Properties

Label 370.2.b.c.149.3
Level $370$
Weight $2$
Character 370.149
Analytic conductor $2.954$
Analytic rank $0$
Dimension $4$
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] = [370,2,Mod(149,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, 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("370.149");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.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: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 149.3
Root \(-1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 370.149
Dual form 370.2.b.c.149.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} -2.44949i q^{3} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +2.44949 q^{6} -0.449490i q^{7} -1.00000i q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -2.44949i q^{3} -1.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +2.44949 q^{6} -0.449490i q^{7} -1.00000i q^{8} -3.00000 q^{9} +(-1.00000 - 2.00000i) q^{10} -4.89898 q^{11} +2.44949i q^{12} -4.00000i q^{13} +0.449490 q^{14} +(2.44949 + 4.89898i) q^{15} +1.00000 q^{16} +4.89898i q^{17} -3.00000i q^{18} -8.44949 q^{19} +(2.00000 - 1.00000i) q^{20} -1.10102 q^{21} -4.89898i q^{22} -0.898979i q^{23} -2.44949 q^{24} +(3.00000 - 4.00000i) q^{25} +4.00000 q^{26} +0.449490i q^{28} +(-4.89898 + 2.44949i) q^{30} -6.44949 q^{31} +1.00000i q^{32} +12.0000i q^{33} -4.89898 q^{34} +(0.449490 + 0.898979i) q^{35} +3.00000 q^{36} +1.00000i q^{37} -8.44949i q^{38} -9.79796 q^{39} +(1.00000 + 2.00000i) q^{40} +2.00000 q^{41} -1.10102i q^{42} -4.00000i q^{43} +4.89898 q^{44} +(6.00000 - 3.00000i) q^{45} +0.898979 q^{46} -0.449490i q^{47} -2.44949i q^{48} +6.79796 q^{49} +(4.00000 + 3.00000i) q^{50} +12.0000 q^{51} +4.00000i q^{52} -7.79796i q^{53} +(9.79796 - 4.89898i) q^{55} -0.449490 q^{56} +20.6969i q^{57} +8.44949 q^{59} +(-2.44949 - 4.89898i) q^{60} +12.0000 q^{61} -6.44949i q^{62} +1.34847i q^{63} -1.00000 q^{64} +(4.00000 + 8.00000i) q^{65} -12.0000 q^{66} -10.4495i q^{67} -4.89898i q^{68} -2.20204 q^{69} +(-0.898979 + 0.449490i) q^{70} -4.89898 q^{71} +3.00000i q^{72} -4.00000i q^{73} -1.00000 q^{74} +(-9.79796 - 7.34847i) q^{75} +8.44949 q^{76} +2.20204i q^{77} -9.79796i q^{78} -1.55051 q^{79} +(-2.00000 + 1.00000i) q^{80} -9.00000 q^{81} +2.00000i q^{82} +14.4495i q^{83} +1.10102 q^{84} +(-4.89898 - 9.79796i) q^{85} +4.00000 q^{86} +4.89898i q^{88} +3.79796 q^{89} +(3.00000 + 6.00000i) q^{90} -1.79796 q^{91} +0.898979i q^{92} +15.7980i q^{93} +0.449490 q^{94} +(16.8990 - 8.44949i) q^{95} +2.44949 q^{96} -2.00000i q^{97} +6.79796i q^{98} +14.6969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} - 8 q^{5} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} - 8 q^{5} - 12 q^{9} - 4 q^{10} - 8 q^{14} + 4 q^{16} - 24 q^{19} + 8 q^{20} - 24 q^{21} + 12 q^{25} + 16 q^{26} - 16 q^{31} - 8 q^{35} + 12 q^{36} + 4 q^{40} + 8 q^{41} + 24 q^{45} - 16 q^{46} - 12 q^{49} + 16 q^{50} + 48 q^{51} + 8 q^{56} + 24 q^{59} + 48 q^{61} - 4 q^{64} + 16 q^{65} - 48 q^{66} - 48 q^{69} + 16 q^{70} - 4 q^{74} + 24 q^{76} - 16 q^{79} - 8 q^{80} - 36 q^{81} + 24 q^{84} + 16 q^{86} - 24 q^{89} + 12 q^{90} + 32 q^{91} - 8 q^{94} + 48 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 2.44949i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(4\) −1.00000 −0.500000
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) 2.44949 1.00000
\(7\) 0.449490i 0.169891i −0.996386 0.0849456i \(-0.972928\pi\)
0.996386 0.0849456i \(-0.0270716\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −3.00000 −1.00000
\(10\) −1.00000 2.00000i −0.316228 0.632456i
\(11\) −4.89898 −1.47710 −0.738549 0.674200i \(-0.764489\pi\)
−0.738549 + 0.674200i \(0.764489\pi\)
\(12\) 2.44949i 0.707107i
\(13\) 4.00000i 1.10940i −0.832050 0.554700i \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) 0.449490 0.120131
\(15\) 2.44949 + 4.89898i 0.632456 + 1.26491i
\(16\) 1.00000 0.250000
\(17\) 4.89898i 1.18818i 0.804400 + 0.594089i \(0.202487\pi\)
−0.804400 + 0.594089i \(0.797513\pi\)
\(18\) 3.00000i 0.707107i
\(19\) −8.44949 −1.93845 −0.969223 0.246185i \(-0.920823\pi\)
−0.969223 + 0.246185i \(0.920823\pi\)
\(20\) 2.00000 1.00000i 0.447214 0.223607i
\(21\) −1.10102 −0.240262
\(22\) 4.89898i 1.04447i
\(23\) 0.898979i 0.187450i −0.995598 0.0937251i \(-0.970123\pi\)
0.995598 0.0937251i \(-0.0298775\pi\)
\(24\) −2.44949 −0.500000
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 4.00000 0.784465
\(27\) 0 0
\(28\) 0.449490i 0.0849456i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −4.89898 + 2.44949i −0.894427 + 0.447214i
\(31\) −6.44949 −1.15836 −0.579181 0.815199i \(-0.696628\pi\)
−0.579181 + 0.815199i \(0.696628\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 12.0000i 2.08893i
\(34\) −4.89898 −0.840168
\(35\) 0.449490 + 0.898979i 0.0759776 + 0.151955i
\(36\) 3.00000 0.500000
\(37\) 1.00000i 0.164399i
\(38\) 8.44949i 1.37069i
\(39\) −9.79796 −1.56893
\(40\) 1.00000 + 2.00000i 0.158114 + 0.316228i
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 1.10102i 0.169891i
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 4.89898 0.738549
\(45\) 6.00000 3.00000i 0.894427 0.447214i
\(46\) 0.898979 0.132547
\(47\) 0.449490i 0.0655648i −0.999463 0.0327824i \(-0.989563\pi\)
0.999463 0.0327824i \(-0.0104368\pi\)
\(48\) 2.44949i 0.353553i
\(49\) 6.79796 0.971137
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) 12.0000 1.68034
\(52\) 4.00000i 0.554700i
\(53\) 7.79796i 1.07113i −0.844493 0.535566i \(-0.820098\pi\)
0.844493 0.535566i \(-0.179902\pi\)
\(54\) 0 0
\(55\) 9.79796 4.89898i 1.32116 0.660578i
\(56\) −0.449490 −0.0600656
\(57\) 20.6969i 2.74138i
\(58\) 0 0
\(59\) 8.44949 1.10003 0.550015 0.835155i \(-0.314622\pi\)
0.550015 + 0.835155i \(0.314622\pi\)
\(60\) −2.44949 4.89898i −0.316228 0.632456i
\(61\) 12.0000 1.53644 0.768221 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 6.44949i 0.819086i
\(63\) 1.34847i 0.169891i
\(64\) −1.00000 −0.125000
\(65\) 4.00000 + 8.00000i 0.496139 + 0.992278i
\(66\) −12.0000 −1.47710
\(67\) 10.4495i 1.27661i −0.769784 0.638304i \(-0.779636\pi\)
0.769784 0.638304i \(-0.220364\pi\)
\(68\) 4.89898i 0.594089i
\(69\) −2.20204 −0.265095
\(70\) −0.898979 + 0.449490i −0.107449 + 0.0537243i
\(71\) −4.89898 −0.581402 −0.290701 0.956814i \(-0.593888\pi\)
−0.290701 + 0.956814i \(0.593888\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 4.00000i 0.468165i −0.972217 0.234082i \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) −1.00000 −0.116248
\(75\) −9.79796 7.34847i −1.13137 0.848528i
\(76\) 8.44949 0.969223
\(77\) 2.20204i 0.250946i
\(78\) 9.79796i 1.10940i
\(79\) −1.55051 −0.174446 −0.0872230 0.996189i \(-0.527799\pi\)
−0.0872230 + 0.996189i \(0.527799\pi\)
\(80\) −2.00000 + 1.00000i −0.223607 + 0.111803i
\(81\) −9.00000 −1.00000
\(82\) 2.00000i 0.220863i
\(83\) 14.4495i 1.58604i 0.609197 + 0.793019i \(0.291492\pi\)
−0.609197 + 0.793019i \(0.708508\pi\)
\(84\) 1.10102 0.120131
\(85\) −4.89898 9.79796i −0.531369 1.06274i
\(86\) 4.00000 0.431331
\(87\) 0 0
\(88\) 4.89898i 0.522233i
\(89\) 3.79796 0.402583 0.201291 0.979531i \(-0.435486\pi\)
0.201291 + 0.979531i \(0.435486\pi\)
\(90\) 3.00000 + 6.00000i 0.316228 + 0.632456i
\(91\) −1.79796 −0.188477
\(92\) 0.898979i 0.0937251i
\(93\) 15.7980i 1.63817i
\(94\) 0.449490 0.0463613
\(95\) 16.8990 8.44949i 1.73380 0.866899i
\(96\) 2.44949 0.250000
\(97\) 2.00000i 0.203069i −0.994832 0.101535i \(-0.967625\pi\)
0.994832 0.101535i \(-0.0323753\pi\)
\(98\) 6.79796i 0.686698i
\(99\) 14.6969 1.47710
\(100\) −3.00000 + 4.00000i −0.300000 + 0.400000i
\(101\) −18.6969 −1.86041 −0.930207 0.367034i \(-0.880373\pi\)
−0.930207 + 0.367034i \(0.880373\pi\)
\(102\) 12.0000i 1.18818i
\(103\) 9.79796i 0.965422i 0.875780 + 0.482711i \(0.160348\pi\)
−0.875780 + 0.482711i \(0.839652\pi\)
\(104\) −4.00000 −0.392232
\(105\) 2.20204 1.10102i 0.214897 0.107449i
\(106\) 7.79796 0.757405
\(107\) 10.4495i 1.01019i −0.863064 0.505095i \(-0.831457\pi\)
0.863064 0.505095i \(-0.168543\pi\)
\(108\) 0 0
\(109\) −13.7980 −1.32160 −0.660802 0.750560i \(-0.729784\pi\)
−0.660802 + 0.750560i \(0.729784\pi\)
\(110\) 4.89898 + 9.79796i 0.467099 + 0.934199i
\(111\) 2.44949 0.232495
\(112\) 0.449490i 0.0424728i
\(113\) 12.8990i 1.21343i 0.794918 + 0.606717i \(0.207514\pi\)
−0.794918 + 0.606717i \(0.792486\pi\)
\(114\) −20.6969 −1.93845
\(115\) 0.898979 + 1.79796i 0.0838303 + 0.167661i
\(116\) 0 0
\(117\) 12.0000i 1.10940i
\(118\) 8.44949i 0.777839i
\(119\) 2.20204 0.201861
\(120\) 4.89898 2.44949i 0.447214 0.223607i
\(121\) 13.0000 1.18182
\(122\) 12.0000i 1.08643i
\(123\) 4.89898i 0.441726i
\(124\) 6.44949 0.579181
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) −1.34847 −0.120131
\(127\) 17.3485i 1.53943i −0.638389 0.769714i \(-0.720399\pi\)
0.638389 0.769714i \(-0.279601\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −9.79796 −0.862662
\(130\) −8.00000 + 4.00000i −0.701646 + 0.350823i
\(131\) 14.2474 1.24481 0.622403 0.782697i \(-0.286157\pi\)
0.622403 + 0.782697i \(0.286157\pi\)
\(132\) 12.0000i 1.04447i
\(133\) 3.79796i 0.329325i
\(134\) 10.4495 0.902698
\(135\) 0 0
\(136\) 4.89898 0.420084
\(137\) 19.5959i 1.67419i −0.547056 0.837096i \(-0.684251\pi\)
0.547056 0.837096i \(-0.315749\pi\)
\(138\) 2.20204i 0.187450i
\(139\) −13.7980 −1.17033 −0.585164 0.810915i \(-0.698970\pi\)
−0.585164 + 0.810915i \(0.698970\pi\)
\(140\) −0.449490 0.898979i −0.0379888 0.0759776i
\(141\) −1.10102 −0.0927227
\(142\) 4.89898i 0.411113i
\(143\) 19.5959i 1.63869i
\(144\) −3.00000 −0.250000
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) 16.6515i 1.37340i
\(148\) 1.00000i 0.0821995i
\(149\) −10.6969 −0.876327 −0.438164 0.898895i \(-0.644371\pi\)
−0.438164 + 0.898895i \(0.644371\pi\)
\(150\) 7.34847 9.79796i 0.600000 0.800000i
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 8.44949i 0.685344i
\(153\) 14.6969i 1.18818i
\(154\) −2.20204 −0.177446
\(155\) 12.8990 6.44949i 1.03607 0.518035i
\(156\) 9.79796 0.784465
\(157\) 11.7980i 0.941580i 0.882245 + 0.470790i \(0.156031\pi\)
−0.882245 + 0.470790i \(0.843969\pi\)
\(158\) 1.55051i 0.123352i
\(159\) −19.1010 −1.51481
\(160\) −1.00000 2.00000i −0.0790569 0.158114i
\(161\) −0.404082 −0.0318461
\(162\) 9.00000i 0.707107i
\(163\) 2.20204i 0.172477i 0.996275 + 0.0862386i \(0.0274847\pi\)
−0.996275 + 0.0862386i \(0.972515\pi\)
\(164\) −2.00000 −0.156174
\(165\) −12.0000 24.0000i −0.934199 1.86840i
\(166\) −14.4495 −1.12150
\(167\) 8.00000i 0.619059i 0.950890 + 0.309529i \(0.100171\pi\)
−0.950890 + 0.309529i \(0.899829\pi\)
\(168\) 1.10102i 0.0849456i
\(169\) −3.00000 −0.230769
\(170\) 9.79796 4.89898i 0.751469 0.375735i
\(171\) 25.3485 1.93845
\(172\) 4.00000i 0.304997i
\(173\) 0.202041i 0.0153609i −0.999971 0.00768045i \(-0.997555\pi\)
0.999971 0.00768045i \(-0.00244479\pi\)
\(174\) 0 0
\(175\) −1.79796 1.34847i −0.135913 0.101935i
\(176\) −4.89898 −0.369274
\(177\) 20.6969i 1.55568i
\(178\) 3.79796i 0.284669i
\(179\) −5.34847 −0.399763 −0.199882 0.979820i \(-0.564056\pi\)
−0.199882 + 0.979820i \(0.564056\pi\)
\(180\) −6.00000 + 3.00000i −0.447214 + 0.223607i
\(181\) −18.6969 −1.38973 −0.694866 0.719139i \(-0.744536\pi\)
−0.694866 + 0.719139i \(0.744536\pi\)
\(182\) 1.79796i 0.133274i
\(183\) 29.3939i 2.17286i
\(184\) −0.898979 −0.0662736
\(185\) −1.00000 2.00000i −0.0735215 0.147043i
\(186\) −15.7980 −1.15836
\(187\) 24.0000i 1.75505i
\(188\) 0.449490i 0.0327824i
\(189\) 0 0
\(190\) 8.44949 + 16.8990i 0.612990 + 1.22598i
\(191\) −3.34847 −0.242287 −0.121143 0.992635i \(-0.538656\pi\)
−0.121143 + 0.992635i \(0.538656\pi\)
\(192\) 2.44949i 0.176777i
\(193\) 14.0000i 1.00774i −0.863779 0.503871i \(-0.831909\pi\)
0.863779 0.503871i \(-0.168091\pi\)
\(194\) 2.00000 0.143592
\(195\) 19.5959 9.79796i 1.40329 0.701646i
\(196\) −6.79796 −0.485568
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) 14.6969i 1.04447i
\(199\) −1.55051 −0.109913 −0.0549564 0.998489i \(-0.517502\pi\)
−0.0549564 + 0.998489i \(0.517502\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) −25.5959 −1.80540
\(202\) 18.6969i 1.31551i
\(203\) 0 0
\(204\) −12.0000 −0.840168
\(205\) −4.00000 + 2.00000i −0.279372 + 0.139686i
\(206\) −9.79796 −0.682656
\(207\) 2.69694i 0.187450i
\(208\) 4.00000i 0.277350i
\(209\) 41.3939 2.86327
\(210\) 1.10102 + 2.20204i 0.0759776 + 0.151955i
\(211\) 22.6969 1.56252 0.781261 0.624205i \(-0.214577\pi\)
0.781261 + 0.624205i \(0.214577\pi\)
\(212\) 7.79796i 0.535566i
\(213\) 12.0000i 0.822226i
\(214\) 10.4495 0.714312
\(215\) 4.00000 + 8.00000i 0.272798 + 0.545595i
\(216\) 0 0
\(217\) 2.89898i 0.196796i
\(218\) 13.7980i 0.934516i
\(219\) −9.79796 −0.662085
\(220\) −9.79796 + 4.89898i −0.660578 + 0.330289i
\(221\) 19.5959 1.31816
\(222\) 2.44949i 0.164399i
\(223\) 4.44949i 0.297960i 0.988840 + 0.148980i \(0.0475990\pi\)
−0.988840 + 0.148980i \(0.952401\pi\)
\(224\) 0.449490 0.0300328
\(225\) −9.00000 + 12.0000i −0.600000 + 0.800000i
\(226\) −12.8990 −0.858027
\(227\) 15.1010i 1.00229i −0.865363 0.501145i \(-0.832912\pi\)
0.865363 0.501145i \(-0.167088\pi\)
\(228\) 20.6969i 1.37069i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −1.79796 + 0.898979i −0.118554 + 0.0592770i
\(231\) 5.39388 0.354891
\(232\) 0 0
\(233\) 9.79796i 0.641886i 0.947099 + 0.320943i \(0.104000\pi\)
−0.947099 + 0.320943i \(0.896000\pi\)
\(234\) −12.0000 −0.784465
\(235\) 0.449490 + 0.898979i 0.0293215 + 0.0586430i
\(236\) −8.44949 −0.550015
\(237\) 3.79796i 0.246704i
\(238\) 2.20204i 0.142737i
\(239\) −26.0454 −1.68474 −0.842369 0.538902i \(-0.818839\pi\)
−0.842369 + 0.538902i \(0.818839\pi\)
\(240\) 2.44949 + 4.89898i 0.158114 + 0.316228i
\(241\) −11.7980 −0.759973 −0.379987 0.924992i \(-0.624071\pi\)
−0.379987 + 0.924992i \(0.624071\pi\)
\(242\) 13.0000i 0.835672i
\(243\) 22.0454i 1.41421i
\(244\) −12.0000 −0.768221
\(245\) −13.5959 + 6.79796i −0.868611 + 0.434306i
\(246\) 4.89898 0.312348
\(247\) 33.7980i 2.15051i
\(248\) 6.44949i 0.409543i
\(249\) 35.3939 2.24300
\(250\) −11.0000 2.00000i −0.695701 0.126491i
\(251\) 6.65153 0.419841 0.209920 0.977718i \(-0.432679\pi\)
0.209920 + 0.977718i \(0.432679\pi\)
\(252\) 1.34847i 0.0849456i
\(253\) 4.40408i 0.276882i
\(254\) 17.3485 1.08854
\(255\) −24.0000 + 12.0000i −1.50294 + 0.751469i
\(256\) 1.00000 0.0625000
\(257\) 4.89898i 0.305590i 0.988258 + 0.152795i \(0.0488274\pi\)
−0.988258 + 0.152795i \(0.951173\pi\)
\(258\) 9.79796i 0.609994i
\(259\) 0.449490 0.0279299
\(260\) −4.00000 8.00000i −0.248069 0.496139i
\(261\) 0 0
\(262\) 14.2474i 0.880210i
\(263\) 26.2474i 1.61849i −0.587473 0.809244i \(-0.699877\pi\)
0.587473 0.809244i \(-0.300123\pi\)
\(264\) 12.0000 0.738549
\(265\) 7.79796 + 15.5959i 0.479025 + 0.958050i
\(266\) −3.79796 −0.232868
\(267\) 9.30306i 0.569338i
\(268\) 10.4495i 0.638304i
\(269\) −10.6969 −0.652204 −0.326102 0.945335i \(-0.605735\pi\)
−0.326102 + 0.945335i \(0.605735\pi\)
\(270\) 0 0
\(271\) 16.4949 1.00199 0.500997 0.865449i \(-0.332967\pi\)
0.500997 + 0.865449i \(0.332967\pi\)
\(272\) 4.89898i 0.297044i
\(273\) 4.40408i 0.266547i
\(274\) 19.5959 1.18383
\(275\) −14.6969 + 19.5959i −0.886259 + 1.18168i
\(276\) 2.20204 0.132547
\(277\) 19.5959i 1.17740i −0.808350 0.588702i \(-0.799639\pi\)
0.808350 0.588702i \(-0.200361\pi\)
\(278\) 13.7980i 0.827547i
\(279\) 19.3485 1.15836
\(280\) 0.898979 0.449490i 0.0537243 0.0268622i
\(281\) 8.20204 0.489293 0.244646 0.969612i \(-0.421328\pi\)
0.244646 + 0.969612i \(0.421328\pi\)
\(282\) 1.10102i 0.0655648i
\(283\) 23.5959i 1.40263i 0.712851 + 0.701316i \(0.247404\pi\)
−0.712851 + 0.701316i \(0.752596\pi\)
\(284\) 4.89898 0.290701
\(285\) −20.6969 41.3939i −1.22598 2.45196i
\(286\) −19.5959 −1.15873
\(287\) 0.898979i 0.0530651i
\(288\) 3.00000i 0.176777i
\(289\) −7.00000 −0.411765
\(290\) 0 0
\(291\) −4.89898 −0.287183
\(292\) 4.00000i 0.234082i
\(293\) 13.5959i 0.794282i 0.917758 + 0.397141i \(0.129998\pi\)
−0.917758 + 0.397141i \(0.870002\pi\)
\(294\) 16.6515 0.971137
\(295\) −16.8990 + 8.44949i −0.983897 + 0.491948i
\(296\) 1.00000 0.0581238
\(297\) 0 0
\(298\) 10.6969i 0.619657i
\(299\) −3.59592 −0.207957
\(300\) 9.79796 + 7.34847i 0.565685 + 0.424264i
\(301\) −1.79796 −0.103633
\(302\) 8.00000i 0.460348i
\(303\) 45.7980i 2.63102i
\(304\) −8.44949 −0.484611
\(305\) −24.0000 + 12.0000i −1.37424 + 0.687118i
\(306\) 14.6969 0.840168
\(307\) 21.1464i 1.20689i −0.797404 0.603445i \(-0.793794\pi\)
0.797404 0.603445i \(-0.206206\pi\)
\(308\) 2.20204i 0.125473i
\(309\) 24.0000 1.36531
\(310\) 6.44949 + 12.8990i 0.366306 + 0.732613i
\(311\) 7.34847 0.416693 0.208347 0.978055i \(-0.433192\pi\)
0.208347 + 0.978055i \(0.433192\pi\)
\(312\) 9.79796i 0.554700i
\(313\) 21.5959i 1.22067i −0.792142 0.610337i \(-0.791034\pi\)
0.792142 0.610337i \(-0.208966\pi\)
\(314\) −11.7980 −0.665797
\(315\) −1.34847 2.69694i −0.0759776 0.151955i
\(316\) 1.55051 0.0872230
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) 19.1010i 1.07113i
\(319\) 0 0
\(320\) 2.00000 1.00000i 0.111803 0.0559017i
\(321\) −25.5959 −1.42862
\(322\) 0.404082i 0.0225186i
\(323\) 41.3939i 2.30322i
\(324\) 9.00000 0.500000
\(325\) −16.0000 12.0000i −0.887520 0.665640i
\(326\) −2.20204 −0.121960
\(327\) 33.7980i 1.86903i
\(328\) 2.00000i 0.110432i
\(329\) −0.202041 −0.0111389
\(330\) 24.0000 12.0000i 1.32116 0.660578i
\(331\) −10.2474 −0.563251 −0.281625 0.959524i \(-0.590874\pi\)
−0.281625 + 0.959524i \(0.590874\pi\)
\(332\) 14.4495i 0.793019i
\(333\) 3.00000i 0.164399i
\(334\) −8.00000 −0.437741
\(335\) 10.4495 + 20.8990i 0.570917 + 1.14183i
\(336\) −1.10102 −0.0600656
\(337\) 35.5959i 1.93903i 0.245026 + 0.969517i \(0.421204\pi\)
−0.245026 + 0.969517i \(0.578796\pi\)
\(338\) 3.00000i 0.163178i
\(339\) 31.5959 1.71605
\(340\) 4.89898 + 9.79796i 0.265684 + 0.531369i
\(341\) 31.5959 1.71101
\(342\) 25.3485i 1.37069i
\(343\) 6.20204i 0.334879i
\(344\) −4.00000 −0.215666
\(345\) 4.40408 2.20204i 0.237108 0.118554i
\(346\) 0.202041 0.0108618
\(347\) 21.7980i 1.17018i 0.810970 + 0.585088i \(0.198940\pi\)
−0.810970 + 0.585088i \(0.801060\pi\)
\(348\) 0 0
\(349\) −16.8990 −0.904582 −0.452291 0.891871i \(-0.649393\pi\)
−0.452291 + 0.891871i \(0.649393\pi\)
\(350\) 1.34847 1.79796i 0.0720787 0.0961049i
\(351\) 0 0
\(352\) 4.89898i 0.261116i
\(353\) 6.00000i 0.319348i 0.987170 + 0.159674i \(0.0510443\pi\)
−0.987170 + 0.159674i \(0.948956\pi\)
\(354\) 20.6969 1.10003
\(355\) 9.79796 4.89898i 0.520022 0.260011i
\(356\) −3.79796 −0.201291
\(357\) 5.39388i 0.285474i
\(358\) 5.34847i 0.282675i
\(359\) 3.10102 0.163666 0.0818328 0.996646i \(-0.473923\pi\)
0.0818328 + 0.996646i \(0.473923\pi\)
\(360\) −3.00000 6.00000i −0.158114 0.316228i
\(361\) 52.3939 2.75757
\(362\) 18.6969i 0.982689i
\(363\) 31.8434i 1.67134i
\(364\) 1.79796 0.0942387
\(365\) 4.00000 + 8.00000i 0.209370 + 0.418739i
\(366\) 29.3939 1.53644
\(367\) 17.3485i 0.905583i −0.891617 0.452791i \(-0.850428\pi\)
0.891617 0.452791i \(-0.149572\pi\)
\(368\) 0.898979i 0.0468625i
\(369\) −6.00000 −0.312348
\(370\) 2.00000 1.00000i 0.103975 0.0519875i
\(371\) −3.50510 −0.181976
\(372\) 15.7980i 0.819086i
\(373\) 7.79796i 0.403763i −0.979410 0.201882i \(-0.935294\pi\)
0.979410 0.201882i \(-0.0647056\pi\)
\(374\) 24.0000 1.24101
\(375\) 26.9444 + 4.89898i 1.39140 + 0.252982i
\(376\) −0.449490 −0.0231807
\(377\) 0 0
\(378\) 0 0
\(379\) −7.59592 −0.390176 −0.195088 0.980786i \(-0.562499\pi\)
−0.195088 + 0.980786i \(0.562499\pi\)
\(380\) −16.8990 + 8.44949i −0.866899 + 0.433450i
\(381\) −42.4949 −2.17708
\(382\) 3.34847i 0.171323i
\(383\) 5.30306i 0.270974i 0.990779 + 0.135487i \(0.0432599\pi\)
−0.990779 + 0.135487i \(0.956740\pi\)
\(384\) −2.44949 −0.125000
\(385\) −2.20204 4.40408i −0.112226 0.224453i
\(386\) 14.0000 0.712581
\(387\) 12.0000i 0.609994i
\(388\) 2.00000i 0.101535i
\(389\) 6.20204 0.314456 0.157228 0.987562i \(-0.449744\pi\)
0.157228 + 0.987562i \(0.449744\pi\)
\(390\) 9.79796 + 19.5959i 0.496139 + 0.992278i
\(391\) 4.40408 0.222724
\(392\) 6.79796i 0.343349i
\(393\) 34.8990i 1.76042i
\(394\) 2.00000 0.100759
\(395\) 3.10102 1.55051i 0.156029 0.0780146i
\(396\) −14.6969 −0.738549
\(397\) 35.7980i 1.79665i −0.439334 0.898324i \(-0.644785\pi\)
0.439334 0.898324i \(-0.355215\pi\)
\(398\) 1.55051i 0.0777201i
\(399\) 9.30306 0.465736
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) −4.20204 −0.209840 −0.104920 0.994481i \(-0.533459\pi\)
−0.104920 + 0.994481i \(0.533459\pi\)
\(402\) 25.5959i 1.27661i
\(403\) 25.7980i 1.28509i
\(404\) 18.6969 0.930207
\(405\) 18.0000 9.00000i 0.894427 0.447214i
\(406\) 0 0
\(407\) 4.89898i 0.242833i
\(408\) 12.0000i 0.594089i
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) −2.00000 4.00000i −0.0987730 0.197546i
\(411\) −48.0000 −2.36767
\(412\) 9.79796i 0.482711i
\(413\) 3.79796i 0.186885i
\(414\) −2.69694 −0.132547
\(415\) −14.4495 28.8990i −0.709298 1.41860i
\(416\) 4.00000 0.196116
\(417\) 33.7980i 1.65509i
\(418\) 41.3939i 2.02464i
\(419\) 13.7980 0.674074 0.337037 0.941491i \(-0.390575\pi\)
0.337037 + 0.941491i \(0.390575\pi\)
\(420\) −2.20204 + 1.10102i −0.107449 + 0.0537243i
\(421\) 19.5959 0.955047 0.477523 0.878619i \(-0.341535\pi\)
0.477523 + 0.878619i \(0.341535\pi\)
\(422\) 22.6969i 1.10487i
\(423\) 1.34847i 0.0655648i
\(424\) −7.79796 −0.378702
\(425\) 19.5959 + 14.6969i 0.950542 + 0.712906i
\(426\) −12.0000 −0.581402
\(427\) 5.39388i 0.261028i
\(428\) 10.4495i 0.505095i
\(429\) 48.0000 2.31746
\(430\) −8.00000 + 4.00000i −0.385794 + 0.192897i
\(431\) −40.2474 −1.93865 −0.969326 0.245780i \(-0.920956\pi\)
−0.969326 + 0.245780i \(0.920956\pi\)
\(432\) 0 0
\(433\) 37.3939i 1.79704i 0.438938 + 0.898518i \(0.355355\pi\)
−0.438938 + 0.898518i \(0.644645\pi\)
\(434\) −2.89898 −0.139155
\(435\) 0 0
\(436\) 13.7980 0.660802
\(437\) 7.59592i 0.363362i
\(438\) 9.79796i 0.468165i
\(439\) −35.3485 −1.68709 −0.843545 0.537058i \(-0.819536\pi\)
−0.843545 + 0.537058i \(0.819536\pi\)
\(440\) −4.89898 9.79796i −0.233550 0.467099i
\(441\) −20.3939 −0.971137
\(442\) 19.5959i 0.932083i
\(443\) 39.3485i 1.86950i −0.355303 0.934751i \(-0.615622\pi\)
0.355303 0.934751i \(-0.384378\pi\)
\(444\) −2.44949 −0.116248
\(445\) −7.59592 + 3.79796i −0.360081 + 0.180041i
\(446\) −4.44949 −0.210689
\(447\) 26.2020i 1.23931i
\(448\) 0.449490i 0.0212364i
\(449\) −3.79796 −0.179237 −0.0896184 0.995976i \(-0.528565\pi\)
−0.0896184 + 0.995976i \(0.528565\pi\)
\(450\) −12.0000 9.00000i −0.565685 0.424264i
\(451\) −9.79796 −0.461368
\(452\) 12.8990i 0.606717i
\(453\) 19.5959i 0.920697i
\(454\) 15.1010 0.708726
\(455\) 3.59592 1.79796i 0.168579 0.0842896i
\(456\) 20.6969 0.969223
\(457\) 2.00000i 0.0935561i −0.998905 0.0467780i \(-0.985105\pi\)
0.998905 0.0467780i \(-0.0148953\pi\)
\(458\) 10.0000i 0.467269i
\(459\) 0 0
\(460\) −0.898979 1.79796i −0.0419151 0.0838303i
\(461\) −14.2020 −0.661455 −0.330727 0.943726i \(-0.607294\pi\)
−0.330727 + 0.943726i \(0.607294\pi\)
\(462\) 5.39388i 0.250946i
\(463\) 28.4949i 1.32427i −0.749384 0.662135i \(-0.769650\pi\)
0.749384 0.662135i \(-0.230350\pi\)
\(464\) 0 0
\(465\) −15.7980 31.5959i −0.732613 1.46523i
\(466\) −9.79796 −0.453882
\(467\) 12.0000i 0.555294i −0.960683 0.277647i \(-0.910445\pi\)
0.960683 0.277647i \(-0.0895545\pi\)
\(468\) 12.0000i 0.554700i
\(469\) −4.69694 −0.216884
\(470\) −0.898979 + 0.449490i −0.0414668 + 0.0207334i
\(471\) 28.8990 1.33159
\(472\) 8.44949i 0.388919i
\(473\) 19.5959i 0.901021i
\(474\) −3.79796 −0.174446
\(475\) −25.3485 + 33.7980i −1.16307 + 1.55076i
\(476\) −2.20204 −0.100930
\(477\) 23.3939i 1.07113i
\(478\) 26.0454i 1.19129i
\(479\) 29.1464 1.33173 0.665867 0.746070i \(-0.268062\pi\)
0.665867 + 0.746070i \(0.268062\pi\)
\(480\) −4.89898 + 2.44949i −0.223607 + 0.111803i
\(481\) 4.00000 0.182384
\(482\) 11.7980i 0.537382i
\(483\) 0.989795i 0.0450372i
\(484\) −13.0000 −0.590909
\(485\) 2.00000 + 4.00000i 0.0908153 + 0.181631i
\(486\) −22.0454 −1.00000
\(487\) 29.3939i 1.33196i 0.745968 + 0.665982i \(0.231987\pi\)
−0.745968 + 0.665982i \(0.768013\pi\)
\(488\) 12.0000i 0.543214i
\(489\) 5.39388 0.243920
\(490\) −6.79796 13.5959i −0.307100 0.614201i
\(491\) −38.6969 −1.74637 −0.873184 0.487390i \(-0.837949\pi\)
−0.873184 + 0.487390i \(0.837949\pi\)
\(492\) 4.89898i 0.220863i
\(493\) 0 0
\(494\) −33.7980 −1.52064
\(495\) −29.3939 + 14.6969i −1.32116 + 0.660578i
\(496\) −6.44949 −0.289591
\(497\) 2.20204i 0.0987750i
\(498\) 35.3939i 1.58604i
\(499\) 25.3485 1.13475 0.567377 0.823458i \(-0.307958\pi\)
0.567377 + 0.823458i \(0.307958\pi\)
\(500\) 2.00000 11.0000i 0.0894427 0.491935i
\(501\) 19.5959 0.875481
\(502\) 6.65153i 0.296872i
\(503\) 17.7980i 0.793572i −0.917911 0.396786i \(-0.870126\pi\)
0.917911 0.396786i \(-0.129874\pi\)
\(504\) 1.34847 0.0600656
\(505\) 37.3939 18.6969i 1.66401 0.832003i
\(506\) −4.40408 −0.195785
\(507\) 7.34847i 0.326357i
\(508\) 17.3485i 0.769714i
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) −12.0000 24.0000i −0.531369 1.06274i
\(511\) −1.79796 −0.0795370
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −4.89898 −0.216085
\(515\) −9.79796 19.5959i −0.431750 0.863499i
\(516\) 9.79796 0.431331
\(517\) 2.20204i 0.0968457i
\(518\) 0.449490i 0.0197494i
\(519\) −0.494897 −0.0217236
\(520\) 8.00000 4.00000i 0.350823 0.175412i
\(521\) −1.79796 −0.0787700 −0.0393850 0.999224i \(-0.512540\pi\)
−0.0393850 + 0.999224i \(0.512540\pi\)
\(522\) 0 0
\(523\) 0.898979i 0.0393096i −0.999807 0.0196548i \(-0.993743\pi\)
0.999807 0.0196548i \(-0.00625672\pi\)
\(524\) −14.2474 −0.622403
\(525\) −3.30306 + 4.40408i −0.144157 + 0.192210i
\(526\) 26.2474 1.14444
\(527\) 31.5959i 1.37634i
\(528\) 12.0000i 0.522233i
\(529\) 22.1918 0.964862
\(530\) −15.5959 + 7.79796i −0.677443 + 0.338722i
\(531\) −25.3485 −1.10003
\(532\) 3.79796i 0.164662i
\(533\) 8.00000i 0.346518i
\(534\) 9.30306 0.402583
\(535\) 10.4495 + 20.8990i 0.451771 + 0.903542i
\(536\) −10.4495 −0.451349
\(537\) 13.1010i 0.565351i
\(538\) 10.6969i 0.461178i
\(539\) −33.3031 −1.43446
\(540\) 0 0
\(541\) 39.5959 1.70236 0.851181 0.524873i \(-0.175887\pi\)
0.851181 + 0.524873i \(0.175887\pi\)
\(542\) 16.4949i 0.708517i
\(543\) 45.7980i 1.96538i
\(544\) −4.89898 −0.210042
\(545\) 27.5959 13.7980i 1.18208 0.591040i
\(546\) −4.40408 −0.188477
\(547\) 18.6969i 0.799423i 0.916641 + 0.399712i \(0.130890\pi\)
−0.916641 + 0.399712i \(0.869110\pi\)
\(548\) 19.5959i 0.837096i
\(549\) −36.0000 −1.53644
\(550\) −19.5959 14.6969i −0.835573 0.626680i
\(551\) 0 0
\(552\) 2.20204i 0.0937251i
\(553\) 0.696938i 0.0296368i
\(554\) 19.5959 0.832551
\(555\) −4.89898 + 2.44949i −0.207950 + 0.103975i
\(556\) 13.7980 0.585164
\(557\) 12.0000i 0.508456i −0.967144 0.254228i \(-0.918179\pi\)
0.967144 0.254228i \(-0.0818214\pi\)
\(558\) 19.3485i 0.819086i
\(559\) −16.0000 −0.676728
\(560\) 0.449490 + 0.898979i 0.0189944 + 0.0379888i
\(561\) −58.7878 −2.48202
\(562\) 8.20204i 0.345982i
\(563\) 5.30306i 0.223497i 0.993736 + 0.111749i \(0.0356452\pi\)
−0.993736 + 0.111749i \(0.964355\pi\)
\(564\) 1.10102 0.0463613
\(565\) −12.8990 25.7980i −0.542664 1.08533i
\(566\) −23.5959 −0.991810
\(567\) 4.04541i 0.169891i
\(568\) 4.89898i 0.205557i
\(569\) 17.5959 0.737659 0.368830 0.929497i \(-0.379759\pi\)
0.368830 + 0.929497i \(0.379759\pi\)
\(570\) 41.3939 20.6969i 1.73380 0.866899i
\(571\) 33.3939 1.39749 0.698745 0.715371i \(-0.253742\pi\)
0.698745 + 0.715371i \(0.253742\pi\)
\(572\) 19.5959i 0.819346i
\(573\) 8.20204i 0.342645i
\(574\) 0.898979 0.0375227
\(575\) −3.59592 2.69694i −0.149960 0.112470i
\(576\) 3.00000 0.125000
\(577\) 1.30306i 0.0542472i −0.999632 0.0271236i \(-0.991365\pi\)
0.999632 0.0271236i \(-0.00863476\pi\)
\(578\) 7.00000i 0.291162i
\(579\) −34.2929 −1.42516
\(580\) 0 0
\(581\) 6.49490 0.269454
\(582\) 4.89898i 0.203069i
\(583\) 38.2020i 1.58217i
\(584\) −4.00000 −0.165521
\(585\) −12.0000 24.0000i −0.496139 0.992278i
\(586\) −13.5959 −0.561642
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 16.6515i 0.686698i
\(589\) 54.4949 2.24542
\(590\) −8.44949 16.8990i −0.347860 0.695720i
\(591\) −4.89898 −0.201517
\(592\) 1.00000i 0.0410997i
\(593\) 24.0000i 0.985562i −0.870153 0.492781i \(-0.835980\pi\)
0.870153 0.492781i \(-0.164020\pi\)
\(594\) 0 0
\(595\) −4.40408 + 2.20204i −0.180550 + 0.0902749i
\(596\) 10.6969 0.438164
\(597\) 3.79796i 0.155440i
\(598\) 3.59592i 0.147048i
\(599\) 27.5959 1.12754 0.563769 0.825932i \(-0.309351\pi\)
0.563769 + 0.825932i \(0.309351\pi\)
\(600\) −7.34847 + 9.79796i −0.300000 + 0.400000i
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 1.79796i 0.0732793i
\(603\) 31.3485i 1.27661i
\(604\) 8.00000 0.325515
\(605\) −26.0000 + 13.0000i −1.05705 + 0.528525i
\(606\) −45.7980 −1.86041
\(607\) 2.69694i 0.109465i −0.998501 0.0547327i \(-0.982569\pi\)
0.998501 0.0547327i \(-0.0174307\pi\)
\(608\) 8.44949i 0.342672i
\(609\) 0 0
\(610\) −12.0000 24.0000i −0.485866 0.971732i
\(611\) −1.79796 −0.0727376
\(612\) 14.6969i 0.594089i
\(613\) 20.2020i 0.815953i −0.912992 0.407976i \(-0.866235\pi\)
0.912992 0.407976i \(-0.133765\pi\)
\(614\) 21.1464 0.853400
\(615\) 4.89898 + 9.79796i 0.197546 + 0.395092i
\(616\) 2.20204 0.0887228
\(617\) 19.5959i 0.788902i −0.918917 0.394451i \(-0.870935\pi\)
0.918917 0.394451i \(-0.129065\pi\)
\(618\) 24.0000i 0.965422i
\(619\) 3.10102 0.124641 0.0623203 0.998056i \(-0.480150\pi\)
0.0623203 + 0.998056i \(0.480150\pi\)
\(620\) −12.8990 + 6.44949i −0.518035 + 0.259018i
\(621\) 0 0
\(622\) 7.34847i 0.294647i
\(623\) 1.70714i 0.0683953i
\(624\) −9.79796 −0.392232
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 21.5959 0.863146
\(627\) 101.394i 4.04928i
\(628\) 11.7980i 0.470790i
\(629\) −4.89898 −0.195335
\(630\) 2.69694 1.34847i 0.107449 0.0537243i
\(631\) 4.24745 0.169088 0.0845441 0.996420i \(-0.473057\pi\)
0.0845441 + 0.996420i \(0.473057\pi\)
\(632\) 1.55051i 0.0616760i
\(633\) 55.5959i 2.20974i
\(634\) −18.0000 −0.714871
\(635\) 17.3485 + 34.6969i 0.688453 + 1.37691i
\(636\) 19.1010 0.757405
\(637\) 27.1918i 1.07738i
\(638\) 0 0
\(639\) 14.6969 0.581402
\(640\) 1.00000 + 2.00000i 0.0395285 + 0.0790569i
\(641\) −1.79796 −0.0710151 −0.0355076 0.999369i \(-0.511305\pi\)
−0.0355076 + 0.999369i \(0.511305\pi\)
\(642\) 25.5959i 1.01019i
\(643\) 32.8990i 1.29741i 0.761040 + 0.648705i \(0.224689\pi\)
−0.761040 + 0.648705i \(0.775311\pi\)
\(644\) 0.404082 0.0159231
\(645\) 19.5959 9.79796i 0.771589 0.385794i
\(646\) 41.3939 1.62862
\(647\) 32.0000i 1.25805i −0.777385 0.629025i \(-0.783454\pi\)
0.777385 0.629025i \(-0.216546\pi\)
\(648\) 9.00000i 0.353553i
\(649\) −41.3939 −1.62485
\(650\) 12.0000 16.0000i 0.470679 0.627572i
\(651\) 7.10102 0.278311
\(652\) 2.20204i 0.0862386i
\(653\) 34.0000i 1.33052i −0.746611 0.665261i \(-0.768320\pi\)
0.746611 0.665261i \(-0.231680\pi\)
\(654\) −33.7980 −1.32160
\(655\) −28.4949 + 14.2474i −1.11339 + 0.556694i
\(656\) 2.00000 0.0780869
\(657\) 12.0000i 0.468165i
\(658\) 0.202041i 0.00787638i
\(659\) 7.59592 0.295895 0.147947 0.988995i \(-0.452733\pi\)
0.147947 + 0.988995i \(0.452733\pi\)
\(660\) 12.0000 + 24.0000i 0.467099 + 0.934199i
\(661\) 47.1918 1.83555 0.917775 0.397101i \(-0.129984\pi\)
0.917775 + 0.397101i \(0.129984\pi\)
\(662\) 10.2474i 0.398278i
\(663\) 48.0000i 1.86417i
\(664\) 14.4495 0.560749
\(665\) −3.79796 7.59592i −0.147279 0.294557i
\(666\) 3.00000 0.116248
\(667\) 0 0
\(668\) 8.00000i 0.309529i
\(669\) 10.8990 0.421379
\(670\) −20.8990 + 10.4495i −0.807398 + 0.403699i
\(671\) −58.7878 −2.26948
\(672\) 1.10102i 0.0424728i
\(673\) 24.0000i 0.925132i −0.886585 0.462566i \(-0.846929\pi\)
0.886585 0.462566i \(-0.153071\pi\)
\(674\) −35.5959 −1.37110
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) 18.0000i 0.691796i 0.938272 + 0.345898i \(0.112426\pi\)
−0.938272 + 0.345898i \(0.887574\pi\)
\(678\) 31.5959i 1.21343i
\(679\) −0.898979 −0.0344997
\(680\) −9.79796 + 4.89898i −0.375735 + 0.187867i
\(681\) −36.9898 −1.41745
\(682\) 31.5959i 1.20987i
\(683\) 23.5959i 0.902873i 0.892303 + 0.451436i \(0.149088\pi\)
−0.892303 + 0.451436i \(0.850912\pi\)
\(684\) −25.3485 −0.969223
\(685\) 19.5959 + 39.1918i 0.748722 + 1.49744i
\(686\) 6.20204 0.236795
\(687\) 24.4949i 0.934539i
\(688\) 4.00000i 0.152499i
\(689\) −31.1918 −1.18831
\(690\) 2.20204 + 4.40408i 0.0838303 + 0.167661i
\(691\) 18.2020 0.692438 0.346219 0.938154i \(-0.387465\pi\)
0.346219 + 0.938154i \(0.387465\pi\)
\(692\) 0.202041i 0.00768045i
\(693\) 6.60612i 0.250946i
\(694\) −21.7980 −0.827439
\(695\) 27.5959 13.7980i 1.04677 0.523386i
\(696\) 0 0
\(697\) 9.79796i 0.371124i
\(698\) 16.8990i 0.639636i
\(699\) 24.0000 0.907763
\(700\) 1.79796 + 1.34847i 0.0679565 + 0.0509673i
\(701\) 5.79796 0.218986 0.109493 0.993988i \(-0.465077\pi\)
0.109493 + 0.993988i \(0.465077\pi\)
\(702\) 0 0
\(703\) 8.44949i 0.318679i
\(704\) 4.89898 0.184637
\(705\) 2.20204 1.10102i 0.0829337 0.0414668i
\(706\) −6.00000 −0.225813
\(707\) 8.40408i 0.316068i
\(708\) 20.6969i 0.777839i
\(709\) 13.7980 0.518193 0.259097 0.965851i \(-0.416575\pi\)
0.259097 + 0.965851i \(0.416575\pi\)
\(710\) 4.89898 + 9.79796i 0.183855 + 0.367711i
\(711\) 4.65153 0.174446
\(712\) 3.79796i 0.142335i
\(713\) 5.79796i 0.217135i
\(714\) 5.39388 0.201861
\(715\) −19.5959 39.1918i −0.732846 1.46569i
\(716\) 5.34847 0.199882
\(717\) 63.7980i 2.38258i
\(718\) 3.10102i 0.115729i
\(719\) −12.4041 −0.462594 −0.231297 0.972883i \(-0.574297\pi\)
−0.231297 + 0.972883i \(0.574297\pi\)
\(720\) 6.00000 3.00000i 0.223607 0.111803i
\(721\) 4.40408 0.164017
\(722\) 52.3939i 1.94990i
\(723\) 28.8990i 1.07476i
\(724\) 18.6969 0.694866
\(725\) 0 0
\(726\) 31.8434 1.18182
\(727\) 8.89898i 0.330045i −0.986290 0.165022i \(-0.947230\pi\)
0.986290 0.165022i \(-0.0527697\pi\)
\(728\) 1.79796i 0.0666368i
\(729\) 27.0000 1.00000
\(730\) −8.00000 + 4.00000i −0.296093 + 0.148047i
\(731\) 19.5959 0.724781
\(732\) 29.3939i 1.08643i
\(733\) 21.5959i 0.797663i −0.917024 0.398832i \(-0.869416\pi\)
0.917024 0.398832i \(-0.130584\pi\)
\(734\) 17.3485 0.640344
\(735\) 16.6515 + 33.3031i 0.614201 + 1.22840i
\(736\) 0.898979 0.0331368
\(737\) 51.1918i 1.88568i
\(738\) 6.00000i 0.220863i
\(739\) 26.2020 0.963858 0.481929 0.876210i \(-0.339936\pi\)
0.481929 + 0.876210i \(0.339936\pi\)
\(740\) 1.00000 + 2.00000i 0.0367607 + 0.0735215i
\(741\) 82.7878 3.04128
\(742\) 3.50510i 0.128676i
\(743\) 38.2474i 1.40316i 0.712589 + 0.701581i \(0.247522\pi\)
−0.712589 + 0.701581i \(0.752478\pi\)
\(744\) 15.7980 0.579181
\(745\) 21.3939 10.6969i 0.783811 0.391906i
\(746\) 7.79796 0.285504
\(747\) 43.3485i 1.58604i
\(748\) 24.0000i 0.877527i
\(749\) −4.69694 −0.171622
\(750\) −4.89898 + 26.9444i −0.178885 + 0.983870i
\(751\) 1.30306 0.0475494 0.0237747 0.999717i \(-0.492432\pi\)
0.0237747 + 0.999717i \(0.492432\pi\)
\(752\) 0.449490i 0.0163912i
\(753\) 16.2929i 0.593745i
\(754\) 0 0
\(755\) 16.0000 8.00000i 0.582300 0.291150i
\(756\) 0 0
\(757\) 5.59592i 0.203387i 0.994816 + 0.101694i \(0.0324261\pi\)
−0.994816 + 0.101694i \(0.967574\pi\)
\(758\) 7.59592i 0.275896i
\(759\) 10.7878 0.391571
\(760\) −8.44949 16.8990i −0.306495 0.612990i
\(761\) −53.1918 −1.92820 −0.964101 0.265535i \(-0.914451\pi\)
−0.964101 + 0.265535i \(0.914451\pi\)
\(762\) 42.4949i 1.53943i
\(763\) 6.20204i 0.224529i
\(764\) 3.34847 0.121143
\(765\) 14.6969 + 29.3939i 0.531369 + 1.06274i
\(766\) −5.30306 −0.191607
\(767\) 33.7980i 1.22037i
\(768\) 2.44949i 0.0883883i
\(769\) 16.2020 0.584261 0.292130 0.956379i \(-0.405636\pi\)
0.292130 + 0.956379i \(0.405636\pi\)
\(770\) 4.40408 2.20204i 0.158712 0.0793561i
\(771\) 12.0000 0.432169
\(772\) 14.0000i 0.503871i
\(773\) 6.00000i 0.215805i 0.994161 + 0.107903i \(0.0344134\pi\)
−0.994161 + 0.107903i \(0.965587\pi\)
\(774\) −12.0000 −0.431331
\(775\) −19.3485 + 25.7980i −0.695018 + 0.926690i
\(776\) −2.00000 −0.0717958
\(777\) 1.10102i 0.0394989i
\(778\) 6.20204i 0.222354i
\(779\) −16.8990 −0.605469
\(780\) −19.5959 + 9.79796i −0.701646 + 0.350823i
\(781\) 24.0000 0.858788
\(782\) 4.40408i 0.157490i
\(783\) 0 0
\(784\) 6.79796 0.242784
\(785\) −11.7980 23.5959i −0.421087 0.842174i
\(786\) 34.8990 1.24481
\(787\) 44.7423i 1.59489i 0.603390 + 0.797446i \(0.293816\pi\)
−0.603390 + 0.797446i \(0.706184\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) −64.2929 −2.28889
\(790\) 1.55051 + 3.10102i 0.0551647 + 0.110329i
\(791\) 5.79796 0.206152
\(792\) 14.6969i 0.522233i
\(793\) 48.0000i 1.70453i
\(794\) 35.7980 1.27042
\(795\) 38.2020 19.1010i 1.35489 0.677443i
\(796\) 1.55051 0.0549564
\(797\) 4.40408i 0.156001i −0.996953 0.0780003i \(-0.975146\pi\)
0.996953 0.0780003i \(-0.0248535\pi\)
\(798\) 9.30306i 0.329325i
\(799\) 2.20204 0.0779026
\(800\) 4.00000 + 3.00000i 0.141421 + 0.106066i
\(801\) −11.3939 −0.402583
\(802\) 4.20204i 0.148379i
\(803\) 19.5959i 0.691525i
\(804\) 25.5959 0.902698
\(805\) 0.808164 0.404082i 0.0284840 0.0142420i
\(806\) −25.7980 −0.908694
\(807\) 26.2020i 0.922356i
\(808\) 18.6969i 0.657756i
\(809\) −45.1918 −1.58886 −0.794430 0.607356i \(-0.792230\pi\)
−0.794430 + 0.607356i \(0.792230\pi\)
\(810\) 9.00000 + 18.0000i 0.316228 + 0.632456i
\(811\) 45.7980 1.60818 0.804092 0.594505i \(-0.202652\pi\)
0.804092 + 0.594505i \(0.202652\pi\)
\(812\) 0 0
\(813\) 40.4041i 1.41703i
\(814\) 4.89898 0.171709
\(815\) −2.20204 4.40408i −0.0771341 0.154268i
\(816\) 12.0000 0.420084
\(817\) 33.7980i 1.18244i
\(818\) 10.0000i 0.349642i
\(819\) 5.39388 0.188477
\(820\) 4.00000 2.00000i 0.139686 0.0698430i
\(821\) −45.5959 −1.59131 −0.795654 0.605751i \(-0.792873\pi\)
−0.795654 + 0.605751i \(0.792873\pi\)
\(822\) 48.0000i 1.67419i
\(823\) 18.6515i 0.650151i −0.945688 0.325076i \(-0.894610\pi\)
0.945688 0.325076i \(-0.105390\pi\)
\(824\) 9.79796 0.341328
\(825\) 48.0000 + 36.0000i 1.67115 + 1.25336i
\(826\) 3.79796 0.132148
\(827\) 12.4949i 0.434490i 0.976117 + 0.217245i \(0.0697071\pi\)
−0.976117 + 0.217245i \(0.930293\pi\)
\(828\) 2.69694i 0.0937251i
\(829\) −47.5959 −1.65307 −0.826537 0.562882i \(-0.809693\pi\)
−0.826537 + 0.562882i \(0.809693\pi\)
\(830\) 28.8990 14.4495i 1.00310 0.501549i
\(831\) −48.0000 −1.66510
\(832\) 4.00000i 0.138675i
\(833\) 33.3031i 1.15388i
\(834\) −33.7980 −1.17033
\(835\) −8.00000 16.0000i −0.276851 0.553703i
\(836\) −41.3939 −1.43164
\(837\) 0 0
\(838\) 13.7980i 0.476643i
\(839\) −33.7980 −1.16684 −0.583418 0.812172i \(-0.698285\pi\)
−0.583418 + 0.812172i \(0.698285\pi\)
\(840\) −1.10102 2.20204i −0.0379888 0.0759776i
\(841\) −29.0000 −1.00000
\(842\) 19.5959i 0.675320i
\(843\) 20.0908i 0.691964i
\(844\) −22.6969 −0.781261
\(845\) 6.00000 3.00000i 0.206406 0.103203i
\(846\) −1.34847 −0.0463613
\(847\) 5.84337i 0.200780i
\(848\) 7.79796i 0.267783i
\(849\) 57.7980 1.98362
\(850\) −14.6969 + 19.5959i −0.504101 + 0.672134i
\(851\) 0.898979 0.0308166
\(852\) 12.0000i 0.411113i
\(853\) 1.59592i 0.0546432i −0.999627 0.0273216i \(-0.991302\pi\)
0.999627 0.0273216i \(-0.00869782\pi\)
\(854\) 5.39388 0.184575
\(855\) −50.6969 + 25.3485i −1.73380 + 0.866899i
\(856\) −10.4495 −0.357156
\(857\) 29.5959i 1.01098i −0.862833 0.505489i \(-0.831312\pi\)
0.862833 0.505489i \(-0.168688\pi\)
\(858\) 48.0000i 1.63869i
\(859\) 20.8536 0.711515 0.355757 0.934578i \(-0.384223\pi\)
0.355757 + 0.934578i \(0.384223\pi\)
\(860\) −4.00000 8.00000i −0.136399 0.272798i
\(861\) −2.20204 −0.0750454
\(862\) 40.2474i 1.37083i
\(863\) 30.7423i 1.04648i −0.852185 0.523241i \(-0.824723\pi\)
0.852185 0.523241i \(-0.175277\pi\)
\(864\) 0 0
\(865\) 0.202041 + 0.404082i 0.00686960 + 0.0137392i
\(866\) −37.3939 −1.27070
\(867\) 17.1464i 0.582323i
\(868\) 2.89898i 0.0983978i
\(869\) 7.59592 0.257674
\(870\) 0 0
\(871\) −41.7980 −1.41627
\(872\) 13.7980i 0.467258i
\(873\) 6.00000i 0.203069i
\(874\) −7.59592 −0.256936
\(875\) 4.94439 + 0.898979i 0.167151 + 0.0303911i
\(876\) 9.79796 0.331042
\(877\) 43.3939i 1.46531i −0.680602 0.732654i \(-0.738282\pi\)
0.680602 0.732654i \(-0.261718\pi\)
\(878\) 35.3485i 1.19295i
\(879\) 33.3031 1.12328
\(880\) 9.79796 4.89898i 0.330289 0.165145i
\(881\) 53.3939 1.79889 0.899443 0.437039i \(-0.143973\pi\)
0.899443 + 0.437039i \(0.143973\pi\)
\(882\) 20.3939i 0.686698i
\(883\) 13.3031i 0.447684i −0.974625 0.223842i \(-0.928140\pi\)
0.974625 0.223842i \(-0.0718599\pi\)
\(884\) −19.5959 −0.659082
\(885\) 20.6969 + 41.3939i 0.695720 + 1.39144i
\(886\) 39.3485 1.32194
\(887\) 24.0454i 0.807366i 0.914899 + 0.403683i \(0.132270\pi\)
−0.914899 + 0.403683i \(0.867730\pi\)
\(888\) 2.44949i 0.0821995i
\(889\) −7.79796 −0.261535
\(890\) −3.79796 7.59592i −0.127308 0.254616i
\(891\) 44.0908 1.47710
\(892\) 4.44949i 0.148980i
\(893\) 3.79796i 0.127094i
\(894\) −26.2020 −0.876327
\(895\) 10.6969 5.34847i 0.357559 0.178780i
\(896\) −0.449490 −0.0150164
\(897\) 8.80816i 0.294096i
\(898\) 3.79796i 0.126740i
\(899\) 0 0
\(900\) 9.00000 12.0000i 0.300000 0.400000i
\(901\) 38.2020 1.27269
\(902\) 9.79796i 0.326236i
\(903\) 4.40408i 0.146559i
\(904\) 12.8990 0.429014
\(905\) 37.3939 18.6969i 1.24301 0.621507i
\(906\) −19.5959 −0.651031
\(907\) 8.89898i 0.295486i −0.989026 0.147743i \(-0.952799\pi\)
0.989026 0.147743i \(-0.0472008\pi\)
\(908\) 15.1010i 0.501145i
\(909\) 56.0908 1.86041
\(910\) 1.79796 + 3.59592i 0.0596018 + 0.119204i
\(911\) 31.8434 1.05502 0.527509 0.849550i \(-0.323126\pi\)
0.527509 + 0.849550i \(0.323126\pi\)
\(912\) 20.6969i 0.685344i
\(913\) 70.7878i 2.34273i
\(914\) 2.00000 0.0661541
\(915\) 29.3939 + 58.7878i 0.971732 + 1.94346i
\(916\) −10.0000 −0.330409
\(917\) 6.40408i 0.211481i
\(918\) 0 0
\(919\) 9.14643 0.301713 0.150856 0.988556i \(-0.451797\pi\)
0.150856 + 0.988556i \(0.451797\pi\)
\(920\) 1.79796 0.898979i 0.0592770 0.0296385i
\(921\) −51.7980 −1.70680
\(922\) 14.2020i 0.467719i
\(923\) 19.5959i 0.645007i
\(924\) −5.39388 −0.177446
\(925\) 4.00000 + 3.00000i 0.131519 + 0.0986394i
\(926\) 28.4949 0.936400
\(927\) 29.3939i 0.965422i
\(928\) 0 0
\(929\) −37.5959 −1.23348 −0.616741 0.787166i \(-0.711547\pi\)
−0.616741 + 0.787166i \(0.711547\pi\)
\(930\) 31.5959 15.7980i 1.03607 0.518035i
\(931\) −57.4393 −1.88250
\(932\) 9.79796i 0.320943i
\(933\) 18.0000i 0.589294i
\(934\) 12.0000 0.392652
\(935\) 24.0000 + 48.0000i 0.784884 + 1.56977i
\(936\) 12.0000 0.392232
\(937\) 8.00000i 0.261349i 0.991425 + 0.130674i \(0.0417142\pi\)
−0.991425 + 0.130674i \(0.958286\pi\)
\(938\) 4.69694i 0.153360i
\(939\) −52.8990 −1.72629
\(940\) −0.449490 0.898979i −0.0146607 0.0293215i
\(941\) 30.2929 0.987519 0.493759 0.869599i \(-0.335622\pi\)
0.493759 + 0.869599i \(0.335622\pi\)
\(942\) 28.8990i 0.941580i
\(943\) 1.79796i 0.0585496i
\(944\) 8.44949 0.275007
\(945\) 0 0
\(946\) −19.5959 −0.637118
\(947\) 33.3939i 1.08516i −0.840006 0.542578i \(-0.817448\pi\)
0.840006 0.542578i \(-0.182552\pi\)
\(948\) 3.79796i 0.123352i
\(949\) −16.0000 −0.519382
\(950\) −33.7980 25.3485i −1.09655 0.822413i
\(951\) 44.0908 1.42974
\(952\) 2.20204i 0.0713686i
\(953\) 2.20204i 0.0713311i 0.999364 + 0.0356656i \(0.0113551\pi\)
−0.999364 + 0.0356656i \(0.988645\pi\)
\(954\) −23.3939 −0.757405
\(955\) 6.69694 3.34847i 0.216708 0.108354i
\(956\) 26.0454 0.842369
\(957\) 0 0
\(958\) 29.1464i 0.941678i
\(959\) −8.80816 −0.284430
\(960\) −2.44949 4.89898i −0.0790569 0.158114i
\(961\) 10.5959 0.341804
\(962\) 4.00000i 0.128965i
\(963\) 31.3485i 1.01019i
\(964\) 11.7980 0.379987
\(965\) 14.0000 + 28.0000i 0.450676 + 0.901352i
\(966\) −0.989795 −0.0318461
\(967\) 52.4949i 1.68812i 0.536247 + 0.844061i \(0.319842\pi\)
−0.536247 + 0.844061i \(0.680158\pi\)
\(968\) 13.0000i 0.417836i
\(969\) −101.394 −3.25724
\(970\) −4.00000 + 2.00000i −0.128432 + 0.0642161i
\(971\) −44.8990 −1.44088 −0.720438 0.693519i \(-0.756059\pi\)
−0.720438 + 0.693519i \(0.756059\pi\)
\(972\) 22.0454i 0.707107i
\(973\) 6.20204i 0.198828i
\(974\) −29.3939 −0.941841
\(975\) −29.3939 + 39.1918i −0.941357 + 1.25514i
\(976\) 12.0000 0.384111
\(977\) 49.5959i 1.58671i −0.608757 0.793357i \(-0.708331\pi\)
0.608757 0.793357i \(-0.291669\pi\)
\(978\) 5.39388i 0.172477i
\(979\) −18.6061 −0.594654
\(980\) 13.5959 6.79796i 0.434306 0.217153i
\(981\) 41.3939 1.32160
\(982\) 38.6969i 1.23487i
\(983\) 48.9444i 1.56108i 0.625104 + 0.780542i \(0.285057\pi\)
−0.625104 + 0.780542i \(0.714943\pi\)
\(984\) −4.89898 −0.156174
\(985\) 2.00000 + 4.00000i 0.0637253 + 0.127451i
\(986\) 0 0
\(987\) 0.494897i 0.0157528i
\(988\) 33.7980i 1.07526i
\(989\) −3.59592 −0.114344
\(990\) −14.6969 29.3939i −0.467099 0.934199i
\(991\) 31.8434 1.01154 0.505769 0.862669i \(-0.331209\pi\)
0.505769 + 0.862669i \(0.331209\pi\)
\(992\) 6.44949i 0.204772i
\(993\) 25.1010i 0.796557i
\(994\) −2.20204 −0.0698445
\(995\) 3.10102 1.55051i 0.0983090 0.0491545i
\(996\) −35.3939 −1.12150
\(997\) 22.0000i 0.696747i −0.937356 0.348373i \(-0.886734\pi\)
0.937356 0.348373i \(-0.113266\pi\)
\(998\) 25.3485i 0.802392i
\(999\) 0 0
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 370.2.b.c.149.3 yes 4
3.2 odd 2 3330.2.d.m.1999.1 4
5.2 odd 4 1850.2.a.s.1.1 2
5.3 odd 4 1850.2.a.v.1.2 2
5.4 even 2 inner 370.2.b.c.149.2 4
15.14 odd 2 3330.2.d.m.1999.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.b.c.149.2 4 5.4 even 2 inner
370.2.b.c.149.3 yes 4 1.1 even 1 trivial
1850.2.a.s.1.1 2 5.2 odd 4
1850.2.a.v.1.2 2 5.3 odd 4
3330.2.d.m.1999.1 4 3.2 odd 2
3330.2.d.m.1999.4 4 15.14 odd 2