Properties

Label 605.2.b.h.364.2
Level $605$
Weight $2$
Character 605.364
Analytic conductor $4.831$
Analytic rank $0$
Dimension $12$
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] = [605,2,Mod(364,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("605.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.b (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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4 x^{11} + x^{10} + 34 x^{9} - 123 x^{8} - 20 x^{7} + 516 x^{6} - 668 x^{5} - 67 x^{4} + 3848 x^{3} + 6697 x^{2} + 4398 x + 1089 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 364.2
Root \(1.15541 + 2.37379i\) of defining polynomial
Character \(\chi\) \(=\) 605.364
Dual form 605.2.b.h.364.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.60777i q^{2} +2.13980i q^{3} -4.80044 q^{4} +(-2.11084 - 0.737808i) q^{5} +5.58011 q^{6} -0.988879i q^{7} +7.30289i q^{8} -1.57876 q^{9} +O(q^{10})\) \(q-2.60777i q^{2} +2.13980i q^{3} -4.80044 q^{4} +(-2.11084 - 0.737808i) q^{5} +5.58011 q^{6} -0.988879i q^{7} +7.30289i q^{8} -1.57876 q^{9} +(-1.92403 + 5.50457i) q^{10} -10.2720i q^{12} +3.07624i q^{13} -2.57876 q^{14} +(1.57876 - 4.51678i) q^{15} +9.44335 q^{16} +1.61889i q^{17} +4.11705i q^{18} +6.58256 q^{19} +(10.1330 + 3.54180i) q^{20} +2.11601 q^{21} +5.18097i q^{23} -15.6268 q^{24} +(3.91128 + 3.11479i) q^{25} +8.02212 q^{26} +3.04117i q^{27} +4.74705i q^{28} +7.31216 q^{29} +(-11.7787 - 4.11705i) q^{30} -2.64291 q^{31} -10.0203i q^{32} +4.22168 q^{34} +(-0.729602 + 2.08736i) q^{35} +7.57876 q^{36} -2.80399i q^{37} -17.1658i q^{38} -6.58256 q^{39} +(5.38813 - 15.4152i) q^{40} -1.38641 q^{41} -5.51805i q^{42} +3.18585i q^{43} +(3.33252 + 1.16482i) q^{45} +13.5108 q^{46} +2.13980i q^{47} +20.2069i q^{48} +6.02212 q^{49} +(8.12263 - 10.1997i) q^{50} -3.46410 q^{51} -14.7673i q^{52} -2.37698i q^{53} +7.93065 q^{54} +7.22168 q^{56} +14.0854i q^{57} -19.0684i q^{58} -12.2438 q^{59} +(-7.57876 + 21.6825i) q^{60} +1.00245 q^{61} +6.89210i q^{62} +1.56121i q^{63} -7.24380 q^{64} +(2.26967 - 6.49345i) q^{65} +9.84499i q^{67} -7.77137i q^{68} -11.0863 q^{69} +(5.44335 + 1.90263i) q^{70} -0.243796 q^{71} -11.5295i q^{72} +13.6688i q^{73} -7.31216 q^{74} +(-6.66503 + 8.36938i) q^{75} -31.5992 q^{76} +17.1658i q^{78} +7.69612 q^{79} +(-19.9334 - 6.96738i) q^{80} -11.2438 q^{81} +3.61542i q^{82} -5.95515i q^{83} -10.1578 q^{84} +(1.19443 - 3.41721i) q^{85} +8.30795 q^{86} +15.6466i q^{87} -9.00000 q^{89} +(3.03759 - 8.69042i) q^{90} +3.04203 q^{91} -24.8710i q^{92} -5.65532i q^{93} +5.58011 q^{94} +(-13.8947 - 4.85666i) q^{95} +21.4414 q^{96} -12.7389i q^{97} -15.7043i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 20 q^{4} - 6 q^{5} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 20 q^{4} - 6 q^{5} - 20 q^{9} - 32 q^{14} + 20 q^{15} + 36 q^{16} + 26 q^{20} - 10 q^{25} + 20 q^{26} + 8 q^{31} + 12 q^{34} + 92 q^{36} - 18 q^{45} - 4 q^{49} + 48 q^{56} - 32 q^{59} - 92 q^{60} + 28 q^{64} - 16 q^{69} - 12 q^{70} + 112 q^{71} + 36 q^{75} - 106 q^{80} - 20 q^{81} - 56 q^{86} - 108 q^{89} + 72 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.60777i 1.84397i −0.387227 0.921984i \(-0.626567\pi\)
0.387227 0.921984i \(-0.373433\pi\)
\(3\) 2.13980i 1.23542i 0.786407 + 0.617708i \(0.211939\pi\)
−0.786407 + 0.617708i \(0.788061\pi\)
\(4\) −4.80044 −2.40022
\(5\) −2.11084 0.737808i −0.943996 0.329958i
\(6\) 5.58011 2.27807
\(7\) 0.988879i 0.373761i −0.982383 0.186881i \(-0.940162\pi\)
0.982383 0.186881i \(-0.0598377\pi\)
\(8\) 7.30289i 2.58196i
\(9\) −1.57876 −0.526255
\(10\) −1.92403 + 5.50457i −0.608431 + 1.74070i
\(11\) 0 0
\(12\) 10.2720i 2.96527i
\(13\) 3.07624i 0.853196i 0.904441 + 0.426598i \(0.140288\pi\)
−0.904441 + 0.426598i \(0.859712\pi\)
\(14\) −2.57876 −0.689204
\(15\) 1.57876 4.51678i 0.407635 1.16623i
\(16\) 9.44335 2.36084
\(17\) 1.61889i 0.392638i 0.980540 + 0.196319i \(0.0628988\pi\)
−0.980540 + 0.196319i \(0.937101\pi\)
\(18\) 4.11705i 0.970397i
\(19\) 6.58256 1.51014 0.755071 0.655643i \(-0.227602\pi\)
0.755071 + 0.655643i \(0.227602\pi\)
\(20\) 10.1330 + 3.54180i 2.26580 + 0.791971i
\(21\) 2.11601 0.461751
\(22\) 0 0
\(23\) 5.18097i 1.08031i 0.841566 + 0.540154i \(0.181634\pi\)
−0.841566 + 0.540154i \(0.818366\pi\)
\(24\) −15.6268 −3.18980
\(25\) 3.91128 + 3.11479i 0.782256 + 0.622957i
\(26\) 8.02212 1.57327
\(27\) 3.04117i 0.585273i
\(28\) 4.74705i 0.897109i
\(29\) 7.31216 1.35783 0.678917 0.734215i \(-0.262450\pi\)
0.678917 + 0.734215i \(0.262450\pi\)
\(30\) −11.7787 4.11705i −2.15049 0.751666i
\(31\) −2.64291 −0.474681 −0.237341 0.971426i \(-0.576276\pi\)
−0.237341 + 0.971426i \(0.576276\pi\)
\(32\) 10.0203i 1.77135i
\(33\) 0 0
\(34\) 4.22168 0.724012
\(35\) −0.729602 + 2.08736i −0.123325 + 0.352829i
\(36\) 7.57876 1.26313
\(37\) 2.80399i 0.460974i −0.973075 0.230487i \(-0.925968\pi\)
0.973075 0.230487i \(-0.0740319\pi\)
\(38\) 17.1658i 2.78466i
\(39\) −6.58256 −1.05405
\(40\) 5.38813 15.4152i 0.851938 2.43736i
\(41\) −1.38641 −0.216520 −0.108260 0.994123i \(-0.534528\pi\)
−0.108260 + 0.994123i \(0.534528\pi\)
\(42\) 5.51805i 0.851454i
\(43\) 3.18585i 0.485837i 0.970047 + 0.242919i \(0.0781048\pi\)
−0.970047 + 0.242919i \(0.921895\pi\)
\(44\) 0 0
\(45\) 3.33252 + 1.16482i 0.496782 + 0.173642i
\(46\) 13.5108 1.99205
\(47\) 2.13980i 0.312123i 0.987747 + 0.156061i \(0.0498797\pi\)
−0.987747 + 0.156061i \(0.950120\pi\)
\(48\) 20.2069i 2.91662i
\(49\) 6.02212 0.860303
\(50\) 8.12263 10.1997i 1.14871 1.44246i
\(51\) −3.46410 −0.485071
\(52\) 14.7673i 2.04786i
\(53\) 2.37698i 0.326503i −0.986584 0.163252i \(-0.947802\pi\)
0.986584 0.163252i \(-0.0521982\pi\)
\(54\) 7.93065 1.07923
\(55\) 0 0
\(56\) 7.22168 0.965037
\(57\) 14.0854i 1.86566i
\(58\) 19.0684i 2.50380i
\(59\) −12.2438 −1.59401 −0.797003 0.603975i \(-0.793583\pi\)
−0.797003 + 0.603975i \(0.793583\pi\)
\(60\) −7.57876 + 21.6825i −0.978414 + 2.79921i
\(61\) 1.00245 0.128350 0.0641752 0.997939i \(-0.479558\pi\)
0.0641752 + 0.997939i \(0.479558\pi\)
\(62\) 6.89210i 0.875297i
\(63\) 1.56121i 0.196693i
\(64\) −7.24380 −0.905475
\(65\) 2.26967 6.49345i 0.281519 0.805414i
\(66\) 0 0
\(67\) 9.84499i 1.20276i 0.798964 + 0.601379i \(0.205382\pi\)
−0.798964 + 0.601379i \(0.794618\pi\)
\(68\) 7.77137i 0.942417i
\(69\) −11.0863 −1.33463
\(70\) 5.44335 + 1.90263i 0.650605 + 0.227408i
\(71\) −0.243796 −0.0289333 −0.0144666 0.999895i \(-0.504605\pi\)
−0.0144666 + 0.999895i \(0.504605\pi\)
\(72\) 11.5295i 1.35877i
\(73\) 13.6688i 1.59982i 0.600122 + 0.799908i \(0.295119\pi\)
−0.600122 + 0.799908i \(0.704881\pi\)
\(74\) −7.31216 −0.850021
\(75\) −6.66503 + 8.36938i −0.769612 + 0.966412i
\(76\) −31.5992 −3.62467
\(77\) 0 0
\(78\) 17.1658i 1.94364i
\(79\) 7.69612 0.865881 0.432940 0.901423i \(-0.357476\pi\)
0.432940 + 0.901423i \(0.357476\pi\)
\(80\) −19.9334 6.96738i −2.22862 0.778977i
\(81\) −11.2438 −1.24931
\(82\) 3.61542i 0.399256i
\(83\) 5.95515i 0.653662i −0.945083 0.326831i \(-0.894019\pi\)
0.945083 0.326831i \(-0.105981\pi\)
\(84\) −10.1578 −1.10830
\(85\) 1.19443 3.41721i 0.129554 0.370648i
\(86\) 8.30795 0.895869
\(87\) 15.6466i 1.67749i
\(88\) 0 0
\(89\) −9.00000 −0.953998 −0.476999 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) 3.03759 8.69042i 0.320190 0.916051i
\(91\) 3.04203 0.318891
\(92\) 24.8710i 2.59298i
\(93\) 5.65532i 0.586429i
\(94\) 5.58011 0.575544
\(95\) −13.8947 4.85666i −1.42557 0.498283i
\(96\) 21.4414 2.18836
\(97\) 12.7389i 1.29344i −0.762727 0.646721i \(-0.776140\pi\)
0.762727 0.646721i \(-0.223860\pi\)
\(98\) 15.7043i 1.58637i
\(99\) 0 0
\(100\) −18.7759 14.9523i −1.87759 1.49523i
\(101\) −15.2811 −1.52053 −0.760264 0.649614i \(-0.774931\pi\)
−0.760264 + 0.649614i \(0.774931\pi\)
\(102\) 9.03357i 0.894456i
\(103\) 8.13220i 0.801290i 0.916233 + 0.400645i \(0.131214\pi\)
−0.916233 + 0.400645i \(0.868786\pi\)
\(104\) −22.4655 −2.20292
\(105\) −4.46655 1.56121i −0.435891 0.152358i
\(106\) −6.19860 −0.602061
\(107\) 6.62096i 0.640072i −0.947405 0.320036i \(-0.896305\pi\)
0.947405 0.320036i \(-0.103695\pi\)
\(108\) 14.5989i 1.40478i
\(109\) 2.84561 0.272560 0.136280 0.990670i \(-0.456485\pi\)
0.136280 + 0.990670i \(0.456485\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 9.33833i 0.882390i
\(113\) 17.7400i 1.66884i 0.551129 + 0.834420i \(0.314197\pi\)
−0.551129 + 0.834420i \(0.685803\pi\)
\(114\) 36.7314 3.44021
\(115\) 3.82256 10.9362i 0.356456 1.01981i
\(116\) −35.1016 −3.25910
\(117\) 4.85666i 0.448998i
\(118\) 31.9290i 2.93930i
\(119\) 1.60088 0.146753
\(120\) 32.9856 + 11.5295i 3.01116 + 1.05250i
\(121\) 0 0
\(122\) 2.61415i 0.236674i
\(123\) 2.96664i 0.267493i
\(124\) 12.6872 1.13934
\(125\) −5.95797 9.46058i −0.532897 0.846180i
\(126\) 4.07126 0.362697
\(127\) 17.2712i 1.53257i 0.642498 + 0.766287i \(0.277898\pi\)
−0.642498 + 0.766287i \(0.722102\pi\)
\(128\) 1.15041i 0.101683i
\(129\) −6.81709 −0.600212
\(130\) −16.9334 5.91878i −1.48516 0.519111i
\(131\) 5.12335 0.447629 0.223815 0.974632i \(-0.428149\pi\)
0.223815 + 0.974632i \(0.428149\pi\)
\(132\) 0 0
\(133\) 6.50935i 0.564432i
\(134\) 25.6734 2.21785
\(135\) 2.24380 6.41941i 0.193115 0.552495i
\(136\) −11.8226 −1.01378
\(137\) 7.27817i 0.621816i 0.950440 + 0.310908i \(0.100633\pi\)
−0.950440 + 0.310908i \(0.899367\pi\)
\(138\) 28.9104i 2.46102i
\(139\) 11.5059 0.975915 0.487957 0.872867i \(-0.337742\pi\)
0.487957 + 0.872867i \(0.337742\pi\)
\(140\) 3.50241 10.0203i 0.296008 0.846867i
\(141\) −4.57876 −0.385601
\(142\) 0.635763i 0.0533521i
\(143\) 0 0
\(144\) −14.9088 −1.24240
\(145\) −15.4348 5.39497i −1.28179 0.448028i
\(146\) 35.6451 2.95001
\(147\) 12.8862i 1.06283i
\(148\) 13.4604i 1.10644i
\(149\) 10.3195 0.845407 0.422703 0.906268i \(-0.361081\pi\)
0.422703 + 0.906268i \(0.361081\pi\)
\(150\) 21.8254 + 17.3808i 1.78203 + 1.41914i
\(151\) 14.9700 1.21824 0.609119 0.793079i \(-0.291523\pi\)
0.609119 + 0.793079i \(0.291523\pi\)
\(152\) 48.0717i 3.89913i
\(153\) 2.55584i 0.206627i
\(154\) 0 0
\(155\) 5.57876 + 1.94996i 0.448097 + 0.156625i
\(156\) 31.5992 2.52996
\(157\) 18.0671i 1.44191i −0.692980 0.720957i \(-0.743703\pi\)
0.692980 0.720957i \(-0.256297\pi\)
\(158\) 20.0697i 1.59666i
\(159\) 5.08627 0.403367
\(160\) −7.39303 + 21.1512i −0.584470 + 1.67215i
\(161\) 5.12335 0.403777
\(162\) 29.3212i 2.30369i
\(163\) 21.4028i 1.67639i 0.545367 + 0.838197i \(0.316390\pi\)
−0.545367 + 0.838197i \(0.683610\pi\)
\(164\) 6.65536 0.519696
\(165\) 0 0
\(166\) −15.5296 −1.20533
\(167\) 12.5761i 0.973168i −0.873634 0.486584i \(-0.838243\pi\)
0.873634 0.486584i \(-0.161757\pi\)
\(168\) 15.4530i 1.19222i
\(169\) 3.53673 0.272056
\(170\) −8.91128 3.11479i −0.683464 0.238893i
\(171\) −10.3923 −0.794719
\(172\) 15.2935i 1.16612i
\(173\) 9.91066i 0.753494i −0.926316 0.376747i \(-0.877043\pi\)
0.926316 0.376747i \(-0.122957\pi\)
\(174\) 40.8026 3.09324
\(175\) 3.08015 3.86778i 0.232837 0.292377i
\(176\) 0 0
\(177\) 26.1993i 1.96926i
\(178\) 23.4699i 1.75914i
\(179\) 2.44335 0.182625 0.0913125 0.995822i \(-0.470894\pi\)
0.0913125 + 0.995822i \(0.470894\pi\)
\(180\) −15.9975 5.59167i −1.19239 0.416778i
\(181\) −14.2018 −1.05561 −0.527804 0.849366i \(-0.676985\pi\)
−0.527804 + 0.849366i \(0.676985\pi\)
\(182\) 7.93290i 0.588026i
\(183\) 2.14504i 0.158566i
\(184\) −37.8361 −2.78931
\(185\) −2.06881 + 5.91878i −0.152102 + 0.435157i
\(186\) −14.7477 −1.08136
\(187\) 0 0
\(188\) 10.2720i 0.749163i
\(189\) 3.00735 0.218752
\(190\) −12.6650 + 36.2342i −0.918818 + 2.62870i
\(191\) 17.4013 1.25912 0.629558 0.776954i \(-0.283236\pi\)
0.629558 + 0.776954i \(0.283236\pi\)
\(192\) 15.5003i 1.11864i
\(193\) 11.0091i 0.792456i −0.918152 0.396228i \(-0.870319\pi\)
0.918152 0.396228i \(-0.129681\pi\)
\(194\) −33.2201 −2.38507
\(195\) 13.8947 + 4.85666i 0.995021 + 0.347793i
\(196\) −28.9088 −2.06492
\(197\) 3.49279i 0.248851i −0.992229 0.124426i \(-0.960291\pi\)
0.992229 0.124426i \(-0.0397088\pi\)
\(198\) 0 0
\(199\) −2.84247 −0.201498 −0.100749 0.994912i \(-0.532124\pi\)
−0.100749 + 0.994912i \(0.532124\pi\)
\(200\) −22.7469 + 28.5637i −1.60845 + 2.01976i
\(201\) −21.0664 −1.48591
\(202\) 39.8496i 2.80381i
\(203\) 7.23084i 0.507505i
\(204\) 16.6292 1.16428
\(205\) 2.92648 + 1.02290i 0.204394 + 0.0714424i
\(206\) 21.2069 1.47755
\(207\) 8.17953i 0.568517i
\(208\) 29.0500i 2.01426i
\(209\) 0 0
\(210\) −4.07126 + 11.6477i −0.280944 + 0.803769i
\(211\) −3.11846 −0.214683 −0.107342 0.994222i \(-0.534234\pi\)
−0.107342 + 0.994222i \(0.534234\pi\)
\(212\) 11.4105i 0.783679i
\(213\) 0.521676i 0.0357447i
\(214\) −17.2659 −1.18027
\(215\) 2.35054 6.72481i 0.160306 0.458628i
\(216\) −22.2093 −1.51115
\(217\) 2.61352i 0.177417i
\(218\) 7.42068i 0.502592i
\(219\) −29.2486 −1.97644
\(220\) 0 0
\(221\) −4.98009 −0.334997
\(222\) 15.6466i 1.05013i
\(223\) 12.3692i 0.828303i −0.910208 0.414152i \(-0.864078\pi\)
0.910208 0.414152i \(-0.135922\pi\)
\(224\) −9.90883 −0.662061
\(225\) −6.17499 4.91751i −0.411666 0.327834i
\(226\) 46.2618 3.07729
\(227\) 13.6169i 0.903786i −0.892072 0.451893i \(-0.850749\pi\)
0.892072 0.451893i \(-0.149251\pi\)
\(228\) 67.6161i 4.47798i
\(229\) −5.84247 −0.386081 −0.193041 0.981191i \(-0.561835\pi\)
−0.193041 + 0.981191i \(0.561835\pi\)
\(230\) −28.5190 9.96834i −1.88049 0.657293i
\(231\) 0 0
\(232\) 53.3999i 3.50588i
\(233\) 23.4398i 1.53559i −0.640693 0.767797i \(-0.721353\pi\)
0.640693 0.767797i \(-0.278647\pi\)
\(234\) −12.6650 −0.827939
\(235\) 1.57876 4.51678i 0.102987 0.294642i
\(236\) 58.7756 3.82597
\(237\) 16.4682i 1.06972i
\(238\) 4.17473i 0.270607i
\(239\) 6.58256 0.425790 0.212895 0.977075i \(-0.431711\pi\)
0.212895 + 0.977075i \(0.431711\pi\)
\(240\) 14.9088 42.6536i 0.962361 2.75328i
\(241\) 12.1627 0.783466 0.391733 0.920079i \(-0.371876\pi\)
0.391733 + 0.920079i \(0.371876\pi\)
\(242\) 0 0
\(243\) 14.9360i 0.958146i
\(244\) −4.81220 −0.308069
\(245\) −12.7117 4.44316i −0.812122 0.283863i
\(246\) −7.73629 −0.493248
\(247\) 20.2495i 1.28845i
\(248\) 19.3009i 1.22561i
\(249\) 12.7428 0.807545
\(250\) −24.6710 + 15.5370i −1.56033 + 0.982645i
\(251\) −1.08627 −0.0685646 −0.0342823 0.999412i \(-0.510915\pi\)
−0.0342823 + 0.999412i \(0.510915\pi\)
\(252\) 7.49448i 0.472108i
\(253\) 0 0
\(254\) 45.0393 2.82602
\(255\) 7.31216 + 2.55584i 0.457905 + 0.160053i
\(256\) −17.4876 −1.09297
\(257\) 24.2494i 1.51263i 0.654205 + 0.756317i \(0.273003\pi\)
−0.654205 + 0.756317i \(0.726997\pi\)
\(258\) 17.7774i 1.10677i
\(259\) −2.77281 −0.172294
\(260\) −10.8954 + 31.1714i −0.675707 + 1.93317i
\(261\) −11.5442 −0.714566
\(262\) 13.3605i 0.825415i
\(263\) 2.49816i 0.154043i −0.997029 0.0770216i \(-0.975459\pi\)
0.997029 0.0770216i \(-0.0245410\pi\)
\(264\) 0 0
\(265\) −1.75375 + 5.01742i −0.107732 + 0.308217i
\(266\) −16.9749 −1.04080
\(267\) 19.2582i 1.17859i
\(268\) 47.2603i 2.88688i
\(269\) −16.0863 −0.980797 −0.490399 0.871498i \(-0.663149\pi\)
−0.490399 + 0.871498i \(0.663149\pi\)
\(270\) −16.7403 5.85129i −1.01878 0.356098i
\(271\) −2.00490 −0.121789 −0.0608944 0.998144i \(-0.519395\pi\)
−0.0608944 + 0.998144i \(0.519395\pi\)
\(272\) 15.2877i 0.926954i
\(273\) 6.50935i 0.393964i
\(274\) 18.9798 1.14661
\(275\) 0 0
\(276\) 53.2190 3.20341
\(277\) 19.3586i 1.16315i 0.813494 + 0.581573i \(0.197562\pi\)
−0.813494 + 0.581573i \(0.802438\pi\)
\(278\) 30.0046i 1.79956i
\(279\) 4.17254 0.249803
\(280\) −15.2438 5.32821i −0.910991 0.318421i
\(281\) 2.91841 0.174098 0.0870488 0.996204i \(-0.472256\pi\)
0.0870488 + 0.996204i \(0.472256\pi\)
\(282\) 11.9403i 0.711037i
\(283\) 0.572327i 0.0340213i −0.999855 0.0170107i \(-0.994585\pi\)
0.999855 0.0170107i \(-0.00541492\pi\)
\(284\) 1.17033 0.0694463
\(285\) 10.3923 29.7320i 0.615587 1.76117i
\(286\) 0 0
\(287\) 1.37099i 0.0809268i
\(288\) 15.8196i 0.932181i
\(289\) 14.3792 0.845836
\(290\) −14.0688 + 40.2503i −0.826149 + 2.36358i
\(291\) 27.2588 1.59794
\(292\) 65.6164i 3.83991i
\(293\) 9.33258i 0.545215i −0.962125 0.272608i \(-0.912114\pi\)
0.962125 0.272608i \(-0.0878860\pi\)
\(294\) 33.6041 1.95983
\(295\) 25.8447 + 9.03357i 1.50474 + 0.525954i
\(296\) 20.4773 1.19022
\(297\) 0 0
\(298\) 26.9109i 1.55890i
\(299\) −15.9379 −0.921714
\(300\) 31.9951 40.1767i 1.84724 2.31960i
\(301\) 3.15042 0.181587
\(302\) 39.0382i 2.24639i
\(303\) 32.6986i 1.87849i
\(304\) 62.1614 3.56520
\(305\) −2.11601 0.739614i −0.121162 0.0423502i
\(306\) −6.66503 −0.381015
\(307\) 6.34982i 0.362404i 0.983446 + 0.181202i \(0.0579987\pi\)
−0.983446 + 0.181202i \(0.942001\pi\)
\(308\) 0 0
\(309\) −17.4013 −0.989927
\(310\) 5.08504 14.5481i 0.288811 0.826277i
\(311\) 22.5589 1.27920 0.639598 0.768710i \(-0.279101\pi\)
0.639598 + 0.768710i \(0.279101\pi\)
\(312\) 48.0717i 2.72153i
\(313\) 25.5778i 1.44574i 0.690984 + 0.722870i \(0.257177\pi\)
−0.690984 + 0.722870i \(0.742823\pi\)
\(314\) −47.1148 −2.65884
\(315\) 1.15187 3.29545i 0.0649005 0.185678i
\(316\) −36.9448 −2.07830
\(317\) 24.8236i 1.39423i −0.716958 0.697117i \(-0.754466\pi\)
0.716958 0.697117i \(-0.245534\pi\)
\(318\) 13.2638i 0.743797i
\(319\) 0 0
\(320\) 15.2905 + 5.34453i 0.854764 + 0.298768i
\(321\) 14.1676 0.790756
\(322\) 13.3605i 0.744552i
\(323\) 10.6564i 0.592939i
\(324\) 53.9752 2.99862
\(325\) −9.58183 + 12.0320i −0.531505 + 0.667418i
\(326\) 55.8134 3.09122
\(327\) 6.08905i 0.336725i
\(328\) 10.1248i 0.559047i
\(329\) 2.11601 0.116659
\(330\) 0 0
\(331\) −5.80044 −0.318821 −0.159411 0.987212i \(-0.550959\pi\)
−0.159411 + 0.987212i \(0.550959\pi\)
\(332\) 28.5873i 1.56893i
\(333\) 4.42685i 0.242590i
\(334\) −32.7955 −1.79449
\(335\) 7.26371 20.7812i 0.396859 1.13540i
\(336\) 19.9822 1.09012
\(337\) 0.0461700i 0.00251504i 0.999999 + 0.00125752i \(0.000400281\pi\)
−0.999999 + 0.00125752i \(0.999600\pi\)
\(338\) 9.22297i 0.501664i
\(339\) −37.9602 −2.06171
\(340\) −5.73378 + 16.4041i −0.310958 + 0.889638i
\(341\) 0 0
\(342\) 27.1007i 1.46544i
\(343\) 12.8773i 0.695309i
\(344\) −23.2659 −1.25441
\(345\) 23.4013 + 8.17953i 1.25988 + 0.440371i
\(346\) −25.8447 −1.38942
\(347\) 31.5643i 1.69446i 0.531225 + 0.847231i \(0.321732\pi\)
−0.531225 + 0.847231i \(0.678268\pi\)
\(348\) 75.1106i 4.02635i
\(349\) −30.3239 −1.62320 −0.811600 0.584213i \(-0.801403\pi\)
−0.811600 + 0.584213i \(0.801403\pi\)
\(350\) −10.0863 8.03230i −0.539134 0.429344i
\(351\) −9.35537 −0.499353
\(352\) 0 0
\(353\) 19.1157i 1.01743i 0.860936 + 0.508714i \(0.169879\pi\)
−0.860936 + 0.508714i \(0.830121\pi\)
\(354\) −68.3217 −3.63126
\(355\) 0.514615 + 0.179875i 0.0273129 + 0.00954676i
\(356\) 43.2040 2.28981
\(357\) 3.42558i 0.181301i
\(358\) 6.37170i 0.336755i
\(359\) −26.8981 −1.41963 −0.709814 0.704390i \(-0.751221\pi\)
−0.709814 + 0.704390i \(0.751221\pi\)
\(360\) −8.50659 + 24.3370i −0.448336 + 1.28267i
\(361\) 24.3301 1.28053
\(362\) 37.0349i 1.94651i
\(363\) 0 0
\(364\) −14.6031 −0.765410
\(365\) 10.0850 28.8527i 0.527871 1.51022i
\(366\) 5.59377 0.292391
\(367\) 8.04226i 0.419803i −0.977723 0.209901i \(-0.932686\pi\)
0.977723 0.209901i \(-0.0673143\pi\)
\(368\) 48.9258i 2.55043i
\(369\) 2.18881 0.113945
\(370\) 15.4348 + 5.39497i 0.802417 + 0.280471i
\(371\) −2.35054 −0.122034
\(372\) 27.1480i 1.40756i
\(373\) 27.7542i 1.43706i −0.695496 0.718530i \(-0.744815\pi\)
0.695496 0.718530i \(-0.255185\pi\)
\(374\) 0 0
\(375\) 20.2438 12.7489i 1.04539 0.658350i
\(376\) −15.6268 −0.805889
\(377\) 22.4940i 1.15850i
\(378\) 7.84245i 0.403372i
\(379\) 18.3151 0.940781 0.470391 0.882458i \(-0.344113\pi\)
0.470391 + 0.882458i \(0.344113\pi\)
\(380\) 66.7008 + 23.3141i 3.42168 + 1.19599i
\(381\) −36.9571 −1.89337
\(382\) 45.3786i 2.32177i
\(383\) 17.4602i 0.892177i −0.894989 0.446088i \(-0.852817\pi\)
0.894989 0.446088i \(-0.147183\pi\)
\(384\) 2.46165 0.125621
\(385\) 0 0
\(386\) −28.7093 −1.46126
\(387\) 5.02970i 0.255674i
\(388\) 61.1524i 3.10455i
\(389\) −13.5589 −0.687461 −0.343731 0.939068i \(-0.611691\pi\)
−0.343731 + 0.939068i \(0.611691\pi\)
\(390\) 12.6650 36.2342i 0.641319 1.83479i
\(391\) −8.38741 −0.424169
\(392\) 43.9789i 2.22127i
\(393\) 10.9630i 0.553009i
\(394\) −9.10839 −0.458874
\(395\) −16.2453 5.67825i −0.817388 0.285704i
\(396\) 0 0
\(397\) 2.42431i 0.121673i 0.998148 + 0.0608363i \(0.0193767\pi\)
−0.998148 + 0.0608363i \(0.980623\pi\)
\(398\) 7.41250i 0.371555i
\(399\) 13.9287 0.697309
\(400\) 36.9356 + 29.4140i 1.84678 + 1.47070i
\(401\) −16.4141 −0.819682 −0.409841 0.912157i \(-0.634416\pi\)
−0.409841 + 0.912157i \(0.634416\pi\)
\(402\) 54.9361i 2.73996i
\(403\) 8.13024i 0.404996i
\(404\) 73.3561 3.64960
\(405\) 23.7338 + 8.29576i 1.17934 + 0.412220i
\(406\) −18.8563 −0.935824
\(407\) 0 0
\(408\) 25.2980i 1.25244i
\(409\) −19.4748 −0.962968 −0.481484 0.876455i \(-0.659902\pi\)
−0.481484 + 0.876455i \(0.659902\pi\)
\(410\) 2.66748 7.63157i 0.131738 0.376896i
\(411\) −15.5739 −0.768202
\(412\) 39.0382i 1.92327i
\(413\) 12.1076i 0.595778i
\(414\) −21.3303 −1.04833
\(415\) −4.39375 + 12.5704i −0.215681 + 0.617054i
\(416\) 30.8248 1.51131
\(417\) 24.6203i 1.20566i
\(418\) 0 0
\(419\) 1.84468 0.0901185 0.0450592 0.998984i \(-0.485652\pi\)
0.0450592 + 0.998984i \(0.485652\pi\)
\(420\) 21.4414 + 7.49448i 1.04623 + 0.365693i
\(421\) −21.1996 −1.03320 −0.516602 0.856226i \(-0.672803\pi\)
−0.516602 + 0.856226i \(0.672803\pi\)
\(422\) 8.13220i 0.395869i
\(423\) 3.37825i 0.164256i
\(424\) 17.3588 0.843019
\(425\) −5.04249 + 6.33192i −0.244596 + 0.307143i
\(426\) −1.36041 −0.0659121
\(427\) 0.991300i 0.0479724i
\(428\) 31.7835i 1.53632i
\(429\) 0 0
\(430\) −17.5367 6.12966i −0.845696 0.295599i
\(431\) 26.3302 1.26828 0.634141 0.773217i \(-0.281354\pi\)
0.634141 + 0.773217i \(0.281354\pi\)
\(432\) 28.7188i 1.38174i
\(433\) 9.13347i 0.438927i −0.975621 0.219463i \(-0.929569\pi\)
0.975621 0.219463i \(-0.0704306\pi\)
\(434\) 6.81545 0.327152
\(435\) 11.5442 33.0274i 0.553501 1.58354i
\(436\) −13.6602 −0.654204
\(437\) 34.1040i 1.63142i
\(438\) 76.2736i 3.64449i
\(439\) −11.0836 −0.528991 −0.264496 0.964387i \(-0.585205\pi\)
−0.264496 + 0.964387i \(0.585205\pi\)
\(440\) 0 0
\(441\) −9.50750 −0.452738
\(442\) 12.9869i 0.617724i
\(443\) 17.6827i 0.840131i 0.907494 + 0.420066i \(0.137993\pi\)
−0.907494 + 0.420066i \(0.862007\pi\)
\(444\) −28.8026 −1.36691
\(445\) 18.9975 + 6.64027i 0.900570 + 0.314779i
\(446\) −32.2560 −1.52737
\(447\) 22.0817i 1.04443i
\(448\) 7.16324i 0.338431i
\(449\) −16.9287 −0.798917 −0.399458 0.916751i \(-0.630802\pi\)
−0.399458 + 0.916751i \(0.630802\pi\)
\(450\) −12.8237 + 16.1029i −0.604516 + 0.759099i
\(451\) 0 0
\(452\) 85.1599i 4.00559i
\(453\) 32.0328i 1.50503i
\(454\) −35.5097 −1.66655
\(455\) −6.42124 2.24443i −0.301032 0.105221i
\(456\) −102.864 −4.81705
\(457\) 32.6109i 1.52547i −0.646709 0.762736i \(-0.723855\pi\)
0.646709 0.762736i \(-0.276145\pi\)
\(458\) 15.2358i 0.711922i
\(459\) −4.92331 −0.229800
\(460\) −18.3500 + 52.4986i −0.855572 + 2.44776i
\(461\) −7.96896 −0.371152 −0.185576 0.982630i \(-0.559415\pi\)
−0.185576 + 0.982630i \(0.559415\pi\)
\(462\) 0 0
\(463\) 25.3879i 1.17988i −0.807449 0.589938i \(-0.799152\pi\)
0.807449 0.589938i \(-0.200848\pi\)
\(464\) 69.0513 3.20563
\(465\) −4.17254 + 11.9375i −0.193497 + 0.553587i
\(466\) −61.1256 −2.83159
\(467\) 16.3070i 0.754599i 0.926091 + 0.377299i \(0.123147\pi\)
−0.926091 + 0.377299i \(0.876853\pi\)
\(468\) 23.3141i 1.07770i
\(469\) 9.73550 0.449544
\(470\) −11.7787 4.11705i −0.543311 0.189905i
\(471\) 38.6601 1.78136
\(472\) 89.4152i 4.11567i
\(473\) 0 0
\(474\) 42.9452 1.97254
\(475\) 25.7462 + 20.5033i 1.18132 + 0.940754i
\(476\) −7.68494 −0.352239
\(477\) 3.75269i 0.171824i
\(478\) 17.1658i 0.785144i
\(479\) 34.7943 1.58979 0.794895 0.606747i \(-0.207526\pi\)
0.794895 + 0.606747i \(0.207526\pi\)
\(480\) −45.2594 15.8196i −2.06580 0.722064i
\(481\) 8.62577 0.393301
\(482\) 31.7174i 1.44469i
\(483\) 10.9630i 0.498833i
\(484\) 0 0
\(485\) −9.39887 + 26.8898i −0.426781 + 1.22100i
\(486\) −38.9497 −1.76679
\(487\) 2.52421i 0.114383i −0.998363 0.0571915i \(-0.981785\pi\)
0.998363 0.0571915i \(-0.0182146\pi\)
\(488\) 7.32078i 0.331396i
\(489\) −45.7977 −2.07105
\(490\) −11.5867 + 33.1492i −0.523435 + 1.49753i
\(491\) 19.3254 0.872143 0.436072 0.899912i \(-0.356369\pi\)
0.436072 + 0.899912i \(0.356369\pi\)
\(492\) 14.2412i 0.642041i
\(493\) 11.8376i 0.533137i
\(494\) 52.8061 2.37586
\(495\) 0 0
\(496\) −24.9580 −1.12065
\(497\) 0.241085i 0.0108141i
\(498\) 33.2304i 1.48909i
\(499\) −1.15753 −0.0518181 −0.0259090 0.999664i \(-0.508248\pi\)
−0.0259090 + 0.999664i \(0.508248\pi\)
\(500\) 28.6009 + 45.4150i 1.27907 + 2.03102i
\(501\) 26.9104 1.20227
\(502\) 2.83273i 0.126431i
\(503\) 17.9890i 0.802089i −0.916059 0.401044i \(-0.868647\pi\)
0.916059 0.401044i \(-0.131353\pi\)
\(504\) −11.4013 −0.507855
\(505\) 32.2560 + 11.2745i 1.43537 + 0.501710i
\(506\) 0 0
\(507\) 7.56792i 0.336103i
\(508\) 82.9096i 3.67852i
\(509\) 11.3500 0.503079 0.251539 0.967847i \(-0.419063\pi\)
0.251539 + 0.967847i \(0.419063\pi\)
\(510\) 6.66503 19.0684i 0.295133 0.844363i
\(511\) 13.5168 0.597949
\(512\) 43.3027i 1.91373i
\(513\) 20.0187i 0.883845i
\(514\) 63.2367 2.78925
\(515\) 6.00000 17.1658i 0.264392 0.756414i
\(516\) 32.7251 1.44064
\(517\) 0 0
\(518\) 7.23084i 0.317705i
\(519\) 21.2069 0.930879
\(520\) 47.4210 + 16.5752i 2.07955 + 0.726870i
\(521\) 18.0243 0.789660 0.394830 0.918754i \(-0.370803\pi\)
0.394830 + 0.918754i \(0.370803\pi\)
\(522\) 30.1045i 1.31764i
\(523\) 18.0409i 0.788874i 0.918923 + 0.394437i \(0.129060\pi\)
−0.918923 + 0.394437i \(0.870940\pi\)
\(524\) −24.5944 −1.07441
\(525\) 8.27630 + 6.59091i 0.361207 + 0.287651i
\(526\) −6.51461 −0.284051
\(527\) 4.27858i 0.186378i
\(528\) 0 0
\(529\) −3.84247 −0.167064
\(530\) 13.0842 + 4.57337i 0.568343 + 0.198655i
\(531\) 19.3301 0.838853
\(532\) 31.2478i 1.35476i
\(533\) 4.26492i 0.184734i
\(534\) −50.2210 −2.17327
\(535\) −4.88500 + 13.9758i −0.211197 + 0.604226i
\(536\) −71.8969 −3.10547
\(537\) 5.22830i 0.225618i
\(538\) 41.9492i 1.80856i
\(539\) 0 0
\(540\) −10.7712 + 30.8160i −0.463519 + 1.32611i
\(541\) 6.34802 0.272923 0.136461 0.990645i \(-0.456427\pi\)
0.136461 + 0.990645i \(0.456427\pi\)
\(542\) 5.22830i 0.224575i
\(543\) 30.3890i 1.30412i
\(544\) 16.2217 0.695499
\(545\) −6.00662 2.09951i −0.257295 0.0899332i
\(546\) 16.9749 0.726457
\(547\) 15.2300i 0.651190i −0.945509 0.325595i \(-0.894435\pi\)
0.945509 0.325595i \(-0.105565\pi\)
\(548\) 34.9384i 1.49250i
\(549\) −1.58263 −0.0675450
\(550\) 0 0
\(551\) 48.1327 2.05052
\(552\) 80.9619i 3.44597i
\(553\) 7.61053i 0.323632i
\(554\) 50.4827 2.14480
\(555\) −12.6650 4.42685i −0.537601 0.187909i
\(556\) −55.2332 −2.34241
\(557\) 40.9027i 1.73310i −0.499089 0.866551i \(-0.666332\pi\)
0.499089 0.866551i \(-0.333668\pi\)
\(558\) 10.8810i 0.460629i
\(559\) −9.80044 −0.414515
\(560\) −6.88989 + 19.7117i −0.291151 + 0.832972i
\(561\) 0 0
\(562\) 7.61053i 0.321031i
\(563\) 17.9993i 0.758582i 0.925277 + 0.379291i \(0.123832\pi\)
−0.925277 + 0.379291i \(0.876168\pi\)
\(564\) 21.9801 0.925529
\(565\) 13.0887 37.4463i 0.550647 1.57538i
\(566\) −1.49250 −0.0627343
\(567\) 11.1188i 0.466944i
\(568\) 1.78042i 0.0747047i
\(569\) −40.7200 −1.70707 −0.853536 0.521034i \(-0.825546\pi\)
−0.853536 + 0.521034i \(0.825546\pi\)
\(570\) −77.5340 27.1007i −3.24754 1.13512i
\(571\) −13.2417 −0.554149 −0.277075 0.960848i \(-0.589365\pi\)
−0.277075 + 0.960848i \(0.589365\pi\)
\(572\) 0 0
\(573\) 37.2354i 1.55553i
\(574\) 3.57521 0.149226
\(575\) −16.1376 + 20.2642i −0.672985 + 0.845077i
\(576\) 11.4362 0.476510
\(577\) 0.659467i 0.0274540i −0.999906 0.0137270i \(-0.995630\pi\)
0.999906 0.0137270i \(-0.00436957\pi\)
\(578\) 37.4976i 1.55969i
\(579\) 23.5574 0.979013
\(580\) 74.0938 + 25.8982i 3.07658 + 1.07537i
\(581\) −5.88892 −0.244313
\(582\) 71.0846i 2.94655i
\(583\) 0 0
\(584\) −99.8221 −4.13067
\(585\) −3.58328 + 10.2516i −0.148150 + 0.423853i
\(586\) −24.3372 −1.00536
\(587\) 12.0747i 0.498378i −0.968455 0.249189i \(-0.919836\pi\)
0.968455 0.249189i \(-0.0801640\pi\)
\(588\) 61.8592i 2.55103i
\(589\) −17.3971 −0.716836
\(590\) 23.5574 67.3969i 0.969844 2.77469i
\(591\) 7.47390 0.307435
\(592\) 26.4791i 1.08828i
\(593\) 38.3249i 1.57382i 0.617070 + 0.786908i \(0.288320\pi\)
−0.617070 + 0.786908i \(0.711680\pi\)
\(594\) 0 0
\(595\) −3.37921 1.18114i −0.138534 0.0484222i
\(596\) −49.5382 −2.02916
\(597\) 6.08233i 0.248933i
\(598\) 41.5624i 1.69961i
\(599\) 4.28803 0.175204 0.0876022 0.996156i \(-0.472080\pi\)
0.0876022 + 0.996156i \(0.472080\pi\)
\(600\) −61.1207 48.6740i −2.49524 1.98711i
\(601\) 28.9413 1.18054 0.590270 0.807206i \(-0.299021\pi\)
0.590270 + 0.807206i \(0.299021\pi\)
\(602\) 8.21555i 0.334841i
\(603\) 15.5429i 0.632956i
\(604\) −71.8624 −2.92404
\(605\) 0 0
\(606\) −85.2703 −3.46387
\(607\) 11.0553i 0.448721i 0.974506 + 0.224361i \(0.0720294\pi\)
−0.974506 + 0.224361i \(0.927971\pi\)
\(608\) 65.9590i 2.67499i
\(609\) 15.4726 0.626981
\(610\) −1.92874 + 5.51805i −0.0780924 + 0.223419i
\(611\) −6.58256 −0.266302
\(612\) 12.2692i 0.495951i
\(613\) 10.5707i 0.426947i 0.976949 + 0.213474i \(0.0684778\pi\)
−0.976949 + 0.213474i \(0.931522\pi\)
\(614\) 16.5589 0.668261
\(615\) −2.18881 + 6.26209i −0.0882612 + 0.252512i
\(616\) 0 0
\(617\) 1.60816i 0.0647421i −0.999476 0.0323710i \(-0.989694\pi\)
0.999476 0.0323710i \(-0.0103058\pi\)
\(618\) 45.3786i 1.82539i
\(619\) 36.9309 1.48438 0.742190 0.670189i \(-0.233787\pi\)
0.742190 + 0.670189i \(0.233787\pi\)
\(620\) −26.7805 9.36068i −1.07553 0.375934i
\(621\) −15.7562 −0.632275
\(622\) 58.8282i 2.35880i
\(623\) 8.89991i 0.356567i
\(624\) −62.1614 −2.48845
\(625\) 5.59622 + 24.3656i 0.223849 + 0.974624i
\(626\) 66.7008 2.66590
\(627\) 0 0
\(628\) 86.7302i 3.46091i
\(629\) 4.53935 0.180996
\(630\) −8.59377 3.00381i −0.342384 0.119674i
\(631\) 43.0150 1.71240 0.856200 0.516644i \(-0.172819\pi\)
0.856200 + 0.516644i \(0.172819\pi\)
\(632\) 56.2039i 2.23567i
\(633\) 6.67289i 0.265223i
\(634\) −64.7342 −2.57092
\(635\) 12.7428 36.4568i 0.505684 1.44674i
\(636\) −24.4163 −0.968171
\(637\) 18.5255i 0.734007i
\(638\) 0 0
\(639\) 0.384897 0.0152263
\(640\) −0.848781 + 2.42833i −0.0335510 + 0.0959882i
\(641\) −22.3057 −0.881024 −0.440512 0.897747i \(-0.645203\pi\)
−0.440512 + 0.897747i \(0.645203\pi\)
\(642\) 36.9457i 1.45813i
\(643\) 32.6187i 1.28636i −0.765716 0.643179i \(-0.777615\pi\)
0.765716 0.643179i \(-0.222385\pi\)
\(644\) −24.5944 −0.969153
\(645\) 14.3898 + 5.02970i 0.566597 + 0.198044i
\(646\) 27.7894 1.09336
\(647\) 9.79766i 0.385186i −0.981279 0.192593i \(-0.938310\pi\)
0.981279 0.192593i \(-0.0616897\pi\)
\(648\) 82.1123i 3.22567i
\(649\) 0 0
\(650\) 31.3768 + 24.9872i 1.23070 + 0.980078i
\(651\) −5.59242 −0.219184
\(652\) 102.743i 4.02372i
\(653\) 28.2492i 1.10548i −0.833355 0.552738i \(-0.813583\pi\)
0.833355 0.552738i \(-0.186417\pi\)
\(654\) 15.8788 0.620911
\(655\) −10.8146 3.78005i −0.422560 0.147699i
\(656\) −13.0923 −0.511169
\(657\) 21.5799i 0.841911i
\(658\) 5.51805i 0.215116i
\(659\) −35.4089 −1.37934 −0.689668 0.724126i \(-0.742244\pi\)
−0.689668 + 0.724126i \(0.742244\pi\)
\(660\) 0 0
\(661\) 34.3615 1.33651 0.668254 0.743933i \(-0.267042\pi\)
0.668254 + 0.743933i \(0.267042\pi\)
\(662\) 15.1262i 0.587896i
\(663\) 10.6564i 0.413861i
\(664\) 43.4898 1.68773
\(665\) −4.80265 + 13.7402i −0.186239 + 0.532822i
\(666\) 11.5442 0.447328
\(667\) 37.8841i 1.46688i
\(668\) 60.3709i 2.33582i
\(669\) 26.4677 1.02330
\(670\) −54.1925 18.9420i −2.09364 0.731795i
\(671\) 0 0
\(672\) 21.2030i 0.817922i
\(673\) 28.8989i 1.11397i −0.830523 0.556985i \(-0.811958\pi\)
0.830523 0.556985i \(-0.188042\pi\)
\(674\) 0.120401 0.00463766
\(675\) −9.47258 + 11.8949i −0.364600 + 0.457833i
\(676\) −16.9779 −0.652995
\(677\) 19.5778i 0.752436i −0.926531 0.376218i \(-0.877224\pi\)
0.926531 0.376218i \(-0.122776\pi\)
\(678\) 98.9912i 3.80174i
\(679\) −12.5972 −0.483438
\(680\) 24.9555 + 8.72277i 0.957000 + 0.334503i
\(681\) 29.1375 1.11655
\(682\) 0 0
\(683\) 6.84643i 0.261971i 0.991384 + 0.130986i \(0.0418142\pi\)
−0.991384 + 0.130986i \(0.958186\pi\)
\(684\) 49.8877 1.90750
\(685\) 5.36989 15.3630i 0.205173 0.586992i
\(686\) −33.5810 −1.28213
\(687\) 12.5017i 0.476971i
\(688\) 30.0851i 1.14698i
\(689\) 7.31216 0.278571
\(690\) 21.3303 61.0252i 0.812031 2.32319i
\(691\) −35.5739 −1.35329 −0.676647 0.736308i \(-0.736568\pi\)
−0.676647 + 0.736308i \(0.736568\pi\)
\(692\) 47.5755i 1.80855i
\(693\) 0 0
\(694\) 82.3124 3.12453
\(695\) −24.2870 8.48911i −0.921259 0.322010i
\(696\) −114.265 −4.33122
\(697\) 2.24443i 0.0850140i
\(698\) 79.0776i 2.99313i
\(699\) 50.1567 1.89710
\(700\) −14.7861 + 18.5671i −0.558860 + 0.701769i
\(701\) −0.307335 −0.0116079 −0.00580394 0.999983i \(-0.501847\pi\)
−0.00580394 + 0.999983i \(0.501847\pi\)
\(702\) 24.3966i 0.920791i
\(703\) 18.4575i 0.696136i
\(704\) 0 0
\(705\) 9.66503 + 3.37825i 0.364006 + 0.127232i
\(706\) 49.8493 1.87610
\(707\) 15.1112i 0.568314i
\(708\) 125.768i 4.72666i
\(709\) 4.14821 0.155789 0.0778947 0.996962i \(-0.475180\pi\)
0.0778947 + 0.996962i \(0.475180\pi\)
\(710\) 0.469071 1.34199i 0.0176039 0.0503641i
\(711\) −12.1504 −0.455674
\(712\) 65.7261i 2.46319i
\(713\) 13.6929i 0.512802i
\(714\) 8.93310 0.334313
\(715\) 0 0
\(716\) −11.7292 −0.438340
\(717\) 14.0854i 0.526028i
\(718\) 70.1439i 2.61775i
\(719\) 2.87391 0.107179 0.0535893 0.998563i \(-0.482934\pi\)
0.0535893 + 0.998563i \(0.482934\pi\)
\(720\) 31.4701 + 10.9998i 1.17282 + 0.409940i
\(721\) 8.04176 0.299491
\(722\) 63.4471i 2.36126i
\(723\) 26.0257i 0.967907i
\(724\) 68.1747 2.53369
\(725\) 28.5999 + 22.7758i 1.06217 + 0.845872i
\(726\) 0 0
\(727\) 27.5703i 1.02253i 0.859424 + 0.511263i \(0.170822\pi\)
−0.859424 + 0.511263i \(0.829178\pi\)
\(728\) 22.2156i 0.823366i
\(729\) −1.77121 −0.0656005
\(730\) −75.2411 26.2992i −2.78480 0.973378i
\(731\) −5.15753 −0.190758
\(732\) 10.2972i 0.380594i
\(733\) 36.9830i 1.36600i −0.730420 0.682998i \(-0.760676\pi\)
0.730420 0.682998i \(-0.239324\pi\)
\(734\) −20.9723 −0.774103
\(735\) 9.50750 27.2006i 0.350690 1.00331i
\(736\) 51.9147 1.91360
\(737\) 0 0
\(738\) 5.70789i 0.210110i
\(739\) 44.9643 1.65404 0.827020 0.562172i \(-0.190034\pi\)
0.827020 + 0.562172i \(0.190034\pi\)
\(740\) 9.93119 28.4128i 0.365078 1.04447i
\(741\) −43.3301 −1.59177
\(742\) 6.12966i 0.225027i
\(743\) 26.6500i 0.977693i 0.872370 + 0.488847i \(0.162582\pi\)
−0.872370 + 0.488847i \(0.837418\pi\)
\(744\) 41.3002 1.51414
\(745\) −21.7828 7.61381i −0.798060 0.278948i
\(746\) −72.3765 −2.64989
\(747\) 9.40177i 0.343993i
\(748\) 0 0
\(749\) −6.54733 −0.239234
\(750\) −33.2461 52.7911i −1.21398 1.92766i
\(751\) 33.6451 1.22773 0.613864 0.789412i \(-0.289614\pi\)
0.613864 + 0.789412i \(0.289614\pi\)
\(752\) 20.2069i 0.736871i
\(753\) 2.32440i 0.0847059i
\(754\) 58.6590 2.13624
\(755\) −31.5992 11.0450i −1.15001 0.401967i
\(756\) −14.4366 −0.525054
\(757\) 1.34307i 0.0488147i −0.999702 0.0244074i \(-0.992230\pi\)
0.999702 0.0244074i \(-0.00776988\pi\)
\(758\) 47.7614i 1.73477i
\(759\) 0 0
\(760\) 35.4677 101.472i 1.28655 3.68076i
\(761\) −1.62094 −0.0587591 −0.0293795 0.999568i \(-0.509353\pi\)
−0.0293795 + 0.999568i \(0.509353\pi\)
\(762\) 96.3754i 3.49131i
\(763\) 2.81396i 0.101872i
\(764\) −83.5340 −3.02216
\(765\) −1.88572 + 5.39497i −0.0681783 + 0.195055i
\(766\) −45.5322 −1.64515
\(767\) 37.6649i 1.36000i
\(768\) 37.4200i 1.35028i
\(769\) 3.62584 0.130751 0.0653755 0.997861i \(-0.479175\pi\)
0.0653755 + 0.997861i \(0.479175\pi\)
\(770\) 0 0
\(771\) −51.8889 −1.86873
\(772\) 52.8488i 1.90207i
\(773\) 22.0996i 0.794867i −0.917631 0.397434i \(-0.869901\pi\)
0.917631 0.397434i \(-0.130099\pi\)
\(774\) −13.1163 −0.471455
\(775\) −10.3372 8.23211i −0.371322 0.295706i
\(776\) 93.0310 3.33962
\(777\) 5.93327i 0.212855i
\(778\) 35.3583i 1.26766i
\(779\) −9.12609 −0.326976
\(780\) −66.7008 23.3141i −2.38827 0.834779i
\(781\) 0 0
\(782\) 21.8724i 0.782155i
\(783\) 22.2375i 0.794703i
\(784\) 56.8690 2.03104
\(785\) −13.3301 + 38.1368i −0.475770 + 1.36116i
\(786\) 28.5889 1.01973
\(787\) 1.84385i 0.0657263i 0.999460 + 0.0328632i \(0.0104626\pi\)
−0.999460 + 0.0328632i \(0.989537\pi\)
\(788\) 16.7670i 0.597298i
\(789\) 5.34557 0.190307
\(790\) −14.8076 + 42.3638i −0.526829 + 1.50724i
\(791\) 17.5427 0.623748
\(792\) 0 0
\(793\) 3.08377i 0.109508i
\(794\) 6.32203 0.224360
\(795\) −10.7363 3.75269i −0.380777 0.133094i
\(796\) 13.6451 0.483638
\(797\) 48.4609i 1.71657i −0.513172 0.858286i \(-0.671530\pi\)
0.513172 0.858286i \(-0.328470\pi\)
\(798\) 36.3229i 1.28582i
\(799\) −3.46410 −0.122551
\(800\) 31.2110 39.1921i 1.10347 1.38565i
\(801\) 14.2089 0.502046
\(802\) 42.8042i 1.51147i
\(803\) 0 0
\(804\) 101.128 3.56650
\(805\) −10.8146 3.78005i −0.381164 0.133229i
\(806\) −21.2018 −0.746800
\(807\) 34.4215i 1.21169i
\(808\) 111.596i 3.92595i
\(809\) −16.5526 −0.581958 −0.290979 0.956729i \(-0.593981\pi\)
−0.290979 + 0.956729i \(0.593981\pi\)
\(810\) 21.6334 61.8923i 0.760120 2.17467i
\(811\) −14.7477 −0.517863 −0.258932 0.965896i \(-0.583370\pi\)
−0.258932 + 0.965896i \(0.583370\pi\)
\(812\) 34.7112i 1.21813i
\(813\) 4.29009i 0.150460i
\(814\) 0 0
\(815\) 15.7911 45.1778i 0.553139 1.58251i
\(816\) −32.7127 −1.14517
\(817\) 20.9710i 0.733683i
\(818\) 50.7858i 1.77568i
\(819\) −4.80265 −0.167818
\(820\) −14.0484 4.91037i −0.490591 0.171478i
\(821\) −41.1891 −1.43751 −0.718754 0.695264i \(-0.755287\pi\)
−0.718754 + 0.695264i \(0.755287\pi\)
\(822\) 40.6130i 1.41654i
\(823\) 2.43428i 0.0848535i −0.999100 0.0424268i \(-0.986491\pi\)
0.999100 0.0424268i \(-0.0135089\pi\)
\(824\) −59.3886 −2.06890
\(825\) 0 0
\(826\) 31.5739 1.09860
\(827\) 42.0173i 1.46108i −0.682868 0.730542i \(-0.739268\pi\)
0.682868 0.730542i \(-0.260732\pi\)
\(828\) 39.2654i 1.36457i
\(829\) 12.9730 0.450570 0.225285 0.974293i \(-0.427669\pi\)
0.225285 + 0.974293i \(0.427669\pi\)
\(830\) 32.7805 + 11.4579i 1.13783 + 0.397709i
\(831\) −41.4236 −1.43697
\(832\) 22.2837i 0.772547i
\(833\) 9.74913i 0.337787i
\(834\) 64.2040 2.22320
\(835\) −9.27875 + 26.5461i −0.321104 + 0.918667i
\(836\) 0 0
\(837\) 8.03754i 0.277818i
\(838\) 4.81049i 0.166176i
\(839\) −30.4876 −1.05255 −0.526274 0.850315i \(-0.676411\pi\)
−0.526274 + 0.850315i \(0.676411\pi\)
\(840\) 11.4013 32.6187i 0.393383 1.12545i
\(841\) 24.4677 0.843713
\(842\) 55.2835i 1.90519i
\(843\) 6.24482i 0.215083i
\(844\) 14.9700 0.515287
\(845\) −7.46547 2.60943i −0.256820 0.0897671i
\(846\) −8.80968 −0.302883
\(847\) 0 0
\(848\) 22.4466i 0.770821i
\(849\) 1.22467 0.0420305
\(850\) 16.5122 + 13.1496i 0.566363 + 0.451028i
\(851\) 14.5274 0.497993
\(852\) 2.50428i 0.0857951i
\(853\) 40.7630i 1.39570i 0.716245 + 0.697849i \(0.245859\pi\)
−0.716245 + 0.697849i \(0.754141\pi\)
\(854\) −2.58508 −0.0884596
\(855\) 21.9365 + 7.66752i 0.750212 + 0.262224i
\(856\) 48.3522 1.65264
\(857\) 5.21553i 0.178159i 0.996025 + 0.0890796i \(0.0283925\pi\)
−0.996025 + 0.0890796i \(0.971607\pi\)
\(858\) 0 0
\(859\) −43.2632 −1.47612 −0.738061 0.674734i \(-0.764258\pi\)
−0.738061 + 0.674734i \(0.764258\pi\)
\(860\) −11.2836 + 32.2821i −0.384769 + 1.10081i
\(861\) −2.93364 −0.0999783
\(862\) 68.6631i 2.33867i
\(863\) 28.5863i 0.973088i −0.873656 0.486544i \(-0.838257\pi\)
0.873656 0.486544i \(-0.161743\pi\)
\(864\) 30.4733 1.03672
\(865\) −7.31216 + 20.9198i −0.248621 + 0.711295i
\(866\) −23.8180 −0.809367
\(867\) 30.7687i 1.04496i
\(868\) 12.5461i 0.425841i
\(869\) 0 0
\(870\) −86.1278 30.1045i −2.92001 1.02064i
\(871\) −30.2856 −1.02619
\(872\) 20.7812i 0.703740i
\(873\) 20.1118i 0.680680i
\(874\) 88.9354 3.00828
\(875\) −9.35537 + 5.89171i −0.316269 + 0.199176i
\(876\) 140.406 4.74389
\(877\) 25.3137i 0.854784i 0.904066 + 0.427392i \(0.140568\pi\)
−0.904066 + 0.427392i \(0.859432\pi\)
\(878\) 28.9034i 0.975443i
\(879\) 19.9699 0.673568
\(880\) 0 0
\(881\) −0.716380 −0.0241355 −0.0120677 0.999927i \(-0.503841\pi\)
−0.0120677 + 0.999927i \(0.503841\pi\)
\(882\) 24.7933i 0.834835i
\(883\) 28.7614i 0.967899i −0.875096 0.483950i \(-0.839202\pi\)
0.875096 0.483950i \(-0.160798\pi\)
\(884\) 23.9066 0.804067
\(885\) −19.3301 + 55.3026i −0.649773 + 1.85898i
\(886\) 46.1124 1.54918
\(887\) 48.5426i 1.62990i 0.579532 + 0.814950i \(0.303235\pi\)
−0.579532 + 0.814950i \(0.696765\pi\)
\(888\) 43.8174i 1.47041i
\(889\) 17.0792 0.572817
\(890\) 17.3163 49.5412i 0.580442 1.66062i
\(891\) 0 0
\(892\) 59.3776i 1.98811i
\(893\) 14.0854i 0.471350i
\(894\) 57.5840 1.92590
\(895\) −5.15753 1.80273i −0.172397 0.0602585i
\(896\) −1.13762 −0.0380051
\(897\) 34.1040i 1.13870i
\(898\) 44.1462i 1.47318i
\(899\) −19.3254 −0.644538
\(900\) 29.6427 + 23.6062i 0.988089 + 0.786874i
\(901\) 3.84806 0.128197
\(902\) 0 0
\(903\) 6.74128i 0.224336i
\(904\) −129.553 −4.30889
\(905\) 29.9776 + 10.4782i 0.996490 + 0.348306i
\(906\) 83.5340 2.77523
\(907\) 32.9984i 1.09569i 0.836578 + 0.547847i \(0.184553\pi\)
−0.836578 + 0.547847i \(0.815447\pi\)
\(908\) 65.3672i 2.16929i
\(909\) 24.1253 0.800185
\(910\) −5.85296 + 16.7451i −0.194024 + 0.555094i
\(911\) 22.9708 0.761056 0.380528 0.924769i \(-0.375742\pi\)
0.380528 + 0.924769i \(0.375742\pi\)
\(912\) 133.013i 4.40451i
\(913\) 0 0
\(914\) −85.0415 −2.81292
\(915\) 1.58263 4.52784i 0.0523201 0.149686i
\(916\) 28.0464 0.926681
\(917\) 5.06638i 0.167306i
\(918\) 12.8388i 0.423744i
\(919\) −54.6875 −1.80398 −0.901988 0.431762i \(-0.857892\pi\)
−0.901988 + 0.431762i \(0.857892\pi\)
\(920\) 79.8659 + 27.9158i 2.63310 + 0.920355i
\(921\) −13.5874 −0.447719
\(922\) 20.7812i 0.684392i
\(923\) 0.749976i 0.0246858i
\(924\) 0 0
\(925\) 8.73384 10.9672i 0.287167 0.360600i
\(926\) −66.2057 −2.17565
\(927\) 12.8388i 0.421682i
\(928\) 73.2698i 2.40520i
\(929\) 47.1128 1.54572 0.772860 0.634576i \(-0.218825\pi\)
0.772860 + 0.634576i \(0.218825\pi\)
\(930\) 31.1301 + 10.8810i 1.02080 + 0.356802i
\(931\) 39.6409 1.29918
\(932\) 112.522i 3.68577i
\(933\) 48.2715i 1.58034i
\(934\) 42.5249 1.39146
\(935\) 0 0
\(936\) 35.4677 1.15930
\(937\) 29.4666i 0.962632i 0.876547 + 0.481316i \(0.159841\pi\)
−0.876547 + 0.481316i \(0.840159\pi\)
\(938\) 25.3879i 0.828945i
\(939\) −54.7314 −1.78609
\(940\) −7.57876 + 21.6825i −0.247192 + 0.707207i
\(941\) 40.6051 1.32369 0.661844 0.749642i \(-0.269774\pi\)
0.661844 + 0.749642i \(0.269774\pi\)
\(942\) 100.817i 3.28478i
\(943\) 7.18293i 0.233908i
\(944\) −115.623 −3.76319
\(945\) −6.34802 2.21884i −0.206501 0.0721789i
\(946\) 0 0
\(947\) 12.2120i 0.396837i −0.980117 0.198418i \(-0.936420\pi\)
0.980117 0.198418i \(-0.0635805\pi\)
\(948\) 79.0546i 2.56757i
\(949\) −42.0487 −1.36496
\(950\) 53.4677 67.1401i 1.73472 2.17831i
\(951\) 53.1177 1.72246
\(952\) 11.6911i 0.378910i
\(953\) 6.22053i 0.201503i 0.994912 + 0.100751i \(0.0321246\pi\)
−0.994912 + 0.100751i \(0.967875\pi\)
\(954\) 9.78613 0.316838
\(955\) −36.7314 12.8388i −1.18860 0.415455i
\(956\) −31.5992 −1.02199
\(957\) 0 0
\(958\) 90.7353i 2.93152i
\(959\) 7.19723 0.232411
\(960\) −11.4362 + 32.7187i −0.369103 + 1.05599i
\(961\) −24.0150 −0.774678
\(962\) 22.4940i 0.725235i
\(963\) 10.4529i 0.336841i
\(964\) −58.3862 −1.88049
\(965\) −8.12263 + 23.2385i −0.261477 + 0.748075i
\(966\) 28.5889 0.919832
\(967\) 51.2195i 1.64711i −0.567238 0.823554i \(-0.691988\pi\)
0.567238 0.823554i \(-0.308012\pi\)
\(968\) 0 0
\(969\) −22.8026 −0.732527
\(970\) 70.1223 + 24.5101i 2.25149 + 0.786970i
\(971\) 16.9708 0.544618 0.272309 0.962210i \(-0.412213\pi\)
0.272309 + 0.962210i \(0.412213\pi\)
\(972\) 71.6995i 2.29976i
\(973\) 11.3779i 0.364759i
\(974\) −6.58256 −0.210919
\(975\) −25.7462 20.5033i −0.824539 0.656630i
\(976\) 9.46648 0.303015
\(977\) 13.1659i 0.421216i 0.977571 + 0.210608i \(0.0675443\pi\)
−0.977571 + 0.210608i \(0.932456\pi\)
\(978\) 119.430i 3.81894i
\(979\) 0 0
\(980\) 61.0219 + 21.3292i 1.94927 + 0.681335i
\(981\) −4.49255 −0.143436
\(982\) 50.3961i 1.60821i
\(983\) 12.7962i 0.408136i 0.978957 + 0.204068i \(0.0654164\pi\)
−0.978957 + 0.204068i \(0.934584\pi\)
\(984\) 21.6650 0.690656
\(985\) −2.57701 + 7.37272i −0.0821103 + 0.234915i
\(986\) 30.8696 0.983088
\(987\) 4.52784i 0.144123i
\(988\) 97.2067i 3.09256i
\(989\) −16.5058 −0.524854
\(990\) 0 0
\(991\) 2.32786 0.0739468 0.0369734 0.999316i \(-0.488228\pi\)
0.0369734 + 0.999316i \(0.488228\pi\)
\(992\) 26.4827i 0.840826i
\(993\) 12.4118i 0.393877i
\(994\) 0.628693 0.0199409
\(995\) 6.00000 + 2.09720i 0.190213 + 0.0664856i
\(996\) −61.1713 −1.93829
\(997\) 19.1613i 0.606843i −0.952856 0.303422i \(-0.901871\pi\)
0.952856 0.303422i \(-0.0981290\pi\)
\(998\) 3.01856i 0.0955509i
\(999\) 8.52742 0.269796
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 605.2.b.h.364.2 yes 12
5.2 odd 4 3025.2.a.bo.1.12 12
5.3 odd 4 3025.2.a.bo.1.1 12
5.4 even 2 inner 605.2.b.h.364.11 yes 12
11.2 odd 10 605.2.j.k.444.12 48
11.3 even 5 605.2.j.k.9.1 48
11.4 even 5 605.2.j.k.269.12 48
11.5 even 5 605.2.j.k.124.11 48
11.6 odd 10 605.2.j.k.124.1 48
11.7 odd 10 605.2.j.k.269.2 48
11.8 odd 10 605.2.j.k.9.11 48
11.9 even 5 605.2.j.k.444.2 48
11.10 odd 2 inner 605.2.b.h.364.12 yes 12
55.4 even 10 605.2.j.k.269.1 48
55.9 even 10 605.2.j.k.444.11 48
55.14 even 10 605.2.j.k.9.12 48
55.19 odd 10 605.2.j.k.9.2 48
55.24 odd 10 605.2.j.k.444.1 48
55.29 odd 10 605.2.j.k.269.11 48
55.32 even 4 3025.2.a.bo.1.2 12
55.39 odd 10 605.2.j.k.124.12 48
55.43 even 4 3025.2.a.bo.1.11 12
55.49 even 10 605.2.j.k.124.2 48
55.54 odd 2 inner 605.2.b.h.364.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.b.h.364.1 12 55.54 odd 2 inner
605.2.b.h.364.2 yes 12 1.1 even 1 trivial
605.2.b.h.364.11 yes 12 5.4 even 2 inner
605.2.b.h.364.12 yes 12 11.10 odd 2 inner
605.2.j.k.9.1 48 11.3 even 5
605.2.j.k.9.2 48 55.19 odd 10
605.2.j.k.9.11 48 11.8 odd 10
605.2.j.k.9.12 48 55.14 even 10
605.2.j.k.124.1 48 11.6 odd 10
605.2.j.k.124.2 48 55.49 even 10
605.2.j.k.124.11 48 11.5 even 5
605.2.j.k.124.12 48 55.39 odd 10
605.2.j.k.269.1 48 55.4 even 10
605.2.j.k.269.2 48 11.7 odd 10
605.2.j.k.269.11 48 55.29 odd 10
605.2.j.k.269.12 48 11.4 even 5
605.2.j.k.444.1 48 55.24 odd 10
605.2.j.k.444.2 48 11.9 even 5
605.2.j.k.444.11 48 55.9 even 10
605.2.j.k.444.12 48 11.2 odd 10
3025.2.a.bo.1.1 12 5.3 odd 4
3025.2.a.bo.1.2 12 55.32 even 4
3025.2.a.bo.1.11 12 55.43 even 4
3025.2.a.bo.1.12 12 5.2 odd 4