Properties

Label 300.2.m.b.241.1
Level $300$
Weight $2$
Character 300.241
Analytic conductor $2.396$
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] = [300,2,Mod(61,300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(300, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("300.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.m (of order \(5\), degree \(4\), 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: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.26265625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 241.1
Root \(1.40799 + 0.132563i\) of defining polynomial
Character \(\chi\) \(=\) 300.241
Dual form 300.2.m.b.61.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 - 0.951057i) q^{3} +(-1.96485 - 1.06740i) q^{5} -1.74037 q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.309017 - 0.951057i) q^{3} +(-1.96485 - 1.06740i) q^{5} -1.74037 q^{7} +(-0.809017 + 0.587785i) q^{9} +(-1.87714 - 1.36382i) q^{11} +(-3.99517 + 2.90266i) q^{13} +(-0.407987 + 2.19853i) q^{15} +(1.15584 - 3.55730i) q^{17} +(-0.523364 + 1.61075i) q^{19} +(0.537803 + 1.65519i) q^{21} +(-7.02120 - 5.10120i) q^{23} +(2.72130 + 4.19458i) q^{25} +(0.809017 + 0.587785i) q^{27} +(0.964854 + 2.96952i) q^{29} +(2.95471 - 9.09368i) q^{31} +(-0.717004 + 2.20671i) q^{33} +(3.41957 + 1.85767i) q^{35} +(-4.34199 + 3.15464i) q^{37} +(3.99517 + 2.90266i) q^{39} +(7.05900 - 5.12866i) q^{41} +2.86270 q^{43} +(2.21700 - 0.291365i) q^{45} +(-2.61505 - 8.04830i) q^{47} -3.97112 q^{49} -3.74037 q^{51} +(-0.415470 - 1.27868i) q^{53} +(2.23256 + 4.68338i) q^{55} +1.69364 q^{57} +(-3.54991 + 2.57916i) q^{59} +(12.4035 + 9.01166i) q^{61} +(1.40799 - 1.02296i) q^{63} +(10.9482 - 1.43885i) q^{65} +(2.85246 - 8.77897i) q^{67} +(-2.68186 + 8.25391i) q^{69} +(0.00728184 + 0.0224112i) q^{71} +(0.827230 + 0.601018i) q^{73} +(3.14835 - 3.88431i) q^{75} +(3.26691 + 2.37355i) q^{77} +(-0.246835 - 0.759681i) q^{79} +(0.309017 - 0.951057i) q^{81} +(0.732396 - 2.25408i) q^{83} +(-6.06812 + 5.75583i) q^{85} +(2.52602 - 1.83526i) q^{87} +(3.93348 + 2.85784i) q^{89} +(6.95307 - 5.05170i) q^{91} -9.56166 q^{93} +(2.74765 - 2.60624i) q^{95} +(-1.06966 - 3.29209i) q^{97} +2.32027 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{3} - 5 q^{5} + 8 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{3} - 5 q^{5} + 8 q^{7} - 2 q^{9} + 8 q^{11} + 5 q^{15} + 3 q^{17} + 5 q^{19} + 7 q^{21} - 7 q^{23} + 5 q^{25} + 2 q^{27} - 3 q^{29} - 3 q^{31} + 7 q^{33} - 10 q^{35} - q^{37} + 10 q^{41} - 12 q^{43} + 5 q^{45} - 33 q^{47} - 8 q^{49} - 8 q^{51} - 19 q^{53} - 15 q^{55} + 10 q^{57} - 38 q^{59} + 46 q^{61} + 3 q^{63} + 25 q^{65} - 8 q^{67} + 2 q^{69} - 25 q^{71} - 26 q^{73} - 5 q^{75} + 23 q^{77} - 16 q^{79} - 2 q^{81} + 8 q^{83} - 30 q^{85} + 3 q^{87} - 30 q^{89} + 25 q^{91} - 22 q^{93} - 25 q^{95} - 14 q^{97} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\)

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
\(3\) −0.309017 0.951057i −0.178411 0.549093i
\(4\) 0 0
\(5\) −1.96485 1.06740i −0.878709 0.477357i
\(6\) 0 0
\(7\) −1.74037 −0.657797 −0.328899 0.944365i \(-0.606677\pi\)
−0.328899 + 0.944365i \(0.606677\pi\)
\(8\) 0 0
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 0 0
\(11\) −1.87714 1.36382i −0.565979 0.411208i 0.267663 0.963513i \(-0.413749\pi\)
−0.833642 + 0.552305i \(0.813749\pi\)
\(12\) 0 0
\(13\) −3.99517 + 2.90266i −1.10806 + 0.805054i −0.982357 0.187014i \(-0.940119\pi\)
−0.125705 + 0.992068i \(0.540119\pi\)
\(14\) 0 0
\(15\) −0.407987 + 2.19853i −0.105342 + 0.567659i
\(16\) 0 0
\(17\) 1.15584 3.55730i 0.280332 0.862772i −0.707428 0.706786i \(-0.750144\pi\)
0.987759 0.155986i \(-0.0498556\pi\)
\(18\) 0 0
\(19\) −0.523364 + 1.61075i −0.120068 + 0.369531i −0.992970 0.118364i \(-0.962235\pi\)
0.872902 + 0.487895i \(0.162235\pi\)
\(20\) 0 0
\(21\) 0.537803 + 1.65519i 0.117358 + 0.361192i
\(22\) 0 0
\(23\) −7.02120 5.10120i −1.46402 1.06367i −0.982293 0.187352i \(-0.940009\pi\)
−0.481728 0.876321i \(-0.659991\pi\)
\(24\) 0 0
\(25\) 2.72130 + 4.19458i 0.544261 + 0.838916i
\(26\) 0 0
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) 0 0
\(29\) 0.964854 + 2.96952i 0.179169 + 0.551425i 0.999799 0.0200341i \(-0.00637749\pi\)
−0.820630 + 0.571459i \(0.806377\pi\)
\(30\) 0 0
\(31\) 2.95471 9.09368i 0.530682 1.63327i −0.222115 0.975020i \(-0.571296\pi\)
0.752798 0.658252i \(-0.228704\pi\)
\(32\) 0 0
\(33\) −0.717004 + 2.20671i −0.124814 + 0.384139i
\(34\) 0 0
\(35\) 3.41957 + 1.85767i 0.578013 + 0.314004i
\(36\) 0 0
\(37\) −4.34199 + 3.15464i −0.713820 + 0.518620i −0.884404 0.466723i \(-0.845435\pi\)
0.170584 + 0.985343i \(0.445435\pi\)
\(38\) 0 0
\(39\) 3.99517 + 2.90266i 0.639740 + 0.464798i
\(40\) 0 0
\(41\) 7.05900 5.12866i 1.10243 0.800963i 0.120975 0.992656i \(-0.461398\pi\)
0.981455 + 0.191693i \(0.0613978\pi\)
\(42\) 0 0
\(43\) 2.86270 0.436558 0.218279 0.975886i \(-0.429956\pi\)
0.218279 + 0.975886i \(0.429956\pi\)
\(44\) 0 0
\(45\) 2.21700 0.291365i 0.330491 0.0434342i
\(46\) 0 0
\(47\) −2.61505 8.04830i −0.381444 1.17397i −0.939027 0.343844i \(-0.888271\pi\)
0.557582 0.830122i \(-0.311729\pi\)
\(48\) 0 0
\(49\) −3.97112 −0.567303
\(50\) 0 0
\(51\) −3.74037 −0.523756
\(52\) 0 0
\(53\) −0.415470 1.27868i −0.0570691 0.175641i 0.918459 0.395517i \(-0.129435\pi\)
−0.975528 + 0.219876i \(0.929435\pi\)
\(54\) 0 0
\(55\) 2.23256 + 4.68338i 0.301038 + 0.631506i
\(56\) 0 0
\(57\) 1.69364 0.224328
\(58\) 0 0
\(59\) −3.54991 + 2.57916i −0.462159 + 0.335778i −0.794378 0.607424i \(-0.792203\pi\)
0.332219 + 0.943202i \(0.392203\pi\)
\(60\) 0 0
\(61\) 12.4035 + 9.01166i 1.58810 + 1.15382i 0.906584 + 0.422025i \(0.138681\pi\)
0.681519 + 0.731800i \(0.261319\pi\)
\(62\) 0 0
\(63\) 1.40799 1.02296i 0.177390 0.128881i
\(64\) 0 0
\(65\) 10.9482 1.43885i 1.35796 0.178468i
\(66\) 0 0
\(67\) 2.85246 8.77897i 0.348483 1.07252i −0.611209 0.791469i \(-0.709317\pi\)
0.959692 0.281052i \(-0.0906835\pi\)
\(68\) 0 0
\(69\) −2.68186 + 8.25391i −0.322858 + 0.993654i
\(70\) 0 0
\(71\) 0.00728184 + 0.0224112i 0.000864195 + 0.00265972i 0.951488 0.307687i \(-0.0995549\pi\)
−0.950623 + 0.310347i \(0.899555\pi\)
\(72\) 0 0
\(73\) 0.827230 + 0.601018i 0.0968200 + 0.0703438i 0.635142 0.772395i \(-0.280942\pi\)
−0.538322 + 0.842739i \(0.680942\pi\)
\(74\) 0 0
\(75\) 3.14835 3.88431i 0.363541 0.448521i
\(76\) 0 0
\(77\) 3.26691 + 2.37355i 0.372299 + 0.270491i
\(78\) 0 0
\(79\) −0.246835 0.759681i −0.0277711 0.0854708i 0.936210 0.351440i \(-0.114308\pi\)
−0.963981 + 0.265969i \(0.914308\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 0 0
\(83\) 0.732396 2.25408i 0.0803909 0.247418i −0.902781 0.430100i \(-0.858478\pi\)
0.983172 + 0.182683i \(0.0584781\pi\)
\(84\) 0 0
\(85\) −6.06812 + 5.75583i −0.658180 + 0.624308i
\(86\) 0 0
\(87\) 2.52602 1.83526i 0.270818 0.196761i
\(88\) 0 0
\(89\) 3.93348 + 2.85784i 0.416948 + 0.302931i 0.776409 0.630230i \(-0.217039\pi\)
−0.359461 + 0.933160i \(0.617039\pi\)
\(90\) 0 0
\(91\) 6.95307 5.05170i 0.728880 0.529562i
\(92\) 0 0
\(93\) −9.56166 −0.991498
\(94\) 0 0
\(95\) 2.74765 2.60624i 0.281903 0.267395i
\(96\) 0 0
\(97\) −1.06966 3.29209i −0.108608 0.334261i 0.881952 0.471339i \(-0.156229\pi\)
−0.990560 + 0.137078i \(0.956229\pi\)
\(98\) 0 0
\(99\) 2.32027 0.233196
\(100\) 0 0
\(101\) −7.58056 −0.754294 −0.377147 0.926154i \(-0.623095\pi\)
−0.377147 + 0.926154i \(0.623095\pi\)
\(102\) 0 0
\(103\) 3.32808 + 10.2428i 0.327926 + 1.00925i 0.970103 + 0.242695i \(0.0780314\pi\)
−0.642177 + 0.766556i \(0.721969\pi\)
\(104\) 0 0
\(105\) 0.710047 3.82626i 0.0692935 0.373404i
\(106\) 0 0
\(107\) −4.34344 −0.419896 −0.209948 0.977713i \(-0.567329\pi\)
−0.209948 + 0.977713i \(0.567329\pi\)
\(108\) 0 0
\(109\) −0.866675 + 0.629677i −0.0830125 + 0.0603121i −0.628517 0.777796i \(-0.716338\pi\)
0.545505 + 0.838108i \(0.316338\pi\)
\(110\) 0 0
\(111\) 4.34199 + 3.15464i 0.412124 + 0.299426i
\(112\) 0 0
\(113\) −15.0167 + 10.9103i −1.41265 + 1.02635i −0.419722 + 0.907653i \(0.637872\pi\)
−0.992930 + 0.118699i \(0.962128\pi\)
\(114\) 0 0
\(115\) 8.35059 + 17.5176i 0.778697 + 1.63352i
\(116\) 0 0
\(117\) 1.52602 4.69661i 0.141081 0.434202i
\(118\) 0 0
\(119\) −2.01158 + 6.19101i −0.184401 + 0.567529i
\(120\) 0 0
\(121\) −1.73554 5.34145i −0.157777 0.485586i
\(122\) 0 0
\(123\) −7.05900 5.12866i −0.636488 0.462436i
\(124\) 0 0
\(125\) −0.869658 11.1465i −0.0777846 0.996970i
\(126\) 0 0
\(127\) −15.3791 11.1735i −1.36467 0.991492i −0.998132 0.0610897i \(-0.980542\pi\)
−0.366540 0.930402i \(-0.619458\pi\)
\(128\) 0 0
\(129\) −0.884623 2.72259i −0.0778867 0.239711i
\(130\) 0 0
\(131\) −0.230228 + 0.708567i −0.0201151 + 0.0619078i −0.960610 0.277899i \(-0.910362\pi\)
0.940495 + 0.339807i \(0.110362\pi\)
\(132\) 0 0
\(133\) 0.910845 2.80329i 0.0789803 0.243076i
\(134\) 0 0
\(135\) −0.962197 2.01846i −0.0828127 0.173721i
\(136\) 0 0
\(137\) 9.00643 6.54355i 0.769471 0.559054i −0.132329 0.991206i \(-0.542246\pi\)
0.901801 + 0.432152i \(0.142246\pi\)
\(138\) 0 0
\(139\) −11.0746 8.04613i −0.939331 0.682464i 0.00892821 0.999960i \(-0.497158\pi\)
−0.948260 + 0.317496i \(0.897158\pi\)
\(140\) 0 0
\(141\) −6.84629 + 4.97412i −0.576562 + 0.418897i
\(142\) 0 0
\(143\) 11.4582 0.958185
\(144\) 0 0
\(145\) 1.27387 6.86455i 0.105789 0.570070i
\(146\) 0 0
\(147\) 1.22714 + 3.77676i 0.101213 + 0.311502i
\(148\) 0 0
\(149\) −10.6283 −0.870701 −0.435351 0.900261i \(-0.643376\pi\)
−0.435351 + 0.900261i \(0.643376\pi\)
\(150\) 0 0
\(151\) −10.4689 −0.851943 −0.425972 0.904737i \(-0.640068\pi\)
−0.425972 + 0.904737i \(0.640068\pi\)
\(152\) 0 0
\(153\) 1.15584 + 3.55730i 0.0934439 + 0.287591i
\(154\) 0 0
\(155\) −15.5122 + 14.7139i −1.24597 + 1.18185i
\(156\) 0 0
\(157\) −17.2987 −1.38059 −0.690295 0.723528i \(-0.742519\pi\)
−0.690295 + 0.723528i \(0.742519\pi\)
\(158\) 0 0
\(159\) −1.08771 + 0.790270i −0.0862613 + 0.0626725i
\(160\) 0 0
\(161\) 12.2195 + 8.87796i 0.963028 + 0.699681i
\(162\) 0 0
\(163\) 4.97293 3.61304i 0.389510 0.282995i −0.375745 0.926723i \(-0.622613\pi\)
0.765255 + 0.643728i \(0.222613\pi\)
\(164\) 0 0
\(165\) 3.76426 3.57053i 0.293047 0.277966i
\(166\) 0 0
\(167\) −0.587188 + 1.80718i −0.0454379 + 0.139844i −0.971202 0.238259i \(-0.923423\pi\)
0.925764 + 0.378103i \(0.123423\pi\)
\(168\) 0 0
\(169\) 3.51874 10.8296i 0.270672 0.833043i
\(170\) 0 0
\(171\) −0.523364 1.61075i −0.0400226 0.123177i
\(172\) 0 0
\(173\) −9.37317 6.81000i −0.712629 0.517755i 0.171392 0.985203i \(-0.445174\pi\)
−0.884021 + 0.467448i \(0.845174\pi\)
\(174\) 0 0
\(175\) −4.73607 7.30011i −0.358013 0.551837i
\(176\) 0 0
\(177\) 3.54991 + 2.57916i 0.266828 + 0.193862i
\(178\) 0 0
\(179\) 6.81312 + 20.9686i 0.509236 + 1.56727i 0.793530 + 0.608531i \(0.208241\pi\)
−0.284294 + 0.958737i \(0.591759\pi\)
\(180\) 0 0
\(181\) 6.38341 19.6461i 0.474475 1.46028i −0.372190 0.928157i \(-0.621393\pi\)
0.846665 0.532127i \(-0.178607\pi\)
\(182\) 0 0
\(183\) 4.73771 14.5812i 0.350222 1.07787i
\(184\) 0 0
\(185\) 11.8987 1.56376i 0.874807 0.114970i
\(186\) 0 0
\(187\) −7.02120 + 5.10120i −0.513441 + 0.373036i
\(188\) 0 0
\(189\) −1.40799 1.02296i −0.102416 0.0744096i
\(190\) 0 0
\(191\) −16.8535 + 12.2448i −1.21948 + 0.886004i −0.996057 0.0887181i \(-0.971723\pi\)
−0.223423 + 0.974722i \(0.571723\pi\)
\(192\) 0 0
\(193\) 4.78053 0.344110 0.172055 0.985087i \(-0.444959\pi\)
0.172055 + 0.985087i \(0.444959\pi\)
\(194\) 0 0
\(195\) −4.75162 9.96777i −0.340271 0.713807i
\(196\) 0 0
\(197\) 5.36207 + 16.5028i 0.382032 + 1.17577i 0.938611 + 0.344978i \(0.112114\pi\)
−0.556579 + 0.830795i \(0.687886\pi\)
\(198\) 0 0
\(199\) 11.0756 0.785129 0.392564 0.919724i \(-0.371588\pi\)
0.392564 + 0.919724i \(0.371588\pi\)
\(200\) 0 0
\(201\) −9.23075 −0.651087
\(202\) 0 0
\(203\) −1.67920 5.16805i −0.117857 0.362726i
\(204\) 0 0
\(205\) −19.3443 + 2.54228i −1.35106 + 0.177561i
\(206\) 0 0
\(207\) 8.67867 0.603210
\(208\) 0 0
\(209\) 3.17920 2.30982i 0.219910 0.159774i
\(210\) 0 0
\(211\) −4.58634 3.33217i −0.315736 0.229396i 0.418618 0.908163i \(-0.362515\pi\)
−0.734354 + 0.678767i \(0.762515\pi\)
\(212\) 0 0
\(213\) 0.0190641 0.0138509i 0.00130625 0.000949047i
\(214\) 0 0
\(215\) −5.62479 3.05565i −0.383607 0.208394i
\(216\) 0 0
\(217\) −5.14229 + 15.8263i −0.349081 + 1.07436i
\(218\) 0 0
\(219\) 0.315974 0.972467i 0.0213515 0.0657132i
\(220\) 0 0
\(221\) 5.70788 + 17.5670i 0.383953 + 1.18169i
\(222\) 0 0
\(223\) 17.2972 + 12.5671i 1.15831 + 0.841559i 0.989563 0.144101i \(-0.0460292\pi\)
0.168743 + 0.985660i \(0.446029\pi\)
\(224\) 0 0
\(225\) −4.66709 1.79395i −0.311140 0.119596i
\(226\) 0 0
\(227\) 18.5770 + 13.4970i 1.23300 + 0.895827i 0.997111 0.0759536i \(-0.0242001\pi\)
0.235888 + 0.971780i \(0.424200\pi\)
\(228\) 0 0
\(229\) −8.68482 26.7291i −0.573909 1.76631i −0.639865 0.768487i \(-0.721010\pi\)
0.0659560 0.997823i \(-0.478990\pi\)
\(230\) 0 0
\(231\) 1.24785 3.84049i 0.0821025 0.252686i
\(232\) 0 0
\(233\) −0.411596 + 1.26676i −0.0269646 + 0.0829885i −0.963633 0.267229i \(-0.913892\pi\)
0.936669 + 0.350217i \(0.113892\pi\)
\(234\) 0 0
\(235\) −3.45258 + 18.6051i −0.225222 + 1.21366i
\(236\) 0 0
\(237\) −0.646223 + 0.469509i −0.0419767 + 0.0304979i
\(238\) 0 0
\(239\) −2.78730 2.02509i −0.180295 0.130992i 0.493977 0.869475i \(-0.335543\pi\)
−0.674272 + 0.738483i \(0.735543\pi\)
\(240\) 0 0
\(241\) 19.4923 14.1620i 1.25561 0.912253i 0.257075 0.966392i \(-0.417241\pi\)
0.998533 + 0.0541389i \(0.0172414\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 7.80267 + 4.23878i 0.498495 + 0.270806i
\(246\) 0 0
\(247\) −2.58453 7.95437i −0.164450 0.506124i
\(248\) 0 0
\(249\) −2.37008 −0.150198
\(250\) 0 0
\(251\) −30.1621 −1.90381 −0.951907 0.306387i \(-0.900880\pi\)
−0.951907 + 0.306387i \(0.900880\pi\)
\(252\) 0 0
\(253\) 6.22264 + 19.1513i 0.391214 + 1.20403i
\(254\) 0 0
\(255\) 7.34928 + 3.99248i 0.460230 + 0.250019i
\(256\) 0 0
\(257\) 10.6862 0.666588 0.333294 0.942823i \(-0.391840\pi\)
0.333294 + 0.942823i \(0.391840\pi\)
\(258\) 0 0
\(259\) 7.55667 5.49024i 0.469548 0.341147i
\(260\) 0 0
\(261\) −2.52602 1.83526i −0.156357 0.113600i
\(262\) 0 0
\(263\) −7.46948 + 5.42689i −0.460588 + 0.334637i −0.793762 0.608229i \(-0.791880\pi\)
0.333174 + 0.942865i \(0.391880\pi\)
\(264\) 0 0
\(265\) −0.548533 + 2.95590i −0.0336961 + 0.181580i
\(266\) 0 0
\(267\) 1.50246 4.62409i 0.0919488 0.282989i
\(268\) 0 0
\(269\) 8.26252 25.4294i 0.503774 1.55046i −0.299047 0.954238i \(-0.596669\pi\)
0.802821 0.596220i \(-0.203331\pi\)
\(270\) 0 0
\(271\) 7.47325 + 23.0003i 0.453968 + 1.39717i 0.872343 + 0.488895i \(0.162600\pi\)
−0.418375 + 0.908274i \(0.637400\pi\)
\(272\) 0 0
\(273\) −6.95307 5.05170i −0.420819 0.305743i
\(274\) 0 0
\(275\) 0.612394 11.5852i 0.0369288 0.698613i
\(276\) 0 0
\(277\) 25.5713 + 18.5787i 1.53643 + 1.11628i 0.952524 + 0.304464i \(0.0984775\pi\)
0.583909 + 0.811819i \(0.301523\pi\)
\(278\) 0 0
\(279\) 2.95471 + 9.09368i 0.176894 + 0.544424i
\(280\) 0 0
\(281\) 7.18851 22.1240i 0.428831 1.31981i −0.470447 0.882428i \(-0.655907\pi\)
0.899278 0.437377i \(-0.144093\pi\)
\(282\) 0 0
\(283\) 7.67355 23.6167i 0.456145 1.40387i −0.413641 0.910440i \(-0.635743\pi\)
0.869786 0.493430i \(-0.164257\pi\)
\(284\) 0 0
\(285\) −3.32776 1.80780i −0.197119 0.107085i
\(286\) 0 0
\(287\) −12.2853 + 8.92576i −0.725175 + 0.526871i
\(288\) 0 0
\(289\) 2.43486 + 1.76903i 0.143227 + 0.104060i
\(290\) 0 0
\(291\) −2.80042 + 2.03462i −0.164163 + 0.119272i
\(292\) 0 0
\(293\) 29.2758 1.71031 0.855156 0.518371i \(-0.173461\pi\)
0.855156 + 0.518371i \(0.173461\pi\)
\(294\) 0 0
\(295\) 9.72806 1.27849i 0.566390 0.0744366i
\(296\) 0 0
\(297\) −0.717004 2.20671i −0.0416048 0.128046i
\(298\) 0 0
\(299\) 42.8580 2.47854
\(300\) 0 0
\(301\) −4.98215 −0.287166
\(302\) 0 0
\(303\) 2.34252 + 7.20954i 0.134574 + 0.414177i
\(304\) 0 0
\(305\) −14.7520 30.9461i −0.844695 1.77197i
\(306\) 0 0
\(307\) 8.73972 0.498802 0.249401 0.968400i \(-0.419766\pi\)
0.249401 + 0.968400i \(0.419766\pi\)
\(308\) 0 0
\(309\) 8.71303 6.33039i 0.495667 0.360123i
\(310\) 0 0
\(311\) 12.5043 + 9.08488i 0.709052 + 0.515156i 0.882868 0.469622i \(-0.155610\pi\)
−0.173816 + 0.984778i \(0.555610\pi\)
\(312\) 0 0
\(313\) 1.26124 0.916343i 0.0712894 0.0517948i −0.551570 0.834129i \(-0.685971\pi\)
0.622859 + 0.782334i \(0.285971\pi\)
\(314\) 0 0
\(315\) −3.85840 + 0.507083i −0.217396 + 0.0285709i
\(316\) 0 0
\(317\) −1.68802 + 5.19520i −0.0948088 + 0.291792i −0.987204 0.159464i \(-0.949024\pi\)
0.892395 + 0.451255i \(0.149024\pi\)
\(318\) 0 0
\(319\) 2.23873 6.89009i 0.125345 0.385771i
\(320\) 0 0
\(321\) 1.34220 + 4.13085i 0.0749140 + 0.230562i
\(322\) 0 0
\(323\) 5.12499 + 3.72352i 0.285162 + 0.207182i
\(324\) 0 0
\(325\) −23.0475 8.85905i −1.27845 0.491412i
\(326\) 0 0
\(327\) 0.866675 + 0.629677i 0.0479273 + 0.0348212i
\(328\) 0 0
\(329\) 4.55115 + 14.0070i 0.250913 + 0.772231i
\(330\) 0 0
\(331\) 0.264458 0.813918i 0.0145359 0.0447370i −0.943525 0.331300i \(-0.892513\pi\)
0.958061 + 0.286563i \(0.0925128\pi\)
\(332\) 0 0
\(333\) 1.65849 5.10432i 0.0908849 0.279715i
\(334\) 0 0
\(335\) −14.9754 + 14.2047i −0.818191 + 0.776084i
\(336\) 0 0
\(337\) −11.9933 + 8.71367i −0.653318 + 0.474664i −0.864400 0.502805i \(-0.832301\pi\)
0.211082 + 0.977468i \(0.432301\pi\)
\(338\) 0 0
\(339\) 15.0167 + 10.9103i 0.815595 + 0.592564i
\(340\) 0 0
\(341\) −17.9486 + 13.0404i −0.971970 + 0.706177i
\(342\) 0 0
\(343\) 19.0938 1.03097
\(344\) 0 0
\(345\) 14.0797 13.3551i 0.758026 0.719015i
\(346\) 0 0
\(347\) −0.361763 1.11339i −0.0194204 0.0597700i 0.940877 0.338749i \(-0.110004\pi\)
−0.960297 + 0.278979i \(0.910004\pi\)
\(348\) 0 0
\(349\) −21.4346 −1.14737 −0.573683 0.819077i \(-0.694486\pi\)
−0.573683 + 0.819077i \(0.694486\pi\)
\(350\) 0 0
\(351\) −4.93831 −0.263587
\(352\) 0 0
\(353\) −1.10094 3.38834i −0.0585970 0.180343i 0.917474 0.397796i \(-0.130225\pi\)
−0.976071 + 0.217453i \(0.930225\pi\)
\(354\) 0 0
\(355\) 0.00961402 0.0518074i 0.000510259 0.00274965i
\(356\) 0 0
\(357\) 6.50961 0.344525
\(358\) 0 0
\(359\) −10.8337 + 7.87116i −0.571782 + 0.415424i −0.835752 0.549107i \(-0.814968\pi\)
0.263970 + 0.964531i \(0.414968\pi\)
\(360\) 0 0
\(361\) 13.0507 + 9.48191i 0.686880 + 0.499048i
\(362\) 0 0
\(363\) −4.54371 + 3.30120i −0.238483 + 0.173268i
\(364\) 0 0
\(365\) −0.983858 2.06390i −0.0514975 0.108029i
\(366\) 0 0
\(367\) −0.440150 + 1.35464i −0.0229757 + 0.0707118i −0.961887 0.273447i \(-0.911836\pi\)
0.938911 + 0.344159i \(0.111836\pi\)
\(368\) 0 0
\(369\) −2.69630 + 8.29835i −0.140364 + 0.431995i
\(370\) 0 0
\(371\) 0.723070 + 2.22538i 0.0375399 + 0.115536i
\(372\) 0 0
\(373\) −20.6564 15.0077i −1.06955 0.777072i −0.0937165 0.995599i \(-0.529875\pi\)
−0.975831 + 0.218527i \(0.929875\pi\)
\(374\) 0 0
\(375\) −10.3322 + 4.27154i −0.533551 + 0.220581i
\(376\) 0 0
\(377\) −12.4743 9.06309i −0.642457 0.466773i
\(378\) 0 0
\(379\) −11.7671 36.2153i −0.604434 1.86026i −0.500634 0.865659i \(-0.666900\pi\)
−0.103800 0.994598i \(-0.533100\pi\)
\(380\) 0 0
\(381\) −5.87428 + 18.0792i −0.300949 + 0.926225i
\(382\) 0 0
\(383\) 4.21946 12.9862i 0.215604 0.663562i −0.783506 0.621384i \(-0.786571\pi\)
0.999110 0.0421775i \(-0.0134295\pi\)
\(384\) 0 0
\(385\) −3.88547 8.15080i −0.198022 0.415403i
\(386\) 0 0
\(387\) −2.31597 + 1.68265i −0.117728 + 0.0855341i
\(388\) 0 0
\(389\) −28.9546 21.0368i −1.46806 1.06661i −0.981171 0.193142i \(-0.938132\pi\)
−0.486888 0.873465i \(-0.661868\pi\)
\(390\) 0 0
\(391\) −26.2619 + 19.0804i −1.32812 + 0.964935i
\(392\) 0 0
\(393\) 0.745032 0.0375819
\(394\) 0 0
\(395\) −0.325890 + 1.75613i −0.0163973 + 0.0883607i
\(396\) 0 0
\(397\) 7.58400 + 23.3412i 0.380630 + 1.17146i 0.939601 + 0.342272i \(0.111196\pi\)
−0.558971 + 0.829187i \(0.688804\pi\)
\(398\) 0 0
\(399\) −2.94756 −0.147562
\(400\) 0 0
\(401\) −25.7068 −1.28373 −0.641867 0.766816i \(-0.721840\pi\)
−0.641867 + 0.766816i \(0.721840\pi\)
\(402\) 0 0
\(403\) 14.5913 + 44.9074i 0.726844 + 2.23700i
\(404\) 0 0
\(405\) −1.62233 + 1.53884i −0.0806144 + 0.0764657i
\(406\) 0 0
\(407\) 12.4529 0.617268
\(408\) 0 0
\(409\) 15.0121 10.9069i 0.742299 0.539312i −0.151131 0.988514i \(-0.548292\pi\)
0.893430 + 0.449202i \(0.148292\pi\)
\(410\) 0 0
\(411\) −9.00643 6.54355i −0.444254 0.322770i
\(412\) 0 0
\(413\) 6.17815 4.48869i 0.304007 0.220874i
\(414\) 0 0
\(415\) −3.84506 + 3.64718i −0.188747 + 0.179033i
\(416\) 0 0
\(417\) −4.23010 + 13.0189i −0.207149 + 0.637539i
\(418\) 0 0
\(419\) 1.45029 4.46354i 0.0708513 0.218058i −0.909361 0.416009i \(-0.863429\pi\)
0.980212 + 0.197951i \(0.0634286\pi\)
\(420\) 0 0
\(421\) 2.84929 + 8.76921i 0.138866 + 0.427385i 0.996171 0.0874228i \(-0.0278631\pi\)
−0.857305 + 0.514808i \(0.827863\pi\)
\(422\) 0 0
\(423\) 6.84629 + 4.97412i 0.332878 + 0.241850i
\(424\) 0 0
\(425\) 18.0668 4.83224i 0.876367 0.234398i
\(426\) 0 0
\(427\) −21.5866 15.6836i −1.04465 0.758983i
\(428\) 0 0
\(429\) −3.54079 10.8974i −0.170951 0.526132i
\(430\) 0 0
\(431\) 8.83198 27.1820i 0.425421 1.30931i −0.477169 0.878812i \(-0.658337\pi\)
0.902590 0.430501i \(-0.141663\pi\)
\(432\) 0 0
\(433\) 1.12286 3.45581i 0.0539612 0.166075i −0.920444 0.390875i \(-0.872173\pi\)
0.974405 + 0.224799i \(0.0721726\pi\)
\(434\) 0 0
\(435\) −6.92223 + 0.909740i −0.331895 + 0.0436187i
\(436\) 0 0
\(437\) 11.8914 8.63959i 0.568842 0.413288i
\(438\) 0 0
\(439\) 14.2446 + 10.3493i 0.679859 + 0.493947i 0.873311 0.487163i \(-0.161968\pi\)
−0.193452 + 0.981110i \(0.561968\pi\)
\(440\) 0 0
\(441\) 3.21270 2.33417i 0.152986 0.111151i
\(442\) 0 0
\(443\) 7.11807 0.338190 0.169095 0.985600i \(-0.445916\pi\)
0.169095 + 0.985600i \(0.445916\pi\)
\(444\) 0 0
\(445\) −4.67825 9.81385i −0.221770 0.465221i
\(446\) 0 0
\(447\) 3.28431 + 10.1081i 0.155343 + 0.478096i
\(448\) 0 0
\(449\) −20.4121 −0.963305 −0.481653 0.876362i \(-0.659963\pi\)
−0.481653 + 0.876362i \(0.659963\pi\)
\(450\) 0 0
\(451\) −20.2453 −0.953315
\(452\) 0 0
\(453\) 3.23505 + 9.95647i 0.151996 + 0.467796i
\(454\) 0 0
\(455\) −19.0540 + 2.50413i −0.893264 + 0.117395i
\(456\) 0 0
\(457\) −16.8375 −0.787624 −0.393812 0.919191i \(-0.628844\pi\)
−0.393812 + 0.919191i \(0.628844\pi\)
\(458\) 0 0
\(459\) 3.02602 2.19853i 0.141243 0.102619i
\(460\) 0 0
\(461\) −14.0162 10.1833i −0.652798 0.474286i 0.211425 0.977394i \(-0.432190\pi\)
−0.864223 + 0.503109i \(0.832190\pi\)
\(462\) 0 0
\(463\) −6.96088 + 5.05738i −0.323500 + 0.235036i −0.737667 0.675164i \(-0.764073\pi\)
0.414168 + 0.910201i \(0.364073\pi\)
\(464\) 0 0
\(465\) 18.7873 + 10.2061i 0.871238 + 0.473298i
\(466\) 0 0
\(467\) 0.258292 0.794942i 0.0119523 0.0367855i −0.944902 0.327352i \(-0.893844\pi\)
0.956855 + 0.290566i \(0.0938437\pi\)
\(468\) 0 0
\(469\) −4.96433 + 15.2786i −0.229231 + 0.705502i
\(470\) 0 0
\(471\) 5.34560 + 16.4521i 0.246312 + 0.758072i
\(472\) 0 0
\(473\) −5.37369 3.90422i −0.247083 0.179516i
\(474\) 0 0
\(475\) −8.18064 + 2.18804i −0.375354 + 0.100394i
\(476\) 0 0
\(477\) 1.08771 + 0.790270i 0.0498030 + 0.0361840i
\(478\) 0 0
\(479\) −10.3365 31.8123i −0.472285 1.45354i −0.849585 0.527452i \(-0.823147\pi\)
0.377300 0.926091i \(-0.376853\pi\)
\(480\) 0 0
\(481\) 8.19015 25.2067i 0.373439 1.14933i
\(482\) 0 0
\(483\) 4.66742 14.3648i 0.212375 0.653623i
\(484\) 0 0
\(485\) −1.41225 + 7.61024i −0.0641269 + 0.345563i
\(486\) 0 0
\(487\) 19.7528 14.3512i 0.895083 0.650316i −0.0421152 0.999113i \(-0.513410\pi\)
0.937198 + 0.348797i \(0.113410\pi\)
\(488\) 0 0
\(489\) −4.97293 3.61304i −0.224884 0.163387i
\(490\) 0 0
\(491\) 11.8501 8.60958i 0.534786 0.388545i −0.287359 0.957823i \(-0.592777\pi\)
0.822145 + 0.569278i \(0.192777\pi\)
\(492\) 0 0
\(493\) 11.6787 0.525981
\(494\) 0 0
\(495\) −4.55900 2.47667i −0.204912 0.111318i
\(496\) 0 0
\(497\) −0.0126731 0.0390037i −0.000568465 0.00174956i
\(498\) 0 0
\(499\) −13.5655 −0.607276 −0.303638 0.952787i \(-0.598201\pi\)
−0.303638 + 0.952787i \(0.598201\pi\)
\(500\) 0 0
\(501\) 1.90018 0.0848937
\(502\) 0 0
\(503\) −12.6475 38.9250i −0.563924 1.73558i −0.671126 0.741343i \(-0.734189\pi\)
0.107202 0.994237i \(-0.465811\pi\)
\(504\) 0 0
\(505\) 14.8947 + 8.09151i 0.662805 + 0.360067i
\(506\) 0 0
\(507\) −11.3869 −0.505709
\(508\) 0 0
\(509\) −9.82240 + 7.13639i −0.435370 + 0.316315i −0.783793 0.621023i \(-0.786718\pi\)
0.348422 + 0.937338i \(0.386718\pi\)
\(510\) 0 0
\(511\) −1.43968 1.04599i −0.0636879 0.0462720i
\(512\) 0 0
\(513\) −1.37018 + 0.995497i −0.0604951 + 0.0439523i
\(514\) 0 0
\(515\) 4.39398 23.6780i 0.193622 1.04338i
\(516\) 0 0
\(517\) −6.06763 + 18.6743i −0.266854 + 0.821293i
\(518\) 0 0
\(519\) −3.58023 + 11.0188i −0.157155 + 0.483672i
\(520\) 0 0
\(521\) 8.10398 + 24.9415i 0.355042 + 1.09271i 0.955985 + 0.293415i \(0.0947918\pi\)
−0.600943 + 0.799292i \(0.705208\pi\)
\(522\) 0 0
\(523\) −12.3978 9.00754i −0.542118 0.393872i 0.282753 0.959193i \(-0.408752\pi\)
−0.824871 + 0.565321i \(0.808752\pi\)
\(524\) 0 0
\(525\) −5.47929 + 6.76013i −0.239136 + 0.295036i
\(526\) 0 0
\(527\) −28.9338 21.0216i −1.26037 0.915716i
\(528\) 0 0
\(529\) 16.1676 + 49.7587i 0.702938 + 2.16342i
\(530\) 0 0
\(531\) 1.35595 4.17317i 0.0588430 0.181100i
\(532\) 0 0
\(533\) −13.3151 + 40.9798i −0.576743 + 1.77503i
\(534\) 0 0
\(535\) 8.53422 + 4.63619i 0.368966 + 0.200440i
\(536\) 0 0
\(537\) 17.8370 12.9593i 0.769722 0.559236i
\(538\) 0 0
\(539\) 7.45435 + 5.41590i 0.321082 + 0.233279i
\(540\) 0 0
\(541\) −7.66742 + 5.57071i −0.329648 + 0.239503i −0.740281 0.672297i \(-0.765308\pi\)
0.410633 + 0.911801i \(0.365308\pi\)
\(542\) 0 0
\(543\) −20.6571 −0.886483
\(544\) 0 0
\(545\) 2.37501 0.312131i 0.101734 0.0133702i
\(546\) 0 0
\(547\) 0.199605 + 0.614321i 0.00853449 + 0.0262665i 0.955233 0.295854i \(-0.0956043\pi\)
−0.946699 + 0.322121i \(0.895604\pi\)
\(548\) 0 0
\(549\) −15.3316 −0.654335
\(550\) 0 0
\(551\) −5.28811 −0.225281
\(552\) 0 0
\(553\) 0.429584 + 1.32212i 0.0182678 + 0.0562224i
\(554\) 0 0
\(555\) −5.16411 10.8331i −0.219204 0.459838i
\(556\) 0 0
\(557\) −12.0297 −0.509716 −0.254858 0.966978i \(-0.582029\pi\)
−0.254858 + 0.966978i \(0.582029\pi\)
\(558\) 0 0
\(559\) −11.4370 + 8.30946i −0.483733 + 0.351453i
\(560\) 0 0
\(561\) 7.02120 + 5.10120i 0.296435 + 0.215373i
\(562\) 0 0
\(563\) −12.8498 + 9.33593i −0.541555 + 0.393462i −0.824662 0.565626i \(-0.808635\pi\)
0.283107 + 0.959088i \(0.408635\pi\)
\(564\) 0 0
\(565\) 41.1513 5.40822i 1.73125 0.227526i
\(566\) 0 0
\(567\) −0.537803 + 1.65519i −0.0225856 + 0.0695114i
\(568\) 0 0
\(569\) 6.77685 20.8570i 0.284100 0.874371i −0.702566 0.711618i \(-0.747963\pi\)
0.986667 0.162753i \(-0.0520374\pi\)
\(570\) 0 0
\(571\) −2.10390 6.47513i −0.0880453 0.270976i 0.897334 0.441353i \(-0.145501\pi\)
−0.985379 + 0.170377i \(0.945501\pi\)
\(572\) 0 0
\(573\) 16.8535 + 12.2448i 0.704067 + 0.511534i
\(574\) 0 0
\(575\) 2.29058 43.3329i 0.0955238 1.80711i
\(576\) 0 0
\(577\) −15.0698 10.9488i −0.627364 0.455806i 0.228122 0.973632i \(-0.426741\pi\)
−0.855486 + 0.517826i \(0.826741\pi\)
\(578\) 0 0
\(579\) −1.47726 4.54655i −0.0613930 0.188948i
\(580\) 0 0
\(581\) −1.27464 + 3.92293i −0.0528809 + 0.162751i
\(582\) 0 0
\(583\) −0.964003 + 2.96690i −0.0399249 + 0.122876i
\(584\) 0 0
\(585\) −8.01158 + 7.59927i −0.331238 + 0.314191i
\(586\) 0 0
\(587\) 11.4963 8.35254i 0.474503 0.344746i −0.324691 0.945820i \(-0.605260\pi\)
0.799194 + 0.601074i \(0.205260\pi\)
\(588\) 0 0
\(589\) 13.1012 + 9.51860i 0.539827 + 0.392207i
\(590\) 0 0
\(591\) 14.0381 10.1993i 0.577450 0.419542i
\(592\) 0 0
\(593\) 40.7850 1.67484 0.837420 0.546559i \(-0.184063\pi\)
0.837420 + 0.546559i \(0.184063\pi\)
\(594\) 0 0
\(595\) 10.5608 10.0173i 0.432949 0.410668i
\(596\) 0 0
\(597\) −3.42255 10.5335i −0.140076 0.431109i
\(598\) 0 0
\(599\) 34.8928 1.42568 0.712841 0.701326i \(-0.247408\pi\)
0.712841 + 0.701326i \(0.247408\pi\)
\(600\) 0 0
\(601\) 10.6287 0.433552 0.216776 0.976221i \(-0.430446\pi\)
0.216776 + 0.976221i \(0.430446\pi\)
\(602\) 0 0
\(603\) 2.85246 + 8.77897i 0.116161 + 0.357507i
\(604\) 0 0
\(605\) −2.29139 + 12.3477i −0.0931582 + 0.502005i
\(606\) 0 0
\(607\) 30.5033 1.23809 0.619045 0.785355i \(-0.287520\pi\)
0.619045 + 0.785355i \(0.287520\pi\)
\(608\) 0 0
\(609\) −4.39620 + 3.19403i −0.178143 + 0.129429i
\(610\) 0 0
\(611\) 33.8091 + 24.5638i 1.36777 + 0.993743i
\(612\) 0 0
\(613\) 10.3337 7.50789i 0.417375 0.303241i −0.359206 0.933258i \(-0.616952\pi\)
0.776581 + 0.630018i \(0.216952\pi\)
\(614\) 0 0
\(615\) 8.39555 + 17.6119i 0.338541 + 0.710179i
\(616\) 0 0
\(617\) −3.68740 + 11.3486i −0.148449 + 0.456879i −0.997438 0.0715308i \(-0.977212\pi\)
0.848989 + 0.528410i \(0.177212\pi\)
\(618\) 0 0
\(619\) −4.48215 + 13.7946i −0.180153 + 0.554454i −0.999831 0.0183705i \(-0.994152\pi\)
0.819678 + 0.572824i \(0.194152\pi\)
\(620\) 0 0
\(621\) −2.68186 8.25391i −0.107619 0.331218i
\(622\) 0 0
\(623\) −6.84570 4.97369i −0.274267 0.199267i
\(624\) 0 0
\(625\) −10.1890 + 22.8295i −0.407561 + 0.913178i
\(626\) 0 0
\(627\) −3.17920 2.30982i −0.126965 0.0922455i
\(628\) 0 0
\(629\) 6.20338 + 19.0920i 0.247345 + 0.761249i
\(630\) 0 0
\(631\) −1.13341 + 3.48828i −0.0451204 + 0.138866i −0.971079 0.238759i \(-0.923259\pi\)
0.925958 + 0.377626i \(0.123259\pi\)
\(632\) 0 0
\(633\) −1.75182 + 5.39156i −0.0696288 + 0.214295i
\(634\) 0 0
\(635\) 18.2910 + 38.3701i 0.725854 + 1.52267i
\(636\) 0 0
\(637\) 15.8653 11.5268i 0.628607 0.456710i
\(638\) 0 0
\(639\) −0.0190641 0.0138509i −0.000754164 0.000547932i
\(640\) 0 0
\(641\) 11.2064 8.14192i 0.442626 0.321587i −0.344051 0.938951i \(-0.611799\pi\)
0.786678 + 0.617364i \(0.211799\pi\)
\(642\) 0 0
\(643\) −27.1641 −1.07125 −0.535624 0.844456i \(-0.679924\pi\)
−0.535624 + 0.844456i \(0.679924\pi\)
\(644\) 0 0
\(645\) −1.16794 + 6.29374i −0.0459878 + 0.247816i
\(646\) 0 0
\(647\) −1.59140 4.89783i −0.0625644 0.192553i 0.914889 0.403706i \(-0.132278\pi\)
−0.977453 + 0.211153i \(0.932278\pi\)
\(648\) 0 0
\(649\) 10.1812 0.399647
\(650\) 0 0
\(651\) 16.6408 0.652204
\(652\) 0 0
\(653\) −9.16957 28.2210i −0.358833 1.10437i −0.953753 0.300590i \(-0.902816\pi\)
0.594920 0.803785i \(-0.297184\pi\)
\(654\) 0 0
\(655\) 1.20869 1.14649i 0.0472274 0.0447969i
\(656\) 0 0
\(657\) −1.02251 −0.0398920
\(658\) 0 0
\(659\) −12.7614 + 9.27170i −0.497114 + 0.361174i −0.807913 0.589301i \(-0.799403\pi\)
0.310800 + 0.950475i \(0.399403\pi\)
\(660\) 0 0
\(661\) 19.4614 + 14.1396i 0.756962 + 0.549965i 0.897977 0.440042i \(-0.145037\pi\)
−0.141015 + 0.990007i \(0.545037\pi\)
\(662\) 0 0
\(663\) 14.9434 10.8570i 0.580354 0.421652i
\(664\) 0 0
\(665\) −4.78192 + 4.53582i −0.185435 + 0.175892i
\(666\) 0 0
\(667\) 8.37366 25.7715i 0.324229 0.997875i
\(668\) 0 0
\(669\) 6.60694 20.3341i 0.255439 0.786161i
\(670\) 0 0
\(671\) −10.9928 33.8323i −0.424372 1.30608i
\(672\) 0 0
\(673\) −25.8914 18.8112i −0.998040 0.725119i −0.0363731 0.999338i \(-0.511580\pi\)
−0.961667 + 0.274220i \(0.911580\pi\)
\(674\) 0 0
\(675\) −0.263932 + 4.99303i −0.0101587 + 0.192182i
\(676\) 0 0
\(677\) 19.7246 + 14.3307i 0.758077 + 0.550775i 0.898320 0.439342i \(-0.144788\pi\)
−0.140243 + 0.990117i \(0.544788\pi\)
\(678\) 0 0
\(679\) 1.86161 + 5.72944i 0.0714420 + 0.219876i
\(680\) 0 0
\(681\) 7.09579 21.8386i 0.271911 0.836856i
\(682\) 0 0
\(683\) −3.44642 + 10.6070i −0.131873 + 0.405865i −0.995091 0.0989680i \(-0.968446\pi\)
0.863217 + 0.504833i \(0.168446\pi\)
\(684\) 0 0
\(685\) −24.6809 + 3.24364i −0.943010 + 0.123933i
\(686\) 0 0
\(687\) −22.7371 + 16.5195i −0.867476 + 0.630258i
\(688\) 0 0
\(689\) 5.37146 + 3.90260i 0.204636 + 0.148677i
\(690\) 0 0
\(691\) −8.76055 + 6.36491i −0.333267 + 0.242133i −0.741816 0.670604i \(-0.766035\pi\)
0.408549 + 0.912737i \(0.366035\pi\)
\(692\) 0 0
\(693\) −4.03813 −0.153396
\(694\) 0 0
\(695\) 13.1714 + 27.6305i 0.499620 + 1.04808i
\(696\) 0 0
\(697\) −10.0851 31.0389i −0.382002 1.17568i
\(698\) 0 0
\(699\) 1.33195 0.0503791
\(700\) 0 0
\(701\) 43.2512 1.63357 0.816787 0.576939i \(-0.195753\pi\)
0.816787 + 0.576939i \(0.195753\pi\)
\(702\) 0 0
\(703\) −2.80889 8.64488i −0.105939 0.326048i
\(704\) 0 0
\(705\) 18.7614 2.46568i 0.706594 0.0928627i
\(706\) 0 0
\(707\) 13.1930 0.496172
\(708\) 0 0
\(709\) 36.0864 26.2183i 1.35525 0.984649i 0.356522 0.934287i \(-0.383963\pi\)
0.998731 0.0503617i \(-0.0160374\pi\)
\(710\) 0 0
\(711\) 0.646223 + 0.469509i 0.0242353 + 0.0176079i
\(712\) 0 0
\(713\) −67.1343 + 48.7759i −2.51420 + 1.82667i
\(714\) 0 0
\(715\) −22.5137 12.2305i −0.841966 0.457396i
\(716\) 0 0
\(717\) −1.06465 + 3.27666i −0.0397602 + 0.122369i
\(718\) 0 0
\(719\) −9.91537 + 30.5164i −0.369781 + 1.13807i 0.577152 + 0.816637i \(0.304164\pi\)
−0.946933 + 0.321432i \(0.895836\pi\)
\(720\) 0 0
\(721\) −5.79208 17.8262i −0.215708 0.663882i
\(722\) 0 0
\(723\) −19.4923 14.1620i −0.724926 0.526689i
\(724\) 0 0
\(725\) −9.83021 + 12.1281i −0.365085 + 0.450427i
\(726\) 0 0
\(727\) 11.0201 + 8.00656i 0.408712 + 0.296947i 0.773080 0.634308i \(-0.218715\pi\)
−0.364368 + 0.931255i \(0.618715\pi\)
\(728\) 0 0
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) 3.30882 10.1835i 0.122381 0.376650i
\(732\) 0 0
\(733\) 8.78355 27.0330i 0.324428 0.998486i −0.647271 0.762260i \(-0.724090\pi\)
0.971698 0.236225i \(-0.0759104\pi\)
\(734\) 0 0
\(735\) 1.62017 8.73064i 0.0597607 0.322035i
\(736\) 0 0
\(737\) −17.3274 + 12.5891i −0.638264 + 0.463726i
\(738\) 0 0
\(739\) −7.85925 5.71008i −0.289107 0.210049i 0.433773 0.901022i \(-0.357182\pi\)
−0.722880 + 0.690974i \(0.757182\pi\)
\(740\) 0 0
\(741\) −6.76639 + 4.91607i −0.248569 + 0.180596i
\(742\) 0 0
\(743\) 34.2029 1.25478 0.627390 0.778705i \(-0.284123\pi\)
0.627390 + 0.778705i \(0.284123\pi\)
\(744\) 0 0
\(745\) 20.8830 + 11.3446i 0.765093 + 0.415635i
\(746\) 0 0
\(747\) 0.732396 + 2.25408i 0.0267970 + 0.0824726i
\(748\) 0 0
\(749\) 7.55917 0.276206
\(750\) 0 0
\(751\) −12.7840 −0.466495 −0.233248 0.972417i \(-0.574935\pi\)
−0.233248 + 0.972417i \(0.574935\pi\)
\(752\) 0 0
\(753\) 9.32060 + 28.6859i 0.339661 + 1.04537i
\(754\) 0 0
\(755\) 20.5698 + 11.1745i 0.748610 + 0.406681i
\(756\) 0 0
\(757\) 26.6200 0.967520 0.483760 0.875201i \(-0.339271\pi\)
0.483760 + 0.875201i \(0.339271\pi\)
\(758\) 0 0
\(759\) 16.2911 11.8362i 0.591329 0.429626i
\(760\) 0 0
\(761\) −20.8028 15.1141i −0.754102 0.547887i 0.142993 0.989724i \(-0.454327\pi\)
−0.897096 + 0.441836i \(0.854327\pi\)
\(762\) 0 0
\(763\) 1.50833 1.09587i 0.0546053 0.0396731i
\(764\) 0 0
\(765\) 1.52602 8.22332i 0.0551734 0.297315i
\(766\) 0 0
\(767\) 6.69607 20.6084i 0.241781 0.744126i
\(768\) 0 0
\(769\) −11.8575 + 36.4937i −0.427593 + 1.31600i 0.472897 + 0.881118i \(0.343208\pi\)
−0.900490 + 0.434877i \(0.856792\pi\)
\(770\) 0 0
\(771\) −3.30222 10.1632i −0.118927 0.366019i
\(772\) 0 0
\(773\) 1.13168 + 0.822215i 0.0407038 + 0.0295730i 0.607951 0.793974i \(-0.291992\pi\)
−0.567247 + 0.823547i \(0.691992\pi\)
\(774\) 0 0
\(775\) 46.1848 12.3529i 1.65901 0.443728i
\(776\) 0 0
\(777\) −7.55667 5.49024i −0.271094 0.196961i
\(778\) 0 0
\(779\) 4.56656 + 14.0544i 0.163614 + 0.503552i
\(780\) 0 0
\(781\) 0.0168959 0.0520001i 0.000604581 0.00186071i
\(782\) 0 0
\(783\) −0.964854 + 2.96952i −0.0344811 + 0.106122i
\(784\) 0 0
\(785\) 33.9895 + 18.4647i 1.21314 + 0.659034i
\(786\) 0 0
\(787\) 3.40614 2.47471i 0.121416 0.0882138i −0.525420 0.850843i \(-0.676092\pi\)
0.646836 + 0.762629i \(0.276092\pi\)
\(788\) 0 0
\(789\) 7.46948 + 5.42689i 0.265920 + 0.193203i
\(790\) 0 0
\(791\) 26.1346 18.9879i 0.929238 0.675131i
\(792\) 0 0
\(793\) −75.7119 −2.68861
\(794\) 0 0
\(795\) 2.98073 0.391737i 0.105716 0.0138935i
\(796\) 0 0
\(797\) −9.77099 30.0720i −0.346106 1.06521i −0.960989 0.276587i \(-0.910797\pi\)
0.614883 0.788619i \(-0.289203\pi\)
\(798\) 0 0
\(799\) −31.6528 −1.11980
\(800\) 0 0
\(801\) −4.86205 −0.171792
\(802\) 0 0
\(803\) −0.733145 2.25639i −0.0258721 0.0796263i
\(804\) 0 0
\(805\) −14.5331 30.4870i −0.512225 1.07452i
\(806\) 0 0
\(807\) −26.7381 −0.941224
\(808\) 0 0
\(809\) −34.0676 + 24.7515i −1.19775 + 0.870218i −0.994062 0.108817i \(-0.965294\pi\)
−0.203691 + 0.979035i \(0.565294\pi\)
\(810\) 0 0
\(811\) −12.2591 8.90674i −0.430474 0.312758i 0.351364 0.936239i \(-0.385718\pi\)
−0.781838 + 0.623481i \(0.785718\pi\)
\(812\) 0 0
\(813\) 19.5652 14.2150i 0.686183 0.498541i
\(814\) 0 0
\(815\) −13.6276 + 1.79099i −0.477356 + 0.0627355i
\(816\) 0 0
\(817\) −1.49823 + 4.61109i −0.0524166 + 0.161322i
\(818\) 0 0
\(819\) −2.65584 + 8.17383i −0.0928025 + 0.285617i
\(820\) 0 0
\(821\) −0.124324 0.382629i −0.00433893 0.0133538i 0.948864 0.315686i \(-0.102235\pi\)
−0.953203 + 0.302332i \(0.902235\pi\)
\(822\) 0 0
\(823\) 0.492983 + 0.358173i 0.0171843 + 0.0124851i 0.596344 0.802729i \(-0.296619\pi\)
−0.579160 + 0.815214i \(0.696619\pi\)
\(824\) 0 0
\(825\) −11.2074 + 2.99760i −0.390192 + 0.104363i
\(826\) 0 0
\(827\) −22.2214 16.1448i −0.772715 0.561410i 0.130069 0.991505i \(-0.458480\pi\)
−0.902784 + 0.430095i \(0.858480\pi\)
\(828\) 0 0
\(829\) 9.62722 + 29.6295i 0.334367 + 1.02908i 0.967033 + 0.254651i \(0.0819607\pi\)
−0.632666 + 0.774425i \(0.718039\pi\)
\(830\) 0 0
\(831\) 9.76738 30.0609i 0.338827 1.04280i
\(832\) 0 0
\(833\) −4.58997 + 14.1265i −0.159033 + 0.489453i
\(834\) 0 0
\(835\) 3.08272 2.92407i 0.106682 0.101192i
\(836\) 0 0
\(837\) 7.73554 5.62020i 0.267379 0.194263i
\(838\) 0 0
\(839\) −31.6468 22.9927i −1.09257 0.793798i −0.112738 0.993625i \(-0.535962\pi\)
−0.979831 + 0.199827i \(0.935962\pi\)
\(840\) 0 0
\(841\) 15.5744 11.3155i 0.537049 0.390189i
\(842\) 0 0
\(843\) −23.2625 −0.801204
\(844\) 0 0
\(845\) −18.4733 + 17.5226i −0.635501 + 0.602796i
\(846\) 0 0
\(847\) 3.02048 + 9.29608i 0.103785 + 0.319417i
\(848\) 0 0
\(849\) −24.8321 −0.852236
\(850\) 0 0
\(851\) 46.5785 1.59669
\(852\) 0 0
\(853\) −16.2468 50.0025i −0.556279 1.71205i −0.692541 0.721379i \(-0.743509\pi\)
0.136261 0.990673i \(-0.456491\pi\)
\(854\) 0 0
\(855\) −0.690983 + 3.72352i −0.0236311 + 0.127342i
\(856\) 0 0
\(857\) −31.0291 −1.05993 −0.529967 0.848018i \(-0.677796\pi\)
−0.529967 + 0.848018i \(0.677796\pi\)
\(858\) 0 0
\(859\) −31.4263 + 22.8325i −1.07225 + 0.779035i −0.976315 0.216353i \(-0.930584\pi\)
−0.0959345 + 0.995388i \(0.530584\pi\)
\(860\) 0 0
\(861\) 12.2853 + 8.92576i 0.418680 + 0.304189i
\(862\) 0 0
\(863\) 2.91445 2.11748i 0.0992092 0.0720797i −0.537075 0.843535i \(-0.680471\pi\)
0.636284 + 0.771455i \(0.280471\pi\)
\(864\) 0 0
\(865\) 11.1479 + 23.3856i 0.379040 + 0.795134i
\(866\) 0 0
\(867\) 0.930033 2.86235i 0.0315856 0.0972104i
\(868\) 0 0
\(869\) −0.572725 + 1.76267i −0.0194284 + 0.0597944i
\(870\) 0 0
\(871\) 14.0863 + 43.3532i 0.477297 + 1.46897i
\(872\) 0 0
\(873\) 2.80042 + 2.03462i 0.0947798 + 0.0688615i
\(874\) 0 0
\(875\) 1.51352 + 19.3989i 0.0511665 + 0.655804i
\(876\) 0 0
\(877\) 25.5323 + 18.5503i 0.862165 + 0.626399i 0.928473 0.371400i \(-0.121122\pi\)
−0.0663082 + 0.997799i \(0.521122\pi\)
\(878\) 0 0
\(879\) −9.04673 27.8430i −0.305139 0.939120i
\(880\) 0 0
\(881\) 1.86270 5.73280i 0.0627560 0.193143i −0.914763 0.403991i \(-0.867623\pi\)
0.977519 + 0.210848i \(0.0676226\pi\)
\(882\) 0 0
\(883\) −1.22550 + 3.77171i −0.0412414 + 0.126928i −0.969557 0.244864i \(-0.921257\pi\)
0.928316 + 0.371792i \(0.121257\pi\)
\(884\) 0 0
\(885\) −4.22205 8.85686i −0.141923 0.297720i
\(886\) 0 0
\(887\) −45.0745 + 32.7485i −1.51345 + 1.09959i −0.548836 + 0.835930i \(0.684929\pi\)
−0.964616 + 0.263657i \(0.915071\pi\)
\(888\) 0 0
\(889\) 26.7652 + 19.4461i 0.897677 + 0.652201i
\(890\) 0 0
\(891\) −1.87714 + 1.36382i −0.0628866 + 0.0456898i
\(892\) 0 0
\(893\) 14.3324 0.479616
\(894\) 0 0
\(895\) 8.99517 48.4726i 0.300676 1.62026i
\(896\) 0 0
\(897\) −13.2438 40.7603i −0.442199 1.36095i
\(898\) 0 0
\(899\) 29.8547 0.995709
\(900\) 0 0
\(901\) −5.02888 −0.167536
\(902\) 0 0
\(903\) 1.53957 + 4.73831i 0.0512337 + 0.157681i
\(904\) 0 0
\(905\) −33.5128 + 31.7881i −1.11400 + 1.05667i
\(906\) 0 0
\(907\) −21.4063 −0.710785 −0.355392 0.934717i \(-0.615653\pi\)
−0.355392 + 0.934717i \(0.615653\pi\)
\(908\) 0 0
\(909\) 6.13280 4.45574i 0.203412 0.147788i
\(910\) 0 0
\(911\) −25.5560 18.5676i −0.846709 0.615170i 0.0775273 0.996990i \(-0.475298\pi\)
−0.924237 + 0.381820i \(0.875298\pi\)
\(912\) 0 0
\(913\) −4.44898 + 3.23237i −0.147240 + 0.106976i
\(914\) 0 0
\(915\) −24.8729 + 23.5928i −0.822272 + 0.779955i
\(916\) 0 0
\(917\) 0.400680 1.23317i 0.0132316 0.0407228i
\(918\) 0 0
\(919\) −5.58626 + 17.1927i −0.184274 + 0.567136i −0.999935 0.0113935i \(-0.996373\pi\)
0.815661 + 0.578530i \(0.196373\pi\)
\(920\) 0 0
\(921\) −2.70072 8.31197i −0.0889918 0.273889i
\(922\) 0 0
\(923\) −0.0941444 0.0683999i −0.00309880 0.00225141i
\(924\) 0 0
\(925\) −25.0483 9.62810i −0.823583 0.316570i
\(926\) 0 0
\(927\) −8.71303 6.33039i −0.286173 0.207917i
\(928\) 0 0
\(929\) 2.75953 + 8.49296i 0.0905373 + 0.278645i 0.986065 0.166361i \(-0.0532016\pi\)
−0.895528 + 0.445006i \(0.853202\pi\)
\(930\) 0 0
\(931\) 2.07834 6.39647i 0.0681149 0.209636i
\(932\) 0 0
\(933\) 4.77620 14.6996i 0.156366 0.481245i
\(934\) 0 0
\(935\) 19.2407 2.52867i 0.629237 0.0826962i
\(936\) 0 0
\(937\) 0.0491192 0.0356872i 0.00160466 0.00116585i −0.586983 0.809600i \(-0.699684\pi\)
0.588587 + 0.808434i \(0.299684\pi\)
\(938\) 0 0
\(939\) −1.26124 0.916343i −0.0411589 0.0299037i
\(940\) 0 0
\(941\) −16.7021 + 12.1348i −0.544473 + 0.395583i −0.825744 0.564046i \(-0.809244\pi\)
0.281271 + 0.959628i \(0.409244\pi\)
\(942\) 0 0
\(943\) −75.7249 −2.46594
\(944\) 0 0
\(945\) 1.67458 + 3.51286i 0.0544740 + 0.114273i
\(946\) 0 0
\(947\) 15.8787 + 48.8696i 0.515988 + 1.58805i 0.781477 + 0.623934i \(0.214466\pi\)
−0.265489 + 0.964114i \(0.585534\pi\)
\(948\) 0 0
\(949\) −5.04948 −0.163913
\(950\) 0 0
\(951\) 5.46256 0.177136
\(952\) 0 0
\(953\) 7.58457 + 23.3429i 0.245688 + 0.756151i 0.995522 + 0.0945251i \(0.0301333\pi\)
−0.749834 + 0.661626i \(0.769867\pi\)
\(954\) 0 0
\(955\) 46.1849 6.06976i 1.49451 0.196413i
\(956\) 0 0
\(957\) −7.24467 −0.234187
\(958\) 0 0
\(959\) −15.6745 + 11.3882i −0.506156 + 0.367744i
\(960\) 0 0
\(961\) −48.8851 35.5171i −1.57694 1.14571i
\(962\) 0 0
\(963\) 3.51391 2.55301i 0.113234 0.0822695i
\(964\) 0 0
\(965\) −9.39304 5.10275i −0.302373 0.164263i
\(966\) 0 0
\(967\) 11.7996 36.3155i 0.379451 1.16783i −0.560976 0.827832i \(-0.689574\pi\)
0.940427 0.339997i \(-0.110426\pi\)
\(968\) 0 0
\(969\) 1.95757 6.02479i 0.0628863 0.193544i
\(970\) 0 0
\(971\) 7.97794 + 24.5536i 0.256024 + 0.787962i 0.993626 + 0.112726i \(0.0359582\pi\)
−0.737602 + 0.675236i \(0.764042\pi\)
\(972\) 0 0
\(973\) 19.2738 + 14.0032i 0.617889 + 0.448923i
\(974\) 0 0
\(975\) −1.30338 + 24.6571i −0.0417415 + 0.789660i
\(976\) 0 0
\(977\) −16.6867 12.1236i −0.533855 0.387868i 0.287943 0.957648i \(-0.407029\pi\)
−0.821798 + 0.569779i \(0.807029\pi\)
\(978\) 0 0
\(979\) −3.48611 10.7291i −0.111417 0.342905i
\(980\) 0 0
\(981\) 0.331041 1.01884i 0.0105693 0.0325290i
\(982\) 0 0
\(983\) −6.83966 + 21.0503i −0.218151 + 0.671401i 0.780763 + 0.624827i \(0.214830\pi\)
−0.998915 + 0.0465741i \(0.985170\pi\)
\(984\) 0 0
\(985\) 7.07940 38.1490i 0.225569 1.21553i
\(986\) 0 0
\(987\) 11.9151 8.65680i 0.379261 0.275549i
\(988\) 0 0
\(989\) −20.0996 14.6032i −0.639130 0.464355i
\(990\) 0 0
\(991\) 1.34709 0.978715i 0.0427916 0.0310899i −0.566184 0.824279i \(-0.691581\pi\)
0.608975 + 0.793189i \(0.291581\pi\)
\(992\) 0 0
\(993\) −0.855804 −0.0271581
\(994\) 0 0
\(995\) −21.7620 11.8221i −0.689900 0.374787i
\(996\) 0 0
\(997\) −7.25453 22.3271i −0.229753 0.707108i −0.997774 0.0666831i \(-0.978758\pi\)
0.768021 0.640425i \(-0.221242\pi\)
\(998\) 0 0
\(999\) −5.36700 −0.169804
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 300.2.m.b.241.1 yes 8
3.2 odd 2 900.2.n.b.541.2 8
5.2 odd 4 1500.2.o.b.49.1 16
5.3 odd 4 1500.2.o.b.49.4 16
5.4 even 2 1500.2.m.a.1201.2 8
25.2 odd 20 1500.2.o.b.949.3 16
25.6 even 5 7500.2.a.e.1.1 4
25.8 odd 20 7500.2.d.c.1249.4 8
25.11 even 5 inner 300.2.m.b.61.1 8
25.14 even 10 1500.2.m.a.301.2 8
25.17 odd 20 7500.2.d.c.1249.5 8
25.19 even 10 7500.2.a.f.1.4 4
25.23 odd 20 1500.2.o.b.949.2 16
75.11 odd 10 900.2.n.b.361.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
300.2.m.b.61.1 8 25.11 even 5 inner
300.2.m.b.241.1 yes 8 1.1 even 1 trivial
900.2.n.b.361.2 8 75.11 odd 10
900.2.n.b.541.2 8 3.2 odd 2
1500.2.m.a.301.2 8 25.14 even 10
1500.2.m.a.1201.2 8 5.4 even 2
1500.2.o.b.49.1 16 5.2 odd 4
1500.2.o.b.49.4 16 5.3 odd 4
1500.2.o.b.949.2 16 25.23 odd 20
1500.2.o.b.949.3 16 25.2 odd 20
7500.2.a.e.1.1 4 25.6 even 5
7500.2.a.f.1.4 4 25.19 even 10
7500.2.d.c.1249.4 8 25.8 odd 20
7500.2.d.c.1249.5 8 25.17 odd 20