Properties

Label 900.2.w.c.289.3
Level $900$
Weight $2$
Character 900.289
Analytic conductor $7.187$
Analytic rank $0$
Dimension $24$
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] = [900,2,Mod(109,900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(900, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("900.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 900.w (of order \(10\), 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: \(7.18653618192\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: no (minimal twist has level 300)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 289.3
Character \(\chi\) \(=\) 900.289
Dual form 900.2.w.c.109.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.913250 + 2.04107i) q^{5} +4.62675i q^{7} +O(q^{10})\) \(q+(-0.913250 + 2.04107i) q^{5} +4.62675i q^{7} +(-4.00366 + 2.90883i) q^{11} +(2.21170 - 3.04414i) q^{13} +(-2.55872 + 0.831378i) q^{17} +(-1.81426 - 5.58371i) q^{19} +(-3.92540 - 5.40285i) q^{23} +(-3.33195 - 3.72802i) q^{25} +(0.370972 - 1.14173i) q^{29} +(1.02048 + 3.14072i) q^{31} +(-9.44353 - 4.22538i) q^{35} +(1.10342 - 1.51873i) q^{37} +(-2.45366 - 1.78269i) q^{41} +10.6626i q^{43} +(-0.246527 - 0.0801015i) q^{47} -14.4068 q^{49} +(9.31711 + 3.02731i) q^{53} +(-2.28079 - 10.8282i) q^{55} +(7.78643 + 5.65717i) q^{59} +(-5.07552 + 3.68758i) q^{61} +(4.19348 + 7.29430i) q^{65} +(-2.43521 + 0.791247i) q^{67} +(-2.68143 + 8.25259i) q^{71} +(2.86534 + 3.94381i) q^{73} +(-13.4584 - 18.5239i) q^{77} +(-3.85443 + 11.8627i) q^{79} +(8.45513 - 2.74724i) q^{83} +(0.639846 - 5.98178i) q^{85} +(-11.7934 + 8.56841i) q^{89} +(14.0845 + 10.2330i) q^{91} +(13.0536 + 1.39629i) q^{95} +(-3.79176 - 1.23202i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67} - 40 q^{71} + 60 q^{73} + 40 q^{77} + 8 q^{79} + 50 q^{83} + 34 q^{85} - 30 q^{91} + 60 q^{95} - 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(451\) \(577\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{10}\right)\)

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 0
\(4\) 0 0
\(5\) −0.913250 + 2.04107i −0.408418 + 0.912795i
\(6\) 0 0
\(7\) 4.62675i 1.74875i 0.485254 + 0.874373i \(0.338727\pi\)
−0.485254 + 0.874373i \(0.661273\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.00366 + 2.90883i −1.20715 + 0.877045i −0.994969 0.100185i \(-0.968056\pi\)
−0.212180 + 0.977231i \(0.568056\pi\)
\(12\) 0 0
\(13\) 2.21170 3.04414i 0.613415 0.844294i −0.383438 0.923567i \(-0.625260\pi\)
0.996853 + 0.0792730i \(0.0252599\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.55872 + 0.831378i −0.620580 + 0.201639i −0.602398 0.798196i \(-0.705788\pi\)
−0.0181824 + 0.999835i \(0.505788\pi\)
\(18\) 0 0
\(19\) −1.81426 5.58371i −0.416219 1.28099i −0.911156 0.412062i \(-0.864809\pi\)
0.494937 0.868929i \(-0.335191\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.92540 5.40285i −0.818502 1.12657i −0.989955 0.141379i \(-0.954846\pi\)
0.171453 0.985192i \(-0.445154\pi\)
\(24\) 0 0
\(25\) −3.33195 3.72802i −0.666390 0.745603i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.370972 1.14173i 0.0688878 0.212015i −0.910686 0.413099i \(-0.864446\pi\)
0.979574 + 0.201084i \(0.0644464\pi\)
\(30\) 0 0
\(31\) 1.02048 + 3.14072i 0.183284 + 0.564090i 0.999915 0.0130708i \(-0.00416068\pi\)
−0.816631 + 0.577161i \(0.804161\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −9.44353 4.22538i −1.59625 0.714219i
\(36\) 0 0
\(37\) 1.10342 1.51873i 0.181401 0.249677i −0.708627 0.705584i \(-0.750685\pi\)
0.890028 + 0.455907i \(0.150685\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.45366 1.78269i −0.383198 0.278410i 0.379464 0.925206i \(-0.376108\pi\)
−0.762663 + 0.646797i \(0.776108\pi\)
\(42\) 0 0
\(43\) 10.6626i 1.62603i 0.582244 + 0.813014i \(0.302175\pi\)
−0.582244 + 0.813014i \(0.697825\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.246527 0.0801015i −0.0359597 0.0116840i 0.290982 0.956729i \(-0.406018\pi\)
−0.326942 + 0.945045i \(0.606018\pi\)
\(48\) 0 0
\(49\) −14.4068 −2.05811
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.31711 + 3.02731i 1.27980 + 0.415833i 0.868511 0.495670i \(-0.165078\pi\)
0.411292 + 0.911504i \(0.365078\pi\)
\(54\) 0 0
\(55\) −2.28079 10.8282i −0.307542 1.46008i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 7.78643 + 5.65717i 1.01371 + 0.736501i 0.964983 0.262311i \(-0.0844847\pi\)
0.0487233 + 0.998812i \(0.484485\pi\)
\(60\) 0 0
\(61\) −5.07552 + 3.68758i −0.649854 + 0.472147i −0.863222 0.504825i \(-0.831557\pi\)
0.213367 + 0.976972i \(0.431557\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 4.19348 + 7.29430i 0.520138 + 0.904747i
\(66\) 0 0
\(67\) −2.43521 + 0.791247i −0.297508 + 0.0966662i −0.453968 0.891018i \(-0.649992\pi\)
0.156460 + 0.987684i \(0.449992\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.68143 + 8.25259i −0.318227 + 0.979403i 0.656178 + 0.754606i \(0.272172\pi\)
−0.974406 + 0.224797i \(0.927828\pi\)
\(72\) 0 0
\(73\) 2.86534 + 3.94381i 0.335363 + 0.461588i 0.943080 0.332566i \(-0.107914\pi\)
−0.607717 + 0.794154i \(0.707914\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −13.4584 18.5239i −1.53373 2.11100i
\(78\) 0 0
\(79\) −3.85443 + 11.8627i −0.433657 + 1.33466i 0.460800 + 0.887504i \(0.347563\pi\)
−0.894457 + 0.447155i \(0.852437\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 8.45513 2.74724i 0.928071 0.301549i 0.194298 0.980943i \(-0.437757\pi\)
0.733774 + 0.679394i \(0.237757\pi\)
\(84\) 0 0
\(85\) 0.639846 5.98178i 0.0694011 0.648816i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −11.7934 + 8.56841i −1.25010 + 0.908249i −0.998228 0.0595118i \(-0.981046\pi\)
−0.251870 + 0.967761i \(0.581046\pi\)
\(90\) 0 0
\(91\) 14.0845 + 10.2330i 1.47646 + 1.07271i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 13.0536 + 1.39629i 1.33927 + 0.143256i
\(96\) 0 0
\(97\) −3.79176 1.23202i −0.384995 0.125092i 0.110123 0.993918i \(-0.464875\pi\)
−0.495119 + 0.868825i \(0.664875\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −9.36896 −0.932246 −0.466123 0.884720i \(-0.654350\pi\)
−0.466123 + 0.884720i \(0.654350\pi\)
\(102\) 0 0
\(103\) −9.91391 3.22123i −0.976847 0.317397i −0.223270 0.974757i \(-0.571673\pi\)
−0.753577 + 0.657360i \(0.771673\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.220683i 0.0213342i 0.999943 + 0.0106671i \(0.00339551\pi\)
−0.999943 + 0.0106671i \(0.996604\pi\)
\(108\) 0 0
\(109\) 5.40941 + 3.93017i 0.518127 + 0.376442i 0.815898 0.578196i \(-0.196243\pi\)
−0.297771 + 0.954637i \(0.596243\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 5.64782 7.77355i 0.531302 0.731274i −0.456026 0.889966i \(-0.650728\pi\)
0.987328 + 0.158692i \(0.0507277\pi\)
\(114\) 0 0
\(115\) 14.6125 3.07787i 1.36262 0.287013i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.84658 11.8385i −0.352615 1.08524i
\(120\) 0 0
\(121\) 4.16882 12.8303i 0.378984 1.16639i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 10.6521 3.39614i 0.952749 0.303760i
\(126\) 0 0
\(127\) −9.40003 12.9380i −0.834118 1.14806i −0.987143 0.159842i \(-0.948902\pi\)
0.153025 0.988222i \(-0.451098\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.80795 + 11.7197i 0.332702 + 1.02395i 0.967843 + 0.251556i \(0.0809422\pi\)
−0.635140 + 0.772397i \(0.719058\pi\)
\(132\) 0 0
\(133\) 25.8344 8.39411i 2.24013 0.727862i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.34717 4.60698i 0.285968 0.393601i −0.641731 0.766930i \(-0.721784\pi\)
0.927699 + 0.373329i \(0.121784\pi\)
\(138\) 0 0
\(139\) −14.5598 + 10.5783i −1.23495 + 0.897242i −0.997251 0.0740969i \(-0.976393\pi\)
−0.237697 + 0.971339i \(0.576393\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 18.6212i 1.55718i
\(144\) 0 0
\(145\) 1.99157 + 1.79987i 0.165391 + 0.149471i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.09001 −0.0892972 −0.0446486 0.999003i \(-0.514217\pi\)
−0.0446486 + 0.999003i \(0.514217\pi\)
\(150\) 0 0
\(151\) 11.3789 0.926004 0.463002 0.886357i \(-0.346772\pi\)
0.463002 + 0.886357i \(0.346772\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −7.34239 0.785384i −0.589755 0.0630836i
\(156\) 0 0
\(157\) 3.98415i 0.317970i −0.987281 0.158985i \(-0.949178\pi\)
0.987281 0.158985i \(-0.0508221\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 24.9976 18.1618i 1.97009 1.43135i
\(162\) 0 0
\(163\) −12.8322 + 17.6620i −1.00509 + 1.38339i −0.0829441 + 0.996554i \(0.526432\pi\)
−0.922148 + 0.386837i \(0.873568\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −14.7118 + 4.78015i −1.13843 + 0.369899i −0.816775 0.576957i \(-0.804240\pi\)
−0.321658 + 0.946856i \(0.604240\pi\)
\(168\) 0 0
\(169\) −0.357976 1.10174i −0.0275366 0.0847490i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −10.0925 13.8911i −0.767317 1.05612i −0.996570 0.0827547i \(-0.973628\pi\)
0.229253 0.973367i \(-0.426372\pi\)
\(174\) 0 0
\(175\) 17.2486 15.4161i 1.30387 1.16535i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4.46392 + 13.7385i −0.333649 + 1.02687i 0.633734 + 0.773551i \(0.281521\pi\)
−0.967384 + 0.253316i \(0.918479\pi\)
\(180\) 0 0
\(181\) 3.83071 + 11.7897i 0.284734 + 0.876322i 0.986478 + 0.163893i \(0.0524051\pi\)
−0.701744 + 0.712429i \(0.747595\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.09213 + 3.63913i 0.153817 + 0.267554i
\(186\) 0 0
\(187\) 7.82590 10.7714i 0.572287 0.787685i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.33930 0.973056i −0.0969081 0.0704078i 0.538276 0.842769i \(-0.319076\pi\)
−0.635184 + 0.772361i \(0.719076\pi\)
\(192\) 0 0
\(193\) 16.3253i 1.17512i −0.809181 0.587560i \(-0.800089\pi\)
0.809181 0.587560i \(-0.199911\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.9652 + 4.21264i 0.923730 + 0.300138i 0.731996 0.681309i \(-0.238589\pi\)
0.191734 + 0.981447i \(0.438589\pi\)
\(198\) 0 0
\(199\) 6.07817 0.430870 0.215435 0.976518i \(-0.430883\pi\)
0.215435 + 0.976518i \(0.430883\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.28252 + 1.71639i 0.370760 + 0.120467i
\(204\) 0 0
\(205\) 5.87941 3.38006i 0.410636 0.236074i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 23.5057 + 17.0779i 1.62593 + 1.18130i
\(210\) 0 0
\(211\) −13.8200 + 10.0408i −0.951409 + 0.691239i −0.951140 0.308761i \(-0.900086\pi\)
−0.000268984 1.00000i \(0.500086\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −21.7631 9.73760i −1.48423 0.664099i
\(216\) 0 0
\(217\) −14.5313 + 4.72151i −0.986450 + 0.320517i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.12828 + 9.62787i −0.210431 + 0.647640i
\(222\) 0 0
\(223\) 0.460700 + 0.634100i 0.0308508 + 0.0424624i 0.824164 0.566352i \(-0.191646\pi\)
−0.793313 + 0.608814i \(0.791646\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 14.0771 + 19.3755i 0.934331 + 1.28600i 0.958146 + 0.286280i \(0.0924186\pi\)
−0.0238153 + 0.999716i \(0.507581\pi\)
\(228\) 0 0
\(229\) 1.71005 5.26299i 0.113003 0.347788i −0.878522 0.477702i \(-0.841470\pi\)
0.991525 + 0.129914i \(0.0414700\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.863314 + 0.280508i −0.0565576 + 0.0183767i −0.337159 0.941448i \(-0.609466\pi\)
0.280602 + 0.959824i \(0.409466\pi\)
\(234\) 0 0
\(235\) 0.388634 0.430027i 0.0253517 0.0280519i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 9.09227 6.60592i 0.588130 0.427302i −0.253516 0.967331i \(-0.581587\pi\)
0.841646 + 0.540030i \(0.181587\pi\)
\(240\) 0 0
\(241\) 16.3840 + 11.9037i 1.05539 + 0.766783i 0.973229 0.229837i \(-0.0738193\pi\)
0.0821564 + 0.996619i \(0.473819\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 13.1570 29.4053i 0.840570 1.87864i
\(246\) 0 0
\(247\) −21.0102 6.82663i −1.33685 0.434368i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 30.6919 1.93725 0.968627 0.248520i \(-0.0799442\pi\)
0.968627 + 0.248520i \(0.0799442\pi\)
\(252\) 0 0
\(253\) 31.4319 + 10.2129i 1.97611 + 0.642077i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.77543i 0.297883i −0.988846 0.148941i \(-0.952413\pi\)
0.988846 0.148941i \(-0.0475866\pi\)
\(258\) 0 0
\(259\) 7.02676 + 5.10524i 0.436622 + 0.317224i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0.711022 0.978638i 0.0438435 0.0603454i −0.786532 0.617549i \(-0.788126\pi\)
0.830376 + 0.557204i \(0.188126\pi\)
\(264\) 0 0
\(265\) −14.6878 + 16.2522i −0.902265 + 0.998364i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7.88763 24.2756i −0.480917 1.48011i −0.837808 0.545965i \(-0.816163\pi\)
0.356891 0.934146i \(-0.383837\pi\)
\(270\) 0 0
\(271\) −1.81499 + 5.58596i −0.110253 + 0.339323i −0.990927 0.134399i \(-0.957090\pi\)
0.880675 + 0.473722i \(0.157090\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 24.1842 + 5.23364i 1.45836 + 0.315600i
\(276\) 0 0
\(277\) 2.88332 + 3.96855i 0.173242 + 0.238447i 0.886805 0.462144i \(-0.152920\pi\)
−0.713563 + 0.700591i \(0.752920\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.400257 + 1.23186i 0.0238773 + 0.0734868i 0.962285 0.272043i \(-0.0876993\pi\)
−0.938408 + 0.345530i \(0.887699\pi\)
\(282\) 0 0
\(283\) 28.7501 9.34149i 1.70902 0.555294i 0.718849 0.695166i \(-0.244669\pi\)
0.990169 + 0.139873i \(0.0446693\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.24807 11.3525i 0.486868 0.670116i
\(288\) 0 0
\(289\) −7.89744 + 5.73783i −0.464555 + 0.337519i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 8.06831i 0.471356i 0.971831 + 0.235678i \(0.0757310\pi\)
−0.971831 + 0.235678i \(0.924269\pi\)
\(294\) 0 0
\(295\) −18.6576 + 10.7263i −1.08629 + 0.624506i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −25.1289 −1.45324
\(300\) 0 0
\(301\) −49.3331 −2.84351
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.89140 13.7272i −0.165561 0.786017i
\(306\) 0 0
\(307\) 14.7750i 0.843255i −0.906769 0.421628i \(-0.861459\pi\)
0.906769 0.421628i \(-0.138541\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −7.40552 + 5.38043i −0.419929 + 0.305096i −0.777609 0.628748i \(-0.783568\pi\)
0.357680 + 0.933844i \(0.383568\pi\)
\(312\) 0 0
\(313\) 7.79128 10.7238i 0.440389 0.606144i −0.529909 0.848054i \(-0.677774\pi\)
0.970299 + 0.241910i \(0.0777740\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −0.751858 + 0.244293i −0.0422286 + 0.0137209i −0.330055 0.943962i \(-0.607067\pi\)
0.287827 + 0.957683i \(0.407067\pi\)
\(318\) 0 0
\(319\) 1.83587 + 5.65021i 0.102789 + 0.316351i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 9.28434 + 12.7788i 0.516595 + 0.711032i
\(324\) 0 0
\(325\) −18.7179 + 1.89768i −1.03828 + 0.105264i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0.370610 1.14062i 0.0204324 0.0628844i
\(330\) 0 0
\(331\) −1.04253 3.20858i −0.0573026 0.176359i 0.918308 0.395866i \(-0.129555\pi\)
−0.975611 + 0.219506i \(0.929555\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0.608960 5.69304i 0.0332711 0.311044i
\(336\) 0 0
\(337\) −10.6189 + 14.6157i −0.578449 + 0.796166i −0.993524 0.113621i \(-0.963755\pi\)
0.415076 + 0.909787i \(0.363755\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −13.2215 9.60597i −0.715983 0.520192i
\(342\) 0 0
\(343\) 34.2694i 1.85037i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.90284 + 0.943191i 0.155833 + 0.0506332i 0.385895 0.922543i \(-0.373893\pi\)
−0.230062 + 0.973176i \(0.573893\pi\)
\(348\) 0 0
\(349\) 0.628744 0.0336559 0.0168280 0.999858i \(-0.494643\pi\)
0.0168280 + 0.999858i \(0.494643\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 17.9651 + 5.83721i 0.956184 + 0.310683i 0.745226 0.666812i \(-0.232342\pi\)
0.210958 + 0.977495i \(0.432342\pi\)
\(354\) 0 0
\(355\) −14.3953 13.0097i −0.764024 0.690482i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −23.4087 17.0074i −1.23546 0.897617i −0.238176 0.971222i \(-0.576550\pi\)
−0.997287 + 0.0736053i \(0.976550\pi\)
\(360\) 0 0
\(361\) −12.5149 + 9.09264i −0.658681 + 0.478560i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −10.6664 + 2.24669i −0.558303 + 0.117597i
\(366\) 0 0
\(367\) 5.11949 1.66342i 0.267235 0.0868299i −0.172334 0.985038i \(-0.555131\pi\)
0.439570 + 0.898209i \(0.355131\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −14.0066 + 43.1079i −0.727187 + 2.23805i
\(372\) 0 0
\(373\) 6.46415 + 8.89714i 0.334701 + 0.460677i 0.942884 0.333120i \(-0.108101\pi\)
−0.608183 + 0.793797i \(0.708101\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.65513 3.65447i −0.136746 0.188215i
\(378\) 0 0
\(379\) −2.18405 + 6.72183i −0.112187 + 0.345277i −0.991350 0.131245i \(-0.958103\pi\)
0.879163 + 0.476522i \(0.158103\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 7.70484 2.50346i 0.393699 0.127921i −0.105476 0.994422i \(-0.533637\pi\)
0.499175 + 0.866501i \(0.333637\pi\)
\(384\) 0 0
\(385\) 50.0996 10.5526i 2.55331 0.537812i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −26.7325 + 19.4223i −1.35539 + 0.984750i −0.356669 + 0.934231i \(0.616088\pi\)
−0.998723 + 0.0505192i \(0.983912\pi\)
\(390\) 0 0
\(391\) 14.5358 + 10.5609i 0.735107 + 0.534086i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −20.6926 18.7008i −1.04116 0.940938i
\(396\) 0 0
\(397\) 11.7615 + 3.82155i 0.590294 + 0.191798i 0.588907 0.808201i \(-0.299559\pi\)
0.00138688 + 0.999999i \(0.499559\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 14.7983 0.738993 0.369496 0.929232i \(-0.379530\pi\)
0.369496 + 0.929232i \(0.379530\pi\)
\(402\) 0 0
\(403\) 11.8178 + 3.83984i 0.588687 + 0.191276i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9.29012i 0.460494i
\(408\) 0 0
\(409\) −19.1618 13.9219i −0.947491 0.688392i 0.00272132 0.999996i \(-0.499134\pi\)
−0.950212 + 0.311604i \(0.899134\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −26.1743 + 36.0258i −1.28795 + 1.77272i
\(414\) 0 0
\(415\) −2.11433 + 19.7664i −0.103789 + 0.970297i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.477059 + 1.46824i 0.0233058 + 0.0717280i 0.962033 0.272933i \(-0.0879938\pi\)
−0.938727 + 0.344661i \(0.887994\pi\)
\(420\) 0 0
\(421\) −5.43760 + 16.7352i −0.265013 + 0.815625i 0.726678 + 0.686978i \(0.241063\pi\)
−0.991691 + 0.128647i \(0.958937\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 11.6249 + 6.76883i 0.563891 + 0.328337i
\(426\) 0 0
\(427\) −17.0615 23.4832i −0.825665 1.13643i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.83527 14.8814i −0.232907 0.716814i −0.997392 0.0721724i \(-0.977007\pi\)
0.764485 0.644641i \(-0.222993\pi\)
\(432\) 0 0
\(433\) 0.217772 0.0707586i 0.0104655 0.00340044i −0.303780 0.952742i \(-0.598249\pi\)
0.314245 + 0.949342i \(0.398249\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −23.0462 + 31.7204i −1.10245 + 1.51739i
\(438\) 0 0
\(439\) 15.7111 11.4147i 0.749848 0.544796i −0.145932 0.989295i \(-0.546618\pi\)
0.895780 + 0.444498i \(0.146618\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.7980i 0.608051i −0.952664 0.304026i \(-0.901669\pi\)
0.952664 0.304026i \(-0.0983309\pi\)
\(444\) 0 0
\(445\) −6.71842 31.8963i −0.318483 1.51203i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −21.1499 −0.998124 −0.499062 0.866566i \(-0.666322\pi\)
−0.499062 + 0.866566i \(0.666322\pi\)
\(450\) 0 0
\(451\) 15.0092 0.706755
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −33.7489 + 19.4022i −1.58217 + 0.909589i
\(456\) 0 0
\(457\) 8.97118i 0.419654i −0.977739 0.209827i \(-0.932710\pi\)
0.977739 0.209827i \(-0.0672901\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 22.2764 16.1847i 1.03751 0.753797i 0.0677146 0.997705i \(-0.478429\pi\)
0.969799 + 0.243907i \(0.0784293\pi\)
\(462\) 0 0
\(463\) −17.2815 + 23.7859i −0.803140 + 1.10543i 0.189206 + 0.981937i \(0.439409\pi\)
−0.992346 + 0.123489i \(0.960591\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.6119 4.09785i 0.583609 0.189626i −0.00230768 0.999997i \(-0.500735\pi\)
0.585917 + 0.810371i \(0.300735\pi\)
\(468\) 0 0
\(469\) −3.66090 11.2671i −0.169045 0.520266i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −31.0156 42.6893i −1.42610 1.96286i
\(474\) 0 0
\(475\) −14.7711 + 25.3682i −0.677747 + 1.16397i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5.58057 + 17.1752i −0.254983 + 0.784757i 0.738850 + 0.673870i \(0.235369\pi\)
−0.993833 + 0.110887i \(0.964631\pi\)
\(480\) 0 0
\(481\) −2.18279 6.71793i −0.0995266 0.306311i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.97746 6.61412i 0.271423 0.300332i
\(486\) 0 0
\(487\) 8.26258 11.3725i 0.374413 0.515336i −0.579681 0.814844i \(-0.696823\pi\)
0.954094 + 0.299508i \(0.0968226\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −22.0310 16.0065i −0.994247 0.722363i −0.0334000 0.999442i \(-0.510634\pi\)
−0.960847 + 0.277079i \(0.910634\pi\)
\(492\) 0 0
\(493\) 3.22980i 0.145463i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −38.1827 12.4063i −1.71273 0.556499i
\(498\) 0 0
\(499\) 8.17654 0.366032 0.183016 0.983110i \(-0.441414\pi\)
0.183016 + 0.983110i \(0.441414\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 9.45805 + 3.07311i 0.421714 + 0.137023i 0.512183 0.858876i \(-0.328837\pi\)
−0.0904697 + 0.995899i \(0.528837\pi\)
\(504\) 0 0
\(505\) 8.55620 19.1227i 0.380746 0.850950i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −13.9758 10.1540i −0.619464 0.450067i 0.233270 0.972412i \(-0.425057\pi\)
−0.852734 + 0.522345i \(0.825057\pi\)
\(510\) 0 0
\(511\) −18.2470 + 13.2572i −0.807200 + 0.586465i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 15.6286 17.2932i 0.688680 0.762031i
\(516\) 0 0
\(517\) 1.22001 0.396406i 0.0536561 0.0174339i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3.43786 10.5807i 0.150615 0.463547i −0.847075 0.531474i \(-0.821638\pi\)
0.997690 + 0.0679269i \(0.0216385\pi\)
\(522\) 0 0
\(523\) −2.20585 3.03609i −0.0964551 0.132759i 0.758062 0.652183i \(-0.226147\pi\)
−0.854517 + 0.519424i \(0.826147\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.22225 7.18781i −0.227485 0.313106i
\(528\) 0 0
\(529\) −6.67462 + 20.5424i −0.290201 + 0.893146i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −10.8535 + 3.52653i −0.470119 + 0.152751i
\(534\) 0 0
\(535\) −0.450429 0.201538i −0.0194738 0.00871326i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 57.6799 41.9069i 2.48445 1.80506i
\(540\) 0 0
\(541\) −15.2752 11.0981i −0.656731 0.477143i 0.208826 0.977953i \(-0.433036\pi\)
−0.865557 + 0.500810i \(0.833036\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −12.9619 + 7.45177i −0.555226 + 0.319199i
\(546\) 0 0
\(547\) 0.147706 + 0.0479926i 0.00631545 + 0.00205201i 0.312173 0.950025i \(-0.398943\pi\)
−0.305858 + 0.952077i \(0.598943\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.04815 −0.300261
\(552\) 0 0
\(553\) −54.8858 17.8335i −2.33398 0.758356i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 19.0371i 0.806626i 0.915062 + 0.403313i \(0.132141\pi\)
−0.915062 + 0.403313i \(0.867859\pi\)
\(558\) 0 0
\(559\) 32.4584 + 23.5824i 1.37285 + 0.997430i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −18.2630 + 25.1369i −0.769694 + 1.05939i 0.226652 + 0.973976i \(0.427222\pi\)
−0.996345 + 0.0854166i \(0.972778\pi\)
\(564\) 0 0
\(565\) 10.7085 + 18.6268i 0.450510 + 0.783635i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12.1573 + 37.4162i 0.509659 + 1.56857i 0.792794 + 0.609490i \(0.208626\pi\)
−0.283135 + 0.959080i \(0.591374\pi\)
\(570\) 0 0
\(571\) 8.78632 27.0415i 0.367696 1.13165i −0.580580 0.814203i \(-0.697174\pi\)
0.948276 0.317448i \(-0.102826\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −7.06267 + 32.6360i −0.294534 + 1.36101i
\(576\) 0 0
\(577\) 13.2014 + 18.1701i 0.549581 + 0.756433i 0.989955 0.141381i \(-0.0451544\pi\)
−0.440375 + 0.897814i \(0.645154\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 12.7108 + 39.1198i 0.527332 + 1.62296i
\(582\) 0 0
\(583\) −46.1085 + 14.9815i −1.90962 + 0.620472i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.45335 13.0114i 0.390182 0.537039i −0.568064 0.822984i \(-0.692308\pi\)
0.958246 + 0.285945i \(0.0923076\pi\)
\(588\) 0 0
\(589\) 15.6854 11.3961i 0.646307 0.469570i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 20.4648i 0.840389i 0.907434 + 0.420194i \(0.138038\pi\)
−0.907434 + 0.420194i \(0.861962\pi\)
\(594\) 0 0
\(595\) 27.6762 + 2.96041i 1.13461 + 0.121365i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 18.5688 0.758699 0.379349 0.925253i \(-0.376148\pi\)
0.379349 + 0.925253i \(0.376148\pi\)
\(600\) 0 0
\(601\) 47.2047 1.92552 0.962761 0.270355i \(-0.0871409\pi\)
0.962761 + 0.270355i \(0.0871409\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 22.3804 + 20.2261i 0.909894 + 0.822310i
\(606\) 0 0
\(607\) 0.0786576i 0.00319261i 0.999999 + 0.00159631i \(0.000508121\pi\)
−0.999999 + 0.00159631i \(0.999492\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.789085 + 0.573304i −0.0319230 + 0.0231934i
\(612\) 0 0
\(613\) −3.12162 + 4.29654i −0.126081 + 0.173536i −0.867391 0.497627i \(-0.834205\pi\)
0.741310 + 0.671163i \(0.234205\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 28.9429 9.40411i 1.16520 0.378595i 0.338349 0.941021i \(-0.390132\pi\)
0.826848 + 0.562426i \(0.190132\pi\)
\(618\) 0 0
\(619\) 9.77918 + 30.0972i 0.393058 + 1.20971i 0.930463 + 0.366385i \(0.119405\pi\)
−0.537405 + 0.843324i \(0.680595\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −39.6439 54.5651i −1.58830 2.18610i
\(624\) 0 0
\(625\) −2.79622 + 24.8431i −0.111849 + 0.993725i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.56070 + 4.80335i −0.0622293 + 0.191522i
\(630\) 0 0
\(631\) −10.4722 32.2301i −0.416891 1.28306i −0.910548 0.413403i \(-0.864340\pi\)
0.493657 0.869657i \(-0.335660\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 34.9920 7.37048i 1.38862 0.292489i
\(636\) 0 0
\(637\) −31.8635 + 43.8564i −1.26248 + 1.73765i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −39.6699 28.8219i −1.56687 1.13840i −0.930080 0.367358i \(-0.880263\pi\)
−0.636788 0.771039i \(-0.719737\pi\)
\(642\) 0 0
\(643\) 14.2509i 0.562000i 0.959708 + 0.281000i \(0.0906660\pi\)
−0.959708 + 0.281000i \(0.909334\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −40.2623 13.0820i −1.58287 0.514307i −0.620079 0.784539i \(-0.712899\pi\)
−0.962795 + 0.270233i \(0.912899\pi\)
\(648\) 0 0
\(649\) −47.6300 −1.86964
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 44.7274 + 14.5328i 1.75032 + 0.568713i 0.996126 0.0879407i \(-0.0280286\pi\)
0.754192 + 0.656654i \(0.228029\pi\)
\(654\) 0 0
\(655\) −27.3983 2.93068i −1.07054 0.114511i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 9.05013 + 6.57531i 0.352543 + 0.256138i 0.749935 0.661511i \(-0.230085\pi\)
−0.397392 + 0.917649i \(0.630085\pi\)
\(660\) 0 0
\(661\) 37.7102 27.3981i 1.46676 1.06566i 0.485218 0.874393i \(-0.338740\pi\)
0.981538 0.191268i \(-0.0612599\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −6.46029 + 60.3958i −0.250519 + 2.34205i
\(666\) 0 0
\(667\) −7.62483 + 2.47746i −0.295235 + 0.0959276i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 9.59412 29.5277i 0.370377 1.13990i
\(672\) 0 0
\(673\) −8.07264 11.1110i −0.311178 0.428299i 0.624570 0.780968i \(-0.285274\pi\)
−0.935748 + 0.352669i \(0.885274\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 21.6428 + 29.7888i 0.831801 + 1.14488i 0.987585 + 0.157085i \(0.0502095\pi\)
−0.155784 + 0.987791i \(0.549790\pi\)
\(678\) 0 0
\(679\) 5.70024 17.5435i 0.218755 0.673259i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 28.6179 9.29850i 1.09503 0.355797i 0.294843 0.955546i \(-0.404733\pi\)
0.800189 + 0.599748i \(0.204733\pi\)
\(684\) 0 0
\(685\) 6.34638 + 11.0391i 0.242483 + 0.421784i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 29.8222 21.6671i 1.13614 0.825451i
\(690\) 0 0
\(691\) 6.76839 + 4.91752i 0.257482 + 0.187071i 0.709036 0.705172i \(-0.249130\pi\)
−0.451554 + 0.892244i \(0.649130\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −8.29438 39.3783i −0.314624 1.49370i
\(696\) 0 0
\(697\) 7.76033 + 2.52148i 0.293943 + 0.0955080i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 3.42495 0.129359 0.0646794 0.997906i \(-0.479398\pi\)
0.0646794 + 0.997906i \(0.479398\pi\)
\(702\) 0 0
\(703\) −10.4820 3.40581i −0.395336 0.128453i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 43.3478i 1.63026i
\(708\) 0 0
\(709\) −40.0330 29.0857i −1.50347 1.09234i −0.968973 0.247168i \(-0.920500\pi\)
−0.534499 0.845169i \(-0.679500\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 12.9630 17.8421i 0.485469 0.668191i
\(714\) 0 0
\(715\) −38.0072 17.0058i −1.42139 0.635980i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 8.08148 + 24.8722i 0.301388 + 0.927578i 0.981000 + 0.194006i \(0.0621481\pi\)
−0.679612 + 0.733572i \(0.737852\pi\)
\(720\) 0 0
\(721\) 14.9038 45.8692i 0.555046 1.70826i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −5.49247 + 2.42121i −0.203985 + 0.0899216i
\(726\) 0 0
\(727\) 20.3475 + 28.0059i 0.754647 + 1.03868i 0.997640 + 0.0686545i \(0.0218706\pi\)
−0.242994 + 0.970028i \(0.578129\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −8.86463 27.2825i −0.327870 1.00908i
\(732\) 0 0
\(733\) 16.6104 5.39704i 0.613518 0.199344i 0.0142577 0.999898i \(-0.495461\pi\)
0.599260 + 0.800554i \(0.295461\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.44814 10.2515i 0.274356 0.377618i
\(738\) 0 0
\(739\) 16.2358 11.7960i 0.597243 0.433922i −0.247656 0.968848i \(-0.579660\pi\)
0.844899 + 0.534926i \(0.179660\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 5.84644i 0.214485i 0.994233 + 0.107243i \(0.0342022\pi\)
−0.994233 + 0.107243i \(0.965798\pi\)
\(744\) 0 0
\(745\) 0.995453 2.22479i 0.0364706 0.0815101i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.02104 −0.0373081
\(750\) 0 0
\(751\) −32.7925 −1.19662 −0.598308 0.801266i \(-0.704160\pi\)
−0.598308 + 0.801266i \(0.704160\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −10.3918 + 23.2252i −0.378196 + 0.845252i
\(756\) 0 0
\(757\) 22.6371i 0.822759i 0.911464 + 0.411379i \(0.134953\pi\)
−0.911464 + 0.411379i \(0.865047\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −29.3923 + 21.3547i −1.06547 + 0.774109i −0.975092 0.221799i \(-0.928807\pi\)
−0.0903767 + 0.995908i \(0.528807\pi\)
\(762\) 0 0
\(763\) −18.1839 + 25.0280i −0.658301 + 0.906073i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 34.4425 11.1910i 1.24365 0.404085i
\(768\) 0 0
\(769\) −4.51902 13.9081i −0.162960 0.501539i 0.835920 0.548851i \(-0.184935\pi\)
−0.998880 + 0.0473119i \(0.984935\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −17.9422 24.6953i −0.645336 0.888229i 0.353550 0.935416i \(-0.384975\pi\)
−0.998886 + 0.0471864i \(0.984975\pi\)
\(774\) 0 0
\(775\) 8.30846 14.2691i 0.298449 0.512561i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.50245 + 16.9348i −0.197146 + 0.606752i
\(780\) 0 0
\(781\) −13.2699 40.8404i −0.474833 1.46138i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 8.13194 + 3.63852i 0.290241 + 0.129865i
\(786\) 0 0
\(787\) 28.8905 39.7644i 1.02984 1.41745i 0.124766 0.992186i \(-0.460182\pi\)
0.905070 0.425262i \(-0.139818\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 35.9663 + 26.1310i 1.27881 + 0.929112i
\(792\) 0 0
\(793\) 23.6065i 0.838290i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 42.3529 + 13.7613i 1.50022 + 0.487450i 0.940081 0.340951i \(-0.110749\pi\)
0.560136 + 0.828401i \(0.310749\pi\)
\(798\) 0 0
\(799\) 0.697388 0.0246718
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −22.9437 7.45487i −0.809667 0.263077i
\(804\) 0 0
\(805\) 14.2405 + 67.6082i 0.501913 + 2.38288i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 24.5060 + 17.8046i 0.861584 + 0.625978i 0.928316 0.371793i \(-0.121257\pi\)
−0.0667312 + 0.997771i \(0.521257\pi\)
\(810\) 0 0
\(811\) −5.05382 + 3.67182i −0.177464 + 0.128935i −0.672971 0.739669i \(-0.734982\pi\)
0.495507 + 0.868604i \(0.334982\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −24.3304 42.3211i −0.852255 1.48244i
\(816\) 0 0
\(817\) 59.5367 19.3447i 2.08293 0.676784i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 5.95524 18.3284i 0.207839 0.639664i −0.791745 0.610851i \(-0.790827\pi\)
0.999585 0.0288127i \(-0.00917263\pi\)
\(822\) 0 0
\(823\) −4.44218 6.11414i −0.154845 0.213126i 0.724546 0.689227i \(-0.242050\pi\)
−0.879391 + 0.476101i \(0.842050\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −18.4412 25.3821i −0.641262 0.882621i 0.357420 0.933944i \(-0.383656\pi\)
−0.998682 + 0.0513225i \(0.983656\pi\)
\(828\) 0 0
\(829\) −8.55625 + 26.3334i −0.297171 + 0.914597i 0.685313 + 0.728249i \(0.259665\pi\)
−0.982484 + 0.186349i \(0.940335\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 36.8629 11.9775i 1.27723 0.414996i
\(834\) 0 0
\(835\) 3.67890 34.3933i 0.127314 1.19023i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 30.5642 22.2062i 1.05519 0.766643i 0.0819999 0.996632i \(-0.473869\pi\)
0.973193 + 0.229990i \(0.0738693\pi\)
\(840\) 0 0
\(841\) 22.2956 + 16.1987i 0.768812 + 0.558575i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.57565 + 0.275506i 0.0886049 + 0.00947770i
\(846\) 0 0
\(847\) 59.3626 + 19.2881i 2.03972 + 0.662747i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −12.5368 −0.429756
\(852\) 0 0
\(853\) 46.9508 + 15.2552i 1.60756 + 0.522329i 0.968962 0.247208i \(-0.0795131\pi\)
0.638602 + 0.769537i \(0.279513\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 15.7692i 0.538667i 0.963047 + 0.269333i \(0.0868034\pi\)
−0.963047 + 0.269333i \(0.913197\pi\)
\(858\) 0 0
\(859\) 7.60223 + 5.52335i 0.259385 + 0.188454i 0.709876 0.704327i \(-0.248751\pi\)
−0.450491 + 0.892781i \(0.648751\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −10.5040 + 14.4575i −0.357560 + 0.492140i −0.949467 0.313867i \(-0.898375\pi\)
0.591907 + 0.806007i \(0.298375\pi\)
\(864\) 0 0
\(865\) 37.5697 7.91343i 1.27741 0.269065i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −19.0748 58.7061i −0.647068 1.99147i
\(870\) 0 0
\(871\) −2.97728 + 9.16312i −0.100881 + 0.310481i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 15.7131 + 49.2844i 0.531199 + 1.66612i
\(876\) 0 0
\(877\) 10.4069 + 14.3238i 0.351415 + 0.483681i 0.947732 0.319068i \(-0.103370\pi\)
−0.596317 + 0.802749i \(0.703370\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 9.82007 + 30.2231i 0.330847 + 1.01824i 0.968732 + 0.248110i \(0.0798094\pi\)
−0.637885 + 0.770131i \(0.720191\pi\)
\(882\) 0 0
\(883\) 32.9158 10.6950i 1.10771 0.359916i 0.302643 0.953104i \(-0.402131\pi\)
0.805064 + 0.593188i \(0.202131\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −16.7639 + 23.0735i −0.562876 + 0.774732i −0.991689 0.128661i \(-0.958932\pi\)
0.428813 + 0.903393i \(0.358932\pi\)
\(888\) 0 0
\(889\) 59.8610 43.4916i 2.00767 1.45866i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.52186i 0.0509271i
\(894\) 0 0
\(895\) −23.9647 21.6579i −0.801051 0.723944i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3.96444 0.132221
\(900\) 0 0
\(901\) −26.3567 −0.878069
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −27.5620 2.94819i −0.916193 0.0980013i
\(906\) 0 0
\(907\) 7.01754i 0.233013i 0.993190 + 0.116507i \(0.0371697\pi\)
−0.993190 + 0.116507i \(0.962830\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −16.9145 + 12.2891i −0.560403 + 0.407157i −0.831606 0.555365i \(-0.812578\pi\)
0.271203 + 0.962522i \(0.412578\pi\)
\(912\) 0 0
\(913\) −25.8602 + 35.5936i −0.855849 + 1.17797i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −54.2240 + 17.6184i −1.79063 + 0.581812i
\(918\) 0 0
\(919\) −18.4658 56.8320i −0.609132 1.87471i −0.465406 0.885097i \(-0.654092\pi\)
−0.143726 0.989618i \(-0.545908\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 19.1916 + 26.4149i 0.631698 + 0.869458i
\(924\) 0 0
\(925\) −9.33837 + 0.946755i −0.307044 + 0.0311291i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −12.4320 + 38.2618i −0.407881 + 1.25533i 0.510585 + 0.859828i \(0.329429\pi\)
−0.918466 + 0.395501i \(0.870571\pi\)
\(930\) 0 0
\(931\) 26.1376 + 80.4434i 0.856626 + 2.63642i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 14.8383 + 25.8102i 0.485263 + 0.844085i
\(936\) 0 0
\(937\) −29.0457 + 39.9780i −0.948881 + 1.30602i 0.00314114 + 0.999995i \(0.499000\pi\)
−0.952022 + 0.306028i \(0.901000\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 18.0130 + 13.0872i 0.587207 + 0.426631i 0.841315 0.540545i \(-0.181782\pi\)
−0.254108 + 0.967176i \(0.581782\pi\)
\(942\) 0 0
\(943\) 20.2546i 0.659579i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 33.9316 + 11.0251i 1.10263 + 0.358266i 0.803114 0.595825i \(-0.203175\pi\)
0.299516 + 0.954091i \(0.403175\pi\)
\(948\) 0 0
\(949\) 18.3428 0.595433
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.66940 + 0.867341i 0.0864704 + 0.0280959i 0.351933 0.936025i \(-0.385525\pi\)
−0.265462 + 0.964121i \(0.585525\pi\)
\(954\) 0 0
\(955\) 3.20919 1.84496i 0.103847 0.0597014i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 21.3153 + 15.4865i 0.688308 + 0.500085i
\(960\) 0 0
\(961\) 16.2568 11.8113i 0.524413 0.381008i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 33.3211 + 14.9091i 1.07264 + 0.479940i
\(966\) 0 0
\(967\) 10.9640 3.56243i 0.352580 0.114560i −0.127372 0.991855i \(-0.540654\pi\)
0.479952 + 0.877295i \(0.340654\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −7.15578 + 22.0232i −0.229640 + 0.706759i 0.768148 + 0.640273i \(0.221179\pi\)
−0.997787 + 0.0664858i \(0.978821\pi\)
\(972\) 0 0
\(973\) −48.9433 67.3646i −1.56905 2.15961i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.85551 + 6.68304i 0.155342 + 0.213809i 0.879593 0.475726i \(-0.157815\pi\)
−0.724252 + 0.689536i \(0.757815\pi\)
\(978\) 0 0
\(979\) 22.2927 68.6100i 0.712479 2.19278i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 18.8202 6.11506i 0.600271 0.195040i 0.00690994 0.999976i \(-0.497800\pi\)
0.593361 + 0.804936i \(0.297800\pi\)
\(984\) 0 0
\(985\) −20.4387 + 22.6157i −0.651232 + 0.720595i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 57.6083 41.8549i 1.83184 1.33091i
\(990\) 0 0
\(991\) −17.3036 12.5718i −0.549666 0.399355i 0.277997 0.960582i \(-0.410330\pi\)
−0.827662 + 0.561227i \(0.810330\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −5.55089 + 12.4060i −0.175975 + 0.393296i
\(996\) 0 0
\(997\) −16.7226 5.43350i −0.529610 0.172081i 0.0319923 0.999488i \(-0.489815\pi\)
−0.561602 + 0.827407i \(0.689815\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 900.2.w.c.289.3 24
3.2 odd 2 300.2.o.a.289.2 yes 24
15.2 even 4 1500.2.m.d.301.1 24
15.8 even 4 1500.2.m.c.301.6 24
15.14 odd 2 1500.2.o.c.949.6 24
25.9 even 10 inner 900.2.w.c.109.3 24
75.29 odd 10 7500.2.d.g.1249.13 24
75.38 even 20 1500.2.m.c.1201.6 24
75.41 odd 10 1500.2.o.c.49.6 24
75.47 even 20 7500.2.a.m.1.1 12
75.53 even 20 7500.2.a.n.1.12 12
75.59 odd 10 300.2.o.a.109.2 24
75.62 even 20 1500.2.m.d.1201.1 24
75.71 odd 10 7500.2.d.g.1249.12 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
300.2.o.a.109.2 24 75.59 odd 10
300.2.o.a.289.2 yes 24 3.2 odd 2
900.2.w.c.109.3 24 25.9 even 10 inner
900.2.w.c.289.3 24 1.1 even 1 trivial
1500.2.m.c.301.6 24 15.8 even 4
1500.2.m.c.1201.6 24 75.38 even 20
1500.2.m.d.301.1 24 15.2 even 4
1500.2.m.d.1201.1 24 75.62 even 20
1500.2.o.c.49.6 24 75.41 odd 10
1500.2.o.c.949.6 24 15.14 odd 2
7500.2.a.m.1.1 12 75.47 even 20
7500.2.a.n.1.12 12 75.53 even 20
7500.2.d.g.1249.12 24 75.71 odd 10
7500.2.d.g.1249.13 24 75.29 odd 10