Properties

Label 1368.2.e.e.379.7
Level $1368$
Weight $2$
Character 1368.379
Analytic conductor $10.924$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1368,2,Mod(379,1368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1368.379");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1368.e (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: \(10.9235349965\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.319794774016000000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2x^{10} + 2x^{8} + 8x^{4} - 32x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 152)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 379.7
Root \(-0.491416 + 1.32609i\) of defining polynomial
Character \(\chi\) \(=\) 1368.379
Dual form 1368.2.e.e.379.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.491416 - 1.32609i) q^{2} +(-1.51702 - 1.30332i) q^{4} +2.08884i q^{5} -2.23607i q^{7} +(-2.47381 + 1.37123i) q^{8} +O(q^{10})\) \(q+(0.491416 - 1.32609i) q^{2} +(-1.51702 - 1.30332i) q^{4} +2.08884i q^{5} -2.23607i q^{7} +(-2.47381 + 1.37123i) q^{8} +(2.76999 + 1.02649i) q^{10} +0.602705 q^{11} -1.29574 q^{13} +(-2.96522 - 1.09884i) q^{14} +(0.602705 + 3.95433i) q^{16} -2.20541 q^{17} +(-2.60270 - 3.49656i) q^{19} +(2.72243 - 3.16881i) q^{20} +(0.296179 - 0.799240i) q^{22} -6.19040i q^{23} +0.636747 q^{25} +(-0.636747 + 1.71826i) q^{26} +(-2.91432 + 3.39216i) q^{28} -8.20902 q^{29} -4.94762 q^{31} +(5.53997 + 1.14398i) q^{32} +(-1.08377 + 2.92457i) q^{34} +4.67079 q^{35} -6.91328 q^{37} +(-5.91576 + 1.73315i) q^{38} +(-2.86428 - 5.16739i) q^{40} -6.53862i q^{41} -0.191885 q^{43} +(-0.914316 - 0.785518i) q^{44} +(-8.20902 - 3.04206i) q^{46} -0.223348i q^{47} +2.00000 q^{49} +(0.312907 - 0.844383i) q^{50} +(1.96566 + 1.68877i) q^{52} -4.83659 q^{53} +1.25895i q^{55} +(3.06617 + 5.53160i) q^{56} +(-4.03404 + 10.8859i) q^{58} -5.60395i q^{59} +11.7743i q^{61} +(-2.43134 + 6.56098i) q^{62} +(4.23945 - 6.78432i) q^{64} -2.70659i q^{65} +6.23902i q^{67} +(3.34565 + 2.87436i) q^{68} +(2.29530 - 6.19388i) q^{70} -12.4867 q^{71} -8.27349 q^{73} +(-3.39730 + 9.16762i) q^{74} +(-0.608784 + 8.69652i) q^{76} -1.34769i q^{77} +15.4017 q^{79} +(-8.25997 + 1.25895i) q^{80} +(-8.67079 - 3.21318i) q^{82} -2.00000 q^{83} -4.60675i q^{85} +(-0.0942954 + 0.254457i) q^{86} +(-1.49098 + 0.826448i) q^{88} -7.44762i q^{89} +2.89736i q^{91} +(-8.06808 + 9.39097i) q^{92} +(-0.296179 - 0.109757i) q^{94} +(7.30375 - 5.43663i) q^{95} -17.6018i q^{97} +(0.982832 - 2.65218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{4} - 12 q^{17} - 24 q^{19} - 4 q^{20} - 44 q^{25} + 44 q^{26} - 20 q^{28} - 40 q^{35} - 4 q^{38} - 24 q^{43} + 4 q^{44} + 24 q^{49} - 4 q^{58} + 8 q^{62} - 8 q^{64} - 12 q^{68} + 4 q^{73} - 48 q^{74} - 12 q^{76} - 32 q^{80} - 8 q^{82} - 24 q^{83} - 8 q^{92}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).

\(n\) \(343\) \(685\) \(1009\) \(1217\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.491416 1.32609i 0.347483 0.937686i
\(3\) 0 0
\(4\) −1.51702 1.30332i −0.758510 0.651661i
\(5\) 2.08884i 0.934158i 0.884216 + 0.467079i \(0.154694\pi\)
−0.884216 + 0.467079i \(0.845306\pi\)
\(6\) 0 0
\(7\) 2.23607i 0.845154i −0.906327 0.422577i \(-0.861126\pi\)
0.906327 0.422577i \(-0.138874\pi\)
\(8\) −2.47381 + 1.37123i −0.874623 + 0.484803i
\(9\) 0 0
\(10\) 2.76999 + 1.02649i 0.875947 + 0.324604i
\(11\) 0.602705 0.181722 0.0908612 0.995864i \(-0.471038\pi\)
0.0908612 + 0.995864i \(0.471038\pi\)
\(12\) 0 0
\(13\) −1.29574 −0.359373 −0.179687 0.983724i \(-0.557508\pi\)
−0.179687 + 0.983724i \(0.557508\pi\)
\(14\) −2.96522 1.09884i −0.792489 0.293677i
\(15\) 0 0
\(16\) 0.602705 + 3.95433i 0.150676 + 0.988583i
\(17\) −2.20541 −0.534890 −0.267445 0.963573i \(-0.586179\pi\)
−0.267445 + 0.963573i \(0.586179\pi\)
\(18\) 0 0
\(19\) −2.60270 3.49656i −0.597101 0.802166i
\(20\) 2.72243 3.16881i 0.608754 0.708568i
\(21\) 0 0
\(22\) 0.296179 0.799240i 0.0631455 0.170399i
\(23\) 6.19040i 1.29079i −0.763850 0.645394i \(-0.776693\pi\)
0.763850 0.645394i \(-0.223307\pi\)
\(24\) 0 0
\(25\) 0.636747 0.127349
\(26\) −0.636747 + 1.71826i −0.124876 + 0.336979i
\(27\) 0 0
\(28\) −2.91432 + 3.39216i −0.550754 + 0.641058i
\(29\) −8.20902 −1.52438 −0.762188 0.647355i \(-0.775875\pi\)
−0.762188 + 0.647355i \(0.775875\pi\)
\(30\) 0 0
\(31\) −4.94762 −0.888618 −0.444309 0.895874i \(-0.646551\pi\)
−0.444309 + 0.895874i \(0.646551\pi\)
\(32\) 5.53997 + 1.14398i 0.979338 + 0.202229i
\(33\) 0 0
\(34\) −1.08377 + 2.92457i −0.185866 + 0.501559i
\(35\) 4.67079 0.789507
\(36\) 0 0
\(37\) −6.91328 −1.13654 −0.568268 0.822843i \(-0.692386\pi\)
−0.568268 + 0.822843i \(0.692386\pi\)
\(38\) −5.91576 + 1.73315i −0.959663 + 0.281154i
\(39\) 0 0
\(40\) −2.86428 5.16739i −0.452883 0.817036i
\(41\) 6.53862i 1.02116i −0.859830 0.510580i \(-0.829431\pi\)
0.859830 0.510580i \(-0.170569\pi\)
\(42\) 0 0
\(43\) −0.191885 −0.0292622 −0.0146311 0.999893i \(-0.504657\pi\)
−0.0146311 + 0.999893i \(0.504657\pi\)
\(44\) −0.914316 0.785518i −0.137838 0.118421i
\(45\) 0 0
\(46\) −8.20902 3.04206i −1.21035 0.448527i
\(47\) 0.223348i 0.0325786i −0.999867 0.0162893i \(-0.994815\pi\)
0.999867 0.0162893i \(-0.00518528\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) 0.312907 0.844383i 0.0442518 0.119414i
\(51\) 0 0
\(52\) 1.96566 + 1.68877i 0.272588 + 0.234190i
\(53\) −4.83659 −0.664357 −0.332178 0.943217i \(-0.607784\pi\)
−0.332178 + 0.943217i \(0.607784\pi\)
\(54\) 0 0
\(55\) 1.25895i 0.169757i
\(56\) 3.06617 + 5.53160i 0.409734 + 0.739192i
\(57\) 0 0
\(58\) −4.03404 + 10.8859i −0.529696 + 1.42939i
\(59\) 5.60395i 0.729573i −0.931091 0.364786i \(-0.881142\pi\)
0.931091 0.364786i \(-0.118858\pi\)
\(60\) 0 0
\(61\) 11.7743i 1.50754i 0.657138 + 0.753770i \(0.271767\pi\)
−0.657138 + 0.753770i \(0.728233\pi\)
\(62\) −2.43134 + 6.56098i −0.308780 + 0.833245i
\(63\) 0 0
\(64\) 4.23945 6.78432i 0.529931 0.848040i
\(65\) 2.70659i 0.335711i
\(66\) 0 0
\(67\) 6.23902i 0.762218i 0.924530 + 0.381109i \(0.124458\pi\)
−0.924530 + 0.381109i \(0.875542\pi\)
\(68\) 3.34565 + 2.87436i 0.405720 + 0.348567i
\(69\) 0 0
\(70\) 2.29530 6.19388i 0.274341 0.740310i
\(71\) −12.4867 −1.48190 −0.740950 0.671560i \(-0.765624\pi\)
−0.740950 + 0.671560i \(0.765624\pi\)
\(72\) 0 0
\(73\) −8.27349 −0.968339 −0.484170 0.874974i \(-0.660878\pi\)
−0.484170 + 0.874974i \(0.660878\pi\)
\(74\) −3.39730 + 9.16762i −0.394928 + 1.06571i
\(75\) 0 0
\(76\) −0.608784 + 8.69652i −0.0698323 + 0.997559i
\(77\) 1.34769i 0.153583i
\(78\) 0 0
\(79\) 15.4017 1.73283 0.866416 0.499323i \(-0.166418\pi\)
0.866416 + 0.499323i \(0.166418\pi\)
\(80\) −8.25997 + 1.25895i −0.923493 + 0.140755i
\(81\) 0 0
\(82\) −8.67079 3.21318i −0.957528 0.354837i
\(83\) −2.00000 −0.219529 −0.109764 0.993958i \(-0.535010\pi\)
−0.109764 + 0.993958i \(0.535010\pi\)
\(84\) 0 0
\(85\) 4.60675i 0.499672i
\(86\) −0.0942954 + 0.254457i −0.0101681 + 0.0274388i
\(87\) 0 0
\(88\) −1.49098 + 0.826448i −0.158939 + 0.0880996i
\(89\) 7.44762i 0.789446i −0.918800 0.394723i \(-0.870841\pi\)
0.918800 0.394723i \(-0.129159\pi\)
\(90\) 0 0
\(91\) 2.89736i 0.303726i
\(92\) −8.06808 + 9.39097i −0.841156 + 0.979076i
\(93\) 0 0
\(94\) −0.296179 0.109757i −0.0305485 0.0113205i
\(95\) 7.30375 5.43663i 0.749349 0.557787i
\(96\) 0 0
\(97\) 17.6018i 1.78719i −0.448870 0.893597i \(-0.648173\pi\)
0.448870 0.893597i \(-0.351827\pi\)
\(98\) 0.982832 2.65218i 0.0992810 0.267910i
\(99\) 0 0
\(100\) −0.965958 0.829886i −0.0965958 0.0829886i
\(101\) 3.73098i 0.371247i 0.982621 + 0.185623i \(0.0594305\pi\)
−0.982621 + 0.185623i \(0.940570\pi\)
\(102\) 0 0
\(103\) −16.4180 −1.61772 −0.808859 0.588003i \(-0.799914\pi\)
−0.808859 + 0.588003i \(0.799914\pi\)
\(104\) 3.20541 1.77676i 0.314316 0.174225i
\(105\) 0 0
\(106\) −2.37678 + 6.41375i −0.230853 + 0.622958i
\(107\) 6.51295i 0.629631i −0.949153 0.314815i \(-0.898057\pi\)
0.949153 0.314815i \(-0.101943\pi\)
\(108\) 0 0
\(109\) −4.83659 −0.463261 −0.231631 0.972804i \(-0.574406\pi\)
−0.231631 + 0.972804i \(0.574406\pi\)
\(110\) 1.66948 + 0.618670i 0.159179 + 0.0589879i
\(111\) 0 0
\(112\) 8.84216 1.34769i 0.835505 0.127345i
\(113\) 14.1309i 1.32933i 0.747143 + 0.664663i \(0.231425\pi\)
−0.747143 + 0.664663i \(0.768575\pi\)
\(114\) 0 0
\(115\) 12.9308 1.20580
\(116\) 12.4533 + 10.6990i 1.15626 + 0.993376i
\(117\) 0 0
\(118\) −7.43134 2.75387i −0.684110 0.253514i
\(119\) 4.93145i 0.452065i
\(120\) 0 0
\(121\) −10.6367 −0.966977
\(122\) 15.6137 + 5.78606i 1.41360 + 0.523845i
\(123\) 0 0
\(124\) 7.50564 + 6.44834i 0.674026 + 0.579078i
\(125\) 11.7743i 1.05312i
\(126\) 0 0
\(127\) 4.16667 0.369732 0.184866 0.982764i \(-0.440815\pi\)
0.184866 + 0.982764i \(0.440815\pi\)
\(128\) −6.91328 8.95581i −0.611053 0.791589i
\(129\) 0 0
\(130\) −3.58918 1.33006i −0.314792 0.116654i
\(131\) 10.2600 0.896418 0.448209 0.893929i \(-0.352062\pi\)
0.448209 + 0.893929i \(0.352062\pi\)
\(132\) 0 0
\(133\) −7.81854 + 5.81983i −0.677954 + 0.504643i
\(134\) 8.27349 + 3.06595i 0.714721 + 0.264858i
\(135\) 0 0
\(136\) 5.45576 3.02413i 0.467828 0.259317i
\(137\) 17.1362 1.46404 0.732021 0.681282i \(-0.238577\pi\)
0.732021 + 0.681282i \(0.238577\pi\)
\(138\) 0 0
\(139\) 20.7389 1.75905 0.879524 0.475854i \(-0.157861\pi\)
0.879524 + 0.475854i \(0.157861\pi\)
\(140\) −7.08568 6.08754i −0.598850 0.514491i
\(141\) 0 0
\(142\) −6.13617 + 16.5585i −0.514936 + 1.38956i
\(143\) −0.780948 −0.0653062
\(144\) 0 0
\(145\) 17.1473i 1.42401i
\(146\) −4.06573 + 10.9714i −0.336482 + 0.907998i
\(147\) 0 0
\(148\) 10.4876 + 9.01023i 0.862075 + 0.740636i
\(149\) 12.5154i 1.02530i −0.858597 0.512651i \(-0.828663\pi\)
0.858597 0.512651i \(-0.171337\pi\)
\(150\) 0 0
\(151\) 3.93133 0.319927 0.159963 0.987123i \(-0.448862\pi\)
0.159963 + 0.987123i \(0.448862\pi\)
\(152\) 11.2332 + 5.08091i 0.911131 + 0.412116i
\(153\) 0 0
\(154\) −1.78716 0.662276i −0.144013 0.0533677i
\(155\) 10.3348i 0.830109i
\(156\) 0 0
\(157\) 1.77676i 0.141801i −0.997483 0.0709003i \(-0.977413\pi\)
0.997483 0.0709003i \(-0.0225872\pi\)
\(158\) 7.56866 20.4241i 0.602131 1.62485i
\(159\) 0 0
\(160\) −2.38960 + 11.5721i −0.188914 + 0.914856i
\(161\) −13.8422 −1.09091
\(162\) 0 0
\(163\) 9.68431 0.758534 0.379267 0.925287i \(-0.376176\pi\)
0.379267 + 0.925287i \(0.376176\pi\)
\(164\) −8.52193 + 9.91922i −0.665451 + 0.774561i
\(165\) 0 0
\(166\) −0.982832 + 2.65218i −0.0762825 + 0.205849i
\(167\) 2.35614 0.182323 0.0911617 0.995836i \(-0.470942\pi\)
0.0911617 + 0.995836i \(0.470942\pi\)
\(168\) 0 0
\(169\) −11.3211 −0.870851
\(170\) −6.10896 2.26383i −0.468536 0.173628i
\(171\) 0 0
\(172\) 0.291094 + 0.250088i 0.0221957 + 0.0190690i
\(173\) 16.9769 1.29073 0.645366 0.763873i \(-0.276705\pi\)
0.645366 + 0.763873i \(0.276705\pi\)
\(174\) 0 0
\(175\) 1.42381i 0.107630i
\(176\) 0.363253 + 2.38330i 0.0273812 + 0.179648i
\(177\) 0 0
\(178\) −9.87620 3.65988i −0.740252 0.274319i
\(179\) 13.9504i 1.04270i 0.853343 + 0.521350i \(0.174571\pi\)
−0.853343 + 0.521350i \(0.825429\pi\)
\(180\) 0 0
\(181\) 9.89523 0.735507 0.367753 0.929923i \(-0.380127\pi\)
0.367753 + 0.929923i \(0.380127\pi\)
\(182\) 3.84216 + 1.42381i 0.284800 + 0.105540i
\(183\) 0 0
\(184\) 8.48847 + 15.3139i 0.625778 + 1.12895i
\(185\) 14.4407i 1.06170i
\(186\) 0 0
\(187\) −1.32921 −0.0972016
\(188\) −0.291094 + 0.338823i −0.0212302 + 0.0247112i
\(189\) 0 0
\(190\) −3.62028 12.3571i −0.262643 0.896476i
\(191\) 16.8403i 1.21852i 0.792969 + 0.609261i \(0.208534\pi\)
−0.792969 + 0.609261i \(0.791466\pi\)
\(192\) 0 0
\(193\) 13.1706i 0.948040i −0.880514 0.474020i \(-0.842802\pi\)
0.880514 0.474020i \(-0.157198\pi\)
\(194\) −23.3416 8.64982i −1.67583 0.621021i
\(195\) 0 0
\(196\) −3.03404 2.60664i −0.216717 0.186189i
\(197\) 22.8074i 1.62496i −0.582990 0.812479i \(-0.698117\pi\)
0.582990 0.812479i \(-0.301883\pi\)
\(198\) 0 0
\(199\) 15.0636i 1.06783i −0.845539 0.533914i \(-0.820721\pi\)
0.845539 0.533914i \(-0.179279\pi\)
\(200\) −1.57519 + 0.873127i −0.111383 + 0.0617394i
\(201\) 0 0
\(202\) 4.94762 + 1.83347i 0.348113 + 0.129002i
\(203\) 18.3559i 1.28833i
\(204\) 0 0
\(205\) 13.6581 0.953925
\(206\) −8.06808 + 21.7718i −0.562130 + 1.51691i
\(207\) 0 0
\(208\) −0.780948 5.12378i −0.0541490 0.355270i
\(209\) −1.56866 2.10739i −0.108507 0.145771i
\(210\) 0 0
\(211\) 10.1285i 0.697277i 0.937257 + 0.348639i \(0.113356\pi\)
−0.937257 + 0.348639i \(0.886644\pi\)
\(212\) 7.33721 + 6.30364i 0.503922 + 0.432935i
\(213\) 0 0
\(214\) −8.63675 3.20057i −0.590396 0.218786i
\(215\) 0.400818i 0.0273355i
\(216\) 0 0
\(217\) 11.0632i 0.751019i
\(218\) −2.37678 + 6.41375i −0.160976 + 0.434394i
\(219\) 0 0
\(220\) 1.64082 1.90986i 0.110624 0.128763i
\(221\) 2.85764 0.192225
\(222\) 0 0
\(223\) −7.53909 −0.504855 −0.252428 0.967616i \(-0.581229\pi\)
−0.252428 + 0.967616i \(0.581229\pi\)
\(224\) 2.55802 12.3878i 0.170915 0.827692i
\(225\) 0 0
\(226\) 18.7389 + 6.94417i 1.24649 + 0.461919i
\(227\) 16.2127i 1.07607i −0.842922 0.538036i \(-0.819166\pi\)
0.842922 0.538036i \(-0.180834\pi\)
\(228\) 0 0
\(229\) 24.4495i 1.61567i −0.589409 0.807835i \(-0.700639\pi\)
0.589409 0.807835i \(-0.299361\pi\)
\(230\) 6.35438 17.1473i 0.418995 1.13066i
\(231\) 0 0
\(232\) 20.3075 11.2565i 1.33326 0.739023i
\(233\) 0.774073 0.0507112 0.0253556 0.999678i \(-0.491928\pi\)
0.0253556 + 0.999678i \(0.491928\pi\)
\(234\) 0 0
\(235\) 0.466538 0.0304336
\(236\) −7.30375 + 8.50131i −0.475434 + 0.553388i
\(237\) 0 0
\(238\) 6.53953 + 2.42339i 0.423895 + 0.157085i
\(239\) 1.20046i 0.0776514i −0.999246 0.0388257i \(-0.987638\pi\)
0.999246 0.0388257i \(-0.0123617\pi\)
\(240\) 0 0
\(241\) 16.7862i 1.08129i 0.841250 + 0.540647i \(0.181820\pi\)
−0.841250 + 0.540647i \(0.818180\pi\)
\(242\) −5.22707 + 14.1053i −0.336009 + 0.906721i
\(243\) 0 0
\(244\) 15.3457 17.8618i 0.982405 1.14348i
\(245\) 4.17768i 0.266902i
\(246\) 0 0
\(247\) 3.37243 + 4.53063i 0.214582 + 0.288277i
\(248\) 12.2395 6.78432i 0.777206 0.430805i
\(249\) 0 0
\(250\) 15.6137 + 5.78606i 0.987498 + 0.365943i
\(251\) 23.2178 1.46549 0.732747 0.680502i \(-0.238238\pi\)
0.732747 + 0.680502i \(0.238238\pi\)
\(252\) 0 0
\(253\) 3.73098i 0.234565i
\(254\) 2.04757 5.52537i 0.128476 0.346693i
\(255\) 0 0
\(256\) −15.2735 + 4.76659i −0.954593 + 0.297912i
\(257\) 3.97673i 0.248062i 0.992278 + 0.124031i \(0.0395821\pi\)
−0.992278 + 0.124031i \(0.960418\pi\)
\(258\) 0 0
\(259\) 15.4586i 0.960548i
\(260\) −3.52756 + 4.10596i −0.218770 + 0.254641i
\(261\) 0 0
\(262\) 5.04191 13.6056i 0.311490 0.840558i
\(263\) 14.3809i 0.886765i −0.896333 0.443382i \(-0.853778\pi\)
0.896333 0.443382i \(-0.146222\pi\)
\(264\) 0 0
\(265\) 10.1029i 0.620614i
\(266\) 3.87545 + 13.2280i 0.237619 + 0.811063i
\(267\) 0 0
\(268\) 8.13145 9.46473i 0.496707 0.578150i
\(269\) −9.28271 −0.565977 −0.282988 0.959123i \(-0.591326\pi\)
−0.282988 + 0.959123i \(0.591326\pi\)
\(270\) 0 0
\(271\) 10.8148i 0.656951i 0.944513 + 0.328475i \(0.106535\pi\)
−0.944513 + 0.328475i \(0.893465\pi\)
\(272\) −1.32921 8.72092i −0.0805953 0.528784i
\(273\) 0 0
\(274\) 8.42098 22.7241i 0.508730 1.37281i
\(275\) 0.383770 0.0231422
\(276\) 0 0
\(277\) 14.0229i 0.842557i 0.906931 + 0.421279i \(0.138419\pi\)
−0.906931 + 0.421279i \(0.861581\pi\)
\(278\) 10.1914 27.5016i 0.611240 1.64944i
\(279\) 0 0
\(280\) −11.5546 + 6.40473i −0.690521 + 0.382756i
\(281\) 30.6277i 1.82710i −0.406730 0.913548i \(-0.633331\pi\)
0.406730 0.913548i \(-0.366669\pi\)
\(282\) 0 0
\(283\) −9.49243 −0.564266 −0.282133 0.959375i \(-0.591042\pi\)
−0.282133 + 0.959375i \(0.591042\pi\)
\(284\) 18.9426 + 16.2742i 1.12404 + 0.965696i
\(285\) 0 0
\(286\) −0.383770 + 1.03561i −0.0226928 + 0.0612367i
\(287\) −14.6208 −0.863039
\(288\) 0 0
\(289\) −12.1362 −0.713892
\(290\) −22.7389 8.42647i −1.33527 0.494819i
\(291\) 0 0
\(292\) 12.5511 + 10.7830i 0.734495 + 0.631029i
\(293\) −9.93934 −0.580663 −0.290331 0.956926i \(-0.593765\pi\)
−0.290331 + 0.956926i \(0.593765\pi\)
\(294\) 0 0
\(295\) 11.7058 0.681536
\(296\) 17.1021 9.47970i 0.994041 0.550996i
\(297\) 0 0
\(298\) −16.5965 6.15027i −0.961412 0.356276i
\(299\) 8.02114i 0.463875i
\(300\) 0 0
\(301\) 0.429068i 0.0247311i
\(302\) 1.93192 5.21329i 0.111169 0.299991i
\(303\) 0 0
\(304\) 12.2579 12.3994i 0.703039 0.711152i
\(305\) −24.5946 −1.40828
\(306\) 0 0
\(307\) 16.9668i 0.968344i 0.874973 + 0.484172i \(0.160879\pi\)
−0.874973 + 0.484172i \(0.839121\pi\)
\(308\) −1.75647 + 2.04447i −0.100084 + 0.116495i
\(309\) 0 0
\(310\) −13.7048 5.07867i −0.778382 0.288449i
\(311\) 34.3174i 1.94596i −0.230884 0.972981i \(-0.574162\pi\)
0.230884 0.972981i \(-0.425838\pi\)
\(312\) 0 0
\(313\) 13.5675 0.766881 0.383440 0.923566i \(-0.374739\pi\)
0.383440 + 0.923566i \(0.374739\pi\)
\(314\) −2.35614 0.873127i −0.132965 0.0492734i
\(315\) 0 0
\(316\) −23.3648 20.0734i −1.31437 1.12922i
\(317\) −2.07669 −0.116638 −0.0583192 0.998298i \(-0.518574\pi\)
−0.0583192 + 0.998298i \(0.518574\pi\)
\(318\) 0 0
\(319\) −4.94762 −0.277013
\(320\) 14.1714 + 8.85554i 0.792204 + 0.495040i
\(321\) 0 0
\(322\) −6.80226 + 18.3559i −0.379075 + 1.02294i
\(323\) 5.74003 + 7.71135i 0.319384 + 0.429071i
\(324\) 0 0
\(325\) −0.825058 −0.0457660
\(326\) 4.75903 12.8423i 0.263578 0.711267i
\(327\) 0 0
\(328\) 8.96596 + 16.1753i 0.495062 + 0.893131i
\(329\) −0.499421 −0.0275339
\(330\) 0 0
\(331\) 20.1739i 1.10886i −0.832231 0.554429i \(-0.812937\pi\)
0.832231 0.554429i \(-0.187063\pi\)
\(332\) 3.03404 + 2.60664i 0.166515 + 0.143058i
\(333\) 0 0
\(334\) 1.15784 3.12445i 0.0633544 0.170962i
\(335\) −13.0323 −0.712032
\(336\) 0 0
\(337\) 1.79760i 0.0979213i 0.998801 + 0.0489606i \(0.0155909\pi\)
−0.998801 + 0.0489606i \(0.984409\pi\)
\(338\) −5.56335 + 15.0127i −0.302606 + 0.816585i
\(339\) 0 0
\(340\) −6.00408 + 6.98853i −0.325617 + 0.379006i
\(341\) −2.98195 −0.161482
\(342\) 0 0
\(343\) 20.1246i 1.08663i
\(344\) 0.474687 0.263119i 0.0255934 0.0141864i
\(345\) 0 0
\(346\) 8.34274 22.5129i 0.448508 1.21030i
\(347\) 21.9853 1.18023 0.590117 0.807318i \(-0.299082\pi\)
0.590117 + 0.807318i \(0.299082\pi\)
\(348\) 0 0
\(349\) 6.85543i 0.366963i −0.983023 0.183481i \(-0.941263\pi\)
0.983023 0.183481i \(-0.0587367\pi\)
\(350\) −1.88810 0.699682i −0.100923 0.0373996i
\(351\) 0 0
\(352\) 3.33897 + 0.689483i 0.177968 + 0.0367496i
\(353\) −12.2940 −0.654344 −0.327172 0.944965i \(-0.606096\pi\)
−0.327172 + 0.944965i \(0.606096\pi\)
\(354\) 0 0
\(355\) 26.0827i 1.38433i
\(356\) −9.70664 + 11.2982i −0.514451 + 0.598803i
\(357\) 0 0
\(358\) 18.4994 + 6.85543i 0.977725 + 0.362321i
\(359\) 14.7691i 0.779484i 0.920924 + 0.389742i \(0.127436\pi\)
−0.920924 + 0.389742i \(0.872564\pi\)
\(360\) 0 0
\(361\) −5.45185 + 18.2010i −0.286940 + 0.957949i
\(362\) 4.86267 13.1220i 0.255576 0.689674i
\(363\) 0 0
\(364\) 3.77619 4.39536i 0.197926 0.230379i
\(365\) 17.2820i 0.904582i
\(366\) 0 0
\(367\) 21.9240i 1.14442i −0.820106 0.572212i \(-0.806085\pi\)
0.820106 0.572212i \(-0.193915\pi\)
\(368\) 24.4789 3.73098i 1.27605 0.194491i
\(369\) 0 0
\(370\) −19.1497 7.09641i −0.995545 0.368925i
\(371\) 10.8149i 0.561484i
\(372\) 0 0
\(373\) −34.6907 −1.79622 −0.898109 0.439774i \(-0.855059\pi\)
−0.898109 + 0.439774i \(0.855059\pi\)
\(374\) −0.653196 + 1.76265i −0.0337759 + 0.0911446i
\(375\) 0 0
\(376\) 0.306261 + 0.552519i 0.0157942 + 0.0284940i
\(377\) 10.6367 0.547820
\(378\) 0 0
\(379\) 33.2666i 1.70879i 0.519622 + 0.854396i \(0.326073\pi\)
−0.519622 + 0.854396i \(0.673927\pi\)
\(380\) −18.1656 1.27165i −0.931877 0.0652344i
\(381\) 0 0
\(382\) 22.3318 + 8.27560i 1.14259 + 0.423417i
\(383\) 33.6303 1.71843 0.859214 0.511616i \(-0.170953\pi\)
0.859214 + 0.511616i \(0.170953\pi\)
\(384\) 0 0
\(385\) 2.81511 0.143471
\(386\) −17.4654 6.47224i −0.888964 0.329428i
\(387\) 0 0
\(388\) −22.9408 + 26.7023i −1.16464 + 1.35561i
\(389\) 18.2006i 0.922808i 0.887190 + 0.461404i \(0.152654\pi\)
−0.887190 + 0.461404i \(0.847346\pi\)
\(390\) 0 0
\(391\) 13.6524i 0.690430i
\(392\) −4.94762 + 2.74246i −0.249892 + 0.138515i
\(393\) 0 0
\(394\) −30.2446 11.2079i −1.52370 0.564646i
\(395\) 32.1718i 1.61874i
\(396\) 0 0
\(397\) 11.1854i 0.561377i 0.959799 + 0.280688i \(0.0905627\pi\)
−0.959799 + 0.280688i \(0.909437\pi\)
\(398\) −19.9756 7.40247i −1.00129 0.371053i
\(399\) 0 0
\(400\) 0.383770 + 2.51791i 0.0191885 + 0.125895i
\(401\) 22.8703i 1.14209i 0.820919 + 0.571044i \(0.193462\pi\)
−0.820919 + 0.571044i \(0.806538\pi\)
\(402\) 0 0
\(403\) 6.41082 0.319346
\(404\) 4.86267 5.65998i 0.241927 0.281595i
\(405\) 0 0
\(406\) 24.3416 + 9.02039i 1.20805 + 0.447675i
\(407\) −4.16667 −0.206534
\(408\) 0 0
\(409\) 1.65290i 0.0817304i −0.999165 0.0408652i \(-0.986989\pi\)
0.999165 0.0408652i \(-0.0130114\pi\)
\(410\) 6.71182 18.1119i 0.331473 0.894483i
\(411\) 0 0
\(412\) 24.9065 + 21.3980i 1.22706 + 1.05420i
\(413\) −12.5308 −0.616601
\(414\) 0 0
\(415\) 4.17768i 0.205074i
\(416\) −7.17836 1.48230i −0.351948 0.0726758i
\(417\) 0 0
\(418\) −3.56546 + 1.04458i −0.174392 + 0.0510920i
\(419\) −23.8615 −1.16571 −0.582856 0.812576i \(-0.698065\pi\)
−0.582856 + 0.812576i \(0.698065\pi\)
\(420\) 0 0
\(421\) −6.17644 −0.301021 −0.150511 0.988608i \(-0.548092\pi\)
−0.150511 + 0.988608i \(0.548092\pi\)
\(422\) 13.4313 + 4.97732i 0.653827 + 0.242292i
\(423\) 0 0
\(424\) 11.9648 6.63208i 0.581062 0.322082i
\(425\) −1.40429 −0.0681180
\(426\) 0 0
\(427\) 26.3281 1.27410
\(428\) −8.48847 + 9.88028i −0.410306 + 0.477581i
\(429\) 0 0
\(430\) −0.531519 0.196968i −0.0256321 0.00949864i
\(431\) 20.9083 1.00712 0.503558 0.863962i \(-0.332024\pi\)
0.503558 + 0.863962i \(0.332024\pi\)
\(432\) 0 0
\(433\) 1.41484i 0.0679927i 0.999422 + 0.0339964i \(0.0108235\pi\)
−0.999422 + 0.0339964i \(0.989177\pi\)
\(434\) 14.6708 + 5.43663i 0.704220 + 0.260967i
\(435\) 0 0
\(436\) 7.33721 + 6.30364i 0.351389 + 0.301889i
\(437\) −21.6451 + 16.1118i −1.03543 + 0.770731i
\(438\) 0 0
\(439\) 13.5912 0.648673 0.324337 0.945942i \(-0.394859\pi\)
0.324337 + 0.945942i \(0.394859\pi\)
\(440\) −1.72632 3.11441i −0.0822989 0.148474i
\(441\) 0 0
\(442\) 1.40429 3.78948i 0.0667951 0.180247i
\(443\) −19.1907 −0.911779 −0.455889 0.890036i \(-0.650679\pi\)
−0.455889 + 0.890036i \(0.650679\pi\)
\(444\) 0 0
\(445\) 15.5569 0.737467
\(446\) −3.70483 + 9.99751i −0.175429 + 0.473396i
\(447\) 0 0
\(448\) −15.1702 9.47970i −0.716725 0.447874i
\(449\) 14.5341i 0.685906i 0.939353 + 0.342953i \(0.111427\pi\)
−0.939353 + 0.342953i \(0.888573\pi\)
\(450\) 0 0
\(451\) 3.94086i 0.185568i
\(452\) 18.4172 21.4369i 0.866270 1.00831i
\(453\) 0 0
\(454\) −21.4994 7.96716i −1.00902 0.373917i
\(455\) −6.05212 −0.283728
\(456\) 0 0
\(457\) −9.61507 −0.449774 −0.224887 0.974385i \(-0.572201\pi\)
−0.224887 + 0.974385i \(0.572201\pi\)
\(458\) −32.4222 12.0149i −1.51499 0.561419i
\(459\) 0 0
\(460\) −19.6162 16.8529i −0.914611 0.785772i
\(461\) 18.6473i 0.868492i 0.900794 + 0.434246i \(0.142985\pi\)
−0.900794 + 0.434246i \(0.857015\pi\)
\(462\) 0 0
\(463\) 26.6447i 1.23829i −0.785279 0.619143i \(-0.787480\pi\)
0.785279 0.619143i \(-0.212520\pi\)
\(464\) −4.94762 32.4612i −0.229687 1.50697i
\(465\) 0 0
\(466\) 0.380392 1.02649i 0.0176213 0.0475512i
\(467\) −20.1919 −0.934369 −0.467185 0.884160i \(-0.654732\pi\)
−0.467185 + 0.884160i \(0.654732\pi\)
\(468\) 0 0
\(469\) 13.9509 0.644192
\(470\) 0.229264 0.618670i 0.0105752 0.0285371i
\(471\) 0 0
\(472\) 7.68431 + 13.8631i 0.353699 + 0.638101i
\(473\) −0.115650 −0.00531760
\(474\) 0 0
\(475\) −1.65726 2.22642i −0.0760405 0.102155i
\(476\) 6.42726 7.48111i 0.294593 0.342896i
\(477\) 0 0
\(478\) −1.59192 0.589926i −0.0728126 0.0269826i
\(479\) 5.80220i 0.265109i −0.991176 0.132555i \(-0.957682\pi\)
0.991176 0.132555i \(-0.0423180\pi\)
\(480\) 0 0
\(481\) 8.95781 0.408441
\(482\) 22.2600 + 8.24900i 1.01391 + 0.375732i
\(483\) 0 0
\(484\) 16.1362 + 13.8631i 0.733462 + 0.630141i
\(485\) 36.7674 1.66952
\(486\) 0 0
\(487\) 3.70928 0.168083 0.0840417 0.996462i \(-0.473217\pi\)
0.0840417 + 0.996462i \(0.473217\pi\)
\(488\) −16.1452 29.1273i −0.730860 1.31853i
\(489\) 0 0
\(490\) 5.53997 + 2.05298i 0.250270 + 0.0927441i
\(491\) 9.68431 0.437047 0.218523 0.975832i \(-0.429876\pi\)
0.218523 + 0.975832i \(0.429876\pi\)
\(492\) 0 0
\(493\) 18.1043 0.815374
\(494\) 7.66528 2.24571i 0.344877 0.101039i
\(495\) 0 0
\(496\) −2.98195 19.5645i −0.133894 0.878473i
\(497\) 27.9211i 1.25243i
\(498\) 0 0
\(499\) 28.0804 1.25705 0.628527 0.777788i \(-0.283658\pi\)
0.628527 + 0.777788i \(0.283658\pi\)
\(500\) 15.3457 17.8618i 0.686278 0.798804i
\(501\) 0 0
\(502\) 11.4096 30.7888i 0.509235 1.37417i
\(503\) 22.9011i 1.02111i 0.859845 + 0.510555i \(0.170560\pi\)
−0.859845 + 0.510555i \(0.829440\pi\)
\(504\) 0 0
\(505\) −7.79343 −0.346803
\(506\) −4.94762 1.83347i −0.219948 0.0815075i
\(507\) 0 0
\(508\) −6.32092 5.43051i −0.280446 0.240940i
\(509\) 38.0190 1.68516 0.842582 0.538568i \(-0.181035\pi\)
0.842582 + 0.538568i \(0.181035\pi\)
\(510\) 0 0
\(511\) 18.5001i 0.818396i
\(512\) −1.18472 + 22.5964i −0.0523575 + 0.998628i
\(513\) 0 0
\(514\) 5.27349 + 1.95423i 0.232604 + 0.0861973i
\(515\) 34.2947i 1.51120i
\(516\) 0 0
\(517\) 0.134613i 0.00592026i
\(518\) 20.4994 + 7.59658i 0.900693 + 0.333775i
\(519\) 0 0
\(520\) 3.71136 + 6.69559i 0.162754 + 0.293621i
\(521\) 35.7095i 1.56446i −0.622989 0.782231i \(-0.714082\pi\)
0.622989 0.782231i \(-0.285918\pi\)
\(522\) 0 0
\(523\) 15.3754i 0.672319i −0.941805 0.336160i \(-0.890872\pi\)
0.941805 0.336160i \(-0.109128\pi\)
\(524\) −15.5646 13.3720i −0.679942 0.584160i
\(525\) 0 0
\(526\) −19.0704 7.06701i −0.831507 0.308136i
\(527\) 10.9115 0.475313
\(528\) 0 0
\(529\) −15.3211 −0.666133
\(530\) −13.3973 4.96471i −0.581941 0.215653i
\(531\) 0 0
\(532\) 19.4460 + 1.36128i 0.843091 + 0.0590191i
\(533\) 8.47235i 0.366978i
\(534\) 0 0
\(535\) 13.6045 0.588174
\(536\) −8.55514 15.4341i −0.369526 0.666653i
\(537\) 0 0
\(538\) −4.56167 + 12.3097i −0.196668 + 0.530709i
\(539\) 1.20541 0.0519207
\(540\) 0 0
\(541\) 19.8352i 0.852780i 0.904539 + 0.426390i \(0.140215\pi\)
−0.904539 + 0.426390i \(0.859785\pi\)
\(542\) 14.3413 + 5.31455i 0.616014 + 0.228280i
\(543\) 0 0
\(544\) −12.2179 2.52295i −0.523839 0.108171i
\(545\) 10.1029i 0.432759i
\(546\) 0 0
\(547\) 15.7838i 0.674868i 0.941349 + 0.337434i \(0.109559\pi\)
−0.941349 + 0.337434i \(0.890441\pi\)
\(548\) −25.9959 22.3339i −1.11049 0.954059i
\(549\) 0 0
\(550\) 0.188591 0.508913i 0.00804154 0.0217001i
\(551\) 21.3657 + 28.7033i 0.910207 + 1.22280i
\(552\) 0 0
\(553\) 34.4394i 1.46451i
\(554\) 18.5957 + 6.89110i 0.790054 + 0.292775i
\(555\) 0 0
\(556\) −31.4613 27.0294i −1.33426 1.14630i
\(557\) 0.429068i 0.0181802i 0.999959 + 0.00909011i \(0.00289351\pi\)
−0.999959 + 0.00909011i \(0.997106\pi\)
\(558\) 0 0
\(559\) 0.248633 0.0105161
\(560\) 2.81511 + 18.4699i 0.118960 + 0.780494i
\(561\) 0 0
\(562\) −40.6151 15.0509i −1.71324 0.634886i
\(563\) 8.17604i 0.344579i −0.985046 0.172290i \(-0.944884\pi\)
0.985046 0.172290i \(-0.0551165\pi\)
\(564\) 0 0
\(565\) −29.5173 −1.24180
\(566\) −4.66473 + 12.5878i −0.196073 + 0.529105i
\(567\) 0 0
\(568\) 30.8897 17.1222i 1.29610 0.718430i
\(569\) 33.8822i 1.42041i 0.703993 + 0.710207i \(0.251399\pi\)
−0.703993 + 0.710207i \(0.748601\pi\)
\(570\) 0 0
\(571\) −34.1362 −1.42855 −0.714277 0.699863i \(-0.753244\pi\)
−0.714277 + 0.699863i \(0.753244\pi\)
\(572\) 1.18472 + 1.01783i 0.0495354 + 0.0425575i
\(573\) 0 0
\(574\) −7.18489 + 19.3885i −0.299892 + 0.809259i
\(575\) 3.94172i 0.164381i
\(576\) 0 0
\(577\) −5.41082 −0.225255 −0.112628 0.993637i \(-0.535927\pi\)
−0.112628 + 0.993637i \(0.535927\pi\)
\(578\) −5.96391 + 16.0936i −0.248066 + 0.669407i
\(579\) 0 0
\(580\) −22.3485 + 26.0129i −0.927970 + 1.08012i
\(581\) 4.47214i 0.185535i
\(582\) 0 0
\(583\) −2.91504 −0.120729
\(584\) 20.4670 11.3449i 0.846932 0.469454i
\(585\) 0 0
\(586\) −4.88435 + 13.1804i −0.201771 + 0.544479i
\(587\) −43.7648 −1.80637 −0.903183 0.429257i \(-0.858776\pi\)
−0.903183 + 0.429257i \(0.858776\pi\)
\(588\) 0 0
\(589\) 12.8772 + 17.2996i 0.530595 + 0.712819i
\(590\) 5.75240 15.5229i 0.236822 0.639067i
\(591\) 0 0
\(592\) −4.16667 27.3374i −0.171249 1.12356i
\(593\) −3.93192 −0.161464 −0.0807322 0.996736i \(-0.525726\pi\)
−0.0807322 + 0.996736i \(0.525726\pi\)
\(594\) 0 0
\(595\) −10.3010 −0.422300
\(596\) −16.3116 + 18.9861i −0.668150 + 0.777703i
\(597\) 0 0
\(598\) 10.6367 + 3.94172i 0.434969 + 0.161189i
\(599\) 18.7742 0.767092 0.383546 0.923522i \(-0.374703\pi\)
0.383546 + 0.923522i \(0.374703\pi\)
\(600\) 0 0
\(601\) 27.3529i 1.11575i −0.829926 0.557874i \(-0.811617\pi\)
0.829926 0.557874i \(-0.188383\pi\)
\(602\) 0.568983 + 0.210851i 0.0231900 + 0.00859365i
\(603\) 0 0
\(604\) −5.96391 5.12378i −0.242668 0.208484i
\(605\) 22.2185i 0.903309i
\(606\) 0 0
\(607\) 33.8391 1.37349 0.686743 0.726901i \(-0.259040\pi\)
0.686743 + 0.726901i \(0.259040\pi\)
\(608\) −10.4189 22.3483i −0.422543 0.906343i
\(609\) 0 0
\(610\) −12.0862 + 32.6146i −0.489354 + 1.32052i
\(611\) 0.289400i 0.0117079i
\(612\) 0 0
\(613\) 15.7997i 0.638144i 0.947730 + 0.319072i \(0.103371\pi\)
−0.947730 + 0.319072i \(0.896629\pi\)
\(614\) 22.4994 + 8.33773i 0.908003 + 0.336484i
\(615\) 0 0
\(616\) 1.84799 + 3.33392i 0.0744578 + 0.134328i
\(617\) 31.4983 1.26807 0.634036 0.773303i \(-0.281397\pi\)
0.634036 + 0.773303i \(0.281397\pi\)
\(618\) 0 0
\(619\) −8.04103 −0.323196 −0.161598 0.986857i \(-0.551665\pi\)
−0.161598 + 0.986857i \(0.551665\pi\)
\(620\) −13.4695 + 15.6781i −0.540950 + 0.629647i
\(621\) 0 0
\(622\) −45.5079 16.8641i −1.82470 0.676190i
\(623\) −16.6534 −0.667203
\(624\) 0 0
\(625\) −21.4108 −0.856433
\(626\) 6.66729 17.9917i 0.266478 0.719093i
\(627\) 0 0
\(628\) −2.31569 + 2.69538i −0.0924060 + 0.107557i
\(629\) 15.2466 0.607922
\(630\) 0 0
\(631\) 30.6449i 1.21996i 0.792419 + 0.609978i \(0.208822\pi\)
−0.792419 + 0.609978i \(0.791178\pi\)
\(632\) −38.1010 + 21.1194i −1.51558 + 0.840083i
\(633\) 0 0
\(634\) −1.02052 + 2.75387i −0.0405299 + 0.109370i
\(635\) 8.70350i 0.345388i
\(636\) 0 0
\(637\) −2.59148 −0.102678
\(638\) −2.43134 + 6.56098i −0.0962575 + 0.259752i
\(639\) 0 0
\(640\) 18.7073 14.4407i 0.739469 0.570820i
\(641\) 6.08412i 0.240308i 0.992755 + 0.120154i \(0.0383389\pi\)
−0.992755 + 0.120154i \(0.961661\pi\)
\(642\) 0 0
\(643\) 6.98648 0.275520 0.137760 0.990466i \(-0.456010\pi\)
0.137760 + 0.990466i \(0.456010\pi\)
\(644\) 20.9988 + 18.0408i 0.827470 + 0.710906i
\(645\) 0 0
\(646\) 13.0467 3.82231i 0.513314 0.150387i
\(647\) 42.0486i 1.65310i −0.562862 0.826551i \(-0.690300\pi\)
0.562862 0.826551i \(-0.309700\pi\)
\(648\) 0 0
\(649\) 3.37753i 0.132580i
\(650\) −0.405446 + 1.09410i −0.0159029 + 0.0429141i
\(651\) 0 0
\(652\) −14.6913 12.6218i −0.575356 0.494307i
\(653\) 15.7745i 0.617303i 0.951175 + 0.308651i \(0.0998777\pi\)
−0.951175 + 0.308651i \(0.900122\pi\)
\(654\) 0 0
\(655\) 21.4314i 0.837395i
\(656\) 25.8559 3.94086i 1.00950 0.153865i
\(657\) 0 0
\(658\) −0.245423 + 0.662276i −0.00956759 + 0.0258182i
\(659\) 4.40556i 0.171616i 0.996312 + 0.0858080i \(0.0273472\pi\)
−0.996312 + 0.0858080i \(0.972653\pi\)
\(660\) 0 0
\(661\) 24.2366 0.942694 0.471347 0.881948i \(-0.343768\pi\)
0.471347 + 0.881948i \(0.343768\pi\)
\(662\) −26.7524 9.91378i −1.03976 0.385310i
\(663\) 0 0
\(664\) 4.94762 2.74246i 0.192005 0.106428i
\(665\) −12.1567 16.3317i −0.471416 0.633316i
\(666\) 0 0
\(667\) 50.8171i 1.96765i
\(668\) −3.57431 3.07081i −0.138294 0.118813i
\(669\) 0 0
\(670\) −6.40429 + 17.2820i −0.247419 + 0.667662i
\(671\) 7.09641i 0.273954i
\(672\) 0 0
\(673\) 37.6208i 1.45018i 0.688656 + 0.725088i \(0.258201\pi\)
−0.688656 + 0.725088i \(0.741799\pi\)
\(674\) 2.38377 + 0.883367i 0.0918194 + 0.0340260i
\(675\) 0 0
\(676\) 17.1743 + 14.7550i 0.660549 + 0.567499i
\(677\) −29.2511 −1.12421 −0.562106 0.827065i \(-0.690009\pi\)
−0.562106 + 0.827065i \(0.690009\pi\)
\(678\) 0 0
\(679\) −39.3589 −1.51046
\(680\) 6.31692 + 11.3962i 0.242243 + 0.437025i
\(681\) 0 0
\(682\) −1.46538 + 3.95433i −0.0561123 + 0.151419i
\(683\) 14.2243i 0.544278i −0.962258 0.272139i \(-0.912269\pi\)
0.962258 0.272139i \(-0.0877310\pi\)
\(684\) 0 0
\(685\) 35.7947i 1.36765i
\(686\) −26.6870 9.88955i −1.01891 0.377585i
\(687\) 0 0
\(688\) −0.115650 0.758778i −0.00440912 0.0289281i
\(689\) 6.26696 0.238752
\(690\) 0 0
\(691\) −27.0135 −1.02764 −0.513821 0.857897i \(-0.671771\pi\)
−0.513821 + 0.857897i \(0.671771\pi\)
\(692\) −25.7544 22.1264i −0.979034 0.841120i
\(693\) 0 0
\(694\) 10.8039 29.1545i 0.410112 1.10669i
\(695\) 43.3202i 1.64323i
\(696\) 0 0
\(697\) 14.4203i 0.546209i
\(698\) −9.09091 3.36887i −0.344096 0.127514i
\(699\) 0 0
\(700\) −1.85568 + 2.15995i −0.0701382 + 0.0816384i
\(701\) 45.2033i 1.70731i 0.520843 + 0.853653i \(0.325618\pi\)
−0.520843 + 0.853653i \(0.674382\pi\)
\(702\) 0 0
\(703\) 17.9932 + 24.1727i 0.678627 + 0.911690i
\(704\) 2.55514 4.08895i 0.0963004 0.154108i
\(705\) 0 0
\(706\) −6.04147 + 16.3029i −0.227374 + 0.613569i
\(707\) 8.34274 0.313761
\(708\) 0 0
\(709\) 14.1576i 0.531698i 0.964015 + 0.265849i \(0.0856523\pi\)
−0.964015 + 0.265849i \(0.914348\pi\)
\(710\) −34.5880 12.8175i −1.29807 0.481031i
\(711\) 0 0
\(712\) 10.2124 + 18.4240i 0.382726 + 0.690468i
\(713\) 30.6277i 1.14702i
\(714\) 0 0
\(715\) 1.63128i 0.0610063i
\(716\) 18.1818 21.1630i 0.679486 0.790898i
\(717\) 0 0
\(718\) 19.5851 + 7.25777i 0.730911 + 0.270858i
\(719\) 5.67260i 0.211552i −0.994390 0.105776i \(-0.966267\pi\)
0.994390 0.105776i \(-0.0337327\pi\)
\(720\) 0 0
\(721\) 36.7118i 1.36722i
\(722\) 21.4570 + 16.1739i 0.798548 + 0.601931i
\(723\) 0 0
\(724\) −15.0113 12.8967i −0.557890 0.479301i
\(725\) −5.22707 −0.194128
\(726\) 0 0
\(727\) 26.1143i 0.968526i −0.874923 0.484263i \(-0.839088\pi\)
0.874923 0.484263i \(-0.160912\pi\)
\(728\) −3.97295 7.16751i −0.147247 0.265646i
\(729\) 0 0
\(730\) −22.9175 8.49265i −0.848214 0.314327i
\(731\) 0.423186 0.0156521
\(732\) 0 0
\(733\) 22.3959i 0.827213i −0.910456 0.413606i \(-0.864269\pi\)
0.910456 0.413606i \(-0.135731\pi\)
\(734\) −29.0732 10.7738i −1.07311 0.397668i
\(735\) 0 0
\(736\) 7.08171 34.2947i 0.261035 1.26412i
\(737\) 3.76029i 0.138512i
\(738\) 0 0
\(739\) −8.39614 −0.308857 −0.154428 0.988004i \(-0.549354\pi\)
−0.154428 + 0.988004i \(0.549354\pi\)
\(740\) −18.8209 + 21.9069i −0.691871 + 0.805314i
\(741\) 0 0
\(742\) 14.3416 + 5.31464i 0.526496 + 0.195106i
\(743\) −37.7837 −1.38615 −0.693075 0.720866i \(-0.743744\pi\)
−0.693075 + 0.720866i \(0.743744\pi\)
\(744\) 0 0
\(745\) 26.1427 0.957794
\(746\) −17.0476 + 46.0030i −0.624156 + 1.68429i
\(747\) 0 0
\(748\) 2.01644 + 1.73239i 0.0737284 + 0.0633425i
\(749\) −14.5634 −0.532135
\(750\) 0 0
\(751\) −43.2902 −1.57968 −0.789841 0.613312i \(-0.789837\pi\)
−0.789841 + 0.613312i \(0.789837\pi\)
\(752\) 0.883191 0.134613i 0.0322067 0.00490882i
\(753\) 0 0
\(754\) 5.22707 14.1053i 0.190359 0.513684i
\(755\) 8.21191i 0.298862i
\(756\) 0 0
\(757\) 31.9115i 1.15984i −0.814672 0.579921i \(-0.803083\pi\)
0.814672 0.579921i \(-0.196917\pi\)
\(758\) 44.1145 + 16.3477i 1.60231 + 0.593777i
\(759\) 0 0
\(760\) −10.6132 + 23.4643i −0.384981 + 0.851140i
\(761\) −12.3826 −0.448869 −0.224435 0.974489i \(-0.572054\pi\)
−0.224435 + 0.974489i \(0.572054\pi\)
\(762\) 0 0
\(763\) 10.8149i 0.391527i
\(764\) 21.9484 25.5471i 0.794064 0.924262i
\(765\) 0 0
\(766\) 16.5265 44.5968i 0.597126 1.61135i
\(767\) 7.26126i 0.262189i
\(768\) 0 0
\(769\) −15.9308 −0.574478 −0.287239 0.957859i \(-0.592737\pi\)
−0.287239 + 0.957859i \(0.592737\pi\)
\(770\) 1.38339 3.73308i 0.0498539 0.134531i
\(771\) 0 0
\(772\) −17.1655 + 19.9801i −0.617801 + 0.719099i
\(773\) −13.8707 −0.498893 −0.249447 0.968389i \(-0.580249\pi\)
−0.249447 + 0.968389i \(0.580249\pi\)
\(774\) 0 0
\(775\) −3.15038 −0.113165
\(776\) 24.1362 + 43.5435i 0.866438 + 1.56312i
\(777\) 0 0
\(778\) 24.1356 + 8.94408i 0.865305 + 0.320661i
\(779\) −22.8627 + 17.0181i −0.819140 + 0.609737i
\(780\) 0 0
\(781\) −7.52580 −0.269294
\(782\) 18.1043 + 6.70899i 0.647407 + 0.239913i
\(783\) 0 0
\(784\) 1.20541 + 7.90867i 0.0430504 + 0.282452i
\(785\) 3.71136 0.132464
\(786\) 0 0
\(787\) 39.2994i 1.40087i −0.713715 0.700436i \(-0.752989\pi\)
0.713715 0.700436i \(-0.247011\pi\)
\(788\) −29.7253 + 34.5993i −1.05892 + 1.23255i
\(789\) 0 0
\(790\) 42.6626 + 15.8097i 1.51787 + 0.562485i
\(791\) 31.5977 1.12349
\(792\) 0 0
\(793\) 15.2564i 0.541770i
\(794\) 14.8328 + 5.49666i 0.526395 + 0.195069i
\(795\) 0 0
\(796\) −19.6327 + 22.8517i −0.695862 + 0.809959i
\(797\) 40.0155 1.41742 0.708711 0.705499i \(-0.249277\pi\)
0.708711 + 0.705499i \(0.249277\pi\)
\(798\) 0 0
\(799\) 0.492573i 0.0174260i
\(800\) 3.52756 + 0.728427i 0.124718 + 0.0257538i
\(801\) 0 0
\(802\) 30.3281 + 11.2388i 1.07092 + 0.396857i
\(803\) −4.98648 −0.175969
\(804\) 0 0
\(805\) 28.9141i 1.01909i
\(806\) 3.15038 8.50131i 0.110967 0.299446i
\(807\) 0 0
\(808\) −5.11604 9.22974i −0.179982 0.324701i
\(809\) −13.2723 −0.466630 −0.233315 0.972401i \(-0.574957\pi\)
−0.233315 + 0.972401i \(0.574957\pi\)
\(810\) 0 0
\(811\) 36.2317i 1.27227i −0.771579 0.636133i \(-0.780533\pi\)
0.771579 0.636133i \(-0.219467\pi\)
\(812\) 23.9237 27.8463i 0.839556 0.977214i
\(813\) 0 0
\(814\) −2.04757 + 5.52537i −0.0717672 + 0.193664i
\(815\) 20.2290i 0.708590i
\(816\) 0 0
\(817\) 0.499421 + 0.670938i 0.0174725 + 0.0234731i
\(818\) −2.19189 0.812259i −0.0766375 0.0284000i
\(819\) 0 0
\(820\) −20.7197 17.8009i −0.723562 0.621636i
\(821\) 7.95152i 0.277510i −0.990327 0.138755i \(-0.955690\pi\)
0.990327 0.138755i \(-0.0443101\pi\)
\(822\) 0 0
\(823\) 41.1653i 1.43493i 0.696594 + 0.717465i \(0.254698\pi\)
−0.696594 + 0.717465i \(0.745302\pi\)
\(824\) 40.6151 22.5129i 1.41489 0.784275i
\(825\) 0 0
\(826\) −6.15784 + 16.6170i −0.214259 + 0.578178i
\(827\) 17.1575i 0.596626i −0.954468 0.298313i \(-0.903576\pi\)
0.954468 0.298313i \(-0.0964239\pi\)
\(828\) 0 0
\(829\) −6.56691 −0.228078 −0.114039 0.993476i \(-0.536379\pi\)
−0.114039 + 0.993476i \(0.536379\pi\)
\(830\) −5.53997 2.05298i −0.192295 0.0712599i
\(831\) 0 0
\(832\) −5.49322 + 8.79071i −0.190443 + 0.304763i
\(833\) −4.41082 −0.152826
\(834\) 0 0
\(835\) 4.92159i 0.170319i
\(836\) −0.366917 + 5.24143i −0.0126901 + 0.181279i
\(837\) 0 0
\(838\) −11.7259 + 31.6425i −0.405065 + 1.09307i
\(839\) −2.12080 −0.0732180 −0.0366090 0.999330i \(-0.511656\pi\)
−0.0366090 + 0.999330i \(0.511656\pi\)
\(840\) 0 0
\(841\) 38.3880 1.32372
\(842\) −3.03520 + 8.19051i −0.104600 + 0.282263i
\(843\) 0 0
\(844\) 13.2007 15.3652i 0.454388 0.528892i
\(845\) 23.6479i 0.813512i
\(846\) 0 0
\(847\) 23.7845i 0.817245i
\(848\) −2.91504 19.1255i −0.100103 0.656772i
\(849\) 0 0
\(850\) −0.690089 + 1.86221i −0.0236699 + 0.0638733i
\(851\) 42.7960i 1.46703i
\(852\) 0 0
\(853\) 4.74136i 0.162341i 0.996700 + 0.0811706i \(0.0258658\pi\)
−0.996700 + 0.0811706i \(0.974134\pi\)
\(854\) 12.9380 34.9133i 0.442730 1.19471i
\(855\) 0 0
\(856\) 8.93076 + 16.1118i 0.305247 + 0.550690i
\(857\) 0.619596i 0.0211650i −0.999944 0.0105825i \(-0.996631\pi\)
0.999944 0.0105825i \(-0.00336858\pi\)
\(858\) 0 0
\(859\) −6.94544 −0.236975 −0.118488 0.992956i \(-0.537805\pi\)
−0.118488 + 0.992956i \(0.537805\pi\)
\(860\) −0.522394 + 0.608049i −0.0178135 + 0.0207343i
\(861\) 0 0
\(862\) 10.2747 27.7262i 0.349956 0.944358i
\(863\) 2.60477 0.0886674 0.0443337 0.999017i \(-0.485884\pi\)
0.0443337 + 0.999017i \(0.485884\pi\)
\(864\) 0 0
\(865\) 35.4621i 1.20575i
\(866\) 1.87620 + 0.695273i 0.0637558 + 0.0236263i
\(867\) 0 0
\(868\) 14.4189 16.7831i 0.489410 0.569656i
\(869\) 9.28271 0.314894
\(870\) 0 0
\(871\) 8.08414i 0.273921i
\(872\) 11.9648 6.63208i 0.405179 0.224591i
\(873\) 0 0
\(874\) 10.7289 + 36.6209i 0.362911 + 1.23872i
\(875\) 26.3281 0.890051
\(876\) 0 0
\(877\) −34.1318 −1.15255 −0.576275 0.817256i \(-0.695494\pi\)
−0.576275 + 0.817256i \(0.695494\pi\)
\(878\) 6.67894 18.0232i 0.225403 0.608252i
\(879\) 0 0
\(880\) −4.97832 + 0.758778i −0.167819 + 0.0255784i
\(881\) −19.1849 −0.646355 −0.323178 0.946338i \(-0.604751\pi\)
−0.323178 + 0.946338i \(0.604751\pi\)
\(882\) 0 0
\(883\) −31.1497 −1.04827 −0.524135 0.851635i \(-0.675611\pi\)
−0.524135 + 0.851635i \(0.675611\pi\)
\(884\) −4.33509 3.72442i −0.145805 0.125266i
\(885\) 0 0
\(886\) −9.43063 + 25.4486i −0.316828 + 0.854962i
\(887\) −16.1960 −0.543808 −0.271904 0.962324i \(-0.587653\pi\)
−0.271904 + 0.962324i \(0.587653\pi\)
\(888\) 0 0
\(889\) 9.31695i 0.312481i
\(890\) 7.64490 20.6298i 0.256258 0.691512i
\(891\) 0 0
\(892\) 11.4370 + 9.82587i 0.382938 + 0.328994i
\(893\) −0.780948 + 0.581308i −0.0261334 + 0.0194527i
\(894\) 0 0
\(895\) −29.1401 −0.974046
\(896\) −20.0258 + 15.4586i −0.669015 + 0.516434i
\(897\) 0 0
\(898\) 19.2735 + 7.14228i 0.643165 + 0.238341i
\(899\) 40.6151 1.35459
\(900\) 0 0
\(901\) 10.6667 0.355358
\(902\) −5.22593 1.93660i −0.174004 0.0644817i
\(903\) 0 0
\(904\) −19.3768 34.9572i −0.644462 1.16266i
\(905\) 20.6696i 0.687079i
\(906\) 0 0
\(907\) 50.5945i 1.67996i −0.542615 0.839982i \(-0.682566\pi\)
0.542615 0.839982i \(-0.317434\pi\)
\(908\) −21.1303 + 24.5949i −0.701234 + 0.816212i
\(909\) 0 0
\(910\) −2.97411 + 8.02565i −0.0985908 + 0.266048i
\(911\) −12.8236 −0.424864 −0.212432 0.977176i \(-0.568138\pi\)
−0.212432 + 0.977176i \(0.568138\pi\)
\(912\) 0 0
\(913\) −1.20541 −0.0398932
\(914\) −4.72500 + 12.7504i −0.156289 + 0.421747i
\(915\) 0 0
\(916\) −31.8656 + 37.0904i −1.05287 + 1.22550i
\(917\) 22.9420i 0.757611i
\(918\) 0 0
\(919\) 20.9469i 0.690974i 0.938423 + 0.345487i \(0.112286\pi\)
−0.938423 + 0.345487i \(0.887714\pi\)
\(920\) −31.9882 + 17.7311i −1.05462 + 0.584576i
\(921\) 0 0
\(922\) 24.7280 + 9.16359i 0.814373 + 0.301787i
\(923\) 16.1795 0.532555
\(924\) 0 0
\(925\) −4.40201 −0.144737
\(926\) −35.3333 13.0936i −1.16112 0.430284i
\(927\) 0 0
\(928\) −45.4777 9.39097i −1.49288 0.308274i
\(929\) −23.9783 −0.786703 −0.393352 0.919388i \(-0.628684\pi\)
−0.393352 + 0.919388i \(0.628684\pi\)
\(930\) 0 0
\(931\) −5.20541 6.99312i −0.170600 0.229190i
\(932\) −1.17428 1.00887i −0.0384650 0.0330465i
\(933\) 0 0
\(934\) −9.92261 + 26.7762i −0.324678 + 0.876145i
\(935\) 2.77651i 0.0908016i
\(936\) 0 0
\(937\) 4.13733 0.135161 0.0675803 0.997714i \(-0.478472\pi\)
0.0675803 + 0.997714i \(0.478472\pi\)
\(938\) 6.85568 18.5001i 0.223846 0.604049i
\(939\) 0 0
\(940\) −0.707747 0.608049i −0.0230842 0.0198324i
\(941\) −3.88722 −0.126720 −0.0633598 0.997991i \(-0.520182\pi\)
−0.0633598 + 0.997991i \(0.520182\pi\)
\(942\) 0 0
\(943\) −40.4767 −1.31810
\(944\) 22.1599 3.37753i 0.721243 0.109929i
\(945\) 0 0
\(946\) −0.0568323 + 0.153362i −0.00184778 + 0.00498624i
\(947\) −49.8475 −1.61983 −0.809914 0.586549i \(-0.800486\pi\)
−0.809914 + 0.586549i \(0.800486\pi\)
\(948\) 0 0
\(949\) 10.7203 0.347995
\(950\) −3.76684 + 1.10358i −0.122212 + 0.0358048i
\(951\) 0 0
\(952\) −6.76215 12.1995i −0.219163 0.395386i
\(953\) 7.37588i 0.238928i −0.992839 0.119464i \(-0.961882\pi\)
0.992839 0.119464i \(-0.0381176\pi\)
\(954\) 0 0
\(955\) −35.1767 −1.13829
\(956\) −1.56459 + 1.82113i −0.0506024 + 0.0588994i
\(957\) 0 0
\(958\) −7.69423 2.85129i −0.248589 0.0921211i
\(959\) 38.3176i 1.23734i
\(960\) 0 0
\(961\) −6.52110 −0.210358
\(962\) 4.40201 11.8788i 0.141926 0.382989i
\(963\) 0 0
\(964\) 21.8778 25.4650i 0.704637 0.820172i
\(965\) 27.5113 0.885619
\(966\) 0 0
\(967\) 38.1528i 1.22691i −0.789729 0.613455i \(-0.789779\pi\)
0.789729 0.613455i \(-0.210221\pi\)
\(968\) 26.3133 14.5854i 0.845740 0.468794i
\(969\) 0 0
\(970\) 18.0681 48.7568i 0.580131 1.56549i
\(971\) 21.2378i 0.681554i 0.940144 + 0.340777i \(0.110690\pi\)
−0.940144 + 0.340777i \(0.889310\pi\)
\(972\) 0 0
\(973\) 46.3735i 1.48667i
\(974\) 1.82280 4.91883i 0.0584062 0.157610i
\(975\) 0 0
\(976\) −46.5594 + 7.09641i −1.49033 + 0.227150i
\(977\) 10.4436i 0.334121i −0.985947 0.167060i \(-0.946573\pi\)
0.985947 0.167060i \(-0.0534275\pi\)
\(978\) 0 0
\(979\) 4.48872i 0.143460i
\(980\) 5.44486 6.33763i 0.173930 0.202448i
\(981\) 0 0
\(982\) 4.75903 12.8423i 0.151867 0.409813i
\(983\) −25.3103 −0.807272 −0.403636 0.914920i \(-0.632254\pi\)
−0.403636 + 0.914920i \(0.632254\pi\)
\(984\) 0 0
\(985\) 47.6410 1.51797
\(986\) 8.89672 24.0078i 0.283329 0.764565i
\(987\) 0 0
\(988\) 0.788825 11.2684i 0.0250959 0.358496i
\(989\) 1.18785i 0.0377713i
\(990\) 0 0
\(991\) 52.6132 1.67131 0.835657 0.549251i \(-0.185087\pi\)
0.835657 + 0.549251i \(0.185087\pi\)
\(992\) −27.4097 5.65998i −0.870258 0.179705i
\(993\) 0 0
\(994\) 37.0259 + 13.7209i 1.17439 + 0.435200i
\(995\) 31.4654 0.997520
\(996\) 0 0
\(997\) 0.312083i 0.00988376i −0.999988 0.00494188i \(-0.998427\pi\)
0.999988 0.00494188i \(-0.00157305\pi\)
\(998\) 13.7992 37.2372i 0.436805 1.17872i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1368.2.e.e.379.7 12
3.2 odd 2 152.2.b.c.75.6 yes 12
4.3 odd 2 5472.2.e.e.5167.7 12
8.3 odd 2 inner 1368.2.e.e.379.5 12
8.5 even 2 5472.2.e.e.5167.6 12
12.11 even 2 608.2.b.c.303.7 12
19.18 odd 2 inner 1368.2.e.e.379.6 12
24.5 odd 2 608.2.b.c.303.8 12
24.11 even 2 152.2.b.c.75.8 yes 12
57.56 even 2 152.2.b.c.75.7 yes 12
76.75 even 2 5472.2.e.e.5167.8 12
152.37 odd 2 5472.2.e.e.5167.5 12
152.75 even 2 inner 1368.2.e.e.379.8 12
228.227 odd 2 608.2.b.c.303.5 12
456.227 odd 2 152.2.b.c.75.5 12
456.341 even 2 608.2.b.c.303.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.2.b.c.75.5 12 456.227 odd 2
152.2.b.c.75.6 yes 12 3.2 odd 2
152.2.b.c.75.7 yes 12 57.56 even 2
152.2.b.c.75.8 yes 12 24.11 even 2
608.2.b.c.303.5 12 228.227 odd 2
608.2.b.c.303.6 12 456.341 even 2
608.2.b.c.303.7 12 12.11 even 2
608.2.b.c.303.8 12 24.5 odd 2
1368.2.e.e.379.5 12 8.3 odd 2 inner
1368.2.e.e.379.6 12 19.18 odd 2 inner
1368.2.e.e.379.7 12 1.1 even 1 trivial
1368.2.e.e.379.8 12 152.75 even 2 inner
5472.2.e.e.5167.5 12 152.37 odd 2
5472.2.e.e.5167.6 12 8.5 even 2
5472.2.e.e.5167.7 12 4.3 odd 2
5472.2.e.e.5167.8 12 76.75 even 2