) 7.60327 0.472444
\(260\) 0.185602 0.0115105
\(261\) 3.98827 0.246868
\(262\) 7.81183i 0.482617i
\(263\) 5.72534i 0.353040i −0.984297 0.176520i \(-0.943516\pi\)
0.984297 0.176520i \(-0.0564840\pi\)
\(264\) 4.81788 8.52820i 0.296520 0.524874i
\(265\) 0.813546i 0.0499757i
\(266\) −5.55795 0.724257i −0.340780 0.0444071i
\(267\) 14.5000 0.887385
\(268\) 0.166608i 0.0101772i
\(269\) 20.6199i 1.25722i −0.777723 0.628608i \(-0.783625\pi\)
0.777723 0.628608i \(-0.216375\pi\)
\(270\) 7.34361i 0.446918i
\(271\) 18.9246i 1.14959i 0.818297 + 0.574795i \(0.194918\pi\)
−0.818297 + 0.574795i \(0.805082\pi\)
\(272\) 12.1187i 0.734802i
\(273\) 5.34638 0.323578
\(274\) 1.79769 0.108602
\(275\) 2.88768 + 1.63135i 0.174134 + 0.0983742i
\(276\) 0.202785i 0.0122062i
\(277\) 2.96097i 0.177907i −0.996036 0.0889537i \(-0.971648\pi\)
0.996036 0.0889537i \(-0.0283523\pi\)
\(278\) 23.3212i 1.39871i
\(279\) 18.0691i 1.08177i
\(280\) 2.52933i 0.151157i
\(281\) −22.1209 −1.31962 −0.659810 0.751433i \(-0.729363\pi\)
−0.659810 + 0.751433i \(0.729363\pi\)
\(282\) 9.42118i 0.561023i
\(283\) 11.3104i 0.672333i −0.941803 0.336166i \(-0.890870\pi\)
0.941803 0.336166i \(-0.109130\pi\)
\(284\) 0.0779902i 0.00462787i
\(285\) −4.55147 0.593103i −0.269606 0.0351324i
\(286\) 23.1800 + 13.0952i 1.37066 + 0.774335i
\(287\) 4.41833i 0.260806i
\(288\) 0.352651 0.0207802
\(289\) 8.11166 0.477156
\(290\) 3.00690 0.176571
\(291\) 9.66557 0.566606
\(292\) 0.139858i 0.00818455i
\(293\) −12.3218 −0.719846 −0.359923 0.932982i \(-0.617197\pi\)
−0.359923 + 0.932982i \(0.617197\pi\)
\(294\) 9.28869i 0.541728i
\(295\) 13.9409i 0.811668i
\(296\) 23.6454i 1.37436i
\(297\) 8.40219 14.8728i 0.487544 0.863009i
\(298\) 25.7188i 1.48985i
\(299\) 32.8867 1.90189
\(300\) 0.0347147i 0.00200426i
\(301\) 9.67548 0.557685
\(302\) −11.5613 −0.665276
\(303\) 4.36136 0.250554
\(304\) 2.28951 17.5697i 0.131312 1.00769i
\(305\) 11.3812i 0.651688i
\(306\) 8.03910i 0.459565i
\(307\) 26.9323 1.53711 0.768553 0.639786i \(-0.220977\pi\)
0.768553 + 0.639786i \(0.220977\pi\)
\(308\) 0.0485020 0.0858540i 0.00276366 0.00489199i
\(309\) 4.28601 0.243823
\(310\) 13.6229i 0.773730i
\(311\) −12.1912 −0.691301 −0.345651 0.938363i \(-0.612342\pi\)
−0.345651 + 0.938363i \(0.612342\pi\)
\(312\) 16.6268i 0.941304i
\(313\) −8.18206 −0.462477 −0.231239 0.972897i \(-0.574278\pi\)
−0.231239 + 0.972897i \(0.574278\pi\)
\(314\) 18.1392 1.02365
\(315\) 1.70554i 0.0960961i
\(316\) 0.186244 0.0104770
\(317\) 19.3644i 1.08762i 0.839210 + 0.543808i \(0.183018\pi\)
−0.839210 + 0.543808i \(0.816982\pi\)
\(318\) −1.22146 −0.0684960
\(319\) 6.08979 + 3.44034i 0.340963 + 0.192622i
\(320\) −7.86382 −0.439601
\(321\) 5.13443i 0.286576i
\(322\) 7.51132i 0.418589i
\(323\) −12.8864 1.67922i −0.717017 0.0934345i
\(324\) 0.00824409 0.000458005
\(325\) −5.62988 −0.312290
\(326\) −34.8145 −1.92820
\(327\) 20.4767i 1.13236i
\(328\) −13.7406 −0.758697
\(329\) 5.65898i 0.311990i
\(330\) 2.44931 4.33556i 0.134830 0.238665i
\(331\) 10.1969i 0.560473i 0.959931 + 0.280237i \(0.0904129\pi\)
−0.959931 + 0.280237i \(0.909587\pi\)
\(332\) 0.482692i 0.0264912i
\(333\) 15.9442i 0.873736i
\(334\) 1.70796 0.0934554
\(335\) 5.05376i 0.276116i
\(336\) 3.86016 0.210589
\(337\) 19.1076 1.04086 0.520428 0.853906i \(-0.325772\pi\)
0.520428 + 0.853906i \(0.325772\pi\)
\(338\) −26.6565 −1.44992
\(339\) −7.64146 −0.415027
\(340\) 0.0982862i 0.00533032i
\(341\) 15.5867 27.5902i 0.844065 1.49409i
\(342\) 1.51878 11.6551i 0.0821263 0.630238i
\(343\) 11.8923i 0.642123i
\(344\) 30.0898i 1.62234i
\(345\) 6.15110i 0.331164i
\(346\) −7.64389 −0.410938
\(347\) 5.65842i 0.303760i 0.988399 + 0.151880i \(0.0485328\pi\)
−0.988399 + 0.151880i \(0.951467\pi\)
\(348\) 0.0732094i 0.00392444i
\(349\) 19.1660i 1.02593i −0.858409 0.512967i \(-0.828546\pi\)
0.858409 0.512967i \(-0.171454\pi\)
\(350\) 1.28586i 0.0687322i
\(351\) 28.9964i 1.54771i
\(352\) 0.538471 + 0.304201i 0.0287006 + 0.0162140i
\(353\) −26.1542 −1.39205 −0.696025 0.718017i \(-0.745050\pi\)
−0.696025 + 0.718017i \(0.745050\pi\)
\(354\) −20.9308 −1.11246
\(355\) 2.36569i 0.125558i
\(356\) 0.453961i 0.0240599i
\(357\) 2.83120i 0.149843i
\(358\) 8.92028i 0.471451i
\(359\) 14.9692i 0.790043i 0.918672 + 0.395022i \(0.129263\pi\)
−0.918672 + 0.395022i \(0.870737\pi\)
\(360\) −5.30406 −0.279549
\(361\) −18.3655 4.86910i −0.966606 0.256269i
\(362\) 9.11242i 0.478938i
\(363\) 9.92106 5.97833i 0.520721 0.313781i
\(364\) 0.167383i 0.00877324i
\(365\) 4.24232i 0.222053i
\(366\) −17.0878 −0.893193
\(367\) 32.8273 1.71357 0.856785 0.515674i \(-0.172459\pi\)
0.856785 + 0.515674i \(0.172459\pi\)
\(368\) 23.7446 1.23778
\(369\) −9.26532 −0.482333
\(370\) 12.0209i 0.624935i
\(371\) 0.733688 0.0380912
\(372\) −0.331680 −0.0171968
\(373\) −0.160453 −0.00830792 −0.00415396 0.999991i \(-0.501322\pi\)
−0.00415396 + 0.999991i \(0.501322\pi\)
\(374\) 6.93463 12.2751i 0.358581 0.634729i
\(375\) 1.05301i 0.0543771i
\(376\) 17.5989 0.907594
\(377\) −11.8728 −0.611479
\(378\) 6.62276 0.340638
\(379\) 4.85119i 0.249189i −0.992208 0.124595i \(-0.960237\pi\)
0.992208 0.124595i \(-0.0397630\pi\)
\(380\) 0.0185687 0.142496i 0.000952552 0.00730989i
\(381\) 3.19188i 0.163525i
\(382\) 16.7412 0.856555
\(383\) 21.5584i 1.10158i 0.834642 + 0.550792i \(0.185674\pi\)
−0.834642 + 0.550792i \(0.814326\pi\)
\(384\) 12.1995i 0.622551i
\(385\) −1.47122 + 2.60422i −0.0749802 + 0.132724i
\(386\) 27.1115 1.37994
\(387\) 20.2897i 1.03138i
\(388\) 0.302607i 0.0153625i
\(389\) −1.78194 −0.0903478 −0.0451739 0.998979i \(-0.514384\pi\)
−0.0451739 + 0.998979i \(0.514384\pi\)
\(390\) 8.45271i 0.428019i
\(391\) 17.4153i 0.880731i
\(392\) 17.3514 0.876379
\(393\) −5.76925 −0.291020
\(394\) 12.8652i 0.648139i
\(395\) −5.64937 −0.284251
\(396\) 0.180038 + 0.101710i 0.00904723 + 0.00511110i
\(397\) −24.5140 −1.23032 −0.615161 0.788402i \(-0.710909\pi\)
−0.615161 + 0.788402i \(0.710909\pi\)
\(398\) 30.2202 1.51480
\(399\) 0.534883 4.10470i 0.0267777 0.205492i
\(400\) −4.06485 −0.203242
\(401\) 13.5931i 0.678808i −0.940641 0.339404i \(-0.889775\pi\)
0.940641 0.339404i \(-0.110225\pi\)
\(402\) −7.58772 −0.378441
\(403\) 53.7903i 2.67949i
\(404\) 0.136544i 0.00679332i
\(405\) −0.250069 −0.0124260
\(406\) 2.71174i 0.134581i
\(407\) −13.7537 + 24.3456i −0.681744 + 1.20676i
\(408\) 8.80478 0.435902
\(409\) −24.0687 −1.19012 −0.595059 0.803682i \(-0.702871\pi\)
−0.595059 + 0.803682i \(0.702871\pi\)
\(410\) −6.98544 −0.344986
\(411\) 1.32764i 0.0654876i
\(412\) 0.134185i 0.00661082i
\(413\) 12.5724 0.618648
\(414\) 15.7514 0.774138
\(415\) 14.6416i 0.718726i
\(416\) −1.04981 −0.0514714
\(417\) 17.2233 0.843431
\(418\) 12.3729 16.4864i 0.605180 0.806375i
\(419\) 36.7457 1.79515 0.897573 0.440865i \(-0.145328\pi\)
0.897573 + 0.440865i \(0.145328\pi\)
\(420\) 0.0313071 0.00152763
\(421\) 5.19903i 0.253385i −0.991942 0.126693i \(-0.959564\pi\)
0.991942 0.126693i \(-0.0404362\pi\)
\(422\) −11.0755 −0.539146
\(423\) 11.8670 0.576993
\(424\) 2.28170i 0.110809i
\(425\) 2.98133i 0.144616i
\(426\) 3.55185 0.172088
\(427\) 10.2640 0.496712
\(428\) −0.160747 −0.00777001
\(429\) −9.67115 + 17.1190i −0.466928 + 0.826515i
\(430\) 15.2971i 0.737690i
\(431\) −16.2337 −0.781949 −0.390974 0.920402i \(-0.627862\pi\)
−0.390974 + 0.920402i \(0.627862\pi\)
\(432\) 20.9358i 1.00727i
\(433\) 38.7358i 1.86153i 0.365624 + 0.930763i \(0.380856\pi\)
−0.365624 + 0.930763i \(0.619144\pi\)
\(434\) 12.2857 0.589732
\(435\) 2.22067i 0.106473i
\(436\) 0.641077 0.0307020
\(437\) 3.29018 25.2489i 0.157391 1.20782i
\(438\) 6.36943 0.304343
\(439\) −33.5838 −1.60287 −0.801434 0.598083i \(-0.795929\pi\)
−0.801434 + 0.598083i \(0.795929\pi\)
\(440\) −8.09889 4.57535i −0.386100 0.218121i
\(441\) 11.7001 0.557148
\(442\) 23.9318i 1.13832i
\(443\) 21.4260 1.01798 0.508991 0.860772i \(-0.330019\pi\)
0.508991 + 0.860772i \(0.330019\pi\)
\(444\) 0.292674 0.0138897
\(445\) 13.7701i 0.652764i
\(446\) 16.8451i 0.797640i
\(447\) −18.9940 −0.898387
\(448\) 7.09190i 0.335061i
\(449\) 2.20285i 0.103959i 0.998648 + 0.0519795i \(0.0165531\pi\)
−0.998648 + 0.0519795i \(0.983447\pi\)
\(450\) −2.69648 −0.127113
\(451\) −14.1474 7.99238i −0.666176 0.376347i
\(452\) 0.239236i 0.0112527i
\(453\) 8.53830i 0.401164i
\(454\) −13.1556 −0.617423
\(455\) 5.07725i 0.238025i
\(456\) 12.7652 + 1.66344i 0.597787 + 0.0778976i
\(457\) 7.87683i 0.368463i 0.982883 + 0.184231i \(0.0589796\pi\)
−0.982883 + 0.184231i \(0.941020\pi\)
\(458\) 20.5890 0.962059
\(459\) 15.3552 0.716719
\(460\) 0.192577 0.00897894
\(461\) 11.1537i 0.519481i −0.965678 0.259741i \(-0.916363\pi\)
0.965678 0.259741i \(-0.0836371\pi\)
\(462\) 3.90998 + 2.20889i 0.181909 + 0.102767i
\(463\) −0.272621 −0.0126698 −0.00633488 0.999980i \(-0.502016\pi\)
−0.00633488 + 0.999980i \(0.502016\pi\)
\(464\) −8.57230 −0.397959
\(465\) 10.0609 0.466563
\(466\) 27.6839i 1.28243i
\(467\) −34.0388 −1.57513 −0.787564 0.616233i \(-0.788658\pi\)
−0.787564 + 0.616233i \(0.788658\pi\)
\(468\) −0.351005 −0.0162252
\(469\) 4.55768 0.210454
\(470\) 8.94693 0.412691
\(471\) 13.3963i 0.617267i
\(472\) 39.0990i 1.79968i
\(473\) −17.5021 + 30.9808i −0.804749 + 1.42450i
\(474\) 8.48197i 0.389590i
\(475\) −0.563246 + 4.32236i −0.0258435 + 0.198323i
\(476\) 0.0886384 0.00406274
\(477\) 1.53856i 0.0704457i
\(478\) 20.2820i 0.927676i
\(479\) 20.1960i 0.922778i −0.887198 0.461389i \(-0.847351\pi\)
0.887198 0.461389i \(-0.152649\pi\)
\(480\) 0.196356i 0.00896240i
\(481\) 47.4646i 2.16420i
\(482\) 32.7209 1.49040
\(483\) 5.54731 0.252411
\(484\) 0.187167 + 0.310605i 0.00850761 + 0.0141184i
\(485\) 9.17901i 0.416797i
\(486\) 22.4063i 1.01637i
\(487\) 5.97405i 0.270710i 0.990797 + 0.135355i \(0.0432175\pi\)
−0.990797 + 0.135355i \(0.956783\pi\)
\(488\) 31.9202i 1.44496i
\(489\) 25.7115i 1.16271i
\(490\) 8.82111 0.398497
\(491\) 0.729652i 0.0329287i 0.999864 + 0.0164644i \(0.00524101\pi\)
−0.999864 + 0.0164644i \(0.994759\pi\)
\(492\) 0.170076i 0.00766761i
\(493\) 6.28729i 0.283165i
\(494\) −4.52129 + 34.6964i −0.203423 + 1.56107i
\(495\) −5.46111 3.08517i −0.245459 0.138668i
\(496\) 38.8373i 1.74385i
\(497\) −2.13347 −0.0956994
\(498\) 21.9829 0.985076
\(499\) −24.6032 −1.10139 −0.550695 0.834706i \(-0.685637\pi\)
−0.550695 + 0.834706i \(0.685637\pi\)
\(500\) −0.0329672 −0.00147434
\(501\) 1.26137i 0.0563541i
\(502\) −21.4831 −0.958838
\(503\) 8.17919i 0.364692i −0.983234 0.182346i \(-0.941631\pi\)
0.983234 0.182346i \(-0.0583691\pi\)
\(504\) 4.78341i 0.213070i
\(505\) 4.14181i 0.184308i
\(506\) 24.0511 + 13.5873i 1.06920 + 0.604031i
\(507\) 19.6866i 0.874311i
\(508\) 0.0999304 0.00443370
\(509\) 12.7190i 0.563758i 0.959450 + 0.281879i \(0.0909577\pi\)
−0.959450 + 0.281879i \(0.909042\pi\)
\(510\) 4.47617 0.198208
\(511\) −3.82589 −0.169248
\(512\) 22.0429 0.974166
\(513\) 22.2620 + 2.90097i 0.982893 + 0.128081i
\(514\) 28.2416i 1.24568i
\(515\) 4.07026i 0.179357i
\(516\) 0.372440 0.0163958
\(517\) 18.1200 + 10.2366i 0.796916 + 0.450206i
\(518\) −10.8409 −0.476322
\(519\) 5.64522i 0.247798i
\(520\) 15.7898 0.692427
\(521\) 6.53428i 0.286272i 0.989703 + 0.143136i \(0.0457186\pi\)
−0.989703 + 0.143136i \(0.954281\pi\)
\(522\) −5.68657 −0.248894
\(523\) 0.662002 0.0289473 0.0144737 0.999895i \(-0.495393\pi\)
0.0144737 + 0.999895i \(0.495393\pi\)
\(524\) 0.180622i 0.00789050i
\(525\) −0.949644 −0.0414459
\(526\) 8.16332i 0.355938i
\(527\) 28.4850 1.24082
\(528\) −6.98270 + 12.3602i −0.303883 + 0.537908i
\(529\) 11.1227 0.483594
\(530\) 1.15997i 0.0503859i
\(531\) 26.3646i 1.14413i
\(532\) 0.128509 + 0.0167460i 0.00557155 + 0.000726029i
\(533\) 27.5821 1.19471
\(534\) −20.6744 −0.894669
\(535\) 4.87597 0.210806
\(536\) 14.1740i 0.612222i
\(537\) 6.58787 0.284287
\(538\) 29.4002i 1.26753i
\(539\) 17.8652 + 10.0927i 0.769507 + 0.434722i
\(540\) 0.169796i 0.00730685i
\(541\) 3.82889i 0.164617i 0.996607 + 0.0823085i \(0.0262293\pi\)
−0.996607 + 0.0823085i \(0.973771\pi\)
\(542\) 26.9832i 1.15903i
\(543\) 6.72976 0.288802
\(544\) 0.555935i 0.0238355i
\(545\) −19.4459 −0.832970
\(546\) −7.62299 −0.326234
\(547\) −14.7797 −0.631936 −0.315968 0.948770i \(-0.602329\pi\)
−0.315968 + 0.948770i \(0.602329\pi\)
\(548\) −0.0415653 −0.00177558
\(549\) 21.5239i 0.918618i
\(550\) −4.11732 2.32602i −0.175563 0.0991817i
\(551\) −1.18782 + 9.11536i −0.0506029 + 0.388327i
\(552\) 17.2516i 0.734277i
\(553\) 5.09483i 0.216654i
\(554\) 4.22181i 0.179368i
\(555\) −8.87774 −0.376839
\(556\) 0.539223i 0.0228681i
\(557\) 33.4642i 1.41792i −0.705247 0.708962i \(-0.749164\pi\)
0.705247 0.708962i \(-0.250836\pi\)
\(558\) 25.7633i 1.09065i
\(559\) 60.4007i 2.55468i
\(560\) 3.66584i 0.154910i
\(561\) 9.06548 + 5.12141i 0.382745 + 0.216226i
\(562\) 31.5404 1.33045
\(563\) −15.6241 −0.658476 −0.329238 0.944247i \(-0.606792\pi\)
−0.329238 + 0.944247i \(0.606792\pi\)
\(564\) 0.217832i 0.00917240i
\(565\) 7.25680i 0.305296i
\(566\) 16.1266i 0.677851i
\(567\) 0.225522i 0.00947105i
\(568\) 6.63490i 0.278394i
\(569\) −2.66835 −0.111863 −0.0559316 0.998435i \(-0.517813\pi\)
−0.0559316 + 0.998435i \(0.517813\pi\)
\(570\) 6.48959 + 0.845659i 0.271819 + 0.0354207i
\(571\) 35.7601i 1.49651i 0.663410 + 0.748256i \(0.269109\pi\)
−0.663410 + 0.748256i \(0.730891\pi\)
\(572\) −0.535958 0.302781i −0.0224095 0.0126599i
\(573\) 12.3638i 0.516507i
\(574\) 6.29975i 0.262946i
\(575\) −5.84146 −0.243606
\(576\) 14.8719 0.619661
\(577\) 23.8081 0.991143 0.495571 0.868567i \(-0.334959\pi\)
0.495571 + 0.868567i \(0.334959\pi\)
\(578\) −11.5658 −0.481073
\(579\) 20.0225i 0.832108i
\(580\) −0.0695241 −0.00288683
\(581\) −13.2044 −0.547809
\(582\) −13.7814 −0.571256
\(583\) −1.32718 + 2.34926i −0.0549662 + 0.0972964i
\(584\) 11.8982i 0.492350i
\(585\) 10.6471 0.440203
\(586\) 17.5686 0.725754
\(587\) 4.18900 0.172898 0.0864492 0.996256i \(-0.472448\pi\)
0.0864492 + 0.996256i \(0.472448\pi\)
\(588\) 0.214769i 0.00885693i
\(589\) 41.2977 + 5.38150i 1.70164 + 0.221741i
\(590\) 19.8772i 0.818330i
\(591\) 9.50128 0.390831
\(592\) 34.2701i 1.40849i
\(593\) 38.4621i 1.57945i −0.613461 0.789725i \(-0.710223\pi\)
0.613461 0.789725i \(-0.289777\pi\)
\(594\) −11.9800 + 21.2060i −0.491546 + 0.870093i
\(595\) −2.68868 −0.110225
\(596\) 0.594659i 0.0243582i
\(597\) 22.3184i 0.913432i
\(598\) −46.8906 −1.91750
\(599\) 42.1022i 1.72025i −0.510086 0.860124i \(-0.670386\pi\)
0.510086 0.860124i \(-0.329614\pi\)
\(600\) 2.95330i 0.120568i
\(601\) 25.0134 1.02032 0.510159 0.860080i \(-0.329587\pi\)
0.510159 + 0.860080i \(0.329587\pi\)
\(602\) −13.7955 −0.562263
\(603\) 9.55754i 0.389213i
\(604\) 0.267314 0.0108769
\(605\) −5.67738 9.42164i −0.230818 0.383044i
\(606\) −6.21852 −0.252610
\(607\) −22.1188 −0.897775 −0.448887 0.893588i \(-0.648180\pi\)
−0.448887 + 0.893588i \(0.648180\pi\)
\(608\) −0.105030 + 0.805998i −0.00425951 + 0.0326875i
\(609\) −2.00269 −0.0811532
\(610\) 16.2276i 0.657037i
\(611\) −35.3271 −1.42918
\(612\) 0.185876i 0.00751361i
\(613\) 17.6194i 0.711642i 0.934554 + 0.355821i \(0.115799\pi\)
−0.934554 + 0.355821i \(0.884201\pi\)
\(614\) −38.4006 −1.54972
\(615\) 5.15893i 0.208028i
\(616\) 4.12623 7.30390i 0.166251 0.294283i
\(617\) 0.650912 0.0262047 0.0131024 0.999914i \(-0.495829\pi\)
0.0131024 + 0.999914i \(0.495829\pi\)
\(618\) −6.11108 −0.245824
\(619\) 4.52383 0.181828 0.0909140 0.995859i \(-0.471021\pi\)
0.0909140 + 0.995859i \(0.471021\pi\)
\(620\) 0.314983i 0.0126500i
\(621\) 30.0861i 1.20731i
\(622\) 17.3825 0.696976
\(623\) 12.4184 0.497533
\(624\) 24.0977i 0.964679i
\(625\) 1.00000 0.0400000
\(626\) 11.6662 0.466273
\(627\) 12.1756 + 9.13774i 0.486248 + 0.364926i
\(628\) −0.419405 −0.0167361
\(629\) −25.1351 −1.00220
\(630\) 2.43179i 0.0968849i
\(631\) 30.6552 1.22036 0.610182 0.792261i \(-0.291096\pi\)
0.610182 + 0.792261i \(0.291096\pi\)
\(632\) 15.8444 0.630258
\(633\) 8.17954i 0.325108i
\(634\) 27.6102i 1.09654i
\(635\) −3.03121 −0.120290
\(636\) 0.0282420 0.00111987
\(637\) −34.8303 −1.38003
\(638\) −8.68295 4.90531i −0.343761 0.194203i
\(639\) 4.47393i 0.176986i
\(640\) 11.5853 0.457951
\(641\) 20.0450i 0.791732i −0.918308 0.395866i \(-0.870445\pi\)
0.918308 0.395866i \(-0.129555\pi\)
\(642\) 7.32078i 0.288928i
\(643\) 4.54366 0.179185 0.0895923 0.995979i \(-0.471444\pi\)
0.0895923 + 0.995979i \(0.471444\pi\)
\(644\) 0.173673i 0.00684369i
\(645\) −11.2973 −0.444831
\(646\) 18.3737 + 2.39427i 0.722903 + 0.0942015i
\(647\) −37.3454 −1.46820 −0.734099 0.679042i \(-0.762395\pi\)
−0.734099 + 0.679042i \(0.762395\pi\)
\(648\) 0.701354 0.0275518
\(649\) −22.7424 + 40.2567i −0.892719 + 1.58021i
\(650\) 8.02721 0.314853
\(651\) 9.07331i 0.355611i
\(652\) 0.804966 0.0315249
\(653\) 20.7486 0.811957 0.405978 0.913883i \(-0.366931\pi\)
0.405978 + 0.913883i \(0.366931\pi\)
\(654\) 29.1961i 1.14166i
\(655\) 5.47883i 0.214076i
\(656\) 19.9147 0.777537
\(657\) 8.02298i 0.313006i
\(658\) 8.06870i 0.314551i
\(659\) 21.3264 0.830759 0.415380 0.909648i \(-0.363649\pi\)
0.415380 + 0.909648i \(0.363649\pi\)
\(660\) −0.0566319 + 0.100245i −0.00220440 + 0.00390203i
\(661\) 47.0683i 1.83075i −0.402608 0.915373i \(-0.631896\pi\)
0.402608 0.915373i \(-0.368104\pi\)
\(662\) 14.5390i 0.565074i
\(663\) −17.6743 −0.686411
\(664\) 41.0643i 1.59360i
\(665\) −3.89807 0.507958i −0.151161 0.0196978i
\(666\) 22.7336i 0.880908i
\(667\) −12.3190 −0.476993
\(668\) −0.0394907 −0.00152794
\(669\) 12.4406 0.480981
\(670\) 7.20576i 0.278383i
\(671\) −18.5668 + 32.8654i −0.716763 + 1.26875i
\(672\) −0.177082 −0.00683108
\(673\) 15.2046 0.586094 0.293047 0.956098i \(-0.405331\pi\)
0.293047 + 0.956098i \(0.405331\pi\)
\(674\) −27.2440 −1.04940
\(675\) 5.15044i 0.198241i
\(676\) 0.616340 0.0237054
\(677\) −16.5878 −0.637522 −0.318761 0.947835i \(-0.603267\pi\)
−0.318761 + 0.947835i \(0.603267\pi\)
\(678\) 10.8954 0.418434
\(679\) 8.27800 0.317680
\(680\) 8.36156i 0.320651i
\(681\) 9.71577i 0.372309i
\(682\) −22.2238 + 39.3386i −0.850993 + 1.50635i
\(683\) 11.8388i 0.452998i −0.974011 0.226499i \(-0.927272\pi\)
0.974011 0.226499i \(-0.0727280\pi\)
\(684\) −0.0351166 + 0.269485i −0.00134272 + 0.0103040i
\(685\) 1.26081 0.0481730
\(686\) 16.9563i 0.647393i
\(687\) 15.2055i 0.580126i
\(688\) 43.6101i 1.66262i
\(689\) 4.58017i 0.174490i
\(690\) 8.77037i 0.333882i
\(691\) 32.1810 1.22422 0.612112 0.790771i \(-0.290320\pi\)
0.612112 + 0.790771i \(0.290320\pi\)
\(692\) 0.176739 0.00671859
\(693\) 2.78233 4.92504i 0.105692 0.187087i
\(694\) 8.06790i 0.306253i
\(695\) 16.3563i 0.620431i
\(696\) 6.22818i 0.236079i
\(697\) 14.6063i 0.553251i
\(698\) 27.3273i 1.03435i
\(699\) −20.4453 −0.773312
\(700\) 0.0297311i 0.00112373i
\(701\) 4.01817i 0.151764i −0.997117 0.0758820i \(-0.975823\pi\)
0.997117 0.0758820i \(-0.0241772\pi\)
\(702\) 41.3437i 1.56042i
\(703\) −36.4411 4.74864i −1.37440 0.179098i
\(704\) 22.7082 + 12.8287i 0.855847 + 0.483498i
\(705\) 6.60755i 0.248855i
\(706\) 37.2913 1.40348
\(707\) 3.73525 0.140479
\(708\) 0.483953 0.0181881
\(709\) 4.15961 0.156218 0.0781088 0.996945i \(-0.475112\pi\)
0.0781088 + 0.996945i \(0.475112\pi\)
\(710\) 3.37305i 0.126588i
\(711\) 10.6840 0.400679
\(712\) 38.6201i 1.44735i
\(713\) 55.8119i 2.09017i
\(714\) 4.03679i 0.151073i
\(715\) 16.2573 + 9.18432i 0.607988 + 0.343474i
\(716\) 0.206251i 0.00770795i
\(717\) 14.9788 0.559393
\(718\) 21.3434i 0.796528i
\(719\) 34.8816 1.30086 0.650432 0.759565i \(-0.274588\pi\)
0.650432 + 0.759565i \(0.274588\pi\)
\(720\) 7.68734 0.286490
\(721\) 3.67072 0.136705
\(722\) 26.1859 + 6.94247i 0.974540 + 0.258372i
\(723\) 24.1653i 0.898717i
\(724\) 0.210693i 0.00783035i
\(725\) 2.10889 0.0783221
\(726\) −14.1457 + 8.52403i −0.524995 + 0.316356i
\(727\) −4.49125 −0.166571 −0.0832856 0.996526i \(-0.526541\pi\)
−0.0832856 + 0.996526i \(0.526541\pi\)
\(728\) 14.2398i 0.527764i
\(729\) −15.7974 −0.585091
\(730\) 6.04880i 0.223876i
\(731\) −31.9855 −1.18303
\(732\) 0.395096 0.0146032
\(733\) 32.7845i 1.21092i 0.795874 + 0.605462i \(0.207012\pi\)
−0.795874 + 0.605462i \(0.792988\pi\)
\(734\) −46.8058 −1.72763
\(735\) 6.51463i 0.240296i
\(736\) −1.08927 −0.0401510
\(737\) −8.24446 + 14.5936i −0.303689 + 0.537563i
\(738\) 13.2107 0.486292
\(739\) 40.4424i 1.48770i 0.668348 + 0.743849i \(0.267002\pi\)
−0.668348 + 0.743849i \(0.732998\pi\)
\(740\) 0.277941i 0.0102173i
\(741\) −25.6242 3.33910i −0.941330 0.122665i
\(742\) −1.04611 −0.0384038
\(743\) 28.7094 1.05325 0.526623 0.850099i \(-0.323458\pi\)
0.526623 + 0.850099i \(0.323458\pi\)
\(744\) −28.2172 −1.03449
\(745\) 18.0379i 0.660857i
\(746\) 0.228777 0.00837611
\(747\) 27.6898i 1.01312i
\(748\) −0.160339 + 0.283819i −0.00586259 + 0.0103775i
\(749\) 4.39734i 0.160675i
\(750\) 1.50140i 0.0548234i
\(751\) 1.48823i 0.0543064i −0.999631 0.0271532i \(-0.991356\pi\)
0.999631 0.0271532i \(-0.00864420\pi\)
\(752\) −25.5066 −0.930131
\(753\) 15.8658i 0.578184i
\(754\) 16.9285 0.616498
\(755\) −8.10849 −0.295098
\(756\) −0.153129 −0.00556923
\(757\) 16.7554 0.608987 0.304493 0.952514i \(-0.401513\pi\)
0.304493 + 0.952514i \(0.401513\pi\)
\(758\) 6.91694i 0.251234i
\(759\) −10.0346 + 17.7624i −0.364233 + 0.644735i
\(760\) 1.57970 12.1226i 0.0573018 0.439734i
\(761\) 13.9024i 0.503962i −0.967732 0.251981i \(-0.918918\pi\)
0.967732 0.251981i \(-0.0810820\pi\)
\(762\) 4.55105i 0.164867i
\(763\) 17.5371i 0.634885i
\(764\) −0.387083 −0.0140042
\(765\) 5.63822i 0.203850i
\(766\) 30.7385i 1.11063i
\(767\) 78.4853i 2.83394i
\(768\) 0.832928i 0.0300557i
\(769\) 31.5810i 1.13884i −0.822047 0.569420i \(-0.807168\pi\)
0.822047 0.569420i \(-0.192832\pi\)
\(770\) 2.09769 3.71316i 0.0755957 0.133813i
\(771\) 20.8572 0.751153
\(772\) −0.626859 −0.0225612
\(773\) 43.0045i 1.54677i −0.633939 0.773383i \(-0.718563\pi\)
0.633939 0.773383i \(-0.281437\pi\)
\(774\) 28.9294i 1.03985i
\(775\) 9.55444i 0.343206i
\(776\) 25.7438i 0.924149i
\(777\) 8.00630i 0.287224i
\(778\) 2.54073 0.0910894
\(779\) 2.75948 21.1762i 0.0988686 0.758718i
\(780\) 0.195440i 0.00699787i
\(781\) 3.85927 6.83135i 0.138096 0.244445i
\(782\) 24.8312i 0.887960i
\(783\) 10.8617i 0.388166i
\(784\) −25.1479 −0.898140
\(785\) 12.7219 0.454064
\(786\) 8.22592 0.293409
\(787\) 37.5328 1.33790 0.668950 0.743307i \(-0.266744\pi\)
0.668950 + 0.743307i \(0.266744\pi\)
\(788\) 0.297463i 0.0105967i
\(789\) −6.02883 −0.214632
\(790\) 8.05500 0.286584
\(791\) −6.54447 −0.232694
\(792\) 15.3164 + 8.65279i 0.544246 + 0.307464i
\(793\) 64.0750i 2.27537i
\(794\) 34.9526 1.24042
\(795\) −0.856670 −0.0303830
\(796\) −0.698738 −0.0247661
\(797\) 0.454063i 0.0160837i 0.999968 + 0.00804187i \(0.00255984\pi\)
−0.999968 + 0.00804187i \(0.997440\pi\)
\(798\) −0.762648 + 5.85257i −0.0269975 + 0.207179i
\(799\) 18.7076i 0.661829i
\(800\) 0.186472 0.00659278
\(801\) 26.0416i 0.920135i
\(802\) 19.3814i 0.684380i
\(803\) 6.92072 12.2505i 0.244227 0.432310i
\(804\) 0.175440 0.00618729
\(805\) 5.26806i 0.185675i
\(806\) 76.6954i 2.70148i
\(807\) −21.7129 −0.764329
\(808\) 11.6163i 0.408660i
\(809\) 2.11976i 0.0745266i 0.999305 + 0.0372633i \(0.0118640\pi\)
−0.999305 + 0.0372633i \(0.988136\pi\)
\(810\) 0.356554 0.0125280
\(811\) −54.9435 −1.92933 −0.964663 0.263486i \(-0.915128\pi\)
−0.964663 + 0.263486i \(0.915128\pi\)
\(812\) 0.0626996i 0.00220033i
\(813\) 19.9278 0.698898
\(814\) 19.6103 34.7124i 0.687340 1.21667i
\(815\) −24.4172 −0.855296
\(816\) −12.7610 −0.446726
\(817\) −46.3728 6.04285i −1.62238 0.211412i
\(818\) 34.3176 1.19989
\(819\) 9.60197i 0.335520i
\(820\) 0.161514 0.00564032
\(821\) 45.3581i 1.58301i −0.611163 0.791505i \(-0.709298\pi\)
0.611163 0.791505i \(-0.290702\pi\)
\(822\) 1.89298i 0.0660252i
\(823\) 18.0345 0.628642 0.314321 0.949317i \(-0.398223\pi\)
0.314321 + 0.949317i \(0.398223\pi\)
\(824\) 11.4156i 0.397681i
\(825\) 1.71783 3.04075i 0.0598070 0.105865i
\(826\) −17.9260 −0.623726
\(827\) −1.68723 −0.0586707 −0.0293353 0.999570i \(-0.509339\pi\)
−0.0293353 + 0.999570i \(0.509339\pi\)
\(828\) −0.364196 −0.0126567
\(829\) 29.3844i 1.02056i −0.860008 0.510280i \(-0.829542\pi\)
0.860008 0.510280i \(-0.170458\pi\)
\(830\) 20.8763i 0.724626i
\(831\) −3.11792 −0.108160
\(832\) −44.2724 −1.53487
\(833\) 18.4446i 0.639066i
\(834\) −24.5574 −0.850354
\(835\) 1.19788 0.0414543
\(836\) −0.286082 + 0.381191i −0.00989434 + 0.0131838i
\(837\) −49.2096 −1.70093
\(838\) −52.3929 −1.80988
\(839\) 16.3384i 0.564066i 0.959405 + 0.282033i \(0.0910087\pi\)
−0.959405 + 0.282033i \(0.908991\pi\)
\(840\) 2.66341 0.0918963
\(841\) −24.5526 −0.846641
\(842\) 7.41289i 0.255465i
\(843\) 23.2934i 0.802268i
\(844\) 0.256082 0.00881472
\(845\) −18.6956 −0.643147
\(846\) −16.9202 −0.581729
\(847\) 8.49681 5.12009i 0.291954 0.175928i
\(848\) 3.30694i 0.113561i
\(849\) −11.9099 −0.408748
\(850\) 4.25085i 0.145803i
\(851\) 49.2484i 1.68821i
\(852\) −0.0821243 −0.00281353
\(853\) 13.4324i 0.459915i 0.973201 + 0.229957i \(0.0738587\pi\)
−0.973201 + 0.229957i \(0.926141\pi\)
\(854\) −14.6347 −0.500789
\(855\) 1.06520 8.17433i 0.0364290 0.279556i
\(856\) −13.6753 −0.467413
\(857\) −35.7851 −1.22240 −0.611198 0.791478i \(-0.709312\pi\)
−0.611198 + 0.791478i \(0.709312\pi\)
\(858\) 13.7893 24.4087i 0.470760 0.833300i
\(859\) 2.41890 0.0825317 0.0412658 0.999148i \(-0.486861\pi\)
0.0412658 + 0.999148i \(0.486861\pi\)
\(860\) 0.353692i 0.0120608i
\(861\) 4.65253 0.158558
\(862\) 23.1463 0.788367
\(863\) 33.1469i 1.12833i 0.825661 + 0.564167i \(0.190803\pi\)
−0.825661 + 0.564167i \(0.809197\pi\)
\(864\) 0.960413i 0.0326739i
\(865\) −5.36104 −0.182281
\(866\) 55.2304i 1.87680i
\(867\) 8.54164i 0.290089i
\(868\) −0.284064 −0.00964177
\(869\) 16.3136 + 9.21611i 0.553400 + 0.312635i
\(870\) 3.16628i 0.107347i
\(871\) 28.4521i 0.964061i
\(872\) 54.5387 1.84691
\(873\) 17.3591i 0.587517i
\(874\) −4.69121 + 36.0004i −0.158683 + 1.21773i
\(875\) 0.901840i 0.0304877i
\(876\) −0.147271 −0.00497583
\(877\) −23.3683 −0.789090 −0.394545 0.918877i \(-0.629098\pi\)
−0.394545 + 0.918877i \(0.629098\pi\)
\(878\) 47.8846 1.61603
\(879\) 12.9749i 0.437633i
\(880\) 11.7380 + 6.63120i 0.395687 + 0.223538i
\(881\) −27.6215 −0.930590 −0.465295 0.885156i \(-0.654052\pi\)
−0.465295 + 0.885156i \(0.654052\pi\)
\(882\) −16.6823 −0.561721
\(883\) 19.3375 0.650758 0.325379 0.945584i \(-0.394508\pi\)
0.325379 + 0.945584i \(0.394508\pi\)
\(884\) 0.553340i 0.0186108i
\(885\) −14.6798 −0.493457
\(886\) −30.5497 −1.02634
\(887\) 57.9130 1.94453 0.972263 0.233888i \(-0.0751451\pi\)
0.972263 + 0.233888i \(0.0751451\pi\)
\(888\) 24.8988 0.835550
\(889\) 2.73366i 0.0916841i
\(890\) 19.6337i 0.658122i
\(891\) 0.722120 + 0.407951i 0.0241919 + 0.0136669i
\(892\) 0.389486i 0.0130409i
\(893\) −3.53433 + 27.1225i −0.118272 + 0.907619i
\(894\) 27.0821 0.905761
\(895\) 6.25624i 0.209123i
\(896\) 10.4481i 0.349047i
\(897\) 34.6300i 1.15626i
\(898\) 3.14088i 0.104812i
\(899\) 20.1492i 0.672014i
\(900\) 0.0623468 0.00207823
\(901\) −2.42545 −0.0808035
\(902\) 20.1717 + 11.3957i 0.671644 + 0.379436i
\(903\) 10.1884i 0.339047i
\(904\) 20.3527i 0.676920i
\(905\) 6.39099i 0.212444i
\(906\) 12.1741i 0.404457i
\(907\) 2.95496i 0.0981179i 0.998796 + 0.0490590i \(0.0156222\pi\)
−0.998796 + 0.0490590i \(0.984378\pi\)
\(908\) 0.304178 0.0100945
\(909\) 7.83290i 0.259801i
\(910\) 7.23925i 0.239979i
\(911\) 58.9818i 1.95415i 0.212888 + 0.977077i \(0.431713\pi\)
−0.212888 + 0.977077i \(0.568287\pi\)
\(912\) −18.5010 2.41087i −0.612631 0.0798319i
\(913\) 23.8856 42.2802i 0.790497 1.39927i
\(914\) 11.2310i 0.371487i
\(915\) −11.9845 −0.396196
\(916\) −0.476049 −0.0157291
\(917\) −4.94102 −0.163167
\(918\) −21.8938 −0.722602
\(919\) 7.25820i 0.239426i 0.992809 + 0.119713i \(0.0381974\pi\)
−0.992809 + 0.119713i \(0.961803\pi\)
\(920\) 16.3832 0.540138
\(921\) 28.3599i 0.934490i
\(922\) 15.9032i 0.523745i
\(923\) 13.3186i 0.438386i
\(924\) −0.0904049 0.0510729i −0.00297410 0.00168018i
\(925\) 8.43084i 0.277204i
\(926\) 0.388708 0.0127737
\(927\) 7.69757i 0.252821i
\(928\) 0.393248 0.0129090
\(929\) −39.9341 −1.31020 −0.655098 0.755544i \(-0.727373\pi\)
−0.655098 + 0.755544i \(0.727373\pi\)
\(930\) −14.3450 −0.470392
\(931\) −3.48463 + 26.7411i −0.114204 + 0.876403i
\(932\) 0.640095i 0.0209670i
\(933\) 12.8375i 0.420280i
\(934\) 48.5332 1.58806
\(935\) 4.86360 8.60913i 0.159057 0.281549i
\(936\) −29.8612 −0.976045
\(937\) 36.7081i 1.19920i −0.800299 0.599601i \(-0.795326\pi\)
0.800299 0.599601i \(-0.204674\pi\)
\(938\) −6.49844 −0.212182
\(939\) 8.61577i 0.281165i
\(940\) −0.206867 −0.00674726
\(941\) 22.2948 0.726790 0.363395 0.931635i \(-0.381618\pi\)
0.363395 + 0.931635i \(0.381618\pi\)
\(942\) 19.1007i 0.622333i
\(943\) 28.6187 0.931953
\(944\) 56.6674i 1.84437i
\(945\) 4.64487 0.151098
\(946\) 24.9549 44.1730i 0.811354 1.43619i
\(947\) −50.9261 −1.65487 −0.827437 0.561558i \(-0.810202\pi\)
−0.827437 + 0.561558i \(0.810202\pi\)
\(948\) 0.196116i 0.00636956i
\(949\) 23.8838i 0.775300i
\(950\) 0.803089 6.16291i 0.0260556 0.199951i
\(951\) 20.3909 0.661220
\(952\) 7.54078 0.244398
\(953\) −41.5830 −1.34701 −0.673504 0.739184i \(-0.735211\pi\)
−0.673504 + 0.739184i \(0.735211\pi\)
\(954\) 2.19371i 0.0710240i
\(955\) 11.7414 0.379944
\(956\) 0.468951i 0.0151669i
\(957\) 3.62270 6.41259i 0.117105 0.207290i
\(958\) 28.7959i 0.930353i
\(959\) 1.13705i 0.0367171i
\(960\) 8.28066i 0.267257i
\(961\) −60.2873 −1.94475
\(962\) 67.6761i 2.18196i
\(963\) −9.22131 −0.297153
\(964\) −0.756559 −0.0243671
\(965\) 19.0146 0.612102
\(966\) −7.90947 −0.254483
\(967\) 33.7443i 1.08514i 0.840010 + 0.542571i \(0.182549\pi\)
−0.840010 + 0.542571i \(0.817451\pi\)
\(968\) 15.9230 + 26.4243i 0.511785 + 0.849309i
\(969\) −1.76824 + 13.5695i −0.0568039 + 0.435914i
\(970\) 13.0876i 0.420219i
\(971\) 56.8920i 1.82575i −0.408239 0.912875i \(-0.633857\pi\)
0.408239 0.912875i \(-0.366143\pi\)
\(972\) 0.518069i 0.0166171i
\(973\) 14.7508 0.472889
\(974\) 8.51792i 0.272932i
\(975\) 5.92831i 0.189858i
\(976\) 46.2630i 1.48084i
\(977\) 43.1130i 1.37931i 0.724140 + 0.689653i \(0.242237\pi\)
−0.724140 + 0.689653i \(0.757763\pi\)
\(978\) 36.6600i 1.17226i
\(979\) −22.4638 + 39.7635i −0.717947 + 1.27085i
\(980\) −0.203958 −0.00651519
\(981\) 36.7756 1.17415
\(982\) 1.04035i 0.0331990i
\(983\) 17.8759i 0.570154i 0.958505 + 0.285077i \(0.0920191\pi\)
−0.958505 + 0.285077i \(0.907981\pi\)
\(984\) 14.4689i 0.461253i
\(985\) 9.02300i 0.287497i
\(986\) 8.96456i 0.285490i
\(987\) −5.95895 −0.189675
\(988\) 0.104539 0.802236i 0.00332584 0.0255225i
\(989\) 62.6707i 1.99281i
\(990\) 7.78656 + 4.39891i 0.247473 + 0.139806i
\(991\) 42.8471i 1.36108i −0.732710 0.680541i \(-0.761745\pi\)
0.732710 0.680541i \(-0.238255\pi\)
\(992\) 1.78163i 0.0565669i
\(993\) 10.7374 0.340742
\(994\) 3.04195 0.0964849
\(995\) 21.1949 0.671925
\(996\) −0.508278 −0.0161054
\(997\) 31.9958i 1.01332i −0.862147 0.506658i \(-0.830881\pi\)
0.862147 0.506658i \(-0.169119\pi\)
\(998\) 35.0798 1.11043
\(999\) 43.4226 1.37383
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.f.a.626.14 yes 40
11.10 odd 2 inner 1045.2.f.a.626.28 yes 40
19.18 odd 2 inner 1045.2.f.a.626.27 yes 40
209.208 even 2 inner 1045.2.f.a.626.13 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.f.a.626.13 40 209.208 even 2 inner
1045.2.f.a.626.14 yes 40 1.1 even 1 trivial
1045.2.f.a.626.27 yes 40 19.18 odd 2 inner
1045.2.f.a.626.28 yes 40 11.10 odd 2 inner