Properties

Label 775.2.f.c.743.4
Level $775$
Weight $2$
Character 775.743
Analytic conductor $6.188$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [775,2,Mod(557,775)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(775, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("775.557");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 775.f (of order \(4\), degree \(2\), 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: \(6.18840615665\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.3317760000.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 25x^{4} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 743.4
Root \(0.578737 + 2.15988i\) of defining polynomial
Character \(\chi\) \(=\) 775.743
Dual form 775.2.f.c.557.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.73205 - 1.73205i) q^{2} +(1.58114 - 1.58114i) q^{3} -4.00000i q^{4} -5.47723i q^{6} +(-1.73205 + 1.73205i) q^{7} +(-3.46410 - 3.46410i) q^{8} -2.00000i q^{9} +O(q^{10})\) \(q+(1.73205 - 1.73205i) q^{2} +(1.58114 - 1.58114i) q^{3} -4.00000i q^{4} -5.47723i q^{6} +(-1.73205 + 1.73205i) q^{7} +(-3.46410 - 3.46410i) q^{8} -2.00000i q^{9} -5.47723i q^{11} +(-6.32456 - 6.32456i) q^{12} +6.00000i q^{14} -4.00000 q^{16} +(1.58114 + 1.58114i) q^{17} +(-3.46410 - 3.46410i) q^{18} +7.00000i q^{19} +5.47723i q^{21} +(-9.48683 - 9.48683i) q^{22} +(3.16228 - 3.16228i) q^{23} -10.9545 q^{24} +(1.58114 + 1.58114i) q^{27} +(6.92820 + 6.92820i) q^{28} -5.47723 q^{29} +(-1.00000 + 5.47723i) q^{31} +(-8.66025 - 8.66025i) q^{33} +5.47723 q^{34} -8.00000 q^{36} +(-4.74342 - 4.74342i) q^{37} +(12.1244 + 12.1244i) q^{38} +9.00000 q^{41} +(9.48683 + 9.48683i) q^{42} +(4.74342 - 4.74342i) q^{43} -21.9089 q^{44} -10.9545i q^{46} +(-6.32456 + 6.32456i) q^{48} +1.00000i q^{49} +5.00000 q^{51} +(7.90569 - 7.90569i) q^{53} +5.47723 q^{54} +12.0000 q^{56} +(11.0680 + 11.0680i) q^{57} +(-9.48683 + 9.48683i) q^{58} +3.00000i q^{59} +10.9545i q^{61} +(7.75478 + 11.2189i) q^{62} +(3.46410 + 3.46410i) q^{63} -8.00000i q^{64} -30.0000 q^{66} +(-8.66025 + 8.66025i) q^{67} +(6.32456 - 6.32456i) q^{68} -10.0000i q^{69} -9.00000 q^{71} +(-6.92820 + 6.92820i) q^{72} +(-4.74342 + 4.74342i) q^{73} -16.4317 q^{74} +28.0000 q^{76} +(9.48683 + 9.48683i) q^{77} +5.47723 q^{79} +11.0000 q^{81} +(15.5885 - 15.5885i) q^{82} +(-7.90569 + 7.90569i) q^{83} +21.9089 q^{84} -16.4317i q^{86} +(-8.66025 + 8.66025i) q^{87} +(-18.9737 + 18.9737i) q^{88} +5.47723 q^{89} +(-12.6491 - 12.6491i) q^{92} +(7.07912 + 10.2414i) q^{93} +(10.3923 - 10.3923i) q^{97} +(1.73205 + 1.73205i) q^{98} -10.9545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 32 q^{16} - 8 q^{31} - 64 q^{36} + 72 q^{41} + 40 q^{51} + 96 q^{56} - 240 q^{66} - 72 q^{71} + 224 q^{76} + 88 q^{81}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/775\mathbb{Z}\right)^\times\).

\(n\) \(251\) \(652\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 1.73205i 1.22474 1.22474i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(3\) 1.58114 1.58114i 0.912871 0.912871i −0.0836263 0.996497i \(-0.526650\pi\)
0.996497 + 0.0836263i \(0.0266502\pi\)
\(4\) 4.00000i 2.00000i
\(5\) 0 0
\(6\) 5.47723i 2.23607i
\(7\) −1.73205 + 1.73205i −0.654654 + 0.654654i −0.954110 0.299456i \(-0.903195\pi\)
0.299456 + 0.954110i \(0.403195\pi\)
\(8\) −3.46410 3.46410i −1.22474 1.22474i
\(9\) 2.00000i 0.666667i
\(10\) 0 0
\(11\) 5.47723i 1.65145i −0.564076 0.825723i \(-0.690768\pi\)
0.564076 0.825723i \(-0.309232\pi\)
\(12\) −6.32456 6.32456i −1.82574 1.82574i
\(13\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(14\) 6.00000i 1.60357i
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 1.58114 + 1.58114i 0.383482 + 0.383482i 0.872355 0.488873i \(-0.162592\pi\)
−0.488873 + 0.872355i \(0.662592\pi\)
\(18\) −3.46410 3.46410i −0.816497 0.816497i
\(19\) 7.00000i 1.60591i 0.596040 + 0.802955i \(0.296740\pi\)
−0.596040 + 0.802955i \(0.703260\pi\)
\(20\) 0 0
\(21\) 5.47723i 1.19523i
\(22\) −9.48683 9.48683i −2.02260 2.02260i
\(23\) 3.16228 3.16228i 0.659380 0.659380i −0.295853 0.955233i \(-0.595604\pi\)
0.955233 + 0.295853i \(0.0956039\pi\)
\(24\) −10.9545 −2.23607
\(25\) 0 0
\(26\) 0 0
\(27\) 1.58114 + 1.58114i 0.304290 + 0.304290i
\(28\) 6.92820 + 6.92820i 1.30931 + 1.30931i
\(29\) −5.47723 −1.01710 −0.508548 0.861034i \(-0.669817\pi\)
−0.508548 + 0.861034i \(0.669817\pi\)
\(30\) 0 0
\(31\) −1.00000 + 5.47723i −0.179605 + 0.983739i
\(32\) 0 0
\(33\) −8.66025 8.66025i −1.50756 1.50756i
\(34\) 5.47723 0.939336
\(35\) 0 0
\(36\) −8.00000 −1.33333
\(37\) −4.74342 4.74342i −0.779813 0.779813i 0.199986 0.979799i \(-0.435910\pi\)
−0.979799 + 0.199986i \(0.935910\pi\)
\(38\) 12.1244 + 12.1244i 1.96683 + 1.96683i
\(39\) 0 0
\(40\) 0 0
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 9.48683 + 9.48683i 1.46385 + 1.46385i
\(43\) 4.74342 4.74342i 0.723364 0.723364i −0.245925 0.969289i \(-0.579092\pi\)
0.969289 + 0.245925i \(0.0790916\pi\)
\(44\) −21.9089 −3.30289
\(45\) 0 0
\(46\) 10.9545i 1.61515i
\(47\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(48\) −6.32456 + 6.32456i −0.912871 + 0.912871i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 5.00000 0.700140
\(52\) 0 0
\(53\) 7.90569 7.90569i 1.08593 1.08593i 0.0899877 0.995943i \(-0.471317\pi\)
0.995943 0.0899877i \(-0.0286828\pi\)
\(54\) 5.47723 0.745356
\(55\) 0 0
\(56\) 12.0000 1.60357
\(57\) 11.0680 + 11.0680i 1.46599 + 1.46599i
\(58\) −9.48683 + 9.48683i −1.24568 + 1.24568i
\(59\) 3.00000i 0.390567i 0.980747 + 0.195283i \(0.0625627\pi\)
−0.980747 + 0.195283i \(0.937437\pi\)
\(60\) 0 0
\(61\) 10.9545i 1.40257i 0.712879 + 0.701287i \(0.247391\pi\)
−0.712879 + 0.701287i \(0.752609\pi\)
\(62\) 7.75478 + 11.2189i 0.984858 + 1.42480i
\(63\) 3.46410 + 3.46410i 0.436436 + 0.436436i
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) −30.0000 −3.69274
\(67\) −8.66025 + 8.66025i −1.05802 + 1.05802i −0.0598086 + 0.998210i \(0.519049\pi\)
−0.998210 + 0.0598086i \(0.980951\pi\)
\(68\) 6.32456 6.32456i 0.766965 0.766965i
\(69\) 10.0000i 1.20386i
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) −6.92820 + 6.92820i −0.816497 + 0.816497i
\(73\) −4.74342 + 4.74342i −0.555175 + 0.555175i −0.927930 0.372755i \(-0.878413\pi\)
0.372755 + 0.927930i \(0.378413\pi\)
\(74\) −16.4317 −1.91014
\(75\) 0 0
\(76\) 28.0000 3.21182
\(77\) 9.48683 + 9.48683i 1.08112 + 1.08112i
\(78\) 0 0
\(79\) 5.47723 0.616236 0.308118 0.951348i \(-0.400301\pi\)
0.308118 + 0.951348i \(0.400301\pi\)
\(80\) 0 0
\(81\) 11.0000 1.22222
\(82\) 15.5885 15.5885i 1.72146 1.72146i
\(83\) −7.90569 + 7.90569i −0.867763 + 0.867763i −0.992224 0.124462i \(-0.960280\pi\)
0.124462 + 0.992224i \(0.460280\pi\)
\(84\) 21.9089 2.39046
\(85\) 0 0
\(86\) 16.4317i 1.77187i
\(87\) −8.66025 + 8.66025i −0.928477 + 0.928477i
\(88\) −18.9737 + 18.9737i −2.02260 + 2.02260i
\(89\) 5.47723 0.580585 0.290292 0.956938i \(-0.406247\pi\)
0.290292 + 0.956938i \(0.406247\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −12.6491 12.6491i −1.31876 1.31876i
\(93\) 7.07912 + 10.2414i 0.734070 + 1.06198i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 10.3923 10.3923i 1.05518 1.05518i 0.0567927 0.998386i \(-0.481913\pi\)
0.998386 0.0567927i \(-0.0180874\pi\)
\(98\) 1.73205 + 1.73205i 0.174964 + 0.174964i
\(99\) −10.9545 −1.10096
\(100\) 0 0
\(101\) −9.00000 −0.895533 −0.447767 0.894150i \(-0.647781\pi\)
−0.447767 + 0.894150i \(0.647781\pi\)
\(102\) 8.66025 8.66025i 0.857493 0.857493i
\(103\) −3.46410 3.46410i −0.341328 0.341328i 0.515538 0.856866i \(-0.327592\pi\)
−0.856866 + 0.515538i \(0.827592\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 27.3861i 2.65998i
\(107\) 10.3923 10.3923i 1.00466 1.00466i 0.00467295 0.999989i \(-0.498513\pi\)
0.999989 0.00467295i \(-0.00148745\pi\)
\(108\) 6.32456 6.32456i 0.608581 0.608581i
\(109\) 7.00000i 0.670478i 0.942133 + 0.335239i \(0.108817\pi\)
−0.942133 + 0.335239i \(0.891183\pi\)
\(110\) 0 0
\(111\) −15.0000 −1.42374
\(112\) 6.92820 6.92820i 0.654654 0.654654i
\(113\) −5.19615 5.19615i −0.488813 0.488813i 0.419119 0.907931i \(-0.362339\pi\)
−0.907931 + 0.419119i \(0.862339\pi\)
\(114\) 38.3406 3.59092
\(115\) 0 0
\(116\) 21.9089i 2.03419i
\(117\) 0 0
\(118\) 5.19615 + 5.19615i 0.478345 + 0.478345i
\(119\) −5.47723 −0.502096
\(120\) 0 0
\(121\) −19.0000 −1.72727
\(122\) 18.9737 + 18.9737i 1.71780 + 1.71780i
\(123\) 14.2302 14.2302i 1.28310 1.28310i
\(124\) 21.9089 + 4.00000i 1.96748 + 0.359211i
\(125\) 0 0
\(126\) 12.0000 1.06904
\(127\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(128\) −13.8564 13.8564i −1.22474 1.22474i
\(129\) 15.0000i 1.32068i
\(130\) 0 0
\(131\) 3.00000 0.262111 0.131056 0.991375i \(-0.458163\pi\)
0.131056 + 0.991375i \(0.458163\pi\)
\(132\) −34.6410 + 34.6410i −3.01511 + 3.01511i
\(133\) −12.1244 12.1244i −1.05131 1.05131i
\(134\) 30.0000i 2.59161i
\(135\) 0 0
\(136\) 10.9545i 0.939336i
\(137\) −11.0680 11.0680i −0.945601 0.945601i 0.0529942 0.998595i \(-0.483124\pi\)
−0.998595 + 0.0529942i \(0.983124\pi\)
\(138\) −17.3205 17.3205i −1.47442 1.47442i
\(139\) −16.4317 −1.39372 −0.696858 0.717209i \(-0.745419\pi\)
−0.696858 + 0.717209i \(0.745419\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −15.5885 + 15.5885i −1.30815 + 1.30815i
\(143\) 0 0
\(144\) 8.00000i 0.666667i
\(145\) 0 0
\(146\) 16.4317i 1.35990i
\(147\) 1.58114 + 1.58114i 0.130410 + 0.130410i
\(148\) −18.9737 + 18.9737i −1.55963 + 1.55963i
\(149\) 9.00000i 0.737309i 0.929567 + 0.368654i \(0.120181\pi\)
−0.929567 + 0.368654i \(0.879819\pi\)
\(150\) 0 0
\(151\) 16.4317i 1.33719i 0.743626 + 0.668595i \(0.233104\pi\)
−0.743626 + 0.668595i \(0.766896\pi\)
\(152\) 24.2487 24.2487i 1.96683 1.96683i
\(153\) 3.16228 3.16228i 0.255655 0.255655i
\(154\) 32.8634 2.64820
\(155\) 0 0
\(156\) 0 0
\(157\) −1.73205 + 1.73205i −0.138233 + 0.138233i −0.772837 0.634604i \(-0.781163\pi\)
0.634604 + 0.772837i \(0.281163\pi\)
\(158\) 9.48683 9.48683i 0.754732 0.754732i
\(159\) 25.0000i 1.98263i
\(160\) 0 0
\(161\) 10.9545i 0.863332i
\(162\) 19.0526 19.0526i 1.49691 1.49691i
\(163\) 13.8564 + 13.8564i 1.08532 + 1.08532i 0.996004 + 0.0893140i \(0.0284675\pi\)
0.0893140 + 0.996004i \(0.471533\pi\)
\(164\) 36.0000i 2.81113i
\(165\) 0 0
\(166\) 27.3861i 2.12558i
\(167\) −1.58114 1.58114i −0.122352 0.122352i 0.643279 0.765632i \(-0.277573\pi\)
−0.765632 + 0.643279i \(0.777573\pi\)
\(168\) 18.9737 18.9737i 1.46385 1.46385i
\(169\) 13.0000i 1.00000i
\(170\) 0 0
\(171\) 14.0000 1.07061
\(172\) −18.9737 18.9737i −1.44673 1.44673i
\(173\) −8.66025 8.66025i −0.658427 0.658427i 0.296581 0.955008i \(-0.404154\pi\)
−0.955008 + 0.296581i \(0.904154\pi\)
\(174\) 30.0000i 2.27429i
\(175\) 0 0
\(176\) 21.9089i 1.65145i
\(177\) 4.74342 + 4.74342i 0.356537 + 0.356537i
\(178\) 9.48683 9.48683i 0.711068 0.711068i
\(179\) −16.4317 −1.22816 −0.614081 0.789243i \(-0.710473\pi\)
−0.614081 + 0.789243i \(0.710473\pi\)
\(180\) 0 0
\(181\) 10.9545i 0.814238i −0.913375 0.407119i \(-0.866533\pi\)
0.913375 0.407119i \(-0.133467\pi\)
\(182\) 0 0
\(183\) 17.3205 + 17.3205i 1.28037 + 1.28037i
\(184\) −21.9089 −1.61515
\(185\) 0 0
\(186\) 30.0000 + 5.47723i 2.19971 + 0.401610i
\(187\) 8.66025 8.66025i 0.633300 0.633300i
\(188\) 0 0
\(189\) −5.47723 −0.398410
\(190\) 0 0
\(191\) −6.00000 −0.434145 −0.217072 0.976156i \(-0.569651\pi\)
−0.217072 + 0.976156i \(0.569651\pi\)
\(192\) −12.6491 12.6491i −0.912871 0.912871i
\(193\) 3.46410 + 3.46410i 0.249351 + 0.249351i 0.820704 0.571353i \(-0.193581\pi\)
−0.571353 + 0.820704i \(0.693581\pi\)
\(194\) 36.0000i 2.58465i
\(195\) 0 0
\(196\) 4.00000 0.285714
\(197\) −6.32456 6.32456i −0.450606 0.450606i 0.444950 0.895556i \(-0.353222\pi\)
−0.895556 + 0.444950i \(0.853222\pi\)
\(198\) −18.9737 + 18.9737i −1.34840 + 1.34840i
\(199\) −16.4317 −1.16481 −0.582405 0.812899i \(-0.697888\pi\)
−0.582405 + 0.812899i \(0.697888\pi\)
\(200\) 0 0
\(201\) 27.3861i 1.93167i
\(202\) −15.5885 + 15.5885i −1.09680 + 1.09680i
\(203\) 9.48683 9.48683i 0.665845 0.665845i
\(204\) 20.0000i 1.40028i
\(205\) 0 0
\(206\) −12.0000 −0.836080
\(207\) −6.32456 6.32456i −0.439587 0.439587i
\(208\) 0 0
\(209\) 38.3406 2.65207
\(210\) 0 0
\(211\) 16.0000 1.10149 0.550743 0.834675i \(-0.314345\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) −31.6228 31.6228i −2.17186 2.17186i
\(213\) −14.2302 + 14.2302i −0.975041 + 0.975041i
\(214\) 36.0000i 2.46091i
\(215\) 0 0
\(216\) 10.9545i 0.745356i
\(217\) −7.75478 11.2189i −0.526429 0.761587i
\(218\) 12.1244 + 12.1244i 0.821165 + 0.821165i
\(219\) 15.0000i 1.01361i
\(220\) 0 0
\(221\) 0 0
\(222\) −25.9808 + 25.9808i −1.74371 + 1.74371i
\(223\) −14.2302 + 14.2302i −0.952928 + 0.952928i −0.998941 0.0460129i \(-0.985348\pi\)
0.0460129 + 0.998941i \(0.485348\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −18.0000 −1.19734
\(227\) −8.66025 + 8.66025i −0.574801 + 0.574801i −0.933466 0.358665i \(-0.883232\pi\)
0.358665 + 0.933466i \(0.383232\pi\)
\(228\) 44.2719 44.2719i 2.93198 2.93198i
\(229\) 5.47723 0.361945 0.180973 0.983488i \(-0.442075\pi\)
0.180973 + 0.983488i \(0.442075\pi\)
\(230\) 0 0
\(231\) 30.0000 1.97386
\(232\) 18.9737 + 18.9737i 1.24568 + 1.24568i
\(233\) 5.19615 + 5.19615i 0.340411 + 0.340411i 0.856522 0.516111i \(-0.172621\pi\)
−0.516111 + 0.856522i \(0.672621\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 12.0000 0.781133
\(237\) 8.66025 8.66025i 0.562544 0.562544i
\(238\) −9.48683 + 9.48683i −0.614940 + 0.614940i
\(239\) −10.9545 −0.708585 −0.354292 0.935135i \(-0.615278\pi\)
−0.354292 + 0.935135i \(0.615278\pi\)
\(240\) 0 0
\(241\) 5.47723i 0.352819i −0.984317 0.176410i \(-0.943552\pi\)
0.984317 0.176410i \(-0.0564483\pi\)
\(242\) −32.9090 + 32.9090i −2.11547 + 2.11547i
\(243\) 12.6491 12.6491i 0.811441 0.811441i
\(244\) 43.8178 2.80515
\(245\) 0 0
\(246\) 49.2950i 3.14294i
\(247\) 0 0
\(248\) 22.4378 15.5096i 1.42480 0.984858i
\(249\) 25.0000i 1.58431i
\(250\) 0 0
\(251\) 10.9545i 0.691439i 0.938338 + 0.345719i \(0.112365\pi\)
−0.938338 + 0.345719i \(0.887635\pi\)
\(252\) 13.8564 13.8564i 0.872872 0.872872i
\(253\) −17.3205 17.3205i −1.08893 1.08893i
\(254\) 0 0
\(255\) 0 0
\(256\) −32.0000 −2.00000
\(257\) −1.73205 + 1.73205i −0.108042 + 0.108042i −0.759061 0.651019i \(-0.774342\pi\)
0.651019 + 0.759061i \(0.274342\pi\)
\(258\) −25.9808 25.9808i −1.61749 1.61749i
\(259\) 16.4317 1.02101
\(260\) 0 0
\(261\) 10.9545i 0.678064i
\(262\) 5.19615 5.19615i 0.321019 0.321019i
\(263\) −1.58114 + 1.58114i −0.0974972 + 0.0974972i −0.754173 0.656676i \(-0.771962\pi\)
0.656676 + 0.754173i \(0.271962\pi\)
\(264\) 60.0000i 3.69274i
\(265\) 0 0
\(266\) −42.0000 −2.57519
\(267\) 8.66025 8.66025i 0.529999 0.529999i
\(268\) 34.6410 + 34.6410i 2.11604 + 2.11604i
\(269\) 5.47723 0.333952 0.166976 0.985961i \(-0.446600\pi\)
0.166976 + 0.985961i \(0.446600\pi\)
\(270\) 0 0
\(271\) 27.3861i 1.66359i −0.555084 0.831794i \(-0.687314\pi\)
0.555084 0.831794i \(-0.312686\pi\)
\(272\) −6.32456 6.32456i −0.383482 0.383482i
\(273\) 0 0
\(274\) −38.3406 −2.31624
\(275\) 0 0
\(276\) −40.0000 −2.40772
\(277\) −4.74342 4.74342i −0.285004 0.285004i 0.550097 0.835101i \(-0.314591\pi\)
−0.835101 + 0.550097i \(0.814591\pi\)
\(278\) −28.4605 + 28.4605i −1.70695 + 1.70695i
\(279\) 10.9545 + 2.00000i 0.655826 + 0.119737i
\(280\) 0 0
\(281\) 21.0000 1.25275 0.626377 0.779520i \(-0.284537\pi\)
0.626377 + 0.779520i \(0.284537\pi\)
\(282\) 0 0
\(283\) 17.3205 + 17.3205i 1.02960 + 1.02960i 0.999548 + 0.0300489i \(0.00956630\pi\)
0.0300489 + 0.999548i \(0.490434\pi\)
\(284\) 36.0000i 2.13621i
\(285\) 0 0
\(286\) 0 0
\(287\) −15.5885 + 15.5885i −0.920158 + 0.920158i
\(288\) 0 0
\(289\) 12.0000i 0.705882i
\(290\) 0 0
\(291\) 32.8634i 1.92648i
\(292\) 18.9737 + 18.9737i 1.11035 + 1.11035i
\(293\) 8.66025 + 8.66025i 0.505937 + 0.505937i 0.913277 0.407339i \(-0.133543\pi\)
−0.407339 + 0.913277i \(0.633543\pi\)
\(294\) 5.47723 0.319438
\(295\) 0 0
\(296\) 32.8634i 1.91014i
\(297\) 8.66025 8.66025i 0.502519 0.502519i
\(298\) 15.5885 + 15.5885i 0.903015 + 0.903015i
\(299\) 0 0
\(300\) 0 0
\(301\) 16.4317i 0.947106i
\(302\) 28.4605 + 28.4605i 1.63772 + 1.63772i
\(303\) −14.2302 + 14.2302i −0.817506 + 0.817506i
\(304\) 28.0000i 1.60591i
\(305\) 0 0
\(306\) 10.9545i 0.626224i
\(307\) 1.73205 1.73205i 0.0988534 0.0988534i −0.655951 0.754804i \(-0.727732\pi\)
0.754804 + 0.655951i \(0.227732\pi\)
\(308\) 37.9473 37.9473i 2.16225 2.16225i
\(309\) −10.9545 −0.623177
\(310\) 0 0
\(311\) −21.0000 −1.19080 −0.595400 0.803429i \(-0.703007\pi\)
−0.595400 + 0.803429i \(0.703007\pi\)
\(312\) 0 0
\(313\) 4.74342 4.74342i 0.268114 0.268114i −0.560226 0.828340i \(-0.689286\pi\)
0.828340 + 0.560226i \(0.189286\pi\)
\(314\) 6.00000i 0.338600i
\(315\) 0 0
\(316\) 21.9089i 1.23247i
\(317\) 24.2487 24.2487i 1.36194 1.36194i 0.490505 0.871438i \(-0.336812\pi\)
0.871438 0.490505i \(-0.163188\pi\)
\(318\) −43.3013 43.3013i −2.42821 2.42821i
\(319\) 30.0000i 1.67968i
\(320\) 0 0
\(321\) 32.8634i 1.83425i
\(322\) 18.9737 + 18.9737i 1.05736 + 1.05736i
\(323\) −11.0680 + 11.0680i −0.615838 + 0.615838i
\(324\) 44.0000i 2.44444i
\(325\) 0 0
\(326\) 48.0000 2.65847
\(327\) 11.0680 + 11.0680i 0.612060 + 0.612060i
\(328\) −31.1769 31.1769i −1.72146 1.72146i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 31.6228 + 31.6228i 1.73553 + 1.73553i
\(333\) −9.48683 + 9.48683i −0.519875 + 0.519875i
\(334\) −5.47723 −0.299700
\(335\) 0 0
\(336\) 21.9089i 1.19523i
\(337\) −14.2302 14.2302i −0.775171 0.775171i 0.203834 0.979005i \(-0.434660\pi\)
−0.979005 + 0.203834i \(0.934660\pi\)
\(338\) 22.5167 + 22.5167i 1.22474 + 1.22474i
\(339\) −16.4317 −0.892446
\(340\) 0 0
\(341\) 30.0000 + 5.47723i 1.62459 + 0.296608i
\(342\) 24.2487 24.2487i 1.31122 1.31122i
\(343\) −13.8564 13.8564i −0.748176 0.748176i
\(344\) −32.8634 −1.77187
\(345\) 0 0
\(346\) −30.0000 −1.61281
\(347\) 22.1359 + 22.1359i 1.18832 + 1.18832i 0.977532 + 0.210788i \(0.0676029\pi\)
0.210788 + 0.977532i \(0.432397\pi\)
\(348\) 34.6410 + 34.6410i 1.85695 + 1.85695i
\(349\) 1.00000i 0.0535288i −0.999642 0.0267644i \(-0.991480\pi\)
0.999642 0.0267644i \(-0.00852039\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.32456 + 6.32456i −0.336622 + 0.336622i −0.855094 0.518472i \(-0.826501\pi\)
0.518472 + 0.855094i \(0.326501\pi\)
\(354\) 16.4317 0.873334
\(355\) 0 0
\(356\) 21.9089i 1.16117i
\(357\) −8.66025 + 8.66025i −0.458349 + 0.458349i
\(358\) −28.4605 + 28.4605i −1.50418 + 1.50418i
\(359\) 18.0000i 0.950004i −0.879985 0.475002i \(-0.842447\pi\)
0.879985 0.475002i \(-0.157553\pi\)
\(360\) 0 0
\(361\) −30.0000 −1.57895
\(362\) −18.9737 18.9737i −0.997234 0.997234i
\(363\) −30.0416 + 30.0416i −1.57678 + 1.57678i
\(364\) 0 0
\(365\) 0 0
\(366\) 60.0000 3.13625
\(367\) −23.7171 23.7171i −1.23802 1.23802i −0.960808 0.277213i \(-0.910589\pi\)
−0.277213 0.960808i \(-0.589411\pi\)
\(368\) −12.6491 + 12.6491i −0.659380 + 0.659380i
\(369\) 18.0000i 0.937043i
\(370\) 0 0
\(371\) 27.3861i 1.42182i
\(372\) 40.9656 28.3165i 2.12397 1.46814i
\(373\) 5.19615 + 5.19615i 0.269047 + 0.269047i 0.828716 0.559669i \(-0.189072\pi\)
−0.559669 + 0.828716i \(0.689072\pi\)
\(374\) 30.0000i 1.55126i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) −9.48683 + 9.48683i −0.487950 + 0.487950i
\(379\) 11.0000i 0.565032i −0.959263 0.282516i \(-0.908831\pi\)
0.959263 0.282516i \(-0.0911690\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −10.3923 + 10.3923i −0.531717 + 0.531717i
\(383\) −17.3925 + 17.3925i −0.888717 + 0.888717i −0.994400 0.105683i \(-0.966297\pi\)
0.105683 + 0.994400i \(0.466297\pi\)
\(384\) −43.8178 −2.23607
\(385\) 0 0
\(386\) 12.0000 0.610784
\(387\) −9.48683 9.48683i −0.482243 0.482243i
\(388\) −41.5692 41.5692i −2.11036 2.11036i
\(389\) 21.9089 1.11083 0.555413 0.831575i \(-0.312560\pi\)
0.555413 + 0.831575i \(0.312560\pi\)
\(390\) 0 0
\(391\) 10.0000 0.505722
\(392\) 3.46410 3.46410i 0.174964 0.174964i
\(393\) 4.74342 4.74342i 0.239274 0.239274i
\(394\) −21.9089 −1.10375
\(395\) 0 0
\(396\) 43.8178i 2.20193i
\(397\) −6.92820 + 6.92820i −0.347717 + 0.347717i −0.859258 0.511542i \(-0.829075\pi\)
0.511542 + 0.859258i \(0.329075\pi\)
\(398\) −28.4605 + 28.4605i −1.42660 + 1.42660i
\(399\) −38.3406 −1.91943
\(400\) 0 0
\(401\) 16.4317i 0.820559i 0.911960 + 0.410279i \(0.134569\pi\)
−0.911960 + 0.410279i \(0.865431\pi\)
\(402\) 47.4342 + 47.4342i 2.36580 + 2.36580i
\(403\) 0 0
\(404\) 36.0000i 1.79107i
\(405\) 0 0
\(406\) 32.8634i 1.63098i
\(407\) −25.9808 + 25.9808i −1.28782 + 1.28782i
\(408\) −17.3205 17.3205i −0.857493 0.857493i
\(409\) −5.47723 −0.270831 −0.135416 0.990789i \(-0.543237\pi\)
−0.135416 + 0.990789i \(0.543237\pi\)
\(410\) 0 0
\(411\) −35.0000 −1.72642
\(412\) −13.8564 + 13.8564i −0.682656 + 0.682656i
\(413\) −5.19615 5.19615i −0.255686 0.255686i
\(414\) −21.9089 −1.07676
\(415\) 0 0
\(416\) 0 0
\(417\) −25.9808 + 25.9808i −1.27228 + 1.27228i
\(418\) 66.4078 66.4078i 3.24811 3.24811i
\(419\) 3.00000i 0.146560i 0.997311 + 0.0732798i \(0.0233466\pi\)
−0.997311 + 0.0732798i \(0.976653\pi\)
\(420\) 0 0
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) 27.7128 27.7128i 1.34904 1.34904i
\(423\) 0 0
\(424\) −54.7723 −2.65998
\(425\) 0 0
\(426\) 49.2950i 2.38835i
\(427\) −18.9737 18.9737i −0.918200 0.918200i
\(428\) −41.5692 41.5692i −2.00932 2.00932i
\(429\) 0 0
\(430\) 0 0
\(431\) −27.0000 −1.30054 −0.650272 0.759701i \(-0.725345\pi\)
−0.650272 + 0.759701i \(0.725345\pi\)
\(432\) −6.32456 6.32456i −0.304290 0.304290i
\(433\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(434\) −32.8634 6.00000i −1.57749 0.288009i
\(435\) 0 0
\(436\) 28.0000 1.34096
\(437\) 22.1359 + 22.1359i 1.05891 + 1.05891i
\(438\) 25.9808 + 25.9808i 1.24141 + 1.24141i
\(439\) 17.0000i 0.811366i −0.914014 0.405683i \(-0.867034\pi\)
0.914014 0.405683i \(-0.132966\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 0 0
\(443\) 3.46410 + 3.46410i 0.164584 + 0.164584i 0.784594 0.620010i \(-0.212871\pi\)
−0.620010 + 0.784594i \(0.712871\pi\)
\(444\) 60.0000i 2.84747i
\(445\) 0 0
\(446\) 49.2950i 2.33419i
\(447\) 14.2302 + 14.2302i 0.673068 + 0.673068i
\(448\) 13.8564 + 13.8564i 0.654654 + 0.654654i
\(449\) 21.9089 1.03395 0.516973 0.856002i \(-0.327059\pi\)
0.516973 + 0.856002i \(0.327059\pi\)
\(450\) 0 0
\(451\) 49.2950i 2.32121i
\(452\) −20.7846 + 20.7846i −0.977626 + 0.977626i
\(453\) 25.9808 + 25.9808i 1.22068 + 1.22068i
\(454\) 30.0000i 1.40797i
\(455\) 0 0
\(456\) 76.6812i 3.59092i
\(457\) −18.9737 18.9737i −0.887551 0.887551i 0.106737 0.994287i \(-0.465960\pi\)
−0.994287 + 0.106737i \(0.965960\pi\)
\(458\) 9.48683 9.48683i 0.443291 0.443291i
\(459\) 5.00000i 0.233380i
\(460\) 0 0
\(461\) 38.3406i 1.78570i 0.450355 + 0.892849i \(0.351297\pi\)
−0.450355 + 0.892849i \(0.648703\pi\)
\(462\) 51.9615 51.9615i 2.41747 2.41747i
\(463\) 9.48683 9.48683i 0.440891 0.440891i −0.451421 0.892311i \(-0.649083\pi\)
0.892311 + 0.451421i \(0.149083\pi\)
\(464\) 21.9089 1.01710
\(465\) 0 0
\(466\) 18.0000 0.833834
\(467\) 24.2487 24.2487i 1.12210 1.12210i 0.130671 0.991426i \(-0.458287\pi\)
0.991426 0.130671i \(-0.0417131\pi\)
\(468\) 0 0
\(469\) 30.0000i 1.38527i
\(470\) 0 0
\(471\) 5.47723i 0.252377i
\(472\) 10.3923 10.3923i 0.478345 0.478345i
\(473\) −25.9808 25.9808i −1.19460 1.19460i
\(474\) 30.0000i 1.37795i
\(475\) 0 0
\(476\) 21.9089i 1.00419i
\(477\) −15.8114 15.8114i −0.723954 0.723954i
\(478\) −18.9737 + 18.9737i −0.867835 + 0.867835i
\(479\) 18.0000i 0.822441i 0.911536 + 0.411220i \(0.134897\pi\)
−0.911536 + 0.411220i \(0.865103\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −9.48683 9.48683i −0.432113 0.432113i
\(483\) 17.3205 + 17.3205i 0.788110 + 0.788110i
\(484\) 76.0000i 3.45455i
\(485\) 0 0
\(486\) 43.8178i 1.98762i
\(487\) 14.2302 + 14.2302i 0.644834 + 0.644834i 0.951740 0.306906i \(-0.0992936\pi\)
−0.306906 + 0.951740i \(0.599294\pi\)
\(488\) 37.9473 37.9473i 1.71780 1.71780i
\(489\) 43.8178 1.98151
\(490\) 0 0
\(491\) 10.9545i 0.494367i 0.968969 + 0.247184i \(0.0795051\pi\)
−0.968969 + 0.247184i \(0.920495\pi\)
\(492\) −56.9210 56.9210i −2.56620 2.56620i
\(493\) −8.66025 8.66025i −0.390038 0.390038i
\(494\) 0 0
\(495\) 0 0
\(496\) 4.00000 21.9089i 0.179605 0.983739i
\(497\) 15.5885 15.5885i 0.699238 0.699238i
\(498\) 43.3013 + 43.3013i 1.94038 + 1.94038i
\(499\) 5.47723 0.245194 0.122597 0.992457i \(-0.460878\pi\)
0.122597 + 0.992457i \(0.460878\pi\)
\(500\) 0 0
\(501\) −5.00000 −0.223384
\(502\) 18.9737 + 18.9737i 0.846836 + 0.846836i
\(503\) −12.1244 12.1244i −0.540598 0.540598i 0.383106 0.923704i \(-0.374854\pi\)
−0.923704 + 0.383106i \(0.874854\pi\)
\(504\) 24.0000i 1.06904i
\(505\) 0 0
\(506\) −60.0000 −2.66733
\(507\) 20.5548 + 20.5548i 0.912871 + 0.912871i
\(508\) 0 0
\(509\) 10.9545 0.485548 0.242774 0.970083i \(-0.421943\pi\)
0.242774 + 0.970083i \(0.421943\pi\)
\(510\) 0 0
\(511\) 16.4317i 0.726895i
\(512\) −27.7128 + 27.7128i −1.22474 + 1.22474i
\(513\) −11.0680 + 11.0680i −0.488663 + 0.488663i
\(514\) 6.00000i 0.264649i
\(515\) 0 0
\(516\) −60.0000 −2.64135
\(517\) 0 0
\(518\) 28.4605 28.4605i 1.25048 1.25048i
\(519\) −27.3861 −1.20212
\(520\) 0 0
\(521\) −27.0000 −1.18289 −0.591446 0.806345i \(-0.701443\pi\)
−0.591446 + 0.806345i \(0.701443\pi\)
\(522\) 18.9737 + 18.9737i 0.830455 + 0.830455i
\(523\) 23.7171 23.7171i 1.03708 1.03708i 0.0377899 0.999286i \(-0.487968\pi\)
0.999286 0.0377899i \(-0.0120318\pi\)
\(524\) 12.0000i 0.524222i
\(525\) 0 0
\(526\) 5.47723i 0.238818i
\(527\) −10.2414 + 7.07912i −0.446122 + 0.308371i
\(528\) 34.6410 + 34.6410i 1.50756 + 1.50756i
\(529\) 3.00000i 0.130435i
\(530\) 0 0
\(531\) 6.00000 0.260378
\(532\) −48.4974 + 48.4974i −2.10263 + 2.10263i
\(533\) 0 0
\(534\) 30.0000i 1.29823i
\(535\) 0 0
\(536\) 60.0000 2.59161
\(537\) −25.9808 + 25.9808i −1.12115 + 1.12115i
\(538\) 9.48683 9.48683i 0.409006 0.409006i
\(539\) 5.47723 0.235921
\(540\) 0 0
\(541\) −4.00000 −0.171973 −0.0859867 0.996296i \(-0.527404\pi\)
−0.0859867 + 0.996296i \(0.527404\pi\)
\(542\) −47.4342 47.4342i −2.03747 2.03747i
\(543\) −17.3205 17.3205i −0.743294 0.743294i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 15.5885 15.5885i 0.666514 0.666514i −0.290393 0.956907i \(-0.593786\pi\)
0.956907 + 0.290393i \(0.0937861\pi\)
\(548\) −44.2719 + 44.2719i −1.89120 + 1.89120i
\(549\) 21.9089 0.935049
\(550\) 0 0
\(551\) 38.3406i 1.63336i
\(552\) −34.6410 + 34.6410i −1.47442 + 1.47442i
\(553\) −9.48683 + 9.48683i −0.403421 + 0.403421i
\(554\) −16.4317 −0.698115
\(555\) 0 0
\(556\) 65.7267i 2.78743i
\(557\) −3.16228 3.16228i −0.133990 0.133990i 0.636931 0.770921i \(-0.280204\pi\)
−0.770921 + 0.636931i \(0.780204\pi\)
\(558\) 22.4378 15.5096i 0.949866 0.656572i
\(559\) 0 0
\(560\) 0 0
\(561\) 27.3861i 1.15624i
\(562\) 36.3731 36.3731i 1.53431 1.53431i
\(563\) −5.19615 5.19615i −0.218992 0.218992i 0.589082 0.808073i \(-0.299490\pi\)
−0.808073 + 0.589082i \(0.799490\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 60.0000 2.52199
\(567\) −19.0526 + 19.0526i −0.800132 + 0.800132i
\(568\) 31.1769 + 31.1769i 1.30815 + 1.30815i
\(569\) 21.9089 0.918469 0.459234 0.888315i \(-0.348124\pi\)
0.459234 + 0.888315i \(0.348124\pi\)
\(570\) 0 0
\(571\) 5.47723i 0.229215i 0.993411 + 0.114607i \(0.0365610\pi\)
−0.993411 + 0.114607i \(0.963439\pi\)
\(572\) 0 0
\(573\) −9.48683 + 9.48683i −0.396318 + 0.396318i
\(574\) 54.0000i 2.25392i
\(575\) 0 0
\(576\) −16.0000 −0.666667
\(577\) −8.66025 + 8.66025i −0.360531 + 0.360531i −0.864008 0.503477i \(-0.832054\pi\)
0.503477 + 0.864008i \(0.332054\pi\)
\(578\) −20.7846 20.7846i −0.864526 0.864526i
\(579\) 10.9545 0.455251
\(580\) 0 0
\(581\) 27.3861i 1.13617i
\(582\) −56.9210 56.9210i −2.35945 2.35945i
\(583\) −43.3013 43.3013i −1.79336 1.79336i
\(584\) 32.8634 1.35990
\(585\) 0 0
\(586\) 30.0000 1.23929
\(587\) −22.1359 22.1359i −0.913648 0.913648i 0.0829090 0.996557i \(-0.473579\pi\)
−0.996557 + 0.0829090i \(0.973579\pi\)
\(588\) 6.32456 6.32456i 0.260820 0.260820i
\(589\) −38.3406 7.00000i −1.57980 0.288430i
\(590\) 0 0
\(591\) −20.0000 −0.822690
\(592\) 18.9737 + 18.9737i 0.779813 + 0.779813i
\(593\) 13.8564 + 13.8564i 0.569014 + 0.569014i 0.931852 0.362838i \(-0.118192\pi\)
−0.362838 + 0.931852i \(0.618192\pi\)
\(594\) 30.0000i 1.23091i
\(595\) 0 0
\(596\) 36.0000 1.47462
\(597\) −25.9808 + 25.9808i −1.06332 + 1.06332i
\(598\) 0 0
\(599\) 12.0000i 0.490307i 0.969484 + 0.245153i \(0.0788383\pi\)
−0.969484 + 0.245153i \(0.921162\pi\)
\(600\) 0 0
\(601\) 5.47723i 0.223421i −0.993741 0.111710i \(-0.964367\pi\)
0.993741 0.111710i \(-0.0356329\pi\)
\(602\) 28.4605 + 28.4605i 1.15996 + 1.15996i
\(603\) 17.3205 + 17.3205i 0.705346 + 0.705346i
\(604\) 65.7267 2.67438
\(605\) 0 0
\(606\) 49.2950i 2.00247i
\(607\) −25.9808 + 25.9808i −1.05453 + 1.05453i −0.0561015 + 0.998425i \(0.517867\pi\)
−0.998425 + 0.0561015i \(0.982133\pi\)
\(608\) 0 0
\(609\) 30.0000i 1.21566i
\(610\) 0 0
\(611\) 0 0
\(612\) −12.6491 12.6491i −0.511310 0.511310i
\(613\) 23.7171 23.7171i 0.957924 0.957924i −0.0412259 0.999150i \(-0.513126\pi\)
0.999150 + 0.0412259i \(0.0131263\pi\)
\(614\) 6.00000i 0.242140i
\(615\) 0 0
\(616\) 65.7267i 2.64820i
\(617\) 8.66025 8.66025i 0.348649 0.348649i −0.510957 0.859606i \(-0.670709\pi\)
0.859606 + 0.510957i \(0.170709\pi\)
\(618\) −18.9737 + 18.9737i −0.763233 + 0.763233i
\(619\) −32.8634 −1.32089 −0.660445 0.750875i \(-0.729632\pi\)
−0.660445 + 0.750875i \(0.729632\pi\)
\(620\) 0 0
\(621\) 10.0000 0.401286
\(622\) −36.3731 + 36.3731i −1.45843 + 1.45843i
\(623\) −9.48683 + 9.48683i −0.380082 + 0.380082i
\(624\) 0 0
\(625\) 0 0
\(626\) 16.4317i 0.656742i
\(627\) 60.6218 60.6218i 2.42100 2.42100i
\(628\) 6.92820 + 6.92820i 0.276465 + 0.276465i
\(629\) 15.0000i 0.598089i
\(630\) 0 0
\(631\) 21.9089i 0.872180i −0.899903 0.436090i \(-0.856363\pi\)
0.899903 0.436090i \(-0.143637\pi\)
\(632\) −18.9737 18.9737i −0.754732 0.754732i
\(633\) 25.2982 25.2982i 1.00551 1.00551i
\(634\) 84.0000i 3.33607i
\(635\) 0 0
\(636\) −100.000 −3.96526
\(637\) 0 0
\(638\) 51.9615 + 51.9615i 2.05718 + 2.05718i
\(639\) 18.0000i 0.712069i
\(640\) 0 0
\(641\) 32.8634i 1.29802i −0.760778 0.649012i \(-0.775182\pi\)
0.760778 0.649012i \(-0.224818\pi\)
\(642\) −56.9210 56.9210i −2.24649 2.24649i
\(643\) 33.2039 33.2039i 1.30943 1.30943i 0.387612 0.921823i \(-0.373300\pi\)
0.921823 0.387612i \(-0.126700\pi\)
\(644\) 43.8178 1.72666
\(645\) 0 0
\(646\) 38.3406i 1.50849i
\(647\) −1.58114 1.58114i −0.0621610 0.0621610i 0.675343 0.737504i \(-0.263996\pi\)
−0.737504 + 0.675343i \(0.763996\pi\)
\(648\) −38.1051 38.1051i −1.49691 1.49691i
\(649\) 16.4317 0.645000
\(650\) 0 0
\(651\) −30.0000 5.47723i −1.17579 0.214669i
\(652\) 55.4256 55.4256i 2.17064 2.17064i
\(653\) 17.3205 + 17.3205i 0.677804 + 0.677804i 0.959503 0.281699i \(-0.0908980\pi\)
−0.281699 + 0.959503i \(0.590898\pi\)
\(654\) 38.3406 1.49924
\(655\) 0 0
\(656\) −36.0000 −1.40556
\(657\) 9.48683 + 9.48683i 0.370117 + 0.370117i
\(658\) 0 0
\(659\) 33.0000i 1.28550i −0.766077 0.642749i \(-0.777794\pi\)
0.766077 0.642749i \(-0.222206\pi\)
\(660\) 0 0
\(661\) 41.0000 1.59472 0.797358 0.603507i \(-0.206231\pi\)
0.797358 + 0.603507i \(0.206231\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 54.7723 2.12558
\(665\) 0 0
\(666\) 32.8634i 1.27343i
\(667\) −17.3205 + 17.3205i −0.670653 + 0.670653i
\(668\) −6.32456 + 6.32456i −0.244704 + 0.244704i
\(669\) 45.0000i 1.73980i
\(670\) 0 0
\(671\) 60.0000 2.31627
\(672\) 0 0
\(673\) 4.74342 4.74342i 0.182845 0.182845i −0.609749 0.792594i \(-0.708730\pi\)
0.792594 + 0.609749i \(0.208730\pi\)
\(674\) −49.2950 −1.89877
\(675\) 0 0
\(676\) 52.0000 2.00000
\(677\) 1.58114 + 1.58114i 0.0607681 + 0.0607681i 0.736838 0.676070i \(-0.236318\pi\)
−0.676070 + 0.736838i \(0.736318\pi\)
\(678\) −28.4605 + 28.4605i −1.09302 + 1.09302i
\(679\) 36.0000i 1.38155i
\(680\) 0 0
\(681\) 27.3861i 1.04944i
\(682\) 61.4484 42.4747i 2.35298 1.62644i
\(683\) −22.5167 22.5167i −0.861576 0.861576i 0.129945 0.991521i \(-0.458520\pi\)
−0.991521 + 0.129945i \(0.958520\pi\)
\(684\) 56.0000i 2.14121i
\(685\) 0 0
\(686\) −48.0000 −1.83265
\(687\) 8.66025 8.66025i 0.330409 0.330409i
\(688\) −18.9737 + 18.9737i −0.723364 + 0.723364i
\(689\) 0 0
\(690\) 0 0
\(691\) 19.0000 0.722794 0.361397 0.932412i \(-0.382300\pi\)
0.361397 + 0.932412i \(0.382300\pi\)
\(692\) −34.6410 + 34.6410i −1.31685 + 1.31685i
\(693\) 18.9737 18.9737i 0.720750 0.720750i
\(694\) 76.6812 2.91078
\(695\) 0 0
\(696\) 60.0000 2.27429
\(697\) 14.2302 + 14.2302i 0.539009 + 0.539009i
\(698\) −1.73205 1.73205i −0.0655591 0.0655591i
\(699\) 16.4317 0.621503
\(700\) 0 0
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 0 0
\(703\) 33.2039 33.2039i 1.25231 1.25231i
\(704\) −43.8178 −1.65145
\(705\) 0 0
\(706\) 21.9089i 0.824552i
\(707\) 15.5885 15.5885i 0.586264 0.586264i
\(708\) 18.9737 18.9737i 0.713074 0.713074i
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 10.9545i 0.410824i
\(712\) −18.9737 18.9737i −0.711068 0.711068i
\(713\) 14.1582 + 20.4828i 0.530230 + 0.767086i
\(714\) 30.0000i 1.12272i
\(715\) 0 0
\(716\) 65.7267i 2.45632i
\(717\) −17.3205 + 17.3205i −0.646846 + 0.646846i
\(718\) −31.1769 31.1769i −1.16351 1.16351i
\(719\) 10.9545 0.408532 0.204266 0.978915i \(-0.434519\pi\)
0.204266 + 0.978915i \(0.434519\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) −51.9615 + 51.9615i −1.93381 + 1.93381i
\(723\) −8.66025 8.66025i −0.322078 0.322078i
\(724\) −43.8178 −1.62848
\(725\) 0 0
\(726\) 104.067i 3.86230i
\(727\) −24.2487 + 24.2487i −0.899335 + 0.899335i −0.995377 0.0960423i \(-0.969382\pi\)
0.0960423 + 0.995377i \(0.469382\pi\)
\(728\) 0 0
\(729\) 7.00000i 0.259259i
\(730\) 0 0
\(731\) 15.0000 0.554795
\(732\) 69.2820 69.2820i 2.56074 2.56074i
\(733\) 3.46410 + 3.46410i 0.127950 + 0.127950i 0.768182 0.640232i \(-0.221162\pi\)
−0.640232 + 0.768182i \(0.721162\pi\)
\(734\) −82.1584 −3.03252
\(735\) 0 0
\(736\) 0 0
\(737\) 47.4342 + 47.4342i 1.74726 + 1.74726i
\(738\) −31.1769 31.1769i −1.14764 1.14764i
\(739\) 43.8178 1.61186 0.805932 0.592008i \(-0.201665\pi\)
0.805932 + 0.592008i \(0.201665\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 47.4342 + 47.4342i 1.74136 + 1.74136i
\(743\) −20.5548 + 20.5548i −0.754083 + 0.754083i −0.975238 0.221156i \(-0.929017\pi\)
0.221156 + 0.975238i \(0.429017\pi\)
\(744\) 10.9545 60.0000i 0.401610 2.19971i
\(745\) 0 0
\(746\) 18.0000 0.659027
\(747\) 15.8114 + 15.8114i 0.578508 + 0.578508i
\(748\) −34.6410 34.6410i −1.26660 1.26660i
\(749\) 36.0000i 1.31541i
\(750\) 0 0
\(751\) −14.0000 −0.510867 −0.255434 0.966827i \(-0.582218\pi\)
−0.255434 + 0.966827i \(0.582218\pi\)
\(752\) 0 0
\(753\) 17.3205 + 17.3205i 0.631194 + 0.631194i
\(754\) 0 0
\(755\) 0 0
\(756\) 21.9089i 0.796819i
\(757\) −14.2302 14.2302i −0.517207 0.517207i 0.399518 0.916725i \(-0.369177\pi\)
−0.916725 + 0.399518i \(0.869177\pi\)
\(758\) −19.0526 19.0526i −0.692020 0.692020i
\(759\) −54.7723 −1.98811
\(760\) 0 0
\(761\) 32.8634i 1.19130i −0.803246 0.595648i \(-0.796895\pi\)
0.803246 0.595648i \(-0.203105\pi\)
\(762\) 0 0
\(763\) −12.1244 12.1244i −0.438931 0.438931i
\(764\) 24.0000i 0.868290i
\(765\) 0 0
\(766\) 60.2495i 2.17690i
\(767\) 0 0
\(768\) −50.5964 + 50.5964i −1.82574 + 1.82574i
\(769\) 47.0000i 1.69486i −0.530904 0.847432i \(-0.678148\pi\)
0.530904 0.847432i \(-0.321852\pi\)
\(770\) 0 0
\(771\) 5.47723i 0.197257i
\(772\) 13.8564 13.8564i 0.498703 0.498703i
\(773\) 22.1359 22.1359i 0.796175 0.796175i −0.186315 0.982490i \(-0.559655\pi\)
0.982490 + 0.186315i \(0.0596546\pi\)
\(774\) −32.8634 −1.18125
\(775\) 0 0
\(776\) −72.0000 −2.58465
\(777\) 25.9808 25.9808i 0.932055 0.932055i
\(778\) 37.9473 37.9473i 1.36048 1.36048i
\(779\) 63.0000i 2.25721i
\(780\) 0 0
\(781\) 49.2950i 1.76391i
\(782\) 17.3205 17.3205i 0.619380 0.619380i
\(783\) −8.66025 8.66025i −0.309492 0.309492i
\(784\) 4.00000i 0.142857i
\(785\) 0 0
\(786\) 16.4317i 0.586098i
\(787\) 9.48683 + 9.48683i 0.338169 + 0.338169i 0.855678 0.517509i \(-0.173141\pi\)
−0.517509 + 0.855678i \(0.673141\pi\)
\(788\) −25.2982 + 25.2982i −0.901212 + 0.901212i
\(789\) 5.00000i 0.178005i
\(790\) 0 0
\(791\) 18.0000 0.640006
\(792\) 37.9473 + 37.9473i 1.34840 + 1.34840i
\(793\) 0 0
\(794\) 24.0000i 0.851728i
\(795\) 0 0
\(796\) 65.7267i 2.32962i
\(797\) −3.16228 3.16228i −0.112014 0.112014i 0.648878 0.760892i \(-0.275238\pi\)
−0.760892 + 0.648878i \(0.775238\pi\)
\(798\) −66.4078 + 66.4078i −2.35081 + 2.35081i
\(799\) 0 0
\(800\) 0 0
\(801\) 10.9545i 0.387056i
\(802\) 28.4605 + 28.4605i 1.00498 + 1.00498i
\(803\) 25.9808 + 25.9808i 0.916841 + 0.916841i
\(804\) 109.545 3.86334
\(805\) 0 0
\(806\) 0 0
\(807\) 8.66025 8.66025i 0.304855 0.304855i
\(808\) 31.1769 + 31.1769i 1.09680 + 1.09680i
\(809\) 16.4317 0.577707 0.288853 0.957373i \(-0.406726\pi\)
0.288853 + 0.957373i \(0.406726\pi\)
\(810\) 0 0
\(811\) −13.0000 −0.456492 −0.228246 0.973604i \(-0.573299\pi\)
−0.228246 + 0.973604i \(0.573299\pi\)
\(812\) −37.9473 37.9473i −1.33169 1.33169i
\(813\) −43.3013 43.3013i −1.51864 1.51864i
\(814\) 90.0000i 3.15450i
\(815\) 0 0
\(816\) −20.0000 −0.700140
\(817\) 33.2039 + 33.2039i 1.16166 + 1.16166i
\(818\) −9.48683 + 9.48683i −0.331699 + 0.331699i
\(819\) 0 0
\(820\) 0 0
\(821\) 49.2950i 1.72041i 0.509950 + 0.860204i \(0.329664\pi\)
−0.509950 + 0.860204i \(0.670336\pi\)
\(822\) −60.6218 + 60.6218i −2.11443 + 2.11443i
\(823\) −14.2302 + 14.2302i −0.496035 + 0.496035i −0.910201 0.414166i \(-0.864073\pi\)
0.414166 + 0.910201i \(0.364073\pi\)
\(824\) 24.0000i 0.836080i
\(825\) 0 0
\(826\) −18.0000 −0.626300
\(827\) 7.90569 + 7.90569i 0.274908 + 0.274908i 0.831072 0.556164i \(-0.187728\pi\)
−0.556164 + 0.831072i \(0.687728\pi\)
\(828\) −25.2982 + 25.2982i −0.879174 + 0.879174i
\(829\) 32.8634 1.14139 0.570696 0.821162i \(-0.306674\pi\)
0.570696 + 0.821162i \(0.306674\pi\)
\(830\) 0 0
\(831\) −15.0000 −0.520344
\(832\) 0 0
\(833\) −1.58114 + 1.58114i −0.0547832 + 0.0547832i
\(834\) 90.0000i 3.11645i
\(835\) 0 0
\(836\) 153.362i 5.30415i
\(837\) −10.2414 + 7.07912i −0.353994 + 0.244690i
\(838\) 5.19615 + 5.19615i 0.179498 + 0.179498i
\(839\) 39.0000i 1.34643i −0.739447 0.673215i \(-0.764913\pi\)
0.739447 0.673215i \(-0.235087\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −1.73205 + 1.73205i −0.0596904 + 0.0596904i
\(843\) 33.2039 33.2039i 1.14360 1.14360i
\(844\) 64.0000i 2.20297i
\(845\) 0 0
\(846\) 0 0
\(847\) 32.9090 32.9090i 1.13077 1.13077i
\(848\) −31.6228 + 31.6228i −1.08593 + 1.08593i
\(849\) 54.7723 1.87978
\(850\) 0 0
\(851\) −30.0000 −1.02839
\(852\) 56.9210 + 56.9210i 1.95008 + 1.95008i
\(853\) 17.3205 + 17.3205i 0.593043 + 0.593043i 0.938452 0.345409i \(-0.112260\pi\)
−0.345409 + 0.938452i \(0.612260\pi\)
\(854\) −65.7267 −2.24912
\(855\) 0 0
\(856\) −72.0000 −2.46091
\(857\) 8.66025 8.66025i 0.295829 0.295829i −0.543549 0.839378i \(-0.682920\pi\)
0.839378 + 0.543549i \(0.182920\pi\)
\(858\) 0 0
\(859\) −38.3406 −1.30816 −0.654082 0.756424i \(-0.726945\pi\)
−0.654082 + 0.756424i \(0.726945\pi\)
\(860\) 0 0
\(861\) 49.2950i 1.67997i
\(862\) −46.7654 + 46.7654i −1.59283 + 1.59283i
\(863\) −30.0416 + 30.0416i −1.02263 + 1.02263i −0.0228913 + 0.999738i \(0.507287\pi\)
−0.999738 + 0.0228913i \(0.992713\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −18.9737 18.9737i −0.644379 0.644379i
\(868\) −44.8755 + 31.0191i −1.52317 + 1.05286i
\(869\) 30.0000i 1.01768i
\(870\) 0 0
\(871\) 0 0
\(872\) 24.2487 24.2487i 0.821165 0.821165i
\(873\) −20.7846 20.7846i −0.703452 0.703452i
\(874\) 76.6812 2.59378
\(875\) 0 0
\(876\) 60.0000 2.02721
\(877\) 36.3731 36.3731i 1.22823 1.22823i 0.263599 0.964632i \(-0.415091\pi\)
0.964632 0.263599i \(-0.0849095\pi\)
\(878\) −29.4449 29.4449i −0.993716 0.993716i
\(879\) 27.3861 0.923711
\(880\) 0 0
\(881\) 38.3406i 1.29173i −0.763453 0.645863i \(-0.776498\pi\)
0.763453 0.645863i \(-0.223502\pi\)
\(882\) 3.46410 3.46410i 0.116642 0.116642i
\(883\) −23.7171 + 23.7171i −0.798143 + 0.798143i −0.982803 0.184659i \(-0.940882\pi\)
0.184659 + 0.982803i \(0.440882\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 12.0000 0.403148
\(887\) 19.0526 19.0526i 0.639722 0.639722i −0.310765 0.950487i \(-0.600585\pi\)
0.950487 + 0.310765i \(0.100585\pi\)
\(888\) 51.9615 + 51.9615i 1.74371 + 1.74371i
\(889\) 0 0
\(890\) 0 0
\(891\) 60.2495i 2.01843i
\(892\) 56.9210 + 56.9210i 1.90586 + 1.90586i
\(893\) 0 0
\(894\) 49.2950 1.64867
\(895\) 0 0
\(896\) 48.0000 1.60357
\(897\) 0 0
\(898\) 37.9473 37.9473i 1.26632 1.26632i
\(899\) 5.47723 30.0000i 0.182676 1.00056i
\(900\) 0 0
\(901\) 25.0000 0.832871
\(902\) −85.3815 85.3815i −2.84289 2.84289i
\(903\) 25.9808 + 25.9808i 0.864586 + 0.864586i
\(904\) 36.0000i 1.19734i
\(905\) 0 0
\(906\) 90.0000 2.99005
\(907\) 6.92820 6.92820i 0.230047 0.230047i −0.582665 0.812712i \(-0.697990\pi\)
0.812712 + 0.582665i \(0.197990\pi\)
\(908\) 34.6410 + 34.6410i 1.14960 + 1.14960i
\(909\) 18.0000i 0.597022i
\(910\) 0 0
\(911\) 5.47723i 0.181469i −0.995875 0.0907343i \(-0.971079\pi\)
0.995875 0.0907343i \(-0.0289214\pi\)
\(912\) −44.2719 44.2719i −1.46599 1.46599i
\(913\) 43.3013 + 43.3013i 1.43306 + 1.43306i
\(914\) −65.7267 −2.17405
\(915\) 0 0
\(916\) 21.9089i 0.723891i
\(917\) −5.19615 + 5.19615i −0.171592 + 0.171592i
\(918\) 8.66025 + 8.66025i 0.285831 + 0.285831i
\(919\) 31.0000i 1.02260i 0.859404 + 0.511298i \(0.170835\pi\)
−0.859404 + 0.511298i \(0.829165\pi\)
\(920\) 0 0
\(921\) 5.47723i 0.180481i
\(922\) 66.4078 + 66.4078i 2.18703 + 2.18703i
\(923\) 0 0
\(924\) 120.000i 3.94771i
\(925\) 0 0
\(926\) 32.8634i 1.07996i
\(927\) −6.92820 + 6.92820i −0.227552 + 0.227552i
\(928\) 0 0
\(929\) −10.9545 −0.359404 −0.179702 0.983721i \(-0.557513\pi\)
−0.179702 + 0.983721i \(0.557513\pi\)
\(930\) 0 0
\(931\) −7.00000 −0.229416
\(932\) 20.7846 20.7846i 0.680823 0.680823i
\(933\) −33.2039 + 33.2039i −1.08705 + 1.08705i
\(934\) 84.0000i 2.74856i
\(935\) 0 0
\(936\) 0 0
\(937\) −8.66025 + 8.66025i −0.282918 + 0.282918i −0.834272 0.551354i \(-0.814112\pi\)
0.551354 + 0.834272i \(0.314112\pi\)
\(938\) −51.9615 51.9615i −1.69660 1.69660i
\(939\) 15.0000i 0.489506i
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 9.48683 + 9.48683i 0.309098 + 0.309098i
\(943\) 28.4605 28.4605i 0.926801 0.926801i
\(944\) 12.0000i 0.390567i
\(945\) 0 0
\(946\) −90.0000 −2.92615
\(947\) −17.3925 17.3925i −0.565181 0.565181i 0.365593 0.930775i \(-0.380866\pi\)
−0.930775 + 0.365593i \(0.880866\pi\)
\(948\) −34.6410 34.6410i −1.12509 1.12509i
\(949\) 0 0
\(950\) 0 0
\(951\) 76.6812i 2.48656i
\(952\) 18.9737 + 18.9737i 0.614940 + 0.614940i
\(953\) 1.58114 1.58114i 0.0512181 0.0512181i −0.681034 0.732252i \(-0.738469\pi\)
0.732252 + 0.681034i \(0.238469\pi\)
\(954\) −54.7723 −1.77332
\(955\) 0 0
\(956\) 43.8178i 1.41717i
\(957\) 47.4342 + 47.4342i 1.53333 + 1.53333i
\(958\) 31.1769 + 31.1769i 1.00728 + 1.00728i
\(959\) 38.3406 1.23808
\(960\) 0 0
\(961\) −29.0000 10.9545i −0.935484 0.353369i
\(962\) 0 0
\(963\) −20.7846 20.7846i −0.669775 0.669775i
\(964\) −21.9089 −0.705638
\(965\) 0 0
\(966\) 60.0000 1.93047
\(967\) −37.9473 37.9473i −1.22030 1.22030i −0.967524 0.252780i \(-0.918655\pi\)
−0.252780 0.967524i \(-0.581345\pi\)
\(968\) 65.8179 + 65.8179i 2.11547 + 2.11547i
\(969\) 35.0000i 1.12436i
\(970\) 0 0
\(971\) −33.0000 −1.05902 −0.529510 0.848304i \(-0.677624\pi\)
−0.529510 + 0.848304i \(0.677624\pi\)
\(972\) −50.5964 50.5964i −1.62288 1.62288i
\(973\) 28.4605 28.4605i 0.912402 0.912402i
\(974\) 49.2950 1.57951
\(975\) 0 0
\(976\) 43.8178i 1.40257i
\(977\) −15.5885 + 15.5885i −0.498719 + 0.498719i −0.911039 0.412320i \(-0.864719\pi\)
0.412320 + 0.911039i \(0.364719\pi\)
\(978\) 75.8947 75.8947i 2.42684 2.42684i
\(979\) 30.0000i 0.958804i
\(980\) 0 0
\(981\) 14.0000 0.446986
\(982\) 18.9737 + 18.9737i 0.605474 + 0.605474i
\(983\) 34.7851 34.7851i 1.10947 1.10947i 0.116251 0.993220i \(-0.462912\pi\)
0.993220 0.116251i \(-0.0370877\pi\)
\(984\) −98.5901 −3.14294
\(985\) 0 0
\(986\) −30.0000 −0.955395
\(987\) 0 0
\(988\) 0 0
\(989\) 30.0000i 0.953945i
\(990\) 0 0
\(991\) 5.47723i 0.173990i −0.996209 0.0869949i \(-0.972274\pi\)
0.996209 0.0869949i \(-0.0277264\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 54.0000i 1.71278i
\(995\) 0 0
\(996\) 100.000 3.16862
\(997\) 6.92820 6.92820i 0.219418 0.219418i −0.588835 0.808253i \(-0.700413\pi\)
0.808253 + 0.588835i \(0.200413\pi\)
\(998\) 9.48683 9.48683i 0.300300 0.300300i
\(999\) 15.0000i 0.474579i
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 775.2.f.c.743.4 yes 8
5.2 odd 4 inner 775.2.f.c.557.3 yes 8
5.3 odd 4 inner 775.2.f.c.557.2 yes 8
5.4 even 2 inner 775.2.f.c.743.1 yes 8
31.30 odd 2 inner 775.2.f.c.743.3 yes 8
155.92 even 4 inner 775.2.f.c.557.4 yes 8
155.123 even 4 inner 775.2.f.c.557.1 8
155.154 odd 2 inner 775.2.f.c.743.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
775.2.f.c.557.1 8 155.123 even 4 inner
775.2.f.c.557.2 yes 8 5.3 odd 4 inner
775.2.f.c.557.3 yes 8 5.2 odd 4 inner
775.2.f.c.557.4 yes 8 155.92 even 4 inner
775.2.f.c.743.1 yes 8 5.4 even 2 inner
775.2.f.c.743.2 yes 8 155.154 odd 2 inner
775.2.f.c.743.3 yes 8 31.30 odd 2 inner
775.2.f.c.743.4 yes 8 1.1 even 1 trivial