Properties

Label 2100.2.bo.i.1349.9
Level $2100$
Weight $2$
Character 2100.1349
Analytic conductor $16.769$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2100,2,Mod(1349,2100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2100.1349");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.bo (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1349.9
Character \(\chi\) \(=\) 2100.1349
Dual form 2100.2.bo.i.1949.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.134063 - 1.72685i) q^{3} +(-2.52603 - 0.786875i) q^{7} +(-2.96405 - 0.463016i) q^{9} +O(q^{10})\) \(q+(0.134063 - 1.72685i) q^{3} +(-2.52603 - 0.786875i) q^{7} +(-2.96405 - 0.463016i) q^{9} +(2.34474 - 1.35373i) q^{11} +1.12489 q^{13} +(-6.39336 + 3.69121i) q^{17} +(0.412264 + 0.238021i) q^{19} +(-1.69747 + 4.25660i) q^{21} +(-2.79845 + 4.84706i) q^{23} +(-1.19693 + 5.05642i) q^{27} -2.20372i q^{29} +(-2.07315 + 1.19693i) q^{31} +(-2.02336 - 4.23051i) q^{33} +(-7.53233 - 4.34879i) q^{37} +(0.150806 - 1.94251i) q^{39} +5.42336 q^{41} +4.16209i q^{43} +(10.7600 + 6.21227i) q^{47} +(5.76166 + 3.97534i) q^{49} +(5.51707 + 11.5353i) q^{51} +(-2.45559 - 4.25321i) q^{53} +(0.466297 - 0.680011i) q^{57} +(-1.15586 - 2.00200i) q^{59} +(-2.26895 - 1.30998i) q^{61} +(7.12295 + 3.50193i) q^{63} +(-12.7169 + 7.34210i) q^{67} +(7.99501 + 5.48234i) q^{69} +9.89729i q^{71} +(3.63180 + 6.29046i) q^{73} +(-6.98810 + 1.57456i) q^{77} +(-3.47478 + 6.01850i) q^{79} +(8.57123 + 2.74481i) q^{81} -11.3005i q^{83} +(-3.80550 - 0.295438i) q^{87} +(-3.48186 + 6.03075i) q^{89} +(-2.84150 - 0.885144i) q^{91} +(1.78899 + 3.74049i) q^{93} -8.79691 q^{97} +(-7.57673 + 2.92689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 18 q^{9} + 36 q^{19} - 22 q^{21} - 36 q^{31} - 24 q^{39} + 36 q^{49} - 2 q^{51} + 72 q^{61} + 14 q^{81} + 40 q^{91} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).

\(n\) \(701\) \(1051\) \(1177\) \(1501\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.134063 1.72685i 0.0774015 0.997000i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.52603 0.786875i −0.954750 0.297411i
\(8\) 0 0
\(9\) −2.96405 0.463016i −0.988018 0.154339i
\(10\) 0 0
\(11\) 2.34474 1.35373i 0.706965 0.408166i −0.102971 0.994684i \(-0.532835\pi\)
0.809936 + 0.586518i \(0.199502\pi\)
\(12\) 0 0
\(13\) 1.12489 0.311987 0.155994 0.987758i \(-0.450142\pi\)
0.155994 + 0.987758i \(0.450142\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.39336 + 3.69121i −1.55062 + 0.895250i −0.552527 + 0.833495i \(0.686336\pi\)
−0.998091 + 0.0617544i \(0.980330\pi\)
\(18\) 0 0
\(19\) 0.412264 + 0.238021i 0.0945799 + 0.0546057i 0.546544 0.837430i \(-0.315943\pi\)
−0.451964 + 0.892036i \(0.649276\pi\)
\(20\) 0 0
\(21\) −1.69747 + 4.25660i −0.370417 + 0.928865i
\(22\) 0 0
\(23\) −2.79845 + 4.84706i −0.583518 + 1.01068i 0.411540 + 0.911392i \(0.364991\pi\)
−0.995058 + 0.0992913i \(0.968342\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.19693 + 5.05642i −0.230350 + 0.973108i
\(28\) 0 0
\(29\) 2.20372i 0.409220i −0.978844 0.204610i \(-0.934407\pi\)
0.978844 0.204610i \(-0.0655926\pi\)
\(30\) 0 0
\(31\) −2.07315 + 1.19693i −0.372348 + 0.214975i −0.674484 0.738290i \(-0.735634\pi\)
0.302136 + 0.953265i \(0.402300\pi\)
\(32\) 0 0
\(33\) −2.02336 4.23051i −0.352222 0.736437i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7.53233 4.34879i −1.23831 0.714937i −0.269559 0.962984i \(-0.586878\pi\)
−0.968748 + 0.248047i \(0.920211\pi\)
\(38\) 0 0
\(39\) 0.150806 1.94251i 0.0241483 0.311051i
\(40\) 0 0
\(41\) 5.42336 0.846986 0.423493 0.905899i \(-0.360804\pi\)
0.423493 + 0.905899i \(0.360804\pi\)
\(42\) 0 0
\(43\) 4.16209i 0.634712i 0.948306 + 0.317356i \(0.102795\pi\)
−0.948306 + 0.317356i \(0.897205\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.7600 + 6.21227i 1.56950 + 0.906153i 0.996227 + 0.0867912i \(0.0276613\pi\)
0.573277 + 0.819362i \(0.305672\pi\)
\(48\) 0 0
\(49\) 5.76166 + 3.97534i 0.823094 + 0.567905i
\(50\) 0 0
\(51\) 5.51707 + 11.5353i 0.772544 + 1.61526i
\(52\) 0 0
\(53\) −2.45559 4.25321i −0.337302 0.584224i 0.646622 0.762810i \(-0.276181\pi\)
−0.983924 + 0.178586i \(0.942848\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.466297 0.680011i 0.0617626 0.0900696i
\(58\) 0 0
\(59\) −1.15586 2.00200i −0.150480 0.260638i 0.780924 0.624626i \(-0.214748\pi\)
−0.931404 + 0.363987i \(0.881415\pi\)
\(60\) 0 0
\(61\) −2.26895 1.30998i −0.290509 0.167726i 0.347662 0.937620i \(-0.386976\pi\)
−0.638172 + 0.769894i \(0.720309\pi\)
\(62\) 0 0
\(63\) 7.12295 + 3.50193i 0.897408 + 0.441202i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −12.7169 + 7.34210i −1.55361 + 0.896980i −0.555772 + 0.831335i \(0.687577\pi\)
−0.997843 + 0.0656452i \(0.979089\pi\)
\(68\) 0 0
\(69\) 7.99501 + 5.48234i 0.962486 + 0.659996i
\(70\) 0 0
\(71\) 9.89729i 1.17459i 0.809372 + 0.587296i \(0.199807\pi\)
−0.809372 + 0.587296i \(0.800193\pi\)
\(72\) 0 0
\(73\) 3.63180 + 6.29046i 0.425070 + 0.736242i 0.996427 0.0844591i \(-0.0269162\pi\)
−0.571357 + 0.820701i \(0.693583\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.98810 + 1.57456i −0.796368 + 0.179438i
\(78\) 0 0
\(79\) −3.47478 + 6.01850i −0.390944 + 0.677134i −0.992574 0.121640i \(-0.961185\pi\)
0.601631 + 0.798774i \(0.294518\pi\)
\(80\) 0 0
\(81\) 8.57123 + 2.74481i 0.952359 + 0.304979i
\(82\) 0 0
\(83\) 11.3005i 1.24040i −0.784446 0.620198i \(-0.787052\pi\)
0.784446 0.620198i \(-0.212948\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.80550 0.295438i −0.407992 0.0316743i
\(88\) 0 0
\(89\) −3.48186 + 6.03075i −0.369076 + 0.639258i −0.989421 0.145070i \(-0.953659\pi\)
0.620345 + 0.784329i \(0.286992\pi\)
\(90\) 0 0
\(91\) −2.84150 0.885144i −0.297870 0.0927883i
\(92\) 0 0
\(93\) 1.78899 + 3.74049i 0.185510 + 0.387871i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −8.79691 −0.893190 −0.446595 0.894736i \(-0.647364\pi\)
−0.446595 + 0.894736i \(0.647364\pi\)
\(98\) 0 0
\(99\) −7.57673 + 2.92689i −0.761490 + 0.294164i
\(100\) 0 0
\(101\) −5.23274 9.06338i −0.520677 0.901840i −0.999711 0.0240431i \(-0.992346\pi\)
0.479034 0.877797i \(-0.340987\pi\)
\(102\) 0 0
\(103\) 1.63440 2.83087i 0.161042 0.278934i −0.774200 0.632941i \(-0.781848\pi\)
0.935243 + 0.354007i \(0.115181\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.49305 + 4.31809i −0.241012 + 0.417445i −0.961003 0.276538i \(-0.910813\pi\)
0.719991 + 0.693984i \(0.244146\pi\)
\(108\) 0 0
\(109\) 2.40043 + 4.15767i 0.229920 + 0.398232i 0.957784 0.287489i \(-0.0928204\pi\)
−0.727864 + 0.685721i \(0.759487\pi\)
\(110\) 0 0
\(111\) −8.51954 + 12.4242i −0.808639 + 1.17925i
\(112\) 0 0
\(113\) 18.8874 1.77678 0.888388 0.459094i \(-0.151826\pi\)
0.888388 + 0.459094i \(0.151826\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −3.33422 0.520840i −0.308249 0.0481517i
\(118\) 0 0
\(119\) 19.0543 4.29333i 1.74671 0.393569i
\(120\) 0 0
\(121\) −1.83480 + 3.17797i −0.166800 + 0.288907i
\(122\) 0 0
\(123\) 0.727074 9.36535i 0.0655580 0.844445i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 7.77289i 0.689732i 0.938652 + 0.344866i \(0.112076\pi\)
−0.938652 + 0.344866i \(0.887924\pi\)
\(128\) 0 0
\(129\) 7.18732 + 0.557983i 0.632808 + 0.0491277i
\(130\) 0 0
\(131\) −2.32600 + 4.02875i −0.203224 + 0.351994i −0.949565 0.313569i \(-0.898475\pi\)
0.746342 + 0.665563i \(0.231809\pi\)
\(132\) 0 0
\(133\) −0.854100 0.925648i −0.0740598 0.0802639i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.50592 + 9.53654i 0.470403 + 0.814762i 0.999427 0.0338451i \(-0.0107753\pi\)
−0.529024 + 0.848607i \(0.677442\pi\)
\(138\) 0 0
\(139\) 20.5928i 1.74665i 0.487134 + 0.873327i \(0.338042\pi\)
−0.487134 + 0.873327i \(0.661958\pi\)
\(140\) 0 0
\(141\) 12.1702 17.7481i 1.02492 1.49466i
\(142\) 0 0
\(143\) 2.63756 1.52280i 0.220564 0.127343i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 7.63726 9.41660i 0.629910 0.776668i
\(148\) 0 0
\(149\) 14.8906 + 8.59708i 1.21988 + 0.704300i 0.964893 0.262643i \(-0.0845942\pi\)
0.254991 + 0.966943i \(0.417928\pi\)
\(150\) 0 0
\(151\) −1.00060 1.73309i −0.0814279 0.141037i 0.822436 0.568858i \(-0.192615\pi\)
−0.903863 + 0.427821i \(0.859281\pi\)
\(152\) 0 0
\(153\) 20.6594 7.98072i 1.67021 0.645203i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −9.11856 15.7938i −0.727741 1.26048i −0.957836 0.287316i \(-0.907237\pi\)
0.230095 0.973168i \(-0.426096\pi\)
\(158\) 0 0
\(159\) −7.67389 + 3.67025i −0.608579 + 0.291070i
\(160\) 0 0
\(161\) 10.8830 10.0418i 0.857701 0.791405i
\(162\) 0 0
\(163\) −17.1563 9.90522i −1.34379 0.775837i −0.356427 0.934323i \(-0.616005\pi\)
−0.987361 + 0.158487i \(0.949339\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.5257i 0.969269i −0.874717 0.484634i \(-0.838953\pi\)
0.874717 0.484634i \(-0.161047\pi\)
\(168\) 0 0
\(169\) −11.7346 −0.902664
\(170\) 0 0
\(171\) −1.11177 0.896392i −0.0850189 0.0685488i
\(172\) 0 0
\(173\) −12.7620 7.36813i −0.970275 0.560188i −0.0709548 0.997480i \(-0.522605\pi\)
−0.899320 + 0.437291i \(0.855938\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3.61212 + 1.72760i −0.271504 + 0.129854i
\(178\) 0 0
\(179\) −1.18770 + 0.685720i −0.0887730 + 0.0512531i −0.543729 0.839261i \(-0.682988\pi\)
0.454956 + 0.890514i \(0.349655\pi\)
\(180\) 0 0
\(181\) 21.3843i 1.58949i −0.606947 0.794743i \(-0.707606\pi\)
0.606947 0.794743i \(-0.292394\pi\)
\(182\) 0 0
\(183\) −2.56633 + 3.74253i −0.189708 + 0.276656i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −9.99384 + 17.3098i −0.730822 + 1.26582i
\(188\) 0 0
\(189\) 7.00225 11.8308i 0.509339 0.860566i
\(190\) 0 0
\(191\) 14.9775 + 8.64724i 1.08373 + 0.625692i 0.931900 0.362714i \(-0.118150\pi\)
0.151830 + 0.988407i \(0.451483\pi\)
\(192\) 0 0
\(193\) −11.0921 + 6.40401i −0.798425 + 0.460971i −0.842920 0.538039i \(-0.819165\pi\)
0.0444950 + 0.999010i \(0.485832\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 9.17207 0.653483 0.326741 0.945114i \(-0.394049\pi\)
0.326741 + 0.945114i \(0.394049\pi\)
\(198\) 0 0
\(199\) −7.16818 + 4.13855i −0.508139 + 0.293374i −0.732068 0.681231i \(-0.761445\pi\)
0.223930 + 0.974605i \(0.428111\pi\)
\(200\) 0 0
\(201\) 10.9739 + 22.9445i 0.774037 + 1.61838i
\(202\) 0 0
\(203\) −1.73405 + 5.56666i −0.121706 + 0.390703i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 10.5390 13.0712i 0.732514 0.908513i
\(208\) 0 0
\(209\) 1.28887 0.0891529
\(210\) 0 0
\(211\) −8.50872 −0.585765 −0.292882 0.956148i \(-0.594614\pi\)
−0.292882 + 0.956148i \(0.594614\pi\)
\(212\) 0 0
\(213\) 17.0912 + 1.32686i 1.17107 + 0.0909152i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 6.17867 1.39218i 0.419435 0.0945073i
\(218\) 0 0
\(219\) 11.3496 5.42827i 0.766935 0.366808i
\(220\) 0 0
\(221\) −7.19180 + 4.15219i −0.483773 + 0.279306i
\(222\) 0 0
\(223\) 5.54451 0.371288 0.185644 0.982617i \(-0.440563\pi\)
0.185644 + 0.982617i \(0.440563\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.36478 3.09736i 0.356073 0.205579i −0.311284 0.950317i \(-0.600759\pi\)
0.667357 + 0.744738i \(0.267426\pi\)
\(228\) 0 0
\(229\) 0.307553 + 0.177566i 0.0203237 + 0.0117339i 0.510127 0.860099i \(-0.329598\pi\)
−0.489804 + 0.871833i \(0.662932\pi\)
\(230\) 0 0
\(231\) 1.78219 + 12.2785i 0.117259 + 0.807867i
\(232\) 0 0
\(233\) −9.33296 + 16.1652i −0.611422 + 1.05901i 0.379578 + 0.925160i \(0.376069\pi\)
−0.991001 + 0.133855i \(0.957264\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 9.92723 + 6.80730i 0.644843 + 0.442182i
\(238\) 0 0
\(239\) 21.1914i 1.37076i 0.728186 + 0.685379i \(0.240364\pi\)
−0.728186 + 0.685379i \(0.759636\pi\)
\(240\) 0 0
\(241\) −1.92350 + 1.11053i −0.123903 + 0.0715356i −0.560671 0.828039i \(-0.689457\pi\)
0.436767 + 0.899574i \(0.356123\pi\)
\(242\) 0 0
\(243\) 5.88897 14.4333i 0.377778 0.925896i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.463750 + 0.267746i 0.0295077 + 0.0170363i
\(248\) 0 0
\(249\) −19.5144 1.51499i −1.23667 0.0960084i
\(250\) 0 0
\(251\) −18.3017 −1.15519 −0.577597 0.816322i \(-0.696010\pi\)
−0.577597 + 0.816322i \(0.696010\pi\)
\(252\) 0 0
\(253\) 15.1535i 0.952690i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.69894 5.59968i −0.605003 0.349299i 0.166004 0.986125i \(-0.446913\pi\)
−0.771007 + 0.636826i \(0.780247\pi\)
\(258\) 0 0
\(259\) 15.6049 + 16.9122i 0.969643 + 1.05087i
\(260\) 0 0
\(261\) −1.02036 + 6.53194i −0.0631585 + 0.404317i
\(262\) 0 0
\(263\) 6.60778 + 11.4450i 0.407453 + 0.705730i 0.994604 0.103748i \(-0.0330836\pi\)
−0.587150 + 0.809478i \(0.699750\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 9.94744 + 6.82116i 0.608774 + 0.417448i
\(268\) 0 0
\(269\) −12.6657 21.9377i −0.772244 1.33757i −0.936330 0.351120i \(-0.885801\pi\)
0.164086 0.986446i \(-0.447532\pi\)
\(270\) 0 0
\(271\) −23.9303 13.8162i −1.45366 0.839273i −0.454976 0.890504i \(-0.650352\pi\)
−0.998687 + 0.0512313i \(0.983685\pi\)
\(272\) 0 0
\(273\) −1.90946 + 4.78818i −0.115566 + 0.289794i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −20.4917 + 11.8309i −1.23122 + 0.710848i −0.967285 0.253691i \(-0.918355\pi\)
−0.263939 + 0.964539i \(0.585022\pi\)
\(278\) 0 0
\(279\) 6.69912 2.58787i 0.401066 0.154932i
\(280\) 0 0
\(281\) 17.3694i 1.03617i −0.855329 0.518085i \(-0.826645\pi\)
0.855329 0.518085i \(-0.173355\pi\)
\(282\) 0 0
\(283\) −6.46037 11.1897i −0.384029 0.665158i 0.607605 0.794239i \(-0.292130\pi\)
−0.991634 + 0.129082i \(0.958797\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −13.6996 4.26750i −0.808660 0.251903i
\(288\) 0 0
\(289\) 18.7500 32.4760i 1.10294 1.91036i
\(290\) 0 0
\(291\) −1.17934 + 15.1910i −0.0691343 + 0.890511i
\(292\) 0 0
\(293\) 11.2345i 0.656326i −0.944621 0.328163i \(-0.893571\pi\)
0.944621 0.328163i \(-0.106429\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 4.03856 + 13.4763i 0.234341 + 0.781974i
\(298\) 0 0
\(299\) −3.14794 + 5.45239i −0.182050 + 0.315320i
\(300\) 0 0
\(301\) 3.27504 10.5136i 0.188770 0.605991i
\(302\) 0 0
\(303\) −16.3527 + 7.82112i −0.939435 + 0.449312i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 31.0165 1.77021 0.885103 0.465395i \(-0.154088\pi\)
0.885103 + 0.465395i \(0.154088\pi\)
\(308\) 0 0
\(309\) −4.66938 3.20189i −0.265632 0.182149i
\(310\) 0 0
\(311\) 0.771357 + 1.33603i 0.0437396 + 0.0757593i 0.887066 0.461642i \(-0.152739\pi\)
−0.843327 + 0.537401i \(0.819406\pi\)
\(312\) 0 0
\(313\) −12.8545 + 22.2646i −0.726579 + 1.25847i 0.231742 + 0.972777i \(0.425558\pi\)
−0.958321 + 0.285694i \(0.907776\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.55545 2.69412i 0.0873629 0.151317i −0.819033 0.573747i \(-0.805489\pi\)
0.906396 + 0.422430i \(0.138823\pi\)
\(318\) 0 0
\(319\) −2.98325 5.16714i −0.167030 0.289304i
\(320\) 0 0
\(321\) 7.12248 + 4.88403i 0.397538 + 0.272600i
\(322\) 0 0
\(323\) −3.51434 −0.195543
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 7.50150 3.58780i 0.414834 0.198406i
\(328\) 0 0
\(329\) −22.2917 24.1591i −1.22898 1.33194i
\(330\) 0 0
\(331\) 0.139978 0.242450i 0.00769391 0.0133262i −0.862153 0.506648i \(-0.830884\pi\)
0.869847 + 0.493322i \(0.164218\pi\)
\(332\) 0 0
\(333\) 20.3127 + 16.3776i 1.11313 + 0.897489i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 5.96891i 0.325147i 0.986696 + 0.162574i \(0.0519795\pi\)
−0.986696 + 0.162574i \(0.948021\pi\)
\(338\) 0 0
\(339\) 2.53211 32.6158i 0.137525 1.77145i
\(340\) 0 0
\(341\) −3.24066 + 5.61298i −0.175491 + 0.303960i
\(342\) 0 0
\(343\) −11.4260 14.5755i −0.616947 0.787004i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.28063 + 7.41426i 0.229796 + 0.398019i 0.957748 0.287610i \(-0.0928607\pi\)
−0.727951 + 0.685629i \(0.759527\pi\)
\(348\) 0 0
\(349\) 7.23833i 0.387459i 0.981055 + 0.193729i \(0.0620584\pi\)
−0.981055 + 0.193729i \(0.937942\pi\)
\(350\) 0 0
\(351\) −1.34641 + 5.68789i −0.0718661 + 0.303597i
\(352\) 0 0
\(353\) 20.5790 11.8813i 1.09531 0.632377i 0.160324 0.987065i \(-0.448746\pi\)
0.934985 + 0.354688i \(0.115413\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −4.85947 33.4797i −0.257190 1.77193i
\(358\) 0 0
\(359\) −31.3993 18.1284i −1.65719 0.956780i −0.974003 0.226537i \(-0.927260\pi\)
−0.683188 0.730242i \(-0.739407\pi\)
\(360\) 0 0
\(361\) −9.38669 16.2582i −0.494036 0.855696i
\(362\) 0 0
\(363\) 5.24192 + 3.59449i 0.275129 + 0.188662i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.730418 1.26512i −0.0381275 0.0660387i 0.846332 0.532656i \(-0.178806\pi\)
−0.884459 + 0.466617i \(0.845473\pi\)
\(368\) 0 0
\(369\) −16.0751 2.51110i −0.836838 0.130723i
\(370\) 0 0
\(371\) 2.85616 + 12.6760i 0.148284 + 0.658105i
\(372\) 0 0
\(373\) −18.3457 10.5919i −0.949907 0.548429i −0.0568547 0.998382i \(-0.518107\pi\)
−0.893052 + 0.449954i \(0.851441\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.47893i 0.127671i
\(378\) 0 0
\(379\) −24.3581 −1.25119 −0.625596 0.780147i \(-0.715144\pi\)
−0.625596 + 0.780147i \(0.715144\pi\)
\(380\) 0 0
\(381\) 13.4226 + 1.04206i 0.687663 + 0.0533863i
\(382\) 0 0
\(383\) −21.8176 12.5964i −1.11483 0.643647i −0.174754 0.984612i \(-0.555913\pi\)
−0.940076 + 0.340965i \(0.889246\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.92711 12.3367i 0.0979606 0.627107i
\(388\) 0 0
\(389\) −10.9380 + 6.31508i −0.554581 + 0.320187i −0.750967 0.660339i \(-0.770413\pi\)
0.196387 + 0.980527i \(0.437079\pi\)
\(390\) 0 0
\(391\) 41.3187i 2.08958i
\(392\) 0 0
\(393\) 6.64524 + 4.55677i 0.335208 + 0.229859i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 8.27166 14.3269i 0.415143 0.719048i −0.580301 0.814402i \(-0.697065\pi\)
0.995443 + 0.0953542i \(0.0303984\pi\)
\(398\) 0 0
\(399\) −1.71296 + 1.35081i −0.0857555 + 0.0676251i
\(400\) 0 0
\(401\) −9.72834 5.61666i −0.485810 0.280482i 0.237025 0.971504i \(-0.423828\pi\)
−0.722835 + 0.691021i \(0.757161\pi\)
\(402\) 0 0
\(403\) −2.33205 + 1.34641i −0.116168 + 0.0670695i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −23.5484 −1.16725
\(408\) 0 0
\(409\) 31.6764 18.2884i 1.56630 0.904303i 0.569703 0.821851i \(-0.307058\pi\)
0.996595 0.0824520i \(-0.0262751\pi\)
\(410\) 0 0
\(411\) 17.2064 8.22943i 0.848727 0.405928i
\(412\) 0 0
\(413\) 1.34440 + 5.96663i 0.0661537 + 0.293599i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 35.5607 + 2.76073i 1.74141 + 0.135194i
\(418\) 0 0
\(419\) 8.29006 0.404996 0.202498 0.979283i \(-0.435094\pi\)
0.202498 + 0.979283i \(0.435094\pi\)
\(420\) 0 0
\(421\) 23.8826 1.16397 0.581984 0.813200i \(-0.302277\pi\)
0.581984 + 0.813200i \(0.302277\pi\)
\(422\) 0 0
\(423\) −29.0168 23.3955i −1.41084 1.13753i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4.70065 + 5.09443i 0.227480 + 0.246537i
\(428\) 0 0
\(429\) −2.27605 4.75884i −0.109889 0.229759i
\(430\) 0 0
\(431\) 9.93859 5.73805i 0.478725 0.276392i −0.241160 0.970485i \(-0.577528\pi\)
0.719885 + 0.694093i \(0.244194\pi\)
\(432\) 0 0
\(433\) −3.31657 −0.159384 −0.0796920 0.996820i \(-0.525394\pi\)
−0.0796920 + 0.996820i \(0.525394\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.30741 + 1.33218i −0.110378 + 0.0637269i
\(438\) 0 0
\(439\) −23.6144 13.6338i −1.12705 0.650705i −0.183862 0.982952i \(-0.558860\pi\)
−0.943192 + 0.332247i \(0.892193\pi\)
\(440\) 0 0
\(441\) −15.2372 14.4509i −0.725582 0.688136i
\(442\) 0 0
\(443\) −20.4555 + 35.4300i −0.971872 + 1.68333i −0.281979 + 0.959421i \(0.590991\pi\)
−0.689893 + 0.723911i \(0.742343\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 16.8422 24.5613i 0.796608 1.16171i
\(448\) 0 0
\(449\) 19.6734i 0.928446i 0.885718 + 0.464223i \(0.153666\pi\)
−0.885718 + 0.464223i \(0.846334\pi\)
\(450\) 0 0
\(451\) 12.7164 7.34179i 0.598790 0.345711i
\(452\) 0 0
\(453\) −3.12695 + 1.49555i −0.146917 + 0.0702671i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −7.95987 4.59563i −0.372347 0.214975i 0.302136 0.953265i \(-0.402300\pi\)
−0.674483 + 0.738290i \(0.735634\pi\)
\(458\) 0 0
\(459\) −11.0119 36.7456i −0.513990 1.71514i
\(460\) 0 0
\(461\) −28.7958 −1.34115 −0.670577 0.741840i \(-0.733953\pi\)
−0.670577 + 0.741840i \(0.733953\pi\)
\(462\) 0 0
\(463\) 25.0825i 1.16568i 0.812586 + 0.582841i \(0.198059\pi\)
−0.812586 + 0.582841i \(0.801941\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 20.2087 + 11.6675i 0.935145 + 0.539907i 0.888435 0.459002i \(-0.151793\pi\)
0.0467103 + 0.998908i \(0.485126\pi\)
\(468\) 0 0
\(469\) 37.9005 8.53977i 1.75008 0.394330i
\(470\) 0 0
\(471\) −28.4961 + 13.6291i −1.31303 + 0.627994i
\(472\) 0 0
\(473\) 5.63436 + 9.75900i 0.259068 + 0.448719i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 5.30921 + 13.7437i 0.243092 + 0.629282i
\(478\) 0 0
\(479\) 8.12075 + 14.0655i 0.371046 + 0.642671i 0.989727 0.142971i \(-0.0456657\pi\)
−0.618680 + 0.785643i \(0.712332\pi\)
\(480\) 0 0
\(481\) −8.47301 4.89189i −0.386336 0.223051i
\(482\) 0 0
\(483\) −15.8817 20.1396i −0.722643 0.916384i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 8.79420 5.07733i 0.398503 0.230076i −0.287335 0.957830i \(-0.592769\pi\)
0.685838 + 0.727754i \(0.259436\pi\)
\(488\) 0 0
\(489\) −19.4049 + 28.2986i −0.877520 + 1.27971i
\(490\) 0 0
\(491\) 25.5734i 1.15411i −0.816704 0.577057i \(-0.804201\pi\)
0.816704 0.577057i \(-0.195799\pi\)
\(492\) 0 0
\(493\) 8.13438 + 14.0892i 0.366354 + 0.634544i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7.78792 25.0008i 0.349336 1.12144i
\(498\) 0 0
\(499\) 4.80838 8.32836i 0.215253 0.372829i −0.738098 0.674693i \(-0.764276\pi\)
0.953351 + 0.301865i \(0.0976092\pi\)
\(500\) 0 0
\(501\) −21.6301 1.67924i −0.966361 0.0750229i
\(502\) 0 0
\(503\) 6.82743i 0.304420i 0.988348 + 0.152210i \(0.0486390\pi\)
−0.988348 + 0.152210i \(0.951361\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.57318 + 20.2640i −0.0698675 + 0.899956i
\(508\) 0 0
\(509\) 7.02977 12.1759i 0.311589 0.539688i −0.667118 0.744952i \(-0.732472\pi\)
0.978707 + 0.205265i \(0.0658055\pi\)
\(510\) 0 0
\(511\) −4.22423 18.7477i −0.186869 0.829347i
\(512\) 0 0
\(513\) −1.69699 + 1.79969i −0.0749237 + 0.0794581i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 33.6391 1.47945
\(518\) 0 0
\(519\) −14.4346 + 21.0503i −0.633609 + 0.924005i
\(520\) 0 0
\(521\) 13.6122 + 23.5771i 0.596363 + 1.03293i 0.993353 + 0.115109i \(0.0367216\pi\)
−0.396990 + 0.917823i \(0.629945\pi\)
\(522\) 0 0
\(523\) 0.528969 0.916202i 0.0231302 0.0400627i −0.854229 0.519898i \(-0.825970\pi\)
0.877359 + 0.479835i \(0.159303\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.83625 15.3048i 0.384913 0.666689i
\(528\) 0 0
\(529\) −4.16269 7.20999i −0.180987 0.313478i
\(530\) 0 0
\(531\) 2.49906 + 6.46922i 0.108450 + 0.280740i
\(532\) 0 0
\(533\) 6.10066 0.264249
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.02491 + 2.14292i 0.0442282 + 0.0924738i
\(538\) 0 0
\(539\) 18.8911 + 1.52137i 0.813698 + 0.0655300i
\(540\) 0 0
\(541\) 13.1032 22.6953i 0.563349 0.975748i −0.433853 0.900984i \(-0.642846\pi\)
0.997201 0.0747644i \(-0.0238205\pi\)
\(542\) 0 0
\(543\) −36.9276 2.86686i −1.58472 0.123029i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 36.6385i 1.56655i 0.621675 + 0.783275i \(0.286452\pi\)
−0.621675 + 0.783275i \(0.713548\pi\)
\(548\) 0 0
\(549\) 6.11875 + 4.93341i 0.261142 + 0.210553i
\(550\) 0 0
\(551\) 0.524531 0.908514i 0.0223458 0.0387040i
\(552\) 0 0
\(553\) 13.5132 12.4687i 0.574640 0.530223i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −17.1032 29.6236i −0.724685 1.25519i −0.959104 0.283055i \(-0.908652\pi\)
0.234419 0.972136i \(-0.424681\pi\)
\(558\) 0 0
\(559\) 4.68187i 0.198022i
\(560\) 0 0
\(561\) 28.5518 + 19.5785i 1.20546 + 0.826606i
\(562\) 0 0
\(563\) −20.6666 + 11.9319i −0.870993 + 0.502868i −0.867678 0.497127i \(-0.834388\pi\)
−0.00331483 + 0.999995i \(0.501055\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −19.4914 13.6780i −0.818561 0.574420i
\(568\) 0 0
\(569\) −27.8326 16.0692i −1.16680 0.673655i −0.213879 0.976860i \(-0.568610\pi\)
−0.952925 + 0.303205i \(0.901943\pi\)
\(570\) 0 0
\(571\) 9.85333 + 17.0665i 0.412349 + 0.714209i 0.995146 0.0984083i \(-0.0313751\pi\)
−0.582797 + 0.812618i \(0.698042\pi\)
\(572\) 0 0
\(573\) 16.9405 24.7046i 0.707697 1.03205i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −6.20731 10.7514i −0.258414 0.447586i 0.707403 0.706810i \(-0.249866\pi\)
−0.965817 + 0.259224i \(0.916533\pi\)
\(578\) 0 0
\(579\) 9.57176 + 20.0129i 0.397789 + 0.831710i
\(580\) 0 0
\(581\) −8.89211 + 28.5455i −0.368907 + 1.18427i
\(582\) 0 0
\(583\) −11.5154 6.64845i −0.476921 0.275351i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 30.6227i 1.26394i −0.774995 0.631968i \(-0.782247\pi\)
0.774995 0.631968i \(-0.217753\pi\)
\(588\) 0 0
\(589\) −1.13958 −0.0469556
\(590\) 0 0
\(591\) 1.22964 15.8388i 0.0505805 0.651522i
\(592\) 0 0
\(593\) 37.6999 + 21.7660i 1.54815 + 0.893823i 0.998283 + 0.0585693i \(0.0186539\pi\)
0.549864 + 0.835254i \(0.314679\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 6.18568 + 12.9332i 0.253163 + 0.529322i
\(598\) 0 0
\(599\) −22.8060 + 13.1670i −0.931827 + 0.537991i −0.887389 0.461022i \(-0.847483\pi\)
−0.0444381 + 0.999012i \(0.514150\pi\)
\(600\) 0 0
\(601\) 18.8846i 0.770317i −0.922850 0.385159i \(-0.874147\pi\)
0.922850 0.385159i \(-0.125853\pi\)
\(602\) 0 0
\(603\) 41.0930 15.8743i 1.67344 0.646450i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 7.16622 12.4123i 0.290868 0.503798i −0.683147 0.730281i \(-0.739389\pi\)
0.974015 + 0.226482i \(0.0727226\pi\)
\(608\) 0 0
\(609\) 9.38034 + 3.74074i 0.380110 + 0.151582i
\(610\) 0 0
\(611\) 12.1037 + 6.98810i 0.489665 + 0.282708i
\(612\) 0 0
\(613\) −16.0421 + 9.26188i −0.647932 + 0.374084i −0.787664 0.616106i \(-0.788709\pi\)
0.139731 + 0.990189i \(0.455376\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 46.6900 1.87967 0.939833 0.341633i \(-0.110980\pi\)
0.939833 + 0.341633i \(0.110980\pi\)
\(618\) 0 0
\(619\) −33.0066 + 19.0564i −1.32665 + 0.765940i −0.984780 0.173808i \(-0.944393\pi\)
−0.341868 + 0.939748i \(0.611059\pi\)
\(620\) 0 0
\(621\) −21.1592 19.9518i −0.849090 0.800636i
\(622\) 0 0
\(623\) 13.5407 12.4941i 0.542498 0.500565i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0.172790 2.22569i 0.00690057 0.0888855i
\(628\) 0 0
\(629\) 64.2092 2.56019
\(630\) 0 0
\(631\) −17.1097 −0.681128 −0.340564 0.940221i \(-0.610618\pi\)
−0.340564 + 0.940221i \(0.610618\pi\)
\(632\) 0 0
\(633\) −1.14071 + 14.6933i −0.0453391 + 0.584007i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6.48121 + 4.47180i 0.256795 + 0.177179i
\(638\) 0 0
\(639\) 4.58260 29.3361i 0.181285 1.16052i
\(640\) 0 0
\(641\) −18.2874 + 10.5583i −0.722310 + 0.417026i −0.815602 0.578613i \(-0.803594\pi\)
0.0932922 + 0.995639i \(0.470261\pi\)
\(642\) 0 0
\(643\) 6.86538 0.270744 0.135372 0.990795i \(-0.456777\pi\)
0.135372 + 0.990795i \(0.456777\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15.4243 8.90522i 0.606391 0.350100i −0.165161 0.986267i \(-0.552814\pi\)
0.771552 + 0.636167i \(0.219481\pi\)
\(648\) 0 0
\(649\) −5.42036 3.12944i −0.212768 0.122841i
\(650\) 0 0
\(651\) −1.57576 10.8563i −0.0617589 0.425492i
\(652\) 0 0
\(653\) 22.8610 39.5964i 0.894619 1.54953i 0.0603437 0.998178i \(-0.480780\pi\)
0.834275 0.551348i \(-0.185886\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −7.85226 20.3268i −0.306346 0.793025i
\(658\) 0 0
\(659\) 6.74688i 0.262821i 0.991328 + 0.131411i \(0.0419506\pi\)
−0.991328 + 0.131411i \(0.958049\pi\)
\(660\) 0 0
\(661\) −43.2369 + 24.9628i −1.68172 + 0.970942i −0.721203 + 0.692724i \(0.756410\pi\)
−0.960518 + 0.278218i \(0.910256\pi\)
\(662\) 0 0
\(663\) 6.20607 + 12.9759i 0.241024 + 0.503940i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 10.6816 + 6.16700i 0.413592 + 0.238787i
\(668\) 0 0
\(669\) 0.743316 9.57457i 0.0287383 0.370174i
\(670\) 0 0
\(671\) −7.09346 −0.273840
\(672\) 0 0
\(673\) 20.0600i 0.773257i 0.922236 + 0.386628i \(0.126360\pi\)
−0.922236 + 0.386628i \(0.873640\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −21.6076 12.4751i −0.830446 0.479458i 0.0235594 0.999722i \(-0.492500\pi\)
−0.854005 + 0.520264i \(0.825833\pi\)
\(678\) 0 0
\(679\) 22.2212 + 6.92206i 0.852773 + 0.265644i
\(680\) 0 0
\(681\) −4.62947 9.67944i −0.177402 0.370917i
\(682\) 0 0
\(683\) −15.4243 26.7156i −0.590194 1.02225i −0.994206 0.107492i \(-0.965718\pi\)
0.404012 0.914754i \(-0.367615\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0.347862 0.507294i 0.0132718 0.0193545i
\(688\) 0 0
\(689\) −2.76226 4.78438i −0.105234 0.182270i
\(690\) 0 0
\(691\) 15.5472 + 8.97619i 0.591444 + 0.341470i 0.765668 0.643236i \(-0.222408\pi\)
−0.174224 + 0.984706i \(0.555742\pi\)
\(692\) 0 0
\(693\) 21.4421 1.43148i 0.814520 0.0543776i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −34.6735 + 20.0188i −1.31335 + 0.758264i
\(698\) 0 0
\(699\) 26.6637 + 18.2838i 1.00851 + 0.691557i
\(700\) 0 0
\(701\) 31.7744i 1.20010i −0.799961 0.600052i \(-0.795147\pi\)
0.799961 0.600052i \(-0.204853\pi\)
\(702\) 0 0
\(703\) −2.07021 3.58570i −0.0780793 0.135237i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.08633 + 27.0119i 0.228900 + 1.01589i
\(708\) 0 0
\(709\) 13.2201 22.8978i 0.496490 0.859946i −0.503502 0.863994i \(-0.667955\pi\)
0.999992 + 0.00404829i \(0.00128862\pi\)
\(710\) 0 0
\(711\) 13.0861 16.2303i 0.490767 0.608683i
\(712\) 0 0
\(713\) 13.3982i 0.501768i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 36.5945 + 2.84099i 1.36665 + 0.106099i
\(718\) 0 0
\(719\) −12.2625 + 21.2393i −0.457314 + 0.792092i −0.998818 0.0486066i \(-0.984522\pi\)
0.541504 + 0.840698i \(0.317855\pi\)
\(720\) 0 0
\(721\) −6.35608 + 5.86478i −0.236713 + 0.218416i
\(722\) 0 0
\(723\) 1.65986 + 3.47048i 0.0617307 + 0.129069i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 49.4804 1.83513 0.917564 0.397589i \(-0.130153\pi\)
0.917564 + 0.397589i \(0.130153\pi\)
\(728\) 0 0
\(729\) −24.1347 12.1044i −0.893878 0.448310i
\(730\) 0 0
\(731\) −15.3631 26.6097i −0.568226 0.984196i
\(732\) 0 0
\(733\) 8.27642 14.3352i 0.305697 0.529482i −0.671720 0.740805i \(-0.734444\pi\)
0.977416 + 0.211324i \(0.0677774\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −19.8785 + 34.4306i −0.732234 + 1.26827i
\(738\) 0 0
\(739\) 8.41010 + 14.5667i 0.309371 + 0.535846i 0.978225 0.207548i \(-0.0665483\pi\)
−0.668854 + 0.743394i \(0.733215\pi\)
\(740\) 0 0
\(741\) 0.524531 0.764935i 0.0192691 0.0281006i
\(742\) 0 0
\(743\) 4.76463 0.174797 0.0873987 0.996173i \(-0.472145\pi\)
0.0873987 + 0.996173i \(0.472145\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −5.23233 + 33.4954i −0.191441 + 1.22553i
\(748\) 0 0
\(749\) 9.69531 8.94590i 0.354259 0.326876i
\(750\) 0 0
\(751\) −4.11749 + 7.13171i −0.150249 + 0.260240i −0.931319 0.364204i \(-0.881341\pi\)
0.781070 + 0.624444i \(0.214674\pi\)
\(752\) 0 0
\(753\) −2.45359 + 31.6044i −0.0894138 + 1.15173i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 3.01624i 0.109627i 0.998497 + 0.0548136i \(0.0174565\pi\)
−0.998497 + 0.0548136i \(0.982544\pi\)
\(758\) 0 0
\(759\) 26.1678 + 2.03152i 0.949832 + 0.0737396i
\(760\) 0 0
\(761\) 7.59504 13.1550i 0.275320 0.476868i −0.694896 0.719110i \(-0.744550\pi\)
0.970216 + 0.242242i \(0.0778829\pi\)
\(762\) 0 0
\(763\) −2.79200 12.3912i −0.101077 0.448593i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.30021 2.25202i −0.0469477 0.0813158i
\(768\) 0 0
\(769\) 33.1611i 1.19582i 0.801563 + 0.597910i \(0.204002\pi\)
−0.801563 + 0.597910i \(0.795998\pi\)
\(770\) 0 0
\(771\) −10.9701 + 15.9979i −0.395079 + 0.576152i
\(772\) 0 0
\(773\) −8.39536 + 4.84706i −0.301960 + 0.174337i −0.643323 0.765595i \(-0.722445\pi\)
0.341363 + 0.939932i \(0.389111\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 31.2969 24.6801i 1.12277 0.885395i
\(778\) 0 0
\(779\) 2.23586 + 1.29087i 0.0801079 + 0.0462503i
\(780\) 0 0
\(781\) 13.3983 + 23.2065i 0.479429 + 0.830395i
\(782\) 0 0
\(783\) 11.1429 + 2.63770i 0.398215 + 0.0942637i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −20.9882 36.3526i −0.748148 1.29583i −0.948710 0.316149i \(-0.897610\pi\)
0.200562 0.979681i \(-0.435723\pi\)
\(788\) 0 0
\(789\) 20.6497 9.87632i 0.735150 0.351606i
\(790\) 0 0
\(791\) −47.7101 14.8620i −1.69638 0.528432i
\(792\) 0 0
\(793\) −2.55231 1.47358i −0.0906352 0.0523283i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 29.8186i 1.05623i 0.849173 + 0.528115i \(0.177101\pi\)
−0.849173 + 0.528115i \(0.822899\pi\)
\(798\) 0 0
\(799\) −91.7232 −3.24493
\(800\) 0 0
\(801\) 13.1127 16.2633i 0.463316 0.574636i
\(802\) 0 0
\(803\) 17.0312 + 9.83298i 0.601019 + 0.346998i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −39.5813 + 18.9309i −1.39333 + 0.666398i
\(808\) 0 0
\(809\) 15.5493 8.97739i 0.546684 0.315628i −0.201099 0.979571i \(-0.564451\pi\)
0.747784 + 0.663942i \(0.231118\pi\)
\(810\) 0 0
\(811\) 4.42584i 0.155412i 0.996976 + 0.0777061i \(0.0247596\pi\)
−0.996976 + 0.0777061i \(0.975240\pi\)
\(812\) 0 0
\(813\) −27.0667 + 39.4719i −0.949270 + 1.38434i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −0.990664 + 1.71588i −0.0346589 + 0.0600311i
\(818\) 0 0
\(819\) 8.01251 + 3.93927i 0.279980 + 0.137649i
\(820\) 0 0
\(821\) 32.5257 + 18.7787i 1.13515 + 0.655381i 0.945226 0.326417i \(-0.105841\pi\)
0.189927 + 0.981798i \(0.439175\pi\)
\(822\) 0 0
\(823\) 31.8982 18.4164i 1.11190 0.641957i 0.172581 0.984995i \(-0.444789\pi\)
0.939321 + 0.343038i \(0.111456\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 14.9737 0.520686 0.260343 0.965516i \(-0.416164\pi\)
0.260343 + 0.965516i \(0.416164\pi\)
\(828\) 0 0
\(829\) 2.95565 1.70645i 0.102654 0.0592674i −0.447794 0.894137i \(-0.647790\pi\)
0.550448 + 0.834869i \(0.314457\pi\)
\(830\) 0 0
\(831\) 17.6830 + 36.9722i 0.613417 + 1.28255i
\(832\) 0 0
\(833\) −51.5102 4.14829i −1.78472 0.143730i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −3.57077 11.9153i −0.123424 0.411854i
\(838\) 0 0
\(839\) −3.71578 −0.128283 −0.0641416 0.997941i \(-0.520431\pi\)
−0.0641416 + 0.997941i \(0.520431\pi\)
\(840\) 0 0
\(841\) 24.1436 0.832539
\(842\) 0 0
\(843\) −29.9944 2.32860i −1.03306 0.0802012i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 7.13544 6.58390i 0.245176 0.226225i
\(848\) 0 0
\(849\) −20.1891 + 9.65599i −0.692887 + 0.331393i
\(850\) 0 0
\(851\) 42.1577 24.3398i 1.44515 0.834357i
\(852\) 0 0
\(853\) 10.5549 0.361393 0.180696 0.983539i \(-0.442165\pi\)
0.180696 + 0.983539i \(0.442165\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −33.4229 + 19.2967i −1.14170 + 0.659163i −0.946852 0.321669i \(-0.895756\pi\)
−0.194852 + 0.980833i \(0.562423\pi\)
\(858\) 0 0
\(859\) 25.9876 + 15.0039i 0.886685 + 0.511928i 0.872857 0.487977i \(-0.162265\pi\)
0.0138282 + 0.999904i \(0.495598\pi\)
\(860\) 0 0
\(861\) −9.20597 + 23.0850i −0.313739 + 0.786736i
\(862\) 0 0
\(863\) 19.0643 33.0204i 0.648958 1.12403i −0.334414 0.942426i \(-0.608538\pi\)
0.983372 0.181602i \(-0.0581283\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −53.5677 36.7325i −1.81925 1.24750i
\(868\) 0 0
\(869\) 18.8157i 0.638280i
\(870\) 0 0
\(871\) −14.3050 + 8.25902i −0.484708 + 0.279846i
\(872\) 0 0
\(873\) 26.0745 + 4.07311i 0.882488 + 0.137854i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −28.7268 16.5855i −0.970037 0.560051i −0.0707893 0.997491i \(-0.522552\pi\)
−0.899247 + 0.437440i \(0.855885\pi\)
\(878\) 0 0
\(879\) −19.4003 1.50613i −0.654357 0.0508006i
\(880\) 0 0
\(881\) 19.8093 0.667393 0.333697 0.942681i \(-0.391704\pi\)
0.333697 + 0.942681i \(0.391704\pi\)
\(882\) 0 0
\(883\) 3.37029i 0.113419i 0.998391 + 0.0567096i \(0.0180609\pi\)
−0.998391 + 0.0567096i \(0.981939\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −31.3008 18.0715i −1.05098 0.606783i −0.128056 0.991767i \(-0.540874\pi\)
−0.922923 + 0.384984i \(0.874207\pi\)
\(888\) 0 0
\(889\) 6.11629 19.6346i 0.205134 0.658522i
\(890\) 0 0
\(891\) 23.8130 5.16732i 0.797767 0.173112i
\(892\) 0 0
\(893\) 2.95730 + 5.12220i 0.0989623 + 0.171408i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 8.99347 + 6.16700i 0.300283 + 0.205910i
\(898\) 0 0
\(899\) 2.63770 + 4.56863i 0.0879722 + 0.152372i
\(900\) 0 0
\(901\) 31.3990 + 18.1282i 1.04605 + 0.603939i
\(902\) 0 0
\(903\) −17.7163 7.06500i −0.589562 0.235109i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −39.9260 + 23.0513i −1.32572 + 0.765405i −0.984635 0.174627i \(-0.944128\pi\)
−0.341086 + 0.940032i \(0.610795\pi\)
\(908\) 0 0
\(909\) 11.3136 + 29.2872i 0.375250 + 0.971394i
\(910\) 0 0
\(911\) 58.0403i 1.92296i 0.274871 + 0.961481i \(0.411365\pi\)
−0.274871 + 0.961481i \(0.588635\pi\)
\(912\) 0 0
\(913\) −15.2979 26.4968i −0.506288 0.876916i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 9.04567 8.34648i 0.298714 0.275625i
\(918\) 0 0
\(919\) 2.66148 4.60983i 0.0877943 0.152064i −0.818784 0.574101i \(-0.805352\pi\)
0.906578 + 0.422037i \(0.138685\pi\)
\(920\) 0 0
\(921\) 4.15818 53.5610i 0.137017 1.76490i
\(922\) 0 0
\(923\) 11.1333i 0.366458i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −6.15519 + 7.63409i −0.202163 + 0.250736i
\(928\) 0 0
\(929\) −20.7113 + 35.8731i −0.679517 + 1.17696i 0.295610 + 0.955309i \(0.404477\pi\)
−0.975127 + 0.221649i \(0.928856\pi\)
\(930\) 0 0
\(931\) 1.42911 + 3.01029i 0.0468373 + 0.0986581i
\(932\) 0 0
\(933\) 2.41054 1.15291i 0.0789175 0.0377445i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −0.523249 −0.0170938 −0.00854690 0.999963i \(-0.502721\pi\)
−0.00854690 + 0.999963i \(0.502721\pi\)
\(938\) 0 0
\(939\) 36.7245 + 25.1827i 1.19846 + 0.821807i
\(940\) 0 0
\(941\) 9.58594 + 16.6033i 0.312493 + 0.541253i 0.978901 0.204333i \(-0.0655026\pi\)
−0.666409 + 0.745587i \(0.732169\pi\)
\(942\) 0 0
\(943\) −15.1770 + 26.2874i −0.494232 + 0.856035i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −15.0654 + 26.0940i −0.489558 + 0.847940i −0.999928 0.0120156i \(-0.996175\pi\)
0.510370 + 0.859955i \(0.329509\pi\)
\(948\) 0 0
\(949\) 4.08536 + 7.07605i 0.132616 + 0.229698i
\(950\) 0 0
\(951\) −4.44383 3.04722i −0.144101 0.0988130i
\(952\) 0 0
\(953\) −17.4015 −0.563691 −0.281846 0.959460i \(-0.590947\pi\)
−0.281846 + 0.959460i \(0.590947\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −9.32285 + 4.45892i −0.301365 + 0.144136i
\(958\) 0 0
\(959\) −6.40407 28.4221i −0.206798 0.917796i
\(960\) 0 0
\(961\) −12.6347 + 21.8840i −0.407571 + 0.705934i
\(962\) 0 0
\(963\) 9.38887 11.6447i 0.302552 0.375246i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 24.9154i 0.801224i −0.916248 0.400612i \(-0.868797\pi\)
0.916248 0.400612i \(-0.131203\pi\)
\(968\) 0 0
\(969\) −0.471144 + 6.06875i −0.0151353 + 0.194956i
\(970\) 0 0
\(971\) 9.45293 16.3730i 0.303359 0.525433i −0.673536 0.739155i \(-0.735225\pi\)
0.976895 + 0.213722i \(0.0685585\pi\)
\(972\) 0 0
\(973\) 16.2039 52.0179i 0.519474 1.66762i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 20.2411 + 35.0586i 0.647571 + 1.12163i 0.983701 + 0.179810i \(0.0575483\pi\)
−0.336131 + 0.941815i \(0.609118\pi\)
\(978\) 0 0
\(979\) 18.8540i 0.602578i
\(980\) 0 0
\(981\) −5.18994 13.4350i −0.165702 0.428946i
\(982\) 0 0
\(983\) −47.0341 + 27.1552i −1.50016 + 0.866116i −0.500156 + 0.865935i \(0.666724\pi\)
−1.00000 0.000180339i \(0.999943\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −44.7078 + 35.2557i −1.42307 + 1.12220i
\(988\) 0 0
\(989\) −20.1739 11.6474i −0.641493 0.370366i
\(990\) 0 0
\(991\) 30.8784 + 53.4830i 0.980886 + 1.69894i 0.658957 + 0.752181i \(0.270998\pi\)
0.321929 + 0.946764i \(0.395669\pi\)
\(992\) 0 0
\(993\) −0.399910 0.274226i −0.0126907 0.00870230i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −10.2738 17.7948i −0.325375 0.563566i 0.656213 0.754576i \(-0.272157\pi\)
−0.981588 + 0.191009i \(0.938824\pi\)
\(998\) 0 0
\(999\) 31.0050 32.8814i 0.980954 1.04032i
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 2100.2.bo.i.1349.9 32
3.2 odd 2 inner 2100.2.bo.i.1349.4 32
5.2 odd 4 2100.2.bi.l.1601.1 yes 16
5.3 odd 4 2100.2.bi.m.1601.8 yes 16
5.4 even 2 inner 2100.2.bo.i.1349.8 32
7.3 odd 6 inner 2100.2.bo.i.1949.13 32
15.2 even 4 2100.2.bi.l.1601.4 yes 16
15.8 even 4 2100.2.bi.m.1601.5 yes 16
15.14 odd 2 inner 2100.2.bo.i.1349.13 32
21.17 even 6 inner 2100.2.bo.i.1949.8 32
35.3 even 12 2100.2.bi.m.101.5 yes 16
35.17 even 12 2100.2.bi.l.101.4 yes 16
35.24 odd 6 inner 2100.2.bo.i.1949.4 32
105.17 odd 12 2100.2.bi.l.101.1 16
105.38 odd 12 2100.2.bi.m.101.8 yes 16
105.59 even 6 inner 2100.2.bo.i.1949.9 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2100.2.bi.l.101.1 16 105.17 odd 12
2100.2.bi.l.101.4 yes 16 35.17 even 12
2100.2.bi.l.1601.1 yes 16 5.2 odd 4
2100.2.bi.l.1601.4 yes 16 15.2 even 4
2100.2.bi.m.101.5 yes 16 35.3 even 12
2100.2.bi.m.101.8 yes 16 105.38 odd 12
2100.2.bi.m.1601.5 yes 16 15.8 even 4
2100.2.bi.m.1601.8 yes 16 5.3 odd 4
2100.2.bo.i.1349.4 32 3.2 odd 2 inner
2100.2.bo.i.1349.8 32 5.4 even 2 inner
2100.2.bo.i.1349.9 32 1.1 even 1 trivial
2100.2.bo.i.1349.13 32 15.14 odd 2 inner
2100.2.bo.i.1949.4 32 35.24 odd 6 inner
2100.2.bo.i.1949.8 32 21.17 even 6 inner
2100.2.bo.i.1949.9 32 105.59 even 6 inner
2100.2.bo.i.1949.13 32 7.3 odd 6 inner