Properties

Label 1815.2.c.d.364.2
Level $1815$
Weight $2$
Character 1815.364
Analytic conductor $14.493$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1815,2,Mod(364,1815)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1815.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.c (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: \(14.4928479669\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 364.2
Root \(-0.854638 + 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 1815.364
Dual form 1815.2.c.d.364.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.53919i q^{2} +1.00000i q^{3} -0.369102 q^{4} +(2.17009 - 0.539189i) q^{5} +1.53919 q^{6} -0.290725i q^{7} -2.51026i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.53919i q^{2} +1.00000i q^{3} -0.369102 q^{4} +(2.17009 - 0.539189i) q^{5} +1.53919 q^{6} -0.290725i q^{7} -2.51026i q^{8} -1.00000 q^{9} +(-0.829914 - 3.34017i) q^{10} -0.369102i q^{12} +6.97107i q^{13} -0.447480 q^{14} +(0.539189 + 2.17009i) q^{15} -4.60197 q^{16} -4.78765i q^{17} +1.53919i q^{18} +7.75872 q^{19} +(-0.800984 + 0.199016i) q^{20} +0.290725 q^{21} -4.00000i q^{23} +2.51026 q^{24} +(4.41855 - 2.34017i) q^{25} +10.7298 q^{26} -1.00000i q^{27} +0.107307i q^{28} -7.41855 q^{29} +(3.34017 - 0.829914i) q^{30} +6.34017 q^{31} +2.06278i q^{32} -7.36910 q^{34} +(-0.156755 - 0.630898i) q^{35} +0.369102 q^{36} -3.41855i q^{37} -11.9421i q^{38} -6.97107 q^{39} +(-1.35350 - 5.44748i) q^{40} +7.41855 q^{41} -0.447480i q^{42} +0.290725i q^{43} +(-2.17009 + 0.539189i) q^{45} -6.15676 q^{46} +5.26180i q^{47} -4.60197i q^{48} +6.91548 q^{49} +(-3.60197 - 6.80098i) q^{50} +4.78765 q^{51} -2.57304i q^{52} -5.75872i q^{53} -1.53919 q^{54} -0.729794 q^{56} +7.75872i q^{57} +11.4186i q^{58} -3.60197 q^{59} +(-0.199016 - 0.800984i) q^{60} +6.68035 q^{61} -9.75872i q^{62} +0.290725i q^{63} -6.02893 q^{64} +(3.75872 + 15.1278i) q^{65} +6.15676i q^{67} +1.76713i q^{68} +4.00000 q^{69} +(-0.971071 + 0.241276i) q^{70} -5.07838 q^{71} +2.51026i q^{72} -1.12783i q^{73} -5.26180 q^{74} +(2.34017 + 4.41855i) q^{75} -2.86376 q^{76} +10.7298i q^{78} -0.921622 q^{79} +(-9.98667 + 2.48133i) q^{80} +1.00000 q^{81} -11.4186i q^{82} +1.70928i q^{83} -0.107307 q^{84} +(-2.58145 - 10.3896i) q^{85} +0.447480 q^{86} -7.41855i q^{87} -4.34017 q^{89} +(0.829914 + 3.34017i) q^{90} +2.02666 q^{91} +1.47641i q^{92} +6.34017i q^{93} +8.09890 q^{94} +(16.8371 - 4.18342i) q^{95} -2.06278 q^{96} +4.68035i q^{97} -10.6442i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 10 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 10 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9} - 16 q^{10} - 4 q^{14} + 10 q^{16} - 4 q^{19} + 14 q^{20} + 16 q^{21} - 18 q^{24} - 2 q^{25} - 16 q^{26} - 16 q^{29} - 2 q^{30} + 16 q^{31} - 52 q^{34} + 12 q^{35} + 10 q^{36} - 12 q^{39} + 12 q^{40} + 16 q^{41} - 2 q^{45} - 24 q^{46} - 22 q^{49} + 16 q^{50} + 8 q^{51} - 6 q^{54} + 76 q^{56} + 16 q^{59} - 20 q^{60} - 4 q^{61} - 66 q^{64} - 28 q^{65} + 24 q^{69} + 24 q^{70} - 24 q^{71} - 16 q^{74} - 8 q^{75} + 36 q^{76} - 12 q^{79} - 58 q^{80} + 6 q^{81} - 24 q^{84} - 44 q^{85} + 4 q^{86} - 4 q^{89} + 16 q^{90} + 16 q^{91} - 24 q^{94} + 44 q^{95} + 22 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).

\(n\) \(727\) \(1211\) \(1696\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.53919i 1.08837i −0.838965 0.544185i \(-0.816839\pi\)
0.838965 0.544185i \(-0.183161\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −0.369102 −0.184551
\(5\) 2.17009 0.539189i 0.970492 0.241133i
\(6\) 1.53919 0.628371
\(7\) 0.290725i 0.109884i −0.998490 0.0549418i \(-0.982503\pi\)
0.998490 0.0549418i \(-0.0174973\pi\)
\(8\) 2.51026i 0.887511i
\(9\) −1.00000 −0.333333
\(10\) −0.829914 3.34017i −0.262442 1.05626i
\(11\) 0 0
\(12\) 0.369102i 0.106551i
\(13\) 6.97107i 1.93343i 0.255861 + 0.966714i \(0.417641\pi\)
−0.255861 + 0.966714i \(0.582359\pi\)
\(14\) −0.447480 −0.119594
\(15\) 0.539189 + 2.17009i 0.139218 + 0.560314i
\(16\) −4.60197 −1.15049
\(17\) 4.78765i 1.16118i −0.814197 0.580588i \(-0.802823\pi\)
0.814197 0.580588i \(-0.197177\pi\)
\(18\) 1.53919i 0.362790i
\(19\) 7.75872 1.77997 0.889987 0.455987i \(-0.150714\pi\)
0.889987 + 0.455987i \(0.150714\pi\)
\(20\) −0.800984 + 0.199016i −0.179105 + 0.0445013i
\(21\) 0.290725 0.0634413
\(22\) 0 0
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) 2.51026 0.512405
\(25\) 4.41855 2.34017i 0.883710 0.468035i
\(26\) 10.7298 2.10429
\(27\) 1.00000i 0.192450i
\(28\) 0.107307i 0.0202791i
\(29\) −7.41855 −1.37759 −0.688795 0.724956i \(-0.741860\pi\)
−0.688795 + 0.724956i \(0.741860\pi\)
\(30\) 3.34017 0.829914i 0.609829 0.151521i
\(31\) 6.34017 1.13873 0.569364 0.822085i \(-0.307189\pi\)
0.569364 + 0.822085i \(0.307189\pi\)
\(32\) 2.06278i 0.364651i
\(33\) 0 0
\(34\) −7.36910 −1.26379
\(35\) −0.156755 0.630898i −0.0264965 0.106641i
\(36\) 0.369102 0.0615171
\(37\) 3.41855i 0.562006i −0.959707 0.281003i \(-0.909333\pi\)
0.959707 0.281003i \(-0.0906671\pi\)
\(38\) 11.9421i 1.93727i
\(39\) −6.97107 −1.11626
\(40\) −1.35350 5.44748i −0.214008 0.861322i
\(41\) 7.41855 1.15858 0.579291 0.815120i \(-0.303329\pi\)
0.579291 + 0.815120i \(0.303329\pi\)
\(42\) 0.447480i 0.0690477i
\(43\) 0.290725i 0.0443351i 0.999754 + 0.0221675i \(0.00705673\pi\)
−0.999754 + 0.0221675i \(0.992943\pi\)
\(44\) 0 0
\(45\) −2.17009 + 0.539189i −0.323497 + 0.0803775i
\(46\) −6.15676 −0.907764
\(47\) 5.26180i 0.767512i 0.923435 + 0.383756i \(0.125370\pi\)
−0.923435 + 0.383756i \(0.874630\pi\)
\(48\) 4.60197i 0.664237i
\(49\) 6.91548 0.987926
\(50\) −3.60197 6.80098i −0.509395 0.961804i
\(51\) 4.78765 0.670406
\(52\) 2.57304i 0.356816i
\(53\) 5.75872i 0.791022i −0.918461 0.395511i \(-0.870568\pi\)
0.918461 0.395511i \(-0.129432\pi\)
\(54\) −1.53919 −0.209457
\(55\) 0 0
\(56\) −0.729794 −0.0975229
\(57\) 7.75872i 1.02767i
\(58\) 11.4186i 1.49933i
\(59\) −3.60197 −0.468936 −0.234468 0.972124i \(-0.575335\pi\)
−0.234468 + 0.972124i \(0.575335\pi\)
\(60\) −0.199016 0.800984i −0.0256928 0.103407i
\(61\) 6.68035 0.855331 0.427665 0.903937i \(-0.359336\pi\)
0.427665 + 0.903937i \(0.359336\pi\)
\(62\) 9.75872i 1.23936i
\(63\) 0.290725i 0.0366279i
\(64\) −6.02893 −0.753616
\(65\) 3.75872 + 15.1278i 0.466212 + 1.87638i
\(66\) 0 0
\(67\) 6.15676i 0.752167i 0.926586 + 0.376084i \(0.122729\pi\)
−0.926586 + 0.376084i \(0.877271\pi\)
\(68\) 1.76713i 0.214296i
\(69\) 4.00000 0.481543
\(70\) −0.971071 + 0.241276i −0.116065 + 0.0288380i
\(71\) −5.07838 −0.602693 −0.301346 0.953515i \(-0.597436\pi\)
−0.301346 + 0.953515i \(0.597436\pi\)
\(72\) 2.51026i 0.295837i
\(73\) 1.12783i 0.132002i −0.997820 0.0660010i \(-0.978976\pi\)
0.997820 0.0660010i \(-0.0210241\pi\)
\(74\) −5.26180 −0.611671
\(75\) 2.34017 + 4.41855i 0.270220 + 0.510210i
\(76\) −2.86376 −0.328496
\(77\) 0 0
\(78\) 10.7298i 1.21491i
\(79\) −0.921622 −0.103691 −0.0518453 0.998655i \(-0.516510\pi\)
−0.0518453 + 0.998655i \(0.516510\pi\)
\(80\) −9.98667 + 2.48133i −1.11654 + 0.277421i
\(81\) 1.00000 0.111111
\(82\) 11.4186i 1.26097i
\(83\) 1.70928i 0.187617i 0.995590 + 0.0938087i \(0.0299042\pi\)
−0.995590 + 0.0938087i \(0.970096\pi\)
\(84\) −0.107307 −0.0117082
\(85\) −2.58145 10.3896i −0.279997 1.12691i
\(86\) 0.447480 0.0482530
\(87\) 7.41855i 0.795352i
\(88\) 0 0
\(89\) −4.34017 −0.460057 −0.230029 0.973184i \(-0.573882\pi\)
−0.230029 + 0.973184i \(0.573882\pi\)
\(90\) 0.829914 + 3.34017i 0.0874806 + 0.352085i
\(91\) 2.02666 0.212452
\(92\) 1.47641i 0.153926i
\(93\) 6.34017i 0.657445i
\(94\) 8.09890 0.835337
\(95\) 16.8371 4.18342i 1.72745 0.429210i
\(96\) −2.06278 −0.210532
\(97\) 4.68035i 0.475217i 0.971361 + 0.237609i \(0.0763635\pi\)
−0.971361 + 0.237609i \(0.923636\pi\)
\(98\) 10.6442i 1.07523i
\(99\) 0 0
\(100\) −1.63090 + 0.863763i −0.163090 + 0.0863763i
\(101\) 8.58145 0.853886 0.426943 0.904279i \(-0.359590\pi\)
0.426943 + 0.904279i \(0.359590\pi\)
\(102\) 7.36910i 0.729650i
\(103\) 6.73820i 0.663935i −0.943291 0.331968i \(-0.892288\pi\)
0.943291 0.331968i \(-0.107712\pi\)
\(104\) 17.4992 1.71594
\(105\) 0.630898 0.156755i 0.0615693 0.0152978i
\(106\) −8.86376 −0.860925
\(107\) 12.2329i 1.18260i −0.806453 0.591298i \(-0.798616\pi\)
0.806453 0.591298i \(-0.201384\pi\)
\(108\) 0.369102i 0.0355169i
\(109\) −6.31351 −0.604725 −0.302362 0.953193i \(-0.597775\pi\)
−0.302362 + 0.953193i \(0.597775\pi\)
\(110\) 0 0
\(111\) 3.41855 0.324474
\(112\) 1.33791i 0.126420i
\(113\) 16.4969i 1.55190i 0.630794 + 0.775950i \(0.282729\pi\)
−0.630794 + 0.775950i \(0.717271\pi\)
\(114\) 11.9421 1.11848
\(115\) −2.15676 8.68035i −0.201118 0.809446i
\(116\) 2.73820 0.254236
\(117\) 6.97107i 0.644476i
\(118\) 5.54411i 0.510377i
\(119\) −1.39189 −0.127594
\(120\) 5.44748 1.35350i 0.497285 0.123557i
\(121\) 0 0
\(122\) 10.2823i 0.930917i
\(123\) 7.41855i 0.668908i
\(124\) −2.34017 −0.210154
\(125\) 8.32684 7.46081i 0.744775 0.667315i
\(126\) 0.447480 0.0398647
\(127\) 4.87217i 0.432336i −0.976356 0.216168i \(-0.930644\pi\)
0.976356 0.216168i \(-0.0693558\pi\)
\(128\) 13.4052i 1.18487i
\(129\) −0.290725 −0.0255969
\(130\) 23.2846 5.78539i 2.04219 0.507412i
\(131\) 8.68035 0.758405 0.379203 0.925314i \(-0.376198\pi\)
0.379203 + 0.925314i \(0.376198\pi\)
\(132\) 0 0
\(133\) 2.25565i 0.195590i
\(134\) 9.47641 0.818637
\(135\) −0.539189 2.17009i −0.0464060 0.186771i
\(136\) −12.0183 −1.03056
\(137\) 12.5958i 1.07613i −0.842902 0.538067i \(-0.819155\pi\)
0.842902 0.538067i \(-0.180845\pi\)
\(138\) 6.15676i 0.524098i
\(139\) −9.91548 −0.841020 −0.420510 0.907288i \(-0.638149\pi\)
−0.420510 + 0.907288i \(0.638149\pi\)
\(140\) 0.0578588 + 0.232866i 0.00488996 + 0.0196808i
\(141\) −5.26180 −0.443123
\(142\) 7.81658i 0.655953i
\(143\) 0 0
\(144\) 4.60197 0.383497
\(145\) −16.0989 + 4.00000i −1.33694 + 0.332182i
\(146\) −1.73594 −0.143667
\(147\) 6.91548i 0.570379i
\(148\) 1.26180i 0.103719i
\(149\) −1.26180 −0.103370 −0.0516851 0.998663i \(-0.516459\pi\)
−0.0516851 + 0.998663i \(0.516459\pi\)
\(150\) 6.80098 3.60197i 0.555298 0.294099i
\(151\) −1.60197 −0.130366 −0.0651832 0.997873i \(-0.520763\pi\)
−0.0651832 + 0.997873i \(0.520763\pi\)
\(152\) 19.4764i 1.57975i
\(153\) 4.78765i 0.387059i
\(154\) 0 0
\(155\) 13.7587 3.41855i 1.10513 0.274585i
\(156\) 2.57304 0.206008
\(157\) 7.10504i 0.567044i −0.958966 0.283522i \(-0.908497\pi\)
0.958966 0.283522i \(-0.0915029\pi\)
\(158\) 1.41855i 0.112854i
\(159\) 5.75872 0.456696
\(160\) 1.11223 + 4.47641i 0.0879293 + 0.353891i
\(161\) −1.16290 −0.0916492
\(162\) 1.53919i 0.120930i
\(163\) 22.9360i 1.79649i 0.439499 + 0.898243i \(0.355156\pi\)
−0.439499 + 0.898243i \(0.644844\pi\)
\(164\) −2.73820 −0.213818
\(165\) 0 0
\(166\) 2.63090 0.204197
\(167\) 4.81432i 0.372543i −0.982498 0.186271i \(-0.940360\pi\)
0.982498 0.186271i \(-0.0596404\pi\)
\(168\) 0.729794i 0.0563049i
\(169\) −35.5958 −2.73814
\(170\) −15.9916 + 3.97334i −1.22650 + 0.304741i
\(171\) −7.75872 −0.593324
\(172\) 0.107307i 0.00818209i
\(173\) 12.8865i 0.979746i −0.871794 0.489873i \(-0.837043\pi\)
0.871794 0.489873i \(-0.162957\pi\)
\(174\) −11.4186 −0.865638
\(175\) −0.680346 1.28458i −0.0514293 0.0971052i
\(176\) 0 0
\(177\) 3.60197i 0.270741i
\(178\) 6.68035i 0.500713i
\(179\) −1.84324 −0.137771 −0.0688853 0.997625i \(-0.521944\pi\)
−0.0688853 + 0.997625i \(0.521944\pi\)
\(180\) 0.800984 0.199016i 0.0597018 0.0148338i
\(181\) 10.2823 0.764278 0.382139 0.924105i \(-0.375187\pi\)
0.382139 + 0.924105i \(0.375187\pi\)
\(182\) 3.11942i 0.231226i
\(183\) 6.68035i 0.493825i
\(184\) −10.0410 −0.740235
\(185\) −1.84324 7.41855i −0.135518 0.545423i
\(186\) 9.75872 0.715544
\(187\) 0 0
\(188\) 1.94214i 0.141645i
\(189\) −0.290725 −0.0211471
\(190\) −6.43907 25.9155i −0.467139 1.88011i
\(191\) −11.5174 −0.833373 −0.416687 0.909050i \(-0.636809\pi\)
−0.416687 + 0.909050i \(0.636809\pi\)
\(192\) 6.02893i 0.435101i
\(193\) 3.86603i 0.278283i 0.990273 + 0.139141i \(0.0444343\pi\)
−0.990273 + 0.139141i \(0.955566\pi\)
\(194\) 7.20394 0.517212
\(195\) −15.1278 + 3.75872i −1.08333 + 0.269168i
\(196\) −2.55252 −0.182323
\(197\) 8.57304i 0.610804i 0.952224 + 0.305402i \(0.0987908\pi\)
−0.952224 + 0.305402i \(0.901209\pi\)
\(198\) 0 0
\(199\) −8.31351 −0.589329 −0.294665 0.955601i \(-0.595208\pi\)
−0.294665 + 0.955601i \(0.595208\pi\)
\(200\) −5.87444 11.0917i −0.415386 0.784302i
\(201\) −6.15676 −0.434264
\(202\) 13.2085i 0.929345i
\(203\) 2.15676i 0.151375i
\(204\) −1.76713 −0.123724
\(205\) 16.0989 4.00000i 1.12440 0.279372i
\(206\) −10.3714 −0.722608
\(207\) 4.00000i 0.278019i
\(208\) 32.0806i 2.22439i
\(209\) 0 0
\(210\) −0.241276 0.971071i −0.0166496 0.0670102i
\(211\) −25.9155 −1.78410 −0.892048 0.451941i \(-0.850732\pi\)
−0.892048 + 0.451941i \(0.850732\pi\)
\(212\) 2.12556i 0.145984i
\(213\) 5.07838i 0.347965i
\(214\) −18.8287 −1.28710
\(215\) 0.156755 + 0.630898i 0.0106906 + 0.0430269i
\(216\) −2.51026 −0.170802
\(217\) 1.84324i 0.125128i
\(218\) 9.71769i 0.658165i
\(219\) 1.12783 0.0762114
\(220\) 0 0
\(221\) 33.3751 2.24505
\(222\) 5.26180i 0.353149i
\(223\) 9.62863i 0.644781i 0.946607 + 0.322390i \(0.104486\pi\)
−0.946607 + 0.322390i \(0.895514\pi\)
\(224\) 0.599701 0.0400692
\(225\) −4.41855 + 2.34017i −0.294570 + 0.156012i
\(226\) 25.3919 1.68904
\(227\) 18.3896i 1.22056i 0.792185 + 0.610281i \(0.208943\pi\)
−0.792185 + 0.610281i \(0.791057\pi\)
\(228\) 2.86376i 0.189657i
\(229\) −17.1506 −1.13334 −0.566672 0.823943i \(-0.691769\pi\)
−0.566672 + 0.823943i \(0.691769\pi\)
\(230\) −13.3607 + 3.31965i −0.880978 + 0.218892i
\(231\) 0 0
\(232\) 18.6225i 1.22263i
\(233\) 4.10731i 0.269079i −0.990908 0.134539i \(-0.957045\pi\)
0.990908 0.134539i \(-0.0429555\pi\)
\(234\) −10.7298 −0.701429
\(235\) 2.83710 + 11.4186i 0.185072 + 0.744864i
\(236\) 1.32950 0.0865428
\(237\) 0.921622i 0.0598658i
\(238\) 2.14238i 0.138870i
\(239\) −4.36683 −0.282467 −0.141234 0.989976i \(-0.545107\pi\)
−0.141234 + 0.989976i \(0.545107\pi\)
\(240\) −2.48133 9.98667i −0.160169 0.644637i
\(241\) 5.20394 0.335215 0.167608 0.985854i \(-0.446396\pi\)
0.167608 + 0.985854i \(0.446396\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) −2.46573 −0.157852
\(245\) 15.0072 3.72875i 0.958774 0.238221i
\(246\) 11.4186 0.728020
\(247\) 54.0866i 3.44145i
\(248\) 15.9155i 1.01063i
\(249\) −1.70928 −0.108321
\(250\) −11.4836 12.8166i −0.726286 0.810592i
\(251\) −8.28231 −0.522775 −0.261388 0.965234i \(-0.584180\pi\)
−0.261388 + 0.965234i \(0.584180\pi\)
\(252\) 0.107307i 0.00675972i
\(253\) 0 0
\(254\) −7.49920 −0.470541
\(255\) 10.3896 2.58145i 0.650623 0.161657i
\(256\) 8.57531 0.535957
\(257\) 11.0205i 0.687441i 0.939072 + 0.343721i \(0.111687\pi\)
−0.939072 + 0.343721i \(0.888313\pi\)
\(258\) 0.447480i 0.0278589i
\(259\) −0.993857 −0.0617553
\(260\) −1.38735 5.58372i −0.0860400 0.346287i
\(261\) 7.41855 0.459197
\(262\) 13.3607i 0.825426i
\(263\) 2.97107i 0.183204i −0.995796 0.0916020i \(-0.970801\pi\)
0.995796 0.0916020i \(-0.0291988\pi\)
\(264\) 0 0
\(265\) −3.10504 12.4969i −0.190741 0.767680i
\(266\) −3.47187 −0.212874
\(267\) 4.34017i 0.265614i
\(268\) 2.27247i 0.138813i
\(269\) 15.8432 0.965980 0.482990 0.875626i \(-0.339551\pi\)
0.482990 + 0.875626i \(0.339551\pi\)
\(270\) −3.34017 + 0.829914i −0.203276 + 0.0505069i
\(271\) 6.28231 0.381623 0.190812 0.981627i \(-0.438888\pi\)
0.190812 + 0.981627i \(0.438888\pi\)
\(272\) 22.0326i 1.33592i
\(273\) 2.02666i 0.122659i
\(274\) −19.3874 −1.17123
\(275\) 0 0
\(276\) −1.47641 −0.0888694
\(277\) 5.12783i 0.308101i −0.988063 0.154051i \(-0.950768\pi\)
0.988063 0.154051i \(-0.0492319\pi\)
\(278\) 15.2618i 0.915342i
\(279\) −6.34017 −0.379576
\(280\) −1.58372 + 0.393497i −0.0946452 + 0.0235159i
\(281\) −21.8888 −1.30578 −0.652889 0.757454i \(-0.726443\pi\)
−0.652889 + 0.757454i \(0.726443\pi\)
\(282\) 8.09890i 0.482282i
\(283\) 25.9649i 1.54345i 0.635954 + 0.771727i \(0.280607\pi\)
−0.635954 + 0.771727i \(0.719393\pi\)
\(284\) 1.87444 0.111228
\(285\) 4.18342 + 16.8371i 0.247804 + 0.997344i
\(286\) 0 0
\(287\) 2.15676i 0.127309i
\(288\) 2.06278i 0.121550i
\(289\) −5.92162 −0.348331
\(290\) 6.15676 + 24.7792i 0.361537 + 1.45509i
\(291\) −4.68035 −0.274367
\(292\) 0.416283i 0.0243611i
\(293\) 10.4163i 0.608526i 0.952588 + 0.304263i \(0.0984101\pi\)
−0.952588 + 0.304263i \(0.901590\pi\)
\(294\) 10.6442 0.620784
\(295\) −7.81658 + 1.94214i −0.455099 + 0.113076i
\(296\) −8.58145 −0.498787
\(297\) 0 0
\(298\) 1.94214i 0.112505i
\(299\) 27.8843 1.61259
\(300\) −0.863763 1.63090i −0.0498694 0.0941599i
\(301\) 0.0845208 0.00487170
\(302\) 2.46573i 0.141887i
\(303\) 8.58145i 0.492991i
\(304\) −35.7054 −2.04785
\(305\) 14.4969 3.60197i 0.830092 0.206248i
\(306\) 7.36910 0.421264
\(307\) 29.0700i 1.65911i 0.558425 + 0.829555i \(0.311406\pi\)
−0.558425 + 0.829555i \(0.688594\pi\)
\(308\) 0 0
\(309\) 6.73820 0.383323
\(310\) −5.26180 21.1773i −0.298850 1.20279i
\(311\) 5.44521 0.308770 0.154385 0.988011i \(-0.450660\pi\)
0.154385 + 0.988011i \(0.450660\pi\)
\(312\) 17.4992i 0.990697i
\(313\) 25.0928i 1.41833i −0.705044 0.709163i \(-0.749073\pi\)
0.705044 0.709163i \(-0.250927\pi\)
\(314\) −10.9360 −0.617154
\(315\) 0.156755 + 0.630898i 0.00883217 + 0.0355471i
\(316\) 0.340173 0.0191362
\(317\) 21.1773i 1.18943i 0.803935 + 0.594717i \(0.202736\pi\)
−0.803935 + 0.594717i \(0.797264\pi\)
\(318\) 8.86376i 0.497055i
\(319\) 0 0
\(320\) −13.0833 + 3.25073i −0.731379 + 0.181721i
\(321\) 12.2329 0.682772
\(322\) 1.78992i 0.0997484i
\(323\) 37.1461i 2.06686i
\(324\) −0.369102 −0.0205057
\(325\) 16.3135 + 30.8020i 0.904911 + 1.70859i
\(326\) 35.3028 1.95524
\(327\) 6.31351i 0.349138i
\(328\) 18.6225i 1.02825i
\(329\) 1.52973 0.0843369
\(330\) 0 0
\(331\) −6.70701 −0.368650 −0.184325 0.982865i \(-0.559010\pi\)
−0.184325 + 0.982865i \(0.559010\pi\)
\(332\) 0.630898i 0.0346250i
\(333\) 3.41855i 0.187335i
\(334\) −7.41014 −0.405465
\(335\) 3.31965 + 13.3607i 0.181372 + 0.729973i
\(336\) −1.33791 −0.0729887
\(337\) 23.7503i 1.29376i −0.762591 0.646881i \(-0.776073\pi\)
0.762591 0.646881i \(-0.223927\pi\)
\(338\) 54.7887i 2.98011i
\(339\) −16.4969 −0.895990
\(340\) 0.952819 + 3.83483i 0.0516739 + 0.207973i
\(341\) 0 0
\(342\) 11.9421i 0.645757i
\(343\) 4.04557i 0.218440i
\(344\) 0.729794 0.0393479
\(345\) 8.68035 2.15676i 0.467334 0.116116i
\(346\) −19.8348 −1.06633
\(347\) 31.1689i 1.67323i 0.547790 + 0.836616i \(0.315469\pi\)
−0.547790 + 0.836616i \(0.684531\pi\)
\(348\) 2.73820i 0.146783i
\(349\) 11.0472 0.591342 0.295671 0.955290i \(-0.404457\pi\)
0.295671 + 0.955290i \(0.404457\pi\)
\(350\) −1.97721 + 1.04718i −0.105687 + 0.0559742i
\(351\) 6.97107 0.372088
\(352\) 0 0
\(353\) 27.4329i 1.46011i 0.683390 + 0.730054i \(0.260505\pi\)
−0.683390 + 0.730054i \(0.739495\pi\)
\(354\) −5.54411 −0.294666
\(355\) −11.0205 + 2.73820i −0.584908 + 0.145329i
\(356\) 1.60197 0.0849041
\(357\) 1.39189i 0.0736666i
\(358\) 2.83710i 0.149945i
\(359\) −19.1506 −1.01073 −0.505365 0.862905i \(-0.668642\pi\)
−0.505365 + 0.862905i \(0.668642\pi\)
\(360\) 1.35350 + 5.44748i 0.0713359 + 0.287107i
\(361\) 41.1978 2.16830
\(362\) 15.8264i 0.831818i
\(363\) 0 0
\(364\) −0.748046 −0.0392083
\(365\) −0.608111 2.44748i −0.0318300 0.128107i
\(366\) 10.2823 0.537465
\(367\) 14.5692i 0.760504i −0.924883 0.380252i \(-0.875837\pi\)
0.924883 0.380252i \(-0.124163\pi\)
\(368\) 18.4079i 0.959577i
\(369\) −7.41855 −0.386194
\(370\) −11.4186 + 2.83710i −0.593622 + 0.147494i
\(371\) −1.67420 −0.0869203
\(372\) 2.34017i 0.121332i
\(373\) 8.81432i 0.456388i −0.973616 0.228194i \(-0.926718\pi\)
0.973616 0.228194i \(-0.0732820\pi\)
\(374\) 0 0
\(375\) 7.46081 + 8.32684i 0.385275 + 0.429996i
\(376\) 13.2085 0.681175
\(377\) 51.7152i 2.66347i
\(378\) 0.447480i 0.0230159i
\(379\) 23.5174 1.20801 0.604005 0.796980i \(-0.293571\pi\)
0.604005 + 0.796980i \(0.293571\pi\)
\(380\) −6.21461 + 1.54411i −0.318803 + 0.0792111i
\(381\) 4.87217 0.249609
\(382\) 17.7275i 0.907019i
\(383\) 19.3028i 0.986329i 0.869936 + 0.493164i \(0.164160\pi\)
−0.869936 + 0.493164i \(0.835840\pi\)
\(384\) −13.4052 −0.684082
\(385\) 0 0
\(386\) 5.95055 0.302875
\(387\) 0.290725i 0.0147784i
\(388\) 1.72753i 0.0877019i
\(389\) 20.0410 1.01612 0.508060 0.861321i \(-0.330363\pi\)
0.508060 + 0.861321i \(0.330363\pi\)
\(390\) 5.78539 + 23.2846i 0.292954 + 1.17906i
\(391\) −19.1506 −0.968488
\(392\) 17.3596i 0.876795i
\(393\) 8.68035i 0.437866i
\(394\) 13.1955 0.664781
\(395\) −2.00000 + 0.496928i −0.100631 + 0.0250032i
\(396\) 0 0
\(397\) 33.3607i 1.67433i −0.546954 0.837163i \(-0.684213\pi\)
0.546954 0.837163i \(-0.315787\pi\)
\(398\) 12.7961i 0.641409i
\(399\) 2.25565 0.112924
\(400\) −20.3340 + 10.7694i −1.01670 + 0.538470i
\(401\) −37.6475 −1.88003 −0.940014 0.341135i \(-0.889189\pi\)
−0.940014 + 0.341135i \(0.889189\pi\)
\(402\) 9.47641i 0.472640i
\(403\) 44.1978i 2.20165i
\(404\) −3.16743 −0.157586
\(405\) 2.17009 0.539189i 0.107832 0.0267925i
\(406\) 3.31965 0.164752
\(407\) 0 0
\(408\) 12.0183i 0.594992i
\(409\) −25.2039 −1.24625 −0.623127 0.782120i \(-0.714138\pi\)
−0.623127 + 0.782120i \(0.714138\pi\)
\(410\) −6.15676 24.7792i −0.304060 1.22376i
\(411\) 12.5958 0.621306
\(412\) 2.48709i 0.122530i
\(413\) 1.04718i 0.0515284i
\(414\) 6.15676 0.302588
\(415\) 0.921622 + 3.70928i 0.0452407 + 0.182081i
\(416\) −14.3798 −0.705027
\(417\) 9.91548i 0.485563i
\(418\) 0 0
\(419\) −17.8432 −0.871700 −0.435850 0.900019i \(-0.643552\pi\)
−0.435850 + 0.900019i \(0.643552\pi\)
\(420\) −0.232866 + 0.0578588i −0.0113627 + 0.00282322i
\(421\) −11.8120 −0.575684 −0.287842 0.957678i \(-0.592938\pi\)
−0.287842 + 0.957678i \(0.592938\pi\)
\(422\) 39.8888i 1.94176i
\(423\) 5.26180i 0.255837i
\(424\) −14.4559 −0.702040
\(425\) −11.2039 21.1545i −0.543471 1.02614i
\(426\) −7.81658 −0.378715
\(427\) 1.94214i 0.0939868i
\(428\) 4.51518i 0.218249i
\(429\) 0 0
\(430\) 0.971071 0.241276i 0.0468292 0.0116354i
\(431\) −16.6803 −0.803464 −0.401732 0.915757i \(-0.631592\pi\)
−0.401732 + 0.915757i \(0.631592\pi\)
\(432\) 4.60197i 0.221412i
\(433\) 28.3135i 1.36066i 0.732906 + 0.680330i \(0.238164\pi\)
−0.732906 + 0.680330i \(0.761836\pi\)
\(434\) −2.83710 −0.136185
\(435\) −4.00000 16.0989i −0.191785 0.771883i
\(436\) 2.33033 0.111603
\(437\) 31.0349i 1.48460i
\(438\) 1.73594i 0.0829463i
\(439\) −27.4452 −1.30989 −0.654944 0.755677i \(-0.727308\pi\)
−0.654944 + 0.755677i \(0.727308\pi\)
\(440\) 0 0
\(441\) −6.91548 −0.329309
\(442\) 51.3705i 2.44345i
\(443\) 0.412408i 0.0195941i −0.999952 0.00979704i \(-0.996881\pi\)
0.999952 0.00979704i \(-0.00311854\pi\)
\(444\) −1.26180 −0.0598822
\(445\) −9.41855 + 2.34017i −0.446482 + 0.110935i
\(446\) 14.8203 0.701761
\(447\) 1.26180i 0.0596809i
\(448\) 1.75276i 0.0828100i
\(449\) −1.33403 −0.0629568 −0.0314784 0.999504i \(-0.510022\pi\)
−0.0314784 + 0.999504i \(0.510022\pi\)
\(450\) 3.60197 + 6.80098i 0.169798 + 0.320601i
\(451\) 0 0
\(452\) 6.08906i 0.286405i
\(453\) 1.60197i 0.0752670i
\(454\) 28.3051 1.32842
\(455\) 4.39803 1.09275i 0.206183 0.0512291i
\(456\) 19.4764 0.912066
\(457\) 11.6514i 0.545030i −0.962151 0.272515i \(-0.912145\pi\)
0.962151 0.272515i \(-0.0878555\pi\)
\(458\) 26.3980i 1.23350i
\(459\) −4.78765 −0.223469
\(460\) 0.796064 + 3.20394i 0.0371167 + 0.149384i
\(461\) 2.05786 0.0958440 0.0479220 0.998851i \(-0.484740\pi\)
0.0479220 + 0.998851i \(0.484740\pi\)
\(462\) 0 0
\(463\) 28.7792i 1.33748i −0.743494 0.668742i \(-0.766833\pi\)
0.743494 0.668742i \(-0.233167\pi\)
\(464\) 34.1399 1.58491
\(465\) 3.41855 + 13.7587i 0.158531 + 0.638046i
\(466\) −6.32192 −0.292857
\(467\) 1.84324i 0.0852952i 0.999090 + 0.0426476i \(0.0135793\pi\)
−0.999090 + 0.0426476i \(0.986421\pi\)
\(468\) 2.57304i 0.118939i
\(469\) 1.78992 0.0826509
\(470\) 17.5753 4.36683i 0.810688 0.201427i
\(471\) 7.10504 0.327383
\(472\) 9.04187i 0.416186i
\(473\) 0 0
\(474\) −1.41855 −0.0651562
\(475\) 34.2823 18.1568i 1.57298 0.833089i
\(476\) 0.513749 0.0235477
\(477\) 5.75872i 0.263674i
\(478\) 6.72138i 0.307429i
\(479\) 26.8371 1.22622 0.613109 0.789998i \(-0.289919\pi\)
0.613109 + 0.789998i \(0.289919\pi\)
\(480\) −4.47641 + 1.11223i −0.204319 + 0.0507660i
\(481\) 23.8310 1.08660
\(482\) 8.00984i 0.364838i
\(483\) 1.16290i 0.0529137i
\(484\) 0 0
\(485\) 2.52359 + 10.1568i 0.114590 + 0.461195i
\(486\) 1.53919 0.0698190
\(487\) 28.5646i 1.29439i 0.762326 + 0.647193i \(0.224057\pi\)
−0.762326 + 0.647193i \(0.775943\pi\)
\(488\) 16.7694i 0.759115i
\(489\) −22.9360 −1.03720
\(490\) −5.73925 23.0989i −0.259273 1.04350i
\(491\) −25.9877 −1.17281 −0.586405 0.810018i \(-0.699457\pi\)
−0.586405 + 0.810018i \(0.699457\pi\)
\(492\) 2.73820i 0.123448i
\(493\) 35.5174i 1.59963i
\(494\) 83.2495 3.74557
\(495\) 0 0
\(496\) −29.1773 −1.31010
\(497\) 1.47641i 0.0662260i
\(498\) 2.63090i 0.117893i
\(499\) 27.5174 1.23185 0.615925 0.787805i \(-0.288782\pi\)
0.615925 + 0.787805i \(0.288782\pi\)
\(500\) −3.07346 + 2.75380i −0.137449 + 0.123154i
\(501\) 4.81432 0.215088
\(502\) 12.7480i 0.568973i
\(503\) 22.6576i 1.01025i 0.863046 + 0.505125i \(0.168554\pi\)
−0.863046 + 0.505125i \(0.831446\pi\)
\(504\) 0.729794 0.0325076
\(505\) 18.6225 4.62702i 0.828690 0.205900i
\(506\) 0 0
\(507\) 35.5958i 1.58087i
\(508\) 1.79833i 0.0797880i
\(509\) 27.8432 1.23413 0.617065 0.786912i \(-0.288322\pi\)
0.617065 + 0.786912i \(0.288322\pi\)
\(510\) −3.97334 15.9916i −0.175942 0.708119i
\(511\) −0.327887 −0.0145049
\(512\) 13.6114i 0.601546i
\(513\) 7.75872i 0.342556i
\(514\) 16.9627 0.748191
\(515\) −3.63317 14.6225i −0.160096 0.644344i
\(516\) 0.107307 0.00472393
\(517\) 0 0
\(518\) 1.52973i 0.0672126i
\(519\) 12.8865 0.565657
\(520\) 37.9748 9.43537i 1.66530 0.413768i
\(521\) 29.7009 1.30122 0.650609 0.759413i \(-0.274514\pi\)
0.650609 + 0.759413i \(0.274514\pi\)
\(522\) 11.4186i 0.499776i
\(523\) 24.7565i 1.08252i 0.840854 + 0.541262i \(0.182053\pi\)
−0.840854 + 0.541262i \(0.817947\pi\)
\(524\) −3.20394 −0.139965
\(525\) 1.28458 0.680346i 0.0560637 0.0296927i
\(526\) −4.57304 −0.199394
\(527\) 30.3545i 1.32226i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) −19.2351 + 4.77924i −0.835521 + 0.207597i
\(531\) 3.60197 0.156312
\(532\) 0.832567i 0.0360963i
\(533\) 51.7152i 2.24004i
\(534\) −6.68035 −0.289087
\(535\) −6.59583 26.5464i −0.285162 1.14770i
\(536\) 15.4551 0.667557
\(537\) 1.84324i 0.0795419i
\(538\) 24.3857i 1.05134i
\(539\) 0 0
\(540\) 0.199016 + 0.800984i 0.00856428 + 0.0344689i
\(541\) 12.5236 0.538431 0.269216 0.963080i \(-0.413236\pi\)
0.269216 + 0.963080i \(0.413236\pi\)
\(542\) 9.66967i 0.415348i
\(543\) 10.2823i 0.441256i
\(544\) 9.87587 0.423425
\(545\) −13.7009 + 3.40417i −0.586881 + 0.145819i
\(546\) 3.11942 0.133499
\(547\) 14.2784i 0.610502i 0.952272 + 0.305251i \(0.0987404\pi\)
−0.952272 + 0.305251i \(0.901260\pi\)
\(548\) 4.64915i 0.198602i
\(549\) −6.68035 −0.285110
\(550\) 0 0
\(551\) −57.5585 −2.45207
\(552\) 10.0410i 0.427375i
\(553\) 0.267938i 0.0113939i
\(554\) −7.89269 −0.335328
\(555\) 7.41855 1.84324i 0.314900 0.0782414i
\(556\) 3.65983 0.155211
\(557\) 3.57918i 0.151655i 0.997121 + 0.0758274i \(0.0241598\pi\)
−0.997121 + 0.0758274i \(0.975840\pi\)
\(558\) 9.75872i 0.413120i
\(559\) −2.02666 −0.0857187
\(560\) 0.721384 + 2.90337i 0.0304840 + 0.122690i
\(561\) 0 0
\(562\) 33.6910i 1.42117i
\(563\) 28.9588i 1.22047i 0.792222 + 0.610234i \(0.208924\pi\)
−0.792222 + 0.610234i \(0.791076\pi\)
\(564\) 1.94214 0.0817789
\(565\) 8.89496 + 35.7998i 0.374214 + 1.50611i
\(566\) 39.9649 1.67985
\(567\) 0.290725i 0.0122093i
\(568\) 12.7480i 0.534896i
\(569\) −25.8264 −1.08270 −0.541350 0.840797i \(-0.682087\pi\)
−0.541350 + 0.840797i \(0.682087\pi\)
\(570\) 25.9155 6.43907i 1.08548 0.269703i
\(571\) −17.1194 −0.716425 −0.358213 0.933640i \(-0.616614\pi\)
−0.358213 + 0.933640i \(0.616614\pi\)
\(572\) 0 0
\(573\) 11.5174i 0.481148i
\(574\) −3.31965 −0.138560
\(575\) −9.36069 17.6742i −0.390368 0.737065i
\(576\) 6.02893 0.251205
\(577\) 22.5692i 0.939567i 0.882782 + 0.469783i \(0.155668\pi\)
−0.882782 + 0.469783i \(0.844332\pi\)
\(578\) 9.11450i 0.379113i
\(579\) −3.86603 −0.160667
\(580\) 5.94214 1.47641i 0.246734 0.0613046i
\(581\) 0.496928 0.0206161
\(582\) 7.20394i 0.298613i
\(583\) 0 0
\(584\) −2.83114 −0.117153
\(585\) −3.75872 15.1278i −0.155404 0.625459i
\(586\) 16.0326 0.662302
\(587\) 3.63317i 0.149957i 0.997185 + 0.0749784i \(0.0238888\pi\)
−0.997185 + 0.0749784i \(0.976111\pi\)
\(588\) 2.55252i 0.105264i
\(589\) 49.1917 2.02691
\(590\) 2.98932 + 12.0312i 0.123068 + 0.495317i
\(591\) −8.57304 −0.352648
\(592\) 15.7321i 0.646584i
\(593\) 12.3051i 0.505310i 0.967556 + 0.252655i \(0.0813037\pi\)
−0.967556 + 0.252655i \(0.918696\pi\)
\(594\) 0 0
\(595\) −3.02052 + 0.750491i −0.123829 + 0.0307671i
\(596\) 0.465732 0.0190771
\(597\) 8.31351i 0.340249i
\(598\) 42.9192i 1.75510i
\(599\) −19.6865 −0.804368 −0.402184 0.915559i \(-0.631749\pi\)
−0.402184 + 0.915559i \(0.631749\pi\)
\(600\) 11.0917 5.87444i 0.452817 0.239823i
\(601\) −25.8843 −1.05584 −0.527921 0.849294i \(-0.677028\pi\)
−0.527921 + 0.849294i \(0.677028\pi\)
\(602\) 0.130094i 0.00530222i
\(603\) 6.15676i 0.250722i
\(604\) 0.591290 0.0240593
\(605\) 0 0
\(606\) 13.2085 0.536557
\(607\) 41.5357i 1.68588i 0.538006 + 0.842941i \(0.319178\pi\)
−0.538006 + 0.842941i \(0.680822\pi\)
\(608\) 16.0045i 0.649070i
\(609\) −2.15676 −0.0873961
\(610\) −5.54411 22.3135i −0.224474 0.903448i
\(611\) −36.6803 −1.48393
\(612\) 1.76713i 0.0714322i
\(613\) 20.6453i 0.833855i −0.908940 0.416927i \(-0.863107\pi\)
0.908940 0.416927i \(-0.136893\pi\)
\(614\) 44.7442 1.80573
\(615\) 4.00000 + 16.0989i 0.161296 + 0.649170i
\(616\) 0 0
\(617\) 8.69472i 0.350036i 0.984565 + 0.175018i \(0.0559984\pi\)
−0.984565 + 0.175018i \(0.944002\pi\)
\(618\) 10.3714i 0.417198i
\(619\) −2.65368 −0.106661 −0.0533303 0.998577i \(-0.516984\pi\)
−0.0533303 + 0.998577i \(0.516984\pi\)
\(620\) −5.07838 + 1.26180i −0.203953 + 0.0506749i
\(621\) −4.00000 −0.160514
\(622\) 8.38121i 0.336056i
\(623\) 1.26180i 0.0505528i
\(624\) 32.0806 1.28425
\(625\) 14.0472 20.6803i 0.561887 0.827214i
\(626\) −38.6225 −1.54367
\(627\) 0 0
\(628\) 2.62249i 0.104649i
\(629\) −16.3668 −0.652588
\(630\) 0.971071 0.241276i 0.0386884 0.00961268i
\(631\) −10.6393 −0.423544 −0.211772 0.977319i \(-0.567923\pi\)
−0.211772 + 0.977319i \(0.567923\pi\)
\(632\) 2.31351i 0.0920265i
\(633\) 25.9155i 1.03005i
\(634\) 32.5958 1.29455
\(635\) −2.62702 10.5730i −0.104250 0.419578i
\(636\) −2.12556 −0.0842839
\(637\) 48.2083i 1.91008i
\(638\) 0 0
\(639\) 5.07838 0.200898
\(640\) 7.22795 + 29.0905i 0.285710 + 1.14990i
\(641\) −35.8576 −1.41629 −0.708145 0.706067i \(-0.750468\pi\)
−0.708145 + 0.706067i \(0.750468\pi\)
\(642\) 18.8287i 0.743109i
\(643\) 12.2146i 0.481697i −0.970563 0.240849i \(-0.922574\pi\)
0.970563 0.240849i \(-0.0774258\pi\)
\(644\) 0.429229 0.0169140
\(645\) −0.630898 + 0.156755i −0.0248416 + 0.00617224i
\(646\) −57.1748 −2.24951
\(647\) 25.9421i 1.01989i 0.860207 + 0.509945i \(0.170334\pi\)
−0.860207 + 0.509945i \(0.829666\pi\)
\(648\) 2.51026i 0.0986123i
\(649\) 0 0
\(650\) 47.4101 25.1096i 1.85958 0.984879i
\(651\) 1.84324 0.0722424
\(652\) 8.46573i 0.331544i
\(653\) 14.3402i 0.561174i 0.959829 + 0.280587i \(0.0905292\pi\)
−0.959829 + 0.280587i \(0.909471\pi\)
\(654\) −9.71769 −0.379992
\(655\) 18.8371 4.68035i 0.736026 0.182876i
\(656\) −34.1399 −1.33294
\(657\) 1.12783i 0.0440007i
\(658\) 2.35455i 0.0917899i
\(659\) 6.52359 0.254123 0.127062 0.991895i \(-0.459445\pi\)
0.127062 + 0.991895i \(0.459445\pi\)
\(660\) 0 0
\(661\) 3.16290 0.123022 0.0615112 0.998106i \(-0.480408\pi\)
0.0615112 + 0.998106i \(0.480408\pi\)
\(662\) 10.3234i 0.401228i
\(663\) 33.3751i 1.29618i
\(664\) 4.29072 0.166512
\(665\) −1.21622 4.89496i −0.0471631 0.189818i
\(666\) 5.26180 0.203890
\(667\) 29.6742i 1.14899i
\(668\) 1.77698i 0.0687532i
\(669\) −9.62863 −0.372264
\(670\) 20.5646 5.10957i 0.794481 0.197400i
\(671\) 0 0
\(672\) 0.599701i 0.0231340i
\(673\) 18.4885i 0.712680i −0.934356 0.356340i \(-0.884024\pi\)
0.934356 0.356340i \(-0.115976\pi\)
\(674\) −36.5562 −1.40809
\(675\) −2.34017 4.41855i −0.0900733 0.170070i
\(676\) 13.1385 0.505327
\(677\) 15.0966i 0.580211i −0.956995 0.290105i \(-0.906310\pi\)
0.956995 0.290105i \(-0.0936903\pi\)
\(678\) 25.3919i 0.975170i
\(679\) 1.36069 0.0522186
\(680\) −26.0806 + 6.48011i −1.00015 + 0.248501i
\(681\) −18.3896 −0.704692
\(682\) 0 0
\(683\) 12.4657i 0.476988i 0.971144 + 0.238494i \(0.0766537\pi\)
−0.971144 + 0.238494i \(0.923346\pi\)
\(684\) 2.86376 0.109499
\(685\) −6.79153 27.3340i −0.259491 1.04438i
\(686\) −6.22690 −0.237744
\(687\) 17.1506i 0.654337i
\(688\) 1.33791i 0.0510072i
\(689\) 40.1445 1.52938
\(690\) −3.31965 13.3607i −0.126377 0.508633i
\(691\) −30.7214 −1.16870 −0.584348 0.811503i \(-0.698650\pi\)
−0.584348 + 0.811503i \(0.698650\pi\)
\(692\) 4.75646i 0.180813i
\(693\) 0 0
\(694\) 47.9748 1.82110
\(695\) −21.5174 + 5.34632i −0.816203 + 0.202797i
\(696\) −18.6225 −0.705884
\(697\) 35.5174i 1.34532i
\(698\) 17.0037i 0.643599i
\(699\) 4.10731 0.155353
\(700\) 0.251117 + 0.474142i 0.00949134 + 0.0179209i
\(701\) −17.9955 −0.679679 −0.339840 0.940483i \(-0.610373\pi\)
−0.339840 + 0.940483i \(0.610373\pi\)
\(702\) 10.7298i 0.404970i
\(703\) 26.5236i 1.00036i
\(704\) 0 0
\(705\) −11.4186 + 2.83710i −0.430047 + 0.106851i
\(706\) 42.2245 1.58914
\(707\) 2.49484i 0.0938281i
\(708\) 1.32950i 0.0499655i
\(709\) −23.5897 −0.885929 −0.442965 0.896539i \(-0.646073\pi\)
−0.442965 + 0.896539i \(0.646073\pi\)
\(710\) 4.21461 + 16.9627i 0.158172 + 0.636597i
\(711\) 0.921622 0.0345635
\(712\) 10.8950i 0.408306i
\(713\) 25.3607i 0.949765i
\(714\) −2.14238 −0.0801765
\(715\) 0 0
\(716\) 0.680346 0.0254257
\(717\) 4.36683i 0.163082i
\(718\) 29.4764i 1.10005i
\(719\) −24.5646 −0.916106 −0.458053 0.888925i \(-0.651453\pi\)
−0.458053 + 0.888925i \(0.651453\pi\)
\(720\) 9.98667 2.48133i 0.372181 0.0924737i
\(721\) −1.95896 −0.0729556
\(722\) 63.4112i 2.35992i
\(723\) 5.20394i 0.193536i
\(724\) −3.79523 −0.141048
\(725\) −32.7792 + 17.3607i −1.21739 + 0.644760i
\(726\) 0 0
\(727\) 8.51130i 0.315667i 0.987466 + 0.157833i \(0.0504509\pi\)
−0.987466 + 0.157833i \(0.949549\pi\)
\(728\) 5.08745i 0.188553i
\(729\) −1.00000 −0.0370370
\(730\) −3.76713 + 0.935998i −0.139428 + 0.0346428i
\(731\) 1.39189 0.0514809
\(732\) 2.46573i 0.0911361i
\(733\) 29.8615i 1.10296i −0.834188 0.551480i \(-0.814063\pi\)
0.834188 0.551480i \(-0.185937\pi\)
\(734\) −22.4247 −0.827711
\(735\) 3.72875 + 15.0072i 0.137537 + 0.553548i
\(736\) 8.25112 0.304140
\(737\) 0 0
\(738\) 11.4186i 0.420323i
\(739\) −36.7526 −1.35197 −0.675983 0.736917i \(-0.736281\pi\)
−0.675983 + 0.736917i \(0.736281\pi\)
\(740\) 0.680346 + 2.73820i 0.0250100 + 0.100658i
\(741\) −54.0866 −1.98692
\(742\) 2.57691i 0.0946015i
\(743\) 2.17501i 0.0797933i −0.999204 0.0398966i \(-0.987297\pi\)
0.999204 0.0398966i \(-0.0127029\pi\)
\(744\) 15.9155 0.583490
\(745\) −2.73820 + 0.680346i −0.100320 + 0.0249259i
\(746\) −13.5669 −0.496719
\(747\) 1.70928i 0.0625391i
\(748\) 0 0
\(749\) −3.55640 −0.129948
\(750\) 12.8166 11.4836i 0.467995 0.419322i
\(751\) −44.4580 −1.62229 −0.811147 0.584842i \(-0.801157\pi\)
−0.811147 + 0.584842i \(0.801157\pi\)
\(752\) 24.2146i 0.883016i
\(753\) 8.28231i 0.301824i
\(754\) −79.5995 −2.89884
\(755\) −3.47641 + 0.863763i −0.126519 + 0.0314356i
\(756\) 0.107307 0.00390272
\(757\) 26.4247i 0.960422i −0.877153 0.480211i \(-0.840560\pi\)
0.877153 0.480211i \(-0.159440\pi\)
\(758\) 36.1978i 1.31476i
\(759\) 0 0
\(760\) −10.5015 42.2655i −0.380928 1.53313i
\(761\) 27.6163 1.00109 0.500546 0.865710i \(-0.333133\pi\)
0.500546 + 0.865710i \(0.333133\pi\)
\(762\) 7.49920i 0.271667i
\(763\) 1.83549i 0.0664493i
\(764\) 4.25112 0.153800
\(765\) 2.58145 + 10.3896i 0.0933325 + 0.375638i
\(766\) 29.7107 1.07349
\(767\) 25.1096i 0.906654i
\(768\) 8.57531i 0.309435i
\(769\) 27.8432 1.00405 0.502027 0.864852i \(-0.332588\pi\)
0.502027 + 0.864852i \(0.332588\pi\)
\(770\) 0 0
\(771\) −11.0205 −0.396894
\(772\) 1.42696i 0.0513575i
\(773\) 18.0267i 0.648374i 0.945993 + 0.324187i \(0.105091\pi\)
−0.945993 + 0.324187i \(0.894909\pi\)
\(774\) −0.447480 −0.0160843
\(775\) 28.0144 14.8371i 1.00631 0.532964i
\(776\) 11.7489 0.421760
\(777\) 0.993857i 0.0356544i
\(778\) 30.8469i 1.10592i
\(779\) 57.5585 2.06225
\(780\) 5.58372 1.38735i 0.199929 0.0496752i
\(781\) 0 0
\(782\) 29.4764i 1.05407i
\(783\) 7.41855i 0.265117i
\(784\) −31.8248 −1.13660
\(785\) −3.83096 15.4186i −0.136733 0.550312i
\(786\) 13.3607 0.476560
\(787\) 35.6391i 1.27040i −0.772349 0.635199i \(-0.780918\pi\)
0.772349 0.635199i \(-0.219082\pi\)
\(788\) 3.16433i 0.112725i
\(789\) 2.97107 0.105773
\(790\) 0.764867 + 3.07838i 0.0272127 + 0.109524i
\(791\) 4.79606 0.170528
\(792\) 0 0
\(793\) 46.5692i 1.65372i
\(794\) −51.3484 −1.82229
\(795\) 12.4969 3.10504i 0.443220 0.110124i
\(796\) 3.06854 0.108761
\(797\) 4.97948i 0.176382i −0.996104 0.0881911i \(-0.971891\pi\)
0.996104 0.0881911i \(-0.0281086\pi\)
\(798\) 3.47187i 0.122903i
\(799\) 25.1917 0.891217
\(800\) 4.82726 + 9.11450i 0.170669 + 0.322246i
\(801\) 4.34017 0.153352
\(802\) 57.9467i 2.04617i
\(803\) 0 0
\(804\) 2.27247 0.0801439
\(805\) −2.52359 + 0.627022i −0.0889449 + 0.0220996i
\(806\) 68.0288 2.39621
\(807\) 15.8432i 0.557709i
\(808\) 21.5417i 0.757833i
\(809\) 31.6697 1.11345 0.556723 0.830698i \(-0.312058\pi\)
0.556723 + 0.830698i \(0.312058\pi\)
\(810\) −0.829914 3.34017i −0.0291602 0.117362i
\(811\) 21.7998 0.765493 0.382747 0.923853i \(-0.374978\pi\)
0.382747 + 0.923853i \(0.374978\pi\)
\(812\) 0.796064i 0.0279364i
\(813\) 6.28231i 0.220330i
\(814\) 0 0
\(815\) 12.3668 + 49.7731i 0.433191 + 1.74348i
\(816\) −22.0326 −0.771296
\(817\) 2.25565i 0.0789153i
\(818\) 38.7936i 1.35639i
\(819\) −2.02666 −0.0708173
\(820\) −5.94214 + 1.47641i −0.207509 + 0.0515585i
\(821\) 10.9360 0.381669 0.190834 0.981622i \(-0.438881\pi\)
0.190834 + 0.981622i \(0.438881\pi\)
\(822\) 19.3874i 0.676212i
\(823\) 45.9709i 1.60244i −0.598367 0.801222i \(-0.704183\pi\)
0.598367 0.801222i \(-0.295817\pi\)
\(824\) −16.9146 −0.589249
\(825\) 0 0
\(826\) 1.61181 0.0560820
\(827\) 22.9711i 0.798782i 0.916781 + 0.399391i \(0.130778\pi\)
−0.916781 + 0.399391i \(0.869222\pi\)
\(828\) 1.47641i 0.0513088i
\(829\) 48.1543 1.67247 0.836234 0.548373i \(-0.184752\pi\)
0.836234 + 0.548373i \(0.184752\pi\)
\(830\) 5.70928 1.41855i 0.198172 0.0492386i
\(831\) 5.12783 0.177882
\(832\) 42.0281i 1.45706i
\(833\) 33.1089i 1.14716i
\(834\) −15.2618 −0.528473
\(835\) −2.59583 10.4475i −0.0898322 0.361550i
\(836\) 0 0
\(837\) 6.34017i 0.219148i
\(838\) 27.4641i 0.948732i
\(839\) 17.9278 0.618935 0.309468 0.950910i \(-0.399849\pi\)
0.309468 + 0.950910i \(0.399849\pi\)
\(840\) −0.393497 1.58372i −0.0135769 0.0546434i
\(841\) 26.0349 0.897755
\(842\) 18.1810i 0.626558i
\(843\) 21.8888i 0.753891i
\(844\) 9.56547 0.329257
\(845\) −77.2460 + 19.1929i −2.65734 + 0.660255i
\(846\) −8.09890 −0.278446
\(847\) 0 0
\(848\) 26.5015i 0.910064i
\(849\) −25.9649 −0.891114
\(850\) −32.5608 + 17.2450i −1.11682 + 0.591498i
\(851\) −13.6742 −0.468746
\(852\) 1.87444i 0.0642173i
\(853\) 9.54799i 0.326917i −0.986550 0.163458i \(-0.947735\pi\)
0.986550 0.163458i \(-0.0522649\pi\)
\(854\) −2.98932 −0.102292
\(855\) −16.8371 + 4.18342i −0.575817 + 0.143070i
\(856\) −30.7077 −1.04957
\(857\) 10.5776i 0.361323i −0.983545 0.180662i \(-0.942176\pi\)
0.983545 0.180662i \(-0.0578239\pi\)
\(858\) 0 0
\(859\) 31.3340 1.06910 0.534552 0.845136i \(-0.320480\pi\)
0.534552 + 0.845136i \(0.320480\pi\)
\(860\) −0.0578588 0.232866i −0.00197297 0.00794066i
\(861\) 2.15676 0.0735020
\(862\) 25.6742i 0.874467i
\(863\) 56.7792i 1.93279i −0.257066 0.966394i \(-0.582756\pi\)
0.257066 0.966394i \(-0.417244\pi\)
\(864\) 2.06278 0.0701772
\(865\) −6.94828 27.9649i −0.236249 0.950836i
\(866\) 43.5798 1.48090
\(867\) 5.92162i 0.201109i
\(868\) 0.680346i 0.0230924i
\(869\) 0 0
\(870\) −24.7792 + 6.15676i −0.840095 + 0.208734i
\(871\) −42.9192 −1.45426
\(872\) 15.8486i 0.536700i
\(873\) 4.68035i 0.158406i
\(874\) −47.7686 −1.61580
\(875\) −2.16904 2.42082i −0.0733270 0.0818386i
\(876\) −0.416283 −0.0140649
\(877\) 5.87832i 0.198497i −0.995063 0.0992483i \(-0.968356\pi\)
0.995063 0.0992483i \(-0.0316438\pi\)
\(878\) 42.2434i 1.42564i
\(879\) −10.4163 −0.351333
\(880\) 0 0
\(881\) 8.21008 0.276605 0.138302 0.990390i \(-0.455835\pi\)
0.138302 + 0.990390i \(0.455835\pi\)
\(882\) 10.6442i 0.358410i
\(883\) 27.0349i 0.909797i 0.890543 + 0.454898i \(0.150324\pi\)
−0.890543 + 0.454898i \(0.849676\pi\)
\(884\) −12.3188 −0.414327
\(885\) −1.94214 7.81658i −0.0652844 0.262752i
\(886\) −0.634773 −0.0213256
\(887\) 48.7442i 1.63667i 0.574742 + 0.818335i \(0.305102\pi\)
−0.574742 + 0.818335i \(0.694898\pi\)
\(888\) 8.58145i 0.287975i
\(889\) −1.41646 −0.0475066
\(890\) 3.60197 + 14.4969i 0.120738 + 0.485938i
\(891\) 0 0
\(892\) 3.55395i 0.118995i
\(893\) 40.8248i 1.36615i
\(894\) −1.94214 −0.0649549
\(895\) −4.00000 + 0.993857i −0.133705 + 0.0332210i
\(896\) 3.89723 0.130197
\(897\) 27.8843i 0.931029i
\(898\) 2.05332i 0.0685203i
\(899\) −47.0349 −1.56870
\(900\) 1.63090 0.863763i 0.0543633 0.0287921i
\(901\) −27.5708 −0.918516
\(902\) 0 0
\(903\) 0.0845208i 0.00281268i
\(904\) 41.4116 1.37733
\(905\) 22.3135 5.54411i 0.741726 0.184292i
\(906\) −2.46573 −0.0819184
\(907\) 32.4657i 1.07801i −0.842304 0.539003i \(-0.818801\pi\)
0.842304 0.539003i \(-0.181199\pi\)
\(908\) 6.78765i 0.225256i
\(909\) −8.58145 −0.284629
\(910\) −1.68195 6.76940i −0.0557562 0.224403i
\(911\) −4.84939 −0.160667 −0.0803337 0.996768i \(-0.525599\pi\)
−0.0803337 + 0.996768i \(0.525599\pi\)
\(912\) 35.7054i 1.18232i
\(913\) 0 0
\(914\) −17.9337 −0.593195
\(915\) 3.60197 + 14.4969i 0.119077 + 0.479254i
\(916\) 6.33033 0.209160
\(917\) 2.52359i 0.0833363i
\(918\) 7.36910i 0.243217i
\(919\) −14.3980 −0.474947 −0.237474 0.971394i \(-0.576319\pi\)
−0.237474 + 0.971394i \(0.576319\pi\)
\(920\) −21.7899 + 5.41402i −0.718392 + 0.178495i
\(921\) −29.0700 −0.957888
\(922\) 3.16743i 0.104314i
\(923\) 35.4017i 1.16526i
\(924\) 0 0
\(925\) −8.00000 15.1050i −0.263038 0.496651i
\(926\) −44.2967 −1.45568
\(927\) 6.73820i 0.221312i
\(928\) 15.3028i 0.502340i
\(929\) 11.1629 0.366243 0.183121 0.983090i \(-0.441380\pi\)
0.183121 + 0.983090i \(0.441380\pi\)
\(930\) 21.1773 5.26180i 0.694430 0.172541i
\(931\) 53.6553 1.75848
\(932\) 1.51602i 0.0496588i
\(933\) 5.44521i 0.178268i
\(934\) 2.83710 0.0928328
\(935\) 0 0
\(936\) −17.4992 −0.571979
\(937\) 48.6453i 1.58917i −0.607152 0.794586i \(-0.707688\pi\)
0.607152 0.794586i \(-0.292312\pi\)
\(938\) 2.75503i 0.0899548i
\(939\) 25.0928 0.818871
\(940\) −1.04718 4.21461i −0.0341553 0.137466i
\(941\) −16.4124 −0.535029 −0.267515 0.963554i \(-0.586202\pi\)
−0.267515 + 0.963554i \(0.586202\pi\)
\(942\) 10.9360i 0.356314i
\(943\) 29.6742i 0.966325i
\(944\) 16.5761 0.539508
\(945\) −0.630898 + 0.156755i −0.0205231 + 0.00509926i
\(946\) 0 0
\(947\) 45.7198i 1.48569i −0.669462 0.742847i \(-0.733475\pi\)
0.669462 0.742847i \(-0.266525\pi\)
\(948\) 0.340173i 0.0110483i
\(949\) 7.86216 0.255216
\(950\) −27.9467 52.7670i −0.906710 1.71199i
\(951\) −21.1773 −0.686720
\(952\) 3.49400i 0.113241i
\(953\) 26.4619i 0.857184i −0.903498 0.428592i \(-0.859010\pi\)
0.903498 0.428592i \(-0.140990\pi\)
\(954\) 8.86376 0.286975
\(955\) −24.9939 + 6.21008i −0.808782 + 0.200953i
\(956\) 1.61181 0.0521296
\(957\) 0 0
\(958\) 41.3074i 1.33458i
\(959\) −3.66192 −0.118249
\(960\) −3.25073 13.0833i −0.104917 0.422262i
\(961\) 9.19779 0.296703
\(962\) 36.6803i 1.18262i
\(963\) 12.2329i 0.394199i
\(964\) −1.92079 −0.0618643
\(965\) 2.08452 + 8.38962i 0.0671031 + 0.270071i
\(966\) −1.78992 −0.0575897
\(967\) 50.5464i 1.62546i −0.582639 0.812731i \(-0.697980\pi\)
0.582639 0.812731i \(-0.302020\pi\)
\(968\) 0 0
\(969\) 37.1461 1.19330
\(970\) 15.6332 3.88428i 0.501951 0.124717i
\(971\) −57.3074 −1.83908 −0.919540 0.392995i \(-0.871439\pi\)
−0.919540 + 0.392995i \(0.871439\pi\)
\(972\) 0.369102i 0.0118390i
\(973\) 2.88267i 0.0924143i
\(974\) 43.9664 1.40877
\(975\) −30.8020 + 16.3135i −0.986454 + 0.522450i
\(976\) −30.7427 −0.984051
\(977\) 45.7875i 1.46487i −0.680836 0.732436i \(-0.738384\pi\)
0.680836 0.732436i \(-0.261616\pi\)
\(978\) 35.3028i 1.12886i
\(979\) 0 0
\(980\) −5.53919 + 1.37629i −0.176943 + 0.0439640i
\(981\) 6.31351 0.201575
\(982\) 40.0000i 1.27645i
\(983\) 55.0805i 1.75679i −0.477932 0.878397i \(-0.658613\pi\)
0.477932 0.878397i \(-0.341387\pi\)
\(984\) 18.6225 0.593663
\(985\) 4.62249 + 18.6042i 0.147285 + 0.592780i
\(986\) 54.6681 1.74099
\(987\) 1.52973i 0.0486920i
\(988\) 19.9635i 0.635123i
\(989\) 1.16290 0.0369780
\(990\) 0 0
\(991\) 40.6947 1.29271 0.646355 0.763037i \(-0.276292\pi\)
0.646355 + 0.763037i \(0.276292\pi\)
\(992\) 13.0784i 0.415239i
\(993\) 6.70701i 0.212840i
\(994\) 2.27247 0.0720785
\(995\) −18.0410 + 4.48255i −0.571939 + 0.142106i
\(996\) 0.630898 0.0199908
\(997\) 32.7610i 1.03755i 0.854911 + 0.518775i \(0.173612\pi\)
−0.854911 + 0.518775i \(0.826388\pi\)
\(998\) 42.3545i 1.34071i
\(999\) −3.41855 −0.108158
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 1815.2.c.d.364.2 6
5.2 odd 4 9075.2.a.ck.1.2 3
5.3 odd 4 9075.2.a.cc.1.2 3
5.4 even 2 inner 1815.2.c.d.364.5 6
11.10 odd 2 165.2.c.a.34.5 yes 6
33.32 even 2 495.2.c.d.199.2 6
44.43 even 2 2640.2.d.i.529.3 6
55.32 even 4 825.2.a.h.1.2 3
55.43 even 4 825.2.a.n.1.2 3
55.54 odd 2 165.2.c.a.34.2 6
165.32 odd 4 2475.2.a.be.1.2 3
165.98 odd 4 2475.2.a.y.1.2 3
165.164 even 2 495.2.c.d.199.5 6
220.219 even 2 2640.2.d.i.529.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.c.a.34.2 6 55.54 odd 2
165.2.c.a.34.5 yes 6 11.10 odd 2
495.2.c.d.199.2 6 33.32 even 2
495.2.c.d.199.5 6 165.164 even 2
825.2.a.h.1.2 3 55.32 even 4
825.2.a.n.1.2 3 55.43 even 4
1815.2.c.d.364.2 6 1.1 even 1 trivial
1815.2.c.d.364.5 6 5.4 even 2 inner
2475.2.a.y.1.2 3 165.98 odd 4
2475.2.a.be.1.2 3 165.32 odd 4
2640.2.d.i.529.3 6 44.43 even 2
2640.2.d.i.529.6 6 220.219 even 2
9075.2.a.cc.1.2 3 5.3 odd 4
9075.2.a.ck.1.2 3 5.2 odd 4