Properties

Label 525.3.c.a.176.3
Level $525$
Weight $3$
Character 525.176
Analytic conductor $14.305$
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] = [525,3,Mod(176,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.176");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(14.3052138789\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.65856.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 14x^{2} + 21 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.3
Root \(1.30710i\) of defining polynomial
Character \(\chi\) \(=\) 525.176
Dual form 525.3.c.a.176.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.30710i q^{2} +(1.82288 + 2.38267i) q^{3} +2.29150 q^{4} +(-3.11438 + 2.38267i) q^{6} +2.64575 q^{7} +8.22359i q^{8} +(-2.35425 + 8.68663i) q^{9} +O(q^{10})\) \(q+1.30710i q^{2} +(1.82288 + 2.38267i) q^{3} +2.29150 q^{4} +(-3.11438 + 2.38267i) q^{6} +2.64575 q^{7} +8.22359i q^{8} +(-2.35425 + 8.68663i) q^{9} -2.61419i q^{11} +(4.17712 + 5.45990i) q^{12} +6.35425 q^{13} +3.45825i q^{14} -1.58301 q^{16} +12.1449i q^{17} +(-11.3542 - 3.07723i) q^{18} -10.2288 q^{19} +(4.82288 + 6.30396i) q^{21} +3.41699 q^{22} -4.30231i q^{23} +(-19.5941 + 14.9906i) q^{24} +8.30561i q^{26} +(-24.9889 + 10.2252i) q^{27} +6.06275 q^{28} +17.3733i q^{29} +39.2915 q^{31} +30.8252i q^{32} +(6.22876 - 4.76534i) q^{33} -15.8745 q^{34} +(-5.39477 + 19.9054i) q^{36} -41.0405 q^{37} -13.3700i q^{38} +(11.5830 + 15.1401i) q^{39} -30.2802i q^{41} +(-8.23987 + 6.30396i) q^{42} +55.8745 q^{43} -5.99042i q^{44} +5.62352 q^{46} +39.9749i q^{47} +(-2.88562 - 3.77178i) q^{48} +7.00000 q^{49} +(-28.9373 + 22.1386i) q^{51} +14.5608 q^{52} -105.002i q^{53} +(-13.3654 - 32.6628i) q^{54} +21.7576i q^{56} +(-18.6458 - 24.3718i) q^{57} -22.7085 q^{58} +41.3640i q^{59} -20.4797 q^{61} +51.3577i q^{62} +(-6.22876 + 22.9827i) q^{63} -46.6235 q^{64} +(6.22876 + 8.14158i) q^{66} +27.1660 q^{67} +27.8300i q^{68} +(10.2510 - 7.84257i) q^{69} -67.8049i q^{71} +(-71.4353 - 19.3604i) q^{72} -60.7895 q^{73} -53.6439i q^{74} -23.4392 q^{76} -6.91650i q^{77} +(-19.7895 + 15.1401i) q^{78} -63.2470 q^{79} +(-69.9150 - 40.9010i) q^{81} +39.5791 q^{82} -89.9435i q^{83} +(11.0516 + 14.4455i) q^{84} +73.0333i q^{86} +(-41.3948 + 31.6693i) q^{87} +21.4980 q^{88} +63.1745i q^{89} +16.8118 q^{91} -9.85875i q^{92} +(71.6235 + 93.6188i) q^{93} -52.2510 q^{94} +(-73.4464 + 56.1906i) q^{96} -19.1660 q^{97} +9.14967i q^{98} +(22.7085 + 6.15445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 12 q^{4} + 14 q^{6} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} - 12 q^{4} + 14 q^{6} - 20 q^{9} + 22 q^{12} + 36 q^{13} + 36 q^{16} - 56 q^{18} + 12 q^{19} + 14 q^{21} + 56 q^{22} - 126 q^{24} - 10 q^{27} + 56 q^{28} + 136 q^{31} - 28 q^{33} + 116 q^{36} - 16 q^{37} + 4 q^{39} - 70 q^{42} + 160 q^{43} - 168 q^{46} - 38 q^{48} + 28 q^{49} - 84 q^{51} - 164 q^{52} - 154 q^{54} - 64 q^{57} - 112 q^{58} - 156 q^{61} + 28 q^{63} + 4 q^{64} - 28 q^{66} + 24 q^{67} + 168 q^{69} + 32 q^{73} - 316 q^{76} + 196 q^{78} + 128 q^{79} - 68 q^{81} - 392 q^{82} - 14 q^{84} - 28 q^{87} - 168 q^{88} - 28 q^{91} + 96 q^{93} - 336 q^{94} - 98 q^{96} + 8 q^{97} + 112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30710i 0.653548i 0.945103 + 0.326774i \(0.105962\pi\)
−0.945103 + 0.326774i \(0.894038\pi\)
\(3\) 1.82288 + 2.38267i 0.607625 + 0.794224i
\(4\) 2.29150 0.572876
\(5\) 0 0
\(6\) −3.11438 + 2.38267i −0.519063 + 0.397112i
\(7\) 2.64575 0.377964
\(8\) 8.22359i 1.02795i
\(9\) −2.35425 + 8.68663i −0.261583 + 0.965181i
\(10\) 0 0
\(11\) 2.61419i 0.237654i −0.992915 0.118827i \(-0.962087\pi\)
0.992915 0.118827i \(-0.0379133\pi\)
\(12\) 4.17712 + 5.45990i 0.348094 + 0.454992i
\(13\) 6.35425 0.488788 0.244394 0.969676i \(-0.421411\pi\)
0.244394 + 0.969676i \(0.421411\pi\)
\(14\) 3.45825i 0.247018i
\(15\) 0 0
\(16\) −1.58301 −0.0989378
\(17\) 12.1449i 0.714405i 0.934027 + 0.357202i \(0.116269\pi\)
−0.934027 + 0.357202i \(0.883731\pi\)
\(18\) −11.3542 3.07723i −0.630792 0.170957i
\(19\) −10.2288 −0.538356 −0.269178 0.963090i \(-0.586752\pi\)
−0.269178 + 0.963090i \(0.586752\pi\)
\(20\) 0 0
\(21\) 4.82288 + 6.30396i 0.229661 + 0.300188i
\(22\) 3.41699 0.155318
\(23\) 4.30231i 0.187057i −0.995617 0.0935284i \(-0.970185\pi\)
0.995617 0.0935284i \(-0.0298146\pi\)
\(24\) −19.5941 + 14.9906i −0.816422 + 0.624608i
\(25\) 0 0
\(26\) 8.30561i 0.319446i
\(27\) −24.9889 + 10.2252i −0.925514 + 0.378713i
\(28\) 6.06275 0.216527
\(29\) 17.3733i 0.599078i 0.954084 + 0.299539i \(0.0968328\pi\)
−0.954084 + 0.299539i \(0.903167\pi\)
\(30\) 0 0
\(31\) 39.2915 1.26747 0.633734 0.773551i \(-0.281521\pi\)
0.633734 + 0.773551i \(0.281521\pi\)
\(32\) 30.8252i 0.963288i
\(33\) 6.22876 4.76534i 0.188750 0.144404i
\(34\) −15.8745 −0.466897
\(35\) 0 0
\(36\) −5.39477 + 19.9054i −0.149855 + 0.552929i
\(37\) −41.0405 −1.10920 −0.554602 0.832116i \(-0.687129\pi\)
−0.554602 + 0.832116i \(0.687129\pi\)
\(38\) 13.3700i 0.351841i
\(39\) 11.5830 + 15.1401i 0.297000 + 0.388207i
\(40\) 0 0
\(41\) 30.2802i 0.738541i −0.929322 0.369270i \(-0.879608\pi\)
0.929322 0.369270i \(-0.120392\pi\)
\(42\) −8.23987 + 6.30396i −0.196187 + 0.150094i
\(43\) 55.8745 1.29941 0.649704 0.760188i \(-0.274893\pi\)
0.649704 + 0.760188i \(0.274893\pi\)
\(44\) 5.99042i 0.136146i
\(45\) 0 0
\(46\) 5.62352 0.122251
\(47\) 39.9749i 0.850530i 0.905069 + 0.425265i \(0.139819\pi\)
−0.905069 + 0.425265i \(0.860181\pi\)
\(48\) −2.88562 3.77178i −0.0601171 0.0785788i
\(49\) 7.00000 0.142857
\(50\) 0 0
\(51\) −28.9373 + 22.1386i −0.567397 + 0.434090i
\(52\) 14.5608 0.280015
\(53\) 105.002i 1.98116i −0.136928 0.990581i \(-0.543723\pi\)
0.136928 0.990581i \(-0.456277\pi\)
\(54\) −13.3654 32.6628i −0.247507 0.604868i
\(55\) 0 0
\(56\) 21.7576i 0.388528i
\(57\) −18.6458 24.3718i −0.327118 0.427575i
\(58\) −22.7085 −0.391526
\(59\) 41.3640i 0.701085i 0.936547 + 0.350542i \(0.114003\pi\)
−0.936547 + 0.350542i \(0.885997\pi\)
\(60\) 0 0
\(61\) −20.4797 −0.335733 −0.167867 0.985810i \(-0.553688\pi\)
−0.167867 + 0.985810i \(0.553688\pi\)
\(62\) 51.3577i 0.828350i
\(63\) −6.22876 + 22.9827i −0.0988692 + 0.364804i
\(64\) −46.6235 −0.728493
\(65\) 0 0
\(66\) 6.22876 + 8.14158i 0.0943751 + 0.123357i
\(67\) 27.1660 0.405463 0.202731 0.979234i \(-0.435018\pi\)
0.202731 + 0.979234i \(0.435018\pi\)
\(68\) 27.8300i 0.409265i
\(69\) 10.2510 7.84257i 0.148565 0.113660i
\(70\) 0 0
\(71\) 67.8049i 0.954999i −0.878632 0.477499i \(-0.841543\pi\)
0.878632 0.477499i \(-0.158457\pi\)
\(72\) −71.4353 19.3604i −0.992157 0.268894i
\(73\) −60.7895 −0.832733 −0.416367 0.909197i \(-0.636697\pi\)
−0.416367 + 0.909197i \(0.636697\pi\)
\(74\) 53.6439i 0.724917i
\(75\) 0 0
\(76\) −23.4392 −0.308411
\(77\) 6.91650i 0.0898246i
\(78\) −19.7895 + 15.1401i −0.253712 + 0.194104i
\(79\) −63.2470 −0.800596 −0.400298 0.916385i \(-0.631093\pi\)
−0.400298 + 0.916385i \(0.631093\pi\)
\(80\) 0 0
\(81\) −69.9150 40.9010i −0.863148 0.504950i
\(82\) 39.5791 0.482672
\(83\) 89.9435i 1.08366i −0.840489 0.541828i \(-0.817732\pi\)
0.840489 0.541828i \(-0.182268\pi\)
\(84\) 11.0516 + 14.4455i 0.131567 + 0.171971i
\(85\) 0 0
\(86\) 73.0333i 0.849224i
\(87\) −41.3948 + 31.6693i −0.475802 + 0.364015i
\(88\) 21.4980 0.244296
\(89\) 63.1745i 0.709826i 0.934899 + 0.354913i \(0.115490\pi\)
−0.934899 + 0.354913i \(0.884510\pi\)
\(90\) 0 0
\(91\) 16.8118 0.184745
\(92\) 9.85875i 0.107160i
\(93\) 71.6235 + 93.6188i 0.770145 + 1.00665i
\(94\) −52.2510 −0.555862
\(95\) 0 0
\(96\) −73.4464 + 56.1906i −0.765067 + 0.585318i
\(97\) −19.1660 −0.197588 −0.0987939 0.995108i \(-0.531498\pi\)
−0.0987939 + 0.995108i \(0.531498\pi\)
\(98\) 9.14967i 0.0933639i
\(99\) 22.7085 + 6.15445i 0.229379 + 0.0621662i
\(100\) 0 0
\(101\) 98.7122i 0.977348i −0.872466 0.488674i \(-0.837481\pi\)
0.872466 0.488674i \(-0.162519\pi\)
\(102\) −28.9373 37.8237i −0.283699 0.370821i
\(103\) 56.2510 0.546126 0.273063 0.961996i \(-0.411963\pi\)
0.273063 + 0.961996i \(0.411963\pi\)
\(104\) 52.2547i 0.502449i
\(105\) 0 0
\(106\) 137.247 1.29478
\(107\) 123.137i 1.15081i −0.817868 0.575406i \(-0.804844\pi\)
0.817868 0.575406i \(-0.195156\pi\)
\(108\) −57.2621 + 23.4312i −0.530205 + 0.216955i
\(109\) 164.539 1.50953 0.754764 0.655996i \(-0.227751\pi\)
0.754764 + 0.655996i \(0.227751\pi\)
\(110\) 0 0
\(111\) −74.8118 97.7861i −0.673980 0.880956i
\(112\) −4.18824 −0.0373950
\(113\) 144.050i 1.27478i 0.770540 + 0.637391i \(0.219986\pi\)
−0.770540 + 0.637391i \(0.780014\pi\)
\(114\) 31.8562 24.3718i 0.279441 0.213787i
\(115\) 0 0
\(116\) 39.8109i 0.343197i
\(117\) −14.9595 + 55.1970i −0.127859 + 0.471769i
\(118\) −54.0667 −0.458192
\(119\) 32.1323i 0.270020i
\(120\) 0 0
\(121\) 114.166 0.943521
\(122\) 26.7690i 0.219418i
\(123\) 72.1477 55.1970i 0.586567 0.448756i
\(124\) 90.0366 0.726101
\(125\) 0 0
\(126\) −30.0405 8.14158i −0.238417 0.0646157i
\(127\) 36.5830 0.288055 0.144028 0.989574i \(-0.453995\pi\)
0.144028 + 0.989574i \(0.453995\pi\)
\(128\) 62.3595i 0.487184i
\(129\) 101.852 + 133.131i 0.789553 + 1.03202i
\(130\) 0 0
\(131\) 33.6855i 0.257141i 0.991700 + 0.128570i \(0.0410389\pi\)
−0.991700 + 0.128570i \(0.958961\pi\)
\(132\) 14.2732 10.9198i 0.108130 0.0827257i
\(133\) −27.0627 −0.203479
\(134\) 35.5086i 0.264989i
\(135\) 0 0
\(136\) −99.8745 −0.734371
\(137\) 39.9749i 0.291788i −0.989300 0.145894i \(-0.953394\pi\)
0.989300 0.145894i \(-0.0466058\pi\)
\(138\) 10.2510 + 13.3990i 0.0742825 + 0.0970943i
\(139\) −194.642 −1.40030 −0.700150 0.713995i \(-0.746884\pi\)
−0.700150 + 0.713995i \(0.746884\pi\)
\(140\) 0 0
\(141\) −95.2470 + 72.8693i −0.675511 + 0.516803i
\(142\) 88.6275 0.624137
\(143\) 16.6112i 0.116162i
\(144\) 3.72679 13.7510i 0.0258805 0.0954929i
\(145\) 0 0
\(146\) 79.4577i 0.544231i
\(147\) 12.7601 + 16.6787i 0.0868036 + 0.113461i
\(148\) −94.0445 −0.635436
\(149\) 203.685i 1.36701i −0.729945 0.683506i \(-0.760454\pi\)
0.729945 0.683506i \(-0.239546\pi\)
\(150\) 0 0
\(151\) 165.749 1.09768 0.548838 0.835929i \(-0.315070\pi\)
0.548838 + 0.835929i \(0.315070\pi\)
\(152\) 84.1171i 0.553402i
\(153\) −105.498 28.5921i −0.689530 0.186876i
\(154\) 9.04052 0.0587047
\(155\) 0 0
\(156\) 26.5425 + 34.6936i 0.170144 + 0.222395i
\(157\) 302.723 1.92817 0.964086 0.265592i \(-0.0855674\pi\)
0.964086 + 0.265592i \(0.0855674\pi\)
\(158\) 82.6699i 0.523227i
\(159\) 250.184 191.405i 1.57349 1.20380i
\(160\) 0 0
\(161\) 11.3828i 0.0707008i
\(162\) 53.4615 91.3856i 0.330009 0.564109i
\(163\) 145.041 0.889819 0.444910 0.895576i \(-0.353236\pi\)
0.444910 + 0.895576i \(0.353236\pi\)
\(164\) 69.3871i 0.423092i
\(165\) 0 0
\(166\) 117.565 0.708221
\(167\) 19.6594i 0.117721i −0.998266 0.0588604i \(-0.981253\pi\)
0.998266 0.0588604i \(-0.0187467\pi\)
\(168\) −51.8412 + 39.6614i −0.308578 + 0.236080i
\(169\) −128.624 −0.761086
\(170\) 0 0
\(171\) 24.0810 88.8534i 0.140825 0.519611i
\(172\) 128.037 0.744399
\(173\) 19.6884i 0.113806i −0.998380 0.0569030i \(-0.981877\pi\)
0.998380 0.0569030i \(-0.0181226\pi\)
\(174\) −41.3948 54.1069i −0.237901 0.310959i
\(175\) 0 0
\(176\) 4.13828i 0.0235129i
\(177\) −98.5568 + 75.4014i −0.556818 + 0.425997i
\(178\) −82.5751 −0.463905
\(179\) 341.745i 1.90919i −0.297910 0.954594i \(-0.596289\pi\)
0.297910 0.954594i \(-0.403711\pi\)
\(180\) 0 0
\(181\) 215.889 1.19276 0.596378 0.802704i \(-0.296606\pi\)
0.596378 + 0.802704i \(0.296606\pi\)
\(182\) 21.9746i 0.120739i
\(183\) −37.3320 48.7965i −0.204000 0.266648i
\(184\) 35.3804 0.192285
\(185\) 0 0
\(186\) −122.369 + 93.6188i −0.657896 + 0.503327i
\(187\) 31.7490 0.169781
\(188\) 91.6026i 0.487248i
\(189\) −66.1144 + 27.0534i −0.349812 + 0.143140i
\(190\) 0 0
\(191\) 44.7112i 0.234090i 0.993127 + 0.117045i \(0.0373422\pi\)
−0.993127 + 0.117045i \(0.962658\pi\)
\(192\) −84.9889 111.089i −0.442650 0.578586i
\(193\) 145.122 0.751925 0.375963 0.926635i \(-0.377312\pi\)
0.375963 + 0.926635i \(0.377312\pi\)
\(194\) 25.0518i 0.129133i
\(195\) 0 0
\(196\) 16.0405 0.0818394
\(197\) 87.4643i 0.443981i −0.975049 0.221991i \(-0.928745\pi\)
0.975049 0.221991i \(-0.0712554\pi\)
\(198\) −8.04446 + 29.6822i −0.0406286 + 0.149910i
\(199\) 65.4170 0.328729 0.164364 0.986400i \(-0.447443\pi\)
0.164364 + 0.986400i \(0.447443\pi\)
\(200\) 0 0
\(201\) 49.5203 + 64.7277i 0.246369 + 0.322028i
\(202\) 129.026 0.638743
\(203\) 45.9653i 0.226430i
\(204\) −66.3098 + 50.7307i −0.325048 + 0.248680i
\(205\) 0 0
\(206\) 73.5254i 0.356919i
\(207\) 37.3725 + 10.1287i 0.180544 + 0.0489309i
\(208\) −10.0588 −0.0483597
\(209\) 26.7399i 0.127942i
\(210\) 0 0
\(211\) 40.5830 0.192337 0.0961683 0.995365i \(-0.469341\pi\)
0.0961683 + 0.995365i \(0.469341\pi\)
\(212\) 240.611i 1.13496i
\(213\) 161.557 123.600i 0.758483 0.580281i
\(214\) 160.952 0.752110
\(215\) 0 0
\(216\) −84.0882 205.498i −0.389297 0.951381i
\(217\) 103.956 0.479058
\(218\) 215.068i 0.986548i
\(219\) −110.812 144.842i −0.505990 0.661377i
\(220\) 0 0
\(221\) 77.1716i 0.349193i
\(222\) 127.816 97.7861i 0.575746 0.440478i
\(223\) −100.959 −0.452733 −0.226367 0.974042i \(-0.572685\pi\)
−0.226367 + 0.974042i \(0.572685\pi\)
\(224\) 81.5559i 0.364089i
\(225\) 0 0
\(226\) −188.288 −0.833131
\(227\) 391.279i 1.72370i 0.507166 + 0.861849i \(0.330693\pi\)
−0.507166 + 0.861849i \(0.669307\pi\)
\(228\) −42.7268 55.8480i −0.187398 0.244947i
\(229\) −6.81176 −0.0297457 −0.0148728 0.999889i \(-0.504734\pi\)
−0.0148728 + 0.999889i \(0.504734\pi\)
\(230\) 0 0
\(231\) 16.4797 12.6079i 0.0713409 0.0545797i
\(232\) −142.871 −0.615821
\(233\) 116.877i 0.501616i −0.968037 0.250808i \(-0.919304\pi\)
0.968037 0.250808i \(-0.0806963\pi\)
\(234\) −72.1477 19.5535i −0.308324 0.0835618i
\(235\) 0 0
\(236\) 94.7857i 0.401634i
\(237\) −115.292 150.697i −0.486462 0.635852i
\(238\) −42.0000 −0.176471
\(239\) 59.9623i 0.250888i −0.992101 0.125444i \(-0.959964\pi\)
0.992101 0.125444i \(-0.0400356\pi\)
\(240\) 0 0
\(241\) 134.753 0.559141 0.279570 0.960125i \(-0.409808\pi\)
0.279570 + 0.960125i \(0.409808\pi\)
\(242\) 149.226i 0.616636i
\(243\) −29.9928 241.142i −0.123427 0.992354i
\(244\) −46.9294 −0.192334
\(245\) 0 0
\(246\) 72.1477 + 94.3039i 0.293283 + 0.383349i
\(247\) −64.9961 −0.263142
\(248\) 323.117i 1.30289i
\(249\) 214.306 163.956i 0.860666 0.658457i
\(250\) 0 0
\(251\) 268.248i 1.06872i 0.845257 + 0.534359i \(0.179447\pi\)
−0.845257 + 0.534359i \(0.820553\pi\)
\(252\) −14.2732 + 52.6648i −0.0566397 + 0.208987i
\(253\) −11.2470 −0.0444547
\(254\) 47.8175i 0.188258i
\(255\) 0 0
\(256\) −268.004 −1.04689
\(257\) 234.129i 0.911007i −0.890234 0.455504i \(-0.849459\pi\)
0.890234 0.455504i \(-0.150541\pi\)
\(258\) −174.014 + 133.131i −0.674474 + 0.516010i
\(259\) −108.583 −0.419239
\(260\) 0 0
\(261\) −150.915 40.9010i −0.578218 0.156709i
\(262\) −44.0301 −0.168054
\(263\) 250.142i 0.951111i −0.879686 0.475555i \(-0.842247\pi\)
0.879686 0.475555i \(-0.157753\pi\)
\(264\) 39.1882 + 51.2228i 0.148440 + 0.194026i
\(265\) 0 0
\(266\) 35.3736i 0.132983i
\(267\) −150.524 + 115.159i −0.563761 + 0.431308i
\(268\) 62.2510 0.232280
\(269\) 340.684i 1.26648i 0.773955 + 0.633241i \(0.218276\pi\)
−0.773955 + 0.633241i \(0.781724\pi\)
\(270\) 0 0
\(271\) −21.2994 −0.0785955 −0.0392977 0.999228i \(-0.512512\pi\)
−0.0392977 + 0.999228i \(0.512512\pi\)
\(272\) 19.2254i 0.0706816i
\(273\) 30.6458 + 40.0569i 0.112255 + 0.146729i
\(274\) 52.2510 0.190697
\(275\) 0 0
\(276\) 23.4902 17.9713i 0.0851093 0.0651133i
\(277\) 226.915 0.819188 0.409594 0.912268i \(-0.365670\pi\)
0.409594 + 0.912268i \(0.365670\pi\)
\(278\) 254.415i 0.915163i
\(279\) −92.5020 + 341.311i −0.331548 + 1.22334i
\(280\) 0 0
\(281\) 235.489i 0.838039i −0.907977 0.419019i \(-0.862374\pi\)
0.907977 0.419019i \(-0.137626\pi\)
\(282\) −95.2470 124.497i −0.337755 0.441479i
\(283\) −368.634 −1.30259 −0.651297 0.758823i \(-0.725775\pi\)
−0.651297 + 0.758823i \(0.725775\pi\)
\(284\) 155.375i 0.547096i
\(285\) 0 0
\(286\) 21.7124 0.0759176
\(287\) 80.1138i 0.279142i
\(288\) −267.767 72.5703i −0.929748 0.251980i
\(289\) 141.502 0.489626
\(290\) 0 0
\(291\) −34.9373 45.6663i −0.120059 0.156929i
\(292\) −139.299 −0.477053
\(293\) 531.625i 1.81442i 0.420677 + 0.907211i \(0.361793\pi\)
−0.420677 + 0.907211i \(0.638207\pi\)
\(294\) −21.8006 + 16.6787i −0.0741519 + 0.0567303i
\(295\) 0 0
\(296\) 337.500i 1.14020i
\(297\) 26.7307 + 65.3257i 0.0900024 + 0.219952i
\(298\) 266.235 0.893407
\(299\) 27.3379i 0.0914312i
\(300\) 0 0
\(301\) 147.830 0.491130
\(302\) 216.650i 0.717383i
\(303\) 235.199 179.940i 0.776233 0.593861i
\(304\) 16.1922 0.0532637
\(305\) 0 0
\(306\) 37.3725 137.896i 0.122132 0.450640i
\(307\) −567.763 −1.84939 −0.924696 0.380706i \(-0.875681\pi\)
−0.924696 + 0.380706i \(0.875681\pi\)
\(308\) 15.8492i 0.0514583i
\(309\) 102.539 + 134.028i 0.331840 + 0.433746i
\(310\) 0 0
\(311\) 42.7531i 0.137470i 0.997635 + 0.0687349i \(0.0218963\pi\)
−0.997635 + 0.0687349i \(0.978104\pi\)
\(312\) −124.506 + 95.2539i −0.399057 + 0.305301i
\(313\) 158.118 0.505168 0.252584 0.967575i \(-0.418720\pi\)
0.252584 + 0.967575i \(0.418720\pi\)
\(314\) 395.688i 1.26015i
\(315\) 0 0
\(316\) −144.931 −0.458642
\(317\) 140.944i 0.444619i 0.974976 + 0.222309i \(0.0713595\pi\)
−0.974976 + 0.222309i \(0.928641\pi\)
\(318\) 250.184 + 327.015i 0.786743 + 1.02835i
\(319\) 45.4170 0.142373
\(320\) 0 0
\(321\) 293.395 224.463i 0.914002 0.699262i
\(322\) 14.8784 0.0462064
\(323\) 124.227i 0.384604i
\(324\) −160.210 93.7247i −0.494477 0.289274i
\(325\) 0 0
\(326\) 189.582i 0.581539i
\(327\) 299.933 + 392.041i 0.917227 + 1.19890i
\(328\) 249.012 0.759182
\(329\) 105.764i 0.321470i
\(330\) 0 0
\(331\) −258.369 −0.780570 −0.390285 0.920694i \(-0.627623\pi\)
−0.390285 + 0.920694i \(0.627623\pi\)
\(332\) 206.106i 0.620801i
\(333\) 96.6196 356.504i 0.290149 1.07058i
\(334\) 25.6967 0.0769362
\(335\) 0 0
\(336\) −7.63464 9.97920i −0.0227221 0.0297000i
\(337\) −328.959 −0.976141 −0.488070 0.872804i \(-0.662299\pi\)
−0.488070 + 0.872804i \(0.662299\pi\)
\(338\) 168.123i 0.497406i
\(339\) −343.225 + 262.586i −1.01246 + 0.774590i
\(340\) 0 0
\(341\) 102.715i 0.301218i
\(342\) 116.140 + 31.4762i 0.339590 + 0.0920357i
\(343\) 18.5203 0.0539949
\(344\) 459.489i 1.33572i
\(345\) 0 0
\(346\) 25.7347 0.0743776
\(347\) 128.635i 0.370707i −0.982672 0.185353i \(-0.940657\pi\)
0.982672 0.185353i \(-0.0593430\pi\)
\(348\) −94.8562 + 72.5703i −0.272575 + 0.208535i
\(349\) −73.4837 −0.210555 −0.105277 0.994443i \(-0.533573\pi\)
−0.105277 + 0.994443i \(0.533573\pi\)
\(350\) 0 0
\(351\) −158.786 + 64.9737i −0.452381 + 0.185110i
\(352\) 80.5830 0.228929
\(353\) 239.685i 0.678995i 0.940607 + 0.339498i \(0.110257\pi\)
−0.940607 + 0.339498i \(0.889743\pi\)
\(354\) −98.5568 128.823i −0.278409 0.363907i
\(355\) 0 0
\(356\) 144.765i 0.406642i
\(357\) −76.5608 + 58.5732i −0.214456 + 0.164071i
\(358\) 446.693 1.24775
\(359\) 180.215i 0.501992i 0.967988 + 0.250996i \(0.0807581\pi\)
−0.967988 + 0.250996i \(0.919242\pi\)
\(360\) 0 0
\(361\) −256.373 −0.710173
\(362\) 282.187i 0.779523i
\(363\) 208.110 + 272.020i 0.573307 + 0.749367i
\(364\) 38.5242 0.105836
\(365\) 0 0
\(366\) 63.7817 48.7965i 0.174267 0.133324i
\(367\) −229.786 −0.626119 −0.313059 0.949734i \(-0.601354\pi\)
−0.313059 + 0.949734i \(0.601354\pi\)
\(368\) 6.81057i 0.0185070i
\(369\) 263.033 + 71.2871i 0.712826 + 0.193190i
\(370\) 0 0
\(371\) 277.808i 0.748809i
\(372\) 164.125 + 214.528i 0.441198 + 0.576687i
\(373\) −441.749 −1.18431 −0.592157 0.805823i \(-0.701723\pi\)
−0.592157 + 0.805823i \(0.701723\pi\)
\(374\) 41.4990i 0.110960i
\(375\) 0 0
\(376\) −328.737 −0.874301
\(377\) 110.394i 0.292822i
\(378\) −35.3614 86.4178i −0.0935487 0.228618i
\(379\) −421.203 −1.11135 −0.555676 0.831399i \(-0.687541\pi\)
−0.555676 + 0.831399i \(0.687541\pi\)
\(380\) 0 0
\(381\) 66.6863 + 87.1653i 0.175030 + 0.228780i
\(382\) −58.4418 −0.152989
\(383\) 595.591i 1.55507i −0.628841 0.777534i \(-0.716470\pi\)
0.628841 0.777534i \(-0.283530\pi\)
\(384\) −148.582 + 113.674i −0.386933 + 0.296025i
\(385\) 0 0
\(386\) 189.688i 0.491419i
\(387\) −131.542 + 485.361i −0.339903 + 1.25416i
\(388\) −43.9190 −0.113193
\(389\) 367.347i 0.944336i −0.881509 0.472168i \(-0.843472\pi\)
0.881509 0.472168i \(-0.156528\pi\)
\(390\) 0 0
\(391\) 52.2510 0.133634
\(392\) 57.5651i 0.146850i
\(393\) −80.2614 + 61.4044i −0.204227 + 0.156245i
\(394\) 114.324 0.290163
\(395\) 0 0
\(396\) 52.0366 + 14.1029i 0.131406 + 0.0356135i
\(397\) −408.346 −1.02858 −0.514290 0.857616i \(-0.671945\pi\)
−0.514290 + 0.857616i \(0.671945\pi\)
\(398\) 85.5062i 0.214840i
\(399\) −49.3320 64.4816i −0.123639 0.161608i
\(400\) 0 0
\(401\) 238.817i 0.595555i −0.954635 0.297777i \(-0.903755\pi\)
0.954635 0.297777i \(-0.0962453\pi\)
\(402\) −84.6052 + 64.7277i −0.210461 + 0.161014i
\(403\) 249.668 0.619524
\(404\) 226.199i 0.559899i
\(405\) 0 0
\(406\) −60.0810 −0.147983
\(407\) 107.288i 0.263606i
\(408\) −182.059 237.968i −0.446223 0.583255i
\(409\) −649.365 −1.58769 −0.793844 0.608121i \(-0.791924\pi\)
−0.793844 + 0.608121i \(0.791924\pi\)
\(410\) 0 0
\(411\) 95.2470 72.8693i 0.231745 0.177297i
\(412\) 128.899 0.312862
\(413\) 109.439i 0.264985i
\(414\) −13.2392 + 48.8495i −0.0319787 + 0.117994i
\(415\) 0 0
\(416\) 195.871i 0.470844i
\(417\) −354.808 463.768i −0.850858 1.11215i
\(418\) −34.9516 −0.0836163
\(419\) 11.5178i 0.0274888i −0.999906 0.0137444i \(-0.995625\pi\)
0.999906 0.0137444i \(-0.00437512\pi\)
\(420\) 0 0
\(421\) −83.9921 −0.199506 −0.0997531 0.995012i \(-0.531805\pi\)
−0.0997531 + 0.995012i \(0.531805\pi\)
\(422\) 53.0458i 0.125701i
\(423\) −347.247 94.1108i −0.820915 0.222484i
\(424\) 863.490 2.03653
\(425\) 0 0
\(426\) 161.557 + 211.170i 0.379241 + 0.495705i
\(427\) −54.1843 −0.126895
\(428\) 282.168i 0.659272i
\(429\) 39.5791 30.2802i 0.0922589 0.0705832i
\(430\) 0 0
\(431\) 694.004i 1.61022i 0.593127 + 0.805109i \(0.297893\pi\)
−0.593127 + 0.805109i \(0.702107\pi\)
\(432\) 39.5575 16.1866i 0.0915684 0.0374690i
\(433\) −116.834 −0.269824 −0.134912 0.990858i \(-0.543075\pi\)
−0.134912 + 0.990858i \(0.543075\pi\)
\(434\) 135.880i 0.313087i
\(435\) 0 0
\(436\) 377.041 0.864772
\(437\) 44.0072i 0.100703i
\(438\) 189.322 144.842i 0.432241 0.330688i
\(439\) −528.073 −1.20290 −0.601450 0.798910i \(-0.705410\pi\)
−0.601450 + 0.798910i \(0.705410\pi\)
\(440\) 0 0
\(441\) −16.4797 + 60.8064i −0.0373690 + 0.137883i
\(442\) −100.871 −0.228214
\(443\) 272.252i 0.614564i −0.951619 0.307282i \(-0.900581\pi\)
0.951619 0.307282i \(-0.0994194\pi\)
\(444\) −171.431 224.077i −0.386107 0.504678i
\(445\) 0 0
\(446\) 131.964i 0.295883i
\(447\) 485.314 371.292i 1.08571 0.830631i
\(448\) −123.354 −0.275344
\(449\) 525.770i 1.17098i −0.810680 0.585490i \(-0.800902\pi\)
0.810680 0.585490i \(-0.199098\pi\)
\(450\) 0 0
\(451\) −79.1581 −0.175517
\(452\) 330.092i 0.730292i
\(453\) 302.140 + 394.925i 0.666975 + 0.871800i
\(454\) −511.439 −1.12652
\(455\) 0 0
\(456\) 200.423 153.335i 0.439525 0.336261i
\(457\) 513.786 1.12426 0.562129 0.827050i \(-0.309983\pi\)
0.562129 + 0.827050i \(0.309983\pi\)
\(458\) 8.90362i 0.0194402i
\(459\) −124.184 303.487i −0.270554 0.661192i
\(460\) 0 0
\(461\) 687.879i 1.49214i 0.665865 + 0.746072i \(0.268063\pi\)
−0.665865 + 0.746072i \(0.731937\pi\)
\(462\) 16.4797 + 21.5406i 0.0356704 + 0.0466246i
\(463\) −781.061 −1.68696 −0.843479 0.537162i \(-0.819496\pi\)
−0.843479 + 0.537162i \(0.819496\pi\)
\(464\) 27.5020i 0.0592715i
\(465\) 0 0
\(466\) 152.769 0.327830
\(467\) 163.353i 0.349792i −0.984587 0.174896i \(-0.944041\pi\)
0.984587 0.174896i \(-0.0559589\pi\)
\(468\) −34.2797 + 126.484i −0.0732472 + 0.270265i
\(469\) 71.8745 0.153251
\(470\) 0 0
\(471\) 551.826 + 721.289i 1.17161 + 1.53140i
\(472\) −340.161 −0.720679
\(473\) 146.067i 0.308809i
\(474\) 196.975 150.697i 0.415560 0.317926i
\(475\) 0 0
\(476\) 73.6313i 0.154688i
\(477\) 912.110 + 247.200i 1.91218 + 0.518239i
\(478\) 78.3765 0.163968
\(479\) 700.159i 1.46171i 0.682533 + 0.730855i \(0.260878\pi\)
−0.682533 + 0.730855i \(0.739122\pi\)
\(480\) 0 0
\(481\) −260.782 −0.542166
\(482\) 176.135i 0.365425i
\(483\) 27.1216 20.7495i 0.0561523 0.0429596i
\(484\) 261.612 0.540520
\(485\) 0 0
\(486\) 315.195 39.2035i 0.648550 0.0806656i
\(487\) −86.5909 −0.177805 −0.0889023 0.996040i \(-0.528336\pi\)
−0.0889023 + 0.996040i \(0.528336\pi\)
\(488\) 168.417i 0.345117i
\(489\) 264.391 + 345.584i 0.540677 + 0.706716i
\(490\) 0 0
\(491\) 741.494i 1.51017i −0.655627 0.755085i \(-0.727596\pi\)
0.655627 0.755085i \(-0.272404\pi\)
\(492\) 165.327 126.484i 0.336030 0.257081i
\(493\) −210.996 −0.427984
\(494\) 84.9560i 0.171976i
\(495\) 0 0
\(496\) −62.1987 −0.125401
\(497\) 179.395i 0.360956i
\(498\) 214.306 + 280.118i 0.430333 + 0.562486i
\(499\) 379.814 0.761151 0.380575 0.924750i \(-0.375726\pi\)
0.380575 + 0.924750i \(0.375726\pi\)
\(500\) 0 0
\(501\) 46.8419 35.8366i 0.0934967 0.0715302i
\(502\) −350.626 −0.698458
\(503\) 465.808i 0.926059i 0.886343 + 0.463029i \(0.153238\pi\)
−0.886343 + 0.463029i \(0.846762\pi\)
\(504\) −189.000 51.2228i −0.375000 0.101632i
\(505\) 0 0
\(506\) 14.7010i 0.0290533i
\(507\) −234.465 306.468i −0.462455 0.604473i
\(508\) 83.8301 0.165020
\(509\) 750.503i 1.47447i −0.675639 0.737233i \(-0.736132\pi\)
0.675639 0.737233i \(-0.263868\pi\)
\(510\) 0 0
\(511\) −160.834 −0.314744
\(512\) 100.868i 0.197009i
\(513\) 255.605 104.592i 0.498256 0.203882i
\(514\) 306.029 0.595387
\(515\) 0 0
\(516\) 233.395 + 305.069i 0.452315 + 0.591219i
\(517\) 104.502 0.202131
\(518\) 141.928i 0.273993i
\(519\) 46.9111 35.8896i 0.0903875 0.0691514i
\(520\) 0 0
\(521\) 726.946i 1.39529i −0.716443 0.697645i \(-0.754231\pi\)
0.716443 0.697645i \(-0.245769\pi\)
\(522\) 53.4615 197.260i 0.102417 0.377893i
\(523\) 624.707 1.19447 0.597234 0.802067i \(-0.296266\pi\)
0.597234 + 0.802067i \(0.296266\pi\)
\(524\) 77.1903i 0.147310i
\(525\) 0 0
\(526\) 326.959 0.621596
\(527\) 477.190i 0.905485i
\(528\) −9.86015 + 7.54356i −0.0186745 + 0.0142871i
\(529\) 510.490 0.965010
\(530\) 0 0
\(531\) −359.314 97.3812i −0.676674 0.183392i
\(532\) −62.0144 −0.116568
\(533\) 192.408i 0.360990i
\(534\) −150.524 196.749i −0.281881 0.368445i
\(535\) 0 0
\(536\) 223.402i 0.416795i
\(537\) 814.265 622.958i 1.51632 1.16007i
\(538\) −445.306 −0.827706
\(539\) 18.2993i 0.0339505i
\(540\) 0 0
\(541\) −291.757 −0.539292 −0.269646 0.962960i \(-0.586907\pi\)
−0.269646 + 0.962960i \(0.586907\pi\)
\(542\) 27.8403i 0.0513659i
\(543\) 393.539 + 514.392i 0.724749 + 0.947315i
\(544\) −374.369 −0.688178
\(545\) 0 0
\(546\) −52.3582 + 40.0569i −0.0958941 + 0.0733643i
\(547\) −204.952 −0.374683 −0.187342 0.982295i \(-0.559987\pi\)
−0.187342 + 0.982295i \(0.559987\pi\)
\(548\) 91.6026i 0.167158i
\(549\) 48.2144 177.900i 0.0878222 0.324044i
\(550\) 0 0
\(551\) 177.707i 0.322517i
\(552\) 64.4941 + 84.2999i 0.116837 + 0.152717i
\(553\) −167.336 −0.302597
\(554\) 296.599i 0.535378i
\(555\) 0 0
\(556\) −446.022 −0.802198
\(557\) 503.883i 0.904637i −0.891857 0.452318i \(-0.850597\pi\)
0.891857 0.452318i \(-0.149403\pi\)
\(558\) −446.125 120.909i −0.799508 0.216683i
\(559\) 355.041 0.635135
\(560\) 0 0
\(561\) 57.8745 + 75.6475i 0.103163 + 0.134844i
\(562\) 307.806 0.547698
\(563\) 108.735i 0.193135i 0.995326 + 0.0965674i \(0.0307863\pi\)
−0.995326 + 0.0965674i \(0.969214\pi\)
\(564\) −218.259 + 166.980i −0.386984 + 0.296064i
\(565\) 0 0
\(566\) 481.840i 0.851307i
\(567\) −184.978 108.214i −0.326239 0.190853i
\(568\) 557.600 0.981690
\(569\) 434.871i 0.764273i 0.924106 + 0.382136i \(0.124812\pi\)
−0.924106 + 0.382136i \(0.875188\pi\)
\(570\) 0 0
\(571\) 119.122 0.208619 0.104310 0.994545i \(-0.466737\pi\)
0.104310 + 0.994545i \(0.466737\pi\)
\(572\) 38.0646i 0.0665466i
\(573\) −106.532 + 81.5029i −0.185920 + 0.142239i
\(574\) 104.716 0.182433
\(575\) 0 0
\(576\) 109.763 405.001i 0.190561 0.703127i
\(577\) 655.417 1.13590 0.567952 0.823061i \(-0.307736\pi\)
0.567952 + 0.823061i \(0.307736\pi\)
\(578\) 184.957i 0.319994i
\(579\) 264.539 + 345.777i 0.456889 + 0.597197i
\(580\) 0 0
\(581\) 237.968i 0.409584i
\(582\) 59.6902 45.6663i 0.102560 0.0784645i
\(583\) −274.494 −0.470830
\(584\) 499.908i 0.856007i
\(585\) 0 0
\(586\) −694.885 −1.18581
\(587\) 736.236i 1.25424i 0.778925 + 0.627118i \(0.215765\pi\)
−0.778925 + 0.627118i \(0.784235\pi\)
\(588\) 29.2399 + 38.2193i 0.0497277 + 0.0649988i
\(589\) −401.903 −0.682348
\(590\) 0 0
\(591\) 208.399 159.437i 0.352620 0.269774i
\(592\) 64.9674 0.109742
\(593\) 832.884i 1.40453i 0.711917 + 0.702263i \(0.247827\pi\)
−0.711917 + 0.702263i \(0.752173\pi\)
\(594\) −85.3869 + 34.9396i −0.143749 + 0.0588209i
\(595\) 0 0
\(596\) 466.744i 0.783127i
\(597\) 119.247 + 155.867i 0.199744 + 0.261084i
\(598\) 35.7333 0.0597546
\(599\) 69.3290i 0.115741i −0.998324 0.0578706i \(-0.981569\pi\)
0.998324 0.0578706i \(-0.0184311\pi\)
\(600\) 0 0
\(601\) −161.720 −0.269085 −0.134543 0.990908i \(-0.542957\pi\)
−0.134543 + 0.990908i \(0.542957\pi\)
\(602\) 193.228i 0.320977i
\(603\) −63.9555 + 235.981i −0.106062 + 0.391345i
\(604\) 379.814 0.628832
\(605\) 0 0
\(606\) 235.199 + 307.427i 0.388117 + 0.507305i
\(607\) −929.608 −1.53148 −0.765740 0.643151i \(-0.777627\pi\)
−0.765740 + 0.643151i \(0.777627\pi\)
\(608\) 315.304i 0.518592i
\(609\) −109.520 + 83.7891i −0.179836 + 0.137585i
\(610\) 0 0
\(611\) 254.010i 0.415729i
\(612\) −241.749 65.5188i −0.395015 0.107057i
\(613\) −297.940 −0.486036 −0.243018 0.970022i \(-0.578137\pi\)
−0.243018 + 0.970022i \(0.578137\pi\)
\(614\) 742.121i 1.20867i
\(615\) 0 0
\(616\) 56.8784 0.0923351
\(617\) 975.575i 1.58116i −0.612360 0.790579i \(-0.709780\pi\)
0.612360 0.790579i \(-0.290220\pi\)
\(618\) −175.187 + 134.028i −0.283474 + 0.216873i
\(619\) 357.034 0.576792 0.288396 0.957511i \(-0.406878\pi\)
0.288396 + 0.957511i \(0.406878\pi\)
\(620\) 0 0
\(621\) 43.9921 + 107.510i 0.0708408 + 0.173124i
\(622\) −55.8824 −0.0898431
\(623\) 167.144i 0.268289i
\(624\) −18.3360 23.9668i −0.0293845 0.0384084i
\(625\) 0 0
\(626\) 206.675i 0.330151i
\(627\) −63.7124 + 48.7435i −0.101615 + 0.0777409i
\(628\) 693.690 1.10460
\(629\) 498.432i 0.792420i
\(630\) 0 0
\(631\) −813.223 −1.28879 −0.644393 0.764695i \(-0.722890\pi\)
−0.644393 + 0.764695i \(0.722890\pi\)
\(632\) 520.118i 0.822971i
\(633\) 73.9778 + 96.6960i 0.116869 + 0.152758i
\(634\) −184.227 −0.290579
\(635\) 0 0
\(636\) 573.298 438.605i 0.901412 0.689630i
\(637\) 44.4797 0.0698269
\(638\) 59.3643i 0.0930475i
\(639\) 588.996 + 159.630i 0.921747 + 0.249812i
\(640\) 0 0
\(641\) 646.727i 1.00893i −0.863431 0.504467i \(-0.831689\pi\)
0.863431 0.504467i \(-0.168311\pi\)
\(642\) 293.395 + 383.495i 0.457001 + 0.597344i
\(643\) −144.561 −0.224822 −0.112411 0.993662i \(-0.535857\pi\)
−0.112411 + 0.993662i \(0.535857\pi\)
\(644\) 26.0838i 0.0405028i
\(645\) 0 0
\(646\) 162.376 0.251357
\(647\) 716.654i 1.10766i −0.832631 0.553828i \(-0.813166\pi\)
0.832631 0.553828i \(-0.186834\pi\)
\(648\) 336.353 574.953i 0.519063 0.887273i
\(649\) 108.133 0.166615
\(650\) 0 0
\(651\) 189.498 + 247.692i 0.291088 + 0.380479i
\(652\) 332.361 0.509756
\(653\) 378.999i 0.580397i 0.956966 + 0.290199i \(0.0937214\pi\)
−0.956966 + 0.290199i \(0.906279\pi\)
\(654\) −512.435 + 392.041i −0.783540 + 0.599452i
\(655\) 0 0
\(656\) 47.9337i 0.0730696i
\(657\) 143.114 528.056i 0.217829 0.803738i
\(658\) −138.243 −0.210096
\(659\) 710.721i 1.07848i 0.842151 + 0.539242i \(0.181289\pi\)
−0.842151 + 0.539242i \(0.818711\pi\)
\(660\) 0 0
\(661\) 91.5045 0.138433 0.0692167 0.997602i \(-0.477950\pi\)
0.0692167 + 0.997602i \(0.477950\pi\)
\(662\) 337.712i 0.510139i
\(663\) −183.875 + 140.674i −0.277337 + 0.212178i
\(664\) 739.659 1.11394
\(665\) 0 0
\(666\) 465.984 + 126.291i 0.699676 + 0.189626i
\(667\) 74.7451 0.112062
\(668\) 45.0495i 0.0674394i
\(669\) −184.037 240.553i −0.275092 0.359571i
\(670\) 0 0
\(671\) 53.5379i 0.0797883i
\(672\) −194.321 + 148.666i −0.289168 + 0.221230i
\(673\) −645.806 −0.959594 −0.479797 0.877380i \(-0.659290\pi\)
−0.479797 + 0.877380i \(0.659290\pi\)
\(674\) 429.981i 0.637954i
\(675\) 0 0
\(676\) −294.741 −0.436008
\(677\) 335.571i 0.495674i −0.968802 0.247837i \(-0.920280\pi\)
0.968802 0.247837i \(-0.0797198\pi\)
\(678\) −343.225 448.627i −0.506231 0.661692i
\(679\) −50.7085 −0.0746811
\(680\) 0 0
\(681\) −932.290 + 713.254i −1.36900 + 1.04736i
\(682\) 134.259 0.196860
\(683\) 113.336i 0.165939i −0.996552 0.0829694i \(-0.973560\pi\)
0.996552 0.0829694i \(-0.0264404\pi\)
\(684\) 55.1818 203.608i 0.0806751 0.297672i
\(685\) 0 0
\(686\) 24.2077i 0.0352882i
\(687\) −12.4170 16.2302i −0.0180742 0.0236247i
\(688\) −88.4496 −0.128561
\(689\) 667.206i 0.968369i
\(690\) 0 0
\(691\) 565.667 0.818620 0.409310 0.912395i \(-0.365769\pi\)
0.409310 + 0.912395i \(0.365769\pi\)
\(692\) 45.1161i 0.0651967i
\(693\) 60.0810 + 16.2832i 0.0866970 + 0.0234966i
\(694\) 168.138 0.242274
\(695\) 0 0
\(696\) −260.435 340.414i −0.374189 0.489100i
\(697\) 367.749 0.527617
\(698\) 96.0501i 0.137608i
\(699\) 278.478 213.051i 0.398395 0.304794i
\(700\) 0 0
\(701\) 872.955i 1.24530i 0.782501 + 0.622650i \(0.213944\pi\)
−0.782501 + 0.622650i \(0.786056\pi\)
\(702\) −84.9268 207.548i −0.120978 0.295652i
\(703\) 419.793 0.597146
\(704\) 121.883i 0.173129i
\(705\) 0 0
\(706\) −313.292 −0.443756
\(707\) 261.168i 0.369403i
\(708\) −225.843 + 172.783i −0.318988 + 0.244043i
\(709\) 1092.04 1.54025 0.770125 0.637894i \(-0.220194\pi\)
0.770125 + 0.637894i \(0.220194\pi\)
\(710\) 0 0
\(711\) 148.899 549.404i 0.209422 0.772720i
\(712\) −519.522 −0.729665
\(713\) 169.044i 0.237088i
\(714\) −76.5608 100.072i −0.107228 0.140157i
\(715\) 0 0
\(716\) 783.109i 1.09373i
\(717\) 142.871 109.304i 0.199262 0.152446i
\(718\) −235.558 −0.328076
\(719\) 901.769i 1.25420i 0.778939 + 0.627099i \(0.215758\pi\)
−0.778939 + 0.627099i \(0.784242\pi\)
\(720\) 0 0
\(721\) 148.826 0.206416
\(722\) 335.103i 0.464132i
\(723\) 245.638 + 321.072i 0.339748 + 0.444083i
\(724\) 494.710 0.683301
\(725\) 0 0
\(726\) −355.556 + 272.020i −0.489747 + 0.374683i
\(727\) −297.506 −0.409224 −0.204612 0.978843i \(-0.565593\pi\)
−0.204612 + 0.978843i \(0.565593\pi\)
\(728\) 138.253i 0.189908i
\(729\) 519.889 511.035i 0.713153 0.701008i
\(730\) 0 0
\(731\) 678.589i 0.928302i
\(732\) −85.5464 111.817i −0.116867 0.152756i
\(733\) −456.966 −0.623419 −0.311709 0.950177i \(-0.600902\pi\)
−0.311709 + 0.950177i \(0.600902\pi\)
\(734\) 300.352i 0.409198i
\(735\) 0 0
\(736\) 132.620 0.180190
\(737\) 71.0171i 0.0963597i
\(738\) −93.1790 + 343.809i −0.126259 + 0.465865i
\(739\) −332.199 −0.449525 −0.224762 0.974414i \(-0.572161\pi\)
−0.224762 + 0.974414i \(0.572161\pi\)
\(740\) 0 0
\(741\) −118.480 154.864i −0.159892 0.208994i
\(742\) 363.122 0.489382
\(743\) 64.5346i 0.0868568i 0.999057 + 0.0434284i \(0.0138280\pi\)
−0.999057 + 0.0434284i \(0.986172\pi\)
\(744\) −769.882 + 589.003i −1.03479 + 0.791670i
\(745\) 0 0
\(746\) 577.408i 0.774005i
\(747\) 781.306 + 211.749i 1.04592 + 0.283466i
\(748\) 72.7530 0.0972633
\(749\) 325.790i 0.434966i
\(750\) 0 0
\(751\) −611.668 −0.814471 −0.407236 0.913323i \(-0.633507\pi\)
−0.407236 + 0.913323i \(0.633507\pi\)
\(752\) 63.2805i 0.0841496i
\(753\) −639.148 + 488.983i −0.848802 + 0.649380i
\(754\) −144.295 −0.191373
\(755\) 0 0
\(756\) −151.501 + 61.9930i −0.200399 + 0.0820014i
\(757\) 207.357 0.273919 0.136960 0.990577i \(-0.456267\pi\)
0.136960 + 0.990577i \(0.456267\pi\)
\(758\) 550.552i 0.726322i
\(759\) −20.5020 26.7980i −0.0270118 0.0353070i
\(760\) 0 0
\(761\) 337.770i 0.443851i 0.975064 + 0.221925i \(0.0712341\pi\)
−0.975064 + 0.221925i \(0.928766\pi\)
\(762\) −113.933 + 87.1653i −0.149519 + 0.114390i
\(763\) 435.328 0.570548
\(764\) 102.456i 0.134104i
\(765\) 0 0
\(766\) 778.494 1.01631
\(767\) 262.837i 0.342682i
\(768\) −488.538 638.565i −0.636117 0.831465i
\(769\) −1042.22 −1.35529 −0.677646 0.735388i \(-0.737000\pi\)
−0.677646 + 0.735388i \(0.737000\pi\)
\(770\) 0 0
\(771\) 557.852 426.788i 0.723544 0.553551i
\(772\) 332.546 0.430760
\(773\) 291.448i 0.377035i −0.982070 0.188517i \(-0.939632\pi\)
0.982070 0.188517i \(-0.0603682\pi\)
\(774\) −634.413 171.939i −0.819655 0.222143i
\(775\) 0 0
\(776\) 157.613i 0.203110i
\(777\) −197.933 258.718i −0.254740 0.332970i
\(778\) 480.157 0.617168
\(779\) 309.729i 0.397598i
\(780\) 0 0
\(781\) −177.255 −0.226959
\(782\) 68.2970i 0.0873363i
\(783\) −177.646 434.138i −0.226878 0.554455i
\(784\) −11.0810 −0.0141340
\(785\) 0 0
\(786\) −80.2614 104.909i −0.102114 0.133472i
\(787\) −293.889 −0.373429 −0.186715 0.982414i \(-0.559784\pi\)
−0.186715 + 0.982414i \(0.559784\pi\)
\(788\) 200.425i 0.254346i
\(789\) 596.006 455.978i 0.755395 0.577919i
\(790\) 0 0
\(791\) 381.122i 0.481822i
\(792\) −50.6117 + 186.745i −0.0639037 + 0.235790i
\(793\) −130.133 −0.164103
\(794\) 533.748i 0.672226i
\(795\) 0 0
\(796\) 149.903 0.188321
\(797\) 568.764i 0.713631i 0.934175 + 0.356816i \(0.116138\pi\)
−0.934175 + 0.356816i \(0.883862\pi\)
\(798\) 84.2836 64.4816i 0.105619 0.0808041i
\(799\) −485.490 −0.607622
\(800\) 0 0
\(801\) −548.774 148.729i −0.685111 0.185679i
\(802\) 312.157 0.389223
\(803\) 158.915i 0.197902i
\(804\) 113.476 + 148.324i 0.141139 + 0.184482i
\(805\) 0 0
\(806\) 326.340i 0.404888i
\(807\) −811.737 + 621.024i −1.00587 + 0.769546i
\(808\) 811.768 1.00466
\(809\) 183.697i 0.227067i −0.993534 0.113534i \(-0.963783\pi\)
0.993534 0.113534i \(-0.0362169\pi\)
\(810\) 0 0
\(811\) −544.663 −0.671594 −0.335797 0.941934i \(-0.609006\pi\)
−0.335797 + 0.941934i \(0.609006\pi\)
\(812\) 105.330i 0.129716i
\(813\) −38.8261 50.7494i −0.0477566 0.0624224i
\(814\) −140.235 −0.172279
\(815\) 0 0
\(816\) 45.8078 35.0455i 0.0561370 0.0429479i
\(817\) −571.527 −0.699543
\(818\) 848.781i 1.03763i
\(819\) −39.5791 + 146.038i −0.0483261 + 0.178312i
\(820\) 0 0
\(821\) 1188.78i 1.44797i 0.689818 + 0.723983i \(0.257691\pi\)
−0.689818 + 0.723983i \(0.742309\pi\)
\(822\) 95.2470 + 124.497i 0.115872 + 0.151456i
\(823\) −1265.15 −1.53724 −0.768621 0.639704i \(-0.779057\pi\)
−0.768621 + 0.639704i \(0.779057\pi\)
\(824\) 462.585i 0.561390i
\(825\) 0 0
\(826\) −143.047 −0.173180
\(827\) 790.941i 0.956398i 0.878252 + 0.478199i \(0.158710\pi\)
−0.878252 + 0.478199i \(0.841290\pi\)
\(828\) 85.6393 + 23.2099i 0.103429 + 0.0280313i
\(829\) 99.1961 0.119658 0.0598288 0.998209i \(-0.480945\pi\)
0.0598288 + 0.998209i \(0.480945\pi\)
\(830\) 0 0
\(831\) 413.638 + 540.664i 0.497759 + 0.650619i
\(832\) −296.257 −0.356079
\(833\) 85.0141i 0.102058i
\(834\) 606.188 463.768i 0.726844 0.556076i
\(835\) 0 0
\(836\) 61.2746i 0.0732950i
\(837\) −981.851 + 401.765i −1.17306 + 0.480006i
\(838\) 15.0549 0.0179652
\(839\) 243.824i 0.290612i 0.989387 + 0.145306i \(0.0464167\pi\)
−0.989387 + 0.145306i \(0.953583\pi\)
\(840\) 0 0
\(841\) 539.170 0.641106
\(842\) 109.786i 0.130387i
\(843\) 561.093 429.267i 0.665591 0.509214i
\(844\) 92.9961 0.110185
\(845\) 0 0
\(846\) 123.012 453.885i 0.145404 0.536507i
\(847\) 302.055 0.356617
\(848\) 166.218i 0.196012i
\(849\) −671.974 878.334i −0.791489 1.03455i
\(850\) 0 0
\(851\) 176.569i 0.207484i
\(852\) 370.208 283.230i 0.434516 0.332429i
\(853\) 1122.06 1.31543 0.657713 0.753268i \(-0.271524\pi\)
0.657713 + 0.753268i \(0.271524\pi\)
\(854\) 70.8240i 0.0829321i
\(855\) 0 0
\(856\) 1012.63 1.18298
\(857\) 871.489i 1.01691i 0.861090 + 0.508453i \(0.169783\pi\)
−0.861090 + 0.508453i \(0.830217\pi\)
\(858\) 39.5791 + 51.7336i 0.0461295 + 0.0602956i
\(859\) −1674.92 −1.94985 −0.974925 0.222533i \(-0.928568\pi\)
−0.974925 + 0.222533i \(0.928568\pi\)
\(860\) 0 0
\(861\) 190.885 146.038i 0.221701 0.169614i
\(862\) −907.129 −1.05235
\(863\) 1320.74i 1.53041i 0.643787 + 0.765205i \(0.277362\pi\)
−0.643787 + 0.765205i \(0.722638\pi\)
\(864\) −315.195 770.288i −0.364810 0.891537i
\(865\) 0 0
\(866\) 152.713i 0.176343i
\(867\) 257.940 + 337.153i 0.297509 + 0.388873i
\(868\) 238.214 0.274441
\(869\) 165.340i 0.190264i
\(870\) 0 0
\(871\) 172.620 0.198186
\(872\) 1353.10i 1.55172i
\(873\) 45.1216 166.488i 0.0516856 0.190708i
\(874\) −57.5217 −0.0658142
\(875\) 0 0
\(876\) −253.925 331.905i −0.289869 0.378887i
\(877\) 344.790 0.393147 0.196573 0.980489i \(-0.437019\pi\)
0.196573 + 0.980489i \(0.437019\pi\)
\(878\) 690.242i 0.786152i
\(879\) −1266.69 + 969.087i −1.44106 + 1.10249i
\(880\) 0 0
\(881\) 518.737i 0.588805i 0.955682 + 0.294403i \(0.0951206\pi\)
−0.955682 + 0.294403i \(0.904879\pi\)
\(882\) −79.4797 21.5406i −0.0901131 0.0244224i
\(883\) 584.008 0.661391 0.330695 0.943738i \(-0.392717\pi\)
0.330695 + 0.943738i \(0.392717\pi\)
\(884\) 176.839i 0.200044i
\(885\) 0 0
\(886\) 355.859 0.401646
\(887\) 263.213i 0.296745i −0.988932 0.148373i \(-0.952597\pi\)
0.988932 0.148373i \(-0.0474035\pi\)
\(888\) 804.153 615.221i 0.905577 0.692817i
\(889\) 96.7895 0.108875
\(890\) 0 0
\(891\) −106.923 + 182.771i −0.120003 + 0.205130i
\(892\) −231.349 −0.259360
\(893\) 408.893i 0.457887i
\(894\) 485.314 + 634.351i 0.542857 + 0.709565i
\(895\) 0 0
\(896\) 164.988i 0.184138i
\(897\) 65.1373 49.8336i 0.0726168 0.0555559i
\(898\) 687.231 0.765291
\(899\) 682.621i 0.759312i
\(900\) 0 0
\(901\) 1275.23 1.41535
\(902\) 103.467i 0.114709i
\(903\) 269.476 + 352.230i 0.298423 + 0.390067i
\(904\) −1184.61 −1.31041
\(905\) 0 0
\(906\) −516.205 + 394.925i −0.569763 + 0.435900i
\(907\) 1501.72 1.65570 0.827849 0.560951i \(-0.189565\pi\)
0.827849 + 0.560951i \(0.189565\pi\)
\(908\) 896.618i 0.987464i
\(909\) 857.476 + 232.393i 0.943318 + 0.255658i
\(910\) 0 0
\(911\) 879.178i 0.965069i 0.875877 + 0.482534i \(0.160284\pi\)
−0.875877 + 0.482534i \(0.839716\pi\)
\(912\) 29.5163 + 38.5806i 0.0323644 + 0.0423033i
\(913\) −235.129 −0.257535
\(914\) 671.567i 0.734756i
\(915\) 0 0
\(916\) −15.6092 −0.0170406
\(917\) 89.1234i 0.0971901i
\(918\) 396.686 162.321i 0.432120 0.176820i
\(919\) 76.9882 0.0837739 0.0418869 0.999122i \(-0.486663\pi\)
0.0418869 + 0.999122i \(0.486663\pi\)
\(920\) 0 0
\(921\) −1034.96 1352.79i −1.12374 1.46883i
\(922\) −899.123 −0.975188
\(923\) 430.849i 0.466792i
\(924\) 37.7634 28.8911i 0.0408694 0.0312674i
\(925\) 0 0
\(926\) 1020.92i 1.10251i
\(927\) −132.429 + 488.631i −0.142857 + 0.527110i
\(928\) −535.535 −0.577085
\(929\) 1629.76i 1.75431i 0.480204 + 0.877157i \(0.340563\pi\)
−0.480204 + 0.877157i \(0.659437\pi\)
\(930\) 0 0
\(931\) −71.6013 −0.0769079
\(932\) 267.823i 0.287364i
\(933\) −101.867 + 77.9336i −0.109182 + 0.0835301i
\(934\) 213.517 0.228605
\(935\) 0 0
\(936\) −453.918 123.021i −0.484955 0.131432i
\(937\) 497.720 0.531185 0.265592 0.964085i \(-0.414432\pi\)
0.265592 + 0.964085i \(0.414432\pi\)
\(938\) 93.9468i 0.100157i
\(939\) 288.229 + 376.742i 0.306953 + 0.401217i
\(940\) 0 0
\(941\) 238.894i 0.253873i −0.991911 0.126936i \(-0.959486\pi\)
0.991911 0.126936i \(-0.0405144\pi\)
\(942\) −942.793 + 721.289i −1.00084 + 0.765700i
\(943\) −130.275 −0.138149
\(944\) 65.4794i 0.0693638i
\(945\) 0 0
\(946\) 190.923 0.201821
\(947\) 667.910i 0.705291i 0.935757 + 0.352645i \(0.114718\pi\)
−0.935757 + 0.352645i \(0.885282\pi\)
\(948\) −264.191 345.322i −0.278682 0.364264i
\(949\) −386.272 −0.407030
\(950\) 0 0
\(951\) −335.824 + 256.924i −0.353127 + 0.270162i
\(952\) −264.243 −0.277566
\(953\) 11.3247i 0.0118832i 0.999982 + 0.00594162i \(0.00189129\pi\)
−0.999982 + 0.00594162i \(0.998109\pi\)
\(954\) −323.114 + 1192.21i −0.338694 + 1.24970i
\(955\) 0 0
\(956\) 137.404i 0.143728i
\(957\) 82.7895 + 108.214i 0.0865094 + 0.113076i
\(958\) −915.174 −0.955296
\(959\) 105.764i 0.110285i
\(960\) 0 0
\(961\) 582.822 0.606475
\(962\) 340.866i 0.354331i
\(963\) 1069.64 + 289.895i 1.11074 + 0.301033i
\(964\) 308.787 0.320318
\(965\) 0 0
\(966\) 27.1216 + 35.4504i 0.0280761 + 0.0366982i
\(967\) −830.324 −0.858660 −0.429330 0.903148i \(-0.641250\pi\)
−0.429330 + 0.903148i \(0.641250\pi\)
\(968\) 938.855i 0.969891i
\(969\) 295.992 226.450i 0.305461 0.233695i
\(970\) 0 0
\(971\) 1217.58i 1.25394i −0.779044 0.626970i \(-0.784295\pi\)
0.779044 0.626970i \(-0.215705\pi\)
\(972\) −68.7286 552.577i −0.0707085 0.568495i
\(973\) −514.974 −0.529264
\(974\) 113.183i 0.116204i
\(975\) 0 0
\(976\) 32.4195 0.0332167
\(977\) 424.579i 0.434574i −0.976108 0.217287i \(-0.930279\pi\)
0.976108 0.217287i \(-0.0697207\pi\)
\(978\) −451.711 + 345.584i −0.461872 + 0.353358i
\(979\) 165.150 0.168693
\(980\) 0 0
\(981\) −387.365 + 1429.29i −0.394867 + 1.45697i
\(982\) 969.203 0.986968
\(983\) 76.7273i 0.0780542i −0.999238 0.0390271i \(-0.987574\pi\)
0.999238 0.0390271i \(-0.0124259\pi\)
\(984\) 453.918 + 593.313i 0.461298 + 0.602961i
\(985\) 0 0
\(986\) 275.792i 0.279708i
\(987\) −252.000 + 192.794i −0.255319 + 0.195333i
\(988\) −148.939 −0.150748
\(989\) 240.389i 0.243063i
\(990\) 0 0
\(991\) 181.271 0.182917 0.0914585 0.995809i \(-0.470847\pi\)
0.0914585 + 0.995809i \(0.470847\pi\)
\(992\) 1211.17i 1.22094i
\(993\) −470.974 615.608i −0.474294 0.619947i
\(994\) 234.486 0.235902
\(995\) 0 0
\(996\) 491.082 375.705i 0.493055 0.377214i
\(997\) 1184.43 1.18800 0.593998 0.804466i \(-0.297549\pi\)
0.593998 + 0.804466i \(0.297549\pi\)
\(998\) 496.453i 0.497448i
\(999\) 1025.56 419.649i 1.02658 0.420069i
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 525.3.c.a.176.3 4
3.2 odd 2 inner 525.3.c.a.176.2 4
5.2 odd 4 525.3.f.a.449.3 8
5.3 odd 4 525.3.f.a.449.6 8
5.4 even 2 21.3.b.a.8.2 4
15.2 even 4 525.3.f.a.449.5 8
15.8 even 4 525.3.f.a.449.4 8
15.14 odd 2 21.3.b.a.8.3 yes 4
20.19 odd 2 336.3.d.c.113.4 4
35.4 even 6 147.3.h.e.128.3 8
35.9 even 6 147.3.h.e.116.2 8
35.19 odd 6 147.3.h.c.116.2 8
35.24 odd 6 147.3.h.c.128.3 8
35.34 odd 2 147.3.b.f.50.2 4
40.19 odd 2 1344.3.d.b.449.1 4
40.29 even 2 1344.3.d.f.449.4 4
45.4 even 6 567.3.r.c.512.3 8
45.14 odd 6 567.3.r.c.512.2 8
45.29 odd 6 567.3.r.c.134.3 8
45.34 even 6 567.3.r.c.134.2 8
60.59 even 2 336.3.d.c.113.3 4
105.44 odd 6 147.3.h.e.116.3 8
105.59 even 6 147.3.h.c.128.2 8
105.74 odd 6 147.3.h.e.128.2 8
105.89 even 6 147.3.h.c.116.3 8
105.104 even 2 147.3.b.f.50.3 4
120.29 odd 2 1344.3.d.f.449.3 4
120.59 even 2 1344.3.d.b.449.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.3.b.a.8.2 4 5.4 even 2
21.3.b.a.8.3 yes 4 15.14 odd 2
147.3.b.f.50.2 4 35.34 odd 2
147.3.b.f.50.3 4 105.104 even 2
147.3.h.c.116.2 8 35.19 odd 6
147.3.h.c.116.3 8 105.89 even 6
147.3.h.c.128.2 8 105.59 even 6
147.3.h.c.128.3 8 35.24 odd 6
147.3.h.e.116.2 8 35.9 even 6
147.3.h.e.116.3 8 105.44 odd 6
147.3.h.e.128.2 8 105.74 odd 6
147.3.h.e.128.3 8 35.4 even 6
336.3.d.c.113.3 4 60.59 even 2
336.3.d.c.113.4 4 20.19 odd 2
525.3.c.a.176.2 4 3.2 odd 2 inner
525.3.c.a.176.3 4 1.1 even 1 trivial
525.3.f.a.449.3 8 5.2 odd 4
525.3.f.a.449.4 8 15.8 even 4
525.3.f.a.449.5 8 15.2 even 4
525.3.f.a.449.6 8 5.3 odd 4
567.3.r.c.134.2 8 45.34 even 6
567.3.r.c.134.3 8 45.29 odd 6
567.3.r.c.512.2 8 45.14 odd 6
567.3.r.c.512.3 8 45.4 even 6
1344.3.d.b.449.1 4 40.19 odd 2
1344.3.d.b.449.2 4 120.59 even 2
1344.3.d.f.449.3 4 120.29 odd 2
1344.3.d.f.449.4 4 40.29 even 2