Properties

Label 336.7.bh.e.241.1
Level $336$
Weight $7$
Character 336.241
Analytic conductor $77.298$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,7,Mod(145,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.145");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 336.bh (of order \(6\), degree \(2\), not 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: \(77.2981720963\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 82x^{6} - 165x^{5} + 5606x^{4} - 7807x^{3} + 102447x^{2} + 132594x + 1162084 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{4}\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 241.1
Root \(-1.59227 + 2.75789i\) of defining polynomial
Character \(\chi\) \(=\) 336.241
Dual form 336.7.bh.e.145.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(13.5000 + 7.79423i) q^{3} +(-181.505 + 104.792i) q^{5} +(223.761 + 259.961i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})\) \(q+(13.5000 + 7.79423i) q^{3} +(-181.505 + 104.792i) q^{5} +(223.761 + 259.961i) q^{7} +(121.500 + 210.444i) q^{9} +(460.778 - 798.091i) q^{11} -1794.79i q^{13} -3267.10 q^{15} +(7212.40 + 4164.08i) q^{17} +(1718.83 - 992.368i) q^{19} +(994.580 + 5253.52i) q^{21} +(5343.69 + 9255.54i) q^{23} +(14150.3 - 24509.1i) q^{25} +3788.00i q^{27} +39717.2 q^{29} +(15848.6 + 9150.17i) q^{31} +(12441.0 - 7182.82i) q^{33} +(-67855.8 - 23736.0i) q^{35} +(29140.0 + 50471.9i) q^{37} +(13989.0 - 24229.6i) q^{39} -73309.8i q^{41} -136517. q^{43} +(-44105.8 - 25464.5i) q^{45} +(20926.0 - 12081.6i) q^{47} +(-17510.7 + 116339. i) q^{49} +(64911.6 + 112430. i) q^{51} +(-12255.9 + 21227.9i) q^{53} +193144. i q^{55} +30939.0 q^{57} +(50090.5 + 28919.8i) q^{59} +(-329986. + 190517. i) q^{61} +(-27520.3 + 78674.6i) q^{63} +(188080. + 325763. i) q^{65} +(-97520.4 + 168910. i) q^{67} +166600. i q^{69} -226460. q^{71} +(-280254. - 161805. i) q^{73} +(382059. - 220582. i) q^{75} +(310577. - 58797.5i) q^{77} +(277989. + 481492. i) q^{79} +(-29524.5 + 51137.9i) q^{81} -529636. i q^{83} -1.74545e6 q^{85} +(536182. + 309565. i) q^{87} +(-41162.6 + 23765.2i) q^{89} +(466575. - 401604. i) q^{91} +(142637. + 247055. i) q^{93} +(-207985. + 360240. i) q^{95} +1.02234e6i q^{97} +223938. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 108 q^{3} - 42 q^{5} + 92 q^{7} + 972 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 108 q^{3} - 42 q^{5} + 92 q^{7} + 972 q^{9} - 126 q^{11} - 756 q^{15} - 2532 q^{17} - 19998 q^{19} - 5886 q^{21} + 15648 q^{23} + 42698 q^{25} + 129468 q^{29} + 42096 q^{31} - 3402 q^{33} - 73524 q^{35} + 9866 q^{37} - 29106 q^{39} + 71764 q^{43} - 10206 q^{45} - 86988 q^{47} + 314588 q^{49} - 22788 q^{51} + 391710 q^{53} - 359964 q^{57} + 553434 q^{59} - 1009104 q^{61} - 181278 q^{63} + 589452 q^{65} - 229762 q^{67} - 208488 q^{71} - 1249290 q^{73} + 1152846 q^{75} + 1009566 q^{77} - 693808 q^{79} - 236196 q^{81} - 1302600 q^{85} + 1747818 q^{87} - 1414692 q^{89} + 766410 q^{91} + 378864 q^{93} - 3047568 q^{95} - 61236 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 13.5000 + 7.79423i 0.500000 + 0.288675i
\(4\) 0 0
\(5\) −181.505 + 104.792i −1.45204 + 0.838338i −0.998597 0.0529456i \(-0.983139\pi\)
−0.453446 + 0.891284i \(0.649806\pi\)
\(6\) 0 0
\(7\) 223.761 + 259.961i 0.652365 + 0.757905i
\(8\) 0 0
\(9\) 121.500 + 210.444i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 460.778 798.091i 0.346189 0.599618i −0.639380 0.768891i \(-0.720809\pi\)
0.985569 + 0.169273i \(0.0541421\pi\)
\(12\) 0 0
\(13\) 1794.79i 0.816926i −0.912775 0.408463i \(-0.866065\pi\)
0.912775 0.408463i \(-0.133935\pi\)
\(14\) 0 0
\(15\) −3267.10 −0.968029
\(16\) 0 0
\(17\) 7212.40 + 4164.08i 1.46802 + 0.847564i 0.999359 0.0358113i \(-0.0114015\pi\)
0.468666 + 0.883376i \(0.344735\pi\)
\(18\) 0 0
\(19\) 1718.83 992.368i 0.250595 0.144681i −0.369442 0.929254i \(-0.620451\pi\)
0.620037 + 0.784573i \(0.287118\pi\)
\(20\) 0 0
\(21\) 994.580 + 5253.52i 0.107394 + 0.567274i
\(22\) 0 0
\(23\) 5343.69 + 9255.54i 0.439195 + 0.760708i 0.997628 0.0688416i \(-0.0219303\pi\)
−0.558432 + 0.829550i \(0.688597\pi\)
\(24\) 0 0
\(25\) 14150.3 24509.1i 0.905621 1.56858i
\(26\) 0 0
\(27\) 3788.00i 0.192450i
\(28\) 0 0
\(29\) 39717.2 1.62849 0.814244 0.580523i \(-0.197152\pi\)
0.814244 + 0.580523i \(0.197152\pi\)
\(30\) 0 0
\(31\) 15848.6 + 9150.17i 0.531992 + 0.307145i 0.741827 0.670591i \(-0.233960\pi\)
−0.209835 + 0.977737i \(0.567293\pi\)
\(32\) 0 0
\(33\) 12441.0 7182.82i 0.346189 0.199873i
\(34\) 0 0
\(35\) −67855.8 23736.0i −1.58264 0.553608i
\(36\) 0 0
\(37\) 29140.0 + 50471.9i 0.575286 + 0.996424i 0.996011 + 0.0892359i \(0.0284425\pi\)
−0.420725 + 0.907188i \(0.638224\pi\)
\(38\) 0 0
\(39\) 13989.0 24229.6i 0.235826 0.408463i
\(40\) 0 0
\(41\) 73309.8i 1.06368i −0.846845 0.531839i \(-0.821501\pi\)
0.846845 0.531839i \(-0.178499\pi\)
\(42\) 0 0
\(43\) −136517. −1.71704 −0.858522 0.512777i \(-0.828617\pi\)
−0.858522 + 0.512777i \(0.828617\pi\)
\(44\) 0 0
\(45\) −44105.8 25464.5i −0.484015 0.279446i
\(46\) 0 0
\(47\) 20926.0 12081.6i 0.201554 0.116367i −0.395826 0.918326i \(-0.629542\pi\)
0.597380 + 0.801958i \(0.296208\pi\)
\(48\) 0 0
\(49\) −17510.7 + 116339.i −0.148839 + 0.988861i
\(50\) 0 0
\(51\) 64911.6 + 112430.i 0.489341 + 0.847564i
\(52\) 0 0
\(53\) −12255.9 + 21227.9i −0.0823225 + 0.142587i −0.904247 0.427010i \(-0.859567\pi\)
0.821925 + 0.569596i \(0.192900\pi\)
\(54\) 0 0
\(55\) 193144.i 1.16090i
\(56\) 0 0
\(57\) 30939.0 0.167063
\(58\) 0 0
\(59\) 50090.5 + 28919.8i 0.243893 + 0.140812i 0.616965 0.786991i \(-0.288362\pi\)
−0.373072 + 0.927803i \(0.621695\pi\)
\(60\) 0 0
\(61\) −329986. + 190517.i −1.45380 + 0.839354i −0.998694 0.0510816i \(-0.983733\pi\)
−0.455109 + 0.890436i \(0.650400\pi\)
\(62\) 0 0
\(63\) −27520.3 + 78674.6i −0.110061 + 0.314639i
\(64\) 0 0
\(65\) 188080. + 325763.i 0.684860 + 1.18621i
\(66\) 0 0
\(67\) −97520.4 + 168910.i −0.324243 + 0.561606i −0.981359 0.192184i \(-0.938443\pi\)
0.657116 + 0.753790i \(0.271776\pi\)
\(68\) 0 0
\(69\) 166600.i 0.507139i
\(70\) 0 0
\(71\) −226460. −0.632726 −0.316363 0.948638i \(-0.602462\pi\)
−0.316363 + 0.948638i \(0.602462\pi\)
\(72\) 0 0
\(73\) −280254. 161805.i −0.720416 0.415933i 0.0944896 0.995526i \(-0.469878\pi\)
−0.814906 + 0.579593i \(0.803211\pi\)
\(74\) 0 0
\(75\) 382059. 220582.i 0.905621 0.522860i
\(76\) 0 0
\(77\) 310577. 58797.5i 0.680295 0.128791i
\(78\) 0 0
\(79\) 277989. + 481492.i 0.563828 + 0.976579i 0.997158 + 0.0753436i \(0.0240053\pi\)
−0.433329 + 0.901236i \(0.642661\pi\)
\(80\) 0 0
\(81\) −29524.5 + 51137.9i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 529636.i 0.926281i −0.886285 0.463141i \(-0.846722\pi\)
0.886285 0.463141i \(-0.153278\pi\)
\(84\) 0 0
\(85\) −1.74545e6 −2.84218
\(86\) 0 0
\(87\) 536182. + 309565.i 0.814244 + 0.470104i
\(88\) 0 0
\(89\) −41162.6 + 23765.2i −0.0583892 + 0.0337110i −0.528910 0.848678i \(-0.677399\pi\)
0.470521 + 0.882389i \(0.344066\pi\)
\(90\) 0 0
\(91\) 466575. 401604.i 0.619152 0.532934i
\(92\) 0 0
\(93\) 142637. + 247055.i 0.177331 + 0.307145i
\(94\) 0 0
\(95\) −207985. + 360240.i −0.242583 + 0.420167i
\(96\) 0 0
\(97\) 1.02234e6i 1.12017i 0.828437 + 0.560083i \(0.189231\pi\)
−0.828437 + 0.560083i \(0.810769\pi\)
\(98\) 0 0
\(99\) 223938. 0.230793
\(100\) 0 0
\(101\) 543849. + 313991.i 0.527854 + 0.304757i 0.740142 0.672450i \(-0.234758\pi\)
−0.212288 + 0.977207i \(0.568092\pi\)
\(102\) 0 0
\(103\) −743176. + 429073.i −0.680112 + 0.392663i −0.799897 0.600137i \(-0.795113\pi\)
0.119785 + 0.992800i \(0.461779\pi\)
\(104\) 0 0
\(105\) −731050. 849319.i −0.631509 0.733674i
\(106\) 0 0
\(107\) −755399. 1.30839e6i −0.616630 1.06804i −0.990096 0.140391i \(-0.955164\pi\)
0.373466 0.927644i \(-0.378169\pi\)
\(108\) 0 0
\(109\) 1.10063e6 1.90635e6i 0.849891 1.47205i −0.0314137 0.999506i \(-0.510001\pi\)
0.881305 0.472548i \(-0.156666\pi\)
\(110\) 0 0
\(111\) 908494.i 0.664283i
\(112\) 0 0
\(113\) 2.31425e6 1.60389 0.801946 0.597397i \(-0.203798\pi\)
0.801946 + 0.597397i \(0.203798\pi\)
\(114\) 0 0
\(115\) −1.93982e6 1.11995e6i −1.27546 0.736388i
\(116\) 0 0
\(117\) 377702. 218066.i 0.235826 0.136154i
\(118\) 0 0
\(119\) 531356. + 2.80671e6i 0.315315 + 1.66554i
\(120\) 0 0
\(121\) 461147. + 798731.i 0.260306 + 0.450863i
\(122\) 0 0
\(123\) 571393. 989682.i 0.307057 0.531839i
\(124\) 0 0
\(125\) 2.65662e6i 1.36019i
\(126\) 0 0
\(127\) 1.08748e6 0.530898 0.265449 0.964125i \(-0.414480\pi\)
0.265449 + 0.964125i \(0.414480\pi\)
\(128\) 0 0
\(129\) −1.84298e6 1.06404e6i −0.858522 0.495668i
\(130\) 0 0
\(131\) −2.58564e6 + 1.49282e6i −1.15015 + 0.664039i −0.948923 0.315506i \(-0.897826\pi\)
−0.201225 + 0.979545i \(0.564492\pi\)
\(132\) 0 0
\(133\) 642585. + 224776.i 0.273134 + 0.0955422i
\(134\) 0 0
\(135\) −396952. 687542.i −0.161338 0.279446i
\(136\) 0 0
\(137\) 833850. 1.44427e6i 0.324285 0.561678i −0.657083 0.753819i \(-0.728210\pi\)
0.981367 + 0.192141i \(0.0615431\pi\)
\(138\) 0 0
\(139\) 3.54942e6i 1.32164i 0.750544 + 0.660820i \(0.229791\pi\)
−0.750544 + 0.660820i \(0.770209\pi\)
\(140\) 0 0
\(141\) 376667. 0.134369
\(142\) 0 0
\(143\) −1.43240e6 826998.i −0.489843 0.282811i
\(144\) 0 0
\(145\) −7.20888e6 + 4.16205e6i −2.36463 + 1.36522i
\(146\) 0 0
\(147\) −1.14316e6 + 1.43409e6i −0.359879 + 0.451465i
\(148\) 0 0
\(149\) 2.02935e6 + 3.51494e6i 0.613477 + 1.06257i 0.990650 + 0.136430i \(0.0435630\pi\)
−0.377173 + 0.926143i \(0.623104\pi\)
\(150\) 0 0
\(151\) −2.76232e6 + 4.78447e6i −0.802310 + 1.38964i 0.115782 + 0.993275i \(0.463063\pi\)
−0.918092 + 0.396368i \(0.870271\pi\)
\(152\) 0 0
\(153\) 2.02374e6i 0.565043i
\(154\) 0 0
\(155\) −3.83547e6 −1.02997
\(156\) 0 0
\(157\) 4.69617e6 + 2.71134e6i 1.21351 + 0.700623i 0.963523 0.267625i \(-0.0862390\pi\)
0.249991 + 0.968248i \(0.419572\pi\)
\(158\) 0 0
\(159\) −330910. + 191051.i −0.0823225 + 0.0475289i
\(160\) 0 0
\(161\) −1.21037e6 + 3.46018e6i −0.290029 + 0.829128i
\(162\) 0 0
\(163\) 1.70824e6 + 2.95875e6i 0.394444 + 0.683197i 0.993030 0.117862i \(-0.0376039\pi\)
−0.598586 + 0.801058i \(0.704271\pi\)
\(164\) 0 0
\(165\) −1.50541e6 + 2.60744e6i −0.335122 + 0.580448i
\(166\) 0 0
\(167\) 8.61704e6i 1.85016i 0.379777 + 0.925078i \(0.376001\pi\)
−0.379777 + 0.925078i \(0.623999\pi\)
\(168\) 0 0
\(169\) 1.60555e6 0.332632
\(170\) 0 0
\(171\) 417676. + 241145.i 0.0835317 + 0.0482270i
\(172\) 0 0
\(173\) −4.46734e6 + 2.57922e6i −0.862801 + 0.498138i −0.864949 0.501859i \(-0.832649\pi\)
0.00214848 + 0.999998i \(0.499316\pi\)
\(174\) 0 0
\(175\) 9.53771e6 1.80565e6i 1.77963 0.336914i
\(176\) 0 0
\(177\) 450815. + 780834.i 0.0812977 + 0.140812i
\(178\) 0 0
\(179\) 4.41115e6 7.64034e6i 0.769118 1.33215i −0.168924 0.985629i \(-0.554029\pi\)
0.938042 0.346522i \(-0.112637\pi\)
\(180\) 0 0
\(181\) 6.71665e6i 1.13270i −0.824163 0.566352i \(-0.808354\pi\)
0.824163 0.566352i \(-0.191646\pi\)
\(182\) 0 0
\(183\) −5.93974e6 −0.969203
\(184\) 0 0
\(185\) −1.05781e7 6.10728e6i −1.67068 0.964568i
\(186\) 0 0
\(187\) 6.64664e6 3.83744e6i 1.01643 0.586836i
\(188\) 0 0
\(189\) −984732. + 847607.i −0.145859 + 0.125548i
\(190\) 0 0
\(191\) −686211. 1.18855e6i −0.0984822 0.170576i 0.812574 0.582858i \(-0.198065\pi\)
−0.911057 + 0.412281i \(0.864732\pi\)
\(192\) 0 0
\(193\) 1.36111e6 2.35751e6i 0.189331 0.327931i −0.755696 0.654922i \(-0.772701\pi\)
0.945027 + 0.326991i \(0.106035\pi\)
\(194\) 0 0
\(195\) 5.86374e6i 0.790808i
\(196\) 0 0
\(197\) −3.38161e6 −0.442308 −0.221154 0.975239i \(-0.570982\pi\)
−0.221154 + 0.975239i \(0.570982\pi\)
\(198\) 0 0
\(199\) −8.34464e6 4.81778e6i −1.05888 0.611347i −0.133760 0.991014i \(-0.542705\pi\)
−0.925123 + 0.379667i \(0.876039\pi\)
\(200\) 0 0
\(201\) −2.63305e6 + 1.52019e6i −0.324243 + 0.187202i
\(202\) 0 0
\(203\) 8.88717e6 + 1.03249e7i 1.06237 + 1.23424i
\(204\) 0 0
\(205\) 7.68229e6 + 1.33061e7i 0.891722 + 1.54451i
\(206\) 0 0
\(207\) −1.29852e6 + 2.24910e6i −0.146398 + 0.253569i
\(208\) 0 0
\(209\) 1.82905e6i 0.200348i
\(210\) 0 0
\(211\) −6.59114e6 −0.701638 −0.350819 0.936443i \(-0.614097\pi\)
−0.350819 + 0.936443i \(0.614097\pi\)
\(212\) 0 0
\(213\) −3.05721e6 1.76508e6i −0.316363 0.182652i
\(214\) 0 0
\(215\) 2.47786e7 1.43059e7i 2.49322 1.43946i
\(216\) 0 0
\(217\) 1.16760e6 + 6.16747e6i 0.114266 + 0.603570i
\(218\) 0 0
\(219\) −2.52229e6 4.36873e6i −0.240139 0.415933i
\(220\) 0 0
\(221\) 7.47364e6 1.29447e7i 0.692397 1.19927i
\(222\) 0 0
\(223\) 6.24541e6i 0.563178i −0.959535 0.281589i \(-0.909138\pi\)
0.959535 0.281589i \(-0.0908615\pi\)
\(224\) 0 0
\(225\) 6.87706e6 0.603747
\(226\) 0 0
\(227\) −7.03151e6 4.05964e6i −0.601134 0.347065i 0.168354 0.985727i \(-0.446155\pi\)
−0.769487 + 0.638662i \(0.779488\pi\)
\(228\) 0 0
\(229\) 2.91787e6 1.68463e6i 0.242974 0.140281i −0.373569 0.927602i \(-0.621866\pi\)
0.616543 + 0.787321i \(0.288533\pi\)
\(230\) 0 0
\(231\) 4.65107e6 + 1.62694e6i 0.377326 + 0.131989i
\(232\) 0 0
\(233\) 821960. + 1.42368e6i 0.0649805 + 0.112550i 0.896685 0.442668i \(-0.145968\pi\)
−0.831705 + 0.555218i \(0.812635\pi\)
\(234\) 0 0
\(235\) −2.53212e6 + 4.38576e6i −0.195110 + 0.337941i
\(236\) 0 0
\(237\) 8.66685e6i 0.651053i
\(238\) 0 0
\(239\) 5.10928e6 0.374254 0.187127 0.982336i \(-0.440082\pi\)
0.187127 + 0.982336i \(0.440082\pi\)
\(240\) 0 0
\(241\) −1.49250e7 8.61698e6i −1.06626 0.615607i −0.139105 0.990278i \(-0.544423\pi\)
−0.927158 + 0.374670i \(0.877756\pi\)
\(242\) 0 0
\(243\) −797162. + 460241.i −0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) −9.01308e6 2.29511e7i −0.612879 1.56065i
\(246\) 0 0
\(247\) −1.78109e6 3.08493e6i −0.118194 0.204718i
\(248\) 0 0
\(249\) 4.12810e6 7.15008e6i 0.267394 0.463141i
\(250\) 0 0
\(251\) 576684.i 0.0364684i −0.999834 0.0182342i \(-0.994196\pi\)
0.999834 0.0182342i \(-0.00580445\pi\)
\(252\) 0 0
\(253\) 9.84902e6 0.608179
\(254\) 0 0
\(255\) −2.35636e7 1.36045e7i −1.42109 0.820467i
\(256\) 0 0
\(257\) 1.27238e7 7.34607e6i 0.749577 0.432769i −0.0759639 0.997111i \(-0.524203\pi\)
0.825541 + 0.564342i \(0.190870\pi\)
\(258\) 0 0
\(259\) −6.60034e6 + 1.88689e7i −0.379898 + 1.08604i
\(260\) 0 0
\(261\) 4.82564e6 + 8.35825e6i 0.271415 + 0.470104i
\(262\) 0 0
\(263\) −4.02385e6 + 6.96951e6i −0.221195 + 0.383120i −0.955171 0.296055i \(-0.904329\pi\)
0.733976 + 0.679175i \(0.237662\pi\)
\(264\) 0 0
\(265\) 5.13730e6i 0.276056i
\(266\) 0 0
\(267\) −740926. −0.0389261
\(268\) 0 0
\(269\) 1.85745e7 + 1.07240e7i 0.954246 + 0.550934i 0.894397 0.447274i \(-0.147605\pi\)
0.0598484 + 0.998207i \(0.480938\pi\)
\(270\) 0 0
\(271\) −1.50184e7 + 8.67088e6i −0.754598 + 0.435667i −0.827353 0.561682i \(-0.810154\pi\)
0.0727548 + 0.997350i \(0.476821\pi\)
\(272\) 0 0
\(273\) 9.42895e6 1.78506e6i 0.463421 0.0877333i
\(274\) 0 0
\(275\) −1.30403e7 2.25865e7i −0.627033 1.08605i
\(276\) 0 0
\(277\) 1.11394e7 1.92941e7i 0.524112 0.907788i −0.475494 0.879719i \(-0.657731\pi\)
0.999606 0.0280691i \(-0.00893583\pi\)
\(278\) 0 0
\(279\) 4.44698e6i 0.204764i
\(280\) 0 0
\(281\) −2.42003e7 −1.09069 −0.545346 0.838211i \(-0.683602\pi\)
−0.545346 + 0.838211i \(0.683602\pi\)
\(282\) 0 0
\(283\) −1.31661e7 7.60147e6i −0.580896 0.335381i 0.180593 0.983558i \(-0.442198\pi\)
−0.761490 + 0.648177i \(0.775532\pi\)
\(284\) 0 0
\(285\) −5.61559e6 + 3.24216e6i −0.242583 + 0.140056i
\(286\) 0 0
\(287\) 1.90577e7 1.64039e7i 0.806167 0.693907i
\(288\) 0 0
\(289\) 2.26104e7 + 3.91623e7i 0.936730 + 1.62246i
\(290\) 0 0
\(291\) −7.96839e6 + 1.38017e7i −0.323364 + 0.560083i
\(292\) 0 0
\(293\) 1.75547e7i 0.697894i 0.937142 + 0.348947i \(0.113461\pi\)
−0.937142 + 0.348947i \(0.886539\pi\)
\(294\) 0 0
\(295\) −1.21223e7 −0.472191
\(296\) 0 0
\(297\) 3.02317e6 + 1.74543e6i 0.115396 + 0.0666242i
\(298\) 0 0
\(299\) 1.66117e7 9.59078e6i 0.621442 0.358790i
\(300\) 0 0
\(301\) −3.05472e7 3.54891e7i −1.12014 1.30136i
\(302\) 0 0
\(303\) 4.89464e6 + 8.47776e6i 0.175951 + 0.304757i
\(304\) 0 0
\(305\) 3.99295e7 6.91599e7i 1.40732 2.43756i
\(306\) 0 0
\(307\) 1.15281e7i 0.398420i −0.979957 0.199210i \(-0.936162\pi\)
0.979957 0.199210i \(-0.0638375\pi\)
\(308\) 0 0
\(309\) −1.33772e7 −0.453408
\(310\) 0 0
\(311\) 2.90011e7 + 1.67438e7i 0.964124 + 0.556637i 0.897440 0.441137i \(-0.145425\pi\)
0.0666840 + 0.997774i \(0.478758\pi\)
\(312\) 0 0
\(313\) −5.17516e7 + 2.98788e7i −1.68768 + 0.974385i −0.731399 + 0.681950i \(0.761132\pi\)
−0.956286 + 0.292435i \(0.905535\pi\)
\(314\) 0 0
\(315\) −3.24939e6 1.71638e7i −0.103961 0.549138i
\(316\) 0 0
\(317\) −3.57873e6 6.19855e6i −0.112344 0.194586i 0.804371 0.594128i \(-0.202503\pi\)
−0.916715 + 0.399541i \(0.869169\pi\)
\(318\) 0 0
\(319\) 1.83008e7 3.16979e7i 0.563765 0.976470i
\(320\) 0 0
\(321\) 2.35510e7i 0.712024i
\(322\) 0 0
\(323\) 1.65292e7 0.490506
\(324\) 0 0
\(325\) −4.39886e7 2.53968e7i −1.28141 0.739825i
\(326\) 0 0
\(327\) 2.97171e7 1.71572e7i 0.849891 0.490685i
\(328\) 0 0
\(329\) 7.82317e6 + 2.73654e6i 0.219682 + 0.0768448i
\(330\) 0 0
\(331\) −1.98576e7 3.43944e7i −0.547574 0.948427i −0.998440 0.0558348i \(-0.982218\pi\)
0.450866 0.892592i \(-0.351115\pi\)
\(332\) 0 0
\(333\) −7.08101e6 + 1.22647e7i −0.191762 + 0.332141i
\(334\) 0 0
\(335\) 4.08775e7i 1.08730i
\(336\) 0 0
\(337\) 5.87064e7 1.53390 0.766948 0.641710i \(-0.221775\pi\)
0.766948 + 0.641710i \(0.221775\pi\)
\(338\) 0 0
\(339\) 3.12424e7 + 1.80378e7i 0.801946 + 0.463004i
\(340\) 0 0
\(341\) 1.46053e7 8.43240e6i 0.368340 0.212661i
\(342\) 0 0
\(343\) −3.41618e7 + 2.14800e7i −0.846560 + 0.532293i
\(344\) 0 0
\(345\) −1.74584e7 3.02388e7i −0.425154 0.736388i
\(346\) 0 0
\(347\) 1.62185e7 2.80912e7i 0.388170 0.672330i −0.604034 0.796959i \(-0.706441\pi\)
0.992203 + 0.124629i \(0.0397741\pi\)
\(348\) 0 0
\(349\) 1.54009e7i 0.362302i −0.983455 0.181151i \(-0.942018\pi\)
0.983455 0.181151i \(-0.0579823\pi\)
\(350\) 0 0
\(351\) 6.79864e6 0.157217
\(352\) 0 0
\(353\) 4.08353e7 + 2.35763e7i 0.928350 + 0.535983i 0.886289 0.463132i \(-0.153274\pi\)
0.0420604 + 0.999115i \(0.486608\pi\)
\(354\) 0 0
\(355\) 4.11037e7 2.37312e7i 0.918746 0.530438i
\(356\) 0 0
\(357\) −1.47028e7 + 4.20321e7i −0.323143 + 0.923796i
\(358\) 0 0
\(359\) 6.82935e6 + 1.18288e7i 0.147603 + 0.255656i 0.930341 0.366695i \(-0.119511\pi\)
−0.782738 + 0.622351i \(0.786177\pi\)
\(360\) 0 0
\(361\) −2.15534e7 + 3.73315e7i −0.458135 + 0.793513i
\(362\) 0 0
\(363\) 1.43772e7i 0.300575i
\(364\) 0 0
\(365\) 6.78236e7 1.39477
\(366\) 0 0
\(367\) 6.56532e7 + 3.79049e7i 1.32818 + 0.766826i 0.985018 0.172450i \(-0.0551682\pi\)
0.343163 + 0.939276i \(0.388502\pi\)
\(368\) 0 0
\(369\) 1.54276e7 8.90714e6i 0.307057 0.177280i
\(370\) 0 0
\(371\) −8.26083e6 + 1.56391e6i −0.161771 + 0.0306260i
\(372\) 0 0
\(373\) −3.25829e7 5.64352e7i −0.627860 1.08749i −0.987980 0.154580i \(-0.950598\pi\)
0.360120 0.932906i \(-0.382736\pi\)
\(374\) 0 0
\(375\) −2.07063e7 + 3.58644e7i −0.392653 + 0.680095i
\(376\) 0 0
\(377\) 7.12838e7i 1.33035i
\(378\) 0 0
\(379\) 4.57899e6 0.0841109 0.0420555 0.999115i \(-0.486609\pi\)
0.0420555 + 0.999115i \(0.486609\pi\)
\(380\) 0 0
\(381\) 1.46810e7 + 8.47609e6i 0.265449 + 0.153257i
\(382\) 0 0
\(383\) 5.46037e7 3.15254e7i 0.971909 0.561132i 0.0720912 0.997398i \(-0.477033\pi\)
0.899818 + 0.436266i \(0.143699\pi\)
\(384\) 0 0
\(385\) −5.02099e7 + 4.32181e7i −0.879848 + 0.757328i
\(386\) 0 0
\(387\) −1.65868e7 2.87292e7i −0.286174 0.495668i
\(388\) 0 0
\(389\) −2.11662e7 + 3.66610e7i −0.359580 + 0.622810i −0.987891 0.155152i \(-0.950413\pi\)
0.628311 + 0.777962i \(0.283747\pi\)
\(390\) 0 0
\(391\) 8.90062e7i 1.48898i
\(392\) 0 0
\(393\) −4.65415e7 −0.766766
\(394\) 0 0
\(395\) −1.00913e8 5.82622e7i −1.63741 0.945357i
\(396\) 0 0
\(397\) −1.22475e7 + 7.07107e6i −0.195738 + 0.113009i −0.594666 0.803973i \(-0.702716\pi\)
0.398928 + 0.916982i \(0.369382\pi\)
\(398\) 0 0
\(399\) 6.92294e6 + 8.04293e6i 0.108986 + 0.126618i
\(400\) 0 0
\(401\) 3.00770e7 + 5.20949e7i 0.466446 + 0.807908i 0.999265 0.0383207i \(-0.0122008\pi\)
−0.532819 + 0.846229i \(0.678868\pi\)
\(402\) 0 0
\(403\) 1.64226e7 2.84448e7i 0.250915 0.434598i
\(404\) 0 0
\(405\) 1.23758e7i 0.186297i
\(406\) 0 0
\(407\) 5.37082e7 0.796632
\(408\) 0 0
\(409\) −3.29559e7 1.90271e7i −0.481685 0.278101i 0.239434 0.970913i \(-0.423038\pi\)
−0.721118 + 0.692812i \(0.756372\pi\)
\(410\) 0 0
\(411\) 2.25140e7 1.29984e7i 0.324285 0.187226i
\(412\) 0 0
\(413\) 3.69030e6 + 1.94927e7i 0.0523855 + 0.276708i
\(414\) 0 0
\(415\) 5.55017e7 + 9.61318e7i 0.776537 + 1.34500i
\(416\) 0 0
\(417\) −2.76650e7 + 4.79172e7i −0.381525 + 0.660820i
\(418\) 0 0
\(419\) 1.11966e8i 1.52211i −0.648690 0.761053i \(-0.724683\pi\)
0.648690 0.761053i \(-0.275317\pi\)
\(420\) 0 0
\(421\) 6.22296e7 0.833970 0.416985 0.908913i \(-0.363087\pi\)
0.416985 + 0.908913i \(0.363087\pi\)
\(422\) 0 0
\(423\) 5.08501e6 + 2.93583e6i 0.0671847 + 0.0387891i
\(424\) 0 0
\(425\) 2.04116e8 1.17846e8i 2.65895 1.53514i
\(426\) 0 0
\(427\) −1.23365e8 4.31531e7i −1.58456 0.554279i
\(428\) 0 0
\(429\) −1.28916e7 2.23290e7i −0.163281 0.282811i
\(430\) 0 0
\(431\) −6.79249e7 + 1.17649e8i −0.848394 + 1.46946i 0.0342477 + 0.999413i \(0.489096\pi\)
−0.882641 + 0.470047i \(0.844237\pi\)
\(432\) 0 0
\(433\) 4.12757e7i 0.508430i 0.967148 + 0.254215i \(0.0818171\pi\)
−0.967148 + 0.254215i \(0.918183\pi\)
\(434\) 0 0
\(435\) −1.29760e8 −1.57642
\(436\) 0 0
\(437\) 1.83698e7 + 1.06058e7i 0.220120 + 0.127087i
\(438\) 0 0
\(439\) −9.91802e7 + 5.72617e7i −1.17228 + 0.676816i −0.954216 0.299118i \(-0.903308\pi\)
−0.218064 + 0.975934i \(0.569974\pi\)
\(440\) 0 0
\(441\) −2.66103e7 + 1.04501e7i −0.310266 + 0.121844i
\(442\) 0 0
\(443\) −6.30057e7 1.09129e8i −0.724717 1.25525i −0.959090 0.283100i \(-0.908637\pi\)
0.234373 0.972147i \(-0.424696\pi\)
\(444\) 0 0
\(445\) 4.98082e6 8.62703e6i 0.0565224 0.0978997i
\(446\) 0 0
\(447\) 6.32689e7i 0.708382i
\(448\) 0 0
\(449\) −4.74196e7 −0.523864 −0.261932 0.965086i \(-0.584360\pi\)
−0.261932 + 0.965086i \(0.584360\pi\)
\(450\) 0 0
\(451\) −5.85079e7 3.37795e7i −0.637800 0.368234i
\(452\) 0 0
\(453\) −7.45825e7 + 4.30602e7i −0.802310 + 0.463214i
\(454\) 0 0
\(455\) −4.26009e7 + 1.21787e8i −0.452257 + 1.29290i
\(456\) 0 0
\(457\) 2.42944e7 + 4.20792e7i 0.254541 + 0.440878i 0.964771 0.263092i \(-0.0847422\pi\)
−0.710230 + 0.703970i \(0.751409\pi\)
\(458\) 0 0
\(459\) −1.57735e7 + 2.73205e7i −0.163114 + 0.282521i
\(460\) 0 0
\(461\) 1.47655e7i 0.150712i −0.997157 0.0753558i \(-0.975991\pi\)
0.997157 0.0753558i \(-0.0240092\pi\)
\(462\) 0 0
\(463\) 1.02866e8 1.03640 0.518200 0.855259i \(-0.326602\pi\)
0.518200 + 0.855259i \(0.326602\pi\)
\(464\) 0 0
\(465\) −5.17788e7 2.98945e7i −0.514983 0.297326i
\(466\) 0 0
\(467\) −1.19585e8 + 6.90423e7i −1.17415 + 0.677899i −0.954655 0.297714i \(-0.903776\pi\)
−0.219500 + 0.975613i \(0.570443\pi\)
\(468\) 0 0
\(469\) −6.57314e7 + 1.24441e7i −0.637169 + 0.120627i
\(470\) 0 0
\(471\) 4.22655e7 + 7.32060e7i 0.404505 + 0.700623i
\(472\) 0 0
\(473\) −6.29041e7 + 1.08953e8i −0.594423 + 1.02957i
\(474\) 0 0
\(475\) 5.61693e7i 0.524105i
\(476\) 0 0
\(477\) −5.95638e6 −0.0548816
\(478\) 0 0
\(479\) 5.88901e6 + 3.40002e6i 0.0535841 + 0.0309368i 0.526553 0.850142i \(-0.323484\pi\)
−0.472969 + 0.881079i \(0.656818\pi\)
\(480\) 0 0
\(481\) 9.05862e7 5.23000e7i 0.814005 0.469966i
\(482\) 0 0
\(483\) −4.33095e7 + 3.72786e7i −0.384363 + 0.330840i
\(484\) 0 0
\(485\) −1.07134e8 1.85561e8i −0.939077 1.62653i
\(486\) 0 0
\(487\) 3.76363e7 6.51879e7i 0.325851 0.564391i −0.655833 0.754906i \(-0.727682\pi\)
0.981684 + 0.190515i \(0.0610157\pi\)
\(488\) 0 0
\(489\) 5.32575e7i 0.455465i
\(490\) 0 0
\(491\) 1.92123e8 1.62306 0.811532 0.584308i \(-0.198634\pi\)
0.811532 + 0.584308i \(0.198634\pi\)
\(492\) 0 0
\(493\) 2.86456e8 + 1.65386e8i 2.39066 + 1.38025i
\(494\) 0 0
\(495\) −4.06460e7 + 2.34670e7i −0.335122 + 0.193483i
\(496\) 0 0
\(497\) −5.06729e7 5.88707e7i −0.412769 0.479546i
\(498\) 0 0
\(499\) 7.28568e7 + 1.26192e8i 0.586366 + 1.01561i 0.994704 + 0.102784i \(0.0327751\pi\)
−0.408338 + 0.912831i \(0.633892\pi\)
\(500\) 0 0
\(501\) −6.71631e7 + 1.16330e8i −0.534094 + 0.925078i
\(502\) 0 0
\(503\) 1.82561e8i 1.43451i −0.696812 0.717254i \(-0.745399\pi\)
0.696812 0.717254i \(-0.254601\pi\)
\(504\) 0 0
\(505\) −1.31615e8 −1.02196
\(506\) 0 0
\(507\) 2.16750e7 + 1.25140e7i 0.166316 + 0.0960227i
\(508\) 0 0
\(509\) 1.05246e8 6.07636e7i 0.798088 0.460776i −0.0447143 0.999000i \(-0.514238\pi\)
0.842802 + 0.538224i \(0.180904\pi\)
\(510\) 0 0
\(511\) −2.06471e7 1.09061e8i −0.154737 0.817347i
\(512\) 0 0
\(513\) 3.75908e6 + 6.51093e6i 0.0278439 + 0.0482270i
\(514\) 0 0
\(515\) 8.99271e7 1.55758e8i 0.658368 1.14033i
\(516\) 0 0
\(517\) 2.22678e7i 0.161141i
\(518\) 0 0
\(519\) −8.04121e7 −0.575200
\(520\) 0 0
\(521\) −6.06815e7 3.50345e7i −0.429085 0.247732i 0.269872 0.962896i \(-0.413019\pi\)
−0.698957 + 0.715164i \(0.746352\pi\)
\(522\) 0 0
\(523\) −1.09457e8 + 6.31947e7i −0.765132 + 0.441749i −0.831135 0.556070i \(-0.812309\pi\)
0.0660031 + 0.997819i \(0.478975\pi\)
\(524\) 0 0
\(525\) 1.42833e8 + 4.99628e7i 0.987074 + 0.345278i
\(526\) 0 0
\(527\) 7.62041e7 + 1.31989e8i 0.520651 + 0.901794i
\(528\) 0 0
\(529\) 1.69079e7 2.92854e7i 0.114215 0.197826i
\(530\) 0 0
\(531\) 1.40550e7i 0.0938745i
\(532\) 0 0
\(533\) −1.31575e8 −0.868946
\(534\) 0 0
\(535\) 2.74218e8 + 1.58320e8i 1.79075 + 1.03389i
\(536\) 0 0
\(537\) 1.19101e8 6.87630e7i 0.769118 0.444050i
\(538\) 0 0
\(539\) 8.47802e7 + 6.75814e7i 0.541412 + 0.431580i
\(540\) 0 0
\(541\) −1.47236e7 2.55020e7i −0.0929869 0.161058i 0.815780 0.578363i \(-0.196308\pi\)
−0.908767 + 0.417305i \(0.862975\pi\)
\(542\) 0 0
\(543\) 5.23511e7 9.06747e7i 0.326984 0.566352i
\(544\) 0 0
\(545\) 4.61351e8i 2.84998i
\(546\) 0 0
\(547\) 2.00583e7 0.122555 0.0612777 0.998121i \(-0.480482\pi\)
0.0612777 + 0.998121i \(0.480482\pi\)
\(548\) 0 0
\(549\) −8.01866e7 4.62957e7i −0.484601 0.279785i
\(550\) 0 0
\(551\) 6.82671e7 3.94140e7i 0.408091 0.235611i
\(552\) 0 0
\(553\) −6.29659e7 + 1.80006e8i −0.372332 + 1.06441i
\(554\) 0 0
\(555\) −9.52031e7 1.64897e8i −0.556893 0.964568i
\(556\) 0 0
\(557\) −6.02294e7 + 1.04320e8i −0.348532 + 0.603676i −0.985989 0.166810i \(-0.946653\pi\)
0.637457 + 0.770486i \(0.279987\pi\)
\(558\) 0 0
\(559\) 2.45019e8i 1.40270i
\(560\) 0 0
\(561\) 1.19639e8 0.677619
\(562\) 0 0
\(563\) 1.59791e8 + 9.22556e7i 0.895423 + 0.516973i 0.875712 0.482833i \(-0.160392\pi\)
0.0197104 + 0.999806i \(0.493726\pi\)
\(564\) 0 0
\(565\) −4.20049e8 + 2.42516e8i −2.32892 + 1.34460i
\(566\) 0 0
\(567\) −1.99003e7 + 3.76746e6i −0.109172 + 0.0206681i
\(568\) 0 0
\(569\) −9.00390e7 1.55952e8i −0.488758 0.846554i 0.511158 0.859487i \(-0.329217\pi\)
−0.999916 + 0.0129327i \(0.995883\pi\)
\(570\) 0 0
\(571\) −1.50724e8 + 2.61062e8i −0.809609 + 1.40228i 0.103527 + 0.994627i \(0.466987\pi\)
−0.913135 + 0.407657i \(0.866346\pi\)
\(572\) 0 0
\(573\) 2.13940e7i 0.113717i
\(574\) 0 0
\(575\) 3.02460e8 1.59098
\(576\) 0 0
\(577\) −3.88168e7 2.24109e7i −0.202066 0.116663i 0.395553 0.918443i \(-0.370553\pi\)
−0.597619 + 0.801780i \(0.703886\pi\)
\(578\) 0 0
\(579\) 3.67500e7 2.12176e7i 0.189331 0.109310i
\(580\) 0 0
\(581\) 1.37685e8 1.18512e8i 0.702033 0.604274i
\(582\) 0 0
\(583\) 1.12945e7 + 1.95627e7i 0.0569983 + 0.0987240i
\(584\) 0 0
\(585\) −4.57033e7 + 7.91605e7i −0.228287 + 0.395404i
\(586\) 0 0
\(587\) 2.88473e8i 1.42623i 0.701045 + 0.713117i \(0.252717\pi\)
−0.701045 + 0.713117i \(0.747283\pi\)
\(588\) 0 0
\(589\) 3.63213e7 0.177753
\(590\) 0 0
\(591\) −4.56517e7 2.63570e7i −0.221154 0.127683i
\(592\) 0 0
\(593\) 2.25115e8 1.29970e8i 1.07954 0.623275i 0.148770 0.988872i \(-0.452468\pi\)
0.930773 + 0.365597i \(0.119135\pi\)
\(594\) 0 0
\(595\) −3.90565e8 4.53751e8i −1.85414 2.15410i
\(596\) 0 0
\(597\) −7.51017e7 1.30080e8i −0.352961 0.611347i
\(598\) 0 0
\(599\) −4.84290e7 + 8.38815e7i −0.225333 + 0.390289i −0.956419 0.291997i \(-0.905680\pi\)
0.731086 + 0.682285i \(0.239014\pi\)
\(600\) 0 0
\(601\) 9.67065e7i 0.445484i −0.974877 0.222742i \(-0.928499\pi\)
0.974877 0.222742i \(-0.0715008\pi\)
\(602\) 0 0
\(603\) −4.73949e7 −0.216162
\(604\) 0 0
\(605\) −1.67402e8 9.66493e7i −0.755951 0.436448i
\(606\) 0 0
\(607\) −1.33896e8 + 7.73047e7i −0.598688 + 0.345652i −0.768525 0.639820i \(-0.779009\pi\)
0.169837 + 0.985472i \(0.445676\pi\)
\(608\) 0 0
\(609\) 3.95019e7 + 2.08655e8i 0.174890 + 0.923798i
\(610\) 0 0
\(611\) −2.16839e7 3.75576e7i −0.0950635 0.164655i
\(612\) 0 0
\(613\) −3.80409e7 + 6.58887e7i −0.165146 + 0.286042i −0.936707 0.350114i \(-0.886143\pi\)
0.771561 + 0.636155i \(0.219476\pi\)
\(614\) 0 0
\(615\) 2.39510e8i 1.02967i
\(616\) 0 0
\(617\) −1.44709e7 −0.0616085 −0.0308043 0.999525i \(-0.509807\pi\)
−0.0308043 + 0.999525i \(0.509807\pi\)
\(618\) 0 0
\(619\) −3.92476e8 2.26596e8i −1.65478 0.955389i −0.975066 0.221914i \(-0.928769\pi\)
−0.679717 0.733475i \(-0.737897\pi\)
\(620\) 0 0
\(621\) −3.50599e7 + 2.02419e7i −0.146398 + 0.0845232i
\(622\) 0 0
\(623\) −1.53886e7 5.38294e6i −0.0636408 0.0222615i
\(624\) 0 0
\(625\) −5.72943e7 9.92366e7i −0.234677 0.406473i
\(626\) 0 0
\(627\) 1.42560e7 2.46921e7i 0.0578356 0.100174i
\(628\) 0 0
\(629\) 4.85365e8i 1.95037i
\(630\) 0 0
\(631\) −2.83654e8 −1.12902 −0.564508 0.825428i \(-0.690934\pi\)
−0.564508 + 0.825428i \(0.690934\pi\)
\(632\) 0 0
\(633\) −8.89804e7 5.13728e7i −0.350819 0.202545i
\(634\) 0 0
\(635\) −1.97384e8 + 1.13960e8i −0.770887 + 0.445072i
\(636\) 0 0
\(637\) 2.08803e8 + 3.14280e7i 0.807826 + 0.121590i
\(638\) 0 0
\(639\) −2.75148e7 4.76571e7i −0.105454 0.182652i
\(640\) 0 0
\(641\) 1.86195e7 3.22500e7i 0.0706960 0.122449i −0.828511 0.559973i \(-0.810811\pi\)
0.899207 + 0.437524i \(0.144145\pi\)
\(642\) 0 0
\(643\) 1.57727e7i 0.0593297i 0.999560 + 0.0296648i \(0.00944399\pi\)
−0.999560 + 0.0296648i \(0.990556\pi\)
\(644\) 0 0
\(645\) 4.46015e8 1.66215
\(646\) 0 0
\(647\) 4.25974e7 + 2.45936e7i 0.157279 + 0.0908049i 0.576574 0.817045i \(-0.304389\pi\)
−0.419295 + 0.907850i \(0.637723\pi\)
\(648\) 0 0
\(649\) 4.61613e7 2.66512e7i 0.168867 0.0974951i
\(650\) 0 0
\(651\) −3.23080e7 + 9.23614e7i −0.117103 + 0.334771i
\(652\) 0 0
\(653\) −9.52792e7 1.65028e8i −0.342183 0.592678i 0.642655 0.766156i \(-0.277833\pi\)
−0.984838 + 0.173477i \(0.944500\pi\)
\(654\) 0 0
\(655\) 3.12872e8 5.41910e8i 1.11338 1.92843i
\(656\) 0 0
\(657\) 7.86372e7i 0.277288i
\(658\) 0 0
\(659\) 2.19319e8 0.766338 0.383169 0.923678i \(-0.374833\pi\)
0.383169 + 0.923678i \(0.374833\pi\)
\(660\) 0 0
\(661\) −1.48603e8 8.57963e7i −0.514547 0.297074i 0.220154 0.975465i \(-0.429344\pi\)
−0.734701 + 0.678392i \(0.762677\pi\)
\(662\) 0 0
\(663\) 2.01788e8 1.16502e8i 0.692397 0.399756i
\(664\) 0 0
\(665\) −1.40188e8 + 2.65398e7i −0.476699 + 0.0902471i
\(666\) 0 0
\(667\) 2.12236e8 + 3.67604e8i 0.715224 + 1.23880i
\(668\) 0 0
\(669\) 4.86781e7 8.43130e7i 0.162576 0.281589i
\(670\) 0 0
\(671\) 3.51145e8i 1.16230i
\(672\) 0 0
\(673\) 3.97407e8 1.30374 0.651869 0.758332i \(-0.273985\pi\)
0.651869 + 0.758332i \(0.273985\pi\)
\(674\) 0 0
\(675\) 9.28403e7 + 5.36014e7i 0.301874 + 0.174287i
\(676\) 0 0
\(677\) 1.13243e8 6.53809e7i 0.364960 0.210710i −0.306294 0.951937i \(-0.599089\pi\)
0.671254 + 0.741227i \(0.265756\pi\)
\(678\) 0 0
\(679\) −2.65770e8 + 2.28761e8i −0.848979 + 0.730757i
\(680\) 0 0
\(681\) −6.32836e7 1.09610e8i −0.200378 0.347065i
\(682\) 0 0
\(683\) 1.22907e8 2.12882e8i 0.385759 0.668154i −0.606115 0.795377i \(-0.707273\pi\)
0.991874 + 0.127223i \(0.0406063\pi\)
\(684\) 0 0
\(685\) 3.49524e8i 1.08744i
\(686\) 0 0
\(687\) 5.25216e7 0.161983
\(688\) 0 0
\(689\) 3.80995e7 + 2.19968e7i 0.116483 + 0.0672513i
\(690\) 0 0
\(691\) −2.21758e8 + 1.28032e8i −0.672116 + 0.388046i −0.796878 0.604140i \(-0.793517\pi\)
0.124762 + 0.992187i \(0.460183\pi\)
\(692\) 0 0
\(693\) 5.01087e7 + 5.82153e7i 0.150561 + 0.174919i
\(694\) 0 0
\(695\) −3.71952e8 6.44240e8i −1.10798 1.91908i
\(696\) 0 0
\(697\) 3.05268e8 5.28740e8i 0.901536 1.56151i
\(698\) 0 0
\(699\) 2.56262e7i 0.0750330i
\(700\) 0 0
\(701\) 3.67117e7 0.106574 0.0532869 0.998579i \(-0.483030\pi\)
0.0532869 + 0.998579i \(0.483030\pi\)
\(702\) 0 0
\(703\) 1.00173e8 + 5.78351e7i 0.288328 + 0.166466i
\(704\) 0 0
\(705\) −6.83672e7 + 3.94718e7i −0.195110 + 0.112647i
\(706\) 0 0
\(707\) 4.00667e7 + 2.11639e8i 0.113377 + 0.598876i
\(708\) 0 0
\(709\) 5.84664e7 + 1.01267e8i 0.164047 + 0.284137i 0.936316 0.351158i \(-0.114212\pi\)
−0.772270 + 0.635295i \(0.780879\pi\)
\(710\) 0 0
\(711\) −6.75514e7 + 1.17002e8i −0.187943 + 0.325526i
\(712\) 0 0
\(713\) 1.95583e8i 0.539587i
\(714\) 0 0
\(715\) 3.46652e8 0.948365
\(716\) 0 0
\(717\) 6.89753e7 + 3.98229e7i 0.187127 + 0.108038i
\(718\) 0 0
\(719\) −2.27783e8 + 1.31511e8i −0.612823 + 0.353813i −0.774069 0.633101i \(-0.781782\pi\)
0.161247 + 0.986914i \(0.448449\pi\)
\(720\) 0 0
\(721\) −2.77837e8 9.71871e7i −0.741282 0.259300i
\(722\) 0 0
\(723\) −1.34325e8 2.32658e8i −0.355421 0.615607i
\(724\) 0 0
\(725\) 5.62011e8 9.73432e8i 1.47479 2.55441i
\(726\) 0 0
\(727\) 4.25452e7i 0.110726i 0.998466 + 0.0553628i \(0.0176315\pi\)
−0.998466 + 0.0553628i \(0.982368\pi\)
\(728\) 0 0
\(729\) −1.43489e7 −0.0370370
\(730\) 0 0
\(731\) −9.84616e8 5.68468e8i −2.52066 1.45531i
\(732\) 0 0
\(733\) −2.07737e8 + 1.19937e8i −0.527475 + 0.304538i −0.739988 0.672621i \(-0.765169\pi\)
0.212513 + 0.977158i \(0.431835\pi\)
\(734\) 0 0
\(735\) 5.72093e7 3.80090e8i 0.144080 0.957247i
\(736\) 0 0
\(737\) 8.98705e7 + 1.55660e8i 0.224499 + 0.388844i
\(738\) 0 0
\(739\) 3.43587e8 5.95110e8i 0.851340 1.47456i −0.0286595 0.999589i \(-0.509124\pi\)
0.879999 0.474975i \(-0.157543\pi\)
\(740\) 0 0
\(741\) 5.55288e7i 0.136478i
\(742\) 0 0
\(743\) 7.22022e8 1.76029 0.880145 0.474705i \(-0.157445\pi\)
0.880145 + 0.474705i \(0.157445\pi\)
\(744\) 0 0
\(745\) −7.36676e8 4.25320e8i −1.78159 1.02860i
\(746\) 0 0
\(747\) 1.11459e8 6.43507e7i 0.267394 0.154380i
\(748\) 0 0
\(749\) 1.71102e8 4.89141e8i 0.407201 1.16410i
\(750\) 0 0
\(751\) 1.18653e8 + 2.05513e8i 0.280129 + 0.485198i 0.971416 0.237382i \(-0.0762894\pi\)
−0.691287 + 0.722580i \(0.742956\pi\)
\(752\) 0 0
\(753\) 4.49481e6 7.78523e6i 0.0105275 0.0182342i
\(754\) 0 0
\(755\) 1.15788e9i 2.69043i
\(756\) 0 0
\(757\) 4.51958e8 1.04186 0.520931 0.853599i \(-0.325585\pi\)
0.520931 + 0.853599i \(0.325585\pi\)
\(758\) 0 0
\(759\) 1.32962e8 + 7.67655e7i 0.304090 + 0.175566i
\(760\) 0 0
\(761\) 2.47772e8 1.43051e8i 0.562210 0.324592i −0.191822 0.981430i \(-0.561440\pi\)
0.754032 + 0.656837i \(0.228106\pi\)
\(762\) 0 0
\(763\) 7.41857e8 1.40446e8i 1.67012 0.316181i
\(764\) 0 0
\(765\) −2.12073e8 3.67321e8i −0.473697 0.820467i
\(766\) 0 0
\(767\) 5.19048e7 8.99018e7i 0.115033 0.199243i
\(768\) 0 0
\(769\) 8.53791e8i 1.87747i −0.344642 0.938734i \(-0.612000\pi\)
0.344642 0.938734i \(-0.388000\pi\)
\(770\) 0 0
\(771\) 2.29028e8 0.499718
\(772\) 0 0
\(773\) 3.74548e8 + 2.16245e8i 0.810902 + 0.468175i 0.847269 0.531164i \(-0.178245\pi\)
−0.0363669 + 0.999339i \(0.511578\pi\)
\(774\) 0 0
\(775\) 4.48525e8 2.58956e8i 0.963565 0.556315i
\(776\) 0 0
\(777\) −2.36173e8 + 2.03286e8i −0.503463 + 0.433355i
\(778\) 0 0
\(779\) −7.27502e7 1.26007e8i −0.153894 0.266552i
\(780\) 0 0
\(781\) −1.04348e8 + 1.80735e8i −0.219043 + 0.379394i
\(782\) 0 0
\(783\) 1.50448e8i 0.313403i
\(784\) 0 0
\(785\) −1.13651e9 −2.34943
\(786\) 0 0
\(787\) 2.78457e8 + 1.60767e8i 0.571260 + 0.329817i 0.757653 0.652658i \(-0.226346\pi\)
−0.186392 + 0.982475i \(0.559680\pi\)
\(788\) 0 0
\(789\) −1.08644e8 + 6.27256e7i −0.221195 + 0.127707i
\(790\) 0 0
\(791\) 5.17840e8 + 6.01616e8i 1.04632 + 1.21560i
\(792\) 0 0
\(793\) 3.41938e8 + 5.92254e8i 0.685690 + 1.18765i
\(794\) 0 0
\(795\) 4.00413e7 6.93536e7i 0.0796906 0.138028i
\(796\) 0 0
\(797\) 7.05947e8i 1.39443i 0.716861 + 0.697216i \(0.245578\pi\)
−0.716861 + 0.697216i \(0.754422\pi\)
\(798\) 0 0
\(799\) 2.01235e8 0.394515
\(800\) 0 0
\(801\) −1.00025e7 5.77495e6i −0.0194631 0.0112370i
\(802\) 0 0
\(803\) −2.58270e8 + 1.49112e8i −0.498801 + 0.287983i
\(804\) 0 0
\(805\) −1.42911e8 7.54880e8i −0.273955 1.44707i
\(806\) 0 0
\(807\) 1.67170e8 + 2.89548e8i 0.318082 + 0.550934i
\(808\) 0 0
\(809\) −7.67123e7 + 1.32870e8i −0.144884 + 0.250946i −0.929330 0.369251i \(-0.879614\pi\)
0.784446 + 0.620197i \(0.212947\pi\)
\(810\) 0 0
\(811\) 3.23998e8i 0.607407i 0.952767 + 0.303704i \(0.0982233\pi\)
−0.952767 + 0.303704i \(0.901777\pi\)
\(812\) 0 0
\(813\) −2.70331e8 −0.503065
\(814\) 0 0
\(815\) −6.20109e8 3.58020e8i −1.14550 0.661355i
\(816\) 0 0
\(817\) −2.34650e8 + 1.35475e8i −0.430283 + 0.248424i
\(818\) 0 0
\(819\) 1.41204e8 + 4.93931e7i 0.257037 + 0.0899114i
\(820\) 0 0
\(821\) −3.54738e8 6.14424e8i −0.641030 1.11030i −0.985203 0.171390i \(-0.945174\pi\)
0.344174 0.938906i \(-0.388159\pi\)
\(822\) 0 0
\(823\) 3.37680e8 5.84879e8i 0.605768 1.04922i −0.386162 0.922431i \(-0.626199\pi\)
0.991930 0.126789i \(-0.0404672\pi\)
\(824\) 0 0
\(825\) 4.06557e8i 0.724035i
\(826\) 0 0
\(827\) −6.68754e8 −1.18236 −0.591180 0.806540i \(-0.701338\pi\)
−0.591180 + 0.806540i \(0.701338\pi\)
\(828\) 0 0
\(829\) 1.58225e8 + 9.13510e7i 0.277722 + 0.160343i 0.632392 0.774649i \(-0.282073\pi\)
−0.354670 + 0.934992i \(0.615407\pi\)
\(830\) 0 0
\(831\) 3.00765e8 1.73647e8i 0.524112 0.302596i
\(832\) 0 0
\(833\) −6.10738e8 + 7.66164e8i −1.05662 + 1.32552i
\(834\) 0 0
\(835\) −9.02998e8 1.56404e9i −1.55106 2.68651i
\(836\) 0 0
\(837\) −3.46608e7 + 6.00343e7i −0.0591102 + 0.102382i
\(838\) 0 0
\(839\) 8.94089e8i 1.51389i 0.653477 + 0.756946i \(0.273310\pi\)
−0.653477 + 0.756946i \(0.726690\pi\)
\(840\) 0 0
\(841\) 9.82631e8 1.65197
\(842\) 0 0
\(843\) −3.26704e8 1.88623e8i −0.545346 0.314856i
\(844\) 0 0
\(845\) −2.91417e8 + 1.68250e8i −0.482997 + 0.278858i
\(846\) 0 0
\(847\) −1.04452e8 + 2.98606e8i −0.171897 + 0.491414i
\(848\) 0 0
\(849\) −1.18495e8 2.05240e8i −0.193632 0.335381i
\(850\) 0 0
\(851\) −3.11430e8 + 5.39412e8i −0.505326 + 0.875250i
\(852\) 0 0
\(853\) 1.10048e9i 1.77311i 0.462621 + 0.886556i \(0.346909\pi\)
−0.462621 + 0.886556i \(0.653091\pi\)
\(854\) 0 0
\(855\) −1.01081e8 −0.161722
\(856\) 0 0
\(857\) 4.37624e8 + 2.52663e8i 0.695279 + 0.401419i 0.805587 0.592478i \(-0.201850\pi\)
−0.110308 + 0.993897i \(0.535184\pi\)
\(858\) 0 0
\(859\) 4.38236e8 2.53016e8i 0.691399 0.399179i −0.112737 0.993625i \(-0.535962\pi\)
0.804136 + 0.594445i \(0.202628\pi\)
\(860\) 0 0
\(861\) 3.85135e8 7.29124e7i 0.603397 0.114233i
\(862\) 0 0
\(863\) −2.25163e8 3.89994e8i −0.350320 0.606771i 0.635986 0.771701i \(-0.280594\pi\)
−0.986305 + 0.164929i \(0.947260\pi\)
\(864\) 0 0
\(865\) 5.40564e8 9.36285e8i 0.835216 1.44664i
\(866\) 0 0
\(867\) 7.04922e8i 1.08164i
\(868\) 0 0
\(869\) 5.12366e8 0.780766
\(870\) 0 0
\(871\) 3.03158e8 + 1.75028e8i 0.458790 + 0.264883i
\(872\) 0 0
\(873\) −2.15147e8 + 1.24215e8i −0.323364 + 0.186694i
\(874\) 0 0
\(875\) −6.90618e8 + 5.94449e8i −1.03089 + 0.887340i
\(876\) 0 0
\(877\) −5.79576e8 1.00386e9i −0.859235 1.48824i −0.872660 0.488329i \(-0.837607\pi\)
0.0134246 0.999910i \(-0.495727\pi\)
\(878\) 0 0
\(879\) −1.36825e8 + 2.36988e8i −0.201465 + 0.348947i
\(880\) 0 0
\(881\) 3.06547e8i 0.448300i 0.974555 + 0.224150i \(0.0719606\pi\)
−0.974555 + 0.224150i \(0.928039\pi\)
\(882\) 0 0
\(883\) −1.52518e8 −0.221533 −0.110767 0.993846i \(-0.535331\pi\)
−0.110767 + 0.993846i \(0.535331\pi\)
\(884\) 0 0
\(885\) −1.63651e8 9.44838e7i −0.236096 0.136310i
\(886\) 0 0
\(887\) −3.21672e8 + 1.85717e8i −0.460938 + 0.266122i −0.712438 0.701735i \(-0.752409\pi\)
0.251501 + 0.967857i \(0.419076\pi\)
\(888\) 0 0
\(889\) 2.43337e8 + 2.82703e8i 0.346340 + 0.402370i
\(890\) 0 0
\(891\) 2.72085e7 + 4.71265e7i 0.0384655 + 0.0666242i
\(892\) 0 0
\(893\) 2.39788e7 4.15325e7i 0.0336723 0.0583222i
\(894\) 0 0
\(895\) 1.84902e9i 2.57912i
\(896\) 0 0
\(897\) 2.99011e8 0.414295
\(898\) 0 0
\(899\) 6.29460e8 + 3.63419e8i 0.866342 + 0.500183i
\(900\) 0 0
\(901\) −1.76789e8 + 1.02069e8i −0.241703 + 0.139547i
\(902\) 0 0
\(903\) −1.35777e8 7.17195e8i −0.184401 0.974034i
\(904\) 0 0
\(905\) 7.03852e8 + 1.21911e9i 0.949589 + 1.64474i
\(906\) 0 0
\(907\) −1.42050e7 + 2.46038e7i −0.0190379 + 0.0329746i −0.875387 0.483422i \(-0.839394\pi\)
0.856349 + 0.516397i \(0.172727\pi\)
\(908\) 0 0
\(909\) 1.52600e8i 0.203171i
\(910\) 0 0
\(911\) −6.83478e6 −0.00904002 −0.00452001 0.999990i \(-0.501439\pi\)
−0.00452001 + 0.999990i \(0.501439\pi\)
\(912\) 0 0
\(913\) −4.22698e8 2.44045e8i −0.555415 0.320669i
\(914\) 0 0
\(915\) 1.07810e9 6.22439e8i 1.40732 0.812519i
\(916\) 0 0
\(917\) −9.66641e8 3.38131e8i −1.25360 0.438507i
\(918\) 0 0
\(919\) −4.42907e8 7.67138e8i −0.570646 0.988387i −0.996500 0.0835954i \(-0.973360\pi\)
0.425854 0.904792i \(-0.359974\pi\)
\(920\) 0 0
\(921\) 8.98523e7 1.55629e8i 0.115014 0.199210i
\(922\) 0 0
\(923\) 4.06447e8i 0.516890i
\(924\) 0 0
\(925\) 1.64936e9 2.08396
\(926\) 0 0
\(927\) −1.80592e8 1.04265e8i −0.226704 0.130888i
\(928\) 0 0
\(929\) −5.94674e8 + 3.43335e8i −0.741706 + 0.428224i −0.822689 0.568492i \(-0.807527\pi\)
0.0809836 + 0.996715i \(0.474194\pi\)
\(930\) 0 0
\(931\) 8.53526e7 + 2.17343e8i 0.105771 + 0.269338i
\(932\) 0 0
\(933\) 2.61010e8 + 4.52082e8i 0.321375 + 0.556637i
\(934\) 0 0
\(935\) −8.04267e8 + 1.39303e9i −0.983933 + 1.70422i
\(936\) 0 0
\(937\) 3.64827e8i 0.443474i −0.975107 0.221737i \(-0.928827\pi\)
0.975107 0.221737i \(-0.0711727\pi\)
\(938\) 0 0
\(939\) −9.31530e8 −1.12512
\(940\) 0 0
\(941\) 2.72677e8 + 1.57430e8i 0.327250 + 0.188938i 0.654620 0.755958i \(-0.272829\pi\)
−0.327369 + 0.944896i \(0.606162\pi\)
\(942\) 0 0
\(943\) 6.78521e8 3.91745e8i 0.809149 0.467162i
\(944\) 0 0
\(945\) 8.99117e7 2.57038e8i 0.106542 0.304580i
\(946\) 0 0
\(947\) −6.59511e8 1.14231e9i −0.776555 1.34503i −0.933917 0.357491i \(-0.883632\pi\)
0.157362 0.987541i \(-0.449701\pi\)
\(948\) 0 0
\(949\) −2.90405e8 + 5.02996e8i −0.339786 + 0.588527i
\(950\) 0 0
\(951\) 1.11574e8i 0.129724i
\(952\) 0 0
\(953\) 1.45853e9 1.68514 0.842570 0.538587i \(-0.181042\pi\)
0.842570 + 0.538587i \(0.181042\pi\)
\(954\) 0 0
\(955\) 2.49102e8 + 1.43819e8i 0.286001 + 0.165123i
\(956\) 0 0
\(957\) 4.94122e8 2.85281e8i 0.563765 0.325490i
\(958\) 0 0
\(959\) 5.62038e8 1.06403e8i 0.637250 0.120642i
\(960\) 0 0
\(961\) −2.76301e8 4.78567e8i −0.311323 0.539228i
\(962\) 0 0
\(963\) 1.83562e8 3.17939e8i 0.205543 0.356012i
\(964\) 0 0
\(965\) 5.70536e8i 0.634893i
\(966\) 0 0
\(967\) 1.14158e8 0.126249 0.0631243 0.998006i \(-0.479894\pi\)
0.0631243 + 0.998006i \(0.479894\pi\)
\(968\) 0 0
\(969\) 2.23144e8 + 1.28832e8i 0.245253 + 0.141597i
\(970\) 0 0
\(971\) −2.39718e8 + 1.38401e8i −0.261844 + 0.151176i −0.625176 0.780484i \(-0.714973\pi\)
0.363331 + 0.931660i \(0.381639\pi\)
\(972\) 0 0
\(973\) −9.22712e8 + 7.94223e8i −1.00168 + 0.862192i
\(974\) 0 0
\(975\) −3.95897e8 6.85714e8i −0.427138 0.739825i
\(976\) 0 0
\(977\) 1.28667e8 2.22858e8i 0.137970 0.238970i −0.788758 0.614703i \(-0.789276\pi\)
0.926728 + 0.375733i \(0.122609\pi\)
\(978\) 0 0
\(979\) 4.38020e7i 0.0466816i
\(980\) 0 0
\(981\) 5.34908e8 0.566594
\(982\) 0 0
\(983\) −4.69243e8 2.70917e8i −0.494012 0.285218i 0.232226 0.972662i \(-0.425399\pi\)
−0.726237 + 0.687444i \(0.758733\pi\)
\(984\) 0 0
\(985\) 6.13781e8 3.54366e8i 0.642250 0.370803i
\(986\) 0 0
\(987\) 8.42836e7 + 9.79189e7i 0.0876580 + 0.101839i
\(988\) 0 0
\(989\) −7.29504e8 1.26354e9i −0.754117 1.30617i
\(990\) 0 0
\(991\) −3.53479e8 + 6.12243e8i −0.363197 + 0.629076i −0.988485 0.151318i \(-0.951648\pi\)
0.625288 + 0.780394i \(0.284982\pi\)
\(992\) 0 0
\(993\) 6.19099e8i 0.632284i
\(994\) 0 0
\(995\) 2.01946e9 2.05006
\(996\) 0 0
\(997\) 1.41068e9 + 8.14455e8i 1.42345 + 0.821829i 0.996592 0.0824896i \(-0.0262871\pi\)
0.426858 + 0.904319i \(0.359620\pi\)
\(998\) 0 0
\(999\) −1.91187e8 + 1.10382e8i −0.191762 + 0.110714i
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 336.7.bh.e.241.1 8
4.3 odd 2 84.7.m.a.73.1 yes 8
7.5 odd 6 inner 336.7.bh.e.145.1 8
12.11 even 2 252.7.z.d.73.4 8
28.3 even 6 588.7.d.b.97.4 8
28.11 odd 6 588.7.d.b.97.5 8
28.19 even 6 84.7.m.a.61.1 8
28.23 odd 6 588.7.m.c.313.4 8
28.27 even 2 588.7.m.c.325.4 8
84.47 odd 6 252.7.z.d.145.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.7.m.a.61.1 8 28.19 even 6
84.7.m.a.73.1 yes 8 4.3 odd 2
252.7.z.d.73.4 8 12.11 even 2
252.7.z.d.145.4 8 84.47 odd 6
336.7.bh.e.145.1 8 7.5 odd 6 inner
336.7.bh.e.241.1 8 1.1 even 1 trivial
588.7.d.b.97.4 8 28.3 even 6
588.7.d.b.97.5 8 28.11 odd 6
588.7.m.c.313.4 8 28.23 odd 6
588.7.m.c.325.4 8 28.27 even 2