Properties

Label 756.2.bp.a.193.19
Level $756$
Weight $2$
Character 756.193
Analytic conductor $6.037$
Analytic rank $0$
Dimension $144$
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] = [756,2,Mod(193,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 2, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.bp (of order \(9\), degree \(6\), 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: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 193.19
Character \(\chi\) \(=\) 756.193
Dual form 756.2.bp.a.709.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.17989 + 1.26802i) q^{3} +(3.75808 - 1.36783i) q^{5} +(2.59104 - 0.535278i) q^{7} +(-0.215726 + 2.99223i) q^{9} +O(q^{10})\) \(q+(1.17989 + 1.26802i) q^{3} +(3.75808 - 1.36783i) q^{5} +(2.59104 - 0.535278i) q^{7} +(-0.215726 + 2.99223i) q^{9} +(-0.974227 - 0.354590i) q^{11} +(-1.95754 + 0.712485i) q^{13} +(6.16854 + 3.15142i) q^{15} +(-0.153243 - 0.265426i) q^{17} +(0.388297 - 0.672550i) q^{19} +(3.73588 + 2.65391i) q^{21} +(0.439761 - 2.49401i) q^{23} +(8.42198 - 7.06688i) q^{25} +(-4.04873 + 3.25696i) q^{27} +(-8.90667 - 3.24176i) q^{29} +(-3.70422 + 1.34823i) q^{31} +(-0.699854 - 1.65371i) q^{33} +(9.00516 - 5.55571i) q^{35} -11.1327 q^{37} +(-3.21312 - 1.64153i) q^{39} +(-4.30886 + 1.56830i) q^{41} +(0.781068 + 4.42966i) q^{43} +(3.28215 + 11.5401i) q^{45} +(7.60578 + 2.76828i) q^{47} +(6.42695 - 2.77385i) q^{49} +(0.155753 - 0.507488i) q^{51} +(4.78182 - 8.28236i) q^{53} -4.14624 q^{55} +(1.31095 - 0.301167i) q^{57} +(10.3022 + 8.64456i) q^{59} +(-7.68941 - 2.79872i) q^{61} +(1.04272 + 7.86846i) q^{63} +(-6.38202 + 5.35515i) q^{65} +(-1.81338 + 10.2842i) q^{67} +(3.68131 - 2.38503i) q^{69} +(0.987174 - 1.70984i) q^{71} +3.18187 q^{73} +(18.8979 + 2.34107i) q^{75} +(-2.71406 - 0.397273i) q^{77} +(0.931268 + 5.28148i) q^{79} +(-8.90692 - 1.29101i) q^{81} +(6.70366 + 2.43993i) q^{83} +(-0.938958 - 0.787879i) q^{85} +(-6.39827 - 15.1187i) q^{87} +(-1.30794 + 2.26541i) q^{89} +(-4.69068 + 2.89390i) q^{91} +(-6.08014 - 3.10625i) q^{93} +(0.539317 - 3.05862i) q^{95} +(1.31999 + 7.48602i) q^{97} +(1.27118 - 2.83862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.17989 + 1.26802i 0.681209 + 0.732089i
\(4\) 0 0
\(5\) 3.75808 1.36783i 1.68066 0.611712i 0.687264 0.726408i \(-0.258812\pi\)
0.993401 + 0.114696i \(0.0365895\pi\)
\(6\) 0 0
\(7\) 2.59104 0.535278i 0.979320 0.202316i
\(8\) 0 0
\(9\) −0.215726 + 2.99223i −0.0719088 + 0.997411i
\(10\) 0 0
\(11\) −0.974227 0.354590i −0.293741 0.106913i 0.190947 0.981600i \(-0.438844\pi\)
−0.484687 + 0.874688i \(0.661067\pi\)
\(12\) 0 0
\(13\) −1.95754 + 0.712485i −0.542923 + 0.197608i −0.598899 0.800824i \(-0.704395\pi\)
0.0559763 + 0.998432i \(0.482173\pi\)
\(14\) 0 0
\(15\) 6.16854 + 3.15142i 1.59271 + 0.813692i
\(16\) 0 0
\(17\) −0.153243 0.265426i −0.0371670 0.0643751i 0.846844 0.531842i \(-0.178500\pi\)
−0.884011 + 0.467467i \(0.845167\pi\)
\(18\) 0 0
\(19\) 0.388297 0.672550i 0.0890814 0.154294i −0.818042 0.575159i \(-0.804940\pi\)
0.907123 + 0.420865i \(0.138274\pi\)
\(20\) 0 0
\(21\) 3.73588 + 2.65391i 0.815235 + 0.579130i
\(22\) 0 0
\(23\) 0.439761 2.49401i 0.0916965 0.520037i −0.904013 0.427505i \(-0.859393\pi\)
0.995710 0.0925322i \(-0.0294961\pi\)
\(24\) 0 0
\(25\) 8.42198 7.06688i 1.68440 1.41338i
\(26\) 0 0
\(27\) −4.04873 + 3.25696i −0.779179 + 0.626802i
\(28\) 0 0
\(29\) −8.90667 3.24176i −1.65393 0.601980i −0.664536 0.747257i \(-0.731371\pi\)
−0.989391 + 0.145276i \(0.953593\pi\)
\(30\) 0 0
\(31\) −3.70422 + 1.34823i −0.665298 + 0.242149i −0.652522 0.757770i \(-0.726289\pi\)
−0.0127760 + 0.999918i \(0.504067\pi\)
\(32\) 0 0
\(33\) −0.699854 1.65371i −0.121829 0.287874i
\(34\) 0 0
\(35\) 9.00516 5.55571i 1.52215 0.939087i
\(36\) 0 0
\(37\) −11.1327 −1.83020 −0.915102 0.403223i \(-0.867890\pi\)
−0.915102 + 0.403223i \(0.867890\pi\)
\(38\) 0 0
\(39\) −3.21312 1.64153i −0.514511 0.262856i
\(40\) 0 0
\(41\) −4.30886 + 1.56830i −0.672931 + 0.244927i −0.655809 0.754927i \(-0.727672\pi\)
−0.0171215 + 0.999853i \(0.505450\pi\)
\(42\) 0 0
\(43\) 0.781068 + 4.42966i 0.119112 + 0.675517i 0.984632 + 0.174642i \(0.0558769\pi\)
−0.865520 + 0.500874i \(0.833012\pi\)
\(44\) 0 0
\(45\) 3.28215 + 11.5401i 0.489274 + 1.72030i
\(46\) 0 0
\(47\) 7.60578 + 2.76828i 1.10942 + 0.403795i 0.830780 0.556602i \(-0.187895\pi\)
0.278637 + 0.960396i \(0.410117\pi\)
\(48\) 0 0
\(49\) 6.42695 2.77385i 0.918136 0.396265i
\(50\) 0 0
\(51\) 0.155753 0.507488i 0.0218098 0.0710625i
\(52\) 0 0
\(53\) 4.78182 8.28236i 0.656834 1.13767i −0.324597 0.945853i \(-0.605229\pi\)
0.981431 0.191817i \(-0.0614381\pi\)
\(54\) 0 0
\(55\) −4.14624 −0.559079
\(56\) 0 0
\(57\) 1.31095 0.301167i 0.173640 0.0398906i
\(58\) 0 0
\(59\) 10.3022 + 8.64456i 1.34123 + 1.12543i 0.981308 + 0.192443i \(0.0616409\pi\)
0.359921 + 0.932983i \(0.382804\pi\)
\(60\) 0 0
\(61\) −7.68941 2.79872i −0.984528 0.358339i −0.200929 0.979606i \(-0.564396\pi\)
−0.783599 + 0.621267i \(0.786618\pi\)
\(62\) 0 0
\(63\) 1.04272 + 7.86846i 0.131371 + 0.991333i
\(64\) 0 0
\(65\) −6.38202 + 5.35515i −0.791592 + 0.664225i
\(66\) 0 0
\(67\) −1.81338 + 10.2842i −0.221540 + 1.25641i 0.647651 + 0.761937i \(0.275752\pi\)
−0.869191 + 0.494477i \(0.835360\pi\)
\(68\) 0 0
\(69\) 3.68131 2.38503i 0.443178 0.287124i
\(70\) 0 0
\(71\) 0.987174 1.70984i 0.117156 0.202920i −0.801484 0.598017i \(-0.795956\pi\)
0.918640 + 0.395097i \(0.129289\pi\)
\(72\) 0 0
\(73\) 3.18187 0.372410 0.186205 0.982511i \(-0.440381\pi\)
0.186205 + 0.982511i \(0.440381\pi\)
\(74\) 0 0
\(75\) 18.8979 + 2.34107i 2.18214 + 0.270324i
\(76\) 0 0
\(77\) −2.71406 0.397273i −0.309296 0.0452734i
\(78\) 0 0
\(79\) 0.931268 + 5.28148i 0.104776 + 0.594213i 0.991310 + 0.131549i \(0.0419952\pi\)
−0.886534 + 0.462664i \(0.846894\pi\)
\(80\) 0 0
\(81\) −8.90692 1.29101i −0.989658 0.143445i
\(82\) 0 0
\(83\) 6.70366 + 2.43993i 0.735823 + 0.267818i 0.682627 0.730767i \(-0.260837\pi\)
0.0531953 + 0.998584i \(0.483059\pi\)
\(84\) 0 0
\(85\) −0.938958 0.787879i −0.101844 0.0854575i
\(86\) 0 0
\(87\) −6.39827 15.1187i −0.685967 1.62090i
\(88\) 0 0
\(89\) −1.30794 + 2.26541i −0.138641 + 0.240133i −0.926982 0.375105i \(-0.877607\pi\)
0.788342 + 0.615238i \(0.210940\pi\)
\(90\) 0 0
\(91\) −4.69068 + 2.89390i −0.491716 + 0.303363i
\(92\) 0 0
\(93\) −6.08014 3.10625i −0.630481 0.322104i
\(94\) 0 0
\(95\) 0.539317 3.05862i 0.0553328 0.313808i
\(96\) 0 0
\(97\) 1.31999 + 7.48602i 0.134024 + 0.760090i 0.975534 + 0.219848i \(0.0705562\pi\)
−0.841510 + 0.540242i \(0.818333\pi\)
\(98\) 0 0
\(99\) 1.27118 2.83862i 0.127759 0.285292i
\(100\) 0 0
\(101\) 0.102391 + 0.580686i 0.0101882 + 0.0577804i 0.989478 0.144683i \(-0.0462163\pi\)
−0.979290 + 0.202464i \(0.935105\pi\)
\(102\) 0 0
\(103\) −13.4888 + 4.90952i −1.32909 + 0.483749i −0.906360 0.422507i \(-0.861150\pi\)
−0.422730 + 0.906256i \(0.638928\pi\)
\(104\) 0 0
\(105\) 17.6698 + 4.86356i 1.72440 + 0.474634i
\(106\) 0 0
\(107\) 2.45480 + 4.25184i 0.237314 + 0.411040i 0.959943 0.280196i \(-0.0903995\pi\)
−0.722628 + 0.691237i \(0.757066\pi\)
\(108\) 0 0
\(109\) −3.25895 + 5.64467i −0.312151 + 0.540661i −0.978828 0.204686i \(-0.934383\pi\)
0.666677 + 0.745347i \(0.267716\pi\)
\(110\) 0 0
\(111\) −13.1353 14.1164i −1.24675 1.33987i
\(112\) 0 0
\(113\) −0.164509 + 0.932979i −0.0154757 + 0.0877673i −0.991567 0.129592i \(-0.958633\pi\)
0.976092 + 0.217359i \(0.0697443\pi\)
\(114\) 0 0
\(115\) −1.75872 9.97420i −0.164002 0.930099i
\(116\) 0 0
\(117\) −1.70963 6.01111i −0.158055 0.555727i
\(118\) 0 0
\(119\) −0.539136 0.605700i −0.0494225 0.0555244i
\(120\) 0 0
\(121\) −7.60310 6.37976i −0.691191 0.579978i
\(122\) 0 0
\(123\) −7.07260 3.61328i −0.637715 0.325799i
\(124\) 0 0
\(125\) 11.9860 20.7604i 1.07206 1.85687i
\(126\) 0 0
\(127\) −8.90354 15.4214i −0.790061 1.36843i −0.925929 0.377699i \(-0.876715\pi\)
0.135868 0.990727i \(-0.456618\pi\)
\(128\) 0 0
\(129\) −4.69530 + 6.21691i −0.413398 + 0.547368i
\(130\) 0 0
\(131\) 3.55592 20.1666i 0.310682 1.76197i −0.284788 0.958591i \(-0.591923\pi\)
0.595470 0.803377i \(-0.296966\pi\)
\(132\) 0 0
\(133\) 0.646091 1.95045i 0.0560232 0.169125i
\(134\) 0 0
\(135\) −10.7605 + 17.7779i −0.926116 + 1.53008i
\(136\) 0 0
\(137\) 15.3866 12.9109i 1.31457 1.10305i 0.327140 0.944976i \(-0.393915\pi\)
0.987427 0.158076i \(-0.0505292\pi\)
\(138\) 0 0
\(139\) −11.3937 9.56042i −0.966398 0.810904i 0.0155838 0.999879i \(-0.495039\pi\)
−0.981982 + 0.188974i \(0.939484\pi\)
\(140\) 0 0
\(141\) 5.46375 + 12.9105i 0.460131 + 1.08726i
\(142\) 0 0
\(143\) 2.15973 0.180605
\(144\) 0 0
\(145\) −37.9061 −3.14793
\(146\) 0 0
\(147\) 11.1004 + 4.87664i 0.915544 + 0.402219i
\(148\) 0 0
\(149\) 9.32756 + 7.82675i 0.764143 + 0.641192i 0.939202 0.343366i \(-0.111567\pi\)
−0.175059 + 0.984558i \(0.556011\pi\)
\(150\) 0 0
\(151\) 12.5900 + 4.58237i 1.02456 + 0.372908i 0.799006 0.601323i \(-0.205360\pi\)
0.225551 + 0.974231i \(0.427582\pi\)
\(152\) 0 0
\(153\) 0.827274 0.401281i 0.0668811 0.0324416i
\(154\) 0 0
\(155\) −12.0766 + 10.1335i −0.970017 + 0.813941i
\(156\) 0 0
\(157\) −5.19728 4.36103i −0.414788 0.348048i 0.411388 0.911460i \(-0.365044\pi\)
−0.826176 + 0.563412i \(0.809488\pi\)
\(158\) 0 0
\(159\) 16.1442 3.70884i 1.28032 0.294130i
\(160\) 0 0
\(161\) −0.195551 6.69747i −0.0154116 0.527834i
\(162\) 0 0
\(163\) 8.65586 + 14.9924i 0.677980 + 1.17430i 0.975588 + 0.219607i \(0.0704776\pi\)
−0.297609 + 0.954688i \(0.596189\pi\)
\(164\) 0 0
\(165\) −4.89210 5.25750i −0.380850 0.409296i
\(166\) 0 0
\(167\) 1.61900 9.18182i 0.125282 0.710511i −0.855858 0.517212i \(-0.826970\pi\)
0.981140 0.193299i \(-0.0619188\pi\)
\(168\) 0 0
\(169\) −6.63426 + 5.56681i −0.510328 + 0.428216i
\(170\) 0 0
\(171\) 1.92866 + 1.30696i 0.147488 + 0.0999459i
\(172\) 0 0
\(173\) 4.41074 3.70105i 0.335342 0.281385i −0.459530 0.888162i \(-0.651982\pi\)
0.794872 + 0.606777i \(0.207538\pi\)
\(174\) 0 0
\(175\) 18.0389 22.8187i 1.36361 1.72493i
\(176\) 0 0
\(177\) 1.19399 + 23.2629i 0.0897460 + 1.74855i
\(178\) 0 0
\(179\) −3.84363 6.65737i −0.287287 0.497595i 0.685874 0.727720i \(-0.259420\pi\)
−0.973161 + 0.230125i \(0.926087\pi\)
\(180\) 0 0
\(181\) −7.31512 12.6702i −0.543729 0.941766i −0.998686 0.0512523i \(-0.983679\pi\)
0.454957 0.890513i \(-0.349655\pi\)
\(182\) 0 0
\(183\) −5.52383 13.0525i −0.408333 0.964866i
\(184\) 0 0
\(185\) −41.8375 + 15.2276i −3.07596 + 1.11956i
\(186\) 0 0
\(187\) 0.0551768 + 0.312923i 0.00403493 + 0.0228832i
\(188\) 0 0
\(189\) −8.74704 + 10.6061i −0.636253 + 0.771480i
\(190\) 0 0
\(191\) 1.87096 + 10.6107i 0.135378 + 0.767764i 0.974596 + 0.223970i \(0.0719018\pi\)
−0.839218 + 0.543794i \(0.816987\pi\)
\(192\) 0 0
\(193\) 8.67419 3.15715i 0.624382 0.227256i −0.0104023 0.999946i \(-0.503311\pi\)
0.634784 + 0.772689i \(0.281089\pi\)
\(194\) 0 0
\(195\) −14.3205 1.77402i −1.02551 0.127040i
\(196\) 0 0
\(197\) −10.8434 18.7813i −0.772559 1.33811i −0.936156 0.351584i \(-0.885643\pi\)
0.163597 0.986527i \(-0.447690\pi\)
\(198\) 0 0
\(199\) 5.42032 + 9.38827i 0.384236 + 0.665517i 0.991663 0.128859i \(-0.0411314\pi\)
−0.607427 + 0.794376i \(0.707798\pi\)
\(200\) 0 0
\(201\) −15.1801 + 9.83481i −1.07072 + 0.693694i
\(202\) 0 0
\(203\) −24.8128 3.63198i −1.74151 0.254915i
\(204\) 0 0
\(205\) −14.0479 + 11.7876i −0.981146 + 0.823279i
\(206\) 0 0
\(207\) 7.36779 + 1.85389i 0.512097 + 0.128854i
\(208\) 0 0
\(209\) −0.616769 + 0.517530i −0.0426628 + 0.0357983i
\(210\) 0 0
\(211\) 2.30865 13.0930i 0.158934 0.901358i −0.796167 0.605077i \(-0.793142\pi\)
0.955101 0.296281i \(-0.0957465\pi\)
\(212\) 0 0
\(213\) 3.33285 0.765663i 0.228363 0.0524624i
\(214\) 0 0
\(215\) 8.99433 + 15.5786i 0.613408 + 1.06245i
\(216\) 0 0
\(217\) −8.87611 + 5.47610i −0.602549 + 0.371742i
\(218\) 0 0
\(219\) 3.75426 + 4.03467i 0.253689 + 0.272637i
\(220\) 0 0
\(221\) 0.489092 + 0.410397i 0.0328999 + 0.0276063i
\(222\) 0 0
\(223\) 10.6778 8.95976i 0.715040 0.599990i −0.210968 0.977493i \(-0.567662\pi\)
0.926008 + 0.377503i \(0.123217\pi\)
\(224\) 0 0
\(225\) 19.3289 + 26.7251i 1.28859 + 1.78167i
\(226\) 0 0
\(227\) 2.17399 + 0.791269i 0.144293 + 0.0525184i 0.413157 0.910660i \(-0.364426\pi\)
−0.268864 + 0.963178i \(0.586648\pi\)
\(228\) 0 0
\(229\) 13.2314 + 11.1025i 0.874355 + 0.733671i 0.965011 0.262211i \(-0.0844516\pi\)
−0.0906551 + 0.995882i \(0.528896\pi\)
\(230\) 0 0
\(231\) −2.69854 3.91021i −0.177551 0.257273i
\(232\) 0 0
\(233\) 15.0313 0.984733 0.492367 0.870388i \(-0.336132\pi\)
0.492367 + 0.870388i \(0.336132\pi\)
\(234\) 0 0
\(235\) 32.3697 2.11156
\(236\) 0 0
\(237\) −5.59821 + 7.41242i −0.363643 + 0.481488i
\(238\) 0 0
\(239\) −11.8507 9.94390i −0.766557 0.643217i 0.173268 0.984875i \(-0.444567\pi\)
−0.939825 + 0.341657i \(0.889012\pi\)
\(240\) 0 0
\(241\) −18.6617 + 15.6590i −1.20210 + 1.00869i −0.202537 + 0.979275i \(0.564919\pi\)
−0.999567 + 0.0294111i \(0.990637\pi\)
\(242\) 0 0
\(243\) −8.87216 12.8174i −0.569149 0.822234i
\(244\) 0 0
\(245\) 20.3589 19.2153i 1.30068 1.22762i
\(246\) 0 0
\(247\) −0.280924 + 1.59320i −0.0178747 + 0.101373i
\(248\) 0 0
\(249\) 4.81570 + 11.3792i 0.305183 + 0.721128i
\(250\) 0 0
\(251\) 1.32366 + 2.29265i 0.0835487 + 0.144711i 0.904772 0.425897i \(-0.140041\pi\)
−0.821223 + 0.570607i \(0.806708\pi\)
\(252\) 0 0
\(253\) −1.31278 + 2.27380i −0.0825336 + 0.142952i
\(254\) 0 0
\(255\) −0.108823 2.12022i −0.00681473 0.132774i
\(256\) 0 0
\(257\) −20.4866 17.1903i −1.27792 1.07230i −0.993527 0.113596i \(-0.963763\pi\)
−0.284394 0.958707i \(-0.591792\pi\)
\(258\) 0 0
\(259\) −28.8452 + 5.95909i −1.79236 + 0.370280i
\(260\) 0 0
\(261\) 11.6215 25.9515i 0.719354 1.60636i
\(262\) 0 0
\(263\) 5.20945 + 29.5442i 0.321228 + 1.82178i 0.534953 + 0.844882i \(0.320329\pi\)
−0.213725 + 0.976894i \(0.568560\pi\)
\(264\) 0 0
\(265\) 6.64162 37.6665i 0.407991 2.31383i
\(266\) 0 0
\(267\) −4.41579 + 1.01445i −0.270242 + 0.0620833i
\(268\) 0 0
\(269\) −1.18287 + 2.04879i −0.0721210 + 0.124917i −0.899831 0.436239i \(-0.856310\pi\)
0.827710 + 0.561157i \(0.189643\pi\)
\(270\) 0 0
\(271\) −0.935621 1.62054i −0.0568349 0.0984409i 0.836208 0.548412i \(-0.184768\pi\)
−0.893043 + 0.449971i \(0.851434\pi\)
\(272\) 0 0
\(273\) −9.20399 2.53337i −0.557051 0.153326i
\(274\) 0 0
\(275\) −10.7108 + 3.89840i −0.645884 + 0.235082i
\(276\) 0 0
\(277\) 2.94888 + 16.7240i 0.177181 + 1.00484i 0.935596 + 0.353073i \(0.114863\pi\)
−0.758415 + 0.651772i \(0.774026\pi\)
\(278\) 0 0
\(279\) −3.23511 11.3747i −0.193681 0.680988i
\(280\) 0 0
\(281\) 3.85516 + 21.8637i 0.229980 + 1.30428i 0.852933 + 0.522021i \(0.174822\pi\)
−0.622953 + 0.782259i \(0.714067\pi\)
\(282\) 0 0
\(283\) 5.21874 29.5969i 0.310222 1.75936i −0.287623 0.957744i \(-0.592865\pi\)
0.597845 0.801612i \(-0.296024\pi\)
\(284\) 0 0
\(285\) 4.51471 2.92497i 0.267428 0.173260i
\(286\) 0 0
\(287\) −10.3249 + 6.36995i −0.609462 + 0.376006i
\(288\) 0 0
\(289\) 8.45303 14.6411i 0.497237 0.861240i
\(290\) 0 0
\(291\) −7.93495 + 10.5064i −0.465155 + 0.615898i
\(292\) 0 0
\(293\) −2.74653 2.30461i −0.160454 0.134637i 0.559026 0.829150i \(-0.311175\pi\)
−0.719480 + 0.694513i \(0.755620\pi\)
\(294\) 0 0
\(295\) 50.5407 + 18.3953i 2.94259 + 1.07102i
\(296\) 0 0
\(297\) 5.09927 1.73738i 0.295889 0.100813i
\(298\) 0 0
\(299\) 0.916096 + 5.19544i 0.0529792 + 0.300460i
\(300\) 0 0
\(301\) 4.39488 + 11.0593i 0.253316 + 0.637449i
\(302\) 0 0
\(303\) −0.615509 + 0.814977i −0.0353601 + 0.0468192i
\(304\) 0 0
\(305\) −32.7256 −1.87386
\(306\) 0 0
\(307\) −9.22311 + 15.9749i −0.526390 + 0.911735i 0.473137 + 0.880989i \(0.343122\pi\)
−0.999527 + 0.0307460i \(0.990212\pi\)
\(308\) 0 0
\(309\) −22.1406 11.3113i −1.25953 0.643478i
\(310\) 0 0
\(311\) 4.63504 26.2866i 0.262829 1.49058i −0.512318 0.858796i \(-0.671213\pi\)
0.775147 0.631781i \(-0.217676\pi\)
\(312\) 0 0
\(313\) 23.3119 19.5610i 1.31767 1.10566i 0.330875 0.943675i \(-0.392656\pi\)
0.986794 0.161981i \(-0.0517883\pi\)
\(314\) 0 0
\(315\) 14.6813 + 28.1440i 0.827200 + 1.58574i
\(316\) 0 0
\(317\) −11.6415 4.23717i −0.653853 0.237983i −0.00627266 0.999980i \(-0.501997\pi\)
−0.647580 + 0.761997i \(0.724219\pi\)
\(318\) 0 0
\(319\) 7.52762 + 6.31642i 0.421466 + 0.353652i
\(320\) 0 0
\(321\) −2.49500 + 8.12941i −0.139258 + 0.453740i
\(322\) 0 0
\(323\) −0.238016 −0.0132436
\(324\) 0 0
\(325\) −11.4513 + 19.8342i −0.635204 + 1.10020i
\(326\) 0 0
\(327\) −11.0027 + 2.52768i −0.608452 + 0.139781i
\(328\) 0 0
\(329\) 21.1887 + 3.10150i 1.16817 + 0.170991i
\(330\) 0 0
\(331\) 17.9295 + 6.52579i 0.985492 + 0.358690i 0.783973 0.620795i \(-0.213190\pi\)
0.201519 + 0.979485i \(0.435412\pi\)
\(332\) 0 0
\(333\) 2.40162 33.3116i 0.131608 1.82547i
\(334\) 0 0
\(335\) 7.25219 + 41.1292i 0.396230 + 2.24713i
\(336\) 0 0
\(337\) −16.8212 + 6.12241i −0.916308 + 0.333509i −0.756769 0.653683i \(-0.773223\pi\)
−0.159539 + 0.987192i \(0.551001\pi\)
\(338\) 0 0
\(339\) −1.37713 + 0.892211i −0.0747957 + 0.0484582i
\(340\) 0 0
\(341\) 4.08682 0.221314
\(342\) 0 0
\(343\) 15.1677 10.6274i 0.818979 0.573824i
\(344\) 0 0
\(345\) 10.5723 13.9985i 0.569196 0.753656i
\(346\) 0 0
\(347\) −14.3108 + 5.20872i −0.768246 + 0.279619i −0.696263 0.717787i \(-0.745155\pi\)
−0.0719834 + 0.997406i \(0.522933\pi\)
\(348\) 0 0
\(349\) −6.61713 2.40844i −0.354207 0.128921i 0.158787 0.987313i \(-0.449242\pi\)
−0.512994 + 0.858392i \(0.671464\pi\)
\(350\) 0 0
\(351\) 5.60501 9.26028i 0.299173 0.494277i
\(352\) 0 0
\(353\) −2.61321 + 2.19274i −0.139087 + 0.116708i −0.709677 0.704527i \(-0.751159\pi\)
0.570590 + 0.821235i \(0.306715\pi\)
\(354\) 0 0
\(355\) 1.37112 7.77598i 0.0727713 0.412706i
\(356\) 0 0
\(357\) 0.131916 1.39829i 0.00698174 0.0740054i
\(358\) 0 0
\(359\) −3.98322 + 6.89914i −0.210226 + 0.364122i −0.951785 0.306765i \(-0.900753\pi\)
0.741559 + 0.670888i \(0.234087\pi\)
\(360\) 0 0
\(361\) 9.19845 + 15.9322i 0.484129 + 0.838536i
\(362\) 0 0
\(363\) −0.881178 17.1683i −0.0462499 0.901100i
\(364\) 0 0
\(365\) 11.9577 4.35226i 0.625897 0.227808i
\(366\) 0 0
\(367\) 6.11912 + 2.22718i 0.319416 + 0.116258i 0.496752 0.867892i \(-0.334526\pi\)
−0.177336 + 0.984150i \(0.556748\pi\)
\(368\) 0 0
\(369\) −3.76317 13.2314i −0.195903 0.688801i
\(370\) 0 0
\(371\) 7.95652 24.0195i 0.413082 1.24703i
\(372\) 0 0
\(373\) 8.62680 3.13990i 0.446679 0.162578i −0.108880 0.994055i \(-0.534727\pi\)
0.555559 + 0.831477i \(0.312504\pi\)
\(374\) 0 0
\(375\) 40.4667 9.29650i 2.08969 0.480069i
\(376\) 0 0
\(377\) 19.7448 1.01691
\(378\) 0 0
\(379\) −7.49943 −0.385220 −0.192610 0.981275i \(-0.561695\pi\)
−0.192610 + 0.981275i \(0.561695\pi\)
\(380\) 0 0
\(381\) 9.04936 29.4853i 0.463613 1.51058i
\(382\) 0 0
\(383\) 7.65983 2.78795i 0.391399 0.142458i −0.138821 0.990317i \(-0.544331\pi\)
0.530220 + 0.847860i \(0.322109\pi\)
\(384\) 0 0
\(385\) −10.7431 + 2.21939i −0.547517 + 0.113111i
\(386\) 0 0
\(387\) −13.4231 + 1.38154i −0.682333 + 0.0702278i
\(388\) 0 0
\(389\) 27.7047 + 10.0837i 1.40468 + 0.511263i 0.929565 0.368658i \(-0.120183\pi\)
0.475119 + 0.879922i \(0.342405\pi\)
\(390\) 0 0
\(391\) −0.729364 + 0.265467i −0.0368855 + 0.0134252i
\(392\) 0 0
\(393\) 29.7672 19.2854i 1.50156 0.972821i
\(394\) 0 0
\(395\) 10.7239 + 18.5744i 0.539580 + 0.934580i
\(396\) 0 0
\(397\) −15.2950 + 26.4917i −0.767633 + 1.32958i 0.171210 + 0.985235i \(0.445232\pi\)
−0.938843 + 0.344345i \(0.888101\pi\)
\(398\) 0 0
\(399\) 3.23551 1.48206i 0.161978 0.0741958i
\(400\) 0 0
\(401\) −4.83088 + 27.3973i −0.241243 + 1.36815i 0.587817 + 0.808994i \(0.299988\pi\)
−0.829059 + 0.559160i \(0.811124\pi\)
\(402\) 0 0
\(403\) 6.29056 5.27841i 0.313355 0.262936i
\(404\) 0 0
\(405\) −35.2388 + 7.33144i −1.75103 + 0.364302i
\(406\) 0 0
\(407\) 10.8458 + 3.94754i 0.537605 + 0.195672i
\(408\) 0 0
\(409\) 8.96999 3.26481i 0.443537 0.161434i −0.110590 0.993866i \(-0.535274\pi\)
0.554128 + 0.832432i \(0.313052\pi\)
\(410\) 0 0
\(411\) 34.5257 + 4.27704i 1.70303 + 0.210971i
\(412\) 0 0
\(413\) 31.3206 + 16.8838i 1.54118 + 0.830799i
\(414\) 0 0
\(415\) 28.5303 1.40050
\(416\) 0 0
\(417\) −1.32049 25.7276i −0.0646648 1.25988i
\(418\) 0 0
\(419\) 5.88681 2.14262i 0.287589 0.104674i −0.194197 0.980962i \(-0.562210\pi\)
0.481787 + 0.876289i \(0.339988\pi\)
\(420\) 0 0
\(421\) 0.967375 + 5.48626i 0.0471470 + 0.267384i 0.999264 0.0383488i \(-0.0122098\pi\)
−0.952117 + 0.305733i \(0.901099\pi\)
\(422\) 0 0
\(423\) −9.92410 + 22.1611i −0.482526 + 1.07751i
\(424\) 0 0
\(425\) −3.16634 1.15246i −0.153590 0.0559023i
\(426\) 0 0
\(427\) −21.4216 3.13561i −1.03667 0.151743i
\(428\) 0 0
\(429\) 2.54824 + 2.73857i 0.123030 + 0.132219i
\(430\) 0 0
\(431\) 4.87104 8.43690i 0.234630 0.406391i −0.724535 0.689238i \(-0.757946\pi\)
0.959165 + 0.282847i \(0.0912788\pi\)
\(432\) 0 0
\(433\) −8.60092 −0.413334 −0.206667 0.978411i \(-0.566262\pi\)
−0.206667 + 0.978411i \(0.566262\pi\)
\(434\) 0 0
\(435\) −44.7250 48.0656i −2.14440 2.30457i
\(436\) 0 0
\(437\) −1.50659 1.26418i −0.0720699 0.0604738i
\(438\) 0 0
\(439\) 14.6860 + 5.34525i 0.700922 + 0.255115i 0.667805 0.744337i \(-0.267234\pi\)
0.0331178 + 0.999451i \(0.489456\pi\)
\(440\) 0 0
\(441\) 6.91355 + 19.8293i 0.329217 + 0.944254i
\(442\) 0 0
\(443\) −6.47957 + 5.43701i −0.307854 + 0.258320i −0.783604 0.621260i \(-0.786621\pi\)
0.475750 + 0.879580i \(0.342177\pi\)
\(444\) 0 0
\(445\) −1.81663 + 10.3026i −0.0861166 + 0.488391i
\(446\) 0 0
\(447\) 1.08104 + 21.0622i 0.0511313 + 0.996207i
\(448\) 0 0
\(449\) 12.8251 22.2137i 0.605253 1.04833i −0.386758 0.922181i \(-0.626405\pi\)
0.992011 0.126148i \(-0.0402615\pi\)
\(450\) 0 0
\(451\) 4.75391 0.223853
\(452\) 0 0
\(453\) 9.04423 + 21.3709i 0.424935 + 1.00409i
\(454\) 0 0
\(455\) −13.6696 + 17.2916i −0.640839 + 0.810641i
\(456\) 0 0
\(457\) −1.44825 8.21344i −0.0677463 0.384209i −0.999763 0.0217919i \(-0.993063\pi\)
0.932016 0.362417i \(-0.118048\pi\)
\(458\) 0 0
\(459\) 1.48492 + 0.575529i 0.0693102 + 0.0268634i
\(460\) 0 0
\(461\) 1.40759 + 0.512321i 0.0655580 + 0.0238612i 0.374591 0.927190i \(-0.377783\pi\)
−0.309033 + 0.951051i \(0.600005\pi\)
\(462\) 0 0
\(463\) −19.8247 16.6349i −0.921333 0.773090i 0.0529082 0.998599i \(-0.483151\pi\)
−0.974241 + 0.225509i \(0.927595\pi\)
\(464\) 0 0
\(465\) −27.0985 3.35696i −1.25666 0.155675i
\(466\) 0 0
\(467\) −11.3477 + 19.6548i −0.525109 + 0.909515i 0.474463 + 0.880275i \(0.342642\pi\)
−0.999572 + 0.0292403i \(0.990691\pi\)
\(468\) 0 0
\(469\) 0.806366 + 27.6174i 0.0372345 + 1.27525i
\(470\) 0 0
\(471\) −0.602350 11.7358i −0.0277548 0.540755i
\(472\) 0 0
\(473\) 0.809773 4.59245i 0.0372334 0.211161i
\(474\) 0 0
\(475\) −1.48260 8.40825i −0.0680264 0.385797i
\(476\) 0 0
\(477\) 23.7512 + 16.0951i 1.08749 + 0.736942i
\(478\) 0 0
\(479\) −5.17236 29.3339i −0.236331 1.34030i −0.839792 0.542908i \(-0.817323\pi\)
0.603461 0.797392i \(-0.293788\pi\)
\(480\) 0 0
\(481\) 21.7927 7.93188i 0.993660 0.361663i
\(482\) 0 0
\(483\) 8.26176 8.15022i 0.375923 0.370848i
\(484\) 0 0
\(485\) 15.2002 + 26.3275i 0.690206 + 1.19547i
\(486\) 0 0
\(487\) 12.1802 21.0968i 0.551938 0.955985i −0.446196 0.894935i \(-0.647222\pi\)
0.998135 0.0610500i \(-0.0194449\pi\)
\(488\) 0 0
\(489\) −8.79764 + 28.6651i −0.397843 + 1.29628i
\(490\) 0 0
\(491\) −6.89390 + 39.0972i −0.311117 + 1.76443i 0.282094 + 0.959387i \(0.408971\pi\)
−0.593211 + 0.805047i \(0.702140\pi\)
\(492\) 0 0
\(493\) 0.504443 + 2.86084i 0.0227190 + 0.128846i
\(494\) 0 0
\(495\) 0.894454 12.4065i 0.0402027 0.557632i
\(496\) 0 0
\(497\) 1.64257 4.95866i 0.0736792 0.222426i
\(498\) 0 0
\(499\) 25.3279 + 21.2526i 1.13383 + 0.951399i 0.999220 0.0394997i \(-0.0125764\pi\)
0.134613 + 0.990898i \(0.457021\pi\)
\(500\) 0 0
\(501\) 13.5529 8.78061i 0.605501 0.392289i
\(502\) 0 0
\(503\) −8.61071 + 14.9142i −0.383933 + 0.664991i −0.991620 0.129185i \(-0.958764\pi\)
0.607688 + 0.794176i \(0.292097\pi\)
\(504\) 0 0
\(505\) 1.17907 + 2.04221i 0.0524679 + 0.0908771i
\(506\) 0 0
\(507\) −14.8865 1.84414i −0.661132 0.0819009i
\(508\) 0 0
\(509\) 6.58159 37.3261i 0.291724 1.65445i −0.388503 0.921448i \(-0.627008\pi\)
0.680227 0.733002i \(-0.261881\pi\)
\(510\) 0 0
\(511\) 8.24436 1.70319i 0.364709 0.0753446i
\(512\) 0 0
\(513\) 0.618357 + 3.98764i 0.0273011 + 0.176059i
\(514\) 0 0
\(515\) −43.9765 + 36.9007i −1.93784 + 1.62604i
\(516\) 0 0
\(517\) −6.42815 5.39386i −0.282710 0.237222i
\(518\) 0 0
\(519\) 9.89716 + 1.22606i 0.434437 + 0.0538180i
\(520\) 0 0
\(521\) 11.7559 0.515037 0.257518 0.966273i \(-0.417095\pi\)
0.257518 + 0.966273i \(0.417095\pi\)
\(522\) 0 0
\(523\) −3.47076 −0.151766 −0.0758829 0.997117i \(-0.524178\pi\)
−0.0758829 + 0.997117i \(0.524178\pi\)
\(524\) 0 0
\(525\) 50.2183 4.04984i 2.19171 0.176749i
\(526\) 0 0
\(527\) 0.925502 + 0.776588i 0.0403155 + 0.0338287i
\(528\) 0 0
\(529\) 15.5862 + 5.67293i 0.677663 + 0.246649i
\(530\) 0 0
\(531\) −28.0890 + 28.9617i −1.21896 + 1.25683i
\(532\) 0 0
\(533\) 7.31736 6.14000i 0.316950 0.265953i
\(534\) 0 0
\(535\) 15.0411 + 12.6210i 0.650284 + 0.545653i
\(536\) 0 0
\(537\) 3.90659 12.7287i 0.168582 0.549286i
\(538\) 0 0
\(539\) −7.24489 + 0.423430i −0.312060 + 0.0182384i
\(540\) 0 0
\(541\) −4.28017 7.41347i −0.184019 0.318730i 0.759227 0.650826i \(-0.225577\pi\)
−0.943245 + 0.332096i \(0.892244\pi\)
\(542\) 0 0
\(543\) 7.43493 24.2251i 0.319064 1.03960i
\(544\) 0 0
\(545\) −4.52646 + 25.6708i −0.193892 + 1.09962i
\(546\) 0 0
\(547\) −28.1571 + 23.6266i −1.20391 + 1.01020i −0.204401 + 0.978887i \(0.565525\pi\)
−0.999510 + 0.0313134i \(0.990031\pi\)
\(548\) 0 0
\(549\) 10.0332 22.4048i 0.428207 0.956212i
\(550\) 0 0
\(551\) −5.63868 + 4.73141i −0.240216 + 0.201565i
\(552\) 0 0
\(553\) 5.24001 + 13.1860i 0.222828 + 0.560727i
\(554\) 0 0
\(555\) −68.6725 35.0838i −2.91499 1.48922i
\(556\) 0 0
\(557\) −13.9154 24.1022i −0.589614 1.02124i −0.994283 0.106778i \(-0.965947\pi\)
0.404669 0.914463i \(-0.367387\pi\)
\(558\) 0 0
\(559\) −4.68504 8.11472i −0.198156 0.343216i
\(560\) 0 0
\(561\) −0.331689 + 0.439180i −0.0140039 + 0.0185422i
\(562\) 0 0
\(563\) −20.1878 + 7.34777i −0.850816 + 0.309672i −0.730373 0.683049i \(-0.760654\pi\)
−0.120443 + 0.992720i \(0.538431\pi\)
\(564\) 0 0
\(565\) 0.657917 + 3.73123i 0.0276788 + 0.156974i
\(566\) 0 0
\(567\) −23.7692 + 1.42263i −0.998214 + 0.0597449i
\(568\) 0 0
\(569\) 3.49844 + 19.8406i 0.146662 + 0.831762i 0.966018 + 0.258476i \(0.0832204\pi\)
−0.819355 + 0.573286i \(0.805668\pi\)
\(570\) 0 0
\(571\) −36.8816 + 13.4238i −1.54345 + 0.561769i −0.966869 0.255272i \(-0.917835\pi\)
−0.576579 + 0.817041i \(0.695613\pi\)
\(572\) 0 0
\(573\) −11.2470 + 14.8919i −0.469852 + 0.622116i
\(574\) 0 0
\(575\) −13.9212 24.1122i −0.580555 1.00555i
\(576\) 0 0
\(577\) 1.63475 + 2.83148i 0.0680557 + 0.117876i 0.898045 0.439903i \(-0.144987\pi\)
−0.829990 + 0.557779i \(0.811654\pi\)
\(578\) 0 0
\(579\) 14.2379 + 7.27393i 0.591706 + 0.302294i
\(580\) 0 0
\(581\) 18.6755 + 2.73364i 0.774790 + 0.113410i
\(582\) 0 0
\(583\) −7.59542 + 6.37331i −0.314570 + 0.263956i
\(584\) 0 0
\(585\) −14.6471 20.2518i −0.605583 0.837307i
\(586\) 0 0
\(587\) −14.9958 + 12.5830i −0.618944 + 0.519356i −0.897471 0.441073i \(-0.854598\pi\)
0.278527 + 0.960428i \(0.410154\pi\)
\(588\) 0 0
\(589\) −0.531588 + 3.01479i −0.0219037 + 0.124222i
\(590\) 0 0
\(591\) 11.0210 35.9094i 0.453343 1.47712i
\(592\) 0 0
\(593\) −20.8803 36.1658i −0.857452 1.48515i −0.874351 0.485293i \(-0.838713\pi\)
0.0168995 0.999857i \(-0.494620\pi\)
\(594\) 0 0
\(595\) −2.85461 1.53882i −0.117028 0.0630855i
\(596\) 0 0
\(597\) −5.50910 + 17.9502i −0.225472 + 0.734651i
\(598\) 0 0
\(599\) 7.16302 + 6.01049i 0.292673 + 0.245582i 0.777287 0.629146i \(-0.216595\pi\)
−0.484614 + 0.874728i \(0.661040\pi\)
\(600\) 0 0
\(601\) 37.3323 31.3256i 1.52282 1.27780i 0.690803 0.723043i \(-0.257257\pi\)
0.832015 0.554753i \(-0.187187\pi\)
\(602\) 0 0
\(603\) −30.3815 7.64463i −1.23723 0.311314i
\(604\) 0 0
\(605\) −37.2995 13.5759i −1.51644 0.551939i
\(606\) 0 0
\(607\) 17.2934 + 14.5109i 0.701919 + 0.588980i 0.922319 0.386430i \(-0.126292\pi\)
−0.220400 + 0.975410i \(0.570736\pi\)
\(608\) 0 0
\(609\) −24.6709 35.7483i −0.999714 1.44859i
\(610\) 0 0
\(611\) −16.8610 −0.682121
\(612\) 0 0
\(613\) −19.7396 −0.797275 −0.398637 0.917109i \(-0.630517\pi\)
−0.398637 + 0.917109i \(0.630517\pi\)
\(614\) 0 0
\(615\) −31.5217 3.90491i −1.27108 0.157461i
\(616\) 0 0
\(617\) 9.35270 + 7.84784i 0.376525 + 0.315942i 0.811337 0.584579i \(-0.198740\pi\)
−0.434811 + 0.900522i \(0.643185\pi\)
\(618\) 0 0
\(619\) −6.06747 + 5.09121i −0.243872 + 0.204633i −0.756528 0.653961i \(-0.773106\pi\)
0.512656 + 0.858594i \(0.328662\pi\)
\(620\) 0 0
\(621\) 6.34241 + 11.5299i 0.254512 + 0.462677i
\(622\) 0 0
\(623\) −2.17629 + 6.56987i −0.0871910 + 0.263216i
\(624\) 0 0
\(625\) 7.10221 40.2787i 0.284089 1.61115i
\(626\) 0 0
\(627\) −1.38395 0.171444i −0.0552698 0.00684682i
\(628\) 0 0
\(629\) 1.70601 + 2.95490i 0.0680232 + 0.117820i
\(630\) 0 0
\(631\) 9.64257 16.7014i 0.383865 0.664873i −0.607746 0.794131i \(-0.707926\pi\)
0.991611 + 0.129258i \(0.0412596\pi\)
\(632\) 0 0
\(633\) 19.3260 12.5209i 0.768141 0.497659i
\(634\) 0 0
\(635\) −54.5540 45.7762i −2.16491 1.81657i
\(636\) 0 0
\(637\) −10.6047 + 10.0090i −0.420173 + 0.396572i
\(638\) 0 0
\(639\) 4.90327 + 3.32271i 0.193970 + 0.131444i
\(640\) 0 0
\(641\) 4.22997 + 23.9893i 0.167074 + 0.947522i 0.946901 + 0.321527i \(0.104196\pi\)
−0.779827 + 0.625995i \(0.784693\pi\)
\(642\) 0 0
\(643\) 0.329571 1.86909i 0.0129970 0.0737096i −0.977619 0.210381i \(-0.932529\pi\)
0.990616 + 0.136672i \(0.0436405\pi\)
\(644\) 0 0
\(645\) −9.14165 + 29.7860i −0.359952 + 1.17282i
\(646\) 0 0
\(647\) 0.204404 0.354039i 0.00803596 0.0139187i −0.861979 0.506943i \(-0.830775\pi\)
0.870015 + 0.493025i \(0.164109\pi\)
\(648\) 0 0
\(649\) −6.97139 12.0748i −0.273651 0.473978i
\(650\) 0 0
\(651\) −17.4166 4.79386i −0.682610 0.187886i
\(652\) 0 0
\(653\) 20.6196 7.50491i 0.806906 0.293690i 0.0945609 0.995519i \(-0.469855\pi\)
0.712345 + 0.701829i \(0.247633\pi\)
\(654\) 0 0
\(655\) −14.2211 80.6517i −0.555663 3.15132i
\(656\) 0 0
\(657\) −0.686415 + 9.52091i −0.0267796 + 0.371446i
\(658\) 0 0
\(659\) −4.66416 26.4518i −0.181690 1.03041i −0.930135 0.367218i \(-0.880310\pi\)
0.748445 0.663197i \(-0.230801\pi\)
\(660\) 0 0
\(661\) 2.57555 14.6066i 0.100177 0.568133i −0.892860 0.450334i \(-0.851305\pi\)
0.993037 0.117799i \(-0.0375839\pi\)
\(662\) 0 0
\(663\) 0.0566843 + 1.10440i 0.00220144 + 0.0428913i
\(664\) 0 0
\(665\) −0.239821 8.21368i −0.00929986 0.318513i
\(666\) 0 0
\(667\) −12.0018 + 20.7877i −0.464711 + 0.804903i
\(668\) 0 0
\(669\) 23.9598 + 2.96813i 0.926338 + 0.114755i
\(670\) 0 0
\(671\) 6.49883 + 5.45317i 0.250885 + 0.210517i
\(672\) 0 0
\(673\) 42.9536 + 15.6338i 1.65574 + 0.602640i 0.989685 0.143262i \(-0.0457593\pi\)
0.666055 + 0.745902i \(0.267982\pi\)
\(674\) 0 0
\(675\) −11.0818 + 56.0419i −0.426539 + 2.15706i
\(676\) 0 0
\(677\) 2.09570 + 11.8853i 0.0805443 + 0.456789i 0.998229 + 0.0594810i \(0.0189446\pi\)
−0.917685 + 0.397308i \(0.869944\pi\)
\(678\) 0 0
\(679\) 7.42724 + 18.6900i 0.285031 + 0.717256i
\(680\) 0 0
\(681\) 1.56173 + 3.69027i 0.0598456 + 0.141411i
\(682\) 0 0
\(683\) 7.29677 0.279203 0.139602 0.990208i \(-0.455418\pi\)
0.139602 + 0.990208i \(0.455418\pi\)
\(684\) 0 0
\(685\) 40.1642 69.5664i 1.53459 2.65800i
\(686\) 0 0
\(687\) 1.53348 + 29.8773i 0.0585060 + 1.13989i
\(688\) 0 0
\(689\) −3.45954 + 19.6200i −0.131798 + 0.747463i
\(690\) 0 0
\(691\) 18.5445 15.5607i 0.705466 0.591956i −0.217857 0.975981i \(-0.569907\pi\)
0.923323 + 0.384024i \(0.125462\pi\)
\(692\) 0 0
\(693\) 1.77423 8.03541i 0.0673974 0.305240i
\(694\) 0 0
\(695\) −55.8953 20.3442i −2.12023 0.771701i
\(696\) 0 0
\(697\) 1.07657 + 0.903350i 0.0407780 + 0.0342168i
\(698\) 0 0
\(699\) 17.7353 + 19.0599i 0.670809 + 0.720912i
\(700\) 0 0
\(701\) −8.97538 −0.338995 −0.169498 0.985531i \(-0.554215\pi\)
−0.169498 + 0.985531i \(0.554215\pi\)
\(702\) 0 0
\(703\) −4.32279 + 7.48729i −0.163037 + 0.282389i
\(704\) 0 0
\(705\) 38.1926 + 41.0452i 1.43842 + 1.54585i
\(706\) 0 0
\(707\) 0.576126 + 1.44977i 0.0216674 + 0.0545242i
\(708\) 0 0
\(709\) 43.0831 + 15.6810i 1.61802 + 0.588911i 0.983004 0.183587i \(-0.0587708\pi\)
0.635017 + 0.772498i \(0.280993\pi\)
\(710\) 0 0
\(711\) −16.0043 + 1.64721i −0.600209 + 0.0617754i
\(712\) 0 0
\(713\) 1.73352 + 9.83126i 0.0649207 + 0.368184i
\(714\) 0 0
\(715\) 8.11642 2.95414i 0.303537 0.110478i
\(716\) 0 0
\(717\) −1.37346 26.7595i −0.0512928 0.999353i
\(718\) 0 0
\(719\) 9.97194 0.371891 0.185945 0.982560i \(-0.440465\pi\)
0.185945 + 0.982560i \(0.440465\pi\)
\(720\) 0 0
\(721\) −32.3220 + 19.9410i −1.20373 + 0.742641i
\(722\) 0 0
\(723\) −41.8746 5.18742i −1.55733 0.192922i
\(724\) 0 0
\(725\) −97.9210 + 35.6403i −3.63669 + 1.32365i
\(726\) 0 0
\(727\) −8.15330 2.96756i −0.302389 0.110061i 0.186369 0.982480i \(-0.440328\pi\)
−0.488759 + 0.872419i \(0.662550\pi\)
\(728\) 0 0
\(729\) 5.78446 26.3731i 0.214239 0.976781i
\(730\) 0 0
\(731\) 1.05605 0.886132i 0.0390594 0.0327748i
\(732\) 0 0
\(733\) −6.01962 + 34.1390i −0.222340 + 1.26095i 0.645366 + 0.763873i \(0.276705\pi\)
−0.867706 + 0.497078i \(0.834406\pi\)
\(734\) 0 0
\(735\) 48.3865 + 3.14339i 1.78476 + 0.115946i
\(736\) 0 0
\(737\) 5.41331 9.37614i 0.199402 0.345374i
\(738\) 0 0
\(739\) −6.94358 12.0266i −0.255424 0.442407i 0.709587 0.704618i \(-0.248882\pi\)
−0.965011 + 0.262211i \(0.915548\pi\)
\(740\) 0 0
\(741\) −2.35166 + 1.52358i −0.0863903 + 0.0559701i
\(742\) 0 0
\(743\) 46.2416 16.8306i 1.69644 0.617454i 0.701029 0.713133i \(-0.252724\pi\)
0.995412 + 0.0956791i \(0.0305023\pi\)
\(744\) 0 0
\(745\) 45.7594 + 16.6550i 1.67649 + 0.610194i
\(746\) 0 0
\(747\) −8.74701 + 19.5326i −0.320036 + 0.714659i
\(748\) 0 0
\(749\) 8.63639 + 9.70267i 0.315567 + 0.354528i
\(750\) 0 0
\(751\) 13.7227 4.99464i 0.500747 0.182257i −0.0792829 0.996852i \(-0.525263\pi\)
0.580030 + 0.814595i \(0.303041\pi\)
\(752\) 0 0
\(753\) −1.34534 + 4.38349i −0.0490269 + 0.159743i
\(754\) 0 0
\(755\) 53.5820 1.95005
\(756\) 0 0
\(757\) −16.9195 −0.614948 −0.307474 0.951556i \(-0.599484\pi\)
−0.307474 + 0.951556i \(0.599484\pi\)
\(758\) 0 0
\(759\) −4.43214 + 1.01820i −0.160876 + 0.0369585i
\(760\) 0 0
\(761\) 40.2651 14.6553i 1.45961 0.531254i 0.514351 0.857580i \(-0.328033\pi\)
0.945257 + 0.326326i \(0.105811\pi\)
\(762\) 0 0
\(763\) −5.42260 + 16.3700i −0.196311 + 0.592634i
\(764\) 0 0
\(765\) 2.56008 2.63962i 0.0925598 0.0954355i
\(766\) 0 0
\(767\) −26.3260 9.58189i −0.950577 0.345982i
\(768\) 0 0
\(769\) −17.4562 + 6.35354i −0.629487 + 0.229114i −0.637008 0.770857i \(-0.719828\pi\)
0.00752124 + 0.999972i \(0.497606\pi\)
\(770\) 0 0
\(771\) −2.37434 46.2600i −0.0855098 1.66601i
\(772\) 0 0
\(773\) −26.1688 45.3256i −0.941225 1.63025i −0.763139 0.646235i \(-0.776343\pi\)
−0.178086 0.984015i \(-0.556991\pi\)
\(774\) 0 0
\(775\) −21.6691 + 37.5320i −0.778378 + 1.34819i
\(776\) 0 0
\(777\) −41.5904 29.5451i −1.49205 1.05993i
\(778\) 0 0
\(779\) −0.618359 + 3.50689i −0.0221550 + 0.125647i
\(780\) 0 0
\(781\) −1.56802 + 1.31573i −0.0561082 + 0.0470804i
\(782\) 0 0
\(783\) 46.6190 15.8836i 1.66603 0.567634i
\(784\) 0 0
\(785\) −25.4969 9.28013i −0.910025 0.331222i
\(786\) 0 0
\(787\) 0.430912 0.156839i 0.0153604 0.00559072i −0.334329 0.942457i \(-0.608510\pi\)
0.349689 + 0.936866i \(0.386287\pi\)
\(788\) 0 0
\(789\) −31.3160 + 41.4646i −1.11488 + 1.47618i
\(790\) 0 0
\(791\) 0.0731532 + 2.50544i 0.00260103 + 0.0890833i
\(792\) 0 0
\(793\) 17.0463 0.605334
\(794\) 0 0
\(795\) 55.5981 36.0206i 1.97186 1.27752i
\(796\) 0 0
\(797\) 5.21846 1.89936i 0.184847 0.0672789i −0.247938 0.968776i \(-0.579753\pi\)
0.432785 + 0.901497i \(0.357531\pi\)
\(798\) 0 0
\(799\) −0.430765 2.44299i −0.0152394 0.0864267i
\(800\) 0 0
\(801\) −6.49648 4.40236i −0.229542 0.155550i
\(802\) 0 0
\(803\) −3.09987 1.12826i −0.109392 0.0398154i
\(804\) 0 0
\(805\) −9.89588 24.9021i −0.348784 0.877685i
\(806\) 0 0
\(807\) −3.99356 + 0.917449i −0.140580 + 0.0322957i
\(808\) 0 0
\(809\) −16.1897 + 28.0413i −0.569198 + 0.985880i 0.427447 + 0.904040i \(0.359413\pi\)
−0.996645 + 0.0818400i \(0.973920\pi\)
\(810\) 0 0
\(811\) 19.3335 0.678890 0.339445 0.940626i \(-0.389761\pi\)
0.339445 + 0.940626i \(0.389761\pi\)
\(812\) 0 0
\(813\) 0.950945 3.09844i 0.0333511 0.108667i
\(814\) 0 0
\(815\) 53.0365 + 44.5029i 1.85779 + 1.55887i
\(816\) 0 0
\(817\) 3.28245 + 1.19472i 0.114838 + 0.0417978i
\(818\) 0 0
\(819\) −7.64733 14.6599i −0.267219 0.512258i
\(820\) 0 0
\(821\) 6.76489 5.67642i 0.236096 0.198108i −0.517061 0.855948i \(-0.672974\pi\)
0.753158 + 0.657840i \(0.228530\pi\)
\(822\) 0 0
\(823\) −9.41473 + 53.3936i −0.328177 + 1.86118i 0.158163 + 0.987413i \(0.449443\pi\)
−0.486339 + 0.873770i \(0.661668\pi\)
\(824\) 0 0
\(825\) −17.5807 8.98174i −0.612083 0.312704i
\(826\) 0 0
\(827\) −11.3137 + 19.5959i −0.393415 + 0.681415i −0.992898 0.118973i \(-0.962040\pi\)
0.599482 + 0.800388i \(0.295373\pi\)
\(828\) 0 0
\(829\) −9.64577 −0.335012 −0.167506 0.985871i \(-0.553571\pi\)
−0.167506 + 0.985871i \(0.553571\pi\)
\(830\) 0 0
\(831\) −17.7269 + 23.4716i −0.614939 + 0.814222i
\(832\) 0 0
\(833\) −1.72114 1.28080i −0.0596340 0.0443772i
\(834\) 0 0
\(835\) −6.47482 36.7205i −0.224070 1.27077i
\(836\) 0 0
\(837\) 10.6063 17.5231i 0.366607 0.605687i
\(838\) 0 0
\(839\) 29.6127 + 10.7781i 1.02234 + 0.372103i 0.798161 0.602444i \(-0.205806\pi\)
0.224183 + 0.974547i \(0.428029\pi\)
\(840\) 0 0
\(841\) 46.6044 + 39.1058i 1.60705 + 1.34847i
\(842\) 0 0
\(843\) −23.1749 + 30.6851i −0.798185 + 1.05685i
\(844\) 0 0
\(845\) −17.3176 + 29.9950i −0.595745 + 1.03186i
\(846\) 0 0
\(847\) −23.1149 12.4604i −0.794237 0.428145i
\(848\) 0 0
\(849\) 43.6869 28.3036i 1.49933 0.971379i
\(850\) 0 0
\(851\) −4.89573 + 27.7650i −0.167823 + 0.951773i
\(852\) 0 0
\(853\) −3.51141 19.9142i −0.120228 0.681849i −0.984028 0.178014i \(-0.943033\pi\)
0.863800 0.503835i \(-0.168078\pi\)
\(854\) 0 0
\(855\) 9.03576 + 2.27359i 0.309016 + 0.0777551i
\(856\) 0 0
\(857\) −3.44257 19.5238i −0.117596 0.666919i −0.985432 0.170069i \(-0.945601\pi\)
0.867836 0.496850i \(-0.165510\pi\)
\(858\) 0 0
\(859\) −6.44898 + 2.34724i −0.220036 + 0.0800867i −0.449686 0.893187i \(-0.648464\pi\)
0.229650 + 0.973273i \(0.426242\pi\)
\(860\) 0 0
\(861\) −20.2595 5.57635i −0.690441 0.190042i
\(862\) 0 0
\(863\) −9.76289 16.9098i −0.332333 0.575617i 0.650636 0.759390i \(-0.274502\pi\)
−0.982969 + 0.183773i \(0.941169\pi\)
\(864\) 0 0
\(865\) 11.5135 19.9420i 0.391471 0.678047i
\(866\) 0 0
\(867\) 28.5388 6.55627i 0.969227 0.222663i
\(868\) 0 0
\(869\) 0.965492 5.47558i 0.0327521 0.185746i
\(870\) 0 0
\(871\) −3.77758 21.4237i −0.127998 0.725915i
\(872\) 0 0
\(873\) −22.6847 + 2.33478i −0.767760 + 0.0790202i
\(874\) 0 0
\(875\) 19.9437 60.2069i 0.674219 2.03536i
\(876\) 0 0
\(877\) −33.4492 28.0672i −1.12950 0.947763i −0.130455 0.991454i \(-0.541644\pi\)
−0.999045 + 0.0436912i \(0.986088\pi\)
\(878\) 0 0
\(879\) −0.318314 6.20182i −0.0107365 0.209182i
\(880\) 0 0
\(881\) 0.828121 1.43435i 0.0279001 0.0483244i −0.851738 0.523968i \(-0.824451\pi\)
0.879638 + 0.475643i \(0.157785\pi\)
\(882\) 0 0
\(883\) 2.42828 + 4.20591i 0.0817183 + 0.141540i 0.903988 0.427558i \(-0.140626\pi\)
−0.822270 + 0.569098i \(0.807293\pi\)
\(884\) 0 0
\(885\) 36.3068 + 85.7908i 1.22044 + 2.88383i
\(886\) 0 0
\(887\) −0.108152 + 0.613359i −0.00363138 + 0.0205946i −0.986570 0.163341i \(-0.947773\pi\)
0.982938 + 0.183936i \(0.0588839\pi\)
\(888\) 0 0
\(889\) −31.3241 35.1915i −1.05058 1.18029i
\(890\) 0 0
\(891\) 8.21959 + 4.41604i 0.275367 + 0.147943i
\(892\) 0 0
\(893\) 4.81511 4.04035i 0.161131 0.135205i
\(894\) 0 0
\(895\) −23.5508 19.7615i −0.787217 0.660554i
\(896\) 0 0
\(897\) −5.50701 + 7.29166i −0.183874 + 0.243462i
\(898\) 0 0
\(899\) 37.3629 1.24612
\(900\) 0 0
\(901\) −2.93113 −0.0976502
\(902\) 0 0
\(903\) −8.83793 + 18.6215i −0.294108 + 0.619686i
\(904\) 0 0
\(905\) −44.8214 37.6096i −1.48991 1.25019i
\(906\) 0 0
\(907\) 3.42149 + 1.24532i 0.113609 + 0.0413501i 0.398199 0.917299i \(-0.369635\pi\)
−0.284590 + 0.958649i \(0.591858\pi\)
\(908\) 0 0
\(909\) −1.75964 + 0.181107i −0.0583634 + 0.00600694i
\(910\) 0 0
\(911\) −15.5558 + 13.0528i −0.515386 + 0.432460i −0.863020 0.505170i \(-0.831430\pi\)
0.347634 + 0.937630i \(0.386985\pi\)
\(912\) 0 0
\(913\) −5.66572 4.75410i −0.187508 0.157338i
\(914\) 0 0
\(915\) −38.6125 41.4965i −1.27649 1.37183i
\(916\) 0 0
\(917\) −1.58123 54.1559i −0.0522168 1.78839i
\(918\) 0 0
\(919\) −25.8975 44.8558i −0.854280 1.47966i −0.877312 0.479921i \(-0.840665\pi\)
0.0230323 0.999735i \(-0.492668\pi\)
\(920\) 0 0
\(921\) −31.1386 + 7.15354i −1.02605 + 0.235717i
\(922\) 0 0
\(923\) −0.714197 + 4.05041i −0.0235081 + 0.133321i
\(924\) 0 0
\(925\) −93.7593 + 78.6734i −3.08279 + 2.58677i
\(926\) 0 0
\(927\) −11.7805 41.4207i −0.386923 1.36043i
\(928\) 0 0
\(929\) −4.73144 + 3.97015i −0.155234 + 0.130257i −0.717096 0.696974i \(-0.754529\pi\)
0.561863 + 0.827230i \(0.310085\pi\)
\(930\) 0 0
\(931\) 0.630013 5.39953i 0.0206478 0.176962i
\(932\) 0 0
\(933\) 38.8007 25.1380i 1.27028 0.822980i
\(934\) 0 0
\(935\) 0.635384 + 1.10052i 0.0207793 + 0.0359908i
\(936\) 0 0
\(937\) −2.05305 3.55599i −0.0670703 0.116169i 0.830540 0.556959i \(-0.188032\pi\)
−0.897610 + 0.440790i \(0.854698\pi\)
\(938\) 0 0
\(939\) 52.3092 + 6.48006i 1.70705 + 0.211469i
\(940\) 0 0
\(941\) 33.2167 12.0899i 1.08283 0.394119i 0.261871 0.965103i \(-0.415660\pi\)
0.820961 + 0.570984i \(0.193438\pi\)
\(942\) 0 0
\(943\) 2.01648 + 11.4360i 0.0656655 + 0.372408i
\(944\) 0 0
\(945\) −18.3647 + 51.8230i −0.597405 + 1.68580i
\(946\) 0 0
\(947\) 4.05842 + 23.0164i 0.131881 + 0.747934i 0.976981 + 0.213326i \(0.0684296\pi\)
−0.845100 + 0.534608i \(0.820459\pi\)
\(948\) 0 0
\(949\) −6.22864 + 2.26704i −0.202190 + 0.0735912i
\(950\) 0 0
\(951\) −8.36290 19.7610i −0.271186 0.640795i
\(952\) 0 0
\(953\) −3.05136 5.28512i −0.0988433 0.171202i 0.812363 0.583152i \(-0.198181\pi\)
−0.911206 + 0.411951i \(0.864848\pi\)
\(954\) 0 0
\(955\) 21.5448 + 37.3168i 0.697175 + 1.20754i
\(956\) 0 0
\(957\) 0.872430 + 16.9978i 0.0282017 + 0.549461i
\(958\) 0 0
\(959\) 32.9564 41.6887i 1.06422 1.34620i
\(960\) 0 0
\(961\) −11.8438 + 9.93815i −0.382059 + 0.320585i
\(962\) 0 0
\(963\) −13.2520 + 6.42810i −0.427041 + 0.207143i
\(964\) 0 0
\(965\) 28.2799 23.7296i 0.910361 0.763883i
\(966\) 0 0
\(967\) −8.59228 + 48.7293i −0.276309 + 1.56703i 0.458463 + 0.888713i \(0.348400\pi\)
−0.734772 + 0.678314i \(0.762711\pi\)
\(968\) 0 0
\(969\) −0.280832 0.301808i −0.00902163 0.00969546i
\(970\) 0 0
\(971\) 0.0633848 + 0.109786i 0.00203412 + 0.00352319i 0.867041 0.498237i \(-0.166019\pi\)
−0.865007 + 0.501761i \(0.832686\pi\)
\(972\) 0 0
\(973\) −34.6389 18.6726i −1.11047 0.598617i
\(974\) 0 0
\(975\) −38.6614 + 8.88175i −1.23815 + 0.284444i
\(976\) 0 0
\(977\) 27.6429 + 23.1951i 0.884374 + 0.742078i 0.967074 0.254497i \(-0.0819098\pi\)
−0.0826996 + 0.996575i \(0.526354\pi\)
\(978\) 0 0
\(979\) 2.07752 1.74324i 0.0663977 0.0557143i
\(980\) 0 0
\(981\) −16.1871 10.9693i −0.516815 0.350221i
\(982\) 0 0
\(983\) 44.0491 + 16.0326i 1.40495 + 0.511360i 0.929643 0.368461i \(-0.120115\pi\)
0.475306 + 0.879821i \(0.342337\pi\)
\(984\) 0 0
\(985\) −66.4399 55.7497i −2.11695 1.77633i
\(986\) 0 0
\(987\) 21.0675 + 30.5270i 0.670586 + 0.971685i
\(988\) 0 0
\(989\) 11.3911 0.362216
\(990\) 0 0
\(991\) 20.2243 0.642447 0.321223 0.947003i \(-0.395906\pi\)
0.321223 + 0.947003i \(0.395906\pi\)
\(992\) 0 0
\(993\) 12.8800 + 30.4345i 0.408733 + 0.965811i
\(994\) 0 0
\(995\) 33.2115 + 27.8678i 1.05288 + 0.883469i
\(996\) 0 0
\(997\) −27.3227 + 22.9265i −0.865318 + 0.726088i −0.963107 0.269119i \(-0.913268\pi\)
0.0977887 + 0.995207i \(0.468823\pi\)
\(998\) 0 0
\(999\) 45.0733 36.2587i 1.42606 1.14717i
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 756.2.bp.a.193.19 144
7.2 even 3 756.2.bq.a.625.3 yes 144
27.7 even 9 756.2.bq.a.277.3 yes 144
189.142 even 9 inner 756.2.bp.a.709.19 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
756.2.bp.a.193.19 144 1.1 even 1 trivial
756.2.bp.a.709.19 yes 144 189.142 even 9 inner
756.2.bq.a.277.3 yes 144 27.7 even 9
756.2.bq.a.625.3 yes 144 7.2 even 3