Properties

Label 1368.2.e.g.379.20
Level $1368$
Weight $2$
Character 1368.379
Analytic conductor $10.924$
Analytic rank $0$
Dimension $40$
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: \(40\)
Twist minimal: no (minimal twist has level 456)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 379.20
Character \(\chi\) \(=\) 1368.379
Dual form 1368.2.e.g.379.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.134537 + 1.40780i) q^{2} +(-1.96380 - 0.378802i) q^{4} -2.61555i q^{5} -4.81248i q^{7} +(0.797481 - 2.71367i) q^{8} +O(q^{10})\) \(q+(-0.134537 + 1.40780i) q^{2} +(-1.96380 - 0.378802i) q^{4} -2.61555i q^{5} -4.81248i q^{7} +(0.797481 - 2.71367i) q^{8} +(3.68217 + 0.351888i) q^{10} -3.49434 q^{11} +1.50149 q^{13} +(6.77501 + 0.647456i) q^{14} +(3.71302 + 1.48778i) q^{16} -5.31012 q^{17} +(3.83470 + 2.07245i) q^{19} +(-0.990775 + 5.13641i) q^{20} +(0.470118 - 4.91934i) q^{22} +2.26423i q^{23} -1.84109 q^{25} +(-0.202006 + 2.11379i) q^{26} +(-1.82298 + 9.45075i) q^{28} -5.12817 q^{29} +1.72573 q^{31} +(-2.59404 + 5.02702i) q^{32} +(0.714407 - 7.47558i) q^{34} -12.5873 q^{35} -10.2996 q^{37} +(-3.43350 + 5.11967i) q^{38} +(-7.09774 - 2.08585i) q^{40} -3.90666i q^{41} +0.342152 q^{43} +(6.86219 + 1.32366i) q^{44} +(-3.18759 - 0.304623i) q^{46} +0.679062i q^{47} -16.1600 q^{49} +(0.247695 - 2.59189i) q^{50} +(-2.94862 - 0.568767i) q^{52} +10.0708 q^{53} +9.13962i q^{55} +(-13.0595 - 3.83786i) q^{56} +(0.689928 - 7.21944i) q^{58} +9.15071i q^{59} -2.65473i q^{61} +(-0.232175 + 2.42948i) q^{62} +(-6.72805 - 4.32821i) q^{64} -3.92721i q^{65} +7.37340i q^{67} +(10.4280 + 2.01148i) q^{68} +(1.69345 - 17.7204i) q^{70} -9.74773 q^{71} -7.16085 q^{73} +(1.38568 - 14.4998i) q^{74} +(-6.74554 - 5.52247i) q^{76} +16.8165i q^{77} -5.21007 q^{79} +(3.89137 - 9.71158i) q^{80} +(5.49980 + 0.525590i) q^{82} +4.80051 q^{83} +13.8889i q^{85} +(-0.0460321 + 0.481681i) q^{86} +(-2.78667 + 9.48251i) q^{88} -14.0944i q^{89} -7.22588i q^{91} +(0.857696 - 4.44650i) q^{92} +(-0.955984 - 0.0913590i) q^{94} +(5.42059 - 10.0299i) q^{95} -13.2574i q^{97} +(2.17411 - 22.7500i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.134537 + 1.40780i −0.0951320 + 0.995465i
\(3\) 0 0
\(4\) −1.96380 0.378802i −0.981900 0.189401i
\(5\) 2.61555i 1.16971i −0.811138 0.584854i \(-0.801152\pi\)
0.811138 0.584854i \(-0.198848\pi\)
\(6\) 0 0
\(7\) 4.81248i 1.81895i −0.415763 0.909473i \(-0.636485\pi\)
0.415763 0.909473i \(-0.363515\pi\)
\(8\) 0.797481 2.71367i 0.281952 0.959428i
\(9\) 0 0
\(10\) 3.68217 + 0.351888i 1.16440 + 0.111277i
\(11\) −3.49434 −1.05358 −0.526792 0.849994i \(-0.676605\pi\)
−0.526792 + 0.849994i \(0.676605\pi\)
\(12\) 0 0
\(13\) 1.50149 0.416438 0.208219 0.978082i \(-0.433233\pi\)
0.208219 + 0.978082i \(0.433233\pi\)
\(14\) 6.77501 + 0.647456i 1.81070 + 0.173040i
\(15\) 0 0
\(16\) 3.71302 + 1.48778i 0.928254 + 0.371946i
\(17\) −5.31012 −1.28789 −0.643947 0.765071i \(-0.722704\pi\)
−0.643947 + 0.765071i \(0.722704\pi\)
\(18\) 0 0
\(19\) 3.83470 + 2.07245i 0.879742 + 0.475452i
\(20\) −0.990775 + 5.13641i −0.221544 + 1.14854i
\(21\) 0 0
\(22\) 0.470118 4.91934i 0.100230 1.04881i
\(23\) 2.26423i 0.472125i 0.971738 + 0.236063i \(0.0758570\pi\)
−0.971738 + 0.236063i \(0.924143\pi\)
\(24\) 0 0
\(25\) −1.84109 −0.368219
\(26\) −0.202006 + 2.11379i −0.0396165 + 0.414549i
\(27\) 0 0
\(28\) −1.82298 + 9.45075i −0.344510 + 1.78602i
\(29\) −5.12817 −0.952277 −0.476139 0.879370i \(-0.657964\pi\)
−0.476139 + 0.879370i \(0.657964\pi\)
\(30\) 0 0
\(31\) 1.72573 0.309950 0.154975 0.987918i \(-0.450470\pi\)
0.154975 + 0.987918i \(0.450470\pi\)
\(32\) −2.59404 + 5.02702i −0.458566 + 0.888661i
\(33\) 0 0
\(34\) 0.714407 7.47558i 0.122520 1.28205i
\(35\) −12.5873 −2.12764
\(36\) 0 0
\(37\) −10.2996 −1.69324 −0.846622 0.532195i \(-0.821367\pi\)
−0.846622 + 0.532195i \(0.821367\pi\)
\(38\) −3.43350 + 5.11967i −0.556987 + 0.830521i
\(39\) 0 0
\(40\) −7.09774 2.08585i −1.12225 0.329802i
\(41\) 3.90666i 0.610118i −0.952333 0.305059i \(-0.901324\pi\)
0.952333 0.305059i \(-0.0986762\pi\)
\(42\) 0 0
\(43\) 0.342152 0.0521777 0.0260888 0.999660i \(-0.491695\pi\)
0.0260888 + 0.999660i \(0.491695\pi\)
\(44\) 6.86219 + 1.32366i 1.03451 + 0.199550i
\(45\) 0 0
\(46\) −3.18759 0.304623i −0.469984 0.0449142i
\(47\) 0.679062i 0.0990514i 0.998773 + 0.0495257i \(0.0157710\pi\)
−0.998773 + 0.0495257i \(0.984229\pi\)
\(48\) 0 0
\(49\) −16.1600 −2.30857
\(50\) 0.247695 2.59189i 0.0350294 0.366549i
\(51\) 0 0
\(52\) −2.94862 0.568767i −0.408900 0.0788737i
\(53\) 10.0708 1.38333 0.691667 0.722216i \(-0.256876\pi\)
0.691667 + 0.722216i \(0.256876\pi\)
\(54\) 0 0
\(55\) 9.13962i 1.23239i
\(56\) −13.0595 3.83786i −1.74515 0.512856i
\(57\) 0 0
\(58\) 0.689928 7.21944i 0.0905920 0.947958i
\(59\) 9.15071i 1.19132i 0.803236 + 0.595660i \(0.203110\pi\)
−0.803236 + 0.595660i \(0.796890\pi\)
\(60\) 0 0
\(61\) 2.65473i 0.339904i −0.985452 0.169952i \(-0.945639\pi\)
0.985452 0.169952i \(-0.0543613\pi\)
\(62\) −0.232175 + 2.42948i −0.0294862 + 0.308545i
\(63\) 0 0
\(64\) −6.72805 4.32821i −0.841006 0.541026i
\(65\) 3.92721i 0.487111i
\(66\) 0 0
\(67\) 7.37340i 0.900804i 0.892826 + 0.450402i \(0.148719\pi\)
−0.892826 + 0.450402i \(0.851281\pi\)
\(68\) 10.4280 + 2.01148i 1.26458 + 0.243928i
\(69\) 0 0
\(70\) 1.69345 17.7204i 0.202406 2.11799i
\(71\) −9.74773 −1.15684 −0.578421 0.815738i \(-0.696331\pi\)
−0.578421 + 0.815738i \(0.696331\pi\)
\(72\) 0 0
\(73\) −7.16085 −0.838114 −0.419057 0.907960i \(-0.637639\pi\)
−0.419057 + 0.907960i \(0.637639\pi\)
\(74\) 1.38568 14.4998i 0.161082 1.68556i
\(75\) 0 0
\(76\) −6.74554 5.52247i −0.773767 0.633470i
\(77\) 16.8165i 1.91641i
\(78\) 0 0
\(79\) −5.21007 −0.586178 −0.293089 0.956085i \(-0.594683\pi\)
−0.293089 + 0.956085i \(0.594683\pi\)
\(80\) 3.89137 9.71158i 0.435068 1.08579i
\(81\) 0 0
\(82\) 5.49980 + 0.525590i 0.607351 + 0.0580417i
\(83\) 4.80051 0.526925 0.263462 0.964670i \(-0.415135\pi\)
0.263462 + 0.964670i \(0.415135\pi\)
\(84\) 0 0
\(85\) 13.8889i 1.50646i
\(86\) −0.0460321 + 0.481681i −0.00496377 + 0.0519410i
\(87\) 0 0
\(88\) −2.78667 + 9.48251i −0.297060 + 1.01084i
\(89\) 14.0944i 1.49400i −0.664823 0.747001i \(-0.731493\pi\)
0.664823 0.747001i \(-0.268507\pi\)
\(90\) 0 0
\(91\) 7.22588i 0.757478i
\(92\) 0.857696 4.44650i 0.0894210 0.463579i
\(93\) 0 0
\(94\) −0.955984 0.0913590i −0.0986022 0.00942296i
\(95\) 5.42059 10.0299i 0.556141 1.02904i
\(96\) 0 0
\(97\) 13.2574i 1.34608i −0.739604 0.673042i \(-0.764987\pi\)
0.739604 0.673042i \(-0.235013\pi\)
\(98\) 2.17411 22.7500i 0.219618 2.29810i
\(99\) 0 0
\(100\) 3.61554 + 0.697410i 0.361554 + 0.0697410i
\(101\) 0.101742i 0.0101237i 0.999987 + 0.00506187i \(0.00161125\pi\)
−0.999987 + 0.00506187i \(0.998389\pi\)
\(102\) 0 0
\(103\) 19.3937 1.91092 0.955460 0.295120i \(-0.0953597\pi\)
0.955460 + 0.295120i \(0.0953597\pi\)
\(104\) 1.19741 4.07455i 0.117415 0.399542i
\(105\) 0 0
\(106\) −1.35490 + 14.1777i −0.131599 + 1.37706i
\(107\) 2.03827i 0.197047i −0.995135 0.0985235i \(-0.968588\pi\)
0.995135 0.0985235i \(-0.0314120\pi\)
\(108\) 0 0
\(109\) 18.0323 1.72718 0.863589 0.504197i \(-0.168212\pi\)
0.863589 + 0.504197i \(0.168212\pi\)
\(110\) −12.8668 1.22962i −1.22680 0.117239i
\(111\) 0 0
\(112\) 7.15993 17.8688i 0.676549 1.68845i
\(113\) 5.54322i 0.521462i 0.965412 + 0.260731i \(0.0839635\pi\)
−0.965412 + 0.260731i \(0.916036\pi\)
\(114\) 0 0
\(115\) 5.92221 0.552249
\(116\) 10.0707 + 1.94256i 0.935041 + 0.180362i
\(117\) 0 0
\(118\) −12.8824 1.23111i −1.18592 0.113333i
\(119\) 25.5548i 2.34261i
\(120\) 0 0
\(121\) 1.21043 0.110039
\(122\) 3.73733 + 0.357160i 0.338362 + 0.0323357i
\(123\) 0 0
\(124\) −3.38899 0.653711i −0.304340 0.0587050i
\(125\) 8.26227i 0.739000i
\(126\) 0 0
\(127\) −12.4962 −1.10886 −0.554430 0.832231i \(-0.687064\pi\)
−0.554430 + 0.832231i \(0.687064\pi\)
\(128\) 6.99842 8.88944i 0.618579 0.785723i
\(129\) 0 0
\(130\) 5.52873 + 0.528355i 0.484901 + 0.0463398i
\(131\) −12.5819 −1.09928 −0.549642 0.835400i \(-0.685236\pi\)
−0.549642 + 0.835400i \(0.685236\pi\)
\(132\) 0 0
\(133\) 9.97362 18.4544i 0.864822 1.60020i
\(134\) −10.3803 0.991994i −0.896718 0.0856952i
\(135\) 0 0
\(136\) −4.23472 + 14.4099i −0.363124 + 1.23564i
\(137\) 1.32093 0.112855 0.0564273 0.998407i \(-0.482029\pi\)
0.0564273 + 0.998407i \(0.482029\pi\)
\(138\) 0 0
\(139\) 1.41682 0.120173 0.0600864 0.998193i \(-0.480862\pi\)
0.0600864 + 0.998193i \(0.480862\pi\)
\(140\) 24.7189 + 4.76809i 2.08913 + 0.402977i
\(141\) 0 0
\(142\) 1.31143 13.7229i 0.110053 1.15160i
\(143\) −5.24671 −0.438752
\(144\) 0 0
\(145\) 13.4130i 1.11389i
\(146\) 0.963399 10.0810i 0.0797315 0.834313i
\(147\) 0 0
\(148\) 20.2264 + 3.90151i 1.66260 + 0.320702i
\(149\) 13.2785i 1.08782i −0.839144 0.543909i \(-0.816943\pi\)
0.839144 0.543909i \(-0.183057\pi\)
\(150\) 0 0
\(151\) −16.2778 −1.32467 −0.662334 0.749208i \(-0.730434\pi\)
−0.662334 + 0.749208i \(0.730434\pi\)
\(152\) 8.68205 8.75340i 0.704207 0.709994i
\(153\) 0 0
\(154\) −23.6742 2.26243i −1.90772 0.182312i
\(155\) 4.51373i 0.362552i
\(156\) 0 0
\(157\) 18.3793i 1.46683i 0.679783 + 0.733413i \(0.262074\pi\)
−0.679783 + 0.733413i \(0.737926\pi\)
\(158\) 0.700946 7.33473i 0.0557643 0.583520i
\(159\) 0 0
\(160\) 13.1484 + 6.78483i 1.03947 + 0.536388i
\(161\) 10.8966 0.858770
\(162\) 0 0
\(163\) −12.3413 −0.966649 −0.483325 0.875441i \(-0.660571\pi\)
−0.483325 + 0.875441i \(0.660571\pi\)
\(164\) −1.47985 + 7.67190i −0.115557 + 0.599075i
\(165\) 0 0
\(166\) −0.645847 + 6.75816i −0.0501274 + 0.524535i
\(167\) 20.7583 1.60632 0.803161 0.595762i \(-0.203150\pi\)
0.803161 + 0.595762i \(0.203150\pi\)
\(168\) 0 0
\(169\) −10.7455 −0.826580
\(170\) −19.5527 1.86857i −1.49963 0.143313i
\(171\) 0 0
\(172\) −0.671918 0.129608i −0.0512333 0.00988251i
\(173\) 0.684931 0.0520743 0.0260372 0.999661i \(-0.491711\pi\)
0.0260372 + 0.999661i \(0.491711\pi\)
\(174\) 0 0
\(175\) 8.86022i 0.669770i
\(176\) −12.9746 5.19882i −0.977994 0.391876i
\(177\) 0 0
\(178\) 19.8421 + 1.89622i 1.48723 + 0.142127i
\(179\) 18.7464i 1.40117i 0.713568 + 0.700586i \(0.247078\pi\)
−0.713568 + 0.700586i \(0.752922\pi\)
\(180\) 0 0
\(181\) −11.8359 −0.879758 −0.439879 0.898057i \(-0.644979\pi\)
−0.439879 + 0.898057i \(0.644979\pi\)
\(182\) 10.1726 + 0.972147i 0.754042 + 0.0720604i
\(183\) 0 0
\(184\) 6.14439 + 1.80568i 0.452970 + 0.133117i
\(185\) 26.9391i 1.98060i
\(186\) 0 0
\(187\) 18.5554 1.35690
\(188\) 0.257230 1.33354i 0.0187604 0.0972586i
\(189\) 0 0
\(190\) 13.3908 + 8.98049i 0.971468 + 0.651513i
\(191\) 17.4611i 1.26344i −0.775197 0.631720i \(-0.782349\pi\)
0.775197 0.631720i \(-0.217651\pi\)
\(192\) 0 0
\(193\) 11.0743i 0.797149i −0.917136 0.398574i \(-0.869505\pi\)
0.917136 0.398574i \(-0.130495\pi\)
\(194\) 18.6638 + 1.78361i 1.33998 + 0.128056i
\(195\) 0 0
\(196\) 31.7349 + 6.12143i 2.26678 + 0.437245i
\(197\) 20.2434i 1.44228i −0.692788 0.721141i \(-0.743618\pi\)
0.692788 0.721141i \(-0.256382\pi\)
\(198\) 0 0
\(199\) 12.1969i 0.864613i −0.901727 0.432307i \(-0.857700\pi\)
0.901727 0.432307i \(-0.142300\pi\)
\(200\) −1.46824 + 4.99613i −0.103820 + 0.353279i
\(201\) 0 0
\(202\) −0.143233 0.0136881i −0.0100778 0.000963092i
\(203\) 24.6792i 1.73214i
\(204\) 0 0
\(205\) −10.2181 −0.713660
\(206\) −2.60917 + 27.3025i −0.181790 + 1.90225i
\(207\) 0 0
\(208\) 5.57505 + 2.23389i 0.386560 + 0.154892i
\(209\) −13.3998 7.24185i −0.926882 0.500929i
\(210\) 0 0
\(211\) 11.2304i 0.773136i 0.922261 + 0.386568i \(0.126339\pi\)
−0.922261 + 0.386568i \(0.873661\pi\)
\(212\) −19.7771 3.81485i −1.35830 0.262005i
\(213\) 0 0
\(214\) 2.86948 + 0.274223i 0.196153 + 0.0187455i
\(215\) 0.894915i 0.0610327i
\(216\) 0 0
\(217\) 8.30505i 0.563783i
\(218\) −2.42601 + 25.3858i −0.164310 + 1.71934i
\(219\) 0 0
\(220\) 3.46211 17.9484i 0.233415 1.21008i
\(221\) −7.97308 −0.536327
\(222\) 0 0
\(223\) −5.86592 −0.392811 −0.196406 0.980523i \(-0.562927\pi\)
−0.196406 + 0.980523i \(0.562927\pi\)
\(224\) 24.1924 + 12.4838i 1.61643 + 0.834106i
\(225\) 0 0
\(226\) −7.80374 0.745767i −0.519097 0.0496077i
\(227\) 13.7884i 0.915168i 0.889166 + 0.457584i \(0.151285\pi\)
−0.889166 + 0.457584i \(0.848715\pi\)
\(228\) 0 0
\(229\) 7.75918i 0.512741i −0.966579 0.256371i \(-0.917473\pi\)
0.966579 0.256371i \(-0.0825268\pi\)
\(230\) −0.796756 + 8.33728i −0.0525365 + 0.549744i
\(231\) 0 0
\(232\) −4.08962 + 13.9162i −0.268497 + 0.913642i
\(233\) −23.5694 −1.54408 −0.772041 0.635573i \(-0.780764\pi\)
−0.772041 + 0.635573i \(0.780764\pi\)
\(234\) 0 0
\(235\) 1.77612 0.115861
\(236\) 3.46631 17.9702i 0.225637 1.16976i
\(237\) 0 0
\(238\) −35.9761 3.43807i −2.33198 0.222857i
\(239\) 13.3670i 0.864640i −0.901720 0.432320i \(-0.857695\pi\)
0.901720 0.432320i \(-0.142305\pi\)
\(240\) 0 0
\(241\) 19.9602i 1.28575i −0.765972 0.642873i \(-0.777742\pi\)
0.765972 0.642873i \(-0.222258\pi\)
\(242\) −0.162848 + 1.70405i −0.0104683 + 0.109540i
\(243\) 0 0
\(244\) −1.00562 + 5.21337i −0.0643782 + 0.333752i
\(245\) 42.2672i 2.70035i
\(246\) 0 0
\(247\) 5.75776 + 3.11175i 0.366357 + 0.197996i
\(248\) 1.37624 4.68307i 0.0873912 0.297375i
\(249\) 0 0
\(250\) 11.6316 + 1.11158i 0.735649 + 0.0703026i
\(251\) 29.8620 1.88487 0.942435 0.334388i \(-0.108530\pi\)
0.942435 + 0.334388i \(0.108530\pi\)
\(252\) 0 0
\(253\) 7.91200i 0.497423i
\(254\) 1.68120 17.5922i 0.105488 1.10383i
\(255\) 0 0
\(256\) 11.5730 + 11.0483i 0.723313 + 0.690521i
\(257\) 0.677951i 0.0422894i −0.999776 0.0211447i \(-0.993269\pi\)
0.999776 0.0211447i \(-0.00673108\pi\)
\(258\) 0 0
\(259\) 49.5666i 3.07992i
\(260\) −1.48764 + 7.71226i −0.0922593 + 0.478294i
\(261\) 0 0
\(262\) 1.69273 17.7128i 0.104577 1.09430i
\(263\) 3.00903i 0.185545i 0.995687 + 0.0927723i \(0.0295729\pi\)
−0.995687 + 0.0927723i \(0.970427\pi\)
\(264\) 0 0
\(265\) 26.3407i 1.61810i
\(266\) 24.6383 + 16.5237i 1.51067 + 1.01313i
\(267\) 0 0
\(268\) 2.79306 14.4799i 0.170613 0.884499i
\(269\) −7.04041 −0.429261 −0.214631 0.976695i \(-0.568855\pi\)
−0.214631 + 0.976695i \(0.568855\pi\)
\(270\) 0 0
\(271\) 22.8229i 1.38639i −0.720750 0.693195i \(-0.756202\pi\)
0.720750 0.693195i \(-0.243798\pi\)
\(272\) −19.7166 7.90031i −1.19549 0.479026i
\(273\) 0 0
\(274\) −0.177714 + 1.85960i −0.0107361 + 0.112343i
\(275\) 6.43341 0.387949
\(276\) 0 0
\(277\) 20.9985i 1.26168i −0.775913 0.630840i \(-0.782710\pi\)
0.775913 0.630840i \(-0.217290\pi\)
\(278\) −0.190614 + 1.99459i −0.0114323 + 0.119628i
\(279\) 0 0
\(280\) −10.0381 + 34.1577i −0.599892 + 2.04132i
\(281\) 5.03139i 0.300148i −0.988675 0.150074i \(-0.952049\pi\)
0.988675 0.150074i \(-0.0479511\pi\)
\(282\) 0 0
\(283\) −1.25113 −0.0743719 −0.0371860 0.999308i \(-0.511839\pi\)
−0.0371860 + 0.999308i \(0.511839\pi\)
\(284\) 19.1426 + 3.69246i 1.13590 + 0.219107i
\(285\) 0 0
\(286\) 0.705877 7.38632i 0.0417394 0.436762i
\(287\) −18.8007 −1.10977
\(288\) 0 0
\(289\) 11.1974 0.658668
\(290\) −18.8828 1.80454i −1.10884 0.105966i
\(291\) 0 0
\(292\) 14.0625 + 2.71255i 0.822944 + 0.158740i
\(293\) −18.5789 −1.08539 −0.542695 0.839930i \(-0.682596\pi\)
−0.542695 + 0.839930i \(0.682596\pi\)
\(294\) 0 0
\(295\) 23.9341 1.39350
\(296\) −8.21374 + 27.9498i −0.477414 + 1.62455i
\(297\) 0 0
\(298\) 18.6935 + 1.78645i 1.08289 + 0.103486i
\(299\) 3.39972i 0.196611i
\(300\) 0 0
\(301\) 1.64660i 0.0949084i
\(302\) 2.18997 22.9159i 0.126018 1.31866i
\(303\) 0 0
\(304\) 11.1550 + 13.4002i 0.639782 + 0.768557i
\(305\) −6.94359 −0.397589
\(306\) 0 0
\(307\) 10.7076i 0.611115i −0.952174 0.305557i \(-0.901157\pi\)
0.952174 0.305557i \(-0.0988428\pi\)
\(308\) 6.37011 33.0241i 0.362971 1.88173i
\(309\) 0 0
\(310\) 6.35443 + 0.607264i 0.360907 + 0.0344903i
\(311\) 13.2171i 0.749472i −0.927132 0.374736i \(-0.877733\pi\)
0.927132 0.374736i \(-0.122267\pi\)
\(312\) 0 0
\(313\) −32.4175 −1.83235 −0.916174 0.400781i \(-0.868739\pi\)
−0.916174 + 0.400781i \(0.868739\pi\)
\(314\) −25.8743 2.47269i −1.46017 0.139542i
\(315\) 0 0
\(316\) 10.2315 + 1.97358i 0.575568 + 0.111023i
\(317\) 14.4866 0.813650 0.406825 0.913506i \(-0.366636\pi\)
0.406825 + 0.913506i \(0.366636\pi\)
\(318\) 0 0
\(319\) 17.9196 1.00330
\(320\) −11.3206 + 17.5975i −0.632843 + 0.983732i
\(321\) 0 0
\(322\) −1.46599 + 15.3402i −0.0816965 + 0.854875i
\(323\) −20.3627 11.0049i −1.13301 0.612332i
\(324\) 0 0
\(325\) −2.76438 −0.153340
\(326\) 1.66037 17.3741i 0.0919593 0.962265i
\(327\) 0 0
\(328\) −10.6014 3.11549i −0.585364 0.172024i
\(329\) 3.26797 0.180169
\(330\) 0 0
\(331\) 5.22689i 0.287296i −0.989629 0.143648i \(-0.954117\pi\)
0.989629 0.143648i \(-0.0458832\pi\)
\(332\) −9.42725 1.81845i −0.517387 0.0998001i
\(333\) 0 0
\(334\) −2.79275 + 29.2235i −0.152813 + 1.59904i
\(335\) 19.2855 1.05368
\(336\) 0 0
\(337\) 18.1981i 0.991312i 0.868519 + 0.495656i \(0.165072\pi\)
−0.868519 + 0.495656i \(0.834928\pi\)
\(338\) 1.44567 15.1276i 0.0786342 0.822831i
\(339\) 0 0
\(340\) 5.26114 27.2750i 0.285325 1.47919i
\(341\) −6.03030 −0.326559
\(342\) 0 0
\(343\) 44.0821i 2.38021i
\(344\) 0.272860 0.928489i 0.0147116 0.0500608i
\(345\) 0 0
\(346\) −0.0921485 + 0.964245i −0.00495393 + 0.0518381i
\(347\) 16.9154 0.908066 0.454033 0.890985i \(-0.349985\pi\)
0.454033 + 0.890985i \(0.349985\pi\)
\(348\) 0 0
\(349\) 28.3766i 1.51896i 0.650528 + 0.759482i \(0.274547\pi\)
−0.650528 + 0.759482i \(0.725453\pi\)
\(350\) −12.4734 1.19203i −0.666732 0.0637165i
\(351\) 0 0
\(352\) 9.06446 17.5661i 0.483137 0.936279i
\(353\) −2.43957 −0.129845 −0.0649227 0.997890i \(-0.520680\pi\)
−0.0649227 + 0.997890i \(0.520680\pi\)
\(354\) 0 0
\(355\) 25.4957i 1.35317i
\(356\) −5.33899 + 27.6786i −0.282966 + 1.46696i
\(357\) 0 0
\(358\) −26.3912 2.52209i −1.39482 0.133296i
\(359\) 24.6073i 1.29872i 0.760479 + 0.649362i \(0.224964\pi\)
−0.760479 + 0.649362i \(0.775036\pi\)
\(360\) 0 0
\(361\) 10.4099 + 15.8945i 0.547890 + 0.836550i
\(362\) 1.59237 16.6626i 0.0836931 0.875768i
\(363\) 0 0
\(364\) −2.73718 + 14.1902i −0.143467 + 0.743767i
\(365\) 18.7295i 0.980349i
\(366\) 0 0
\(367\) 18.9695i 0.990201i −0.868836 0.495100i \(-0.835131\pi\)
0.868836 0.495100i \(-0.164869\pi\)
\(368\) −3.36869 + 8.40713i −0.175605 + 0.438252i
\(369\) 0 0
\(370\) −37.9249 3.62431i −1.97162 0.188419i
\(371\) 48.4657i 2.51621i
\(372\) 0 0
\(373\) −20.4231 −1.05747 −0.528734 0.848788i \(-0.677333\pi\)
−0.528734 + 0.848788i \(0.677333\pi\)
\(374\) −2.49638 + 26.1223i −0.129085 + 1.35075i
\(375\) 0 0
\(376\) 1.84275 + 0.541540i 0.0950328 + 0.0279278i
\(377\) −7.69988 −0.396564
\(378\) 0 0
\(379\) 26.0452i 1.33785i 0.743330 + 0.668925i \(0.233245\pi\)
−0.743330 + 0.668925i \(0.766755\pi\)
\(380\) −14.4443 + 17.6433i −0.740976 + 0.905082i
\(381\) 0 0
\(382\) 24.5817 + 2.34916i 1.25771 + 0.120194i
\(383\) 23.1300 1.18189 0.590944 0.806712i \(-0.298755\pi\)
0.590944 + 0.806712i \(0.298755\pi\)
\(384\) 0 0
\(385\) 43.9843 2.24165
\(386\) 15.5905 + 1.48991i 0.793534 + 0.0758344i
\(387\) 0 0
\(388\) −5.02193 + 26.0349i −0.254950 + 1.32172i
\(389\) 17.1821i 0.871166i −0.900148 0.435583i \(-0.856542\pi\)
0.900148 0.435583i \(-0.143458\pi\)
\(390\) 0 0
\(391\) 12.0233i 0.608047i
\(392\) −12.8873 + 43.8529i −0.650905 + 2.21490i
\(393\) 0 0
\(394\) 28.4986 + 2.72349i 1.43574 + 0.137207i
\(395\) 13.6272i 0.685658i
\(396\) 0 0
\(397\) 28.3706i 1.42388i 0.702242 + 0.711939i \(0.252183\pi\)
−0.702242 + 0.711939i \(0.747817\pi\)
\(398\) 17.1708 + 1.64093i 0.860692 + 0.0822524i
\(399\) 0 0
\(400\) −6.83601 2.73915i −0.341801 0.136957i
\(401\) 6.28011i 0.313614i 0.987629 + 0.156807i \(0.0501200\pi\)
−0.987629 + 0.156807i \(0.949880\pi\)
\(402\) 0 0
\(403\) 2.59116 0.129075
\(404\) 0.0385402 0.199802i 0.00191745 0.00994050i
\(405\) 0 0
\(406\) −34.7434 3.32027i −1.72429 0.164782i
\(407\) 35.9903 1.78398
\(408\) 0 0
\(409\) 2.75238i 0.136097i 0.997682 + 0.0680483i \(0.0216772\pi\)
−0.997682 + 0.0680483i \(0.978323\pi\)
\(410\) 1.37471 14.3850i 0.0678919 0.710424i
\(411\) 0 0
\(412\) −38.0854 7.34638i −1.87633 0.361930i
\(413\) 44.0376 2.16695
\(414\) 0 0
\(415\) 12.5560i 0.616349i
\(416\) −3.89492 + 7.54801i −0.190964 + 0.370072i
\(417\) 0 0
\(418\) 11.9978 17.8899i 0.586833 0.875024i
\(419\) 33.3577 1.62963 0.814816 0.579719i \(-0.196838\pi\)
0.814816 + 0.579719i \(0.196838\pi\)
\(420\) 0 0
\(421\) 0.929028 0.0452781 0.0226390 0.999744i \(-0.492793\pi\)
0.0226390 + 0.999744i \(0.492793\pi\)
\(422\) −15.8102 1.51091i −0.769629 0.0735499i
\(423\) 0 0
\(424\) 8.03130 27.3289i 0.390034 1.32721i
\(425\) 9.77642 0.474226
\(426\) 0 0
\(427\) −12.7759 −0.618267
\(428\) −0.772101 + 4.00275i −0.0373209 + 0.193480i
\(429\) 0 0
\(430\) 1.25986 + 0.120399i 0.0607559 + 0.00580616i
\(431\) −34.4951 −1.66157 −0.830786 0.556592i \(-0.812109\pi\)
−0.830786 + 0.556592i \(0.812109\pi\)
\(432\) 0 0
\(433\) 24.9055i 1.19688i −0.801166 0.598442i \(-0.795787\pi\)
0.801166 0.598442i \(-0.204213\pi\)
\(434\) 11.6918 + 1.11734i 0.561226 + 0.0536338i
\(435\) 0 0
\(436\) −35.4117 6.83066i −1.69591 0.327129i
\(437\) −4.69250 + 8.68266i −0.224473 + 0.415348i
\(438\) 0 0
\(439\) −20.5120 −0.978984 −0.489492 0.872008i \(-0.662818\pi\)
−0.489492 + 0.872008i \(0.662818\pi\)
\(440\) 24.8020 + 7.28868i 1.18239 + 0.347474i
\(441\) 0 0
\(442\) 1.07267 11.2245i 0.0510219 0.533895i
\(443\) −25.9849 −1.23458 −0.617289 0.786736i \(-0.711769\pi\)
−0.617289 + 0.786736i \(0.711769\pi\)
\(444\) 0 0
\(445\) −36.8646 −1.74755
\(446\) 0.789184 8.25805i 0.0373689 0.391030i
\(447\) 0 0
\(448\) −20.8294 + 32.3786i −0.984097 + 1.52974i
\(449\) 36.4806i 1.72163i −0.508920 0.860814i \(-0.669955\pi\)
0.508920 0.860814i \(-0.330045\pi\)
\(450\) 0 0
\(451\) 13.6512i 0.642810i
\(452\) 2.09978 10.8858i 0.0987654 0.512023i
\(453\) 0 0
\(454\) −19.4113 1.85505i −0.911018 0.0870618i
\(455\) −18.8996 −0.886028
\(456\) 0 0
\(457\) 23.2770 1.08885 0.544425 0.838809i \(-0.316748\pi\)
0.544425 + 0.838809i \(0.316748\pi\)
\(458\) 10.9234 + 1.04390i 0.510416 + 0.0487781i
\(459\) 0 0
\(460\) −11.6300 2.24335i −0.542253 0.104597i
\(461\) 14.2845i 0.665298i −0.943051 0.332649i \(-0.892058\pi\)
0.943051 0.332649i \(-0.107942\pi\)
\(462\) 0 0
\(463\) 15.6276i 0.726275i −0.931736 0.363137i \(-0.881706\pi\)
0.931736 0.363137i \(-0.118294\pi\)
\(464\) −19.0410 7.62961i −0.883956 0.354196i
\(465\) 0 0
\(466\) 3.17095 33.1810i 0.146892 1.53708i
\(467\) 8.66870 0.401140 0.200570 0.979679i \(-0.435721\pi\)
0.200570 + 0.979679i \(0.435721\pi\)
\(468\) 0 0
\(469\) 35.4843 1.63851
\(470\) −0.238954 + 2.50042i −0.0110221 + 0.115336i
\(471\) 0 0
\(472\) 24.8320 + 7.29752i 1.14299 + 0.335895i
\(473\) −1.19560 −0.0549736
\(474\) 0 0
\(475\) −7.06005 3.81557i −0.323937 0.175070i
\(476\) 9.68023 50.1846i 0.443693 2.30021i
\(477\) 0 0
\(478\) 18.8181 + 1.79836i 0.860719 + 0.0822549i
\(479\) 3.41248i 0.155920i 0.996956 + 0.0779602i \(0.0248407\pi\)
−0.996956 + 0.0779602i \(0.975159\pi\)
\(480\) 0 0
\(481\) −15.4647 −0.705130
\(482\) 28.0999 + 2.68538i 1.27992 + 0.122316i
\(483\) 0 0
\(484\) −2.37705 0.458515i −0.108048 0.0208416i
\(485\) −34.6754 −1.57453
\(486\) 0 0
\(487\) 41.8116 1.89467 0.947333 0.320250i \(-0.103767\pi\)
0.947333 + 0.320250i \(0.103767\pi\)
\(488\) −7.20408 2.11710i −0.326114 0.0958367i
\(489\) 0 0
\(490\) −59.5037 5.68650i −2.68810 0.256890i
\(491\) 13.0613 0.589448 0.294724 0.955582i \(-0.404772\pi\)
0.294724 + 0.955582i \(0.404772\pi\)
\(492\) 0 0
\(493\) 27.2312 1.22643
\(494\) −5.15536 + 7.68713i −0.231951 + 0.345860i
\(495\) 0 0
\(496\) 6.40767 + 2.56751i 0.287713 + 0.115285i
\(497\) 46.9108i 2.10424i
\(498\) 0 0
\(499\) 7.12405 0.318916 0.159458 0.987205i \(-0.449025\pi\)
0.159458 + 0.987205i \(0.449025\pi\)
\(500\) −3.12977 + 16.2255i −0.139967 + 0.725624i
\(501\) 0 0
\(502\) −4.01754 + 42.0397i −0.179312 + 1.87632i
\(503\) 6.92730i 0.308873i −0.988003 0.154437i \(-0.950644\pi\)
0.988003 0.154437i \(-0.0493562\pi\)
\(504\) 0 0
\(505\) 0.266112 0.0118418
\(506\) 11.1385 + 1.06446i 0.495167 + 0.0473209i
\(507\) 0 0
\(508\) 24.5400 + 4.73359i 1.08879 + 0.210019i
\(509\) −5.92205 −0.262490 −0.131245 0.991350i \(-0.541897\pi\)
−0.131245 + 0.991350i \(0.541897\pi\)
\(510\) 0 0
\(511\) 34.4614i 1.52448i
\(512\) −17.1108 + 14.8061i −0.756199 + 0.654342i
\(513\) 0 0
\(514\) 0.954420 + 0.0912095i 0.0420977 + 0.00402308i
\(515\) 50.7252i 2.23522i
\(516\) 0 0
\(517\) 2.37288i 0.104359i
\(518\) −69.7799 6.66854i −3.06595 0.292999i
\(519\) 0 0
\(520\) −10.6572 3.13188i −0.467348 0.137342i
\(521\) 16.9113i 0.740898i 0.928853 + 0.370449i \(0.120796\pi\)
−0.928853 + 0.370449i \(0.879204\pi\)
\(522\) 0 0
\(523\) 20.3406i 0.889434i −0.895671 0.444717i \(-0.853304\pi\)
0.895671 0.444717i \(-0.146696\pi\)
\(524\) 24.7083 + 4.76604i 1.07939 + 0.208206i
\(525\) 0 0
\(526\) −4.23611 0.404826i −0.184703 0.0176512i
\(527\) −9.16384 −0.399183
\(528\) 0 0
\(529\) 17.8733 0.777098
\(530\) 37.0825 + 3.54380i 1.61076 + 0.153933i
\(531\) 0 0
\(532\) −26.5768 + 32.4628i −1.15225 + 1.40744i
\(533\) 5.86580i 0.254076i
\(534\) 0 0
\(535\) −5.33119 −0.230488
\(536\) 20.0090 + 5.88014i 0.864257 + 0.253984i
\(537\) 0 0
\(538\) 0.947196 9.91149i 0.0408365 0.427315i
\(539\) 56.4684 2.43227
\(540\) 0 0
\(541\) 24.8364i 1.06780i −0.845548 0.533900i \(-0.820726\pi\)
0.845548 0.533900i \(-0.179274\pi\)
\(542\) 32.1300 + 3.07052i 1.38010 + 0.131890i
\(543\) 0 0
\(544\) 13.7747 26.6941i 0.590583 1.14450i
\(545\) 47.1642i 2.02029i
\(546\) 0 0
\(547\) 22.8518i 0.977071i −0.872544 0.488535i \(-0.837531\pi\)
0.872544 0.488535i \(-0.162469\pi\)
\(548\) −2.59404 0.500370i −0.110812 0.0213748i
\(549\) 0 0
\(550\) −0.865532 + 9.05695i −0.0369064 + 0.386190i
\(551\) −19.6650 10.6279i −0.837758 0.452762i
\(552\) 0 0
\(553\) 25.0733i 1.06623i
\(554\) 29.5617 + 2.82508i 1.25596 + 0.120026i
\(555\) 0 0
\(556\) −2.78234 0.536693i −0.117998 0.0227609i
\(557\) 5.88751i 0.249462i 0.992191 + 0.124731i \(0.0398067\pi\)
−0.992191 + 0.124731i \(0.960193\pi\)
\(558\) 0 0
\(559\) 0.513737 0.0217288
\(560\) −46.7368 18.7271i −1.97499 0.791366i
\(561\) 0 0
\(562\) 7.08319 + 0.676908i 0.298786 + 0.0285536i
\(563\) 6.33319i 0.266912i −0.991055 0.133456i \(-0.957393\pi\)
0.991055 0.133456i \(-0.0426075\pi\)
\(564\) 0 0
\(565\) 14.4985 0.609959
\(566\) 0.168323 1.76134i 0.00707515 0.0740346i
\(567\) 0 0
\(568\) −7.77363 + 26.4522i −0.326174 + 1.10991i
\(569\) 19.8209i 0.830937i −0.909607 0.415469i \(-0.863618\pi\)
0.909607 0.415469i \(-0.136382\pi\)
\(570\) 0 0
\(571\) −35.3004 −1.47728 −0.738639 0.674101i \(-0.764531\pi\)
−0.738639 + 0.674101i \(0.764531\pi\)
\(572\) 10.3035 + 1.98747i 0.430811 + 0.0831001i
\(573\) 0 0
\(574\) 2.52939 26.4677i 0.105575 1.10474i
\(575\) 4.16866i 0.173845i
\(576\) 0 0
\(577\) 28.4776 1.18554 0.592769 0.805373i \(-0.298035\pi\)
0.592769 + 0.805373i \(0.298035\pi\)
\(578\) −1.50646 + 15.7636i −0.0626604 + 0.655681i
\(579\) 0 0
\(580\) 5.08087 26.3404i 0.210971 1.09373i
\(581\) 23.1024i 0.958448i
\(582\) 0 0
\(583\) −35.1909 −1.45746
\(584\) −5.71064 + 19.4322i −0.236308 + 0.804111i
\(585\) 0 0
\(586\) 2.49955 26.1554i 0.103255 1.08047i
\(587\) −28.0180 −1.15643 −0.578214 0.815885i \(-0.696250\pi\)
−0.578214 + 0.815885i \(0.696250\pi\)
\(588\) 0 0
\(589\) 6.61767 + 3.57649i 0.272676 + 0.147367i
\(590\) −3.22002 + 33.6944i −0.132566 + 1.38718i
\(591\) 0 0
\(592\) −38.2426 15.3236i −1.57176 0.629795i
\(593\) 45.6450 1.87442 0.937208 0.348771i \(-0.113401\pi\)
0.937208 + 0.348771i \(0.113401\pi\)
\(594\) 0 0
\(595\) 66.8399 2.74017
\(596\) −5.02993 + 26.0764i −0.206034 + 1.06813i
\(597\) 0 0
\(598\) −4.78612 0.457387i −0.195719 0.0187040i
\(599\) 20.9807 0.857248 0.428624 0.903483i \(-0.358998\pi\)
0.428624 + 0.903483i \(0.358998\pi\)
\(600\) 0 0
\(601\) 0.458660i 0.0187091i −0.999956 0.00935456i \(-0.997022\pi\)
0.999956 0.00935456i \(-0.00297769\pi\)
\(602\) 2.31808 + 0.221528i 0.0944780 + 0.00902883i
\(603\) 0 0
\(604\) 31.9663 + 6.16607i 1.30069 + 0.250894i
\(605\) 3.16595i 0.128714i
\(606\) 0 0
\(607\) 30.1779 1.22488 0.612441 0.790516i \(-0.290188\pi\)
0.612441 + 0.790516i \(0.290188\pi\)
\(608\) −20.3656 + 13.9011i −0.825935 + 0.563766i
\(609\) 0 0
\(610\) 0.934169 9.77518i 0.0378234 0.395785i
\(611\) 1.01960i 0.0412487i
\(612\) 0 0
\(613\) 15.1288i 0.611045i −0.952185 0.305523i \(-0.901169\pi\)
0.952185 0.305523i \(-0.0988311\pi\)
\(614\) 15.0742 + 1.44057i 0.608343 + 0.0581366i
\(615\) 0 0
\(616\) 45.6344 + 13.4108i 1.83866 + 0.540337i
\(617\) 3.05065 0.122815 0.0614073 0.998113i \(-0.480441\pi\)
0.0614073 + 0.998113i \(0.480441\pi\)
\(618\) 0 0
\(619\) −14.3298 −0.575962 −0.287981 0.957636i \(-0.592984\pi\)
−0.287981 + 0.957636i \(0.592984\pi\)
\(620\) −1.70981 + 8.86407i −0.0686677 + 0.355990i
\(621\) 0 0
\(622\) 18.6070 + 1.77819i 0.746073 + 0.0712987i
\(623\) −67.8290 −2.71751
\(624\) 0 0
\(625\) −30.8158 −1.23263
\(626\) 4.36136 45.6374i 0.174315 1.82404i
\(627\) 0 0
\(628\) 6.96211 36.0932i 0.277818 1.44028i
\(629\) 54.6921 2.18072
\(630\) 0 0
\(631\) 11.4416i 0.455482i −0.973722 0.227741i \(-0.926866\pi\)
0.973722 0.227741i \(-0.0731340\pi\)
\(632\) −4.15493 + 14.1384i −0.165274 + 0.562396i
\(633\) 0 0
\(634\) −1.94899 + 20.3943i −0.0774041 + 0.809960i
\(635\) 32.6844i 1.29704i
\(636\) 0 0
\(637\) −24.2640 −0.961374
\(638\) −2.41085 + 25.2272i −0.0954463 + 0.998754i
\(639\) 0 0
\(640\) −23.2508 18.3047i −0.919067 0.723557i
\(641\) 13.6910i 0.540760i −0.962754 0.270380i \(-0.912851\pi\)
0.962754 0.270380i \(-0.0871494\pi\)
\(642\) 0 0
\(643\) 7.58609 0.299166 0.149583 0.988749i \(-0.452207\pi\)
0.149583 + 0.988749i \(0.452207\pi\)
\(644\) −21.3987 4.12764i −0.843226 0.162652i
\(645\) 0 0
\(646\) 18.2323 27.1861i 0.717340 1.06962i
\(647\) 27.2526i 1.07141i 0.844405 + 0.535705i \(0.179954\pi\)
−0.844405 + 0.535705i \(0.820046\pi\)
\(648\) 0 0
\(649\) 31.9757i 1.25516i
\(650\) 0.371911 3.89169i 0.0145875 0.152645i
\(651\) 0 0
\(652\) 24.2359 + 4.67493i 0.949153 + 0.183084i
\(653\) 3.86565i 0.151274i 0.997135 + 0.0756372i \(0.0240991\pi\)
−0.997135 + 0.0756372i \(0.975901\pi\)
\(654\) 0 0
\(655\) 32.9085i 1.28584i
\(656\) 5.81226 14.5055i 0.226931 0.566345i
\(657\) 0 0
\(658\) −0.439663 + 4.60065i −0.0171399 + 0.179352i
\(659\) 33.7642i 1.31527i −0.753338 0.657633i \(-0.771558\pi\)
0.753338 0.657633i \(-0.228442\pi\)
\(660\) 0 0
\(661\) −7.29497 −0.283741 −0.141871 0.989885i \(-0.545312\pi\)
−0.141871 + 0.989885i \(0.545312\pi\)
\(662\) 7.35841 + 0.703209i 0.285993 + 0.0273310i
\(663\) 0 0
\(664\) 3.82832 13.0270i 0.148568 0.505547i
\(665\) −48.2685 26.0865i −1.87177 1.01159i
\(666\) 0 0
\(667\) 11.6114i 0.449594i
\(668\) −40.7651 7.86327i −1.57725 0.304239i
\(669\) 0 0
\(670\) −2.59461 + 27.1501i −0.100238 + 1.04890i
\(671\) 9.27655i 0.358117i
\(672\) 0 0
\(673\) 20.7118i 0.798380i 0.916868 + 0.399190i \(0.130709\pi\)
−0.916868 + 0.399190i \(0.869291\pi\)
\(674\) −25.6192 2.44831i −0.986816 0.0943055i
\(675\) 0 0
\(676\) 21.1021 + 4.07043i 0.811618 + 0.156555i
\(677\) −22.9317 −0.881336 −0.440668 0.897670i \(-0.645258\pi\)
−0.440668 + 0.897670i \(0.645258\pi\)
\(678\) 0 0
\(679\) −63.8009 −2.44846
\(680\) 37.6899 + 11.0761i 1.44534 + 0.424750i
\(681\) 0 0
\(682\) 0.811298 8.48945i 0.0310662 0.325078i
\(683\) 22.5142i 0.861483i 0.902475 + 0.430741i \(0.141748\pi\)
−0.902475 + 0.430741i \(0.858252\pi\)
\(684\) 0 0
\(685\) 3.45495i 0.132007i
\(686\) −62.0588 5.93068i −2.36942 0.226434i
\(687\) 0 0
\(688\) 1.27042 + 0.509048i 0.0484342 + 0.0194073i
\(689\) 15.1212 0.576073
\(690\) 0 0
\(691\) −13.4002 −0.509766 −0.254883 0.966972i \(-0.582037\pi\)
−0.254883 + 0.966972i \(0.582037\pi\)
\(692\) −1.34507 0.259453i −0.0511318 0.00986293i
\(693\) 0 0
\(694\) −2.27575 + 23.8135i −0.0863861 + 0.903948i
\(695\) 3.70575i 0.140567i
\(696\) 0 0
\(697\) 20.7448i 0.785767i
\(698\) −39.9485 3.81770i −1.51207 0.144502i
\(699\) 0 0
\(700\) 3.35627 17.3997i 0.126855 0.657647i
\(701\) 33.0858i 1.24963i −0.780772 0.624816i \(-0.785174\pi\)
0.780772 0.624816i \(-0.214826\pi\)
\(702\) 0 0
\(703\) −39.4959 21.3454i −1.48962 0.805057i
\(704\) 23.5101 + 15.1242i 0.886070 + 0.570016i
\(705\) 0 0
\(706\) 0.328213 3.43443i 0.0123525 0.129257i
\(707\) 0.489633 0.0184145
\(708\) 0 0
\(709\) 19.4606i 0.730858i −0.930839 0.365429i \(-0.880922\pi\)
0.930839 0.365429i \(-0.119078\pi\)
\(710\) −35.8928 3.43011i −1.34703 0.128730i
\(711\) 0 0
\(712\) −38.2476 11.2400i −1.43339 0.421237i
\(713\) 3.90746i 0.146335i
\(714\) 0 0
\(715\) 13.7230i 0.513212i
\(716\) 7.10118 36.8142i 0.265384 1.37581i
\(717\) 0 0
\(718\) −34.6422 3.31059i −1.29283 0.123550i
\(719\) 32.5024i 1.21213i −0.795414 0.606067i \(-0.792746\pi\)
0.795414 0.606067i \(-0.207254\pi\)
\(720\) 0 0
\(721\) 93.3319i 3.47586i
\(722\) −23.7767 + 12.5167i −0.884878 + 0.465823i
\(723\) 0 0
\(724\) 23.2434 + 4.48348i 0.863834 + 0.166627i
\(725\) 9.44144 0.350646
\(726\) 0 0
\(727\) 11.3190i 0.419800i 0.977723 + 0.209900i \(0.0673139\pi\)
−0.977723 + 0.209900i \(0.932686\pi\)
\(728\) −19.6087 5.76250i −0.726746 0.213572i
\(729\) 0 0
\(730\) −26.3675 2.51982i −0.975903 0.0932626i
\(731\) −1.81687 −0.0671993
\(732\) 0 0
\(733\) 14.7845i 0.546079i 0.962003 + 0.273040i \(0.0880290\pi\)
−0.962003 + 0.273040i \(0.911971\pi\)
\(734\) 26.7053 + 2.55210i 0.985710 + 0.0941998i
\(735\) 0 0
\(736\) −11.3823 5.87351i −0.419559 0.216500i
\(737\) 25.7652i 0.949072i
\(738\) 0 0
\(739\) 33.9300 1.24813 0.624067 0.781371i \(-0.285479\pi\)
0.624067 + 0.781371i \(0.285479\pi\)
\(740\) 10.2046 52.9030i 0.375128 1.94475i
\(741\) 0 0
\(742\) 68.2299 + 6.52042i 2.50480 + 0.239372i
\(743\) 14.5846 0.535056 0.267528 0.963550i \(-0.413793\pi\)
0.267528 + 0.963550i \(0.413793\pi\)
\(744\) 0 0
\(745\) −34.7306 −1.27243
\(746\) 2.74766 28.7516i 0.100599 1.05267i
\(747\) 0 0
\(748\) −36.4390 7.02882i −1.33234 0.256999i
\(749\) −9.80913 −0.358418
\(750\) 0 0
\(751\) −13.8729 −0.506229 −0.253114 0.967436i \(-0.581455\pi\)
−0.253114 + 0.967436i \(0.581455\pi\)
\(752\) −1.01030 + 2.52137i −0.0368418 + 0.0919449i
\(753\) 0 0
\(754\) 1.03592 10.8399i 0.0377259 0.394766i
\(755\) 42.5754i 1.54948i
\(756\) 0 0
\(757\) 13.4956i 0.490506i −0.969459 0.245253i \(-0.921129\pi\)
0.969459 0.245253i \(-0.0788710\pi\)
\(758\) −36.6664 3.50404i −1.33178 0.127272i
\(759\) 0 0
\(760\) −22.8949 22.7083i −0.830487 0.823718i
\(761\) −19.7088 −0.714442 −0.357221 0.934020i \(-0.616276\pi\)
−0.357221 + 0.934020i \(0.616276\pi\)
\(762\) 0 0
\(763\) 86.7799i 3.14164i
\(764\) −6.61430 + 34.2901i −0.239297 + 1.24057i
\(765\) 0 0
\(766\) −3.11184 + 32.5624i −0.112435 + 1.17653i
\(767\) 13.7397i 0.496111i
\(768\) 0 0
\(769\) 18.8060 0.678163 0.339081 0.940757i \(-0.389884\pi\)
0.339081 + 0.940757i \(0.389884\pi\)
\(770\) −5.91751 + 61.9210i −0.213252 + 2.23148i
\(771\) 0 0
\(772\) −4.19499 + 21.7478i −0.150981 + 0.782720i
\(773\) −0.638576 −0.0229680 −0.0114840 0.999934i \(-0.503656\pi\)
−0.0114840 + 0.999934i \(0.503656\pi\)
\(774\) 0 0
\(775\) −3.17723 −0.114130
\(776\) −35.9762 10.5725i −1.29147 0.379531i
\(777\) 0 0
\(778\) 24.1889 + 2.31163i 0.867215 + 0.0828758i
\(779\) 8.09635 14.9809i 0.290082 0.536746i
\(780\) 0 0
\(781\) 34.0619 1.21883
\(782\) 16.9265 + 1.61758i 0.605289 + 0.0578447i
\(783\) 0 0
\(784\) −60.0022 24.0425i −2.14294 0.858661i
\(785\) 48.0719 1.71576
\(786\) 0 0
\(787\) 5.69613i 0.203045i −0.994833 0.101522i \(-0.967629\pi\)
0.994833 0.101522i \(-0.0323714\pi\)
\(788\) −7.66824 + 39.7540i −0.273170 + 1.41618i
\(789\) 0 0
\(790\) −19.1843 1.83336i −0.682548 0.0652280i
\(791\) 26.6766 0.948511
\(792\) 0 0
\(793\) 3.98605i 0.141549i
\(794\) −39.9401 3.81689i −1.41742 0.135456i
\(795\) 0 0
\(796\) −4.62020 + 23.9522i −0.163759 + 0.848964i
\(797\) 0.349816 0.0123911 0.00619557 0.999981i \(-0.498028\pi\)
0.00619557 + 0.999981i \(0.498028\pi\)
\(798\) 0 0
\(799\) 3.60590i 0.127568i
\(800\) 4.77587 9.25522i 0.168852 0.327221i
\(801\) 0 0
\(802\) −8.84114 0.844907i −0.312191 0.0298347i
\(803\) 25.0225 0.883024
\(804\) 0 0
\(805\) 28.5005i 1.00451i
\(806\) −0.348607 + 3.64784i −0.0122792 + 0.128490i
\(807\) 0 0
\(808\) 0.276096 + 0.0811376i 0.00971301 + 0.00285441i
\(809\) −11.1848 −0.393236 −0.196618 0.980480i \(-0.562996\pi\)
−0.196618 + 0.980480i \(0.562996\pi\)
\(810\) 0 0
\(811\) 11.3206i 0.397520i −0.980048 0.198760i \(-0.936309\pi\)
0.980048 0.198760i \(-0.0636914\pi\)
\(812\) 9.34854 48.4650i 0.328069 1.70079i
\(813\) 0 0
\(814\) −4.84203 + 50.6672i −0.169713 + 1.77588i
\(815\) 32.2794i 1.13070i
\(816\) 0 0
\(817\) 1.31205 + 0.709092i 0.0459029 + 0.0248080i
\(818\) −3.87480 0.370297i −0.135479 0.0129471i
\(819\) 0 0
\(820\) 20.0662 + 3.87062i 0.700743 + 0.135168i
\(821\) 16.9782i 0.592542i −0.955104 0.296271i \(-0.904257\pi\)
0.955104 0.296271i \(-0.0957432\pi\)
\(822\) 0 0
\(823\) 5.17146i 0.180266i −0.995930 0.0901329i \(-0.971271\pi\)
0.995930 0.0901329i \(-0.0287292\pi\)
\(824\) 15.4661 52.6282i 0.538788 1.83339i
\(825\) 0 0
\(826\) −5.92468 + 61.9961i −0.206146 + 2.15712i
\(827\) 0.733529i 0.0255073i −0.999919 0.0127536i \(-0.995940\pi\)
0.999919 0.0127536i \(-0.00405972\pi\)
\(828\) 0 0
\(829\) 18.3783 0.638304 0.319152 0.947703i \(-0.396602\pi\)
0.319152 + 0.947703i \(0.396602\pi\)
\(830\) 17.6763 + 1.68924i 0.613553 + 0.0586345i
\(831\) 0 0
\(832\) −10.1021 6.49875i −0.350226 0.225304i
\(833\) 85.8113 2.97319
\(834\) 0 0
\(835\) 54.2942i 1.87893i
\(836\) 23.5712 + 19.2974i 0.815228 + 0.667414i
\(837\) 0 0
\(838\) −4.48785 + 46.9610i −0.155030 + 1.62224i
\(839\) −37.9165 −1.30902 −0.654511 0.756052i \(-0.727125\pi\)
−0.654511 + 0.756052i \(0.727125\pi\)
\(840\) 0 0
\(841\) −2.70187 −0.0931678
\(842\) −0.124989 + 1.30789i −0.00430739 + 0.0450727i
\(843\) 0 0
\(844\) 4.25412 22.0543i 0.146433 0.759142i
\(845\) 28.1055i 0.966858i
\(846\) 0 0
\(847\) 5.82519i 0.200156i
\(848\) 37.3932 + 14.9832i 1.28409 + 0.514525i
\(849\) 0 0
\(850\) −1.31529 + 13.7632i −0.0451141 + 0.472075i
\(851\) 23.3207i 0.799423i
\(852\) 0 0
\(853\) 46.5801i 1.59487i 0.603404 + 0.797436i \(0.293811\pi\)
−0.603404 + 0.797436i \(0.706189\pi\)
\(854\) 1.71883 17.9858i 0.0588170 0.615463i
\(855\) 0 0
\(856\) −5.53120 1.62548i −0.189053 0.0555578i
\(857\) 25.6585i 0.876477i 0.898859 + 0.438238i \(0.144397\pi\)
−0.898859 + 0.438238i \(0.855603\pi\)
\(858\) 0 0
\(859\) −15.5918 −0.531986 −0.265993 0.963975i \(-0.585700\pi\)
−0.265993 + 0.963975i \(0.585700\pi\)
\(860\) −0.338996 + 1.75743i −0.0115597 + 0.0599280i
\(861\) 0 0
\(862\) 4.64087 48.5622i 0.158069 1.65404i
\(863\) 31.1083 1.05894 0.529470 0.848329i \(-0.322391\pi\)
0.529470 + 0.848329i \(0.322391\pi\)
\(864\) 0 0
\(865\) 1.79147i 0.0609118i
\(866\) 35.0620 + 3.35072i 1.19146 + 0.113862i
\(867\) 0 0
\(868\) −3.14597 + 16.3094i −0.106781 + 0.553579i
\(869\) 18.2058 0.617588
\(870\) 0 0
\(871\) 11.0711i 0.375128i
\(872\) 14.3804 48.9337i 0.486981 1.65710i
\(873\) 0 0
\(874\) −11.5921 7.77424i −0.392110 0.262968i
\(875\) −39.7620 −1.34420
\(876\) 0 0
\(877\) −0.487909 −0.0164755 −0.00823776 0.999966i \(-0.502622\pi\)
−0.00823776 + 0.999966i \(0.502622\pi\)
\(878\) 2.75962 28.8768i 0.0931327 0.974544i
\(879\) 0 0
\(880\) −13.5978 + 33.9356i −0.458381 + 1.14397i
\(881\) 13.5269 0.455732 0.227866 0.973693i \(-0.426825\pi\)
0.227866 + 0.973693i \(0.426825\pi\)
\(882\) 0 0
\(883\) 34.7988 1.17107 0.585537 0.810646i \(-0.300884\pi\)
0.585537 + 0.810646i \(0.300884\pi\)
\(884\) 15.6575 + 3.02022i 0.526619 + 0.101581i
\(885\) 0 0
\(886\) 3.49592 36.5815i 0.117448 1.22898i
\(887\) −18.9849 −0.637449 −0.318725 0.947847i \(-0.603255\pi\)
−0.318725 + 0.947847i \(0.603255\pi\)
\(888\) 0 0
\(889\) 60.1377i 2.01696i
\(890\) 4.95965 51.8979i 0.166248 1.73962i
\(891\) 0 0
\(892\) 11.5195 + 2.22202i 0.385701 + 0.0743989i
\(893\) −1.40732 + 2.60400i −0.0470942 + 0.0871397i
\(894\) 0 0
\(895\) 49.0321 1.63896
\(896\) −42.7802 33.6798i −1.42919 1.12516i
\(897\) 0 0
\(898\) 51.3574 + 4.90799i 1.71382 + 0.163782i
\(899\) −8.84984 −0.295159
\(900\) 0 0
\(901\) −53.4773 −1.78159
\(902\) −19.2182 1.83659i −0.639895 0.0611518i
\(903\) 0 0
\(904\) 15.0425 + 4.42061i 0.500305 + 0.147027i
\(905\) 30.9574i 1.02906i
\(906\) 0 0
\(907\) 20.6905i 0.687016i 0.939150 + 0.343508i \(0.111615\pi\)
−0.939150 + 0.343508i \(0.888385\pi\)
\(908\) 5.22308 27.0777i 0.173334 0.898603i
\(909\) 0 0
\(910\) 2.54270 26.6069i 0.0842896 0.882010i
\(911\) 29.8333 0.988420 0.494210 0.869342i \(-0.335457\pi\)
0.494210 + 0.869342i \(0.335457\pi\)
\(912\) 0 0
\(913\) −16.7746 −0.555160
\(914\) −3.13161 + 32.7693i −0.103584 + 1.08391i
\(915\) 0 0
\(916\) −2.93920 + 15.2375i −0.0971138 + 0.503461i
\(917\) 60.5500i 1.99954i
\(918\) 0 0
\(919\) 35.6710i 1.17668i 0.808615 + 0.588338i \(0.200218\pi\)
−0.808615 + 0.588338i \(0.799782\pi\)
\(920\) 4.72285 16.0709i 0.155708 0.529843i
\(921\) 0 0
\(922\) 20.1098 + 1.92180i 0.662280 + 0.0632911i
\(923\) −14.6361 −0.481753
\(924\) 0 0
\(925\) 18.9625 0.623484
\(926\) 22.0005 + 2.10249i 0.722981 + 0.0690920i
\(927\) 0 0
\(928\) 13.3027 25.7794i 0.436682 0.846251i
\(929\) 5.05272 0.165774 0.0828872 0.996559i \(-0.473586\pi\)
0.0828872 + 0.996559i \(0.473586\pi\)
\(930\) 0 0
\(931\) −61.9687 33.4907i −2.03094 1.09761i
\(932\) 46.2856 + 8.92814i 1.51613 + 0.292451i
\(933\) 0 0
\(934\) −1.16626 + 12.2038i −0.0381612 + 0.399320i
\(935\) 48.5325i 1.58718i
\(936\) 0 0
\(937\) 5.91078 0.193097 0.0965484 0.995328i \(-0.469220\pi\)
0.0965484 + 0.995328i \(0.469220\pi\)
\(938\) −4.77395 + 49.9548i −0.155875 + 1.63108i
\(939\) 0 0
\(940\) −3.48794 0.672798i −0.113764 0.0219443i
\(941\) 19.2287 0.626837 0.313418 0.949615i \(-0.398526\pi\)
0.313418 + 0.949615i \(0.398526\pi\)
\(942\) 0 0
\(943\) 8.84559 0.288052
\(944\) −13.6143 + 33.9767i −0.443107 + 1.10585i
\(945\) 0 0
\(946\) 0.160852 1.68316i 0.00522975 0.0547243i
\(947\) −26.5034 −0.861245 −0.430623 0.902532i \(-0.641706\pi\)
−0.430623 + 0.902532i \(0.641706\pi\)
\(948\) 0 0
\(949\) −10.7519 −0.349022
\(950\) 6.32140 9.42580i 0.205093 0.305813i
\(951\) 0 0
\(952\) 69.3475 + 20.3795i 2.24757 + 0.660504i
\(953\) 37.0464i 1.20005i 0.799981 + 0.600025i \(0.204843\pi\)
−0.799981 + 0.600025i \(0.795157\pi\)
\(954\) 0 0
\(955\) −45.6703 −1.47786
\(956\) −5.06345 + 26.2501i −0.163764 + 0.848990i
\(957\) 0 0
\(958\) −4.80409 0.459105i −0.155213 0.0148330i
\(959\) 6.35694i 0.205276i
\(960\) 0 0
\(961\) −28.0219 −0.903931
\(962\) 2.08058 21.7712i 0.0670805 0.701932i
\(963\) 0 0
\(964\) −7.56095 + 39.1978i −0.243522 + 1.26247i
\(965\) −28.9655 −0.932432
\(966\) 0 0
\(967\) 49.4739i 1.59097i −0.605970 0.795487i \(-0.707215\pi\)
0.605970 0.795487i \(-0.292785\pi\)
\(968\) 0.965299 3.28472i 0.0310259 0.105575i
\(969\) 0 0
\(970\) 4.66512 48.8159i 0.149788 1.56739i
\(971\) 13.1840i 0.423095i −0.977368 0.211548i \(-0.932150\pi\)
0.977368 0.211548i \(-0.0678503\pi\)
\(972\) 0 0
\(973\) 6.81840i 0.218588i
\(974\) −5.62521 + 58.8624i −0.180243 + 1.88607i
\(975\) 0 0
\(976\) 3.94967 9.85708i 0.126426 0.315517i
\(977\) 28.8518i 0.923049i 0.887127 + 0.461525i \(0.152697\pi\)
−0.887127 + 0.461525i \(0.847303\pi\)
\(978\) 0 0
\(979\) 49.2506i 1.57406i
\(980\) 16.0109 83.0042i 0.511449 2.65147i
\(981\) 0 0
\(982\) −1.75723 + 18.3877i −0.0560754 + 0.586775i
\(983\) −9.02606 −0.287887 −0.143943 0.989586i \(-0.545978\pi\)
−0.143943 + 0.989586i \(0.545978\pi\)
\(984\) 0 0
\(985\) −52.9476 −1.68705
\(986\) −3.66360 + 38.3361i −0.116673 + 1.22087i
\(987\) 0 0
\(988\) −10.1283 8.29191i −0.322226 0.263801i
\(989\) 0.774712i 0.0246344i
\(990\) 0 0
\(991\) −12.9609 −0.411717 −0.205858 0.978582i \(-0.565999\pi\)
−0.205858 + 0.978582i \(0.565999\pi\)
\(992\) −4.47661 + 8.67529i −0.142133 + 0.275441i
\(993\) 0 0
\(994\) −66.0410 6.31123i −2.09469 0.200180i
\(995\) −31.9015 −1.01135
\(996\) 0 0
\(997\) 5.01059i 0.158687i 0.996847 + 0.0793435i \(0.0252824\pi\)
−0.996847 + 0.0793435i \(0.974718\pi\)
\(998\) −0.958448 + 10.0292i −0.0303391 + 0.317470i
\(999\) 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.g.379.20 40
3.2 odd 2 456.2.e.a.379.21 yes 40
4.3 odd 2 5472.2.e.g.5167.33 40
8.3 odd 2 inner 1368.2.e.g.379.22 40
8.5 even 2 5472.2.e.g.5167.4 40
12.11 even 2 1824.2.e.a.1519.37 40
19.18 odd 2 inner 1368.2.e.g.379.21 40
24.5 odd 2 1824.2.e.a.1519.7 40
24.11 even 2 456.2.e.a.379.19 40
57.56 even 2 456.2.e.a.379.20 yes 40
76.75 even 2 5472.2.e.g.5167.3 40
152.37 odd 2 5472.2.e.g.5167.34 40
152.75 even 2 inner 1368.2.e.g.379.19 40
228.227 odd 2 1824.2.e.a.1519.8 40
456.227 odd 2 456.2.e.a.379.22 yes 40
456.341 even 2 1824.2.e.a.1519.38 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.2.e.a.379.19 40 24.11 even 2
456.2.e.a.379.20 yes 40 57.56 even 2
456.2.e.a.379.21 yes 40 3.2 odd 2
456.2.e.a.379.22 yes 40 456.227 odd 2
1368.2.e.g.379.19 40 152.75 even 2 inner
1368.2.e.g.379.20 40 1.1 even 1 trivial
1368.2.e.g.379.21 40 19.18 odd 2 inner
1368.2.e.g.379.22 40 8.3 odd 2 inner
1824.2.e.a.1519.7 40 24.5 odd 2
1824.2.e.a.1519.8 40 228.227 odd 2
1824.2.e.a.1519.37 40 12.11 even 2
1824.2.e.a.1519.38 40 456.341 even 2
5472.2.e.g.5167.3 40 76.75 even 2
5472.2.e.g.5167.4 40 8.5 even 2
5472.2.e.g.5167.33 40 4.3 odd 2
5472.2.e.g.5167.34 40 152.37 odd 2